diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/4vdledyGERk.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/4vdledyGERk.srt new file mode 100644 index 0000000000000000000000000000000000000000..05f84630f8712aba2827a86b95f036b1072aee16 --- /dev/null +++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/4vdledyGERk.srt @@ -0,0 +1,1517 @@ +1 +00:00:20,650 --> 00:00:25,130 +Assalamualaikum warahmatullahi wabarakatuh. Today, + +2 +00:00:25,250 --> 00:00:30,470 +inshallah, we will study a passage, a reading + +3 +00:00:30,470 --> 00:00:34,250 +passage about The Clown Doctor. + +4 +00:00:36,890 --> 00:00:39,870 +Open your book, page 18. + +5 +00:00:42,950 --> 00:00:45,450 +Look at the first paragraph. + +6 +00:00:47,470 --> 00:00:48,890 +The introduction. + +7 +00:00:52,680 --> 00:00:58,740 +We have two kinds of questions, W-H questions and + +8 +00:00:58,740 --> 00:01:06,500 +matching questions. W-H questions about the + +9 +00:01:06,500 --> 00:01:10,800 +paragraphs of this passage and matching questions + +10 +00:01:10,800 --> 00:01:17,420 +about the meaning of some phrases. The + +11 +00:01:17,420 --> 00:01:22,410 +introduction, all over the world, Children in + +12 +00:01:22,410 --> 00:01:26,570 +hospital are being treated with a new kind of + +13 +00:01:26,570 --> 00:01:31,430 +medicine, laughter. So there is a new kind of + +14 +00:01:31,430 --> 00:01:39,550 +medicine. What is it? Laughter. Lucy is 23 and + +15 +00:01:39,550 --> 00:01:42,150 +works for Theodora Children's Trust. + +16 +00:01:44,830 --> 00:01:52,660 +How old is she? She is 23. And where does she + +17 +00:01:52,660 --> 00:01:58,680 +work? She works in a hospital. She works for + +18 +00:01:58,680 --> 00:02:04,180 +Theodora Children's Trust. She is one of the many + +19 +00:02:04,180 --> 00:02:09,440 +clown doctors. Is she a doctor? No. She is a clown + +20 +00:02:09,440 --> 00:02:12,720 +doctor. She is a clown doctor. + +21 +00:02:15,230 --> 00:02:19,390 +She is one of the many clown doctors who bring a + +22 +00:02:19,390 --> 00:02:25,230 +smile to the faces of sick children. This is a + +23 +00:02:25,230 --> 00:02:30,910 +hospital for children and Lucy is a clown doctor + +24 +00:02:30,910 --> 00:02:33,830 +who helps children smile. + +25 +00:02:36,030 --> 00:02:43,110 +Question. Read the introduction. What is the new + +26 +00:02:43,110 --> 00:02:48,710 +kind of medicine? Laughter. Yes. So the answer is + +27 +00:02:48,710 --> 00:02:50,050 +laughter. + +28 +00:02:53,450 --> 00:03:00,130 +Now the passage. I'm a Theodora clown doctor. Who + +29 +00:03:00,130 --> 00:03:04,790 +is speaking? Lucy. Yes. I am a Theodora clown + +30 +00:03:04,790 --> 00:03:13,070 +doctor. I call myself Dr. Lulu. I spend two days a + +31 +00:03:13,070 --> 00:03:18,650 +week. in children's hospitals being extremely + +32 +00:03:18,650 --> 00:03:23,130 +silly with my friend and colleague, Dr. Chikers. + +33 +00:03:23,950 --> 00:03:27,030 +So how many clown doctors are there in this + +34 +00:03:27,030 --> 00:03:34,750 +hospital? Two. Lucy and Chikers. Lucy, whose name + +35 +00:03:34,750 --> 00:03:42,770 +is Lulu, and Dr. Chikers. Yes. They are extremely + +36 +00:03:42,770 --> 00:03:49,520 +silly. They are silly. With what? With each other. + +37 +00:03:51,460 --> 00:03:55,660 +Now, we make funny faces. So because they are + +38 +00:03:55,660 --> 00:04:04,580 +clown doctors, what is their job? They make funny. + +39 +00:04:04,760 --> 00:04:12,260 +We make funny faces. Tell jokes and do magic + +40 +00:04:12,260 --> 00:04:19,140 +tricks. As I walk into the wards, into the wards + +41 +00:04:19,140 --> 00:04:26,220 +of the hospital, I blow bubbles, shake hands, + +42 +00:04:26,780 --> 00:04:32,360 +shake hands with the kids. We shake hands with the + +43 +00:04:32,360 --> 00:04:37,200 +children and make up nonsense songs. We make + +44 +00:04:37,200 --> 00:04:41,940 +strange songs, new songs, simple songs. + +45 +00:04:45,170 --> 00:04:49,890 +for those children well enough to sing. We make + +46 +00:04:49,890 --> 00:04:56,250 +songs for the children who can sing. Who can sing. + +47 +00:04:57,230 --> 00:05:02,410 +We make special balloons to make balloon animals. + +48 +00:05:03,090 --> 00:05:09,650 +So we make balloon animals and tell funny stories + +49 +00:05:09,650 --> 00:05:17,780 +about them, about these animals. So them refer to + +50 +00:05:17,780 --> 00:05:24,880 +what? To animals. And we refer to what? To Lulu + +51 +00:05:24,880 --> 00:05:27,280 +and Chicares. + +52 +00:05:29,720 --> 00:05:36,660 +We often meet kids who one week look really sick. + +53 +00:05:37,700 --> 00:05:42,160 +Then we go back the next week, and they are racing + +54 +00:05:42,160 --> 00:05:46,620 +about healing. Hi there, Dr. Lulu. Hi, Dr. + +55 +00:05:46,720 --> 00:05:51,500 +Chikers. So at one week, they are ill. The next + +56 +00:05:51,500 --> 00:05:56,580 +week, they are good. They are very well. So the + +57 +00:05:56,580 --> 00:06:00,180 +next week, they come to us saying, hello, hello, + +58 +00:06:00,480 --> 00:06:04,590 +how are you, Dr. Chikers, Dr. Lulu? Yes. A + +59 +00:06:04,590 --> 00:06:12,330 +question. What is, who is Dr. Lulu? Lucy. Lucy. + +60 +00:06:12,790 --> 00:06:18,150 +Yes. Who is Dr. Chakirs? Her friend or her + +61 +00:06:18,150 --> 00:06:25,350 +colleague. Who asked about the person? Who about + +62 +00:06:25,350 --> 00:06:29,890 +the person? Yes. Now, in what ways? It means how? + +63 +00:06:30,990 --> 00:06:35,450 +I'll give examples. How is their job extremely + +64 +00:06:35,450 --> 00:06:40,890 +silly? Extremely, very, very silly. Very, very + +65 +00:06:40,890 --> 00:06:46,450 +simple. Give example. Example about their job. + +66 +00:06:49,530 --> 00:06:57,610 +They make funny faces. + +67 +00:07:00,000 --> 00:07:04,080 +This is one another example. They tell jokes. + +68 +00:07:05,280 --> 00:07:13,060 +Another example. They do magic tricks. Also, they + +69 +00:07:13,060 --> 00:07:20,900 +blow bubbles. Also, they shake hands with the + +70 +00:07:20,900 --> 00:07:26,100 +kids. They make up nonsense songs. + +71 +00:07:29,140 --> 00:07:33,300 +We take special balloons to make balloon animals. + +72 +00:07:36,660 --> 00:07:40,780 +That's clear. Isn't it? Yes. So, + +73 +00:07:44,320 --> 00:07:50,920 +number one, Lucy is Dr. Lulu. Dr. Chiquers is her + +74 +00:07:50,920 --> 00:07:56,370 +colleague. Watch number two, the answer. They make + +75 +00:07:56,370 --> 00:07:59,750 +funny faces, tell jokes and do magic tricks. + +76 +00:07:59,930 --> 00:08:04,710 +That's it. They blow bubbles, shake hands with the + +77 +00:08:04,710 --> 00:08:08,770 +kids and make up nonsense songs. They take special + +78 +00:08:08,770 --> 00:08:12,670 +balloons to make balloon animals and tell funny + +79 +00:08:12,670 --> 00:08:16,930 +stories. It's clear? It's clear, yes. Now we have, + +80 +00:08:17,070 --> 00:08:21,240 +they are really They are running about shouting. + +81 +00:08:21,740 --> 00:08:27,140 +This is from the exercise. Give me a phrase or a + +82 +00:08:27,140 --> 00:08:31,680 +sentence meaning the same as this one. So it's the + +83 +00:08:31,680 --> 00:08:38,820 +same as they are racing about healing. So this is + +84 +00:08:38,820 --> 00:08:42,360 +the + +85 +00:08:42,360 --> 00:08:47,940 +meaning of what? The meaning of this. This is a + +86 +00:08:47,940 --> 00:08:52,140 +question number one, the first one. So they are + +87 +00:08:52,140 --> 00:08:56,020 +running about shouting. It means, or it is the + +88 +00:08:56,020 --> 00:09:01,300 +same as from the paragraph. They are racing about + +89 +00:09:01,300 --> 00:09:05,300 +healing. The second one. + +90 +00:09:08,260 --> 00:09:08,940 +Yes. + +91 +00:09:19,690 --> 00:09:26,510 +I'm naturally a very cheerful person. I have a + +92 +00:09:26,510 --> 00:09:31,830 +happy personality. What does it mean? It means I'm + +93 +00:09:31,830 --> 00:09:36,890 +naturally a very cheerful person. It means I have + +94 +00:09:36,890 --> 00:09:42,830 +a happy personality, happy character. I have + +95 +00:09:42,830 --> 00:09:48,890 +always been a clown. She was a clown. And now she + +96 +00:09:48,890 --> 00:09:54,210 +is a clown. She, I have been a clown. In fact, my + +97 +00:09:54,210 --> 00:10:00,010 +father is a clown. Lucy's father, what is his job? + +98 +00:10:00,550 --> 00:10:07,260 +A clown. In fact, my father's clown, my father's + +99 +00:10:07,260 --> 00:10:11,120 +clown and I started working with him when I was + +100 +00:10:11,120 --> 00:10:14,920 +eight years old. She started working with her + +101 +00:10:14,920 --> 00:10:21,280 +father when she was young. Yes, I knew it was just + +102 +00:10:21,280 --> 00:10:26,240 +the job for me and I became a clown doctor because + +103 +00:10:26,240 --> 00:10:28,840 +I think it's a great way to cheer up sick + +104 +00:10:28,840 --> 00:10:30,820 +frightened children in hospital. + +105 +00:10:33,640 --> 00:10:38,860 +A clown doctor is a job. But in addition to the + +106 +00:10:38,860 --> 00:10:43,700 +job, it is good. My job is a teacher. In addition, + +107 +00:10:44,020 --> 00:10:49,710 +I'm happy. So here, She says, I knew it was just + +108 +00:10:49,710 --> 00:10:54,690 +the job for me. It is a job. And I became a clown + +109 +00:10:54,690 --> 00:10:59,970 +doctor because I think it's a great way to cheer + +110 +00:10:59,970 --> 00:11:05,630 +up sick, frightened children. It helps people. It + +111 +00:11:05,630 --> 00:11:11,330 +helps children. So Lucy helps children to be + +112 +00:11:11,330 --> 00:11:13,850 +cheerful, to be happy, to smile. + +113 +00:11:16,790 --> 00:11:23,590 +Which children? The sick children and the + +114 +00:11:23,590 --> 00:11:25,250 +frightened children. + +115 +00:11:27,910 --> 00:11:32,310 +In hospital + +116 +00:11:32,310 --> 00:11:37,430 +or in the hospital? Without the. If I say in the + +117 +00:11:37,430 --> 00:11:41,170 +hospital, it is a visit. In hospital, I am + +118 +00:11:41,170 --> 00:11:49,940 +patient. I wear a fancy coat. I wear a fancy coat. + +119 +00:11:50,680 --> 00:11:56,300 +It means I wear a strange coat. Yes. + +120 +00:11:59,560 --> 00:12:07,840 +A yellow shirt. Yellow shirt. And tights with big + +121 +00:12:07,840 --> 00:12:16,520 +strips. Ah, tights. Trousers. Trousers for women. + +122 +00:12:17,600 --> 00:12:25,240 +Trousers or tights. Cologne. With big strips. Yes. + +123 +00:12:25,600 --> 00:12:32,960 +Also, I have a red rubber. Rubber. Ring. And with + +124 +00:12:32,960 --> 00:12:39,210 +a red rubber nose. Nose made of rubber. and wear + +125 +00:12:39,210 --> 00:12:46,370 +my hair in a crazy plaits. And I have hair with + +126 +00:12:46,370 --> 00:12:52,970 +plaits. You know plaits? Like this. Like this. So, + +127 +00:12:54,130 --> 00:12:56,530 +this is a plait. + +128 +00:13:00,990 --> 00:13:07,050 +Yes. Now, how did Lucy became a Theodora clown + +129 +00:13:07,050 --> 00:13:07,430 +doctor? + +130 +00:13:13,320 --> 00:13:20,260 +She's always been a clown. She or I? She. She's + +131 +00:13:20,260 --> 00:13:24,120 +always. She have or she has? She has. She's always + +132 +00:13:24,120 --> 00:13:30,340 +been a clown. In fact, her father, her father, her + +133 +00:13:30,340 --> 00:13:35,600 +father is a clown and she started working with him + +134 +00:13:35,600 --> 00:13:42,990 +when she was eight years old. Uh-huh. Why does she + +135 +00:13:42,990 --> 00:13:48,310 +like her job? Why does she like her job? Because + +136 +00:13:48,310 --> 00:13:58,970 +it's great. It's a great way to cheer up sick, + +137 +00:13:59,330 --> 00:14:06,650 +frightened children in hospital. Yes. Now, what + +138 +00:14:06,650 --> 00:14:12,950 +does she wear? She wears a fancy coat, a yellow + +139 +00:14:12,950 --> 00:14:20,090 +shirt, and tights with big strips. Also, I have a + +140 +00:14:20,090 --> 00:14:24,890 +red rubber nose and wear my hair in a crazy plait. + +141 +00:14:26,030 --> 00:14:31,790 +So this is the answer. I have a happy personality. + +142 +00:14:32,010 --> 00:14:38,570 +It's the same as I am naturally A very cheerful + +143 +00:14:38,570 --> 00:14:43,870 +person. I am naturally a very cheerful person. We + +144 +00:14:43,870 --> 00:14:49,090 +say nature, but natural. Natural, naturally. + +145 +00:14:50,650 --> 00:14:57,610 +Nature, natural. Question number three, how did + +146 +00:14:57,610 --> 00:15:00,550 +Lucy become a Theodora Clown doctor, a clown + +147 +00:15:00,550 --> 00:15:04,530 +doctor in Theodora Hospital? She's always been a + +148 +00:15:04,530 --> 00:15:09,170 +clown. She worked with her father, who was a clown + +149 +00:15:09,170 --> 00:15:12,570 +when she was eight, or something like this. The + +150 +00:15:12,570 --> 00:15:21,480 +same. Number four. Why does she like her job? It's + +151 +00:15:21,480 --> 00:15:24,040 +a great way to cheer up sick, frightened children + +152 +00:15:24,040 --> 00:15:28,900 +in hospital. Number five, what does she wear? She + +153 +00:15:28,900 --> 00:15:32,880 +wears a fancy coat, a yellow short and tights with + +154 +00:15:32,880 --> 00:15:37,340 +big strips. She has a red rubber nose and wears + +155 +00:15:37,340 --> 00:15:43,520 +her hair in a crazy plaits. This is very easy. The + +156 +00:15:43,520 --> 00:15:52,210 +idea is easy. And funny, yes. Now, second + +157 +00:15:52,210 --> 00:15:52,830 +paragraph. + +158 +00:15:55,930 --> 00:16:04,450 +Being a clown in a hospital is very tiring, both + +159 +00:16:04,450 --> 00:16:10,350 +physically and emotionally. Because I am a clown + +160 +00:16:10,350 --> 00:16:16,390 +doctor in hospital, it means because I am. Because + +161 +00:16:16,390 --> 00:16:22,190 +I am a clown in hospital, This is very tiring. + +162 +00:16:22,710 --> 00:16:28,190 +Tiring or tired? I am tired and the work is + +163 +00:16:28,190 --> 00:16:35,110 +tiring. It's very tiring. For two things, both + +164 +00:16:35,110 --> 00:16:40,750 +physically and emotionally. Physically and + +165 +00:16:40,750 --> 00:16:45,430 +emotionally. We have to learn not to show our + +166 +00:16:45,430 --> 00:16:50,230 +feelings. If you show your feelings, it is not + +167 +00:16:50,230 --> 00:16:54,010 +good. Because I am a clown doctor, I should be + +168 +00:16:54,010 --> 00:16:59,310 +happy all the time. If I am sad, I should not show + +169 +00:16:59,310 --> 00:17:04,110 +my sadness. I should show my happiness, even if I + +170 +00:17:04,110 --> 00:17:08,790 +am not happy. So here, we have to learn not to + +171 +00:17:08,790 --> 00:17:12,630 +show our feelings. Otherwise, + +172 +00:17:18,870 --> 00:17:27,190 +We said we have therefore, moreover, however, and + +173 +00:17:27,190 --> 00:17:32,010 +we can add otherwise. Otherwise means if the + +174 +00:17:32,010 --> 00:17:37,650 +previous sentence is not like this, if the + +175 +00:17:37,650 --> 00:17:41,330 +previous sentence is different, this is the + +176 +00:17:41,330 --> 00:17:47,250 +result. If it is not like this, This is the + +177 +00:17:47,250 --> 00:17:54,450 +result. Otherwise, or the same, we'd be useless. + +178 +00:17:56,110 --> 00:18:01,650 +So it means if we show our feelings, so we are + +179 +00:18:01,650 --> 00:18:07,330 +useless. Now I am angry. If I came and show my + +180 +00:18:07,330 --> 00:18:12,010 +anger, no, we don't want you now. Why? Because we + +181 +00:18:12,010 --> 00:18:15,930 +want someone to cheer up children, to make + +182 +00:18:15,930 --> 00:18:21,010 +children smile. So if you are sad, don't come. + +183 +00:18:21,950 --> 00:18:28,030 +Don't come to us. So here, we've to learn not to + +184 +00:18:28,030 --> 00:18:32,390 +show our feelings. Otherwise, if the contrary, + +185 +00:18:33,190 --> 00:18:38,870 +we'd be useless. We will be of no use. Clown + +186 +00:18:38,870 --> 00:18:44,530 +doctors are sensitive, sensitive. Feeling. About + +187 +00:18:44,530 --> 00:18:49,070 +feeling. But this is not a sight most people see. + +188 +00:18:50,930 --> 00:18:54,570 +These clown doctors are people like us. And they + +189 +00:18:54,570 --> 00:18:56,430 +are sensitive. Sometimes they are happy. Sometimes + +190 +00:18:56,430 --> 00:19:01,750 +they are sad. Angry. Hungry. And something like + +191 +0 + +223 +00:21:34,090 --> 00:21:37,230 +been in and out of hospital. She comes to the + +224 +00:21:37,230 --> 00:21:40,170 +hospital, and she leaves the hospital, comes to + +225 +00:21:40,170 --> 00:21:42,530 +the hospital, leaves the hospital. Why? Because of + +226 +00:21:42,530 --> 00:21:46,410 +operations. Because she is sick. She comes to the + +227 +00:21:46,410 --> 00:21:49,870 +hospital many times. After she goes, she comes + +228 +00:21:49,870 --> 00:21:55,150 +again. So she's been in and out, in and out of + +229 +00:21:55,150 --> 00:21:58,610 +hospital for operations. Why she comes at first? + +230 +00:21:58,710 --> 00:22:03,550 +For the operation. She leaves. She comes again. + +231 +00:22:04,590 --> 00:22:08,710 +For operations, so many times. Not one time, many + +232 +00:22:08,710 --> 00:22:13,230 +times. And she's always on my mind. She's always + +233 +00:22:13,230 --> 00:22:17,050 +on my mind. Always I think of her. I'm thinking of + +234 +00:22:17,050 --> 00:22:23,250 +her now. So what would be useless? What would be + +235 +00:22:23,250 --> 00:22:23,650 +useless? + +236 +00:22:26,320 --> 00:22:36,260 +Showing our feelings showing showing our feelings + +237 +00:22:36,260 --> 00:22:39,760 +If + +238 +00:22:39,760 --> 00:22:46,820 +we show our feelings so we are useless If we don't + +239 +00:22:46,820 --> 00:22:53,000 +show our feelings you are good Now we would be of + +240 +00:22:53,990 --> 00:22:59,310 +We would be no help at all. It means we'd be + +241 +00:22:59,310 --> 00:23:06,810 +useless. We'd be useless. I'm always thinking + +242 +00:23:06,810 --> 00:23:11,950 +about her. I'm always thinking about her. It's the + +243 +00:23:11,950 --> 00:23:20,730 +same as what? She's always on my mind. She's + +244 +00:23:20,730 --> 00:23:24,530 +always on my mind. So this is the answer. + +245 +00:23:27,550 --> 00:23:31,630 +So what would be useless? + +246 +00:23:34,550 --> 00:23:41,370 +Showing your feelings. The synonyms. We'd be no + +247 +00:23:41,370 --> 00:23:45,290 +help at all. We'd be useless. I'm always thinking + +248 +00:23:45,290 --> 00:23:48,630 +about her. She's always on my mind. + +249 +00:23:57,480 --> 00:24:04,380 +Yes, the last one was + +250 +00:24:04,380 --> 00:24:09,640 +the one before the last. At lunchtime, page 19, + +251 +00:24:10,040 --> 00:24:13,860 +second page. At lunchtime, at the time of lunch, + +252 +00:24:15,580 --> 00:24:22,260 +we eat in the hospital cafeteria. At lunchtime, we + +253 +00:24:22,260 --> 00:24:25,540 +eat where? What do we eat? In the hospital + +254 +00:24:25,540 --> 00:24:34,420 +cafeteria. And that's really useful. So eating in + +255 +00:24:34,420 --> 00:24:39,520 +the cafeteria is useful. Good. Because why? + +256 +00:24:40,600 --> 00:24:44,120 +Because why is it useful to eat in the hospital + +257 +00:24:44,120 --> 00:24:48,620 +cafeteria? Why? Because we meet the nurses and + +258 +00:24:48,620 --> 00:24:56,180 +doctors. We meet because we meet The nurses and + +259 +00:24:56,180 --> 00:25:02,520 +doctors. And they tell us about particular kids. + +260 +00:25:05,700 --> 00:25:12,440 +They tell us about some children who they think + +261 +00:25:12,440 --> 00:25:15,560 +will + +262 +00:25:15,560 --> 00:25:22,220 +benefit from a clown doctor visit, who will be + +263 +00:25:22,220 --> 00:25:27,470 +happy if we visit them. So the doctors and nurses + +264 +00:25:27,470 --> 00:25:33,550 +Usually tell us about some children who need help + +265 +00:25:33,550 --> 00:25:43,030 +Who need our visit? Yes, so This is the answer if + +266 +00:25:43,030 --> 00:25:47,730 +a child is frightened If + +267 +00:25:47,730 --> 00:25:51,960 +a child is frightened Perhaps they are being given + +268 +00:25:51,960 --> 00:25:55,160 +an injection. Some children are frightened. Why? + +269 +00:25:55,940 --> 00:25:59,480 +Because the doctor or the nurse is giving them an + +270 +00:25:59,480 --> 00:26:05,060 +injection. So they are frightened. Sometimes they + +271 +00:26:05,060 --> 00:26:11,600 +take medicine, nasty medicine, bad medicine. So + +272 +00:26:11,600 --> 00:26:17,070 +they feel frightened. So what's here the job of + +273 +00:26:17,070 --> 00:26:23,990 +the clown doctors? To distract them, to make them + +274 +00:26:23,990 --> 00:26:27,810 +laugh and to pay their attention to some other + +275 +00:26:27,810 --> 00:26:33,490 +thing. So here, if a child is frightened, perhaps + +276 +00:26:33,490 --> 00:26:36,610 +they are being given an injection because of the + +277 +00:26:36,610 --> 00:26:43,980 +injection or some nasty medicine We can distract + +278 +00:26:43,980 --> 00:26:48,700 +them. We can distract them, pay their attention to + +279 +00:26:48,700 --> 00:26:54,360 +some other thing. So the nurses can do their job. + +280 +00:26:55,440 --> 00:26:58,980 +So Lucy and she cares, come to the children who + +281 +00:26:58,980 --> 00:27:06,540 +are frightened and try to laugh, make faces, to + +282 +00:27:06,540 --> 00:27:14,080 +distract them in order to help nurses do their job + +283 +00:27:14,080 --> 00:27:20,080 +better? Yes. Now, the answer is because they meet + +284 +00:27:20,080 --> 00:27:24,240 +the nurses and doctors. Why is it useful to eat in + +285 +00:27:24,240 --> 00:27:27,800 +the hospital cafeteria? Because they meet the + +286 +00:27:27,800 --> 00:27:30,880 +nurses and doctors and they tell them about + +287 +00:27:30,880 --> 00:27:34,820 +particular kids who they think will benefit from a + +288 +00:27:34,820 --> 00:27:36,600 +clown doctor visit. + +289 +00:27:39,170 --> 00:27:42,830 +The last paragraph, + +290 +00:27:44,590 --> 00:27:51,350 +about six o'clock, about + +291 +00:27:51,350 --> 00:27:58,530 +six o'clock, Dr. Chikaz and I, both of us, I and + +292 +00:27:58,530 --> 00:28:03,810 +Dr. Chikaz, or Dr. Chikaz and I, it is better if + +293 +00:28:03,810 --> 00:28:09,860 +it's something good to say someone and I. But if + +294 +00:28:09,860 --> 00:28:15,100 +it is something bad, I and someone. I and Ali + +295 +00:28:15,100 --> 00:28:21,500 +broke the window. But Ali and I got high marks. + +296 +00:28:22,740 --> 00:28:27,560 +Something good, someone and I. Something bad, I + +297 +00:28:27,560 --> 00:28:32,320 +and someone. About six o'clock, Dr. Chakirs and I + +298 +00:28:32,320 --> 00:28:40,950 +take off our makeup. Our makeup and change our + +299 +00:28:40,950 --> 00:28:45,750 +clothes. At six o'clock at the end of the day, we + +300 +00:28:45,750 --> 00:28:50,850 +change clothes and remove the makeup. We are + +301 +00:28:50,850 --> 00:28:54,790 +totally exhausted. We are very exhausted. We are + +302 +00:28:54,790 --> 00:28:59,870 +tired, tired, extremely tired. Sometimes I have a + +303 +00:28:59,870 --> 00:29:04,270 +night out with friends. Sometimes I go out with my + +304 +00:29:04,270 --> 00:29:13,440 +friends. It helps me unwind. If I go out, it helps + +305 +00:29:13,440 --> 00:29:20,480 +me to relax. It helps me relax. I feel happy. When + +306 +00:29:20,480 --> 00:29:25,180 +I finally fall into bed, I crash out. When I go to + +307 +00:29:25,180 --> 00:29:31,700 +bed, I sleep quickly. I have deep sleep quickly + +308 +00:29:31,700 --> 00:29:38,040 +because I'm tired. At weekends, at the end of the + +309 +00:29:38,040 --> 00:29:42,960 +weeks, on Saturdays or on Fridays, we are often + +310 +00:29:42,960 --> 00:29:47,980 +asked to participate. The people of the hospital + +311 +00:29:47,980 --> 00:29:51,940 +ask us to come to share with them something, to + +312 +00:29:51,940 --> 00:29:55,120 +share with them, to participate with them in + +313 +00:29:55,120 --> 00:30:01,190 +events, in the occasions to raise money. to have + +314 +00:30:01,190 --> 00:30:06,890 +money, to collect money from the rich. So in some + +315 +00:30:06,890 --> 00:30:11,910 +events, in some occasions, we go to collect money + +316 +00:30:11,910 --> 00:30:17,450 +from whom? From the rich. At weekends, we are + +317 +00:30:17,450 --> 00:30:21,110 +often asked to participate in events to raise + +318 +00:30:21,110 --> 00:30:26,190 +money for what? For Theodora Children's Trust. + +319 +00:30:27,930 --> 00:30:33,110 +It's a charity. This hospital is a charity. Not + +320 +00:30:33,110 --> 00:30:37,870 +commercialized. No, it is for something good. For + +321 +00:30:37,870 --> 00:30:42,830 +the goodness of people. Charity. So we are paid. + +322 +00:30:43,410 --> 00:30:48,610 +The money we get, our salary, are paid with the + +323 +00:30:48,610 --> 00:30:53,690 +money people give. from the money people give. So + +324 +00:30:53,690 --> 00:30:58,730 +they take their salaries from the money people + +325 +00:30:58,730 --> 00:31:02,550 +give, or with the money people give. Being a clown + +326 +00:31:02,550 --> 00:31:06,350 +doctor, because I am a clown doctor, makes the + +327 +00:31:06,350 --> 00:31:09,450 +worries of everything, of everyday life seem + +328 +00:31:09,450 --> 00:31:13,530 +small. Because this is my job, a clown doctor, + +329 +00:31:14,210 --> 00:31:21,120 +every worries seem small. I don't worry a lot + +330 +00:31:21,120 --> 00:31:24,440 +because this is my job. My job is to make people + +331 +00:31:24,440 --> 00:31:27,920 +smile, to make people happy. So if there are many + +332 +00:31:27,920 --> 00:31:34,080 +problems, it seems to me small because it's my + +333 +00:31:34,080 --> 00:31:41,970 +job. All in all, I feel privileged, lucky. I'm + +334 +00:31:41,970 --> 00:31:47,270 +lucky to do this job. I am lucky to do this job. + +335 +00:31:47,850 --> 00:31:52,790 +Question. What does she do after work? What does + +336 +00:31:52,790 --> 00:31:53,930 +she do after work? + +337 +00:31:57,210 --> 00:32:06,230 +She has a night out with friends. She has a night + +338 +00:32:06,230 --> 00:32:09,820 +out with friends. Yes. + +339 +00:32:13,220 --> 00:32:17,500 +Where does the money for Lucy's salary come from? + +340 +00:32:19,180 --> 00:32:26,340 +From the people. We are paid with the money people + +341 +00:32:26,340 --> 00:32:32,240 +give. With the money we are paid. With the money + +342 +00:32:32,240 --> 00:32:33,100 +people give. + +343 +00:32:35,880 --> 00:32:42,690 +I'm out for the evening with friends. It's a, I + +344 +00:32:42,690 --> 00:32:45,910 +have a night out with friends. This one. + +345 +00:32:49,510 --> 00:32:52,590 +Yes. It helps me relax. + +346 +00:32:55,270 --> 00:33:02,990 +It helps me unwind. It helps me unwind. I go to + +347 +00:33:02,990 --> 00:33:08,470 +bed and immediately fall into a deep sleep. I + +348 +00:33:08,470 --> 00:33:17,730 +finally fall into bed. I crash out. I'm lucky to + +349 +00:33:17,730 --> 00:33:25,310 +have this job. I feel privileged to do this job. + +350 +00:33:26,430 --> 00:33:30,710 +So this is the answer. Sometimes she has a night + +351 +00:33:30,710 --> 00:33:35,270 +out with friends to unwind, to relax. So this is + +352 +00:33:35,270 --> 00:33:39,240 +the answer for number Eight, what does she do + +353 +00:33:39,240 --> 00:33:44,260 +after work? After work, sometimes she has a night + +354 +00:33:44,260 --> 00:33:51,120 +out with friends. Why? To rewind, to relax. Nine, + +355 +00:33:51,540 --> 00:33:54,780 +where does the money for Lucy's salary come from? + +356 +00:33:56,460 --> 00:34:01,700 +The Theodora Children's Trust. It's a charity. So + +357 +00:34:01,700 --> 00:34:08,000 +she is paid with the money people give. The + +358 +00:34:08,000 --> 00:34:13,760 +meaning, I go out for the evening with friends + +359 +00:34:13,760 --> 00:34:19,240 +equals to or the same as the same as I have a + +360 +00:34:19,240 --> 00:34:24,480 +night out with friends. It helps me relax. It + +361 +00:34:24,480 --> 00:34:26,180 +helps me unwind. + +362 +00:34:29,240 --> 00:34:33,120 +I go to bed and immediately fall into a deep + +363 +00:34:33,120 --> 00:34:39,680 +sleep. I fall into bed and crash out. I'm lucky to + +364 +00:34:39,680 --> 00:34:46,160 +have this job. I feel privileged to do this job. + +365 +00:34:48,160 --> 00:34:54,580 +Now quickly, we want to put two things. We have + +366 +00:34:54,580 --> 00:34:58,840 +the doctor and we have the clown doctor. Doctor + +367 +00:34:58,840 --> 00:35:04,120 +and the clown doctor. Page 19, this exercise + +368 +00:35:04,120 --> 00:35:07,740 +number two. Which of these things did you think + +369 +00:35:07,740 --> 00:35:13,400 +of? Which do clowns do? Which do doctors do? So we + +370 +00:35:13,400 --> 00:35:21,960 +have clowns and doctors. Which do both do? Both + +371 +00:35:21,960 --> 00:35:31,100 +means clown and doctor. Number one. Wear funny + +372 +00:35:31,100 --> 00:35:39,830 +clothes. Clown. Yes. Make children feel better. + +373 +00:35:41,790 --> 00:35:49,130 +Clown and doctor. So both. Number three. Who can + +374 +00:35:49,130 --> 00:35:55,470 +read? Who can read? Yes. Perform operations. + +375 +00:35:55,610 --> 00:35:58,670 +Perform operations. Doctor. Doctor. Yes. + +376 +00:36:01,850 --> 00:36:08,600 +Next. We read rubber nose clown. Clown. Very + +377 +00:36:08,600 --> 00:36:09,720 +good. Yes. + +378 +00:36:12,960 --> 00:36:19,920 +Clown. Yes. You understand? Yes. Here. Yes. + +379 +00:36:23,020 --> 00:36:25,000 +Doctor. Yes. + +380 +00:36:29,820 --> 00:36:34,500 +Do magic tricks. Clown. Clown. Very good. + +381 +00:36:38,810 --> 00:36:47,470 +Yes Clown give injection doctor. Yes Doctor give + +382 +00:36:47,470 --> 00:36:53,610 +injection but clowns don't Give injection make + +383 +00:36:53,610 --> 00:37:04,380 +funny faces Clown Give medicine Doctor so this is + +384 +00:37:04,380 --> 00:37:09,720 +a very easy exercise now the last Exercise very + +385 +00:37:09,720 --> 00:37:24,640 +simple. So this is the answer The + +386 +00:37:24,640 --> 00:37:29,910 +answer clowns who can read Mm-hmm Clowns wear + +387 +00:37:29,910 --> 00:37:34,230 +funny clothes, make children feel tired, wear + +388 +00:37:34,230 --> 00:37:38,810 +rubber noses, tell jokes, do magic tricks, make + +389 +00:37:38,810 --> 00:37:43,250 +funny faces. Yes, these are for the clowns. What + +390 +00:37:43,250 --> 00:37:43,910 +about for the doctor? + +391 +00:37:58,620 --> 00:38:02,460 +So we have one for the two. What are they? Make + +392 +00:38:02,460 --> 00:38:07,620 +children feel better. And here, make children feel + +393 +00:38:07,620 --> 00:38:09,240 +better for both of them. + +394 +00:38:12,120 --> 00:38:14,420 +Finally, we have this grammar spot quickly. + +395 +00:38:19,710 --> 00:38:25,710 +Complete these sentences from the text. All over + +396 +00:38:25,710 --> 00:38:32,870 +the world, children in hospitals are being + +397 +00:38:32,870 --> 00:38:37,550 +treated. + +398 +00:38:50,150 --> 00:38:57,770 +It's a charity. So we are paid. We are paid. + +399 +00:39:01,130 --> 00:39:08,110 +So this one and this one, what tense are they? The + +400 +00:39:08,110 --> 00:39:09,770 +first one, what tense is it? + +401 +00:39:12,690 --> 00:39:17,110 +Very good. Yes, it is a present continuous passive + +402 +00:39:17,110 --> 00:39:18,170 +being. + +403 +00:39:20,750 --> 00:39:27,070 +Treated, continuous, passive are present, present, + +404 +00:39:27,170 --> 00:39:29,170 +continuous, passive. What about this? + +405 +00:39:32,690 --> 00:39:36,410 +Present, simple, passive. So what these are? The + +406 +00:39:36,410 --> 00:39:41,550 +first one is present, continuous, passive. And the + +407 +00:39:41,550 --> 00:39:47,330 +other one is present, simple, passive. Number two. + +408 +00:39:47,950 --> 00:39:52,060 +This is number one. Number two, complete these + +409 +00:39:52,060 --> 00:40:00,100 +passive sentences. People of all ages love clowns, + +410 +00:40:00,480 --> 00:40:02,480 +love clowns. + +411 +00:40:04,420 --> \ No newline at end of file diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/4vdledyGERk_raw.json b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/4vdledyGERk_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..e56571170fdf6f19a498188a27df4e1253ae22ba --- /dev/null +++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/4vdledyGERk_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 4889, "start": 20.65, "end": 48.89, "text": " Assalamualaikum warahmatullahi wabarakatuh. Today, inshallah, we will study a passage, a reading passage about The Clown Doctor. Open your book, page 18. Look at the first paragraph. 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W-H questions about the paragraphs of this passage and matching questions about the meaning of some phrases. 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So there is a new kind of medicine. What is it? Laughter. Lucy is 23 and works for Theodora Children's Trust. How old is she? 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This is a hospital for children and Lucy is a clown doctor who helps children smile. Question. Read the introduction. 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To animals. And we refer to what? To Lulu and Chicares. 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Hi there, Dr. Lulu. Hi, Dr. Chikers. So at one week, they are ill. The next week, they are good. They are very well. 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A question. What is, who is Dr. Lulu? Lucy. Lucy. Yes. Who is Dr. Chakirs? Her friend or her colleague. Who asked about the person? Who about the person? Yes. Now, in what ways? 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How is their job extremely silly? Extremely, very, very silly. Very, very simple. Give example. Example about their job. 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They tell jokes. Another example. They do magic tricks. Also, they blow bubbles. Also, they shake hands with the kids. 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That's clear. Isn't it? Yes. So, number one, Lucy is Dr. Lulu. 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This is from the exercise. Give me a phrase or a sentence meaning the same as this one. So it's the same as they are racing about healing. So this is the meaning of what? 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So they are running about shouting. It means, or it is the same as from the paragraph. They are racing about healing. The second one. 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But in addition to the job, it is good. My job is a teacher. In addition, I'm happy. 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The sick children and the frightened children. In hospital or in the hospital? Without the. If I say in the hospital, it is a visit. In hospital, I am patient.", "tokens": [3013, 2227, 30, 440, 4998, 2227, 293, 264, 28839, 2227, 13, 682, 4530, 420, 294, 264, 4530, 30, 9129, 264, 13, 759, 286, 584, 294, 264, 4530, 11, 309, 307, 257, 3441, 13, 682, 4530, 11, 286, 669, 4537, 13], "avg_logprob": -0.2932545615405571, "compression_ratio": 1.5304347826086957, "no_speech_prob": 0.0, "words": [{"start": 676.79, "end": 677.15, "word": " Which", "probability": 0.69482421875}, {"start": 677.15, "end": 677.65, "word": " children?", "probability": 0.77197265625}, {"start": 678.21, "end": 678.43, "word": " The", "probability": 0.78857421875}, {"start": 678.43, "end": 680.11, "word": " sick", "probability": 0.85888671875}, {"start": 680.11, "end": 682.49, "word": " children", "probability": 0.5556640625}, {"start": 682.49, "end": 682.99, "word": " and", "probability": 0.72607421875}, {"start": 682.99, "end": 683.59, "word": " the", "probability": 0.5322265625}, {"start": 683.59, "end": 683.99, "word": " frightened", "probability": 0.95849609375}, {"start": 683.99, "end": 685.25, "word": " children.", "probability": 0.8359375}, {"start": 687.91, "end": 688.57, "word": " In", "probability": 0.424072265625}, {"start": 688.57, "end": 692.31, "word": " hospital", "probability": 0.62353515625}, {"start": 692.31, "end": 692.63, "word": " or", "probability": 0.6474609375}, {"start": 692.63, "end": 692.79, "word": " in", "probability": 0.90380859375}, {"start": 692.79, "end": 692.93, "word": " the", "probability": 0.83984375}, {"start": 692.93, "end": 693.47, "word": " hospital?", "probability": 0.919921875}, {"start": 694.91, "end": 695.57, "word": " Without", "probability": 0.404052734375}, {"start": 695.57, "end": 695.91, "word": " the.", "probability": 0.39990234375}, {"start": 696.21, "end": 696.77, "word": " If", "probability": 0.865234375}, {"start": 696.77, "end": 696.91, "word": " I", "probability": 0.98046875}, {"start": 696.91, "end": 697.09, "word": " say", "probability": 0.90625}, {"start": 697.09, "end": 697.29, "word": " in", "probability": 0.79931640625}, {"start": 697.29, "end": 697.43, "word": " the", "probability": 0.88232421875}, {"start": 697.43, "end": 697.83, "word": " hospital,", "probability": 0.89794921875}, {"start": 698.01, "end": 698.11, "word": " it", "probability": 0.92041015625}, {"start": 698.11, "end": 698.23, "word": " is", "probability": 0.8466796875}, {"start": 698.23, "end": 698.33, "word": " a", "probability": 0.94775390625}, {"start": 698.33, "end": 698.59, "word": " visit.", "probability": 0.94873046875}, {"start": 699.79, "end": 699.97, "word": " In", "probability": 0.94970703125}, {"start": 699.97, "end": 700.37, "word": " hospital,", "probability": 0.6943359375}, {"start": 700.65, "end": 700.97, "word": " I", "probability": 0.99072265625}, {"start": 700.97, "end": 701.17, "word": " am", "probability": 0.8759765625}, {"start": 701.17, "end": 702.15, "word": " patient.", "probability": 0.6435546875}], "temperature": 1.0}, {"id": 26, "seek": 73116, "start": 704.04, "end": 731.16, "text": " I wear a fancy coat. I wear a fancy coat. It means I wear a strange coat. Yes. A yellow shirt. Yellow shirt. And tights with big strips. Ah, tights.", "tokens": [286, 3728, 257, 10247, 10690, 13, 286, 3728, 257, 10247, 10690, 13, 467, 1355, 286, 3728, 257, 5861, 10690, 13, 1079, 13, 316, 5566, 8336, 13, 17550, 8336, 13, 400, 4524, 82, 365, 955, 19842, 13, 2438, 11, 4524, 82, 13], "avg_logprob": -0.20982143211932408, "compression_ratio": 1.5520833333333333, "no_speech_prob": 0.0, "words": [{"start": 704.04, "end": 704.28, "word": " I", "probability": 0.84326171875}, {"start": 704.28, "end": 704.8, "word": " wear", "probability": 0.93798828125}, {"start": 704.8, "end": 705.72, "word": " a", "probability": 0.9697265625}, {"start": 705.72, "end": 706.12, "word": " fancy", "probability": 0.966796875}, {"start": 706.12, "end": 706.78, "word": " coat.", "probability": 0.974609375}, {"start": 707.0, "end": 707.88, "word": " I", "probability": 0.61962890625}, {"start": 707.88, "end": 708.24, "word": " wear", "probability": 0.953125}, {"start": 708.24, "end": 708.92, "word": " a", "probability": 0.99169921875}, {"start": 708.92, "end": 709.32, "word": " fancy", "probability": 0.96630859375}, {"start": 709.32, "end": 709.94, "word": " coat.", "probability": 0.96044921875}, {"start": 710.68, "end": 710.9, "word": " It", "probability": 0.8984375}, {"start": 710.9, "end": 711.36, "word": " means", "probability": 0.92919921875}, {"start": 711.36, "end": 713.18, "word": " I", "probability": 0.818359375}, {"start": 713.18, "end": 713.52, "word": " wear", "probability": 0.9287109375}, {"start": 713.52, "end": 713.9, "word": " a", "probability": 0.986328125}, {"start": 713.9, "end": 714.42, "word": " strange", "probability": 0.8994140625}, {"start": 714.42, "end": 714.98, "word": " coat.", "probability": 0.9677734375}, {"start": 715.86, "end": 716.3, "word": " Yes.", "probability": 0.84423828125}, {"start": 719.56, "end": 720.64, "word": " A", "probability": 0.6005859375}, {"start": 720.64, "end": 721.02, "word": " yellow", "probability": 0.84814453125}, {"start": 721.02, "end": 721.76, "word": " shirt.", "probability": 0.970703125}, {"start": 722.8, "end": 723.24, "word": " Yellow", "probability": 0.71826171875}, {"start": 723.24, "end": 724.0, "word": " shirt.", "probability": 0.94970703125}, {"start": 725.38, "end": 725.42, "word": " And", "probability": 0.83642578125}, {"start": 725.42, "end": 726.96, "word": " tights", "probability": 0.89501953125}, {"start": 726.96, "end": 727.5, "word": " with", "probability": 0.8994140625}, {"start": 727.5, "end": 727.84, "word": " big", "probability": 0.9296875}, {"start": 727.84, "end": 728.68, "word": " strips.", "probability": 0.49853515625}, {"start": 729.72, "end": 730.02, "word": " Ah,", "probability": 0.2149658203125}, {"start": 730.42, "end": 731.16, "word": " tights.", "probability": 0.9560546875}], "temperature": 1.0}, {"id": 27, "seek": 75748, "start": 732.42, "end": 757.48, "text": " Trousers. Trousers for women. Trousers or tights. Cologne. With big strips. Yes. Also, I have a red rubber. Rubber. Ring. And with a red rubber nose. 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And I have hair with plaits. You know plaits? Like this. Like this. So, this is a plait. Yes. 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She or I? She. She's always. She have or she has? She has. She's always been a clown. 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Why does she like her job? Why does she like her job? Because it's great. It's a great way to cheer up sick, frightened children in hospital. Yes. 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I am naturally a very cheerful person. We say nature, but natural. Natural, naturally. 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She's always been a clown. She worked with her father, who was a clown when she was eight, or something like this. The same. Number four. Why does she like her job?", "tokens": [14464, 1230, 1045, 11, 577, 630, 22698, 1813, 257, 440, 378, 3252, 2033, 648, 4631, 11, 257, 22209, 4631, 294, 440, 378, 3252, 15645, 30, 1240, 311, 1009, 668, 257, 22209, 13, 1240, 2732, 365, 720, 3086, 11, 567, 390, 257, 22209, 562, 750, 390, 3180, 11, 420, 746, 411, 341, 13, 440, 912, 13, 5118, 1451, 13, 1545, 775, 750, 411, 720, 1691, 30], "avg_logprob": -0.19910037517547607, "compression_ratio": 1.4835164835164836, "no_speech_prob": 0.0, "words": [{"start": 894.61, "end": 894.97, "word": " Question", "probability": 0.76025390625}, {"start": 894.97, "end": 895.25, "word": " number", "probability": 0.86767578125}, {"start": 895.25, "end": 895.71, "word": " three,", "probability": 0.8056640625}, {"start": 896.73, "end": 897.11, "word": " how", "probability": 0.8173828125}, {"start": 897.11, "end": 897.61, "word": " did", "probability": 0.93505859375}, {"start": 897.61, "end": 897.97, "word": " Lucy", "probability": 0.85205078125}, {"start": 897.97, "end": 898.43, "word": " become", "probability": 0.463623046875}, {"start": 898.43, "end": 898.65, "word": " a", "probability": 0.978515625}, {"start": 898.65, "end": 899.07, "word": " Theodora", "probability": 0.9202473958333334}, {"start": 899.07, "end": 899.47, "word": " Clown", "probability": 0.754150390625}, {"start": 899.47, "end": 899.87, "word": " doctor,", "probability": 0.45458984375}, {"start": 900.21, "end": 900.37, "word": " a", "probability": 0.91015625}, {"start": 900.37, "end": 900.55, "word": " clown", "probability": 0.82080078125}, {"start": 900.55, "end": 900.89, "word": " doctor", "probability": 0.92919921875}, {"start": 900.89, "end": 901.15, "word": " in", "probability": 0.87255859375}, {"start": 901.15, "end": 901.57, "word": " Theodora", "probability": 0.8527018229166666}, {"start": 901.57, "end": 901.95, "word": " Hospital?", "probability": 0.62939453125}, {"start": 902.77, "end": 903.25, "word": " She's", "probability": 0.892333984375}, {"start": 903.25, "end": 903.77, "word": " always", "probability": 0.91015625}, {"start": 903.77, "end": 904.35, "word": " been", "probability": 0.744140625}, {"start": 904.35, "end": 904.53, "word": " a", "probability": 0.99462890625}, {"start": 904.53, "end": 904.91, "word": " clown.", "probability": 0.9462890625}, {"start": 905.31, "end": 905.59, "word": " She", "probability": 0.89501953125}, {"start": 905.59, "end": 906.13, "word": " worked", "probability": 0.869140625}, {"start": 906.13, "end": 906.41, "word": " with", "probability": 0.89306640625}, {"start": 906.41, "end": 906.63, "word": " her", "probability": 0.9658203125}, {"start": 906.63, "end": 907.39, "word": " father,", "probability": 0.76904296875}, {"start": 907.75, "end": 908.21, "word": " who", "probability": 0.9072265625}, {"start": 908.21, "end": 908.57, "word": " was", "probability": 0.9521484375}, {"start": 908.57, "end": 908.83, "word": " a", "probability": 0.998046875}, {"start": 908.83, "end": 909.17, "word": " clown", "probability": 0.95166015625}, {"start": 909.17, "end": 909.65, "word": " when", "probability": 0.892578125}, {"start": 909.65, "end": 909.85, "word": " she", "probability": 0.92041015625}, {"start": 909.85, "end": 910.13, "word": " was", "probability": 0.95849609375}, {"start": 910.13, "end": 910.51, "word": " eight,", "probability": 0.84521484375}, {"start": 910.89, "end": 911.05, "word": " or", "probability": 0.95849609375}, {"start": 911.05, "end": 911.31, "word": " something", "probability": 0.86865234375}, {"start": 911.31, "end": 911.53, "word": " like", "probability": 0.9375}, {"start": 911.53, "end": 911.85, "word": " this.", "probability": 0.9375}, {"start": 911.99, "end": 912.57, "word": " The", "probability": 0.47900390625}, {"start": 912.57, "end": 912.83, "word": " same.", "probability": 0.8994140625}, {"start": 913.87, "end": 914.51, "word": " Number", "probability": 0.85888671875}, {"start": 914.51, "end": 915.33, "word": " four.", "probability": 0.935546875}, {"start": 916.21, "end": 916.37, "word": " Why", "probability": 0.755859375}, {"start": 916.37, "end": 919.13, "word": " does", "probability": 0.943359375}, {"start": 919.13, "end": 919.41, "word": " she", "probability": 0.9033203125}, {"start": 919.41, "end": 919.77, "word": " like", "probability": 0.90771484375}, {"start": 919.77, "end": 920.05, "word": " her", "probability": 0.94873046875}, {"start": 920.05, "end": 920.37, "word": " job?", "probability": 0.974609375}], "temperature": 1.0}, {"id": 34, "seek": 94844, "start": 921.1, "end": 948.44, "text": " It's a great way to cheer up sick, frightened children in hospital. Number five, what does she wear? She wears a fancy coat, a yellow short and tights with big strips. She has a red rubber nose and wears her hair in a crazy plaits. This is very easy. The idea is easy. And funny, yes.", "tokens": [467, 311, 257, 869, 636, 281, 12581, 493, 4998, 11, 28839, 2227, 294, 4530, 13, 5118, 1732, 11, 437, 775, 750, 3728, 30, 1240, 20877, 257, 10247, 10690, 11, 257, 5566, 2099, 293, 4524, 82, 365, 955, 19842, 13, 1240, 575, 257, 2182, 11593, 6690, 293, 20877, 720, 2578, 294, 257, 3219, 499, 1001, 82, 13, 639, 307, 588, 1858, 13, 440, 1558, 307, 1858, 13, 400, 4074, 11, 2086, 13], "avg_logprob": -0.18077256716787815, "compression_ratio": 1.4540816326530612, "no_speech_prob": 0.0, "words": [{"start": 921.1, "end": 921.48, "word": " It's", "probability": 0.84033203125}, {"start": 921.48, "end": 921.64, "word": " a", "probability": 0.86279296875}, {"start": 921.64, "end": 921.94, "word": " great", "probability": 0.916015625}, {"start": 921.94, "end": 922.22, "word": " way", "probability": 0.95703125}, {"start": 922.22, "end": 922.42, "word": " to", "probability": 0.9697265625}, {"start": 922.42, "end": 922.68, "word": " cheer", "probability": 0.919921875}, 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Being a clown in a hospital is very tiring, both physically and emotionally. Because I am a clown doctor in hospital, it means because I am. Because I am a clown in hospital,", "tokens": [823, 11, 1150, 18865, 13, 8891, 257, 22209, 294, 257, 4530, 307, 588, 35182, 11, 1293, 9762, 293, 17991, 13, 1436, 286, 669, 257, 22209, 4631, 294, 4530, 11, 309, 1355, 570, 286, 669, 13, 1436, 286, 669, 257, 22209, 294, 4530, 11], "avg_logprob": -0.20134943317283283, "compression_ratio": 1.584, "no_speech_prob": 0.0, "words": [{"start": 950.53, "end": 950.95, "word": " Now,", "probability": 0.84228515625}, {"start": 951.93, "end": 952.21, "word": " second", "probability": 0.7666015625}, {"start": 952.21, "end": 952.83, "word": " paragraph.", "probability": 0.9345703125}, {"start": 955.93, "end": 957.01, "word": " Being", "probability": 0.80615234375}, {"start": 957.01, "end": 957.67, "word": " a", "probability": 0.986328125}, {"start": 957.67, "end": 958.05, "word": " clown", "probability": 0.92919921875}, {"start": 958.05, "end": 959.35, "word": " in", "probability": 0.92236328125}, {"start": 959.35, "end": 959.49, "word": " a", "probability": 0.93212890625}, {"start": 959.49, "end": 959.91, "word": " hospital", "probability": 0.900390625}, {"start": 959.91, "end": 960.77, "word": " is", "probability": 0.93603515625}, {"start": 960.77, "end": 961.45, "word": " very", "probability": 0.8671875}, {"start": 961.45, "end": 962.37, "word": " tiring,", "probability": 0.96044921875}, {"start": 963.23, "end": 964.45, "word": " both", "probability": 0.857421875}, {"start": 964.45, "end": 965.19, "word": " physically", "probability": 0.951171875}, {"start": 965.19, "end": 965.89, "word": " and", "probability": 0.93896484375}, {"start": 965.89, "end": 966.73, "word": " emotionally.", "probability": 0.85498046875}, {"start": 968.75, "end": 969.31, "word": " Because", "probability": 0.85009765625}, {"start": 969.31, "end": 969.59, "word": " I", "probability": 0.99267578125}, {"start": 969.59, "end": 969.77, "word": " am", "probability": 0.9189453125}, {"start": 969.77, "end": 969.97, "word": " a", "probability": 0.99169921875}, {"start": 969.97, "end": 970.35, "word": " clown", "probability": 0.92431640625}, {"start": 970.35, "end": 971.87, "word": " doctor", "probability": 0.88671875}, {"start": 971.87, "end": 972.09, "word": " in", "probability": 0.91845703125}, {"start": 972.09, "end": 972.71, "word": " hospital,", "probability": 0.5576171875}, {"start": 973.29, "end": 973.49, "word": " it", "probability": 0.235595703125}, {"start": 973.49, "end": 974.03, "word": " means", "probability": 0.92138671875}, {"start": 974.03, "end": 974.41, "word": " because", "probability": 0.677734375}, {"start": 974.41, "end": 974.71, "word": " I", "probability": 0.9765625}, {"start": 974.71, "end": 975.37, "word": " am.", "probability": 0.93603515625}, {"start": 975.71, "end": 976.39, "word": " Because", "probability": 0.88916015625}, {"start": 976.39, "end": 976.69, "word": " I", "probability": 0.99755859375}, {"start": 976.69, "end": 976.97, "word": " am", "probability": 0.94189453125}, {"start": 976.97, "end": 977.23, "word": " a", "probability": 0.9921875}, {"start": 977.23, "end": 977.49, "word": " clown", "probability": 0.9541015625}, {"start": 977.49, "end": 977.73, "word": " in", "probability": 0.9453125}, {"start": 977.73, "end": 978.25, "word": " hospital,", "probability": 0.6484375}], "temperature": 1.0}, {"id": 36, "seek": 100609, "start": 979.47, "end": 1006.09, "text": " This is very tiring. Tiring or tired? I am tired and the work is tiring. It's very tiring. For two things, both physically and emotionally. Physically and emotionally. 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Because I am a clown doctor, I should be happy all the time. If I am sad, I should not show my sadness. I should show my happiness, even if I am not happy. So here, we have to learn not to show our feelings. 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Otherwise means if the previous sentence is not like this, if the previous sentence is different, this is the result. 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Otherwise, or the same, we'd be useless. So it means if we show our feelings, so we are useless. Now I am angry. If I came and show my anger, no, we don't want you now. Why? 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About feeling. But this is not a sight most people see. These clown doctors are people like us. And they are sensitive. Sometimes they are happy. Sometimes they are sad. Angry. Hungry. And something like this. But the people don't see this. They think that they are happy all the time. They are happy all the time. 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They are close to us. 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So this girl is from Bosnia. She is sick. And this is Lucy. She's working with this girl, the little girl. 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She comes to the hospital, and she leaves the hospital, comes to the hospital, leaves the hospital. Why? Because of operations. Because she is sick. She comes to the hospital many times. After she goes, she comes again. So she's been in and out, in and out of hospital for operations. Why she comes at first? 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Shin comes again. For operations, so many times. Not one time, many times. And she's always on my mind. She's always on my mind. Always I think of her. I'm thinking of her now. So what would be useless? 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It means we'd be useless. We'd be useless. I'm always thinking about her. I'm always thinking about her. It's the same as what? She's always on my mind.", "tokens": [492, 576, 312, 572, 854, 412, 439, 13, 467, 1355, 321, 1116, 312, 14115, 13, 492, 1116, 312, 14115, 13, 286, 478, 1009, 1953, 466, 720, 13, 286, 478, 1009, 1953, 466, 720, 13, 467, 311, 264, 912, 382, 437, 30, 1240, 311, 1009, 322, 452, 1575, 13], "avg_logprob": -0.14979272472615146, "compression_ratio": 1.5739130434782609, "no_speech_prob": 0.0, "words": [{"start": 1373.99, "end": 1374.23, "word": " We", "probability": 0.5048828125}, {"start": 1374.23, "end": 1374.37, "word": " would", "probability": 0.71435546875}, {"start": 1374.37, "end": 1374.57, "word": " be", "probability": 0.83984375}, {"start": 1374.57, "end": 1374.87, "word": " no", "probability": 0.84912109375}, {"start": 1374.87, "end": 1375.15, "word": " help", "probability": 0.912109375}, {"start": 1375.15, "end": 1375.37, "word": " at", "probability": 0.96533203125}, {"start": 1375.37, "end": 1375.77, "word": " all.", "probability": 0.951171875}, {"start": 1376.37, "end": 1376.47, "word": " It", "probability": 0.8876953125}, {"start": 1376.47, "end": 1376.81, "word": " means", "probability": 0.923828125}, {"start": 1376.81, "end": 1378.97, "word": " we'd", "probability": 0.71435546875}, {"start": 1378.97, "end": 1379.31, "word": " be", "probability": 0.95556640625}, {"start": 1379.31, "end": 1380.81, "word": " useless.", "probability": 0.92041015625}, {"start": 1381.65, "end": 1381.93, "word": " We'd", "probability": 0.766357421875}, {"start": 1381.93, "end": 1382.71, "word": " be", "probability": 0.95556640625}, {"start": 1382.71, "end": 1383.81, "word": " useless.", "probability": 0.9130859375}, {"start": 1385.29, "end": 1386.13, "word": " I'm", "probability": 0.977783203125}, {"start": 1386.13, "end": 1386.41, "word": " always", "probability": 0.900390625}, {"start": 1386.41, "end": 1386.81, "word": " thinking", "probability": 0.8623046875}, {"start": 1386.81, "end": 1387.31, "word": " about", "probability": 0.90673828125}, {"start": 1387.31, "end": 1387.75, "word": " her.", "probability": 0.93798828125}, {"start": 1389.05, "end": 1389.27, "word": " I'm", "probability": 0.926025390625}, {"start": 1389.27, "end": 1389.63, "word": " always", "probability": 0.89501953125}, {"start": 1389.63, "end": 1390.11, "word": " thinking", "probability": 0.85888671875}, {"start": 1390.11, "end": 1390.51, "word": " about", "probability": 0.9052734375}, {"start": 1390.51, "end": 1390.89, "word": " her.", "probability": 0.93359375}, {"start": 1391.43, "end": 1391.83, "word": " It's", "probability": 0.9208984375}, {"start": 1391.83, "end": 1391.95, "word": " the", "probability": 0.91650390625}, {"start": 1391.95, "end": 1392.15, "word": " same", "probability": 0.9111328125}, {"start": 1392.15, "end": 1392.61, "word": " as", "probability": 0.9619140625}, {"start": 1392.61, "end": 1393.25, "word": " what?", "probability": 0.36669921875}, {"start": 1395.61, "end": 1396.45, "word": " She's", "probability": 0.717529296875}, {"start": 1396.45, "end": 1397.13, "word": " always", "probability": 0.9033203125}, {"start": 1397.13, "end": 1398.05, "word": " on", "probability": 0.92236328125}, {"start": 1398.05, "end": 1399.09, "word": " my", "probability": 0.96826171875}, {"start": 1399.09, "end": 1399.53, "word": " mind.", "probability": 0.880859375}], "temperature": 1.0}, {"id": 52, "seek": 142863, "start": 1400.39, "end": 1428.63, "text": " She's always on my mind. So this is the answer. So what would be useless? Showing your feelings. The synonyms. We'd be no help at all. We'd be useless. I'm always thinking about her. 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At lunchtime, page 19, second page. At lunchtime, at the time of lunch, we eat in the hospital cafeteria. At lunchtime, we eat where? What do we eat? 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So eating in the cafeteria is useful. Good. Because why? Because why is it useful to eat in the hospital cafeteria? Why? Because we meet the nurses and doctors. 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And they tell us about particular kids. 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So what's here the job of the clown doctors? To distract them, to make them laugh and to pay their attention to some other thing. 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I and Ali broke the window. But Ali and I got high marks. Something good, someone and I. Something bad, I and someone. 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At six o'clock at the end of the day, we change clothes and remove the makeup. We are totally exhausted. We are very exhausted. We are tired, tired, extremely tired. Sometimes I have a night out with friends. Sometimes I go out with my friends.", "tokens": [2621, 6567, 293, 1319, 527, 5534, 13, 1711, 2309, 277, 6, 9023, 412, 264, 917, 295, 264, 786, 11, 321, 1319, 5534, 293, 4159, 264, 6567, 13, 492, 366, 3879, 17992, 13, 492, 366, 588, 17992, 13, 492, 366, 5868, 11, 5868, 11, 4664, 5868, 13, 4803, 286, 362, 257, 1818, 484, 365, 1855, 13, 4803, 286, 352, 484, 365, 452, 1855, 13], "avg_logprob": -0.16760254511609674, "compression_ratio": 1.7073170731707317, "no_speech_prob": 0.0, "words": [{"start": 1717.37, "end": 1718.07, "word": " Our", "probability": 0.5244140625}, {"start": 1718.07, "end": 1718.43, "word": " makeup", "probability": 0.7646484375}, {"start": 1718.43, "end": 1719.71, "word": " and", "probability": 0.446044921875}, {"start": 1719.71, "end": 1720.65, "word": " change", "probability": 0.78515625}, {"start": 1720.65, "end": 1720.95, "word": " our", "probability": 0.8759765625}, {"start": 1720.95, "end": 1721.57, "word": " clothes.", "probability": 0.72802734375}, {"start": 1723.05, "end": 1723.75, "word": " At", "probability": 0.8359375}, {"start": 1723.75, "end": 1723.93, "word": " six", "probability": 0.62158203125}, {"start": 1723.93, "end": 1724.07, "word": " o", "probability": 0.98583984375}, {"start": 1724.07, "end": 1724.17, "word": "'clock", "probability": 0.954345703125}, {"start": 1724.17, "end": 1724.33, "word": " at", "probability": 0.755859375}, {"start": 1724.33, "end": 1724.43, "word": " the", "probability": 0.91943359375}, {"start": 1724.43, "end": 1724.51, "word": " end", "probability": 0.90087890625}, {"start": 1724.51, "end": 1724.63, "word": " of", "probability": 0.96826171875}, {"start": 1724.63, "end": 1724.73, "word": " the", "probability": 0.91943359375}, {"start": 1724.73, "end": 1725.03, "word": " day,", "probability": 0.9599609375}, {"start": 1725.25, "end": 1725.75, "word": " we", "probability": 0.93603515625}, {"start": 1725.75, "end": 1726.01, "word": " change", "probability": 0.85546875}, {"start": 1726.01, "end": 1726.43, "word": " clothes", "probability": 0.673828125}, {"start": 1726.43, "end": 1726.89, "word": " and", "probability": 0.9287109375}, {"start": 1726.89, "end": 1727.45, "word": " remove", "probability": 0.9072265625}, {"start": 1727.45, "end": 1728.83, "word": " the", "probability": 0.8115234375}, {"start": 1728.83, "end": 1729.17, "word": " makeup.", "probability": 0.92138671875}, {"start": 1730.09, "end": 1730.63, "word": " We", "probability": 0.9423828125}, {"start": 1730.63, "end": 1730.85, "word": " are", "probability": 0.93994140625}, {"start": 1730.85, "end": 1731.41, "word": " totally", "probability": 0.8662109375}, {"start": 1731.41, "end": 1732.03, "word": " exhausted.", "probability": 0.95361328125}, {"start": 1732.75, "end": 1732.85, "word": " We", "probability": 0.96240234375}, {"start": 1732.85, "end": 1733.07, "word": " are", "probability": 0.943359375}, {"start": 1733.07, "end": 1733.37, "word": " very", "probability": 0.85205078125}, {"start": 1733.37, "end": 1734.03, "word": " exhausted.", "probability": 0.9384765625}, {"start": 1734.45, "end": 1734.55, "word": " We", "probability": 0.9638671875}, {"start": 1734.55, "end": 1734.79, "word": " are", "probability": 0.9375}, {"start": 1734.79, "end": 1735.23, "word": " tired,", "probability": 0.78271484375}, {"start": 1735.93, "end": 1736.49, "word": " tired,", "probability": 0.76806640625}, {"start": 1736.73, "end": 1737.23, "word": " extremely", "probability": 0.82080078125}, {"start": 1737.23, "end": 1737.65, "word": " tired.", "probability": 0.80322265625}, {"start": 1738.31, "end": 1739.01, "word": " Sometimes", "probability": 0.9033203125}, {"start": 1739.01, "end": 1739.31, "word": " I", "probability": 0.912109375}, {"start": 1739.31, "end": 1739.65, "word": " have", "probability": 0.91357421875}, {"start": 1739.65, "end": 1739.87, "word": " a", "probability": 0.99560546875}, {"start": 1739.87, "end": 1740.13, "word": " night", "probability": 0.88916015625}, {"start": 1740.13, "end": 1740.51, "word": " out", "probability": 0.90380859375}, {"start": 1740.51, "end": 1740.79, "word": " with", "probability": 0.89794921875}, {"start": 1740.79, "end": 1741.29, "word": " friends.", "probability": 0.77099609375}, {"start": 1742.61, "end": 1743.29, "word": " Sometimes", "probability": 0.9189453125}, {"start": 1743.29, "end": 1743.53, "word": " I", "probability": 0.98681640625}, {"start": 1743.53, "end": 1743.69, "word": " go", "probability": 0.97021484375}, {"start": 1743.69, "end": 1743.95, "word": " out", "probability": 0.8974609375}, {"start": 1743.95, "end": 1744.11, "word": " with", "probability": 0.896484375}, {"start": 1744.11, "end": 1744.27, "word": " my", "probability": 0.966796875}, {"start": 1744.27, "end": 1744.67, "word": " friends.", "probability": 0.78173828125}], "temperature": 1.0}, {"id": 64, "seek": 177266, "start": 1746.08, "end": 1772.66, "text": " It helps me unwind. 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I crash out. I'm lucky to have this job. I feel privileged to do this job. So this is the answer. Sometimes she has a night out with friends to unwind, to relax. 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I feel privileged to do this job. Now quickly, we want to put two things. We have the doctor and we have the clown doctor. Doctor and the clown doctor. Page 19, this exercise number two. Which of these things did you think of?", "tokens": [286, 478, 6356, 281, 362, 341, 1691, 13, 286, 841, 25293, 281, 360, 341, 1691, 13, 823, 2661, 11, 321, 528, 281, 829, 732, 721, 13, 492, 362, 264, 4631, 293, 321, 362, 264, 22209, 4631, 13, 10143, 293, 264, 22209, 4631, 13, 21217, 1294, 11, 341, 5380, 1230, 732, 13, 3013, 295, 613, 721, 630, 291, 519, 295, 30], "avg_logprob": -0.13319672619710204, "compression_ratio": 1.5548780487804879, "no_speech_prob": 0.0, "words": [{"start": 2078.64, "end": 2078.98, "word": " I'm", "probability": 0.638916015625}, {"start": 2078.98, "end": 2079.3, "word": " lucky", "probability": 0.84130859375}, {"start": 2079.3, "end": 2079.68, "word": " to", "probability": 0.96630859375}, {"start": 2079.68, "end": 2080.0, "word": " have", "probability": 0.94873046875}, {"start": 2080.0, "end": 2080.24, "word": " this", "probability": 0.94384765625}, {"start": 2080.24, "end": 2080.6, "word": " job.", "probability": 0.97314453125}, {"start": 2081.82, "end": 2082.06, "word": " I", "probability": 0.9951171875}, {"start": 2082.06, "end": 2082.38, "word": " feel", "probability": 0.96875}, {"start": 2082.38, "end": 2082.98, "word": " privileged", "probability": 0.896484375}, {"start": 2082.98, "end": 2084.04, "word": " to", "probability": 0.96044921875}, {"start": 2084.04, "end": 2084.42, "word": " do", "probability": 0.9619140625}, {"start": 2084.42, "end": 2085.5, "word": " this", "probability": 0.94287109375}, {"start": 2085.5, "end": 2086.16, "word": " job.", "probability": 0.97216796875}, {"start": 2088.16, "end": 2088.92, "word": " Now", "probability": 0.943359375}, {"start": 2088.92, "end": 2089.54, "word": " quickly,", "probability": 0.48486328125}, {"start": 2090.48, "end": 2090.74, "word": " we", "probability": 0.95947265625}, {"start": 2090.74, "end": 2091.1, "word": " want", "probability": 0.87744140625}, {"start": 2091.1, "end": 2091.42, "word": " to", "probability": 0.9677734375}, {"start": 2091.42, "end": 2091.88, "word": " put", "probability": 0.92578125}, {"start": 2091.88, "end": 2093.08, "word": " two", "probability": 0.92138671875}, {"start": 2093.08, "end": 2093.6, "word": " things.", "probability": 0.8671875}, {"start": 2094.1, "end": 2094.28, "word": " We", "probability": 0.9541015625}, {"start": 2094.28, "end": 2094.58, "word": " have", "probability": 0.9482421875}, {"start": 2094.58, "end": 2094.76, "word": " the", "probability": 0.91064453125}, {"start": 2094.76, "end": 2095.1, "word": " doctor", "probability": 0.81591796875}, {"start": 2095.1, "end": 2095.84, "word": " and", "probability": 0.7216796875}, {"start": 2095.84, "end": 2095.98, "word": " we", "probability": 0.95556640625}, {"start": 2095.98, "end": 2096.2, "word": " have", "probability": 0.94775390625}, {"start": 2096.2, "end": 2096.38, "word": " the", "probability": 0.9130859375}, {"start": 2096.38, "end": 2096.7, "word": " clown", "probability": 0.9150390625}, {"start": 2096.7, "end": 2097.14, "word": " doctor.", "probability": 0.92431640625}, {"start": 2098.32, "end": 2098.84, "word": " Doctor", "probability": 0.9423828125}, {"start": 2098.84, "end": 2099.66, "word": " and", "probability": 0.912109375}, {"start": 2099.66, "end": 2099.8, "word": " the", "probability": 0.8740234375}, {"start": 2099.8, "end": 2100.06, "word": " clown", "probability": 0.9521484375}, {"start": 2100.06, "end": 2100.48, "word": " doctor.", "probability": 0.92431640625}, {"start": 2101.18, "end": 2101.4, "word": " Page", "probability": 0.85791015625}, {"start": 2101.4, "end": 2102.0, "word": " 19,", "probability": 0.88427734375}, {"start": 2103.5, "end": 2103.72, "word": " this", "probability": 0.9306640625}, {"start": 2103.72, "end": 2104.12, "word": " exercise", "probability": 0.904296875}, {"start": 2104.12, "end": 2104.38, "word": " number", "probability": 0.59912109375}, {"start": 2104.38, "end": 2104.78, "word": " two.", "probability": 0.7919921875}, {"start": 2105.56, "end": 2105.84, "word": " Which", "probability": 0.8896484375}, {"start": 2105.84, "end": 2106.06, "word": " of", "probability": 0.96923828125}, {"start": 2106.06, "end": 2106.36, "word": " these", "probability": 0.84814453125}, {"start": 2106.36, "end": 2106.8, "word": " things", "probability": 0.849609375}, {"start": 2106.8, "end": 2107.1, "word": " did", "probability": 0.9423828125}, {"start": 2107.1, "end": 2107.34, "word": " you", "probability": 0.96435546875}, {"start": 2107.34, "end": 2107.74, "word": " think", "probability": 0.9130859375}, {"start": 2107.74, "end": 2108.16, "word": " of?", "probability": 0.9658203125}], "temperature": 1.0}, {"id": 77, "seek": 213454, "start": 2109.2, "end": 2134.54, "text": " Which do clowns do? Which do doctors do? So we have clowns and doctors. Which do both do? Both means clown and doctor. Number one. Wear funny clothes. Clown. Yes.", "tokens": [3013, 360, 22209, 82, 360, 30, 3013, 360, 8778, 360, 30, 407, 321, 362, 22209, 82, 293, 8778, 13, 3013, 360, 1293, 360, 30, 6767, 1355, 22209, 293, 4631, 13, 5118, 472, 13, 34514, 4074, 5534, 13, 2033, 648, 13, 1079, 13], "avg_logprob": -0.14516715046971343, "compression_ratio": 1.4954128440366972, "no_speech_prob": 0.0, "words": [{"start": 2109.2, "end": 2109.56, "word": " Which", "probability": 0.6591796875}, {"start": 2109.56, "end": 2109.92, "word": " do", "probability": 0.912109375}, {"start": 2109.92, "end": 2110.92, "word": " clowns", "probability": 0.84814453125}, {"start": 2110.92, "end": 2111.24, "word": " do?", "probability": 0.9638671875}, {"start": 2111.64, "end": 2111.84, "word": " Which", "probability": 0.87744140625}, {"start": 2111.84, "end": 2112.12, "word": " do", "probability": 0.947265625}, {"start": 2112.12, "end": 2112.6, "word": " doctors", "probability": 0.84326171875}, {"start": 2112.6, "end": 2112.94, "word": " do?", "probability": 0.96533203125}, {"start": 2113.1, "end": 2113.22, "word": " So", "probability": 0.9013671875}, {"start": 2113.22, "end": 2113.4, "word": " we", "probability": 0.75146484375}, {"start": 2113.4, "end": 2113.76, "word": " have", "probability": 0.94970703125}, {"start": 2113.76, "end": 2115.12, "word": " clowns", "probability": 0.869873046875}, {"start": 2115.12, "end": 2116.28, "word": " and", "probability": 0.9169921875}, {"start": 2116.28, "end": 2117.88, "word": " doctors.", "probability": 0.8798828125}, {"start": 2118.46, "end": 2119.14, "word": " Which", "probability": 0.8779296875}, {"start": 2119.14, "end": 2119.5, "word": " do", "probability": 0.94580078125}, {"start": 2119.5, "end": 2120.16, "word": " both", "probability": 0.8701171875}, {"start": 2120.16, "end": 2120.54, "word": " do?", "probability": 0.95458984375}, {"start": 2121.52, "end": 2121.96, "word": " Both", "probability": 0.7451171875}, {"start": 2121.96, "end": 2122.48, "word": " means", "probability": 0.9267578125}, {"start": 2122.48, "end": 2124.36, "word": " clown", "probability": 0.90087890625}, {"start": 2124.36, "end": 2125.24, "word": " and", "probability": 0.93359375}, {"start": 2125.24, "end": 2125.98, "word": " doctor.", "probability": 0.92919921875}, {"start": 2127.12, "end": 2127.3, "word": " Number", "probability": 0.8583984375}, {"start": 2127.3, "end": 2127.54, "word": " one.", "probability": 0.8388671875}, {"start": 2129.92, "end": 2130.34, "word": " Wear", "probability": 0.67333984375}, {"start": 2130.34, "end": 2131.1, "word": " funny", "probability": 0.96044921875}, {"start": 2131.1, "end": 2131.88, "word": " clothes.", "probability": 0.75537109375}, {"start": 2133.06, "end": 2134.02, "word": " Clown.", "probability": 0.936767578125}, {"start": 2134.24, "end": 2134.54, "word": " Yes.", "probability": 0.650390625}], "temperature": 1.0}, {"id": 78, "seek": 216615, "start": 2136.81, "end": 2166.15, "text": " Make children feel bitter. Clown and doctor. So both. Number three. Who can read? Who can read? Yes. Perform operations. Perform operations. Doctor. Doctor. Yes. Next. We read rubber noise clown.", "tokens": [4387, 2227, 841, 13871, 13, 2033, 648, 293, 4631, 13, 407, 1293, 13, 5118, 1045, 13, 2102, 393, 1401, 30, 2102, 393, 1401, 30, 1079, 13, 19351, 7705, 13, 19351, 7705, 13, 10143, 13, 10143, 13, 1079, 13, 3087, 13, 492, 1401, 11593, 5658, 22209, 13], "avg_logprob": -0.21841755763013312, "compression_ratio": 1.4961832061068703, "no_speech_prob": 0.0, "words": [{"start": 2136.81, "end": 2137.33, "word": " Make", "probability": 0.65771484375}, {"start": 2137.33, "end": 2138.09, "word": " children", "probability": 0.83642578125}, {"start": 2138.09, "end": 2139.25, "word": " feel", "probability": 0.94384765625}, {"start": 2139.25, "end": 2139.83, "word": " bitter.", "probability": 0.6748046875}, {"start": 2141.79, "end": 2142.71, "word": " Clown", "probability": 0.8994140625}, {"start": 2142.71, "end": 2144.07, "word": " and", "probability": 0.7607421875}, {"start": 2144.07, "end": 2144.87, "word": " doctor.", "probability": 0.8515625}, {"start": 2145.27, "end": 2145.41, "word": " So", "probability": 0.814453125}, {"start": 2145.41, "end": 2145.89, "word": " both.", "probability": 0.75830078125}, {"start": 2147.39, "end": 2147.89, "word": " Number", "probability": 0.7578125}, {"start": 2147.89, "end": 2148.57, "word": " three.", "probability": 0.83642578125}, {"start": 2148.91, "end": 2149.01, "word": " Who", "probability": 0.89892578125}, {"start": 2149.01, "end": 2149.13, "word": " can", "probability": 0.95068359375}, {"start": 2149.13, "end": 2149.43, "word": " read?", "probability": 0.97998046875}, {"start": 2150.61, "end": 2150.75, "word": " Who", "probability": 0.64794921875}, {"start": 2150.75, "end": 2150.91, "word": " can", "probability": 0.94921875}, {"start": 2150.91, "end": 2151.13, "word": " read?", "probability": 0.97802734375}, {"start": 2151.47, "end": 2151.69, "word": " Yes.", "probability": 0.900390625}, {"start": 2153.81, "end": 2154.55, "word": " Perform", "probability": 0.767578125}, {"start": 2154.55, "end": 2155.47, "word": " operations.", "probability": 0.91650390625}, {"start": 2155.61, "end": 2155.87, "word": " Perform", "probability": 0.53857421875}, {"start": 2155.87, "end": 2156.87, "word": " operations.", "probability": 0.94384765625}, {"start": 2156.99, "end": 2157.45, "word": " Doctor.", "probability": 0.7509765625}, {"start": 2157.69, "end": 2158.07, "word": " Doctor.", "probability": 0.58349609375}, {"start": 2158.37, "end": 2158.67, "word": " Yes.", "probability": 0.91552734375}, {"start": 2161.85, "end": 2162.77, "word": " Next.", "probability": 0.82421875}, {"start": 2163.69, "end": 2164.53, "word": " We", "probability": 0.8857421875}, {"start": 2164.53, "end": 2164.91, "word": " read", "probability": 0.89892578125}, {"start": 2164.91, "end": 2165.27, "word": " rubber", "probability": 0.95263671875}, {"start": 2165.27, "end": 2165.73, "word": " noise", "probability": 0.837890625}, {"start": 2165.73, "end": 2166.15, "word": " clown.", "probability": 0.496826171875}], "temperature": 1.0}, {"id": 79, "seek": 219450, "start": 2167.22, "end": 2194.5, "text": " Clown. Very good. Yes. Clown. Yes. You understand? Yes. Here. Yes. Doctor. Yes. Do magic tricks. Clown. Clown. Very good.", "tokens": [2033, 648, 13, 4372, 665, 13, 1079, 13, 2033, 648, 13, 1079, 13, 509, 1223, 30, 1079, 13, 1692, 13, 1079, 13, 10143, 13, 1079, 13, 1144, 5585, 11733, 13, 2033, 648, 13, 2033, 648, 13, 4372, 665, 13], "avg_logprob": -0.3125000104308128, "compression_ratio": 1.4878048780487805, "no_speech_prob": 0.0, "words": [{"start": 2167.22, "end": 2167.88, "word": " Clown.", "probability": 0.7042236328125}, {"start": 2168.06, "end": 2168.6, "word": " Very", "probability": 0.73828125}, {"start": 2168.6, "end": 2168.94, "word": " good.", "probability": 0.9169921875}, {"start": 2169.18, "end": 2169.72, "word": " Yes.", "probability": 0.8984375}, {"start": 2172.96, "end": 2174.04, "word": " Clown.", "probability": 0.6517333984375}, {"start": 2174.2, "end": 2174.74, "word": " Yes.", "probability": 0.93310546875}, {"start": 2175.4, "end": 2175.54, "word": " You", "probability": 0.529296875}, {"start": 2175.54, "end": 2175.8, "word": " understand?", "probability": 0.83447265625}, {"start": 2176.64, "end": 2176.96, "word": " Yes.", "probability": 0.67529296875}, {"start": 2177.84, "end": 2178.12, "word": " Here.", "probability": 0.53564453125}, {"start": 2178.96, "end": 2179.92, "word": " Yes.", "probability": 0.80322265625}, {"start": 2183.02, "end": 2184.1, "word": " Doctor.", "probability": 0.83984375}, {"start": 2184.56, "end": 2185.0, "word": " Yes.", "probability": 0.9599609375}, {"start": 2189.82, "end": 2189.96, "word": " Do", "probability": 0.3994140625}, {"start": 2189.96, "end": 2191.22, "word": " magic", "probability": 0.454833984375}, {"start": 2191.22, "end": 2191.82, "word": " tricks.", "probability": 0.8603515625}, {"start": 2191.98, "end": 2192.48, "word": " Clown.", "probability": 0.957275390625}, {"start": 2192.76, "end": 2193.38, "word": " Clown.", "probability": 0.719482421875}, {"start": 2193.66, "end": 2194.2, "word": " Very", "probability": 0.8173828125}, {"start": 2194.2, "end": 2194.5, "word": " good.", "probability": 0.9267578125}], "temperature": 1.0}, {"id": 80, "seek": 222035, "start": 2198.81, "end": 2220.35, "text": " Yes Clown give injection doctor. Yes Doctor give injection but clowns don't Give injection make funny faces Clown Give medicine", "tokens": [1079, 2033, 648, 976, 22873, 4631, 13, 1079, 10143, 976, 22873, 457, 22209, 82, 500, 380, 5303, 22873, 652, 4074, 8475, 2033, 648, 5303, 7195], "avg_logprob": -0.36748796701431274, "compression_ratio": 1.391304347826087, "no_speech_prob": 0.0, "words": [{"start": 2198.81, "end": 2200.21, "word": " Yes", "probability": 0.38037109375}, {"start": 2200.21, "end": 2201.61, "word": " Clown", "probability": 0.542327880859375}, {"start": 2201.61, "end": 2202.27, "word": " give", "probability": 0.5546875}, {"start": 2202.27, "end": 2203.73, "word": " injection", "probability": 0.5458984375}, {"start": 2203.73, "end": 2205.09, "word": " doctor.", "probability": 0.32861328125}, {"start": 2205.35, "end": 2205.65, "word": " Yes", "probability": 0.96337890625}, {"start": 2205.65, "end": 2207.03, "word": " Doctor", "probability": 0.52978515625}, {"start": 2207.03, "end": 2207.47, "word": " give", "probability": 0.77197265625}, {"start": 2207.47, "end": 2208.11, "word": " injection", "probability": 0.828125}, {"start": 2208.11, "end": 2208.77, "word": " but", "probability": 0.6591796875}, {"start": 2208.77, "end": 2209.77, "word": " clowns", "probability": 0.795654296875}, {"start": 2209.77, "end": 2210.71, "word": " don't", "probability": 0.933837890625}, {"start": 2210.71, "end": 2212.31, "word": " Give", "probability": 0.7333984375}, {"start": 2212.31, "end": 2212.83, "word": " injection", "probability": 0.830078125}, {"start": 2212.83, "end": 2213.61, "word": " make", "probability": 0.8935546875}, {"start": 2213.61, "end": 2214.09, "word": " funny", "probability": 0.9140625}, {"start": 2214.09, "end": 2214.89, "word": " faces", "probability": 0.92529296875}, {"start": 2214.89, "end": 2217.27, "word": " Clown", "probability": 0.823486328125}, {"start": 2217.27, "end": 2219.65, "word": " Give", "probability": 0.76318359375}, {"start": 2219.65, "end": 2220.35, "word": " medicine", "probability": 0.9091796875}], "temperature": 1.0}, {"id": 81, "seek": 224838, "start": 2221.52, "end": 2248.38, "text": " Doctor so this is a very easy exercise now the last Exercise very simple. So this is the answer The answer clowns who can read Mm-hmm", "tokens": [10143, 370, 341, 307, 257, 588, 1858, 5380, 586, 264, 1036, 44307, 588, 2199, 13, 407, 341, 307, 264, 1867, 440, 1867, 22209, 82, 567, 393, 1401, 8266, 12, 10250], "avg_logprob": -0.2086693577228054, "compression_ratio": 1.3267326732673268, "no_speech_prob": 0.0, "words": [{"start": 2221.52, "end": 2222.02, "word": " Doctor", "probability": 0.69482421875}, {"start": 2222.02, "end": 2222.98, "word": " so", "probability": 0.36962890625}, {"start": 2222.98, "end": 2223.98, "word": " this", "probability": 0.87255859375}, {"start": 2223.98, "end": 2224.38, "word": " is", "probability": 0.9560546875}, {"start": 2224.38, "end": 2224.68, "word": " a", "probability": 0.9970703125}, {"start": 2224.68, "end": 2225.0, "word": " very", "probability": 0.86865234375}, {"start": 2225.0, "end": 2225.84, "word": " easy", "probability": 0.9169921875}, {"start": 2225.84, "end": 2226.62, "word": " exercise", "probability": 0.93408203125}, {"start": 2226.62, "end": 2227.44, "word": " now", "probability": 0.71240234375}, {"start": 2227.44, "end": 2227.74, "word": " the", "probability": 0.904296875}, {"start": 2227.74, "end": 2228.0, "word": " last", "probability": 0.88720703125}, {"start": 2228.0, "end": 2229.28, "word": " Exercise", "probability": 0.7705078125}, {"start": 2229.28, "end": 2229.72, "word": " very", "probability": 0.81201171875}, {"start": 2229.72, "end": 2230.12, "word": " simple.", "probability": 0.9580078125}, {"start": 2230.4, "end": 2230.5, "word": " So", "probability": 0.97119140625}, {"start": 2230.5, "end": 2230.68, "word": " this", "probability": 0.943359375}, {"start": 2230.68, "end": 2230.76, "word": " is", "probability": 0.95068359375}, {"start": 2230.76, "end": 2230.88, "word": " the", "probability": 0.9306640625}, {"start": 2230.88, "end": 2231.6, "word": " answer", "probability": 0.962890625}, {"start": 2231.6, "end": 2244.64, "word": " The", "probability": 0.8642578125}, {"start": 2244.64, "end": 2245.04, "word": " answer", "probability": 0.92578125}, {"start": 2245.04, "end": 2245.86, "word": " clowns", "probability": 0.794677734375}, {"start": 2245.86, "end": 2246.04, "word": " who", "probability": 0.71435546875}, {"start": 2246.04, "end": 2246.16, "word": " can", "probability": 0.9453125}, {"start": 2246.16, "end": 2246.4, "word": " read", "probability": 0.72265625}, {"start": 2246.4, "end": 2248.2, "word": " Mm", "probability": 0.205810546875}, {"start": 2248.2, "end": 2248.38, "word": "-hmm", "probability": 0.9228515625}], "temperature": 1.0}, {"id": 82, "seek": 226391, "start": 2248.91, "end": 2263.91, "text": " Clowns wear funny clothes, make children feel tired, wear rubber noses, tell jokes, do magic tricks, make funny faces. Yes, these are for the clowns. What about for the doctor?", "tokens": [2033, 648, 82, 3728, 4074, 20123, 392, 279, 11, 652, 2227, 841, 5868, 11, 3728, 11593, 3269, 279, 11, 980, 14439, 11, 360, 5585, 11733, 11, 652, 4074, 8475, 13, 1079, 11, 613, 366, 337, 264, 22209, 82, 13, 708, 466, 337, 264, 4631, 30], "avg_logprob": -0.2741168342206789, "compression_ratio": 1.3937007874015748, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2248.91, "end": 2249.39, "word": " Clowns", "probability": 0.9070638020833334}, {"start": 2249.39, "end": 2249.91, "word": " wear", "probability": 0.77685546875}, {"start": 2249.91, "end": 2250.23, "word": " funny", "probability": 0.86279296875}, {"start": 2250.23, "end": 2251.07, "word": " clothes,", "probability": 0.6790771484375}, {"start": 2251.17, "end": 2251.53, "word": " make", "probability": 0.87890625}, {"start": 2251.53, "end": 2251.93, "word": " children", "probability": 0.83740234375}, {"start": 2251.93, "end": 2252.95, "word": " feel", "probability": 0.61279296875}, {"start": 2252.95, "end": 2253.45, "word": " tired,", "probability": 0.607421875}, {"start": 2254.03, "end": 2254.23, "word": " wear", "probability": 0.88525390625}, {"start": 2254.23, "end": 2254.79, "word": " rubber", "probability": 0.7578125}, {"start": 2254.79, "end": 2255.87, "word": " noses,", "probability": 0.824951171875}, {"start": 2256.19, "end": 2256.53, "word": " tell", "probability": 0.857421875}, {"start": 2256.53, "end": 2256.91, "word": " jokes,", "probability": 0.89599609375}, {"start": 2257.21, "end": 2257.37, "word": " do", "probability": 0.88427734375}, {"start": 2257.37, "end": 2257.77, "word": " magic", "probability": 0.89794921875}, {"start": 2257.77, "end": 2258.23, "word": " tricks,", "probability": 0.9140625}, {"start": 2258.59, "end": 2258.81, "word": " make", "probability": 0.91796875}, {"start": 2258.81, "end": 2259.11, "word": " funny", "probability": 0.916015625}, {"start": 2259.11, "end": 2259.53, "word": " faces.", "probability": 0.92724609375}, {"start": 2260.25, "end": 2260.79, "word": " Yes,", "probability": 0.64306640625}, {"start": 2261.17, "end": 2261.35, "word": " these", "probability": 0.71875}, {"start": 2261.35, "end": 2262.05, "word": " are", "probability": 0.92333984375}, {"start": 2262.05, "end": 2262.27, "word": " for", "probability": 0.93603515625}, {"start": 2262.27, "end": 2262.41, "word": " the", "probability": 0.865234375}, {"start": 2262.41, "end": 2263.11, "word": " clowns.", "probability": 0.8828125}, {"start": 2263.17, "end": 2263.25, "word": " What", "probability": 0.822265625}, {"start": 2263.25, "end": 2263.41, "word": " about", "probability": 0.9052734375}, {"start": 2263.41, "end": 2263.55, "word": " for", "probability": 0.55126953125}, {"start": 2263.55, "end": 2263.63, "word": " the", "probability": 0.88623046875}, {"start": 2263.63, "end": 2263.91, "word": " doctor?", "probability": 0.73681640625}], "temperature": 1.0}, {"id": 83, "seek": 229442, "start": 2278.62, "end": 2294.42, "text": " So we have one for the two. What are they? Make children feel better. And here, make children feel better for both of them. Finally, we have this grammar spot quickly.", "tokens": [407, 321, 362, 472, 337, 264, 732, 13, 708, 366, 436, 30, 4387, 2227, 841, 1101, 13, 400, 510, 11, 652, 2227, 841, 1101, 337, 1293, 295, 552, 13, 6288, 11, 321, 362, 341, 22317, 4008, 2661, 13], "avg_logprob": -0.23998397359481224, "compression_ratio": 1.3770491803278688, "no_speech_prob": 0.0, "words": [{"start": 2278.62, "end": 2279.16, "word": " So", "probability": 0.060028076171875}, {"start": 2279.16, "end": 2279.7, "word": " we", "probability": 0.76953125}, {"start": 2279.7, "end": 2279.98, "word": " have", "probability": 0.94970703125}, {"start": 2279.98, "end": 2280.24, "word": " one", "probability": 0.90234375}, {"start": 2280.24, "end": 2280.48, "word": " for", "probability": 0.94580078125}, {"start": 2280.48, "end": 2280.62, "word": " the", "probability": 0.919921875}, {"start": 2280.62, "end": 2280.84, "word": " two.", "probability": 0.94677734375}, {"start": 2281.06, "end": 2281.14, "word": " What", "probability": 0.888671875}, {"start": 2281.14, "end": 2281.26, "word": " are", "probability": 0.943359375}, {"start": 2281.26, "end": 2281.48, "word": " they?", "probability": 0.9130859375}, {"start": 2282.18, "end": 2282.46, "word": " Make", "probability": 0.77685546875}, {"start": 2282.46, "end": 2284.0, "word": " children", "probability": 0.84326171875}, {"start": 2284.0, "end": 2284.78, "word": " feel", "probability": 0.966796875}, {"start": 2284.78, "end": 2285.02, "word": " better.", "probability": 0.77001953125}, {"start": 2285.16, "end": 2285.26, "word": " And", "probability": 0.91796875}, {"start": 2285.26, "end": 2285.58, "word": " here,", "probability": 0.85888671875}, {"start": 2286.38, "end": 2286.66, "word": " make", "probability": 0.91455078125}, {"start": 2286.66, "end": 2287.06, "word": " children", "probability": 0.85205078125}, {"start": 2287.06, "end": 2287.62, "word": " feel", "probability": 0.96923828125}, {"start": 2287.62, "end": 2288.24, "word": " better", "probability": 0.91357421875}, {"start": 2288.24, "end": 2288.66, "word": " for", "probability": 0.50048828125}, {"start": 2288.66, "end": 2288.88, "word": " both", "probability": 0.88134765625}, {"start": 2288.88, "end": 2289.04, "word": " of", "probability": 0.96923828125}, {"start": 2289.04, "end": 2289.24, "word": " them.", "probability": 0.88818359375}, {"start": 2292.12, "end": 2292.66, "word": " Finally,", "probability": 0.6337890625}, {"start": 2292.76, "end": 2292.88, "word": " we", "probability": 0.9638671875}, {"start": 2292.88, "end": 2293.08, "word": " have", "probability": 0.94677734375}, {"start": 2293.08, "end": 2293.28, "word": " this", "probability": 0.935546875}, {"start": 2293.28, "end": 2293.54, "word": " grammar", "probability": 0.91650390625}, {"start": 2293.54, "end": 2293.96, "word": " spot", "probability": 0.9453125}, {"start": 2293.96, "end": 2294.42, "word": " quickly.", "probability": 0.478759765625}], "temperature": 1.0}, {"id": 84, "seek": 231755, "start": 2299.71, "end": 2317.55, "text": " Complete these sentences from the text. All over the world, children in hospitals are being treated.", "tokens": [34687, 613, 16579, 490, 264, 2487, 13, 1057, 670, 264, 1002, 11, 2227, 294, 13014, 366, 885, 8668, 13], "avg_logprob": -0.29003907442092897, "compression_ratio": 1.1744186046511629, "no_speech_prob": 0.0, "words": [{"start": 2299.71, "end": 2300.41, "word": " Complete", "probability": 0.42529296875}, {"start": 2300.41, "end": 2300.93, "word": " these", "probability": 0.82958984375}, {"start": 2300.93, "end": 2301.43, "word": " sentences", "probability": 0.95263671875}, {"start": 2301.43, "end": 2301.79, "word": " from", "probability": 0.87890625}, {"start": 2301.79, "end": 2301.99, "word": " the", "probability": 0.919921875}, {"start": 2301.99, "end": 2302.47, "word": " text.", "probability": 0.96875}, {"start": 2304.57, "end": 2305.45, "word": " All", "probability": 0.7998046875}, {"start": 2305.45, "end": 2305.71, "word": " over", "probability": 0.91796875}, {"start": 2305.71, "end": 2305.95, "word": " the", "probability": 0.92578125}, {"start": 2305.95, "end": 2306.55, "word": " world,", "probability": 0.95068359375}, {"start": 2307.65, "end": 2308.37, "word": " children", "probability": 0.78173828125}, {"start": 2308.37, "end": 2308.73, "word": " in", "probability": 0.93994140625}, {"start": 2308.73, "end": 2309.41, "word": " hospitals", "probability": 0.44775390625}, {"start": 2309.41, "end": 2311.97, "word": " are", "probability": 0.88037109375}, {"start": 2311.97, "end": 2312.87, "word": " being", "probability": 0.9208984375}, {"start": 2312.87, "end": 2317.55, "word": " treated.", "probability": 0.82470703125}], "temperature": 1.0}, {"id": 85, "seek": 235817, "start": 2330.15, "end": 2358.17, "text": " It's a charity. So we are paid. We are paid. So this one and this one, what tense are they? The first one, what tense is it? Very good. Yes, it is a present continuous passive being.", "tokens": [467, 311, 257, 16863, 13, 407, 321, 366, 4835, 13, 492, 366, 4835, 13, 407, 341, 472, 293, 341, 472, 11, 437, 18760, 366, 436, 30, 440, 700, 472, 11, 437, 18760, 307, 309, 30, 4372, 665, 13, 1079, 11, 309, 307, 257, 1974, 10957, 14975, 885, 13], "avg_logprob": -0.29209184646606445, "compression_ratio": 1.4409448818897639, "no_speech_prob": 0.0, "words": [{"start": 2330.15, "end": 2330.51, "word": " It's", "probability": 0.80908203125}, {"start": 2330.51, "end": 2330.73, "word": " a", "probability": 0.40966796875}, {"start": 2330.73, "end": 2331.15, "word": " charity.", "probability": 0.9580078125}, {"start": 2332.55, "end": 2332.55, "word": " So", "probability": 0.89013671875}, {"start": 2332.55, "end": 2333.19, "word": " we", "probability": 0.7119140625}, {"start": 2333.19, "end": 2333.89, "word": " are", "probability": 0.89111328125}, {"start": 2333.89, "end": 2335.21, "word": " paid.", "probability": 0.321533203125}, {"start": 2336.27, "end": 2336.49, "word": " We", "probability": 0.56298828125}, {"start": 2336.49, "end": 2337.25, "word": " are", "probability": 0.9423828125}, {"start": 2337.25, "end": 2337.77, "word": " paid.", "probability": 0.7587890625}, {"start": 2341.13, "end": 2341.91, "word": " So", "probability": 0.90087890625}, {"start": 2341.91, "end": 2342.21, "word": " this", "probability": 0.908203125}, {"start": 2342.21, "end": 2342.69, "word": " one", "probability": 0.93017578125}, {"start": 2342.69, "end": 2343.35, "word": " and", "probability": 0.8486328125}, {"start": 2343.35, "end": 2343.65, "word": " this", "probability": 0.9521484375}, {"start": 2343.65, "end": 2344.07, "word": " one,", "probability": 0.9267578125}, {"start": 2345.33, "end": 2345.51, "word": " what", "probability": 0.896484375}, {"start": 2345.51, "end": 2346.03, "word": " tense", "probability": 0.283447265625}, {"start": 2346.03, "end": 2346.53, "word": " are", "probability": 0.460205078125}, {"start": 2346.53, "end": 2346.91, "word": " they?", "probability": 0.87841796875}, {"start": 2347.91, "end": 2348.11, "word": " The", "probability": 0.83935546875}, {"start": 2348.11, "end": 2348.43, "word": " first", "probability": 0.8935546875}, {"start": 2348.43, "end": 2348.71, "word": " one,", "probability": 0.9296875}, {"start": 2348.87, "end": 2348.99, "word": " what", "probability": 0.9169921875}, {"start": 2348.99, "end": 2349.27, "word": " tense", "probability": 0.85595703125}, {"start": 2349.27, "end": 2349.45, "word": " is", "probability": 0.87353515625}, {"start": 2349.45, "end": 2349.77, "word": " it?", "probability": 0.923828125}, {"start": 2352.69, "end": 2353.47, "word": " Very", "probability": 0.62548828125}, {"start": 2353.47, "end": 2353.73, "word": " good.", "probability": 0.923828125}, {"start": 2353.85, "end": 2354.03, "word": " Yes,", "probability": 0.95458984375}, {"start": 2354.27, "end": 2354.43, "word": " it", "probability": 0.9384765625}, {"start": 2354.43, "end": 2354.61, "word": " is", "probability": 0.935546875}, {"start": 2354.61, "end": 2354.73, "word": " a", "probability": 0.3994140625}, {"start": 2354.73, "end": 2355.07, "word": " present", "probability": 0.94091796875}, {"start": 2355.07, "end": 2356.17, "word": " continuous", "probability": 0.80126953125}, {"start": 2356.17, "end": 2357.11, "word": " passive", "probability": 0.8857421875}, {"start": 2357.11, "end": 2358.17, "word": " being.", "probability": 0.285400390625}], "temperature": 1.0}, {"id": 86, "seek": 238863, "start": 2360.75, "end": 2388.63, "text": " Treated, continuous, passive are present, present, continuous, passive. What about this? Present, simple, passive. So what these are? The first one is present, continuous, passive. And the other one is present, simple, passive. Number two. This is number one.", "tokens": [20298, 292, 11, 10957, 11, 14975, 366, 1974, 11, 1974, 11, 10957, 11, 14975, 13, 708, 466, 341, 30, 33253, 11, 2199, 11, 14975, 13, 407, 437, 613, 366, 30, 440, 700, 472, 307, 1974, 11, 10957, 11, 14975, 13, 400, 264, 661, 472, 307, 1974, 11, 2199, 11, 14975, 13, 5118, 732, 13, 639, 307, 1230, 472, 13], "avg_logprob": -0.26614584773778915, "compression_ratio": 1.911764705882353, "no_speech_prob": 0.0, "words": [{"start": 2360.7500000000005, "end": 2361.4300000000003, "word": " Treated,", "probability": 0.5721435546875}, {"start": 2361.4300000000003, "end": 2362.11, "word": " continuous,", "probability": 0.69873046875}, {"start": 2363.31, "end": 2363.97, "word": " passive", "probability": 0.8896484375}, {"start": 2363.97, "end": 2365.71, "word": " are", "probability": 0.2296142578125}, {"start": 2365.71, "end": 2366.39, "word": " present,", "probability": 0.865234375}, {"start": 2366.71, "end": 2367.07, "word": " present,", "probability": 0.57177734375}, {"start": 2367.17, "end": 2367.57, "word": " continuous,", "probability": 0.8408203125}, {"start": 2367.79, "end": 2368.13, "word": " passive.", "probability": 0.92822265625}, {"start": 2368.51, "end": 2368.63, "word": " What", "probability": 0.7978515625}, {"start": 2368.63, "end": 2368.81, "word": " about", "probability": 0.89404296875}, {"start": 2368.81, "end": 2369.17, "word": " this?", "probability": 0.923828125}, {"start": 2372.69, "end": 2373.37, "word": " Present,", "probability": 0.80322265625}, {"start": 2373.53, "end": 2373.95, "word": " simple,", "probability": 0.87255859375}, {"start": 2374.09, "end": 2374.29, "word": " passive.", "probability": 0.93310546875}, {"start": 2374.61, "end": 2374.81, "word": " So", "probability": 0.83837890625}, {"start": 2374.81, "end": 2375.43, "word": " what", "probability": 0.66357421875}, {"start": 2375.43, "end": 2375.65, "word": " these", "probability": 0.4638671875}, {"start": 2375.65, "end": 2375.95, "word": " are?", "probability": 0.86767578125}, {"start": 2376.41, "end": 2376.41, "word": " The", "probability": 0.83349609375}, {"start": 2376.41, "end": 2377.45, "word": " first", "probability": 0.8369140625}, {"start": 2377.45, "end": 2377.85, "word": " one", "probability": 0.923828125}, {"start": 2377.85, "end": 2378.35, "word": " is", "probability": 0.94189453125}, {"start": 2378.35, "end": 2379.17, "word": " present,", "probability": 0.7998046875}, {"start": 2379.31, "end": 2379.99, "word": " continuous,", "probability": 0.85888671875}, {"start": 2380.15, "end": 2380.47, "word": " passive.", "probability": 0.9326171875}, {"start": 2381.23, "end": 2381.43, "word": " And", "probability": 0.91943359375}, {"start": 2381.43, "end": 2381.55, "word": " the", "probability": 0.92138671875}, {"start": 2381.55, "end": 2381.75, "word": " other", "probability": 0.88427734375}, {"start": 2381.75, "end": 2382.01, "word": " one", "probability": 0.9248046875}, {"start": 2382.01, "end": 2382.35, "word": " is", "probability": 0.9453125}, {"start": 2382.35, "end": 2383.13, "word": " present,", "probability": 0.837890625}, {"start": 2383.75, "end": 2384.01, "word": " simple,", "probability": 0.95654296875}, {"start": 2384.35, "end": 2384.93, "word": " passive.", "probability": 0.9345703125}, {"start": 2386.43, "end": 2387.11, "word": " Number", "probability": 0.83251953125}, {"start": 2387.11, "end": 2387.33, "word": " two.", "probability": 0.85107421875}, {"start": 2387.95, "end": 2388.15, "word": " This", "probability": 0.775390625}, {"start": 2388.15, "end": 2388.23, "word": " is", "probability": 0.93798828125}, {"start": 2388.23, "end": 2388.37, "word": " number", "probability": 0.90380859375}, {"start": 2388.37, "end": 2388.63, "word": " one.", "probability": 0.92578125}], "temperature": 1.0}, {"id": 87, "seek": 241790, "start": 2389.68, "end": 2417.9, "text": " Number two, complete these passive sentences. People of all ages love clown, love clown. So it means in the passive, clowns are loved. So this is the active and this is the passive.", "tokens": [5118, 732, 11, 3566, 613, 14975, 16579, 13, 3432, 295, 439, 12357, 959, 22209, 11, 959, 22209, 13, 407, 309, 1355, 294, 264, 14975, 11, 22209, 82, 366, 4333, 13, 407, 341, 307, 264, 4967, 293, 341, 307, 264, 14975, 13], "avg_logprob": -0.16322544713815054, "compression_ratio": 1.5166666666666666, "no_speech_prob": 0.0, "words": [{"start": 2389.68, "end": 2389.98, "word": " Number", "probability": 0.490478515625}, {"start": 2389.98, "end": 2390.22, "word": " two,", "probability": 0.78564453125}, {"start": 2391.08, "end": 2391.44, "word": " complete", "probability": 0.7724609375}, {"start": 2391.44, "end": 2392.06, "word": " these", "probability": 0.84375}, {"start": 2392.06, "end": 2392.76, "word": " passive", "probability": 0.93994140625}, {"start": 2392.76, "end": 2393.72, "word": " sentences.", "probability": 0.94775390625}, {"start": 2395.5, "end": 2396.0, "word": " People", "probability": 0.7587890625}, {"start": 2396.0, "end": 2396.52, "word": " of", "probability": 0.96923828125}, {"start": 2396.52, "end": 2396.9, "word": " all", "probability": 0.94580078125}, {"start": 2396.9, "end": 2397.62, "word": " ages", "probability": 0.87646484375}, {"start": 2397.62, "end": 2398.94, "word": " love", "probability": 0.8701171875}, {"start": 2398.94, "end": 2400.1, "word": " clown,", "probability": 0.9453125}, {"start": 2400.48, "end": 2401.34, "word": " love", "probability": 0.9375}, {"start": 2401.34, "end": 2402.48, "word": " clown.", "probability": 0.939453125}, {"start": 2404.42, "end": 2404.74, "word": " So", "probability": 0.88232421875}, {"start": 2404.74, "end": 2405.32, "word": " it", "probability": 0.8232421875}, {"start": 2405.32, "end": 2406.04, "word": " means", "probability": 0.931640625}, {"start": 2406.04, "end": 2406.44, "word": " in", "probability": 0.83740234375}, {"start": 2406.44, "end": 2406.6, "word": " the", "probability": 0.91650390625}, {"start": 2406.6, "end": 2407.1, "word": " passive,", "probability": 0.94384765625}, {"start": 2407.78, "end": 2408.84, "word": " clowns", "probability": 0.8466796875}, {"start": 2408.84, "end": 2410.38, "word": " are", "probability": 0.93408203125}, {"start": 2410.38, "end": 2412.82, "word": " loved.", "probability": 0.8623046875}, {"start": 2414.44, "end": 2415.54, "word": " So", "probability": 0.9248046875}, {"start": 2415.54, "end": 2415.8, "word": " this", "probability": 0.91064453125}, {"start": 2415.8, "end": 2415.96, "word": " is", "probability": 0.94482421875}, {"start": 2415.96, "end": 2416.1, "word": " the", "probability": 0.91357421875}, {"start": 2416.1, "end": 2416.48, "word": " active", "probability": 0.9462890625}, {"start": 2416.48, "end": 2417.12, "word": " and", "probability": 0.71533203125}, {"start": 2417.12, "end": 2417.34, "word": " this", "probability": 0.94384765625}, {"start": 2417.34, "end": 2417.48, "word": " is", "probability": 0.94677734375}, {"start": 2417.48, "end": 2417.62, "word": " the", "probability": 0.91015625}, {"start": 2417.62, "end": 2417.9, "word": " passive.", "probability": 0.9326171875}], "temperature": 1.0}, {"id": 88, "seek": 244542, "start": 2419.22, "end": 2445.42, "text": " People of all ages love clowns. Clowns are loved by people of all ages. So change the first one into passive, begin with clowns. So the answer is clowns are loved, are plus plus plus participle by people of all ages. The second one.", "tokens": [3432, 295, 439, 12357, 959, 22209, 82, 13, 2033, 648, 82, 366, 4333, 538, 561, 295, 439, 12357, 13, 407, 1319, 264, 700, 472, 666, 14975, 11, 1841, 365, 22209, 82, 13, 407, 264, 1867, 307, 22209, 82, 366, 4333, 11, 366, 1804, 1804, 1804, 3421, 306, 538, 561, 295, 439, 12357, 13, 440, 1150, 472, 13], "avg_logprob": -0.14978448250170412, "compression_ratio": 1.7007299270072993, "no_speech_prob": 0.0, "words": [{"start": 2419.22, "end": 2419.64, "word": " People", "probability": 0.619140625}, {"start": 2419.64, "end": 2419.84, "word": " of", "probability": 0.970703125}, {"start": 2419.84, "end": 2420.04, "word": " all", "probability": 0.9267578125}, {"start": 2420.04, "end": 2420.3, "word": " ages", "probability": 0.91845703125}, {"start": 2420.3, "end": 2420.7, "word": " love", "probability": 0.9306640625}, {"start": 2420.7, "end": 2421.6, "word": " clowns.", "probability": 0.888427734375}, {"start": 2422.3, "end": 2423.06, "word": " Clowns", "probability": 0.9762369791666666}, {"start": 2423.06, "end": 2423.44, "word": " are", "probability": 0.9453125}, {"start": 2423.44, "end": 2423.78, "word": " loved", "probability": 0.89892578125}, {"start": 2423.78, "end": 2424.54, "word": " by", "probability": 0.97216796875}, {"start": 2424.54, "end": 2425.58, "word": " people", "probability": 0.8876953125}, {"start": 2425.58, "end": 2425.82, "word": " of", "probability": 0.96923828125}, {"start": 2425.82, "end": 2426.0, "word": " all", "probability": 0.95263671875}, {"start": 2426.0, "end": 2426.32, "word": " ages.", "probability": 0.9189453125}, {"start": 2427.78, "end": 2428.54, "word": " So", "probability": 0.84130859375}, {"start": 2428.54, "end": 2429.28, "word": " change", "probability": 0.65087890625}, {"start": 2429.28, "end": 2429.46, "word": " the", "probability": 0.9208984375}, {"start": 2429.46, "end": 2429.74, "word": " first", "probability": 0.89453125}, {"start": 2429.74, "end": 2430.12, "word": " one", "probability": 0.93212890625}, {"start": 2430.12, "end": 2430.56, "word": " into", "probability": 0.82421875}, {"start": 2430.56, "end": 2430.94, "word": " passive,", "probability": 0.86962890625}, {"start": 2432.2, "end": 2432.74, "word": " begin", "probability": 0.8173828125}, {"start": 2432.74, "end": 2433.18, "word": " with", "probability": 0.912109375}, {"start": 2433.18, "end": 2434.64, "word": " clowns.", "probability": 0.860107421875}, {"start": 2434.8, "end": 2434.92, "word": " So", "probability": 0.93505859375}, {"start": 2434.92, "end": 2435.1, "word": " the", "probability": 0.89794921875}, {"start": 2435.1, "end": 2435.32, "word": " answer", "probability": 0.9580078125}, {"start": 2435.32, "end": 2435.7, "word": " is", "probability": 0.9482421875}, {"start": 2435.7, "end": 2437.7, "word": " clowns", "probability": 0.833251953125}, {"start": 2437.7, "end": 2438.5, "word": " are", "probability": 0.93310546875}, {"start": 2438.5, "end": 2439.36, "word": " loved,", "probability": 0.73193359375}, {"start": 2439.86, "end": 2440.24, "word": " are", "probability": 0.9404296875}, {"start": 2440.24, "end": 2440.68, "word": " plus", "probability": 0.444580078125}, {"start": 2440.68, "end": 2440.9, "word": " plus", "probability": 0.7353515625}, {"start": 2440.9, "end": 2441.08, "word": " plus", "probability": 0.8310546875}, {"start": 2441.08, "end": 2441.94, "word": " participle", "probability": 0.765380859375}, {"start": 2441.94, "end": 2442.98, "word": " by", "probability": 0.71435546875}, {"start": 2442.98, "end": 2443.8, "word": " people", "probability": 0.9677734375}, {"start": 2443.8, "end": 2444.0, "word": " of", "probability": 0.96923828125}, {"start": 2444.0, "end": 2444.14, "word": " all", "probability": 0.951171875}, {"start": 2444.14, "end": 2444.5, "word": " ages.", "probability": 0.89794921875}, {"start": 2444.72, "end": 2444.88, "word": " The", "probability": 0.88623046875}, {"start": 2444.88, "end": 2445.12, "word": " second", "probability": 0.904296875}, {"start": 2445.12, "end": 2445.42, "word": " one.", "probability": 0.92529296875}], "temperature": 1.0}, {"id": 89, "seek": 247375, "start": 2446.65, "end": 2473.75, "text": " She is giving her an injection. So here, she is being given an injection. What tense is it? The first one? Present? Simple? Passive? The second one? Present?", "tokens": [1240, 307, 2902, 720, 364, 22873, 13, 407, 510, 11, 750, 307, 885, 2212, 364, 22873, 13, 708, 18760, 307, 309, 30, 440, 700, 472, 30, 33253, 30, 21532, 30, 10319, 488, 30, 440, 1150, 472, 30, 33253, 30], "avg_logprob": -0.29062500447034834, "compression_ratio": 1.4766355140186915, "no_speech_prob": 0.0, "words": [{"start": 2446.65, "end": 2446.93, "word": " She", "probability": 0.6923828125}, {"start": 2446.93, "end": 2447.17, "word": " is", "probability": 0.900390625}, {"start": 2447.17, "end": 2447.75, "word": " giving", "probability": 0.8779296875}, {"start": 2447.75, "end": 2450.13, "word": " her", "probability": 0.176513671875}, {"start": 2450.13, "end": 2451.51, "word": " an", "probability": 0.89990234375}, {"start": 2451.51, "end": 2452.01, "word": " injection.", "probability": 0.87548828125}, {"start": 2452.81, "end": 2452.95, "word": " So", "probability": 0.6728515625}, {"start": 2452.95, "end": 2453.53, "word": " here,", "probability": 0.802734375}, {"start": 2454.59, "end": 2454.87, "word": " she", "probability": 0.83837890625}, {"start": 2454.87, "end": 2457.35, "word": " is", "probability": 0.607421875}, {"start": 2457.35, "end": 2458.99, "word": " being", "probability": 0.80029296875}, {"start": 2458.99, "end": 2459.99, "word": " given", "probability": 0.85302734375}, {"start": 2459.99, "end": 2462.89, "word": " an", "probability": 0.94140625}, {"start": 2462.89, "end": 2463.33, "word": " injection.", "probability": 0.86376953125}, {"start": 2464.11, "end": 2464.35, "word": " What", "probability": 0.78857421875}, {"start": 2464.35, "end": 2464.63, "word": " tense", "probability": 0.79541015625}, {"start": 2464.63, "end": 2464.81, "word": " is", "probability": 0.86181640625}, {"start": 2464.81, "end": 2464.97, "word": " it?", "probability": 0.82861328125}, {"start": 2465.03, "end": 2465.09, "word": " The", "probability": 0.84326171875}, {"start": 2465.09, "end": 2465.35, "word": " first", "probability": 0.89208984375}, {"start": 2465.35, "end": 2465.71, "word": " one?", "probability": 0.931640625}, {"start": 2467.07, "end": 2468.01, "word": " Present?", "probability": 0.77880859375}, {"start": 2468.83, "end": 2469.51, "word": " Simple?", "probability": 0.77734375}, {"start": 2470.11, "end": 2470.49, "word": " Passive?", "probability": 0.957763671875}, {"start": 2470.95, "end": 2471.23, "word": " The", "probability": 0.841796875}, {"start": 2471.23, "end": 2471.57, "word": " second", "probability": 0.89453125}, {"start": 2471.57, "end": 2471.93, "word": " one?", "probability": 0.92724609375}, {"start": 2472.81, "end": 2473.75, "word": " Present?", "probability": 0.7880859375}], "temperature": 1.0}, {"id": 90, "seek": 249567, "start": 2474.8, "end": 2495.68, "text": " Continuous. Passive. And these are the answers. The first answer, R being created. 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So if I say do it means do, does, and did. 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First, tenses. So they help us to make tenses or to form tenses. Also, they help us to make questions. Questions and negatives.", "tokens": [814, 854, 505, 281, 1254, 1451, 721, 13, 2386, 11, 10688, 279, 13, 407, 436, 854, 505, 281, 652, 10688, 279, 420, 281, 1254, 10688, 279, 13, 2743, 11, 436, 854, 505, 281, 652, 1651, 13, 27738, 293, 40019, 13], "avg_logprob": -0.22217987514123683, "compression_ratio": 1.528301886792453, "no_speech_prob": 0.0, "words": [{"start": 140.18, "end": 140.46, "word": " They", "probability": 0.6181640625}, {"start": 140.46, "end": 140.78, "word": " help", "probability": 0.89208984375}, {"start": 140.78, "end": 141.3, "word": " us", "probability": 0.93994140625}, {"start": 141.3, "end": 142.06, "word": " to", "probability": 0.9404296875}, {"start": 142.06, "end": 142.6, "word": " form", "probability": 0.91943359375}, {"start": 142.6, "end": 143.6, "word": " four", "probability": 0.80810546875}, {"start": 143.6, "end": 144.12, "word": " things.", "probability": 0.88232421875}, {"start": 144.94, "end": 145.4, "word": " First,", "probability": 0.73974609375}, {"start": 148.8, "end": 149.56, "word": " tenses.", "probability": 0.54632568359375}, {"start": 150.56, "end": 151.06, "word": " So", "probability": 0.80908203125}, {"start": 151.06, "end": 151.48, "word": " they", "probability": 0.70556640625}, {"start": 151.48, "end": 151.78, "word": " help", "probability": 0.90185546875}, {"start": 151.78, "end": 152.06, "word": " us", "probability": 0.93115234375}, {"start": 152.06, "end": 152.3, "word": " to", "probability": 0.9560546875}, {"start": 152.3, "end": 152.6, "word": " make", "probability": 0.9443359375}, {"start": 152.6, "end": 153.26, "word": " tenses", "probability": 0.843994140625}, {"start": 153.26, "end": 153.88, "word": " or", "probability": 0.6865234375}, {"start": 153.88, "end": 154.1, "word": " to", "probability": 0.93798828125}, {"start": 154.1, "end": 154.44, "word": " form", "probability": 0.921875}, {"start": 154.44, "end": 155.28, "word": " tenses.", "probability": 0.881103515625}, {"start": 155.98, "end": 156.3, "word": " Also,", "probability": 0.8896484375}, {"start": 156.78, "end": 157.0, "word": " they", "probability": 0.88134765625}, {"start": 157.0, "end": 157.24, "word": " help", "probability": 0.900390625}, {"start": 157.24, "end": 157.52, "word": " us", "probability": 0.9306640625}, {"start": 157.52, "end": 157.82, "word": " to", "probability": 0.95849609375}, {"start": 157.82, "end": 159.06, "word": " make", "probability": 0.8076171875}, {"start": 159.06, "end": 159.58, "word": " questions.", "probability": 0.9091796875}, {"start": 161.58, "end": 162.62, "word": " Questions", "probability": 0.50830078125}, {"start": 162.62, "end": 165.12, "word": " and", "probability": 0.90771484375}, {"start": 165.12, "end": 166.42, "word": " negatives.", "probability": 0.8642578125}], "temperature": 1.0}, {"id": 6, "seek": 19737, "start": 172.25, "end": 197.37, "text": " And short answer. Very good. Short answer. Now, if I ask you to deal with the first one with the tenses,", "tokens": [400, 2099, 1867, 13, 4372, 665, 13, 16881, 1867, 13, 823, 11, 498, 286, 1029, 291, 281, 2028, 365, 264, 700, 472, 365, 264, 18760, 82, 11], "avg_logprob": -0.19308035341756685, "compression_ratio": 1.2209302325581395, "no_speech_prob": 0.0, "words": [{"start": 172.24999999999997, "end": 172.98999999999998, "word": " And", "probability": 0.4521484375}, {"start": 172.98999999999998, "end": 173.73, "word": " short", "probability": 0.89208984375}, {"start": 173.73, "end": 174.75, "word": " answer.", "probability": 0.92236328125}, {"start": 175.13, "end": 175.29, "word": " Very", "probability": 0.8212890625}, {"start": 175.29, "end": 175.63, "word": " good.", "probability": 0.9208984375}, {"start": 178.31, "end": 178.91, "word": " Short", "probability": 0.94189453125}, {"start": 178.91, "end": 179.49, "word": " answer.", "probability": 0.95166015625}, {"start": 188.87, "end": 189.61, "word": " Now,", "probability": 0.92333984375}, {"start": 189.87, "end": 192.25, "word": " if", "probability": 0.92529296875}, {"start": 192.25, "end": 192.39, "word": " I", "probability": 0.99853515625}, {"start": 192.39, "end": 192.69, "word": " ask", "probability": 0.8818359375}, {"start": 192.69, "end": 193.01, "word": " you", "probability": 0.96533203125}, {"start": 193.01, "end": 193.71, "word": " to", "probability": 0.966796875}, {"start": 193.71, "end": 193.91, "word": " deal", "probability": 0.982421875}, {"start": 193.91, "end": 194.13, "word": " with", "probability": 0.908203125}, {"start": 194.13, "end": 194.29, "word": " the", "probability": 0.9208984375}, {"start": 194.29, "end": 194.55, "word": " first", "probability": 0.8876953125}, {"start": 194.55, "end": 194.91, "word": " one", "probability": 0.9326171875}, {"start": 194.91, "end": 196.29, "word": " with", "probability": 0.54296875}, {"start": 196.29, "end": 196.47, "word": " the", "probability": 0.888671875}, {"start": 196.47, "end": 197.37, "word": " tenses,", "probability": 0.5634765625}], "temperature": 1.0}, {"id": 7, "seek": 22993, "start": 202.19, "end": 229.93, "text": " Yes. Today, Inshallah, we will discuss the tenses and the questions. Next time, we will deal with negatives and short answers. 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And present perfect continuous. Yes, so these are six tenses. We will deal with them throughout the whole syllabus.", "tokens": [400, 1791, 10957, 13, 400, 1974, 2176, 10957, 13, 1079, 11, 370, 613, 366, 2309, 18760, 82, 13, 492, 486, 2028, 365, 552, 3710, 264, 1379, 48077, 13], "avg_logprob": -0.21672952997273412, "compression_ratio": 1.3047619047619048, "no_speech_prob": 0.0, "words": [{"start": 265.61, "end": 266.57, "word": " And", "probability": 0.39990234375}, {"start": 266.57, "end": 267.53, "word": " past", "probability": 0.73876953125}, {"start": 267.53, "end": 269.83, "word": " continuous.", "probability": 0.826171875}, {"start": 271.23, "end": 272.19, "word": " And", "probability": 0.82958984375}, {"start": 272.19, "end": 273.63, "word": " present", "probability": 0.8857421875}, {"start": 273.63, "end": 276.59, "word": " perfect", "probability": 0.9111328125}, {"start": 276.59, "end": 279.61, "word": " continuous.", "probability": 0.8173828125}, {"start": 282.27, "end": 282.95, "word": " Yes,", "probability": 0.81689453125}, {"start": 283.23, "end": 283.53, "word": " so", "probability": 0.923828125}, {"start": 283.53, "end": 283.85, "word": " these", "probability": 0.8359375}, {"start": 283.85, "end": 284.21, "word": " are", "probability": 0.943359375}, {"start": 284.21, "end": 284.87, "word": " six", "probability": 0.84228515625}, {"start": 284.87, "end": 286.49, "word": " tenses.", "probability": 0.68408203125}, {"start": 286.77, "end": 286.97, "word": " We", "probability": 0.95458984375}, {"start": 286.97, "end": 287.13, "word": " will", "probability": 0.8916015625}, {"start": 287.13, "end": 287.33, "word": " deal", "probability": 0.98046875}, {"start": 287.33, "end": 287.53, "word": " with", "probability": 0.9072265625}, {"start": 287.53, "end": 287.85, "word": " them", "probability": 0.89501953125}, {"start": 287.85, "end": 288.69, "word": " throughout", "probability": 0.84228515625}, {"start": 288.69, "end": 289.03, "word": " the", "probability": 0.92431640625}, {"start": 289.03, "end": 289.51, "word": " whole", "probability": 0.90283203125}, {"start": 289.51, "end": 289.91, "word": " syllabus.", "probability": 0.90087890625}], "temperature": 1.0}, {"id": 10, "seek": 31960, "start": 291.8, "end": 319.6, "text": " Today, just we want to use the names of these senses. We just want to know them, the names of these senses. Also, we have two passives, passive forms, present, symbol, passive, and past, symbol,", "tokens": [2692, 11, 445, 321, 528, 281, 764, 264, 5288, 295, 613, 17057, 13, 492, 445, 528, 281, 458, 552, 11, 264, 5288, 295, 613, 17057, 13, 2743, 11, 321, 362, 732, 1320, 1539, 11, 14975, 6422, 11, 1974, 11, 5986, 11, 14975, 11, 293, 1791, 11, 5986, 11], "avg_logprob": -0.21890943390982492, "compression_ratio": 1.652542372881356, "no_speech_prob": 0.0, "words": [{"start": 291.8, "end": 292.24, "word": " Today,", "probability": 0.7646484375}, {"start": 292.48, "end": 292.72, "word": " just", "probability": 0.75537109375}, {"start": 292.72, "end": 292.92, "word": " we", "probability": 0.84765625}, {"start": 292.92, "end": 293.26, "word": " want", "probability": 0.89208984375}, {"start": 293.26, "end": 293.48, "word": " to", "probability": 0.970703125}, {"start": 293.48, "end": 294.26, "word": " use", "probability": 0.8740234375}, {"start": 294.26, "end": 294.56, "word": " the", "probability": 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"probability": 0.9423828125}, {"start": 339.24, "end": 340.98, "word": " the", "probability": 0.8525390625}, {"start": 340.98, "end": 341.26, "word": " first", "probability": 0.8974609375}, {"start": 341.26, "end": 341.84, "word": " question", "probability": 0.92578125}], "temperature": 1.0}, {"id": 12, "seek": 37119, "start": 342.61, "end": 371.19, "text": " Which tense uses does, did and do in the negative and in the question? Present simple and past simple. Yes. So here we use do, does in the negative and did in the past simple.", "tokens": [3013, 18760, 4960, 775, 11, 630, 293, 360, 294, 264, 3671, 293, 294, 264, 1168, 30, 33253, 2199, 293, 1791, 2199, 13, 1079, 13, 407, 510, 321, 764, 360, 11, 775, 294, 264, 3671, 293, 630, 294, 264, 1791, 2199, 13], "avg_logprob": -0.24051338895445779, "compression_ratio": 1.5575221238938053, "no_speech_prob": 0.0, "words": [{"start": 342.61, "end": 343.13, "word": " Which", "probability": 0.720703125}, {"start": 343.13, "end": 344.19, "word": " tense", "probability": 0.7421875}, {"start": 344.19, "end": 345.59, "word": " uses", "probability": 0.439208984375}, {"start": 345.59, "end": 346.91, "word": " does,", "probability": 0.272705078125}, {"start": 347.51, "end": 347.85, "word": " did", "probability": 0.970703125}, {"start": 347.85, "end": 348.47, "word": " and", "probability": 0.59765625}, {"start": 348.47, "end": 349.07, "word": " do", "probability": 0.9541015625}, {"start": 349.07, "end": 349.67, "word": " in", "probability": 0.8359375}, {"start": 349.67, "end": 349.87, "word": " the", "probability": 0.88818359375}, {"start": 349.87, "end": 350.41, "word": " negative", "probability": 0.9130859375}, {"start": 350.41, "end": 350.83, "word": " and", "probability": 0.884765625}, {"start": 350.83, "end": 351.25, "word": " in", "probability": 0.89306640625}, {"start": 351.25, "end": 351.75, "word": " the", "probability": 0.91845703125}, {"start": 351.75, "end": 352.85, "word": " question?", "probability": 0.95849609375}, {"start": 353.35, "end": 353.89, "word": " Present", "probability": 0.80615234375}, {"start": 353.89, "end": 355.35, "word": " simple", "probability": 0.6767578125}, {"start": 355.35, "end": 356.47, "word": " and", "probability": 0.499267578125}, {"start": 356.47, "end": 357.71, "word": " past", "probability": 0.81591796875}, {"start": 357.71, "end": 358.15, "word": " simple.", "probability": 0.96728515625}, {"start": 358.31, "end": 358.51, "word": " Yes.", "probability": 0.50390625}, {"start": 358.85, "end": 359.03, "word": " So", "probability": 0.94677734375}, {"start": 359.03, "end": 359.57, "word": " here", "probability": 0.78662109375}, {"start": 359.57, "end": 360.17, "word": " we", "probability": 0.71923828125}, {"start": 360.17, "end": 360.57, "word": " use", "probability": 0.8427734375}, {"start": 360.57, "end": 361.19, "word": " do,", "probability": 0.86572265625}, {"start": 362.47, "end": 362.97, "word": " does", "probability": 0.9541015625}, {"start": 362.97, "end": 363.81, "word": " in", "probability": 0.85498046875}, {"start": 363.81, "end": 364.13, "word": " the", "probability": 0.90869140625}, {"start": 364.13, "end": 365.33, "word": " negative", "probability": 0.94091796875}, {"start": 365.33, "end": 366.45, "word": " and", "probability": 0.450439453125}, {"start": 366.45, "end": 367.17, "word": " did", "probability": 0.96044921875}, {"start": 367.17, "end": 369.29, "word": " in", "probability": 0.880859375}, {"start": 369.29, "end": 369.53, "word": " the", "probability": 0.91015625}, {"start": 369.53, "end": 369.99, "word": " past", "probability": 0.8857421875}, {"start": 369.99, "end": 371.19, "word": " simple.", "probability": 0.90283203125}], "temperature": 1.0}, {"id": 13, "seek": 40120, "start": 373.1, "end": 401.2, "text": " So the first question, which tense is used did, does, do in the negative and in the question? Present simple and past simple. Another question, which tense is used have? Here, yes. Here, have.", "tokens": [407, 264, 700, 1168, 11, 597, 18760, 307, 1143, 630, 11, 775, 11, 360, 294, 264, 3671, 293, 294, 264, 1168, 30, 33253, 2199, 293, 1791, 2199, 13, 3996, 1168, 11, 597, 18760, 307, 1143, 362, 30, 1692, 11, 2086, 13, 1692, 11, 362, 13], "avg_logprob": -0.2739470095738121, "compression_ratio": 1.6218487394957983, "no_speech_prob": 0.0, "words": [{"start": 373.1, "end": 373.36, "word": " So", "probability": 0.78564453125}, {"start": 373.36, "end": 373.56, "word": " the", "probability": 0.6767578125}, {"start": 373.56, "end": 373.78, "word": " first", "probability": 0.89208984375}, {"start": 373.78, "end": 374.36, "word": " question,", "probability": 0.919921875}, {"start": 375.48, "end": 375.64, "word": " which", "probability": 0.83056640625}, {"start": 375.64, "end": 376.0, "word": " tense", "probability": 0.64892578125}, {"start": 376.0, "end": 376.28, "word": " is", "probability": 0.58740234375}, {"start": 376.28, "end": 376.66, "word": " used", "probability": 0.89697265625}, {"start": 376.66, "end": 377.9, "word": " did,", "probability": 0.68505859375}, {"start": 378.24, "end": 379.36, "word": " does,", "probability": 0.919921875}, {"start": 380.18, "end": 380.5, "word": " do", "probability": 0.9580078125}, {"start": 380.5, "end": 380.98, "word": " in", "probability": 0.70703125}, {"start": 380.98, "end": 381.1, "word": " the", "probability": 0.91943359375}, {"start": 381.1, "end": 381.42, "word": " negative", "probability": 0.9296875}, {"start": 381.42, "end": 381.68, "word": " and", "probability": 0.85400390625}, {"start": 381.68, "end": 381.84, "word": " in", "probability": 0.9189453125}, {"start": 381.84, "end": 381.98, "word": " the", "probability": 0.9248046875}, {"start": 381.98, "end": 382.44, "word": " question?", "probability": 0.96337890625}, {"start": 383.0, "end": 384.04, "word": " Present", "probability": 0.41162109375}, {"start": 384.04, "end": 384.56, "word": " simple", "probability": 0.80712890625}, {"start": 384.56, "end": 385.4, "word": " and", "probability": 0.84765625}, {"start": 385.4, "end": 386.28, "word": " past", "probability": 0.7392578125}, {"start": 386.28, "end": 387.24, "word": " simple.", "probability": 0.951171875}, {"start": 387.82, "end": 388.24, "word": " Another", "probability": 0.84619140625}, {"start": 388.24, "end": 388.78, "word": " question,", "probability": 0.91650390625}, {"start": 389.68, "end": 390.04, "word": " which", "probability": 0.9150390625}, {"start": 390.04, "end": 390.44, "word": " tense", "probability": 0.90478515625}, {"start": 390.44, "end": 390.84, "word": " is", "probability": 0.912109375}, {"start": 390.84, "end": 391.52, "word": " used", "probability": 0.87939453125}, {"start": 391.52, "end": 392.14, "word": " have?", "probability": 0.90283203125}, {"start": 395.34, "end": 396.38, "word": " Here,", "probability": 0.31591796875}, {"start": 397.1, "end": 397.66, "word": " yes.", "probability": 0.474853515625}, {"start": 399.38, "end": 400.42, "word": " Here,", "probability": 0.599609375}, {"start": 400.56, "end": 401.2, "word": " have.", "probability": 0.95556640625}], "temperature": 1.0}, {"id": 14, "seek": 42965, "start": 403.31, "end": 429.65, "text": " And here have. The third question, which tense is use B? The continuous here and the past continuous B and the present simple passive. We use B. Uh-huh.", "tokens": [400, 510, 362, 13, 440, 2636, 1168, 11, 597, 18760, 307, 764, 363, 30, 440, 10957, 510, 293, 264, 1791, 10957, 363, 293, 264, 1974, 2199, 14975, 13, 492, 764, 363, 13, 4019, 12, 18710, 13], "avg_logprob": -0.3194679118491508, "compression_ratio": 1.3660714285714286, "no_speech_prob": 0.0, "words": [{"start": 403.31, "end": 403.71, "word": " And", "probability": 0.445068359375}, {"start": 403.71, "end": 404.11, "word": " here", "probability": 0.853515625}, {"start": 404.11, "end": 404.83, "word": " have.", "probability": 0.53173828125}, {"start": 406.85, "end": 407.63, "word": " The", "probability": 0.89501953125}, {"start": 407.63, "end": 407.89, "word": " third", "probability": 0.9189453125}, {"start": 407.89, "end": 408.51, "word": " question,", "probability": 0.92529296875}, {"start": 409.83, "end": 410.11, "word": " which", "probability": 0.92578125}, {"start": 410.11, "end": 410.57, "word": " tense", "probability": 0.7001953125}, {"start": 410.57, "end": 411.05, "word": " is", "probability": 0.52392578125}, {"start": 411.05, "end": 412.63, "word": " use", "probability": 0.69921875}, {"start": 412.63, "end": 413.45, "word": " B?", "probability": 0.51806640625}, {"start": 414.85, "end": 416.09, "word": " The", "probability": 0.68017578125}, {"start": 416.09, "end": 416.59, "word": " continuous", "probability": 0.8154296875}, {"start": 416.59, "end": 417.87, "word": " here", "probability": 0.5126953125}, {"start": 417.87, "end": 419.05, "word": " and", "probability": 0.630859375}, {"start": 419.05, "end": 419.21, "word": " the", "probability": 0.82080078125}, {"start": 419.21, "end": 419.49, "word": " past", "probability": 0.91943359375}, {"start": 419.49, "end": 420.17, "word": " continuous", "probability": 0.85986328125}, {"start": 420.17, "end": 420.85, "word": " B", "probability": 0.73046875}, {"start": 420.85, "end": 422.43, "word": " and", "probability": 0.63623046875}, {"start": 422.43, "end": 422.65, "word": " the", "probability": 0.75146484375}, {"start": 422.65, "end": 423.61, "word": " present", "probability": 0.90380859375}, {"start": 423.61, "end": 425.45, "word": " simple", "probability": 0.6669921875}, {"start": 425.45, "end": 426.05, "word": " passive.", "probability": 0.89111328125}, {"start": 426.51, "end": 426.63, "word": " We", "probability": 0.939453125}, {"start": 426.63, "end": 426.91, "word": " use", "probability": 0.87548828125}, {"start": 426.91, "end": 427.53, "word": " B.", "probability": 0.98193359375}, {"start": 428.95, "end": 429.49, "word": " Uh", "probability": 0.70263671875}, {"start": 429.49, "end": 429.65, "word": "-huh.", "probability": 0.6494140625}], "temperature": 1.0}, {"id": 15, "seek": 44772, "start": 430.34, "end": 447.72, "text": " And here we use B. So this is the first exercise. Is it clear? Yes. Now, we will clean this and", "tokens": [400, 510, 321, 764, 363, 13, 407, 341, 307, 264, 700, 5380, 13, 1119, 309, 1850, 30, 1079, 13, 823, 11, 321, 486, 2541, 341, 293], "avg_logprob": -0.24001736552626998, "compression_ratio": 1.0909090909090908, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 430.34, "end": 430.76, "word": " And", "probability": 0.363525390625}, {"start": 430.76, "end": 431.12, "word": " here", "probability": 0.8544921875}, {"start": 431.12, "end": 431.42, "word": " we", "probability": 0.75634765625}, {"start": 431.42, "end": 431.82, "word": " use", "probability": 0.8623046875}, {"start": 431.82, "end": 432.22, "word": " B.", "probability": 0.309326171875}, {"start": 432.64, "end": 433.04, "word": " So", "probability": 0.9169921875}, {"start": 433.04, "end": 433.42, "word": " this", "probability": 0.78857421875}, {"start": 433.42, "end": 433.84, "word": " is", "probability": 0.9560546875}, {"start": 433.84, "end": 434.48, "word": " the", "probability": 0.923828125}, {"start": 434.48, "end": 434.98, "word": " first", "probability": 0.8916015625}, {"start": 434.98, "end": 436.14, "word": " exercise.", "probability": 0.96044921875}, {"start": 439.64, "end": 440.48, "word": " Is", "probability": 0.80908203125}, {"start": 440.48, "end": 440.62, "word": " it", "probability": 0.92919921875}, {"start": 440.62, "end": 440.9, "word": " clear?", "probability": 0.890625}, {"start": 441.66, "end": 442.0, "word": " Yes.", "probability": 0.79833984375}, {"start": 443.06, "end": 443.58, "word": " Now,", "probability": 0.68994140625}, {"start": 444.72, "end": 446.14, "word": " we", "probability": 0.94091796875}, {"start": 446.14, "end": 446.34, "word": " will", "probability": 0.89794921875}, {"start": 446.34, "end": 446.64, "word": " clean", "probability": 0.798828125}, {"start": 446.64, "end": 447.06, "word": " this", "probability": 0.9462890625}, {"start": 447.06, "end": 447.72, "word": " and", "probability": 0.69091796875}], "temperature": 1.0}, {"id": 16, "seek": 50024, "start": 471.4, "end": 500.24, "text": " Now look here. That's enough. Now present simple, past simple, present perfect simple, present continuous, past continuous, present perfect continuous, present simple passive,", "tokens": [823, 574, 510, 13, 663, 311, 1547, 13, 823, 1974, 2199, 11, 1791, 2199, 11, 1974, 2176, 2199, 11, 1974, 10957, 11, 1791, 10957, 11, 1974, 2176, 10957, 11, 1974, 2199, 14975, 11], "avg_logprob": -0.16544117778539658, "compression_ratio": 1.8526315789473684, "no_speech_prob": 0.0, "words": [{"start": 471.4, "end": 471.7, "word": " Now", "probability": 0.8857421875}, {"start": 471.7, "end": 471.94, "word": " look", "probability": 0.66650390625}, {"start": 471.94, "end": 472.32, "word": " here.", "probability": 0.869140625}, {"start": 477.28, "end": 478.24, "word": " That's", "probability": 0.9189453125}, {"start": 478.24, "end": 478.58, "word": " enough.", "probability": 0.869140625}, {"start": 484.02, "end": 484.98, "word": " Now", "probability": 0.92626953125}, {"start": 484.98, "end": 485.42, "word": " present", "probability": 0.54296875}, {"start": 485.42, "end": 485.88, "word": " simple,", "probability": 0.474609375}, {"start": 487.2, "end": 487.48, "word": " past", "probability": 0.84423828125}, {"start": 487.48, "end": 487.9, "word": " simple,", "probability": 0.96142578125}, {"start": 488.94, "end": 489.24, "word": " present", "probability": 0.919921875}, {"start": 489.24, "end": 489.74, "word": " perfect", "probability": 0.89111328125}, {"start": 489.74, "end": 490.16, "word": " simple,", "probability": 0.96630859375}, {"start": 491.5, "end": 491.82, "word": " present", "probability": 0.92236328125}, {"start": 491.82, "end": 492.3, "word": " continuous,", "probability": 0.873046875}, {"start": 493.54, "end": 493.78, "word": " past", "probability": 0.8896484375}, {"start": 493.78, "end": 494.26, "word": " continuous,", "probability": 0.8701171875}, {"start": 495.22, "end": 495.52, "word": " present", "probability": 0.92626953125}, {"start": 495.52, "end": 496.02, "word": " perfect", "probability": 0.9150390625}, {"start": 496.02, "end": 496.64, "word": " continuous,", "probability": 0.84423828125}, {"start": 498.32, "end": 498.66, "word": " present", "probability": 0.9169921875}, {"start": 498.66, "end": 499.8, "word": " simple", "probability": 0.95068359375}, {"start": 499.8, "end": 500.24, "word": " passive,", "probability": 0.89697265625}], "temperature": 1.0}, {"id": 17, "seek": 52704, "start": 501.3, "end": 527.04, "text": " Past, simple, passive. The first question, which tense uses the auxiliary verbs do, does, did to make the negative and the question? This is it, do, does, and did.", "tokens": [18408, 11, 2199, 11, 14975, 13, 440, 700, 1168, 11, 597, 18760, 4960, 264, 43741, 30051, 360, 11, 775, 11, 630, 281, 652, 264, 3671, 293, 264, 1168, 30, 639, 307, 309, 11, 360, 11, 775, 11, 293, 630, 13], "avg_logprob": -0.40167683508338, "compression_ratio": 1.3442622950819672, "no_speech_prob": 0.0, "words": [{"start": 501.3, "end": 501.8, "word": " Past,", "probability": 0.7041015625}, {"start": 501.92, "end": 502.26, "word": " simple,", "probability": 0.85986328125}, {"start": 502.4, "end": 502.86, "word": " passive.", "probability": 0.92138671875}, {"start": 503.68, "end": 503.82, "word": " The", "probability": 0.86669921875}, {"start": 503.82, "end": 504.06, "word": " first", "probability": 0.89892578125}, {"start": 504.06, "end": 504.68, "word": " question,", "probability": 0.921875}, {"start": 507.24, "end": 507.5, "word": " which", "probability": 0.669921875}, {"start": 507.5, "end": 507.94, "word": " tense", "probability": 0.398681640625}, {"start": 507.94, "end": 508.68, "word": " uses", "probability": 0.452392578125}, {"start": 508.68, "end": 508.88, "word": " the", "probability": 0.517578125}, {"start": 508.88, "end": 509.2, "word": " auxiliary", "probability": 0.98779296875}, {"start": 509.2, "end": 509.84, "word": " verbs", "probability": 0.87451171875}, {"start": 509.84, "end": 510.32, "word": " do,", "probability": 0.689453125}, {"start": 510.68, "end": 510.98, "word": " does,", "probability": 0.6796875}, {"start": 511.46, "end": 511.74, "word": " did", "probability": 0.96435546875}, {"start": 511.74, "end": 512.38, "word": " to", "probability": 0.771484375}, {"start": 512.38, "end": 512.9, "word": " make", "probability": 0.94287109375}, {"start": 512.9, "end": 513.72, "word": " the", "probability": 0.74658203125}, {"start": 513.72, "end": 514.28, "word": " negative", "probability": 0.9287109375}, {"start": 514.28, "end": 514.7, "word": " and", "probability": 0.85693359375}, {"start": 514.7, "end": 514.84, "word": " the", "probability": 0.70361328125}, {"start": 514.84, "end": 515.24, "word": " question?", "probability": 0.95361328125}, {"start": 516.32, "end": 516.48, "word": " This", "probability": 0.748046875}, {"start": 516.48, "end": 516.84, "word": " is", "probability": 0.95556640625}, {"start": 516.84, "end": 520.16, "word": " it,", "probability": 0.09149169921875}, {"start": 520.84, "end": 522.3, "word": " do,", "probability": 0.92626953125}, {"start": 523.78, "end": 524.2, "word": " does,", "probability": 0.97216796875}, {"start": 525.54, "end": 526.14, "word": " and", "probability": 0.91943359375}, {"start": 526.14, "end": 527.04, "word": " did.", "probability": 0.6279296875}], "temperature": 1.0}, {"id": 18, "seek": 55565, "start": 530.65, "end": 555.65, "text": " Then the other question, which tense use the auxiliary verbs have? Present perfect. Present perfect simple. And present perfect continuous. Which tense use the auxiliary verbs be? Present continuous.", "tokens": [1396, 264, 661, 1168, 11, 597, 18760, 764, 264, 43741, 30051, 362, 30, 33253, 2176, 13, 33253, 2176, 2199, 13, 400, 1974, 2176, 10957, 13, 3013, 18760, 764, 264, 43741, 30051, 312, 30, 33253, 10957, 13], "avg_logprob": -0.3570523584211195, "compression_ratio": 1.7241379310344827, "no_speech_prob": 0.0, "words": [{"start": 530.65, "end": 530.93, "word": " Then", "probability": 0.449462890625}, {"start": 530.93, "end": 531.45, "word": " the", "probability": 0.70263671875}, {"start": 531.45, "end": 531.83, "word": " other", "probability": 0.77490234375}, {"start": 531.83, "end": 532.35, "word": " question,", "probability": 0.90771484375}, {"start": 532.65, "end": 532.79, "word": " which", "probability": 0.8212890625}, {"start": 532.79, "end": 533.15, "word": " tense", "probability": 0.65234375}, {"start": 533.15, "end": 534.75, "word": " use", "probability": 0.28662109375}, {"start": 534.75, "end": 535.01, "word": " the", "probability": 0.83740234375}, {"start": 535.01, "end": 535.33, "word": " auxiliary", "probability": 0.91259765625}, {"start": 535.33, "end": 535.81, "word": " verbs", "probability": 0.85498046875}, {"start": 535.81, "end": 536.57, "word": " have?", "probability": 0.6015625}, {"start": 536.87, "end": 537.17, "word": " Present", "probability": 0.67724609375}, {"start": 537.17, "end": 537.61, "word": " perfect.", "probability": 0.77099609375}, {"start": 539.37, "end": 540.37, "word": " Present", "probability": 0.4482421875}, {"start": 540.37, "end": 541.79, "word": " perfect", "probability": 0.82568359375}, {"start": 541.79, "end": 542.21, "word": " simple.", "probability": 0.5302734375}, {"start": 544.97, "end": 544.97, "word": " And", "probability": 0.64404296875}, {"start": 544.97, "end": 545.45, "word": " present", "probability": 0.8427734375}, {"start": 545.45, "end": 546.17, "word": " perfect", "probability": 0.92919921875}, {"start": 546.17, "end": 546.67, "word": " continuous.", "probability": 0.85107421875}, {"start": 549.91, "end": 550.91, "word": " Which", "probability": 0.73193359375}, {"start": 550.91, "end": 551.91, "word": " tense", "probability": 0.9111328125}, {"start": 551.91, "end": 552.63, "word": " use", "probability": 0.71435546875}, {"start": 552.63, "end": 552.81, "word": " the", "probability": 0.91162109375}, {"start": 552.81, "end": 553.07, "word": " auxiliary", "probability": 0.912109375}, {"start": 553.07, "end": 553.59, "word": " verbs", "probability": 0.75732421875}, {"start": 553.59, "end": 554.07, "word": " be?", "probability": 0.83984375}, {"start": 554.59, "end": 555.03, "word": " Present", "probability": 0.6943359375}, {"start": 555.03, "end": 555.65, "word": " continuous.", "probability": 0.83154296875}], "temperature": 1.0}, {"id": 19, "seek": 58892, "start": 561.97, "end": 588.93, "text": " Past continuous Present simple passive Past simple passive By the end of this exercise, we just know the names of the tenses and something about the auxiliary verbs in them. Now, we will discuss another one. What is it?", "tokens": [18408, 10957, 33253, 2199, 14975, 18408, 2199, 14975, 3146, 264, 917, 295, 341, 5380, 11, 321, 445, 458, 264, 5288, 295, 264, 18760, 82, 293, 746, 466, 264, 43741, 30051, 294, 552, 13, 823, 11, 321, 486, 2248, 1071, 472, 13, 708, 307, 309, 30], "avg_logprob": -0.2043138606392819, "compression_ratio": 1.4379084967320261, "no_speech_prob": 0.0, "words": [{"start": 561.97, "end": 562.31, "word": " Past", "probability": 0.55322265625}, {"start": 562.31, "end": 562.81, "word": " continuous", "probability": 0.8525390625}, {"start": 562.81, "end": 563.29, "word": " Present", "probability": 0.325439453125}, {"start": 563.29, "end": 563.61, "word": " simple", "probability": 0.76708984375}, {"start": 563.61, "end": 563.99, "word": " passive", "probability": 0.9296875}, {"start": 563.99, "end": 570.63, "word": " Past", "probability": 0.86572265625}, {"start": 570.63, "end": 570.99, "word": " simple", "probability": 0.9189453125}, {"start": 570.99, "end": 571.35, "word": " passive", "probability": 0.93798828125}, {"start": 571.35, "end": 571.93, "word": " By", "probability": 0.63818359375}, {"start": 571.93, "end": 574.29, "word": " the", "probability": 0.92529296875}, {"start": 574.29, "end": 574.49, "word": " end", "probability": 0.9052734375}, {"start": 574.49, "end": 574.65, "word": " of", "probability": 0.96923828125}, {"start": 574.65, "end": 574.81, "word": " this", "probability": 0.93408203125}, {"start": 574.81, "end": 575.31, "word": " exercise,", "probability": 0.93212890625}, {"start": 576.25, "end": 576.37, "word": " we", "probability": 0.9130859375}, {"start": 576.37, "end": 576.81, "word": " just", "probability": 0.89697265625}, {"start": 576.81, "end": 577.67, "word": " know", "probability": 0.85986328125}, {"start": 577.67, "end": 577.95, "word": " the", "probability": 0.908203125}, {"start": 577.95, "end": 578.35, "word": " names", "probability": 0.86865234375}, {"start": 578.35, "end": 578.57, "word": " of", "probability": 0.96826171875}, {"start": 578.57, "end": 578.73, "word": " the", "probability": 0.873046875}, {"start": 578.73, "end": 579.43, "word": " tenses", "probability": 0.6279296875}, {"start": 579.43, "end": 580.03, "word": " and", "probability": 0.8251953125}, {"start": 580.03, "end": 581.27, "word": " something", "probability": 0.66943359375}, {"start": 581.27, "end": 582.01, "word": " about", "probability": 0.8916015625}, {"start": 582.01, "end": 582.27, "word": " the", "probability": 0.88671875}, {"start": 582.27, "end": 582.63, "word": " auxiliary", "probability": 0.93408203125}, {"start": 582.63, "end": 583.11, "word": " verbs", "probability": 0.9267578125}, {"start": 583.11, "end": 583.93, "word": " in", "probability": 0.935546875}, {"start": 583.93, "end": 584.39, "word": " them.", "probability": 0.90478515625}, {"start": 584.81, "end": 585.57, "word": " Now,", "probability": 0.93603515625}, {"start": 585.85, "end": 586.53, "word": " we", "probability": 0.9287109375}, {"start": 586.53, "end": 586.75, "word": " will", "probability": 0.8857421875}, {"start": 586.75, "end": 587.37, "word": " discuss", "probability": 0.8916015625}, {"start": 587.37, "end": 587.77, "word": " another", "probability": 0.89794921875}, {"start": 587.77, "end": 588.15, "word": " one.", "probability": 0.93017578125}, {"start": 588.41, "end": 588.53, "word": " What", "probability": 0.87939453125}, {"start": 588.53, "end": 588.65, "word": " is", "probability": 0.93798828125}, {"start": 588.65, "end": 588.93, "word": " it?", "probability": 0.95263671875}], "temperature": 1.0}, {"id": 20, "seek": 60205, "start": 590.2, "end": 602.06, "text": " Making questions. Making questions using the auxiliary verbs. So now the auxiliary verbs with the questions. I will clean this again.", "tokens": [14595, 1651, 13, 14595, 1651, 1228, 264, 43741, 30051, 13, 407, 586, 264, 43741, 30051, 365, 264, 1651, 13, 286, 486, 2541, 341, 797, 13], "avg_logprob": -0.23798077152325556, "compression_ratio": 1.488888888888889, "no_speech_prob": 0.0, "words": [{"start": 590.2, "end": 590.74, "word": " Making", "probability": 0.60595703125}, {"start": 590.74, "end": 591.54, "word": " questions.", "probability": 0.88720703125}, {"start": 592.06, "end": 592.9, "word": " Making", "probability": 0.685546875}, {"start": 592.9, "end": 593.62, "word": " questions", "probability": 0.94873046875}, {"start": 593.62, "end": 594.68, "word": " using", "probability": 0.57080078125}, {"start": 594.68, "end": 595.04, "word": " the", "probability": 0.65283203125}, {"start": 595.04, "end": 595.42, "word": " auxiliary", "probability": 0.962890625}, {"start": 595.42, "end": 596.32, "word": " verbs.", "probability": 0.93798828125}, {"start": 596.9, "end": 597.0, "word": " So", "probability": 0.88232421875}, {"start": 597.0, "end": 597.42, "word": " now", "probability": 0.8740234375}, {"start": 597.42, "end": 597.84, "word": " the", "probability": 0.496337890625}, {"start": 597.84, "end": 598.18, "word": " auxiliary", "probability": 0.82080078125}, {"start": 598.18, "end": 598.62, "word": " verbs", "probability": 0.92041015625}, {"start": 598.62, "end": 598.92, "word": " with", "probability": 0.900390625}, {"start": 598.92, "end": 599.06, "word": " the", "probability": 0.701171875}, {"start": 599.06, "end": 599.68, "word": " questions.", "probability": 0.9326171875}, {"start": 600.62, "end": 600.9, "word": " I", "probability": 0.98486328125}, {"start": 600.9, "end": 601.04, "word": " will", "probability": 0.91064453125}, {"start": 601.04, "end": 601.32, "word": " clean", "probability": 0.7392578125}, {"start": 601.32, "end": 601.68, "word": " this", "probability": 0.94482421875}, {"start": 601.68, "end": 602.06, "word": " again.", "probability": 0.94140625}], "temperature": 1.0}, {"id": 21, "seek": 65227, "start": 624.81, "end": 652.27, "text": " Now, I come from Scotland. I come from Scotland. This is a statement. The question using where.", "tokens": [823, 11, 286, 808, 490, 11180, 13, 286, 808, 490, 11180, 13, 639, 307, 257, 5629, 13, 440, 1168, 1228, 689, 13], "avg_logprob": -0.2085597761299299, "compression_ratio": 1.2151898734177216, "no_speech_prob": 0.0, "words": [{"start": 624.81, "end": 625.13, "word": " Now,", "probability": 0.85205078125}, {"start": 625.71, "end": 626.31, "word": " I", "probability": 0.75439453125}, {"start": 626.31, "end": 627.49, "word": " come", "probability": 0.90283203125}, {"start": 627.49, "end": 628.17, "word": " from", "probability": 0.9052734375}, {"start": 628.17, "end": 629.07, "word": " Scotland.", "probability": 0.81298828125}, {"start": 630.09, "end": 630.65, "word": " I", "probability": 0.62060546875}, {"start": 630.65, "end": 631.87, "word": " come", "probability": 0.91552734375}, {"start": 631.87, "end": 633.73, "word": " from", "probability": 0.89794921875}, {"start": 633.73, "end": 636.09, "word": " Scotland.", "probability": 0.81396484375}, {"start": 639.53, "end": 640.93, "word": " This", "probability": 0.89599609375}, {"start": 640.93, "end": 641.21, "word": " is", "probability": 0.95751953125}, {"start": 641.21, "end": 641.37, "word": " a", "probability": 0.98828125}, {"start": 641.37, "end": 641.99, "word": " statement.", "probability": 0.91650390625}, {"start": 643.01, "end": 644.41, "word": " The", "probability": 0.865234375}, {"start": 644.41, "end": 644.97, "word": " question", "probability": 0.921875}, {"start": 644.97, "end": 647.29, "word": " using", "probability": 0.491455078125}, {"start": 647.29, "end": 652.27, "word": " where.", "probability": 0.525390625}], "temperature": 1.0}, {"id": 22, "seek": 67771, "start": 653.29, "end": 677.71, "text": " Again, I come from Scotland. Make questions using where. So, the question here ends with question mark. Yes? Where does you come from? Where does you? 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So, where do you come from? Where do you come from? Where do you come from? Where do you come from? I come from Scotland. I come from Palestine. 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Because all of us, or most of us, come from Palestine. So when I ask you, where do you come from? Say, I am from, or I come from Gaza. I come from Rafah. I come from Khan Yunis. I come from Jabalia. I come from Bethlehem, et cetera. 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Number two, I was born in Gaza in 1994. I want to make two questions. 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So, the question, uh-huh, where, where, yes, where, teacher did, because it's fast.", "tokens": [400, 365, 562, 13, 407, 11, 264, 1168, 11, 2232, 12, 18710, 11, 689, 11, 689, 11, 2086, 11, 689, 11, 5027, 630, 11, 570, 309, 311, 2370, 13], "avg_logprob": -0.4986979325612386, "compression_ratio": 1.1785714285714286, "no_speech_prob": 0.0, "words": [{"start": 770.83, "end": 771.39, "word": " And", "probability": 0.43017578125}, {"start": 771.39, "end": 771.95, "word": " with", "probability": 0.89111328125}, {"start": 771.95, "end": 773.41, "word": " when.", "probability": 0.529296875}, {"start": 775.69, "end": 776.37, "word": " So,", "probability": 0.763671875}, {"start": 777.93, "end": 778.13, "word": " the", "probability": 0.921875}, {"start": 778.13, "end": 778.71, "word": " question,", "probability": 0.9169921875}, {"start": 781.67, "end": 781.91, "word": " uh", "probability": 0.18408203125}, {"start": 781.91, "end": 782.41, "word": "-huh,", "probability": 0.701416015625}, {"start": 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Where? Yes? Where do you live? Yes. Here, we don't have a helping verb like was, so we use do. Yes. Where do you? Do or does? Do. Why?", "tokens": [2305, 30, 2305, 30, 1079, 30, 2305, 360, 291, 1621, 30, 1079, 13, 1692, 11, 321, 500, 380, 362, 257, 4315, 9595, 411, 390, 11, 370, 321, 764, 360, 13, 1079, 13, 2305, 360, 291, 30, 1144, 420, 775, 30, 1144, 13, 1545, 30], "avg_logprob": -0.1769965238041348, "compression_ratio": 1.3523809523809525, "no_speech_prob": 0.0, "words": [{"start": 883.4215937499999, "end": 883.96, "word": " Where?", "probability": 0.7880859375}, {"start": 885.06, "end": 885.82, "word": " Where?", "probability": 0.60693359375}, {"start": 887.54, "end": 888.32, "word": " Yes?", "probability": 0.8017578125}, {"start": 889.58, "end": 890.62, "word": " Where", "probability": 0.76171875}, {"start": 890.62, "end": 891.72, "word": " do", "probability": 0.84423828125}, {"start": 891.72, "end": 891.86, "word": " you", "probability": 0.97314453125}, {"start": 891.86, "end": 892.12, "word": " live?", "probability": 0.93017578125}, {"start": 892.34, "end": 892.6, "word": " Yes.", "probability": 0.84619140625}, {"start": 892.86, "end": 893.44, "word": " Here,", "probability": 0.8310546875}, {"start": 893.66, "end": 894.1, "word": " we", "probability": 0.9638671875}, {"start": 894.1, "end": 894.46, "word": " don't", "probability": 0.98193359375}, {"start": 894.46, "end": 895.08, "word": " have", "probability": 0.9541015625}, {"start": 895.08, "end": 896.3, "word": " a", "probability": 0.953125}, {"start": 896.3, "end": 896.58, "word": " helping", "probability": 0.82421875}, {"start": 896.58, "end": 897.1, "word": " verb", "probability": 0.89990234375}, {"start": 897.1, "end": 897.48, "word": " like", "probability": 0.70068359375}, {"start": 897.48, "end": 898.0, "word": " was,", "probability": 0.56396484375}, {"start": 898.54, "end": 898.8, "word": " so", "probability": 0.94384765625}, {"start": 898.8, "end": 899.0, "word": " we", "probability": 0.9228515625}, {"start": 899.0, "end": 899.42, "word": " use", "probability": 0.8720703125}, {"start": 899.42, "end": 900.94, "word": " do.", "probability": 0.7880859375}, {"start": 901.28, "end": 901.74, "word": " Yes.", "probability": 0.78759765625}, {"start": 903.04, "end": 903.62, "word": " Where", "probability": 0.8447265625}, {"start": 903.62, "end": 906.84, "word": " do", "probability": 0.873046875}, {"start": 906.84, "end": 908.0, "word": " you?", "probability": 0.97509765625}, {"start": 909.08, "end": 909.38, "word": " Do", "probability": 0.9345703125}, {"start": 909.38, "end": 909.6, "word": " or", "probability": 0.900390625}, {"start": 909.6, "end": 909.92, "word": " does?", "probability": 0.95751953125}, {"start": 910.54, "end": 911.36, "word": " Do.", "probability": 0.86962890625}, {"start": 911.48, "end": 911.78, "word": " Why?", "probability": 0.85302734375}], "temperature": 1.0}, {"id": 31, "seek": 94126, "start": 913.16, "end": 941.26, "text": " Because it is in the present. If it is in the past, we use dead. If the subject is he or she, we use does. Yes. Now, where do you live? 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Yes. We don't use, do you have? We use have got. Because the answer with have got. If it's with have, do we have? Do you have? But have got?", "tokens": [1012, 867, 2283, 30, 1079, 13, 492, 500, 380, 764, 11, 360, 291, 362, 30, 492, 764, 362, 658, 13, 1436, 264, 1867, 365, 362, 658, 13, 759, 309, 311, 365, 362, 11, 360, 321, 362, 30, 1144, 291, 362, 30, 583, 362, 658, 30], "avg_logprob": -0.3104619617047517, "compression_ratio": 1.4403669724770642, "no_speech_prob": 0.0, "words": [{"start": 973.42, "end": 973.92, "word": " How", "probability": 0.11651611328125}, {"start": 973.92, "end": 973.94, "word": " many", "probability": 0.908203125}, {"start": 973.94, "end": 976.88, "word": " words?", "probability": 0.81982421875}, {"start": 980.72, "end": 981.36, "word": " Yes.", "probability": 0.2117919921875}, {"start": 985.66, "end": 986.3, "word": " We", "probability": 0.55419921875}, {"start": 986.3, "end": 986.6, "word": " don't", "probability": 0.973388671875}, {"start": 986.6, "end": 986.96, "word": " use,", "probability": 0.84814453125}, {"start": 987.04, "end": 987.36, "word": " do", "probability": 0.52294921875}, {"start": 987.36, "end": 987.52, "word": " you", "probability": 0.970703125}, {"start": 987.52, "end": 987.86, "word": " have?", "probability": 0.955078125}, {"start": 988.08, "end": 988.16, "word": " We", "probability": 0.89599609375}, {"start": 988.16, "end": 988.62, "word": " use", "probability": 0.8486328125}, {"start": 988.62, "end": 990.42, "word": " have", "probability": 0.71923828125}, {"start": 990.42, "end": 991.0, "word": " got.", "probability": 0.92822265625}, {"start": 992.12, "end": 992.76, "word": " Because", "probability": 0.708984375}, {"start": 992.76, "end": 993.02, "word": " the", "probability": 0.8994140625}, {"start": 993.02, "end": 993.26, "word": " answer", "probability": 0.955078125}, {"start": 993.26, "end": 993.46, "word": " with", "probability": 0.38671875}, {"start": 993.46, "end": 993.88, "word": " have", "probability": 0.92822265625}, {"start": 993.88, "end": 994.24, "word": " got.", "probability": 0.94482421875}, {"start": 995.54, "end": 995.76, "word": " If", "probability": 0.91015625}, {"start": 995.76, "end": 995.96, "word": " it's", "probability": 0.7197265625}, {"start": 995.96, "end": 996.14, "word": " with", "probability": 0.90185546875}, {"start": 996.14, "end": 996.6, "word": " have,", "probability": 0.9443359375}, {"start": 997.56, "end": 997.74, "word": " do", "probability": 0.8994140625}, {"start": 997.74, "end": 997.92, "word": " we", "probability": 0.88427734375}, {"start": 997.92, "end": 998.16, "word": " have?", "probability": 0.94970703125}, {"start": 998.36, "end": 998.46, "word": " Do", "probability": 0.904296875}, {"start": 998.46, "end": 998.64, "word": " you", "probability": 0.966796875}, {"start": 998.64, "end": 998.98, "word": " have?", "probability": 0.95166015625}, {"start": 999.36, "end": 999.66, "word": " But", "probability": 0.93359375}, {"start": 999.66, "end": 999.98, "word": " have", "probability": 0.8876953125}, {"start": 999.98, "end": 1000.28, "word": " got?", "probability": 0.9404296875}], "temperature": 1.0}, {"id": 34, "seek": 102731, "start": 1001.55, "end": 1027.31, "text": " How many brothers and sisters have you got? How many brothers and sisters have you got?", "tokens": [1012, 867, 8452, 293, 11589, 362, 291, 658, 30, 1012, 867, 8452, 293, 11589, 362, 291, 658, 30], "avg_logprob": -0.20990953633659765, "compression_ratio": 1.6603773584905661, "no_speech_prob": 0.0, "words": [{"start": 1001.55, "end": 1002.03, "word": " How", "probability": 0.293212890625}, {"start": 1002.03, "end": 1004.03, "word": " many", "probability": 0.90673828125}, {"start": 1004.03, "end": 1004.53, "word": " brothers", "probability": 0.8076171875}, {"start": 1004.53, "end": 1008.81, "word": " and", "probability": 0.8505859375}, {"start": 1008.81, "end": 1011.01, "word": " sisters", "probability": 0.8330078125}, {"start": 1011.01, "end": 1015.49, "word": " have", "probability": 0.85400390625}, {"start": 1015.49, "end": 1016.35, "word": " you", "probability": 0.97216796875}, {"start": 1016.35, "end": 1022.39, "word": " got?", "probability": 0.822265625}, {"start": 1024.21, "end": 1025.19, "word": " How", "probability": 0.79345703125}, {"start": 1025.19, "end": 1025.43, "word": " many", "probability": 0.90576171875}, {"start": 1025.43, "end": 1025.85, "word": " brothers", "probability": 0.8173828125}, {"start": 1025.85, "end": 1026.17, "word": " and", "probability": 0.9453125}, {"start": 1026.17, "end": 1026.51, "word": " sisters", "probability": 0.81005859375}, {"start": 1026.51, "end": 1026.77, "word": " have", "probability": 0.9384765625}, {"start": 1026.77, "end": 1026.89, "word": " you", "probability": 0.966796875}, {"start": 1026.89, "end": 1027.31, "word": " got?", "probability": 0.9267578125}], "temperature": 1.0}, {"id": 35, "seek": 105684, "start": 1028.31, "end": 1056.85, "text": " I have got two brothers and a sister. I will ask you a question. How many brothers and sisters do you have? Or have you got? I have five brothers. Five brothers. MashaAllah. And four sisters. I'm the fifth. You are the fifth? Yes. MashaAllah. MashaAllah. Someone else. How many brothers and sisters have you got?", "tokens": [286, 362, 658, 732, 8452, 293, 257, 4892, 13, 286, 486, 1029, 291, 257, 1168, 13, 1012, 867, 8452, 293, 11589, 360, 291, 362, 30, 1610, 362, 291, 658, 30, 286, 362, 1732, 8452, 13, 9436, 8452, 13, 376, 12137, 26022, 13, 400, 1451, 11589, 13, 286, 478, 264, 9266, 13, 509, 366, 264, 9266, 30, 1079, 13, 376, 12137, 26022, 13, 376, 12137, 26022, 13, 8734, 1646, 13, 1012, 867, 8452, 293, 11589, 362, 291, 658, 30], "avg_logprob": -0.2054984169670298, "compression_ratio": 1.9085365853658536, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1028.31, "end": 1028.61, "word": " I", "probability": 0.8154296875}, {"start": 1028.61, "end": 1028.81, "word": " have", "probability": 0.90576171875}, {"start": 1028.81, "end": 1029.23, "word": " got", "probability": 0.908203125}, {"start": 1029.23, "end": 1029.79, "word": " two", "probability": 0.89111328125}, {"start": 1029.79, "end": 1030.11, "word": " brothers", "probability": 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One brother and a sister. Yes. Mashallah. Rabbina zidhum. Is it clear? Yes. Now, we will deal with other questions according... Can I clean it now? Yes.", "tokens": [286, 362, 472, 3708, 293, 257, 4892, 13, 1485, 3708, 293, 257, 4892, 13, 1079, 13, 42039, 13492, 13, 36753, 1426, 710, 327, 14645, 13, 1119, 309, 1850, 30, 1079, 13, 823, 11, 321, 486, 2028, 365, 661, 1651, 4650, 485, 1664, 286, 2541, 309, 586, 30, 1079, 13], "avg_logprob": -0.32531249821186065, "compression_ratio": 1.4307692307692308, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1058.74, "end": 1059.48, "word": " I", "probability": 0.1751708984375}, {"start": 1059.48, "end": 1060.22, "word": " have", "probability": 0.88525390625}, {"start": 1060.22, "end": 1060.66, "word": " one", "probability": 0.6396484375}, {"start": 1060.66, "end": 1060.92, "word": " brother", "probability": 0.86328125}, {"start": 1060.92, "end": 1061.34, "word": " and", "probability": 0.85498046875}, {"start": 1061.34, "end": 1061.44, "word": " a", "probability": 0.319580078125}, {"start": 1061.44, "end": 1061.66, "word": " sister.", "probability": 0.6259765625}, {"start": 1062.2, "end": 1062.38, "word": " One", "probability": 0.466796875}, {"start": 1062.38, "end": 1062.7, "word": " brother", "probability": 0.90185546875}, {"start": 1062.7, "end": 1063.12, "word": " and", "probability": 0.9423828125}, {"start": 1063.12, "end": 1064.2, "word": " a", "probability": 0.875}, {"start": 1064.2, "end": 1064.66, "word": " sister.", "probability": 0.8388671875}, {"start": 1065.28, "end": 1065.58, "word": " Yes.", "probability": 0.8349609375}, {"start": 1065.94, "end": 1066.3, "word": " Mashallah.", "probability": 0.71435546875}, {"start": 1066.46, "end": 1066.6, "word": " Rabbina", "probability": 0.494140625}, {"start": 1066.6, "end": 1067.02, "word": " zidhum.", "probability": 0.5487467447916666}, {"start": 1069.58, "end": 1069.96, "word": " Is", "probability": 0.87451171875}, {"start": 1069.96, "end": 1070.34, "word": " it", "probability": 0.94580078125}, {"start": 1070.34, "end": 1071.7, "word": " clear?", "probability": 0.85693359375}, {"start": 1072.04, "end": 1072.28, "word": " Yes.", "probability": 0.8251953125}, {"start": 1073.08, "end": 1073.46, "word": " Now,", "probability": 0.78759765625}, {"start": 1074.06, "end": 1074.36, "word": " we", "probability": 0.9599609375}, {"start": 1074.36, "end": 1074.56, "word": " will", "probability": 0.89013671875}, {"start": 1074.56, "end": 1074.82, "word": " deal", "probability": 0.9765625}, {"start": 1074.82, "end": 1075.1, "word": " with", "probability": 0.90185546875}, {"start": 1075.1, "end": 1075.74, "word": " other", "probability": 0.890625}, {"start": 1075.74, "end": 1076.44, "word": " questions", "probability": 0.9599609375}, {"start": 1076.44, "end": 1081.0, "word": " according...", "probability": 0.49041748046875}, {"start": 1081.0, "end": 1081.54, "word": " Can", "probability": 0.822265625}, {"start": 1081.54, "end": 1081.66, "word": " I", "probability": 0.9970703125}, {"start": 1081.66, "end": 1081.86, "word": " clean", "probability": 0.91015625}, {"start": 1081.86, "end": 1081.98, "word": " it", "probability": 0.94775390625}, {"start": 1081.98, "end": 1082.28, "word": " now?", "probability": 0.94189453125}, {"start": 1082.62, "end": 1083.34, "word": " Yes.", "probability": 0.94970703125}], "temperature": 1.0}, {"id": 37, "seek": 111593, "start": 1112.65, "end": 1115.93, "text": " Now, this is the exercise", "tokens": [823, 11, 341, 307, 264, 5380], "avg_logprob": -0.24372208969933645, "compression_ratio": 0.8125, "no_speech_prob": 0.0, "words": [{"start": 1112.6499999999999, "end": 1113.6299999999999, "word": " Now,", "probability": 0.7431640625}, {"start": 1113.6299999999999, "end": 1114.61, "word": " this", "probability": 0.9326171875}, {"start": 1114.61, "end": 1115.03, "word": " is", "probability": 0.94921875}, {"start": 1115.03, "end": 1115.45, "word": " the", "probability": 0.93212890625}, {"start": 1115.45, "end": 1115.93, "word": " exercise", "probability": 0.96240234375}], "temperature": 1.0}, {"id": 38, "seek": 114127, "start": 1117.21, "end": 1141.27, "text": " About making questions The first exercise making questions with you Why with you? Because all the answers all the statements begin with I If it is begin with I I must use you Yes, I come from Scotland", "tokens": [7769, 1455, 1651, 440, 700, 5380, 1455, 1651, 365, 291, 1545, 365, 291, 30, 1436, 439, 264, 6338, 439, 264, 12363, 1841, 365, 286, 759, 309, 307, 1841, 365, 286, 286, 1633, 764, 291, 1079, 11, 286, 808, 490, 11180], "avg_logprob": -0.2299923722336932, "compression_ratio": 1.5112781954887218, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1117.21, "end": 1117.77, "word": " About", "probability": 0.477294921875}, {"start": 1117.77, "end": 1118.61, "word": " making", "probability": 0.88037109375}, {"start": 1118.61, "end": 1119.29, "word": " questions", "probability": 0.95263671875}, {"start": 1119.29, "end": 1120.61, "word": " The", "probability": 0.51953125}, {"start": 1120.61, "end": 1121.11, "word": " first", "probability": 0.83935546875}, {"start": 1121.11, "end": 1122.19, "word": " exercise", "probability": 0.8173828125}, {"start": 1122.19, "end": 1123.03, "word": " making", "probability": 0.31640625}, {"start": 1123.03, "end": 1123.53, "word": " questions", "probability": 0.95361328125}, {"start": 1123.53, "end": 1123.83, "word": " with", "probability": 0.9111328125}, {"start": 1123.83, "end": 1124.19, "word": " you", "probability": 0.865234375}, {"start": 1124.19, "end": 1125.53, "word": " Why", "probability": 0.72021484375}, {"start": 1125.53, "end": 1125.75, "word": " with", "probability": 0.89990234375}, {"start": 1125.75, "end": 1126.01, "word": " you?", "probability": 0.96435546875}, {"start": 1126.69, "end": 1127.23, "word": " Because", "probability": 0.6142578125}, {"start": 1127.23, "end": 1127.81, "word": " all", "probability": 0.93701171875}, {"start": 1127.81, "end": 1128.03, "word": " the", "probability": 0.923828125}, {"start": 1128.03, "end": 1128.67, "word": " answers", "probability": 0.89111328125}, {"start": 1128.67, "end": 1129.11, "word": " all", "probability": 0.646484375}, {"start": 1129.11, "end": 1129.31, "word": " the", "probability": 0.92333984375}, {"start": 1129.31, "end": 1129.87, "word": " statements", "probability": 0.85400390625}, {"start": 1129.87, "end": 1130.63, "word": " begin", "probability": 0.83642578125}, {"start": 1130.63, "end": 1130.97, "word": " with", "probability": 0.90869140625}, {"start": 1130.97, "end": 1131.29, "word": " I", "probability": 0.7998046875}, {"start": 1131.29, "end": 1132.73, "word": " If", "probability": 0.517578125}, {"start": 1132.73, "end": 1133.67, "word": " it", "probability": 0.94775390625}, {"start": 1133.67, "end": 1133.79, "word": " is", "probability": 0.84521484375}, {"start": 1133.79, "end": 1134.05, "word": " begin", "probability": 0.63720703125}, {"start": 1134.05, "end": 1134.23, "word": " with", "probability": 0.9130859375}, {"start": 1134.23, "end": 1134.57, "word": " I", "probability": 0.9658203125}, {"start": 1134.57, "end": 1135.43, "word": " I", "probability": 0.61572265625}, {"start": 1135.43, "end": 1135.73, "word": " must", "probability": 0.84521484375}, {"start": 1135.73, "end": 1136.09, "word": " use", "probability": 0.87548828125}, {"start": 1136.09, "end": 1136.75, "word": " you", "probability": 0.9423828125}, {"start": 1136.75, "end": 1139.19, "word": " Yes,", "probability": 0.85986328125}, {"start": 1139.33, "end": 1139.91, "word": " I", "probability": 0.998046875}, {"start": 1139.91, "end": 1140.31, "word": " come", "probability": 0.83203125}, {"start": 1140.31, "end": 1140.73, "word": " from", "probability": 0.89111328125}, {"start": 1140.73, "end": 1141.27, "word": " Scotland", "probability": 0.77734375}], "temperature": 1.0}, {"id": 39, "seek": 117057, "start": 1142.49, "end": 1170.57, "text": " I come from Palestine. I come from Egypt. I come from Gaza, Rafah, et cetera. Where? The question was where. So where do you come from? Where do you come from? It means where are you from? Where are you from? Where do you come from? The same. 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Two questions. Yes, who can read the first one? Yes. Where were you born? Yes, again. When were you born? The second one. Yes. So where were you born? 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I was born in Scotland, in Palestine, etc. I was... The second one, when were you born? I was born in 1994, in 1993, etc. Number three, I live in Milan. Where? Where do you live? 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Yes. Where do you live? I live in Palestine. I live in Gaza, et cetera. Number four. Yes. Have you got? Because I use have got, I say have you got? If I say have, do you have? 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Number five. Yes. I am studying English because I need it for my job. Why you read? Why you? Why I am make inversion are you?", "tokens": [1079, 13, 5118, 1732, 13, 1079, 13, 286, 669, 7601, 3669, 570, 286, 643, 309, 337, 452, 1691, 13, 1545, 291, 1401, 30, 1545, 291, 30, 1545, 286, 669, 652, 43576, 366, 291, 30], "avg_logprob": -0.3482142993382045, "compression_ratio": 1.2242990654205608, "no_speech_prob": 0.0, "words": [{"start": 1257.59, "end": 1258.19, "word": " Yes.", "probability": 0.30810546875}, {"start": 1259.63, "end": 1260.25, "word": " Number", "probability": 0.81005859375}, {"start": 1260.25, "end": 1260.57, "word": " five.", "probability": 0.693359375}, {"start": 1263.93, "end": 1264.19, "word": " Yes.", "probability": 0.63037109375}, {"start": 1265.07, "end": 1265.27, "word": " I", "probability": 0.28759765625}, {"start": 1265.27, "end": 1265.49, "word": " am", "probability": 0.810546875}, {"start": 1265.49, "end": 1265.81, "word": " studying", "probability": 0.86962890625}, {"start": 1265.81, "end": 1266.37, "word": " English", "probability": 0.96533203125}, {"start": 1266.37, "end": 1266.79, "word": " because", "probability": 0.8642578125}, {"start": 1266.79, "end": 1267.07, "word": " I", "probability": 0.98388671875}, {"start": 1267.07, "end": 1267.33, "word": " need", "probability": 0.8681640625}, {"start": 1267.33, "end": 1267.55, "word": " it", "probability": 0.953125}, {"start": 1267.55, "end": 1267.83, "word": " for", "probability": 0.95068359375}, {"start": 1267.83, "end": 1268.19, "word": " my", "probability": 0.97216796875}, {"start": 1268.19, "end": 1268.53, "word": " job.", "probability": 0.970703125}, {"start": 1268.95, "end": 1269.35, "word": " Why", "probability": 0.9404296875}, {"start": 1269.35, "end": 1269.73, "word": " you", "probability": 0.763671875}, {"start": 1269.73, "end": 1270.15, "word": " read?", "probability": 0.43701171875}, {"start": 1270.39, "end": 1270.65, "word": " Why", "probability": 0.9150390625}, {"start": 1270.65, "end": 1270.91, "word": " you?", "probability": 0.7529296875}, {"start": 1273.61, "end": 1274.39, "word": " Why", "probability": 0.80712890625}, {"start": 1274.39, "end": 1275.65, "word": " I", "probability": 0.87255859375}, {"start": 1275.65, "end": 1277.75, "word": " am", "probability": 0.95068359375}, {"start": 1277.75, "end": 1280.95, "word": " make", "probability": 0.39404296875}, {"start": 1280.95, "end": 1282.09, "word": " inversion", "probability": 0.92724609375}, {"start": 1282.09, "end": 1283.85, "word": " are", "probability": 0.55517578125}, {"start": 1283.85, "end": 1284.11, "word": " you?", "probability": 0.9736328125}], "temperature": 1.0}, {"id": 44, "seek": 130983, "start": 1285.16, "end": 1309.84, "text": " You and here are, are you. So why are you studying English? Why are you studying English? Because I need it for my job. Because I need it for my job. 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Someone else, why are you studying English?", "tokens": [1171, 264, 5454, 13, 8734, 1646, 11, 983, 366, 291, 7601, 3669, 30], "avg_logprob": -0.22586495216403688, "compression_ratio": 0.9142857142857143, "no_speech_prob": 0.0, "words": [{"start": 1320.23, "end": 1321.07, "word": " For", "probability": 0.71923828125}, {"start": 1321.07, "end": 1321.27, "word": " the", "probability": 0.82666015625}, {"start": 1321.27, "end": 1321.89, "word": " university.", "probability": 0.74169921875}, {"start": 1323.63, "end": 1324.47, "word": " Someone", "probability": 0.7119140625}, {"start": 1324.47, "end": 1324.81, "word": " else,", "probability": 0.92578125}, {"start": 1325.17, "end": 1325.41, "word": " why", "probability": 0.78564453125}, {"start": 1325.41, "end": 1326.13, "word": " are", "probability": 0.685546875}, {"start": 1326.13, "end": 1326.75, "word": " you", "probability": 0.96826171875}, {"start": 1326.75, "end": 1326.99, "word": " studying", "probability": 0.94091796875}, {"start": 1326.99, "end": 1327.41, "word": " English?", "probability": 0.96484375}], "temperature": 1.0}, {"id": 46, "seek": 135850, "start": 1328.94, "end": 1358.5, "text": " Because I love it. 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And here, brothers and sisters. 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Sorry. I have been studying English for three years. The question was how long? How long have you been studying English? I have been studying English for three years.", "tokens": [1079, 11, 1230, 2309, 13, 4919, 13, 286, 362, 668, 7601, 3669, 337, 1045, 924, 13, 440, 1168, 390, 577, 938, 30, 1012, 938, 362, 291, 668, 7601, 3669, 30, 286, 362, 668, 7601, 3669, 337, 1045, 924, 13], "avg_logprob": -0.21289061866700648, "compression_ratio": 1.6727272727272726, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 1384.69, "end": 1385.01, "word": " Yes,", "probability": 0.623046875}, {"start": 1385.09, "end": 1385.21, "word": " number", "probability": 0.9189453125}, {"start": 1385.21, "end": 1385.51, "word": " six.", "probability": 0.76416015625}, {"start": 1385.67, "end": 1385.85, "word": " Sorry.", "probability": 0.82470703125}, {"start": 1386.57, "end": 1386.69, "word": " I", "probability": 0.953125}, {"start": 1386.69, "end": 1386.81, "word": " have", "probability": 0.492431640625}, {"start": 1386.81, "end": 1386.97, "word": " been", "probability": 0.919921875}, {"start": 1386.97, "end": 1387.29, "word": " studying", "probability": 0.9375}, {"start": 1387.29, "end": 1387.67, "word": " English", "probability": 0.970703125}, {"start": 1387.67, "end": 1387.97, "word": " for", "probability": 0.95263671875}, {"start": 1387.97, "end": 1388.35, "word": " three", "probability": 0.8720703125}, {"start": 1388.35, "end": 1388.79, "word": " years.", "probability": 0.9296875}, {"start": 1389.45, "end": 1389.57, "word": " The", "probability": 0.8603515625}, {"start": 1389.57, "end": 1389.93, "word": " question", "probability": 0.9150390625}, {"start": 1389.93, "end": 1390.19, "word": " was", "probability": 0.6552734375}, {"start": 1390.19, "end": 1390.53, "word": " how", "probability": 0.59423828125}, {"start": 1390.53, "end": 1390.91, "word": " long?", "probability": 0.931640625}, {"start": 1392.97, "end": 1393.63, "word": " How", "probability": 0.5458984375}, {"start": 1393.63, "end": 1393.99, "word": " long", "probability": 0.94482421875}, {"start": 1393.99, "end": 1399.09, "word": " have", "probability": 0.5908203125}, {"start": 1399.09, "end": 1399.45, "word": " you", "probability": 0.966796875}, {"start": 1399.45, "end": 1400.35, "word": " been", "probability": 0.8740234375}, {"start": 1400.35, "end": 1400.77, "word": " studying", "probability": 0.9423828125}, {"start": 1400.77, "end": 1401.21, "word": " English?", "probability": 0.95703125}, {"start": 1401.83, "end": 1402.01, "word": " I", "probability": 0.86328125}, {"start": 1402.01, "end": 1402.15, "word": " have", "probability": 0.90771484375}, {"start": 1402.15, "end": 1402.27, "word": " been", "probability": 0.9130859375}, {"start": 1402.27, "end": 1402.57, "word": " studying", "probability": 0.9453125}, {"start": 1402.57, "end": 1402.83, "word": " English", "probability": 0.97412109375}, {"start": 1402.83, "end": 1403.17, "word": " for", "probability": 0.94677734375}, {"start": 1403.17, "end": 1403.87, "word": " three", "probability": 0.71875}, {"start": 1403.87, "end": 1403.93, "word": " years.", "probability": 0.8955078125}], "temperature": 1.0}, {"id": 49, "seek": 143200, "start": 1404.08, "end": 1432.0, "text": " three years or for five years, for 12 years, et cetera. How long for the duration of time? So how long have you been studying English? Number seven, I have been to, it means I visited the United States, Canada, Japan, and Australia. 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Which countries have you been to? Which countries have you been to?", "tokens": [3013, 3517, 362, 291, 668, 281, 30, 3013, 3517, 362, 291, 668, 281, 30, 3013, 3517, 362, 291, 668, 281, 30], "avg_logprob": -0.36789771779017016, "compression_ratio": 2.2666666666666666, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1437.92, "end": 1439.18, "word": " Which", "probability": 0.54541015625}, {"start": 1439.18, "end": 1439.74, "word": " countries", "probability": 0.7890625}, {"start": 1439.74, "end": 1443.48, "word": " have", "probability": 0.0977783203125}, {"start": 1443.48, "end": 1446.1, "word": " you", "probability": 0.8876953125}, {"start": 1446.1, "end": 1446.5, "word": " been", "probability": 0.82861328125}, {"start": 1446.5, "end": 1451.8, "word": " to?", "probability": 0.873046875}, {"start": 1452.12, "end": 1453.38, "word": " Which", "probability": 0.420654296875}, {"start": 1453.38, "end": 1454.9, "word": " countries", "probability": 0.77734375}, {"start": 1454.9, "end": 1455.16, "word": " have", "probability": 0.90380859375}, {"start": 1455.16, "end": 1455.38, "word": " you", "probability": 0.962890625}, {"start": 1455.38, "end": 1455.72, "word": " been", "probability": 0.904296875}, {"start": 1455.72, "end": 1456.08, "word": " to?", "probability": 0.939453125}, {"start": 1456.4, "end": 1457.16, "word": " Which", "probability": 0.41259765625}, {"start": 1457.16, "end": 1458.24, "word": " countries", "probability": 0.77294921875}, {"start": 1458.24, "end": 1458.94, "word": " have", "probability": 0.9384765625}, {"start": 1458.94, "end": 1459.22, "word": " you", "probability": 0.96875}, {"start": 1459.22, "end": 1459.6, "word": " been", "probability": 0.90673828125}, {"start": 1459.6, "end": 1460.1, "word": " to?", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 51, "seek": 148565, "start": 1460.95, "end": 1485.65, "text": " Which countries have you been to? I have been to the United States, Canada, Japan and Australia. Number eight. I went to Canada three years ago. When? Yes.", "tokens": [3013, 3517, 362, 291, 668, 281, 30, 286, 362, 668, 281, 264, 2824, 3040, 11, 6309, 11, 3367, 293, 7060, 13, 5118, 3180, 13, 286, 1437, 281, 6309, 1045, 924, 2057, 13, 1133, 30, 1079, 13], "avg_logprob": -0.18581081242174716, "compression_ratio": 1.2380952380952381, "no_speech_prob": 0.0, "words": [{"start": 1460.95, "end": 1461.83, "word": " Which", "probability": 0.67529296875}, {"start": 1461.83, "end": 1462.43, "word": " countries", "probability": 0.78369140625}, {"start": 1462.43, "end": 1462.97, "word": " have", "probability": 0.94580078125}, {"start": 1462.97, "end": 1463.17, "word": " you", "probability": 0.966796875}, {"start": 1463.17, "end": 1463.43, "word": " been", "probability": 0.9033203125}, {"start": 1463.43, "end": 1463.85, "word": " to?", "probability": 0.9521484375}, {"start": 1465.51, "end": 1465.79, "word": " I", "probability": 0.90966796875}, {"start": 1465.79, "end": 1465.97, "word": " have", "probability": 0.82275390625}, {"start": 1465.97, "end": 1466.15, "word": " been", "probability": 0.90625}, {"start": 1466.15, "end": 1466.73, "word": " to", "probability": 0.9638671875}, {"start": 1466.73, "end": 1467.33, "word": " the", "probability": 0.86328125}, {"start": 1467.33, "end": 1467.83, "word": " United", "probability": 0.91455078125}, {"start": 1467.83, "end": 1468.49, "word": " States,", "probability": 0.93310546875}, {"start": 1469.09, "end": 1469.63, "word": " Canada,", "probability": 0.94873046875}, {"start": 1470.85, "end": 1471.25, "word": " Japan", "probability": 0.89892578125}, {"start": 1471.25, "end": 1472.11, "word": " and", "probability": 0.56787109375}, {"start": 1472.11, "end": 1473.17, "word": " Australia.", "probability": 0.93408203125}, {"start": 1474.67, "end": 1475.87, "word": " Number", "probability": 0.81591796875}, {"start": 1475.87, "end": 1476.43, "word": " eight.", "probability": 0.7587890625}, {"start": 1477.37, "end": 1477.67, "word": " I", "probability": 0.99365234375}, {"start": 1477.67, "end": 1477.99, "word": " went", "probability": 0.88818359375}, {"start": 1477.99, "end": 1478.21, "word": " to", "probability": 0.97265625}, {"start": 1478.21, "end": 1478.67, "word": " Canada", "probability": 0.9541015625}, {"start": 1478.67, "end": 1480.25, "word": " three", "probability": 0.890625}, {"start": 1480.25, "end": 1481.39, "word": " years", "probability": 0.92822265625}, {"start": 1481.39, "end": 1482.11, "word": " ago.", "probability": 0.8828125}, {"start": 1483.31, "end": 1483.57, "word": " When?", "probability": 0.5048828125}, {"start": 1484.75, "end": 1485.65, "word": " Yes.", "probability": 0.5537109375}], "temperature": 1.0}, {"id": 52, "seek": 151759, "start": 1489.25, "end": 1517.59, "text": " Yes, because went in the past. So here I use dead. Here I use do. Here I use dead. So when did you go to Canada? When did you go to Canada? Three years ago. Last year. 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So here is the end of this exercise. Who can make number two quickly? The question number two quickly. Where were you born? Another one. When were you born? Yes, next. Again. 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Number eight and the last one. When did you go to Canada? Very good. Now we will deal with if I want to show you something. These are the questions. 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Yes. Yes. Next. Someone else? Yes. 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Why are you studying English? Six. How long have you been studying English? Yes, seven. Which country have you been? And number eight. When did you learn English? Thank you. 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This is the answer of the present and the past simple. 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Now we look here. I want you to answer this exercise about what? Making questions.", "tokens": [440, 1974, 2199, 14975, 11, 264, 1791, 2199, 14975, 293, 439, 264, 661, 10688, 279, 13, 823, 321, 574, 510, 13, 286, 528, 291, 281, 1867, 341, 5380, 466, 437, 30, 14595, 1651, 13], "avg_logprob": -0.30892857653754097, "compression_ratio": 1.3416666666666666, "no_speech_prob": 0.0, "words": [{"start": 1725.33, "end": 1725.49, "word": " The", "probability": 0.384765625}, {"start": 1725.49, "end": 1726.27, "word": " present", "probability": 0.80859375}, {"start": 1726.27, "end": 1727.35, "word": " simple", "probability": 0.8466796875}, {"start": 1727.35, "end": 1727.87, "word": " passive,", "probability": 0.8818359375}, {"start": 1728.23, "end": 1728.59, "word": " the", "probability": 0.69482421875}, {"start": 1728.59, "end": 1728.93, "word": " past", "probability": 0.552734375}, {"start": 1728.93, "end": 1730.35, "word": " simple", "probability": 0.845703125}, {"start": 1730.35, "end": 1730.79, "word": " passive", "probability": 0.94091796875}, {"start": 1730.79, "end": 1731.65, "word": " and", "probability": 0.53662109375}, {"start": 1731.65, "end": 1731.93, "word": " all", "probability": 0.93310546875}, {"start": 1731.93, "end": 1732.07, "word": " the", "probability": 0.91357421875}, {"start": 1732.07, "end": 1732.25, "word": " other", "probability": 0.9052734375}, {"start": 1732.25, "end": 1732.81, "word": " tenses.", "probability": 0.6334228515625}, {"start": 1733.69, "end": 1734.11, "word": " Now", "probability": 0.88134765625}, {"start": 1734.11, "end": 1736.61, "word": " we", "probability": 0.55126953125}, {"start": 1736.61, "end": 1738.69, "word": " look", "probability": 0.80615234375}, {"start": 1738.69, "end": 1739.13, "word": " here.", "probability": 0.85693359375}, {"start": 1740.59, "end": 1741.75, "word": " I", "probability": 0.442626953125}, {"start": 1741.75, "end": 1743.57, "word": " want", "probability": 0.87109375}, {"start": 1743.57, "end": 1743.81, "word": " you", "probability": 0.96337890625}, {"start": 1743.81, "end": 1744.65, "word": " to", "probability": 0.9736328125}, {"start": 1744.65, "end": 1745.97, "word": " answer", "probability": 0.955078125}, {"start": 1745.97, "end": 1746.23, "word": " this", "probability": 0.939453125}, {"start": 1746.23, "end": 1746.73, "word": " exercise", "probability": 0.9560546875}, {"start": 1746.73, "end": 1747.31, "word": " about", "probability": 0.603515625}, {"start": 1747.31, "end": 1747.69, "word": " what?", "probability": 0.90283203125}, {"start": 1749.61, "end": 1750.77, "word": " Making", "probability": 0.7685546875}, {"start": 1750.77, "end": 1751.43, "word": " questions.", "probability": 0.8544921875}], "temperature": 1.0}, {"id": 61, "seek": 178386, "start": 1755.0, "end": 1783.86, "text": " Here, the answer in full and the question needs just the verb and the subject. Number one, who can read B, then make a question with A. Yes. I stayed at home and watched television. 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What did you do? So here, did you. Very good. What did you do last night? I stayed at home and watched TV. Number two. Yes.", "tokens": [440, 1168, 11, 437, 630, 291, 360, 1036, 1818, 30, 708, 630, 291, 360, 30, 407, 510, 11, 630, 291, 13, 4372, 665, 13, 708, 630, 291, 360, 1036, 1818, 30, 286, 9181, 412, 1280, 293, 6337, 3558, 13, 5118, 732, 13, 1079, 13], "avg_logprob": -0.24583334657880995, "compression_ratio": 1.4434782608695653, "no_speech_prob": 0.0, "words": [{"start": 1784.73, "end": 1784.97, "word": " The", "probability": 0.5107421875}, {"start": 1784.97, "end": 1785.63, "word": " question,", "probability": 0.8935546875}, {"start": 1786.69, "end": 1787.47, "word": " what", "probability": 0.51806640625}, {"start": 1787.47, "end": 1787.81, "word": " did", "probability": 0.96435546875}, {"start": 1787.81, "end": 1788.11, "word": " you", "probability": 0.9697265625}, {"start": 1788.11, "end": 1788.45, "word": " do", "probability": 0.95703125}, {"start": 1788.45, "end": 1790.15, "word": " last", "probability": 0.4892578125}, {"start": 1790.15, "end": 1790.61, "word": " night?", "probability": 0.88037109375}, {"start": 1790.99, "end": 1791.29, "word": " What", "probability": 0.59228515625}, {"start": 1791.29, "end": 1791.85, "word": " did", "probability": 0.9580078125}, {"start": 1791.85, "end": 1792.17, "word": " you", "probability": 0.96728515625}, {"start": 1792.17, "end": 1792.59, "word": " do?", "probability": 0.96240234375}, {"start": 1792.73, "end": 1793.13, "word": " So", "probability": 0.89990234375}, {"start": 1793.13, "end": 1793.75, "word": " here,", "probability": 0.67041015625}, {"start": 1794.79, "end": 1795.31, "word": " did", "probability": 0.869140625}, {"start": 1795.31, "end": 1797.13, "word": " you.", "probability": 0.88720703125}, {"start": 1798.75, "end": 1799.15, "word": " Very", "probability": 0.69482421875}, {"start": 1799.15, "end": 1799.37, "word": " good.", "probability": 0.9140625}, {"start": 1799.63, "end": 1799.83, "word": " What", "probability": 0.89013671875}, {"start": 1799.83, "end": 1800.01, "word": " did", "probability": 0.96337890625}, {"start": 1800.01, "end": 1800.21, "word": " you", "probability": 0.966796875}, {"start": 1800.21, "end": 1800.55, "word": " do", "probability": 0.9609375}, {"start": 1800.55, "end": 1801.01, "word": " last", "probability": 0.8662109375}, {"start": 1801.01, "end": 1801.55, "word": " night?", "probability": 0.87646484375}, {"start": 1802.17, "end": 1802.39, "word": " I", "probability": 0.99267578125}, {"start": 1802.39, "end": 1802.93, "word": " stayed", "probability": 0.9287109375}, {"start": 1802.93, "end": 1803.25, "word": " at", "probability": 0.900390625}, {"start": 1803.25, "end": 1803.65, "word": " home", "probability": 0.89453125}, {"start": 1803.65, "end": 1803.87, "word": " and", "probability": 0.92431640625}, {"start": 1803.87, "end": 1804.37, "word": " watched", "probability": 0.82666015625}, {"start": 1804.37, "end": 1805.19, "word": " TV.", "probability": 0.83154296875}, {"start": 1807.75, "end": 1808.63, "word": " Number", "probability": 0.65185546875}, {"start": 1808.63, "end": 1808.87, "word": " two.", "probability": 0.7841796875}, {"start": 1810.59, "end": 1811.31, "word": " Yes.", "probability": 0.85009765625}], "temperature": 1.0}, {"id": 63, "seek": 184331, "start": 1813.49, "end": 1843.31, "text": " Horror stories and science fiction. What kind of books do you like reading? Do you like reading? Very good. Do you like reading? I like reading horror stories and science fiction. Here, as if there were I like. Number three. 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Very good You Because I have have you Have you ever been to the United States? Yes, I have I Went there last year again Yes Did you", "tokens": [8266, 12, 10250, 13, 4372, 665, 509, 1436, 286, 362, 362, 291, 3560, 291, 1562, 668, 281, 264, 2824, 3040, 30, 1079, 11, 286, 362, 286, 31809, 456, 1036, 1064, 797, 1079, 2589, 291], "avg_logprob": -0.18470982568604605, "compression_ratio": 1.2280701754385965, "no_speech_prob": 0.0, "words": [{"start": 1846.58, "end": 1846.98, "word": " Mm", "probability": 0.54833984375}, {"start": 1846.98, "end": 1847.24, "word": "-hmm.", "probability": 0.867919921875}, {"start": 1847.24, "end": 1847.84, "word": " Very", "probability": 0.77001953125}, {"start": 1847.84, "end": 1848.16, "word": " good", "probability": 0.91943359375}, {"start": 1848.16, "end": 1850.64, "word": " You", "probability": 0.1920166015625}, {"start": 1850.64, "end": 1853.88, "word": " Because", "probability": 0.88916015625}, {"start": 1853.88, "end": 1854.64, "word": " I", "probability": 0.99609375}, {"start": 1854.64, "end": 1854.9, "word": " have", "probability": 0.9326171875}, {"start": 1854.9, "end": 1855.96, "word": " have", "probability": 0.8984375}, {"start": 1855.96, "end": 1856.3, "word": " you", "probability": 0.97412109375}, {"start": 1856.3, "end": 1857.88, "word": " Have", "probability": 0.5595703125}, {"start": 1857.88, "end": 1858.02, "word": " you", "probability": 0.9716796875}, {"start": 1858.02, "end": 1858.26, "word": " ever", "probability": 0.880859375}, {"start": 1858.26, "end": 1858.46, "word": " been", "probability": 0.916015625}, {"start": 1858.46, "end": 1858.62, "word": " to", "probability": 0.97265625}, {"start": 1858.62, "end": 1858.76, "word": " the", "probability": 0.92529296875}, {"start": 1858.76, "end": 1859.0, "word": " United", "probability": 0.94677734375}, {"start": 1859.0, "end": 1859.6, "word": " States?", "probability": 0.9404296875}, {"start": 1860.98, "end": 1861.32, "word": " Yes,", "probability": 0.927734375}, {"start": 1861.34, "end": 1861.46, "word": " I", "probability": 0.99951171875}, {"start": 1861.46, "end": 1861.84, "word": " have", "probability": 0.95361328125}, {"start": 1861.84, "end": 1863.52, "word": " I", "probability": 0.796875}, {"start": 1863.52, "end": 1863.72, "word": " Went", "probability": 0.5732421875}, {"start": 1863.72, "end": 1864.0, "word": " there", "probability": 0.91845703125}, {"start": 1864.0, "end": 1864.72, "word": " last", "probability": 0.87744140625}, {"start": 1864.72, "end": 1865.06, "word": " year", "probability": 0.93701171875}, {"start": 1865.06, "end": 1866.52, "word": " again", "probability": 0.80126953125}, {"start": 1866.52, "end": 1869.4, "word": " Yes", "probability": 0.96533203125}, {"start": 1869.4, "end": 1874.04, "word": " Did", "probability": 0.95947265625}, {"start": 1874.04, "end": 1874.54, "word": " you", "probability": 0.97412109375}], "temperature": 1.0}, {"id": 65, "seek": 189835, "start": 1875.23, "end": 1898.35, "text": " Like it? 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The question? What is teacher doing? Yes. Again. Again. 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No, I haven't, just a CD player. Yes, thank you very much, indeed. Inshallah, next time we hope to meet you at the same room. 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"word": " same", "probability": 0.9111328125}, {"start": 2259.0, "end": 2259.22, "word": " room.", "probability": 0.9482421875}, {"start": 2259.6, "end": 2259.84, "word": " Thank", "probability": 0.90087890625}, {"start": 2259.84, "end": 2259.94, "word": " you", "probability": 0.96337890625}, {"start": 2259.94, "end": 2260.08, "word": " very", "probability": 0.845703125}, {"start": 2260.08, "end": 2260.32, "word": " much.", "probability": 0.91064453125}], "temperature": 1.0}], "language": "en", "language_probability": 1.0, "duration": 2261.043, "duration_after_vad": 2075.2118749999936} \ No newline at end of file diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/z4FIPvnrQEs_raw.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/z4FIPvnrQEs_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..7a871e46c027f21b2c9fa17207b585d84cca740c --- /dev/null +++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/z4FIPvnrQEs_raw.srt @@ -0,0 +1,1988 @@ +1 +00:00:21,040 --> 00:00:27,140 +Assalamualaikum warahmatullahi wabarakatuh Good + +2 +00:00:27,140 --> 00:00:32,080 +afternoon Today inshallah we are going to study + +3 +00:00:32,080 --> 00:00:39,680 +verb patterns Verb patterns we have five patterns + +4 +00:00:39,680 --> 00:00:47,580 +Verbs plus Infinitive + +5 +00:00:47,580 --> 00:00:56,790 +plus ing Gerund verbs plus gerund Like enjoy I + +6 +00:00:56,790 --> 00:01:03,350 +enjoy playing football I enjoy playing football + +7 +00:01:03,350 --> 00:01:11,730 +Number two verbs plus two plus infinitive I wanted + +8 +00:01:11,730 --> 00:01:20,910 +to study English I wanted to study English also + +9 +00:01:20,910 --> 00:01:29,070 +number three verbs plus object plus to plus + +10 +00:01:29,070 --> 00:01:36,910 +infinitive he asked me to study English he wanted + +11 +00:01:36,910 --> 00:01:43,150 +me to play football number + +12 +00:01:43,150 --> 00:01:45,910 +four we'll have + +13 +00:01:48,760 --> 00:01:55,140 +some verbs with object and infinitive without to + +14 +00:01:55,140 --> 00:02:06,560 +he let me go he made me study hard he helped me go + +15 +00:02:06,560 --> 00:02:13,160 +to school number five and the last one some verbs + +16 +00:02:13,160 --> 00:02:17,150 +are used with preposition So after the + +17 +00:02:17,150 --> 00:02:20,150 +preposition, we use gerund. + +18 +00:02:23,850 --> 00:02:30,790 +Thank you for coming early. He succeeded in + +19 +00:02:30,790 --> 00:02:38,570 +playing well. So this is our subject for today. We + +20 +00:02:38,570 --> 00:02:44,240 +will have five patterns. of verbs. We call them + +21 +00:02:44,240 --> 00:02:45,620 +verb patterns. + +22 +00:02:48,000 --> 00:02:52,920 +The first exercise, we will study a thank you + +23 +00:02:52,920 --> 00:02:59,080 +letter from Soonhee when she went home to South + +24 +00:02:59,080 --> 00:03:03,420 +Korea. She sent this letter to her friend in + +25 +00:03:03,420 --> 00:03:10,350 +Australia. Dear Sandy and family, So this letter + +26 +00:03:10,350 --> 00:03:18,870 +is to Sandy and her family. I just wanted to say, + +27 +00:03:19,530 --> 00:03:26,290 +so here we have 14 verbs. These 14 verbs are + +28 +00:03:26,290 --> 00:03:31,970 +classified into five groups. The first group with + +29 +00:03:31,970 --> 00:03:36,920 +ing the second with two the third with object and + +30 +00:03:36,920 --> 00:03:41,240 +two the fourth with object and without two the + +31 +00:03:41,240 --> 00:03:49,360 +fifth with preposition and ing so this one i just + +32 +00:03:49,360 --> 00:03:55,560 +wanted to say the first verb is wanted wanted is + +33 +00:03:55,560 --> 00:04:02,220 +from number two verbs plus infinitive with two so + +34 +00:04:02,220 --> 00:04:13,820 +I just wanted to say thank you for for having + +35 +00:04:13,820 --> 00:04:21,120 +for having yeah + +36 +00:04:21,120 --> 00:04:26,700 +so for + +37 +00:04:26,700 --> 00:04:28,400 +next + +38 +00:04:29,750 --> 00:04:33,510 +Thank you for having me as your guest in your + +39 +00:04:33,510 --> 00:04:38,270 +beautiful home. I had a great time. + +40 +00:04:40,890 --> 00:04:47,830 +I really enjoyed meeting + +41 +00:04:47,830 --> 00:04:56,470 +your + +42 +00:04:56,470 --> 00:05:05,180 +friends. friends you all made me made me made me + +43 +00:05:05,180 --> 00:05:16,220 +feel made me feel so the verb here is made me so + +44 +00:05:16,220 --> 00:05:21,080 +welcome you all made me feel welcome so welcome + +45 +00:05:21,080 --> 00:05:28,100 +you know how much i missed my family at first But + +46 +00:05:28,100 --> 00:05:34,320 +you were so kind that I soon stopped feeling + +47 +00:05:34,320 --> 00:05:42,640 +homesick. + +48 +00:05:44,420 --> 00:05:50,020 +I can't find the words to tell you how grateful I + +49 +00:05:50,020 --> 00:05:53,500 +am. I'd like + +50 +00:05:56,180 --> 00:06:06,460 +I'd like to call. I'd like to call you. What's a + +51 +00:06:06,460 --> 00:06:11,140 +good time to call? Yes, again. + +52 +00:06:14,080 --> 00:06:18,860 +Dear Sandy and family, I just wanted to say thank + +53 +00:06:18,860 --> 00:06:22,560 +you for having me as your guest in your beautiful + +54 +00:06:22,560 --> 00:06:28,180 +home. I had a great time. I really enjoyed meeting + +55 +00:06:28,180 --> 00:06:34,420 +your friends. You made me feel so welcome. You + +56 +00:06:34,420 --> 00:06:38,480 +know how much I missed my family at first, but you + +57 +00:06:38,480 --> 00:06:42,820 +were so kind that I soon stopped feeling homesick. + +58 +00:06:43,340 --> 00:06:48,960 +I can't find words to tell you how grateful I am. + +59 +00:06:49,760 --> 00:06:55,180 +I'd like to call you once a good time To call + +60 +00:06:55,180 --> 00:07:04,200 +someone, read. Yes. Dear Sandy and family, I just + +61 +00:07:04,200 --> 00:07:09,780 +wanted to say thank you for having me as your + +62 +00:07:09,780 --> 00:07:14,300 +guest in your beautiful home. I had a great time. + +63 +00:07:14,880 --> 00:07:23,340 +I really enjoyed meeting you friends. You all made + +64 +00:07:23,690 --> 00:07:26,590 +to feel so welcome. + +65 +00:07:28,470 --> 00:07:33,030 +Thank you, yes? Thank you. You know how much I + +66 +00:07:33,030 --> 00:07:38,470 +miss my family, Akbar. But you were so kind that I + +67 +00:07:38,470 --> 00:07:42,150 +soon stopped feeling homesick. I cannot find the + +68 +00:07:42,150 --> 00:07:48,150 +words to tell you how grateful I am. I would like + +69 +00:07:48,150 --> 00:07:55,470 +to call you Mm-hmm. And this is the answer Mm-hmm. + +70 +00:07:55,490 --> 00:08:03,330 +So after wanted we use to After for thank you for + +71 +00:08:03,330 --> 00:08:15,130 +we use having Enjoy meeting Made me feel without + +72 +00:08:15,130 --> 00:08:20,710 +to without ing Stopped + +73 +00:08:21,810 --> 00:08:28,230 +Feeling gave up feeling finished gave up feeling + +74 +00:08:28,230 --> 00:08:38,430 +Uh-huh. I'd like To call I'd like to call you How + +75 +00:08:38,430 --> 00:08:47,390 +many are they? Six Ten percent Now + +76 +00:08:47,390 --> 00:08:49,590 +Complete + +77 +00:09:00,080 --> 00:09:06,800 +You know that on my way home... Now Soonhee is + +78 +00:09:06,800 --> 00:09:10,320 +traveling to South Korea and she wrote this letter + +79 +00:09:10,320 --> 00:09:15,060 +when she was in Korea. She thanked Sandy and her + +80 +00:09:15,060 --> 00:09:20,760 +family. You know that on my way home I stopped to + +81 +00:09:20,760 --> 00:09:26,340 +visit. Here stopped to visit. + +82 +00:09:29,560 --> 00:09:34,400 +She stopped the journey in order to visit. She + +83 +00:09:34,400 --> 00:09:38,600 +stopped an activity to do something. So we have + +84 +00:09:38,600 --> 00:09:45,880 +two stops. Stop means giving up. Stop with two + +85 +00:09:45,880 --> 00:09:52,500 +means stop one activity in order to do something + +86 +00:09:52,500 --> 00:09:59,330 +else. When I say the teacher stopped smoking + +87 +00:09:59,330 --> 00:10:07,610 +stopped smoking it means he gave up smoking he + +88 +00:10:07,610 --> 00:10:11,310 +doesn't smoke anymore in the past he was smoking + +89 +00:10:11,310 --> 00:10:18,530 +but now no but when I say Ali stopped to smoke + +90 +00:10:18,530 --> 00:10:24,950 +stopped to smoke it means he stopped shopping He + +91 +00:10:24,950 --> 00:10:29,930 +stopped talking. He stopped playing. Why? In order + +92 +00:10:29,930 --> 00:10:36,210 +to smoke. He left something to do something else. + +93 +00:10:36,890 --> 00:10:40,410 +He stopped something, interrupted something to do + +94 +00:10:40,410 --> 00:10:44,730 +something else. In order to do something else. So + +95 +00:10:44,730 --> 00:10:49,170 +I gave up smoking. It means I stopped smoking. I + +96 +00:10:49,170 --> 00:10:53,810 +don't smoke. But when I say I stopped to smoke, it + +97 +00:10:53,810 --> 00:10:59,030 +means I stopped talking to you in order to smoke. + +98 +00:10:59,490 --> 00:11:02,890 +Where's the teacher? He stopped to smoke. Look, + +99 +00:11:03,110 --> 00:11:08,610 +he's smoking. Where is the teacher? He stopped to + +100 +00:11:08,610 --> 00:11:13,710 +smoke. He stopped, interrupted the activity in + +101 +00:11:13,710 --> 00:11:16,590 +order to smoke. But when I say I stopped smoking, + +102 +00:11:17,500 --> 00:11:26,940 +It means he gave up smoking. So here, I stopped to + +103 +00:11:26,940 --> 00:11:32,140 +visit. It means she stopped the journey in order + +104 +00:11:32,140 --> 00:11:40,020 +to visit her aunt. So here, I stopped to visit my + +105 +00:11:40,020 --> 00:11:46,800 +aunt in Perth. It was so hot. In Perth, it was so + +106 +00:11:46,800 --> 00:11:56,380 +hot. It was over 35 degrees all the time. But I + +107 +00:11:56,380 --> 00:11:59,620 +absolutely loved it. So she loved the hot weather. + +108 +00:12:01,240 --> 00:12:09,760 +My aunt wanted me + +109 +00:12:09,760 --> 00:12:13,240 +to + +110 +00:12:13,240 --> 00:12:14,480 +stay. + +111 +00:12:17,320 --> 00:12:22,480 +You understand? Wanted me to stay longer. I + +112 +00:12:22,480 --> 00:12:29,940 +visited my aunt. She wanted me to stay longer. But + +113 +00:12:29,940 --> 00:12:40,410 +I wanted to see. So I wanted to see So with want, + +114 +00:12:40,730 --> 00:12:47,470 +we use want to or wanted me to. Want object and to + +115 +00:12:47,470 --> 00:12:54,370 +or want and to. Two bars with object and without + +116 +00:12:54,370 --> 00:12:59,430 +object. Both of them are with to. He wanted me to + +117 +00:12:59,430 --> 00:13:03,010 +come early. He wants to come early. Both are + +118 +00:13:03,010 --> 00:13:03,250 +correct. + +119 +00:13:06,540 --> 00:13:09,620 +But I wanted to see my parents and my brother + +120 +00:13:09,620 --> 00:13:20,380 +Sangchu. But she's invited me to go back. To come + +121 +00:13:20,380 --> 00:13:26,460 +back to here. To go back to Perth. So she invited + +122 +00:13:26,460 --> 00:13:38,930 +me to go. invited me to go, wanted me to go. Yes. + +123 +00:13:39,270 --> 00:13:45,850 +To go back. And I'd love, I'd love, I'd love, I'd + +124 +00:13:45,850 --> 00:13:54,710 +like, I'd like to do that. So she agreed to go + +125 +00:13:54,710 --> 00:14:01,860 +back to Perth in her answer. I'm thinking of + +126 +00:14:01,860 --> 00:14:09,060 +thinking of going because we have of preposition + +127 +00:14:09,060 --> 00:14:15,500 +so we use going I'm + +128 +00:14:15,500 --> 00:14:24,480 +thinking of going next year again You know that on + +129 +00:14:24,480 --> 00:14:28,800 +my way home, I stopped to visit my aunt in Perth. + +130 +00:14:29,280 --> 00:14:34,500 +It was so hot. It was over 35 degrees all the + +131 +00:14:34,500 --> 00:14:39,980 +time. But I absolutely loved it. My aunt wanted me + +132 +00:14:39,980 --> 00:14:44,340 +to visit to stay longer, but I wanted to see my + +133 +00:14:44,340 --> 00:14:49,490 +parents and my brother Sanghee. But she's invited + +134 +00:14:49,490 --> 00:14:54,410 +me to go back and I'd love to do that. I'm + +135 +00:14:54,410 --> 00:14:59,410 +thinking of going next year. I'm thinking of going + +136 +00:14:59,410 --> 00:15:00,710 +next year. + +137 +00:15:05,210 --> 00:15:11,250 +Yes? You know that on my way home, I stopped to + +138 +00:15:11,250 --> 00:15:15,230 +visit my aunt in Paris. It was so hot. It was over + +139 +00:15:15,230 --> 00:15:20,260 +35 degrees all the time. But I absolutely loved + +140 +00:15:20,260 --> 00:15:25,020 +it. My aunt wanted me to stay longer, but I wanted + +141 +00:15:25,020 --> 00:15:31,100 +to see my parents and my brother. But she invited + +142 +00:15:31,100 --> 00:15:35,520 +me to go back and I'd love to do that. I am + +143 +00:15:35,520 --> 00:15:40,500 +thinking of going next year. Thank you. So this it + +144 +00:15:40,500 --> 00:15:46,300 +is would. And this is, is, has. + +145 +00:15:48,740 --> 00:15:54,320 +Anything else? And this is I am. And the answer? + +146 +00:15:56,600 --> 00:16:03,200 +Who can read again? Yeah? You know that on my way + +147 +00:16:03,200 --> 00:16:07,220 +home, I stopped to visit my aunt in bed. It was so + +148 +00:16:07,220 --> 00:16:12,810 +hot. It was over 35 degrees all the time. But I + +149 +00:16:12,810 --> 00:16:18,110 +absolutely loved it. My aunt wanted me to stay + +150 +00:16:18,110 --> 00:16:21,650 +longer. But I wanted to see my parents and my + +151 +00:16:21,650 --> 00:16:26,930 +brother. Thank you. But she invented me to go back + +152 +00:16:26,930 --> 00:16:31,050 +and I'd love to do that. I'm thinking of going + +153 +00:16:31,050 --> 00:16:34,870 +next year. Thank you. Thank you. Some other one + +154 +00:16:34,870 --> 00:16:35,210 +again. + +155 +00:16:38,760 --> 00:16:42,500 +You know that on my way home, I stopped to visit + +156 +00:16:42,500 --> 00:16:48,580 +my aunt in Beirut. It was so hot. It was over 35 + +157 +00:16:48,580 --> 00:16:56,100 +degrees all the time, but I absolutely loved it. + +158 +00:16:56,440 --> 00:17:01,200 +My aunt wanted me to stay longer, but I wanted to + +159 +00:17:01,200 --> 00:17:04,820 +see my parents and my brother. + +160 +00:17:10,010 --> 00:17:18,630 +But she has wanted me to go back and + +161 +00:17:18,630 --> 00:17:23,110 +I would love to do that. I'm thinking of going + +162 +00:17:23,110 --> 00:17:26,070 +next year. And this is the answer. + +163 +00:17:30,190 --> 00:17:34,010 +The last + +164 +00:17:34,010 --> 00:17:34,310 +one. + +165 +00:17:47,190 --> 00:17:53,270 +The last part of the letter. Anyway, I'm looking + +166 +00:17:53,270 --> 00:17:58,630 +forward to hearing from you very soon. This is + +167 +00:17:58,630 --> 00:18:03,030 +important. I'm looking forward to. I'm looking + +168 +00:18:03,030 --> 00:18:08,210 +forward to. To here is a preposition. It's very + +169 +00:18:08,210 --> 00:18:12,150 +important. Don't forget after looking forward to + +170 +00:18:12,150 --> 00:18:18,960 +we use having or leaving. or seeing meeting ing + +171 +00:18:18,960 --> 00:18:23,900 +form so anyway i'm looking forward to hearing from + +172 +00:18:23,900 --> 00:18:27,280 +you very soon sometimes we can use i look forward + +173 +00:18:27,280 --> 00:18:31,800 +to i'm looking forward to is informal i look + +174 +00:18:31,800 --> 00:18:37,180 +forward to is formal hearing + +175 +00:18:37,180 --> 00:18:46,070 +from you very soon let me let me know so This let + +176 +00:18:46,070 --> 00:18:56,210 +let me we use no without to So three verbs let + +177 +00:18:56,210 --> 00:19:05,830 +make and help me go Three verbs object and verb + +178 +00:19:05,830 --> 00:19:13,050 +without to or without ing So let me know if you + +179 +00:19:13,050 --> 00:19:19,510 +ever want to visit Seoul. My brother and I could + +180 +00:19:19,510 --> 00:19:25,770 +take you to a Norbag. Norbag is sinning room. + +181 +00:19:26,270 --> 00:19:31,130 +Sinning room in the language of Korea. Sinning + +182 +00:19:31,130 --> 00:19:38,620 +room in Australia. It's a bit like karaoke. So + +183 +00:19:38,620 --> 00:19:43,140 +this is in the Australian language. And this is in + +184 +00:19:43,140 --> 00:19:47,380 +the Seoul language. In English, a sinning room. + +185 +00:19:47,540 --> 00:19:57,660 +Sinning. Love to you all. Soon he. P.S. Post + +186 +00:19:57,660 --> 00:20:03,500 +script. Post script. Do you like the picture of + +187 +00:20:03,500 --> 00:20:10,300 +Sangchul and me? The picture. Again. Anyway, I'm + +188 +00:20:10,300 --> 00:20:14,240 +looking forward to hearing from you very soon. Let + +189 +00:20:14,240 --> 00:20:17,680 +me know if you ever want to visit Seoul. My + +190 +00:20:17,680 --> 00:20:22,060 +brother and I could take you to a Norbank, a + +191 +00:20:22,060 --> 00:20:27,300 +singing room. It's a bit like karaoke. Love to you + +192 +00:20:27,300 --> 00:20:32,840 +all. Soonhee. P.S. Do you like the picture of + +193 +00:20:32,840 --> 00:20:39,520 +Sangchul and me? And this is the answer. Who can + +194 +00:20:39,520 --> 00:20:47,140 +read? Yes. Anyway, I am looking forward to hearing + +195 +00:20:47,140 --> 00:20:55,860 +from you very soon. Let me know if + +196 +00:20:55,860 --> 00:20:59,900 +you ever want to visit Seoul. My brother and I + +197 +00:20:59,900 --> 00:21:05,060 +could take you to an old bank ceiling room. It's a + +198 +00:21:05,060 --> 00:21:09,960 +bit like Karok. Love to you all. Soon he asked, do + +199 +00:21:09,960 --> 00:21:13,940 +you like the picture of Sang Shool and me? Thank + +200 +00:21:13,940 --> 00:21:18,460 +you. Someone else? Anyway, I'm looking forward + +201 +00:21:18,460 --> 00:21:21,560 +hearing from you very soon. Let me know if you + +202 +00:21:21,560 --> 00:21:26,280 +ever want to visit Seoul. My brother and I could + +203 +00:21:26,280 --> 00:21:31,520 +take you to a Norbank, a ceiling room. It is a bit + +204 +00:21:31,520 --> 00:21:36,880 +like Karok. Love to you all, Songhee. Post script, + +205 +00:21:37,120 --> 00:21:41,240 +do you like the picture of Sangchul and me? Thank + +206 +00:21:41,240 --> 00:21:44,680 +you very much. Now after reading this letter and + +207 +00:21:44,680 --> 00:21:51,580 +choosing the correct word after some verbs, we're + +208 +00:21:51,580 --> 00:21:56,300 +going to classify these verbs into five groups. + +209 +00:21:56,920 --> 00:22:02,500 +Five groups. Don't forget these five groups. It is + +210 +00:22:02,500 --> 00:22:04,540 +the lesson of our unit. + +211 +00:22:15,640 --> 00:22:24,440 +Before classifying them, we are going to do + +212 +00:22:24,440 --> 00:22:31,650 +this exercise. their patterns so the name of this + +213 +00:22:31,650 --> 00:22:38,490 +subject is their patterns complete these examples + +214 +00:22:38,490 --> 00:22:45,690 +from soon his letter number a um i really enjoyed + +215 +00:22:45,690 --> 00:22:50,830 +uh-huh i'm really enjoyed meeting yes + +216 +00:22:57,150 --> 00:23:00,630 +From the letter itself from the letter number two. + +217 +00:23:01,130 --> 00:23:12,350 +I just wanted To say uh-huh wanted to say To + +218 +00:23:12,350 --> 00:23:23,330 +say thank you my aunt Wanted me To + +219 +00:23:23,330 --> 00:23:25,630 +stay + +220 +00:23:31,160 --> 00:23:48,920 +longer Number D you all made me feel me feel The + +221 +00:23:48,920 --> 00:23:56,860 +last one thank you for having + +222 +00:24:00,250 --> 00:24:08,430 +Me as your guest. So these are five examples of + +223 +00:24:08,430 --> 00:24:14,970 +the verb patterns. Who can read them? Yeah? I + +224 +00:24:14,970 --> 00:24:20,570 +really enjoyed meeting you recently. Two? I just + +225 +00:24:20,570 --> 00:24:26,010 +wanted to say thank you. Three? My aunt wanted me + +226 +00:24:26,010 --> 00:24:27,750 +to stay in Hong Kong. + +227 +00:24:33,490 --> 00:24:40,370 +And the last one Yes, + +228 +00:24:40,570 --> 00:24:47,270 +so These five groups are as follows number one or + +229 +00:24:47,270 --> 00:24:51,010 +number eight Number one or number eight or the + +230 +00:24:51,010 --> 00:24:54,610 +first group? we have enjoy + +231 +00:24:57,170 --> 00:25:02,430 +Enjoy is filled with ng Enjoyed and the group of + +232 +00:25:02,430 --> 00:25:09,950 +enjoy The group of enjoy or the group take ng now + +233 +00:25:09,950 --> 00:25:14,810 +the second group The second group wanted + +234 +00:25:17,400 --> 00:25:25,180 +Wanted to say. Wanted to go. Wanted to play. So + +235 +00:25:25,180 --> 00:25:30,640 +the name of the first group is enjoy. And the name + +236 +00:25:30,640 --> 00:25:34,100 +of the second group is want. This is example. Just + +237 +00:25:34,100 --> 00:25:42,260 +example. It is a verb plus id. A verb plus two. + +238 +00:25:42,660 --> 00:25:48,110 +The third one. The third buttons. So if this is + +239 +00:25:48,110 --> 00:25:51,710 +number one, number two, number three, so it is + +240 +00:25:51,710 --> 00:25:59,750 +wanted me to. Wanted plus object, me, him, Ali, + +241 +00:26:00,390 --> 00:26:06,170 +them, and the verb with two. + +242 +00:26:07,570 --> 00:26:09,350 +What's the difference between number two and + +243 +00:26:09,350 --> 00:26:13,560 +number three? Number two without object. Number + +244 +00:26:13,560 --> 00:26:20,240 +three with object. Object and two. So there are + +245 +00:26:20,240 --> 00:26:26,580 +some verbs like want takes object plus two. + +246 +00:26:28,040 --> 00:26:32,060 +This is the third one. What about number four or + +247 +00:26:32,060 --> 00:26:37,880 +number D? You all made me feel. So this verb is + +248 +00:26:37,880 --> 00:26:43,850 +made. The group of made. Made, lit, and help. + +249 +00:26:43,970 --> 00:26:51,490 +Three. Just three. Made, help, and lit. Let me go. + +250 +00:26:51,970 --> 00:26:59,050 +Help me go. Made me go. It is the fourth pattern. + +251 +00:27:00,150 --> 00:27:04,670 +Made plus object plus infinitive + +252 +00:27:05,820 --> 00:27:11,060 +without two but here object and infinitive with + +253 +00:27:11,060 --> 00:27:16,380 +two here infinitive with two here infinitive with + +254 +00:27:16,380 --> 00:27:23,840 +ing the last one the last group prepositions some + +255 +00:27:23,840 --> 00:27:28,720 +verbs are connected with prepositions after this + +256 +00:27:28,720 --> 00:27:34,780 +preposition we use the gerund the ing form the + +257 +00:27:34,780 --> 00:27:38,140 +infinitive with ing why because it is a + +258 +00:27:38,140 --> 00:27:43,480 +preposition so here thank you thank thank you for + +259 +00:27:43,480 --> 00:27:51,840 +so after four we use having playing me as your + +260 +00:27:51,840 --> 00:27:56,760 +guest so these groups don't forget them in this + +261 +00:27:56,760 --> 00:28:04,540 +arrangement grant to object and to So these are + +262 +00:28:04,540 --> 00:28:07,140 +the answers. I want someone also again to read + +263 +00:28:07,140 --> 00:28:09,300 +them. Number one. Yes. + +264 +00:28:13,100 --> 00:28:13,660 +Two. + +265 +00:28:19,000 --> 00:28:19,560 +Three. + +266 +00:28:24,560 --> 00:28:25,120 +Four. + +267 +00:28:28,900 --> 00:28:29,980 +And the last one. + +268 +00:28:34,380 --> 00:28:40,680 +So these are five. We have 14. We have 14 verbs. + +269 +00:28:41,100 --> 00:28:42,720 +Now look here. + +270 +00:28:45,020 --> 00:28:52,680 +Look here. We want to put + +271 +00:28:52,680 --> 00:28:59,380 +the verbs in this chart. The first one is enjoyed. + +272 +00:29:00,080 --> 00:29:05,160 +What about the second one? From the letter. Mm + +273 +00:29:05,160 --> 00:29:16,860 +-hmm. The second one is Yes Stopped + +274 +00:29:16,860 --> 00:29:25,600 +stopped and feeling stopped feeling So + +275 +00:29:25,600 --> 00:29:32,200 +here we have enjoyed and here we have stopped Yes + +276 +00:29:32,200 --> 00:29:32,900 +here + +277 +00:29:38,490 --> 00:29:54,650 +Wanted to say Next would like yeah would like to + +278 +00:29:54,650 --> 00:30:03,090 +call Next + +279 +00:30:04,730 --> 00:30:17,410 +Stop to visit Wanted + +280 +00:30:17,410 --> 00:30:22,270 +to see Wanted + +281 +00:30:22,270 --> 00:30:30,390 +to see Would + +282 +00:30:30,390 --> 00:30:32,910 +love to do + +283 +00:30:41,420 --> 00:30:49,380 +would love to do yes how many five how many here + +284 +00:30:49,380 --> 00:30:59,980 +two so number three number three wanted me wanted + +285 +00:30:59,980 --> 00:31:12,130 +me to stay wanted me to wanted me to Next. + +286 +00:31:14,850 --> 00:31:20,310 +Invited me to go. + +287 +00:31:24,810 --> 00:31:26,210 +Next. + +288 +00:31:28,410 --> 00:31:39,310 +Made me feel. Made me feel. Made me feel. + +289 +00:31:41,410 --> 00:31:55,090 +made me let me know let me know and + +290 +00:31:55,090 --> 00:32:02,890 +the last one thank you for having thank + +291 +00:32:02,890 --> 00:32:08,250 +you for having + +292 +00:32:13,520 --> 00:32:24,160 +thinking of going looking + +293 +00:32:24,160 --> 00:32:30,760 +forward looking forward + +294 +00:32:30,760 --> 00:32:37,140 +to hearing looking + +295 +00:32:37,140 --> 00:32:43,010 +forward to Looking forward to hearing. How many? + +296 +00:32:44,930 --> 00:32:55,730 +1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. How + +297 +00:32:55,730 --> 00:33:01,030 +many are they in the letter? Fourteen. So here we + +298 +00:33:01,030 --> 00:33:09,010 +wrote the fourteen verbs into this chart. Okay? + +299 +00:33:10,150 --> 00:33:14,690 +Yes, who can read? The first one, the first group. + +300 +00:33:18,170 --> 00:33:19,050 +Number two. + +301 +00:33:28,030 --> 00:33:29,950 +Number three. + +302 +00:33:31,730 --> 00:33:32,010 +Yeah. + +303 +00:33:37,310 --> 00:33:40,020 +And This one. + +304 +00:33:43,160 --> 00:33:49,920 +And the last one with prepositions. Thank you. + +305 +00:33:55,920 --> 00:34:04,520 +These groups enjoyed and stopped with ING. Wanted, + +306 +00:34:05,560 --> 00:34:10,920 +would like, Stopped, wanted, would love with + +307 +00:34:10,920 --> 00:34:18,900 +infinitive, with to Wanted me, invited me, object + +308 +00:34:18,900 --> 00:34:22,700 +and to Made, + +309 +00:34:23,580 --> 00:34:30,360 +let, object and the verb without to The last one + +310 +00:34:30,360 --> 00:34:40,410 +preposition and ing Thank you for thinking of + +311 +00:34:40,410 --> 00:34:47,030 +looking forward to. This too is a preposition. So + +312 +00:34:47,030 --> 00:34:50,130 +after it we use ing form. + +313 +00:34:54,590 --> 00:34:56,390 +And this is the answer. + +314 +00:35:04,530 --> 00:35:06,130 +Or someone to read again. + +315 +00:35:09,250 --> 00:35:09,530 +Yes. + +316 +00:35:14,030 --> 00:35:15,370 +Number two. + +317 +00:35:23,790 --> 00:35:28,990 +And would love to. + +318 +00:35:29,810 --> 00:35:36,790 +Would love to do. Yeah. Mhm. + +319 +00:35:39,470 --> 00:35:40,410 +Mhm. + +320 +00:35:42,650 --> 00:35:44,550 +Four. Yes. + +321 +00:35:47,150 --> 00:35:52,770 +No. Yes. The last one preposition. Yeah. Thank you + +322 +00:35:52,770 --> 00:35:56,790 +for having thinking of going looking forward + +323 +00:35:59,050 --> 00:36:02,490 +Hearing. Yes. So verb plus ing verb plus two + +324 +00:36:02,490 --> 00:36:08,190 +infinitive verb plus somebody and two infinitive + +325 +00:36:08,190 --> 00:36:14,590 +verb plus somebody infinitive Without two without + +326 +00:36:14,590 --> 00:36:23,410 +two and here is preposition and ing Look + +327 +00:36:23,410 --> 00:36:32,270 +at this example after the 14 verbs, we have a + +328 +00:36:32,270 --> 00:36:38,090 +group of other verbs. We want also to write them + +329 +00:36:38,090 --> 00:36:46,810 +in the same chart. So after the 14 verbs, we want + +330 +00:36:46,810 --> 00:36:51,810 +to add something. Choose from here. So promise. + +331 +00:36:54,710 --> 00:36:56,210 +Promise, what is it? + +332 +00:37:05,920 --> 00:37:15,160 +Here Promise to promise to uh-huh the second one + +333 +00:37:15,160 --> 00:37:25,760 +Promised and uh-huh succeed in Here + +334 +00:37:25,760 --> 00:37:29,660 +succeed in + +335 +00:37:30,280 --> 00:37:36,860 +Preposition Yes + +336 +00:37:36,860 --> 00:37:40,940 +here + +337 +00:37:40,940 --> 00:37:53,300 +let Let me let him let Ali let me Yes + +338 +00:38:00,740 --> 00:38:11,600 +with somebody tell me to so we have till and here + +339 +00:38:11,600 --> 00:38:18,040 +we have let ask + +340 +00:38:18,040 --> 00:38:25,780 +also asked me + +341 +00:38:25,780 --> 00:38:35,570 +to so the verb is Help me + +342 +00:38:35,570 --> 00:38:39,290 +go. + +343 +00:38:39,970 --> 00:38:43,170 +Help me teach. + +344 +00:38:46,730 --> 00:38:50,230 +Finish here. + +345 +00:38:53,090 --> 00:39:06,230 +Finish writing. Finish playing. uh-huh need uh-huh + +346 +00:39:06,230 --> 00:39:11,250 +need need + +347 +00:39:11,250 --> 00:39:20,350 +to need to with the promise promise to need to so + +348 +00:39:20,350 --> 00:39:27,090 +we have promise and need uh-huh hate + +349 +00:39:29,110 --> 00:39:31,610 +Hate ing, yes. Hate. + +350 +00:39:35,070 --> 00:39:40,570 +I hate eating in front of the people. I hate + +351 +00:39:40,570 --> 00:39:46,710 +coming late. I hate reading silently. Something + +352 +00:39:46,710 --> 00:39:55,890 +like this. Yeah, yes, next. Forget. Forget. Two, + +353 +00:39:57,130 --> 00:39:57,510 +yes. + +354 +00:40:03,320 --> 00:40:12,140 +Yeah. Don't mind mind IG. Yes. Don't mind. + +355 +00:40:16,280 --> 00:40:25,440 +Yeah. And look forward to look + +356 +00:40:25,440 --> 00:40:39,080 +forward to to IG. IG. So in addition to the 14 + +357 +00:40:39,080 --> 00:40:49,000 +verbs, we have another 12. What are they? With IG, + +358 +00:40:49,340 --> 00:40:56,540 +we use finish, hate, and mind. Don't mind. Would + +359 +00:40:56,540 --> 00:41:02,960 +you mind? I don't mind. Finish, hate, mind with + +360 +00:41:02,960 --> 00:41:07,990 +IG. And with two, in addition to the previous + +361 +00:41:07,990 --> 00:41:15,550 +ones, promised to need to forget two. And in + +362 +00:41:15,550 --> 00:41:20,330 +addition to the object and two, we have till and + +363 +00:41:20,330 --> 00:41:24,270 +ask. He told me to come early. He asked me to give + +364 +00:41:24,270 --> 00:41:30,840 +him some money. And here, somebody and without to + +365 +00:41:30,840 --> 00:41:37,920 +let me go help me go the last one preposition verb + +366 +00:41:37,920 --> 00:41:43,200 +plus prepositions and the ing form so succeeded in + +367 +00:41:43,200 --> 00:41:50,210 +succeed in solving succeed in playing succeed in + +368 +00:41:50,210 --> 00:41:54,930 +taking look forward to meeting look forward to + +369 +00:41:54,930 --> 00:42:00,470 +having look forward to hearing you understand ah + +370 +00:42:00,470 --> 00:42:08,410 +also we have who can read this again again yes + +371 +00:42:08,410 --> 00:42:16,230 +enjoyed meeting finish hate don't mind don't mind + +372 +00:42:16,230 --> 00:42:22,790 +yes plus two + +373 +00:42:22,790 --> 00:42:27,050 +plus infinity yes and + +374 +00:42:27,050 --> 00:42:34,090 +object and two yeah verb somebody to plus infinity + +375 +00:42:34,090 --> 00:42:41,510 +tell me to ask me to and here yeah + +376 +00:42:46,580 --> 00:42:57,660 +And the last one Yes, + +377 +00:42:57,900 --> 00:43:07,640 +so we have 14 verbs and and 12 now how many 26 + +378 +00:43:07,640 --> 00:43:11,340 +Yes now + +379 +00:43:13,940 --> 00:43:19,000 +These are the answers. Some other one. You can + +380 +00:43:19,000 --> 00:43:21,740 +read it quickly. All of them. Yes. + +381 +00:43:28,970 --> 00:43:32,910 +forget need verb plus somebody plus two plus + +382 +00:43:32,910 --> 00:43:37,270 +infinitive tell and ask verb plus somebody plus + +383 +00:43:37,270 --> 00:43:40,870 +infinitive without to let and tell preposition + +384 +00:43:40,870 --> 00:43:45,950 +plus ing succeed and plot forward to yeah again + +385 +00:43:45,950 --> 00:43:48,870 +again yeah + +386 +00:44:13,170 --> 00:44:22,450 +prepositions plus ing succeed and For what? Two. + +387 +00:44:22,750 --> 00:44:26,510 +Yes. You understand this? Easy or difficult? You + +388 +00:44:26,510 --> 00:44:31,070 +have to keep them by heart. By heart. Not without + +389 +00:44:31,070 --> 00:44:34,790 +understanding. No. By heart. Yeah. + +390 +00:44:41,050 --> 00:44:44,250 +So here we have + +391 +00:44:49,740 --> 00:44:57,420 +Yeah. This exercise, in fact, these exercises are + +392 +00:44:57,420 --> 00:45:02,220 +two exercises or three exercises. Why? Because we + +393 +00:45:02,220 --> 00:45:06,420 +want to make these six sentences into eighteen + +394 +00:45:06,420 --> 00:45:11,580 +sentences. Eighteen sentences. What's with this? + +395 +00:45:12,160 --> 00:45:15,040 +What's with this? What's with this? With three. + +396 +00:45:16,010 --> 00:45:20,210 +Not choose. No, not choose. So here in these + +397 +00:45:20,210 --> 00:45:23,970 +sentences, two verbs are correct. So we can make + +398 +00:45:23,970 --> 00:45:30,950 +two sentences with the same. And one is not. Two + +399 +00:45:30,950 --> 00:45:36,530 +okay and one not. Take the correct verb. The first + +400 +00:45:36,530 --> 00:45:45,410 +one. My father promised to mend my bike. Okay. So + +401 +00:45:45,410 --> 00:45:48,270 +this is pipe. + +402 +00:45:49,650 --> 00:45:57,950 +My father tried to mend my bike. So this is with + +403 +00:45:57,950 --> 00:46:07,510 +okay. Now she asked her son to turn down his + +404 +00:46:07,510 --> 00:46:09,850 +music. Asked. + +405 +00:46:12,420 --> 00:46:18,100 +She wanted her son to turn down his music. How + +406 +00:46:18,100 --> 00:46:22,040 +many + +407 +00:46:22,040 --> 00:46:28,860 +now? Four. Two and two. Now by three. I can't + +408 +00:46:28,860 --> 00:46:33,880 +stand going on long walks. + +409 +00:46:37,360 --> 00:46:40,600 +So this can't stand with the verb plus? + +410 +00:46:56,810 --> 00:47:02,530 +I love going + +411 +00:47:02,530 --> 00:47:07,550 +on long walks. Another one. Love and can't stand. + +412 +00:47:07,690 --> 00:47:15,590 +With what? with ing uh-huh now next we we need to + +413 +00:47:15,590 --> 00:47:28,690 +go we'd we'd love to go shopping number five she + +414 +00:47:28,690 --> 00:47:38,730 +made me do the cooking She helped me do the + +415 +00:47:38,730 --> 00:47:46,110 +cooking. Do you understand? Number six. I started + +416 +00:47:46,110 --> 00:47:49,590 +working + +417 +00:47:49,590 --> 00:47:53,350 +for + +418 +00:47:53,350 --> 00:48:02,550 +the bank 20 years ago. I stopped working for the + +419 +00:48:02,550 --> 00:48:08,120 +bank 20 years ago. How many new ones? Three. Can't + +420 +00:48:08,120 --> 00:48:14,920 +stand, love with ing and started with ing. You + +421 +00:48:14,920 --> 00:48:18,840 +understand? So we have three verbs can't stand, + +422 +00:48:19,920 --> 00:48:26,200 +love and started. Also how many sentences did we + +423 +00:48:26,200 --> 00:48:31,880 +make? Six and six. How many? Twelve. Now we're + +424 +00:48:31,880 --> 00:48:38,620 +going to make another six. New ones. So the answer + +425 +00:48:38,620 --> 00:48:44,240 +here is number two, A and B. Number three, B and + +426 +00:48:44,240 --> 00:48:50,160 +C. Four, A and B. Five, B and C. And six, A and B. + +427 +00:48:50,420 --> 00:48:54,580 +Now we want to make new sentences. With what? With + +428 +00:48:54,580 --> 00:49:06,500 +this one. With Kotin. With couldn't. So we + +429 +00:49:06,500 --> 00:49:18,620 +use my father. My father couldn't without + +430 +00:49:18,620 --> 00:49:24,900 +you. And this is a new group. Must, couldn't, can. + +431 +00:49:25,950 --> 00:49:32,430 +should these are another group the model takes the + +432 +00:49:32,430 --> 00:49:37,990 +infinitive without two without object so this is + +433 +00:49:37,990 --> 00:49:47,650 +group number six group number six should must may + +434 +00:49:47,650 --> 00:49:54,480 +might can Could all the models take infinitive + +435 +00:49:54,480 --> 00:50:01,660 +without to except for need to and ought to. You + +436 +00:50:01,660 --> 00:50:05,560 +understand? So this is another group. So here + +437 +00:50:05,560 --> 00:50:11,640 +couldn't without to. Number two, she made, she + +438 +00:50:11,640 --> 00:50:22,510 +made. So here we use couldn't. Here, she made her + +439 +00:50:22,510 --> 00:50:24,610 +son turn. + +440 +00:50:26,370 --> 00:50:32,950 +She made her son turn. You understand? This is + +441 +00:50:32,950 --> 00:50:40,590 +another one. Number three, I refused to + +442 +00:50:40,590 --> 00:50:48,520 +go to go on a long walks. Or I refuse without ed, + +443 +00:50:48,780 --> 00:50:55,240 +the same. So this is a new one. A new one. What's + +444 +00:50:55,240 --> 00:51:02,880 +it? Refuse. A new one. You understand? Number + +445 +00:51:02,880 --> 00:51:10,080 +four. We enjoy going. + +446 +00:51:11,860 --> 00:51:18,160 +After enjoy, going. so the third one is we enjoy + +447 +00:51:18,160 --> 00:51:26,740 +going shopping number five she wanted she + +448 +00:51:26,740 --> 00:51:31,420 +wanted me to + +449 +00:51:31,420 --> 00:51:38,990 +do she wanted me to do You understand? Simple. + +450 +00:51:39,150 --> 00:51:44,730 +Yes, and the last one I decided Also this a new + +451 +00:51:44,730 --> 00:51:57,190 +one I decided Decided To work You + +452 +00:51:57,190 --> 00:52:05,470 +understand? So again, couldn't mend Made her son + +453 +00:52:05,470 --> 00:52:19,280 +turn Refuse to go. Enjoy going. Wanted me to do. I + +454 +00:52:19,280 --> 00:52:26,600 +decided to work. So now we are going to make 18 + +455 +00:52:26,600 --> 00:52:34,040 +sentences. Two the same and one is different. Who + +456 +00:52:34,040 --> 00:52:38,280 +can make the first one? Three sentences. Two the + +457 +00:52:38,280 --> 00:52:42,600 +same and one is different. Yes. Number one, my + +458 +00:52:42,600 --> 00:52:46,020 +father couldn't mend my bike. No, no. The first, + +459 +00:52:46,760 --> 00:52:52,260 +the similar. My father promised to mend my bike. + +460 +00:52:52,700 --> 00:52:58,400 +My father tried to mend my bike. My father + +461 +00:52:58,400 --> 00:53:02,040 +couldn't mend my bike. Yes. You understand? So + +462 +00:53:02,040 --> 00:53:05,520 +with this and this, the same. And with this, a + +463 +00:53:05,520 --> 00:53:11,960 +different one. Son asked her son to turn down his + +464 +00:53:11,960 --> 00:53:21,040 +music. She, yes. She wanted her son to turn down + +465 +00:53:21,040 --> 00:53:25,600 +his music. She made her son turn down his music. + +466 +00:53:26,080 --> 00:53:28,080 +Number three. Good. + +467 +00:53:31,180 --> 00:53:36,880 +I can't stand going on long walks. I love going on + +468 +00:53:36,880 --> 00:53:40,950 +long walks. I refuse to go on long walk. You + +469 +00:53:40,950 --> 00:53:45,630 +understand? Yes. Easy. Yes. We need to go + +470 +00:53:45,630 --> 00:53:52,290 +shopping. We love to go shopping. We enjoy going + +471 +00:53:52,290 --> 00:53:57,550 +shopping. Very good. Number five, she made me do + +472 +00:53:57,550 --> 00:54:05,230 +the cooking. She helped me do the cooking. She + +473 +00:54:05,230 --> 00:54:13,050 +wanted Yes. And number six, the last one. Yeah. I + +474 +00:54:13,050 --> 00:54:17,390 +started working for the bank 20 years ago. I + +475 +00:54:17,390 --> 00:54:21,490 +stopped working for the bank 20 years ago. I + +476 +00:54:21,490 --> 00:54:25,510 +decided to work for the bank 20 years ago. Do you + +477 +00:54:25,510 --> 00:54:30,310 +understand? So this is three exercises in one. So + +478 +00:54:30,310 --> 00:54:36,170 +the answer here is this is the strange one. + +479 +00:54:39,050 --> 00:54:46,090 +So after we choose the two, this is with the third + +480 +00:54:46,090 --> 00:54:51,870 +verb. Couldn't mend. My father couldn't mend my + +481 +00:54:51,870 --> 00:54:58,450 +bike. She made her son turn. I refused to go on + +482 +00:54:58,450 --> 00:55:03,720 +long walks. We enjoyed going shopping. She wanted + +483 +00:55:03,720 --> 00:55:09,620 +me to do the cooking. I decided to work for the + +484 +00:55:09,620 --> 00:55:14,560 +bank 20 years ago. Also, don't forget that we have + +485 +00:55:14,560 --> 00:55:17,760 +two + +486 +00:55:17,760 --> 00:55:23,420 +things. Don't forget it. What's the difference + +487 +00:55:23,420 --> 00:55:30,180 +between this and this? Here, they stop to talk to + +488 +00:55:30,180 --> 00:55:36,020 +each other. They stopped shopping. Why? In order + +489 +00:55:36,020 --> 00:55:41,400 +to talk. Now they were shopping at first, then + +490 +00:55:41,400 --> 00:55:46,880 +they left the shopping. Why? In order to talk. + +491 +00:55:47,260 --> 00:55:52,980 +This one. They stopped talking. They gave up + +492 +00:55:52,980 --> 00:56:00,780 +talking. But here they... to talk. Talking. + +493 +00:56:01,060 --> 00:56:05,100 +Stopped to talk. Stopped talking. Example + +494 +00:56:05,100 --> 00:56:12,840 +complete. Here I soon stopped feeling. + +495 +00:56:15,300 --> 00:56:24,700 +Stopped feeling. And here I stopped to visit. + +496 +00:56:28,190 --> 00:56:31,410 +You understand the difference between stop? Thank + +497 +00:56:31,410 --> 00:56:33,570 +you very much. Thank you very much. + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/5kawOfcrw3A_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/5kawOfcrw3A_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..47e15ca893b46f8e87fdbba18e801e756786302b --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/5kawOfcrw3A_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 4976, "start": 21.08, "end": 49.76, "text": "بسم الله الرحمن الرحيم اليوم المحاضرة التالتة في اللي هو التقارير وروابطها هنستكمل تعريفنا للروابط اللي تستخدم في تكوين التقارير المركبة من التقارير البسيطة كما ذكرنا في المحاضرات السابقة هناك خمس روابط وهي الـNeffy الـ Negation اللي هي not أداتها وفي عندنا ال conjunction الإخترار وأداتها أو هي ال and", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 45595, 20498, 9673, 5016, 46958, 25720, 16712, 6027, 2655, 3660, 8978, 13672, 1829, 31439, 16712, 4587, 9640, 13546, 4032, 2288, 14407, 3555, 9566, 11296, 8032, 1863, 14851, 24793, 1211, 37279, 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اسمه؟ رمز الجمع .. اه .. تمام؟ فهي نهيأش اسمه .. الرمز هذا الـ biconditional طيب، مع مين بتعامل؟ مع two statements .. مع two statements .. بنحط بينهم زي ما هيك كيف بنقرا هذه ال statement؟ ب .. if and only .. 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" الجواب", "probability": 0.92529296875}], "temperature": 1.0}, {"id": 16, "seek": 37877, "start": 357.93, "end": 378.77, "text": "مباشرة solution ف determine whether the following statements are true or false المثال الأول A فبنحلل المركبات بنستنتج لجملة ال compound statement فبقولي one is all الواحد عدد فردي true ولا false true", "tokens": [2304, 3555, 33599, 25720, 3827, 6156, 6997, 1968, 264, 3480, 12363, 366, 2074, 420, 7908, 9673, 12984, 6027, 16247, 12610, 316, 6156, 3555, 1863, 5016, 1211, 1211, 9673, 31747, 3555, 9307, 44945, 14851, 29399, 7435, 5296, 7435, 2304, 37977, 2423, 14154, 5629, 6156, 3555, 39648, 1829, 472, 307, 439, 2423, 14407, 24401, 6225, 3215, 3215, 6156, 2288, 16254, 2074, 49429, 7908, 2074], "avg_logprob": -0.21726190286969382, "compression_ratio": 1.3979057591623036, "no_speech_prob": 0.0, "words": [{"start": 357.93, "end": 358.61, "word": "مباشرة", "probability": 0.86102294921875}, {"start": 358.61, "end": 359.51, "word": " solution", "probability": 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"probability": 0.79541015625}, {"start": 771.69, "end": 772.81, "word": " بنعمله", "probability": 0.9033203125}, {"start": 772.81, "end": 773.45, "word": " عمود", "probability": 0.9459635416666666}, {"start": 773.45, "end": 773.69, "word": " و", "probability": 0.72607421875}, {"start": 773.69, "end": 774.13, "word": " اليسار", "probability": 0.958984375}, {"start": 774.13, "end": 774.57, "word": " عمود", "probability": 0.9611002604166666}, {"start": 774.57, "end": 774.79, "word": " و", "probability": 0.81005859375}, {"start": 774.79, "end": 775.47, "word": " بنقارن", "probability": 0.9591064453125}, {"start": 775.47, "end": 775.93, "word": " فيه", "probability": 0.92822265625}, {"start": 775.93, "end": 776.13, "word": " إيش", "probability": 0.7314453125}, {"start": 776.13, "end": 776.61, "word": " قيمة", "probability": 0.9978841145833334}, {"start": 776.61, "end": 777.03, "word": " الصدق", "probability": 0.9913736979166666}, {"start": 777.03, "end": 777.85, "word": " فهنعمل", 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true false اه فالجهة هذه true then true true بعدين false false true if if then آسف أنا معلق مع الجدول الصحيح اه true then false false false then true true true تمام هذه if then تمام", "tokens": [2304, 3555, 33599, 25720, 12399, 23032, 3555, 3615, 995, 5551, 12610, 44049, 39896, 29538, 2074, 2074, 7908, 7908, 2074, 7908, 2074, 7908, 1975, 3224, 6156, 6027, 7435, 3224, 3660, 29538, 2074, 550, 2074, 2074, 39182, 9957, 7908, 7908, 2074, 498, 498, 550, 19753, 3794, 5172, 41850, 3714, 30241, 4587, 20449, 25724, 3215, 12610, 31767, 5016, 1829, 5016, 1975, 3224, 2074, 550, 7908, 7908, 7908, 550, 2074, 2074, 2074, 46811, 10943, 29538, 498, 550, 46811, 10943], "avg_logprob": -0.2650082209392598, "compression_ratio": 1.96875, "no_speech_prob": 0.0, "words": [{"start": 805.07, "end": 805.71, "word": "مباشرة،", "probability": 0.7885498046875}, {"start": 805.71, "end": 805.89, "word": " طبعا", "probability": 0.9051513671875}, {"start": 805.89, "end": 806.05, "word": " أول", "probability": 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"probability": 0.8525390625}, {"start": 1052.14, "end": 1052.64, "word": " given", "probability": 0.89599609375}, {"start": 1052.64, "end": 1053.2, "word": " compound", "probability": 0.9326171875}, {"start": 1053.2, "end": 1054.0, "word": " statements", "probability": 0.7001953125}, {"start": 1054.0, "end": 1054.98, "word": " ترجم", "probability": 0.8473307291666666}, {"start": 1054.98, "end": 1055.8, "word": " الجمال", "probability": 0.7140299479166666}, {"start": 1055.8, "end": 1056.48, "word": " المركبة", "probability": 0.87939453125}, {"start": 1056.48, "end": 1056.66, "word": " أو", "probability": 0.7119140625}, {"start": 1056.66, "end": 1057.14, "word": " التقارير", "probability": 0.926513671875}, {"start": 1057.14, "end": 1057.72, "word": " المركبة", "probability": 0.9892578125}, {"start": 1057.72, "end": 1058.4, "word": " إلى", "probability": 0.86865234375}, {"start": 1058.4, "end": 1059.04, "word": " into", "probability": 0.53125}, {"start": 1059.04, "end": 1059.3, "word": " 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احنا", "probability": 0.80810546875}, {"start": 1123.96, "end": 1124.3, "word": " هنقول", "probability": 0.9140625}, {"start": 1124.3, "end": 1124.5, "word": " له", "probability": 0.6015625}], "temperature": 1.0}, {"id": 51, "seek": 115077, "start": 1125.21, "end": 1150.77, "text": "let e denotes the statement ليه اياش a natural number is even is even بعد ال statement الأول and let d denotes", "tokens": [2631, 308, 1441, 17251, 264, 5629, 32239, 3224, 1975, 1829, 33599, 257, 3303, 1230, 307, 754, 307, 754, 39182, 2423, 5629, 16247, 12610, 293, 718, 274, 1441, 17251], "avg_logprob": -0.44154094005453176, "compression_ratio": 1.1981132075471699, "no_speech_prob": 0.0, "words": [{"start": 1125.21, "end": 1125.71, "word": "let", "probability": 0.313232421875}, {"start": 1125.71, "end": 1126.69, "word": " e", "probability": 0.3837890625}, {"start": 1126.69, "end": 1128.47, "word": " denotes", "probability": 0.731689453125}, {"start": 1128.47, "end": 1130.15, "word": " the", "probability": 0.24755859375}, {"start": 1130.15, "end": 1130.83, "word": " statement", "probability": 0.9560546875}, {"start": 1130.83, "end": 1131.79, "word": " ليه", "probability": 0.526611328125}, {"start": 1131.79, "end": 1132.15, "word": " اياش", "probability": 0.5958251953125}, {"start": 1132.15, "end": 1133.79, "word": " a", "probability": 0.61474609375}, {"start": 1133.79, "end": 1134.21, "word": " natural", "probability": 0.919921875}, {"start": 1134.21, "end": 1134.77, "word": " number", "probability": 0.97265625}, {"start": 1134.77, "end": 1135.11, "word": " is", "probability": 0.97021484375}, {"start": 1135.11, "end": 1135.49, "word": " even", "probability": 0.90234375}, {"start": 1135.49, "end": 1144.61, "word": " is", "probability": 0.61376953125}, {"start": 1144.61, "end": 1145.09, "word": " even", "probability": 0.896484375}, {"start": 1145.09, "end": 1145.51, "word": " بعد", "probability": 0.2054443359375}, {"start": 1145.51, "end": 1145.63, "word": " ال", "probability": 0.94091796875}, {"start": 1145.63, "end": 1145.91, "word": " statement", "probability": 0.8466796875}, {"start": 1145.91, "end": 1146.27, "word": " الأول", "probability": 0.7052001953125}, {"start": 1146.27, "end": 1147.09, "word": " and", "probability": 0.6259765625}, {"start": 1147.09, "end": 1148.83, "word": " let", "probability": 0.9345703125}, {"start": 1148.83, "end": 1149.39, "word": " d", "probability": 0.81201171875}, {"start": 1149.39, "end": 1150.77, "word": " denotes", "probability": 0.939453125}], "temperature": 1.0}, {"id": 52, "seek": 118182, "start": 1154.2, "end": 1181.82, "text": "A natural number is divisible يقبل القسمة by two فإذا ال statement is B A E if and only if D فده هو الرمز", "tokens": [32, 3303, 1230, 307, 25974, 964, 7251, 4587, 36150, 25062, 38251, 3660, 538, 732, 6156, 28814, 15730, 2423, 5629, 307, 363, 316, 462, 498, 293, 787, 498, 413, 6156, 3215, 3224, 31439, 34892, 2304, 11622], "avg_logprob": -0.3298610986934768, "compression_ratio": 1.0826446280991735, "no_speech_prob": 0.0, "words": [{"start": 1154.2, "end": 1155.28, "word": "A", "probability": 0.08441162109375}, {"start": 1155.28, "end": 1155.8, "word": " natural", "probability": 0.8544921875}, {"start": 1155.8, "end": 1156.4, "word": " number", "probability": 0.96142578125}, {"start": 1156.4, "end": 1156.96, "word": " is", "probability": 0.814453125}, {"start": 1156.96, "end": 1162.1, "word": " divisible", "probability": 0.89794921875}, {"start": 1162.1, "end": 1162.52, "word": " يقبل", "probability": 0.7906901041666666}, {"start": 1162.52, "end": 1163.32, "word": " القسمة", "probability": 0.9822591145833334}, {"start": 1163.32, "end": 1163.54, "word": " by", "probability": 0.9013671875}, {"start": 1163.54, "end": 1165.34, "word": " two", "probability": 0.6943359375}, {"start": 1165.34, "end": 1166.68, "word": " فإذا", "probability": 0.6188151041666666}, {"start": 1166.68, "end": 1166.86, "word": " ال", "probability": 0.78466796875}, {"start": 1166.86, "end": 1167.32, "word": " statement", "probability": 0.9033203125}, {"start": 1167.32, "end": 1172.42, "word": " is", "probability": 0.52490234375}, {"start": 1172.42, "end": 1176.84, "word": " B", "probability": 0.10382080078125}, {"start": 1176.84, "end": 1177.72, "word": " A", "probability": 0.463134765625}, {"start": 1177.72, "end": 1178.1, "word": " E", "probability": 0.9814453125}, {"start": 1178.1, "end": 1179.04, "word": " if", "probability": 0.72265625}, {"start": 1179.04, "end": 1179.3, "word": " and", "probability": 0.94921875}, {"start": 1179.3, "end": 1179.5, "word": " only", "probability": 0.921875}, {"start": 1179.5, "end": 1179.94, "word": " if", "probability": 0.9794921875}, {"start": 1179.94, "end": 1180.54, "word": " D", "probability": 0.83154296875}, {"start": 1180.54, "end": 1181.28, "word": " فده", "probability": 0.79296875}, {"start": 1181.28, "end": 1181.42, "word": " هو", "probability": 0.96630859375}, {"start": 1181.42, "end": 1181.82, "word": " الرمز", "probability": 0.9912109375}], "temperature": 1.0}, {"id": 53, "seek": 121067, "start": 1182.55, "end": 1210.67, "text": "فهذه جملة ثنائية الشرطية فهذه جملة ثنائية الشرطية ممكن تحويلها لرموز E if and only if D إيش معناته E يعني عدد اللي بيكون زوجي فقط وإذا فقط يقبل قسمة على اتنين نشوف كمان مثل أتوقع بقدر أمسح هنا بي", "tokens": [5172, 3224, 24192, 10874, 2304, 37977, 38637, 1863, 16373, 10632, 25124, 2288, 9566, 10632, 6156, 3224, 24192, 10874, 2304, 37977, 38637, 1863, 16373, 10632, 25124, 2288, 9566, 10632, 3714, 43020, 6055, 5016, 2407, 26895, 11296, 5296, 2288, 2304, 2407, 11622, 462, 498, 293, 787, 498, 413, 11933, 1829, 8592, 20449, 8315, 47395, 462, 37495, 22653, 6225, 3215, 3215, 13672, 1829, 4724, 1829, 30544, 30767, 29245, 1829, 6156, 47432, 4032, 28814, 15730, 6156, 47432, 7251, 4587, 36150, 12174, 38251, 3660, 15844, 1975, 2655, 1863, 9957, 8717, 8592, 38688, 9122, 2304, 7649, 50113, 1211, 5551, 2655, 30543, 3615, 4724, 28543, 2288, 5551, 2304, 3794, 5016, 34105, 4724, 1829], "avg_logprob": -0.16851635096229126, "compression_ratio": 1.7106598984771573, "no_speech_prob": 0.0, "words": [{"start": 1182.55, "end": 1182.95, "word": "فهذه", "probability": 0.8116861979166666}, {"start": 1182.95, "end": 1183.37, "word": " جملة", "probability": 0.9554036458333334}, {"start": 1183.37, "end": 1184.53, "word": " ثنائية", "probability": 0.9486083984375}, {"start": 1184.53, "end": 1185.21, "word": " الشرطية", "probability": 0.97802734375}, {"start": 1185.21, "end": 1186.23, "word": " فهذه", "probability": 0.812255859375}, {"start": 1186.23, "end": 1186.59, "word": " جملة", "probability": 0.9627278645833334}, {"start": 1186.59, "end": 1187.09, "word": " ثنائية", "probability": 0.9840087890625}, {"start": 1187.09, "end": 1187.53, "word": " الشرطية", "probability": 0.9921875}, {"start": 1187.53, "end": 1187.73, "word": " ممكن", "probability": 0.913818359375}, {"start": 1187.73, "end": 1188.09, "word": " تحويلها", "probability": 0.75}, {"start": 1188.09, "end": 1188.61, "word": " لرموز", "probability": 0.97041015625}, {"start": 1188.61, "end": 1189.25, "word": " E", "probability": 0.1451416015625}, {"start": 1189.25, "end": 1189.81, "word": " if", "probability": 0.85888671875}, {"start": 1189.81, "end": 1189.97, "word": " and", "probability": 0.92431640625}, {"start": 1189.97, "end": 1190.15, "word": " only", "probability": 0.91650390625}, {"start": 1190.15, "end": 1190.41, "word": " if", "probability": 0.97216796875}, {"start": 1190.41, "end": 1190.59, "word": " D", "probability": 0.394775390625}, {"start": 1190.59, "end": 1190.79, "word": " إيش", "probability": 0.77099609375}, {"start": 1190.79, "end": 1191.21, "word": " معناته", "probability": 0.9607747395833334}, {"start": 1191.21, "end": 1191.71, "word": " E", "probability": 0.53955078125}, {"start": 1191.71, "end": 1192.37, "word": " يعني", "probability": 0.970703125}, {"start": 1192.37, "end": 1192.95, "word": " عدد", "probability": 0.9602864583333334}, {"start": 1192.95, "end": 1193.49, "word": " اللي", "probability": 0.869140625}, {"start": 1193.49, "end": 1193.77, "word": " بيكون", "probability": 0.7913411458333334}, {"start": 1193.77, "end": 1194.29, "word": " زوجي", "probability": 0.9597981770833334}, {"start": 1194.29, "end": 1195.19, "word": " فقط", "probability": 0.76171875}, {"start": 1195.19, "end": 1195.45, "word": " وإذا", "probability": 0.8660481770833334}, {"start": 1195.45, "end": 1195.87, "word": " فقط", "probability": 0.9873046875}, {"start": 1195.87, "end": 1196.45, "word": " يقبل", "probability": 0.96142578125}, {"start": 1196.45, "end": 1197.19, "word": " قسمة", "probability": 0.8639322916666666}, {"start": 1197.19, "end": 1197.49, "word": " على", "probability": 0.61669921875}, {"start": 1197.49, "end": 1198.25, "word": " اتنين", "probability": 0.77593994140625}, {"start": 1198.25, "end": 1200.87, "word": " نشوف", "probability": 0.90087890625}, {"start": 1200.87, "end": 1201.31, "word": " كمان", "probability": 0.9293619791666666}, {"start": 1201.31, "end": 1202.31, "word": " مثل", "probability": 0.828125}, {"start": 1202.31, "end": 1203.07, "word": " أتوقع", "probability": 0.7760009765625}, {"start": 1203.07, "end": 1203.39, "word": " بقدر", "probability": 0.9197591145833334}, {"start": 1203.39, "end": 1203.69, "word": " أمسح", "probability": 0.9595947265625}, {"start": 1203.69, "end": 1203.97, "word": " هنا", "probability": 0.96240234375}, {"start": 1203.97, "end": 1210.67, "word": " بي", "probability": 0.727783203125}], "temperature": 1.0}, {"id": 54, "seek": 122128, "start": 1212.7, "end": 1221.28, "text": "A matrix has an inverse المصفوفة إليها معكوس whenever its determinant is not zero", "tokens": [32, 8141, 575, 364, 17340, 9673, 9381, 5172, 38688, 3660, 11933, 20292, 11296, 20449, 4117, 41779, 5699, 1080, 41296, 307, 406, 4018], "avg_logprob": -0.36311140526895935, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 1212.7, "end": 1212.92, "word": "A", "probability": 0.1318359375}, {"start": 1212.92, "end": 1213.48, "word": " matrix", "probability": 0.8798828125}, {"start": 1213.48, "end": 1214.08, "word": " has", "probability": 0.93310546875}, {"start": 1214.08, "end": 1214.4, "word": " an", "probability": 0.908203125}, {"start": 1214.4, "end": 1214.88, "word": " inverse", "probability": 0.8349609375}, {"start": 1214.88, "end": 1215.7, "word": " المصفوفة", "probability": 0.816162109375}, {"start": 1215.7, "end": 1215.88, "word": " إليها", "probability": 0.6430257161458334}, {"start": 1215.88, "end": 1216.38, "word": " معكوس", "probability": 0.8517252604166666}, {"start": 1216.38, "end": 1217.22, "word": " whenever", "probability": 0.91259765625}, {"start": 1217.22, "end": 1218.24, "word": " its", "probability": 0.80126953125}, {"start": 1218.24, "end": 1219.78, "word": " determinant", "probability": 0.8447265625}, {"start": 1219.78, "end": 1220.66, "word": " is", "probability": 0.9365234375}, {"start": 1220.66, "end": 1220.94, "word": " not", "probability": 0.93994140625}, {"start": 1220.94, "end": 1221.28, "word": " zero", "probability": 0.75341796875}], "temperature": 1.0}, {"id": 55, "seek": 125850, "start": 1228.68, "end": 1258.5, "text": "فهنا على الملاحظة في المحاضرة الماضية كما لو كنتش تستخدم if then منها whenever قلنا ايش اكيو و whenever بي اكيو و whenever بي فإذا هنا بالنسبة لنا اللي بيكون الأولى هي جواب الشرط و اللي بعد whenever هي الشرط هنعملهم نعملهم مع بعض أول شيء برضه زي بطوي طبعا احنا ممكن نكتب بشكل مطول زي هيك او نحط اختصارة هي I من كلمة inverse هتشملها a matrix", "tokens": [5172, 3224, 8315, 15844, 9673, 15040, 5016, 19913, 3660, 8978, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 9122, 15042, 45164, 9122, 29399, 8592, 6055, 14851, 9778, 40448, 498, 550, 9154, 11296, 5699, 12174, 1211, 8315, 1975, 1829, 8592, 1975, 4117, 1829, 2407, 4032, 5699, 4724, 1829, 1975, 4117, 1829, 2407, 4032, 5699, 4724, 1829, 6156, 28814, 15730, 34105, 20666, 1863, 35457, 3660, 5296, 8315, 13672, 1829, 4724, 1829, 30544, 16247, 12610, 7578, 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{"start": 1230.52, "end": 1231.74, "word": " المحاضرة", "probability": 0.9189453125}, {"start": 1231.74, "end": 1232.28, "word": " الماضية", "probability": 0.97265625}, {"start": 1232.28, "end": 1232.8, "word": " كما", "probability": 0.39892578125}, {"start": 1232.8, "end": 1232.86, "word": " لو", "probability": 0.669921875}, {"start": 1232.86, "end": 1233.08, "word": " كنتش", "probability": 0.5587565104166666}, {"start": 1233.08, "end": 1233.48, "word": " تستخدم", "probability": 0.953369140625}, {"start": 1233.48, "end": 1233.7, "word": " if", "probability": 0.8857421875}, {"start": 1233.7, "end": 1234.0, "word": " then", "probability": 0.830078125}, {"start": 1234.0, "end": 1234.56, "word": " منها", "probability": 0.90771484375}, {"start": 1234.56, "end": 1235.06, "word": " whenever", "probability": 0.86181640625}, {"start": 1235.06, "end": 1235.5, "word": " قلنا", "probability": 0.779296875}, {"start": 1235.5, "end": 1235.74, "word": " ايش", "probability": 0.6033935546875}, 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given statement", "tokens": [1353, 855, 300, 264, 5629, 1975, 2407, 264, 2212, 5629], "avg_logprob": -0.31267756765538995, "compression_ratio": 1.108695652173913, "no_speech_prob": 0.0, "words": [{"start": 1846.28, "end": 1846.48, "word": "to", "probability": 0.298095703125}, {"start": 1846.48, "end": 1846.9, "word": " show", "probability": 0.96484375}, {"start": 1846.9, "end": 1849.36, "word": " that", "probability": 0.89306640625}, {"start": 1849.36, "end": 1851.32, "word": " the", "probability": 0.80029296875}, {"start": 1851.32, "end": 1851.92, "word": " statement", "probability": 0.8837890625}, {"start": 1851.92, "end": 1852.16, "word": " او", "probability": 0.65576171875}, {"start": 1852.16, "end": 1852.28, "word": " the", "probability": 0.705078125}, {"start": 1852.28, "end": 1852.5, "word": " given", "probability": 0.88671875}, {"start": 1852.5, "end": 1853.06, "word": " statement", "probability": 0.9326171875}], "temperature": 1.0}, {"id": 79, "seek": 187848, "start": 1857.94, "end": 1878.48, "text": "is always true اختصارا في جميع اللياش احتمالا انها دايما صحيح تمام فهذه هي طريقتنا في كل تعامل مع رياضة ان شاء الله هذه هنكرر الفيلم بشوف السؤال بحاول افسره و يمكن اصيغه بصيغة اخرى دي مهم جدا ويش و بعدين نحاول نتعامل معه من وين بدنا ايش المطلوب و كيف بدنا نوصل", "tokens": [271, 1009, 2074, 1975, 46456, 9381, 9640, 995, 8978, 10874, 2304, 40228, 13672, 1829, 33599, 1975, 33753, 2304, 6027, 995, 16472, 11296, 11778, 47302, 15042, 20328, 5016, 1829, 5016, 46811, 10943, 6156, 3224, 24192, 39896, 23032, 16572, 38149, 8315, 8978, 28242, 37279, 10943, 1211, 20449, 12602, 1829, 46958, 3660, 16472, 13412, 16606, 21984, 29538, 8032, 1863, 37983, 2288, 27188, 1829, 19528, 4724, 8592, 38688, 21136, 33604, 6027, 4724, 5016, 995, 12610, 1975, 36178, 2288, 3224, 4032, 7251, 43020, 1975, 9381, 1829, 17082, 3224, 4724, 9381, 1829, 17082, 3660, 1975, 34740, 7578, 11778, 1829, 3714, 16095, 10874, 28259, 4032, 1829, 8592, 4032, 39182, 9957, 8717, 5016, 995, 12610, 8717, 2655, 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0.8935546875}, {"start": 1977.01, "end": 1977.21, "word": " أي", "probability": 0.81689453125}, {"start": 1977.21, "end": 1977.89, "word": " استفسار،", "probability": 0.8687744140625}, {"start": 1977.89, "end": 1977.95, "word": " أي", "probability": 0.8896484375}, {"start": 1977.95, "end": 1978.71, "word": " صعوبة،", "probability": 0.79951171875}, {"start": 1978.71, "end": 1979.35, "word": " بنفسرها", "probability": 0.8797607421875}, {"start": 1979.35, "end": 1979.47, "word": " إن", "probability": 0.57958984375}, {"start": 1979.47, "end": 1979.57, "word": " شاء", "probability": 0.98291015625}, {"start": 1979.57, "end": 1979.67, "word": " الله", "probability": 0.96240234375}, {"start": 1979.67, "end": 1979.97, "word": " عشان", "probability": 0.84130859375}, {"start": 1979.97, "end": 1980.53, "word": " الأمر", "probability": 0.9716796875}, {"start": 1980.53, "end": 1980.69, "word": " يكون", "probability": 0.969482421875}, {"start": 1980.69, "end": 1980.99, "word": " واضح", "probability": 0.953125}], "temperature": 1.0}, {"id": 84, "seek": 198720, "start": 1982.12, "end": 1987.2, "text": "تمام الخطوة اللي ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه", "tokens": [39237, 10943, 33962, 9566, 2407, 3660, 13672, 1829, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224, 1975, 1829, 3224], "avg_logprob": -0.2803442132645759, "compression_ratio": 4.25, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 1982.12, "end": 1982.32, "word": "تمام", "probability": 0.61126708984375}, {"start": 1982.32, "end": 1982.52, "word": " الخطوة", "probability": 0.9459228515625}, {"start": 1982.52, "end": 1982.62, "word": " اللي", "probability": 0.5972900390625}, {"start": 1982.62, "end": 1983.0, "word": " ايه", "probability": 0.6033528645833334}, {"start": 1983.0, "end": 1983.1, "word": " ايه", "probability": 0.6031901041666666}, {"start": 1983.1, "end": 1983.14, "word": " ايه", "probability": 0.6439615885416666}, {"start": 1983.14, "end": 1983.18, "word": " ايه", "probability": 0.7274576822916666}, {"start": 1983.18, "end": 1983.18, "word": " ايه", "probability": 0.78271484375}, {"start": 1983.18, "end": 1983.24, "word": " ايه", "probability": 0.8077799479166666}, {"start": 1983.24, "end": 1983.28, "word": " ايه", "probability": 0.8331705729166666}, {"start": 1983.28, "end": 1983.34, "word": " ايه", "probability": 0.8611653645833334}, {"start": 1983.34, "end": 1983.4, "word": " ايه", "probability": 0.89111328125}, {"start": 1983.4, "end": 1983.44, "word": " ايه", "probability": 0.9140625}, {"start": 1983.44, "end": 1983.48, "word": " ايه", "probability": 0.9298502604166666}, {"start": 1983.48, "end": 1983.54, "word": " ايه", "probability": 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هنقول ايه عشان اعلق from the table we see that the given statement is a tautology from or by the table", "tokens": [6027, 25957, 3215, 46811, 10943, 8717, 44510, 10721, 8717, 8592, 2655, 17082, 1211, 32771, 995, 22488, 3660, 498, 550, 2074, 550, 2074, 2074, 7908, 550, 7908, 2074, 2074, 550, 2074, 2074, 7908, 550, 1340, 2074, 1975, 1829, 8592, 50239, 1975, 12984, 3555, 2655, 16472, 3224, 256, 1375, 1793, 6055, 9566, 1211, 3615, 256, 1375, 1793, 45164, 19446, 23032, 1211, 3615, 33599, 23032, 1211, 3615, 11778, 47302, 15042, 2074, 256, 1375, 1793, 37495, 22653, 11778, 47302, 15042, 2074, 1975, 15730, 1975, 8315, 8032, 1863, 39648, 1975, 1829, 3224, 6225, 8592, 7649, 1975, 30241, 4587, 490, 264, 3199, 321, 536, 300, 264, 2212, 5629, 307, 257, 256, 1375, 1793, 490, 420, 538, 264, 3199], "avg_logprob": -0.2887168057196963, "compression_ratio": 1.8165938864628821, "no_speech_prob": 0.0, "words": [{"start": 2001.4199999999998, "end": 2002.1399999999999, "word": "العمد", "probability": 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table", "probability": 0.90673828125}, {"start": 2023.34, "end": 2023.54, "word": " we", "probability": 0.87158203125}, {"start": 2023.54, "end": 2023.78, "word": " see", "probability": 0.919921875}, {"start": 2023.78, "end": 2024.12, "word": " that", "probability": 0.9501953125}, {"start": 2024.12, "end": 2024.54, "word": " the", "probability": 0.724609375}, {"start": 2024.54, "end": 2025.18, "word": " given", "probability": 0.488525390625}, {"start": 2025.18, "end": 2025.66, "word": " statement", "probability": 0.87744140625}, {"start": 2025.66, "end": 2025.98, "word": " is", "probability": 0.9560546875}, {"start": 2025.98, "end": 2026.18, "word": " a", "probability": 0.9580078125}, {"start": 2026.18, "end": 2026.5, "word": " tautology", "probability": 0.951171875}, {"start": 2026.5, "end": 2028.72, "word": " from", "probability": 0.90380859375}, {"start": 2028.72, "end": 2029.14, "word": " or", "probability": 0.428955078125}, {"start": 2029.14, "end": 2029.36, "word": " by", 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2036.14, "word": " the", "probability": 0.767578125}, {"start": 2036.14, "end": 2036.42, "word": " given", "probability": 0.85693359375}, {"start": 2036.42, "end": 2037.16, "word": " statement", "probability": 0.92529296875}, {"start": 2037.16, "end": 2042.32, "word": " is", "probability": 0.94775390625}, {"start": 2042.32, "end": 2042.64, "word": " a", "probability": 0.986328125}, {"start": 2042.64, "end": 2043.14, "word": " tautology", "probability": 0.9482421875}, {"start": 2043.14, "end": 2049.18, "word": " أي", "probability": 0.64892578125}, {"start": 2049.18, "end": 2049.88, "word": " سؤال", "probability": 0.9864908854166666}, {"start": 2049.88, "end": 2050.76, "word": " فهذا", "probability": 0.8693033854166666}, {"start": 2050.76, "end": 2050.94, "word": " هو", "probability": 0.9609375}, {"start": 2050.94, "end": 2051.5, "word": " التعريف", "probability": 0.9923095703125}, {"start": 2051.5, "end": 2052.4, "word": " وهكذا", "probability": 0.7701822916666666}, {"start": 2052.4, 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if the conditional statement if the conditional .. جملة الشرطية if B then Q is autotology، دايما true، then it is called an implication، بسميها تضمين، هذا طبعا زي ما تشوف في كل سياستنا دايما رموز، دايما رموز، ليه شوفنا رموز؟ سهم", "tokens": [2631, 4238, 363, 293, 4238, 1249, 312, 732, 12363, 1975, 1829, 732, 12363, 12399, 2199, 12399, 14679, 12399, 3714, 5172, 47341, 8592, 12399, 13412, 5172, 2655, 9673, 12984, 6027, 23758, 9122, 33911, 22807, 3714, 5172, 47341, 8592, 12399, 16472, 31439, 732, 12363, 39894, 3615, 10943, 1211, 498, 264, 27708, 5629, 498, 264, 27708, 4386, 10874, 2304, 37977, 25124, 2288, 9566, 10632, 498, 363, 550, 1249, 307, 1476, 310, 1793, 12399, 11778, 47302, 15042, 2074, 12399, 550, 309, 307, 1219, 364, 37814, 12399, 4724, 38251, 1829, 11296, 6055, 11242, 2304, 9957, 12399, 23758, 23032, 3555, 3615, 995, 30767, 1829, 19446, 6055, 8592, 38688, 8978, 28242, 8608, 25528, 14851, 8315, 11778, 47302, 15042, 12602, 2304, 2407, 11622, 12399, 11778, 47302, 15042, 12602, 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solution", "probability": 0.74072265625}, {"start": 2246.57, "end": 2246.77, "word": " لان", "probability": 0.818115234375}, {"start": 2246.77, "end": 2246.91, "word": " هذا", "probability": 0.465576171875}, {"start": 2246.91, "end": 2247.09, "word": " مهم", "probability": 0.980224609375}, {"start": 2247.09, "end": 2247.31, "word": " جدا", "probability": 0.991943359375}, {"start": 2247.31, "end": 2247.49, "word": " ان", "probability": 0.426513671875}, {"start": 2247.49, "end": 2248.31, "word": " نفسر", "probability": 0.7569986979166666}, {"start": 2248.31, "end": 2248.63, "word": " السؤال", "probability": 0.99072265625}, {"start": 2248.63, "end": 2248.83, "word": " هذه", "probability": 0.72900390625}, {"start": 2248.83, "end": 2249.43, "word": " السياسة", "probability": 0.974853515625}], "temperature": 1.0}, {"id": 95, "seek": 227603, "start": 2250.53, "end": 2276.03, "text": "أرجو أن يكون هناك شاهدين من المثال المثال المطلوب المباشر له والسياسة التي نتبعها والحقيقة هذه سنستخدمها دائما وهذه ستساعدكم كثيرا في المثاق وإن شاء الله في المثاقات الأخرى كيف نتعامل مع الأمثلة كيف نتعامل مع البراهين أيش المعطيات أيش المطلوب وكيف نتعامل فإذا احنا أول الشيء we have to show المطلوب مننا that", "tokens": [10721, 47341, 2407, 14739, 7251, 30544, 34105, 4117, 13412, 40294, 3215, 9957, 9154, 9673, 12984, 6027, 9673, 12984, 6027, 9673, 9566, 1211, 37746, 9673, 3555, 33599, 2288, 46740, 16070, 3794, 25528, 3794, 3660, 38392, 8717, 2655, 3555, 3615, 11296, 16070, 5016, 38436, 28671, 29538, 8608, 1863, 14851, 9778, 40448, 11296, 11778, 16373, 15042, 37037, 24192, 8608, 2655, 3794, 995, 22488, 24793, 9122, 12984, 13546, 995, 8978, 9673, 12984, 995, 4587, 4032, 28814, 1863, 13412, 16606, 21984, 8978, 9673, 12984, 995, 4587, 9307, 16247, 34740, 7578, 9122, 33911, 8717, 2655, 3615, 10943, 1211, 20449, 16247, 2304, 12984, 37977, 9122, 33911, 8717, 2655, 3615, 10943, 1211, 20449, 2423, 26890, 40294, 9957, 36632, 8592, 9673, 3615, 9566, 1829, 9307, 36632, 8592, 9673, 9566, 1211, 37746, 4032, 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2254.53, "end": 2254.97, "word": " المطلوب", "probability": 0.9576416015625}, {"start": 2254.97, "end": 2255.45, "word": " المباشر", "probability": 0.9071044921875}, {"start": 2255.45, "end": 2255.67, "word": " له", "probability": 0.59521484375}, {"start": 2255.67, "end": 2256.51, "word": " والسياسة", "probability": 0.8783203125}, {"start": 2256.51, "end": 2256.59, "word": " التي", "probability": 0.496826171875}, {"start": 2256.59, "end": 2257.07, "word": " نتبعها", "probability": 0.9046875}, {"start": 2257.07, "end": 2257.51, "word": " والحقيقة", "probability": 0.781341552734375}, {"start": 2257.51, "end": 2257.69, "word": " هذه", "probability": 0.2379150390625}, {"start": 2257.69, "end": 2259.03, "word": " سنستخدمها", "probability": 0.8727213541666666}, {"start": 2259.03, "end": 2259.41, "word": " دائما", "probability": 0.9451497395833334}, {"start": 2259.41, "end": 2260.07, "word": " وهذه", "probability": 0.731689453125}, {"start": 2260.07, "end": 2260.61, "word": " ستساعدكم", "probability": 0.87548828125}, {"start": 2260.61, "end": 2260.89, "word": " كثيرا", "probability": 0.890380859375}, {"start": 2260.89, "end": 2261.03, "word": " في", "probability": 0.88818359375}, {"start": 2261.03, "end": 2261.61, "word": " المثاق", "probability": 0.74603271484375}, {"start": 2261.61, "end": 2261.91, "word": " وإن", "probability": 0.806640625}, {"start": 2261.91, "end": 2262.03, "word": " شاء", "probability": 0.983642578125}, {"start": 2262.03, "end": 2262.15, "word": " الله", "probability": 0.955078125}, {"start": 2262.15, "end": 2262.29, "word": " في", "probability": 0.896484375}, {"start": 2262.29, "end": 2262.67, "word": " المثاقات", "probability": 0.978515625}, {"start": 2262.67, "end": 2263.03, "word": " الأخرى", "probability": 0.9791666666666666}, {"start": 2263.03, "end": 2263.59, "word": " كيف", "probability": 0.854248046875}, {"start": 2263.59, "end": 2264.01, "word": " نتعامل", "probability": 0.99013671875}, {"start": 2264.01, "end": 2264.13, "word": " مع", "probability": 0.9638671875}, {"start": 2264.13, "end": 2264.55, "word": " الأمثلة", "probability": 0.9580078125}, {"start": 2264.55, "end": 2264.93, "word": " كيف", "probability": 0.7080078125}, {"start": 2264.93, "end": 2265.15, "word": " نتعامل", "probability": 0.99736328125}, {"start": 2265.15, "end": 2265.29, "word": " مع", "probability": 0.9921875}, {"start": 2265.29, "end": 2265.73, "word": " البراهين", "probability": 0.7989501953125}, {"start": 2265.73, "end": 2266.13, "word": " أيش", "probability": 0.538818359375}, {"start": 2266.13, "end": 2266.65, "word": " المعطيات", "probability": 0.94580078125}, {"start": 2266.65, "end": 2266.81, "word": " أيش", "probability": 0.930419921875}, {"start": 2266.81, "end": 2267.17, "word": " المطلوب", "probability": 0.9736328125}, {"start": 2267.17, "end": 2267.39, "word": " وكيف", "probability": 0.8268229166666666}, {"start": 2267.39, "end": 2267.79, "word": " نتعامل", "probability": 0.98447265625}, {"start": 2267.79, "end": 2268.17, "word": " فإذا", "probability": 0.4947916666666667}, {"start": 2268.17, "end": 2268.33, "word": " احنا", "probability": 0.7530924479166666}, {"start": 2268.33, "end": 2268.55, "word": " أول", "probability": 0.941162109375}, {"start": 2268.55, "end": 2269.23, "word": " الشيء", "probability": 0.7789713541666666}, {"start": 2269.23, "end": 2269.45, "word": " we", "probability": 0.1748046875}, {"start": 2269.45, "end": 2269.87, "word": " have", "probability": 0.96923828125}, {"start": 2269.87, "end": 2270.03, "word": " to", "probability": 0.9794921875}, {"start": 2270.03, "end": 2270.37, "word": " show", "probability": 0.970703125}, {"start": 2270.37, "end": 2272.93, "word": " المطلوب", "probability": 0.970703125}, {"start": 2272.93, "end": 2273.43, "word": " مننا", "probability": 0.84521484375}, {"start": 2273.43, "end": 2276.03, "word": " that", "probability": 0.880859375}], "temperature": 1.0}, {"id": 96, "seek": 230031, "start": 2276.79, "end": 2300.31, "text": "اللي هو implication بي .. if b then b is a tautology فهي البنية او that is بمعنى آخر ممكن نفسر that is if b then b is always true", "tokens": [6027, 20292, 31439, 37814, 4724, 1829, 4386, 498, 272, 550, 272, 307, 257, 256, 1375, 1793, 6156, 3224, 1829, 29739, 1863, 10632, 1975, 2407, 300, 307, 4724, 2304, 3615, 1863, 7578, 19753, 34740, 3714, 43020, 8717, 36178, 2288, 300, 307, 498, 272, 550, 272, 307, 1009, 2074], "avg_logprob": -0.26611329056322575, "compression_ratio": 1.2424242424242424, "no_speech_prob": 0.0, "words": [{"start": 2276.79, "end": 2277.09, "word": "اللي", "probability": 0.788818359375}, {"start": 2277.09, "end": 2277.21, "word": " هو", "probability": 0.81298828125}, {"start": 2277.21, "end": 2277.71, "word": " implication", "probability": 0.92822265625}, {"start": 2277.71, "end": 2278.85, "word": " بي", "probability": 0.5079345703125}, {"start": 2278.85, "end": 2279.11, "word": " ..", "probability": 0.47509765625}, {"start": 2279.11, "end": 2279.33, "word": " if", "probability": 0.9208984375}, {"start": 2279.33, "end": 2279.55, "word": " b", "probability": 0.283447265625}, {"start": 2279.55, "end": 2279.77, "word": " then", "probability": 0.73193359375}, {"start": 2279.77, "end": 2280.01, "word": " b", "probability": 0.7255859375}, {"start": 2280.01, "end": 2280.49, "word": " is", "probability": 0.9375}, {"start": 2280.49, "end": 2280.87, "word": " a", "probability": 0.96337890625}, {"start": 2280.87, "end": 2281.35, "word": " tautology", "probability": 0.9560546875}, {"start": 2281.35, "end": 2290.49, "word": " فهي", "probability": 0.8697916666666666}, {"start": 2290.49, "end": 2291.07, "word": " البنية", "probability": 0.4573160807291667}, {"start": 2291.07, "end": 2291.67, "word": " او", "probability": 0.5931396484375}, {"start": 2291.67, "end": 2292.19, "word": " that", "probability": 0.5634765625}, {"start": 2292.19, "end": 2292.59, "word": " is", "probability": 0.970703125}, {"start": 2292.59, "end": 2293.15, "word": " بمعنى", "probability": 0.98603515625}, {"start": 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"seek": 232867, "start": 2302.9, "end": 2328.68, "text": "فهذه السياسة قعدت سياغة المطلوب سياسة مهمة جدا في حل مسائل الرياضيات أو في البراهين فهذه بدنا نتعلمها ان شاء الله شوية شوية و نتعود عليها لأنها حد ساعدنا كتير في دراسة الرياضية تمام خلاص كيف بنثبت جدول الصدق اذا we will use truth table تمام", "tokens": [5172, 3224, 24192, 21136, 25528, 3794, 3660, 12174, 22488, 2655, 8608, 1829, 5718, 118, 3660, 9673, 9566, 1211, 37746, 8608, 25528, 3794, 3660, 3714, 16095, 3660, 10874, 28259, 8978, 11331, 1211, 47524, 16373, 1211, 2423, 16572, 46958, 1829, 9307, 34051, 8978, 2423, 26890, 40294, 9957, 6156, 3224, 24192, 47525, 8315, 8717, 2655, 3615, 19528, 11296, 16472, 13412, 16606, 21984, 13412, 2407, 10632, 13412, 2407, 10632, 4032, 8717, 2655, 3615, 23328, 25894, 11296, 5296, 33456, 11296, 11331, 3215, 8608, 995, 22488, 8315, 9122, 2655, 13546, 8978, 11778, 23557, 3794, 3660, 2423, 16572, 46958, 10632, 46811, 10943, 16490, 1211, 33546, 9122, 33911, 44945, 12984, 3555, 2655, 10874, 3215, 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a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/6BraapxPBi4_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/6BraapxPBi4_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..c889110ff8f22656012dd47e22365d93ee1a4ba0 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/6BraapxPBi4_postprocess.srt @@ -0,0 +1,2672 @@ +1 +00:00:19,660 --> 00:00:24,000 +بسم الله الرحمن الرحيم نواصل مع العلاقات في + +2 +00:00:24,000 --> 00:00:28,420 +المحاضرة الأخيرة شرحنا اللي هو العلاقات التكافؤ + +3 +00:00:28,420 --> 00:00:33,520 +equivalence relations وتحدثنا أن العلاقة بتكون + +4 +00:00:33,520 --> 00:00:36,980 +علاقة تكافؤ إذا تحقق فيها تلت خواص اللي هي خاصية + +5 +00:00:36,980 --> 00:00:41,680 +الانعكاس والتماثل والتعدىأه فطبعا شوفنا بعض + +6 +00:00:41,680 --> 00:00:44,380 +الأمثلة الآن بنكمل ان شاء الله و نشوف بعض الأمور + +7 +00:00:44,380 --> 00:00:49,660 +الجديدة و كيف نتعامل مع هذه المفاهيم نفحص إذا كان + +8 +00:00:49,660 --> 00:00:54,560 +المثال مُعطى كأعداد و كأزواج مرتبة لل relation أو + +9 +00:00:54,560 --> 00:00:58,560 +إذا كانت مُعطية بشكل عام و هكذا فعنا المثال التالت + +10 +00:00:58,560 --> 00:01:02,900 +فيه أن ال relation معرفة على ال Z اللي هو الأعداد + +11 +00:01:02,900 --> 00:01:07,380 +الصحيحة بشكل عام فهذا المثال التالت يعني في هذا + +12 +00:01:07,380 --> 00:01:12,290 +المثال عندنا مجموعة X هي Zفهذه ال relation معرفة + +13 +00:01:12,290 --> 00:01:15,310 +من Z ل Z لأنه جال ال X و Y وين موجودة؟ في ال Z، ال + +14 +00:01:15,310 --> 00:01:18,790 +cross في ال Z ما هي العلاقة؟ بقول ال X إيه علاقة + +15 +00:01:18,790 --> 00:01:23,470 +مع ال Y إذا كان حاصل ضربهم موجب بمعنى إن هدول + +16 +00:01:23,470 --> 00:01:25,690 +العددين بيكونوا إيه علاقة مع بعض إذا كانوا يا تنين + +17 +00:01:25,690 --> 00:01:28,710 +موجبين مع بعض يا تنين سالبين مع بعض فهذه المفهومة + +18 +00:01:28,710 --> 00:01:31,510 +فهذه النقطة احنا حاولنا نفهم ليش العلاقة فبقولي + +19 +00:01:31,510 --> 00:01:36,070 +أنا بقول عنه في عددين صحيحين اللي هم علاقة مع بعض + +20 +00:01:36,070 --> 00:01:39,180 +إذا حاصل ضربهم موجب بمعنى يكون نفس الإشارةيا اتنين + +21 +00:01:39,180 --> 00:01:42,540 +موجبين مع بعض، يا اتنين سالبين مع بعض، تمام، إيش + +22 +00:01:42,540 --> 00:01:45,440 +السؤال؟ determine whether R is reflexive, + +23 +00:01:45,720 --> 00:01:50,180 +symmetric, transitive or not؟ فهنا سؤال مفتوح، + +24 +00:01:50,180 --> 00:01:53,940 +ماجلناش اثبت زي هذا they prove or disapprove ولا + +25 +00:01:53,940 --> 00:01:57,390 +قال لا ايه اثبت انه خطأ زي بعض الأسئلةجال حد دي + +26 +00:01:57,390 --> 00:02:00,850 +طبعا ماعلي اثبات هل هي transitive هل هي symmetric + +27 +00:02:00,850 --> 00:02:04,450 +هل هي reflexive او لأ و بدنا نفحص فنبدأ الفحص + +28 +00:02:04,450 --> 00:02:07,890 +بالترتيب و نبدأ بال reflexive كهو مراتب روحاني + +29 +00:02:07,890 --> 00:02:11,650 +الترتيب مش مهم لكن احنا عرفنا بهذا الشكل مش ضروري + +30 +00:02:11,650 --> 00:02:16,610 +فممكن ننتظم بهذا الترتيب R is reflexive + +31 +00:02:19,010 --> 00:02:23,610 +reflexive طبعا اللي هو H كافق for all x تنتمي لل + +32 +00:02:23,610 --> 00:02:28,310 +capital X اللي هي Z في هذا السؤال بدنا إيش XX تكون + +33 +00:02:28,310 --> 00:02:32,370 +تنتمي لل R كل عنصر اللي علاقة مع نفسه فده سؤالنا + +34 +00:02:32,370 --> 00:02:36,450 +الأول هل هذا صحيح ولا لأ لإن بقول determined فإيش + +35 +00:02:36,450 --> 00:02:43,890 +رأيكوا؟ هل كل عدد صحيح علاقة مع نفسه؟ ليش؟ الواحد + +36 +00:02:43,890 --> 00:02:47,070 +اللي علاقة مع نفسها نعم السالب واحد اللي علاقة مع + +37 +00:02:47,070 --> 00:02:51,720 +نفسها نعمطب والباقي؟الصفر الشمال اللي ليه علاقة مع + +38 +00:02:51,720 --> 00:02:56,320 +نفسه؟ لأ لأن صفر في صفر مش مش positive اه فوين + +39 +00:02:56,320 --> 00:03:00,520 +ننتبهه؟ جميع الأعداد الصحيحة مايعدد صفر كل عدد + +40 +00:03:00,520 --> 00:03:04,240 +اللي ليه علاقة مع نفسه إلا الصفر مثال واحد يكفي إن + +41 +00:03:04,240 --> 00:03:07,460 +هياش not reflexive فإذا نقاشها دي not reflexive + +42 +00:03:07,460 --> 00:03:14,760 +ليش؟ 00 لا تنتمي للR ليش؟ لأن 0 ضرب 0 تساوي 0 ليست + +43 +00:03:14,760 --> 00:03:18,960 +أكبر من صفر فإذا نقاش العلاقة not reflexive thus + +44 +00:03:19,710 --> 00:03:28,250 +الـ R is not reflexive بس + +45 +00:03:28,250 --> 00:03:32,490 +واحدة تكون مش متحقق لأنه جالي for all ده بأكد + +46 +00:03:32,490 --> 00:03:35,030 +عليهش معناه for all طب الواحد اللي علاقة مع نفسه + +47 +00:03:35,030 --> 00:03:38,390 +اه سالب واحد اه كل الإعداد إلا الصفر يكفي شوف مثال + +48 +00:03:38,390 --> 00:03:41,450 +واحد خلاها مش reflexive لأنه جالي for all لازم + +49 +00:03:41,450 --> 00:03:44,450 +يكون كل عنصر في المجموع اللي علاقة مع نفسه طب + +50 +00:03:44,450 --> 00:03:47,090 +الصفر ماليش علاقة مع نفسه إذا مختلف الشرط ف it's + +51 +00:03:47,090 --> 00:03:47,790 +not reflexive + +52 +00:03:51,870 --> 00:03:55,310 +أه هو إيش بيقول العدد هو بيقول إيش إيش مات + +53 +00:03:55,310 --> 00:03:58,430 +reflexive إنها كاسة اللي هو أنصر هو العلاقة مع + +54 +00:03:58,430 --> 00:04:01,470 +نفسه بدّي ال X مع ال X مش مع ال X مع ال Y X مع + +55 +00:04:01,470 --> 00:04:04,590 +نفسها هل إيه علاقة ولا لا فده ده بدأ أشهر أنا ع ال + +56 +00:04:04,590 --> 00:04:07,030 +reflexive إيش ده أشتغل واحد مع الواحد صح ولا خطأ + +57 +00:04:07,030 --> 00:04:11,200 +صح مع مع مين مع نفسهاه هيك ما هيك ال reflexive هذه + +58 +00:04:11,200 --> 00:04:14,760 +خاصية ال reflexive واضح؟ اه فالreflexivish بيقول + +59 +00:04:14,760 --> 00:04:18,760 +بدنا كل عنصر إيه له علاقة مع نفسه هيك معناته ان + +60 +00:04:18,760 --> 00:04:21,860 +أنا كاذب لأنه قلنا أن أنا كاذب تمام نيجي نفحص + +61 +00:04:21,860 --> 00:04:27,620 +الخاصية التانية وهي خاصية ال symmetric التماثرلأ + +62 +00:04:27,620 --> 00:04:32,120 +ال X و Y و المعكوس كل زوج و معكوس موجودين ولا لأ R + +63 +00:04:32,120 --> 00:04:36,540 +is symmetric خلينا نحسب جالكوتل التعريف Symmetric + +64 +00:04:36,540 --> 00:04:43,100 +اللي يتوا كافق ان X Y في ال R implies Y X في ال R + +65 +00:04:43,100 --> 00:04:47,920 +بده اكتبه كمان مرة التعريف عشان نتذكره فدي العلاقة + +66 +00:04:47,920 --> 00:04:54,610 +طبعابدنا نشوف هل دي symmetric ولا لا طبعا إذا بدنا + +67 +00:04:54,610 --> 00:04:58,070 +نحاول نخمن و بعدين نشوف prove or disapprove إيش + +68 +00:04:58,070 --> 00:05:02,010 +رأيكوا؟ هل جيت احنا بيقول XY في الار إذا حاصل + +69 +00:05:02,010 --> 00:05:06,590 +ضربهم لا يساوي zero طب لو غيرنا الترتيببتغيرش ليش؟ + +70 +00:05:06,590 --> 00:05:09,830 +لأنه ضرب إبدالي ضرب على عدد صحيح إبدالي فإذا هي S + +71 +00:05:09,830 --> 00:05:12,810 +Symmetric بدنا نثبت إنها Symmetric كيف بنثبت إنها + +72 +00:05:12,810 --> 00:05:16,730 +Symmetric؟ الشرط هو جملة شرطية تعريف الـ Symmetric + +73 +00:05:16,730 --> 00:05:19,870 +جملة شرطية كيف بنثبت الجملة الشرطية؟ نفترض إن + +74 +00:05:19,870 --> 00:05:23,790 +الشرط صحيح وبنثبت جواب الشرط إذا إن هي .. طبعا لو + +75 +00:05:23,790 --> 00:05:26,690 +جالي هل هي reflexive ولا لأ؟ بدأ أقول أولا إيش؟ it + +76 +00:05:26,690 --> 00:05:31,870 +is reflexive R is .. آسف Symmetric وبدنا نثبت هذا + +77 +00:05:31,870 --> 00:05:33,010 +الكلب Symmetric + +78 +00:05:36,990 --> 00:05:40,110 +Symmetric طبعا بنعمله prove لهذا الكلام ي prove + +79 +00:05:40,110 --> 00:05:44,990 +انها symmetric فقلنا هي جملة شرطية بنبدأ نجيل + +80 +00:05:44,990 --> 00:05:49,150 +البرهان انه نفترض ان الشرط صحيح فبقول له assume أو + +81 +00:05:49,150 --> 00:05:57,990 +let نفس الشيخ الاشي assume ان X Y تنتمي لل R ايش + +82 +00:05:57,990 --> 00:06:00,890 +بده اثبت؟ بده اثبت ان Y X تنتمي لل R كونه من + +83 +00:06:00,890 --> 00:06:06,110 +الأمثل اللي في البداية خلينا نكتب التفاصيل we want + +84 +00:06:06,840 --> 00:06:14,960 +to prove or to show to prove that Y X تنتمي لل R + +85 +00:06:14,960 --> 00:06:18,960 +ممتاز زي ما احنا ممكن نحكي ناشرة فور الان XY في ال + +86 +00:06:18,960 --> 00:06:25,860 +R ماذا تعني XY في ال R تعني ان X في Y positiveهذا + +87 +00:06:25,860 --> 00:06:28,440 +تعريف الـ A طيب أنا إيش بدى أعمل؟ هذا المطلوب بدى + +88 +00:06:28,440 --> 00:06:32,640 +أعكس وهذا يؤدي إن YX is positive من خواص الأعداد + +89 +00:06:32,640 --> 00:06:35,320 +الصحيحة لأنه إيش؟ الدرب إبدالي إذا بدنا نحط إن + +90 +00:06:35,320 --> 00:06:38,860 +الدرب على الأعداد الصحيحة يتمتع بخاصية الإبدال هذا + +91 +00:06:38,860 --> 00:06:43,140 +إيش يعني بالتعريف؟ إن YX في الـ A اتغير الترتيب + +92 +00:06:43,140 --> 00:06:48,610 +لإيش؟ لأن هذا تعريف الـ A إذا و هو المطلوب إثباتهR + +93 +00:06:48,610 --> 00:06:53,090 +is symmetric فالإشباط واضح وكتبناها بشكل تفصيل + +94 +00:06:53,090 --> 00:06:55,750 +يعني واضحة الصورة شفوية نعرفنا إن خمن إنها + +95 +00:06:55,750 --> 00:06:59,230 +symmetric أه لأنه جولنا تغيير التبديل هو تغيير + +96 +00:06:59,230 --> 00:07:02,970 +ترتيب في الضرب والضرب إبدالي في العملية الصحيحة أي + +97 +00:07:02,970 --> 00:07:06,650 +سؤال واضح تمام فإذا إنها symmetric نشوف عملية + +98 +00:07:06,650 --> 00:07:11,950 +الـtransitive الخاصية + +99 +00:07:11,950 --> 00:07:17,550 +التالتة الـR is transitive + +100 +00:07:19,290 --> 00:07:28,910 +اللي هي تكافئ XY في الـR and YZ في الـR يؤدي XZ في + +101 +00:07:28,910 --> 00:07:34,870 +الـR بدنا نثبت على ده الكلمة طبعا علمت استفهام اه + +102 +00:07:34,870 --> 00:07:39,090 +برضه نحاول إذا بنقدر نخمنإيش راح نشوف؟ إحنا راجعين + +103 +00:07:39,090 --> 00:07:43,070 +XY في الـR يعني يا إما الـXY التنين positive أو + +104 +00:07:43,070 --> 00:07:47,570 +التنين negative طيب و YZ في الـR يعني التنين برضه + +105 +00:07:47,570 --> 00:07:49,570 +positive و أنا negative نبدأ نحلل مش عارفين مش + +106 +00:07:49,570 --> 00:07:52,930 +واضح أحس ولا كتير إذا كانت XY positive يعني الـY + +107 +00:07:52,930 --> 00:07:56,150 +positive و YZ بدي يكون positive يعني كمان الـZ + +108 +00:07:56,150 --> 00:07:58,910 +positive إذا إن الـX و الـZ positive إذا صح طب لو + +109 +00:07:58,910 --> 00:08:01,570 +كانوا negative معناته Y negative بتخلي Z كمان + +110 +00:08:01,570 --> 00:08:03,770 +الـnegative بتصير صح إذا إيه يا إيش؟ Transitive + +111 +00:08:03,770 --> 00:08:06,750 +فإذا واضح إنه تخمينينا Transitive بتم علينا يا إيش + +112 +00:08:06,750 --> 00:08:14,210 +نثبتفإذا إيش؟ إيش؟ R is transitive اه نعملها proof + +113 +00:08:16,040 --> 00:08:19,480 +لهذا الكلام فاحنا قدرنا نخمن انها transit لو + +114 +00:08:19,480 --> 00:08:22,920 +ماقدرناش نخمن بنحاول نثبت بس انا بتدعي نتعلم كي + +115 +00:08:22,920 --> 00:08:27,820 +بننبرهم نيجي نشوف ايش التعريف جملة شرطية ببدأ + +116 +00:08:27,820 --> 00:08:31,800 +الوراني ان افترض ان الشرط صحيح فحقوله assume او + +117 +00:08:31,800 --> 00:08:39,880 +let نفس المعنى ايش xy في الار and yz في الارأه + +118 +00:08:39,880 --> 00:08:43,640 +فشايفين احنا نتعلم أشياء حتى التعريف كله وين ما + +119 +00:08:43,640 --> 00:08:46,980 +كان جملة شرطية بدي أبرهنها إيش كانت الجملة الشرطية + +120 +00:08:46,980 --> 00:08:50,460 +هذا هو المطلوب هو تعريف أي مكان أنا هذا بتعامل مع + +121 +00:08:50,460 --> 00:08:54,680 +جملة شرطية أه بينا نثبت إن مين إنه x و إنه xz في + +122 +00:08:54,680 --> 00:08:58,020 +ال R مطلوب خليني برضه أكتبها لإن احنا في الأمثلة + +123 +00:08:58,020 --> 00:09:06,620 +اللي ممكن في البداية we want to show اللي هو إيش + +124 +00:09:06,620 --> 00:09:10,620 +xz في ال Rأه طبعا إذا بدنا نكتب اللي هو يكافئ مين + +125 +00:09:10,620 --> 00:09:14,940 +بدنا xz positive يعني هذا مطلوب ممتاز نبدأ في + +126 +00:09:14,940 --> 00:09:18,380 +المعطيات هدول الفرضيات اللي هم عاطويات طيب إيش + +127 +00:09:18,380 --> 00:09:25,860 +معناه أن xy في ال R و yz في ال R يكافئ أن xy + +128 +00:09:25,860 --> 00:09:31,260 +positive and اللي هو yz positive مظبوط تعريف ال R + +129 +00:09:37,860 --> 00:09:43,580 +لش؟ لأنها .. طب هل .. هل صفر واحد تنتمي لل R أصلا؟ + +130 +00:09:43,580 --> 00:09:52,000 +وإذا كانت شرط false فال statement true؟ لأكيف؟ + +131 +00:09:52,000 --> 00:09:55,780 +كيف؟ أنا بقول .. انا بقول إذا كانت X Y .. أبدأ هنا + +132 +00:09:55,780 --> 00:10:00,020 +إذا كانت X Y في ال R فمعكوسة موجود صفر واحد مش + +133 +00:10:00,020 --> 00:10:03,040 +موجود أصلا مش بده في معكوسة يعني إذا كان الشرط + +134 +00:10:03,040 --> 00:10:06,620 +false فبدور شرط يبقى مش شرط فواضحة؟ أه فالصفر مش + +135 +00:10:06,620 --> 00:10:09,320 +موجود و لا الصفر صفر أنا بقول كل زوج موجود nation + +136 +00:10:09,320 --> 00:10:13,400 +-group ال get الواحد والاتنين موجودة نعم لأنه حصف + +137 +00:10:13,400 --> 00:10:16,240 +ضربه طب اتنين وواحد موجودة برضه نعم فانت إذا كان + +138 +00:10:16,240 --> 00:10:19,260 +الأول موجود التاني موجود طب الواحد مش موجود مش بده + +139 +00:10:19,260 --> 00:10:21,970 +في عكسهطبعا، زي ما عملنا، تبهي؟ قبل قول ده، بقى + +140 +00:10:21,970 --> 00:10:24,910 +اتعلمنا من المنطق إذا الشرط falls، ما تدوريش على + +141 +00:10:24,910 --> 00:10:27,190 +إشي، لكن إذا الشرط تتروح، دي تتدوري على جواب + +142 +00:10:27,190 --> 00:10:30,570 +الشرط، تمام؟ أه فإحنا بنفترض إذا الشرط تتحقق، + +143 +00:10:30,570 --> 00:10:34,110 +بنشوف جواب الشرط، الشرط مش موجود، خلاص، تمام، أه، + +144 +00:10:34,110 --> 00:10:39,990 +الآن أنا بدي أوصل لهنا، كيف ممكن نوصل؟ كيف؟ إيش + +145 +00:10:39,990 --> 00:10:48,090 +دليلك؟ هو صح، معناه مطلوب، طب ليش؟ إذن؟ + +146 +00:10:50,390 --> 00:10:54,450 +بس لو بدنا طالب في ابتدائي أو في عدالة بتشرحله + +147 +00:10:54,450 --> 00:10:57,490 +إياها، إيش بتشرحله إياها؟ في طريق تاني، يا إما بدك + +148 +00:10:57,490 --> 00:11:00,290 +تحلل إيش الاحتمالات، إنه بتكون التنين positive + +149 +00:11:00,290 --> 00:11:03,570 +وبالتالي ال Y positive، وحاصف ضربة مع ال Z + +150 +00:11:03,570 --> 00:11:06,330 +positive، لازم يكون ال Z positive أو بطريقة أسهل، + +151 +00:11:06,330 --> 00:11:09,590 +لو ضربناهم في بعض هدول، لو ضربناهم في بعض، فهذا + +152 +00:11:09,590 --> 00:11:16,540 +يؤدي إن X في Y تربية في Z positive، ولا لأ؟كميتين + +153 +00:11:16,540 --> 00:11:20,760 +موجبتين حصل ضربهم يتموا موجب طب أنا إيش بديه دايما + +154 +00:11:20,760 --> 00:11:24,740 +عينا عن المطلوب XZ ممكن أتخلص من Y تربيع نعم لو + +155 +00:11:24,740 --> 00:11:28,900 +جسمت على كمية موجب المتباينة لاتتغير وهذا يؤدي إن + +156 +00:11:28,900 --> 00:11:33,260 +XZ positive هو المطلوب وهذا يؤدي إن XZ في الأعلى + +157 +00:11:33,260 --> 00:11:36,800 +فبدأ أفسر أنا تمام واضحة أنت ما أحنا قلنا خمننا صح + +158 +00:11:36,800 --> 00:11:45,540 +لكن كيف بنشرحها كيف نحط الدليل the same signإذا Z + +159 +00:11:45,540 --> 00:11:49,420 +لن تكون إشارتها زي ال Y، ممكن، ممكن، بس هذه عملية + +160 +00:11:49,420 --> 00:11:53,140 +أيه، برضه، كله، يعني دايما هنبقى معنين بالحل + +161 +00:11:53,140 --> 00:11:55,860 +الصحيح، مش ضروري نفس الحل، أكتر من الحل ممكن يكون + +162 +00:11:55,860 --> 00:11:59,760 +صحيح، المهم يكون حل رياضي صحيح، فالآن طبعا و هو + +163 +00:11:59,760 --> 00:12:03,780 +المطلوب، thus R is a transit + +164 +00:12:07,640 --> 00:12:12,300 +فهنا طبعا التفاصيل يمكن مهمة لكن مش هي الأهم أهم + +165 +00:12:12,300 --> 00:12:15,060 +حاجة بنتعلمها كيف نتعامل كيف نثبت أنها reflexive + +166 +00:12:15,060 --> 00:12:18,340 +كيف نثبت أنها symmetric كيف نثبت أنها transitive و + +167 +00:12:18,340 --> 00:12:20,760 +هنا الشرطية ده ممكن احنا ماثبتناش ان انا reflexive + +168 +00:12:20,760 --> 00:12:22,980 +اثبتنا ان انا ليست reflexive لكن كيف نثبت أنها + +169 +00:12:22,980 --> 00:12:27,480 +transitive و symmetric خلينا + +170 +00:12:27,480 --> 00:12:33,330 +نشوف كمان مثالأه برضه هنا يمكن أول مثال على ال + +171 +00:12:33,330 --> 00:12:35,230 +equivalence relation طبعا احنا قلنا فيه أننا تلت + +172 +00:12:35,230 --> 00:12:40,430 +مفاهيم خاصية الانعكاس خاصية التماثل وخاصية التعدى + +173 +00:12:40,430 --> 00:12:43,330 +أه كلهم إذا اجتمعوا بنقول على علاقة علاقة تكافؤ + +174 +00:12:43,330 --> 00:12:46,570 +فنشوف علاقة تتوفى فيها التلاتة فاحنا شوفنا يمكن + +175 +00:12:46,570 --> 00:12:49,870 +تلت أمثلة في المثال الأول كانت اللي هو ال + +176 +00:12:49,870 --> 00:12:52,880 +symmetric مش متوفر الباقي متوفرفي التاني كانت الـ + +177 +00:12:52,880 --> 00:12:56,020 +Symmetric وحيدة متوفرة والباقي مش متوفر شفنا مثال + +178 +00:12:56,020 --> 00:12:58,880 +تالت الـ Reflexion مش متوفر والباقي متوفر فإذا + +179 +00:12:58,880 --> 00:13:01,060 +مافيش حاجة تقول إذا واحدة متوفرة تانية بدأت تتوفر + +180 +00:13:01,060 --> 00:13:04,560 +أو لا، فالأمور دي مستقلين، كل واحدة بنحاول نعمل + +181 +00:13:04,560 --> 00:13:07,740 +المعيار اتحقق أو يتحقق أو لا يتحقق، مالوش علاقة + +182 +00:13:07,740 --> 00:13:11,590 +بالخاصية الأخرىإنه إذا تأفرت واحدة لازم تتوفر، لأ + +183 +00:13:11,590 --> 00:13:13,970 +هالجيت بيقول لي أثبت إنها equivalence relation أول + +184 +00:13:13,970 --> 00:13:16,810 +مثال فمدينة برضه نبدأ دايما بالمثال البسيط + +185 +00:13:16,810 --> 00:13:19,790 +المجموعة من عنصرين بيقول لي أثبت إنها إيش + +186 +00:13:19,790 --> 00:13:22,170 +equivalence relation إيش معناته؟ يعني نثبت إنها + +187 +00:13:22,170 --> 00:13:25,530 +reflexive وsymmetric وtransitive لإننا نثبت التلت + +188 +00:13:25,530 --> 00:13:33,070 +إيش خواص التلت خواص أو مميزات للعلاقة أو التلت + +189 +00:13:33,070 --> 00:13:39,000 +حلال فهذا المثال الرابعفالان كان المثال التالت حدد + +190 +00:13:39,000 --> 00:13:43,100 +هل انها reflexive ولا لأ؟ هل symmetric ولا لأ؟ هل + +191 +00:13:43,100 --> 00:13:45,780 +transitive ولا لأ؟ الآن لأ اثبت انها reflexive + +192 +00:13:45,780 --> 00:13:48,400 +واثبت انها symmetric واثبت انها transitive هذا + +193 +00:13:48,400 --> 00:13:51,340 +معناه انه اثبت انها equivalence relation فطبعا + +194 +00:13:51,340 --> 00:13:55,880 +نبدأ بالحل فالان على طول بدي اثبت ان R is + +195 +00:13:55,880 --> 00:13:57,260 +reflexive + +196 +00:13:59,090 --> 00:14:02,850 +معنى equivalence relation؟ تلت خواص متحققة طبعا + +197 +00:14:02,850 --> 00:14:06,710 +مثال بسيط، ايش بده اثبت؟ for all x طب مين الـx هنا + +198 +00:14:06,710 --> 00:14:09,230 +فيها؟ مافيش الـ0 و الـ1؟ بدنا الـ0 اللي علاقة مع + +199 +00:14:09,230 --> 00:14:11,950 +نفسها صح و لا مش صح؟ الـ0 و الـ0 تنتمي؟ هي الـR + +200 +00:14:11,950 --> 00:14:15,230 +موجودة طب الـ1 اللي علاقة مع نفسها برضه صح لأن + +201 +00:14:15,230 --> 00:14:17,970 +واحد واحد تنتمي زنن بتاعة العملية فابد أقوله هناك + +202 +00:14:17,970 --> 00:14:21,670 +الجواب لأن المثال بسيط، عدد عناصر المجموعة محدود، + +203 +00:14:21,670 --> 00:14:26,330 +بيش مقدر أفحص كل واحد على حدة فالـ0 و الـ0 تنتمي و + +204 +00:14:26,330 --> 00:14:32,690 +واحد واحد تنتميخلصنا كل عناصر المجموعة إذا الـ R + +205 +00:14:32,690 --> 00:14:37,890 +is reflex خلصنا + +206 +00:14:37,890 --> 00:14:40,990 +لأنه جالس for all X مين عناصر الـ X؟ الـ 0 و الـ 1 + +207 +00:14:40,990 --> 00:14:43,770 +كل عنصر يتعلق مع نفسه نعم إيش ما تقلي يتعلق مع + +208 +00:14:43,770 --> 00:14:48,650 +نفسه يعني إيش؟ XX تنتمي للـ R أثبتناها أي سؤال + +209 +00:14:48,650 --> 00:14:56,310 +تمام؟ ننتقل للخطوة التانية الـ R is symmetricأزواج + +210 +00:14:56,310 --> 00:15:00,410 +مرتبة بيقول الـ X يعني إذا كان زوج موجود عكسه + +211 +00:15:00,410 --> 00:15:04,550 +موجود إذا كان أي زوج بتطلع على أزواج الموجودة و + +212 +00:15:04,550 --> 00:15:07,490 +بشوف عكسها موجود بيقولها بتفحص كل واحد على حدا زي + +213 +00:15:07,490 --> 00:15:11,650 +ما اتعلمنا فإذا إحنا بنلاحظ هنا إنه في إننا حالتين + +214 +00:15:11,650 --> 00:15:15,110 +إذا العلاقة مُقطية بشكل سرد أزواج مرتبة فإيها + +215 +00:15:15,110 --> 00:15:18,110 +طريقة للفحص زي ما بنعمل في هذا المثال وإذا أُقطت + +216 +00:15:18,110 --> 00:15:22,510 +العلاقة بطريقة الوصوفة المميزة أو صورة العلاقةفي + +217 +00:15:22,510 --> 00:15:25,190 +طريقة للإثبات فمختلفين زي ما انتم لاحظين في + +218 +00:15:25,190 --> 00:15:27,870 +الأمثلة فالان بدنا نفحص كيف لما تكون أزواج مرتبة + +219 +00:15:27,870 --> 00:15:31,210 +زي هيك هل الواحد و واحد مين معكوث و نفسه فهنقول له + +220 +00:15:31,210 --> 00:15:35,770 +ها واحد واحد تنتمي لل R و واحد واحد تنتمي لل R + +221 +00:15:35,770 --> 00:15:39,670 +الحقيقة بداش تفحص الحق 00 نفس الشيء ايش معكوثها + +222 +00:15:39,670 --> 00:15:46,770 +نفسها تنتمي و 00 تنتمي نجي لان 01 مين معكوثها 101 + +223 +00:15:46,770 --> 00:15:51,940 +تنتمي و لا تنتميبين تميهم طبعا بدا فحص الرابع ما + +224 +00:15:51,940 --> 00:15:55,100 +هو موجود هنا لأنه ال and إيش؟ symmetric لأنه ال + +225 +00:15:55,100 --> 00:15:58,540 +and قاسف، commutative فخلصنا، إذا كل زوج موجود من + +226 +00:15:58,540 --> 00:16:02,100 +الأربعة و معكوسه موجود إذا فعلا الإلاقة is + +227 +00:16:02,100 --> 00:16:10,500 +symmetric thus R is symmetric هذا + +228 +00:16:10,500 --> 00:16:14,900 +المفهوم بشكل عام إنه إذا الزوج وجد بدور على معكوسه + +229 +00:16:14,900 --> 00:16:21,290 +مش موجود خلاص، مابديش أعمل إشي، تمام؟الآن الخاصية + +230 +00:16:21,290 --> 00:16:25,010 +التالتة والاخيرة خاصية التعدى هل ال R transitive + +231 +00:16:25,010 --> 00:16:29,230 +طبعا هي نعم لأن جالب proof ما علي بس بدي أثبتها إن + +232 +00:16:29,230 --> 00:16:37,430 +هي فعلا تتمتع بخاصية التعدى فهنا تلاتة R is + +233 +00:16:37,430 --> 00:16:39,290 +transitive + +234 +00:16:41,020 --> 00:16:44,520 +أه طبعا مش غلط أننا نكتب التعريف قدامنا بس أنا + +235 +00:16:44,520 --> 00:16:47,080 +مابديش أننا نعيد لإن هو دي .. خلينا نحفظ التعريف + +236 +00:16:47,080 --> 00:16:50,080 +أو يكون قدامنا زي ما حكينا ملخص عشان نعرف أشي اللي + +237 +00:16:50,080 --> 00:16:53,200 +بدنا نعمله فده أسلوب كتير فعال أنه كيف نحفظ + +238 +00:16:53,200 --> 00:16:56,800 +التعريفات و كيف نستخدمها و نتعامل معاها تمام إيش + +239 +00:16:56,800 --> 00:17:00,260 +بدنا نعمل؟ بدنا نبدأ بزوج واحد و نشوف نهايته و + +240 +00:17:00,260 --> 00:17:03,400 +نشوف مين ببدأ بنهايته عشان نشوف زوجين الآن فمثلا + +241 +00:17:03,400 --> 00:17:06,620 +نبدأ من واحد واحد و بنسأل نفسنا مين ببدأ بواحد + +242 +00:17:06,620 --> 00:17:12,820 +غيرهواحد وزيرو هل التالت موجود اذا بنا ممكن نكتب + +243 +00:17:12,820 --> 00:17:19,570 +هيك او ان هل واحد وزيرو موجود نعم اذا هذي truetrue + +244 +00:17:19,570 --> 00:17:24,770 +خلاص فديه الصح متحققين اه الآن في غيره مبدأ بواحد + +245 +00:17:24,770 --> 00:17:28,850 +لأ خلصنا اذا واحد واحد خلصنا منه اذا هذا ممكن نقول + +246 +00:17:28,850 --> 00:17:33,650 +هذا فحصناه نيجي نفحص zero zero تبداية طبعا البداية + +247 +00:17:33,650 --> 00:17:36,850 +مهمة لأن الترتيب مهم بدنا اللي ببدو ب zero مين فيه + +248 +00:17:36,850 --> 00:17:44,020 +في zero واحدهل الزوج 01 ينتمي؟ اه true ممتاز لإنه + +249 +00:17:44,020 --> 00:17:47,600 +لما بيبدأ stop مين اللي بالنص بن stop تمام طيب مين + +250 +00:17:47,600 --> 00:17:51,080 +بيبدأ ب0 غيره؟ خلصنا مافيش غيره إذا هذا برضه خلص + +251 +00:17:51,080 --> 00:17:57,880 +01 نبدأ ال gate 01 01 مين بيبدأ ب1؟ في اتنين بيبدأ + +252 +00:17:57,880 --> 00:18:06,290 +ب1 11 وفي عندنا مين؟ 10 التنتيجة بينفحص 10هل + +253 +00:18:06,290 --> 00:18:10,730 +التالت اللي بيكمل هذه سلسلة التعدي موجود ولا لأ؟ + +254 +00:18:10,730 --> 00:18:16,330 +هذا بيدينا 01 تنتمي؟ true وهذا يؤدي لمين؟ 00 + +255 +00:18:16,330 --> 00:18:18,250 +تنتمي؟ برضه true + +256 +00:18:21,650 --> 00:18:25,070 +فإذا فعلًا صح فإذا فعلًا هنا في التعد في سلسلة + +257 +00:18:25,070 --> 00:18:29,230 +تتكوّل من اتنين و لازم التالت يكون ماذا ملازم + +258 +00:18:29,230 --> 00:18:32,310 +اللهم بينفعش يكون تنين و التالت لأ طب التنين مش + +259 +00:18:32,310 --> 00:18:35,810 +موجودين مدورش على أي جواب الشرط واضح فانا بدور على + +260 +00:18:35,810 --> 00:18:39,680 +اتنين من نوع معين اللي هو الشرطإنه نهاية الأول + +261 +00:18:39,680 --> 00:18:43,140 +بداية التاني إذا اتحقق هيك بدي الزوج التالت اللي + +262 +00:18:43,140 --> 00:18:46,280 +بكمل السلسة اللي بيكون بمداية الأول ونهاية التاني + +263 +00:18:46,280 --> 00:18:50,060 +في هذه الصورة تمام إذا هذا فحصناه و هذا خلصنا منه + +264 +00:18:50,060 --> 00:18:52,980 +لأن نيجي على one zero مين بيبدأ ب zero إيش + +265 +00:18:52,980 --> 00:18:58,400 +الاحتمالات one zero ولا لأ اه one zero فبدنا + +266 +00:18:58,400 --> 00:19:03,620 +الأزواج اللي بتبدأ ب zero في zero zero و zero one + +267 +00:19:03,620 --> 00:19:04,060 +تمام + +268 +00:19:06,980 --> 00:19:10,940 +zero one تنتمي لل R فهل مكمل السلسلة موجود اللي هو + +269 +00:19:10,940 --> 00:19:15,940 +one zero طبعا نعم true اه و هل مكمل السلسلة اللي + +270 +00:19:15,940 --> 00:19:21,360 +هو one one منتمي موجود اه فانا فحصهم كله بكل + +271 +00:19:21,360 --> 00:19:27,860 +الاحتمالات الممكنة اذا فعلا هي transitive R + +272 +00:19:27,860 --> 00:19:29,700 +is transitive + +273 +00:19:34,960 --> 00:19:39,080 +متابعين؟ خلصنا واحد و اتنين و تلاتة كلهم أثبتناهم + +274 +00:19:39,080 --> 00:19:43,460 +إذا فعلا إيه علاقة التكافئة فنكتب له واحد اتنين + +275 +00:19:43,460 --> 00:19:49,580 +and three implies R is an equivalence relation + +276 +00:19:49,580 --> 00:20:00,740 +فهنا + +277 +00:20:00,740 --> 00:20:06,320 +هذا مثال علىrelation معطية بشكل أزواج مرتبة بشكل + +278 +00:20:06,320 --> 00:20:12,100 +صريح بطريقة السرد فهنا كيف نتعامل معها طبعا كله + +279 +00:20:12,100 --> 00:20:15,740 +كيف نفحص أي واحدة من الخواص التلاتة طبعا بالتالي + +280 +00:20:15,740 --> 00:20:20,020 +بنفحص ال equivalence relationجابل ما نستمر في + +281 +00:20:20,020 --> 00:20:25,240 +الأمثلة خلّينا نشوف بس ملاحظة مهمة بقول لأي مجموعة + +282 +00:20:25,240 --> 00:20:30,220 +غير فارغة دايما بقدر أعرف عليها على الأقل إيش + +283 +00:20:30,220 --> 00:20:35,120 +علاقتين تكافؤ ما هم لو أخدت أنا ال X cross ال X كل + +284 +00:20:35,120 --> 00:20:38,240 +إش موجودبأضمن أنه تكون reflexive، ليش؟ لأن كل شيء + +285 +00:20:38,240 --> 00:20:41,500 +موجود، كل الأزواد المرتبة الممكنة، إذا كل X مع X + +286 +00:20:41,500 --> 00:20:45,140 +ما تكون موجودة، طيب، ما زال، طب X Y موجودة، لازم + +287 +00:20:45,140 --> 00:20:47,360 +تكون Y و X موجودة، لأن أنا أخد كل الاحتمالات، كل + +288 +00:20:47,360 --> 00:20:49,880 +الأزواد المرتبة، و برضه بالـ Transit، فإذا أخدت كل + +289 +00:20:49,880 --> 00:20:52,740 +شيء، إذا نهاش، مافيش حاجة مفقودة، مش صحيح يكون + +290 +00:20:52,740 --> 00:20:55,420 +حاجة مفقودة، بتكون نهاش، بتكون دايما equivalence + +291 +00:20:55,420 --> 00:20:59,860 +relation، في كمان واحدةبسموها علاقة القطرية + +292 +00:20:59,860 --> 00:21:04,020 +diagonal relation أو بيسموها العلاقة المحايدة مما + +293 +00:21:04,020 --> 00:21:07,620 +تتكون من الأزواج الـ XX ليه أحداث الأول تبعها + +294 +00:21:07,620 --> 00:21:10,760 +بيساوي الأحداث التانية Delta X بيعملولها هذا رمزها + +295 +00:21:10,760 --> 00:21:14,660 +طبعا رمز الـ Delta من وين؟ من Diagonal D في + +296 +00:21:14,660 --> 00:21:17,300 +اللاتينيش مقابل الـD Delta هذه capital Delta + +297 +00:21:17,300 --> 00:21:19,680 +بتعرفوا يمكن Small Delta في تعريف الأبسلون Delta + +298 +00:21:19,680 --> 00:21:22,360 +Definition هذه capital Delta برضه بتضروا عليكم + +299 +00:21:22,360 --> 00:21:26,080 +للمميز أو كذا أه فهذه الرمز تبعها فهي عبارة عن + +300 +00:21:26,080 --> 00:21:29,200 +مين؟كل الأزواج اللي حدا فيها الأول يساوي الإحداث + +301 +00:21:29,200 --> 00:21:32,540 +التاني لكل X تنتمي لكبتر X برضه دايما إيش + +302 +00:21:32,540 --> 00:21:36,040 +equivalence relation ليش؟ لأن العناصر زي ما فحصنا + +303 +00:21:36,040 --> 00:21:40,180 +طوي XX طبعا هذا بيقول إنها reflexive ليش؟ لأن كل + +304 +00:21:40,180 --> 00:21:43,480 +أنصر ماعيش اللي علاقة مع نفسه جالي كل الأزواج بحيث + +305 +00:21:43,480 --> 00:21:46,960 +X تنتمي لكبتر X طيب و بعد ليه symmetric؟ لأن كل + +306 +00:21:46,960 --> 00:21:50,380 +زوج عكسه نفسه طيب ليش transitive؟ نفس القضية لأن + +307 +00:21:50,380 --> 00:21:53,900 +نهايته و البداية واحدة اه فتختلفش فدي دايما + +308 +00:21:53,900 --> 00:21:59,120 +equivalence relationبتكون ايش يعني واحد واحد، مين + +309 +00:21:59,120 --> 00:22:01,520 +كمان بيبدأ بواحد، ايش هي لنفسه، احنا مابحثعش حتى، + +310 +00:22:01,520 --> 00:22:05,440 +نبادية هي اصلا، trivia صحيح؟ اه فخص، فمافيش غيره + +311 +00:22:05,440 --> 00:22:09,020 +بيكون، تمام؟ اه فهي انا، انا، انا، انا، انا، انا، + +312 +00:22:09,020 --> 00:22:09,220 +انا، انا، انا، انا، انا، انا، انا، انا، انا، انا، + +313 +00:22:09,220 --> 00:22:09,620 +انا، انا، انا، انا، انا، انا، انا، انا، انا، انا، + +314 +00:22:09,620 --> 00:22:10,200 +انا، انا، انا، انا، انا، انا، انا، انا، انا، انا، + +315 +00:22:10,200 --> 00:22:19,560 +انا، انا، انا، انا، انا، انا، انا، انا، انا، انا + +316 +00:22:19,590 --> 00:22:22,990 +فدي ملاحظة عامة، إذا أي مجموعة غير فارغة بقدر + +317 +00:22:22,990 --> 00:22:26,590 +ألاقي عليها علاقتين تكافؤ هم العلاقة القطرية أو + +318 +00:22:26,590 --> 00:22:29,370 +العلاقة المحايدة، طبعا ليش محايدة؟ لأن X العلاقة + +319 +00:22:29,370 --> 00:22:32,470 +مع نفسها فقط، زي الدالة المحايدة بتخلي X متغيرهاش، + +320 +00:22:32,470 --> 00:22:35,710 +فبسموها محايدة، اه و إذا بناخد كل شيء، لما ناخد كل + +321 +00:22:35,710 --> 00:22:41,110 +شيء بتكون برضه اللي هي علاقة تكافؤنشوف مزيد من + +322 +00:22:41,110 --> 00:22:46,290 +الأمثلة على إثبات علاقات التكافؤ، فيها مثال مهم، + +323 +00:22:46,290 --> 00:22:51,330 +المثال مهم، بيقول إنه برضه هيعرف العلاقة على الـZ، + +324 +00:22:51,330 --> 00:22:58,270 +الإعداد الصحيحة كلها، إحنا هنا، إيش العلاقة؟ بيقول + +325 +00:22:58,270 --> 00:23:02,450 +إنه بد الفرق بينهم يقبل قسمة تلاتةاللي هي مرت + +326 +00:23:02,450 --> 00:23:06,450 +علينا المعنى بس كتبينها ياش تلاتة K for some K هذا + +327 +00:23:06,450 --> 00:23:10,430 +معناه تقبل القسمة اه فاحنا هنا المثال الأول بعد + +328 +00:23:10,430 --> 00:23:15,370 +الملاحظة وعنا اللي هو .. عنا المجموعة اللي بنشر + +329 +00:23:15,370 --> 00:23:18,470 +عليها هي مجموعة الأعداد الصحيحة أكد عليها وهي ال R + +330 +00:23:18,470 --> 00:23:24,660 +قدامفبقول اللي بدي X ناقص Y الأول ناقص التاني يقبل + +331 +00:23:24,660 --> 00:23:28,620 +القسمة على تلاتة بيساوي تلاتة في K يعني المضاعفات + +332 +00:23:28,620 --> 00:23:31,700 +التلاتة هي معناها بيقول اللي اثبت ان ال R an + +333 +00:23:31,700 --> 00:23:34,200 +equivalence relation هذا السؤال مباشر اثبت انها + +334 +00:23:34,200 --> 00:23:37,100 +equivalence relation يعني اثبت انها reflexive، + +335 +00:23:37,100 --> 00:23:41,860 +symmetric وtransitive فنبدأ فيهم بالترتيب واحد R + +336 +00:23:41,860 --> 00:23:47,160 +is reflexiveبدنا نفرض علامة السفهام we want to + +337 +00:23:47,160 --> 00:23:50,660 +prove يعني علامة السفهام بيوفر عليا كتابة I want + +338 +00:23:50,660 --> 00:23:55,040 +to prove R is reflex ماعناء انعكاس بدنا كل عنصر + +339 +00:23:55,040 --> 00:23:57,900 +اللي له علاقة مع نفسه بدنا كل عنصر اللي له علاقة + +340 +00:23:57,900 --> 00:24:01,360 +مع نفسه طبعا بكيف بتبدأ البرهان ممكن احاول افكر + +341 +00:24:01,360 --> 00:24:07,730 +نرسم نخربش اشي نعمل هامشفسؤالنا هل جيت هل X تنتمي + +342 +00:24:07,730 --> 00:24:13,210 +لل R؟ سؤال، طب إيش يعني؟ هل X ناقص X تساوي 3 في K + +343 +00:24:13,210 --> 00:24:17,330 +for some K؟ إيش رأيكوا؟ ليش؟ لأن وعدد صفر تساوي 3 + +344 +00:24:17,330 --> 00:24:17,970 +في مين؟ + +345 +00:24:27,600 --> 00:24:32,960 +كيف نكتبه؟ اشتغليه في reflexive for all + +346 +00:24:51,290 --> 00:24:57,430 +لت X تنتمي لـ Z بـAny Element + +347 +00:24:59,950 --> 00:25:04,550 +فانا بدي أشتغل بشكل عام إيش ممكن أستخدم؟ هذا هو + +348 +00:25:04,550 --> 00:25:08,170 +عدد عشوائي أو عنصر عشوائي لكن إشماله عدد صحيح إيش + +349 +00:25:08,170 --> 00:25:11,590 +ممكن أستخدم؟ خواصة لعدد الصحيحة بشكل عام طب هال X + +350 +00:25:11,590 --> 00:25:13,870 +ممكن يكون positive ولا لا و انا ممكن أستخدم إن + +351 +00:25:13,870 --> 00:25:16,550 +خاصيته positive؟ لأ لإن أنا بدي أشتغل بشكل عام هو + +352 +00:25:16,550 --> 00:25:18,270 +ممكن يكون positive ممكن يكون negative ممكن يكون + +353 +00:25:18,270 --> 00:25:22,610 +zero بس بقدر أستخدم إنه عدد صحيح فقط ممتاز الآن + +354 +00:25:22,610 --> 00:25:29,280 +هذا هو المطلوب thenX ناقص X تساوي صفر ولا بتعرفوش + +355 +00:25:29,280 --> 00:25:33,140 +هذا الكلام؟ اه العارفين هو من التدالي ويساوي صفر + +356 +00:25:33,140 --> 00:25:38,120 +في مين؟ في تلاتة أو تلاتة في صفر بمعنى احنا هنا + +357 +00:25:38,120 --> 00:25:44,160 +احنا احنا اختارنا K تساوي Zeroهي في Z ولا مش في Z؟ + +358 +00:25:44,160 --> 00:25:46,680 +ممكن لأنه قال لي for some إيش معنى for some؟ + +359 +00:25:46,680 --> 00:25:49,920 +ادّيني مثال يكفي بدي أقل صحيحة إذا قدرنا ناجي مثال + +360 +00:25:49,920 --> 00:25:52,860 +على ال K و لا ماقدرناهاش ليه الصفر صحيح هذا إيش + +361 +00:25:52,860 --> 00:25:57,800 +معناته؟ إن X X تنتمي لل R هاي التعريف ولا لأ؟ إذا + +362 +00:25:57,800 --> 00:26:02,760 +قدرت أكتب الفرق بينهم الإحداث الأول ناقص الإحداث + +363 +00:26:02,760 --> 00:26:06,360 +التاني بيساوي مضاعفات ال K إذا إيش؟ ينتمي لل + +364 +00:26:06,360 --> 00:26:10,840 +relation هو بالتالي R is reflex + +365 +00:26:14,590 --> 00:26:17,450 +فاحنا أثبتنا إنها فعلا علاقة إيش علاقة إيه إيه إيه + +366 +00:26:17,450 --> 00:26:17,830 +إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه + +367 +00:26:17,830 --> 00:26:20,670 +إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه + +368 +00:26:20,670 --> 00:26:22,970 +إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه + +369 +00:26:22,970 --> 00:26:27,350 +إيه + +370 +00:26:27,350 --> 00:26:27,730 +إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه + +371 +00:26:27,730 --> 00:26:31,410 +إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه + +372 +00:26:31,410 --> 00:26:43,430 +إيه إيه إيه + +373 +00:26:43,430 --> 00:26:54,080 +إإتنين R is symmetric سيماترك نثبت ان انا سيماترك + +374 +00:26:54,080 --> 00:27:00,160 +سيماترك الشيء اذا زوج موجود عكسه يكون موجود فتعريف + +375 +00:27:00,160 --> 00:27:03,980 +السيماترك جملة شرطية تعريف ال reflexive باستخدام + +376 +00:27:03,980 --> 00:27:07,300 +for all تعريفنا كيف نثبت ال for all تعريف + +377 +00:27:07,300 --> 00:27:10,380 +السيماترك جملة شرطية كيف نثبت جملة شرطية نفترض ان + +378 +00:27:10,380 --> 00:27:14,830 +الشرط صحيح فسأقول له assume أو letكله معنى واحد x + +379 +00:27:14,830 --> 00:27:19,070 +y تنتمي لل R نكتب + +380 +00:27:19,070 --> 00:27:22,090 +كمان مرة مش مشكلة we want to prove أو to show نفس + +381 +00:27:22,090 --> 00:27:28,050 +المعنى why x تنتمي لل R اللي هي ايه تكافئ تكافئ x + +382 +00:27:28,050 --> 00:27:32,350 +ناقص y تسوى تلاتة في K او خلينا نقول في M for some + +383 +00:27:32,350 --> 00:27:39,610 +Mتكافئ هذه ال statement for some M تنتمي لزر، + +384 +00:27:39,610 --> 00:27:44,710 +مظبوط؟ هيك معناها؟ لا يا هداي ده انا اقول ايش؟ Y X + +385 +00:27:44,710 --> 00:27:48,410 +ايش بيعمل؟ بيقول لمين؟ الاول ناقص التاني، صحيح + +386 +00:27:48,410 --> 00:27:52,950 +التعريف الاول ناقص التاني، صحيح، صحيح، هذا + +387 +00:27:52,950 --> 00:27:57,270 +المطلوب، ممتاز، هذا المطلوب نبدأ من المعطى، and + +388 +00:27:57,270 --> 00:28:02,010 +now X Y في الانقلاب، قلت أنا assume، ليه ليه؟ نفس + +389 +00:28:02,010 --> 00:28:12,700 +المعنىتكافئ X ناقص Y تساوي تلاتة K for someكيف + +390 +00:28:12,700 --> 00:28:16,120 +الذنب ممتاز هذا مد تعريف ممكن احط الدليل تعريف + +391 +00:28:16,120 --> 00:28:20,060 +الان احنا ايه المطلوب ايش بدنا نعمل لنوصل لهنا نضر + +392 +00:28:20,060 --> 00:28:23,680 +في سالب one لأ مش ابدال لإن ال minus مش ابدال بدنا + +393 +00:28:23,680 --> 00:28:26,180 +نضر في سالب one طبعا ممكن انت .. انت قصدك انه ايش + +394 +00:28:26,180 --> 00:28:29,100 +حاجات نضر في سالب one طيب خلاص ماشي بس انا انا ب + +395 +00:28:29,100 --> 00:28:33,080 +.. بركز على المصطلح فبدنا نضر في سالب one فهذا + +396 +00:28:33,080 --> 00:28:39,410 +يؤديY ناقص X تساوي ثالث ثلاثة في K، مظبوط؟ من خواص + +397 +00:28:39,410 --> 00:28:42,450 +الأعداد الصحيحة، أه لإن أنا إيش مطلوب؟ بديّها + +398 +00:28:42,450 --> 00:28:47,170 +تلاتة في .. إيش بتساوي؟ تلاتة في سالب K، طب هل هذه + +399 +00:28:47,170 --> 00:28:50,010 +مفهوة تكون M؟ نعم، إذا ال K عدد صحيح فالسالب تبقى + +400 +00:28:50,010 --> 00:28:54,170 +عدد صحيح، فإذا هذه بتساوي تلاتة M، where M تساوي + +401 +00:28:54,170 --> 00:28:57,530 +سالب K تنتمي للذنب، وهو المطلوب، فالعملية سهلة + +402 +00:28:57,530 --> 00:29:04,310 +جدا، فإذا ThusYX تنتمي للـR وبالتالي and hence + +403 +00:29:04,310 --> 00:29:10,790 +الـR is symmetric خلصنا بس هاد أيش الخاتمة تبعت + +404 +00:29:10,790 --> 00:29:14,890 +للبرهة فالخطوة الأساسية شفنا كيبنا دايما عيننا على + +405 +00:29:14,890 --> 00:29:18,230 +المطلوب عشان هيك بنقول وطبعا ممكن نفسر إيش المطلوب + +406 +00:29:18,230 --> 00:29:20,930 +عشان نعرف وين رايحين إحنا نقول لك وإننا مضرون ندور + +407 +00:29:20,930 --> 00:29:24,110 +في الـ1 طب لو درابت مسموح لا مش مسموح، مسموح لأن + +408 +00:29:24,110 --> 00:29:26,630 +الطرفين أعداد صحيحة خواص الأعداد الصحيحة + +409 +00:29:30,850 --> 00:29:41,150 +واضح؟ في أي صعوبة في الخطوات؟ متابعين؟ نجي للخاصية + +410 +00:29:41,150 --> 00:29:47,590 +التالتة والاخيرة التعدى R is transitive + +411 +00:29:48,820 --> 00:29:52,180 +أه برضه جملة شرطية فنبدأ بإن الشرط صحيح ونقول له + +412 +00:29:52,180 --> 00:29:59,480 +assume أو let x, y تنتمي لل R and y, z تنتمي لل R + +413 +00:29:59,480 --> 00:30:03,920 +مطلوب x, z في ال R ممكن أكتبها و ممكن مكتباش خليني + +414 +00:30:03,920 --> 00:30:09,540 +أحطها هامشبدنا XZ تنتمي لل R سؤال يعني بدنا X ناقص + +415 +00:30:09,540 --> 00:30:15,780 +Z تساوي تلاتة في M for some M for some M تنتمي لل + +416 +00:30:15,780 --> 00:30:18,120 +Z هذا علامة استفاهة ما ده مطلوب قال ليه عشان إيش + +417 +00:30:18,120 --> 00:30:22,340 +كل شوية طالع عليه و اين رايح أنا اه انفك هدولة + +418 +00:30:22,340 --> 00:30:27,760 +طبعا هذا على طول معناته ان X ناقص Y تساوي K for + +419 +00:30:27,760 --> 00:30:34,210 +some K واش كمان تلاتة K صحيحو احنا بدنا تلاتة and + +420 +00:30:34,210 --> 00:30:41,430 +صحيح تلاتة K and Y ناقص Z تساوي تلاتة إيش أل + +421 +00:30:41,430 --> 00:30:45,410 +بإنفعش تحطي نفسه لإن زي ما اتعلمنا في قابلية + +422 +00:30:45,410 --> 00:30:49,430 +القسمة قلنا ال 21 بتقبل قسمها تلاتة إيش لإن السبعة + +423 +00:30:49,430 --> 00:30:53,110 +هو ال factor بختلف عن ال 18 ال factor 6 فده بتغيّر + +424 +00:30:53,110 --> 00:30:55,950 +لإنه قال for some مش بالضرورة إن there exist يكون + +425 +00:30:55,950 --> 00:30:59,770 +كلهم متساوين و اتعلمنا أكتر من بعض فتلاتة L طبعا + +426 +00:30:59,770 --> 00:31:07,310 +for someK و L في الـ Z لو كتبت كل واحدة تابعة + +427 +00:31:07,310 --> 00:31:12,430 +لناقص ممكن ولو كتبتهم مع بعض كله صحيحلأ نجمح الأهم + +428 +00:31:12,430 --> 00:31:16,190 +طبعا بدنا احنا إيش؟ بدنا X ناقص Z بتخلص من ال Y + +429 +00:31:16,190 --> 00:31:19,510 +إيش لو جمعناهم بروحوا مع بعض فطبعا هدول المعادلتين + +430 +00:31:19,510 --> 00:31:24,390 +الصحيحتين is an X ناقص Z تسوي تلاتة K زائد تلاتة N + +431 +00:31:24,390 --> 00:31:28,630 +معادلتين صحيحتين إيش مع الطرف اليمين مع اليمين + +432 +00:31:28,630 --> 00:31:31,210 +اليسار مع اليسار بتام و متساوي لإن المقدار متكافئ + +433 +00:31:31,210 --> 00:31:36,880 +طبعا بدي أخد تلاتة عامل مشتركK زائد L وتساوي تلاتة + +434 +00:31:36,880 --> 00:31:41,960 +في M نعم لأن M تساوي K زائد L تنتمي لل Z كلامي صح + +435 +00:31:41,960 --> 00:31:45,640 +ولا مش صح أفسر عندي عددين صحيحين مجموعة بتعملوا + +436 +00:31:45,640 --> 00:31:50,540 +عدد صحيح فانا فعلا في المكان الصحيح فخلاص الان بس + +437 +00:31:50,540 --> 00:31:56,640 +اللي هو نختم فهذا معناته طبعا هذا كان مطلوب الان + +438 +00:31:56,640 --> 00:32:02,740 +هذا معناته ان XZ في ال R اذا XZ في ال R وبالتالي + +439 +00:32:03,750 --> 00:32:11,710 +thus R is transitive طبعاً + +440 +00:32:11,710 --> 00:32:15,170 +واحد واثنين وثلاثة بيثبتوا انها فعلا علاقة تكافأت + +441 +00:32:15,170 --> 00:32:24,250 +واحد اتنين and three implies R is an equivalence + +442 +00:32:24,250 --> 00:32:24,650 +relation + +443 +00:32:33,580 --> 00:32:40,440 +أي سؤال فهذه علاقة الحقيقة اللي هي المضاعفات + +444 +00:32:40,440 --> 00:32:44,080 +التلاتة علاقة مهمة اللي لها تطبيقات عامة ممكن + +445 +00:32:44,080 --> 00:32:47,760 +الدور اللي قامت بيه التلاتة يقوم بيه أي عدد صحيح + +446 +00:32:47,760 --> 00:32:51,880 +موجب في أقنع هنا تعليق عليها فأرجو أن الأمور تكون + +447 +00:32:51,880 --> 00:32:55,200 +واضحة واحنا نشوف كمثال كيف نتعامل مع التعريفات + +448 +00:32:55,200 --> 00:33:00,980 +بشكل عامبقول هنا let M be any arbitrary fixed + +449 +00:33:00,980 --> 00:33:04,660 +positive integer and let فبقول هنا هذا الملاحظة .. + +450 +00:33:04,660 --> 00:33:07,320 +المثال هذا اللي هو .. ممكن .. ممكن .. ممكن .. ممكن + +451 +00:33:07,320 --> 00:33:09,060 +.. ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. + +452 +00:33:09,060 --> 00:33:09,080 +ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. + +453 +00:33:09,080 --> 00:33:09,840 +ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. + +454 +00:33:09,840 --> 00:33:11,020 +ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. + +455 +00:33:11,020 --> 00:33:11,040 +ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. + +456 +00:33:11,040 --> 00:33:11,760 +ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. + +457 +00:33:11,760 --> 00:33:12,500 +ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. + +458 +00:33:12,500 --> 00:33:12,540 +ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. ممكن .. + +459 +00:33:12,540 --> 00:33:19,880 +ممكن .. ممكن .. ممكن .. ممكن .. ممكن + +460 +00:33:19,880 --> 00:33:25,900 +.. ممكن ..XY بحيث الفرق بينهم يقبل قسم على M بديل + +461 +00:33:25,900 --> 00:33:29,100 +3 انا بدي أحط M مرة تانية جاهدين هذا المثال بدنا + +462 +00:33:29,100 --> 00:33:33,240 +نعيش نعمم التلاتة مالهاش خصوصية طب لو أخدنا 2 برضه + +463 +00:33:33,240 --> 00:33:36,820 +صح لو أخدنا 10 برضه صح أي عدد صحيح موجب ممكن يقوم + +464 +00:33:36,820 --> 00:33:39,960 +ينسى التلاتة هو البرهان نفس الخطوات أيدي نسخه خطوة + +465 +00:33:39,960 --> 00:33:43,500 +بخطوة بس مجرد يعيش اختلاف بديل 3 حصلت تاخد العشرة + +466 +00:33:43,500 --> 00:33:47,760 +على المشترك و هكذا تمام فبقول لي for some k ال R + +467 +00:33:47,760 --> 00:33:51,060 +ها دي بيسموها دايما علاقة تكافةاللي زي ما .. اللي + +468 +00:33:51,060 --> 00:33:54,340 +بنجح مع التلتة بنجح مع أي عدد صحيح موجود، تمام؟ اه + +469 +00:33:54,340 --> 00:33:57,380 +و إيش بيسموها؟ congrance relation بيسموها علاقة + +470 +00:33:57,380 --> 00:34:01,740 +congrance relation modulo .. modulo M اه بالنسبة + +471 +00:34:01,740 --> 00:34:05,740 +إيش؟ علاقة تطابق بيسموها .. إيش؟ بالنسبة ل M على + +472 +00:34:05,740 --> 00:34:08,080 +ال Z طبعا لإن أحنا قولنا إيش؟ من عام نشطوا لإنا + +473 +00:34:08,080 --> 00:34:11,620 +علاقة على ال Z لإنا من Z ل Z اه و طبعا بيكتبوها + +474 +00:34:11,620 --> 00:34:15,150 +بهذا الشكلإلى بعض التطبيقات في الرياضيات بيقولوا X + +475 +00:34:15,150 --> 00:34:19,830 +تكافئ ال Y Module و M هدولة العددين متكافئين + +476 +00:34:19,830 --> 00:34:24,250 +بالنسبة لمين بالنسبة للتلاتة بالنسبة للتلاتة فهم + +477 +00:34:24,250 --> 00:34:27,850 +مايشيلهم نفس الخواص اه ممكن نشوفها بهذا الشكل + +478 +00:34:27,850 --> 00:34:30,970 +الموديول وهذه علاقة مشهورة إلى بعض التطبيقات في + +479 +00:34:30,970 --> 00:34:34,410 +الرياضيات فإذا التلاتة مالهاش أي خصوصية أي عدد + +480 +00:34:34,410 --> 00:34:36,470 +صحيح ممكن يقوم مقام التلاتة + +481 +00:34:40,080 --> 00:34:45,240 +فطبعا ممكن انتوا يا بتشغلوها بشكل عام على ال M بس + +482 +00:34:45,240 --> 00:34:47,260 +تنتبهوا ال M اللي كنا نستخدمه هنا البنبط نستخدمه + +483 +00:34:47,260 --> 00:34:49,800 +لإن صارت مشغولة أو طبعا اللي بتكون تفهم ممكن + +484 +00:34:49,800 --> 00:34:52,580 +تاخدوا بدل ال M تاخدوا أربعة خمسة بدل التلاتة و + +485 +00:34:52,580 --> 00:34:55,500 +تقيدوا نفس القطوات و التعميم بكون سهل جدا خلينا + +486 +00:34:55,500 --> 00:35:00,590 +نشوف مثال جديدتلاتة مثال التالت let R الآن بدل + +487 +00:35:00,590 --> 00:35:05,730 +الفرق قال خلينا ناخد المجموع بيسوي تلاتة K for + +488 +00:35:05,730 --> 00:35:09,430 +some K determine الآن هل بالتامها equivalence + +489 +00:35:09,430 --> 00:35:12,830 +relation ولا لأ فبقول لي هل اللي هي reflexive؟ هل + +490 +00:35:12,830 --> 00:35:16,750 +هي symmetric؟ هل هي transitive or not؟ هنا سؤال + +491 +00:35:16,750 --> 00:35:20,750 +prove or disprove أه إيش رأيكوا؟ فده المثال التالت + +492 +00:35:20,750 --> 00:35:25,730 +لو غيرنا بدل الطرح عملناها جمع ليش؟ إيش اللي + +493 +00:35:25,730 --> 00:35:34,810 +اختلف؟أشمالها، من اللي بختل؟ ال transitive؟ لأ، + +494 +00:35:34,810 --> 00:35:38,930 +ولا ال symmetric، بقول جامعة أسهل من الطرح، ال + +495 +00:35:38,930 --> 00:35:43,590 +reflexive بختللأنه عندنا عددين مجموح بتمش يقبل + +496 +00:35:43,590 --> 00:35:47,690 +القسمة على تلاتة لأن الفرق هنا كان صفر و الصفر + +497 +00:35:47,690 --> 00:35:51,270 +يقبل القسمة على أي عدد لكن المجموع يعني لو أخدت هل + +498 +00:35:51,270 --> 00:35:55,010 +الواحد لعلاقة مع الواحد لأ واحد زائد واحد اتنين لأ + +499 +00:35:55,010 --> 00:35:57,810 +تقبل القسمة على تلاتة لكن الفرق بينهم صفر يقبل + +500 +00:35:57,810 --> 00:36:01,970 +القسمة على تلاتة كان فهنا شوفت الفرق فهنا ال + +501 +00:36:01,970 --> 00:36:06,650 +reflex فيش الشرط بيختلف فهنا solutionاحنا بنفحص + +502 +00:36:06,650 --> 00:36:09,850 +الكل، الحقيقة بنفحص الكل بالترتيب، طبعا هي مش + +503 +00:36:09,850 --> 00:36:12,310 +equivalent relation، بيقوللي افحص هل reflexive أه + +504 +00:36:12,310 --> 00:36:15,030 +و لا لأ، symmetric أه و لا لأ، transitive أه و لا + +505 +00:36:15,030 --> 00:36:18,930 +لأ، خلينا نمشي فيهم واحدة واحدة، ممتاز، فأول شيء R + +506 +00:36:18,930 --> 00:36:25,280 +is reflexive، نفحصيعني احنا يمكن جاوبنا بشكل سريع + +507 +00:36:25,280 --> 00:36:28,000 +أنه هي equivalence ولا لأ مش equivalence إذا في + +508 +00:36:28,000 --> 00:36:30,960 +واحدة على الأقل reflexive قولنا لأ بسهولة فإذا مش + +509 +00:36:30,960 --> 00:36:35,920 +reflexive أه هل R reflexive؟ No ليش؟ مثال عكسي + +510 +00:36:35,920 --> 00:36:42,040 +واحد واحد لا تنتمي لل R ليش؟ since واحد زائد واحد + +511 +00:36:42,040 --> 00:36:48,980 +لا تساوي تلاتة K for all K تنتمي لل Z مستحيل تكون + +512 +00:36:48,980 --> 00:36:52,680 +تقبل قصبة على تلاتةواحد بيقولي طب ليش صارت for all + +513 +00:36:52,680 --> 00:36:56,620 +ما كانت for some فانا نفيت .. نفيتها الآن فانا + +514 +00:36:56,620 --> 00:37:00,640 +بيقول انها إيش .. إيش غير صحيحة بيدقوله x زائد .. + +515 +00:37:00,640 --> 00:37:03,840 +اللي هي x زائد x بتسوي تلاتة K بيقوله هذا غير صحيح + +516 +00:37:03,840 --> 00:37:08,700 +فكانت for some صارت إيش for all ماقدرش ألاقي عدد K + +517 +00:37:08,700 --> 00:37:13,020 +و أخلي التنين تسوي تلاتة في K ماقدرش فلكله مستحيل + +518 +00:37:13,020 --> 00:37:16,800 +واضحة هالي؟أه فإذا الواحد مانعش علاقة مع نفسه يكفي + +519 +00:37:16,800 --> 00:37:19,280 +طبعا الواحد يقول ال zero اللي علاقة مع نفسه أه صح + +520 +00:37:19,280 --> 00:37:23,200 +لكن التلاتة اللي علاقة مع نفسها أه لكن الواحد لأ + +521 +00:37:23,200 --> 00:37:26,680 +التنم لأ بدنا نشوف من اللي له علاقة مش كله بنجح + +522 +00:37:26,680 --> 00:37:30,140 +يلديت مثال عكسي واحد يكفي لأنه أنا بدأ أثبت أنهياش + +523 +00:37:30,140 --> 00:37:37,420 +أنها false بدأ أعمل disapprove أنها reflexive تمام + +524 +00:37:37,420 --> 00:37:45,410 +نيجي نفحص ال symmetric R is symmetricالحقيقة هذه + +525 +00:37:45,410 --> 00:37:52,050 +سهلة جدا فعلا symmetric فبقول هنا let x y تنتمي لل + +526 +00:37:52,050 --> 00:38:02,010 +R هذا يؤدى ان x زائد y تسوى 3k for some k for some + +527 +00:38:02,010 --> 00:38:07,090 +k تنتمي لل z طبعا ممكن الجامعه يشمله إبدالى + +528 +00:38:07,090 --> 00:38:12,810 +الجامعه إبدالى أسهل من الطرحيعني ال K المرة الفاتة + +529 +00:38:12,810 --> 00:38:18,290 +اتغيرناها من K ل-K لأقل مش محتاجين حتى for some K + +530 +00:38:18,290 --> 00:38:24,930 +تنتمي لل Z فهذا معناته أن YX تنتمي لل R فإذا ال R + +531 +00:38:24,930 --> 00:38:25,470 +is symmetric + +532 +00:38:33,190 --> 00:38:36,550 +طبعا هنا واحد يقول كيف جيبت المثال العكسي لو + +533 +00:38:36,550 --> 00:38:40,410 +حاولنا نثبت قولنا x زائد x تساوي 2x مش ضروري تكون + +534 +00:38:40,410 --> 00:38:42,910 +أيش من مضاعفات التلاتة طبعا عشان نديله مثال عكسي + +535 +00:38:42,910 --> 00:38:46,050 +لو ال x فيها تلاتة بتديني التلاتة يعني كان هنا من + +536 +00:38:46,050 --> 00:38:49,950 +وين جيبنا حاولنا نقول إيش x زائد x تساوي 2x + +537 +00:38:49,950 --> 00:38:54,110 +فالسؤال هل هذه تلاتة k دائما لأ إذا ال x بتساويش + +538 +00:38:54,110 --> 00:38:57,110 +من مضاعفات التلاتة بتظبطش واضحة فكيف نجيب المثال + +539 +00:38:57,110 --> 00:39:04,560 +العكسي إذا حد سأل تمام نفحص الخاصية الأخيرةR is a + +540 +00:39:04,560 --> 00:39:05,260 +transitive + +541 +00:39:08,020 --> 00:39:11,520 +أه كما ذكرنا في محاضرات سابقة في ال prove or + +542 +00:39:11,520 --> 00:39:14,520 +disapprove إذا قدرت أخمن ممتاز ماقدرتش بحاول أثبت + +543 +00:39:14,520 --> 00:39:17,800 +و أشوف وين الصقوبة خيا نحاول نثبت فنقوله هنا إيش + +544 +00:39:17,800 --> 00:39:22,580 +ناخد عنصرين ذوجين من خواص معينة اللي هو نهاية + +545 +00:39:22,580 --> 00:39:29,400 +الأول و بداية التاني فقوله let xy في ال R and yz + +546 +00:39:29,400 --> 00:39:34,500 +في ال R بده أشوف بنجح أخلي xz في ال R ولا لأ فطبعا + +547 +00:39:34,500 --> 00:39:41,970 +من التعريفأه فإذا أنا عايش فيه عندي X زاد Y تساوي + +548 +00:39:41,970 --> 00:39:48,770 +تلاتة K and هذا implies طبعا Y زاد Z تساوي تلاتة N + +549 +00:39:48,770 --> 00:39:56,930 +مثلا تمام for some for some اللي هو يعيش K وN في Z + +550 +00:39:59,090 --> 00:40:02,730 +طب ليش نطرحهم؟ عشان المرة دي كان طرح جمعناهم زبط + +551 +00:40:02,730 --> 00:40:06,290 +الآن لو طرحناهم بظبط مظبطش لو طرحناهم يصير X زاخر + +552 +00:40:06,290 --> 00:40:09,970 +Z أنا إيش بدي؟ أنا إيش في الـHام إيش بدي؟ بدي X + +553 +00:40:09,970 --> 00:40:15,830 +زائد Z تساوي 3M هذا المطلوب ولا لأ؟ مش هيك مطلوب؟ + +554 +00:40:15,830 --> 00:40:19,910 +فإيش ممكن نعمل؟ فالطرح مظبطش، بضيع الـY، أه لكن لو + +555 +00:40:19,910 --> 00:40:28,020 +جمعنا، إيش بيصير؟ 3X زائد Zزي اتنين Y تساوي تلاتة + +556 +00:40:28,020 --> 00:40:31,380 +K زي تلاتة N الطرح مش هيصبح لإنه بدي انا X زي زيت + +557 +00:40:31,380 --> 00:40:35,440 +طيب إيش ما أنا بدي؟ بدي X زي زيت طيب لو نجلنا ال Y + +558 +00:40:35,440 --> 00:40:41,960 +على الطرف التاني بنفع + +559 +00:40:41,960 --> 00:40:48,520 +أخد تلاتة عامل مشترك؟ K وينها؟طيب، بديها جيت + +560 +00:40:48,520 --> 00:40:52,360 +المثال العكسي، يلّا، ما زال واضح، إذا واضح، إذا + +561 +00:40:52,360 --> 00:40:56,180 +الـY مش من المضاعفات التلاتة، هيفشل العملية، إذا + +562 +00:40:56,180 --> 00:41:01,580 +نادي أشملها، false، العملية false، R is not + +563 +00:41:01,580 --> 00:41:05,160 +transitive، + +564 +00:41:05,160 --> 00:41:08,500 +آه، بديها جيت مثال عكسي، كون الـSi، transitive، + +565 +00:41:08,500 --> 00:41:13,060 +آه، فعل، ليش؟ sinceبدنا ناخد ال Y مش من ضعف + +566 +00:41:13,060 --> 00:41:19,280 +التلاتة مثلا ناخد ال .. ال .. اتنين و واحد تنتمي + +567 +00:41:19,280 --> 00:41:26,160 +لل R and ايش كمان اللي هو واحد و تلاتة تنتمي لل R + +568 +00:41:26,160 --> 00:41:33,500 +لكن .. اه ثواني .. اه بدنا يام .. اه بصحيح بدنا + +569 +00:41:33,500 --> 00:41:39,560 +يامن تنتمي بدنا المجموعة دي صح واحد و اتنينطيب .. + +570 +00:41:39,560 --> 00:41:45,500 +طيب هل اتنين اتنين تنتمي؟ لأ .. لأ .. لأن اربعة مش + +571 +00:41:45,500 --> 00:41:48,280 +مضاعفات التلاتة فخلاص هذا يكفي .. اه وضحكت مني + +572 +00:41:48,280 --> 00:41:51,260 +واناشي انا طبعا كنت مركز ان ال Y بتكون مش مضاعفات + +573 +00:41:51,260 --> 00:41:53,880 +التلاتة طبعا بده انتبه جيد انكوا نباتوني ان انا + +574 +00:41:53,880 --> 00:41:56,500 +بده انتبه انه طبعا بده ال Y تكون مش مضاعفات + +575 +00:41:56,500 --> 00:41:59,880 +التلاتة واحد اتنين اربعة كذا لكن بده انتبه تتأكد + +576 +00:41:59,880 --> 00:42:02,620 +انه فعلا في ال R مش بده اكتب كلام مش اه فانتكون + +577 +00:42:02,620 --> 00:42:06,080 +المجموع من مضاعفات التلاتة فإذا هذه فعلا انها not + +578 +00:42:06,080 --> 00:42:11,890 +a transitواضح فينيو مثال جيد انه حاولنا نبرهن و من + +579 +00:42:11,890 --> 00:42:14,890 +البرهان لما لاجينا فيه صعوبة عرفنا كيف نجيب المثال + +580 +00:42:14,890 --> 00:42:25,810 +العكسي كمان بساعد مثال + +581 +00:42:25,810 --> 00:42:26,350 +جديد + +582 +00:42:29,610 --> 00:42:36,050 +let R be a relation on a set X prove that R is + +583 +00:42:36,050 --> 00:42:40,010 +reflexive if and only if ال diagonal relation + +584 +00:42:40,010 --> 00:42:48,410 +subset من R فخلينا نعيد السؤال R is reflexive if + +585 +00:42:48,410 --> 00:42:52,750 +and only if delta X subset من R هذا هو المطلوب + +586 +00:42:56,150 --> 00:43:01,650 +فزي ما انتوا شايفين المنهج واحد طبعا فيه اختلاف في + +587 +00:43:01,650 --> 00:43:06,370 +التفاصيل فالمطلوب prove that جملة ايش ثنائية + +588 +00:43:06,370 --> 00:43:10,970 +الشرطية فبدنا نعملها two parts prove اه فطبعا ممكن + +589 +00:43:10,970 --> 00:43:14,350 +اكتب I will want او على طول مباشرة واحد للاتجاه + +590 +00:43:14,350 --> 00:43:22,510 +الاول R is reflexive implies Delta X subset من ال + +591 +00:43:22,510 --> 00:43:25,710 +R هذا المطلوب الجزء الاول من two parts prove + +592 +00:43:29,230 --> 00:43:33,470 +فانا بحاول يعني أنوى شوية عشان لو شفته في كتاب ما + +593 +00:43:33,470 --> 00:43:37,230 +تستغربوش كيف بكتبه هو نفس الأشياء لكن أحيانا طريقة + +594 +00:43:37,230 --> 00:43:40,810 +التعبير بتختلف لكن كله بيصب في نفس القالب الحقيقة + +595 +00:43:40,810 --> 00:43:44,610 +نفس الموضوع ممتاز جملة شرطية إيش هنعمل اشترض إن + +596 +00:43:44,610 --> 00:43:48,510 +الشرط صحيح و اثبت جواب الشرط فقوله assume أولت نفس + +597 +00:43:48,510 --> 00:43:52,950 +المعنى تستخدم مع نفس الاصطلاع assume R is + +598 +00:43:52,950 --> 00:43:54,270 +reflexive + +599 +00:43:56,090 --> 00:44:00,090 +ممكن نعمل معناها وده يكافئ for all X تنتمي + +600 +00:44:00,090 --> 00:44:09,030 +للcapital X، XX تنتمي للR إيش بتثبت؟ بتثبت إن + +601 +00:44:09,030 --> 00:44:15,050 +Delta X subset من الR نكتبها عشان نركز we want to + +602 +00:44:15,050 --> 00:44:22,450 +prove Delta X subset من الRفهذه علاقة subset بتبدأ + +603 +00:44:22,450 --> 00:44:27,990 +من الطرف اليسار ووصل الآن بدي أخد إيش أنصر في الـ + +604 +00:44:27,990 --> 00:44:33,410 +delta X ما هي عناصر الـ delta X؟ XX XX فانا هقوله + +605 +00:44:33,410 --> 00:44:38,410 +الآن let اللي هو إذا هذا موجود ممكن أسميه أنصر + +606 +00:44:38,410 --> 00:44:43,890 +تاني، تفرجش XX تنتمل الـ delta X بـany element طب + +607 +00:44:43,890 --> 00:44:47,510 +مش اختارنا XX لإنه .. بس هي subset يعني يا بدي + +608 +00:44:47,510 --> 00:44:53,480 +أثبت إنها subset بدي أثبت إنه هنا N هو Pلأ بنفعش + +609 +00:44:53,480 --> 00:44:58,840 +أنه أما لأن عناصر الـ delta X إيش تعريفها؟ بس + +610 +00:44:58,840 --> 00:45:03,060 +بنفعش نختار X و X خلّيها Y و Y إذا كانت برايحك ليش + +611 +00:45:03,060 --> 00:45:07,560 +مشكلة لكن عن عناصر ال delta X الدياجونال كل + +612 +00:45:07,560 --> 00:45:09,560 +الأحداث الأول يساوي الأحداث التانية شرحتها قبل + +613 +00:45:09,560 --> 00:45:10,240 +قليل صح؟ + +614 +00:45:13,820 --> 00:45:16,360 +أنا بتثبت هذا مطلوب .. ايه ده .. ايه ده ما هو + +615 +00:45:16,360 --> 00:45:19,980 +معطيها .. بتثبت هذا الكلام فبتاخد عنصر منها .. اه + +616 +00:45:19,980 --> 00:45:22,960 +زي ما اتعلمنا تمام خليني أشرحها مرة تانية .. اوضح + +617 +00:45:22,960 --> 00:45:27,140 +.. اوضح .. خليني اوضح .. بس واحدة واحدة .. اه + +618 +00:45:27,140 --> 00:45:32,600 +مطلوب نثبت subsetماذا يعني علاق الـ Subset؟ بدنا + +619 +00:45:32,600 --> 00:45:37,280 +عنصر في الطرف اليسار نوصله لليمين اتعلمنا في + +620 +00:45:37,280 --> 00:45:40,020 +المحادرات الماضية أنا بدي أخد عنصر عشوائي و ليكن + +621 +00:45:40,020 --> 00:45:43,500 +خليني أسميه A طب أنا عندي معلومات إن الـ A في الـ + +622 +00:45:43,500 --> 00:45:46,620 +Delta X إيش عناصر الـ Delta X؟ بدي يكون عنصر إيش + +623 +00:45:46,620 --> 00:45:50,340 +قطري XX يعني ممكن أنا .. ممكن أنا مشيت بسرعة شوية + +624 +00:45:50,340 --> 00:45:55,840 +فكرنا نتقدمين فمافيش مفروض أقوله، أقوله LetA تنتمي + +625 +00:45:55,840 --> 00:45:59,560 +للـ Delta X B على إلمة، مظبوط؟ آه، الأعرفين دي + +626 +00:45:59,560 --> 00:46:02,280 +معلومات، زي ما اتعلمنا إن هذا زوج مرتب ولا هو زوج + +627 +00:46:02,280 --> 00:46:05,520 +مرتب، واش كمان؟ واحداثي الأول يساوي واحداثي + +628 +00:46:05,520 --> 00:46:10,460 +التاني، A تساوي YY، ليش؟ تعريف الـ Delta X هو هيك، + +629 +00:46:10,460 --> 00:46:13,400 +آه، لأن Delta X إيش متساوي؟ عناصر واحداثيها الأول + +630 +00:46:13,400 --> 00:46:15,680 +يساوي واحداثيها التاني، فانا إيش عندي معلومات + +631 +00:46:15,680 --> 00:46:19,390 +معروفة باستخدامها؟ آهزي ما كنا نقول احنا أخدنا + +632 +00:46:19,390 --> 00:46:22,770 +عناصر من ال Z فكل عدد صحيح بدأ الصحيح تبقى واصل + +633 +00:46:22,770 --> 00:46:26,130 +عدد صحيح فانا عندي معلومة مزال العنصر العشوائي هو + +634 +00:46:26,130 --> 00:46:29,290 +في ال diagonal relation اذا نيش يكون زوج أحداثي + +635 +00:46:29,290 --> 00:46:33,510 +الأول يساوي أحداثي الثاني واضحة؟ اه تمام طيب YY في + +636 +00:46:33,510 --> 00:46:36,650 +ال delta X انا وين بدي أوصلها لل R بما ان ال R + +637 +00:46:36,650 --> 00:46:40,630 +reflexive هي معطوية اذا نيش ان ال YY تكون في ال A + +638 +00:46:40,630 --> 00:46:45,670 +فإن ايش؟ هذا ينتمي ان YY تنتمي لل R ليش؟ لأن ال R + +639 +00:46:45,670 --> 00:46:54,320 +reflexivereflex وهو المطلوب التجاه التاني thus + +640 +00:46:54,320 --> 00:47:00,700 +اللي هو delta x subset من ال R نيجي للتجاه التاني + +641 +00:47:00,700 --> 00:47:07,250 +لأن هذا if and only ifفالحقيقة البروهين سهل جدا + +642 +00:47:07,250 --> 00:47:10,850 +لكن المهم ليش كيف نكتب هذا المهم الآن للتجاه + +643 +00:47:10,850 --> 00:47:17,590 +التاني Delta X subset من R implies R is reflexive + +644 +00:47:17,590 --> 00:47:25,550 +العكس البداية تصير نهاية Assume Delta X subset من + +645 +00:47:25,550 --> 00:47:32,780 +R Assume Delta X subset من Rوحدة واحدة، بس عشان + +646 +00:47:32,780 --> 00:47:35,280 +نبدأ، إيش معنى الـreflexive for all؟ إذا كتبت في + +647 +00:47:35,280 --> 00:47:39,040 +الـreflexive for all، بتاخد عنصر إيه؟ عشوائي في + +648 +00:47:39,040 --> 00:47:44,960 +الـX، عشان كلمة for all، فإيش بعدين، هقولّه؟ let X + +649 +00:47:44,960 --> 00:47:47,200 +تنتمي لكبتل X be an element + +650 +00:47:52,260 --> 00:47:56,780 +مطلوب اثبت ان X X سنتامل الـ A طيب الآن وين طريقة + +651 +00:47:56,780 --> 00:48:00,560 +بتستميد من المعتف الغالب بما انه ال diagonal + +652 +00:48:00,560 --> 00:48:03,760 +relation كل X X في ال diagonal relation اه فلأي + +653 +00:48:03,760 --> 00:48:08,180 +عنصر X تعريف ال Delta X لو تذكرتوا ايش تعريفها وين + +654 +00:48:08,180 --> 00:48:16,580 +اكتبها Delta X تساوي X X such that X سنتامل كبتة X + +655 +00:48:16,580 --> 00:48:23,090 +هيك تعريفهابما أن ال X تنتمي لل X كل زوج إحداثيه + +656 +00:48:23,090 --> 00:48:25,350 +الأول يساوي إحداثيه التاني هو اللي موجود في المحطة + +657 +00:48:25,350 --> 00:48:30,470 +القطرية هك تعريفه فده على طول XX تنتمي لل Delta X + +658 +00:48:30,470 --> 00:48:35,480 +من وين تعريف ال Delta Xفتبتدى شوية تتعود عليها + +659 +00:48:35,480 --> 00:48:39,140 +لأنه أول مرة بنستخدمها تكون غريبة بس هيك معناته أن + +660 +00:48:39,140 --> 00:48:46,100 +العلاقة القطرية عناصرها XXYY بما أو بعن آخر أزواج + +661 +00:48:46,100 --> 00:48:49,540 +مرتبة الإحداث الأول يساوي الإحداث التاني فعلا طول + +662 +00:48:49,540 --> 00:48:55,220 +تمام الآن من subset إذن XX في ال R وهو المطلوب XX + +663 +00:48:55,220 --> 00:48:59,820 +تنتمي لل R ليش؟ لأن ال Delta X subset من ال R وهو + +664 +00:48:59,820 --> 00:49:01,960 +المطلوب إذن ال R فعلا Reflex + +665 +00:49:13,330 --> 00:49:19,350 +فجيد احنا نتعلم نحلل المطلوب نحلل الحل و طبعا نعمل + +666 +00:49:19,350 --> 00:49:23,610 +هامش و برضه نتعلم كيف نكتب بطريقة البرهان الرياضي + +667 +00:49:23,610 --> 00:49:30,070 +كيف بنبدأ و الخطوات اه تمام جيد فدي مكان مناسب انه + +668 +00:49:30,070 --> 00:49:31,430 +نوقف ان شاء الله المرة الجاية + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/6BraapxPBi4_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/6BraapxPBi4_raw.json new file mode 100644 index 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طبعا اللي هو H كافق for all x تنتمي لل capital X اللي هي Z في هذا السؤال بدنا إيش XX تكون تنتمي لل R كل عنصر اللي علاقة مع نفسه فده سؤالنا الأول هل هذا صحيح ولا لأ لإن بقول determined فإيش رأيكوا؟ هل كل عدد صحيح علاقة مع نفسه؟ ليش؟ الواحد اللي علاقة مع نفسها نعم السالب واحد اللي علاقة مع نفسها نعم", "tokens": [33115, 2021, 488, 23032, 3555, 3615, 995, 13672, 1829, 31439, 389, 9122, 31845, 4587, 337, 439, 2031, 6055, 29399, 2304, 1829, 24976, 4238, 1783, 13672, 1829, 39896, 1176, 8978, 23758, 21136, 33604, 6027, 47525, 8315, 11933, 1829, 8592, 27050, 6055, 30544, 6055, 29399, 2304, 1829, 24976, 497, 28242, 18871, 9381, 2288, 13672, 1829, 11203, 995, 28671, 20449, 8717, 36178, 3224, 6156, 3215, 3224, 8608, 33604, 6027, 8315, 16247, 12610, 8032, 1211, 23758, 20328, 5016, 1829, 5016, 49429, 5296, 10721, 5296, 28814, 1863, 4724, 39648, 9540, 6156, 28814, 1829, 8592, 12602, 10721, 1829, 4117, 14407, 22807, 8032, 1211, 28242, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 11203, 995, 28671, 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"word": " رأيكوا؟", "probability": 0.8277180989583334}, {"start": 156.91, "end": 157.07, "word": " هل", "probability": 0.96875}, {"start": 157.07, "end": 157.41, "word": " كل", "probability": 0.97802734375}, {"start": 157.41, "end": 158.03, "word": " عدد", "probability": 0.9534505208333334}, {"start": 158.03, "end": 158.57, "word": " صحيح", "probability": 0.9937744140625}, {"start": 158.57, "end": 159.07, "word": " علاقة", "probability": 0.73779296875}, {"start": 159.07, "end": 159.19, "word": " مع", "probability": 0.9892578125}, {"start": 159.19, "end": 159.57, "word": " نفسه؟", "probability": 0.88232421875}, {"start": 159.57, "end": 161.25, "word": " ليش؟", "probability": 0.912109375}, {"start": 161.25, "end": 163.89, "word": " الواحد", "probability": 0.6559651692708334}, {"start": 163.89, "end": 164.01, "word": " اللي", "probability": 0.977294921875}, {"start": 164.01, "end": 164.29, "word": " علاقة", "probability": 0.9571940104166666}, {"start": 164.29, "end": 164.45, "word": " مع", "probability": 0.9921875}, {"start": 164.45, "end": 164.91, "word": " نفسها", "probability": 0.890625}, {"start": 164.91, "end": 165.33, "word": " نعم", "probability": 0.74951171875}, {"start": 165.33, "end": 166.29, "word": " السالب", "probability": 0.7691243489583334}, {"start": 166.29, "end": 166.51, "word": " واحد", "probability": 0.95849609375}, {"start": 166.51, "end": 166.65, "word": " اللي", "probability": 0.994140625}, {"start": 166.65, "end": 166.91, "word": " علاقة", "probability": 0.96826171875}, {"start": 166.91, "end": 167.07, "word": " مع", "probability": 0.99609375}, {"start": 167.07, "end": 167.41, "word": " نفسها", "probability": 0.8876953125}, {"start": 167.41, "end": 167.65, "word": " نعم", "probability": 0.986572265625}], "temperature": 1.0}, {"id": 7, "seek": 16923, "start": 168.39, "end": 169.23, "text": "طب والباقي؟", "tokens": [9566, 3555, 16070, 3555, 995, 38436, 22807], "avg_logprob": -0.2420654222369194, "compression_ratio": 0.7241379310344828, "no_speech_prob": 0.0, "words": [{"start": 168.39, "end": 168.67, "word": "طب", "probability": 0.873779296875}, {"start": 168.67, "end": 169.23, "word": " والباقي؟", "probability": 0.779296875}], "temperature": 1.0}, {"id": 8, "seek": 19896, "start": 170.42, "end": 198.96, "text": "الصفر الشمال اللي ليه علاقة مع نفسه؟ لأ لأن صفر في صفر مش مش positive اه فوين ننتبهه؟ جميع الأعداد الصحيحة مايعدد صفر كل عدد اللي ليه علاقة مع نفسه إلا الصفر مثال واحد يكفي إن هياش not reflexive فإذا نقاشها دي not reflexive ليش؟ 00 لا تنتمي للR ليش؟ لأن 0 ضرب 0 تساوي 0 ليست أكبر من صفر فإذا نقاش العلاقة not reflexive thus", "tokens": [6027, 9381, 5172, 2288, 25124, 2304, 6027, 13672, 1829, 32239, 3224, 11203, 995, 28671, 20449, 8717, 36178, 3224, 22807, 5296, 10721, 5296, 33456, 20328, 5172, 2288, 8978, 20328, 5172, 2288, 37893, 37893, 3353, 1975, 3224, 6156, 2407, 9957, 8717, 29399, 3555, 3224, 3224, 22807, 10874, 2304, 40228, 16247, 22488, 18513, 31767, 5016, 1829, 5016, 3660, 19446, 1829, 22488, 3215, 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"probability": 0.696044921875}, {"start": 175.8, "end": 176.32, "word": " فوين", "probability": 0.6900227864583334}, {"start": 176.32, "end": 177.36, "word": " ننتبهه؟", "probability": 0.8159993489583334}, {"start": 177.36, "end": 177.88, "word": " جميع", "probability": 0.9710286458333334}, {"start": 177.88, "end": 178.52, "word": " الأعداد", "probability": 0.95166015625}, {"start": 178.52, "end": 179.2, "word": " الصحيحة", "probability": 0.98125}, {"start": 179.2, "end": 179.58, "word": " مايعدد", "probability": 0.57440185546875}, {"start": 179.58, "end": 179.9, "word": " صفر", "probability": 0.8681640625}, {"start": 179.9, "end": 180.22, "word": " كل", "probability": 0.93798828125}, {"start": 180.22, "end": 180.52, "word": " عدد", "probability": 0.9794921875}, {"start": 180.52, "end": 180.58, "word": " اللي", "probability": 0.8623046875}, {"start": 180.58, "end": 180.64, "word": " ليه", "probability": 0.6234130859375}, {"start": 180.64, "end": 180.86, "word": " علاقة", "probability": 0.9803059895833334}, {"start": 180.86, "end": 181.02, "word": " مع", "probability": 0.9912109375}, {"start": 181.02, "end": 181.3, "word": " نفسه", "probability": 0.9978841145833334}, {"start": 181.3, "end": 181.44, "word": " إلا", "probability": 0.849365234375}, {"start": 181.44, "end": 181.86, "word": " الصفر", "probability": 0.9671223958333334}, {"start": 181.86, "end": 182.92, "word": " مثال", "probability": 0.7261962890625}, {"start": 182.92, "end": 183.4, "word": " واحد", "probability": 0.817138671875}, {"start": 183.4, "end": 184.12, "word": " يكفي", "probability": 0.9812825520833334}, {"start": 184.12, "end": 184.24, "word": " إن", "probability": 0.328369140625}, {"start": 184.24, "end": 184.52, "word": " هياش", "probability": 0.53826904296875}, {"start": 184.52, "end": 184.74, "word": " not", "probability": 0.859375}, {"start": 184.74, "end": 185.36, "word": " reflexive", "probability": 0.9814453125}, {"start": 185.36, "end": 185.76, "word": " فإذا", "probability": 0.8756510416666666}, {"start": 185.76, "end": 186.14, "word": " نقاشها", "probability": 0.6739501953125}, {"start": 186.14, "end": 186.34, "word": " دي", "probability": 0.87353515625}, {"start": 186.34, "end": 186.84, "word": " not", "probability": 0.88818359375}, {"start": 186.84, "end": 187.46, "word": " reflexive", "probability": 0.982666015625}, {"start": 187.46, "end": 187.9, "word": " ليش؟", "probability": 0.7936197916666666}, {"start": 187.9, "end": 188.32, "word": " 00", "probability": 0.495849609375}, {"start": 188.32, "end": 189.34, "word": " لا", "probability": 0.9033203125}, {"start": 189.34, "end": 190.0, "word": " تنتمي", "probability": 0.9857177734375}, {"start": 190.0, "end": 190.48, "word": " للR", "probability": 0.6268310546875}, {"start": 190.48, "end": 191.2, "word": " ليش؟", "probability": 0.89501953125}, {"start": 191.2, "end": 191.5, "word": " لأن", "probability": 0.921875}, {"start": 191.5, "end": 192.04, "word": " 0", "probability": 0.4482421875}, {"start": 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reflexive", "probability": 0.984619140625}, {"start": 198.36, "end": 198.96, "word": " thus", "probability": 0.6416015625}], "temperature": 1.0}, {"id": 9, "seek": 22779, "start": 199.71, "end": 227.79, "text": "الـ R is not reflexive بس واحدة تكون مش متحقق لأنه جالي for all ده بأكد عليهش معناه for all طب الواحد اللي علاقة مع نفسه اه سالب واحد اه كل الإعداد إلا الصفر يكفي شوف مثال واحد خلاها مش reflexive لأنه جالي for all لازم يكون كل عنصر في المجموع اللي علاقة مع نفسه طب الصفر ماليش علاقة مع نفسه إذا مختلف الشرط ف it's not reflexive", "tokens": [6027, 39184, 497, 307, 406, 23802, 488, 4724, 3794, 36764, 24401, 3660, 6055, 30544, 37893, 44650, 5016, 4587, 4587, 5296, 33456, 3224, 10874, 6027, 1829, 337, 439, 11778, 3224, 4724, 10721, 4117, 3215, 47356, 8592, 20449, 8315, 3224, 337, 439, 23032, 3555, 2423, 14407, 24401, 13672, 1829, 11203, 995, 28671, 20449, 8717, 36178, 3224, 1975, 3224, 8608, 6027, 3555, 36764, 24401, 1975, 3224, 28242, 33688, 22488, 18513, 11933, 15040, 31767, 5172, 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symmetric التماثر", "tokens": [40294, 39896, 4117, 19446, 39896, 4117, 2423, 23802, 488, 29538, 16490, 33546, 10632, 2423, 23802, 488, 4032, 46958, 5016, 22807, 1975, 3224, 6156, 6027, 33115, 2021, 592, 742, 4724, 1829, 39648, 47525, 8315, 28242, 18871, 9381, 2288, 11933, 1829, 3224, 46740, 11203, 995, 28671, 20449, 8717, 36178, 3224, 39896, 4117, 20449, 8315, 47395, 16472, 41850, 9122, 45636, 3555, 5296, 33456, 3224, 12174, 1211, 8315, 14739, 41850, 9122, 45636, 3555, 46811, 10943, 8717, 1829, 7435, 1829, 8717, 5172, 5016, 9381, 33962, 33546, 10632, 16712, 7649, 10632, 37037, 1829, 16490, 33546, 10632, 2423, 32330, 16712, 2304, 5718, 104, 2288], "avg_logprob": -0.25685587251672937, "compression_ratio": 1.8232323232323233, "no_speech_prob": 0.0, "words": [{"start": 249.78, "end": 250.06, "word": "اه", "probability": 0.2030029296875}, {"start": 250.06, "end": 250.34, "word": " هيك", "probability": 0.93798828125}, {"start": 250.34, "end": 250.4, "word": " ما", "probability": 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الاشي assume ان X Y تنتمي لل R ايش بده اثبت؟ بده اثبت ان Y X تنتمي لل R كونه من الأمثل اللي في البداية خلينا نكتب التفاصيل we want", "tokens": [50, 32497, 17475, 23032, 3555, 3615, 995, 4724, 1863, 25957, 43761, 7081, 46740, 15730, 2423, 28820, 10943, 7251, 7081, 16472, 11296, 32330, 6156, 4587, 1211, 8315, 39896, 10874, 2304, 37977, 13412, 2288, 9566, 10632, 44945, 44510, 10721, 8717, 7435, 26895, 2423, 26890, 3224, 7649, 16472, 3224, 8717, 5172, 2655, 43042, 16472, 25124, 2288, 9566, 20328, 5016, 1829, 5016, 6156, 3555, 39648, 46740, 6552, 34051, 718, 8717, 36178, 25124, 1829, 9778, 2423, 33599, 1829, 6552, 16472, 1783, 398, 6055, 29399, 2304, 1829, 24976, 497, 1975, 1829, 8592, 47525, 3224, 1975, 12984, 3555, 2655, 22807, 47525, 3224, 1975, 12984, 3555, 2655, 16472, 398, 1783, 6055, 29399, 2304, 1829, 24976, 497, 9122, 11536, 3224, 9154, 16247, 2304, 12984, 1211, 13672, 1829, 8978, 29739, 28259, 10632, 16490, 20292, 8315, 8717, 4117, 2655, 3555, 16712, 5172, 33546, 26895, 321, 528], 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38456, "start": 366.84, "end": 384.56, "text": "to prove or to show to prove that Y X تنتمي لل R ممتاز زي ما احنا ممكن نحكي ناشرة فور الان XY في ال R ماذا تعني XY في ال R تعني ان X في Y positive", "tokens": [1353, 7081, 420, 281, 855, 281, 7081, 300, 398, 1783, 6055, 29399, 2304, 1829, 24976, 497, 3714, 2304, 2655, 31377, 30767, 1829, 19446, 1975, 5016, 8315, 3714, 43020, 8717, 5016, 4117, 1829, 8717, 33599, 25720, 6156, 13063, 2423, 7649, 48826, 8978, 2423, 497, 3714, 45636, 995, 37279, 22653, 48826, 8978, 2423, 497, 37279, 22653, 16472, 1783, 8978, 398, 3353], "avg_logprob": -0.2579427073399226, "compression_ratio": 1.4482758620689655, "no_speech_prob": 2.3245811462402344e-06, "words": [{"start": 366.84, "end": 367.04, "word": "to", "probability": 0.5986328125}, {"start": 367.04, "end": 367.46, "word": " prove", "probability": 0.9296875}, {"start": 367.46, "end": 367.66, "word": " or", "probability": 0.428955078125}, {"start": 367.66, "end": 367.82, "word": " to", "probability": 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الإبدال هذا إيش يعني بالتعريف؟ إن YX في الـ A اتغير الترتيب لإيش؟ لأن هذا تعريف الـ A إذا و هو المطلوب إثباته", "tokens": [3224, 15730, 37279, 16572, 5172, 2423, 39184, 316, 23032, 1829, 3555, 41850, 11933, 1829, 8592, 47525, 7578, 5551, 25957, 1211, 22807, 23758, 9673, 9566, 1211, 37746, 47525, 7578, 5551, 3615, 4117, 3794, 37037, 15730, 7251, 33604, 16254, 36145, 398, 55, 307, 3353, 9154, 16490, 14407, 9381, 16247, 22488, 18513, 31767, 5016, 1829, 5016, 3660, 5296, 33456, 3224, 11933, 1829, 8592, 22807, 32748, 25513, 11933, 44510, 6027, 1829, 11933, 15730, 47525, 8315, 8717, 5016, 9566, 36145, 32748, 25513, 15844, 16247, 22488, 18513, 31767, 5016, 1829, 5016, 3660, 7251, 39237, 2655, 3615, 4724, 9778, 33546, 10632, 33688, 44510, 6027, 23758, 11933, 1829, 8592, 37495, 22653, 20666, 2655, 3615, 16572, 5172, 22807, 36145, 398, 55, 8978, 2423, 39184, 316, 1975, 2655, 17082, 13546, 16712, 43500, 1829, 3555, 5296, 28814, 1829, 8592, 22807, 5296, 33456, 23758, 37279, 16572, 5172, 2423, 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المفهوم بشكل عام إنه إذا الزوج وجد بدور على معكوسه مش موجود خلاص، مابديش أعمل إشي، تمام؟", "tokens": [3555, 9957, 46811, 1829, 16095, 23032, 3555, 3615, 995, 4724, 28259, 6156, 5016, 9381, 34892, 16758, 3615, 19446, 31439, 3714, 29245, 23328, 34105, 5296, 33456, 3224, 2423, 293, 11933, 1829, 8592, 22807, 32330, 5296, 33456, 3224, 2423, 293, 12174, 32277, 5172, 12399, 800, 325, 1166, 6156, 9778, 1211, 9381, 8315, 12399, 11933, 15730, 28242, 30767, 29245, 3714, 29245, 23328, 9154, 16247, 25513, 27884, 4032, 20449, 4117, 41779, 3224, 3714, 29245, 23328, 11933, 15730, 6156, 3615, 15040, 33688, 15040, 28671, 307, 32330, 8807, 497, 307, 32330, 23758, 9673, 5172, 3224, 20498, 4724, 8592, 28820, 6225, 10943, 36145, 3224, 11933, 15730, 6024, 110, 29245, 49610, 3215, 47525, 13063, 15844, 20449, 4117, 41779, 3224, 37893, 3714, 29245, 23328, 16490, 1211, 33546, 12399, 3714, 16758, 16254, 8592, 5551, 25957, 1211, 11933, 8592, 1829, 12399, 46811, 10943, 22807], "avg_logprob": -0.2574626805622186, 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نشوف كمثال كيف نتعامل مع التعريفات بشكل عام", "tokens": [10721, 1829, 8608, 33604, 6027, 6156, 3224, 24192, 11203, 995, 28671, 21542, 38436, 28671, 13672, 1829, 39896, 9673, 11242, 45761, 5172, 9307, 16712, 1211, 9307, 3660, 11203, 995, 28671, 3714, 16095, 3660, 13672, 1829, 5296, 11296, 6055, 9566, 21292, 4587, 9307, 6225, 10943, 3660, 3714, 43020, 32748, 13063, 13672, 1829, 12174, 10943, 2655, 4724, 1829, 3224, 16712, 1211, 9307, 3660, 7251, 4587, 20498, 4724, 1829, 3224, 36632, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3555, 8978, 5551, 4587, 1863, 3615, 34105, 37279, 20292, 4587, 25894, 11296, 6156, 10721, 47341, 2407, 14739, 16247, 2304, 13063, 6055, 30544, 4032, 46958, 5016, 3660, 4032, 39319, 8315, 8717, 8592, 38688, 9122, 2304, 12984, 6027, 9122, 33911, 8717, 2655, 3615, 10943, 1211, 20449, 16712, 3615, 16572, 5172, 9307, 4724, 8592, 28820, 6225, 10943], "avg_logprob": -0.1583969445173977, "compression_ratio": 1.9866071428571428, "no_speech_prob": 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المطلوب", "probability": 0.9876708984375}], "temperature": 1.0}, {"id": 110, "seek": 260571, "start": 2576.15, "end": 2605.71, "text": "فزي ما انتوا شايفين المنهج واحد طبعا فيه اختلاف في التفاصيل فالمطلوب prove that جملة ايش ثنائية الشرطية فبدنا نعملها two parts prove اه فطبعا ممكن اكتب I will want او على طول مباشرة واحد للاتجاه الاول R is reflexive implies Delta X subset من ال R هذا المطلوب الجزء الاول من two parts prove", "tokens": [5172, 11622, 1829, 19446, 16472, 2655, 14407, 13412, 995, 33911, 9957, 9673, 1863, 3224, 7435, 36764, 24401, 23032, 3555, 3615, 995, 8978, 3224, 1975, 46456, 15040, 5172, 8978, 16712, 5172, 33546, 26895, 6156, 45340, 9566, 1211, 37746, 7081, 300, 10874, 2304, 37977, 1975, 1829, 8592, 38637, 1863, 16373, 10632, 25124, 2288, 9566, 10632, 6156, 44510, 8315, 8717, 25957, 1211, 11296, 732, 3166, 7081, 1975, 3224, 6156, 9566, 3555, 3615, 995, 3714, 43020, 1975, 4117, 2655, 3555, 286, 486, 528, 1975, 2407, 15844, 23032, 12610, 3714, 3555, 33599, 25720, 36764, 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على", "probability": 0.8955078125}, {"start": 2592.31, "end": 2592.51, "word": " طول", "probability": 0.990478515625}, {"start": 2592.51, "end": 2592.97, "word": " مباشرة", "probability": 0.95166015625}, {"start": 2592.97, "end": 2593.87, "word": " واحد", "probability": 0.925048828125}, {"start": 2593.87, "end": 2594.35, "word": " للاتجاه", "probability": 0.820068359375}, {"start": 2594.35, "end": 2594.81, "word": " الاول", "probability": 0.797607421875}, {"start": 2594.81, "end": 2596.13, "word": " R", "probability": 0.6904296875}, {"start": 2596.13, "end": 2596.81, "word": " is", "probability": 0.91064453125}, {"start": 2596.81, "end": 2598.39, "word": " reflexive", "probability": 0.98095703125}, {"start": 2598.39, "end": 2599.75, "word": " implies", "probability": 0.9033203125}, {"start": 2599.75, "end": 2600.69, "word": " Delta", "probability": 0.347412109375}, {"start": 2600.69, "end": 2601.17, "word": " X", "probability": 0.86767578125}, {"start": 2601.17, "end": 2602.09, "word": 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263427, "start": 2609.23, "end": 2634.27, "text": "فانا بحاول يعني أنوى شوية عشان لو شفته في كتاب ما تستغربوش كيف بكتبه هو نفس الأشياء لكن أحيانا طريقة التعبير بتختلف لكن كله بيصب في نفس القالب الحقيقة نفس الموضوع ممتاز جملة شرطية إيش هنعمل اشترض إن الشرط صحيح و اثبت جواب الشرط فقوله assume أولت نفس المعنى تستخدم مع نفس الاصطلاع assume R is reflexive", "tokens": [5172, 7649, 995, 4724, 5016, 995, 12610, 37495, 22653, 14739, 2407, 7578, 13412, 2407, 10632, 6225, 8592, 7649, 45164, 13412, 5172, 47395, 8978, 9122, 2655, 16758, 19446, 6055, 14851, 17082, 25513, 2407, 8592, 9122, 33911, 4724, 4117, 2655, 3555, 3224, 31439, 8717, 36178, 16247, 8592, 1829, 16606, 44381, 5551, 5016, 1829, 7649, 995, 23032, 16572, 28671, 16712, 3615, 3555, 13546, 39894, 46456, 46538, 44381, 28242, 3224, 4724, 1829, 9381, 3555, 8978, 8717, 36178, 25062, 6027, 3555, 21542, 38436, 28671, 8717, 36178, 9673, 2407, 11242, 45367, 3714, 2304, 2655, 31377, 10874, 2304, 37977, 13412, 2288, 9566, 10632, 11933, 1829, 8592, 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-0,0 +1,2423 @@ +1 +00:00:19,760 --> 00:00:23,420 +بسم الله الرحمن الرحيم اليوم إن شاء الله موضوعنا + +2 +00:00:23,420 --> 00:00:27,160 +اللي هو الأساسي اللي هو التكافؤ العددي للمجموعات + +3 +00:00:27,160 --> 00:00:30,560 +آه لكن في كان مثال أو proposition أخير في ال + +4 +00:00:30,560 --> 00:00:34,200 +section الماضي خمسة واحد خلينا نشوفه على السريع و + +5 +00:00:34,200 --> 00:00:37,180 +ننتقل ل section خمسة اثنين اللي بتحدث عن اللي هو + +6 +00:00:37,180 --> 00:00:41,540 +التكافؤ العددي للمجموعات فطبعا احنا كنا فيهن نظرية + +7 +00:00:41,540 --> 00:00:45,760 +أثبتنا أنه فيهن معيار للمجموعة أن تكون finite و + +8 +00:00:45,760 --> 00:00:49,910 +يمكن هذا يكون بديل للتعريف بتكون الـ X finite if + +9 +00:00:49,910 --> 00:00:53,230 +and only if يا تكون Phi يعني فيها Zero من العناصر + +10 +00:00:53,230 --> 00:00:56,790 +يا إما تكافئ N sub K أو فيه bijection بينها و + +11 +00:00:56,790 --> 00:00:59,050 +بينها ونصب K يعني فيها K من العناصر الـ K طبعا ما + +12 +00:00:59,050 --> 00:01:02,210 +زال K تنتمي للـ N يعني K أكبر أو تساوي صفر يا فيها Zero من + +13 +00:01:02,210 --> 00:01:05,070 +العناصر يا فيها واحد أو اثنين أو عشرة من العناصر و + +14 +00:01:05,070 --> 00:01:09,470 +هكذا آه طبعا متفقنا إذا ماكنتش Phi و كان فيها K من + +15 +00:01:09,470 --> 00:01:12,750 +العناصر بنرقم العناصر ممكن من X1 إلى XK فدي كانت + +16 +00:01:12,750 --> 00:01:15,670 +آخر ملاحظة حكيناها آه الحالة دلوقتي هنطبق على هذا + +17 +00:01:15,670 --> 00:01:18,980 +المفهوم إن شاء الله بالنسبة للـ proposition برضه مهم عندي + +18 +00:01:18,980 --> 00:01:22,960 +مجموعتين finite مجموعة فيها عشرة مجموعة فيها + +19 +00:01:22,960 --> 00:01:27,580 +عشرين الاتحاد تبعهم جدش بيكون فيه ثلاثين دائما، + +20 +00:01:27,580 --> 00:01:30,960 +أقل أو يساوي ثلاثين آه فلكن هو مش بشكل متمتم و + +21 +00:01:30,960 --> 00:01:33,740 +finite آه فهي العنوان تبع الـ proposition the + +22 +00:01:33,740 --> 00:01:39,750 +union of two finite sets is finite اتحاد مجموعتين + +23 +00:01:39,750 --> 00:01:43,410 +منتهيتين بتمه منتهى فطبعا نص الـ proposition بشكل + +24 +00:01:43,410 --> 00:01:49,510 +دقيق أو شكل صريح if A and B are finite sets then A + +25 +00:01:49,510 --> 00:01:54,750 +union B is finite خلينا نشوف البرهان مع بعض في هذا ال + +26 +00:01:54,750 --> 00:01:59,410 +proposition خمسة + +27 +00:01:59,410 --> 00:02:01,130 +ثلاثة will prove + +28 +00:02:03,840 --> 00:02:06,780 +طبعا زي ما شايفين اليوم شرطية فنبدأ نقول نفترض أن + +29 +00:02:06,780 --> 00:02:11,920 +الشرط صحيح Assume A + +30 +00:02:11,920 --> 00:02:22,140 +and B are finite sets فدول + +31 +00:02:22,140 --> 00:02:26,080 +مجموعتين finite بدنا نثبت أن الاتحاد finite + +32 +00:02:35,280 --> 00:02:43,520 +to prove that A union B is finite + +33 +00:02:47,460 --> 00:02:51,380 +فهذه البواطيات والمطلوب طبعا إيش معنى finite؟ يا + +34 +00:02:51,380 --> 00:02:53,560 +بده يستخدم التعريف هنا ليست infinite أو بده يستخدم + +35 +00:02:53,560 --> 00:02:57,900 +النظرية السابقة أثبت أنها يا Phi يا تكافئ أنصب K + +36 +00:02:57,900 --> 00:03:01,140 +من الـ K معينة تمام؟ آه طبعا زي الملاحظة اللي + +37 +00:03:01,140 --> 00:03:04,460 +حكيناها أنه لما ناخد الاتحاد مش دائما إذا فيه خمس + +38 +00:03:04,460 --> 00:03:07,800 +أو عشرة بيطلع 15 فبده ناخد بعض الاحتمالات في عين + +39 +00:03:07,800 --> 00:03:10,840 +الاعتبار لكن الفكرة الرئيسية احنا حكيناها لكن بدا + +40 +00:03:10,840 --> 00:03:14,930 +شوية تفصيلات عشان نشتغل صح طيب الـ M من المعطيات + +41 +00:03:14,930 --> 00:03:18,930 +الـ A finite في النظرية السابقة يا في يا تكافئ N + +42 +00:03:18,930 --> 00:03:22,490 +sub K فيها bijection بينها ونصب K والـ B برضه + +43 +00:03:22,490 --> 00:03:26,630 +finite إذا يا في يا تكافئ N sub M M + +44 +00:03:26,630 --> 00:03:28,710 +مختلفة مش لإنهم يكونوا نفس العناصر واحدة فيها + +45 +00:03:28,710 --> 00:03:31,170 +عشرة الثانية مترو كل عشر ربما يكون 15 لكنها + +46 +00:03:31,170 --> 00:03:34,210 +finite فبناخد دول احتمالات مع بعض ونشوف كيف + +47 +00:03:34,210 --> 00:03:38,070 +بدنا نشتغل فنبدأ الاحتمال الأول طبعا ماينفعش + +48 +00:03:38,070 --> 00:03:42,750 +أشتغلهم كلهم مع بعض لما يكونوا مجموعتين منفصلتين + +49 +00:03:42,750 --> 00:03:45,550 +مافيش بينهم تقاطع غير لما يكون فيه عناصر مشتركة + +50 +00:03:45,550 --> 00:03:48,270 +بيطلع العدد مختلف ولا لأ؟ لما يكونوا هكذا بدأنا + +51 +00:03:48,270 --> 00:03:50,370 +ناخد الاحتمالات دول كل واحدة على حتة نبدأ + +52 +00:03:50,370 --> 00:03:55,470 +بالاحتمالين الأسهل لو كانت واحدة فيهم Phi والـ B + +53 +00:03:55,470 --> 00:04:00,690 +لا تساوي Phi then أو إيش ما كانت الـ B بيكون الـ A + +54 +00:04:00,690 --> 00:04:04,090 +مش ضرورة مش قضية إيه اتحاد الـ B في هذه الحالة؟ + +55 +00:04:04,090 --> 00:04:07,810 +في ساوي؟ الـ B لأنه إيش مال الـ A finite وهذا شماله + +56 +00:04:07,810 --> 00:04:08,470 +finite + +57 +00:04:13,650 --> 00:04:18,190 +نستنتج على جهة خلصناه العكس هو يمكن أن نقضهم مع + +58 +00:04:18,190 --> 00:04:22,810 +بعض لو كانت الـ A ليست Phi والـ B هي اللي Phi برضه + +59 +00:04:22,810 --> 00:04:28,430 +الاتحاد بده يساوي A والـ A إيش مالها؟ finite كتبناها + +60 +00:04:28,430 --> 00:04:33,820 +في أول البرهان ممتاز فيه أيضا احتمال أنهم يكونوا + +61 +00:04:33,820 --> 00:04:36,540 +متساويين وليس اثنتين Phi أو متساويين أو حتى لو + +62 +00:04:36,540 --> 00:04:39,260 +كانوا متساويين وليس اثنتين Phi إيش بيكون اتحادهم + +63 +00:04:39,260 --> 00:04:42,060 +واحدة منهم لو كانوا كلهم متطابقين فهذه هناخدها مع + +64 +00:04:42,060 --> 00:04:47,960 +بعض if A تساوي B كانوا Phi أو مش Phi نفس نفس + +65 +00:04:47,960 --> 00:04:52,980 +القدرة then اتحادهم بيساوي نفسهم A union B يساوي A + +66 +00:04:52,980 --> 00:04:59,330 +يساوي B is final فدول أول احتمالات سهلة وبرهانهم + +67 +00:04:59,330 --> 00:05:02,590 +سهل أخدناهم على جهة لأنه بدأ يأخد الحالة الأخيرة + +68 +00:05:02,590 --> 00:05:05,390 +هي اللي بدها شغل الحالة الرابعة أو الأخيرة الآن + +69 +00:05:05,390 --> 00:05:09,790 +هناخد الحالة الأخيرة اللي هي إيش؟ أن الـ A لا تساوي + +70 +00:05:09,790 --> 00:05:13,110 +B ولا واحدة فيهم Phi ولا واحدة فيهم Phi الآن بدأش + +71 +00:05:13,110 --> 00:05:20,390 +يأخد الحالة الأخيرة assume A لا تساوي Phi B لا تساوي + +72 +00:05:20,390 --> 00:05:26,480 +Phi و A لا تساوي B لا تساوي 100 ناخد الحالة لهذه اللي + +73 +00:05:26,480 --> 00:05:30,380 +هي اللي بدها شغل ناخد الحالة اللي بدها شغل اللي هي + +74 +00:05:30,380 --> 00:05:34,260 +غير متساويين ولا واحدة فيهم فارغة فده واحدة فيها + +75 +00:05:34,260 --> 00:05:37,980 +عشرة والثاني إيش فيه؟ 15 فالاتحاد يكون أصغر + +76 +00:05:37,980 --> 00:05:41,700 +أو يساوي 25 نشوف كيف نعرف العدد بالظبط إنه + +77 +00:05:41,700 --> 00:05:46,120 +إيش بيساوي 15 و لا 25 و لا 24 هنعمل الـ trick + +78 +00:05:46,120 --> 00:05:49,740 +البسيط قبل هيك ممكن يكون ذكرته لكن هنشوف طبعا و + +79 +00:05:49,740 --> 00:05:53,920 +نكتشف يكون لو فيه خمسة وعشرة الاتحاد خمسة عشر لو كانت + +80 +00:05:53,920 --> 00:05:57,320 +قاطعة of five فهذا معناه فانا سؤالي الآن كيف أكتب + +81 +00:05:57,320 --> 00:06:02,140 +اتحاد مجموعتين على صورة اتحاد من مجموعتين منفصلتين + +82 +00:06:02,140 --> 00:06:06,260 +تقطعهم five و نسميهم six فيه trick بسيط ومشهور + +83 +00:06:06,260 --> 00:06:10,940 +أنا ذكرته لكن بأذكركم فيه مرتين هي عندي مجموعة A + +84 +00:06:11,500 --> 00:06:17,100 +وهي مجموعة B وهي A وهي B من الاتحاد اثنتين مع بعض + +85 +00:06:17,100 --> 00:06:24,520 +لو أخدت هي الـ A من الاتحاد مين تم من الاتحاد؟ B + +86 +00:06:24,520 --> 00:06:30,260 +ناقص A فإذا هنا هذه ملاحظة أنه we know that واتوقع + +87 +00:06:30,260 --> 00:06:36,160 +مرة عالية هي exercise أو لحظة we know that A union + +88 +00:06:36,160 --> 00:06:42,220 +B إيش بتساوي؟ A union B ناقص إيش؟ لأن هذه المنطقة + +89 +00:06:42,220 --> 00:06:46,060 +هي مين؟ B ناقص A اللي تم صح؟ واضحة ولا مش + +90 +00:06:46,060 --> 00:06:51,600 +واضحة؟ تم فهذا trick مشهور كيف أكتب اتحاد عام + +91 +00:06:51,600 --> 00:06:55,480 +اتحاد عشوائي على صورة disjoint union اتحاد من + +92 +00:06:55,480 --> 00:06:58,260 +مجموعتين منفصلتين فدائما هذا الـ trick اللي بينعمل + +93 +00:06:58,260 --> 00:07:01,000 +فهذا الـ trick اللي بينعمل ممتاز الآن بدنا نبدأ + +94 +00:07:01,000 --> 00:07:03,920 +نشتغل علم يعني كل هدفنا العناصر المشتركة ما نعدهاش + +95 +00:07:03,920 --> 00:07:08,520 +إلا مرة واحدة ما نعدهاش إلا مرة واحدة فهنشوف عملية + +96 +00:07:08,520 --> 00:07:17,980 +البرهان نبدأ الآن الـ B ناقص A هي subset من مين؟ من + +97 +00:07:17,980 --> 00:07:22,860 +الـ B و لا لأ؟ هي subset من الـ B والـ B finite إذن + +98 +00:07:22,860 --> 00:07:25,720 +هذه برضه finite نظرية خمسة واحد اللي أصغر من الـ + +99 +00:07:25,720 --> 00:07:34,360 +finite finite implies B ناقص A is finite طب هل + +100 +00:07:34,360 --> 00:07:41,110 +ممكن هذه تكون Phi؟ لأ لأنه قلت A لا تساوي B and B + +101 +00:07:41,110 --> 00:07:46,890 +ناقص A لا تساوي Phi ليش؟ لأن الـ A لا تساوي ممتاز + +102 +00:07:46,890 --> 00:07:51,250 +فإذا نصلنا عشان هيك احنا خدنا الحل هذه المجموعة اللي + +103 +00:07:51,250 --> 00:07:54,390 +بنشترط عليها يمين B ناقص A الآن بنركز عليها بدنا + +104 +00:07:54,390 --> 00:07:57,620 +نشترط شوية لأنه احنا عندنا معلومات عن الـ A تبعين + +105 +00:07:57,620 --> 00:08:00,220 +معايا يا إخوان؟ احنا الـ A عندنا معلومات لكن الـ B + +106 +00:08:00,220 --> 00:08:03,400 +ناقص A ما عندنا إيش؟ ما عندنا معلومات لكن هنشتق + +107 +00:08:03,400 --> 00:08:06,620 +المعلومات هنستنتج المعلومات بكل سهولة أولا الـ B + +108 +00:08:06,620 --> 00:08:09,420 +ناقص A هذا جزء من الـ B إذا هي subset من الـ finite + +109 +00:08:09,420 --> 00:08:12,660 +فاينيت طب الـ finite إيش الاحتمالية؟ يا في يا + +110 +00:08:12,660 --> 00:08:16,760 +تكافئ N sub K طب هي ممكن تكون Phi؟ مستحيل مزال مش مش + +111 +00:08:16,760 --> 00:08:22,500 +في تكون تكافئ N sub K for some K فإذا بس + +112 +00:08:23,850 --> 00:08:29,490 +ب ماذا يعني تكافئ N sub k؟ بقدر أرقم العناصر على صورة B + +113 +00:08:29,490 --> 00:08:33,730 +واحد B K B + +114 +00:08:33,730 --> 00:08:44,960 +واحد B اثنين B K B ناقص إيش؟ B ناقص ممتاز فإذا + +115 +00:08:44,960 --> 00:08:48,380 +أنا دول العناصر اللي هنا إيش هرقمهم؟ B واحد B + +116 +00:08:48,380 --> 00:08:52,540 +اثنين B جدش ومعاشرة فـ B واحد لـ B عشرة الآن بنفس + +117 +00:08:52,540 --> 00:08:56,400 +الاسلوب برضه الـ A مش Phi و finite إذا برضه بقدر + +118 +00:08:56,400 --> 00:09:02,720 +أرقم عناصرها similarly A + +119 +00:09:02,720 --> 00:09:12,320 +لا تساوي Phi is finite implies A تساوي A واحد A + +120 +00:09:12,320 --> 00:09:19,970 +اثنين A جدش لأ عشرة وعشرة ليه؟ m for some عدد + +121 +00:09:19,970 --> 00:09:23,490 +حقيقي عدد صحيح m صح واحدة فيها عشرة واحدة فيها + +122 +00:09:23,490 --> 00:09:27,300 +عشرين واحدة فيها خمسة واحدة فيها خمسة عشر مش عادة بس + +123 +00:09:27,300 --> 00:09:30,440 +رقمناه فإذا احنا هنا إيش استخدمنا؟ استخدمنا + +124 +00:09:30,440 --> 00:09:35,140 +النظرية السابقة مع الملاحظة بقدر أرقمهم إيش معناه + +125 +00:09:35,140 --> 00:09:39,140 +تقعد الكلام؟ الآن بدنا إيش؟ نعمل اتحاد الاتحاد + +126 +00:09:39,140 --> 00:09:42,920 +هيتكون من هدول مع هدول فيه عصر مشترك بينهم؟ لأ + +127 +00:09:42,920 --> 00:09:46,580 +جدش هيكون عدد العناصر؟ K زائد m أحسنته + +128 +00:09:46,580 --> 00:09:54,600 +فبنثبت أنه هادي finite فبتكافئ N sub K خلينا نكتب + +129 +00:09:54,600 --> 00:10:03,520 +We will prove that there + +130 +00:10:03,520 --> 00:10:11,620 +is a bisection F + +131 +00:10:11,620 --> 00:10:18,800 +من A union B ليش بتساوي N sub K بس بعد الصورة طبعا تكتب + +132 +00:10:18,800 --> 00:10:23,920 +اختصارا متابعين معاه؟ آه هي نفسها لمين؟ لمين ضايق + +133 +00:10:23,920 --> 00:10:29,660 +أنك متابعينه؟ مثل N sub m K زي N sub m يعني عدد العدد + +134 +00:10:29,660 --> 00:10:34,960 +الصغير K زي N تمام بدناش نلاقي bijection نشوف كيف + +135 +00:10:34,960 --> 00:10:39,960 +نكتب الـ bijection سهل جدا الـ bijection وفكرته من + +136 +00:10:39,960 --> 00:10:45,350 +وين؟ كيف بتعلم الولد الصغير عملية العد؟ وبتتذكروا + +137 +00:10:45,350 --> 00:10:48,950 +اللي له أخ أو له أخت أو قريب أو من أخيه الصغير + +138 +00:10:48,950 --> 00:10:52,230 +بتعلم العد؟ إيش بيقولوا له؟ بيقولوا هاي مجموعة فيها + +139 +00:10:52,230 --> 00:10:56,190 +أربع تفاحات وهي مجموعة فيها ثلاث تفاحات فإذا أربع زائد + +140 +00:10:56,190 --> 00:10:58,690 +الثلاث إيش بيساوي؟ بيقولوا هاي واحد اثنين ثلاث + +141 +00:10:58,690 --> 00:11:02,710 +أربع، خلاص بتعد المجموعة الثانية بتبدأ تعد من وين؟ + +142 +00:11:02,710 --> 00:11:06,010 +خمسة، ستة، سبعة فإيه اللي هنعمله؟ واضحة؟ هاي + +143 +00:11:06,010 --> 00:11:08,810 +الفكرة كيف نطبق على هذا المثال؟ هاي عندنا + +144 +00:11:08,810 --> 00:11:14,910 +مجموعتين، هاي مجموعة وهاي مجموعة، هنبدأ نعدّ لهنّ؟ K + +145 +00:11:14,910 --> 00:11:20,150 +K plus one K plus two K plus one واضحة؟ + +146 +00:11:44,940 --> 00:12:00,140 +F من A union B إلى M sub K plus M sub B given by F of + +147 +00:12:00,140 --> 00:12:06,040 +X تساوي نرجع للمثال، ليش عملنا؟ لما كنا ناخذ من P + +148 +00:12:06,040 --> 00:12:10,860 +نقول P1 كأيش رقمها؟ واحد P2 كبنا عدّت اثنين فهنقول + +149 +00:12:10,860 --> 00:12:15,480 +لهذه بتساوي J اللي هو الرقم إذا كانت ال X بتساوي + +150 +00:12:15,480 --> 00:12:20,960 +PJ، مصبوخ؟ P1 إيش رقمها؟ واحد P2 إيش رقمها؟ اثنين + +151 +00:12:20,960 --> 00:12:26,300 +PK إيش رقمها؟ K طيب الآن A1 إيش رقمها؟ K plus واحد + +152 +00:12:26,300 --> 00:12:28,080 +طب إذا ب AJ إيش رقمها؟ + +153 +00:12:33,030 --> 00:12:36,490 +واضحة ولا مش واضحة؟ من هنا، من وين بدي أعدّ؟ أيه + +154 +00:12:36,490 --> 00:12:39,910 +واحد، إيش رقمها؟ k plus one أيه خمسة، إيش رقمها؟ k + +155 +00:12:39,910 --> 00:12:44,430 +plus خمسة لأن K خلصت في الأول، خلصت أعدّ، هي عشرة، + +156 +00:12:44,430 --> 00:12:46,550 +بعدين بدي أعدّ إحداث، لما تحط إيديك أول مرة + +157 +00:12:46,550 --> 00:12:49,390 +تستخدمهم، مظبوط، فدهي، طبعًا هذي one to one and onto + +158 +00:12:49,390 --> 00:12:58,790 +to two exercise عبايدك، + +159 +00:12:58,790 --> 00:12:59,690 +و هذا exercise + +160 +00:13:02,330 --> 00:13:06,610 +ففكرة مباشرة وهذه هي فكرة اللي بتتعلمها في ابتدائي + +161 +00:13:06,610 --> 00:13:11,690 +و بيحطوها بس بلغة أبسط لا يساعد فهذه إذا أي فتوفة + +162 +00:13:11,690 --> 00:13:14,630 +يناجست اتحادهم تكون final فاحنا حلقين .. غطينا كلّ + +163 +00:13:14,630 --> 00:13:20,730 +احتمالات .. بيكون هيك خلصنا ودا نهاية ال .. أي + +164 +00:13:20,730 --> 00:13:26,170 +استفسار؟ أي سؤال؟ ففكرة بسيطة ونشوف احنا كيف طبعًا + +165 +00:13:26,170 --> 00:13:29,230 +زي إن كنت بدأنا في عندي عدة أمثلة الآن إنك صار + +166 +00:13:29,230 --> 00:13:32,810 +الأمور متقدمة شوية كده بنكون الدوال اتعلمنا إنه + +167 +00:13:32,810 --> 00:13:35,750 +كان في صعوبة في البداية لأنه لسه كان أول مرة + +168 +00:13:35,750 --> 00:13:39,710 +بنتعامل لكن شفنا بعض الـ tricks بعض الملاحظات بعض + +169 +00:13:39,710 --> 00:13:43,450 +الإرشادات بدأت خزينتنا أو إيه اللي خلفية تبعتنا + +170 +00:13:43,450 --> 00:13:46,410 +تزداد عنها صار أمثلة ومتعددة وممكن نفيد منها و + +171 +00:13:46,410 --> 00:13:50,930 +نقلّدها ونقلّتها نشوف مين المثال بيناسب شغلنا نعمله + +172 +00:13:50,930 --> 00:13:54,290 +كمان مرة أحيانًا ممكن ما ينطبقش تمامًا بحتاج بعض + +173 +00:13:54,290 --> 00:13:56,970 +التعليق لكن بدينا أفكار من وين نبدأ كيف نشتغل + +174 +00:13:56,970 --> 00:13:59,250 +وطبعًا ممكن يكون فيه تطابق وممكن يكون فيه تعديل + +175 +00:13:59,250 --> 00:14:03,990 +بسيط فالي هي طريقة في التعليق الآن ننتقل للـ + +176 +00:14:03,990 --> 00:14:08,890 +section 5-2 هيتحدث عن موضوع بيتطبّق في الموضوع + +177 +00:14:08,890 --> 00:14:12,650 +الماضي وبرضه هذا هيقوي معرفتنا ويمكن يدّينا + +178 +00:14:12,650 --> 00:14:16,870 +زاوية أخرى للنظر تساعدنا .. تساعدنا في العمل طبعًا + +179 +00:14:16,870 --> 00:14:22,080 +مع زاوية أخرى العنوان equipotence of sets طبعًا + +180 +00:14:22,080 --> 00:14:28,280 +equipotence مصطلح جاي من المقطع equality تساوي + +181 +00:14:28,280 --> 00:14:30,400 +.. تساوي .. تساوي .. تساوي .. تساوي .. تساوي .. + +182 +00:14:30,400 --> 00:14:31,080 +تساوي .. تساوي .. تساوي .. تساوي .. تساوي .. تساوي + +183 +00:14:31,080 --> 00:14:31,560 +.. تساوي .. تساوي .. تساوي .. تساوي .. تساوي .. + +184 +00:14:31,560 --> 00:14:35,300 +تساوي .. تساوي .. تساوي .. تساوي .. تساوي .. تساوي + +185 +00:14:35,300 --> 00:14:39,280 +.. تساوي .. تساوي .. تساوي .. تساوي .. تساوي .. + +186 +00:14:39,280 --> 00:14:43,260 +تساوي .. تساوي وقاعة فيها أربعين مقعد فهدولة + +187 +00:14:43,260 --> 00:14:46,040 +بنفعوا يقعدوا على هدولة بنفعوا القاعة بتتسع فهذا + +188 +00:14:46,040 --> 00:14:49,740 +تكافؤ بقول إن عدد مقاعد القاعة يكافئ على الطالبات + +189 +00:14:49,740 --> 00:14:52,240 +المجموعة إذا هدول مجموعتين متكافئتين لما ييجوا + +190 +00:14:52,240 --> 00:14:54,540 +الطالبات يدخلوا في القاع القاع بتكافئهم فهذا + +191 +00:14:54,540 --> 00:14:56,840 +التكافؤ العددي فعشان هيك في ناس بيحطوا مصطلح + +192 +00:14:56,840 --> 00:15:01,460 +numerically equivalent sets المجموعات المتكافئة + +193 +00:15:01,460 --> 00:15:05,260 +عدديًا equivalent sets المجموعات المتكافئة عدديًا + +194 +00:15:05,260 --> 00:15:08,800 +مش متساوية لأنه هد مجموع الطالبات وهد قاعة فيها + +195 +00:15:08,800 --> 00:15:13,850 +كراسي هدول نفس المجمل، فواضح؟ فبننظر علشان بيهمنا + +196 +00:15:13,850 --> 00:15:16,950 +إيش بيهمنا بالمجموعة، العدد تبعها، إيش نوع العناصر + +197 +00:15:16,950 --> 00:15:19,790 +بيهمنا ه، فأقول المجموعتين، فيها أربعين، أربعين + +198 +00:15:19,790 --> 00:15:23,330 +كرسي، فيها أربعين طالبة، فيها أربعين تفاحة، المهمّ + +199 +00:15:23,330 --> 00:15:28,460 +بالمين عدد العناصر، فحننظر من هذا الزمن تمام فأنا + +200 +00:15:28,460 --> 00:15:32,420 +طبعًا كمقدمة بقول لي two finite sets X and Y have + +201 +00:15:32,420 --> 00:15:35,600 +the same number of elements if and only if there + +202 +00:15:35,600 --> 00:15:38,240 +is a bijection F احنا اللي بتاوي حاكيناها ده اللي + +203 +00:15:38,240 --> 00:15:43,960 +تلعب ليش بقول إن المجموعة اللي فيها أربعين طالبة و + +204 +00:15:43,960 --> 00:15:47,540 +القاعة اللي فيها أربعين مقعد متكافئين لأن كل مقعد + +205 +00:15:47,540 --> 00:15:50,680 +.. كل طالبة لها مقعد فهي فيه تناظر هي عملية العدّ + +206 +00:15:50,680 --> 00:15:53,560 +ليش أنا بقول هذا العنصر الأول إذا هذا بقابل لعدد + +207 +00:15:53,560 --> 00:15:56,840 +واحد في الأعداد الطبيعية هذا العنصر رقم اثنين يعني + +208 +00:15:56,840 --> 00:15:59,740 +بقابل لعدد رقم اثنين فهذه عملية بقدر ألاقي تناظر + +209 +00:15:59,740 --> 00:16:02,380 +هذا اللي بقدر أكافئ ليش هدول أربعين وهدول أربعين + +210 +00:16:02,380 --> 00:16:06,320 +يعني فيه تناظر في هذا المقعد للطالبة فاطمة هذا + +211 +00:16:06,320 --> 00:16:09,540 +المقعد لعائشة هذا لخديجة هي التناظر فإذا هذه عملية + +212 +00:16:09,540 --> 00:16:13,280 +العدّ فلما أقول إنهم متكافئين عدديًا لكل عنصر + +213 +00:16:13,280 --> 00:16:16,710 +يقابل عنصر والعكس صحيح تناظر واحد لواحد فهذه + +214 +00:16:16,710 --> 00:16:18,970 +الطريقة اللي أنت عاملها مع العدد طب ليش ما يقولوا + +215 +00:16:18,970 --> 00:16:21,970 +ليش هذه فيها عشرة وهذه فيها عشرة لأن عشرة تنطبق مع + +216 +00:16:21,970 --> 00:16:25,070 +الـ finite لو كانت infinite طب هذي فيها infinite و + +217 +00:16:25,070 --> 00:16:27,310 +هذي فيها infinite كيف بدأ أقارن الـ infinite مع الـ + +218 +00:16:27,310 --> 00:16:32,230 +infinite ما ينفعش فهذا هو الطريقة الصحيحة اللي بتنفع + +219 +00:16:32,230 --> 00:16:36,900 +تنطبق على الـ finite وعلى الـ infinites فطبعًا .. لأن + +220 +00:16:36,900 --> 00:16:40,620 +هنا بقول لأ رغم أن كلمة اللي هو the same number + +221 +00:16:40,620 --> 00:16:43,120 +ما تطبقش مع الـ infinity وبعدين هنشوف إن مجموعها + +222 +00:16:43,120 --> 00:16:46,380 +infinite ومجموعها infinite لكن مختلفين، ما يكفيش + +223 +00:16:46,380 --> 00:16:49,620 +بعض، فإذا ناقش عملية اللي هو العدد مش .. مش .. مش + +224 +00:16:49,620 --> 00:16:54,920 +مناسبة كتعريف، آه فبقول لي does not apply when X + +225 +00:16:54,920 --> 00:16:58,520 +and Y are infinite sets it seems natural يبدو يعني + +226 +00:16:58,520 --> 00:17:01,140 +العلماء هم بيفكروا لقوا إنه من الطبيعي كلمة + +227 +00:17:01,140 --> 00:17:04,500 +التناظر one to one هي التعريف المناسب عشان أخارن + +228 +00:17:04,500 --> 00:17:08,240 +بين مجموعتين وفعلا نجحوا وحطوا التعريف اللي هنشوفه + +229 +00:17:08,240 --> 00:17:11,800 +بعد قليل two infinite sets that are in one to one + +230 +00:17:11,800 --> 00:17:16,040 +correspondence have or are of the same size ممكن + +231 +00:17:16,040 --> 00:17:20,460 +أقول إن عددهم متساوي أو لهم نفس الحجم الحقيقي عدد + +232 +00:17:20,460 --> 00:17:24,790 +العدد ففي عندنا التعريف التالي في عندنا التعريف + +233 +00:17:24,790 --> 00:17:28,030 +التالي، إذا عشان أقارن بين مجموعتين من حيث العدد، + +234 +00:17:28,030 --> 00:17:30,630 +واكتشف بيكونوا متكافئتين عدديًا، إذا قدرت ألاجد + +235 +00:17:30,630 --> 00:17:34,670 +بينهم تناظر واحد لواحد، اللي هو إيش؟ Bijection Two + +236 +00:17:34,670 --> 00:17:39,350 +sets X and Y are said to be equipotent يعني + +237 +00:17:39,350 --> 00:17:43,350 +متكافئتين عدديًا، denoted by إيش الرمز؟ كالعادة، + +238 +00:17:43,350 --> 00:17:47,030 +شوفوا احنا، مبادئ مبادئ، في مفهوم تكافؤ المجموعات + +239 +00:17:47,030 --> 00:17:53,540 +عدديًا، إيش الرمز سببه؟ X تكافئ Y عدديًا زي إشارة + +240 +00:17:53,540 --> 00:17:56,840 +النفي بس طبعًا واضحة من الصياغ لما .. مش الـ + +241 +00:17:56,840 --> 00:18:00,460 +statement عشان أقول إن دي يساوي وإن دي تكافئ زي + +242 +00:18:00,460 --> 00:18:03,420 +ما أحط الـ bride لما أحط الـ bride مع الدالة تفاضل + +243 +00:18:03,420 --> 00:18:06,940 +لما أحطها على مجموعة مكملة فالصياغ بيوضع فده هو + +244 +00:18:06,940 --> 00:18:10,100 +الرمز فده ليش المفهوم؟ إيش المصطلح؟ Equipotence + +245 +00:18:10,100 --> 00:18:13,640 +تكافؤ المجموعة العددية إيش رمزه؟ هاي الرمز تبعه + +246 +00:18:13,640 --> 00:18:17,660 +إيش تعريفه؟ بقول إيه؟ if there is إيش؟ if there + +247 +00:18:17,660 --> 00:18:20,490 +exists أو there is نفس المعنى a bijection فإذا أنا + +248 +00:18:20,490 --> 00:18:29,810 +بقول الـ X تكافئ الـ Y there exists a bijection f + +249 +00:18:29,810 --> 00:18:36,670 +من X إلى Y فده هو التعريف هي الرمز وهي التعريف واضح؟ + +250 +00:18:36,670 --> 00:18:41,580 +أي استفسار؟ تمام، هنبدأ نشوف بعض الأمثلة البسيطة و + +251 +00:18:41,580 --> 00:18:44,860 +نؤكد على التعريف وبعدين نطور حالنا لأنه الآن برضه + +252 +00:18:44,860 --> 00:18:48,760 +تقريبًا بنفس الدائرة لو جالي أثبت إنه مجموعتين + +253 +00:18:48,760 --> 00:18:51,640 +متكافئتين عدديًا، إيش مطلب مني؟ ألاقي a bijection + +254 +00:18:51,640 --> 00:18:55,400 +بينهم الـ infinite دالة من مجموعة على نفسها، هنا + +255 +00:18:55,400 --> 00:18:58,240 +مجموعتين مختلفتين وتكون one to one وليست onto، + +256 +00:18:58,240 --> 00:19:01,000 +بس كان one to one وليست onto، الآن بدي دالة بين + +257 +00:19:01,000 --> 00:19:04,740 +مجموعتين مختلفتين one to one و onto فتقريبًا بننظر + +258 +00:19:04,740 --> 00:19:10,140 +بنفس الدائرة بس مع اختلاف نبدأ بمثال بسيط جدًا عشان + +259 +00:19:10,140 --> 00:19:13,920 +بس نقلّش نثبت المفهوم، نثبت المفهوم، وين احنا + +260 +00:19:13,920 --> 00:19:19,440 +وصلنا؟ وصلنا هنا، تمام؟ + +261 +00:19:19,440 --> 00:19:24,120 +فإذا هذا التعليق باختصار، ونشوف المثال الأول، هو + +262 +00:19:24,120 --> 00:19:28,930 +يبقى مثال بسيط طبعًا فيها دي مجموعتين الـ X تساوي + +263 +00:19:28,930 --> 00:19:33,610 +واحد اثنين ثلاثة والـ Y تساوي عدد الـ pi وعدد جزر + +264 +00:19:33,610 --> 00:19:37,850 +الخمسة والعدد e هدول كلهم عدد حقيقية إيش بيميزهم؟ + +265 +00:19:37,850 --> 00:19:41,930 +كلهم غير نسبية آه كلهم عدد غير نسبي لا الـ pi نسبي + +266 +00:19:41,930 --> 00:19:45,470 +ولا جزر الخمسة نسبي ولا الـ e نسبي اللي هي 2.7 والـ + +267 +00:19:45,470 --> 00:19:48,090 +pi ثلاثة point واحد كذا كذا وجزر الخمسة بيساوي + +268 +00:19:48,090 --> 00:19:51,150 +اثنين كثر كلهم ولا عدد فيهم مقدر أحطه على صورة بس + +269 +00:19:51,150 --> 00:19:54,310 +ط ومقامه كله عدد غير نسبي هذه المجموعة كافية؟ هذه + +270 +00:19:54,310 --> 00:19:57,830 +المجموعة عدديًا ولا لأ؟ واضح ثلاثة وثلاثة طيب لو + +271 +00:19:57,830 --> 00:20:00,770 +قلت بدنا نجيب .. بدنا دالة من هالهال تكون one to + +272 +00:20:00,770 --> 00:20:04,110 +one and onto فعنا هنا الـ X فاكروا مع بعض + +273 +00:20:04,110 --> 00:20:07,810 +عملوها اكتبوا السؤال بشكل مختلف هو Y تساوي مين؟ الـ + +274 +00:20:07,810 --> 00:20:12,290 +pi والجزر الخمسة والـ e آه فانا بدأ بالده الحلّ + +275 +00:20:12,290 --> 00:20:14,810 +كيف بدأ أتبيّن إن هدول متكافئة في إيه هنا؟ بدأ يعرف + +276 +00:20:14,810 --> 00:20:17,450 +دالة من X إلى Y تكون one to one and onto كيف + +277 +00:20:17,450 --> 00:20:22,720 +بدأ يعرف .. كيف بدأ بدأ السؤال؟ let F من X إلى Y be + +278 +00:20:22,720 --> 00:20:27,100 +given by أحسنتوا جيدًا by طبعًا هذه دالة عدد عناصر + +279 +00:20:27,100 --> 00:20:30,060 +محدود دلوقت ده قاعد ولا ممكن ندّي كل عنصر وش صوته + +280 +00:20:30,060 --> 00:20:39,120 +ممكن مين عندها مثال أو عندها حل اختراع أعرفولي + +281 +00:20:39,120 --> 00:20:42,280 +الدالة بدي الدالة سهلة جدا إيش بدنا نعرفها عفواً في + +282 +00:20:42,280 --> 00:20:43,060 +واحد إيش بدنا نعرفها + +283 +00:20:52,100 --> 00:20:55,380 +خلصنا فعدي ده اللي اتعرفت ولا ما اتعرفتش فعرفت كل + +284 +00:20:55,380 --> 00:20:58,900 +عناصر الـ domain وكل عنصر له صورة ده لـ one to one + +285 +00:20:58,900 --> 00:21:01,700 +ولا مش one to one لإنه ما فيش عنصر راح له صورتين + +286 +00:21:01,700 --> 00:21:04,180 +انتوا ولا مش انتوا انتوا هطلنا كل الـ domain بدي + +287 +00:21:04,180 --> 00:21:13,190 +إثبات ولا خلص خلص then f is a bijection طبعاً واضح، بس + +288 +00:21:13,190 --> 00:21:15,330 +هنا بس أنا عايش فهذه مقدمة كانت مثالها البسيط، بس + +289 +00:21:15,330 --> 00:21:18,070 +إيش الفكرة؟ فواضح ليش هذه التناظر؟ هذه مجموعة + +290 +00:21:18,070 --> 00:21:20,770 +متساوي المجموعة؟ لأ، ولا subset منها، لكنهم + +291 +00:21:20,770 --> 00:21:23,610 +متكافئتين، فيها تلت عناصر وفيها تلت عناصر، فنبدأ + +292 +00:21:23,610 --> 00:21:29,550 +بالمثال البسيط هذا، تمام، نظرية + +293 +00:21:38,830 --> 00:21:43,350 +عملية التكافؤ العددي، هذه علاقة، أنا عندي + +294 +00:21:43,350 --> 00:21:46,590 +مجموعتين، ممكن أقول مجموعة تساوي مجموعة، علاقة + +295 +00:21:46,590 --> 00:21:50,430 +التساوي أو ممكن أقول تساوي تكافؤها عددي، هذه + +296 +00:21:50,430 --> 00:21:56,220 +علاقة، كعلاقة، هل هي علاقة تكافؤ ولا لا؟ بدنا نشوف + +297 +00:21:56,220 --> 00:21:59,320 +النظرية بتقول نعم هي علاقة تكافؤ، يعني هذه العلاقة + +298 +00:21:59,320 --> 00:22:03,580 +هي علاقة اللي هو reflexive, symmetric, و transitive + +299 +00:22:03,580 --> 00:22:07,400 +فبقول لو أخدت مجموعة تشوف النظرية let S be a non + +300 +00:22:07,400 --> 00:22:11,200 +-empty collection of non-empty sets هي علاقة مع من + +301 +00:22:11,200 --> 00:22:15,040 +معرفها، إيش عدسرها؟ مجموعات، إذا إيش بدي أخد؟ بدي + +302 +00:22:15,040 --> 00:22:18,320 +أعرف علاقة على مجموعة من المجموعات فالمجموعة + +303 +00:22:18,320 --> 00:22:22,240 +الكبيرة هي S إيش عناصرها؟ مجموعات إيش بدي أدرس؟ + +304 +00:22:22,240 --> 00:22:25,320 +بدي أدرس علاقة المجموعات هذه لجوه الـ S هل هي + +305 +00:22:25,320 --> 00:22:30,580 +متكافئة عددياً ولا لا؟ متكافئة عددياً ولا لا؟ بقول + +306 +00:22:30,580 --> 00:22:35,900 +define a relation R on S مجموعة المجموعات X, Y في الـ + +307 +00:22:35,900 --> 00:22:39,340 +R و أنا عديتهم رمز كبير X و Y ليش؟ عشان هم مجموعات + +308 +00:22:39,340 --> 00:22:43,640 +عشان العناصر هنا مجموعات لأن الـ S مجموعة مجموعات if + +309 +00:22:43,640 --> 00:22:47,820 +and only if X تكافئ Y عددياً، هذه العلاقة بقول هذول + +310 +00:22:47,820 --> 00:22:51,600 +ألهم علاقة مع بعض إذا كانوا متكافئين عددياً يعني + +311 +00:22:51,600 --> 00:22:55,020 +هذه المجموعة هذول أشمالهم تمتكافئين بصبوط إذا + +312 +00:22:55,020 --> 00:22:59,320 +بنتموا لمين للأرض بعد و هكذا بقول لي then إيش + +313 +00:22:59,320 --> 00:23:01,520 +النتيجة؟ إيش النظر اللي بتقول؟ R is an equivalence + +314 +00:23:01,520 --> 00:23:06,500 +relation ليه؟ هذه العلاقة reflexive, symmetric, و transitive و + +315 +00:23:06,500 --> 00:23:13,820 +transitive فهذه نظرية خمسة خمسة طب ليش بتنهار + +316 +00:23:13,820 --> 00:23:21,060 +reflexive, symmetric, و transitive أول شيء إيش معناها؟ + +317 +00:23:21,060 --> 00:23:24,780 +reflexive أرجعلكوا عشان الـ quiz يعني كل مجموعة + +318 +00:23:24,780 --> 00:23:27,680 +اللي علاقة مع نفسها كل عنصر اللي هو مجموعة كل X + +319 +00:23:27,680 --> 00:23:31,220 +تكافئ نفسها عددياً واضحة ولا مش واضحة طب لو قلتلك + +320 +00:23:31,220 --> 00:23:34,820 +أعطيني بيجيبشن بين X و بين نفسهامين عنده + +321 +00:23:34,820 --> 00:23:38,320 +bijection بين مجموعة نفسها؟ اخلطوا مش مشكلة + +322 +00:23:38,320 --> 00:23:41,700 +اتعلموا احكوا احكوا إيش هي؟ بدي دالة بدي bijection + +323 +00:23:41,700 --> 00:23:45,760 +من X لـ X الـ identity الـ identity صحيح فهي خلصنا + +324 +00:23:45,760 --> 00:23:49,440 +أثبتنا أننا نفلكسها فخلصنا؟ طب هي symmetric لو + +325 +00:23:49,440 --> 00:23:52,980 +قلنا إن الـ X تكافئ الـ Y إيش معناه؟ في bijection من + +326 +00:23:52,980 --> 00:23:57,720 +X لـ Y طب كيف ده تصير من Y لـ X؟ G inverse فهي صارت + +327 +00:23:57,720 --> 00:24:02,420 +إيش؟ أثبتها إيش تم نثبت؟ إنها transitive X تكافئ الـ Y + +328 +00:24:02,420 --> 00:24:06,040 +يعني فيه bijection من X لـ Y و Y تكافئ الـ Z يعني + +329 +00:24:06,040 --> 00:24:09,840 +فيه bijection من Y لـ Z مين بدي bijection من X لـ Z؟ + +330 +00:24:09,840 --> 00:24:14,740 +إيش أعمل؟ composition .. composition .. أه فعلاً + +331 +00:24:14,740 --> 00:24:17,200 +شرحتوا ليها الـ exercise تكتبوها في البيت الـ proof + +332 +00:24:17,200 --> 00:24:26,140 +exercise حدثوا ليها شوفوا عليكم تكتبوا notation + +333 +00:24:26,140 --> 00:24:33,100 +أه طبعاً كالعادة منحبش نكتب كتير في رياضيات فالآن + +334 +00:24:33,100 --> 00:24:36,680 +احنا هنتعامل مع bijection بشكل كثير لأن التعريف + +335 +00:24:36,680 --> 00:24:39,360 +اعتمد على bijection فبعد ما اكتب there exists a + +336 +00:24:39,360 --> 00:24:43,600 +bijection F from X to Y إيش بده أكتب هنا؟ there + +337 +00:24:43,600 --> 00:24:48,600 +exists F من X بده يساهمش لحطوة كلمة bijection بده + +338 +00:24:48,600 --> 00:24:52,840 +يختصرها فبكتب إن كل دالة بيحط سهم كل احنا اتفقنا + +339 +00:24:52,840 --> 00:24:58,100 +الدالة بنحط اسم الدالة نقطتين فوق بعض الـ domain سهم + +340 +00:24:58,100 --> 00:25:01,980 +الـ codomain طيب لو كانت bijection بنحط بدل السهم + +341 +00:25:01,980 --> 00:25:04,520 +بنحطها ده معناه إنك تشوف هنا يوجد دالة من X لـ Y + +342 +00:25:04,520 --> 00:25:08,180 +وهي one to one and onto اختصار فده رمز هنستخدمه + +343 +00:25:08,180 --> 00:25:12,920 +رمز هنستخدمه نشوف أمثلة + +344 +00:25:21,160 --> 00:25:29,060 +المثال الأول بدنا نثبت إنه الفترة من واحد لاتنين + +345 +00:25:29,060 --> 00:25:35,040 +تكافئ الفترة من zero لاتنين إيش الفترات هدول هم + +346 +00:25:35,040 --> 00:25:38,280 +مجموعات من الأعداد الحقيقية يعني إيش الفترة من + +347 +00:25:38,280 --> 00:25:41,320 +واحد لاتنين كل الأعداد الحقيقية اللي أكبر من واحد + +348 +00:25:41,320 --> 00:25:43,960 +وأصغر من اتنين واللي من صفر لاتنين نفس الشيء اللي + +349 +00:25:43,960 --> 00:25:46,860 +أكبر من صفر وأصغر من اتنين فأنا بدنا نثبت إن هدول + +350 +00:25:46,860 --> 00:25:53,060 +المجموعتين متكافئتين فهذا المثال الأول طبعاً أنا في + +351 +00:25:53,060 --> 00:25:57,480 +عندي هي حط الأعداد هي الصفر وهي الواحد وهي الاتنين + +352 +00:25:57,480 --> 00:26:01,980 +المجموعة الأولى اللي هنا من صفر من واحد لاتنين + +353 +00:26:01,980 --> 00:26:10,200 +والتانية من وين من صفر لاتنين طبعاً + +354 +00:26:10,200 --> 00:26:12,300 +أنا ممكن البعض الناس يقول إيه غريبة طبعاً دي جداً + +355 +00:26:12,300 --> 00:26:17,970 +مرتين لأ عدد عناصرهم متساوي عدد عناصرهم متساوي بدنا + +356 +00:26:17,970 --> 00:26:22,510 +نثبت إنهم فعلاً كعدد عناصر متكافئتين مجموعتين + +357 +00:26:22,510 --> 00:26:28,610 +مختلفتين ظاهرياً واحدة ضعف الثانية لكنهم في الحقيقة + +358 +00:26:28,610 --> 00:26:32,550 +عدد عناصرهم واحد طبعاً هذا عشان هم الفنانين فلنثبت + +359 +00:26:32,550 --> 00:26:37,290 +إنهم متكافئتين فالآن إيش بدنا بدنا bijection من 1 + +360 +00:26:37,290 --> 00:26:39,950 +,2 لـ 0,2 هي حتى الآن هي النظرية الوحيدة اللي + +361 +00:26:39,950 --> 00:26:42,890 +معناها أو هو التعريف أسئلة معناها نظرية فإذا هنا + +362 +00:26:42,890 --> 00:26:56,170 +we have to find f من 1 إلى 2 لمن؟ لـ 0 إلى 2 بدنا + +363 +00:26:56,170 --> 00:27:00,150 +دالة من 0 إلى 1 أو اكتبوا كيابة لكي أقولوا مثال + +364 +00:27:00,150 --> 00:27:06,970 +لكم بالتصيب find f such that f + +365 +00:27:06,970 --> 00:27:13,950 +is one to one and onto by bijection فبدنا نعرف + +366 +00:27:13,950 --> 00:27:25,630 +دالة للـ F من 1,2 إلى 0,2 بـ given bar بدنا + +367 +00:27:25,630 --> 00:27:26,530 +نعرف الـ F + +368 +00:27:31,280 --> 00:27:34,640 +نفكر مع بعض فأقول احنا بندور في نفس الدائرة وإن + +369 +00:27:34,640 --> 00:27:37,760 +كان بشكل مختلف دايماً مطلوب مني أجيب دالة من عندي + +370 +00:27:37,760 --> 00:27:41,320 +دالة مناسبة طبعاً لما كل نسبة infinite بدنا هي تكون + +371 +00:27:41,320 --> 00:27:43,920 +one to one وليس أنتم من المجموع على نفسها لكن في + +372 +00:27:43,920 --> 00:27:47,460 +التكافئة والعدد دي دالة بين مجموعتين وبدنا هي تكون + +373 +00:27:47,460 --> 00:27:51,500 +one to one و onto one to one and onto أه بنفع أدور + +374 +00:27:51,500 --> 00:27:56,920 +في دفتر الـ calculus؟ ليش بنفعش أعداد حقيقية أعداد + +375 +00:27:56,920 --> 00:28:01,210 +حقيقية فيه في المعطيات دوال؟ ما فيش هدول أعداد حقيقية + +376 +00:28:01,210 --> 00:28:04,470 +بنفع أدور في دفتر الـ calculus فبدنا دالة من دفتر + +377 +00:28:04,470 --> 00:28:07,990 +الـ calculus من الـ calculus دالة فيها جمع فيها طرح + +378 +00:28:07,990 --> 00:28:12,650 +فيها sin فيها cos تكون one to one and onto خلينا + +379 +00:28:12,650 --> 00:28:17,390 +نفكر مع بعض .. خلينا نفكر مع بعض كيف بنوجد الدالة + +380 +00:28:17,390 --> 00:28:22,410 +المناسبة إن + +381 +00:28:22,410 --> 00:28:27,170 +شو بنعمل نوع ما نحنا؟ إيش احنا بنعمل؟ خلينا طبعاً + +382 +00:28:27,170 --> 00:28:31,770 +كنقطة بداية ممكن واحد يحاول ودايماً في try and + +383 +00:28:31,770 --> 00:28:34,170 +error الواحد بيحاول وممكن يخطأ لكن بتعلم من + +384 +00:28:34,170 --> 00:28:37,210 +أخطائه وبيشوف إذا هالي فشلة بدور على جهة ثانية + +385 +00:28:37,210 --> 00:28:40,770 +لحد ما ينجح ممكن أنا طريقة تفكير بتفكر بالطريقة + +386 +00:28:40,770 --> 00:28:45,730 +التالية بدي دالة تنقل الواحد للصفر تنقل الواحد + +387 +00:28:45,730 --> 00:28:51,930 +للصفر وتنقل الاتنين للاتنين تنقل الاتنين للاتنين في + +388 +00:28:51,930 --> 00:28:57,050 +هنا سمعت كلام X ناقص واحد جيد بس واحدة واحدة جربي + +389 +00:28:57,050 --> 00:28:59,970 +اكتبي في رياضة اكتبي اه بتنقل الاتنين .. بتنقل + +390 +00:28:59,970 --> 00:29:05,890 +الواحد للصفر وبتنقل الاتنين للواحد إيش نعمل؟ + +391 +00:29:05,890 --> 00:29:12,830 +عادي مبدئياً نجلت الواحد للصفر ونجلت الاتنين للاتنين + +392 +00:29:12,830 --> 00:29:16,950 +صح؟ ممتفقين؟ طيب إذا بقيتش تبدأش اجرب هل هي one to + +393 +00:29:16,950 --> 00:29:19,990 +one أنت ولا أنت ولا أنا اجرب اه a given by أول + +394 +00:29:19,990 --> 00:29:25,940 +شيء واحد is one to one كيف نفترض أنها one to one؟ + +395 +00:29:25,940 --> 00:29:30,880 +let x1 و x2 وين؟ في الـ domain مين تنتمي لمين؟ واحد + +396 +00:29:30,880 --> 00:29:34,260 +واتنينها شايف؟ بدنا نكون دقيقين، هه نتعلم فاحنا + +397 +00:29:34,260 --> 00:29:37,740 +بناخد عنصرين في الـ domain الدالة صورهم متساوي such + +398 +00:29:37,740 --> 00:29:48,180 +that f of x1 تساوي f of x2 then إيش أعمل؟ + +399 +00:29:51,130 --> 00:29:56,930 +2 في x1 ناقص 1 سواء 2 و في x2 ناقص 1 وهذا يودّي x1 + +400 +00:29:56,930 --> 00:30:01,070 +سواء x2 ولا في حد عنده اعتراض؟ اه x مع 2 و y مع 1 + +401 +00:30:01,070 --> 00:30:04,790 +فإذا الدالة فعلاً one to one انجحنا نجاح فاحنا نص + +402 +00:30:04,790 --> 00:30:10,010 +الطريق انجحنا is one to one فممتاز ماشيين بالطريق + +403 +00:30:10,010 --> 00:30:17,370 +إن شاء الله الصحيح نثبت أنها onto f is onto كيف + +404 +00:30:17,370 --> 00:30:20,410 +نثبت أنها onto ناخد عنصر في المجال المقابل let y + +405 +00:30:21,770 --> 00:30:25,290 +أو نحسب اللي ماشي، كله صح تخلينا نشتغل عليها، من + +406 +00:30:25,290 --> 00:30:31,370 +وين؟ من 0 و 2 بدنا ندور على X، بدنا X .. خلينا + +407 +00:30:31,370 --> 00:30:37,230 +نعمل الهمش بدنا X وين؟ من 1 و 2، بحيث F of X تساوي + +408 +00:30:37,230 --> 00:30:40,980 +Y، صح؟ عارجي على كل قنده، واحنا مهارة بنحاول + +409 +00:30:40,980 --> 00:30:44,740 +نتعلمها طيب، إيش معناه أقل في X؟ اتنين في X نقص + +410 +00:30:44,740 --> 00:30:49,180 +واحدة تساوي Y إيش بنعمل في الهامش؟ بنحل لـ X بدلة + +411 +00:30:49,180 --> 00:30:53,480 +الـ Y آه، فهذا بيقدي إن X مش بنساوي Y على اتنين + +412 +00:30:53,480 --> 00:30:58,820 +زائد واحد إيش بتثبت؟ بتديها حاجتين، إن X فعلاً بين + +413 +00:30:58,820 --> 00:31:01,880 +الواحد وبين الاتنين وإن صورتها بتساوي Y وإن + +414 +00:31:01,880 --> 00:31:03,800 +صورتها بتساوي Y طيب، نشوف + +415 +00:31:14,340 --> 00:31:20,140 +X تساوي Y على 2 زائد 1 ثم أول شيء بدي أثبت إن X بين + +416 +00:31:20,140 --> 00:31:24,840 +1 و 2 كيف؟ أنا عندي الـ Y وين أخدتها الـ Y؟ الـ Y من + +417 +00:31:24,840 --> 00:31:29,000 +0 إلى 2 مظبوط؟ بدي أنا أشوف الـ X بين الـ 0 وبين الـ + +418 +00:31:29,000 --> 00:31:32,680 +1 وبين الـ 2 إيش أعمل؟ أكسب على 2 فده بيقول إن 0 + +419 +00:31:32,680 --> 00:31:39,320 +على Y على 2 على 1 أجمع 1 للطرفين بيصير 1 أقل من Y + +420 +00:31:39,320 --> 00:31:45,390 +على 2 زائد 1 أقل من 2 صح ولا مش صح؟ اه فإذا إيش then + +421 +00:31:45,390 --> 00:31:51,810 +خلينا نكتبها white بتكتب الـhammer implies x تنتمي + +422 +00:31:51,810 --> 00:31:55,590 +للزيرو لواحد لاتنين وهو الـايه المكتوبة الأول اتنين + +423 +00:31:55,590 --> 00:32:08,640 +تمام آخر حاجة and وهي الـhammer f of x تساوي F of Y ع + +424 +00:32:08,640 --> 00:32:13,440 +2 زائد 1 وتساوي Y لإيش؟ إيش الدالة بتعمل؟ الدالة + +425 +00:32:13,440 --> 00:32:16,500 +بتطرح واحد وبتطرح اتنين فمية لمية، اه فإذا فعلا + +426 +00:32:16,500 --> 00:32:26,900 +الدالة plus F ازمها وهو المطلوب، وهو المطلوب تمام؟ + +427 +00:32:26,900 --> 00:32:30,510 +أي سؤال؟ فياريت هذه نتدرب عليها وناخد فترتين + +428 +00:32:30,510 --> 00:32:33,450 +مختلفتين دائما ممكن نشتغل بهذه الشكلة فالحقيقة أنه + +429 +00:32:33,450 --> 00:32:38,770 +هذا وهنعممه بعد شوية كل فترة تكافئ فترة فإيه زمان + +430 +00:32:38,770 --> 00:32:42,990 +مش أكبر منها طلع عدديا متكافئتين .. متكافئتين + +431 +00:32:42,990 --> 00:32:50,510 +بقوله الصدمة بصحي منها صدمة فاللي مصدوم أن واحد + +432 +00:32:50,510 --> 00:32:56,040 +اتنين تكافئ Zero اتنين يشوف المثال اللي بعده سالب + +433 +00:32:56,040 --> 00:33:03,640 +باية اتنين باية اتنين الفترة هالي تكافئ كل الـ infinity ما هي نص الـ infinity انفنتي مش نص الـ + +434 +00:33:03,640 --> 00:33:05,740 +infinity انفنتي انفنتي هذي المظبوط هذي فبعدين نثبت + +435 +00:33:05,740 --> 00:33:09,400 +أو إيه كيف نثبت إيه إيش التانية اه مش هنحلوها لسه + +436 +00:33:09,400 --> 00:33:15,500 +هنحلوها مع بعض هنحلوها مع بعض فمعين من الـمدور + +437 +00:33:15,500 --> 00:33:20,920 +function معين مع بعض أكيد هنخشهم مع بعض هنقشها مع + +438 +00:33:20,920 --> 00:33:24,940 +بعض فهنا + +439 +00:33:24,940 --> 00:33:33,920 +F تخلصناه مثال + +440 +00:33:33,920 --> 00:33:40,340 +رحم اتنين اه let F من سالب بايع اتنين لبايع اتنين + +441 +00:33:40,340 --> 00:33:49,840 +للـ R + +442 +00:33:49,840 --> 00:33:50,660 +be given by f of x تساوي وين بتدوروا جاعدين؟ في + +443 +00:33:54,780 --> 00:34:03,200 +تفاقد الأحرار في دالة مشهورة جدا ارجعوا + +444 +00:34:03,200 --> 00:34:10,940 +على تفاضل باه و الدالة هادي one to one and unto + +445 +00:34:10,940 --> 00:34:14,160 +عشان انها inverse tan inverse فهي بيبدأ تركها يقول + +446 +00:34:14,160 --> 00:34:17,220 +باجي عليك وخلاص + +447 +00:34:17,220 --> 00:34:18,040 +باجي تتذكروا احنا كيف عرفنا التان inverse؟ طبعا + +448 +00:34:28,040 --> 00:34:31,100 +التان في الأصل معرفة على كل الـ R معدى عدد فردي في + +449 +00:34:31,100 --> 00:34:35,860 +بايع 2 فهي معرفة من سالب بايع 2 لبايع 2 و من بايع + +450 +00:34:35,860 --> 00:34:39,680 +2 لتلاتة بايع 2 و هكذا عشان نخليها one to one + +451 +00:34:39,680 --> 00:34:43,120 +أخدنا جزء فهي حصلت one to one لما أخدنا فترة من + +452 +00:34:43,120 --> 00:34:46,080 +الفترات طبعا هي انتوا على طول لأن كلها رسمتها + +453 +00:34:46,080 --> 00:34:49,720 +بتتذكروا الرسم كيف؟ هيّا، بس درسوها من الفترة اللي + +454 +00:34:49,720 --> 00:34:53,180 +بديها، ده .. من سلة باعتنا ماباعتنا واش مهل، أغطّط + +455 +00:34:53,180 --> 00:34:56,700 +كل الـ R من سلة infinite إلى infinite، أه فهو one + +456 +00:34:56,700 --> 00:34:59,460 +to one and unto طبعا عشان تفتحوها one to one يمكن + +457 +00:34:59,460 --> 00:35:02,060 +صعب نفبتها بالتعريف لكن ممكن تجي لـ الـ calculus إن + +458 +00:35:02,060 --> 00:35:05,340 +التفاضل و إنها تزايدية و هكذا، تزايدية تاني، + +459 +00:35:05,340 --> 00:35:08,740 +فبتطلع one to one، فعشان هيك نرجع لـ الـ calculus + +460 +00:35:08,740 --> 00:35:10,900 +فهو one to one و unto فعلا، لإن الـ .. الـ .. الـ .. + +461 +00:35:10,900 --> 00:35:13,860 +الـ .. هو إيش من هنا أعرفها؟ المادة تبعها كل R، + +462 +00:35:13,860 --> 00:35:16,680 +ارجع لتفاضل بها، فهو one to one and unto فليه ف + +463 +00:35:16,680 --> 00:35:19,480 +فاحنا إيش عملنا .. يعني نحكي أنتوا أنه بتغفل كل + +464 +00:35:21,070 --> 00:35:24,130 +المجال وخلاص؟ لأ إن المجال تبعها، الـ calculus + +465 +00:35:24,130 --> 00:35:26,330 +بيساوي اه، فأطول هذي إيش المجال تبعها بيساوي اه، + +466 +00:35:26,330 --> 00:35:30,330 +بيساوي اه طيب إيش .. إيش .. إيش نثبتناه المثاليين + +467 +00:35:30,330 --> 00:35:33,530 +مع بعض؟ أثبتنا إنه كل فترة تقريبا تكافئ فترة، + +468 +00:35:33,530 --> 00:35:37,370 +نعملنا كام مثال، الحقيقة كل فترة مفتوحة تكافئ فترة + +469 +00:35:37,370 --> 00:35:40,410 +مفتوحة و الفترة باية اتنين باية اتنين تكافئ الـ ا .. + +470 +00:35:40,410 --> 00:35:44,350 +طب الـ باية اتنين باية اتنين سالب باية اتنين بتكافئ + +471 +00:35:44,350 --> 00:35:46,830 +واحد zero مثلا بتكافئ ا .. فإيه صار .. كل أي فترة + +472 +00:35:46,830 --> 00:35:50,910 +تكافئ أي فترة مفتوحة .. أي فترة مفتوحة .. ان شاء + +473 +00:35:50,910 --> 00:35:54,450 +الله تاخد الفترة من صفر لواحد من عشر .. تكافئ كل الـ + +474 +00:35:54,450 --> 00:35:58,170 +.. أي فترة مفتوحة تكافئ الـ ا .. تكافئ الـ ا .. و + +475 +00:35:58,170 --> 00:36:01,770 +ادي + +476 +00:36:06,210 --> 00:36:09,530 +أه فده لسه هنجيله .. هنديعله مرة تانية أي فترة + +477 +00:36:09,530 --> 00:36:11,730 +مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة .. أي + +478 +00:36:11,730 --> 00:36:11,950 +فترة مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة .. + +479 +00:36:11,950 --> 00:36:12,690 +أي فترة مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة + +480 +00:36:12,690 --> 00:36:17,970 +.. أي فترة مفتوحة .. أي فترة مفتوحة .. أي فترة + +481 +00:36:17,970 --> 00:36:22,630 +مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة .. أي + +482 +00:36:22,630 --> 00:36:25,770 +فترة مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة .. + +483 +00:36:25,770 --> 00:36:28,710 +أي فترة مفتوحة .. أي فلأن هو إيش العلاقة؟ هي علاقة + +484 +00:36:28,710 --> 00:36:31,230 +إيش؟ equivalence relation، يعني transitive فأنا + +485 +00:36:31,230 --> 00:36:34,270 +عندي أي فترة تكافئ سالب بايع اتنين على بايع اتنين + +486 +00:36:34,270 --> 00:36:36,430 +وسالب بايع اتنين على بايع اتنين بتكافئ لأ لإن + +487 +00:36:36,430 --> 00:36:40,650 +سهولة عشان التهن إذا كل فترة مفتوحة تكافئ أ فترة + +488 +00:36:40,650 --> 00:36:44,710 +transitive نشوف مثال المخلخة بدها شوية شغل عشان + +489 +00:36:44,710 --> 00:36:47,530 +اللي هو النقطة اللي جوا بدها شوية شغل موجودة في + +490 +00:36:47,530 --> 00:36:54,650 +الكتاب نشوف مثال مختلف نوعا ما بقولي إذا في عندي + +491 +00:36:54,650 --> 00:37:01,580 +مجموعة وإيه بجبعتين؟ الأولى ناقص التانية يكافئ + +492 +00:37:01,580 --> 00:37:05,840 +التانية ناقص الأولى فدوله مجبعتين متكافئتين خلينا + +493 +00:37:05,840 --> 00:37:10,480 +نشوف البرهان أو الحل ونشوف رسمه ممكن تساعدنا نشوف + +494 +00:37:10,480 --> 00:37:18,600 +رسمه ممكن تساعدنا هذا + +495 +00:37:18,600 --> 00:37:21,860 +يمكن تكون أسهل من الأمثلة الماضية التصور تبعها + +496 +00:37:21,860 --> 00:37:28,340 +يكون أسهل هي عندنا مجموعتين طبعا هذه X وهذه Y طبعا + +497 +00:37:28,340 --> 00:37:34,940 +هذه المنطقة .. هذه X ناقص Y وهذه المنطقة Y ناقص S + +498 +00:37:34,940 --> 00:37:41,120 +لأن الاتحاد مشترك فهذه هي الفكرة .. فهذه هي الفكرة + +499 +00:37:41,120 --> 00:37:45,140 +واضحة إذا منطق الكلام .. الكلام منطقي فبدنا نبرهنه + +500 +00:37:45,140 --> 00:37:49,100 +.. بدنا نكتبه بلغة رياضية مايواضحة من الصورة .. + +501 +00:37:49,100 --> 00:37:53,830 +الصورة مش مرهقة فالآن دعنا هذا المثال التالدطب + +502 +00:37:53,830 --> 00:38:01,590 +عشان ده عنده موضوع prove that if ف assume x + +503 +00:38:01,590 --> 00:38:09,690 +ناقص y تكافئ y ناقص x بدنا نثبت ان x تكافئ y كيف + +504 +00:38:09,690 --> 00:38:13,950 +بدنا نثبتها؟ بدي bijection من x لـ y بدنا دالة من x + +505 +00:38:13,950 --> 00:38:18,820 +لـ y نرجع على دفتر الـ calculus؟ ولا خلاص نسكره الآن؟ + +506 +00:38:18,820 --> 00:38:23,140 +مانفعش الآن، مانفعش، مانفعش، بدنا إذا بنعرف دالة F + +507 +00:38:23,140 --> 00:38:26,440 +من X لـ Y تكون one to one عند أنتم، من وين بدنا + +508 +00:38:26,440 --> 00:38:29,960 +ندور عليها؟ بالمعطيات، في في المعطيات، نعم، هاي و + +509 +00:38:29,960 --> 00:38:32,820 +مش هدية السوم، إذا بقدر ألاقي دالة one to one عند + +510 +00:38:32,820 --> 00:38:37,360 +أنتم، من X ناقص Y لـ Y ناقص X، هذا يؤدي، there + +511 +00:38:37,360 --> 00:38:44,290 +exist G اختصارا، هاي bijection معناها، صح؟ بعدين + +512 +00:38:44,290 --> 00:38:47,050 +مكتوبة bijection، الإكتوبة بدا الشكل، اتعودتوا على + +513 +00:38:47,050 --> 00:38:50,210 +الرمز الجديد؟ يعني فيه bijection من X نقص Y لـ Y + +514 +00:38:50,210 --> 00:38:53,310 +نقصي، الآن أنا جاهز أعرف الدالة، شوفت الفكرة اللي + +515 +00:38:53,310 --> 00:38:55,850 +احنا قولنا فيها، بالله في حول الدائرة، نفس + +516 +00:38:55,850 --> 00:38:59,590 +الدائرة، و نفس الأفكار تتكرر بشكل بس إيش، متقارن، + +517 +00:38:59,590 --> 00:39:05,650 +هعرفه دالة، let F من X لـ Y be given + +518 +00:39:09,620 --> 00:39:13,140 +G of X to Z طبعا هعتمد في تعريف عالميين على الـ G + +519 +00:39:13,140 --> 00:39:17,320 +الفكرة مرت علينا تقريبا مشابهة لكن إيش ميزة الـ G + +520 +00:39:17,320 --> 00:39:21,700 +معرفة على جزء من الـ X مش على كل الـ X معرفة من وين؟ + +521 +00:39:21,700 --> 00:39:26,400 +من X ناقص Y فبتكمل الدمان طب إذن أول شي هعرفها G + +522 +00:39:26,400 --> 00:39:32,940 +of X إذا الـ X وين؟ في الـ X ناقص Y بتام هنا الفرق + +523 +00:39:32,940 --> 00:39:35,060 +هنا الباقي إيش عرفها؟ + +524 +00:39:38,550 --> 00:39:43,410 +أولش هنا انا هي الـ domain الـ domain كل X المنطقة + +525 +00:39:43,410 --> 00:39:49,490 +هذه انا معرف عليها G هذه المنطقة مش معرف عليها G + +526 +00:39:49,490 --> 00:39:54,190 +صح؟ بدي اكمل انا عشان يكون اقص من X لكي اتعرف على + +527 +00:39:54,190 --> 00:39:58,070 +كل الـ G هذا بيشبه اول مثال يمكن حليناه في الـ + +528 +00:39:58,070 --> 00:40:02,330 +infinite cell ايش اعرفها هنا؟ الـ identity بنفع نفس + +529 +00:40:02,330 --> 00:40:05,190 +الشيء لأن هدول إيش فيه؟ هدول عناصر بيكافؤوا هدول + +530 +00:40:05,190 --> 00:40:07,670 +فيه تناظر بين هدول وبين هدول طب هذا كيف بناظر + +531 +00:40:07,670 --> 00:40:10,730 +نفسه؟ لأنه نفسه مشترك فكل عنصر هو بناظر نفسه هنا + +532 +00:40:10,730 --> 00:40:17,470 +لأنه مشترك فدي هسميها X زي X وين تنتمي للتقاطة لأن + +533 +00:40:17,470 --> 00:40:21,890 +هذه المنطقة هي التقاطة فهي تكمل من كل الـ X فالـ X + +534 +00:40:21,890 --> 00:40:30,110 +مما تتكون تتكون من X ناقص Y إتحاد التقاطة ففي X + +535 +00:40:30,110 --> 00:40:35,290 +ناقص Y جي معرفة أدت الغلط وخدمتني بس أي مقدرة الجي + +536 +00:40:35,290 --> 00:40:39,170 +طيب في الباقي الـ identity إيه بتصرف؟ بالنسبة لهذه + +537 +00:40:39,170 --> 00:40:42,590 +one to one أد one to one تعرف تفكروها ولا لا؟ + +538 +00:40:42,590 --> 00:40:43,490 +المفروض تعرف + +539 +00:40:57,520 --> 00:41:00,500 +is one to one شفتوا الأفكار كام تتكرر ده؟ ده يمكن + +540 +00:41:00,500 --> 00:41:05,300 +الأول مرة تكون غريبة افهمتوا منها 5% تتكرر كمان + +541 +00:41:05,300 --> 00:41:09,860 +مرة بترتفع نسبة الفهم 10% 20% مع التكرار أرجو أنه + +542 +00:41:09,860 --> 00:41:14,020 +نسبة تعلى عن الـ 50% و هكذا بيصير في الأمر كويس + +543 +00:41:14,020 --> 00:41:22,920 +slit x1 و x2 في domain الـ F لأ ركزوا مش غير تحطوا + +544 +00:41:22,920 --> 00:41:26,280 +مستطيل و أنتوا شاطرين بالتزويج و بالأمور زي هيك + +545 +00:41:26,280 --> 00:41:28,740 +عشان تتبعوا اتركزوا هنا وهنا و أنتوا تشتغلوا اه + +546 +00:41:28,740 --> 00:41:32,500 +فأنا مش هروح للـ G انا بشغل على الـ F بداشي أدي الـ F + +547 +00:41:32,500 --> 00:41:35,880 +one to one إيش أعمل؟ عنصرين في الـ domain تبع الـ F + +548 +00:41:35,880 --> 00:41:41,180 +اه so what are we going to solve؟ + +549 +00:41:41,180 --> 00:41:45,980 +بدي + +550 +00:41:45,980 --> 00:41:49,700 +أستخدم التعريف التعريف ده لمعرفة متعددة القاعدة + +551 +00:41:49,700 --> 00:41:50,480 +أربع حالة + +552 +00:41:54,410 --> 00:42:00,610 +طبعا لو كانوا التنين في X-Y إيش التعريف؟ G of X1 + +553 +00:42:00,610 --> 00:42:07,310 +تساوي G of X2 إذا كان X1 و X2 في X-Y وناخد برضه + +554 +00:42:07,310 --> 00:42:11,310 +التانية السهلة لو كانوا التنين في التقاطة X1 تساوي + +555 +00:42:11,310 --> 00:42:16,990 +X2 إذا X1 و X2 في X مقاطع الواحد لما يكونوا التنين + +556 +00:42:16,990 --> 00:42:20,870 +مع بعض يا في المنطقة الأولى يا في المنطقة التانية + +557 +00:42:20,870 --> 00:42:26,990 +بيتعمل حالتين كل واحد في منطقة مختلفة ف G of X1 + +558 +00:42:26,990 --> 00:42:33,990 +تساوي X2 لو كانت X1 في المنطقة الـ minus و X2 في + +559 +00:42:33,990 --> 00:42:41,730 +التقاطع و هنا العكس X1 تساوي G of X2 إذا X1 في + +561 +00:42:41,730 --> 00:42:50,650 +التقاطع و X2 في X ما قصر طبعا كالعادة فيه اثنتين + +562 +00:42:50,650 --> 00:42:54,650 +هيدوني X1 تساوي X2 واحدة فيهم واضحة واثنتين هيدوني + +563 +00:42:54,650 --> 00:42:58,050 +contradiction طبعا هالي ليش بتديني X1 لأنه G is + +564 +00:42:58,050 --> 00:43:04,010 +one to one اه فهذا يؤدي طبعا كله بينهم ان X1 تساوي + +565 +00:43:04,010 --> 00:43:09,230 +X1 ليش لأنه G is one to one وطبعا X1 تساوي X2 لأنه + +566 +00:43:09,230 --> 00:43:17,030 +مفت الباقي contradiction ليش هالي بقولي ان G of X1 + +567 +00:43:17,030 --> 00:43:23,100 +تساوي G of X2 X2 وين؟ في التقاطع، وهل ممكن تكون الـG من + +568 +00:43:23,100 --> 00:43:27,820 +وين لوين الـG؟ من X ناقص Y لـ Y ناقص X، عمره ما + +569 +00:43:27,820 --> 00:43:30,240 +بتكون الصورة هنا، الصورة هنا لازم تكون، فده + +570 +00:43:30,240 --> 00:43:35,580 +مستحيل، فهذا Contradiction هأضحك مرة في الثانية + +571 +00:43:35,580 --> 00:43:42,820 +نفسي Contradiction، ليش؟ لأن X2 لا تنتمي للـG of X + +572 +00:43:42,820 --> 00:43:48,880 +ناقص Y مرة ثانية الـG من أين تأخذ عناصر؟ من هنا إلى + +573 +00:43:48,880 --> 00:43:52,340 +هنا، لا تودّههم إلى التقاطع فلما تكون X2 في + +574 +00:43:52,340 --> 00:43:55,380 +التقاطع، فممكن أن يكون صورة مستحيلة نفس القضية، + +575 +00:43:55,380 --> 00:43:58,780 +لما تكون X1 في التقاطع، مستحيل أن تكون صورة مستحيل + +576 +00:43:58,780 --> 00:44:02,060 +أن تكون صورة، فنفس الأفكار تتكرر، فأرجعوا أن الفهم + +577 +00:44:02,060 --> 00:44:09,200 +.. نسبة الفهم تزداد Contradiction لأن + +578 +00:44:09,200 --> 00:44:16,070 +X1 الآن لا تنتمي، خلاص P or P P P or contradiction P + +579 +00:44:16,070 --> 00:44:19,550 +وبالتالي + +580 +00:44:19,550 --> 00:44:26,850 +F is one to one هنثبت + +581 +00:44:26,850 --> 00:44:32,670 +on to برضه برضه سريعة سهلة و برضه هنستخدم ال trick + +582 +00:44:32,670 --> 00:44:36,950 +برضه صعب خلنا نستخدمها في الإعادة إفادة كما يُقال + +583 +00:44:36,950 --> 00:44:44,120 +اثنين F is onto .. اه هحسب ال image مش هستخدم + +584 +00:44:44,120 --> 00:44:48,680 +الصورة الثانية هاخد ال Y و أجيبها صورة مين هحسب ال + +585 +00:44:48,680 --> 00:44:54,250 +image مباشرة فهو هحسب F of X فيه trick مشهور + +586 +00:44:54,250 --> 00:44:56,850 +بنعملهش نعمل ده لمعرفة بالتيزيق بنجذّق ال domain + +587 +00:44:56,850 --> 00:45:04,550 +فحكته بال X على صورة مين X ناقص Y اتحاد X تقاطع ال + +588 +00:45:04,550 --> 00:45:07,650 +Y مش هيك عملناها مش هيك عرفناها عملناها جزئين + +589 +00:45:07,650 --> 00:45:12,350 +الرسم مثلا محيطة الطريق واضح تمام معروف أن ال F + +590 +00:45:12,350 --> 00:45:20,000 +تتوزع عن اتحاد فده بيساوي F(x-y) اتحاد F(x تقاطع + +591 +00:45:20,000 --> 00:45:24,920 +ال y ليش عملت هيك؟ لأن ال f تعريفة هنا هي g + +592 +00:45:24,920 --> 00:45:28,040 +وتعريفة + +593 +00:45:28,040 --> 00:45:30,700 +هنا identity يعني المجموعة العنصر بتعمل زي ما هو و + +594 +00:45:30,700 --> 00:45:34,020 +المجموعة بتعمل زي ما هي فدي ليست إلا x تقاطع ال y + +595 +00:45:34,020 --> 00:45:41,060 +في حد عنده أي مشكلة هنا؟ سهل حتى الآن، ولا لأ؟ فهو + +596 +00:45:41,060 --> 00:45:44,080 +فيه trick بسيط الآن، ده طبعا هو مش صعب لكنه بنتبه، + +597 +00:45:44,080 --> 00:45:47,300 +الان ال G اشملها one to one and onto اشملها + +598 +00:45:47,300 --> 00:45:49,820 +one to one and onto ان ال domain صورة مين؟ + +599 +00:45:49,820 --> 00:45:52,340 +المجال المقابل، إذا بقى ال G دالة من وين لو وين، + +600 +00:45:52,340 --> 00:45:55,340 +عنكم مكتوب، من X ناقص Y لـ Y ناقص X، فده إيش + +601 +00:45:55,340 --> 00:46:01,980 +بيساوي؟ Y ناقص X، إتحاد التقاطع، يعني مين؟ يعني Y، + +602 +00:46:01,980 --> 00:46:07,560 +بس عكس للصورة، يعني إحنا قاعد الصورة هيكفكنا هادي + +603 +00:46:07,560 --> 00:46:10,620 +مع هادي .. هادي صارت هادي مع هادي .. إيش صارت؟ + +604 +00:46:10,620 --> 00:46:14,060 +واحد .. فنجلنا من هناك لهناك .. كل هذا مصطلح واحد + +605 +00:46:14,060 --> 00:46:19,140 +.. وي زي إيش وي on .. + +606 +00:46:19,140 --> 00:46:24,700 +is on .. وهو المضمون .. فإن شاء الله المحاضرة + +607 +00:46:24,700 --> 00:46:25,260 +تجيبنا كذلك diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/I64ZBj8Mh0U_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/I64ZBj8Mh0U_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..a1ef6b12f8deb3f801fb68c72120ec798c7a08bf --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/I64ZBj8Mh0U_raw.srt @@ -0,0 +1,2260 @@ +1 +00:00:20,690 --> 00:00:24,830 +بسم الله الرحمن الرحيم هنستكمل محاضراتنا في قواعد + +2 +00:00:24,830 --> 00:00:28,270 +الاستدلال وزي ما احنا شوفنا في المحاضرة الأخيرة + +3 +00:00:28,270 --> 00:00:33,930 +وقفنا عند هذه النظرية اتوقع ان الكل بيقدر يثبت هذه + +4 +00:00:33,930 --> 00:00:38,410 +القوانين فهتتركها ك exercise الأمور واضحة القانون + +5 +00:00:38,410 --> 00:00:41,550 +الأول implication التاني implication والتالت تكافؤ + +6 +00:00:41,550 --> 00:00:45,690 +فالقضية اتوقع واضحة ولا تستحق انه نكرر نفس + +7 +00:00:45,690 --> 00:00:54,640 +العملياتخلّينا نشوف مثال على مودس طولنس ومودس + +8 +00:00:54,640 --> 00:00:58,340 +بولنس خلّينا نستفهمها بأمثلة واقعية نفهم الأمور + +9 +00:00:58,340 --> 00:01:05,870 +طبعا واحد فيهم كان بيقول أنهif b then q and b + +10 +00:01:05,870 --> 00:01:12,170 +implies q و بعدين if b هذه كلها مع بعض طبعا then q + +11 +00:01:12,170 --> 00:01:21,610 +and not q مظبوط then not b then not + +12 +00:01:21,610 --> 00:01:30,780 +q then not bمظبوط فهدولة هما القانونين فهذا modus + +13 +00:01:30,780 --> 00:01:37,400 +bonnas وهذا modus tollens خلينا نشوف مثال و نشوف + +14 +00:01:37,400 --> 00:01:41,340 +كيف أن هذا الأمر فعلا منطقي ولا لأ فلو أخد ال + +15 +00:01:41,340 --> 00:01:45,800 +statement اللي هي جملة شرطية if b then q if I am + +16 +00:01:45,800 --> 00:01:50,520 +in Gaza then I am in Palestineإذا كنت فانا في غزة + +17 +00:01:50,520 --> 00:01:54,100 +فانا في فلسطين هذه جملة شرطية هذه جملة شرطية تشوف + +18 +00:01:54,100 --> 00:01:59,940 +الكلام فالآن فهذه ايش فهذه P وهذه Q فالآن لو كان + +19 +00:01:59,940 --> 00:02:04,920 +أنا عند P هذه جملة شرطية بتكون قاعدة من هو في غزة + +20 +00:02:04,920 --> 00:02:07,640 +فهو في فلسطين فالآن لو أنا عندي معلومة إن أنا في + +21 +00:02:07,640 --> 00:02:10,960 +غزةمنطقيا وان انا في فلسطين و انا ممكن اكون في مصر + +22 +00:02:10,960 --> 00:02:14,760 +فانا في فلسطين فانا مثلا لو قلت ان انا مثلا هي بي + +23 +00:02:14,760 --> 00:02:20,000 +I am in Gaza بالتأكيد الاستنتاج المنطقي ان من .. + +24 +00:02:20,000 --> 00:02:22,960 +ان في فلسطين فشوفين عند القاعدة كده بتقول اه فايش + +25 +00:02:22,960 --> 00:02:25,920 +الاستنتاج منطقي ولا مش منطقي كل الكل عارف ومش + +26 +00:02:25,920 --> 00:02:28,860 +متأكد ان الكلام صحيح فهذه زي هيك القاعدة فانا بحط + +27 +00:02:28,860 --> 00:02:32,380 +القاعدة قا قاعدة شرطية فإذا الشرط صحيح فالاستنتاج + +28 +00:02:32,380 --> 00:02:37,660 +لازم يكون صحيح فهذه ايش اللي هو ايش modus bonoنشوف + +29 +00:02:37,660 --> 00:02:41,960 +اللي هو modestliness I am not in Palestine إذا أنا + +30 +00:02:41,960 --> 00:02:45,540 +مستحيل أن أكون في غزة إذا أنا مش في فلسطين ممكن + +31 +00:02:45,540 --> 00:02:50,160 +أكون في نابس ولا في غزة؟ لا واضح؟ فهذا إذا هذا إيش + +32 +00:02:50,160 --> 00:02:54,540 +مستحيل يكون not you فإيش not be على طول فهذا كمثال + +33 +00:02:54,540 --> 00:02:59,260 +لنفهم كيف أن المنطق ونطبقه على مثال واضح يساعدنا + +34 +00:02:59,260 --> 00:03:06,370 +على الفهم فهذه نهاية هذا ال sectionالان هنتقل لل + +35 +00:03:06,370 --> 00:03:17,270 +section الرابع في هذا ال chapter هنستكمل + +36 +00:03:17,270 --> 00:03:21,570 +فيه بعض المصطلحات و بعض قواعد الاستدلال طبعا + +37 +00:03:21,570 --> 00:03:25,710 +العنوان contradiction التناقض contradiction + +38 +00:03:25,710 --> 00:03:29,970 +التناقض تمام + +39 +00:03:30,800 --> 00:03:35,180 +فاحنا مر علينا ما يعرف بالـ tautology أو القضية + +40 +00:03:35,180 --> 00:03:38,980 +مطلقة الصواب وهي صحيحة دائما لجميع الاحتمالات + +41 +00:03:38,980 --> 00:03:42,880 +المنطقية عكسها اللي هو الخطأ دائما بنسميه + +42 +00:03:42,880 --> 00:03:46,160 +contradiction فإذا ال contradiction هو statement + +43 +00:03:46,160 --> 00:03:50,980 +إيش مطلقة الخطأ دائما خاطئة دائما خاطئة فهنا + +44 +00:03:50,980 --> 00:03:55,420 +التعريفa statement where the truth values are all + +45 +00:03:55,420 --> 00:03:59,840 +false دايماً true for every assignment of truth + +46 +00:03:59,840 --> 00:04:03,780 +value to its component لكل احتمالات مركبة اذا كانت + +47 +00:04:03,780 --> 00:04:08,380 +مركبة او بسيطة فبنسميها contradiction التناقض بس + +48 +00:04:08,380 --> 00:04:11,940 +التناقض هو عكس من الـ tautology عكس قضية التقرير + +49 +00:04:11,940 --> 00:04:16,980 +المطلق الصواب ايش هو التناقض فهذا هو التناقض اللي + +50 +00:04:16,980 --> 00:04:23,580 +هنتعامل معاه نشوف مثالshow that بي and not بي ممكن + +51 +00:04:23,580 --> 00:04:26,860 +شفناها في القانون النقد النقيد انه مايوجدش شيء و + +52 +00:04:26,860 --> 00:04:30,220 +ضده لايجتمعان هذه قاعدة و المروحة فشيء و ضده + +53 +00:04:30,220 --> 00:04:33,120 +مايجتمعونش ف بي and not بي is a contradiction + +54 +00:04:33,120 --> 00:04:37,720 +خلينا نشوف اللي هو هذا المثال و نحله مع بعض فعنا + +55 +00:04:37,720 --> 00:04:41,960 +المثال we want to show is a contradiction ايش + +56 +00:04:41,960 --> 00:04:45,540 +معناته؟ بنعمل جدول و يظهروا دايما ايش؟ false اه + +57 +00:04:45,540 --> 00:04:47,180 +فإذن solution + +58 +00:04:49,200 --> 00:04:51,740 +خلّينا نعمل جدول by truth table + +59 +00:05:02,500 --> 00:05:07,140 +و في احتمالين اه فال B طبعا يا true يا false بدنا + +60 +00:05:07,140 --> 00:05:12,120 +نحسب not B و بعدين نحسب ال end بعدين B and not B + +61 +00:05:12,120 --> 00:05:16,960 +فطبعا false true نيجي ليا true and false .. false + +62 +00:05:16,960 --> 00:05:21,220 +false and true .. false اه فإذا فعلا هذه إيش + +63 +00:05:21,220 --> 00:05:28,700 +contradiction فإذا from the table we + +64 +00:05:28,700 --> 00:05:40,970 +see thatB and not B is a contradiction واضح + +65 +00:05:40,970 --> 00:05:44,770 +مثال بسيط بس عشان نوضح الصورة و ده ايه اشهر مثال + +66 +00:05:44,770 --> 00:05:48,050 +ال contradiction الشيء و ضده ده مابيجتمعوش + +67 +00:05:50,710 --> 00:05:55,510 +تمام كأي نقطة عالية زي ما حكينا أنه نفي التطولوجي + +68 +00:05:55,510 --> 00:05:58,810 +contradiction والعكس صحيح فبقول the negation of + +69 +00:05:58,810 --> 00:06:01,730 +our totology is a contradiction ف in other words + +70 +00:06:01,730 --> 00:06:05,370 +if small t لو بنرمز لتطولوجي بعض الأحيان هنرمز ل + +71 +00:06:05,370 --> 00:06:12,090 +بsmall t تطولوجي then not T is a contradiction فلو + +72 +00:06:12,090 --> 00:06:15,970 +أنا عند statement تطولوجينموذلة برمز T عشان نذكرنا + +73 +00:06:15,970 --> 00:06:19,290 +زي ما قلنا الرمز المناسب فلو بتدعي فيها تديني + +74 +00:06:19,290 --> 00:06:22,250 +contradiction اللي هي عشان نموذلة برمز small c + +75 +00:06:22,250 --> 00:06:24,930 +Contradiction فعشان نموذلة عشان برمز C و العكس + +76 +00:06:24,930 --> 00:06:27,850 +صحيح لو أنا فيها عندي contradiction النفي تبعها + +77 +00:06:27,850 --> 00:06:33,070 +Totology لأن هو واضح عكس ال true force و العكس + +78 +00:06:33,070 --> 00:06:38,230 +الصحيح فهذه الأمور لازم نعرفها و واضح من التعريف + +79 +00:06:39,670 --> 00:06:43,190 +الأن النظرية السابعة في هذا الـ chapter وعلى ما + +80 +00:06:43,190 --> 00:06:46,690 +أعتقد أنها الأخيرة هنشوف كيف ممكن نتعامل مع + +81 +00:06:46,690 --> 00:06:51,190 +Totology و Contradiction القوانين اللي بتتعامل مع + +82 +00:06:51,190 --> 00:06:54,350 +Totology و Contradiction القوانين اللي هو المنطق + +83 +00:06:54,350 --> 00:06:57,090 +اللي بتحكم التعامل مع هذا النوعين من ال statement + +84 +00:06:57,090 --> 00:07:01,010 +لان دول اللي احنا كنا فيما سبق كانت المقدمة كله + +85 +00:07:01,010 --> 00:07:05,590 +statements عشوائية عامة let B Q B N statement الان + +86 +00:07:05,590 --> 00:07:12,210 +نشوف المقدمة المقدمة مهمة جدا let Tsmall t small c + +87 +00:07:12,210 --> 00:07:17,870 +and b a tautology a contradiction and an arbitrary + +88 +00:07:17,870 --> 00:07:22,450 +statement respectively طبعا هذا ع التتوالي أو ع + +89 +00:07:22,450 --> 00:07:26,550 +التتابع فهذه طريقة مختصرة فداني تلات رموز ورا بعض + +90 +00:07:26,550 --> 00:07:29,670 +و قاللي كل واحدة فيهم مش إيش هيوعلى التتابع ايش + +91 +00:07:29,670 --> 00:07:32,490 +معناته؟ يعني هيش المفروض يقول يحكيلي بالتفصيل + +92 +00:07:32,490 --> 00:07:36,710 +بيقول let T be a tautology الأولى الأولى let C be + +93 +00:07:36,710 --> 00:07:39,890 +a contradiction and let B be an arbitrary + +94 +00:07:39,890 --> 00:07:41,910 +statement يعني زي any statement نفس المعنى + +95 +00:07:41,910 --> 00:07:45,170 +arbitrary يعني any statement واضح؟فانعرفهم بس طبعا + +96 +00:07:45,170 --> 00:07:47,970 +مدن ما تقول كل واحدة let let let عاملهم مع بعض و + +97 +00:07:47,970 --> 00:07:50,550 +respectively من على التتابع يعني ال T للأولى و ال + +98 +00:07:50,550 --> 00:07:53,930 +C للتانية و ال B للأخيرة ما همش هنرتبهم ع كيفي لأ + +99 +00:07:53,930 --> 00:07:58,090 +الترتيب المعطق له فإذا هو هستخدم تلت رموز الرموز + +100 +00:07:58,090 --> 00:08:00,870 +وين ما تظهر ال T شمالها هي تقرير مطلق الصواب + +101 +00:08:00,870 --> 00:08:03,270 +Totology وين ما تظهر small c فهي contradiction + +102 +00:08:03,270 --> 00:08:06,900 +يعني دايما false و ال B أي statementفي أي + +103 +00:08:06,900 --> 00:08:10,020 +statement؟ بينفع الـC تكون أي statement؟ لأ، لازم + +104 +00:08:10,020 --> 00:08:12,560 +تكون contradiction والـT is tautology، لكن الـB ما + +105 +00:08:12,560 --> 00:08:14,800 +ينطبق على الـB، ينطبق على أي statement، ما ينطبق + +106 +00:08:14,800 --> 00:08:17,040 +على الـC، بس على ال contradiction، ينطبق مش على أي + +107 +00:08:17,040 --> 00:08:19,920 +statement، ما ينطبق على الـT، بس على الـTautology، + +108 +00:08:19,920 --> 00:08:22,980 +تمام، then واضح، هذه الطريقة كيف نقرأ النظريات، + +109 +00:08:22,980 --> 00:08:28,380 +مهم جدا، بنندقق ونفهم الأمور، أول شيءStatement and + +110 +00:08:28,380 --> 00:08:32,740 +tautology بتكافئ ال statement نفسها أول قانون فال + +111 +00:08:32,740 --> 00:08:35,760 +statement مع tautology تكافئ ال statement نفسها طب + +112 +00:08:35,760 --> 00:08:39,440 +ليش؟ لأنه لما تكون ال .. الجيهة ال tautology اسمه + +113 +00:08:39,440 --> 00:08:43,580 +دايما true عشان ال and تكون true لازم بس ال B تكون + +114 +00:08:43,580 --> 00:08:46,260 +true لأن دي معرف، هدا ثابت، متغيرش، فال B هو + +115 +00:08:46,260 --> 00:08:49,900 +المتغير true and true true طب false and true false + +116 +00:08:49,900 --> 00:08:52,590 +مين اللي بيخليها true؟ ال Bومي اللي بيخلّيها + +117 +00:08:52,590 --> 00:08:55,390 +force؟ الـB، إذا هي زيها زي الـB مش هنقش التكافأة، + +118 +00:08:55,390 --> 00:08:59,110 +مش نقش قيمة الصدق، إذا هذه قيمة الصدق للآن معتمدة + +119 +00:08:59,110 --> 00:09:00,890 +على الـB، مش على الـTautology، لأن الـTautology + +120 +00:09:00,890 --> 00:09:05,470 +ثابت، كأنه إيش، ماليش دعوة، في الـR، آه، لكن بي + +121 +00:09:05,470 --> 00:09:08,830 +أور تي تكافئ تي، مش بي، ليش؟ لأنه ما زال + +122 +00:09:08,830 --> 00:09:11,610 +الـTautology true، إذا هذه دايما true، ها + +123 +00:09:11,610 --> 00:09:13,830 +الـTautology، ليش؟ لأنه أنا ضمنت إن واحدة true، + +124 +00:09:13,830 --> 00:09:17,510 +خلصت، ماليش دعوة في الـB، أي ما كانت الـB مع الـR، + +125 +00:09:17,510 --> 00:09:22,210 +دايما true، واضح؟دول الأول قانونين اي statement + +126 +00:09:22,210 --> 00:09:25,570 +معته تقول جي كيف اتعامل معها مع الـ A و مع الـ R + +127 +00:09:25,570 --> 00:09:34,420 +اتنينB or C or Contradiction تكافئ الـ B ليش؟ لأن + +128 +00:09:34,420 --> 00:09:37,560 +Contradiction دايماً False هلجيت لو الـ B true + +129 +00:09:37,560 --> 00:09:41,520 +بتكون الكل true لو الـ B false، الكل false إذا مين + +130 +00:09:41,520 --> 00:09:44,520 +اللي بيحدد ال truth value الـ B؟ زيها دي، تشوف + +131 +00:09:44,520 --> 00:09:48,320 +هدول أيش، بتتعضع، بس هنا أيش؟ الـ tautology مع ال + +132 +00:09:48,320 --> 00:09:52,020 +and أدتنا حاجة و Contradiction مع ال or أدتنا نفس + +133 +00:09:52,020 --> 00:09:55,200 +ال statement هناك العكس، B and Contradiction + +134 +00:09:55,200 --> 00:09:57,260 +دايماً False لأن في واحدة False، اللي هو + +135 +00:09:57,260 --> 00:10:00,490 +Contradictionهو صحيح؟ أه فإيه ليش بتكافئ؟ + +136 +00:10:00,490 --> 00:10:03,570 +Contradiction فدول القوانين اللي انا هتمدهم على + +137 +00:10:03,570 --> 00:10:10,810 +طول C Contradiction implies B أي statement ليش؟ + +138 +00:10:10,810 --> 00:10:14,170 +لأنه إذا كان ال إيش المعطى false فالاستنتاج دايما + +139 +00:10:14,170 --> 00:10:17,990 +صح بيكون دايما true فلو أنا عندي statement if C + +140 +00:10:17,990 --> 00:10:22,330 +then أي شيء if false then anything true هذا + +141 +00:10:22,330 --> 00:10:27,160 +المنطقة اللي بنحكي عليه if false thenanything true + +142 +00:10:27,160 --> 00:10:29,980 +فهذه هيك بتقول if false لأن ال quadratic يعني + +143 +00:10:29,980 --> 00:10:35,740 +false و أي حاجة true العكس بي implies tautology + +144 +00:10:35,740 --> 00:10:39,680 +ليش؟ لأنه إذا أنا بدي أوفر بالوعد ضروري إيش؟ الوعد + +145 +00:10:39,680 --> 00:10:42,800 +ماوعدتش، مافيش مشكلة فإذا ال B .. ال B بغض النظر، + +146 +00:10:42,800 --> 00:10:47,200 +لو مثلا ال Q true إذا كانت ال B true مافيش مشكلة، + +147 +00:10:47,200 --> 00:10:50,540 +طب ال B false برضه مافيش مشكلة لأنه إيش؟ لأنه تمة + +148 +00:10:50,540 --> 00:10:53,760 +true، واضح؟فده القواعد طبعا احنا بنحاول نفسر ليش + +149 +00:10:53,760 --> 00:10:56,680 +هذا الكلام شفوي عشان الواحد يتعود عليهم و يشوف ان + +150 +00:10:56,680 --> 00:10:59,820 +هو ايش منطقيا او انه ممكن يساعد في الحفظ حتى لو + +151 +00:10:59,820 --> 00:11:02,780 +القانون الـC لو كتبه و حاول يفسره هذا الشكل ممكن + +152 +00:11:02,780 --> 00:11:06,920 +يتذكروا انه صحيح او طبعا أسهل جدول بيأكد ان هذا + +153 +00:11:06,920 --> 00:11:11,220 +الكلام صحيحخلّينا عشان نتعامل مع الـ tautology و + +154 +00:11:11,220 --> 00:11:14,980 +ال contradiction الأول مرة نعمل واحدة فيهم أوتنتين + +155 +00:11:14,980 --> 00:11:18,720 +كمثال كيف نعمل جدول صدق ل statement تحتوي على + +156 +00:11:18,720 --> 00:11:21,060 +tautology أو على contradiction لأنه مش arbitrary + +157 +00:11:21,060 --> 00:11:29,260 +فخلّينا نحاول نثبت بعض هدولا ال statement نعمل + +158 +00:11:29,260 --> 00:11:35,140 +C نعمل C تمام فهذه theorem + +159 +00:11:36,670 --> 00:11:41,590 +one seven بدي اعمل مثال بتطول جيه ومثال مع ال + +160 +00:11:41,590 --> 00:11:44,410 +contradiction خليها هي موجودة ال C خلينا ال C لأنه + +161 +00:11:44,410 --> 00:11:48,990 +بسيط ويمكن الناس تسموه سغربة منه شوية ابروف فنبدأ + +162 +00:11:48,990 --> 00:11:53,550 +بال C حد طبعا على الجزئين أولا بال death bit خلينا + +163 +00:11:53,550 --> 00:11:58,010 +نقول هنا B أسف C implies B بال death bit C implies + +164 +00:11:58,010 --> 00:12:02,090 +B هذا السؤال هذا المطلوبفهذا المطلوب الأول بحاجة + +165 +00:12:02,090 --> 00:12:05,150 +للمطلوب التالي فهنا طبعا في طريقة معتمدة لأنه لما + +166 +00:12:05,150 --> 00:12:08,690 +أحط أن هذا علم تستفهام أنه هذا مطلوب مش .. مش الحل + +167 +00:12:08,690 --> 00:12:12,310 +لأنه دايما لما بدي أنا القارئ بدي أكتب اللي بدي + +168 +00:12:12,310 --> 00:12:15,110 +أعرف أن هذا بدأ الحل لأ ده هو المطلوب بنفع الحل + +169 +00:12:15,110 --> 00:12:17,870 +يبدأ بالمطلوب لأ بنتهي بالمطلوب فانا أحط انه ليش + +170 +00:12:17,870 --> 00:12:19,910 +علم تستفهام لأ نثبت هذا النقطة فإذا الحل إيش + +171 +00:12:19,910 --> 00:12:25,030 +نقوله؟ we want بس نقوله إيش؟ we want to show أو to + +172 +00:12:25,030 --> 00:12:29,530 +prove that if C then B is a tautology + +173 +00:12:33,860 --> 00:12:40,080 +ممتاز by truth table by truth table او tables فاني + +174 +00:12:40,080 --> 00:12:45,650 +اعمل جدول طبعا اكمل statement أساسي هنا واحدةهي + +175 +00:12:45,650 --> 00:12:49,570 +اللي بتاعة خطقيا الـ C ثابت الـ C و التطوريجي زيها + +176 +00:12:49,570 --> 00:12:52,150 +اه فهنا احنا بدنا ايش من اللي اللي الا احتمالات + +177 +00:12:52,150 --> 00:12:55,150 +الـ C الا احتمالات؟ لأ اه مالاسي احتمالات ثابتة + +178 +00:12:55,150 --> 00:12:59,310 +القيمة الصدق طبعا ثابتة فلا تعد احنا بندور على + +179 +00:12:59,310 --> 00:13:01,990 +الاش على المتغير اللي ياله احتمالات اللي ياله + +180 +00:13:01,990 --> 00:13:04,950 +احتمالات اللي هو ايش مش معروف اللي هو arbitrary هو + +181 +00:13:04,950 --> 00:13:08,130 +اللي بيحددنا الجدول فاحنا عايش حيكون بس عندنا + +182 +00:13:08,130 --> 00:13:11,650 +statement واحدة هنستخدم الـ C هنستخدمها عشان نطبق + +183 +00:13:11,650 --> 00:13:14,610 +لكن مابتدينااش احتمالات جديدة فاحنا عندنا بيه + +184 +00:13:14,610 --> 00:13:19,890 +أساسيالـ C مساعد و فى عنا بس احتمالين يا true يا + +185 +00:13:19,890 --> 00:13:25,650 +false الـ C false false تمام أي سؤال واضحة اخوات + +186 +00:13:25,650 --> 00:13:28,730 +ان الـ tautology و الـ C مابنعدوش مستقلين لإنهم مش + +187 +00:13:28,730 --> 00:13:35,550 +ثوابت كأنهم ثوابت احنا اش بدنا C then B تمام false + +188 +00:13:35,550 --> 00:13:40,550 +then anything true false then anything true اه + +189 +00:13:40,550 --> 00:13:44,090 +فإذن واضح انه من الجدول انه tautology therefore + +190 +00:13:46,500 --> 00:13:55,580 +C implies B فأثبتنا إن فعلًا الـ C implies B فهذه + +191 +00:13:55,580 --> 00:13:57,900 +أول واحدة طبعًا مرهقنة زي ما تشوفين سهل جدًا بس + +192 +00:13:57,900 --> 00:14:00,280 +عشان يمكن الجديد الواحد يلتخم أول ما يشوف كيف تعمل + +193 +00:14:00,280 --> 00:14:05,160 +الجدول و إيش اللي بده يعمله فوضحنا لكوا يعنى فخلاص + +194 +00:14:05,160 --> 00:14:08,780 +أثبت إن الـ tautology يعني إيش implication تضمين + +195 +00:14:08,780 --> 00:14:14,040 +نشوف التاني هيا نعمل التاني عشان كيف نتعامل مع + +196 +00:14:14,040 --> 00:14:19,370 +التطولوجيافالان بدنا نثبت ان اي statement implies + +197 +00:14:19,370 --> 00:14:27,570 +tautology نفس السلوك we have to show او we want to + +198 +00:14:27,570 --> 00:14:33,610 +show that if B then tautology is a tautology + +199 +00:14:36,990 --> 00:14:41,290 +طبعا بالـ truth table تمام فنعمل جدول برضه أكمل + +200 +00:14:41,290 --> 00:14:44,490 +احتمال بس اثنين الـ tautology زي الـ contradiction + +201 +00:14:44,490 --> 00:14:49,070 +فعنا بيه أساسي و هو يا true يا false عندنا الـT + +202 +00:14:49,070 --> 00:14:54,110 +مساعد لكنه دايما الـ true شوف الفرق هنا إيش كل رمز + +203 +00:14:54,110 --> 00:14:59,230 +و دقة الاستخدام الـ true capital T الـ tautology + +204 +00:14:59,230 --> 00:15:02,710 +small T فننتبه إنه إيش ده كل واحدة رمزة و إيش + +205 +00:15:02,710 --> 00:15:07,190 +بتستخدم الآن بدنا إيشif B then T true then true + +206 +00:15:07,190 --> 00:15:13,450 +true if B then T false then true true فواضح أنه + +207 +00:15:13,450 --> 00:15:20,770 +totality فإذا therefore B implies T وهو المطلوب + +208 +00:15:20,770 --> 00:15:27,130 +فأمر بسيط قواعد الجداول الصحيح عملية سهلة لكن إذا + +209 +00:15:27,130 --> 00:15:29,910 +في أي إضافة في تنويب بنوّح كيف نتعامل معاه فأمور + +210 +00:15:29,910 --> 00:15:36,040 +سهلة وهذه قواعدها البسيطةاه تمام هذا section هيك + +211 +00:15:36,040 --> 00:15:39,740 +بسيط وخفيف فهيك احنا بكون انتهينا من قواعد + +212 +00:15:39,740 --> 00:15:43,580 +الاستدلال الآن ان شاء الله هنتقل على ال section + +213 +00:15:43,580 --> 00:15:50,620 +التالي و هنشوف موضوع جديد هيتحدث فيه عن اللي هو + +214 +00:15:50,620 --> 00:15:57,260 +التفكير الاستدلالي التفكير + +215 +00:15:57,260 --> 00:16:02,870 +الاستدلاليفده section قصير لكن احنا ماشيين على + +216 +00:16:02,870 --> 00:16:05,290 +تقسيم الكتاب فملتزمين + +217 +00:16:12,400 --> 00:16:18,720 +طبعا ال section الخامس deductive reasoning التفكير + +218 +00:16:18,720 --> 00:16:24,840 +المنطق أو التفكير الاستدلالي او التفكير القياسي + +219 +00:16:24,840 --> 00:16:28,220 +طرق التفكير القياسي المنطقي القياسي المنطقي هذا + +220 +00:16:28,220 --> 00:16:33,840 +بالنسبة للعنوان باللغة العربية تمامالهدف الرئيسي + +221 +00:16:33,840 --> 00:16:37,540 +من هذا ال section الهدف الأساسي المباشر من ال + +222 +00:16:37,540 --> 00:16:42,960 +section بحد ذاته هنتعلم فيه طرق جديدة لإثبات + +223 +00:16:42,960 --> 00:16:48,300 +التضمين والتكافؤ بديلة لجداول الصدقهدفنا الرئيسي + +224 +00:16:48,300 --> 00:16:54,500 +من هذا ال section هو أن يتعلم كيف يثبت تضمين أو + +225 +00:16:54,500 --> 00:16:58,080 +تكافؤ بطريقة غير جدا والصدق فالان من أنا وطالع صار + +226 +00:16:58,080 --> 00:17:01,560 +لما يديني مثلا قانون هقول كيف تثبتيه truth table + +227 +00:17:01,560 --> 00:17:04,120 +بطلت بدي هي زي الأول صار فيه يا truth table يا + +228 +00:17:04,120 --> 00:17:06,560 +deductive reasoning هتعلم طريقة جديدة هذا هو الهدف + +229 +00:17:06,560 --> 00:17:09,490 +الرئيسيطيب، بس خلينا نمهد ما هو الـ deductive + +230 +00:17:09,490 --> 00:17:12,810 +reasoning ما هو التفكير اللي هو الاستدلالي أو اللي + +231 +00:17:12,810 --> 00:17:15,690 +هو التفكير المنطق .. المنطق القياسي أو القياسي + +232 +00:17:15,690 --> 00:17:20,230 +المنطقي اه فطبعا بقوللي بشكل عام هناك طريقتين + +233 +00:17:20,230 --> 00:17:25,230 +أساسيتين لاللي هو التفكير المنطقي الصحيح التفكير + +234 +00:17:25,230 --> 00:17:28,930 +المنطقي الصحيح في التفكير اللي هو يسموه الاستقرائي + +235 +00:17:29,250 --> 00:17:33,270 +inductive reasoning والتفكير الاستدلالي احيانا + +236 +00:17:33,270 --> 00:17:36,230 +ممكن يعرفوه الصمباطي اللي هو deductive فيه + +237 +00:17:36,230 --> 00:17:40,270 +inductive و فيه deductive اه اللي هو ايش اه فعنا + +238 +00:17:40,270 --> 00:17:43,350 +ال inductive كيف inductive ال inductive بيجي من + +239 +00:17:43,350 --> 00:17:47,390 +الأمثلة و بيستنتج القاعدة للقاعدة ال deductiveمن + +240 +00:17:47,390 --> 00:17:51,650 +القاعدة للمثال بحط القاعدة و بعدين بشوف مين المثال + +241 +00:17:51,650 --> 00:17:54,910 +واضح فهو هذا ال deductive و هذا ال deductive بشكل + +242 +00:17:54,910 --> 00:17:58,290 +عام زي برضه في التعليم فيه بتعلم بحط القاعدة و + +243 +00:17:58,290 --> 00:18:01,690 +بعدين بدي الأنفلة فيه العكس بتعلم الجزء و بعدين + +244 +00:18:01,690 --> 00:18:05,250 +بياخد الكل و هكذا الطرقتين للتعليم و للتفكير و هذه + +245 +00:18:05,250 --> 00:18:11,980 +أمور إيش أساسيةفهذه النقطة بيمشي من الخاص المثال + +246 +00:18:11,980 --> 00:18:16,220 +للقاعدة ال deductive بالعكس بيجي من القاعدة العامة + +247 +00:18:16,220 --> 00:18:20,980 +لمن؟ للأمثلة اللي هي الخاصة فاحنا سميناها مرة top + +248 +00:18:20,980 --> 00:18:24,820 +to bottom لأن القاعدة هي القمة و ال bottom هي + +249 +00:18:24,820 --> 00:18:30,400 +الأمثلأحنا هدفنا ال deductive reasoning خلينا نركز + +250 +00:18:30,400 --> 00:18:34,160 +عليها بعدين ممكن نرجع ال inductive في مواضيع أخرى + +251 +00:18:34,160 --> 00:18:37,020 +فبقوللي الفكرة الرئيسية في ال deductive reasoning + +252 +00:18:37,020 --> 00:18:42,040 +اللي هو إذا كان في عندنا قاعدة عامة something is + +253 +00:18:42,040 --> 00:18:45,660 +true for a class of thing في عندنا قاعدة عامة + +254 +00:18:45,660 --> 00:18:50,040 +لمجموعة من الأشياء بتنطبق عليها فهي القاعدة العامة + +255 +00:18:50,040 --> 00:18:54,560 +فمثلا بأقول جميع طالبات الرياضيات أسكياء فهذه + +256 +00:18:54,560 --> 00:18:58,440 +قاعدةفأنا بأقول فاطمة طالبة الرياضيات، إذا فاطمة + +257 +00:18:58,440 --> 00:19:01,640 +ذكية، هيك يعني، فإذا في قاعدة، فأنا بدأ أشوف أي + +258 +00:19:01,640 --> 00:19:05,900 +مثال هيانطبق عليه القاعدة، فبصير أنا، فهو إيش بقول + +259 +00:19:05,900 --> 00:19:07,840 +ليه؟ a class of things في مجموعة، مثلا مجموعة + +260 +00:19:07,840 --> 00:19:11,880 +طالبة الرياضيات أو كذا، يعني كمثال، فإذا كان هذا + +261 +00:19:11,880 --> 00:19:16,440 +ال truth applied to all، ليه؟ لجمية member of the + +262 +00:19:16,440 --> 00:19:19,200 +class، فأنا بس أثبت إن واحدة فعلا ينتمي للمجموعة + +263 +00:19:19,200 --> 00:19:21,660 +اللي بتنطبق عليها القاعدة، إذا بده ينتمي عليه مين؟ + +264 +00:19:21,660 --> 00:19:26,550 +القاعدة، بده ينطبق عليه القاعدةفبقول لي المفتاح + +265 +00:19:26,550 --> 00:19:29,870 +لهذا التفكير وجهة خليني أمسح الجزء هذا أتوقع أنه + +266 +00:19:29,870 --> 00:19:30,830 +كل خلص منه + +267 +00:19:33,910 --> 00:19:37,330 +فإذن بيصير عندنا الخطوة الأساسية بعد ما نعرف + +268 +00:19:37,330 --> 00:19:42,630 +القاعدة إنه نثبت إن هذا الجزء إيش بينتمي لهذا + +269 +00:19:42,630 --> 00:19:45,430 +الصنف لهذه المجموعة اللي بتنطبق عليها القاعدة فإذا + +270 +00:19:45,430 --> 00:19:47,890 +عشان أثبت إن فاطمة ذكية بدي أثبت إنها طالبة + +271 +00:19:47,890 --> 00:19:51,590 +رياضيات فهي صار هيك القاعدة فبقول طبعا ف miss + +272 +00:19:51,590 --> 00:19:57,390 +categorizing لو أنا ماقدرش أصنف صحأه مايصيرش فيه + +273 +00:19:57,390 --> 00:20:01,650 +خطأ في تقبيل القاعدة، كل استنتاج غير صحيح، فهذا هو + +274 +00:20:01,650 --> 00:20:03,850 +الـ deductive reason كيف لدينا القاعدة و كيف نمشي + +275 +00:20:03,850 --> 00:20:05,150 +للأمثلة + +276 +00:20:07,030 --> 00:20:11,210 +أه طبعا الصورة العامة أو الأشهر في الـ deductive + +277 +00:20:11,210 --> 00:20:14,790 +reasoning أنه فيه أنا فيه بيكون عندي اللي هو اللي + +278 +00:20:14,790 --> 00:20:17,390 +ما يُعرف بيه اللي هو deductive reasoning اللي هو + +279 +00:20:17,390 --> 00:20:20,650 +عبارة عن الـ syllogism اللي هو عبارة عن القياس + +280 +00:20:20,650 --> 00:20:26,710 +المنطقي القياس المنطقي فالصورة تبعته لها تلت خطوات + +281 +00:20:26,710 --> 00:20:30,710 +تلت خطوات زي ما جيبنا المثال فبقى عندي إيش بيقوليه + +282 +00:20:30,710 --> 00:20:35,020 +فيه قاعدةevery x has the characteristic y زي ما + +283 +00:20:35,020 --> 00:20:37,900 +قلنا كل طالبة رياضيات ذكية او جميع طالبات الرياضة + +284 +00:20:37,900 --> 00:20:41,320 +الذكية فانا every x has the characteristic y فانا + +285 +00:20:41,320 --> 00:20:45,520 +عندي قلت كل طالب رياضيات في الخاصية الذكاء مثلا + +286 +00:20:45,520 --> 00:20:48,260 +فهنا القاعدة العامة فهذه القاعدة الصورة العامة + +287 +00:20:48,580 --> 00:20:52,320 +فبقول لي بعدين ايش بقول هذه طلبة رياضيات فاطمة + +288 +00:20:52,320 --> 00:20:57,440 +طلبة رياضيات this thing is X ايش الاستنتاج اذا X + +289 +00:20:57,440 --> 00:21:02,420 +is Y has the characteristic Y therefore الاستنتاج + +290 +00:21:02,420 --> 00:21:06,380 +this thing has the characteristic Y فهذه الصورة + +291 +00:21:06,380 --> 00:21:10,520 +العامة واضحة والمثال بهذا الشكل بيكون بهذه الصورة + +292 +00:21:10,520 --> 00:21:15,800 +فانا في عندي قاعدة جميع طلبة الرياضيات أذكيةفاطمة + +293 +00:21:15,800 --> 00:21:19,900 +طالبة رياضيات ليه إيش؟ this thing هذه الطالبة + +294 +00:21:19,900 --> 00:21:22,980 +طالبة رياضيات إيش الاستنتاج المنطقي بيقول إنه فإذن + +295 +00:21:22,980 --> 00:21:27,180 +فاطمة طالبة ذكية فهذه قاعدة منطقية والكلام بيكون + +296 +00:21:27,180 --> 00:21:30,400 +هناك إيش ينطبق مع المنطق لما أنا باستنتج أي إنسان + +297 +00:21:30,400 --> 00:21:35,020 +يعرف منطق بيقول والله استنتاج صحيح ليش فاطمة ذكية؟ + +298 +00:21:35,020 --> 00:21:38,920 +لأ ضمن قواعد المنطق هذا استنتاج بيكون استنتاج صحيح + +299 +00:21:40,350 --> 00:21:46,670 +نشوف مثال أخر + +300 +00:21:46,670 --> 00:21:50,610 +من + +301 +00:21:50,610 --> 00:21:56,110 +الرياضيات All numbers ending in 0 or 5 are + +302 +00:21:56,110 --> 00:22:00,230 +divisible by 5 كل عدد ينتهي في 0 أو 5 يقبل قسم على + +303 +00:22:00,230 --> 00:22:04,030 +5، قاعدة رياضيةتمام؟ فإيه القاعدة؟ شوف كمثال من + +304 +00:22:04,030 --> 00:22:08,250 +اللي هو الرياضيات فالآن لو جبت أنا أي عدد وبينتهي + +305 +00:22:08,250 --> 00:22:11,290 +بصفر او خمسة بقى بقدر أني أسنتش من غير ما اجرب ولا + +306 +00:22:11,290 --> 00:22:13,770 +يعمل اي حاسب انه يقبل قسم على خمسة صح؟ فإيه + +307 +00:22:13,770 --> 00:22:16,330 +القاعدة؟ فبعد الشكل اللي بنفكر فمثلا الخمسة + +308 +00:22:16,330 --> 00:22:19,990 +وتلاتين بتنتهي بخمسة إذا انت تقبل قسم على خمسة + +309 +00:22:19,990 --> 00:22:23,750 +معروففتدكيف المنطق؟ اه فهذا الأمور خد اثبات لو + +310 +00:22:23,750 --> 00:22:26,730 +واحد جالي اثبت انه لو انا في عندي نظرية اه هذه + +311 +00:22:26,730 --> 00:22:29,630 +النظرية الاولى بقوللي ايه ماهي خاصية القسم على + +312 +00:22:29,630 --> 00:22:33,330 +خمسة بقول كل عدد ينتهي بصفر او خمسة يقبل قسم على + +313 +00:22:33,330 --> 00:22:36,690 +خمسة فلو بقوللي اثبتلي او افحصلي خمسة تلاتين تقبل + +314 +00:22:36,690 --> 00:22:40,590 +قسم على خمسة ولا لا بقوللي الخمسة تلاتين تنتهي + +315 +00:22:40,590 --> 00:22:43,370 +بخمسة اذا اني ايه تنطبق عليها النظرية فاني تقبل + +316 +00:22:43,370 --> 00:22:45,550 +قسم على خمسة من غير ما اعمل اي حاسب ولا شيء حتى لو + +317 +00:22:45,550 --> 00:22:48,010 +جيبت رقم مهول بيم + +318 +00:22:50,400 --> 00:22:53,800 +حاول على الحساب لأن القاعدة أو القاعدة الشمالية + +319 +00:22:53,800 --> 00:22:57,200 +أنا متأكد أنها صحيحة نظرية مثبتة واضح فهذا هو + +320 +00:22:57,200 --> 00:22:59,800 +التفكير المنطق الاستدلالي + +321 +00:23:02,650 --> 00:23:05,970 +أه فطبعا إحنا زي ما حكينا موضوعنا الـ deductive + +322 +00:23:05,970 --> 00:23:08,670 +reasoning ممكن بيسموه أحيانا الـ deductive logic + +323 +00:23:08,670 --> 00:23:12,250 +اللي هو المنطق اللي هو الاستدلالي أو اللي هو ال + +324 +00:23:12,250 --> 00:23:14,770 +logical deductive يعني كل واحد المصارعة نفس المعنى + +325 +00:23:14,770 --> 00:23:19,830 +أو بشكل اللي هو غير رسمي بالعامية يعني بيصيب واحد + +326 +00:23:19,830 --> 00:23:22,970 +top down logical لإنه يجيب من القاعدة الألمية من + +327 +00:23:22,970 --> 00:23:28,250 +القمة اللي هي القاعدة العلمية طبعا إلى اللي هو + +328 +00:23:28,250 --> 00:23:30,930 +القاعة اللي هو القاعدة العامة اللي هو القاعدة + +329 +00:23:30,930 --> 00:23:36,470 +الأساسية للعملينفهي عملية دايمًا بتيجي إنه أنا إيش + +330 +00:23:36,470 --> 00:23:43,930 +اللي هي تفكير منطقي من مُعطَى أو أكتر one or more + +331 +00:23:43,930 --> 00:23:47,610 +statements أنا في عندي مقدمات بيسموها بيسموها + +332 +00:23:47,610 --> 00:23:51,650 +premises أنا في عندي مقدمات to reach a logically + +333 +00:23:51,650 --> 00:23:56,990 +certain conclusion للوصول إلى استنتاج صحيح منطقيًا + +334 +00:23:56,990 --> 00:24:00,370 +مؤكد إن صحته منطقيًا فتتعامل زي ما بحنا نعمل في + +335 +00:24:00,370 --> 00:24:04,870 +رياضات في مُعطَياتفي استنتاج او نظرية ايش المعطيات + +336 +00:24:04,870 --> 00:24:08,070 +و ايش القاعدة فعنا في عندي بديني statements اللي + +337 +00:24:08,070 --> 00:24:10,990 +هو ايش معطع دلوقت انا عارف انهم صحيحين و بدأ اثبت + +338 +00:24:10,990 --> 00:24:14,170 +انه ايش و بدأ استنتج منهم استنتاج صحيح استنتاج + +339 +00:24:14,170 --> 00:24:20,300 +صحيح اه فهذا هو التفكير لصدالي بشكل عامفطبعا زي ما + +340 +00:24:20,300 --> 00:24:23,180 +احنا حكينا The deductive reasoning is a method for + +341 +00:24:23,180 --> 00:24:27,440 +verification that used logic هي طريقة للإثبات + +342 +00:24:27,440 --> 00:24:31,420 +Verification إثبات أشملها تستخدم المنطق عشان قواعد + +343 +00:24:31,420 --> 00:24:33,980 +المنطق هي الحكاية من إن هذا كلام صحيح أو غير صحيح + +344 +00:24:33,980 --> 00:24:37,320 +to draw a conclusion لاشتقاق أو لوصول إلى + +345 +00:24:37,320 --> 00:24:41,670 +استنتاجات تعتمد على مين؟على معطيات اللي بيسميها + +346 +00:24:41,670 --> 00:24:44,450 +statement accepted as true اللي هي ال premises + +347 +00:24:44,450 --> 00:24:47,270 +معطيات او مقدمات بيسموها بالمنطقى احنا في رياضة + +348 +00:24:47,270 --> 00:24:50,350 +بيقول معطيات بيسموها بيسموها premises او بيسموها + +349 +00:24:50,350 --> 00:24:55,950 +hypothesis معطيات او مقدمات بعد هيكفأنا باخد من + +350 +00:24:55,950 --> 00:24:59,470 +هدولة المعطيات، من هدولة اللي هم المقدمات عشان + +351 +00:24:59,470 --> 00:25:03,650 +أوصل لمن؟ للاستنتاج، للاستنتاج بطريقة صحية، فهذا + +352 +00:25:03,650 --> 00:25:06,070 +تفكير ايش؟ تفكير بيسموه تفكير رياضي، زي ما نقول + +353 +00:25:06,070 --> 00:25:11,150 +مثلا جميع الطالبات الرياضيات أذكية، فاطمة طالبة + +354 +00:25:11,150 --> 00:25:14,030 +الرياضيات، هذي ايش؟ معطة، هذي صار معطة، ايش .. ايش + +355 +00:25:14,030 --> 00:25:16,730 +استنتاج منطقي؟ اذا فاطمة طالبة ذكية، هذا استنتاج + +356 +00:25:16,730 --> 00:25:19,690 +منطقي، فدولك بيسموهم ايش؟ معطيات، مقدمات، + +357 +00:25:19,690 --> 00:25:25,250 +فالاستنتاج المنطقي صحيح على طبق لقواعد المنطفبقول + +358 +00:25:25,250 --> 00:25:29,490 +لي if all premises are true إذا كل المعطيات، كل + +359 +00:25:29,490 --> 00:25:36,010 +المقدمات صحيحة واللي هو ال terms واضحين، البنود + +360 +00:25:36,010 --> 00:25:39,270 +واضحة and the rules of deductive logic are + +361 +00:25:39,270 --> 00:25:43,470 +followed واستخدمنا أو اتبعنا قواعد المنطق، هذا مهم + +362 +00:25:43,470 --> 00:25:46,650 +جدا عشان نقول له هذا هي أمشي ده فبالتأكيد إن + +363 +00:25:46,650 --> 00:25:50,910 +الاسمتاج اللي وصلناله بتكون بالضروري صحيح فهناشي + +364 +00:25:50,910 --> 00:25:55,460 +بدناه إذا المعطيات صحيحةو احنا اتبعنا قواعد المنطق + +365 +00:25:55,460 --> 00:25:58,840 +إذا إيش إن الإنتاج اللي وصلنا له بيكون صحيح فده هو + +366 +00:25:58,840 --> 00:26:02,180 +إيش لب موضوعنا يا أخوان لب الموضوع تبعنا اللي هو + +367 +00:26:02,180 --> 00:26:05,340 +بنشتغل على ال deductive reasoning فهذه المقدمة + +368 +00:26:05,340 --> 00:26:11,700 +مهمة جدا عشان نفهم هذا الكلامتمام فهذا يمكن مقدمة + +369 +00:26:11,700 --> 00:26:14,440 +سريع عن الـ deductive reasoning بشكل عام لكن كما + +370 +00:26:14,440 --> 00:26:16,740 +بدأت ال section هدفنا الرئيس في هذا ال section + +371 +00:26:16,740 --> 00:26:20,260 +الآن اللي هو هدفنا القريب و هدفنا البعيد التفكير + +372 +00:26:20,260 --> 00:26:26,700 +هداك اللي هو إيش كيف أثبت قوانين تضمين أو تكافؤ + +373 +00:26:26,700 --> 00:26:30,560 +باستخدام قواعد الاستدلال أو بالتفكير المنطقي ف in + +374 +00:26:30,560 --> 00:26:33,540 +this section we will use deductive method to prove + +375 +00:26:33,540 --> 00:26:37,570 +implications and equivalentsهل ممكن نستخدم الطريقة + +376 +00:26:37,570 --> 00:26:41,870 +الجديدة لإثبات إن في حاجة Contradiction؟ لأ، احنا + +377 +00:26:41,870 --> 00:26:45,710 +استخدمنا truth table بشكل عامالـ truth table هي + +378 +00:26:45,710 --> 00:26:50,370 +أداة أو وسيلة أن أجيب قيمة الصح لأي statement طبعا + +379 +00:26:50,370 --> 00:26:54,690 +بستنتج كيف تضمن أن الجملة الشرطية دايما صحية كيف + +380 +00:26:54,690 --> 00:26:58,410 +equivalence بشوف الطرفين true مع بعض أو false مع + +381 +00:26:58,410 --> 00:27:03,250 +بعض فإذا ال truth table أداة واسعة تستخدم لماذا + +382 +00:27:03,250 --> 00:27:06,790 +لمواضيع متعددة لكن هذه الطريقة البديلة الجديدة + +383 +00:27:06,790 --> 00:27:11,430 +طريقة جديدة للبرهان مش نفس الشيءمش كل شيء بنفعله + +384 +00:27:11,430 --> 00:27:14,310 +truth table بنفعله deductive reasoning هنا بس + +385 +00:27:14,310 --> 00:27:18,290 +محدود ان انا بثبت فيه اللي هو التضمين والتكاثر + +386 +00:27:18,290 --> 00:27:22,090 +واضح؟ اه فايش اللي هو implication and equivalence + +387 +00:27:22,090 --> 00:27:30,080 +اه في عندنا تقريبا 16 قانونملخصين في النظرية من 1 + +388 +00:27:30,080 --> 00:27:35,260 +1 ل 1 6 أو ل 1 7 فهدول هم بيسموهم قواعد مهمة جدا، + +389 +00:27:35,260 --> 00:27:38,380 +هنسميهم قواعد الاستدلال، توافقوا ان انا ايش قلنا؟ + +390 +00:27:38,380 --> 00:27:42,200 +انا فيه عندي مقدمات صحيحة اتبعت قواعد المنطق، اللي + +391 +00:27:42,200 --> 00:27:44,640 +هم هدول القوانين، اللي هم هدول القوانين، إذا + +392 +00:27:44,640 --> 00:27:48,760 +الاستنتاج صحيح، فنامين بدلليلي على إن استنتاجي + +393 +00:27:48,760 --> 00:27:51,240 +صحيح ولا لا، زي القواعد اللي استخدمتها القواعد + +394 +00:27:51,240 --> 00:27:54,150 +الصحيحةفبنفعش .. ممكن ازمنتكوا في المحاضرة الماضية + +395 +00:27:54,150 --> 00:27:57,690 +جالسة هل بنفع لما دخل النافع الآن دخليها نافي نافي + +396 +00:27:57,690 --> 00:28:00,730 +وان؟ لأ، هذا مش قانون، لكن إيش؟ فيه De Morgan's + +397 +00:28:00,730 --> 00:28:03,970 +Law، فزال ما نقوله إيش؟ لما دخل النافع على الآن، + +398 +00:28:03,970 --> 00:28:06,850 +نفيت الجزء إيه؟ انه حولت الار؟ هذا الكلام صحيح، + +399 +00:28:06,850 --> 00:28:10,070 +لكن التاني مش صحيح، لأن مافيش قاعدة، من دليلات؟ + +400 +00:28:10,070 --> 00:28:13,570 +نظرية، نظرية قانون، مايقوله نظرية واحد تلاتة أو De + +401 +00:28:13,570 --> 00:28:16,470 +Morgan's Law، فده هو إيش؟ بيسميه قواعد الاستدلال + +402 +00:28:16,730 --> 00:28:20,870 +فبقول ليش are very useful tools أدوات مهمة جدا + +403 +00:28:20,870 --> 00:28:26,910 +وأساسية justifying logical equivalence بتثبت بتثبت + +404 +00:28:26,910 --> 00:28:30,790 +اللي هو التكافؤ المنطقي و التضمين اللي بتلوزون + +405 +00:28:30,790 --> 00:28:34,090 +التكافؤ مين والتضمين اللي هو هدفنا في الموضوع أو + +406 +00:28:34,090 --> 00:28:39,940 +في هذا sectionهنستخدم 16 قانون أو نسميهم Rules of + +407 +00:28:39,940 --> 00:28:43,580 +Inference طبعاً في على الموقع ملخص لهذه القوانين + +408 +00:28:43,580 --> 00:28:45,860 +معملون جدول عشان أسهل عليكم بعد ما تتطلعوا على + +409 +00:28:45,860 --> 00:28:48,660 +نظريات موجودين فيها أكتر من ال section أنا رصصلكم + +410 +00:28:48,660 --> 00:28:52,900 +إياهم رص ورا بعض قوانين الاستدلال في sheet عليها + +411 +00:28:52,900 --> 00:28:55,420 +قوانين الاستدلال اللي بنستخدمها كلها في النظرية + +412 +00:28:55,420 --> 00:28:59,040 +لأن مهم هذه وانت بتدرسيها وانت بتستخدم الكون قدامك + +413 +00:28:59,040 --> 00:29:03,660 +عشان ترجعيلهاموجودة على الموقع ممكن يتنزلوها قواعد + +414 +00:29:03,660 --> 00:29:07,640 +الاستدلال rules of inference قواعد الاستدلال بنفس + +415 +00:29:07,640 --> 00:29:14,060 +العنوان موجودة طبعا هدوله 16 قانون 20 قانون 15 + +416 +00:29:14,060 --> 00:29:19,020 +قانون هذا العدد مش حصري ولا أنه أساسي هل هدوله + +417 +00:29:19,020 --> 00:29:21,680 +أساسيين و الباجي مش طاقم منهم أو كذا لأ هدول + +418 +00:29:21,680 --> 00:29:26,300 +القوانين طبعا اختيروا بشكل بشكل مافي منهم أساسي في + +419 +00:29:26,300 --> 00:29:29,720 +منهم ممكن نستغنى عنه وممكن نشتق واحد من التاني فهم + +420 +00:29:29,720 --> 00:29:33,100 +مش مستقلين عن بعض مش هم الأساسيين والباقي بيشتق + +421 +00:29:33,100 --> 00:29:37,600 +منه لأ وإنما اختيره بشكل اختيار يمكن نقول المؤلف + +422 +00:29:37,600 --> 00:29:41,600 +ليس الا لكن في منهم طبعا دايما القاعدة اللي احنا + +423 +00:29:41,600 --> 00:29:45,580 +بنهتم فيها بتكون أهم اللي بنستخدمها أكتر و هي اللي + +424 +00:29:45,580 --> 00:29:48,080 +بنحفظها واضح فدول القوانين اللي تكونوا قدامكوا + +425 +00:29:48,080 --> 00:29:51,920 +القانون مع الاستخدام هيبين أن هو مهم و بنحفظه أكتر + +426 +00:29:52,050 --> 00:29:55,730 +فطبعا إن هدول مش بضروري إن هم استقلين عن بعض ممكن + +427 +00:29:55,730 --> 00:30:00,950 +أشتق واحد منهم من التاني بشكل مناسب فطبعا هنشوف + +428 +00:30:00,950 --> 00:30:04,530 +بعد قليل إن Contrapositive law هذا قانون طب هل هذا + +429 +00:30:04,530 --> 00:30:07,550 +مافيش قانون يسد عنه؟ لأ ممكن أشتقه لو نسيته ممكن + +430 +00:30:07,550 --> 00:30:11,730 +أشتقه من قوانين أخرى باستخدام اللي هو التعريفات + +431 +00:30:11,730 --> 00:30:17,210 +وقواعد الاستدلال تمام + +432 +00:30:18,180 --> 00:30:21,240 +فهذه بس مقدمة عن الـ deductive reasoning + +433 +00:30:21,240 --> 00:30:25,540 +والاستخدام اللي بدنا نستخدمه والان بدنا نبدأ اللي + +434 +00:30:25,540 --> 00:30:32,300 +هو انحل بعض الأنفلة فهنا هذا المثال هو مثالنا + +435 +00:30:32,300 --> 00:30:38,000 +الأول ويحتوي المثال في نصه ما هو المقصود بعملية + +436 +00:30:38,000 --> 00:30:41,060 +الـ deductive reasoning أو التفكير الاستدلالي + +437 +00:30:41,060 --> 00:30:44,760 +فبقول لي approve the contrapositive law هذا قانون + +438 +00:30:44,760 --> 00:30:49,680 +مر علينا سابقابرهننا باستخدام جداول الصدق اللي انا + +439 +00:30:49,680 --> 00:30:53,260 +هنشوف له بقى إيش برهان بديل بطريقة أخرى بطريقة + +440 +00:30:53,260 --> 00:30:56,900 +بديلة طبعا نشوف إيش بدقول using relevant + +441 +00:30:56,900 --> 00:31:00,460 +definitions and other rules of inference باستخدام + +442 +00:31:00,460 --> 00:31:04,700 +التعريفات الذات العلاقة وإيش وقواعد الاستدلال هذا + +443 +00:31:04,700 --> 00:31:08,840 +هو detective reasoning بهذا الموضوع إثبات التضمين + +444 +00:31:09,170 --> 00:31:12,150 +والتكافؤ بالطريقة الـ productive reasoning إيش + +445 +00:31:12,150 --> 00:31:15,550 +معناته؟ إنه بدي أثبت باستخدام التعريفات ذات + +446 +00:31:15,550 --> 00:31:18,830 +الإلاقة وقواعد الاستدالة اللي احنا لقصناهم في + +447 +00:31:18,830 --> 00:31:24,150 +النظريات من 1 ل7 فبدنا + +448 +00:31:24,150 --> 00:31:28,430 +نبدأ نشتغل واحدة واحدة خلينا نتعلم هذا مثلنا الأول + +449 +00:31:28,430 --> 00:31:32,990 +هنشتغله خطوة خطوة ببطء شديد عشان .. لأن مثلنا + +450 +00:31:32,990 --> 00:31:38,710 +الأول حد ما نستوعب فهذا المثال الأول solution + +451 +00:31:43,080 --> 00:31:47,500 +أول شيء عشان أستخدم الـ deductive reasoning بدي + +452 +00:31:47,500 --> 00:31:51,940 +أطلع على القانون وكما قدمنا وحكينا فيها أن نوعين + +453 +00:31:51,940 --> 00:31:53,780 +من القانون هيتعامل معاهم في ال deductive reasoning + +454 +00:31:53,780 --> 00:31:57,140 +يا تكافؤ يا تضمين القانون اللي أمامكوا تكافؤ ولا + +455 +00:31:57,140 --> 00:32:03,150 +تضمين؟ تكافؤ هذي أول سؤال التكافؤممكن أبدأ منه من + +456 +00:32:03,150 --> 00:32:07,050 +الجزء اليسار أو اليمين في حرية، في التضمين لأ، في + +457 +00:32:07,050 --> 00:32:09,730 +عندنا بداية إجبارية، فإذا هنا ما زال القانون + +458 +00:32:09,730 --> 00:32:14,410 +تتكافأ، ممكن أبدأ منه، مانعاش من أي جزء، احنا ممكن + +459 +00:32:14,410 --> 00:32:18,110 +نبدأ، خلّينا نبدأ من اليسار، نبدأ من طرف اليسار، + +460 +00:32:18,110 --> 00:32:22,750 +فإذا احنا هنبدأish، if B then AQبدنا تمنا ماشيين + +461 +00:32:22,750 --> 00:32:26,650 +لحد ما نوصل ان هذا يكافئ if not Q then not B + +462 +00:32:26,650 --> 00:32:29,690 +باستخدام كيف بدنا نمشيه؟ بقواعد الاستدلال + +463 +00:32:29,690 --> 00:32:34,790 +والتعريفات دايما وكل خطوة هحط الدليل تبعي هنا انت + +464 +00:32:34,790 --> 00:32:36,910 +عملت هذه الخطوة ليش ده ايه؟ ليش؟ ليش؟ ليش؟ مابنعمل + +465 +00:32:36,910 --> 00:32:41,140 +الدليل؟ وهذا مهم جدا يا أخواتعشان نتعلم طرق + +466 +00:32:41,140 --> 00:32:44,760 +البرهان الرياضي ونقدر نحكم على عملنا انه صح ولا + +467 +00:32:44,760 --> 00:32:50,440 +خطأ بنحط الدليل عشان نعرف انه حلنا صح لانه من + +468 +00:32:50,440 --> 00:32:54,380 +المشكلات الكبرى في البراهين الرياضية ان الطلبة + +469 +00:32:54,380 --> 00:32:58,260 +بيكتب برهان وبيتعب وممكن يكتب صفحة او صفحتين وممكن + +470 +00:32:58,260 --> 00:33:02,120 +يجد ان الحل تبقى صفر كله خطأ ليش؟ لأنه كتب كلام + +471 +00:33:02,120 --> 00:33:06,020 +غير منطقي غير صحيح فلازم انا قبل اي اعمل اي خطوة + +472 +00:33:06,020 --> 00:33:09,260 +اشوف دليلي عشان اعرف ان هذه الخطوة صحيحة او غير + +473 +00:33:09,460 --> 00:33:15,060 +صحيحة صحيحة او غير صحيحة تمام احنا بدأنا فإذا احنا + +474 +00:33:15,060 --> 00:33:19,820 +بدنا نوصل بالتكافئ إلى الصورة المطلوبة فالان طبعا + +475 +00:33:19,820 --> 00:33:23,620 +زي اي هدأ في عندي حاجات خاصة بالموضوع وفي عندي + +476 +00:33:23,620 --> 00:33:27,620 +حاجات خاصة عامة لكل الرياضيات انا بدأ ابدأ من هنا + +477 +00:33:27,620 --> 00:33:32,620 +و اوصل لمين ل not q not b كيف ممكن اعمل ايش هي + +478 +00:33:32,620 --> 00:33:37,440 +نقطة البداية اه الحقيقةفي من الخبرة من التجربة + +479 +00:33:37,440 --> 00:33:41,180 +بيقول إذا فينا جملة شرطية ممكن يساعدنا لأن معظم + +480 +00:33:41,180 --> 00:33:44,340 +القوانين بتلاجواها بممكن أتعامل مع ال or و ال and + +481 +00:33:44,340 --> 00:33:47,600 +بشكل أكتر من ال if then فإذا أول خطوة لازم نعملها + +482 +00:33:47,600 --> 00:33:50,880 +نستخدم التعريف و نحولها ل and فإذا احنا هنقول اللي + +483 +00:33:50,880 --> 00:33:55,740 +هو هذا to cafe not be and not to queue طب ليش + +484 +00:33:55,740 --> 00:33:58,480 +الخطوة دي؟ مين عملناها؟ by definition أو نقول + +485 +00:33:58,480 --> 00:34:04,840 +definitionهي دليلنا دليلنا اه فانا لما حطيتها حافظ + +486 +00:34:04,840 --> 00:34:08,320 +التعريف او الطلاع على التعريف اذا خطوتك صح طب انا + +487 +00:34:08,320 --> 00:34:11,060 +حطيتها من عجلي ممكن تكون غلط لكن انا عارف دي + +488 +00:34:11,060 --> 00:34:14,280 +التعريف هذا الكلام الطلاع على التعريف تكافؤ طب هي + +489 +00:34:14,280 --> 00:34:17,780 +تكافؤ ولا implies؟ اه تكافؤ في القانون شايفة؟ عشان + +490 +00:34:17,780 --> 00:34:21,020 +اتأكد طب لو عملت implies صح ولا غلط؟ غلط ممكن تكون + +491 +00:34:21,020 --> 00:34:25,080 +غلط ده الأمور دقيقة و بدنا نتعلم الدقة نتعلم الدقة + +492 +00:34:25,080 --> 00:34:28,700 +لأنه ممكنالتساهُر يدّينا إيش؟ يودّينا في مكان + +493 +00:34:28,700 --> 00:34:31,920 +خاطئ، في مكان خاطئ، فهذه الخطوة الأولى، تمام، + +494 +00:34:31,920 --> 00:34:34,980 +الأنها بدأنا نعمل، إيش ممكن أعمل؟ ممكن أعمل + +495 +00:34:34,980 --> 00:34:38,440 +DeMorgans، ممكن، بس الإنسان طبعا أول ما يشوف حاجة + +496 +00:34:38,440 --> 00:34:42,000 +برا بده يدخلها جوا، لكن أنا خلّيني أتأنى شوية + +497 +00:34:43,100 --> 00:34:47,020 +خلّيني أتقن شويه احنا وين بدنا نوصل وده طريقة + +498 +00:34:47,020 --> 00:34:52,360 +بنتعلمها احنا بدنا نوصل لـQ.B جيد لو جينا نعمل + +499 +00:34:52,360 --> 00:34:55,900 +خليني أمسح هان عشان أنا أعرف وين رايح هذا مهم جدا + +500 +00:34:55,900 --> 00:35:00,620 +في البرهان مش أني أبدأ من طرف و تمني ماشي و أشوف + +501 +00:35:00,620 --> 00:35:05,710 +وين واصل لأ أعرف وين رايحفي البرهان، مش كل حاجة + +502 +00:35:05,710 --> 00:35:11,010 +كتبتيها حتى لو كانت صحيحة، إنها مفيدة، أنا بدي + +503 +00:35:11,010 --> 00:35:15,990 +الحاجة تكون صحيحة وتؤدي إلى الهدف، وتخدم الهدف، + +504 +00:35:15,990 --> 00:35:18,030 +عشان هذي كتير قعدت طلب، وليش مقولك؟ طب أنا اللي + +505 +00:35:18,030 --> 00:35:21,440 +كاتبه صح، ليش مش حاطط العلمات؟ما مفيدش صح إنه يتوي + +506 +00:35:21,440 --> 00:35:25,640 +صح لكن مش هو اللي بيأديك للحل الصحيح للحل الصحيح + +507 +00:35:25,640 --> 00:35:30,000 +فاحنا هذه الأمور ملاحظات مهمة جدا هنتعلمها و هناخد + +508 +00:35:30,000 --> 00:35:33,740 +فيها أمثلة متعددة لحد ان شاء الله ما ننجح و لترسخ + +509 +00:35:33,740 --> 00:35:37,740 +عنا بالاستخدام أنا أين رايح أنا هادي و أود أوصل + +510 +00:35:37,740 --> 00:35:43,650 +هناأه فده هامش مش هي الحالة not Q then not B طيب + +511 +00:35:43,650 --> 00:35:48,090 +هادي واضح اللي كبدا روح مش واضح ولا واضح مش واضح + +512 +00:35:48,090 --> 00:35:52,860 +طب خليني أعمل تعريف على هادي إيش تكافئ notnot .. + +513 +00:35:52,860 --> 00:35:56,540 +هذه هي اللي هيجيب صلاة التاشرة الشرط هذه not q and + +514 +00:35:56,540 --> 00:36:01,940 +not not b صح؟ عشان انتبهوا الآن انتبهوا معايا هذه + +515 +00:36:01,940 --> 00:36:06,900 +هي الخمنة شوية لانه شوية هذه كأنها سميها a وهذه + +516 +00:36:06,900 --> 00:36:11,920 +سميها b لما if b then a إيش ده تكون؟ not للكل + +517 +00:36:11,920 --> 00:36:18,220 +وإيش؟ و a اللي هي not q و not b واضحة؟ أه ومش غلط + +518 +00:36:18,220 --> 00:36:23,550 +تعملوا الرموز هذه خطوة وسيطة واضح؟وقفوني أنا هلجيت + +519 +00:36:23,550 --> 00:36:27,470 +من ده مش اي اول مثال اللي بنعمله ببطء هنا صعب + +520 +00:36:27,470 --> 00:36:32,190 +نعيده بعدين لإنه هنتقدم بس هذا اول مثال طيب هلجيت + +521 +00:36:32,190 --> 00:36:38,410 +هذا ممكن ابسطه عشان اعرف أين رايح انا نعم نط نط Q + +522 +00:36:38,410 --> 00:36:43,790 +and P بدي اوصل اذا انا أين رايح اه هاي هدفي هاي + +523 +00:36:43,790 --> 00:36:48,430 +هدفي طيب نقارن بين ما بدنا نروح له دي طبعا نط و + +524 +00:36:48,430 --> 00:36:53,590 +بين اللي عندنا بعيد ولا جريب جريب جداهل كان دا + +525 +00:36:53,590 --> 00:36:56,830 +أدقن النط لأ لإننا بدنا نرط على النط وهذه ممكن + +526 +00:36:56,830 --> 00:37:00,530 +نشوفها ملاحظة نصيحة إذا انت الهدف اللي بدك توصيله + +527 +00:37:00,530 --> 00:37:03,370 +فيه if then خلّي النط برة دخليهاش لإنه في الآخر + +528 +00:37:03,370 --> 00:37:07,250 +بدك يجاها لإنه بالآخر بدنا نرجع ولا لأ فالنط ماحنا + +529 +00:37:07,250 --> 00:37:10,710 +محتاجة فإذا ما اتصبعش أنا وده يمكن حتى في الحسابات + +530 +00:37:11,190 --> 00:37:14,430 +هل دايما انا بشوف أقواص بفكها؟ لأ انا ممكن دايما + +531 +00:37:14,430 --> 00:37:17,830 +بحتاج التحليل مش ضروري افكه فلازم ايش ما نعملش + +532 +00:37:17,830 --> 00:37:21,110 +العملية بتسرع بدنا ايش نتقن و نشوف احنا وين رايحين + +533 +00:37:21,110 --> 00:37:26,610 +فالان واضح من هنا ما علي الا اغير الترتيب ممكن + +534 +00:37:26,610 --> 00:37:31,550 +اغير الترتيب نعم قانون إيش الإبدال هذه and ال and + +535 +00:37:31,550 --> 00:37:38,530 +إبدالية فاروح أعمله نط نط why نط Q and B من وين + +536 +00:37:38,530 --> 00:37:40,250 +هذا commutative law + +537 +00:37:43,020 --> 00:37:48,600 +اه اللي بتكتبش حصن على طول ليش لحد ما ترسخ القواعد + +538 +00:37:48,600 --> 00:37:52,140 +هذه ما تعمليش حاجة ماعنكيش داليل عليها لأنه ممكن + +539 +00:37:52,140 --> 00:37:56,540 +تكون خطوة خطأ فانا بدي نلزم نفسنا عشان نتعلم صح + +540 +00:37:56,540 --> 00:38:01,750 +بدنا نلزم نفسنا و نكتب عشانبسيطة يعني انا .. يعني + +541 +00:38:01,750 --> 00:38:05,250 +ممكن ات .. مش ضروري مثلا في عندي خمس خطوات انسيت + +542 +00:38:05,250 --> 00:38:08,890 +خطوة بسيطة لكن لو اتعودنا هنحفظهم فانا ممكن ايش + +543 +00:38:08,890 --> 00:38:12,930 +نتسهل لكن كلهم م .. م .. م .. نسيهم مينفعش هو احنا + +544 +00:38:12,930 --> 00:38:15,810 +ايش قلنا دايما و أنت في البيت بتحلي ال exercise + +545 +00:38:15,810 --> 00:38:18,790 +هتعودي تكتبي هتلاقي حالك اتعودتي في الامتحان فدي + +546 +00:38:18,790 --> 00:38:22,550 +مهمة جدا واضح؟ اه فدي committed flow خلصنا هذا + +547 +00:38:22,550 --> 00:38:24,810 +اللي هو اللي بدناهي اه اذا بدنا نعمل الخطوة دي + +548 +00:38:24,810 --> 00:38:27,810 +ممكن نعملها كمان مرة مافيش مشكلة عشان نوصل فدي + +549 +00:38:27,810 --> 00:38:34,790 +عبارة عن نطق نطقnot not b إيش هذا double negation + +550 +00:38:34,790 --> 00:38:40,290 +نفي + +551 +00:38:40,290 --> 00:38:43,170 +المزدوج هذا القانون يا بتحطوا رقم النظرية اللي + +552 +00:38:43,170 --> 00:38:47,290 +الاسم مش عافظينه رقم النظرية كله صح قواعد إسلال + +553 +00:38:47,290 --> 00:38:49,650 +موجودة خلاص نالي إيه زي ما أحنا شايفين هذا إيش + +554 +00:38:49,650 --> 00:38:54,290 +ماله يكافئ not q then not b من وين جيبت هذه الخطوة + +555 +00:38:54,290 --> 00:38:55,090 +تعريف + +556 +00:39:05,640 --> 00:39:11,920 +definition فإذن بدأنا من طرف مشينا باستخدام + +557 +00:39:11,920 --> 00:39:16,620 +التعريفات ذات العلاقة وقواعد الاستدلال ووصلنا + +558 +00:39:16,620 --> 00:39:19,560 +للمطلوب فإذا فعلا هذا يكافئ هذا بدأنا فيها + +559 +00:39:19,560 --> 00:39:23,120 +والتكافئ كله تكافئ إذا فعلا يكافئ بعض هذا ده + +560 +00:39:23,120 --> 00:39:26,940 +بيسموه فانا أثبت القانون باستخدام اللي هو ال + +561 +00:39:26,940 --> 00:39:32,740 +deductive reasoningواضح؟ طبعا الوضوح عشرة في المية + +562 +00:39:32,740 --> 00:39:35,360 +اشتريت في المية جيد لانه لسه اول مثال ان شاء الله + +563 +00:39:35,360 --> 00:39:38,360 +في اقل من خمس او سبع امثلة شوية شوية الامور ان شاء + +564 +00:39:38,360 --> 00:39:41,600 +الله هتتضدح اكتر نكتفي بعد القدر ان شاء الله + +565 +00:39:41,600 --> 00:39:43,860 +نلاقاش المحاضرة الجاية هنكمل + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/IiQLVUdLX2g_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/IiQLVUdLX2g_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..9ba3188dc50836a0e089d401f723606f1aca2bcd --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/IiQLVUdLX2g_postprocess.srt @@ -0,0 +1,2264 @@ +1 +00:00:19,670 --> 00:00:23,750 +بسم الله الرحمن الرحيم ان شاء الله هنواصل مع اللي + +2 +00:00:23,750 --> 00:00:28,710 +هو الاخترانات او الدوال و بدنا نشتغل احنا على اللي + +3 +00:00:28,710 --> 00:00:34,410 +هو injective و surjective و bijective خلينا نسترجع + +4 +00:00:34,410 --> 00:00:37,910 +التعريفات على السريع و نكمل مع الأمثلة لأنه + +5 +00:00:37,910 --> 00:00:43,950 +تعريفات أساسية فبنقول على الدالة F انها injective + +6 +00:00:43,950 --> 00:00:47,090 +يعني one to one + +7 +00:00:59,690 --> 00:01:06,310 +أي عنصرين في الـ domain طبعاً F دالة من X إلى Y + +8 +00:01:06,310 --> 00:01:15,550 +فعنا F of X1 تساوي F of X2 implies X1 تساوي X2 + +9 +00:01:16,640 --> 00:01:22,180 +تعريف الـ one to one نعيد بس نتذكر بمعنى آخر أنه + +10 +00:01:22,180 --> 00:01:25,500 +الصور المتساوي أو العناصر المختلفة تؤدي لصور + +11 +00:01:25,500 --> 00:01:29,840 +مختلفة طبعا ده ممكن نكتبه بشكل مختلف for all x one + +12 +00:01:29,840 --> 00:01:37,340 +in x for all x two in + +13 +00:01:37,340 --> 00:01:43,100 +x ال contrapositive x one لا تساوي x two implies f + +14 +00:01:43,100 --> 00:01:48,730 +of x one لا تساويF of X two فالعناصر المختلفة + +15 +00:01:48,730 --> 00:01:50,990 +بتروح لصور مختلفة دي معناته اللي هو ايش بيسميها + +16 +00:01:50,990 --> 00:01:54,930 +تطبيق اللي بيسموها دالة متباينة او اقتران متباين + +17 +00:01:54,930 --> 00:01:58,430 +يعني بيأدي ليش اختلاف العناصر يؤدي لاختلاف الصور + +18 +00:01:58,430 --> 00:02:01,930 +فهذه يدل هذا التعريف او هذا متكافئين في الغالب + +19 +00:02:01,930 --> 00:02:04,710 +بيستخدم هذا لأنه ايش فيه سهولة بالتعامل مع اللي + +20 +00:02:04,710 --> 00:02:07,930 +يساوي اكتر من التعامل مع اللي لا يساوي في عندنا + +21 +00:02:07,930 --> 00:02:15,690 +تعريف اخر ان ال F بيسميها surjectiveسيرجيكتف او on + +22 +00:02:15,690 --> 00:02:20,730 +to التعليم الصلاح الاخر بين قصين اش يكافئ for all + +23 +00:02:20,730 --> 00:02:24,670 +y في المجال المقابل كل عنصر المجال المقابل هو صورة + +24 +00:02:24,670 --> 00:02:30,210 +there exist x في ال domain بحيث y تساوي f of x + +25 +00:02:30,210 --> 00:02:36,090 +بحيث y تساوي f of x او برضه هذا يكافئ تعريف اخر ان + +26 +00:02:36,090 --> 00:02:46,100 +ال image بيساوي yبساوي Y بساوي image ال F تعريفين + +27 +00:02:46,100 --> 00:02:50,860 +متكافئين بنجرب مين أسهل بالنسبة لنا اتنين ممكن + +28 +00:02:50,860 --> 00:02:55,780 +نستخدمه اه طبعا اخر حاجة بس للمراجعة bijective + +29 +00:02:55,780 --> 00:03:01,380 +اللي يشملها بدى تكون injective and surjective + +30 +00:03:01,380 --> 00:03:06,180 +injective and F is surjective + +31 +00:03:08,460 --> 00:03:12,740 +فيمكن هذا مختصر للمحاضرة الأخيرة فدول المصطلحات أو + +32 +00:03:12,740 --> 00:03:17,920 +هذه المفاهيم مهم جدا نحفظها و نعرفها و طبعا الأهم + +33 +00:03:17,920 --> 00:03:21,710 +نعرف نتعامل معاهادّينا أمثلة كيف نثبت أن الدالة + +34 +00:03:21,710 --> 00:03:24,310 +one to one و أمثلة كيف نتعامل مع أن نثبت أن الدالة + +35 +00:03:24,310 --> 00:03:27,150 +one to و أو نثبت أنها ليست one to one أو ليست one + +36 +00:03:27,150 --> 00:03:30,710 +to طبعا من التعريف من التعريف آه شوفنا احنا المثال + +37 +00:03:30,710 --> 00:03:33,370 +الأول خلّيني نشوف طبعا ال page اتفاقية قدامنا + +38 +00:03:33,370 --> 00:03:36,290 +التعريف طبعا بيسموها one to one correspondence ليه + +39 +00:03:36,290 --> 00:03:40,390 +ايش؟ دالة تناظرية واحد إلى واحد أو اقتران تناظر + +40 +00:03:40,390 --> 00:03:46,230 +بيسموه في عندنا المثال رقم اتنينخلّينا نقرعه مع + +41 +00:03:46,230 --> 00:03:49,870 +بعض وبنعلق عليه ونشوف إيش الهدف منه في شاهد من + +42 +00:03:49,870 --> 00:03:55,470 +المثال let f a function من X ل Y be an injection + +43 +00:03:55,470 --> 00:03:59,290 +إيش يعني؟ one to one فهي injective function one to + +44 +00:03:59,290 --> 00:04:04,770 +one and let A capital A sub one و capital A two be + +45 +00:04:04,770 --> 00:04:09,330 +subsets of X أخد مجموعتين ديوسيتين من ال XShow + +46 +00:04:09,330 --> 00:04:15,410 +that، ايش المطلوب تقاطع الصور هو subset من صورة + +47 +00:04:15,410 --> 00:04:21,830 +التقاطع، ايش الهدف؟ احنا فيه نظرية تلات عشرة نظرية + +48 +00:04:21,830 --> 00:04:28,560 +تلات عشرة، theoremتلاتة عشر أيش بتقول جزء منها بيه + +49 +00:04:28,560 --> 00:04:34,760 +بقول لإنه صورة التقاطع على أي family هو صبصة من + +50 +00:04:34,760 --> 00:04:39,920 +تقاطع الصورة من تقاطع الصورة اه فقولنا هنا مافيش + +51 +00:04:39,920 --> 00:04:46,190 +تساوي جامة تبقي للجامع فهذا بشكل عام لأي دالةهدفنا + +52 +00:04:46,190 --> 00:04:49,650 +نثبت إنه ممكن يصير إن الطرف زي ما هو الطرف اليسار + +53 +00:04:49,650 --> 00:04:53,390 +صبصت من اليمين، بدنا نثبت إنه اليمين صبصت من إيش + +54 +00:04:53,390 --> 00:04:55,830 +من اليسار، وبالتالي فيصيب تساوي، وبالسار يصيب + +55 +00:04:55,830 --> 00:04:58,910 +تساوي، طب هل هذا دايما صح؟ لأ، لأنه في النظرية جات + +56 +00:04:58,910 --> 00:05:01,690 +لأ مش دايما صح، أي إيش ماله إذا كانت الدالة one to + +57 +00:05:01,690 --> 00:05:04,790 +one؟إذا الدالة one to one بيصبح أيش فيه تساوي؟ + +58 +00:05:04,790 --> 00:05:10,010 +بشكل عام، نظرية 13 لأي دالة، لأي دالة الكلام صحيح، + +59 +00:05:10,010 --> 00:05:12,550 +طب لو الدالة one to one، بيصير فيه تساوي، بيصير + +60 +00:05:12,550 --> 00:05:15,570 +فيه تساوي، فبننمهد هذا البرهان بدل ما نشتر على + +61 +00:05:15,570 --> 00:05:18,650 +اللي هو أي family من المجموعات، هناخد بس مجموعتين، + +62 +00:05:18,650 --> 00:05:22,950 +عشان نفهم هذه أسلوبفعال جدا في عندنا نظرية في + +63 +00:05:22,950 --> 00:05:26,710 +عندنا مفهوم مدينية بشكل عام نبدأ نفهم و ناخد أمثلة + +64 +00:05:26,710 --> 00:05:30,270 +عدد صغير صغير من الاش من العناصر و هكذا بنقدر + +65 +00:05:30,270 --> 00:05:33,610 +نتصور الصورة العام بنقدر نتصور الصورة العام فطبعا + +66 +00:05:33,610 --> 00:05:39,220 +هنا جلنا ان صورة التقاط عصابس دايما صحفالطرف الأول + +67 +00:05:39,220 --> 00:05:42,500 +اللي هو اليمين صبصت من اليسار في المثال دايما صح، + +68 +00:05:42,500 --> 00:05:46,180 +إذا المهم أن اليمين صبصت من اليسار، فادانا المثال + +69 +00:05:46,180 --> 00:05:49,240 +أنه بدل ما عندي family من ال 6 ما لنهاية ممكن + +70 +00:05:49,240 --> 00:05:52,180 +تكون، اداني بس مجموعتين، فأنا معنى كيف أثبت أن + +71 +00:05:52,180 --> 00:05:56,000 +اليمين صبصت من اليسار، واضحة فكرة المثال؟ واضح + +72 +00:05:56,000 --> 00:06:00,950 +الشاهد؟ تمام، نيجيناخد المثال على عفويته من غير + +73 +00:06:00,950 --> 00:06:04,030 +اللي عمه اختبعه و ايش الهدف منه هو عبارة مدينة + +74 +00:06:04,030 --> 00:06:07,870 +موطيات فوق و بيقوللي اثبت انه مجموعة صبست من + +75 +00:06:07,870 --> 00:06:10,790 +التانية واحدة من المهارات الأساسية هناخد عنصر و + +76 +00:06:10,790 --> 00:06:13,890 +نوصله من اليسار لليمين و لا لأ مش اذا اتعلمنا طب + +77 +00:06:13,890 --> 00:06:17,790 +ايش نسميه X ولا Y؟ Y أنسب لأنه صورة هو لأنه هو + +78 +00:06:17,790 --> 00:06:25,830 +صورة فهنبدأ البرهان solutionlet Y تنتمي لل F of A1 + +79 +00:06:25,830 --> 00:06:32,130 +تقاطع F of A2 بدأنا بأنصر من الطرف اليسار بدنا + +80 +00:06:32,130 --> 00:06:32,950 +نوصله لليمين + +81 +00:06:37,170 --> 00:06:40,910 +أتوقع إن الكل بيبدأ .. بيعرف يبدأ إيش اللي هو + +82 +00:06:40,910 --> 00:06:44,770 +علاقة subset و لا لأ طيب إيش ممكن نعمل الآن؟ مين + +83 +00:06:44,770 --> 00:06:48,390 +عنده فكرة؟ ننفق التقاطة أحسن يعني فالإنسان .. يعني + +84 +00:06:48,390 --> 00:06:51,330 +زي ما قلنا الرياضية فيها صعوبة فيها صعوبة لكن مش + +85 +00:06:51,330 --> 00:06:54,570 +سحر يعني الناس بتتعلم و أحنا ممكن نتعلم زيهم آه + +86 +00:06:54,570 --> 00:06:57,590 +فالأمور هي .. بنبدأ نشوف الآن كيف الناس بتفكر كيف + +87 +00:06:57,590 --> 00:07:01,110 +الناس بتعمل و نحاول آه ممكن ننفع بعض الحياة ممكن + +88 +00:07:01,110 --> 00:07:04,550 +نفشل .. لكن بتعلم و الواحد خبراء فنفق التقاطة فده + +89 +00:07:04,550 --> 00:07:12,350 +معناته impliesإن الـ Y تنتمي للـ F of A1 و Y تنتمي + +90 +00:07:12,350 --> 00:07:21,010 +للـ F of A2 تعريف التقاطع تعريف التقاطع تمام إيش + +91 +00:07:21,010 --> 00:07:28,070 +كمان ممكن نعمل؟ ممكن نعمل تعريف الصورة Y إيش + +92 +00:07:28,070 --> 00:07:32,150 +معناه؟ Y في صورة مجموعة يعني Y صورة عنصر من + +93 +00:07:32,150 --> 00:07:35,630 +المجموعة خلينا .. بدي أمحيها أنا جيت هنا أتوقع + +94 +00:07:35,630 --> 00:07:36,590 +مناسب نمحيها + +95 +00:07:43,610 --> 00:07:48,170 +فهذا يؤدي أن Y تساوي أو خلّيني أكتبها بالشكل + +96 +00:07:48,170 --> 00:07:56,370 +التالي There exists X1 في الـ A1 و Y تساوي F of X1 + +97 +00:07:56,370 --> 00:08:00,470 +هي سورة + +98 +00:08:00,470 --> 00:08:04,870 +عنصر من الـ A1 ممكن أكتبها أن Y تساوي F of X1 for + +99 +00:08:04,870 --> 00:08:08,590 +some X1 in A أو There exists الطريقتين صح ولا لأ؟ + +100 +00:08:08,750 --> 00:08:13,510 +تفقين؟ لسه ميتها X1 مش X عشان أربطها مع A1 هذا + +101 +00:08:13,510 --> 00:08:17,810 +بسهل التعامل طبعا زي ما بقيد و بكرر مافيش رمز غلط + +102 +00:08:17,810 --> 00:08:22,230 +مافيش تسمية غلط لكن في تسمية أنسب أسهل أيضا الآن + +103 +00:08:22,230 --> 00:08:33,030 +there exist X2 في ال A2 والY تساوي F of X2واضح؟ اي + +104 +00:08:33,030 --> 00:08:37,430 +سؤال اتوقع انه المفروض كل الطالبات يعرفوا يعملوا + +105 +00:08:37,430 --> 00:08:40,650 +دول الخطوطين لأنه سهلين من تعرفها طيب احنا في + +106 +00:08:40,650 --> 00:08:45,250 +الطريق الصحيح نشوف وين نتطلع على المطلوب مش دايما + +107 +00:08:45,250 --> 00:08:49,270 +انا على المطلوب تمام انا بدي اوصل ان ال Y اللي + +108 +00:08:49,270 --> 00:08:54,500 +بدأت فيها هي F of A1 تقاطع ال A2وقت إيش ال Y + +109 +00:08:54,500 --> 00:08:57,760 +بتكون؟ ممكن أكتب بشكل معين إيش معناة Y في F في + +110 +00:08:57,760 --> 00:09:02,060 +التقاطع؟ يعني Y بتساوي عنصر من التقاطع فأنا إيش + +111 +00:09:02,060 --> 00:09:06,700 +عندي صار؟ قال لي ال Y بتساوي F of X1 و ال Y بتساوي + +112 +00:09:06,700 --> 00:09:11,020 +F of X2 لو كدرت أثبت إن X1 تساوي X2 في التقاطع + +113 +00:09:11,020 --> 00:09:14,680 +انتهت العملية لو كدرت أثبت إن X1 تساوي X2 انتهت + +114 +00:09:14,680 --> 00:09:17,740 +العملية طب كيف أثبت إن X1 تساوي X2؟ هنشوف إيش + +115 +00:09:17,740 --> 00:09:22,220 +معناه معطيات بقول لي الدالة one to oneأه فلو كنت + +116 +00:09:22,220 --> 00:09:25,960 +أثبت أن صورة X1 تساوي صورة X2 بقدر أستنتج أن X1 + +117 +00:09:25,960 --> 00:09:31,200 +تساوي X2 طب هل في عندي ما يدل؟ نعم Y تساوي F of X1 + +118 +00:09:31,200 --> 00:09:38,100 +نفس ال Y بتساوي F of X2 فإذن هنا يؤدي أن F of X1 + +119 +00:09:38,100 --> 00:09:44,250 +بتساوي Y في نفس الوقت بتساوي F of X2فشايفين الواحد + +120 +00:09:44,250 --> 00:09:48,830 +يفكر وين هو إيش المعطيات ويعرف كيف بيبدأ وكيف + +121 +00:09:48,830 --> 00:09:52,470 +بينتهي ويشوف دايما وين رايحه ويفكر واتوقع أن + +122 +00:09:52,470 --> 00:09:56,230 +العملية مش صعبة أن العملية مش صعبة F of X1 تساوي F + +123 +00:09:56,230 --> 00:09:59,570 +of X تساوية الصور لازم تساوي العناصر تعريف ال one + +124 +00:09:59,570 --> 00:10:04,990 +to one فهذا يؤدي أن X1 تساوي X2 ليش؟ لأن ال F is + +125 +00:10:04,990 --> 00:10:07,950 +one to one ممكن اكتب اختصارا بيد الشكل one to one + +126 +00:10:07,950 --> 00:10:11,690 +بنكتب اختصارا بيد الصورةأه فهذه هو لأنها one to + +127 +00:10:11,690 --> 00:10:15,350 +one كانت مظبطتش أه فهذه مهم جدا المعطى أن الدالة + +128 +00:10:15,350 --> 00:10:18,850 +one to one ممتاز إذا إيش أصبح إذا X1 و X2 وين + +129 +00:10:18,850 --> 00:10:22,370 +موجودة في التقاطع لأنه التنتين موجودين فهذا يؤدي + +130 +00:10:22,370 --> 00:10:28,780 +إن X1 تساوي X2وخلّيني أسمي القيمة المشتركة X0 + +131 +00:10:28,780 --> 00:10:31,880 +تسميها دي لعندي هنا أنا متفقين بس إذا بدني أسميها + +132 +00:10:31,880 --> 00:10:36,180 +F of X1 ما خلاص مايفيه قيمة مشتركة فالجدران عندي + +133 +00:10:36,180 --> 00:10:40,100 +X1 بتساوي 2 و X2 بتساوي 2 فانا بسميهم القيمة + +134 +00:10:40,100 --> 00:10:43,460 +المشتركة هي 2 أو X0 في هذا الشكل وين موجودة؟ في + +135 +00:10:43,460 --> 00:10:48,580 +التقاطةتقاطع اتنين لأن لو قلت انا X واحد في + +136 +00:10:48,580 --> 00:10:51,600 +التقاطع طبعا ليش ماخدداش X اتنين لأ التنتين هم هم + +137 +00:10:51,600 --> 00:10:56,100 +التنتين ممتاز مزال X Zero في التقاطع اذا صورتها + +138 +00:10:56,100 --> 00:11:01,080 +وين في صورة التقاطع على طول فهذا يؤدي F of X واحد + +139 +00:11:01,080 --> 00:11:05,800 +اللي هي Y وتساوي F of X اتنين وتساوي F of X Zero + +140 +00:11:05,800 --> 00:11:11,230 +وين موجودة في صورة إيش التقاطعإذا العنصر انوجد + +141 +00:11:11,230 --> 00:11:15,930 +صورة وين بتكون؟ في صورة المجموعة إذا عنصر ما انوجد + +142 +00:11:15,930 --> 00:11:19,230 +في مجموعة صورة وين بتكون؟ في صورة المجموعة خلاص + +143 +00:11:19,230 --> 00:11:22,450 +إذاً Y وصلناها لمين للطرف اليسار انتهى البرهن + +144 +00:11:22,450 --> 00:11:27,290 +بدأنا من عنصر Y في الطرف اليسار وصلناه بطريقة + +145 +00:11:27,290 --> 00:11:33,860 +رياضية صحيحة للطرف اليمين انتهى البرهنF of A1 + +146 +00:11:33,860 --> 00:11:41,020 +تقاطع F الـ A2 subset من صورة التقاطع F of A1 + +147 +00:11:41,020 --> 00:11:48,540 +تقاطع A2 وهو المطلوب أي سؤال واضح؟ بدنا نبني عليه + +148 +00:11:48,540 --> 00:11:52,900 +الآن إذا فهمنا الفكرة تاعة المجموعتين الآن هنعمل + +149 +00:11:52,900 --> 00:11:56,380 +لو فينا تلاتة بنفس الطريقة لو عندنا عشرة نفس + +150 +00:11:56,380 --> 00:12:04,990 +الطريقة فهذه النظريةنظرية 3.13 Images of + +151 +00:12:04,990 --> 00:12:09,350 +intersections under injective functions نظرية 3.13 + +152 +00:12:09,350 --> 00:12:12,310 +كانت تحت أي فункشن، تحت أي فункشن، تحت أي فункشن، + +153 +00:12:12,310 --> 00:12:12,770 +تحت أي فункشن، تحت أي فункشن، تحت أي فункشن، تحت + +154 +00:12:12,770 --> 00:12:13,170 +أي فункشن، تحت أي فункشن، تحت أي فункشن، تحت أي + +155 +00:12:13,170 --> 00:12:13,710 +فункشن، تحت أي فункشن، تحت أي فункشن، تحت أي + +156 +00:12:13,710 --> 00:12:17,990 +فункشن، تحت أي فункشن، تحت أي فункشن، تحت أي + +157 +00:12:17,990 --> 00:12:18,290 +فункشن، تحت أي فункشن، تحت أي فункشن، تحت أي + +158 +00:12:18,290 --> 00:12:21,750 +فункشن، تحت أي فункشن، تحت أي فункشن، تحت أي + +159 +00:12:21,750 --> 00:12:26,310 +فункشن،and let a sub gamma اسمه الـ gamma في + +160 +00:12:26,310 --> 00:12:29,570 +الكيبة الـ gamma بيبقى family of subsets of X ليه + +161 +00:12:29,570 --> 00:12:32,290 +subsets من X؟ عشان ياخد صوره، ضروري يكونوا من ال + +162 +00:12:32,290 --> 00:12:38,110 +domain then صورة التقاطع تساوي تقاطع الصور واحد + +163 +00:12:38,110 --> 00:12:41,810 +يقول يعني لغاية النظرية السابقة؟ لأ، هذه كانت عامة + +164 +00:12:41,810 --> 00:12:45,610 +لكل دالة هذه خاصة بالدوال ال injective ال one to + +165 +00:12:45,610 --> 00:12:50,040 +one واضح يا أخوات؟ لازم من أول يومنقرأ بدقة + +166 +00:12:50,040 --> 00:12:53,940 +وبطريقة صحيحة عندك نظرية في تناقض بين نظريتين؟ لأ + +167 +00:12:53,940 --> 00:12:58,100 +لو دالة عامة بتكون subset اللي هي نظرية تلاتة عشرة + +168 +00:12:58,100 --> 00:13:00,820 +طب لو دالة injective بتكون انها دي صحيحة أو كمان + +169 +00:13:00,820 --> 00:13:03,880 +أضافنا لصارت تساوي صارت تساوي لأن في معلومة إضافية + +170 +00:13:03,880 --> 00:13:08,820 +زي معلومة إضافية تمام خليني أشوف البرهان مع بعض + +171 +00:13:08,820 --> 00:13:14,610 +طبعا في نص من البرهان معموله خالص ان هوإن اليسار + +172 +00:13:14,610 --> 00:13:17,690 +صبست من اليمين انعمل نظرية تلاتة عشرة تم الطرف + +173 +00:13:17,690 --> 00:13:21,310 +الاش التاني أنه بدنا نجويه بإن اليمين صبست من + +174 +00:13:21,310 --> 00:13:32,250 +اليسار فهذه نظرية تلاتة تلتاش البرهان approved by + +175 +00:13:32,250 --> 00:13:41,210 +theorem تلاتة عشرة we have الاتجاه الأول اللي هو + +176 +00:13:41,210 --> 00:13:49,520 +إيش صورةالتقاطع a sub gamma subset من تقاطع الصورة + +177 +00:13:49,520 --> 00:13:53,780 +فهذا + +178 +00:13:53,780 --> 00:13:58,040 +الاتجاه الأول من النظرية دايما صح هذا دالة one to + +179 +00:13:58,040 --> 00:14:01,700 +one مش one to one لأي دالة الكلام صحيح الآن بنعمل + +180 +00:14:01,700 --> 00:14:07,120 +اتجاه التاني فناخد عنصلة y تنتمي لمين؟ لبطرف + +181 +00:14:07,120 --> 00:14:15,240 +اليمين gamma تنتمي لل gamma F of a gammaبتعيد حل + +182 +00:14:15,240 --> 00:14:19,420 +المثال بس مع تعميم، مع تعميم إيش عملنا بالمثال؟ + +183 +00:14:19,420 --> 00:14:24,060 +إيش أول شي فكينا؟ فكينا بتقاطع، فده إيش معناته؟ + +184 +00:14:24,060 --> 00:14:30,600 +for all Gamma in Gamma Y تنتمي لل F of A Gamma بدل + +185 +00:14:30,600 --> 00:14:33,640 +ما أعمل and، بدي أعمل and إلى مدى نهاية، for all + +186 +00:14:33,640 --> 00:14:38,610 +صارت، متابعين؟ومتابعين التناظر مع المثال واضح + +187 +00:14:38,610 --> 00:14:42,170 +ممتاز هذا تعريف التقاطة انت ماهم ايش بعدين عملنا + +188 +00:14:42,170 --> 00:14:47,930 +فكّينا الصورة فكّينا الصورة for all Gamma in Gamma + +189 +00:14:47,930 --> 00:14:51,290 +there exist X Gamma أسميها ما سميناها X واحد X + +190 +00:14:51,290 --> 00:14:55,030 +اتنين نسميها عشان نربطها بال A فعنا A Gamma نسميها + +191 +00:14:55,030 --> 00:15:01,190 +X اسمه X Gamma تنتمي لل A Gamma بحيث Y تساوي F of + +192 +00:15:01,190 --> 00:15:06,470 +X Gammaزي ما عملنا ده هي نفسها دي بس إيش تعنيها + +193 +00:15:06,470 --> 00:15:11,330 +there exist فكانت for all كانت and وها كذا تمام + +194 +00:15:11,330 --> 00:15:19,410 +تمت الخطوة الآن إيش صار؟كل الصور F of X1 تساوي F + +195 +00:15:19,410 --> 00:15:23,490 +of X2 تساوي F of X3 لأن كلهم بيساوي Y لأي X Gamma + +196 +00:15:23,490 --> 00:15:27,230 +F of X Gamma بتساوي Y ودالة one to one لازم + +197 +00:15:27,230 --> 00:15:29,170 +العناصر .. لازم العناصر تتساوى .. لازم العناصر + +198 +00:15:29,170 --> 00:15:33,010 +تتساوى .. لازم العناصر تتساوى ال one to one بتسمحش + +199 +00:15:33,010 --> 00:15:36,190 +لعنصرين مختلفين يروح لصورتين مختلفتين بديها تسمح + +200 +00:15:36,190 --> 00:15:39,090 +لعشر عناصر مختلفة تروح لصور مختلفة .. لنفس الصورة؟ + +201 +00:15:39,090 --> 00:15:42,250 +مفهوش، فيادة أولىأه فإذن نفس القضية فلان إيش + +202 +00:15:42,250 --> 00:15:44,330 +بتكتب؟ لأنه مابديش عديد .. طبعا مش هعمله هذا + +203 +00:15:44,330 --> 00:15:47,650 +الصورة بس مابدي عيد الكتاب هجد السورة عندي .. هدي + +204 +00:15:47,650 --> 00:15:52,210 +إيش معناته؟ أن Y تساوي F of X1 تساوي F of X2 تساوي + +205 +00:15:52,210 --> 00:15:55,050 +F of X3 إلى مالة نهاية مش عارفين جداش تفهم اللي + +206 +00:15:55,050 --> 00:15:58,790 +فيها صح؟ أه و الدالة one to one مازالت ساوة الصورة + +207 +00:15:58,790 --> 00:16:02,090 +إذا انها تساوية العناصر فهذا بيقول ل .. أه فلان + +208 +00:16:02,090 --> 00:16:05,810 +since F is one to one X Gamma أو خلينا نكتب على + +209 +00:16:05,810 --> 00:16:11,520 +كلهم for all Gamma in GammaX Gamma كلهم بيسووا + +210 +00:16:11,520 --> 00:16:14,760 +قيمة مشترك وليه يكون X0؟ هيك بدك تبقى سوى كيف نكتب + +211 +00:16:14,760 --> 00:16:18,840 +أن X1 تسوى X2 تسوى X0، الآن كلهم بيبقوا بيسووا X0، + +212 +00:16:18,840 --> 00:16:23,420 +أه، اللي هو إيه؟ ليه هذا الكلام صحيح؟ لأن الواقف + +213 +00:16:23,420 --> 00:16:28,400 +is one to one، injective، تسوى X0، كلهم متساوى + +214 +00:16:29,210 --> 00:16:35,250 +تمام، إذا صارت، هذا يؤدي إن الـY اللي هي بتساوي F + +215 +00:16:35,250 --> 00:16:42,450 +of X جامعة بتساوى مين؟ طبعا الـ X0، آه جابل مزال + +216 +00:16:42,450 --> 00:16:45,770 +كلهم بيساوي X0، كلهم بتساوي X0 وموجود العنصر هذا + +217 +00:16:45,770 --> 00:16:55,490 +في التقاطة فهذا يؤدي إن X0 اشمالها في التقاطة إيه + +218 +00:16:55,490 --> 00:17:00,890 +جامعة؟ لأ، تفضلفما زال كلهم متساويين طبعاً A1 في + +219 +00:17:00,890 --> 00:17:06,330 +A1 و X أسل X1 في A1 و X2 في A2 و كلهم بيسووا X0 + +220 +00:17:06,330 --> 00:17:09,670 +إذا أنها أنصر مشترك إذا أنهم موجود في التقاطع نفس + +221 +00:17:09,670 --> 00:17:12,550 +الفكرة تماما إذا فهمت المثال هتفهم ما ده الكلام بس + +222 +00:17:12,550 --> 00:17:17,610 +تعني تمام إذا وين صورته Y تساوي F of X0 وين موجودة + +223 +00:17:17,610 --> 00:17:24,070 +في صورة التقاطع في صورة التقاطع نفس البرهان الماضي + +224 +00:17:24,070 --> 00:17:29,200 +بس مع التعميمنفس البرهان بس مع التعميم بدل ما كانت + +225 +00:17:29,200 --> 00:17:34,920 +عنصرين صارت عدد عشوائة من العناصر لأنه family أي + +226 +00:17:34,920 --> 00:17:38,280 +family تكان عناصراتين، عشرة، مليون، مالة، نهاية، + +227 +00:17:38,280 --> 00:17:41,880 +كله صح لكن نفس الفكرة تمام فخلاص بدأنا بعنصر + +228 +00:17:41,880 --> 00:17:45,640 +باليمين وصلنا اليسار، إذن اليمين subset من اليسار + +229 +00:17:45,640 --> 00:17:52,440 +Thus اللي هو إيش؟ تقاطع الصور subset، لسه احنا + +230 +00:17:52,440 --> 00:18:00,290 +باليزوية هادةتقاطع الصور هو subset من صورة التقاطع + +231 +00:18:00,290 --> 00:18:05,610 +طبعا واحد و اتنين بدوا تساوي اللي بندور عليه هذه + +232 +00:18:05,610 --> 00:18:09,170 +اتنين واحد + +233 +00:18:09,170 --> 00:18:19,110 +و اتنين implies تقاطع الصور يساوي صورة التقاطع وهو + +234 +00:18:19,110 --> 00:18:22,970 +المظلومة اي سؤال + +235 +00:18:26,000 --> 00:18:30,460 +فهنا شفنا ان بعض الدوال بتخلي هذا تساوي لكن بشكل + +236 +00:18:30,460 --> 00:18:36,560 +عام هذا فيش تساوي تمام + +237 +00:18:36,560 --> 00:18:45,520 +الآن هنتقل لموضوع اخر مهم اه طبعا احنا كل function + +238 +00:18:45,520 --> 00:18:50,550 +هي relationوكل relation لها inverse relation + +239 +00:18:50,550 --> 00:18:57,050 +فالسؤال + +240 +00:18:57,050 --> 00:19:00,570 +اللى هنجاوب عليه الآن فانا ال function ك relation + +241 +00:19:00,570 --> 00:19:03,490 +ممكن اجيب منها ال inverse relation هل ال inverse + +242 +00:19:03,490 --> 00:19:07,530 +relation بتامها function؟يعني هل معكوث كل دالة هو + +243 +00:19:07,530 --> 00:19:11,410 +دالة؟ ليس بالضروري، فاحنا دائما نكون دقيقين، زي ما + +244 +00:19:11,410 --> 00:19:14,750 +قلنا احنا، عندنا دالتين، الدالتين هما مش + +245 +00:19:14,750 --> 00:19:17,570 +relations، و relation مجموعات كنا نتحدث عن اتحاد + +246 +00:19:17,570 --> 00:19:21,170 +المجموعات، لكن هل اتحاد الدوال بتامه دالة، ده سؤال + +247 +00:19:21,170 --> 00:19:24,570 +آخر، هنا نفس القضية، عشان نفهم الموضوع، كل + +248 +00:19:24,570 --> 00:19:27,190 +function هي relation، وكل relation لها inverse، + +249 +00:19:27,190 --> 00:19:30,650 +اذا كل function لها inverse relation، لكن هل كل + +250 +00:19:30,650 --> 00:19:34,130 +function لها inverse function؟لأ موضوع مختلف واضح؟ + +251 +00:19:34,130 --> 00:19:36,530 +اه فك relation بقدر أجيب ال inverse لكن هل ال + +252 +00:19:36,530 --> 00:19:39,130 +inverse اللي هو relation بتامه function هذا سؤال + +253 +00:19:39,130 --> 00:19:42,150 +مختلف عشان هيك هنشوف المثال التالي اللي بيأكد على + +254 +00:19:42,150 --> 00:19:46,570 +هذه الفكرة اللي بيأكد على هذه الفكرةفإذا نشاهد من + +255 +00:19:46,570 --> 00:19:50,030 +المثال إنه أي function بقدر أحسب ال inverse + +256 +00:19:50,030 --> 00:19:53,350 +relation تبعتها ك relation لكن هل بقى يالها + +257 +00:19:53,350 --> 00:19:56,030 +inverse function؟ هذا موضوع آخر فإيش بيقول ليه؟ + +258 +00:19:56,030 --> 00:20:00,630 +هيديني مجموعتين X وY ومعرف بينهم function طبعا هي + +259 +00:20:00,630 --> 00:20:04,030 +function لأنه غطت كل ال domain وكل عنصر له صورة + +260 +00:20:04,030 --> 00:20:07,970 +واحدة بيقول ليه وجد ال F inverse؟ هذا السؤال غريب؟ + +261 +00:20:07,970 --> 00:20:10,650 +لأ بدي أجدها كإيش؟ ك inverse relation ك inverse + +262 +00:20:10,650 --> 00:20:13,270 +relation بعدين بيقول ليه؟ هل ال F inverse ك + +263 +00:20:13,270 --> 00:20:16,640 +relation هي function؟ بدنا نشوفخلّينا نشوف مع بعض + +264 +00:20:16,640 --> 00:20:22,840 +فهذا مثال solution فأول شي F inverse ك relation + +265 +00:20:22,840 --> 00:20:29,700 +تساوي على طول أحسنتي بس علينا نغير الترتيب اتنين + +266 +00:20:29,700 --> 00:20:37,920 +لل B و واحد و C و أربع و D اشمل هذه عبارة عن + +267 +00:20:37,920 --> 00:20:43,740 +relation من وين ل وين من Y ل X صارت مظبوط؟فدائما + +268 +00:20:43,740 --> 00:20:47,300 +بتصير بالعكس فدي is a relation ك relation مافيش + +269 +00:20:47,300 --> 00:20:51,680 +مشكلة is a relation خليني بس أكد على هذه المعلومة + +270 +00:20:51,680 --> 00:20:57,060 +أه هل هي function؟ لأ ليش؟ غطت كل ال domain غطت كل + +271 +00:20:57,060 --> 00:21:00,920 +ال domain لكن في عندنا عنصر الواحد له صورتين فليست + +272 +00:21:00,920 --> 00:21:05,500 +a function ليست function F inverse is not a + +273 +00:21:05,500 --> 00:21:09,880 +function لأن الواحد له صورتين مختلفتين since + +274 +00:21:12,310 --> 00:21:19,410 +وحد C وواحد A تنتمي ل F inverse وواحد A تنتمي ل F + +275 +00:21:19,410 --> 00:21:23,190 +inverse وواحد + +276 +00:21:23,190 --> 00:21:27,890 +A تنتمي ل F inverse وواحد A تنتمي ل F inverse + +277 +00:21:27,890 --> 00:21:29,130 +وواحد A تنتمي ل F inverse وواحد A تنتمي ل F + +278 +00:21:29,130 --> 00:21:29,150 +inverse وواحد A تنتمي ل F inverse وواحد A تنتمي ل + +279 +00:21:29,150 --> 00:21:30,350 +inverse وواحد A تنتمي ل F inverse وواحد A تنتمي ل + +280 +00:21:30,350 --> 00:21:36,500 +F inverse وواحد A تنتمي ل F inverse وفإذا هنا أرجو + +281 +00:21:36,500 --> 00:21:41,580 +ننتبه إن تعريف اللي هو أو رمز F inverse بيستخدم + +282 +00:21:41,580 --> 00:21:45,680 +لمعاني مختلفة بيستخدم F inverse للمجموعات الصورة + +283 +00:21:45,680 --> 00:21:49,060 +العكسية للمجموعة فهذا لا يتحدث عن الدالة العكسية + +284 +00:21:49,060 --> 00:21:53,300 +وبيتحدث إنه نستخدمه هنا كإيش؟ كعلاقة عكسية لما + +285 +00:21:53,300 --> 00:21:56,740 +نستخدمه دالة عكسية هذا إيش رمز آخر فبيستخدم بتلات + +286 +00:21:56,740 --> 00:22:00,280 +أماكن نفس الرمز فبديكون واضح من الصياق ماذا المعنى + +287 +00:22:00,280 --> 00:22:04,070 +فيه ماذا يعني فيهفالسؤال اللي بيطرح نفسه وقت إيش + +288 +00:22:04,070 --> 00:22:08,230 +بيكون العلاقة العكسية لدالة بتكون دالة؟ أه طبعا + +289 +00:22:08,230 --> 00:22:11,490 +يمكن أننا نشوف تفاضل بقى، هنشوف اللي هو نظرية + +290 +00:22:11,490 --> 00:22:17,770 +بتتحدث عن ذلك في نظرية بتتحدث ما هي الشروط اللي + +291 +00:22:17,770 --> 00:22:21,970 +إذا توفرت في الدالة، بيكون معكوسة كعلاقة بيتم + +292 +00:22:21,970 --> 00:22:25,510 +دالة، بيتم دالة، ليش هذه ما زبطتش معناها؟ هنشوف + +293 +00:22:25,510 --> 00:22:29,230 +وين اختلت الشروط و وين الشروط اللي يجب أن تتوفر، + +294 +00:22:29,230 --> 00:22:36,590 +نظريةlet F from X to Y be a bijection يعني دالة + +295 +00:22:36,590 --> 00:22:40,250 +one to one and unto دالة injective و Serjective + +296 +00:22:40,250 --> 00:22:44,730 +بنفس الوقت then F inverse from X to Y is a + +297 +00:22:44,730 --> 00:22:49,070 +bijection أيضا إيش النتيجة بتقول؟ بتقول إذا الدالة + +298 +00:22:49,070 --> 00:22:53,470 +الأصلية كانت bijection فالمعكوز تبعها هو دالة مش + +299 +00:22:53,470 --> 00:22:58,840 +بس هيك و bijectionObjects فهذه نظرية قوية جدا اه + +300 +00:22:58,840 --> 00:23:02,140 +بتقول ليه؟ إذا الدالة كانت one to one and unto + +301 +00:23:02,140 --> 00:23:07,720 +فمعكوسها بيتم دالة وبل و one to one and unto و one + +302 +00:23:07,720 --> 00:23:16,160 +to one and unto تمام تعليق بسيط بس في تفاضل ده مر + +303 +00:23:16,160 --> 00:23:19,920 +علينا كنا بنثبت أن الدالة إليها inverse إيش كنتوا + +304 +00:23:19,920 --> 00:23:23,510 +تعملوا؟تثبت .. كنتوا فيها one to one to one و بس + +305 +00:23:23,510 --> 00:23:27,530 +اه و ماكنوش يذكروا الانتوا طب مين الغلط؟ تفاضل بقى + +306 +00:23:27,530 --> 00:23:32,710 +ولا هنا؟ التنين صح .. التنين صح بس في تفاضل بقى .. + +307 +00:23:32,710 --> 00:23:35,190 +في تفاضل بقى كل الدوا اللي كنتوا اتعاملوا معاها + +308 +00:23:35,190 --> 00:23:37,670 +كانوا يتعاملوا معاها انتوا على طول ماكانش يذكرها + +309 +00:23:37,670 --> 00:23:40,110 +.. كانت دي قياه دايما انتوا .. بدوش يهيش اصعب + +310 +00:23:40,110 --> 00:23:43,930 +الموضوع فكل ال .. لو جهتوا تفاضل بقى هتلاقوا كل + +311 +00:23:43,930 --> 00:23:45,390 +الدوا اللي اتعاملتوا معاها كانت انتوا + +312 +00:23:45,390 --> 00:23:48,010 +automatically بس ماكانش معرفكوا انتوا بس كانت دي + +313 +00:23:48,010 --> 00:23:53,120 +قياه جاهزة بس رأه بس هنا .. فهذا هو إيش .. هذا + +314 +00:23:53,120 --> 00:23:56,020 +الأصل فهذه الصورة الكاملة هنا كانت الصورة إيش + +315 +00:23:56,020 --> 00:23:59,340 +مجتزقة مبيديك جزء من الصورة و جزء مايهاش مغطي لك + +316 +00:23:59,340 --> 00:24:01,780 +إياه لسه مبيديك إياه أنه طيبا صح فهذه هو الأصل + +317 +00:24:01,780 --> 00:24:04,200 +عشان الدالة تكون عندنا .. هنشوف بالبرهان عشان + +318 +00:24:04,200 --> 00:24:07,600 +الدالة المعكسية تكون موجودة لازم تكون الدالة one + +319 +00:24:07,600 --> 00:24:10,900 +to one and on two هنشوف ليش هذا الكلام صحيح ا + +320 +00:24:10,900 --> 00:24:21,160 +proof فهذه نظرية 314 ا proofكما ذكرت قبل قليل + +321 +00:24:21,160 --> 00:24:25,420 +قراعة دقيقة للموضوع بدي أثبت أن ال F inverse هي + +322 +00:24:25,420 --> 00:24:29,820 +دالة و هي injective و injective و injective و + +323 +00:24:29,820 --> 00:24:31,120 +injective و injective و injective و injective و + +324 +00:24:31,120 --> 00:24:31,160 +injective و injective و injective و injective و + +325 +00:24:31,160 --> 00:24:32,360 +injective و injective و injective و injective و + +326 +00:24:32,360 --> 00:24:33,200 +injective و injective و injective و injective و + +327 +00:24:33,200 --> 00:24:35,860 +injective و injective و injective و injective و + +328 +00:24:35,860 --> 00:24:36,500 +injective و injective و injective و injective و + +329 +00:24:36,500 --> 00:24:36,520 +injective و injective و injective و injective و + +330 +00:24:36,520 --> 00:24:36,800 +injective و injective و injective و injective و + +331 +00:24:36,800 --> 00:24:43,530 +injective و injective و injective و injectطبعا لو + +332 +00:24:43,530 --> 00:24:46,210 +شوفنا المثال الماضي بيلاقيها إنه اختل الشرط كانت + +333 +00:24:46,210 --> 00:24:49,510 +الدالة إيش يمكن في المثال؟ وين الاختل؟ مش أنته + +334 +00:24:49,510 --> 00:24:53,530 +أتوقع .. مش أنته لأنه .. إيش؟ التلاتة مش صورة حده + +335 +00:24:53,530 --> 00:24:57,910 +.. مش أنته مغطتش كل المجال المقابل هل one to one؟ + +336 +00:24:57,910 --> 00:25:00,330 +لأنها ال A بتروح لواحد و ال C بتروح لوحد فاختل + +337 +00:25:00,330 --> 00:25:06,650 +الشرط تاني الحقيقة تمام ماشي واكتشف بتكون ال F a + +338 +00:25:06,650 --> 00:25:10,590 +function أول شيء بدنا يا تكون هي a function من وين + +339 +00:25:10,590 --> 00:25:19,140 +لوين كمان is a functionمن X ل Y من Y ل X from Y to + +340 +00:25:19,140 --> 00:25:24,000 +X هيكون دقيقين فعشان تكون function أولا تكون + +341 +00:25:24,000 --> 00:25:27,740 +relation و بعدين تكون ال domain بيغطي كل المجموعة + +342 +00:25:27,740 --> 00:25:30,860 +الأولى اللي هي ال Y هنا و كل عنصر له صورة وحيدة + +343 +00:25:30,860 --> 00:25:37,520 +تلت شروط تلت شروط فأول شيء طبعا الشرط الأول Zero F + +344 +00:25:37,520 --> 00:25:40,440 +inverse subset من Y cross ال X + +345 +00:25:43,370 --> 00:25:46,330 +إن هي relation من Y ل X هتكون، مظبوط؟ هذا الشرط + +346 +00:25:46,330 --> 00:25:48,870 +الأول، ليه مش مرقم في التعريف، فانا حاططله الـ 0 + +347 +00:25:48,870 --> 00:25:54,350 +هل هذا الكلام صحيح ولا بده إثبات؟ دايما صحيح هذا، + +348 +00:25:54,350 --> 00:25:57,690 +لأنه .. لأي relation .. لأي relation .. ال .. ال + +349 +00:25:57,690 --> 00:26:00,430 +.. ال .. عكسها، ال relation العكسية دايما موجودة و + +350 +00:26:00,430 --> 00:26:03,010 +هي من Y ل X، ب .. ب .. بإيش؟ by definition، by + +351 +00:26:03,010 --> 00:26:09,810 +definition by definition of إيش؟ inverse relation + +352 +00:26:09,810 --> 00:26:11,610 +inverse relation + +353 +00:26:17,520 --> 00:26:22,980 +فدائما كعلاقة أي علاقة من A ل B R inverse بتكون + +354 +00:26:22,980 --> 00:26:26,700 +علاقة من B ل A شفناها بالتعريف فهذا دائما معروف + +355 +00:26:26,700 --> 00:26:31,860 +إذا هذا الشرط الأول معروف واحد الشرط التاني بدنا + +356 +00:26:31,860 --> 00:26:38,780 +ال domain يساوي كل ال Y domain ال F inverse بيساوي + +357 +00:26:38,780 --> 00:26:44,360 +Yالمجموعة الأولى لأنه بايجيكشن تمام بس كيفنا + +358 +00:26:44,360 --> 00:26:49,460 +نبدأها واحدة واحدة كنا في مثال ماضي أثبتنا لأن ودا + +359 +00:26:49,460 --> 00:26:53,380 +كيش ماله جالي ال image لدالة بي say why لإن هي + +360 +00:26:53,380 --> 00:26:57,900 +قريش أنته فبنستخدم هذا العقيقة فاحنا عندنا بمثال + +361 +00:26:57,900 --> 00:27:04,470 +سابق أثبتناهاdomain العلاقة العكسية بيساوي image + +362 +00:27:04,470 --> 00:27:08,830 +العلاقة الأصلية أثبتناه مثال هذا مثال رجعوله طبعا + +363 +00:27:08,830 --> 00:27:11,250 +مابينفعش أعيده طبعا هل المثال بنفع دليل؟ لأ + +364 +00:27:11,250 --> 00:27:14,030 +مابينفعش بس أنا مابينفعش أعيده لإن أنا حلته فبنفع + +365 +00:27:14,030 --> 00:27:17,190 +أستشتري فيه فبنفع أساسيه فهذا مثال في الامتحان + +366 +00:27:17,190 --> 00:27:22,360 +يعني لما .. لأ بينفعش في الامتحانفهذا مثال تمام + +367 +00:27:22,360 --> 00:27:26,280 +الدالة Onto إذا ال image بيساوي بيساوي المجال + +368 +00:27:26,280 --> 00:27:30,960 +المقابل اللي هو Y و يساوي Y ليش؟ لأن ال F is Onto + +369 +00:27:30,960 --> 00:27:36,060 +بالتحديد هبدأ أشوف أن التنتين مهمين ال Onto مضروري + +370 +00:27:36,060 --> 00:27:38,900 +و ال injected فهي استخدمنا ال Onto استخدمناها في + +371 +00:27:38,900 --> 00:27:42,220 +إثبات مين الخاصية رقم واحد من خواص الدالة واضح؟ + +372 +00:27:42,220 --> 00:27:49,310 +فإذا هو يساوي Y و هو المطلوب نشوف الشرط التانيهيش + +373 +00:27:49,310 --> 00:27:57,470 +الشرط التاني إذا XY في الـ F inverse and XZ في الـ + +374 +00:27:57,470 --> 00:28:01,650 +F inverse يؤدى أنه مين؟ أن Y تساوي Z، متذكرين نوت + +375 +00:28:01,650 --> 00:28:04,650 +عليه في الدالة؟ أه بينفعش عنصر أروح لثورتين + +376 +00:28:04,650 --> 00:28:07,550 +مختلفتين، بس الدالة اللي بشتغل عليها هي مين؟ F + +377 +00:28:07,550 --> 00:28:11,270 +أسالب واحد الآن أو F inverse تمام، كجملة شرطية إيش + +378 +00:28:11,270 --> 00:28:16,070 +هبدأ؟ هفترض إن الشرط صحيح، هقوله let أو assume XY + +379 +00:28:16,070 --> 00:28:21,770 +تنتمي للـ F inverse and XZ تنتمي للـ F inverse + +380 +00:28:23,840 --> 00:28:28,860 +تمام؟ في خاصية دايما استخدمناها لما يكون الزوج في + +381 +00:28:28,860 --> 00:28:32,880 +العكس وين بيكون اللي بعكوسه؟ في العلاقة العصرية + +382 +00:28:32,880 --> 00:28:39,140 +دايما صحيح العلاقات فهذا يؤدي ان YX تنتمي لل F و + +383 +00:28:39,140 --> 00:28:45,450 +ZX تنتمي لل Fطبعاً هذا ليس إلا تعريف R inverse + +384 +00:28:45,450 --> 00:28:48,730 +خليني أكتبلكوا إياها الميشكة علاقة عكسية لا يمكن + +385 +00:28:48,730 --> 00:28:51,430 +استخدامها لأنه لسه هي ما ثبتتش هنا دالة مافيه عشان + +386 +00:28:51,430 --> 00:28:56,350 +أعمل معاها كدالة تمام؟ ممتاز لكن ال F دالة ماذا + +387 +00:28:56,350 --> 00:29:02,590 +يعني هذا؟ فهذا يعني إن X تساوي F of Y و إيش كمان؟ + +388 +00:29:02,590 --> 00:29:09,470 +و X تساوي F of Zمظبوط؟ باللغة، انتبهوا، فالفهم + +389 +00:29:09,470 --> 00:29:14,430 +العميق اللي بنركز عليه، مش دايما Y F of X أنا عندي + +390 +00:29:14,430 --> 00:29:18,890 +زوج مرتب في دالة، بتكون التانية صورة الأولى، + +391 +00:29:18,890 --> 00:29:21,650 +انتبهوا، لا الترتيب، احنا عايشنا المفاهيم، طب إيه + +392 +00:29:21,650 --> 00:29:25,530 +صار عندي؟ صار عندي F of Y تساوي F of Z وكله بيساوي + +393 +00:29:25,530 --> 00:29:30,510 +X، فهذا بيقوللي إن F of Y تساوي F of Z، طب و + +394 +00:29:30,510 --> 00:29:34,070 +الدالة one to one، إذا Y تساوي Z، ليش؟ لأن الـF is + +395 +00:29:34,070 --> 00:29:38,200 +one to oneفشايفين؟ عشان نثبت ان ال domain بيساوي + +396 +00:29:38,200 --> 00:29:42,340 +كل y استخدامنا انها onto وعشان نثبت ان العنصرين + +397 +00:29:42,340 --> 00:29:45,300 +المختلفين بيروح لصور مختلفة استخدامنا انها one to + +398 +00:29:45,300 --> 00:29:49,000 +one وهو المطلوب أثبتنا ان y تساوزه فإذا هنا فعلا + +399 +00:29:49,000 --> 00:29:55,940 +انهياش ده خلصنا من الجزء الأول مفهوم؟ + +400 +00:29:55,940 --> 00:30:01,460 +أي استفسار؟ أي سؤال؟ واضح؟ انتبعين؟ انتقل للجزء + +401 +00:30:01,460 --> 00:30:04,860 +التاني اجيب ده أثبت انهياش انها bijectionأتنين + +402 +00:30:04,860 --> 00:30:10,020 +طبعا الترقيم هنا يمكن سيء خلّيني أحط هذه capital I + +403 +00:30:10,020 --> 00:30:13,280 +عشان أميز بين الترقيم و بين الترقيم وخلّيها دي ايش + +404 +00:30:13,280 --> 00:30:18,440 +اتنين باللاتيني عشان بس القراها تكون صحيحة مابديش + +405 +00:30:18,440 --> 00:30:23,780 +الرقم يتكرر فانا قسمت البرهان لقسمين القسم الأول I + +406 +00:30:23,780 --> 00:30:26,760 +اللي هو او ايش او واحد باللاتيني و القسم اللي هو + +407 +00:30:26,760 --> 00:30:28,640 +death بتنا ده لأ القسم التالي بdeath بتنا ايش + +408 +00:30:28,640 --> 00:30:35,630 +بيجيكشن F inverse is bijectionطبعا bijection يعني + +409 +00:30:35,630 --> 00:30:42,410 +حاجتين واحد F inverse is one to one F inverse is + +410 +00:30:42,410 --> 00:30:46,590 +one to one و بعدين هثبت انها one to one كيف بنثبت + +411 +00:30:46,590 --> 00:30:49,770 +ده لما انها one to one ناخد عنصرين في ال domain + +412 +00:30:49,770 --> 00:30:55,990 +صورهم متساوية هاخد عنصرين let X1 و X2 domain F + +413 +00:30:55,990 --> 00:31:00,750 +inverse هو مين هو ال Y ينتمي إلى ال Y such that + +414 +00:31:05,360 --> 00:31:09,840 +F inverse الدالة اللي بشتر عليها تساوي F inverse + +415 +00:31:09,840 --> 00:31:13,600 +of X2 فهنا بس بدنا تركيز عشان احنا ايش نشتري على + +416 +00:31:13,600 --> 00:31:17,040 +مين على دالة F inverse ممكن تسموها G زي مغلباكوا، + +417 +00:31:17,040 --> 00:31:20,140 +اه لكن إيه بقى ده الشكل، مطلوب أثبت أن X1 تساوي X2 + +418 +00:31:21,410 --> 00:31:24,830 +هنعمل trick بسيط تقريبا نفس العملية قيمتين + +419 +00:31:24,830 --> 00:31:30,470 +متساويتين خلّيني أسميهم Y خلّيني أسميهم Y let Y + +420 +00:31:30,470 --> 00:31:35,740 +تساوي F inverse of X1 تساوي F inverse of X2تسمي + +421 +00:31:35,740 --> 00:31:38,680 +هذه قيمة مشتركة زي ما توقع من ال X0 مسموح ولا مش + +422 +00:31:38,680 --> 00:31:42,120 +مسموح؟ مسموح مش عشان أنا بعمله عشان هيك المنطق + +423 +00:31:42,120 --> 00:31:46,480 +بيقول و لا لأ قيمتين متساويتين قيمة مش مشتركة تمام + +424 +00:31:46,480 --> 00:31:49,240 +ليش بيحملت استخدام هذه اللي هوية زي ما ممكن نعمل + +425 +00:31:49,240 --> 00:31:51,860 +في القرآن في حاجة اسمها زي العمل اللي مسموح فيه؟ + +426 +00:31:51,860 --> 00:31:56,020 +ليش بتعمل هيك؟إيش معناته إن Y تساوي F inverse of + +427 +00:31:56,020 --> 00:32:00,480 +X1؟ يعني X Y و X و X واحد و Y في ال F inverse بدي + +428 +00:32:00,480 --> 00:32:02,820 +أروح عنها ليش بدي أعمل بدي أستفيد من ال F لأن + +429 +00:32:02,820 --> 00:32:06,100 +المعطيات كلها على ال F فدايما بحاول أنتقل من F + +430 +00:32:06,100 --> 00:32:08,880 +inverse اللي بدي أثبت إليها معلومات معلومات عنها + +431 +00:32:08,880 --> 00:32:12,000 +قليلة بروح للأصل اللي عندي معلومات عنه كتيرة وهذه + +432 +00:32:12,000 --> 00:32:16,200 +مهمة جدا في ال F inverse و في ال F فهذا معناته إن + +433 +00:32:16,200 --> 00:32:22,440 +X واحد و Y في ال F inverse and X اتنين و Y في ال F + +434 +00:32:22,440 --> 00:32:26,710 +inverseالـ notation تبعت الدالة مكتوبة بطريقتين + +435 +00:32:26,710 --> 00:32:31,550 +مختلفتين طب ليش عملت هيك؟ عشان هنا لأي علاقة بقدر + +436 +00:32:31,550 --> 00:32:38,270 +أعكس الترتيب فده معناته أن Y و X1 تنتمي لل F و Y و + +437 +00:32:38,270 --> 00:32:41,910 +X2 تنتمي لل F + +438 +00:32:46,750 --> 00:32:52,890 +إيه صار عندى؟ صار عندى عنصر لصورتين تحت ال F و ال + +439 +00:32:52,890 --> 00:32:59,650 +F function كأن Y صورتها X1 و Y صورتها X2 مستحيل + +440 +00:32:59,650 --> 00:33:04,830 +إلا إذا X1 تسوى X2 هذا يؤدي إن X1 تسوى X2 ليش؟ لأن + +441 +00:33:04,830 --> 00:33:08,830 +ال F is a functionهذا مُعطى هو احنا f inverse + +442 +00:33:08,830 --> 00:33:13,130 +عناها function وهو المطلوب بدأنا من أنصرين في + +443 +00:33:13,130 --> 00:33:17,030 +domain ال f inverse صورهم متساوية أوصلنا ان + +444 +00:33:17,030 --> 00:33:22,070 +الأنصرين متساوية فإذا هذا انها one to one thus f + +445 +00:33:22,070 --> 00:33:26,980 +inverse is one to oneمتابعين؟ اه واحد يقول انت مش + +446 +00:33:26,980 --> 00:33:30,100 +هاجي تشتغل على ال F لأ انا اين بدأت بدأت عنصرين في + +447 +00:33:30,100 --> 00:33:33,620 +domain F inverse صورهم تحت ال F inverse متساوية + +448 +00:33:33,620 --> 00:33:36,520 +بعدين اشتغلت بطريقة رياضية روحت على ال F و هم ما + +449 +00:33:36,520 --> 00:33:39,220 +روحت المهم انا بشتغل بطريقة رياضية صالحة وصلت لمين + +450 +00:33:39,220 --> 00:33:43,440 +للهدف تبعي X1 سو X2 اذا انتهى البرهات نثبت انها + +451 +00:33:43,440 --> 00:33:48,680 +Onto اتنين F inverse is Onto او surjective نفس + +452 +00:33:48,680 --> 00:33:54,470 +المعنىتمام البرهان الحقيقة سهل و هنستخدم فيه زي ما + +453 +00:33:54,470 --> 00:33:57,070 +توي عملنا في الدالة هلجيت انا عندي ايش بده اثبت + +454 +00:33:57,070 --> 00:34:00,010 +ايش معانطه بده استخدم التعريف التاني بدي اثبت ان + +455 +00:34:00,010 --> 00:34:03,910 +ال image بيساوي Y هنثبت ان ال image يساوي و بعدي + +456 +00:34:03,910 --> 00:34:10,010 +image F inverse طبعا هو domain ال F مثال ماضي + +457 +00:34:10,010 --> 00:34:14,130 +domain ال F و بما انه ال F function اذا ال domain + +458 +00:34:14,130 --> 00:34:19,270 +ايش بيساوي بيساوي X و هو المطلوب و هو المطلوب بكل + +459 +00:34:19,270 --> 00:34:25,250 +سهولةالـ image مثال هذا لأي علاقة هذا الكلام صحيح + +460 +00:34:25,250 --> 00:34:29,470 +ده هو استخدمناه قلنا domain العلاقة بيساوياش image + +461 +00:34:29,470 --> 00:34:32,790 +للعلاقة العكسية وحطينا مراعظ على ما قد اتذكر في + +462 +00:34:32,790 --> 00:34:38,610 +شبتر تلاتة في العلاقات و العكسية طيب بما انه هذه + +463 +00:34:38,610 --> 00:34:41,250 +ال f function ايش ال domain كل x وهو المطلوب احنا + +464 +00:34:41,250 --> 00:34:44,490 +نستطيع نشتغل على f inverse من و لا و ان؟ من y ل x + +465 +00:34:49,090 --> 00:34:53,310 +is on وهو المطلوب أي سؤال + +466 +00:34:57,110 --> 00:35:02,810 +هنا كأي أي علاقة image الـR inverse بيسوي domain + +467 +00:35:02,810 --> 00:35:06,230 +الـR والعكس صحيح فاحنا استخدمنا هذه العلاقة طيب + +468 +00:35:06,230 --> 00:35:08,550 +domain الـF، الـF احنا معطيها ايه؟ اول شي انها + +469 +00:35:08,550 --> 00:35:12,570 +function domainها مين؟ X على طول ولا لأ؟ وإيش + +470 +00:35:12,570 --> 00:35:15,210 +واحنا بدنا إيش بدنا يثبت؟ F inverse ذالك من Y لX + +471 +00:35:15,210 --> 00:35:17,510 +يعني بدنا إيش المجال المقابل تبع حاجة يكون image + +472 +00:35:17,510 --> 00:35:22,730 +اللي هو X وهو المطلوب وهو المطلوبفإذن كل هذه + +473 +00:35:22,730 --> 00:35:27,690 +العلاقات أو كل هذه الأمور مطلوبة وهذه نهاية ال + +474 +00:35:27,690 --> 00:35:27,970 +section + +475 +00:35:51,560 --> 00:35:55,840 +composition of functions آخر موضوع هنتحدث فيه اللي + +476 +00:35:55,840 --> 00:35:59,540 +هو التركيب أو ال composition طبعا الموضوع بسيط + +477 +00:35:59,540 --> 00:36:08,000 +هنمر عليه عشان بس الصورة تكتمل بشكل عام فطبعا + +478 +00:36:08,000 --> 00:36:12,520 +زي ما انتوا عارفين ال composition عندنا دالتين + +479 +00:36:12,520 --> 00:36:15,920 +بنجيب التركيب اللي هو بسموها إيش ال composition + +480 +00:36:17,550 --> 00:36:21,870 +طبعا مهم الصورة العامة أنه يكون في عندنا علاقة + +481 +00:36:21,870 --> 00:36:27,930 +بالشكل التالي هي عندنا X طبعا هنا دي عملية من + +482 +00:36:27,930 --> 00:36:33,310 +عملية التعاون طبعا في عندنا عملية كبرى بنجسمها على + +483 +00:36:33,310 --> 00:36:37,150 +مرحلتين ال F بتقوم بالجزء الأول وال G بتكمل + +484 +00:36:37,150 --> 00:36:41,550 +العملية فبنعمل على مرحلتين فعندنا هنا X وعندنا هنا + +485 +00:36:41,550 --> 00:36:50,010 +Y وعندنا هنا Zففي عندنا الدالة الأولى F من X ل Y و + +486 +00:36:50,010 --> 00:36:55,010 +الدالة التانية من Y ل Z G طبعا فالمهم هنا عشان + +487 +00:36:55,010 --> 00:37:00,650 +أعمل composition أن يكون الـ domain التانية بيساوي + +488 +00:37:00,650 --> 00:37:04,250 +المجال المقابل للأولى عشان هي عشان أقدر أشتغل لأنه + +489 +00:37:04,250 --> 00:37:09,020 +بدي أخد Y عشان عند ال F بتاخد من؟ بتاخد Xبتوديها ل + +490 +00:37:09,020 --> 00:37:14,100 +Y و الـ G بتوديها لمين؟ ل Z فهنا هنا F و هنا G + +491 +00:37:14,100 --> 00:37:18,540 +طبعا فلازم ايش؟ بتاخد من هنا تكون فإذا صارت صورة و + +492 +00:37:18,540 --> 00:37:22,280 +الـ G بتكمل اه فبقول لي let F be a function from X + +493 +00:37:22,280 --> 00:37:26,920 +to Y و الـ G من Y ل Z فنهاية الأولى بداية التانية + +494 +00:37:26,920 --> 00:37:30,470 +مهم جدا ك domaina B2 function the composition + +495 +00:37:30,470 --> 00:37:33,730 +التركيب of the two functions is the function + +496 +00:37:33,730 --> 00:37:38,050 +فتركيب الدالتين دالة أخرى فهذه عملية من أهم + +497 +00:37:38,050 --> 00:37:41,770 +العمليات العدوان أنا عندي دالتين ممكن أجمحهم ممكن + +498 +00:37:41,770 --> 00:37:45,250 +ممكن أضربهم و أكون دالة ممكن أه ممكن نجسمهم على + +499 +00:37:45,250 --> 00:37:49,650 +بعض بشرف طبعا بس هذه العمليات ليش هنا مش هيدرسهم + +500 +00:37:49,650 --> 00:37:54,650 +الجمع و الدرب و الجسم؟ لأ مش ماخدناهم هذا السبب + +501 +00:37:54,650 --> 00:38:00,650 +لأن هنااحنا بندرس بشكل مجرد، بشكل عام عمليات + +502 +00:38:00,650 --> 00:38:04,690 +الحسابية دي بتنفع لو كانت الدوال بتتعرف على أعداد + +503 +00:38:04,690 --> 00:38:08,710 +وبالتالي العمليات الجامعة والطرح معرفة ولا لأ هنا + +504 +00:38:08,710 --> 00:38:12,050 +بشر على دوال بشكل عام فال composition معرف بغض + +505 +00:38:12,050 --> 00:38:16,650 +النظر كانت المجموعات هذه أعداد أو غير أعدادأه فانا + +506 +00:38:16,650 --> 00:38:20,190 +بتعمل عملية عامة كل اللي بنشتغله اللي بتشوفيه فيه + +507 +00:38:20,190 --> 00:38:23,410 +بينفع بغض النظر إيش نوع العناصر اللي في مجموعة ال + +508 +00:38:23,410 --> 00:38:27,310 +domain أو في الصور هذا عشان أعرف الجامع بدي F of X + +509 +00:38:27,310 --> 00:38:30,990 +زائد F of A بيكون هدول الصور و أعرف أجمعهم هل كل + +510 +00:38:30,990 --> 00:38:34,650 +صور بنجمعه؟ لأ مش ضروري إلا إذا كانت دالة من R لR + +511 +00:38:34,650 --> 00:38:37,770 +أو من مجموعة أعداد إلى مجموعة أعداد فعشان هيك احنا + +512 +00:38:37,770 --> 00:38:42,150 +مش هنعرفهم لأنهم مش دايما معرفين مش كل دالة بقدر + +513 +00:38:42,150 --> 00:38:45,370 +أعمل إيش الجامعة تبعها إلا إذا كانت دالة على مين؟ + +514 +00:38:45,370 --> 00:38:48,630 +على الأعدادعلى أرقام فطبعا هنا ال composition + +515 +00:38:48,630 --> 00:38:52,830 +دايما معرف واش معرف فهي دالة فانا بكون بدأت + +516 +00:38:52,830 --> 00:38:56,370 +بدالتين ال composition هو دالة من وين لوين من ال + +517 +00:38:56,370 --> 00:39:00,030 +domain الأولى إلى ال code main للأخيرة للتانية + +518 +00:39:00,030 --> 00:39:06,310 +شوفتوا واضحة زي ال translation زي التعدي تشبهها + +519 +00:39:06,310 --> 00:39:09,210 +فالعنصر المشترك اللي هو ال Y اللي بالنص يرد يروح + +520 +00:39:09,210 --> 00:39:14,230 +صارت عنصر من X ل Z طب كيف بيعرفها؟ أنا عشان أعرف + +521 +00:39:14,230 --> 00:39:17,600 +ال function فيها عندي حاجتين دايمابدي ال domain و + +522 +00:39:17,600 --> 00:39:20,140 +ال codomain المجال و المجال المقابل وش بدي كمان + +523 +00:39:20,140 --> 00:39:24,180 +قاعدة التعريف العلاقة كيف العلاقة فبقول عشان تحسب + +524 +00:39:24,180 --> 00:39:28,560 +الدالة الجديدة عن ال X إيش تحسب تحسب صورتها تحت ال + +525 +00:39:28,560 --> 00:39:33,040 +F و بتحسب من G للصورة و بصيب قيمة ال G للصورة بعد + +526 +00:39:33,040 --> 00:39:35,480 +التتواصل ده ما أنتوا عارفين بس أحنا بس بنأكد نحاول + +527 +00:39:35,480 --> 00:39:40,780 +نقرأ التعريفبمعنى آخر لو بدك تكتبها على صورة علاقة + +528 +00:39:40,780 --> 00:39:44,380 +أزواج مرتبة فهذه طريقة أنك تكتبها بطريقة الدوال Y + +529 +00:39:44,380 --> 00:39:47,700 +تساوي F of X طب بدك تكتبها على صورة علاقة فالـ G + +530 +00:39:47,700 --> 00:39:51,180 +circle F كأزواج مرتبة أيش بتساوي؟ X و Z لأن هي + +531 +00:39:51,180 --> 00:39:56,680 +subset من مين؟ من X cross Z يعني أنت مؤلد X cross + +532 +00:39:56,680 --> 00:40:01,060 +Z بحيthere exists Y في الـ Y في عامل مشترك في عامل + +533 +00:40:01,060 --> 00:40:04,780 +مساعد Y اللي هو وصلهم لبعض ال X بتروحش ل Z على طول + +534 +00:40:04,780 --> 00:40:07,920 +بتروح عن طريق ال Y فقولي there exists Y in capital + +535 +00:40:07,920 --> 00:40:12,980 +Y such that X و Y في ال F و Y و Z في ال G فهذه + +536 +00:40:12,980 --> 00:40:15,740 +طريقة كتابة أخرى جديدة علينا طبعا لأن بس كياش + +537 +00:40:15,740 --> 00:40:21,550 +كارلش فهذا هو ال composition فهذه ال compositionبس + +538 +00:40:21,550 --> 00:40:24,850 +نديكم مثال من الـ Calculus سريع بس عشان نسترجع + +539 +00:40:24,850 --> 00:40:28,490 +التعريف و نؤكد على اللي هو الباب فوق + +540 +00:40:39,600 --> 00:40:44,500 +مثال بسيط من ال calculus طبعا ال F من R ل R و G من + +541 +00:40:44,500 --> 00:40:48,280 +R ل R two function given by F of X X تربيه زائد + +542 +00:40:48,280 --> 00:40:50,460 +اتنين و G of X الجزر التربيه على X تربيه زائد + +543 +00:40:50,460 --> 00:40:56,660 +اربعة بقولي اوجد G circle F لل X و F circle G لل X + +544 +00:40:56,660 --> 00:41:03,160 +طبعا تقرأ F circle G solution فF circle G of X + +545 +00:41:03,160 --> 00:41:12,220 +طبقا للتعريف هي F G of X وتساوي FG X هو جزر + +546 +00:41:12,220 --> 00:41:18,560 +التربيع للـ X تربيع زائد 4 هذه سهلة فالـ F بتربع + +547 +00:41:18,560 --> 00:41:23,940 +اللي جواها و بتجمعله 2 فهذه ستكون X تربيع زائد 6 + +548 +00:41:23,940 --> 00:41:31,960 +Calculus ألف فهذه بكل سهولة لكن G Circle F أهم + +549 +00:41:31,960 --> 00:41:37,420 +حاجة هي G للـ F of X والـ G للـ F of X يمين X + +550 +00:41:37,420 --> 00:41:42,560 +تربيع زائد 2مظبوط؟ طيب الجيش اللي بتعمل بتربع اللي + +551 +00:41:42,560 --> 00:41:46,300 +جواها و بتضيفله أربعة و بتاخد الجزر التربيعي بدنا + +552 +00:41:46,300 --> 00:41:50,820 +نربع X تربيع زائد اتنين لكل تربيع زائد أربعة + +553 +00:41:50,820 --> 00:41:55,000 +وتساوي الجزر التربيعي X أُص أربعة زائد أربعة X + +554 +00:41:55,000 --> 00:41:56,960 +تربيع زائد 8 + +555 +00:42:00,650 --> 00:42:03,850 +فهذا سؤال calculus ألف الكل بيعرف يعمل و أتوقع و + +556 +00:42:03,850 --> 00:42:08,270 +يمكن من الثانوية عارفينه الشاهد من المثال عملية ال + +557 +00:42:08,270 --> 00:42:11,970 +circle ليس إبدالية فدول بيساويش بعض فعملية ال + +558 +00:42:11,970 --> 00:42:15,810 +composition ليس عملية إبدالية فهذا مثال مشهور على + +559 +00:42:15,810 --> 00:42:19,810 +العمليات الغير إبدالية زي ضربش المصففات برضه غير + +560 +00:42:19,810 --> 00:42:23,390 +إبدالي نفس القضية عملية ال composition لدوال غير + +561 +00:42:23,390 --> 00:42:28,180 +إبدالي طيب إيش حصية ممكن ت .. ت ..اللي هو تتوفر + +562 +00:42:28,180 --> 00:42:31,740 +فيها، فاحنا فيها خواص .. خواص كتير مشهورة الإبدال + +563 +00:42:31,740 --> 00:42:35,660 +و إيش؟ و التجميع، هل إيه خاصية التجميع؟ هنشوف إنه + +564 +00:42:35,660 --> 00:42:37,800 +هذا الكلام صحيح ال composition اللي هو خاصية + +565 +00:42:37,800 --> 00:42:40,320 +التجميع، لكن هذا خليه لنا المرة الجاية إن شاء الله + +566 +00:42:40,320 --> 00:42:41,220 +عشان نمزج المتحف + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/NTo9q63N_fY_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/NTo9q63N_fY_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..bccc9d129891a93a1d3009bc62a84ef5f76be15e --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/NTo9q63N_fY_postprocess.srt @@ -0,0 +1,2544 @@ +1 +00:00:20,860 --> 00:00:23,920 +بسم الله الرحمن الرحيم ان شاء الله اليوم هنكمل مع + +2 +00:00:23,920 --> 00:00:28,400 +اللي هو ال compliments مكملات المجموعات فبس نتذكر + +3 +00:00:28,400 --> 00:00:32,200 +احنا عرفنا حاجتين فيما يعرف بيه اللي هو المكملة + +4 +00:00:32,200 --> 00:00:35,060 +النسبية او ال relative compliment لو في عندنا + +5 +00:00:35,060 --> 00:00:41,180 +مجموعتين a و b فعرفنا اللي هو a minus ال b وهي + +6 +00:00:41,180 --> 00:00:46,060 +مكملة ال b في ال a وتساوي عناصر اللي موجودة في ال + +7 +00:00:46,060 --> 00:00:50,890 +a و غير موجودة في ال b x such that x تنتمي لل aand + +8 +00:00:50,890 --> 00:00:55,830 +X لا تنتمي لل B فهذه تسموها relative complement of + +9 +00:00:55,830 --> 00:01:01,310 +B in A أو تجاوزا ال difference between A and B بس + +10 +00:01:01,310 --> 00:01:04,070 +ننتبه أن هذه العملية ليست إبدالية، ليست إبدالية + +11 +00:01:04,070 --> 00:01:10,010 +بعدين عرفنا المكملة A' طبعا نسبة لمجموعة مرجعية + +12 +00:01:10,010 --> 00:01:13,630 +بنسميها ال universal set أي عبارة عن U اللي هي ال + +13 +00:01:13,630 --> 00:01:17,880 +universal ناقص Aفهي العناصر اللي موجودة في ال U + +14 +00:01:17,880 --> 00:01:21,180 +خارج ال A وغير موجودة في ال A أو باختصار العاصر + +15 +00:01:21,180 --> 00:01:25,180 +عايش خارج ال A أيضا تحدثنا عن بعض الخواص فقولنا + +16 +00:01:25,180 --> 00:01:28,600 +مكملة المكملة بتدينا المجموعة نفسها مكملة ال Phi U + +17 +00:01:28,600 --> 00:01:33,300 +مكملة ال U prime أو ال U هي ال Phi تقاطع أي مجموعة + +18 +00:01:33,300 --> 00:01:37,410 +مع مكملتها Phiالتحاد المجموعة مع مكملتها بيدينا كل + +19 +00:01:37,410 --> 00:01:40,870 +ال universal set و طبعا إذا كانت ال A subset من ال + +20 +00:01:40,870 --> 00:01:44,070 +B فال contrapositive بتصير مكملة ال B subset من + +21 +00:01:44,070 --> 00:01:47,710 +مكملة ال A و طبعا النقطة الأخيرة مهمة هشوف عليها + +22 +00:01:47,710 --> 00:01:51,630 +تتبقى قرابة متعددة بقدر أكتب ال A minus B بديهش + +23 +00:01:51,630 --> 00:01:54,700 +عبارة عن إيه تقاطة مكملة ال Bلأنه إيش بدنا العناصر + +24 +00:01:54,700 --> 00:01:58,800 +اللي خارج ال B؟ العناصر لإنه من هنا هذا هي A تنتمي + +25 +00:01:58,800 --> 00:02:03,200 +ل A و B و X لا تنتمي ل B طبعا إيش X لا تنتمي ل B؟ + +26 +00:02:03,200 --> 00:02:06,920 +يعني X في المكملة و في N بصير تقاطة فدي النقطة ان + +27 +00:02:06,920 --> 00:02:09,440 +شاء الله هنشوف بعض التطبيقات عليها لكن بعض قليل + +28 +00:02:11,120 --> 00:02:15,760 +فينا نظرية De Morgan's theorem ويمكن هذا بيؤكد + +29 +00:02:15,760 --> 00:02:19,140 +اللي هو التشابه الوثيقة أو العلاقة الوثيقة بين ال + +30 +00:02:19,140 --> 00:02:23,540 +logic وعمليات ال logic و بين المجموعات و العمليات + +31 +00:02:23,540 --> 00:02:28,140 +على المجموعات فطبعا هنا بيقول let a let for any + +32 +00:02:28,140 --> 00:02:32,220 +sets a و b that are subsets of a universal set U + +33 +00:02:32,220 --> 00:02:36,370 +we have طبعا هنا بتتحدث عن المكملةفإذا اتحدث عن + +34 +00:02:36,370 --> 00:02:38,770 +مكملة لازم يكون فيها أنهياش universal set، مجموعة + +35 +00:02:38,770 --> 00:02:41,950 +مرجعية، مجموعة كبرى، اللي هي capital U اه طبعا ال + +36 +00:02:41,950 --> 00:02:44,370 +Demorgan's أشمالها كانت بتدخل النفي على ال and و + +37 +00:02:44,370 --> 00:02:48,430 +ال or طبعا بلغة المجموعات النفي هو المكملة و ال + +38 +00:02:48,430 --> 00:02:51,730 +and و ال or إيش هيصيروا؟ تقاطعوا اتحاد فالفرع + +39 +00:02:51,730 --> 00:02:56,080 +الأول بيقوللي مكملة الاتحاد هي تقاطع المكملاتمكملة + +40 +00:02:56,080 --> 00:03:00,480 +الاتحاد هي تقاطع المكملات هي دخلت على ايش صارت نفي + +41 +00:03:00,480 --> 00:03:04,100 +الطرفين والاخر صارت and فالاتحاد صار تقاطع وكل + +42 +00:03:04,100 --> 00:03:06,840 +مجموعة صارت المكملة استبدلناها بالمكملة تبعتها + +43 +00:03:06,840 --> 00:03:12,100 +بنفس الاسلوب مكملة التقاطع اتحاد المكملات اتحاد + +44 +00:03:12,100 --> 00:03:16,320 +المكملات طبعا البرهان exercise هتركه لأنه ما علينا + +45 +00:03:16,320 --> 00:03:18,780 +نحط التعريف و من demorgan's تبع ال logic + +46 +00:03:18,780 --> 00:03:23,980 +demorgan's law حسيبه exerciseخلّيني أشوف بعض + +47 +00:03:23,980 --> 00:03:30,100 +الأمثلة كيف نشتغل مع التعريفات هذه و مع النظريات و + +48 +00:03:30,100 --> 00:03:36,950 +كيف نحل بعض الأمثلةالمثال الأول بيقول let A, B and + +49 +00:03:36,950 --> 00:03:42,710 +C be any sets مقدمة زي ما اتعودين فطبعا المفروض + +50 +00:03:42,710 --> 00:03:47,030 +انه نعرف نقرأ وما نلتخمش نتعود كيف ناخد المعلومات + +51 +00:03:47,030 --> 00:03:51,150 +وناخد الملاحظات على السؤال على النظرية على أي اشي + +52 +00:03:51,150 --> 00:03:54,650 +كيف نتعامل معاه طيب ايش المطلوب بيقول decide قرر + +53 +00:03:54,650 --> 00:04:00,650 +او حدد whether the setA تقاطع B-C is the same as + +54 +00:04:00,650 --> 00:04:03,490 +the third يعني هل المجموعة تساوي المجموعة التالية + +55 +00:04:03,490 --> 00:04:09,070 +فخليني أعيد صياغة المثال أو السؤال الأول فبقول هل + +56 +00:04:09,070 --> 00:04:19,730 +المجموعة A تقاطع B-C تساويA تقاطع ال B minus A + +57 +00:04:19,730 --> 00:04:24,350 +تقاطع ال C يعني بمعنى أخر هل التقاطع بتوزع على ال + +58 +00:04:24,350 --> 00:04:28,550 +minus فده السؤال فبقول ال decide هدول متساويين ولا + +59 +00:04:28,550 --> 00:04:30,830 +لأ بدنا نحل مع بعض solution + +60 +00:04:33,410 --> 00:04:37,070 +السؤال بمعنى آخر هو approve or disapprove هي صيغة + +61 +00:04:37,070 --> 00:04:40,690 +أخرى ل approve or disapprove بدنا نقرر هل هذه + +62 +00:04:40,690 --> 00:04:44,850 +صحيحة و طبعا و نثبت أو هى خاطئة و ندى مثال عكسى + +63 +00:04:44,850 --> 00:04:49,070 +طبعا ممكن احنا بهذا النوع من الأسئلة اللى يعتبر + +64 +00:04:49,070 --> 00:04:51,750 +فيه أصعب من السؤال لما اقول prove مباشرة او + +65 +00:04:51,750 --> 00:04:54,390 +disapprove بيكون داني جزء من الجواب لأن انا بدى + +66 +00:04:54,390 --> 00:04:57,890 +اقرر اولا هل هي true وديها برهان او هل هي false + +67 +00:04:57,890 --> 00:05:02,200 +وديها مثال عكسىفي هذه الحالة إذا قدرت أنا أخمن + +68 +00:05:02,200 --> 00:05:06,280 +بطريقة ما بمساعدة رسم بمساعدة بعض التجريب بقى بقدر + +69 +00:05:06,280 --> 00:05:09,320 +أخمن إنها true أو false و بعدين بكون إيش بكمل الحل + +70 +00:05:09,320 --> 00:05:12,260 +طيب ماقدرتش إيش ممكن نعمل في هذا المثال اللي + +71 +00:05:12,260 --> 00:05:16,900 +هنشوفه هنا ممكن نحاول نثبت نحاول نثبت إذا إذا + +72 +00:05:16,900 --> 00:05:19,540 +البرهان مشي صح و أنا متأكد إن البرهان صحيفة بكون + +73 +00:05:19,540 --> 00:05:23,230 +أنا إيش أثبتت إنها صحيحة بنفس الوقتلاجيت فيه صعوبة + +74 +00:05:23,230 --> 00:05:25,950 +في البروحانة في مشاكل ممكن اكتشف انها مش .. بشكل + +75 +00:05:25,950 --> 00:05:29,450 +عام صحيحة لأنه حلاجي انه ايش مش جادر انا اثبتها و + +76 +00:05:29,450 --> 00:05:32,310 +.. و أثناء الاثبات بلاجي وين المشكلة و وين الخلل + +77 +00:05:32,310 --> 00:05:35,630 +هذا ممكن كمان يديني ايش و كيف اجيب المثال عكسي .. + +78 +00:05:35,630 --> 00:05:38,730 +كيف اجيب المثال عكسي فذا احنا ب .. بأحد الطرح في + +79 +00:05:38,730 --> 00:05:41,850 +ال prove or disprove ان نحاول ايش نعمل prove نعمل + +80 +00:05:41,850 --> 00:05:44,610 +prove و أنا هذا اللي بدنا نحاول طيب لو حاولنا بدنا + +81 +00:05:44,610 --> 00:05:48,460 +نعمل عملية prove لهذهطبعاً في طريقتين تعريف تساوي + +82 +00:05:48,460 --> 00:05:51,960 +المجموعات for all X X في الأولى F and all F X في + +83 +00:05:51,960 --> 00:05:55,400 +الثانية طريقة تانية ممكن استخدم أياشأ نظرية وسهلة + +84 +00:05:55,400 --> 00:05:58,680 +على حالي طريقة مختصرة طيب تساوي مجموعات زي أي + +85 +00:05:58,680 --> 00:06:02,040 +تساوي ببدأ من طرف يوصل للطرف الآخر وقلنا نصيحة + +86 +00:06:02,040 --> 00:06:04,940 +عامة نبدأ من وين؟ من الكبير فخلينا نبدأ من الطرف + +87 +00:06:04,940 --> 00:06:07,180 +الكبير اللي هو اليمين فالقاهنة ال solution خلينا + +88 +00:06:07,180 --> 00:06:13,740 +نبدأ من الطرف اليمين A تقاطع ال B ناقص A تقاطع ال + +89 +00:06:13,740 --> 00:06:19,270 +C بدي أشتغل عليهاالشاهد من المثال يوحى نشوف انه في + +90 +00:06:19,270 --> 00:06:22,750 +اخر فرع فرع ايه في نظرية اتنين خمسة بيقول لي بقدر + +91 +00:06:22,750 --> 00:06:27,130 +اكتب ال minus بدل ال 8 تقاطع مع المكملة فهذا يساوي + +92 +00:06:27,130 --> 00:06:34,130 +الاولى تقاطع مكملة التانية هذا ماشي اللي هو ايه + +93 +00:06:34,130 --> 00:06:37,370 +تقاطع ال c لكل prime من وين جبته هذا من نظرية + +94 +00:06:37,370 --> 00:06:40,550 +اتنين خمسة اتنين خمسة الفرع ايه اذا حابين + +95 +00:06:40,550 --> 00:06:44,950 +بالتخصيزةفإذن بدلنا هذه عبارة عن إيش؟ هي هذه X + +96 +00:06:44,950 --> 00:06:50,410 +وهذه Y ف X ناقص Y تساوي X تقاطع مكملة ال Y بشكل + +97 +00:06:50,410 --> 00:06:55,050 +عام اللي هي A و B تمام؟ تمام، إيش ممكن أعمل الآن؟ + +98 +00:06:55,050 --> 00:06:58,850 +ممكن أعمل DeMorgans، آه لا أيه، هد هي فهذا يساوي، + +99 +00:06:58,850 --> 00:07:07,300 +بدك تبهان، بيساوي A تقاطع ال B تقاطعA' Union C' + +100 +00:07:07,880 --> 00:07:11,900 +نظرية اتنين ستة او دي مورجان كله صح نظرية اتنين + +101 +00:07:11,900 --> 00:07:20,240 +ستة تمام انتبعين ممتاز ايش ممكن نعمل الانممكن نعمل + +102 +00:07:20,240 --> 00:07:24,480 +توزيع في عندنا تقاطع تقاطع واتحاد طب كيف؟ هدول فيه + +103 +00:07:24,480 --> 00:07:28,220 +تقاطع اين؟ بدي اعمل هذه كتلة واحدة اه مافتاح حاش + +104 +00:07:28,220 --> 00:07:32,980 +الآن واخد هذه الأولى مع التانية و بعدين مع التالتة + +105 +00:07:32,980 --> 00:07:39,680 +فهذا بدي اعمله توزيع A تقاطع ال B تقاطع ال A prime + +106 +00:07:39,680 --> 00:07:47,160 +اتحاد برضه نفسها الأولى A تقاطع ال B تقاطع ال C + +107 +00:07:47,160 --> 00:07:47,560 +prime + +108 +00:07:50,950 --> 00:07:55,730 +distributive law قانون التوسع طبعا زي ما حكيت + +109 +00:07:55,730 --> 00:08:00,010 +دايما انا بشتغل بشوف ايش ممكن اعمل و اين عيني على + +110 +00:08:00,010 --> 00:08:03,290 +المطلوب عيني على المطلوب عشان ماتوهش لإن في ممكن + +111 +00:08:03,290 --> 00:08:06,650 +اعمل عمليات صحيحة لكن غير مفيدة احنا برياضة تبنينا + +112 +00:08:06,650 --> 00:08:10,150 +حاجة صحيحة و مفيدة اه اذا عملنا حاجة غلط مشكلة و + +113 +00:08:10,150 --> 00:08:12,890 +اذا عملنا حاجات غير مفيدة بتتوهنا بتودينا ياش بعيد + +114 +00:08:12,890 --> 00:08:16,370 +عن الهدف اللي بدنايا وين احنا رايحين احنا رايحين + +115 +00:08:16,370 --> 00:08:21,320 +على الطرف هذااللي هي عبارة عن A تقاطع B ناقص C + +116 +00:08:21,320 --> 00:08:26,180 +اللي هي ايش؟ B تقاطع C' ممكن نكتبها كهمش فهذه ممكن + +117 +00:08:26,180 --> 00:08:30,600 +احطها بهمش احطها بوين طرف معين فانا رايح هنا اللي + +118 +00:08:30,600 --> 00:08:35,970 +هي عبارة عن A تقاطع B تقاطع C'طيب ممتاز هذا انا + +119 +00:08:35,970 --> 00:08:40,090 +وين رايح؟ وين انا وصلت؟ هي هنا ايه التقاطع بيه + +120 +00:08:40,090 --> 00:08:43,790 +تقاطع C prime؟ بديها هيها موجودة، اذا انت اما تخلص + +121 +00:08:43,790 --> 00:08:47,290 +من هذا، اه ايش هتخلص منه؟ امحيه وخلاص؟ مع ايه بدنا + +122 +00:08:47,290 --> 00:08:50,490 +ياه؟ لأ بدنا نتخلص بطريقة رياضية صحيحة، بنخلص + +123 +00:08:50,490 --> 00:08:55,200 +بطريقة رياضية صحيحة، ممتازفي عندنا A و A' هذي زي + +124 +00:08:55,200 --> 00:08:59,760 +زي تناقض وموجودة في النظرية أن A تقاطع A' تساوي + +125 +00:08:59,760 --> 00:09:03,720 +فعلا طب كيف أوصلهم لبعض إبدال و أعيش و تجميع إبدال + +126 +00:09:03,720 --> 00:09:09,160 +و تجميع فإذا هذا يساوي يساوي A تقاطع A' خليهم مع + +127 +00:09:09,160 --> 00:09:13,400 +بعض تقاطع ال B أرجو أن يكون الكلام هذا بدأ يوضح + +128 +00:09:13,400 --> 00:09:16,560 +معناه كيف أنه يتعامل و ليست تجميع و ليست توزيع + +129 +00:09:16,560 --> 00:09:24,020 +وقال إبدال بعدين اتحادهذا عبارة عن ايه؟ تقاطع الـ + +130 +00:09:24,020 --> 00:09:27,400 +B تقاطع الـ C' خلّيني أعملهم مع بعض، إيش عملناه؟ + +131 +00:09:27,400 --> 00:09:31,200 +عملنا commutative law و associative law و + +132 +00:09:31,200 --> 00:09:34,920 +associative laws + +133 +00:09:36,700 --> 00:09:41,480 +تجميع و إبقاش و إبدال إبدال في الفقرة الأولى + +134 +00:09:41,480 --> 00:09:45,660 +وبعدين إيه و تجميع و في التانية بس تجميع واضح تمام + +135 +00:09:45,660 --> 00:09:49,140 +الآن في عندنا نظرية اتنين خمسة بتقول A تقاطع A + +136 +00:09:49,140 --> 00:09:55,680 +برايم بيساوي في تقاطع ال B واحدة واحدة Union A + +137 +00:09:55,680 --> 00:09:59,900 +تقاطع B تقاطع C برايم ليس إلا B ناقص C فانا + +138 +00:09:59,900 --> 00:10:04,640 +استخدمت نظرية اتنين خمسة اتنين خمسةفي الحالتين + +139 +00:10:04,640 --> 00:10:14,620 +استخدمت نظرية اتنين خمسة اي سؤال متابعين تمام بي و + +140 +00:10:14,620 --> 00:10:18,580 +في مين بين عناصر مشتركة مافيش اه مافيش اطلاق فدي + +141 +00:10:18,580 --> 00:10:25,460 +بتسوي في فدي في اتحاد ايه تقاطع b minus c اه هذا + +142 +00:10:25,460 --> 00:10:30,420 +من وين جيبناه اللي هو ايه في تقاطع ال b تسوي فيفده + +143 +00:10:30,420 --> 00:10:36,060 +واضحة تمام اه طيب في اتحاد اي حاجة اي حاجة جيبناها + +144 +00:10:36,060 --> 00:10:41,700 +بالمحايدة فتساوي a تقاطع b minus c هتتوقع نظرية + +145 +00:10:41,700 --> 00:10:47,280 +نينس اربع theoremاتنين اربع وهو المطلوب فهي + +146 +00:10:47,280 --> 00:10:52,480 +نتخلصنا منه بطريقة رياضية صحيحة خطوة خطوة step by + +147 +00:10:52,480 --> 00:10:57,260 +step وهو المطلوب اذا نشتغلت true لو انا في مرحلة + +148 +00:10:57,260 --> 00:11:00,800 +ما لجأت انه في صعوبة وبشوف الصعوبة وينها ايش اللي + +149 +00:11:00,800 --> 00:11:04,300 +مشعليني امشي واصل للمطلوب بقدر اجيب المثال العكسي + +150 +00:11:04,300 --> 00:11:11,080 +اذا قدرنا فإذا ممكن هنا نعلق thus aليه إيش تقاطع + +151 +00:11:11,080 --> 00:11:18,840 +ال B minus C فعلا يساوي A تقاطع ال B minus A تقاطع + +152 +00:11:18,840 --> 00:11:21,760 +ال C فصار عندنا إيش التقاطع بتوزع على ال minus + +153 +00:11:21,760 --> 00:11:30,900 +صحيح أي سؤال؟ متبين؟ صح، إذا ننتقل لنقطة تانية + +154 +00:11:30,900 --> 00:11:36,740 +مثال آخر في عندنا مثال جديد من أسئلة الكتاب + +155 +00:11:44,460 --> 00:11:49,220 +سؤال مباشر الان بروفما جاليش prove or disprove او + +156 +00:11:49,220 --> 00:11:54,480 +decide جالي prove that for any sets A وB لأي + +157 +00:11:54,480 --> 00:11:59,320 +مجموعات A وB الفرق بين المكملات يسوى الفرق بين + +158 +00:11:59,320 --> 00:12:03,400 +المجموعات بس مع عكس الترتيب اه فبقولي A' ناقص B' + +159 +00:12:03,840 --> 00:12:08,980 +تسوى B ناقص A انعكست العملية انعكست العملية طبعا + +160 +00:12:08,980 --> 00:12:11,520 +ما زال جالي prove اذا انا على طول بدي اقوله prove + +161 +00:12:11,520 --> 00:12:15,240 +مش بدي اقولله خطأ ولا صح خلاص prove او solution + +162 +00:12:15,240 --> 00:12:19,430 +كله صحبروف طبعا خلّيني أعيد السياغة مافيش تساوي + +163 +00:12:19,430 --> 00:12:22,950 +مجموعات بس الـ A و الـ B أنسات بدنا نثبت تساوي + +164 +00:12:22,950 --> 00:12:27,070 +مجموعات إيش نعمل؟ نبدأ من أي طرف اللي بدنا إيه؟ من + +165 +00:12:27,070 --> 00:12:33,330 +وين نبدأ؟ نبدأ من الطرف اليسار A'-B' إيش ممكن + +166 +00:12:33,330 --> 00:12:36,870 +نعمل؟ ال trick اللي استخدمنا نظرية 2.5 نحول من + +167 +00:12:36,870 --> 00:12:44,190 +minus لتقاطع فهذا مفيد جدا فأي A' تقاطع من؟ B' لكل + +168 +00:12:44,190 --> 00:12:50,950 +برايم نظرية 2.5طبعا ننتبه في ناس مكملة مين أيش ما + +169 +00:12:50,950 --> 00:12:54,230 +تكون مكملة بي براين في هذا السؤال او ايش كانت + +170 +00:12:54,230 --> 00:12:58,390 +مكملة اي تقاطع او بي تقاطع سي ما أيش ما تكون احنا + +171 +00:12:58,390 --> 00:13:03,530 +بنقول في عندي مجموعة ما X ناقص مجموعة ما Y ايش + +172 +00:13:03,530 --> 00:13:07,570 +بتساوي الأولى تقاطع التانية بغض النظر إيش هي فارجو + +173 +00:13:07,570 --> 00:13:11,610 +أنه نقدر نفكر بيد الشمول بيد العمومية عشان نقدر + +174 +00:13:11,610 --> 00:13:15,970 +نشتغل صح تماماحنا وان رايحين؟ رايحين على B ناقص A + +175 +00:13:15,970 --> 00:13:19,930 +ليه B تقاطع H A' طيب إيش ممكن أعمل؟ double + +176 +00:13:19,930 --> 00:13:23,890 +negation أو H مكملة المكمل هي المجموعة نفسها فده + +177 +00:13:23,890 --> 00:13:28,950 +بيسوي A' تقاطع ال B نظرية برضه اتنين خمسة بس الفرع + +178 +00:13:28,950 --> 00:13:34,400 +الأولتمام اش نعمل ابدال لان اين رايح دايما عيني + +179 +00:13:34,400 --> 00:13:38,160 +على اين رايح احنا رايح على B ناقص A يعني B تقاطع + +180 +00:13:38,160 --> 00:13:41,260 +ال A هي دي رايحين حابين يكتبوها هنا على طول هذا + +181 +00:13:41,260 --> 00:13:44,400 +عبارة عن ايه؟ B تقاطع ال A' وانا وصلت هنا اش اعمل + +182 +00:13:44,400 --> 00:13:49,000 +ابدال؟ وتساوي B تقاطع ال A' competitive law + +183 +00:13:49,000 --> 00:13:54,260 +competitive law خلصنا وهو B ناقص A نظرية 2.5 + +184 +00:14:01,810 --> 00:14:06,990 +وهو المطلوب فهذه الحقيقة الفرع هذا كتير بساعدنا أن + +185 +00:14:06,990 --> 00:14:10,690 +نحول ال minus لتقاطه وبعدين نقدر نشتغل بخواص + +186 +00:14:10,690 --> 00:14:17,970 +التقاط وخواص الاتحاد و هكذا أي سؤال نشوف مثال جديد + +187 +00:14:17,970 --> 00:14:24,440 +المثال رقم تلاتة let a and b be six prove thatب + +188 +00:14:24,440 --> 00:14:28,620 +sub set من a prime if and only if a تقاطع ال b + +189 +00:14:28,620 --> 00:14:34,040 +يساوي 5 في عندنا جملة ايش ثنائية الشرطية خليني + +190 +00:14:34,040 --> 00:14:39,480 +اعيد صياغة السؤالالمثال التالت طبعا المقدمة واضحة + +191 +00:14:39,480 --> 00:14:44,700 +مافيش ده عنصيغة بس مجموعة فبقول بي subset من a + +192 +00:14:44,700 --> 00:14:48,760 +prime if and only if طبعا بتافت هنا true فممكن + +193 +00:14:48,760 --> 00:14:54,720 +اعملها تكافؤ اللي هو ايش a تقاطع ال b يساوي في هذا + +194 +00:14:54,720 --> 00:14:56,780 +هو المطلوب solution + +195 +00:14:58,930 --> 00:15:03,110 +فمرة تانية عشان ابرهن اللي هو if and only if + +196 +00:15:03,110 --> 00:15:06,450 +statement فيه انا طريقتين two parts theorem وهذا + +197 +00:15:06,450 --> 00:15:10,390 +بننصح فيه خصوصا احنا في مبادئ الرياضيات لأنه الشغل + +198 +00:15:10,390 --> 00:15:14,390 +في التكافؤ بده دقة شديدة لأنه اذا اي خطوة ماكانتش + +199 +00:15:14,390 --> 00:15:17,230 +تكافؤ بكون اللي بالبرهان نص راحأه بيكونوا يقولوا + +200 +00:15:17,230 --> 00:15:19,990 +احنا أثبتنا النص و النص التاني ماعملناهوش فاحنا + +201 +00:15:19,990 --> 00:15:23,190 +هنستخدم طريقة ايش two parts proof بننصح فيها + +202 +00:15:23,190 --> 00:15:27,090 +نجسمها لمين ل two implications او ل two + +203 +00:15:27,090 --> 00:15:31,610 +conditional statements فحنستخدم two parts proof we + +204 +00:15:31,610 --> 00:15:37,930 +will use two parts proof + +205 +00:15:39,450 --> 00:15:41,490 +ايش معناه two parts؟ يعني حاجات اسمها two + +206 +00:15:41,490 --> 00:15:45,410 +conditional الأول implies التاني والتاني implies + +207 +00:15:45,410 --> 00:15:49,690 +الأول فنبدأ بالطرف الأول أو بالجزء الأول زي ما + +208 +00:15:49,690 --> 00:15:52,990 +اقول لما اش two parts جزئين نبدأ بال part first + +209 +00:15:52,990 --> 00:16:00,770 +part الجزء الأولفالجزء الأول من اليسار implies إيش + +210 +00:16:00,770 --> 00:16:08,130 +اليمين فعنا B subset من A' implies A تقاطع الـ B + +211 +00:16:08,130 --> 00:16:16,590 +يساوي فاي هذا مطلوب تمام كالعادة لكل حفظ assume إن + +212 +00:16:16,590 --> 00:16:20,970 +الشرط صحيح the condition is true assume B subset + +213 +00:16:20,970 --> 00:16:27,960 +من A' B subset من A' بدنا نثبت إن هذه فايWe want + +214 +00:16:27,960 --> 00:16:38,880 +to prove A تقاطع الـ B تساوي 5 أي سؤالهنا في + +215 +00:16:38,880 --> 00:16:43,940 +ملاحظة مهمة و برضه ممكن نعتبرها كنصيحة عامة كيف + +216 +00:16:43,940 --> 00:16:48,420 +نثبت أن مجموعة ما في لو روحنا على التعريف بدنا + +217 +00:16:48,420 --> 00:16:51,640 +نقول for all x, x في الأولى, if and only if, x في + +218 +00:16:51,640 --> 00:16:54,040 +التانية طبعا x and تملى الفيها دي يشمل + +219 +00:16:54,040 --> 00:16:56,700 +Contradiction ففي صعوبة في الوصول إليها ومستحيل + +220 +00:16:56,700 --> 00:17:00,840 +أوصلها أي Contradiction بدها عملية لذلك نصيحة طبعا + +221 +00:17:00,840 --> 00:17:05,160 +مش قاعدة عشان نثبت أن مجموعة ما فيا هنستخدم a + +222 +00:17:05,160 --> 00:17:09,280 +proof by contradiction indirect proofأه فلتسهيل + +223 +00:17:09,280 --> 00:17:13,340 +العملية عشان تثبتي إذا جالك تثبتي مجموعة ما في من + +224 +00:17:13,340 --> 00:17:17,420 +الطرق الفعالة بتنجح في الغالب إذا مش دايما عن طريق + +225 +00:17:17,420 --> 00:17:19,760 +اللي هو approved by contradiction احنا نفترض إنه + +226 +00:17:19,760 --> 00:17:22,620 +مطلوب خطأ و نوصل لمين ل contradiction فانا إيش + +227 +00:17:22,620 --> 00:17:27,360 +هقوله الآن هقوله assumeإيش؟ المطلوب false، مظبوط؟ + +228 +00:17:27,360 --> 00:17:30,420 +مش هيك اتعلمناه، فهقوله assume ان هذه لا تساوي + +229 +00:17:30,420 --> 00:17:34,720 +فيه، فهقوله ايه؟ تقاطع ال B لا تساوي فيه، إيش + +230 +00:17:34,720 --> 00:17:37,060 +معملة أنا جاهد؟ معمة اللي جايش approved by + +231 +00:17:37,060 --> 00:17:37,780 +contradiction + +232 +00:17:44,470 --> 00:17:47,930 +طبعا لو قلت indirect proof بقبلها لكن ال indirect + +233 +00:17:47,930 --> 00:17:50,190 +proof فيه كمان اللي هو contrapositive لكن ايه او + +234 +00:17:50,190 --> 00:17:51,910 +by contradiction فاحنا بدنا بالظبط by + +235 +00:17:51,910 --> 00:17:56,450 +contradiction للدقة الأكثر ممتاز واضح فإذا هذه + +236 +00:17:56,450 --> 00:18:00,810 +نصيحة عشان نثبت إن مجموعة فارغة من الأفضل نستخدم + +237 +00:18:00,810 --> 00:18:03,630 +proof by contradiction أه بقول من الأفضل مش دايما + +238 +00:18:03,630 --> 00:18:07,290 +الشرط لكنه هذه طريقة فعالة و الحقيقة بيعتمدوا + +239 +00:18:07,290 --> 00:18:10,530 +عليها في معظم الأحيان إذا مش في كل الأحيان ممتاز + +240 +00:18:10,530 --> 00:18:15,540 +ماذا يعني إنه مجموعة غير فارغة؟أحسنتي، يعني انت + +241 +00:18:15,540 --> 00:18:17,840 +فاكري مع نفسك حتى إيش بيقولي إن هذا الصف مش فاضي، + +242 +00:18:17,840 --> 00:18:20,440 +إيش يعني؟ فيه على الأقل طالبة، فيه إيش، إذا ناشي + +243 +00:18:20,440 --> 00:18:24,260 +نقوله، there exists X تنتمي لهذا التقاطة، فده + +244 +00:18:24,260 --> 00:18:30,440 +بيقوللي implies there exists X، X تنتمي لمن؟ للـA + +245 +00:18:30,440 --> 00:18:33,280 +تقاطة على الـB، مش للفاي، لللي مش فارق، لللي مش + +246 +00:18:33,280 --> 00:18:36,780 +فارق، تقاطة على الـB، من وين جيبنا هذا؟ مين نقوله + +247 +00:18:36,780 --> 00:18:41,360 +دليلنا؟ تعريف الفايما شوفوا أيش معناه فاضي؟ مافيش + +248 +00:18:41,360 --> 00:18:43,500 +فيه ولا عنصر طب ايش اللي مش فاضي؟ فيه على الأقل + +249 +00:18:43,500 --> 00:18:47,520 +أنصر واضح؟ تمام، ممتاز، لأ الآن بندور على + +250 +00:18:47,520 --> 00:18:52,680 +contradiction نحاول نفسر أيش معناه أنه يوجد عنصر + +251 +00:18:52,680 --> 00:19:00,040 +now X تنتمي للـA تقاطع الـB، ماذا تعني؟ and X + +252 +00:19:00,040 --> 00:19:04,680 +تنتمي للـB تعريف ماهيش؟ التقاطعof intersection + +253 +00:19:04,680 --> 00:19:09,380 +ممتاز انا وان بدور على contradiction يا بدى نطق + +254 +00:19:09,380 --> 00:19:13,060 +ايه اللي هو يا X لا تنتمي لل B يا X لا تنتمي لل A + +255 +00:19:13,060 --> 00:19:16,400 +هي اللي عندى بدى حالة كون هي الجملة اللي عندى بدى + +256 +00:19:16,400 --> 00:19:20,820 +اوصل انه بي and not بيإيش وين ندور؟ ندور .. إيش + +257 +00:19:20,820 --> 00:19:24,580 +المعطيات؟ قول لإن الـB subset من الـA' فاللي في + +258 +00:19:24,580 --> 00:19:27,480 +الـB وين؟ موجود في الـA' أه هو EO هتوصل + +259 +00:19:27,480 --> 00:19:30,900 +للcontradiction صحيح فهذا على طول implies مش تكافؤ + +260 +00:19:30,900 --> 00:19:36,500 +X تنتمي للـA and X تنتمي للـA' ليش؟ لأن الـB + +261 +00:19:36,500 --> 00:19:39,780 +subset من A' فكل اللي في الصغيرة موجود في الكبير + +262 +00:19:39,780 --> 00:19:44,520 +طبعا دي إيش معناته؟ X لا تنتمي فهذا X تنتمي للـA + +263 +00:19:44,520 --> 00:19:49,720 +and X لا تنتمي للـA طبعا تعريف الـPrimeطبعا + +264 +00:19:49,720 --> 00:19:55,760 +contradiction وانتهى + +265 +00:19:55,760 --> 00:19:59,180 +البرهان طبعا ممكن أعلق و أقوله إيش فبالتالي إنها + +266 +00:19:59,180 --> 00:20:03,040 +بتسوي file لكن لو ما كتبتش إيش صحيح thus أو + +267 +00:20:03,040 --> 00:20:09,660 +therefore أيه تقاطع ال B فعلا هو فارق لأن لو كان + +268 +00:20:09,660 --> 00:20:13,080 +في عنصر واحد الدنيا تناقض مستحيل إذا المستحيل يكون + +269 +00:20:13,080 --> 00:20:16,700 +في أي عنصر إذا نشمله فارق أي سؤال + +270 +00:20:19,770 --> 00:20:26,470 +بنروح لتجاه التاني او الجزء التاني اتنين + +271 +00:20:26,470 --> 00:20:35,150 +فهنقول له ايش a تقاطع ال b يساوي five implies b + +272 +00:20:35,150 --> 00:20:40,370 +subset من a prime هذا مطلوب كالعادة هقوله ايش + +273 +00:20:40,370 --> 00:20:46,510 +assume ان ال b true او الشرط صحيح تساوي five we + +274 +00:20:46,510 --> 00:20:54,050 +want to prove جواب الشرطto prove that + +275 +00:20:54,050 --> 00:21:04,210 +B is a subset of A' فمشيين + +276 +00:21:04,210 --> 00:21:09,800 +على نفس المنهجأحياناً بنختصر أحياناً بنكتب بشكل + +277 +00:21:09,800 --> 00:21:13,240 +مفصل لكن ماغيرناش المنهج كيف نتعامل مع جملة + +278 +00:21:13,240 --> 00:21:16,880 +الشرطية كيف نتعامل مع جملة ثنائية الشرطية الآن + +279 +00:21:16,880 --> 00:21:23,160 +برضه بتمر علينا متعددة كيف نثبت subset اتعلمت ولا + +280 +00:21:23,160 --> 00:21:27,320 +لسه ناخد عنصر عشوائي من الطرف اليسار نفس الطريقة + +281 +00:21:27,320 --> 00:21:38,470 +let x be anyElement such that أو أندتز كله صح ال X + +282 +00:21:38,470 --> 00:21:45,230 +تنتمي لمين؟ لل B للطرف اليسار بدنا نوصلها بطريقة + +283 +00:21:45,230 --> 00:21:51,250 +صحيحة إلى ال A إبراى بدنا نشوف إيش فيها عندنا أنا + +284 +00:21:51,250 --> 00:21:58,460 +عندي تقاطع في و بس هي المعطمة و ال X في ال Bفانا + +285 +00:21:58,460 --> 00:22:02,120 +بدي إياها تكون في ال A' بمعنى بدي إياها ما تكونش + +286 +00:22:02,120 --> 00:22:05,280 +في ال A ممكن أعملها مش واقعي نفكر بصوت عالي بدنا + +287 +00:22:05,280 --> 00:22:10,820 +إيش نوصل X أنا مطلوب X تنتمي لل A' سؤال يعني X لا + +288 +00:22:10,820 --> 00:22:17,320 +تنتمي لل A فكر بسؤالأه فاللي في ال B مستحيل يكون + +289 +00:22:17,320 --> 00:22:21,660 +في ال A فهذا على طول يؤدي أن X لا تنتمي لل A ليش؟ + +290 +00:22:21,660 --> 00:22:25,920 +لأن A تقاطع ال B بيساوي فيه لأن لو كان في ال A صار + +291 +00:22:25,920 --> 00:22:29,640 +فيه إيش في التقاطع X في ال B وفي ال A مع بعض بيصيح + +292 +00:22:29,640 --> 00:22:33,120 +في التقاطع فمشكلة طبعا مزال مش في ال A إذا وين؟ في + +293 +00:22:33,120 --> 00:22:37,460 +المكملة تعريف + +294 +00:22:37,460 --> 00:22:42,200 +المكملة إبراهيم وهو المطلوب therefore + +295 +00:22:44,660 --> 00:22:49,120 +الـ B subset من A' بدأنا من عنصر من الـ B عشوائي + +296 +00:22:49,120 --> 00:22:53,660 +وصلنا للـ A' إذا هذا إثبات أنه علاقة ال subset + +297 +00:22:53,660 --> 00:22:58,180 +فطبعا فزي ما شايفين الخطوط العريضة الهيكلية واحدة + +298 +00:22:58,180 --> 00:23:00,840 +التفاصيل بتختلف من مثال لمثال لكن أنا بدأت من + +299 +00:23:00,840 --> 00:23:04,320 +اليسار بعنصر عشوائي وصلت لليمين بطريقة رياضية + +300 +00:23:04,320 --> 00:23:14,080 +صحيحة فإذا انتهى الجرهن نشوف كمان مثال مثال الرابع + +301 +00:23:15,110 --> 00:23:20,090 +نفس الطريقة let a b c b six prove that برهان مباشر + +302 +00:23:20,090 --> 00:23:24,230 +و لا if then و لا if and only if إثبات تساوي + +303 +00:23:24,230 --> 00:23:24,970 +مجموعات + +304 +00:23:31,830 --> 00:23:36,550 +فزي ما انتوا شايفين احنا بنشوف المسألة، بنفهمها، + +305 +00:23:36,550 --> 00:23:39,410 +بنكتبها، بنشوف ايش نوع ال statement المطلوبة، هل + +306 +00:23:39,410 --> 00:23:43,450 +هي جملة مباشرة، مطلوب مباشر، هل هو جملة شرطية + +307 +00:23:43,450 --> 00:23:47,130 +المطلوب، جملة ثنائية الشرطية، لازم نعرف و نفصل و + +308 +00:23:47,130 --> 00:23:50,290 +نشوف الطريقة المناسبة، نختار الطريقة، نصمم الطريقة + +309 +00:23:50,290 --> 00:23:53,870 +زي ما اتفقنا، و هكذا، ففش لاقيت اثبات مجموعة تساوي + +310 +00:23:53,870 --> 00:24:03,200 +مجموعةبعد المثال الرابع اللي هو a-b-c تساوي a-b + +311 +00:24:03,200 --> 00:24:10,690 +union c solution أكم طريقة للحلعلى الأقل أنا مذكر + +312 +00:24:10,690 --> 00:24:14,930 +طريقتين طريقة التعريف التساوي أقول له for all X X + +313 +00:24:14,930 --> 00:24:17,350 +في الأولى F and all ل F X التانية هذه الطريقة + +314 +00:24:17,350 --> 00:24:20,830 +تعريفه دايما بتنفع لكن ممكن تكون طويلة شوية + +315 +00:24:20,830 --> 00:24:25,230 +الطريقة التانية ممكن نحول من ال minus لتقاطع زي ما + +316 +00:24:25,230 --> 00:24:28,010 +شوفنا في المثال الأول والتاني خلينا نعمل اشترا + +317 +00:24:28,010 --> 00:24:31,370 +عليها لأ ده هتكون مقتصر أكتر اه طبعا تساوي مجموعات + +318 +00:24:31,370 --> 00:24:34,030 +ببدأ من أي طرف بدي إياه إيش رأيكوا نبدأ من اليمين + +319 +00:24:34,030 --> 00:24:37,420 +ولا اليسارنبدأ من اليمين، ماشي لإن هو طبعا طول + +320 +00:24:37,420 --> 00:24:41,740 +تقريبا طول واحد هيا نبدأ من طرف اليمين فالآن A + +321 +00:24:41,740 --> 00:24:48,220 +ناقص B Union C طبقا لنظرية 2 5 بيساوي الأول تقاطة + +322 +00:24:48,220 --> 00:24:57,180 +مكملة التاني C لكل براي، نظرية 2 5 الان + +323 +00:24:57,180 --> 00:25:03,200 +إيش نعمل؟ De Morgan's، اه فده يساويA تقاطع B' + +324 +00:25:03,780 --> 00:25:09,760 +تقاطع C' نظرية 2.6 أو D مورجان كله صح المهم اذكر + +325 +00:25:09,760 --> 00:25:15,560 +الدليل و بأي صيغة بدك إياها إيش + +326 +00:25:15,560 --> 00:25:21,340 +نعمل؟كله تقاطع مافيش أمامي إلا يا تبديل يا تجميع + +327 +00:25:21,340 --> 00:25:24,220 +طب مين .. أيش .. أيش عمل؟ اتطلع على المطلوب وين + +328 +00:25:24,220 --> 00:25:28,800 +رايحين احنا؟ رايحين على اليسار اليسار إيش بيساوي؟ + +329 +00:25:28,800 --> 00:25:35,590 +عبارة عن إيه؟ تقاطع الـB' تقاطع الـC'وصلنا ولا مش + +330 +00:25:35,590 --> 00:25:38,450 +وصلين؟ وصلين احنا بس طبعا بدنا نكتبها .. بدنا + +331 +00:25:38,450 --> 00:25:41,930 +نكتبها فطبعا هذا بيقوللي ايش؟ غير الأقواس يعني ايش + +332 +00:25:41,930 --> 00:25:47,730 +عمل تجميع فهذا تساوي a تقاطع ال b prime تقاطع ال c + +333 +00:25:47,730 --> 00:25:52,110 +prime associative law طبعا يعمل الان بس حطيهاش + +334 +00:25:52,110 --> 00:26:00,570 +النظرية ناقص b اتقع ناقص c نظرية اتنين خمسة وهو + +335 +00:26:00,570 --> 00:26:08,090 +المطلوبواضح فدائما بكتب و بوصل و بعمل و بطلع على + +336 +00:26:08,090 --> 00:26:10,770 +المطلوب عشان اعرف ايش اللي بده اعمله فبساعدني كتير + +337 +00:26:10,770 --> 00:26:14,390 +لأن في أشياء كتير صحيحة لكن مين المفيد وين عهو + +338 +00:26:14,390 --> 00:26:18,470 +الهدف تبعي اللي بيحدد وين بده اوصل للهدف اللي انا + +339 +00:26:18,470 --> 00:26:24,210 +رايحني اي سؤال فارجو + +340 +00:26:24,210 --> 00:26:28,190 +ان هذه الأمثلة تكون دتنا فكرة كافية نحل أمثلة + +341 +00:26:28,190 --> 00:26:31,810 +الكتاب نحل القال و نكون جيش نتمكن من الموضوع فهذه + +342 +00:26:31,810 --> 00:26:32,610 +نهاية هذا ال session + +343 +00:26:44,740 --> 00:26:49,280 +في اتنين خمسة موضوعنا Venn diagrams اللي هو مخططات + +344 +00:26:49,280 --> 00:26:53,740 +Venn هذا الرسم في الرياضيات بشكل عام عبارة عن أداء + +345 +00:26:53,740 --> 00:26:59,260 +مساعدة بتساعدنا في فهم المواضيع في أحيانا في + +346 +00:26:59,260 --> 00:27:02,060 +الأسئلة اللي prove و disprove نعرف إنها true ولا + +347 +00:27:02,060 --> 00:27:05,220 +false أو نخمن وبالتالي اتحللنا جزء من السؤال + +348 +00:27:05,220 --> 00:27:10,810 +وبعدين نعرف إيش اللي بدنا إياهفالحقيقة أن الـ Venn + +349 +00:27:10,810 --> 00:27:15,210 +Diagram عبارة عن أداة بتساعدنا خصوصا في التعرف على + +350 +00:27:15,210 --> 00:27:20,690 +العمليات تبع المجموعة وهي الاتحاد والتقاطعوالمكمل + +351 +00:27:20,690 --> 00:27:26,570 +أول فرق طبعا Vin هو عالم انجليزي عالم رياضيات و + +352 +00:27:26,570 --> 00:27:31,850 +logic اسمه John Vin طبعا ولد في ال 1834 وتوفى في + +353 +00:27:31,850 --> 00:27:38,070 +ال 1923 فده عالم عاش مدة طويلة صحيح فطبعا نسبة + +354 +00:27:38,070 --> 00:27:44,120 +لهذا العالمطبعا كيف القواعد الرسم طبعا في عرف + +355 +00:27:44,120 --> 00:27:47,160 +متعرف عليه طبعا انا ممكن ارسم اي حد تساعدني ممكن + +356 +00:27:47,160 --> 00:27:51,740 +لكن عرفا كيف المتعرف عليه بقولي بنرسم ال universal + +357 +00:27:51,740 --> 00:27:54,960 +set اللي هي ايش عبارة عن مجموعة تخيولية مش حقيقية + +358 +00:27:54,960 --> 00:27:57,880 +لان بيقولوله لا توجد universal set ولكن احنا ممكن + +359 +00:27:57,880 --> 00:28:02,700 +مؤقتا عرفا نتفق على مجموعة مرجعية ما برسموه على + +360 +00:28:02,700 --> 00:28:05,500 +صورة مستطيل برسموه على صورة مستطيل ال universal + +361 +00:28:05,500 --> 00:28:11,540 +set فبنرسموه بهذا الشكل مستطيل معينوبحطه في القاع + +362 +00:28:11,540 --> 00:28:14,800 +في أحد الزواييه في اليمين أو اليسار فهذا yes ال + +363 +00:28:14,800 --> 00:28:18,060 +universe إذاً هذا هو الإطار العمل تبعي مش هخرج عن + +364 +00:28:18,060 --> 00:28:21,680 +هذا الإطار هذا المستطيل طيب المجموعات المجموعات + +365 +00:28:21,680 --> 00:28:24,940 +الأخرى اللي طبعا كلها جواها هتكون لأن أي إطار + +366 +00:28:24,940 --> 00:28:28,540 +العمل تبعي هي المرجية بتكون عبارة عن دوائر برسمها + +367 +00:28:28,540 --> 00:28:32,340 +كدوائر برسمها كدوائر فهذا المبدأ العام فهذا هو + +368 +00:28:32,340 --> 00:28:35,840 +المبدأ العام طبعا + +369 +00:28:36,810 --> 00:28:40,950 +بنتفق على أمور و هي متفق عليها رياضيا بالرغم أن ال + +370 +00:28:40,950 --> 00:28:46,170 +Venn diagram يعني هي أسهل كتير من البراهين لكن هي + +371 +00:28:46,170 --> 00:28:51,230 +اسمها ليست إلا أداة مساعدة لا تعتبر بديل للبرهان + +372 +00:28:51,230 --> 00:28:54,630 +فعمر الرسم ما كان برهان في الرياضيات ولا كان حل + +373 +00:28:54,630 --> 00:28:57,650 +إلا إذا جالك أقول و هأرسمي بده رسمة هذا سؤال لكن + +374 +00:28:57,650 --> 00:29:01,350 +هو لا يعتبر برهان فهو ليس .. اه فبقول ليه it is + +375 +00:29:01,350 --> 00:29:04,750 +never a substitute for a real proof ليست بديل + +376 +00:29:04,750 --> 00:29:10,300 +للبرهان الحقيقى إنما هي أداة مساعدةأداء مساعد أيضا + +377 +00:29:10,300 --> 00:29:14,560 +طبعا في استخدامها محدود إذا كتر المجموعات بيصير + +378 +00:29:14,560 --> 00:29:18,860 +عملية غير عملية الرسم بيصير ايش صعب أن أقدر أوضح + +379 +00:29:18,860 --> 00:29:21,500 +فبقول إذا أكتر من تلت مجموعات بيصير عملية الرسم + +380 +00:29:21,500 --> 00:29:25,140 +صعبة شوية فهذا بيخلي استخدام هذا ال Venn diagrams + +381 +00:29:25,140 --> 00:29:29,420 +محدودطبعاً في صور نمطية طبعاً مابتجيهش كل الحالات + +382 +00:29:29,420 --> 00:29:33,820 +فهذه أشهر الصور في الصورة الأولى في عنا اللي هو + +383 +00:29:33,820 --> 00:29:36,760 +الاتحاد فهو هي ال A و ال B و المظلة اللي هو + +384 +00:29:36,760 --> 00:29:39,580 +الاتحاد لأنه يا في ال A يا في ال B طبعاً زي ما + +385 +00:29:39,580 --> 00:29:43,560 +تشايفين اليوم المعاتين تقطعهم file يسمونهم + +386 +00:29:43,560 --> 00:29:47,280 +disjoint منفصلين نرسمهم مبعد عن بعض نرسمهم مبعد عن + +387 +00:29:47,280 --> 00:29:50,160 +بعض زي ما الرسم التاني في الرسم التالتة المكملة + +388 +00:29:50,160 --> 00:29:53,620 +اللي خارج ال A واضح كل اللي في ال universe معدى ال + +389 +00:29:53,620 --> 00:29:57,180 +A كل ال universeطبعا التقاطع واضح لعناص المشتركة + +390 +00:29:57,180 --> 00:30:01,080 +زي الرسمة الرابعة لها طبعا subset جزء جوا زي + +391 +00:30:01,080 --> 00:30:06,660 +الرسمة الخامسة طبعا المكمل اللي هي A ناقص B عناصر + +392 +00:30:06,660 --> 00:30:10,340 +في الـA خارج الـB فانا بدي كل الـA مع ده التقاطع + +393 +00:30:10,340 --> 00:30:14,040 +اللي مع الـB بس بدي جزء من الـA وخارج الـB فهذه + +394 +00:30:14,040 --> 00:30:17,220 +رسمات نمطية طبعا تتكسس جميع الحلال وإنما هذه الصور + +395 +00:30:17,220 --> 00:30:20,160 +النمطية المتعرفة عليها تفضل ما تذكرتش ليه ال + +396 +00:30:20,160 --> 00:30:23,550 +universe كله؟وين؟ كله موجود، كله موجود، هي اللي هو + +397 +00:30:23,550 --> 00:30:28,590 +المرجعية المستطيل، وين؟ في الأخيرة؟ لأ، الأخيرة مش + +398 +00:30:28,590 --> 00:30:32,510 +مكملة، مكملة نسبية، مش مكملة مطلقة، مكملة الـA + +399 +00:30:32,510 --> 00:30:37,090 +بالنسبة للـB، فهي عناصر الـL خارج الـB، بس، + +400 +00:30:37,090 --> 00:30:41,350 +ماديكيش المكملة العامة، هي U ناقص الـA، فمختلفة، + +401 +00:30:41,350 --> 00:30:44,790 +هنا لأ، فهذه بعض الصور النمطية اللي متعرف عليها + +402 +00:30:44,790 --> 00:30:48,730 +خليني أشوف بعض الأمثلة، كيف نستخدم هذه الرسمات في + +403 +00:30:48,730 --> 00:30:53,610 +حل بعض المسائلالسؤال الأول رسم مباشر مابدوش شيء + +404 +00:30:53,610 --> 00:30:57,870 +بقول draw a Venn diagram for A تقاطع ال B' أي إيش + +405 +00:30:57,870 --> 00:31:01,890 +بتساوي A يونيو A ناقص B نشوف الرسمة و نقارن خلينا + +406 +00:31:01,890 --> 00:31:13,010 +نحلهم مع بعض نشوف فعلا بطلع نفس الشيء ولا لأ فده + +407 +00:31:13,010 --> 00:31:17,640 +المثال الأولSolution فطبعا إيش هنرسمهم هنرسم + +408 +00:31:17,640 --> 00:31:23,120 +مستطيل عبارة عن ال universal set المجموعة المرجعية + +409 +00:31:23,120 --> 00:31:28,420 +أو ال U بدوا مجموعتين A و B طبعا نبدأ من B عشان + +410 +00:31:28,420 --> 00:31:33,070 +بدنا B' فلو في عندنا مجموعة B هيهادائرة بنعملها + +411 +00:31:33,070 --> 00:31:37,150 +طبعا مش .. مدناش نجيب فرجار و كذا تقريبي كله اه + +412 +00:31:37,150 --> 00:31:41,390 +ايش المكملة؟ خارج المكملة ما في الخارج فهذه مكملة + +413 +00:31:41,390 --> 00:31:45,210 +ال B فهذه مكملة ال B ممكن طبعا نظللها بشكل كامل او + +414 +00:31:45,210 --> 00:31:50,890 +نحط خطوط بدنا ايش؟ فهذه هي B prime طيب بدنا + +415 +00:31:50,890 --> 00:31:54,250 +تقاطحها مع ال A بدنا نجيب A و نجيب التقاطع هي ال A + +416 +00:31:55,400 --> 00:32:00,060 +هي الـ A تقاطعها مع B' وين تقاطعها مع B'؟ اللي + +417 +00:32:00,060 --> 00:32:04,980 +مشترك، مش مع الـ B، مع الـ B' اللي هو A مظبوط؟ + +418 +00:32:04,980 --> 00:32:08,300 +اللي هي فعلاً A ناقص B، لو تظهرت الرسمة فعلاً هي A + +419 +00:32:08,300 --> 00:32:16,270 +ناقص B فدهي .. فهذا الأحمر هو مين؟ A تقاطع B'هي + +420 +00:32:16,270 --> 00:32:19,450 +الصورة النمطية هيك الصورة النمطية طبعا بيبقى بعيد + +421 +00:32:19,450 --> 00:32:22,390 +احتمال و هذا احتمال ولا لأ فهذه الصورة النمطية + +422 +00:32:22,390 --> 00:32:25,910 +الصورة النمطية زي ما رسمنا ايش ايه ناقص فيه بنعمله + +423 +00:32:25,910 --> 00:32:29,810 +متقاطة فهذه طبعا احنا في احتمالات متعددة بس نحكي + +424 +00:32:29,810 --> 00:32:34,770 +المثال الأشهر اه فالصورة النمطية اه عشان اقارن هي + +425 +00:32:34,770 --> 00:32:38,610 +فعلا ايه ناقص فيه بتطلع نفس الرسم اي سؤال + +426 +00:32:41,620 --> 00:32:45,440 +نشوف مثال والحقيقة ده مثال الحقيقة هو أكتر استخدام + +427 +00:32:45,440 --> 00:32:49,820 +للـ diagrams إنه إيش بده أقرر true or false true + +428 +00:32:49,820 --> 00:32:53,300 +or false use then .. then diagrams to decide + +429 +00:32:53,300 --> 00:32:58,640 +whether the following are true or false الأولى دي + +430 +00:32:58,640 --> 00:33:01,960 +مرجان أحنا عارفين أنها true فخليني أشوف أكيد من ال + +431 +00:33:01,960 --> 00:33:06,540 +diagram إنها فعلا true خليني أرسمها مع بعض ونشوف + +432 +00:33:06,540 --> 00:33:07,880 +ليش فعلا هي true + +433 +00:33:16,850 --> 00:33:22,650 +المثال التاني solution الفرع الأول خليني أبدأ + +434 +00:33:22,650 --> 00:33:27,590 +برسمة اللي هي الطرف اليسار فبد الإتحاد والصورة + +435 +00:33:27,590 --> 00:33:32,630 +النمطية للاتحاد مش هذه كل احتمالات قال لي هي A وB + +436 +00:33:32,630 --> 00:33:36,870 +هيك بارسمهم والاتحاد هو كل هذا هو بدوش الاتحاد بده + +437 +00:33:36,870 --> 00:33:42,030 +المكملة مين المكملة الخارج خارج هذه الصورة فهذا + +438 +00:33:42,030 --> 00:33:42,570 +الخارج + +439 +00:33:45,230 --> 00:33:49,490 +خارج الاتحاد، هذا الاتحاد و هذا الخارج، طبعا ليش + +440 +00:33:49,490 --> 00:33:51,690 +مش بعض عن بعض، ممكن، لكن احنا قولنا هذه الصورة + +441 +00:33:51,690 --> 00:33:57,910 +النمطية، فهذه الأزرق هي union B الكل الـ prime + +442 +00:33:57,910 --> 00:34:01,810 +المكمل، تمام، بدنا نرسم الرسمة التانية، طبعا يمكن + +443 +00:34:01,810 --> 00:34:05,500 +صعب ارسم مع نفس الرسمة، خدنا نرسم مع الرسمةو نقارن + +444 +00:34:05,500 --> 00:34:08,820 +بين الرسمتين بس بدي احاول ايش اثبت بعض الأمور عشان + +445 +00:34:08,820 --> 00:34:12,460 +تسهل المقارنة عشان تسهل المقارنة فهي المستطيل اللي + +446 +00:34:12,460 --> 00:34:16,900 +هو ال U طبعا اللي هو ال U وهي الاتحاد نفس الرسمة + +447 +00:34:16,900 --> 00:34:22,840 +مشابهة ايش بده الآن بده A' تقاطع B' نبدأ نحسبهم + +448 +00:34:22,840 --> 00:34:27,960 +واحدة واحدة هى ال A وين A' خارج ال A خارج ال A + +449 +00:34:27,960 --> 00:34:34,000 +خليه بيعمله بالأحمر هى خارج ال Aخارج ال A بنعمله + +450 +00:34:34,000 --> 00:34:38,980 +بعد الشكل هاي خارج ال A كله من A و برا خارج ال A + +451 +00:34:38,980 --> 00:34:44,000 +تمام؟ هاي الأحمر خارج ال A طيب خارج ال B بدنا + +452 +00:34:44,000 --> 00:34:47,220 +نعمله بالأزرق هاي ال B اللي قاعد في الأحمر A prime + +453 +00:34:47,220 --> 00:34:52,500 +B prime خارج ال B هاي بي وهاي خارجها خارج ال B + +454 +00:34:58,220 --> 00:35:02,480 +لما يقول لتقاطع بدي عناصر مشتركة بين خارج ال A و + +455 +00:35:02,480 --> 00:35:05,760 +خارج ال B يعني إيش بالنسبالي؟ المناطق اللي فيها + +456 +00:35:05,760 --> 00:35:10,000 +أزرق و أحمر المناطق اللي فيها أزرق و أحمر هيها هذه + +457 +00:35:10,000 --> 00:35:13,380 +المناطق فيها أزرق و أحمر وهذه المناطق طب هل هي نفس + +458 +00:35:13,380 --> 00:35:18,060 +الشيء نفسها فإذا هذه فعلا هي true فإذا فعلا true + +459 +00:35:18,060 --> 00:35:19,460 +فإذا هذه الأولى true + +460 +00:35:24,810 --> 00:35:29,030 +فهي مافيش مشكلة نعمل رسمتين منفصلتين بس نثبت + +461 +00:35:29,030 --> 00:35:33,370 +الأمور المشتركة عشان نقدر نقارنها فزي ما احنا + +462 +00:35:33,370 --> 00:35:41,990 +عارفين نظرية هذه true نشوف فرقة B بقول لي في عندنا + +463 +00:35:41,990 --> 00:35:46,970 +A و B و الـ A ليست subset من الـ B فهي ال universe + +464 +00:35:46,970 --> 00:35:51,230 +او ال universal set الـ A ليست subset هتكون بعيد + +465 +00:35:51,230 --> 00:35:58,060 +عنها يعني لأ مش شريعني subset تحتويها وليست subset + +466 +00:35:58,060 --> 00:36:02,720 +فيها على الأقل عنصر في الـA ليس في الـB فهذه A وB + +467 +00:36:02,720 --> 00:36:07,700 +ممكن يكون دقاطة مش شرط مش شرطفهنا إيش معنى subset؟ + +468 +00:36:07,700 --> 00:36:10,900 +قلنا تحتويها جوا، طب إيش بدنا فيها؟ إذا في جزء على + +469 +00:36:10,900 --> 00:36:13,700 +الأقل خارج، على الأقل جزء فيه خارج، هيك و هيك أحنا + +470 +00:36:13,700 --> 00:36:17,360 +عرفناها، قلنا إن there exist at least X موجودة في + +471 +00:36:17,360 --> 00:36:20,240 +الـA و غير موجودة في الـB، إيه معناه؟ طيب إيش + +472 +00:36:20,240 --> 00:36:23,720 +بيقوللي؟ بيقوللي إذا في عنصر في الـA، عنصر في الـA + +473 +00:36:23,720 --> 00:36:28,820 +وين يكون؟ ياها، ياهاهل بالضروري يكون خارج الـ B؟ + +474 +00:36:28,820 --> 00:36:33,900 +واضح أنه لا، ها هي مرة تانية، هي الـ A ليست subset + +475 +00:36:33,900 --> 00:36:38,180 +من الـ B فعنصر في الـ A ممكن يكون خارج وممكن يكون + +476 +00:36:38,180 --> 00:36:41,180 +في المشترك، هذا لا ينقض، إذا نشملها ال statement، + +477 +00:36:41,180 --> 00:36:43,900 +false، او طبعا ممكن أجيب له لو أنه جلب prove or + +478 +00:36:43,900 --> 00:36:49,280 +disapprove، بدي counter example، فهذه false، فهذه + +479 +00:36:49,280 --> 00:36:54,000 +false، متابعين؟ + +480 +00:36:54,000 --> 00:37:09,300 +في أي استفسار؟ننتقل للفرق التالت والاخير بقوللي + +481 +00:37:09,300 --> 00:37:16,520 +ال A و ال B subset من مجموعة كبيرة X فبقوللي هل ال + +482 +00:37:16,520 --> 00:37:19,220 +minus بتوزع الاتحاد ده وشوفناه في المثال بتوزع + +483 +00:37:19,220 --> 00:37:22,590 +الطقات و هل بتوزع الاتحاد هيك معناهاهنشوف مع بعض + +484 +00:37:22,590 --> 00:37:27,690 +فنبدأ بالرسمة و برضه هرسم جهتين و أقارن هي ال + +485 +00:37:27,690 --> 00:37:32,990 +universal في مجموعة كبيرة X ممتاز هي X كبيرة هنحط + +486 +00:37:32,990 --> 00:37:36,650 +فيها A و B طبعا متوقع انهم يتقاطعوا هيك الصورة + +487 +00:37:36,650 --> 00:37:40,430 +النمطية ال A subset من ال X و ال B subset من ال X + +488 +00:37:40,430 --> 00:37:45,600 +و بدنا X ناقص A و X ناقص B فهي مجموعتين A و Bهي A + +489 +00:37:45,600 --> 00:37:50,360 +وهي B صورة نمطية كمثال و هذا بتوضح الصورة طب بده + +490 +00:37:50,360 --> 00:37:54,680 +إيش X ناقص A العناصر اللي في ال X خارج ال A X ناقص + +491 +00:37:54,680 --> 00:38:00,440 +A هي الأحمر خارج ال A خارج ال A واحدة واحدة اللي + +492 +00:38:00,440 --> 00:38:05,660 +بدنا نرسم احنا إيش X ناقص ال A الخطوط الحمرة هذه و + +493 +00:38:05,660 --> 00:38:08,880 +المناطق اللي فيها الخطوط الحمرة بعدين بده إيش X + +494 +00:38:08,880 --> 00:38:13,300 +ناقص B اللي في ال X خارج ال B الخطوط الزرجة هي B + +495 +00:38:19,320 --> 00:38:22,800 +خارج ال B بس U و ال X مش مابديش أخد المكمل على ال + +496 +00:38:22,800 --> 00:38:27,560 +U هاي الصورة ال إيش الطرف اليسار خلينا نعيد الصورة + +497 +00:38:27,560 --> 00:38:32,940 +بس إيش نعمل نمثل الطرف اليمين هاي ال U وهي ال X + +498 +00:38:32,940 --> 00:38:36,640 +صورة مشابهة لهذه وهي ال A و ال B بنفس الأسلوب + +499 +00:38:36,640 --> 00:38:39,540 +مابنفعش أرسمهم الآن بعيد عن بعض عشان بدي أقارن + +500 +00:38:39,540 --> 00:38:44,410 +فبدي أثبت هي ال A و هي ال Bطيب، إيش بده؟ بده + +501 +00:38:44,410 --> 00:38:48,090 +الاتحاد أولا، بعدين ناخد X ناقص الاتحاد، الاتحاد + +502 +00:38:48,090 --> 00:38:53,170 +هذه المجموعة، إيش اللي هو X ناقص؟ خارج هدول، خارج + +503 +00:38:53,170 --> 00:39:00,890 +الاتحاد، مظبوط؟ طبعا هذه X، خارج الاتحادفنقارن + +504 +00:39:00,890 --> 00:39:06,810 +الأسود مع من؟ مع الاتحاد، صحيح، false، لأ ليش؟ لأن + +505 +00:39:06,810 --> 00:39:10,430 +الاتحاد اسمها اتحاد، توي لما قلنا تقاطع بدنا + +506 +00:39:10,430 --> 00:39:13,110 +المنطقة اللي فيها الخطين مع بعض، أزرق و أحمر، طب + +507 +00:39:13,110 --> 00:39:17,670 +لو اتحاد أي واحد يكون يكفي، فهذه جوا الاتحاد، وهذه + +508 +00:39:17,670 --> 00:39:21,410 +جوا الاتحاد، ما عدا بس التقاطع، فهنا مختلفة تماما + +509 +00:39:21,570 --> 00:39:26,050 +أه فلما بيقول تقاطع بدي إيش المناطق المشتركة اللي + +510 +00:39:26,050 --> 00:39:30,130 +فيها الخطين النوعين أه لكن لما يقول اتحاد بس اللي + +511 +00:39:30,130 --> 00:39:32,790 +فيها على الأقل واحد من الخطين مش هيك معناها إذا + +512 +00:39:32,790 --> 00:39:38,630 +هذه برضه false فهذه false ف + +513 +00:39:38,630 --> 00:39:41,650 +C برضه false بمساعدة الرسم + +514 +00:39:51,170 --> 00:39:54,490 +تمام فاحنا هنكتفي بهذا القدر من هذا الموضوع طبعا + +515 +00:39:54,490 --> 00:39:57,850 +قبل هيك حد حدثنا عنه و لما نحتاج ممكن نحل بعض + +516 +00:39:57,850 --> 00:40:04,110 +الأمثلة باستخدام ال Venn diagrams اعيد ايش اخر + +517 +00:40:04,110 --> 00:40:10,450 +واحدة تمام فاحنا بدنا نحل الطرف اليسار X ماقص A + +518 +00:40:10,450 --> 00:40:17,460 +المناطق اللي فيها الخطوط الحمرةو X ناقص P المناطق + +519 +00:40:17,460 --> 00:40:21,720 +اللي فيها الخطوط الزرقاء طب إيه؟ اتحادهم أي منطقة + +520 +00:40:21,720 --> 00:40:25,240 +فيها خط على الأقل فبما يهم هدف الاتحاد ولا لأ؟ أه + +521 +00:40:25,240 --> 00:40:28,380 +فاشلة المناطق الفاضية هي الخارج الاتحاد تمام إذا + +522 +00:40:28,380 --> 00:40:32,260 +كل ال X معدى التقاطع معدى التقاطع وهذا معناها لو + +523 +00:40:32,260 --> 00:40:36,080 +طلعنا عليها طيب لما يقول لي X ناقص الاتحاد هي + +524 +00:40:36,080 --> 00:40:39,800 +الاتحاد الخارج بس اللي برا جوا فهل متساويين؟ واضح + +525 +00:40:39,800 --> 00:40:49,640 +أنه لأالآن ننتقل to the section 2 + +526 +00:40:49,640 --> 00:41:05,620 +-6 Indexed Families of Sets ممكن + +527 +00:41:05,620 --> 00:41:13,210 +نترجمها عائلات مؤرشفة من المجموعاتindexed family + +528 +00:41:13,210 --> 00:41:18,670 +ممكن يسميها عائلات مؤرشفة من المجموعة طبعا من كلمة + +529 +00:41:18,670 --> 00:41:23,030 +index اللي هو الدليل هو الدليل عملية تكشيف بيسموها + +530 +00:41:23,030 --> 00:41:27,990 +أو أرشفة عملية indexing عملية الأرشفة أو اللي هو + +531 +00:41:27,990 --> 00:41:35,950 +التكشيف كيف بدي أرتب مجموعة من العناصر المعينةطبعا + +532 +00:41:35,950 --> 00:41:39,810 +أول شي خلينا نتحدث عن الفرق بين كلمة المصطلح + +533 +00:41:39,810 --> 00:41:45,510 +family و set ايش الفرق بينهم فالحقيقة لو جالي ما + +534 +00:41:45,510 --> 00:41:48,830 +هي ال set بقوله collection of objects طب ال family + +535 +00:41:48,830 --> 00:41:52,010 +برضه collection of objects طب ايش الفرق بينهم؟ + +536 +00:41:54,990 --> 00:41:59,170 +بالنسبة للمجموعة، اتفقنا إن التكرار ما لهوش قيمة، + +537 +00:41:59,170 --> 00:42:03,210 +لو فيها مجموعة، فيها عنصر مكرر مرتين، بعدهش، في ال + +538 +00:42:03,210 --> 00:42:06,870 +family التكرار له قيمة، له أهمية، في ال family + +539 +00:42:06,870 --> 00:42:11,090 +التكرار له أهمية، فده هو الفرق بين التنتيجةفهنا + +540 +00:42:11,090 --> 00:42:14,390 +طبعا بيقوللي هنا recall that a set is a collection + +541 +00:42:14,390 --> 00:42:17,630 +of objects or elements that are all distinct ففيش + +542 +00:42:17,630 --> 00:42:22,450 +تقرار كلهم مختلفين على بعض بيقوللي roughly + +543 +00:42:22,450 --> 00:42:26,970 +speaking بشكل تقريبي a family is to be considered + +544 +00:42:27,550 --> 00:42:32,270 +العُرف، الاتفاق، هنتفق to be as a collection of + +545 +00:42:32,270 --> 00:42:35,550 +not necessarily distinct objects، مش بدروي يكونوا + +546 +00:42:35,550 --> 00:42:38,890 +وياش مختلفين، ممكن يكون فيه تكرار، ممكن يكون فيه + +547 +00:42:38,890 --> 00:42:42,570 +تكرار، طبعا هنسميهم members، مش هنسميهم elements، + +548 +00:42:42,570 --> 00:42:45,530 +عناصر المجموعة هنسميهم elements، طبعا عناصر اللي + +549 +00:42:45,530 --> 00:42:48,450 +في الفم اللي هنسميهم أعضاء، members، هنسميهم + +550 +00:42:48,450 --> 00:42:53,580 +members، طبعا بس أنثرة بسيطةاللي قدامنا هذه بين + +551 +00:42:53,580 --> 00:42:57,360 +الأقواس عبارة عن مجموعة إذا مجموعة ففيها عنصرين + +552 +00:42:57,360 --> 00:43:02,560 +إذا family فيها تلت عناصر كمجموعة فيها عنصرين ك + +553 +00:43:02,560 --> 00:43:05,840 +family فيها three members three members تلت أعضاء + +554 +00:43:05,840 --> 00:43:09,220 +فهنا is a family with three members بنأكد على أنه + +555 +00:43:09,220 --> 00:43:14,240 +إيش التكرار مهم في ال family آه لكن في اللي ليش + +556 +00:43:14,240 --> 00:43:17,340 +مالوش قيمة في المجموعة طبعا ممكن تكون ضروري يكون + +557 +00:43:17,340 --> 00:43:21,900 +فيه تكرار لأأحنا بيقولش نطن السلم مش بالضروري + +558 +00:43:21,900 --> 00:43:25,060 +يكونوا مش لكن ممكن يكونوا كله مختلف لكن لو اتكرروا + +559 +00:43:25,060 --> 00:43:33,360 +مهم التكرار بيأخذ بعين الاعتبار تمام + +560 +00:43:33,360 --> 00:43:37,480 +إيش الهدف من الموضوع؟ حين احنا فسرنا العنوان إيش + +561 +00:43:37,480 --> 00:43:41,020 +معناه family و إيش معناه set و إيش الفرق بينهم؟ + +562 +00:43:41,020 --> 00:43:44,430 +إيش الهدف الرئيسي من هذا ال section؟الهدف الرئيسي + +563 +00:43:44,430 --> 00:43:48,350 +في هذا ال section بدنا نتعلم كيف نتعامل مع مجموعة + +564 +00:43:48,350 --> 00:43:52,650 +كبيرة من المجموعات بدل ما نقول مجموعة من المجموعات + +565 +00:43:52,650 --> 00:43:55,830 +هنقول family of six عائلة من المجموعات بس هي أول + +566 +00:43:55,830 --> 00:43:58,070 +نقطة إذا احنا بدل ما نقول مجموعة من المجموعات + +567 +00:43:58,070 --> 00:44:03,050 +المصطلح شوية جيل مزعج شوية فبنقول عائلة من + +568 +00:44:03,050 --> 00:44:07,590 +المجموعات family of six هذه النقطة الأولة طيب لما + +569 +00:44:07,590 --> 00:44:08,830 +يكون انا عندي فضل + +570 +00:44:13,860 --> 00:44:17,200 +هي عضو في ال family بدا تكون المجموعة member + +571 +00:44:17,200 --> 00:44:24,280 +هتحاول مع family of six family of six ممكن ممكن + +572 +00:44:24,280 --> 00:44:26,720 +هدقق بشكل عام بس احنا هدفنا الرئيسي طبعا ال family + +573 +00:44:26,720 --> 00:44:30,020 +بشكل عام collection of objects هدول ال objects + +574 +00:44:30,020 --> 00:44:33,500 +ضروري يكونوا مجموعات مش شرط مش شرط لكن احنا في هذا + +575 +00:44:33,500 --> 00:44:36,960 +المصاد ايش هدفنا هتعامل مع family of six موضوعنا + +576 +00:44:36,960 --> 00:44:39,320 +الرئيسي لكن هل كل family هي family of six مش + +577 +00:44:39,320 --> 00:44:41,580 +بالضروري واضح الفرق تمام + +578 +00:44:46,550 --> 00:44:52,970 +أه صحيح و هي family أه و في تكرار بس بالنسبة ك .. + +579 +00:44:52,970 --> 00:44:57,530 +ك ستة كم عنصر فيها نين ك family تلاتة بس ايه الفرق + +580 +00:44:57,530 --> 00:45:00,990 +مش مشكلة تمام اذا نقول ان احنا هدفنا الرئيسي ان + +581 +00:45:00,990 --> 00:45:04,710 +نتعامل مع عدد كبير من المجموعات طبعا بشكل عام لو + +582 +00:45:04,710 --> 00:45:07,710 +انا جالي في عندي three sets ايش ممكن ارمزلهم ABC + +583 +00:45:07,710 --> 00:45:11,910 +بكل سهولة طب لو في عندي خمساشإيش بده أبدا أقول A,B + +584 +00:45:11,910 --> 00:45:15,190 +,C,D و أعدله كل الحروف؟ لأ، من الأفضل أقوله A1,A2 + +585 +00:45:15,190 --> 00:45:18,770 +,A3 و هكذا فهذه عملية الترقيم، عملية التسمية هي + +586 +00:45:18,770 --> 00:45:22,790 +عملية indexing، عملية أرشفة، لو بده أرشف كتب، إيش + +587 +00:45:22,790 --> 00:45:26,350 +بده أعمل؟ ممكن إيش، بده أحط لهم إيش، طابعة معينة + +588 +00:45:26,540 --> 00:45:30,660 +أرقمهم ترقيم معين أسميهم تسمية معينة أقسمهم تقسيم + +589 +00:45:30,660 --> 00:45:33,780 +معين وارتبهم ولا لأ فهذا هو الهدف فهذا هدفنا + +590 +00:45:33,780 --> 00:45:37,820 +الرئيسي كيف نتعامل مع مجموعة كبيرة من المجموعات + +591 +00:45:37,820 --> 00:45:41,240 +اللي هنسميها عائلة من المجموعات وطبعا هذا بت .. ب + +592 +00:45:41,240 --> 00:45:46,460 +.. ب .. ب .. ب ..بيتضمن او بيتطلب اني ايش ارقمهم + +593 +00:45:46,460 --> 00:45:50,620 +بشكل معين اسميهم بشكل معين هذه العملية التسمية او + +594 +00:45:50,620 --> 00:45:53,920 +الترقيم بيسموها عملية ايش ارشفة او indexing او + +595 +00:45:53,920 --> 00:45:57,360 +عملية index فهو هذا ليش باختصار بيقول لي بهذا + +596 +00:45:57,360 --> 00:46:00,920 +الشكل لو انا في عندي عشرة او خمساش بدي اسميهم a1, + +597 +00:46:01,020 --> 00:46:06,260 +a2, a10طبعا هل بالضروري انا ارقم ترقيم؟ لأ مش + +598 +00:46:06,260 --> 00:46:11,020 +بالضروري ممكن اسميهم ايش a a a sub a او a alpha a + +599 +00:46:11,020 --> 00:46:14,680 +beta a gamma ممكن بطريقة معينة فهذه المجموعة اللي + +600 +00:46:14,680 --> 00:46:18,380 +أخدنا منها الأسماء اللي أخدنا منها الأرقام بسموها + +601 +00:46:18,380 --> 00:46:23,360 +عمل ايش مجموعة القرشفة indexing set indexing set + +602 +00:46:23,360 --> 00:46:27,690 +فهي الصيغة العامةبها دا الشكل فهدول الأرقام + +603 +00:46:27,690 --> 00:46:31,490 +بيسموها اللي هي the set indexes the family set + +604 +00:46:31,490 --> 00:46:37,690 +بيستخدمنها للترقيم أو للتسميح بشكل عام بقول let + +605 +00:46:37,690 --> 00:46:41,290 +capital gamma be a set capital gamma عبارة عن + +606 +00:46:41,290 --> 00:46:44,470 +مجموعة اللي ان شاء الله بشرح مثال يوضح الأمور and + +607 +00:46:44,470 --> 00:46:48,130 +assume that with each element gamma of capital + +608 +00:46:48,130 --> 00:46:51,670 +gamma هدول الرمزة دي small gamma والأولة capital + +609 +00:46:51,670 --> 00:46:57,520 +gamma والتانية small gamma فهديsmall gamma و هذه + +610 +00:46:57,520 --> 00:47:02,240 +capital gamma فبقول لكل عنصر .. طبعا زي ما تعرفين + +611 +00:47:02,240 --> 00:47:06,000 +بنقول small لل element و capital للمجموعة بقول لكل + +612 +00:47:06,000 --> 00:47:11,160 +عنصر small gamma بتنتمي لcapital gamma احنا هنصحب + +613 +00:47:11,160 --> 00:47:15,180 +او هيش هيكون فيه مقابلها مجموعة capital A sub + +614 +00:47:15,180 --> 00:47:19,320 +gamma فبنتحدث الآن عن family خلينا نشوف المثال .. + +615 +00:47:19,320 --> 00:47:25,210 +نحاول نقرب الصورةافترض أنه في مكتبة كبيرة من الكتب + +616 +00:47:25,210 --> 00:47:31,070 +بدنا ن archefها بطريقة معينة بحيث يسهل الوصول إلى + +617 +00:47:31,070 --> 00:47:35,450 +الكتب إيش ما عملنا؟ جيبنا بطاقات أو طوابع وحطينا + +618 +00:47:35,450 --> 00:47:37,950 +على هدول الطوابع أسمها أنا عارف الكتب، بدي أ + +619 +00:47:37,950 --> 00:47:41,730 +archefهم، فعملت تقسيمة فانا المجموعة اللي فيها + +620 +00:47:41,730 --> 00:47:45,110 +الطوابع هي ال capital gamma طريقة التسمية، طريقة + +621 +00:47:45,110 --> 00:47:48,310 +الأرشفة، طريقة الترقيم، فهي capital gamma، بعدين + +622 +00:47:48,310 --> 00:47:51,470 +إيش عملت؟روحت أخدت من هذه المجموعة الطوابع اللي هي + +623 +00:47:51,470 --> 00:47:54,830 +capital gamma كل طابع و لزجت عليه كتاب المناسب على + +624 +00:47:54,830 --> 00:47:58,310 +كتاب المناسب فهذا اللي عملته لكل small gamma روحت + +625 +00:47:58,310 --> 00:48:02,550 +جيبت الكتاب اللي هو a و روحت لزجتها عليه فصارت a + +626 +00:48:02,550 --> 00:48:06,030 +sub gamma فماشي عملت أرشفت ال family of sets اللي + +627 +00:48:06,030 --> 00:48:09,330 +هي مجموعة الكتب بالاستخدام من مجموعة الطوابع أو + +628 +00:48:09,330 --> 00:48:12,380 +البطاقات اللي هي capital gammaواضحة هي كل العملية + +629 +00:48:12,380 --> 00:48:19,080 +فهي كل عملية عملية ترتيب مناسب تسمية مناسبة طرقين + +630 +00:48:19,080 --> 00:48:23,560 +مناسب لمائش لعائلة كبيرة من المجموعات عشان أسهل + +631 +00:48:23,560 --> 00:48:27,340 +التعامل عشان نسهل التعامل فدي بيسموها إيش index + +632 +00:48:27,340 --> 00:48:30,760 +index family of six كيف الرمز إلها كيف صارت بعد + +633 +00:48:30,760 --> 00:48:33,810 +مرتبته خلاص كل كتاب و الطبيعة تبعتهوالطوابع من وين + +634 +00:48:33,810 --> 00:48:37,110 +جبتم؟ من طريقة معينة يعني إيش الطوابع؟ يعني طريقة + +635 +00:48:37,110 --> 00:48:41,790 +الأرشفة بأي أساس أرشفة الكتب؟ هل أرشفتم حسب التخصص + +636 +00:48:41,790 --> 00:48:42,910 +علمي أدبي؟ + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/O98m-m2qojg_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/O98m-m2qojg_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..027279e09457d8f9bb8e2c191b0457a651940d77 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/O98m-m2qojg_postprocess.srt @@ -0,0 +1,2160 @@ +1 +00:00:20,970 --> 00:00:25,030 +بسم الله الرحمن الرحيم هنواصل دراستنا في نظرية + +2 +00:00:25,030 --> 00:00:30,490 +المجموعات أو اللي هو المجموعات بشكل عام فهذا هو ال + +3 +00:00:30,490 --> 00:00:34,630 +section التاني العنوان تبعه specification of sets + +4 +00:00:34,630 --> 00:00:39,690 +تخصيص المجموعات ففي هذا ال section احنا هنتحدث كيف + +5 +00:00:39,690 --> 00:00:46,310 +بنبني مجموعة من مجموعة معطيةأو بمعنى آخر زي ما هو + +6 +00:00:46,310 --> 00:00:52,490 +العلوان بيقول كيف بنخصص مجموعة خاصة من مجموعة عامة + +7 +00:00:52,490 --> 00:00:56,190 +من مجموعة عامة هذا الموضوع اللي هنبدأ فيه لكن + +8 +00:00:56,190 --> 00:01:00,530 +الموضوع الأهم هنتعرف على مفهوم ما يُعرف بال power + +9 +00:01:00,530 --> 00:01:04,170 +set مجموعة القوة فهذا يمكن اللي هم أهم نقطتين + +10 +00:01:04,170 --> 00:01:08,080 +هنتحدث عنهم في هذا sectionفبالنسبة لـ + +11 +00:01:08,080 --> 00:01:13,540 +specification of sets فاحنا أحيانا بنكون مجموعة + +12 +00:01:13,540 --> 00:01:17,700 +جديدة من مجموعة معطية فاحنا أحد الطرق أنه إيش + +13 +00:01:17,700 --> 00:01:23,740 +نعمل؟ نختار عناصر مجموعة قديمة معطية بتحقق خاصية + +14 +00:01:23,740 --> 00:01:26,760 +إضافية يعني فاحنا فيها أننا مثلا مجموعة كبيرة فيها + +15 +00:01:26,760 --> 00:01:31,080 +عناصر كتيرة عموغ عامة بدنا إيش؟ هذه العناصر بتحقق + +16 +00:01:31,080 --> 00:01:34,600 +خاصية أخرى بدنا نخصص مثلا إحنا نتحدث عن مجموعة + +17 +00:01:34,600 --> 00:01:39,020 +الإعداد الحقيقية كلهاطب احنا في موضوع ما مش مهتمين + +18 +00:01:39,020 --> 00:01:42,180 +احنا الا بالاعداد الموجبة مثلا الحقيقية الموجبة + +19 +00:01:42,180 --> 00:01:45,960 +فبنعمل عملية تخصيص فبدنا مجموعة جزئية اه ففي طريقة + +20 +00:01:45,960 --> 00:01:49,060 +متعرف عليها في الرياضات كيف نبني المجموعة الجديدة + +21 +00:01:49,060 --> 00:01:52,820 +بدلالة المجموعة السابقة كيف نخصص العام فهي عملية + +22 +00:01:52,820 --> 00:01:55,060 +specification طبعا ايش بنعمل؟ بنقول احنا بدنا + +23 +00:01:55,060 --> 00:01:59,080 +عناصر الموجودة في المجموعة الأصلية اللي عليهم شرط + +24 +00:01:59,080 --> 00:02:05,400 +إضافي بحقق خصية إضافية معطية لناSome Probability + +25 +00:02:05,400 --> 00:02:09,420 +أو Particular Probability الطريقة العامة لذلك لو + +26 +00:02:09,420 --> 00:02:13,960 +احنا عندنا مجموعة عامة A capital A ايش بنعمل فبدنا + +27 +00:02:13,960 --> 00:02:17,280 +العناصر الخاصية ممكن نرمزلها ب open sentence P of + +28 +00:02:17,280 --> 00:02:21,300 +X Probability معينة خاصية إضافية فبدنا عناصر ال A + +29 +00:02:21,300 --> 00:02:26,220 +اللي بتحقق ال P of X بمعنى بلغة المنطق أن P of X + +30 +00:02:26,220 --> 00:02:28,990 +تكون اللي هياش trueالـ B of X تكون إليها إتره + +31 +00:02:28,990 --> 00:02:32,750 +فالكتابة بنكتب X تنتمي لـ A إذا احنا دراستنا + +32 +00:02:32,750 --> 00:02:35,770 +الأساسية المرجعانية المرجعة تبعنا من capital A + +33 +00:02:35,770 --> 00:02:38,330 +المجموعة القديمة هي المرجعانة بس بدنا يأكل capital + +34 +00:02:38,330 --> 00:02:42,410 +A لأ بدنا عناصر ال capital A اللي بيحققوا خاصية ما + +35 +00:02:42,410 --> 00:02:47,210 +B of X فبدنا عناصر المجموعة Aاللي فيهم الـ P of X + +36 +00:02:47,210 --> 00:02:50,570 +تكون الـ True Statement الـ True Statement فهذه + +37 +00:02:50,570 --> 00:02:53,770 +طريقة متعرفة عليها وأكيد مرت عليكم كتير لكن الآن + +38 +00:02:53,770 --> 00:02:59,570 +احنا بدنا إيش نركز عليها أو بدنا نوضحها ونأكد على + +39 +00:02:59,570 --> 00:03:03,810 +كيف استخدامهافطبعا كيف بنقراها؟ بنقول إيه؟ the set + +40 +00:03:03,810 --> 00:03:08,510 +is A كيف بنقراها؟ X تنتمي ل A أو the set of all X + +41 +00:03:08,510 --> 00:03:12,470 +in A in capital A such that B of X is true فهذه + +42 +00:03:12,470 --> 00:03:14,990 +نقطين فوق بعض بنقراهم such that فبحنا بنقول هذه + +43 +00:03:14,990 --> 00:03:19,850 +مجموعة عناصر ال A بحيث B of X is true B of X is + +44 +00:03:19,850 --> 00:03:22,970 +true هذه الطريقة في الكتابة بيسموها set builder + +45 +00:03:22,970 --> 00:03:25,950 +notation طريقة اللي هو بناء المجموعات من مجموعات + +46 +00:03:25,950 --> 00:03:29,630 +معطية set builder notation طريقة بناء المجموعات + +47 +00:03:31,190 --> 00:03:34,810 +خلّينا بس نشوف أنثية بسيطة على هذا الموضوع لأنه + +48 +00:03:34,810 --> 00:03:38,370 +موضوع نستخدمه كتير و أتوقع مش جديد لكن حابنا نمر + +49 +00:03:38,370 --> 00:03:42,330 +عليه كمفهوم و احنا ندرس المجموعات ندرسها بشكل عام + +50 +00:03:42,330 --> 00:03:49,150 +فطبعا المثال الأول مديني مجموعة مكتوبة بطريقة set + +51 +00:03:49,150 --> 00:03:52,370 +builder notation هيه بده الأعداد الحقيقية اللي + +52 +00:03:52,370 --> 00:03:56,940 +متحقق المعادلة هذهبمعنى آخر بيده مجموعة الحل يعني + +53 +00:03:56,940 --> 00:04:01,460 +مجموعة الحل لمعادلة x تكعيب زائد اتنين اكثر بزايد + +54 +00:04:01,460 --> 00:04:04,860 +اكتر بالثاوزيه فبقول اكتبهم بشكل صريح between + +55 +00:04:04,860 --> 00:04:08,400 +braces يعني الأقواص الخاصة بالمجموعات بدنا نكتبهم + +56 +00:04:08,400 --> 00:04:13,200 +بشكل صريح فهذا المثال الأول فما علينا إلا إيش نحل + +57 +00:04:13,200 --> 00:04:19,200 +المعادلة و نجيب مجموعة الحل نجيب مجموعة الحل فعنا + +58 +00:04:19,200 --> 00:04:25,060 +المعادلة x تكعيبزائد اتنين X تربية زائد X تساوي + +59 +00:04:25,060 --> 00:04:30,180 +Zero لو حللناها ناخد ال X عامل مشترك بتصيرت X + +60 +00:04:30,180 --> 00:04:34,200 +تربية زائد اتنين X زائد واحد تساوي Zero ممكن تتحلل + +61 +00:04:34,200 --> 00:04:39,100 +هذهبصير x زائد واحد لكل تربية تساوي zero تديني + +62 +00:04:39,100 --> 00:04:44,940 +حالين x تساوي zero او x تساوي سالب واحد فإذا هذه + +63 +00:04:44,940 --> 00:04:50,280 +المجموعة thus المجموعة اللي كانت مكتوبة بطريقة set + +64 +00:04:50,280 --> 00:04:55,100 +builder notation x تكأي بهذه الخاصية بدنا ال P of + +65 +00:04:55,100 --> 00:05:00,000 +x هذه تكون trueاللي بتحقق المعادلة هي الحل فبدنا x + +66 +00:05:00,000 --> 00:05:05,320 +تكعيب زاد 2x تربية زاد x تساوي 0 هذه ليس إلا + +67 +00:05:05,320 --> 00:05:11,320 +مجموعة تتكون من عنصرين الصفر والسالب واحد فطبعا + +68 +00:05:11,320 --> 00:05:15,660 +الشاهد أنه المجموعة كانت مكتوبة بطريقته set + +69 +00:05:15,660 --> 00:05:19,710 +builder notation طبعا كتبناها بشكل صحيحفهذا اللي + +70 +00:05:19,710 --> 00:05:22,570 +هو الرمز متعرف عليه يستخدم كثيرًا في الرياضية + +71 +00:05:22,570 --> 00:05:26,310 +فيعني احنا هنا ممكن نعبر عن مجموعة حل أي معادلة + +72 +00:05:26,310 --> 00:05:29,510 +بهذه الطريقة طب انا مهتم بالحلول الحقيقية بكتوب + +73 +00:05:29,510 --> 00:05:31,970 +هذه الشكلة طب مهتم بالحلول الصحيحة .. العداد + +74 +00:05:31,970 --> 00:05:35,310 +الصحيحة مثلا بقول X أنتميل الـN الـZ بدي أعداد + +75 +00:05:35,310 --> 00:05:39,030 +نسبية بحط X أنتميل الـQ بدي أعداد مركبة بحط X + +76 +00:05:39,030 --> 00:05:42,030 +أنتميل الـC و هكذا فهذه أسلوب متعرف عليه في + +77 +00:05:42,030 --> 00:05:46,990 +الرياضية خلينا نشوف كمان مثال هنا العكسبتديني + +78 +00:05:46,990 --> 00:05:51,270 +المجموعة بطريقة ال third بدي أكتبها بطريقة set + +79 +00:05:51,270 --> 00:05:55,050 +builder notation أكتبها بشكل مختصر بديها عناصر في + +80 +00:05:55,050 --> 00:05:58,910 +مجموعة ما بيحققوا خاصية معينة اللي هي open + +81 +00:05:58,910 --> 00:06:03,630 +sentence فدي عملية عكس المثال الأول بدنا نروح من + +82 +00:06:03,630 --> 00:06:07,090 +طريقة ال third إلى طريقة set builder notation أو + +83 +00:06:07,090 --> 00:06:11,610 +الصفة المميزة بس مع استخدام مجموعة مرجعية solution + +84 +00:06:11,610 --> 00:06:18,010 +فطبعا هذه هي المجموعة اللي عندناهي تلاتة .. ستة .. + +85 +00:06:18,010 --> 00:06:25,250 +تسعة .. اتناش تساوي فأول شيء بدي عناصر وين موجودة؟ + +86 +00:06:25,250 --> 00:06:27,690 +في الان ممكن أقول لإن كلهم أعداد طبيعية فدي أنا + +87 +00:06:27,690 --> 00:06:31,390 +مابتنياش أعداد طبيعية طب كل الأعداد الطبيعية؟ لأ + +88 +00:06:31,390 --> 00:06:35,590 +ماخدتش الواحد ماخدتش الأربعة إيه ميزتهم هنا؟ + +89 +00:06:35,590 --> 00:06:40,610 +مضاعفات التلاتة تلاتة .. ستة .. تسعة كم ممكن أعبر + +90 +00:06:40,610 --> 00:06:45,980 +على مضاعفات التلاتة؟تلاتة في .. في X؟ لأ هم تلاتة + +91 +00:06:45,980 --> 00:06:48,820 +في X هل هي X تساوي تلاتة في X؟ مانفعش أعرف حاجة + +92 +00:06:48,820 --> 00:06:52,700 +بنفسها لأ ممكن أقول تلاتة أنا أو أقول X تقبل قسمها + +93 +00:06:52,700 --> 00:06:56,420 +تلاتة يا إما X is divisible by three أو إن أقول إن + +94 +00:06:56,420 --> 00:07:00,180 +هيش بيساوي تلاتة في M و ال M صح من إتجار الطريقتين + +95 +00:07:00,180 --> 00:07:04,260 +الصحيحة فبقول such that خدعي نكتب هنا X is + +96 +00:07:04,260 --> 00:07:10,860 +divisible by three divisible by ال three أه دي + +97 +00:07:10,860 --> 00:07:16,510 +الطريقةأو وتساوي طريقة أخرى X تنتمي لـnatural + +98 +00:07:16,510 --> 00:07:19,830 +number إيش معناه تقبل قسمة عرفناها المرة فاتر X + +99 +00:07:19,830 --> 00:07:24,350 +متساوي مضاعفات التلاتة تلاتة في N for all ولا for + +100 +00:07:24,350 --> 00:07:29,130 +some for some N تنتمي لمين لل Z مثلا هي بتعريف + +101 +00:07:29,130 --> 00:07:33,380 +القسمةتعريف القسمة فبتطلع هل هذا الكلام صحيح نعم + +102 +00:07:33,380 --> 00:07:37,620 +ليش التلاتة الأولى لأنها تلاتة في واحد ليش الستة + +103 +00:07:37,620 --> 00:07:41,700 +لأنها تلاتة في اتنين هي بتقبل تلاتة في عدد ما مش + +104 +00:07:41,700 --> 00:07:46,900 +في كل الأعداد في عدد ما ممكن زد و ممكن أن ممكن أن + +105 +00:07:46,900 --> 00:07:52,460 +لكن زد غلط صح و أن صح ليش لأن اشتراتينا تكون جزئية + +106 +00:07:52,460 --> 00:07:55,940 +اول شي تكون عدد طبيعي يعني عدد صحيح موجه بشماله من + +107 +00:07:55,940 --> 00:07:59,200 +المضاعفات التلاتة ممكن نكتب بهذا الصورة فهذه بس + +108 +00:07:59,890 --> 00:08:04,730 +أمور سريعة أدى الطريقة في الكتابة وكيف نفهمها وكيف + +109 +00:08:04,730 --> 00:08:07,710 +لو عندنا مجموعة كيف نكتبها بها الطريقة المفيدة + +110 +00:08:07,710 --> 00:08:14,230 +والمتعارفة عليها واضح فهذا عمر بسيط ومررنا عليه + +111 +00:08:14,230 --> 00:08:20,090 +بها ده السرعة تصدري بصبتش زي القسمة كيف هل الستة + +112 +00:08:20,090 --> 00:08:21,910 +بتساوي تلاتة في كل الإعداد + +113 +00:08:25,710 --> 00:08:29,330 +لأ أنا هي .. هاي المجموعة معرفة هيا إيش عن أسرها؟ + +114 +00:08:29,330 --> 00:08:32,770 +تلاتة، ستة، تسعة، اتناشر اللي هي بمعنى أخر مضاعفات + +115 +00:08:32,770 --> 00:08:36,450 +التلاتة كيف بأعبر عن مضاعفات التلاتة؟ هو كل عدد + +116 +00:08:36,450 --> 00:08:41,240 +بقدرته بعصور التلاتة ضرب عدد مامش كل الأعداد + +117 +00:08:41,240 --> 00:08:44,400 +الأخرى هو تلاتة في كل الأعداد الأخرى ولا في عدد ما + +118 +00:08:44,400 --> 00:08:47,780 +الواحد وعشرين من مضاعفات تلاتة ليش لأنها تلاتة في + +119 +00:08:47,780 --> 00:08:51,440 +سبعة ولا تلاتة في كل الأعداد الأخرى بعدد واحد بس + +120 +00:08:51,440 --> 00:08:56,140 +at least عشان ايه there exist واضح زي القسم تماما + +121 +00:08:56,140 --> 00:09:00,200 +زي تعريف القسم هو يعني مضاعفات تعريف القسم تمام + +122 +00:09:00,200 --> 00:09:06,920 +ننتقل لنقطة أهم في هذا section طبعا فهي ال power + +123 +00:09:06,920 --> 00:09:12,760 +set مجموعة القوةمجموعة القوة فإحنا إذا عندنا + +124 +00:09:12,760 --> 00:09:19,000 +مجموعة ممكن نكون منها مجموعة جزئية هذه طريقة أيضا + +125 +00:09:19,000 --> 00:09:22,100 +ممكن نكون منها حاجة بسموها مجموعة القوة فهذه + +126 +00:09:22,100 --> 00:09:27,500 +مجموعة مهمةبتشبهش المجموعة الجزئية إلى علاقة + +127 +00:09:27,500 --> 00:09:30,920 +بالمجموعة المعطية كبط ال A مثلا لكن كيف علاقتها + +128 +00:09:30,920 --> 00:09:34,280 +علاقة جديدة بدنا نتعلمها و نشوف كيف متعامل معها + +129 +00:09:34,280 --> 00:09:38,340 +فبقول هنا نشوف التعريف let A be a set إذا ال power + +130 +00:09:38,340 --> 00:09:41,900 +set معرفة لأي set لأنه جالي S بيه a set يعني إيه؟ + +131 +00:09:41,900 --> 00:09:47,480 +أي set يعني أني، عام، فمافيش حاجة تخصصthe power + +132 +00:09:47,480 --> 00:09:51,740 +set of A إذا هو بيعرف ال power لأي مجموعة، هل في + +133 +00:09:51,740 --> 00:09:55,960 +مجموعة ما لهاش power set؟ لأ، جلّت A بيقى set، + +134 +00:09:55,960 --> 00:09:58,180 +جلّي إلها خاصية معينة عشان يعرف ال power set؟ ما + +135 +00:09:58,180 --> 00:10:02,680 +جلّش، بيشتغل بشكل عام، فإذا هذا الكلام أي مجموعة + +136 +00:10:02,680 --> 00:10:05,880 +إلها power set، ممتاز، فهذا هو المفهوم، the power + +137 +00:10:05,880 --> 00:10:10,930 +set of A is the setالـ power set عبارة عن إيه؟ هل + +138 +00:10:10,930 --> 00:10:15,750 +عبارة عن statement ولا عدد ولا function ولا إيش؟ + +139 +00:10:15,750 --> 00:10:20,250 +مجموعة فال power set لمجموعة ما هو مجموعة أخرى + +140 +00:10:20,250 --> 00:10:25,350 +فشوف نقرأ بدقة و بنفهم طيب is the set whose + +141 +00:10:25,350 --> 00:10:28,590 +elements are مين عناصره؟ كيف بتكون هذه المجموعة + +142 +00:10:28,590 --> 00:10:33,070 +الجديدة؟ أنا عندي مجموعة إيه؟ شوف الصورة كيفأخوات + +143 +00:10:33,070 --> 00:10:36,830 +هي عندنا ايه؟ بدنا نكون منها بطريقة ما مجموعة + +144 +00:10:36,830 --> 00:10:40,530 +جديدة اللي احنا نرمزها بالرمز power of a power of + +145 +00:10:40,530 --> 00:10:44,030 +a تمام؟ اللي هي ده الرمز طبعاً ده حرف ال B من كلمة + +146 +00:10:44,030 --> 00:10:47,070 +power اه بس بكتبوه بشكل مختلف زي ما الرياضيات كيف + +147 +00:10:47,070 --> 00:10:49,830 +نعملها R مختلفة فإنها متعارف عليه في العُرف + +148 +00:10:49,830 --> 00:10:53,450 +بالرياضيات بيميزوها شوية بيميزوها شوية من كلمة B + +149 +00:10:53,450 --> 00:10:56,390 +power بيعملوها بده الشكل فانا عندي مجموعة بده أكون + +150 +00:10:56,390 --> 00:10:59,810 +منها مجموعة ما power of a مين عنصرها؟ طب أنا + +151 +00:10:59,810 --> 00:11:04,450 +مجموعةإذا كيف تكون؟ تبدأ بقوس و تبتدي بقوس من + +152 +00:11:04,450 --> 00:11:08,350 +أقواص المجموعات، إذا هي مجموعة، من عناصرها؟ جالي + +153 +00:11:08,350 --> 00:11:13,550 +عناصرها إشمالها are the subsets of A فعناصرها + +154 +00:11:13,550 --> 00:11:19,730 +عبارة عن مجموعات إشمالهم مجموعات جزئية من ال A فده + +155 +00:11:19,730 --> 00:11:24,960 +هو تعريفهاأه فإذا أنا عندي مجموعة capital A كونت + +156 +00:11:24,960 --> 00:11:30,200 +منها مجموعة جديدة اسمها مجموعة القوة مما تتكون من + +157 +00:11:30,200 --> 00:11:34,240 +المجموعات الجزئية لل A من المجموعات الجزئية لل A + +158 +00:11:34,240 --> 00:11:37,400 +فهذا هو التعريف واضح؟ طبعا هنشوف الأمثل عشان + +159 +00:11:37,400 --> 00:11:39,420 +الأمور ان شاء الله تكون أوضح بس هذا مبدأيا كيف + +160 +00:11:39,420 --> 00:11:43,760 +نقرأ التعريف كيف نقرأ التعريف طبعا الملاحظة أه + +161 +00:11:43,760 --> 00:11:50,000 +طبعا ممكن أمسح هنشوف المكتوب مرة تانيةفي الملاحظة + +162 +00:11:50,000 --> 00:11:55,300 +بس احنا شرحنا مباشرة فأول ملاحظة هذا هو ال power + +163 +00:11:55,300 --> 00:11:58,920 +of A إيش تعريفها بلغة الرموز؟ هي عبارة عن كل + +164 +00:11:58,920 --> 00:12:03,100 +المجموعات ال B اللي هي جزئية من مين؟ من ال A اللي + +165 +00:12:03,100 --> 00:12:05,840 +هي جزئية من ال A لأنه مش بيقول تتكون من إيش؟ من + +166 +00:12:05,840 --> 00:12:09,680 +المجموعات الجزئية لل capital A فهذه power لل A هي + +167 +00:12:09,680 --> 00:12:15,660 +علاقتها مع ال A الملاحظة التانيةاحنا عرفنا في ال + +168 +00:12:15,660 --> 00:12:20,960 +section الماضي كتبنا ملاحظة كل مجموعة هي مجموعة + +169 +00:12:20,960 --> 00:12:25,260 +جزئية من نفسها إذا دائما و أبدا كل مجموعة تنتمي لل + +170 +00:12:25,260 --> 00:12:28,700 +power ال set للمجموعة نفسها فإذا الملاحظات بتقول + +171 +00:12:28,700 --> 00:12:34,640 +بما أن ال a subset من نفسها في حد عنده مشكلة في + +172 +00:12:34,640 --> 00:12:40,980 +هذه العلاقة متفقين إذا هذا يؤديإن الـ A تنتمي لل + +173 +00:12:40,980 --> 00:12:45,840 +power of A وانتبهوا للعلاقة ال A subset من A لكن + +174 +00:12:45,840 --> 00:12:48,900 +هي بالنسبة لل power of A تشمل عنصر هي عنصر لأن + +175 +00:12:48,900 --> 00:12:52,760 +عناصر ال power مجموعات بيقولوا ليه whose elements + +176 +00:12:52,760 --> 00:12:56,220 +are the subsets of A وال subsets of A إيش مالهم + +177 +00:12:56,220 --> 00:13:00,270 +مجموعات مجموعات فإذا هذه أول ملاحظةالملاحظة + +178 +00:13:00,270 --> 00:13:02,630 +التانية كان عندنا نظرية اتنين واحد اول نظريش + +179 +00:13:02,630 --> 00:13:07,230 +بيقوللي الفاي subset من اي set اذا برضه الفاي + +180 +00:13:07,230 --> 00:13:12,110 +اشملها تنتمي لل power of a تنتمي لل power of a + +181 +00:13:12,110 --> 00:13:15,570 +فإذا هنا بيقوللي ده ايش فيه دايما جال يجيب ال + +182 +00:13:15,570 --> 00:13:18,830 +power of a بحط عنصرين وانا مغمل الفاي و المجموعة + +183 +00:13:18,830 --> 00:13:24,290 +نفسها الفاي و المجموعة نفسها واضح؟ هذا اول ملاحظة + +184 +00:13:24,290 --> 00:13:29,640 +نبدأ نشوف بعض الأمثلة البسيطة للحساباتنبدأ بالمثال + +185 +00:13:29,640 --> 00:13:30,500 +الأول + +186 +00:13:34,760 --> 00:13:39,140 +بالمثال الأول بقول لي احسب من ال power set + +187 +00:13:39,140 --> 00:13:42,560 +للمجموعة capital A اللي بتتكون من عنصر واحد وهو + +188 +00:13:42,560 --> 00:13:46,980 +الواحد وهو الواحد فده المثال الأول عندنا ال A + +189 +00:13:46,980 --> 00:13:51,140 +تساوي واحد بدنا ال power of A خلينا نحسبها مع بعض + +190 +00:13:51,140 --> 00:13:56,220 +طبعا الملاحظة الماضية على طول مش هحط five وحط ال A + +191 +00:13:56,220 --> 00:13:58,960 +نفسها بممكن احط ال A نفسها اللي هي اكتب ببادئ + +192 +00:13:58,960 --> 00:14:04,320 +الشكل احط Aفي غيرهم؟ لأ في subset تانية مجموعة + +193 +00:14:04,320 --> 00:14:08,160 +مكوّنة من عنصر بقدر اجزئها اكتر من هيك؟ لأ انتهت + +194 +00:14:08,160 --> 00:14:17,240 +فهذه صح ممكن اكتب هذه Phi A صح فهذه ال power set + +195 +00:14:17,240 --> 00:14:22,280 +فانتبهوا عناصرها مجموعات عناصر مجموعة القوة + +196 +00:14:22,280 --> 00:14:26,180 +مجموعات اي مجموعات مجموعات جزئية من ال capital A + +197 +00:14:26,180 --> 00:14:32,420 +اه تمامواضح؟ أه هاي المثال الأول نشوف كمان مثال + +198 +00:14:32,420 --> 00:14:38,100 +find the power set of capital A بتتكون من تلت + +199 +00:14:38,100 --> 00:14:45,680 +عناصر a,b,c الحروف الأبجدية a,b,c خلّينا أيضا انحل + +200 +00:14:45,680 --> 00:14:50,480 +مع بعض فهذا أن capital A فيها تلت عناصر يمكن نقول + +201 +00:14:50,480 --> 00:14:53,580 +إن كانت فيها عنصر خلينا نكبر المجموعة شوية و نشوف + +202 +00:14:53,580 --> 00:14:57,310 +كيف بدنا نحسب ال power setPower of A طبعا زي ما + +203 +00:14:57,310 --> 00:15:00,630 +قلت و أنا مغمّد باخد Phi و ممكن أخد المجموعة نفسها + +204 +00:15:00,630 --> 00:15:03,770 +بس خلّيني أحطها بالترتيب بالآخر أو الشاهد عده + +205 +00:15:03,770 --> 00:15:05,310 +بيوضّح ليش أنا عملت بالترتيب + +206 +00:15:07,830 --> 00:15:11,270 +فطبعا احنا لو بدنا نيجي و ان شاء الله هنتعلم كيف + +207 +00:15:11,270 --> 00:15:14,570 +انا بدي مجموعات جزئية كيف ممكن اجزء هذه المجموعة؟ + +208 +00:15:14,570 --> 00:15:18,390 +ممكن اخد كل عنصر و يكون مجموعة جزئية فانا ممكن اخد + +209 +00:15:18,390 --> 00:15:21,890 +مجموعة جزئية فيها عنصر واحد زي ال A و فيها عنصر + +210 +00:15:21,890 --> 00:15:27,290 +واحد زي ال B و فيها عنصر واحد زي ال Cلأن احنا + +211 +00:15:27,290 --> 00:15:32,250 +باشين بدأنا من مجموعات جزئية فيها صفر من العناصر + +212 +00:15:32,250 --> 00:15:34,370 +بعدين شوفنا مين المجموعات الجزئية اللي فيها عنصر + +213 +00:15:34,370 --> 00:15:37,850 +واحد A B C هاي الاحتمالات ممكن ادور على مجموعات + +214 +00:15:37,850 --> 00:15:44,690 +جزئية فيها عنصرين زي مين A و B و A و Cو B و C + +215 +00:15:44,690 --> 00:15:47,130 +خلّيني بس ده أحطها تحت أنا مافيش عندي وزر و B و C + +216 +00:15:47,130 --> 00:15:51,450 +طيب في احتمال غيره؟ لأ بعدين بدنا مجموعات جزيرة + +217 +00:15:51,450 --> 00:15:55,850 +فيها تلت عناصر نلاقي نفسها فهيهم أكم واحدة تمانية + +218 +00:15:55,850 --> 00:16:01,710 +تمانية فهنا هل بقدر أستقرق قاعدة عامة ما هو + +219 +00:16:01,710 --> 00:16:05,350 +الأعداد ناصر؟ اتنين أسئلت لما كان في عنصر واحد + +220 +00:16:05,350 --> 00:16:08,270 +التتنين عنصرين ال power لما كان في ال ايه تلت + +221 +00:16:08,270 --> 00:16:10,530 +عناصر كانت ال power في ايه في ايه اش تمان عناصر + +222 +00:16:10,530 --> 00:16:18,440 +الحقيقة دي قاعدة عامة انه اتنين أسئلتفعنا نظري عدد + +223 +00:16:18,440 --> 00:16:23,680 +عناصر ال power set عدد عناصر مجموعة القوة لمجموعة + +224 +00:16:23,680 --> 00:16:30,360 +ما A بقول إذا كانت ال A consists of N elements إذا + +225 +00:16:30,360 --> 00:16:33,060 +كانت المجموعة المُعطَرة بتتكون من N من العناصر + +226 +00:16:33,060 --> 00:16:37,880 +then the مجموعة القوة the power set of A contains + +227 +00:16:37,880 --> 00:16:42,980 +exactly two أُس N elements تحتوي على اتنين أُس N + +228 +00:16:42,980 --> 00:16:47,730 +من العناصر2 أثنان من العناصر الحقيقة هذا المثال + +229 +00:16:47,730 --> 00:16:52,650 +إذا فهمناه سنستطيع أن نفهم البرهان لأنه سيمشي بنفس + +230 +00:16:52,650 --> 00:16:59,910 +الطريقة مع التعميم مع التعميم prove + +231 +00:16:59,910 --> 00:17:04,310 +فالحقيقة + +232 +00:17:04,310 --> 00:17:06,790 +فكرة البرهان هي فكرة اللي حلينا فيها المثال الأخير + +233 +00:17:08,000 --> 00:17:13,820 +حنبدأ نشوف أكم مجموعة فيها 0 من العناصر واحدة اللي + +234 +00:17:13,820 --> 00:17:16,140 +هي الـ Phi أكم مجموعة جزئية، أنا عندي مجموعة + +235 +00:17:16,140 --> 00:17:20,920 +capital A فيها N من العناصر فابد أعد أكم مجموعة + +236 +00:17:20,920 --> 00:17:23,900 +فيها صفر من العناصر الـ Phi، مافيش غيرها، واحدةطب + +237 +00:17:23,900 --> 00:17:27,140 +أكم مجموعة فيها عنصر .. بدي أعدهم أكم مجموعة فيها + +238 +00:17:27,140 --> 00:17:29,980 +عنصرين و هكذا .. بدي أن أعد زي ما عملنا هنا لحد ما + +239 +00:17:29,980 --> 00:17:32,940 +نوصل لمين .. أكم مجموعة فيها N من العناصر اللي هي + +240 +00:17:32,940 --> 00:17:37,180 +ال A .. اللي هي ال A فهنبرهن بهذه الطريقة فنقول له + +241 +00:17:37,180 --> 00:17:42,700 +أول شيء let A be a set .. ممكن بس اللي هو واضح let + +242 +00:17:42,700 --> 00:17:50,180 +A be a set with N elements .. اه فيها N من العناصر + +243 +00:17:50,180 --> 00:17:51,480 +.. N elements + +244 +00:17:56,760 --> 00:18:00,980 +هذه مقدمة ممكن ناخدها تمام خلّيني اكتب تحت شوية + +245 +00:18:00,980 --> 00:18:09,320 +فأول خطوة first of all في عندنا مجموعة فيها صفر من + +246 +00:18:09,320 --> 00:18:11,280 +عصرها المجموعة الخالية و دايما هذه موجودة في ال + +247 +00:18:11,280 --> 00:18:16,280 +power فانا عند ال five تنتمي لل power of a فهذا + +248 +00:18:16,280 --> 00:18:24,390 +معناته thus we haveone mt set هذي ال one بدي + +249 +00:18:24,390 --> 00:18:27,670 +اكتبها بالطريقة التالية بدي اعملها بال binomial + +250 +00:18:27,670 --> 00:18:31,350 +coefficients and zero مش هذي بيساوي واحد بدي + +251 +00:18:31,350 --> 00:18:34,170 +اكتبها مؤقتا و انا دي بوضح ليش اه في عندي one + +252 +00:18:34,170 --> 00:18:41,370 +تساوي c and إيش إيش ال subset subsets we have one + +253 +00:18:41,370 --> 00:18:47,830 +اللي هو mt subsets عندنا إيش مجموعة خالية واحدة mt + +254 +00:18:47,830 --> 00:18:50,310 +subset + +255 +00:18:53,320 --> 00:19:00,750 +of A فكان مجموعة جزئية خالية من الـ A واحدةمتفقين؟ + +256 +00:19:00,750 --> 00:19:06,050 +واضح؟ تمام الآن بدنا نشوف نعد أكم مجموعة جزئية من + +257 +00:19:06,050 --> 00:19:10,190 +ال A بتحتوي على عنصر واحد N كل عنصر بيكوّن زي ما + +258 +00:19:10,190 --> 00:19:13,550 +توي شوفنا هي ال A و ال B و ال C ال A بتعملي واحدة + +259 +00:19:13,550 --> 00:19:15,870 +و ال B بتعملي واحدة و ال C بتعملي واحدة مثلا لو + +260 +00:19:15,870 --> 00:19:20,410 +كانوا A واحد A اتنين A N كل عنصر بيعملي مجموعة + +261 +00:19:20,410 --> 00:19:26,950 +فانا بدي اكتب هذه و اقول له fourevery X تنتمي للـ + +262 +00:19:26,950 --> 00:19:29,870 +A لأن أنا دول مش عارفهم أنا مش زمن زيتاوي معروفين + +263 +00:19:29,870 --> 00:19:35,670 +مجموعة الـ X أشمالها موجودة في ال power of A + +264 +00:19:35,670 --> 00:19:41,690 +مظبوط؟ انتبهوا للرموز للعنصر X بيعمللي إيش؟ مجموعة + +265 +00:19:41,690 --> 00:19:46,370 +جزئية بتكون في ال power of A ال X في ال A بتكون + +266 +00:19:46,370 --> 00:19:49,630 +مجموعة جزئية subset من ال A يعني تنتمي لل power of + +267 +00:19:49,630 --> 00:19:57,930 +A فبالتالي thusالـ A has أكم واحدة زي هي N .. N is + +268 +00:19:57,930 --> 00:20:03,870 +subsets .. اللي هي تحتوي على أنصر واحد .. subsets + +269 +00:20:03,870 --> 00:20:08,970 +containing .. containing exactly one element + +270 +00:20:09,510 --> 00:20:15,990 +Exactly بس بالان برضه ده كتوبة بالتوافيق has an و + +271 +00:20:15,990 --> 00:20:20,930 +الان ممكن اكتبها صورة sn1 subsets containing + +272 +00:20:20,930 --> 00:20:27,510 +exactly ايش one element وهدي + +273 +00:20:27,510 --> 00:20:31,850 +ممكن نثبتها عن طريق التوافيق ليش بعمل التوافيق + +274 +00:20:31,850 --> 00:20:36,570 +ممكن الان اوضحفي المرة الأولى لما كنا فيها بندور + +275 +00:20:36,570 --> 00:20:39,610 +على مجموعات جزئية فيها ash صفر من العناصر أنا + +276 +00:20:39,610 --> 00:20:42,470 +بتختار صفر من ash من n لإنه أنا هى قدام المجموعة + +277 +00:20:42,470 --> 00:20:48,830 +بتكون هيك هي capital A فيها مين؟ فيها a1, a2, an + +278 +00:20:49,790 --> 00:20:53,490 +ببدأ اختار اكم مجموعة فيها فوق الصفر قولنا في اللي + +279 +00:20:53,490 --> 00:20:56,370 +هي واحد يعني اختار صفر من ان الان ماعندي ايش بدي + +280 +00:20:56,370 --> 00:20:59,370 +اعمل اختار واحد في كل مرة واحد من ان عملية + +281 +00:20:59,370 --> 00:21:02,210 +احتمالات اللي هي الاحتمالات الموجودة فبعمل ايش + +282 +00:21:02,210 --> 00:21:06,890 +بعمل توافيخ بيسموها ليش ليش مش تبديل لأن الترتيب + +283 +00:21:06,890 --> 00:21:11,910 +مش مهم اه هنا لما كنت بختار ااختار a,b تب بي سي بي + +284 +00:21:11,910 --> 00:21:15,110 +اي نفسها ماتفرجش فانا بدي توافق اه فبدي أحطها بيد + +285 +00:21:15,110 --> 00:21:18,950 +الشكل فالان بعدين عشان نعمل بدنا المجموعات الجزئية + +286 +00:21:18,950 --> 00:21:22,110 +اللي بتحتوي على عنصرين اه جديش بيكونوا اختار اتنين + +287 +00:21:22,110 --> 00:21:25,710 +من ان يعني اختار اتنين من ان اه فهنا هنمشي بنفس + +288 +00:21:25,710 --> 00:21:34,310 +الطريقة فهنا هنقول ليش continuing in + +289 +00:21:34,310 --> 00:21:35,130 +the same way + +290 +00:21:37,920 --> 00:21:44,580 +بنفس الطريقة a has جداش بيكون c and two مش عارفين + +291 +00:21:44,580 --> 00:21:47,840 +جداش بيكونوا .. حسابها يمكن بده شوية حسابات اه + +292 +00:21:47,840 --> 00:21:52,060 +subsets .. subsets ايش معنو مادولة subsets + +293 +00:21:52,060 --> 00:21:58,780 +containing exactly two elements containing exactly + +294 +00:21:58,780 --> 00:22:01,440 +two elements + +295 +00:22:04,130 --> 00:22:08,570 +و هكذا بتمني ماشي لور وقفت لحد ما اختار n من n + +296 +00:22:08,570 --> 00:22:15,650 +اختار من n و ال n بشكل نهائي finally finally a has + +297 +00:22:15,650 --> 00:22:20,210 +cnn و الحقيقة بتساوي واحد و لا كم عنصر او كم + +298 +00:22:20,210 --> 00:22:23,190 +مجموعة فيها a مجموعة من نفس العدد العناصر فشل ال a + +299 +00:22:23,190 --> 00:22:27,630 +اللي فيها نفس العدد العناصر one اللي هو subsets او + +300 +00:22:27,630 --> 00:22:31,430 +subset containing containing + +301 +00:22:34,460 --> 00:22:41,160 +exactly جداش n elements ممتازة + +302 +00:22:41,160 --> 00:22:47,060 +دكتور اه تفضل احسبها + +303 +00:22:47,060 --> 00:22:49,900 +من خلاص التوافق من خلاص التوافق مابديش اضايق عليها + +304 +00:22:49,900 --> 00:22:52,560 +وقت من خلاص التوافق طبعا احنا عارفينهم ليش لأن لو + +305 +00:22:52,560 --> 00:22:55,700 +كانت مجموعة فيها n فالشيء اللي بيبقى نفسه لكن ممكن + +306 +00:22:55,700 --> 00:23:00,460 +نحسبها من إيش من تعريف التوافق تمام + +307 +00:23:01,930 --> 00:23:05,110 +الخطوة الأخيرة إيش نعمل؟ إحنا شوفنا أكم subset + +308 +00:23:05,110 --> 00:23:08,650 +فيها zero، واحدة، أكم subset فيها واحد، جيبناهم، + +309 +00:23:08,650 --> 00:23:12,050 +أكم subset فيها اتنين، الأن، طب أكم ال bar set إيش + +310 +00:23:12,050 --> 00:23:14,970 +مالها؟ مجموحهم كلهم دول ولا لأ؟ أه فنقوله هنا + +311 +00:23:14,970 --> 00:23:15,710 +Therefore + +312 +00:23:19,830 --> 00:23:29,690 +الـ power of A has جداش CNN0 زائد CNN1 اللي هي عدد + +313 +00:23:29,690 --> 00:23:34,170 +المجموعات اللي فيها صفر من العناصر زائد عدد + +314 +00:23:34,170 --> 00:23:39,250 +المجموعات اللي فيها عنصر واحد و هكذا لعند فين عدد + +315 +00:23:39,250 --> 00:23:41,950 +المجموعات اللي فيها أكثر من العناصر فهي دول عدد + +316 +00:23:41,950 --> 00:23:45,230 +العناصر الـ power of 6 of A، مظبوط؟ طيب، هذا إيش + +317 +00:23:45,230 --> 00:23:45,930 +فيساوي؟ + +318 +00:23:50,630 --> 00:23:56,990 +By Binomial Theorem هوضحها + +319 +00:23:56,990 --> 00:24:05,480 +الأن Binomial Theorem هذا ليش بيساوي هيك؟X زائد Y + +320 +00:24:05,480 --> 00:24:09,720 +أُس N إيش بتساوي؟ قلنا بتساوي C N Zero X أُس N بس + +321 +00:24:09,720 --> 00:24:13,840 +ال X هنا إيش بتساوي؟ واحد فواحد أُس N راحت بعدين C + +322 +00:24:13,840 --> 00:24:19,340 +N واحد إيش؟ Y أُس واحد X أُس N ماقص واحد طب ال X + +323 +00:24:19,340 --> 00:24:21,480 +بتساوي واحد و ال Y بتساوي واحد اختفى المعاملة + +324 +00:24:21,480 --> 00:24:25,180 +واضحة لو تبدأ لم تش تنتهي C N N Y أُس N اللي هي + +325 +00:24:25,180 --> 00:24:31,410 +بتساوي واحد إيش بتساوي؟ اتنين أُس N وهو المطلوبوهو + +326 +00:24:31,410 --> 00:24:34,830 +المطلوب فإذا هنا البرهان بيعتمد على مين أول شي على + +327 +00:24:34,830 --> 00:24:39,070 +احتمالات وهي احتمالات توافقية لأن الترتيب مش مهم + +328 +00:24:39,070 --> 00:24:41,930 +وبنستخدم binomial theorem لما نجمع استخدمنا + +329 +00:24:41,930 --> 00:24:46,450 +binomial theorem فهذا هو البرهان فهذا هو البرهن + +330 +00:24:46,450 --> 00:24:50,950 +خلّيني أشوف ماشي + +331 +00:24:53,130 --> 00:24:56,630 +أه طبعا هو برهان يعني مش كتير يعني في فكر متكرر + +332 +00:24:56,630 --> 00:24:59,090 +عملية عدب بيسموها دي من البرهين اللي فيها بنا بعد + +333 +00:24:59,090 --> 00:25:03,770 +العناصر إيش متوقع عندي فدي شغل أقرب للإيش شغل + +334 +00:25:03,770 --> 00:25:07,070 +احتمالات شغل احتمالات وبنعندي أكم احتمال عندي من + +335 +00:25:07,070 --> 00:25:09,790 +المجموعات اللي فيها صفر من العناصر أكم احتمال عندي + +336 +00:25:09,790 --> 00:25:12,810 +من مجموعة من subsets فيها واحد أنصر فدي طريقة + +337 +00:25:12,810 --> 00:25:17,070 +تستخدم في بعض البرهين طبعا في عملية عدب إيش + +338 +00:25:17,070 --> 00:25:18,230 +الاحتمالات الممكنة + +339 +00:25:22,170 --> 00:25:24,650 +والله طبعا ايه؟ شوفي دايما عملية رياضة ما تبصي + +340 +00:25:24,650 --> 00:25:27,470 +مواقع التعليم تراكمة، اه فالاشي اللي بتمنع عليك في + +341 +00:25:27,470 --> 00:25:30,050 +المصادق بتك تتعلميه، احنا مش هنجيبلك حاجة غريبة + +342 +00:25:30,050 --> 00:25:33,230 +يعني، هو احنا ضمن اللي بنشرحه وضمن أساس الكتاب، + +343 +00:25:33,230 --> 00:25:35,170 +فاي موضوع، انت الحاجة اللي بتحتاجيها بتختاريها، + +344 +00:25:35,170 --> 00:25:38,170 +احنا شرحناها توافق، بالقدر اللي شرحناه، فاحنا مش + +345 +00:25:38,170 --> 00:25:41,310 +محتاجينه انه ايش أشياء غريبة، و احنا مش يعني مش .. + +346 +00:25:41,310 --> 00:25:44,090 +مش .. مش .. مش مفاهيمنا الرئيسية توافق، احنا كل + +347 +00:25:44,090 --> 00:25:44,650 +اللي اشتغلناه ع + +348 +00:25:51,810 --> 00:25:58,630 +خلّينا نشوف تطبيق و نعلّق عليه بدنا نوجد مجموعة + +349 +00:25:58,630 --> 00:26:03,370 +القوة للمجموعة الخالية فعندي مجموعة خالية إيش + +350 +00:26:03,370 --> 00:26:05,150 +رايكوا هذه؟ كم أنصار؟ + +351 +00:26:11,470 --> 00:26:17,510 +أول شيء مجموعة القوة للـ Phi نحسبها يا أخوان، نحسب + +352 +00:26:17,510 --> 00:26:20,950 +ما هو الواحد فيها الـ Phi ومين فيها كمان؟ نفسها، + +353 +00:26:20,950 --> 00:26:23,470 +ما هي بتساوي، مافيش تكرار، في غيرها؟ في أي مجموعة + +354 +00:26:23,470 --> 00:26:26,780 +جزئية من الـ Phi غيرها؟ لأوهذا يتوافق مع النظرية + +355 +00:26:26,780 --> 00:26:29,880 +لأنه قلنا إيهاش عدد عناصر الـ Phi 0 و ال power + +356 +00:26:29,880 --> 00:26:33,400 +setage يكون 2 أز 0 يساوا 1 فالكلام سليم فالكلام + +357 +00:26:33,400 --> 00:26:36,900 +متوافق وحتى لو التخمته النظرية بيكون مرجعة إنه مش + +358 +00:26:36,900 --> 00:26:40,240 +أتكدوا حالته صح ولا لأ فهذا بيشبه لما كنا نقول في + +359 +00:26:40,240 --> 00:26:44,760 +جدول الصدق أكا محتمال في 2 أس N عدد ال statementأه + +360 +00:26:44,760 --> 00:26:47,880 +فانا بعرف الاحتمالات متوقع حق بس المهم أذكرها صح + +361 +00:26:47,880 --> 00:26:51,380 +فلما يقول لي جيب بواسطة لمجموعة ما فيها أربع عناصر + +362 +00:26:51,380 --> 00:26:54,700 +بدي أعرف الجواب بتطلع ال 16 بس أكتبهم صح فانا هذه + +363 +00:26:54,700 --> 00:26:57,600 +بتديني مرجعية و بتساعدني في التأكد من الجواب + +364 +00:26:57,600 --> 00:27:03,780 +التأكد من الجواب خليني أشوف أنثى أهم شويةفهذه كلها + +365 +00:27:03,780 --> 00:27:08,980 +أمثلة بسيطة الشاهد منها أو الهدف منها أنه المفهوم + +366 +00:27:08,980 --> 00:27:13,280 +يكون واضح من غير أمثلة صعب نتعامل مع الصورة العامة + +367 +00:27:13,280 --> 00:27:17,120 +المجردة فدائما أول تعريف حتى لو أنت بتدرس الموضوع + +368 +00:27:17,120 --> 00:27:20,900 +بشكل مستقل شوف التعريف حوله بأمثلة بسيطة عشان إيش + +369 +00:27:20,900 --> 00:27:26,690 +الأمر يبدأ يكون واضح وملموس بالنسبالكالسؤال بيقول + +370 +00:27:26,690 --> 00:27:33,750 +لي هل ال power set of A اتحاد ال power set of B .. + +371 +00:27:33,750 --> 00:27:38,610 +بنوقف اه .. بيسجل هيك و لا واقف؟ بيسجل .. بيسجل + +372 +00:27:38,610 --> 00:27:43,280 +الصوت و الغرفةوالـ Power Point، تمام فهل الـ Power + +373 +00:27:43,280 --> 00:27:47,620 +Set للإقلا مجموعة ما إيه؟ اتحاد، حاضر، حاضر، + +374 +00:27:47,620 --> 00:27:51,040 +بنقيت، بس أحنا نستغل الوقت ال Power Set of B + +375 +00:27:51,040 --> 00:27:57,060 +بيساوي ال Power Set للاتحاد بلغة أخرى، هل علاقة ال + +376 +00:27:57,060 --> 00:28:00,600 +Power Set بتتوزع على الاتحاد؟ هذا السؤال تبعنا، + +377 +00:28:00,600 --> 00:28:03,900 +فاكروا فيه مع بعضفهو بيقول ليه السؤال هل هذا + +378 +00:28:03,900 --> 00:28:08,840 +الكلام صحيح وإذا كان yes ليش yes يعني اثبته وإذا + +379 +00:28:08,840 --> 00:28:13,340 +كان no ليش no اعمل a disapproval اثبت انها خطأ فهل + +380 +00:28:13,340 --> 00:28:19,720 +ال statement true و لا او false و بدنا نشوف مين + +381 +00:28:19,720 --> 00:28:23,300 +بيقول true و مين بيقول false + +382 +00:28:26,230 --> 00:28:31,250 +المحايدين هم الأغلبية، لا طبعا الأغلبية هم الغلط، + +383 +00:28:31,250 --> 00:28:35,770 +واللي جاله force هم نصح، هي force، هي force و + +384 +00:28:35,770 --> 00:28:40,190 +هتشوف ليش force مع بعض، فلو حاولنا نحلل، انتبهوا + +385 +00:28:40,190 --> 00:28:43,250 +هنا، احنا قولنا ان كل مجموعة تنتمي ل power set + +386 +00:28:43,250 --> 00:28:50,680 +لنفسهابشكل عام لما نقول A union B تتوقع تكون أكبر + +387 +00:28:50,680 --> 00:28:54,760 +ولا أصغر من ال A و ال B أكبر أكبر صحيح فعدد + +388 +00:28:54,760 --> 00:28:57,800 +عناصرها المفروض يكون أكبر فبالتالي ال power + +389 +00:28:57,800 --> 00:29:02,640 +للاتحاد متوقع يكون أكبر بكتير بشكل عام اه طبعا + +390 +00:29:02,640 --> 00:29:05,580 +احنا بنحنا بنحطها قاعدة تكون في قاعدة دائما لو في + +391 +00:29:05,580 --> 00:29:09,280 +انا مثال عكس واحد بيقول انه خطأ اه فهذه العلاقة + +392 +00:29:09,280 --> 00:29:16,250 +الجواب خطأ فاولش الجواب noبدي نديله مثال فهينا + +393 +00:29:16,250 --> 00:29:20,370 +نقول له مثال عكسي او .. فده طبعا solution احنا + +394 +00:29:20,370 --> 00:29:24,410 +يعني نعطيه مثال؟ اه طبعا هذا اللي بيقولي why + +395 +00:29:24,410 --> 00:29:27,670 +بتديله مثال فده معناته انه disapprove يعني + +396 +00:29:27,670 --> 00:29:32,490 +solution فهينا نديله مثال عكسي + +397 +00:29:43,200 --> 00:29:46,300 +Counter Example أو مثلًا مثلًا مثلًا مثلًا مثلًا + +398 +00:29:46,300 --> 00:29:46,560 +مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا + +399 +00:29:46,560 --> 00:29:52,160 +مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن + +400 +00:29:52,160 --> 00:29:52,900 +مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن + +401 +00:29:52,900 --> 00:30:03,440 +مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن + +402 +00:30:03,440 --> 00:30:04,220 +مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن + +403 +00:30:04,220 --> 00:30:04,240 +مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن مثلن + +404 +00:30:04,240 --> 00:30:10,940 +مثلن مثلن مثلن مثلن + +405 +00:30:10,940 --> 00:30:16,740 +مثلن مثلأخدها نفسها ولا subset من ال A؟ بدي أكبرها + +406 +00:30:16,740 --> 00:30:19,260 +شوية، بدي أخد لها عنصر فيها مختلف، لأ من فعلا، لو + +407 +00:30:19,260 --> 00:30:22,300 +واحد مش هيظبط، فخليني مثلا أخد فيها مثلا الواحد + +408 +00:30:22,300 --> 00:30:25,960 +والتلاتة مثلا أو التلاتة من فعلا، تمام؟ اه طبعا + +409 +00:30:25,960 --> 00:30:29,720 +then فعلى + +410 +00:30:29,720 --> 00:30:38,060 +طول أنا عندي ال A union B الاتحاد في عنصر اتنين، + +411 +00:30:38,060 --> 00:30:40,280 +هو الموجود هنا الاتحاد، اتبعوا المرة عليكم، احنا + +412 +00:30:40,280 --> 00:30:46,510 +هندرسه بالتفصيلفهي عناصر تلت عناصر تلت عناصر فهذا + +413 +00:30:46,510 --> 00:30:53,230 +دائما و أبدا ينتمي لل power للاتحاد و لا لأ لأن هي + +414 +00:30:53,230 --> 00:31:02,170 +المجموعة نفسها لكن هذا العنصر لا ينتمي لاتحاد ال + +415 +00:31:02,170 --> 00:31:06,450 +powers اللي + +416 +00:31:06,450 --> 00:31:10,660 +هو بيساوي خليني أكتبها هناإيش بيساوي اتحاد ال + +417 +00:31:10,660 --> 00:31:12,600 +powers؟ خلّيني أكتب ال power of A و ال power of B + +418 +00:31:12,600 --> 00:31:16,680 +ال power of A مين فيها؟ فيها ال Phi فيها مجموعة + +419 +00:31:16,680 --> 00:31:22,080 +الواحد و مجموعة التنين و ال A نفسها طيب ال power + +420 +00:31:22,080 --> 00:31:26,180 +of B مين فيها؟ فيها ال Phi أكتوبها كمان مرة؟ لأ و + +421 +00:31:26,180 --> 00:31:30,100 +فيها مجموعة الواحد مكتوبة مجموعة التلاتة و مين + +422 +00:31:30,100 --> 00:31:36,500 +كمان؟ مجموعة ال B فهل هذا العنصر موجود هنا؟ مش + +423 +00:31:36,500 --> 00:31:40,110 +موجودمش موجود، يعني هدا أكم أنصر فيها شوفوا، واحد، + +424 +00:31:40,110 --> 00:31:43,230 +اتنين، تلاتة، أربعة، خمسة، ستة، لكن هذه ال power + +425 +00:31:43,230 --> 00:31:47,070 +أكم أنصر فيها تمانية، فمش .. مش .. مش سوية فده + +426 +00:31:47,070 --> 00:31:50,950 +مثال عكسي على إنه ليس العلاقة مش دايما صح هذه، فده + +427 +00:31:50,950 --> 00:31:54,490 +مش قاعد، فال power بتوزعش على الاتحاد نعم + +428 +00:32:02,900 --> 00:32:05,780 +وهذه من الأسئلة الصعبة تعتبر لما يقولك سؤال prove + +429 +00:32:05,780 --> 00:32:08,500 +or disprove هذا السؤال يعتبر صعب لأن أول شي لك + +430 +00:32:08,500 --> 00:32:11,680 +تقرر هل ال statement true و تبرهينها أو false و + +431 +00:32:11,680 --> 00:32:14,420 +تديها disprove اه طبعا هذه تعتمد فيها شوية خبرة و + +432 +00:32:14,420 --> 00:32:18,360 +بتحاول تحلي المثال و تتوقع انه صح ولا لأ ممكن + +433 +00:32:18,360 --> 00:32:21,220 +تحاول تجيبي أمثلة بسيطة او مثلا بتساعدني برسمة او + +434 +00:32:21,220 --> 00:32:23,360 +كذا بدا معلومات مافيش قاعدة عامة + +435 +00:32:29,190 --> 00:32:33,110 +ماشي يعني قضية البرهان موضوع مختلف انا عندي قاعدة + +436 +00:32:33,110 --> 00:32:37,210 +يعني اذا جالب proof ماده عملية سهلة بدي اثبت لكن + +437 +00:32:37,210 --> 00:32:39,970 +اذا انا مش عارف هى proof ولا disproof دي مشكلة في + +438 +00:32:39,970 --> 00:32:43,710 +الأول اه فانا بدي اؤكد اللي لو عرفت انها true بدي + +439 +00:32:43,710 --> 00:32:46,910 +ابتدى برهن معروف طب عرفت انها false بدي ادي مثال + +440 +00:32:46,910 --> 00:32:50,190 +عكسي بدي ادي مثال عكسي وانا بدى شوية تجريب وشوية + +441 +00:32:50,190 --> 00:32:55,050 +خبرة نشوف مثال اخر نشوف مثال جديد + +442 +00:33:00,990 --> 00:33:06,930 +مثال التالت بقول prove that فهي أدانا جزء من الحل + +443 +00:33:06,930 --> 00:33:09,850 +ماقلناش prove or disprove فهذا يعتبر أسهل من + +444 +00:33:09,850 --> 00:33:15,210 +المثال السابق prove that if A and B are any sets + +445 +00:33:15,210 --> 00:33:20,810 +such that ال A subset من ال B then ال power set + +446 +00:33:20,810 --> 00:33:24,590 +بتحافظ على علاقة ال subset إذا كانت عند ال A + +447 +00:33:24,590 --> 00:33:28,190 +subset من ال B فمجموعة قوة ال A بتامها subset من + +448 +00:33:28,190 --> 00:33:33,270 +مجموعة قوة ال Bقوة الـ B نبرهنها مع بعض خلّيني أول + +449 +00:33:33,270 --> 00:33:35,630 +شي نفهم السؤال زي ما تقولنا فيه أربع خطوات رئيسية + +450 +00:33:35,630 --> 00:33:40,230 +لحل المسائل نفهم السؤال، نعيد سياقته، بعدين نحدد + +451 +00:33:40,230 --> 00:33:44,550 +طريقة الحل أو نبتكر طريقة الحل أو نصمم طريقة الحل، + +452 +00:33:44,550 --> 00:33:47,050 +بعدين الخطوة التالتة نطبق الطريقة، الخطوة الرابعة + +453 +00:33:47,050 --> 00:33:50,910 +نتأكد أن حلنا صحيح فخلينا نحاول نفهم السؤال أولا + +454 +00:33:50,910 --> 00:33:55,310 +فالسؤال مش بيقول إيه؟ بيقول if A and B are any set + +455 +00:33:55,310 --> 00:33:59,130 +فإحنا عندنا جملة الـ A والـ B، ممكن اكتب باختصار + +456 +00:34:00,000 --> 00:34:06,860 +sets او any sets such that اه ممكن اكتب بقياش ال a + +457 +00:34:06,860 --> 00:34:11,180 +subset من ال b ليش بدنا نثبت then يعني implies + +458 +00:34:11,180 --> 00:34:17,180 +power of a subset من power of b يعني اثبتوا ان + +459 +00:34:17,180 --> 00:34:20,100 +واحد يطره ولا لأ؟ هيك معناه ده فده هو المطلوب فده + +460 +00:34:20,100 --> 00:34:26,760 +هو السؤال solution يعاد نصيبته طبعا اذا بده كمان + +461 +00:34:26,760 --> 00:34:33,930 +ان نوضح بنوضح تمامأه فاللي أنا جملة شرطية بتمر + +462 +00:34:33,930 --> 00:34:37,530 +علينا مرة و مرتين و عشرات المرة هتمر هنبدأ نفترض + +463 +00:34:37,530 --> 00:34:41,030 +أن الشرط صحيح فهبدأ أقول Assume أو Let كله صح + +464 +00:34:41,030 --> 00:34:49,450 +Assume ال A و ال B are any sets such that + +465 +00:34:52,360 --> 00:34:56,940 +الـ A subset من الـ B إيش المطلوب إثبت أن ال power + +466 +00:34:56,940 --> 00:35:03,680 +of A subset من ال power of B؟ we have to show that + +467 +00:35:03,680 --> 00:35:15,000 +power of A subset من ال power of B أي سؤال ممتازة + +468 +00:35:15,000 --> 00:35:20,900 +فهي المطلوب المطلوب نظرة خارجية بيقول بيثبت علاقة + +469 +00:35:20,900 --> 00:35:26,420 +subsetبتثبت علاقة subset ال power of A مجموعة ال + +470 +00:35:26,420 --> 00:35:29,080 +subset من المجموعة الأخرى هي ال power of B فنبدأ + +471 +00:35:29,080 --> 00:35:31,560 +من أول السؤال نبدأ واحدة واحدة زي ما بنبدأش + +472 +00:35:31,560 --> 00:35:36,460 +بالتدريج فال علاقة subset اتفقنا أن علاقة subset + +473 +00:35:36,460 --> 00:35:43,680 +تكافئ for all X X في الأولى then X في التانى فهذا + +474 +00:35:43,680 --> 00:35:48,730 +هو التعريففممكن اكتب هذا بشكل كبير بس مانيش اكتب + +475 +00:35:48,730 --> 00:35:51,670 +عشان نبدأ احنا اول مثال يمكن افصلها كتير والان + +476 +00:35:51,670 --> 00:35:56,650 +نحاول نختصر عشان اتعامل مع الجملة المكافئة التعريف + +477 +00:35:56,650 --> 00:36:00,950 +هي فيها for all كيف نتعامل؟ بنقول له let x be any + +478 +00:36:00,950 --> 00:36:03,890 +element صح؟ اذا هنبدأ البرنامج نقول له let x be + +479 +00:36:03,890 --> 00:36:10,470 +any element let بس بدي احطها capital X be any + +480 +00:36:10,470 --> 00:36:18,270 +elementليش capital؟ طب ال X غلط؟ لأ فيش رمز غلط + +481 +00:36:18,270 --> 00:36:22,590 +قولنا لكن capital مهم لأنه عناصر ال power إيش + +482 +00:36:22,590 --> 00:36:25,450 +مالهم؟ إنهم مجموعات فده بيذكر إن دول مجموعات يعني + +483 +00:36:25,450 --> 00:36:28,170 +أنصر في ال power لكن هي مجموعة نفسها subset تمام + +484 +00:36:28,650 --> 00:36:33,190 +بعدين إيش صار بدي أثبت جملة شرطية X in A then X in + +485 +00:36:33,190 --> 00:36:35,530 +B بديش أكتب الآن بقوله we want to prove بدي أحاول + +486 +00:36:35,530 --> 00:36:39,570 +أقتصر لأن أحنا بس أول مرة فصلناها طيب فبدي أفترض + +487 +00:36:39,570 --> 00:36:43,790 +أنه X في الأولى فبدي أقول أنه X في ال power of A + +488 +00:36:43,790 --> 00:36:46,730 +فبقوله هنا إيش ممكن أكمل الجملة أو أكتب من الجديد + +489 +00:36:46,730 --> 00:36:56,290 +and let X مالها تنتمي لل power of Aفهذه ليش كتبنا + +490 +00:36:56,290 --> 00:36:59,830 +الجمعتين هدول؟ عشان التعريف التعريف فيه for all + +491 +00:36:59,830 --> 00:37:03,970 +فقلنا له let X be any element طيب البعد ال for all + +492 +00:37:03,970 --> 00:37:06,290 +ليش فيه؟ جملة شرطية فقلنا لنا افترض ان الشرط صحيح + +493 +00:37:06,290 --> 00:37:11,370 +هدا هم متابعين؟ واضح ليش كتبنا الجمعتين هدول؟ واضح + +494 +00:37:11,370 --> 00:37:15,390 +ولا مش واضح؟ واضح تمام أيش المطلوب أصبح؟ بدي أثبت + +495 +00:37:15,390 --> 00:37:18,110 +ان كابتن ال X وين؟ في ال power of B خليني اكتب + +496 +00:37:18,110 --> 00:37:26,930 +بهذه we haveto prove أو to show that X تنتمي + +497 +00:37:26,930 --> 00:37:31,870 +للpower of B فهذه مهارة أساسية في هذا الشبطب + +498 +00:37:31,870 --> 00:37:36,910 +بيتعلمها كيف أثبت أن مجموعة ما subset من مجموعة ما + +499 +00:37:36,910 --> 00:37:40,790 +فهي بدأ أثبت هذه ال statement فدائما بتاخد عنصر + +500 +00:37:40,790 --> 00:37:46,270 +عشوائي موجود في الأولى ووصله بطريقة زيادية صحيحة + +501 +00:37:46,270 --> 00:37:49,800 +للتاني هذه علاقة إيش subset واضحةيعني أكتر مرة هذه + +502 +00:37:49,800 --> 00:37:52,840 +المرة فصلناها بالتفصيل على الآخر لأنه كان أول مثال + +503 +00:37:52,840 --> 00:37:55,360 +الآن نفس التفصيل بس باختصار في أمورنا عملناها + +504 +00:37:55,360 --> 00:38:00,160 +شفوية لأنه قدمنا شوية ممتاز فنبدأ نشوف هلجيت أنا + +505 +00:38:00,160 --> 00:38:05,500 +عندي ال X تنتمي لل power of B ماذا يعني capital X + +506 +00:38:05,500 --> 00:38:08,980 +تنتمي لل power of A هلجيت ممكن أقول هنا now إذا + +507 +00:38:08,980 --> 00:38:15,200 +بدا بدا بدامن التعريف هذه تعني أو ممكن أحط تكافأ + +508 +00:38:15,200 --> 00:38:20,620 +أو implies إن ال X subset من مين؟ لأ مش تكافأ، + +509 +00:38:20,620 --> 00:38:25,520 +implies من وين جبته هذا؟ من التعريف definition of + +510 +00:38:25,520 --> 00:38:29,160 +power of A تعريف ال power، ماشي؟ تذكروا لما + +511 +00:38:29,160 --> 00:38:31,500 +كتبناها؟ أولا كتبناها على اللوحة و بعدين مسحناها و + +512 +00:38:31,500 --> 00:38:34,220 +قلنا هي و مكتوب في الملاحظة و مكتوب عنكم طيب إيش + +513 +00:38:34,220 --> 00:38:37,700 +معناه التنتمي؟ شوفوا الإعلاقة X تنتمي لل power of + +514 +00:38:37,700 --> 00:38:45,290 +A يعني ال X subset من capital Aيعني ال X الصبع فال + +515 +00:38:45,290 --> 00:38:51,520 +X subset من ال A أنا وين رايح؟بدي ال X تكون في ال + +516 +00:38:51,520 --> 00:38:57,120 +power of B بمعنى ال X subset من ال B فهل بقدر أوصل + +517 +00:38:57,120 --> 00:39:01,080 +من X subset في ال A ل X subset في ال B؟ إيش بدي + +518 +00:39:01,080 --> 00:39:05,600 +علاقة إيش؟ تعدي متوفرة ولا مش متوفرة؟ متوفرة لأن + +519 +00:39:05,600 --> 00:39:08,700 +ال A subset من ال B فاللي subset من ال A ويندو + +520 +00:39:08,700 --> 00:39:13,720 +يكون subset من ال B أه فهد مباشرة فهد يؤديإن ال X + +521 +00:39:13,720 --> 00:39:18,000 +subset من ال B، مين دليلك إن ال A subset من ال B؟ + +522 +00:39:18,000 --> 00:39:21,580 +وممكن أقوله إيش؟ ونظرية جديش؟ إتنين إتنين على ما + +523 +00:39:21,580 --> 00:39:25,260 +أعتقد، إن علاقة ال subset إيش مالها؟ Transitive، + +524 +00:39:25,260 --> 00:39:30,860 +علاقة تعديمظبوط؟ انتبعين؟ لأنه قلنا هي إيش ال X + +525 +00:39:30,860 --> 00:39:36,140 +جزء من ال A و ال A جزء من ال B فبتكون الصغير جزء + +526 +00:39:36,140 --> 00:39:39,620 +من الكبير خالص واضحة؟ أه وصلنا ولا ماوصلناش؟ + +527 +00:39:39,620 --> 00:39:42,700 +أوصلنا بس كيف نكتب؟ بما أن ال X سبسط من ال B لأن + +528 +00:39:42,700 --> 00:39:46,960 +ال X وين مالها تنتمي لل power of B أرجو التدقيق في + +529 +00:39:46,960 --> 00:39:52,300 +العلاقات سبسط إيش تعني و تنتمي إيش تعني ال B من + +530 +00:39:52,300 --> 00:40:00,170 +وين جيبت هي ده؟ من تعريفباور of B فخلصنا + +531 +00:40:00,170 --> 00:40:04,110 +بدأنا من عنصر في ال capital H في ال power of A + +532 +00:40:04,110 --> 00:40:08,310 +بدأنا وصلنا بطريقة رياضية صحيحة أنه في ال power of + +533 +00:40:08,310 --> 00:40:12,010 +B إذا ننتهى إثبات ال subset thus أو therefore + +534 +00:40:12,010 --> 00:40:18,010 +power of A subset من ال power of B وهو المطلوب + +535 +00:40:23,760 --> 00:40:28,260 +واضح؟ ففي عندنا هيكلية خارجية، في أمور عامة وفي + +536 +00:40:28,260 --> 00:40:31,140 +تفاصيل، في عندنا أمور عامة كيف أتعامل مع جملة + +537 +00:40:31,140 --> 00:40:34,880 +شرطية، في عندي أمور عامة كيف أقف بالعلاقة subset، + +538 +00:40:34,880 --> 00:40:38,920 +و بعدين في تفاصيل، كيف أوصل بالعلاقة بشكل عام، + +539 +00:40:38,920 --> 00:40:40,680 +فهذه نهاية ال section ان شاء الله المرة الجاية + +540 +00:40:40,680 --> 00:40:41,060 +بنكمل + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/O98m-m2qojg_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/O98m-m2qojg_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..8535a28735801eeb12a3dd1618824af1ac41832a --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/O98m-m2qojg_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 4409, "start": 20.97, "end": 44.09, "text": "بسم الله الرحمن الرحيم هنواصل دراستنا في نظرية المجموعات أو اللي هو المجموعات بشكل عام فهذا هو ال section التاني العنوان تبعه specification of sets تخصيص المجموعات ففي هذا ال section احنا هنتحدث كيف بنبني مجموعة من مجموعة معطية", "tokens": 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هو كل عدد بقدرته بعصور التلاتة ضرب عدد ما", "tokens": [1211, 10721, 41850, 39896, 4386, 8032, 47302, 9673, 7435, 2304, 45367, 3660, 20449, 28480, 3660, 8032, 25528, 11933, 1829, 8592, 18871, 5551, 3794, 2288, 11296, 22807, 6055, 1211, 9307, 3660, 12399, 8608, 2655, 3660, 12399, 6055, 3794, 27884, 12399, 1975, 2655, 1863, 33599, 2288, 13672, 1829, 39896, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 3714, 11242, 45761, 5172, 9307, 16712, 1211, 9307, 3660, 9122, 33911, 4724, 10721, 3615, 3555, 2288, 18871, 3714, 11242, 45761, 5172, 9307, 16712, 1211, 9307, 3660, 22807, 31439, 28242, 6225, 3215, 3215, 4724, 28543, 43500, 3224, 4724, 3615, 9381, 13063, 16712, 1211, 9307, 3660, 48812, 25513, 6225, 3215, 3215, 19446], "avg_logprob": -0.2086309512456258, "compression_ratio": 1.8409090909090908, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 505.71, "end": 505.99, "word": "لأ", "probability": 0.892333984375}, {"start": 505.99, "end": 506.17, "word": " أنا", "probability": 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there exist واضح زي القسم تماما زي تعريف القسم هو يعني مضاعفات تعريف القسم تمام ننتقل لنقطة أهم في هذا section طبعا فهي ال power set مجموعة القوة", "tokens": [2304, 8592, 28242, 16247, 22488, 18513, 16247, 34740, 7578, 31439, 6055, 1211, 9307, 3660, 8978, 28242, 16247, 22488, 18513, 16247, 34740, 7578, 49429, 8978, 6225, 3215, 3215, 19446, 2423, 14407, 24401, 4032, 3615, 46309, 9957, 9154, 3714, 11242, 45761, 5172, 9307, 6055, 1211, 9307, 3660, 32239, 8592, 5296, 33456, 11296, 6055, 1211, 9307, 3660, 8978, 8608, 3555, 27884, 49429, 6055, 1211, 9307, 3660, 8978, 28242, 16247, 22488, 18513, 16247, 34740, 7578, 4724, 22488, 3215, 36764, 24401, 4724, 3794, 412, 1935, 6225, 8592, 7649, 1975, 1829, 3224, 456, 2514, 4032, 46958, 5016, 30767, 1829, 25062, 38251, 46811, 10943, 995, 30767, 1829, 37279, 16572, 5172, 25062, 38251, 31439, 37495, 22653, 3714, 11242, 45761, 5172, 9307, 37279, 16572, 5172, 25062, 38251, 46811, 10943, 8717, 29399, 4587, 1211, 5296, 1863, 47432, 3660, 5551, 16095, 8978, 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555.42, "word": " نكون", "probability": 0.81201171875}, {"start": 555.42, "end": 555.8, "word": " منها", "probability": 0.97705078125}, {"start": 555.8, "end": 556.18, "word": " مجموعة", "probability": 0.89365234375}, {"start": 556.18, "end": 556.78, "word": " جزئية", "probability": 0.9339599609375}, {"start": 556.78, "end": 557.42, "word": " هذه", "probability": 0.58935546875}, {"start": 557.42, "end": 557.98, "word": " طريقة", "probability": 0.97900390625}, {"start": 557.98, "end": 559.0, "word": " أيضا", "probability": 0.82958984375}, {"start": 559.0, "end": 559.34, "word": " ممكن", "probability": 0.97509765625}, {"start": 559.34, "end": 559.74, "word": " نكون", "probability": 0.9453125}, {"start": 559.74, "end": 560.06, "word": " منها", "probability": 0.984375}, {"start": 560.06, "end": 560.4, "word": " حاجة", "probability": 0.9449869791666666}, {"start": 560.4, "end": 560.9, "word": " بسموها", "probability": 0.79248046875}, {"start": 560.9, "end": 561.46, "word": " مجموعة", "probability": 0.97138671875}, {"start": 561.46, "end": 561.9, "word": " القوة", "probability": 0.9886067708333334}, {"start": 561.9, "end": 562.1, "word": " فهذه", "probability": 0.8349609375}, {"start": 562.1, "end": 562.42, "word": " مجموعة", "probability": 0.96748046875}, {"start": 562.42, "end": 563.34, "word": " مهمة", "probability": 0.9894205729166666}], "temperature": 1.0}, {"id": 24, "seek": 58567, "start": 565.32, "end": 585.68, "text": "بتشبهش المجموعة الجزئية إلى علاقة بالمجموعة المعطية كبط ال A مثلا لكن كيف علاقتها علاقة جديدة بدنا نتعلمها و نشوف كيف متعامل معها فبقول هنا نشوف التعريف let A be a set إذا ال power set معرفة لأي set لأنه جالي S بيه a set يعني إيه؟ أي set يعني أني، عام، فمافيش حاجة تخصص", "tokens": [3555, 2655, 8592, 3555, 3224, 8592, 9673, 7435, 2304, 2407, 27884, 25724, 11622, 19986, 10632, 30731, 11203, 995, 28671, 20666, 2304, 7435, 2304, 2407, 27884, 9673, 3615, 9566, 10632, 9122, 3555, 9566, 2423, 316, 50113, 15040, 44381, 9122, 33911, 11203, 995, 38149, 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" جالي", "probability": 0.6290690104166666}, {"start": 580.2, "end": 580.42, "word": " S", "probability": 0.89599609375}, {"start": 580.42, "end": 580.9, "word": " بيه", "probability": 0.6272786458333334}, {"start": 580.9, "end": 581.0, "word": " a", "probability": 0.4462890625}, {"start": 581.0, "end": 581.2, "word": " set", "probability": 0.9775390625}, {"start": 581.2, "end": 581.48, "word": " يعني", "probability": 0.9658203125}, {"start": 581.48, "end": 581.9, "word": " إيه؟", "probability": 0.61749267578125}, {"start": 581.9, "end": 582.2, "word": " أي", "probability": 0.875}, {"start": 582.2, "end": 582.76, "word": " set", "probability": 0.9296875}, {"start": 582.76, "end": 583.3, "word": " يعني", "probability": 0.84912109375}, {"start": 583.3, "end": 583.84, "word": " أني،", "probability": 0.53125}, {"start": 583.84, "end": 584.48, "word": " عام،", "probability": 0.8733723958333334}, {"start": 584.48, "end": 584.96, "word": " فمافيش", "probability": 0.82879638671875}, {"start": 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{"start": 772.3, "end": 772.76, "word": " elements", "probability": 0.90576171875}, {"start": 772.76, "end": 773.18, "word": " are", "probability": 0.9560546875}, {"start": 773.18, "end": 773.56, "word": " the", "probability": 0.8603515625}, {"start": 773.56, "end": 774.14, "word": " subsets", "probability": 0.930908203125}, {"start": 774.14, "end": 774.38, "word": " of", "probability": 0.9833984375}, {"start": 774.38, "end": 774.62, "word": " A", "probability": 0.96044921875}, {"start": 774.62, "end": 774.92, "word": " وال", "probability": 0.3701171875}, {"start": 774.92, "end": 775.44, "word": " subsets", "probability": 0.916259765625}, {"start": 775.44, "end": 775.62, "word": " of", "probability": 0.95654296875}, {"start": 775.62, "end": 775.72, "word": " A", "probability": 0.96826171875}, {"start": 775.72, "end": 775.88, "word": " إيش", "probability": 0.8512369791666666}, {"start": 775.88, "end": 776.22, "word": " مالهم", "probability": 0.8365885416666666}, {"start": 776.22, "end": 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{"start": 1025.47, "end": 1025.61, "word": " اللي", "probability": 0.901611328125}, {"start": 1025.61, "end": 1025.91, "word": " حلينا", "probability": 0.8313802083333334}, {"start": 1025.91, "end": 1026.07, "word": " فيها", "probability": 0.9365234375}, {"start": 1026.07, "end": 1026.39, "word": " المثال", "probability": 0.9641927083333334}, {"start": 1026.39, "end": 1026.79, "word": " الأخير", "probability": 0.9466145833333334}], "temperature": 1.0}, {"id": 44, "seek": 104348, "start": 1028.0, "end": 1043.48, "text": "حنبدأ نشوف أكم مجموعة فيها 0 من العناصر واحدة اللي هي الـ Phi أكم مجموعة جزئية، أنا عندي مجموعة capital A فيها N من العناصر فابد أعد أكم مجموعة فيها صفر من العناصر الـ Phi، مافيش غيرها، واحدة", "tokens": [5016, 1863, 44510, 10721, 8717, 8592, 38688, 5551, 24793, 3714, 7435, 2304, 2407, 27884, 8978, 11296, 1958, 9154, 18863, 1863, 33546, 2288, 36764, 24401, 3660, 13672, 1829, 39896, 2423, 39184, 41435, 5551, 24793, 3714, 7435, 2304, 2407, 27884, 10874, 11622, 19986, 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with N elements .. اه فيها N من العناصر .. 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113878, "start": 1133.32, "end": 1138.78, "text": "of A فكان مجموعة جزئية خالية من الـ A واحدة", "tokens": [2670, 316, 6156, 41361, 3714, 7435, 2304, 2407, 27884, 10874, 11622, 19986, 10632, 16490, 6027, 10632, 9154, 2423, 39184, 316, 36764, 24401, 3660], "avg_logprob": -0.1889648406455914, "compression_ratio": 1.028169014084507, "no_speech_prob": 0.0, "words": [{"start": 1133.32, "end": 1133.64, "word": "of", "probability": 0.2900390625}, {"start": 1133.64, "end": 1134.36, "word": " A", "probability": 0.59521484375}, {"start": 1134.36, "end": 1136.22, "word": " فكان", "probability": 0.78076171875}, {"start": 1136.22, "end": 1136.68, "word": " مجموعة", "probability": 0.89951171875}, {"start": 1136.68, "end": 1137.1, "word": " جزئية", "probability": 0.95556640625}, {"start": 1137.1, "end": 1137.48, "word": " خالية", "probability": 0.9925130208333334}, {"start": 1137.48, "end": 1137.62, "word": " من", "probability": 0.97900390625}, {"start": 1137.62, "end": 1137.8, "word": " الـ", 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"end": 2108.34, "word": " من", "probability": 0.99609375}, {"start": 2108.34, "end": 2108.5, "word": " ال", "probability": 0.8681640625}, {"start": 2108.5, "end": 2108.72, "word": " power", "probability": 0.8349609375}, {"start": 2108.72, "end": 2109.0, "word": " of", "probability": 0.9814453125}, {"start": 2109.0, "end": 2109.26, "word": " B", "probability": 0.97705078125}, {"start": 2109.26, "end": 2111.86, "word": " أي", "probability": 0.6982421875}, {"start": 2111.86, "end": 2112.44, "word": " سؤال", "probability": 0.9899088541666666}, {"start": 2112.44, "end": 2115.0, "word": " ممتازة", "probability": 0.78154296875}, {"start": 2115.0, "end": 2116.14, "word": " فهي", "probability": 0.92626953125}, {"start": 2116.14, "end": 2116.72, "word": " المطلوب", "probability": 0.989501953125}, {"start": 2116.72, "end": 2118.3, "word": " المطلوب", "probability": 0.947021484375}, {"start": 2118.3, "end": 2119.24, "word": " نظرة", "probability": 0.9173177083333334}, {"start": 2119.24, "end": 2119.82, "word": " خارجية", "probability": 0.9925537109375}, {"start": 2119.82, "end": 2120.06, "word": " بيقول", "probability": 0.890625}, {"start": 2120.06, "end": 2120.58, "word": " بيثبت", "probability": 0.62392578125}, {"start": 2120.58, "end": 2120.9, "word": " علاقة", "probability": 0.9879557291666666}, {"start": 2120.9, "end": 2121.3, "word": " subset", "probability": 0.9521484375}], "temperature": 1.0}, {"id": 89, "seek": 214430, "start": 2122.18, "end": 2144.3, "text": "بتثبت علاقة subset ال power of A مجموعة ال subset من المجموعة الأخرى هي ال power of B فنبدأ من أول السؤال نبدأ واحدة واحدة زي ما بنبدأش بالتدريج فال علاقة subset اتفقنا أن علاقة subset تكافئ for all X X في الأولى then X في التانى فهذا هو التعريف", "tokens": [3555, 2655, 12984, 3555, 2655, 11203, 995, 28671, 25993, 2423, 1347, 295, 316, 3714, 7435, 2304, 2407, 27884, 2423, 25993, 9154, 9673, 7435, 2304, 2407, 27884, 16247, 34740, 7578, 39896, 2423, 1347, 295, 363, 6156, 1863, 44510, 10721, 9154, 5551, 12610, 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element صح؟ اذا هنبدأ البرنامج نقول له let x be any element let بس بدي احطها capital X be any element", "tokens": [5172, 2304, 43020, 1975, 4117, 2655, 3555, 23758, 4724, 8592, 28820, 9122, 3555, 13546, 4724, 3794, 3714, 7649, 1829, 8592, 1975, 4117, 2655, 3555, 6225, 8592, 7649, 8717, 44510, 10721, 1975, 5016, 8315, 1975, 12610, 50113, 6027, 7251, 43020, 1975, 5172, 36520, 11296, 9122, 2655, 13546, 4032, 6027, 7649, 8717, 5016, 995, 12610, 8717, 46456, 9381, 2288, 6225, 8592, 7649, 1975, 2655, 3615, 10943, 1211, 20449, 25724, 2304, 37977, 9673, 4117, 31845, 19986, 3660, 16712, 3615, 16572, 5172, 39896, 8978, 11296, 337, 439, 9122, 33911, 8717, 2655, 3615, 10943, 1211, 22807, 44945, 39648, 46740, 718, 2031, 312, 604, 4478, 20328, 5016, 22807, 1975, 15730, 8032, 1863, 44510, 10721, 2423, 26890, 8315, 2304, 7435, 8717, 39648, 46740, 718, 2031, 312, 604, 4478, 718, 4724, 3794, 4724, 16254, 1975, 5016, 9566, 11296, 4238, 1783, 312, 604, 4478], "avg_logprob": -0.2233455823186566, 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" x", "probability": 0.5673828125}, {"start": 2160.61, "end": 2160.75, "word": " be", "probability": 0.92236328125}, {"start": 2160.75, "end": 2160.95, "word": " any", "probability": 0.93505859375}, {"start": 2160.95, "end": 2161.27, "word": " element", "probability": 0.951171875}, {"start": 2161.27, "end": 2161.85, "word": " صح؟", "probability": 0.7915852864583334}, {"start": 2161.85, "end": 2161.99, "word": " اذا", "probability": 0.7049560546875}, {"start": 2161.99, "end": 2162.41, "word": " هنبدأ", "probability": 0.849609375}, {"start": 2162.41, "end": 2162.71, "word": " البرنامج", "probability": 0.698388671875}, {"start": 2162.71, "end": 2162.93, "word": " نقول", "probability": 0.834716796875}, {"start": 2162.93, "end": 2163.03, "word": " له", "probability": 0.7119140625}, {"start": 2163.03, "end": 2163.27, "word": " let", "probability": 0.9580078125}, {"start": 2163.27, "end": 2163.61, "word": " x", "probability": 0.9091796875}, {"start": 2163.61, "end": 2163.89, "word": " be", 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2173.43, "end": 2188.17, "text": "ليش capital؟ طب ال X غلط؟ لأ فيش رمز غلط قولنا لكن capital مهم لأنه عناصر ال power إيش مالهم؟ إنهم مجموعات فده بيذكر إن دول مجموعات يعني أنصر في ال power لكن هي مجموعة نفسها subset تمام", "tokens": [20292, 8592, 4238, 22807, 23032, 3555, 2423, 1783, 32771, 1211, 9566, 22807, 5296, 10721, 8978, 8592, 12602, 2304, 11622, 32771, 1211, 9566, 12174, 12610, 8315, 44381, 4238, 3714, 16095, 5296, 33456, 3224, 18871, 33546, 2288, 2423, 1347, 11933, 1829, 8592, 3714, 6027, 16095, 22807, 36145, 16095, 3714, 7435, 2304, 45367, 9307, 6156, 3215, 3224, 4724, 1829, 8848, 37983, 36145, 11778, 12610, 3714, 7435, 2304, 45367, 9307, 37495, 22653, 14739, 9381, 2288, 8978, 2423, 1347, 44381, 39896, 3714, 7435, 2304, 2407, 27884, 8717, 36178, 11296, 25993, 46811, 10943], "avg_logprob": -0.2862215983596715, "compression_ratio": 1.6236559139784945, "no_speech_prob": 0.0, "words": [{"start": 2173.4300000000003, "end": 2174.05, "word": "ليش", "probability": 0.58465576171875}, 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"probability": 0.7109375}, {"start": 2184.75, "end": 2184.93, "word": " دول", "probability": 0.793212890625}, {"start": 2184.93, "end": 2185.35, "word": " مجموعات", "probability": 0.89990234375}, {"start": 2185.35, "end": 2185.45, "word": " يعني", "probability": 0.773193359375}, {"start": 2185.45, "end": 2185.85, "word": " أنصر", "probability": 0.8243815104166666}, {"start": 2185.85, "end": 2185.95, "word": " في", "probability": 0.9482421875}, {"start": 2185.95, "end": 2186.03, "word": " ال", "probability": 0.9306640625}, {"start": 2186.03, "end": 2186.17, "word": " power", "probability": 0.833984375}, {"start": 2186.17, "end": 2186.37, "word": " لكن", "probability": 0.89111328125}, {"start": 2186.37, "end": 2186.53, "word": " هي", "probability": 0.609375}, {"start": 2186.53, "end": 2186.91, "word": " مجموعة", "probability": 0.93818359375}, {"start": 2186.91, "end": 2187.27, "word": " نفسها", "probability": 0.9908854166666666}, {"start": 2187.27, "end": 2187.55, "word": " subset", "probability": 0.253173828125}, {"start": 2187.55, "end": 2188.17, "word": " تمام", "probability": 0.881591796875}], "temperature": 1.0}, {"id": 92, "seek": 221415, "start": 2188.65, "end": 2214.15, "text": "بعدين إيش صار بدي أثبت جملة شرطية X in A then X in B بديش أكتب الآن بقوله we want to prove بدي أحاول أقتصر لأن أحنا بس أول مرة فصلناها طيب فبدي أفترض أنه X في الأولى فبدي أقول أنه X في ال power of A فبقوله هنا إيش ممكن أكمل الجملة أو أكتب من الجديد and let X مالها تنتمي لل power of A", "tokens": [3555, 22488, 9957, 11933, 1829, 8592, 20328, 9640, 4724, 16254, 5551, 12984, 3555, 2655, 10874, 2304, 37977, 13412, 2288, 9566, 10632, 1783, 294, 316, 550, 1783, 294, 363, 4724, 16254, 8592, 5551, 4117, 2655, 3555, 6024, 48506, 4724, 39648, 3224, 321, 528, 281, 7081, 4724, 16254, 5551, 5016, 995, 12610, 5551, 38149, 9381, 2288, 5296, 33456, 5551, 5016, 8315, 4724, 3794, 5551, 12610, 3714, 25720, 6156, 36520, 8315, 11296, 23032, 1829, 3555, 6156, 3555, 16254, 5551, 5172, 2655, 43042, 14739, 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"word": " فصلناها", "probability": 0.8309326171875}, {"start": 2198.19, "end": 2198.67, "word": " طيب", "probability": 0.9518229166666666}, {"start": 2198.67, "end": 2199.19, "word": " فبدي", "probability": 0.8693033854166666}, {"start": 2199.19, "end": 2199.57, "word": " أفترض", "probability": 0.93896484375}, {"start": 2199.57, "end": 2199.75, "word": " أنه", "probability": 0.45263671875}, {"start": 2199.75, "end": 2200.43, "word": " X", "probability": 0.4140625}, {"start": 2200.43, "end": 2200.63, "word": " في", "probability": 0.900390625}, {"start": 2200.63, "end": 2201.09, "word": " الأولى", "probability": 0.9576822916666666}, {"start": 2201.09, "end": 2201.49, "word": " فبدي", "probability": 0.8942057291666666}, {"start": 2201.49, "end": 2201.77, "word": " أقول", "probability": 0.968017578125}, {"start": 2201.77, "end": 2201.95, "word": " أنه", "probability": 0.4830322265625}, {"start": 2201.95, "end": 2202.27, "word": " X", "probability": 0.355224609375}, {"start": 2202.27, "end": 2202.49, "word": " في", "probability": 0.79443359375}, {"start": 2202.49, "end": 2203.01, "word": " ال", "probability": 0.34033203125}, {"start": 2203.01, "end": 2203.27, "word": " power", "probability": 0.61474609375}, {"start": 2203.27, "end": 2203.53, "word": " of", "probability": 0.9765625}, {"start": 2203.53, "end": 2203.79, "word": " A", "probability": 0.88671875}, {"start": 2203.79, "end": 2204.39, "word": " فبقوله", "probability": 0.832275390625}, {"start": 2204.39, "end": 2204.57, "word": " هنا", "probability": 0.85400390625}, {"start": 2204.57, "end": 2204.75, "word": " إيش", "probability": 0.7734375}, {"start": 2204.75, "end": 2204.93, "word": " ممكن", "probability": 0.8427734375}, {"start": 2204.93, "end": 2205.31, "word": " أكمل", "probability": 0.9541015625}, {"start": 2205.31, "end": 2205.67, "word": " الجملة", "probability": 0.962890625}, {"start": 2205.67, "end": 2205.99, "word": " أو", "probability": 0.8486328125}, {"start": 2205.99, "end": 2206.27, "word": " أكتب", "probability": 0.9857177734375}, {"start": 2206.27, "end": 2206.37, "word": " من", "probability": 0.9716796875}, {"start": 2206.37, "end": 2206.73, "word": " الجديد", "probability": 0.9049479166666666}, {"start": 2206.73, "end": 2207.01, "word": " and", "probability": 0.78857421875}, {"start": 2207.01, "end": 2207.41, "word": " let", "probability": 0.97021484375}, {"start": 2207.41, "end": 2210.31, "word": " X", "probability": 0.81787109375}, {"start": 2210.31, "end": 2210.95, "word": " مالها", "probability": 0.7908528645833334}, {"start": 2210.95, "end": 2212.15, "word": " تنتمي", "probability": 0.9876708984375}, {"start": 2212.15, "end": 2213.15, "word": " لل", "probability": 0.794921875}, {"start": 2213.15, "end": 2213.57, "word": " power", "probability": 0.68017578125}, {"start": 2213.57, "end": 2213.93, "word": " of", "probability": 0.9833984375}, {"start": 2213.93, "end": 2214.15, "word": " A", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 93, "seek": 224071, "start": 2214.83, "end": 2240.71, "text": "فهذه ليش كتبنا الجمعتين هدول؟ عشان التعريف التعريف فيه for all فقلنا له let X be any element طيب البعد ال for all ليش فيه؟ جملة شرطية فقلنا لنا افترض ان الشرط صحيح هدا هم متابعين؟ واضح ليش كتبنا الجمعتين هدول؟ واضح ولا مش واضح؟ واضح تمام أيش المطلوب أصبح؟ بدي أثبت ان كابتن ال X وين؟ في ال power of B خليني اكتب بهذه we have", "tokens": [5172, 3224, 24192, 32239, 8592, 9122, 2655, 3555, 8315, 25724, 2304, 34268, 9957, 8032, 3215, 12610, 22807, 6225, 8592, 7649, 16712, 3615, 16572, 5172, 16712, 3615, 16572, 5172, 8978, 3224, 337, 439, 6156, 4587, 1211, 8315, 46740, 718, 1783, 312, 604, 4478, 23032, 1829, 3555, 29739, 22488, 2423, 337, 439, 32239, 8592, 8978, 3224, 22807, 10874, 2304, 37977, 13412, 2288, 9566, 10632, 6156, 4587, 1211, 8315, 5296, 8315, 1975, 5172, 2655, 43042, 16472, 25124, 2288, 9566, 20328, 5016, 1829, 5016, 8032, 28259, 8032, 2304, 44650, 16758, 3615, 9957, 22807, 4032, 46958, 5016, 32239, 8592, 9122, 2655, 3555, 8315, 25724, 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"word": " عشان", "probability": 0.9259440104166666}, {"start": 2217.75, "end": 2218.37, "word": " التعريف", "probability": 0.993896484375}, {"start": 2218.37, "end": 2219.15, "word": " التعريف", "probability": 0.930419921875}, {"start": 2219.15, "end": 2219.37, "word": " فيه", "probability": 0.6728515625}, {"start": 2219.37, "end": 2219.57, "word": " for", "probability": 0.8857421875}, {"start": 2219.57, "end": 2219.83, "word": " all", "probability": 0.94189453125}, {"start": 2219.83, "end": 2220.21, "word": " فقلنا", "probability": 0.74176025390625}, {"start": 2220.21, "end": 2220.37, "word": " له", "probability": 0.8427734375}, {"start": 2220.37, "end": 2220.53, "word": " let", "probability": 0.8251953125}, {"start": 2220.53, "end": 2220.99, "word": " X", "probability": 0.408935546875}, {"start": 2220.99, "end": 2221.17, "word": " be", "probability": 0.716796875}, {"start": 2221.17, "end": 2221.37, "word": " any", "probability": 0.91796875}, {"start": 2221.37, "end": 2221.71, "word": " element", "probability": 0.96337890625}, {"start": 2221.71, "end": 2222.31, "word": " طيب", "probability": 0.9111328125}, {"start": 2222.31, "end": 2222.99, "word": " البعد", "probability": 0.636962890625}, {"start": 2222.99, "end": 2223.61, "word": " ال", "probability": 0.3154296875}, {"start": 2223.61, "end": 2223.77, "word": " for", "probability": 0.55712890625}, {"start": 2223.77, "end": 2223.97, "word": " all", "probability": 0.9560546875}, {"start": 2223.97, "end": 2224.09, "word": " ليش", "probability": 0.6829833984375}, {"start": 2224.09, "end": 2224.39, "word": " فيه؟", "probability": 0.9259440104166666}, {"start": 2224.39, "end": 2224.61, "word": " جملة", "probability": 0.9459635416666666}, {"start": 2224.61, "end": 2225.01, "word": " شرطية", "probability": 0.9879150390625}, {"start": 2225.01, "end": 2225.27, "word": " فقلنا", "probability": 0.938720703125}, {"start": 2225.27, "end": 2225.35, "word": " لنا", "probability": 0.46484375}, {"start": 2225.35, "end": 2225.55, "word": " افترض", "probability": 0.9366455078125}, {"start": 2225.55, "end": 2225.69, "word": " ان", "probability": 0.69970703125}, {"start": 2225.69, "end": 2225.95, "word": " الشرط", "probability": 0.9259440104166666}, {"start": 2225.95, "end": 2226.29, "word": " صحيح", "probability": 0.9761962890625}, {"start": 2226.29, "end": 2226.49, "word": " هدا", "probability": 0.5}, {"start": 2226.49, "end": 2226.73, "word": " هم", "probability": 0.790771484375}, {"start": 2226.73, "end": 2228.47, "word": " متابعين؟", "probability": 0.814453125}, {"start": 2228.47, "end": 2228.77, "word": " واضح", "probability": 0.95166015625}, {"start": 2228.77, "end": 2228.95, "word": " ليش", "probability": 0.9775390625}, {"start": 2228.95, "end": 2229.23, "word": " كتبنا", "probability": 0.9964599609375}, {"start": 2229.23, "end": 2229.59, "word": " الجمعتين", "probability": 0.9656982421875}, {"start": 2229.59, "end": 2231.09, "word": " هدول؟", "probability": 0.9705810546875}, {"start": 2231.09, "end": 2231.37, "word": " واضح", "probability": 0.9580078125}, {"start": 2231.37, "end": 2231.49, "word": " ولا", "probability": 0.6669921875}, {"start": 2231.49, "end": 2231.67, "word": " مش", "probability": 0.9833984375}, {"start": 2231.67, "end": 2232.21, "word": " واضح؟", "probability": 0.962646484375}, {"start": 2232.21, "end": 2232.91, "word": " واضح", "probability": 0.9567057291666666}, {"start": 2232.91, "end": 2233.33, "word": " تمام", "probability": 0.914794921875}, {"start": 2233.33, "end": 2233.75, "word": " أيش", "probability": 0.6204833984375}, {"start": 2233.75, "end": 2234.13, "word": " المطلوب", "probability": 0.97998046875}, {"start": 2234.13, "end": 2234.81, "word": " أصبح؟", "probability": 0.9393310546875}, {"start": 2234.81, "end": 2235.05, "word": " بدي", "probability": 0.75146484375}, {"start": 2235.05, "end": 2235.39, "word": " أثبت", "probability": 0.98486328125}, {"start": 2235.39, "end": 2235.49, "word": " ان", "probability": 0.413818359375}, {"start": 2235.49, 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شاء الله نواصل احنا + +2 +00:00:23,550 --> 00:00:28,110 +بدأنا بداية مختصرة اللي هو الـdenominable and non + +3 +00:00:28,110 --> 00:00:31,130 +-denominable sets وبشكل خاص بدأنا من ال infinite + +4 +00:00:31,130 --> 00:00:36,050 +set المجموعة غير المنتهية او اللانهائية فانهيت بس + +5 +00:00:36,050 --> 00:00:40,680 +اللي هو التعريف لانه مهم جدافبنقول على مجموعة x + +6 +00:00:40,680 --> 00:00:44,640 +إنها infinite إذا كان فيه بقدر ألاقي منها proper + +7 +00:00:44,640 --> 00:00:48,520 +subset y بحيث إنه هذه ال proper subset y بقدر + +8 +00:00:48,520 --> 00:00:51,740 +ألاقي اللي هو bijection بينها وبين ال x نفسها + +9 +00:00:51,740 --> 00:00:57,180 +بمعنى آخر فيه بشكل مكافئإن بقدر ألاقي اللي هو one + +10 +00:00:57,180 --> 00:01:01,040 +to one function من X لنفسها بحيث تكون اللي هو ال + +11 +00:01:01,040 --> 00:01:04,460 +image اللي هو F of X بربر subset من X بربر subset + +12 +00:01:04,460 --> 00:01:07,500 +من X فدولة صورتين متكافئتين و احنا بنشتغل مع + +13 +00:01:07,500 --> 00:01:10,380 +الصورة التانية أسهل في التطبيق أسهل في التطبيق + +14 +00:01:10,380 --> 00:01:14,400 +طبعا هو متكافئتين طبعا اللي ما هي ال finite اللي + +15 +00:01:14,400 --> 00:01:17,160 +غير infinite اللي هو ال negation ل ال infinite + +16 +00:01:17,160 --> 00:01:22,100 +فالمجموعة إذا ماكنتش infinite بسميها finiteفطبعا + +17 +00:01:22,100 --> 00:01:26,640 +احنا شفنا اول مثال وانه مجموعة الاعداد الطبيعية اي + +18 +00:01:26,640 --> 00:01:30,240 +الاعداد الصحيحة الموجبة هي infinite set واجدرنا + +19 +00:01:30,240 --> 00:01:33,020 +اللاجي دالة طبعا ممكن يكون فيه اكتر من دالة احنا + +20 +00:01:33,020 --> 00:01:37,400 +اخدنا f of x بتساوي 2x زي 2x وظبطت معنا طبعا ممكن + +21 +00:01:37,400 --> 00:01:40,900 +ان نشوف خيارات اخرى لكن هذا قد الغرض لانه بده لاجي + +22 +00:01:40,900 --> 00:01:46,630 +الدالةخلّينا نشوف كمان نظرية نبدأ نشوف مين الأمثل + +23 +00:01:46,630 --> 00:01:49,850 +اللي هتكون متعارف علينا ومعروفة طبعا من هنا نطالة + +24 +00:01:49,850 --> 00:01:52,450 +احنا عارفين ان الان infinite فهذه تعتبر نظرية ممكن + +25 +00:01:52,450 --> 00:01:55,870 +تستخدمها في أي مكان ال proposition النظرية التانية + +26 +00:01:55,870 --> 00:01:59,630 +او proposition خمسة اتنين المجموعة الخالية و ال + +27 +00:01:59,630 --> 00:02:02,410 +singleton sets يعني المجموعة متكونة من عنصر واحد + +28 +00:02:02,410 --> 00:02:08,220 +هدولة ايش finite set are finiteفنشوف نص الـ + +29 +00:02:08,220 --> 00:02:11,620 +proposition هذا العنوان تبعه The empty set is + +30 +00:02:11,620 --> 00:02:16,060 +finite طبعا واضح لأنه فيها zero من العناصر و + +31 +00:02:16,060 --> 00:02:20,080 +singleton set finite لأنه فيها عنصر واحد فهذا واضح + +32 +00:02:20,080 --> 00:02:23,840 +لكن تشوف كيف البرهان في ضوء مين في ضوء التعريف في + +33 +00:02:23,840 --> 00:02:29,280 +ضوء التعريف نشوف التعريف كيف نثبت أن مجموعة + +34 +00:02:29,280 --> 00:02:32,100 +infinite شوفنا كيف نثبت أنها finite خليني أشوف مع + +35 +00:02:32,100 --> 00:02:35,040 +بعض مثال فهذا proposition خمسة اتنين + +36 +00:02:39,420 --> 00:02:45,680 +خمسة اتنين approved ونبدأ من الفرع الأول بدنا نثبت + +37 +00:02:45,680 --> 00:02:51,580 +انه Phi is finite طبعا زي ما احنا شايفين التعريف + +38 +00:02:51,580 --> 00:02:55,680 +عرف ال infinite ماعرفش ال finite جال ف ال finite + +39 +00:02:55,680 --> 00:02:59,280 +هي ال negation لذلك من الأنسب انه نثبتها عن طريق + +40 +00:02:59,280 --> 00:03:03,020 +ال contradiction by contradiction فهنبدأ by + +41 +00:03:03,020 --> 00:03:04,920 +contradiction هنقول له assume + +42 +00:03:08,120 --> 00:03:13,660 +فاي is infinite ايش بنعمل approved by + +43 +00:03:13,660 --> 00:03:16,860 +contradiction خليني بس اكتب تحت عشان احافظ على + +44 +00:03:16,860 --> 00:03:24,420 +المساحة approved by contradiction يعني وقت إيش + +45 +00:03:24,420 --> 00:03:28,200 +بنتهي البرهان لما أوصل لcontradiction تمام ايش + +46 +00:03:28,200 --> 00:03:33,400 +معناه الـ finite التعريف فده معناته there exists F + +47 +00:03:34,110 --> 00:03:39,090 +من وين لوين من ال X لنفسها اللي هي فيه such that + +48 +00:03:39,090 --> 00:03:43,870 +هذا التعريف اللي بدنا نتمكن منه نحفظه نستخدمه ال F + +49 +00:03:43,870 --> 00:03:51,720 +is one to one andF of Phi إبرابر من مين؟ من الـ + +50 +00:03:51,720 --> 00:03:57,020 +Phi فاحنا بنطبق التعريف على X بتساوي Phi تمام؟ أه، + +51 +00:03:57,020 --> 00:04:00,520 +بدأ أوصل ل contradiction الحقيقة من نظريات سابقة + +52 +00:04:00,520 --> 00:04:05,640 +أثبتنا إن صورة الـ Phi تساوي Phi أثبتنا من نظريات + +53 +00:04:05,640 --> 00:04:10,540 +سابقة، طبعا ايش دليل هنا؟ Definition of infinite + +54 +00:04:10,540 --> 00:04:15,150 +setInfinite set هذا اللي استخدمته اه فاستخدمت + +55 +00:04:15,150 --> 00:04:18,770 +التعريف لان حتى الان طب الآن هذا ايش بيأدي طب F of + +56 +00:04:18,770 --> 00:04:22,590 +Phi ايش بتسووا Phi ابرابر من ال Phi ليش لأن في + +57 +00:04:22,590 --> 00:04:26,070 +نظرية بتقولي F of Phi تسووا Phi هاي دليلي صحيح + +58 +00:04:26,070 --> 00:04:33,860 +تمام ايش رأيكوا ايش نعمل بعد هيكخلص البرهام ولا + +59 +00:04:33,860 --> 00:04:37,320 +ماخلصش؟ اه Contradiction .. اه ليش؟ لأن الـ Phi + +60 +00:04:37,320 --> 00:04:39,620 +بيبقى أيش معنى تبروبرت؟ لا تسووا Phi؟ + +61 +00:04:39,620 --> 00:04:42,040 +Contradiction .. اه فده معناته أن Phi لا تسووا Phi + +62 +00:04:42,040 --> 00:04:44,220 +فده أيش؟ Contradiction .. خلص البرهام + +63 +00:04:44,220 --> 00:04:45,860 +Contradiction + +64 +00:04:48,000 --> 00:04:51,300 +فمهم جدا نعرف نبدأ البرهان وهذا بنحاول ان اعلمكوا + +65 +00:04:51,300 --> 00:04:54,680 +ياه وكيف نعرف ان البرهان انتهى Contradiction لانه + +66 +00:04:54,680 --> 00:04:57,260 +دي ايش معناته ان هي subset طبعا بيحصل set صح لأن + +67 +00:04:57,260 --> 00:05:00,120 +الـ Phi Subset من أي set بما فيها من نفسها ولا + +68 +00:05:00,120 --> 00:05:03,020 +تساوي ال Phi Contradiction Phi لا تساوي Phi مانفعش + +69 +00:05:03,020 --> 00:05:09,240 +واحد ده يساوي واحد Contradiction مستحيل نشوف بي بي + +70 +00:05:09,240 --> 00:05:12,940 +بنفس المنهج برضه بي Contradiction طبعا Singleton + +71 +00:05:12,940 --> 00:05:15,420 +set يعني مجموعة من عنصر واحد خدنا ناخد مجموعة من + +72 +00:05:15,420 --> 00:05:21,810 +عنصر واحد فنقول هنا letA او X اذا حبينا نسميها X + +73 +00:05:21,810 --> 00:05:28,270 +تساوي مجموعة بين عنصر واحد بـ a singleton set + +74 +00:05:28,270 --> 00:05:31,770 +Singleton + +75 +00:05:31,770 --> 00:05:37,710 +set مطلوب اثبت ان ال X finite بنثبت ان ال X finite + +76 +00:05:37,710 --> 00:05:47,480 +by contradiction assume X is infiniteعشان بنعمل + +77 +00:05:47,480 --> 00:05:53,080 +prove by contradictionبس عشان الواحد تابع كل جملة + +78 +00:05:53,080 --> 00:05:58,460 +بنكتبها إلى سبب العمل مش عشوائي كله له أسبابه + +79 +00:05:58,460 --> 00:06:01,500 +المنطقية و احنا فاتعلمنا التفكير الاستدالي في + +80 +00:06:01,500 --> 00:06:05,200 +أقلنا دليل ليش بنعمل كل خطوة، ممتاز، بنفس العملية + +81 +00:06:05,200 --> 00:06:07,360 +عشان إن المهارة تتكرر معاكوا، يمكن أول مثال كان + +82 +00:06:07,360 --> 00:06:10,000 +صعوبة، إيش معناه not infinite؟ بقدر ألاقي ديالة + +83 +00:06:10,000 --> 00:06:14,040 +one to one من X لنفسها و تكون إيش ال image proper + +84 +00:06:14,040 --> 00:06:19,180 +subset فعلى طول بنفس الطريقة there exists F من X + +85 +00:06:19,180 --> 00:06:30,360 +لنفسهاsuch that f is one to one and f of x is + +86 +00:06:30,360 --> 00:06:33,880 +proper من + +87 +00:06:33,880 --> 00:06:39,840 +ال x اه خليكم معانا اه طيب f of x برضه مرت علينا + +88 +00:06:39,840 --> 00:06:46,500 +بنظرية ف f of x f of x اللي هي تساوي x لأنه مجموعة + +89 +00:06:46,500 --> 00:06:51,650 +من عنصر واحدمرت علينا قبل هيك ال proper من ال X + +90 +00:06:51,650 --> 00:06:54,970 +برضه ال contradiction زي توي + +91 +00:06:59,380 --> 00:07:03,060 +Contradiction فإذن هدول المجموعتين أول احنا أول + +92 +00:07:03,060 --> 00:07:08,060 +مثال على ال infinite set هي ال natural number وعنا + +93 +00:07:08,060 --> 00:07:11,840 +مثالين على ال finite set هم مين ال five و أي + +94 +00:07:11,840 --> 00:07:15,820 +مجموعة من عنصر واحد فدول أول أمثلة بنقابلهم على + +95 +00:07:15,820 --> 00:07:20,300 +المصطلح الجديد finite أو infinite في أي استفسار؟ + +96 +00:07:20,300 --> 00:07:27,780 +متابعين؟ اه طيب ماشي هنشوف نقطة جديدة نظرية + +97 +00:07:28,940 --> 00:07:34,560 +نظرية يعني كل أمثلاتنا جاية نظريات ونشوف بعدها + +98 +00:07:34,560 --> 00:07:38,720 +هنشوف أمثلة متنوعة طبعا عنوان النظرية عشان نفهم + +99 +00:07:38,720 --> 00:07:41,400 +إيش اللي بدنا نقوله a subset of a finite set is + +100 +00:07:41,400 --> 00:07:45,160 +finite and a superset of infinite set is infinite + +101 +00:07:45,160 --> 00:07:49,420 +منطق الأمر غير نستوعب المجموعة هالجت finite إيش + +102 +00:07:49,420 --> 00:07:53,060 +يعني صغيرة طب و ال subset أصغر منها فاللي أصغر من + +103 +00:07:53,060 --> 00:07:58,640 +ال finite finite واضح بالعاميةو ال infinite كبيرة + +104 +00:07:58,640 --> 00:08:01,320 +اللي أكبر منها بتاعةها infinite اللي هي ال super + +105 +00:08:01,320 --> 00:08:05,340 +set شوف انتبهوا لكن infinite أصغر منها مفتوح ممكن + +106 +00:08:05,340 --> 00:08:07,540 +يكون infinite و ممكن يكون finite انتبهوا هذه اه + +107 +00:08:07,540 --> 00:08:11,020 +فال infinite اللي أكبر من ال infinite infinite و + +108 +00:08:11,020 --> 00:08:13,920 +اللي أصغر من ال finite finite لكن أصغر من infinite + +109 +00:08:13,920 --> 00:08:16,700 +مش معروف و أكبر من ال finite مش معروف ممكن يكون + +110 +00:08:16,700 --> 00:08:18,960 +finite و ممكن يكون infinite واضحة زي ما كنا بنعمل + +111 +00:08:18,960 --> 00:08:21,720 +بياش بال diverge و ال converge قلنا إذا الكبيرة + +112 +00:08:21,720 --> 00:08:25,070 +converge يعني finite فاللي أصغر convergeوإذا + +113 +00:08:25,070 --> 00:08:29,110 +الصغيرة diverse فالأكبر diverse هاي نفس القضية لأن + +114 +00:08:29,110 --> 00:08:31,130 +اللي أكبر من ال infinite infinite لكن الاتجاه + +115 +00:08:31,130 --> 00:08:37,590 +التاني بيفشر نفس العملية نشوف النص بشكل كامل + +116 +00:08:37,590 --> 00:08:44,670 +every super set of an infinite set is infinite كل + +117 +00:08:44,670 --> 00:08:48,650 +مجموعة أكبر من مجموعة تحتوي super يعني تحتوي عكس + +118 +00:08:48,650 --> 00:08:54,480 +subset بتكون infiniteو every subset of a finite + +119 +00:08:54,480 --> 00:09:01,560 +set is finite نشوف البرهان مع بعض فهنا كله بنتدرب + +120 +00:09:01,560 --> 00:09:05,520 +أمثلة كيف نستخدم التعريف و طبعا بنطور أدوات ممكن + +121 +00:09:05,520 --> 00:09:11,640 +فيما بعد هدول نظريات نستخدمها و تسهل عليها theorem + +122 +00:09:13,670 --> 00:09:16,990 +خمسة واحد أول نظرية يعني هذه أهم من نتائج المهمة + +123 +00:09:16,990 --> 00:09:21,550 +جدا اللي هنعتمد عليها لأن النظرية every super set + +124 +00:09:21,550 --> 00:09:25,190 +of an infinite set كيف بدنا نعبر عنها هذا بتقول لو + +125 +00:09:25,190 --> 00:09:29,890 +أنت عندك مجموعة X infinite أي مجموعة تحتويها بدت + +126 +00:09:29,890 --> 00:09:32,570 +تكون infinite هي المطلوب فهي نعبر أولش ناخد + +127 +00:09:32,570 --> 00:09:38,930 +infinite set ال proof فنقول له let X be an + +128 +00:09:38,930 --> 00:09:44,430 +infinite setفي عندنا مجموعة infinite بدي أثبت أن + +129 +00:09:44,430 --> 00:09:48,410 +أي مجموعة أكبر منها في إيش final إيش بدنا نثبت؟ + +130 +00:09:48,410 --> 00:09:55,410 +نريد .. خلينا نكتب to prove for all capital Y أي + +131 +00:09:55,410 --> 00:10:00,270 +مجموعة Y تحتوي ال X أكتب بها هيك يعني ال X subset + +132 +00:10:00,270 --> 00:10:05,250 +من ال Y هي super set إيش لازم تكون؟ Y is infinite + +133 +00:10:05,250 --> 00:10:12,910 +Y is infinite هذا المطلوبفنعبّرنا عنه إيش معنات + +134 +00:10:12,910 --> 00:10:18,090 +every super set for all Y أي مجموعة كبيرة Y تحتوى + +135 +00:10:18,090 --> 00:10:21,750 +الـ X والـ X finite بدا تكون برضه الـ Y infinite + +136 +00:10:21,750 --> 00:10:27,060 +تكون الـ Y infiniteأه فإذن بدنا نثبت هذا الكلام اه + +137 +00:10:27,060 --> 00:10:31,840 +ممتاز for all y هتقوله let y تكون أي super set + +138 +00:10:31,840 --> 00:10:36,480 +فهنبدأ البراني فهذه مهارات ممتازة انه يتعلم let y + +139 +00:10:36,480 --> 00:10:44,130 +be a set such thatأه هي بكتب هيك يا بكتب X subset + +140 +00:10:44,130 --> 00:10:47,090 +إيه اللي بدلون إياها كله اللي بيريحكوا X subset من + +141 +00:10:47,090 --> 00:10:50,150 +ال Y يمكن هذي إحنا متعودين عليها فال Y هي الكبيرة + +142 +00:10:50,150 --> 00:10:53,430 +هي ال super set هي ال Y مطلوب أثبت إن ال Y + +143 +00:10:53,430 --> 00:10:56,830 +infinite إذا إيش مطلوب؟ مطلوب أداة جدال التعريف + +144 +00:10:56,830 --> 00:11:00,110 +اللي هنستخدم من Y ل Y أنا مدشن على ال Y تكون one + +145 +00:11:00,110 --> 00:11:03,430 +to one و تكون اللي هو ال image proper subset + +146 +00:11:03,430 --> 00:11:07,090 +proper subset بحكتب عشان هو ده المثال المهم we + +147 +00:11:07,090 --> 00:11:10,450 +want to find + +148 +00:11:14,120 --> 00:11:17,700 +ع مين بشتغل أنا؟ على ال Y المطلوب أثبت أن ال Y is + +149 +00:11:17,700 --> 00:11:29,200 +infinite من Y ل Y such that G F F is one to one + +150 +00:11:29,200 --> 00:11:37,820 +and صورة ال Y برابر من ال Y برابر من ال Y بدنا + +151 +00:11:37,820 --> 00:11:38,940 +ندور على دالة + +152 +00:11:42,810 --> 00:11:48,770 +فبدنا نعرف الـ F لازم أكتب له let F وعرف و بعدين + +153 +00:11:48,770 --> 00:11:50,750 +نفسي بيتناه one to one و بتحقق الشرطين هدول زي ما + +154 +00:11:50,750 --> 00:11:54,290 +أعمله في مثال ال natural number مين عنده اقتراح + +155 +00:11:54,290 --> 00:11:59,090 +على ان يتعرف لل F اعملوا + +156 +00:11:59,090 --> 00:12:04,450 +عصف ذهني زي ما بيقولوا اقترحواعرفوني ال F بدنا + +157 +00:12:04,450 --> 00:12:08,550 +دالة مناسبة نجرب اه بنجيب دالة هذا نقطة البداية + +158 +00:12:08,550 --> 00:12:13,390 +بدنا نجيب دالة بتحقيق الشرطين بتكون one to one و + +159 +00:12:13,390 --> 00:12:17,210 +إيش و ليست أنتوا اللي هي بتحقيق الشرطين one to one + +160 +00:12:17,210 --> 00:12:21,250 +و ال image proper subset من المجال المقابل طب ما + +161 +00:12:21,250 --> 00:12:24,590 +مثلا انت تفكر ان انا انا انا انا انا انا انا انا + +162 +00:12:24,590 --> 00:12:26,350 +انا انا انا انا انا انا انا انا انا انا انا انا + +163 +00:12:26,350 --> 00:12:26,430 +انا انا انا انا انا انا انا انا انا انا انا انا + +164 +00:12:26,430 --> 00:12:26,770 +انا انا انا انا انا انا انا انا انا انا انا انا + +165 +00:12:26,770 --> 00:12:26,770 +انا انا انا انا انا انا انا انا انا انا انا انا + +166 +00:12:26,770 --> 00:12:31,230 +انا انا انا + +167 +00:12:31,230 --> 00:12:38,810 +اناولا طفاح ولا موز ولا بوردجان؟ مش عارفين، ممتاز، + +168 +00:12:38,810 --> 00:12:41,590 +احنا اللي بده اوصله اليه، لما أنا لسه قالت مش + +169 +00:12:41,590 --> 00:12:44,430 +عارفين ايش عناصر الواد، الواد بقى بجموعة عامة، + +170 +00:12:44,430 --> 00:12:50,830 +عناصرها مش معروفة،بنك دوال ال calculus سكروه + +171 +00:12:50,830 --> 00:12:55,130 +مانفعناش لأن وداك معرف على دوال هيش ريال لريال اه + +172 +00:12:55,130 --> 00:12:59,250 +بدنا نشوف مكان اخر نعرف منه بدنا نشوف مكان اخر + +173 +00:12:59,250 --> 00:13:02,730 +بدنا بنك اخر بنك ال calculus مفلس بالنسبالنا غير + +174 +00:13:02,730 --> 00:13:09,320 +مناسب بدنا ندور على مكان مناسبطيب، من وين نعرف؟ من + +175 +00:13:09,320 --> 00:13:13,800 +وين نعرف؟ إيش في عينكوا؟ في هذا النوع، في الغالب، + +176 +00:13:13,800 --> 00:13:17,480 +بدي أعتمد على دوال معطية في السؤال، في الغالب، هذه + +177 +00:13:17,480 --> 00:13:21,520 +كنصيحة، كإرشاد، بدنا نتعرف على دوال معطية في + +178 +00:13:21,520 --> 00:13:25,080 +السؤال، في عيننا دوال معطية في السؤال؟ إيش مالها + +179 +00:13:25,080 --> 00:13:28,740 +ال X؟ Infinite، إيش معنات Infinite؟ بقدر ألاقي + +180 +00:13:28,740 --> 00:13:32,710 +دالة، في أيه المفتاح؟ آه، هاي هنا، بدي دوالفو بس + +181 +00:13:32,710 --> 00:13:35,230 +واحدة واحدة بس أنا بدي أعرف ده لوحدة ماني بس إذا + +182 +00:13:35,230 --> 00:13:39,050 +ال F معرفة فإذا ال F معرفة هذي هي إيش بيصير عندي + +183 +00:13:39,050 --> 00:13:42,210 +أنا إي حاجة أشتغل عليها خليني أشوف كيف .. طبعا + +184 +00:13:42,210 --> 00:13:45,210 +الأمثلة في البداية فشيء طبيعي أن أنتوا تكونوا بعاد + +185 +00:13:45,210 --> 00:13:48,710 +عنها شوية شوية الأمور تتحسن تمام فانا بدي أدور على + +186 +00:13:48,710 --> 00:13:52,010 +ال F الآن بدي أشوف وين مظادر إذا إحنا بنتعلم هنا + +187 +00:13:53,050 --> 00:13:55,890 +تفكير المجرد تتذكر لما تقول إن احنا عرفنا ال + +188 +00:13:55,890 --> 00:13:58,450 +composition ماعرفناش الجمع أو الطرح للدوال بشكل + +189 +00:13:58,450 --> 00:14:01,670 +عام لإنه مش ضروري كل عناصر بيكون فيها جمع زي هنا + +190 +00:14:01,670 --> 00:14:05,430 +إيش عرفنا إنه 2X معرفة لإن هو مش أرقام إيش معرفنا + +191 +00:14:05,430 --> 00:14:08,810 +إن الجمع معرف ال sign معرفة مش معرفة على ال Y لإن + +192 +00:14:08,810 --> 00:14:11,610 +ال Y مش عارفين إيش عناصرها بشكل عام نشتغل فالآن + +193 +00:14:11,610 --> 00:14:14,930 +هنشوف كيف بنجيب الدالة من المعطيات لإن هو دي معرفة + +194 +00:14:14,930 --> 00:14:18,750 +و هتتكرر معنا فالآن نبدأ نقول له ال gate X أشمالها + +195 +00:14:18,750 --> 00:14:25,400 +is infinite X is infiniteو هذه المهارة حكيناها قبل + +196 +00:14:25,400 --> 00:14:28,300 +ايه عندك معلومات اكتبوها حتى لو بالهمش تشوف انت + +197 +00:14:28,300 --> 00:14:31,880 +إيش عندك إمكانيات و انت دايما عينك وين على المطلوب + +198 +00:14:31,880 --> 00:14:34,860 +هينحطينا المطلوب و نقولنا بندور على جيه دورنا في + +199 +00:14:34,860 --> 00:14:38,000 +دفاضر ال calculus قولنا بتبفع ناس بندور في مكان + +200 +00:14:38,000 --> 00:14:42,380 +آخر فندورش أن مواطيات تفتحنا الباب للحل ولا بتفتحش + +201 +00:14:42,380 --> 00:14:46,160 +اه فال excess finite implies there exist ايش + +202 +00:14:46,160 --> 00:14:51,910 +يسميها ال F مشغول هنسميها اسم جديد جيهمن X ل X + +203 +00:14:51,910 --> 00:15:05,850 +such that G is one to one and G of X برابر من Xهذا + +204 +00:15:05,850 --> 00:15:10,910 +معناه infinite هتطيها في السؤال، هتطيها في الهامش، + +205 +00:15:10,910 --> 00:15:13,110 +هتطيها على الأقل جانبية، لكن هذا مُعطَب، نحاول + +206 +00:15:13,110 --> 00:15:17,630 +نستفيد منه فالآن بنتعلمها دي المهارة، هنعرف الـF + +207 +00:15:17,630 --> 00:15:21,570 +بدلالة الـG كيف؟ نفكر مع بعض، نفكر مع بعض، إحنا + +208 +00:15:21,570 --> 00:15:31,470 +إيش عندنا الصورة؟ عندنا Y كبيرة وفيها X جواهاو جوا + +209 +00:15:31,470 --> 00:15:36,750 +عناصر كل ال Y اللي في ال X معرف عليهم ال G شايفها + +210 +00:15:36,750 --> 00:15:41,390 +معرف عليهم مش معروفة بشكل صريح لكن معرفة معرفة و + +211 +00:15:41,390 --> 00:15:45,610 +بتام عندنا الباقي بتام عندنا الباقي بدنا ياها من Y + +212 +00:15:45,610 --> 00:15:50,730 +ل Y نعمل كمان نسخة من ال Y كمان نسخة من ال Y فبدنا + +213 +00:15:50,730 --> 00:15:55,470 +دالة من hand ل handفانا هعرف .. وانتبه okay بنفكر + +214 +00:15:55,470 --> 00:15:58,570 +عشان نتعرف .. هبدأ أقوله let F مش هيك قلناه .. مش + +215 +00:15:58,570 --> 00:16:01,650 +هيك حلينا natural number .. بدنا نكرر .. هقوله let + +216 +00:16:01,650 --> 00:16:10,010 +F من Y إلى Y be given by .. بدأ أعرف ال F .. by F + +217 +00:16:10,010 --> 00:16:16,830 +of X تساويلو كانت ال X في ال capital X فال G معرف + +218 +00:16:16,830 --> 00:16:24,930 +عليها فهقوله تساوي G of X إذا X وين في ال capital + +219 +00:16:24,930 --> 00:16:29,830 +X ممتازة بتنفعه ولا بتنفعش؟ تنفع لأن ال G هذه + +220 +00:16:29,830 --> 00:16:32,970 +الدالة بتقدر الغرض اشمالها one to one و اشمالها + +221 +00:16:32,970 --> 00:16:38,010 +بتزغر كذا not onto بتزغر الصورة كأنها طيب في عندي + +222 +00:16:38,010 --> 00:16:45,100 +هنا مكان إضافي اللي هو إيش بيمثل هناY ناقص X ما + +223 +00:16:45,100 --> 00:16:49,460 +تبقى لأنه مفهوش .. مفهو .. ده اللي اوقفها من Y ل Y + +224 +00:16:49,460 --> 00:16:53,980 +لازم الناس اللي هيجي تغطي كل ال domain كيف اعرفها؟ + +225 +00:16:53,980 --> 00:16:58,360 +كيف نعرفها؟ X اه .. ايه؟ X من ان اعرفها identity + +226 +00:16:58,360 --> 00:17:02,570 +functionبدنا نعرفه Identity Function ايه اسمه لك + +227 +00:17:02,570 --> 00:17:05,450 +يا حبي؟ نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي + +228 +00:17:05,450 --> 00:17:07,130 +نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي + +229 +00:17:07,130 --> 00:17:07,450 +نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي + +230 +00:17:07,450 --> 00:17:10,410 +نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي + +231 +00:17:10,410 --> 00:17:14,930 +نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي + +232 +00:17:14,930 --> 00:17:16,730 +نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي + +233 +00:17:16,730 --> 00:17:24,410 +نفسي نفسي نفسي نفسي نفسي نفسي نفسي + +234 +00:17:24,410 --> 00:17:30,070 +نفسي نفسي نمش أنتوا لكن أنا إيش عملت مش على كل + +235 +00:17:30,070 --> 00:17:33,790 +اللي عرفتها identity بس على جزء عندي جزء فانا إيش + +236 +00:17:33,790 --> 00:17:37,450 +اللي بده أعمله عشان بس نفكر مع بعض هذا الجزء بديش + +237 +00:17:37,450 --> 00:17:41,510 +أصغره صورته مش هتصغر لإن احنا إيش بنعمل بناخد + +238 +00:17:41,510 --> 00:17:45,170 +المجموعة و بنخلي صورتها أصغر proper subset مظبوط + +239 +00:17:45,170 --> 00:17:47,990 +فكأنه الدالة اللي بتأول عليها هي دالة بتعمل عمل + +240 +00:17:47,990 --> 00:17:52,370 +تصغير للصورة فبالنسبة لل identity هذا الجزء بتنجله + +241 +00:17:52,370 --> 00:17:56,220 +زي ما هو بيصغرهاش لكن مين اللي بيصغراللي جوه ال X + +242 +00:17:56,220 --> 00:17:59,420 +ليه ال G بتقوم بعملية تصغير يكفيني، بتديش كل + +243 +00:17:59,420 --> 00:18:01,940 +الدالة جزء منها، لو جزء منها صغر يكفي، بتقدي + +244 +00:18:01,940 --> 00:18:05,740 +الغرض، فهذه هنثبت أنه بتحقق الشرطين، هنثبت أن هذه + +245 +00:18:05,740 --> 00:18:09,060 +الدالة هي التعريف الصحيح، فبدنا ننتبه، لما نعرف + +246 +00:18:09,060 --> 00:18:11,840 +الدالة، نشوف الدالة ممكن تتعرف ولا لأ، في عنا + +247 +00:18:11,840 --> 00:18:15,320 +مجموعة مجرد عامةلا يمكنني أن أعرف عليها عمليات + +248 +00:18:15,320 --> 00:18:18,560 +حسابية أو أعرف دوال الـ Calculus طيب، من الدوال + +249 +00:18:18,560 --> 00:18:20,360 +التي تنفع أن تتعرف دائما؟ لو Identity تنفع أن + +250 +00:18:20,360 --> 00:18:23,380 +تتعرف دائما، لأنه لا يوجد أي عملية حسابية لأي + +251 +00:18:23,380 --> 00:18:26,160 +مجموعة؟ أو نحن استفدنا من هذا الـL مُعرّف، أيش ما + +252 +00:18:26,160 --> 00:18:29,120 +تكون تكون الـG مُعرّف أصلا استفدنا منها، لنرى هل + +253 +00:18:29,120 --> 00:18:32,360 +هذه تنفع ولا لا تنفع؟ هل هناك أحد عنده الصفصار + +254 +00:18:32,360 --> 00:18:35,380 +متبعين؟ فإذن هذا المفتاح، هذه الصعوبة التي أتكلم + +255 +00:18:35,380 --> 00:18:39,340 +عنها كيف نكون الـF؟ طبعا لسه الأمثلة تتعدد معنا + +256 +00:18:39,340 --> 00:18:39,820 +وشوية ش + +257 +00:18:43,680 --> 00:18:47,020 +أي استفسار؟ متابعين؟ تمام، نثبت إن الـ App هي one + +258 +00:18:47,020 --> 00:18:54,640 +-to-one وإن ليش ليست on فنبدأ .. نعم .. أه بس + +259 +00:18:54,640 --> 00:18:57,220 +بتاخدوا .. تشوفوا مع بعض كيف بيكون، على أنه بتاخد + +260 +00:18:57,220 --> 00:18:59,920 +عنصرين من ال domain طب لو عنصرين ممكن يكونوا في X + +261 +00:18:59,920 --> 00:19:03,000 +و ال G بتحللنا المشكلة، طب لو واحد هنا و واحد هنا، + +262 +00:19:03,000 --> 00:19:05,680 +إيش بيصير؟ هنشتغلها كلها، خليني أنا أخدها واحدة + +263 +00:19:05,680 --> 00:19:10,020 +واحدةخلّيني أخدها واحدة واحدة ده نبدأ خطوة خطوة و + +264 +00:19:10,020 --> 00:19:15,380 +نشوف إيش الاحتمالات والنظرة الأولية بالسهولة صح + +265 +00:19:15,380 --> 00:19:20,300 +ولا مش صح فهيبدأ أثبت أن F is one to one F is one + +266 +00:19:20,300 --> 00:19:24,680 +to one بدنا نثبت طبعا كالعادة هاخد عنصرين من ال + +267 +00:19:24,680 --> 00:19:31,640 +domain let X1 X2 من domain ال F؟ Y فننتبه و نركز + +268 +00:19:31,640 --> 00:19:34,420 +في الحل تنتبه من ال Y such that + +269 +00:19:37,280 --> 00:19:44,720 +F of X1 تساوي F of X2 إيش مطلوب مني؟ مطلوب مني + +270 +00:19:44,720 --> 00:19:48,980 +أثبت إن X1 تساوي X2 هذا هو الهدف تبعي أوصلنا ال F + +271 +00:19:48,980 --> 00:19:53,260 +هنا معرفة بالتجزيق اللي عبارة عن اتحاد يعني اتحاد + +272 +00:19:53,260 --> 00:19:57,520 +إيش؟ يعني or ففي عندي الحقيقة أربع احتمالاتيا + +273 +00:19:57,520 --> 00:20:01,800 +العنصرين مع بعض في الـ X، يا العنصرين مع بعض خارج + +274 +00:20:01,800 --> 00:20:05,400 +الـ X في Y ناقص X، أو واحد دي هو واحد برا، الأول + +275 +00:20:05,400 --> 00:20:08,180 +أو التاني، فعندي أربع احتمالات، أربع احتمالات، + +276 +00:20:08,180 --> 00:20:10,600 +لحقيقة الاحتمالات التانية ممكن أضمهم مع بعض، بس + +277 +00:20:10,600 --> 00:20:12,860 +حتى لو خلينا نكتبهم بالتفصيل، متفرجش كتير، و هم + +278 +00:20:12,860 --> 00:20:15,260 +متشابهين، لأنه احنا قولنا X واحد و X اتنين من + +279 +00:20:15,260 --> 00:20:17,120 +الأول و الأتنين التاني، متفرجش معنا كتير، لكن + +280 +00:20:17,120 --> 00:20:20,720 +خلينا نشتغلهم بالتفصيل، فهذا يؤدي، في عندي أربع + +281 +00:20:20,720 --> 00:20:27,080 +احتمالاتلو كانوا X1 و X2 في الـ Capital X إيش + +282 +00:20:27,080 --> 00:20:30,060 +تعريفهم؟ بدي أستخدم التعريف الآن بس التعريف هيدينا + +283 +00:20:30,060 --> 00:20:32,960 +أربع احتمالات وهذه المهارة هتيجي معنا أكتر من مرة + +284 +00:20:32,960 --> 00:20:35,880 +هذا ال trick اللي هنا بنستخدمه ففي عندنا أربع + +285 +00:20:35,880 --> 00:20:39,620 +احتمالات خلينا نعملهم بيد الشكل عشان مافيش واسعة + +286 +00:20:39,620 --> 00:20:47,280 +فإما تكون G of X1 تساوي G of X2 وقتاش إذا X1 و X2 + +287 +00:20:47,280 --> 00:20:52,170 +وين موجودين؟ في ال Capital Xهي التعريف إذا التنين + +288 +00:20:52,170 --> 00:20:55,990 +مع بعض يوما ال X فإيه ان تعريف ال F ال F بتكون G + +289 +00:20:55,990 --> 00:21:00,190 +لو سمحت هنا فإذا كانت X1 في ال capital X إيش تعريف + +290 +00:21:00,190 --> 00:21:04,590 +ال F؟ G و X2 نفس القضية طيب، الآن لو كانوا التنين + +291 +00:21:04,590 --> 00:21:08,370 +برا طبعا بينهم هدولة كلهم Or لأنها دي هاش اتحاد + +292 +00:21:08,370 --> 00:21:11,150 +فأو لو كانوا التنين برا دي وكنت عارفهم ال identity + +293 +00:21:11,150 --> 00:21:16,390 +X1 تساوي X2 وقتهاش إذا X1 و X2 موجودين في ال Y + +294 +00:21:16,390 --> 00:21:23,220 +ناقص Xأه طبعا كله بينهم R أو طبعا لو كانت X1 في ال + +295 +00:21:23,220 --> 00:21:30,280 +X و X2 في ال Y ناقص X إيش بيكون؟ ال X1 في ال X إيش + +296 +00:21:30,280 --> 00:21:34,340 +تعريف ال F؟ F of X .. G of X1 و ال X2 من برة إيش + +297 +00:21:34,340 --> 00:21:40,500 +بيكون تعريفها؟ X2 نفس القضية لو كانت X2 في ال X و + +298 +00:21:40,500 --> 00:21:45,500 +X1 في ال Y ناقص X بتشبهها إيش بيكون؟ تعريف ال A of + +299 +00:21:45,500 --> 00:21:53,980 +X1 X1و X2 جي و X2 طبعا كله R R R هدولة أربع + +300 +00:21:53,980 --> 00:21:57,620 +احتمالات واحدة منهم بتكون على الأقل صحية واحدة + +301 +00:21:57,620 --> 00:22:04,150 +منهم بتكون صحيةواضحة فهذه دالة يعني هذه ايش نتعلم + +302 +00:22:04,150 --> 00:22:08,810 +منها كيف اثبت انه دالة معرفة بالتيزيق اختراع متعدد + +303 +00:22:08,810 --> 00:22:13,270 +القاعدة كيف اثبت انه one to one كيف اثبت انه one + +304 +00:22:13,270 --> 00:22:18,690 +to one فكل احتمال بديني باش تغلق و بداشه طبعا اخر + +305 +00:22:18,690 --> 00:22:22,710 +احتمال جاهز هدف ان اوصل ان X1 تساوي X2 مظبوط هذا + +306 +00:22:22,710 --> 00:22:25,380 +جاهزأه طبعا عشان بينهم or بينفع أعمل + +307 +00:22:25,380 --> 00:22:28,180 +simplification وأقول ما هي x1 سو x2 وخلصت وجهها + +308 +00:22:28,180 --> 00:22:30,940 +للباقي لأ عشان or مافيش simplification فإيش لازم + +309 +00:22:30,940 --> 00:22:33,800 +نقول عن دي؟ يا contradiction or anything تؤدي + +310 +00:22:33,800 --> 00:22:37,820 +anything أو أيضا بتنسيقون تكافئوا قولوا يطلع x1 سو + +311 +00:22:37,820 --> 00:22:43,810 +x2 أه فهذا يؤدي الآن بدي أكتبهم بالشكل التاليطيب، + +312 +00:22:43,810 --> 00:22:47,730 +هذا الأخير معروف، طيب الأول بتديني برضه X1 تساوي + +313 +00:22:47,730 --> 00:22:53,190 +X2، ليش؟ لأن الـ G is one to one لأن الـ G is one + +314 +00:22:53,190 --> 00:22:56,910 +to one، يمكن أكتبهم بشكل، بنفس الأسلوب أفضل، هذا + +315 +00:22:56,910 --> 00:23:02,250 +يؤدي X1 تساوي X2، ليش؟ لأن الـ G is one to one، + +316 +00:23:02,250 --> 00:23:06,150 +بنفس المنهج، والأخيرة ما أحنا جاهزة، X1 تساوي X2 + +317 +00:23:06,150 --> 00:23:10,630 +لأنه طبعاً R، بدنا نشوف كله R، هذه طبعاً من الأول، + +318 +00:23:10,630 --> 00:23:15,530 +من التعريففيش مشكلة، فهذا الاحتمال الرابع، بدنا + +319 +00:23:15,530 --> 00:23:19,510 +نشوف الاحتمالين التانين إيش بتتوقعوا من الاحتمال + +320 +00:23:19,510 --> 00:23:23,950 +اللي في النص يدونا X1 تساوي X2 ولا Contradiction؟ + +321 +00:23:23,950 --> 00:23:28,790 +هي اللي بنفعلها، إيش بتدونا؟ Contradiction، + +322 +00:23:28,790 --> 00:23:34,390 +Contradiction، ليش؟أه ليش مينفعش هال gate لما يقول + +323 +00:23:34,390 --> 00:23:40,430 +لي x2 بتساوي صورة x1 أه ليش لأن ال g من y متودة من + +324 +00:23:40,430 --> 00:23:44,890 +x ل x فلما يقول x1 في x صورة هو أنك تكون في x هو + +325 +00:23:44,890 --> 00:23:48,230 +x1 ومش بتقول في y نقص x يعني ليست في ال x فده + +326 +00:23:48,230 --> 00:23:50,710 +contradiction فهنا contradiction + +327 +00:23:53,360 --> 00:23:59,240 +Contradiction، ليش؟ أكتبلكوا السبب لأن X2 اللي هي + +328 +00:23:59,240 --> 00:24:08,780 +إيش في الأول تنتمي للـG of X subset من الـX and X2 + +329 +00:24:08,780 --> 00:24:12,320 +لا تنتمي للـX، هاي الـContradiction X2 في الـY + +330 +00:24:12,320 --> 00:24:15,620 +ناقص X، إيش معناته؟ في الـY وليست في الـX، أه + +331 +00:24:15,620 --> 00:24:19,000 +التانية زيها، تشبهها بس العكس، اتضحوا، برضه + +332 +00:24:19,000 --> 00:24:26,640 +Contradiction، لو سمحتواأه ليش؟ لأن X1 تنتمي لصورة + +333 +00:24:26,640 --> 00:24:32,200 +G of X وهي بربع صفر من X و X1 نشمالها لا تنتمي لل + +334 +00:24:32,200 --> 00:24:37,200 +X لأنه إيش بيقول هنا؟ X1 خارج ال X طب X1 صورة .. + +335 +00:24:37,200 --> 00:24:40,600 +صورة G والـ G من وين لوين؟ من X لX، بينفعش تكون + +336 +00:24:40,600 --> 00:24:45,540 +خارج، فcontradiction تمام؟ الآن B or contradiction + +337 +00:24:45,540 --> 00:24:49,180 +or contradiction or B؟ بيدينا B، idempotency + +338 +00:24:49,180 --> 00:24:51,940 +ونظرية واحد سبعة، وهو المطلوب + +339 +00:24:59,060 --> 00:25:07,200 +أه فهنا هذا يؤدي إن X1 تساوي X2 نظرية 1 7 و P or B + +340 +00:25:07,200 --> 00:25:12,760 +تكافئ بي I don't want to answer تمام و هو المطلوب + +341 +00:25:12,760 --> 00:25:18,760 +فإذا أثبتنا نبدأ له one to one thus FG احنا بنشر + +342 +00:25:18,760 --> 00:25:23,440 +على F is one to one أي سؤال + +343 +00:25:26,020 --> 00:25:29,200 +واضح؟ فإذن هذه .. يمكن أول مثال هيمر علينا عدة + +344 +00:25:29,200 --> 00:25:33,020 +أمثلة كيف نثبت إن ده لمتعددة القاعدة إنها one to + +345 +00:25:33,020 --> 00:25:37,400 +one نفس الطريقة نشوف الخطوة التانية بإن نثبت إنها + +346 +00:25:37,400 --> 00:25:42,400 +جاية F of Y برابر من ال Y هذا المطلوب التاني إذا + +347 +00:25:42,400 --> 00:25:49,910 +حبينا نرقم بنرقم مطلوب إيه؟شوفنا في المثال السابق + +348 +00:25:49,910 --> 00:25:53,590 +وفي الملاحظة عشان اثبت ايش مطلوب اثبت ان هناك عنصر + +349 +00:25:53,590 --> 00:25:57,970 +في ال Y غير موجود في ال F of Y خليني اكتبها We + +350 +00:25:57,970 --> 00:26:08,410 +have to find Y تنتمي لل Y and Y لا تنتمي لل F of Y + +351 +00:26:08,410 --> 00:26:13,370 +بدنا عنصر الزيادة بدنا عنصر الزيادة بدنا ندور على + +352 +00:26:13,370 --> 00:26:19,200 +هذا العنصر بدنا ندور على عنصر الزيادةوين الـ G؟ + +353 +00:26:19,200 --> 00:26:22,640 +طبعا في المثال الماضي كنا عارفين أن الصور كلها + +354 +00:26:22,640 --> 00:26:25,380 +زوجية فاخدنا له واحد فرد الواحد تذكروا المثال تبع + +355 +00:26:25,380 --> 00:26:27,860 +المعادرة السابعة طب الآن احنا عارفين الصور ايش + +356 +00:26:27,860 --> 00:26:30,980 +بتكون بالظبط مش عارفين برضه نفس الخضية لما يكون + +357 +00:26:30,980 --> 00:26:35,060 +الشغل عام يطلع المعطيات إيش عندنا معطيات؟ عندنا من + +358 +00:26:35,060 --> 00:26:39,660 +المعطيات أن الـ G of X برابر subset برابر subset + +359 +00:26:39,660 --> 00:26:42,900 +ماعنش تقريبا نفس المجموعة هي عندنا .. إيش الصورة؟ + +360 +00:26:42,900 --> 00:26:48,460 +خلينا نشوفما هيي ال X و F of X وينها؟ جواها ال F + +361 +00:26:48,460 --> 00:26:52,480 +of X بس هيي ال X و هيي ال F of X ال brother subset + +362 +00:26:52,480 --> 00:26:59,300 +وهان ال X ففي عنصرها الزيادة صح؟ من الأول هل هذا + +363 +00:26:59,300 --> 00:27:02,800 +هو بتام عنصر الزيادة؟ الحقيقة نعم هو المرشح + +364 +00:27:02,800 --> 00:27:05,180 +والحقيقة هو اللي بنجح لأنه زي ما قلنا مين اللي + +365 +00:27:05,180 --> 00:27:12,290 +بيظغر ال .. آسف ال G هذي هذي G مش Fمهي أياش + +366 +00:27:12,290 --> 00:27:15,990 +بتنجولها نفسها لإن ال Fاش بتعمل جوا ال X زي ما هي + +367 +00:27:15,990 --> 00:27:20,990 +.. اه زي ما هي فهذه مش صورة أي حد تحت ال G و طب و + +368 +00:27:20,990 --> 00:27:24,030 +ال Fاش بتعمل جوا العنصر X لإن هي بتحرفها G مش + +369 +00:27:24,030 --> 00:27:27,790 +تعرفها G إذا هو هيتمه برضه مش صورة حد اه فحناخد ال + +370 +00:27:27,790 --> 00:27:35,730 +answer ده ال A البرهان since G of capital X برابر + +371 +00:27:35,730 --> 00:27:47,080 +من ال X ايش فيه؟We have X تنتمي للكابتل X and أو + +372 +00:27:47,080 --> 00:27:55,260 +there exist و X شمالها لا تنتمي لل G of X فهذا هو + +373 +00:27:55,260 --> 00:28:01,140 +العنصر اللي بندور عليه خلينا نسميه Y عشان + +374 +00:28:01,140 --> 00:28:05,420 +نطبق مع الكلام اللي تحتهل هذا ال Y اللي بدور عليه؟ + +375 +00:28:05,420 --> 00:28:12,000 +بدنا نثبت إن هو نفسه إنه هو العنصر اللي بدور عليه + +376 +00:28:12,000 --> 00:28:15,360 +هو نفس العنصر اللي بدور عليه فاحنا بدنا نثبت إن + +377 +00:28:15,360 --> 00:28:19,460 +هذا ال Y فعلا ينتمي ل F of Y + +378 +00:28:22,700 --> 00:28:26,320 +هو ينتمي لل Y ولا ينتمي لل F of Y فهنا خلّينا + +379 +00:28:26,320 --> 00:28:31,760 +نحطها claim ادعاء Y هي اللي بدور عليها تنتمي لل Y + +380 +00:28:31,760 --> 00:28:36,480 +and Y لا تنتمي لل F of Y هو العنصر اللي بدور عليه + +381 +00:28:36,480 --> 00:28:39,700 +بدنا نثبت هذا الكلام فنثبت هذا الكلام prove + +382 +00:28:42,620 --> 00:28:46,560 +فهذا الجزئية بس عشان احط البرهان بنطب و نقدر نخرج + +383 +00:28:46,560 --> 00:28:51,880 +تمام اول شئ Y تنتمي ل Y بسهولة لأن ال Y في ال X و + +384 +00:28:51,880 --> 00:28:56,180 +ال X برابر subset من ال X فإذا هنا Y تنتمي ل X + +385 +00:28:56,180 --> 00:29:00,760 +implies Y تنتمي ل Y لإيش؟ لأن X subset من Y من + +386 +00:29:00,760 --> 00:29:03,800 +البداية أخدناها ولا لأ؟ مش هيقولنا هي super set + +387 +00:29:03,800 --> 00:29:09,600 +فدي أخدناها تمام بتام الجزء التاني الجزء التاني + +388 +00:29:09,600 --> 00:29:15,300 +هعمله by contradictionهعمله by contradiction نفترض + +389 +00:29:15,300 --> 00:29:22,280 +ان ال Y في ال F of Y assume Y تنتمي لل F of Y + +390 +00:29:22,280 --> 00:29:27,660 +خلينا بس نتابع الكلام نكون أتوقع هي نفس الخيار + +391 +00:29:27,660 --> 00:29:30,180 +صحيح بس هتأكد عشان ما نروحش بعيد + +392 +00:30:07,060 --> 00:30:16,310 +لأ تابعغالبا الكلام صحيح فال Y تساوي تنتمي لل F of + +393 +00:30:16,310 --> 00:30:20,350 +Y نوصل إلى Contradiction نعمل By Contradiction + +394 +00:30:20,350 --> 00:30:24,570 +prove للجزء هذا By Contradiction و اتعلمنا انه + +395 +00:30:24,570 --> 00:30:27,930 +احنا ممكن ضمن البرهان نعمل اجزاء زي ما بدنا + +396 +00:30:27,930 --> 00:30:32,490 +Contradiction ايش معناه ان ال Y في صورة ال capital + +397 +00:30:32,490 --> 00:30:37,470 +Y ان هي صورة عنصر من ال capital Y Y تساوي F of X + +398 +00:30:38,210 --> 00:30:44,850 +for some x تنتمي للـ y طيب إيش تعريف ال F محيتها + +399 +00:30:44,850 --> 00:30:51,960 +أنا احتماليةفالـ Y يا بتساوي G of X إذا الـ X + +400 +00:30:51,960 --> 00:30:57,440 +تنتمي للـ X أو بتساوي X إذا الـ X تنتمي لمن؟ للـ Y + +401 +00:30:57,440 --> 00:31:01,460 +ناقص X بدنا نثبت أن التنتين احكمالين أور أن + +402 +00:31:01,460 --> 00:31:04,500 +التنتين Contradiction، بنوصل لـ Contradiction طيب، + +403 +00:31:04,500 --> 00:31:10,420 +هل بنفع أن الـ Y تساوي G of X؟ احنا من وين اخترنا + +404 +00:31:10,420 --> 00:31:16,530 +الـ Y؟ الـ Y شمالهاهي لا تنتمي لل G of X فهذا + +405 +00:31:16,530 --> 00:31:20,150 +مستحيل Contradiction اه Contradiction فهذا + +406 +00:31:20,150 --> 00:31:24,670 +Contradiction Or + +407 +00:31:24,670 --> 00:31:30,450 +فده الأول طيب بنفعل Y تساوي X طب ال X .. ايش ال X؟ + +408 +00:31:30,450 --> 00:31:35,850 +وين موجودة ال X؟ ال X موجودة في ال Y و ال X لا + +409 +00:31:35,850 --> 00:31:40,810 +تنتمي لل X ال X لا تنتمي لل X + +410 +00:31:46,070 --> 00:31:52,810 +بنفعش ليش تكون X لأنه لو X تنتمي لل Y ولا تنتمي لل + +411 +00:31:52,810 --> 00:31:57,390 +X بيدينا برضه contradiction لأن ال Y موجودة في ال + +412 +00:31:57,390 --> 00:31:59,650 +X صحيح فهذا برضه contradiction فهذا أيش برضه + +413 +00:31:59,650 --> 00:32:05,700 +contradiction وهو الموضوعفإذن ليش هذا الكلام غير + +414 +00:32:05,700 --> 00:32:09,600 +صحيح؟ لأن ال Y في ال X أصلا، ماينفعش تكون خارج، ف + +415 +00:32:09,600 --> 00:32:13,620 +Y تسوى X لأنه .. طبعا هنا ليش؟ لأن ال Y تنتمي لل + +416 +00:32:13,620 --> 00:32:19,340 +X، طبعا هنا ليش؟ لأن ال Y لا تنتمي لمين؟ لل G of + +417 +00:32:19,340 --> 00:32:24,280 +X، فهنا طبعا هي كل واحدة وسبب تتحدث، وانتهت العمل + +418 +00:32:27,540 --> 00:32:31,420 +طبعاً الأمور شوية زي ما حكينا مش .. مش سالسة أو مش + +419 +00:32:31,420 --> 00:32:35,060 +مباشرة فلكن احنا بنحاول نشوف اللي هو البنية + +420 +00:32:35,060 --> 00:32:38,880 +الأساسية للشغل آه كيبنا نثبت إنها infinite بندور + +421 +00:32:38,880 --> 00:32:42,840 +على دالة وتعلمنا إنه ما زال مجموعة مجردة ماينفعش + +422 +00:32:42,840 --> 00:32:45,660 +أجيب دوال من دوال ال calculus لإنه مش معرفين ممكن + +423 +00:32:45,660 --> 00:32:49,600 +يكونواأه فشوفنا من المعطيات استفدنا جيبنا الدالة F + +424 +00:32:49,600 --> 00:32:54,280 +عرفناها ب G طبعا مش بشكل متطابق تماما كملنا من عنا + +425 +00:32:54,280 --> 00:32:57,580 +وانجحنا اه طبعا فاثبتنا انها one to one وانجحنا + +426 +00:32:57,580 --> 00:33:00,720 +نثبت انها one to one تم ندوي على عنصر زيادة موجود + +427 +00:33:00,720 --> 00:33:03,860 +في المجموع او مش موجود في الصورة ولاجناها من .. + +428 +00:33:03,860 --> 00:33:06,820 +برضه من المعطيات ولاجناها برضه من المعطيات طبعا + +429 +00:33:06,820 --> 00:33:12,010 +اختارناها بشكل مناسب واثبتنا فعلا انهبيحقق الشروط + +430 +00:33:12,010 --> 00:33:15,710 +فطبعا احنا قلنا افترض ان هو صورة بنتظر تقول ده + +431 +00:33:15,710 --> 00:33:19,530 +contradiction مستحيل فطبعا ايش معنى الصورة؟ اه وهي + +432 +00:33:19,530 --> 00:33:23,650 +الاحتمالين طب لو كان G of X بتكون ال Y وين؟ لو + +433 +00:33:23,650 --> 00:33:27,510 +كانت تنتمي لل G of X فده مستحيل و لو كانت X بتكون + +434 +00:33:27,510 --> 00:33:31,330 +وين؟ في ال capital X اه لإيه؟ لأن ال Y بال capital + +435 +00:33:31,330 --> 00:33:35,110 +X و ايش ويش ويش ال Y؟ بقول ايش؟ Y ناقص X مينفعش + +436 +00:33:35,110 --> 00:33:44,150 +فصارت contradictionنشوف فرع بيه السهل فرع بيه هذا + +437 +00:33:44,150 --> 00:33:50,210 +كله ايه طبع نظرية الأولى + +438 +00:33:50,210 --> 00:33:52,650 +بعدين بنعلق على امتحان اخر خلينا نكمل نرجع + +439 +00:33:52,650 --> 00:33:56,970 +الامتحانكل مجزّي من الـ finite set هو finite + +440 +00:33:56,970 --> 00:34:00,610 +خلّيني أولا أحط الجملة لأن البرهان هي تعمل على + +441 +00:34:00,610 --> 00:34:05,170 +السابق بسهولة لأنه عملية negation و هنعملها بشكل + +442 +00:34:05,170 --> 00:34:10,730 +مباشر فخلّيني أشوف هنا البرهان بشكل مشابه let X be + +443 +00:34:10,730 --> 00:34:18,150 +a finite set إيش المطلوب؟ + +444 +00:34:18,150 --> 00:34:26,240 +we have to prove thatنفس العملية الماضية بس اختلاف + +445 +00:34:26,240 --> 00:34:33,440 +انه بدل super set subset for all y such that y + +446 +00:34:33,440 --> 00:34:48,240 +subset من ال X ال Y is finite ال + +447 +00:34:48,240 --> 00:34:56,380 +Y is finite فطبعا كالعادة بدنا نبداش let Ybe a set + +448 +00:34:56,380 --> 00:35:01,800 +such that طبعا عشان for all ال Y subset من ال X + +449 +00:35:01,800 --> 00:35:06,340 +بدنا يثبت ان ال Y finite طبعا زي حتى اللي مر علينا + +450 +00:35:06,340 --> 00:35:09,560 +كل ال finite اللي عملناها by contradiction assume + +451 +00:35:09,560 --> 00:35:13,060 +Y + +452 +00:35:13,060 --> 00:35:18,660 +is infinite افترض + +453 +00:35:18,660 --> 00:35:22,790 +ان ال Y infinite بدنا يفرض ان هذا المستحيلالعملية + +454 +00:35:22,790 --> 00:35:27,930 +بس انتباه انتبهوا ال Y infinite وال X أكبر منها + +455 +00:35:27,930 --> 00:35:30,970 +لازم تكون infinite بالباش بالنظرية توي أثمتناها + +456 +00:35:30,970 --> 00:35:36,710 +الفرع اللي اتصابها أثمتها X is infinite مين دليلي + +457 +00:35:36,710 --> 00:35:44,170 +نظرية خمسة واحد A فرع A طبعا contradiction لأن X + +458 +00:35:44,170 --> 00:35:45,550 +شمالها finite + +459 +00:35:52,200 --> 00:35:56,240 +فهذه برهانة قصيرة جدا بيد السهولة اعتمد على فرع A + +460 +00:35:56,240 --> 00:36:01,160 +فهو المهم ففرع A هو الأساسي + +461 +00:36:01,160 --> 00:36:15,420 +ففرع A هو الأساسي نظرية + +462 +00:36:15,420 --> 00:36:16,060 +5-2 + +463 +00:36:20,810 --> 00:36:24,970 +طبعاً ممكن تستخدميها ممكن تستخدميها مهمة جدا إذا + +464 +00:36:24,970 --> 00:36:28,070 +قدرت تثبت فالجيت انا مثلا لو قالك اثبت ان ال Z + +465 +00:36:28,070 --> 00:36:28,450 +infinite + +466 +00:36:33,450 --> 00:36:36,670 +على طول مباشرة فإن واضح ما زال أثبتنا أن نحن + +467 +00:36:36,670 --> 00:36:40,110 +ماشيين بيد الشكل للحقيقة ليش أثبتنا أن N هي ال + +468 +00:36:40,110 --> 00:36:42,830 +infinite هي أصغر infinite 6 للحقيقة فلجيت ال Z + +469 +00:36:42,830 --> 00:36:45,130 +infinite على طول و ال Q infinite و ال R infinite + +470 +00:36:45,130 --> 00:36:48,310 +كل المجموعات الأكبر منها infinite كلها infinite + +471 +00:36:48,310 --> 00:36:53,210 +على طول هذا كام مثال فهذه نظرية مهمة جداالنظرية + +472 +00:36:53,210 --> 00:36:56,790 +التانية برضه نظرية مهمة طبعاً العنوان العريض الـ + +473 +00:36:56,790 --> 00:37:00,750 +how و لا النتيجة اللي بعده بيقول لي no bijections + +474 +00:37:00,750 --> 00:37:03,810 +أو no bijection between infinite and finite set + +475 +00:37:03,810 --> 00:37:08,450 +مستحيل أقدر ألاجي تناظر بين مجموعتين واحدة finite + +476 +00:37:08,450 --> 00:37:12,010 +واحدة infinite هذا مستحيل نتخيله مع بعض ما هوش + +477 +00:37:12,010 --> 00:37:15,730 +معاه التناظر كل عنصر له نظير في المجموعة التانية + +478 +00:37:15,730 --> 00:37:19,090 +فهذا بيقول ان واش عناصرهم بتكون متساوي لعدد ولا لأ + +479 +00:37:19,090 --> 00:37:21,090 +اه فهو بيقول لي إذا كانت واحدة infinite واحدة + +480 +00:37:21,090 --> 00:37:24,500 +finite مستحيل إذا الكلام يكون صحيحبنشوف كيف بنثبت + +481 +00:37:24,500 --> 00:37:30,400 +هذه الحقيقة النظرية اللي هو بشكل مباشر let G from + +482 +00:37:30,400 --> 00:37:34,870 +X to Y be a one to one correspondenceهذه اسمها + +483 +00:37:34,870 --> 00:37:36,710 +يعني اسم by ejection one to one correspondence هو + +484 +00:37:36,710 --> 00:37:41,470 +المصطلح الآخر بقول إذا X infinite فال Y infinite + +485 +00:37:41,470 --> 00:37:45,170 +فهذه أول جزء من النظرية أنا لجيت one to one + +486 +00:37:45,170 --> 00:37:47,730 +correspondence بين مجموعتين إذا واحدة infinite + +487 +00:37:47,730 --> 00:37:50,450 +التانية لازم تكون infinite طب واحد يقول التانية + +488 +00:37:50,450 --> 00:37:52,830 +جالة إذا كانت ال X infinite فال Y infinite طب + +489 +00:37:52,830 --> 00:37:57,190 +والعكس لو ال F infiniteبرضه صح، ليش؟ لأن الـ F in + +490 +00:37:57,190 --> 00:38:00,090 +a bijection is an F in a G inverse as if G is in a + +491 +00:38:00,090 --> 00:38:02,750 +bijection، G inverse برضه bijection، من Y لأكس، + +492 +00:38:02,750 --> 00:38:06,290 +فالعملية ماشية باتجاهين، بس ودانا اسم العنوان وانت + +493 +00:38:06,290 --> 00:38:10,210 +تطبقي واتعممي، فده هو العنوان الرئيسي، إذا عندي + +494 +00:38:10,210 --> 00:38:13,430 +مجموعتين بينهم bijection، فواحدة Infinite، التانية + +495 +00:38:13,430 --> 00:38:16,410 +لازم تكون Infinite، طبعا بالنسبة يادر اتجاه من X ل + +496 +00:38:16,410 --> 00:38:19,110 +Y، بستخدم الـG كbijection، طب من Y ل X، إيش + +497 +00:38:19,110 --> 00:38:21,450 +هستخدم؟ G inverse، وهي بتكون bijection على طول + +498 +00:38:21,450 --> 00:38:25,200 +النظرية السابقة، فده بس ملاحظة سريعةخلّينا نشوف + +499 +00:38:25,200 --> 00:38:32,880 +البرهة فاحنا بدنا نشوف البرهة وإن + +500 +00:38:32,880 --> 00:38:35,400 +شاء الله بنبني على بعض ما تعلمناه في البرهان + +501 +00:38:35,400 --> 00:38:44,440 +السابق مع بعض الإختلافات القليلة theorem 5-2 + +502 +00:38:44,440 --> 00:38:50,540 +approved طبعا فيه مواطيات let g from a be a + +503 +00:38:50,540 --> 00:38:55,410 +bijection خلّينا نكتبها لإن محتاجينهاlet g من x ل + +504 +00:38:55,410 --> 00:39:00,190 +y be a bijection one to one يعني bijection اتعود + +505 +00:39:00,190 --> 00:39:04,570 +على المصطلح هى اه بقوللي if x is infinite اذا هدا + +506 +00:39:04,570 --> 00:39:11,110 +يشمله الشرط بنفترض ان هو ياش معطق assume x + +507 +00:39:11,110 --> 00:39:20,350 +is infinite ايش مطلوب اثبت ان ال y infinite we + +508 +00:39:20,350 --> 00:39:29,560 +haveto prove Y is infinite تمام + +509 +00:39:29,560 --> 00:39:33,560 +فهذا كل ما بقى دي رياضيات ماعملتش كل هذا معلومات + +510 +00:39:33,560 --> 00:39:37,240 +جديدة معلومات قديمة أسف طيب بدي أثبت أن ال Y + +511 +00:39:37,240 --> 00:39:41,200 +infinite يعني إيش بدي بدي دالة F من Y ل Y one to + +512 +00:39:41,200 --> 00:39:48,120 +one و proper subset we mustFind او have to find a + +513 +00:39:48,120 --> 00:39:58,820 +function F من Y ل Y such that F is one to one and + +514 +00:39:58,820 --> 00:40:05,620 +F ال Y اقرب من ال Y فبد ان هدول الشرطين يتحقق فبد + +515 +00:40:05,620 --> 00:40:06,400 +اعرف ال F + +516 +00:40:09,410 --> 00:40:16,590 +من Y ل Y بي given by هذا ليهيش مفتاح الحل هذا ال + +517 +00:40:16,590 --> 00:40:21,050 +use الأول فكيف + +518 +00:40:21,050 --> 00:40:26,700 +بدنا نعرف ال Fبنفع نجيب من دفاتر ال calculus؟ لأ، + +519 +00:40:26,700 --> 00:40:29,820 +اه هنا نفعي، شوف ده العملية بتدل، لإن ال Y جالي + +520 +00:40:29,820 --> 00:40:34,420 +مجموعة، إيش عناصرها مش عارف، أعداد، مش أعداد، + +521 +00:40:34,420 --> 00:40:38,060 +فواكه، كراسي، مش عارف، مجموعة، أي مجموعة، العمليات + +522 +00:40:38,060 --> 00:40:40,880 +الحسابية معرفة مش معرفة، مش عارف، دهش مشاكل عامة، + +523 +00:40:40,880 --> 00:40:45,010 +إذا أين بده أدور؟في المعطيات عن دوال اتساعدني بدي + +524 +00:40:45,010 --> 00:40:48,650 +ادور عن دوال اتساعدني في دوال في المعطيات نعم قال + +525 +00:40:48,650 --> 00:40:52,510 +لي فيه G قال ليه فيه G بس هنا الصورة مختلفة عن + +526 +00:40:52,510 --> 00:40:57,650 +الصورة الماضية كنا هناك نشتغل في X و Y مجموعة أكبر + +527 +00:40:57,650 --> 00:41:00,370 +منها الآن ال X و Y دولة مش ضرورة تكون سبسط من بعض + +528 +00:41:00,370 --> 00:41:06,130 +بشكل عام فاحنا عندنا الصورة التالية هي في عندنا X + +529 +00:41:06,530 --> 00:41:11,970 +الرسم بيساعد و في عندنا Y و في عندنا G و احنا + +530 +00:41:11,970 --> 00:41:16,030 +بندور على دالة F من Y ل Y نعمل كمان نسخة من Y + +531 +00:41:16,030 --> 00:41:26,050 +بندور على F من Y ل Y بندور على function F من Y ل Y + +532 +00:41:26,050 --> 00:41:31,150 +بدنا انعرفها بشكل مناسب تكون one to one و ليست + +533 +00:41:31,150 --> 00:41:38,810 +انتوا ال G one to one ايش نعمل؟بدنا نعرف الـ F + +534 +00:41:38,810 --> 00:41:43,990 +الأمور أصعب من السابق أصعب من السابق لكن هنا بنشوف + +535 +00:41:43,990 --> 00:41:48,410 +الأمثلة و بن count هنعمل .. مين أداتنا؟ الـ G + +536 +00:41:48,410 --> 00:41:52,190 +اتفقنا؟ إذا إحنا ندور على المعطيات وهي الـ G بدنا + +537 +00:41:52,190 --> 00:41:56,570 +نعمل ال trickبدنا نبدأ من ال Y و بدنا نستخدم ال G + +538 +00:41:56,570 --> 00:42:02,050 +بنفع أبدأ من ال Y مع ال G؟ لأ ال Y .. ال G من وين؟ + +539 +00:42:02,050 --> 00:42:06,250 +من X ل Y لكن ممكن أبدأ بمين؟ بال G inverse بال G + +540 +00:42:06,250 --> 00:42:08,890 +inverse لإن هو دي إيش one two bijection فال + +541 +00:42:08,890 --> 00:42:14,280 +inverse معروف فانا هبدأ من Y في ال G inverseالـ G + +542 +00:42:14,280 --> 00:42:18,900 +inverse وين بيوديني؟ بيوديني على ال X فانا هبدأ من + +543 +00:42:18,900 --> 00:42:24,200 +Y بالـ G inverse ووداني على ال X بدي ارجع لل Y مين + +544 +00:42:24,200 --> 00:42:29,260 +ممكن يرجعني لل Y؟ ممكن يرجعني ال G ممكن يرجعني .. + +545 +00:42:29,260 --> 00:42:34,100 +انا ال G inverse من وين لوين؟ ال G inverse من Y ل + +546 +00:42:34,100 --> 00:42:38,800 +Xأه ممكن ال G ترجعني لل Y بس بكون أنا ليش ماعملتش + +547 +00:42:38,800 --> 00:42:41,980 +إشي أنا بده أروح من Y ل X بكون ليش لأن ال G + +548 +00:42:41,980 --> 00:42:45,120 +inverse مع ال G هذي one to one and unto مابتنفعش + +549 +00:42:45,120 --> 00:42:48,140 +مين اللي بيقوم بعملية التصغير اللي قلنا عنه اللي + +550 +00:42:48,140 --> 00:42:51,880 +بيدينا صورة مش unto ال F فلازم ندخل ال F على الخط + +551 +00:42:52,320 --> 00:42:55,280 +بدنا ندخل الـ F في العملية لأنه قلنا مين اللي + +552 +00:42:55,280 --> 00:42:58,860 +بيصغر فيه دالة بتصغر في العملية بتصغر الصورة الـ F + +553 +00:42:58,860 --> 00:43:04,920 +هندخل الـ F بشكل مناسب مانفعش أبدأ من الـ G مباشرة + +554 +00:43:04,920 --> 00:43:07,660 +بدنا نبدأ بالـ G inverse فهنعرف الـ F بشكل التالي + +555 +00:43:07,660 --> 00:43:13,660 +given by F بدنا ن .. لأ ال F بدنا .. هي اللي بدنا + +556 +00:43:13,660 --> 00:43:18,560 +نعرفها بدنا نعرفها فإيش كيف الـ G في عندنا دالة + +557 +00:43:18,560 --> 00:43:19,320 +أخرة احنا لأ + +558 +00:43:33,720 --> 00:43:39,620 +لسه مش كافي الأمور فلسه الجيل حد مش نافع بدنا ندور + +559 +00:43:39,620 --> 00:43:43,600 +ع كمان دالةبيدنا command دلّة فالـ G لحالة مش + +560 +00:43:43,600 --> 00:43:47,800 +مكافية للتركيز في عندنا command دلّة اه فعندنا + +561 +00:43:47,800 --> 00:43:50,280 +command .. في عندنا command دلّة X is infinite في + +562 +00:43:50,280 --> 00:43:55,060 +command دلّة فالعملية هنا ماضبطتش فالان X is + +563 +00:43:55,060 --> 00:44:00,500 +infinite implies there exist function الجي والاف + +564 +00:44:00,500 --> 00:44:08,800 +موجودين خلينا نسمي اسم جديد H من X ل X such that H + +565 +00:44:08,800 --> 00:44:15,620 +is one to one andH of X برابر من X فالعملية الآن + +566 +00:44:15,620 --> 00:44:20,920 +مختلفة شوية فحستخدم الـH الـH فالآن G inverse + +567 +00:44:20,920 --> 00:44:25,820 +بتودينا من Y لX اللي بيظغر مين الـH أسف مش الـF + +568 +00:44:25,820 --> 00:44:28,280 +اللي أفضل دي المطلوبة صح هي بتظغر بس هذا مطلوب مش + +569 +00:44:28,280 --> 00:44:32,420 +معطف لكن H هي اللي بتظغر بتاخدنا من وين لوين من X + +570 +00:44:32,420 --> 00:44:37,820 +لنفسها من X لنفسها بتدينا H او بعدين الـG بترجعنا + +571 +00:44:37,820 --> 00:44:42,400 +للـY فبكون بدينا من Y ورجعنا للـY فحنعرفالان اه + +572 +00:44:42,400 --> 00:44:45,900 +فهنا يمكن هذه الخطوة هتكون قبل فهذه الخطوة هتيجي + +573 +00:44:45,900 --> 00:44:57,480 +بعد فهقوله هنا let F من Y ل Y be given by F of X + +574 +00:44:57,480 --> 00:45:03,040 +تساوي كيف عرفناها؟ ابدينا بإيش؟ G inverse أول شيء + +575 +00:45:03,040 --> 00:45:08,780 +G inverse بعدين إيش ركبنا؟ H بعدين ركبنا ال G of X + +576 +00:45:10,070 --> 00:45:13,550 +خلّينا .. طبعا ممكن احنا و احنا بنحاول .. بن .. بن + +577 +00:45:13,550 --> 00:45:16,710 +.. بن .. بنخربش، بنعمل مسودة، بنعمل هامش، بنحاول، + +578 +00:45:16,710 --> 00:45:21,410 +نشوف شغلنا صح ولا مش صح الـG inverse ده لأن أيد + +579 +00:45:21,410 --> 00:45:28,410 +الرسمها دي مرة تانية، بطريقة مختلفة بدنا دالة من + +580 +00:45:28,410 --> 00:45:32,450 +واي لوين؟ من واي لواي، نشوف الصورة، بنتعلم هذه + +581 +00:45:32,450 --> 00:45:38,330 +المهارة، فانا بدأت من وايG inverse وين بتوديها؟ ال + +582 +00:45:38,330 --> 00:45:41,630 +X ال G دالة من X ل Y خدت ال inverse تبعها طب ال + +583 +00:45:41,630 --> 00:45:46,470 +inverse exist نعم لأنه الدالة one to one هلجيت من + +584 +00:45:46,470 --> 00:45:51,630 +X طبقت ال H وين وددتها؟ على ال X و طب ليش دخلت ال + +585 +00:45:51,630 --> 00:45:55,830 +H؟ ماوددتكاش مكان جديد خلتك في نفس المحل بس H + +586 +00:45:55,830 --> 00:45:59,410 +بتلعب دور ال H تصغير بتصغر الصورة هي مهمة جدا لإن + +587 +00:45:59,410 --> 00:46:03,470 +هيهاهي اللي بتزغر الصورة بعد هي ايش عملت طبقت الجي + +588 +00:46:03,470 --> 00:46:08,510 +كمان مرة وين رجعتني الجي لل one فالصورة صحيحة + +589 +00:46:08,510 --> 00:46:12,970 +فالصورة صحيحة تم أثبت ان هذه ال F فعلا one to one + +590 +00:46:12,970 --> 00:46:16,450 +و انها ايش و بتدينا الصورة not onto يعني الصورة + +591 +00:46:16,450 --> 00:46:22,750 +أصغر فبنثبت ان ال F one to one و انها بيش بتزغر + +592 +00:46:22,750 --> 00:46:30,150 +الصورة فال Fis one to one هدا واحد هنثبته ويمكن + +593 +00:46:30,150 --> 00:46:36,910 +هدا سهل أعمله بسرعة خل الجزء التاني هو الأصعب + +594 +00:46:36,910 --> 00:46:41,550 +فغالبنا نعمل هذا الجزء السهل فناخد عنصرين let X1 و + +595 +00:46:41,550 --> 00:46:52,190 +X2 في ال Y such that F of X1 تساوي F of X2 بداية + +596 +00:46:52,190 --> 00:46:56,370 +ال one to one كالعادةما يمكننا فعله باستخدام تعريف + +597 +00:46:56,370 --> 00:47:04,770 +الدالة كالعادة فهذا بيقول لي G of H of G of X1 + +598 +00:47:04,770 --> 00:47:13,250 +تساوي G of H of G inverse of X2 مشاكل اللي هو + +599 +00:47:13,250 --> 00:47:19,230 +تعريف الدالة Circle تلاتة مع بعضالان بدي اوصل ان + +600 +00:47:19,230 --> 00:47:24,110 +X1 تساوي X2 هذي ال X1 في عليها اغلفة متعددة تلت + +601 +00:47:24,110 --> 00:47:27,810 +اغلفة بدي احاول انتزعهم واحدة واحدة لحد ما اوصل ان + +602 +00:47:27,810 --> 00:47:32,430 +X1 تساوي X2 بس بنتزعهم بطريقة رياضية صحية كيف + +603 +00:47:32,430 --> 00:47:35,190 +ننتزع ال G؟ + +604 +00:47:36,700 --> 00:47:43,240 +فيه أسهل .. فيه أسهل أن قيمتين الـG and قيمة معينة + +605 +00:47:43,240 --> 00:47:48,140 +Y1 تساوي الـG and Y2 والـG مالها one to one and on + +606 +00:47:48,140 --> 00:47:50,880 +two فبتدينا اللي جوا لازم يساوي اللي جوا .. اه + +607 +00:47:50,880 --> 00:47:57,500 +فهنا على طول يؤدي Hof G inverse of X تساوي H of G + +608 +00:47:57,500 --> 00:48:02,240 +inverse of X2 ليش؟ لأن الـ F أو S في الـ G is one + +609 +00:48:02,240 --> 00:48:06,680 +to one هي one to one and unto نفس الفكرة ما الـ H + +610 +00:48:06,680 --> 00:48:12,720 +برضه one to one فهذا يؤدي إن G inverse of X تساوي + +611 +00:48:12,720 --> 00:48:16,950 +G inverse of X2 لأن الـ H is one to oneطب وال G + +612 +00:48:16,950 --> 00:48:20,590 +inverse برضه one to one نعم لأنه بيجيكشن و هذا + +613 +00:48:20,590 --> 00:48:25,590 +يؤدي ان X1 تساوي X2 لأنه G inverse is one to one + +614 +00:48:25,590 --> 00:48:32,350 +وهو المطلوب تمت جزئية خليها للمرة الجاية لان فيها + +615 +00:48:32,350 --> 00:48:34,990 +صعوبة خلينا نأخر + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/RblLD1z_wGY_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/RblLD1z_wGY_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..938fd75d065d52c5e521b7066a0e81d6da6409f1 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/RblLD1z_wGY_postprocess.srt @@ -0,0 +1,1700 @@ +1 +00:00:19,670 --> 00:00:24,030 +بسم الله الرحمن الرحيم هنواصل مع الأعداد الأصلية + +2 +00:00:24,030 --> 00:00:28,710 +ال cardinal numbers وبشكل خاص مع جمع ال cardinal + +3 +00:00:28,710 --> 00:00:33,190 +numbers فكنا عرفنا ال addition of cardinal number + +4 +00:00:33,190 --> 00:00:37,430 +لو في عندي two cardinal numbers A وB فالصورة + +5 +00:00:37,970 --> 00:00:42,370 +النمطية عنا two cardinal number A and B بدي أجيب + +6 +00:00:42,370 --> 00:00:46,850 +مجموعة تقابل ال cardinal number A و أجيب مجموعة + +7 +00:00:46,850 --> 00:00:50,330 +تقابل ال cardinal number B بحيث أنه تقطعهم يسووا + +8 +00:00:50,330 --> 00:00:56,650 +Phi اه و بعدين بروح باخد ايش A زات B تساوي + +9 +00:00:56,650 --> 00:01:02,170 +cardinality لالاتحاد تحت هذا الشرط اه فهذه هي + +10 +00:01:02,170 --> 00:01:09,230 +الطريقةفكان فينا سؤال منطقي وسؤال علمي أساسي هل + +11 +00:01:09,230 --> 00:01:14,470 +هذا التعريف يعتبر تعريف علمي قابل للتطبيق فهو طبعا + +12 +00:01:14,470 --> 00:01:17,330 +بيقول عشان انت تجيب الجامعة بدك تجيب مجموعتين A و + +13 +00:01:17,330 --> 00:01:21,470 +B تعطوهم Phi و بعدين تجيب الاتحاد طب أنا لو أداني + +14 +00:01:21,470 --> 00:01:24,130 +أي two cardinal numbers بقدر أجيب المجموعتين A و B + +15 +00:01:24,130 --> 00:01:27,770 +بعد الشروط فكان عن نظرية نعم بقدر أجيب نقطة تانية + +16 +00:01:28,860 --> 00:01:32,720 +إنسان آخر جاب مجموعتين مختلفتين لأنه ماحددش إن + +17 +00:01:32,720 --> 00:01:35,480 +هدولة مش unique الـA والـB طب بيختلف الجواب قال + +18 +00:01:35,480 --> 00:01:39,320 +للا فبهذه الحالة إن هذا فعلا تعريف علمي لأ دايما + +19 +00:01:39,320 --> 00:01:42,040 +في إمكانية أن أطبقه إذا ما بقدر أجيب الـA والـB + +20 +00:01:42,040 --> 00:01:45,920 +تاني شغلة لو اختلف التطبيق من إنسان لإنسان تحت + +21 +00:01:45,920 --> 00:01:48,420 +الشروط نفسه بيطلع الناتج نفسه لو بعتمد مش على + +22 +00:01:48,420 --> 00:01:50,940 +الإنسان اللي بيعمل عملية وإنما بعتمد على الشروط + +23 +00:01:50,940 --> 00:01:54,540 +طبعته فده يعتبر تعريف علمي صحيح وبنقول إن هذا ال + +24 +00:01:54,540 --> 00:01:57,960 +addition أشمله is well defined تعريف علمي صحيحفهذه + +25 +00:01:57,960 --> 00:02:00,900 +كانت نظرية 6 3 الآن خلّيني نشوف بعض الأمثلة و + +26 +00:02:00,900 --> 00:02:04,900 +نتقدّم في الموضوع نبدأ بمثال بسيط جدا بقول find + +27 +00:02:04,900 --> 00:02:08,080 +the cardinal sum طبعا تلاتة زائد خمسة ماعرفش أقول + +28 +00:02:08,080 --> 00:02:14,630 +تلاتة زائد خمسة لو عملناها معداد صحيحة أوحقيقية طب + +29 +00:02:14,630 --> 00:02:16,890 +لو عملناهم ك cardinal number التلاتة cardinal + +30 +00:02:16,890 --> 00:02:19,370 +number نعم و الخمسة cardinal number نعم لأنه + +31 +00:02:19,370 --> 00:02:21,590 +يقولنا أيش ال cardinal number الصفر و كل الأعداد + +32 +00:02:21,590 --> 00:02:24,850 +الطبيعية و طبعا في اللي هو ال transfinite cardinal + +33 +00:02:24,850 --> 00:02:27,490 +number اللي بقابل المجموعات ال infinite set + +34 +00:02:27,490 --> 00:02:30,770 +فبقوللي ك cardinal number نجيب التلاتة و الخمسة + +35 +00:02:30,770 --> 00:02:35,710 +أنا هنا مثال بسيط جدا بس بدنا نوضعاللي هو إيش نعمل + +36 +00:02:35,710 --> 00:02:39,910 +.. نكرس الفكرة فاحنا عندنا هنا الـ A بتساوي تلاتة + +37 +00:02:39,910 --> 00:02:43,470 +والـ B بتساوي خمسة، مظبوط؟ نعم، بدنا A زائد B، + +38 +00:02:43,470 --> 00:02:48,050 +solution فبدنا نجيب مجموعة فيها تلت عناصر، مجموعة + +39 +00:02:48,050 --> 00:02:51,590 +فيها خمس عناصر، تقاطحهم بيساوي فاي، و هي نجيب + +40 +00:02:51,590 --> 00:02:57,690 +الاتحاد، فطبعا إيش ناخد؟ واحد، اتنين، تلاتة، + +41 +00:02:57,690 --> 00:03:03,150 +التفكير بكل بساطة، مية لمية، بدنا الآن B أحسنتي + +42 +00:03:04,160 --> 00:03:11,560 +خمسة، ستة، سبعة، تمانية، تسعة خمسة، ستة، سبعة، + +43 +00:03:11,560 --> 00:03:18,080 +تمانية، تسعة خمسة، + +44 +00:03:18,080 --> 00:03:22,480 +ستة، سبعة، تمانية، تسعة خمسة، + +45 +00:03:22,480 --> 00:03:27,760 +ستة، سبعة، تمانية، تسعة خمسة، + +46 +00:03:27,760 --> 00:03:32,540 +ستة، سبعة، تمانية، تسعةبقى لأ بس عشان تكون سهولة + +47 +00:03:32,540 --> 00:03:40,340 +صح صح فطبعا then ال cardinality لل a تساوي تلاتة + +48 +00:03:40,340 --> 00:03:45,820 +ال cardinality لل b تساوي خمسة و ايش كمان و a + +49 +00:03:45,820 --> 00:03:51,140 +تقاطع ال b بيساوي fiveفبالتالي اللي هو تلاتة زائد + +50 +00:03:51,140 --> 00:03:56,140 +خمسة بديه يساوي ال cardinality للاتحاد A union B + +51 +00:03:56,140 --> 00:04:01,260 +وهو ايش بتساوي؟ واحد اتنين تلاتة اربع خمسة ستة + +52 +00:04:01,260 --> 00:04:04,700 +سبعة تمانية وبالتالي ايش بيساوي اه طبعا ال + +53 +00:04:04,700 --> 00:04:11,600 +cardinality لهذا الكلام هو يساوي تمانية فهذه هي + +54 +00:04:11,600 --> 00:04:14,900 +الفكرة تماما اللي هو كيف بنعلم اي طفل صغير كيف + +55 +00:04:14,900 --> 00:04:20,230 +بنعلمه يجمعبشكل بسيط فهذا هو كيف طبقنا التعريف + +56 +00:04:20,230 --> 00:04:26,250 +فهذا بس مثال مباشر كيف ممكن نطبق التعريف تمام + +57 +00:04:26,250 --> 00:04:30,270 +جالما نبدأ بالأمثلة الحقيقية اللي بدأ شغل نشوف + +58 +00:04:30,270 --> 00:04:35,040 +فيها نظرية ببعض الخواصطبعا ده عملية دائما في + +59 +00:04:35,040 --> 00:04:37,460 +الرياضيات إذا فيها عملية بنسأل هل عملية دي + +60 +00:04:37,460 --> 00:04:41,140 +إبدالية؟ هل إلها خاصية التجميع؟ هل إلها خاصية + +61 +00:04:41,140 --> 00:04:44,500 +التوزيع؟ إذا فيها عملية أخرى مع حواها؟ كذا أسئلة + +62 +00:04:44,500 --> 00:04:48,020 +طبيعية موجودة في معظم مواضيع الرياضيات فبقول + +63 +00:04:48,020 --> 00:04:51,360 +addition of cardinal number is commutative الخاصية + +64 +00:04:51,360 --> 00:04:55,760 +الإبدال and associative وخاصية التجميع طبعا + +65 +00:04:55,760 --> 00:04:59,000 +التجميع مهم جدا لأنه بتفتح الباب أنه أنا هنا بجمع + +66 +00:04:59,000 --> 00:05:02,490 +عددين وممكن أجمع تلاتة عن طريق التجميع وها كذاطبعا + +67 +00:05:02,490 --> 00:05:07,750 +نص النظرية let x, y and z be arbitrary cardinal + +68 +00:05:07,750 --> 00:05:12,570 +numbers أي أعداد أصلية أولا عملية الإبدال + +69 +00:05:12,570 --> 00:05:17,390 +commutativity x زائد y تصيب y زائد x بدون أي مشاكل + +70 +00:05:17,390 --> 00:05:20,010 +تبدأ من التلاتة تبدأ من الخمسة تطلع الجهة التامنية + +71 +00:05:20,940 --> 00:05:27,540 +B associativity لخاصية التجميع بدي أجمع تلت أعداد + +72 +00:05:27,540 --> 00:05:31,560 +X Y و Z أجمع الأول و التاني و الناتج مع التالت أو + +73 +00:05:31,560 --> 00:05:34,720 +التاني مع التالت و الناتج مع الأول كله نفس الشيء + +74 +00:05:34,720 --> 00:05:40,720 +خلينا نشوف البرهان مع بعض نظرية + +75 +00:05:40,720 --> 00:05:47,660 +6-4 prove نبدأ بالفرع الأولطبعا هنا اللي بدنا نأكد + +76 +00:05:47,660 --> 00:05:50,260 +عليه نفس الطريقة اللي نشتغل عليها عشان أبدأ أجمع + +77 +00:05:50,260 --> 00:05:53,220 +بدحولها من لغة ال cardinal number إلى لغة + +78 +00:05:53,220 --> 00:05:56,560 +المجموعات واستفيد من معلوماتي في chapter 5 و فيما + +79 +00:05:56,560 --> 00:06:01,900 +سبق و عشان إيش أخد المعلومات فطبعا هنا بالنسبة + +80 +00:06:01,900 --> 00:06:10,580 +للأول عندنا x و y فنقول له let x و y be sets such + +81 +00:06:10,580 --> 00:06:17,960 +that تقطعهم يساوي فيوإيش كمان؟ وإن الـ X بتساوي + +82 +00:06:17,960 --> 00:06:21,740 +الـ cardinality للـ capital X مثلاً و ال small y + +83 +00:06:21,740 --> 00:06:26,800 +بتساوي ال cardinality لل capital Y عشان أبدأ أشتغل + +84 +00:06:26,800 --> 00:06:30,060 +اه then فاحنا أول شي بدنا نبدأ نشتغل على مجموعة + +85 +00:06:30,060 --> 00:06:35,340 +أنا بعرف إن X زائد Y إيش بتساوي؟ cardinality لل X + +86 +00:06:35,340 --> 00:06:41,280 +إتحاد ال Y مظبوط؟ هاي البدايةإيش بدنا نعمل؟ بدنا + +87 +00:06:41,280 --> 00:06:44,720 +نبدّل مين من كنا نبدّل؟ الاتحاد لإن الاتحاد في + +88 +00:06:44,720 --> 00:06:50,060 +المعلومات السابقة فهذه تساوي ال cardinality لل Y + +89 +00:06:50,060 --> 00:06:54,300 +اتحاد ال X مين دليلنا؟ إن الاتحاد commutative لإن + +90 +00:06:54,300 --> 00:06:59,380 +اتحاد المجموعات commutative اللي هو Union is + +91 +00:06:59,380 --> 00:07:04,880 +commutative طبعا طبعا طبقا للتعريف هي Y و X + +92 +00:07:04,880 --> 00:07:09,300 +تخطوحهم بسوء فائزة وهذه عبارة عن أيش؟ Y زي X بكل + +93 +00:07:09,300 --> 00:07:14,830 +بساطةفبكل بساطة الموضوع حولته من موضوع جديد لموضوع + +94 +00:07:14,830 --> 00:07:20,030 +قديم استخدمت معلومات قديمة و أثبتت المعلومة لجديدة + +95 +00:07:20,030 --> 00:07:27,430 +نشوف عملية اللي هو associativity ليهخصية التجميع + +96 +00:07:27,430 --> 00:07:31,150 +بس هنا عشان تلاتة نشوف كيف نشتغل مع التلاتة مع بعض + +97 +00:07:32,960 --> 00:07:37,080 +فبدنا تلت مجموعات هذا بي .. لا أسف واحد واثنين + +98 +00:07:37,080 --> 00:07:47,540 +الأرقام مش مشكلة نلتزم فهنقول let X, Y and Z مثلا + +99 +00:07:47,540 --> 00:07:51,520 +ب 6 such that + +100 +00:07:55,570 --> 00:07:58,810 +كل تنتين مع بعض يكون في عشان انا اجمع كل تنتين مع + +101 +00:07:58,810 --> 00:08:04,710 +بعض فبدي x تقاطع ال y يساوي اللي هو x تقاطع ال z + +102 +00:08:04,710 --> 00:08:10,710 +يساوي y تقاطع ال z يساوي في كل تنتين في مع بعض لان + +103 +00:08:10,710 --> 00:08:14,540 +بالاخر انا بدي اجيب تلاتة في عندي تلت تلتمجموعة + +104 +00:08:14,540 --> 00:08:18,620 +فيها تلت عناصر والتانية أربعة والتالتة خمسة بدي + +105 +00:08:18,620 --> 00:08:21,240 +أجمعهم كلهم عن بعض ليش ولا عنصر يتكرر ولا ماتن تان + +106 +00:08:21,240 --> 00:08:24,960 +مش شرط يكون مش شرك للتلتة لأ بديهم كلهم يكونوا + +107 +00:08:24,960 --> 00:08:29,720 +disjoint منفصلين عن بعض طبعا لسه كمان بي such that + +108 +00:08:29,720 --> 00:08:36,820 +and cardinality لكبتل X بتساوي small x cardinality + +109 +00:08:36,820 --> 00:08:42,240 +لكبتل Y بتساوي small y cardinality ل Z تساوي small + +110 +00:08:42,240 --> 00:08:53,230 +zتمام الآن then نبدأ من طرف X زائد Y زائد Z إيش + +111 +00:08:53,230 --> 00:08:57,350 +بتساوي طبقا لهذا التعريف طبعا أنا لازم أجيب ال Y + +112 +00:08:57,350 --> 00:09:04,830 +زائد Z أولا فده عبارة عن cardinality لل X اتحاد من + +113 +00:09:04,830 --> 00:09:06,810 +Y اتحاد ال Z + +114 +00:09:10,060 --> 00:09:15,100 +طبعا هنا بس كملاحظة بما انه تقطع ال X مع ال Y يعني + +115 +00:09:15,100 --> 00:09:18,780 +هاد ممكن يعملها كأنها مجموعة A بما انه هاد تقطعها + +116 +00:09:18,780 --> 00:09:21,820 +مع ال Y Phi و مع ال Z Phi برضه تقطعها مع الاتحاد + +117 +00:09:21,820 --> 00:09:25,260 +Phi بقدر أشتغل عليها بدل شكل فكل الشروط متحقق خلاص + +118 +00:09:25,260 --> 00:09:29,180 +الآن نستخدم ال associative لمن؟ لل union فده + +119 +00:09:29,180 --> 00:09:34,380 +بتساوي cardinality لل X union Y مع بعض بعدين مع ال + +120 +00:09:34,380 --> 00:09:38,720 +Z لأنه ال union is associative + +121 +00:09:41,410 --> 00:09:51,370 +خلصنا وهذا يساوي X زائد Y زائد Z لا يساقل فإذا هذه + +122 +00:09:51,370 --> 00:09:55,330 +العملية مع ال cardinal number من حصن الحظ تتمتع + +123 +00:09:55,330 --> 00:09:58,770 +بالخواص الطبيعي اللي احنا متعودين عليها وهي ليش + +124 +00:09:58,770 --> 00:10:05,590 +الإبدال والتجميل أي سؤالجال ما نبدأ في الأنثى اللي + +125 +00:10:05,590 --> 00:10:08,830 +فيها عنها بعض الرموز متعارف عليها مشهورة فاحنا + +126 +00:10:08,830 --> 00:10:13,550 +طبعا عندنا أشهر infinite set هي الـN فطبعا + +127 +00:10:13,550 --> 00:10:16,310 +الـcardinality تبعيتها عبارة عن transfinite number + +128 +00:10:16,310 --> 00:10:20,790 +بدنا نديله رمز طبعا بيقدرش يقدي من الأعداد اللي + +129 +00:10:20,790 --> 00:10:24,290 +بنعرفه مافيش عدد حقيقي لأنه infinite فبنديله رمز + +130 +00:10:24,290 --> 00:10:28,810 +فهذا الرمز هانعمله هذا الرمز اللي قدامكوا يقرأ ألف + +131 +00:10:28,810 --> 00:10:33,860 +null هذا الحرف طبعا بنكتب بهذا الشكلحرف مائل هيك + +132 +00:10:33,860 --> 00:10:37,320 +زي هي طبعا تشبه ال X لكن بتنكتبش بدا الشكل لإن + +133 +00:10:37,320 --> 00:10:41,340 +بتنكتبها دولة منفصلين زي ال X بيسموها ألف null و + +134 +00:10:41,340 --> 00:10:43,820 +أتوقع أن هو ده إيش باللغة العبرية اللي هدا الحرف + +135 +00:10:43,820 --> 00:10:48,320 +الحرف الألف باللغة العبرية ألف null تقرأ إنه طبعا + +136 +00:10:48,320 --> 00:10:51,800 +zero اللي هو إيش أو null تقرأ بدا الشكل فده هو ال + +137 +00:10:51,800 --> 00:10:55,530 +cardinality هنديله هذا الرمز هنديله هذا الرمزعشان + +138 +00:10:55,530 --> 00:10:58,130 +نتعامل معاه، هنتعامل معاه كتير لإنه من المجموعات + +139 +00:10:58,130 --> 00:11:02,030 +الأساسية يعني هو من أشهر الاتمين لـ Transfinite + +140 +00:11:02,030 --> 00:11:05,910 +Cardinal Number من أشهر الأعداد الأصلية غير + +141 +00:11:05,910 --> 00:11:09,850 +المنتهية، غير المنتهية في كمان رمز الـR برضه + +142 +00:11:09,850 --> 00:11:12,750 +مجموعة مهمة لإنه هي أول مجموعة non-denumerable هي + +143 +00:11:12,750 --> 00:11:15,870 +أول مجموعة أو أشهر مجموعة non-denumerable هنديها + +144 +00:11:15,870 --> 00:11:19,970 +حرف small c طبعا small c مر علينا كتير نستخدم، مش + +145 +00:11:19,970 --> 00:11:22,910 +حرف يعني غريبأه طبعا استخدمناها لـ Contradiction + +146 +00:11:22,910 --> 00:11:25,250 +استخدمناها في أشياء أخرى نستخدمها أحيانا بشكل + +147 +00:11:25,250 --> 00:11:28,090 +عشوائي أه لكن هنا بتكون طبعا واضح من السياق إيش + +148 +00:11:28,090 --> 00:11:31,270 +اللي بيرمزله طب ليش اختار حرف الـC من كلمة + +149 +00:11:31,270 --> 00:11:35,250 +continuum continuum continuum أه ليش continuum من + +150 +00:11:35,250 --> 00:11:40,090 +خواص الأعداد الحقيقية أن خط الأعداد هذا ماله إيش + +151 +00:11:40,090 --> 00:11:45,550 +ماله بيسموه مستمر مافيش فيه ولا فراغ أي نقطة على + +152 +00:11:45,550 --> 00:11:50,370 +خط الأعداد تمثل عدد حقيقيمن خواص الأعداد الحقيقية + +153 +00:11:50,370 --> 00:11:55,710 +وهذا يجعله مكتار جداً كل نقطة على قط الأعداد تمثل + +154 +00:11:55,710 --> 00:11:59,110 +أعداد حقيقية جد ما نجيب لو جيبنا أكبر مايكروسكوب + +155 +00:11:59,110 --> 00:12:03,490 +كل نقطة أعداد حقيقية فهذه ميزة من ميازة الأعداد + +156 +00:12:03,490 --> 00:12:05,910 +الحقيقية وهذا اللي خلّى الأعداد الحقيقية هي + +157 +00:12:05,910 --> 00:12:09,070 +المناسبة إن نشغل calculus نشغل limit ونشغل تفاضل + +158 +00:12:09,070 --> 00:12:13,610 +ماينفعش نشغل على الـQ ماينفعش نشغل على الـZ الـR + +159 +00:12:13,610 --> 00:12:17,290 +لأن كل وين ما تمشي فيه أعداد حقيقيةأه فدي مهمة جدا + +160 +00:12:17,290 --> 00:12:22,350 +فمن كلمة continuum هناخد حرف الـC فإذا هدولة على + +161 +00:12:22,350 --> 00:12:25,490 +اتراك اتنين cardinal number مشهورين، اتنين + +162 +00:12:25,490 --> 00:12:28,610 +infinite لكن مختلفين عن بعض طبعا مين أكبر من مين + +163 +00:12:28,610 --> 00:12:33,530 +الـC أكبر من ألف null، هنتعامل معه تمام، المثال + +164 +00:12:33,530 --> 00:12:38,690 +الأول، بدنا نجيب هدولة من صراع أعداد، نتعود عليهم + +165 +00:12:38,690 --> 00:12:44,320 +ألف null زائد ألف nullبدنا نجيب مجموع هدولة + +166 +00:12:44,320 --> 00:12:50,480 +العددين ال cardinal number تمام فخلينا نبدأ نفكر + +167 +00:12:50,480 --> 00:12:57,920 +مع بعض و نشوف كيف بدنا نحل ايش تتوقع الجواب ال if + +168 +00:12:57,920 --> 00:13:04,520 +not احسنته تمام فهذا المثال الاول solution ايش + +169 +00:13:04,520 --> 00:13:10,170 +بدنابدنا مجموعتين، كل مجموعة الـ Cardinal تلها ألف + +170 +00:13:10,170 --> 00:13:14,570 +null لكن تقطوحهم بيسووا five مين مجموعات الـ + +171 +00:13:14,570 --> 00:13:18,010 +Cardinal number اللي هالف null؟ الـ N أشهر واحدة و + +172 +00:13:18,010 --> 00:13:21,990 +الـ Z و الـ Q و N cross N زي بدكم و Uneven و + +173 +00:13:21,990 --> 00:13:25,350 +Unequal بس احنا بدنا نختار تنتين من هدول تقطوحهم + +174 +00:13:25,350 --> 00:13:29,460 +بيسووا fiveالـ even و الـ odd بنفعش أخد n و z + +175 +00:13:29,460 --> 00:13:32,580 +تقطعهم بيسويش five ولا n و q ولا n و z فحناخد ال + +176 +00:13:32,580 --> 00:13:40,400 +even و ال odd فحقوله هنا let اله يش a تساوي n even + +177 +00:13:40,400 --> 00:13:44,840 +إذا بنذكركوا إياها هي عبارة عن اتنين n such that n + +178 +00:13:44,840 --> 00:13:52,510 +تنتمي للn الإعداد الطبيعية الزوجية andB تساوي N O + +179 +00:13:52,510 --> 00:13:59,050 +اللي هي أعدادها 2 N زائد 1 أو ناقص واحد بحيث N + +180 +00:13:59,050 --> 00:14:01,270 +تنتمي للـ N تبدأ من الواحد اللي هي الـ A تبدأ من + +181 +00:14:01,270 --> 00:14:05,110 +الـ O طبعا على طول هدول المجموعتين هتروحوا في الـ + +182 +00:14:05,110 --> 00:14:08,690 +Phi ولا في عدد زوج وفرد مع بعض؟ لأ مافيش اه طبعا + +183 +00:14:08,690 --> 00:14:17,650 +and ال cardinality للـ A تساوي ال cardinalityللـ N + +184 +00:14:17,650 --> 00:14:20,930 +و تساوي ألف null على طول لأن الـ Denimrable + +185 +00:14:20,930 --> 00:14:24,930 +أثبتناها صح لأنها infinite subset من Denimrable كل + +186 +00:14:24,930 --> 00:14:27,710 +infinite subset من Denimrable Denimrable مستحيل و + +187 +00:14:27,710 --> 00:14:30,030 +مافيش أصغر من Denimrable او ايش كمان و ال + +188 +00:14:30,030 --> 00:14:35,210 +cardinality لل B بتساوي ال cardinality لل N أيضا + +189 +00:14:35,210 --> 00:14:39,950 +بتساوي ألف null إذن فده هي المنهج اللي متبعينه + +190 +00:14:39,950 --> 00:14:48,670 +جيبنا مجموعتين تحتهم Phiوكل عدد مجموعة تقابل فأصبح + +191 +00:14:48,670 --> 00:14:53,350 +الف null زاد الف null بيساوي ال cardinality لمن؟ + +192 +00:14:53,350 --> 00:14:59,090 +لل A union B للاتحاد او هذا ايش بيساوي؟ بيساوي ال + +193 +00:14:59,090 --> 00:15:04,650 +cardinality لل un even اتحاد ال N O اللي هي ليس + +194 +00:15:04,650 --> 00:15:10,970 +الا N أحسنتي بتساوي ال cardinality لل N وتساوي من؟ + +195 +00:15:10,970 --> 00:15:14,930 +الف nullالذن الف null زي الف null بتساوي الف null + +196 +00:15:14,930 --> 00:15:18,610 +وهذا شيء مش غريب المفروض يكون عندنا ليش infinite + +197 +00:15:18,610 --> 00:15:22,030 +زي infinite تساوي infinity غير لكن لو جالنا مثلا + +198 +00:15:22,030 --> 00:15:26,250 +واحد زي واحد اتنين بيسويش واحد لكن عشان انه + +199 +00:15:26,250 --> 00:15:32,530 +infinite بيطلع نفس العدد نشوف + +200 +00:15:32,530 --> 00:15:41,940 +كمان مثال بيقول اي او جد الف null زي Cالف نل زائد + +201 +00:15:41,940 --> 00:15:45,240 +C هدول two cardinal number تو اتعرفنا عليهم فدول + +202 +00:15:45,240 --> 00:15:49,400 +اعداد ادنا لها مرموز عشان هنبدأ نشتري عليهم بدنا + +203 +00:15:49,400 --> 00:15:54,180 +نجيب الالف نل مع نفسها الان الف نل مع ال C بدنا + +204 +00:15:54,180 --> 00:16:00,240 +مجموعتين solution مجموعة تكون الف null ال cardinal + +205 +00:16:00,240 --> 00:16:03,700 +تتبعتها والتانية ال cardinal تتبعتها الهايه ال C + +206 +00:16:03,700 --> 00:16:09,300 +تقطوحهم بيساوي five هذا مثال رقم اتنينأه طبعا مين + +207 +00:16:09,300 --> 00:16:11,800 +بنعرف إن الcardinality لها ألف نال اكتار طوى + +208 +00:16:11,800 --> 00:16:16,820 +وقولناهم N even, N odd, N zq و هكذا طب مين + +209 +00:16:16,820 --> 00:16:20,940 +الcardinality لها C؟ ال R و إيش غيرها؟ أي open + +210 +00:16:20,940 --> 00:16:24,320 +interval أي open interval أصلا احنا مين النظرية + +211 +00:16:24,320 --> 00:16:27,520 +اللي أثبتناها C؟ أثبتناها ع 01 ع 01 أثبتناها بعدين + +212 +00:16:27,520 --> 00:16:31,080 +قولنا إن ال R تكافئها فهي non-denominable أه طيب + +213 +00:16:31,080 --> 00:16:37,570 +مين ناخد؟الفترة مفتوحة تقاطعها مع الـ N فاي مافيش + +214 +00:16:37,570 --> 00:16:39,850 +ولا عدد بين الصفر و بين ال one فهنا دول هناخد + +215 +00:16:39,850 --> 00:16:45,150 +التنتين هدول فهنقول له let .. خلّيني نكتب مع بعض + +216 +00:16:45,150 --> 00:16:50,130 +and بي + +217 +00:16:50,130 --> 00:16:55,810 +مع الكتابة بتوضح للي مش واضحانه then أول شيء ايه + +218 +00:16:55,810 --> 00:16:59,800 +تقاطع ال بي بسوا فاي ولا لأ؟مافيش ولا عدد طبيعي + +219 +00:16:59,800 --> 00:17:02,960 +بين الصفر و الواحد هذا مفتوح اه مافيش ولا عدد + +220 +00:17:02,960 --> 00:17:06,200 +طبيعي لإنه ايش العداد واحد اتنين و هكذا اه فده أول + +221 +00:17:06,200 --> 00:17:12,380 +حاجة طبعا add طبعا ال cardinality لل a ألف null + +222 +00:17:12,380 --> 00:17:18,480 +مظبوط اه و ال cardinality لل b بتساوي c ليش لأن + +223 +00:17:18,480 --> 00:17:24,080 +هذه تكافئ ال Rتساوى C السبب لأن الـ 01 تكافئ الـ + +224 +00:17:24,080 --> 00:17:26,840 +real number هذا بيحتمل عليها كتير الـ 01 هذا مثال + +225 +00:17:26,840 --> 00:17:30,420 +نموذج جيد نتعامل معاه نموذج جيد نتعامل معاه هو + +226 +00:17:30,420 --> 00:17:32,960 +والـ R هنروح عليهم طبعا أي open interval بقدر + +227 +00:17:32,960 --> 00:17:36,020 +الغرض بس هذا إيه ميزة إيه ميزة لأنه بيريحنا أي + +228 +00:17:36,020 --> 00:17:41,080 +تقاطع ما الآن بيساوفها إذاً thus بالنسبة عنا إيش + +229 +00:17:41,080 --> 00:17:45,180 +بده هو ألف null زائد C ألف null زائد C بتساوى ال + +230 +00:17:45,180 --> 00:17:49,760 +cardinality لمين لـ A union B اللي هم عبارة عن إيش + +231 +00:17:50,780 --> 00:17:56,740 +الـ Natural number اتحاد 01 فبنتش + +232 +00:17:56,740 --> 00:18:03,440 +نشوف جداش بيساوي إيش متوقعين الجواب؟ C هو Infinite + +233 +00:18:03,440 --> 00:18:07,860 +بس من الـ Infinite الكبيرة فيه طبعا هنا التعامل مع + +234 +00:18:07,860 --> 00:18:11,000 +الـ C شوية ميجيش زي هداك هداك مثال كان سهل ع طول + +235 +00:18:11,000 --> 00:18:14,400 +طلعت مباشرة أثبتنا أنه بيساوي ألف null ألف null زي + +236 +00:18:14,400 --> 00:18:18,120 +ألف null بيساوي ألف null بشكل مباشرفي هذه المواضيع + +237 +00:18:18,120 --> 00:18:20,920 +خصوصا لما نكون نتعامل مع الـ C هنستخدم طريقة تانية + +238 +00:18:20,920 --> 00:18:25,540 +عشان أثبت أن X يساوي Y هثبت أن X أصغر تساوي Y وY + +239 +00:18:25,540 --> 00:18:28,660 +أصغر تساوي X هذا السلوب اللي هنستخدمه خصوصا لما + +240 +00:18:28,660 --> 00:18:31,760 +نتعامل مع الـ real numbers مع الـ C لأنه العملية + +241 +00:18:31,760 --> 00:18:35,660 +شوية كبيرة ومافيش طريقة مباشرة فهنستخدم الطريقة + +242 +00:18:35,660 --> 00:18:41,380 +غير المباشرة فأول شيء هثبت أنه طبعا احنا هنثبت ان + +243 +00:18:41,380 --> 00:18:44,100 +هيش خلنا نكتب + +244 +00:18:46,880 --> 00:18:53,300 +will prove that ألف null زائد C تساوي C تمام فأول + +245 +00:18:53,300 --> 00:18:56,820 +شي هثبت أنه هذه أصغر منها وتساوي هذه طبعا أسهل + +246 +00:18:56,820 --> 00:18:59,800 +المفروض لأن واضح أنها أكبر بشكل أكبر بشكل زائد + +247 +00:18:59,800 --> 00:19:05,500 +طبعا أول شي واحد عشان أثبت أنه C أصغر أو تساوي ألف + +248 +00:19:05,500 --> 00:19:10,080 +null زائد C بدأ أثبت هذا الكلام هذا المطلوبوبتش + +249 +00:19:10,080 --> 00:19:12,940 +بيكون cardinal number أصغر من cardinal number إذا + +250 +00:19:12,940 --> 00:19:15,540 +المجموع اللي بتقابله تكافئ subset من المجموع + +251 +00:19:15,540 --> 00:19:19,120 +التاني، مظبوط؟ فقلنا إحنا بالنسبة للسيمين بيقابلها + +252 +00:19:19,120 --> 00:19:23,600 +01 أو R، خلّي دايما التفكير عنها البدائل، وبالنسبة + +253 +00:19:23,600 --> 00:19:27,020 +لهذه عبارة عن مين؟ عبارة عن الاتحاد، وهذا سهل جدا، + +254 +00:19:27,020 --> 00:19:31,360 +ليش؟ لأن كل مجموعة هي subset من الاتحاد، كل مجموعة + +255 +00:19:31,360 --> 00:19:35,600 +هي subset من الاتحاد، فهذه سهلة، فبتش بتكافئ، + +256 +00:19:35,600 --> 00:19:40,530 +بتكافئ نفسها يعني، وهي subsetفالان هنا عشان نشتغل + +257 +00:19:40,530 --> 00:19:47,950 +هنا ان اللي هو الـ C اللي هو 01 اشمالها subset من + +258 +00:19:47,950 --> 00:19:53,830 +N union 01 اللي هو AB صح؟ كل مجموعة بتكون subset + +259 +00:19:53,830 --> 00:19:57,530 +من الاتحاد ولا لأ؟ واضحة هذه ولا مش واضحة؟ اه تمام + +260 +00:19:57,530 --> 00:20:02,470 +هذا معناته على طول ان ال cardinality لهذه المجموعة + +261 +00:20:02,470 --> 00:20:10,480 +01أقل أو يساوي الـ cardinality للـ N union 01 فهذه + +262 +00:20:10,480 --> 00:20:13,740 +فكرة مباشرة، واضحة عادي لأنه احنا مش مانعات أصغر + +263 +00:20:13,740 --> 00:20:16,620 +من أو يساوي، تكافئ، سبصل، طب يعني تكافئ نفسي على + +264 +00:20:16,620 --> 00:20:18,940 +طول، مافيش داعي أن أحط تكافئ، فهذا على طول إيش بقى + +265 +00:20:18,940 --> 00:20:24,200 +تديلي إن الـ C أقل أو تساوي ألف null زائد C، فهذا + +266 +00:20:24,200 --> 00:20:29,180 +واحد، فهذا لاتجاه السهل زي ما احنا متوقعين، نشوف + +267 +00:20:29,180 --> 00:20:34,810 +الآن لاتجاه التانيبدنا نثبت إن الـAlpha Null زائد + +268 +00:20:34,810 --> 00:20:41,650 +C أقل أو تساوي C فبدّي + +269 +00:20:41,650 --> 00:20:48,190 +الـUnunion 01 تكافئ subset من مين؟ بنفع أخد 01؟ + +270 +00:20:48,190 --> 00:20:55,070 +لأ، رأيت أنا بدي أدور، هاي عنيN مع 01 بديها تكافئ + +271 +00:20:55,070 --> 00:20:59,470 +subset معينة وليكن X بنفع أخد من ال 01؟ بنفعش + +272 +00:20:59,470 --> 00:21:06,870 +لإنها كبيرة لإنها مش cross لكن إيش ممكن نعمل ناخد + +273 +00:21:06,870 --> 00:21:12,580 +ال R فدي subset من ال Rفهذه اللي هي المرونة اللي + +274 +00:21:12,580 --> 00:21:16,140 +بدنا نتعلمها إذا بدنا حاجة .. بدنا مجموعة + +275 +00:21:16,140 --> 00:21:20,840 +القاردنات اللي لها الـC وصغيرة 01 مجموعة القاردنات + +276 +00:21:20,840 --> 00:21:25,600 +اللي لها الـC وكبيرة R فبنشتغل بهذا الشكل و نتحرك + +277 +00:21:25,600 --> 00:21:29,480 +اه فطبعا كيف بدي أشوف إن هذا تكافئ ال X أصلا كل + +278 +00:21:29,480 --> 00:21:35,480 +هذه برضه صبصة من الـA كل ال union ال now ال .. ال + +279 +00:21:35,480 --> 00:21:35,880 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +280 +00:21:35,880 --> 00:21:35,920 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +281 +00:21:35,920 --> 00:21:36,040 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +282 +00:21:36,040 --> 00:21:42,280 +ال .. ال ..union 01 subset من ال R و لا لأ واضح + +283 +00:21:42,280 --> 00:21:45,760 +هادي و لا مش واضح ليش لأن ال 01 subset من ال R و + +284 +00:21:45,760 --> 00:21:48,500 +ال N subset من ال R فاتحادهم subset من ال R على + +285 +00:21:48,500 --> 00:21:51,240 +طول هذا بيقوللي ان ال cardinality أصغر من ال + +286 +00:21:51,240 --> 00:21:58,300 +cardinality N union 01 أقل أو تساوي cardinality لل + +287 +00:21:58,300 --> 00:22:04,240 +R فهذا trick مشهورإنه تكون في عيننا مرونة زي ما + +288 +00:22:04,240 --> 00:22:09,420 +انا حاولت أفكر نقول من Alpha null نحط NZQ NO + +289 +00:22:09,420 --> 00:22:14,240 +Uneven الـC من هي؟ R01 ولو أي فترة مفتوحة ممكنها + +290 +00:22:14,240 --> 00:22:17,880 +خلّي يكون عندنا المرونة هادى عشان نستوعب فده بيقول + +291 +00:22:17,880 --> 00:22:22,740 +له أن ألف null زائد C أقل أو تساوي C طبعا واحد + +292 +00:22:22,740 --> 00:22:28,840 +واتنين بيدون المطلوب implies ألف null زائد C تساوي + +293 +00:22:28,840 --> 00:22:35,820 +Cهذه الطريقة المعتمدة في إثبات التعامل مع الـ C أو + +294 +00:22:35,820 --> 00:22:38,920 +Cardinality للـ Real Numbers أو للـ 01 + +295 +00:22:43,010 --> 00:22:47,790 +فطبعا زي ما حكي هنا الأمر مش غريب مع الـ Infinity + +296 +00:22:47,790 --> 00:22:50,150 +Infinity زائد Infinity بتساوي Infinity كله تحت هذا + +297 +00:22:50,150 --> 00:22:53,310 +العنوان العريض بس مع التفاصيل هنا فالف null زائد + +298 +00:22:53,310 --> 00:22:57,010 +الف null الف null الف null زائد C، C مش الف null + +299 +00:22:57,010 --> 00:22:59,450 +طبعا ال Infinity مختلفين ونشوف مين ال Infinity + +300 +00:22:59,450 --> 00:23:02,230 +المناسبة وهذا اللي خلانا نشتغل قولنا هنا في ال + +301 +00:23:02,230 --> 00:23:04,590 +cardinality مش كل ال Infinity زي بعض ومش كل ال + +302 +00:23:04,590 --> 00:23:07,730 +infinite set مع بعض في عندنا الآن هي أصغر infinite + +303 +00:23:07,730 --> 00:23:11,600 +set لكن في أكبر منها ال R ومين أكبر من ال R؟الـ + +304 +00:23:11,600 --> 00:23:15,420 +Power of R وها كذا فأرجو أن هذه الصورة تكون واضحة + +305 +00:23:15,420 --> 00:23:20,440 +ويعني حاضرة للجميع نشوف مثال برضه يعتبر مثال طبيعي + +306 +00:23:20,440 --> 00:23:26,260 +جدا بيقول لي prove that if A is any transfinite + +307 +00:23:26,260 --> 00:23:28,660 +cardinal number يعني إيش Infinite يعني بيقابل + +308 +00:23:28,660 --> 00:23:31,780 +المجموعة فA زاد واحد تسوى A طبعا مش غريب لأن + +309 +00:23:31,780 --> 00:23:33,940 +Infinite زاد واحد تسوى Infinite بنفس السياق اللي + +310 +00:23:33,940 --> 00:23:39,750 +بنشتغل في نفس الدائرة تقريباخلّينا نشوف كيف بدنا + +311 +00:23:39,750 --> 00:23:47,490 +نبرهن هذا أو نحل هذا المثال طبعا + +312 +00:23:47,490 --> 00:23:52,450 +بالأول لازم نحط المعطيات و نحول للغة المجموعات + +313 +00:23:52,450 --> 00:23:55,650 +فهذا الشبطر علشان هي بتعمل الشبطر الأول لأنه بنرجع + +314 +00:23:55,650 --> 00:23:58,890 +للغة المجموعات في الشبطر آسف بتعمل الشبطر الخامسة + +315 +00:23:58,890 --> 00:24:05,050 +مثال رقم تلاتة هناخد مجموعة مجموعتين طبعا أول شي + +316 +00:24:05,050 --> 00:24:13,110 +نبدأ بالمجموعة solution let Abe a set such that + +317 +00:24:13,110 --> 00:24:15,930 +الـ cardinality لها بتسوي small a + +318 +00:24:19,060 --> 00:24:25,360 +أه .. أه وجاية دايما نختار .. جاية دايما نختار ال + +319 +00:24:25,360 --> 00:24:30,020 +.. الرمز المناسب و بعيد و أكرر مافيش رمز غلط و رمز + +320 +00:24:30,020 --> 00:24:34,500 +صح لكن في رمز أنسب من الرمز و بيسهل و الحقيقة ده و + +321 +00:24:34,500 --> 00:24:39,860 +أنا يعني بصلح في ال quiz أه الطالب اخترت X محل Y + +322 +00:24:39,860 --> 00:24:43,100 +احنا بنقول احنا أفضل تختار Y لأنه صورة خربطت في + +323 +00:24:43,100 --> 00:24:47,030 +الحل و هذا الشيء لأن الإنسان دايما الاشي المألوفهو + +324 +00:24:47,030 --> 00:24:50,130 +اللي بيخلّينا نتعود نكتب بأحيان بدون .. بشكل + +325 +00:24:50,130 --> 00:24:52,810 +تلقائم غير ما .. فدائما اختيار .. نتعود نختار + +326 +00:24:52,810 --> 00:24:55,950 +الرموز الصحيحة بيريحنا كتير، اه بيريحنا كتير، اه + +327 +00:24:55,950 --> 00:24:58,770 +فخلاص خلينا نربط small a مع capital a، منطقي، اه + +328 +00:24:58,770 --> 00:25:01,930 +بلاش نتوقف بقعد small a لو انها x مقابل x ولا y + +329 +00:25:01,930 --> 00:25:05,030 +ممكن نرقبت، لكن خلاص في ربط هنا، في ربط، تمام، + +330 +00:25:05,030 --> 00:25:07,090 +الان بدي مجموعة تانية عشان ال coordinate اللي لها + +331 +00:25:07,090 --> 00:25:11,260 +واحدوبدي تقاطوحها مع الـ A يساوي 5 نحن نحتاج لعنصر + +332 +00:25:11,260 --> 00:25:14,620 +من خارج الـ A أحسنتي اه فشوف احنا ماحطتش كتب تمشي + +333 +00:25:14,620 --> 00:25:17,960 +ورا بعض لإنه بدي مرتبطة في الـ A نقوله الآن ممكن + +334 +00:25:17,960 --> 00:25:29,500 +نكتب كم مرة let أي عنصر X لا تنتمي للـ A and let B + +335 +00:25:29,500 --> 00:25:31,240 +تساوي مجموعة الـ X + +336 +00:25:34,290 --> 00:25:37,850 +فطبعاً بهذا الاختيار كانت تقاطع Phi وطبعاً + +337 +00:25:37,850 --> 00:25:43,650 +Cardinality للـ B بتساوية واحدة فاحنا هنشتغل على + +338 +00:25:43,650 --> 00:25:47,490 +هذه المجموعة فالان بعد ما اخترنا ال A و ال B بشكل + +339 +00:25:47,490 --> 00:25:52,930 +مناسب الان ممكن نبدأ نشتغل فطبعا صار عندنا ال A + +340 +00:25:52,930 --> 00:25:57,090 +زائد واحد ليست الا Cardinality لل A Union B + +341 +00:26:02,920 --> 00:26:07,620 +طبعا هبدأ اعمل مثل المثال السابق هعملها اصغر من او + +342 +00:26:07,620 --> 00:26:11,880 +يساوي اصغر من او يساوي من الاسهل الطرف اليمين اصغر + +343 +00:26:11,880 --> 00:26:15,780 +او يساوي اليسار لان a اقل او سوا بسهولة طبعا بنفس + +344 +00:26:15,780 --> 00:26:21,760 +الاسلوب انا عندي اللي هو ال a nowsubset من A union + +345 +00:26:21,760 --> 00:26:26,420 +B، الـ trick هذا مشهور، فهذا على طول بيقول إن الـ + +346 +00:26:26,420 --> 00:26:31,760 +cardinality للـ A أقل أو تساوي الـ cardinality للـ + +347 +00:26:31,760 --> 00:26:36,000 +A union B، وضعها هذه، مش ضروري أقول أنتوا كافئ + +348 +00:26:36,000 --> 00:26:39,880 +نفسي خلاص، مباشرة هنستخدمها، فهذا يؤدي إن الـ A + +349 +00:26:39,880 --> 00:26:46,260 +أقل أو تساوي A زائد 1، فده واحد، فهذا الجزء الأول + +350 +00:26:50,250 --> 00:26:54,790 +طرق متعددة دائمة نرتب الكتابة تبعنا البرهان تبعنا + +351 +00:26:54,790 --> 00:26:59,090 +يا بنحط عنوانه بنرقمه أو بنشتغل و بنرقم المعادلة + +352 +00:26:59,090 --> 00:27:01,050 +اللي بدنا نشتغل تماما ده يعنى إذا جاءت المعادلة + +353 +00:27:01,050 --> 00:27:03,790 +التانية بدنا نثبت العكس بدنا نثبت أن الـ A زائد + +354 +00:27:03,790 --> 00:27:07,090 +واحد أصغر أتساوي الـ A فالآن احنا جاعدين إذا بنعمل + +355 +00:27:07,090 --> 00:27:12,170 +هامش أو كذا بنحاول نثبت أن الـ A union الـ B + +356 +00:27:12,170 --> 00:27:19,080 +إشمالته كافة X subset من الـ A هذا السؤالبدنا نفكر + +357 +00:27:19,080 --> 00:27:26,420 +بهذه الطريقة طبعا الآن ماعناش ال trick اللى كنا + +358 +00:27:26,420 --> 00:27:30,720 +نستفيد منه مرة 01 و مرة R نكبر و نزغر ملزمين هنا + +359 +00:27:30,720 --> 00:27:37,300 +في الـ A فإيش ممكن نعمل؟ أزغر المجال المقابل لمين؟ + +360 +00:27:40,110 --> 00:27:45,330 +وحدة وحدة، لأ هي بتحكي فيه منه، بس بدنا نحط الأمور + +361 +00:27:45,330 --> 00:27:50,990 +بالنصابة، احنا حاليا هنعمل برضه trick مشهور، بدنا + +362 +00:27:50,990 --> 00:27:53,950 +نثبت أنه نجيب دالة من مجموعة لمجموعة تكون one to + +363 +00:27:53,950 --> 00:27:57,890 +one، وبالتالي بيصير الدالة تكافئ ال image، وهو + +364 +00:27:57,890 --> 00:28:01,450 +صبصة من المجموعة التانية، فهنعمل بهاي عيننا الـA، + +365 +00:28:02,400 --> 00:28:07,440 +وش جيبناله؟ ضفناله أنصر X كوّننا إيش بي فهذه كلها + +366 +00:28:07,440 --> 00:28:13,260 +مع بعض إشمالها بي مظبوط أو عيننا مجوهنا إيش A + +367 +00:28:13,260 --> 00:28:17,060 +فبدنا + +368 +00:28:17,060 --> 00:28:25,700 +دالة من A union B هي لأ مش هذه B لأ آسفة هذه ال B + +369 +00:28:25,700 --> 00:28:32,320 +هذه A union B بدنا دالةخلّينا نركز و نفكر مع بعض + +370 +00:28:32,320 --> 00:28:36,940 +من A union B لـ A تكون one to one بدنا إياها تكون + +371 +00:28:36,940 --> 00:28:41,920 +one to one أه طبعا معروف، هروح ندور على المعطيات، + +372 +00:28:41,920 --> 00:28:47,500 +في أنا في المعطيات دوال احكي + +373 +00:28:47,500 --> 00:28:51,260 +بصوت عالي، إيش في عندك دوال؟ اقرأوا مع بعض، إيش في + +374 +00:28:51,260 --> 00:28:55,580 +معلومات؟ إيش الـ A؟ الـ A transfinite يعني الـ A + +375 +00:28:55,580 --> 00:28:59,890 +infiniteو الـ infinite شمالها يوجد دالة منها + +376 +00:28:59,890 --> 00:29:04,990 +لنفسها one to one و ليست unto فنبدأ الآن a is + +377 +00:29:04,990 --> 00:29:10,050 +trans finite + +378 +00:29:10,050 --> 00:29:20,790 +implies a is infinite implies there exists a + +379 +00:29:20,790 --> 00:29:28,530 +function from a to a such that سميتها g أناG is + +380 +00:29:28,530 --> 00:29:36,230 +one to one and G of A is proper من الـ A فعندي + +381 +00:29:36,230 --> 00:29:40,410 +دالة من أين إلى أين من A إلى A من هنا إلى هنا + +382 +00:29:40,410 --> 00:29:45,440 +اسمها G أنا الآن أريد دالة من الاتحاديعني إيش بده + +383 +00:29:45,440 --> 00:29:49,120 +أعمل؟ بده أكبر ال domain، أضافله عنصر، بده أضافله + +384 +00:29:49,120 --> 00:29:54,720 +عنصر، فبدنا نعرف ال F، بدنا نعرف ال F، بنفع ال F + +385 +00:29:54,720 --> 00:29:59,660 +تعتمد على ال G؟ بنفع، بس domain الجي صغير، بدنا + +386 +00:29:59,660 --> 00:30:05,670 +نعرف إيش؟ صورة ال X هذه، وين ممكن تروح؟هل جيت أي + +387 +00:30:05,670 --> 00:30:08,850 +عنصر .. كده أنا بدي أعرف ده اللي من .. من A union + +388 +00:30:08,850 --> 00:30:14,110 +B لـ A إذا العنصر في الـ A F تساوي G طب العنصر + +389 +00:30:14,110 --> 00:30:17,470 +اللي في الـ B اللي هو العنصر الوحيد وين اوديه؟ بدي + +390 +00:30:17,470 --> 00:30:21,370 +اوديه ل .. ل .. لأ لـ A و بدي اتويت .. ده أفضل ان + +391 +00:30:21,370 --> 00:30:26,160 +تكون one to oneبيدوديله عنصر A مايكونش صورة، طب + +392 +00:30:26,160 --> 00:30:29,860 +موجود؟ نعم، هذا الفكرة مرة تعالى انا جابله هيك، + +393 +00:30:29,860 --> 00:30:32,640 +شفتوا انت كده؟ بس بودقة، اه لو انه كان جالي اي + +394 +00:30:32,640 --> 00:30:34,780 +دالة كان ماانتبهتش كتير، لكن عشان احافظنا one to + +395 +00:30:34,780 --> 00:30:39,440 +one، بدلان ال X تروح لصورة ماتكونش صورة، لأنه + +396 +00:30:39,440 --> 00:30:46,240 +مافيش في عندي هنا، في عندي جوة ال A، G of Aفال X + +397 +00:30:46,240 --> 00:30:48,540 +ممكن تذهب للصور و تبطل one to one فبديها تذهب + +398 +00:30:48,540 --> 00:30:53,180 +لعنصر إيش هنا برا عشان هي قبل ما كنتش F بدأ من + +399 +00:30:53,180 --> 00:31:02,480 +أستفيد من هذه فالأن هذا إيش معناته there + +400 +00:31:02,480 --> 00:31:13,480 +exists B تنتمي لل A ناقص ال G of A الآن let Fمن A + +401 +00:31:13,480 --> 00:31:22,920 +union B إلى الـ A B given by F أه سميناها احنا ال + +402 +00:31:22,920 --> 00:31:27,000 +X مستخدمة خلينا .. فهي .. هي .. هي برضه لو سميناها + +403 +00:31:27,000 --> 00:31:30,540 +A ك .. و اسمه A مستخدمة كان حرف مختلف خلينا نسميها + +404 +00:31:30,540 --> 00:31:37,830 +Z تساوي أه بتساوي G of Zإذا الـ Z تنتمي للـ A + +405 +00:31:37,830 --> 00:31:42,710 +وتساوي بي إذا الـ Z تساوي X العنصر اللي هو فيه + +406 +00:31:42,710 --> 00:31:47,130 +طبعا بتنتمي للـ B هو الوحيد مظبوط واضحة هيك الصورة + +407 +00:31:47,130 --> 00:31:51,530 +A تمام فالآن بنثبت إن الـ F is one to one وده + +408 +00:31:51,530 --> 00:31:58,660 +هتركه exercise is one to one exerciseماذا متوقعين + +409 +00:31:58,660 --> 00:32:02,200 +يطلع معناه؟ أربع حالات احدين تانية Contradiction + +410 +00:32:02,200 --> 00:32:05,740 +اتنين اتنين يدّونا ان الـ A زد واحد تساوي زد اتنين + +411 +00:32:05,740 --> 00:32:09,900 +تمام مازال هذه one to one طبعا مش شرط تكون on to + +412 +00:32:09,900 --> 00:32:15,140 +لإنه مش عارف مش on to الحقيقة هي فهذا يؤدي ان الـ + +413 +00:32:15,140 --> 00:32:22,900 +A union B ال domain من بكافئ ال image وهو صبصت من + +414 +00:32:22,900 --> 00:32:27,420 +مين؟ من المجال المقابلفي عندنا دالة من A union B + +415 +00:32:27,420 --> 00:32:30,520 +للـ A one to one ال trick مشهور عملناه أكتر من مرة + +416 +00:32:30,520 --> 00:32:34,200 +صار ال domain يكافئ ال image و ال image subset + +417 +00:32:34,200 --> 00:32:40,680 +فهذا بيقول لإنه ال cardinality لل A union B أقل أو + +418 +00:32:40,680 --> 00:32:44,840 +تساوي ال cardinality لمن؟ لل A إيش ال cardinality + +419 +00:32:44,840 --> 00:32:50,800 +هذه؟ A زائد واحد أقل أو تساوي A وهذا رقم اتنين + +420 +00:32:50,800 --> 00:32:55,160 +فواحد و اتنين بيخلصولنا السؤال + +421 +00:32:57,330 --> 00:33:05,310 +1 و 2 implies a زائد 1 يساوي فهنا زي ما انتوا + +422 +00:33:05,310 --> 00:33:10,390 +شايفين في أفكار بتتكرر معنا أرجو أنها اتساعدنا في + +423 +00:33:10,390 --> 00:33:15,810 +الفهم بشكل أفضل فهذه نهاية هذا ال section ان شاء + +424 +00:33:15,810 --> 00:33:19,850 +الله المرة الجاية بنكمل مع اللي هو ضرب الأعداد + +425 +00:33:19,850 --> 00:33:20,670 +الأصلية + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/RfkTkQEL2Xs_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/RfkTkQEL2Xs_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..51a4bd932bf0a7d8e87534283edfccb86e918d04 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/RfkTkQEL2Xs_postprocess.srt @@ -0,0 +1,2252 @@ +1 +00:00:19,940 --> 00:00:23,240 +بسم الله الرحمن الرحيم احنا ان شاء الله هنواصل مع + +2 +00:00:23,240 --> 00:00:29,640 +العلاقات relations ارجو انه نكون دايما متذكرين + +3 +00:00:29,640 --> 00:00:35,180 +حاطين في عقولنا التعريف البسيط جدا للعلاقة هي ليست + +4 +00:00:35,180 --> 00:00:38,180 +الا subset من ال Cartesian product فانا بقول + +5 +00:00:38,180 --> 00:00:44,000 +relation are من مجموعة ما Aلمجموعة ما B أي + +6 +00:00:44,000 --> 00:00:48,600 +مجموعتين متساويتين غير متساويتين التعريف عام فال + +7 +00:00:48,600 --> 00:00:52,160 +relation من مجموعة A لمجموعة B هي أي subset من الـ + +8 +00:00:52,160 --> 00:00:56,260 +Cartesian product A cross الـB فده التعريف اتبسطه + +9 +00:00:56,260 --> 00:01:00,820 +طبعا شفنا بعض المصالحات المتعلقة زي المجال وزي + +10 +00:01:00,820 --> 00:01:04,160 +المدى لل relation اه في ممكن و الاش و العلاقة + +11 +00:01:04,160 --> 00:01:08,200 +العكسية وذكرنا ان أكد ان كل relation اللي عايش is + +12 +00:01:08,200 --> 00:01:12,040 +inverse relation لأ طبعا عكس الدولةبدأنا نشوف بعض + +13 +00:01:12,040 --> 00:01:17,240 +الأمثلة ووصلنا للمثال الرابع المثال الرابع خلينا + +14 +00:01:17,240 --> 00:01:20,580 +نقرأه مع بعض ونشوف كيف بدنا نوضحه أو ايش اللي هو + +15 +00:01:20,580 --> 00:01:24,940 +التعليقات الموجودة عليه نبدأ القراءة زي ما اتعلمنا + +16 +00:01:24,940 --> 00:01:29,480 +كيف نقرأ تعريف كيف نقرأ نظرية كيف نقرأ مسألة ما + +17 +00:01:29,480 --> 00:01:34,340 +مثال أو سؤال تقريبا نفس السياسة فببدأ بالمقدمةlet + +18 +00:01:34,340 --> 00:01:38,520 +R be a relation from A to B إذا أنا فيه الـ R هي + +19 +00:01:38,520 --> 00:01:42,960 +دي ترمز لعلاقة من مجموعة capital A لمجموعة أخرى + +20 +00:01:42,960 --> 00:01:48,220 +capital B and let D subset من ال A وأخد مجموعة + +21 +00:01:48,220 --> 00:01:51,640 +جزئية من المجموعة A المجموعة الأولى ممكن طبعا + +22 +00:01:51,640 --> 00:01:56,640 +الإنسان يحاول يفهم السؤال يرسم هي عندنا A + +23 +00:02:01,620 --> 00:02:05,640 +في عندنا مجموعة A و في عندنا مجموعة B و في عندنا + +24 +00:02:05,640 --> 00:02:09,820 +relation بينهم و في عندنا هنا مجموعة جزئية D صفصف + +25 +00:02:09,820 --> 00:02:15,100 +من ال A يمكن تساعدنا في الفهم و هكذا طيب ماشي اه + +26 +00:02:15,100 --> 00:02:18,960 +الآن بيقولي by the restriction of R to D we mean + +27 +00:02:19,540 --> 00:02:23,200 +إيش جاعت بالدينة؟ بالدينة تعريف جوا السؤال اشي + +28 +00:02:23,200 --> 00:02:27,580 +طبعا ده غريب؟ ممنوع؟ أه لأ مش ممنوع لإن احنا بنطور + +29 +00:02:27,580 --> 00:02:31,700 +طالب كيف يفهم يعني انت مش ضروري كل شيء في المستقبل + +30 +00:02:31,700 --> 00:02:34,500 +تتعاملي معاه يكون درستيه في الجامعة أو في المدرسة + +31 +00:02:34,500 --> 00:02:38,140 +ممكن أي مفهوم جديد بدك تشوفه تعريفه وكيف تفهمه + +32 +00:02:38,140 --> 00:02:41,910 +وكيف تشرحيهأه هذا شئ طبيعي فهو بده يديني تعريف كيف + +33 +00:02:41,910 --> 00:02:45,930 +نتعامل معاه بيقول لي by the restriction of R to D + +34 +00:02:45,930 --> 00:02:50,690 +إذا في أنا مفهوم هو إيش تقييد ال relation لل D أو + +35 +00:02:50,690 --> 00:02:54,670 +بمعنى آخر تخصيص أنا عندي relation معرفة على ال A + +36 +00:02:54,670 --> 00:02:59,090 +كلهابده ياخد منها حالة خاصة بس بده يعرفها على ال D + +37 +00:02:59,090 --> 00:03:02,770 +يعني إيش؟ بده ياخد بس الجزء اللي خاص بال D بجزء من + +38 +00:03:02,770 --> 00:03:06,050 +ال A مش كل ال A فهذا متقيل أنا بديش relation بشكل + +39 +00:03:06,050 --> 00:03:10,450 +عام بدي جزء منها خاص أنا بدي مهتم في هذا السؤال + +40 +00:03:10,740 --> 00:03:13,640 +بجزء من ال relation مش بكل ال relation فبسموه + +41 +00:03:13,640 --> 00:03:17,680 +تقييد ال relation او تخصيص the restriction of R to + +42 +00:03:17,680 --> 00:03:21,500 +D العلاقة معرفة على مجموعة كبيرة A الان انا معنى + +43 +00:03:21,500 --> 00:03:25,760 +ان اش ادرس جزء من العلاقة اللي هو خاص بجزء من ال A + +44 +00:03:25,760 --> 00:03:30,540 +كيف جزقنا العلاقة تجزيئ ال A اخدنا جزء اللي هو + +45 +00:03:30,540 --> 00:03:35,700 +subset D تمام we mean هي تعريف يعني هذا يعني تكافئ + +46 +00:03:35,960 --> 00:03:38,800 +the relation إذا انتقيد ال relation the + +47 +00:03:38,800 --> 00:03:40,980 +restriction of a relation إيش ماله؟ عبارة عن ال + +48 +00:03:40,980 --> 00:03:43,540 +relation هنتبه .. قولنا domain ال relation إيش + +49 +00:03:43,540 --> 00:03:47,520 +ماله؟ set مش relation هنتبه كل كلمة إلها معنى وكيف + +50 +00:03:47,520 --> 00:03:50,220 +نتعامل معاها بقول عبارة عن ال relation أه إيش + +51 +00:03:50,220 --> 00:03:54,220 +الرمز تبعها؟ المفهوم the restriction of R to D هاي + +52 +00:03:54,220 --> 00:03:58,280 +المصطلح طيب إيش رمزه؟ R اللي هو و هذا الخط D + +53 +00:03:58,280 --> 00:04:01,660 +restricted to D هيك تنكتب RD هاي الرمز طيب إيش + +54 +00:04:01,660 --> 00:04:04,420 +تعريفه؟ قال لي هي أزواج مرتبة طبعا هو قال لي ال + +55 +00:04:04,420 --> 00:04:07,930 +relation من وين؟من ال R هي لانوش قلنا هي تخصيص ال + +56 +00:04:07,930 --> 00:04:12,070 +R هي من ال R طب كل ال R لأ بشرط الاحداث الاول يكون + +57 +00:04:12,070 --> 00:04:16,590 +وين في ال D اه فانا طبعا ال relation اشملها ماخدة + +58 +00:04:16,590 --> 00:04:20,310 +كل الأزواج المرتبة احداثيها الاول من A بشكل عام + +59 +00:04:20,310 --> 00:04:23,830 +والتاني من B انا مهتم بالاول لانه مهتم بال A جالي + +60 +00:04:23,830 --> 00:04:27,090 +تاخدش كل الأزواج المرتبة خد بس الحالات اللي فيها + +61 +00:04:27,090 --> 00:04:31,290 +ال X وين في ال D اه فإذا الاحداث الاول هنا خد + +62 +00:04:31,290 --> 00:04:35,780 +الزوج المرتب طب الاحداث الاول برا بدنا نحملهواضح؟ + +63 +00:04:35,780 --> 00:04:38,480 +فده يسموه تقييد اه بعدين انا باخد الحالة العاملة + +64 +00:04:38,480 --> 00:04:41,720 +كل .. كل أزواجي المرتبة في ال relation بدي اخد ايه + +65 +00:04:41,720 --> 00:04:44,520 +اش بعضهم ايه؟ طب ايش الشرط؟ ان يكون اليحداها في + +66 +00:04:44,520 --> 00:04:48,540 +الأول في ال D اه فانا اعمل ايه التقييد تمام طبعا X + +67 +00:04:48,540 --> 00:04:51,620 +تنتمي ل D اه from D to B طبعا هى ال relation تمام + +68 +00:04:51,620 --> 00:04:56,000 +من ون لوين صارت التقييد صارت relation بس من D لB + +69 +00:04:56,000 --> 00:05:00,880 +هد ايش اسمها؟R restricted to D ففيه relation أصلية + +70 +00:05:00,880 --> 00:05:04,340 +وهذه relation حالة خاصة منها تقييد عليها فهذه + +71 +00:05:04,340 --> 00:05:07,940 +الصورة بتفقد و تبدح لنا طيب هذا إيش تعريف لسه + +72 +00:05:07,940 --> 00:05:12,480 +مابدأش السؤال طب إيش المطلوب prove that prove that + +73 +00:05:12,480 --> 00:05:16,500 +هاي المطلوب بيقول لي R restricted to D ك relation + +74 +00:05:16,500 --> 00:05:22,340 +إيش بتساوي بتساوي ال R تقاطع D across ال image لل + +75 +00:05:22,340 --> 00:05:26,420 +Rأه فهو بدي واش بيقوللي هذه كان relation ممكن + +76 +00:05:26,420 --> 00:05:32,000 +أكتبها تساوي R على أزواج مرتبة طب الطرف تقاطع مين + +77 +00:05:32,000 --> 00:05:35,920 +بينفع أجيب مجموعتين تقطعهم من نوع مختلف مش عايز + +78 +00:05:35,920 --> 00:05:39,260 +فيه ده هيطلع فيه لكن هو اش بيقوللي هنا في طب على + +79 +00:05:39,260 --> 00:05:42,540 +الطرفين تساوي مجموعات فلازم تطلع المجموع اللي على + +80 +00:05:42,540 --> 00:05:45,530 +اليسار أزواج مرتبة لأنه relation هي تعريفها صح؟طب + +81 +00:05:45,530 --> 00:05:48,450 +على الطرف اليمين لازم تكون من نفس الجنس لأنهم + +82 +00:05:48,450 --> 00:05:52,370 +متساويتين طب ال R أزواج مرتبة و هان أزواج مرتبة + +83 +00:05:52,370 --> 00:05:56,830 +كيف ال D عناصر عادية لإن صفصت من ال A طب و ال M + +84 +00:05:56,830 --> 00:06:00,590 +ماشي من ال B صفصت من ال B صح تذكروا فإذا نقاش أخد + +85 +00:06:00,590 --> 00:06:02,610 +صفصت من ال A بصفصت من ال B Sir Cartesian أبو دك + +86 +00:06:02,610 --> 00:06:05,410 +أزواج مرتبة مع أزواج مرتبة صارت مجموعة من أزواج + +87 +00:06:05,410 --> 00:06:08,590 +مرتبة بقول اللي هي نفسها مين ال R restricted to D + +88 +00:06:08,940 --> 00:06:11,980 +فهي نفهم السؤال و كيف بنطق السؤال و كل الأمور + +89 +00:06:11,980 --> 00:06:17,160 +منسجمة و ايش بتاعنا منطقية و صحية اه بدنا نثبتها + +90 +00:06:17,160 --> 00:06:23,400 +نبدأ الحل و خطوة خطوة بعد ما فهمنا السؤال و قرأناه + +91 +00:06:23,400 --> 00:06:29,660 +الآن بدنا نبدأ الحل فهذا المثال الرابع ولا التالت + +92 +00:06:29,660 --> 00:06:38,810 +الرابع solution تمام نيجي نشوف ال proofالجملة إيش + +93 +00:06:38,810 --> 00:06:42,970 +نوحة؟ simple لا جملة شرطية ولا فيها or ولا and ولا + +94 +00:06:42,970 --> 00:06:46,990 +أي شيء simple statement ده ده نوع الأول نقطة طيب + +95 +00:06:46,990 --> 00:06:52,290 +هذه ال statement إيش نوحة؟ إيش نويتش؟ بتثبت بتثبت + +96 +00:06:52,290 --> 00:06:54,670 +تساوي مجموعات أو تساوي relation ما هي relation + +97 +00:06:54,670 --> 00:06:57,690 +مجموعة كل relation مجموعة لكن العكس غير صحيح + +98 +00:06:57,690 --> 00:07:01,190 +فتساوي تساوي مجموعة كيف بنسبح تساوي المجموعات؟ + +99 +00:07:01,190 --> 00:07:04,990 +بنبدأ من طرف مشينا تكافؤ خلصنا إذا مامشيناش تكافؤ + +100 +00:07:04,990 --> 00:07:07,940 +بنضطر نبدأ من الطرف التاني ونرجع نفس المبدأفابد + +101 +00:07:07,940 --> 00:07:11,880 +أبدأ من الطرف الأول فهنا بدنا نبدأ من اللي هو + +102 +00:07:11,880 --> 00:07:19,540 +الطرف الأول فهنقوله let نقوله x ولا xy؟ xy لإن + +103 +00:07:19,540 --> 00:07:22,480 +احنا عارفين هذي relation أزواج مرتبة مباشرة بقوله + +104 +00:07:22,480 --> 00:07:32,020 +let xy be any elementand let او such that كله صح + +105 +00:07:32,020 --> 00:07:38,000 +and let x y وين موجودة في الطرف وين اليسار + +106 +00:07:38,000 --> 00:07:45,470 +restricted to D are restricted to Dفي حد عنده أي + +107 +00:07:45,470 --> 00:07:49,090 +اعتراض على البداية؟ طب كل واحد فاهم البداية ليش + +108 +00:07:49,090 --> 00:07:53,450 +كانت صحيحة ومنطقية؟ تمام؟ ممتاز ايش ممكن نعمل؟ + +109 +00:07:53,450 --> 00:07:57,930 +نشوف التعريف وينه التعريف؟ في السؤال ايش معناه x y + +110 +00:07:57,930 --> 00:08:02,030 +في ال R دي؟ مين R دي؟ هي كل x y هي هي عناصر x y + +111 +00:08:02,030 --> 00:08:05,890 +ايش مالهم؟ هم x y في ال R و ال x في ال D طب كيف + +112 +00:08:05,890 --> 00:08:11,900 +بده اقرأ such that يعني and؟هي أزواج المرتبة في ال + +113 +00:08:11,900 --> 00:08:16,620 +relation اللي فيها الإحداث الأول من الـD فإذا أنا + +114 +00:08:16,620 --> 00:08:24,660 +هذه على طول تكافئ XY تنتمي للـR و X تنتمي للـD + +115 +00:08:24,660 --> 00:08:29,100 +طبعا هذا تعريف R restricted to D فهذا definition + +116 +00:08:29,100 --> 00:08:36,340 +of R restricted to Dماهم اه طيب انا بساعد دليل تبع + +117 +00:08:36,340 --> 00:08:41,500 +اه تعرف ممتاز و اين رايحين احنا رايحين على ال R اه + +118 +00:08:41,500 --> 00:08:44,000 +بدنا هي تكون في ال R ممكن انا ايش اه مالهامش و + +119 +00:08:44,000 --> 00:08:47,640 +بدنا هي تكون في ال D cross ال image بدنا هي تكون + +120 +00:08:47,640 --> 00:08:51,280 +في ال D cross ال image هي في ال R موجودة تم أمشي + +121 +00:08:51,280 --> 00:08:57,680 +منها تكون X في ال D و بدي Y في ال range و بدي Y + +122 +00:08:57,680 --> 00:09:01,120 +تكون في ال image أسف اللي هو في المدى بدنا هي تكون + +123 +00:09:01,120 --> 00:09:06,300 +في ال image طيبالأن الجزء الأول هذا يقولنا جاهز + +124 +00:09:06,300 --> 00:09:10,020 +بدنا نحاول نكوّن زوج مرتب تاني عشان نعمل التقاطع و + +125 +00:09:10,020 --> 00:09:13,880 +لا لأ عشان نصبح تقاطع بدي كمان x y ايش تكون تكون + +126 +00:09:13,880 --> 00:09:17,200 +في ال D cross ال M مش يعني ممكن نعمل تفسير وين + +127 +00:09:17,200 --> 00:09:23,080 +رايحين احنا رايحين بدنا x y تكون في ال R تقاطع D + +128 +00:09:23,080 --> 00:09:30,370 +cross ال M اه صح هذا مطلوب اه طب هداش يكافئX Y في + +129 +00:09:30,370 --> 00:09:37,510 +ال R and X Y في ال D across ال image طيب هذا موجود + +130 +00:09:37,510 --> 00:09:43,430 +هذا ايش X في ال D and Y في ال image يعني طبعا هذا + +131 +00:09:43,430 --> 00:09:48,810 +عشان انا بفسر المطلوب مش غلط نعمل هامش ورجع حتى لو + +132 +00:09:48,810 --> 00:09:53,730 +كتبنا we want مش غلط هذا هو المطلوب بتطلع هى الهدف + +133 +00:09:54,250 --> 00:09:57,270 +و هاي اللي بإيديا، هاي اللي بملكه أنا، هاي + +134 +00:09:57,270 --> 00:10:00,650 +المعطيات تبعتها الأول جاهز، عشان هي كده تشكوا عن + +135 +00:10:00,650 --> 00:10:03,910 +مرة، واضح و ال X في ال D كمان عندي، إيش تم؟ بدي + +136 +00:10:03,910 --> 00:10:07,850 +أثبت إن ال Y في ال image بدنا نمتثبت إن ال Y في ال + +137 +00:10:07,850 --> 00:10:11,510 +image من وين ممكن نجيبها؟ نتذكر، إيش تعريف ال + +138 +00:10:11,510 --> 00:10:15,890 +image؟ ال image هو الإحداث التاني في كل زوج مرتب + +139 +00:10:15,890 --> 00:10:18,950 +في الأرض طب فيه عندنا زوج مرتب في الأرض؟ نعم أه، + +140 +00:10:18,950 --> 00:10:22,610 +بقدر أستنتج منه إن ال Y في الأرض طب هل بقدر تمني + +141 +00:10:22,610 --> 00:10:26,690 +أستمر تكافؤ؟مش عارف، مش متأكد، طب ايش أعمل؟ مش + +142 +00:10:26,690 --> 00:10:30,990 +ضرور، مش ضرور نمشي تكافؤ، اصلا نقوله الآن، ممكن + +143 +00:10:30,990 --> 00:10:39,410 +أقوله كالتالي Now x y تنتمي لل R implies y تنتمي ل + +144 +00:10:39,410 --> 00:10:43,970 +image ال R، تعريف ال image، definition of ال image + +145 +00:10:45,050 --> 00:10:49,130 +مظبوط لأن كل زوج مرتب عشان يكون إحداثيه الأول في + +146 +00:10:49,130 --> 00:10:53,110 +ال domain و إحداثيه التاني في ال image طبعا صار + +147 +00:10:53,110 --> 00:10:56,810 +عندي ال X في ال D و ال Y في ال image الزوج المرتب + +148 +00:10:56,810 --> 00:11:01,150 +في ال Cartesian product it follows that أو حطه + +149 +00:11:01,150 --> 00:11:07,310 +implies بس نكتب بطريقة أفضل it followsthat لأن كل + +150 +00:11:07,310 --> 00:11:09,650 +برهان .. كل statement بكتبها في البرهان تكون true + +151 +00:11:09,650 --> 00:11:13,730 +فهذه true وهذه true إيش بده يصير is an xy يعني عمل + +152 +00:11:13,730 --> 00:11:17,930 +conjunction بس مكتبهاش إنه x في ال D و I مايواضحة + +153 +00:11:17,930 --> 00:11:23,530 +ان x y one موجودة في ال D Cartesian image ال R إيش + +154 +00:11:23,530 --> 00:11:26,570 +ده ليه لك؟ تعريف ال Cartesian مديش أكتبها مش ضروري + +155 +00:11:27,110 --> 00:11:31,190 +لان اتقدمنا شويه ممتاز XY في ال .. في ال .. في ال + +156 +00:11:31,190 --> 00:11:34,390 +Cartesian و XY في ال R ولا هذي صارت غلط ما هي صحيح + +157 +00:11:34,390 --> 00:11:37,550 +استخدام ده لكنها true ايش بعملها كمان كنت .. ايش + +158 +00:11:37,550 --> 00:11:41,410 +صارت وين؟ في التقاطع صارت في التقاطع اه and hence + +159 +00:11:41,410 --> 00:11:45,050 +XY + +160 +00:11:45,050 --> 00:11:53,150 +تنتمي لإيش؟ لل R تقاطع D Cartesian image ال R + +161 +00:12:00,090 --> 00:12:03,410 +طبعا فهنا السياسة بما انه مش قادر انا امشي تكافؤ + +162 +00:12:03,410 --> 00:12:07,230 +بسلاسة وخايف يكون فيه خطوة من خطوات ليس التكافؤ + +163 +00:12:07,230 --> 00:12:11,470 +لكن انا ماشي بالاتجاه اللي هو implies 100% ايش + +164 +00:12:11,470 --> 00:12:16,610 +بدأت؟ بدأت من زوج في الطرف اليسار وصلت لليمين + +165 +00:12:16,610 --> 00:12:20,910 +بimplies اكيد اذا انا افبتت subset مش متأكد انه + +166 +00:12:20,910 --> 00:12:25,330 +التساوي فإذا احنا ايش عملنا فهو نقوله ايش Thus ايش + +167 +00:12:25,330 --> 00:12:31,370 +صار؟ صار عندنا الأوللأ subset من التاني احنا عملنا + +168 +00:12:31,370 --> 00:12:37,030 +implies فانت قد إلى subset R تقاطع D across ال + +169 +00:12:37,030 --> 00:12:44,650 +image فده أثبتناه فده ممكن الرقم واحد اه فضل + +170 +00:12:48,370 --> 00:12:51,570 +أين DX في الـD؟ true صح ولا لأ؟ أه ممكن أعمل + +171 +00:12:51,570 --> 00:12:54,670 +simplification بس مكتوبش كل شي يعني حقيقة شوية + +172 +00:12:54,670 --> 00:12:56,810 +بنتقدم بنبطل الاشي نقوله simplification و بعدين + +173 +00:12:56,810 --> 00:12:59,610 +نعمله conjunction هادي مع هادي و بعدين هادي واضحة؟ + +174 +00:12:59,610 --> 00:13:04,150 +لأن كله true تمام؟ أه و بعدين أصار هيها في الـA و + +175 +00:13:04,150 --> 00:13:07,910 +هيها في ال Cartesian إذا في التقاطة نفسه لأن XY + +176 +00:13:07,910 --> 00:13:13,390 +نفسهاطبعا ماغيرناش اذا انا مازال مش متأكد انه في + +177 +00:13:13,390 --> 00:13:16,770 +تكافؤ ممكن ماتعادلش حقا كتير لإنه تكافؤ دقيقة نبدأ + +178 +00:13:16,770 --> 00:13:22,170 +نعمل بالعكس مافيش مشكلة فالان نبدأ بالعكس let X Y + +179 +00:13:22,170 --> 00:13:25,650 +تنتمي لل R تقاطع ال Cartesian product + +180 +00:13:28,360 --> 00:13:31,920 +ممتاز، ليش بدأت البداية التانية؟ متبقين معايا؟ + +181 +00:13:31,920 --> 00:13:34,840 +عشان انا بدأ أثبت انه subset من التانية، اه لأنه + +182 +00:13:34,840 --> 00:13:37,640 +مامشيتش تكافه ومش متأكد فبدأ من الطرف التانية، + +183 +00:13:37,640 --> 00:13:40,840 +ممتاز، اه ليش بدأ اعمل؟ تعريف تقاطه، هاي انت + +184 +00:13:40,840 --> 00:13:44,420 +وفكيته، اه فهادي طبعا، ليش اكتب تكافه؟ مهمنيش + +185 +00:13:44,420 --> 00:13:46,540 +تكافه، انا واضح انه ماشي، انا بدأ امشي in place، + +186 +00:13:46,540 --> 00:13:52,950 +هذا المهتم فيهفأمشي implies إذا x y تنتمي لل R and + +187 +00:13:52,950 --> 00:14:00,850 +x y تنتمي لل D كارتيسيا image ال R ممتاز إيش ممكن + +188 +00:14:00,850 --> 00:14:04,630 +نعمل؟ أين رايحين؟ رايحين هنا بدنا x y في ال R + +189 +00:14:04,630 --> 00:14:08,750 +موجودة و بدنا x في ال D ممكن نجيب x في ال D؟ نعم + +190 +00:14:08,750 --> 00:14:15,490 +من وين؟ من كارتيسيا فهذه تؤدي x y في ال R and x في + +191 +00:14:15,490 --> 00:14:21,450 +ال Dand why في الـ image انتبهوا للدقة أنا بكتب + +192 +00:14:21,450 --> 00:14:25,030 +بسرعة بس بتكونوا تابعين معايا وين الزوج المرتب ايش + +193 +00:14:25,030 --> 00:14:28,170 +تعريف التقاطع اذا الأنصر نفسه في التنتين طب في ال + +194 +00:14:28,170 --> 00:14:31,250 +Cartesian الإحداث الأول في الأولى و الإحداث التاني + +195 +00:14:31,250 --> 00:14:34,350 +في التانية ايش عمل ال and هذه زيادة ماديش هيها ايش + +196 +00:14:34,350 --> 00:14:37,850 +ممكن انا اتخلص منها simplification بال and ف + +197 +00:14:37,850 --> 00:14:44,050 +simplificationXY في الـR و X في الـD طبعا كل واحد + +198 +00:14:44,050 --> 00:14:50,690 +التعريفات B and Q implies B وهو المطلوب إثباته XY + +199 +00:14:50,690 --> 00:14:54,810 +تنتمي للـR تقاطع أو what is restricted to D تعريف + +200 +00:14:54,810 --> 00:15:01,470 +definition فإيش صار إنه Thus الطرف اليسار subset + +201 +00:15:01,470 --> 00:15:04,990 +من الطرف اليمين العكس اليمين طبعا subset من اليسار + +202 +00:15:04,990 --> 00:15:11,460 +الآنimage الـ R subset من R restricted to D وهذا + +203 +00:15:11,460 --> 00:15:15,720 +الجزء التالي طبعا واحد واثنين يؤدوا إلى التساوي + +204 +00:15:15,720 --> 00:15:21,860 +واحد and two implies R restricted to D تساوي D أو + +205 +00:15:21,860 --> 00:15:28,300 +R تقاطع D cross الimage طبعا هذه أيش؟ عشان يكون + +206 +00:15:28,300 --> 00:15:31,160 +جواب كامل ونموذجي + +207 +00:15:33,410 --> 00:15:37,870 +أي سؤال؟ في أي استفسار؟ طبعا هنا، حكاية + +208 +00:15:37,870 --> 00:15:43,210 +الـsimplification بتشككني أن التكافؤ مش صحيح، بدها + +209 +00:15:43,210 --> 00:15:46,490 +دقة، فهذه أسهل وأوضح، وهذا احنا اللي بننصح فيه + +210 +00:15:46,490 --> 00:15:51,310 +دائما، خصوصا في طالبات، المبتدئات، طالبات المبادئ، + +211 +00:15:51,310 --> 00:15:55,170 +التكافؤ بده تكون متأكدة مليون المية، مش مليون + +212 +00:15:55,170 --> 00:16:01,530 +المية، ان هو كل خطوة التكافؤ متابعين؟ + +213 +00:16:01,530 --> 00:16:03,030 +ننتقل للمثال التالف + +214 +00:16:14,000 --> 00:16:17,720 +فأرجو هذه طريقة التحليل تحليل المعطيات وتحليل + +215 +00:16:17,720 --> 00:16:22,360 +المطلوب اتوقع انها سياسة مهمة جدا و بتساعدنا كيف + +216 +00:16:22,360 --> 00:16:27,020 +نفكر ايش المعانا ايش اللي بدنايا و كيف نوصل و كيف + +217 +00:16:27,020 --> 00:16:30,960 +نوصل كيف الطريقة الصحيحة الرياضية و نمشي فيها و زي + +218 +00:16:30,960 --> 00:16:36,450 +ما انتوا شايفين مافيش لا سحرولا في اختراع ولا شيء + +219 +00:16:36,450 --> 00:16:39,410 +بنمشي من التعريفات و هوين هدفنا بنقول كيف بدنا + +220 +00:16:39,410 --> 00:16:43,210 +نوصل هل المعطيات تؤدي للمطلوب ولا ماتؤديش بس بنرتب + +221 +00:16:43,210 --> 00:16:47,690 +.. بنرتب و بنمشي خطوة خطوة السؤال الخامس تقريبا + +222 +00:16:47,690 --> 00:16:52,030 +على نفس النمط برضه بديني تعريف جديد و يشغل عليه + +223 +00:16:52,030 --> 00:16:57,190 +let R be a relation from A to B and let X subset + +224 +00:16:57,190 --> 00:17:02,800 +من A define برضه بديني تعريف جديد R ال Xبديوا + +225 +00:17:02,800 --> 00:17:07,920 +يديني ايش صورة subset R of X من ال relation كأنه + +226 +00:17:07,920 --> 00:17:11,560 +بدي ايش كيف مجموعة تحت ال R بتصور اللي بيسموها + +227 +00:17:11,560 --> 00:17:15,760 +صورة المجموعة صورة المجموعة R of X ما هي؟ هل هي + +228 +00:17:15,760 --> 00:17:20,500 +relation؟ لأ مجموعة عادية هي Y في ال B هي Y في ال + +229 +00:17:20,500 --> 00:17:25,440 +B اذا احنا متوقعين ال R of X يتكون subset من ال B + +230 +00:17:25,440 --> 00:17:28,820 +subset من ال B لو ده نرسم صورة هي subset من ال B + +231 +00:17:28,820 --> 00:17:33,270 +خلينا نرسم الصورةمش غلط لأنها بتساعدنا خلينا نرسم + +232 +00:17:33,270 --> 00:17:37,110 +الصور تقولنا دايما الرسم إيش أداة مساعدة في + +233 +00:17:37,110 --> 00:17:41,270 +الرياضيات ليست أداة حل وليست أداة برهان لكنها أداة + +234 +00:17:41,270 --> 00:17:45,450 +مساعدة فبرضه عندنا هذه المعطيات هي في عندنا A وهي + +235 +00:17:45,450 --> 00:17:50,590 +في عندنا كمان مجموعة BY في عندنا relation R وفي + +236 +00:17:50,590 --> 00:17:55,690 +عندنا مجموعة X subset من ال A capital X وفي عندنا + +237 +00:17:55,690 --> 00:18:01,030 +صورتها R of X subset من ال B لأنه قال ليش كل + +238 +00:18:01,030 --> 00:18:05,250 +عناصرها مين؟ في ال B في ال B إيش ما لهم؟ هما إيش؟ + +239 +00:18:05,250 --> 00:18:09,270 +هما ال Y اللي هي ال .. إيش؟ الإحداث التاني من زوج + +240 +00:18:09,270 --> 00:18:14,930 +مرتب XY في ال R for some X تنتمي لcapital Xإيش + +241 +00:18:14,930 --> 00:18:20,930 +بيبعنى؟ أنا باخد Y ليش؟ فانا يندي بدي هنا X وين + +242 +00:18:20,930 --> 00:18:25,700 +صورتها؟ هنا Yفبدّي العناصر اللي إيش الصور اللي + +243 +00:18:25,700 --> 00:18:28,800 +عناصرهم وين زو الإحداثيهم الأول من وين جاي من ال X + +244 +00:18:28,800 --> 00:18:33,580 +مش من كل ال A فهذه صورة يعني إشماله كأنه R of X أو + +245 +00:18:33,580 --> 00:18:37,740 +هي هي بالظبط إشمالها هي سبسط من ال image ال image + +246 +00:18:37,740 --> 00:18:41,680 +مين هو ال image كل الصور الممكنة ال image طب هد + +247 +00:18:41,680 --> 00:18:45,380 +إشماله بدوش كل الصور الممكنة بدو بس صور العناصر + +248 +00:18:45,380 --> 00:18:48,660 +اللي في ال X اللي هي جزء من ال A جزء من ال A كأنه + +249 +00:18:48,660 --> 00:18:53,870 +ممكن أسميها إيش هي ال image لل RRestricted to X + +250 +00:18:53,870 --> 00:18:58,710 +اللي تعوي عرفناها هي image ال R restricted to X + +251 +00:18:58,710 --> 00:19:03,310 +هذه جانبية مش هي الأساس فهو هنا ايش بعرف باختصار + +252 +00:19:03,310 --> 00:19:09,730 +بعرف صورة subset من ايش من ال A او من ال domain او + +253 +00:19:09,730 --> 00:19:10,630 +من ال A بشكل عام + +254 +00:19:14,360 --> 00:19:23,260 +المعطيات تمام ا proof that if D subset من A and E + +255 +00:19:23,260 --> 00:19:30,190 +subset من Aصورة التقاطع أخد مجموعتين جزئيتين من + +256 +00:19:30,190 --> 00:19:37,270 +الـA أخد D و أخد E مجموعتين من الـA فبقوللي صورة + +257 +00:19:37,270 --> 00:19:42,510 +تقاطعهم صورة التقاطع اشمالها subset من تقاطع الصور + +258 +00:19:42,510 --> 00:19:48,330 +صورة التقاطع هي subset من تقاطع الصور واضحة؟ اه + +259 +00:19:48,330 --> 00:19:51,530 +بدنا نكتبها واحدة واحدة ودي بدأ الحل فده المثال + +260 +00:19:51,530 --> 00:19:52,210 +الخامس + +261 +00:19:55,760 --> 00:19:59,860 +أه طبعا بنفس الصورة في أنا في عندي مين؟ في عندي R + +262 +00:19:59,860 --> 00:20:03,660 +of D و في عندي R of E + +263 +00:20:06,440 --> 00:20:09,560 +ها هي العملية زي ما عملنا ال X كمان مثال يقول لي + +264 +00:20:09,560 --> 00:20:13,320 +أي subset بتتحدث عن صورتها أي subset capital X من + +265 +00:20:13,320 --> 00:20:16,640 +ال A صورتها بتكون subset من ال B طب خدوا كمان two + +266 +00:20:16,640 --> 00:20:20,300 +subsets D و A وين صورهم ده تكون؟ subset من ال B + +267 +00:20:20,300 --> 00:20:24,560 +فبقوللي صورة التقاطع subset من تقاطع طبعا موجودة + +268 +00:20:24,560 --> 00:20:28,780 +في ال B أكيد لكن أشملها هي subset من تقاطع الصورة + +269 +00:20:28,780 --> 00:20:34,920 +فالبطلوب جملة شرطية compound statement بقوللي D + +270 +00:20:35,260 --> 00:20:41,280 +subset من الـA and E subset من الـA implies صورة + +271 +00:20:41,280 --> 00:20:49,680 +التقاطع subset من تقاطع الصور R E هذا المطلوب + +272 +00:20:49,680 --> 00:20:52,180 +solution + +273 +00:20:56,410 --> 00:21:01,410 +فطبعا جملة شرطية اذا سؤال المثال الماضي كان جملة + +274 +00:21:01,410 --> 00:21:03,690 +بسيطة هي اللي بدنا نتعلمه في البداية هنا جملة + +275 +00:21:03,690 --> 00:21:07,190 +شرطية كيف البرهان نفترض ان الشرط صحيح فهنبدأ + +276 +00:21:07,190 --> 00:21:15,350 +البرهان نقول له assume D subset من A and E subset + +277 +00:21:15,350 --> 00:21:20,850 +من Eمن الـ A، مطلوب نثبت هذه العلاقة، علاقة إيش؟ + +278 +00:21:20,850 --> 00:21:25,610 +subset، هنبدأ بعنصر فيها و نوصل للطرف التاني، + +279 +00:21:25,610 --> 00:21:31,370 +العنصر اللي هان زوج مرتب ولا عنصر عادي؟ بقى عيب + +280 +00:21:32,150 --> 00:21:36,770 +حاضر، حاضر، بين أيه؟ اه، فإذا احنا في عيننا تعريف + +281 +00:21:36,770 --> 00:21:41,710 +جديد بيتحدث عن صورة مجموعة جزئية من المجموعة + +282 +00:21:41,710 --> 00:21:43,950 +الأولى، اللي هي كبة الـA اللي هو عملناها الصورة + +283 +00:21:43,950 --> 00:21:49,270 +تبع الـX والآن سأل سؤال بخصوص هذا التعريف الجديد + +284 +00:21:49,630 --> 00:21:53,530 +بقولّي هل صورة التقاطع أثبت إن صورة التقاطع هي + +285 +00:21:53,530 --> 00:21:57,130 +subset من تقاطع الصور صور بس إيش مش صور أنصر صور + +286 +00:21:57,130 --> 00:22:00,710 +مجموعة صور subset واضحة الصورة إيش باختصار هيك + +287 +00:22:00,710 --> 00:22:05,690 +المثال أو هيك السؤال فالأن طبعا الجملة الشرطية جلب + +288 +00:22:05,690 --> 00:22:08,410 +prove that نبدأ واحدة واحدة زي ما قلنا نوغل برفق + +289 +00:22:08,410 --> 00:22:12,210 +من الخارج لداخل أه بقول if then سيبقى من التفاصيل + +290 +00:22:12,210 --> 00:22:15,730 +إذا جملة شرطية بدأنا قلنا assume إن ال condition + +291 +00:22:15,730 --> 00:22:21,130 +true افترض إن الشرط صحيحمطلوب اثبات جواب الشرط + +292 +00:22:21,130 --> 00:22:25,230 +جواب الشرط ممكن اكتبها او ممكن اختصف تمام جواب + +293 +00:22:25,230 --> 00:22:29,510 +الشرط simple statement عبارة عن ايش علاقة subset + +294 +00:22:29,510 --> 00:22:34,130 +استغلنا عليها سابقا كثير هنبدأ من عنصر عشوائي من + +295 +00:22:34,130 --> 00:22:38,490 +الطرف اليسار و نوصله الييمين تمامأنا أتقدمنا الآن + +296 +00:22:38,490 --> 00:22:42,470 +مش أي مجموعة بأشتغل بأشتغل على صورة الصورة عناصرها + +297 +00:22:42,470 --> 00:22:46,690 +أزواج مرتبة ولا عناصر؟ عناصر ليه؟ إيش هيه؟ جال + +298 +00:22:46,690 --> 00:22:50,750 +الصور إيه الصبصة من الـBY ومن الأفضل أسميها X ولا + +299 +00:22:50,750 --> 00:22:54,570 +Y؟ أقول له let X be .. Y أفضل لأنه بيوحيله إنها + +300 +00:22:54,570 --> 00:22:57,570 +صورة إنها في الـB لأنه أنا بدي أشهر في عندي صورة + +301 +00:22:57,570 --> 00:23:02,390 +ذهنية نمطية إن X في الـA وY في الـB وأنا أين رايح؟ + +302 +00:23:02,390 --> 00:23:05,290 +رايح هنا هذا هو الـA الشترة التقاطي فبدي أقول له + +303 +00:23:05,290 --> 00:23:13,830 +هنا letWhy be any element such that + +304 +00:23:16,590 --> 00:23:21,490 +Y في الطرف اليسارى اللى هو إيش صورة التقاطع دي + +305 +00:23:21,490 --> 00:23:26,810 +تقاطع ال E طب لو حطيت لك X غلط لأ مافيش رمز غلط و + +306 +00:23:26,810 --> 00:23:31,890 +رمز صح بس في رمز أنسب F بساعدنا أكتر بساعدنا أكتر + +307 +00:23:31,890 --> 00:23:37,850 +لأنه لو أنا قلتلك إن X بتساوي F of Y تتغلب فيها + +308 +00:23:37,850 --> 00:23:41,710 +لما لو قلت Y F of X دايما أريحلك ولا لأ فهذه هي + +309 +00:23:41,710 --> 00:23:45,580 +النقطة لإن دايما إيش في رموز متعودين عليهابتكون + +310 +00:23:45,580 --> 00:23:49,060 +فيها رياحية في التعامل معها لكن مافيش أيش غلط + +311 +00:23:49,060 --> 00:23:51,300 +ممتاز + +312 +00:23:52,380 --> 00:23:57,260 +إيش ممكن نعمله؟ نفسر إيش معناته؟ اللي هو إيش صورة + +313 +00:23:57,260 --> 00:24:00,980 +مجموعة أنا عندي بدل ال X إيش؟ عندي تخاطر مجموعتين، + +314 +00:24:00,980 --> 00:24:04,360 +نفس الشيء فهذا بيقول لي طبقا للتعريف ال Y إيش + +315 +00:24:04,360 --> 00:24:08,420 +معناه؟ هي عنصر في ال B بحيث إن ال X Y في ال R و ال + +316 +00:24:08,420 --> 00:24:11,820 +X هي عنصر في مين؟ في المجموعة اللي بياخد صورتها + +317 +00:24:11,820 --> 00:24:15,960 +فهذا معناته هذا implies أنا مهتم بـimplies مش مهتم + +318 +00:24:15,960 --> 00:24:23,170 +بالتكافر أنا بدا أبسط فهذا implies إن X Yتنتمي للـ + +319 +00:24:23,170 --> 00:24:29,520 +R من وين جيبت الـ X من التعريف sum Xوين موجودة sum + +320 +00:24:29,520 --> 00:24:33,200 +X في الـ D تقاطع الـ E أحسنته؟ نعم لأن هي الـ X + +321 +00:24:33,200 --> 00:24:36,340 +فيها هذه الصورة العامة وهذا مثال عليها الصورة + +322 +00:24:36,340 --> 00:24:39,120 +العامة بيقولي لأي مجموعة كابت الـ X طب عندك أنت + +323 +00:24:39,120 --> 00:24:43,260 +إيش مطلوب؟ بدك التقاطع، بدك تشر على التقاطع تمام؟ + +324 +00:24:43,260 --> 00:24:47,280 +وين رايحين احنا؟ بدنا نفصل الـ D لحال و الـ E لحال + +325 +00:24:47,280 --> 00:24:50,700 +فكيف ممكن نفصلها؟ من تعريف التقاطع + +326 +00:24:59,120 --> 00:25:04,420 +X such that X + +327 +00:25:04,420 --> 00:25:08,580 +تنتمي إلى D و X تنتمي إلى E تعريف التقاطة + +328 +00:25:08,580 --> 00:25:14,900 +Definition of intersection وهنا تعريف R لـ X + +329 +00:25:19,470 --> 00:25:23,390 +هي التعريف بس بدل X أنا عندي صورة مين؟ صورة X ولا + +330 +00:25:23,390 --> 00:25:28,130 +صورة التقاطع؟ حطوا X محلها فإيش قال لي؟ قال لي ال + +331 +00:25:28,130 --> 00:25:32,750 +Y موجودة في الصورة إذا كانت هي إحداثي تاني من زوج + +332 +00:25:32,750 --> 00:25:35,910 +مرتب إحداثي الأول من وين جبته؟ من المجموعة زي ما + +333 +00:25:35,910 --> 00:25:39,410 +عملنا الصورة شايفة؟ هي ال X وهي ال Y بس بدل + +334 +00:25:39,410 --> 00:25:43,740 +capital X إيش عندي السؤال؟ تقاطع واضحيت؟تمام؟ + +335 +00:25:43,740 --> 00:25:49,440 +ممتاز الان ايش عندي؟ عندي xy في ال R for some x في + +336 +00:25:49,440 --> 00:25:54,160 +ال D هذا ايه اشماله؟ معناته ان ال Y في صورة ال D + +337 +00:25:54,160 --> 00:25:57,360 +اه بتبدأ .. بتبدأ .. بتبدأ .. جزئها هذه جزئين فإذا + +338 +00:25:57,360 --> 00:26:04,840 +هذا بيقول ليه؟إن ال Y في R ال D ليش X Y في ال R ال + +339 +00:26:04,840 --> 00:26:08,060 +Y إحداث تاني من زوج مرتب ال X وين موجودة في ال D + +340 +00:26:08,060 --> 00:26:14,320 +إذا ال Y وين في صورة ال D أيضًا X Y في ال R و X في + +341 +00:26:14,320 --> 00:26:19,440 +ال E إذا ال Y وين في صورة ال E and Y تنتمي ل R of + +342 +00:26:19,440 --> 00:26:26,760 +E طبعًا تعرف نفسه خلص نصل إلى التقاطة تقاطة + +343 +00:26:26,760 --> 00:26:29,240 +ال R of E وهو المطلوب + +344 +00:26:31,800 --> 00:26:40,800 +R of D تقاطع الـ E هو subset من R of D تقاطع R الـ + +345 +00:26:40,800 --> 00:26:48,740 +E وهو المطلوب أي سؤال؟ لأ لأ احنا اللي عندنا هنا + +346 +00:26:48,740 --> 00:26:54,940 +هذا هيالتعريفش بيقول ما هو صورة المجموعة هي كل + +347 +00:26:54,940 --> 00:26:58,140 +إحداث تاني Y إذا الإحداث الأول تبع وين؟ في + +348 +00:26:58,140 --> 00:27:01,960 +المجموعة فما هي R of D هي كل إحداث تاني من زوج + +349 +00:27:01,960 --> 00:27:04,420 +مرتب الإحداث الأول تبعه في ال D موجود ال X في ال D + +350 +00:27:04,420 --> 00:27:08,220 +إذا ال Y وين؟ في صورة ال D طب XY في ال R و X في ال + +351 +00:27:08,220 --> 00:27:13,600 +E إذا ال Y وين؟ في صورة ال E و بس و خلصت طبعا هذه + +352 +00:27:13,600 --> 00:27:17,300 +subset صحية لكن العكس غير صحية ممكن تجربوها غالبا + +353 +00:27:17,300 --> 00:27:26,650 +أن العكس غير صحيةتمام الآن ننتقل لمفهوم مهم جدا + +354 +00:27:26,650 --> 00:27:31,090 +يمكن هو المفهوم الأساسي في دراسة الألاقات ما يُعرف + +355 +00:27:31,090 --> 00:27:36,810 +بـ equivalence relations علاقات التكافؤ فإحنا في + +356 +00:27:36,810 --> 00:27:41,270 +معمضة تحدثنا عن الألاقات بشكل عام الآن هنخصص .. + +357 +00:27:41,270 --> 00:27:46,150 +هندرس نوع خاص من الألاقات نوع خاص من الألاقات تسمى + +358 +00:27:46,150 --> 00:27:50,870 +علاقات التكافؤفهذه أيش علاقة ولها كمان شرط هنسميها + +359 +00:27:50,870 --> 00:27:54,830 +علاقة التكافؤ فهي علاقة ويلها بعض الخواصة هنبدأ + +360 +00:27:54,830 --> 00:27:59,990 +بالتعريف في هذا التعريف هنعرف علاقة التكافؤ كهدف + +361 +00:27:59,990 --> 00:28:04,370 +رئيسي لكن علاقة التكافؤ تعرف بتلت مفاهيم رئيسية + +362 +00:28:04,370 --> 00:28:10,500 +وهي الانعكاسوالتماثل والتعدى فبدنا تلت مفاهيم + +363 +00:28:10,500 --> 00:28:14,140 +ونربطهم بالتكافئة بعلاقة بفهم التكافئة فإن عندنا + +364 +00:28:14,140 --> 00:28:18,840 +أربع مفاهيم في تلت مفاهيم مستقلة عن بعض كلهم إذا + +365 +00:28:18,840 --> 00:28:21,940 +ارتبطوا إذا اتحققوا بسمي العلاقة علاقة التكافئة + +366 +00:28:21,940 --> 00:28:28,690 +فأول مقدمة let R be a relation on asset Xإذاً من + +367 +00:28:28,690 --> 00:28:33,190 +هنا نطالع بدي أشتغل على علاقة R من مجموعة على + +368 +00:28:33,190 --> 00:28:37,170 +نفسها بنفع أشتغل أي مفهوم من المفاهيم التالية على + +369 +00:28:37,170 --> 00:28:41,570 +علاقة عامة من A ل B و الـB غير عن الـA؟ لأ، فأول + +370 +00:28:41,570 --> 00:28:45,970 +ملاحظة الـ equivalence relations و ما يتعلق بها + +371 +00:28:45,970 --> 00:28:51,850 +بينفعش يشتغل، بينفعش أعرفه لعلاقة من أي مجموعة لأي + +372 +00:28:51,850 --> 00:28:54,590 +مجموعة أخرى، لازم المجموعة على نفسها، بدي أشتغل + +373 +00:28:54,590 --> 00:28:59,050 +على مجموعة نفسها، فهو هنا قال ليه؟A relation on X + +374 +00:29:01,360 --> 00:29:06,400 +فإذن هي إيش؟ أول شيء هي علاقة من مجموعة إلى نفسها + +375 +00:29:06,400 --> 00:29:09,600 +اللي أنا بديش أسميها capital X أسميها capital X مش + +376 +00:29:09,600 --> 00:29:14,800 +خضيع then المفهوم الأول علاقة التماثل اللي هو إيش + +377 +00:29:14,800 --> 00:29:18,360 +reflexive اللي يسموها تماثل بيعرفوها علاقة + +378 +00:29:18,360 --> 00:29:24,680 +reflexive علاقة تماثل وقت إيش؟ if and only if ال X + +379 +00:29:24,680 --> 00:29:31,510 +انعكاس مش علاقة انعكاس reflexive انعكاسإذاً أول + +380 +00:29:31,510 --> 00:29:36,830 +مفهوم اللي هو العلاقة تكون علاقة in a cast اللي هو + +381 +00:29:36,830 --> 00:29:40,450 +إيش reflexive relation وقت إيش هي if and only if + +382 +00:29:40,450 --> 00:29:44,350 +relation X related to X for all X تنتمي لcapital X + +383 +00:29:44,350 --> 00:29:49,260 +بمعنى إن كل عنصر في المجموعة له علاقة مع نفسههي + +384 +00:29:49,260 --> 00:29:52,660 +انعكاس، مع انعكاس يعني زي إيش؟ زي في مرآة، تنعكس، + +385 +00:29:52,660 --> 00:29:55,360 +فصورة ليش بيشوف ده في المرآة، بيشوف نفسه، فجميع + +386 +00:29:55,360 --> 00:29:59,620 +عنصر له علاقة مع نفسه، لجميع عناصر المجموعة، بدنا + +387 +00:29:59,620 --> 00:30:02,680 +كل عنصر يكون له علاقة مع نفسه، for all X in + +388 +00:30:02,680 --> 00:30:06,200 +capital X، هذه معنات reflexive، علاقة انعكس، + +389 +00:30:06,200 --> 00:30:10,500 +اتنين، بي، علاقة الواي ال symmetric، التماثل، + +390 +00:30:10,500 --> 00:30:14,380 +symmetric، أه إيش علاقتها؟ بيقوللي إذا كانت جملة + +391 +00:30:14,380 --> 00:30:17,740 +شرطية التعريف، شوف انتبهوا، في الأول، كيف التعريف؟ + +392 +00:30:18,090 --> 00:30:23,650 +Quant Equal Y باستخدام ال quantifier for all X X X + +393 +00:30:23,650 --> 00:30:26,690 +تنتمي لل R يعني هي X related to X يعني X X تنتمي + +394 +00:30:26,690 --> 00:30:30,910 +لل R فالتانية بقول ليه إذا كانت ال X related لل Y + +395 +00:30:30,910 --> 00:30:36,540 +لازم ال Y تكون related لل X بمعنى آخرإذا كان زوج + +396 +00:30:36,540 --> 00:30:41,700 +ما موجود ع صورة XY لازم معقوسه يكون موجود جملة + +397 +00:30:41,700 --> 00:30:45,040 +شرطية إذا وجد زوج معقوسه لازم يكون موجود هذا ال + +398 +00:30:45,040 --> 00:30:48,440 +symmetric هذا التماثل هذا التماثل جملة شرطية اه + +399 +00:30:48,440 --> 00:30:51,900 +فانا بدي أشوف زوج موجود العكس لازم يكون موجود طب + +400 +00:30:51,900 --> 00:30:54,540 +زوج مش موجود مانيش ده هو بعكسه اه فهي نهيجة مش + +401 +00:30:54,540 --> 00:30:58,980 +جملة شرطية متساويين صح؟ ايش متساويين؟ موجود نفسه + +402 +00:30:58,980 --> 00:31:04,900 +يكونهي جملة شرطية إذا وجد زوج ما لازم عكس يكون + +403 +00:31:04,900 --> 00:31:06,200 +موجود عشان تكون تماثل + +404 +00:31:08,930 --> 00:31:14,610 +علاقة are is طبعا مش I'd is transitive if and only + +405 +00:31:14,610 --> 00:31:19,950 +if هنا شرطين في عندنا أول شي مُعطَين بدنا زوجين + +406 +00:31:19,950 --> 00:31:22,610 +يكونوا موجودين التالت يكون موجود في ال .. في ال + +407 +00:31:22,610 --> 00:31:27,530 +symmetric كل زوج لازم عكسه يكون موجود في التلاتة + +408 +00:31:27,530 --> 00:31:30,190 +.. في تلاتة في عندنا علاقة عمالة تع .. اللي هو + +409 +00:31:30,190 --> 00:31:36,920 +علاقة تعدي إيش بتقول بتقوللي نهايةالأول هي بداية + +410 +00:31:36,920 --> 00:31:42,500 +التاني A نهاية الأول بداية التاني ايش تؤدي انه + +411 +00:31:42,500 --> 00:31:46,780 +امحي المعنى المشترك Y لازم X Z تكون في ال A لازم X + +412 +00:31:46,780 --> 00:31:50,440 +تكون related لل Z فبقول إذا لجيت زوجين إذا لجيت + +413 +00:31:50,440 --> 00:31:56,820 +زوجيننهاية الأول بداية للتاني لازم بداية الأول مع + +414 +00:31:56,820 --> 00:32:00,220 +نهاية التاني يكون لهم علاقة مع بعض بهذا المعنى فهي + +415 +00:32:00,220 --> 00:32:04,660 +علاقة تعدي زي ما قلنا ليش في أنا في عندي مرحلة أو + +416 +00:32:04,660 --> 00:32:09,820 +محطة وسطة ال Y محطة وسطةالـ X بتوصل للـ Y والـ Y + +417 +00:32:09,820 --> 00:32:13,380 +بتوصل للـ Z لازم يكون فيه علاقة مباشرة بين الـ X و + +418 +00:32:13,380 --> 00:32:16,580 +بين الـ Z بها ده المعنى فهذه علاقة تعدي وشوفناها + +419 +00:32:16,580 --> 00:32:20,220 +زي في ال implies ولها ده نفس العملية لو في عملية + +420 +00:32:20,220 --> 00:32:24,100 +تعدي في حلقة وسيطة ببدأ من الأول للأخير من الأول + +421 +00:32:24,100 --> 00:32:27,920 +للأخر إذا عملنا هى دول تلاتة هى أول و تاني متكرر + +422 +00:32:27,920 --> 00:32:33,590 +من Y من X لZ من الأول للأخر فهذه ال transitالمفهوم + +423 +00:32:33,590 --> 00:32:36,830 +الرابع والأخير بيجمحهم اللي هو المفهوم الرئيسي + +424 +00:32:36,830 --> 00:32:40,170 +وماكنتش بقول على علاقة ان علاقة التكافؤ إذا كانت + +425 +00:32:40,170 --> 00:32:44,410 +تلاتة مع بعض كانت reflexive، symmetric وtransitive + +426 +00:32:44,410 --> 00:32:48,690 +إلى خاصية الانعكاس، خاصية التماثل وخاصية التعد + +427 +00:32:48,690 --> 00:32:51,950 +فبدنا نفهم دول الأربع مع بعض طبعا الرابع مقتمد على + +428 +00:32:51,950 --> 00:32:56,250 +التلاتة الأولى لكن هنفهمهم بالترتيب نبدأ كالعادة + +429 +00:32:56,250 --> 00:33:00,250 +بأمثلة بسيطة نبدأ بأمثلة بسيطة المثال الأول + +430 +00:33:04,790 --> 00:33:08,450 +طبعا هنكرر الأمر و نعيد المثال التعريف و نذكر ان + +431 +00:33:08,450 --> 00:33:13,490 +شاء الله بالتفصيل عشان نوضحه بصيغ مكافئة أخرى + +432 +00:33:13,490 --> 00:33:17,510 +بدأنا بمجموعة بسيطة capital X و تو H بتتكون من + +433 +00:33:17,510 --> 00:33:22,310 +عصوين 1 و 2وجلّت R بيكون relation on X إذا نحن + +434 +00:33:22,310 --> 00:33:25,850 +عشان ندرس المفاهيم الأربعة لازم يكون في ال + +435 +00:33:25,850 --> 00:33:28,250 +relation when من مجموعة على نفسها يعني relation + +436 +00:33:28,250 --> 00:33:31,130 +على الاش على مجموعة بنسميها اختصارا بدا ما نقول من + +437 +00:33:31,130 --> 00:33:35,130 +X ل X بنقول on X تمام given by عرف ال relation + +438 +00:33:35,130 --> 00:33:38,450 +تتكون من تلت أزواج مرتبة الواحد والواحد والواحد + +439 +00:33:38,450 --> 00:33:42,450 +والتنين والتنين والتنينأه طبعا مثال بسيط ومباشر + +440 +00:33:42,450 --> 00:33:45,850 +لأنه احنا في البداية show that ال R is reflexive + +441 +00:33:45,850 --> 00:33:51,110 +وtransitive لكن not symmetric فهيلاقها تتمتع + +442 +00:33:51,110 --> 00:33:55,450 +بخاصية الانعكاس وخاصية التعدي لكن لا تتمتع بخاصية + +443 +00:33:55,450 --> 00:33:59,930 +التمر خلينا نبدأ فيهم واحدة واحدة solution فأول + +444 +00:33:59,930 --> 00:34:04,150 +شيء بدي أثبت أن ال R is reflexive + +445 +00:34:08,650 --> 00:34:11,890 +خلّيني أكتب بها عادة كتابة Reflexive إيش معنات + +446 +00:34:11,890 --> 00:34:16,730 +Reflexive ده هي صياغتها بشكل مختلف For all X تنتمي + +447 +00:34:16,730 --> 00:34:24,290 +لـX XX تنتمي لـR اللي هي هذه نفسها فهذا هو المطلوب + +448 +00:34:25,190 --> 00:34:27,990 +فال statement اللي كتبناها ممكن يعدي صياغتها + +449 +00:34:27,990 --> 00:34:32,970 +بالشكل التالي جالي إيش؟ جالي X related to X for + +450 +00:34:32,970 --> 00:34:37,070 +all X تنتمي لكاميتال X هيها بعادة صياغة واضح فها + +451 +00:34:37,070 --> 00:34:40,190 +دي معناه reflect بدنا نشوف إيش بدنا نعمل؟ بدنا كل + +452 +00:34:40,190 --> 00:34:42,670 +هنصر في ال X اللي علاقة مع نفسه، مين عناصر ال X؟ + +453 +00:34:42,670 --> 00:34:45,510 +الواحد اللي علاقة مع نفسها نعم، واحد واحد في ال R + +454 +00:34:45,510 --> 00:34:50,790 +صح فأول شيء واحد واحد تنتمي لل R طيب مين كمان؟ + +455 +00:34:50,790 --> 00:34:54,920 +اتنين من اللي علاقة مع نفسها؟ نعمأه تمشي أفحصه + +456 +00:34:54,920 --> 00:34:59,080 +خلصت مش هيجلي for all small x in capital X capital + +457 +00:34:59,080 --> 00:35:01,920 +X خلصوا أولا صرا في هذا المثال الواحد والاتنين + +458 +00:35:01,920 --> 00:35:06,180 +فحصهم نعم الاتنين اتحققوا نعم هداش معناته أن هي + +459 +00:35:06,180 --> 00:35:11,420 +فعلا reflex R + +460 +00:35:11,420 --> 00:35:18,740 +is reflex فهذا هو المعنى وكيف بنطبقهطبعا عشان + +461 +00:35:18,740 --> 00:35:23,100 +المثال مجموعة تتكون من عدد عناصر محدود فحصنا كل + +462 +00:35:23,100 --> 00:35:26,040 +عنصر بالدور طب لو ماكنتش بنشوف طريقة عامة هنشوف + +463 +00:35:26,040 --> 00:35:28,800 +أمثلة مختلفة لكنها دي هو الصورة إيش meant for all + +464 +00:35:28,800 --> 00:35:31,520 +ويعني إيش كل عنصر أيه علاقة مع نفسه كل عنصر من + +465 +00:35:31,520 --> 00:35:34,500 +المجموعة أكام عنصر اتنين فعلا كل واحد له علاقة مع + +466 +00:35:34,500 --> 00:35:39,440 +نفسه is an reflex طيب بقول هي transitive أيضا ال R + +467 +00:35:39,440 --> 00:35:44,520 +is transitiveإيش معناه الـ Transit؟ فخلّيني أقعد + +468 +00:35:44,520 --> 00:35:49,840 +صياغتها صياغتها بتقول لي دي جملة شرطية إذا XY في + +469 +00:35:49,840 --> 00:35:59,220 +الـR and YZ في الـR then XZ في الـR هذا المطلوب + +470 +00:36:01,100 --> 00:36:07,440 +فكيف بدنا نفحصها؟ بدنا نشوف زوجين بداية التاني + +471 +00:36:07,440 --> 00:36:12,060 +نهاية الأول ونشوف التالت صح ولا لأ فبنبدأ نفحص كل + +472 +00:36:12,060 --> 00:36:17,160 +زوجين على حدة نشوف .. نبدأ من الأول واحد .. واحد + +473 +00:36:17,160 --> 00:36:21,840 +وواحد في الأرضبدنا زوج اخر بدنا اي زوج بدنا واحد + +474 +00:36:21,840 --> 00:36:25,480 +يبدأ بالواحد غيره في غير الواحد واحد يبدأ بالواحد + +475 +00:36:25,480 --> 00:36:31,020 +الواحد اتنين and واحد اتنين تنتمي لل R لازم تؤدي + +476 +00:36:31,020 --> 00:36:35,620 +ان واحد اتنين تنتمي لل R true ولا مش true؟ true + +477 +00:36:35,620 --> 00:36:39,960 +لان التلاتة ده الموجودين ولا لأ هاي واحدبدايته + +478 +00:36:39,960 --> 00:36:44,040 +نهايته واحد واللي بعده بدايته واحد ممكن احذف + +479 +00:36:44,040 --> 00:36:47,320 +الواحد والواحد اللي في النص نعم واحد اتنين موجودة + +480 +00:36:47,320 --> 00:36:50,860 +نعم يعني هنا بدنا ننتبه ممكن يمكن التلوين يوضح + +481 +00:36:50,860 --> 00:36:55,870 +الصورة فدا واحد ودا واحد متشابهينبدي ماروحه ماليش + +482 +00:36:55,870 --> 00:36:58,750 +دعوة اتشابه هنا اي ال Y طبعا X بيساوي Y بالصدفة + +483 +00:36:58,750 --> 00:37:01,470 +لكن انا بحكي بشكل عام فهذه اللي بده يكون انا فيها + +484 +00:37:01,470 --> 00:37:05,050 +عندي اذا كان زوجين انواجده بهذه الشروط مش اي زوجين + +485 +00:37:05,050 --> 00:37:08,910 +باللي ليش معناته نهاية الأول بداية التاني لازم ليش + +486 +00:37:08,910 --> 00:37:11,990 +احذف المتكرر واشوف الزوج اللي بتبقى منتمي ولا مش + +487 +00:37:11,990 --> 00:37:15,910 +منتمي؟ منتمي فإذا هذه اسمها ال true فهذه ال true + +488 +00:37:15,910 --> 00:37:20,350 +طيب نشوف كمان بدنا نشوف كل أزواج اللي على هذه + +489 +00:37:20,350 --> 00:37:27,130 +الشكلةلازم نفحص كل الأزواج اللي على هذه الشاكلة + +490 +00:37:27,130 --> 00:37:32,730 +طيب في عنصر آخر بيبدأ بواحد غير الواحد اتنين؟ لأ + +491 +00:37:32,730 --> 00:37:35,650 +إذا نخلص من واحد واحد خلصنا منه اللي هو نهايته + +492 +00:37:35,650 --> 00:37:38,130 +واحد و بدنا ندور على الأزواج اللي بتبدأ بواحد ما + +493 +00:37:38,130 --> 00:37:42,270 +خلصنا ناخد التاني واحد اتنين في الار بدنا العناصر + +494 +00:37:42,270 --> 00:37:46,950 +اللي بتبدأ باتنين تشيلة اتنين اتنين هل هذا يؤدي ان + +495 +00:37:46,950 --> 00:37:54,610 +واحد اتنين موجودة في الار؟ اه trueصح اه طيب في غير + +496 +00:37:54,610 --> 00:37:57,890 +اتنين اتنين تبدأ بتنين؟ لأ فانا بدي افحص كل زوجين + +497 +00:37:57,890 --> 00:38:00,530 +على هذه الصورة bye نبدأ نقش طلعة التالت اتنين + +498 +00:38:00,530 --> 00:38:05,290 +اتنين في حد ببدأ بتنين؟ لأ اذا انخلصنا .. اذا + +499 +00:38:05,290 --> 00:38:10,710 +انخلصنافإذا فعلًا إذا لجيت زوجين بالشروط اللي + +500 +00:38:10,710 --> 00:38:15,470 +حكيناها نهاية الأول بداية التاني يؤدي إنه فيه تالت + +501 +00:38:15,470 --> 00:38:18,530 +موجود اللي هو إيش بتتكون من بداية الأول و نهاية + +502 +00:38:18,530 --> 00:38:25,450 +التاني نشيل المشترك ففعلا اتحققمش كل .. كل زوجين + +503 +00:38:25,450 --> 00:38:30,410 +بهذا الشرط كل زوجين موجودين التالت بيكون مكمل إلهم + +504 +00:38:30,410 --> 00:38:35,830 +بالشروط هذه إذا لجيت XY وYZ لازم X يكون موجودين + +505 +00:38:35,830 --> 00:38:41,050 +فعلا فإذا إيش معناته إنه transitive thus R is + +506 +00:38:41,050 --> 00:38:47,570 +transitive R + +507 +00:38:47,570 --> 00:38:48,690 +is not symmetric + +508 +00:38:55,010 --> 00:38:57,190 +بدنا نثبت انها not symmetric طبعا اسمها not + +509 +00:38:57,190 --> 00:39:02,150 +symmetric اذا كانت XY في الار لازم YX تكون في الار + +510 +00:39:02,150 --> 00:39:06,650 +كل زوج اذا انوجد معقوس يكون موجود نشوف واحد واحد + +511 +00:39:06,650 --> 00:39:11,150 +من معقوسه نفسه موجودة طب واحد اتنين؟أتنين واحد مش + +512 +00:39:11,150 --> 00:39:15,030 +موجودة فإيش بتكتبله؟ بتقول واحد اتنين موجودة وعكسه + +513 +00:39:15,030 --> 00:39:19,490 +غير موجود بتقول واحد اتنين موجودة في ال R بط أو + +514 +00:39:19,490 --> 00:39:24,030 +and كل صح بيه بط بتعني and and اتنين one لا تنتمي + +515 +00:39:24,030 --> 00:39:29,090 +لل R فهذا بيقوللي ان ال R is not C + +516 +00:39:34,290 --> 00:39:37,810 +فهنا أول مثال، ومن بعد هنا نتعرف كيف نشتغل + +517 +00:39:37,810 --> 00:39:41,950 +بالتعريف، فأول بالنسبة إلا التعريف اللي هو + +518 +00:39:41,950 --> 00:39:45,470 +الانعكاس ال reflexive، statement فيها for all، بنا + +519 +00:39:45,470 --> 00:39:48,850 +يتحدث بقى، بالنسبة لاللي هو ال symmetric و ال + +520 +00:39:48,850 --> 00:39:52,370 +transitive، جملة شرطية، بنا إذا الشرط اتحقق، بنا + +521 +00:39:52,370 --> 00:39:57,250 +يجيب الشرط يتحقق، نشوف كمان مثال + +522 +00:40:10,190 --> 00:40:13,550 +طبعا هذا هو المثال ان شاء الله مع افكار الأنثى + +523 +00:40:13,550 --> 00:40:23,950 +بشكل عامة مع المجموعات التدوية ايضا مثال بسيط تلت + +524 +00:40:23,950 --> 00:40:28,970 +عناصر المجموعة وعرفنا relation عليها بتتكون من خمس + +525 +00:40:28,970 --> 00:40:35,660 +أزواجP A A C C A و P B اثبت ان ال R هذه الحالة + +526 +00:40:35,660 --> 00:40:42,340 +سيمتريك لكن ليست reflexive ولا transient نبدأ انها + +527 +00:40:42,340 --> 00:40:50,740 +سيمتريك واحد R is symmetric ايش + +528 +00:40:50,740 --> 00:40:58,820 +معناه سيمتريك يعني XY في ال R implies YX في ال + +529 +00:41:02,150 --> 00:41:06,790 +فبدنا نشوف كل زؤوف نفحص معقوسه موجود ولا لا، فالآن + +530 +00:41:06,790 --> 00:41:12,410 +ال A بي موجودة في ال R، هل المعقوسة موجود؟ نعم، بي + +531 +00:41:12,410 --> 00:41:15,970 +A موجودة في ال R، إذا مافيش مشكلة، إذا كان الشرط + +532 +00:41:15,970 --> 00:41:18,790 +صحيح، برضه يهوض الشرط صحيح، إذا ندروه، إذا ال + +533 +00:41:18,790 --> 00:41:22,920 +statement ندروهطيب الجد اللي بعده .. فنفحص الزوج + +534 +00:41:22,920 --> 00:41:26,200 +اللي بعده PA ما هو مفحوظ هنا لأنه دهاش ابدالية + +535 +00:41:26,200 --> 00:41:30,280 +فهنا فحصنا أول واحد و تاني واحد نفحص الآن AC + +536 +00:41:30,280 --> 00:41:35,000 +موجودة في الـR هل معكوسة موجودة؟ نعم موجودة في + +537 +00:41:35,000 --> 00:41:38,300 +الـR فإذا أنا عايش بالـD زي ما تقولنا مفهومها كل + +538 +00:41:38,300 --> 00:41:43,440 +زوج وعكسه موجود فالأول والتاني ومعكس بعض تمامتالت + +539 +00:41:43,440 --> 00:41:47,620 +والرابع عكس بعض موجودين طب الخامس عكسه موجود نعم + +540 +00:41:47,620 --> 00:41:53,980 +لأنه نفسه فممكن برضه للتأكيد BB تنتمي لل R and BB + +541 +00:41:53,980 --> 00:41:59,060 +تنتمي لل R زي + +542 +00:41:59,060 --> 00:42:02,980 +المثال السابق هيوا واحد اتنين عكسه مش موجود بتبطل + +543 +00:42:02,980 --> 00:42:06,640 +symmetric طبعا لأنه لازم الكل هذه قاعدة عامة كل + +544 +00:42:06,640 --> 00:42:11,960 +صحيحة دائمة فهنا بيقولي thus R is symmetric + +545 +00:42:16,750 --> 00:42:20,690 +بدنا نثبت إنه ليست reflexive وليست transitive طيب + +546 +00:42:20,690 --> 00:42:28,000 +نشوف R is not transitive نبدأ فيهاالـ Transitive + +547 +00:42:28,000 --> 00:42:33,180 +تمام ايش معناه الـ Transitive كل زوجين بداية + +548 +00:42:33,180 --> 00:42:37,900 +التاني نهاية الأول يؤدي لزوج تالت من بداية الأول + +549 +00:42:37,900 --> 00:42:41,820 +لنهاية التاني اه فإذا قدرنا نلاقي زوجين موجودين + +550 +00:42:41,820 --> 00:42:45,500 +والزوج التالت المكمل مش موجود بتكون اختل الشرط + +551 +00:42:45,500 --> 00:42:51,070 +فبدنا نشوف زوجين موجودين والمكمل مش موجودA,B وB,A + +552 +00:42:51,070 --> 00:42:54,830 +لازم A,A موجودة، موجودة؟ لأ فإذا هذا بتدي الخارج + +553 +00:42:54,830 --> 00:43:01,390 +فانا عنده بتقوله A,B تنتمي لل R and B,A تنتمي لل R + +554 +00:43:01,390 --> 00:43:10,010 +لكن but أو and كله صح A,A لا تنتمي لل R فهذا بيقدي + +555 +00:43:10,010 --> 00:43:15,010 +إنها ليست a transit is not a transit + +556 +00:43:18,600 --> 00:43:22,200 +فلمّا أجي مثال عكسي بتكون ال statement false أصبح + +557 +00:43:22,200 --> 00:43:26,420 +اه بدال statement true دائما لجت مثال فإذا بطل في + +558 +00:43:26,420 --> 00:43:31,900 +صحيح إذا not a trend تمام تلاتة ال R is not + +559 +00:43:31,900 --> 00:43:35,160 +reflexive not reflexive + +560 +00:43:39,720 --> 00:43:45,120 +ما هو نفس + +561 +00:43:45,120 --> 00:43:49,720 +المثال خلصنا مافيش دا أفحص كمان a a لا تنتمي لل R + +562 +00:43:49,720 --> 00:43:53,740 +implies R is not reflexive + +563 +00:44:12,060 --> 00:44:13,920 +بنوقفها ان شاء الله الساعة تنتهي و بنكمل + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/SuCRM6Nv8Fg_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/SuCRM6Nv8Fg_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..bac57d090faae1aaac1f1d75d41af1cfb5c84aca --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/SuCRM6Nv8Fg_postprocess.srt @@ -0,0 +1,3024 @@ +1 +00:00:20,810 --> 00:00:24,780 +بسم الله الرحمن الرحيمفاليوم ان شاء الله هنواصل مع + +2 +00:00:24,780 --> 00:00:28,200 +المجموعات في المحاضرة الماضية يمكن احنا أخدنا + +3 +00:00:28,200 --> 00:00:31,840 +مقدمة سريعة سارجعنا فيها بعض المفاهيم طبعا مفهوم + +4 +00:00:31,840 --> 00:00:34,860 +المجموعات من المفاهيم الأساسية اللي جمر علينا في + +5 +00:00:34,860 --> 00:00:39,100 +مرحلة مبكرة من الدراسة لكن احنا في هذه في هذا + +6 +00:00:39,100 --> 00:00:43,060 +المساق هنركز كيف نتعامل مع مفهوم المجموعات و ال + +7 +00:00:43,060 --> 00:00:47,080 +operations و اللي على المجموعات بطريقة المجردة + +8 +00:00:47,080 --> 00:00:50,580 +بطريقة البراهين كيف نتعامل معهم من هذه الناحية في + +9 +00:00:50,580 --> 00:00:55,250 +هذا المساق ان شاء اللهفإن شاء الله أول مفهوم بتعلق + +10 +00:00:55,250 --> 00:00:59,270 +بالتعامل مع المجموعات واللي ممكن نشتغل عليه وفي + +11 +00:00:59,270 --> 00:01:04,230 +عليه عمليات حسابية هو مفهوم تساوي المجموعات فطبعا + +12 +00:01:04,230 --> 00:01:07,770 +احنا فيه عنا المفهوم عنا الرمز تبعه وفيه عنا + +13 +00:01:07,770 --> 00:01:11,510 +التعريف تبعه فيه يمكن تلت نقاط بنتحدث عنهافأول شي + +14 +00:01:11,510 --> 00:01:14,910 +أنا ببيبندي مجموعتين هذه المجموعتين هدول ممكن أدرس + +15 +00:01:14,910 --> 00:01:18,330 +علاقة التساوي وقت إيش بقول مجموعة ألف تساوي مجموعة + +16 +00:01:18,330 --> 00:01:21,470 +باق وقت إيش بقول asset A capital A تساوي asset + +17 +00:01:21,470 --> 00:01:24,810 +capital B أول شي إيش الرمز هو علاقة التساوي + +18 +00:01:24,810 --> 00:01:27,950 +المتعرف عليها بين الأعداد فأنا بقول ليش two sets + +19 +00:01:27,950 --> 00:01:30,990 +أه طبعا في الآخر يمكن كتبها A تساوي ال B هذا هو + +20 +00:01:30,990 --> 00:01:34,800 +الرمزإذا المفهوم مفهوم التساوي للمجموعات equality + +21 +00:01:34,800 --> 00:01:38,400 +of sets هذا هو إيش المصطلح اللي بتتعامل معاه إيش + +22 +00:01:38,400 --> 00:01:41,800 +الرمز تبعه علاقة التساوي المتعرف عليها بالأرقام + +23 +00:01:41,800 --> 00:01:45,400 +طيب ما هو التعريف بجوجتش بقول على أن two sets are + +24 +00:01:45,400 --> 00:01:49,320 +equal أه فبقول ليه two sets capital A and capital + +25 +00:01:49,320 --> 00:01:53,160 +B are said to be equal or identical متطابقين أو + +26 +00:01:53,160 --> 00:01:56,800 +متساويين if they contain the same elements إذا + +27 +00:01:56,800 --> 00:01:59,890 +احتووا على نفس العناصإذا كانت عناصرهم هي نفس + +28 +00:01:59,890 --> 00:02:04,570 +العناصر، عناصر الـA هي نفس عناصر الـB، وهكذا، اه، + +29 +00:02:04,570 --> 00:02:07,590 +فطبعا الرمز بقول إذا كانت الـA و الـB متساويين + +30 +00:02:07,590 --> 00:02:11,250 +فبكتب A تساوي B، وبنقرأها A تساوي B، فده هو الرمز، + +31 +00:02:11,250 --> 00:02:13,810 +وماكنتش بقول A تساوي B إذا كانوا بينهم بحتوى على + +32 +00:02:13,810 --> 00:02:19,980 +نفس العناصر، بحتوى على نفس العناصرخلّينا نشوف إيه + +33 +00:02:19,980 --> 00:02:23,840 +كيف متعامل منطقيا بالرموز ماذا تعني يحتوي على جميع + +34 +00:02:23,840 --> 00:02:28,720 +العناصر بلغة الرموز فهنا ملاحظة a تساوي b means + +35 +00:02:28,720 --> 00:02:34,140 +يعني تكافئ بمعنى for all x لكل العناصر طب ما هو ال + +36 +00:02:34,140 --> 00:02:37,800 +universe؟كل العناصر اللي أنا قولش مقوليه ويقوليه + +37 +00:02:37,800 --> 00:02:41,380 +بحتوى جميع العناصر بمعنى العنصر اللي موجود في الـA + +38 +00:02:41,380 --> 00:02:45,500 +لازم يكون موجود في الـB واللي في الـB لازم يكون + +39 +00:02:45,500 --> 00:02:50,100 +موجود في الـA فهو بيقول للتعريف تبعها for all X X + +40 +00:02:50,100 --> 00:02:55,620 +تنتمي للـA if and only if X تنتمي للـB بيعني فكل + +41 +00:02:55,620 --> 00:02:58,560 +عنصر إذا كان موجود في الـA لازم يكون في الـB وعكس + +42 +00:02:58,560 --> 00:03:00,540 +إذا كان موجود في الـB لازم يكون في الـA هذا معناه + +43 +00:03:00,540 --> 00:03:04,250 +أنهم يحتووا على نفس العناصر بلغة الرموزfor all x + +44 +00:03:04,250 --> 00:03:08,630 +أي أنصر أي ما كان إذا نوجد في الأولى لازم ينوجد في + +45 +00:03:08,630 --> 00:03:11,950 +التانية و العكس صحيح إذا نوجد في التانية لازم + +46 +00:03:11,950 --> 00:03:15,490 +ينوجد في الأولى واضح؟ أه فهذه لغة الرموز اللي احنا + +47 +00:03:15,490 --> 00:03:18,010 +بيقولنا نتعامل معها و نكتب بطريقة الرموز عشان + +48 +00:03:18,010 --> 00:03:21,410 +نتعامل مع المفهوم كيف بتأثبت ان هم متساويتين؟ + +49 +00:03:21,410 --> 00:03:25,170 +بتأثبت من for all x, x أنتمي لل a, if and only if, + +50 +00:03:25,250 --> 00:03:30,460 +x أنتمي لل bأه واضح؟ متابعين؟ خليني أشوف بعض + +51 +00:03:30,460 --> 00:03:32,820 +الأمثلة البسيطة وبعدين طبعا هنرجع للتعريف كيف + +52 +00:03:32,820 --> 00:03:37,820 +نتعامل معاه منطقيا أو بالبرهان هنشوف مثال بسيط + +53 +00:03:37,820 --> 00:03:41,680 +بيقول لي show that capital A وتساوية على حروف + +54 +00:03:41,680 --> 00:03:47,500 +الأبجدية ABC is equal to the set capital B وتساوية + +55 +00:03:47,500 --> 00:03:51,700 +على الحروف BCA هدول المجموعتين متساويتين لو أقوللي + +56 +00:03:51,700 --> 00:03:56,260 +showأه طبعا ليش؟ نفس العناصر ال A موجودة في ال + +57 +00:03:56,260 --> 00:03:58,900 +capital A و موجودة في ال capital B ال small b + +58 +00:03:58,900 --> 00:04:01,500 +موجودة في ال capital A و موجودة في ال capital B و + +59 +00:04:01,500 --> 00:04:04,160 +ال small c موجودة في التنتين فكل العناصر هم + +60 +00:04:04,160 --> 00:04:05,840 +بيحتووا على نفس العناصر ال A و ال B بيحتووا على + +61 +00:04:05,840 --> 00:04:09,820 +من؟ على التلات حروف A,B,C فإذا هم متساوينطبعا إيش + +62 +00:04:09,820 --> 00:04:12,640 +مستنتج الشياط من المثال؟ ترتيب العناصر ما لهوش + +63 +00:04:12,640 --> 00:04:15,360 +أهمية في المجموعات لأنه جالي يحتوى على جميع + +64 +00:04:15,360 --> 00:04:17,780 +العناصر، ما جاليش نفس الترتيب، ما جاليش العنصر + +65 +00:04:17,780 --> 00:04:20,900 +الأول يساوي العنصر الأول، لأ، جالي نفس العناصر، + +66 +00:04:20,900 --> 00:04:24,660 +بغض النظر إيش، مين، ترتيب، فأنا بتحدث عن مجموعة + +67 +00:04:24,660 --> 00:04:28,800 +طالبات مبادئ الرياضيات، هذه هي المجموعة، في + +68 +00:04:28,800 --> 00:04:31,300 +المحاضرة اليوم، مين جاعد أول، في المحاضرة التانية، + +69 +00:04:31,300 --> 00:04:34,040 +مين جاعد آخر، مابيهمنيش، هذه هي المجموعة، فالترتيب + +70 +00:04:34,040 --> 00:04:37,570 +ما لهوش قيمة في المجموعاتفطبعا عشان اجيبه بعد + +71 +00:04:37,570 --> 00:04:40,410 +السؤال ببساطة ماهي التعريف ليش هدول equal لإنهم + +72 +00:04:40,410 --> 00:04:43,270 +يحتووا على نفس العناصر لإنهم يحتووا على نفس + +73 +00:04:43,270 --> 00:04:52,010 +العناصر فده المثال الأول solution ال a and b are + +74 +00:04:52,010 --> 00:04:56,990 +equal and b are + +75 +00:04:56,990 --> 00:05:07,190 +equal ليش since they contains او containthe same + +76 +00:05:07,190 --> 00:05:11,230 +element من + +77 +00:05:11,230 --> 00:05:17,030 +التعريف أخدت الجواب من التعريف لأنهم بيحتوي على + +78 +00:05:17,030 --> 00:05:24,350 +نفس العناصر بكل بصرة أي سؤال؟ + +79 +00:05:24,350 --> 00:05:28,570 +نشوف + +80 +00:05:28,570 --> 00:05:32,010 +كدا مثال برضه بسيط عشان نأكد على المفهوم و بعض + +81 +00:05:32,010 --> 00:05:36,190 +الملاحظاتبقول لي في عندي مجموعة capital A بتساوي + +82 +00:05:36,190 --> 00:05:41,530 +عناصر 1 4 1 فقى كم عنصر فيه في الـ A؟ عنصرين، + +83 +00:05:41,530 --> 00:05:44,430 +التكرار مالهوش قيمة في المجموعات، فهد فيها عنصرين + +84 +00:05:44,430 --> 00:05:47,290 +الواحد والاربع ولا فيها عنصر تاني؟ أي عناصر، طيب + +85 +00:05:47,290 --> 00:05:50,730 +والـ B بتساوي الواحد والاربع، هدول هم متساويين، + +86 +00:05:50,730 --> 00:05:54,360 +ليش؟لأنه محتوى على نفس العناصر فالشاهد الأهم من + +87 +00:05:54,360 --> 00:05:57,820 +المثال أن التكرار برضه مالهوش أهمية زي الترتيب + +88 +00:05:57,820 --> 00:06:01,400 +مالهوش أهمية و التكرار كأنه لم يكن مابنعدش فأنا + +89 +00:06:01,400 --> 00:06:05,040 +بقول من عناصر الـ A واحد و أربع بتقول الواحد ظهرت + +90 +00:06:05,040 --> 00:06:08,020 +مرتين ماليش داعو أنا بقول من العناصر واحد و أربع + +91 +00:06:08,020 --> 00:06:14,060 +واضح؟ فهنا برضه نقول هنا مثال رقم اتنين مثال رقم + +92 +00:06:14,060 --> 00:06:21,440 +اتنين ف solution فيها أن الـ A will be havethe + +93 +00:06:21,440 --> 00:06:26,020 +same elements + +94 +00:06:26,020 --> 00:06:30,940 +فبالتالي + +95 +00:06:30,940 --> 00:06:36,930 +متساويين A تساوي ال Bفدولا مثالين بسيطين واتعلمنا + +96 +00:06:36,930 --> 00:06:41,790 +منهم أن الترتيب مش مهم والتكرار مالهوش قيمة العنصر + +97 +00:06:41,790 --> 00:06:45,630 +مكتوب أكتر من مرة كأنه يعتبر خطأ مطبع انا عندي + +98 +00:06:45,630 --> 00:06:50,110 +قائمة طالبات هذه الشعبة طب في اسم انطبع مرتين في + +99 +00:06:50,110 --> 00:06:52,870 +الآخر انا بتحصل ليه علامة ولا علامتين علامة في + +100 +00:06:52,870 --> 00:06:55,650 +الآخر أنا مايش ممكن أصحي هذا الخطأ فانا بهمني كم + +101 +00:06:55,650 --> 00:06:59,430 +طالبة عندي عندي تسعين طالبة اللي كتب الاسم أكتر من + +102 +00:06:59,430 --> 00:07:03,190 +مرة مالهوش قيمة مالهوش قيمة نفس الاش نفس القضية + +103 +00:07:07,120 --> 00:07:09,200 +لسه ماوصلناش، واحدة واحدة، لسه ماعرفناش إيش معناه + +104 +00:07:09,200 --> 00:07:12,920 +subset، إيش جزئي، واحدة واحدة، احنا لسه عرفنا إيش + +105 +00:07:12,920 --> 00:07:16,800 +مجموعة، تعرفنا عليه إيش بنقصد فيه، وبعدين عرفنا + +106 +00:07:16,800 --> 00:07:19,460 +التساوي، لسه ماعرفناش الفترة، هنجيها، تمام، + +107 +00:07:19,460 --> 00:07:25,720 +ملاحظة، ملاحظة، البعض بيسقط في خطأ، بدنا نميز هال + +108 +00:07:25,720 --> 00:07:31,920 +gate، بيقولّي بشكل عامالـ A لا تساوي A بين هدول + +109 +00:07:31,920 --> 00:07:36,360 +الأقواص، ليش؟ لأن الـ A هذه لحالة عنصر، وهديك + +110 +00:07:36,360 --> 00:07:39,640 +مجموعة تحتوي على عنصر الـ A، فهدول فيهم فرق، طب + +111 +00:07:39,640 --> 00:07:42,900 +إيش ال small a تكون؟ أي ما كانت، أي عنصر ما كانت، + +112 +00:07:42,900 --> 00:07:45,890 +حتى لو كانت مجموعة نفسها، لكن هدول أيش؟رمزين + +113 +00:07:45,890 --> 00:07:49,730 +مختلفين، مفهومين مختلفين، هذه عبارة عن عنصر ما + +114 +00:07:49,730 --> 00:07:54,070 +إيه، هذه عبارة عن مجموعة تحتوي على عنصر إيه، فبقول + +115 +00:07:54,070 --> 00:07:56,750 +هنا الـA is an element، عنصر، بغض النظر إيش + +116 +00:07:56,750 --> 00:08:00,390 +محتوياته أو إيش نوعيته، لكن الـA عبارة عن مجموعة + +117 +00:08:00,390 --> 00:08:03,750 +تحتوي على عنصر إيه، فبننفرق في رمزي هدول اللي اللي + +118 +00:08:03,750 --> 00:08:06,910 +أقواص مهمين جدا، وإذا انكتبوه، دايما نبيع إنه فيه + +119 +00:08:06,910 --> 00:08:11,040 +مجموعة، طبعا يسع ناصر المجموعة موضوع آخرموضوع آخر + +120 +00:08:11,040 --> 00:08:15,040 +فبننفرق بين هدول الرمزين فهنا مافيش تساوي إيش ممكن + +121 +00:08:15,040 --> 00:08:19,100 +أحط بدل لأدم التساوي ينتمي ينتمي بس مش مجموعة + +122 +00:08:19,100 --> 00:08:23,100 +جزئية بس ينتمي العلاقة الوحيدة بين a ومجموعة ال a + +123 +00:08:23,100 --> 00:08:26,960 +ينتمي بس هذه العلاقة الصحية غير هيك أي علاقة غير + +124 +00:08:26,960 --> 00:08:29,680 +صحية ولا subset صحيحة لسه معرفنهاش ولا التساوي + +125 +00:08:29,680 --> 00:08:34,740 +صحيح انتبهوا لهذا النقر طب نيجي لمفهوم ال subset + +126 +00:08:34,740 --> 00:08:39,420 +المجموعة الجزئية subsetبنعرف إيش معناهات subset + +127 +00:08:39,420 --> 00:08:45,580 +طبعا بي ساعدنا يمكن رسم مساعد Venn diagram تقريبا + +128 +00:08:45,580 --> 00:08:50,340 +فطبعا subset هي جزء فهي عندنا مجموعة كبيرة B في + +129 +00:08:50,340 --> 00:08:53,900 +عندنا مجموعة صغيرة جواها A فده هو المفهوم فانا + +130 +00:08:53,900 --> 00:08:56,840 +بقول على ال A subset من ال B خلينا نشوف التعريف + +131 +00:08:56,840 --> 00:09:00,360 +طبعا زي المنهج اللي اتبعناه في الشتر الأول أيضا + +132 +00:09:00,360 --> 00:09:05,530 +ماتتبعه في عندنا مقدمة للتعريف مقدمة للنظريةبتقول + +133 +00:09:05,530 --> 00:09:08,630 +يا دول الرموز كي بده تستخدمهم؟ Let capital A و + +134 +00:09:08,630 --> 00:09:11,750 +capital B be two sets إذا ما إيه ليه؟ هينطبق على + +135 +00:09:11,750 --> 00:09:14,570 +ال A و ال B بينطبق على أي مجموعات A و B مش + +136 +00:09:14,570 --> 00:09:19,690 +statements مش أرقام و إنما مجموعات تمام التعريف أو + +137 +00:09:19,690 --> 00:09:26,060 +الجزء الأول من التعريفإذا كل عنصر في الـ A هو عنصر + +138 +00:09:26,060 --> 00:09:29,500 +في الـ B موجود في الـ B بقول أنا أن الـ A subset + +139 +00:09:29,500 --> 00:09:34,560 +من الـ B فدهو فكل عناصر الـ A بنفس الوقت موجودة في + +140 +00:09:34,560 --> 00:09:38,760 +الـ B يعني مثلا نحن نقول قسم الرياضيات أو طالبات + +141 +00:09:38,760 --> 00:09:41,520 +قسم رياضية مجموعة جزئية من الجامعة كل طالبة في قسم + +142 +00:09:41,520 --> 00:09:44,860 +رياضية طالب في الجامعة الإسلاميةواضح؟ فالكل أنصر + +143 +00:09:44,860 --> 00:09:48,280 +ينتمي لمين؟ لمجموعة أكبر فبقول ليش if every + +144 +00:09:48,280 --> 00:09:51,900 +element of A is an element of B then we say that A + +145 +00:09:51,900 --> 00:09:56,120 +is a subset of B ما هو الرمز؟ رمز زي أصغر من أو + +146 +00:09:56,120 --> 00:10:00,470 +يساوي بس بدل ما يزاوي حدعلى صورة جوس، على صورة + +147 +00:10:00,470 --> 00:10:03,310 +جوس، والتساوي ده له معنى، هنأكد عليه أنه فيه + +148 +00:10:03,310 --> 00:10:06,490 +احتمال التساوي، فممكن اكتبها بهذا الشكل، فالـ A + +149 +00:10:06,490 --> 00:10:10,130 +أصغر من الـ B، جوا الـ B، الـ B تحتوي الـ A، طب لو + +150 +00:10:10,130 --> 00:10:14,510 +عكست الترتيب، تكون الـ B تحتوي الـ A، بقرأها بشكل + +151 +00:10:14,510 --> 00:10:18,410 +آخر، زي ما بنقول إيهاش، الخمسة أصغر من الستة، + +152 +00:10:18,410 --> 00:10:21,910 +والستة أكبر من الخمسة، فنفس القضية، بقول إن الـ A، + +153 +00:10:21,910 --> 00:10:25,830 +إيهاش، subset من الـ B، والـ B بسميها super set من + +154 +00:10:25,830 --> 00:10:29,150 +الـ A، هنسميها، هي جاي تقريبا،واضح؟ فهو ممكن + +155 +00:10:29,150 --> 00:10:31,710 +يكتبها بالطريقتين، طبعا الأولى هي الأكثر شيوعة، + +156 +00:10:31,710 --> 00:10:35,110 +هذي نادر جدا، نادر جدا، وقت إيش نكتبها؟ في الغالب + +157 +00:10:35,110 --> 00:10:38,190 +لما أنا إيش كتبت ال B وما تمش وصح على يسارها، + +158 +00:10:38,190 --> 00:10:40,910 +بكتبها على اليمين ال A بس بغير الاتجاه، في الغالب + +159 +00:10:40,910 --> 00:10:45,150 +هيك، بقول إذا ال A صبصت من ال B، ال B إيش بيسميها؟ + +160 +00:10:45,250 --> 00:10:49,250 +Super 6 Super 6 هي الكبيرة هي الكبيرة sub يعني + +161 +00:10:49,250 --> 00:10:53,790 +صغيرة جزء هذه كيش هي الكل الأكبر وهكذا فطبعا هي + +162 +00:10:53,790 --> 00:10:58,410 +الصورة هذه جزء من هذه وهذه تحتوي ال A ال B تحتوي + +163 +00:10:58,410 --> 00:11:02,530 +ال A بمعنى Super 6 من ال A أي سؤال طبعا المفهوم + +164 +00:11:02,530 --> 00:11:06,070 +مرة عليكم بس بنأكد عليه والمصطلحات تمام طيب زي ما + +165 +00:11:06,070 --> 00:11:08,930 +عملنا سياسة التساوي بنشوف إيش يعني بالرموز كي بدأ + +166 +00:11:08,930 --> 00:11:14,410 +أثبت إن ال A صفصت من ال B هنشوف الرمز remarkالـ A + +167 +00:11:14,410 --> 00:11:17,870 +subset من الـ B means يعني تكافئ .. إيش قال ليه؟ + +168 +00:11:17,870 --> 00:11:21,470 +every element of A is for all .. كل العناصر .. أي + +169 +00:11:21,470 --> 00:11:24,590 +عنصر موجود في الـ A بدي يكون موجود في الـ B طب + +170 +00:11:24,590 --> 00:11:29,230 +العكس مفتوح .. مش معروف .. فهي اتجاه واحد فكنا في + +171 +00:11:29,230 --> 00:11:32,970 +التساوي if and only if .. في ال subset if then .. + +172 +00:11:32,970 --> 00:11:35,870 +if then .. العنصر الموجود في الـ A بدي يكون في الـ + +173 +00:11:35,870 --> 00:11:39,670 +B العكس مش عارفين .. مش عارفين .. تمام؟ فهذا هو + +174 +00:11:39,670 --> 00:11:42,930 +الرمز .. فهذا هو الرمز وهذه اللي هنتعامل عليها + +175 +00:11:43,600 --> 00:11:48,820 +ملاحظة رقم 2 حكت زميلتكوا قبل قليل التساوي ممكن + +176 +00:11:48,820 --> 00:11:52,480 +ينكتب بلغة ال subset بس ايش الأولى subset من + +177 +00:11:52,480 --> 00:11:56,180 +التانية والتانية subset من الأولى لأنه نفس العناصر + +178 +00:11:56,180 --> 00:11:59,940 +فكل عنصر في ال A موجود في ال B وكل عنصر في ال B + +179 +00:11:59,940 --> 00:12:04,960 +موجود في ال A فبقدر اكتبها ان هذه if and only ifA + +180 +00:12:04,960 --> 00:12:09,000 +subset من الـ B والـ B subset من الـ A فالتساوي هي + +181 +00:12:09,000 --> 00:12:13,000 +تعريف آخر له ممكن أعرفه مباشرة ممكن أعرفه بدلالة + +182 +00:12:13,000 --> 00:12:18,000 +من ال subset بدلالة ال subset طبعا ماحد يسأل بقدر + +183 +00:12:18,000 --> 00:12:21,440 +أجيب هذا التعريف من التعريف الأصلي طبعا for all + +184 +00:12:21,440 --> 00:12:28,040 +مين بقدر يجيب منياه بسهولة لو جينا الآن A تساوي + +185 +00:12:28,040 --> 00:12:35,030 +الـ B قولنا تكافئ means for all XX تنتمي للـA if + +186 +00:12:35,030 --> 00:12:39,950 +and only if X تنتمي للـB بعد هيك إيش نعمل؟ نحوّل + +187 +00:12:39,950 --> 00:12:44,250 +الـF لـand on الـF إلى and by conditional فهذه + +188 +00:12:44,250 --> 00:12:52,050 +تكافئ for all X X تنتمي للـA then X تنتمي للـB and + +189 +00:12:52,050 --> 00:12:58,770 +X تنتمي للـB then X تنتمي للـA، مصبوط؟طيب، ها، بده + +190 +00:12:58,770 --> 00:13:01,430 +أوصل لمين؟ بده أوصل لـ for .. ل .. ل .. ل .. بده + +191 +00:13:01,430 --> 00:13:03,870 +أوزع كل واحدة لحال، عشان يصير هذه الـ sub set و + +192 +00:13:03,870 --> 00:13:07,310 +sub set، بنفع أوزع الـ for all على الـ and نعم من + +193 +00:13:07,310 --> 00:13:10,770 +قواعد ال quantifiers اللي أخدناها، جولة في علاقات + +194 +00:13:10,770 --> 00:13:13,390 +مسموحة و في علاقات فين هم تكافئوا و فين هم been + +195 +00:13:13,390 --> 00:13:15,650 +obliged و فين ما ذكرناهم مش ممكن .. إيه، مش ممكن + +196 +00:13:15,650 --> 00:13:19,570 +نقول غير مسموحة، فهذا يكافئ، ممكن أوزع ال for all، + +197 +00:13:19,570 --> 00:13:25,210 +for all x, x تنتمي لل a, then x تنتمي لل b and for + +198 +00:13:25,210 --> 00:13:33,630 +all xX تنتمي للـB ثم X تنتمي للـA الآن، مين هذه؟ + +199 +00:13:33,630 --> 00:13:37,590 +هذه ليست إلا A صبصة من الـB تعريف أيه مفزوظ، مصبوط + +200 +00:13:37,590 --> 00:13:44,070 +طيب والتانية ليست إلا B صبصة من الـAوهو اللي بدنا + +201 +00:13:44,070 --> 00:13:47,010 +يعني فانا ممكن أجيبها من المنطق من وين جبتها صح + +202 +00:13:47,010 --> 00:13:51,210 +يمكن أنا فهمتها لكن ممكن أبرهنها من قواعد المنطق + +203 +00:13:51,210 --> 00:13:54,230 +اللي اتعلمناها قواعد ال quantifiers اللي اتعلمناها + +204 +00:13:54,230 --> 00:13:58,310 +و ال and و كل هذه الأمور ففعلا التساوي ممكن ينكتب + +205 +00:13:58,310 --> 00:14:02,070 +على صورة أن الأولى صبصت من التانية و التانية صبصت + +206 +00:14:02,070 --> 00:14:08,670 +من الأولى and واضح؟ أي سؤالنشوف بعض الأمثلة و + +207 +00:14:08,670 --> 00:14:12,110 +دايما بنبدأ بالأمثلة البسيطة عشان الأمر يرسخ و + +208 +00:14:12,110 --> 00:14:16,830 +المفهوم يكون واضح بدون أي غبش بقول لي let a تساوي + +209 +00:14:16,830 --> 00:14:22,730 +واحد و اتنين و small a كمش متغير هنا كحرف كحرف + +210 +00:14:22,730 --> 00:14:27,310 +اللي هو حرف أبيض و ال b هي الحروف a و b و العداد + +211 +00:14:27,310 --> 00:14:29,610 +واحد اتنين و تلاتة طبعا فال a سبسكت من ال bهذا + +212 +00:14:29,610 --> 00:14:32,750 +سؤال مباشر مش مطلوب فيه، بس مثال توضيحي، فطبعا + +213 +00:14:32,750 --> 00:14:36,250 +واضح، ليش؟ لأن كل عناصر الـA موجودة في الـB الواحد + +214 +00:14:36,250 --> 00:14:38,970 +موجودة في الـB ولا مش موجودة؟ صح، الاتنين موجودة + +215 +00:14:38,970 --> 00:14:41,150 +ولا مش موجودة؟ موجودة، الـA موجودة ولا مش موجودة؟ + +216 +00:14:41,150 --> 00:14:43,650 +موجودة، انتهت العملية، فكل عناصر الـA موجودة في + +217 +00:14:43,650 --> 00:14:47,410 +الـB، إذا نهيش فعلا الـA subset من الـB، واضح؟ هذا + +218 +00:14:47,410 --> 00:14:50,670 +المثال البسيط جدا، مش المعنى، بدي أختبر، كل عناصر + +219 +00:14:50,670 --> 00:14:55,270 +الـA موجودة في الـB، انتهت العملية، نشوف مثال آخر + +220 +00:14:56,090 --> 00:15:03,690 +ال A هي 123 وال B 312 فال A subset من ال B صح؟ صح + +221 +00:15:03,690 --> 00:15:07,050 +لأن ال 1 موجودة في ال B نعم ال 2 موجودة في ال B + +222 +00:15:07,050 --> 00:15:11,250 +نعم التلاتة موجودة في ال B نعم فدي subset اه في + +223 +00:15:11,250 --> 00:15:15,450 +طالبة بتقول ايه طب هدول متساويين صح متساويين وهل + +224 +00:15:15,450 --> 00:15:18,690 +ال subset ينفي التساوي لأ عشان هيك الإشارة إيش هي + +225 +00:15:18,690 --> 00:15:24,100 +الإشارة؟أصغر من أو يساوي تقريبا فيه تساوي محتمل هو + +226 +00:15:24,100 --> 00:15:27,480 +جالي كل عناصر الـA موجودة في الـB جالي لازم الـB + +227 +00:15:27,480 --> 00:15:30,620 +تكون أكبر؟ لأ جالي لازم يكون في عناصر الـB عناصر + +228 +00:15:30,620 --> 00:15:34,600 +زيادة؟ لأ فانا إيش ماختبر؟ هاي الواحد موجودة نعم + +229 +00:15:34,600 --> 00:15:37,520 +التنين موجودة نعم التلاتة موجودة نعم انتهت العملية + +230 +00:15:37,520 --> 00:15:40,580 +أبطل على الـB أنا أن فيها زيادة ولا مافيهاش زيادة؟ + +231 +00:15:40,580 --> 00:15:43,880 +لأ بس أنا بتبطلع عناصر الـA موجودة في الـBانتهت + +232 +00:15:43,880 --> 00:15:47,800 +العملية واضح وهذا رمز برضه رمز موفق الحقيقة أن + +233 +00:15:47,800 --> 00:15:51,840 +الاحتمال التساوي موجود احتمال التساوي موجود أي + +234 +00:15:51,840 --> 00:15:55,500 +سؤال فإذا subset لا تنفي التساوي ممكن التساوي يكون + +235 +00:15:55,500 --> 00:15:59,520 +موجود فيا أكبر منها أو تساويها فهذا الفراغ ممكن + +236 +00:15:59,520 --> 00:16:02,060 +ينعدم في ال subset ممكن مايكونش فيه فراغ يكونوا + +237 +00:16:02,060 --> 00:16:07,400 +متطابقين فال subset تحتمل التساوي لكن مش دايم مش + +238 +00:16:07,400 --> 00:16:14,790 +دايم ف remark هنا remark منفصلبقول لـ every set is + +239 +00:16:14,790 --> 00:16:19,870 +a subset of itself بس مرتبط بالسابق بما أنه عناصر + +240 +00:16:19,870 --> 00:16:23,110 +كل مجموعة موجودة في نفسها إذاً كل مجموعة هي مجموعة + +241 +00:16:23,110 --> 00:16:26,310 +جزئية من نفسها لأن التساوي كلها محتمل فكل مجموعة + +242 +00:16:26,310 --> 00:16:30,230 +هي مجموعة جزئية من نفسها بمعنى آخر لأي مجموعة + +243 +00:16:30,230 --> 00:16:33,410 +capital A capital A is a subset من capital A + +244 +00:16:33,410 --> 00:16:36,150 +دايماً هذا صحيح فلأن التساوي موجود زي ما بقول + +245 +00:16:36,150 --> 00:16:40,150 +التلاتة أصغر أو يسووا تلاتة كل عدد أصغر من A أو + +246 +00:16:40,150 --> 00:16:45,780 +يسووا نفسه فنفس القضيةكل مجموعة subset من نفسها + +247 +00:16:45,780 --> 00:16:52,200 +واضح؟ أي تعليق؟ أي استفسار؟ ولا اعتراض كمان؟ + +248 +00:16:52,200 --> 00:16:56,360 +متفقين؟ تمام proper subset + +249 +00:16:58,820 --> 00:17:03,300 +طيب، لو بدنا ننفي التساوي، مصطلح جديد، مفهوم جديد، + +250 +00:17:03,300 --> 00:17:07,260 +فإذا الـ Subset هذه تحتمل التساوي، طب لو أنا بدي + +251 +00:17:07,260 --> 00:17:10,660 +أكون دقيق و بديش أخد التساوي بالإعتبار، زي ما احنا + +252 +00:17:10,660 --> 00:17:17,600 +فيه عندنا، بالنسبة هنا، اللي بنقارن، القارن دايما + +253 +00:17:17,600 --> 00:17:20,690 +مع من أصغر من أو يساويفأصغر منه يساوي، بتحتتمل + +254 +00:17:20,690 --> 00:17:23,910 +التساوي، لكن لما بدنا ننفي التساوي، بنحط أصغر منه، + +255 +00:17:23,910 --> 00:17:27,210 +نفس القضية، ففي عندنا مفهوم بيميز هذه الأمور، اللي + +256 +00:17:27,210 --> 00:17:31,290 +هو إيش، بيسموه proper subset، يعني جزئية صحيحة أو + +257 +00:17:31,290 --> 00:17:35,470 +إيش، ممكن تكون إيش، لوصافية فعلا إن فيه الجزء من، + +258 +00:17:35,470 --> 00:17:40,770 +التساوي منفي، ففي عندنا التعريفWe say that asset + +259 +00:17:40,770 --> 00:17:49,330 +capital A is a proper subset of asset + +260 +00:17:49,330 --> 00:17:51,150 +capital B and right + +261 +00:17:56,230 --> 00:18:00,690 +الـ A subset من الـ B و لا تساويها هي subset + +262 +00:18:00,690 --> 00:18:04,490 +والتساوي إيش مانفي الاحتمال التساوي بده يلغي .. + +263 +00:18:04,490 --> 00:18:09,070 +يلغي الاحتمال التساوي بدنا نلغي واضحة؟ فإذا ال + +264 +00:18:09,070 --> 00:18:12,930 +proper يعني إيش؟ هي جزء والتساوي إيش ماله؟ بدناش + +265 +00:18:12,930 --> 00:18:16,890 +إيه ففي هذه الحالة بنميز تمام أه طبعا قلنا أحنا + +266 +00:18:16,890 --> 00:18:21,630 +subset و super set proper subset proper super set + +267 +00:18:21,630 --> 00:18:27,590 +نفس المصطلح proper subset تمام؟لأ هي .. بس لأ هي + +268 +00:18:27,590 --> 00:18:34,830 +.. انت عندك علاقة هذه بقراها باتجاهين ال A sub 6 + +269 +00:18:34,830 --> 00:18:38,410 +من ال B طب ال B هي super 6 من ال A زي ما بقوليش + +270 +00:18:38,410 --> 00:18:42,830 +الخمسة أصغر من الستة و الستة أكبر من الخمسة فقراها + +271 +00:18:42,830 --> 00:18:47,000 +من الجهة التانية يعني قراها من الجهة التانيةنشوف + +272 +00:18:47,000 --> 00:18:50,520 +بعض الأمثلة طبعا مجموعة الأعداد الصحيحة Z هي + +273 +00:18:50,520 --> 00:18:53,680 +proper subset من ال Q ليش؟ لأنها متساويهاش في + +274 +00:18:53,680 --> 00:18:57,800 +أعداد نسبية غير صحيحة ولا لأ؟ لكن كل عدد صحيح هو + +275 +00:18:57,800 --> 00:19:01,920 +عدد نسبي فكل عناصر ال Z موجودة في ال Q لكن في في + +276 +00:19:01,920 --> 00:19:05,660 +ال Q عناصر الزيادة مافيش تساوي بتطبقوش مع بعض ال Z + +277 +00:19:05,660 --> 00:19:09,800 +جزء من ال Q والتساوي غير موجود لأن ال Q أكبر فعلا + +278 +00:19:09,800 --> 00:19:15,140 +في عناصر الزيادة واضح؟ هذا مثال مشهور نشوف كمان + +279 +00:19:15,140 --> 00:19:21,300 +مثاللو أخدنا مجموعة ال A تساوي سالب واحد Zero واحد + +280 +00:19:21,300 --> 00:19:24,540 +وال B واحد و سالب واحد و Zero فال A subset من ال B + +281 +00:19:24,540 --> 00:19:28,520 +متفقين لكن هل هي proper؟ لأ لأنهم متساويين هدول هم + +282 +00:19:28,520 --> 00:19:31,700 +متساويين مينفعش إيش أقول proper أه فهنا إيش ال A + +283 +00:19:31,700 --> 00:19:35,560 +subset من ال B لكن ال A is not a proper subset of + +284 +00:19:35,560 --> 00:19:39,560 +Bواضح؟ اه فهي ايش معناه proper؟ بنفي التساوي، إذا + +285 +00:19:39,560 --> 00:19:43,760 +أنا متأكد أن التساوي احتماله أصبح غير وارد، اه + +286 +00:19:43,760 --> 00:19:46,740 +فبقول proper subset، بكون دقيق، اه فانا بقول عنصر + +287 +00:19:46,740 --> 00:19:49,420 +هذا أصغر من أو يساوي العنصر، طب أنا لو في عندي + +288 +00:19:49,420 --> 00:19:52,180 +معلومة أن التساوي مش موجود، بحط أصغر، وانا مطمئن، + +289 +00:19:52,180 --> 00:19:58,280 +في عندي معلومة زيادة، أي سؤال؟خلّينا نتفق على بعض + +290 +00:19:58,280 --> 00:20:03,460 +الرموز if A is not a subset of B بنم في علاقة، + +291 +00:20:03,460 --> 00:20:05,640 +بنقول A subset من B وبنم فيها، بنحط ال slash + +292 +00:20:05,640 --> 00:20:08,540 +المعروف .. متعرف عليها ال slash النفسي زي يساوي لا + +293 +00:20:08,540 --> 00:20:13,140 +يساوي، ينتمي لا ينتمي، و هكذا فده الرمز متعارف + +294 +00:20:13,140 --> 00:20:20,200 +عليه ممكن استخدامهتمام؟ خلّينا لو بدنا نثبت أنه + +295 +00:20:20,200 --> 00:20:24,480 +مجموعة ليست subset خلّينا نشوف كيف ممكن نعملها + +296 +00:20:24,480 --> 00:20:28,300 +بلغة الرموز بلغة الرموز عشان كده ده مصطلح يمر + +297 +00:20:28,300 --> 00:20:32,540 +علينا مرات عديدة خلّينا نعمله قلنا إنه اسمها + +298 +00:20:32,540 --> 00:20:37,420 +subsetfor all X X تنتمي للـ A then X تنتمي للـ B + +299 +00:20:37,420 --> 00:20:41,740 +طب بدي أنفيها؟ بنعمل نجاش؟ و لا لأ؟ طب إيش؟ كيف + +300 +00:20:41,740 --> 00:20:44,760 +بننفي؟ نفي الـ for all there exist و بننفي اللي + +301 +00:20:44,760 --> 00:20:47,380 +جوا بس واحدة واحدة ماتحطولوش نفي مرتين زي ما انتوا + +302 +00:20:47,380 --> 00:20:50,620 +عاملين في ال quiz البعض لأ أنا لما أنفي ال for all + +303 +00:20:50,620 --> 00:20:52,800 +بصير there exist و بعدين بننفي اللي جوا أه بقى + +304 +00:20:52,800 --> 00:20:55,780 +النفي بتتوزعش مرتين واضح؟ فأرجو الأخطاء اللي قادمة + +305 +00:20:55,780 --> 00:20:58,620 +ماتتكررش ف there exist بعدين بدنا ننفي اللي جوا + +306 +00:20:58,620 --> 00:21:02,380 +الجملة جملة شرطية اللي هي إيه إيش؟ P then Q خليني + +307 +00:21:02,380 --> 00:21:12,510 +أكتبها هناB then Q و تكافئ not B and not Q بيصير + +308 +00:21:12,510 --> 00:21:17,210 +B and not Q مين ال B X تنتمي ل A و مين ال not Q X + +309 +00:21:17,210 --> 00:21:21,750 +لا تنتمي ل B نفعامتبعين؟ واضحة ولا مش واضحة؟ + +310 +00:21:21,750 --> 00:21:25,350 +واضحة؟ اه فهي هاد الشرط، فإذا أصبحت هيك، فماديش + +311 +00:21:25,350 --> 00:21:28,390 +بقول إن الـA ليس subset من الـB، إذا كدرت لاجي + +312 +00:21:28,390 --> 00:21:31,410 +عنصر موجود في الـA وليس موجود في الـB، هيك صرا، + +313 +00:21:31,410 --> 00:21:34,690 +مصموط، there exist X موجودة في الـA وغير موجودة في + +314 +00:21:34,690 --> 00:21:37,890 +الـB، وده منطقي، ليش مش subset؟ لأن فيها عناصر مش + +315 +00:21:37,890 --> 00:21:40,990 +.. مش موجودة في الـB، في عناصر خارج الـB، فبتكون + +316 +00:21:40,990 --> 00:21:45,500 +ليست subsetأي سؤال شوفوا كيف جيبناها من المنطق + +317 +00:21:45,500 --> 00:21:48,460 +شوفوا كيف فسرناها و كيف احتجناها ما درسناها في شبط + +318 +00:21:48,460 --> 00:21:54,020 +واحد نشوف مثال خلينا نطبق على هذا الكلام فأصبح + +319 +00:21:54,020 --> 00:21:58,520 +الآن عشان أثبت أن مجموعة ما ليست مجموعة جزئية من + +320 +00:21:58,520 --> 00:22:02,100 +مجموعة أخرى يكفي أن ألاقي عنصر موجود في المجموعة A + +321 +00:22:02,100 --> 00:22:05,800 +و غير موجود في ال B المثال بقول اثبت أن ال A ليست + +322 +00:22:05,800 --> 00:22:10,600 +سبسط من ال B مين يحل الليه؟الـ Zero موجودة في الـ + +323 +00:22:10,600 --> 00:22:13,280 +A وليس في الـ B يكفي يكفي بس بالـ There exists + +324 +00:22:13,280 --> 00:22:16,620 +مثال واحد يكفي There exists لأنه موجود على أقل مرة + +325 +00:22:16,620 --> 00:22:20,200 +واحد هيكفى فالـ Zero موجودة في الـ A وليس في الـ B + +326 +00:22:20,200 --> 00:22:25,260 +هذا بتدل على أنه ليست مجموعة جزئية فهنا هذا مثال + +327 +00:22:25,260 --> 00:22:30,980 +وهي ال solution Zero تنتمي للـ A and Zero لا تنتمي + +328 +00:22:30,980 --> 00:22:38,820 +للـ B implies الـ A ليست subset من الـ B أي سؤالهم + +329 +00:22:38,820 --> 00:22:42,420 +تابعين؟ اه فاحنا لسه نمشي واحدة واحدة مادخلناش في + +330 +00:22:42,420 --> 00:22:45,820 +البراهين لكن اللي مش فاهم هذه الأمور صعب ان يمشي + +331 +00:22:45,820 --> 00:22:50,600 +على الأصعب فلازم نفهم السهل و نمشي بالتدريج و نوصل + +332 +00:22:50,600 --> 00:22:57,980 +للدرجة الأعلى نظرية الأولى نظرية 2 1 النظرية + +333 +00:22:57,980 --> 00:23:03,280 +الأولى في شبطر 2 عنوان النظرية المجموعة الفارغة هي + +334 +00:23:03,280 --> 00:23:06,660 +مجموعة جزئية من أي مجموعة هي مجموعة جزئية من أي + +335 +00:23:06,660 --> 00:23:11,970 +مجموعة النصبقول ليه؟ The empty set phi is a subset + +336 +00:23:11,970 --> 00:23:16,670 +of every set خلّينا أول شي نفهمها بالشفا و هيك زي + +337 +00:23:16,670 --> 00:23:19,430 +ما اتعلمونا في بعض الحلات و بعدين نشوف البرهان + +338 +00:23:19,430 --> 00:23:23,250 +للنظرية طيب كيف بدي أقول أن الـA subset من أي + +339 +00:23:23,250 --> 00:23:26,810 +مجموعة؟ بدي جميع عناصر الـPhi .. آسف الـPhi subset + +340 +00:23:26,810 --> 00:23:30,330 +من أي مجموعة؟ بدي جميع عناصر الـPhi تكون موجودة في + +341 +00:23:30,330 --> 00:23:33,590 +الـA طب مين جميع عناصر الـPhi؟ مفيش ولا عنصر طب + +342 +00:23:33,590 --> 00:23:37,440 +بمعنى آخركيف ممكن تكون ليس subset ال file إذا قدرت + +343 +00:23:37,440 --> 00:23:39,660 +تلاقي answer موجود في ال file و هذا مستحيل و ليس + +344 +00:23:39,660 --> 00:23:41,840 +موجود في ال A إذا المستحيل هذا الكلام يكون ليس + +345 +00:23:41,840 --> 00:23:46,240 +subset لازم تكون subset خلينا نشوف البرهان مع بعض + +346 +00:23:46,240 --> 00:23:56,390 +فهذه نظرية 8 1طبعا خليني أكتب النص بلغة الرموز + +347 +00:23:56,390 --> 00:24:00,890 +بقول الـ Phi is a subset of every set إيش معناه + +348 +00:24:00,890 --> 00:24:03,390 +every set؟ لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +349 +00:24:03,390 --> 00:24:03,610 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +350 +00:24:03,610 --> 00:24:04,030 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +351 +00:24:04,030 --> 00:24:05,610 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +352 +00:24:05,610 --> 00:24:06,310 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +353 +00:24:06,310 --> 00:24:07,490 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +354 +00:24:07,490 --> 00:24:08,110 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +355 +00:24:08,110 --> 00:24:10,910 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +356 +00:24:13,590 --> 00:24:17,390 +of proof من ال universe هنا كل المجموعات مجموعات + +357 +00:24:17,390 --> 00:24:20,850 +كل المجموعات لان بيقول every set every set ايه ايش + +358 +00:24:20,850 --> 00:24:25,210 +بتحتوي على ال file اه هي ايش super set لل file هي + +359 +00:24:25,210 --> 00:24:29,690 +super set لل file تمام بدنا نثبت هذه لل statement + +360 +00:24:29,690 --> 00:24:34,250 +statement تحتوي على ال quantifier اه ايش عمل افتح + +361 +00:24:34,250 --> 00:24:38,250 +الدليل تبعك في section 177 عملنا ارشادات كيف + +362 +00:24:38,250 --> 00:24:41,170 +نتعامل مع for all مرت علينا for all في ال + +363 +00:24:41,170 --> 00:24:43,050 +induction بنفع نعمل induction هنا + +364 +00:24:46,230 --> 00:24:50,490 +لأ ليش؟ لأن ال universe مش أعداد صحيحة هنا إيش + +365 +00:24:50,490 --> 00:24:53,650 +العناصر؟ مجموعات فاحنا إيش قولنا أول ما شوف for + +366 +00:24:53,650 --> 00:24:56,230 +all أقول induction لأ قولنا بدنا for all بدنا ال + +367 +00:24:56,230 --> 00:24:58,710 +universe يشكون مجموعة من الأعداد الصحيحة بتبدأ من + +368 +00:24:58,710 --> 00:25:02,810 +الأعداد الصحيح N0 وبتمشي N0 زي 1 N0 زي 2 وإلا + +369 +00:25:02,810 --> 00:25:05,870 +مانفعش فال induction بتعامل مع إيه اللي هو + +370 +00:25:05,870 --> 00:25:09,710 +quantifier for all وإيش universe خاص universe خاص + +371 +00:25:09,710 --> 00:25:13,420 +مش أي شيء فإذا أنا دي مانفعشطيب في عندنا كان إرشاد + +372 +00:25:13,420 --> 00:25:16,600 +قال لي عشان تتعامل مع for all ابدأ ال statement + +373 +00:25:16,600 --> 00:25:20,260 +بايش بال proof let A be any set لأن لما نقول B any + +374 +00:25:20,260 --> 00:25:23,120 +set إذا ما ينطبق على ال capital A ينطبق على جميع + +375 +00:25:23,120 --> 00:25:26,280 +المجموعات لأن زي ما كنا نعمل في مقدمة النظريات let + +376 +00:25:26,280 --> 00:25:29,420 +B be any statement إذا ما ينطبق على ال B ينطبق على + +377 +00:25:29,420 --> 00:25:31,700 +جميع ال statement فبنفس الطريقة لو رجعتوا + +378 +00:25:31,700 --> 00:25:34,480 +للإرشادات قولوا عشان تثبت for all إيش اللي بتبدأ + +379 +00:25:34,480 --> 00:25:38,360 +let X be any element in the universe فهنقول له let + +380 +00:25:38,360 --> 00:25:46,700 +A be any setlet capital A be any set إيش بدّي + +381 +00:25:46,700 --> 00:25:49,500 +أثبت؟ بدّي أثبت إن الـ Phi subset من الـ A بيكون + +382 +00:25:49,500 --> 00:25:52,320 +البروحان انتهى ولا لأ؟ نعم لأنه إيش بدّي؟ بيقوللي + +383 +00:25:52,320 --> 00:25:55,660 +Phi is a subset of every set يعني أي set، لكل + +384 +00:25:55,660 --> 00:26:04,460 +المجموعات، لأي مجموع We want to prove Phi + +385 +00:26:04,460 --> 00:26:10,160 +subset من الـ A ممتاز إيش عملنا؟ صعب اللي عملته؟ + +386 +00:26:15,890 --> 00:26:19,430 +الكل بيعرف يعمل اللي عملته ولا لأ؟ أمور سهلة ومش + +387 +00:26:19,430 --> 00:26:23,390 +هيه statement أمامك فسرناها for all جاعدين نتعلم + +388 +00:26:23,390 --> 00:26:27,110 +كيف نتعامل مع for all بنقول له let العنصر يامكان + +389 +00:26:27,110 --> 00:26:29,710 +بإيش بياني باليان ال universe ما هو ال universe؟ + +390 +00:26:29,710 --> 00:26:32,630 +كل المجموعات يعني بتكون ال a,k,z لو جالي for all + +391 +00:26:32,630 --> 00:26:36,930 +اكسبت من ال R بقوله X real number و هكذا واضحة؟ + +392 +00:26:36,930 --> 00:26:43,940 +صعبة؟ صعبة ولا سهلة؟ مفهومها؟أكمل أكمل طيب فاي + +393 +00:26:43,940 --> 00:26:48,360 +subset من ال a ماذا تعني فسرناها الملاحظات نكتبش + +394 +00:26:48,360 --> 00:26:52,780 +كلام انمل الصفحات كل شي مهم هذا يكافئ المطلوب for + +395 +00:26:52,780 --> 00:26:57,900 +all x x تنتمي للفاي then x تنتمي لل a هذا هو + +396 +00:26:57,900 --> 00:27:02,840 +المطلوب صح ولا مش صح بجيبش حاجة من عندى أنا بجيب + +397 +00:27:02,840 --> 00:27:06,770 +من اللي تعلمناها من السابقنعتمد chapter one هو + +398 +00:27:06,770 --> 00:27:09,790 +القاعدة الأساسية تبعاتنا والإرشادات وبنتعلم أمور + +399 +00:27:09,790 --> 00:27:12,610 +طيب بدنا نثبت هذه ال statement مش هذا هو المطلوب + +400 +00:27:12,610 --> 00:27:16,330 +we want to prove إيش بتبدأ ال statement for all x + +401 +00:27:16,330 --> 00:27:22,150 +ممكن أعمل عليها نفس القاعدة أقوله let x بس ال x + +402 +00:27:22,150 --> 00:27:26,650 +إيش هذه answer let x be any element let x be any + +403 +00:27:26,650 --> 00:27:32,030 +element تمام let x be any element + +404 +00:27:34,950 --> 00:27:41,690 +إيش مطلوب؟ بدي أثبت إن هذا صحيح We want to prove + +405 +00:27:41,690 --> 00:27:47,870 +that ماقتش بتقول ال for all P of X true إذا لكل X + +406 +00:27:47,870 --> 00:27:50,670 +ال P of X كانت true ما هي ال P of X في هذا ال + +407 +00:27:50,670 --> 00:27:54,130 +statement؟ اللي هي الجملة الشرطية X تنتمي لفاي + +408 +00:27:54,130 --> 00:28:01,990 +then X تنتمي لإيه؟ is true بدنا نثبتشوفتوا بقى هذا + +409 +00:28:01,990 --> 00:28:05,690 +التحليل أنا بعمله بالتفصيل طبعا فيما بعد هذا ممكن + +410 +00:28:05,690 --> 00:28:10,850 +نعمله ضمن الحلكمرحلة ابتدائية أو مبدئية صح ممكن + +411 +00:28:10,850 --> 00:28:13,790 +نعمله بهامش ممكن نعمله شفاوي بس هذا لازم نفهمه + +412 +00:28:13,790 --> 00:28:17,930 +لازم نكون في مكان ما عارفين إحنا إيش بنشتغل واضح + +413 +00:28:17,930 --> 00:28:22,170 +بنحلل، متابعين معاه؟ تمام، بدي أثبت إن جملة شرطية + +414 +00:28:22,170 --> 00:28:25,330 +تكون true وقت إيش بتكون الجملة الشرطية true؟ يا + +415 +00:28:25,330 --> 00:28:28,090 +الأول false والتاني إيش ما يكون يكون، يا الأول + +416 +00:28:28,090 --> 00:28:30,990 +true والتاني true طيب نتطلع على الأول X and Tamil + +417 +00:28:30,990 --> 00:28:34,490 +Phiما هي تنتم؟ ما رأيكوا فيها؟ هل هذه ممكن تكون + +418 +00:28:34,490 --> 00:28:38,410 +حقيقية؟ حطيتها ملاحظة إنه دايماً خاطئ فأقول له هنا + +419 +00:28:38,410 --> 00:28:48,090 +X تنتم لفاي هو خاطئ، لذلك الوصف X تنتم لفاي ثم X + +420 +00:28:48,090 --> 00:28:50,090 +تنتم لإيه هو حقيقية؟ + +421 +00:28:52,790 --> 00:28:56,310 +خلص البرحانة ولا ماخلصش؟ خلص مش هاد البداية وصلتله + +422 +00:28:56,310 --> 00:29:00,090 +ولا ماوصلتلهوش والبرحانة انتهت ممكن بدي أقلق thus + +423 +00:29:00,090 --> 00:29:04,970 +fi subset من هنا إذا حابين نعمل خاتمة جيد + +424 +00:29:04,970 --> 00:29:11,790 +ماكتبتوها أخر جملة مش مشكلة واضح؟فهي و ما اتعلمناه + +425 +00:29:11,790 --> 00:29:16,810 +بنحلل المطلوب بنشوف ال statement بدي أبرهنها بتعلم + +426 +00:29:16,810 --> 00:29:19,650 +كيف أتعامل معاها و هتعلم معاها كل واحدة لحال يمكن + +427 +00:29:19,650 --> 00:29:22,770 +احنا اشهر مثال كان في section 188 هو ايش if then + +428 +00:29:22,770 --> 00:29:25,710 +كيف نتعامل معاها نقول له assume b is true we want + +429 +00:29:25,710 --> 00:29:28,230 +to prove q is true هيبدأنا نتعامل مع مين مع for + +430 +00:29:28,230 --> 00:29:35,140 +all برضه جملة شرطية جملة شرطية أي سؤال واضحطب واحد + +431 +00:29:35,140 --> 00:29:38,440 +طالب تقول ليه؟ طب ليش ماقلتش assume أنه الـP true؟ + +432 +00:29:38,440 --> 00:29:41,460 +لأن هذا الاحتمال مش وارد، فليش أدور على حاجة عبث + +433 +00:29:41,460 --> 00:29:43,560 +مش مصحية؟ خلاص أنا عارف إنها default، انتهى + +434 +00:29:43,560 --> 00:29:46,420 +العملية، فليش أثبت .. أفترض إنها true؟ فيه احتمال + +435 +00:29:46,420 --> 00:29:49,860 +إنها تكون true غير وارد إطلاقًا، فمزال الشرط + +436 +00:29:49,860 --> 00:29:52,520 +false، إذا ال statement الشرطية دايما true + +437 +00:29:52,520 --> 00:29:57,000 +والبرهان انتهى أي سؤال؟ + +438 +00:30:03,940 --> 00:30:09,360 +كمية النظرية نظرية 2-2 subset relation is + +439 +00:30:09,360 --> 00:30:13,240 +transitive علاقة الـ subset علاقة إلى خاصية التعدى + +440 +00:30:13,240 --> 00:30:21,720 +بمعنى خلّينا نقرأ و نعمل رسمة مساعدة بقول let A, B + +441 +00:30:21,720 --> 00:30:27,200 +and C be sets شايفين المنهج؟ بتكرر معنى إذا الأن + +442 +00:30:27,200 --> 00:30:32,250 +اللي بدي أذكرCapital A وCapital B وCapital C ليش + +443 +00:30:32,250 --> 00:30:36,570 +بتتحدث عن مجموعات ليست أرقام وليست statement تمام + +444 +00:30:36,570 --> 00:30:42,970 +الجملة الموجودة بقوللي if A subset من الـB و الـB + +445 +00:30:42,970 --> 00:30:47,850 +subset من الـC هي transitive then A subset من الـC + +446 +00:30:47,850 --> 00:30:51,570 +خلينا نعمل رسمة و بعدين نشوف البرهان و نحلل فهي + +447 +00:30:51,570 --> 00:30:54,660 +بقوللي هي في عندي مجموعة Aهي مجموعة جزئية من + +448 +00:30:54,660 --> 00:30:57,660 +مجموعة أكبر منها B والـ B مجموعة جزئية من مجموعة + +449 +00:30:57,660 --> 00:31:00,760 +أصغر منها C فهل ال A جزء من ال C؟ بالتأكيد + +450 +00:31:00,760 --> 00:31:06,500 +بالتأكيد اه فانتوا طالبات في قسم الرياضيات فإذا + +451 +00:31:06,500 --> 00:31:09,280 +انتوا طالبات قسم الرياضيات وانتوا قسم الرياضيات في + +452 +00:31:09,280 --> 00:31:11,920 +كلية العلوم فانتوا طالبات كلية العلوم والكلية + +453 +00:31:11,920 --> 00:31:13,640 +العلوم في الجامعة الإسلامية انه طالبات في الجامعة + +454 +00:31:13,640 --> 00:31:18,460 +الإسلامية صح ولا لأ نفس القالةواضح؟ أه فالـ C هي + +455 +00:31:18,460 --> 00:31:20,960 +الأكبر لأنها بتحتوى الـ B و الـ B بتحتوى ال A فإذا + +456 +00:31:20,960 --> 00:31:23,080 +تقلش ال C بتحتوى ال A و لا بتحتوى أشهر، بتحتوى + +457 +00:31:23,080 --> 00:31:27,260 +أشهر واضحة؟ أه تمام، نشوف البرهان خلّينا نشوف + +458 +00:31:27,260 --> 00:31:30,800 +البرهان مع بعض، بدنا نحلل بالطريقة الماضية + +459 +00:31:30,800 --> 00:31:34,940 +فالبرهان + +460 +00:31:34,940 --> 00:31:39,940 +ليس سحر ولا فهلوة ولا شيء، فيه قواعد، فيه قواعد و + +461 +00:31:39,940 --> 00:31:47,890 +بنتعلم بعض الخبرات فهذه theoremإتنين إتنين طبعاً + +462 +00:31:47,890 --> 00:31:51,250 +في عندي مقدمة وفي عندي جملة شرطية خليني أبدأ + +463 +00:31:51,250 --> 00:31:56,390 +البرهان أفضل على طول و أفسرفكيف بدي أبرهن؟ أنا + +464 +00:31:56,390 --> 00:32:00,530 +عندي معطيات قاللي let a, b, c, b, 6 ممكن هذا عيد + +465 +00:32:00,530 --> 00:32:03,450 +كتبت، هذا صار عندي معطى فعندي معطى من الـ a و ال b + +466 +00:32:03,450 --> 00:32:06,450 +و ال c، إيش مالهم؟ هو عبارة عن مجموعات فبدي أقوله + +467 +00:32:06,450 --> 00:32:14,590 +هنا let a, b, c, b, 6 any 6 فهذا معطى فكل مقدمة في + +468 +00:32:14,590 --> 00:32:18,450 +النظرية تعتبر إيش؟ معطيات إيش المطلوب؟ إيش + +469 +00:32:18,450 --> 00:32:22,210 +القاعدة؟ بيقوللي قاعدة، في جملة شرطية بدي أثبت إن + +470 +00:32:22,210 --> 00:32:23,390 +الجملة الشرطية صحيحة + +471 +00:32:25,850 --> 00:32:35,050 +we want to prove that ايش جملة شرطية a subset من + +472 +00:32:35,050 --> 00:32:43,870 +ال b and b subset من ال c then a ممكن اعمل هيك a + +473 +00:32:43,870 --> 00:32:48,930 +subset من ال c is it true او كيف اكتبأو implies + +474 +00:32:48,930 --> 00:32:52,630 +يعني بحطها if then is true ك statement هذا مطلوب؟ + +475 +00:32:52,630 --> 00:32:56,550 +أه فإيش مطلوب مني أثبت؟ هل بدي أعمل اختبار الجملة + +476 +00:32:56,550 --> 00:32:59,410 +الشرطية لو بتش بتكون true ولا false؟ لأ بدي أثبت + +477 +00:32:59,410 --> 00:33:02,670 +إن أنا true دايما، نظرية، بدي أثبت إنها true يعني + +478 +00:33:02,670 --> 00:33:04,050 +بدي أثبت ال communication علشان هيك دايما في + +479 +00:33:04,050 --> 00:33:07,450 +ريادات بيستخدموش تضمين لأنه أنا مطلوب إن أثبت إنها + +480 +00:33:07,450 --> 00:33:13,060 +true واضح؟ هذا هو المطلوبواضح؟ تمام هذا المطلوب + +481 +00:33:13,060 --> 00:33:16,880 +اصنعه جملة شرطية كيف نبدأ برهان الجملة الشرطية + +482 +00:33:16,880 --> 00:33:21,340 +المباشر افترض ان الشرط صحيح فإيش حداله الآن فيعني + +483 +00:33:21,340 --> 00:33:27,240 +عندي هذا معطى المعطى التاني assume that + +484 +00:33:28,060 --> 00:33:35,180 +A subset من الـ B and الـ B subset من الـ C افترض + +485 +00:33:35,180 --> 00:33:38,380 +ان المعطف صحيح ايش المطلوب اثمت انه جواهب الشرط + +486 +00:33:38,380 --> 00:33:47,480 +صحيح we have to show that الـ A subset من الـ C + +487 +00:33:50,450 --> 00:33:55,150 +أرجو متابعة التسلسل المنطقي اللي ماشيين فيه بنفسر + +488 +00:33:55,150 --> 00:33:58,730 +كل شيء و كل خطوة بنفسرها أه بحتاج تفسير أكتر من + +489 +00:33:58,730 --> 00:34:03,250 +فسرها ممتاز ماذا يعني A subset من الـC تو كتب لها + +490 +00:34:03,250 --> 00:34:11,550 +تكافئ for all X X in A then X in C هذا هو المطلوب + +491 +00:34:13,230 --> 00:34:17,850 +شايفين؟ انت باين؟ انا بجيبش حاجة فجأة تسقط من + +492 +00:34:17,850 --> 00:34:21,670 +السماء، بفسر، واحدة واحدة، انا هذا بدي أثبته، إيش + +493 +00:34:21,670 --> 00:34:23,610 +بدي أعمله؟ لأنه وصلت لهذه المرحلة، طبعا أنا كنت + +494 +00:34:23,610 --> 00:34:28,110 +هنا، هي دي فسرتها، فصار المطلوب مني الآن، حددته + +495 +00:34:28,110 --> 00:34:31,290 +أكتر، صار هذا الكلام جملة بعد الشرط كيف بدي أتعامل + +496 +00:34:31,290 --> 00:34:38,670 +معها؟ let X be any element let X be any element + +497 +00:34:43,610 --> 00:34:46,970 +إيش صار بدنا؟ لنثبت إن الجملة الشرطية صحيحة We + +498 +00:34:46,970 --> 00:34:57,110 +have to show that X تنتمي للـA implies X تنتمي + +499 +00:34:57,110 --> 00:35:00,690 +للـC أو الجملة الشرطية is true ولا لأ؟ بس هيك + +500 +00:35:00,690 --> 00:35:06,300 +معناهاهك معناه ولا مش هيك؟ لأنه أنا عايش for all x + +501 +00:35:06,300 --> 00:35:09,560 +b of x بدي أثبت إن if b of x is true طبعا ممكن + +502 +00:35:09,560 --> 00:35:12,800 +أعملها زي نظرية الأولى بس هل ال x of a true ولا + +503 +00:35:12,800 --> 00:35:16,720 +false مش معروفة فهدي مختلف عن ذاك المثال مثال فريد + +504 +00:35:16,720 --> 00:35:20,920 +من نوعه تبع ال file فانا بدي أثبت إن هذا true تمام + +505 +00:35:20,920 --> 00:35:24,820 +جملة شرطية إيش بدي أعملها assume x تنتمي لل a + +506 +00:35:24,820 --> 00:35:34,400 +assume x تنتمي لل a طبعا واحدغشيم بقولك تعالي + +507 +00:35:34,400 --> 00:35:37,500 +نرياضة كل شوية أسيوم زي ما بده في واحدة أسيوم أنا + +508 +00:35:37,500 --> 00:35:42,150 +عملتها من عجلةأنا في واحدة عملتها مزاجا ولا كلها + +509 +00:35:42,150 --> 00:35:47,710 +بسبب؟ وكلها بسبب طبق من القواعد صح ولا مش صح؟ اه + +510 +00:35:47,710 --> 00:35:49,830 +فهو ماعيش بيقول اه قلت اه و رياضة كلها أسيوم افترض + +511 +00:35:49,830 --> 00:35:52,610 +افترض افترض زي ما بدكم عشوائية ما هي القضية + +512 +00:35:52,610 --> 00:35:57,190 +عشوائية شايفينها؟ لأ كل خطوة بنسأل نفسنا كيف نعمل + +513 +00:35:57,190 --> 00:36:01,430 +و إيش نعمل فالعمر منطقي مش عشوائي ممتاز إيش بده + +514 +00:36:01,430 --> 00:36:04,490 +أثبت؟ X سنتمل الـC هي آخر مطلة بقدر أفسر أكتر من + +515 +00:36:04,490 --> 00:36:13,440 +هيك؟ مش حاجة ده we haveto show that X تنتمي للـC + +516 +00:36:13,440 --> 00:36:17,100 +بقدر أفسر أكتر من هيك؟ لأ، شوفتوا أحنا إيش ماشيين؟ + +517 +00:36:17,100 --> 00:36:19,880 +ماشيين خطوة خطوة، كل خطوة بنفسرها طب كيف نتعامل + +518 +00:36:19,880 --> 00:36:23,320 +معاها؟ بتحتاج تفسير، بتتفسر، بتتفسر، صار بدي أثبت + +519 +00:36:23,320 --> 00:36:27,220 +إن X تنتمي للـC تتفسر أكتر من هيك؟ لأ، إيش معنى X + +520 +00:36:27,220 --> 00:36:30,120 +تنتمي للـC؟ ماعناش معنى، يعني غير إنها بدي عنصر + +521 +00:36:30,120 --> 00:36:33,880 +موجود في الـC، ممتاز، الآن أنا وين موجود؟ X في + +522 +00:36:33,880 --> 00:36:38,430 +الـA، بدأ أوصلها للـCأتطلع على المعطيات X موجودة + +523 +00:36:38,430 --> 00:36:41,370 +في الـ A ومش في عنده معطيات؟ الـ A صبصت من الـ B + +524 +00:36:41,370 --> 00:36:45,970 +فكل عنصر في الـ A وين موجود؟ في الـ B فالآن X + +525 +00:36:45,970 --> 00:36:50,830 +تنتمي للـ A implies X تنتمي للـ B ليش؟ لأن الـ A + +526 +00:36:50,830 --> 00:36:53,550 +صبصت من الـ B، هاي دليل ممكن أكتبها بهذا الشكل + +527 +00:36:53,550 --> 00:36:57,430 +لوقت أكتب since A صبصت من الـ B X تنتمي للـ A + +528 +00:36:57,430 --> 00:37:01,090 +implies تؤدي أن X في الـ B ممتاز اللي في الـ B وين + +529 +00:37:01,090 --> 00:37:04,770 +بيكون؟ بيكون في الـ C فهنا نكتب هنا + +530 +00:37:08,940 --> 00:37:14,780 +implies X تنتمي للـC لإيش؟ لأن الـB subset من الـA + +531 +00:37:14,780 --> 00:37:21,020 +من الـC آسف طيب بعدين وصلنا أحسنتوا أنا إيه اللي + +532 +00:37:21,020 --> 00:37:24,480 +بدي إياه خلص البرهات ماعناش بقول we want to prove + +533 +00:37:24,480 --> 00:37:27,880 +that X تنتمي للـC بدأنا من المعطيات استخدمنا + +534 +00:37:27,880 --> 00:37:34,020 +المعطيات و إيش وصلنا للمطلوب انتهى البرهان واضح؟ + +535 +00:37:34,020 --> 00:37:37,580 +أه طبعاهيك تكون أول مثال يمكن أن أنا كتبته + +536 +00:37:37,580 --> 00:37:43,000 +بالتفصيل لكن لو بدأ لخصه أصبح عشان أثبت أنه إيش + +537 +00:37:43,000 --> 00:37:47,020 +بدنا نثبت A subset من ال C إيش صارت الخطة خدي عنصر + +538 +00:37:47,020 --> 00:37:50,660 +عشوائي في ال A ووصليه في إيش لل C هيك صارت لو بدأ + +539 +00:37:50,660 --> 00:37:55,210 +لخصها أنه بدأ أخد أي عنصرموجود في الـA يكون موجود + +540 +00:37:55,210 --> 00:37:58,690 +في الـC هذه ملخصة بس هذه أول مرة فاكفكناها + +541 +00:37:58,690 --> 00:38:02,790 +وفسرناها خطوة خطوة ممكن نلخصها طبعا نختصر دائما مع + +542 +00:38:02,790 --> 00:38:05,930 +المراحل المتقدمة بنصير نختصر بعض الخطوات لكن في + +543 +00:38:05,930 --> 00:38:13,970 +البداية لازم نفسر نشوف بعض الأمثلة مثال الأول in + +544 +00:38:13,970 --> 00:38:16,310 +each of the following determine whether the + +545 +00:38:16,310 --> 00:38:21,680 +statement is true or false true or falseالمثال + +546 +00:38:21,680 --> 00:38:28,620 +الأول هل ال X تنتمي لمجموعة X؟ true متفقين المثال + +547 +00:38:28,620 --> 00:38:36,580 +الأول هو true طبعا solution مجموعة + +548 +00:38:36,580 --> 00:38:41,310 +الواحد تساوي مجموعة مجموعة الواحدغلط هدولة عمرين + +549 +00:38:41,310 --> 00:38:46,110 +مختلفين هدولة اه اه لإنها جاين ساوي هل هذه فيها + +550 +00:38:46,110 --> 00:38:50,070 +نفس العناصر لأ هذه عناصرها مين مجموعة الواحد هذه + +551 +00:38:50,070 --> 00:38:53,350 +عناصرها مين الواحد نفسه فهذه مختلفة فهذه false + +552 +00:38:53,350 --> 00:38:58,240 +فهذه مختلفة falseأه فهنا زي ما دي أقول أيش مثلا + +553 +00:38:58,240 --> 00:39:02,220 +اللي هو أيش مجموعة أقسام جاء الجامعة الإسلامية + +554 +00:39:02,220 --> 00:39:04,860 +فيها قسم رياضيات فيها قسم اللغة العربية ومجموعة + +555 +00:39:04,860 --> 00:39:08,120 +كليات أه هل فيها قسم اللغة العربية اللي هو قسم + +556 +00:39:08,120 --> 00:39:11,360 +رياضياته لأ رياضيات جزء من العلوم فالعلوم كلية أه + +557 +00:39:11,360 --> 00:39:14,520 +فهنا مختلف الأمر أه فهنا أيش التقسيم اللي بجسمه أه + +558 +00:39:14,520 --> 00:39:18,300 +فهذه أيش مختلفين وإنما أيش ممكن نحط علاقة تنتمي + +559 +00:39:18,300 --> 00:39:22,770 +أحسنتم تبسط من فعل لألأ مينفعش، ايش معنى subset؟ + +560 +00:39:22,770 --> 00:39:25,590 +كل عناصر الأولى عناصر من التانية، هل الواحد عناصر + +561 +00:39:25,590 --> 00:39:28,410 +من التانية؟ لأ، الواحد مش عناصر التانية، مجموعة + +562 +00:39:28,410 --> 00:39:31,090 +الواحد هي اللي عناصر التانية، زي ما هي الرياضيات + +563 +00:39:31,090 --> 00:39:34,490 +مش من كليات الجامعة الإسلامية، الرياضيات اشمال قسم + +564 +00:39:34,490 --> 00:39:37,910 +في كلية العلوم، مختلف المفهوم، المفهوم مختلف + +565 +00:39:37,910 --> 00:39:42,590 +والتقسيم مختلفلكن هيها .. شوفت مجموعة الواحد + +566 +00:39:42,590 --> 00:39:46,630 +والتانين تنتمي لمجموعة .. مجموعة الواحد والتانين + +567 +00:39:46,630 --> 00:39:50,470 +كأنصر والتلاتة كأنصر إيش معانا تنتمي؟ لإن أنصر من + +568 +00:39:50,470 --> 00:39:56,370 +ضمن العناصر فهذه true ف C true فأرجو هذا الرموز + +569 +00:39:56,370 --> 00:40:03,010 +نفرق فيها و نستخدمها بهذه الدقة الفاي تساوي مجموعة + +570 +00:40:03,010 --> 00:40:08,650 +الفايfalse مختلفين هذه مجموعة فارغة هذه مجموعة + +571 +00:40:08,650 --> 00:40:12,470 +فيها عنصر هذه مجموعة فيها عنصر مختلف تماما فهذه + +572 +00:40:12,470 --> 00:40:17,290 +false أشبهلكوا إياها هلجيت صينية فاضية فهي صينية + +573 +00:40:17,290 --> 00:40:20,110 +فاضية صينية فاضية فيها كباية فاضية الصينية صارت + +574 +00:40:20,110 --> 00:40:23,350 +فاضية ولا مليانة ورغم أن فيها كباية فاضية واضح + +575 +00:40:23,350 --> 00:40:27,970 +فالفرق ففرق هذه مجموعة فيها عنصر فارغ مانيش ده + +576 +00:40:27,970 --> 00:40:28,890 +ولكن فيها حاجة + +577 +00:40:32,860 --> 00:40:36,160 +لأن إيش مقناة subset؟ كل عناصر الأولى، من عناصر + +578 +00:40:36,160 --> 00:40:39,360 +الأولى؟ الواحد، بدنا نكون جوا من عناصر، هل الواحد + +579 +00:40:39,360 --> 00:40:42,320 +من عناصر التانية؟ لأ، مجموعة الواحد هي اللي من + +580 +00:40:42,320 --> 00:40:44,560 +عناصر التانية، زي ما قلنا إن الرياضيات مش من + +581 +00:40:44,560 --> 00:40:49,780 +القليات، هي جوا كلية، بطلعش أنا على التفاصيل، بطلع + +582 +00:40:49,780 --> 00:40:53,060 +من الخارج كعناصر، بيهمنا، بيادة شخصية تنتمي .. + +583 +00:40:53,060 --> 00:41:00,960 +تنتمي .. صح، زي الوق، زي الـC، تشبه الـC مثال آخر + +584 +00:41:03,190 --> 00:41:06,450 +in each of the following determine whether the + +585 +00:41:06,450 --> 00:41:09,370 +statement is true or false زي السؤال السابع بس + +586 +00:41:09,370 --> 00:41:13,310 +ضافة بقول if it is true prove it لما احنا بقول + +587 +00:41:13,310 --> 00:41:18,930 +نثبت الصحة with a false disapprove it اذا انا انا + +588 +00:41:18,930 --> 00:41:19,790 +انا انا انا انا انا انا انا انا انا انا انا انا + +589 +00:41:19,790 --> 00:41:19,950 +انا انا انا انا انا انا انا انا انا انا انا انا + +590 +00:41:19,950 --> 00:41:22,750 +انا انا انا انا انا انا انا انا انا انا انا انا + +591 +00:41:22,750 --> 00:41:23,270 +انا انا انا انا انا انا انا انا انا انا انا انا + +592 +00:41:23,270 --> 00:41:28,830 +انا انا انا انا انا انا انا انا انا + +593 +00:41:33,850 --> 00:41:39,370 +خلّينا نحلهم مع بعض نشوف إيش الأسئلة و نحلها + +594 +00:41:39,370 --> 00:41:46,890 +المثال الأول إذا كانت ال X في ال A هذا المثال رقم + +595 +00:41:46,890 --> 00:41:52,250 +اتنين وال solution وهي A إذا ال X في ال A و ال A + +596 +00:41:52,250 --> 00:41:58,790 +تنتمي لل B فال X ضروري تكون في ال B مش + +597 +00:41:58,790 --> 00:42:03,330 +ضروري زي توي هذه نفس الآية للقضية فهذه falseفدى + +598 +00:42:03,330 --> 00:42:10,690 +force بدنا ماشي مثال عكسى counter example بدنا + +599 +00:42:10,690 --> 00:42:17,710 +مثال عكسى نعم لو ال A سبسطم ال B طبعا طبعا تعريفها + +600 +00:42:17,710 --> 00:42:21,230 +فهنا مش بالضرورة لأن هنا التعامل مع ال A كان عنصر + +601 +00:42:21,230 --> 00:42:24,430 +من ال B فمش ضرورى عناصر ال A تكون زى ما توي شفنا + +602 +00:42:24,430 --> 00:42:30,030 +الواحد زى المثال قبل قليل بدنا مثال بدنا مثال عكسى + +603 +00:42:30,030 --> 00:42:35,820 +تمامبدنا مثال عكسي بدنا مثال عكسي بدنا عنصر يكون + +604 +00:42:35,820 --> 00:42:39,140 +موجود في الـA فبدنا نعرف الـA أول شيء فنقول له + +605 +00:42:39,140 --> 00:42:43,140 +مثلا let capital A تساوي مجموعة مين الواحد مثلا + +606 +00:42:43,140 --> 00:42:46,220 +ودائما لما تدي مثال عكسي حاولي تديه أبسط ما يكون + +607 +00:42:46,220 --> 00:42:49,240 +ماتعجديش حالك وماتتهيش عشان ما تغلطيش عشان يكون + +608 +00:42:49,240 --> 00:42:52,060 +المثال واضح فانا بدأ أثبت أن هذا ال statement غلط + +609 +00:42:52,060 --> 00:42:55,940 +يعني إيش؟ بدأ أثبت أن الشرط صحيح وجواب الشرط خطأ + +610 +00:42:55,940 --> 00:42:59,540 +هيك معناته لإن هي شملة شرطية فبدنا ال جتحنا بدنا + +611 +00:42:59,540 --> 00:43:04,790 +مجموعة Aفيها عنصر X والـ A هي عنصر من الـ B لكن + +612 +00:43:04,790 --> 00:43:07,790 +الـ X مش عنصر من الـ B فناخد مثلا مجموعة الواحد + +613 +00:43:07,790 --> 00:43:13,770 +فالآن الواحد تنتمي لل A بتنعرف ال B and let B ال X + +614 +00:43:13,770 --> 00:43:19,870 +بساوة واحدة خلصنا عشان مايكون مثال ملموس أه إيش + +615 +00:43:19,870 --> 00:43:23,790 +مالها ال B تحتوي على ال A أه وممكن .. بس ميداشي + +616 +00:43:23,790 --> 00:43:26,870 +تكون تحتوي على ال واحد ولا تكون مثلا اتنين في أي + +617 +00:43:26,870 --> 00:43:32,560 +اختارأريد أن أثبت أن الجملة الـJH فالس فالآن + +618 +00:43:32,560 --> 00:43:38,920 +الواحد تنتمي للـA صح؟ والـA تنتمي للـB صح؟أيها؟ + +619 +00:43:38,920 --> 00:43:45,220 +لكن but الواحد لا تنتمي لل B هل الواحد من عناصر ال + +620 +00:43:45,220 --> 00:43:48,100 +.. يمكن الكتابة بدأت شكل أسهل لو حطيت إنه بدل ال A + +621 +00:43:48,100 --> 00:43:50,720 +مجموعة الواحد كانت اتخنته شوية لكن واضح إن الواحد + +622 +00:43:50,720 --> 00:43:55,160 +من عناصر ال B لأ واضح من عناصر ال B A وال A + +623 +00:43:55,160 --> 00:43:57,980 +عناصرها الواحد ماليش دعوة أنا بتطلع على عناصر ال B + +624 +00:43:57,980 --> 00:44:00,880 +بتطلع اتطلع على النظر الخارجية ماليش دعوة + +625 +00:44:00,880 --> 00:44:04,120 +بالتفاصيل ماليش دعوة بالتفاصل أي سؤال + +626 +00:44:07,920 --> 00:44:13,280 +فهذا بيقدر أنه يحصل statement false فهذا + +627 +00:44:13,280 --> 00:44:15,240 +يمكن أن يكون أول مثال على الكافرين دي ب counter + +628 +00:44:15,240 --> 00:44:18,480 +example ان شاء الله مع التكرار الأمور تكون أفضل من + +629 +00:44:18,480 --> 00:44:26,580 +هك و أوضح مثال Bإذا X تنتمي للـ B و A subset من + +630 +00:44:26,580 --> 00:44:31,340 +الـ B فالـ X ليست في الـ A هذي False صحيح و ممكن + +631 +00:44:31,340 --> 00:44:36,840 +مع الرسم تساعدنا بي فالس خلينا نعمل رسم مساعد هي + +632 +00:44:36,840 --> 00:44:41,750 +عندي A و هي عندي Bبقول لي في عنصر موجود في ال B + +633 +00:44:41,750 --> 00:44:45,330 +وين عناصر ال B؟ يا هان يا هان ضروري يكون خارج ال + +634 +00:44:45,330 --> 00:44:48,650 +ايه؟ لأ واضح انه مش ضروري انه مش ضروري فهذه طبعا + +635 +00:44:48,650 --> 00:44:51,150 +لما يقولي طب ممكن تكون صح لأ انا اش بده أقول قاعد + +636 +00:44:51,150 --> 00:44:54,090 +تكون دايما صح هيك معاك لأ مش احتمال فلما بده اقول + +637 +00:44:54,090 --> 00:44:56,690 +ان القاعد ده بده تكون دايما صحيحة مش ان احتمال + +638 +00:44:56,690 --> 00:45:01,130 +تكون صحيحة اه في بعض الأحيان لأ بنفعل فبندليه مثال + +639 +00:45:01,130 --> 00:45:09,730 +عكسي counter example مثال عكسي اوتمام فناخد ايش ال + +640 +00:45:09,730 --> 00:45:14,850 +a مثلا تساوي واحد اتنين ببساطة اه بده يعني ايش ال + +641 +00:45:14,850 --> 00:45:20,460 +a subset من ال b بي تساوي عشان تكون subsetواحد + +642 +00:45:20,460 --> 00:45:25,080 +اتنين على اقله تلاتة تمام فبقوللي ال X بدا تكون في + +643 +00:45:25,080 --> 00:45:28,960 +ال B وماتكونش في ال A برضه جملة شرطية بدياش فانا + +644 +00:45:28,960 --> 00:45:33,400 +عندي مثلا انه بدا تكون في ال B وال A صبصت مظبوط + +645 +00:45:33,400 --> 00:45:37,780 +وماتكونش بتكون اه بعد المية ليست في ال A بدا + +646 +00:45:37,780 --> 00:45:42,100 +مفيهاش ده تصير جوا ال A فاشفي عندي الأول شي الواحد + +647 +00:45:42,100 --> 00:45:47,770 +تنتمي لل Bالـ A سبسط من ال B صح ولا مش صح لكن + +648 +00:45:47,770 --> 00:45:55,350 +الواحد تنتمي لل A نفيتها دي مظبوط؟ أه لكن الواحد + +649 +00:45:55,350 --> 00:45:59,170 +تنتمي لل A فهي مثال بتدل عنها دي مش قاعدة لأن + +650 +00:45:59,170 --> 00:46:06,470 +القاعدة بتكون دائما صحيحة دائما صحيحة أي سؤال؟ + +651 +00:46:06,470 --> 00:46:09,930 +نشوف + +652 +00:46:09,930 --> 00:46:14,940 +مثال تالتهو نهاية ال section هنا ان شاء الله prove + +653 +00:46:14,940 --> 00:46:21,160 +that for any sets a,b,c تلت مجموعات إذا ال a بربر + +654 +00:46:21,160 --> 00:46:25,040 +من ال b و ال b بربر subset من ال c فال a بربر + +655 +00:46:25,040 --> 00:46:27,980 +subset من ال c فبرضه علاقة بربر subset is + +656 +00:46:27,980 --> 00:46:37,260 +transitive بدنا نثبتها بدنا نثبتها مثال + +657 +00:46:37,260 --> 00:46:45,020 +التالت و solutionطبعا هذا المثال اللي هو أهم + +658 +00:46:45,020 --> 00:46:49,480 +بالنسبالنا كيف نبرهن لأنه براهين النظريات بدنا + +659 +00:46:49,480 --> 00:46:53,480 +نفهمها و نعرف نشتغل زيها مش نعرف نحفظها اه فهنا + +660 +00:46:53,480 --> 00:46:56,800 +بدينا كيف نتعامل زي ما اتعلمنا في النظرية طبعا + +661 +00:46:56,800 --> 00:47:00,820 +prove that for any sets A,B,C إذا أنا فيه عندي + +662 +00:47:00,820 --> 00:47:07,260 +معطع أن الـA و الـB sets ممكن أقوله إيش let A,B,C + +663 +00:47:07,260 --> 00:47:13,170 +أو and C كله صح بيه sixanysets نفس المعنى كلمة any + +664 +00:47:13,170 --> 00:47:17,010 +هذي ايش ومفهومة ضمنيا حتى لما ذكرتها ايش بقول ايه + +665 +00:47:17,010 --> 00:47:24,630 +اثبت if جملة شرطية we want to prove نكتب هنا ايش + +666 +00:47:24,630 --> 00:47:29,770 +المطلوب فالله يقولني ايش prove that we want او + +667 +00:47:29,770 --> 00:47:36,850 +have to كله صح to prove thatجملة شرطية الـ A + +668 +00:47:36,850 --> 00:47:42,070 +proper subset من الـ B and الـ B proper subset من + +669 +00:47:42,070 --> 00:47:49,110 +الـ C then او implies if then true implies الـ A + +670 +00:47:49,110 --> 00:47:55,590 +proper من الـ C هذا المطلوب في طالبة عندها صعوبة + +671 +00:47:55,590 --> 00:48:00,300 +في اللي كتبناه؟ امتبعين؟واضح؟ يعني احنا جيت في هذه + +672 +00:48:00,300 --> 00:48:04,260 +المرحلة بنأكد على هذه المفهومة بعد هيك شوية هنتقدم + +673 +00:48:04,260 --> 00:48:07,260 +حاسيب تركيز على أمور أخرى متقدمة فارجعوا إن الأمر + +674 +00:48:07,260 --> 00:48:11,240 +إذا فيه مشكلة نحله الآن هذا وقت المناسب تمام؟ إيش + +675 +00:48:11,240 --> 00:48:17,760 +المطلوب؟ جملة صارطية كيف أثبت؟ Assume that Assume + +676 +00:48:17,760 --> 00:48:27,880 +that الـA proper subset من الـB and الـB + +677 +00:48:29,000 --> 00:48:36,760 +بربر subset من الـ C ممتاز ايش المطلوب؟ we have to + +678 +00:48:36,760 --> 00:48:44,740 +show that ال A بربر من ال C وتكافئ ايش معناته + +679 +00:48:44,740 --> 00:48:50,300 +بربر؟ subset ولا تساوي ان ال A subset من ال C and + +680 +00:48:50,300 --> 00:48:56,200 +ال A لا تساوي ال C ممتاز + +681 +00:49:01,970 --> 00:49:06,430 +بدنا نثبت هذا الكلام ايش بيكافئ جملة فيها + +682 +00:49:06,430 --> 00:49:09,110 +conjunction استثمار فيها conjunction عشان تكون + +683 +00:49:09,110 --> 00:49:12,250 +true بتثبت أن هذه true وهذه true فخلينا نقسم على + +684 +00:49:12,250 --> 00:49:15,850 +مرحلتين فنبدأ من الجزء الأول بدنا نثبت أن ال A + +685 +00:49:15,850 --> 00:49:20,190 +subset من ال C بدنا نثبت أن ال A subset من ال C + +686 +00:49:20,190 --> 00:49:26,850 +فده أول جزء بدنا نثبت أن ال A subset من ال C تمام؟ + +687 +00:49:26,850 --> 00:49:32,350 +اه فيه أن احنامقطيات سهل هذا الجزء لأنه ايش قلنا + +688 +00:49:32,350 --> 00:49:35,570 +بدنا نثبت ان البروبر transitive طب ما احنا في + +689 +00:49:35,570 --> 00:49:39,190 +subset transitive طب و البروبر تتضمن ضمنيا انه + +690 +00:49:39,190 --> 00:49:43,050 +يكون subset فانا عندي من الخطوة الأولى هدول مقطيات + +691 +00:49:43,050 --> 00:49:46,810 +assume that ال A subset من ال B يعني A أسف البروبر + +692 +00:49:46,810 --> 00:49:50,130 +subset يعني subset فبما أننا هنا نقوله ايش ال A + +693 +00:49:50,130 --> 00:49:54,010 +subset البروبر subset من ال B implies اللي هو مين + +694 +00:49:54,010 --> 00:49:59,730 +ال A subset من ال Bوالـ B proper subset من الـ C + +695 +00:49:59,730 --> 00:50:04,670 +implies الـ B subset من الـ C هذه و هذه و نظرية + +696 +00:50:04,670 --> 00:50:08,190 +اتنين اتنين ايش يؤدوا ان الـ A subset من الـ C اه + +697 +00:50:08,190 --> 00:50:15,230 +اذا thus ممكن اكتب الـ A subset من الـ C من وين؟ + +698 +00:50:15,230 --> 00:50:21,460 +theorem اتنين اتنينفانا الجزء السهل وده شيء متوقع + +699 +00:50:21,460 --> 00:50:25,460 +ممكن احط اشي يساوي و اقول for all x لكن انا بدل ما + +700 +00:50:25,460 --> 00:50:28,480 +أعمل بشكل مطول باعيد برهان نظرية اتنين اتنين + +701 +00:50:28,480 --> 00:50:32,660 +استخدمت النظرية واضح الفرق؟ اه فالان انا مافصلتش + +702 +00:50:32,660 --> 00:50:35,540 +ليش لأن استفادت من النظرية استفادت من النظرية + +703 +00:50:35,540 --> 00:50:39,880 +فالجزء الاول سهل متفقين؟ اه ممكن اعمل بشكل مطول اه + +704 +00:50:39,880 --> 00:50:44,360 +بس بكون اطول هذا اقصر البرهان الجزء التاني بدنا + +705 +00:50:44,360 --> 00:50:51,560 +نثبت ان ال A لا تساوي ال Cلأ تساوي الـ C على ان + +706 +00:50:51,560 --> 00:50:57,200 +تستفهى ايش + +707 +00:50:57,200 --> 00:51:03,560 +معناه لأ تساوي يساوي يعني هذه سبسط من الأولى + +708 +00:51:03,560 --> 00:51:07,640 +والتانية سبسط من الأولى فاحنا عندنا خلينا بس + +709 +00:51:07,640 --> 00:51:10,540 +أفسرها هنا تساوي + +710 +00:51:13,190 --> 00:51:16,490 +لاتساوي، لاتساوي، إيش معناه؟ إيش تكافئ؟ نفي إن + +711 +00:51:16,490 --> 00:51:21,290 +الـA subset من الـC and C subset من الـA، ممتاز + +712 +00:51:21,290 --> 00:51:26,830 +خلينا ننفيها، كيف بننفيها هذه؟ DeMorgans يعني إيش؟ + +713 +00:51:26,830 --> 00:51:33,290 +A ليست subset من الـC or C ليست subset من الـAصح + +714 +00:51:33,290 --> 00:51:37,590 +ولا لأ؟ دي مورجانز شايفين؟ اه اللي اتعلمناه ممتاز + +715 +00:51:37,590 --> 00:51:41,310 +انا ايش بدي اثبت؟ بدي اثبت انه يا هاذي true يا + +716 +00:51:41,310 --> 00:51:44,670 +هاذي true عشان .. بدي اثبت ان ال or true وقت ايش + +717 +00:51:44,670 --> 00:51:47,330 +بيكون ال or true؟ على الأقل واحدة true طيب احنا + +718 +00:51:47,330 --> 00:51:51,560 +ايش في أول خطوة أثبتنا؟الـ A subset من ال C is + +719 +00:51:51,560 --> 00:51:57,360 +true يعني A ليست subset أدي شمالها false طب عشان + +720 +00:51:57,360 --> 00:52:00,440 +تكون ال R true إيش لازم تكون؟ لازم تكون ال can يه + +721 +00:52:00,440 --> 00:52:03,100 +true فإذا لازم أثبت إن وديك true فهنا دي ده أقولله + +722 +00:52:03,100 --> 00:52:13,200 +since ال A subset من ال C we have to show that ال + +723 +00:52:13,200 --> 00:52:20,540 +إيش ال C ليست subset من مين؟ من ال Aهي اللي تبقى + +724 +00:52:20,540 --> 00:52:26,600 +وهذا issue كافة كتبناها قبل قليل there exist X X + +725 +00:52:26,600 --> 00:52:35,940 +تنتمي لل A .. آسف لل C and X لا تنتمي لل A فهذا هو + +726 +00:52:35,940 --> 00:52:39,920 +المطلوب فهذا هو المطلوب + +727 +00:52:43,300 --> 00:52:46,820 +فكيف نثبته؟ بدنا ندور على X موجودة في الـC و غير + +728 +00:52:46,820 --> 00:52:47,480 +موجودة في الـA + +729 +00:52:53,190 --> 00:52:57,650 +في جيابنا و لا في الشنط و لا وين؟ في المعطيات .. + +730 +00:52:57,650 --> 00:53:02,070 +في المعطيات طيب هل ممكن أذكر ال X بشكل صريح؟ أقول + +731 +00:53:02,070 --> 00:53:05,550 +X بتساوي واحد و لا بتساوي صفر؟ ليش؟ لأن ال A و ال + +732 +00:53:05,550 --> 00:53:08,430 +B و ال C دول عايش مجموعات عامة، إيش عناصرهم؟ مش + +733 +00:53:08,430 --> 00:53:11,790 +معروف، إذا وين بدنا ندور في المعطيات؟ مين موقف + +734 +00:53:11,790 --> 00:53:14,750 +يقول لي there exists؟اتطلعوا احنا ايش استخدمنا في + +735 +00:53:14,750 --> 00:53:18,590 +المعطيات استخدمنا انهم subset استخدمنا انهم proper + +736 +00:53:18,590 --> 00:53:23,230 +لأ ما استخدمناش انهم proper ايش معناه ان الـB + +737 +00:53:23,230 --> 00:53:27,250 +proper subset من الـC ان الـB تسويش الـC يعني هناك + +738 +00:53:27,250 --> 00:53:31,090 +عنصر موجود في الـC غير موجود في الـB اه فالان بدي + +739 +00:53:31,090 --> 00:53:36,970 +اكتبله هنا بي برابر من الـC implies there exists X + +740 +00:53:36,970 --> 00:53:42,110 +X تنتمي للـC and X ليستفي الـ B بنفس المفهوم + +741 +00:53:42,110 --> 00:53:46,490 +السابق مظلة proper إذا في عناصر في الـ C زيادة مش + +742 +00:53:46,490 --> 00:53:49,990 +هي الـ C كبيرة بتحتوى الـ B والتساوي غير محتمل + +743 +00:53:49,990 --> 00:53:53,010 +ليش؟ لأن الـ C فيها عناصر زيادة معناته هذا الكلام + +744 +00:53:53,010 --> 00:53:57,650 +ممتاز أنا إيش بديها؟ أنا بدي X تنتمي للـ A ممكن + +745 +00:53:57,650 --> 00:54:03,060 +أوصلها، كيف أوصلها؟الـ A سبسط من الـ B كل أنصار في + +746 +00:54:03,060 --> 00:54:06,300 +الـ A موجود في الـ B الـ Contrapositive كل أنصار + +747 +00:54:06,300 --> 00:54:09,160 +غير موجود في الـ B مستحيل يكون في الـ A + +748 +00:54:09,160 --> 00:54:14,180 +Contrapositive فهذه تؤدي there exists X X تنتمي + +749 +00:54:14,180 --> 00:54:19,020 +للـ C و X لا تنتمي للـ A من أين جلبنا هذا الدليل؟ + +750 +00:54:19,020 --> 00:54:23,380 +طبعا هذا بإيش؟ هذا يؤدي لهذا هذا ليش؟ لأن الـ A + +751 +00:54:23,380 --> 00:54:28,240 +سبسط من الـ B طيب أكتبلكم على السريع إيش معناة A + +752 +00:54:28,240 --> 00:54:29,220 +سبسط من الـ B؟ + +753 +00:54:36,330 --> 00:54:46,070 +مظبوط؟ إيش الـ Contrapositive تبعتها؟ وضحكت؟ + +754 +00:54:46,070 --> 00:54:49,830 +فما زال X غير موجودة في الـP إذاً هي ماير موجودة + +755 +00:54:49,830 --> 00:54:56,870 +في الـA وهو المطلوب وهو المطلوب هذه نهاية ال + +756 +00:54:56,870 --> 00:54:57,850 +section إن شاء الله المرة جديدة + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/SuCRM6Nv8Fg_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/SuCRM6Nv8Fg_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..185d409a987e0343b4437518364946758c3abdd6 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/SuCRM6Nv8Fg_raw.srt @@ -0,0 +1,3040 @@ +1 +00:00:20,810 --> 00:00:24,780 +بسم الله الرحمن الرحيمفاليوم ان شاء الله هنواصل مع + +2 +00:00:24,780 --> 00:00:28,200 +المجموعات في المحاضرة الماضية يمكن احنا أخدنا + +3 +00:00:28,200 --> 00:00:31,840 +مقدمة سريعة سارجعنا فيها بعض المفاهيم طبعا مفهوم + +4 +00:00:31,840 --> 00:00:34,860 +المجموعات من المفاهيم الأساسية اللي جمر علينا في + +5 +00:00:34,860 --> 00:00:39,100 +مرحلة مبكرة من الدراسة لكن احنا في هذه في هذا + +6 +00:00:39,100 --> 00:00:43,060 +المساق هنركز كيف نتعامل مع مفهوم المجموعات و ال + +7 +00:00:43,060 --> 00:00:47,080 +operations و اللي على المجموعات بطريقة المجردة + +8 +00:00:47,080 --> 00:00:50,580 +بطريقة البراهين كيف نتعامل معهم من هذه الناحية في + +9 +00:00:50,580 --> 00:00:55,250 +هذا المساق ان شاء اللهفإن شاء الله أول مفهوم بتعلق + +10 +00:00:55,250 --> 00:00:59,270 +بالتعامل مع المجموعات واللي ممكن نشتغل عليه وفي + +11 +00:00:59,270 --> 00:01:04,230 +عليه عمليات حسابية هو مفهوم تساوي المجموعات فطبعا + +12 +00:01:04,230 --> 00:01:07,770 +احنا فيه عنا المفهوم عنا الرمز تبعه وفيه عنا + +13 +00:01:07,770 --> 00:01:11,510 +التعريف تبعه فيه يمكن تلت نقاط بنتحدث عنهافأول شي + +14 +00:01:11,510 --> 00:01:14,910 +أنا ببيبندي مجموعتين هذه المجموعتين هدول ممكن أدرس + +15 +00:01:14,910 --> 00:01:18,330 +علاقة التساوي وقت إيش بقول مجموعة ألف تساوي مجموعة + +16 +00:01:18,330 --> 00:01:21,470 +باق وقت إيش بقول asset A capital A تساوي asset + +17 +00:01:21,470 --> 00:01:24,810 +capital B أول شي إيش الرمز هو علاقة التساوي + +18 +00:01:24,810 --> 00:01:27,950 +المتعرف عليها بين الأعداد فأنا بقول ليش two sets + +19 +00:01:27,950 --> 00:01:30,990 +أه طبعا في الآخر يمكن كتبها A تساوي ال B هذا هو + +20 +00:01:30,990 --> 00:01:34,800 +الرمزإذا المفهوم مفهوم التساوي للمجموعات equality + +21 +00:01:34,800 --> 00:01:38,400 +of sets هذا هو إيش المصطلح اللي بتتعامل معاه إيش + +22 +00:01:38,400 --> 00:01:41,800 +الرمز تبعه علاقة التساوي المتعرف عليها بالأرقام + +23 +00:01:41,800 --> 00:01:45,400 +طيب ما هو التعريف بجوجتش بقول على أن two sets are + +24 +00:01:45,400 --> 00:01:49,320 +equal أه فبقول ليه two sets capital A and capital + +25 +00:01:49,320 --> 00:01:53,160 +B are said to be equal or identical متطابقين أو + +26 +00:01:53,160 --> 00:01:56,800 +متساويين if they contain the same elements إذا + +27 +00:01:56,800 --> 00:01:59,890 +احتووا على نفس العناصإذا كانت عناصرهم هي نفس + +28 +00:01:59,890 --> 00:02:04,570 +العناصر، عناصر الـA هي نفس عناصر الـB، وهكذا، اه، + +29 +00:02:04,570 --> 00:02:07,590 +فطبعا الرمز بقول إذا كانت الـA و الـB متساويين + +30 +00:02:07,590 --> 00:02:11,250 +فبكتب A تساوي B، وبنقرأها A تساوي B، فده هو الرمز، + +31 +00:02:11,250 --> 00:02:13,810 +وماكنتش بقول A تساوي B إذا كانوا بينهم بحتوى على + +32 +00:02:13,810 --> 00:02:19,980 +نفس العناصر، بحتوى على نفس العناصرخلّينا نشوف إيه + +33 +00:02:19,980 --> 00:02:23,840 +كيف متعامل منطقيا بالرموز ماذا تعني يحتوي على جميع + +34 +00:02:23,840 --> 00:02:28,720 +العناصر بلغة الرموز فهنا ملاحظة a تساوي b means + +35 +00:02:28,720 --> 00:02:34,140 +يعني تكافئ بمعنى for all x لكل العناصر طب ما هو ال + +36 +00:02:34,140 --> 00:02:37,800 +universe؟كل العناصر اللي أنا قولش مقوليه ويقوليه + +37 +00:02:37,800 --> 00:02:41,380 +بحتوى جميع العناصر بمعنى العنصر اللي موجود في الـA + +38 +00:02:41,380 --> 00:02:45,500 +لازم يكون موجود في الـB واللي في الـB لازم يكون + +39 +00:02:45,500 --> 00:02:50,100 +موجود في الـA فهو بيقول للتعريف تبعها for all X X + +40 +00:02:50,100 --> 00:02:55,620 +تنتمي للـA if and only if X تنتمي للـB بيعني فكل + +41 +00:02:55,620 --> 00:02:58,560 +عنصر إذا كان موجود في الـA لازم يكون في الـB وعكس + +42 +00:02:58,560 --> 00:03:00,540 +إذا كان موجود في الـB لازم يكون في الـA هذا معناه + +43 +00:03:00,540 --> 00:03:04,250 +أنهم يحتووا على نفس العناصر بلغة الرموزfor all x + +44 +00:03:04,250 --> 00:03:08,630 +أي أنصر أي ما كان إذا نوجد في الأولى لازم ينوجد في + +45 +00:03:08,630 --> 00:03:11,950 +التانية و العكس صحيح إذا نوجد في التانية لازم + +46 +00:03:11,950 --> 00:03:15,490 +ينوجد في الأولى واضح؟ أه فهذه لغة الرموز اللي احنا + +47 +00:03:15,490 --> 00:03:18,010 +بيقولنا نتعامل معها و نكتب بطريقة الرموز عشان + +48 +00:03:18,010 --> 00:03:21,410 +نتعامل مع المفهوم كيف بتأثبت ان هم متساويتين؟ + +49 +00:03:21,410 --> 00:03:25,170 +بتأثبت من for all x, x أنتمي لل a, if and only if, + +50 +00:03:25,250 --> 00:03:30,460 +x أنتمي لل bأه واضح؟ متابعين؟ خليني أشوف بعض + +51 +00:03:30,460 --> 00:03:32,820 +الأمثلة البسيطة وبعدين طبعا هنرجع للتعريف كيف + +52 +00:03:32,820 --> 00:03:37,820 +نتعامل معاه منطقيا أو بالبرهان هنشوف مثال بسيط + +53 +00:03:37,820 --> 00:03:41,680 +بيقول لي show that capital A وتساوية على حروف + +54 +00:03:41,680 --> 00:03:47,500 +الأبجدية ABC is equal to the set capital B وتساوية + +55 +00:03:47,500 --> 00:03:51,700 +على الحروف BCA هدول المجموعتين متساويتين لو أقوللي + +56 +00:03:51,700 --> 00:03:56,260 +showأه طبعا ليش؟ نفس العناصر ال A موجودة في ال + +57 +00:03:56,260 --> 00:03:58,900 +capital A و موجودة في ال capital B ال small b + +58 +00:03:58,900 --> 00:04:01,500 +موجودة في ال capital A و موجودة في ال capital B و + +59 +00:04:01,500 --> 00:04:04,160 +ال small c موجودة في التنتين فكل العناصر هم + +60 +00:04:04,160 --> 00:04:05,840 +بيحتووا على نفس العناصر ال A و ال B بيحتووا على + +61 +00:04:05,840 --> 00:04:09,820 +من؟ على التلات حروف A,B,C فإذا هم متساوينطبعا إيش + +62 +00:04:09,820 --> 00:04:12,640 +مستنتج الشياط من المثال؟ ترتيب العناصر ما لهوش + +63 +00:04:12,640 --> 00:04:15,360 +أهمية في المجموعات لأنه جالي يحتوى على جميع + +64 +00:04:15,360 --> 00:04:17,780 +العناصر، ما جاليش نفس الترتيب، ما جاليش العنصر + +65 +00:04:17,780 --> 00:04:20,900 +الأول يساوي العنصر الأول، لأ، جالي نفس العناصر، + +66 +00:04:20,900 --> 00:04:24,660 +بغض النظر إيش، مين، ترتيب، فأنا بتحدث عن مجموعة + +67 +00:04:24,660 --> 00:04:28,800 +طالبات مبادئ الرياضيات، هذه هي المجموعة، في + +68 +00:04:28,800 --> 00:04:31,300 +المحاضرة اليوم، مين جاعد أول، في المحاضرة التانية، + +69 +00:04:31,300 --> 00:04:34,040 +مين جاعد آخر، مابيهمنيش، هذه هي المجموعة، فالترتيب + +70 +00:04:34,040 --> 00:04:37,570 +ما لهوش قيمة في المجموعاتفطبعا عشان اجيبه بعد + +71 +00:04:37,570 --> 00:04:40,410 +السؤال ببساطة ماهي التعريف ليش هدول equal لإنهم + +72 +00:04:40,410 --> 00:04:43,270 +يحتووا على نفس العناصر لإنهم يحتووا على نفس + +73 +00:04:43,270 --> 00:04:52,010 +العناصر فده المثال الأول solution ال a and b are + +74 +00:04:52,010 --> 00:04:56,990 +equal and b are + +75 +00:04:56,990 --> 00:05:07,190 +equal ليش since they contains او containthe same + +76 +00:05:07,190 --> 00:05:11,230 +element من + +77 +00:05:11,230 --> 00:05:17,030 +التعريف أخدت الجواب من التعريف لأنهم بيحتوي على + +78 +00:05:17,030 --> 00:05:24,350 +نفس العناصر بكل بصرة أي سؤال؟ + +79 +00:05:24,350 --> 00:05:28,570 +نشوف + +80 +00:05:28,570 --> 00:05:32,010 +كدا مثال برضه بسيط عشان نأكد على المفهوم و بعض + +81 +00:05:32,010 --> 00:05:36,190 +الملاحظاتبقول لي في عندي مجموعة capital A بتساوي + +82 +00:05:36,190 --> 00:05:41,530 +عناصر 1 4 1 فقى كم عنصر فيه في الـ A؟ عنصرين، + +83 +00:05:41,530 --> 00:05:44,430 +التكرار مالهوش قيمة في المجموعات، فهد فيها عنصرين + +84 +00:05:44,430 --> 00:05:47,290 +الواحد والاربع ولا فيها عنصر تاني؟ أي عناصر، طيب + +85 +00:05:47,290 --> 00:05:50,730 +والـ B بتساوي الواحد والاربع، هدول هم متساويين، + +86 +00:05:50,730 --> 00:05:54,360 +ليش؟لأنه محتوى على نفس العناصر فالشاهد الأهم من + +87 +00:05:54,360 --> 00:05:57,820 +المثال أن التكرار برضه مالهوش أهمية زي الترتيب + +88 +00:05:57,820 --> 00:06:01,400 +مالهوش أهمية و التكرار كأنه لم يكن مابنعدش فأنا + +89 +00:06:01,400 --> 00:06:05,040 +بقول من عناصر الـ A واحد و أربع بتقول الواحد ظهرت + +90 +00:06:05,040 --> 00:06:08,020 +مرتين ماليش داعو أنا بقول من العناصر واحد و أربع + +91 +00:06:08,020 --> 00:06:14,060 +واضح؟ فهنا برضه نقول هنا مثال رقم اتنين مثال رقم + +92 +00:06:14,060 --> 00:06:21,440 +اتنين ف solution فيها أن الـ A will be havethe + +93 +00:06:21,440 --> 00:06:26,020 +same elements + +94 +00:06:26,020 --> 00:06:30,940 +فبالتالي + +95 +00:06:30,940 --> 00:06:36,930 +متساويين A تساوي ال Bفدولا مثالين بسيطين واتعلمنا + +96 +00:06:36,930 --> 00:06:41,790 +منهم أن الترتيب مش مهم والتكرار مالهوش قيمة العنصر + +97 +00:06:41,790 --> 00:06:45,630 +مكتوب أكتر من مرة كأنه يعتبر خطأ مطبع انا عندي + +98 +00:06:45,630 --> 00:06:50,110 +قائمة طالبات هذه الشعبة طب في اسم انطبع مرتين في + +99 +00:06:50,110 --> 00:06:52,870 +الآخر انا بتحصل ليه علامة ولا علامتين علامة في + +100 +00:06:52,870 --> 00:06:55,650 +الآخر أنا مايش ممكن أصحي هذا الخطأ فانا بهمني كم + +101 +00:06:55,650 --> 00:06:59,430 +طالبة عندي عندي تسعين طالبة اللي كتب الاسم أكتر من + +102 +00:06:59,430 --> 00:07:03,190 +مرة مالهوش قيمة مالهوش قيمة نفس الاش نفس القضية + +103 +00:07:07,120 --> 00:07:09,200 +لسه ماوصلناش، واحدة واحدة، لسه ماعرفناش إيش معناه + +104 +00:07:09,200 --> 00:07:12,920 +subset، إيش جزئي، واحدة واحدة، احنا لسه عرفنا إيش + +105 +00:07:12,920 --> 00:07:16,800 +مجموعة، تعرفنا عليه إيش بنقصد فيه، وبعدين عرفنا + +106 +00:07:16,800 --> 00:07:19,460 +التساوي، لسه ماعرفناش الفترة، هنجيها، تمام، + +107 +00:07:19,460 --> 00:07:25,720 +ملاحظة، ملاحظة، البعض بيسقط في خطأ، بدنا نميز هال + +108 +00:07:25,720 --> 00:07:31,920 +gate، بيقولّي بشكل عامالـ A لا تساوي A بين هدول + +109 +00:07:31,920 --> 00:07:36,360 +الأقواص، ليش؟ لأن الـ A هذه لحالة عنصر، وهديك + +110 +00:07:36,360 --> 00:07:39,640 +مجموعة تحتوي على عنصر الـ A، فهدول فيهم فرق، طب + +111 +00:07:39,640 --> 00:07:42,900 +إيش ال small a تكون؟ أي ما كانت، أي عنصر ما كانت، + +112 +00:07:42,900 --> 00:07:45,890 +حتى لو كانت مجموعة نفسها، لكن هدول أيش؟رمزين + +113 +00:07:45,890 --> 00:07:49,730 +مختلفين، مفهومين مختلفين، هذه عبارة عن عنصر ما + +114 +00:07:49,730 --> 00:07:54,070 +إيه، هذه عبارة عن مجموعة تحتوي على عنصر إيه، فبقول + +115 +00:07:54,070 --> 00:07:56,750 +هنا الـA is an element، عنصر، بغض النظر إيش + +116 +00:07:56,750 --> 00:08:00,390 +محتوياته أو إيش نوعيته، لكن الـA عبارة عن مجموعة + +117 +00:08:00,390 --> 00:08:03,750 +تحتوي على عنصر إيه، فبننفرق في رمزي هدول اللي اللي + +118 +00:08:03,750 --> 00:08:06,910 +أقواص مهمين جدا، وإذا انكتبوه، دايما نبيع إنه فيه + +119 +00:08:06,910 --> 00:08:11,040 +مجموعة، طبعا يسع ناصر المجموعة موضوع آخرموضوع آخر + +120 +00:08:11,040 --> 00:08:15,040 +فبننفرق بين هدول الرمزين فهنا مافيش تساوي إيش ممكن + +121 +00:08:15,040 --> 00:08:19,100 +أحط بدل لأدم التساوي ينتمي ينتمي بس مش مجموعة + +122 +00:08:19,100 --> 00:08:23,100 +جزئية بس ينتمي العلاقة الوحيدة بين a ومجموعة ال a + +123 +00:08:23,100 --> 00:08:26,960 +ينتمي بس هذه العلاقة الصحية غير هيك أي علاقة غير + +124 +00:08:26,960 --> 00:08:29,680 +صحية ولا subset صحيحة لسه معرفنهاش ولا التساوي + +125 +00:08:29,680 --> 00:08:34,740 +صحيح انتبهوا لهذا النقر طب نيجي لمفهوم ال subset + +126 +00:08:34,740 --> 00:08:39,420 +المجموعة الجزئية subsetبنعرف إيش معناهات subset + +127 +00:08:39,420 --> 00:08:45,580 +طبعا بي ساعدنا يمكن رسم مساعد Venn diagram تقريبا + +128 +00:08:45,580 --> 00:08:50,340 +فطبعا subset هي جزء فهي عندنا مجموعة كبيرة B في + +129 +00:08:50,340 --> 00:08:53,900 +عندنا مجموعة صغيرة جواها A فده هو المفهوم فانا + +130 +00:08:53,900 --> 00:08:56,840 +بقول على ال A subset من ال B خلينا نشوف التعريف + +131 +00:08:56,840 --> 00:09:00,360 +طبعا زي المنهج اللي اتبعناه في الشتر الأول أيضا + +132 +00:09:00,360 --> 00:09:05,530 +ماتتبعه في عندنا مقدمة للتعريف مقدمة للنظريةبتقول + +133 +00:09:05,530 --> 00:09:08,630 +يا دول الرموز كي بده تستخدمهم؟ Let capital A و + +134 +00:09:08,630 --> 00:09:11,750 +capital B be two sets إذا ما إيه ليه؟ هينطبق على + +135 +00:09:11,750 --> 00:09:14,570 +ال A و ال B بينطبق على أي مجموعات A و B مش + +136 +00:09:14,570 --> 00:09:19,690 +statements مش أرقام و إنما مجموعات تمام التعريف أو + +137 +00:09:19,690 --> 00:09:26,060 +الجزء الأول من التعريفإذا كل عنصر في الـ A هو عنصر + +138 +00:09:26,060 --> 00:09:29,500 +في الـ B موجود في الـ B بقول أنا أن الـ A subset + +139 +00:09:29,500 --> 00:09:34,560 +من الـ B فدهو فكل عناصر الـ A بنفس الوقت موجودة في + +140 +00:09:34,560 --> 00:09:38,760 +الـ B يعني مثلا نحن نقول قسم الرياضيات أو طالبات + +141 +00:09:38,760 --> 00:09:41,520 +قسم رياضية مجموعة جزئية من الجامعة كل طالبة في قسم + +142 +00:09:41,520 --> 00:09:44,860 +رياضية طالب في الجامعة الإسلاميةواضح؟ فالكل أنصر + +143 +00:09:44,860 --> 00:09:48,280 +ينتمي لمين؟ لمجموعة أكبر فبقول ليش if every + +144 +00:09:48,280 --> 00:09:51,900 +element of A is an element of B then we say that A + +145 +00:09:51,900 --> 00:09:56,120 +is a subset of B ما هو الرمز؟ رمز زي أصغر من أو + +146 +00:09:56,120 --> 00:10:00,470 +يساوي بس بدل ما يزاوي حدعلى صورة جوس، على صورة + +147 +00:10:00,470 --> 00:10:03,310 +جوس، والتساوي ده له معنى، هنأكد عليه أنه فيه + +148 +00:10:03,310 --> 00:10:06,490 +احتمال التساوي، فممكن اكتبها بهذا الشكل، فالـ A + +149 +00:10:06,490 --> 00:10:10,130 +أصغر من الـ B، جوا الـ B، الـ B تحتوي الـ A، طب لو + +150 +00:10:10,130 --> 00:10:14,510 +عكست الترتيب، تكون الـ B تحتوي الـ A، بقرأها بشكل + +151 +00:10:14,510 --> 00:10:18,410 +آخر، زي ما بنقول إيهاش، الخمسة أصغر من الستة، + +152 +00:10:18,410 --> 00:10:21,910 +والستة أكبر من الخمسة، فنفس القضية، بقول إن الـ A، + +153 +00:10:21,910 --> 00:10:25,830 +إيهاش، subset من الـ B، والـ B بسميها super set من + +154 +00:10:25,830 --> 00:10:29,150 +الـ A، هنسميها، هي جاي تقريبا،واضح؟ فهو ممكن + +155 +00:10:29,150 --> 00:10:31,710 +يكتبها بالطريقتين، طبعا الأولى هي الأكثر شيوعة، + +156 +00:10:31,710 --> 00:10:35,110 +هذي نادر جدا، نادر جدا، وقت إيش نكتبها؟ في الغالب + +157 +00:10:35,110 --> 00:10:38,190 +لما أنا إيش كتبت ال B وما تمش وصح على يسارها، + +158 +00:10:38,190 --> 00:10:40,910 +بكتبها على اليمين ال A بس بغير الاتجاه، في الغالب + +159 +00:10:40,910 --> 00:10:45,150 +هيك، بقول إذا ال A صبصت من ال B، ال B إيش بيسميها؟ + +160 +00:10:45,250 --> 00:10:49,250 +Super 6 Super 6 هي الكبيرة هي الكبيرة sub يعني + +161 +00:10:49,250 --> 00:10:53,790 +صغيرة جزء هذه كيش هي الكل الأكبر وهكذا فطبعا هي + +162 +00:10:53,790 --> 00:10:58,410 +الصورة هذه جزء من هذه وهذه تحتوي ال A ال B تحتوي + +163 +00:10:58,410 --> 00:11:02,530 +ال A بمعنى Super 6 من ال A أي سؤال طبعا المفهوم + +164 +00:11:02,530 --> 00:11:06,070 +مرة عليكم بس بنأكد عليه والمصطلحات تمام طيب زي ما + +165 +00:11:06,070 --> 00:11:08,930 +عملنا سياسة التساوي بنشوف إيش يعني بالرموز كي بدأ + +166 +00:11:08,930 --> 00:11:14,410 +أثبت إن ال A صفصت من ال B هنشوف الرمز remarkالـ A + +167 +00:11:14,410 --> 00:11:17,870 +subset من الـ B means يعني تكافئ .. إيش قال ليه؟ + +168 +00:11:17,870 --> 00:11:21,470 +every element of A is for all .. كل العناصر .. أي + +169 +00:11:21,470 --> 00:11:24,590 +عنصر موجود في الـ A بدي يكون موجود في الـ B طب + +170 +00:11:24,590 --> 00:11:29,230 +العكس مفتوح .. مش معروف .. فهي اتجاه واحد فكنا في + +171 +00:11:29,230 --> 00:11:32,970 +التساوي if and only if .. في ال subset if then .. + +172 +00:11:32,970 --> 00:11:35,870 +if then .. العنصر الموجود في الـ A بدي يكون في الـ + +173 +00:11:35,870 --> 00:11:39,670 +B العكس مش عارفين .. مش عارفين .. تمام؟ فهذا هو + +174 +00:11:39,670 --> 00:11:42,930 +الرمز .. فهذا هو الرمز وهذه اللي هنتعامل عليها + +175 +00:11:43,600 --> 00:11:48,820 +ملاحظة رقم 2 حكت زميلتكوا قبل قليل التساوي ممكن + +176 +00:11:48,820 --> 00:11:52,480 +ينكتب بلغة ال subset بس ايش الأولى subset من + +177 +00:11:52,480 --> 00:11:56,180 +التانية والتانية subset من الأولى لأنه نفس العناصر + +178 +00:11:56,180 --> 00:11:59,940 +فكل عنصر في ال A موجود في ال B وكل عنصر في ال B + +179 +00:11:59,940 --> 00:12:04,960 +موجود في ال A فبقدر اكتبها ان هذه if and only ifA + +180 +00:12:04,960 --> 00:12:09,000 +subset من الـ B والـ B subset من الـ A فالتساوي هي + +181 +00:12:09,000 --> 00:12:13,000 +تعريف آخر له ممكن أعرفه مباشرة ممكن أعرفه بدلالة + +182 +00:12:13,000 --> 00:12:18,000 +من ال subset بدلالة ال subset طبعا ماحد يسأل بقدر + +183 +00:12:18,000 --> 00:12:21,440 +أجيب هذا التعريف من التعريف الأصلي طبعا for all + +184 +00:12:21,440 --> 00:12:28,040 +مين بقدر يجيب منياه بسهولة لو جينا الآن A تساوي + +185 +00:12:28,040 --> 00:12:35,030 +الـ B قولنا تكافئ means for all XX تنتمي للـA if + +186 +00:12:35,030 --> 00:12:39,950 +and only if X تنتمي للـB بعد هيك إيش نعمل؟ نحوّل + +187 +00:12:39,950 --> 00:12:44,250 +الـF لـand on الـF إلى and by conditional فهذه + +188 +00:12:44,250 --> 00:12:52,050 +تكافئ for all X X تنتمي للـA then X تنتمي للـB and + +189 +00:12:52,050 --> 00:12:58,770 +X تنتمي للـB then X تنتمي للـA، مصبوط؟طيب، ها، بده + +190 +00:12:58,770 --> 00:13:01,430 +أوصل لمين؟ بده أوصل لـ for .. ل .. ل .. ل .. بده + +191 +00:13:01,430 --> 00:13:03,870 +أوزع كل واحدة لحال، عشان يصير هذه الـ sub set و + +192 +00:13:03,870 --> 00:13:07,310 +sub set، بنفع أوزع الـ for all على الـ and نعم من + +193 +00:13:07,310 --> 00:13:10,770 +قواعد ال quantifiers اللي أخدناها، جولة في علاقات + +194 +00:13:10,770 --> 00:13:13,390 +مسموحة و في علاقات فين هم تكافئوا و فين هم been + +195 +00:13:13,390 --> 00:13:15,650 +obliged و فين ما ذكرناهم مش ممكن .. إيه، مش ممكن + +196 +00:13:15,650 --> 00:13:19,570 +نقول غير مسموحة، فهذا يكافئ، ممكن أوزع ال for all، + +197 +00:13:19,570 --> 00:13:25,210 +for all x, x تنتمي لل a, then x تنتمي لل b and for + +198 +00:13:25,210 --> 00:13:33,630 +all xX تنتمي للـB ثم X تنتمي للـA الآن، مين هذه؟ + +199 +00:13:33,630 --> 00:13:37,590 +هذه ليست إلا A صبصة من الـB تعريف أيه مفزوظ، مصبوط + +200 +00:13:37,590 --> 00:13:44,070 +طيب والتانية ليست إلا B صبصة من الـAوهو اللي بدنا + +201 +00:13:44,070 --> 00:13:47,010 +يعني فانا ممكن أجيبها من المنطق من وين جبتها صح + +202 +00:13:47,010 --> 00:13:51,210 +يمكن أنا فهمتها لكن ممكن أبرهنها من قواعد المنطق + +203 +00:13:51,210 --> 00:13:54,230 +اللي اتعلمناها قواعد ال quantifiers اللي اتعلمناها + +204 +00:13:54,230 --> 00:13:58,310 +و ال and و كل هذه الأمور ففعلا التساوي ممكن ينكتب + +205 +00:13:58,310 --> 00:14:02,070 +على صورة أن الأولى صبصت من التانية و التانية صبصت + +206 +00:14:02,070 --> 00:14:08,670 +من الأولى and واضح؟ أي سؤالنشوف بعض الأمثلة و + +207 +00:14:08,670 --> 00:14:12,110 +دايما بنبدأ بالأمثلة البسيطة عشان الأمر يرسخ و + +208 +00:14:12,110 --> 00:14:16,830 +المفهوم يكون واضح بدون أي غبش بقول لي let a تساوي + +209 +00:14:16,830 --> 00:14:22,730 +واحد و اتنين و small a كمش متغير هنا كحرف كحرف + +210 +00:14:22,730 --> 00:14:27,310 +اللي هو حرف أبيض و ال b هي الحروف a و b و العداد + +211 +00:14:27,310 --> 00:14:29,610 +واحد اتنين و تلاتة طبعا فال a سبسكت من ال bهذا + +212 +00:14:29,610 --> 00:14:32,750 +سؤال مباشر مش مطلوب فيه، بس مثال توضيحي، فطبعا + +213 +00:14:32,750 --> 00:14:36,250 +واضح، ليش؟ لأن كل عناصر الـA موجودة في الـB الواحد + +214 +00:14:36,250 --> 00:14:38,970 +موجودة في الـB ولا مش موجودة؟ صح، الاتنين موجودة + +215 +00:14:38,970 --> 00:14:41,150 +ولا مش موجودة؟ موجودة، الـA موجودة ولا مش موجودة؟ + +216 +00:14:41,150 --> 00:14:43,650 +موجودة، انتهت العملية، فكل عناصر الـA موجودة في + +217 +00:14:43,650 --> 00:14:47,410 +الـB، إذا نهيش فعلا الـA subset من الـB، واضح؟ هذا + +218 +00:14:47,410 --> 00:14:50,670 +المثال البسيط جدا، مش المعنى، بدي أختبر، كل عناصر + +219 +00:14:50,670 --> 00:14:55,270 +الـA موجودة في الـB، انتهت العملية، نشوف مثال آخر + +220 +00:14:56,090 --> 00:15:03,690 +ال A هي 123 وال B 312 فال A subset من ال B صح؟ صح + +221 +00:15:03,690 --> 00:15:07,050 +لأن ال 1 موجودة في ال B نعم ال 2 موجودة في ال B + +222 +00:15:07,050 --> 00:15:11,250 +نعم التلاتة موجودة في ال B نعم فدي subset اه في + +223 +00:15:11,250 --> 00:15:15,450 +طالبة بتقول ايه طب هدول متساويين صح متساويين وهل + +224 +00:15:15,450 --> 00:15:18,690 +ال subset ينفي التساوي لأ عشان هيك الإشارة إيش هي + +225 +00:15:18,690 --> 00:15:24,100 +الإشارة؟أصغر من أو يساوي تقريبا فيه تساوي محتمل هو + +226 +00:15:24,100 --> 00:15:27,480 +جالي كل عناصر الـA موجودة في الـB جالي لازم الـB + +227 +00:15:27,480 --> 00:15:30,620 +تكون أكبر؟ لأ جالي لازم يكون في عناصر الـB عناصر + +228 +00:15:30,620 --> 00:15:34,600 +زيادة؟ لأ فانا إيش ماختبر؟ هاي الواحد موجودة نعم + +229 +00:15:34,600 --> 00:15:37,520 +التنين موجودة نعم التلاتة موجودة نعم انتهت العملية + +230 +00:15:37,520 --> 00:15:40,580 +أبطل على الـB أنا أن فيها زيادة ولا مافيهاش زيادة؟ + +231 +00:15:40,580 --> 00:15:43,880 +لأ بس أنا بتبطلع عناصر الـA موجودة في الـBانتهت + +232 +00:15:43,880 --> 00:15:47,800 +العملية واضح وهذا رمز برضه رمز موفق الحقيقة أن + +233 +00:15:47,800 --> 00:15:51,840 +الاحتمال التساوي موجود احتمال التساوي موجود أي + +234 +00:15:51,840 --> 00:15:55,500 +سؤال فإذا subset لا تنفي التساوي ممكن التساوي يكون + +235 +00:15:55,500 --> 00:15:59,520 +موجود فيا أكبر منها أو تساويها فهذا الفراغ ممكن + +236 +00:15:59,520 --> 00:16:02,060 +ينعدم في ال subset ممكن مايكونش فيه فراغ يكونوا + +237 +00:16:02,060 --> 00:16:07,400 +متطابقين فال subset تحتمل التساوي لكن مش دايم مش + +238 +00:16:07,400 --> 00:16:14,790 +دايم ف remark هنا remark منفصلبقول لـ every set is + +239 +00:16:14,790 --> 00:16:19,870 +a subset of itself بس مرتبط بالسابق بما أنه عناصر + +240 +00:16:19,870 --> 00:16:23,110 +كل مجموعة موجودة في نفسها إذاً كل مجموعة هي مجموعة + +241 +00:16:23,110 --> 00:16:26,310 +جزئية من نفسها لأن التساوي كلها محتمل فكل مجموعة + +242 +00:16:26,310 --> 00:16:30,230 +هي مجموعة جزئية من نفسها بمعنى آخر لأي مجموعة + +243 +00:16:30,230 --> 00:16:33,410 +capital A capital A is a subset من capital A + +244 +00:16:33,410 --> 00:16:36,150 +دايماً هذا صحيح فلأن التساوي موجود زي ما بقول + +245 +00:16:36,150 --> 00:16:40,150 +التلاتة أصغر أو يسووا تلاتة كل عدد أصغر من A أو + +246 +00:16:40,150 --> 00:16:45,780 +يسووا نفسه فنفس القضيةكل مجموعة subset من نفسها + +247 +00:16:45,780 --> 00:16:52,200 +واضح؟ أي تعليق؟ أي استفسار؟ ولا اعتراض كمان؟ + +248 +00:16:52,200 --> 00:16:56,360 +متفقين؟ تمام proper subset + +249 +00:16:58,820 --> 00:17:03,300 +طيب، لو بدنا ننفي التساوي، مصطلح جديد، مفهوم جديد، + +250 +00:17:03,300 --> 00:17:07,260 +فإذا الـ Subset هذه تحتمل التساوي، طب لو أنا بدي + +251 +00:17:07,260 --> 00:17:10,660 +أكون دقيق و بديش أخد التساوي بالإعتبار، زي ما احنا + +252 +00:17:10,660 --> 00:17:17,600 +فيه عندنا، بالنسبة هنا، اللي بنقارن، القارن دايما + +253 +00:17:17,600 --> 00:17:20,690 +مع من أصغر من أو يساويفأصغر منه يساوي، بتحتتمل + +254 +00:17:20,690 --> 00:17:23,910 +التساوي، لكن لما بدنا ننفي التساوي، بنحط أصغر منه، + +255 +00:17:23,910 --> 00:17:27,210 +نفس القضية، ففي عندنا مفهوم بيميز هذه الأمور، اللي + +256 +00:17:27,210 --> 00:17:31,290 +هو إيش، بيسموه proper subset، يعني جزئية صحيحة أو + +257 +00:17:31,290 --> 00:17:35,470 +إيش، ممكن تكون إيش، لوصافية فعلا إن فيه الجزء من، + +258 +00:17:35,470 --> 00:17:40,770 +التساوي منفي، ففي عندنا التعريفWe say that asset + +259 +00:17:40,770 --> 00:17:49,330 +capital A is a proper subset of asset + +260 +00:17:49,330 --> 00:17:51,150 +capital B and right + +261 +00:17:56,230 --> 00:18:00,690 +الـ A subset من الـ B و لا تساويها هي subset + +262 +00:18:00,690 --> 00:18:04,490 +والتساوي إيش مانفي الاحتمال التساوي بده يلغي .. + +263 +00:18:04,490 --> 00:18:09,070 +يلغي الاحتمال التساوي بدنا نلغي واضحة؟ فإذا ال + +264 +00:18:09,070 --> 00:18:12,930 +proper يعني إيش؟ هي جزء والتساوي إيش ماله؟ بدناش + +265 +00:18:12,930 --> 00:18:16,890 +إيه ففي هذه الحالة بنميز تمام أه طبعا قلنا أحنا + +266 +00:18:16,890 --> 00:18:21,630 +subset و super set proper subset proper super set + +267 +00:18:21,630 --> 00:18:27,590 +نفس المصطلح proper subset تمام؟لأ هي .. بس لأ هي + +268 +00:18:27,590 --> 00:18:34,830 +.. انت عندك علاقة هذه بقراها باتجاهين ال A sub 6 + +269 +00:18:34,830 --> 00:18:38,410 +من ال B طب ال B هي super 6 من ال A زي ما بقوليش + +270 +00:18:38,410 --> 00:18:42,830 +الخمسة أصغر من الستة و الستة أكبر من الخمسة فقراها + +271 +00:18:42,830 --> 00:18:47,000 +من الجهة التانية يعني قراها من الجهة التانيةنشوف + +272 +00:18:47,000 --> 00:18:50,520 +بعض الأمثلة طبعا مجموعة الأعداد الصحيحة Z هي + +273 +00:18:50,520 --> 00:18:53,680 +proper subset من ال Q ليش؟ لأنها متساويهاش في + +274 +00:18:53,680 --> 00:18:57,800 +أعداد نسبية غير صحيحة ولا لأ؟ لكن كل عدد صحيح هو + +275 +00:18:57,800 --> 00:19:01,920 +عدد نسبي فكل عناصر ال Z موجودة في ال Q لكن في في + +276 +00:19:01,920 --> 00:19:05,660 +ال Q عناصر الزيادة مافيش تساوي بتطبقوش مع بعض ال Z + +277 +00:19:05,660 --> 00:19:09,800 +جزء من ال Q والتساوي غير موجود لأن ال Q أكبر فعلا + +278 +00:19:09,800 --> 00:19:15,140 +في عناصر الزيادة واضح؟ هذا مثال مشهور نشوف كمان + +279 +00:19:15,140 --> 00:19:21,300 +مثاللو أخدنا مجموعة ال A تساوي سالب واحد Zero واحد + +280 +00:19:21,300 --> 00:19:24,540 +وال B واحد و سالب واحد و Zero فال A subset من ال B + +281 +00:19:24,540 --> 00:19:28,520 +متفقين لكن هل هي proper؟ لأ لأنهم متساويين هدول هم + +282 +00:19:28,520 --> 00:19:31,700 +متساويين مينفعش إيش أقول proper أه فهنا إيش ال A + +283 +00:19:31,700 --> 00:19:35,560 +subset من ال B لكن ال A is not a proper subset of + +284 +00:19:35,560 --> 00:19:39,560 +Bواضح؟ اه فهي ايش معناه proper؟ بنفي التساوي، إذا + +285 +00:19:39,560 --> 00:19:43,760 +أنا متأكد أن التساوي احتماله أصبح غير وارد، اه + +286 +00:19:43,760 --> 00:19:46,740 +فبقول proper subset، بكون دقيق، اه فانا بقول عنصر + +287 +00:19:46,740 --> 00:19:49,420 +هذا أصغر من أو يساوي العنصر، طب أنا لو في عندي + +288 +00:19:49,420 --> 00:19:52,180 +معلومة أن التساوي مش موجود، بحط أصغر، وانا مطمئن، + +289 +00:19:52,180 --> 00:19:58,280 +في عندي معلومة زيادة، أي سؤال؟خلّينا نتفق على بعض + +290 +00:19:58,280 --> 00:20:03,460 +الرموز if A is not a subset of B بنم في علاقة، + +291 +00:20:03,460 --> 00:20:05,640 +بنقول A subset من B وبنم فيها، بنحط ال slash + +292 +00:20:05,640 --> 00:20:08,540 +المعروف .. متعرف عليها ال slash النفسي زي يساوي لا + +293 +00:20:08,540 --> 00:20:13,140 +يساوي، ينتمي لا ينتمي، و هكذا فده الرمز متعارف + +294 +00:20:13,140 --> 00:20:20,200 +عليه ممكن استخدامهتمام؟ خلّينا لو بدنا نثبت أنه + +295 +00:20:20,200 --> 00:20:24,480 +مجموعة ليست subset خلّينا نشوف كيف ممكن نعملها + +296 +00:20:24,480 --> 00:20:28,300 +بلغة الرموز بلغة الرموز عشان كده ده مصطلح يمر + +297 +00:20:28,300 --> 00:20:32,540 +علينا مرات عديدة خلّينا نعمله قلنا إنه اسمها + +298 +00:20:32,540 --> 00:20:37,420 +subsetfor all X X تنتمي للـ A then X تنتمي للـ B + +299 +00:20:37,420 --> 00:20:41,740 +طب بدي أنفيها؟ بنعمل نجاش؟ و لا لأ؟ طب إيش؟ كيف + +300 +00:20:41,740 --> 00:20:44,760 +بننفي؟ نفي الـ for all there exist و بننفي اللي + +301 +00:20:44,760 --> 00:20:47,380 +جوا بس واحدة واحدة ماتحطولوش نفي مرتين زي ما انتوا + +302 +00:20:47,380 --> 00:20:50,620 +عاملين في ال quiz البعض لأ أنا لما أنفي ال for all + +303 +00:20:50,620 --> 00:20:52,800 +بصير there exist و بعدين بننفي اللي جوا أه بقى + +304 +00:20:52,800 --> 00:20:55,780 +النفي بتتوزعش مرتين واضح؟ فأرجو الأخطاء اللي قادمة + +305 +00:20:55,780 --> 00:20:58,620 +ماتتكررش ف there exist بعدين بدنا ننفي اللي جوا + +306 +00:20:58,620 --> 00:21:02,380 +الجملة جملة شرطية اللي هي إيه إيش؟ P then Q خليني + +307 +00:21:02,380 --> 00:21:12,510 +أكتبها هناB then Q و تكافئ not B and not Q بيصير + +308 +00:21:12,510 --> 00:21:17,210 +B and not Q مين ال B X تنتمي ل A و مين ال not Q X + +309 +00:21:17,210 --> 00:21:21,750 +لا تنتمي ل B نفعامتبعين؟ واضحة ولا مش واضحة؟ + +310 +00:21:21,750 --> 00:21:25,350 +واضحة؟ اه فهي هاد الشرط، فإذا أصبحت هيك، فماديش + +311 +00:21:25,350 --> 00:21:28,390 +بقول إن الـA ليس subset من الـB، إذا كدرت لاجي + +312 +00:21:28,390 --> 00:21:31,410 +عنصر موجود في الـA وليس موجود في الـB، هيك صرا، + +313 +00:21:31,410 --> 00:21:34,690 +مصموط، there exist X موجودة في الـA وغير موجودة في + +314 +00:21:34,690 --> 00:21:37,890 +الـB، وده منطقي، ليش مش subset؟ لأن فيها عناصر مش + +315 +00:21:37,890 --> 00:21:40,990 +.. مش موجودة في الـB، في عناصر خارج الـB، فبتكون + +316 +00:21:40,990 --> 00:21:45,500 +ليست subsetأي سؤال شوفوا كيف جيبناها من المنطق + +317 +00:21:45,500 --> 00:21:48,460 +شوفوا كيف فسرناها و كيف احتجناها ما درسناها في شبط + +318 +00:21:48,460 --> 00:21:54,020 +واحد نشوف مثال خلينا نطبق على هذا الكلام فأصبح + +319 +00:21:54,020 --> 00:21:58,520 +الآن عشان أثبت أن مجموعة ما ليست مجموعة جزئية من + +320 +00:21:58,520 --> 00:22:02,100 +مجموعة أخرى يكفي أن ألاقي عنصر موجود في المجموعة A + +321 +00:22:02,100 --> 00:22:05,800 +و غير موجود في ال B المثال بقول اثبت أن ال A ليست + +322 +00:22:05,800 --> 00:22:10,600 +سبسط من ال B مين يحل الليه؟الـ Zero موجودة في الـ + +323 +00:22:10,600 --> 00:22:13,280 +A وليس في الـ B يكفي يكفي بس بالـ There exists + +324 +00:22:13,280 --> 00:22:16,620 +مثال واحد يكفي There exists لأنه موجود على أقل مرة + +325 +00:22:16,620 --> 00:22:20,200 +واحد هيكفى فالـ Zero موجودة في الـ A وليس في الـ B + +326 +00:22:20,200 --> 00:22:25,260 +هذا بتدل على أنه ليست مجموعة جزئية فهنا هذا مثال + +327 +00:22:25,260 --> 00:22:30,980 +وهي ال solution Zero تنتمي للـ A and Zero لا تنتمي + +328 +00:22:30,980 --> 00:22:38,820 +للـ B implies الـ A ليست subset من الـ B أي سؤالهم + +329 +00:22:38,820 --> 00:22:42,420 +تابعين؟ اه فاحنا لسه نمشي واحدة واحدة مادخلناش في + +330 +00:22:42,420 --> 00:22:45,820 +البراهين لكن اللي مش فاهم هذه الأمور صعب ان يمشي + +331 +00:22:45,820 --> 00:22:50,600 +على الأصعب فلازم نفهم السهل و نمشي بالتدريج و نوصل + +332 +00:22:50,600 --> 00:22:57,980 +للدرجة الأعلى نظرية الأولى نظرية 2 1 النظرية + +333 +00:22:57,980 --> 00:23:03,280 +الأولى في شبطر 2 عنوان النظرية المجموعة الفارغة هي + +334 +00:23:03,280 --> 00:23:06,660 +مجموعة جزئية من أي مجموعة هي مجموعة جزئية من أي + +335 +00:23:06,660 --> 00:23:11,970 +مجموعة النصبقول ليه؟ The empty set phi is a subset + +336 +00:23:11,970 --> 00:23:16,670 +of every set خلّينا أول شي نفهمها بالشفا و هيك زي + +337 +00:23:16,670 --> 00:23:19,430 +ما اتعلمونا في بعض الحلات و بعدين نشوف البرهان + +338 +00:23:19,430 --> 00:23:23,250 +للنظرية طيب كيف بدي أقول أن الـA subset من أي + +339 +00:23:23,250 --> 00:23:26,810 +مجموعة؟ بدي جميع عناصر الـPhi .. آسف الـPhi subset + +340 +00:23:26,810 --> 00:23:30,330 +من أي مجموعة؟ بدي جميع عناصر الـPhi تكون موجودة في + +341 +00:23:30,330 --> 00:23:33,590 +الـA طب مين جميع عناصر الـPhi؟ مفيش ولا عنصر طب + +342 +00:23:33,590 --> 00:23:37,440 +بمعنى آخركيف ممكن تكون ليس subset ال file إذا قدرت + +343 +00:23:37,440 --> 00:23:39,660 +تلاقي answer موجود في ال file و هذا مستحيل و ليس + +344 +00:23:39,660 --> 00:23:41,840 +موجود في ال A إذا المستحيل هذا الكلام يكون ليس + +345 +00:23:41,840 --> 00:23:46,240 +subset لازم تكون subset خلينا نشوف البرهان مع بعض + +346 +00:23:46,240 --> 00:23:56,390 +فهذه نظرية 8 1طبعا خليني أكتب النص بلغة الرموز + +347 +00:23:56,390 --> 00:24:00,890 +بقول الـ Phi is a subset of every set إيش معناه + +348 +00:24:00,890 --> 00:24:03,390 +every set؟ لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +349 +00:24:03,390 --> 00:24:03,610 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +350 +00:24:03,610 --> 00:24:04,030 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +351 +00:24:04,030 --> 00:24:05,610 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +352 +00:24:05,610 --> 00:24:06,310 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +353 +00:24:06,310 --> 00:24:07,490 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +354 +00:24:07,490 --> 00:24:08,110 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +355 +00:24:08,110 --> 00:24:08,110 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +356 +00:24:08,110 --> 00:24:10,910 +.. لكل .. لكل .. لكل .. لكل .. لكل .. لكل + +357 +00:24:13,590 --> 00:24:17,390 +of proof من ال universe هنا كل المجموعات مجموعات + +358 +00:24:17,390 --> 00:24:20,850 +كل المجموعات لان بيقول every set every set ايه ايش + +359 +00:24:20,850 --> 00:24:25,210 +بتحتوي على ال file اه هي ايش super set لل file هي + +360 +00:24:25,210 --> 00:24:29,690 +super set لل file تمام بدنا نثبت هذه لل statement + +361 +00:24:29,690 --> 00:24:34,250 +statement تحتوي على ال quantifier اه ايش عمل افتح + +362 +00:24:34,250 --> 00:24:38,250 +الدليل تبعك في section 177 عملنا ارشادات كيف + +363 +00:24:38,250 --> 00:24:41,170 +نتعامل مع for all مرت علينا for all في ال + +364 +00:24:41,170 --> 00:24:43,050 +induction بنفع نعمل induction هنا + +365 +00:24:46,230 --> 00:24:50,490 +لأ ليش؟ لأن ال universe مش أعداد صحيحة هنا إيش + +366 +00:24:50,490 --> 00:24:53,650 +العناصر؟ مجموعات فاحنا إيش قولنا أول ما شوف for + +367 +00:24:53,650 --> 00:24:56,230 +all أقول induction لأ قولنا بدنا for all بدنا ال + +368 +00:24:56,230 --> 00:24:58,710 +universe يشكون مجموعة من الأعداد الصحيحة بتبدأ من + +369 +00:24:58,710 --> 00:25:02,810 +الأعداد الصحيح N0 وبتمشي N0 زي 1 N0 زي 2 وإلا + +370 +00:25:02,810 --> 00:25:05,870 +مانفعش فال induction بتعامل مع إيه اللي هو + +371 +00:25:05,870 --> 00:25:09,710 +quantifier for all وإيش universe خاص universe خاص + +372 +00:25:09,710 --> 00:25:13,420 +مش أي شيء فإذا أنا دي مانفعشطيب في عندنا كان إرشاد + +373 +00:25:13,420 --> 00:25:16,600 +قال لي عشان تتعامل مع for all ابدأ ال statement + +374 +00:25:16,600 --> 00:25:20,260 +بايش بال proof let A be any set لأن لما نقول B any + +375 +00:25:20,260 --> 00:25:23,120 +set إذا ما ينطبق على ال capital A ينطبق على جميع + +376 +00:25:23,120 --> 00:25:26,280 +المجموعات لأن زي ما كنا نعمل في مقدمة النظريات let + +377 +00:25:26,280 --> 00:25:29,420 +B be any statement إذا ما ينطبق على ال B ينطبق على + +378 +00:25:29,420 --> 00:25:31,700 +جميع ال statement فبنفس الطريقة لو رجعتوا + +379 +00:25:31,700 --> 00:25:34,480 +للإرشادات قولوا عشان تثبت for all إيش اللي بتبدأ + +380 +00:25:34,480 --> 00:25:38,360 +let X be any element in the universe فهنقول له let + +381 +00:25:38,360 --> 00:25:46,700 +A be any setlet capital A be any set إيش بدّي + +382 +00:25:46,700 --> 00:25:49,500 +أثبت؟ بدّي أثبت إن الـ Phi subset من الـ A بيكون + +383 +00:25:49,500 --> 00:25:52,320 +البروحان انتهى ولا لأ؟ نعم لأنه إيش بدّي؟ بيقوللي + +384 +00:25:52,320 --> 00:25:55,660 +Phi is a subset of every set يعني أي set، لكل + +385 +00:25:55,660 --> 00:26:04,460 +المجموعات، لأي مجموع We want to prove Phi + +386 +00:26:04,460 --> 00:26:10,160 +subset من الـ A ممتاز إيش عملنا؟ صعب اللي عملته؟ + +387 +00:26:15,890 --> 00:26:19,430 +الكل بيعرف يعمل اللي عملته ولا لأ؟ أمور سهلة ومش + +388 +00:26:19,430 --> 00:26:23,390 +هيه statement أمامك فسرناها for all جاعدين نتعلم + +389 +00:26:23,390 --> 00:26:27,110 +كيف نتعامل مع for all بنقول له let العنصر يامكان + +390 +00:26:27,110 --> 00:26:29,710 +بإيش بياني باليان ال universe ما هو ال universe؟ + +391 +00:26:29,710 --> 00:26:32,630 +كل المجموعات يعني بتكون ال a,k,z لو جالي for all + +392 +00:26:32,630 --> 00:26:36,930 +اكسبت من ال R بقوله X real number و هكذا واضحة؟ + +393 +00:26:36,930 --> 00:26:43,940 +صعبة؟ صعبة ولا سهلة؟ مفهومها؟أكمل أكمل طيب فاي + +394 +00:26:43,940 --> 00:26:48,360 +subset من ال a ماذا تعني فسرناها الملاحظات نكتبش + +395 +00:26:48,360 --> 00:26:52,780 +كلام انمل الصفحات كل شي مهم هذا يكافئ المطلوب for + +396 +00:26:52,780 --> 00:26:57,900 +all x x تنتمي للفاي then x تنتمي لل a هذا هو + +397 +00:26:57,900 --> 00:27:02,840 +المطلوب صح ولا مش صح بجيبش حاجة من عندى أنا بجيب + +398 +00:27:02,840 --> 00:27:06,770 +من اللي تعلمناها من السابقنعتمد chapter one هو + +399 +00:27:06,770 --> 00:27:09,790 +القاعدة الأساسية تبعاتنا والإرشادات وبنتعلم أمور + +400 +00:27:09,790 --> 00:27:12,610 +طيب بدنا نثبت هذه ال statement مش هذا هو المطلوب + +401 +00:27:12,610 --> 00:27:16,330 +we want to prove إيش بتبدأ ال statement for all x + +402 +00:27:16,330 --> 00:27:22,150 +ممكن أعمل عليها نفس القاعدة أقوله let x بس ال x + +403 +00:27:22,150 --> 00:27:26,650 +إيش هذه answer let x be any element let x be any + +404 +00:27:26,650 --> 00:27:32,030 +element تمام let x be any element + +405 +00:27:34,950 --> 00:27:41,690 +إيش مطلوب؟ بدي أثبت إن هذا صحيح We want to prove + +406 +00:27:41,690 --> 00:27:47,870 +that ماقتش بتقول ال for all P of X true إذا لكل X + +407 +00:27:47,870 --> 00:27:50,670 +ال P of X كانت true ما هي ال P of X في هذا ال + +408 +00:27:50,670 --> 00:27:54,130 +statement؟ اللي هي الجملة الشرطية X تنتمي لفاي + +409 +00:27:54,130 --> 00:28:01,990 +then X تنتمي لإيه؟ is true بدنا نثبتشوفتوا بقى هذا + +410 +00:28:01,990 --> 00:28:05,690 +التحليل أنا بعمله بالتفصيل طبعا فيما بعد هذا ممكن + +411 +00:28:05,690 --> 00:28:10,850 +نعمله ضمن الحلكمرحلة ابتدائية أو مبدئية صح ممكن + +412 +00:28:10,850 --> 00:28:13,790 +نعمله بهامش ممكن نعمله شفاوي بس هذا لازم نفهمه + +413 +00:28:13,790 --> 00:28:17,930 +لازم نكون في مكان ما عارفين إحنا إيش بنشتغل واضح + +414 +00:28:17,930 --> 00:28:22,170 +بنحلل، متابعين معاه؟ تمام، بدي أثبت إن جملة شرطية + +415 +00:28:22,170 --> 00:28:25,330 +تكون true وقت إيش بتكون الجملة الشرطية true؟ يا + +416 +00:28:25,330 --> 00:28:28,090 +الأول false والتاني إيش ما يكون يكون، يا الأول + +417 +00:28:28,090 --> 00:28:30,990 +true والتاني true طيب نتطلع على الأول X and Tamil + +418 +00:28:30,990 --> 00:28:34,490 +Phiما هي تنتم؟ ما رأيكوا فيها؟ هل هذه ممكن تكون + +419 +00:28:34,490 --> 00:28:38,410 +حقيقية؟ حطيتها ملاحظة إنه دايماً خاطئ فأقول له هنا + +420 +00:28:38,410 --> 00:28:48,090 +X تنتم لفاي هو خاطئ، لذلك الوصف X تنتم لفاي ثم X + +421 +00:28:48,090 --> 00:28:50,090 +تنتم لإيه هو حقيقية؟ + +422 +00:28:52,790 --> 00:28:56,310 +خلص البرحانة ولا ماخلصش؟ خلص مش هاد البداية وصلتله + +423 +00:28:56,310 --> 00:29:00,090 +ولا ماوصلتلهوش والبرحانة انتهت ممكن بدي أقلق thus + +424 +00:29:00,090 --> 00:29:04,970 +fi subset من هنا إذا حابين نعمل خاتمة جيد + +425 +00:29:04,970 --> 00:29:11,790 +ماكتبتوها أخر جملة مش مشكلة واضح؟فهي و ما اتعلمناه + +426 +00:29:11,790 --> 00:29:16,810 +بنحلل المطلوب بنشوف ال statement بدي أبرهنها بتعلم + +427 +00:29:16,810 --> 00:29:19,650 +كيف أتعامل معاها و هتعلم معاها كل واحدة لحال يمكن + +428 +00:29:19,650 --> 00:29:22,770 +احنا اشهر مثال كان في section 188 هو ايش if then + +429 +00:29:22,770 --> 00:29:25,710 +كيف نتعامل معاها نقول له assume b is true we want + +430 +00:29:25,710 --> 00:29:28,230 +to prove q is true هيبدأنا نتعامل مع مين مع for + +431 +00:29:28,230 --> 00:29:35,140 +all برضه جملة شرطية جملة شرطية أي سؤال واضحطب واحد + +432 +00:29:35,140 --> 00:29:38,440 +طالب تقول ليه؟ طب ليش ماقلتش assume أنه الـP true؟ + +433 +00:29:38,440 --> 00:29:41,460 +لأن هذا الاحتمال مش وارد، فليش أدور على حاجة عبث + +434 +00:29:41,460 --> 00:29:43,560 +مش مصحية؟ خلاص أنا عارف إنها default، انتهى + +435 +00:29:43,560 --> 00:29:46,420 +العملية، فليش أثبت .. أفترض إنها true؟ فيه احتمال + +436 +00:29:46,420 --> 00:29:49,860 +إنها تكون true غير وارد إطلاقًا، فمزال الشرط + +437 +00:29:49,860 --> 00:29:52,520 +false، إذا ال statement الشرطية دايما true + +438 +00:29:52,520 --> 00:29:57,000 +والبرهان انتهى أي سؤال؟ + +439 +00:30:03,940 --> 00:30:09,360 +كمية النظرية نظرية 2-2 subset relation is + +440 +00:30:09,360 --> 00:30:13,240 +transitive علاقة الـ subset علاقة إلى خاصية التعدى + +441 +00:30:13,240 --> 00:30:21,720 +بمعنى خلّينا نقرأ و نعمل رسمة مساعدة بقول let A, B + +442 +00:30:21,720 --> 00:30:27,200 +and C be sets شايفين المنهج؟ بتكرر معنى إذا الأن + +443 +00:30:27,200 --> 00:30:32,250 +اللي بدي أذكرCapital A وCapital B وCapital C ليش + +444 +00:30:32,250 --> 00:30:36,570 +بتتحدث عن مجموعات ليست أرقام وليست statement تمام + +445 +00:30:36,570 --> 00:30:42,970 +الجملة الموجودة بقوللي if A subset من الـB و الـB + +446 +00:30:42,970 --> 00:30:47,850 +subset من الـC هي transitive then A subset من الـC + +447 +00:30:47,850 --> 00:30:51,570 +خلينا نعمل رسمة و بعدين نشوف البرهان و نحلل فهي + +448 +00:30:51,570 --> 00:30:54,660 +بقوللي هي في عندي مجموعة Aهي مجموعة جزئية من + +449 +00:30:54,660 --> 00:30:57,660 +مجموعة أكبر منها B والـ B مجموعة جزئية من مجموعة + +450 +00:30:57,660 --> 00:31:00,760 +أصغر منها C فهل ال A جزء من ال C؟ بالتأكيد + +451 +00:31:00,760 --> 00:31:06,500 +بالتأكيد اه فانتوا طالبات في قسم الرياضيات فإذا + +452 +00:31:06,500 --> 00:31:09,280 +انتوا طالبات قسم الرياضيات وانتوا قسم الرياضيات في + +453 +00:31:09,280 --> 00:31:11,920 +كلية العلوم فانتوا طالبات كلية العلوم والكلية + +454 +00:31:11,920 --> 00:31:13,640 +العلوم في الجامعة الإسلامية انه طالبات في الجامعة + +455 +00:31:13,640 --> 00:31:18,460 +الإسلامية صح ولا لأ نفس القالةواضح؟ أه فالـ C هي + +456 +00:31:18,460 --> 00:31:20,960 +الأكبر لأنها بتحتوى الـ B و الـ B بتحتوى ال A فإذا + +457 +00:31:20,960 --> 00:31:23,080 +تقلش ال C بتحتوى ال A و لا بتحتوى أشهر، بتحتوى + +458 +00:31:23,080 --> 00:31:27,260 +أشهر واضحة؟ أه تمام، نشوف البرهان خلّينا نشوف + +459 +00:31:27,260 --> 00:31:30,800 +البرهان مع بعض، بدنا نحلل بالطريقة الماضية + +460 +00:31:30,800 --> 00:31:34,940 +فالبرهان + +461 +00:31:34,940 --> 00:31:39,940 +ليس سحر ولا فهلوة ولا شيء، فيه قواعد، فيه قواعد و + +462 +00:31:39,940 --> 00:31:47,890 +بنتعلم بعض الخبرات فهذه theoremإتنين إتنين طبعاً + +463 +00:31:47,890 --> 00:31:51,250 +في عندي مقدمة وفي عندي جملة شرطية خليني أبدأ + +464 +00:31:51,250 --> 00:31:56,390 +البرهان أفضل على طول و أفسرفكيف بدي أبرهن؟ أنا + +465 +00:31:56,390 --> 00:32:00,530 +عندي معطيات قاللي let a, b, c, b, 6 ممكن هذا عيد + +466 +00:32:00,530 --> 00:32:03,450 +كتبت، هذا صار عندي معطى فعندي معطى من الـ a و ال b + +467 +00:32:03,450 --> 00:32:06,450 +و ال c، إيش مالهم؟ هو عبارة عن مجموعات فبدي أقوله + +468 +00:32:06,450 --> 00:32:14,590 +هنا let a, b, c, b, 6 any 6 فهذا معطى فكل مقدمة في + +469 +00:32:14,590 --> 00:32:18,450 +النظرية تعتبر إيش؟ معطيات إيش المطلوب؟ إيش + +470 +00:32:18,450 --> 00:32:22,210 +القاعدة؟ بيقوللي قاعدة، في جملة شرطية بدي أثبت إن + +471 +00:32:22,210 --> 00:32:23,390 +الجملة الشرطية صحيحة + +472 +00:32:25,850 --> 00:32:35,050 +we want to prove that ايش جملة شرطية a subset من + +473 +00:32:35,050 --> 00:32:43,870 +ال b and b subset من ال c then a ممكن اعمل هيك a + +474 +00:32:43,870 --> 00:32:48,930 +subset من ال c is it true او كيف اكتبأو implies + +475 +00:32:48,930 --> 00:32:52,630 +يعني بحطها if then is true ك statement هذا مطلوب؟ + +476 +00:32:52,630 --> 00:32:56,550 +أه فإيش مطلوب مني أثبت؟ هل بدي أعمل اختبار الجملة + +477 +00:32:56,550 --> 00:32:59,410 +الشرطية لو بتش بتكون true ولا false؟ لأ بدي أثبت + +478 +00:32:59,410 --> 00:33:02,670 +إن أنا true دايما، نظرية، بدي أثبت إنها true يعني + +479 +00:33:02,670 --> 00:33:04,050 +بدي أثبت ال communication علشان هيك دايما في + +480 +00:33:04,050 --> 00:33:07,450 +ريادات بيستخدموش تضمين لأنه أنا مطلوب إن أثبت إنها + +481 +00:33:07,450 --> 00:33:13,060 +true واضح؟ هذا هو المطلوبواضح؟ تمام هذا المطلوب + +482 +00:33:13,060 --> 00:33:16,880 +اصنعه جملة شرطية كيف نبدأ برهان الجملة الشرطية + +483 +00:33:16,880 --> 00:33:21,340 +المباشر افترض ان الشرط صحيح فإيش حداله الآن فيعني + +484 +00:33:21,340 --> 00:33:27,240 +عندي هذا معطى المعطى التاني assume that + +485 +00:33:28,060 --> 00:33:35,180 +A subset من الـ B and الـ B subset من الـ C افترض + +486 +00:33:35,180 --> 00:33:38,380 +ان المعطف صحيح ايش المطلوب اثمت انه جواهب الشرط + +487 +00:33:38,380 --> 00:33:47,480 +صحيح we have to show that الـ A subset من الـ C + +488 +00:33:50,450 --> 00:33:55,150 +أرجو متابعة التسلسل المنطقي اللي ماشيين فيه بنفسر + +489 +00:33:55,150 --> 00:33:58,730 +كل شيء و كل خطوة بنفسرها أه بحتاج تفسير أكتر من + +490 +00:33:58,730 --> 00:34:03,250 +فسرها ممتاز ماذا يعني A subset من الـC تو كتب لها + +491 +00:34:03,250 --> 00:34:11,550 +تكافئ for all X X in A then X in C هذا هو المطلوب + +492 +00:34:13,230 --> 00:34:17,850 +شايفين؟ انت باين؟ انا بجيبش حاجة فجأة تسقط من + +493 +00:34:17,850 --> 00:34:21,670 +السماء، بفسر، واحدة واحدة، انا هذا بدي أثبته، إيش + +494 +00:34:21,670 --> 00:34:23,610 +بدي أعمله؟ لأنه وصلت لهذه المرحلة، طبعا أنا كنت + +495 +00:34:23,610 --> 00:34:28,110 +هنا، هي دي فسرتها، فصار المطلوب مني الآن، حددته + +496 +00:34:28,110 --> 00:34:31,290 +أكتر، صار هذا الكلام جملة بعد الشرط كيف بدي أتعامل + +497 +00:34:31,290 --> 00:34:38,670 +معها؟ let X be any element let X be any element + +498 +00:34:43,610 --> 00:34:46,970 +إيش صار بدنا؟ لنثبت إن الجملة الشرطية صحيحة We + +499 +00:34:46,970 --> 00:34:57,110 +have to show that X تنتمي للـA implies X تنتمي + +500 +00:34:57,110 --> 00:35:00,690 +للـC أو الجملة الشرطية is true ولا لأ؟ بس هيك + +501 +00:35:00,690 --> 00:35:06,300 +معناهاهك معناه ولا مش هيك؟ لأنه أنا عايش for all x + +502 +00:35:06,300 --> 00:35:09,560 +b of x بدي أثبت إن if b of x is true طبعا ممكن + +503 +00:35:09,560 --> 00:35:12,800 +أعملها زي نظرية الأولى بس هل ال x of a true ولا + +504 +00:35:12,800 --> 00:35:16,720 +false مش معروفة فهدي مختلف عن ذاك المثال مثال فريد + +505 +00:35:16,720 --> 00:35:20,920 +من نوعه تبع ال file فانا بدي أثبت إن هذا true تمام + +506 +00:35:20,920 --> 00:35:24,820 +جملة شرطية إيش بدي أعملها assume x تنتمي لل a + +507 +00:35:24,820 --> 00:35:34,400 +assume x تنتمي لل a طبعا واحدغشيم بقولك تعالي + +508 +00:35:34,400 --> 00:35:37,500 +نرياضة كل شوية أسيوم زي ما بده في واحدة أسيوم أنا + +509 +00:35:37,500 --> 00:35:42,150 +عملتها من عجلةأنا في واحدة عملتها مزاجا ولا كلها + +510 +00:35:42,150 --> 00:35:47,710 +بسبب؟ وكلها بسبب طبق من القواعد صح ولا مش صح؟ اه + +511 +00:35:47,710 --> 00:35:49,830 +فهو ماعيش بيقول اه قلت اه و رياضة كلها أسيوم افترض + +512 +00:35:49,830 --> 00:35:52,610 +افترض افترض زي ما بدكم عشوائية ما هي القضية + +513 +00:35:52,610 --> 00:35:57,190 +عشوائية شايفينها؟ لأ كل خطوة بنسأل نفسنا كيف نعمل + +514 +00:35:57,190 --> 00:36:01,430 +و إيش نعمل فالعمر منطقي مش عشوائي ممتاز إيش بده + +515 +00:36:01,430 --> 00:36:04,490 +أثبت؟ X سنتمل الـC هي آخر مطلة بقدر أفسر أكتر من + +516 +00:36:04,490 --> 00:36:13,440 +هيك؟ مش حاجة ده we haveto show that X تنتمي للـC + +517 +00:36:13,440 --> 00:36:17,100 +بقدر أفسر أكتر من هيك؟ لأ، شوفتوا أحنا إيش ماشيين؟ + +518 +00:36:17,100 --> 00:36:19,880 +ماشيين خطوة خطوة، كل خطوة بنفسرها طب كيف نتعامل + +519 +00:36:19,880 --> 00:36:23,320 +معاها؟ بتحتاج تفسير، بتتفسر، بتتفسر، صار بدي أثبت + +520 +00:36:23,320 --> 00:36:27,220 +إن X تنتمي للـC تتفسر أكتر من هيك؟ لأ، إيش معنى X + +521 +00:36:27,220 --> 00:36:30,120 +تنتمي للـC؟ ماعناش معنى، يعني غير إنها بدي عنصر + +522 +00:36:30,120 --> 00:36:33,880 +موجود في الـC، ممتاز، الآن أنا وين موجود؟ X في + +523 +00:36:33,880 --> 00:36:38,430 +الـA، بدأ أوصلها للـCأتطلع على المعطيات X موجودة + +524 +00:36:38,430 --> 00:36:41,370 +في الـ A ومش في عنده معطيات؟ الـ A صبصت من الـ B + +525 +00:36:41,370 --> 00:36:45,970 +فكل عنصر في الـ A وين موجود؟ في الـ B فالآن X + +526 +00:36:45,970 --> 00:36:50,830 +تنتمي للـ A implies X تنتمي للـ B ليش؟ لأن الـ A + +527 +00:36:50,830 --> 00:36:53,550 +صبصت من الـ B، هاي دليل ممكن أكتبها بهذا الشكل + +528 +00:36:53,550 --> 00:36:57,430 +لوقت أكتب since A صبصت من الـ B X تنتمي للـ A + +529 +00:36:57,430 --> 00:37:01,090 +implies تؤدي أن X في الـ B ممتاز اللي في الـ B وين + +530 +00:37:01,090 --> 00:37:04,770 +بيكون؟ بيكون في الـ C فهنا نكتب هنا + +531 +00:37:08,940 --> 00:37:14,780 +implies X تنتمي للـC لإيش؟ لأن الـB subset من الـA + +532 +00:37:14,780 --> 00:37:21,020 +من الـC آسف طيب بعدين وصلنا أحسنتوا أنا إيه اللي + +533 +00:37:21,020 --> 00:37:24,480 +بدي إياه خلص البرهات ماعناش بقول we want to prove + +534 +00:37:24,480 --> 00:37:27,880 +that X تنتمي للـC بدأنا من المعطيات استخدمنا + +535 +00:37:27,880 --> 00:37:34,020 +المعطيات و إيش وصلنا للمطلوب انتهى البرهان واضح؟ + +536 +00:37:34,020 --> 00:37:37,580 +أه طبعاهيك تكون أول مثال يمكن أن أنا كتبته + +537 +00:37:37,580 --> 00:37:43,000 +بالتفصيل لكن لو بدأ لخصه أصبح عشان أثبت أنه إيش + +538 +00:37:43,000 --> 00:37:47,020 +بدنا نثبت A subset من ال C إيش صارت الخطة خدي عنصر + +539 +00:37:47,020 --> 00:37:50,660 +عشوائي في ال A ووصليه في إيش لل C هيك صارت لو بدأ + +540 +00:37:50,660 --> 00:37:55,210 +لخصها أنه بدأ أخد أي عنصرموجود في الـA يكون موجود + +541 +00:37:55,210 --> 00:37:58,690 +في الـC هذه ملخصة بس هذه أول مرة فاكفكناها + +542 +00:37:58,690 --> 00:38:02,790 +وفسرناها خطوة خطوة ممكن نلخصها طبعا نختصر دائما مع + +543 +00:38:02,790 --> 00:38:05,930 +المراحل المتقدمة بنصير نختصر بعض الخطوات لكن في + +544 +00:38:05,930 --> 00:38:13,970 +البداية لازم نفسر نشوف بعض الأمثلة مثال الأول in + +545 +00:38:13,970 --> 00:38:16,310 +each of the following determine whether the + +546 +00:38:16,310 --> 00:38:21,680 +statement is true or false true or falseالمثال + +547 +00:38:21,680 --> 00:38:28,620 +الأول هل ال X تنتمي لمجموعة X؟ true متفقين المثال + +548 +00:38:28,620 --> 00:38:36,580 +الأول هو true طبعا solution مجموعة + +549 +00:38:36,580 --> 00:38:41,310 +الواحد تساوي مجموعة مجموعة الواحدغلط هدولة عمرين + +550 +00:38:41,310 --> 00:38:46,110 +مختلفين هدولة اه اه لإنها جاين ساوي هل هذه فيها + +551 +00:38:46,110 --> 00:38:50,070 +نفس العناصر لأ هذه عناصرها مين مجموعة الواحد هذه + +552 +00:38:50,070 --> 00:38:53,350 +عناصرها مين الواحد نفسه فهذه مختلفة فهذه false + +553 +00:38:53,350 --> 00:38:58,240 +فهذه مختلفة falseأه فهنا زي ما دي أقول أيش مثلا + +554 +00:38:58,240 --> 00:39:02,220 +اللي هو أيش مجموعة أقسام جاء الجامعة الإسلامية + +555 +00:39:02,220 --> 00:39:04,860 +فيها قسم رياضيات فيها قسم اللغة العربية ومجموعة + +556 +00:39:04,860 --> 00:39:08,120 +كليات أه هل فيها قسم اللغة العربية اللي هو قسم + +557 +00:39:08,120 --> 00:39:11,360 +رياضياته لأ رياضيات جزء من العلوم فالعلوم كلية أه + +558 +00:39:11,360 --> 00:39:14,520 +فهنا مختلف الأمر أه فهنا أيش التقسيم اللي بجسمه أه + +559 +00:39:14,520 --> 00:39:18,300 +فهذه أيش مختلفين وإنما أيش ممكن نحط علاقة تنتمي + +560 +00:39:18,300 --> 00:39:22,770 +أحسنتم تبسط من فعل لألأ مينفعش، ايش معنى subset؟ + +561 +00:39:22,770 --> 00:39:25,590 +كل عناصر الأولى عناصر من التانية، هل الواحد عناصر + +562 +00:39:25,590 --> 00:39:28,410 +من التانية؟ لأ، الواحد مش عناصر التانية، مجموعة + +563 +00:39:28,410 --> 00:39:31,090 +الواحد هي اللي عناصر التانية، زي ما هي الرياضيات + +564 +00:39:31,090 --> 00:39:34,490 +مش من كليات الجامعة الإسلامية، الرياضيات اشمال قسم + +565 +00:39:34,490 --> 00:39:37,910 +في كلية العلوم، مختلف المفهوم، المفهوم مختلف + +566 +00:39:37,910 --> 00:39:42,590 +والتقسيم مختلفلكن هيها .. شوفت مجموعة الواحد + +567 +00:39:42,590 --> 00:39:46,630 +والتانين تنتمي لمجموعة .. مجموعة الواحد والتانين + +568 +00:39:46,630 --> 00:39:50,470 +كأنصر والتلاتة كأنصر إيش معانا تنتمي؟ لإن أنصر من + +569 +00:39:50,470 --> 00:39:56,370 +ضمن العناصر فهذه true ف C true فأرجو هذا الرموز + +570 +00:39:56,370 --> 00:40:03,010 +نفرق فيها و نستخدمها بهذه الدقة الفاي تساوي مجموعة + +571 +00:40:03,010 --> 00:40:08,650 +الفايfalse مختلفين هذه مجموعة فارغة هذه مجموعة + +572 +00:40:08,650 --> 00:40:12,470 +فيها عنصر هذه مجموعة فيها عنصر مختلف تماما فهذه + +573 +00:40:12,470 --> 00:40:17,290 +false أشبهلكوا إياها هلجيت صينية فاضية فهي صينية + +574 +00:40:17,290 --> 00:40:20,110 +فاضية صينية فاضية فيها كباية فاضية الصينية صارت + +575 +00:40:20,110 --> 00:40:23,350 +فاضية ولا مليانة ورغم أن فيها كباية فاضية واضح + +576 +00:40:23,350 --> 00:40:27,970 +فالفرق ففرق هذه مجموعة فيها عنصر فارغ مانيش ده + +577 +00:40:27,970 --> 00:40:28,890 +ولكن فيها حاجة + +578 +00:40:32,860 --> 00:40:36,160 +لأن إيش مقناة subset؟ كل عناصر الأولى، من عناصر + +579 +00:40:36,160 --> 00:40:39,360 +الأولى؟ الواحد، بدنا نكون جوا من عناصر، هل الواحد + +580 +00:40:39,360 --> 00:40:42,320 +من عناصر التانية؟ لأ، مجموعة الواحد هي اللي من + +581 +00:40:42,320 --> 00:40:44,560 +عناصر التانية، زي ما قلنا إن الرياضيات مش من + +582 +00:40:44,560 --> 00:40:49,780 +القليات، هي جوا كلية، بطلعش أنا على التفاصيل، بطلع + +583 +00:40:49,780 --> 00:40:53,060 +من الخارج كعناصر، بيهمنا، بيادة شخصية تنتمي .. + +584 +00:40:53,060 --> 00:41:00,960 +تنتمي .. صح، زي الوق، زي الـC، تشبه الـC مثال آخر + +585 +00:41:03,190 --> 00:41:06,450 +in each of the following determine whether the + +586 +00:41:06,450 --> 00:41:09,370 +statement is true or false زي السؤال السابع بس + +587 +00:41:09,370 --> 00:41:13,310 +ضافة بقول if it is true prove it لما احنا بقول + +588 +00:41:13,310 --> 00:41:18,930 +نثبت الصحة with a false disapprove it اذا انا انا + +589 +00:41:18,930 --> 00:41:19,790 +انا انا انا انا انا انا انا انا انا انا انا انا + +590 +00:41:19,790 --> 00:41:19,950 +انا انا انا انا انا انا انا انا انا انا انا انا + +591 +00:41:19,950 --> 00:41:22,750 +انا انا انا انا انا انا انا انا انا انا انا انا + +592 +00:41:22,750 --> 00:41:22,750 +انا انا انا انا انا انا انا انا انا انا انا انا + +593 +00:41:22,750 --> 00:41:23,270 +انا انا انا انا انا انا انا انا انا انا انا انا + +594 +00:41:23,270 --> 00:41:23,270 +انا انا انا انا انا انا انا انا انا انا انا انا + +595 +00:41:23,270 --> 00:41:28,830 +انا انا انا انا انا انا انا انا انا + +596 +00:41:28,830 --> 00:41:28,830 +انا + +597 +00:41:33,850 --> 00:41:39,370 +خلّينا نحلهم مع بعض نشوف إيش الأسئلة و نحلها + +598 +00:41:39,370 --> 00:41:46,890 +المثال الأول إذا كانت ال X في ال A هذا المثال رقم + +599 +00:41:46,890 --> 00:41:52,250 +اتنين وال solution وهي A إذا ال X في ال A و ال A + +600 +00:41:52,250 --> 00:41:58,790 +تنتمي لل B فال X ضروري تكون في ال B مش + +601 +00:41:58,790 --> 00:42:03,330 +ضروري زي توي هذه نفس الآية للقضية فهذه falseفدى + +602 +00:42:03,330 --> 00:42:10,690 +force بدنا ماشي مثال عكسى counter example بدنا + +603 +00:42:10,690 --> 00:42:17,710 +مثال عكسى نعم لو ال A سبسطم ال B طبعا طبعا تعريفها + +604 +00:42:17,710 --> 00:42:21,230 +فهنا مش بالضرورة لأن هنا التعامل مع ال A كان عنصر + +605 +00:42:21,230 --> 00:42:24,430 +من ال B فمش ضرورى عناصر ال A تكون زى ما توي شفنا + +606 +00:42:24,430 --> 00:42:30,030 +الواحد زى المثال قبل قليل بدنا مثال بدنا مثال عكسى + +607 +00:42:30,030 --> 00:42:35,820 +تمامبدنا مثال عكسي بدنا مثال عكسي بدنا عنصر يكون + +608 +00:42:35,820 --> 00:42:39,140 +موجود في الـA فبدنا نعرف الـA أول شيء فنقول له + +609 +00:42:39,140 --> 00:42:43,140 +مثلا let capital A تساوي مجموعة مين الواحد مثلا + +610 +00:42:43,140 --> 00:42:46,220 +ودائما لما تدي مثال عكسي حاولي تديه أبسط ما يكون + +611 +00:42:46,220 --> 00:42:49,240 +ماتعجديش حالك وماتتهيش عشان ما تغلطيش عشان يكون + +612 +00:42:49,240 --> 00:42:52,060 +المثال واضح فانا بدأ أثبت أن هذا ال statement غلط + +613 +00:42:52,060 --> 00:42:55,940 +يعني إيش؟ بدأ أثبت أن الشرط صحيح وجواب الشرط خطأ + +614 +00:42:55,940 --> 00:42:59,540 +هيك معناته لإن هي شملة شرطية فبدنا ال جتحنا بدنا + +615 +00:42:59,540 --> 00:43:04,790 +مجموعة Aفيها عنصر X والـ A هي عنصر من الـ B لكن + +616 +00:43:04,790 --> 00:43:07,790 +الـ X مش عنصر من الـ B فناخد مثلا مجموعة الواحد + +617 +00:43:07,790 --> 00:43:13,770 +فالآن الواحد تنتمي لل A بتنعرف ال B and let B ال X + +618 +00:43:13,770 --> 00:43:19,870 +بساوة واحدة خلصنا عشان مايكون مثال ملموس أه إيش + +619 +00:43:19,870 --> 00:43:23,790 +مالها ال B تحتوي على ال A أه وممكن .. بس ميداشي + +620 +00:43:23,790 --> 00:43:26,870 +تكون تحتوي على ال واحد ولا تكون مثلا اتنين في أي + +621 +00:43:26,870 --> 00:43:32,560 +اختارأريد أن أثبت أن الجملة الـJH فالس فالآن + +622 +00:43:32,560 --> 00:43:38,920 +الواحد تنتمي للـA صح؟ والـA تنتمي للـB صح؟أيها؟ + +623 +00:43:38,920 --> 00:43:45,220 +لكن but الواحد لا تنتمي لل B هل الواحد من عناصر ال + +624 +00:43:45,220 --> 00:43:48,100 +.. يمكن الكتابة بدأت شكل أسهل لو حطيت إنه بدل ال A + +625 +00:43:48,100 --> 00:43:50,720 +مجموعة الواحد كانت اتخنته شوية لكن واضح إن الواحد + +626 +00:43:50,720 --> 00:43:55,160 +من عناصر ال B لأ واضح من عناصر ال B A وال A + +627 +00:43:55,160 --> 00:43:57,980 +عناصرها الواحد ماليش دعوة أنا بتطلع على عناصر ال B + +628 +00:43:57,980 --> 00:44:00,880 +بتطلع اتطلع على النظر الخارجية ماليش دعوة + +629 +00:44:00,880 --> 00:44:04,120 +بالتفاصيل ماليش دعوة بالتفاصل أي سؤال + +630 +00:44:07,920 --> 00:44:13,280 +فهذا بيقدر أنه يحصل statement false فهذا + +631 +00:44:13,280 --> 00:44:15,240 +يمكن أن يكون أول مثال على الكافرين دي ب counter + +632 +00:44:15,240 --> 00:44:18,480 +example ان شاء الله مع التكرار الأمور تكون أفضل من + +633 +00:44:18,480 --> 00:44:26,580 +هك و أوضح مثال Bإذا X تنتمي للـ B و A subset من + +634 +00:44:26,580 --> 00:44:31,340 +الـ B فالـ X ليست في الـ A هذي False صحيح و ممكن + +635 +00:44:31,340 --> 00:44:36,840 +مع الرسم تساعدنا بي فالس خلينا نعمل رسم مساعد هي + +636 +00:44:36,840 --> 00:44:41,750 +عندي A و هي عندي Bبقول لي في عنصر موجود في ال B + +637 +00:44:41,750 --> 00:44:45,330 +وين عناصر ال B؟ يا هان يا هان ضروري يكون خارج ال + +638 +00:44:45,330 --> 00:44:48,650 +ايه؟ لأ واضح انه مش ضروري انه مش ضروري فهذه طبعا + +639 +00:44:48,650 --> 00:44:51,150 +لما يقولي طب ممكن تكون صح لأ انا اش بده أقول قاعد + +640 +00:44:51,150 --> 00:44:54,090 +تكون دايما صح هيك معاك لأ مش احتمال فلما بده اقول + +641 +00:44:54,090 --> 00:44:56,690 +ان القاعد ده بده تكون دايما صحيحة مش ان احتمال + +642 +00:44:56,690 --> 00:45:01,130 +تكون صحيحة اه في بعض الأحيان لأ بنفعل فبندليه مثال + +643 +00:45:01,130 --> 00:45:09,730 +عكسي counter example مثال عكسي اوتمام فناخد ايش ال + +644 +00:45:09,730 --> 00:45:14,850 +a مثلا تساوي واحد اتنين ببساطة اه بده يعني ايش ال + +645 +00:45:14,850 --> 00:45:20,460 +a subset من ال b بي تساوي عشان تكون subsetواحد + +646 +00:45:20,460 --> 00:45:25,080 +اتنين على اقله تلاتة تمام فبقوللي ال X بدا تكون في + +647 +00:45:25,080 --> 00:45:28,960 +ال B وماتكونش في ال A برضه جملة شرطية بدياش فانا + +648 +00:45:28,960 --> 00:45:33,400 +عندي مثلا انه بدا تكون في ال B وال A صبصت مظبوط + +649 +00:45:33,400 --> 00:45:37,780 +وماتكونش بتكون اه بعد المية ليست في ال A بدا + +650 +00:45:37,780 --> 00:45:42,100 +مفيهاش ده تصير جوا ال A فاشفي عندي الأول شي الواحد + +651 +00:45:42,100 --> 00:45:47,770 +تنتمي لل Bالـ A سبسط من ال B صح ولا مش صح لكن + +652 +00:45:47,770 --> 00:45:55,350 +الواحد تنتمي لل A نفيتها دي مظبوط؟ أه لكن الواحد + +653 +00:45:55,350 --> 00:45:59,170 +تنتمي لل A فهي مثال بتدل عنها دي مش قاعدة لأن + +654 +00:45:59,170 --> 00:46:06,470 +القاعدة بتكون دائما صحيحة دائما صحيحة أي سؤال؟ + +655 +00:46:06,470 --> 00:46:09,930 +نشوف + +656 +00:46:09,930 --> 00:46:14,940 +مثال تالتهو نهاية ال section هنا ان شاء الله prove + +657 +00:46:14,940 --> 00:46:21,160 +that for any sets a,b,c تلت مجموعات إذا ال a بربر + +658 +00:46:21,160 --> 00:46:25,040 +من ال b و ال b بربر subset من ال c فال a بربر + +659 +00:46:25,040 --> 00:46:27,980 +subset من ال c فبرضه علاقة بربر subset is + +660 +00:46:27,980 --> 00:46:37,260 +transitive بدنا نثبتها بدنا نثبتها مثال + +661 +00:46:37,260 --> 00:46:45,020 +التالت و solutionطبعا هذا المثال اللي هو أهم + +662 +00:46:45,020 --> 00:46:49,480 +بالنسبالنا كيف نبرهن لأنه براهين النظريات بدنا + +663 +00:46:49,480 --> 00:46:53,480 +نفهمها و نعرف نشتغل زيها مش نعرف نحفظها اه فهنا + +664 +00:46:53,480 --> 00:46:56,800 +بدينا كيف نتعامل زي ما اتعلمنا في النظرية طبعا + +665 +00:46:56,800 --> 00:47:00,820 +prove that for any sets A,B,C إذا أنا فيه عندي + +666 +00:47:00,820 --> 00:47:07,260 +معطع أن الـA و الـB sets ممكن أقوله إيش let A,B,C + +667 +00:47:07,260 --> 00:47:13,170 +أو and C كله صح بيه sixanysets نفس المعنى كلمة any + +668 +00:47:13,170 --> 00:47:17,010 +هذي ايش ومفهومة ضمنيا حتى لما ذكرتها ايش بقول ايه + +669 +00:47:17,010 --> 00:47:24,630 +اثبت if جملة شرطية we want to prove نكتب هنا ايش + +670 +00:47:24,630 --> 00:47:29,770 +المطلوب فالله يقولني ايش prove that we want او + +671 +00:47:29,770 --> 00:47:36,850 +have to كله صح to prove thatجملة شرطية الـ A + +672 +00:47:36,850 --> 00:47:42,070 +proper subset من الـ B and الـ B proper subset من + +673 +00:47:42,070 --> 00:47:49,110 +الـ C then او implies if then true implies الـ A + +674 +00:47:49,110 --> 00:47:55,590 +proper من الـ C هذا المطلوب في طالبة عندها صعوبة + +675 +00:47:55,590 --> 00:48:00,300 +في اللي كتبناه؟ امتبعين؟واضح؟ يعني احنا جيت في هذه + +676 +00:48:00,300 --> 00:48:04,260 +المرحلة بنأكد على هذه المفهومة بعد هيك شوية هنتقدم + +677 +00:48:04,260 --> 00:48:07,260 +حاسيب تركيز على أمور أخرى متقدمة فارجعوا إن الأمر + +678 +00:48:07,260 --> 00:48:11,240 +إذا فيه مشكلة نحله الآن هذا وقت المناسب تمام؟ إيش + +679 +00:48:11,240 --> 00:48:17,760 +المطلوب؟ جملة صارطية كيف أثبت؟ Assume that Assume + +680 +00:48:17,760 --> 00:48:27,880 +that الـA proper subset من الـB and الـB + +681 +00:48:29,000 --> 00:48:36,760 +بربر subset من الـ C ممتاز ايش المطلوب؟ we have to + +682 +00:48:36,760 --> 00:48:44,740 +show that ال A بربر من ال C وتكافئ ايش معناته + +683 +00:48:44,740 --> 00:48:50,300 +بربر؟ subset ولا تساوي ان ال A subset من ال C and + +684 +00:48:50,300 --> 00:48:56,200 +ال A لا تساوي ال C ممتاز + +685 +00:49:01,970 --> 00:49:06,430 +بدنا نثبت هذا الكلام ايش بيكافئ جملة فيها + +686 +00:49:06,430 --> 00:49:09,110 +conjunction استثمار فيها conjunction عشان تكون + +687 +00:49:09,110 --> 00:49:12,250 +true بتثبت أن هذه true وهذه true فخلينا نقسم على + +688 +00:49:12,250 --> 00:49:15,850 +مرحلتين فنبدأ من الجزء الأول بدنا نثبت أن ال A + +689 +00:49:15,850 --> 00:49:20,190 +subset من ال C بدنا نثبت أن ال A subset من ال C + +690 +00:49:20,190 --> 00:49:26,850 +فده أول جزء بدنا نثبت أن ال A subset من ال C تمام؟ + +691 +00:49:26,850 --> 00:49:32,350 +اه فيه أن احنامقطيات سهل هذا الجزء لأنه ايش قلنا + +692 +00:49:32,350 --> 00:49:35,570 +بدنا نثبت ان البروبر transitive طب ما احنا في + +693 +00:49:35,570 --> 00:49:39,190 +subset transitive طب و البروبر تتضمن ضمنيا انه + +694 +00:49:39,190 --> 00:49:43,050 +يكون subset فانا عندي من الخطوة الأولى هدول مقطيات + +695 +00:49:43,050 --> 00:49:46,810 +assume that ال A subset من ال B يعني A أسف البروبر + +696 +00:49:46,810 --> 00:49:50,130 +subset يعني subset فبما أننا هنا نقوله ايش ال A + +697 +00:49:50,130 --> 00:49:54,010 +subset البروبر subset من ال B implies اللي هو مين + +698 +00:49:54,010 --> 00:49:59,730 +ال A subset من ال Bوالـ B proper subset من الـ C + +699 +00:49:59,730 --> 00:50:04,670 +implies الـ B subset من الـ C هذه و هذه و نظرية + +700 +00:50:04,670 --> 00:50:08,190 +اتنين اتنين ايش يؤدوا ان الـ A subset من الـ C اه + +701 +00:50:08,190 --> 00:50:15,230 +اذا thus ممكن اكتب الـ A subset من الـ C من وين؟ + +702 +00:50:15,230 --> 00:50:21,460 +theorem اتنين اتنينفانا الجزء السهل وده شيء متوقع + +703 +00:50:21,460 --> 00:50:25,460 +ممكن احط اشي يساوي و اقول for all x لكن انا بدل ما + +704 +00:50:25,460 --> 00:50:28,480 +أعمل بشكل مطول باعيد برهان نظرية اتنين اتنين + +705 +00:50:28,480 --> 00:50:32,660 +استخدمت النظرية واضح الفرق؟ اه فالان انا مافصلتش + +706 +00:50:32,660 --> 00:50:35,540 +ليش لأن استفادت من النظرية استفادت من النظرية + +707 +00:50:35,540 --> 00:50:39,880 +فالجزء الاول سهل متفقين؟ اه ممكن اعمل بشكل مطول اه + +708 +00:50:39,880 --> 00:50:44,360 +بس بكون اطول هذا اقصر البرهان الجزء التاني بدنا + +709 +00:50:44,360 --> 00:50:51,560 +نثبت ان ال A لا تساوي ال Cلأ تساوي الـ C على ان + +710 +00:50:51,560 --> 00:50:57,200 +تستفهى ايش + +711 +00:50:57,200 --> 00:51:03,560 +معناه لأ تساوي يساوي يعني هذه سبسط من الأولى + +712 +00:51:03,560 --> 00:51:07,640 +والتانية سبسط من الأولى فاحنا عندنا خلينا بس + +713 +00:51:07,640 --> 00:51:10,540 +أفسرها هنا تساوي + +714 +00:51:13,190 --> 00:51:16,490 +لاتساوي، لاتساوي، إيش معناه؟ إيش تكافئ؟ نفي إن + +715 +00:51:16,490 --> 00:51:21,290 +الـA subset من الـC and C subset من الـA، ممتاز + +716 +00:51:21,290 --> 00:51:26,830 +خلينا ننفيها، كيف بننفيها هذه؟ DeMorgans يعني إيش؟ + +717 +00:51:26,830 --> 00:51:33,290 +A ليست subset من الـC or C ليست subset من الـAصح + +718 +00:51:33,290 --> 00:51:37,590 +ولا لأ؟ دي مورجانز شايفين؟ اه اللي اتعلمناه ممتاز + +719 +00:51:37,590 --> 00:51:41,310 +انا ايش بدي اثبت؟ بدي اثبت انه يا هاذي true يا + +720 +00:51:41,310 --> 00:51:44,670 +هاذي true عشان .. بدي اثبت ان ال or true وقت ايش + +721 +00:51:44,670 --> 00:51:47,330 +بيكون ال or true؟ على الأقل واحدة true طيب احنا + +722 +00:51:47,330 --> 00:51:51,560 +ايش في أول خطوة أثبتنا؟الـ A subset من ال C is + +723 +00:51:51,560 --> 00:51:57,360 +true يعني A ليست subset أدي شمالها false طب عشان + +724 +00:51:57,360 --> 00:52:00,440 +تكون ال R true إيش لازم تكون؟ لازم تكون ال can يه + +725 +00:52:00,440 --> 00:52:03,100 +true فإذا لازم أثبت إن وديك true فهنا دي ده أقولله + +726 +00:52:03,100 --> 00:52:13,200 +since ال A subset من ال C we have to show that ال + +727 +00:52:13,200 --> 00:52:20,540 +إيش ال C ليست subset من مين؟ من ال Aهي اللي تبقى + +728 +00:52:20,540 --> 00:52:26,600 +وهذا issue كافة كتبناها قبل قليل there exist X X + +729 +00:52:26,600 --> 00:52:35,940 +تنتمي لل A .. آسف لل C and X لا تنتمي لل A فهذا هو + +730 +00:52:35,940 --> 00:52:39,920 +المطلوب فهذا هو المطلوب + +731 +00:52:43,300 --> 00:52:46,820 +فكيف نثبته؟ بدنا ندور على X موجودة في الـC و غير + +732 +00:52:46,820 --> 00:52:47,480 +موجودة في الـA + +733 +00:52:53,190 --> 00:52:57,650 +في جيابنا و لا في الشنط و لا وين؟ في المعطيات .. + +734 +00:52:57,650 --> 00:53:02,070 +في المعطيات طيب هل ممكن أذكر ال X بشكل صريح؟ أقول + +735 +00:53:02,070 --> 00:53:05,550 +X بتساوي واحد و لا بتساوي صفر؟ ليش؟ لأن ال A و ال + +736 +00:53:05,550 --> 00:53:08,430 +B و ال C دول عايش مجموعات عامة، إيش عناصرهم؟ مش + +737 +00:53:08,430 --> 00:53:11,790 +معروف، إذا وين بدنا ندور في المعطيات؟ مين موقف + +738 +00:53:11,790 --> 00:53:14,750 +يقول لي there exists؟اتطلعوا احنا ايش استخدمنا في + +739 +00:53:14,750 --> 00:53:18,590 +المعطيات استخدمنا انهم subset استخدمنا انهم proper + +740 +00:53:18,590 --> 00:53:23,230 +لأ ما استخدمناش انهم proper ايش معناه ان الـB + +741 +00:53:23,230 --> 00:53:27,250 +proper subset من الـC ان الـB تسويش الـC يعني هناك + +742 +00:53:27,250 --> 00:53:31,090 +عنصر موجود في الـC غير موجود في الـB اه فالان بدي + +743 +00:53:31,090 --> 00:53:36,970 +اكتبله هنا بي برابر من الـC implies there exists X + +744 +00:53:36,970 --> 00:53:42,110 +X تنتمي للـC and X ليستفي الـ B بنفس المفهوم + +745 +00:53:42,110 --> 00:53:46,490 +السابق مظلة proper إذا في عناصر في الـ C زيادة مش + +746 +00:53:46,490 --> 00:53:49,990 +هي الـ C كبيرة بتحتوى الـ B والتساوي غير محتمل + +747 +00:53:49,990 --> 00:53:53,010 +ليش؟ لأن الـ C فيها عناصر زيادة معناته هذا الكلام + +748 +00:53:53,010 --> 00:53:57,650 +ممتاز أنا إيش بديها؟ أنا بدي X تنتمي للـ A ممكن + +749 +00:53:57,650 --> 00:54:03,060 +أوصلها، كيف أوصلها؟الـ A سبسط من الـ B كل أنصار في + +750 +00:54:03,060 --> 00:54:06,300 +الـ A موجود في الـ B الـ Contrapositive كل أنصار + +751 +00:54:06,300 --> 00:54:09,160 +غير موجود في الـ B مستحيل يكون في الـ A + +752 +00:54:09,160 --> 00:54:14,180 +Contrapositive فهذه تؤدي there exists X X تنتمي + +753 +00:54:14,180 --> 00:54:19,020 +للـ C و X لا تنتمي للـ A من أين جلبنا هذا الدليل؟ + +754 +00:54:19,020 --> 00:54:23,380 +طبعا هذا بإيش؟ هذا يؤدي لهذا هذا ليش؟ لأن الـ A + +755 +00:54:23,380 --> 00:54:28,240 +سبسط من الـ B طيب أكتبلكم على السريع إيش معناة A + +756 +00:54:28,240 --> 00:54:29,220 +سبسط من الـ B؟ + +757 +00:54:36,330 --> 00:54:46,070 +مظبوط؟ إيش الـ Contrapositive تبعتها؟ وضحكت؟ + +758 +00:54:46,070 --> 00:54:49,830 +فما زال X غير موجودة في الـP إذاً هي ماير موجودة + +759 +00:54:49,830 --> 00:54:56,870 +في الـA وهو المطلوب وهو المطلوب هذه نهاية ال + +760 +00:54:56,870 --> 00:54:57,850 +section إن شاء الله المرة جديدة + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/TK4jrOuwY4g.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/TK4jrOuwY4g.srt new file mode 100644 index 0000000000000000000000000000000000000000..fbd3ecc7ed9ba6f134dd0b07b8eceeb86ab8cc2f --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/TK4jrOuwY4g.srt @@ -0,0 +1,2567 @@ +1 +00:00:20,720 --> 00:00:23,960 +بسم الله الرحمن الرحيم اه اليوم إن شاء الله احنا + +2 +00:00:23,960 --> 00:00:28,820 +هنبدأ موضوع جديد اللي هو قواعد التكميم لكن تم فينا + +3 +00:00:28,820 --> 00:00:32,920 +مثال على اللي هو deductive reasoning أو إثبات + +4 +00:00:32,920 --> 00:00:37,620 +باستخدام قواعد الاستدلال طبعا احنا ذكرنا أن الإثبات + +5 +00:00:37,620 --> 00:00:40,760 +باستخدام قواعد الاستدلال هو طريقة بديلة لجدول + +6 +00:00:40,760 --> 00:00:45,700 +الصدق تستخدم في إثبات التكافؤ أو التضمين طبعا في + +7 +00:00:45,700 --> 00:00:50,140 +كل خطوة نطبق قاعدة من القواعد لأن هذا التفكير + +8 +00:00:50,140 --> 00:00:54,260 +الاستدلالي القاعدة موجودة ونطبق عليها أمثلة فعنا + +9 +00:00:54,260 --> 00:00:59,320 +أكثر من مرة نطبق القاعدة في الإثبات طبعا عندنا + +10 +00:00:59,320 --> 00:01:05,190 +مثال آخر وهو سؤال تضمين اللي أمامنا if P then Q or + +11 +00:01:05,190 --> 00:01:11,350 +P if P then R and P implies Q and R كما ذكرنا إذا + +12 +00:01:11,350 --> 00:01:14,990 +كان القانون قانون تكافؤ ففيه حرية في البداية مع + +13 +00:01:14,990 --> 00:01:18,450 +نصيحة أنه نبدأ من الكبير للصغير لأنه دائما التبسيط + +14 +00:01:18,450 --> 00:01:21,910 +أسهل من الإضافة لكن إذا كان تضمين اللي البداية + +15 +00:01:21,910 --> 00:01:27,120 +إجبارية ما فيش خيار لازم نبدأ من اليسار فنبدأ في هذا + +16 +00:01:27,120 --> 00:01:32,520 +المثال السابع ونبدأ الـ solution ده هنبدأ طبعا من + +17 +00:01:32,520 --> 00:01:42,280 +اليسار if b then q or if b then r كله معاه and b + +18 +00:01:42,280 --> 00:01:50,960 +بنحاول نوصل لـ q or r طبعا في أكثر من مرة شفنا أن تعريف + +19 +00:01:50,960 --> 00:01:55,340 +الـ if then بيساعدنا كثير لأنه بيحول على متغير أو + +20 +00:01:55,340 --> 00:02:00,060 +أكثر على متغير أو أكثر بس لا عشان المثال هذا and + +21 +00:02:00,060 --> 00:02:04,380 +which اللي هو الجملة الشرطية إلى and و nephew أو or + +22 +00:02:04,380 --> 00:02:09,260 +وبالتالي في عندنا قوانين كثير توزيع التجميع وهكذا + +23 +00:02:09,260 --> 00:02:12,350 +بيصير في عندنا مرونة في العمل الآن إن شاء الله هذا + +24 +00:02:12,350 --> 00:02:16,350 +المثال طبعا ممكن ينحل بالطريقة السابقة أن نستخدم + +25 +00:02:16,350 --> 00:02:20,690 +التعريف لكن احنا هنحلّنه بطريقة مختصرة خلّيني أعمل + +26 +00:02:20,690 --> 00:02:24,350 +توزيع عنا and و are سيبنا من الأقواس الآن فلو + +27 +00:02:24,350 --> 00:02:30,570 +استخدمنا التوزيع بدينا if b then q and b هاي واحدة + +28 +00:02:30,570 --> 00:02:37,070 +or if b then r and b هدول بستخدام التوزيع + +29 +00:02:41,980 --> 00:02:48,580 +distributive law تمام؟ الآن بنظرة فاحصة if B then + +30 +00:02:48,580 --> 00:02:52,960 +Q and B modus ponens بتديني على طول B بس كيف قانون + +31 +00:02:52,960 --> 00:02:55,920 +modus ponens؟ implies ولا تكافؤ؟ implies إذا لازم + +32 +00:02:55,920 --> 00:02:58,980 +نحط هنا implies هذا مهم هو القانون احنا ما نمشي + +33 +00:02:58,980 --> 00:03:04,140 +تكافؤ أو implies حسب القانون فهذا بتديني Q or بنفس + +34 +00:03:04,140 --> 00:03:09,140 +الطريقة if B then R and B مش بتديني R اه لأنه ايش + +35 +00:03:09,140 --> 00:03:14,110 +الشرط فهذا الشرط استخدمنا modus ponens modus ponens + +36 +00:03:14,110 --> 00:03:20,890 +والسؤال انحل أبش .. أبسط طريقة انحل بصفر فطبعا ده + +37 +00:03:20,890 --> 00:03:25,670 +أحد الطرق أنا هنا عملنا توزيع واضح الآن استخدمناه + +38 +00:03:25,670 --> 00:03:29,570 +modus volumens ايش بتقول إذا ايش إذا وعدنا بنوفي + +39 +00:03:29,570 --> 00:03:33,170 +بالوعد إذا وعدنا بنوفي بالوعد بس المرة كان الـ Q + +40 +00:03:33,170 --> 00:03:37,290 +هنقرر modus volumens هذا قانون مهم جدا طبعا فهذا + +41 +00:03:37,290 --> 00:03:41,050 +حل سريع طبعا الحل الثاني ممكن يجيب عن طريق التعريف + +42 +00:03:41,050 --> 00:03:46,550 +لكنه حل أطول شوية فدول سبع أمثلة أرجو أنه بيكونوا + +43 +00:03:46,550 --> 00:03:52,190 +كافيا لتوضيح الموضوع طبعا لابد من العمل والتدريب + +44 +00:03:52,190 --> 00:03:56,530 +والتطبيق باليد حتى الأمور تتمكن احنا بنحاول بس نُدّي + +45 +00:03:56,530 --> 00:04:00,930 +الأفكار الرئيسية ونوضح وبيجي دور الطالب أنه يتدرب + +46 +00:04:00,930 --> 00:04:07,900 +ويطبق هادي ما تعلمه فالآن هننتقل لموضوع جديد هو + +47 +00:04:07,900 --> 00:04:14,280 +عنوان quantification rules قواعد التكميم طبعا + +48 +00:04:14,280 --> 00:04:17,880 +quantification من quantity يعني كمية فبيترجموها .. + +49 +00:04:17,880 --> 00:04:23,180 +بيعرفوها قواعد التكميم من كمية تكميم من كمية ليس + +50 +00:04:23,180 --> 00:04:26,700 +تكميم اللي لقفوها تكميم من كمية اللي هو نستحدث عن + +51 +00:04:26,700 --> 00:04:31,020 +الكمية فموضوعنا الرئيس اللي احنا بنوصله في هذا + +52 +00:04:31,020 --> 00:04:35,940 +section كيف نتعامل مع المصطلحات for all و there + +53 +00:04:35,940 --> 00:04:41,260 +exist نتحدث هنا عن كميات، جميع كمية، بعض، اللي هو + +54 +00:04:41,260 --> 00:04:44,340 +جزء، اللي هو there exist، بعض، بيسموه ايه؟ فاحنا + +55 +00:04:44,340 --> 00:04:47,800 +هنا نتحدث عن الكميات، فهو ايش؟ بيسموه تكميم بشكل + +56 +00:04:47,800 --> 00:04:52,840 +عام، هيتحدث عنهم و كيف نتعامل معاهم جملة تحتوي على + +57 +00:04:52,840 --> 00:04:56,520 +هذول المصطلحين for all who there exist وطبعا كيف + +58 +00:04:56,520 --> 00:04:59,200 +بيصير منهم statement وكيف بيصير true وكيف بيصير + +59 +00:04:59,200 --> 00:05:02,840 +false وهكذا متعمن جميع القواعد اللي بتستخدم هذول + +60 +00:05:02,840 --> 00:05:07,810 +المصطلحين فقبل ما نبدأ باستخدام for all و there + +61 +00:05:07,810 --> 00:05:12,590 +exist بنبدأ في تمهيد ما يعرف بالـ open sentence + +62 +00:05:12,590 --> 00:05:16,630 +جملة مفتوحة اه طبعا اتفقنا في البداية أن الـ + +63 +00:05:16,630 --> 00:05:20,730 +statement هي عبارة عن جملة فيها بتدينا معلومة أو + +64 +00:05:20,730 --> 00:05:25,210 +خبر وهذا يا بيكون true يا false بعض الـ sentences + +65 +00:05:25,210 --> 00:05:28,950 +بحد ذاتها ليست statement وإنما كمان تحتوي على + +66 +00:05:28,950 --> 00:05:33,730 +متغير تحتوي على متغير إذا عوّضنا عن المتغير بقيمة + +67 +00:05:33,730 --> 00:05:38,470 +ما بتصبح statement بتصبح .. بتصبح statement هذه الـ + +68 +00:05:38,470 --> 00:05:41,510 +sentence اللي من هذا النوع هنسميها open sentence + +69 +00:05:41,510 --> 00:05:45,450 +جملة مفتوحة لأنه لسه مفتوح على جميع الاحتمالات لما + +70 +00:05:45,450 --> 00:05:49,950 +بنعود عنها بتصير statement وبتختلف فهذه طبعا .. + +71 +00:05:49,950 --> 00:05:53,830 +طبعا ممكن يكون فيها متغير أو أكثر أو متغير أو أكثر + +72 +00:05:53,830 --> 00:05:56,410 +بنسميها open sentence أصابعين المثال + +73 +00:05:59,280 --> 00:06:02,780 +لو أخذنا X تربيع تساوي 9 مر علينا إن هذه ليست + +74 +00:06:02,780 --> 00:06:06,180 +statement صح ولا لا؟ هذه ليست statement لو عوّضنا + +75 +00:06:06,180 --> 00:06:10,600 +X تساوي 3 بتصير statement و true لو عوّضنا X تساوي 4 + +76 +00:06:10,600 --> 00:06:14,300 +بتصير statement لكن false لكن false فهذا النوع من + +77 +00:06:14,300 --> 00:06:17,320 +الـ sentences اللي بيحتوي على variable أو أكثر + +78 +00:06:17,320 --> 00:06:20,840 +هنسميها open sentence طبعا مش بس تحتوي على + +79 +00:06:20,840 --> 00:06:23,940 +variables وايه كمان؟ وبتصير statement يعني على + +80 +00:06:23,940 --> 00:06:29,340 +سبيل المثال لو أخذت مثلا X زائد 1 هل هدى هدى فيها + +81 +00:06:29,340 --> 00:06:32,700 +variable لكن هل هدى open sentence لا لأنه جات + +82 +00:06:32,700 --> 00:06:35,340 +متعوّض عن X بصيرش statement فإن إذا فينا إنها + +83 +00:06:35,340 --> 00:06:38,420 +معيارين للـ open sentence إنها بتحتوي على variable + +84 +00:06:38,420 --> 00:06:41,720 +أو أكثر وإذا عوضنا عن الـ variables بقيمة معينة + +85 +00:06:41,720 --> 00:06:44,820 +بصير statement لكن إن أعوض عن X بصير statement لا + +86 +00:06:44,820 --> 00:06:50,840 +فمهم جدا إنه ناخد التعريف كاملا وبشكل دقيقة فإنه + +87 +00:06:50,840 --> 00:06:55,620 +التعريف open sentence a sentence containing one or + +88 +00:06:55,620 --> 00:06:58,920 +more values إذا أول معيار بتحتوي عشان .. becomes a + +89 +00:06:58,920 --> 00:07:02,100 +statement ممكن ننسيش مهلا ممكن تصير statement تصير + +90 +00:07:02,100 --> 00:07:05,960 +تقرير وابتداش only when the variables are replaced + +91 +00:07:05,960 --> 00:07:10,660 +فقط عندما نستبدل المتغيرات بـ certain values بقيم + +92 +00:07:10,660 --> 00:07:13,600 +معينة ايش .. ايش بيسميها open sentence فالـ open + +93 +00:07:13,600 --> 00:07:17,540 +sentence هي عبارة عن statement .. آسف عبارة عن .. + +94 +00:07:17,540 --> 00:07:20,760 +عن جملة تحتوي على متغير أو أكثر إذا استبدلنا + +95 +00:07:20,760 --> 00:07:23,750 +المتغيرات بقيم معينة بالصير statement بصير + +96 +00:07:23,750 --> 00:07:26,550 +statement طبعا في مصطلح آخر زي ما قلنا statement + +97 +00:07:26,550 --> 00:07:28,990 +فيه بيسموها preposition اه برضه الـ open sentence + +98 +00:07:28,990 --> 00:07:33,470 +بيسموها prepositional predicate مصطلح آخر احنا + +99 +00:07:33,470 --> 00:07:37,090 +هنركز على مصطلح open sentence احنا هنستخدم open + +100 +00:07:37,090 --> 00:07:42,870 +sentence أي سؤال اه طبعا قلنا مازال open فيها + +101 +00:07:42,870 --> 00:07:45,410 +variable أو أكثر في عندنا رمز احنا اتعودنا للـ + +102 +00:07:45,410 --> 00:07:48,550 +statement نقولها بي كيو capital أو small الآن هذه + +103 +00:07:48,550 --> 00:07:51,430 +بتحتوي على variables فهنعملها بالرمز زي الدوال + +104 +00:07:51,430 --> 00:07:54,410 +نقول احنا f of x فببساطة أننا هنقول هنا بي of x إذا + +105 +00:07:54,410 --> 00:07:57,930 +كان متغير واحد طب أكثر بي of x one x two وهكذا + +106 +00:07:57,930 --> 00:08:03,010 +فهذا الرمز اللي هنستخدمه هذا الرمز اللي هنستخدمه + +107 +00:08:03,010 --> 00:08:07,750 +عشان نوضح أن هذه open sentence نشوف بعض الأمثلة + +108 +00:08:12,680 --> 00:08:15,960 +الـ statement الأولى أو المثال الأول عندنا هنا في + +109 +00:08:15,960 --> 00:08:20,840 +عندنا open sentence example one ففي عندنا P of X X + +110 +00:08:20,840 --> 00:08:25,500 +زائد واحد تساوي Zero فهذه open sentence لأنها + +111 +00:08:25,500 --> 00:08:28,840 +بتحتوي على متغير واحد لو عوّضنا عن الـ X بالقيمة + +112 +00:08:28,840 --> 00:08:33,040 +بيصير statement في عصابين المثال بي of زيرو زيرو + +113 +00:08:33,040 --> 00:08:36,680 +زائد واحد تساوي زيرو هذه statement وهي ليش false + +114 +00:08:36,680 --> 00:08:40,080 +هي statement انها false اه لكن هي statement بغض + +115 +00:08:40,080 --> 00:08:42,520 +النظر هي false ولا true لكن صارت statement فهذه + +116 +00:08:42,520 --> 00:08:46,520 +open sentence لكن بي سالب واحد سالب واحد زائد واحد + +117 +00:08:46,520 --> 00:08:50,360 +تساوي زيرو true اه فجاير لما نعوض صارت ايش صارت + +118 +00:08:50,360 --> 00:08:53,660 +statement فهي open sentence لما نعوض عن بعض القيام + +119 +00:08:53,660 --> 00:08:59,420 +بتصير statement فهذا هو الرمز وهذه هي مثال على الـ + +120 +00:08:59,420 --> 00:09:02,920 +open sentences نشوف مثال آخر + +121 +00:09:05,740 --> 00:09:10,860 +نشوف مثال آخر مثال هنا في عندنا open sentence فيها + +122 +00:09:10,860 --> 00:09:17,260 +متغيرين B of X and Y X زائد Y تساوي واحد هذه open + +123 +00:09:17,260 --> 00:09:21,320 +sentence فيه متغيرين لو عوضنا عن الـ X و الـ Y فمثلا + +124 +00:09:21,320 --> 00:09:25,900 +B of 01 عبارة عن 0 زائد 1 تساوي 1 فدي صارت + +125 +00:09:25,900 --> 00:09:30,380 +statement وهي true وهي الـ true لكن لو قولنا B of + +126 +00:09:30,380 --> 00:09:36,320 +11 1 زائد 1 تساوي 1 statement لكن false فزي ما احنا + +127 +00:09:36,320 --> 00:09:40,580 +شايفين تحتوي على متغير المثال الأول متغير واحد + +128 +00:09:40,580 --> 00:09:44,140 +المثال الثاني متغيرين لما بنبدل المتغيرات بقيم + +129 +00:09:44,140 --> 00:09:47,820 +معينة بتصير statement فهذا هو المعيار هذا هو ايش + +130 +00:09:47,820 --> 00:09:51,560 +المحدد اللي بيحدد انها open sentence فهذه الـ open + +131 +00:09:51,560 --> 00:09:54,280 +sentence ببساطة وهذه أمثلة بسيطة على الـ open + +132 +00:09:54,280 --> 00:10:01,520 +sentences أي سؤال طبعا في التعامل مع الـ open + +133 +00:10:01,520 --> 00:10:06,200 +sentences في عندنا قيم بتتعوّض محل الـ variables + +134 +00:10:06,200 --> 00:10:11,300 +هدول القيم من وين بدنا ناخدهم فهنا مهم جدا نعرف + +135 +00:10:11,300 --> 00:10:15,260 +المجال اللي بدنا ناخد منه القيم هذا المجال هو + +136 +00:10:15,260 --> 00:10:18,400 +عبارة عن مجموعة من الأشياء عبارة عن مجموعة من + +137 +00:10:18,400 --> 00:10:23,220 +الأشياء أو من العناصر بيسموه the universe الكون أو + +138 +00:10:23,220 --> 00:10:27,460 +the domain of discourse مجال الدراسة المجالمجال + +139 +00:10:27,460 --> 00:10:30,340 +الدراسة ممكن زي الدالة مش الدالة في قيم بتعوّض منها + +140 +00:10:30,340 --> 00:10:32,960 +وهنا زي نفس القضية مازال هي open sentence في + +141 +00:10:32,960 --> 00:10:36,560 +متغير بدنا نعوض عن المتغير من وين مسموح نعوض من + +142 +00:10:36,560 --> 00:10:39,960 +مين اللي بدنا نشتغل عليه مجال الدراسة أو إيش + +143 +00:10:39,960 --> 00:10:43,400 +المجال بشكل آخر أو الـ universe اللي هو الكون تبعنا + +144 +00:10:43,400 --> 00:10:46,320 +أو المجموعة المرجعية فبقول لي the set of all + +145 +00:10:46,320 --> 00:10:50,000 +objects مجموعة جميع العناصر that can be considered + +146 +00:10:50,000 --> 00:10:55,370 +اللي ممكن ناخدها بعين الاعتبار ممكن اللي نستخدمها + +147 +00:10:55,370 --> 00:10:59,750 +in an open sentence is called the universe or the + +148 +00:10:59,750 --> 00:11:04,090 +domain of discourse مجال الدراسة اه فإذا مجال open + +149 +00:11:04,090 --> 00:11:06,570 +sentence إيش معنى open sentence إنها بيصير + +150 +00:11:06,570 --> 00:11:09,870 +statement لما نعود بقيم معينة هدول القيم من وين + +151 +00:11:09,870 --> 00:11:11,970 +بدنا ناخدهم هذه المجموعة اللي بدنا ناخدها القيم + +152 +00:11:11,970 --> 00:11:14,650 +بتسميها الـ universe طبعا كل open sentence اللي هي + +153 +00:11:14,650 --> 00:11:17,310 +universe ممكن يكون مختلف عن الآخر فهو مرتبط بالـ + +154 +00:11:17,310 --> 00:11:19,830 +open sentence فانا عندي open sentence اللي هي + +155 +00:11:19,830 --> 00:11:23,470 +مجال من وين باخد فيه القيم فهذا ما يُعرف بالـ + +156 +00:11:23,470 --> 00:11:30,540 +universe أي سؤال اه طبعا ملاحظة عامة وده يمكن كتير + +157 +00:11:30,540 --> 00:11:33,940 +موجود في الرياضيات أن أحيانا ممكن يكون الـ domain + +158 +00:11:33,940 --> 00:11:37,240 +معروف من السياق وأحيانا بيكون طبعا الشيء مُعطى + +159 +00:11:37,240 --> 00:11:40,960 +بشكل صريح طبعا إذا أُعطى بشكل صريح انتهت العملية + +160 +00:11:40,960 --> 00:11:44,380 +ليش؟ هي أدمع النص إذا ما أُعطيش بنشوف السياق ع إيش + +161 +00:11:44,380 --> 00:11:47,660 +بيدل إيش اللي ليش مجال الدراسة تبعتنا بنشوف السياق + +162 +00:11:47,660 --> 00:11:50,240 +وين إحنا بنشتغل؟ هل إحنا بنشتغل calculus A أو B + +163 +00:11:50,240 --> 00:11:53,600 +فعنا real numbers هل المساق هو تحليل مُركّب في + +164 +00:11:53,600 --> 00:11:57,680 +أعداد مُركّبة هو يعني وها كده للمجال بعدين فبقول لي + +165 +00:11:57,680 --> 00:12:00,960 +in many cases the universe will be understood from + +166 +00:12:00,960 --> 00:12:03,900 +the context اه في كتير من الأحيان هنفهم الـ + +167 +00:12:03,900 --> 00:12:06,760 +universe من السياق اه لكن بيقول لي في بعض الأحيان + +168 +00:12:06,760 --> 00:12:09,460 +however there are times when it is it must be + +169 +00:12:09,460 --> 00:12:12,220 +specified explicitly في بعض الأحيان بتكون الموضوع + +170 +00:12:12,220 --> 00:12:15,560 +حساس بتدينايا بشكل صريح وإلا عشان ما يصيرش أي لبس + +171 +00:12:15,560 --> 00:12:20,890 +أو يصير أي مشاكل بتدينايا بشكل صريح فالكون له دور + +172 +00:12:20,890 --> 00:12:24,590 +أساسي في التعامل مع الـ open sentences كما سنرى في + +173 +00:12:24,590 --> 00:12:30,800 +الأمثلة أو في دراستنا القادمة في عندنا هنا موضوع + +174 +00:12:30,800 --> 00:12:34,680 +آخر أو مصطلح آخر بتعلق بالـ open sentence فأول + +175 +00:12:34,680 --> 00:12:39,500 +مصطلح هو المجال أو الـ universe الآن هيتحدث عن حاجة + +176 +00:12:39,500 --> 00:12:43,760 +اسمها truth set طبعا الـ open sentence مش statement + +177 +00:12:43,760 --> 00:12:48,540 +لكن بيصير statement إذا عوضنا فيها بقيم اللي بعوض + +178 +00:12:48,540 --> 00:12:54,100 +فيها وبتديني true بسميها مجموعة الصدق فانا ألجتش + +179 +00:12:54,100 --> 00:12:58,110 +فيه عندنا طبعا أولا في عيننا قيمة صدق في عيننا + +180 +00:12:58,110 --> 00:13:02,290 +truth value قيمة الصدق وفي عيننا truth table جدول + +181 +00:13:02,290 --> 00:13:05,370 +الصدق وفي عيننا اليوم مصطلح تالت truth set مجموعة + +182 +00:13:05,370 --> 00:13:09,130 +الصدق، تمام؟ أنا في عين دي open sentence، إذا V + +183 +00:13:09,130 --> 00:13:13,450 +variables، بدي أعوض عنهم، لما أعوض أي قيمة، من وين + +184 +00:13:13,450 --> 00:13:16,270 +بيعود؟ من الـ universe، من المجال، طب إذا عوضت + +185 +00:13:16,270 --> 00:13:20,050 +ودتني true، بتكون اديش مجموعة الصدق، truth set، + +186 +00:13:20,050 --> 00:13:24,520 +إذا كل القيم المسموح عوض فيها هي الـ universe القيم + +187 +00:13:24,520 --> 00:13:28,400 +اللي بعوض فيها و تديني true هي truth set مجموعة + +188 +00:13:28,400 --> 00:13:33,860 +الصدر واضح الفرق بين الـ universe و truth set فكل + +189 +00:13:33,860 --> 00:13:36,560 +truth set هي مجموعة جزئية من الـ universe والعكس + +190 +00:13:36,560 --> 00:13:41,140 +غير صحيح فبقول لي the collection of objects جميع + +191 +00:13:41,140 --> 00:13:43,460 +العناصر from the universe شايف يام لأ أخد من الـ + +192 +00:13:43,460 --> 00:13:47,680 +universe لأن هو المجال المسموح أخد منه بقاش كمان + +193 +00:13:47,680 --> 00:13:50,940 +that may be substituted to make an open sentence a + +194 +00:13:50,940 --> 00:13:54,760 +true statement a true statement is called the + +195 +00:13:54,760 --> 00:13:59,580 +truth set of the sentence فهو متعلق بكل sentence + +196 +00:13:59,580 --> 00:14:03,500 +إلها truth set خليني أشوف بعض الأمثلة + +197 +00:14:08,410 --> 00:14:12,930 +خلّينا نشوف بعض الأمثلة عشان نثبت هذا المفهوم أو + +198 +00:14:12,930 --> 00:14:17,950 +نقربه بشكل عملي فهي في عندنا مثال في عندنا open + +199 +00:14:17,950 --> 00:14:22,510 +sentence P of X، X تربيع أقل من خمسة عبارة عن + +200 +00:14:22,510 --> 00:14:25,850 +متباينة فهي open sentence ولا statement هذه؟ true + +201 +00:14:25,850 --> 00:14:32,210 +ولا false؟ هو الـ X فهي open sentence في هذا المثال + +202 +00:14:32,210 --> 00:14:36,010 +هنوضح دور الـ universe في انه إيه بيحدد الـ truth + +203 +00:14:36,010 --> 00:14:39,490 +set ممكن تختلف لإنه لما بتحل هذه مثلا على الريال + +204 +00:14:39,490 --> 00:14:41,890 +غير لما بتحلي على أعداد الصحيحة غير لما بتحلي على + +205 +00:14:41,890 --> 00:14:44,790 +أعداد الطبيعية وهكذا فالـ universe مهم جدا لأن ويش + +206 +00:14:44,790 --> 00:14:48,130 +جال ليه؟ هي مجموعة اللي باخد من الـ universe بعوضه + +207 +00:14:48,130 --> 00:14:51,620 +بالدين الـ true فتغير الـ universe ممكن يغير مجموعة + +208 +00:14:51,620 --> 00:14:55,320 +الصدق .. مجموعة الصدق فبقول لي the truth set of + +209 +00:14:55,320 --> 00:14:59,140 +this sentence depends on the universe we choose + +210 +00:14:59,140 --> 00:15:03,480 +تعتمد على المجال اللي بنختاره .. على المجال اللي + +211 +00:15:03,480 --> 00:15:09,440 +بنختاره على سبيل المثال لو اخترنا الـ universe يكون + +212 +00:15:09,440 --> 00:15:12,580 +مجموعة الأعداد الطبيعية يعني الأعداد الصحيحة + +213 +00:15:12,580 --> 00:15:16,060 +الموجبة أنا يعني واحد اثنين ثلاثة وهكذا بتكون + +214 +00:15:16,060 --> 00:15:19,540 +اللي هو مجموعة الصدق الشيء الواحد والاثنين لإن + +215 +00:15:19,540 --> 00:15:22,980 +واحد تربيع واحد أقل من خمسة نعم اثنين تربيع أربع + +216 +00:15:22,980 --> 00:15:26,140 +أقل من خمسة نعم طب ثلاثة تربيع لأ أربع تربيع لأ + +217 +00:15:26,140 --> 00:15:29,440 +فالاعداد الصحيحة الموجبة اللي مربحها أصغر من خمسة + +218 +00:15:29,440 --> 00:15:32,080 +في الشيء اثنين الواحد والاثنين فهذه مجموعة الصدق + +219 +00:15:32,080 --> 00:15:34,940 +بسميها مجموعة الصدق بس إيه اسم لما يكون الـ universe + +220 +00:15:34,940 --> 00:15:38,380 +هو الـ natural number الأعداد الصحية على الموجة + +221 +00:15:38,380 --> 00:15:43,220 +طبعا فهذا مثال لو غيرنا الـ universe أخدنا الأعداد + +222 +00:15:43,220 --> 00:15:47,460 +الحقيقية كلها بيصير مجموعة الصدق الـ open interval + +223 +00:15:47,460 --> 00:15:52,210 +من سالب جذر الخمسة إلى جذر الخمسة تصير مايلة نهائية + +224 +00:15:52,210 --> 00:15:56,510 +من القيم جميع الأعداد الحقيقية المحصورة بين سالب + +225 +00:15:56,510 --> 00:16:00,570 +جذر الخمسة وجذر الخمسة فإذا الـ universe بيلعب دور + +226 +00:16:00,570 --> 00:16:04,050 +أساسي في تحديد مجموعة الصدق وهذا مفهوم مجموعة + +227 +00:16:04,050 --> 00:16:08,370 +الصدق لأنه لما نعوض أي عدد حقيقي بين سالب جذر + +228 +00:16:08,370 --> 00:16:10,930 +الخمسة وبين موجب جذر الخمسة عوضي بيحقق إيش؟ + +229 +00:16:10,930 --> 00:16:13,330 +بيخليها true بيخليها true اللي هو مجموعة الحل + +230 +00:16:13,330 --> 00:16:16,490 +تقريبا نفس المعنى مجموعة الحل بمعنى آخر لكن إحنا + +231 +00:16:16,490 --> 00:16:19,590 +بنأخذها من ماشي من زاوية أخرى اللي هي قيمة الصدق + +232 +00:16:19,590 --> 00:16:23,090 +أو مجموعة الصدق اللي بتخلي الـ statement true ما هو + +233 +00:16:23,090 --> 00:16:25,610 +الحل هو القيم اللي بتحقق المعادلة اللي هي بتخليها + +234 +00:16:25,610 --> 00:16:29,930 +true نفس المعنى أي سؤال فواضح فهنا دور الـ universe + +235 +00:16:29,930 --> 00:16:33,270 +أساسي في تحديد اللي هو مجموعة الصدق + +236 +00:16:36,080 --> 00:16:40,180 +كمان مصطلح آخر طبعا إحنا الـ statement ما نعرف + +237 +00:16:40,180 --> 00:16:43,120 +اكتشف إيه إيه بتكون متكافئين equivalent إذا كانوا + +238 +00:16:43,120 --> 00:16:46,120 +true مع بعض أو false مع بعض بجميع الاحتمالات + +239 +00:16:46,120 --> 00:16:49,580 +المنطقية الممكن طب عندنا open sentences هل ممكن + +240 +00:16:49,580 --> 00:16:53,380 +يكونوا equivalent في ممكن أقارنهم نعم اه فبقول + +241 +00:16:53,380 --> 00:16:57,040 +equivalent open sentences ممكن يتحدث عن open + +242 +00:16:57,040 --> 00:17:01,420 +sentences متكافئين منطقياً إيش التعريف؟ بقول لي with + +243 +00:17:01,420 --> 00:17:07,040 +a universe specified بما أن الـ universe بيلعب دور + +244 +00:17:07,040 --> 00:17:11,300 +أساسي في مجموعة الصدق يعني وبالتالي هيعلق ع دور + +245 +00:17:11,300 --> 00:17:15,200 +أساسي في قيمة الصدق تبعات الـ statement واحنا طبعا + +246 +00:17:15,200 --> 00:17:17,960 +بنعرف انه التكافؤ إيش؟ true مع بعض أو false مع بعض + +247 +00:17:17,960 --> 00:17:22,220 +فلازم أول خطوة أحدد مين اللي هو الـ universe لازم + +248 +00:17:22,220 --> 00:17:25,340 +أقول إيش الـ universe محدد with a universe + +249 +00:17:25,340 --> 00:17:30,860 +specified Two open sentences B of X and Q of X are + +250 +00:17:30,860 --> 00:17:34,900 +equivalent وقت إيش بيكونوا متكافئتين if they have + +251 +00:17:34,900 --> 00:17:39,840 +the same truth set إذا كان لهم نفس مجموعات الصدق + +252 +00:17:39,840 --> 00:17:43,460 +نفس مجموعة الصدق فده هو المعيار فانا عندي open + +253 +00:17:43,460 --> 00:17:46,760 +sentences open sentences بجيب مجموعة الصدق تعتمد + +254 +00:17:46,760 --> 00:17:49,000 +على مين؟ على الـ universe عشان انك مهم بجيب مجموعة + +255 +00:17:49,000 --> 00:17:51,840 +الصدق تعتمد على الـ universe إذا طلعوا نفس المجموعة + +256 +00:17:51,840 --> 00:17:55,740 +بتكونوا إيش؟ equivalent sentences open sentences + +257 +00:17:56,690 --> 00:18:01,770 +خلّيني أشوف مثال اه فطبعا هنا عشان أدرس الـ + +258 +00:18:01,770 --> 00:18:04,550 +equivalent أو التكافؤ لل open sentences أول + +259 +00:18:04,550 --> 00:18:07,770 +خطوة لازم أعرفه الـ universe أُحدد الـ universe بقول + +260 +00:18:07,770 --> 00:18:11,230 +لي let the universe be the set A مجموعة الأعداد + +261 +00:18:11,230 --> 00:18:17,650 +الحقيقية مجموعة الأعداد الحقيقية اه فبقول لي الـ + +262 +00:18:17,650 --> 00:18:21,250 +sentence هي في ND2 open sentences هذا هذا مثال + +263 +00:18:22,310 --> 00:18:26,630 +وهي A طبعا عندنا الـ universe بيساوي R فعندنا الـ B + +264 +00:18:26,630 --> 00:18:33,870 +of X هي 4X زائد 2 تساوي 10 وعندك U of X X تساوي 2 + +265 +00:18:33,870 --> 00:18:38,470 +فبقولي هدولة open sentences على الـ R متكافئين ليش؟ + +266 +00:18:38,470 --> 00:18:43,400 +لأن main truth set هنا الـ truth set مين اللي + +267 +00:18:43,400 --> 00:18:47,180 +بتخليها؟ ما يوجد إلا اثنين وهنا طبعا أوضح الـ truth + +268 +00:18:47,180 --> 00:18:51,360 +set برضه اثنين فدول الـ two statements إثمهما + +269 +00:18:51,360 --> 00:18:55,980 +متكافئين فدول الـ two sentences متكافئين two open + +270 +00:18:55,980 --> 00:18:59,620 +sentences متكافئين لأن ما يوجد إلا قيمة واحدة + +271 +00:18:59,620 --> 00:19:02,340 +الاثنين اللي بتخليهم اثنين true غير هيك لأ فالهم + +272 +00:19:02,340 --> 00:19:04,220 +نفس مجموعة الصفر تفضل + +273 +00:19:07,410 --> 00:19:10,910 +يعني؟ يعني أربع X تساوي ثمانية يعني X تساوي اثنين، + +274 +00:19:10,910 --> 00:19:21,710 +في حل آخر؟ أربع X تساوي عشر، تمام، اه، أي سؤال؟ + +275 +00:19:21,710 --> 00:19:27,790 +تمام، نشوف مثال آخر، اه، بيقول لي أول open + +276 +00:19:27,790 --> 00:19:32,590 +sentence هي X تربيعها تساوي أربع، والثانية برضه X + +277 +00:19:32,590 --> 00:19:37,470 +تساوي اثنين فبرضه بنشغل على الـ R فلو شفنا هنا الـ + +278 +00:19:37,470 --> 00:19:46,230 +truth set سالب اثنين واثنين لكن هنا الـ truth set بس + +279 +00:19:46,230 --> 00:19:51,530 +اثنين فهذا هدولة إثمهما غير متكافئين غير متكافئين + +280 +00:19:51,530 --> 00:19:55,710 +أي سؤال؟ طبعا لو غيرنا الـ universe خليناه الـ natural + +281 +00:19:55,710 --> 00:19:59,430 +number نصيبهما متكافئان فهدول على الـ R مش متكافئان + +282 +00:19:59,430 --> 00:20:03,990 +لكن على الأعداد الصحيحة الموجبة متكافئانالنسالي + +283 +00:20:03,990 --> 00:20:08,190 +ببطل موجود فواضح الـ universe اللي هو دور أساسي في + +284 +00:20:08,190 --> 00:20:11,510 +دراسة الـ open sentences ودراسة تكافؤ الـ open + +285 +00:20:11,510 --> 00:20:17,110 +sentences ودراسة الـ truth sets مجموعات الحل أي + +286 +00:20:17,110 --> 00:20:17,750 +سؤال + +287 +00:20:21,600 --> 00:20:28,280 +تمام فهذا تمهيد سريع عن الـ open sentences والآن + +288 +00:20:28,280 --> 00:20:32,000 +هندخل على الموضوع الرئيسي في هذا الموضوع فاحنا كنا + +289 +00:20:32,000 --> 00:20:35,920 +بالمقدمة عشان نوصل لمصطلح الرئيسي وهو التعامل مع for + +290 +00:20:35,920 --> 00:20:39,140 +all و there exist هدول الـ for all و there exist + +291 +00:20:39,140 --> 00:20:44,540 +بسموهم universal and existential quantifiers مكممات + +292 +00:20:44,540 --> 00:20:49,580 +الشمول والوجود مكممات الوجود والشمول universal + +293 +00:20:49,580 --> 00:20:52,340 +يعني شامل اللي هو بقى الكون كله existential + +294 +00:20:52,340 --> 00:20:56,380 +existence اللي هو existence اللي هو الوجود الوجود + +295 +00:20:56,380 --> 00:21:00,120 +فهدول مصطلحين مهمين وهو الهدف الرئيسي أن نتعامل + +296 +00:21:00,120 --> 00:21:03,180 +معاهم في هذا section دراسة هدول المصطلحين + +297 +00:21:03,180 --> 00:21:09,610 +الرئيسية فاحنا ذكرنا إن الـ open sentence عشان + +298 +00:21:09,610 --> 00:21:13,730 +أعملها statement بدي أبدل الـ variables بقيم معينة + +299 +00:21:13,730 --> 00:21:16,990 +بيصير statement هذه طريقة لكن هل هذه الطريقة + +300 +00:21:16,990 --> 00:21:20,890 +الوحيدة؟ لا في طريقة بديلة استخدام المكممات + +301 +00:21:20,890 --> 00:21:25,290 +فاستخدام المكممات هي طريقة بتخلي الـ open sentence + +302 +00:21:25,290 --> 00:21:29,690 +statement في عندنا مكممين رئيسيين مكمم الشمول اللي + +303 +00:21:29,690 --> 00:21:33,110 +هو for all ومكمم الوجود اللي هي there exists اللي + +304 +00:21:33,110 --> 00:21:39,310 +هي بعض أو يوجد فطبعا الهدف الرئيسي اللي نتعامل + +305 +00:21:39,310 --> 00:21:41,750 +معها في المكممات يا جماعة هي الـ open sentence عشان + +306 +00:21:41,750 --> 00:21:44,570 +هيك احنا مهدنا عرفنا الـ open sentence وبعض + +307 +00:21:44,570 --> 00:21:48,810 +المصطلحات المتعلقة بالـ open sentences فبقول let P + +308 +00:21:48,810 --> 00:21:52,510 +of X be an open sentence هيعرف اللي هو المكممين + +309 +00:21:52,510 --> 00:21:57,170 +الرئيسيين الأول الأول فيه رمز له الرمز هو capital A + +310 +00:21:57,170 --> 00:22:00,490 +مقلوبة capital A مقلوبة الفوق تحته واللي تحت فوق + +311 +00:22:00,490 --> 00:22:04,190 +فده الرمز طب كيف بنقراها؟ for all بنقراها فأول شيء + +312 +00:22:04,190 --> 00:22:07,950 +إيش بيسموه؟ هذا بيسموه universal quantifier مكمم + +313 +00:22:07,950 --> 00:22:11,450 +الشمول طبعا capital A جاية من all بس مقلوبة عشان + +314 +00:22:11,450 --> 00:22:14,950 +رمز خاص ومصطلح معروف زي ما بنعرف مثلا الـ plus + +315 +00:22:14,950 --> 00:22:19,310 +للجمع الـ R الـ bold هذه لمين؟ للـ real numbers فده + +316 +00:22:19,310 --> 00:22:25,010 +رمز معروف ومحدد بدناش إيش إنه يتخربط مع إشي ثاني + +317 +00:22:25,010 --> 00:22:28,630 +يصير في عندنا لبس مع إشي ثاني فماخدش capital a + +318 +00:22:28,630 --> 00:22:31,670 +لحظة لأنه تُستخدم كثير أخد capital A وقلبوها فهذا + +319 +00:22:31,670 --> 00:22:35,250 +مصطلح معروف هذا رمز معروف للهو إيش للـ for all اللي + +320 +00:22:35,250 --> 00:22:39,490 +هو إيش اللي هو بكمم الشمول من كلمة all يعني الجميع + +321 +00:22:39,490 --> 00:22:44,170 +الكل فبتحدث عن كمية كل الكمية فهي كمية أه فإذا هذا + +322 +00:22:44,170 --> 00:22:48,390 +إيش universal quantifier أه الآن انتبهوا the + +323 +00:22:48,390 --> 00:22:53,130 +statement open sentence مع مكمّم أصبحت statement + +324 +00:22:53,130 --> 00:22:56,170 +open sentence مع مكمّم مش جال statement صارت + +325 +00:22:56,170 --> 00:22:59,270 +statement إذا هذه الـ statement عشان أدرسها زي ما + +326 +00:22:59,270 --> 00:23:01,970 +كنا بندرس الـ and و الـ or بدنا نشوف وقتاش true و + +327 +00:23:01,970 --> 00:23:04,970 +وقتاش false آه كان عندي two statement نخلت عليهم + +328 +00:23:04,970 --> 00:23:07,890 +الـ and بدي أعرف وقتاش بقول عنها true إذا كانت true + +329 +00:23:07,890 --> 00:23:11,310 +و غيرك بكون false نفس القضية عندي open sentence + +330 +00:23:11,310 --> 00:23:14,970 +دخلت عليها المكمّم for all أصبحت statement بدي + +331 +00:23:14,970 --> 00:23:17,830 +أعرفها وقتاش بتكون true و وقتاش بتكون false فبقول + +332 +00:23:17,830 --> 00:23:22,740 +ليه؟ for all x b of x كيف تقرأها؟ هدي زي ما قرأنا + +333 +00:23:22,740 --> 00:23:26,400 +for all x b of x نقرأها بيادة شكل هذا رمز وهذه + +334 +00:23:26,400 --> 00:23:31,300 +قراته is it true when b of x بتكون هذه الـ + +335 +00:23:31,300 --> 00:23:34,600 +statement اللي فيها المكمم الـ true لما تكون الـ + +336 +00:23:34,600 --> 00:23:38,680 +open sentence الـ true لجميع عناصر الـ universe + +337 +00:23:38,680 --> 00:23:41,380 +لجميع عناصر الـ universe عشان أنا أشوف قولت تشمل + +338 +00:23:41,380 --> 00:23:46,300 +جميع عناصر الـ universe بمعنى آخر لما تكون الـ open + +339 +00:23:46,300 --> 00:23:49,820 +sentence مجموعة الصدق تبعتها تساوي الـ universe + +340 +00:23:49,820 --> 00:23:54,080 +مجموعة الصدق تبعتها تساوي الـ universe for all x in + +341 +00:23:54,080 --> 00:23:57,520 +the universe غير هيك بتكون false يعني لو في واحدة + +342 +00:23:57,520 --> 00:24:02,700 +فيهم قيمة من قيم الـ Universe ما خلتتش true بتكون + +343 +00:24:02,700 --> 00:24:06,940 +false لأنه شمول لما أقول كل الـ real numbers مثلا + +344 +00:24:06,940 --> 00:24:10,740 +مربعها أكبر أو يساوي zero في عدد حقيقي مربعه + +345 +00:24:10,740 --> 00:24:15,820 +negative لا بيدل المعنى شمول كله قاعدة شاملة تنطبق + +346 +00:24:15,820 --> 00:24:20,720 +على الجميع فهذا المكمم الأول واضح؟ طبعا هنشوف + +347 +00:24:20,720 --> 00:24:25,400 +أمثلة متعددة عشان ننعمق في هذا الفهم الرمز الثاني أو + +348 +00:24:25,400 --> 00:24:30,200 +المكمم الثاني capital E مقلوبة يمين يسار نفس الشيء + +349 +00:24:30,200 --> 00:24:34,020 +نفس المبدأ لماذا؟ قلبوا الـA طبعا الـA لا يمكن أن + +350 +00:24:34,020 --> 00:24:36,980 +تتغير لأنها يمين يسار مظبوط لأنها سيمتري فقلبوها + +351 +00:24:36,980 --> 00:24:41,580 +فوق تحت الـA برضه فوق تحت سيمتري قلبوها يمين يسار + +352 +00:24:41,860 --> 00:24:46,280 +فطبعا هذا إيش يسمونه existential quantifier مكمم + +353 +00:24:46,280 --> 00:24:49,460 +الوجود من existence طبعا والـ E من exist والـ E من + +354 +00:24:49,460 --> 00:24:54,460 +exist واضح تمام ناسم القضية the statement open + +355 +00:24:54,460 --> 00:24:58,260 +sentence مع مكمم الوجود أصبحت statement كيف + +356 +00:24:58,260 --> 00:25:02,680 +بنقراها there exist x such that b of x there exist + +357 +00:25:02,680 --> 00:25:06,960 +x such that b of x هذه الـ statement وقت إيش بتكون + +358 +00:25:06,960 --> 00:25:11,280 +true؟ بتقول it is true when there exists at least + +359 +00:25:11,280 --> 00:25:15,920 +one x in the universe that makes such that p of x + +360 +00:25:15,920 --> 00:25:21,420 +is true هنا الوجود موجود، موجود طلاب في الجامعة + +361 +00:25:21,420 --> 00:25:23,700 +الإسلامية، لو لجيت طالب يكون الـ statement صحيحة، + +362 +00:25:23,700 --> 00:25:27,440 +تمام؟ موجود، موجود، بيهمنيش قد إيش موجود، المهم إن + +363 +00:25:27,440 --> 00:25:31,300 +هو موجود، فعلى أقل واحد أو أكثر أو أقل مش مهم .. لا + +364 +00:25:31,300 --> 00:25:35,140 +مافيش أقل .. أقل شيء واحد فبتقول الـ B of X تكون + +365 +00:25:35,140 --> 00:25:39,220 +true أقل مرة واحدة طيب لما تكون for all دائماً + +366 +00:25:39,220 --> 00:25:42,880 +true لكل الـ universe .. لكل الـ universe واضح؟ أه + +367 +00:25:42,880 --> 00:25:46,260 +فين هذا الـ exist وهناك اللي هو إيش الـ for all أو + +368 +00:25:46,260 --> 00:25:51,320 +الشمول نشوف بعض الأمثلة عشان نبدأ نتعود على + +369 +00:25:51,320 --> 00:25:54,240 +التعريفين determine whether the following + +370 +00:25:54,240 --> 00:25:57,060 +statements are true or false بنتحدد كل statement + +371 +00:25:57,060 --> 00:26:01,640 +من الـ statements التالية هل هي true and false طبعا + +372 +00:26:01,640 --> 00:26:05,560 +هنا أرجو وإحنا بندرس وإحنا بنحل دائماً نركز اه + +373 +00:26:05,560 --> 00:26:08,020 +ماكنتش بقول sentence, open sentence, statement + +374 +00:26:08,020 --> 00:26:12,590 +الكلام دقيق لأن كل مصطلح له معنى مختلف والـ get + +375 +00:26:12,590 --> 00:26:15,950 +open sentence لما أقوم بيصير statement لما أحط محق + +376 +00:26:15,950 --> 00:26:18,690 +quantifier من الاثنين بيصير statement فننتبه + +377 +00:26:18,690 --> 00:26:22,690 +للمصطلحات مهمة جداً نتعود على هذه الأمور عشان هذه + +378 +00:26:22,690 --> 00:26:26,950 +في لب الموضوع تبعنا ونتعلم الدقة لأنه بيأثر على + +379 +00:26:26,950 --> 00:26:32,050 +العمل تبعنا نبدأ بمثال بسيط ناخد Universe صغير + +380 +00:26:32,050 --> 00:26:36,730 +شوية من أربع عناصر U 1 2 3 4 بيه the domain of + +381 +00:26:36,730 --> 00:26:40,400 +discourse يعني الـ universe مجال الدراسة خلّينا نحل + +382 +00:26:40,400 --> 00:26:46,920 +هنا أو نساعد نعمل هامش تمام فهي الـ universe أربع + +383 +00:26:46,920 --> 00:26:51,060 +مجموعات بقول اللي بدنا نشوف true ولا false أول + +384 +00:26:51,060 --> 00:26:56,680 +statement عندنا for all x إيش؟ x زائد 2 تنتمي لـ U + +385 +00:26:56,680 --> 00:27:01,400 +خلّيني أحدد مين الـ open sentence هنا؟ x زائد 2 + +386 +00:27:01,400 --> 00:27:06,480 +تنتمي لـ U أه هذه open sentence هيك لكن مع for all + +387 +00:27:06,480 --> 00:27:09,000 +صارت statement، هذه open، ليش؟ لما أعود على X + +388 +00:27:09,000 --> 00:27:11,400 +القيمة، بعرف true ولا false، هي عناصر الـU معروفة + +389 +00:27:11,400 --> 00:27:14,280 +ولا لأ؟ فلما أعرف مثلا الـ4 تنتمي، الخمسة لا + +390 +00:27:14,280 --> 00:27:16,980 +تنتمي، ولا لأ؟ أه، فإذا أنا عايش، هدي عايش، open + +391 +00:27:16,980 --> 00:27:20,400 +sentence، مع تعويت، بصير statement، true أو false، + +392 +00:27:20,400 --> 00:27:24,540 +فلما يقول لي for all X، X زائد 2 تنتمي للـU، إيش + +393 +00:27:24,540 --> 00:27:28,180 +بدي أعمل؟ المفروض أفحص، هال gate، نشوف B of 1 + +394 +00:27:28,180 --> 00:27:31,480 +عبارة عن واحد زائد اثنين تساوي ثلاثة تنتمي ولا + +395 +00:27:31,480 --> 00:27:37,650 +تنتمي؟ true طيب، B of 2 تساوي أربعة تنتمي ولا تنتمي + +396 +00:27:37,650 --> 00:27:43,910 +تنتمي تنتمي + +397 +00:27:43,910 --> 00:27:48,040 +تنتمي تنتمي تنتمي تنتمي تنتمي تنتمي تنتمي تنتمي إذا + +398 +00:27:48,040 --> 00:27:50,740 +.. إذا .. إذا الـ statement كلها إيش؟ false لأن + +399 +00:27:50,740 --> 00:27:53,640 +لازم الكل .. آه وماكنتش بقول على هذه الـ statement + +400 +00:27:53,640 --> 00:27:58,480 +true لما تكون B of one true وB of اثنين true وB + +401 +00:27:58,480 --> 00:28:02,220 +of three true وB of four true شمول كله بيكون صح + +402 +00:28:02,220 --> 00:28:05,940 +إذا واحدة غلط انتهت ببطل true واضح؟ إيش معناه + +403 +00:28:05,940 --> 00:28:09,400 +شمول؟ لما لاجيت واحدة false بوقف لما لاجي واحدة + +404 +00:28:09,400 --> 00:28:13,850 +false بوقف فإذا هذه إيش مالها؟ false فواضح إيش + +405 +00:28:13,850 --> 00:28:17,310 +معناه for all وقت إيش بتكون true لازم الكل شمول + +406 +00:28:17,310 --> 00:28:22,430 +مافيش استثناء آه لاجيت واحدة خلاص ما نفعش أقول آه الكل + +407 +00:28:22,430 --> 00:28:26,050 +قاعدة استثناء بيظبطش أنه في قليل استثناء لا ولا + +408 +00:28:26,050 --> 00:28:30,650 +استثناء شمول كله بدي يكون true واضح هذا المثال + +409 +00:28:30,650 --> 00:28:33,650 +الأول خلينا نشوف كمان مثال + +410 +00:28:36,290 --> 00:28:41,650 +There exists x بحيث x زائد واحد تساوي أربعة فهنا .. + +411 +00:28:41,650 --> 00:28:45,950 +خلّينا نشوف برضه نحاول نحلل P of x x زائد واحد + +412 +00:28:45,950 --> 00:28:49,570 +تساوي أربعة واكتشف تكون true إذا كده تلاقي قيمة من + +413 +00:28:49,570 --> 00:28:52,650 +قيم الـ U تخليها صح في قيمة لما تجمعها للواحد + +414 +00:28:52,650 --> 00:28:56,610 +بتساوي أربعة نعم ثلاثة بما أن P of the three is + +415 +00:28:56,610 --> 00:28:59,610 +true انتهى لأن عبارة عن مين ثلاثة زائد واحد تساوي + +416 +00:28:59,610 --> 00:29:03,630 +أربعة true إذا هذه true خلاص لاجينا قيمة انتهى مرة + +417 +00:29:03,630 --> 00:29:07,710 +واحدة هل يوجد عدد لما أضيف الواحد بيساوي أربعة نعم + +418 +00:29:07,710 --> 00:29:11,830 +يوجد على كم واحد موجود بيهمنيش exist موجود وبس + +419 +00:29:11,830 --> 00:29:15,810 +ماجليش اثنين ثلاثة اثنين موجود يعني على الأقل واحد + +420 +00:29:15,810 --> 00:29:20,090 +بيكفي واضح مدى .. ضروري أفحص الباقي لا لكن في + +421 +00:29:20,090 --> 00:29:23,050 +الشمول لازم أفحص الجميع في الـ exist اديني مثال + +422 +00:29:23,050 --> 00:29:26,810 +واحد اديني واحد يخليها true بيكفي يخليها true + +423 +00:29:26,810 --> 00:29:32,820 +بيكفي هذا معناته التعريف بأبسط صورة خلينا نشوف + +424 +00:29:32,820 --> 00:29:38,380 +مثال أصعب شوية نكبر المجموعة ناخد الـ domain كل الـ + +425 +00:29:38,380 --> 00:29:41,680 +real numbers مال نهاية من العناصر؟ مال نهاية من + +426 +00:29:41,680 --> 00:29:44,660 +العناصر؟ كيف بدنا نشتغل؟ هل بنقدر نشتغل بالبساطة + +427 +00:29:44,660 --> 00:29:48,860 +هذه؟ طبعًا لا لكن شوية معلومات نقدر نشتغل لإن + +428 +00:29:48,860 --> 00:29:51,660 +ما أقدرش أعوض الكل في هذه الحالة زي المثال الأول + +429 +00:29:51,660 --> 00:30:00,510 +نشوف نقدر نحكم عليها true ولا false في أدابي أول + +430 +00:30:00,510 --> 00:30:05,330 +واحد there exists X X أكبر أو تساوي سالب واحد + +431 +00:30:05,330 --> 00:30:10,290 +بمعنى يوجد عدد حقيقي أكبر أو يساوي سالب واحد نعم + +432 +00:30:10,290 --> 00:30:14,030 +ايش نديله؟ نديله مثال نديله مثال ايش هي الـ zero + +433 +00:30:14,030 --> 00:30:18,870 +لإيش؟ الـ zero أكبر أو تساوي سالب واحد فهنا عندنا أو + +434 +00:30:18,870 --> 00:30:22,550 +سالب واحد P of X X أكثر أو تساوي سالب واحد فـ P of + +435 +00:30:22,550 --> 00:30:27,970 +سالب واحد نترول خلاص يزرناها نترول خلاص يكفي موجود + +436 +00:30:27,970 --> 00:30:31,610 +ولا مش موجود؟ موجود هتسالب واحد عدد حقيقي و يخلي + +437 +00:30:31,610 --> 00:30:37,270 +الـ P of X true انتهى تمام فالـ exist بدنا بس مثال + +438 +00:30:37,270 --> 00:30:43,270 +بدنا واحد يخلّيها true نشوف اللي بعدها X أكبر أو + +439 +00:30:43,270 --> 00:30:48,970 +تساوي خمسة دائمًا؟ طبعًا لا، ليش؟ لأن P of أربعة + +440 +00:30:48,970 --> 00:30:54,710 +false، آه، ما ينفعش، في استثناء، مع الـ for all بدور + +441 +00:30:54,710 --> 00:30:57,510 +على استثناء، إذا ما فيش استثناء هي صحيحة، إذا لاقيت + +442 +00:30:57,510 --> 00:31:02,090 +استثناء بتكون false، فدي false، لأنه لازم يكون + +443 +00:31:02,090 --> 00:31:04,610 +الكل، هل جميع الأعداد الحقيقية أكبر تساوي خمسة؟ + +444 +00:31:04,610 --> 00:31:09,650 +طبعًا لا، فهيك ممكن نترجمها مثال آخر، ربما حكيناها + +445 +00:31:09,650 --> 00:31:14,290 +قبل قليل أو بشكل مختلف For all X، طبعًا X ايه؟ يعني + +446 +00:31:14,290 --> 00:31:17,350 +كل الـ Real Numbers، لأنه برجع لمين؟ للكون، مطلق + +447 +00:31:17,350 --> 00:31:19,870 +الـ X أكبر يساوي Zero، True، هذه من خواص العداد + +448 +00:31:19,870 --> 00:31:23,390 +الحقيقية، Calculus، فهذا مثال كيف نستخدم الـ For + +449 +00:31:23,390 --> 00:31:27,030 +All، كنا بنستخدمها، وهذا مثال استخدمها، فهذه True، + +450 +00:31:27,030 --> 00:31:33,590 +لأنه دائمًا قيمة المطلق عامة بتكون موجبة مثال آخر + +451 +00:31:33,590 --> 00:31:38,830 +there exists x بطلق الـ X أقل من 0 بقدر ألاقي عدد + +452 +00:31:38,830 --> 00:31:41,210 +حقيقي القيمة بتلقاه L و Negative؟ مستحيل فديو + +453 +00:31:41,210 --> 00:31:45,290 +false ما فيش ولا عدد حقيقي بيحقق هذا الكلام إذا مش + +454 +00:31:45,290 --> 00:31:53,310 +موجود مش موجود مطلقًا مثال آخر for all x لكل الـ + +455 +00:31:53,310 --> 00:31:58,210 +real numbers يعني الـ X يا positive يا negative آه + +456 +00:31:58,210 --> 00:32:01,830 +في صفر في صفر إذا هاذي ايش الكلام غير صحيح يعني + +457 +00:32:01,830 --> 00:32:05,890 +طبعًا كلهم بيحققوا فشلت صفر فشوفوا عشانها أشمول بس + +458 +00:32:05,890 --> 00:32:09,570 +أديته مثال مرة واحدة فشل إذا هاذي ايش false لأنه + +459 +00:32:09,570 --> 00:32:15,890 +هنا بالنسبة لهذا الأخير الـ P of X P of Zero is + +460 +00:32:15,890 --> 00:32:21,270 +false فهذه false فايه معناه شمول؟ لا يقبل أي + +461 +00:32:21,270 --> 00:32:25,270 +استثناء حتى استثناء واحد من مال نهاية مال نهاية + +462 +00:32:25,270 --> 00:32:29,070 +من الحلال كل الأعداد الحقيقية يا موجبة يا سالبة + +463 +00:32:29,070 --> 00:32:40,570 +إلا الـ 0 بيفتشل، بتلط الـ for all صحيح فدي false أي + +464 +00:32:40,570 --> 00:32:49,360 +سؤال؟ بنشوف بعض هنا المناحظة كيف بنترجم بالاستخدام + +465 +00:32:49,360 --> 00:32:51,600 +for all و they exist + +466 +00:32:54,710 --> 00:32:58,990 +بيقول لي بشكل عام إذا كان في عندنا sentence أو + +467 +00:32:58,990 --> 00:33:04,910 +statement الحقيقة in the form for all P of X are Q + +468 +00:33:04,910 --> 00:33:09,290 +of X لما يكون في عندي all two statements P of X are + +469 +00:33:09,290 --> 00:33:13,410 +Q of X فهذه ممكن نترجمها أحد الطرق طبعًا مش + +470 +00:33:13,410 --> 00:33:17,270 +الطريقة الوحيدة إن نترجمها for all لأن all if P + +471 +00:33:17,270 --> 00:33:21,690 +of X then Q of X فلما يكون في عندي statement على + +472 +00:33:21,690 --> 00:33:26,690 +صورة all P of X are Q of X ممكن نترجمها for all X + +473 +00:33:26,690 --> 00:33:32,890 +P of X then Q of X بالشكل المقابل مع some هذه + +474 +00:33:32,890 --> 00:33:36,630 +الشمول هذه الـ existence لكن جملة زي some P of X + +475 +00:33:36,630 --> 00:33:41,250 +are Q of X بنترجمها there exists X such that P of + +476 +00:33:41,250 --> 00:33:46,620 +X and Q of X فهنا اتقعدت طرق الترجمة كيف نترجم فعنا + +477 +00:33:46,620 --> 00:33:51,020 +في معقول استخدمنا if then و مع some استخدمنا and + +478 +00:33:51,020 --> 00:33:54,240 +كرابط كرابط المناسب هذه ليست الطريقة الوحيدة لكن + +479 +00:33:54,240 --> 00:33:59,940 +أحد الطرق المشهورة في الترجمة خليني أشوف تطبيق على + +480 +00:33:59,940 --> 00:34:01,400 +هذا الكلام + +481 +00:34:06,990 --> 00:34:11,490 +طبعًا وغيره يعني نطبق كيف نترجم باستخدام المكممات + +482 +00:34:11,490 --> 00:34:15,370 +for all who there exist translate the following + +483 +00:34:15,370 --> 00:34:19,850 +statements into logical language بنستخدم اللغة + +484 +00:34:19,850 --> 00:34:23,250 +المنطق أو رموز المنطق using a quantifier باستخدام + +485 +00:34:23,250 --> 00:34:28,230 +مكممة ضروري نستخدم المكممات and specify وحدد the + +486 +00:34:28,230 --> 00:34:31,450 +domain of discourse in each case وحدد الـ universe + +487 +00:34:31,450 --> 00:34:38,240 +أو مجال الدراسة في كل حالة هيا نبدأ بالمثال الأول A + +488 +00:34:38,240 --> 00:34:40,740 +example solution + +489 +00:34:42,780 --> 00:34:47,520 +All mathematics students جميع طلاب الرياضيات + +490 +00:34:47,520 --> 00:34:52,260 +study math 2450 اللي هي مبادئ الرياضيات جميع طلاب + +491 +00:34:52,260 --> 00:34:55,680 +الرياضيات بيدرسوا مبادئ الرياضيات هذا المصاد + +492 +00:34:55,680 --> 00:35:00,080 +أجباري على الجامعة تمام نعبر عنها آه فطبعًا عشان + +493 +00:35:00,080 --> 00:35:03,380 +أترجم صح الـ domain of discourse بيلعب دور أساسي + +494 +00:35:03,380 --> 00:35:07,460 +بيلعب دور أساسي فهل جيت خليني نختار الـ universe + +495 +00:35:07,460 --> 00:35:08,920 +أول شيء universe + +496 +00:35:12,260 --> 00:35:17,960 +ماذا تختار الكون؟ أو Mathematics student ماشي The + +497 +00:35:17,960 --> 00:35:27,600 +set of all mathematics students + +498 +00:35:27,600 --> 00:35:32,600 +جميع طلاب الرياضية تمام + +499 +00:35:33,640 --> 00:35:37,600 +إذا أنا أخدت all mathematic students هذه صارت هي + +500 +00:35:37,600 --> 00:35:41,740 +كلها for all عبرت عنها تم عندي بس جملة واحدة open + +501 +00:35:41,740 --> 00:35:46,540 +sentence P of X أشملها بقول لكل طالب رياضيات يعني + +502 +00:35:46,540 --> 00:35:49,420 +جميع .. يعني بنوع ما أنا .. كل طالب رياضة بيدرس + +503 +00:35:49,420 --> 00:35:54,860 +مبادئ رياضية هعبر عنها X studies لأن كل تعود بشكل + +504 +00:35:54,860 --> 00:36:01,520 +عام ليه variable studies math ألفين واربعمية وخمسين + +505 +00:36:01,520 --> 00:36:09,360 +فهذه الـ sentence الآن كيف نترجم الـ statement كيف + +506 +00:36:09,360 --> 00:36:13,500 +نترجم الـ statement هل هذه الـ statement على صورة + +507 +00:36:13,500 --> 00:36:18,800 +all P of X are Q of X؟ لا فهذه بتقول لي all P of X + +508 +00:36:18,800 --> 00:36:22,980 +.. all P of X و بس بس ما فيش فيها جملة تانية لأن + +509 +00:36:22,980 --> 00:36:26,540 +هناك ترجمناها لأن الجملة .. الخاصية الأولى عملناها + +510 +00:36:26,540 --> 00:36:29,400 +مع مين؟ مع الـ universe اللي هو ايه؟ اللي هو أنه + +511 +00:36:29,400 --> 00:36:32,540 +يكون طالب رياضيات في الـ universe و التاني يشتم + +512 +00:36:32,540 --> 00:36:35,180 +يدرس .. يدرس مبادئ رياضيات بس هاي الجملة تانية + +513 +00:36:35,180 --> 00:36:41,350 +فأنا على طول بترجمها for all X P of X بس طب يشوف إن + +514 +00:36:41,350 --> 00:36:45,870 +الترجمة الصحية أو لا كيف نقرأها for all x ايش يعني + +515 +00:36:45,870 --> 00:36:49,010 +in you يعني ايش معناه for all x كل طالب رياضيات + +516 +00:36:49,010 --> 00:36:52,310 +هتبسط بالترجمة لأن ايش for all x in the universe + +517 +00:36:52,310 --> 00:36:54,750 +هتبسط بالترجمة لأن ايش معناه ايش كيف تقرأ for all + +518 +00:36:54,750 --> 00:36:58,790 +x in the universe هيك معناها جميع طلبة الرياضيات + +519 +00:36:58,790 --> 00:37:03,290 +لأن هي الـ universe ايش ماله x studies لو ايش math + +520 +00:37:03,290 --> 00:37:07,770 +ألفين و أربعمية و خمسين لكن لو احنا غيرنا الـ + +521 +00:37:07,770 --> 00:37:11,910 +universe خلينا جميع الطلاب لو جيت أقراها جميع + +522 +00:37:11,910 --> 00:37:15,410 +الطلاب يدرسوا رياضة لا صار في كمان شرط إذا كان + +523 +00:37:15,410 --> 00:37:18,590 +طالب رياضيات فهو يدرس المبادئ بيصير مختلفة بيصير + +524 +00:37:18,590 --> 00:37:22,350 +بدا جملتين مختلفة فالآن مهم جدًا إن أنا ايش أترجم + +525 +00:37:22,350 --> 00:37:25,350 +بترجمة صحيحة فالـ universe بيلعب دور أساسي فانا كيف + +526 +00:37:25,350 --> 00:37:29,010 +قادر أقرأها for all x in the universe هيك معناها + +527 +00:37:29,010 --> 00:37:33,010 +for all x in the universe هذه الترجمة صحيحة لو + +528 +00:37:33,010 --> 00:37:39,100 +غيرنا ممكن نستخدم هيك if then كل طلبة مثلًا أو كل + +529 +00:37:39,100 --> 00:37:47,040 +الناس بيختلف الأمر نشوف مثال آخر some + +530 +00:37:47,040 --> 00:37:51,200 +Arabs are not Muslims بعض العرب غير مسلمين نفس + +531 +00:37:51,200 --> 00:37:54,780 +الطريقة فأول خطوة لازم أحدد الـ universe لأنه بيلعب + +532 +00:37:54,780 --> 00:38:00,420 +دور أساسي فيه الترجمة العرب مجموعة جميع العرب the + +533 +00:38:00,420 --> 00:38:03,960 +set of + +534 +00:38:03,960 --> 00:38:11,790 +all Arabs جميع اللي هو يعيش العرب تمام العملية قالت + +535 +00:38:11,790 --> 00:38:14,750 +اللي هو يعيش التحديد اللي هو جنس العرب هل جيت بدنا + +536 +00:38:14,750 --> 00:38:21,930 +الـ statement ايش تم؟ X is not Muslim ممكن نعمل + +537 +00:38:21,930 --> 00:38:26,210 +بهذه الصورة فالـ statement الآن فالـ statement + +538 +00:38:29,510 --> 00:38:34,470 +some يعني there exist بعض يوجد شوفنا نفس المعنى + +539 +00:38:34,470 --> 00:38:40,110 +بعض يوجد مش الكل مش الشمول there exist x وين in + +540 +00:38:40,110 --> 00:38:44,810 +the universe يوجد بعض وين العرب بعض العرب أشمالهم + +541 +00:38:44,810 --> 00:38:51,010 +غير مسلمين P of x بعض العرب غير مسلمين there exist + +542 +00:38:51,010 --> 00:38:52,630 +x P of x + +543 +00:38:56,810 --> 00:39:00,010 +بيصير not P of X there exists X not P of X صحيح + +544 +00:39:00,010 --> 00:39:03,810 +صحيح فالمهم جدًا احنا عشان هيك بنحدد احنا ايش بنرمز + +545 +00:39:03,810 --> 00:39:07,410 +الـ P of X زي ما مرت علينا قبلها آه فهنا الطريقة + +546 +00:39:07,410 --> 00:39:10,830 +لكن لو أنا اتبعت الـ universe مش كل العرب كل الناس + +547 +00:39:10,830 --> 00:39:14,650 +آه صحيح ما ينفعش أقول there exist بعض الناس غير + +548 +00:39:14,650 --> 00:39:19,510 +مسلمين لا بيصير ايش يوجد بعض الناس هم عرب و غير + +549 +00:39:19,510 --> 00:39:22,240 +مسلمين بيصير it was statement شايفينها بننظر على + +550 +00:39:22,240 --> 00:39:27,280 +الملاحظة فمهم جدًا إنه لما نترجم نقرأ there exists + +551 +00:39:27,280 --> 00:39:31,240 +x ايش معناته ايش x يعني؟ في الـ universe يوجد بعض + +552 +00:39:31,240 --> 00:39:34,920 +العرب خلاص ترجمة غير مسلمين الترجمة تولد ما ترجمتش + +553 +00:39:34,920 --> 00:39:40,540 +الترجمة فمهم إنه ايش نتأكد إنه الرمز بيعبر بشكل + +554 +00:39:40,540 --> 00:39:46,000 +صحيح مثال تالت + +555 +00:39:49,230 --> 00:39:54,610 +The equation X تربيع زائد X تساوي 5 has a solution + +556 +00:39:54,610 --> 00:39:58,990 +طبعًا هذا الـ statement ما فيش فيها ولا all ولا some + +557 +00:39:58,990 --> 00:40:04,370 +ولا أي مكمم ظاهرا لكن الحقيقة بتحتوي على مكمم + +558 +00:40:04,370 --> 00:40:05,950 +أشياء + +559 +00:40:07,960 --> 00:40:11,280 +آه إلا حل يعني يوجد لها حل هيك بترجمه مش بنحنا نقول + +560 +00:40:11,280 --> 00:40:15,820 +معادلة إلا حل يعني يوجد لها حل فهنا بننتبه هنا + +561 +00:40:15,820 --> 00:40:20,760 +الشاهد من المثال إن بعض الstatements تحتوي على + +562 +00:40:20,760 --> 00:40:24,920 +مكمن بس بشكل ضمني مش بشكل إيش صريح مش بشكل صريح + +563 +00:40:24,920 --> 00:40:31,220 +فهذه خلينا نترجمها مع بعض فنبدأ هذا C فنبدأ نحدد + +564 +00:40:31,220 --> 00:40:36,860 +الuniverse إيش الuniverse في رأيكوا؟ R مثلا real + +565 +00:40:36,860 --> 00:40:40,220 +numbers لأنه الأعداد هي اللي بتحقق المعادلة اه فال O + +566 +00:40:40,220 --> 00:40:45,920 +اللي هو إيش بنقوله هنا P of X إيش هي X ربيع زائد + +567 +00:40:45,920 --> 00:40:49,180 +X يساوي خمسة مش open sentence شفناها هذه هي P of + +568 +00:40:49,180 --> 00:40:53,160 +X اه فإذا الstatement statement + +569 +00:40:55,140 --> 00:41:02,720 +There exists x P of x يوجد قيمة لما أوضت متحقق + +570 +00:41:02,720 --> 00:41:05,900 +المعادلة يعني إيش يعني وجد حل هذا تعريف الحل ما هو + +571 +00:41:05,900 --> 00:41:09,180 +الحل هو اللي بيحقق المعادلة اللي بيخلي P of x + +572 +00:41:09,180 --> 00:41:14,730 +true يعني نفس المعنى أي سؤال ممكن ترجمها بهذا الشكل + +573 +00:41:14,730 --> 00:41:19,070 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من الصياغ واضح من + +585 +00:42:19,000 --> 00:42:23,640 +أي طالب رياضيات أي متخصص رياضية أنها تعني للكل + +586 +00:42:23,640 --> 00:42:27,140 +ولا إيش ما هي متطابقة في الفرض لو حطينا من ال + +587 +00:42:27,140 --> 00:42:31,500 +universe الnatural تختلف الترجمة بس بسبب يمكن + +588 +00:42:31,500 --> 00:42:35,320 +تختلف أنها صح أو لا أو أو أو أو false بس اه لكن + +589 +00:42:35,320 --> 00:42:36,140 +الترجمة مش هتختلف + +590 +00:42:38,960 --> 00:42:41,500 +أنا بأقولك يعني بس ممكن يختلف اللي.. اللي هو ال + +591 +00:42:41,500 --> 00:42:43,620 +state اللي هو الtrue أو الfalse لكن التاريخ ما + +592 +00:42:43,620 --> 00:42:46,940 +بتختلفش بدناش ندور على حل احنا.. ما هي الحلول مش + +593 +00:42:46,940 --> 00:42:55,860 +.. مش موضوع خليني أشوف كمان مثال all integers are + +594 +00:42:55,860 --> 00:43:00,710 +rational numbers هذا المثال نفس الشيء زي المثال + +595 +00:43:00,710 --> 00:43:04,230 +السابق الأولاني All Mathematics Students Study + +596 +00:43:04,230 --> 00:43:08,430 +Maths 1450 نفس المثال بس خليني أحله بالطريقة + +597 +00:43:08,430 --> 00:43:12,030 +الثانية نعمل what نعمل two open sentences ونعمل + +598 +00:43:12,030 --> 00:43:15,690 +if then طبعا ممكن هذا يتبع يتمد على أنه مين يحدد + +599 +00:43:15,690 --> 00:43:17,830 +الdomain of discourse فأنا بدي أحله الآن بالطريقة + +600 +00:43:17,830 --> 00:43:21,990 +الثانية بدي أحله بالطريقة الثانية فبدي أكبر ال + +601 +00:43:21,990 --> 00:43:26,270 +universe فخلي الuniverse مش الintegers خليه R + +602 +00:43:27,350 --> 00:43:31,110 +عشان بدي أعملها open sentence فلما جيت أقول له for + +603 +00:43:31,110 --> 00:43:34,430 +all x P of x مش هيظبط معه فأعمل two + +604 +00:43:34,430 --> 00:43:38,770 +statements الآن P of x إيش ده تكون؟ x is an + +605 +00:43:38,770 --> 00:43:44,050 +integer لسه بدي أعبر عنه وفيه أندي كمان Q of x + +606 +00:43:44,050 --> 00:43:51,790 +x is a rational number فالآن + +607 +00:43:51,790 --> 00:43:53,250 +لما نترجم الstatement + +608 +00:43:56,030 --> 00:44:01,550 +فإيش بتصير؟ أوكي for all for all 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b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/VmIP06NfAs4_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..066578e83ba63af8a109f108d1611d5a60fb45cf --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/VmIP06NfAs4_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 4649, "start": 20.81, "end": 46.49, "text": "بسم الله الرحمن الرحيم هنستكمل مع بعض الإرشادات و بعض الكلام العام عن البرهان الرياضي و كما ذكرنا في المحاضرة الماضية هذه الصفحات ممكن تكون دليل معنا و طبعا احنا هنتطرق لهذه الملاحظات في حينها مع الأمثلة و كيف نطبقها لكن جيد ان ناخد فكرة عامة و تكون هذه تمهيد و ان شاء الله لما نرجع نذكركوا فيها و نديكوا مثال كيف نطبقها بشكل عام", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8032, 1863, 14851, 24793, 1211, 20449, 45030, 11242, 33688, 2288, 8592, 18513, 9307, 4032, 45030, 11242, 2423, 28820, 10943, 18863, 10943, 18871, 2423, 26890, 3224, 7649, 2423, 16572, 46958, 1829, 4032, 9122, 15042, 29910, 37983, 8315, 8978, 9673, 5016, 46958, 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true طيب فأنا بدي أجي أحللها إيش احتمالاتها؟ طب لو الأول لو ال B false إيش مطلوب مني؟", "tokens": [30543, 2655, 11933, 1829, 8592, 29538, 39894, 30544, 20328, 5016, 1829, 5016, 3660, 22807, 35186, 11933, 15042, 16247, 12610, 7908, 16070, 2655, 7649, 1829, 36632, 44049, 38207, 34051, 16247, 12610, 2074, 16070, 2655, 7649, 1829, 2074, 23032, 1829, 3555, 6156, 10721, 8315, 4724, 16254, 5551, 7435, 1829, 5551, 5016, 1211, 1211, 11296, 11933, 1829, 8592, 1975, 33753, 2304, 6027, 9307, 11296, 22807, 23032, 3555, 45164, 16247, 12610, 45164, 2423, 363, 7908, 11933, 1829, 8592, 3714, 9566, 1211, 37746, 9154, 1829, 22807], "avg_logprob": -0.16615854058323837, "compression_ratio": 1.6568047337278107, "no_speech_prob": 0.0, "words": [{"start": 572.52, "end": 572.94, "word": "وقت", "probability": 0.68994140625}, {"start": 572.94, "end": 573.1, "word": " إيش", "probability": 0.771728515625}, {"start": 573.1, "end": 573.3, "word": " هذه", "probability": 0.48193359375}, {"start": 573.3, "end": 573.62, 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"probability": 0.9951171875}, {"start": 703.91, "end": 705.01, "word": " واقعة", "probability": 0.7861328125}, {"start": 705.01, "end": 705.63, "word": " فبفترض", "probability": 0.96025390625}, {"start": 705.63, "end": 705.83, "word": " إنه", "probability": 0.552490234375}, {"start": 705.83, "end": 705.95, "word": " B", "probability": 0.8388671875}, {"start": 705.95, "end": 706.25, "word": " true", "probability": 0.97705078125}, {"start": 706.25, "end": 706.61, "word": " و", "probability": 0.65625}, {"start": 706.61, "end": 706.91, "word": " بثبت", "probability": 0.9176025390625}, {"start": 706.91, "end": 707.11, "word": " إنه", "probability": 0.748046875}, {"start": 707.11, "end": 707.27, "word": " إيش", "probability": 0.93408203125}, {"start": 707.27, "end": 707.41, "word": " ال", "probability": 0.2154541015625}, {"start": 707.41, "end": 707.71, "word": " AQ", "probability": 0.728515625}, {"start": 707.71, "end": 707.87, "word": " true", "probability": 0.9423828125}, {"start": 707.87, "end": 708.19, "word": " بيكون", "probability": 0.6424967447916666}, {"start": 708.19, "end": 708.59, "word": " انتهت", "probability": 0.9099934895833334}, {"start": 708.59, "end": 709.15, "word": " العملية", "probability": 0.9168294270833334}], "temperature": 1.0}, {"id": 32, "seek": 72719, "start": 710.69, "end": 727.19, "text": "فبقول لي the direct way to proceed is to assume that P is true شفتوا القاعدة اللي شرحناها؟ فهي هيك البداية نفترض ان P true and show او deduce الا استقرق او اثبت او اشتق او اوصل ان هيك ال Q is true وضعت", "tokens": [5172, 3555, 39648, 32239, 264, 2047, 636, 281, 8991, 307, 281, 6552, 300, 430, 307, 2074, 13412, 5172, 2655, 14407, 25062, 995, 22488, 3660, 13672, 1829, 13412, 2288, 5016, 8315, 11296, 22807, 6156, 3224, 1829, 39896, 4117, 29739, 28259, 10632, 8717, 5172, 2655, 43042, 16472, 430, 2074, 293, 855, 1975, 2407, 4172, 4176, 42963, 44713, 4587, 2288, 4587, 1975, 2407, 1975, 12984, 3555, 2655, 1975, 2407, 1975, 8592, 2655, 4587, 1975, 2407, 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"end": 724.71, "word": " اشتق", "probability": 0.936279296875}, {"start": 724.71, "end": 724.99, "word": " او", "probability": 0.862548828125}, {"start": 724.99, "end": 725.41, "word": " اوصل", "probability": 0.9059244791666666}, {"start": 725.41, "end": 725.61, "word": " ان", "probability": 0.90380859375}, {"start": 725.61, "end": 725.87, "word": " هيك", "probability": 0.80517578125}, {"start": 725.87, "end": 726.01, "word": " ال", "probability": 0.70166015625}, {"start": 726.01, "end": 726.13, "word": " Q", "probability": 0.49072265625}, {"start": 726.13, "end": 726.31, "word": " is", "probability": 0.69970703125}, {"start": 726.31, "end": 726.55, "word": " true", "probability": 0.9697265625}, {"start": 726.55, "end": 727.19, "word": " وضعت", "probability": 0.6420084635416666}], "temperature": 1.0}, {"id": 33, "seek": 74875, "start": 727.51, "end": 748.75, "text": "أه فهذه القاعدة العامة فلما يديني جملة شرطية كبدا برا هنا بقوله ببدأ البرهان assume P is true وبتمني أشغل لحد ما وصل ان Q is true بكون البرهان صحيح وواضح ليش شرحناها بالتفصيل ضمن قواعد المنطق فبقوللي الصيغة العامة الصورة العامة لبرهان جملة شرطية هي صورته العامة صورته العامة", "tokens": [10721, 3224, 6156, 3224, 24192, 25062, 995, 22488, 3660, 18863, 10943, 3660, 6156, 1211, 15042, 7251, 3215, 9957, 1829, 10874, 2304, 37977, 13412, 2288, 9566, 10632, 9122, 3555, 28259, 4724, 23557, 34105, 4724, 39648, 3224, 4724, 44510, 10721, 2423, 26890, 3224, 7649, 6552, 430, 307, 2074, 46599, 39237, 22653, 5551, 8592, 17082, 1211, 5296, 24401, 19446, 4032, 36520, 16472, 1249, 307, 2074, 4724, 30544, 2423, 26890, 3224, 7649, 20328, 5016, 1829, 5016, 4032, 2407, 46958, 5016, 32239, 8592, 13412, 2288, 5016, 8315, 11296, 20666, 2655, 5172, 9381, 26895, 48812, 27842, 12174, 14407, 22488, 9673, 1863, 9566, 4587, 6156, 3555, 39648, 20292, 31767, 1829, 17082, 3660, 18863, 10943, 3660, 31767, 13063, 3660, 18863, 10943, 3660, 5296, 26890, 3224, 7649, 10874, 2304, 37977, 13412, 2288, 9566, 10632, 39896, 20328, 13063, 47395, 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"word": " ضمن", "probability": 0.94091796875}, {"start": 740.99, "end": 741.37, "word": " قواعد", "probability": 0.978515625}, {"start": 741.37, "end": 741.79, "word": " المنطق", "probability": 0.95458984375}, {"start": 741.79, "end": 742.63, "word": " فبقوللي", "probability": 0.78741455078125}, {"start": 742.63, "end": 743.07, "word": " الصيغة", "probability": 0.984375}, {"start": 743.07, "end": 743.93, "word": " العامة", "probability": 0.99609375}, {"start": 743.93, "end": 744.39, "word": " الصورة", "probability": 0.9765625}, {"start": 744.39, "end": 744.79, "word": " العامة", "probability": 0.9954427083333334}, {"start": 744.79, "end": 745.29, "word": " لبرهان", "probability": 0.9500732421875}, {"start": 745.29, "end": 745.61, "word": " جملة", "probability": 0.9607747395833334}, {"start": 745.61, "end": 746.17, "word": " شرطية", "probability": 0.995849609375}, {"start": 746.17, "end": 746.63, "word": " هي", "probability": 0.71484375}, {"start": 746.63, "end": 746.93, "word": " 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biconditional statement تمام اه طبعا زى ما اقول ان التعريف هي ايش two conditional من biconditional ثنائية الشرطية", "tokens": [6027, 1863, 45367, 16712, 7649, 1829, 13672, 7578, 3714, 43020, 7251, 29973, 25894, 8315, 4032, 26895, 3224, 11203, 995, 28671, 20666, 7435, 2304, 37977, 25124, 2288, 9566, 10632, 2423, 39184, 34472, 684, 2628, 2423, 39184, 34472, 684, 2628, 5296, 15042, 7251, 30544, 2074, 1975, 1829, 8592, 4724, 1829, 30544, 4724, 1829, 30544, 1993, 1860, 4724, 1829, 30544, 6055, 4117, 31845, 10721, 3660, 4724, 1829, 30544, 6055, 4117, 31845, 10721, 3660, 6156, 39319, 8315, 8032, 29399, 24401, 12984, 18871, 2423, 34472, 684, 2628, 5629, 46811, 10943, 1975, 3224, 23032, 3555, 3615, 995, 30767, 7578, 19446, 1975, 39648, 16472, 16712, 3615, 16572, 5172, 39896, 1975, 1829, 8592, 732, 27708, 9154, 34472, 684, 2628, 38637, 1863, 16373, 10632, 25124, 2288, 9566, 10632], "avg_logprob": -0.20807292088866233, "compression_ratio": 1.9194915254237288, "no_speech_prob": 0.0, "words": 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بيكون", "probability": 0.9278971354166666}, {"start": 794.39, "end": 794.91, "word": " تكافأة", "probability": 0.9818359375}, {"start": 794.91, "end": 795.13, "word": " فاحنا", "probability": 0.93408203125}, {"start": 795.13, "end": 795.59, "word": " هنتحدث", "probability": 0.81268310546875}, {"start": 795.59, "end": 795.83, "word": " عن", "probability": 0.99658203125}, {"start": 795.83, "end": 796.25, "word": " ال", "probability": 0.953125}, {"start": 796.25, "end": 797.23, "word": " biconditional", "probability": 0.8072916666666666}, {"start": 797.23, "end": 797.83, "word": " statement", "probability": 0.96875}, {"start": 797.83, "end": 798.83, "word": " تمام", "probability": 0.7333984375}, {"start": 798.83, "end": 799.15, "word": " اه", "probability": 0.678466796875}, {"start": 799.15, "end": 799.43, "word": " طبعا", "probability": 0.9940185546875}, {"start": 799.43, "end": 799.57, "word": " زى", "probability": 0.8974609375}, {"start": 799.57, "end": 799.65, "word": " ما", "probability": 0.9775390625}, {"start": 799.65, "end": 799.81, "word": " اقول", "probability": 0.775634765625}, {"start": 799.81, "end": 799.93, "word": " ان", "probability": 0.52197265625}, {"start": 799.93, "end": 800.37, "word": " التعريف", "probability": 0.972900390625}, {"start": 800.37, "end": 800.57, "word": " هي", "probability": 0.6640625}, {"start": 800.57, "end": 800.85, "word": " ايش", "probability": 0.6881917317708334}, {"start": 800.85, "end": 801.13, "word": " two", "probability": 0.703125}, {"start": 801.13, "end": 801.69, "word": " conditional", "probability": 0.92041015625}, {"start": 801.69, "end": 801.89, "word": " من", "probability": 0.9072265625}, {"start": 801.89, "end": 802.73, "word": " biconditional", "probability": 0.9425455729166666}, {"start": 802.73, "end": 803.17, "word": " ثنائية", "probability": 0.9576416015625}, {"start": 803.17, "end": 803.73, "word": " الشرطية", "probability": 0.9898681640625}], "temperature": 1.0}, {"id": 37, "seek": 81458, "start": 804.78, "end": 814.58, "text": "إذا عشان أثبتها الطريقة الأولى أنه أجسمها لحالتين if P implies Q and if Q implies V طب كيف أثبت كل واحدة زي ما اتعلمنا سابقة؟", "tokens": [28814, 15730, 6225, 8592, 7649, 5551, 12984, 3555, 2655, 11296, 41950, 16572, 28671, 16247, 12610, 7578, 14739, 3224, 5551, 7435, 38251, 11296, 5296, 5016, 6027, 2655, 9957, 498, 430, 18779, 1249, 293, 498, 1249, 18779, 691, 23032, 3555, 9122, 33911, 5551, 12984, 3555, 2655, 28242, 36764, 24401, 3660, 30767, 1829, 19446, 1975, 2655, 3615, 19528, 8315, 8608, 16758, 28671, 22807], "avg_logprob": -0.23488730192184448, "compression_ratio": 1.342281879194631, "no_speech_prob": 0.0, "words": [{"start": 804.78, "end": 805.08, "word": "إذا", "probability": 0.50872802734375}, {"start": 805.08, "end": 805.6, "word": " عشان", "probability": 0.8301595052083334}, {"start": 805.6, "end": 806.16, "word": " أثبتها", "probability": 0.917578125}, {"start": 806.16, "end": 807.22, "word": " الطريقة", "probability": 0.8994140625}, 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"probability": 0.95849609375}, {"start": 1554.61, "end": 1554.75, "word": " the", "probability": 0.91015625}, {"start": 1554.75, "end": 1555.15, "word": " universe", "probability": 0.85888671875}, {"start": 1555.15, "end": 1555.91, "word": " نفعش", "probability": 0.651397705078125}, {"start": 1555.91, "end": 1556.25, "word": " نستخدم", "probability": 0.995361328125}, {"start": 1556.25, "end": 1556.55, "word": " حاجة", "probability": 0.9920247395833334}, {"start": 1556.55, "end": 1557.03, "word": " خاصة", "probability": 0.9855143229166666}, {"start": 1557.03, "end": 1557.33, "word": " لو", "probability": 0.9208984375}, {"start": 1557.33, "end": 1557.99, "word": " بيستخدم", "probability": 0.89658203125}, {"start": 1557.99, "end": 1558.27, "word": " عنصر", "probability": 0.9728190104166666}, {"start": 1558.27, "end": 1558.63, "word": " معين", "probability": 0.99560546875}], "temperature": 1.0}, {"id": 69, "seek": 158785, "start": 1559.13, "end": 1587.85, "text": "أه .. اه .. then since X 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{"start": 1580.35, "end": 1580.53, "word": " ليش", "probability": 0.9853515625}, {"start": 1580.53, "end": 1580.85, "word": " بنبدأ", "probability": 0.8780924479166666}, {"start": 1580.85, "end": 1581.01, "word": " بعد", "probability": 0.51123046875}, {"start": 1581.01, "end": 1581.35, "word": " الصورة؟", "probability": 0.8629150390625}, {"start": 1581.35, "end": 1581.57, "word": " عشان", "probability": 0.9928385416666666}, {"start": 1581.57, "end": 1581.67, "word": " هي", "probability": 0.966796875}, {"start": 1581.67, "end": 1582.23, "word": " فانا", "probability": 0.5869954427083334}, {"start": 1582.23, "end": 1582.41, "word": " ما", "probability": 0.93115234375}, {"start": 1582.41, "end": 1583.19, "word": " ينطبق", "probability": 0.898046875}, {"start": 1583.19, "end": 1583.37, "word": " على", "probability": 0.9169921875}, {"start": 1583.37, "end": 1583.51, "word": " ال", "probability": 0.9013671875}, {"start": 1583.51, "end": 1583.79, "word": " X", "probability": 0.98486328125}, 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"duration_after_vad": 2382.5499999999947} \ No newline at end of file diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/VmIP06NfAs4_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/VmIP06NfAs4_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..989248cc4992b85804c39bab3334122d5c4b5d1b --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/VmIP06NfAs4_raw.srt @@ -0,0 +1,2480 @@ +1 +00:00:20,810 --> 00:00:25,390 +بسم الله الرحمن الرحيم هنستكمل مع بعض الإرشادات و + +2 +00:00:25,390 --> 00:00:29,690 +بعض الكلام العام عن البرهان الرياضي و كما ذكرنا في + +3 +00:00:29,690 --> 00:00:34,890 +المحاضرة الماضية هذه الصفحات ممكن تكون دليل معنا و + +4 +00:00:34,890 --> 00:00:38,230 +طبعا احنا هنتطرق لهذه الملاحظات في حينها مع + +5 +00:00:38,230 --> 00:00:41,510 +الأمثلة و كيف نطبقها لكن جيد ان ناخد فكرة عامة و + +6 +00:00:41,510 --> 00:00:44,370 +تكون هذه تمهيد و ان شاء الله لما نرجع نذكركوا فيها + +7 +00:00:44,370 --> 00:00:47,480 +و نديكوا مثال كيف نطبقها بشكل عامفطبعا احنا + +8 +00:00:47,480 --> 00:00:51,020 +اتذكرنا فيه هو فيه أربع قواعد للبرهان كيف ممكن + +9 +00:00:51,020 --> 00:00:55,580 +نستخدم المعطيات ممكن نستخدم نظرية مثبتة سابقا وكيف + +10 +00:00:55,580 --> 00:00:59,280 +نستبدل ب statement ب statement تكافئها وبعض الأمور + +11 +00:00:59,280 --> 00:01:04,380 +المشابهة أيضا قلنا فيه خمس صرخ برهان رئيسية وهي + +12 +00:01:04,380 --> 00:01:07,620 +البرهان المباشر تبدأ من المعطيات حتى تنتهي + +13 +00:01:07,620 --> 00:01:12,660 +بالمطلوبفي عندنا البرهان اللي هو ناخد حالات نجسم + +14 +00:01:12,660 --> 00:01:16,520 +المطلوب لعدد حالات عدد منتهي من الحالات و نبرهن كل + +15 +00:01:16,520 --> 00:01:21,380 +حالة على جهة وبالتالي بيكون برهاننا الكل النقطة + +16 +00:01:21,380 --> 00:01:23,080 +التالتة أو الطريقة التالتة اللي هي by + +17 +00:01:23,080 --> 00:01:26,500 +contrapositive وهي تعتبر طريقة مرهان غير مباشر + +18 +00:01:26,500 --> 00:01:29,280 +وتنطبق على ال statements اللي هو ال conditional + +19 +00:01:29,280 --> 00:01:32,520 +statements فقط و يتلش غير مباشر لأنه بدل ما انا + +20 +00:01:32,520 --> 00:01:38,070 +ابقوا برهنif B then Q ببرهن اليوم للمكافئة if not + +21 +00:01:38,070 --> 00:01:41,690 +Q then not P الطريقة الرابعة هي طريقة البرهان by + +22 +00:01:41,690 --> 00:01:44,490 +contradiction برضه نوع ثاني من ال indirect proof + +23 +00:01:44,490 --> 00:01:48,570 +هو في هنا ببدأ أني بأنفي اللي هو المطلوب لحد ما + +24 +00:01:48,570 --> 00:01:51,510 +أوصل ل contradiction بكون انتهى البرهان الطريقة + +25 +00:01:51,510 --> 00:01:56,090 +الخامسة اللي هي البرهان باستخدام الاستخدام الرياضي + +26 +00:01:56,090 --> 00:01:59,070 +اللي هو هيكون موضوع ان شاء الله في اللي هو الجزء + +27 +00:01:59,070 --> 00:02:03,360 +التاني من المحاضرة أو في section 1-8جامل ما نبدأ + +28 +00:02:03,360 --> 00:02:05,960 +بالبرهين الرياضية والتطبيقات خلّينا ناخد بعض + +29 +00:02:05,960 --> 00:02:09,540 +النصائح العامة اللي هي برضه إرشادات ممكن تساعدنا + +30 +00:02:09,540 --> 00:02:13,880 +في دراسة البرهين الرياضية ودراسة رياضية فطبعا بقول + +31 +00:02:13,880 --> 00:02:17,000 +هنا advances for writing proof بعض النصائح + +32 +00:02:17,000 --> 00:02:20,540 +والإرشادات لكتابة البرهان طبعا بقول ليه ليس هناك + +33 +00:02:20,540 --> 00:02:25,210 +طريقة وحيدة وموحدة لكتابة البرهانأه طبعا لأن الناس + +34 +00:02:25,210 --> 00:02:27,710 +في وجهات نظر و دايما أحيانا بتكون يعني كله صحيح + +35 +00:02:27,710 --> 00:02:33,110 +لكن في فرقات فردية في الكتابة أو في التعبير لكن + +36 +00:02:33,110 --> 00:02:36,910 +هناك بعض التقنيات اللي ممكن تستخدمها و بتكون دايما + +37 +00:02:36,910 --> 00:02:39,790 +مفيدة في كتابة البرهان مافيش قاعدة واحدة مافيش + +38 +00:02:39,790 --> 00:02:43,630 +قالب معين لكن في إرشادات عامة قواعد عامة مفيدة جدا + +39 +00:02:43,630 --> 00:02:47,310 +في كتابة البرهان فطبعا احنا هيحنمر على بعض هذه + +40 +00:02:47,310 --> 00:02:53,160 +الإرشادات و بعض هذه النصحةالنصيحة الأولى والسؤال + +41 +00:02:53,160 --> 00:02:57,540 +الأول كيف نبدأ how to start أنا عندي نظرية بدأ + +42 +00:02:57,540 --> 00:03:01,860 +برهنها عندي سؤال جالي approve كذا كذا إيش بدي + +43 +00:03:01,860 --> 00:03:05,780 +أعمل؟ فهذه طبعا هي يمكن الموضوع الأساسي و الصعوبة + +44 +00:03:05,780 --> 00:03:09,640 +الأولى من وين أبدأ وكيف أنتهي طبعا و أيه طبعا نجي + +45 +00:03:09,640 --> 00:03:12,580 +النقطة التانية كيف أحكم أن حل صحيح أو انتهى أو + +46 +00:03:12,580 --> 00:03:15,020 +ماانتهاش هذا موضوع أخر لكن احنا بنركز الآن على + +47 +00:03:15,020 --> 00:03:20,830 +البدايةBegin a proof ابدأ البرهان دايما انك تعيد + +48 +00:03:20,830 --> 00:03:25,730 +كتابة المعطيات بصورة أخرى زي ما حكينا احنا عشان + +49 +00:03:25,730 --> 00:03:28,350 +اللي هو انحل مسألة فيه أربع خطوات الخطوة الأولى + +50 +00:03:28,350 --> 00:03:31,990 +فهم المسألة فهم المسألة بيحتاج أحيانا لعيد صياغة + +51 +00:03:31,990 --> 00:03:37,990 +المعطيات والمطلوب بصورة مناسبةrewriting عادة كتابة + +52 +00:03:37,990 --> 00:03:41,210 +what you are given and what you are asked to prove + +53 +00:03:41,210 --> 00:03:44,090 +المعطيات و المطلوب ممكن أن أعيد سيارته لأنه احنا + +54 +00:03:44,090 --> 00:03:47,670 +هنستخدم المعطيات و هنوصل للمطلوب فأنا بقيد سيارته + +55 +00:03:47,670 --> 00:03:50,770 +بشكل مناسب يكون أوضح لي عشان أعرف إيش اللي معي إيش + +56 +00:03:50,770 --> 00:03:54,530 +إمكانياتي و إيش هدف اللي بده أوصله in a more + +57 +00:03:54,530 --> 00:03:57,870 +convenient form في صيغة أنسب إلي .. أنسب إلي فدي + +58 +00:03:57,870 --> 00:04:00,690 +أول خطوةالخطوة التانية، طبعا هذا إيش بيقولها؟ إيش + +59 +00:04:00,690 --> 00:04:03,190 +معناته؟ بيفسره بشكل أفضل، بيقول في الغالب هذا + +60 +00:04:03,190 --> 00:04:07,390 +بيتضمن إن أحول الكلمات ال statement إلى رموز، + +61 +00:04:07,390 --> 00:04:09,670 +بتسهل العمرو إن كيف يصير إيش، بالنسبة لي مألوف + +62 +00:04:09,670 --> 00:04:15,250 +أكتر، and utilizing the definition أو إن أنا بأسحد + +63 +00:04:15,250 --> 00:04:18,210 +أو باسحد التعريف، أثبت إن الدالة differentiable، + +64 +00:04:18,210 --> 00:04:20,590 +إيش معناة differentiable؟ بدات سحدة، أثبت إنها دي + +65 +00:04:20,590 --> 00:04:23,010 +implication، يعني إيش implication؟ يعني جملة شرطية + +66 +00:04:23,010 --> 00:04:25,230 +إنها إيش تتولج زي ما حاولنا نعمل، إنها تتولج دائما + +67 +00:04:25,460 --> 00:04:29,140 +فانا باستحضر المصطلحة أثبت أنها differentiable إيش + +68 +00:04:29,140 --> 00:04:31,040 +يعني differentiable يعني عشان أعرف إيش بتعمل أنا + +69 +00:04:31,040 --> 00:04:36,160 +إيش مطلوب فانا باستحضر التعريف و الحدود ال terms + +70 +00:04:36,160 --> 00:04:40,020 +used in the statement و كل المصطلحات و الكلمات + +71 +00:04:40,020 --> 00:04:43,140 +اللي مستخدمة وين في اللي هو التقارير المُعطية ال + +72 +00:04:43,140 --> 00:04:47,510 +statements المُعطية فده مهم جدافهذه أول شيء كيف + +73 +00:04:47,510 --> 00:04:51,090 +نبدأ نعيد صياغة المعطيات والمطلوب بشكل مناسب حتى + +74 +00:04:51,090 --> 00:04:54,950 +نفهم السؤال بشكل أوضح نقول الخطوة الأولى نفهم + +75 +00:04:54,950 --> 00:05:00,390 +المسألة نفهم المسألة النصيحة التانية justify each + +76 +00:05:00,390 --> 00:05:05,090 +stepبرر كل خطوة أو اللي هو ادي دليل على كل خطوة، + +77 +00:05:05,090 --> 00:05:09,570 +هذه مهم جدا في البرهان اللي احنا حاولنا نتعلمه عن + +78 +00:05:09,570 --> 00:05:12,870 +طريق الـ deductive reasoning كل خطوة نحط الدليل، + +79 +00:05:12,870 --> 00:05:15,790 +مهم جدا لأنه أنا لازم أسأل نفسي أنا عملت هذه + +80 +00:05:15,790 --> 00:05:19,730 +الخطوة صحيحة ولا غير صحيحة؟ طب صحيحة إيش دليل؟ في + +81 +00:05:19,730 --> 00:05:26,470 +نظرية، اللي هو بديهيةفي قاعدة منطق أو كذا فلازم + +82 +00:05:26,470 --> 00:05:29,610 +دايما أبرر و لا إذا ماقدرتش أبرر إذا في عندي علامة + +83 +00:05:29,610 --> 00:05:32,310 +الصفقة ممكن يكون هذه الخطوة غير صحية طبعا ممكن + +84 +00:05:32,310 --> 00:05:34,470 +تكون صحية لكن أنا بدي دايما أكون دليل عشان أكون + +85 +00:05:34,470 --> 00:05:37,850 +مطمئن إن فعلا هذه صحية فبقول لي as a general rule + +86 +00:05:37,850 --> 00:05:41,570 +كقاعدة عامة when you write a step in a proof ask + +87 +00:05:41,570 --> 00:05:45,210 +yourself إسأل نفسك إسألي نفسك if deducing that + +88 +00:05:45,210 --> 00:05:49,590 +step هل استنتاج هذه الخطوة هل الوصول لهذه الخطوة + +89 +00:05:49,590 --> 00:05:55,520 +هي validهل هو صحيح؟ هل هو صحيح؟ + +90 +00:05:55,520 --> 00:05:58,220 +in the sense that إيش معناه صحيح؟ آه كيف بيقول + +91 +00:05:58,220 --> 00:06:00,880 +صحيح؟ زي ما قلنا إنه بيستخدم إيش؟ أحد قواعد + +92 +00:06:00,880 --> 00:06:04,160 +المنطقة، أحد النظريات السابقة that it uses one of + +93 +00:06:04,160 --> 00:06:07,360 +the four basic rules above أو بيستخدم أحد الأربع + +94 +00:06:07,360 --> 00:06:10,280 +قواعد اللي ذكرناهاطبعا بشكل عام بدي أكون فيه دليل + +95 +00:06:10,280 --> 00:06:14,200 +في نظرية سابقة اعتمدت عليها في قاعدة منطق في أحد + +96 +00:06:14,200 --> 00:06:17,100 +القواعد يعني استبدلت statement ب statement تكافئها + +97 +00:06:17,100 --> 00:06:21,500 +دايما صح و هكذا فلازم يكون عندي دليل على الخطوة + +98 +00:06:21,500 --> 00:06:26,810 +تبعتيبقول لي إذا كانت ال step بتتبع as a result of + +99 +00:06:26,810 --> 00:06:29,830 +the use of a tautology بس تخدمها تطولوجي معين أنه + +100 +00:06:29,830 --> 00:06:33,530 +statement دايما صحيح أو قادة منطق بقول لي هو بشكل + +101 +00:06:33,530 --> 00:06:36,930 +عام ممكن أنا ذكرت ليس من الضروري أنه نكتب ال + +102 +00:06:36,930 --> 00:06:39,970 +tautology نكتب كدليل لكن احنا في البداية بدنا نكتب + +103 +00:06:39,970 --> 00:06:45,360 +عشان نتعود عليهفبقول لي مش ضروري تعمل sight تعمل + +104 +00:06:45,360 --> 00:06:49,280 +إشارة لل-tautology في البرهان لأن زي ما حكينا لما + +105 +00:06:49,280 --> 00:06:53,220 +نتقدم مش هنبدأ نحط أشياء صارت واضحة قواعد أساسية + +106 +00:06:53,220 --> 00:06:56,640 +يعني احنا لما .. لما نيجي مثلا نجمع مانقولش ان + +107 +00:06:56,640 --> 00:06:58,980 +احنا في قاعدة الجامعة ان واحد زاد واحد سوى اتنين + +108 +00:06:58,980 --> 00:07:02,120 +خلاص بصير الأمور بالنسبة لنا واضحة ومتفق عليها + +109 +00:07:02,120 --> 00:07:05,300 +وبديهية بالنسبة لنا فلكن في البداية لازم نتعود + +110 +00:07:05,300 --> 00:07:11,310 +عليهافبقولي في الحقيقة مع الممارسة انت تكتب ال + +111 +00:07:11,310 --> 00:07:15,790 +proof من غير ما انك اتفكر في ال tautology بشكل + +112 +00:07:15,790 --> 00:07:18,950 +يعني بشكل صريح بصير عملية عملية روتينية زي احنا + +113 +00:07:18,950 --> 00:07:22,470 +بنشبه سياقة السيارة الواحد اول ما يتعلم بيكون مهم + +114 +00:07:22,470 --> 00:07:24,210 +بيحط يديك على ال clutch على ال brake و بعدين بيصير + +115 +00:07:24,210 --> 00:07:26,490 +عملها قليلا من غير ما يشعروهي نفس القضية بصير احنا + +116 +00:07:26,490 --> 00:07:29,250 +نستخدم ال totology بس احنا متعودين عليه ولكن + +117 +00:07:29,250 --> 00:07:31,870 +عارفين المنطقة لو جالي برر ليش بجيبله المبرر لكن + +118 +00:07:31,870 --> 00:07:34,610 +انا بعملها بشكل آلي اه لكن مش ضروري احنا نكتبها في + +119 +00:07:34,610 --> 00:07:37,030 +المجتمعات المتقدمة لكن في المجتمعات الأولى لازم + +120 +00:07:37,030 --> 00:07:40,530 +نتعود نكتبها عشان نتعود نفكر بالطريقة المنطقية + +121 +00:07:40,530 --> 00:07:44,490 +الصحيةلكن هو بيقوللي إيش القاعدة اللي مافيش غنى + +122 +00:07:44,490 --> 00:07:47,090 +عنها، إنه لازم كل خطوة تكون مبررة، يعني أنا + +123 +00:07:47,090 --> 00:07:49,810 +ماكتبتش، لكن لو سألني ليش عملتي هيك، بقوله، آه، + +124 +00:07:49,810 --> 00:07:53,650 +فلازم كل خطوة تكون أيش مبررة، مقومة عليها الدليل، + +125 +00:07:53,650 --> 00:07:56,710 +كتبته أو ماكتبتش بشكل صريح، لكن الدليل موجود، + +126 +00:07:56,710 --> 00:08:00,210 +موجود في عقلي شفوي، آه، أو بقدر أكتبه بشكل صريح + +127 +00:08:02,020 --> 00:08:05,520 +تمام فهذه نصايح عامة للبرهان يعني فاحنا بدنا نعرف + +128 +00:08:05,520 --> 00:08:08,480 +كيف بنبدأ وهذه نصايح عامة أنه نعيد كتابة المعطيات + +129 +00:08:08,480 --> 00:08:12,220 +والمطلوب وطبعا وهم جدا أنه كل خطوة بنعملها في + +130 +00:08:12,220 --> 00:08:16,560 +البرهان كلها دليل وقائمة على دليل صحيح على قانون + +131 +00:08:16,560 --> 00:08:20,200 +صحيح حتى أضمن أنه كل خطواتي صحيح وبالتالي برهاني + +132 +00:08:20,200 --> 00:08:25,300 +في الآخر يكون صحيحالان نصائح أخرى كيف بنبرهن + +133 +00:08:25,300 --> 00:08:29,100 +statement شرطية conditional statement طبعا بيمروا + +134 +00:08:29,100 --> 00:08:32,280 +علينا كتير في الرياضيات أه بيقوللي اثبت ان if F is + +135 +00:08:32,280 --> 00:08:35,700 +differentiable then F is continuous كيف أبدأ و كيف + +136 +00:08:35,700 --> 00:08:39,060 +أنتهي و ليش هذا البداية و النهاية صحيحة ضمن ما + +137 +00:08:39,060 --> 00:08:45,230 +تعلمناه من قواعد المنطقةأه طبعا لو قاللي اثبت if b + +138 +00:08:45,230 --> 00:08:50,530 +then q ايش معناه اثبت؟ اثبت انها true اه ممكن + +139 +00:08:50,530 --> 00:08:54,350 +يكونوا ممكن يكونوا false فلما يقوللي prove this + +140 +00:08:54,350 --> 00:09:00,550 +statement اثبت هذه التقرير يعني اثبت صحته اثبت + +141 +00:09:00,550 --> 00:09:04,570 +صحته تمام؟ اه فعشان هيك احنا في الرياضية احيانا + +142 +00:09:04,570 --> 00:09:08,670 +كتير اديش بنحولهاimplies لأننا مهتمين بإنها تكون + +143 +00:09:08,670 --> 00:09:11,790 +صحيحة انها تكون tautology انها تكون tautology + +144 +00:09:11,790 --> 00:09:14,510 +فبنعمل implies وعشانك في بعض الناس مفارقوش بين + +145 +00:09:14,510 --> 00:09:18,110 +هدول الإشارتين فدائما مطلوب في الرياضيات إثبات + +146 +00:09:18,110 --> 00:09:21,090 +الجملة الشرطية تكون صحيحة يعني تكون implication + +147 +00:09:21,090 --> 00:09:24,130 +تضمين وفي بعض الحالات نقول ان ال if and only if a + +148 +00:09:24,130 --> 00:09:27,310 +term يونها equivalent لأننا مهتمين تكون صحيحة تكون + +149 +00:09:27,310 --> 00:09:32,940 +صحيحة ممتاز إذا الأن أرجع لأصلها if B then Qوقت + +150 +00:09:32,940 --> 00:09:37,560 +إيش هذه بتكون صحيحة؟ يا إما الأول false والتاني أي + +151 +00:09:37,560 --> 00:09:42,440 +شيء أو الأول true والتاني true طيب فأنا بدي أجي + +152 +00:09:42,440 --> 00:09:46,660 +أحللها إيش احتمالاتها؟ طب لو الأول لو ال B false + +153 +00:09:46,660 --> 00:09:52,230 +إيش مطلوب مني؟ولا شيء ..ولا شيء .. إذا بي فالس فال + +154 +00:09:52,230 --> 00:09:56,810 +if then true إذا لما تكون ال بي فالس مش مطلوب مني + +155 +00:09:56,810 --> 00:10:00,430 +أثبت ولا حاجة، هذه الاحتمال الأول، فلو ال بي فالس + +156 +00:10:00,430 --> 00:10:03,190 +مش مطلوب مني ولا حاجة فهذا الاحتمال الأشمالي مش + +157 +00:10:03,190 --> 00:10:05,570 +مطلوب مني أشطل عليه، فإذا أنا ده أشمنع بطل عش عليه + +158 +00:10:06,160 --> 00:10:09,000 +مش مطلوب مني حاجة، لأ، طب إذا ال B true، هاي + +159 +00:10:09,000 --> 00:10:12,240 +الاحتمال التاني، لازم أثبت إن ال Q true، لأن هو .. + +160 +00:10:12,240 --> 00:10:14,540 +لأن هو إيش مطلوب؟ هو أنا بدي أثبت إنه بدي أدرس + +161 +00:10:14,540 --> 00:10:17,220 +حالات ال statement ولا بدي أثبت إنها true؟ أنا + +162 +00:10:17,220 --> 00:10:20,220 +مهتم إن ال statement ماكتش true، if then ماكتش + +163 +00:10:20,220 --> 00:10:23,840 +true، إذا ال B false، تبطلعيش على ال Q، صح؟ إذا مش + +164 +00:10:23,840 --> 00:10:27,160 +مطلوب مني إيش، إذا ال B true، اثبتي إن ال Q true + +165 +00:10:27,460 --> 00:10:31,580 +فصارت القاعدة اللي أمامكم إذا بدنا نثبت جملة شرطية + +166 +00:10:31,580 --> 00:10:35,080 +بنبدأ ندرس الحالة الوحيدة أن الـ be true التانية + +167 +00:10:35,080 --> 00:10:39,040 +مافيش داعي ندرسها، واضح؟ فبنفترض أن الـ be true، + +168 +00:10:39,040 --> 00:10:42,100 +إذا هذه الاحتمال اللي بدناه ندرسه، التاني مافيه + +169 +00:10:42,100 --> 00:10:45,520 +أيش داعي، و بنثبت أن الـ Q أتره، فإذا لما أتعامل + +170 +00:10:45,520 --> 00:10:48,760 +مع أي جملة شرطية أصبح المطلوب مني عشان أثبت أن + +171 +00:10:48,760 --> 00:10:52,280 +جملة شرطية true أفرض أن الـ B true أدرس حالة الـ B + +172 +00:10:52,280 --> 00:10:56,540 +true و أثبت أن الـ Q أتره، فنشوف إيش كانتطبعا + +173 +00:10:56,540 --> 00:10:59,520 +بيقول ليه اللي هو the most famous exam اللي هو + +174 +00:10:59,520 --> 00:11:03,580 +أشهر مثال وبنتشر جدا اللي هو إيش الجملة الشرطية بي + +175 +00:11:03,580 --> 00:11:05,900 +implies the Q ووضحنا ليش كتابنا implies لإن ما + +176 +00:11:05,900 --> 00:11:09,800 +تفوت إنها true طبعا إيش تبدأ هي بيقول لي برهانة + +177 +00:11:09,800 --> 00:11:13,420 +بيبدأ خطوة بعد خطوة إيش from the condition B إن + +178 +00:11:13,420 --> 00:11:17,840 +بفترض إن ال B true و بوصل لمين إن ال Q true هي كل + +179 +00:11:17,840 --> 00:11:20,220 +الكلام اللي موجود هذا الكلام هنوضحه بشكل أفضل + +180 +00:11:20,790 --> 00:11:25,250 +فبقولي since B then the Q is false only when B is + +181 +00:11:25,250 --> 00:11:27,410 +true and the Q is false هذه الحالة الوحيدة اللي + +182 +00:11:27,410 --> 00:11:29,690 +بتكون فيها false وانا اللي بدي أثبت إنها إيش إنها + +183 +00:11:29,690 --> 00:11:32,070 +لا يمكن تحدث بدي أثبت إنها يمكن تحدث لإن بدي أثبت + +184 +00:11:32,070 --> 00:11:34,890 +إنها دايما true يعني هذا الحالة الوحيدة من أربعة + +185 +00:11:34,890 --> 00:11:40,210 +لا يمكن حدوثها فبقولي it is suffix يكفي to show + +186 +00:11:40,210 --> 00:11:43,350 +that this situation cannot happen بدي أثبت إن هذه + +187 +00:11:43,350 --> 00:11:47,270 +الحالة غير واقعة فبفترض إنه B true و بثبت إنه إيش + +188 +00:11:47,270 --> 00:11:51,730 +ال AQ true بيكون انتهت العمليةفبقول لي the direct + +189 +00:11:51,730 --> 00:11:55,270 +way to proceed is to assume that P is true شفتوا + +190 +00:11:55,270 --> 00:11:58,510 +القاعدة اللي شرحناها؟ فهي هيك البداية نفترض ان P + +191 +00:11:58,510 --> 00:12:04,710 +true and show او deduce الا استقرق او اثبت او اشتق + +192 +00:12:04,710 --> 00:12:08,690 +او اوصل ان هيك ال Q is true وضعتأه فهذه القاعدة + +193 +00:12:08,690 --> 00:12:11,510 +العامة فلما يديني جملة شرطية كبدا برا هنا بقوله + +194 +00:12:11,510 --> 00:12:15,410 +ببدأ البرهان assume P is true وبتمني أشغل لحد ما + +195 +00:12:15,410 --> 00:12:19,130 +وصل ان Q is true بكون البرهان صحيح وواضح ليش + +196 +00:12:19,130 --> 00:12:23,070 +شرحناها بالتفصيل ضمن قواعد المنطق فبقوللي الصيغة + +197 +00:12:23,070 --> 00:12:26,930 +العامة الصورة العامة لبرهان جملة شرطية هي صورته + +198 +00:12:26,930 --> 00:12:32,760 +العامة صورته العامةDirect proof of B implies Q هذا + +199 +00:12:32,760 --> 00:12:35,160 +ال direct طبعا لأن في Contrapositive indirect فهذا + +200 +00:12:35,160 --> 00:12:37,320 +ال direct ايش بيقول كده بيبدأ؟ بيقول لي ايش تبدأ + +201 +00:12:37,320 --> 00:12:40,200 +assume B يعني assume ان B true يعني هذ المعنية + +202 +00:12:40,200 --> 00:12:43,440 +وبتمني ماشي لحد ما وصل ليش therefore Q is true + +203 +00:12:43,440 --> 00:12:47,800 +انتهى البرهانفأي جملة شرطية ببدبيه طبعا بمشي + +204 +00:12:47,800 --> 00:12:51,020 +بطريقة منطقية صحية رياضية صحية على محط بوصلكيه و + +205 +00:12:51,020 --> 00:12:54,080 +بكون انتهى البرهان فعشان هيك لما تشوفوا أي برهان + +206 +00:12:54,080 --> 00:12:57,480 +جملة شرطية و تقولوه ليش بدبيه هاي المبرر ليش + +207 +00:12:57,480 --> 00:13:04,010 +مبدبيه كيف نبدأ واضح اي سؤال تمامالنوع التاني اللى + +208 +00:13:04,010 --> 00:13:07,030 +ممكن يمر علينا ويله علاقة بالجملة الشرطية الـ + +209 +00:13:07,030 --> 00:13:11,510 +biconditional الـ biconditional لما يكون true ايش + +210 +00:13:11,510 --> 00:13:14,910 +بيكون بيكون totality بيكون تكافأة بيكون تكافأة + +211 +00:13:14,910 --> 00:13:19,150 +فاحنا هنتحدث عن ال biconditional statement تمام اه + +212 +00:13:19,150 --> 00:13:21,690 +طبعا زى ما اقول ان التعريف هي ايش two conditional + +213 +00:13:21,690 --> 00:13:26,160 +من biconditional ثنائية الشرطيةإذا عشان أثبتها + +214 +00:13:26,160 --> 00:13:30,720 +الطريقة الأولى أنه أجسمها لحالتين if P implies Q + +215 +00:13:30,720 --> 00:13:33,660 +and if Q implies V طب كيف أثبت كل واحدة زي ما + +216 +00:13:33,660 --> 00:13:38,660 +اتعلمنا سابقة؟فهذا بيسموه two parts approved اللي + +217 +00:13:38,660 --> 00:13:43,640 +هو البرهان على شقين البرهان على شقين فإيش صيغته؟ + +218 +00:13:43,640 --> 00:13:48,260 +فبقوللي إيش بجسمه لجثئين بثبت أن P implies Q زي ما + +219 +00:13:48,260 --> 00:13:52,160 +اتعلمنا قبل قليل وبعدين بثبت أن Q implies Q بيكون + +220 +00:13:52,160 --> 00:13:55,940 +النتيجة أنه صارت تكافأت الاتجاهين صحيحين، فهذه + +221 +00:13:55,940 --> 00:13:59,240 +الصيغة العامة طب هل هذه الطريقة الوحيدة؟ لأ، في + +222 +00:13:59,240 --> 00:14:01,680 +طريقة تانية إن أنا أمشي أتكافأ مرة واحدة بدل ما + +223 +00:14:01,680 --> 00:14:04,820 +أعملها جزءين أعملها جزء واحد بس هذا بده دقة وبده + +224 +00:14:04,820 --> 00:14:09,760 +انتباهفي بعض الحلقات يقولون أنه يمكن أن نثبت + +225 +00:14:09,760 --> 00:14:17,820 +باستخدام نفس الرابط نمشي if and when left مع تكافة + +226 +00:14:20,560 --> 00:14:23,220 +إن هذه القضية زي ما اتعلمنا في detective reasoning + +227 +00:14:23,220 --> 00:14:25,920 +ممكن أبدأ من أي طرف أوصل للتاني نفترض أنه هنبدأ من + +228 +00:14:25,920 --> 00:14:30,560 +اليسار من B بتمني ماشي و بأستدلها بصياغة كونهش + +229 +00:14:30,560 --> 00:14:33,780 +مكافئة دايما لأنه لم يتمشي تكافئة لحد ما انتهي من + +230 +00:14:33,780 --> 00:14:38,040 +مين بال Q فهذه طبعا القضية بدها انتباه و هنشوف أنه + +231 +00:14:38,040 --> 00:14:42,600 +ببنصحش فيها كتيربنصحش فيها كتير لأن أي قانون إذا + +232 +00:14:42,600 --> 00:14:46,500 +كان تكافأ و استبدلتيه بتضمين صح لكن العكس غير صحيح + +233 +00:14:46,500 --> 00:14:49,380 +إذا كان القانون تضمين و حطيتيه تكافأ بيكون غلط لأن + +234 +00:14:49,380 --> 00:14:52,200 +هذا زي الطريق في اتجاهين بديك تروح من الشمال + +235 +00:14:52,200 --> 00:14:55,220 +للجنوب مسموح تروح من الجنوب للشمال مسموح هذا + +236 +00:14:55,220 --> 00:14:58,160 +التكافأ طب لو كانت اتجاه واحد الشرطة هيخالفك إذا + +237 +00:14:58,160 --> 00:15:01,000 +روحت في اتجاه المخالف ودي نفس الشيء ففي مشكلة ففي + +238 +00:15:01,000 --> 00:15:04,340 +مشكلة بده انتباهفطبعا الصيغة العامة ايش بيكون by + +239 +00:15:04,340 --> 00:15:08,060 +conditional proof ببدأ من بي بتمنع امشي تكافؤ جبت + +240 +00:15:08,060 --> 00:15:10,860 +ال statement تكافحها و تانية و تالتة و N لحد ما + +241 +00:15:10,860 --> 00:15:14,440 +وصل ل Q بس لازم يكون كل الخطوات تكافؤ و انا متأكد + +242 +00:15:14,440 --> 00:15:18,480 +مليون المية ان كله تكافؤ اذا شكيت في مشكلة بدي + +243 +00:15:18,480 --> 00:15:22,160 +ارجع اتأكد بدي ارجع اتأكد فدي مهم جدا فده طريق + +244 +00:15:22,160 --> 00:15:24,700 +تاني يا two parts نعملها two conditional + +245 +00:15:24,700 --> 00:15:28,260 +statements او نمشي تكافؤ وهدي اقل حدوثة اقل + +246 +00:15:28,260 --> 00:15:31,660 +استخدام لان فيها صعوبة احيانا لكن هذه هي الشائعة + +247 +00:15:31,660 --> 00:15:37,580 +اكترفهذه اول شيء كيف نتعامل مع الجمال الشرطية و + +248 +00:15:37,580 --> 00:15:40,880 +كيف نتعامل مع الجمال الثنائية الشرطية فهذه نصاحي + +249 +00:15:40,880 --> 00:15:46,300 +عامة و سنطبقها ان شاء الله في أثناء المثاق نقطة + +250 +00:15:46,300 --> 00:15:51,600 +جديدة أخرى و اكتش أستخدم البرهان بالتناقضطبعا .. + +251 +00:15:51,600 --> 00:15:53,580 +السؤال قال لي طيب لأ احنا مانا مانا مانا ماناش .. + +252 +00:15:53,580 --> 00:15:57,440 +ده السؤال بس ده مرحلة احنا بيتعلم كرياضيين انا عند + +253 +00:15:57,440 --> 00:16:00,600 +برهان و ماجليش السؤال مين أستخدم؟ direct؟ + +254 +00:16:00,600 --> 00:16:03,440 +indirect؟ contrapositive؟ إيش أستخدم الطريقة + +255 +00:16:03,440 --> 00:16:06,140 +المناسبة؟ فهنا بدينا نصيحة عامة وقت إيش أستخدم + +256 +00:16:06,140 --> 00:16:08,720 +prove by contradiction؟ بقولي prove by + +257 +00:16:08,720 --> 00:16:11,260 +contradiction is a natural way to proceed when + +258 +00:16:11,260 --> 00:16:13,960 +negating the conclusion gives you something + +259 +00:16:13,960 --> 00:16:18,160 +concrete to manipulate طبعا احنا زي ما قلنا في + +260 +00:16:18,160 --> 00:16:21,780 +عندنا مسألة معطية بدنا نبرهنحطأيا خدنا المعطيات + +261 +00:16:21,780 --> 00:16:26,600 +فسرناها و كتبناها بأوضح معنى و المطلوب و وضحناه طب + +262 +00:16:26,600 --> 00:16:30,700 +بدي أبدأ من وين أبدأ مش عارف أبدأ مش عارف أبدأ روح + +263 +00:16:30,700 --> 00:16:34,840 +أنف المطلوب ألاقي لأ إداني إيش عمق أحسن ممكن أبدأ + +264 +00:16:34,840 --> 00:16:38,060 +أه فيدياني حاجات ممكن أشتر عليها أه المعطيات مش + +265 +00:16:38,060 --> 00:16:40,960 +قادرة أبدأ فيها طب المطلوب مقدرش أبدأ فيهالمعطيات + +266 +00:16:40,960 --> 00:16:43,940 +أحاول أبدأ منها أن أشتغل فيه شغل ممكن أعمله مش + +267 +00:16:43,940 --> 00:16:47,920 +قادر فبأنف المطلوب لأجلها أداني نقطة بداية نقطة + +268 +00:16:47,920 --> 00:16:50,300 +بداية فهذا بتديني إيش أنه إذا استخدم إيش and + +269 +00:16:50,300 --> 00:16:54,800 +direct proof فإن إذا عجزت أني أبدأ من المعطيات أنف + +270 +00:16:54,800 --> 00:16:58,060 +المطلوب و أشوف إنه ممكن يديني بداية أنسب ولا لأ + +271 +00:16:58,060 --> 00:17:00,720 +واضح؟ فبيديني إيش؟ بيديني حاجة أقدر أشتغل معها + +272 +00:17:00,720 --> 00:17:05,600 +نفي؟ طبعا نفي المطلوب عيد ونكرر المطلوب ليس جزء من + +273 +00:17:05,600 --> 00:17:08,520 +الحال نفي المطلوب ممكن يكون جزء من الحال بالإيش + +274 +00:17:08,520 --> 00:17:12,530 +approved by contradictionفطبعا إيش الصيغة العامة + +275 +00:17:12,530 --> 00:17:15,190 +زي ما اتعلمنا بنبدأ بنفري المطلوب عشان أثبت بيه + +276 +00:17:15,190 --> 00:17:19,450 +بقوله not بيه و بتمني واصل .. أشتغل في مرحلة ما + +277 +00:17:19,450 --> 00:17:22,610 +هوصل إن الـQ true لازم أتمني واصل لسه ما انتهاش + +278 +00:17:22,610 --> 00:17:26,390 +البرهان هوصل إنه not Q is true صار الشيء و نقيده + +279 +00:17:26,390 --> 00:17:29,650 +صحيحين contradiction انتهى البرهان فدائما الصيغة + +280 +00:17:29,650 --> 00:17:32,490 +العامة ببرهان بقى contradiction بوصل ل statement + +281 +00:17:32,490 --> 00:17:35,990 +ما إنها true بوصل إنه ال negation تبعها برضه true + +282 +00:17:35,990 --> 00:17:39,370 +الشيء و ضده لا يجتمع عن تناقض انتهى البرهان انتهى + +283 +00:17:39,370 --> 00:17:45,490 +البرهان أي سؤالبعض الملاحظات على البرهان by + +284 +00:17:45,490 --> 00:17:49,690 +contradiction بيقول لي في وجهين مهمين لل proof by + +285 +00:17:49,690 --> 00:17:54,470 +contradiction و لازم نمشي نلاحظهم و نهتم بيهم + +286 +00:17:54,470 --> 00:17:59,550 +فبقول لي أن طريقة البرهان بالتناقض تصلح مع أي + +287 +00:17:59,550 --> 00:18:02,830 +statement أي ما كانت مركبة بسيطة conditional by + +288 +00:18:02,830 --> 00:18:05,910 +conditional أي ما كانت ممكن أنفيها بانفيها و بشتغل + +289 +00:18:05,910 --> 00:18:09,150 +و لما أوصل لتناقض ما بيبقى بينفع معاها لكن ال + +290 +00:18:09,150 --> 00:18:13,410 +direct proof في الغالب بدي أبدأ نمش if thenالـ + +291 +00:18:13,410 --> 00:18:16,870 +Contrapositive مابتنفعش اللي مع ال F then فبنتبه + +292 +00:18:16,870 --> 00:18:19,450 +لكن ال Contradiction مع أي statement بنفيها و + +293 +00:18:19,450 --> 00:18:23,170 +بشتغل فاش مشكلة لكن ال Contrapositive مع F then و + +294 +00:18:23,170 --> 00:18:27,130 +البرهان المباشر في الغالب هو F then لأن بقول B + +295 +00:18:27,130 --> 00:18:32,630 +implies Q ببدأ من B و بوصل لQ هذه نقطة أولى نقطة + +296 +00:18:32,630 --> 00:18:37,240 +تانيةطبعا احنا بنبدأ إيش لو شفتوا الهيكلية قولنا + +297 +00:18:37,240 --> 00:18:42,100 +not B ووصلنا ل Q و not Q طب Q وين هذه؟ موجودة في + +298 +00:18:42,100 --> 00:18:46,580 +المعطيات؟ موجودة في المطلوب؟ مش ضروري هذه Q جملة + +299 +00:18:46,580 --> 00:18:49,680 +ما مش عارفين اوى كيف تطلع معنا فهذه نقطة الصعوبة + +300 +00:18:49,680 --> 00:18:53,920 +هذه نقطة الصعوبة لأن هو باعتمد يعني لو احنا لقصنا + +301 +00:18:53,920 --> 00:18:57,760 +البرهان كله بدأنا من not B وانتهينا ب + +302 +00:18:57,760 --> 00:19:02,160 +contradictionطيب، البداية تحتوي على النهاية؟ لأ، + +303 +00:19:02,160 --> 00:19:05,560 +هذه نقطة صعوبة، مين هي الـQ؟ ومين هي نط الـQ؟ طبعا + +304 +00:19:05,560 --> 00:19:08,060 +مش عارفينه، شوفنا أمثل أنه بندور على ال + +305 +00:19:08,060 --> 00:19:09,980 +contradiction، مين هي مش عارفينها، فهذه نقطة + +306 +00:19:09,980 --> 00:19:12,280 +صعوبة، فهذه نقطة صعوبة في ال proof by + +307 +00:19:12,280 --> 00:19:12,660 +contradiction + +308 +00:19:16,040 --> 00:19:20,720 +أه فبالتالي البرهان بيقبل بالتناقض إله ميزة وإله + +309 +00:19:20,720 --> 00:19:25,060 +عيب إله نقطة قوة ونقطة ضعف نقطة قوته إن ده طفلة + +310 +00:19:25,060 --> 00:19:27,720 +معطلة جديدة اللي هو نافي المطلوب فبتداني إيش؟ + +311 +00:19:27,720 --> 00:19:31,920 +إتداني بدائل للبداية لكن وين نقطة ضعفه؟ إن الـQ و + +312 +00:19:31,920 --> 00:19:35,240 +الـNot Q مش معروفين من أصلا .. مسبقا الجملة اللي + +313 +00:19:35,240 --> 00:19:37,920 +بدها تعمل تناقض هي ونقيدها مش معروفة مسبقا فدي + +314 +00:19:37,920 --> 00:19:42,080 +نقطة إيش؟ نقطة ضعف أو نقطة صعوبةأه فطبعا هذا في ال + +315 +00:19:42,080 --> 00:19:46,160 +.. في ال .. we don't know the proposition to use + +316 +00:19:46,160 --> 00:19:50,920 +for a cue will be do the job أه طبعا يمكن نقطة قوة + +317 +00:19:50,920 --> 00:19:54,160 +يعني هي نقطة ضعف و نقطة قوة بنفس الوقت ضعف لإنه مش + +318 +00:19:54,160 --> 00:19:57,060 +عارفها مصباح طب قوة إذا لجيت أي واحدة بتقدي الغرض + +319 +00:19:57,060 --> 00:20:00,640 +إذا لجيت أي واحدة بتقدي الغرض طبعا في بعض الأحيان + +320 +00:20:00,640 --> 00:20:04,700 +هذا بحتاج إنه أتعمق في المسألة بشكل كتير عشان + +321 +00:20:04,700 --> 00:20:09,390 +أدوّل على cue مناسبةأه فبيحتاج أنه ندخل جوا + +322 +00:20:09,390 --> 00:20:12,950 +المسألة و ندور على EQ مناسبة هي اللي بتدينا + +323 +00:20:12,950 --> 00:20:16,330 +التناقض وبالتالي نوصل لنهاية البرهان طبعا هذا مع + +324 +00:20:16,330 --> 00:20:22,290 +الخبرة و مع الممارسة نقطة أخرى بالنسبة للبرهين + +325 +00:20:22,290 --> 00:20:27,250 +prove by experiment البرهان بالتجربةطبعا التجربة + +326 +00:20:27,250 --> 00:20:31,370 +والأمثلة لا تعتبر برهان لكنها بتساعد في البرهان هي + +327 +00:20:31,370 --> 00:20:36,330 +ليست طريقة برهان وانما هي إيش أداء مساعدة أداء + +328 +00:20:36,330 --> 00:20:39,810 +مساعدة فبقول .. بيقول رغم أنه we cannot generally + +329 +00:20:39,810 --> 00:20:43,310 +prove a statement by experiment نقدرش نثبت تقرير + +330 +00:20:43,310 --> 00:20:47,150 +ما إنه صحيح بالتجربة لكن many proves can be done + +331 +00:20:47,150 --> 00:20:51,270 +with the help بمساعدة التجربة كأداة مساعدة وليست + +332 +00:20:51,270 --> 00:20:56,780 +طريقة من طريق البرهانفبقول لي بشكل عام الواحد + +333 +00:20:56,780 --> 00:21:00,380 +دايما عنده statement معقدة مش فاهمها بشكل عام + +334 +00:21:00,380 --> 00:21:03,320 +بيبدأ يديه أمثلة بسيطة وبعدين بيبدأ يستقرأ ويفهم + +335 +00:21:03,320 --> 00:21:07,520 +الصورة العامة يفهم الصورة العامة فبقول looks at + +336 +00:21:07,520 --> 00:21:11,720 +simple cases to gain insight حتى يكتسب رؤية أوضح + +337 +00:21:11,720 --> 00:21:16,520 +وعمق رؤية أعمق فإيش؟ وبالتالي هذا ممكن يوضحله + +338 +00:21:16,520 --> 00:21:19,600 +الصورة العامة يقدر يستقرأ الصورة العامة فطبعا هنا + +339 +00:21:19,600 --> 00:21:24,520 +مثال بسيطبقول لي إنه أي عدد فردي هو مجموع عددين + +340 +00:21:24,520 --> 00:21:28,260 +صحيحين متتاليين بدي أثبته هذا الكلام طب لو حاولت + +341 +00:21:28,260 --> 00:21:32,120 +أثبته أشي أطلع بعض الأمثلة التلاتة واحد زائد اتنين + +342 +00:21:32,120 --> 00:21:35,840 +الخمسة اتنين زائد تلاتة السبعة تلاتة زائد أربعة + +343 +00:21:35,840 --> 00:21:39,360 +طيب لو بدي أبره إنه بشكل عام العدد الفردي بنعبر + +344 +00:21:39,360 --> 00:21:42,720 +عنه اتنين n زائد واحد وواضح من هذا الكلام هو عبارة + +345 +00:21:42,720 --> 00:21:47,660 +عن n زائد n زائد 1 وهو المطلوبإذا كتبت أستقرأ من + +346 +00:21:47,660 --> 00:21:49,900 +هذا الكلام، اللي هو يبقى عن العدد و اللي بعده N + +347 +00:21:49,900 --> 00:21:52,340 +زائد N زائد 1، بتطلع 2N زائد 1، و هو عدد فارق، + +348 +00:21:52,340 --> 00:21:54,700 +انتهى البرهان، فانا من الأمثلة، ده ممكن أستقرأ + +349 +00:21:54,700 --> 00:21:58,440 +مثلين و تلاتة، لكن لو بدل تلت أمثلة، أديت تلاتة + +350 +00:21:58,440 --> 00:22:01,220 +مليون مثال، لا يعتبر برهان، لكن هذا يعتبر برهان + +351 +00:22:01,220 --> 00:22:03,420 +الآن، لأن هو ده الصورة العامة، لأن هو ده الصورة + +352 +00:22:03,420 --> 00:22:06,640 +العامة، لكنه ساعدني، الأمثلة ساعدتني على الفهم و + +353 +00:22:06,640 --> 00:22:11,400 +كيف أتوقع أني أحط الصورة العامة، الصورة العامة، + +354 +00:22:11,400 --> 00:22:19,380 +فدي بعض الأمور، تمامفيمكن احنا مرنا على بعض الأمور + +355 +00:22:19,380 --> 00:22:22,760 +كيف نبرهن الجملة الشرطية أو التضمين، كيف نبرهن + +356 +00:22:22,760 --> 00:22:25,880 +التكافؤ، الآن برضه هنمره على command statements + +357 +00:22:25,880 --> 00:22:31,200 +مهمة ومشهورة كيف نبرهنها Proving uniqueness، اثبات + +358 +00:22:31,200 --> 00:22:35,800 +الوحدانية، احنا هى قطع ناشي؟ لأ، بس ماشيين + +359 +00:22:35,800 --> 00:22:40,350 +بالترتيبلو أنا في بعض الرياضيات بمر عليها نظرية + +360 +00:22:40,350 --> 00:22:44,690 +بيقولك أنها مثلا الحل الوحيد أو يوجد عنصر وحيد، + +361 +00:22:44,690 --> 00:22:48,330 +كيف أثبته؟ في طريقة مشهورة في الرياضيات، بأفترض أن + +362 +00:22:48,330 --> 00:22:52,690 +هناك حلين و بأثبت أنهم متساويةهذه متعارفة في + +363 +00:22:52,690 --> 00:22:55,150 +الرياضيات يعني لو أنا أقل هذه المعادلة إلى حل وحيد + +364 +00:22:55,150 --> 00:22:58,290 +بفترض إنه لحالين وبوصل إن هدول حاليين متساويين أو + +365 +00:22:58,290 --> 00:23:01,910 +لتناقض أو لتناقض فبكون هذه هي الطريقة العامة فبقول + +366 +00:23:01,910 --> 00:23:05,110 +لي to prove an object is unique عشان نثبت إن شئ ما + +367 +00:23:05,110 --> 00:23:09,230 +هو وحيد unique فبقول assume that a and b are two + +368 +00:23:09,230 --> 00:23:12,570 +objects نفترض إنه في عنصرين بهذه الصفات وبنستخدم + +369 +00:23:12,570 --> 00:23:15,250 +المعطيات والمعلومات اللي عنا ونثبت إن هدول عيش + +370 +00:23:15,250 --> 00:23:18,550 +مستحيل يكونوا مختلفين إذا فيش الواحد وحيد مستحيل + +371 +00:23:18,550 --> 00:23:20,770 +يكونوا اتنين مختلفين إذا نعيش متساويين فهذه + +372 +00:23:20,770 --> 00:23:25,900 +الطريقة العامةتمام فهذا بالنسبة للـ uniqueness + +373 +00:23:25,900 --> 00:23:30,280 +ننتقل لنوع آخر من ال statements statements تحتوي + +374 +00:23:30,280 --> 00:23:34,520 +على مكممات وفي عنا نوعين من المكممات مكمم الشمول + +375 +00:23:34,520 --> 00:23:38,080 +for all ومكمم الوجود there exists نبدأ في + +376 +00:23:38,080 --> 00:23:41,880 +statement تحتوي على مكمم الشمول for all أنا بدي + +377 +00:23:41,880 --> 00:23:48,400 +أثبت statement for all x b of x كيف بدي أثبتها؟اه + +378 +00:23:48,400 --> 00:23:51,020 +ايه دي اللي هي طريقة عامة؟ اللي هي طريقة عامة في + +379 +00:23:51,020 --> 00:23:54,020 +البرهان طبعا انا بدأت فاهم ان هذه true وماكنتش + +380 +00:23:54,020 --> 00:23:57,060 +بتكون true اذا كانت P of X طولة كل X في ال + +381 +00:23:57,060 --> 00:24:01,120 +universe في ال universe اه فطبعا اذا ال universe + +382 +00:24:01,120 --> 00:24:04,680 +كبير بشكل عام صعب اني ابدأ اجرب كل واحدة بالدور مش + +383 +00:24:04,680 --> 00:24:08,200 +هخلص خلنا ال natural number مثلا ماهي نهاية عمرا + +384 +00:24:08,200 --> 00:24:12,080 +ما بخلص فبدنا طريقة عامة كيف نتعامل مع هذه الجملة + +385 +00:24:12,510 --> 00:24:17,570 +أه فالبرهان بنبدأ بنقوله خد عنصر X من ال domain + +386 +00:24:17,570 --> 00:24:21,270 +عنصر عشوائي واتفقنا يمكن .. بتتذكر لما كنا نكتب + +387 +00:24:21,270 --> 00:24:25,230 +مقدمات نظريات نقول لما نقول let P be any statement + +388 +00:24:25,230 --> 00:24:28,170 +ما ينطبق على ال P بالنظرية ينطبق على أي statement + +389 +00:24:28,170 --> 00:24:31,950 +فهنا نفس القضية لما نقوله let X be any object in + +390 +00:24:31,950 --> 00:24:35,010 +the universe إذا أي شغل حنشتغله على X بنتمي على X + +391 +00:24:35,010 --> 00:24:37,130 +بنطبق على جميع عناصر ال universe ويكون البرهان + +392 +00:24:37,130 --> 00:24:41,570 +انتهى البرهان انتهىفهذه هي الطريقة فهذه هي ايش + +393 +00:24:41,570 --> 00:24:45,150 +الطريقة بس طبعا هنا مهم جدا انه انا مستخدمش اي + +394 +00:24:45,150 --> 00:24:49,250 +خاصية خاصة لل X وانما استخدم خواصة عامة لكل عناصر + +395 +00:24:49,250 --> 00:24:52,410 +ال universe لكل عناصر ال universe بكون اشتغل ما + +396 +00:24:52,410 --> 00:24:55,790 +انطبق على X بانطبق على اي عنصر فبالتالي ما هو صحيح + +397 +00:24:55,790 --> 00:25:01,390 +لل X صحيح لكل العناصر فبقول ليهفبقول لـ to prove a + +398 +00:25:01,390 --> 00:25:03,770 +statement of the form for all x P of x we must + +399 +00:25:03,770 --> 00:25:06,810 +show that P of x is true for every object فده كلام + +400 +00:25:06,810 --> 00:25:11,390 +حكيناه a direct proof is begun by letting x + +401 +00:25:11,390 --> 00:25:16,330 +represent an arbitrary object in the universe في + +402 +00:25:16,330 --> 00:25:22,170 +الدمين التابع للدراسة and then showing that P of x + +403 +00:25:22,170 --> 00:25:29,470 +هنا في كلمة ناقصةP of X is true for the object + +404 +00:25:29,470 --> 00:25:34,130 +فبكون انتهى، هذا العنصر اللي أخدناه بيمثل جميع + +405 +00:25:34,130 --> 00:25:39,890 +العناصر، بيمثل جميع العناصر فانتهىفبقول لي طبعا + +406 +00:25:39,890 --> 00:25:43,810 +هنا بأكد in the proof انتبهي وانا بنأكد الكلام + +407 +00:25:43,810 --> 00:25:49,550 +اللي حاكيناه we may use ممكن نستخدم ايش فقط خواص + +408 +00:25:49,550 --> 00:25:53,730 +ال X اللي اشملها المشتركة لجميع العناصر shared by + +409 +00:25:53,730 --> 00:25:56,550 +every element of the universe نفعش نستخدم حاجة + +410 +00:25:56,550 --> 00:26:00,810 +خاصة لو بيستخدم عنصر معينأه .. اه .. then since X + +411 +00:26:00,810 --> 00:26:04,370 +is an arbitrary ممكن نستنتج ان ال statement for + +412 +00:26:04,370 --> 00:26:08,710 +all x P of X is true لكل ال X فالصورة العامة كيف + +413 +00:26:08,710 --> 00:26:12,850 +بنبرهن بدي أثبت بقول لببدل برهان let X be an + +414 +00:26:12,850 --> 00:26:14,950 +arbitrary object in the universe فعشان هيك لما + +415 +00:26:14,950 --> 00:26:17,530 +تقرأوا برهان اتلاقوا ال statement for all X + +416 +00:26:17,530 --> 00:26:20,530 +هتلاقوه بعدي بعد الشكل طب ليش؟ هي المبررة واضح ليش + +417 +00:26:20,530 --> 00:26:23,790 +بنبدأ بعد الصورة؟ عشان هي فانا ما ينطبق على ال X + +418 +00:26:23,790 --> 00:26:26,650 +ما جاله arbitrary ينطبق على الكل فمزال أثبتت + +419 +00:26:26,650 --> 00:26:31,700 +اشتغلت اشتغلتP of X is true ما ينطبق على ال X + +420 +00:26:31,700 --> 00:26:34,880 +ينطبق على كل العناصر لأن ال X arbitrary لأن ال X + +421 +00:26:34,880 --> 00:26:37,840 +arbitrary طبعا بقول ال universe بشكل عام لازم يكون + +422 +00:26:37,840 --> 00:26:41,560 +موضح بشكل صريح أو الخواص تبع العناصر يكون موضح + +423 +00:26:41,560 --> 00:26:44,720 +اللي بدأ استخدمها ايش ال X ايش بتمثل عناصر ايش + +424 +00:26:44,720 --> 00:26:47,520 +خواصها المشتركة ايش خواصها المشتركة + +425 +00:26:50,670 --> 00:26:55,170 +النوع التاني من التكميم اللي هو مكمم الوجود اللي + +426 +00:26:55,170 --> 00:26:58,250 +هو ال statement there exists x P of X كيف ممكن + +427 +00:26:58,250 --> 00:27:03,780 +نثبت نعمأه بدنا ياها تكون على الأقل لعنصر على + +428 +00:27:03,780 --> 00:27:07,800 +الأقل لعنصر ففي البرهان هنا في قد الطرق الحقيقة مش + +429 +00:27:07,800 --> 00:27:11,140 +زي for all مالاش طريقة واحدة أه لو اجدرت أنا أسمي + +430 +00:27:11,140 --> 00:27:13,880 +العنصر هذا اللي هو بيخلي ال P of X true بتكون + +431 +00:27:13,880 --> 00:27:18,500 +صحيحة بتكون صحيحة أه مثلا لو أنا مثلا بدي أقول إنه + +432 +00:27:18,500 --> 00:27:22,180 +هذه القاعة غير فارغة أه يعني إيش يوجد طالبات في + +433 +00:27:22,180 --> 00:27:24,860 +هذه القاعة لو أنا بعرف إن فاطمة موجودة في هذه + +434 +00:27:24,860 --> 00:27:27,780 +القاعة أنتهت العملية قلت فاطمة موجودة في القاعة K + +435 +00:27:27,780 --> 00:27:33,080 +أو ال 518 أنتهت المثلةفلمّا يقول لي اثبت ان القاعة + +436 +00:27:33,080 --> 00:27:38,780 +الـ518 فيها طالبان بقوله انا شفت فاطمة موجودة في + +437 +00:27:38,780 --> 00:27:41,740 +القاعة انتهت السؤال اثبت هذا يا طبعا فإن لما أسمي + +438 +00:27:41,740 --> 00:27:45,540 +الانصار بكون انتهت المثل فبقول لي هناك عدة طرق + +439 +00:27:45,850 --> 00:27:49,210 +الطريقة الأولى اللي هي إيش؟ إنه أسمي هذه التسمية + +440 +00:27:49,210 --> 00:27:51,710 +أو إنشاء العنصر اللي بيحقق الخاصية بيسموها + +441 +00:27:51,710 --> 00:27:56,410 +constructive method اللي هو طريقة البناء أو أعمل + +442 +00:27:56,410 --> 00:28:00,710 +البرهان in a constructive proof we actually name + +443 +00:28:00,710 --> 00:28:05,150 +an object بنسميه بنقول فاطمة موجودة an object A in + +444 +00:28:05,150 --> 00:28:08,330 +the universe طبعا في ال domain تبعنا بحيث إنه P of + +445 +00:28:08,330 --> 00:28:11,430 +A is true طبعا .. طبعا .. وبالتالي بيكون إيش؟ + +446 +00:28:11,430 --> 00:28:17,560 +البرهان انتهى مباشرة البرهان انتهىطبعا في بعض برضه + +447 +00:28:17,560 --> 00:28:20,680 +ال constructive proof بنقدرش نسميه بشكل صريح .. + +448 +00:28:20,680 --> 00:28:25,040 +بنقدرش نسميه بشكل صريح لكن بنثبت أن هناك عنصر فعلا + +449 +00:28:25,040 --> 00:28:29,500 +موجود زي اللي هو البرهان مثلا طبعا أحيانا بتكون + +450 +00:28:29,500 --> 00:28:32,780 +التسمية سهلة و أحيانا بتكون صعبة أن أنا عنصر مثلا + +451 +00:28:32,780 --> 00:28:37,770 +لو قاللي هناك عدد أولي زوجييوجد عدد أول زوجين عامل + +452 +00:28:37,770 --> 00:28:42,290 +تنين خلاص سمينا مثال آخر there exists an even + +453 +00:28:42,290 --> 00:28:46,050 +prime number S2 is an even prime number انتهت + +454 +00:28:46,050 --> 00:28:50,090 +العملية لكن في بعض الأحيان بتكون التسمية مش سهلة + +455 +00:28:50,090 --> 00:28:52,950 +طبعا بقول لي another strategy to prove there + +456 +00:28:52,950 --> 00:28:56,270 +exists xP of x is to show that there must be some + +457 +00:28:56,270 --> 00:29:00,470 +objectيجب أن يكون هناك عنصر لكن مش قادر أسميه بشكل + +458 +00:29:00,470 --> 00:29:04,610 +صريح مش قادر أسميه بشكل صريح without ever actually + +459 +00:29:04,610 --> 00:29:08,010 +producing a particular object من غير ما نسمي عنصر + +460 +00:29:08,010 --> 00:29:12,450 +بحد ذاته لكن واضح أن المعطيات بتقدي أن هناك وجود + +461 +00:29:12,450 --> 00:29:15,830 +عنصر طبعا أمثل على ذلك يمكن لو رجعتوا برهان ال + +462 +00:29:15,830 --> 00:29:17,630 +main value theorem في ال calculus أو ال rule + +463 +00:29:17,630 --> 00:29:20,750 +theorem بيقولوا في هناك عنصر من غير ما يسميه وحتى + +464 +00:29:20,750 --> 00:29:23,370 +بنعرف أنه مافيش طريقة لحسابه مافيش طريقة لحسابه + +465 +00:29:23,370 --> 00:29:28,570 +لكنه بنثبت أنه موجود بنثبت أنه موجودطبعا طريقة + +466 +00:29:28,570 --> 00:29:30,890 +أخرى لإثبات الـ there exists عن طريق ال + +467 +00:29:30,890 --> 00:29:34,050 +contradiction أن فيها بيصير for all ممكن يتعامل + +468 +00:29:34,050 --> 00:29:39,950 +معاها زي ال for all نقطة + +469 +00:29:39,950 --> 00:29:44,130 +أخيرة بالبرهين اللي هي علاقة بالبرهين وهي ليست + +470 +00:29:44,130 --> 00:29:50,350 +برهانهي disapproving أحيانا بيقولك disapprove أو + +471 +00:29:50,350 --> 00:29:53,910 +بتلاقوا في الأسلحة السابقة approve or disapprove + +472 +00:29:53,910 --> 00:29:59,790 +طيب بشكل عام approve يعني if بتصحت prove if بتصحت + +473 +00:29:59,790 --> 00:30:04,510 +ال statement disapprove if خطأ ال statement مرة + +474 +00:30:04,510 --> 00:30:09,200 +تانيةapprove the statement يعني اثبت صحة ال + +475 +00:30:09,200 --> 00:30:12,400 +statement disapprove the statement اثبت خطأ ال + +476 +00:30:12,400 --> 00:30:14,820 +statement اثبت خطأ ال statement فبقول ليه + +477 +00:30:14,820 --> 00:30:17,140 +disapproving a statement is proving that a + +478 +00:30:17,140 --> 00:30:21,480 +statement is false اثبات ان الجملة false تمام كيف + +479 +00:30:21,480 --> 00:30:24,780 +ممكن نثبت هذا الكلام اه دايما احنا فيهاش القاعدة + +480 +00:30:24,780 --> 00:30:28,320 +بتكون صحيحة دائما مالياش استثناء اذا لجينا استثناء + +481 +00:30:28,320 --> 00:30:32,060 +اذا القاعدة خاطئة فبندى مثال بسموه مثال عكسي بسموه + +482 +00:30:32,060 --> 00:30:36,790 +مثال العكسي فبقول برغمالبرهان بالمثال ليس برهان + +483 +00:30:36,790 --> 00:30:40,790 +ليس برهان على صحة ال statement لكن هو disprove + +484 +00:30:40,790 --> 00:30:44,050 +ببرهن على خطأ ال statement المثال إذا في استثناء + +485 +00:30:44,050 --> 00:30:46,690 +إذا القاعدة غير صحيحة احنا في قواعد رياضية مافيش + +486 +00:30:46,690 --> 00:30:50,770 +استثناء اه فبقول ليه أن البرهان بالرياضيات غير + +487 +00:30:50,770 --> 00:30:54,590 +شرعية not legitimate you can disprove statements + +488 +00:30:54,590 --> 00:30:58,670 +by giving بس مثال واحد يكفي شوفينملايين الأمثلة لا + +489 +00:30:58,670 --> 00:31:03,430 +تكفي للبرهان مثال واحد يكفي لل disapprove لأنه خطأ + +490 +00:31:03,430 --> 00:31:07,490 +المثال by a single example called counter example + +491 +00:31:07,490 --> 00:31:13,160 +مثال عكسي مثال عكسي بيسموه مثال عكسيفطبعا مثال + +492 +00:31:13,160 --> 00:31:17,960 +بسيط بيقول لو أنا قلت فيه قاعدة مجموع أي عددين غير + +493 +00:31:17,960 --> 00:31:22,240 +نسبيين بيكون غير نسبي فهذا ال statement خطأ ليش؟ + +494 +00:31:22,240 --> 00:31:24,820 +يزر التنين غير نسبي و سالب يزر التنين غير نسبي + +495 +00:31:24,820 --> 00:31:28,360 +مجموعهم صفر نسبي إذا القاعدة مش صحية، انتهى، فأنا + +496 +00:31:28,360 --> 00:31:30,960 +بدهش ولا أدور ولا أغلب حالي، مدالة ده مثلها العكس + +497 +00:31:30,960 --> 00:31:35,780 +إذا القاعدة غير صحية، إذا القاعدة غير صحيةلأ فهذه + +498 +00:31:35,780 --> 00:31:38,860 +بعض الإرشادات زي ما حكيتها دول الورقات تكون معنا + +499 +00:31:38,860 --> 00:31:42,900 +دليل ان شاء الله أثناء ال course وممكن نحتاجها + +500 +00:31:42,900 --> 00:31:46,620 +فيما بعد أيضا في بعض الكورسات الأخرى حسب الاحتياج + +501 +00:31:46,620 --> 00:31:51,300 +فان + +502 +00:31:51,300 --> 00:31:52,960 +شاء الله هذه الأمور ان شاء الله هنرجع لها في + +503 +00:31:52,960 --> 00:31:57,140 +مكانها لكن أنا حبيت أنه ناخد صورة عامة حتى أنه + +504 +00:31:57,140 --> 00:32:01,880 +يسهل علينا في المرات القادمة لما نرجع وطبعا وعشان + +505 +00:32:01,880 --> 00:32:05,270 +احنا برضه قريبين منالـ Logic + +506 +00:32:52,230 --> 00:32:54,830 +خلّينا نحاول .. يعني جد ما نقدر ناخد في هذه + +507 +00:32:54,830 --> 00:32:58,100 +المحاضرةmathematical induction ال section الأخير + +508 +00:32:58,100 --> 00:33:01,220 +في هذا ال chapter وهي طريقة من الطرق الخامسة اللي + +509 +00:33:01,220 --> 00:33:04,860 +ذكرناها طريقة الإثبات اللي هو استقرار رياضي + +510 +00:33:04,860 --> 00:33:08,160 +mathematical induction الاستقرار الرياضي وهي طريقة + +511 +00:33:08,160 --> 00:33:13,270 +من الطرق المهمة طبعا تستخدمش يعني في كل مكانتستخدم + +512 +00:33:13,270 --> 00:33:15,710 +للتعامل مع نوع معين من ال statement هنشوفه بعد + +513 +00:33:15,710 --> 00:33:20,310 +قليل لكنها من الأدوات المهمة في الرياضيات لابد من + +514 +00:33:20,310 --> 00:33:24,310 +كل متخصص في الرياضيات يكون بيعرف هذه الأداة وبيعرف + +515 +00:33:24,310 --> 00:33:29,830 +يستخدمها في المكان وبالطريقة الصحيةفالـ + +516 +00:33:29,830 --> 00:33:34,050 +Mathematical Induction فطبعاً هذه عبارة عن طريقة + +517 +00:33:34,050 --> 00:33:39,530 +مفيدة للتعامل مع نوع معين من ال statement وهو جملة + +518 +00:33:39,530 --> 00:33:43,530 +تحتوي على quantifier اللي هي for all جملة شمول + +519 +00:33:43,530 --> 00:33:48,290 +مكمم الشمول for all and b of n طيب بنفع مع أي جملة + +520 +00:33:48,290 --> 00:33:52,160 +فيها for all؟ لأهنا ال universe من نوع خاص ال + +521 +00:33:52,160 --> 00:33:57,380 +universe عبارة عن مجموعة من الأعداد الصحيحة ال + +522 +00:33:57,380 --> 00:34:02,980 +universe بتبدأ من عدد صحيح معين N0 و بتمشي على + +523 +00:34:02,980 --> 00:34:08,700 +التتابع N0 plus one N0 plus two و هكذا إلى ما لا + +524 +00:34:08,700 --> 00:34:14,120 +نهايةالان زيرو يعني عدد صحيح أي عدد صحيح الان زيرو + +525 +00:34:14,120 --> 00:34:17,420 +أي عدد صحيح ممكن يكون سالب عشرة ممكن يكون خمسة أي + +526 +00:34:17,420 --> 00:34:20,360 +عدد صحيح فإذا إحنا في عندنا ال mathematical + +527 +00:34:20,360 --> 00:34:24,220 +induction بيستخدم مع statement فيه for all and P + +528 +00:34:24,220 --> 00:34:27,440 +of N بشرط آخر أن تكون أول شي فيها for all + +529 +00:34:27,440 --> 00:34:30,600 +والuniversity يكون يبدأ من عدد صحيح معين ويمشي على + +530 +00:34:30,600 --> 00:34:33,600 +التتابع مافعش يفط اتنين لازم يمشي واحد واحد + +531 +00:34:33,600 --> 00:34:37,040 +بالترتيب ويبدأ من عدد صحيح ويمشي عدد صحيح على + +532 +00:34:37,040 --> 00:34:38,600 +متتابعة متتابعة + +533 +00:34:40,740 --> 00:34:43,940 +هذه الملاحظة الأولى طبعا ما إيش المبدأ بيقول + +534 +00:34:43,940 --> 00:34:49,640 +المبدأ بيقول ما يلقى بيقول ما يلقى if P of N is an + +535 +00:34:49,640 --> 00:34:52,940 +open sentence طبعا هي الجملة for all and P of N فP + +536 +00:34:52,940 --> 00:34:57,220 +of N بتكون open sentence مكمّم الشمول is an open + +537 +00:34:57,220 --> 00:35:01,780 +sentence involving the natural number and such + +538 +00:35:01,780 --> 00:35:05,980 +that احنا هنبدأ الآن في البداية هذي بشكل عام هنبدأ + +539 +00:35:05,980 --> 00:35:12,270 +مؤقتا أن U تساوي Nيعني هناخد الـ N 0 1 هنبدأ بالـ + +540 +00:35:12,270 --> 00:35:16,350 +N 0 تساوي واحد للتبصير فهناخد ايش كمثال ان N 0 + +541 +00:35:16,350 --> 00:35:18,770 +تساوي واحد ف U تساوي capital N اللي هي ال natural + +542 +00:35:18,770 --> 00:35:23,050 +number فبقولي اه فعبارة عن open sentence ايش ال + +543 +00:35:23,050 --> 00:35:26,510 +universe ال natural number ال universe ال natural + +544 +00:35:26,510 --> 00:35:30,590 +number اه such that انا بدي اثبت ان for all N + +545 +00:35:30,590 --> 00:35:33,850 +تنتمي لل natural number B of N is true بدي اثبت + +546 +00:35:33,850 --> 00:35:38,190 +ايش مطلوب مني اثبت بقولي لازم تعمل خطوة تاليةإن بي + +547 +00:35:38,190 --> 00:35:42,630 +of one is true لازم تثبت أنه بي of واحد true طبعا + +548 +00:35:42,630 --> 00:35:44,970 +لو بدى أثبتها بشكل عام بدي بي واحد بي اتنين بي + +549 +00:35:44,970 --> 00:35:48,270 +تلاتة طب لو أكتش بده أوقف ممكنش طويلة جدا ماقدرش + +550 +00:35:48,270 --> 00:35:53,030 +أخلص فبقول أثبت أنه بي of one is true and أثبت أنه + +551 +00:35:53,030 --> 00:35:58,230 +إذا كانت بي of ك is true then بي of ك plus one is + +552 +00:35:58,230 --> 00:36:02,180 +trueإذا بدك تثبت حاجتين إنه في نقطة بداية وفي + +553 +00:36:02,180 --> 00:36:06,580 +علاقة متتالية ال K مع ال K plus one عشان هيك لازم + +554 +00:36:06,580 --> 00:36:10,660 +ال university تكون تتابع K مع K plus one إذا كانت + +555 +00:36:10,660 --> 00:36:14,500 +true عند ال K فهي لازم تكون true عند ال K plus one + +556 +00:36:14,800 --> 00:36:18,440 +إذا اثبتت إن هدول التانية صحيح، إيش النتيجة؟ then + +557 +00:36:18,440 --> 00:36:22,480 +P of N is true for every natural number N يعني + +558 +00:36:22,480 --> 00:36:25,820 +إيش؟ for all N تنتمي للـN بمعنى آخر إن ال + +559 +00:36:25,820 --> 00:36:29,760 +statement for all N تنتمي للـnatural طبعا للوز P + +560 +00:36:29,760 --> 00:36:36,150 +of N is trueأه طبعا يمكن الأول واه لأ الأمور تكون + +561 +00:36:36,150 --> 00:36:41,390 +شوية صعبة لإيه كيف أنه باثبت عند الواحد واثبتت إذا + +562 +00:36:41,390 --> 00:36:43,890 +كانت صحيحة عند ال K فصحيحة عند ال K plus one صارت + +563 +00:36:43,890 --> 00:36:49,870 +صحيحة للكل صارت صحيحة للكل أنا في عندي مثال ايه من + +564 +00:36:49,870 --> 00:36:55,190 +الواقع ممكن ايه وإيه إيش يقربلنا الصورة يقربلنا + +565 +00:36:55,190 --> 00:37:01,710 +الصورة افترضوا أنه فيه ان احنا شارع طويل مالة + +566 +00:37:01,710 --> 00:37:07,110 +نهاية وبدناانضيقه بإضاءات فبنحط لمبات على قطوات + +567 +00:37:07,110 --> 00:37:10,890 +متباعدة فإي حطينا العمود الأول وهي لمبة والعمود + +568 +00:37:10,890 --> 00:37:14,390 +التاني وهي لمبة والعمود التالت وهي لمبة وبدنا نوره + +569 +00:37:14,390 --> 00:37:19,900 +كله طبعا إلى ما لنهار تمام؟فأول شيء الشرط التاني + +570 +00:37:19,900 --> 00:37:23,420 +بيقول لي خلّي كل عمودين ينشبكوا مع بعض كل عمود + +571 +00:37:23,420 --> 00:37:27,360 +يوصل الكهربا للي بعده كل عمود يوصل الكهربا للي + +572 +00:37:27,360 --> 00:37:32,320 +بعده هايو إذا وصلت ل K توصل إيش ل K plus one وصلت + +573 +00:37:32,320 --> 00:37:36,560 +ل 2 توصل ل 3 وصلت ل 100 إذا بضمن توصل لمين ل 100 + +574 +00:37:36,560 --> 00:37:39,160 +plus one لأنهم مشبوكين مع بعض طيب الأول إيش بيقول + +575 +00:37:39,160 --> 00:37:43,770 +ليه اضمن إن الأول يتوصل بمصدر للكهربامش عارف ايش + +576 +00:37:43,770 --> 00:37:49,370 +برمزولة واضحة هي HP of one فالان اذا وصلت كهربا + +577 +00:37:49,370 --> 00:37:53,610 +للأول هيضيق الأول طب ما الأول بيقاش بوصل للتاني + +578 +00:37:53,610 --> 00:37:57,730 +ضاق و هكذا اذا نقولهم اضاق ولا بياضاقوش فهي الفكرة + +579 +00:37:57,730 --> 00:38:03,820 +فهي الفكرةانتبهوا هال gate دايما بشكل عام أول خطوة + +580 +00:38:03,820 --> 00:38:08,280 +اللي هي P of 1 سهلة وبسيطة لكنها مهمة يعني الآن لو + +581 +00:38:08,280 --> 00:38:12,500 +بدنا نضيق شارع طويل مين أكتر إشي بيكلفنا أنه نعمل + +582 +00:38:12,500 --> 00:38:16,420 +خطوط ونوصل لعامدة طيب لو واحد في آخر إشي نسي يشبك + +583 +00:38:16,420 --> 00:38:19,920 +الفيشة ويوصل كل عمل على الفاضل شفرة عملها بسيطة + +584 +00:38:19,920 --> 00:38:23,580 +فدي مهمة جدا فلازم P of 1 دايما هي خطوة بسيطة + +585 +00:38:23,580 --> 00:38:27,970 +وسهلة لكنها مهمة من غير أبيش كل عمل مابمشيشفهذه + +586 +00:38:27,970 --> 00:38:31,390 +المثال عليها فانا مازال ضمنت ان كل واحد يوصل للي + +587 +00:38:31,390 --> 00:38:34,630 +بعده اذا انا وصلت لان كلهم يعيش ووصلت لهم الكهربا + +588 +00:38:34,630 --> 00:38:40,430 +نفس القضية صحت ال statement ووصلت للكلفطبعا بيقول + +589 +00:38:40,430 --> 00:38:42,690 +لي in order to apply the principle of mathematical + +590 +00:38:42,690 --> 00:38:45,890 +induction to prove a theorem the theorem must be + +591 +00:38:45,890 --> 00:38:51,410 +capable to being broken down into cases طبعا لازم + +592 +00:38:51,410 --> 00:38:53,630 +تكون على الصورة اللي احنا حاطناها for all n, p, or + +593 +00:38:53,630 --> 00:38:56,610 +x one cases for each natural number لازم تكون أيش + +594 +00:38:56,610 --> 00:38:59,510 +عبارة عن حاليات n تسوى واحد, n تسوى اتنين وها كذا + +595 +00:39:01,130 --> 00:39:04,590 +أه فطبعا بيقول اللي لازم هيش انبرهن ان واحد صح و + +596 +00:39:04,590 --> 00:39:08,770 +اتنين صح عشان نثبت ال .. العملية فبقول ال + +597 +00:39:08,770 --> 00:39:12,570 +condition اللي أول بيسموه الحالة الأساسية base + +598 +00:39:12,570 --> 00:39:17,690 +step الخطوة الأساسية و طبعا بشكل عام اثباتها بكون + +599 +00:39:17,690 --> 00:39:21,990 +بشكل عام سهل زي ما حكيناوطبعا هذا بيبقى ايش بديل + +600 +00:39:21,990 --> 00:39:24,870 +Assure us that the theorem is true for at least + +601 +00:39:24,870 --> 00:39:28,490 +one أنت سوّع فاحنا هنا بنضمن أنه في عمود موصول على + +602 +00:39:28,490 --> 00:39:31,910 +الأقل هذا هينوّع بتعمل عملية ما يستمر فهذه هي + +603 +00:39:31,910 --> 00:39:36,790 +العملية الأساسية أو الخطوة الأساسيةال condition + +604 +00:39:36,790 --> 00:39:41,750 +التاني بيسموه inductive step خطوة الاستقرار لإنه + +605 +00:39:41,750 --> 00:39:46,770 +ياشتغل عملية متتابعة to verify this condition عشان + +606 +00:39:46,770 --> 00:39:51,150 +نثبت هذا الشرط التاني we must prove an auxiliary + +607 +00:39:51,150 --> 00:39:56,510 +theorem نظرية مساعدة طيب الآن الشرط التاني إيش هو + +608 +00:39:56,510 --> 00:40:03,950 +الشرط التاني بيقول if P of K is true implies P of + +609 +00:40:03,950 --> 00:40:10,540 +K plus one is trueمظبوط؟ هو هيك هذه جملة شرطية كيف + +610 +00:40:10,540 --> 00:40:16,340 +بنبرهن الجملة الشرطية؟ نفترض أن الشرط صحيح و بنثبت + +611 +00:40:16,340 --> 00:40:20,400 +أن جواب الشرط صحيح فبقول عبارة عن نظرية من + +612 +00:40:20,400 --> 00:40:25,800 +المُعطَى فيها من المُعطَى + +613 +00:40:25,800 --> 00:40:28,860 +P of K is true هذا مُعطَى بيعتبر لأنه هي الشباب ده + +614 +00:40:28,860 --> 00:40:32,720 +منه و وين ال conclusion اللي بدي أوصله P of K plus + +615 +00:40:32,720 --> 00:40:39,570 +one is true P of K plus one is trueأه فطبعا ال .. + +616 +00:40:39,570 --> 00:40:42,090 +هذا اللي احنا ال B of K is true عبارة قلنا سميناها + +617 +00:40:42,090 --> 00:40:44,790 +معطى hypothesis بسموه اللي هو إيش induction + +618 +00:40:44,790 --> 00:40:47,770 +hypothesis اللي هو إيش شرط اللي إيش ال induction + +619 +00:40:47,770 --> 00:40:53,470 +أو الاستقرار أه أو معطى الاستقرار أتوقع .. ماشي + +620 +00:40:53,470 --> 00:40:55,290 +نوقفها إن شاء الله المرة الجاية بنبدأ مع الأمثلة + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/_z6q3CdweFc.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/_z6q3CdweFc.srt new file mode 100644 index 0000000000000000000000000000000000000000..e17933413a0c4b151a770cfe024d4bd3b0151917 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/_z6q3CdweFc.srt @@ -0,0 +1,2083 @@ +1 +00:00:21,230 --> 00:00:25,550 +بسم الله الرحمن الرحيم في المحاضرة اليوم إن شاء + +2 +00:00:25,550 --> 00:00:29,510 +الله هنكمل إحنا في section واحد تلاتة لكن الآن + +3 +00:00:29,510 --> 00:00:34,870 +وقفنا عند نقطة نظرية الأولى وهذه أول نظرية هتدينا + +4 +00:00:34,870 --> 00:00:38,810 +ما يُعرف بقواعد الاستدلال أو القوانين المنطقية + +5 +00:00:38,810 --> 00:00:42,990 +اللي هنستخدمها في دراستنا ده المنطق وطبعا بشكل + +6 +00:00:42,990 --> 00:00:48,260 +أساسي في دراستنا فيما بعد في اللواء الرياضية عنا + +7 +00:00:48,260 --> 00:00:51,840 +النظرية الأولى اللي إحنا رقمناها واحد نقطة واحد + +8 +00:00:51,840 --> 00:00:56,580 +وإحنا هنستخدم هذا الترقيم العدد الأول هيرمز لرمز + +9 +00:00:56,580 --> 00:00:58,640 +الchapter فهذه هي النظرية الأولى في الchapter + +10 +00:00:58,640 --> 00:01:03,300 +الأول هذا كذا هنستخدم الترقيم طبعا فده أول ما + +11 +00:01:03,300 --> 00:01:05,640 +نستخدم نظرية نكتب نظرية واحد واحد نعرف أنه هي + +12 +00:01:05,640 --> 00:01:08,360 +النظرية الأولى في الchapter الأول فإحنا هتتبع هذه + +13 +00:01:08,360 --> 00:01:12,780 +السياسة في ترقيم النظريات وما شابه اه الآن فإحنا + +14 +00:01:12,780 --> 00:01:16,790 +عندنا هنا نظرية اللي إحنا ممكن ن .. طبعا ال .. أو + +15 +00:01:16,790 --> 00:01:21,830 +theorem ممكن نعربها نظرية أو مبرهنة هي هتدينا اللي + +16 +00:01:21,830 --> 00:01:26,070 +هي عبارة عن قاعدة معينة صحيحة دائما فهي تعتبر + +17 +00:01:26,070 --> 00:01:30,660 +قاعدة بنستخدمها في كل مكان جيد جدا أنه أو من المهم + +18 +00:01:30,660 --> 00:01:35,740 +جدا أنه نتعود كيف نقرأ النظرية كيف نقرأ النظرية + +19 +00:01:35,740 --> 00:01:38,200 +اللي هي طبعا نظرية فيها معطيات وفيها استنتاج + +20 +00:01:38,200 --> 00:01:42,460 +والاستنتاج ده بيكون كقاعدة دائما صحيح فنتعود في + +21 +00:01:42,460 --> 00:01:45,100 +هذا النوع من النظريات و النظريات كل الرياضيات + +22 +00:01:45,100 --> 00:01:48,380 +اللي حد يجي في اللي هو اللي دراستنا التالية إن شاء + +23 +00:01:48,380 --> 00:01:51,940 +الله كيف بدنا نقرأ النظرية فنشوف إن النظرية هنا + +24 +00:01:51,940 --> 00:02:00,610 +بدت بتقديم let b and q be any two statements اه هنا + +25 +00:02:00,610 --> 00:02:04,110 +إيش بيعني هذه الجملة؟ هنا جملة بتمهد لي إن أنا + +26 +00:02:04,110 --> 00:02:09,390 +هستخدم رمزين small b و small q فهنا بتقول هدول اللي + +27 +00:02:09,390 --> 00:02:13,330 +هيش بيرمزه وده سياسة عامة في الرياضيات لما نستخدم + +28 +00:02:13,330 --> 00:02:17,110 +رمز لازم نحدد ليش برمز هل هو ال P هنا عدد ولا + +29 +00:02:17,110 --> 00:02:19,970 +مجموعة ولا إيش نوعه فبقول هنا ال P و ال Q + +30 +00:02:19,970 --> 00:02:22,750 +statements هذه النقطة الأولى بدنا ننتبه إليها وهذا + +31 +00:02:22,750 --> 00:02:25,550 +السياسة عامة في قراءتكم لأي نظرية لازم تتبعوا لها + +32 +00:02:25,550 --> 00:02:29,010 +الكلام النقطة الثانية جالي any statements وحقيقة + +33 +00:02:29,010 --> 00:02:32,670 +في .. لقدام شوية هنبطل نحكي any المهم هنا إيش + +34 +00:02:32,670 --> 00:02:38,460 +بيحكي أنه بيقول لي أي قانون في هذه النظرية بدو يستخدم + +35 +00:02:38,460 --> 00:02:42,620 +الرمزين بي و Q بينطبق على أي two statements على أي + +36 +00:02:42,620 --> 00:02:44,960 +two statements إذا هدول ال statements مالهموش أي + +37 +00:02:44,960 --> 00:02:47,520 +خصوصية مجليش هدول ال statements مثلًا tautology + +38 +00:02:47,520 --> 00:02:51,680 +مجليش هدول إكاش تضمين مجليش أي حاجة عنهم إذا ما + +39 +00:02:51,680 --> 00:02:56,700 +يلي القوانين التالية تنطبق على جميع التقارير على + +40 +00:02:56,700 --> 00:02:59,680 +إيش any two statements إذا إن دول ال P و ال Q ما + +41 +00:02:59,680 --> 00:03:02,480 +زالهم بيرمزوا لأي statements بشكل عام إذا إن + +42 +00:03:02,480 --> 00:03:06,520 +القوانين اللي هتتضمنهم في هذه النظرية تنطبق على + +43 +00:03:06,520 --> 00:03:10,120 +جميع ال statements واضح؟ اه فإن كل كلام إحنا إيش + +44 +00:03:10,120 --> 00:03:12,720 +مافيش عندنا كلام إنشائي في الرياضيات كلامنا علمي + +45 +00:03:12,720 --> 00:03:17,000 +ومُدقق كل كلمة إلها دور ما بنحطش كلام زيادة فلازم + +46 +00:03:17,000 --> 00:03:21,040 +كل كلمة نفهمها و نعرف إيش بتدل علينا طبعا then فال + +47 +00:03:21,040 --> 00:03:24,140 +gate هذه هو وعد المقدمة الآن هيبدأ يدينا القواعد + +48 +00:03:24,710 --> 00:03:28,590 +القاعدة الأولى أو القانون الأول سماه قاعدة الإضافة + +49 +00:03:28,590 --> 00:03:32,750 +law of addition قاعدة الإضافة إلها اسم طبعا مش كل + +50 +00:03:32,750 --> 00:03:35,530 +قانون إله اسم صحيح فيها نظرية فيه فغور لكن مش كل + +51 +00:03:35,530 --> 00:03:38,390 +نظرية إلها اسم فده هو اسم القانون طبعا هذا بيساعدنا + +52 +00:03:38,390 --> 00:03:42,070 +أنه نستخدمه إيش بيقول القانون القانون الحقيقة هو + +53 +00:03:42,070 --> 00:03:46,420 +قانون تضمين إيش يعني قانون تضمين؟ يعني هو جملة + +54 +00:03:46,420 --> 00:03:50,440 +شرطية صائبة دائما، مطلقة الصواب، tautology، مظبوط؟ + +55 +00:03:50,440 --> 00:03:54,480 +اه، إيش بيقول لي؟ بيقول لي إن الجملة if P then P or + +56 +00:03:54,480 --> 00:04:00,070 +Q دائما صحيحة أو بمعنى آخر P implies P or Q + +57 +00:04:00,070 --> 00:04:05,210 +implies P or Q طبعا ليس إنه قانون الإضافة لأنه بدأ + +58 +00:04:05,210 --> 00:04:09,250 +بstatement وانتهى ب two statements فأضاف بدأ بجزء + +59 +00:04:09,250 --> 00:04:12,230 +وانتهى بجزئين فهي التسمية عشان نتذكر إيش التسمية + +60 +00:04:12,230 --> 00:04:16,630 +فهو قانون الإضافة طبعا هذا القانون دائما صحليش + +61 +00:04:16,630 --> 00:04:20,690 +دائما صح؟ خلّينا نشوف، هو عبارة عن جملة شرطية، صح؟ + +62 +00:04:20,690 --> 00:04:23,390 +الجملة الشرطية بتكون هنا صحيحة دائما، وما كانتش + +63 +00:04:23,390 --> 00:04:26,610 +بيكون الجملة الشرطية صحيحة، يا إما الأول، الأول + +64 +00:04:26,610 --> 00:04:29,570 +false، بغض النظر عن التاني، مظبوط، اللي هو إيش، + +65 +00:04:29,570 --> 00:04:33,610 +الشرط صحيح، لإن مافيش وعد، مافيش مشكلة، أو إذا + +66 +00:04:33,610 --> 00:04:37,330 +الأول true، لازم التاني يكون true طب نشوف، لو كانت + +67 +00:04:37,330 --> 00:04:39,910 +ال B False، مافيش مشكلة، مظبوط؟ إذا أنا ده + +68 +00:04:39,910 --> 00:04:43,990 +ما بيبناهاش نفحصه طب لو ال B True، B or Q، دايما + +69 +00:04:43,990 --> 00:04:46,630 +ال True لإن جزء أنا ضامن إن جزء True، بغض النظر + +70 +00:04:46,630 --> 00:04:50,390 +عن ال Q، ما زال B True، B or Q، دايما True، + +71 +00:04:50,390 --> 00:04:53,350 +فواضح؟ فإن أنا جيت حللت أنا تحليل هيك شفوي، + +72 +00:04:53,350 --> 00:04:56,050 +و هنثبتها، ممكن نثبتها بسهولة، فواضح ليش القانون + +73 +00:04:56,050 --> 00:05:01,210 +True؟ و ليش هو تضمين؟ و ليش هو إضافة؟ في أي سؤال؟ + +74 +00:05:01,210 --> 00:05:05,110 +اه، اه، فإيه القانون الأول القانون التاني يعتبر + +75 +00:05:05,110 --> 00:05:09,950 +عكسه اللي هو مش إضافة يعني زي حدث أول حدث اللي هو + +76 +00:05:09,950 --> 00:05:13,370 +law of simplification قانون اللي هو إيش التبسيط + +77 +00:05:13,370 --> 00:05:16,970 +بنسميه حدث أو تبسيط Simplification تبسيط إحنا اه + +78 +00:05:16,970 --> 00:05:21,050 +بنعمل سؤال يسميه حدث العكس هنا بقول بي and كيو + +79 +00:05:21,050 --> 00:05:25,690 +implies بي بي and كيو implies بي فهنا إيش؟ ليش + +80 +00:05:25,690 --> 00:05:30,320 +حدث؟ لأنه بدأ بجزئين وانتهى بجزء في الفرق، بس انتبه + +81 +00:05:30,320 --> 00:05:33,860 +هنا طبعا في الأول الاضافة or في التاني في التحديث + +82 +00:05:33,860 --> 00:05:37,620 +and، مهم جدا، طبعا انحللوا شفاويا ليش هذا true؟ + +83 +00:05:37,620 --> 00:05:40,640 +بقول ال B and Q إذا كانت هذه false مافيش مشكلة + +84 +00:05:40,640 --> 00:05:45,040 +أصلا، فدائما ال if then true، مظبوط؟ لكن لو كان + +85 +00:05:45,040 --> 00:05:47,340 +هذا ال true مش معناه، إن ال B و ال Q true، فبشكل + +86 +00:05:47,340 --> 00:05:52,860 +خاص ال B true، بكل بساطة، واضح؟ فهذا هو القانون، + +87 +00:05:52,860 --> 00:05:58,920 +تفضلي ليش هذا true؟ لأن هو جملة شرطية وقلنا الجملة + +88 +00:05:58,920 --> 00:06:01,820 +الشرطية بتكون false وقتاش إذا كان الأول true + +89 +00:06:01,820 --> 00:06:05,200 +و التاني false بس طيب فلو كان الأول false no + +90 +00:06:05,200 --> 00:06:08,540 +problem always true طب لو كان true معناته ال B و + +91 +00:06:08,540 --> 00:06:10,760 +ال Q true لأن وقتاش بتكون عندي true إذا التاني + +92 +00:06:10,760 --> 00:06:14,320 +true بشكل خاص ال B true ولا لأ أنا عارف إن ال B و + +93 +00:06:14,320 --> 00:06:19,230 +ال Q true فالB true ولا مش true true أي سؤالأي + +94 +00:06:19,230 --> 00:06:24,250 +سؤال القانون التالت disjunctive syllogism + +95 +00:06:24,250 --> 00:06:30,690 +disjunctive مرت علينا فصل syllogism سنسميها كقياس + +96 +00:06:30,690 --> 00:06:35,410 +مُمتقي فاصل سنعرفها قياس مُمتقي فاصل ممكن نعبر عن + +97 +00:06:35,410 --> 00:06:40,290 +القانون باسم آخر the way that affirms by denying + +98 +00:06:40,460 --> 00:06:45,400 +طريقة الإثبات بالنفي طريقة الإثبات بالنفي خلّينا + +99 +00:06:45,400 --> 00:06:48,580 +طبعا قانون الفصل المنطقي مش كتير يعني يكون واضحة + +100 +00:06:48,580 --> 00:06:52,760 +لكن زي ما فسّرنا إيش ليش إضافة و ليش حدث ممكن نفسر + +101 +00:06:52,760 --> 00:06:57,540 +الثانية الإثبات بالنفي إيش بيقول لي بيقول P or q and + +102 +00:06:57,540 --> 00:07:02,400 +not P then Q أو implies Q فانا بدي أثبت إنه Q + +103 +00:07:02,400 --> 00:07:06,760 +true إيش عملت نفية ال P فأنا أثبت صحة ال Q عن طريق + +104 +00:07:06,760 --> 00:07:11,820 +نفي ال P عشان هيك التسمية the way of إيش that + +105 +00:07:11,820 --> 00:07:16,160 +affirms إثبات by denying عشان أثبت صحة ال Q نفية + +106 +00:07:16,160 --> 00:07:20,360 +ال P اه إثبات عن طريق النفي إثبات صحة شيء ما عن + +107 +00:07:20,360 --> 00:07:23,180 +طريق النفي هذا بس أول اسم بس هو ده القانون إحنا + +108 +00:07:23,180 --> 00:07:26,240 +نعرفه كام بدنا نعرفه كام طب عن إيش برضه نفسر + +109 +00:07:26,240 --> 00:07:30,320 +شفاويا بقول لي هل جيت P or كيو؟ إذا إيش فيه؟ يا + +110 +00:07:30,320 --> 00:07:33,000 +على الأقل واحدة صح، يا التنتين صح، هذا بيكون true، + +111 +00:07:33,000 --> 00:07:35,960 +مظبوط؟ طب لو عرفت إن ال P خطأ، لازم ال Q تكون + +112 +00:07:35,960 --> 00:07:39,420 +true، ولا لأ؟ فهيك بقول هو تماما، أنت .. أندي جملة + +113 +00:07:39,420 --> 00:07:44,080 +إيش؟ جملة اختيارية، جملة اللي هو إيش؟ بيخيرني، + +114 +00:07:44,080 --> 00:07:47,480 +بيقول لي يا بتختار يا P، يا Q، طب P أنتفي هذا + +115 +00:07:47,480 --> 00:07:50,900 +الخيار، إيش بيتبقى؟ Q، لو فينا جواق سؤال اختيار + +116 +00:07:50,900 --> 00:07:54,680 +من المتعدد، أنا قلت أندي الاختيارات P or Q، طب + +117 +00:07:54,680 --> 00:07:58,810 +ال P عرفت أنا .. أنت أكيد أنا خطأ واضحة فهذا الفصل + +118 +00:07:58,810 --> 00:08:02,970 +فش منطق جدا يعني إحنا بشتغل عليه دايما فهذا قانون + +119 +00:08:02,970 --> 00:08:06,750 +منطقي صحيح وبيسموه قانون الفصل القياس المنطق + +120 +00:08:06,750 --> 00:08:13,210 +الفاصل مهم جدا ها هنشوف اللي هو إيش البرهان هبرهن + +121 +00:08:13,210 --> 00:08:16,730 +واحدة من تلاتة واترك الباقي exercise لأن نفس + +122 +00:08:16,730 --> 00:08:20,330 +الطريقة ما علينا إلا أن نعيد نفس الخطوة فاختاروا + +123 +00:08:20,330 --> 00:08:23,510 +واحدة من تلاتة أبرهن القيامة التالتة عشان هي إيش + +124 +00:08:23,510 --> 00:08:28,340 +بقى هنا أطول شوية وليكن فإحنا جيت هنا approve و هاي + +125 +00:08:28,340 --> 00:08:34,560 +C تمام اه بدي أبرهن حاجة بدي أحل أي مسألة في + +126 +00:08:34,560 --> 00:08:39,260 +الرياضيات زي ما حكينا مهم جدا أحدد إيش المطلوب و + +127 +00:08:39,260 --> 00:08:43,860 +إيش المعطيات و ممكن أعيد صياغة المطلوب هذه الخطوة + +128 +00:08:43,860 --> 00:08:47,930 +بيسموها الخطوة الأولى هي فهم السؤال وفاهم السؤال + +129 +00:08:47,930 --> 00:08:51,370 +وتحديد المطلوب منه بشكل أساسي فهذه خطوة من أربع + +130 +00:08:51,370 --> 00:08:55,490 +خطوات في عالم اسمه بوليا جورج بوليا جاهز له فيه + +131 +00:08:55,490 --> 00:08:58,870 +أربع خطوات لحل أي مسألة رياضية ولحقيقة يمكن حل أي + +132 +00:08:58,870 --> 00:09:01,870 +مسألة في اللي هو في الحياة حتى فيه بقال أربع خطوات + +133 +00:09:01,870 --> 00:09:05,270 +أولا تفهم المسألة الخطوة الثانية اللي هو تعرف + +134 +00:09:05,270 --> 00:09:09,370 +طريقة الحل أو صممها وهذه أصعب خطوة وهذه أصعب خطوة + +135 +00:09:09,370 --> 00:09:12,940 +الخطوة الثالثة التطبيق الطريقة وهذه أسهل لأنه خلاص + +136 +00:09:12,940 --> 00:09:15,340 +مازال عارف إن الطريقة خطوات عملية في الغالب بتكون + +137 +00:09:15,340 --> 00:09:18,720 +عملية آلية والخطوة الرابعة التحقق إن الجواب صحيح + +138 +00:09:18,720 --> 00:09:21,300 +أو إن الطريقة صحيحة إن الطريقة صحيحة فهذه إن شاء + +139 +00:09:21,300 --> 00:09:24,140 +الله الخطوات هنكررها مع بعض وعشان نصير إننا + +140 +00:09:24,140 --> 00:09:27,600 +بنسميها منهج في التعامل مع الرياضيات مع البراهين + +141 +00:09:27,600 --> 00:09:31,260 +مع المسائل مهمة جدا وهذه بتريحنا في دراستنا + +142 +00:09:31,260 --> 00:09:34,340 +الرياضيات وحتى إن شاء الله تنعكس على الحياة وكيف + +143 +00:09:34,340 --> 00:09:37,560 +نتعامل مع المسائل، إذا أول حاجة نفهم إيش السؤال + +144 +00:09:37,560 --> 00:09:42,080 +السؤال بيقول لي أثبت أن P or Q and not P implies + +145 +00:09:42,080 --> 00:09:45,580 +Q إيش معنى هذا الكلام؟ يعني بدي أثبت أن الجملة + +146 +00:09:45,580 --> 00:09:49,160 +الشرطية إنها Tautology، بظبط، خلّيني نكتب هذا + +147 +00:09:49,160 --> 00:09:52,280 +الكلام، ممكن هذا اللي عاملنا نفكر فيه شفوي أو نحطه + +148 +00:09:52,280 --> 00:09:54,840 +على هامش أو ممكن نكتبه، كل هذا بيساعد، فإذا أول + +149 +00:09:54,840 --> 00:09:58,660 +خطة نقول we want to show or have to show that + +150 +00:10:05,520 --> 00:10:19,660 +P or Q and not P then Q is a tautology تمام؟ + +151 +00:10:19,660 --> 00:10:22,360 +إذا أنا هنا إيش حددنا المطلوب يفهمنا السؤال واضح + +152 +00:10:22,360 --> 00:10:25,320 +السؤال ولا بده توضيح كمان؟ إذا واضح خلاص ما بده + +153 +00:10:25,320 --> 00:10:29,020 +توضيح، بحاول أوضحه واضح، الأخوات مهم جدا هنا مهم جدا + +154 +00:10:29,020 --> 00:10:32,080 +نفهم السؤال ممتاز، إذا هي أنا عندي السؤال واضح + +155 +00:10:32,080 --> 00:10:36,090 +السؤال الآن ما هي طريقة الحل؟ truth table فعشان + +156 +00:10:36,090 --> 00:10:45,590 +نستخدم جداول الصدق we will use truth tables جداول + +157 +00:10:45,590 --> 00:10:49,270 +الصدق ممتاز، فشايفين حددنا المطلوب، افهمنا السؤال + +158 +00:10:49,270 --> 00:10:53,250 +حددنا الطريقة، هنطبق، نعمل جدول الصدق، ممتاز، هاي جدول + +159 +00:10:53,250 --> 00:10:56,170 +الصدق، اتعلمنا جدول الصدق من الأدوات السهلة + +160 +00:10:56,170 --> 00:10:59,150 +والبسيطة وأتوقع الكل هيتمكن منها إن شاء الله + +161 +00:10:59,150 --> 00:11:02,490 +فبنطلع على ال statement أكمل statement بسيطة إثنتين + +162 +00:11:02,490 --> 00:11:06,790 +المركبات الأساسية، two statements تقريرين إذا في + +163 +00:11:06,790 --> 00:11:10,470 +عندنا عمودين أساسيين وفي عندنا إيش أربع احتمالات + +164 +00:11:10,470 --> 00:11:15,290 +هي P وهي Q وهذا هو سطر العناوين، خلينا نسميه، وفي + +165 +00:11:15,290 --> 00:11:20,590 +عندنا أربع احتمالات هي إثنين وهي إثنين تمام ممتاز + +166 +00:11:20,590 --> 00:11:26,430 +الآن نوزع الاحتمالات، true true و false false، true + +167 +00:11:26,430 --> 00:11:32,880 +false or true false true false، أي سؤال، الآن بدنا + +168 +00:11:32,880 --> 00:11:36,580 +نبدأ إيش؟ نحسب قيم الصدق لهذه ال statement جزء جزء + +169 +00:11:36,580 --> 00:11:40,260 +حتى نوصل لمين؟ للصورة الأخيرة اللي هي إيش مطلوبة؟ + +170 +00:11:40,260 --> 00:11:44,400 +مين أول حاجة مطلوبة؟ الـ not .. الـ not .. الـ not .. ممكن، + +171 +00:11:44,400 --> 00:11:47,700 +بس إيش الـ not؟ لأ، تتنصح، اه فإنا أبدأ أبدأ بالنط، مش + +172 +00:11:47,700 --> 00:11:51,740 +مشكلة، تتنصح، لأن هدول جزئين منفصلين، فإنا فيه على + +173 +00:11:51,740 --> 00:11:57,240 +طول false false true true ممتاز، بعدين الجوس + +174 +00:11:57,240 --> 00:12:00,980 +الداخلي، الجوس الصغير هذا P or Q، اه واحنا + +175 +00:12:00,980 --> 00:12:03,560 +نقول إن هذه بتكون دائما true ما عدا في حالة واحدة، + +176 +00:12:03,560 --> 00:12:08,160 +إذا الثانية false، إذا true true، false، ممتاز، + +177 +00:12:08,160 --> 00:12:11,220 +على طول، إذا متأكد، بتأكد منهم، إذا متأكد من + +178 +00:12:11,220 --> 00:12:14,740 +الترتيب، متعود على الترتيب، وهذه يمكن ميزة أخرى، + +179 +00:12:14,740 --> 00:12:17,080 +إن أنا اعتمد الترتيب، هذا ما يغيرهش، طبعا نقول إن مش + +180 +00:12:17,080 --> 00:12:19,040 +هذا هو الترتيب الوحيد اللي بدأنا فيه، طبعا الأول + +181 +00:12:19,040 --> 00:12:22,720 +حرين، أول عمودين، اختيارهم حر، بس يغطي الاحتمالات + +182 +00:12:22,720 --> 00:12:25,540 +الأربعة كلها بشكل صحيح، اه طب لو أنا بدأت false + +183 +00:12:25,540 --> 00:12:28,660 +false مثلا، صح ولا صح؟ لكن لو أنا اتعودت على ترتيب + +184 +00:12:28,660 --> 00:12:31,640 +معين، بأتمنى إن أنا اختارت كل الاختيارات، وأيضا + +185 +00:12:31,640 --> 00:12:34,120 +ممكن يسهل علي الحسابات، لأنه أنا حاصرت حفظهم، ممكن + +186 +00:12:34,120 --> 00:12:37,180 +يسهل علي الحسابات تمام؟ وفي حاجة ثانية، ممكن أكوش + +187 +00:12:37,180 --> 00:12:39,980 +كتير بيسهل علي التصليح، لأن أنا بكون هذا الحل + +188 +00:12:39,980 --> 00:12:42,660 +النموذج بيحل .. بيسهل .. لأن هذا الحل النموذج بيحل + +189 +00:12:42,660 --> 00:12:46,020 +بطريقة هذه، طيب هل جيت بعد هيك عشان أعمل الجوس + +190 +00:12:46,020 --> 00:12:53,210 +الكبير؟ الجوس الكبير P or Q and not P، ممتاز، إذا في + +191 +00:12:53,210 --> 00:12:56,830 +إن and، ال and بين مين؟ بين هدول العمودين، اه false + +192 +00:12:56,830 --> 00:13:00,470 +true، اه ده بده حساب، false false and true false + +193 +00:13:00,470 --> 00:13:08,230 +true and true true false، ممتاز، أي سؤال، الآن الجملة + +194 +00:13:08,230 --> 00:13:11,530 +الأخيرة اللي كلها مع بعض بدنا نشوف إن هي فعلا + +195 +00:13:11,530 --> 00:13:17,370 +Tautology، يعني دائما صحيحة، P and not P then Q نشوف + +196 +00:13:17,370 --> 00:13:22,150 +فاحنا بدنا F، ال F كيف ماشية؟ ال F، ال F جاية من and + +197 +00:13:22,150 --> 00:13:28,450 +لمن لـ Q لـ and سهم في ال F then، جيد نعمل هذه + +198 +00:13:28,450 --> 00:13:30,830 +لأن الترتيب فيها مهم، فبيده دقة، فتمام + +199 +00:13:44,930 --> 00:13:50,190 +أي سؤال .. أي سؤال .. اه واضح من الجدول إن فعلا + +200 +00:13:50,190 --> 00:13:53,350 +البرهان انتهى، وإن فعلا إنها إيش؟ Tautology فنكتب هنا + +201 +00:13:53,350 --> 00:14:00,970 +by the table or from the table from the table we + +202 +00:14:00,970 --> 00:14:05,910 +see that، اللي هو ممكن تقبلوا إن هذه طول الجهاد + +203 +00:14:05,910 --> 00:14:10,450 +المطلوب أو الـ implies كله صح اللي بريحكم، اللون + +204 +00:14:10,450 --> 00:14:16,170 +بعبر على إنه إيش؟ الحل انتهى implies الـQ وهو + +205 +00:14:16,170 --> 00:14:23,920 +المطلوب، أي سؤال؟ تعليق بسيط ونصيحة لهذا البرهان ول + +206 +00:14:23,920 --> 00:14:28,940 +غيره، اقعوا اتحاولوا انتوا وانتوا بتحلوا، طلعت + +207 +00:14:28,940 --> 00:14:32,900 +واحدة فيهم false، إذا حالك فيه خطأ، لأنه جالك برهنة + +208 +00:14:32,900 --> 00:14:35,840 +يعني هذا صح ماشي تقوليله إنه ليش السؤال غلط في + +209 +00:14:35,840 --> 00:14:38,700 +الغالب، السؤال صحيح تمام؟ ماشي تقوليله إنه ليش + +210 +00:14:38,700 --> 00:14:41,000 +false أو تروح انت، انت عارف إن طلعة معاك في + +211 +00:14:41,000 --> 00:14:44,330 +الحسابات false تحط true، اقع تعملي هذا الكلام، لأن + +212 +00:14:44,330 --> 00:14:48,070 +انت مازال صار معاك خلل، هذه طريقة إنك تكتشف إنه في + +213 +00:14:48,070 --> 00:14:52,490 +حالك في خطأ من ما، فهذه فرصة لك إنك تراجع، فمازال + +214 +00:14:52,490 --> 00:14:56,470 +طلع معاك في أحد الحسابات شيء مش متوقع، إذا في خطأ + +215 +00:14:56,470 --> 00:14:59,070 +من ما، بتقول إيه؟ فرصة إنك تراجع الحسابات في مكان ما + +216 +00:14:59,070 --> 00:15:01,990 +عملتي حاجة غلط، واضح؟ فإن إيش؟ أمركم اتحاولوا في + +217 +00:15:01,990 --> 00:15:05,430 +الرياضيات إنكوا إيش؟ اتدلسوا على المصحى حولكم + +218 +00:15:05,430 --> 00:15:08,270 +وخارجه، لأ، هذه فرصة مازالت جيتوا في خلل، حاولوا + +219 +00:15:08,270 --> 00:15:11,400 +تدوروا على الخلل، اه تمام، فهذه مهمة جدا إنه فرصة إنه + +220 +00:15:11,400 --> 00:15:14,760 +يعرف إنه في خطأ ودائما تشخيص الخطأ ومعرفة الخطأ + +221 +00:15:14,760 --> 00:15:17,700 +هذه أول خطوة على خطأ، إيش؟ على طريق الحل أو طريق + +222 +00:15:17,700 --> 00:15:30,120 +المعالجة، فمهم جدا ننتبه لهذه النقاط، أي سؤال، تمام + +223 +00:15:31,520 --> 00:15:35,220 +ننتقل الآن في مصطلح كان في العنوان، المصطلح الثالث + +224 +00:15:35,220 --> 00:15:39,040 +والأخير، كان في عندنا Tautology تقرير مطلق الصواب + +225 +00:15:39,040 --> 00:15:41,900 +كان في عندنا التضمين Implications وكان عندنا ال + +226 +00:15:41,900 --> 00:15:46,060 +Equivalence طبعا التكافؤ مر علينا قبل هيك وقلنا أن + +227 +00:15:46,060 --> 00:15:48,900 +الـ two statements بيكونوا متفقين وكافئين إذا كانوا + +228 +00:15:48,900 --> 00:15:51,960 +يا true مع بعض يا false مع بعض في جميع الاحتمالات + +229 +00:15:51,960 --> 00:15:56,440 +المنطقية الممكنة الممكنة، الآن هنشوف تعريف آخر، هنشوف + +230 +00:15:56,440 --> 00:16:00,440 +تعريف آخر، مش أقارن ال statement مع بعض مباشرة عن + +231 +00:16:00,440 --> 00:16:03,040 +طريق اللي هي ال by conditional، عن طريق الجملة + +232 +00:16:03,040 --> 00:16:07,860 +الثنائية الشرطية كما سمينا الجملة الشرطية لما تكون + +233 +00:16:07,860 --> 00:16:11,380 +Tautology سميناها تضمين، الجملة الثنائية الشرطية لما + +234 +00:16:11,380 --> 00:16:14,740 +تكون Tautology هنسميها Equivalence، واضح؟ هنسميها + +235 +00:16:14,740 --> 00:16:17,500 +تكافؤ، إذا حيصير عندنا تعريفين لتكافؤ، هصير + +236 +00:16:17,500 --> 00:16:20,320 +عندنا تعريفين لتكافؤ، خلينا نقرأ التعريف مع بعض، و + +237 +00:16:20,320 --> 00:16:24,640 +بعدين بنشوف إذا في تعليقات، بيقول لي Let P,Q be two + +238 +00:16:24,640 --> 00:16:27,040 +statements، صح، زي شوفنا نفسنا السياسية النظرية برضه + +239 +00:16:27,040 --> 00:16:30,000 +إيش ب .. ب .. ب .. بماهل، فإذا وين ما استخدم ال + +240 +00:16:30,000 --> 00:16:32,040 +capital P و capital Q دول إيه؟ مش برمزه ل + +241 +00:16:32,040 --> 00:16:35,520 +statements برمزه لتقارير، لتقارير، طيب بيقول لي + +242 +00:16:35,520 --> 00:16:38,080 +compound or simple، هنا بيأكد إنه أي statement بشكل + +243 +00:16:38,080 --> 00:16:41,480 +عام، هنا طبعا لو لاحظنا في مبادئ الرياضيات بكرا في + +244 +00:16:41,480 --> 00:16:44,180 +المثلقات مش هيركزلكوا عليها، مازال جالي إنّي أو + +245 +00:16:44,180 --> 00:16:47,810 +جالي statements كلام عام، إذا إيش؟ باخده على مطلقه + +246 +00:16:47,810 --> 00:16:50,750 +العموم، دائما العموم هو إيش؟ الأصل، إذا كان في حاجة + +247 +00:16:50,750 --> 00:16:53,630 +تخصصه زي في القواعد الشرقية دائما النص على عمومه + +248 +00:16:53,630 --> 00:16:55,950 +إلا إذا في حاجة تقيده أو تخصصه، هنا نفس الشيء + +249 +00:16:55,950 --> 00:16:59,190 +بالرياضيات، مازال جلّت and statement، مافيش تخصيص + +250 +00:16:59,190 --> 00:17:02,310 +خلاص، بس بشغل على كل statement خصص، باخد التخصيص + +251 +00:17:02,310 --> 00:17:05,510 +واضح؟ اه فهنا طبعا كلمة simple أو compound بس عشان + +252 +00:17:05,510 --> 00:17:07,950 +كوا مبادئ ولا ويقفم مفهومة ضمنية، ده الكلام لإنه + +253 +00:17:07,950 --> 00:17:11,970 +جل بي two statements، يعني and statements بشكل عام + +254 +00:17:11,970 --> 00:17:15,650 +تمام، هل جيت بيحط التعريف؟ ما هو التعريب؟ بيقول لي + +255 +00:17:15,650 --> 00:17:20,370 +إذا كانت الجملة الثنائية الشرطية P if and only if + +256 +00:17:20,370 --> 00:17:23,670 +Q is a tautology زي ما حكيت، إذا إيش؟ ما لا + +257 +00:17:23,670 --> 00:17:27,130 +بيسميها تكافؤ، ع فإذا الجملة الشرطية لما تكون + +258 +00:17:27,130 --> 00:17:30,070 +Tautology إيش بيسميها؟ تضمين، والجملة الثنائية الشرطية + +259 +00:17:30,070 --> 00:17:33,310 +إذا كانت Tautology إيش بيسميها؟ تكافؤ، تكافؤ، إيش + +260 +00:17:33,310 --> 00:17:37,530 +الرمز؟ زي ما عملنا تضمين ساهم بخطين أفقيين، نفس + +261 +00:17:37,530 --> 00:17:40,090 +القضية، ساهم بخطين أفقيين بس اتجاهين، لإن هي إيش + +262 +00:17:40,090 --> 00:17:42,050 +إيه؟ two .. ال .. ال .. ال .. ال .. ال by + +263 +00:17:42,050 --> 00:17:44,870 +conditional, two if then، وإذا إيه؟ إيش مالها؟ two + +264 +00:17:44,870 --> 00:17:48,590 +تضمين يعني، هتكون التكافؤ تضمين بالاتجاهين، واضح؟ + +265 +00:17:48,590 --> 00:17:54,270 +نفس القضية طبعا، إيش نخرقها؟ P is equivalent to Q + +266 +00:17:56,290 --> 00:17:59,770 +إذا نهدى تعريف آخر للتكافؤ، بنأكد عليه، وصار في + +267 +00:17:59,770 --> 00:18:02,990 +عيننا رمزين للتكافؤ، الرمز اللي أمامنا هذا السهم + +268 +00:18:02,990 --> 00:18:06,670 +في اتجاهين، وفي عيننا التلات خطوط للتكافؤ، طيب + +269 +00:18:06,670 --> 00:18:09,910 +وقتاش نستخدم هذا ووقتاش نستخدم هذا؟ دائما بدكوا + +270 +00:18:09,910 --> 00:18:13,680 +بدون أي فرق، اللي بتحبوه، هذا مطلع، ليش حرية تم، + +271 +00:18:13,680 --> 00:18:16,200 +مافيش بينهم فرق، مافيش بينهم فرق، وهي الملاحظة + +272 +00:18:16,200 --> 00:18:19,920 +بتقول .. بتقول لي P to Q أو P to Q، رمز التاني، هنستخدمهم بشكل متبادل بدون أي فرق، + +273 +00:18:19,920 --> 00:18:23,840 +have the same meaning، نفس المعنى، نفس الاستخدام، + +274 +00:18:23,840 --> 00:18:27,880 +and we will use the two notations interchangeably، + +275 +00:18:27,880 --> 00:18:30,980 +بشكل متبادل، مرة بنستخدم هذا ومرة بنستخدم هذا، + +276 +00:18:30,980 --> 00:18:33,500 +اللي بريحنا، اللي بيجي أبسط، اللي متعودين عليه، + +277 +00:18:33,500 --> 00:18:35,580 +اللي بيجي على بالنا أسرع، مافيش أي فرق إطلاقا إن + +278 +00:18:35,580 --> 00:18:40,390 +رموز P if and only if P equivalent برضه؟ لأ، مش رموز P + +279 +00:18:40,390 --> 00:18:46,050 +if and only if P، رموز التكافؤ إنها جملة P if and only if من + +280 +00:18:46,050 --> 00:18:51,190 +Q. + +281 +00:18:51,190 --> 00:18:57,970 +أي جملة، لأ، وتكون Tautology، مطلقة الصواب إيش + +282 +00:18:57,970 --> 00:19:01,770 +ال equivalent؟ وين؟ إن الرمز اللي بنحكي عنه F and + +283 +00:19:01,770 --> 00:19:06,150 +only F مطلقة الصواب أه أه أه ده في التفسير لما + +284 +00:19:06,150 --> 00:19:09,150 +تكون في جملة بهذا المعنى ما هو طبعا في نصوص + +285 +00:19:09,150 --> 00:19:13,230 +النظريات لما يقولك أنه الجملة التالية تكافئ الجملة + +286 +00:19:13,230 --> 00:19:15,350 +التالية هذا معناه أنها إيش؟ أنها صحيحة، نظرية، + +287 +00:19:15,350 --> 00:19:19,130 +قاعدة، فبديها يقول جملة if and only if وصحيحة عشان + +288 +00:19:19,130 --> 00:19:20,690 +أيك برضه في النظرياتش بتقولك implies if and only if + +289 +00:19:20,690 --> 00:19:23,970 +بتقول differentiability implies continuity هي إيش + +290 +00:19:23,970 --> 00:19:28,610 +في الأصل؟ جملة شرطية لكن اشملها صحيحة واضح؟ أي + +291 +00:19:28,610 --> 00:19:29,290 +سؤال؟ + +292 +00:19:32,160 --> 00:19:34,560 +الحقيقة في بعض الكتب بيميزوش من الرمزين بس هذا + +293 +00:19:34,560 --> 00:19:38,180 +الكلام دقيق، لكن احنا أي نص في نظرية رياضية بيكون + +294 +00:19:38,180 --> 00:19:40,920 +صحيح و بنثبته فهو إيش فبكون إيش بدل حلق + +295 +00:19:40,920 --> 00:19:44,820 +implications أو equivalents إن شاء الله هنأجي هناك + +296 +00:19:44,820 --> 00:19:46,940 +و هنأكد على هذه المعلومة هنربط بينهم بإذن الله + +297 +00:19:46,940 --> 00:19:48,900 +تمام + +298 +00:19:50,290 --> 00:19:54,030 +في أنها نقطة مهمة وبرضه تستخدم كثيرا في الرياضيات + +299 +00:19:54,030 --> 00:19:56,850 +اللي هي علاقة بالجملة الشرطية انتبه يا إخوان في + +300 +00:19:56,850 --> 00:19:59,710 +كلام نحكيه عام وفي كلام بنخصصها فاحنا بيقولنا إيش + +301 +00:19:59,710 --> 00:20:02,530 +Tautology بشكل عام أي statement إيش ما يكون الرابط + +302 +00:20:02,530 --> 00:20:05,030 +ك simple compound الـ Tautology مطلقة الصواب + +303 +00:20:05,030 --> 00:20:10,250 +التضمين نوع خاص من الجملة هو تقرير شرطي و Tautology + +304 +00:20:10,250 --> 00:20:13,890 +في نفس الوقت التكافؤ ثنائية الشرطية و Tautology + +305 +00:20:13,890 --> 00:20:17,090 +فإيش بيكون كلام تقرير ففيه حاجة اسمها ال Converse + +306 +00:20:17,090 --> 00:20:19,930 +اللي هي العكس و في عندنا حاجة اسمها Contra positive + +307 +00:20:19,930 --> 00:20:23,170 +Contra positive Contra برضه عكس بس positive يعني + +308 +00:20:23,170 --> 00:20:27,150 +المعكوس الإيجابي فطبعا في زي ما بيحكوا مثلا في + +309 +00:20:27,150 --> 00:20:30,370 +الكورة Contra attack هجوم عكس يعني ف Contra + +310 +00:20:30,370 --> 00:20:35,090 +positive يعني معكوس إيجابي هنشوف الفرق بينهم طبعا + +311 +00:20:35,090 --> 00:20:37,750 +هذه مصطلحات مهمة بتمر علينا في الرياضيات زي ما + +312 +00:20:37,750 --> 00:20:41,660 +أكيد مر عليكم لما قلنا أثبت أنه في نظرية إذا كانت + +313 +00:20:41,660 --> 00:20:44,340 +الدالة متصلة عن نقطة .. آسف .. إذا كانت الدالة + +314 +00:20:44,340 --> 00:20:47,520 +قابلة للاشتقاء عن نقطة ما فيها متصلة عن نفس النقطة + +315 +00:20:47,520 --> 00:20:50,760 +والعكس غير صحيح، صح؟ مرت عليكم فقط في رياضيات ولا + +316 +00:20:50,760 --> 00:20:53,360 +مرتش؟ أه، فإذا .. طب إيش هو العكس؟ بدنا نفهم، لأن + +317 +00:20:53,360 --> 00:20:56,060 +هذا مصطلح إيش يستخدم، وفي حاجة اسمها اللي هو إيش + +318 +00:20:56,060 --> 00:20:58,800 +المعكوس الإيجابي، وبدنا نميز بينهم، لأن المصطلحين + +319 +00:20:58,800 --> 00:21:01,640 +يستخدموا في رياضيات، بدنا نعرف إيش الفرق بينهم، + +320 +00:21:01,640 --> 00:21:05,920 +وكيف نتعامل معهم، تمام فعنا two statements, B and + +321 +00:21:05,920 --> 00:21:11,420 +Q فأول شيء ما هو عكس الجملة الشرطية أني بعكس الدور + +322 +00:21:11,420 --> 00:21:14,840 +بعكس دور اللي هو اللي بيصير الشرط هو جواب الشرط + +323 +00:21:14,840 --> 00:21:18,780 +وجواب الشرط بيصير الشرط أو بمعنى هيك بالعامية بعكس + +324 +00:21:18,780 --> 00:21:22,100 +اتجاه السهم إذا عكست اتجاه السهم بيصيرش إيش ما هو + +325 +00:21:22,100 --> 00:21:24,960 +اللي بيسموه ال converts أي عكس مباشر بعكس إيش + +326 +00:21:24,960 --> 00:21:30,500 +اتجاه السهم فكاد ما تكون if b then q بخليها if q + +327 +00:21:30,500 --> 00:21:33,340 +then b فهذا بيسموه ال converts هذا بيسموه المعكس + +328 +00:21:33,340 --> 00:21:38,120 +معكس مباشر تمام؟ طب ما هو ال contrapositive؟ بعكس + +329 +00:21:38,120 --> 00:21:43,680 +الترتيب لكن مع أني أنفي الجزئين بعكس الترتيب مع + +330 +00:21:43,680 --> 00:21:47,080 +نفي الجزئين طب هنا في نفي و في عكس و بتسميه + +331 +00:21:47,080 --> 00:21:51,120 +positive ليش؟ لأن هنا هذا التغيير لا يؤثر على قيمة + +332 +00:21:51,120 --> 00:21:54,930 +الصدق لل statement بتكافئها هتشوف انها بتكافئه لما + +333 +00:21:54,930 --> 00:21:58,310 +عملنا العمليتين هدولة جيبنا statement جديدة لكن + +334 +00:21:58,310 --> 00:22:00,990 +إذا جيبنا statement جمالها تغيير إيجابي اللي صار، + +335 +00:22:00,990 --> 00:22:03,830 +تغيير إيجابي، ماغيرناش العصر، رغم كل العمليات + +336 +00:22:03,830 --> 00:22:09,090 +ماغيرناش العصر، عكس لكنه إيجابي لأنه ماغيرش قيمة + +337 +00:22:09,090 --> 00:22:12,350 +الصدق الأصلي، قيمة الصدق الأصلي، فدول المصطلحين + +338 +00:22:12,350 --> 00:22:16,590 +بدنا نعرفهم، نعرف كيف نتعامل معهم، إن شاء الله، + +339 +00:22:16,590 --> 00:22:20,780 +خليني أشوف مثال بسيط و أنأكد على اللي هو عشان نميز + +340 +00:22:20,780 --> 00:22:24,580 +بينهم ال converts الحقيقة هنثبت أنه لا يكافئ + +341 +00:22:24,580 --> 00:22:28,100 +الجملة الأصلية لكن ال contrapositive بيكافئ الجملة + +342 +00:22:28,100 --> 00:22:32,000 +الشرطية الأصلية فنبدأ بإنه ننفي أنهم متكافئين مع + +343 +00:22:32,000 --> 00:22:35,500 +ال inverse بقول it is their mind حدد هل ب if b then + +344 +00:22:35,500 --> 00:22:41,280 +Q و ال converts تبعها متكافئين ولا لأ فخلينا نتبع + +345 +00:22:41,280 --> 00:22:44,560 +سياستنا في حل هذه المسألة فأول شيء بدنا نفهم + +346 +00:22:44,560 --> 00:22:47,860 +المثلة، إيه ما هو المطلوب؟ و إيه ما هو المعطيات؟ + +347 +00:22:47,860 --> 00:22:52,920 +فهو بيقول إيه؟ اختبر هل الجملة اللي هو الشرطية P + +348 +00:22:52,920 --> 00:22:58,540 +then Q تكافئ المعقوس تبعها ولا لأ؟ فإيش أنا بدي + +349 +00:22:58,540 --> 00:23:01,460 +إيش؟ بدي أفحص، أشوف التكافئ و أشوف مش عارف إنهم + +350 +00:23:01,460 --> 00:23:04,080 +متكافئين ولا لأ طب نحن عرفنا الجواب إنه إيش ماله؟ + +351 +00:23:05,640 --> 00:23:08,960 +مسبقا أنا عرفنا إنه لأ طيب إذا اسم الطلب مني أن + +352 +00:23:08,960 --> 00:23:13,940 +أجيب القيمة صدق لل if b then Q و ل if Q then B و أقارن + +353 +00:23:13,940 --> 00:23:18,140 +بينهم اه فاذا احنا إيش نقول هنا الحل example + +354 +00:23:18,140 --> 00:23:25,900 +solution we want to determine عشان بس كلمة + +355 +00:23:25,900 --> 00:23:29,920 +converse بحددها determine whether + +356 +00:23:30,830 --> 00:23:35,450 +بنعيد صياغة السؤال عشان نوضح if b then q is + +357 +00:23:35,450 --> 00:23:41,130 +equivalent to + +358 +00:23:41,130 --> 00:23:45,750 +if q then b هي ال converse or not فهي السؤال + +359 +00:23:45,750 --> 00:23:49,670 +فسرناها بشكل أدق أو بشكل واضح ما هي كلمة converse + +360 +00:23:49,670 --> 00:23:55,250 +فسرناها ككلمة إيش الطريقة طيب truth tip إذا هنا by + +361 +00:23:55,250 --> 00:24:04,290 +truth tables جداول الصدق ونعمل جدول صدق أربع + +362 +00:24:04,290 --> 00:24:17,230 +في B و Q في B و في Q و في أربع احتمالات الـ + +363 +00:24:17,230 --> 00:24:21,510 +true الـ true الـ false الـ false الـ true الـ + +364 +00:24:21,510 --> 00:24:23,850 +false الـ true الـ false الـ false الـ false الـ + +365 +00:24:23,850 --> 00:24:27,490 +true الـ true ماذا في عمليات؟ بس نحسب الاتنين + +366 +00:24:27,490 --> 00:24:32,750 +العمودين بي then كيو نبدأ فيها و احنا عارفين ان + +367 +00:24:32,750 --> 00:24:35,070 +هذي دايما true في اللي في حالة واحد ده اللي هيها + +368 +00:24:35,070 --> 00:24:40,170 +فده true false true true طبعا ممكن نحسبها ليها مش + +369 +00:24:40,170 --> 00:24:44,310 +متعودة التدريب يخلينا نحسب بسرعة عدم التدريب شوية + +370 +00:24:44,310 --> 00:24:49,290 +وقت مش صعب مافي دور صدق حاجة صعبة في طول أو قصر في + +371 +00:24:49,290 --> 00:24:56,520 +فترة الحل تمام لأن نعكس if q then b بعدين ننتبه aq + +372 +00:24:56,520 --> 00:25:02,500 +then b true then true true false then true true + +373 +00:25:02,500 --> 00:25:10,860 +true then false false true then false then false + +374 +00:25:10,860 --> 00:25:19,020 +true نقارن true true مش زي بعض إذا نشملهم غير + +375 +00:25:19,020 --> 00:25:22,880 +متكافئين غير متكافئين شايفين في اختلاف في هنا + +376 +00:25:22,880 --> 00:25:27,720 +اختلاف و في هنا اختلاف أو بنجيب ال by conditional + +377 +00:25:27,720 --> 00:25:32,560 +طبعا هذا طريقة تانية اه طبعا هنا زميلوت كو نبهتنا + +378 +00:25:32,560 --> 00:25:35,920 +لنقطة مهمة إن الجسر في أنا طريقتين عشان ننفذ ننفذ + +379 +00:25:35,920 --> 00:25:40,060 +التكافة يا إما بعمل عموديا زي هيك أو طبعا أنه في ده + +380 +00:25:40,060 --> 00:25:43,380 +عندي تعريفين صلاة تكافؤ أو بعمل كمان عمود هنا اللي + +381 +00:25:43,380 --> 00:25:45,360 +هو if and only if و بثبت إنها دايما true إنها + +382 +00:25:45,360 --> 00:25:48,720 +tautology طبعا مش هتطلع تطولش لكن من أسهل هذه + +383 +00:25:48,720 --> 00:25:52,320 +الطريقة لإنه بدي أضيف عمود زيادة ومش هيسبشي ومش + +384 +00:25:52,320 --> 00:25:54,860 +هيسهللي إشي فهذه الطريقة أسهل يعني كان المفروض إن + +385 +00:25:54,860 --> 00:25:59,620 +إيش نعمل نعمل if b then Q if and only if طبعا هذا مش + +386 +00:25:59,620 --> 00:26:04,090 +جزء من الحل اللي هو إيش if Q then B فهنا ممكن أشتغل + +387 +00:26:04,090 --> 00:26:07,310 +عليها و أشوف إنها مش تتولج طريقتها لكن اشملها ده + +388 +00:26:07,310 --> 00:26:11,670 +زيادة في العمل و مش هيسهل أي شيء فإذا هنا نقول على + +389 +00:26:11,670 --> 00:26:15,130 +طول نستنتج أو نعلق إن الحل من ال table بنوع ما + +390 +00:26:15,130 --> 00:26:25,330 +يتطلع إنهم غير متكافئين from the table we see that + +391 +00:26:25,330 --> 00:26:35,880 +if b then q is not equivalent to نفس الشيء is not + +392 +00:26:35,880 --> 00:26:43,020 +equivalent to if you then be أو تنتين not + +393 +00:26:43,020 --> 00:26:50,480 +equivalent أي سؤال فإذا هنا ياش فيه فرق اللي بعكوس + +394 +00:26:50,480 --> 00:26:54,160 +لا يكافئ لأنه يعني عارفين إنه differentiability + +395 +00:26:54,160 --> 00:26:57,700 +then continuity صح لكن العكس غير صحيح هذا مثال + +396 +00:26:57,700 --> 00:26:59,340 +مشهور في التفاضل + +397 +00:27:04,350 --> 00:27:09,590 +أي سؤال بعد ما عرفنا التكافؤ و شوفنا اللي هو + +398 +00:27:09,590 --> 00:27:12,810 +المصطلحين هدول المهمين اللي هو المعكوس في المعكوس + +399 +00:27:12,810 --> 00:27:16,650 +الإيجابي نستكمل مع قواعد الاستدلال و النظرية رقم + +400 +00:27:16,650 --> 00:27:19,750 +اتنين واحد اتنين في هذا الشطر النظرية رقم اتنين في + +401 +00:27:19,750 --> 00:27:23,530 +شطر الأول نفس الطريقة شوف انتوا إيش هذا منهج مهم + +402 +00:27:23,530 --> 00:27:26,510 +جدا نتعلم كيف نقرأ نظريات في الرياضيات لأن لازم + +403 +00:27:26,510 --> 00:27:29,570 +نفهم النظرية نفهم إيش المعطيات نفهم إيش المطلوب + +404 +00:27:29,570 --> 00:27:32,490 +عشان نقدر نبرهن و نفهم البراهين أو نعرف إيش و + +405 +00:27:32,490 --> 00:27:36,190 +نكوّن برهان أو نكتب برهان رياضي صحيح فمقدمة زي + +406 +00:27:36,190 --> 00:27:39,950 +المرة اللي فاتت نفس المقدمة let p and q be any two + +407 +00:27:39,950 --> 00:27:43,590 +statements يعني ما يلي القوانين هتستخدم الرمزين p + +408 +00:27:43,590 --> 00:27:47,250 +و q على إنهم يشتقاريها فإذا ما ينطبق أي قانون + +409 +00:27:47,250 --> 00:27:50,590 +ينطبق على ال p و ال q في هذه النظرية مش في شكل عام + +410 +00:27:50,590 --> 00:27:53,560 +احنا بنقدم لل course ولا بنقدم للنظرية؟ للنظرية + +411 +00:27:53,560 --> 00:27:57,380 +فإذاً هذا خاص بالنظرية فإذا أي قانون حنكتبه بنطبق + +412 +00:27:57,380 --> 00:28:01,260 +على أي two statements بـ p and q طب لو غيرت + +413 +00:28:01,260 --> 00:28:04,120 +رموزهم صاروا a و b ال statements بنطبق عليهم لأن + +414 +00:28:04,120 --> 00:28:10,360 +هذا بس مجرد رمز تمام القانون الأول طبعا قانون سهل + +415 +00:28:10,360 --> 00:28:14,260 +جدا قانون double negation النفي المزدوج باختصار + +416 +00:28:14,260 --> 00:28:18,820 +نفي النفي إثبات بس فإذا نفيت مرتين برجع لمين للأصل + +417 +00:28:18,820 --> 00:28:22,780 +فهيش نفي النفي إثبات طبعا هنا قوانين تكافر نظرية + +418 +00:28:22,780 --> 00:28:26,500 +لو انتبهنا نظرية واحد كانت قوانين كلها تضمين كانت + +419 +00:28:26,500 --> 00:28:29,640 +قوانين يعني قانون جملة شرطية لكنها true دائما هنا + +420 +00:28:29,640 --> 00:28:34,850 +جملة ثنائية الشرطية لكنها true دائما بالمعنى هذا أو + +421 +00:28:34,850 --> 00:28:39,110 +إن هاتين مع بعض يا true مع بعض يا false مع بعض + +422 +00:28:39,110 --> 00:28:44,030 +القانون الأول قانون سهل، القانون الثاني قانون + +423 +00:28:44,030 --> 00:28:48,010 +الإبدال competitive law لأ مش addition مش قانون + +424 +00:28:48,010 --> 00:28:51,090 +الجامعة هذا قانون الإبدال، قانون الإبدال إيش + +425 +00:28:51,090 --> 00:28:56,290 +بيقول لي؟ بيقول لي عملية الـ and والـ or عمليات إبدالية + +426 +00:28:56,290 --> 00:28:59,530 +الترتيب فيها غير مهم، وهذا ممكن اكتشفناه من أول + +427 +00:28:59,530 --> 00:29:02,630 +التعريف لكننا بنؤكد عليها، ده قانون فإذا بتبدأ + +428 +00:29:02,630 --> 00:29:06,030 +بالأولى تبدأ بالثانية، اللي إيش؟ الترتيب غير مهم، و + +429 +00:29:06,030 --> 00:29:09,050 +عملياً بتبدأ العملية أو خاصية مهمة في الرياضيات في + +430 +00:29:09,050 --> 00:29:11,910 +العمليات الحسابية، هاي هنا حتى في العمليات على + +431 +00:29:11,910 --> 00:29:15,890 +الدوال اللي هو مثلاً في بعض العمليات إبدالية وبعدها + +432 +00:29:15,890 --> 00:29:19,930 +غير إبدالي، مظبوط، أو هنا برضه هنا في المنطق الـ or + +433 +00:29:19,930 --> 00:29:24,030 +والـ and عملية إبدالية، فقال طبعاً كتير من الـ .. زي ما + +434 +00:29:24,030 --> 00:29:27,230 +حكينا عمليات الرياضية بتكون إبدالية ومش إبدالية + +435 +00:29:27,230 --> 00:29:31,030 +حتى في بعض الأمور في حياتنا أشياء إبدالية ومش + +436 +00:29:31,030 --> 00:29:34,150 +إبدالية، آه، البست البنطلون ولا الجربان، جابل + +437 +00:29:34,150 --> 00:29:36,930 +تفرقش، إبدالي إيه إبدالية، لكن لبس الجربان و + +438 +00:29:36,930 --> 00:29:42,700 +الحذاء غير إبدالي، مظبوط؟ فالترتيب + +439 +00:29:42,700 --> 00:29:46,160 +أحياناً بيكون مهم وأحياناً غير مهم، مظبوط؟ فهذه + +440 +00:29:46,160 --> 00:29:52,080 +العملية، نعم commutative، commutative إبدال، إبدال هذه + +441 +00:29:52,080 --> 00:29:58,340 +عملية associative، تجميعية، إبدالية، + +442 +00:29:58,340 --> 00:30:01,080 +بقى ماشي، زي اللي احتجناه من القوانين، احنا بناخد + +443 +00:30:01,080 --> 00:30:05,000 +القوانين، فإذاً الـ and والـ or عمليات إبدالية + +444 +00:30:06,010 --> 00:30:07,790 +قوانين الحيادية + +445 +00:30:12,190 --> 00:30:15,610 +إيش حيادية؟ يعني ما بتأثرش، زي ما بقول محايدة جمعي + +446 +00:30:15,610 --> 00:30:19,130 +يعني أي جمعي لأي صفر لأي حاجة بتتغيرش، محايدة ضرب + +447 +00:30:19,130 --> 00:30:22,550 +بيقدر بأي حاجة بواحد بتتغيرش، فهنا في عن عملية بتأثرش + +448 +00:30:22,550 --> 00:30:27,850 +فبصير هي بي or بي تكافئ بي، بي and بي تكافئ بي، فإذا + +449 +00:30:27,850 --> 00:30:31,330 +أي statement لما أعملها and أو or مع نفسها بتأثرش + +450 +00:30:31,330 --> 00:30:34,550 +هذه عملية حيادية ما بتدخلش شيء جديد أو بتحدث شيء جديد + +451 +00:30:34,550 --> 00:30:40,340 +فهي عملية حيادية، القانون الرابع برضه قانون تكافئ + +452 +00:30:40,340 --> 00:30:43,360 +Contrapositive law اللي هو احنا إيش مهديناله آه + +453 +00:30:43,360 --> 00:30:46,340 +فبيقول لي if P then Q تكافئ اللي هو + +454 +00:30:46,340 --> 00:30:50,760 +الـ contrapositive and if not Q then not P + +455 +00:30:50,760 --> 00:30:53,420 +هذا شيء منطقي جداً طبعاً يا إخوان احنا زي ما احنا + +456 +00:30:53,420 --> 00:30:56,760 +بقوله نشوف المثال تبع التفاضل if differentiable + +457 +00:30:56,760 --> 00:31:00,140 +then continuous، إيش الـ contrapositive؟ if not + +458 +00:31:00,140 --> 00:31:03,560 +continuous then not differentiable، في دالة مش + +459 +00:31:03,560 --> 00:31:06,120 +continuous بيكون differentiable مستحيل، آه فإنها + +460 +00:31:06,120 --> 00:31:08,460 +نفس القضية في دولة يشتت يعني يا صح مع بعض يا true + +461 +00:31:08,460 --> 00:31:11,000 +مع بعض مكافئين تماماً، فالـ statement والـ + +462 +00:31:11,000 --> 00:31:12,800 +contrapositive متكافئين، عشان إيه؟ بيسمونها + +463 +00:31:12,800 --> 00:31:16,140 +contrapositive، كلمة positive لأنه تكافئها آه + +464 +00:31:16,140 --> 00:31:19,760 +بنسبة واحدة منهم زي تول أن هي أخر واحدة حاضر + +465 +00:31:26,290 --> 00:31:32,030 +لأ لأ احنا أثبتنا إن الـ converse بيكافحش لكن الـ + +466 +00:31:32,030 --> 00:31:40,870 +contrapositive بيكافح، فهنا الـ theorem واحد + +467 +00:31:40,870 --> 00:31:45,330 +اثنين approved، وهنثبت طبعاً دي اللي بسيبها كله + +468 +00:31:45,330 --> 00:31:50,020 +exercise، اللي بسيبه exercise ضروري لأنه طبعاً احنا + +469 +00:31:50,020 --> 00:31:53,420 +ما نعرفش نقيد نحنا نحاول ندى الأفكار وما نعرفش عملية + +470 +00:31:53,420 --> 00:31:56,620 +عملية تكرارية ولا لو إني مش واثق إنه لازم إنه + +471 +00:31:56,620 --> 00:31:59,520 +إنكم قادرين كان بس يبقاش exercise، فبدنا بس نقيد + +472 +00:31:59,520 --> 00:32:03,900 +الخطوة زي ما حكينا بدنا نحدد السؤال وبعدين نحدد + +473 +00:32:03,900 --> 00:32:07,600 +الطريقة ونطبق ونشوف الحل، فطبعاً أنا مطلوب إني أثبت + +474 +00:32:07,600 --> 00:32:11,080 +تكافئ إذا بس باختصار بدي أقوله we want to show الـ + +475 +00:32:11,080 --> 00:32:14,020 +statement هادي تكافئ الـ statement هادي، فإذا السؤال + +476 +00:32:14,020 --> 00:32:26,860 +we want to show that if P then Q is equivalent to + +477 +00:32:26,860 --> 00:32:36,680 +if not Q then not P، تمام، إيش الأداة؟ truth table، we + +478 +00:32:36,680 --> 00:32:45,720 +will use truth tables، هنستخدم جدول، فنعمل جدول مع + +479 +00:32:45,720 --> 00:32:56,090 +بعض، هذا كان statement أساسية بين 2 P Q، أربع + +480 +00:32:56,090 --> 00:33:07,230 +احتمالات true + +481 +00:33:07,230 --> 00:33:12,650 +true false false، العمودي الثاني true false true + +482 +00:33:12,650 --> 00:33:18,010 +false، إيش بدنا نحسب؟ ممكن نحسب P then Q أولاً أو + +483 +00:33:18,010 --> 00:33:21,550 +بعدين تبهي، مش ترتيب، أو نعمل النفي، آه؟ خيه نعمل + +484 +00:33:21,550 --> 00:33:31,850 +النفي؟ نعم؟ أسهل، أحسنتي، كلامك سليم، فإنا آخذ + +485 +00:33:31,850 --> 00:33:36,750 +بترتيب اللي اقترحته زميلتكم، not Q فبتصير تكون false + +486 +00:33:36,750 --> 00:33:42,090 +true، false true، بعدين ناخد not P واللي هو إيش + +487 +00:33:42,090 --> 00:33:48,150 +false false true true، ممتاز، حاجات هنحسب P then Q و + +488 +00:33:48,150 --> 00:33:56,030 +بعدين هنحسب not Q then not P، ممتاز، نبدأ بي then + +489 +00:33:56,030 --> 00:33:59,530 +Q يمكن تكونوا حافظين true then true true true + +490 +00:33:59,530 --> 00:34:05,810 +then false false، بعدين الباقي true true، ممتاز نيجي + +491 +00:34:05,810 --> 00:34:08,810 +الآن زي اسم اللي اتقدمت الحقيقة طريقة أسهل بدون + +492 +00:34:08,810 --> 00:34:12,050 +أن نرجع لجوا نمشي لقدام false then anything true + +493 +00:34:12,050 --> 00:34:17,370 +true then false false false then true true true + +494 +00:34:17,370 --> 00:34:22,840 +then true، طبعاً بالمقارنة واضح إنه فعلاً متكافئ مافيش + +495 +00:34:22,840 --> 00:34:26,060 +داعي نعمل if and only if هذه أسهل الطريقة واحنا + +496 +00:34:26,060 --> 00:34:29,060 +هندمد عليها طبعاً اللي بتعمل if and only if مش غلط + +497 +00:34:29,060 --> 00:34:33,260 +لكن أنا ماشي لا أنصح بذلك لإنه بس مجرد وقت زيادة + +498 +00:34:33,260 --> 00:34:43,540 +مش مشكلة، فإذاً هنا from the table we see that بي then + +499 +00:34:43,540 --> 00:34:48,400 +ثم Q تكافئ تماماً if not Q then not P + +500 +00:34:53,430 --> 00:34:58,950 +أي سؤال؟ فطرق بسيطة وسهلة وبدنا إن شاء الله نتمكن + +501 +00:34:58,950 --> 00:35:07,990 +منها في هذا الموضوع De Morgan's + +502 +00:35:07,990 --> 00:35:11,050 +laws، قوانين العالم De Morgan's + +503 +00:35:17,710 --> 00:35:22,410 +نظرية ثالثة في هذا الـ chapter، نفس السياسة let P + +504 +00:35:22,410 --> 00:35:26,010 +and Q be any two statements، أتوقع إيش؟ كله يتعود + +505 +00:35:26,010 --> 00:35:31,590 +ويفهم هذه السياسة تمام، حدين القوانين القانون الأول + +506 +00:35:31,590 --> 00:35:36,170 +الحقيقة دي Morgan's، لو بتتحدث كيف ندخل النفي على الـ + +507 +00:35:36,170 --> 00:35:40,980 +and والـ or، كيف ندخل النفي على الـ and والـ or، ممكن + +508 +00:35:40,980 --> 00:35:44,360 +نسميها توزيع النفي لكن هي مش توزيع بالمعنى الدقيق + +509 +00:35:44,360 --> 00:35:48,620 +لأنه لما بوزع بصير عملية وبحافظ على العملية يعني + +510 +00:35:48,620 --> 00:35:51,500 +أنا بوزع الضرب على الجمع بضرب كل واحدة بخليها + +511 +00:35:51,500 --> 00:35:54,560 +تتجمع بجمع ببدأ تتجمع لكن هنا لأ، لما أدخل النفي + +512 +00:35:54,560 --> 00:35:57,380 +على الـ and بصير or، فهي مش توزيع بالمعنى الدقيق + +513 +00:35:57,380 --> 00:36:03,220 +وإنما هي إدخال النفي على الـ and والـ or، فأول شيء + +514 +00:36:03,220 --> 00:36:06,910 +بقول إذا بدأ أدخل النفي على statement فيها and بنفي + +515 +00:36:06,910 --> 00:36:13,730 +جزئين وبحول الـ and لـ or، القانون الثاني لو دخلت + +516 +00:36:13,730 --> 00:36:16,390 +النفي على الـ or نفس السياسة بنفي جزئين بس بعكس + +517 +00:36:16,390 --> 00:36:20,110 +فإذاً هنا النفي بيحول الـ and لـ or والـ or لـ and، إذا + +518 +00:36:20,110 --> 00:36:23,430 +هذه من القضية وإيش كمان؟ مش بس هيك بعمل حاجتين، بنفي + +519 +00:36:23,430 --> 00:36:27,890 +جزئين وبيقلب الـ and or أو الـ or and، واضح؟ فهدول + +520 +00:36:27,890 --> 00:36:31,250 +دي Morgan's law، فهدول العاملين طبعاً هدول أثبتناهم + +521 +00:36:31,250 --> 00:36:34,390 +صح؟ هدول كان exercise كانوا؟ diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/e5jENMYP4AM_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/e5jENMYP4AM_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..aa4c4ae075bd8261e2289ca9d2c005bc8d24a21e --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/e5jENMYP4AM_postprocess.srt @@ -0,0 +1,2456 @@ +1 +00:00:19,790 --> 00:00:24,770 +بسم الله الرحمن الرحيم فاحنا في المحاضرة الأخيرة + +2 +00:00:24,770 --> 00:00:29,370 +بدأنا الحديث عن اتحاد الدوال union of functions + +3 +00:00:29,370 --> 00:00:36,560 +وذكرناإن اتحاد الدوال قد يبدو لأول وهلة مصطلح غريب + +4 +00:00:36,560 --> 00:00:40,140 +لكن لو رجعنا الدالة لأصلها إن هي عبارة عن relation + +5 +00:00:40,140 --> 00:00:44,140 +وال relation هي مجموعة من الأزواج المرتبة فببدأ + +6 +00:00:44,140 --> 00:00:49,440 +المصطلح ياخد مكانه الطبيعي فعندنا احنا دالتين يعني + +7 +00:00:49,440 --> 00:00:52,900 +مجموعتين من الأزواج المرتبة ممكن يتحدث عن اتحاده + +8 +00:00:52,900 --> 00:00:57,660 +فهذا ليس هناك شيء جديد في هذا الموضوعلكن الجديد + +9 +00:00:57,660 --> 00:01:01,740 +إذا أخدنا اتحاد دالتين هل الناتج بيتم دالة ولا لأ + +10 +00:01:01,740 --> 00:01:05,300 +هذا هو الموضوع المهم اه فانا أتحدث عن اتحاد + +11 +00:01:05,300 --> 00:01:09,000 +الدالتين كاتحاد مجموعتين من أزواج المرتبة شيء + +12 +00:01:09,000 --> 00:01:12,720 +طبيعي وشيء قديم ليس فيه أي شيء جديد لكن النقطة + +13 +00:01:12,720 --> 00:01:16,900 +واجتيش بحافظ أن اتحاد الدالتين بيتم دالة فهذا هو + +14 +00:01:16,900 --> 00:01:20,820 +الموضوع اللي بهمنا بهذا الموضوع طبعا قلنا الموضوع + +15 +00:01:20,820 --> 00:01:25,910 +اللي بيعبر عن ذلك هو الدوال متعددة القاعدةاللي هي + +16 +00:01:25,910 --> 00:01:30,110 +أكتر من قاعدة في التعريف متعددة القاعدة في التعريف + +17 +00:01:30,110 --> 00:01:34,710 +هي الموضوع اللي بتطابق أو ممكن أن هي تسميته على + +18 +00:01:34,710 --> 00:01:38,250 +انه unions of function فاحنا وصلنا لهذه النقطة + +19 +00:01:38,250 --> 00:01:42,010 +احنا أخدنا اللي هو كمصطلح وشوفنا بعض الأمثلة الآن + +20 +00:01:42,010 --> 00:01:45,690 +عندنا نظرية لأن زي ما قلنا السؤال الرئيسي السؤال + +21 +00:01:45,690 --> 00:01:48,390 +الرئيسي مش انه لما باخد .. بعرف اخد اتحاد دالتين + +22 +00:01:48,390 --> 00:01:51,770 +ولا باخدش لأ دايما باخد لأنه كمجموعتين لكن السؤال + +23 +00:01:51,770 --> 00:01:55,650 +الرئيسي هو اكتشف ان اتحاد الدالتين هو دالةلأنه + +24 +00:01:55,650 --> 00:01:58,650 +كاياش بيكون مجموعة، اتحاد أي مجموعتين مجموعة، بس + +25 +00:01:58,650 --> 00:02:01,550 +هناك أزواج مرتبة، لا يسألنا، طب هاللي بيتموا دالة، + +26 +00:02:01,550 --> 00:02:05,490 +هذا النظرية بتقولنا إيش الشروط اللي بتحافظ على إن + +27 +00:02:05,490 --> 00:02:08,950 +اتحاد دالتين يكون دالة، مش دايما صح، شوفنا مرة + +28 +00:02:08,950 --> 00:02:13,650 +مثال تم الاتحاد دالة، ومثال لأ فقد خاصية الدالة، + +29 +00:02:13,650 --> 00:02:17,350 +فبنشوف وقت إيش بيحافظ على إن يكون الاتحاد الدالتين + +30 +00:02:17,350 --> 00:02:23,550 +بيكون دالة، و وقت إيش ما بيكونش، فنظريةlet f be a + +31 +00:02:23,550 --> 00:02:27,410 +function from a to c و ال g function from b to d + +32 +00:02:27,410 --> 00:02:30,790 +في عندنا two functions الأولى ال domain تبعها a + +33 +00:02:30,790 --> 00:02:33,710 +والثانية ال domain تبعها b وفي عندنا مجال مقابل مش + +34 +00:02:33,710 --> 00:02:40,030 +كتير مهم طيب ايش بيقوللي such that هنا شرطF of X + +35 +00:02:40,030 --> 00:02:45,310 +تساوي G of X for all X وين؟ في المنطقة المشتركة + +36 +00:02:45,310 --> 00:02:49,110 +للمجالين بتقاطع الـA و الـB من الـA و الـB دمين + +37 +00:02:49,110 --> 00:02:53,350 +الـF و دمين الـG هاي الشرط طبعنا فبقول لـthen the + +38 +00:02:53,350 --> 00:02:57,130 +union H الunion المظلو بالرمز H عشان نخرج نظرية صح + +39 +00:02:57,130 --> 00:03:02,410 +the union H إيش يعني H؟ هو رمز الاتحاد of F and G + +40 +00:03:02,410 --> 00:03:06,230 +الاتحاد حرمظله بالرمز H هدا هو I و مكتوبالـ H + +41 +00:03:06,230 --> 00:03:09,270 +إشماله هي رمز للاتحاد عشان أنا بدل مكتوب الـ runs + +42 +00:03:09,270 --> 00:03:13,970 +الكبير بدي أكتبه بشكل صغير سميته H إشماله define + +43 +00:03:13,970 --> 00:03:18,790 +of the function بيعرف دالة إذا هنا هو إيش؟ مؤخص + +44 +00:03:18,790 --> 00:03:23,430 +النظرية وقت إيش بيكون اتحاد الدالتين دالة إذا + +45 +00:03:23,430 --> 00:03:27,790 +كانوا في المنطقة المشتركة للمجالين متساويتين هذا + +46 +00:03:27,790 --> 00:03:31,150 +المهم طبعا هذا شيء منطقى ليش؟ لأنه أنا في عندي في + +47 +00:03:31,150 --> 00:03:36,250 +المنطقة المشتركة ممكن أطبق Fممكن اطبق G طب إذا ال + +48 +00:03:36,250 --> 00:03:39,530 +F بتوديها على الشرب وال G بتوديها على الغرب بتامها + +49 +00:03:39,530 --> 00:03:42,430 +دالة، مينفعش لإن هو ده العنصر ال X اللي في + +50 +00:03:42,430 --> 00:03:46,290 +المشترك، مش ماله، ال F ممكن تطبقه، تتطبق عليه، وال + +51 +00:03:46,290 --> 00:03:49,230 +G بتتطبق عليه، لازم يودونه نفس الصورة، لإنه مهم إن + +52 +00:03:49,230 --> 00:03:51,570 +العنصر يكون له صورة واحدة، يكون له عنصر صورة + +53 +00:03:51,570 --> 00:03:54,850 +واحدة، لكن في المناطق البعيدة ال F وينما تود، تود، + +54 +00:03:54,850 --> 00:03:58,530 +لإن العنصر اللي مش في التقاطع، تتطبق عليه F لحالها + +55 +00:03:58,780 --> 00:04:01,880 +والعنصر اللي في domain الـ G ومش في التقاطة ومتضمن + +56 +00:04:01,880 --> 00:04:04,940 +ان الـ G لحالة عليه ففيش احتمال ان انا اخد صورتين + +57 +00:04:04,940 --> 00:04:08,420 +لكن في العنصر المشترك ممكن ان تصير عندى صورتين + +58 +00:04:08,420 --> 00:04:11,240 +لازم الصورتين يكونوا متساويتين عشان عارف ان تكون + +59 +00:04:11,240 --> 00:04:15,580 +دالة عشان عارف ان تكون دالة فهو طبعا بس البقيات + +60 +00:04:15,580 --> 00:04:19,970 +بتكون دالة من وين لوين يا اخواتمن اتحاد المجالين + +61 +00:04:19,970 --> 00:04:24,410 +إلى اتحاد المجالين المقابلين A Union B الـ A هي + +62 +00:04:24,410 --> 00:04:28,270 +مين؟ Domain الـ F والـ B Domain الـ G إلى وين؟ C + +63 +00:04:28,270 --> 00:04:32,350 +وD الـ C تمثل المجال المقابل للـ F والـ D تمثل + +64 +00:04:32,350 --> 00:04:35,750 +المجال المقابل للـ G طبعاً كام معرفة زي ما تشاهد + +65 +00:04:35,750 --> 00:04:39,510 +في متعددة مقاعدة إذا كانت الـ X في Domain الـ F + +66 +00:04:39,510 --> 00:04:43,850 +إيش معرفة الاتحاد؟ F of X وإذا كانت في Domain الـ + +67 +00:04:43,850 --> 00:04:47,250 +G إيش تعريفها؟ G of Xفهذا بيأكد النقطة طب أنص + +68 +00:04:47,250 --> 00:04:50,670 +المشترك من أين أعرفه أحسبه من فوق أو من تحت حسبته + +69 +00:04:50,670 --> 00:04:54,050 +من فوق أو من تحت سيان لأنهم متساويين هذا المهم آه + +70 +00:04:54,050 --> 00:04:56,710 +لكن لو أنه ماكانش متساويين مفهش ساعتها أنا بدأ + +71 +00:04:56,710 --> 00:05:00,610 +أقول هجل أنا أخد X معينة كبت من المتعدد القاعدة + +72 +00:05:00,610 --> 00:05:03,990 +إذا ال X في ال A مين بده أحفظ بها F of X وإذا ال X + +73 +00:05:03,990 --> 00:05:07,590 +في ال B وينده أقولها G of X طب لو ال X مشتركة ممكن + +74 +00:05:07,590 --> 00:05:10,630 +أطبق من هنا و أطبق من هنا طب لاتديني ناتج واحد ما + +75 +00:05:10,630 --> 00:05:14,220 +هو جالي شرط إن مصورة متساوية إذا مشترك واضحية؟و ده + +76 +00:05:14,220 --> 00:05:17,220 +هتشوف الصورة كلها كيف و ايه التعريف فإذا فعلا + +77 +00:05:17,220 --> 00:05:21,260 +اتحاد الدول هو ليس الا إيش ده اللي متعددة القاعدة + +78 +00:05:21,260 --> 00:05:25,120 +ده اللي متعددة القاعدة خليني أشوف البرهان مع بعض + +79 +00:05:25,120 --> 00:05:34,460 +فهذه نظرية تلاتة تمانية approve + +80 +00:05:36,980 --> 00:05:40,900 +أه فطبعا زي ما حكينا فيه أننا دالتين أخد اتحادهم + +81 +00:05:40,900 --> 00:05:44,060 +كمجموعة مافيش مشكلة إيش مطلوب أثبت أن ال each + +82 +00:05:44,060 --> 00:05:47,320 +function بدأ نثبت ال each function أه ال function + +83 +00:05:47,320 --> 00:05:55,180 +فيها تلت شروط شرط خفي وفيه شرطين واضحين الشرطين + +84 +00:05:55,180 --> 00:05:58,060 +الواضحين أن ال domain يساوي المجموعة الأولى صح + +85 +00:05:58,060 --> 00:06:01,860 +والشرط التاني أنه لكل عنصر صورة واحدة مش ذاكرين + +86 +00:06:01,860 --> 00:06:07,200 +أنه جال ال domain يساوي ال X وإذا كانت X وZفي الـ + +87 +00:06:07,200 --> 00:06:11,320 +function و X و Y في الـ function لازم ال Y تساوي + +88 +00:06:11,320 --> 00:06:15,540 +ال Z يعني صورتين متساويتين ما هو الشرط الخفي قال + +89 +00:06:15,540 --> 00:06:18,160 +لي هي ال function عبارة عن مين عبارة عن relation + +90 +00:06:18,160 --> 00:06:22,320 +من X ل Y فانا مبدأ أثبت أن ال H function من A + +91 +00:06:22,320 --> 00:06:25,880 +union B ل C union D أول شي بتثبت أنها في relation + +92 +00:06:25,880 --> 00:06:30,520 +من هذه المجموعة لهذه المجموعة و بعدين بتغطي كل + +93 +00:06:30,520 --> 00:06:34,700 +المجال و بعدين لكل عنصر صورة واحدة فاحنا هنثبت تلت + +94 +00:06:34,700 --> 00:06:40,160 +حاجات فأولمطلوب هرمزه بالرمز Zero عشان اتمنى ماشي + +95 +00:06:40,160 --> 00:06:44,340 +مع التعريف بدي اثبت ان ال H subset من وين؟ H معات + +96 +00:06:44,340 --> 00:06:46,760 +relation يعني subset من ال Cartesian product + +97 +00:06:46,760 --> 00:06:50,600 +Cartesian product لمين؟ مين عند المجوعة الأولى؟ A + +98 +00:06:50,600 --> 00:07:00,080 +union B cross C union D فهذا المطلوب الأولفلازم + +99 +00:07:00,080 --> 00:07:05,800 +تكون هي relation من اتحاد المجالين إلى اتحاد + +100 +00:07:05,800 --> 00:07:10,380 +المجالين المقابلين لازم هذا الشرط الأول تمام فطبعا + +101 +00:07:10,380 --> 00:07:13,700 +بتثبت علاقة subset بتاخد عنصر في ليش؟ في الطرف + +102 +00:07:13,700 --> 00:07:19,560 +اليسار كيف صورة العنصر؟زوج مرتب لأنه كارتيسة فابدأ + +103 +00:07:19,560 --> 00:07:23,740 +أقول له let x y تنتمي لل h be any element لو ما + +104 +00:07:23,740 --> 00:07:27,500 +كتبتش معروفة ضمنيا مطلوب اوصل هذا زوج المرتب لمين + +105 +00:07:27,500 --> 00:07:34,760 +لطرف اليمين لطرف اليمين ممتاز ايش ممكن نستخدم نبدأ + +106 +00:07:34,760 --> 00:07:40,680 +نقرأ ايش ال h اتحاد اه فهذا بيقول ليه ان ال x y + +107 +00:07:40,680 --> 00:07:48,450 +تنتمي يا اما لل F orالـ X Y تنتمي للـ G ليش؟ لأن + +108 +00:07:48,450 --> 00:07:53,770 +الـ H هي ليست إلا F Union G كاتحاد مجموعتين لسه + +109 +00:07:53,770 --> 00:07:57,810 +نشتغل بالـ H في النقطة الأولى واضح؟ ممتاز أنا بدي + +110 +00:07:57,810 --> 00:08:01,890 +أوصل لهنا إيش معناة ال X و ال Y في ال F؟ وين ال X + +111 +00:08:01,890 --> 00:08:05,750 +بتكون؟ في domain ال F و ال Y في الصورة المقابلة + +112 +00:08:05,750 --> 00:08:12,390 +فده يؤدي X تنتمي لل A ليه domain ال F and ال Y + +113 +00:08:12,390 --> 00:08:16,590 +تنتمي لل Cor ممكن ادلها and اعملها ده طبعا مش + +114 +00:08:16,590 --> 00:08:21,850 +مشكلة وال X في domain الجي اللي هو B and ال Y في + +115 +00:08:21,850 --> 00:08:25,450 +المجال المقابل للجي اللي هو مين ال D لأن ال F + +116 +00:08:25,450 --> 00:08:32,590 +function من A ل C وال G function من B لD مش هيك + +117 +00:08:32,590 --> 00:08:35,570 +تعريفهم؟ اه ممتاز هي احنا وصلنا وهي عيني على + +118 +00:08:35,570 --> 00:08:40,310 +المطلوب بدنا نوصل هناالان انا ايش بدي؟ بدي يكون + +119 +00:08:40,310 --> 00:08:43,430 +الـ X في الـ A union B لأن الـ Cartesian product + +120 +00:08:43,430 --> 00:08:46,250 +هنا يشماله، بدي يكون الـ X هنا و الـ Y هنا، هي الـ + +121 +00:08:46,250 --> 00:08:49,430 +Cartesian product، مظبوط؟ فانا بدي أجيب X في الـ A + +122 +00:08:49,430 --> 00:08:53,390 +مع الـ B و الـ Y في الـ C أو في الـ D، إيش ممكن + +123 +00:08:53,390 --> 00:08:57,970 +نعمل؟ توزيع، إيش؟ توزيع و .. و .. و .. و .. و .. و + +124 +00:08:57,970 --> 00:08:58,250 +.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و + +125 +00:08:58,250 --> 00:08:58,630 +.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و + +126 +00:08:58,630 --> 00:08:58,870 +.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و + +127 +00:08:58,870 --> 00:09:00,890 +.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و + +128 +00:09:00,890 --> 00:09:03,840 +.. و .. و .. و .. و .. و .. و .. و .. و ..X تنتمي + +129 +00:09:03,840 --> 00:09:11,320 +لـ A كتلة واحدة معاهم بالتفصيل خلّيني أخد هذه كلها + +130 +00:09:11,320 --> 00:09:17,640 +ككتلة واحدة و Y تنتمي ل C هي كتلة مع مين؟ R X + +131 +00:09:17,640 --> 00:09:19,900 +تنتمي ل B هي واحدة + +132 +00:09:22,480 --> 00:09:27,420 +and هذي كلها غطوها عملوها كتلة واحدة فالتوزيع على + +133 +00:09:27,420 --> 00:09:31,720 +الأخر يا مع الأولى and مع التانية اللي هي نفس + +134 +00:09:31,720 --> 00:09:36,680 +الكتلة اللي هي إيش بس خينا أعمل الجواز صح اللي هو + +135 +00:09:36,680 --> 00:09:46,480 +X تنتمي لل A and Y تنتمي لل C هذي كتلة or إيش Y + +136 +00:09:46,480 --> 00:09:55,230 +تنتمي لل D توزيع هذا جوز كبيرمن ضوء ممتاز الآن + +137 +00:09:55,230 --> 00:10:01,970 +نوزع كمان مرة فهنا يا عندي X تنتمي لل A or X تنتمي + +138 +00:10:01,970 --> 00:10:12,150 +لل B and Y تنتمي لل C or X تنتمي لل B مظبوط فهذا + +139 +00:10:12,150 --> 00:10:20,700 +بيصير تنتين andX تنتمي للـA أو Y تنتمي للـD وY + +140 +00:10:20,700 --> 00:10:28,430 +تنتمي للـC أو Y تنتمي للـD توزيع مرتينفي حد عنده + +141 +00:10:28,430 --> 00:10:31,890 +مشكلة في التوزيع فانا عشان هم أربع مش ثلاثة في + +142 +00:10:31,890 --> 00:10:34,530 +التوزيع أنا متعود واحدة وتنتين صح؟ طب إيه كي + +143 +00:10:34,530 --> 00:10:38,510 +بتعمل؟ بعتبر أن هذه كلها كتلة واحدة وهي تنتين و + +144 +00:10:38,510 --> 00:10:41,950 +بعدين كمان مرة تنتين و واحدة و تنتين و واحدة توزيع + +145 +00:10:41,950 --> 00:10:47,730 +الآن أنا مين بديه؟ بدي هذه هذي بديها؟ لأ إيش ممكن + +146 +00:10:47,730 --> 00:10:51,750 +أعمل؟ تبسيط لأنه and انتبهوا مش or فجيت أعمل تبسيط + +147 +00:10:51,750 --> 00:10:55,520 +فهذه ممكن ألغيهابالتبسيط وهذه ممكن تلغيها بالتبسيط + +148 +00:10:55,520 --> 00:11:00,360 +بتام عندي تنتين اللي بدي اياه فهذا يؤدي ان X تنتمي + +149 +00:11:00,360 --> 00:11:08,100 +ل A Union B مش هذه هي A and ال Y تنتمي لمين؟ C + +150 +00:11:08,100 --> 00:11:11,500 +Union D والتانتين هذه حزب تماشي فعملت هنا + +151 +00:11:11,500 --> 00:11:15,420 +simplification عملت ومش عملت تعريف الاتحاد فهنا + +152 +00:11:15,420 --> 00:11:20,020 +simplification and + +153 +00:11:20,630 --> 00:11:26,290 +definition of union خلصنا إذا كارتيسيا روين موجود + +154 +00:11:26,290 --> 00:11:30,750 +في الأول الـ cross product كارتيسيا روين موجود مع + +155 +00:11:30,750 --> 00:11:39,550 +من؟ مع التاني و هو المطلوب و هو المطلوب واضح؟ أي + +156 +00:11:39,550 --> 00:11:47,910 +سؤال؟ تمام ننتقل للي بعده الآن + +157 +00:11:47,910 --> 00:11:52,870 +الشرط الأولللدالة أو شرط رقم واحد بدنا domain الـ + +158 +00:11:52,870 --> 00:12:00,910 +H إيش يساوي A union الـ B فهنا الشرط رقم واحد وهو + +159 +00:12:00,910 --> 00:12:04,870 +الشرط التاني فأول شي هي فعلًا كانت relation فإذا + +160 +00:12:04,870 --> 00:12:09,030 +اتحاد ال two functions هو relation من اتحاد ال two + +161 +00:12:09,030 --> 00:12:13,730 +domains لاتحاد من ال two co domains أو اللي هو ال + +162 +00:12:13,730 --> 00:12:18,140 +relation الشرط التاني على الجدع كان co functionبدأ + +163 +00:12:18,140 --> 00:12:21,100 +تغطي كل ال domain تبعها ال domain تبعها من a union + +164 +00:12:21,100 --> 00:12:25,160 +b صار لأن هي علاقة من وين لوين من a union b ل c + +165 +00:12:25,160 --> 00:12:29,500 +union d اه بدنا نثبت ايش هذا تساوي مجموعات و ايش + +166 +00:12:29,500 --> 00:12:32,580 +عناصرهم اذا كانوا مرتبوا عناصر عادية عناصر عادية + +167 +00:12:32,580 --> 00:12:35,420 +لأنه ال domain ال domain اللي هو x لحدها في الأول + +168 +00:12:35,420 --> 00:12:41,380 +فطبعا هنبدأ نثبت فنقول له let x تنتمي للطرف الأول + +169 +00:12:41,380 --> 00:12:49,780 +domain ال h be any element ممتاز ايش ممكن نعملفي + +170 +00:12:49,780 --> 00:12:54,460 +نقطة الحقيقة السهلة + +171 +00:12:54,460 --> 00:12:59,150 +اللي هي الاتجاه الأول، إيش هو؟هل جيت في أي + +172 +00:12:59,150 --> 00:13:02,710 +relation .. في أي relation ال domain ايش بيكون + +173 +00:13:02,710 --> 00:13:06,630 +subset من المجموعة الأولى أو يساويها في ال + +174 +00:13:06,630 --> 00:13:09,530 +function لازم يساويها فهذه عملية .. عملية بديهية + +175 +00:13:09,530 --> 00:13:13,550 +ان هذا subset من هذا دايما صحيح لأي relation .. + +176 +00:13:13,550 --> 00:13:17,250 +لأي relation توتة تعريف domain ال relation ايش هو + +177 +00:13:17,250 --> 00:13:20,430 +هو دايما subset من المجموعة الأولى فهذه دايما + +178 +00:13:20,430 --> 00:13:23,310 +معروفة لأنه ما زال هو في domain ال H domain ال H + +179 +00:13:23,310 --> 00:13:26,950 +شماله دايما subset فهذه مابتداش برعان الحقيقة ممكن + +180 +00:13:26,950 --> 00:13:32,000 +ايش نمحيهاممكن نمحيها فدي دايما حقيقة موجودة فأول + +181 +00:13:32,000 --> 00:13:39,000 +شيء domain ال H subset من ال A union B بالتعريف by + +182 +00:13:39,000 --> 00:13:43,200 +definition definition لمين؟ لتعريف ال relation فده + +183 +00:13:43,200 --> 00:13:46,920 +الاتجاه الأول دايما صح فده واحد المهم هالجيت + +184 +00:13:46,920 --> 00:13:51,660 +لاتجاه التاني هو المهم فالتساوي وكافئ ال أولة + +185 +00:13:51,660 --> 00:13:54,360 +subset من التانية والتانية subset من الأولة الآن + +186 +00:13:54,360 --> 00:14:00,820 +نمشي بالاتجاه التانيlet X تنتمي للـ A union الـ B + +187 +00:14:00,820 --> 00:14:08,800 +نعم، ليش؟ ركزي معاه شوية، domain وهي الـ A، إيش + +188 +00:14:08,800 --> 00:14:13,260 +الـ A؟ الزوج يشتغلون A cross الـ C أو B cross الـ + +189 +00:14:13,260 --> 00:14:17,960 +D زي ما حتشغليه، ممتاز إيش معناة اتحاد؟ إنه إيش، + +190 +00:14:17,960 --> 00:14:22,040 +لا في الأولة، يا في التانية or X تنتمي للـ B + +191 +00:14:25,720 --> 00:14:29,780 +صحيح فانا بدون ده واصل لل H و ال H هي مين؟ هي F + +192 +00:14:29,780 --> 00:14:34,740 +Union G طيب هنا مهم جدا لو ماكنتش العلاقة هذه اللي + +193 +00:14:34,740 --> 00:14:37,660 +أصلا ال F و ال G functions كان هذا الكلام غير صحيح + +194 +00:14:37,660 --> 00:14:40,840 +لكن بما أنه ال F function إذا ال A هو مين؟ هو + +195 +00:14:40,840 --> 00:14:45,360 +domain ال F فده على طول بيقول إن ال X تنتمي ل + +196 +00:14:45,360 --> 00:14:52,280 +domain ال FOr X تنتمي لـ domain الـ G لأن الـ F + +197 +00:14:52,280 --> 00:14:57,340 +function من A لـ C و الـ G function من B لD ممتاز، + +198 +00:14:57,340 --> 00:15:01,360 +ايش معناه ان انا عند وصلهم بدي وصلهم ل domain الـ + +199 +00:15:01,360 --> 00:15:01,600 +H + +200 +00:15:09,380 --> 00:15:14,460 +إيش معناته إن الـ X في domain الـ F؟ معناته إن هذه + +201 +00:15:14,460 --> 00:15:19,680 +إحداثي أول من زوج مرتب موجود في الـ F فهذا بيقول + +202 +00:15:19,680 --> 00:15:25,980 +ليه؟ إيه؟ اللي هو إيش؟ XY تنتمي للـ F خلينا نكتب + +203 +00:15:25,980 --> 00:15:31,860 +for some Y there exists Y تنتمي للـ C such that XY + +204 +00:15:31,860 --> 00:15:36,120 +تنتمي للـ F هذا الأولى إكمالات ال domain or there + +205 +00:15:36,120 --> 00:15:43,070 +existsزت تنتمي للـ D بحيث ان الـ X والـ Z تنتمي + +206 +00:15:43,070 --> 00:15:51,550 +لمين؟ للـ G الـ X تنتمي فإذا تكون ياش عنصر في الـ + +207 +00:15:51,550 --> 00:15:54,530 +G بدنا نوصل إنه ياش الـ XY + +208 +00:15:57,760 --> 00:16:03,800 +تكون في إيش؟ في الـH بدنا الـXY في الـH في داعي + +209 +00:16:03,800 --> 00:16:09,940 +نروح في هذا التوضيح ولا في طريق مختصرة + +210 +00:16:09,940 --> 00:16:25,720 +اه + +211 +00:16:25,720 --> 00:16:34,000 +تمامممتازة، أه الآن عندنا ال H بتساوي subset فإيش + +212 +00:16:34,000 --> 00:16:39,500 +معناته أنه توجد اللي هي في ال C و اللي موجود .. + +213 +00:16:39,500 --> 00:16:42,080 +احنا إيش فيه عندنا؟ اللي موجود فيه مجموعة H بيكون + +214 +00:16:42,080 --> 00:16:47,060 +موجود في الاتحاد فال Y موجودة في مين؟ في C اتحاد + +215 +00:16:47,060 --> 00:16:49,680 +ال D و لا لأ؟ اللي موجود في ال C بيكون موجود في + +216 +00:16:49,680 --> 00:16:53,060 +الاتحاد و اللي موجود في ال F1 بيكون في الاتحاد + +217 +00:16:53,060 --> 00:16:57,570 +اللي هو مين؟ Hلأن دائماً كل مجموعة هي سبسط من + +218 +00:16:57,570 --> 00:17:02,150 +اتحادها اللي هي قانون الإضافة قانون الإضافة or + +219 +00:17:02,150 --> 00:17:06,250 +there exists z تنتمي اللي موجود في ال D وين موجود؟ + +220 +00:17:06,250 --> 00:17:11,430 +في ال C union ال D وال XZ وين موجودة؟ في ال Hأه + +221 +00:17:11,430 --> 00:17:16,310 +ليش؟ لأنه قانون الإضافة لأن الـF subset من H تساوي + +222 +00:17:16,310 --> 00:17:21,010 +مين؟ تساوي F union الـG والـG subset من الـH تساوي + +223 +00:17:21,010 --> 00:17:25,970 +F union الـG نفس القضية الـC subset من D union C + +224 +00:17:25,970 --> 00:17:29,930 +والـD subset من D union C أو العكس طبعا كله مع ال + +225 +00:17:29,930 --> 00:17:32,570 +computer واضحت كل الخطوات التي بقيت استخدامها لأنه + +226 +00:17:32,570 --> 00:17:36,550 +قاعد بكبر مع الاتحاد إضافة في إضافة ممتاز الآن + +227 +00:17:36,550 --> 00:17:41,750 +عندي زوج مرتبأحداث الأول تبع وين بيكون؟ في domain + +228 +00:17:41,750 --> 00:17:45,450 +العلاقة و لا لأ؟ ايه التعريف؟ ما زال XY في الـH + +229 +00:17:45,450 --> 00:17:49,570 +وين الـX بتكون؟ هذا طبعا كله implies إذا X وين + +230 +00:17:49,570 --> 00:17:54,830 +موجودة؟ في domain الـH أو نفس القضية X وين موجودة؟ + +231 +00:17:54,830 --> 00:17:59,070 +في domain الـH طبعا أي دوبوتنز الآن is an X في + +232 +00:17:59,070 --> 00:18:07,810 +domain الـH وهو المطلوب فthus A union B subset من + +233 +00:18:07,810 --> 00:18:14,620 +domainالـ H واحد و اتنين بيخلوا ياش انت ساوي انت + +234 +00:18:14,620 --> 00:18:19,460 +واحد + +235 +00:18:19,460 --> 00:18:29,220 +and اتنين يؤدي A union B تساوي domain الـ H تمام + +236 +00:18:29,220 --> 00:18:32,300 +فهنا النقطة انه احنا نتذكر ان ال F دي جزء من + +237 +00:18:32,300 --> 00:18:35,480 +الاتحاد بالاضافة بتنحل المثلة + +238 +00:18:46,510 --> 00:18:54,750 +الشرط التالت اللي هو رقم 2 إذا صورتين لعنصر تنتمي + +239 +00:18:54,750 --> 00:19:01,950 +لل H and X Z تنتمي لل H implies Y تساوي Z الشرط + +240 +00:19:01,950 --> 00:19:07,390 +التالت أنه لكل عنصر X هناك صورة واحدة فهذه جملة + +241 +00:19:07,390 --> 00:19:11,660 +شرطية سنبدأ البرهان أن نفترض أن الشرط صحيحassume + +242 +00:19:11,660 --> 00:19:19,940 +أو let نفس المعنى كله صح تنتمي للـH and XZ تنتمي + +243 +00:19:19,940 --> 00:19:28,760 +للـH بدي أثبت أنه Y تسوي Z تمام، + +244 +00:19:28,760 --> 00:19:33,200 +إيش نعمل؟ نستخدم تعريف إن الـH هي إتحاد فهذا + +245 +00:19:33,200 --> 00:19:45,040 +معناته إن XY تنتمي للـFor x,y تنتمي للـG and x,z + +246 +00:19:45,040 --> 00:19:51,840 +تنتمي للـF or x,z تنتمي لمن؟ للـG لأن الـH هي + +247 +00:19:51,840 --> 00:19:58,480 +اتحاد اتبعين؟ إذا مشيت بسرعة واقفوني بجف و بعيد + +248 +00:19:58,480 --> 00:20:02,260 +إذا في نقطة مش واضحة في نقطة مش اتبعين هبنرجع + +249 +00:20:02,260 --> 00:20:11,030 +أكمل؟أه تمام الآن بدنا نستفيد ان ال F و ال G دوال + +250 +00:20:11,030 --> 00:20:14,510 +عشان بتوصل الاشهده في white horizontal ايش نعمل + +251 +00:20:14,510 --> 00:20:22,520 +توزيع لو عملنا توزيع فهنا بتصير عندناXY هنعمل .. + +252 +00:20:22,520 --> 00:20:25,840 +بدي أختصر الآن خطوة واحدة زي ما توي عملنا لما نوزع + +253 +00:20:25,840 --> 00:20:28,960 +تنتين ما هتنتينش بدون الناتج أربعة بتيني الناتج + +254 +00:20:28,960 --> 00:20:32,640 +أربعة بدي أخد هذه كتلة مع ال .. مع ال and فإيش + +255 +00:20:32,640 --> 00:20:39,920 +هتصير ها دي هتصير بصي or تنتمي لل F and XZ تنتمي + +256 +00:20:39,920 --> 00:20:50,250 +لل F هي واحدة or XY في ال F andXZ في الـ G هيتنتين + +257 +00:20:50,250 --> 00:21:01,550 +or التانية الان XY في ال G and XZ في ال F or XY في + +258 +00:21:01,550 --> 00:21:09,290 +ال G and XZ في ال Gتوزيع بدا مرحلتين بس انا اختصرت + +259 +00:21:09,290 --> 00:21:12,930 +اه زي ما توي عملتي التوزيع اللي عنده اي مشكلة انه + +260 +00:21:12,930 --> 00:21:15,230 +هذا الكلام صحيح تعيدها في البيت مابتديش اضايق واجت + +261 +00:21:15,230 --> 00:21:19,690 +فبتكون وزعوها على مرحلتين هتوصلوا لهذا الكلام الان + +262 +00:21:19,690 --> 00:21:28,210 +ال ghost الأول عندي عنصر x و y في ال F و x و z في + +263 +00:21:28,210 --> 00:21:33,470 +ال F بتديني y تساوي z ليش لأن ال F function + +264 +00:21:33,470 --> 00:21:35,150 +والاخير + +265 +00:21:37,640 --> 00:21:44,640 +والاخير هى فى كمان or وهى فى كمان or والاخير زى X + +266 +00:21:44,640 --> 00:21:47,920 +Y في الـ G و X Z في الـ G و الـ G function مش + +267 +00:21:47,920 --> 00:21:57,280 +بتدينى Y تساوي Z مش مشاكل أول جوس و آخر جوس جالى + +268 +00:21:57,280 --> 00:22:01,120 +عنصر اللى سورتين مرة تحت ال F مفهش مرة تحت ال G + +269 +00:22:01,120 --> 00:22:09,830 +مفهش طب نيجى للأقواس اللى فى الوسطفهذا الجوزوهذا + +270 +00:22:09,830 --> 00:22:13,970 +الجزء هما اللي بدهم شوية شغل أما الأول والأخير + +271 +00:22:13,970 --> 00:22:18,630 +سهلين صح؟ المفجين أن الأول والأخر سهلين لأن ال F + +272 +00:22:18,630 --> 00:22:22,170 +function فبنفعش ال X تكون صورتين مختلفتين وال G + +273 +00:22:22,170 --> 00:22:25,910 +function بنفعش ال X تكون صورتين مختلفتين Y و Z أنا + +274 +00:22:25,910 --> 00:22:29,850 +بتدوصل أن Y تسوى Z وكله بينهم R بنفع أعمل + +275 +00:22:29,850 --> 00:22:33,470 +Simplification؟ لأ، إيش لازم يطلع أي دم تنسي؟ لازم + +276 +00:22:33,470 --> 00:22:35,890 +كله يطلع نفس الصورة فانا طلعت في الأولى والأخيرة + +277 +00:22:35,890 --> 00:22:42,400 +صح طيب نشوفالان ايش معناه ان X Y في ال F و X Z في + +278 +00:22:42,400 --> 00:22:46,800 +ال G؟ يعني ال X عنصر مشترك في domain ال F و ال G + +279 +00:22:46,800 --> 00:22:51,180 +فماذا بيقدي هذا؟ مازال عنصر مشترك، ايه صوره؟ + +280 +00:22:51,180 --> 00:22:56,050 +متساوية، اذا صوره متساويةمش مباشرة إذا بدنا نعمل + +281 +00:22:56,050 --> 00:23:00,030 +حطوة مشتركة يعني هنا معناته ان X في domain ال F + +282 +00:23:00,030 --> 00:23:03,970 +مظبوط لأي relation إذا زوج مرتب في العلاقة إيش + +283 +00:23:03,970 --> 00:23:07,410 +بيكون الأنص الأول؟ في ال domain و هنا الأنص الأول + +284 +00:23:07,410 --> 00:23:10,730 +في ال domain طب إذا ال X شمالها في التقاطع إذا ال + +285 +00:23:10,730 --> 00:23:14,230 +X في التقاطع ممكن نكتبها على جهة معينة ممكن نعملها + +286 +00:23:14,230 --> 00:23:21,740 +خلينا نعملها هنا في عين دي هنا XYفي الـ F and XZ + +287 +00:23:21,740 --> 00:23:27,120 +في الـ J implies X تنتمي لمن؟ للـ A تقاطع الـ B + +288 +00:23:27,120 --> 00:23:31,120 +لأن الـ domain الـ F و domain الـ G صح؟ واضحة؟ + +289 +00:23:31,120 --> 00:23:35,680 +واضحة؟ ما زال الـ X بالتقاطع، زي أن صورهم متساوية + +290 +00:23:35,680 --> 00:23:41,860 +هذا يؤدي إن Y تساوي F of X بدأ تساوي من؟ G of X + +291 +00:23:41,860 --> 00:23:46,370 +وتساوي Z صح؟بقى لإن هو ال gate X مشترك إذاً F + +292 +00:23:46,370 --> 00:23:50,510 +تساوي G صح؟ من الشرط و هذا الشرط المهم طب في عند + +293 +00:23:50,510 --> 00:23:55,410 +ال F إيه صورة ال X؟ Y اسمها وعند ال G صورة ال X؟ Z + +294 +00:23:55,410 --> 00:23:59,790 +إذاً Y تساوي Z إذا ممكن اكتب هنا Y تساوي Z التانية + +295 +00:23:59,790 --> 00:24:03,850 +بنفس الطريقة التانية بنفس الطريقة بس العكس التالتة + +296 +00:24:03,850 --> 00:24:12,820 +إيه؟XY تنتمي للـG و XZ تنتمي للـF يعني X تنتمي + +297 +00:24:12,820 --> 00:24:18,660 +للـA تقاطع الـB وهذا يؤدي إلى Y تساوي G of X تساوي + +298 +00:24:18,660 --> 00:24:22,940 +F of X تساوي Z بس اختلف الدور تبع الـZ والـY فإذا + +299 +00:24:22,940 --> 00:24:30,100 +برضه أيش؟ Y تساوي Z بأي دم بتنسي Y تساوي Z بي أو + +300 +00:24:30,100 --> 00:24:35,780 +بي تكافئ بي أي دم بتنسي وهو المطلوبوهو المطلوب + +301 +00:24:35,780 --> 00:24:39,640 +فهنا مهم جدا وكيف اتخلصنا من هذين الجثين تاوي تاوي + +302 +00:24:39,640 --> 00:24:42,020 +كان simplification اللي كان بينهم and لإن أنا + +303 +00:24:42,020 --> 00:24:44,140 +ماقدرش أعمل simplification لكن مع ال aid and + +304 +00:24:44,140 --> 00:24:47,180 +redundancy حلت المشكلة وكله طلع أن ال white سوى + +305 +00:24:47,180 --> 00:24:51,720 +وزد في الأربعة احتمالا وكل واحدة لها سبب مختلف لها + +306 +00:24:51,720 --> 00:24:57,900 +سبب مختلف فهنا المهم الدور الأساسي أن العنصر + +307 +00:24:57,900 --> 00:25:00,920 +المشترك يكون الصور متساوي + +308 +00:25:03,460 --> 00:25:25,580 +خلّيني أشوف مثال بسيط على هذا الموضوع حاضر فامديني + +309 +00:25:25,580 --> 00:25:31,160 +دالتين الدالة الأولى من سالب infinity ل zero فهنا + +310 +00:25:31,160 --> 00:25:37,520 +عندناdomain الأولى يساوي domain ال F بيساوي من + +311 +00:25:37,520 --> 00:25:42,520 +سالب infinity ل zero و ال B و هو domain ال G + +312 +00:25:42,520 --> 00:25:46,880 +بيساوي من where ل when من zero ل infinity طبعا + +313 +00:25:46,880 --> 00:25:54,360 +مغلق هنافبقوللي أول شيء أوجد الاتحاد و بعدين هل هو + +314 +00:25:54,360 --> 00:25:58,540 +دالة و لا لأ لأننا نعكس ترتيب الجواب نعكس ترتيب + +315 +00:25:58,540 --> 00:26:02,420 +الجواب هاي دالتين ايش شرط عشان يكون الاتحاد دالة + +316 +00:26:02,420 --> 00:26:05,380 +بدي في التقاطع يتساوي هاي الشرط الوحيد النظرية + +317 +00:26:05,380 --> 00:26:09,320 +بتقول عشان أكتر فانا عندي الآن اللي هو تقاطع + +318 +00:26:09,320 --> 00:26:12,660 +الـdominant خدعيني أعملها بدأ الشكل عشان الاسم مش + +319 +00:26:12,660 --> 00:26:19,930 +مهم ايش بيساوي؟ Zero F Zeroلأنه بيقول سالب X تربيع + +320 +00:26:19,930 --> 00:26:23,930 +تساوي G of Zero وليه بتساويش بتساوي إذا الشروط + +321 +00:26:23,930 --> 00:26:29,310 +النظرية اتحقت إذا الاتحاد ده ال Thus F Union G + +322 +00:26:29,310 --> 00:26:32,870 +function من وين لوين من اتحادها دول اتحاده مش + +323 +00:26:32,870 --> 00:26:37,670 +ديكون R من سالب infinity ل infinity لوين لاتحاد + +324 +00:26:37,670 --> 00:26:43,190 +المجالين المقابلين R اتحاد الـR ويساوي Aتطبيق على + +325 +00:26:43,190 --> 00:26:48,190 +النظرية واضحة ولا فصل؟ اه فهنا a union b ايش union + +326 +00:26:48,190 --> 00:26:54,150 +a union b؟ ايش بيساوي؟ بيساوي a فنجلناها هنا طبعا + +327 +00:26:54,150 --> 00:26:59,930 +c هي ايش؟ بتساوي d في هذه الحالة c تساوي d تساوي a + +328 +00:26:59,930 --> 00:27:03,590 +صح؟ مش هيك معطى؟ اه بهمناش المجال المقابل ما هو + +329 +00:27:03,590 --> 00:27:06,470 +واسع بالزيادة مش مشكلة اه فهذه دي ايش؟ function + +330 +00:27:06,470 --> 00:27:07,910 +thus is a function + +331 +00:27:13,230 --> 00:27:19,630 +كيف تعريفها؟ كيف تعريفها؟ النظرية جلتلي كيف عرف؟ + +332 +00:27:19,630 --> 00:27:24,390 +جلتلي هي F of X اللي هي سالب X تربيع إذا ال X وين؟ + +333 +00:27:24,390 --> 00:27:27,970 +في دمين ال F اللي هو أصغر في دمين ال F اللي هو من + +334 +00:27:27,970 --> 00:27:34,890 +سالب Infinity ل Zero و بتساوي X تربية إذا ال X في + +335 +00:27:34,890 --> 00:27:39,650 +دمين ال G اللي هو من وين؟ من Zero ل Infinityخلّيني + +336 +00:27:39,650 --> 00:27:44,570 +أكتبها كمان مرة عشان في ناس عندهم اللي هو بيقع فيه + +337 +00:27:44,570 --> 00:27:48,410 +بعض الخطأ زي + +338 +00:27:48,410 --> 00:27:51,810 +ما حكينا إيش الاتحاد بالدينة؟ دالة إيش مالها؟ + +339 +00:27:51,810 --> 00:27:55,810 +متعددة قاعدة إيش معنات X من سالب Infinite ل Zero؟ + +340 +00:27:55,810 --> 00:27:59,630 +يعني X أصغر أو تساوي Zero لأنه مغلق وإيش معنات X + +341 +00:27:59,630 --> 00:28:04,110 +من Zero لما لا نهاية أكبر أو يساوي Zero؟ فهي تعريف + +342 +00:28:04,110 --> 00:28:08,440 +الدالة، في حاجة غريبة شايفينها؟بقول الـ Zero ظهر + +343 +00:28:08,440 --> 00:28:13,580 +مرتين، في مشكلة؟ لأ، أه، فممكن تظهر، بس إيش .. ليش + +344 +00:28:13,580 --> 00:28:17,400 +مفيش مشكلة؟ طب لو جالي إيه أحسب H of Zero، هذه H، + +345 +00:28:17,400 --> 00:28:20,280 +ممكن أعود فوق أو تحت، بديني نفس النتيجة، مش هتفرق + +346 +00:28:20,280 --> 00:28:23,700 +معاه، فهذه تم الدالة، واضح؟ فإن هو يعني أنا .. و + +347 +00:28:23,700 --> 00:28:26,060 +احنا بشرح في ال calculus، لما أحط اللي يساوي + +348 +00:28:26,060 --> 00:28:29,550 +مرتين، يحتاجوا الطلبةلأ إذا كانت بتديني النقطة + +349 +00:28:29,550 --> 00:28:32,130 +المشتركة بتديني نفس القيمة مافيش مشكلة واضحية؟ و + +350 +00:28:32,130 --> 00:28:34,570 +أي نظرية هيك بتقول ف الـ zero موجودة فوق و موجودة + +351 +00:28:34,570 --> 00:28:37,910 +تحت طب في مشكلة؟ لأ ليش؟ لأن لو عادت في القاعدة + +352 +00:28:37,910 --> 00:28:39,850 +الأولى أو في القاعدة التانية بتديني نفس الناتج + +353 +00:28:39,850 --> 00:28:42,470 +عشان هيك الشرط عشان هيك الشرط أنه في التقاط عشان + +354 +00:28:42,470 --> 00:28:46,230 +يكون نفس الناتج نفس الصورة لو ماحطناش في مكان ما + +355 +00:28:46,230 --> 00:28:50,830 +صح لكن هي هيك تعريفة مباشرة بس لو نحطت يعني مش + +356 +00:28:50,830 --> 00:28:55,950 +مشكلة تنحل بعد الشكل تمام فاد نهاية هذا ال section + +357 +00:29:05,580 --> 00:29:08,800 +فهنا شفنا التعريف الدالة في ال section الماضي + +358 +00:29:08,800 --> 00:29:12,920 +وشفنا بعض الأمور البسيطة وإذا اتحاد الدوال هو ليس + +359 +00:29:12,920 --> 00:29:18,200 +إلا دوال متعددة القاعدة وطبعا عشان انا اتحاد + +360 +00:29:18,200 --> 00:29:22,920 +الدالتين يكون يتم دالة إيش الشرط أنه في التقاطع + +361 +00:29:22,920 --> 00:29:26,720 +المجالين تكون الدالتين متساويتين هي بكل اختصار + +362 +00:29:26,720 --> 00:29:34,170 +الآن ننتقل لموضوع آخر العنوانimages and inverse + +363 +00:29:34,170 --> 00:29:41,770 +images of sets صور وصور عكسية للمجموعات صور وصور + +364 +00:29:41,770 --> 00:29:50,370 +عكسية للمجموعات في دراساتنا السابقة قلنا احنا في + +365 +00:29:50,370 --> 00:29:55,180 +عندنا functionبتكون هي إياش علاقة بين مجموعتين صح؟ + +366 +00:29:55,180 --> 00:29:58,060 +علاقة بين مجموعتين بشرطين إن ال domain بيساوي + +367 +00:29:58,060 --> 00:30:00,780 +المجموعة الأولى كلها و لكل عنصر في ال domain فيه + +368 +00:30:00,780 --> 00:30:04,460 +صورة واحدة، مظبوط؟ أه، مش هذا الشاهد إحنا في عنا + +369 +00:30:04,460 --> 00:30:08,300 +ممكن نكتب إن y تساوي f of x، مظبوط؟ هذه الصورة + +370 +00:30:08,300 --> 00:30:10,900 +اللي متعودين عليها من ال calculus و اللي اتعودنا + +371 +00:30:10,900 --> 00:30:14,140 +عليه كمان الآن هذه ال statement مش بتكافئ، بتكافئ + +372 +00:30:14,140 --> 00:30:18,770 +إن x y تنتمي لل fفدولا two statements ايش مالهم + +373 +00:30:18,770 --> 00:30:23,370 +متكافئتين صحيح مجرد notation كتبت في الجهة اليمين + +374 +00:30:23,370 --> 00:30:28,490 +صح كتبت في اليسار ايش برضه صح طبعا برضه مش هدف + +375 +00:30:28,490 --> 00:30:32,650 +شاهد ايش اللي بدي يعني احنا ايش بيسمي ال y في هذه + +376 +00:30:32,650 --> 00:30:37,830 +الحالةصورة الـ X image و ال X إيش بيسميها pre + +377 +00:30:37,830 --> 00:30:41,510 +image يتقع في ال domain لكن هي بيسميها pre image، + +378 +00:30:41,510 --> 00:30:45,130 +مظبوط؟ أه في عدو المصطلحين المتعودين إذا كانت Y + +379 +00:30:45,130 --> 00:30:50,090 +تساوي F of X أو بمعنى آخر إذا XY كزوج ينتمي لل F + +380 +00:30:50,090 --> 00:30:54,150 +ال Y بيسميها صورة و ال X بيسميها إيش؟اللي هو + +381 +00:30:54,150 --> 00:30:57,450 +الصورة القابلية preimage أو إيش الأصل تبع الصورة + +382 +00:30:57,450 --> 00:31:00,670 +من وين إجت ال Y صحيح فهذا بيسميها image و preimage + +383 +00:31:00,670 --> 00:31:04,190 +اه فهذا الكلام نتحدث فيه عن إيش ال X و ال Y عادلوا + +384 +00:31:04,190 --> 00:31:09,030 +إيش تسميهم عناصر فبتنعمم هذا المفهوم لمين مش لعنصر + +385 +00:31:09,030 --> 00:31:13,010 +واحد لمجموعة من العناصر فهذا هو العنوان بنتحدث عن + +386 +00:31:13,010 --> 00:31:16,290 +ال image و ال preimage بس هنسمي inverse image + +387 +00:31:16,290 --> 00:31:21,010 +للمجموعات مش عنصر واحد زي هنا لعدد عناصر لعدد + +388 +00:31:21,010 --> 00:31:26,810 +عناصر فهذا هو هدفهذا الـ Section فمفهوم الـ Image + +389 +00:31:26,810 --> 00:31:30,470 +و الـ Preimage بدنا نعمّمه من اللي نتحدث فيه عن + +390 +00:31:30,470 --> 00:31:34,110 +عناصر زي X و Y إلى مجموعة من العناصر و التكن + +391 +00:31:34,110 --> 00:31:37,910 +مجموعة capital A و مجموعة capital B واضح؟ هذا + +392 +00:31:37,910 --> 00:31:40,510 +الهدف من الـ Section، هذا النقطة الأولى، اه فاحنا + +393 +00:31:40,510 --> 00:31:46,490 +هنتحدث عن هذا المفهوم باللي هو بتعمل تمام، خلّيني + +394 +00:31:46,490 --> 00:31:51,470 +أحاول نشرح التعريفبقول في عندي دالة F من X ل Y هي + +395 +00:31:51,470 --> 00:31:55,930 +عندنا capital X ال domain وفي عندنا capital Y + +396 +00:31:55,930 --> 00:32:01,150 +المجال المقابل وفي عندنا بينهم ايش دالة F + +397 +00:32:04,010 --> 00:32:10,430 +تمام جالي let a و b be subsets of x and y + +398 +00:32:10,430 --> 00:32:15,310 +respectively إيش يعني؟ يعني ال x subset من ال x ال + +399 +00:32:15,310 --> 00:32:19,870 +a as if و ال y subset من مين؟ ال b subset من وين؟ + +400 +00:32:19,870 --> 00:32:27,180 +من ال y على الترتيب على الترتيب بده يعرفما هو + +401 +00:32:27,180 --> 00:32:30,740 +معناه أن الـA سبسيط من الـX والـB سبسيط من الـY؟ + +402 +00:32:30,740 --> 00:32:33,920 +مثلًا، عندما أقول X وY في الـF، أين تكون الـX؟ في + +403 +00:32:33,920 --> 00:32:37,160 +الـX، وأين تكون الـY؟ في الـY هؤلاء عندما يكونوا + +404 +00:32:37,160 --> 00:32:40,800 +عناصر، الآن نفس الشيء عندما أتحدث عن صورة، بدل من + +405 +00:32:40,800 --> 00:32:43,240 +أن أقول صورة عنصر، أقول صورة مجموعة، أين تكون + +406 +00:32:43,240 --> 00:32:46,280 +المجموعة؟ من الـdomain، وأنا أتحدث عن الصورة + +407 +00:32:46,280 --> 00:32:48,780 +العكسية، المجموعة أين تكون؟ من المجال المقابل، + +408 +00:32:48,780 --> 00:32:51,600 +العكس عندما أتحدث عن صورة X، أين تكون الـX؟ من + +409 +00:32:51,600 --> 00:32:56,540 +الـdomain، أين تكون الصورة؟ في المجال المقابأنصر + +410 +00:32:56,540 --> 00:32:59,960 +من المجال المقابل بيكون من الصورة القابلية في ال + +411 +00:32:59,960 --> 00:33:03,660 +domain في نفس العملية تمام فاحنا هنعرف مفهومين + +412 +00:33:03,660 --> 00:33:08,940 +الصورة والصورة العكسية ما هي صورة الـ A ما هي صورة + +413 +00:33:08,940 --> 00:33:12,100 +الـ A بيقولي the image of A under F طبعا تحت + +414 +00:33:12,100 --> 00:33:16,160 +الدالة F لأن اذا اختلفت الدالة هتختلف الصورةأيش + +415 +00:33:16,160 --> 00:33:20,060 +الرمز تبعها؟ F of A هذا رمز جديد بالنسبالك انتوا + +416 +00:33:20,060 --> 00:33:23,180 +كنتوا بتاعي ما متعودين انه ايش؟ F of X عنصر اه + +417 +00:33:23,180 --> 00:33:26,020 +جيتنا نعمل ايه؟ صورة مجموعة فهم نتحدث عن صورة + +418 +00:33:26,020 --> 00:33:29,540 +مجموعة هاي التعامل صورة المجموعة عبارة عن ايش؟ + +419 +00:33:29,540 --> 00:33:32,500 +عبارة عن مجموعة هذه أول نقطة فصورة المجموعة مش + +420 +00:33:32,500 --> 00:33:37,280 +عنصر مجموعة فهي سره هاي الرمز تبعها ايش بتتكون؟ + +421 +00:33:37,440 --> 00:33:41,460 +بتكون من عناصر من المجال المقابل small y in + +422 +00:33:41,460 --> 00:33:44,220 +capital Y إيش معلومة؟ أي عنصر من المجال المقابل؟ + +423 +00:33:44,220 --> 00:33:48,460 +لأ عبارة عن صور لأن هي في المجال المقابل فهي صور + +424 +00:33:48,460 --> 00:33:53,320 +صور لمين؟ لعناصر من الـA هي F of X for some X + +425 +00:33:53,320 --> 00:33:57,780 +تنتمي للـAباختصار شديد هي عبارة عن صور العناصر + +426 +00:33:57,780 --> 00:34:02,060 +اللي في الـA فصورة المجموعة A هي المجموعة التي + +427 +00:34:02,060 --> 00:34:06,120 +تتكون من صور عناصر الـA واضحة؟ اه فديها من التعريف + +428 +00:34:06,120 --> 00:34:11,240 +التالي هي عبارة عن صور عناصر الـA فصورة مجموعة هي + +429 +00:34:11,240 --> 00:34:15,870 +صورة عناصر المجموعةفما إيش صورة مجموعة ما هي + +430 +00:34:15,870 --> 00:34:20,550 +مجموعة صور عناصر هذه المجموعة باقتصار شديد واضحة؟ + +431 +00:34:20,550 --> 00:34:23,750 +أه فطبعا هي عند ال A فبياخد كل العناصر اللي هنا + +432 +00:34:23,750 --> 00:34:27,270 +وين بيوديهم؟ بيوديهم على المجموعة هنا، إيش اسمها + +433 +00:34:27,270 --> 00:34:32,230 +هذه؟ F في ال A فهذه بتروح هنا طبعا إيش علاقتها بال + +434 +00:34:32,230 --> 00:34:35,130 +B؟ موضوع تاني، ماليش دعوة أنا، بس أنا بدي أقول، + +435 +00:34:35,130 --> 00:34:39,340 +بدي أعرف التعريف الأساسيالعكس الآن، لو أخدنا + +436 +00:34:39,340 --> 00:34:44,560 +مجموعة B من المجال المقابل، مجموعة جزئية من المجال + +437 +00:34:44,560 --> 00:34:49,360 +المقابل، بدي أشوف الصور اللي هنا وين أصلهم، بدي + +438 +00:34:49,360 --> 00:34:52,320 +أشوف الصور هدولة من وين أصلهم، فبدي أجيب مين فهدي + +439 +00:34:52,320 --> 00:34:57,360 +هدي F، بدي أجيب هدي من وين جاية، من F inverseبنجيب + +440 +00:34:57,360 --> 00:35:01,660 +ف inverse ال B احنا + +441 +00:35:01,660 --> 00:35:05,520 +العنصر سميناه pre image لكن للمجموع هنسميه inverse + +442 +00:35:05,520 --> 00:35:09,660 +image و مختلف المصطلح مختلف فبقوللي the inverse + +443 +00:35:09,660 --> 00:35:14,600 +image of B ايش رمزه ف السالب واحد ال B ايش بنقرعها + +444 +00:35:15,740 --> 00:35:18,760 +F inverse of B او الاش ال inverse image of B هي + +445 +00:35:18,760 --> 00:35:23,740 +قرايتها عبارة عن ايش برضه مجموعة فصورة مجموعة من + +446 +00:35:23,740 --> 00:35:28,000 +المجال هي مجموعة في المجال المقابل والصورة العكسية + +447 +00:35:28,000 --> 00:35:31,640 +لمجموعة من المجال المقابل هي مجموعة من وين من ال + +448 +00:35:31,640 --> 00:35:35,700 +domain مجموعة من ال domain مما تتكون من عناصر من + +449 +00:35:35,700 --> 00:35:41,060 +ال domain اشمالهم صورهم في ال Bهي Y تساوي F of X + +450 +00:35:41,060 --> 00:35:44,740 +for some Y تنتمي للـ B عبارة عن عناصر في ال domain + +451 +00:35:44,740 --> 00:35:51,620 +صورهم في الـ B يعني باختصار بالعامية مين هي أنا + +452 +00:35:51,620 --> 00:35:56,760 +عندي بيه بيه مش تحتوي صور تحتوي على صور السؤال + +453 +00:35:56,760 --> 00:36:00,720 +هدول الصور من وين اجوا فبدني مجموعة تتكون من عناصر + +454 +00:36:00,720 --> 00:36:04,040 +اللي عملولي الصور هدولفهي عبارة عن العناصر اللي + +455 +00:36:04,040 --> 00:36:07,840 +صورهم في الـP عبارة عن العناصر اللي صورهم في الـP + +456 +00:36:07,840 --> 00:36:11,640 +فهذا التعريف طبعا هنشوف الأمثلة و كيف نتعامل معاهم + +457 +00:36:11,640 --> 00:36:18,810 +واحدة واحدة ملاحظات الملاحظة الأولى مهمة جداهنا + +458 +00:36:18,810 --> 00:36:24,410 +بنستخدم الرمز F inverse الـ B هذه الـ F inverse هل + +459 +00:36:24,410 --> 00:36:29,250 +معناته أن الدالة هي اللي هي دالة عكسية؟ ليس + +460 +00:36:29,250 --> 00:36:33,090 +بالضرورة لما حط التعريف جلي الـ F function جلي + +461 +00:36:33,090 --> 00:36:36,450 +إلها inverse هل كل دالة لها inverse؟ لأ لكن كل + +462 +00:36:36,450 --> 00:36:40,770 +دالة لها inverse image واضح؟ لأنه في التعريف جلي + +463 +00:36:40,770 --> 00:36:44,310 +.. جلي شرط على الدالة ولا جلي أي دالة؟ أي دالة + +464 +00:36:44,310 --> 00:36:49,930 +فبقولي هذا الرمزلا يرمز لمعكوس الدالة وإنما هو خاص + +465 +00:36:49,930 --> 00:36:54,650 +بمعكوس المجموعة الصورة العكسية الصورة العكسية طبعا + +466 +00:36:54,650 --> 00:36:57,490 +للأسف نفسي أخدمها في نفس الرمز لكن المعنى مختلف + +467 +00:36:57,490 --> 00:37:01,150 +ففي اختلاف لما أقول أنا F inverse لمجموعة دايما + +468 +00:37:01,150 --> 00:37:04,430 +معرف لكن لما أقول F inverse ل X مش دايما معرف + +469 +00:37:04,430 --> 00:37:09,710 +لأنصر مختلف فبقول ايه does not denote the inverse + +470 +00:37:09,710 --> 00:37:13,210 +function فهذا الرمز مانوش دعوة بالدالة العكسية + +471 +00:37:13,210 --> 00:37:19,140 +بالدالة العكسيةهذه الملاحظة الأولى الملاحظة + +472 +00:37:19,140 --> 00:37:25,200 +التانية أسهل أمثلة على التعريف تبعنا إحنا قلنا + +473 +00:37:25,200 --> 00:37:29,580 +بناخد مجموعة من ال domain بنجيب صورة المجموعة طب + +474 +00:37:29,580 --> 00:37:36,120 +مين أشهر subset من ال X؟ ال Phi أو X نفسها طب لو + +475 +00:37:36,120 --> 00:37:41,290 +أخدنا ال A تساوي X مين صورة ال X؟ليس إلا المدى لأن + +476 +00:37:41,290 --> 00:37:46,030 +S صورة الـ X هي صور كل عناصر في الـ X لما جيب صور + +477 +00:37:46,030 --> 00:37:48,270 +عناصر كل ال domain ليش ما كنت جيبت .. جيبت المدى + +478 +00:37:48,270 --> 00:37:52,490 +.. جيبت المدى فبقوللي صورة ال X هي ال image of F + +479 +00:37:52,490 --> 00:37:54,850 +ال image هو مين؟ هو المدى، اللي بمعنى المدى، هذه + +480 +00:37:54,850 --> 00:37:58,470 +النقطة الأولى، طب العكس لو أخدت ال P بتساوي كل ال + +481 +00:37:58,470 --> 00:38:01,410 +Y، بنفع ولا بينفع، عشان بنفع، سبسيط من ال Y، مين + +482 +00:38:01,410 --> 00:38:04,370 +الصورة العكسية؟ كل ال domain، كل ال domain، لأنه + +483 +00:38:04,370 --> 00:38:09,090 +بشكل عامصورة subset بيكون subset وصورة العكسية ل + +484 +00:38:09,090 --> 00:38:13,610 +subset بيكون subset هنا فهنا هنا بتكون F inverse + +485 +00:38:13,610 --> 00:38:17,530 +of B فإذا ال A أخدتها كل X إيش بيطلع؟ بيطلع ال + +486 +00:38:17,530 --> 00:38:20,030 +image وإذا أخدت ال B بيساوي كل ال Y إيش بيطلع ال + +487 +00:38:20,030 --> 00:38:25,670 +inverse image؟ كل ال X فدولة ملاحظتين قبل ما ناخد + +488 +00:38:25,670 --> 00:38:31,850 +الأمثلة نبدأ بالأمثلة وكالعادة نبدأ بمثال بسيط جدا + +489 +00:38:33,260 --> 00:38:42,140 +مثال مجموعات صغيرة ودالة بسيطة المثال + +490 +00:38:42,140 --> 00:38:46,260 +الأول مديني + +491 +00:38:46,260 --> 00:38:53,860 +دالةمن X ل Y ال X تتكون من الأعداد من 0 ل 4 وال Y + +492 +00:38:53,860 --> 00:39:00,620 +من 5 ل 7 ومديني subset من ال X أخدت بس تلت عناصر 0 + +493 +00:39:00,620 --> 00:39:06,440 +1 و 2 فبده صورة A و الداني B subset من ال Y بده + +494 +00:39:06,440 --> 00:39:12,580 +الصورة العكسية ل B فده مثال مباشر solution فبده F + +495 +00:39:12,580 --> 00:39:19,160 +ل Aكيف بدنا نحسبها؟ هتطلع مجموعة طبعا قلنا باختصار + +496 +00:39:19,160 --> 00:39:23,160 +شديد ما هي صورة المجموعة؟ هي صور العناصر اللي في + +497 +00:39:23,160 --> 00:39:27,640 +المجموعة يعني إيش بده؟ بده صورة الـ Zero وبده صورة + +498 +00:39:27,640 --> 00:39:32,240 +الواحد وبده صورة التنين واضحاتش التعريف؟ إيش معناه + +499 +00:39:32,240 --> 00:39:37,320 +صورة مجموعة؟ مجموعة صور عناصر المجموعة واضحة؟ واضح + +500 +00:39:37,320 --> 00:39:40,320 +التعريف الآن كمثال؟ تمام إيش بيساوي؟ إيه الصورة + +501 +00:39:40,320 --> 00:39:45,050 +الـ Zero؟خمسة ومين صورة الواحد؟ ستة ومين صورة + +502 +00:39:45,050 --> 00:39:50,090 +التانية؟ سبعة فهي فواضح المعنى مبدأيا ايش معناته + +503 +00:39:50,090 --> 00:39:54,090 +ايش صورة مجموعة، مجموعة صور عناصر المجموعة، مين + +504 +00:39:54,090 --> 00:39:57,210 +عناصر في هذا المثال الـA؟ صفر واحد واتنين، مين + +505 +00:39:57,210 --> 00:40:00,970 +صورهم؟ هدا هي فكانوا يجيبوا صورة الـA، فجيبوا صورة + +506 +00:40:00,970 --> 00:40:07,830 +الـA نشوف F inverse الـBالـ B بتساوي خمسة أو ستة، + +507 +00:40:07,830 --> 00:40:10,550 +إيش مدينة الـ X versus M إيش؟ بدّي العناصر اللي + +508 +00:40:10,550 --> 00:40:14,910 +صورهم خمسة أو ستة، مين العناصر اللي صورهم خمسة؟ في + +509 +00:40:14,910 --> 00:40:18,550 +عندي الصفر، ومين كمان صورته خمسة؟ والتلاتة + +510 +00:40:18,550 --> 00:40:22,690 +والاربعة، هدول كلهم صورهم خمسة، فبد العناصر اللي + +511 +00:40:22,690 --> 00:40:25,970 +صورهم خمسة، ومين العناصر اللي صورهم ستة؟ الواحد + +512 +00:40:26,500 --> 00:40:30,140 +فهذه بسميها إيش الصورة العكسية الصور تعون ال P من + +513 +00:40:30,140 --> 00:40:34,340 +وين اجه من هدول العناصر واضحة فوضحة التعريف + +514 +00:40:34,340 --> 00:40:39,480 +المبدئيا فهذا هو التعريف بشكله أبسط صورة يمكن له + +515 +00:40:39,480 --> 00:40:46,060 +نشوف مثال آخرفإذا صورة الـA بدي صورة عناصر الـA + +516 +00:40:46,060 --> 00:40:50,340 +الصورة العكسية للـB بدي عناصر صورهم في الـB صورهم + +517 +00:40:50,340 --> 00:40:55,020 +في الـB نشوف مثال آخر ناخد دالة متقدمة شوية + +518 +00:40:55,020 --> 00:40:58,680 +ومتعودين عليها الدالة التربيعية من real numbers ل + +519 +00:40:58,680 --> 00:41:02,820 +real numbers بقول يجيب صورة المجموعة اللي عبارة عن + +520 +00:41:02,820 --> 00:41:06,160 +فترة من سالب واحد لواحد وصورة العكسية برضه لفترة + +521 +00:41:06,160 --> 00:41:09,260 +من سالب اتنين ل zero خلينا نبدأ فيهم واحدة واحدة + +522 +00:41:12,020 --> 00:41:16,480 +Solution فبتوقف الـ A والـ A مدينا إياه إيش بتساوي + +523 +00:41:16,480 --> 00:41:18,600 +من سالب واحد لواحد، مجموعة + +524 +00:41:27,010 --> 00:41:31,110 +طبعا هنا مش زي المثال السابق بدّي صور العناصر اللي + +525 +00:41:31,110 --> 00:41:34,830 +في الـA بس هدولة مش تلت عناصر ولا ألف ولا مليون ما + +526 +00:41:34,830 --> 00:41:37,430 +لا نهاية خلينا نحط التعريف و نشوف كيف بدنا نعمل + +527 +00:41:37,430 --> 00:41:42,130 +فبدنا صور العناصر اللي في الـA اللي هم من سالب + +528 +00:41:42,130 --> 00:41:47,050 +واحد لواحد مصبوط؟ هيك معناته ايش معناته F of A صور + +529 +00:41:47,050 --> 00:41:49,330 +العناصر اللي في الـA و الـA عندنا فترة من سالب + +530 +00:41:49,330 --> 00:41:54,410 +واحد لواحد تمام ايش ممكن اعمل؟ ايش معناته F of X؟ + +531 +00:41:54,410 --> 00:41:58,710 +X تربيه في هذا المثالو ال X وين موجودة؟ بين سالب + +532 +00:41:58,710 --> 00:42:02,410 +واحد و واحد ممكن أعيد كتابة هذا الكلام بهاد الصورة + +533 +00:42:02,410 --> 00:42:07,770 +و لا لأ؟ فماذا أصبح السؤال؟ أصبح السؤال ممكن أقراه + +534 +00:42:07,770 --> 00:42:12,250 +بالصورة التالية بقول إذا كانت ال X محصورة بين سالب + +535 +00:42:12,250 --> 00:42:15,070 +واحد و واحد، بتكون ال X سربيع وين موجودة، هيك أصبح + +536 +00:42:15,070 --> 00:42:19,650 +السؤال، من مين و مين؟ من صفر لواحد، صحيح، فهذا + +537 +00:42:19,650 --> 00:42:25,250 +بيساوي من صفر لواحدهوضح على اللي بتشايفين النقطة + +538 +00:42:25,250 --> 00:42:30,690 +الجواب صحيح هيك بس نقول ليش والله + +539 +00:42:30,690 --> 00:42:35,290 +واضح ده الجميع واضح الجواب ولا انا اوضحه واضح اه + +540 +00:42:35,290 --> 00:42:38,470 +طبعا بتقول ان ده مطلق ال X اقل او يسوى احد بتربط + +541 +00:42:38,470 --> 00:42:41,190 +الطرفين بصير X ربيع اقل او يسوى احد ال X ربيع ده + +542 +00:42:41,190 --> 00:42:48,950 +positive واضحة؟ واضحة ولا اعيد؟ واضحة خلاص مهما + +543 +00:42:48,950 --> 00:42:53,820 +هذا مجموعة هذه فترة هذه عيش عبارة عن ايشهذه عبارة + +544 +00:42:53,820 --> 00:42:57,580 +عن كل الـ real numbers اللي محصورة بين الصفر وبين + +545 +00:42:57,580 --> 00:43:01,100 +الواحد، هيك معناها، هذا رمز مشهور في الرياش من + +546 +00:43:01,100 --> 00:43:05,260 +الفترات، الفترات نوع خاص من المجموعات، هي عبارة عن + +547 +00:43:05,260 --> 00:43:06,340 +مجموعات جزئية من الأرض + +548 +00:43:09,050 --> 00:43:14,190 +هذا رمز خاص، هذا الجثث المربع ليس خاص كمجموعة، + +549 +00:43:14,190 --> 00:43:18,810 +إنما كفترة، والفترة نوع خاص من المجموعات، واضح؟ مش + +550 +00:43:18,810 --> 00:43:26,390 +فيها عنصرين هذه، هذه لا تساوي مجموعة 01، هذه فيها + +551 +00:43:26,390 --> 00:43:30,790 +عنصرين، هذه مالة نهاية، مالة نهاية من العناصر، هذه + +552 +00:43:30,790 --> 00:43:35,840 +الفترة فيها أعداد أكتر من Zهو أضحى بل أكتر من + +553 +00:43:35,840 --> 00:43:38,400 +الـQ، تزعلوش، أكتر من كل الـRational Numbers، + +554 +00:43:38,400 --> 00:43:41,260 +ففيها أعداد كتيرة واضحية في الفرق بينهم، فهذا مجرد + +555 +00:43:41,260 --> 00:43:47,730 +رمز لفترة هيك بتعني، هذا معناها، هذا معناهافإذا + +556 +00:43:47,730 --> 00:43:53,250 +هذه هو الأول نشوف إذا أخدنا B الفترة من سالب 2 لـ + +557 +00:43:53,250 --> 00:43:58,350 +0 فبدنا F inverse الـ B بدنا العناصر اللي في ال + +558 +00:43:58,350 --> 00:44:04,030 +domain اللي صورهم إيش في الـ B بحيث F of X تنتمي + +559 +00:44:04,030 --> 00:44:10,070 +للـ B اللي هي من 0 و 2 فلو جينا نفسر بدنا ال real + +560 +00:44:10,070 --> 00:44:15,390 +numbers اللي فيهم X تربيه أشمالها من سالب 2 لـ 0 + +561 +00:44:17,780 --> 00:44:21,640 +فبقول ليه؟ مين العناصر اللي مربع بيكون أصغر من + +562 +00:44:21,640 --> 00:44:25,220 +Zero و أكبر و يسوى سلب اتنين؟ مافيش الا Zero مافيش + +563 +00:44:25,220 --> 00:44:28,840 +الا Zero مافيش + +564 +00:44:28,840 --> 00:44:32,360 +الا Zero لأن ال Except بيبقى دايما Positive وتسوى + +565 +00:44:32,360 --> 00:44:35,620 +Zero فقط عند ال Zero مش مستحيل تكون سلب اتنين ولا + +566 +00:44:35,620 --> 00:44:38,600 +سلب واحد ولا سلب واحد و نصف فالقيمة الوحيدة هي إيش + +567 +00:44:38,600 --> 00:44:46,380 +ال Zero ملاحظة + +568 +00:44:52,150 --> 00:44:57,450 +عشان نتعامل مع التعريف احنا فيه عندنا تعريفين + +569 +00:44:57,450 --> 00:45:05,850 +التعريف الأول في هذه النقطة مهمة جدا عندنا f of a + +570 +00:45:05,850 --> 00:45:15,290 +تساوي f of x بحيث x تنتمي لل aكيف نتعامل مع + +571 +00:45:15,290 --> 00:45:18,250 +التعريف في البراهين؟ قبل أن نبدأ ناخد النظريات، في + +572 +00:45:18,250 --> 00:45:22,230 +عندنا تعليقين مهمين على هذا التعريف فالنظرية أول + +573 +00:45:22,230 --> 00:45:25,470 +ملاحظة تقول، لو كان في أندي عنصر في الـA، وين + +574 +00:45:25,470 --> 00:45:28,850 +صورته بتكون؟ في صورة الـA، هذا دايما صحيح، إذا + +575 +00:45:28,850 --> 00:45:32,130 +العنصر موجود في مجموعة، فصورته بتكون في صورة + +576 +00:45:32,130 --> 00:45:37,560 +المجموعة، لكن العكس غير صحيحإذا في صورة عنصر ما في + +577 +00:45:37,560 --> 00:45:41,440 +صورة مجموعة مش بالضرورة العنصر يكون في المجموعة + +578 +00:45:41,440 --> 00:45:46,320 +فبقول إذا كانت F of X في F of A ليس من الضرورة + +579 +00:45:46,320 --> 00:45:50,400 +تكون ال X في F of A هنشوف مثال عشان نوضع فإذا هذه + +580 +00:45:50,400 --> 00:45:54,040 +مش F and only F هذا التعريف بده التعامل بدقة مش F + +581 +00:45:54,040 --> 00:46:00,120 +and only F هنشوف لكن بالنسبة للصورة العكسية الكلام + +582 +00:46:00,120 --> 00:46:04,600 +F and only Fهذا يقول لي إيش بتساوي؟ بتساوي X تنتمي + +583 +00:46:04,600 --> 00:46:12,100 +لـX such that F of X تنتمي لـB فبقوللي الـX بتكون + +584 +00:46:12,100 --> 00:46:16,340 +في F inverse of B if and only if صورتها في الـB + +585 +00:46:16,340 --> 00:46:20,620 +هذا الكلام بالتجاهية فإذا أنا بعرف هذه بقدر أستنتج + +586 +00:46:20,620 --> 00:46:25,640 +هذه والعكس صحيحهنا إذا بعرف هذه بستنتج هذه لكن إذا + +587 +00:46:25,640 --> 00:46:29,580 +بعرف هذه بقدرش أرجع جوه بالسنتج التاني لإيش؟ + +588 +00:46:29,580 --> 00:46:32,900 +الملاحظة فهنا الأولى ملاحظة مهمة جدا وهذه مفتاح + +589 +00:46:32,900 --> 00:46:37,320 +للعمل في كل البراهين وفي كل دراستنا القادمة عشان + +590 +00:46:37,320 --> 00:46:40,760 +نشوف إن الأول مش دايما مش تكافأه هنديكم مثال عكسي + +591 +00:46:40,760 --> 00:46:44,040 +إن الاتجاه الأول صحيح لكن عكسه غير صحيح في عندنا + +592 +00:46:44,040 --> 00:46:50,990 +مثال بسيط في عندنا مثال بسيطأه طبعا السبب خدنا + +593 +00:46:50,990 --> 00:46:55,170 +نشوف المثال وبعدين بنلخص إيش السبب بشكل عام ففي + +594 +00:46:55,170 --> 00:47:00,490 +عندنا مثال ناخد الدالة التربيعية وناخد مجموعة A + +595 +00:47:00,490 --> 00:47:08,130 +تساوي مجموعة الاتنين فما هي صورة الـA؟ هي صورة + +596 +00:47:08,130 --> 00:47:13,190 +الاتنين يعني أربع، مظبوط؟ متفقين؟ متبعين؟ أه طب + +597 +00:47:13,190 --> 00:47:19,150 +الآن لو ريحنا نشوف صورة السالب اتنينأيش بتساوي؟ + +598 +00:47:19,150 --> 00:47:24,950 +أربع تنتمي لل F في A ولا بتتميش؟ ها هي عندي صورة + +599 +00:47:24,950 --> 00:47:28,390 +تنتمي لصورة المجموعة هل بالضروري سالب اتنين تنتمي + +600 +00:47:28,390 --> 00:47:34,070 +لل A؟ لأ مش بالضروري but سالب اتنين لا تنتمي لل A + +601 +00:47:35,740 --> 00:47:40,060 +التنين تنتمي وين صورتها؟ تنتمي للصورة لكن صورة + +602 +00:47:40,060 --> 00:47:45,700 +تنتمي العنصر مش بضروري ينتمي ليش؟ لأن الصورة بتيجي + +603 +00:47:45,700 --> 00:47:49,460 +من أكتر من عنصر أنا في عندي صورة موجودة هذه وين + +604 +00:47:49,460 --> 00:47:52,860 +أصلها؟ ممكن يكون في الـA وممكن مايكونش زي هنا هذه + +605 +00:47:52,860 --> 00:47:56,200 +الأربعة وين أصلها؟ أصلها اتنين وسالب اتنين إليها + +606 +00:47:56,200 --> 00:47:59,880 +أصلين فمين واحد ينتمي وواحد لا ينتمي لأن ايش؟ + +607 +00:47:59,880 --> 00:48:04,460 +الصورة ممكن يكونها أكتر من أصل لكن ليش؟ العنصر ليه + +608 +00:48:04,460 --> 00:48:07,930 +صورة واحدة؟فهي تقديك ديك صح F and only F لكن العكس + +609 +00:48:07,930 --> 00:48:11,010 +غير صحيح فواضحة دي ملاحظة مهمة جدا بس لو العنصر + +610 +00:48:11,010 --> 00:48:13,370 +إلا صورتين مايكونش function مايكونش function فاحنا + +611 +00:48:13,370 --> 00:48:16,590 +في ال function ممكن الصورة يكونها أكتر من أصل و + +612 +00:48:16,590 --> 00:48:19,410 +الأصول هدول تتوزع على أكتر من مجموعة لكن العنصر + +613 +00:48:19,410 --> 00:48:23,670 +صورة واحدة عشان هيك هذه F and only F لكن هديك بس + +614 +00:48:23,670 --> 00:48:25,850 +تجاه واحد وده مهم جدا ننتبهله + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/gWNV6nTT2VQ_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/gWNV6nTT2VQ_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..da31bb84fbdf87b1643c610e0b1ab6b3df93c64b --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/gWNV6nTT2VQ_raw.srt @@ -0,0 +1,2692 @@ +1 +00:00:21,380 --> 00:00:24,740 +بسم الله الرحمن الرحيم نواصل في مصداق مبادئ + +2 +00:00:24,740 --> 00:00:29,580 +الرياضيات ونظرية المجموعات اليوم إن شاء الله + +3 +00:00:29,580 --> 00:00:33,240 +هنواصل في الموضوع اللي هو التفكير الاستدلالي أو + +4 +00:00:33,240 --> 00:00:37,460 +التفكير اللي هو القياسي المنطقي أو الاستنباطي ببعض + +5 +00:00:37,460 --> 00:00:41,990 +الأحيان بيعربه طبعا هو deductive reasoningاحنا + +6 +00:00:41,990 --> 00:00:45,010 +طبعا بدأنا في الحديث عن هذا الموضوع وعملنا مقدمة + +7 +00:00:45,010 --> 00:00:48,490 +ان شاء الله اليوم هنستكمل خلينا بس نسترجع بعض + +8 +00:00:48,490 --> 00:00:51,910 +الأمور الأساسية فقولنا ال deductive reasoning هو + +9 +00:00:51,910 --> 00:00:57,970 +واحد من النوعين من التفكيرات الرئيسية أو التفكيرات + +10 +00:00:57,970 --> 00:01:01,570 +المنطقية الرئيسية وهو inductive و deductive في ال + +11 +00:01:01,570 --> 00:01:06,330 +inductive بنروح من الأمثلة إلى القاعدة فهي نمشي من + +12 +00:01:06,330 --> 00:01:11,050 +قاعدة الهرم إلى قمتهأه اللي هي إيش؟ Down-Top اللي + +13 +00:01:11,050 --> 00:01:13,710 +هو إيش؟ هد بيسموه induction استقرار لكن إحنا + +14 +00:01:13,710 --> 00:01:17,030 +لمعنية في ال deductive reasoning بنيجي من القاعدة + +15 +00:01:17,030 --> 00:01:21,330 +للأمثلة من قمة الهرم إلى قاعد الهرم من القاعدة + +16 +00:01:21,330 --> 00:01:24,510 +للهرم عشان إيش بيسموه بالعامية Top-Down من القاعدة + +17 +00:01:24,510 --> 00:01:27,810 +بنشوف مين و الأمثلة فكل عمليتنا في ال deductive + +18 +00:01:27,810 --> 00:01:32,010 +reasoning في عندنا نظرية في عندنا قاعدة بتام دورنا + +19 +00:01:32,010 --> 00:01:35,510 +نشوف إن هذا المثال اللي عندنا ينطبق عليه القاعدة + +20 +00:01:35,510 --> 00:01:37,850 +ولا لأ إذا انطبق عليه القاعدة فالاستنتاج صحيح + +21 +00:01:37,960 --> 00:01:41,180 +مثلًا، على سبيل المثال، إن نظريتي فيه ثغور، فهذه + +22 +00:01:41,180 --> 00:01:45,000 +قاعدة، إذا في عندنا مثلث قائم الزاوية، فطول الوطر + +23 +00:01:45,000 --> 00:01:48,420 +أو مربع طول الوطر يساوي مجموع مربعات طول دلعين + +24 +00:01:48,420 --> 00:01:52,120 +الآخرين، فبتصير أنا فيه من كل أي مثال، اديني أي + +25 +00:01:52,120 --> 00:01:55,860 +مثلث، إذا أثبت أنه قائم الزاوية، بقدر أطبق عليه + +26 +00:01:55,860 --> 00:01:58,820 +القاعدة، فانا عند القاعدة موجودة وفي عندي أمثلة + +27 +00:01:58,820 --> 00:02:01,880 +متعددة، أمثلة متعددة، فهذا هو what is deductive + +28 +00:02:01,880 --> 00:02:04,750 +reasoningطبعا احنا قلنا هذا هو بشكل عام الـ + +29 +00:02:04,750 --> 00:02:08,430 +deductive reasoning طب بهذا ال section هنستخدمه + +30 +00:02:08,430 --> 00:02:11,970 +لإثبات التضمين والتكافأة و بعدين هنستخدمه + +31 +00:02:11,970 --> 00:02:13,550 +استخدامات متعددة في الرياضيات لكن في هذا ال + +32 +00:02:13,550 --> 00:02:17,570 +section بشكل خاص هنستخدمه كطريقة بديلة لجداول + +33 +00:02:17,570 --> 00:02:22,670 +الصدق لإثباتنوعين من القوانين التكافؤ والتضمين طب + +34 +00:02:22,670 --> 00:02:25,330 +لو طلعتوا على اللي هو مقواعد الاستدلال اللي هم + +35 +00:02:25,330 --> 00:02:29,990 +تقريبا 18 قاعدة نظرية من واحد واحد لواحد سبعة مع + +36 +00:02:29,990 --> 00:02:33,490 +بعض إضافات تفيفة بنلاقيها كلها يا تضمين يا تكافؤ + +37 +00:02:33,490 --> 00:02:37,350 +يا تضمين يا تكافؤ يا عبنان نستخدمها بـ deductive + +38 +00:02:37,350 --> 00:02:40,520 +reasoningفطب ليش الطريقة اللي هنسميها deductive + +39 +00:02:40,520 --> 00:02:42,940 +reasoning ونشوفها مثال؟ لأنه أنا دايما بقى أشوف + +40 +00:02:42,940 --> 00:02:46,520 +القاعدة هذه و بقى أشوف الخطوة اللي بشتر عليها + +41 +00:02:46,520 --> 00:02:49,760 +تنطبق عليها القاعدة ولا لا؟ زي المثال، هل هذا قائم + +42 +00:02:49,760 --> 00:02:52,340 +زيها تنطبق عليه في غرفه ولا لا؟ فنفس القضية، أنا + +43 +00:02:52,340 --> 00:02:55,500 +عندي خطوة هذه، بدي أعمل عملية معينة، طيب إيش + +44 +00:02:55,500 --> 00:02:58,940 +دليلي؟ عشان استدلالي، النظرية، إذا هذه تنطبق عليها + +45 +00:02:58,940 --> 00:03:01,820 +النظرية، إذا خطوتي صح، لا تنطبق النظرية إذا الخطوة + +46 +00:03:01,820 --> 00:03:05,040 +بتكون غير صحيحة، فإنها عشان هي كذا تفكير استدل + +47 +00:03:05,450 --> 00:03:08,950 +واتفقنا إن كل خطوة نحط الدليل عشان نتعود التفكير + +48 +00:03:08,950 --> 00:03:14,090 +المنطقي الصحيح ونحكم على برهاننا على حالنا إنه صح + +49 +00:03:14,090 --> 00:03:17,910 +أو غير صحيح طول ما عندك دليل إذا حالك صح لو دليلك + +50 +00:03:17,910 --> 00:03:21,610 +مش صحيح بيكون فيه شك إن حالك ممكن يكون غير صحيح + +51 +00:03:21,610 --> 00:03:25,350 +فأحنا أخدنا مثال الآن خلينا نشوف كمان مثال ونأكد + +52 +00:03:25,350 --> 00:03:33,240 +على هذه الأفكار فالمثال التاني على هذا الموضوعأه + +53 +00:03:33,240 --> 00:03:37,360 +بطبعا صيغ مدعدي ده الممكن المثال لكن الشاهد اللي + +54 +00:03:37,360 --> 00:03:42,380 +هو prove the disjunction syllogism قانون أخدناها + +55 +00:03:42,380 --> 00:03:46,460 +من القوانين بتاعة الاستدلال اللي هو P or Q and not + +56 +00:03:46,460 --> 00:03:51,000 +P implies Q تضمين احنا قولنا يا equivalence يا + +57 +00:03:51,000 --> 00:03:55,890 +implicationsطيب إيش الطريقة؟ By deductive + +58 +00:03:55,890 --> 00:03:59,730 +reasoning باستخدام التفكير الاستدلالي بدناش نعمل + +59 +00:03:59,730 --> 00:04:04,930 +truth table فبدنا نشوف كيف بدنا نبره، دعونا نشوف + +60 +00:04:04,930 --> 00:04:09,490 +الحل فهذا + +61 +00:04:09,490 --> 00:04:16,130 +المثال رقم اتنين دعونا نعلق و بنبدأ اللي هو هي + +62 +00:04:16,130 --> 00:04:23,650 +solution و ده هو الحلأه كما ذكرنا تستخدم التفكير + +63 +00:04:23,650 --> 00:04:27,750 +الاستدلالي اثبات التكافؤ أو التضمين طبعا التكافؤ و + +64 +00:04:27,750 --> 00:04:31,070 +التضمين بنلاقي ان في statement او ال .. ال .. ال + +65 +00:04:31,070 --> 00:04:31,650 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +66 +00:04:31,650 --> 00:04:31,750 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +67 +00:04:31,750 --> 00:04:31,850 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +68 +00:04:31,850 --> 00:04:32,810 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +69 +00:04:32,810 --> 00:04:32,910 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +70 +00:04:32,910 --> 00:04:33,370 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +71 +00:04:33,370 --> 00:04:34,190 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +72 +00:04:34,190 --> 00:04:36,810 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +73 +00:04:36,810 --> 00:04:36,950 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +74 +00:04:36,950 --> 00:04:38,530 +ال .. ال .. ال .. ال .. ال .. الفي قانون التكافؤ + +75 +00:04:38,530 --> 00:04:42,130 +ممكن أبدأ من أي طرف من الطرفين و أوصل للتالي و + +76 +00:04:42,130 --> 00:04:46,310 +طبعا الاتنين صحيحين طبعا الاتنين ممكن تكون واحدة + +77 +00:04:46,310 --> 00:04:48,950 +أسهل من التانية دايما كقاعدة أبدأ من الكبير و أروح + +78 +00:04:48,950 --> 00:04:51,310 +لصغير أسهل ما تروح من الصغير للكبير هذه قاعدة + +79 +00:04:51,310 --> 00:04:56,710 +دايما التبسيط أفضل أو أسهل من الإضافة التبسيط أسهل + +80 +00:04:56,710 --> 00:05:00,410 +من الإضافة أو الحدث فهذه قاعدة لكن في التضمين ليس + +81 +00:05:00,410 --> 00:05:03,630 +خياري يعني لازم أبدأ من اليسار و أوصل لليمين لأن + +82 +00:05:03,630 --> 00:05:07,230 +هو يشمله هذا سهل في اتجاه واحدوالتكافؤ ايش؟ سهمين، + +83 +00:05:07,230 --> 00:05:09,730 +فهذه طريقة اتجاه واحد، هذه طريقة اتجاهين، فاحنا + +84 +00:05:09,730 --> 00:05:15,390 +فيها اننا يا تضمين بشكل عام اتجاه واحد، اه فانزال + +85 +00:05:15,390 --> 00:05:18,930 +باش ملؤ، رايح على اليمين، او في عندنا تكافؤ، هذه + +86 +00:05:18,930 --> 00:05:21,610 +اللي هي ايش نفسها هذه، نفس الشيء، مصبوط؟ فهذه + +87 +00:05:21,610 --> 00:05:24,630 +اتجاهين، تبدأ من هنا لهنا صح، تبدأ من هنا لهنا صح، + +88 +00:05:24,630 --> 00:05:27,390 +من اليمين لليسار أو يسار، لكن هنا ايش؟ من اليسار + +89 +00:05:27,390 --> 00:05:29,630 +لليمين، اذا هنا مافيش عندنا + +90 +00:05:32,300 --> 00:05:41,270 +خيار هنبدأ من الطرف اليسار فهي بي or qand not a + +91 +00:05:41,270 --> 00:05:45,130 +cube not P تمام فده هو الطرف اليساري حنا نبدأ منه + +92 +00:05:45,130 --> 00:05:50,570 +و بدنا نوصل للطرف اليمين باستخدام قوانين المنطق أو + +93 +00:05:50,570 --> 00:05:54,410 +قواعد الاستدلال فانا بدي اشوف اي خطوة بدي اعملها + +94 +00:05:54,410 --> 00:05:57,190 +بدي اشوفها لي مين القاعدة اللي بتطبق عليها و + +95 +00:05:57,190 --> 00:06:00,590 +استخدمها عشان ايه تفكير استدالي بدي اعملها كمثال + +96 +00:06:00,590 --> 00:06:04,770 +على القاعدة تبعتي كمثال من أمثلة القاعدةفطبعا احنا + +97 +00:06:04,770 --> 00:06:08,710 +ايش واضح انه بدنا نتخلص من بعض الأشياء لإن طرف + +98 +00:06:08,710 --> 00:06:12,090 +اليمين كبير هينتهي بواحد في تالت statements وان + +99 +00:06:12,090 --> 00:06:15,850 +كانوا مش مستقلين هينتهي الطرف ب statement واحدة بي + +100 +00:06:15,850 --> 00:06:20,490 +or كيو و not بي بدي ايش اكيو بدي اكيو فإذا هدفنا + +101 +00:06:20,490 --> 00:06:25,350 +نتخلص من ال بي ايش ممكن نعمل نفكر في هذه العملية + +102 +00:06:25,350 --> 00:06:30,670 +ايش ممكن نعمل ممكن نعمل توزيعفي عندنا or وفي عندنا + +103 +00:06:30,670 --> 00:06:34,670 +and عمليتين مختلفتين إذا التوزيع عمليتين من نفس + +104 +00:06:34,670 --> 00:06:38,830 +الجنس يكون تجميع فده نعمل توزيع ممكن نعمل توزيع + +105 +00:06:38,830 --> 00:06:41,910 +طبعا القانون موجود قانون التوزيع البلاجي إيش اللي + +106 +00:06:41,910 --> 00:06:47,430 +هو P اللي هو إيش and اللي هو Q or R هيك ماشي و + +107 +00:06:47,430 --> 00:06:55,020 +بيقول يكافرB and Q او B and R هذا هو قانون التوزيع + +108 +00:06:55,020 --> 00:06:58,960 +فبتستخدمه عشان اوصل لهذا الاستخدام كأنه هذه هي ال + +109 +00:06:58,960 --> 00:07:01,480 +B تبعتي في هذا القانون اللي ممكن اعيد تسميتها و + +110 +00:07:01,480 --> 00:07:06,240 +دولة من Q او R فانا طبعاالقانون مش مهم المسميات + +111 +00:07:06,240 --> 00:07:09,800 +الرموز إنما إيش بدنا نشوف اللي هو المعنى الأصلي + +112 +00:07:09,800 --> 00:07:12,720 +تبعه المضمون ما هو المضمون في three statements + +113 +00:07:12,720 --> 00:07:17,220 +تنتين بينهم عملية or وفي تالت بينهم إيش and مع مين + +114 +00:07:17,220 --> 00:07:20,960 +مع كل ال or مع القصة إذا أحنا بنعرف نقراها من + +115 +00:07:20,960 --> 00:07:24,120 +اليسار لليمين نفسها صحيح لأنه إبدال أو ممكن نعمل + +116 +00:07:24,120 --> 00:07:28,440 +خطوة أولا إبدال نعمل إبدال فإذا طبعا قانون الإبدال + +117 +00:07:28,440 --> 00:07:32,960 +قانون تضمين ولا implies تضمين ولا تكافه فاحنا + +118 +00:07:32,960 --> 00:07:33,840 +جيتنا نعمله إيش + +119 +00:07:42,030 --> 00:07:47,310 +Commutative law استخدمنا + +120 +00:07:47,310 --> 00:07:49,170 +قانين الابدال + +121 +00:07:50,910 --> 00:07:54,290 +كيف اعملت؟ عشان اسمها استدلال عندي two statements + +122 +00:07:54,290 --> 00:07:58,430 +هي واحدة و هي واحدة وبينهم N عشان اوصل للغرض تبعي + +123 +00:07:58,430 --> 00:08:01,310 +طبقت ال what ال commutative law فايها ناية في عندي + +124 +00:08:01,310 --> 00:08:04,090 +قاعدة تدلقوا what ال commutative law هذه القاعدة و + +125 +00:08:04,090 --> 00:08:07,550 +كمثال بدلت طبعا ليش بعد المثال مش قاعدة لأن هي + +126 +00:08:07,550 --> 00:08:10,110 +statement هي statement غير عن الأصل غير عن القاعدة + +127 +00:08:10,110 --> 00:08:13,630 +الأصلية فده يعتبر كمثال على القاعدة الأصلية عملنا + +128 +00:08:13,630 --> 00:08:17,210 +إبدال الآن احنا جاهزين نعمل توزيع نعمل توزيع و + +129 +00:08:17,210 --> 00:08:25,110 +التوزيع إيش ماله تكافؤnot B and B or not B and Q + +130 +00:08:25,110 --> 00:08:32,550 +ايش عملنا؟ Distributed beautiful + +131 +00:08:32,550 --> 00:08:39,230 +قانون التوزيع فصار عندي مثال في and and or طبقت + +132 +00:08:39,230 --> 00:08:41,330 +عليه قاعدة التوزيع لاني بتقول ايش مازال في عندك + +133 +00:08:41,330 --> 00:08:44,410 +and و or مقدر تتوزع فدي القاعدة و هي ايش الدليل + +134 +00:08:44,410 --> 00:08:49,840 +الآن بدنا نبدأ نبصر بدنا نبدأ نبصر اهNot B and B + +135 +00:08:49,840 --> 00:08:54,080 +Contradiction هذي مرت علينا فدى إيش مالها برضه إيش + +136 +00:08:54,080 --> 00:08:59,760 +تكافئ Contradiction or Not B and Q من وين جبنا هذا + +137 +00:08:59,760 --> 00:09:03,900 +الكلام هذى قاعدة أو بديهية تعتبروها بي and not بي + +138 +00:09:03,900 --> 00:09:08,040 +تكافئ Contradiction مثال أثبتناها احنا كم مثال + +139 +00:09:08,040 --> 00:09:12,880 +فإيش دليلنا على الخطوة إن الشيء ونقيده لا يجتمعان + +140 +00:09:12,880 --> 00:09:16,260 +ف بي and not بي Contradiction Contradiction تمام + +141 +00:09:17,390 --> 00:09:22,930 +بدينا الان احنا بدنا Q فلازم نتخلص من ال C و not B + +142 +00:09:22,930 --> 00:09:27,210 +بقدر اي مين اتخلص اولا من ال C في عندي نظرية واحد + +143 +00:09:27,210 --> 00:09:31,230 +سبعة بتقولي C or anything anything من غير ما نبدل + +144 +00:09:31,230 --> 00:09:34,330 +ليش؟ لأن هذي false إذا لازم تاني تكون true عشان + +145 +00:09:34,330 --> 00:09:37,610 +هذي true كلها فهذه false لازم هذي true طبعا هذه + +146 +00:09:37,610 --> 00:09:42,050 +تضمين ولا implies أو تكافأ تكافأ برضه خانون نظرية + +147 +00:09:42,050 --> 00:09:49,800 +فهذه تكافأ not B and Q إيش دليلي؟وحد سبعة وحد سبعة + +148 +00:09:49,800 --> 00:09:55,920 +وحد + +149 +00:09:55,920 --> 00:10:01,440 +سبعة وحد سبعة وحد سبعة وحد سبعة وحد سبعة وحد سبعة + +150 +00:10:01,440 --> 00:10:09,680 +وحد سبعة وحد سبعةامتبعين؟ أي سؤال تمام ايش بدنا + +151 +00:10:09,680 --> 00:10:14,460 +احنا؟ بدنا Q اه بقدر اتخلص من النطبي نعم في قانون + +152 +00:10:14,460 --> 00:10:19,500 +التبسيط قانون التبسيط وقانون التبسيط implies ال Q + +153 +00:10:19,500 --> 00:10:21,300 +ايش عملنا؟ simplification + +154 +00:10:25,790 --> 00:10:29,710 +قانون التبسيط Simplification Law وهو المطلوب اثبته + +155 +00:10:29,710 --> 00:10:34,050 +فاحنا هنا في كل خطوة و احنا وين رايحين عارفين و لا + +156 +00:10:34,050 --> 00:10:37,550 +بشوف كمثال بطبق عليه القواعد الاستدلال فعشان هيك + +157 +00:10:37,550 --> 00:10:43,530 +هو تفكير استدلالي او قواعد الاستدلال بنستخدمها في + +158 +00:10:43,530 --> 00:10:48,190 +البرحة أي سؤال فارجو الانتباه للدقة اللي بنشتغل + +159 +00:10:48,190 --> 00:10:48,690 +فيها تفضل + +160 +00:10:53,620 --> 00:10:56,800 +على الصفحة الموقع مش موجودين rules of inference + +161 +00:10:56,800 --> 00:11:00,780 +برجحها rules of inference اذا مش موجودين برجحها + +162 +00:11:00,780 --> 00:11:03,060 +موجودين يعني ان شاء الله بحاول انزلها مرة تانية + +163 +00:11:03,060 --> 00:11:07,220 +ولا هى مافيش مشكلة تمام فهذا كمان مثال فهذه هي + +164 +00:11:07,220 --> 00:11:11,880 +تفكير الاستدلالي وكيف بنثبت التضمين او التكافؤ + +165 +00:11:11,880 --> 00:11:21,390 +خلينا نشوف مثال جديد المثال التالتApprove the + +166 +00:11:21,390 --> 00:11:26,740 +following exportation law قانون التصديرB and Q + +167 +00:11:26,740 --> 00:11:33,240 +then R تكافئ B then Q then R فدولة two statements + +168 +00:11:33,240 --> 00:11:37,860 +متكافئتين فبدنا نثبته مش بجداول الصدق طبعا في + +169 +00:11:37,860 --> 00:11:41,680 +أمامي طريقتين الحقيقة أي قانون تضمين أو تكافئه في + +170 +00:11:41,680 --> 00:11:46,200 +طريقتين للإثبات الآن جداول الصدق أو الـ deductive + +171 +00:11:46,200 --> 00:11:49,380 +reasoning فطبعا إذا السؤال ماحددش اختار أي طريقة + +172 +00:11:49,380 --> 00:11:53,020 +من الطريقتين إذا حدد التزمي بالتحديد لأني محدد قال + +173 +00:11:53,020 --> 00:11:56,110 +لي إيش بروق أنا مش محددلكن احنا مازال عنوان بدنا + +174 +00:11:56,110 --> 00:12:03,430 +نشتغلها كمثال إضافي على detective reason نبدأ + +175 +00:12:03,430 --> 00:12:08,370 +هنا وبعدين بنكمل هذا المثال التالت solution + +176 +00:12:11,380 --> 00:12:15,300 +فهذه عملية تكافئ، فإذا في عندنا حرية في البداية، + +177 +00:12:15,300 --> 00:12:19,480 +ابدي من الطرف اليمين أو اليسار، كله صحيح، طبعا ده + +178 +00:12:19,480 --> 00:12:22,520 +ما بنحاول نشوف مين أسهل كبداية، ممكن تكون أسهل، + +179 +00:12:22,520 --> 00:12:25,120 +ممكن تكون تنتين متكافئتين لبدايتين، وممكن تكون + +180 +00:12:25,120 --> 00:12:28,200 +واحدة أسهل من التانية، لكن تنتين صح، لكن إيش؟ في + +181 +00:12:28,200 --> 00:12:32,670 +ممكن تكون واحدة أسهل من التانية، من هنا نبدأاللي + +182 +00:12:32,670 --> 00:12:35,990 +هو دايما نبدأ من الأطول، نبدأ من الأطول دايما، فهي + +183 +00:12:35,990 --> 00:12:38,910 +القضية، حبينا نبدأ من اليسار، من اليمين، نتوقع C + +184 +00:12:38,910 --> 00:12:42,970 +يعني، انا تقييمي انه C يعني، خينا نبدأ من اليسار، + +185 +00:12:42,970 --> 00:12:51,070 +فهنا هي B and Q then R، نبدأ من اليسارهو فدائما + +186 +00:12:51,070 --> 00:12:54,590 +أنا ببدأ من ال .. طبعا من .. من بداية و في + +187 +00:12:54,590 --> 00:12:57,010 +الرياضيات بشكل عام نبدأ من المعطيات و نوصل للمطلوب + +188 +00:12:57,010 --> 00:13:00,250 +لو فيها نظرية لكن هدولة من قوانين إذا لطال الضمين + +189 +00:13:00,250 --> 00:13:02,830 +ببدأ من اليسار و بدأ أوصل لليمين و إذا تكافأ و + +190 +00:13:02,830 --> 00:13:05,890 +ببدأ من الطرف و بوصل للطرف كله صحيح فبنحاول نوصل + +191 +00:13:05,890 --> 00:13:11,670 +إلى هناكفواضح لو حاولنا نتعمق في الطرف اليمين اللى + +192 +00:13:11,670 --> 00:13:16,810 +بدنا نوصله بنلاقي ان عملية ال grouping هذه الأمور + +193 +00:13:16,810 --> 00:13:20,210 +اللى مع بعض اختلفت في الطرف اليسار ال B مع ال Q مع + +194 +00:13:20,210 --> 00:13:24,370 +بعض و ال R لحال في الطرف اليمين ال Q مع ال R لحال + +195 +00:13:24,370 --> 00:13:28,110 +و ال B لحال فهذا يمكن اياش نظرة عالسريع فزن كل هدف + +196 +00:13:28,110 --> 00:13:32,490 +الآن يعدي الترتيب للطرف اليسار بحيث انه يبقى + +197 +00:13:32,490 --> 00:13:36,610 +الترتيب يختلف بدل ما هي B مع Q بده حط ال Q مع ال R + +198 +00:13:36,950 --> 00:13:40,430 +مين اللي بيخلّي القادة التبديل يختلف؟ يا إبدال يا + +199 +00:13:40,430 --> 00:13:46,990 +توزيع طيب في إبدال و توزيع لل if then لأ لكن ال if + +200 +00:13:46,990 --> 00:13:50,590 +then اللي هتعريف بتتحول ل and وهذا هيدينا مرونة + +201 +00:13:50,590 --> 00:13:53,750 +عشان هيك دايما التعريف ال if then اللي حطيناه قول + +202 +00:13:53,750 --> 00:13:57,210 +لك و هالجيت هتبين أهميته الآن بتبين أهميته بحول ال + +203 +00:13:57,210 --> 00:14:00,730 +if then أو الجملة الشرطية إلى and فبالتالي بتديني + +204 +00:14:00,730 --> 00:14:04,810 +مرونة في التحركعدد خيارات بتساعدني على الحل + +205 +00:14:04,810 --> 00:14:08,970 +فخلّينا نستخدم التعريف وكل تعريف هو تكافئ إذا هذا + +206 +00:14:08,970 --> 00:14:17,170 +يكافئ not الـ P and Q and not R هذا definition + +207 +00:14:17,170 --> 00:14:21,990 +تعريف ال if then ممكن اختصار ال definition أو + +208 +00:14:21,990 --> 00:14:29,820 +definition of if then أي سؤالالان ممكن نعمل طيب في + +209 +00:14:29,820 --> 00:14:33,780 +ممكن حد يقترح انه ندخل النافي على الكل لأ انا لأ + +210 +00:14:33,780 --> 00:14:37,000 +أنصح لأنه بطلع انا واني بتدوصل؟ بتدوصل في الآخر if + +211 +00:14:37,000 --> 00:14:39,340 +then و if then لازم يكون في نافي ورا و ممكن تكتب + +212 +00:14:39,340 --> 00:14:43,660 +بعد ايش بتساوي اذا ايش ممكن نعمل؟ نعمل ا دي end و + +213 +00:14:43,660 --> 00:14:48,010 +endإذا تجميع و أنا قلتش هذا فيه بدل ما كانت ال B + +214 +00:14:48,010 --> 00:14:50,750 +مع ال Q بتخلي ال Q مع ال R بينفع ولا بينفعاش؟ + +215 +00:14:50,750 --> 00:14:53,850 +بينفع عملي التجميع ليش؟ لأنه and و and إذا أنا على + +216 +00:14:53,850 --> 00:14:57,750 +طول هنا أخلي كلشي زي ما هو جوا أو آسف الأقل برا و + +217 +00:14:57,750 --> 00:15:04,010 +أخليها بي and Q and not R إيش عملنا اللي هو + +218 +00:15:04,010 --> 00:15:07,930 +associative associative + +219 +00:15:07,930 --> 00:15:16,860 +law قانون التجميع أي سؤالأي سؤالتمام، الآن بدنا + +220 +00:15:16,860 --> 00:15:20,120 +نقترب، الآن إيش بدنا نبدأ؟ نرجع واحدة واحدة .. + +221 +00:15:20,120 --> 00:15:25,520 +نرجع واحدة واحدة حتى نوصل للخطوة السابقة فأنا إما + +222 +00:15:25,520 --> 00:15:29,680 +بدأ أعمل ال B then هادي مع بعض، بس هنا بحتاج أنه + +223 +00:15:29,680 --> 00:15:31,640 +عشان دايما احنا إيش اللي بدنا .. خلينا نحط + +224 +00:15:31,640 --> 00:15:35,960 +القاعدة، قولنا اللي هو إحنا بدنا نوصل لحاجة تؤدي + +225 +00:15:35,960 --> 00:15:41,740 +إلى حاجة فبدنا اللي هو A then B إيش تكافئ؟ not B + +226 +00:15:41,740 --> 00:15:49,050 +and not Bهذه الـ A وهذه الـ B فهذه مافيش فيها not + +227 +00:15:49,050 --> 00:15:54,590 +ممكن ندخل فيها not كيف ممكن ندخل فيها not؟ الطريقة + +228 +00:15:54,590 --> 00:15:58,050 +تانية double negation double negation ممتاز فهذا + +229 +00:15:58,050 --> 00:16:07,490 +يكافئ not b and not not q and not r ونحط أقواس + +230 +00:16:07,490 --> 00:16:12,970 +عشان تكون الأمور سليمة فهنا double negation double + +231 +00:16:12,970 --> 00:16:14,350 +negation + +232 +00:16:16,050 --> 00:16:19,970 +فدائما لما انا بتطلع وين انا رايح بفكر ايش اللي + +233 +00:16:19,970 --> 00:16:22,450 +بديا ايش اللي بدي اعمل الخطوة العملية مش قالية و + +234 +00:16:22,450 --> 00:16:25,670 +هذه جزء اللي فيه الصعب في الرياضيات العملية اللي + +235 +00:16:25,670 --> 00:16:29,110 +بدنا نفكر و ايش الخطوة اللازمة الأمور مش قالية مش + +236 +00:16:29,110 --> 00:16:32,750 +قالية فبنفكر عملنا double negation اه الآن ايش + +237 +00:16:32,750 --> 00:16:37,490 +نعمل تمام هى عنا A و هى not B تمام اذا ايش ممكن + +238 +00:16:37,490 --> 00:16:42,610 +نعمل انه هذا يكافئ خليني اكتب هنا احسن خليني نكمل + +239 +00:16:42,610 --> 00:16:42,890 +هنا + +240 +00:16:51,690 --> 00:16:57,630 +انكمل هنا فطبعا هذا U كافق هاي نط هاي A و B عبارة + +241 +00:16:57,630 --> 00:17:03,010 +عن بي then ال نط هتطلع مع التعريف اللي هو not Q + +242 +00:17:03,010 --> 00:17:11,290 +and not R هذا شوه تعريف ولا لأ تعريف اللي هو ال F + +243 +00:17:11,290 --> 00:17:15,960 +thenأي سؤال أتوقع واضح أن الحل انتهينا الآن وهذا + +244 +00:17:15,960 --> 00:17:22,660 +كمان مرة تعريف هو Q then R ويكافئ P then Q then R + +245 +00:17:22,660 --> 00:17:24,440 +كمان مرة تعريف + +246 +00:17:28,970 --> 00:17:33,310 +فواضح انه دايما انا لما اطلع وين انا رايح بيساعدني + +247 +00:17:33,310 --> 00:17:37,130 +انا لو عملت كل العمليات الممكنة هتوغر و هعمل حاجات + +248 +00:17:37,130 --> 00:17:39,950 +مش مالاش لازم لو انا حاول تدخل و اعمل DeMorgans + +249 +00:17:39,950 --> 00:17:43,250 +الحقيقة محتاجناش فانا اش لانه انا عارف وين بده + +250 +00:17:43,250 --> 00:17:46,710 +اروح فبديش اتسرع دايما عيني على المطلوب وهذه قاعدة + +251 +00:17:46,710 --> 00:17:50,290 +في الرياضيات و في البراهين دايما انت هيي وين انت و + +252 +00:17:50,290 --> 00:17:53,790 +وين رايحا دايما تكون فينا دليل عشان مانتهج عشان + +253 +00:17:53,790 --> 00:18:03,200 +مانتهج اي سؤالوهو المطلوب اثباته اتبعين + +254 +00:18:03,200 --> 00:18:14,000 +نشوف مثال use + +255 +00:18:14,000 --> 00:18:17,020 +deductive reasoning to prove that + +256 +00:18:19,660 --> 00:18:23,100 +هنا طبعا شوفنا هي هذا الجزء من هنا بس عشان النقلة + +257 +00:18:23,100 --> 00:18:27,540 +فهي A وهذه كلها not وهذه بيه يعني لو احنا طلعنا + +258 +00:18:27,540 --> 00:18:34,800 +بيه بمقارنة هذه A وهذه not وهذه ايش كلها بيه فA ال + +259 +00:18:34,800 --> 00:18:39,450 +not بيه ونفي برا شمالهاA then B فدي كلها B فدي + +260 +00:18:39,450 --> 00:18:43,450 +كلها كتلة واحدة بتعمليها و الرموزة دي بتساعدنا و + +261 +00:18:43,450 --> 00:18:47,930 +هذا الرسم بيساعدنا عشان ننتبه مين A و مين F هل أنا + +262 +00:18:47,930 --> 00:18:52,190 +بدي أخد بـQ and dot R؟ لأ كلها بيه مع النفر واضحة؟ + +263 +00:18:52,190 --> 00:18:55,470 +اللي صارت السؤال واضحة الآن تمام؟ و بعدين طبقنا + +264 +00:18:55,470 --> 00:19:01,180 +كمان مرةUse deductive reasoning to prove that اه + +265 +00:19:01,180 --> 00:19:05,720 +زي ما حكيت لما يجيني سؤال تكافؤ او تضمين اصبح من + +266 +00:19:05,720 --> 00:19:09,460 +الآن وطالع انه طريقتين اذا لم يذكر انت حرا اختار + +267 +00:19:09,460 --> 00:19:12,620 +الطريقة المناسبة اذا ذكر زي ما تقول قاعدة الشرقية + +268 +00:19:12,620 --> 00:19:16,020 +لا اجتهاد مع النصب ده الحدد الطريقةأنا مش مخيّر، + +269 +00:19:16,020 --> 00:19:19,360 +مانيش اشتهد الطريقة اللي بتناسبني فإذا لازم هنا + +270 +00:19:19,360 --> 00:19:22,180 +ملزمين نستخدم اللي هو الـ deductive reasoning + +271 +00:19:22,180 --> 00:19:26,360 +الطريقة اللي احنا بنحاول نتعلمها و نعطي عليها أي + +272 +00:19:26,360 --> 00:19:31,100 +أكتر من المثال فعنا طبعا طرفين نلاحظ أن الطرفين + +273 +00:19:31,100 --> 00:19:35,400 +تقريبا متكافئين من حيث الطول فأتوقع أيه المبدأ كله + +274 +00:19:35,400 --> 00:19:38,920 +صحيح خلنا نبدأ باليمين المرة هذه كان مثال نبدأ من + +275 +00:19:38,920 --> 00:19:49,120 +اليمين خلنا نبدأ من اليمين B and Qthen are and are + +276 +00:19:49,120 --> 00:19:55,100 +are are are are are are are are are are are are + +277 +00:19:55,100 --> 00:19:55,160 +are are are are are are are are are are are are + +278 +00:19:55,160 --> 00:19:55,180 +are are are are are are are are are are are are + +279 +00:19:55,180 --> 00:19:55,600 +are are are are are are are are are are are are + +280 +00:19:55,600 --> 00:19:57,060 +are are are are are are are are are are are are + +281 +00:19:57,060 --> 00:19:57,100 +are are are are are are are are are are are are + +282 +00:19:57,100 --> 00:19:57,500 +are are are are are are are are are are are are + +283 +00:19:57,500 --> 00:20:03,020 +are are are are are are are are are are are are + +284 +00:20:03,020 --> 00:20:03,020 +are are are are are are are are are are are are + +285 +00:20:03,020 --> 00:20:03,520 +are are are are are are are are are are are are + +286 +00:20:03,520 --> 00:20:03,520 +are are are are are are are are are are are are + +287 +00:20:03,520 --> 00:20:03,520 +are are are are are are are are are are are are + +288 +00:20:03,520 --> 00:20:03,520 +are are are are are are are are are are are are + +289 +00:20:03,520 --> 00:20:03,520 +are are are are are are are are are are are are + +290 +00:20:03,520 --> 00:20:03,520 +are are are are are are are are are are are are + +291 +00:20:03,520 --> 00:20:03,520 +are are are are are are are are are are are are + +292 +00:20:03,520 --> 00:20:03,520 +are are are are are are are are are are are are + +293 +00:20:03,520 --> 00:20:03,520 +are are are are are are are are are are are are + +294 +00:20:03,520 --> 00:20:09,020 +are + +295 +00:20:09,020 --> 00:20:11,610 +are are areفالطرف اللي على اليمين اللي احنا بدنا + +296 +00:20:11,610 --> 00:20:15,190 +نعمله الـP مع الـQ والـR مع الـS وان رايحين نخل + +297 +00:20:15,190 --> 00:20:18,830 +الـP مع الـR الكلام بالعامية ونخل الـQ مع الـS إذا + +298 +00:20:18,830 --> 00:20:22,290 +بدنا عملية إيش تجميع توزيع إبدال هذا اللي بيخلينا + +299 +00:20:22,290 --> 00:20:26,170 +إيش نعيد توزيع المواقع تبعت من ال statements هذه + +300 +00:20:26,170 --> 00:20:30,550 +هي إيش الأداء فإيش ممكن نعمل طبعا ال employees هذه + +301 +00:20:30,550 --> 00:20:34,630 +بتأيخنا نحولها بإيش بالتعريف نحولها بالتعريف فده + +302 +00:20:34,630 --> 00:20:41,900 +عبارة عن نطب الأولB and Q كلها كأنها A and نفي + +303 +00:20:41,900 --> 00:20:50,970 +الطرف التاني R or S فهذا تعريف واحدة واحدةفهنا من + +304 +00:20:50,970 --> 00:20:54,550 +الصعوبات اللي بتقال بعض الطلبة ان القانون هو بسيط + +305 +00:20:54,550 --> 00:20:58,390 +عارفه لكن لما يتعقد شوية بيلتخم الناس لأن زي ما + +306 +00:20:58,390 --> 00:21:03,210 +حكينا هذه كلها كتلة اللي يمكن يسميها ايه وهذه كلها + +307 +00:21:03,210 --> 00:21:06,930 +كتلة الآن زي ما احنا أحيانا نتطلع بدنا ننظر نظرة + +308 +00:21:06,930 --> 00:21:10,210 +خارجية بدناش ندخل بالتفاصيل الآنأنا مركز على ال if + +309 +00:21:10,210 --> 00:21:14,010 +then فانا هيبهمني ها دي a و ها دي b و كل one كلهم + +310 +00:21:14,010 --> 00:21:18,090 +زي بعض حتى لو عملت خطوة وسيطة قلت اللي هي not a أد + +311 +00:21:18,090 --> 00:21:21,150 +not b بعدين رجعت ال a و ال b إيش هم مش غلط حصولها + +312 +00:21:21,150 --> 00:21:23,870 +في البداية عالمة اتدرب بعدين يصير الأمور تمشي + +313 +00:21:23,870 --> 00:21:28,250 +بسهولة و بشكل شفوي أكتر واضح يا أخوات؟فده مهم جدا + +314 +00:21:28,250 --> 00:21:31,890 +إنه نقاط نركز وكيف نطبق القاعدة هتشوف كل الستادالة + +315 +00:21:31,890 --> 00:21:35,030 +القاعدة العامة معروفة تعريف ال إيش ال if then بس + +316 +00:21:35,030 --> 00:21:38,750 +هذه تطبيقة أمثلة متعددة مثال بسيط أو معقد هيختلف + +317 +00:21:38,750 --> 00:21:44,050 +من مثال إلى آخر لكن احنا مع التدريب ومع النظرة هذه + +318 +00:21:44,050 --> 00:21:47,910 +اللي بنتحدث عنها بنقدر نطبق بشكل صحيح فده التعريف + +319 +00:21:48,940 --> 00:21:53,260 +الآن بدنا نتطلع إيش ممكن نعمل إذا بدنا نعيد اللي + +320 +00:21:53,260 --> 00:21:56,340 +هو التوزيع ما زال بدنا نعيد التوزيع هنا في حاجز + +321 +00:21:56,340 --> 00:21:59,960 +النفي لازم أدخل النفي عشان أخليهم حرين و أخلي + +322 +00:21:59,960 --> 00:22:04,200 +بينهم and و or وبالتالي بقدر أستخدم توزيع و استخدم + +323 +00:22:04,200 --> 00:22:07,560 +اللي هو إيش تجميع و هكذا فالآن ندخل نستخدم دي + +324 +00:22:07,560 --> 00:22:11,580 +مورغانز خلّي ال not برا لإنه برضه لازم ترجع في إيش + +325 +00:22:11,580 --> 00:22:17,240 +if then فخلّي لأ الحقيقة لأ إذا ممكن ندخل النفي + +326 +00:22:17,240 --> 00:22:23,230 +لبرا خالصممتاز مهم جدا فبما أن الطرف اللي بدوصله + +327 +00:22:23,230 --> 00:22:26,630 +لأخير هو مش if then الجوس الكبير وإنما if then + +328 +00:22:26,630 --> 00:22:30,850 +داخلية إذا النفل الخارجي مالهوش هش مالهوش داعي + +329 +00:22:30,850 --> 00:22:35,530 +مالهوش داعي فممكن أدخله و هذا هيساعد معاه فده + +330 +00:22:35,530 --> 00:22:41,810 +عبارة عن not B and Q or not not أعملها ولا أختصرهم + +331 +00:22:41,810 --> 00:22:46,930 +لا ليهاش double negation R or S فده يشمل إيش عملنا + +332 +00:22:46,930 --> 00:22:52,450 +دي مورجانزمش توزيع دي Morgan's law and double + +333 +00:22:52,450 --> 00:22:57,730 +negation عملناها خطوطين and double negation + +334 +00:22:59,140 --> 00:23:03,540 +لأن واش هي بأصل نفي الأولى ال and or و نفي التانية + +335 +00:23:03,540 --> 00:23:06,520 +النفي التاني فيها نفي صارت هي نعملنا قطوطين مع بعض + +336 +00:23:06,520 --> 00:23:10,620 +فهذا national شغل صحيح لأن هاي دليلي دي ايش دليلي + +337 +00:23:10,620 --> 00:23:16,000 +دي emergency بنفع بنفع هاي a وهذه كلها b هذه كلها + +338 +00:23:16,000 --> 00:23:20,720 +a وهذه كلها b كلها مع بعض b وهذه كلها a ايش بدتصير + +339 +00:23:20,720 --> 00:23:25,180 +not a or not b مع نفي النفي اعملنا ده بال negation + +340 +00:23:26,680 --> 00:23:30,000 +متابعين؟ بقى إذا لجيتوني أسرعت شوية ممكن نبطّى + +341 +00:23:30,000 --> 00:23:32,460 +فإذا double negation مش واضح بنا إيه ده بنعمل + +342 +00:23:32,460 --> 00:23:32,940 +خطوطات + +343 +00:23:36,060 --> 00:23:39,140 +هو مش توزيع .. يعني توزيع بالعامية بقبلها توزيع + +344 +00:23:39,140 --> 00:23:41,740 +ماشي بس أنا عايز أجيب زي ما قولت هي A و هي B إيش + +345 +00:23:41,740 --> 00:23:47,000 +ده تصير؟ not A or not B الـB فيها نفيه فصارت نفيه + +346 +00:23:47,000 --> 00:23:50,600 +فعملت خطواتين كمان عشان هيك بقول إذا أنا ماشي + +347 +00:23:50,600 --> 00:23:54,340 +بسرعة بدي أبطل في خطواتين عملت فقولت دي مرجاز؟ أه + +348 +00:23:54,340 --> 00:24:00,280 +وفي double negation واضح؟ أي سؤال؟ تمام الآن إيش + +349 +00:24:00,280 --> 00:24:06,840 +ممكن نعمل؟ الآن في عندنا orو or بدنا ندخل النفي + +350 +00:24:06,840 --> 00:24:10,620 +كمان مرة لإنه واضح إن الامر لسه في عوائق في + +351 +00:24:10,620 --> 00:24:14,440 +التجميع اللي بدنا نياه فالجيت not be or not to be + +352 +00:24:14,440 --> 00:24:17,100 +هذا المثال أسهل في ال demorganism ده كان أعصاب + +353 +00:24:17,100 --> 00:24:19,660 +فشوفتم انتوا كيف القاعدة موجودة demorganism هي + +354 +00:24:19,660 --> 00:24:25,260 +النظرية لكن الأمثلة اللي بتستخدمها متعددة or R or + +355 +00:24:25,260 --> 00:24:30,700 +S برضه demorganism demorganism law او demorganism + +356 +00:24:30,700 --> 00:24:37,470 +اختصارا مافيش عندنا مانعأي سؤال ممتاز اه دايما + +357 +00:24:37,470 --> 00:24:42,430 +اتعلموا و انت بتبرهنه و انت بتبرهنه شوفوا وين وصلت + +358 +00:24:42,430 --> 00:24:47,430 +و انت وين هدفك و اين رايحة وصلنا لهنا و احنا وضحنا + +359 +00:24:47,430 --> 00:24:50,830 +الهدف من الأول بدنا نعيد اللي هو توزيع هدول مع بعض + +360 +00:24:50,830 --> 00:24:55,370 +و تجميحهم احنا جاهزين الآن نعم جاهزين في عندي or + +361 +00:24:55,370 --> 00:24:59,880 +or or اذا في عندنا تجميعحتقول لطالب طب التجميع + +362 +00:24:59,880 --> 00:25:02,380 +كانوا تلاتة لأ ماني ماشي من تلاتة و انا ممكن + +363 +00:25:02,380 --> 00:25:05,540 +اعملهم ايش كل تنتين اعملهم كأنها كتلة واحدة اه فهي + +364 +00:25:05,540 --> 00:25:08,840 +ده ايش تلاتة لكن ممكن ايش تتوسع لاربع او خمسة و + +365 +00:25:08,840 --> 00:25:13,020 +هكذا اه فإذا عملية ايش اللي هو التجميع واضح فإذا + +366 +00:25:13,020 --> 00:25:16,100 +هي تلاتة لهذه القاعدة الأصلية لكن ممكن اطبقها مرة + +367 +00:25:16,100 --> 00:25:20,160 +و مرتين و تلاتة فممكن استخدمها أكثر من مرة اه فإذا + +368 +00:25:20,160 --> 00:25:24,700 +حبين كأنه هذا أول مثل خليني ايش أكمل هنا طبعا كل + +369 +00:25:24,700 --> 00:25:28,010 +القوانين تكافوا بل تزنتكافه القانون بحطه تكافه + +370 +00:25:28,010 --> 00:25:30,630 +implies بحطه implies و إلا بيصير اندي خطأ طيب + +371 +00:25:30,630 --> 00:25:34,530 +فخليني أعملها على مرحلتين خليني أعمل هذه ككتلة + +372 +00:25:34,530 --> 00:25:39,070 +واحدة و أوزق ويا اندي R و R فهذه كلها A و B و C + +373 +00:25:39,070 --> 00:25:43,110 +فإذا هذه ممكن أخدها مع R و أخلي ال S لحالي فخليني + +374 +00:25:43,110 --> 00:25:50,650 +أعملها not B or not Q كتلة واحدة or R هذه كمان + +375 +00:25:50,650 --> 00:25:57,520 +كتلة or Sأيش عملت؟ خلّيني أعيد كمان مرة، عملت هذه، + +376 +00:25:57,520 --> 00:26:01,520 +سكرتها، بديش أدخل في تفاصيلها، كإعتبرتها إيه؟ وهي + +377 +00:26:01,520 --> 00:26:05,760 +صارت ايه؟ or تنتين؟ هي تلاتة صارت، فقولنا بعد ما + +378 +00:26:05,760 --> 00:26:09,780 +هي التاني مع التالت، الأول مع التاني، والكل مع + +379 +00:26:09,780 --> 00:26:14,700 +التالت عملنا، واضح؟مرة تانية .. اه هذه سكرت .. هذه + +380 +00:26:14,700 --> 00:26:18,140 +اغلقوها .. هذه كأنها كتلة واحدة .. اصلا عندي تلاتة + +381 +00:26:18,140 --> 00:26:22,060 +.. الكتلة و R و S كانت ايش؟ الكتلة لحال و R و S + +382 +00:26:22,060 --> 00:26:25,480 +لحال .. ايش عملت الكتلة مع R و S لحال؟ هذا هو .. + +383 +00:26:25,480 --> 00:26:27,700 +هذا روح ال associative .. ال associative law .. + +384 +00:26:27,700 --> 00:26:31,140 +هذا روحه .. انه فيه تلت أجزاء .. A, B, C أو B,Q,R + +385 +00:26:31,140 --> 00:26:34,140 +.. اي مجد النظر .. اه في باب يقوللي خد الأول مع + +386 +00:26:34,140 --> 00:26:37,340 +التاني و بعدين مع التالت الناتج أو العكس .. خلي + +387 +00:26:37,340 --> 00:26:39,900 +الأول لحال و خد التاني مع التالت و بعدين نجمع مع + +388 +00:26:39,900 --> 00:26:42,810 +مين؟ مع الأول .. نفس القضية .. فماشي عملنا؟بعد ما + +389 +00:26:42,810 --> 00:26:47,550 +كانت التاني مع التالت وبعدين مع الأول وقلنا الأول + +390 +00:26:47,550 --> 00:26:50,830 +مع التاني هذا كله سميناه أول وبعدين الناتج مع + +391 +00:26:50,830 --> 00:26:58,970 +التالت فده associative law قانون + +392 +00:26:58,970 --> 00:27:05,430 +التجميع طبعا الدليل أو ليش نعمل نفس العملية كله + +393 +00:27:05,430 --> 00:27:08,710 +اخر طبعا عشان هو بس ده أول مثال كان ممكن أعملهم مع + +394 +00:27:08,710 --> 00:27:13,590 +بعض الأربعة مع بعض بس عشان أوضحالان احنا قولنا ايش + +395 +00:27:13,590 --> 00:27:16,570 +هدفنا؟ بدنا الـR تيجي جنب الـP بدنا الـR تروح مع + +396 +00:27:16,570 --> 00:27:20,070 +الـP فإيش نعمل؟ كمان مرة associative في جوه الجثر + +397 +00:27:20,070 --> 00:27:23,130 +الكبير اه فكمان مرة associative هي جت تلاتة تركزي + +398 +00:27:23,130 --> 00:27:26,350 +علينا خلي الـS لحالي بدنا ماشي نستخدمها فدي not B + +399 +00:27:26,350 --> 00:27:32,970 +لحال or not Q or R الكتلة هيك هي associative صح؟ + +400 +00:27:32,970 --> 00:27:35,790 +بدلنا هذه في البداية و هذه الـS خليها لحالي برضه + +401 +00:27:35,790 --> 00:27:39,950 +associative ت + +402 +00:27:39,950 --> 00:27:46,830 +flowفهنا احنا صحيح هذا هدف قصير المدى نتعلم الـ + +403 +00:27:46,830 --> 00:27:49,930 +deductive reasoning والإثبات لكن هدفنا كيف نتعلم + +404 +00:27:49,930 --> 00:27:52,690 +كيف بنفكر في الرياضيات كيف كل خطوة بنعملها بدليل + +405 +00:27:52,690 --> 00:27:58,220 +عشان أتأكد أنه حل صحيح فضللأ لسه لسه واحدة واحدة + +406 +00:27:58,220 --> 00:28:00,980 +associative ايش ال associative؟ كانت الأولى مع + +407 +00:28:00,980 --> 00:28:05,140 +التانية و الناتج مع التالت عكست قلت افصل الأولى + +408 +00:28:05,140 --> 00:28:08,280 +لحال و اعمل التانية مع التالتة associative ماعملتش + +409 +00:28:08,280 --> 00:28:11,820 +ابدال انت بدي تعمل خطوطين بخطوة لسه واحدة واحدة + +410 +00:28:11,820 --> 00:28:15,730 +عشان اتأكد انه حل صحبتقدم بسيط بعمل خطوات يعني زي + +411 +00:28:15,730 --> 00:28:17,670 +ما تبقى عملت ال double negation ممكن لكن احنا + +412 +00:28:17,670 --> 00:28:21,350 +بنحاول كيف نمشي خطوة خطوة لأنه لسه مبتدئين زي اللي + +413 +00:28:21,350 --> 00:28:24,410 +بتعلم الماشي خطوة خطوة بيسندع حاجة بعدين بيصير + +414 +00:28:24,410 --> 00:28:27,750 +يجري جراي تمام فواحدة هنا نفس الشيء فاحنا لسه + +415 +00:28:27,750 --> 00:28:30,910 +بنتمش بنحبه لسه واحدة واحدة فين المبادئ احنا لسه + +416 +00:28:30,910 --> 00:28:34,690 +في المرحلة الأولى انا بسميها مرحلة حفر الأرض + +417 +00:28:34,690 --> 00:28:37,730 +وتسوية الأرض بدنا لسه نحط الأساسات و نعلى في + +418 +00:28:37,730 --> 00:28:42,440 +البنيان فتستعجلوشالان ايش قلنا؟ بدنا نبدل فعنا كل + +419 +00:28:42,440 --> 00:28:46,720 +هدفنا نجرب ال R من الأسف طب إيش نعمل؟ نبدل بدنا + +420 +00:28:46,720 --> 00:28:52,380 +لايهاش نبدل فنعمل إبدال فنعمل إبدال not B or R or + +421 +00:28:52,380 --> 00:28:56,340 +not Q بس عجلش لأنه بديش أجع في خطأ و بدي يكون دليل + +422 +00:28:56,340 --> 00:29:00,560 +فهذا عملنا commutative commutative + +423 +00:29:00,560 --> 00:29:05,090 +lawفأزملتكم عملت خطوطين هذين مع بعض بدا توصل لها + +424 +00:29:05,090 --> 00:29:09,090 +بسرعة حتى يمكن كمان عمل كمان associative كمان وحطت + +425 +00:29:09,090 --> 00:29:12,030 +ال R مع ال S لأ أنا مابديش أستعجب عشان ماجعش + +426 +00:29:12,030 --> 00:29:15,270 +بالغطأ فالآن كل خطوة بعملها هيلي دليل إذا أن أنا + +427 +00:29:15,270 --> 00:29:19,190 +ماتي صح لأنه بنفع .. بنفع أبدل ال or بنفع أه إذا + +428 +00:29:19,190 --> 00:29:23,770 +صح الآن إيش قلنا؟ بدنا ال R مع ال B ممكن أفصلهم + +429 +00:29:23,770 --> 00:29:26,570 +هذين مع بعض وعي الترتيب؟ نعم قانون التجميع .. + +430 +00:29:26,570 --> 00:29:33,570 +قانون التجميع فمرة تانية تجميع not B or Ror نطق + +431 +00:29:33,570 --> 00:29:37,990 +you هي جث الكبير or as إيش هذه associative؟ + +432 +00:29:40,340 --> 00:29:45,100 +associative law قانون التجميع فمعليش الحل شوية + +433 +00:29:45,100 --> 00:29:48,620 +يمكن يعتبر طويل لكن بدنا شوية نتعلم و نشوف أنه كل + +434 +00:29:48,620 --> 00:29:52,380 +خطوة ماشيين صح و عارفين كيف بنمشي بهذه الطريقة + +435 +00:29:52,380 --> 00:29:55,680 +الآن اقتربنا جدا إيش ممكن نعمل؟ زي ما عملنا أول + +436 +00:29:55,680 --> 00:29:59,720 +ممكن برضه نعمل الجوس الكبير اللي هو التجميع نعيد + +437 +00:29:59,720 --> 00:30:05,610 +عمله و نروح نحط ال Q مع مين مع ال Sواضح؟ فالآن + +438 +00:30:05,610 --> 00:30:11,450 +عملنا عدد التوزيع الآن بدي أرجع أيش؟ ارجع لأن عشان + +439 +00:30:11,450 --> 00:30:15,350 +أوصل للتوزيع عملت قدت خطوات أنا هدف الرئيسي أعيد + +440 +00:30:15,350 --> 00:30:19,170 +تبديلهم لكن الإبدال مش واضح إنه موجود في الأول + +441 +00:30:19,170 --> 00:30:22,390 +انتميتني أبسط أبسط تحت موسيقى المرحلة بقدر فيها + +442 +00:30:22,390 --> 00:30:26,070 +أبدل بدلت؟ الآن بدي أرجع لمين؟ للوضع النموذج + +443 +00:30:26,070 --> 00:30:29,270 +التابع أو ليش؟ لهدف اللي بدي أوصل له فنعمل كمان + +444 +00:30:29,270 --> 00:30:38,160 +associative الآنnot B or R or not Q or S برضه S + +445 +00:30:38,160 --> 00:30:44,550 +safe دكتور هو صح لو من آخر خطوة أخدناها هنا لبشكل + +446 +00:30:44,550 --> 00:30:48,090 +عام بشكل عام لو عملنا خطوطين مع بعض مافيش عندي + +447 +00:30:48,090 --> 00:30:51,310 +معنى زي ما توي عملت أنا عملت آه لكن بده تكون أمور + +448 +00:30:51,310 --> 00:30:56,410 +إيش واضحة وما نعملش قفزات مش واضحة بحيث ان واعو + +449 +00:30:56,410 --> 00:30:59,070 +تيجي معانا بالصدفة لأ بده تكون الأمور واضحة في بعض + +450 +00:30:59,070 --> 00:31:02,770 +الأمور بديهية ممكن نعملها مع بعض مافيش مشكلة فضل + +451 +00:31:02,770 --> 00:31:06,990 +فلو احنا في الامتحان مثلا نعملنا إدار وفشقنا يعني + +452 +00:31:06,990 --> 00:31:10,530 +عن الخطوط الأساسية يعني عملتي خطوطين مع بعض أه + +453 +00:31:10,530 --> 00:31:14,820 +بعدين أنا قاعد بحكيبعض الخطوات نتساهل فيهم، لكن + +454 +00:31:14,820 --> 00:31:17,680 +بعض الخطوات الرئيسية لأ، خطوات الفرعية لأ، وبعدين + +455 +00:31:17,680 --> 00:31:21,220 +تكتب إن زي ما عملنا هيو، De Morgan's End، خطوطين + +456 +00:31:21,220 --> 00:31:23,760 +مع بعض، ماعندي مشكلة، بس المهم تعرف أنت إيش اللي + +457 +00:31:23,760 --> 00:31:27,020 +بتعمليه، مش الأمور بالصدفة تيجي معاك، بدنا نعرف، + +458 +00:31:27,020 --> 00:31:30,120 +لأن القضية الصدفة ممكن تنجح مرة، و تفشل عشرات + +459 +00:31:30,120 --> 00:31:33,060 +المرات، بدنا يكون لنا دليل، إنت شايفها، ماعندي + +460 +00:31:33,060 --> 00:31:36,560 +معنى، أنا كل هدف إنك تتعلم كيف تمشي من خطوة لخطوة + +461 +00:31:36,560 --> 00:31:41,730 +بطريقة منطقية، وإيش طريق دليلك على إنكأي سؤال + +462 +00:31:41,730 --> 00:31:45,990 +أتوقع أنه اقتربنا جدا من المطلوب بدنا if B then R + +463 +00:31:45,990 --> 00:31:50,210 +إيش بدنا نحولها للتعريف not B and not R ماعالين + +464 +00:31:50,210 --> 00:31:52,810 +نعمل Demorganism بطريقة عكسية لأن ال Demorganism + +465 +00:31:52,810 --> 00:31:55,390 +تمشي من اليمين لليسار انتوا كاف أو من اليسار + +466 +00:31:55,390 --> 00:31:57,230 +لليمين خليني أعمل هنا + +467 +00:32:00,610 --> 00:32:04,770 +فهنا نعمل دي مورجانز مرتين طبعا ناخد ال not برا + +468 +00:32:04,770 --> 00:32:11,350 +فبصير be and not are or و نفس القضية ناخد ال not + +469 +00:32:11,350 --> 00:32:18,410 +برا هو إيش بدوياها a q then s بصير q and not s دي + +470 +00:32:18,410 --> 00:32:24,970 +مورجانز دي مورجانز قوانين + +471 +00:32:24,970 --> 00:32:31,190 +العالم دي مورجانز أتوقع وصلنا الآن آخر شي التعريفB + +472 +00:32:31,190 --> 00:32:35,530 +then R او Q then S + +473 +00:32:40,990 --> 00:32:46,430 +فأهم شاهد من الموضوع أن كل خطوة لما بعملها في عندي + +474 +00:32:46,430 --> 00:32:50,610 +قاعدة مستند إلها هذا مثال على قاعدة عامة في عندي + +475 +00:32:50,610 --> 00:32:54,010 +قاعدة الإبدال قاعدة التوزيع قاعدة الـ Demorganism + +476 +00:32:54,010 --> 00:32:57,410 +و هكذا فمزال أنا ماشي صح وعندي الدليل عشان هيك + +477 +00:32:57,410 --> 00:33:00,730 +تفكير استدلالي يمكن يكون كويس إذا أنا شغلي صح وانا + +478 +00:33:00,730 --> 00:33:03,890 +بقدر أحاجش فيه أي حد مستحيل حد يقدر يقول على حالنا + +479 +00:33:03,890 --> 00:33:06,850 +غلط مزال دليلنا صح واستخدمناه في المكان الصحي حاجة + +480 +00:33:06,850 --> 00:33:09,970 +مهم طب ما الـ Commitment if law قانوننظرية تب وين + +481 +00:33:09,970 --> 00:33:12,370 +استخدمتيه؟ في المكان الصحيح، في عينينا من + +482 +00:33:12,370 --> 00:33:15,670 +الرياضات، نعرف القانون بشكل صحيح و نعرف نستخدمه في + +483 +00:33:15,670 --> 00:33:18,730 +المكان الصحيح، ماينفعش بعد ما اوزع اروح اي عمل + +484 +00:33:18,730 --> 00:33:22,070 +ابدال او عمل associative، ماينفعش، فده ايش التجميع + +485 +00:33:22,070 --> 00:33:25,150 +معروف، التوزيع معروف، و ال committed في معروف و + +486 +00:33:25,150 --> 00:33:29,790 +وين استخدمه؟ في المكان المناسب الصحيح، اي سؤال + +487 +00:33:31,330 --> 00:33:35,510 +فاحنا هنا بدأنا ندخل شوية رياضيات بس بطريقة غير + +488 +00:33:35,510 --> 00:33:38,530 +مباشرة أو منطقية، هذه هي البراهين بس براهين منطقية + +489 +00:33:38,530 --> 00:33:42,670 +ولكن برضه .. لكن بتستخدم لواش طريقة الرياضيات أو + +490 +00:33:42,670 --> 00:33:46,890 +هيكالية الرياضيات بالاستدلال وإن كل خطوة أنا بدياش + +491 +00:33:46,890 --> 00:33:54,170 +أكون عارفة، طبعاأحنا قلنا سيان ممكن ممكن أنا قلت + +492 +00:33:54,170 --> 00:33:59,310 +يعني أنا مش متأكد من كلامك بدي أجرب لكن احنا قلت + +493 +00:33:59,310 --> 00:34:04,350 +مازال في تكافؤ أنا ممكن أبدأ من أي طرف صحيح في بعض + +494 +00:34:04,350 --> 00:34:07,210 +الأحيان بيكون في طرف أفضل من طرف وممكن يكونوا سيان + +495 +00:34:07,210 --> 00:34:10,610 +طيب بس هنا ملاحظة لو استخدمنا truth table في عندنا + +496 +00:34:10,610 --> 00:34:15,010 +أربع statements أساسيين بدنا جدول من 16 احتمالفهنا + +497 +00:34:15,010 --> 00:34:17,910 +هذا بيهاملنا اسم التدريب الرياضي أنه طريقة تعتبر + +498 +00:34:17,910 --> 00:34:23,310 +أقصر لمن لأ اللي هو للبرهين في التضمين وفي التكافؤ + +499 +00:34:23,310 --> 00:34:32,830 +وطبعا هي بتعلمنا البرهين الرياضية مثال + +500 +00:34:32,830 --> 00:34:40,230 +جديد نشوف كمان مثالprove the tautology اثبت + +501 +00:34:40,230 --> 00:34:43,270 +القانون يعني اللي هو القانون دايما صحيح بغض النظر + +502 +00:34:43,270 --> 00:34:46,470 +عن المسمى هو بده يتفاقش واحد هيستخدم الإشارة + +503 +00:34:46,470 --> 00:34:49,710 +التانية للتكافؤ ساهم في التجاهين اللي حكينا عنها + +504 +00:34:49,710 --> 00:34:54,850 +لأ مش تضمين تكافؤ بس بالرمز الآخر by deductive + +505 +00:34:54,850 --> 00:34:57,770 +method باستخدام طريقة ال deductive reasoning أو + +506 +00:34:57,770 --> 00:35:00,710 +طريقة ال deductive فنبدأ نحل هنا + +507 +00:35:08,590 --> 00:35:16,970 +مثال الخاص و solution أه الآن في تكافؤ واليمين + +508 +00:35:16,970 --> 00:35:22,130 +أكبر من الشمال إذا نصيحة مش قاعدة ابدأ من اليمين + +509 +00:35:22,130 --> 00:35:24,590 +اه مازال اللي جيت الهديك الأطول دايما البداية من + +510 +00:35:24,590 --> 00:35:28,530 +الأطول أحسن من الأقصر وممكن تجربه و تشوف الفرق أنا + +511 +00:35:28,530 --> 00:35:32,410 +ببدأ من اليمين و أحلل كل حل اللي بتوقع أنه أقصر ان + +512 +00:35:32,410 --> 00:35:37,290 +تحله من اليسار و تشوف الفرق عشان تشاهد من النصيحة + +513 +00:35:39,310 --> 00:35:45,310 +then be and equal طبعا استخدم الرمزين المعطوه ال + +514 +00:35:45,310 --> 00:35:48,850 +بدكيه كله صح نفس الرمزين قولنا مافيش فين و مافيه + +515 +00:35:48,850 --> 00:35:53,230 +فرق عملية زوق شخصي استخدم ال بدكيه فدول الرمزين + +516 +00:35:53,230 --> 00:35:58,490 +اللي تكافؤ نفس المعنى نفس المعنى فطبعا نبدأ بإيش + +517 +00:35:58,490 --> 00:36:03,410 +العمليةفتكعفق برضه نستخدم التعريف لأن في الآخر أنا + +518 +00:36:03,410 --> 00:36:06,830 +أشماليه بدي أتخلص من تكرار ال B ال B مكررة في + +519 +00:36:06,830 --> 00:36:09,390 +اليمين مش موجودة في اليسار إلا مرة واحدة فبدي + +520 +00:36:09,390 --> 00:36:13,650 +أحاول أتخلص منهم من التكرار تبعه فنستخدم التعريف + +521 +00:36:13,650 --> 00:36:20,490 +notbe and not .. شوف انا ابني اتعود على .. في بعض + +522 +00:36:20,490 --> 00:36:24,210 +الطالبات الأمور بالنسبة لهم بدأت تتضح طبعا مش شرط + +523 +00:36:24,210 --> 00:36:27,330 +ان كلنا نتضح منها أول مرة و أيضا في المحاضرة بيكون + +524 +00:36:27,330 --> 00:36:30,230 +الجو في شويه ضغط في البيت ممكن يبهدوه لما تكون + +525 +00:36:30,230 --> 00:36:33,970 +واحدة مركزة تقدر تعمل هذا الكلام فهذه .. بس + +526 +00:36:33,970 --> 00:36:36,370 +اعتبرنا هذه كلها كتلة واحدة و هذه كتلة واحدة طبعا + +527 +00:36:36,370 --> 00:36:39,950 +المهم هذه واضحة كتلة لأنها بسيطة لكن هذه المركبة + +528 +00:36:39,950 --> 00:36:43,980 +اعتبرناها كتلة واحدةأه فقلنا not الكتلة هذه ال + +529 +00:36:43,980 --> 00:36:47,040 +statement هذه مع بعض فإنهياش فهذا هو قضية + +530 +00:36:47,040 --> 00:36:50,900 +الرياضيات أنه لو بيحط القانون بشكل بسيط كيف نطبقه + +531 +00:36:50,900 --> 00:36:53,940 +بأمور مركبة في الغالب و هذا اللي بيخلي الرياضيات + +532 +00:36:53,940 --> 00:36:57,140 +فيها شيء من الصعوبة لكن إن شاء الله إذا استخدمنا + +533 +00:36:57,140 --> 00:37:01,400 +القواعد اللي هاجي فيها عملية أسهل طبعا بدي أوصل في + +534 +00:37:01,400 --> 00:37:04,340 +الآخر ل if then فانصح أنه نخلي ال if not برا بس + +535 +00:37:04,340 --> 00:37:06,160 +هذا تعريف الدليل + +536 +00:37:08,810 --> 00:37:11,470 +Definition دليلنا بالشغل و ألا لو أنا عملتها .. + +537 +00:37:11,470 --> 00:37:13,850 +عشان دايما ليش ده الدليل؟ عشان أعرف أن هذا الخطوة + +538 +00:37:13,850 --> 00:37:16,870 +من وين جيبتها أنا مازال في عندي دليل إذا أن هي صح + +539 +00:37:16,870 --> 00:37:20,170 +دليل صحيح لو أنا عملتها و متردد و مش عارف عن أين + +540 +00:37:20,170 --> 00:37:23,510 +عملتها إذا ممكن تكون خطأ فهذا مهم جدا نتعلم + +541 +00:37:23,510 --> 00:37:26,630 +التفكير الاستدامة الآن إيش بدنا نعمل؟ بدنا نحاول + +542 +00:37:26,630 --> 00:37:30,870 +نتخلص من ال B طبعا ال B كله I فنعمل إيه دي ال + +543 +00:37:30,870 --> 00:37:36,420 +associative؟be and not .. اه لسه بينفعش في نفي جوا + +544 +00:37:36,420 --> 00:37:40,480 +في نفي بينفعش فده مش and في حاجز هنا فلازم اعمل + +545 +00:37:40,480 --> 00:37:46,060 +اوش توزيه اللي هو De Morgan's be and not be or not + +546 +00:37:46,060 --> 00:37:49,340 +to you فبنستخدم القاعدة بشكل صحيح اه فلما تقول + +547 +00:37:49,340 --> 00:37:53,280 +associative فمش حواجز بينهم و هنا لما بعد ما عملنا + +548 +00:37:53,280 --> 00:38:00,610 +الآن هنبين و نعلق عليها De Morgan's لأأه فواضح لما + +549 +00:38:00,610 --> 00:38:04,730 +.. دايما انت برضه عشان تعرف انه حالك صح ولا خطأ + +550 +00:38:04,730 --> 00:38:07,670 +حلليه بالطريقتين تشوف الفرق الآن لو حاولنا نعمل + +551 +00:38:07,670 --> 00:38:10,210 +مباشرة تقوللي هذه في ايه and و and و associative + +552 +00:38:10,210 --> 00:38:13,390 +طب هنا لما دخلنا صارت and و or distributive زي + +553 +00:38:13,390 --> 00:38:16,040 +اللي واحدة فيهم غلطعادي صح أنا متأكد إذا ليش + +554 +00:38:16,040 --> 00:38:18,400 +الأولى كانت مش صحيحة لو استعجلنا وعملنا + +555 +00:38:18,400 --> 00:38:21,380 +associative كان وجعنا في الغلط لأن ال and لازم + +556 +00:38:21,380 --> 00:38:26,120 +تدخل أولا لأن في القانون مافيش حواجز جالي a and b + +557 +00:38:26,120 --> 00:38:30,220 +and c بي and q and ر مافيش بينهم إشي فمهم جدا + +558 +00:38:30,220 --> 00:38:35,300 +نستخدم القاعدة بشكل صحيح الآن إيش ممكن نعمل توزيع + +559 +00:38:35,300 --> 00:38:39,140 +توزيع الآن Distributive بدنا نعمل لأن بي and و ا و + +560 +00:38:39,140 --> 00:38:43,840 +ا فنعمل توزيع خلّي ال and اللي لازم نافي براB and + +561 +00:38:43,840 --> 00:38:55,640 +not B or B and not Q قانون + +562 +00:38:55,640 --> 00:39:02,460 +التوزيع أي سؤال تمام مرت علينا B and not B + +563 +00:39:02,460 --> 00:39:09,330 +contradiction فادى يكافئcontradiction or be and + +564 +00:39:09,330 --> 00:39:15,210 +not equal ليش؟ لأن الشيء نقيته contradiction لا + +565 +00:39:15,210 --> 00:39:19,310 +يجتمع ف be and not be تكافئ Contradiction الآن ال + +566 +00:39:19,310 --> 00:39:22,790 +contradiction ممكن أخلص منها لأن هذا هدفي وهذا + +567 +00:39:22,790 --> 00:39:28,770 +نظرية من واحد سبعة بتقول false or anything تكافئ + +568 +00:39:28,770 --> 00:39:35,540 +anything فإذا هذه يكافئالنط برا زي ما هي ولكن هذا + +569 +00:39:35,540 --> 00:39:40,420 +اللي جوا ممكن أستبدله بجملة مكافئة بي and not q + +570 +00:39:40,420 --> 00:39:46,400 +هذه نظريةواحد سبعة القانون ما لهاش اسم بقى استخدم + +571 +00:39:46,400 --> 00:39:49,240 +النظرية طبعا وين ما كان استخدمتي اسم النظرية + +572 +00:39:49,240 --> 00:39:52,640 +استخدمتي اسم القانون حطيت القانون مثلا بدي تقولي + +573 +00:39:52,640 --> 00:39:55,060 +committed في جول ت بدي ماتقولي committed في جول ت + +574 +00:39:55,060 --> 00:39:59,660 +بدي + +575 +00:39:59,660 --> 00:40:03,040 +ماتقولي committed صح هذا دليل يعتبر نفس الشيء فيا + +576 +00:40:03,040 --> 00:40:07,320 +إما القانون بنصه أو باسمه أو بنظريته كله استدلال + +577 +00:40:07,320 --> 00:40:11,500 +مقبول كله استدلال مقبول خلصنا أتوقع فهذا التعريف + +578 +00:40:16,250 --> 00:40:24,010 +definition وهو المطلوب أي سؤال فارجو أنه بدت + +579 +00:40:24,010 --> 00:40:28,450 +الطريقة تكون أوضح طبعا عشان نستوعب لابد من التدريب + +580 +00:40:28,450 --> 00:40:33,950 +عشان نبدأ كيف بنشتغلنا نحاول نقلد الشغل هذا و شوية + +581 +00:40:33,950 --> 00:40:37,250 +شوية نتعود على هذه العمليات + +582 +00:40:43,140 --> 00:40:48,320 +وجدت قدامنا مثال سادس وهو سؤال امتحان سابق سؤال + +583 +00:40:48,320 --> 00:40:52,480 +امتحان سابق عشان برضه نطلع على مستوى الأسئلة في + +584 +00:40:52,480 --> 00:40:57,920 +الامتحانات مش غلط نشوف ايش اللي ممكن انقابله فطبعا + +585 +00:40:57,920 --> 00:41:03,510 +النص في احد الامتحانات السابقة proveاللي هو B then + +586 +00:41:03,510 --> 00:41:08,630 +R and Q then R تكافئ B or Q then R By deductive + +587 +00:41:08,630 --> 00:41:12,730 +method فهنا محدد الطريقة وال statement المعطية هي + +588 +00:41:12,730 --> 00:41:19,310 +statement تكافئ فهذا + +589 +00:41:19,310 --> 00:41:25,030 +أحد أسئلة امتحانات سابقة على الموضوع فخلينا نحله + +590 +00:41:25,030 --> 00:41:26,290 +مع بعض + +591 +00:41:32,430 --> 00:41:39,910 +المثال السادس solution فعندنا + +592 +00:41:39,910 --> 00:41:46,510 +تكافؤ و نبدأ من اليسار لأنه أطول فهذه نصيحة و في + +593 +00:41:46,510 --> 00:41:51,070 +الغالب منها بتنجح طبعا النصيحة أو الإرشاد مش قاعدة + +594 +00:41:51,070 --> 00:41:55,170 +وإنما من و نوقع الخبرة بنتعلم بعض الأمور و بنحاول + +595 +00:41:55,170 --> 00:42:04,180 +نستفيد منهاطبعا يمكن انا محيت لو طبعا بدنا نرجع + +596 +00:42:04,180 --> 00:42:10,080 +رجوع الخطوة اللي جابل هذه اللي هي ال C اللي + +597 +00:42:10,080 --> 00:42:14,120 +عملناها و حذفناها في نظرية واحد سبعة هنا الخطوة + +598 +00:42:14,120 --> 00:42:17,980 +اللي جابل هذه الحذف واضح انه حذف بده اتخلص منه طب + +599 +00:42:17,980 --> 00:42:21,220 +لو انا بده اطلع من هنا و بده ازيد مش عارف ايش ازيد + +600 +00:42:21,520 --> 00:42:24,240 +هي الصعوبة عشان هيك بنقول الكبير للي صغير فدايما + +601 +00:42:24,240 --> 00:42:29,060 +لما يقابلني واحد ناقص واحد فهو صفر وبتخلص منه حذف + +602 +00:42:29,060 --> 00:42:32,640 +لكن لو أنا بدي أضيف الصفر طب الصفر هدف اضيف واحد + +603 +00:42:32,640 --> 00:42:36,260 +ناقص واحد ولا اتنين ناقص اتنين ولا خمس ناقص خمس + +604 +00:42:36,260 --> 00:42:39,940 +فهي الصعوبة اللي هو صور متعددة فهينا دايما فدايما + +605 +00:42:39,940 --> 00:42:43,780 +الحذف أسهل من الإضافة فالحذف أسهل من الإضافة عشان + +606 +00:42:43,780 --> 00:42:47,600 +هيك بندأ من الكبير و بنوصل لصغير عن طريق الحذف أي + +607 +00:42:47,600 --> 00:42:51,420 +سؤالتمام فانحنا هنبدأ من الطويل طبعا واضح بدنا + +608 +00:42:51,420 --> 00:42:54,520 +نوصل في الآخر ل if then و في ending انا if then و + +609 +00:42:54,520 --> 00:42:57,800 +if then نستخدمهاش .. اه موجود بدنا نستخدمهاش + +610 +00:42:57,800 --> 00:43:04,520 +تعريفات فالأول be and not are و نكتب ال are و ال + +611 +00:43:04,520 --> 00:43:07,000 +nothing بشكل مختلف طريقة مناسبة عشان نكون واضح + +612 +00:43:07,000 --> 00:43:16,220 +فهذا الأول and برضه not a queue and not are فهذا + +613 +00:43:16,220 --> 00:43:16,720 +تعريف + +614 +00:43:21,380 --> 00:43:27,700 +definition اي سؤال تمام ايش الخطة؟ وين رايحين؟ + +615 +00:43:27,700 --> 00:43:30,980 +بدنا نجمع ال B مع ال Q ونخل ال R لحالها دي مورجانز + +616 +00:43:30,980 --> 00:43:37,000 +عكسي؟ بدنا R فطبعا كله and لكن في حواجز لازم ندخل + +617 +00:43:37,000 --> 00:43:41,770 +عشان نقدر ايش؟ نشوف الصورة فنستخدم دي مورجانزnot b + +618 +00:43:41,770 --> 00:43:47,670 +and not or not not are are دي مورجانز و double + +619 +00:43:47,670 --> 00:43:52,970 +negation خلصنا منها and نفس القضية not q or are + +620 +00:43:52,970 --> 00:43:57,930 +نفس السياسة فهنا دي مورجانز و double negation دي + +621 +00:43:57,930 --> 00:44:07,330 +مورجانز laws and double negation طبعا double + +622 +00:44:07,330 --> 00:44:09,850 +negation اتغلبت فيها قولي not not b تكافئ بي + +623 +00:44:16,280 --> 00:44:23,040 +not not B to B كف بكف بكف بكف بكف بكف بكف بكف بكف + +624 +00:44:23,040 --> 00:44:24,480 +بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف + +625 +00:44:24,480 --> 00:44:24,480 +بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف + +626 +00:44:24,480 --> 00:44:25,920 +بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف + +627 +00:44:25,920 --> 00:44:26,020 +بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف + +628 +00:44:26,020 --> 00:44:26,020 +بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف بكف + +629 +00:44:26,020 --> 00:44:36,080 +بكف بكف بكف بكف + +630 +00:44:36,080 --> 00:44:43,730 +بpr وpr هو توزية لكنه يعني بإيش لأ توزية هو توزية + +631 +00:44:43,730 --> 00:44:47,590 +بس من الزاوية الأخرى التوزية أحيانا احنا بنقول + +632 +00:44:47,590 --> 00:44:51,170 +بنوزع الدرب على الجامعة توزية و بناخد عامل مشترك + +633 +00:44:51,170 --> 00:44:55,190 +عملية عامل مشترك هي توزية بس إيش من زاوية أخرى من + +634 +00:44:55,190 --> 00:44:57,950 +زاوية أخرى اه فهنا احنا بدأ ناخد ال R كأن عامل + +635 +00:44:57,950 --> 00:45:02,030 +مشترك وهي توزية بدي أعملها و أوضحلكم إياها ليش هي + +636 +00:45:02,030 --> 00:45:10,190 +توزية فهي عبارة عن not be andنطق U or R هذا + +637 +00:45:10,190 --> 00:45:11,110 +distributive + +638 +00:45:18,810 --> 00:45:22,230 +توزيع، ليش؟ الآن من هنا إلى هنا قد تكون الرؤية + +639 +00:45:22,230 --> 00:45:25,130 +صعبة لكن من هنا إلى هنا تتفقنا تdistribute وعشان + +640 +00:45:25,130 --> 00:45:27,710 +هو تكافئ فتتقدم صح طب ما هي جايش كأنها اخت عامل + +641 +00:45:27,710 --> 00:45:31,270 +مشترك .. كأنها اخت عامل مشترك طبعا دي بالعمية لكن + +642 +00:45:31,270 --> 00:45:35,430 +هو قانون توزيع هو .. هو توزيع لأنه تكافئ روحت من + +643 +00:45:35,430 --> 00:45:38,750 +اليمين لليسار صح وروحت من اليسار لليمين صح من فوق + +644 +00:45:38,750 --> 00:45:42,390 +لتحت صح ومن تحت لفوق صح مازال من تحت لفوق صح إذا + +645 +00:45:42,390 --> 00:45:46,440 +من فوق لتحت أيضا صح لأنه تكافئأي سؤال وصلنا إلى حد + +646 +00:45:46,440 --> 00:45:51,720 +كبير آه الآن بدنا ناخد نفي خارج جدًا عشان كله أفضل + +647 +00:45:51,720 --> 00:45:57,740 +فنبدأ ناخد نفي من هنا أولًا فننفي بيصير PRQ De + +648 +00:45:57,740 --> 00:46:02,120 +Morgan's and ممكن أعمل كمان double negation not + +649 +00:46:02,120 --> 00:46:09,360 +not R لأ لأ لأ هذي زي ما هي إذا التخنتوا بدي + +650 +00:46:09,360 --> 00:46:14,410 +أجيلها بس اشتغلت على هذينفس القضية دي مورجانز + +651 +00:46:14,410 --> 00:46:18,150 +بالاتجاه التاني برضه كأنه باخد النفي عامل مشترك لأ + +652 +00:46:18,150 --> 00:46:21,450 +من هنا ل هنا واضحة هذا بدل نفي هذا فبرضه هنا دي + +653 +00:46:21,450 --> 00:46:26,070 +مورجانز دي مورجانز + +654 +00:46:29,550 --> 00:46:32,130 +الان بدنا ناخد النافي كمان مرة خارج جدا عشان + +655 +00:46:32,130 --> 00:46:36,870 +التعريف لإن ممكن نحط ناشم ونرايح فالنافي خالص بدها + +656 +00:46:36,870 --> 00:46:40,310 +عدد التعاملها كتلة واحدة فالنافي تبعت لبرا فدي زي + +657 +00:46:40,310 --> 00:46:47,110 +ما هي و ال R هتصير N و هدي هتصير منفية not R برضه + +658 +00:46:47,110 --> 00:46:51,330 +دي مورجانس لسه دي + +659 +00:46:51,330 --> 00:46:54,790 +مورجانس double negation double negation معه double + +660 +00:46:54,790 --> 00:47:04,650 +negation صحيح andbubble negation any + +661 +00:47:04,650 --> 00:47:14,250 +سؤال الخطوة الأخيرة تعرف بيكون وصلنا بيرك يو then + +662 +00:47:14,250 --> 00:47:17,330 +اه + +663 +00:47:17,330 --> 00:47:25,010 +بي + +664 +00:47:26,000 --> 00:47:30,660 +or q then r وهذا من أين جلبناه من التعريف + +665 +00:47:35,470 --> 00:47:40,670 +فعلى الرغم انه احنا اتوقعنا انه ماشينا من اليسار + +666 +00:47:40,670 --> 00:47:44,850 +الييمين يكون أسهل قد يكون اللي هو العكس من اليمين + +667 +00:47:44,850 --> 00:47:48,050 +لليسار أسهل لو ماشينا هيك الحال بيلاجيه أسهل طبعا + +668 +00:47:48,050 --> 00:47:50,950 +انه قولنا دا يا رشاد مش قاعد لأنه يمكن غلبنا انه + +669 +00:47:50,950 --> 00:47:53,850 +بنشوف دي مورجانز من الزاوية الأخرى بنشوف ال + +670 +00:47:53,850 --> 00:47:58,370 +distributed من الزاوية الأخرى لكن ممكن نتغلب عليه + +671 +00:47:58,370 --> 00:48:03,370 +أي سؤال؟أه فان شاء الله تم مثال واحد ان شاء الله + +672 +00:48:03,370 --> 00:48:06,830 +المرة جايب نعمله و عشان ننهي هذا الموضوع و ندخل في + +673 +00:48:06,830 --> 00:48:10,990 +موضوع اخر نكتفي اليوم بهذا القدر ان شاء الله + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/gy1w1H0Z7YE.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/gy1w1H0Z7YE.srt new file mode 100644 index 0000000000000000000000000000000000000000..af6d02897ef55ee37820d41c10d7fbd084c6f255 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/gy1w1H0Z7YE.srt @@ -0,0 +1,2591 @@ +1 +00:00:19,670 --> 00:00:27,150 +بسم الله الرحمن الرحيم إن شاء الله هنا هنواصل مع ال + +2 +00:00:27,150 --> 00:00:30,790 +cardinal numbers وإن شاء الله تكون هي آخر المحاضرة + +3 +00:00:30,790 --> 00:00:35,270 +الأخيرة فكنا في المحاضرة السابقة توقفنا عند هذا + +4 +00:00:35,270 --> 00:00:39,970 +المثال طبعا بس على السريع كنا احنا عرفنا أنه إذا + +5 +00:00:39,970 --> 00:00:44,310 +كان في عندي عدد A cardinal number وعدد B cardinal + +6 +00:00:44,310 --> 00:00:48,410 +number وجبت مجموعة capital A متقابل ومجموعة capital B + +7 +00:00:48,410 --> 00:00:53,950 +للـ B فقلنا A أس B ليست إلا الـ cardinality لمين؟ للـ + +8 +00:00:53,950 --> 00:00:58,230 +اللي هو A أس B طبعا هذا رمز، رمز جديد وهو يرمز + +9 +00:00:58,230 --> 00:01:02,610 +لجميع الدوال من B لـ A من B لـ A اه فطبعا احنا كنا في + +10 +00:01:02,610 --> 00:01:06,490 +هذا السؤال يمكن بدأنا نناقش فيه وحطينا بعض الخطوط + +11 +00:01:06,490 --> 00:01:11,790 +فطبعا احنا قلنا أن الـ A وبتقابل أو تساوي خليني + +12 +00:01:11,790 --> 00:01:16,130 +نكتب cardinality لـ capital A جيبنا المجموعات هذه و + +13 +00:01:16,130 --> 00:01:20,890 +في عندنا small b تساوي الـ cardinality للـ capital B + +14 +00:01:20,890 --> 00:01:25,550 +وفي عندنا small x cardinality للـ capital X وفي + +15 +00:01:25,550 --> 00:01:33,080 +عندنا small y cardinality للـ capital Y وفي عندنا + +16 +00:01:33,080 --> 00:01:38,840 +معلومات أن الـ A أقل أو تساوي B فقلنا هذا يؤدي أو + +17 +00:01:38,840 --> 00:01:43,960 +if and only if طبعا نفس الشيء أن الـ A تكافئ B0 + +18 +00:01:43,960 --> 00:01:47,300 +subset من الـ B هذا كله كتبناه المرة اللي فاتت بس + +19 +00:01:47,300 --> 00:01:53,400 +بنعيده وX أقل أو تساوي Y معناته أن الـ X تكافئ Y0 + +20 +00:01:53,400 --> 00:02:01,170 +subset من الـ Y طب إيش المطلوب؟ مطلوب A أس X أقل أو + +21 +00:02:01,170 --> 00:02:06,210 +تساوي B أس Y if and only if هذا المطلوب أنه الـ + +22 +00:02:06,210 --> 00:02:13,210 +A أس X تكافئ Z subset من B أس Y هذا هو المطلوب + +23 +00:02:13,210 --> 00:02:18,230 +وجفنا يعني وكنا بندور على الـ Z صح؟ subset صح + +24 +00:02:18,230 --> 00:02:26,500 +يعني بدنا تكافئ subset وسألنا السؤال التالي هل + +25 +00:02:26,500 --> 00:02:32,480 +بنفع Z ناخدها B0 أو الـ Y0؟ قلنا لأ لأن + +26 +00:02:32,480 --> 00:02:38,540 +عناصر الـ B0 أو Y0 هم دوال من Y0 لـ B0 بدنا يكونوا + +27 +00:02:38,540 --> 00:02:42,420 +دوال هنا من Y لـ B، ما ينفعش لأنه لو أنا عند الصورة + +28 +00:02:42,420 --> 00:02:50,950 +كالتالي، هيعندي الـ B الـ Y وجواها Y0 وهي عندي الـ + +29 +00:02:50,950 --> 00:02:56,430 +B وsubset منها الـ B0 وأنا عندي دالة اللي هي + +30 +00:02:56,430 --> 00:03:00,690 +مثلا اللي بنقول F من هان لهان هي عناصر مين؟ اللي هو + +31 +00:03:00,690 --> 00:03:06,450 +B0 is Y0 هل الدالة من Y0 لـ B هي دالة من Y لـ B؟ لأ + +32 +00:03:06,450 --> 00:03:09,330 +لأن أهم حاجة في الدالة أن الـ domain يساوي كل + +33 +00:03:09,330 --> 00:03:13,110 +المجموعة الأولى فـ domain الـ F بيساوي Y0 بيساويش كل + +34 +00:03:13,110 --> 00:03:16,490 +الـ Y فإذا هي ليست دالة من Y لـ B طبعا المجال + +35 +00:03:16,490 --> 00:03:19,450 +المقابل فيه مشكلة كتير لو وسعت وعاء اللي + +36 +00:03:19,450 --> 00:03:22,950 +بيحتوي الصور ما بخسرش كتير أو أزغرته المهم إنه يحتوي + +37 +00:03:22,950 --> 00:03:25,890 +الصور لكن المشكلة أن الـ domain لما يكون فيه جزء + +38 +00:03:25,890 --> 00:03:29,310 +الجزء هنا F تشتغلش هنا مش معرفة هنا فما ينفعش تكون + +39 +00:03:29,310 --> 00:03:34,810 +دالة من Y لـ B لكن باين إنه فشلنا في حاجة والاتجاه + +40 +00:03:34,810 --> 00:03:37,910 +التفكير كان اتجاه صحيح لأن هذا هو العلاقات + +41 +00:03:37,910 --> 00:03:40,950 +الموجودة طب هي ما زبطتش مش معناته إنه هنغلقها + +42 +00:03:40,950 --> 00:03:45,690 +تمامًا بدنا نقترب منها بدنا نقترب منها صحيح الـ B0 + +43 +00:03:45,690 --> 00:03:50,210 +ليس subset لكن تكافئ subset ممكن تكافئ subset هي + +44 +00:03:50,210 --> 00:03:54,550 +مش بالضبط subset لكن تقريبًا تشبه subset منها + +45 +00:03:54,550 --> 00:03:58,010 +تشبهها أو تكافئها فهذا اللي هنعمل هذا اللي هنعمل + +46 +00:03:58,010 --> 00:04:02,770 +اه فطبعا أول شيء في عين النظرية أثبتناها في أول + +47 +00:04:02,770 --> 00:04:07,370 +الـ Section بما أن الـ A تكافئ الـ B0 والـ X + +48 +00:04:07,370 --> 00:04:13,010 +تكافئ الـ Y0 فإذا A أُس X تكافئ B0 أُس Y0، هذا صح، + +49 +00:04:13,010 --> 00:04:17,690 +اه، وأنا بعدين هثبت أن B أُس Y0 تكافئ Z أخرى من + +50 +00:04:17,690 --> 00:04:20,690 +هنا، فحش طل عليها، صحيح هي مش subset لكن تكافئ + +51 +00:04:20,690 --> 00:04:22,770 +subset اللي هي المجموعة اللي احنا بندور عليها، + +52 +00:04:22,770 --> 00:04:28,250 +فإذا أول شيء أننا بنكمل الحل By theorem + +53 +00:04:30,880 --> 00:04:34,920 +6.6 لأنه احنا .. لش هالنظرية اللي قلناها اثبتنا أنه + +54 +00:04:34,920 --> 00:04:37,500 +.. أنه ال .. ال .. عملية اختيار ال .. ال .. + +55 +00:04:37,500 --> 00:04:41,800 +المجموعات لا تؤثر اه فأنا ما عندي بدي أجيب اللي هو + +56 +00:04:41,800 --> 00:04:45,260 +A أُس B جيبنا A وB طب لو بدلناهم X وY بيطلع نفس + +57 +00:04:45,260 --> 00:04:47,560 +الجواب فهي نفس القضية ليش؟ لأنه بيكونوا متكافئين + +58 +00:04:47,560 --> 00:04:51,200 +اه فإذا by theorem إيش في عندنا؟ في عندنا الـ A أُس + +59 +00:04:51,200 --> 00:04:57,800 +X تكافئ اللي هو إيش؟ B أُس 0 أُس Y0 هذه نقطة هل + +60 +00:04:57,800 --> 00:05:00,660 +وجدنا بده اثبت؟ اه ب .. فإذا الـ cardinality بتساوي + +61 +00:05:00,660 --> 00:05:03,240 +الـ cardinality الآن لو اثبتت أن الـ cardinality + +62 +00:05:03,240 --> 00:05:05,780 +اللي هي هذه أصغر أو تساوي الـ cardinality اللي هي + +63 +00:05:05,780 --> 00:05:12,680 +هذه بكون إنتهى فبدأ أكتب we will prove بدل ما اثبت + +64 +00:05:12,680 --> 00:05:19,400 +هذه بدي اثبت أن B أُس Y0 تكافئ Z + +65 +00:05:19,400 --> 00:05:25,180 +subset من الـ BY ما ننفعش ناخدها هي الـ Z بدي أخدها + +66 +00:05:25,180 --> 00:05:30,760 +تكافئ مجموعة Z بدي أخدها تكافئ مجموعة Z تمام فهذه + +67 +00:05:30,760 --> 00:05:35,740 +الخطوة فالسؤال كيف نختار الـ Z طبعا زي ما مرت + +68 +00:05:35,740 --> 00:05:39,520 +علينا نفس الفكرة أكثر من مرة ممكن أريح نفسي بدل ما + +69 +00:05:39,520 --> 00:05:45,130 +أختار الـ Z أخد دالة one to one من الأولى للتانية + +70 +00:05:45,130 --> 00:05:48,250 +وش الـ Z بتكون الـ image بتكون الـ image فهنعمل + +71 +00:05:48,250 --> 00:05:54,390 +بهذه الطريقة فهنبدأ نعرف دالة فنكتب هنا هقول له + +72 +00:05:54,390 --> 00:06:01,730 +let بـ psi من وين لوين؟ من B زيرو أس Y زيرو إلى + +73 +00:06:01,730 --> 00:06:11,370 +B أس Y B given by B given by B given by B + +74 +00:06:11,370 --> 00:06:11,710 +given by B given by B given by B given by B + +75 +00:06:11,710 --> 00:06:12,150 +given by B given by B given by B given by B + +76 +00:06:12,150 --> 00:06:12,390 +given by B given by B given by B given by B + +77 +00:06:12,390 --> 00:06:16,710 +given by B given by B given by psi of F فهنا عندنا + +78 +00:06:16,710 --> 00:06:19,870 +احنا كنا إيش المشكلة؟ ليش ما كناش ناخدها subset لأن + +79 +00:06:19,870 --> 00:06:24,190 +الدالة اللي هنا ما بنفعش تكون دالة من Y لـ B اه وين + +80 +00:06:24,190 --> 00:06:28,830 +مشكلتها؟ أن الـ domain تبعها صغير بدنا نكبّره فـ الآن + +81 +00:06:28,830 --> 00:06:32,870 +أنا بدي أخد الدالة هذه F اللي هي بتنتمي للـ B of 0 + +82 +00:06:32,870 --> 00:06:36,750 +Y0 واخليها دالة من Y لـ B فعندي دالة من subset من + +83 +00:06:36,750 --> 00:06:39,490 +الـ Y بدي اخليها دالة على كل الـ Y طب هذه الدالة إيش + +84 +00:06:39,490 --> 00:06:41,910 +بدي تكون؟ أي دالة بدي أحافظ أنها تكون one to one + +85 +00:06:41,910 --> 00:06:44,560 +أصلًا هي مش one to one هو بدي أحافظ على أي شيء عندي + +86 +00:06:44,560 --> 00:06:50,770 +قيود؟ لأ بس كل همه أنها تتمّها دالة فكما قلنا، وين + +87 +00:06:50,770 --> 00:06:54,290 +الـ I تبعها؟ الـ domain تبعها صغير، جسّر معناه مش + +88 +00:06:54,290 --> 00:06:58,450 +مكافئة، إيش نعمل؟ نمده، نمده، فهنعرفها، اه فالـ + +89 +00:06:58,450 --> 00:07:02,250 +Psi of F دي إيش ده تكون؟ دالة، من وين بتروح؟ دالة + +90 +00:07:02,250 --> 00:07:05,970 +بدل ما هي من Y0 لـ B، هيبقى تصير دالة صورتها من Y لـ + +91 +00:07:05,970 --> 00:07:09,050 +B، فإذا نعدّي function اه طبعا ممكن احنا نتعود + +92 +00:07:09,050 --> 00:07:12,690 +نكتب Psi وF تساوي حاجة معينة لكن احنا عارفين + +93 +00:07:12,690 --> 00:07:16,510 +إنها G، بدنا نعرفها الصورة دالة مش قادر أكتبها بشكل + +94 +00:07:16,510 --> 00:07:20,130 +صريح ما فيش علاقة واضحة أو قاعدة واضحة بس بتكتبها + +95 +00:07:20,130 --> 00:07:24,050 +بطريقة جديدة الصورة دالة مظبوط عشان أعرف الدالة + +96 +00:07:24,050 --> 00:07:28,130 +إيش بدي ثلاث حاجات بدي الـ domain والـ .. والـ .. و + +97 +00:07:28,130 --> 00:07:30,790 +الـ co domain أو اللي هو المجال المقابل وبدي قاعدة + +98 +00:07:30,790 --> 00:07:34,830 +التعريف فـ أنا بدي أعرفها الصورة فـ إيش let given by F + +99 +00:07:34,830 --> 00:07:39,290 +of X أو Epsilon F اللي هي دالة من وين لوين؟ من Y لـ + +100 +00:07:39,290 --> 00:07:45,130 +B defined بـ قاعدة بعرف الصورة يا إخواني بنعرف + +101 +00:07:45,130 --> 00:07:48,950 +الصورة هي الصورة دالة دالة من وين لوين؟ من Y لـ B + +102 +00:07:48,950 --> 00:07:53,010 +كيف بدأت تكون دالة؟ بدأت أعرفها بـ Psi F مش هذي + +103 +00:07:53,010 --> 00:07:58,650 +دالة of X طبعا الرمز شوية مش مقلوب لأن هي دالة + +104 +00:07:58,650 --> 00:08:02,310 +لـ Psi تنتمي لـ F لدالة طب الصورة دالة إذا المعرفة + +105 +00:08:02,310 --> 00:08:07,630 +على X معرفة على X كيف بدنا نعرفها؟ طبعا هي الـ + +106 +00:08:07,630 --> 00:08:10,570 +domain letter تبع الصورة بدي أعرف الـ NG بدي أكبّر + +107 +00:08:10,570 --> 00:08:16,220 +هذه بدل ما كانت الـ F من هان لهان بدي الـ NG من هان + +108 +00:08:16,220 --> 00:08:21,760 +لهان طبعا المنطق أن أنا اللي عندي ما رميتوش اعتمد + +109 +00:08:21,760 --> 00:08:24,980 +عليه فأنا بدي أعرف الـ G أكبر الـ domain طيب في الـ + +110 +00:08:24,980 --> 00:08:28,560 +domain اللي معرف عليه F خليها معرفة تمام أكمل في + +111 +00:08:28,560 --> 00:08:34,220 +الخارج فـ هقول له بتساوي F of X إذا كانت الـ X في الـ Y + +112 +00:08:34,220 --> 00:08:39,200 +Zero تمّ أعرفها وين؟ لما الـ X تكون في الـ Y ناقص Y + +113 +00:08:39,200 --> 00:08:44,610 +Zero ما تبقتش تابعين؟ قاعدة ولا تابعين؟ فمرة ثانية بس + +114 +00:08:44,610 --> 00:08:48,670 +الصعوبة وين؟ أنه أنا بأخذ دالة بوديها لدالة، + +115 +00:08:48,670 --> 00:08:52,670 +بوديها لدالة، طيب إيش الفرق؟ الدالة اللي بستخدم + +116 +00:08:52,670 --> 00:08:55,970 +عليها دومينها صغير، الدالة اللي بتطلع الناتج من + +117 +00:08:55,970 --> 00:08:59,650 +الصورة اللي بتكون دالة دومينها كبير شوية فطبعا + +118 +00:08:59,650 --> 00:09:02,530 +أنا بحافظ على الدالة في الدومين المعطى وبدأ أشوف + +119 +00:09:02,530 --> 00:09:05,610 +كيف أعرفها على الدومين الخارج، كيف نعرفها؟ + +120 +00:09:08,320 --> 00:09:14,440 +X ده identity؟ لأ لأن الـ B مش subset وين نوديها؟ + +121 +00:09:14,440 --> 00:09:16,900 +نوديها على أي صورة .. أي عنصر في الـ B لأنه أنا + +122 +00:09:16,900 --> 00:09:18,440 +ما بديش هي اللي هتكون one term ولا one term + +123 +00:09:18,440 --> 00:09:22,740 +ما بديها تكون ده بس تمام إنه مش معرفة هنا أعرفها اه + +124 +00:09:22,740 --> 00:09:25,740 +مين الدوال المشهورة؟ فيه طبعا الـ identity ما تظبطش + +125 +00:09:25,740 --> 00:09:29,180 +لأنه إيش؟ هذا العنصر بيمشي مش subset لكن مين ده + +126 +00:09:29,180 --> 00:09:32,160 +الأخرى؟ الـ constant function الـ constant function + +127 +00:09:32,160 --> 00:09:38,740 +فحنعرفها بيه؟ وإيش الـ B؟ أي عنصر في الـ B؟ fourSome + +128 +00:09:38,740 --> 00:09:44,380 +B تنتمي لمين؟ للـ capital B تكون في الـ B في الـ + +129 +00:09:44,380 --> 00:09:47,660 +B0 ما يهمنيش حتى لو كانت الصورة السابقة ليش؟ لأنه مش + +130 +00:09:47,660 --> 00:09:49,620 +معنى تكون one to one أو one to two ما بديش ولا إشي، + +131 +00:09:49,620 --> 00:09:53,660 +أي المهم تكون عرفت على ما تبقى، هي كانت معرفة على + +132 +00:09:53,660 --> 00:09:56,500 +جزء من الـ domain، عرفناها على باقي الـ domain، + +133 +00:09:56,500 --> 00:10:00,780 +واضح؟ اه، الآن طيب نشوف أن هذا التصميم، هذا + +134 +00:10:00,780 --> 00:10:05,140 +التركيب صح ولا مش صح؟ طبعا كل اللي بده يعني الكلام + +135 +00:10:05,140 --> 00:10:08,200 +ده ما لهوش بس one to one عشان أخد الـ Z هي الـ image + +136 +00:10:08,200 --> 00:10:13,540 +وخلصنا نثبت إنها one to one if psi is one to one + +137 +00:10:13,540 --> 00:10:18,720 +نثبت طبعا من وين بده أبدأ؟ عنصرين في الـ domain إيش + +138 +00:10:18,720 --> 00:10:22,860 +عناصر الـ domain اللي بـ psi دوال من Y0 لـ B0 فده + +139 +00:10:22,860 --> 00:10:29,340 +أقول له F1 وF2 تنتمي لـ B0 أس Y0 صورهم متساوية such + +140 +00:10:29,340 --> 00:10:38,210 +that بـ Psi of F1 تساوي بـ Psi of F2 البداية، في حد + +141 +00:10:38,210 --> 00:10:43,050 +عنده مشكلة في البداية؟ كيف نبدأ one to one؟ فأرجو + +142 +00:10:43,050 --> 00:10:48,010 +أن هذه البدايات تكون و احنا في نهاية المساق نعرف + +143 +00:10:48,010 --> 00:10:52,610 +نبدأ صح تمام، إيش مطلوب لو بدي أعمل هامش؟ أنا + +144 +00:10:52,610 --> 00:10:56,740 +بحاول أثبت أن F1 تساوي F2 ولا لأ؟ ما هو إيش معنى + +145 +00:10:56,740 --> 00:11:01,340 +one to one؟ خذ عنصرين من المجال صورهم متساوية و + +146 +00:11:01,340 --> 00:11:04,900 +أثبت إنهم العنصرين متساوين صح؟ إيش يكون العنصرين؟ + +147 +00:11:04,900 --> 00:11:09,480 +هم أرقام، هم دوال، هم مجموعات، أي مكان، الكلام + +148 +00:11:09,480 --> 00:11:12,500 +بشكل عام طيب، إذا نرجع للسؤال وقت إيش بتكون الدالة + +149 +00:11:12,500 --> 00:11:15,880 +بتساوي الدالة؟ في شرطين، الشرط الأول أن تكونوا من + +150 +00:11:15,880 --> 00:11:18,780 +نفس المجموعة لنفس المجموعة، تلقائياً نفس المجال لنفس + +151 +00:11:18,780 --> 00:11:23,110 +المجال المقابل، وهذا مضمون، من هنا الآن ما يعني أن F1 + +152 +00:11:23,110 --> 00:11:28,330 +في B0 وY0 هي ده لا من Y0 ولا B0 و F2 زيها إذا هذا + +153 +00:11:28,330 --> 00:11:31,570 +الشرط الأول تحقق، إيش الشرط الثاني؟ صورهم متساوي + +154 +00:11:31,570 --> 00:11:35,250 +على جميع عناصر الـ domain، أكتبهم مرة واحدة فعشان + +155 +00:11:35,250 --> 00:11:39,330 +أثبت هذا الكلام هذا يكافئ if and only if في عندنا + +156 +00:11:39,330 --> 00:11:44,550 +شرطين، في عندنا إنه لازم الـ F1 والـ F2 يكونوا دوال + +157 +00:11:44,550 --> 00:11:51,530 +من Y0 لـ B0، اثنين for all X في الـ domain اللي هو Y0 + +158 +00:11:51,530 --> 00:11:57,090 +بدنا F1 of X تساوي F2 of X للمرة الثالثة أو الرابعة أو + +159 +00:11:57,090 --> 00:12:02,010 +خلال آخر محاضرتين، هذه بوضحها صح؟ واضح أنه عشان + +160 +00:12:02,010 --> 00:12:05,670 +دالتين تساووا في شرطين، يكونوا من نفس المجال لنفس + +161 +00:12:05,670 --> 00:12:09,350 +المجال المقابل، متحقق ولا مش متحقق؟ متحقق لأنه إيش + +162 +00:12:09,350 --> 00:12:13,310 +معناه أنهم في الـ P of 0 of Y of 0؟ هذا معناه هذا + +163 +00:12:13,310 --> 00:12:16,490 +المجموعة، هيك تعريفها، مظبوط، مين هذه المجموعة؟ هي + +164 +00:12:16,490 --> 00:12:21,350 +كل الدوال اللي من Y of 0 لـ P of 0، فهذا صح، واضح؟ + +165 +00:12:22,410 --> 00:12:26,550 +واضح ولا لأ؟ الشرط الثاني، نريد أن يكون على كل + +166 +00:12:26,550 --> 00:12:29,350 +عناصر الـ domain الصور متساوية، قيمهم متساوية على + +167 +00:12:29,350 --> 00:12:31,610 +كل الـ domain، نريد أن نثبت هذا، هذا أريد أن أثبته، + +168 +00:12:31,610 --> 00:12:33,930 +طب كيف أثبته؟ for all، تريد أن تأخذ عناصر في الـ + +169 +00:12:33,930 --> 00:12:42,810 +domain، فسأقول له الآن، لتكن X تنتمي لمن؟ لـ Y0، بدي + +170 +00:12:42,810 --> 00:12:46,550 +أثبت إن F1 تساوي F2 طبعاً زي ما حكينا سابقاً هذه + +171 +00:12:46,550 --> 00:12:48,770 +النقطة وصلت إليها ووقفت عليها لأن أنا مش قادر + +172 +00:12:48,770 --> 00:12:51,930 +أحلها كمعادلة، بدنا نستخدمها الآن، طب هل جئت هاذول + +173 +00:12:51,930 --> 00:12:56,870 +الدوال من وين لوين؟ من Y لـ B، هاذول الصور، هاذول الصور + +174 +00:12:56,870 --> 00:12:59,710 +طيب و الـ Y0 subset من Y، إذا أنا ممكن أطبقهم ولا + +175 +00:12:59,710 --> 00:13:02,370 +ممكن أطبقهم على الـ X؟ بقدر لأن أنا أخذت الـ X هنا يا + +176 +00:13:02,370 --> 00:13:05,830 +خوان، أخذت الـ X هنا جوا الـ Y ولا مش جوا؟ جوا الـ Y + +177 +00:13:05,830 --> 00:13:08,870 +إذا أنا مقدر أطبق الدالتين هاذول، فده بيقول لي بـ Psi + +178 +00:13:08,870 --> 00:13:17,450 +of F1 of X تساوي بـ Psi F2 of X، فحولت لعنصر الآن + +179 +00:13:17,450 --> 00:13:22,330 +بقدر أستخدم التعريف، الـ X وين في الـ Y0؟ إذا إيش + +180 +00:13:22,330 --> 00:13:27,570 +تعريف Psi of X؟ هيها، إذا هذا يؤدي إن F1 of X وإيش + +181 +00:13:27,570 --> 00:13:31,710 +تعريفها؟ F2 of X لأن الـ X وين في الـ Y0؟ إذا وين شغل + +182 +00:13:31,710 --> 00:13:35,490 +كله فوق؟ واضح؟ اه، وهو المطلوب، مش هذا كده بتدور + +183 +00:13:35,490 --> 00:13:44,130 +عليه؟ اه، إذا Thus F1 تساوي F2 وبالتالي and hence + +184 +00:13:44,130 --> 00:13:49,310 +Psi is one to one، فمهم جداً نعرف احنا إيش اللي + +185 +00:13:49,310 --> 00:13:52,570 +بنشتغل فيه وإيش واحنا رايحين وإيش المطلوب دائماً + +186 +00:13:52,570 --> 00:13:56,090 +زي ما بنعيد وبنكرر اه فهي دالة one to one، ممتاز + +187 +00:13:56,090 --> 00:13:59,730 +الـ trick اللي مشهور، ما زال دالة one to one واحنا + +188 +00:13:59,730 --> 00:14:04,010 +نشتغل من هال لهان، إذا المجال يشابه إيش ما له؟ يكافئ + +189 +00:14:04,010 --> 00:14:09,250 +الـ image، اه it follows أو therefore كله صح that + +190 +00:14:09,250 --> 00:14:14,790 +المجال اللي هو مين؟ بي أس زيرو، بي أس زيرو أس واي أس + +191 +00:14:14,790 --> 00:14:21,190 +زيرو، يكافئ الـ image، بصي بي أس زيرو واي زيرو، والـ + +192 +00:14:21,190 --> 00:14:26,330 +image وين بيكون؟ subset من المجال المقابل، subset من + +193 +00:14:26,330 --> 00:14:28,270 +وين؟ من بي أس واي + +194 +00:14:33,630 --> 00:14:37,670 +فالآن نجمع هذا اسمه ناتو، الـ cardinality أصغر أو تساوي + +195 +00:14:37,670 --> 00:14:40,850 +الـ cardinality واحنا كنا هذه باسمه يكافئ اه يكافئ + +196 +00:14:40,850 --> 00:14:46,990 +اه it follows أو therefore الـ + +197 +00:14:46,990 --> 00:14:55,550 +cardinality للـ A أُس X تساوي الـ cardinality هذه + +198 +00:14:55,550 --> 00:14:59,460 +الملاحظة كتبناها في بداية الشرح، مش يقول إن هاذول + +199 +00:14:59,460 --> 00:15:02,820 +يكافؤوا هاذول، فهذول متساويين وهذه إيش بتقول ليه؟ + +200 +00:15:02,820 --> 00:15:08,900 +أنه هذه أصغر أو تساوي الـ cardinality للـ B أُس 1 + +201 +00:15:08,900 --> 00:15:17,300 +وطبعاً هذا معناه إن A أُس X أقل أو تساوي B أُس 1 وهو + +202 +00:15:17,300 --> 00:15:20,760 +المطلوب، وهو المطلوب + +203 +00:15:30,770 --> 00:15:37,590 +أي سؤال؟ خلّيني أشوف نظرية، نظرية + +204 +00:15:37,590 --> 00:15:43,070 +7، نظرية مألوفة بالنسبة لنا إذا بتتعامل مع الأعداد + +205 +00:15:43,070 --> 00:15:47,050 +الحقيقية مثلاً فهو بيقول لي هذه النظرية صحيحة برضه + +206 +00:15:47,050 --> 00:15:50,710 +في الـ cardinal number لما نضرب ونعني نفس الأساس + +207 +00:15:50,710 --> 00:15:56,030 +بنجمع الأسس، فبيقول لي A أُس X ضرب A أُس Y تساوي A أُس + +208 +00:15:56,030 --> 00:15:59,550 +X زائد Y، دعونا نشوف كيف بدنا نبرهن هذه النظرية + +209 +00:16:01,910 --> 00:16:09,510 +approved فدي theorem ستة سبعة approved من وين + +210 +00:16:09,510 --> 00:16:13,670 +نبدأ؟ بدنا نحول من لغة الـ cardinal number للغة + +211 +00:16:13,670 --> 00:16:21,390 +المجموعات، فهو ياخذ مجموعات let capital A capital X + +212 +00:16:21,390 --> 00:16:28,450 +خليكم معايا لو سمحتوا capital Y ب six such that + +213 +00:16:30,430 --> 00:16:36,530 +بينفع اخذ أي مجموعات ولا في قيود؟ إيش العمليات + +214 +00:16:36,530 --> 00:16:41,470 +اللي عندي؟ في عمليات أسس وضرب وجمع، في ثالث عمليات + +215 +00:16:41,470 --> 00:16:47,290 +معايا لأن فيش تقاطع، تقاطع مين؟ X و Y لأنه بدي اجمع + +216 +00:16:47,290 --> 00:16:52,850 +X مع Y such that اللي هو X تقاطع الـ Y يساوي فاي، هي + +217 +00:16:52,850 --> 00:16:56,190 +فاي واحد طبعاً، وان كل مجموعة تقابل cardinal number + +218 +00:16:56,190 --> 00:17:01,410 +cardinality للـ capital A تساوي ايه؟ Cardinality + +219 +00:17:01,410 --> 00:17:06,690 +للـ X، مش B، تساوي small x and Cardinality للـ capital Y تساوي small y، ممتاز + +220 +00:17:06,690 --> 00:17:13,390 +فأرجو أن هذه الأمور تكون واضحة بالنسبة للثلاث + +221 +00:17:13,390 --> 00:17:17,490 +عمليات اللي عرفناها، بالنسبة للجامع بس هو اللي بدنا + +222 +00:17:17,490 --> 00:17:20,790 +نتقاطعه يساوي فاي مجموعتين، لكن بالضرب والـ + +223 +00:17:20,790 --> 00:17:23,730 +exponential، أي مجموعات تؤدي الغرض طبعاً تحت الشروط + +224 +00:17:23,730 --> 00:17:27,050 +المعروفة، فالآن أنا بدي أحول صيغة السؤال بالنسبة + +225 +00:17:27,050 --> 00:17:30,790 +لنا then بالنسبة لنا عنا A أُس X هي ليس إلا الـ + +226 +00:17:30,790 --> 00:17:39,140 +Cardinality للمجموعة A أُس X، والـ A أُس Y ليست إلا + +227 +00:17:39,140 --> 00:17:46,880 +Cardinality لـ A أُس Y، والـ A أُس X زائد Y ليست + +228 +00:17:46,880 --> 00:17:53,020 +إلا Cardinality لـ A أُس X إتحاد Y الاتحاد الـ Y + +229 +00:17:53,020 --> 00:17:59,500 +طبعاً صارت عشان انطقته حنّفان فأصبح مطلوب إيش؟ بدنا + +230 +00:18:03,620 --> 00:18:07,000 +ضرب هذه مع هذه يعني بدنا الـ Cartesian product + +231 +00:18:07,000 --> 00:18:14,280 +اه .. اه Therefore we + +232 +00:18:14,280 --> 00:18:25,980 +want to prove that الـ cardinality لمن؟ للـ A أُس X + +233 +00:18:25,980 --> 00:18:32,640 +كارتيسيان A أُس Y، مظبوط لأن هذه إيش ده ده دربها + +234 +00:18:32,640 --> 00:18:35,860 +ده؟ Cardinality للـ Cartesian product يساوي + +235 +00:18:35,860 --> 00:18:42,420 +Cardinality للـ A أُس X Union Y، هذا المطلوب طبعاً + +236 +00:18:42,420 --> 00:18:48,160 +هذا إيش ماله؟ يكافئ if and only if، إيش يكافئ؟ مين معايا + +237 +00:18:48,160 --> 00:18:48,820 +مركز؟ + +239 +00:18:51,530 --> 00:18:55,570 +مظبوط أو مجموعة تكافئ مجموعة، فالـ cardinality بنقول + +240 +00:18:55,570 --> 00:18:58,390 +أنه Cardinality ل two sets بيساووا بعض if and only + +241 +00:18:58,390 --> 00:19:02,410 +if المجموعتين متكافئتين، if and only if، بدنا نشترط + +242 +00:19:02,410 --> 00:19:09,290 +على هذا الكلام times A أُس Y تكافئ equibotent للـ A + +243 +00:19:09,290 --> 00:19:15,750 +أُس X union A أُس Y، فهذا هو المطلوب، أي سؤال + +244 +00:19:16,630 --> 00:19:19,230 +فالحقيقة احنا مش هنعمل أصغر من أو يساوي، أصغر من أو + +245 +00:19:19,230 --> 00:19:22,570 +يساوي في هذا المثال، هنعمل bijection مباشرةً، فبدنا + +246 +00:19:22,570 --> 00:19:28,930 +نعرف بـ Psi من هنا لهنا، تأخذ زوج مرتب، لأنه + +247 +00:19:28,930 --> 00:19:33,240 +Cartesian، الـ Cartesian هنا زوج مرتب من إيش؟ من + +248 +00:19:33,240 --> 00:19:37,300 +الدوال، دالة الأولى من X لـ A والدالة الثانية من Y لـ + +249 +00:19:37,300 --> 00:19:41,080 +A، توديها لدوال عادية، مش زوج مرتب من إيش؟ من + +250 +00:19:41,080 --> 00:19:46,080 +الاتحاد، للـ إيش؟ فيمكن نعمل صورة diagram مبسط في + +251 +00:19:46,080 --> 00:19:52,980 +عنا زوج مرتب F of G، بدنا نوديه لدالة معينة وليكن H + +252 +00:19:54,290 --> 00:20:00,430 +الـ F ده اللي من وين لوين؟ من X لـ A، الـ G ده اللي + +253 +00:20:00,430 --> 00:20:06,390 +من وين لوين؟ من Y لـ A، الصورة Y ده تكون ده اللي من X + +254 +00:20:06,390 --> 00:20:12,490 +union الـ Y للـ A، فهي الصورة، فخليني أبدأ أكتب و + +255 +00:20:12,490 --> 00:20:20,010 +نفكر مع بعض، لتكن ساية from A أُس X across A أُس Y + +256 +00:20:20,010 --> 00:20:31,250 +إلى A أُس X union الـ Y be given by، إبصي of f g + +257 +00:20:31,250 --> 00:20:36,550 +تساوي، في + +258 +00:20:36,550 --> 00:20:42,250 +حد عنده فكرة إيه؟ عندي دالتين من x لـ a ومن y لـ a + +259 +00:20:42,250 --> 00:20:50,450 +ليش فيهم bijection؟ لأ ما فيش bijection + +260 +00:20:52,010 --> 00:20:59,230 +ما فيش إيه؟ Byjection، فانا شوف مرتان خلينا نفكر مع + +261 +00:20:59,230 --> 00:20:59,610 +بعض + +262 +00:21:02,470 --> 00:21:06,790 +مش ضروري، هل كل الدوال اللي بتروح للـ R بتدي نفس + +263 +00:21:06,790 --> 00:21:10,810 +الصورة؟ فالـ Sin دالة من R لـ R والـ Cos دالة من R + +264 +00:21:10,810 --> 00:21:13,970 +لـ R والدالة التربيعية دالة من R لـ R، مش ضروري تودي + +265 +00:21:13,970 --> 00:21:16,850 +نفس الصورة، بتودي على نفس الوعاء، على نفس + +266 +00:21:16,850 --> 00:21:20,750 +الوعاء، طب مرة تنقل، ركزوا معايا، هي عندي دالتين، + +267 +00:21:20,750 --> 00:21:27,430 +من X لـ A ومن Y لـ A، والمجالين تقاطعهم فاي، بينفع + +268 +00:21:27,430 --> 00:21:32,580 +أعمل، مين بيخلي الـ domain يتحد؟ اتحاد الدوال، اه + +269 +00:21:32,580 --> 00:21:36,420 +اتحاد الدوال، فدي هسميها F Union G + +270 +00:21:39,390 --> 00:21:44,490 +لأ، بس دي الشرط عشان تكافؤ، بس عشان أقعد أعمل .. + +271 +00:21:44,490 --> 00:21:47,510 +وكتش بيكون اتحاد الدالتين دالة إذا كانوا في + +272 +00:21:47,510 --> 00:21:50,630 +التقاطع متساويين، طبعاً التقاطع في الـ domain بس، اه + +273 +00:21:50,630 --> 00:21:53,930 +في انت .. انت جبت نظريتين مع بعض، في نظرية بتقول + +274 +00:21:53,930 --> 00:21:57,830 +وكتش اتحاد الدالتين بيكون دالة إذا كانوا في تقاطع + +275 +00:21:57,830 --> 00:22:00,650 +المجالين متساويين، إذا كانوا في تقاطع فيه، بتحقق، + +276 +00:22:00,650 --> 00:22:03,930 +لأنه إيش؟ ما فيشش وعد، فإذا الجملة الشرطية دائماً صح + +277 +00:22:04,180 --> 00:22:08,980 +لكن هناك بيقول المجالين المتقاطعون فاي والمجالين + +278 +00:22:08,980 --> 00:22:11,600 +المقابلين المتقاطعون فاي عشان أضمن أن الاتحاد تم + +279 +00:22:11,600 --> 00:22:15,840 +بيجيكشن، هذه مختلفة تماماً فهذه نشوف أن هذا الكلام + +280 +00:22:15,840 --> 00:22:25,520 +صحيح، نشوف أن هذا الكلام صحيح، ممتاز + +281 +00:22:25,520 --> 00:22:31,630 +بدنا نثبت أن هذه one to one and onto واحد بصي is + +282 +00:22:31,630 --> 00:22:34,610 +one to one طبعًا واضح أن هذا الكلام صحيح ليش هي + +283 +00:22:34,610 --> 00:22:37,450 +بأخذ دالتين فالاتحاد بيصير دالة لإنه تقاطع فيا على + +284 +00:22:37,450 --> 00:22:41,470 +طول بيصير دالة من وين لوين من أيش H فعلاً بتساوي F + +285 +00:22:41,470 --> 00:22:45,370 +Union G بتكون دالة من X Union Y لنفس ال A لإن كلهم + +286 +00:22:45,370 --> 00:22:50,690 +بيودوا على ال A اه تمام البداية المعروفة بدنا ناخد + +287 +00:22:50,690 --> 00:22:55,170 +عنصرين من ال domain أيش العنصرين في ال domainأسواج + +288 +00:22:55,170 --> 00:23:05,930 +مرتبة يعني F1 G1 F2 G2 let F1 G1 and F2 G2 تنتمي + +289 +00:23:05,930 --> 00:23:18,470 +لمين لل A أُس X times و A أُس Y تمام + +290 +00:23:18,470 --> 00:23:19,970 +such that + +291 +00:23:22,920 --> 00:23:33,830 +بـ Psi F1 G1 تساوي بـ Psi F2 G2 ما هو المطلوب؟ أن + +292 +00:23:33,830 --> 00:23:38,690 +الزوج المرتب يساوي الزوج المرتب يعني بدي F1 تساوي + +293 +00:23:38,690 --> 00:23:43,350 +F2 و بدي G1 تساوي G2 هدول كلهم دوال و هدول كلهم + +294 +00:23:43,350 --> 00:23:48,130 +دوال طبعًا كمل التعريف هذا أيش معناه؟ F1 union G1 + +295 +00:23:48,130 --> 00:23:55,010 +تساوي F2 union G2 مطلوب بدي F1 تساوي F2 هذا مطلوب + +296 +00:23:55,010 --> 00:24:00,370 +بدي G1 تساوي G2 نفس الفكرة تتكرر معنا يمكن ليش + +297 +00:24:00,370 --> 00:24:04,250 +لثالث أو رابع مرة عشان أساوي الدول يتساوي بدي + +298 +00:24:04,250 --> 00:24:07,930 +شرطين يكون لهم نفس المجال ونفس المجال المقابل + +299 +00:24:07,930 --> 00:24:11,610 +وبيدي صورهم تتساوي على كل عناصر الدمين المشترك + +300 +00:24:11,610 --> 00:24:14,590 +المتساوي طيب نشوف فاحنا عندنا الـ Agents اللي توي + +301 +00:24:14,590 --> 00:24:20,870 +اللي كنا نتبقه مرتين أولًا على F1 و F2 F1 و F2 من + +302 +00:24:20,870 --> 00:24:25,060 +وين بيكونوا؟ من A أُس X إحداه في أول إذاً أول شرط + +303 +00:24:25,060 --> 00:24:28,360 +متحقق دائمًا والـ G1 و G2 من وين بيكونوا؟ من A أُس + +304 +00:24:28,360 --> 00:24:30,960 +Y إذاً أول شرط إنهم يلهم نفس ال domain مين + +305 +00:24:30,960 --> 00:24:34,080 +domainهم المشترك لل F؟ X ومين domainهم المشترك لل + +306 +00:24:34,080 --> 00:24:39,400 +G؟ Y المجال المقابل برضه A تمام الشرط الثاني بنا + +307 +00:24:39,400 --> 00:24:42,820 +نثبتهم واحدة واحدة بنا نثبت إنه لكل عناصر ال + +308 +00:24:42,820 --> 00:24:46,900 +domain الأول X F1 تسوي F2 ولكل عناصر ال domain + +309 +00:24:46,900 --> 00:24:49,660 +الثاني Y G1 تسوي G2 فنبدأ + +310 +00:24:52,330 --> 00:25:01,410 +let X تنتمي للـ Capital X ممتاز أيش تعريف أن هدول + +311 +00:25:01,410 --> 00:25:06,150 +اتحاد كيف تعريف الاتحاد متعددة القاعدة ممتاز أو + +312 +00:25:06,150 --> 00:25:10,070 +كيف تعريفها هي بتكون F إذا ال X في domain ال F و + +313 +00:25:10,070 --> 00:25:14,270 +بتكون G إذا كانت ال X في domain ال G فطبعًا بتستخدم + +314 +00:25:14,270 --> 00:25:16,430 +القاعدة ده اللي دائمًا قلنا بنحطها بنقدرش نحلها + +315 +00:25:16,430 --> 00:25:25,410 +بنوقفها شوية فهذا يؤدي then F1 union G1 of X تساوي + +316 +00:25:25,410 --> 00:25:31,270 +F2 union G2 of X أذكركم التعريف تبع الـH هذا خلينا + +317 +00:25:31,270 --> 00:25:35,770 +نكتبه هنا عشان + +318 +00:25:35,770 --> 00:25:40,450 +بس تتابعوا ما أحب أحكي شفوي أحسن يكون قدامنا و + +319 +00:25:40,450 --> 00:25:42,870 +طبعًا بدي أكتب الكياب بالـH بصغرها العامة هل جيت إن + +320 +00:25:42,870 --> 00:25:49,860 +احنا H تساوي F union G اه فكان إن الـH of X إذا + +321 +00:25:49,860 --> 00:25:55,700 +بترجع للتعريف أو للنظرية بتساوي F of X إذا الـX في + +322 +00:25:55,700 --> 00:26:00,740 +Capital X اللي هو domain الـF وتساوي + +323 +00:26:00,740 --> 00:26:06,530 +G of X إذا الـX في الـY اللي هو main domain الـ G + +324 +00:26:06,530 --> 00:26:10,770 +عشان هيك قولنا متعددة القاعدة إذا بتتذكر تمام فأنا + +325 +00:26:10,770 --> 00:26:15,070 +وصلت لها هنا ال X وين في ال Capital X إذا ناشت + +326 +00:26:15,070 --> 00:26:21,330 +عارف الاتحاد F فهذا يؤدي إنه F1 of X تساوي F2 of X + +327 +00:26:21,330 --> 00:26:26,970 +بعيد كمان مرة هلجيت أنا هاي هادي إتش وهادي إتش بده + +328 +00:26:26,970 --> 00:26:32,050 +أشوف ال X وين في ال Capital X اللي هو domain من ال + +329 +00:26:32,050 --> 00:26:38,120 +F F1 و F2 إذا وين هي ده و ده و ده وبتابعين واضحة + +330 +00:26:38,120 --> 00:26:44,140 +إذا خلاص اثبت أن F1 تسوى F2 إذا thus F1 تسوى F2 + +331 +00:26:44,140 --> 00:26:49,900 +هاي الجزء الأول اه لإن ناخد عنصر وين في ال Y عشان + +332 +00:26:49,900 --> 00:26:57,160 +اثبت G1 تسوى G2 اه then بنفس الطريقة F1 union G1 of + +333 +00:26:57,160 --> 00:27:03,220 +X تساوي F2 union G2 of X ولما الـ X تكون في الـ Y + +334 +00:27:03,220 --> 00:27:08,540 +أيّش بيكون التعريف؟ G فده يؤدي إنه G1 of X تساوي G2 + +335 +00:27:08,540 --> 00:27:18,660 +of X Thus G1 تساوي G2 فالآن Therefore F1 + +336 +00:27:18,660 --> 00:27:28,260 +G1 تساوي F2 G2 وبالتالي and hence if Psi is one to + +337 +00:27:28,260 --> 00:27:34,200 +one أي سؤال فأرجو أن هذه المهارة اللي اتكررت أكثر + +338 +00:27:34,200 --> 00:27:37,820 +من مرة كيف نتعامل لما نثبت دالة تساوي دالة وهذه + +339 +00:27:37,820 --> 00:27:41,540 +كانت عندنا نظرية أساسية نظرية تلاتة سبعة في اللي + +340 +00:27:41,540 --> 00:27:49,660 +هو chapter تلاتة نشوف ال onto الآن if Psi is onto + +341 +00:27:51,840 --> 00:27:56,140 +فحناخد عنصر من المجال المقابل اللي هو نسميه H وين + +342 +00:27:56,140 --> 00:28:03,680 +تنتمي لل A أُس X Union ال Y ونعمل الهامش تبعنا هاي + +343 +00:28:03,680 --> 00:28:08,460 +التعريفة تمام فاحنا + +344 +00:28:10,690 --> 00:28:14,510 +مشيين على نفس النهج لكن التفاصيل بتختلف نفس + +345 +00:28:14,510 --> 00:28:17,850 +البداية و نفس النهاية التفاصيل بتختلف احنا عايش + +346 +00:28:17,850 --> 00:28:23,650 +بندور بدنا الـH تساوي بـPsi of FG for some F of G + +347 +00:28:23,650 --> 00:28:28,370 +وين في الـCartesian لإن هو عديدها اللي من A أُس X + +348 +00:28:28,370 --> 00:28:32,730 +across A أُس Y فبندور على F والـG طب بعدين أيش + +349 +00:28:32,730 --> 00:28:40,010 +تعريفها؟ F union الـG F union الـG فالسؤال كيف + +350 +00:28:40,010 --> 00:28:46,370 +اختار الـF والـG كيف اختار الـF والـG المفتاح هنا + +351 +00:28:46,370 --> 00:28:54,110 +المفتاح هنا أيش الصورة الـH معرفة على الاتحاد على + +352 +00:28:54,110 --> 00:28:57,950 +X وY بده خليها أخد أيش لإن مش بده أكبر ال domain + +353 +00:28:57,950 --> 00:29:01,090 +بده أزاغره بده أقسم نصين ال domain بدي أقسم ال + +354 +00:29:01,090 --> 00:29:04,890 +domain نصين أخلي النص الأول اللي هو X اعرف عليه F + +355 +00:29:04,890 --> 00:29:10,770 +والنص الثاني اعرف عليه Y هذا أيش بيسموه restriction + +356 +00:29:10,770 --> 00:29:15,290 +تقييد لما نظغر ال domains مرت علينا كمثال في ال + +357 +00:29:15,290 --> 00:29:18,890 +relations طبعًا لما بدي أكبر ال domain بيسموها + +358 +00:29:18,890 --> 00:29:23,430 +extension تمديد لما بدي أعمل أيش بقيد بعمل تقييد + +359 +00:29:23,430 --> 00:29:26,450 +فأنا دالة معرفة على مجموعة كبيرة بدي أخليها على + +360 +00:29:26,450 --> 00:29:29,750 +جزء منها فال domain عند مين ال domain ال domain + +361 +00:29:29,750 --> 00:29:35,290 +تبع هذه من وين لوين domain ال H من X union Y إلى + +362 +00:29:35,290 --> 00:29:42,220 +ال A ال F وين domainها بدي F من X لـ A و بدي جي + +363 +00:29:42,220 --> 00:29:46,380 +بدور عليهم من Y ل A فايش اعملها أخد restriction + +364 +00:29:46,380 --> 00:29:51,660 +للـ H أخد الـ H معرفة على الإتحاد هي الصورة الـ H + +365 +00:29:51,660 --> 00:29:54,160 +معرفة على الإتحاد هم disjoint طبعًا خلينا ناخدهم + +366 +00:29:54,160 --> 00:29:58,940 +disjoint فهذه X وهذه Y الـ H معرفة على الكل الجزء + +367 +00:29:58,940 --> 00:30:02,700 +هذا هعرف منه ده الـ F والجزء اللي هعرف عليه ده + +368 +00:30:02,700 --> 00:30:08,120 +لمين جي فده اللي هنعمله فهنقوله الآن and فمش دائمًا + +369 +00:30:08,120 --> 00:30:11,120 +بتكون معادلة لو بنحلها في أحيان الكتاب بتكون تعمق + +370 +00:30:11,120 --> 00:30:16,580 +و نفهم هقول له let F تساوي H restricted to X + +371 +00:30:16,580 --> 00:30:24,080 +الرمزة ده اللي استخدمناها and G تساوي H restricted + +372 +00:30:24,080 --> 00:30:28,440 +to Y يعني الـ F المعرف على نص الدمين الأول و الـ G + +373 +00:30:28,440 --> 00:30:34,920 +الـ H معرف على نص الدمين التالي then طبعًا الـ F + +374 +00:30:36,540 --> 00:30:40,400 +تنتمي لمين؟ هي معرفة بس على الـ X و من أين صورها؟ + +375 +00:30:40,400 --> 00:30:45,120 +كله في الـ A لأن الـ X صورها في الـ A and الـ G أو + +376 +00:30:45,120 --> 00:30:51,760 +غلطولة أخذ الزوج المرتب بدل مكتوب مرتين فـ FG تنتمي + +377 +00:30:51,760 --> 00:30:59,260 +للـ A أُس X times A أُس Y هذه دالة بس من X معرفة + +378 +00:30:59,260 --> 00:31:02,400 +بتروح للـ A لأن الـ H بالـ A و هذه دالة من Y لـ A + +379 +00:31:02,400 --> 00:31:08,060 +and هي الشرط الأول الشرط الثاني بـ Psi of FG أيش + +380 +00:31:08,060 --> 00:31:10,260 +بيساوي F Union G + +381 +00:31:13,160 --> 00:31:16,260 +لأ أنا بدور عليهم دائمًا احنا بناخد عنصر في المجال + +382 +00:31:16,260 --> 00:31:19,920 +المقابل وبدنا نقول هو صورة مين من ال domain + +383 +00:31:19,920 --> 00:31:23,440 +فبختارهم زي ما قولنا يقول Y تساوي F of X بنحل ال X + +384 +00:31:23,440 --> 00:31:27,320 +بدلالة ال Y فالآن ال H معطية أنا بديتها H مطلوب + +385 +00:31:27,320 --> 00:31:31,620 +أدور على F of G جبتهم بدلالة ال H صح؟ اه بس طبعًا + +386 +00:31:31,620 --> 00:31:35,960 +مش معادلة مش أرقام لإن هل هذا الكلام فعلًا هذا + +387 +00:31:35,960 --> 00:31:40,600 +بيسوي H؟ نعم، لو طلعنا على التعريف، أيش معناه أن H + +388 +00:31:40,600 --> 00:31:43,660 +تسوي الاتحاد؟ هي بيسوي F X لما X تمهي X، إذاً هي + +389 +00:31:43,660 --> 00:31:45,220 +فعلًا F، هي ال restriction، هذا معناه ال + +390 +00:31:45,220 --> 00:31:47,960 +restriction، إنه جسمتها نصين، جسمت ال domain، + +391 +00:31:47,960 --> 00:31:51,700 +ومتعددة القاعدة في جزء على ال X المعرفة F، هذا + +392 +00:31:51,700 --> 00:31:54,720 +القاعدة الأولى، وعلى ال Y معرفة G، القاعدة + +393 +00:31:54,720 --> 00:32:01,480 +الثانية، فدي ليست إلا H، طبقًا للتعريف، ففعلًا + +394 +00:32:01,480 --> 00:32:03,260 +الدالة بـPsi Onto + +395 +00:32:07,480 --> 00:32:12,400 +طبعًا هذه باستعمخ لمفهوم الاتحاد الـ Psi is onto + +396 +00:32:12,400 --> 00:32:19,840 +طبعًا 1 و 2 بيخلص البرهان implies A أُس X times A + +397 +00:32:19,840 --> 00:32:27,220 +أُس Y تكافئ A أُس X union Y وبالتالي A أُس X في A + +398 +00:32:27,220 --> 00:32:33,720 +أُس Y تساوي A أُس X زائد 1 وهو المطلوب أي سؤال + +399 +00:32:41,970 --> 00:32:46,890 +طبعًا لديق الوقت ممكن نمر على بعض النظريات بس سريع + +400 +00:32:46,890 --> 00:32:51,290 +وممكن نثبت بس حاجة أخرى لإنها يمكن أهم طبعًا خواص + +401 +00:32:51,290 --> 00:32:55,490 +الأسس معروف طبعًا قلنا لما نضرب الأساس لنفس الأساس + +402 +00:32:55,490 --> 00:32:59,090 +فنجمع الأسس أيضًا لو رفعنا مقدار ال أس ورفعناه + +403 +00:32:59,090 --> 00:33:02,470 +لكمان أس فنضرب الأسس موجودة هذه النظرية مش هثبتها + +404 +00:33:02,470 --> 00:33:09,200 +مش وقت أيضًا في نظرية أخرى لو بدّي أنا عندي حاصل ضرب + +405 +00:33:09,200 --> 00:33:13,380 +ده عددين و رفعتلهم أس بقدر أوزّي الأس على العددين + +406 +00:33:13,380 --> 00:33:16,720 +فهي A أس X B أس X هذه كل الخواص للـExperimental + +407 +00:33:16,720 --> 00:33:19,300 +الموجودة في الـReal numbers طامعا صحيح على + +408 +00:33:19,300 --> 00:33:25,560 +الcardinal number فنظرية 6 8 و 6 9 مش هبرهنهم فيما + +409 +00:33:25,560 --> 00:33:28,240 +تبقى هبرهن نظرية 16 + +410 +00:33:31,920 --> 00:33:35,840 +بقول 2 أُس ألف null تساوي C ألف null اللي هي + +411 +00:33:35,840 --> 00:33:38,320 +الcardinality لـnatural number أو للـdenominable + +412 +00:33:38,320 --> 00:33:41,340 +sets والـC هي الcardinality للـreal numbers أو أي + +413 +00:33:41,340 --> 00:33:44,520 +مجموعة كافية مش للـnon-denominable مش كلهم واحد + +414 +00:33:44,520 --> 00:33:46,740 +الـdenominable كلهم متكافئين لكن الـnon + +415 +00:33:46,740 --> 00:33:49,780 +-denominable مش كلهم متكافئين في مجموعات متعددة + +416 +00:33:49,780 --> 00:33:57,440 +خلّيني أحاول أنبرهن هذه النظرية لإن جيد معلومة + +417 +00:33:57,440 --> 00:34:01,160 +أتوقع أنها أهم من السابق وفكرة البرهانة ممكن تكون + +418 +00:34:01,160 --> 00:34:05,620 +أهم طبعًا أنا بدأ أجيب المجموعات و أبدأ أشتغل الـ + +419 +00:34:05,620 --> 00:34:09,680 +proof طبعًا + +420 +00:34:09,680 --> 00:34:13,720 +بدنا مجموعة من عنصرين خليها ناخد الـ 0 1 و بدنا + +421 +00:34:13,720 --> 00:34:16,640 +مجموعة تكون كاردناتية لألف null في أكثر من + +422 +00:34:16,640 --> 00:34:19,780 +المجموعة في الـ N و في الـ Z و في الـ Q و الحقيقة + +423 +00:34:19,780 --> 00:34:22,240 +يمكن نحتاج في حياتنا أن نتنقل من واحدة لواحدة زي ما + +424 +00:34:22,240 --> 00:34:26,000 +نشوف و الـ C هي كاردناتية لـ real number و لأي + +425 +00:34:26,000 --> 00:34:29,080 +فترة مفتوحة 01 على سبيل المثال المشهور و هكذا + +426 +00:34:29,080 --> 00:34:35,090 +فبدنا نشوف إيش المناسب في الغالب مع الـ C بقدرش + +427 +00:34:35,090 --> 00:34:38,690 +أعمل تساوي بالظبط، هنعمل أصغر من أو يساوي و أصغر + +428 +00:34:38,690 --> 00:34:44,050 +من أو يساوي، فطبعا احنا خلينا نبدأ اللي هو بهذا + +429 +00:34:44,050 --> 00:34:49,710 +الشكل، فاحنا عندنا 2 أس ألف null تساوي C، هذا + +430 +00:34:49,710 --> 00:34:54,370 +الكلام if and only if، 2 أس ألف null أقل أو تساوي + +431 +00:34:54,370 --> 00:34:58,110 +C and C أقل أو تساوي 2 أس ألف null، هنعمل بهذا + +432 +00:34:58,110 --> 00:35:02,280 +الشكل يا أخوان هنشتغل بيه أقل من أو يساوي مش صعب أن + +433 +00:35:02,280 --> 00:35:06,200 +نجيب bijection بين المجموعات المناسبة فهنعمل بهذا + +434 +00:35:06,200 --> 00:35:11,560 +الشكل فطبعا هبدأ بالأولى + +435 +00:35:11,560 --> 00:35:19,800 +اثنين أس ألف null واحد أقل أو تساوي C أعتقد احنا + +436 +00:35:19,800 --> 00:35:28,760 +هنمشي بهذا الشكل هو الشكل الأسهل الأول تمام + +437 +00:35:29,990 --> 00:35:33,590 +2 ألف null أقل ألف سوى C ممتاز نبدأ بهذا هذا يمكن + +438 +00:35:33,590 --> 00:35:38,390 +يكون أوضح فهأخد مجموعات الآن هحوله بلغة المجموعات + +439 +00:35:38,390 --> 00:35:41,590 +let + +440 +00:35:41,590 --> 00:35:48,650 +A تساوي مجموعة Zero واحد ليش ال coordinate لها + +441 +00:35:48,650 --> 00:35:55,350 +اتنين ومقابل الالف null أشهر شيء أخد ال N طبعاً + +442 +00:35:55,350 --> 00:36:05,480 +and B تساوي and B تساوي N و هاخد برضه مقابل الـ CR + +443 +00:36:05,480 --> 00:36:08,680 +آه + +444 +00:36:08,680 --> 00:36:15,820 +طبعاً then بالنسبة لنا اتنين ألف null تساوي ال + +445 +00:36:15,820 --> 00:36:24,570 +cardinality لمن لل A أس بي اللي هي إيش A أُس N والـ + +446 +00:36:24,570 --> 00:36:31,610 +C هنعملها إنها R أو 01 هأخدها خلّيني أقول هنا بي و + +447 +00:36:31,610 --> 00:36:39,210 +مجموعة C تساوي 01 and cardinality + +448 +00:36:39,210 --> 00:36:48,330 +ل .. اللي هو أو الـ C تساوي cardinality للـ C لل + +449 +00:36:48,330 --> 00:36:57,750 +capital C منتبه عشان أثبت أن ألف نل أصغر أو تساوي + +450 +00:36:57,750 --> 00:37:03,230 +الـC هثبت أن هذه المجموعة تكافئ subset من الـC We + +451 +00:37:03,230 --> 00:37:16,570 +will prove that A أُس B تكافئ subset Z من الـC هذا + +452 +00:37:16,570 --> 00:37:21,050 +اللي هنعمل طبعا كالعادة بدل ما اخد Z هاخد دالة one + +453 +00:37:21,050 --> 00:37:28,350 +to one آه فهعرف دالة هاخدها image let F من A أس بي + +454 +00:37:28,350 --> 00:37:39,430 +إلى C بي given by سميتها F عشان نرجع للسابق إيش + +455 +00:37:39,430 --> 00:37:45,090 +عناصرها؟ عناصر آه لأ مش F ده بصير بصير + +456 +00:37:47,880 --> 00:37:53,400 +لأن عناصرها دوال أنا خلينا نعمل الصورة تبعتنا عشان + +457 +00:37:53,400 --> 00:37:59,140 +نفكر صح إيش عناصرها اللي هان؟ دوال F من وين لوين + +458 +00:37:59,140 --> 00:38:05,760 +من B إلى A وال B هي مين؟ هي ال N وال A هي مين؟ 01 + +459 +00:38:05,760 --> 00:38:11,120 +تمام بدي اودّيها لوين؟ بدي اودّيها لـ C إيش + +460 +00:38:11,120 --> 00:38:16,080 +عناصرها؟ من 01 يعني Zero Point، X1، X2 و هكذا + +461 +00:38:16,080 --> 00:38:19,540 +متعودة جاب لك شفناها عشان ذلك احنا زغرناها شوية + +462 +00:38:19,540 --> 00:38:25,480 +فبدنا دالة تروح لعدد حقيقي بين الصفر وبين الواحد + +463 +00:38:25,480 --> 00:38:30,160 +مين عنده اقتراح فبصيف + +464 +00:38:30,160 --> 00:38:37,020 +F بدي تسوي عدد كيه بدي اكتبه؟ Zero Point أف اف اي + +465 +00:38:37,020 --> 00:38:38,580 +اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي + +466 +00:38:38,580 --> 00:38:45,540 +اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي + +467 +00:38:45,540 --> 00:38:49,520 +اي اي اي اي اي اي اي اي اي + +468 +00:38:49,520 --> 00:38:50,060 +اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي + +469 +00:38:50,060 --> 00:38:50,880 +اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي + +470 +00:38:50,880 --> 00:38:53,140 +اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي + +471 +00:38:53,140 --> 00:38:54,620 +اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي + +472 +00:39:04,800 --> 00:39:09,740 +لأ مرة ثانية فانا هي عندي الدالة F ال F هذه معرفة + +473 +00:39:09,740 --> 00:39:14,520 +على ال N كيف تاخد يعني ال F إيش بتاخد فال F معرفة + +474 +00:39:14,520 --> 00:39:18,780 +F في واحد و أنت تنتمي لل A F في التانية تنتمي لل A + +475 +00:39:18,780 --> 00:39:22,880 +و هكذا فهم يا صفر يا واحد فانا بدي أخليهم هدول ال + +476 +00:39:22,880 --> 00:39:27,220 +F يتعرف عدد حقيقي إيش عملتم؟ خناد الصور عملتم خناد + +477 +00:39:27,220 --> 00:39:30,020 +كل الصور صورة الواحد الخانة الأولى صورة التانية + +478 +00:39:30,020 --> 00:39:31,420 +الخانة الثانية و هكذا + +479 +00:39:34,510 --> 00:39:37,870 +آه طبعا مش مشكلة في آية دي بيكون عدد بيكون عدد + +480 +00:39:37,870 --> 00:39:40,910 +حقيقي آه فنثبتها بس one to one بدناياها بس + +481 +00:39:40,910 --> 00:39:44,410 +بدناياها تكون one to one لإن و احنا إيش بدنا ندور + +482 +00:39:44,410 --> 00:39:48,730 +على إيش على Z subset و احنا إيش هناخدها ال image + +483 +00:39:48,730 --> 00:39:51,330 +بس إذا one to one ناخدها ال image فده اللي هادي + +484 +00:39:51,330 --> 00:39:54,810 +one to one بدنا نسترجع بعض الأفكار نشوف إن ال size + +485 +00:39:54,810 --> 00:40:03,420 +one to one نثبت let F1 و F2 تنتمي لل domain اللي هو + +486 +00:40:03,420 --> 00:40:15,240 +domain ب A أُس B such that ب Psi F1 تساوي ب Psi F2 + +487 +00:40:15,240 --> 00:40:17,080 +ممتاز + +488 +00:40:18,830 --> 00:40:23,990 +آه إيش هذا يقدي بالتعريف zero point of واحد of + +489 +00:40:23,990 --> 00:40:29,610 +واحد of واحد of اتنين and so on يساوي zero point + +490 +00:40:29,610 --> 00:40:37,390 +of اتنين الواحد of اتنين الاتنين and so on تمام؟ + +491 +00:40:38,980 --> 00:40:41,400 +ممتاز فال Memorized Form بيقول اللي لازم كل + +492 +00:40:41,400 --> 00:40:45,540 +خاناتها تتطابع فهذا بيقول لي انه بيكتبهم مرة واحدة + +493 +00:40:45,540 --> 00:40:51,100 +آه ممكن أقول F1 of N اللي هو واحد اتنين for all + +494 +00:40:51,100 --> 00:40:53,480 +and اكتبه بيقول اكتبه آه واضح؟ كل خانة ده تساوي + +495 +00:40:53,480 --> 00:40:57,040 +خانة ولا أوضح؟ بيبقى اختصرها فيا عزيزي لازم تكون + +496 +00:40:57,040 --> 00:41:05,230 +F1 تساوي F2 of 1 F1 of N تساوي F2 of N كل خانة + +497 +00:41:05,230 --> 00:41:09,530 +تساوي الخانة المقابلة وهاكذا بمعنى آخر F1 of N + +498 +00:41:09,530 --> 00:41:15,830 +تساوي F2 of N for all N تنتمي لل N صح؟ لأن كل + +499 +00:41:15,830 --> 00:41:21,710 +الخنات طيب أنا عايش بدور كنت أن F1 تساوي F2 صح؟ + +500 +00:41:21,710 --> 00:41:26,930 +سؤال الرئيس اللي اتكرر عدة مرات أعيد القصة من + +501 +00:41:26,930 --> 00:41:33,050 +بداية أخذنا عنصرين من ال domain دوالة صورهم + +502 +00:41:33,050 --> 00:41:35,510 +متساوية، إيش مكتوب تثبت العنصرين متساويين؟ F1 + +503 +00:41:35,510 --> 00:41:38,090 +تساوي F2، ده اللي الثاني، عشان يكونوا متساويين، + +504 +00:41:38,090 --> 00:41:41,430 +يبقوا يكونوا من نفس المجموعة لنفس المجموعة، صح تم + +505 +00:41:41,430 --> 00:41:44,190 +صورهم متساوي على كل ال domain، مين ال domain هم؟ + +506 +00:41:44,190 --> 00:41:47,990 +N، بدنا صورهم تكون على كل ال N متساوي، هذا هي، + +507 +00:41:47,990 --> 00:41:50,110 +واضحة؟ لأن ال domain هم N، لما أكتب بعد الكلمة، + +508 +00:41:50,110 --> 00:41:55,290 +هم خلصوا، آه، فهذا بيقول إن F1 تساوي F2، وهذا يعني + +509 +00:41:55,290 --> 00:42:02,280 +إيش؟ Psi is one to one Thus صار الـ domain اللي هو + +510 +00:42:02,280 --> 00:42:08,300 +A أُس B يكافئ ال image للـ + +511 +00:42:08,300 --> 00:42:13,260 +A أُس B اللي هو subset من مين؟ من C اللي هي 01 + +512 +00:42:13,260 --> 00:42:20,700 +طبعا فهذا بيقدّي أنه 2 ألف null تمام شمالها أصغر + +513 +00:42:20,700 --> 00:42:27,700 +أو يساوي C لأن واحد ال cardinality إليها هيك نشوف + +514 +00:42:27,700 --> 00:42:37,840 +الاتجاه الثاني C أصغر أو تساوي 2 أس ال 12 الحقيقة + +515 +00:42:37,840 --> 00:42:41,820 +مش هنشتغل على نفس المجموعات هنغير الآن هناخد + +516 +00:42:41,820 --> 00:42:49,910 +المجموعة اللي هو X أو C من مقابل ال C هناخدها R لـ + +517 +00:42:49,910 --> 00:42:53,850 +C تساوي R فال cardinality لها ال C وهناخد + +518 +00:42:53,850 --> 00:42:59,230 +الطبعا الاثنين هنخليها 01 ولا هنغير بس بدي اخذ .. + +519 +00:42:59,230 --> 00:43:04,950 +بديش اخذ الآن بدي اخذ ال Q الآن المجموعة ب .. آه + +520 +00:43:04,950 --> 00:43:09,870 +تمام هعملها بشكل مختلف تماماً أنا عندي اثنين أُس ال + +521 +00:43:09,870 --> 00:43:12,750 +cardinality هي عبارة عن cardinality ل H أكبر من + +522 +00:43:12,750 --> 00:43:15,430 +cardinality لل power فاحنا في عندنا علاقة إيش + +523 +00:43:15,430 --> 00:43:20,670 +يعملنا فيه ال power بنقول ال Cardinality ل Power + +524 +00:43:20,670 --> 00:43:28,250 +لأي مجموعة تساوي 2 ل Cardinality للمجموعة صح؟ + +525 +00:43:28,250 --> 00:43:32,110 +عممناها هذه فتساوي Cardinality للمجموعة + +526 +00:43:32,110 --> 00:43:38,130 +فهنستخدمها هذه هنستخدم هذه العلاقة طبعاً لأي مجموعة + +527 +00:43:38,130 --> 00:43:41,330 +احنا بس أنا هحط ال Q هنا أثبتناها ده كمثال + +528 +00:43:41,330 --> 00:43:48,080 +الحقيقة مش نظرية مثال رقم 3 هيهمثال رقم ثلاثة + +529 +00:43:48,080 --> 00:43:51,600 +المرة اللي فاتتنا هنا لأ جابل ال cardinality في + +530 +00:43:51,600 --> 00:43:59,460 +مثال أنا متذكر انه عملناه مثال مثال رقم اثنين ال + +531 +00:43:59,460 --> 00:44:01,520 +cardinality لل power of a بتساوي اثنين لل + +532 +00:44:01,520 --> 00:44:06,300 +cardinality of a هنستخدم هذه الفكرة نرجع لنظرية + +533 +00:44:06,300 --> 00:44:13,440 +تبعتها فهنشتغل عليها فهي ال C و هاخد ل ألف null + +534 +00:44:13,440 --> 00:44:19,050 +اللي هي ال cardinality of Q and اللي هي اللي ال B + +535 +00:44:19,050 --> 00:44:24,890 +تساوي Q فطبعاً + +536 +00:44:24,890 --> 00:44:32,150 +then ال cardinality لل R اللي هي بتساوي C أو ال C + +537 +00:44:32,150 --> 00:44:36,970 +بتساوي C small c and باستخدام هذه القاعدة + +538 +00:44:36,970 --> 00:44:46,060 +cardinality ل ال power of Q بتساوى 2 cardinality + +539 +00:44:46,060 --> 00:44:50,200 +لل Q بتساوى 2 نقصة ألف null لأن ال Q شمالها + +540 +00:44:50,200 --> 00:44:54,480 +denomable فانا حاجة تلعب على هذا الكلام فالآن عشان + +541 +00:44:54,480 --> 00:45:00,940 +أثبت أن ال C أصغر أو متساوي هذا الكلام بدنا نثبت + +542 +00:45:00,940 --> 00:45:12,300 +we will prove that ال R تكافئ subset z من من من + +543 +00:45:12,300 --> 00:45:18,180 +اللي هو power of a cube power of a cube فانا بدي + +544 +00:45:18,180 --> 00:45:22,020 +أستفيد أيها هذه بتساوي هذه فهي المجموعة power of a + +545 +00:45:22,020 --> 00:45:26,000 +cube هنستبدلها بدأت بشكل مش هنستخدم قصص الآن هنا + +546 +00:45:26,000 --> 00:45:31,650 +هنشتغل على طول على المجموعات مباشرة فجيد إن نشوف + +547 +00:45:31,650 --> 00:45:38,630 +نوع جديد من الدوال فكرة جديدة كل هذه أفكار بتعلمنا + +548 +00:45:38,630 --> 00:45:42,510 +فطبعاً نفس القضية هعرف ده لمن R ل power of Q تكون + +549 +00:45:42,510 --> 00:45:46,030 +one to one نفس الفكرة مش هعرف ال Z هأخدها ال + +550 +00:45:46,030 --> 00:45:50,870 +image let الجت هدول عناصر ال R عدد حقيقية ومين + +551 +00:45:50,870 --> 00:45:54,490 +عناصر ال power of Q سبسط من ال Q مجموعات أحسنة + +552 +00:45:54,490 --> 00:46:02,270 +فإذا هنسميها F الآن من R لل power of Q بالشكل + +553 +00:46:02,270 --> 00:46:12,710 +التالي be given by اللي هو F of أي عدد R اسمه R + +554 +00:46:12,710 --> 00:46:17,470 +تساوي بدي أعمل subset ال subset هي كل العناصر بدي + +555 +00:46:17,470 --> 00:46:20,830 +أعمل subset من ال Q subset من ال Q بدي أعمل منها + +556 +00:46:20,830 --> 00:46:26,570 +مجموعة شوف كيف بنعمل مجموعة such that X أصغر من R + +557 +00:46:29,050 --> 00:46:35,130 +أصغر ولا أكبر؟ أعتقد ما تفرقش طبعا + +558 +00:46:35,130 --> 00:46:40,710 +زي ما احنا بنحكي دائماً في أشياء كثيرة تجيش من أول + +559 +00:46:40,710 --> 00:46:44,370 +مرة و تجي مع المحاولات طبعاً أنا أول شيء الشكل + +560 +00:46:44,370 --> 00:46:48,390 +الأول فكرة ممكن اتقالها بدي عدد و أوديه لمجموعة + +561 +00:46:48,390 --> 00:46:51,970 +بدي أوديه لمجموعة طبعا خلنا نفهم الدالة أولا إيش + +562 +00:46:51,970 --> 00:46:56,590 +يعني دالة أي real number لو بقول لي أف أوف واحد هي مين؟ + +563 +00:46:57,330 --> 00:47:03,010 +هي كل الأعداد النسبية اللي أصغر من واحد مظبوط؟ هيك + +564 +00:47:03,010 --> 00:47:08,930 +معناته طيب لو جالي F of سالب اثنين هي كل الأعداد + +565 +00:47:08,930 --> 00:47:13,360 +النسبية اللي أصغر من سالب اثنين هذه صورتها طبعا كل + +566 +00:47:13,360 --> 00:47:15,780 +ما دول صبست من الـQ ولا لأ؟ لأن هو بيقول لي إيه + +567 +00:47:15,780 --> 00:47:19,680 +الـQ وهكذا صبست من الـQ إذا المهم نتمو هدول لل + +568 +00:47:19,680 --> 00:47:23,160 +power واضحة بس نثبت أنها one to one هنثبت أن هذه + +569 +00:47:23,160 --> 00:47:26,600 +الدالة one to one يمكن أثناء البرهان يشوفنا ليش + +570 +00:47:26,600 --> 00:47:29,100 +الاختيار بعد الشكل عشان أحافظ أنها one to one + +571 +00:47:29,100 --> 00:47:35,010 +خليني أثبت أن الـ F one to one F is one to one نأخذ + +572 +00:47:35,010 --> 00:47:39,050 +عنصرين من الـ domain R1 وR2 تنتمي للـ capital R + +573 +00:47:39,050 --> 00:47:47,790 +such that صورهم متساوي F of R1 تساوي F of R2 بدنا + +574 +00:47:47,790 --> 00:47:53,750 +نثبت أن R1 تساوي R2 طبعا + +575 +00:47:53,750 --> 00:47:59,170 +نستخدم التعريف واحدة واحدة، طب إيش هذه؟ إذا + +576 +00:47:59,170 --> 00:48:06,770 +المجموعة X تنتمي لـ Q بحيث X أقل من R1 بيبقى تساوي + +577 +00:48:06,770 --> 00:48:14,930 +المجموعة اللي هي X تنتمي لـ Q بحيث X أقل من R2 + +578 +00:48:14,930 --> 00:48:25,060 +مطلوب إن X R1 تساوي R2، هنثبت هذاسنثبت هذا يا إما + +579 +00:48:25,060 --> 00:48:30,280 +by contradiction أو نثبت إن الاحتمالين التانيين مش + +580 +00:48:30,280 --> 00:48:35,820 +ممكن يحصلوا حالة الأعداد الحقيقية أي أعداد حقيقية + +581 +00:48:35,820 --> 00:48:39,460 +فيها ثلاثة احتمالات يا الأول يساوي الثاني يا الأول + +582 +00:48:39,460 --> 00:48:43,120 +أصغر من الثاني أكبر منه فسننفع الاحتمالين وتم أنها + +583 +00:48:43,120 --> 00:48:48,340 +تتساوي سننفع الاحتمالين فلجيت أقول له هيا نمشي by + +584 +00:48:48,340 --> 00:48:53,590 +contradiction assume R1 لا تساوي R2 Proved by + +585 +00:48:53,590 --> 00:48:57,230 +Contradiction Proved by Contradiction ماهو Proved + +586 +00:48:57,230 --> 00:49:00,710 +by Contradiction؟ أن R1 تساوي R2 وهكذا الهدف، + +587 +00:49:00,710 --> 00:49:03,270 +مظبوط؟ أخذنا عنصرين من الـ domain نريد أن يكونوا أصغر + +588 +00:49:03,270 --> 00:49:05,570 +ومتساوي ونريد أن يكونوا متساويين تمامًا، ماهو + +589 +00:49:05,570 --> 00:49:10,770 +معناه أنهم ليسوا متساويين؟ يا R1 أقل من R2 أو R1 + +590 +00:49:10,770 --> 00:49:14,050 +أكبر من R2؟ أثبت أن الاثنين يؤديا لـ Contradiction + +591 +00:49:14,050 --> 00:49:24,780 +الآن أول شيء إذا R1 أقل من R2 ثم .. مجموعات آه .. + +592 +00:49:24,780 --> 00:49:32,320 +لما تكون دائما واضح أن R1 أصغر من R2 فكل عنصر هنا + +593 +00:49:32,320 --> 00:49:36,860 +بيكون هنا ليش؟ لأن اللي أصغر .. X أصغر من R1 بيكون + +594 +00:49:36,860 --> 00:49:40,480 +أصغر من R2 فعلى طول هذه بتكون subset من هذه و + +595 +00:49:40,480 --> 00:49:44,220 +العكس غير صحيح أشمالها؟ + +596 +00:49:46,220 --> 00:49:48,900 +آه طبعا لكن العكس غير صحيح لأن كيف .. كيف هدول + +597 +00:49:48,900 --> 00:49:53,300 +المجموعات خلينا نشوف نعملهم على خط الأعداد هاي خط + +598 +00:49:53,300 --> 00:49:56,260 +الأعداد بس بدنا نأخذ الأعداد النسبية آه هي عندنا + +599 +00:49:56,260 --> 00:50:02,180 +R1 وهي R2 مين المجموعة الأولى F of R1 مين هيها هذه + +600 +00:50:02,180 --> 00:50:05,940 +اللي هي كل أعداد هي عبارة عن مين F of R1 مظبوط + +601 +00:50:05,940 --> 00:50:11,110 +ومين F of R2 الأعداد اللي أصغر من R2 فإذا المجموعة + +602 +00:50:11,110 --> 00:50:15,070 +هذه subset من هذه فلما يكونوا مش متساويين مستحيل + +603 +00:50:15,070 --> 00:50:19,590 +يتساوي المجموعات لذا R1 أكبر بتكون في عنصر موجود + +604 +00:50:19,590 --> 00:50:24,730 +هنا ومش موجود هنا فطبعا بما أن الـ R1 أكبر من R2 + +605 +00:50:24,730 --> 00:50:28,390 +then بقدر ألاقي عدد و ليكل A ممكن أخذ الأشرطة + +606 +00:50:28,390 --> 00:50:37,020 +متوسط وممكن ألاقي عدد A such that الـ A بين الـ R2 + +607 +00:50:37,020 --> 00:50:42,740 +والـ R1 مازالهم مش متساويين وهذه حقيقة كل عددين + +608 +00:50:42,740 --> 00:50:45,520 +نسبيين في A زي مش غير متساويين فيه بين عدد نسبي + +609 +00:50:45,520 --> 00:50:48,640 +تاريخ إيش إيش هو مجموحهم مع اثنين متوسطهم يعني + +610 +00:50:48,640 --> 00:50:51,560 +النص والثلت إيش بينهم اجمعيهم مجموحهم مع اثنين + +611 +00:50:51,560 --> 00:50:56,920 +بيطلع عدد نسبي ف there exist A طبعا في Q فإيش ماله + +612 +00:50:56,920 --> 00:51:01,980 +هذا العدد؟ هو كذا، فهذا بيقول إن الـA وين موجودة؟ + +613 +00:51:01,980 --> 00:51:09,720 +موجودة في الـF of R2 لكن مش موجودة and A غير + +614 +00:51:09,720 --> 00:51:14,180 +موجودة في الـF of R1، مظبوط؟ لأن A برا الـR1 و A، + +615 +00:51:14,180 --> 00:51:16,480 +طبعا هذا يشمل الـcontradiction لأنهم متساويين، + +616 +00:51:16,480 --> 00:51:18,160 +لازم كل عناصرهم متساوية، فكانت contradiction + +617 +00:51:18,160 --> 00:51:22,480 +الثانية زيها، contradiction + +618 +00:51:24,850 --> 00:51:28,070 +الثانية زيها تماما بس العكس آه واضحة لما تكون + +619 +00:51:28,070 --> 00:51:33,810 +الثانية زيها خلينا يمكن أكتبها مش مشكلة لو كانت R1 + +620 +00:51:33,810 --> 00:51:40,210 +أكبر من R2 then there exist a تنتمي لـ الـ Q such + +621 +00:51:40,210 --> 00:51:48,040 +that اللي هو إيش؟ R1 أكبر من A أكبر من R2 هذا إيش + +622 +00:51:48,040 --> 00:51:53,480 +يؤدي إن الـ A موجودة في الـ F of R1 لكن غير موجودة + +623 +00:51:53,480 --> 00:52:01,240 +في الـ F of R2 طبعا Contradiction فبتمش + +624 +00:52:01,240 --> 00:52:05,940 +عندنا الاحتمال إن R1 تساوي R2 وهذا يؤدي إن الـ F is + +625 +00:52:05,940 --> 00:52:11,050 +one to one وهذا يؤدي أن الـ F is one to one فخلاص ما + +626 +00:52:11,050 --> 00:52:15,770 +زال الـ F one to one إذا صارت الـ R تكافئ الـ image + +627 +00:52:15,770 --> 00:52:22,610 +اللي هو sub set من مين من power لـ Q آه فطبعا هذا + +628 +00:52:22,610 --> 00:52:25,790 +بيقول أن الـ cardinality اللي هي الـ C أصغر أو تساوي + +629 +00:52:25,790 --> 00:52:31,170 +الـ cardinality اللي هي 2 أس ألفنا فهد واحد واثنين + +630 +00:52:31,170 --> 00:52:32,670 +بينه البرهان + +631 +00:52:37,920 --> 00:52:44,280 +فطبعا واحد واثنين يؤدي أن 2 أس ألف null تساوي + +632 +00:52:44,280 --> 00:52:52,580 +C فإذن أثبتنا أن الـ power set للـ Q تكافئ R هيك + +633 +00:52:52,580 --> 00:52:55,700 +معناته الـ power set للـ Q اللي هي كاردناتية لاثنين + +634 +00:52:55,700 --> 00:53:00,040 +والـ power set للـ N والـ power set للـ Z تكافئ الـ R + +635 +00:53:00,040 --> 00:53:04,400 +تكافئ الـ R فيهم عدد عناصر تكافئ الـ real numbers + +636 +00:53:04,400 --> 00:53:06,000 +الـ real numbers + +637 +00:53:09,980 --> 00:53:14,640 +طبعا ممكن نتيجة برضه على أنه الـ cardinality لأي + +638 +00:53:14,640 --> 00:53:18,340 +مجموعة أصغر من الـ power بنثبت أن الف null أقل من C + +639 +00:53:18,340 --> 00:53:24,280 +وأيضا ممكن كمثال نثبت أن CC تساوي C بطريقة أخرى + +640 +00:53:24,280 --> 00:53:27,600 +أثبتناها بس الآن باستخدام هذا الكلام بما أن هذا + +641 +00:53:27,600 --> 00:53:33,860 +الكلام صحيح فC ضرب C ممكن أكتبه 2 أس الف null في 2 + +642 +00:53:33,860 --> 00:53:38,260 +أس الف null والنظرية السابقة إيش بتقول ليه؟ مجموعهم + +643 +00:53:38,260 --> 00:53:43,510 +وهذا أثبتنا أنه يساوي الف null هو يساوي C فهذا + +644 +00:53:43,510 --> 00:53:46,690 +المثال بسهولة هذا أثبتناه قبل هيك لكن هذه طريقة + +645 +00:53:46,690 --> 00:53:52,270 +أخرى باستخدام الأساس فممكن أكثر أقدر منه فيمكن هذه + +646 +00:53:52,270 --> 00:53:58,110 +تكون آخر جزء بالنسبة للشرح فهذه نهاية المحاضرة + +647 +00:53:58,110 --> 00:54:03,890 +ونهاية هذا المساق أرجو أن تكون هذه المحاضرات مفيدة + +648 +00:54:03,890 --> 00:54:09,750 +لكم لجميع من يشاهد هذه المحاضرات وبالتوفيق مبارك + +649 +00:54:09,750 --> 00:54:10,170 +الله فيكم diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/gy1w1H0Z7YE_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/gy1w1H0Z7YE_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..a10dcfa91ba65bbb774850797658857cfe9d432f --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/gy1w1H0Z7YE_postprocess.srt @@ -0,0 +1,2596 @@ +1 +00:00:19,670 --> 00:00:27,150 +بسم الله الرحمن الرحيم ان شاء الله هنا هنواصلمع ال + +2 +00:00:27,150 --> 00:00:30,790 +cardinal numbers و ان شاء الله تكون هي آد المحاضرة + +3 +00:00:30,790 --> 00:00:35,270 +الأخيرة فكننا في المحاضرة السابقة توقفنا عند هذا + +4 +00:00:35,270 --> 00:00:39,970 +المثال طبعا بس على السريع كنا احنا عرفنا انه اذا + +5 +00:00:39,970 --> 00:00:44,310 +كان في عندي عدد A cardinal number و عدد B cardinal + +6 +00:00:44,310 --> 00:00:48,410 +number و جبت مجموعة capital A متقابل و capital B + +7 +00:00:48,410 --> 00:00:53,950 +لل B فقلنا A أس B ليست الا ال cardinality لمين لأ + +8 +00:00:53,950 --> 00:00:58,230 +اللي هو A أس Bطبعاً هذا رمز رمز جديد وهو يرمز + +9 +00:00:58,230 --> 00:01:02,610 +لجميع الدوال من B لA من B لA اه فطبعا احنا كنا في + +10 +00:01:02,610 --> 00:01:06,490 +هذا السؤال يمكن بدأنا نناقش فيه وحطينا بعض الخطوط + +11 +00:01:06,490 --> 00:01:11,790 +فطبعا احنا قلنا ان ال A و بتقابل او تساوي خليني + +12 +00:01:11,790 --> 00:01:16,130 +نكتب cardinality لcapital A جيبنا المجموعات هذهو + +13 +00:01:16,130 --> 00:01:20,890 +في عندنا small b تساوي ال cardinality للcapital B + +14 +00:01:20,890 --> 00:01:25,550 +و في عندنا small x cardinality للcapital X و في + +15 +00:01:25,550 --> 00:01:33,080 +عندنا small y cardinality للcapital Yوفي عندنا + +16 +00:01:33,080 --> 00:01:38,840 +معلومات ان ال A أقل أو تساوي B فقولنا هذا يؤدي أو + +17 +00:01:38,840 --> 00:01:43,960 +if and only if طبعا نفس الشيء ان ال A تكافئ B0 + +18 +00:01:43,960 --> 00:01:47,300 +subset من ال B هذا كله كتبناه المرة اللي فاترة بس + +19 +00:01:47,300 --> 00:01:53,400 +بنعيده و X أقل أو تساوي Y معناته ان ال X تكافئ Y0 + +20 +00:01:53,400 --> 00:02:01,170 +subset من ال Y طب ايش المطلوب؟ مطلوب A أس X أقلأو + +21 +00:02:01,170 --> 00:02:06,210 +تساوي بي أس واي if and only if هذا المطلوب أنه الـ + +22 +00:02:06,210 --> 00:02:13,210 +A أس X تكافئ Z subset من بي أس واي هذا هو المطلوب + +23 +00:02:13,210 --> 00:02:18,230 +و جفنا يعني و كنا بندور على الـ Z صح؟ subset صح + +24 +00:02:18,230 --> 00:02:26,500 +يعني بدنا تكافئ subsetو سألنا السؤال التالي هل + +25 +00:02:26,500 --> 00:02:32,480 +بنفع Z ناخدها B أو الـ 0 و Y أو الـ 0؟ قلنا لأ لأن + +26 +00:02:32,480 --> 00:02:38,540 +عناصر الـ B0 أو Y0 هم دوال من Y0 ل B0 بدنا يكونوا + +27 +00:02:38,540 --> 00:02:42,420 +دوال هنا من Y ل B، مانفعش لأنه لو أنا عند الصورة + +28 +00:02:42,420 --> 00:02:50,950 +كالتالي، هيعندي الـ B الـ Yو جواها Y0 وهي عندي الـ + +29 +00:02:50,950 --> 00:02:56,430 +B و subset منها الـ B0 و انا عندي دالة اللى هى + +30 +00:02:56,430 --> 00:03:00,690 +مثلا اللى بنقول F من هان لهان هى عناصر مين اللى هو + +31 +00:03:00,690 --> 00:03:06,450 +B0 is Y0 هل الدالة من Y0 ل B هي دالة من Y ل B لأ + +32 +00:03:06,450 --> 00:03:09,330 +لأن أهم حاجة في الدالة ان ال domain يسوى كل + +33 +00:03:09,330 --> 00:03:13,110 +المجموع الأولى ف domain ال Fبيساوي Y0 بيساويش كل + +34 +00:03:13,110 --> 00:03:16,490 +ال Y فإذا هي ليست دهلة من Y ل B طبعا المجال + +35 +00:03:16,490 --> 00:03:19,450 +المقابل فيش فيه مشكلة كتير لو وثعت وعاء اللي + +36 +00:03:19,450 --> 00:03:22,950 +بيحتوي الصور مابخسرش كتير أو زغرته المهم إنه يحتوي + +37 +00:03:22,950 --> 00:03:25,890 +الصور لكن المشكلة أن ال domain لما يكون فيه جزء + +38 +00:03:25,890 --> 00:03:29,310 +الجزء هنا F تشتغلش هنا مش معرفة هنا فمنفعش تكون + +39 +00:03:29,310 --> 00:03:34,810 +دهلة من Y ل B لكنبايمًا إنه فشلنا في حاجة والاتجاه + +40 +00:03:34,810 --> 00:03:37,910 +التفكير كان اتجاه صحيح لأن هذا هو العلاقات + +41 +00:03:37,910 --> 00:03:40,950 +الموجودة طب هي ما زبطتش مش معناته إنه هي نغلقها + +42 +00:03:40,950 --> 00:03:45,690 +تمامًا بدنا نقترب منها بدنا نقترب منها صحيح الـ B0 + +43 +00:03:45,690 --> 00:03:50,210 +ليس subset لكن تكافئ subset ممكن تكافئ subset هي + +44 +00:03:50,210 --> 00:03:54,550 +مش بالظبط subset لكن تقريبًا تشبه subset منها + +45 +00:03:54,550 --> 00:03:58,010 +تشبهها أو تكافئها فهذا اللي هنعمل هذا اللي هنعمل + +46 +00:03:58,010 --> 00:04:02,770 +آه فطبعًاأول شيء في عيني النظرية أثبتناها في أول + +47 +00:04:02,770 --> 00:04:07,370 +الـ Section بما أن الـ A تكافئ الـ B0 و الـ X + +48 +00:04:07,370 --> 00:04:13,010 +تكافئ الـ Y0 فإذا A أُس X تكافئ B0 أُس Y0، هذا صح، + +49 +00:04:13,010 --> 00:04:17,690 +أه، و أنا بعدين هثبت أن B أُس Y0 تكافئ Z أخرى من + +50 +00:04:17,690 --> 00:04:20,690 +هنا، فحش طل عليها، صحيح هي مش subset لكن تكافئ + +51 +00:04:20,690 --> 00:04:22,770 +subset اللي هي المجموعة اللي احنا بتدور عليها، + +52 +00:04:22,770 --> 00:04:28,250 +فإذا أول شيء أننا بنكمل الحل By theorem + +53 +00:04:30,880 --> 00:04:34,920 +6 6 لأنه احنا .. لش هالنظر اللي قلناها اثبتنا انه + +54 +00:04:34,920 --> 00:04:37,500 +.. انه ال .. ال .. عملية اختيار ال .. ال .. + +55 +00:04:37,500 --> 00:04:41,800 +المجموعات لا يؤثر اه فانا ماعنديه بدي أجيب اللي هو + +56 +00:04:41,800 --> 00:04:45,260 +A أُس B جيبنا A و B طب لو بدلناهم X و Y بيطلع نفس + +57 +00:04:45,260 --> 00:04:47,560 +الجواب فهي نفس القضية ليش؟ لأنه بيكونوا متكافئين + +58 +00:04:47,560 --> 00:04:51,200 +اه فإذا by theorem إيش في عندنا؟ في عندنا ال A أُس + +59 +00:04:51,200 --> 00:04:57,800 +X تكافئ اللي هو إيش؟ B أُس 0 أُس Y 0 هذه نقطةهل + +60 +00:04:57,800 --> 00:05:00,660 +جدتش بده اثبت؟ اه ب .. فإذا ال cardinality بتساوي + +61 +00:05:00,660 --> 00:05:03,240 +ال cardinality الان لو اثبتت ان ال cardinality + +62 +00:05:03,240 --> 00:05:05,780 +اللي هي هذه اصغر او تساوي ال cardinality اللي هي + +63 +00:05:05,780 --> 00:05:12,680 +هذه بكون انتهى فبدا اكتب we will prove بدل ما اثبت + +64 +00:05:12,680 --> 00:05:19,400 +هذه بدي اثبت ان بي اصيزي رو واي زي رو تكافئ Z + +65 +00:05:19,400 --> 00:05:25,180 +subset من ال BYمانفعدش أخدها هي الـ Z بدي أخدها + +66 +00:05:25,180 --> 00:05:30,760 +تكافئ مجموعة Z بدي أخدها تكافئ مجموعة Z تمام فهذه + +67 +00:05:30,760 --> 00:05:35,740 +الخطوة فالسؤال كيف نختار الـ Z طبعا زي ما مرت + +68 +00:05:35,740 --> 00:05:39,520 +علينا نفس الفكرة أكتر من مرة ممكن أريح نفسي بدل ما + +69 +00:05:39,520 --> 00:05:45,130 +أختار الـ Z أخد دالة one to one منالأولى للتانية + +70 +00:05:45,130 --> 00:05:48,250 +وش الـ z بتكون الـ image بتكون الـ image فهنعمل + +71 +00:05:48,250 --> 00:05:54,390 +بهذه الطريقة فهنبدأ نعرف دالة فنكتب هنا هقول له + +72 +00:05:54,390 --> 00:06:01,730 +let بـ psi من وين لوين من بي زيرو أس واي زيرو إلى + +73 +00:06:01,730 --> 00:06:11,370 +بي أس واي بي given by بي given by بي given by بي + +74 +00:06:11,370 --> 00:06:11,710 +given by بي given by بي given by بي given by بي + +75 +00:06:11,710 --> 00:06:12,150 +given by بي given by بي given by بي given by بي + +76 +00:06:12,150 --> 00:06:12,390 +given by بي given by بي given by بي given by بي + +77 +00:06:12,390 --> 00:06:16,710 +given by بي given by بي given bypsi of F فهناعنا + +78 +00:06:16,710 --> 00:06:19,870 +احنا كنا ايش المشكلة ليش ماكناش ناخدها subset لأن + +79 +00:06:19,870 --> 00:06:24,190 +الدالة اللي هنا مابنفعش تكون دالة من Y ل B اه وين + +80 +00:06:24,190 --> 00:06:28,830 +مشكلتها ان ال domain تبعها صغير بدنا نكبره فالان + +81 +00:06:28,830 --> 00:06:32,870 +انا بدي اخد الدالة هذه F اللي هي بتنتمي لل B of 0 + +82 +00:06:32,870 --> 00:06:36,750 +Y 0 واخليها دالة من Y ل B فعندي دالة من subset من + +83 +00:06:36,750 --> 00:06:39,490 +ال Y بدي اخليها دالة على كل ال Y طب هذه الدالة ايش + +84 +00:06:39,490 --> 00:06:41,910 +بدي تكون اي دالة بدي احافظ انها تكون one to one + +85 +00:06:41,910 --> 00:06:44,560 +اصلا هي مش one to oneهو بدي حافظ على أي شيء عندي + +86 +00:06:44,560 --> 00:06:50,770 +قيود؟ لأ بس كل همه انها تتمها دالةفكما قلنا، وين + +87 +00:06:50,770 --> 00:06:54,290 +الـ I تبعها؟ الـ domain تبعها صغير، جسّر معناه، مش + +88 +00:06:54,290 --> 00:06:58,450 +مكافئة، إيش نعمل؟ نمده، نمده، فهنعرفها، آه فالـ + +89 +00:06:58,450 --> 00:07:02,250 +Psi of F دي إيش ده تكون؟ دالة، من وين بتروح؟ دالة + +90 +00:07:02,250 --> 00:07:05,970 +بدل ما هي من Y0 ل B، هيبقى تصير دالة صورتها من Y ل + +91 +00:07:05,970 --> 00:07:09,050 +B، فإذا نعدّي function، آه طبعا، ممكن إحنا نتعود + +92 +00:07:09,050 --> 00:07:12,690 +نكتب Psi و F تساوي، حاجة معينة، لكن إحنا عارفين + +93 +00:07:12,690 --> 00:07:16,510 +إنها G، بدنا نعرفهاالصورة دالة مش جادر أكتبها بشكل + +94 +00:07:16,510 --> 00:07:20,130 +صريح مافيش علاقة واضحة أو قاعدة واضحة بس بتكتبها + +95 +00:07:20,130 --> 00:07:24,050 +بطريقة جديدة الصورة دالة مظبوط عشان أعرف الدالة + +96 +00:07:24,050 --> 00:07:28,130 +إيش بدي تلت حاجات بدي ال domain و ال .. و ال .. و + +97 +00:07:28,130 --> 00:07:30,790 +ال co domain أو اللي هو المجال المقابل و بدي قاعدة + +98 +00:07:30,790 --> 00:07:34,830 +التعريف فانا بدي أعرفها الصورة فإيش let given by F + +99 +00:07:34,830 --> 00:07:39,290 +of X أو Epsilon F اللي هي دالة من وين لوين من Y ل + +100 +00:07:39,290 --> 00:07:45,130 +B definedباي قاعد بعرف الصورة يا أخواتي بنعرف + +101 +00:07:45,130 --> 00:07:48,950 +الصورة هي الصورة دالة دالة من وين لوين؟ من Y ل B + +102 +00:07:48,950 --> 00:07:53,010 +كيف بدأت تكون دالة؟ بدأت أعرفها بـPsi F مش هذي + +103 +00:07:53,010 --> 00:07:58,650 +دالة of X طبعا الرمز شوية مش مقلوف لأن هي دالة + +104 +00:07:58,650 --> 00:08:02,310 +لـPsi تنجل لـF لدالة طب الصورة دالة إذا المعرفة + +105 +00:08:02,310 --> 00:08:07,630 +على X معرفة على X كيف بدنا نعرفها؟ طبعا هي ال + +106 +00:08:07,630 --> 00:08:10,570 +domain letter تبع الصورة بدي أعرف ال NG بدي أكبر + +107 +00:08:10,570 --> 00:08:16,220 +هذهبدل ما كانت الـ F من هان لهان بدي الـ NG من هان + +108 +00:08:16,220 --> 00:08:21,760 +لهان طبعا المنطق ان انا اللي عندي مارمهوش اعتمد + +109 +00:08:21,760 --> 00:08:24,980 +عليه فانا بدي اعرف الـ G اكبر ال domain طيب في ال + +110 +00:08:24,980 --> 00:08:28,560 +domain اللي معرف عليه F خليها معرفة بتام اكمل في + +111 +00:08:28,560 --> 00:08:34,220 +الخارج فحقوله بتساوي F of X إذا كانت ال X في ال Y + +112 +00:08:34,220 --> 00:08:39,200 +Zero تم أعرفها وين لما ال X تكون في ال Y ناقص Y + +113 +00:08:39,200 --> 00:08:44,610 +Zero ماتبقىتبعين؟ قاعد ولا متبعين؟ فمرة تانية، بس + +114 +00:08:44,610 --> 00:08:48,670 +الصقوبة وين؟ أنه أنا باخد دالة بوديها لدالة، + +115 +00:08:48,670 --> 00:08:52,670 +بوديها لدالة، طيب إيش الفرق؟ الدالة اللي بستخل + +116 +00:08:52,670 --> 00:08:55,970 +عليها دمينها صغير، الدالة اللي بتطلع الناتج من + +117 +00:08:55,970 --> 00:08:59,650 +الصورة اللي بتكون دالة دمينها كبيرة شوية، فطبعا + +118 +00:08:59,650 --> 00:09:02,530 +أنا بحافظ على الدالة في الدمين المعطى وبدأ أشوف + +119 +00:09:02,530 --> 00:09:05,610 +كيف أعرفها على الدمين الخارج، كيف نعرفها؟ + +120 +00:09:08,320 --> 00:09:14,440 +X ده identity؟ لأ لأن الـB مش subset وين نوديها؟ + +121 +00:09:14,440 --> 00:09:16,900 +وديها على أي صورة .. أي عنصر في الـB لأنه أنا + +122 +00:09:16,900 --> 00:09:18,440 +مابديش هي اللي هتكون one term و لا one term + +123 +00:09:18,440 --> 00:09:22,740 +مابديها تكون ده بس تم إنه مش معرفة هنا أعرفها أه + +124 +00:09:22,740 --> 00:09:25,740 +مين الدوالي المشهورة؟ فيه طبعا الـidentity ماتظبطش + +125 +00:09:25,740 --> 00:09:29,180 +لأنه إيش؟ هذا العنصر بتمش مش subset لكن مين ده + +126 +00:09:29,180 --> 00:09:32,160 +الأخرى؟ ال constant function ال constant function + +127 +00:09:32,160 --> 00:09:38,740 +فحنعرفها بيه؟ ويش الـB؟ أي عنصر في الـB؟ fourSome + +128 +00:09:38,740 --> 00:09:44,380 +B تنتمي لمين؟ للـ Capital B تكون في الـ B في الـ + +129 +00:09:44,380 --> 00:09:47,660 +B0 بهمنيش حتى لو كانت الصورة السابقة، ليش؟ لأنه مش + +130 +00:09:47,660 --> 00:09:49,620 +معنى تكون one to one أو one to two، بديش ولا إشي، + +131 +00:09:49,620 --> 00:09:53,660 +أي المهم تكون عرفت على ما تبقى، هي كانت معرفة على + +132 +00:09:53,660 --> 00:09:56,500 +جزء من ال domain، أعرفناه على باقي ال domain، + +133 +00:09:56,500 --> 00:10:00,780 +واضح؟ أه، الآن طيب نشوف أن هذا التصميم، هذا + +134 +00:10:00,780 --> 00:10:05,140 +التركيب صح ولا مش صح؟طبعا كل اللي بده يعني الكولة + +135 +00:10:05,140 --> 00:10:08,200 +ده ليهاش بس one to one عشان أخد الـ z هي ال image + +136 +00:10:08,200 --> 00:10:13,540 +و خلصنا نثبت إنها one to one if psi is one to one + +137 +00:10:13,540 --> 00:10:18,720 +نثبت طبعا من وين بده أبدأ عنصرين في ال domain إيش + +138 +00:10:18,720 --> 00:10:22,860 +عناصر ال domain اللي بـ psi دوال من Y0 ل B0 فده + +139 +00:10:22,860 --> 00:10:29,340 +أقوله F1 و F2 تنتمي ل B0 أس Y0 صورهم متساوية such + +140 +00:10:29,340 --> 00:10:38,210 +thatبـ Psi of F1 تساوي بـ Psi of F2 البداية، في حد + +141 +00:10:38,210 --> 00:10:43,050 +عنده مشكلة في البداية؟ كيف نبدأ one to one؟ فأرجو + +142 +00:10:43,050 --> 00:10:48,010 +أن هذه البدايات تكون و احنا في نهاية المساق نعرف + +143 +00:10:48,010 --> 00:10:52,610 +نبدأ صح تمام، إيش مطلوب لو بدي أعمل هامش؟ أنا + +144 +00:10:52,610 --> 00:10:56,740 +بحاول أثبت أن F1 تساوي F2 ولا لأ؟ما هو إيش معنى + +145 +00:10:56,740 --> 00:11:01,340 +one to one؟ خُد عنصرين من المجال صورهم متساوية و + +146 +00:11:01,340 --> 00:11:04,900 +أثبت إنهم العنصرين متساوين صح؟ إيش ميكون العنصرين؟ + +147 +00:11:04,900 --> 00:11:09,480 +هم أرقام، هم دوال، هم مجموعات، أي مكان، الكلام + +148 +00:11:09,480 --> 00:11:12,500 +بشكل عام طيب، إذا نجل السؤال وقت إيش بتكون الدالة + +149 +00:11:12,500 --> 00:11:15,880 +بتساوي الدالة؟ في شرطين الشرط الأول أن تكونوا من + +150 +00:11:15,880 --> 00:11:18,780 +نفس المجموعة لنفس المجموعة تلقلهم نفس المجال لنفس + +151 +00:11:18,780 --> 00:11:23,110 +المجال المقابل وهذا مضمون، من هنالأن ما يعني أن F1 + +152 +00:11:23,110 --> 00:11:28,330 +في B0 وY0 هي ده لا من Y0 ولا B0 و F2 زيها إذا هذا + +153 +00:11:28,330 --> 00:11:31,570 +الشرط الأول اتحقق إيش الشرط التاني صورهم متساوي + +154 +00:11:31,570 --> 00:11:35,250 +على جميع عناصر ال domain أكتبهم مرة واحدة فعشان + +155 +00:11:35,250 --> 00:11:39,330 +أثبت هذا الكلام هذا يكافئ if and only if في عندنا + +156 +00:11:39,330 --> 00:11:44,550 +شرطين في عندنا إنه لازم ال F1والـ F2 يكونوا دوال + +157 +00:11:44,550 --> 00:11:51,530 +من Y0 ل B0 اتنين for all X في ال domain اللي هو Y0 + +158 +00:11:51,530 --> 00:11:57,090 +بدنا F1 of X سوى F2 of X للمرة تالتة او الرابعة او + +159 +00:11:57,090 --> 00:12:02,010 +خلال اخر محاضرتين هذي بوضحها صح؟واضح انه عشان + +160 +00:12:02,010 --> 00:12:05,670 +دالتين اتساووا في شرطين يكونوا من نفس المجال لنفس + +161 +00:12:05,670 --> 00:12:09,350 +المجال المقابل متحقق ولا مش متحقق؟ متحقق لأنه ايش + +162 +00:12:09,350 --> 00:12:13,310 +معناه انهم في الـP of 0 of Y of 0؟ هد معناه هد + +163 +00:12:13,310 --> 00:12:16,490 +المجموعة، هيك تعريفها، مظبوط، مين هد المجموعة؟ هي + +164 +00:12:16,490 --> 00:12:21,350 +كل الدوال اللي من Y of 0 لP of 0، فهد صح، واضح؟ + +165 +00:12:22,410 --> 00:12:26,550 +واضح ولا لأ؟ الشرط التاني، نريد أن يكون على كل + +166 +00:12:26,550 --> 00:12:29,350 +عناصر ال domain الصور متساوية، قيمهم متساوية على + +167 +00:12:29,350 --> 00:12:31,610 +كل ال domain، نريد أن نثبت هذا، هذا أريد أن أثبته، + +168 +00:12:31,610 --> 00:12:33,930 +طب كيف أثبته؟ for all، تريد أن تاخد عناصر في ال + +169 +00:12:33,930 --> 00:12:42,810 +domain، فسأقول له الآن، لت X تنتمي لمن؟ ل Y0بدي + +170 +00:12:42,810 --> 00:12:46,550 +أثبت إن F1 تساوي F2 طبعا زي ما حكينا سابقا هذه + +171 +00:12:46,550 --> 00:12:48,770 +النقطة وصلت إليها ووقفت عليها لإن أنا مش قادر + +172 +00:12:48,770 --> 00:12:51,930 +أحلها كمعادلة بدنا نستخدمها الآن طب هل جيت هدول + +173 +00:12:51,930 --> 00:12:56,870 +الدوال من وين لوين من Y ل B هدول الصور هدول الصور + +174 +00:12:56,870 --> 00:12:59,710 +طيب و ال Y0 subset من Y إذا أنا ممكن أطبقهم ولا + +175 +00:12:59,710 --> 00:13:02,370 +ممكن أطبقهم على ال X بقدر لإن أنا أخدت ال X هنا يا + +176 +00:13:02,370 --> 00:13:05,830 +خوان أخدت ال X هنا جوا ال Y ولا مش جوا جوا ال Y + +177 +00:13:05,830 --> 00:13:08,870 +إذا أنا مقدر أطبق الدالتين هدول فده بيقولني بـPsi + +178 +00:13:08,870 --> 00:13:17,450 +of F1 of Xتساوي بـ Psi F2 of X فحولت لعنصر الآن + +179 +00:13:17,450 --> 00:13:22,330 +بقدر استخدم التعريف ال X وين في ال Y0 إذا إيش + +180 +00:13:22,330 --> 00:13:27,570 +تعريف Psi of X؟ هيها إذا هذا يؤدي إن F1 of X و إيش + +181 +00:13:27,570 --> 00:13:31,710 +تعريفها؟ F2 of X لأن ال X وين في ال Y0 إذا وين شغل + +182 +00:13:31,710 --> 00:13:35,490 +كله فوق واضح؟ أه و هو المطلوب مش هذا كده بتدور + +183 +00:13:35,490 --> 00:13:44,130 +عليه؟ أه إذا ThusF1 تساوي F2 وبالتالي and hence + +184 +00:13:44,130 --> 00:13:49,310 +Psi is one to one فمهم جدا نعرف احنا ايش اللي + +185 +00:13:49,310 --> 00:13:52,570 +بنشتغل فيه و ايش و احنا رايحين و ايش المطلوب دايما + +186 +00:13:52,570 --> 00:13:56,090 +زي ما بنعيد و بنكتر اه فهي دالة one to one ممتاز + +187 +00:13:56,090 --> 00:13:59,730 +ال trick اللي مشهور ما زال دالة one to one و احنا + +188 +00:13:59,730 --> 00:14:04,010 +نشتغل من هال لهان اذا المجال يشاب ايش ما له يكافئ + +189 +00:14:04,010 --> 00:14:09,250 +ال image اه it follows او therefore كله صحthat + +190 +00:14:09,250 --> 00:14:14,790 +المجال اللي هو مين بي أس زيرو بي أس زيرو أس واي أس + +191 +00:14:14,790 --> 00:14:21,190 +زيرو تكافئ ال image بصي بي أس زيرو واي زيرو وال + +192 +00:14:21,190 --> 00:14:26,330 +image وين بيكون subset من المجال المقابل subset من + +193 +00:14:26,330 --> 00:14:28,270 +وين من بي أس واي + +194 +00:14:33,630 --> 00:14:37,670 +فالان نجمع هذا اسمه ناتو ال cardinality أصغر تساوي + +195 +00:14:37,670 --> 00:14:40,850 +ال cardinality و احنا كنا هذي باسمه يكافر اه يكافر + +196 +00:14:40,850 --> 00:14:46,990 +اه it follows او therefore ال + +197 +00:14:46,990 --> 00:14:55,550 +cardinality لل A أُس X تساوي ال cardinality هذه + +198 +00:14:55,550 --> 00:14:59,460 +الملاحظة كتبناها في بداية الشرحمش يقول إن هدول + +199 +00:14:59,460 --> 00:15:02,820 +يكافؤوا هدول فهدول متساويين وهدي إيش بتقول ليه؟ + +200 +00:15:02,820 --> 00:15:08,900 +إنه هدي أصغر أو تساوي ال cardinality لل B أس 1 + +201 +00:15:08,900 --> 00:15:17,300 +وطبعا هذا معناته إن A أس X أقل أو تساوي B أس 1 وهو + +202 +00:15:17,300 --> 00:15:20,760 +المطلوب وهو المطلوب + +203 +00:15:30,770 --> 00:15:37,590 +أي سؤال؟ خلّيني أشوف نظرية نظرية + +204 +00:15:37,590 --> 00:15:43,070 +7 نظرية مألوفة بالنسبالنا إذا بتتعامل مع الأعداد + +205 +00:15:43,070 --> 00:15:47,050 +الحقيقية مثلا فهو بيقول لي هذه النظرية صحيحة برضه + +206 +00:15:47,050 --> 00:15:50,710 +في الcardinal number لما نضرب ونعنى نفس الأساس + +207 +00:15:50,710 --> 00:15:56,030 +بنجمع الأسس فبيقول لي A أس X ضرب A أس Y تساوي A أس + +208 +00:15:56,030 --> 00:15:59,550 +X زائد Y دعونا نشوف كيف بدنا نبرهن هذه النظرية + +209 +00:16:01,910 --> 00:16:09,510 +approved فدي theorem ستة سبعة approved من وين + +210 +00:16:09,510 --> 00:16:13,670 +نبدأ؟ بدنا نحوّل من لغة الcardinal number للغة + +211 +00:16:13,670 --> 00:16:21,390 +المجموعات فهو ياخد مجموعات let capital A capital X + +212 +00:16:21,390 --> 00:16:28,450 +خليكم معايا لو سمحتوا capital Y ب six such that + +213 +00:16:30,430 --> 00:16:36,530 +بينفع اخد اي مجموعات ولا في قيود؟ ايش العمليات + +214 +00:16:36,530 --> 00:16:41,470 +اللي عندي؟ في عمليات أسس وضرب و جمع في تالت عمليات + +215 +00:16:41,470 --> 00:16:47,290 +معايا لأن فيش تقاطع تقاطع مين؟ X و Y لأنه بدي اجمع + +216 +00:16:47,290 --> 00:16:52,850 +X مع Y such that اللي هو X تقاطع ال Y يساوي في هي + +217 +00:16:52,850 --> 00:16:56,190 +واحد طبعا وان كل مجموعة تقابل cardinal number + +218 +00:16:56,190 --> 00:17:01,410 +cardinalityللـ capital A تساوي ايه؟ Cardinality + +219 +00:17:01,410 --> 00:17:06,690 +للـ B تساوي اسمه ايه؟ اسف لل X، مش B، تساوي small + +220 +00:17:06,690 --> 00:17:13,390 +x andCardinality للـ capital Y تساوي small y ممتاز + +221 +00:17:13,390 --> 00:17:17,490 +فأرجو أن هذه الأمور تكون واضحة بالنسبة للتلت + +222 +00:17:17,490 --> 00:17:20,790 +عمليات اللي عرفناها بالنسبة للجامع بس هو اللي بدنا + +223 +00:17:20,790 --> 00:17:23,730 +نتقاطه يساوي file مجموعتين لكن بالضرب وال + +224 +00:17:23,730 --> 00:17:27,050 +exponential أي مجموعات تؤدي الغرض طبعا تحت الشروط + +225 +00:17:27,050 --> 00:17:30,790 +المعروفة فالآن أنا بدي أحول صيغة السؤال بالنسبة + +226 +00:17:30,790 --> 00:17:39,140 +لنا then بالنسبة لنا عنا A أُس Xهي ليس إلا الـ + +227 +00:17:39,140 --> 00:17:46,880 +Cardinality للمجموع A أُس X والـ A أُس Y ليست إلا + +228 +00:17:46,880 --> 00:17:53,020 +Cardinality لـ A أُس Y والـ A أُس X زائد Y ليست + +229 +00:17:53,020 --> 00:17:59,500 +إلا Cardinality لـ A أُس A X إتحاد Yالاتحاد الـ Y + +230 +00:17:59,500 --> 00:18:03,620 +طبعا صارت عشان انطقته حُنفان فأصبح مطلوب ايش؟ بدنا + +231 +00:18:03,620 --> 00:18:07,000 +ضرب هادي مع هادي يعني بدنا الـ Cartesian product + +232 +00:18:07,000 --> 00:18:14,280 +اه .. اه Therefore we + +233 +00:18:14,280 --> 00:18:25,980 +want to prove that ال cardinalityلمن؟ لل A أُس X + +234 +00:18:25,980 --> 00:18:32,640 +كارتيسيان A أُس Y مظبوط لأن هذه ايش ده ده دربها + +235 +00:18:32,640 --> 00:18:35,860 +ده؟ Cardinality للـ Cartesian product يساوي + +236 +00:18:35,860 --> 00:18:42,420 +Cardinality لل A أُس X Union Y هذا المطلوب طبعا + +237 +00:18:42,420 --> 00:18:48,160 +هذا اشماله يكافئ F and only F ايش يكافئ؟ مين معايا + +238 +00:18:48,160 --> 00:18:48,820 +مركز؟ + +239 +00:18:51,530 --> 00:18:55,570 +مظبوط أو مجموعة تكافئ مجموعة فالcardinality بنقول + +240 +00:18:55,570 --> 00:18:58,390 +انه cardinality ل two sets بيسووا بعض if and only + +241 +00:18:58,390 --> 00:19:02,410 +if المجموعتين متكافئتين if and only if بدنا نشتر + +242 +00:19:02,410 --> 00:19:09,290 +على هذا الكلام times A أُس Y تكافئ equibotent لل A + +243 +00:19:09,290 --> 00:19:15,750 +أُس X union A أُس Y فهذا هو المطلوب أي سؤال + +244 +00:19:16,630 --> 00:19:19,230 +فالحقيقة احنا مش هنعمل اصغر من او يساوي اصغر من او + +245 +00:19:19,230 --> 00:19:22,570 +يساوي في هذا المثال، هنعمل bijection مباشرة، فبدنا + +246 +00:19:22,570 --> 00:19:28,930 +نعرف بـPsi من هنا لهنا، تاخد زوج مرتب، لأنه + +247 +00:19:28,930 --> 00:19:33,240 +Cartesian، الـCartesian هنا زوج مرتب من إيش؟من + +248 +00:19:33,240 --> 00:19:37,300 +الدوال دالة الأولى من X ل A والدالة التانية من Y ل + +249 +00:19:37,300 --> 00:19:41,080 +A توديها لدوال عادية مش زوج مرتب من إيهش من + +250 +00:19:41,080 --> 00:19:46,080 +الاتحاد لل إيهش فيمكن نعمل صورة diagram مبسط في + +251 +00:19:46,080 --> 00:19:52,980 +عنا زوج مرتب F of G بدنا نوديه لدالة معينة وليكن H + +252 +00:19:54,290 --> 00:20:00,430 +الـ F ده اللي من وين لوين من X ل A الـ G ده اللي + +253 +00:20:00,430 --> 00:20:06,390 +من وين لوين من Y ل A الصورة Y ده تكون ده اللي من X + +254 +00:20:06,390 --> 00:20:12,490 +union ال Y لل A فهي الصورة فخليني أبدأ أكتب و + +255 +00:20:12,490 --> 00:20:20,010 +انفكر مع بعض لتب ساية from A أُس X across A أُس Y + +256 +00:20:20,010 --> 00:20:31,250 +إلى A أُس X union ال Ybe given by إبصي of f g + +257 +00:20:31,250 --> 00:20:36,550 +تساوي في + +258 +00:20:36,550 --> 00:20:42,250 +حد عنده فكرة أيه عندي دالتين من x ل a و من y ل a + +259 +00:20:42,250 --> 00:20:50,450 +ليش فيهم bijection لأ مافيش bijection + +260 +00:20:52,010 --> 00:20:59,230 +مافيش ايه؟ Byjection فانا شوف مرتان خلينا نفكر مع + +261 +00:20:59,230 --> 00:20:59,610 +بعض + +262 +00:21:02,470 --> 00:21:06,790 +مش ضروري، هل كل الدوال اللي بتروح للـR بتدي نفس + +263 +00:21:06,790 --> 00:21:10,810 +الصورة؟ فالـSin دالة من R لـR والـCos دالة من R + +264 +00:21:10,810 --> 00:21:13,970 +لـR والدالة التربيهية دالة من R لـR، مش ضروري تودي + +265 +00:21:13,970 --> 00:21:16,850 +نفس الصورة، بتودي على نفس الواعاء، على نفس + +266 +00:21:16,850 --> 00:21:20,750 +الواعاء، طب مرة تنقل، ركزوا معايا، هي عندي دالتين، + +267 +00:21:20,750 --> 00:21:27,430 +من X لـA ومن Y لـA، والمجالين تقاطعهم في، بينفع + +268 +00:21:27,430 --> 00:21:32,580 +أعمل، مين بيخلي ال domain يتحد؟اتحاد الدول اه + +269 +00:21:32,580 --> 00:21:36,420 +اتحاد الدول فدي هسميها F Union G + +270 +00:21:39,390 --> 00:21:44,490 +لأ، بس دي الشرط عشان تكافؤ، بس عشان أقعد أعمل .. + +271 +00:21:44,490 --> 00:21:47,510 +وكتش بيكون اتحاد الدالتين دالة إذا كانوا في + +272 +00:21:47,510 --> 00:21:50,630 +التقاطع متساوين، طبعا التقاطع في ال domain بس، اه + +273 +00:21:50,630 --> 00:21:53,930 +في انت .. انت جبت نظريتين مع بعض، في نظرية بتقول + +274 +00:21:53,930 --> 00:21:57,830 +وكتش اتحاد الدالتين بيكون دالة إذا كانوا في تقاطع + +275 +00:21:57,830 --> 00:22:00,650 +المجالين متساوين، إذا كانوا في تقاطع فيه، بتحقق، + +276 +00:22:00,650 --> 00:22:03,930 +لأنه إيش؟ مافيشش وعد، فإذا الجملة الشرطية دايما صح + +277 +00:22:04,180 --> 00:22:08,980 +لكن هناك بيقول المجالين المتقاطعون فيه والمجالين + +278 +00:22:08,980 --> 00:22:11,600 +المقابلين المتقاطعون فيه عشان أضمن ان الاتحاد تم + +279 +00:22:11,600 --> 00:22:15,840 +بيجيكشن هذه مختلفة تمام فهذه نشوف ان هذا الكلام + +280 +00:22:15,840 --> 00:22:25,520 +صحيح نشوف ان هذا الكلام صحيح ممتاز + +281 +00:22:25,520 --> 00:22:31,630 +بدنا نثبت ان هذه one to one and unto واحدبصي is + +282 +00:22:31,630 --> 00:22:34,610 +one to one طبعا واضح ان هذا الكلام صحيح ليش هي + +283 +00:22:34,610 --> 00:22:37,450 +باخد دالتين فالاتحاد بيصير دالة لإنه تقاطع فيا على + +284 +00:22:37,450 --> 00:22:41,470 +طول بيصير دالة من وين لوين من ايش H فعلا بتساوي F + +285 +00:22:41,470 --> 00:22:45,370 +Union G بتكون دالة من X Union Y لنفس ال A لإن كلهم + +286 +00:22:45,370 --> 00:22:50,690 +بيودوا على ال A اه تمام البداية المعروفة بدنا ناخد + +287 +00:22:50,690 --> 00:22:55,170 +عنصرين من ال domain ايش العنصرين في ال domainأسواج + +288 +00:22:55,170 --> 00:23:05,930 +مرتبة يعني F1 G1 F2 G2 let F1 G1 and F2 G2 تنتمي + +289 +00:23:05,930 --> 00:23:18,470 +لمين لل A أُس X times و A A أُس Y تمام + +290 +00:23:18,470 --> 00:23:19,970 +such that + +291 +00:23:22,920 --> 00:23:33,830 +بـ Psi F1 G1 تساوي بـ Psi F2 G2ما هو المطلوب؟ ان + +292 +00:23:33,830 --> 00:23:38,690 +الزوج المرتب يساوي الزوج المرتب يعني بدي F1 تساوي + +293 +00:23:38,690 --> 00:23:43,350 +F2 و بدي G1 تساوي G2 هدول كلهم دوال و هدول كلهم + +294 +00:23:43,350 --> 00:23:48,130 +دوال طبعا كمل التعريف هذا ايش معناته؟ F1 union G1 + +295 +00:23:48,130 --> 00:23:55,010 +تساوي F2 union G2 مطلوب بدي F1 تساوي F2 هذا مطلوب + +296 +00:23:55,010 --> 00:24:00,370 +بدي G1 تساوي G2نفس الفكرة تتكرر معنا يمكن ليش + +297 +00:24:00,370 --> 00:24:04,250 +لتالت أو رابع مرة عشان أساوي الدول يتساوي بدي + +298 +00:24:04,250 --> 00:24:07,930 +شرطين يكون لهم نفس المجال ونفس المجال المقابل + +299 +00:24:07,930 --> 00:24:11,610 +وبيدي صورهم تتساوي على كل عناصر الدمين المشترك + +300 +00:24:11,610 --> 00:24:14,590 +المتساوي طيب نشوف فاحنا عندنا الـ Agents اللي توي + +301 +00:24:14,590 --> 00:24:20,870 +اللي كنا نتبقه مرتين أولا على F1 و F2 F1 و F2 من + +302 +00:24:20,870 --> 00:24:25,060 +وين بيكونوا؟من A أُس X إحداه في أول إذاً أول شرط + +303 +00:24:25,060 --> 00:24:28,360 +متحقق دائماً والـ G1 و G2 من وين بيكونوا؟ من A أُس + +304 +00:24:28,360 --> 00:24:30,960 +Y إذاً أول شرط إنهم يلهم نفس ال domain مين + +305 +00:24:30,960 --> 00:24:34,080 +domainهم المشترك لل F؟ X ومين domainهم المشترك لل + +306 +00:24:34,080 --> 00:24:39,400 +G؟ Y المجال المقابل برضه A تمام الشرط التاني بنا + +307 +00:24:39,400 --> 00:24:42,820 +نثبتهم واحدة واحدة بنا نثبت إنه لكل عناصر ال + +308 +00:24:42,820 --> 00:24:46,900 +domain الأول X F1 تسوي F2 ولكل عناصر ال domain + +309 +00:24:46,900 --> 00:24:49,660 +التاني Y G1 تسوي G2 فنبدأ + +310 +00:24:52,330 --> 00:25:01,410 +let X تنتمي للـ Capital X ممتاز ايش تعريف ان هدول + +311 +00:25:01,410 --> 00:25:06,150 +اتحاد كيف تعريف الاتحاد متعددة القاعدة ممتاز او + +312 +00:25:06,150 --> 00:25:10,070 +كيف تعريفها هي بتكون F إذا ال X في domain ال F و + +313 +00:25:10,070 --> 00:25:14,270 +بتكون G إذا كانت ال X في domain ال G فطبعا بتستخدم + +314 +00:25:14,270 --> 00:25:16,430 +القاعدة ده اللي دايما قلنا بنحطها بنقدرش نحلها + +315 +00:25:16,430 --> 00:25:25,410 +بنوقفها شوية فهذا يؤدي thenF1 union G1 of X تساوي + +316 +00:25:25,410 --> 00:25:31,270 +F2 union G2 of X أذكركم التعريف تبع الـH هذا خلينا + +317 +00:25:31,270 --> 00:25:35,770 +نكتبه هنا عشان + +318 +00:25:35,770 --> 00:25:40,450 +بس تتابعوا ما أحب أحكي شفوي أحسن يكون قدامنا و + +319 +00:25:40,450 --> 00:25:42,870 +طبعا بدي أكتب الكياب بالـH بصغرها العامة هل جيت إن + +320 +00:25:42,870 --> 00:25:49,860 +احنا H تساوي F union Gأه فكان إن الـH of X إذا + +321 +00:25:49,860 --> 00:25:55,700 +بترجع للتعريف أو للنظرية بتساوي F of X إذا الـX في + +322 +00:25:55,700 --> 00:26:00,740 +capital X اللي هو domain الـF وتساوي + +323 +00:26:00,740 --> 00:26:06,530 +G of X إذا الـX في الـY اللي هو maindomain الـ G + +324 +00:26:06,530 --> 00:26:10,770 +عشان هيك قولنا متعددة القاعدة إذا بتتذكر تمام فأنا + +325 +00:26:10,770 --> 00:26:15,070 +وصلت لها هنا ال X وين في ال capital X إذا ناشت + +326 +00:26:15,070 --> 00:26:21,330 +عارف الاتحاد F فهذا يؤدي إنه F1 of X تساوي F2 of X + +327 +00:26:21,330 --> 00:26:26,970 +بعيد كمان مرة هلجيت أنا هاي هادي إتش وهادي إتش بده + +328 +00:26:26,970 --> 00:26:32,050 +أشوف ال X وين في ال capital X اللي هو domain من ال + +329 +00:26:32,050 --> 00:26:38,120 +F F1 و F2 إذا وين هي ده و ده و دهوبتابعين واضحة + +330 +00:26:38,120 --> 00:26:44,140 +اذا خلاص اثبت ان F1 تسوى F2 اذا thus F1 تسوى F2 + +331 +00:26:44,140 --> 00:26:49,900 +هاي الجزء الاول اه لان ناخد عنصر وين في ال Y عشان + +332 +00:26:49,900 --> 00:26:57,160 +اثبت G1 تسوى G2 اه thenبنفس الطريقة F1 union G1 of + +333 +00:26:57,160 --> 00:27:03,220 +X تساوي F2 union G2 of X ولمّا الـ X تكون في الـ Y + +334 +00:27:03,220 --> 00:27:08,540 +إيش بيكون التعريف؟ G فده يؤدي إنه G1 of X تساوي G2 + +335 +00:27:08,540 --> 00:27:18,660 +of X Thus G1 تساوي G2 فالآن Therefore F1 + +336 +00:27:18,660 --> 00:27:28,260 +G1تساوي F2G2 وبالتالي and hence if Psi is one to + +337 +00:27:28,260 --> 00:27:34,200 +one أي سؤال فأرجو أنه هذه المهارة اللي اتكررت أكتر + +338 +00:27:34,200 --> 00:27:37,820 +من مرة كيف نتعامل لما نثبت دالة تساوي دالة وهذه + +339 +00:27:37,820 --> 00:27:41,540 +كانت عندنا نظرية أساسية نظرية تلاتة سبعة في اللي + +340 +00:27:41,540 --> 00:27:49,660 +هو chapter تلاتة نشوف ال onto الآن if Psi is onto + +341 +00:27:51,840 --> 00:27:56,140 +فحناخد عنصر من المجال المقابل اللي هو نسميه H وين + +342 +00:27:56,140 --> 00:28:03,680 +تنتمي لل A أُس X Union ال Y ونعمل الهامش تبعنا هاي + +343 +00:28:03,680 --> 00:28:08,460 +التعريفة تمام فاحنا + +344 +00:28:10,690 --> 00:28:14,510 +مشيين على نفس النهج لكن التفاصيل بتختلف نفس + +345 +00:28:14,510 --> 00:28:17,850 +البداية و نفس النهاية التفاصيل بتختلف احنا عايش + +346 +00:28:17,850 --> 00:28:23,650 +بندور بدنا الـH تساوي بـPsi of FG for some F of G + +347 +00:28:23,650 --> 00:28:28,370 +وين في الـCartesian لأن هو عديدها اللي من A أُس X + +348 +00:28:28,370 --> 00:28:32,730 +across A أُس Y فبندور على F والـG طب بعدين ايش + +349 +00:28:32,730 --> 00:28:40,010 +تعريفها؟ F union الـGF union الـG فالسؤال كيف + +350 +00:28:40,010 --> 00:28:46,370 +اختار الـF والـG كيف اختار الـF والـG المفتاح هنا + +351 +00:28:46,370 --> 00:28:54,110 +المفتاح هنا ايش الصورة الـH معرفة على الاتحاد على + +352 +00:28:54,110 --> 00:28:57,950 +X وY بده خليها اخد ايش لان مش بده اكبر ال domain + +353 +00:28:57,950 --> 00:29:01,090 +بده ازاغره بده اقسم نصين ال domainبدي اقسم ال + +354 +00:29:01,090 --> 00:29:04,890 +domain نصين اخلي النص الاول اللي هو X اعرف عليه F + +355 +00:29:04,890 --> 00:29:10,770 +والنص التاني اعرف عليه Y هذا ايش بيسموهrestriction + +356 +00:29:10,770 --> 00:29:15,290 +تقييد لما نظغر ال domains مرت علينا كمثال في ال + +357 +00:29:15,290 --> 00:29:18,890 +relations طبعا لما بدي أكبر ال domain بيسموها + +358 +00:29:18,890 --> 00:29:23,430 +extension تمديد لما بدي أعمل إيش بقيد بعمل تقييد + +359 +00:29:23,430 --> 00:29:26,450 +فانا دالة معرفة على مجموعة كبيرة بدي أخليها على + +360 +00:29:26,450 --> 00:29:29,750 +جزء منها فال domain عند مين ال domain ال domain + +361 +00:29:29,750 --> 00:29:35,290 +تبع هذه من وين لوين domain ال H من X union Y إلى + +362 +00:29:35,290 --> 00:29:42,220 +ال A ال F وين domainها بدي Fمن X لـ A و بدي جي + +363 +00:29:42,220 --> 00:29:46,380 +بدور عليهم من Y ل A فكيش أعملها أخد restriction + +364 +00:29:46,380 --> 00:29:51,660 +للـ H أخد الـ H معرفة على الإتحاد هي الصورة الـ H + +365 +00:29:51,660 --> 00:29:54,160 +معرفة على الإتحاد هم disjoint طبعا خلينا ناخدهم + +366 +00:29:54,160 --> 00:29:58,940 +disjoint فهذه X وهذه Y الـ H معرفة على الكل الجزء + +367 +00:29:58,940 --> 00:30:02,700 +هذا هعرف منه ده الـ F والجزء اللي هعرف عليه ده + +368 +00:30:02,700 --> 00:30:08,120 +لمين جي فده اللي هنعمله فهنقوله الآن andفمش دايما + +369 +00:30:08,120 --> 00:30:11,120 +بتكون معادلة لو بنحلها في أحيان الكتاب بتكون تعمق + +370 +00:30:11,120 --> 00:30:16,580 +و نفهم هقول له let F تساوي H restricted to X + +371 +00:30:16,580 --> 00:30:24,080 +الرمزة ده اللي استخدمناها and G تساوي H restricted + +372 +00:30:24,080 --> 00:30:28,440 +to Y يعني الـ F المعرف على نص الدمين الأول و الـ G + +373 +00:30:28,440 --> 00:30:34,920 +الـ H معرف على نص الدمين التالي then طبعا الـ F + +374 +00:30:36,540 --> 00:30:40,400 +تنتمي لمين؟ هي معرفة بس على الـ X و من أين صورها؟ + +375 +00:30:40,400 --> 00:30:45,120 +كله في الـ A لأن الـ X صورها في الـ A and الـ G أو + +376 +00:30:45,120 --> 00:30:51,760 +غلطولة أخد الزوج المرتب بدل مكتوب مرتينفـ FG تنتمي + +377 +00:30:51,760 --> 00:30:59,260 +للـ A أُس X times A أُس Y هذه دالة بس من X معرفة + +378 +00:30:59,260 --> 00:31:02,400 +بتروح للـ A لأن الـ H بالـ A و هذه دالة من Y لـ A + +379 +00:31:02,400 --> 00:31:08,060 +and هي الشرط الأول الشرط التاني بـ Psi of FG إيش + +380 +00:31:08,060 --> 00:31:10,260 +بيساوي F Union G + +381 +00:31:13,160 --> 00:31:16,260 +لأ انا بدور عليهم دايما احنا بناخد عنصر في المجال + +382 +00:31:16,260 --> 00:31:19,920 +المقابل وبدنا نقول هو صورة مين من ال domain + +383 +00:31:19,920 --> 00:31:23,440 +فبختارهم زي ما قولنا يقول Y تساوي F of X بنحل ال X + +384 +00:31:23,440 --> 00:31:27,320 +بدلالة ال Y فالان ال H معطية انا بديتها H مطلوب + +385 +00:31:27,320 --> 00:31:31,620 +ادور على F of G جبتهم بدلالة ال H صح؟ اه بس طبعا + +386 +00:31:31,620 --> 00:31:35,960 +مش معادلة مش أرقام لأنفهل هذا الكلام فعلًا هذا + +387 +00:31:35,960 --> 00:31:40,600 +بيسوي H؟ نعم، لو طلعنا على التعريف، إيش معناه أن H + +388 +00:31:40,600 --> 00:31:43,660 +تسوي الاتحاد؟ هي بيسوي F X لما X تمهي X، إذاً هي + +389 +00:31:43,660 --> 00:31:45,220 +فعلاً F، هي ال restriction، هذا معناه ال + +390 +00:31:45,220 --> 00:31:47,960 +restriction، إنه جسمتها نصين، جسمت ال domain، + +391 +00:31:47,960 --> 00:31:51,700 +ومتعددة القاعدة في جزء على ال X المعرفة F، هذا + +392 +00:31:51,700 --> 00:31:54,720 +القاعدة الأولى، وعلى ال Y معرفة G، القاعدة + +393 +00:31:54,720 --> 00:32:01,480 +التانية، فدي ليست إلا H، طبقًا للتعريف، ففعلاً + +394 +00:32:01,480 --> 00:32:03,260 +الدالة بـPsi Onto + +395 +00:32:07,480 --> 00:32:12,400 +طبعاً هذه باستعمخ لمفهوم الاتحاد الـ Psi is onto + +396 +00:32:12,400 --> 00:32:19,840 +طبعاً 1 و 2 بيخلص البرهان implies A أُس X times A + +397 +00:32:19,840 --> 00:32:27,220 +أُس Y تكافئ A أُس X union Y وبالتالي A أُس X في A + +398 +00:32:27,220 --> 00:32:33,720 +أُس Y تساوي A أُس X زائد 1 وهو المطلوب أي سؤال + +399 +00:32:41,970 --> 00:32:46,890 +طبعاً لديق الوقت ممكن نمر على بعض النظريات بس سريع + +400 +00:32:46,890 --> 00:32:51,290 +وممكن نثبت بس حاجة أخرى لأنها يمكن أهم طبعا خواص + +401 +00:32:51,290 --> 00:32:55,490 +الأسس معروف طبعا قلنا لما نضرب الأساس لنفس الأساس + +402 +00:32:55,490 --> 00:32:59,090 +فنجمع الأسس أيضا لو رفعنا مقدار ال أس ورفعناه + +403 +00:32:59,090 --> 00:33:02,470 +لكمان أس فنضرب الأسس موجودة هذه النظرية مش هثبتها + +404 +00:33:02,470 --> 00:33:09,200 +مش وقت أيضا في نظرية أخرىلو بدّي انا عندي حاصل ضرب + +405 +00:33:09,200 --> 00:33:13,380 +ده عددين و رفعتلهم أس بقدر أوزّي الأس على العددين + +406 +00:33:13,380 --> 00:33:16,720 +فهي A أس X B أس X هذه كل الخواص للـExperimental + +407 +00:33:16,720 --> 00:33:19,300 +الموجودة في الـReal numbers طامعا صحيح على + +408 +00:33:19,300 --> 00:33:25,560 +الcardinal number فنظرية 6 8 و 6 9 مش هبرهنهم فيما + +409 +00:33:25,560 --> 00:33:28,240 +تبقى هبرهن نظرية 16 + +410 +00:33:31,920 --> 00:33:35,840 +بقول 2 أُس ألف null تساوي C ألف null اللي هي + +411 +00:33:35,840 --> 00:33:38,320 +الcardinality لـnatural number أو للـdenominable + +412 +00:33:38,320 --> 00:33:41,340 +sets والـC هي الcardinality للـreal numbers أو أي + +413 +00:33:41,340 --> 00:33:44,520 +مجموعة كافية مش للـnon-denominable مش كلهم واحد + +414 +00:33:44,520 --> 00:33:46,740 +الـdenominable كلهم متكافئين لكن الـnon + +415 +00:33:46,740 --> 00:33:49,780 +-denominable مش كلهم متكافئين في مجموعات متعددة + +416 +00:33:49,780 --> 00:33:57,440 +خلّيني أحاول أنبرهن هذه النظرية لأنه جيد معلومة + +417 +00:33:57,440 --> 00:34:01,160 +أتوقع أنها أهم من السابق وفكرة البرهانة ممكن تكون + +418 +00:34:01,160 --> 00:34:05,620 +أهمطبعاً أنا بدأ أجيب المجموعات و أبدأ أشتغل الـ + +419 +00:34:05,620 --> 00:34:09,680 +proof طبعاً + +420 +00:34:09,680 --> 00:34:13,720 +بدنا مجموعة من عنصرين خليها ناخد الـ 01 و بدنا + +421 +00:34:13,720 --> 00:34:16,640 +مجموعة تكون كاردناتية لألف null في أكتر من + +422 +00:34:16,640 --> 00:34:19,780 +المجموعة في الـ N و في الـ Z و في الـ Q و الحقيقة + +423 +00:34:19,780 --> 00:34:22,240 +يمكن نحتاج حياتنا أن نتنقل من واحدة لواحدة زي ما + +424 +00:34:22,240 --> 00:34:26,000 +نشوف و الـ C هي كاردناتية لـ real number و لأي + +425 +00:34:26,000 --> 00:34:29,080 +فترة مفتوحة 01 على سبيل المثال المشهور و هكذا + +426 +00:34:29,080 --> 00:34:35,090 +فبدنا نشوف إيش المناسبفي الغالب مع الـ C بقدرش + +427 +00:34:35,090 --> 00:34:38,690 +أعمل تساوي بالظبط، هنعمل أصغر من أو يساوي و أصغر + +428 +00:34:38,690 --> 00:34:44,050 +من أو يساوي، فطبعا احنا خلينا نبدأ اللي هو بهذا + +429 +00:34:44,050 --> 00:34:49,710 +الشكل، فاحنا عندنا 2 أس ألف null تساوي C، هذا + +430 +00:34:49,710 --> 00:34:54,370 +الكلام if and only if، 2 أس ألف null أقل أو تساوي + +431 +00:34:54,370 --> 00:34:58,110 +C and C أقل أو تساوي 2 أس ألف null، هنعمل بهذا + +432 +00:34:58,110 --> 00:35:02,280 +الشكل يا أخوانهنشتغل بيه أقل من أو يساوي مش صعب ان + +433 +00:35:02,280 --> 00:35:06,200 +نجيب bijection بين المجموعات المناسبة فهنعمل بهذا + +434 +00:35:06,200 --> 00:35:11,560 +الشكل فطبعا هبدأ بالأولى + +435 +00:35:11,560 --> 00:35:19,800 +اثنين أسالف null واحد أقل أو تساوي C اتوقع احنا + +436 +00:35:19,800 --> 00:35:28,760 +هنمشي بهذا الشكل هو الشكل الأسهل الأول تمام + +437 +00:35:29,990 --> 00:35:33,590 +2 ألف null أقل ألف سوى C ممتاز نبدأ بهذا هذا يمكن + +438 +00:35:33,590 --> 00:35:38,390 +يكون أوضح فهأخد مجموعات الآن هحوله بلغة المجموعات + +439 +00:35:38,390 --> 00:35:41,590 +let + +440 +00:35:41,590 --> 00:35:48,650 +A تساوي مجموعة Zero واحد ليش ال coordinate لها + +441 +00:35:48,650 --> 00:35:55,350 +اتنين ومقابل الالف null أشهر شيء أخد ال N طبعاً + +442 +00:35:55,350 --> 00:36:05,480 +and B تساوي andB تساوي N و هاخد برضه مقابل الـ CR + +443 +00:36:05,480 --> 00:36:08,680 +اه + +444 +00:36:08,680 --> 00:36:15,820 +طبعاً then بالنسبة لنا اتنين ألف null تساوي ال + +445 +00:36:15,820 --> 00:36:24,570 +cardinality لمن لل A أسبيواللي هي إيش A أُس N والـ + +446 +00:36:24,570 --> 00:36:31,610 +C هنعملها إنها R أو 01 هأخدها خلّيني أقول هنا بي و + +447 +00:36:31,610 --> 00:36:39,210 +مجموعة C تساوي 01 and cardinality + +448 +00:36:39,210 --> 00:36:48,330 +ل .. اللي هو أو الـ C تساوي cardinality للـ C لل + +449 +00:36:48,330 --> 00:36:57,750 +capital C منتبهعشان أثبت أن ألف نل أصغر أو تساوي + +450 +00:36:57,750 --> 00:37:03,230 +الـC هثبت أن هذه المجموعة تكافئ subset من الـC We + +451 +00:37:03,230 --> 00:37:16,570 +will prove that A أُس B تكافئ subset Z من الـCهذا + +452 +00:37:16,570 --> 00:37:21,050 +اللي هنعمل طبعا كالعادة بدل ما اخد Z هاخد دالة one + +453 +00:37:21,050 --> 00:37:28,350 +to one اه فهعرف دالة هاخدها image let F من A أس بي + +454 +00:37:28,350 --> 00:37:39,430 +إلى C بي given by سميتها F عشان نرجع للسابق ايش + +455 +00:37:39,430 --> 00:37:45,090 +عناصرها؟ عناصر اه لأ مش F ده بصير بصير + +456 +00:37:47,880 --> 00:37:53,400 +لأن عناصرها دوال انا خلينا نعمل الصورة تبعتنا عشان + +457 +00:37:53,400 --> 00:37:59,140 +نفكر صح ايش عناصرها اللي هان؟ دوال F من وين لوين + +458 +00:37:59,140 --> 00:38:05,760 +من B إلى A وال B هي مين؟ هي ال N وال A هي مين؟ 01 + +459 +00:38:05,760 --> 00:38:11,120 +تمامبدي اودّيها لوين؟ بدي اودّيها لـ C إيش + +460 +00:38:11,120 --> 00:38:16,080 +عناصرها؟ من 01 يعني Zero Point، X1، X2 و هكذا + +461 +00:38:16,080 --> 00:38:19,540 +متعودة جاب لك شفناها عشان ذلك احنا زغرناها شوية + +462 +00:38:19,540 --> 00:38:25,480 +فبدنا دالة تروح لعدد حقيقي بين الصفر وبين الواحد + +463 +00:38:25,480 --> 00:38:30,160 +مين عنده اقتراح فبصيف + +464 +00:38:30,160 --> 00:38:37,020 +F بدي تسوي عدد كيه بدي اكتبه؟ Zero Pointأف اف اي + +465 +00:38:37,020 --> 00:38:38,580 +اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي + +466 +00:38:38,580 --> 00:38:45,540 +اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي + +467 +00:38:45,540 --> 00:38:49,520 +اي اي اي اي اي اي اي اي اي + +468 +00:38:49,520 --> 00:38:50,060 +اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي + +469 +00:38:50,060 --> 00:38:50,880 +اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي + +470 +00:38:50,880 --> 00:38:53,140 +اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي + +471 +00:38:53,140 --> 00:38:54,620 +اي اي اي اي اي اي اي اي اي اي اي اي اي اي اي + +472 +00:39:04,800 --> 00:39:09,740 +لأ مرة تانية فانا هي عندي الدالة F ال F هذه معرفة + +473 +00:39:09,740 --> 00:39:14,520 +على ال N كيف تاخد يعني ال F ايش بتاخد فال F معرفة + +474 +00:39:14,520 --> 00:39:18,780 +F في واحد و انت تنتمي لل A F في التانية تنتمي لل A + +475 +00:39:18,780 --> 00:39:22,880 +و هكذا فهم يا صفر يا واحد فانا بدي أخليهم هدول ال + +476 +00:39:22,880 --> 00:39:27,220 +F يتعرف عدد حقيقي ايش عملتم؟ خناد الصور عملتم خناد + +477 +00:39:27,220 --> 00:39:30,020 +كل الصور صورة الواحد الخانة الأولى صورة التانية + +478 +00:39:30,020 --> 00:39:31,420 +الخانة التانية و هكذا + +479 +00:39:34,510 --> 00:39:37,870 +أه طبعا مش مشكلة في آية دي بيكون عدد بيكون عدد + +480 +00:39:37,870 --> 00:39:40,910 +حقيقي اه فنثبتها بس one to one بدناياها بس + +481 +00:39:40,910 --> 00:39:44,410 +بدناياها تكون one to one لإن و أحنا إيش بدنا ندور + +482 +00:39:44,410 --> 00:39:48,730 +على إيش على Z subset و أحنا إيش هناخدها ال image + +483 +00:39:48,730 --> 00:39:51,330 +بس إذا one to one ناخدها ال image فده اللي هادي + +484 +00:39:51,330 --> 00:39:54,810 +one to one بدنا نسترجع بعض الأفكار نشوف إن ال size + +485 +00:39:54,810 --> 00:40:03,420 +one to one نثبتlet F1 و F2 تنتمي لل domain اللي هو + +486 +00:40:03,420 --> 00:40:15,240 +main بA أُس B such that بـ Psi F1 تساوي بـ Psi F2 + +487 +00:40:15,240 --> 00:40:17,080 +ممتاز + +488 +00:40:18,830 --> 00:40:23,990 +اه ايش هذا يقدي بالتعريف zero point of واحد of + +489 +00:40:23,990 --> 00:40:29,610 +واحد of واحد of اتنين and so on يساوي zero point + +490 +00:40:29,610 --> 00:40:37,390 +of اتنين الواحد of اتنين الاتنين and so on تمام؟ + +491 +00:40:38,980 --> 00:40:41,400 +ممتاز فالـ Memorized Form بيقول اللي لازم كل + +492 +00:40:41,400 --> 00:40:45,540 +خاناتها تتطابع فهذا بيقول لي انه بيكتبهم مرة واحدة + +493 +00:40:45,540 --> 00:40:51,100 +اه ممكن اقول F1 of N اللي هو واحد اتنين for all + +494 +00:40:51,100 --> 00:40:53,480 +and اكتبه بيقول اكتبه اه واضح؟ كل خانة ده تساوي + +495 +00:40:53,480 --> 00:40:57,040 +خانة ولا اوضح؟ بيبقى اختصرها فيا عزيزي لازم تكون + +496 +00:40:57,040 --> 00:41:05,230 +F1 تساوي F2 of 1F1 of N تساوي F2 of N كل خانة + +497 +00:41:05,230 --> 00:41:09,530 +تساوي الخانة المقابلة وها كذا بمعنى آخر F1 of N + +498 +00:41:09,530 --> 00:41:15,830 +تساوي F2 of N for all N تنتمي للـ N صح؟ لأن كل + +499 +00:41:15,830 --> 00:41:21,710 +الخنات طيب أنا عايش بدور كنت أن F1 تساوي F2 صح؟ + +500 +00:41:21,710 --> 00:41:26,930 +سؤال الرئيس اللي اتكرر عدة مرات أعيد القصة من + +501 +00:41:26,930 --> 00:41:33,050 +بدايةأخدنا عنصرين من ال domain دوالة صورهم + +502 +00:41:33,050 --> 00:41:35,510 +متساوية، إيش مكتوب تثبت العنصرين متساويين؟ F1 + +503 +00:41:35,510 --> 00:41:38,090 +تساوي F2، ده اللي تاني، عشان يكونوا متساويين، + +504 +00:41:38,090 --> 00:41:41,430 +يبقوا يكونوا من نفس المجموعة لنفس المجموعة، صح تم + +505 +00:41:41,430 --> 00:41:44,190 +صورهم متساوي على كل ال domain، مين ال domain هم؟ + +506 +00:41:44,190 --> 00:41:47,990 +N، بدنا صورهم تكون على كل ال N متساوي، هذا هي، + +507 +00:41:47,990 --> 00:41:50,110 +واضحية؟ لأن ال domain هم N، لما أكتب بعد الكلمة، + +508 +00:41:50,110 --> 00:41:55,290 +هم خلصوا، أه، فهذا بيقول إن F1 تساوي F2، وهذا يعني + +509 +00:41:55,290 --> 00:42:02,280 +إيش؟ Psi is one to oneThus صار الـ domain اللي هو + +510 +00:42:02,280 --> 00:42:08,300 +A أُس B يكافئ الـ image للـ + +511 +00:42:08,300 --> 00:42:13,260 +A أُس B اللي هو subset من مين؟ من C اللي هي 01 + +512 +00:42:13,260 --> 00:42:20,700 +طبعا فهذا بيقدّي أنه 2 ألف null تمام أشمالها أصغر + +513 +00:42:20,700 --> 00:42:27,700 +أو يساوي C لأن واحد ال cardinality إليها هيك نشوف + +514 +00:42:27,700 --> 00:42:37,840 +الاتجاه التانيC أصغر أو تساوي 2 أس الـ12 الحقيقة + +515 +00:42:37,840 --> 00:42:41,820 +مش هنشتغل على نفس المجموعات هنغير الآن هناخد + +516 +00:42:41,820 --> 00:42:49,910 +المجموعة اللي هو X أو C من مقابل الـC هناخدهاR لـ + +517 +00:42:49,910 --> 00:42:53,850 +C تساوي R فالـ cardinality لها الـ C و هناخد + +518 +00:42:53,850 --> 00:42:59,230 +الطبعا الاتنين هنخليها 01 ولا هنغير بس بدي اخد .. + +519 +00:42:59,230 --> 00:43:04,950 +بديش اخد الآن بدي اخد الـ Q الآن المجموعة ب .. اه + +520 +00:43:04,950 --> 00:43:09,870 +تمام هعملها بشكل مختلف تماما انا عندي اتنين أُس ال + +521 +00:43:09,870 --> 00:43:12,750 +cardinality هي عبارة عن cardinality لـ H أكبر من + +522 +00:43:12,750 --> 00:43:15,430 +cardinality لل power فاحنا في عندنا علاقة إيش + +523 +00:43:15,430 --> 00:43:20,670 +يعملنا فيه ال powerبنقول الـ Cardinality لـ Power + +524 +00:43:20,670 --> 00:43:28,250 +لأي مجموعة تساوي 2 لـ Cardinality للمجموعة صح؟ + +525 +00:43:28,250 --> 00:43:32,110 +عمّمناها هذه فتساوي Cardinality للمجموعة + +526 +00:43:32,110 --> 00:43:38,130 +فهنستخدمها هذه هنستخدم هذه العلاقة طبعا لأي مجموعة + +527 +00:43:38,130 --> 00:43:41,330 +احنا بس أنا هحط الـ Q هنا أثبتناها ده كمثال + +528 +00:43:41,330 --> 00:43:48,080 +الحقيقة مش نظرية مثال رقم 3 هيهمثال رقم تلاتة + +529 +00:43:48,080 --> 00:43:51,600 +المرة اللي فاتتنا هنا لأ جابل ال cardinality في + +530 +00:43:51,600 --> 00:43:59,460 +مثال انا متذكر انه عملناه مثال مثال رقم اتنين ال + +531 +00:43:59,460 --> 00:44:01,520 +cardinality لل power of a بتساوي اتنين لل + +532 +00:44:01,520 --> 00:44:06,300 +cardinality of a هنستخدم هذه الفكرة نرجع لنظرية + +533 +00:44:06,300 --> 00:44:13,440 +تبعتها فهنشتغل عليها فهي ال C و هاخد لالف null + +534 +00:44:13,440 --> 00:44:19,050 +اللي هي ال cardinality of Q andاللي هي اللي ال B + +535 +00:44:19,050 --> 00:44:24,890 +تساوي Q فطبعا + +536 +00:44:24,890 --> 00:44:32,150 +then ال cardinality لل R اللي هي بتساوي C أو ال C + +537 +00:44:32,150 --> 00:44:36,970 +بتساوي C small c and باستخدام هذه القاعدة + +538 +00:44:36,970 --> 00:44:46,060 +cardinality ل ال power of Qبتساوى 2 cardinality + +539 +00:44:46,060 --> 00:44:50,200 +للـ Q بتساوى 2 نقصة الف null لأن الـ Q أشمالها + +540 +00:44:50,200 --> 00:44:54,480 +denomable فانا حاجة تلعب على هذا الكلام فالآن عشان + +541 +00:44:54,480 --> 00:45:00,940 +أثبت أن الـ C أصغر أو متساوي هذا الكلام بدنا نثبت + +542 +00:45:00,940 --> 00:45:12,300 +we will prove that ال Rتكافئ subset z من من من + +543 +00:45:12,300 --> 00:45:18,180 +اللي هو power of a cube power of a cube فانا بدي + +544 +00:45:18,180 --> 00:45:22,020 +أستفيد أيها هذه بتساوي هذه فهي المجموعة power of a + +545 +00:45:22,020 --> 00:45:26,000 +cube هنستبدلها بدأت بشكل مش هنستخدم قصص الآن هنا + +546 +00:45:26,000 --> 00:45:31,650 +هنشتغل على طول على المجموعات مباشرةفجيد إن نشوف + +547 +00:45:31,650 --> 00:45:38,630 +نوع جديد من الدوال فكرة جديدة كل هذه أفكار بتعلمنا + +548 +00:45:38,630 --> 00:45:42,510 +فطبعا نفس القضية هعرف ده لمن R ل power of Q تكون + +549 +00:45:42,510 --> 00:45:46,030 +one to one نفس الفكرة مش هعرف الـ Z هأخدها ال + +550 +00:45:46,030 --> 00:45:50,870 +image let الجت هدول عناصر الـ R عدد حقيقية ومين + +551 +00:45:50,870 --> 00:45:54,490 +عناصر ال power of Q سبسط من الـ Q مجموعات أحسنة + +552 +00:45:54,490 --> 00:46:02,270 +فإذا هنسميها F الآن من Rللـ power of Q بالشكل + +553 +00:46:02,270 --> 00:46:12,710 +التالي be given by اللي هو F of أي عدد R اسمه R + +554 +00:46:12,710 --> 00:46:17,470 +تساوي بدي أعمل subset ال subset هي كل العناصر بدي + +555 +00:46:17,470 --> 00:46:20,830 +أعمل subset من ال Q subset من ال Q بدي أعمل منها + +556 +00:46:20,830 --> 00:46:26,570 +مجموعة شوف كيف بنعمل مجموعة such that X أصغر من R + +557 +00:46:29,050 --> 00:46:35,130 +أصغر ولا أكبر؟ أتوقع ماتفرجش طبعا + +558 +00:46:35,130 --> 00:46:40,710 +زي ما احنا بنحكي دايما في أشياء كتيرة تجيش من أول + +559 +00:46:40,710 --> 00:46:44,370 +مرة و تجي مع المحاولات طبعا انا أول شيء الشكل + +560 +00:46:44,370 --> 00:46:48,390 +الأول فكرة ممكن اتقالها بدي عدد و اوديه لمجموعة + +561 +00:46:48,390 --> 00:46:51,970 +بدي اوديه لمجموعة طبعا خلنا نفهم الدالة أولا إيش + +562 +00:46:51,970 --> 00:46:56,590 +يعني دال اي real number لو بقوللي أفف واحد هي مين؟ + +563 +00:46:57,330 --> 00:47:03,010 +هي كل الاعداد النسبية اللي اصغر من واحد مظبوط؟ هيك + +564 +00:47:03,010 --> 00:47:08,930 +معناته طيب لو جالي F of سالب اتنين هي كل الاعداد + +565 +00:47:08,930 --> 00:47:13,360 +النسبيةاللي أصغر من سالب اتنين هذه صورتها طبعا كل + +566 +00:47:13,360 --> 00:47:15,780 +ما دول صبصت من الـQ و لا لأ؟ لأن هو بيقول لي ايه + +567 +00:47:15,780 --> 00:47:19,680 +الـQ و هكذا صبصت من الـQ إذا المهم نتمو هدول لل + +568 +00:47:19,680 --> 00:47:23,160 +power واضحة بس نثبت انها one to one هنثبت ان هذه + +569 +00:47:23,160 --> 00:47:26,600 +الدالة one to one يمكن أثناء البرهان يشوفنا ليش + +570 +00:47:26,600 --> 00:47:29,100 +الاختيار بعد الشكل عشان أحافظ انها one to one + +571 +00:47:29,100 --> 00:47:35,010 +خليني أثبت ان ال F one to one F is one to oneناخد + +572 +00:47:35,010 --> 00:47:39,050 +عنصرين من الـ domain R1 وR2 تنتمي للـ capital R + +573 +00:47:39,050 --> 00:47:47,790 +such that صورهم متساوي F of R1 تساوي F of R2 بدنا + +574 +00:47:47,790 --> 00:47:53,750 +نثبت أن R1 تساوي R2 طبعا + +575 +00:47:53,750 --> 00:47:59,170 +نستخدم التعريفواحدة واحدة، طب إيش هذه؟ إذا + +576 +00:47:59,170 --> 00:48:06,770 +المجموعة X تنتمي لـ Q بحيث X أقل من R1 بيبقى تساوي + +577 +00:48:06,770 --> 00:48:14,930 +المجموعة اللي هي X تنتمي لـ Q بحيث X أقل من R2 + +578 +00:48:14,930 --> 00:48:25,060 +مطلوب إن X R1 تساوي R2، هنثبت هذاسنثبت هذا يا إما + +579 +00:48:25,060 --> 00:48:30,280 +by contradiction أو نثبت إن الاحتمالين التانيين مش + +580 +00:48:30,280 --> 00:48:35,820 +ممكن يحصلوا حالة الأعداد الحقيقية أي أعداد حقيقية + +581 +00:48:35,820 --> 00:48:39,460 +فيها تلات احتمالات يا الأول يساوي التاني يا الأول + +582 +00:48:39,460 --> 00:48:43,120 +أصغر من التاني أكبر منه فسننفع الاحتمالين وتم أنها + +583 +00:48:43,120 --> 00:48:48,340 +تتساوي سننفع الاحتمالين فلجيت أقول له هيا نمشي by + +584 +00:48:48,340 --> 00:48:53,590 +contradiction assumeR1 لا تساوي R2 Proved by + +585 +00:48:53,590 --> 00:48:57,230 +Contradiction Proved by Contradiction ماهو Proved + +586 +00:48:57,230 --> 00:49:00,710 +by Contradiction؟ أن R1 تساوي R2 وهكذا الهدف، + +587 +00:49:00,710 --> 00:49:03,270 +مصبوط؟ أخدنا عنصرهم الـ domain نريد أن يكونوا أصغر + +588 +00:49:03,270 --> 00:49:05,570 +ومتساوي ونريد أن يكونوا متساويين تمامًا، ماهو + +589 +00:49:05,570 --> 00:49:10,770 +معناه أنهم ليسوا متساويين؟ يا R1 أقل من R2 أو R1 + +590 +00:49:10,770 --> 00:49:14,050 +أكبر من R2؟ حثبت أن الاتنين يؤدوا لـ Contradiction + +591 +00:49:14,050 --> 00:49:24,780 +الآن أول شيءإذا R1 أقل من R2 ثم .. مجموعات أه .. + +592 +00:49:24,780 --> 00:49:32,320 +لما تكون دايما واضح أن R1 أصغر من R2 فكل عنصر هنا + +593 +00:49:32,320 --> 00:49:36,860 +بيكون هنا ليش؟ لأن اللي أصغر .. X أصغر من R1 بيكون + +594 +00:49:36,860 --> 00:49:40,480 +أصغر من R2 فعلى طول هذه بتكون subset من هذه و + +595 +00:49:40,480 --> 00:49:44,220 +العكس غير صحيح أشمالها؟ + +596 +00:49:46,220 --> 00:49:48,900 +أه طبعا لكن العكس غير صحيح لأن كيف .. كيف هدول + +597 +00:49:48,900 --> 00:49:53,300 +المجموعات خلينا نشوف نعملهم على خط الاعداد هاي خط + +598 +00:49:53,300 --> 00:49:56,260 +الاعداد بس بدنا ناخد الاعداد النسبية اه هي عندنا + +599 +00:49:56,260 --> 00:50:02,180 +R1 وهي R2 مين المجموعة الأولى F of R1 مين هيها هذه + +600 +00:50:02,180 --> 00:50:05,940 +اللي هي كل اعداد هي عبارة عن مين F of R1 مظبوط + +601 +00:50:05,940 --> 00:50:11,110 +ومين F of R2 العداد اللي أصغر من R2فإذا المجموعة + +602 +00:50:11,110 --> 00:50:15,070 +هذه subset من هذه فلما يكونوا مش متساويين مستحيل + +603 +00:50:15,070 --> 00:50:19,590 +يتساوي المجموعات لذا R1 أكبر بتكون في عنصر موجود + +604 +00:50:19,590 --> 00:50:24,730 +هنا و مش موجود هنا فطبعا بما أن ال R1 أكبر من R2 + +605 +00:50:24,730 --> 00:50:28,390 +then بقدر ألاقي عدد و ليكل A ممكن أخد الاشرار + +606 +00:50:28,390 --> 00:50:37,020 +متوسط و ممكن ألاقي عدد A such thatالـ A بين الـ R2 + +607 +00:50:37,020 --> 00:50:42,740 +و الـ R1 مزالهم مش متساويين وهذه حقيقة كل عددين + +608 +00:50:42,740 --> 00:50:45,520 +نسبيين في A زي مش غير متساويين فيه بين عدد نسبي + +609 +00:50:45,520 --> 00:50:48,640 +تاريخ ايش ايش هو مجموحهم مع اتنين متوسطهم يعني + +610 +00:50:48,640 --> 00:50:51,560 +النص والتلت ايش بينهم اجمعيهم مجموحهم مع اتنين + +611 +00:50:51,560 --> 00:50:56,920 +بيطلع عدد نسبي ف there exist A طبعا في Qفإيش ماله + +612 +00:50:56,920 --> 00:51:01,980 +هذا العدد؟ هو كذا، فهذا بيقول إن الـA وين موجودة؟ + +613 +00:51:01,980 --> 00:51:09,720 +موجودة في الـF of R2 لكن مش موجودة and A غير + +614 +00:51:09,720 --> 00:51:14,180 +موجودة في الـF of R1، مظبوط؟ لأن A برا الـR1 و A، + +615 +00:51:14,180 --> 00:51:16,480 +طبعا هذا يشمل الـcontradiction لأنهم متساويين، + +616 +00:51:16,480 --> 00:51:18,160 +لازم كل عناصرهم متساوية، فكانت contradiction + +617 +00:51:18,160 --> 00:51:22,480 +التاني زيه، contradiction + +618 +00:51:24,850 --> 00:51:28,070 +التانية زيها تماما بس العكس اه واضحة لما تكون + +619 +00:51:28,070 --> 00:51:33,810 +التانية زيها خلينا يمكن اكتبها مش مشكلة لو كانت R1 + +620 +00:51:33,810 --> 00:51:40,210 +أكبر من R2 then there exist a تنتمي ل ال Q such + +621 +00:51:40,210 --> 00:51:48,040 +thatاللي هو إيش؟ R1 أكبر من A أكبر من R2 هذا إيش + +622 +00:51:48,040 --> 00:51:53,480 +يؤدي إن الـ A موجودة في ال F of R1 لكن غير موجودة + +623 +00:51:53,480 --> 00:52:01,240 +في ال F of R2 طبعا Contradiction فبتمش + +624 +00:52:01,240 --> 00:52:05,940 +عندنا الاحتمال إن R1 تساوي R2 وهذا يؤدي إن ال F is + +625 +00:52:05,940 --> 00:52:11,050 +one to oneوهذا يؤدى ان ال F is one to one فخلاص ما + +626 +00:52:11,050 --> 00:52:15,770 +زال ال F one to one اذا صارت ال R تكافئ ال image + +627 +00:52:15,770 --> 00:52:22,610 +اللى هو sub set من مين من power ل Q اه فطبعا هذا + +628 +00:52:22,610 --> 00:52:25,790 +بيقول ان ال cardinality اللى هى ال C اصغر او تساوى + +629 +00:52:25,790 --> 00:52:31,170 +ال cardinality اللى هى 2 أسالفنا فهد واحد و اتنين + +630 +00:52:31,170 --> 00:52:32,670 +بينه البرغم + +631 +00:52:37,920 --> 00:52:44,280 +فطبعاً واحد واتنين يؤدي ان اتنين أسالف null تساوي + +632 +00:52:44,280 --> 00:52:52,580 +C فإذن أثبتنا ان ال power set لل Q تكافئ R هيك + +633 +00:52:52,580 --> 00:52:55,700 +معناته ال power set لل Q اللي هي كاردناتية لاتنين + +634 +00:52:55,700 --> 00:53:00,040 +وال power set لل N وال power set لل Z يكافئ ال R + +635 +00:53:00,040 --> 00:53:04,400 +يكافئ ال R فيهم عداد عناصر يكافئ ال real numbers + +636 +00:53:04,400 --> 00:53:06,000 +ال real numbers + +637 +00:53:09,980 --> 00:53:14,640 +طبعاً ممكن نتيجة برضه على انه ال cardinality لأي + +638 +00:53:14,640 --> 00:53:18,340 +مجموعة أصغر من ال power بنثبت ان الف null أقل من C + +639 +00:53:18,340 --> 00:53:24,280 +وأيضا ممكن كمثال نثبت ان CC تساوي C بطريقة أخرى + +640 +00:53:24,280 --> 00:53:27,600 +أثبتناها بس الآن باستخدام هذا الكلام بما أن هذا + +641 +00:53:27,600 --> 00:53:33,860 +الكلام صحيح فC ضرب C ممكن اكتبه 2 أس الف null في 2 + +642 +00:53:33,860 --> 00:53:38,260 +أس الف null والنظرية السابقة ايش بتقول ليه؟مجموعهم + +643 +00:53:38,260 --> 00:53:43,510 +وهذا أثبتنا أنه يساوي الف null هو يساوي Cفهذا + +644 +00:53:43,510 --> 00:53:46,690 +المثال بسهولة هذا أثبتناه قبل هيك لكن هذه طريقة + +645 +00:53:46,690 --> 00:53:52,270 +أخرى باستخدام الأساس فممكن أكتر أقدر منه فيمكن هذه + +646 +00:53:52,270 --> 00:53:58,110 +تكون أخر جزء بالنسبة للشرح فهذه نهاية المحاضرة + +647 +00:53:58,110 --> 00:54:03,890 +ونهاية هذا المساق أرجو أن تكون هذه المحاضرات مفيدة + +648 +00:54:03,890 --> 00:54:09,750 +لكم لجميع من يشاهد هذه المحاضرات وبالتوفيق مبارك + +649 +00:54:09,750 --> 00:54:10,170 +الله فيكم + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/mUJTBUAt-Mc_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/mUJTBUAt-Mc_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..4306eba5e6f14362f51619c68d4f97565be2cfee --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/mUJTBUAt-Mc_postprocess.srt @@ -0,0 +1,1780 @@ +1 +00:00:19,740 --> 00:00:23,180 +بسم الله الرحمن الرحيم نواصل مع ال cardinal number + +2 +00:00:23,180 --> 00:00:28,080 +الاعداد الأصلية باختصار شديد احنا قلنا ان هذه ال + +3 +00:00:28,080 --> 00:00:33,580 +cardinal numbers لها علاقة وثيقة بالمجموعات وهي بس + +4 +00:00:33,580 --> 00:00:39,060 +لتعبر عن حجم المجموعات فكل cardinal number N بدوا + +5 +00:00:39,060 --> 00:00:42,260 +يقابلوا مجموعة بحيث ان ال cardinal number لهذه + +6 +00:00:42,260 --> 00:00:45,980 +المجموعة بيساوي N والعكس صحيح لو في عندنا مجموعة A + +7 +00:00:45,980 --> 00:00:50,170 +بنتحدث عن ال cardinal number لل Aأيضًا من + +8 +00:00:50,170 --> 00:00:53,730 +المعلومات المهمة أن الـ cardinality للـ 5 بتساوي 0 + +9 +00:00:53,730 --> 00:00:56,870 +وهي المجموعة الوحيدة اللي هي cardinality بتساوي 0 + +10 +00:00:56,870 --> 00:01:00,610 +و ال finite set ال cardinality number بتساوي عدد + +11 +00:01:00,610 --> 00:01:05,370 +العناصر إذا كانت بالكافة N K فهما K و بدنا بنقارن + +12 +00:01:05,370 --> 00:01:08,570 +الآن بعد هيك إذا المجموعتين متكافئتين بيكون ال + +13 +00:01:08,570 --> 00:01:11,550 +cardinality number متساوي F and all F و بعدين + +14 +00:01:11,550 --> 00:01:15,150 +بيقولنا إنه أصغر من أو يساوي إذا المجموعة كافة + +15 +00:01:15,150 --> 00:01:21,260 +subsetفإذا الـ A تكافئ subset من الـ B بنقول إن + +16 +00:01:21,260 --> 00:01:27,100 +cardinality للـ A أقل أو تساوي cardinality للـ B + +17 +00:01:27,100 --> 00:01:30,920 +طيب أصغر من .. أصغر من .. زي ما عملنا تعريف الـ + +18 +00:01:30,920 --> 00:01:34,920 +proper subset بدا تكون أقل من أو يساوي ولا تساوي + +19 +00:01:34,920 --> 00:01:40,060 +أقل من أو تساوي ولا تساوي فيمكن هذا اختصارا وقفنا + +20 +00:01:40,060 --> 00:01:43,790 +في نهاية المحاضرة الماضية عند هذه النظريةوزي ما + +21 +00:01:43,790 --> 00:01:48,690 +قلنا إنه فينا الصفر هو أصغر cardinal number طبعا + +22 +00:01:48,690 --> 00:01:52,870 +أكبر منه الواحد أكبر منه التنين ممكن نوصل لل + +23 +00:01:52,870 --> 00:01:57,230 +cardinality لل N هذا عدد كبير اللي هو أصغر + +24 +00:01:57,230 --> 00:02:01,250 +infinite set أصغر transfinite cardinal number + +25 +00:02:01,250 --> 00:02:05,090 +بالمعنى، مظبوط؟ أه، أه، وقلنا هذا يشمل أصغر من ال + +26 +00:02:05,090 --> 00:02:08,870 +cardinality لمن؟ لل R ال real numbers هذا أكبر منه + +27 +00:02:08,870 --> 00:02:14,320 +أثبتناها برضه فالسؤال هل في أعداد بعد هيك؟الجواب + +28 +00:02:14,320 --> 00:02:17,040 +نعم عن طريق النظرية هنشوف انه في cardinal number + +29 +00:02:17,040 --> 00:02:19,320 +أكبر من هيك في cardinal number أكبر من هيك ما + +30 +00:02:19,320 --> 00:02:24,440 +بيجفوش بنتن نزيد بدون توقف فكان عندنا النظرية + +31 +00:02:24,440 --> 00:02:27,400 +التالية بتقول طبعا الكافر انه بيجفوش لو عندي + +32 +00:02:27,400 --> 00:02:30,000 +مجموعة ال cardinal number إلها معين بقدر أجيب + +33 +00:02:30,000 --> 00:02:32,140 +cardinal number كبير الزيادة بقيه عشان أجيب ال + +34 +00:02:32,140 --> 00:02:34,940 +power للمجموعة هذه و ال power set و هكذا و هذه + +35 +00:02:34,940 --> 00:02:37,940 +العملية بتجفش كل مجموعة كل power set فهي مجموعة + +36 +00:02:37,940 --> 00:02:42,670 +فإلها power set و هكذافبقول إذا كانت ال X is a set + +37 +00:02:42,670 --> 00:02:46,530 +فال cardinality لل X دايما هو أبدا أصغر مش أصغر من + +38 +00:02:46,530 --> 00:02:50,490 +أو يساوي أصغر يعني إيه أيش بكبر بشكل واضح و بشكل + +39 +00:02:50,490 --> 00:02:54,410 +صريح لل cardinality لل power of X خلينا نشوف + +40 +00:02:54,410 --> 00:03:00,770 +البرهان مع بعض فنبدأ برهان هذه النظرية ال proof + +41 +00:03:00,770 --> 00:03:08,250 +هذه نظرية 6 2خلّينا طبعا قبل ما نبدأ البرهان و + +42 +00:03:08,250 --> 00:03:11,150 +ندّيناكوا بعض الأمور اللي هتمر علينا في البرهان + +43 +00:03:11,150 --> 00:03:15,430 +نرجع لها بعد قليل لو كانت المجموعة X بتساوي في + +44 +00:03:15,430 --> 00:03:17,710 +خلّينا ناخدها دي على جهة قبل ما نبدأ نشتغل لإنه + +45 +00:03:17,710 --> 00:03:21,050 +بدنا مجموعة ما تكونش خالية عند الشغل فلو كانت ال X + +46 +00:03:21,050 --> 00:03:26,690 +بتساوي في if X تساوي في then إيش ال cardinality + +47 +00:03:26,690 --> 00:03:33,060 +لها؟ صفرطب والـ cardinality للـ power واحد، مظبوط + +48 +00:03:33,060 --> 00:03:37,120 +أصغر من cardinality للـ power of X اللي بتساوي + +49 +00:03:37,120 --> 00:03:40,480 +واحد، هذا مرة علينة قبلك نظرية لأنه 2 أُس 0 صح؟ أه + +50 +00:03:40,480 --> 00:03:43,920 +إذا المجموعة finite فال power set للمجموعة بيساوي + +51 +00:03:43,920 --> 00:03:47,540 +2 أُس عدد عناصر المجموعة فإذا ناشت لو كانت فيه + +52 +00:03:47,540 --> 00:03:51,400 +الكلام صحيح فال cardinality للمجموعة أقل من + +53 +00:03:51,400 --> 00:03:54,680 +cardinality للpower set للمجموعة أه الآن نشتر على + +54 +00:03:54,680 --> 00:04:01,210 +إن ال X غير فارغة assumeالـ X لا تساوي الـ Far + +55 +00:04:01,210 --> 00:04:07,090 +طبعا بدي أثبت إن ال cardinality أقل من cardinality + +56 +00:04:07,090 --> 00:04:09,830 +للpower طب هذا إيش معناته بالتعريف؟ بدي أثبت إنها + +57 +00:04:09,830 --> 00:04:14,110 +أصغر منها أو تساويها و لا تساويها لأن هيك اللي هو + +58 +00:04:14,110 --> 00:04:16,510 +التعريف لأنه أنا .. بنقول مرة تانية خاين اكتبها + +59 +00:04:16,510 --> 00:04:20,590 +كامة مرة cardinality للـ A أقل من cardinality للـ + +60 +00:04:20,590 --> 00:04:26,770 +B هذا issue كافةيكافئ أن الـ cardinality للـ A أقل + +61 +00:04:26,770 --> 00:04:31,130 +أو يساوي ال cardinality لل B أن A لا تساوي + +62 +00:04:31,130 --> 00:04:36,450 +cardinality لل A لا تساوي cardinality لل B فحنشتغل + +63 +00:04:36,450 --> 00:04:40,630 +على هذا التعريف فطبعا هنبدأ نثبت أن H أقل من أو + +64 +00:04:40,630 --> 00:04:47,330 +تساوي فإذن أول شيء هنثبت أن cardinality لل X أقل + +65 +00:04:47,330 --> 00:04:51,170 +أو تساوي cardinality لل power of X + +66 +00:04:53,890 --> 00:04:58,270 +طبعا إيش مطلوب؟ بدي أدور على مجموعة subset من ال + +67 +00:04:58,270 --> 00:05:02,450 +power of X تكون تكافئة ال X هذه طريقة مر علينا + +68 +00:05:02,450 --> 00:05:05,450 +برضه مثال إن ممكن أنا بدل ما أدور على المجموعة + +69 +00:05:05,450 --> 00:05:10,170 +أدور على دالة بتكون one to one فبالتالي بتصير + +70 +00:05:10,170 --> 00:05:13,970 +المجموعة الأولى Xتكافئ الـ image والـ image دائما + +71 +00:05:13,970 --> 00:05:17,590 +صبصة من المقابل هذه طريقة بديلة فالآن بدنا دالة + +72 +00:05:17,590 --> 00:05:21,930 +الحقيقة بدنا دالة بين ال X و بين ال power of X + +73 +00:05:21,930 --> 00:05:25,230 +خلينا برضه نحاول زي ما عملنا في نهاية المثال + +74 +00:05:25,230 --> 00:05:31,290 +الماضي عشان نفهم لو أخدنا مثال توضيح هنا لو أخدنا + +75 +00:05:31,290 --> 00:05:39,910 +مثلا ال X تساوي 1 2 3 مثلا تفضلي من عندكبصي مظبوط + +76 +00:05:39,910 --> 00:05:43,930 +بس انا بدي .. بدي دال ل .. اه بس هي لأ لأ لأ ال X + +77 +00:05:43,930 --> 00:05:47,650 +اشمالها تنتمي لل power of X مش سبسات منها ال X + +78 +00:05:47,650 --> 00:05:51,350 +تنتمي انتبهوا اه مابداش ننسى ال X تنتمي اه هاي + +79 +00:05:51,350 --> 00:05:54,330 +مثلا هاي .. هاي .. هاي نشوف مثال هاي ال X مين ال + +80 +00:05:54,330 --> 00:05:59,650 +power of X فيها الفاي أحسنتي و فيها ال X و فيها ال + +81 +00:05:59,650 --> 00:06:03,910 +واحد و فيها التنين و فيها التلاتة و فيها واحد + +82 +00:06:03,910 --> 00:06:07,810 +اتنين و فيها واحد و تلاتة و فيها اتنين و تلاتة + +83 +00:06:08,680 --> 00:06:12,100 +خلصوا اتوقع تمانية لازم يكونوا هنا صاروا تمانية + +84 +00:06:12,100 --> 00:06:15,820 +واحد اتنين تلاتة اربع خمسة ستة سبعة تمانية تمام + +85 +00:06:15,820 --> 00:06:19,320 +فال + +86 +00:06:19,320 --> 00:06:23,420 +X تنتمي فبنفعش وإلا كان سهل فالان بدي أدور على + +87 +00:06:23,420 --> 00:06:36,340 +دالة هنعرف دالة let F من X لل power of X be given + +88 +00:06:36,340 --> 00:06:36,740 +by + +89 +00:06:41,100 --> 00:06:44,300 +بدي دالة من ال X لل power of X تكون one to one + +90 +00:06:44,300 --> 00:06:48,180 +فطبعا زي ما احنا بنحكي و بنحاول نأكد على هذا + +91 +00:06:48,180 --> 00:06:52,860 +الكلام طيب ليش في غرابة؟ لأ مافيش غرابة أنا بدي + +92 +00:06:52,860 --> 00:06:55,460 +دالة بين مجموعتين هي المجموعة الأولى وهي المجموعة + +93 +00:06:55,460 --> 00:06:59,230 +التانيةطب إيش كذا ممكن أكوّن دالة؟ أنا بس بدي + +94 +00:06:59,230 --> 00:07:03,050 +شرطين بدي أغطي كل ال domain واش تكون أو بعدين + +95 +00:07:03,050 --> 00:07:04,890 +أبديها تكون one to one بعدين إيش بديها عشان تكون + +96 +00:07:04,890 --> 00:07:08,170 +دالة؟ بدي كل عنصر الصورة وحيدة فأنا لو كان ال + +97 +00:07:08,170 --> 00:07:10,170 +domain زيك بدي صورة الواحد، إيش صورة الواحد + +98 +00:07:10,170 --> 00:07:12,810 +أوديها؟ ممكن أوديها ل fight، ممكن أوديها لمجموعة + +99 +00:07:12,810 --> 00:07:16,330 +الواحد، ممكن أوديها لل X، هي المجال المقابل، أه + +100 +00:07:16,330 --> 00:07:20,270 +فهنا بدنا نحاول نوسع اللي هو الخيال تبعنا وتوسعنا، + +101 +00:07:20,270 --> 00:07:22,770 +احنا متعودين على الدوال دايما من أعداد لأعداد، مش + +102 +00:07:22,770 --> 00:07:25,620 +بالضروريةعشان هيك لما كان يقولنا مجموعة ما قلنا + +103 +00:07:25,620 --> 00:07:28,460 +بنسكر دفتر ال calculus لأن العناص المش عارفينها، + +104 +00:07:28,460 --> 00:07:31,160 +ممكن تكون العناص المجموعات، ممكن تكون كراسة، ممكن + +105 +00:07:31,160 --> 00:07:34,120 +تكون طاولات، ممكن تكون بنا أدمين، مش عارفين، كل شي + +106 +00:07:34,120 --> 00:07:37,480 +بنفع، كل شي بنفع نعم، اه فالان احنا هنعرف دالة + +107 +00:07:37,480 --> 00:07:44,160 +بسهولة أن f of x مسموعة مجموعة xيعني على سبيل + +108 +00:07:44,160 --> 00:07:47,680 +المثال عن ايش نعمل الواحد تروح لمجموعة الواحد يعني + +109 +00:07:47,680 --> 00:07:50,660 +زي هيك ممكن نعمل كام مثال الواحد تروح لمجموعة + +110 +00:07:50,660 --> 00:07:52,880 +الواحد التانية تروح لمجموعة التانية التلاتة تكون + +111 +00:07:52,880 --> 00:07:56,520 +المجموعة التلاتة دالة ولا مش دالة دالة غطت كل ال + +112 +00:07:56,520 --> 00:07:59,700 +domain صح اه طيب ماغطتش كل المجال المقابل مش + +113 +00:07:59,700 --> 00:08:03,080 +بالضرورة مش مش انتم ولا يكن او ايش هذه الدالة كمان + +114 +00:08:03,080 --> 00:08:06,740 +one to one one to one فالدالة هذه one to one then + +115 +00:08:09,930 --> 00:08:14,270 +is one to one واضحة ولا لأ لأن هو واضح أنه ايه + +116 +00:08:14,270 --> 00:08:18,410 +صورة طبعا بشكل عام هنا ده بصيحة كمثال فلو كانت X1 + +117 +00:08:18,410 --> 00:08:21,790 +تساوي X2 فمجموعة ال X1 بتساوي مجموعة X2 وده لا + +118 +00:08:21,790 --> 00:08:24,650 +يمكن يكون اللي إذا كانت X1 تساوي X2 تعرف تثبتها + +119 +00:08:24,650 --> 00:08:30,130 +ولا نثبتها نثبتها خلينا نشوف then خلينا نثبت F is + +120 +00:08:30,130 --> 00:08:35,030 +one to one خلينا نثبتها بلاش أنه ده مش جواب نثبت + +121 +00:08:35,030 --> 00:08:44,570 +فنقوله letX1 و X2 تنتمي للـ Capital X Such that F + +122 +00:08:44,570 --> 00:08:52,290 +of X1 تساوي F of X2 إيش بأعمل؟ بستخدم التعريف زي + +123 +00:08:52,290 --> 00:08:57,270 +معرفة فده بيقوللي مجموعة الـ X1 تساوي مجموعة الـ + +124 +00:08:57,270 --> 00:09:03,210 +X2تعريف فهذا بالضرورة تكون X1 سوى X2 و لا لأ لأنه + +125 +00:09:03,210 --> 00:09:06,850 +مازال هادي بتسويها إذا هدول العناصر نفس العناصر + +126 +00:09:06,850 --> 00:09:11,350 +مافيش عنصر واحد مافيش احتمال آخر فده يؤدي X1 تسوى + +127 +00:09:11,350 --> 00:09:17,390 +X2 إذا F is one to one الآن + +128 +00:09:17,390 --> 00:09:21,810 +هنستخدم ال trick المشهور تبعنا إذا دالة one to one + +129 +00:09:21,810 --> 00:09:25,050 +إذا أنا بتصير bijection لما main أصغر المجال + +130 +00:09:25,050 --> 00:09:27,450 +المقابل فهنا it follows + +131 +00:09:30,310 --> 00:09:38,090 +that الـ domain يكافئ من ال image f of x و ال + +132 +00:09:38,090 --> 00:09:43,490 +image subset من من المجال المقابل ال power of x + +133 +00:09:44,770 --> 00:09:49,150 +فإيش عملنا؟ أثبتنا إن الـ X كافة سبسط من الـ power + +134 +00:09:49,150 --> 00:09:53,670 +إذا ال cardinality أيش؟ أقل أو تساوي فده يؤدي إن + +135 +00:09:53,670 --> 00:09:58,170 +ال cardinality لل X أقل أو تساوي احنا قاعدين + +136 +00:09:58,170 --> 00:10:05,270 +نثبتها cardinality لل power of X فده واحد خلصنا + +137 +00:10:05,270 --> 00:10:11,210 +واحدمتابعين؟ فده trick مشهور أنه أنا بدل ما أبحث + +138 +00:10:11,210 --> 00:10:14,050 +عن مجموعة و بعدين أجيب أنا تكافئ لأ بجيب ده اللي + +139 +00:10:14,050 --> 00:10:16,670 +one to one و أخبره أنه خلصت لأ دي أسهل كتير لأنه + +140 +00:10:16,670 --> 00:10:19,090 +في الآخر أن أنا بدي أجيب أولشي المجموعة و بعدين + +141 +00:10:19,090 --> 00:10:21,230 +أجيب bijection لأ أبحث عن ده لو تكون one to one + +142 +00:10:21,230 --> 00:10:25,290 +أسهل الكتير الآن رقم اتنين بدنا نثبت أن ال + +143 +00:10:25,290 --> 00:10:32,610 +cardinality لل A لل X أسف لاتساوي ال cardinality + +144 +00:10:32,610 --> 00:10:41,410 +لل power of Xهنعملها by contradiction Assume ال + +145 +00:10:41,410 --> 00:10:46,890 +cardinality لل X تساوي ال cardinality لل power of + +146 +00:10:46,890 --> 00:10:48,950 +X proved by contradiction + +147 +00:10:58,900 --> 00:11:03,080 +طيب، ماذا يعني إن الـ cardinality متساوية؟ إن هدول + +148 +00:11:03,080 --> 00:11:11,140 +متكافئين، فطبعاً هذا يؤدي إن هناك G من X بيجيكشن + +149 +00:11:11,140 --> 00:11:20,520 +للpower of X، للpower of X، تمام، هنا هنستخدم برضه + +150 +00:11:20,520 --> 00:11:24,570 +ال trickاستخدمناها سابقًا، مش بحذافيره، لكن نفس + +151 +00:11:24,570 --> 00:11:28,210 +الفكرة الأساسية لما أثبتنا إن الـ 01 non + +152 +00:11:28,210 --> 00:11:31,390 +-denominable قُلنا لو كانت denominable تكثق الـN + +153 +00:11:31,390 --> 00:11:34,650 +فهناك bijection وأثبتنا مستحيل يكون ده اللي تكون + +154 +00:11:34,650 --> 00:11:37,330 +on it مستحيل يتغطي لأن عناصرها كتيرة، هنا نفس + +155 +00:11:37,330 --> 00:11:40,930 +الفكرة إن هنا عناصر كتيرة جدًا فمستحيل ألاقي + +156 +00:11:40,930 --> 00:11:44,230 +bijection فبدأ أثبت إن هناك عنصر في الـP of X وما + +157 +00:11:44,230 --> 00:11:47,800 +يشبهه، ولا يمكن يكون صورة، لا يمكن يكون صورةفبدنا + +158 +00:11:47,800 --> 00:11:50,940 +نشوف اللي هو العنصر اللي صمناه خلف خلافة ده + +159 +00:11:50,940 --> 00:11:53,960 +المخالف تذكروا كيف استختمنا لما اختارنا الـ Z؟ + +160 +00:11:53,960 --> 00:11:56,120 +قلنا خلّي الخانة الأولى الشمالية تختلف مع صورة + +161 +00:11:56,120 --> 00:11:58,900 +الواحد الخانة التانية تختلف مع صورة التين فإذا + +162 +00:11:58,900 --> 00:12:02,380 +ضمننا إنه يخالف الجميع فبالتالي هو مش صورة اتحادة + +163 +00:12:02,380 --> 00:12:06,500 +هنا هنعمل حاجة مشابه، هنعمل حاجة مشابه، هنختار + +164 +00:12:06,500 --> 00:12:10,200 +مجموع عنصر هنا العنصر إيه شبه العنصر هنا؟ مجموعة + +165 +00:12:10,200 --> 00:12:16,770 +بدي تكون، بدي تكون مجموعة فهأختار let S تساويX + +166 +00:12:16,770 --> 00:12:24,390 +تنتمي للcapital X such that X لا تنتمي لل G of X + +167 +00:12:24,390 --> 00:12:27,910 +طبعا + +168 +00:12:27,910 --> 00:12:34,990 +الكتابة شوية غريبة خلينا نحاول نفهمها مع بعض في + +169 +00:12:34,990 --> 00:12:39,390 +المثال طبعا هذا الأحمر هو ال Fخلّينا على سبيل + +170 +00:12:39,390 --> 00:12:42,070 +المثال نشوف كيف أن هذا الكلام منطقي، كيف أن هذا + +171 +00:12:42,070 --> 00:12:45,790 +الكلام منطقي، طبعا الصور، وين بتكون الصور؟ في ال + +172 +00:12:45,790 --> 00:12:49,350 +power، يعني إيش بتكون الصور؟ مجموعات، فأول شيء + +173 +00:12:49,350 --> 00:12:54,370 +أقول تنتمي أو لا تنتمي، شيء منطقي، أشملها؟ أنا بدي + +174 +00:12:54,370 --> 00:12:58,110 +أختار مجموعة زي ما نقولها هي الشخصية المخالفةهنا + +175 +00:12:58,110 --> 00:13:01,710 +بدأ اوضحها اول الشيء تنتمي او لا تنتمي شيء منطق + +176 +00:13:01,710 --> 00:13:04,810 +لأن الـG of X شمالها مجموعة نشوف عصابي المثال هذه + +177 +00:13:04,810 --> 00:13:08,650 +كانت الأحمر F خلّيني نغيّر لو أخدنا عصابي المثال + +178 +00:13:08,650 --> 00:13:14,730 +ناخد هنا قلنا G الواحد تساوي مثلا مجموعة الواحد + +179 +00:13:14,730 --> 00:13:19,910 +فالواحد تنتمي لجي of واحد ولا تنتميش تنتمي لكن لو + +180 +00:13:19,910 --> 00:13:24,490 +قلنا ناخد G التنين تساوي المجموعة واحد التنين مش + +181 +00:13:24,490 --> 00:13:30,770 +هي ضمن هنا لأ بديش التنين واحد تلاتةفهل ال S تنتمي + +182 +00:13:30,770 --> 00:13:34,530 +لل G of 2؟ لأ، واضحة كيف الصورة؟ او واحد كذا، ممكن + +183 +00:13:34,530 --> 00:13:37,250 +طبعا خيارات، إذا لا تكون إيش، وإيه بدي أحاول و + +184 +00:13:37,250 --> 00:13:40,050 +أعمل بدأ الشكل، فالآن طبعا أول شيء، بدي أثبت أن + +185 +00:13:40,050 --> 00:13:43,250 +هذه ال S لا يمكن تكون صورة لحدها، لا يمكن تكون + +186 +00:13:43,250 --> 00:13:48,990 +صورة لحدها، أول شيء، then ال S subset من ال X ولا + +187 +00:13:48,990 --> 00:13:53,120 +مش subset من ال X؟ليش؟ لأن هي تعريفة بتقول كل + +188 +00:13:53,120 --> 00:13:55,700 +عناصر ال X اللي عليهم كمان شرط إضافي فبياخدش من + +189 +00:13:55,700 --> 00:13:59,080 +برا ال X ومزالها subset من ال X في وين بتكون؟ في + +190 +00:13:59,080 --> 00:14:07,780 +ال power of X and hence ال S تنتمي لل power of X + +191 +00:14:07,780 --> 00:14:11,040 +إذا هذه موجودة .. ليش موجودة في المجال المقابل؟ + +192 +00:14:11,040 --> 00:14:14,580 +بدي أثبت إنها مش صورة و هذا بناقد إنها أنتم و هذا + +193 +00:14:14,580 --> 00:14:19,950 +بناقد إنها أنتمتمام الان بما ان الدالة on to لازم + +194 +00:14:19,950 --> 00:14:27,950 +هذه الاس تكون صورة now g is on to implies there + +195 +00:14:27,950 --> 00:14:33,350 +exists a في ال X الدالة من وين لوين من ال X لل F + +196 +00:14:33,350 --> 00:14:37,090 +of X في عنصر ينجد يكون صورة حدى ففي عنصر في ال + +197 +00:14:37,090 --> 00:14:46,820 +domain such that هذه الاس صورة هذا العنصرالـ G on + +198 +00:14:46,820 --> 00:14:50,180 +2 يعني كل عناصر المجال المقابل كل اللي في الـ + +199 +00:14:50,180 --> 00:14:54,140 +power هي الصور الآن بدنا نشوف إنه فيه تناقض ففي + +200 +00:14:54,140 --> 00:15:00,780 +عندنا احتمالين الـ A في الـ X والـ S وين subset من + +201 +00:15:00,780 --> 00:15:05,620 +الـ X هي عندنا الـ X والـ S مجموعة هنا وعندنا الـ + +202 +00:15:05,620 --> 00:15:08,160 +A الـ A وين بتكون يا هن يا هن بالدفع بيننا + +203 +00:15:08,160 --> 00:15:12,800 +احتمالين بيؤدوا لقتنا التناقض فلو كانت الـ A تنتمي + +204 +00:15:12,800 --> 00:15:14,000 +للـ S then + +205 +00:15:16,430 --> 00:15:23,250 +إيش تعريف الـS يا أخوات؟ هاي شرطة إذا بتنتمي إذا + +206 +00:15:23,250 --> 00:15:26,430 +إيش تعريف لازم تكون؟ لاتنتمي للـG of A فلو الـA + +207 +00:15:26,430 --> 00:15:30,150 +تنتمي للـS وما تتحققش الشرط الصفة المميزة فإذا + +208 +00:15:30,150 --> 00:15:34,850 +بيقول إن الـA لاتنتمي للـG of A فده الصفة المميزة، + +209 +00:15:34,850 --> 00:15:39,970 +ماشي؟ فده هي طب الـG of A إيش بتساوي؟ تساوي S مش + +210 +00:15:39,970 --> 00:15:44,950 +هيك اختارناها فصارت الـA تنتمي للـS وA لاتنتمي + +211 +00:15:44,950 --> 00:15:50,220 +للـS Contradictionفهذا الاحتمال الأول مستحيل اذا + +212 +00:15:50,220 --> 00:15:55,860 +الاحتمال التاني واضحة ولا عيد؟ اه فهنا عشان احنا + +213 +00:15:55,860 --> 00:15:59,520 +اختارناها بشكل مخالف هي المخالفة بها الشكل لو كانت + +214 +00:15:59,520 --> 00:16:07,300 +ال A لان لا تنتمي لل Sإيش الصفة المميزة؟ إذا إيش + +215 +00:16:07,300 --> 00:16:12,460 +مالها؟ لازم تنتمي، لازم تنتمي، then الـA بدا تنتمي + +216 +00:16:12,460 --> 00:16:16,660 +للـG of A، اللي هي إيش؟ اللي هي S، لها تنتمي + +217 +00:16:16,660 --> 00:16:25,280 +وتنتمي Contradiction فإذا + +218 +00:16:25,280 --> 00:16:32,130 +في هنا تناقض فلفرضية تبعتنا غير صحيحةthus هذا + +219 +00:16:32,130 --> 00:16:36,450 +الكلام غير صحيح cardinality of X لا تساوي + +220 +00:16:36,450 --> 00:16:43,570 +cardinality of power of X طبعا واحد واثنين ينهوا + +221 +00:16:43,570 --> 00:16:48,210 +البرهام أقل + +222 +00:16:48,210 --> 00:16:55,010 +من ال cardinality لل power of Xفادي الصورة طبعا زى + +223 +00:16:55,010 --> 00:16:57,210 +ما حكينا ممكن تكون شوية غريبة المثال هذا ممكن + +224 +00:16:57,210 --> 00:17:04,550 +يساعدنا شوية نفهم كيف يعني لو هنا ع سبيل المثال لو + +225 +00:17:04,550 --> 00:17:08,490 +بدي أنا أشوف لو بصرف G تلاتة إيش بتساوي مثلا لو + +226 +00:17:08,490 --> 00:17:14,090 +قولنا G of تلاتة مثلا بتساوي إيش؟ نقول اتنين + +227 +00:17:15,360 --> 00:17:17,980 +فده السبب اللي بده يجيب الـ S الآن، مين الـ S؟ إيش + +228 +00:17:17,980 --> 00:17:23,000 +بتساوي الـ S؟ المجموعة بتنتمي لصورة، مافيش للواحد، + +229 +00:17:23,000 --> 00:17:25,640 +ع سبيل المثال هنا، مظبوط؟ أه، فلو بدنا نيجي نحسب + +230 +00:17:25,640 --> 00:17:29,820 +الـ S هنا فالـ S إيش بتساوي؟ بتساوي X تنتمي للـ X + +231 +00:17:29,820 --> 00:17:35,920 +such that X تنتمي لتنتمي للـ G of X، أسف، مين اللي + +232 +00:17:35,920 --> 00:17:39,480 +بنتميش؟ الواحد بتنتمي، زي مش موجودة، التنين ما + +233 +00:17:39,480 --> 00:17:46,900 +بتعرف، والتنين لتنتمي والتلاتة، مظبوطصحيح فهي بعد + +234 +00:17:46,900 --> 00:17:52,680 +المعنى عشان بس نفهم البرهان لكن الواحد لأ فهكذا + +235 +00:17:52,680 --> 00:17:56,280 +هذا كان مثال بسيط ودائما هذه الطريقة طريقة مهمة + +236 +00:17:56,280 --> 00:17:59,400 +جدا لما انتوا تشوفوا اي نظرية اي موضوع مش قادرين + +237 +00:17:59,400 --> 00:18:02,320 +تصوروه كله بشكل عام يبدو مثال بسيط هذا بيساعدنا + +238 +00:18:02,320 --> 00:18:07,510 +على تصور الصورة العامةخلّينا ننهي هذا الموضوع بهو + +239 +00:18:07,510 --> 00:18:11,490 +إيش الدليل من هذه النظرية أو الشاهد من هذه النظرية + +240 +00:18:11,490 --> 00:18:17,990 +بقول ليه the significance of the theorem مهمية + +241 +00:18:17,990 --> 00:18:27,810 +النظريةأشمالها بتقول لإنه it is furnishes بتنتج أو + +242 +00:18:27,810 --> 00:18:31,190 +هي طريقة to construct a far-reaching sequence + +243 +00:18:31,190 --> 00:18:35,910 +مجموعة غير قابلة نوصل لنهايتها مش صحيح نوصل + +244 +00:18:35,910 --> 00:18:40,050 +نهايتها of new transfinite cardinal numbersفطبعا + +245 +00:18:40,050 --> 00:18:43,330 +احنا طبعا قلنا ايش ال cardinal number ال R هو كون + +246 +00:18:43,330 --> 00:18:46,630 +الاكبر واحد بنعرفه لأ في اكبر منه ال power of R + +247 +00:18:46,630 --> 00:18:50,010 +وفي اكبر منه power power ال R و هكذا اه فإذا انا + +248 +00:18:50,010 --> 00:18:53,490 +اقولها مافيش حاجة تقولها ده اكبر cardinal number + +249 +00:18:53,490 --> 00:18:56,530 +في اصغر cardinal number اللي هو ال zero لكن مافيش + +250 +00:18:56,530 --> 00:19:03,330 +حاجة اسمها اكبر cardinal number فهذا section قصير + +251 +00:19:03,330 --> 00:19:05,090 +بهذا الشكل انتهى + +252 +00:19:13,000 --> 00:19:18,760 +ننتقل لـ section اللي هو جديد طبعا احنا كان عنوان + +253 +00:19:18,760 --> 00:19:23,140 +ال chapter Cardinal Numbers and Cardinal + +254 +00:19:23,140 --> 00:19:26,740 +Arithmeticics العمليات الحسابية فطبعا احنا في ال + +255 +00:19:26,740 --> 00:19:29,080 +session الماضي اتعرفنا مين هو ال cardinal number + +256 +00:19:29,080 --> 00:19:32,780 +وشوفنا كيف نقارن مين أكبر من مين الآن هندخل على + +257 +00:19:32,780 --> 00:19:36,280 +العمليات الحسابية و هنبدأ بعملية الجمع ف addition + +258 +00:19:36,280 --> 00:19:43,450 +of cardinal numbers عملية الجمع تمامعملية الجمع + +259 +00:19:43,450 --> 00:19:48,390 +هنا هنعرف الجمع بالطريقة البسيطة الطريقة الفطرية + +260 +00:19:48,390 --> 00:19:51,750 +اللى بنتعلم فيها لعقل الجمع لو بنعلم أي طفل صغير + +261 +00:19:51,750 --> 00:19:55,410 +كيف يجمع تلاتة زائد اتنين بتساوي خمسة كيف بيعملوا + +262 +00:19:55,410 --> 00:19:57,530 +كام جمع و المجموعة فيها تلاتة تفاحات و المجموعة + +263 +00:19:57,530 --> 00:20:01,050 +فيها تفاحتين و بيبدأ يعيد تلاتة اربعة خمسة و هكذا + +264 +00:20:01,050 --> 00:20:03,450 +فنفس القضية فاحنا هنجيب المجموعات عن طريق + +265 +00:20:03,450 --> 00:20:07,130 +المجموعات فهنجيب مجمعتين واحدة ال cardinal number + +266 +00:20:07,130 --> 00:20:11,050 +اللي عدد A والتانية B طبعا بس هنا فيدنا شرط ان + +267 +00:20:11,050 --> 00:20:15,360 +التقاطه يسوا fiveلأن التقاطة تحدث بدل تكرار بدل + +268 +00:20:15,360 --> 00:20:18,880 +تكرار نعمل اتحاد و نهدد لأن المجموعتين مع بعض + +269 +00:20:18,880 --> 00:20:21,940 +بيطلع المجموع بيطلع المجموع فنشوف كيف التعريف مع + +270 +00:20:21,940 --> 00:20:25,940 +بعض let small a and small b be cardinal numbers + +271 +00:20:25,940 --> 00:20:30,360 +فانا عندي عددين أصليينمطلب مني أن أحصل على a b من + +272 +00:20:30,360 --> 00:20:36,000 +ايه؟ آسف a زائد b بقول لي the cardinal sum يعني + +273 +00:20:36,000 --> 00:20:40,580 +المجموع ك cardinal number كعدد أصلي of a and b هذه + +274 +00:20:40,580 --> 00:20:43,320 +المفهوم ال cardinal sum اسمه اللي هو الجمع على + +275 +00:20:43,320 --> 00:20:47,180 +العداد الأصلي طيب ماهو الرمز تبعه؟ نفس العملية + +276 +00:20:47,180 --> 00:20:51,440 +اللي هي ال cross هذه أو ال plus هذه زائد نفس + +277 +00:20:51,440 --> 00:20:55,300 +العملية نفس الرمز طيب is the cardinal number مين؟ + +278 +00:20:55,360 --> 00:20:59,860 +اللي هو طبع الاتحاد طبع الاتحاد طبع الاتحاد طبع + +279 +00:20:59,860 --> 00:21:08,080 +الاتحاد طبع الاتحاد طبع الاتحاد + +280 +00:21:08,080 --> 00:21:09,280 +طبع الاتحاد طبع الاتحاد طبع الاتحاد طبع الاتحاد + +281 +00:21:09,280 --> 00:21:10,340 +طبع الاتحاد طبع الاتحاد طبع الاتحاد طبع الاتحاد + +282 +00:21:10,340 --> 00:21:10,960 +طبع الاتحاد طبع الاتحاد طبع الاتحاد طبع الاتحاد + +283 +00:21:10,960 --> 00:21:20,040 +طبع الاتحاد طبع الاتحاد طبع الاتحاد طبع الاتحاد + +284 +00:21:20,040 --> 00:21:26,140 +طبع الاتحاد طبع الTwo cardinal numbers A and B + +285 +00:21:26,140 --> 00:21:31,560 +مطلوب منها جيب A زي B إيش يعمل؟ جال نجيب مجموعتين + +286 +00:21:31,560 --> 00:21:37,260 +capital A و capital B جيب + +287 +00:21:37,260 --> 00:21:40,400 +مجموعتين زي ما قلنا بنجيب اتنين زي تلاتة جيب + +288 +00:21:40,400 --> 00:21:44,280 +مجموعة فيها تلات تفاحات و مجموعة فيها تفاحتين و + +289 +00:21:44,280 --> 00:21:49,110 +جيب الاتحادبينفع ياخد أي مجموعة تانية بالشرط ان + +290 +00:21:49,110 --> 00:21:54,090 +الـ A تقاطع الـ B يساوي 5 فبعد ما اجيب الاتحاد ايش + +291 +00:21:54,090 --> 00:21:58,770 +هروح اجيب ال cardinality اعدهم ايش هذا بيساوي A + +292 +00:21:58,770 --> 00:22:04,180 +زاد Bيساوي a زاد b فهذه العملية تمام فبقول ليه ال + +293 +00:22:04,180 --> 00:22:08,180 +where a and b are disjoint sits such that بدنا + +294 +00:22:08,180 --> 00:22:11,440 +اللي هو مقابل ال a مجموعة ال cardinality بتساوي + +295 +00:22:11,440 --> 00:22:14,480 +small a ومقابل ال b مجموعة ال cardinality بتساوي + +296 +00:22:14,480 --> 00:22:18,200 +small b طبعا بس يكونوا disjoint بقدر أجيب بهذه + +297 +00:22:18,200 --> 00:22:21,900 +الصورة واضحة فالعملية بسيطة وسهلة في الطريقة + +298 +00:22:21,900 --> 00:22:26,860 +العملية قبل ما نبدأ نشوف الأمثلة و نشوف بعض الخواص + +299 +00:22:26,860 --> 00:22:31,860 +في عندنا نظريةعنوان النظرية addition of cardinal + +300 +00:22:31,860 --> 00:22:36,540 +numbers is well defined ماذا يعني هذا؟ هذا سؤال + +301 +00:22:36,540 --> 00:22:40,780 +أحياناً بنقابله في الرياضيات أنا فيه عندي تعريف لو + +302 +00:22:40,780 --> 00:22:44,560 +رجعنا للتعريف بقول عشان تجيبي المجموع A زائد B + +303 +00:22:44,560 --> 00:22:50,260 +جيبلي مجموعتين A و B تقطعهم يساوي Phi و بعدين جيب + +304 +00:22:50,260 --> 00:22:55,520 +الاتحاد و أعدهل هذا تعريف يُعتبر تعريف علمي؟ نعم، + +305 +00:22:55,520 --> 00:22:58,160 +هناك نقطة دائماً في هذا السؤال الذي نطرحه، لماذا؟ + +306 +00:22:58,160 --> 00:23:01,320 +لأنه يقول إنك تريد أن تجلب الـA و الـB، طب أنا جبت + +307 +00:23:01,320 --> 00:23:04,740 +الـA و الـB، و إجت طالب أخر جابت مجموعتين X و Y، + +308 +00:23:04,740 --> 00:23:07,920 +هل الناتج باعتمد على الاختيار للمجموعتين هؤلاء، أو + +309 +00:23:07,920 --> 00:23:10,880 +ليس باعتمد؟ لو كان باعتمد، فهو ليس تعريف علمي + +310 +00:23:11,290 --> 00:23:14,590 +فبنثبت إن هذا لا يعتمد لأنه بكل جيب وبعدين هل + +311 +00:23:14,590 --> 00:23:17,430 +دايما بقدر أجيب المجموعات دول ولا ممكن أعجز + +312 +00:23:17,430 --> 00:23:20,170 +وبالتالي مش هقدر أجيب المجموع فهنا السؤال المطروح + +313 +00:23:20,170 --> 00:23:23,070 +بهذا الشكل عشان هيك بده أقول إن هذا التعريف تعريف + +314 +00:23:23,070 --> 00:23:26,510 +علمي كامل دايما أنا بقدر أجيب المجموعاتين A و B + +315 +00:23:26,510 --> 00:23:30,570 +تقطعهم يساوي Phi ولو أحد آخر جاب مجموعتين مختلفتين + +316 +00:23:30,570 --> 00:23:33,270 +بنفس الشروط لازم يطلع نفس الجوابعشان يكون تعريف + +317 +00:23:33,270 --> 00:23:36,170 +علمى صحيح لا يعتمد على الإنسان اللى بيجري العملية + +318 +00:23:36,170 --> 00:23:40,710 +وإنما بيعتمد على التعريف العلمى تبعته وبالتالي هو + +319 +00:23:40,710 --> 00:23:43,750 +تعريف علمى لا يعتمد على الشخص اللى بيجري العملية + +320 +00:23:43,750 --> 00:23:47,530 +وإنما يعتمد على الخواص والأمور العامة اللى بتجري + +321 +00:23:47,530 --> 00:23:53,160 +فعنا هنا النظرية بتقول التاليlet A and B be + +322 +00:23:53,160 --> 00:23:56,900 +cardinal numbers أنا مطلوب مني أجيب A زائد B أول + +323 +00:23:56,900 --> 00:24:00,520 +شيء بيقوللي دايما و أبدا بتقدر تلاقي مجموعتين + +324 +00:24:00,520 --> 00:24:03,580 +واحدة ال cardinality تبعتها small a و واحدة ال + +325 +00:24:03,580 --> 00:24:08,780 +cardinality small b و هم disjoint فدايما ممكن فحدش + +326 +00:24:08,780 --> 00:24:11,680 +يقوللي رجيب ليه اللي هو أربعة زائد خمسة يقوللي مش + +327 +00:24:11,680 --> 00:24:14,120 +هملاقي مجموعتين مستحيل لازم يلاقي مجموعتين + +328 +00:24:14,120 --> 00:24:18,360 +فالنظرية بتقوللي إيش بتقدر تلاقي مجموعتينإتنين طيب + +329 +00:24:18,360 --> 00:24:22,140 +لو انا اديت اللي هو بقول جيبه المجموع اللي هو A + +330 +00:24:22,140 --> 00:24:26,900 +زائد B للمئة طالب اللي هنا أو أقل وكل واحدة لجت + +331 +00:24:26,900 --> 00:24:29,360 +مجموعتين مختلفتين لازم يطلع الجواب نفس الجواب مش + +332 +00:24:29,360 --> 00:24:31,660 +هتقول انا لجت مجموعتين مختلفتين فطلع مع الجواب + +333 +00:24:31,660 --> 00:24:34,980 +مختلف لأ لازم يطلع نفس الجواب النهاية .. اه فكيف + +334 +00:24:34,980 --> 00:24:38,340 +بده اعبر عنها بقول لو كان في عندنا مجموعة اربع + +335 +00:24:38,340 --> 00:24:44,220 +مجموعاتA1 B1 و A2 و B2 هما عبارة عن مجموعات بحيث + +336 +00:24:44,220 --> 00:24:51,420 +طبعا انا مقابل ال A ايش جبت جبت A1 و A2 فال + +337 +00:24:51,420 --> 00:24:56,240 +cardinata بعتهم متساوين و مقابل ال B في طالب جابت + +338 +00:24:56,240 --> 00:25:01,150 +B1 و في طالب جابت B2أه طبعا الطالب الأولى لما جابت + +339 +00:25:01,150 --> 00:25:05,230 +A1 وB1 بدوا تقطوحهم يساوي الفائد والتانية جابت A2 + +340 +00:25:05,230 --> 00:25:08,850 +وB2 تقطوحهم يساوي الفائد طب الأولى جابت الاتحاد + +341 +00:25:08,850 --> 00:25:12,630 +وجابت المجموع بطلع محارة قبل والتانية جابت الاتحاد + +342 +00:25:12,630 --> 00:25:15,010 +وجابت المجموع طالما حارة خمس لازم يكون متساوين + +343 +00:25:15,010 --> 00:25:17,870 +دايما بطلع متساوين فهذه النظرية بتقول بها الشكل + +344 +00:25:17,870 --> 00:25:22,390 +خلينا نشوف البرهان مع بعضخلّينا نشوف البرهان مع + +345 +00:25:22,390 --> 00:25:27,130 +بعض فبالتالي لو أنا بدأ أجمع تلاتة زائد أربعة + +346 +00:25:27,130 --> 00:25:29,890 +أجيبت تلاتة تفاحات وأربعة تفاحات ولا تلاتة + +347 +00:25:29,890 --> 00:25:32,390 +بوردجانات وأربعة بوردجانات ما بيختلفش الجواب + +348 +00:25:32,390 --> 00:25:36,290 +المجموعة لو تغيرت المجموعات بس يحققوا الشرطين أن + +349 +00:25:36,290 --> 00:25:40,350 +يكونوا كل مجموعة بتعبر عن عدد ولو يكونوا disjoint + +350 +00:25:40,350 --> 00:25:45,990 +فالنتج ما بيختلفش فالنتج لن يختلف نشوف البرهان مع + +351 +00:25:45,990 --> 00:25:50,190 +بعض تفضل اه + +352 +00:25:55,760 --> 00:26:00,000 +كأرقام، بديك تجيب مجموعتين مختلفتين، يعني انت مثلا + +353 +00:26:00,000 --> 00:26:04,400 +تعلم طفل الجامع، بديك تعلمه اتنين زي التلاتة + +354 +00:26:04,400 --> 00:26:09,280 +بيساوي خمسة، بدي تكون عندك خمس كورات أو خمس طفحات، + +355 +00:26:09,280 --> 00:26:12,240 +بينفعش تعملينه مجموعتين من أربع طفحات، تقولها هذه + +356 +00:26:12,240 --> 00:26:14,720 +المجموعة الأولى، خلصنا منها، و تروح بعدين تاخد + +357 +00:26:14,720 --> 00:26:17,920 +منها عنصر وده، فمافيش تكون عنصر مشترك، صح؟ فهذا هو + +358 +00:26:17,920 --> 00:26:18,320 +المعنى + +359 +00:26:22,000 --> 00:26:25,640 +أربعة زي التقطع بيسووا تمانية، طب كيف بدك تثبتيها؟ + +360 +00:26:25,640 --> 00:26:28,700 +بدك تجيبي مجموعتين، مجموعة فيها أربعة طفاحات و + +361 +00:26:28,700 --> 00:26:31,640 +مجموعة فيها أربعة طفاحات، بدكون عندك كام طفاحة + +362 +00:26:31,640 --> 00:26:34,300 +عشان لازم تكون تمانية، بينفع تعملي مجموعتين في + +363 +00:26:34,300 --> 00:26:37,500 +سبعة أو بستة تقولي أنا بدي أعملهم مرتين، أخلصت + +364 +00:26:37,500 --> 00:26:40,000 +المجموع الأولى خلاص امحيها و أعمل كمان مجموع + +365 +00:26:40,000 --> 00:26:44,390 +تانية، بينفعشواضحة؟ فلا يجب أن يكون تكرار، فلازم + +366 +00:26:44,390 --> 00:26:48,330 +يكون هذه المنفصلات هيانة مجموعة و هيانة مجموعة، لا + +367 +00:26:48,330 --> 00:26:53,230 +يمكن أن يكون فيهم عنصر مشترك مرة هنا و مرة هنا، لم + +368 +00:26:53,230 --> 00:26:56,550 +تُوضح الفكرة؟ كأنك تستطيع تعمل هذه عملية الجامعة + +369 +00:26:56,550 --> 00:27:00,310 +بالظبط بعد الصورة، طبعا هو ليش؟ لأنه عندما يعمل + +370 +00:27:00,310 --> 00:27:04,490 +الاتحاد عنصر المتكرر، ليس مرتين، صح ولا لأ؟ فلا + +371 +00:27:04,490 --> 00:27:09,250 +يجب أن يكون عنصر متكرر، نشوف البرهان، فهذه نظرية 6 + +372 +00:27:09,250 --> 00:27:09,570 +-3 + +373 +00:27:14,050 --> 00:27:19,390 +approved طبعا بالنسبة لكل المقدمات معطيات ايش + +374 +00:27:19,390 --> 00:27:22,430 +المعطيات ان ال a و ال b cardinal numbers فنبدأ + +375 +00:27:22,430 --> 00:27:27,430 +بواحد بدي الاقي مجموعة a و مجموعة b الأولى + +376 +00:27:27,430 --> 00:27:29,690 +cardinal تبعتها small a و التانى ال cardinal + +377 +00:27:29,690 --> 00:27:34,750 +تبعتها small b و الأهم يكون دوسيون يكونوا دوسيون + +378 +00:27:34,750 --> 00:27:40,530 +مين عنده نقطة بدايةأول ما بدّينا ال cardinal + +379 +00:27:40,530 --> 00:27:43,230 +numbers قلنا كل cardinal number بيبقى بالمجموع + +380 +00:27:43,230 --> 00:27:48,930 +فالـ A هن على طول اللي هو القاعدة C1 implies there + +381 +00:27:48,930 --> 00:27:55,190 +exist six X و Y بدي أسميهم مش هم ال A و ال B بدور + +382 +00:27:55,190 --> 00:27:58,010 +عليهم لأنهم لسه ممكن يكونوا مت disjoint القاعدة + +383 +00:27:58,010 --> 00:27:59,810 +بتقول يوجد such that + +384 +00:28:03,260 --> 00:28:08,040 +الـ Cardinality للـ X تساوي Small a والـ + +385 +00:28:08,040 --> 00:28:15,020 +Cardinality andالـ cardinality للـ Y تساوي small p + +386 +00:28:15,020 --> 00:28:19,100 +فهذه أول قاعدة يقولنا كل cardinal number يقابله + +387 +00:28:19,100 --> 00:28:22,860 +مجموعة لأن هذا ياش لا ينفك عنها، لا ينفك عنها تمت + +388 +00:28:22,860 --> 00:28:25,820 +عندنا مشكلة التي التقاطع يساوي في فأنا عندي + +389 +00:28:25,820 --> 00:28:29,380 +مجموعتين تقطعهم يساوي في أو لو يساوي في مش عارف + +390 +00:28:29,380 --> 00:28:33,280 +بدنا نعمل trick بسيط و نكون ال A و ال B نحافظ على + +391 +00:28:33,280 --> 00:28:36,880 +ال cardinality لكن نضمن أنه التقاطع يساوي في + +392 +00:28:36,880 --> 00:28:42,900 +الفكرة قبل ذلك مرت عليناكيف أكوّن مجموعة كافة الـ + +393 +00:28:42,900 --> 00:28:47,660 +X لكن تقاطع .. أو مجموعة كافة الـ Y لكن التقاطع مع + +394 +00:28:47,660 --> 00:28:53,180 +الـ X .. التقاطع بينتان ما بعد يكون فاية اتنين X و + +395 +00:28:53,180 --> 00:28:57,560 +Y اضربها في اتنين يعني اه Cartesian product .. + +396 +00:28:57,560 --> 00:29:06,080 +Cartesian product الآن هنعرف let A تساوي X across + +397 +00:29:06,080 --> 00:29:12,800 +اتنينفهذه تكافئ ال X لأنها مش رابطة في واحد لأن هي + +398 +00:29:12,800 --> 00:29:16,400 +مش نفس الأزواج كيف هذه تكافئ ال X؟ من ال bijection + +399 +00:29:16,400 --> 00:29:25,840 +X تروح ل X اتنين فهذه bijection and let B تساوي Y + +400 +00:29:25,840 --> 00:29:31,180 +cross من الواحد مثلا اي عدد غير اتنين cross الواحد + +401 +00:29:31,180 --> 00:29:37,950 +then على طول ال cardinalityللـ A تساوي ال + +402 +00:29:37,950 --> 00:29:43,550 +cardinality لل X تساوي A لأن هم متكافئين بسهولة فى + +403 +00:29:43,550 --> 00:29:48,550 +حد عنده مشكلة أنه يثبت أن X تكافئ هذه فى حد عنده + +404 +00:29:48,550 --> 00:29:54,130 +مشكلة ماحدش عنده مشكلة ايش ال bijection F من X ل X + +405 +00:29:54,130 --> 00:29:58,090 +cross الواحد ايش بتساوي F من X تساوي الزوج X1 X1 + +406 +00:29:58,090 --> 00:30:04,960 +على طول and نفس القضية cardinalityللـ B تساوي ال + +407 +00:30:04,960 --> 00:30:10,220 +cardinality لل Y تساوي B ايش كمان ال A تقطع ال B + +408 +00:30:10,220 --> 00:30:14,400 +فاي ليش؟ لأن مافيش عنصر مشارك بينهم هدولة لأن + +409 +00:30:14,400 --> 00:30:17,060 +مافيش واحد احداثي تبقى اتنين و هنا احداثي تبقى + +410 +00:30:17,060 --> 00:30:19,960 +اتنين بالصحيح هذا كله دايما الاحداث التاني اتنين و + +411 +00:30:19,960 --> 00:30:23,500 +دايما الاحداث التاني واحد فهذا trick بسيط تذكروا + +412 +00:30:23,500 --> 00:30:28,800 +لما اثبتنا ان ال infinite union of ال Y دربنا + +413 +00:30:28,800 --> 00:30:31,500 +الأنب واحد و اتنين و تلتة ضمننا انهم هم disjoint + +414 +00:30:31,500 --> 00:30:37,370 +على طول نفس الفكرةنفس الفكرة فإذا دائما و أبدا + +415 +00:30:37,370 --> 00:30:41,830 +بقدر أجيب المجموعات أه إذا ماحدش يقول لي أنا مش + +416 +00:30:41,830 --> 00:30:45,910 +قادر أجيب مجموعتين disjoint لأ انت بس جيب أولا من + +417 +00:30:45,910 --> 00:30:49,630 +قاعدة C1 جيب مجموعتين ومنهم على طول بتعمل disjoint + +418 +00:30:49,630 --> 00:30:52,910 +انك تضرب في 11 و 1 و 2 بيصيروا مختلفين عن بعض + +419 +00:30:52,910 --> 00:30:59,230 +اتنينطبعاً فيها جملة شرطية نفترض إن هدولة مجموعات + +420 +00:30:59,230 --> 00:31:12,010 +assume كل الشرط صحيح a1, b1, a2 and b2 are sets + +421 +00:31:12,010 --> 00:31:22,010 +such that ال cardinality لل a1 تساوي ال + +422 +00:31:22,010 --> 00:31:30,600 +cardinality لل a2الـ cardinality للـ B1 تساوي ال + +423 +00:31:30,600 --> 00:31:37,800 +cardinality للـ B2 ايش كمان؟ و A1 تقاطع B1 يساوي + +424 +00:31:37,800 --> 00:31:45,780 +Phi andA2 تقاطع B2 يساوي 5 إيش بده يثبت إن + +425 +00:31:45,780 --> 00:31:48,600 +الcardinality للاتحاد يساوي الcardinality للاتحاد + +426 +00:31:48,600 --> 00:31:51,880 +نظرية سابقة أه الآن إيش معناته إن الcardinality + +427 +00:31:51,880 --> 00:31:57,780 +يساوي الcardinality فده معناته إن A1 تكافئ A2 وB1 + +428 +00:31:57,780 --> 00:32:03,380 +تكافئ B2 وتقاطع مع تقاطع 5 وتقاطع مع تقاطع 5 + +429 +00:32:03,380 --> 00:32:08,220 +فالاتحاد يكافئ الاتحاد نظرية أه فده يؤدي إن A1 + +430 +00:32:08,220 --> 00:32:14,680 +اتحاد B1تكافئ اتنين اتحاد بيتنين مش عارف نظرية + +431 +00:32:14,680 --> 00:32:17,540 +جداش في chapter .. في chapter ايش؟ في chapter خمسة + +432 +00:32:17,540 --> 00:32:21,480 +في chapter خمسة خمسة جداش اللي هو ايش قال ال union + +433 +00:32:21,480 --> 00:32:26,520 +of bijections is a bijection اه بتذكروها النظرية و + +434 +00:32:26,520 --> 00:32:29,600 +هدى معناها اه بتشوف رحام النظرية طبعا هداش معناته + +435 +00:32:29,600 --> 00:32:39,200 +ال cardinality تساوي ال cardinality وهو + +436 +00:32:39,200 --> 00:32:44,950 +المطلوبفما زال حافظنا على أنه تقاطع في و تقاطع في + +437 +00:32:44,950 --> 00:32:47,370 +يتشير إلى يتشير إلى يتشير الكلام إلى يتشير الكلام + +438 +00:32:47,370 --> 00:32:49,890 +إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام + +439 +00:32:49,890 --> 00:32:51,070 +إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام + +440 +00:32:51,070 --> 00:32:52,090 +إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام + +441 +00:32:52,090 --> 00:32:52,310 +إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام + +442 +00:32:52,310 --> 00:32:52,650 +إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام + +443 +00:32:52,650 --> 00:32:54,390 +إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام + +444 +00:32:54,390 --> 00:32:56,790 +إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام + +445 +00:32:56,790 --> 00:33:00,450 +إلى يتشير الكلام إلى + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/n56Jirv5D38.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/n56Jirv5D38.srt new file mode 100644 index 0000000000000000000000000000000000000000..21cdd8cae7ed75f36d8e751de81a6dbf83b79126 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/n56Jirv5D38.srt @@ -0,0 +1,2295 @@ +1 +00:00:19,740 --> 00:00:23,460 +بسم الله الرحمن الرحيم، هنواصل مع الـdenumerable + +2 +00:00:23,460 --> 00:00:27,440 +sets وطبعا الـsection خمسة تلاتة هو مكمل لـsection + +3 +00:00:27,440 --> 00:00:31,520 +خمسة اتنين بيتحدث عن اللي هو examples and + +4 +00:00:31,520 --> 00:00:35,920 +probabilities of denumerable setsأه فطبعا احنا لو + +5 +00:00:35,920 --> 00:00:39,240 +شوفنا اللي هو الصورة اللي بنتحدث عنها عشان نشوف + +6 +00:00:39,240 --> 00:00:44,240 +صورة كلية للموضوع فاحنا ال .. النقطة اللي هنوصلها + +7 +00:00:44,240 --> 00:00:49,440 +و بنتحدث عنها يعني يمكن ذكرناها و هنأكد عليها أن + +8 +00:00:49,440 --> 00:00:52,860 +الـdenumerable sets هي أصغر infinite set أصغر + +9 +00:00:52,860 --> 00:00:56,440 +infinite set و كان في عندنا نظرية شوفنا احنا لو + +10 +00:00:56,440 --> 00:01:00,540 +أخدنا infinite subset من denumerable تمت + +11 +00:01:00,540 --> 00:01:04,480 +denumerableوعنا برضه نتيجة مهمة أن أي subset من + +12 +00:01:04,480 --> 00:01:07,720 +countable بتكون countable فشوفنا الآن إيش علاقة + +13 +00:01:07,720 --> 00:01:10,800 +الأصغر من الـsubset من الـcountable بتم الـ + +14 +00:01:10,800 --> 00:01:14,360 +countable بعدين بدنا نتحدث لو بدنا طب نكبر هي + +15 +00:01:14,360 --> 00:01:18,520 +عندنا denumerable دفناها عنصر تم الـdenumerable طب ضفنا + +16 +00:01:18,520 --> 00:01:21,640 +لها finite number of elements طب ما الـdenumerables + +17 +00:01:21,640 --> 00:01:25,800 +فالآن بدنا نمشي برضه بنفس الاتجاه لو وسعنا وقت إيش + +18 +00:01:25,800 --> 00:01:28,960 +بتبطل المجموعة denumerable وقت إيش بدها تصير non- + +19 +00:01:28,960 --> 00:01:33,080 +denumerable فهنتمنا نكبر فيها لحد ما إيش الـK لطف + +20 +00:01:33,080 --> 00:01:36,680 +زي ما بقول واتبطلناش denumerable فالآن احنا أولا + +21 +00:01:36,680 --> 00:01:39,980 +ضفنا answer ضفنا finite number of answer الآن هشوف + +22 +00:01:39,980 --> 00:01:44,540 +نظرية لو ضفنا denumerable للـdenumerable إيش بتصير؟ + +23 +00:01:44,540 --> 00:01:48,870 +خلينا نشوف فالعنوان the union of two denumerable sets + +24 +00:01:48,870 --> 00:01:52,570 +is denumerable حتى لو تفنعها كمان denumerable بتامها + +25 +00:01:52,570 --> 00:01:57,690 +denumerable فعنا نظرية if A and B are denumerable sets + +26 +00:01:57,690 --> 00:02:04,160 +then A union B is denumerable نشوف البراحة فاحنا + +27 +00:02:04,160 --> 00:02:08,060 +ماشيين بيدا الاتجاه حد ما نوصل وين الـnon- + +28 +00:02:08,060 --> 00:02:14,500 +denumerable بتكون فهذه نظرية خمسة تسعة أو هي + +29 +00:02:14,500 --> 00:02:21,300 +البرهان above طبعا جملة شرطية فنبدأ ان الشرط صحيح + +30 +00:02:21,300 --> 00:02:27,060 +assume الـA is denumerable بتكتب اختصارا to + +31 +00:02:27,060 --> 00:02:32,010 +capital N يعني مظبوط و الـB is denumerable and الـ + +32 +00:02:32,010 --> 00:02:38,430 +B is denumerable مطلوب نثبت أن الاتحاد is denumerable + +33 +00:02:38,430 --> 00:02:46,390 +بدنا نثبت أن الـA union B is denumerable we want to + +34 +00:02:46,390 --> 00:02:55,170 +prove A union B is denumerable تمام + +35 +00:02:55,170 --> 00:03:03,890 +مرة علينا نظريات بتقول لو مجموعتين متكافئتين أو + +36 +00:03:03,890 --> 00:03:08,190 +مجموعة X تكافئ Y قلنا و W تكافئ V فالاتحاد يكافئ + +37 +00:03:08,190 --> 00:03:12,490 +الاتحاد تحت بعض الشروط صح فهل ممكن استخدم الفكرة + +38 +00:03:12,490 --> 00:03:18,920 +هذه هنا ولا لأ؟ قلنا فيها نظرية جت للـunion of a + +39 +00:03:18,920 --> 00:03:23,340 +bijection أو the union of two bijections is a + +40 +00:03:23,340 --> 00:03:27,060 +bijection أو قلنا انه من معنانها انه اذا كان في + +41 +00:03:27,060 --> 00:03:32,760 +عندي X تكافئ الـY و W تكافئ الـV بس بشرط تقاطع + +42 +00:03:32,760 --> 00:03:35,260 +الأولى مع الأولى في و التانية مع التانية في في + +43 +00:03:35,260 --> 00:03:38,640 +الاتحاد وكفي الاتحاد ممكن نستخدم هذا الكلام هنا + +44 +00:03:38,640 --> 00:03:43,460 +ممكن ليش لأ بس بنا ناخد احتمالات هذه فالان الـA و + +45 +00:03:43,460 --> 00:03:48,340 +الـB اي مجموعتين تقاطعهم في أو مش في مش معروف فلو + +46 +00:03:48,340 --> 00:03:50,900 +كان تقاطعهم في ممكن أبدأ أشتغل على هذا الموضوع + +47 +00:03:50,900 --> 00:04:01,980 +فأنا أخد هذه الحالة case one A تقاطع الـB يساوي Φ + +48 +00:04:04,100 --> 00:04:08,980 +فإذا هنا ممكن اتحدث عن اتحاد بدون مشاكل طيب بينفع + +49 +00:04:08,980 --> 00:04:13,900 +أقول ما زال الـA تكافئ الـN و الـB تكافئ الـN إذا + +50 +00:04:13,900 --> 00:04:19,860 +A Union B يكافئ N اتحاد الـN منفعش لأن احنا بدنا + +51 +00:04:19,860 --> 00:04:22,540 +برضه ادى و التقطع عن Φ و بدنا التنتيان اللى + +52 +00:04:22,540 --> 00:04:26,440 +بنوزن معاهم يكون اتحاد و ايه تقطع عن Φ طيب مازال + +53 +00:04:26,440 --> 00:04:29,820 +كتبنا case one اذا نادي ندرسها يعني مش هنلغيها طيب + +54 +00:04:29,820 --> 00:04:33,600 +إننا نعمل trick بسيط كيف نتغلب على الموضوع كيف + +55 +00:04:33,600 --> 00:04:40,100 +أستبدل الان و الان بمين؟ أن إيه؟ والتانية I'm not + +56 +00:04:40,100 --> 00:04:46,420 +فنستبدل الـN بشيء توزنها ولكن تحته سيكون في فهنا + +57 +00:04:46,420 --> 00:04:53,420 +أول شيء فإحنا عندنا since أو على طول نكتب A تكافئ + +58 +00:04:53,420 --> 00:05:03,620 +الـN وهذه تكافئ الـN even and الـB تكافئ الـN وهذه + +59 +00:05:03,620 --> 00:05:05,400 +تكافئ الـN ا + +60 +00:05:17,720 --> 00:05:26,200 +Since A تقاطع الـB يساوي Φ and N E تقاطع الـN O + +61 +00:05:26,200 --> 00:05:27,520 +يساوي Φ + +62 +00:05:32,840 --> 00:05:40,220 +A union الـB يكافئ N E union N O اللي هو إيش + +63 +00:05:40,220 --> 00:05:44,140 +بيساوي بيساوي N وهو المطلوب، وعن النظرية، النظرية + +64 +00:05:44,140 --> 00:05:50,220 +أتوقع 5-6 theorem 5-6 عشان ترجعوا وتتأكد، وهو + +65 +00:05:50,220 --> 00:05:56,920 +المطلوب، انتهت العملية فهذا الاحتمال الأول الآن + +66 +00:05:56,920 --> 00:06:04,160 +case 2 A تقاطع الـB لا يساوي Φ في عناصر مشتركة + +67 +00:06:04,160 --> 00:06:06,340 +بينهم اه تفضلي + +68 +00:06:09,790 --> 00:06:14,170 +لأ احنا دي من طرق اللي هو البرهان by cases أحيانا + +69 +00:06:14,170 --> 00:06:18,590 +أنا في عندي المعطيات كلها بشكلها العام بقدرش + +70 +00:06:18,590 --> 00:06:21,250 +أعملها مرة واحدة أنا كل المعلومات عن الـA و الـB + +71 +00:06:21,250 --> 00:06:24,970 +إنهم دي نمروا اشتقطوحهم مش معروف طب هل بقدر أشتغل + +72 +00:06:24,970 --> 00:06:27,870 +الصورة العامة مرة واحدة مش جادة فعملت حالتين + +73 +00:06:27,870 --> 00:06:31,190 +جسمتها نصين لأن مافيش عندي برهان لجميع الحالات مع + +74 +00:06:31,190 --> 00:06:35,690 +بعض فبضطر أعملها حالات متعددة كل حالة بقدر أعليجها + +75 +00:06:35,690 --> 00:06:40,230 +بطريقة مختلفة واضحت؟ لأ، فواحدة قولنا تذكرناها من + +76 +00:06:40,230 --> 00:06:43,270 +ضمن إيش؟ proved by cases، اتطلعوا عليه في section + +77 +00:06:43,270 --> 00:06:48,310 +1-7، proved by cases وبلجأله + +78 +00:06:48,310 --> 00:06:52,990 +إذا ما قدرتش أعمل الحالة العامة مرة واحدة، فبجسمها، + +79 +00:06:52,990 --> 00:06:57,440 +وده شيء مبدع عام في أي مسألة ما بيقولك الحمل اللي + +80 +00:06:57,440 --> 00:07:01,480 +يجيك لما يتجسم، بنحمل، وعادي مسألة، كلها كبيرة، لأ، + +81 +00:07:01,480 --> 00:07:05,420 +أبدأ، ودائما احنا هيك نفكر، يعني عندنا مسألة، ممكن + +82 +00:07:05,420 --> 00:07:07,760 +احنا نقول الاحتمالات كلها، لأ نبدأ بالحالات + +83 +00:07:07,760 --> 00:07:11,850 +السهلة، طيب، ها دي بتشتغل، طيب، بس فده شرط ماشي إذا + +84 +00:07:11,850 --> 00:07:15,830 +أنا الحلقة خلصت منها طب أشوف لو الشرط ما كانش متحقق + +85 +00:07:15,830 --> 00:07:20,710 +فيه شرط تاني بعودة على جهة وهكذا نبدأ الآن هنعمل + +86 +00:07:20,710 --> 00:07:24,210 +برضه trick مشهور هنا الـtrick دايما مشهور كيف أكتب + +87 +00:07:24,210 --> 00:07:28,610 +الاتحاد على صورة اتحاد منفصل disjoint union معروف + +88 +00:07:28,610 --> 00:07:32,290 +فهي عندنا الـA وعندنا الـB فكرة مرت علينا قبل هيك + +89 +00:07:32,290 --> 00:07:37,720 +هي A و هي B هذه المنطقة إيش اسمها بيناقص A بيناقص B + +90 +00:07:37,720 --> 00:07:42,280 +بيناقص A هسميها C فهنعمل الـtrick البسيط فهقوله + +91 +00:07:42,280 --> 00:07:51,220 +let C تساوي B ناقص A then أول شيء C تقاطع الـA + +92 +00:07:51,220 --> 00:07:58,380 +بيساوي Φ صح؟ بسميتها C ليها الـB وإيش كمان؟ و A + +93 +00:07:58,380 --> 00:08:04,280 +union B يساوي A union C صح؟ فانا الآن حولته من + +94 +00:08:04,280 --> 00:08:10,960 +اتحاد عام الى اتحاد disjoint مجموعتين منفصلتين طيب + +95 +00:08:10,960 --> 00:08:14,240 +إيش .. طب ليش ما اشتغلتش من أول زي هيك وحتى لو كانت + +96 +00:08:14,240 --> 00:08:17,820 +Φ لأن الـC ما عنديش كل المعلومات عنها ما عنديش كل + +97 +00:08:17,820 --> 00:08:21,120 +المعلومات عنها الآن بدي معلومات عن الـC عن الـB + +98 +00:08:21,120 --> 00:08:23,320 +والـA عندي معلومات عنهم منهم دي نمروا لكن الـC مش + +99 +00:08:23,320 --> 00:08:27,500 +دي نمروابدي أبدأ أشتق وأستقرق بعض المعلومات عن + +100 +00:08:27,500 --> 00:08:31,540 +الـC من المعطيات إيش كل اللي بعرفه عن الـC؟ إنها + +101 +00:08:31,540 --> 00:08:37,500 +subset من الـB أحسنتي Now الـC subset من الـB + +102 +00:08:37,500 --> 00:08:41,860 +الـB .. أنا بدي معلومات عن الـC في أي اتجاه؟ + +103 +00:08:41,860 --> 00:08:44,760 +إنها denumerable، إنها finite وهكذا اه الـC + +104 +00:08:44,760 --> 00:08:48,100 +subset من الـB و الـB denumerable إيش الـC؟ لأ + +105 +00:08:48,100 --> 00:08:54,570 +لأ انتبهوا النظرية بتقول يعني إيه إيش countable؟ + +106 +00:08:54,570 --> 00:08:57,550 +subset من denumerable دايما countable اه فدي إيش + +107 +00:08:57,550 --> 00:09:01,890 +countable؟ now C subset من B implies C is + +108 +00:09:01,890 --> 00:09:06,850 +countable is countable طيب بنشوف إيش معنى + +109 +00:09:06,850 --> 00:09:09,870 +countable؟ يا finite يا denumerable إذا denumerable + +110 +00:09:09,870 --> 00:09:14,790 +صارت الحالة الأولى لإن C is denumerable وتقطوحها مع + +111 +00:09:14,790 --> 00:09:18,650 +الـA؟ في صارت الحالة الأولى وإذا finite آخر مثال + +112 +00:09:18,650 --> 00:09:22,680 +إن هنا في النظر المحاضرة الماضية فإيه الصارة؟ هي أي + +113 +00:09:22,680 --> 00:09:26,600 +صارة عندها الـgate الـC countable وأنا إيش بدور؟ + +114 +00:09:26,600 --> 00:09:30,780 +بقول A union B اللي بدرسها وختابت A union C فالـC + +115 +00:09:30,780 --> 00:09:33,660 +يا finite والـA denumerable الـdenumerable اتحاد + +116 +00:09:33,660 --> 00:09:37,760 +finite هنا في المعادلة الماضية أو الـC countable + +117 +00:09:37,760 --> 00:09:39,600 +يعني الـdenumerable ممكن تكون و الـdenumerable + +118 +00:09:39,600 --> 00:09:42,020 +اتحاد denumerable الـdenumerable إذا كانت تقاطع + +119 +00:09:42,020 --> 00:09:45,360 +في و هو في فبنقول خلصت، إذا كانت تقاطع في و هو في + +120 +00:09:45,360 --> 00:09:45,640 +فبنقول خلصت، إذا كانت تقاطع في و هو في فبنقول + +121 +00:09:45,640 --> 00:09:45,760 +خلصت، إذا كانت تقاطع في و هو في فبنقول خلصت، إذا + +122 +00:09:45,760 --> 00:09:56,160 +كانت تقاطع في و هو في فبنقول خلص C is finite or C is + +123 +00:09:56,160 --> 00:10:01,660 +denumerable اكتب اختصارا تكافئ N هو هذا يؤدي + +124 +00:10:01,660 --> 00:10:08,680 +على طول الـA union C is denumerable أو تكافئ N + +125 +00:10:08,680 --> 00:10:13,380 +خلينا نكتب اختصار ما عنديش مكان كتير وهذا مثال + +126 +00:10:13,380 --> 00:10:19,150 +نهينا في المحاضرة الماضية مظبوط ارجعوله or الـA + +127 +00:10:19,150 --> 00:10:24,950 +Union C برضه تنمرة بلوينها ده هذه Case 1 تنطبق + +128 +00:10:24,950 --> 00:10:27,690 +عليها الحالة الأولى، ليش؟ لأنه عشان الحالة الأولى + +129 +00:10:27,690 --> 00:10:32,250 +التقطع يساوي فيه وينطبق وخلصت، انتهت الحالة فعشان + +130 +00:10:32,250 --> 00:10:34,210 +هيك ما قدرش أعالجه مرة واحدة، هذه الحالة لازم + +131 +00:10:34,210 --> 00:10:47,170 +أثبتها عشان أستخدمها فيما بعد متبعين؟ + +132 +00:10:47,170 --> 00:10:53,150 +اه نمشي كمان طيب الاتحاد دينامرابول دينامرابول طب + +133 +00:10:53,150 --> 00:10:56,810 +تلاتة دينامرابول اتحادهم دينامرابول وعشرة + +134 +00:10:56,810 --> 00:11:00,730 +دينامرابول اتحادهم دينامرابول نتيجة بقول ليه؟ + +135 +00:11:00,730 --> 00:11:04,250 +finite union يعني عدد محدود عشرة، خمسة، مية، ألف + +136 +00:11:04,250 --> 00:11:07,930 +of denumerable sets is denumerable تعميم للنظرية + +137 +00:11:07,930 --> 00:11:15,410 +النتيجة بشكل نص واضح وصريح let A1, A2, AN be + +138 +00:11:15,410 --> 00:11:19,130 +denumerable sets عندنا مجموعة من المجموعات القابلة + +139 +00:11:19,130 --> 00:11:23,710 +للعدد then the union J من 1 ل N AJ is denumerable + +140 +00:11:23,710 --> 00:11:34,130 +عملية تعميم البرهان بالـinduction هتركه exercise أن + +141 +00:11:34,130 --> 00:11:40,190 +ال statement for all n أكبر من أو يساوى 2، ليش؟ لأن + +142 +00:11:40,190 --> 00:11:42,590 +اتحاده، لأن اتحاده يشتغل على أكثر من عنصر، أجل من + +143 +00:11:42,590 --> 00:11:45,610 +عنصر يعني، صحيح طبعًا الجملة إذا كانت الـ a واحد لـ a + +144 +00:11:45,610 --> 00:11:49,230 +undenumerable فالاتحاد denumerable طبعًا الـ b of two + +145 +00:11:49,230 --> 00:11:53,670 +is true ليش؟ نظرية، بعدين induction و induction + +146 +00:11:53,670 --> 00:11:58,890 +hypothesis وخلصت، فده exercise هذه كتبناها بشكل + +147 +00:11:58,890 --> 00:12:05,870 +صريح، التكملة عليكم احنا + +148 +00:12:05,870 --> 00:12:08,670 +أثبتنا لما عم بتسوي توقف نظريًا إن أنت عميم + +149 +00:12:10,230 --> 00:12:15,650 +Induction نشوف مثال، مثال حقيقة أثبتناها قبل هيك بس + +150 +00:12:15,650 --> 00:12:19,790 +بطريقة مختلفة، هنشوف إثبات جديد، أثبتنا إن الـ Z + +151 +00:12:19,790 --> 00:12:22,290 +-denumerable أدّينا إيه بإيجيكشن مباشر بينها وبين + +152 +00:12:22,290 --> 00:12:25,330 +الآن، الآن ممكن أثبتها بسهولة عن طريق أن أكتبها على + +153 +00:12:25,330 --> 00:12:29,450 +صورة اتحاد مجموعتين denumerable بكل سهولة، هنستفيد + +154 +00:12:29,450 --> 00:12:33,730 +من النظرية بقى، فنشوف كيف، في فكرة سهلة وممكن نستفيد + +155 +00:12:33,730 --> 00:12:40,420 +منها، مثال Solution طبعًا ايش الـ Z؟ الـ Z عبارة عن + +156 +00:12:40,420 --> 00:12:44,080 +الـ Natural number مع الأعداد السالبة والصفر، فالـ + +157 +00:12:44,080 --> 00:12:47,200 +Natural طبعًا كلهم Denumerable لأنها بتكافئ نفسها، + +158 +00:12:47,200 --> 00:12:51,000 +تم أثبت أن الـ Zero والسالب يكافئ الآن، فبس بدي + +159 +00:12:51,000 --> 00:12:57,620 +أعرف هذه المجموعة، let A تساوي واحد ناقص X such + +160 +00:12:57,620 --> 00:13:03,980 +that X تنتمي لـ N اللي هي إيش بتساوي؟ zero سالب + +161 +00:13:03,980 --> 00:13:07,980 +واحد، سالب اثنين وهاكذا، مظبوط؟ لما نعوض x بتساوي + +162 +00:13:07,980 --> 00:13:11,560 +واحد، بدينا صفر، x بتساوي اثنين، اه فهذه المجموعة، + +163 +00:13:11,560 --> 00:13:17,060 +اه then بس عشان أؤكد على الفكرة، إيش معناه، فـ z + +164 +00:13:17,060 --> 00:13:25,400 +عبارة عن مين؟ إن اتحاد الـA، الـ N طبعًا نمبربل + +165 +00:13:25,400 --> 00:13:28,000 +بالتأكيد، لأن هذا المقياس، هذا المعيار تبع النمربل + +166 +00:13:28,000 --> 00:13:30,660 +هذا المقياس عليه كله، و الـ A ثبتنا أن الـ A نمبربل + +167 +00:13:30,660 --> 00:13:38,300 +خلص السؤال، نعم نعم الـ A هو نمبربل لا أريد أن أكتب + +168 +00:13:38,300 --> 00:13:44,380 +بالتفصيل، لأن من الـ bijection بينها وبين الـ N؟ + +169 +00:13:44,380 --> 00:13:53,170 +الـ F بدي ده لمن الـ N لـ A given by ايش نعرف ده + +170 +00:13:53,170 --> 00:13:59,110 +لمن n ل a تكون بيجيكشن واحد نقص اكس بديكي هيه سؤال + +171 +00:13:59,110 --> 00:14:05,050 +بديكي الحلقة is a bijection a bijection طبعًا + +172 +00:14:05,050 --> 00:14:10,790 +التفاصيل كلها بترك exercise now a is a bijection + +173 +00:14:10,790 --> 00:14:15,130 +therefore z + +174 +00:14:15,130 --> 00:14:18,590 +تسوي اتحاد ال n is innumerable + +175 +00:14:23,410 --> 00:14:29,250 +طبعًا النظرية خمسة تسعة بكل + +176 +00:14:29,250 --> 00:14:33,770 +سهولة، أه فإن النظريات هذه بتساعدنا، مش دائمًا مطلوب + +177 +00:14:33,770 --> 00:14:39,050 +إن أجيب bijection، ممكن أستخدم طرق مختلفة أو حتى لو + +178 +00:14:39,050 --> 00:14:41,510 +مش قادر أجيب ال bijection كله، ممكن جزئيًا هنا أسهل + +179 +00:14:41,510 --> 00:14:44,950 +بعد ما أشتغل على كل ال Z أشتغلت على جزء منه، فهذه + +180 +00:14:44,950 --> 00:14:52,330 +النظريات بتساعد هم + +181 +00:14:52,330 --> 00:14:52,830 +تابعين + +182 +00:14:57,710 --> 00:15:02,790 +فده بس مثال والسرجاع وفكرة جديدة وكيف نشتغل مع + +183 +00:15:02,790 --> 00:15:06,570 +الـdenumerable، نرجع لفكرتنا الرئيسية اللي حكينا + +184 +00:15:06,570 --> 00:15:09,790 +فيها من أول المحاضرة، احنا بدأنا من الـdenumerable + +185 +00:15:09,790 --> 00:15:13,470 +بدأنا نكبر فيها دفنالها عنصر دفنالها finite set + +186 +00:15:13,470 --> 00:15:16,790 +بعدين دفنالها الـdenumerable، تم الـdenumerable طب لو + +187 +00:15:16,790 --> 00:15:20,070 +ضربنا، عملنا Cartesian product، طبعًا الـCartesian + +188 +00:15:20,070 --> 00:15:23,510 +product مين أكبر الاتحاد ولا الـCartesian؟ الـ + +189 +00:15:23,510 --> 00:15:27,350 +Cartesian، احنا لو مجموعة بس عشان أنا أكد، عشان إذا + +190 +00:15:27,350 --> 00:15:30,290 +عندنا مجموعة فيها خمسة ومجموعة فيها عشرة، الاتحاد + +191 +00:15:30,290 --> 00:15:35,590 +أقل أو يساوي خمسة عشر، حد لحظة، خمسة عشر، لكن الـ Cartesian + +192 +00:15:35,590 --> 00:15:40,570 +خمسين على طول، فشفت الفرق، فإيه احنا بنكبر الآن فهو + +193 +00:15:40,570 --> 00:15:43,690 +بيقول لي في نظرية بيقول لي الـ Cartesian product N + +194 +00:15:43,690 --> 00:15:48,470 +cross الـN برضه دينامرابل، مازال دينامرابل، نشوف + +195 +00:15:48,470 --> 00:15:49,430 +البرهان + +196 +00:15:52,440 --> 00:15:56,140 +يعني لو أخذنا كل الأزواج المرتبة من الـnatural + +197 +00:15:56,140 --> 00:16:00,360 +numbers بتامها المجموعة denumerable قابلة للعدد + +198 +00:16:00,360 --> 00:16:07,880 +نظرية 15 approve + +199 +00:16:07,880 --> 00:16:14,960 +الآن + +200 +00:16:14,960 --> 00:16:17,680 +طبعًا بدي أثبت إنها denumerable، يا بدي أستخدم + +201 +00:16:17,680 --> 00:16:21,320 +النظريات إذا قدرت، يا بدي أجيب bijection بينها وبين + +202 +00:16:21,320 --> 00:16:26,990 +الآن، الحقيقة في صعوبة، مش هنحيبها بـ bijection، هنعمل + +203 +00:16:26,990 --> 00:16:31,130 +الـ trick بسيط، خلينا نشرحه مع بعض، هنعمل بطريقة غير + +204 +00:16:31,130 --> 00:16:35,750 +مباشرة، مش هثبت أنها بتكافئ ال N هثبت أن مجموعته + +205 +00:16:35,750 --> 00:16:43,930 +كافئ ال N بس بطريقة شوية مختلفة، هعرف دالة let F من + +206 +00:16:43,930 --> 00:16:49,860 +N cross ال N إلى ال N هو المفروض أن يكون بيجيكشن + +207 +00:16:49,860 --> 00:16:52,840 +بين M and H من N cross ل N ل N مش هيك التعريف + +208 +00:16:52,840 --> 00:16:57,880 +المباشر، وفيه نظريات مديلة let F من N be given by + +209 +00:16:57,880 --> 00:17:01,760 +طبعًا + +210 +00:17:01,760 --> 00:17:04,620 +أنا في الأصل بتدور على ده، لتكون one to one and + +211 +00:17:04,620 --> 00:17:09,230 +onto، وين الصعوبة اللي ممكن نقبلها؟ أنا بدي أخد عنصر + +212 +00:17:09,230 --> 00:17:14,090 +اللي هو زوج مرتب، فبدي أقول له F of N and M أو X و + +213 +00:17:14,090 --> 00:17:17,970 +Y مثلاً خلينا ناخدهم N و M عشان العداد صحيح بدي زوج + +214 +00:17:17,970 --> 00:17:22,530 +مرتّب يصير عياش عدد واحد، عدد طبيعي كمان هنعرفها في + +215 +00:17:22,530 --> 00:17:31,790 +trick طبعًا 2 أس N في 2 M ناقص 1، 2 + +216 +00:17:31,790 --> 00:17:38,110 +أس N نعم، خلّينا نشوف .. خلّينا نشوف اثنين أس N + +217 +00:17:38,110 --> 00:17:41,190 +يعني مثلاً ايش نجيب؟ ايش عن نزاوج مرتب؟ واحد واحد + +218 +00:17:41,190 --> 00:17:47,910 +ايش صورة الواحد واحد؟ خلّينا نشوف F of واحد واحد + +219 +00:17:47,910 --> 00:17:54,490 +بيساوي إيش؟ اثنين أس واحد اثنين، مش هنطلع + +220 +00:17:54,490 --> 00:17:56,790 +projection، مش هنطلع projection، لكنها one to one + +221 +00:17:56,790 --> 00:18:00,550 +طيب ايش ناخد مثلاً؟ F of واحد اثنين مثلاً، إيش بتساوي + +222 +00:18:00,550 --> 00:18:07,260 +اثنين في ثلاثة ستة صح؟ 2 أس واحد في ثلاثة ستة، طيب F + +223 +00:18:07,260 --> 00:18:11,820 +of اثنين واحد مثلاً ده تصير أربعة في واحد أربعة + +224 +00:18:13,130 --> 00:18:16,490 +فالأمور شوية صعبة إنه مش عملية ترتيب ومين .. أصلاً + +225 +00:18:16,490 --> 00:18:20,350 +الأزواج مرتبة أه؟ الأزواجة المرتبة هي مش مرتبة كيف + +226 +00:18:20,350 --> 00:18:22,470 +مش مرتبة؟ هي مش مرتبة بالنسبة لبعض، مين جاب ال .. + +227 +00:18:22,470 --> 00:18:26,030 +مين؟ مين الزوج؟ هذا جاب لهذا ولا هذا جاب لهذا؟ في + +228 +00:18:26,030 --> 00:18:29,370 +الترتيب، مش عارفين، أه تمام؟ فالعملية بدها شوية + +229 +00:18:29,370 --> 00:18:32,850 +دقة، طبعًا أكيد اللي .. اللي حطوها ده قضية فيه + +230 +00:18:32,850 --> 00:18:36,450 +محاولات متعددة لما يوصل لهذه الصورة، أه فهذه الدالة + +231 +00:18:36,450 --> 00:18:40,570 +هنثبت إنها one to one ليست onto أه لأنه زي ما + +232 +00:18:40,570 --> 00:18:43,800 +شوفين مثلاً هي ليش العداد الفردية مش جاية تطلع، طب + +233 +00:18:43,800 --> 00:18:48,220 +ممكن نأخذها من هناك؟ ايش كنت تعملي مثلاً؟ نأخذها من + +234 +00:18:48,220 --> 00:18:54,420 +هناك، لأنك تريد تغيير الدالة، فنثبت أنها one to one + +235 +00:18:54,420 --> 00:18:58,120 +طيب هذه هذه بيساعدنا هنشوف أنه بده يساعد نعمل الـ + +236 +00:18:58,120 --> 00:19:01,220 +trick، فطبعًا هذه كل الأفكار بتساعدنا إنه مش دائمًا + +237 +00:19:01,220 --> 00:19:04,420 +نلاقي contradiction وإذا ما لاقيناها مش أخر المطاف + +238 +00:19:04,420 --> 00:19:07,480 +في بعض ال trick هتعاملها، فنثبت أنها one to one + +239 +00:19:13,520 --> 00:19:18,280 +F is one to one طبعًا + +240 +00:19:18,280 --> 00:19:27,440 +كالعادة هناخد عنصرين من ال domain N1 M1 N2 M2 في + +241 +00:19:27,440 --> 00:19:38,540 +ال N across ال N such that F of N1 M1 تساوي F of + +242 +00:19:38,540 --> 00:19:40,220 +N2 M2 + +243 +00:19:42,550 --> 00:19:49,250 +ايش عمل؟ نعود نستخدم تعريف الدالة، فهذا يؤدي 2 + +244 +00:19:49,250 --> 00:19:55,510 +أس N1 في 2 M1 ناقص واحد بتساوي 2 + +245 +00:19:55,510 --> 00:19:58,950 +أس N2 في 2 M2 ناقص واحد + +246 +00:20:01,620 --> 00:20:08,000 +بدي أثبت أن N1 تساوي N2 و M1 تساوي M2، مظبوط عشان + +247 +00:20:08,000 --> 00:20:11,260 +أثبت أن الزوج المرتب يساوي الزوج المرتب، فبدي + +248 +00:20:11,260 --> 00:20:14,760 +الإحداثي الأول يساوي الإحداثي الأول والإحداثي الثاني + +249 +00:20:14,760 --> 00:20:20,960 +يساوي الإحداثي الثاني، اه هنا طبعًا ليش اختاره بهذا + +250 +00:20:20,960 --> 00:20:24,840 +الشكل و 2 M ناقص واحد، اه كل هذا أثناء البرهان + +251 +00:20:24,840 --> 00:20:28,860 +الـ one to one هيبين ليش هذا الاختيار، الحقيقة الـ + +252 +00:20:28,860 --> 00:20:32,480 +trick اللي بدي أعمله هو بروح أجسم على اثنين واحدة + +253 +00:20:32,480 --> 00:20:39,500 +منهم، هروح أجسم فلازم أعرف طبعًا هتصير ايش عندي 2 + +254 +00:20:39,500 --> 00:20:44,380 +أس N2 ناقص N1، وان بيصير هنا في عندي عدد فردي و + +255 +00:20:44,380 --> 00:20:48,400 +الطرف الثاني عدد زوجي بس بشرط إذا كان الأس طب على + +256 +00:20:48,400 --> 00:20:52,760 +اثنين موجب، بدي إيه يكون اثنين، فعشان يكون العدد + +257 +00:20:52,760 --> 00:20:55,220 +اللي لها ده يكون موجب، إيش لازم يكون؟ لازم يكون إن + +258 +00:20:55,220 --> 00:20:58,180 +N2 أكبر من N1، فهذا احتمال، الاحتمال + +259 +00:20:58,180 --> 00:21:00,440 +الثاني، لو كان العكس، بنقول الثاني على الطرف + +260 +00:21:00,440 --> 00:21:04,160 +الثاني، فبأخذ بيش الاحتمالين، فهنأخذ اللي هو + +261 +00:21:04,160 --> 00:21:14,050 +الاحتمالين، if n1 أكبر من n2 then n1 هي الكبيرة ننقل + +262 +00:21:14,050 --> 00:21:20,770 +الاثنين عندها بتصير عندنا 2 أس n1 ناقص n2 في 2m1 + +263 +00:21:20,770 --> 00:21:26,950 +ناقص 1 تساوي 2m2 ناقص 1، طبعًا هذا contradiction هذا + +264 +00:21:26,950 --> 00:21:30,070 +زوجي وهذا فردي، صح؟ لأن هي الأس تبعت وإيش؟ موجبة + +265 +00:21:30,070 --> 00:21:32,870 +بقى، في 2 هنا، فهذا إيش contradiction؟ + +266 +00:21:39,020 --> 00:21:43,680 +واضحة ولا عيد؟ اه هل جيت احنا الجسم دي واضحة ولا + +267 +00:21:43,680 --> 00:21:47,120 +مش واضحة؟ الجسمين اه لما تكون n واحد أكبر من n + +268 +00:21:47,120 --> 00:21:50,000 +اثنين يعني هذا الأُسّ موجب، يعني إيش فيها دي + +269 +00:21:50,000 --> 00:21:53,060 +2 أس N1 ناقص N2 تربيع، لأن كل معدات أُسّها + +270 +00:21:53,060 --> 00:21:55,960 +طبيعية فالفرق فيها رقم، واحد اثنين هل جيتها دي + +271 +00:21:55,960 --> 00:21:59,960 +فيها 2 ضرب أي شيء، زوجي 2 M ناقص واحد + +272 +00:21:59,960 --> 00:22:03,780 +2 M ناقص واحد فردي، فردي يساوي زوجي ومستحيل + +273 +00:22:03,780 --> 00:22:12,280 +contradiction طب العكس، إذا N1 أصغر من N2 ثم 2N1-1 + +274 +00:22:12,280 --> 00:22:19,340 +ستكون 2-N2-N1، فـ 2N2-1 برضه Contradiction نفس الشيء + +275 +00:22:19,340 --> 00:22:22,420 +Contradiction، ما تعملش الاحتمال واحد إنهم بيساويوا + +276 +00:22:22,420 --> 00:22:30,490 +بعض، Thus N1 تساوي N2، هذا نص اللي بدنا نعرفه، أن واحد + +277 +00:22:30,490 --> 00:22:33,390 +تساوي أن اثنين، بدي أنا كمان M1 تساوي M2 + +278 +00:22:33,390 --> 00:22:37,310 +طب مازال إن N1 تساوي N2 بقدر أجسم اختصر + +279 +00:22:37,310 --> 00:22:44,050 +منهم then، صحيح + +280 +00:22:44,050 --> 00:22:47,370 +على طول مظبوط، بس المعنى هي الفكرة إنه بالتتابع + +281 +00:22:47,370 --> 00:22:50,290 +العملية مش سهلة جدًّا it follows + +282 +00:22:53,890 --> 00:22:59,930 +that اثنين أم واحد ناقص واحد تساوي اثنين أم اثنين + +283 +00:22:59,930 --> 00:23:04,750 +ناقص واحد ودا يؤدي إلى أم واحد تساوي أم اثنين آه فطبعًا + +284 +00:23:04,750 --> 00:23:11,150 +hence نعم الزوج المرتب يساوي الزوج المرتب أم واحد + +285 +00:23:11,150 --> 00:23:19,830 +تساوي إن اثنين أم اثنين وبالتالي and F is one to + +286 +00:23:19,830 --> 00:23:24,150 +one فأثبتنا إنها one to one رغم أن البرهان لم يكن + +287 +00:23:24,150 --> 00:23:27,430 +سهل، بده بعض التفكير لأن هذه المشكلة إن أنا في + +288 +00:23:27,430 --> 00:23:31,810 +عندي أربعة عناصر أو في عندي زوج مرتب وطرف الثاني + +289 +00:23:31,810 --> 00:23:36,210 +ما عنصر يعني غير عن مرة فكرة من الكارتيزية إلى + +290 +00:23:36,210 --> 00:23:38,650 +الكارتيزية كانت سهلة لأنه بقارن فعندي معادلات + +291 +00:23:38,650 --> 00:23:41,570 +متعددة في عندي .. كان عندي معادلتين أخذت منها + +292 +00:23:41,570 --> 00:23:44,250 +شرطين أو نتيجتين لكن أنا ما عندي معادلة واحدة و + +293 +00:23:44,250 --> 00:23:47,410 +بدأت أنتج منها مرتين فكانت العملية بدها دليلة + +294 +00:23:47,410 --> 00:23:52,640 +تمامًا دي on to مش on two يمكن زي ما احنا شايفين + +295 +00:23:52,640 --> 00:23:58,740 +لكن في trick بسيط ومر علينا قبل هيك في تعريف ال + +296 +00:23:58,740 --> 00:24:02,730 +infinite set قلنا في أول ما عرفنا الـ Infinite set + +297 +00:24:02,730 --> 00:24:07,790 +قلنا هي مجموعة وكافة proper subset منها وقلنا بدل + +298 +00:24:07,790 --> 00:24:11,390 +ما ندور على proper subset وبعدين نجيب ال + +299 +00:24:11,390 --> 00:24:14,850 +bijection أخذنا اللي هو الـ F تكون one to one + +300 +00:24:14,850 --> 00:24:18,210 +وأخذنا الـ proper هي الصورة آه .. ب .. ب .. ب .. + +301 +00:24:18,210 --> 00:24:21,470 +لأ اعتمادًا على أيش فكرة إذا لوجد ده اللي one to + +302 +00:24:21,470 --> 00:24:25,050 +one فدائمًا بقدر أخليها bijection كيف؟ أظغر المجال + +303 +00:24:25,050 --> 00:24:32,460 +المقابل أظغر المجال المقابل فالآن آه now بما أن ال + +304 +00:24:32,460 --> 00:24:39,400 +F is one to one F is one to one implies N cross + +305 +00:24:39,400 --> 00:24:47,540 +الـ N ما هي جت لها شمالها تكافئ F N cross ال N + +306 +00:24:47,540 --> 00:24:53,080 +المدى مظبوط طبعًا جت له وين ده لوين احنا بس نشوف + +307 +00:24:53,080 --> 00:24:56,540 +الصورة الرئيسية احنا بدأنا F من وين لوين يا أخوات؟ + +308 +00:24:58,180 --> 00:25:03,020 +لأ لأ، مظبوط؟ أثبتناه، واضح إن بالنسبة لما أخذنا + +309 +00:25:03,020 --> 00:25:06,140 +بعض الأمثلة إنه المجال المقابل اللي هو الآن أكبر + +310 +00:25:06,140 --> 00:25:10,340 +من اللازم، صح؟ متابعين؟ آه، فإيش روحنا عملناه؟ + +311 +00:25:10,340 --> 00:25:13,380 +صغرناه، أخذنا بس المدى على الجد، على المدى، + +312 +00:25:13,380 --> 00:25:20,220 +بـSubjection، صح؟ طيب، هذه شمالها، صح؟ مشكلة المدى + +313 +00:25:20,220 --> 00:25:24,720 +هو subset من المجال المقابل؟ نشوف مع بعض، طيب، + +314 +00:25:24,720 --> 00:25:27,360 +الآن إذا قدرنا أثبت أن هذه denominable انتهت + +315 +00:25:27,360 --> 00:25:31,780 +العملية لأن هي هذي تكافئ denominable وعملية التعداد + +316 +00:25:31,780 --> 00:25:36,040 +تصبح denominable، طيب، الآن هذه subset من مين؟ من + +317 +00:25:36,040 --> 00:25:40,870 +الآن طيب ليش .. مش ضروري هذه subset من denominable + +318 +00:25:40,870 --> 00:25:44,210 +إذا كانت infinite انتهت العملية لأن infinite + +319 +00:25:44,210 --> 00:25:46,710 +subset من denominable is denominable طيب ليش هذه + +320 +00:25:46,710 --> 00:25:51,850 +infinite؟ ليش هذه infinite؟ لأن هذه تكافئ هذه + +321 +00:25:51,850 --> 00:25:56,350 +ومستحيل تكون finite آه لأن مستحيل تكون finite آه + +322 +00:25:56,350 --> 00:25:59,870 +فهذه subset من ال end وهذه تكافئها فهي على طول + +323 +00:25:59,870 --> 00:26:02,750 +denominable كيف بدنا نكتفي؟ فإذا هذه تكافئها فهذه + +324 +00:26:02,750 --> 00:26:04,310 +تكافئها since + +325 +00:26:09,610 --> 00:26:18,690 +N cross الـ N is infinite we + +326 +00:26:18,690 --> 00:26:28,330 +have F of N cross ال N is infinite وهذا + +327 +00:26:28,330 --> 00:26:33,450 +يؤدي إلى أن F of N cross ال N is innumerable + +328 +00:26:38,430 --> 00:26:44,030 +هذه نظرية نظرية جدًّاش infinite subset of + +329 +00:26:44,030 --> 00:26:51,850 +denumerable set is denumerable نظرية خمسة ثمانية + +330 +00:26:51,850 --> 00:26:58,350 +صحيح خلاص مع ذلك عملية equivalence relation + +331 +00:26:58,350 --> 00:27:05,390 +therefore n x n is denumerable + +332 +00:27:09,360 --> 00:27:12,740 +ليش؟ لأن علاقة التكافئة في واحدة شمالها + +333 +00:27:12,740 --> 00:27:16,600 +equivalence relation وبشكل خاص شمالها transitive + +334 +00:27:16,600 --> 00:27:20,820 +is transitive + +335 +00:27:20,820 --> 00:27:26,620 +فاحنا ليش أثبتنا أن cross الان تكافئ هذه المجموعة + +336 +00:27:26,620 --> 00:27:29,480 +و هذه المجموعة تكافئ الان فإذا الأولى تكافئ + +337 +00:27:29,480 --> 00:27:34,440 +الثالثة وهو المطلوب فهنا ما قدرناش نوصل مباشرة لكن + +338 +00:27:34,440 --> 00:27:36,960 +وصلنا بهذه الطريقة غير المباشرة + +339 +00:27:39,990 --> 00:27:44,610 +هذه واحدة من الحيل التي نجعلها أحيانًا عندما + +340 +00:27:44,610 --> 00:27:49,550 +الأمور لا تصبح مجموعة كبيرة ولا نستطيع الإجابة بشكل + +341 +00:27:49,550 --> 00:27:50,050 +مباشر + +342 +00:27:59,530 --> 00:28:04,450 +مزيد من التوسع دائمًا حاضر فزي ما احنا شايفين احنا + +343 +00:28:04,450 --> 00:28:06,770 +كل ما لقينا بدينا يعني الممكن الفكرة اللي ماشيين + +344 +00:28:06,770 --> 00:28:11,070 +فيها جالسين بنكبر كل ما قاش وانا نوصل هل هتوجه + +345 +00:28:11,070 --> 00:28:15,850 +مرحلة ونبطل denumerable بنشوف بنكبر denumerable + +346 +00:28:15,850 --> 00:28:19,590 +بنكبر denumerable بدنا نشوف وقت إيش الكلب بده يطف + +347 +00:28:19,590 --> 00:28:23,370 +ويتبطل المجموعة denumerable لمّا جدًّاش نكبرها جدًّاش + +348 +00:28:23,370 --> 00:28:30,420 +نضيف لها فعنا نتيجة خمسة خمسة Infinite union of + +349 +00:28:30,420 --> 00:28:36,740 +disjoint denumerable sets is denumerable كان في + +350 +00:28:36,740 --> 00:28:43,440 +عندنا نتيجة نتيجة اللي هو finite union بس ما قالليش + +351 +00:28:43,440 --> 00:28:46,660 +disjoint هناك بشكل عام اللي هو إيش احنا بدأنا + +352 +00:28:46,660 --> 00:28:50,520 +بنظرية المحاضرة وبعدها نتيجة مباشرة كان finite + +353 +00:28:50,520 --> 00:28:56,280 +union بدون disjoint الآن infinite union بس حط شرط + +354 +00:28:56,280 --> 00:28:59,400 +إنه لازم يكونوا disjoint المجموعات is denumerable + +355 +00:28:59,400 --> 00:29:02,840 +فالآن إحنا حلينا خدنا أي اتحاد ما لا نهاية من + +356 +00:29:02,840 --> 00:29:06,880 +المجموعات بس يكونوا disjoint بده يدمّر اتحاد denumerable + +357 +00:29:07,640 --> 00:29:12,300 +نشوف البرهان والفكرة تبعها البرهان وإيش بدنا + +358 +00:29:12,300 --> 00:29:19,240 +نشتغل معها for each k تنتمي إلى لأن لأي عدد طبيعي let + +359 +00:29:19,240 --> 00:29:25,860 +a sub k be a denumerable set satisfying a j تقاطع + +360 +00:29:25,860 --> 00:29:30,740 +a k تساوي five for all j لا تساوي k نحاول نفهم هذا + +361 +00:29:30,740 --> 00:29:36,940 +الكلام هو يعبر عن جميع المجموعات مقاومة في ال + +362 +00:29:36,940 --> 00:29:41,320 +Disjoint ما هو معنى الـ Disjoint؟ كل اثنين + +363 +00:29:41,320 --> 00:29:44,060 +تقاطعوهم فيها، ليس فقط كلهم تقاطعوهم مع بعض فيها، + +364 +00:29:44,060 --> 00:29:51,520 +لكن كل اثنينفعبّر عنه أن أي جي تقاطع أي ك لأي جي + +365 +00:29:51,520 --> 00:29:55,600 +لا تساوي ك طبعًا التبليش مجال لا تساوي لأن لو بيساووا + +366 +00:29:55,600 --> 00:29:58,580 +بعض ما بيكون تقاطعهم بيساوي نفسهم ما عندش منطقي لما + +367 +00:29:58,580 --> 00:30:01,600 +يقولوا كل مجموعتين المختلفتين تقاطعهم فيه هيك + +368 +00:30:01,600 --> 00:30:06,240 +معناته فبقول الاتحاد is denumerable الاتحاد is + +369 +00:30:06,240 --> 00:30:12,840 +denumerable نشوف البرهان Corollary خمسة + +370 +00:30:12,840 --> 00:30:14,940 +خمسة Approved + +371 +00:30:18,740 --> 00:30:23,740 +خلّينا نبدأ بالمعطيات، كلّه يكون صحيح، وإذا أردنا + +372 +00:30:23,740 --> 00:30:28,160 +أن نثبت بأنه نمبربول فكلّه مُعطى، ما هي فكرة + +373 +00:30:28,160 --> 00:30:32,100 +البرهان لكي نتابع مع بعض؟ طبعًا احنا في عندنا نظرية + +374 +00:30:32,100 --> 00:30:35,720 +بتقول إن اتحاد الـ bijections بيموّوا bijection بس + +375 +00:30:35,720 --> 00:30:40,540 +في شرط بدنا تقاطع كل المجالات Phi وبدنا تقاطع + +376 +00:30:40,540 --> 00:30:44,500 +المجالات المقابلة يساوي Phi بالنسبة لو بدنا احنا + +377 +00:30:44,500 --> 00:30:48,700 +احنا إيش الصورة تقريبًا تعميم ل case one من النظرية + +378 +00:30:48,700 --> 00:30:52,280 +السابقة أو من النتيجة السابقة فانا عندي هاي A1 + +379 +00:30:52,280 --> 00:31:00,520 +تكافئ أنا في عندي A2 تكافئ أنا وهكذا في المرة + +380 +00:31:00,520 --> 00:31:04,440 +الماضية كانت الانتين كنا سهلة واحدة N O N E وخلصنا + +381 +00:31:04,440 --> 00:31:10,120 +العملية الآن هدول تقطعوا حنفية جاهز بس أنا بدي أجيب + +382 +00:31:10,120 --> 00:31:16,800 +أستبدل الان بمجموعات تقطعوا حنفية لمّا كانت الانتين + +383 +00:31:16,800 --> 00:31:20,300 +العملية سهلة جبنا N O N E فالآن كيف بدنا نجيب + +384 +00:31:20,300 --> 00:31:24,600 +مهلة نهاية من المجموعات هنا كلهم تقطعوا حنفاي فهي + +385 +00:31:24,600 --> 00:31:28,000 +الفكرة اللي بدنا نشتغل عليها، هنعمل ترك بسيط، + +386 +00:31:28,000 --> 00:31:31,260 +هنعمل ترك، كل هذه تركات بنتعلمها مع بعض، العملية + +387 +00:31:31,260 --> 00:31:36,960 +سهلة جدًا، يعني الفكرة يعني فعلاً فكرة .. فكرة واضحة + +388 +00:31:36,960 --> 00:31:40,440 +وسهلة، بس طبعًا كيف تجين الأول مرة، هي القضية، احنا + +389 +00:31:40,440 --> 00:31:41,920 +إيش اللي هنعمله؟ + +390 +00:31:43,800 --> 00:31:48,440 +العملية هنشوف إننا نتحدث عن عدد العناصر مظبوط + +391 +00:31:48,440 --> 00:31:52,560 +فبدنا مجموعة عدد العناصر زي الان بالضبط لكن كل + +392 +00:31:52,560 --> 00:31:55,680 +واحدة مختلفة طب لما أنا أضرب عدد العناصر الان + +393 +00:31:55,680 --> 00:31:59,440 +بواحد بتعمل نفس الشيء كيف ممكن أضربه في واحد لو + +394 +00:31:59,440 --> 00:32:02,340 +عملت له كارتيزار و دخلت مع عنصر واحد لو عملت له + +395 +00:32:02,340 --> 00:32:06,960 +كارتيزار و دخلت مع عنصر واحد فالآن هذه المجموعة بدي + +396 +00:32:06,960 --> 00:32:11,460 +أستبدلها بأن أحسنتي + +397 +00:32:12,370 --> 00:32:17,950 +آه حالجين وهذه حالجين + +398 +00:32:17,950 --> 00:32:20,510 +هذه تقطعوا فيهم ولا مش فيهم لأن ولا واحد هذه + +399 +00:32:20,510 --> 00:32:23,150 +الأحداث الثانية دائمًا واحد هذه الأحداث الثانية + +400 +00:32:23,150 --> 00:32:26,210 +دائمًا اثنين عمره ما بيصير هذا وهكذا فهي الفكرة + +401 +00:32:26,210 --> 00:32:30,390 +فهي الفكرة اللي بدنا نعملها آه فطبعًا اللي هو ال + +402 +00:32:30,390 --> 00:32:34,070 +bijection واضح ضروري أكتبه ولا لأ مظنّنيش لأن في + +403 +00:32:34,070 --> 00:32:39,230 +ضرورة أن نكتبه ما فيش داعي أن نكتب اللي هو ال + +404 +00:32:39,230 --> 00:32:49,790 +bijection خلّيني أكتبه مش مشكلة فالآن for each K + +405 +00:32:49,790 --> 00:32:58,270 +تنتمي إلى ال N let FK من .. بدي أثبت هذا الكلام إنّه + +406 +00:32:58,270 --> 00:33:07,650 +دائمًا صح على السريع من N إلى N across ال K be + +407 +00:33:07,650 --> 00:33:19,950 +given by فك الان تساوي ان ومين وك يعني هنا إيش + +408 +00:33:19,950 --> 00:33:24,930 +بتسمي هذه الدالة F1 F2 هاي بسمي بكتب الكلام اللي + +409 +00:33:24,930 --> 00:33:30,350 +شرحته فإيش تعمل هاي العنصر من إيش بيصير كلّه من إيش + +410 +00:33:30,350 --> 00:33:33,810 +أزواج ان واحد أو ان اثنين أو ان ثلاث فطبعًا هذه + +411 +00:33:33,810 --> 00:33:38,250 +بيجيكشن البرهان هتركه في ال exercise given by let + +412 +00:33:38,250 --> 00:33:46,800 +F then FK is a bijection exercise + +413 +00:33:46,800 --> 00:33:52,500 +آه + +414 +00:33:52,500 --> 00:33:56,840 +تفضلي لأ + +415 +00:33:56,840 --> 00:34:00,380 +بس بزيده يعني بدل مجموعة الواحد تقولي مجموعة + +416 +00:34:00,380 --> 00:34:05,440 +الاثنين لأ بصير ضربت المجموعة ب اثنين ضعفها مش مش + +417 +00:34:05,440 --> 00:34:11,890 +نفسها هل جت لها دي عدد عناصرها مئة؟ وهذا عدد عناصرها + +418 +00:34:11,890 --> 00:34:15,110 +واحد؟ جدًّاش المجموع الكارتيزيان بتاع مئة؟ لكن لما + +419 +00:34:15,110 --> 00:34:18,530 +تقول هنا مئة وهنا اثنين تصبحين اثنين أنا بديها + +420 +00:34:18,530 --> 00:34:22,490 +تكافئ واضحة طول لأ؟ آه فما بيدّي أنا أضعف العدد، + +421 +00:34:22,490 --> 00:34:25,470 +أنا بدي نفس العدد لما أنا بثبت الإحداثي الثاني + +422 +00:34:25,470 --> 00:34:28,910 +ما بتغيرش عدد العناصر بس بدل مكتوبهم اللي هو and + +423 +00:34:28,910 --> 00:34:36,670 +بدل مكتوبة هنا الـ and مين بناظر؟ إن واحد ما بدش + +424 +00:34:36,670 --> 00:34:39,450 +يديها احتماليا في كل أعداد ماهي مقابلة للتنظير الصحيح + +425 +00:34:39,450 --> 00:34:42,270 +له واضح لكن لما تصير إن مع الواحد ولا إن مع + +426 +00:34:42,270 --> 00:34:45,490 +التانين فصار إيه لو تشعب ممكن يزيدوا عدد العناصر + +427 +00:34:45,490 --> 00:34:52,370 +واضحات تمام فـ this is a bijection طبعًا فالآن now + +428 +00:34:52,370 --> 00:34:55,530 +كل + +429 +00:34:55,530 --> 00:35:05,370 +a k تكافئ لليمين and across الـ k مظبوط وليه إيش + +430 +00:35:05,370 --> 00:35:13,150 +بيجيكشن وإيش كمان and a j تقاطع الـ a k تساوي five + +431 +00:35:13,150 --> 00:35:16,590 +وهادي + +432 +00:35:16,590 --> 00:35:22,030 +تساوي إيش كمان اللي + +433 +00:35:22,030 --> 00:35:29,510 +ليمين اللي هو n اه بتجيب الباقي كله اللي هو عبارة + +434 +00:35:29,510 --> 00:35:37,420 +عن اللي هو n cross j تقاطع N across الـ K برضه + +435 +00:35:37,420 --> 00:35:40,060 +بيساوي Phi هذا اللي عملناه، الكلام اللي شرحناه أنه + +436 +00:35:40,060 --> 00:35:43,080 +اللي جت عنا على الجهة هذه كله تقاطع Phi معطى، صح؟ + +437 +00:35:43,080 --> 00:35:46,740 +وبهذا الـ trick صار تقاطع كله Phi، صح؟ أه، فالآن + +438 +00:35:46,740 --> 00:35:50,040 +بقدر أخد الاتحاد على طول، فالاتحاد، يجب أن يكافئ + +439 +00:35:50,040 --> 00:35:54,280 +الاتحاد نظرية تعميم لنظرية اللي هو إيش؟ أن الـ + +440 +00:35:54,280 --> 00:35:58,680 +union of two bijections is a bijection أه، implies + +441 +00:35:58,680 --> 00:36:00,380 +اتحاد + +442 +00:36:02,190 --> 00:36:11,950 +J من واحد لـ infinity AJ يكافئ اتحاد J من واحد + +443 +00:36:11,950 --> 00:36:20,170 +لـ infinity N across الـJ بس + +444 +00:36:20,170 --> 00:36:24,990 +اللي جينا احنا حلنا المشكلة طب اتحاد هدول هل + +445 +00:36:24,990 --> 00:36:27,730 +بيتموا denumerable من اتحاد هذا + +446 +00:36:35,840 --> 00:36:39,860 +هذا تمرين في الكتاب هذا السؤال في الكتاب اثبت أن + +447 +00:36:39,860 --> 00:36:45,460 +هذه تساوي هذه هذا تمرين في الكتاب موجود وهو + +448 +00:36:45,460 --> 00:36:47,920 +المطلوب لماذا ما دي دي نمرة مش لو اثبتناه عشان ذلك + +449 +00:36:47,920 --> 00:36:50,880 +احنا حطينا النظرية جابنا النظرية لأن المنطق يقول + +450 +00:36:50,880 --> 00:36:53,500 +لماذا ما انتماش فيها اتحاد لماذا روحت على الكارتسية + +451 +00:36:53,500 --> 00:36:57,420 +وبعدها رجعت للاتحاد عشان مديها فخلاص وهي دي نمرة + +452 +00:36:57,420 --> 00:37:01,200 +وهو المطلوب وهو المطلوب + +453 +00:37:11,410 --> 00:37:18,130 +أي سؤال؟ تمام فاحنا يعني يمكن إن إحنا ماشيين في + +454 +00:37:18,130 --> 00:37:22,010 +اتجاه بنكبر وبنمرّج بعض المجموعات اللي بنعرفها + +455 +00:37:22,010 --> 00:37:25,390 +طبعًا وحدة القياس الـ Merge يعتبر أنها الـ natural + +456 +00:37:25,390 --> 00:37:29,970 +number شفنا الـ Z لأنها denumerable نمشي إلى + +457 +00:37:29,970 --> 00:37:33,050 +قدام، مين الأكبر من الـ Z؟ الـ Q مشهورة طب هل الـ + +458 +00:37:33,050 --> 00:37:36,870 +Q denumerable ولا لأ؟ Denumerable الـ Q is + +459 +00:37:36,870 --> 00:37:44,560 +denumerable وهذه نتيجة نتيجة بـ مجموعة الأعداد النسبية + +460 +00:37:44,560 --> 00:37:50,880 +is denumerable corollary + +461 +00:37:50,880 --> 00:37:54,660 +a + +462 +00:37:54,660 --> 00:38:03,520 +proof خلينا + +463 +00:38:03,520 --> 00:38:08,080 +نشوف البرهان مع بعض ونشوف إيش الأفكار الموجودة فيه + +464 +00:38:10,340 --> 00:38:13,840 +طبعًا مش هأتراعب مع الـ Q مش هقدر أدي بيجيكشن بين + +465 +00:38:13,840 --> 00:38:17,860 +الـ Q بين الـ N أول شيء هأجزئها إلى طبعًا زي ما + +466 +00:38:17,860 --> 00:38:21,240 +اتعلمنا في المثال تبع الـ Z لو أنا قدرت أجزئها + +467 +00:38:21,240 --> 00:38:24,160 +عبارة عن نصفين، العداد الصحيح اللي هو ليش الموجب + +468 +00:38:24,160 --> 00:38:27,060 +بالحال والسالب بالحال وطبعًا السالب والموجب + +469 +00:38:27,060 --> 00:38:30,140 +متكافئين وواضح العملية فدي أول خطوة خلينا نعملها + +470 +00:38:30,140 --> 00:38:37,220 +ملاحظة first of all هذه + +471 +00:38:37,220 --> 00:38:42,600 +الـ Q بقدر أكتبها على صورة Eq minus الأعداد النسبية + +472 +00:38:42,600 --> 00:38:48,880 +السالبة اتحاد الصفر اتحاد الأعداد النسبية الموجبة + +473 +00:38:48,880 --> 00:38:52,940 +مظبوط + +474 +00:38:52,940 --> 00:39:00,140 +أه فطبعًا هادي تكافئ هادي صح إيش الدالة بينهم F of + +475 +00:39:00,140 --> 00:39:05,730 +X صار سالب X السالب والموجب صح؟ والصفر الزيادة لو + +476 +00:39:05,730 --> 00:39:07,990 +قدرت أثبت أنها دي denumerable فاللي تكفيها + +477 +00:39:07,990 --> 00:39:11,090 +denumerable Automatic وضفنا عليها عنصر denumerable + +478 +00:39:11,090 --> 00:39:14,330 +Proposition صالحة فإحنا هنجزئ المثال مش هنشتر + +479 +00:39:14,330 --> 00:39:20,010 +عليها مرة واحدة هنجزئها هنجزئها اه فإذا بينا نثبت + +480 +00:39:20,010 --> 00:39:29,530 +أن الـ Q plus is denumerable we will prove Q plus + +481 +00:39:30,290 --> 00:39:35,630 +اللي هي تساوي X تنتمي لـ Q such that X is positive + +482 +00:39:35,630 --> 00:39:44,090 +is denumerable هنثبت + +483 +00:39:44,090 --> 00:39:49,670 +أن العداد النسبي denumerable طيب نبدأ نفكر عشان الأمر + +484 +00:39:49,670 --> 00:39:53,370 +يعني يرسخ والفكرة تيجي بالنسبة للعدد النسبي لما + +485 +00:39:53,370 --> 00:39:55,530 +أقول عدد نسبي إيش بيجي على بالك؟ نعم + +486 +00:39:58,640 --> 00:40:01,520 +ممتاز إذا هو فيه بسط ومقام والبسط والمقام دول إيش + +487 +00:40:01,520 --> 00:40:05,320 +بيكونوا أعداد صحيحة natural natural إذا كانوا إيش Q + +488 +00:40:05,320 --> 00:40:09,080 +plus عشان هيك هناخد ناخد Q plus فإذا هذه اللي هو + +489 +00:40:09,080 --> 00:40:16,740 +إيش الملاحظة على طول فهنا let X تنتمي لـ Q plus + +490 +00:40:16,740 --> 00:40:27,510 +عشان هيك اخذنا then X تساوي B على Q for some طبعًا + +491 +00:40:27,510 --> 00:40:32,870 +احنا عندنا مثلًا النص نكتبها واحد على اتنين أو اتنين + +492 +00:40:32,870 --> 00:40:36,370 +على أربعة أو خمسة على عشرة لكن لما بدي أعمل أنا + +493 +00:40:36,370 --> 00:40:39,150 +تمثيل حقيقي لازم أعملها بشكل إنه إيش يكون كل + +494 +00:40:39,150 --> 00:40:42,230 +المعاملات المشتركة تكون محذوفة فده بنعبر عنه إنه + +495 +00:40:42,230 --> 00:40:45,930 +يكون إيش المعامل المشترك الأعظم يكون بواحد فدائمًا + +496 +00:40:45,930 --> 00:40:49,770 +هذا الكلام متوفر لأي عدد نسبي x ممكن نكتبها بهذا + +497 +00:40:49,770 --> 00:40:54,880 +الشكل for some P و Q وين موجودين في الـ natural + +498 +00:40:54,880 --> 00:40:58,400 +number الآن عشان هي أنا أخدت الـ plus لأنهم موجبين + +499 +00:40:58,400 --> 00:41:04,620 +السؤال اللي بيخلّيني أعملها where for some with + +500 +00:41:04,620 --> 00:41:08,260 +greatest + +501 +00:41:08,260 --> 00:41:11,300 +common + +502 +00:41:11,300 --> 00:41:13,880 +divisor اللي هو العام المشترك الأعظم + +503 +00:41:19,700 --> 00:41:25,160 +divisor ما يسمونه ليش العامل المشترك أو العامل + +504 +00:41:25,160 --> 00:41:32,680 +المشترك الأكبر greatest common divisor of B and Q + +505 +00:41:32,680 --> 00:41:37,020 +is one بواحد، لا أريد أن يتم ولا عامل مشترك، كله + +506 +00:41:37,020 --> 00:41:41,720 +بدأ يختصر، تمام فهذا سيساعدنا، الآن سنعرف دالة، + +507 +00:41:41,720 --> 00:41:45,720 +مين عرف دالة؟ سنستطيع أن نثبت أن الـQ تكافئ الـN + +508 +00:41:45,720 --> 00:41:53,520 +ولا الـN cross الـN واضح إن كل عدد نسبي بيصير عددين + +509 +00:41:53,520 --> 00:41:57,000 +طبيعيين فإذا أسهل أشتغل على مين على N نقرص الـ N + +510 +00:41:57,000 --> 00:42:02,780 +أسهل أشتغل على الـ N نقرص الـ N فالآن هنعرف الدالة + +511 +00:42:02,780 --> 00:42:07,820 +بالشكل التالي هنعرفها هل هي one to one and onto + +512 +00:42:07,820 --> 00:42:13,900 +أتوقع مش شرط هي one to one and onto لأ مش هتطلع + +513 +00:42:13,900 --> 00:42:18,760 +one to one and onto لكن العملية سهلة let F + +514 +00:42:21,380 --> 00:42:34,900 +من Q plus إلى N across الـ N B given by F + +515 +00:42:34,900 --> 00:42:41,120 +of B على Q اتفقنا إن كل عدد هنا مكتوب بهذه الشكل و + +516 +00:42:41,120 --> 00:42:44,340 +طبعًا طب ليش أنا بدي المعامل المشتركة بواحد عشان + +517 +00:42:44,340 --> 00:42:48,520 +لما .. ده اللي هتكون معرفة ما نفعش أقوله مثلًا الجد + +518 +00:42:48,520 --> 00:42:54,720 +أقوله F of نص هذي بيكون F of 2 على 4 طب كيف بدي + +519 +00:42:54,720 --> 00:42:57,260 +أعرفها؟ أنا مش عارف كيف بدي أعرف الدالة دي بي كيو + +520 +00:42:57,260 --> 00:43:01,900 +لو أنا هذا ما حاططوش بالصورة صار هذا بدي أعرفه + +521 +00:43:01,900 --> 00:43:05,980 +إيه؟ وكيف ممكن أعرفه؟ واحد اتنين وأنا كيف بدي + +522 +00:43:05,980 --> 00:43:09,160 +أعرفه اتنين أربعة؟ هدول ليه يساوي بعض؟ فبتبطل + +523 +00:43:09,160 --> 00:43:13,540 +دالة فلازم أحطه بصورة نموذجية بصورة قياسية عشان + +524 +00:43:13,540 --> 00:43:17,830 +أقدر أعرف صح عشان أقدر أعرف صح فطبعًا زي ما بنحكي + +525 +00:43:17,830 --> 00:43:21,430 +دائمًا الرياضيات مش فيها أي شيء زيادة مش بدي قول كل + +526 +00:43:21,430 --> 00:43:27,170 +كلمة مهمة وإلا بنخسر كتير من الأشياء لو لها الدقة + +527 +00:43:27,170 --> 00:43:31,690 +الموجودة تمام الدالة دي سهل نثبت أنها one to one + +528 +00:43:31,690 --> 00:43:40,490 +طبعًا مش onto الحقيقة ممكن نشوف أنها مش onto then F + +529 +00:43:40,490 --> 00:43:46,890 +is one to one طبعًا بضمن إن هذه الأمور بقدر أثبتها + +530 +00:43:46,890 --> 00:43:50,150 +one to one لأن كل عنصر قوله representation صحيح + +531 +00:43:50,150 --> 00:43:53,810 +one to one مش هنثبتها أنتم هنعمل trick تبع توي + +532 +00:43:53,810 --> 00:43:58,110 +نفس الـ trick فما زال one to one بتصير عندنا مين الـ + +533 +00:43:58,110 --> 00:44:03,730 +Q plus H تكافئ شوف متابعين ولا لأ أنا كنت أقف من + +534 +00:44:03,730 --> 00:44:07,650 +وين لوين من الـ Q plus لإن نقرص الآن one to one فقط + +535 +00:44:07,650 --> 00:44:12,110 +بتكافئ ليش الـ image مظبوط نفس الـ trick اللي هي F + +536 +00:44:13,290 --> 00:44:18,690 +وفي Q Plus وهذا subset من مين؟ من الـ N نقرص في + +537 +00:44:18,690 --> 00:44:23,510 +الـ N أه هلّجت هذه الـ Denominable إذا هذه Infinite + +538 +00:44:23,510 --> 00:44:26,930 +انتهت العملية طب هذه Infinite ليش؟ لأن الـ Q Plus + +539 +00:44:26,930 --> 00:44:29,890 +Infinite لأن الـ Q Plus شمالها أكبر من الـ N + +540 +00:44:29,890 --> 00:44:38,890 +Infinite أه فالآن الـ subset and F of Q Plus is + +541 +00:44:38,890 --> 00:44:45,840 +Infinite implies F of Q plus is denumerable + +542 +00:44:45,840 --> 00:44:52,720 +وبالتالي + +543 +00:44:52,720 --> 00:45:00,000 +Q plus is denumerable + +544 +00:45:00,000 --> 00:45:03,740 +والباقي + +545 +00:45:03,740 --> 00:45:11,530 +زي ما حكينا طبعًا Q minus تكافئ Q plus Q minus تكافئ + +546 +00:45:11,530 --> 00:45:21,850 +EQ plus implies EQ minus is denumerable طبعًا + +547 +00:45:21,850 --> 00:45:30,510 +فبتمن إن الاتحاد تبقى homodenumerable therefore EQ + +548 +00:45:30,510 --> 00:45:36,270 +is denumerable مع + +549 +00:45:36,270 --> 00:45:37,690 +النظريات السابقة + +550 +00:45:50,290 --> 00:45:56,430 +فطبعًا يمكن بدت اللي هو الصورة تكتمل شيئًا فشيئًا، + +551 +00:45:56,430 --> 00:46:00,630 +الآن مرتانة في عندنا عنوان الـ denumerable sets are + +552 +00:46:00,630 --> 00:46:05,450 +the smallest infinite sets فطبعًا كل موضوعنا الأساسي + +553 +00:46:05,450 --> 00:46:08,890 +اللي بندور حواليه يمكن أو اللي احنا بنوصل لتصور + +554 +00:46:08,890 --> 00:46:13,270 +التالي أو الحقيقة التالية احنا بنجيس المجموعات من + +555 +00:46:13,270 --> 00:46:17,170 +حيث الحجم أو عدد العناصر فعنا طبعًا أصغر مجموعة هي + +556 +00:46:17,170 --> 00:46:19,670 +الـ five ما فيش فيها ولا عنصر بعدين ببدأ المجموعة + +557 +00:46:19,670 --> 00:46:23,190 +فيها عنصر واحد finite فيها خمس عناصر بنتمنا نكبر + +558 +00:46:23,190 --> 00:46:26,570 +خلص الـ finite تجينا الـ infinite أصغر infinite set + +559 +00:46:26,570 --> 00:46:28,770 +هي الـ natural number، هي الـ denumerable، طب في + +560 +00:46:28,770 --> 00:46:32,630 +أكبر منها في كل الـ infinite زي بعض، لأ، هنوصل لها + +561 +00:46:32,630 --> 00:46:35,210 +دي الحقيقة، آه، لكن فأصغر infinite هي + +562 +00:46:35,210 --> 00:46:37,570 +الـdenumerable set، بعدين فيه الـnon-denumerable، + +563 +00:46:37,570 --> 00:46:40,230 +حنسميهم، أو الـuncountable، مش قادرين، ممكنش نتخيل + +564 +00:46:40,230 --> 00:46:43,070 +عددهم، ولا نعدهم، ولا نرقمهم، عناصرهم، فاحنا + +565 +00:46:43,070 --> 00:46:46,350 +ماشيين بهذا الاتجاه، آه فالمرة الماضية كان العنوان + +566 +00:46:46,350 --> 00:46:50,530 +هذا في نظرية قالت لنا أنه any اللي هو الـ .. الـ .. + +567 +00:46:50,530 --> 00:46:53,050 +الـ .. كده، واستخدمناها infinite subset من + +568 +00:46:53,050 --> 00:46:54,870 +denumerable to denumerable مافيش أصغر من + +569 +00:46:54,870 --> 00:46:56,630 +denumerable مافيش infinite أصغر من denumerable + +570 +00:46:56,630 --> 00:47:00,970 +الآن هنشوف بشكل مختلف أنه أنا عندي أي infinite set + +571 +00:47:00,970 --> 00:47:04,010 +بقدر ألاقي منها subset تكون denumerable فانا بقدر + +572 +00:47:04,010 --> 00:47:07,410 +ألاقي مجموعة صغيرة، فبقول every infinite set + +573 +00:47:07,410 --> 00:47:11,210 +contains a denumerable subset، آه خلّي البرهان إن + +574 +00:47:11,210 --> 00:47:12,190 +شاء الله في المرة القادمة diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/n56Jirv5D38_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/n56Jirv5D38_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..84b98044dec3c2e220177b04cf2c8fc33dc422e7 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/n56Jirv5D38_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 3311, "start": 19.74, "end": 33.12, "text": "بسم الله الرحمن الرحيم، هنواصل مع الـdenominable sets وطبعا ال section خمسة تلاتة هو مكمل لsection خمسة اتنين بيتحدث عن اللي هو examples and 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.. النقطة اللي هنوصلها و بنتحدث عنها يعني يمكن ذكرناها و هنأكد عليها أن الـdenominable sets هي أصغر infinite set أصغر infinite set و كان في عندنا نظرية شوفنا احنا لو أخدنا infinite subset من denominable تمت denominable", "tokens": [10721, 3224, 6156, 9566, 3555, 3615, 995, 1975, 5016, 8315, 45164, 13412, 38688, 8315, 13672, 1829, 31439, 31767, 13063, 3660, 13672, 1829, 44945, 2655, 24401, 12984, 18871, 11296, 6225, 8592, 7649, 8717, 8592, 38688, 20328, 13063, 3660, 28242, 10632, 5296, 19528, 2407, 11242, 45367, 6156, 39319, 8315, 2423, 4386, 28239, 47432, 3660, 13672, 1829, 8032, 1863, 2407, 36520, 11296, 4032, 44945, 2655, 24401, 12984, 18871, 11296, 37495, 22653, 7251, 43020, 29910, 37983, 8315, 11296, 4032, 8032, 1863, 10721, 4117, 3215, 25894, 11296, 14739, 2423, 39184, 1556, 6981, 712, 6352, 39896, 5551, 9381, 17082, 2288, 13785, 992, 5551, 9381, 17082, 2288, 13785, 992, 4032, 25961, 8978, 43242, 8315, 8717, 19913, 2288, 10632, 13412, 38688, 8315, 1975, 5016, 8315, 45164, 5551, 9778, 3215, 8315, 13785, 25993, 9154, 1441, 6981, 712, 46811, 2655, 1441, 6981, 712], "avg_logprob": -0.13759327635391436, "compression_ratio": 1.9678714859437751, "no_speech_prob": 0.0, "words": [{"start": 34.88, "end": 35.18, "word": "أه", "probability": 0.472900390625}, {"start": 35.18, "end": 35.54, "word": " فطبعا", "probability": 0.92265625}, {"start": 35.54, "end": 35.74, "word": " احنا", "probability": 0.87646484375}, {"start": 35.74, "end": 35.92, "word": " لو", "probability": 0.95849609375}, {"start": 35.92, "end": 36.32, "word": " شوفنا", "probability": 0.8626302083333334}, {"start": 36.32, "end": 36.44, "word": " اللي", "probability": 0.867919921875}, {"start": 36.44, "end": 36.54, "word": " هو", "probability": 0.97705078125}, {"start": 36.54, "end": 37.02, "word": " الصورة", "probability": 0.9895833333333334}, {"start": 37.02, "end": 37.12, "word": " اللي", "probability": 0.931884765625}, {"start": 37.12, "end": 37.6, "word": " بنتحدث", "probability": 0.883056640625}, {"start": 37.6, "end": 37.9, "word": " عنها", "probability": 0.99560546875}, {"start": 37.9, "end": 38.28, "word": " عشان", "probability": 0.9765625}, {"start": 38.28, "end": 39.24, "word": " نشوف", "probability": 0.9840494791666666}, {"start": 39.24, "end": 39.7, "word": " صورة", "probability": 0.9918619791666666}, {"start": 39.7, "end": 40.18, "word": " كلية", "probability": 0.840087890625}, {"start": 40.18, "end": 40.88, "word": " للموضوع", "probability": 0.95302734375}, {"start": 40.88, "end": 42.28, "word": " فاحنا", "probability": 0.8776041666666666}, {"start": 42.28, "end": 42.76, "word": " ال", "probability": 0.351806640625}, {"start": 42.76, "end": 42.96, "word": " ..", "probability": 0.73388671875}, {"start": 42.96, "end": 43.54, "word": " النقطة", "probability": 0.9322916666666666}, {"start": 43.54, "end": 43.6, "word": " اللي", "probability": 0.90625}, {"start": 43.6, "end": 44.24, "word": " هنوصلها", "probability": 0.9111328125}, {"start": 44.24, "end": 44.48, "word": " و", "probability": 0.9111328125}, {"start": 44.48, "end": 45.18, "word": " بنتحدث", "probability": 0.872802734375}, {"start": 45.18, "end": 45.62, "word": " عنها", "probability": 0.997314453125}, {"start": 45.62, "end": 46.08, "word": " يعني", "probability": 0.955810546875}, {"start": 46.08, "end": 46.32, "word": " يمكن", "probability": 0.7254638671875}, {"start": 46.32, "end": 47.12, "word": " ذكرناها", "probability": 0.981689453125}, {"start": 47.12, "end": 47.66, "word": " و", "probability": 0.9619140625}, {"start": 47.66, "end": 48.26, "word": " هنأكد", "probability": 0.9419921875}, {"start": 48.26, "end": 48.72, "word": " عليها", "probability": 0.98876953125}, {"start": 48.72, "end": 49.44, "word": " أن", "probability": 0.42529296875}, {"start": 49.44, "end": 50.26, "word": " الـdenominable", "probability": 0.657568359375}, {"start": 50.26, "end": 50.58, "word": " sets", "probability": 0.90869140625}, {"start": 50.58, "end": 50.86, "word": " هي", "probability": 0.87060546875}, {"start": 50.86, "end": 51.4, "word": " أصغر", "probability": 0.982421875}, {"start": 51.4, "end": 51.82, "word": " infinite", "probability": 0.8603515625}, {"start": 51.82, "end": 52.2, "word": " set", "probability": 0.9541015625}, {"start": 52.2, "end": 52.86, "word": " أصغر", "probability": 0.9212646484375}, {"start": 52.86, "end": 53.28, "word": " infinite", "probability": 0.953125}, {"start": 53.28, "end": 53.62, "word": " set", "probability": 0.98046875}, {"start": 53.62, "end": 54.22, "word": " و", "probability": 0.96826171875}, {"start": 54.22, "end": 54.42, "word": " كان", "probability": 0.61572265625}, {"start": 54.42, "end": 54.6, "word": " في", "probability": 0.970703125}, {"start": 54.6, "end": 55.04, "word": " عندنا", "probability": 0.800537109375}, {"start": 55.04, "end": 55.6, "word": " نظرية", "probability": 0.9833984375}, {"start": 55.6, "end": 56.0, "word": " شوفنا", "probability": 0.8575846354166666}, {"start": 56.0, "end": 56.18, "word": " احنا", "probability": 0.9060872395833334}, {"start": 56.18, "end": 56.44, "word": " لو", "probability": 0.98095703125}, {"start": 56.44, "end": 57.2, "word": " أخدنا", "probability": 0.9755859375}, {"start": 57.2, "end": 58.14, "word": " infinite", "probability": 0.95654296875}, {"start": 58.14, "end": 58.92, "word": " subset", "probability": 0.98046875}, {"start": 58.92, "end": 59.46, "word": " من", "probability": 0.9951171875}, {"start": 59.46, "end": 60.06, "word": " denominable", "probability": 0.8234049479166666}, {"start": 60.06, "end": 60.54, "word": " تمت", "probability": 0.736083984375}, {"start": 60.54, "end": 60.96, "word": " denominable", "probability": 0.85009765625}], "temperature": 1.0}, {"id": 3, "seek": 7750, "start": 61.46, "end": 77.5, "text": "وعنا برضه نتيجة مهمة أن أي subset من countable بتكون countable فشوفنا الآن إيش علاقة الأصغر من ال subset من ال countable بتم ال countable بعدين بدنا نتحدث لو بدنا طب نكبر هي عندنا denomable دفناها عنصر تم ال denomable", "tokens": [2407, 3615, 8315, 4724, 43042, 3224, 8717, 31371, 7435, 3660, 3714, 16095, 3660, 14739, 36632, 25993, 9154, 1207, 712, 39894, 30544, 1207, 712, 6156, 8592, 38688, 8315, 6024, 48506, 11933, 1829, 8592, 11203, 995, 28671, 16247, 9381, 17082, 2288, 9154, 2423, 25993, 9154, 2423, 1207, 712, 4724, 39237, 2423, 1207, 712, 39182, 9957, 47525, 8315, 8717, 2655, 24401, 12984, 45164, 47525, 8315, 23032, 3555, 8717, 4117, 26890, 39896, 43242, 8315, 1441, 298, 712, 11778, 5172, 8315, 11296, 18871, 9381, 2288, 46811, 2423, 1441, 298, 712], "avg_logprob": -0.23183139257652816, "compression_ratio": 1.8076923076923077, "no_speech_prob": 0.0, "words": [{"start": 61.46, "end": 62.04, "word": "وعنا", "probability": 0.66064453125}, {"start": 62.04, "end": 62.48, "word": " برضه", "probability": 0.9143880208333334}, {"start": 62.48, "end": 62.94, "word": " نتيجة", "probability": 0.994384765625}, {"start": 62.94, "end": 63.42, "word": " مهمة", "probability": 0.9869791666666666}, {"start": 63.42, "end": 63.58, "word": " أن", 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68.64, "end": 68.84, "word": " ال", "probability": 0.89892578125}, {"start": 68.84, "end": 69.28, "word": " subset", "probability": 0.818359375}, {"start": 69.28, "end": 69.6, "word": " من", "probability": 0.986328125}, {"start": 69.6, "end": 69.98, "word": " ال", "probability": 0.796875}, {"start": 69.98, "end": 70.46, "word": " countable", "probability": 0.95751953125}, {"start": 70.46, "end": 70.68, "word": " بتم", "probability": 0.54345703125}, {"start": 70.68, "end": 70.8, "word": " ال", "probability": 0.5078125}, {"start": 70.8, "end": 71.2, "word": " countable", "probability": 0.96435546875}, {"start": 71.2, "end": 71.9, "word": " بعدين", "probability": 0.763427734375}, {"start": 71.9, "end": 72.18, "word": " بدنا", "probability": 0.708251953125}, {"start": 72.18, "end": 72.76, "word": " نتحدث", "probability": 0.9898681640625}, {"start": 72.76, "end": 72.9, "word": " لو", "probability": 0.73876953125}, {"start": 72.9, "end": 73.2, "word": " بدنا", "probability": 0.962646484375}, {"start": 73.2, "end": 73.38, "word": " طب", "probability": 0.759765625}, {"start": 73.38, "end": 73.88, "word": " نكبر", "probability": 0.9187825520833334}, {"start": 73.88, "end": 74.36, "word": " هي", "probability": 0.56005859375}, {"start": 74.36, "end": 74.64, "word": " عندنا", "probability": 0.60302734375}, {"start": 74.64, "end": 75.54, "word": " denomable", "probability": 0.487060546875}, {"start": 75.54, "end": 75.96, "word": " دفناها", "probability": 0.682861328125}, {"start": 75.96, "end": 76.46, "word": " عنصر", "probability": 0.88232421875}, {"start": 76.46, "end": 76.94, "word": " تم", "probability": 0.91455078125}, {"start": 76.94, "end": 77.1, "word": " ال", "probability": 0.42041015625}, {"start": 77.1, "end": 77.5, "word": " denomable", "probability": 0.7716471354166666}], "temperature": 1.0}, {"id": 4, "seek": 10514, "start": 77.96, "end": 105.14, "text": "طب ضفنا لها finite number of elements طبما الـdenimrables فالآن بدنا نمشي برضه بنفس الاتجاه لو وسعنا وقت إيش بتبطل المجموعة denimrable وقت إيش بدها تصير non-denimrable فهنتمنا نكبر فيها لحد ما إيش الـK لطف زي ما بقول واتبطلناش denimrable فالآن احنا أولا ضفنا answer ضفنا finite number of answer الآن هشوف نظرية لو ضفنا denimrable للـdenimrable إيش بتصير؟ خلينا نشوف", "tokens": [9566, 3555, 48812, 5172, 8315, 5296, 11296, 19362, 1230, 295, 4959, 23032, 3555, 15042, 2423, 39184, 1556, 332, 5305, 904, 6156, 6027, 148, 48506, 47525, 8315, 8717, 2304, 8592, 1829, 4724, 43042, 3224, 44945, 36178, 2423, 9307, 7435, 40294, 45164, 4032, 3794, 3615, 8315, 4032, 38149, 11933, 1829, 8592, 39894, 3555, 9566, 1211, 9673, 7435, 2304, 45367, 3660, 1441, 332, 424, 638, 4032, 38149, 11933, 1829, 8592, 47525, 11296, 6055, 9381, 13546, 2107, 12, 1556, 332, 424, 638, 6156, 3224, 1863, 39237, 8315, 8717, 4117, 26890, 8978, 11296, 5296, 24401, 19446, 11933, 1829, 8592, 2423, 39184, 42, 5296, 9566, 5172, 30767, 1829, 19446, 4724, 39648, 4032, 9307, 3555, 9566, 1211, 1863, 33599, 1441, 332, 424, 638, 6156, 6027, 148, 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0.90576171875}, {"start": 80.74, "end": 81.12, "word": " طبما", "probability": 0.7010091145833334}, {"start": 81.12, "end": 81.64, "word": " الـdenimrables", "probability": 0.6300048828125}, {"start": 81.64, "end": 82.24, "word": " فالآن", "probability": 0.77392578125}, {"start": 82.24, "end": 82.68, "word": " بدنا", "probability": 0.959716796875}, {"start": 82.68, "end": 83.38, "word": " نمشي", "probability": 0.9901123046875}, {"start": 83.38, "end": 83.62, "word": " برضه", "probability": 0.93603515625}, {"start": 83.62, "end": 83.86, "word": " بنفس", "probability": 0.938232421875}, {"start": 83.86, "end": 84.26, "word": " الاتجاه", "probability": 0.8717041015625}, {"start": 84.26, "end": 84.44, "word": " لو", "probability": 0.89208984375}, {"start": 84.44, "end": 84.94, "word": " وسعنا", "probability": 0.827880859375}, {"start": 84.94, "end": 85.52, "word": " وقت", "probability": 0.821533203125}, {"start": 85.52, "end": 85.8, "word": " إيش", "probability": 0.8118489583333334}, {"start": 85.8, "end": 86.36, "word": " بتبطل", "probability": 0.84521484375}, {"start": 86.36, "end": 87.02, "word": " المجموعة", "probability": 0.888671875}, {"start": 87.02, "end": 87.88, "word": " denimrable", "probability": 0.8055419921875}, {"start": 87.88, "end": 88.1, "word": " وقت", "probability": 0.748291015625}, {"start": 88.1, "end": 88.24, "word": " إيش", "probability": 0.9928385416666666}, {"start": 88.24, "end": 88.48, "word": " بدها", "probability": 0.865234375}, {"start": 88.48, "end": 88.74, "word": " تصير", "probability": 0.8883463541666666}, {"start": 88.74, "end": 88.96, "word": " non", "probability": 0.90673828125}, {"start": 88.96, "end": 89.44, "word": "-denimrable", "probability": 0.91015625}, {"start": 89.44, "end": 90.12, "word": " فهنتمنا", "probability": 0.714599609375}, {"start": 90.12, "end": 90.48, "word": " نكبر", "probability": 0.95166015625}, {"start": 90.48, "end": 90.88, "word": " فيها", "probability": 0.9951171875}, {"start": 90.88, "end": 91.48, "word": " لحد", "probability": 0.9716796875}, {"start": 91.48, "end": 91.66, "word": " ما", "probability": 0.98974609375}, {"start": 91.66, "end": 92.02, "word": " إيش", "probability": 0.9295247395833334}, {"start": 92.02, "end": 92.64, "word": " الـK", "probability": 0.515380859375}, {"start": 92.64, "end": 93.08, "word": " لطف", "probability": 0.8154296875}, {"start": 93.08, "end": 93.26, "word": " زي", "probability": 0.89697265625}, {"start": 93.26, "end": 93.32, "word": " ما", "probability": 0.98291015625}, {"start": 93.32, "end": 93.58, "word": " بقول", "probability": 0.827392578125}, {"start": 93.58, "end": 94.36, "word": " واتبطلناش", "probability": 0.7645786830357143}, {"start": 94.36, "end": 94.98, "word": " denimrable", "probability": 0.7677001953125}, {"start": 94.98, "end": 95.86, "word": " فالآن", "probability": 0.8970947265625}, {"start": 95.86, "end": 96.42, "word": " احنا", "probability": 0.77099609375}, {"start": 96.42, "end": 96.68, "word": " أولا", "probability": 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{"start": 101.02, "end": 102.16, "word": " denimrable", "probability": 0.9227294921875}, {"start": 102.16, "end": 103.32, "word": " للـdenimrable", "probability": 0.7672119140625}, {"start": 103.32, "end": 103.8, "word": " إيش", "probability": 0.8904622395833334}, {"start": 103.8, "end": 104.54, "word": " بتصير؟", "probability": 0.86474609375}, {"start": 104.54, "end": 104.8, "word": " خلينا", "probability": 0.6610107421875}, {"start": 104.8, "end": 105.14, "word": " نشوف", "probability": 0.9977213541666666}], "temperature": 1.0}, {"id": 5, "seek": 12233, "start": 105.69, "end": 122.33, "text": "فالعنوان the union of two denomable sets is denomable حتى لو تفنعها كمان denomable بتامها denomable فعنا نظرية if A and B are denomable sets then A union B is denomable نشوف البراحة", "tokens": [5172, 6027, 3615, 1863, 2407, 7649, 264, 11671, 295, 732, 1441, 298, 712, 6352, 307, 1441, 298, 712, 11331, 49975, 45164, 6055, 5172, 1863, 3615, 11296, 9122, 2304, 7649, 1441, 298, 712, 39894, 10943, 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0.68121337890625}], "temperature": 1.0}, {"id": 6, "seek": 15104, "start": 123.66, "end": 151.04, "text": "فاحنا ماشيين بيدا الاتجاه حد ما نوصل وين ال non-denominable بتكون فهذه نظرية خمسة تسعة او هي البرهة above طبعا جملة شرطية فنبدأ ان الشرط صحيح assume ال A is denominable بتكتب اختصارا to capital N يعني مظبوط و ال B is denominable and", "tokens": [5172, 39319, 8315, 3714, 33599, 1829, 9957, 4724, 25708, 995, 2423, 9307, 7435, 40294, 11331, 3215, 19446, 8717, 2407, 36520, 4032, 9957, 2423, 2107, 12, 1556, 6981, 712, 39894, 30544, 6156, 3224, 24192, 8717, 19913, 2288, 10632, 16490, 2304, 3794, 3660, 6055, 3794, 27884, 1975, 2407, 39896, 2423, 26890, 3224, 3660, 3673, 23032, 3555, 3615, 995, 10874, 2304, 37977, 13412, 2288, 9566, 10632, 6156, 1863, 44510, 10721, 16472, 25124, 2288, 9566, 20328, 5016, 1829, 5016, 6552, 2423, 316, 307, 1441, 6981, 712, 39894, 4117, 2655, 3555, 1975, 46456, 9381, 9640, 995, 281, 4238, 426, 37495, 22653, 3714, 19913, 3555, 2407, 9566, 4032, 2423, 363, 307, 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is denomable تمام مرة علينا نظريات", "tokens": [6027, 39184, 363, 307, 1441, 298, 712, 3714, 9566, 1211, 37746, 8717, 12984, 3555, 2655, 14739, 2423, 9307, 5016, 18513, 307, 1441, 298, 712, 47525, 8315, 8717, 12984, 3555, 2655, 14739, 2423, 39184, 316, 11671, 363, 307, 1441, 298, 712, 321, 528, 281, 7081, 316, 11671, 363, 307, 1441, 298, 712, 46811, 10943, 3714, 25720, 11203, 9957, 995, 8717, 19913, 16572, 9307], "avg_logprob": -0.24404762093982998, "compression_ratio": 1.544776119402985, "no_speech_prob": 0.0, "words": [{"start": 151.65, "end": 152.01, "word": "الـ", "probability": 0.702880859375}, {"start": 152.01, "end": 152.29, "word": " B", "probability": 0.56591796875}, {"start": 152.29, "end": 152.97, "word": " is", "probability": 0.77490234375}, {"start": 152.97, "end": 153.83, "word": " denomable", "probability": 0.5045572916666666}, {"start": 153.83, "end": 156.45, "word": " مطلوب", "probability": 0.78912353515625}, {"start": 156.45, "end": 156.81, "word": " نثبت", 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bijection a bijection طبعا التفاصيل كلها بترك exercise now a is a bijection therefore z تسوي اتحاد ال n is innumerable", "tokens": [70, 5709, 538, 1975, 1829, 8592, 8717, 3615, 28480, 11778, 3224, 5296, 27842, 297, 5296, 257, 6055, 30544, 4724, 1829, 7435, 1829, 4117, 8592, 1863, 36764, 24401, 8717, 4587, 9381, 1975, 4117, 3794, 4724, 16254, 4117, 1829, 39896, 3224, 8608, 33604, 6027, 4724, 16254, 4117, 1829, 21542, 1211, 28671, 307, 257, 3228, 1020, 313, 257, 3228, 1020, 313, 23032, 3555, 3615, 995, 16712, 5172, 33546, 26895, 28242, 11296, 39894, 31747, 5380, 586, 257, 307, 257, 3228, 1020, 313, 4412, 710, 6055, 3794, 45865, 1975, 2655, 5016, 18513, 2423, 297, 307, 7714, 15583, 712], "avg_logprob": -0.3816489260247413, "compression_ratio": 1.472636815920398, "no_speech_prob": 0.0, "words": [{"start": 830.11, "end": 830.65, "word": "given", "probability": 0.689453125}, {"start": 830.65, "end": 831.61, "word": " by", "probability": 0.9326171875}, {"start": 831.61, "end": 832.49, "word": 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"word": " كله", "probability": 0.936767578125}, {"start": 880.27, "end": 880.45, "word": " ممكن", "probability": 0.92236328125}, {"start": 880.45, "end": 880.89, "word": " جزئيا", "probability": 0.817138671875}, {"start": 880.89, "end": 881.09, "word": " هنا", "probability": 0.71923828125}, {"start": 881.09, "end": 881.51, "word": " أسهل", "probability": 0.986328125}, {"start": 881.51, "end": 881.81, "word": " بعد", "probability": 0.67529296875}, {"start": 881.81, "end": 881.93, "word": " ما", "probability": 0.58251953125}, {"start": 881.93, "end": 882.11, "word": " أشتغل", "probability": 0.82353515625}, {"start": 882.11, "end": 882.23, "word": " على", "probability": 0.84423828125}, {"start": 882.23, "end": 882.43, "word": " كل", "probability": 0.9453125}, {"start": 882.43, "end": 882.57, "word": " ال", "probability": 0.8427734375}, {"start": 882.57, "end": 882.75, "word": " Z", "probability": 0.35498046875}, {"start": 882.75, "end": 883.17, "word": " أشتغلت", "probability": 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طب لو ضربنا عملنا Cartesian product طبعا الـCartesian product مين أكبر الاتحاد ولا الـCartesian؟", "tokens": [5172, 3215, 3224, 4724, 3794, 50113, 6027, 16070, 3794, 47341, 45761, 4032, 5172, 4117, 25720, 10874, 16254, 41891, 4032, 4117, 33911, 8717, 8592, 2655, 17082, 1211, 20449, 2423, 39184, 1556, 332, 424, 638, 8717, 47341, 3615, 5296, 5172, 4117, 43500, 8315, 34892, 19986, 1829, 3794, 10632, 13672, 1829, 11331, 4117, 1829, 8315, 8978, 11296, 9154, 5551, 12610, 9673, 5016, 46958, 25720, 1975, 5016, 8315, 47525, 10721, 8315, 9154, 2423, 39184, 1556, 332, 424, 638, 47525, 10721, 8315, 8717, 4117, 26890, 8978, 11296, 11778, 5172, 1863, 6027, 11296, 18871, 9381, 2288, 11778, 5172, 1863, 6027, 11296, 19362, 992, 39182, 9957, 11778, 5172, 1863, 6027, 11296, 2423, 39184, 1556, 332, 424, 638, 46811, 2423, 39184, 1556, 332, 424, 638, 23032, 3555, 45164, 48812, 25513, 8315, 6225, 42213, 8315, 22478, 42434, 1674, 23032, 3555, 3615, 995, 2423, 39184, 34, 446, 42434, 1674, 3714, 9957, 5551, 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"word": " متابعين؟", "probability": 0.837158203125}, {"start": 1508.98, "end": 1509.18, "word": " أه،", "probability": 0.5691731770833334}, {"start": 1509.18, "end": 1509.38, "word": " فإيش", "probability": 0.974365234375}, {"start": 1509.38, "end": 1509.62, "word": " روحنا", "probability": 0.9229736328125}, {"start": 1509.62, "end": 1510.34, "word": " عملناه؟", "probability": 0.92900390625}, {"start": 1510.34, "end": 1511.26, "word": " زغرناه،", "probability": 0.87939453125}, {"start": 1511.26, "end": 1511.6, "word": " أخدنا", "probability": 0.994140625}, {"start": 1511.6, "end": 1511.84, "word": " بس", "probability": 0.94775390625}, {"start": 1511.84, "end": 1512.14, "word": " المدى", "probability": 0.93994140625}, {"start": 1512.14, "end": 1512.28, "word": " على", "probability": 0.52880859375}, {"start": 1512.28, "end": 1513.0, "word": " الجد،", "probability": 0.9083658854166666}, {"start": 1513.0, "end": 1513.1, "word": " على", "probability": 0.82958984375}, {"start": 1513.1, "end": 1513.38, "word": " المدى،", "probability": 0.83319091796875}, {"start": 1513.38, "end": 1514.08, "word": " بـSubjection،", "probability": 0.6732584635416666}, {"start": 1514.08, "end": 1514.9, "word": " صح؟", "probability": 0.9817708333333334}, {"start": 1514.9, "end": 1515.34, "word": " طيب،", "probability": 0.9627685546875}, {"start": 1515.34, "end": 1515.58, "word": " هذه", "probability": 0.484375}, {"start": 1515.58, "end": 1518.16, "word": " شمالها،", "probability": 0.786572265625}, {"start": 1518.16, "end": 1518.9, "word": " صح؟", "probability": 0.9923502604166666}], "temperature": 1.0}, {"id": 63, "seek": 153640, "start": 1519.34, "end": 1536.4, "text": "مشكلة المدى هو subset من المجال المقابل؟ نشوف مع بعض، طيب، الآن إذا كدرت أثبت أن هذه denominable انتهت العملية لأن هي هذي تكافح denominable وعملية التعدد تصبح denominable، طيب، الآن هذه subset من مين؟ من الان", "tokens": [2304, 8592, 28820, 3660, 9673, 3215, 7578, 31439, 25993, 9154, 9673, 7435, 6027, 9673, 4587, 16758, 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"probability": 0.71142578125}, {"start": 1526.52, "end": 1527.02, "word": " denominable", "probability": 0.5468343098958334}, {"start": 1527.02, "end": 1527.36, "word": " انتهت", "probability": 0.8610026041666666}, {"start": 1527.36, "end": 1527.86, "word": " العملية", "probability": 0.9864908854166666}, {"start": 1527.86, "end": 1528.38, "word": " لأن", "probability": 0.76318359375}, {"start": 1528.38, "end": 1528.64, "word": " هي", "probability": 0.442138671875}, {"start": 1528.64, "end": 1528.98, "word": " هذي", "probability": 0.4031168619791667}, {"start": 1528.98, "end": 1529.46, "word": " تكافح", "probability": 0.84326171875}, {"start": 1529.46, "end": 1530.06, "word": " denominable", "probability": 0.79248046875}, {"start": 1530.06, "end": 1531.1, "word": " وعملية", "probability": 0.7969970703125}, {"start": 1531.1, "end": 1531.78, "word": " التعدد", "probability": 0.6958821614583334}, {"start": 1531.78, "end": 1532.02, "word": " تصبح", "probability": 0.7357584635416666}, {"start": 1532.02, "end": 1532.88, "word": " denominable،", "probability": 0.798583984375}, {"start": 1532.88, "end": 1533.42, "word": " طيب،", "probability": 0.9072265625}, {"start": 1533.42, "end": 1533.84, "word": " الآن", "probability": 0.801513671875}, {"start": 1533.84, "end": 1534.3, "word": " هذه", "probability": 0.81201171875}, {"start": 1534.3, "end": 1534.8, "word": " subset", "probability": 0.943359375}, {"start": 1534.8, "end": 1535.12, "word": " من", "probability": 0.9921875}, {"start": 1535.12, "end": 1535.7, "word": " مين؟", "probability": 0.7947591145833334}, {"start": 1535.7, "end": 1536.04, "word": " من", "probability": 0.978515625}, {"start": 1536.04, "end": 1536.4, "word": " الان", "probability": 0.598388671875}], "temperature": 1.0}, {"id": 64, "seek": 156431, "start": 1537.01, "end": 1564.31, "text": "طيب ليش .. مش جروري هذه subset من denominable إذا كانت infinite انتهت العملية لأن infinite subset من denominable is denominable طيب ليش هذه infinite؟ ليش هذه infinite؟ لأن هذه تكافئ هذه ومستحيل تكون finite أه لأن مستحيل تكون finite أه فهذه subset من ال end وهذه تكافئها فهي على طول denominable كيف بدنا نكتفه؟ فإذا هذه تكافئها فهذه تكافئها since", "tokens": [9566, 1829, 3555, 32239, 8592, 4386, 37893, 10874, 2288, 13063, 1829, 29538, 25993, 9154, 1441, 6981, 712, 11933, 15730, 25961, 2655, 13785, 16472, 47395, 2655, 18863, 42213, 10632, 5296, 33456, 13785, 25993, 9154, 1441, 6981, 712, 307, 1441, 6981, 712, 23032, 1829, 3555, 32239, 8592, 29538, 13785, 22807, 32239, 8592, 29538, 13785, 22807, 5296, 33456, 29538, 6055, 4117, 31845, 19986, 29538, 4032, 2304, 14851, 5016, 26895, 6055, 30544, 19362, 5551, 3224, 5296, 33456, 3714, 14851, 5016, 26895, 6055, 30544, 19362, 5551, 3224, 6156, 3224, 24192, 25993, 9154, 2423, 917, 4032, 3224, 24192, 6055, 4117, 31845, 19986, 11296, 6156, 3224, 1829, 15844, 23032, 12610, 1441, 6981, 712, 9122, 33911, 47525, 8315, 8717, 4117, 2655, 5172, 3224, 22807, 6156, 28814, 15730, 29538, 6055, 4117, 31845, 19986, 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"word": " طيب", "probability": 0.8453776041666666}, {"start": 1546.25, "end": 1546.49, "word": " ليش", "probability": 0.95703125}, {"start": 1546.49, "end": 1546.71, "word": " هذه", "probability": 0.857421875}, {"start": 1546.71, "end": 1547.79, "word": " infinite؟", "probability": 0.708984375}, {"start": 1547.79, "end": 1548.21, "word": " ليش", "probability": 0.75146484375}, {"start": 1548.21, "end": 1548.65, "word": " هذه", "probability": 0.90185546875}, {"start": 1548.65, "end": 1549.57, "word": " infinite؟", "probability": 0.872314453125}, {"start": 1549.57, "end": 1549.91, "word": " لأن", "probability": 0.970703125}, {"start": 1549.91, "end": 1550.79, "word": " هذه", "probability": 0.578125}, {"start": 1550.79, "end": 1551.43, "word": " تكافئ", "probability": 0.9796142578125}, {"start": 1551.43, "end": 1551.85, "word": " هذه", "probability": 0.59326171875}, {"start": 1551.85, "end": 1552.61, "word": " ومستحيل", "probability": 0.92529296875}, {"start": 1552.61, "end": 1552.85, "word": " تكون", "probability": 0.926513671875}, {"start": 1552.85, "end": 1553.25, "word": " finite", "probability": 0.91552734375}, {"start": 1553.25, "end": 1553.95, "word": " أه", "probability": 0.644775390625}, {"start": 1553.95, "end": 1554.27, "word": " لأن", "probability": 0.678955078125}, {"start": 1554.27, "end": 1554.79, "word": " مستحيل", "probability": 0.799407958984375}, {"start": 1554.79, "end": 1555.17, "word": " تكون", "probability": 0.98828125}, {"start": 1555.17, "end": 1555.75, "word": " finite", "probability": 0.96337890625}, {"start": 1555.75, "end": 1556.35, "word": " أه", "probability": 0.83984375}, {"start": 1556.35, "end": 1556.63, "word": " فهذه", "probability": 0.9576822916666666}, {"start": 1556.63, "end": 1556.89, "word": " subset", "probability": 0.94873046875}, {"start": 1556.89, "end": 1557.15, "word": " من", "probability": 0.99560546875}, {"start": 1557.15, "end": 1557.31, "word": " ال", "probability": 0.85986328125}, {"start": 1557.31, "end": 1557.51, "word": " end", "probability": 0.126220703125}, {"start": 1557.51, "end": 1557.75, "word": " وهذه", "probability": 0.7740071614583334}, {"start": 1557.75, "end": 1558.47, "word": " تكافئها", "probability": 0.991796875}, {"start": 1558.47, "end": 1559.45, "word": " فهي", "probability": 0.6263834635416666}, {"start": 1559.45, "end": 1559.61, "word": " على", "probability": 0.97021484375}, {"start": 1559.61, "end": 1559.87, "word": " طول", "probability": 0.9931640625}, {"start": 1559.87, "end": 1560.43, "word": " denominable", "probability": 0.9197591145833334}, {"start": 1560.43, "end": 1561.23, "word": " كيف", "probability": 0.759033203125}, {"start": 1561.23, "end": 1561.43, "word": " بدنا", "probability": 0.749267578125}, {"start": 1561.43, "end": 1561.87, "word": " نكتفه؟", "probability": 0.71630859375}, {"start": 1561.87, "end": 1562.01, "word": " فإذا", "probability": 0.84326171875}, {"start": 1562.01, "end": 1562.25, "word": " هذه", "probability": 0.8095703125}, {"start": 1562.25, "end": 1562.65, "word": " تكافئها", "probability": 0.9123046875}, {"start": 1562.65, "end": 1562.75, "word": " فهذه", "probability": 0.750244140625}, {"start": 1562.75, "end": 1563.43, "word": " تكافئها", "probability": 0.995703125}, {"start": 1563.43, "end": 1564.31, "word": " since", "probability": 0.736328125}], "temperature": 1.0}, {"id": 65, "seek": 159345, "start": 1569.61, "end": 1593.45, "text": "N cross الـ N is infinite we have F of N cross ال N is infinite وهذا يؤدي أن F of N cross ال N is innumerable", "tokens": [45, 3278, 2423, 39184, 426, 307, 13785, 321, 362, 479, 295, 426, 3278, 2423, 426, 307, 13785, 37037, 15730, 7251, 33604, 16254, 14739, 479, 295, 426, 3278, 2423, 426, 307, 7714, 15583, 712], "avg_logprob": -0.3010110171402202, "compression_ratio": 1.4, "no_speech_prob": 0.0, "words": [{"start": 1569.6100000000001, "end": 1570.73, "word": "N", "probability": 0.3291015625}, {"start": 1570.73, "end": 1571.85, "word": " cross", "probability": 0.3232421875}, {"start": 1571.85, "end": 1572.13, "word": " الـ", "probability": 0.69970703125}, {"start": 1572.13, "end": 1572.37, "word": " N", "probability": 0.8017578125}, {"start": 1572.37, "end": 1573.49, "word": " is", "probability": 0.87158203125}, {"start": 1573.49, "end": 1574.19, "word": " infinite", "probability": 0.8984375}, {"start": 1574.19, "end": 1578.69, "word": " we", "probability": 0.10931396484375}, {"start": 1578.69, "end": 1580.53, "word": " have", "probability": 0.96728515625}, {"start": 1580.53, "end": 1581.35, "word": " F", "probability": 0.7783203125}, {"start": 1581.35, "end": 1582.05, "word": " of", "probability": 0.50634765625}, {"start": 1582.05, "end": 1582.23, "word": " N", "probability": 0.9072265625}, {"start": 1582.23, "end": 1582.61, "word": " cross", "probability": 0.90869140625}, {"start": 1582.61, "end": 1582.85, "word": " ال", "probability": 0.84765625}, {"start": 1582.85, "end": 1583.13, "word": " N", "probability": 0.8671875}, {"start": 1583.13, "end": 1584.51, "word": " is", "probability": 0.94140625}, {"start": 1584.51, "end": 1585.19, "word": " infinite", "probability": 0.9189453125}, {"start": 1585.19, "end": 1588.33, "word": " وهذا", "probability": 0.88037109375}, {"start": 1588.33, "end": 1588.87, "word": " يؤدي", "probability": 0.892578125}, {"start": 1588.87, "end": 1589.79, "word": " أن", "probability": 0.26318359375}, {"start": 1589.79, "end": 1590.25, "word": " F", "probability": 0.84228515625}, {"start": 1590.25, "end": 1590.55, "word": " of", "probability": 0.87890625}, {"start": 1590.55, "end": 1590.89, "word": " N", "probability": 0.9736328125}, {"start": 1590.89, "end": 1591.23, "word": " cross", "probability": 0.93603515625}, {"start": 1591.23, "end": 1591.47, "word": " ال", "probability": 0.953125}, {"start": 1591.47, "end": 1591.77, "word": " N", "probability": 0.98046875}, {"start": 1591.77, "end": 1592.89, "word": " is", "probability": 0.94482421875}, {"start": 1592.89, "end": 1593.45, "word": " innumerable", "probability": 0.78076171875}], "temperature": 1.0}, {"id": 66, "seek": 162539, "start": 1598.43, "end": 1625.39, "text": "هذه نظرية نظرية جداش infinite subset of denumerable set is denumerable نظرية خمسة تمانية صحيح خلاص مع ذلك عملية equivalence relation therefore n x n is denumerable", "tokens": [3224, 24192, 8717, 19913, 2288, 10632, 8717, 19913, 2288, 10632, 10874, 3215, 33599, 13785, 25993, 295, 1441, 15583, 712, 992, 307, 1441, 15583, 712, 8717, 19913, 2288, 10632, 16490, 2304, 3794, 3660, 46811, 7649, 10632, 20328, 5016, 1829, 5016, 16490, 1211, 33546, 20449, 29910, 23275, 6225, 42213, 10632, 9052, 655, 9721, 4412, 297, 2031, 297, 307, 1441, 15583, 712], "avg_logprob": -0.288802078862985, "compression_ratio": 1.4489795918367347, "no_speech_prob": 0.0, "words": [{"start": 1598.43, "end": 1598.77, "word": "هذه", "probability": 0.853759765625}, {"start": 1598.77, "end": 1599.29, "word": " نظرية", "probability": 0.9732666015625}, {"start": 1599.29, "end": 1600.59, "word": " نظرية", 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"probability": 0.9378255208333334}, {"start": 1649.08, "end": 1649.48, "word": " تكافئ", "probability": 0.995849609375}, {"start": 1649.48, "end": 1650.4, "word": " التالتة", "probability": 0.8760986328125}, {"start": 1650.4, "end": 1650.76, "word": " وهو", "probability": 0.7509765625}, {"start": 1650.76, "end": 1651.26, "word": " المطلوب", "probability": 0.990234375}, {"start": 1651.26, "end": 1652.36, "word": " فهنا", "probability": 0.94921875}, {"start": 1652.36, "end": 1652.92, "word": " ماقدرناش", "probability": 0.7876953125}, {"start": 1652.92, "end": 1653.18, "word": " نوصل", "probability": 0.978515625}, {"start": 1653.18, "end": 1653.86, "word": " مباشرة", "probability": 0.9820556640625}, {"start": 1653.86, "end": 1654.44, "word": " لكن", "probability": 0.88330078125}, {"start": 1654.44, "end": 1654.94, "word": " وصلنا", "probability": 0.8346354166666666}, {"start": 1654.94, "end": 1655.3, "word": " بهذه", "probability": 0.963623046875}, {"start": 1655.3, "end": 1655.8, "word": " الطريقة", "probability": 0.990234375}, {"start": 1655.8, "end": 1656.34, "word": " غير", "probability": 0.995361328125}, {"start": 1656.34, "end": 1656.96, "word": " المباشرة", "probability": 0.9925537109375}], "temperature": 1.0}, {"id": 68, "seek": 167005, "start": 1659.99, "end": 1670.05, "text": "هذه واحدة التركيات التي نجعلها أحياناً عندما الأمور لا تصبح مجموعة كبيرة ولا نستطيع إجابة بشكل مباشر", "tokens": [3224, 24192, 36764, 24401, 3660, 16712, 31747, 1829, 9307, 38392, 8717, 7435, 30241, 11296, 5551, 5016, 1829, 7649, 995, 14111, 43242, 15042, 16247, 2304, 13063, 20193, 6055, 9381, 49628, 3714, 7435, 2304, 2407, 27884, 9122, 3555, 48923, 49429, 8717, 14851, 9566, 40228, 11933, 7435, 16758, 3660, 4724, 8592, 28820, 3714, 3555, 33599, 2288], "avg_logprob": -0.39872685185185186, "compression_ratio": 1.4488188976377954, "no_speech_prob": 0.0, "words": [{"start": 1659.99, "end": 1660.53, "word": "هذه", "probability": 0.66943359375}, {"start": 1660.53, "end": 1660.91, "word": " 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"end": 1667.91, "word": " نستطيع", "probability": 0.888427734375}, {"start": 1667.91, "end": 1668.43, "word": " إجابة", "probability": 0.5142822265625}, {"start": 1668.43, "end": 1669.55, "word": " بشكل", "probability": 0.9187825520833334}, {"start": 1669.55, "end": 1670.05, "word": " مباشر", "probability": 0.9835205078125}], "temperature": 1.0}, {"id": 69, "seek": 170773, "start": 1679.53, "end": 1707.73, "text": "مزيد من التوسع دائما حاضر فزي ما احنا شايفين احنا كل ما لقوا بدينا يعني الممكن الفكرة اللي ماشيين فيها جاعدين بنكبر كل ما قاش وانا نوصل هل هتوجه مرحلة ونبطل denim rubble بنشوف بنكبر denim rubble بنكبر denim rubble بدنا نشوف وقت إيش الكلب بده يطف ويتبطل المجموعة denim rubble لمّا جداش نكبرها جداش نضفلها فعنا نتيجة خمسة خمسة", "tokens": [2304, 11622, 25708, 9154, 16712, 41779, 3615, 11778, 16373, 15042, 11331, 46958, 2288, 6156, 11622, 1829, 19446, 1975, 5016, 8315, 13412, 995, 33911, 9957, 1975, 5016, 8315, 28242, 19446, 5296, 4587, 14407, 4724, 16254, 8315, 37495, 22653, 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خمسة", "probability": 0.9693603515625}], "temperature": 1.0}, {"id": 70, "seek": 172182, "start": 1708.86, "end": 1721.82, "text": "Infinite union of disjoint denumerable sets is denumerable كان في عندنا نتيجة نتيجة اللي هو finite union", "tokens": [4575, 5194, 642, 11671, 295, 717, 48613, 1441, 15583, 712, 6352, 307, 1441, 15583, 712, 25961, 8978, 43242, 8315, 8717, 31371, 7435, 3660, 8717, 31371, 7435, 3660, 13672, 1829, 31439, 19362, 11671], "avg_logprob": -0.37642045454545453, "compression_ratio": 1.2745098039215685, "no_speech_prob": 0.0, "words": [{"start": 1708.86, "end": 1709.62, "word": "Infinite", "probability": 0.7107747395833334}, {"start": 1709.62, "end": 1710.1, "word": " union", "probability": 0.70361328125}, {"start": 1710.1, "end": 1710.42, "word": " of", "probability": 0.95263671875}, {"start": 1710.42, "end": 1711.2, "word": " disjoint", "probability": 0.84423828125}, {"start": 1711.2, "end": 1712.28, "word": " denumerable", "probability": 0.5375162760416666}, {"start": 1712.28, "end": 1712.66, "word": " sets", "probability": 0.931640625}, {"start": 1712.66, "end": 1713.02, "word": " is", "probability": 0.849609375}, {"start": 1713.02, "end": 1715.5, "word": " denumerable", "probability": 0.8829752604166666}, {"start": 1715.5, "end": 1716.52, "word": " كان", "probability": 0.72021484375}, {"start": 1716.52, "end": 1716.74, "word": " في", "probability": 0.53955078125}, {"start": 1716.74, "end": 1717.1, "word": " عندنا", "probability": 0.62359619140625}, {"start": 1717.1, "end": 1717.66, "word": " نتيجة", "probability": 0.99267578125}, {"start": 1717.66, "end": 1719.92, "word": " نتيجة", "probability": 0.6796875}, {"start": 1719.92, "end": 1720.22, "word": " اللي", "probability": 0.530517578125}, {"start": 1720.22, "end": 1720.68, "word": " هو", "probability": 0.9033203125}, {"start": 1720.68, "end": 1721.08, "word": " finite", "probability": 0.9150390625}, {"start": 1721.08, "end": 1721.82, "word": " union", "probability": 0.93994140625}], "temperature": 1.0}, {"id": 71, "seek": 174688, "start": 1722.62, "end": 1746.88, "text": "بس ما قالليش disjoint هناك بشكل عام اللي هو إيش احنا بدأنا بنظرية المحاضرة و بعدها نتيجة مباشرة كان finite union بدون disjoint الآن infinite union بس حط شرط إنه لازم يكونوا disjoint المجموعات is inimitable فالآن إحنا حلا خدنا أي اتحاد مالا نهاية من المجموعات بس يكونوا disjoint بدمر اتحاد inimitable", "tokens": [3555, 3794, 19446, 50239, 20292, 8592, 717, 48613, 34105, 4117, 4724, 8592, 28820, 6225, 10943, 13672, 1829, 31439, 11933, 1829, 8592, 1975, 5016, 8315, 47525, 10721, 8315, 44945, 19913, 2288, 10632, 9673, 5016, 46958, 25720, 4032, 39182, 11296, 8717, 31371, 7435, 3660, 3714, 3555, 33599, 25720, 25961, 19362, 11671, 47525, 11536, 717, 48613, 6024, 48506, 13785, 11671, 4724, 3794, 11331, 9566, 13412, 2288, 9566, 36145, 3224, 5296, 31377, 2304, 7251, 30544, 14407, 717, 48613, 9673, 7435, 2304, 45367, 9307, 307, 45945, 16772, 6156, 6027, 148, 48506, 11933, 5016, 8315, 11331, 15040, 16490, 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يكونوا", "probability": 0.98193359375}, {"start": 1737.3, "end": 1737.74, "word": " disjoint", "probability": 0.87939453125}, {"start": 1737.74, "end": 1738.48, "word": " المجموعات", "probability": 0.93330078125}, {"start": 1738.48, "end": 1738.9, "word": " is", "probability": 0.37353515625}, {"start": 1738.9, "end": 1739.4, "word": " inimitable", "probability": 0.342529296875}, {"start": 1739.4, "end": 1740.04, "word": " فالآن", "probability": 0.85107421875}, {"start": 1740.04, "end": 1740.24, "word": " إحنا", "probability": 0.8055826822916666}, {"start": 1740.24, "end": 1740.44, "word": " حلا", "probability": 0.2811279296875}, {"start": 1740.44, "end": 1740.74, "word": " خدنا", "probability": 0.9246419270833334}, {"start": 1740.74, "end": 1741.0, "word": " أي", "probability": 0.92431640625}, {"start": 1741.0, "end": 1741.64, "word": " اتحاد", "probability": 0.9671630859375}, {"start": 1741.64, "end": 1742.34, "word": " مالا", "probability": 0.5604654947916666}, {"start": 1742.34, "end": 1742.72, "word": " نهاية", "probability": 0.9153645833333334}, {"start": 1742.72, "end": 1742.84, "word": " من", "probability": 0.9873046875}, {"start": 1742.84, "end": 1743.5, "word": " المجموعات", "probability": 0.9869140625}, {"start": 1743.5, "end": 1743.88, "word": " بس", "probability": 0.9931640625}, {"start": 1743.88, "end": 1744.2, "word": " يكونوا", "probability": 0.9910481770833334}, {"start": 1744.2, "end": 1744.7, "word": " disjoint", "probability": 0.932373046875}, {"start": 1744.7, "end": 1745.4, "word": " بدمر", "probability": 0.727783203125}, {"start": 1745.4, "end": 1746.08, "word": " اتحاد", "probability": 0.9775390625}, {"start": 1746.08, "end": 1746.88, "word": " inimitable", "probability": 0.54669189453125}], "temperature": 1.0}, {"id": 72, "seek": 177120, "start": 1747.64, "end": 1771.2, "text": "نشوف البرهان و الفكرة تبعها البرهان و إيش بدنا نشتغل معاها for each k تنتمي لأن لأي عدد طبيعي let a sub k be a denominable set satisfying a j تقاطع a k تساوي five for all j لا تساوي k نحاول نفهم هذا الكلام", "tokens": [1863, 8592, 38688, 2423, 26890, 3224, 7649, 4032, 27188, 4117, 25720, 6055, 3555, 3615, 11296, 2423, 26890, 3224, 7649, 4032, 11933, 1829, 8592, 47525, 8315, 8717, 8592, 2655, 17082, 1211, 20449, 995, 11296, 337, 1184, 350, 6055, 29399, 2304, 1829, 5296, 33456, 5296, 10721, 1829, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 718, 257, 1422, 350, 312, 257, 1441, 6981, 712, 992, 18348, 257, 361, 6055, 4587, 41193, 3615, 257, 350, 6055, 3794, 995, 45865, 1732, 337, 439, 361, 20193, 6055, 3794, 995, 45865, 350, 8717, 5016, 995, 12610, 8717, 5172, 16095, 23758, 2423, 28820, 10943], "avg_logprob": -0.23179767549652414, "compression_ratio": 1.5049019607843137, "no_speech_prob": 0.0, "words": [{"start": 1747.64, "end": 1748.26, "word": "نشوف", "probability": 0.8063151041666666}, {"start": 1748.26, "end": 1749.2, "word": " البرهان", "probability": 0.7777099609375}, {"start": 1749.2, "end": 1749.76, "word": " و", "probability": 0.810546875}, {"start": 1749.76, "end": 1750.28, "word": " الفكرة", "probability": 0.7528483072916666}, {"start": 1750.28, "end": 1750.66, "word": " تبعها", "probability": 0.8197021484375}, {"start": 1750.66, "end": 1751.24, "word": " البرهان", "probability": 0.7852783203125}, {"start": 1751.24, "end": 1751.68, "word": " و", "probability": 0.8681640625}, {"start": 1751.68, "end": 1751.86, "word": " إيش", "probability": 0.73193359375}, {"start": 1751.86, "end": 1752.3, "word": " بدنا", "probability": 0.947509765625}, {"start": 1752.3, "end": 1753.6, "word": " نشتغل", "probability": 0.99248046875}, {"start": 1753.6, "end": 1754.06, "word": " معاها", "probability": 0.8658854166666666}, {"start": 1754.06, "end": 1754.82, "word": " for", "probability": 0.4951171875}, {"start": 1754.82, "end": 1755.28, "word": " each", "probability": 0.94921875}, {"start": 1755.28, "end": 1756.1, "word": " k", "probability": 0.351806640625}, {"start": 1756.1, "end": 1756.7, "word": " تنتمي", "probability": 0.908935546875}, {"start": 1756.7, "end": 1757.0, "word": " لأن", "probability": 0.4814453125}, {"start": 1757.0, "end": 1757.42, "word": " لأي", "probability": 0.816650390625}, {"start": 1757.42, "end": 1757.7, "word": " عدد", "probability": 0.9855143229166666}, {"start": 1757.7, "end": 1758.18, "word": " طبيعي", "probability": 0.977783203125}, {"start": 1758.18, "end": 1759.24, "word": " let", "probability": 0.58056640625}, {"start": 1759.24, "end": 1759.56, "word": " a", "probability": 0.6396484375}, {"start": 1759.56, "end": 1759.78, "word": " sub", "probability": 0.771484375}, {"start": 1759.78, "end": 1760.2, "word": " k", "probability": 0.94091796875}, {"start": 1760.2, "end": 1760.52, "word": " be", "probability": 0.73681640625}, {"start": 1760.52, "end": 1760.76, "word": " a", "probability": 0.931640625}, {"start": 1760.76, "end": 1761.16, "word": " denominable", "probability": 0.5791829427083334}, {"start": 1761.16, "end": 1761.56, "word": " set", "probability": 0.9794921875}, {"start": 1761.56, "end": 1762.78, "word": " satisfying", "probability": 0.908203125}, {"start": 1762.78, "end": 1763.88, "word": " a", "probability": 0.70556640625}, {"start": 1763.88, "end": 1764.48, "word": " j", "probability": 0.55810546875}, {"start": 1764.48, "end": 1765.86, "word": " تقاطع", "probability": 0.895751953125}, {"start": 1765.86, "end": 1766.1, "word": " a", "probability": 0.89501953125}, {"start": 1766.1, "end": 1766.26, "word": " k", "probability": 0.8046875}, {"start": 1766.26, "end": 1766.68, "word": " تساوي", "probability": 0.75592041015625}, {"start": 1766.68, "end": 1767.04, "word": " five", "probability": 0.418701171875}, {"start": 1767.04, "end": 1767.86, "word": " for", "probability": 0.95263671875}, {"start": 1767.86, "end": 1768.42, "word": " all", "probability": 0.953125}, {"start": 1768.42, "end": 1768.68, "word": " j", "probability": 0.92236328125}, {"start": 1768.68, "end": 1768.86, "word": " لا", "probability": 0.420654296875}, {"start": 1768.86, "end": 1769.22, "word": " تساوي", "probability": 0.9803466796875}, {"start": 1769.22, "end": 1769.46, "word": " k", "probability": 0.67138671875}, {"start": 1769.46, "end": 1770.26, "word": " نحاول", "probability": 0.9564208984375}, {"start": 1770.26, "end": 1770.54, "word": " نفهم", "probability": 0.9752604166666666}, {"start": 1770.54, "end": 1770.74, "word": " هذا", "probability": 0.662109375}, {"start": 1770.74, "end": 1771.2, "word": " الكلام", "probability": 0.931640625}], "temperature": 1.0}, {"id": 73, "seek": 178522, "start": 1772.72, "end": 1785.22, "text": "هو يعبّر أن جميع المجموعات مقاومة في الـ Disjoint ما هو معنى الـ Disjoint؟ كل تنتين تقاطعوهم فيها، ليس فقط كلهم تقاطعوهم مع بعض فيها، لكن كل تنتين", "tokens": [3224, 2407, 7251, 3615, 3555, 11703, 2288, 14739, 10874, 2304, 40228, 9673, 7435, 2304, 45367, 9307, 3714, 4587, 995, 20498, 3660, 8978, 2423, 39184, 4208, 5134, 686, 19446, 31439, 20449, 1863, 7578, 2423, 39184, 4208, 48613, 22807, 28242, 6055, 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"word": " فقط", "probability": 0.735107421875}, {"start": 1782.56, "end": 1783.0, "word": " كلهم", "probability": 0.8818359375}, {"start": 1783.0, "end": 1783.42, "word": " تقاطعوهم", "probability": 0.8640950520833334}, {"start": 1783.42, "end": 1783.54, "word": " مع", "probability": 0.53857421875}, {"start": 1783.54, "end": 1783.72, "word": " بعض", "probability": 0.9921875}, {"start": 1783.72, "end": 1784.06, "word": " فيها،", "probability": 0.7848307291666666}, {"start": 1784.06, "end": 1784.22, "word": " لكن", "probability": 0.324951171875}, {"start": 1784.22, "end": 1784.66, "word": " كل", "probability": 0.939453125}, {"start": 1784.66, "end": 1785.22, "word": " تنتين", "probability": 0.98974609375}], "temperature": 1.0}, {"id": 74, "seek": 181494, "start": 1787.08, "end": 1814.94, "text": "فعبّر عنه أن اي جي تقاطع أي ك لأي جي لتساوي ك طبعا التبليش مجال لاتساوي لأن لو بيساووا بعض ما بيكون تقاطعهم بيساوي نفسهم ماعندش منطقي لما يقولوا كل مجموعتين المختلفتين تقاطعهم فيه هيك معناته 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"word": " بيجيكشن", "probability": 0.7406877790178571}, {"start": 2014.37, "end": 2015.41, "word": " البرهان", "probability": 0.8360595703125}, {"start": 2015.41, "end": 2015.73, "word": " هتركه", "probability": 0.843505859375}, {"start": 2015.73, "end": 2015.83, "word": " في", "probability": 0.505859375}, {"start": 2015.83, "end": 2015.93, "word": " ال", "probability": 0.30029296875}, {"start": 2015.93, "end": 2016.21, "word": " exercise", "probability": 0.28857421875}, {"start": 2016.21, "end": 2017.35, "word": " given", "probability": 0.44580078125}, {"start": 2017.35, "end": 2017.83, "word": " by", "probability": 0.98876953125}, {"start": 2017.83, "end": 2018.25, "word": " let", "probability": 0.837890625}, {"start": 2018.25, "end": 2018.53, "word": " F", "probability": 0.52001953125}, {"start": 2018.53, "end": 2018.89, "word": " then", "probability": 0.81982421875}], "temperature": 1.0}, {"id": 83, "seek": 204586, "start": 2021.1, "end": 2045.86, "text": "FK is a bijection exercise اه تفضلي لأ بس بزيده يعني بدل مجموعة الواحد تقولي مجموعة التنين لأ بصير تضربت المجموعة باتنين ضعفها مش مش نفسها", "tokens": [37, 42, 307, 257, 3228, 1020, 313, 5380, 1975, 3224, 6055, 5172, 11242, 20292, 5296, 10721, 4724, 3794, 4724, 11622, 25708, 3224, 37495, 22653, 47525, 1211, 3714, 7435, 2304, 2407, 27884, 2423, 14407, 24401, 6055, 39648, 1829, 3714, 7435, 2304, 2407, 27884, 16712, 1863, 9957, 5296, 10721, 4724, 9381, 13546, 6055, 11242, 25513, 2655, 9673, 7435, 2304, 45367, 3660, 4724, 9307, 1863, 9957, 48812, 3615, 5172, 11296, 37893, 37893, 8717, 36178, 11296], "avg_logprob": -0.2060145515285126, "compression_ratio": 1.4679487179487178, "no_speech_prob": 0.0, "words": [{"start": 2021.1, "end": 2021.78, "word": "FK", "probability": 0.625732421875}, {"start": 2021.78, "end": 2022.1, "word": " is", "probability": 0.43603515625}, {"start": 2022.1, "end": 2022.24, "word": " a", "probability": 0.68310546875}, {"start": 2022.24, "end": 2023.08, "word": " bijection", 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عدد عناصرها مية؟ وهذا عدد عناصرها واحد؟ جدتش المجموع الكارتيسيان بتام مية؟ لكن لما تقول هنا مية و هنا اتنين تصبحين متين أنا بديها تكافئ واضحة طول لأ؟ اه فمابيديش انا اضعف العدد، انا بدي نفس العدد لما انا بثبت الإحداث التاني مابتغيرش العدد العناصر بس بدل مكتوبهم اللي هو and بدل مكتوبه هنا ال and مين بناظر؟", "tokens": [3224, 1211, 10874, 36081, 11296, 11778, 1829, 6225, 3215, 3215, 18871, 33546, 2288, 11296, 3714, 10632, 22807, 37037, 15730, 6225, 3215, 3215, 18871, 33546, 2288, 11296, 36764, 24401, 22807, 10874, 3215, 2655, 8592, 9673, 7435, 2304, 45367, 33251, 9640, 31371, 3794, 1829, 7649, 39894, 10943, 3714, 10632, 22807, 44381, 5296, 15042, 6055, 39648, 34105, 3714, 10632, 4032, 34105, 1975, 2655, 1863, 9957, 6055, 9381, 49628, 9957, 44650, 9957, 41850, 4724, 16254, 11296, 6055, 4117, 31845, 19986, 4032, 46958, 5016, 3660, 23032, 12610, 5296, 10721, 22807, 1975, 3224, 6156, 15042, 21292, 16254, 8592, 1975, 8315, 1975, 11242, 3615, 5172, 18863, 3215, 3215, 12399, 1975, 8315, 4724, 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صحيح نترال نترال إذا كانوا إيش Q plus عشان هيك هناخد ناخد Q plus فإذا هذه اللي هو إيش الملاحظة على طول فهنا let X تنتمي لـ Q plus عشان هيك ناخدنا then X تساوي B على Q", "tokens": [2304, 2304, 2655, 31377, 11933, 15730, 31439, 8978, 3224, 4724, 9381, 47395, 3714, 4587, 10943, 16070, 10721, 46538, 4032, 6027, 3555, 995, 3224, 11778, 12610, 11933, 1829, 8592, 4724, 1829, 30544, 14407, 5551, 22488, 18513, 20328, 5016, 1829, 5016, 8717, 2655, 2288, 6027, 8717, 2655, 2288, 6027, 11933, 15730, 25961, 14407, 11933, 1829, 8592, 1249, 1804, 6225, 8592, 7649, 39896, 4117, 8032, 1863, 47283, 3215, 8717, 47283, 3215, 1249, 1804, 6156, 28814, 15730, 29538, 13672, 1829, 31439, 11933, 1829, 8592, 9673, 15040, 5016, 19913, 3660, 15844, 23032, 12610, 6156, 3224, 8315, 718, 1783, 6055, 29399, 2304, 1829, 5296, 39184, 1249, 1804, 6225, 8592, 7649, 39896, 4117, 8717, 47283, 3215, 8315, 550, 1783, 6055, 3794, 995, 45865, 363, 15844, 1249], "avg_logprob": -0.3356770910322666, "compression_ratio": 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"probability": 0.8492838541666666}, {"start": 2441.41, "end": 2441.79, "word": " بنعبر", "probability": 0.7965494791666666}, {"start": 2441.79, "end": 2442.03, "word": " عنه", "probability": 0.914794921875}, {"start": 2442.03, "end": 2442.23, "word": " انه", "probability": 0.5604248046875}, {"start": 2442.23, "end": 2442.37, "word": " يكون", "probability": 0.70654296875}, {"start": 2442.37, "end": 2442.57, "word": " ايش", "probability": 0.81396484375}, {"start": 2442.57, "end": 2443.43, "word": " المعامل", "probability": 0.985107421875}, {"start": 2443.43, "end": 2443.91, "word": " المشترك", "probability": 0.993896484375}, {"start": 2443.91, "end": 2444.27, "word": " الأعظم", "probability": 0.86187744140625}, {"start": 2444.27, "end": 2444.55, "word": " يكون", "probability": 0.986328125}, {"start": 2444.55, "end": 2445.33, "word": " بسواحى", "probability": 0.591552734375}, {"start": 2445.33, "end": 2445.93, "word": " فدائما", "probability": 0.66790771484375}, {"start": 2445.93, "end": 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{"start": 2452.12, "end": 2452.46, "word": " و", "probability": 0.904296875}, {"start": 2452.46, "end": 2452.7, "word": " Q", "probability": 0.51806640625}, {"start": 2452.7, "end": 2452.96, "word": " وين", "probability": 0.5037841796875}, {"start": 2452.96, "end": 2453.56, "word": " موجودين", "probability": 0.9888916015625}, {"start": 2453.56, "end": 2454.48, "word": " في", "probability": 0.5517578125}, {"start": 2454.48, "end": 2454.62, "word": " الـ", "probability": 0.8505859375}, {"start": 2454.62, "end": 2454.88, "word": " natural", "probability": 0.370849609375}, {"start": 2454.88, "end": 2455.34, "word": " number", "probability": 0.9736328125}, {"start": 2455.34, "end": 2455.64, "word": " الآن", "probability": 0.64111328125}, {"start": 2455.64, "end": 2456.62, "word": " عشان", "probability": 0.84326171875}, {"start": 2456.62, "end": 2456.7, "word": " هي", "probability": 0.51611328125}, {"start": 2456.7, "end": 2456.84, "word": " أنا", "probability": 0.484130859375}, {"start": 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كله بدا اختصر، تمام فهذا سيساعدنا، الآن سنعرف دالة، مين العرف دالة؟ سنستطيع أن نثبت أن الـQ تكافئ الـN ولا الـN cross الـN", "tokens": [67, 592, 271, 284, 19446, 7251, 38251, 11536, 3224, 32239, 8592, 18863, 10943, 1211, 9673, 8592, 2655, 31747, 1975, 2407, 18863, 10943, 1211, 9673, 8592, 2655, 31747, 42963, 4117, 26890, 6636, 2689, 25974, 284, 295, 363, 293, 1249, 307, 472, 7251, 3794, 2407, 11703, 5016, 12399, 20193, 5551, 16572, 3215, 14739, 7251, 39237, 49429, 6225, 10943, 1211, 37893, 2655, 31747, 12399, 28242, 3224, 4724, 28259, 1975, 46456, 9381, 2288, 12399, 46811, 10943, 6156, 3224, 15730, 8608, 1829, 3794, 995, 22488, 8315, 12399, 6024, 48506, 8608, 1863, 3615, 28480, 11778, 6027, 3660, 12399, 3714, 9957, 18863, 28480, 11778, 6027, 3660, 22807, 8608, 1863, 14851, 9566, 40228, 14739, 8717, 12984, 3555, 2655, 14739, 2423, 39184, 48, 6055, 4117, 31845, 19986, 2423, 39184, 45, 49429, 2423, 39184, 45, 3278, 2423, 39184, 45], "avg_logprob": -0.3831730821957955, "compression_ratio": 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العملية طب هذه Infinite ليش؟ لأن الـ Q Plus Infinite لأن الـ Q Plus شمالها أكبر من الـ N Infinite أه فالأن ال subset and F of Q Plus is Infinite", "tokens": [38688, 1829, 1249, 7721, 37037, 15730, 25993, 9154, 3714, 9957, 22807, 9154, 2423, 39184, 426, 8717, 4587, 2288, 9381, 8978, 2423, 39184, 426, 5551, 3224, 8032, 1211, 7435, 2655, 29538, 2423, 39184, 6458, 6981, 712, 11933, 15730, 29538, 43368, 16472, 47395, 2655, 18863, 42213, 10632, 23032, 3555, 29538, 43368, 32239, 8592, 22807, 5296, 33456, 2423, 39184, 1249, 7721, 43368, 5296, 33456, 2423, 39184, 1249, 7721, 13412, 2304, 6027, 11296, 5551, 4117, 26890, 9154, 2423, 39184, 426, 43368, 5551, 3224, 6156, 6027, 33456, 2423, 25993, 293, 479, 295, 1249, 7721, 307, 43368], "avg_logprob": -0.3529211985676185, "compression_ratio": 1.8, "no_speech_prob": 0.0, "words": [{"start": 2653.29, "end": 2653.69, "word": "وفي", "probability": 0.62060546875}, {"start": 2653.69, "end": 2654.03, "word": " Q", "probability": 0.46875}, {"start": 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{"start": 2675.67, "end": 2675.97, "word": " Q", "probability": 0.92236328125}, {"start": 2675.97, "end": 2676.59, "word": " Plus", "probability": 0.845703125}, {"start": 2676.59, "end": 2678.89, "word": " is", "probability": 0.91552734375}, {"start": 2678.89, "end": 2679.41, "word": " Infinite", "probability": 0.76318359375}], "temperature": 1.0}, {"id": 106, "seek": 270982, "start": 2681.62, "end": 2709.82, "text": "implies F of Q plus is denumerable وبالتالي Q plus is denumerable والباقي زي ما حكينا طبعا Q minus تكافئ Q plus Q minus", "tokens": [332, 564, 530, 479, 295, 1249, 1804, 307, 1441, 15583, 712, 46599, 6027, 2655, 6027, 1829, 1249, 1804, 307, 1441, 15583, 712, 4032, 6027, 3555, 995, 38436, 30767, 1829, 19446, 11331, 4117, 1829, 8315, 23032, 3555, 3615, 995, 1249, 3175, 6055, 4117, 31845, 19986, 1249, 1804, 1249, 3175], "avg_logprob": -0.34885203108495594, "compression_ratio": 1.345132743362832, "no_speech_prob": 0.0, "words": [{"start": 2681.62, "end": 2682.48, "word": 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"word": " والباقي", "probability": 0.6150390625}, {"start": 2703.74, "end": 2703.9, "word": " زي", "probability": 0.6771240234375}, {"start": 2703.9, "end": 2703.96, "word": " ما", "probability": 0.962890625}, {"start": 2703.96, "end": 2704.32, "word": " حكينا", "probability": 0.9642333984375}, {"start": 2704.32, "end": 2704.62, "word": " طبعا", "probability": 0.845458984375}, {"start": 2704.62, "end": 2704.88, "word": " Q", "probability": 0.35888671875}, {"start": 2704.88, "end": 2705.44, "word": " minus", "probability": 0.87890625}, {"start": 2705.44, "end": 2706.7, "word": " تكافئ", "probability": 0.810791015625}, {"start": 2706.7, "end": 2706.92, "word": " Q", "probability": 0.55810546875}, {"start": 2706.92, "end": 2707.42, "word": " plus", "probability": 0.94580078125}, {"start": 2707.42, "end": 2709.28, "word": " Q", "probability": 0.7626953125}, {"start": 2709.28, "end": 2709.82, "word": " minus", "probability": 0.9833984375}], "temperature": 1.0}, {"id": 107, "seek": 273769, "start": 2710.75, "end": 2737.69, "text": "تكافئ EQ plus implies EQ minus is denumerable طبعا فبتم ان الاتحاد تبقى homodenumerable therefore EQ is denumerable مع النظريات السابقة", "tokens": [2655, 4117, 31845, 19986, 33580, 1804, 18779, 33580, 3175, 307, 1441, 15583, 712, 23032, 3555, 3615, 995, 6156, 3555, 39237, 16472, 2423, 9307, 5016, 18513, 6055, 3555, 4587, 7578, 3655, 378, 268, 15583, 712, 4412, 33580, 307, 1441, 15583, 712, 20449, 28239, 19913, 16572, 9307, 21136, 16758, 28671], "avg_logprob": -0.31138392857142855, "compression_ratio": 1.2805755395683454, "no_speech_prob": 0.0, "words": [{"start": 2710.75, "end": 2711.53, "word": "تكافئ", "probability": 0.748748779296875}, {"start": 2711.53, "end": 2713.03, "word": " EQ", "probability": 0.1717529296875}, {"start": 2713.03, "end": 2713.69, "word": " plus", "probability": 0.1737060546875}, {"start": 2713.69, "end": 2714.77, "word": " implies", "probability": 0.76318359375}, {"start": 2714.77, "end": 2715.47, "word": " EQ", 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"end": 2731.03, "word": " is", "probability": 0.916015625}, {"start": 2731.03, "end": 2731.73, "word": " denumerable", "probability": 0.9181315104166666}, {"start": 2731.73, "end": 2736.27, "word": " مع", "probability": 0.98193359375}, {"start": 2736.27, "end": 2736.99, "word": " النظريات", "probability": 0.968994140625}, {"start": 2736.99, "end": 2737.69, "word": " السابقة", "probability": 0.9783528645833334}], "temperature": 1.0}, {"id": 108, "seek": 276233, "start": 2750.29, "end": 2762.33, "text": "فطبعا يمكن بدت اللي هو الصورة تكتمل شيئا فشيئا، الآن مرتانة في عندنا عنوان الـdenominable sets are the smallest infinite sets", "tokens": [5172, 9566, 3555, 3615, 995, 7251, 43020, 47525, 2655, 13672, 1829, 31439, 31767, 13063, 3660, 6055, 4117, 39237, 1211, 44049, 19986, 995, 6156, 8592, 1829, 19986, 995, 12399, 6024, 48506, 3714, 43500, 7649, 3660, 8978, 43242, 8315, 18871, 2407, 7649, 2423, 39184, 1556, 6981, 712, 6352, 366, 264, 16998, 13785, 6352], "avg_logprob": 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"duration_after_vad": 2646.18312499999} \ No newline at end of file diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/pV7ba4YK3IA.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/pV7ba4YK3IA.srt new file mode 100644 index 0000000000000000000000000000000000000000..864efc8a572ca6d48f7f108c36f43554c29b0e92 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/pV7ba4YK3IA.srt @@ -0,0 +1,1875 @@ +1 +00:00:20,500 --> 00:00:25,720 +بسم الله الرحمن الرحيم نستكمل مع الـdenumerable + +2 +00:00:25,720 --> 00:00:31,720 +sets وجدنا عند نظرية طبعا اللي هو العنوان الرئيسي + +3 +00:00:31,720 --> 00:00:36,080 +لها أن الـdenumerable sets هما أصغر infinite sets + +4 +00:00:36,080 --> 00:00:39,960 +فطبعا بتقول every infinite set contains a + +5 +00:00:39,960 --> 00:00:43,460 +denumerable set يعني مستحيل تكون infinite set وتكون + +6 +00:00:43,460 --> 00:00:46,740 +صغيرة جدا بحيث ما ألاقيش فيها جواها Denumerable جواها + +7 +00:00:46,740 --> 00:00:49,920 +Denumerable فده بيدينا الإحساس أن الـ Denumerable + +8 +00:00:49,920 --> 00:00:54,500 +هي أصغر Infinite Set خلّيني أشوف البرهان فكرة مرت + +9 +00:00:54,500 --> 00:00:59,460 +علينا مش بنفس الصيغة لكن بشكل مشابه لما نشوفها مع + +10 +00:00:59,460 --> 00:01:05,560 +بعض هنتذكر استخدمناها في أكثر من منبع ال proof every + +11 +00:01:05,560 --> 00:01:08,880 +infinite set contains a denumerable subset فناخد + +12 +00:01:08,880 --> 00:01:19,090 +infinite set let X an infinite set ايش + +13 +00:01:19,090 --> 00:01:23,790 +المطلوب؟ بدنا نلاقي subset من ال X تكون denumerable + +14 +00:01:23,790 --> 00:01:27,790 +بدنا نلاقي مجموعة من ال X تكون denumerable اه طبعا + +15 +00:01:27,790 --> 00:01:29,710 +هي نفس الفكرة اللي احنا عملناها أكثر من مرة قولنا + +16 +00:01:29,710 --> 00:01:32,650 +كأنه هذه ال X مجموعة عشوائية فيها أنا كيس من + +17 +00:01:32,650 --> 00:01:36,090 +القرات و بناخد و بنقدر نرقم طبعا هنا بدنا نرقم إلى + +18 +00:01:36,090 --> 00:01:38,670 +مالا نهاية عشانها denumerable بدنا نرقم واحد اثنين + +19 +00:01:38,670 --> 00:01:42,380 +ثلاثة إلى مالانهاية فهي نفس الفكرة تماما طبعا ايش + +20 +00:01:42,380 --> 00:01:45,140 +اللي بيخليني أختار دائما من ال X انها infinite فهي + +21 +00:01:45,140 --> 00:01:49,260 +مش فارغة بالتأكيد لأنه لو فارغة finite بنعرف فإذن + +22 +00:01:49,260 --> 00:01:55,740 +أول شيء فهذا بيؤدي أن X لا تساوي Φ وهذا يؤدي + +23 +00:01:55,740 --> 00:02:00,380 +there exists X1 تنتمي لل X فهي أول عنصر اللي + +24 +00:02:00,380 --> 00:02:06,280 +وجدناه بنرتبه و بناخده على جهة تمام برضه بما أن ال + +25 +00:02:06,280 --> 00:02:11,670 +X is infinite بقدر ألاقي X2 X is infinite + +26 +00:02:11,670 --> 00:02:18,510 +implies there exist X2 في ال X معنى ال X1 واتوقع + +27 +00:02:18,510 --> 00:02:21,590 +أن هذه الفكرة استخدمناها أكثر من مرة بنحذف العنصر + +28 +00:02:21,590 --> 00:02:26,110 +فبنلاقي عنصر جديد وهكذا فبنفس الأسلوب continuing + +29 +00:02:26,110 --> 00:02:29,990 +in + +30 +00:02:29,990 --> 00:02:30,830 +the same way + +31 +00:02:37,850 --> 00:02:44,190 +We can find XK + +32 +00:02:44,190 --> 00:02:53,310 +تنتمي لـ X معدى X1 لـ XK-1 فانا لما لجيت X2 بقدر + +33 +00:02:53,310 --> 00:03:00,110 +أجي X3 بعدها و X4 طبعا هذا الكلام for all K تنتمي + +34 +00:03:00,110 --> 00:03:05,620 +لمن؟ لـ natural number دي العملية مستمرة لسه، دا + +35 +00:03:05,620 --> 00:03:08,960 +كون المجموعة منها، هنشوف هل جيت بس نقوله let Y + +36 +00:03:08,960 --> 00:03:14,060 +فدول العناصر اللي لجتهم بدي أحطهم في وعاء جديد + +37 +00:03:14,060 --> 00:03:20,380 +سميه Y تساوي XK such that XK تنتمي لل N طبعا ففي + +38 +00:03:20,380 --> 00:03:24,880 +عندي بس شيء أهم بدي أتأكد منهم ال Y subset من ال X + +39 +00:03:24,880 --> 00:03:27,300 +ولا لأ؟ لأن كل العناصر اللي أخدت منها من ال X + +40 +00:03:27,300 --> 00:03:32,200 +وطبعا denumerable لأن هي مرقمة، ما فيش أوضح من هاتف + +41 +00:03:32,200 --> 00:03:41,060 +and denumerable and why is the name of it؟ + +42 +00:03:41,060 --> 00:03:45,200 +لأن أنا كنت عنصر بأخد و كنت برقمه فعملية واضحة + +43 +00:03:45,200 --> 00:03:49,920 +بهذا الشكل فهنا أرجو أنه يعني دائما نشوف الأفكار + +44 +00:03:49,920 --> 00:03:53,680 +تتكرر و نتعلمها و تبدأ الإنسان يستخدم نفس الفكرة + +45 +00:03:53,680 --> 00:03:59,200 +في مكان آخر فممكن يستخدمها في أكثر من مكان فتادي + +46 +00:03:59,200 --> 00:04:00,580 +نهاية ال section + +47 +00:04:05,750 --> 00:04:11,190 +نشوف ال section الأخير اللي هيكمل لنا الصورة في + +48 +00:04:11,190 --> 00:04:14,530 +uncountable و non uncountable sets + +49 +00:04:20,880 --> 00:04:23,960 +فطبعا زي ما حكيت أنا في المحاضرات السابقة احنا + +50 +00:04:23,960 --> 00:04:27,220 +بدأنا من denumerable وبدأنا نكبر فيها وانضفنا لها + +51 +00:04:27,220 --> 00:04:31,440 +عنصر finite number of elements بعدين denumerable + +52 +00:04:31,440 --> 00:04:34,520 +اتحاد، denumerable حتى denumerable كارتيزي بوداك مع + +53 +00:04:34,520 --> 00:04:37,480 +denumerable ما زلنا جد ما بنكبر ما زلنا denumerable طب + +54 +00:04:37,480 --> 00:04:40,360 +هل هذا الكلام إلى مدى نهاية فيش كل المجموعات + +55 +00:04:40,360 --> 00:04:43,380 +denumerable؟ هنشوف طبعا هنبقى لنا non-denumerable + +56 +00:04:43,380 --> 00:04:48,480 +system لأ في مجموعات non-denumerable فطبعا السؤال + +57 +00:04:48,480 --> 00:04:52,600 +اللي احنا توي طرحنا هل كل infinite set denumerable؟ + +58 +00:04:52,600 --> 00:04:57,760 +فطبعا واضح أن الجواب لا فطبعا يوجد ما يعرف + +59 +00:04:57,760 --> 00:05:00,700 +بالـnon-denumerable sets يعني مجموعات not denumerable + +60 +00:05:00,700 --> 00:05:04,280 +طبعا ايش معناه not denumerable بشكل صريح؟ طبعا إنها + +61 +00:05:04,280 --> 00:05:06,660 +بدأت تكون غير قابلة للعدد، هذا المعنى الاصطلاحي + +62 +00:05:06,660 --> 00:05:10,800 +اللغوي المعنى الاصطلاحي بدأت تكون infinite و لا + +63 +00:05:10,800 --> 00:05:13,990 +تكافئ الآن infinite لأن الـ set اللي بيسموها برضه + +64 +00:05:13,990 --> 00:05:18,450 +uncountable لأن countable يا finite يا denumerable + +65 +00:05:18,450 --> 00:05:21,390 +طب uncountable أو non-denumerable نفس المعنى + +66 +00:05:21,390 --> 00:05:26,130 +infinite وغير قابلة للعدد أو إياته كافية فهنا بنقول + +67 +00:05:26,130 --> 00:05:28,690 +أن a set X is said to be non-denumerable or + +68 +00:05:28,690 --> 00:05:32,910 +uncountable if it is not countable هذا المعنى اللي + +69 +00:05:32,910 --> 00:05:36,790 +على طول لأنه هي ولا finite ولا denumerable بمعنى + +70 +00:05:36,790 --> 00:05:40,780 +آخر it is infinite and not denumerable، اه ما أقدرش + +71 +00:05:40,780 --> 00:05:44,800 +ايش، لا تكافئ لان، ولا تكافئ لان، فاحنا عندنا يمكن ال + +72 +00:05:44,800 --> 00:05:47,620 +set اللي هو المجموعات، فيه الصغار جدا اللي هم ال + +73 +00:05:47,620 --> 00:05:50,860 +finite، بعدين الأكبر شوية اللي هم infinite لكن + +74 +00:05:50,860 --> 00:05:54,180 +denumerable، والآن ال infinite و not denumerable، + +75 +00:05:54,180 --> 00:05:57,740 +في هذه الصورة، فاحنا هنتحدث عنهم بشكل اللي هو + +76 +00:05:57,740 --> 00:06:03,620 +تفصيلي أكثر طبعاً زي ما احنا شوفنا تسلسل الان هي + +77 +00:06:03,620 --> 00:06:06,640 +المعيار الأساسي واحدة القياس لل infinite set + +78 +00:06:06,640 --> 00:06:10,920 +و denumerable لجينا ال z رغم أنها أكبر منها ظاهريا + +79 +00:06:10,920 --> 00:06:15,160 +لكن عدد العناصر متساوي وال Q زي هيك فصار الهدف ان + +80 +00:06:15,160 --> 00:06:19,920 +أشتغل على بعد هيك ال R هرق الـ R denumerable اللي حصل + +81 +00:06:19,920 --> 00:06:24,760 +.. الحقيقة لا فهذه مجموعة كبيرة فاحنا مشينا Z, Q + +82 +00:06:24,760 --> 00:06:28,960 +لجينا كله denumerable لكن عند الـ R لا عشان أثبت أن + +83 +00:06:28,960 --> 00:06:33,200 +الـ R non-denumerable هاخد فترة صغيرة أول طبعا لأنه + +84 +00:06:33,200 --> 00:06:36,560 +شوفنا احنا في ما سبق أن الـ R تكافئ من سالب ما لا نهاية + +85 +00:06:36,560 --> 00:06:40,320 +لما لا نهاية وقلنا كل open interval يكافئ open interval + +86 +00:06:40,320 --> 00:06:44,630 +فللبعض اللي قاعدة بيدينا مرونة وتسهيل في العمل تسهيل + +87 +00:06:44,630 --> 00:06:47,130 +في العملية، لأنه ما بديش أن ألتزم، يعني زي ما + +88 +00:06:47,130 --> 00:06:50,290 +تشوفنا أنه إثبات الـ Z-denumerable بطريقة ثانية، + +89 +00:06:50,290 --> 00:06:52,730 +فلما صار عندي نظريات، صار بديني تسهيل، آه، بديني + +90 +00:06:52,730 --> 00:06:55,230 +بدائل، وهذا بديني سهولة، فالآن احنا هنشتغل على + +91 +00:06:55,230 --> 00:06:58,290 +الفترة 01، إذا قدرت أثبت أن هذه المجموعة non + +92 +00:06:58,290 --> 00:07:00,450 +-denumerable، بتكون الـ R non-denumerable، لأنكوا + +93 +00:07:00,450 --> 00:07:03,410 +كافئها على طول، آه، آه، فطبعا، ليش بدي أشتغل على + +94 +00:07:03,410 --> 00:07:07,250 +الـ 01؟ لأن الأعداد الحقيقية في الـ 01، بيكون الجزء + +95 +00:07:07,250 --> 00:07:10,550 +الصحيح فيها صفر، بالتام مش إلا جزء كسر لأن هو بين + +96 +00:07:10,550 --> 00:07:13,250 +صفر وبين واحد فهذا بدينا بعض السهولة في التعامل و + +97 +00:07:13,250 --> 00:07:16,270 +طبعا أنا دائما بدي المفاد الأسهل وبعدين التعميم + +98 +00:07:16,270 --> 00:07:19,710 +خلاص بشتغل على النظرية فطبعا أول شيء من بعض + +99 +00:07:19,710 --> 00:07:23,430 +الحقائق من خواص الأعداد الحقيقية هنديها على صورة + +100 +00:07:23,430 --> 00:07:27,760 +نظريات بس بدون برهان أي عدد بين الـ zero بين ال one + +101 +00:07:27,760 --> 00:07:32,880 +طبعا بإيش بنكتبه؟ صفر فاصلة واللي هم خانات العشرية + +102 +00:07:32,880 --> 00:07:35,700 +طبعا الخانات العشرية ايش بتقول؟ يا صفر يا واحد يا + +103 +00:07:35,700 --> 00:07:38,880 +تسعة هم دول اللي هيش ال digits ولا لأ أنا بكتب أي + +104 +00:07:38,880 --> 00:07:42,040 +عدد ما زال هو بين أصغر بإيش ما له بين الصفر وبين + +105 +00:07:42,040 --> 00:07:45,000 +الواحد يعني أكبر من صفر وأصغر من واحد يعني هو موجب + +106 +00:07:45,000 --> 00:07:48,520 +لكنه أصغر من واحد إذا الجزء الصحيح فيه أقل من صفر + +107 +00:07:48,520 --> 00:07:53,890 +أطولهو 9 من 10، 99 من 100، 98 من 1000، كله آه بعد + +108 +00:07:53,890 --> 00:07:56,310 +الشكل، طبعا هدول الخانات بيكونوا من صفر لتسعة، + +109 +00:07:56,310 --> 00:07:59,150 +هدول الأرقام، هدول ال digits، هدول اللي بنحكي عنه، + +110 +00:07:59,150 --> 00:08:02,370 +فكل عدد هنعمله بعد الشكل، هتمد على هذه الخواص وعلى + +111 +00:08:02,370 --> 00:08:07,960 +هذه الصورة آه في عندنا ملاحظة مهمة جدا زي ما عملنا في + +112 +00:08:07,960 --> 00:08:13,060 +المحاضرة السابقة لما قلنا في عدد النسبة بنحطه على + +113 +00:08:13,060 --> 00:08:16,020 +صورة كسر بس هذه الكسر قليل و أكثر من صورة فبدي + +114 +00:08:16,020 --> 00:08:19,500 +الصورة القياسية اللي ما فيش عامل مشترك هنا نفس + +115 +00:08:19,500 --> 00:08:23,320 +القضية لأني حطيت العدد وكتبته بشكل كسر عشرة و + +116 +00:08:23,320 --> 00:08:26,880 +خانة طب هل هذه العملية unique ولا في أكثر من + +117 +00:08:26,880 --> 00:08:31,310 +طريقة للكتابة؟ في أكثر من طريقة للكتابة لو استخدمنا + +118 +00:08:31,310 --> 00:08:34,890 +الـ Geometric Series كأنه ممكن أن أثبت أن هذا + +119 +00:08:34,890 --> 00:08:39,870 +العدد صفر وثلاثة وواحد وبعدين كله تسعات إلى مال + +120 +00:08:39,870 --> 00:08:45,750 +نهاية ممكن أو بيساوي مش يمكن 32% لما تكون تسعة في + +121 +00:08:45,750 --> 00:08:49,830 +النهاية دي ملاحظة عامة إذا كان أي عدد كسري وفي + +122 +00:08:49,830 --> 00:08:53,580 +الآخر كله تسعة تسعة تسعة إلى مالانهاية ده بتقرب على + +123 +00:08:53,580 --> 00:08:55,660 +طول بيساوي على طول عن طريق اللي هو الـ Geometric + +124 +00:08:55,660 --> 00:08:58,920 +Series متذكرين في تفاضل باك كيف كنا نثبت أنه أيش + +125 +00:08:58,920 --> 00:09:03,600 +نعملها عبارة عن مثلا هذه كده بدي أعملها التسعة هذه + +126 +00:09:03,600 --> 00:09:07,060 +تسعة من ألف زائد تسعة من عشرة آلاف وهكذا بنعملها + +127 +00:09:07,060 --> 00:09:09,220 +Infinite Series وبعدين نجمعها عن طريق الـ + +128 +00:09:09,220 --> 00:09:12,740 +Geometric Series بتنجمعها على طول بهذا الشكل فالآن + +129 +00:09:13,920 --> 00:09:19,040 +فهعتاج فيه اللي هو البرهان إن هذا الصورة أو هذه + +130 +00:09:19,040 --> 00:09:22,000 +الصورة مين اللي بده يستخدمها فيهم ودول متساويين + +131 +00:09:22,000 --> 00:09:27,780 +بديش يكون عنده صورتين متشابهتين وكل واحدة كتابتها + +132 +00:09:27,780 --> 00:09:31,020 +مختلفة زي ما عملنا في مين؟ في الـP على Q، متذكرين؟ + +133 +00:09:31,020 --> 00:09:33,920 +نفس القضية، عشان بدي أنا أكون في عندي اللي هو + +134 +00:09:33,920 --> 00:09:37,360 +تمثيل وحيد عشان أعتمد عليه وإلا بيصير عندي يعني + +135 +00:09:37,360 --> 00:09:41,630 +غلطة في أن نكون عارفين الدالة فبدنا تمثيل وحيد آه + +136 +00:09:41,630 --> 00:09:44,730 +فدائما هذه الصيغة الأخيرة هسميها هي الصيغة + +137 +00:09:44,730 --> 00:09:48,130 +القياسية الصيغة القياسية مش هنسمح يكون تسعات إلى + +138 +00:09:48,130 --> 00:09:53,510 +ما لا نهاية فبقول لي أي عدد كسري بيكون في الآخر كله + +139 +00:09:53,510 --> 00:09:58,630 +تسعات ممكن ايش أعدله واوش ويصير أنه ايش زيادة + +140 +00:09:58,630 --> 00:10:01,510 +بواحد equal to one that ends with an infinite + +141 +00:10:01,510 --> 00:10:05,230 +string of zero ممكن أحوله لأصفار في الآخر وين + +142 +00:10:05,230 --> 00:10:09,300 +التكرار أضيف واحد و أحول الباقي لأصفار، أه فهذه + +143 +00:10:09,300 --> 00:10:14,620 +الطريقة اللي هنعتمدها، فهذا الكلام صحيح، فهنعتمد الصورة + +144 +00:10:14,620 --> 00:10:17,900 +القياسية زي ما احنا في العدد النسبي يقول لنا إن المعامل + +145 +00:10:17,900 --> 00:10:21,680 +المشترك يكون واحد ما فيش أي معامل كله يكون اختصر + +146 +00:10:21,680 --> 00:10:24,540 +وخلصنا هنا نفس القضية دائماً هنعتبر إنه حاطط في ال + +147 +00:10:24,540 --> 00:10:27,640 +normal form صار أصفار في الآخر فبيقول لي a decimal + +148 +00:10:27,640 --> 00:10:31,540 +representation of a real number X is in normalized + +149 +00:10:31,540 --> 00:10:36,360 +form في الوضع القياسي، يعني if and only if there is + +150 +00:10:36,360 --> 00:10:41,030 +no k such that for all n أكبر من k xj بساوي 9، ما + +151 +00:10:41,030 --> 00:10:44,130 +بديش كله بعد خانة معينة كله تسعات وتسعات، إذا كان + +152 +00:10:44,130 --> 00:10:47,130 +كله تسعات وتسعات، بتعمله Normalization، زي هذا + +153 +00:10:47,130 --> 00:10:51,290 +المثال، فهذا وضع غير قياسي، إذا صار هيك، بتحاولوا + +154 +00:10:51,290 --> 00:10:54,230 +الوضع القياسي، فأي عدد اللي هو هذه الخاصية، إنه في + +155 +00:10:54,230 --> 00:10:57,170 +الآخر كل الخانات تسعة تسعة تسعة لنهاية، بتعمله + +156 +00:10:57,170 --> 00:11:00,210 +Normalization، أو بتعمله Normalization، فاحنا + +157 +00:11:00,210 --> 00:11:04,920 +هنشتغل على كل عدد بهذه الصورة بقدر أضع ه في هذا الشكل + +158 +00:11:04,920 --> 00:11:08,540 +اتفقنا مصفوفة وبعدين كل عدد إذا كان بنتي كله تسعات + +159 +00:11:08,540 --> 00:11:12,280 +بنحاوله لمين؟ لـ Normalized form، لـ Normalized form + +160 +00:11:12,280 --> 00:11:17,300 +فهذا الوضع القياسي تماماً، الآن هذه بتأكد الكلام اللي + +161 +00:11:17,300 --> 00:11:20,860 +بدي أحكي عليه فبيقول لي two decimal numbers in + +162 +00:11:20,860 --> 00:11:23,940 +normalized form لما نحطه بالوضع القياسي اسمهم + +163 +00:11:23,940 --> 00:11:29,300 +بيساوي بعض if and only if كل خانة بتساوي الخانة + +164 +00:11:29,300 --> 00:11:33,580 +المقابلة فبدي أول خانة عشرية تساوي أول خانة عشرية + +165 +00:11:33,580 --> 00:11:37,160 +ثاني خانة عشرية تساوي ثاني خانة عشرية يعني بمعنى + +166 +00:11:37,160 --> 00:11:43,590 +خليني أشوف هي عندنا مثلاً اللي هو X تساوي 0 X1 X2 و + +167 +00:11:43,590 --> 00:11:50,230 +هكذا وفي عندنا Y تساوي 0 Y1 Y2 خذنا خانة أولى وهكذا + +168 +00:11:50,230 --> 00:11:55,690 +متى هدول بيساوي بعض؟ إذا X1 تساوي Y1، X2 تساوي Y2 و + +169 +00:11:55,690 --> 00:11:59,350 +هكذا، طبعاً ليش بدي أعمل normalize form؟ لأن لو حولته + +170 +00:11:59,350 --> 00:12:02,450 +عشان المثال بيصير إيش؟ الوضع اختلف هيعندي عددين + +171 +00:12:02,450 --> 00:12:07,350 +متساويين لكن الخانات شمالهم هيو هذا بيساوي هذا لكن + +172 +00:12:07,350 --> 00:12:10,500 +هل كل خانة تساوي خانة؟ لأ، لكن عندما أقول إنه Normalized + +173 +00:12:10,500 --> 00:12:13,740 +Form فأعرف عن الكلام، واضح؟ أه، فهنا هي اللي بدنا + +174 +00:12:13,740 --> 00:12:16,700 +نحطها في الوضع القياسي عشان نتفق ونبدأ نشتغل ونبدأ + +175 +00:12:16,700 --> 00:12:20,640 +نشتغل، أه، فلأن هذا راح نعتمد عليه تمعن فهذا + +176 +00:12:20,640 --> 00:12:24,140 +تمهيد وبعض الخواص، الآن في عندنا نظرية أساسية + +177 +00:12:25,490 --> 00:12:30,010 +النظرية الرئيسية بيقول ليه؟ المجموعة من صفر لواحد + +178 +00:12:30,010 --> 00:12:32,830 +اللي هي مجموعة كل الأعداد الحقيقية اللي أكبر من + +179 +00:12:32,830 --> 00:12:36,010 +صفر وأصغر من واحد is non-denominable is non + +180 +00:12:36,010 --> 00:12:40,350 +-denominable، شوفتوا كل اللي احنا عملناه في الأول + +181 +00:12:40,350 --> 00:12:44,750 +كبرنا من الانفينتي وروحنا بالشرق باتجاه الغرب، تمت + +182 +00:12:44,750 --> 00:12:48,500 +denominable، أول ما دخلنا على الـreal numbers الأمور + +183 +00:12:48,500 --> 00:12:51,560 +خرجت عن السيطرة، بطّت الـdenominable، واخدنا فترة + +184 +00:12:51,560 --> 00:12:55,600 +نموذجية من صفر لواحد، فبيقول الـopen interval نأكد + +185 +00:12:55,600 --> 00:12:59,580 +عليها، هي الفترة 01 اللي هي كل عدد حقيقي اللي أكبر + +186 +00:12:59,580 --> 00:13:02,180 +من صفر أصغر من واحد of real numbers is a non + +187 +00:13:02,180 --> 00:13:05,960 +-denominable set، فهنشوف البرهان ونشوف فكرة البرهان + +188 +00:13:05,960 --> 00:13:11,960 +مع بعض، فدي theorem 512 + +189 +00:13:13,190 --> 00:13:16,850 +هنثبتها by contradiction، لأن كل شغلنا معه اللي هو + +190 +00:13:16,850 --> 00:13:23,010 +denomable، فنعملها by contradiction prove، assume + +191 +00:13:23,010 --> 00:13:26,070 +01 + +192 +00:13:26,070 --> 00:13:32,650 +is denomable، نفترض + +193 +00:13:32,650 --> 00:13:38,030 +عليه prove by contradiction، طبعاً prove by + +194 +00:13:38,030 --> 00:13:39,870 +contradiction + +195 +00:13:42,170 --> 00:13:45,050 +أو فكرة البرهان يمكن برضه تساعدنا في التخيل ليش + +196 +00:13:45,050 --> 00:13:48,970 +الأعداد الحقيقية هذه أعدادها مهولة وخرجة عن السيطرة + +197 +00:13:48,970 --> 00:13:51,590 +ايه معنى الـ numerical؟ بقدر ألاقي bijection + +198 +00:13:51,590 --> 00:13:55,890 +بينها وبين الـ N، فده implies there exists a + +199 +00:13:55,890 --> 00:14:03,730 +bijection F من اللي هو بدنا ياها من N لـ Zero لـ Zero + +200 +00:14:03,730 --> 00:14:08,710 +لـ N، بس عشان الفكرة بالترتيب طبعاً احنا عارفين يقول + +201 +00:14:08,710 --> 00:14:10,490 +bijection، فالـ inverse تبعه bijection + +202 +00:14:14,630 --> 00:14:23,910 +من N لـ 01، ناخدها من N إلى 01، تمام ممتاز + +203 +00:14:26,010 --> 00:14:30,110 +الآن بدنا بس اللي هو الآن رقم، أثبتوا أن هذه ليست + +204 +00:14:30,110 --> 00:14:34,530 +قُنطة، مستحيل تغطي، ما عندي عدد عناصر كافية من الـ N + +205 +00:14:34,530 --> 00:14:38,350 +يغطي كل الـ01، لأنها كبيرة جداً، فده هي إيش الفكرة، + +206 +00:14:38,350 --> 00:14:41,470 +فتلاحظوا أننا لم نصل إيش لـContradiction، إيش بدنا + +207 +00:14:41,470 --> 00:14:43,630 +الـContradiction؟ ما زال دي Bijection، بدي أثبتوا + +208 +00:14:43,630 --> 00:14:46,930 +أن هذه ليست قُنطة، فهذا تناقض، يعني في عنصر هنا مش + +209 +00:14:46,930 --> 00:14:50,090 +صورة حدا، مش صورة حدا، فاحنا جينا إيش اللي بدنا + +210 +00:14:50,090 --> 00:14:53,270 +نعمله؟ بس إيش؟ نسمي، نسمي الصور هدول بس عشان + +211 +00:14:53,270 --> 00:14:58,840 +نكتبهم، let f of one، نشوف طبعاً مع المقدمة اللي + +212 +00:14:58,840 --> 00:15:01,640 +عملناها، f of واحد وين ده؟ تكون عدد هنا إذا بقدر + +213 +00:15:01,640 --> 00:15:06,420 +أكتبه كيف على صورة 0. بدي أرقمه عشان هو دي + +214 +00:15:06,420 --> 00:15:10,520 +f of واحد، بدي أعمل حاجتين عشان واحد، فبدي أحط واحد + +215 +00:15:10,520 --> 00:15:14,480 +وعشان الخانة الأولى كمان واحد زي ما بعمل بالمصفوفات + +216 +00:15:14,480 --> 00:15:18,520 +إذا مرت عليكم، فبدي رقمين، رقم عشان الواحد ورقم عشان + +217 +00:15:18,520 --> 00:15:21,480 +الخانة، بعدين لجينا لـ A1 + +218 +00:15:47,290 --> 00:15:48,690 +A1A2A3A4A5A6A7A8A9A10A11A12A13A14A15A16A17A18A20A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21 + +219 +00:15:49,960 --> 00:15:55,060 +لو كان الكلام صحيح، لو كانت الـ 01 denomable + +220 +00:15:55,060 --> 00:16:00,480 +المفروض هدول الصور شمالهم يغطوا كل الـ 01، نشوف + +221 +00:16:00,480 --> 00:16:04,100 +كيف بدنا نلاقي عدد بين الـ 01 ولا واحد من هدول + +222 +00:16:04,100 --> 00:16:06,700 +بيساويش ولا واحد من هدول بيساويش ولا واحد من هدول + +223 +00:16:06,700 --> 00:16:16,140 +هنعمل trick بسيط الآن، now let z تساوي طبعاً هو عايش + +224 +00:16:19,370 --> 00:16:28,570 +point z1 z2 وهكذا z3 وهكذا، بي let z be where؟ + +225 +00:16:28,570 --> 00:16:36,830 +بدنا نعرفه بالشكل التالي، z z sub j، هذه الخانات بدنا + +226 +00:16:36,830 --> 00:16:40,050 +نعرفهم بالشكل التالي، شوفوا كيف الفكرة اللي عامة + +227 +00:16:40,050 --> 00:16:45,190 +فهذا بدنا نعمله حزب معارضة يعني مخالف على طول، بديش + +228 +00:16:45,190 --> 00:16:51,180 +يا يساوي صورة الواحد، فطبعاً بالمقدمة اللي حكيتها إذا + +229 +00:16:51,180 --> 00:16:53,640 +اختلف معاه بخانة واحدة بيساويهاش، لأن كل دول طبعاً + +230 +00:16:53,640 --> 00:16:56,620 +إنه Normalized for، بدي أؤكد إن كل خانة بتتطابق + +231 +00:16:56,620 --> 00:17:01,480 +عشان تتساوي، فإذا اختلف بخانة واحدة انتهى، فبدي إذا + +232 +00:17:01,480 --> 00:17:07,420 +كانت مثلاً A11 بتساوي سبعة خليه + +233 +00:17:07,420 --> 00:17:17,090 +يصبح ثلاثة، فإذا هو يختلف مع الـA11 بشكل عام + +234 +00:17:17,090 --> 00:17:22,330 +فببدأ + +235 +00:17:22,330 --> 00:17:27,110 +نشتغل على الخانة القطرية فأنا بدي إياه يختلف مع + +236 +00:17:27,110 --> 00:17:33,210 +مين؟ بروح بتطلع على إيه؟ بتطلع على A11، فأول شيء في + +237 +00:17:33,210 --> 00:17:36,570 +هذا الـ Z بدي إياه يختلف مع صورة الواحد، أندوين في + +238 +00:17:36,570 --> 00:17:40,310 +الخانة الأولى ويختلف عن صورة الاثنين في الخانة + +239 +00:17:40,310 --> 00:17:43,350 +الثانية وهكذا إذاً هيختلف عن كل الصورة في هذه + +240 +00:17:43,350 --> 00:17:47,750 +الصورة طبعاً دول أرقام بشكل عام ويساوي سبعة إذا + +241 +00:17:47,750 --> 00:17:51,470 +كانت Ajj تساوي سبعة .. بلا تساوي سبعة فيعمل .. + +242 +00:17:51,470 --> 00:17:52,790 +شوف مرة ثانية + +243 +00:17:56,410 --> 00:18:00,850 +بنعيد بس عملية اللي هو إيش مخالفة معارضة نقول زي + +244 +00:18:00,850 --> 00:18:04,450 +حزب المعارضة فبيقول بتطلع هو طبعاً بدنا نبدأ لأن بدنا + +245 +00:18:04,450 --> 00:18:10,630 +نجيب Z1، بروح بتطلع بتطلع على إيش؟ f of 1 + +246 +00:18:10,630 --> 00:18:14,160 +بتطلع على A11، بدي Z1 ده دي لا تساوي + +247 +00:18:14,160 --> 00:18:17,140 +A11، فإذا A11 بتساوي سبعة بأخليها + +248 +00:18:17,140 --> 00:18:19,940 +ثلاثة، المهم ما تساويهاش أي حاجة، الأرقام ثلاثة وسبعة + +249 +00:18:19,940 --> 00:18:23,140 +دول عشوائية ممكن أغيرهم وإذا بتساوي السبعة بحطها + +250 +00:18:23,140 --> 00:18:26,760 +سبعة، إذا تأكدنا إن إيش Z1 لا تساوي A11 + +251 +00:18:26,760 --> 00:18:30,720 +إذا Z2 لا تساوي f of 2 على طول مباشرة لأنه + +252 +00:18:30,720 --> 00:18:32,460 +اختلفت فيها مع الخانة الأولى تمام + +253 +00:18:36,790 --> 00:18:40,250 +ماشي، أنا بدي أجيبه، ليش؟ بدي أجيبه يكون هنا، أه + +254 +00:18:40,250 --> 00:18:44,690 +مهم، أه، ليش؟ إيش بعلمنا هذا الكلام؟ إنه هنا أنا + +255 +00:18:44,690 --> 00:18:50,990 +بختاره تقريباً بشكل عشوائي بس بغير تغيير بسيط، + +256 +00:18:50,990 --> 00:18:54,790 +جيبت عدد، هل الـZ موجودة هنا ولا مش موجودة؟ موجودة + +257 +00:18:54,790 --> 00:19:01,350 +لأن هي 0. مظبوط، لكن ما هي القضية؟ إيش معنى ليست + +258 +00:19:01,350 --> 00:19:05,490 +قُنطة؟ بقدر ألاقي عنصر بين الـ 01 مش الصورة، فعند + +259 +00:19:05,490 --> 00:19:08,450 +الفراد أنا لجيته، بعد ما أتفرضته، مظبوط؟ أه، أنا + +260 +00:19:08,450 --> 00:19:12,780 +لجيته، في عدد بقى بالشكل ولا ما في شيء؟ في عدد + +261 +00:19:12,780 --> 00:19:16,940 +وبين الـ 01، هل بيساوي واحد من الصور دول؟ مطلقاً + +262 +00:19:16,940 --> 00:19:19,760 +لأ، لأن كيف اختارته، بالدياية يختلف، هدول مالها + +263 +00:19:19,760 --> 00:19:23,200 +نهاية طبعاً، عشان هي صعوبة الاختيار بس، بالدياية + +264 +00:19:23,200 --> 00:19:26,360 +إيش؟ يختلف مع الأول بالخانة الأولى ومع الثاني + +265 +00:19:26,360 --> 00:19:29,140 +بالخانة الثانية وهكذا، فالعملية مش عادة ما + +266 +00:19:29,140 --> 00:19:31,860 +هيش، ما هيش، معناته إنه ليست قُنطة، إنه في عنصر مش + +267 +00:19:31,860 --> 00:19:34,900 +صورة حدى، وأنا لجيته هذا، بس إيش صممته بهذه + +268 +00:19:34,900 --> 00:19:37,820 +الطريقة، دي عملية تصميم مش فرضية تصميم، صممته + +269 +00:19:37,820 --> 00:19:39,120 +العدد بهذه الصورة، + +270 +00:19:42,440 --> 00:19:52,000 +then الـ z أولاً بتنتمي للـ 01، مظبوط، and z لا تساوي + +271 +00:19:52,000 --> 00:19:59,460 +f of k أو for all k تنتمي للـ N، مستحيل تكون أي صورة + +272 +00:19:59,460 --> 00:20:05,770 +بالصور صح، واضحة ولا أنا أيضا كمان؟ أخذ أي عددين، + +273 +00:20:05,770 --> 00:20:09,970 +معناه يقولنا حزب معارضة، هذا بيقول أنا اثنين، + +274 +00:20:09,970 --> 00:20:12,650 +بيقول له أنا مش اثنين، هذا بيقول له أنا سبعة، بيقول له مش + +275 +00:20:12,650 --> 00:20:15,370 +سبعة، أنا خمسة، مش خمسة، فأي عددين، المهم مخالف + +276 +00:20:15,370 --> 00:20:18,670 +الثلاثة والسبعة مالهم مش خصوصية، مالهم مش أي + +277 +00:20:18,670 --> 00:20:22,510 +خصوصية، بس طبعاً ليش مجلس واحد اثنين؟ بده ترتيب + +278 +00:20:22,510 --> 00:20:25,730 +معين، فهذا ترتيبه سهل إنه بده يختلف مع الأول + +279 +00:20:25,730 --> 00:20:28,050 +بالخانة الأولى ومع الثاني بالخانة الثانية، طب ليش + +280 +00:20:28,050 --> 00:20:31,550 +مع الأول مش بالخانة العاشرة؟ بين two فأبدأ ترتيب + +281 +00:20:31,550 --> 00:20:34,050 +معين فلما أقول مع الأول بالخانة الأولى يختلف مع + +282 +00:20:34,050 --> 00:20:37,690 +الثاني بالخانة الثانية فإذا أنا ضاع من إنه إيش هذا + +283 +00:20:37,690 --> 00:20:40,550 +الـ Z لا يمكن يساوي F of 1 لأنه اختلف معاه بالخانة + +284 +00:20:40,550 --> 00:20:42,890 +الأولى و لا يمكن يساوي F of 2 لأنه اختلف معاه + +285 +00:20:42,890 --> 00:20:45,330 +بالخانة الثانية لأن اتفقنا في المقدمات إنه إيش + +286 +00:20:45,330 --> 00:20:47,930 +مثلا إذا في ال Normalized form ما كانت بتساوي كل + +287 +00:20:47,930 --> 00:20:51,030 +خاناتهم بتساوي اختلف بخانة إذا مختلف إذا مختلف + +288 +00:20:51,030 --> 00:20:57,250 +فطبعا هذا إيش contradiction فهذا يؤدي إن F is not + +289 +00:20:57,250 --> 00:20:58,630 +onto contradiction + +290 +00:21:04,050 --> 00:21:06,790 +أه، فطبعًا واضح من الـ «الثابت» ‏«الثابت» + +291 +00:21:06,790 --> 00:21:09,290 +‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» + +292 +00:21:09,290 --> 00:21:11,250 +‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» + +293 +00:21:11,250 --> 00:21:12,650 +‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» + +294 +00:21:12,650 --> 00:21:17,730 +‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» + +295 +00:21:17,730 --> 00:21:22,110 +‏«الثابت» ‏«الثابت» + +296 +00:21:22,110 --> 00:21:29,950 +‏«الثابت» ‏«الثابت» + +297 +00:21:29,950 --> 00:21:38,010 +‏طبعا الآن نتيجة الهدف الأكبر أن الـ R نفسها non + +298 +00:21:38,010 --> 00:21:44,470 +-denominable طبعا هذا الكلام إحنا شرحناه قبل ذلك + +299 +00:21:44,470 --> 00:21:49,270 +بس نؤكد عليه كل + +300 +00:21:49,270 --> 00:22:00,330 +ريخ خمسة سبعة prove طبعا + +301 +00:22:00,330 --> 00:22:06,440 +إحنا بنعرف أن الـ R الـ R تشملها تكافئ سالب باية 2 + +302 +00:22:06,440 --> 00:22:10,540 +لباية 2 نعملها بشكل صريح و هذه تكافئ صفر واحد ممكن + +303 +00:22:10,540 --> 00:22:14,600 +نعملها يمكن ما نعملهاش بشكل صريح تنعملها طبعا على طول + +304 +00:22:14,600 --> 00:22:19,420 +و هذه علاقة الـ Transitive فهذا يؤدي أن الـ R is + +305 +00:22:19,420 --> 00:22:19,980 +non-denominable + +306 +00:22:29,540 --> 00:22:32,380 +فارجعوا أن تكونوا واضحة الفكرة لو اشتغلنا على أرض + +307 +00:22:32,380 --> 00:22:37,980 +مباشرة كانت هتكون كبير العملية لأنه ركزنا أنه بيبدأ + +308 +00:22:37,980 --> 00:22:41,000 +بصفر كذا و أنا فصار عندي عملية تركيز و هذا سهل + +309 +00:22:41,000 --> 00:22:48,920 +التعمم و التعميم بعدين بيجي بيجي بهذا الشكل نشوف + +310 +00:22:48,920 --> 00:22:49,520 +مثال + +311 +00:23:13,420 --> 00:23:17,480 +show that the set of all irrational numbers is not + +312 +00:23:17,480 --> 00:23:22,040 +denominable مجموعة كل أعداد غير النسبية برضه non + +313 +00:23:22,040 --> 00:23:27,680 +-denominable مثال + +314 +00:23:27,680 --> 00:23:31,680 +طبعا + +315 +00:23:31,680 --> 00:23:38,120 +الكلام هنا هو شيء منطقي يعني لأن إحنا عند ال Q و + +316 +00:23:38,120 --> 00:23:42,040 +هو denominable يعني كل عدد نسبي دنيا مربوط طيب إيش + +317 +00:23:42,040 --> 00:23:44,680 +هي العدد الحقيقية؟ تتكون من النسبية و الغير نسبية + +318 +00:23:44,680 --> 00:23:49,720 +إذا ال mainly العدد هو هائل جدا و خلى ال R تصير + +319 +00:23:49,720 --> 00:23:52,680 +non-denominable مش العدد النسبي و إنما غير النسبية + +320 +00:23:52,680 --> 00:23:57,720 +فإحنا ده اللي إيش اللي هنثبته فطبعا بس لتسميات + +321 +00:23:57,720 --> 00:24:04,920 +solution let X تساوي R ما عدا Q هذا ليه إيش؟ لعدد + +322 +00:24:04,920 --> 00:24:06,860 +النسبية B + +323 +00:24:09,170 --> 00:24:21,970 +the set of irrational number فدى + +324 +00:24:21,970 --> 00:24:27,490 +مجموعة لعداد غير النسبية بدنا نثبت أنها non + +325 +00:24:27,490 --> 00:24:36,330 +-denominable باي contradiction هنعملها assume x is + +326 +00:24:36,330 --> 00:24:37,270 +denominable + +327 +00:24:43,730 --> 00:24:48,850 +طب لو كانت ال X denomable إيش بدي يصير؟ ال R عبارة + +328 +00:24:48,850 --> 00:24:56,070 +عن إيه؟ X إتحاد Q أه و إحنا عندنا نظرية denomable + +329 +00:24:56,070 --> 00:24:59,150 +لو هذه denomable لازم تكون denomable is denomable + +330 +00:24:59,150 --> 00:25:05,910 +طبعا خلصنا contradiction + +331 +00:25:05,910 --> 00:25:05,950 +contradiction + +332 +00:25:15,520 --> 00:25:26,140 +فأنا خلصنا ال chapter أسرع مما توقعنا ممكن + +333 +00:25:26,140 --> 00:25:28,560 +يعني هو اللي اللي اللي اللي لازم فهمته ده شيء + +334 +00:25:28,560 --> 00:25:29,000 +ممتاز + +335 +00:25:50,360 --> 00:25:51,760 +السلام عليكم ورحمة الله وبركاته + +336 +00:26:16,840 --> 00:26:20,620 +خلينا في ما تبقى من الوقت ناخد مقدمة عن الشبطة + +337 +00:26:21,510 --> 00:26:24,830 +chapter 6 وإن شاء الله يعني بنشوف إحنا عايش .. + +338 +00:26:24,830 --> 00:26:28,530 +ماشيين يعني ونشوف إيش العلاقة مع الموضوع عشان نشوف + +339 +00:26:28,530 --> 00:26:33,130 +.. زي ما حكينا كيف هنعيد أفكار في chapter 5 + +340 +00:26:33,130 --> 00:26:36,890 +الحقيقة و هذا هيساعدنا كتير إن شاء الله في تثبيت + +341 +00:26:36,890 --> 00:26:40,730 +مفاهيم في chapter 5 طبعاً العنوان cardinal numbers + +342 +00:26:40,730 --> 00:26:46,580 +and cardinal arithmetic Cardinal يسمونها أعداد + +343 +00:26:46,580 --> 00:26:50,920 +أصلية أو نوع من الأعداد نتعرف على نوع جديد من + +344 +00:26:50,920 --> 00:26:54,360 +أنظمة الأعداد طبعا هنعرف الأعداد الطبيعية الأعداد + +345 +00:26:54,360 --> 00:26:57,400 +الصحيحة النسبية الحقيقية و المركبة يمكن اللي هي فيها + +346 +00:26:57,400 --> 00:27:00,890 +التخيل جزر السالب واحد أه فدولا نوع جديد من الأعداد + +347 +00:27:00,890 --> 00:27:03,310 +يسمون Cardinal Number طبعا Cardinal Arithmetic + +348 +00:27:03,310 --> 00:27:06,010 +العمليات الحسابية على Cardinal Numbers العمليات + +349 +00:27:06,010 --> 00:27:09,310 +الحسابية على هذه الأعداد الجديدة اللي إحنا هتعرف + +350 +00:27:09,310 --> 00:27:13,730 +عليها فإحنا كل اللي بدنا نعمله بشكل رئيسي إنه + +351 +00:27:13,730 --> 00:27:19,300 +هنحول الكلام اللي كنا بنحكيه إلى عدد العناصر إيش + +352 +00:27:19,300 --> 00:27:22,660 +معناه Denumerable تكافئ الـ N فهذه بنحط عدد + +353 +00:27:22,660 --> 00:27:26,580 +عناصرها بالساوية مثلا عدد معين مثلا A طيب ال R non + +354 +00:27:26,580 --> 00:27:29,600 +-denumerable إذا عدد عناصرها عدد مختلف نسميه C + +355 +00:27:29,600 --> 00:27:32,620 +طبعا برضه ال finite برضه عدد عناصرها واضح هذا فيها + +356 +00:27:32,620 --> 00:27:35,680 +صفر من عناصر Phi هذا في عنصر واحد single to set + +357 +00:27:35,680 --> 00:27:39,220 +هذا في عشر عناصر N عشرة و هكذا فبنشتغل معاهم بعد + +358 +00:27:39,220 --> 00:27:44,200 +الشكل فدولة كلهم اللي أي عدد بيرمز لعدد عناصر + +359 +00:27:44,200 --> 00:27:47,400 +مجموعة معينة هنسميه cardinal number هنسميه + +360 +00:27:47,400 --> 00:27:53,430 +cardinal number فإحنا بنتعرف على مفهوم ال cardinal + +361 +00:27:53,430 --> 00:27:57,010 +numbers إيش هو ال cardinal number كتعريف خواص ال + +362 +00:27:57,010 --> 00:28:03,090 +cardinal number و بعدين عملية الحسابية عليهم فنبدأ + +363 +00:28:03,090 --> 00:28:05,090 +بما هو ال cardinal numbers + +364 +00:28:16,710 --> 00:28:20,890 +الحقيقة إحنا مش هنددي تعريف مباشر لل cardinal + +365 +00:28:20,890 --> 00:28:26,210 +number وإنما هنحط قواعد و هنرقمها ب .. اللي هو + +366 +00:28:26,210 --> 00:28:30,190 +حروف C1 من كلمة cardinal number و هدول القواعد + +367 +00:28:30,190 --> 00:28:33,330 +اللي تنطبق على أي عدد نسميه cardinal number فبقول + +368 +00:28:33,330 --> 00:28:35,330 +we will not define a cardinal number but we will + +369 +00:28:35,330 --> 00:28:38,910 +introduce it as a primitive concept يفشق اللي هو + +370 +00:28:38,910 --> 00:28:41,810 +مبدأه و طبعا يشمل إيه له علاقة بمين؟ حجم + +371 +00:28:41,810 --> 00:28:45,170 +المجموعات زي ما حكيت فإنا بدي أقول عدد عنصر رمح طيب + +372 +00:28:45,170 --> 00:28:48,070 +ليه فإحنا لجأنا لل cardinal numbers لأنه ما فيش + +373 +00:28:48,070 --> 00:28:52,230 +نظام عدد يتعامل مع المجموعات لأن ال infinite هي + +374 +00:28:52,230 --> 00:28:57,030 +عدد حقيقي ولا عدد مركب فإذا هذه العداد اللي + +375 +00:28:57,030 --> 00:29:00,770 +هتتضمن infinite و أنواع مختلفة من ال infinite بدها + +376 +00:29:00,770 --> 00:29:03,530 +يش نوع جديد من العداد بيسموها ال cardinal numbers + +377 +00:29:03,530 --> 00:29:07,920 +ففي عندنا قواعد لل cardinal numbers القاعدة الأولى + +378 +00:29:07,920 --> 00:29:12,840 +C1 من كلمة Cardinal بقول لكل مجموعة يصحبها + +379 +00:29:12,840 --> 00:29:16,100 +Cardinal number فإذا إحنا مرتبط تعريف Cardinal + +380 +00:29:16,100 --> 00:29:20,080 +number بعدد أياش المجموعات أنا عندي مجموعة فيه + +381 +00:29:20,080 --> 00:29:23,020 +Cardinal number بيقابلها و عكس صحيح فيه Cardinal + +382 +00:29:23,020 --> 00:29:26,540 +number لازم يقابله مجموعة إيش ما لها عدد عناصر أيه + +383 +00:29:26,540 --> 00:29:29,740 +يساوي هذا Cardinal number فDenoted by طبعا الرمز + +384 +00:29:29,740 --> 00:29:33,260 +من كلمة Cardinal الحلو هو أول أربع حروف فطبعا + +385 +00:29:33,260 --> 00:29:36,920 +نقراها Cardinal of A and for each cardinal number + +386 +00:29:36,920 --> 00:29:41,440 +N، العكس، there is a set such that cardinal number + +387 +00:29:41,440 --> 00:29:46,160 +of A بيساوي N فإنه إيش العملية مرتبطة مرتبط مباشر + +388 +00:29:46,160 --> 00:29:50,200 +و وثيق بالمجموعات فدول الأعداد مش أعداد لأي شيء + +389 +00:29:50,200 --> 00:29:53,900 +و إنما التعامل مع المجموعات من حيث عدد العناصر أو + +390 +00:29:53,900 --> 00:29:58,180 +من حيث الحجم من حيث الحجم فإذا ما فيش حاجة مثلا + +391 +00:29:58,180 --> 00:30:02,340 +cardinal number بيعبر عن اللي هو وزن معين ولا عن + +392 +00:30:02,340 --> 00:30:06,820 +طول، مسافة، لأ cardinal number بيعبر عن عدد عناصر + +393 +00:30:06,820 --> 00:30:10,220 +مجموعة فكل مجموعة بيقبلها cardinal number و كل + +394 +00:30:10,220 --> 00:30:13,940 +cardinal number لازم يتحدث عن مجموعة أو عدد عناصر + +395 +00:30:13,940 --> 00:30:18,290 +مجموعة، فهذه القاعدة الأولى القاعدة الثانية + +396 +00:30:18,290 --> 00:30:21,570 +المجموعة الوحيدة الكاردنالدية تبعتها بتساوي صفر هي + +397 +00:30:21,570 --> 00:30:25,010 +الـ Phi و هذا شيء منطقي فالمجموعة فارغة يعني أن + +398 +00:30:25,010 --> 00:30:27,310 +عدد عناصرها صفر و هذا بيأكد إحنا كيف المفهوم اللي + +399 +00:30:27,310 --> 00:30:29,590 +بنمشي معاه فهي الـ Phi + +400 +00:30:32,690 --> 00:30:34,950 +إذا كانت المجموعة طبعاً اللي إحنا متعودين عليه + +401 +00:30:34,950 --> 00:30:40,750 +السهل finite و مش MT تكافئان K ففي هذه الحالة كدهش + +402 +00:30:40,750 --> 00:30:42,890 +ال cardinal number K زي اللي إحنا متعارفينه فإحنا + +403 +00:30:42,890 --> 00:30:45,110 +بدنااش .. طبعا كل الهدف من تعريف ال cardinal + +404 +00:30:45,110 --> 00:30:47,790 +number هو التعامل مع ال infinite sets و ليس مع ال + +405 +00:30:47,790 --> 00:30:51,530 +finite ولكن بدنا دايما لما بنعمم حاجة بدنااش تلغي + +406 +00:30:51,530 --> 00:30:55,110 +الماضي بدناها تنسجم مع الماضي و تطوره و من غير + +407 +00:30:55,110 --> 00:30:59,170 +تناقض ينطبق على السابق و اللاحق بشكل مناسب + +408 +00:31:09,810 --> 00:31:16,130 +القاعدة الرابعة بنقول إذا كان في عندنا مجموعتين و + +409 +00:31:16,130 --> 00:31:20,950 +ال cardinal number تبعهم بتساوى if and only if هم + +410 +00:31:20,950 --> 00:31:25,170 +متكافئتين فالآن إحنا صار عندنا هاي الكلام اللي + +411 +00:31:25,170 --> 00:31:29,950 +بنحكي عنه ممكن أعبر مجموعتين متكافئتين عدديًا أو + +412 +00:31:29,950 --> 00:31:32,250 +ال cardinal number للمجموعة الأولى بيساوي ال + +413 +00:31:32,250 --> 00:31:33,930 +cardinal number للمجموعة الثانية فإحنا هننظر + +414 +00:31:33,930 --> 00:31:37,130 +لموضوع التكافئة من زاوية أخرى الآن أنه عايش ال + +415 +00:31:37,130 --> 00:31:41,210 +cardinal number متساوين فهو إحنا نتحدث عن عدد + +416 +00:31:41,210 --> 00:31:44,190 +العناصر كنا نحكيها بشكل غير رسمي الآن هنعبّر عنها + +417 +00:31:44,190 --> 00:31:48,470 +بشكل رسمي أن X تكافئ ال Y يعني ال cardinal number + +418 +00:31:48,470 --> 00:31:51,590 +لل X بيساوي ال cardinal number لل Y نفس البعض فدول + +419 +00:31:51,590 --> 00:31:56,700 +الأربع قواعد هنعتمد عليهم أه هدولة يعتبر ال + +420 +00:31:56,700 --> 00:31:59,600 +cardinal number لل N يساوي ال cardinal number لل Z + +421 +00:31:59,600 --> 00:32:02,460 +يساوي ال cardinal number للـ Q لكن لا يساوي ال + +422 +00:32:02,460 --> 00:32:06,320 +cardinal number للـ R 100% صحيح فاحنا هنبدأ نعدّد ب + +423 +00:32:06,320 --> 00:32:08,880 +.. عشان هيك أنا قلت إن هذا الشطر بيدعم الشطر + +424 +00:32:08,880 --> 00:32:12,240 +الماضي، هنحكي عن نفس المفاهيم لكن من زاوية أخرى .. + +425 +00:32:12,240 --> 00:32:19,610 +من زاوية أخرى، نشوف مثال بسيط جدا ويقول show that + +426 +00:32:19,610 --> 00:32:23,990 +الواحد is a cardinal number، الواحد يعتبر cardinal + +427 +00:32:23,990 --> 00:32:26,570 +number، الواحد احنا متعرفينه على إيه؟ اللي متعرفينه هو + +428 +00:32:26,570 --> 00:32:31,390 +يعتبر cardinal number، كيف بدنا نتعاون مع هذا + +429 +00:32:31,390 --> 00:32:37,350 +الموضوع؟ بدنا مجموعة قدر عنصرها واحد تمام، فبتكون + +430 +00:32:37,350 --> 00:32:42,290 +إيش؟ العملية صحيحة، فهنا هذا المثال الأول solution + +431 +00:32:42,290 --> 00:32:47,070 +فنقول له let a تساوي singleton set أي أي singleton + +432 +00:32:47,070 --> 00:32:51,130 +set يعني إذا الواحد بده يلخمكه بلاش، لأنه عشانها + +433 +00:32:51,130 --> 00:32:57,530 +مكرر أي عدل من عنصر واحد، فطبعا then cardinal + +434 +00:32:57,530 --> 00:33:03,610 +number of a بيساوي واحد، وهذا يؤدي إن الواحد is a + +435 +00:33:03,610 --> 00:33:04,230 +cardinal number + +436 +00:33:13,070 --> 00:33:16,730 +بس بقدرش أقول إن هذا card number، لأنه أنا فيه عندي + +437 +00:33:16,730 --> 00:33:21,870 +مسافة بين اللي هو بين تان واحد كيلو، لأ لأن هي + +438 +00:33:21,870 --> 00:33:26,110 +تعبر عن عدد عناصر مجموعة ما، فهذه النقطة مهمة جدا + +439 +00:33:26,110 --> 00:33:32,250 +طبعا تبقى للقواعد، احنا استغلنا، تمام، نشوف كمان مثال + +440 +00:33:32,250 --> 00:33:37,530 +نؤكد على نفس المعلومة، بس نعمّم شوية، فاحنا جيت احنا + +441 +00:33:37,530 --> 00:33:40,230 +إيش cardinal number؟ اتعرفنا عليهم، الـ zero + +442 +00:33:40,230 --> 00:33:42,990 +cardinal number لأن هو إيش؟ هو عدد عناصر الـ five + +443 +00:33:42,990 --> 00:33:47,210 +الواحدة ده هو كل finite، أي حاجة المية المية الـ + +444 +00:33:47,210 --> 00:33:50,390 +100 هالجيت فاق نحن ناني الواحد، نشوف بقولي find the + +445 +00:33:50,390 --> 00:33:53,770 +cardinal number of A وجيت 100 على طول ماحن بدنا + +446 +00:33:53,770 --> 00:33:57,890 +نؤكد هتنلموه عشان بدنا نسوي الأرض ونجفّ على أرض + +447 +00:33:57,890 --> 00:34:03,590 +ثابتة و نطور شغلفهنا مثال تاني solution، فطبعا ليش + +448 +00:34:03,590 --> 00:34:10,450 +لأن هذه الـ A شمالها تكافئ أنمية واضحة هذه اه، فلأن + +449 +00:34:10,450 --> 00:34:14,530 +هي بتكافئ أنمية ولا لأ؟ لأن أي A واحد تكافئ الواحد + +450 +00:34:14,530 --> 00:34:20,230 +فده يؤدي إن ال cardinal number للـ A يساوي 100 + +451 +00:34:20,230 --> 00:34:26,200 +فاحنا بنؤكد على هذه المفاهيم الأساسية، فإذا واضح إن + +452 +00:34:26,200 --> 00:34:31,340 +أي صفر Cardinal number، أي عدد طبيعي Cardinal + +453 +00:34:31,340 --> 00:34:35,960 +number، سنضيف أجزاء من عدد Cardinal number، هل يوجد + +454 +00:34:35,960 --> 00:34:42,360 +غيرهم؟ يوجد غيرهم، سنشوف، تمام + +455 +00:34:42,360 --> 00:34:47,780 +هذه السؤال اللي بتحكيها كل وقت، نستخدم القواعد + +456 +00:34:54,260 --> 00:34:57,060 +فبكل شغل يبقى استخدم اللي هو ياشق القواعد اللي هو + +457 +00:34:57,060 --> 00:35:01,220 +من C1 لـ C4، فهذا الواشل طبعا، فانا هتواشل استخدم + +458 +00:35:01,220 --> 00:35:11,980 +القاعدة C4 و C3، مثال التالف بقول + +459 +00:35:11,980 --> 00:35:13,760 +اثبت ان ال cardinality اللي انت صحيح الـ + +460 +00:35:13,760 --> 00:35:21,760 +cardinality اللي هي Z solution، كيف + +461 +00:35:21,760 --> 00:35:26,910 +نعملها if and و if، بنرجع للمبادئ F and only F + +462 +00:35:26,910 --> 00:35:30,910 +باستخدامتيها في أي اتجاه صح؟ زي الشارع في اتجاهين اه + +463 +00:35:30,910 --> 00:35:34,210 +روحت منه اه دي اه، مش ضروري ملزمة انك تروح + +464 +00:35:34,210 --> 00:35:39,690 +الاتجاهين، مش ملزمة اه، مسموح لك اه، تمام، فهذا يؤدي + +465 +00:35:39,690 --> 00:35:46,370 +إن ال cardinality للـ Z تساوي ال cardinality للـ I + +466 +00:35:46,370 --> 00:35:54,770 +بكل سهولة، فهدولة نقطة البداية ونقطة الانطلاق، و + +467 +00:35:54,770 --> 00:36:03,650 +يكفي اليوم كمقدم، فهنا نفس المواضيع بس هناخده من + +468 +00:36:03,650 --> 00:36:07,890 +زاوية أخرى، فهنا الموضوع عرفينه بس هننزله من زاوية + +469 +00:36:07,890 --> 00:36:10,870 +أخرى وهكذا إن شاء الله يوم الأربعة بنكمل diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/pV7ba4YK3IA_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/pV7ba4YK3IA_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..2becb07f0a98bab354c9080d6f1b18269e6b3192 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/pV7ba4YK3IA_raw.srt @@ -0,0 +1,1876 @@ +1 +00:00:20,500 --> 00:00:25,720 +بسم الله الرحمن الرحيم نستكمل مع الـdenominable + +2 +00:00:25,720 --> 00:00:31,720 +sets وجفنا عند نظرية طبعا اللي هو العنوان الرئيسي + +3 +00:00:31,720 --> 00:00:36,080 +لها أن الـdenominable sets هما أصغر infinite sets + +4 +00:00:36,080 --> 00:00:39,960 +فطبعا بتقول every infinite set contains a + +5 +00:00:39,960 --> 00:00:43,460 +denominable set يعني مستحيل تكون infinite setوتكون + +6 +00:00:43,460 --> 00:00:46,740 +صغيرة جدا بحيث ملاقيش فيها جواها Denominable جواها + +7 +00:00:46,740 --> 00:00:49,920 +Denominable فده بيدينا الاحساس أن الـ Denominable + +8 +00:00:49,920 --> 00:00:54,500 +هي أصغر Infinite Set خلّيني أشوف البرهان فكرة مرت + +9 +00:00:54,500 --> 00:00:59,460 +علينا مش بنفس الصيغة لكن بشكل مشابه لما نشوفها مع + +10 +00:00:59,460 --> 00:01:05,560 +بعض هنتذكر استخدمناها في أكتر منبع ال proof every + +11 +00:01:05,560 --> 00:01:08,880 +infinite set contains a denominable subset فناخد + +12 +00:01:08,880 --> 00:01:19,090 +infinite set let Xan infinite set ايش + +13 +00:01:19,090 --> 00:01:23,790 +المطلوب؟ بدنا نلاقي subset من ال X تكون denomable + +14 +00:01:23,790 --> 00:01:27,790 +بدنا نلاقي مجموعة من ال X تكون denomable اه طبعا + +15 +00:01:27,790 --> 00:01:29,710 +هي نفس الفكرة اللي احنا عملناها اكتر من مرة قولنا + +16 +00:01:29,710 --> 00:01:32,650 +كأنه هذه ال X مجموعة عشوائية فيها انا كيس من + +17 +00:01:32,650 --> 00:01:36,090 +القرات و بناخد و بنقدر نرقم طبعا هنا بدنا نرقم إلى + +18 +00:01:36,090 --> 00:01:38,670 +مالة نهاية عشانها denomable بدنا نرقم واحد اتنين + +19 +00:01:38,670 --> 00:01:42,380 +تلاتة إلى مالة نهاية فهي نفس الفكرة تماماطبعا ايش + +20 +00:01:42,380 --> 00:01:45,140 +اللي بيخليني اختار دايما من ال X انها infinite فهي + +21 +00:01:45,140 --> 00:01:49,260 +مش فارغة بالتأكيد لأنه لو فارغة finite بنعرف فإذن + +22 +00:01:49,260 --> 00:01:55,740 +أول شيء فهذا بيؤدي ان X لا تساوي في وهذا يؤدي + +23 +00:01:55,740 --> 00:02:00,380 +there exists X one تنتمي لل X فهي أول عنصر اللي + +24 +00:02:00,380 --> 00:02:06,280 +وجدناه بنرتبه و بناخده على جهة تمام برضه بما أن ال + +25 +00:02:06,280 --> 00:02:11,670 +X is infiniteبقدر ألاقي X اتنين X is infinite + +26 +00:02:11,670 --> 00:02:18,510 +implies there exist X2 في ال X معنى ال X1 و اتوقع + +27 +00:02:18,510 --> 00:02:21,590 +ان هذه الفكرة استخدمناها أكتر من مرة بنحذف العنصر + +28 +00:02:21,590 --> 00:02:26,110 +فبنلاقي عنصر جديد و هكذا فبنفس الاسلوب continuing + +29 +00:02:26,110 --> 00:02:29,990 +in + +30 +00:02:29,990 --> 00:02:30,830 +the same way + +31 +00:02:37,850 --> 00:02:44,190 +We can find XK + +32 +00:02:44,190 --> 00:02:53,310 +تنتمي لـ X معدى X1 لـ XK-1 فانا لما لجيت X2 بقدر + +33 +00:02:53,310 --> 00:03:00,110 +أجي X3 بعدها و X4 طبعا هذا الكلام for all K تنتمي + +34 +00:03:00,110 --> 00:03:05,620 +لمن؟ لـ natural number دي العملية مستمرةلسة، دا + +35 +00:03:05,620 --> 00:03:08,960 +كون المجموعة منها، هنشوف هل جيت بس نقوله let Y + +36 +00:03:08,960 --> 00:03:14,060 +فدول العناصر اللي لجيتهم بدي أحطهم في وعاء جديد + +37 +00:03:14,060 --> 00:03:20,380 +سميه Y تساوي XK such that XK تنتمي للأن طبعا ففي + +38 +00:03:20,380 --> 00:03:24,880 +عندي بس شيئ أهم بدي أتأكد منهم ال Y subset من ال X + +39 +00:03:24,880 --> 00:03:27,300 +ولا لأ؟ لأن كل العناصر اللي أخدت منها من ال X + +40 +00:03:27,300 --> 00:03:32,200 +وطبعا denomable لأن هي مرقمة، مافيش أوضح من هاتف + +41 +00:03:32,200 --> 00:03:41,060 +and denomableand why is the name of it؟ + +42 +00:03:41,060 --> 00:03:45,200 +لأن أنا كنت عنصر باخد و كنت برقمه فعملية واضحة + +43 +00:03:45,200 --> 00:03:49,920 +بهذا الشكل فهنا أرجو أنه يعني دائما نشوف الأفكار + +44 +00:03:49,920 --> 00:03:53,680 +تتكرر و نتعلمها و تبدأ الإنسان يستخدم نفس الفكرة + +45 +00:03:53,680 --> 00:03:59,200 +في مكان آخر فممكن يستخدمها في أكتر من مكان فتادي + +46 +00:03:59,200 --> 00:04:00,580 +نهاية ال section + +47 +00:04:05,750 --> 00:04:11,190 +نشوف ال section الأخير اللي هيكمل لنا الصورة في + +48 +00:04:11,190 --> 00:04:14,530 +indenmarable و non indenmarable sets + +49 +00:04:20,880 --> 00:04:23,960 +فطبعا زي ما حكيت انا في المحاضرات السابقة احنا + +50 +00:04:23,960 --> 00:04:27,220 +بدأنا من denomable وبدأنا نكبر فيها وانضفنا لها + +51 +00:04:27,220 --> 00:04:31,440 +عنصر finite number of elements بعدين denomable + +52 +00:04:31,440 --> 00:04:34,520 +اتحاد، denomable حتى denomable كارتيسا بوداك مع + +53 +00:04:34,520 --> 00:04:37,480 +denomable ما زلنا جد ما بنكبر ما زلنا denomable طب + +54 +00:04:37,480 --> 00:04:40,360 +هل هذا الكلام إلى مدى نهاية فيش كل المجموعات + +55 +00:04:40,360 --> 00:04:43,380 +denomable؟ هنشوف طبعا هنبقى لنا non-denomable + +56 +00:04:43,380 --> 00:04:48,480 +system لأ في مجموعات non-denomableفطبعا السؤال + +57 +00:04:48,480 --> 00:04:52,600 +اللي احنا توي طرحنا هل كل infinite set denomable؟ + +58 +00:04:52,600 --> 00:04:57,760 +فطبعا واضح أن الجيابة لا فطبعا يوجد ما يُعرف + +59 +00:04:57,760 --> 00:05:00,700 +بالـnon-denomable sets يعني مجموعات not denomable + +60 +00:05:00,700 --> 00:05:04,280 +طبعا إيش معناه not denomable بشكل صريح؟ طبعا إنها + +61 +00:05:04,280 --> 00:05:06,660 +بدأت تكون غير خابرة للعدد، هذا المعنى الإصطلاع + +62 +00:05:06,660 --> 00:05:10,800 +اللغوي المعنى الإصطلاح بدأت تكون infinite و لا + +63 +00:05:10,800 --> 00:05:13,990 +تكافئ الآنinfinite لأن الـ gate اللي بيسموها برضه + +64 +00:05:13,990 --> 00:05:18,450 +uncountable لأن countable يا finite يا denumerable + +65 +00:05:18,450 --> 00:05:21,390 +طب uncountable أو non-denumerable نفس المعنى + +66 +00:05:21,390 --> 00:05:26,130 +infinite و غير قابل للعدد أوياته كافية فهنا بنقول + +67 +00:05:26,130 --> 00:05:28,690 +أن asset X is said to be non-denumerable or + +68 +00:05:28,690 --> 00:05:32,910 +uncountable if it is not countable هذا المعنى اللي + +69 +00:05:32,910 --> 00:05:36,790 +على طول لأنه هي ولا finite ولا denumerable بمعنى + +70 +00:05:36,790 --> 00:05:40,780 +آخر it is infinite and notdenumerable، اه ماقدرش + +71 +00:05:40,780 --> 00:05:44,800 +ايش، لاتكافئلان، ولا تكافئلان، فاحنا عندنا يمكن ال + +72 +00:05:44,800 --> 00:05:47,620 +gate اللي هو المجموعات، فيه الصغار جدا اللي هم ال + +73 +00:05:47,620 --> 00:05:50,860 +finite، بعدين الأكبر شوية اللي هم infinite لكن + +74 +00:05:50,860 --> 00:05:54,180 +denumerable، والان ال infinite و not denumerable، + +75 +00:05:54,180 --> 00:05:57,740 +في هذه الصورة، فاحنا هنتحدث عنهم بشكل اللي هو + +76 +00:05:57,740 --> 00:06:03,620 +تفصيلي أكترطبعاً زي ما احنا شوفنا تسلسل الان هي + +77 +00:06:03,620 --> 00:06:06,640 +المعيار الأساسي واحدة القياس لل infinite set + +78 +00:06:06,640 --> 00:06:10,920 +وdenominable لجينا ال z رغم أنها أكبر منها ظاهريا + +79 +00:06:10,920 --> 00:06:15,160 +لكن عدد العناصر متساوي و ال Q زي هيك فصار الهدف ان + +80 +00:06:15,160 --> 00:06:19,920 +اشتغل على بعد هيك ال Rهرق الـ R denomable اللي حصل + +81 +00:06:19,920 --> 00:06:24,760 +.. الحقيقة لأ فهذه مجموعة كبيرة فاحنا مشينا Z, Q + +82 +00:06:24,760 --> 00:06:28,960 +لجينا كله denomable لكن عند الـ R لأ عشان أثبت أن + +83 +00:06:28,960 --> 00:06:33,200 +الـ R non-denomable هاخد فترة صغيرة أول طبعا لإنه + +84 +00:06:33,200 --> 00:06:36,560 +شوفنا احنا في ما سبق أن الـ R تكافئ من سالب باية 2 + +85 +00:06:36,560 --> 00:06:40,320 +لباية 2 وقلنا كل open interval يكافئ open interval + +86 +00:06:40,320 --> 00:06:44,630 +فلبعض اللي قاعدة بيدينا مرونة وتسهيل في العملتسهيل + +87 +00:06:44,630 --> 00:06:47,130 +في العملية، لأنه ما بديش أن ألتزم، يعني زي ما + +88 +00:06:47,130 --> 00:06:50,290 +تشوفنا أنه إثبات الـ Z-denumerable بطريقة تانية، + +89 +00:06:50,290 --> 00:06:52,730 +فلما صار عندي نظريات، صار بديني تسهيل، آه، بديني + +90 +00:06:52,730 --> 00:06:55,230 +بدائل، و هذا بديني سهولة، فالآن إحنا هنشتغل على + +91 +00:06:55,230 --> 00:06:58,290 +الفترة 01، إذا كدرت أثبت أن هذه المجموعة non + +92 +00:06:58,290 --> 00:07:00,450 +-denumerable، بتكون الـ R non-denumerable، لإنكوا + +93 +00:07:00,450 --> 00:07:03,410 +كافئها على طوط، آه، آه، فطبعا، ليش بدي أشتغل على + +94 +00:07:03,410 --> 00:07:07,250 +الـ 01؟ لأن الإعداد الحقيقي في الـ 01، بيكون الجزء + +95 +00:07:07,250 --> 00:07:10,550 +الصحيح فيها صفر،بالتام مش إلا جزء أكسر لأن هو بين + +96 +00:07:10,550 --> 00:07:13,250 +صفر و بين واحد فهذا بدينا بعض السهولة في التعامل و + +97 +00:07:13,250 --> 00:07:16,270 +طبعا أنا دايما بدي المفاد الأسهل و بعدين التعميم + +98 +00:07:16,270 --> 00:07:19,710 +خلاص بشتغل على النظرية فطبعا أول شيء من بعض + +99 +00:07:19,710 --> 00:07:23,430 +الحقائق من خواص العداد الحقيقية هنديها على صورة + +100 +00:07:23,430 --> 00:07:27,760 +نظريات بس بدون برهان أي عددبين الـ zero بين ال one + +101 +00:07:27,760 --> 00:07:32,880 +طبعا بإيش بنكتبه؟ صفر فاصلة و اللي هم خنات العشرية + +102 +00:07:32,880 --> 00:07:35,700 +طبعا الخنات العشرية إيش بتقول؟ يا صفر يا واحد يا + +103 +00:07:35,700 --> 00:07:38,880 +تسعة هم دول اللي هيش ال digits و لا لأ أنا بكتب أي + +104 +00:07:38,880 --> 00:07:42,040 +عدد ما زال هو بين أصغر بإيش ما له بين الصفر وبين + +105 +00:07:42,040 --> 00:07:45,000 +الواحد يعني أكبر من صفر وأصغر من واحد يعني هو موجب + +106 +00:07:45,000 --> 00:07:48,520 +لكنه أصغر من واحد إذا الجزء الصحيح فيه أقل من صفر + +107 +00:07:48,520 --> 00:07:53,890 +أطولهو 9 من 10، 99 من 100، 98 من 1000، كله آه بعد + +108 +00:07:53,890 --> 00:07:56,310 +الشكل، طبعا هدول الخناتش بيكونوا من صفر لتسعة، + +109 +00:07:56,310 --> 00:07:59,150 +هدول الأرقام، هدول ال digits، هدول اللي بنحكي عنه، + +110 +00:07:59,150 --> 00:08:02,370 +فكل عدد هنعمله بعد الشكل، هتمد على هذه الخواص وعلى + +111 +00:08:02,370 --> 00:08:07,960 +هذه الصورةأه في عنا ملاحظة مهمة جدا زي ما عملنا في + +112 +00:08:07,960 --> 00:08:13,060 +المحاضرة السابقة لما قلنا في عدد النسبة بنحطه على + +113 +00:08:13,060 --> 00:08:16,020 +صورة كسر بس هذه الكسر قليل و أكتر من صورة فبدي + +114 +00:08:16,020 --> 00:08:19,500 +الصورة القياسية اللي مافيش عامل مشترك هنا نفس + +115 +00:08:19,500 --> 00:08:23,320 +القضية لأنا بحطيت العدد و كتبته بشكل كسر عشرة و + +116 +00:08:23,320 --> 00:08:26,880 +خانات طب هل هذه العملية unique ولا في أكتر من + +117 +00:08:26,880 --> 00:08:31,310 +طريقة للكتابة؟ في أكتر من طريقة للكتابةلو استخدمنا + +118 +00:08:31,310 --> 00:08:34,890 +الـ Geometric Series كادة ممكن أن أثبت أن هذا + +119 +00:08:34,890 --> 00:08:39,870 +العدد صفر و تلاتة و واحد و بعدين كله تسعات إلى مال + +120 +00:08:39,870 --> 00:08:45,750 +نهاية ممكن أو بيساوي مش يمكن 32% لما تكون تسعة في + +121 +00:08:45,750 --> 00:08:49,830 +النهاية دي ملاحظة عامة إذا كان أي عدد كسري و في + +122 +00:08:49,830 --> 00:08:53,580 +الآخر كله تسعة تسعة تسعة إلى مال نهاية ده بتقربعلى + +123 +00:08:53,580 --> 00:08:55,660 +طول بيساوي على طول عن طريق اللي هو الـ Geometric + +124 +00:08:55,660 --> 00:08:58,920 +Series متذكرين في تفاضل باك كيف كنا نثبت أنه أياش + +125 +00:08:58,920 --> 00:09:03,600 +نعملها عبارة عن مثلا هذه كده بدي أعملها التسعة هذه + +126 +00:09:03,600 --> 00:09:07,060 +تسعة من ألف زائد تسعة من عشر تلاف و هكذا بنعملها + +127 +00:09:07,060 --> 00:09:09,220 +Infinite Series و بعدين نجمعها عن طريق الـ + +128 +00:09:09,220 --> 00:09:12,740 +Geometric Series بتنجمعها على طول بهذا الشكل فالان + +129 +00:09:13,920 --> 00:09:19,040 +فهعتاج فيه اللي هو البرهان إن هذا الصورة أو هذه + +130 +00:09:19,040 --> 00:09:22,000 +الصورة مين اللي بده يستخدمها فيهم ودول متساويين + +131 +00:09:22,000 --> 00:09:27,780 +بديش يكون عنده صورتين متشابهتين وكل واحدة كتابتها + +132 +00:09:27,780 --> 00:09:31,020 +مختلفة زي ما عملنا في مين؟ في الـP على Q، متذكرين؟ + +133 +00:09:31,020 --> 00:09:33,920 +نفس القضية، عشان بدي انا اكون في عندي اللي هو + +134 +00:09:33,920 --> 00:09:37,360 +تمثيل وحيد عشان اعتمد عليه وإلا بيصير عندي يعني + +135 +00:09:37,360 --> 00:09:41,630 +غلبتنا في ان نكون عارفين الدالة فبدنا تمثيل وحيدأه + +136 +00:09:41,630 --> 00:09:44,730 +فدائما هذه الصيغة الأخيرة هسميها هي الصيغة + +137 +00:09:44,730 --> 00:09:48,130 +القياسية الصيغة القياسية مش هنسمح يكون تسعات إلى + +138 +00:09:48,130 --> 00:09:53,510 +ما لنهاية فبقوللي أي عدد كسري بيكون في الآخر كله + +139 +00:09:53,510 --> 00:09:58,630 +تسعات ممكن إيش أعدله و إيش و يصير انه إيش زيادة + +140 +00:09:58,630 --> 00:10:01,510 +بواحد equal to one that ends with an infinite + +141 +00:10:01,510 --> 00:10:05,230 +string of zero ممكن أحوله لأصفار في الآخر وين + +142 +00:10:05,230 --> 00:10:09,300 +التكرار أضيف واحد و أحول الباقي لأصفارأه فهذه + +143 +00:10:09,300 --> 00:10:14,620 +الطريقة هانعتمدها فهذا الكلام صحيحفحنعتمد الصورة + +144 +00:10:14,620 --> 00:10:17,900 +القياسية زي ما احنا في العدد نسب يقولنا إن المعامل + +145 +00:10:17,900 --> 00:10:21,680 +المشترك يكون واحد مافيش أي معامل كله يكون اختصر + +146 +00:10:21,680 --> 00:10:24,540 +وخلص هنا نفس القضية دايما حنعتبر إنه حاط في ال + +147 +00:10:24,540 --> 00:10:27,640 +normal form صار أصفر في الآخر فبقول لي a decimal + +148 +00:10:27,640 --> 00:10:31,540 +representation of a real number X is in normalized + +149 +00:10:31,540 --> 00:10:36,360 +form في الوضع القياسي يعني if and only if there is + +150 +00:10:36,360 --> 00:10:41,030 +no k such that for all n أكبر من k xj بسوة 9ما + +151 +00:10:41,030 --> 00:10:44,130 +بديش كله بعد خانة معينة كله ساعة و تسعات، إذا كان + +152 +00:10:44,130 --> 00:10:47,130 +كله ساعة و تسعات، بتعمله Normalization، زي هذا + +153 +00:10:47,130 --> 00:10:51,290 +المثال، فهذا وضع غير قياسي، إذا صار هيكش، بتحاولوا + +154 +00:10:51,290 --> 00:10:54,230 +الوضع القياسي، فأي عدد اللي هو هذه الخاصية، إنه في + +155 +00:10:54,230 --> 00:10:57,170 +الآخر كل الخنات تسعة و تسعة و تسعة لنهاية، بتعمله + +156 +00:10:57,170 --> 00:11:00,210 +Normalization، او بتعمله Normalization، فاحنا + +157 +00:11:00,210 --> 00:11:04,920 +هنشتغل على كل عددبهذه الصورة بقدر اوضعه بهذه الشكل + +158 +00:11:04,920 --> 00:11:08,540 +اتفقنا مصبور وبعدين كل عدد إذا كان بنتي كله تسعات + +159 +00:11:08,540 --> 00:11:12,280 +بنحاوله لمين لـ Normalized form لـ Normalized form + +160 +00:11:12,280 --> 00:11:17,300 +فهذا الوضع القياسي تمامالان هذي بتأكد الكلام اللي + +161 +00:11:17,300 --> 00:11:20,860 +بدي أحكي عليه فبقول لي two decimal numbers in + +162 +00:11:20,860 --> 00:11:23,940 +normalized form لما نحطه بالوضع القياسي اسمهم + +163 +00:11:23,940 --> 00:11:29,300 +بيسووا بعض if and only if كل خانة بتسووا الخانة + +164 +00:11:29,300 --> 00:11:33,580 +المقابلة فبدي أول خانة عشرية تسووا أول خانة عشرية + +165 +00:11:33,580 --> 00:11:37,160 +تاني خانة عشرية تسووا تاني خانة عشرية يعني بمعنى + +166 +00:11:37,160 --> 00:11:43,590 +خليني أشوف هي عندنا مثلا اللي هو Xتساوي 0 X1 X2 و + +167 +00:11:43,590 --> 00:11:50,230 +هكذا و في عنا Y تساوي 0 XY1 عدي خانة أولى و هكذا + +168 +00:11:50,230 --> 00:11:55,690 +فوقتش هدول بيساوي بعض إذا X1 سوا Y1 X2 سوا Y2 و + +169 +00:11:55,690 --> 00:11:59,350 +هكذا طبعا ليش بدي أعمل normalize form لإن لو حولته + +170 +00:11:59,350 --> 00:12:02,450 +عشان المثال بيصير إيش الوضع اختلف هيعندي عددين + +171 +00:12:02,450 --> 00:12:07,350 +متساويين لكن الخنات اشمالهم هيو هذا بيساوي هذا لكن + +172 +00:12:07,350 --> 00:12:10,500 +هل كل خانة بيساوي خانة لألكن عندما أقول إنه Wallet + +173 +00:12:10,500 --> 00:12:13,740 +Form فأعرف عن الكلام، واضح؟ أه، فهنا هي اللي بدنا + +174 +00:12:13,740 --> 00:12:16,700 +نحطه الوضع للقياس عشان نتفق ونبدأ نشتغل، ونبدأ + +175 +00:12:16,700 --> 00:12:20,640 +نشتغل، أه، فلأن هذا راح نعتمد عليه، تمع، فهذا + +176 +00:12:20,640 --> 00:12:24,140 +تمهيد وبعض الخواص، الآن في عندنا نظرية أساسية + +177 +00:12:25,490 --> 00:12:30,010 +النظرية الرئيسية بيقول ليه المجموعة من صفر لواحد + +178 +00:12:30,010 --> 00:12:32,830 +اللي هي مجموعة كل الأعداد الحقيقية اللي أكبر من + +179 +00:12:32,830 --> 00:12:36,010 +صفر و أصغر من واحد is non-denominable is non + +180 +00:12:36,010 --> 00:12:40,350 +-denominable شوفتوا كل اللي احنا عملناه في الأول + +181 +00:12:40,350 --> 00:12:44,750 +كبرنا من الان وروحنا بالشرق باتجاه الغرب تمت + +182 +00:12:44,750 --> 00:12:48,500 +denominableأول ما دخلنا على الـreal numbers الأمور + +183 +00:12:48,500 --> 00:12:51,560 +خرجت عن السيطرة بطّت الـdenominable واخدنا فترة + +184 +00:12:51,560 --> 00:12:55,600 +نموذجية من صفر لواحد فبقول الـopen interval نأكد + +185 +00:12:55,600 --> 00:12:59,580 +عليها هي الفترة 01 اللي هي كل عدد الحقية اللي أكبر + +186 +00:12:59,580 --> 00:13:02,180 +من صفر أصغر من واحد of real numbers is a non + +187 +00:13:02,180 --> 00:13:05,960 +-denominable set فهنشوف البرهان ونشوف فكرة البرهان + +188 +00:13:05,960 --> 00:13:11,960 +مع بعض فدي theorem 512 + +189 +00:13:13,190 --> 00:13:16,850 +حنثبتها by contradiction لأن كل شغلنا معاه اللي هو + +190 +00:13:16,850 --> 00:13:23,010 +denomable فنعملها by contradiction prove assume + +191 +00:13:23,010 --> 00:13:26,070 +01 + +192 +00:13:26,070 --> 00:13:32,650 +is denomable نفترض + +193 +00:13:32,650 --> 00:13:38,030 +عليه prove by contradiction طبعا prove by + +194 +00:13:38,030 --> 00:13:39,870 +contradiction + +195 +00:13:42,170 --> 00:13:45,050 +أو فكرة البرهان يمكن برضه تساعدنا في التخيل ليش + +196 +00:13:45,050 --> 00:13:48,970 +الأعداد الحقيقية هذه أعدادها مهول وخرجة عن السيطرة + +197 +00:13:48,970 --> 00:13:51,590 +ايه معناه الـ numerical؟ بقدر ألاقي bijection + +198 +00:13:51,590 --> 00:13:55,890 +بينها و بين ال N فده implies there exists a + +199 +00:13:55,890 --> 00:14:03,730 +bijection F من اللي هو بدنا ياها من N Zero ل Zero + +200 +00:14:03,730 --> 00:14:08,710 +N بس عشان الفكرة بالترتيب طبعا احنا عارفين يقول + +201 +00:14:08,710 --> 00:14:10,490 +bijection فال inverse تبعه bijection + +202 +00:14:14,630 --> 00:14:23,910 +من N لـ 01 ناخدها من N إلى 01 تمام ممتاز + +203 +00:14:26,010 --> 00:14:30,110 +الآن بدنا بس اللي هو الانرقم، أثبتوا أن هذه ليست + +204 +00:14:30,110 --> 00:14:34,530 +قُنطة، مستحيل تغطي، ماعندي عدد عناصر كافية من الآن + +205 +00:14:34,530 --> 00:14:38,350 +يغطي كل الـ01، لأنها كبيرة جدا، فده هي إيش الفكرة، + +206 +00:14:38,350 --> 00:14:41,470 +فتلاحظوا أننا لم نصل إيش لـContradiction، إيش بدنا + +207 +00:14:41,470 --> 00:14:43,630 +الـContradiction؟ ما زال دي Bijection، بدي أثبتوا + +208 +00:14:43,630 --> 00:14:46,930 +أن هذه ليست قُنطة، فهذا تناقض، يعني في عنصر هنا مش + +209 +00:14:46,930 --> 00:14:50,090 +صورة حدا، مش صورة حدا، فاحنا جيت إيش اللي بدنا + +210 +00:14:50,090 --> 00:14:53,270 +نعمله، بس إيش، نسمي، نسمي الصور هدول، بس عشان + +211 +00:14:53,270 --> 00:14:58,840 +نكتبهم،let f of one نشوف طبعاً مع المقدمة اللي + +212 +00:14:58,840 --> 00:15:01,640 +عملناها f of واحد وين ده تكون عدد هنا إذا بقدر + +213 +00:15:01,640 --> 00:15:06,420 +أكتبه كيف على صورة zero point بدي أرقمه عشان هو دي + +214 +00:15:06,420 --> 00:15:10,520 +f of واحد بدي أعمل حاجتين عشان واحد فبدي أحط واحد + +215 +00:15:10,520 --> 00:15:14,480 +وعشان الخانة الأولى كمان واحد زي ما بعمل بالمصففات + +216 +00:15:14,480 --> 00:15:18,520 +إذا مرت عليكم فبدي رقمين رقم عشان الواحد ورقم عشان + +217 +00:15:18,520 --> 00:15:21,480 +الخانة بعدين لجيت a واحد + +218 +00:15:47,290 --> 00:15:48,690 +A1A2A3A4A5A6A7A8A9A10A11A12A13A14A15A16A17A18A20A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21A21 + +219 +00:15:49,960 --> 00:15:55,060 +لو كان الكلام صحيح لو كانت الـ 01 denomable + +220 +00:15:55,060 --> 00:16:00,480 +المفروض هدول الصور الشمالهم يغطوا كل الـ 01 نشوف + +221 +00:16:00,480 --> 00:16:04,100 +كيف بدنا نلاقي عدد بين الـ 01 و لا واحد من هدول + +222 +00:16:04,100 --> 00:16:06,700 +بيسويش و لا واحد من هدول بيسويش و لا واحد من هدول + +223 +00:16:06,700 --> 00:16:16,140 +هنعمل trick بسيط الآن now let z تساوي طبعا هو عايش + +224 +00:16:19,370 --> 00:16:28,570 +point z1 z2 و هكذا z3 و هكذا بي let z be where؟ + +225 +00:16:28,570 --> 00:16:36,830 +بدنا نعرف بالشكل التالي z z sub j هذه الخنات بدنا + +226 +00:16:36,830 --> 00:16:40,050 +نعرفهم بالشكل التالي شوفوا كيف الفكرة اللي عامة + +227 +00:16:40,050 --> 00:16:45,190 +فهذا بدنا نعمله حزب معارضة يعني مخالف على طول بديش + +228 +00:16:45,190 --> 00:16:51,180 +يا يساوي صورة الواحدفطبعا بالمقدمة اللي حكيتها إذا + +229 +00:16:51,180 --> 00:16:53,640 +اختلف معاه بخانة واحدة بيساويهاش لأن كل دول طبعا + +230 +00:16:53,640 --> 00:16:56,620 +انه Normalize for بدي ازالة ان كل خانة بتتطابق + +231 +00:16:56,620 --> 00:17:01,480 +عشان تتساوي فإذا اختلف بخانة واحدة انتهى فبدي اذا + +232 +00:17:01,480 --> 00:17:07,420 +كانت مثلا ا واحد واحد مثلا ايش بتساوي سبعة خليه + +233 +00:17:07,420 --> 00:17:17,090 +يشمله سميه تلاتةفإذا هو يختلف مع الـA11 بشكل عام + +234 +00:17:17,090 --> 00:17:22,330 +فبدا + +235 +00:17:22,330 --> 00:17:27,110 +نشتغل على الخانة القطرية فأنا بدي إياه يختلف مع + +236 +00:17:27,110 --> 00:17:33,210 +مين بروح بتطلع على إيه؟ بتطلع على A11 فأول شيء في + +237 +00:17:33,210 --> 00:17:36,570 +هذا الـZ بدي إياه يختلف مع صورة الواحد أندوين في + +238 +00:17:36,570 --> 00:17:40,310 +الخانة الأولىو يختلف عن صورة التنين في الخانة + +239 +00:17:40,310 --> 00:17:43,350 +التانية و هكذا إذاً هيختلف عن كل الصورة في هذه + +240 +00:17:43,350 --> 00:17:47,750 +الصورة طبعا دول أرقام بشكل عام و يساوي سبعة إذا + +241 +00:17:47,750 --> 00:17:51,470 +كانت AJJ بتساوي سبعة .. بلا تساوي سبعة فيعمل .. + +242 +00:17:51,470 --> 00:17:52,790 +شوف مرة تانية + +243 +00:17:56,410 --> 00:18:00,850 +بنعيد بس عملية اللي هو إيش مخالفة معارضة نقول زي + +244 +00:18:00,850 --> 00:18:04,450 +حزب المعارضة فبقول بتطلع هو طبعا بدي نبدأ لإن بدي + +245 +00:18:04,450 --> 00:18:10,630 +أجيب زد واحد بروح بتطلع بتطلع على إيش أفف واحد + +246 +00:18:10,630 --> 00:18:14,160 +بتطلع على إيه واحد واحدبدي ازد واحد ده دي لا تساوي + +247 +00:18:14,160 --> 00:18:17,140 +اي واحد واحد فإذا اي واحد واحد بتساوي سبعة باخليها + +248 +00:18:17,140 --> 00:18:19,940 +تلاتة المهم ماتساويهاش أي حاجة الأرقام تلاتة وسبعة + +249 +00:18:19,940 --> 00:18:23,140 +دولة عشوائية ممكن أغيرهم وإذا بتساوي السبعة بحطها + +250 +00:18:23,140 --> 00:18:26,760 +سبعة إذا انضمنت إنه إيش ازد واحد لا تساوي اي واحد + +251 +00:18:26,760 --> 00:18:30,720 +واحد إذا ازد لا تساوي أفوفان على طول مباشرة لإنه + +252 +00:18:30,720 --> 00:18:32,460 +اختلفت فيها مع الخانة الأولى تمام + +253 +00:18:36,790 --> 00:18:40,250 +ماشي أنا بدي أجيبه، ليش؟ بدي أجيبه يكون هنا، أه + +254 +00:18:40,250 --> 00:18:44,690 +مهم، أه ليش؟ إيش بعلمنا هذا الكلام؟ إنه هنا أنا + +255 +00:18:44,690 --> 00:18:50,990 +بختاره تقريبا بشكل عشوائي، بس بغير تغيير بسيط، + +256 +00:18:50,990 --> 00:18:54,790 +جيبت عدد، هل الـZ موجودة هنا ولا مش موجودة؟ موجودة + +257 +00:18:54,790 --> 00:19:01,350 +لأن هي 0.مظبوط، لكن ما هي القضية؟ إيش معناه ليست + +258 +00:19:01,350 --> 00:19:05,490 +أنتوا؟ بقدر ألاقي عنصر بين الـ01 مش الصورة، فعند + +259 +00:19:05,490 --> 00:19:08,450 +الفراد أنا لجيته، بعد ما أتفرضته، مظبوط؟ أه، أنا + +260 +00:19:08,450 --> 00:19:12,780 +لجيته، في عدد بقى الشكل ولا مافيه الشيء؟فيه عدد + +261 +00:19:12,780 --> 00:19:16,940 +وبين الـ 01 هل بيساوي واحد من الصورة دول؟ مطلقاً + +262 +00:19:16,940 --> 00:19:19,760 +لأ، لأن كيف اختارته، بالدياية يختلف، هدول مالها + +263 +00:19:19,760 --> 00:19:23,200 +نهاية طبعا، عشان هي الصعوبة الاختيار بس، بالدياية + +264 +00:19:23,200 --> 00:19:26,360 +إيش، يختلف مع الأول بالخانة الأولى، ومع التاني + +265 +00:19:26,360 --> 00:19:29,140 +بالخانة التانية، وها كذا، فالعملية مش عادة، ما + +266 +00:19:29,140 --> 00:19:31,860 +هيش، ما هيش، معناته إنه ليست قُنته، إنه في عنصر مش + +267 +00:19:31,860 --> 00:19:34,900 +صورة حدى، وانا لجيته هذا، بس بيش، صممته بهذه + +268 +00:19:34,900 --> 00:19:37,820 +الطريقة، دي عملية تصميم، مش فرضية، تصميم، صممتي + +269 +00:19:37,820 --> 00:19:39,120 +العدد بهذه الصورة، + +270 +00:19:42,440 --> 00:19:52,000 +then الـ z أولا بتنتمي للـ 01 مصبوط and z لا تساوي + +271 +00:19:52,000 --> 00:19:59,460 +f of k أو for all k تنتمي لل N مستحيل تكون أي صورة + +272 +00:19:59,460 --> 00:20:05,770 +بالصور صح واضحة ولا أنا أيضا كمان؟أخذ أي عددين، + +273 +00:20:05,770 --> 00:20:09,970 +معناه يقولنا حزب وعارضة هذا بيقول أنا اتنين، + +274 +00:20:09,970 --> 00:20:12,650 +بيقوله أنا مش اتنين هذا بيقوله أنا سبعة، بيقوله مش + +275 +00:20:12,650 --> 00:20:15,370 +سبعة أنا خمسة مش خمسة، فأي عددين، المهم مخالف + +276 +00:20:15,370 --> 00:20:18,670 +التلاتة والسبعة مالهم مش خصوصية، مالهم مش اي + +277 +00:20:18,670 --> 00:20:22,510 +خصوصية بس طبعا ليش مجلس واحد اتنين؟ بده ترتيب + +278 +00:20:22,510 --> 00:20:25,730 +معين، فهذا ترتيبه سهل أنه بده يختلف مع الأول + +279 +00:20:25,730 --> 00:20:28,050 +بالخانة الأولى ومع التاني بالخانة التانية طب ليش + +280 +00:20:28,050 --> 00:20:31,550 +مع الأول مش بالخانة العاشرة؟ بين twoفأبدوا ترتيب + +281 +00:20:31,550 --> 00:20:34,050 +معين فلما أقول مع الأول بالخانة الأولى يختلف مع + +282 +00:20:34,050 --> 00:20:37,690 +التاني بالخانة التانية فإذا أنا ضاع من إنه إيش هذا + +283 +00:20:37,690 --> 00:20:40,550 +الـ Z لا يمكن يساوي F of 1 لأنه اختلف معاه بالخانة + +284 +00:20:40,550 --> 00:20:42,890 +الأولى و لا يمكن يساوي F of 2 لأنه اختلف معاه + +285 +00:20:42,890 --> 00:20:45,330 +بالخانة التانية لأن اتفقنا في المقدمات إنه إيش + +286 +00:20:45,330 --> 00:20:47,930 +مثلا إذا في ال Normalized form ماكنتش بتساوي كل + +287 +00:20:47,930 --> 00:20:51,030 +خاناتهم بتساوي اختلف بخانة إذا مختلف إذا مختلف + +288 +00:20:51,030 --> 00:20:57,250 +فطبعا هذا إيش contradiction فهذا يؤدي إن F is not + +289 +00:20:57,250 --> 00:20:58,630 +onto contradiction + +290 +00:21:04,050 --> 00:21:06,790 +أه، فطبعًا واضح من الـ «الثابت» ‏«الثابت» + +291 +00:21:06,790 --> 00:21:09,290 +‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» + +292 +00:21:09,290 --> 00:21:11,250 +‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» + +293 +00:21:11,250 --> 00:21:12,650 +‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» + +294 +00:21:12,650 --> 00:21:17,730 +‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» ‏«الثابت» + +295 +00:21:17,730 --> 00:21:22,110 +‏«الثابت» ‏«الثابت» + +296 +00:21:22,110 --> 00:21:29,950 +‏«الثابت» ‏«الثابت» + +297 +00:21:29,950 --> 00:21:38,010 +‏«طبعا الان نتيجة الهدف الأكبر ان الـ R نفسها non + +298 +00:21:38,010 --> 00:21:44,470 +-denominable طبعا هذا الكلام احنا شرحناه قبل ذلك + +299 +00:21:44,470 --> 00:21:49,270 +بس نؤكد عليه كل + +300 +00:21:49,270 --> 00:22:00,330 +ريخ خمسة سبعة prove طبعا + +301 +00:22:00,330 --> 00:22:06,440 +احنا بنعرف ان الـ Rالـ R اشملها تكافئ سالب باية 2 + +302 +00:22:06,440 --> 00:22:10,540 +لباية 2 نعملها بشكل صريح و هذه تكافئ صفر واحد ممكن + +303 +00:22:10,540 --> 00:22:14,600 +نعملها يمكن ماعملاش بشكل صريح تنعملها طبعا على طول + +304 +00:22:14,600 --> 00:22:19,420 +و هذه علاقة الـ Transitive فهذا يؤدي ان الـ R is + +305 +00:22:19,420 --> 00:22:19,980 +non-denominable + +306 +00:22:29,540 --> 00:22:32,380 +فارجعوا أن تكونوا واضحة الفكرة لو اشتغلنا على أرض + +307 +00:22:32,380 --> 00:22:37,980 +مباشرة كانت تهنأ كبير العملية لأنه ركزنا أنه ببدأ + +308 +00:22:37,980 --> 00:22:41,000 +بصفر كذا و انا فصار عندي عملية تركيز و هذا سهل + +309 +00:22:41,000 --> 00:22:48,920 +التعمم و التعميم بعدين بيجي بيجي بهذا الشكل نشوف + +310 +00:22:48,920 --> 00:22:49,520 +مثال + +311 +00:23:13,420 --> 00:23:17,480 +show that the set of all irrational numbers is not + +312 +00:23:17,480 --> 00:23:22,040 +denominable مجموعة كل أعداد غير النسبية برضه non + +313 +00:23:22,040 --> 00:23:27,680 +-denominable مثال + +314 +00:23:27,680 --> 00:23:31,680 +طبعا + +315 +00:23:31,680 --> 00:23:38,120 +الكلام هنا هو شيء منطقي يعني لأن احنا عند ال Q و + +316 +00:23:38,120 --> 00:23:42,040 +هو denominableيعني كل عدد نسبية دنيا مربوط طيب إيش + +317 +00:23:42,040 --> 00:23:44,680 +هي العدد الحقيقية؟ تتكون من النسبية والغير نسبية + +318 +00:23:44,680 --> 00:23:49,720 +إذا ال mainly العدد هو هائل جدا وخلّى ال R تصير + +319 +00:23:49,720 --> 00:23:52,680 +non-denominable مش العدد النسبي وانما غير النسبية + +320 +00:23:52,680 --> 00:23:57,720 +فاحنا ده اللي إيش اللي هنثبته فطبعا بس لت تسميات + +321 +00:23:57,720 --> 00:24:04,920 +solution let X تساوي R ما عدا Q هذا ليه إيش؟ لعدد + +322 +00:24:04,920 --> 00:24:06,860 +النسبية B + +323 +00:24:09,170 --> 00:24:21,970 +the set of irrational number فدى + +324 +00:24:21,970 --> 00:24:27,490 +مجموعة لعداد غير النسوية بدنا نثبت انها non + +325 +00:24:27,490 --> 00:24:36,330 +-denominable باي contradiction هنعملها assume x is + +326 +00:24:36,330 --> 00:24:37,270 +denominable + +327 +00:24:43,730 --> 00:24:48,850 +طب لو كانت ال X denomable إيش بدي يصير؟ ال R عبارة + +328 +00:24:48,850 --> 00:24:56,070 +عن إيه؟ X إتحاد Q أه و إحنا عندنا نظرية denomable + +329 +00:24:56,070 --> 00:24:59,150 +لو هذه denomable لازم تكون denomable is denomable + +330 +00:24:59,150 --> 00:25:05,910 +طبعا خلصنا contradiction + +331 +00:25:05,910 --> 00:25:05,950 +contradiction + +332 +00:25:15,520 --> 00:25:26,140 +فانا خلصنا ال chapter أسرع مما توقعنا ممكن + +333 +00:25:26,140 --> 00:25:28,560 +يعني هو اللي اللي اللي اللي لازم فاهمته ده شيء + +334 +00:25:28,560 --> 00:25:29,000 +ممتاز + +335 +00:25:50,360 --> 00:25:51,760 +السلام عليكم ورحمة الله وبركاته + +336 +00:26:16,840 --> 00:26:20,620 +خلّينا في ما تبقى من الوقت ناخد مقدمة عن الشبطة + +337 +00:26:21,510 --> 00:26:24,830 +chapter 6 وإن شاء الله يعني بنشوف إحنا عايش .. + +338 +00:26:24,830 --> 00:26:28,530 +ماشيين يعني ونشوف إيش العلاقة مع الموضوع عشان نشوف + +339 +00:26:28,530 --> 00:26:33,130 +.. زي ما حكينا كيف هنعيد أفكار في chapter 5 + +340 +00:26:33,130 --> 00:26:36,890 +الحقيقة و هذا هيساعدنا كتير إن شاء الله في تثبيت + +341 +00:26:36,890 --> 00:26:40,730 +مفاهيم في chapter 5 طبعاً العنوان cardinal numbers + +342 +00:26:40,730 --> 00:26:46,580 +and cardinal arithmeticCardinal يسمونها أعداد + +343 +00:26:46,580 --> 00:26:50,920 +أصلية أو نوع من الأعداد نتعرف على نوع جديد من + +344 +00:26:50,920 --> 00:26:54,360 +أنظمة الأعداد طبعا هنعرف الأعداد الطبيعية الأعداد + +345 +00:26:54,360 --> 00:26:57,400 +الصحيحة النسبية الحقية و المركبة يمكن اللي هي فيها + +346 +00:26:57,400 --> 00:27:00,890 +التخيل جزر السالب واحدأه فدولا نوع جديد من الأعداد + +347 +00:27:00,890 --> 00:27:03,310 +يسمون Cardinal Number طبعا Cardinal Arithmetic + +348 +00:27:03,310 --> 00:27:06,010 +العمليات الحسابية على Cardinal Numbers العمليات + +349 +00:27:06,010 --> 00:27:09,310 +الحسابية على هذه الأعداد الجديدة اللي احنا هتعرف + +350 +00:27:09,310 --> 00:27:13,730 +عليها فاحنا كل اللي بدنا نعمله بشكل رئيسي انه + +351 +00:27:13,730 --> 00:27:19,300 +هنحول الكلام اللي كنا بنحكيه إلى عدد العناصرإيش + +352 +00:27:19,300 --> 00:27:22,660 +معناة Denumerable تكافئ الـ N فهذه بنحط عدد + +353 +00:27:22,660 --> 00:27:26,580 +عناصرها بالساوية مثلا عدد معين مثلا A طيب ال R non + +354 +00:27:26,580 --> 00:27:29,600 +-denumerable إذا عدد عناصرها عدد مختلف نسميه C + +355 +00:27:29,600 --> 00:27:32,620 +طبعا برضه ال finite برضه عدد عناصرها واضح هذا فيها + +356 +00:27:32,620 --> 00:27:35,680 +صفر من عناصر Phi هذا في عنصر واحد single to set + +357 +00:27:35,680 --> 00:27:39,220 +هذا في عشر عناصر N عشرة و هكذا فبنشتغل معاهم بعد + +358 +00:27:39,220 --> 00:27:44,200 +الشكل فدولة كلهم اللي أي عدد بيرمز لعدد عناصر + +359 +00:27:44,200 --> 00:27:47,400 +مجموعة معينة هنسميه cardinal number هنسميه + +360 +00:27:47,400 --> 00:27:53,430 +cardinal numberفاحنا بنتعرف على مفهوم ال cardinal + +361 +00:27:53,430 --> 00:27:57,010 +numbers ايش هو ال cardinal number كتعريف خواص ال + +362 +00:27:57,010 --> 00:28:03,090 +cardinal number و بعدين عملية الحسابية عليهم فنبدأ + +363 +00:28:03,090 --> 00:28:05,090 +بما هو ال cardinal numbers + +364 +00:28:16,710 --> 00:28:20,890 +الحقيقة احنا مش هنددي تعريف مباشر لل cardinal + +365 +00:28:20,890 --> 00:28:26,210 +number وانما هنحط قواعد و هنرقمها ب .. اللي هو + +366 +00:28:26,210 --> 00:28:30,190 +حروف C1 من كلمة cardinal number و هدول القواعد + +367 +00:28:30,190 --> 00:28:33,330 +اللي تنطبق على أي عدد نسميه cardinal number فبقول + +368 +00:28:33,330 --> 00:28:35,330 +we will not define a cardinal number but we will + +369 +00:28:35,330 --> 00:28:38,910 +introduce it as a primitive concept يفشق اللي هو + +370 +00:28:38,910 --> 00:28:41,810 +مبدأه و طبعا اشمله إيه له علاقة بمين؟ حجم + +371 +00:28:41,810 --> 00:28:45,170 +المجموعات زي ما حكيتفأنا بدي أقول عدد عنصر رمح طيب + +372 +00:28:45,170 --> 00:28:48,070 +ليه فإحنا لجأنا لل cardinal numbers لأنه مافيش + +373 +00:28:48,070 --> 00:28:52,230 +نظام عدد يتعامل مع المجموعات لأن ال infinite هي + +374 +00:28:52,230 --> 00:28:57,030 +عدد حقيقي ولا عدد مركّب فإذا هذه العداد اللي + +375 +00:28:57,030 --> 00:29:00,770 +هتتضمن infinite وعنواع مختلفة من ال infinite بدها + +376 +00:29:00,770 --> 00:29:03,530 +يش نوع جديد من العداد بيسموها ال cardinal numbers + +377 +00:29:03,530 --> 00:29:07,920 +ففي عندنا قواعد لل cardinal numbersالقاعدة الأولى + +378 +00:29:07,920 --> 00:29:12,840 +C1 من كلمة Cardinal بقول لكل مجموعة يصحبها + +379 +00:29:12,840 --> 00:29:16,100 +Cardinal number فإذا إحنا مرتبط تعريف Cardinal + +380 +00:29:16,100 --> 00:29:20,080 +number بعدد أياش المجموعات أنا عندي مجموعة فيه + +381 +00:29:20,080 --> 00:29:23,020 +Cardinal number بيقابلها وعكس صحيح فيه Cardinal + +382 +00:29:23,020 --> 00:29:26,540 +number لازم تقابله مجموعة إيش ما لها عدد عناصر أيه + +383 +00:29:26,540 --> 00:29:29,740 +يساوي هذا Cardinal number فDenoted by طبعا الرمز + +384 +00:29:29,740 --> 00:29:33,260 +من كلمة Cardinal الحلو هو أول أربع حروف فطبعا + +385 +00:29:33,260 --> 00:29:36,920 +نقراها Cardinal of Aand for each cardinal number + +386 +00:29:36,920 --> 00:29:41,440 +N، العكس، there is a set such that cardinal number + +387 +00:29:41,440 --> 00:29:46,160 +of A بيساوي N فانهيش العملية مرتبطة مرتبط مباشر + +388 +00:29:46,160 --> 00:29:50,200 +ووثيق بالمجموعات فدول الاعداد مش اعداد لأي شيء + +389 +00:29:50,200 --> 00:29:53,900 +وانما التعامل مع المجموعات من حيث عدد العناصر او + +390 +00:29:53,900 --> 00:29:58,180 +من حيث الحجم من حيث الحجمفإذا مافيش حاجة مثلا + +391 +00:29:58,180 --> 00:30:02,340 +cardinal number بيعبر عن اللي هو وزن معين ولا عن + +392 +00:30:02,340 --> 00:30:06,820 +طول، مسافة، لأ cardinal number بيعبر عن عدد عناصر + +393 +00:30:06,820 --> 00:30:10,220 +مجموعة فكل مجموعة بيقبلها cardinal number وكل + +394 +00:30:10,220 --> 00:30:13,940 +cardinal number لازم يتحدث عن مجموعة أو عدد عناصر + +395 +00:30:13,940 --> 00:30:18,290 +مجموعة، فهذه القاعدة الأولىالقاعدة التانية + +396 +00:30:18,290 --> 00:30:21,570 +المجموعة الوحيدة الكاردنالدية تبعتها بتساوي صفر هي + +397 +00:30:21,570 --> 00:30:25,010 +الـ Phi و هذا شيء منطقي فالمجموعة فارغة يعني أن + +398 +00:30:25,010 --> 00:30:27,310 +عضو عناصرها صفر و هذا بيأكد احنا كيف المفهوم اللي + +399 +00:30:27,310 --> 00:30:29,590 +بنمشي معاه فهي الـ Phi + +400 +00:30:32,690 --> 00:30:34,950 +إذا كانت المجموعة طبعاً اللي احنا متعودين عليه + +401 +00:30:34,950 --> 00:30:40,750 +السهل finite ومش MT تكافئان K ففي هذه الحالة كدهش + +402 +00:30:40,750 --> 00:30:42,890 +ال cardinal number K زي اللي احنا متعارفينه فاحنا + +403 +00:30:42,890 --> 00:30:45,110 +بدنااش .. طبعا كل الهدف من تعريف ال cardinal + +404 +00:30:45,110 --> 00:30:47,790 +number هو التعامل مع ال infinite sets و ليس مع ال + +405 +00:30:47,790 --> 00:30:51,530 +finite ولكن بدنا دايما لما بنعمم حاجة بدنااش تلغي + +406 +00:30:51,530 --> 00:30:55,110 +الماضي بدناها تنسجم مع الماضي و تطوره و من غير + +407 +00:30:55,110 --> 00:30:59,170 +تناقض ينطبق على السابق و اللاحق بشكل مناسب + +408 +00:31:09,810 --> 00:31:16,130 +القاعدة الرابعةبنقول إذا كان في عندنا مجموعتين و + +409 +00:31:16,130 --> 00:31:20,950 +ال cardinal number تبعهم بتساوى if and only if هم + +410 +00:31:20,950 --> 00:31:25,170 +متكافئتين فالان احنا صار عندنا هاي الكلام اللي + +411 +00:31:25,170 --> 00:31:29,950 +بنحكي عنه ممكن أعبر مجموعتين متكافئتين عدديًا أو + +412 +00:31:29,950 --> 00:31:32,250 +ال cardinal number للمجموعة الأولى بيساوي ال + +413 +00:31:32,250 --> 00:31:33,930 +cardinal number للمجموعة التانية فاحنا هننظر + +414 +00:31:33,930 --> 00:31:37,130 +لموضوع التكافئة من زاوية أخرى الآن أنه عايش ال + +415 +00:31:37,130 --> 00:31:41,210 +cardinal number متساويفهو احنا نتحدث عن عدد + +416 +00:31:41,210 --> 00:31:44,190 +العناصر كنا نحكيها بشكل غير رسمي الان هنعبّر عنها + +417 +00:31:44,190 --> 00:31:48,470 +بشكل رسمي ان X تكافئ ال Y يعني ال cardinal number + +418 +00:31:48,470 --> 00:31:51,590 +لل X بيساوي ال cardinal number لل Y نفس البعض فدول + +419 +00:31:51,590 --> 00:31:56,700 +الأربع قواعد هنعتمد عليهمأه هدولة يعتبر ال + +420 +00:31:56,700 --> 00:31:59,600 +cardinal number لل N يساوي ال cardinal number لل Z + +421 +00:31:59,600 --> 00:32:02,460 +يساوي ال cardinal number لل Q لكن لا يساوي ال + +422 +00:32:02,460 --> 00:32:06,320 +cardinal number لل R 100% صحيح فاحنا هنبدأ نعدر ب + +423 +00:32:06,320 --> 00:32:08,880 +.. عشان هيك أنا قلت ان هذا الشبطر بيدعم الشبطر + +424 +00:32:08,880 --> 00:32:12,240 +الماضي هنحكي عن نفس المفاهيم لكن من زاوية أخرة .. + +425 +00:32:12,240 --> 00:32:19,610 +من زاوية أخرةنشوف مثال بسيط جدا ويقول show that + +426 +00:32:19,610 --> 00:32:23,990 +الواحد is a cardinal number الواحد يعتبر cardinal + +427 +00:32:23,990 --> 00:32:26,570 +number الواحد احنا متعرفينه على ايه اللي متعرفه هو + +428 +00:32:26,570 --> 00:32:31,390 +يعتبر cardinal number كيف بدنا نتعاون مع هذا + +429 +00:32:31,390 --> 00:32:37,350 +الموضوع؟ بدنا مجموعة قدر عنصرها واحدتمام فبتكون + +430 +00:32:37,350 --> 00:32:42,290 +ايش؟ العملية صحيحة فهنا هذا المثال الأول solution + +431 +00:32:42,290 --> 00:32:47,070 +فنقول له let a تساوي singleton set اي اي singleton + +432 +00:32:47,070 --> 00:32:51,130 +set يعني اذا الواحد بده يلخمكه بلاش لأنه عشانها + +433 +00:32:51,130 --> 00:32:57,530 +مكرر اي عدل من عنصر واحد فطبعا then cardinal + +434 +00:32:57,530 --> 00:33:03,610 +number of a بيساوي واحد وهذا يؤدي ان الواحد is a + +435 +00:33:03,610 --> 00:33:04,230 +cardinal number + +436 +00:33:13,070 --> 00:33:16,730 +بس بقدرش أقول إن هذا card number لأنه أنا فيه عندي + +437 +00:33:16,730 --> 00:33:21,870 +مسافة بين اللي هو بنين تان واحد كيلو لأ لأن هي + +438 +00:33:21,870 --> 00:33:26,110 +تعبر عن عدد عناصر مجموعة ما فهذه النقطة مهمة جدا + +439 +00:33:26,110 --> 00:33:32,250 +طبعا تبقى للقواعد احنا استغلنا تمام نشوف كمان مثال + +440 +00:33:32,250 --> 00:33:37,530 +نأكد على نفس المعلومةبس نعمم شوية فاحنا جيت احنا + +441 +00:33:37,530 --> 00:33:40,230 +ايش cardinal number اتعرفنا عليهم الـ zero + +442 +00:33:40,230 --> 00:33:42,990 +cardinal number لإن هو ايش؟ هو عدد عناصر الـ five + +443 +00:33:42,990 --> 00:33:47,210 +الواحدة ده هو كل finite اي حاجة المية المية الـ + +444 +00:33:47,210 --> 00:33:50,390 +100 هالجيت فاق نحن ناني الواحد نشوف بقولي find the + +445 +00:33:50,390 --> 00:33:53,770 +cardinal number of A وجيت 100 على طول ماحن بدنا + +446 +00:33:53,770 --> 00:33:57,890 +نأكد هتنلموه عشان بدنا نسوي الأرض و نجف على أرض + +447 +00:33:57,890 --> 00:34:03,590 +ثابتة و نطور شغلفهنا مثال تاني solution فطبعا ليش + +448 +00:34:03,590 --> 00:34:10,450 +لأن هذه ال A شمالها تكافئ أنمية واضحة هذه اه فلأن + +449 +00:34:10,450 --> 00:34:14,530 +هي بتكافئ أنمية ولا لأ لأن أي A واحد تكافئ الواحد + +450 +00:34:14,530 --> 00:34:20,230 +فده يؤدي ان ال cardinal number لل A يساوي 100 + +451 +00:34:20,230 --> 00:34:26,200 +فاحنا بنأكد على هذه المفاهيم الأساسيةفإذا واضح إن + +452 +00:34:26,200 --> 00:34:31,340 +أي صفر Cardinal number أي عدد طبيعي Cardinal + +453 +00:34:31,340 --> 00:34:35,960 +number سنضيف أجزاء من عدد Cardinal number هل يوجد + +454 +00:34:35,960 --> 00:34:42,360 +غيرهم؟ يوجد غيرهم سنشوف تمام + +455 +00:34:42,360 --> 00:34:47,780 +هذه السؤال اللي تحكتيها كل وقت نستخدم القواعد + +456 +00:34:54,260 --> 00:34:57,060 +فبكل شغل يبقى استخدم اللي هو ياشق القواعد اللي هو + +457 +00:34:57,060 --> 00:35:01,220 +من C1 ل C4 فهذا الواشل طبعا فانا هتواشل استخدم + +458 +00:35:01,220 --> 00:35:11,980 +القاعدة C4 و C3 مثال التالف بقول + +459 +00:35:11,980 --> 00:35:13,760 +اثبت ان ال cardinality اللي انت صحيح ال + +460 +00:35:13,760 --> 00:35:21,760 +cardinality اللي هي Z solution كيف + +461 +00:35:21,760 --> 00:35:26,910 +نعملها if and و ifبنرجع للمبادئ F and only F + +462 +00:35:26,910 --> 00:35:30,910 +بستخدمتيها في أي اتجاه صح زي الشارع في اتجاهين اه + +463 +00:35:30,910 --> 00:35:34,210 +روحت منه اه دي اه مش ضروري ملزمة انك تروح + +464 +00:35:34,210 --> 00:35:39,690 +الاتجاهين مش ملزمة اه مسموح لك اه تمام فهذا يؤدي + +465 +00:35:39,690 --> 00:35:46,370 +ان ال cardinality لل Z تساوي ال cardinality لل I + +466 +00:35:46,370 --> 00:35:54,770 +بكل سهولة فهدولة نقطة البداية و نقطة الانطلاقو + +467 +00:35:54,770 --> 00:36:03,650 +يكفي اليوم كمقدم فهنا نفس المواضيع بس هناخده من + +468 +00:36:03,650 --> 00:36:07,890 +زاوية أخرى فهنا الموضوع عرفينه بس هننزله من زاوية + +469 +00:36:07,890 --> 00:36:10,870 +أخرى و هكذا ان شاء الله يوم الأربعة بنكمل + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/qExcn0_xmbU_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/qExcn0_xmbU_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..26c3dbf7b312a59b371b0cbb8b2d15ef619cc046 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/qExcn0_xmbU_raw.srt @@ -0,0 +1,2760 @@ +1 +00:00:22,000 --> 00:00:25,540 +إن شاء الله هنواصل احنا مع دراسة الـ Cartesian + +2 +00:00:25,540 --> 00:00:30,260 +product و ال relations أو العلاقات فطبعا احنا ال + +3 +00:00:30,260 --> 00:00:34,180 +.. ال Cartesian product هو الأداة الأساسية أو هو + +4 +00:00:34,180 --> 00:00:37,120 +المدخل لدراسة ال relations و من ثم دراسة ال + +5 +00:00:37,120 --> 00:00:40,860 +functions فاحنا تبقالنا بعض الأمثلة في هذا الموضوع + +6 +00:00:40,860 --> 00:00:44,540 +خلينا نستكمل ففي المحاضرة الماضية شوفنا المثال + +7 +00:00:44,540 --> 00:00:48,940 +الأول اليوم هنشوف المثال التاني نقرأه مع بعض prove + +8 +00:00:48,940 --> 00:00:57,040 +thatA x B → F if and only if A → F or B → F فاحنا + +9 +00:00:57,040 --> 00:01:01,140 +في عندنا statement عبارة عن by conditional if and + +10 +00:01:01,140 --> 00:01:03,960 +only if خلينا نسترجى كيف نتعامل معاها و نبدأ + +11 +00:01:03,960 --> 00:01:07,640 +نتعامل معاها خطوة خطوةفإن أعيد صياغة السؤال + +12 +00:01:07,640 --> 00:01:14,060 +فالسؤال prove that A cross ال B تساوي فاي if and + +13 +00:01:14,060 --> 00:01:20,600 +only if هذا المطلوب ايش A تساوي فاي or B تساوي فاي + +14 +00:01:20,600 --> 00:01:25,220 +فهذا هو السؤالفدي عادة صياغة للسؤال فاحنا فيها + +15 +00:01:25,220 --> 00:01:29,360 +إننا statement مركبة تحتوي على الرابط if and only + +16 +00:01:29,360 --> 00:01:31,840 +if طبعاً نثبت إنها true عشان هيك عملنا تكافؤ + +17 +00:01:31,840 --> 00:01:35,480 +فطبعاً زي ما اتعلمنا فيه طريقتين للبرهان في طريقة + +18 +00:01:35,480 --> 00:01:39,020 +اللي هو one part proof أمشي بتكافؤ من طرف للطرف + +19 +00:01:39,020 --> 00:01:42,300 +التاني أو أعملها two parts وطبعاً هذا احنا اللي + +20 +00:01:42,300 --> 00:01:45,720 +بنفضله لأنه عملية ال one part دي بدأ دقة شديدة + +21 +00:01:45,720 --> 00:01:49,740 +لأنه أي خطأ استخدمنا فيه علاقة حطينا تكافؤ وليس + +22 +00:01:49,740 --> 00:01:52,970 +التكافؤ بيكون احنا إيش اخسرنا نص البرهاناخسرنا نص + +23 +00:01:52,970 --> 00:01:56,130 +البرعان لذلك انا هستخدم ايضا two parts proof اه + +24 +00:01:56,130 --> 00:02:05,510 +فهنا solutions او solution we will use two parts + +25 +00:02:05,510 --> 00:02:09,450 +proof اه + +26 +00:02:09,450 --> 00:02:13,870 +فنبدأ بالجزء الاول الجزء الاول من هذه الى هذه ممكن + +27 +00:02:13,870 --> 00:02:18,170 +اكتبها بشكل كامل او اختصارا ممكن احط السهم الى + +28 +00:02:18,170 --> 00:02:22,840 +اليميناختصارا متعرف عليه اه فانا بدي اعمل اتجاه + +29 +00:02:22,840 --> 00:02:27,140 +الاول من اليسار لليمين من اليسار لليمين ممكن + +30 +00:02:27,140 --> 00:02:30,900 +اكتبها بشكل كامل لو حبينا نختصر هذا العرف متعرف + +31 +00:02:30,900 --> 00:02:34,440 +عليه تمام فانا بدي اعمل من الاولة لتانية جملة + +32 +00:02:34,440 --> 00:02:38,140 +شرطية اشحب ده افترض ان الشرط صحيح فهقول له assume + +33 +00:02:40,770 --> 00:02:45,290 +A B أو A cross الـ B that ممكن نكتبها ممكن ما + +34 +00:02:45,290 --> 00:02:51,170 +نكتبهاش ماشي الحل بمشي A cross ال B تساوي فاي + +35 +00:02:51,170 --> 00:03:00,310 +المطلوب جواب الشرط we want to prove A + +36 +00:03:00,310 --> 00:03:08,970 +تساوي فاي او B تساوي فاأه فهي الجملة فكتناها + +37 +00:03:08,970 --> 00:03:13,110 +اعتبرناها كالعادة ممكن نفرض إن الشرط صحيح مطلوب + +38 +00:03:13,110 --> 00:03:16,370 +جواب الشرط كما هو واضح جواب الشرط عبارة عن + +39 +00:03:16,370 --> 00:03:21,190 +statement فيها or عشان أثبتها إنها true لازم أثبت + +40 +00:03:21,190 --> 00:03:23,630 +على أقل واحدة فيهم إنها true زي ما اتعلمنا في + +41 +00:03:23,630 --> 00:03:26,030 +المنطقة يعني كل الكلام زي ما تشايفين كل اللي + +42 +00:03:26,030 --> 00:03:31,210 +اتعلمناه بنطبقهطيب مين أثبت فيهم؟ ممكن يعملي حيرة + +43 +00:03:31,210 --> 00:03:38,070 +مؤقتا او كيف اعمل ممكن نريح حالنا و نعمل prove by + +44 +00:03:38,070 --> 00:03:41,990 +contradiction ننفي المطلوب ننفي المطلوب فخلينا + +45 +00:03:41,990 --> 00:03:45,510 +نشتغل بعد الصورة و هي طبعا لأن في جميع الأحوال انا + +46 +00:03:45,510 --> 00:03:50,310 +بدي أثبت ان ال A تصوّي فيأو الـ B تساوي فاي وإثبات + +47 +00:03:50,310 --> 00:03:54,150 +إن مجموعة ما فاي من أفضل الطرق إياش اللي هو prove + +48 +00:03:54,150 --> 00:03:57,610 +by contradiction طب أنا بدل منفذ جزء منها وعندي + +49 +00:03:57,610 --> 00:04:00,850 +احتمالين لأ بنفيها كلها مرة واحدة فخلّيني أقول له + +50 +00:04:00,850 --> 00:04:05,130 +assume not + +51 +00:04:07,130 --> 00:04:13,110 +A تساوي فاي او B تساوي فاي اه اه اه اه اه اه اه اه + +52 +00:04:13,110 --> 00:04:13,490 +اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه + +53 +00:04:13,490 --> 00:04:14,190 +اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه + +54 +00:04:14,190 --> 00:04:15,390 +اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه + +55 +00:04:15,390 --> 00:04:15,470 +اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه + +56 +00:04:15,470 --> 00:04:16,710 +اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه + +57 +00:04:16,710 --> 00:04:24,330 +اه اه اه اه اه اه اه اه اه + +58 +00:04:24,330 --> 00:04:25,650 +اه اه + +59 +00:04:30,290 --> 00:04:35,970 +في أي استفسار والبداية ليش عملناها؟ فمهم جداً طبعا + +60 +00:04:35,970 --> 00:04:39,510 +استخدام الديمورجان لما نفيت الـor صارت and ونفينا + +61 +00:04:39,510 --> 00:04:43,750 +الجزئين تمام الآن صار عندي أشياء ممكن أنا أشتغل + +62 +00:04:43,750 --> 00:04:47,110 +فيها طبعا أنا بدي أوصل ل contradiction ماذا يعني + +63 +00:04:47,110 --> 00:04:51,230 +إن مجموعة ما ليست فارغة على الأقل فيها عنصر فالآن + +64 +00:04:51,230 --> 00:04:56,210 +من هذا الكلام implies there exist X such that X + +65 +00:04:56,210 --> 00:05:01,040 +تنتمي للـA لأن الـA بتسوي شفارة andthere exist ايش + +66 +00:05:01,040 --> 00:05:06,060 +نقول؟ X برضه؟ لا نغير الاسم ليش بنغير؟ لأنه أنا + +67 +00:05:06,060 --> 00:05:10,040 +بقول في عنصر ما هو X لو قلت كمان مرة X أنا فرضت أن + +68 +00:05:10,040 --> 00:05:13,140 +عنصرهم متساويين وده مش بالضروري مين بيقولك معلومات + +69 +00:05:13,140 --> 00:05:16,160 +انه؟ أنا بقول هذه الغرفة مش فاضية فيها طالبة + +70 +00:05:16,160 --> 00:05:18,740 +والغرفة التانية ممكن مش فاضية ممكن فيها طالب خلينا + +71 +00:05:18,740 --> 00:05:21,360 +نروح ع شجرة الطلاب مش بالضروري تكون نفسها لأنه + +72 +00:05:21,360 --> 00:05:25,440 +موجود فيها حد واضح؟أه فتمام فإن there exists Y + +73 +00:05:25,440 --> 00:05:29,820 +such that Y تنتمي للـ B طبعا من تعريف الـ Phi يعني + +74 +00:05:29,820 --> 00:05:34,020 +definition of Phi إيش معناه الفارغ مافيه عنصر طب + +75 +00:05:34,020 --> 00:05:38,700 +غير الفارغ الأقل فيها عنصر ممتاز احنا بندور على + +76 +00:05:38,700 --> 00:05:43,540 +contradiction بندور على contradiction ممتاز عندي X + +77 +00:05:43,540 --> 00:05:46,640 +في الـ A و Y في الـ B الـ X الزوج و الـ B بتكون في + +78 +00:05:46,640 --> 00:05:48,760 +الـ Cartesian product لإن بحاول أشوف الموقعيات و + +79 +00:05:48,760 --> 00:05:53,780 +أن أدور على contradiction فهذا معناته أن X Yتنتمل + +80 +00:05:53,780 --> 00:05:57,420 +الـ A cross الـ B طبعا Contradiction لأن هذا + +81 +00:05:57,420 --> 00:06:01,520 +معناته أنه ليست Phi فهذا معناته أن A cross الـ B + +82 +00:06:01,520 --> 00:06:05,460 +لا تساوي Phi طبعا هذا تعريف الـ Cartesian product + +83 +00:06:05,460 --> 00:06:08,500 +او + +84 +00:06:08,500 --> 00:06:14,040 +هذا تعريف الـ Phi طبعا وصلنا لأنه قال ليش؟ بيسووا + +85 +00:06:14,040 --> 00:06:14,900 +Phi Contradiction + +86 +00:06:18,420 --> 00:06:22,300 +فالبرهان انتهى، ايش معناته؟ انه ايش؟ هذه الـ A + +87 +00:06:22,300 --> 00:06:25,640 +فالس، اذا عكسها، اللي هو من غيرنا فيه، اترو فممكن + +88 +00:06:25,640 --> 00:06:31,280 +نعلق هنا، هذا ليس ضروري، thus A تساوي فاي او B + +89 +00:06:31,280 --> 00:06:37,140 +تساوي فاي فالكارتيس يعني بيكونش فاي إلا إذا واحدة + +90 +00:06:37,140 --> 00:06:39,980 +على أقل فاي، عملنا اتجاه واحد، بدنا نعمل الآن + +91 +00:06:39,980 --> 00:06:43,500 +لاتجاه التاني، فضلوا، لو سمحتوا + +92 +00:06:48,850 --> 00:06:54,330 +صحيح اه طبعا احنا انا مش .. مش .. مش نفسي اللي + +93 +00:06:54,330 --> 00:06:56,950 +بعملها بس implies انا من اول بديت implies في مرحلة + +94 +00:06:56,950 --> 00:07:02,390 +ما اه طبعابس تعليق بسيط طبعا أنا معنى انه اوصل ل + +95 +00:07:02,390 --> 00:07:04,930 +contradiction فانا مش ضروري ان انا امشي تكافأ ومش + +96 +00:07:04,930 --> 00:07:07,870 +بدي اسوي مجموعات فانا مابديش اقعد ادقق واشوف + +97 +00:07:07,870 --> 00:07:10,190 +انهمين تكافأ ومن ال .. انا بدي اوصل ل ال + +98 +00:07:10,190 --> 00:07:13,590 +contradiction المهم اوصله بأي طريقة بتكافأ و بين + +99 +00:07:13,590 --> 00:07:16,230 +ال lies بهمنيش المهم اوصله ان هي دي تكونت ايه في + +100 +00:07:16,230 --> 00:07:18,930 +عندي بي and not بي is true وها دي ايش مستحيلة + +101 +00:07:18,930 --> 00:07:22,110 +واضحة؟ اه فعشان ايك انا مادققتش كتير لو بدي ادقق + +102 +00:07:22,110 --> 00:07:24,790 +بدي اشوف لكن انا مش معنى في هذا الكلام فهذا دايما + +103 +00:07:24,790 --> 00:07:29,610 +احنا مزالإحنا عشان هيك إحنا لما نعمل برهان في if + +104 +00:07:29,610 --> 00:07:32,270 +and only if نمشي في الوهم نكون دقيقين لكن هنا لما + +105 +00:07:32,270 --> 00:07:34,690 +نمشي باتجاه واحد بيقول فيه شوية حرية فيه أكتر + +106 +00:07:34,690 --> 00:07:38,690 +والرؤية أوضح والرؤية أيش فيها مرونة وفيها سعة + +107 +00:07:38,690 --> 00:07:41,790 +وبدائي المتعددة، المهم إنه أنا بمشي و بقدر أستنتج + +108 +00:07:41,790 --> 00:07:44,290 +إن الخطوة الأولى true واللي بعدها بقدر أجيبها + +109 +00:07:44,290 --> 00:07:47,750 +بطريقة منطقية رياضية نطرو وهاكذا، فأنا مش معنى + +110 +00:07:47,750 --> 00:07:48,810 +كتير بالتعريف + +111 +00:07:52,090 --> 00:07:57,930 +طبعاً هذا على خاصة في أي سؤال تعليق آخر تمام الآن + +112 +00:07:57,930 --> 00:08:01,450 +بدنا نمشي لاتجاه التاني الجزء التاني من البرهان + +113 +00:08:01,450 --> 00:08:05,190 +طبعا احنا ممكن نحلل و نشوف أنه وين فيه تكافأة بس + +114 +00:08:05,190 --> 00:08:08,670 +مش هيفيدنا مدلاش نضيع وجهتيه الآن الجزء التاني من + +115 +00:08:08,670 --> 00:08:11,850 +البرهان لاتجاه التاني ممكن نكتبه صهم إلى اليسار + +116 +00:08:11,850 --> 00:08:15,220 +يعني بدنا نمشي من اليمين إلى اليساراختصارا بدل ما + +117 +00:08:15,220 --> 00:08:18,260 +اكتبله اليمين implies اليسار بحط الـ sign بهذا + +118 +00:08:18,260 --> 00:08:22,240 +الشكل متعرف عليه تمام وين ال statement هنبدأ نفضل + +119 +00:08:22,240 --> 00:08:28,440 +انفترضاش ان اليمين true فهنقول لها الآن assume a + +120 +00:08:28,440 --> 00:08:37,100 +تساوي five او b تساوي five ايش المطلوب؟ we want to + +121 +00:08:37,100 --> 00:08:44,630 +prove that a cross ال b تساوي fiveفالعكس الآن + +122 +00:08:44,630 --> 00:08:49,790 +مشينا بالاتجاه العكسي هنا كنا بدأنا أن هذا معطى و + +123 +00:08:49,790 --> 00:08:54,270 +هذا بطلوب الآن نعكس الترتيب برضه سؤال تقليدي + +124 +00:08:54,270 --> 00:08:57,690 +مجموعة بدأت بيثبت أنها Phi أفضل طريقة approved by + +125 +00:08:57,690 --> 00:09:00,750 +contradiction أفترض أنها ليست Phi فحنقوله الآن + +126 +00:09:00,750 --> 00:09:08,610 +assume A cross B لا تساوي Phi approved by + +127 +00:09:08,610 --> 00:09:13,510 +contradictionContradiction طريقة فعالة وهذا هو + +128 +00:09:13,510 --> 00:09:17,910 +المعتمد في الغالب فهي الطريقة الأفضل عشان أثبت أن + +129 +00:09:17,910 --> 00:09:20,630 +المجموعة تنفع ايش معناه أنها مش فاية؟ فيها علاقة + +130 +00:09:20,630 --> 00:09:25,550 +العنصر بس العناصر دي أزواج مرتبة فهذا يؤدي there + +131 +00:09:25,550 --> 00:09:31,670 +exist XY تنتمي للـA cross الـB طبعا ممكن اكتبها + +132 +00:09:31,670 --> 00:09:35,050 +بالشكل there exist XY و XY تنتمي كله صح بس أتوقع + +133 +00:09:35,050 --> 00:09:39,230 +مفهومة فطبعا هذا تعريف الـFile Definition of File + +134 +00:09:41,120 --> 00:09:44,200 +أه فطبعا هنا هي تعريف لأنه زي ما تاوي شوفنا احنا + +135 +00:09:44,200 --> 00:09:47,360 +استخدمنا بالاتجاهين يعني إذا هذه صح هذه صح و العكس + +136 +00:09:47,360 --> 00:09:49,980 +صحيح فانا ممكن أحط تكافو هنا ليش؟ لأن تاوي استخدمت + +137 +00:09:49,980 --> 00:09:54,560 +قولت .. قولت إنه X Y تنتمي implies ليست Phi و ليست + +138 +00:09:54,560 --> 00:09:57,220 +Phi ليش؟ برضه implies هذه، فإذا هي ممكن نمشي + +139 +00:09:57,220 --> 00:09:59,940 +بالاتجاهين، إذا ان هي تكافو فعلا لأنه تعريفمافيش + +140 +00:09:59,940 --> 00:10:02,900 +اختلاف، ممتاز، آه، الآن أنا واقعي بدي أدوّل على + +141 +00:10:02,900 --> 00:10:06,220 +contradiction وعندي معطيات، هدولة معطيات، إيش ممكن + +142 +00:10:06,220 --> 00:10:09,820 +أعمل؟ أفسر الكارتيسيا، آه، أفسر الكارتيسيا أو اللي + +143 +00:10:09,820 --> 00:10:12,760 +هو تعريف الكارتيسيا فده implies اللي هو فيه عندي + +144 +00:10:12,760 --> 00:10:18,160 +أنهيش X تنتمي للـA وY تنتمي للـB و there exists X + +145 +00:10:18,160 --> 00:10:25,570 +وY طبعاً هذا تعريف definition of A cross الـBطب + +146 +00:10:25,570 --> 00:10:29,230 +هذا ايش معناته؟ معناته ان A لا تساوي في و هذا + +147 +00:10:29,230 --> 00:10:33,250 +معناته ان ب لا تساوي في برضه تعريف الفي مرة تانية + +148 +00:10:33,250 --> 00:10:37,980 +definition of فيطيب وين؟ وصلنا لـ Contradiction؟ + +149 +00:10:37,980 --> 00:10:44,240 +نعم بي and كيو و إيش؟ و هنا not بي or not كيو لو + +150 +00:10:44,240 --> 00:10:47,580 +عملنا disjunction سولوجزم بطلع Contradiction على + +151 +00:10:47,580 --> 00:10:51,380 +طول بس هي واضحة فالانواعي بيقولي مثلا بي or كيو و + +152 +00:10:51,380 --> 00:10:54,620 +هذي true لحالها اذا not بي بيقول إيش يكون؟ بيكون + +153 +00:10:54,620 --> 00:10:58,430 +إيش كيو و كيو not كيو Contradictionفممكن أعملها + +154 +00:10:58,430 --> 00:11:01,710 +بأكتر من طريقة، لكن مستحيل أدوة الأربع .. + +155 +00:11:01,710 --> 00:11:04,390 +الـDominant يكونوا مع بعض true، لا رغم أن هذا + +156 +00:11:04,390 --> 00:11:07,930 +بينها or، لأنه ممكن أنا .. طبعا لأن ممكن أعمل هنا + +157 +00:11:07,930 --> 00:11:11,130 +simplification، إذا حبينا نكتب بالتفصيل، طبعا هذا + +158 +00:11:11,130 --> 00:11:16,030 +implies .. خلينا ناخد واحدة، not file، طيب ونعمل + +159 +00:11:16,030 --> 00:11:22,950 +هنا conjunction and إيش؟A تساوي فاى او B تساوي فاى + +160 +00:11:22,950 --> 00:11:25,190 +اذا حبينا نعمل بالتفصيل بس ال contradiction واصلة + +161 +00:11:25,190 --> 00:11:28,370 +اللي مش واضح اقل بنوضح هلجيت هذه كلها true واضحة + +162 +00:11:28,370 --> 00:11:32,850 +اه فهذه كلها true اذا اي جزء منها true طيب ال B + +163 +00:11:32,850 --> 00:11:37,190 +اللي هي false و B or Q لازم ال Q تكون true فده ايش + +164 +00:11:37,190 --> 00:11:45,770 +بيقدى انه B تساوي فاىالفصل المنطقي مظبوط هي بي or + +165 +00:11:45,770 --> 00:11:49,330 +كيو and not بي أو not كيو كله صح تفرج لأنه a في + +166 +00:11:49,330 --> 00:11:56,090 +إيش commutative واضحة؟ واضحة؟ بكل بساطة عندك بي or + +167 +00:11:56,090 --> 00:11:58,830 +كيو بدنا نقول على الأقل واحدة true إذا واحدة false + +168 +00:11:58,830 --> 00:12:02,450 +لازم التانية تكون true طيب ال بي فاي و ال بي + +169 +00:12:02,450 --> 00:12:04,910 +لاتساو فاي بلّا أنها true إذا كانت contradiction + +170 +00:12:08,440 --> 00:12:11,600 +يعني إذا ما شوفناش مباشرة بنشوفها بهذا التفصيل + +171 +00:12:11,600 --> 00:12:18,120 +فإذا البرهان انتهى إذا ما فرضناه عكس هو الصحيح + +172 +00:12:18,120 --> 00:12:23,620 +اللي هو تبع ال proof a cross ال b تساوي five العكس + +173 +00:12:23,620 --> 00:12:31,000 +هو الصحيح متابعين؟ حتى + +174 +00:12:31,000 --> 00:12:37,930 +وين؟hand اه ممتاز و بتطلع على طول contradiction + +175 +00:12:37,930 --> 00:12:41,210 +صحيح صحيح اه دي ممكن اه اه ولا addition ولا شي + +176 +00:12:41,210 --> 00:12:45,090 +ممتاز اه تطلع النفي برا بتصير عكس هذي تمام اه + +177 +00:12:45,090 --> 00:12:52,270 +ممتاز أسهل صحيح ال حلين + +178 +00:12:52,270 --> 00:12:56,390 +الطرفينيعني بدك السؤال الأصلي لأنه if and و ليف + +179 +00:12:56,390 --> 00:13:01,090 +ممكن ممكن بس أنا دايما اللي تكافئ بده دقة شديدة أه + +180 +00:13:01,090 --> 00:13:04,430 +لكن هيك الأمور واضحة و احنا ماشيين و بتفيه تثالث + +181 +00:13:04,430 --> 00:13:07,870 +المنطقي و احنا ماشي متأكدين منه وماشيين فيه ممكن + +182 +00:13:07,870 --> 00:13:15,850 +خليني أشوف مثال جديد خليني + +183 +00:13:15,850 --> 00:13:16,910 +أشوف مثال جديد + +184 +00:13:23,540 --> 00:13:29,580 +approved or disapproved الـ power للكارتيسيان ال + +185 +00:13:29,580 --> 00:13:33,120 +product بيساوي الكارتيسيان ال product لل power ايش + +186 +00:13:33,120 --> 00:13:40,560 +رايكوا true ولا false؟ false ليش؟ + +187 +00:13:40,560 --> 00:13:44,140 +ليش؟ يعني انت .. يعني مش هي يا .. يا .. يا عبيد يا + +188 +00:13:44,140 --> 00:13:48,520 +أسود وبالصدفة نعم + +189 +00:13:51,260 --> 00:13:55,660 +بشكل عام الـ Cartesian product بتدّينا مجموعة + +190 +00:13:55,660 --> 00:14:01,360 +كبيرة وال power بتقول 2 أُس عدد عناصر المجموعة + +191 +00:14:01,360 --> 00:14:05,600 +يعني على سبيل المثال لو كانت ال A فيها أنصر واحد + +192 +00:14:06,300 --> 00:14:11,140 +والـ B فيها عنصر واحد الـ Cartesian ايش بيكون؟ + +193 +00:14:11,140 --> 00:14:14,800 +بيكون واحد، بس طيب ال power of H تكون اتنين و أس + +194 +00:14:14,800 --> 00:14:19,000 +واحد اتنين طيب نمشي للتانية ال power للواحد اتنين + +195 +00:14:19,000 --> 00:14:22,500 +و درب اتنين أربعة فإذا في اختلاف في الاعداد + +196 +00:14:22,500 --> 00:14:26,740 +فالمثال واحد عكسي مباشرة فهذا المثال عكسي فالعملية + +197 +00:14:26,740 --> 00:14:29,580 +مختلفة فإذا أول شيء false طبعا ال proof or + +198 +00:14:29,580 --> 00:14:33,380 +disbelief بدناهياش counter example المثال التالت + +199 +00:14:34,300 --> 00:14:38,100 +Solution أول شيء false The statement false بدنا + +200 +00:14:38,100 --> 00:14:43,080 +نديله مثال أو counter example مثال + +201 +00:14:43,080 --> 00:14:51,440 +عكسي أه يمكن زي ما حكيت let A تساوي من عنصر واحد و + +202 +00:14:51,440 --> 00:14:57,260 +ال B تساوي من عنصر واحد then أه بدي أحسب A cross + +203 +00:14:57,260 --> 00:15:01,320 +ال B فيها بس عنصر واحد اللي هو زوج مرتب واحد و + +204 +00:15:01,320 --> 00:15:09,930 +اتنينبنكتب بشكل دقيق فإذا and بالتالي power of a + +205 +00:15:09,930 --> 00:15:15,890 +cross b من ما يتكون من الـ Phi و من هذه المجموعة + +206 +00:15:15,890 --> 00:15:18,570 +فقط لأن المجموعة من عصر واحد كنا فيها اتنين و من a + +207 +00:15:18,570 --> 00:15:23,910 +cross b هذا الكلام طبعا ال a cross b لا تنتمي + +208 +00:15:23,910 --> 00:15:29,180 +للتانية لكن power of aبدي أعملها مرة واحدة cross + +209 +00:15:29,180 --> 00:15:32,640 +power of B بتساوي power الـ A عبارة عن Phi و A + +210 +00:15:32,640 --> 00:15:37,200 +مظبوط لأنه برضه عنصر واحد و power ال B Phi و B و + +211 +00:15:37,200 --> 00:15:41,200 +ال Phi مكتوبة بكتبهاش كمان مرة فاش B لأ لسه بيضرب + +212 +00:15:41,200 --> 00:15:46,860 +لأ مش اتحاد Cartesian إذا بدي أكتبها كمان مرة Phi + +213 +00:15:46,860 --> 00:15:58,170 +of B و تساوي بتساوي Phi Phi و Phi و B و Phi of Bو + +214 +00:15:58,170 --> 00:16:07,270 +بعدين A و Phi و B و A و B هاي الأربع عناصر لأ صح + +215 +00:16:07,270 --> 00:16:10,950 +بس مجموعة كمجموعة ال A هي مين هي مجموعة الواحد و + +216 +00:16:10,950 --> 00:16:14,190 +ال B مجموعة التانية فانا يا بكتب ال A يا بكتب + +217 +00:16:14,190 --> 00:16:17,450 +الطرف هذا هي ال A كتابتها من الطرف اليسار صح + +218 +00:16:17,450 --> 00:16:20,470 +كتابتها من الطرف اليمين صح فدي ال A فطبعا واضح أنه + +219 +00:16:20,470 --> 00:16:26,270 +A غير متساوي فطبعا لا تساوي power ال A cross ال B + +220 +00:16:27,740 --> 00:16:32,960 +لأن هذه المجموعة A×B لا تنتمي لها، مختلفة تماما، + +221 +00:16:32,960 --> 00:16:37,020 +مختلفة تماما، فإذا الـ Power لا تتوزع على الـ + +222 +00:16:37,020 --> 00:16:42,190 +Cartesian Productأه فهذه نهاية ال section هذا فهنا + +223 +00:16:42,190 --> 00:16:44,970 +كانت مقدمة عن الـ Cartesian product عشان ندخل + +224 +00:16:44,970 --> 00:16:49,030 +بموضوعنا الرئيسي الأول يمكن الشبطر عنوانه + +225 +00:16:49,030 --> 00:16:53,250 +relations and functions العلاقات والدوال فهنبدأ + +226 +00:16:53,250 --> 00:16:57,530 +بالموضوع الرئيسي وهو الأول ال relations العلاقات + +227 +00:16:57,530 --> 00:16:58,650 +العلاقات + +228 +00:17:01,050 --> 00:17:05,830 +تعريف العلاقات تعريف بسيط جدا و أرجو أن نفهمه بهذه + +229 +00:17:05,830 --> 00:17:09,610 +البساطة خلينا بس نبدأ بمقدمة وبعدين هنحط التعريف + +230 +00:17:09,610 --> 00:17:15,910 +بشكل رسمي الأمر بسيط جدا طبعا باعتماد اعتماد رئيسي + +231 +00:17:15,910 --> 00:17:20,630 +على الأزواج المرتبةطبعاً أنا في عندي بدي أجيب + +232 +00:17:20,630 --> 00:17:24,450 +علاقة بين عنصرين ودول العنصرين بنتموا لمجموعتين + +233 +00:17:24,450 --> 00:17:29,370 +فانا الصورة النمطية في عندنا مجموعة ما A وفي عندنا + +234 +00:17:29,370 --> 00:17:36,230 +مجموعة ما B هناخد عنصر small a من capital A وعنصر + +235 +00:17:36,230 --> 00:17:40,990 +small b من المجموعة B ونعمل بينهم علاقة ونعمل + +236 +00:17:40,990 --> 00:17:46,940 +بينهم علاقة ما نربطهم مع بعض نربطهم مع بعضمن كلمة + +237 +00:17:46,940 --> 00:17:50,820 +الـ relation أشهر إيش نسمي إيش نرمزها بالرمز R لـ + +238 +00:17:50,820 --> 00:17:54,780 +relation فبنعمل relation R نتحدث عن علاقة فهو + +239 +00:17:54,780 --> 00:17:59,020 +بيقول لي given sets A و B not necessarily distinct + +240 +00:17:59,020 --> 00:18:01,480 +طبعا أنا بدي أجيب علاقة بين مجموعتين مش بالضروري + +241 +00:18:01,480 --> 00:18:04,400 +تكون المجموعتين مختلفتين أنا ممكن أجيب علاقة من + +242 +00:18:04,400 --> 00:18:07,800 +مجموعة عناصرة نفسها زي احنا متعودين أنه مثلا إيش + +243 +00:18:07,800 --> 00:18:12,530 +أجيب اللي هو علاقة أقارنالعداد مع نفسها مثلا ممكن + +244 +00:18:12,530 --> 00:18:15,770 +استساوية علاقة و هكذا مش بالضروري يكون المجموعتين + +245 +00:18:15,770 --> 00:18:18,610 +اللي بدي أجيب علاقة بين عناصرهم يكونوا مختلفتين أي + +246 +00:18:18,610 --> 00:18:20,970 +.. أي مجموعتين بقدر أشتغلهم بما فيهم المجموعتين + +247 +00:18:20,970 --> 00:18:26,330 +المتساويتين المتطابقتين اه we say that an element + +248 +00:18:26,330 --> 00:18:30,270 +small a of the set capital A is related to another + +249 +00:18:30,270 --> 00:18:33,850 +element زي ما عملنا الصورة small b وهو عنصر من + +250 +00:18:33,850 --> 00:18:37,220 +المجموعة capital B by a relation Rطبعًا فاحنا + +251 +00:18:37,220 --> 00:18:40,700 +بنتحدث إيه أزاي واضح إنه بنعمل A وB دايما في بتحدث + +252 +00:18:40,700 --> 00:18:45,060 +عن عنصرين فبنتحدث عن أزواج مرتبة و بزاد أقول علاقة + +253 +00:18:45,060 --> 00:18:48,520 +من إلى في ترتيب آه العلاقة من المجموعة الأولى إلى + +254 +00:18:48,520 --> 00:18:51,980 +المجموعة التانية فبيدنا زوج مرتب فاحنا بنتحدث عن + +255 +00:18:51,980 --> 00:18:56,480 +أزواج مرتبة A وB فهنا النقطة الأساسية الشاهدة من + +256 +00:18:56,480 --> 00:19:01,040 +الكلام إنه تعريف العلاقات بيعتمد على الـ Cartesian + +257 +00:19:01,040 --> 00:19:03,740 +product على الضرب الـDcardأه، فبقول إن هي + +258 +00:19:03,740 --> 00:19:06,420 +Mathematical .. Mathematical .. Mathematical + +259 +00:19:06,420 --> 00:19:11,100 +Definition of a relation can be precisely given in + +260 +00:19:11,100 --> 00:19:13,960 +terms of ordered pairs فاحنا التعريف الرياضي + +261 +00:19:13,960 --> 00:19:19,360 +للعلاقة هنعرفه بدلالة مين Its أزواج المرتبة، يعني + +262 +00:19:19,360 --> 00:19:22,660 +طبعا إيش، بدلالة الـ Cartesian product مين بيولد + +263 +00:19:22,660 --> 00:19:25,480 +الأزواج المرتبة؟ الـ Cartesian product للمجموعة + +264 +00:19:25,480 --> 00:19:29,480 +فهذه هي نقطة البداية فإذا إحنا هنعرف ال relations + +265 +00:19:29,480 --> 00:19:34,990 +بدلالة الأزواج المرتبةعلاقة بين مجموعتين يعني بدنا + +266 +00:19:34,990 --> 00:19:38,470 +كارتيسن ال product للمجموعتين ناخد الأزواج المرتبة + +267 +00:19:38,470 --> 00:19:42,990 +ونتحدث عن relation ما عن ال relation ما ما هي ال + +268 +00:19:42,990 --> 00:19:48,450 +relation تعريف بسيط جدا فالعملية واسعة وال + +269 +00:19:48,450 --> 00:19:52,550 +relations احتمالاتها متعددة جدا ال relation are + +270 +00:19:52,550 --> 00:19:56,980 +سوف اشوف التعريف fromasset capital A to asset + +271 +00:19:56,980 --> 00:20:00,760 +capital B اذا متحدث عن علاقة بين مجموعتين من الى + +272 +00:20:00,760 --> 00:20:06,440 +ترتيب مهم اه ايش ايه ايش هي ليست الا مجموعة جزئية + +273 +00:20:06,440 --> 00:20:09,840 +من ال Cartesian product فانا هي عندي ال A و ال B + +274 +00:20:09,840 --> 00:20:16,530 +اروح اجيب A cross ال Bواخد أي subset من الـ + +275 +00:20:16,530 --> 00:20:21,270 +Cartesian product يعتبر علاقة، يعتبر علاقة، فإذاً + +276 +00:20:21,270 --> 00:20:25,650 +ايش؟ هذه بكل بساطة أي subset من الـ Cartesian + +277 +00:20:25,650 --> 00:20:30,730 +product of A and B is a relation from A to Bهو فده + +278 +00:20:30,730 --> 00:20:33,990 +تعريف بسيط جدا فازن فيه ان اي اش ات اي ا كيب دي + +279 +00:20:33,990 --> 00:20:36,870 +عرف relation بكل بساطة خدي Cartesian product وخدي + +280 +00:20:36,870 --> 00:20:39,390 +subset من ال Cartesian product اي subset بتديني + +281 +00:20:39,390 --> 00:20:42,650 +relation مافيش ولا شرط الا ان يكون subset من + +282 +00:20:42,650 --> 00:20:46,430 +Cartesian product فتعريف بسيط جدا لذلك العملية + +283 +00:20:46,430 --> 00:20:50,450 +واسعة لإن مافيش قيود كتيرة مافيش قيود كتيرة ايه + +284 +00:20:50,450 --> 00:20:55,130 +السؤال؟قبل ما نبدأ بالأمثلة بس مجرد اللي هو بعض + +285 +00:20:55,130 --> 00:20:59,470 +العلاقات طبعا احنا عندنا الـR subset من A cross + +286 +00:20:59,470 --> 00:21:03,550 +الـB، اذا عناصر relation أزواج مرتبة، أزواج مرتبة، + +287 +00:21:03,550 --> 00:21:08,510 +اذا احنا بنتحدث عن A وB تنتمي للـR، معناته ان الـA + +288 +00:21:08,510 --> 00:21:12,870 +لعلاقة مع الـB يعني A وB تنتمي للـR، طبعا هذه + +289 +00:21:12,870 --> 00:21:16,990 +طريقة الكتابة، في طريقة أخرى ممكن نكتب بادئ وكافئ + +290 +00:21:16,990 --> 00:21:22,630 +ان الـA is R related to Bis R related to B؟ طبعا + +291 +00:21:22,630 --> 00:21:26,290 +يمكن أشهر مثال على علاقات علاقة التساوي نقول إنه + +292 +00:21:26,290 --> 00:21:30,650 +عدد يساوي عدد A إذا كانوا متطابقين مثلا فإذا نكتب + +293 +00:21:30,650 --> 00:21:37,870 +A تساوي B مثلا هذا علاقة فإذا نكتب ARB هل هي علاقة + +294 +00:21:37,870 --> 00:21:43,010 +تساوي؟هل هي علاقة أصغر من أو علاقة أكبر من أو أي + +295 +00:21:43,010 --> 00:21:45,330 +علاقة بنكتبها ده الشكل أو بنكتبها ده الشكل لأنه + +296 +00:21:45,330 --> 00:21:48,450 +أزواج مرتبة لأنه هي ياش مجموعة جزئية من الـ + +297 +00:21:48,450 --> 00:21:51,750 +Cartesian product فالرمزين متعرف عليهم ممكن أنا + +298 +00:21:51,750 --> 00:21:55,890 +هستخدمها ده أكتر لأنه واضح ومباشر فده بنكتبها طبعا + +299 +00:21:55,890 --> 00:22:01,070 +إيش نقراها؟ A is R related to B A is R related to + +300 +00:22:01,070 --> 00:22:04,570 +B أو إن الـA is related to B اختصارا إذا كانت الـR + +301 +00:22:04,570 --> 00:22:11,140 +واضحة من الصياقنبدأ ببعض الأمثلة و كسياستنا نبدأ + +302 +00:22:11,140 --> 00:22:16,140 +بأمثلة بسيطة نرسخ مفهوم أن ال relation أي subset + +303 +00:22:16,140 --> 00:22:19,420 +من الـ Cartesian product بهذه البساطة فإيش ما + +304 +00:22:19,420 --> 00:22:27,300 +نتصور subset هي relation فهنا مديني مجموعتين A و B + +305 +00:22:27,300 --> 00:22:31,180 +كل مجموعة فيها عنصرين الـ A فيها الحروف الأبجدية A + +306 +00:22:31,180 --> 00:22:35,020 +و B و الـ B فيها الوعد والسلب واحد اه فطبعا انا + +307 +00:22:35,020 --> 00:22:38,210 +لما بدي اجي اه خليني ..أوضح بعض الأمور في هذا + +308 +00:22:38,210 --> 00:22:41,990 +المثال لو جيت على A cross الـ B أكم عنصر فيها + +309 +00:22:41,990 --> 00:22:46,910 +أربعة اللي هي مين؟ A مع الواحد والـ A مع السالب + +310 +00:22:46,910 --> 00:22:50,490 +واحد ومين فيها كمان؟ B مع الواحد والـ B مع السالب + +311 +00:22:50,490 --> 00:22:55,210 +واحد فأي subset من هذه المجموعة تُعتبر relation هو + +312 +00:22:55,210 --> 00:23:01,310 +إيش أخد؟ أخد الـ A و الواحد وأخد الـ B و الواحد + +313 +00:23:01,310 --> 00:23:03,490 +وسأب الباقى، هاي subset، كوّن relation ولا + +314 +00:23:03,490 --> 00:23:07,420 +ماكوّنش، كوّن relationأه ممكن تاخدش ولا إشي الفاي + +315 +00:23:07,420 --> 00:23:11,360 +لإنه إيش قال لي subset قال لي إيش non empty subset + +316 +00:23:11,360 --> 00:23:16,000 +لأ أه هي شوف هذه الصورة الأن نمطي أي subset من A x + +317 +00:23:16,000 --> 00:23:19,340 +B هي relation طب الفاي subset ولا مش subset؟ أه + +318 +00:23:19,340 --> 00:23:22,620 +موضوع طب ال .. ال .. ال A x B كلها برضه subset + +319 +00:23:22,620 --> 00:23:25,340 +relation فدولة أصغر relation هي الفاي و أكبر + +320 +00:23:25,340 --> 00:23:28,600 +relation A x B وما بينهماأي subset تعتبر ال + +321 +00:23:28,600 --> 00:23:31,500 +relation فاحنا دينا مثال لو أخد عنصر واحد هنا ممكن + +322 +00:23:31,500 --> 00:23:34,580 +إش كان عندي أمامي أخد ولا عنصر أخد واحد اتنين + +323 +00:23:34,580 --> 00:23:37,140 +تلاتة أربع هذه الاحتمالات كلها و بجيب كل ال + +324 +00:23:37,140 --> 00:23:40,840 +relations الممكنة بين ال A و بين ال B واضح فهي هي + +325 +00:23:40,840 --> 00:23:46,180 +التعريف بهذه البساطة لأن مافيش شروط مافيش شروط + +326 +00:23:46,180 --> 00:23:51,630 +نشوف كمان مثالفي المثال التاني أخدنا الـ A تساوي B + +327 +00:23:51,630 --> 00:23:56,670 +فبدنا نعمل relation من A ل A من A ل A بنفع؟ بنفع + +328 +00:23:56,670 --> 00:23:59,410 +هو قال لي not necessary this thing ممكن يختلفوا + +329 +00:23:59,410 --> 00:24:03,390 +ممكن ممكن يتطابقوا الـ A و الـ B ممكن كله وارد + +330 +00:24:03,390 --> 00:24:07,430 +فطبعا أنا عندي الـ A تلاتة .. تلاتة عناصر لو عملت + +331 +00:24:07,430 --> 00:24:10,410 +A cross الـ A هيديهم تسعة عناصر بدونش نكتبهم أخدنا + +332 +00:24:10,410 --> 00:24:14,110 +منهم تلاتة بس الواحد واحدو اتنين اتنين و واحد + +333 +00:24:14,110 --> 00:24:17,150 +تلاتة هذي relation نعم لأنه صبست من a cross ال a + +334 +00:24:17,150 --> 00:24:21,170 +واضحة اه فهذهاش relation بدناش طبعا السؤال مش طالب + +335 +00:24:21,170 --> 00:24:25,150 +فيه اشي مش طالب فيه اشي فهذهاش relation لأنه ان ال + +336 +00:24:25,150 --> 00:24:31,330 +a cross ال a إذا بدنا نوضح هي واحد واحدواحد اتنين + +337 +00:24:31,330 --> 00:24:35,090 +وواحد تلاتة اخد اول ادم شاطر ابولاكي وانا اخد + +338 +00:24:35,090 --> 00:24:39,190 +التنين بعدين عندنا اتنين واحد اتنين اتنين واتنين + +339 +00:24:39,190 --> 00:24:41,590 +تلاتة اخد من السطر هذا بس العنصر اللي في النص + +340 +00:24:41,590 --> 00:24:47,910 +بعدين تلاتة واحد وتلاتة اتنين وتلاتة تلاتة اه فهنا + +341 +00:24:47,910 --> 00:24:53,680 +ايش اخد في ال relation اخد الاولوالتالت والخامس + +342 +00:24:53,680 --> 00:24:59,200 +وبس A بس أخد تلت عناصر مافيش معنى subset كله يعتبر + +343 +00:24:59,200 --> 00:25:02,700 +relation فأي subset من ال Cartesian product هي + +344 +00:25:02,700 --> 00:25:06,260 +relation وممكن ال A تساوي بيه ممكن مافيش شي قيول + +345 +00:25:07,950 --> 00:25:11,710 +تمام حالة خاصة إذا الـ A سوّت الـ B ممكن أقول + +346 +00:25:11,710 --> 00:25:14,830 +relation from A to A طب عشان هم متساويين الترتيب + +347 +00:25:14,830 --> 00:25:17,550 +هنا مالهوش أهمية كتير فممكن اختصارا أقول relation + +348 +00:25:17,550 --> 00:25:22,290 +on A لأنه إذا قلت من A لـ A فانا مش ضروري أعرف مين + +349 +00:25:22,290 --> 00:25:24,730 +البداية و يومين النهاية لأنهم واحدة لأنهم متطابقين + +350 +00:25:24,730 --> 00:25:29,810 +فبقول باختصار relation on A لما يتساووا مع بعض لو + +351 +00:25:29,810 --> 00:25:36,530 +قلت من A ل A صحلأ لأ لأ واضح لأ بس هذه حالة خاصة + +352 +00:25:36,530 --> 00:25:41,110 +الترتيب مهم إذا العلاقة من من A ل B بقول من A ل B + +353 +00:25:41,110 --> 00:25:45,570 +ومختلفين طب من A ل A صح المصطلح في مصطلح بديل من A + +354 +00:25:45,570 --> 00:25:49,710 +ل A نعم on A لما تكون من A ل نفسها أه ممكن أستبدل + +355 +00:25:49,710 --> 00:25:52,770 +و أقول on A لكن إذا قلت أنا on A هي العلاقة من A ل + +356 +00:25:52,770 --> 00:25:55,710 +B و ال A و ال B مختلفين لما أقول on A من البداية و + +357 +00:25:55,710 --> 00:25:59,050 +من النهاية توضحش لكن لما يتطبق البداية و النهاية + +358 +00:25:59,050 --> 00:26:03,310 +أذكر واحدة فيه وانتهت لأن هي واحدة المجموعةلو سمحت + +359 +00:26:03,310 --> 00:26:09,270 +اه اه طالع ما هو طالع لما ال A تساوي بيه بيذكروش + +360 +00:26:09,270 --> 00:26:12,410 +اللي واحدة فيهم خلاص صحيح صحيح ما هي بيساووا بعض + +361 +00:26:12,410 --> 00:26:15,990 +بيساووا بعض فما إذا تساووا بيذكروش المجموعتين بقول + +362 +00:26:15,990 --> 00:26:19,130 +ايه و خلاص زي المثال التاني هاي قلت A تساوي واحد + +363 +00:26:19,130 --> 00:26:24,230 +اتنين تلاتة و اين ال B اختفت لأنها بتطبيقها فزي ما + +364 +00:26:24,230 --> 00:26:29,460 +بتطبيقها بسميها شمرتينفكلامك صحيح لكن في العرفة لا + +365 +00:26:29,460 --> 00:26:34,720 +يذكر لأنه هي الـA فهي الـA هي البداية و هي النهاية + +366 +00:26:34,720 --> 00:26:40,000 +فهي بتقوم مقام الـB بس ماذكرش الـB بشكل صريح أي + +367 +00:26:40,000 --> 00:26:46,510 +استفسار؟ أي سؤال آخر؟ واضحة الصورة؟تمام، مفهوم + +368 +00:26:46,510 --> 00:26:49,590 +جديد، فإذا هذه ال relation و أرجو أن يتعامل معها + +369 +00:26:49,590 --> 00:26:53,330 +بهذه البساطة، مافيش قيود إطلاقًا، أي subset من ال + +370 +00:26:53,330 --> 00:26:56,350 +Cartesian product هي relation من A ل B، من ال + +371 +00:26:56,350 --> 00:26:59,570 +Cartesian product of A and B Inverse relation، + +372 +00:26:59,570 --> 00:27:03,390 +العلاقة العكسيةالعلاقة العكسية، لو كان في عندي + +373 +00:27:03,390 --> 00:27:07,590 +علاقة، هل بقدر أعرف ال inverse تبعها؟ وهل كل علاقة + +374 +00:27:07,590 --> 00:27:11,250 +لها inverse ولا لأ؟ احنا في نعرف الدوال، هل كل ده + +375 +00:27:11,250 --> 00:27:14,530 +اللي لها inverse function؟ لأ، هل كل relation لها + +376 +00:27:14,530 --> 00:27:17,980 +inverse relation؟ نعمأي relation اللي هي inverse + +377 +00:27:17,980 --> 00:27:21,300 +relation فش شرط فش شرط زي ما كنا ندوس في التفاضل + +378 +00:27:21,300 --> 00:27:23,600 +بالأ ال functions احنا هنشوف ال function و هنشوف + +379 +00:27:23,600 --> 00:27:26,280 +الشروط هذه مرة تانية لكن بالنسبة لل relation زي ما + +380 +00:27:26,280 --> 00:27:29,340 +هو تعريفها بسيط أيضا كل relation اللي هي inverse + +381 +00:27:29,340 --> 00:27:32,720 +بشكل بسيط جدا خلينا نقرا التعريف و نشوف احنا هي + +382 +00:27:32,720 --> 00:27:36,600 +الصورة عندنا ال R من A لB ال inverse من وين يكون + +383 +00:27:36,600 --> 00:27:42,020 +العكس من B لA فالinverse من B لA هي ال R inverse + +384 +00:27:42,450 --> 00:27:48,570 +إيش بنعمل؟ نقرأ البداية أو مقدمة التعريف let A and + +385 +00:27:48,570 --> 00:27:51,930 +B be two sets not necessarily distinct شايف بيتم + +386 +00:27:51,930 --> 00:27:55,030 +مركزلكوا على النقطة دي أرجو ماحدش يقول إنه لازم + +387 +00:27:55,030 --> 00:27:57,430 +يكونوا مختلفين لما نشوف الـA بتساوي الـB ونقول + +388 +00:27:57,430 --> 00:28:00,090 +إنهم نفس المجموع نلتخم، لأ not necessarily + +389 +00:28:00,090 --> 00:28:03,650 +distinct and let RB a relation from A to B، في + +390 +00:28:03,650 --> 00:28:07,250 +عندي علاقة من A لB، بده يعرف المفهوم الجديد، ده + +391 +00:28:07,250 --> 00:28:11,890 +كله مقدمةthe inverse of a relation R is the + +392 +00:28:11,890 --> 00:28:15,330 +relation معكوث العلاقة أشماله علاقة مش دالة ولا + +393 +00:28:15,330 --> 00:28:18,890 +مجموعة جديدة هو علاقة ومطبعا علاقة دالة لكن العكس + +394 +00:28:18,890 --> 00:28:22,550 +غير صحيح كل علاقة دالة لأنها subset لكن مش كل .. + +395 +00:28:22,550 --> 00:28:26,630 +أسف كل علاقة مجموعة ولكن ليس كل مجموعة علاقة تمام + +396 +00:28:27,680 --> 00:28:32,120 +فإيش الرمز تبعها؟ هذا الرمز كيف بنقرأه؟ R inverse + +397 +00:28:32,120 --> 00:28:36,020 +مش R أسالب واحد تقرأ R inverse فعندي مفهوم inverse + +398 +00:28:36,020 --> 00:28:40,540 +relation الرمز تبعه R inverse هذا الرمز إيش ماله؟ + +399 +00:28:40,540 --> 00:28:44,140 +هي عبارة عن relation من و لا وين؟ من B لA عكس + +400 +00:28:44,140 --> 00:28:51,070 +الترتيب such thatB is related بالعلاقة العكسية by + +401 +00:28:51,070 --> 00:28:55,670 +R inverse to A if and only if A is related to B + +402 +00:28:55,670 --> 00:28:58,850 +يعني إيش بعكس؟ بعكس ذور الـA والـB، بعكس ذور + +403 +00:28:58,850 --> 00:29:02,030 +الترتيب أو بمعنى آخر، بعكس ترتيب الأزواج المرتبة، + +404 +00:29:02,030 --> 00:29:07,130 +بمعنى آخر، ما هي الـR inverse؟ هي BA بشرط إن A وB + +405 +00:29:07,130 --> 00:29:13,680 +تنتمي للـRبمعنى آخر إن عندي أن الـ A والـ B تنتمي + +406 +00:29:13,680 --> 00:29:19,540 +للـ R if and only if بي A تنتمي للـ A اندرس + +407 +00:29:21,930 --> 00:29:25,710 +فما هي باختصار إذا عندي relation في أزواج مرتبة + +408 +00:29:25,710 --> 00:29:28,550 +كيف بدي أجيب الـR inverse؟ أعكس الترتيب، عندي + +409 +00:29:28,550 --> 00:29:32,110 +أزواج مرتبة أعكس الترتيب أجيب الـR inverse، هل في + +410 +00:29:32,110 --> 00:29:35,270 +علاقة ماقدرش أعكس ترتيبها؟ لأ، إذا كل علاقة لها + +411 +00:29:35,270 --> 00:29:37,930 +inverse، و هذا عشان ليش التبسيط، إذا عندي أزواج + +412 +00:29:37,930 --> 00:29:41,370 +مرتبة AB، بعكس الترتيب أكون حسبت مين؟ الـR + +413 +00:29:41,370 --> 00:29:47,360 +inverse، زي ما هنشوف بالأمثلةفالعملية بسيطة جداً + +414 +00:29:47,360 --> 00:29:51,140 +والتعريفات بهذا الشكل هاي مدينا مثال نبدأ بمثال + +415 +00:29:51,140 --> 00:29:55,580 +بسيط مديني مجموعة A تتكون من الواحد والاتنين + +416 +00:29:55,580 --> 00:29:59,120 +ومجموعة B من سالب واحد وزير وسالب اتنين ومديني ال + +417 +00:29:59,120 --> 00:30:03,280 +relation من A لB ايش تعريفها؟ هي واحد سالب واحد + +418 +00:30:03,280 --> 00:30:08,700 +واتنين سالب اتنين بقول يوجد R inverse هذا المثال + +419 +00:30:08,700 --> 00:30:15,590 +الأول لجديد فهي الـ Rهي واحد سالب واحد و اتنين + +420 +00:30:15,590 --> 00:30:22,050 +سالب اتنين بده ال R inverse مافيش أسهل من هيك سالب + +421 +00:30:22,050 --> 00:30:24,410 +واحد و واحد و سالب اتنين + +422 +00:30:27,580 --> 00:30:34,900 +فهذا هو ببساطة ما علينا إلا نعكس الترتيب فإذا كانت + +423 +00:30:34,900 --> 00:30:39,700 +ال 1 سالب 1 في ال R فإعكس الترتيب بيكون سالب واحد + +424 +00:30:39,700 --> 00:30:43,660 +واحد في ال R inverse و هكذا فهذا المفهوم الأساسي + +425 +00:30:45,890 --> 00:30:49,510 +واضح؟ اه طبعا دائما نحن نحط الأمثلة البسيطة ليست + +426 +00:30:49,510 --> 00:30:52,870 +هي هدفنا الرئيسي لكن هي ايش ضروري عشان نفهم ليش + +427 +00:30:52,870 --> 00:30:56,570 +الأصعب نفهم الاش الأكبر الأمثلة الأكبر اه لازم + +428 +00:30:56,570 --> 00:30:59,450 +نفهم هذا الكلام طبعا مش هدفنا انه ندينا و نجيب و + +429 +00:30:59,450 --> 00:31:03,050 +نحسب لكن هدفنا نفهم المفهوم عشان نتعامل معه عشان + +430 +00:31:03,050 --> 00:31:07,090 +نقدر نتعامل معه خليني نشوف زيادة من الأمثلة نشوف + +431 +00:31:07,090 --> 00:31:12,090 +مثال جديد مديني + +432 +00:31:12,090 --> 00:31:18,590 +relationعلاقة قابلية القسمة بقول ليه؟ اوجد R + +433 +00:31:18,590 --> 00:31:23,630 +inverse إذا كانت الـR خلّينا نكتب الـR مثال رقم 2 + +434 +00:31:23,630 --> 00:31:28,550 +الـR هي علاقة من الـnatural number أو الأعداد + +435 +00:31:28,550 --> 00:31:31,510 +الصحيحة الموجبة إلى الأعداد الصحيحة فالـA تساوي N + +436 +00:31:31,510 --> 00:31:38,750 +والـB تساوي Z فهي N M تنتمي للـN across الـZ such + +437 +00:31:38,750 --> 00:31:46,960 +that N divides الـMdivides M يعني إيش؟ الأولى تقسم + +438 +00:31:46,960 --> 00:31:50,920 +التانية أو بمعنى آخر التانية تقبل القسمة على + +439 +00:31:50,920 --> 00:31:54,480 +الأولى فطبعا بدنا ناخد الأول من وين؟ من ال natural + +440 +00:31:54,480 --> 00:31:57,120 +number لو بدنا نجيب أمثلة نفهم العلاقة، مين فيه في + +441 +00:31:57,120 --> 00:32:01,400 +العلاقة؟ واحد واحد تنتمي للعلاقة؟ نعم، لأن الواحد + +442 +00:32:01,400 --> 00:32:05,580 +تقسم الواحد ومين كمان مع الواحد اللي علاقة؟ السالب + +443 +00:32:05,580 --> 00:32:11,070 +واحد، برضه صح ومين كمان؟ الواحد والزيرو، صحوالواحد + +444 +00:32:11,070 --> 00:32:16,870 +و الخمسة في مشكلة كل هذا في الار في الار و الواحد + +445 +00:32:16,870 --> 00:32:19,810 +و الخمسة في الار فهذه بعض الأمثلة من كمان ناخد + +446 +00:32:19,810 --> 00:32:24,790 +مثال أصعب شوية اتنين مع مين؟ مع زاد او ناقص اتنين + +447 +00:32:24,790 --> 00:32:32,200 +مع زاد و ناقص مين؟ اربع في الار و هكذافأرجعوا أن + +448 +00:32:32,200 --> 00:32:36,700 +الخضية تكون نفهم إيش المقصود فالأول يقسم التاني أو + +449 +00:32:36,700 --> 00:32:40,400 +التاني يقبل القسم على الأول الأول عدد صحيح موجب + +450 +00:32:40,400 --> 00:32:43,940 +natural number والتاني أي عدد صحيح الصفر بنفع + +451 +00:32:43,940 --> 00:32:47,380 +الناقص بنفع والموجب بنفع واضحة العلاقة إيش + +452 +00:32:47,380 --> 00:32:53,020 +تعريفها؟ نحسب ال inverse مع بعض solution R inverse + +453 +00:32:53,020 --> 00:32:57,790 +تساوينمشي واحدة واحدة زي ما شوفنا المثال البسيط + +454 +00:32:57,790 --> 00:33:01,970 +لنتطور ال gate هذي كانت علاقة من N ل Z إيش هتصير؟ + +455 +00:33:01,970 --> 00:33:07,450 +من Z ل N فهتصير من Z across ال N بدو ينكس الترتيب + +456 +00:33:07,450 --> 00:33:13,570 +such that إيش نعمل؟ M N تان تامي such that + +457 +00:33:13,570 --> 00:33:22,470 +ماتغيروش التعريف زي ما هي نشوف ليش such that N + +458 +00:33:22,470 --> 00:33:29,610 +divides ال Mنشوف ليش هذا الكلام صحيح تمام بس انتبه + +459 +00:33:29,610 --> 00:33:36,660 +ان الدور هنا اختلف فيالعلاقة الأصلية لو بنفهمها + +460 +00:33:36,660 --> 00:33:41,380 +طبعا احنا هذا هو الأصل انه نحاول نحيد الرموز شوية + +461 +00:33:41,380 --> 00:33:45,500 +ايش معناته العلاقة الأول يقسم التاني طب ايه صار + +462 +00:33:45,500 --> 00:33:50,020 +هنا صار التاني يقسم الأول ال relation العكسية صار + +463 +00:33:50,020 --> 00:33:53,320 +الان ايش دورها الآن الان هي التاني هي الاحداث + +464 +00:33:53,320 --> 00:33:56,660 +التاني يقسم الأول طب نشوف نشوف هذا الكلام صحيح ولا + +465 +00:33:56,660 --> 00:34:02,440 +لأ نشوف هال gateالتنين والاربعة في ال R مهم لازم + +466 +00:34:02,440 --> 00:34:05,500 +يكون في ال inverse اربعة والتنين صح ولا مش صح؟ + +467 +00:34:06,670 --> 00:34:09,850 +أربعة أو اتنين تنتمل الـR inverse شوفوا يعني الـN + +468 +00:34:09,850 --> 00:34:14,150 +بتسوي أربعة والـN بتسوي اتنين هل الـN تقسم الأربعة + +469 +00:34:14,150 --> 00:34:18,290 +الصح؟ ان عكس الدور اه صار إيش؟ التاني يقسم الأول + +470 +00:34:18,290 --> 00:34:22,250 +إيش كانت ال relation؟ الأول يقسم التاني بس رتبناها + +471 +00:34:22,250 --> 00:34:25,110 +بشكل صحيح مافيش داعي أعيش أعكس التاني بس بدي أعكس + +472 +00:34:25,110 --> 00:34:29,130 +الزوج المرتب فهي نفس البساطة الزوج المرتب XY بيصير + +473 +00:34:29,130 --> 00:34:34,770 +YX AB بيصير BA MNM صار MN و الباقي نفس الشيء + +474 +00:34:37,450 --> 00:34:42,270 +بصير عكس .. بصير انت بتكتبش .. ايه صح .. صح .. صح + +475 +00:34:42,270 --> 00:34:44,910 +.. ممكن يعني هذه ممكن تكتب أكتر من طريقة بس أنا + +476 +00:34:44,910 --> 00:34:47,370 +عملتها بالطريقة البسيطة زي المثال الأول المهم في + +477 +00:34:47,370 --> 00:34:50,810 +الآخر انت كده تتأكد انه حالك صح خدي أمثلة جولنا + +478 +00:34:50,810 --> 00:34:53,430 +اتنين و أربعة في ال R طب يازم يكون اربعة و اتنين + +479 +00:34:53,430 --> 00:34:59,350 +في R بنطبق عليها ولا بنطبقش تتأكدي منهاهو بده يحسب + +480 +00:34:59,350 --> 00:35:02,770 +على inverse بس اتأكدنا إنه كتبتنا صح ولا لأ فعكسنا + +481 +00:35:02,770 --> 00:35:04,810 +الأزواج المرابطة بإمكان .. بس هذه الطريقة هي + +482 +00:35:04,810 --> 00:35:09,850 +الأبسط شيء عندك XY خليها YX عندك N M خليها M N و + +483 +00:35:09,850 --> 00:35:13,690 +بس بتحصل على ال inverse خليني أشوف مثال + +484 +00:35:19,650 --> 00:35:23,250 +في عندنا الان relation من R إلى R طبعا الـ R هنا + +485 +00:35:23,250 --> 00:35:26,690 +الـ real numbers و بنكتبها بشكل مختلف عشان رمز ال + +486 +00:35:26,690 --> 00:35:30,750 +relation غير و رمز ال R غير فانتبهوا أنه شوفوا كيف + +487 +00:35:30,750 --> 00:35:34,370 +دقة الرموز فالـ R العادية ال relation لكن هذه الـ + +488 +00:35:34,370 --> 00:35:39,510 +R ال bold بيسموها اللي هي الغامقة أو المفقمة هذه + +489 +00:35:39,510 --> 00:35:43,190 +للـ real numbers معروفة real numbers فهذا المثال + +490 +00:35:43,190 --> 00:35:51,650 +رقم تلاتة فهذا طبعا عندنا الـ R تساويXY تنتمي من R + +491 +00:35:51,650 --> 00:35:57,950 +إلى الريالز بحيث X أكبر من Y بده R inverse بنعمل + +492 +00:35:57,950 --> 00:36:03,830 +زي تاوي ما علينا لا نعكس الترتيب طبعا هنا فيششي + +493 +00:36:03,830 --> 00:36:10,170 +مشكلة لأن المجموعة ال A و ال B نفسها طبعا بحيث X + +494 +00:36:10,170 --> 00:36:16,340 +أكبر من YX أكبر من Y طبعا اختلفت الآن فعلا دي + +495 +00:36:16,340 --> 00:36:19,580 +inverse لأنه قال لي في الأول مين الأول أكبر من + +496 +00:36:19,580 --> 00:36:23,200 +التاني في ال R و اكتشف العدد في ال R إذا الأول + +497 +00:36:23,200 --> 00:36:26,540 +أكبر من التاني إذا الزوج المرتب في ال R إذا الأول + +498 +00:36:26,540 --> 00:36:29,820 +أكبر من التاني إيش صار الآن التاني أكبر من الأول + +499 +00:36:29,820 --> 00:36:33,360 +انعكست العلاقة فعنا هنا ع سبيل المثال لو بنعملهامش + +500 +00:36:33,360 --> 00:36:38,030 +إيش في عنا؟ عنا الواحد مع ال zero في ال Rلكن الـ 0 + +501 +00:36:38,030 --> 00:36:41,010 +و الـ 1 في الـ R inverse بنطبق ولا بنتبقش؟ في + +502 +00:36:41,010 --> 00:36:45,550 +الأول هايه الـ X1 أكبر من Y في التاني الـ X1 + +503 +00:36:45,550 --> 00:36:49,130 +الاصارات أشملها أكبر من Y، صح فطبعا بندنعيد + +504 +00:36:49,130 --> 00:36:51,290 +كتابتها بندنعيد كتابتها و بنغير الترتيب لكنها دي + +505 +00:36:51,290 --> 00:36:56,830 +أثّل طريقة زي المثال السابق، تفضل لا، لا، احنا يا + +506 +00:36:56,830 --> 00:36:59,630 +بنغيرها يا بنغيرها، مفهومش نغيرها مرتين زي اللي + +507 +00:36:59,630 --> 00:37:01,830 +بيصير نافي نافي إثبات فاللي بتغيره مرتين بترجع + +508 +00:37:01,830 --> 00:37:05,750 +لنفس النقطة فهي القضية، هل بنطبق هذا المثال صح ولا + +509 +00:37:05,750 --> 00:37:10,410 +مش صح؟يعني هذه انا كيف ممكن اكتبها؟ ده ايه اتكتبت؟ + +510 +00:37:10,410 --> 00:37:17,710 +من ال Y هنا صفر صح؟ اه فانت بيلا الترتيب يعني انك + +511 +00:37:17,710 --> 00:37:21,890 +تكتبيها هذه بالترتيب ليش تقول ايه؟ X Y تنتمي لل R + +512 +00:37:21,890 --> 00:37:29,310 +across ال R بحيث X اه Y اهعكس الـ I، يا بتعكسي هنا + +513 +00:37:29,310 --> 00:37:32,910 +يا هنا، ماينفعش تعكسي مرتين، هل جاء الكلام صحيح؟ + +514 +00:37:32,910 --> 00:37:37,070 +أه، فعناشي بنقول الإلاقة الأول أكبر من التاني، ال + +515 +00:37:37,070 --> 00:37:40,250 +inverse التاني أكبر من الأول أو الأول أصغر من + +516 +00:37:40,250 --> 00:37:44,110 +التاني، تناكس العمل، فانتبهوا لهذه النقاط، بدناش + +517 +00:37:44,110 --> 00:37:47,250 +نعكس مرتين، وطبعا أمثلة بسيطة بتأكد إن حالنا صح + +518 +00:37:47,250 --> 00:37:50,690 +ولا لأ، لأن هنا طبعا المثال الأول كان سهل جدا، كل + +519 +00:37:50,690 --> 00:37:56,250 +أزواج مرتبة عكسناها بسهولة تمام + +520 +00:37:57,500 --> 00:38:02,960 +ننتقل لنقطة جديدة domain and image of a relation + +521 +00:38:02,960 --> 00:38:07,760 +المجال والمدى للعلاقة طبعا شايف زي ما شوفين + +522 +00:38:07,760 --> 00:38:11,680 +مصطلحات بتشابه الدالة لأن زي ما هنشوف أن الدوال هي + +523 +00:38:11,680 --> 00:38:15,910 +علاقات كل دالة علاقة لكن العكس غير صحيحأه فهنا في + +524 +00:38:15,910 --> 00:38:21,730 +مفاهيم اللي هو موحدة طبعا هنا بيستخدم مصالح image + +525 +00:38:21,730 --> 00:38:24,950 +اللي هي الصورة بولاية وما بيستخدمش كلمة range + +526 +00:38:24,950 --> 00:38:28,530 +هيستخدمها بشريقة مختلفة عن ال calculus فاحنا هنا + +527 +00:38:28,530 --> 00:38:31,770 +بنتحدث عن ال domain يعني المجال وال image اللي هو + +528 +00:38:31,770 --> 00:38:37,940 +ال مدى باللغة العربية بترجمه تمامفعنا تعريف بده + +529 +00:38:37,940 --> 00:38:42,320 +يعرفنا اللي هو مجال ال relation لأنه زي ما شوفنا + +530 +00:38:42,320 --> 00:38:46,040 +في الأمثلة إحنا عنا علاقة من A ل B هل العلاقة لازم + +531 +00:38:46,040 --> 00:38:49,000 +تغطي كل ال A؟ شوفنا في الأمثلة لأ مش بالضروري بص + +532 +00:38:49,000 --> 00:38:53,340 +صحيح أه لإن شوفتوا الأمثلة الماضية أخدنا بص subset + +533 +00:38:53,340 --> 00:38:56,620 +من ال Cartesian إذا في بعض العناصر إيش مش داخلة + +534 +00:38:56,620 --> 00:38:59,920 +فبعض العناصر ال A مش داخلة طبعا المدى لإنا نغطي كل + +535 +00:38:59,920 --> 00:39:03,500 +ال B برضه مش بالضروري فبدنا نشوف إيش اللي بنغطيه + +536 +00:39:03,500 --> 00:39:08,650 +بالظبطمقدمة للتعريف let R be a relation from asset + +537 +00:39:08,650 --> 00:39:12,670 +A to asset B طبعا أنا بتتحدث عن إيش مجال relation + +538 +00:39:12,670 --> 00:39:15,290 +فبتكون عندي relation و بتتحدث عن إيش image + +539 +00:39:15,290 --> 00:39:19,350 +relation أول شيء التعريف الأول ال domain فما هو + +540 +00:39:19,350 --> 00:39:23,380 +domain ال R هذا مفهومإيش رمزه؟ domain الـR طبعا + +541 +00:39:23,380 --> 00:39:26,800 +نقراها domain بس أخد أول تلات حروف domain الـR ما + +542 +00:39:26,800 --> 00:39:31,020 +هو domain الـR؟ عبارة عن مجموعة أول شيء نقرا صح هو + +543 +00:39:31,020 --> 00:39:34,900 +مجموعة ف domain ال relation مجموعة طب إيش عناصرها؟ + +544 +00:39:34,900 --> 00:39:39,240 +عناصر عادية و الأزواج مرتبة عناصر عادية A تنتمي لل + +545 +00:39:39,240 --> 00:39:43,060 +capital A فبدنا عناصر الـA اللي إيش مالها؟ اللي + +546 +00:39:43,060 --> 00:39:47,300 +إليها علاقة مع حدا من الـB فبدوا إيش؟ هو كل A في + +547 +00:39:47,300 --> 00:39:53,660 +الـA بحيثA لعلاقة مع أحد ما من الـ B for some B in + +548 +00:39:53,660 --> 00:39:58,860 +B بمعنى آخر ببساطة شديدة ما هو ال domain بتطلع على + +549 +00:39:58,860 --> 00:40:01,900 +الزوج المرتب اللي في ال R وبياخد الإحداثيات الأولى + +550 +00:40:03,520 --> 00:40:07,400 +مجموعة الإحداثيات الأولى باخد إيش هيزوج مرتب في + +551 +00:40:07,400 --> 00:40:10,360 +الـR باخد الإحداث الأول والإحداث الأول بكون مجموعة + +552 +00:40:10,360 --> 00:40:12,840 +عادية بتكون إيش هذه هي ال domain هذه هي ال domain + +553 +00:40:12,840 --> 00:40:17,300 +ال image العكس باخد الإحداث التاني ال image باخد + +554 +00:40:17,300 --> 00:40:24,230 +الإحداث التاني فالصورةالنمطية هي الـA وين بيكون ال + +555 +00:40:24,230 --> 00:40:29,990 +domain؟ subset من الـA فdomain الـR وهي الـB وهي + +556 +00:40:29,990 --> 00:40:34,550 +طبعا في علاقة وين ال image؟ subset image الـR وهي + +557 +00:40:34,550 --> 00:40:40,870 +الـR طبعا علاقة فهذه الصورة النمطية فأنا بشكل عام + +558 +00:40:40,870 --> 00:40:47,200 +إذا عندي زوج مرتب موجود في ال relationالإحداث + +559 +00:40:47,200 --> 00:40:51,020 +الأول وين بيكون؟ في الـ Domain فالـ A في الـ + +560 +00:40:51,020 --> 00:40:54,720 +Domain والتاني وين بيكون؟ في الـ Image فانا زوج + +561 +00:40:54,720 --> 00:40:59,080 +مرتب هي علاقة في إحداثيين إحداثي أول بيكون في الـ + +562 +00:40:59,080 --> 00:41:01,900 +Domain والتاني وين بيكون؟ في الـ Image في المدى + +563 +00:41:01,900 --> 00:41:06,320 +فطبعا الـ Image هو كل عناصر في الـ B بحيث أنه هي + +564 +00:41:06,320 --> 00:41:09,660 +إحداثي تاني من زوج مرتب هي الـ B اللي هي تقية + +565 +00:41:09,660 --> 00:41:14,460 +شمالها زوج مرتب أو إحداثي تاني من زوج مرتب فده هو + +566 +00:41:14,460 --> 00:41:15,000 +التعريف + +567 +00:41:17,840 --> 00:41:23,680 +نبدأ بالأمثلة البسيطة كالعادة فالصورة + +568 +00:41:23,680 --> 00:41:28,000 +أرجو أن تنتبع في الذهن الصورة هذه بهذا الشكل + +569 +00:41:28,000 --> 00:41:31,920 +والترتيب عشان بدي أضطر أمحي عشان الأمثلة تتطلع + +570 +00:41:31,920 --> 00:41:40,280 +نبدأ بالمثال البسيط والذي يوضح لنا الفكرة الأساسية + +571 +00:41:43,460 --> 00:41:46,800 +هي في عندنا مجموعتين ولا مش مدينا إياهم؟ مش مدينا + +572 +00:41:46,800 --> 00:41:49,900 +إياهم بشكل صريح مش محتاجينهم مدينا ال relation + +573 +00:41:49,900 --> 00:41:53,380 +مدينا ال relation بيقول لي أوجد ال domain و ال + +574 +00:41:53,380 --> 00:41:57,940 +image وهذا اللي بديها بالظبط أنا ما علي إلا أخد من + +575 +00:41:57,940 --> 00:42:02,240 +ال relation solutiondomain ال relation إيش بأعمل + +576 +00:42:02,240 --> 00:42:06,460 +باخد الإحداث الأول فواحد واحد في ال relation إذا + +577 +00:42:06,460 --> 00:42:10,620 +إنه الأولى في ال domain واحد سالب اتنين إذا إن + +578 +00:42:10,620 --> 00:42:13,120 +الواحد في ال domain بس مكتبوش كمان مرة لأنه مجموعة + +579 +00:42:13,120 --> 00:42:16,980 +وفي مين والتنين اللي علاقة مع الخمسة فهذا هو ال + +580 +00:42:16,980 --> 00:42:21,460 +domain بكل بساطة زي ما حكينا هو الإحداثيات الأولى + +581 +00:42:21,460 --> 00:42:25,120 +من الأزواج المرتبة اللي في ال relation مش أي أزواج + +582 +00:42:25,120 --> 00:42:29,500 +مرتب بكل بساطة ال image إننا ناخد الإحداث التاني + +583 +00:42:33,780 --> 00:42:38,140 +وخمسة واحد و ساله اتنين وخمسة فهذا هو الأصل هذا + +584 +00:42:38,140 --> 00:42:41,420 +المفهوم بكل بساطة مع الأمثلة البسيطة طبعا مع تقدم + +585 +00:42:41,420 --> 00:42:44,620 +الأمثلة الحسابات بتصعب لكن هذا هو ايش المفهوم + +586 +00:42:44,620 --> 00:42:48,640 +الأساسي لما يكونوا الأزواج عددهم محدود الحساب سهل + +587 +00:42:48,640 --> 00:42:53,160 +لما يكتروا الحساب بيصعب لكن هذا هو المفهوم فضل + +588 +00:42:53,160 --> 00:42:58,510 +لأنها مجموعةلأن المجموعة والتكرار ما لهوش قيمة + +589 +00:42:58,510 --> 00:43:02,010 +اللي كتبنا واحد واحد كمجموعة ما لهوش قيمة التكرار + +590 +00:43:02,010 --> 00:43:06,130 +واضح؟ ماشي + +591 +00:43:06,130 --> 00:43:10,030 +بنفع انا اكوّن من العنصر اكتر من زوج مرتب، بنفع + +592 +00:43:10,030 --> 00:43:13,190 +كارتيسان بوداكر، لكن لما ده رجحهم كمجموعة اكتب بس + +593 +00:43:13,190 --> 00:43:16,530 +اخد الاحداث الاول احداث الاول التكرار مالهوش قيمة + +594 +00:43:16,530 --> 00:43:19,570 +لو كتبت واحد واحد واتنين اكمع عنصر فيها كمجموعة + +595 +00:43:19,570 --> 00:43:23,070 +اتنين فالتكرار مالهوش قيمة زي ما اتفقنا تذكروا في + +596 +00:43:23,070 --> 00:43:29,200 +البداية خليني اشوف مثال جديدخلّينا نشوف مثال جديد + +597 +00:43:29,200 --> 00:43:34,680 +مثال توي شفناه فزوج مرتب الإحداث الأول من ال + +598 +00:43:34,680 --> 00:43:38,780 +natural number والتاني من ال Z والأول يقسم التاني + +599 +00:43:38,780 --> 00:43:43,220 +فبدنا ال domain وبدنا ال image solution + +600 +00:43:45,110 --> 00:43:48,910 +domain الـ R يساوي كل الـ natural number هل كل + +601 +00:43:48,910 --> 00:43:52,670 +عنصر له علاقة مع عنصر ما؟ هل كل عدد طبيعي بيقسم + +602 +00:43:52,670 --> 00:43:57,590 +عدد ما؟ نعم، كلهم بيقسم الصفر، يكفي، فالواحد تقسم + +603 +00:43:57,590 --> 00:44:00,310 +الصفر، إذا موجودة، الواحد، التنين بتقسم الصفر، + +604 +00:44:00,310 --> 00:44:03,350 +موجودة، التلاتة بتقسم الصفر، موجودة، طيب بقاشك إيه + +605 +00:44:03,350 --> 00:44:08,450 +رأيكوا في ال image؟ و ال image برضه كل Z لأن كل + +606 +00:44:08,450 --> 00:44:10,970 +عدد صحيح يقبل قسم علها عدد طبيعي + +607 +00:44:14,550 --> 00:44:16,490 +إيش معنهم؟ كلهم يقبل القصب على واحد أصلا + +608 +00:44:20,090 --> 00:44:24,650 +فانا مين الأزواج؟ مين العناصر اللي في الـR؟ قلنا + +609 +00:44:24,650 --> 00:44:29,330 +واحد مع نفسها ومع الـ0 ومع السلب واحد وكذا، إذن + +610 +00:44:29,330 --> 00:44:32,830 +الواحد موجودة، التنين مع نفسها، لإنها علاقة، لإنها + +611 +00:44:32,830 --> 00:44:37,070 +تقسم نفسها وكذا، كل عدد صحيح يقسم نفسه، إذن موجود، + +612 +00:44:37,070 --> 00:44:40,490 +طيب، كل عدد صحيح لو كان موجب أو سالب يقبل قسم على + +613 +00:44:40,490 --> 00:44:43,790 +عدد آخر، نعم، بقاه، فإذن إيش موجود في الـimage، + +614 +00:44:43,790 --> 00:44:46,010 +فإن الحسابات طبعا أصعب، لكن نفس الأشياء + +615 +00:44:48,860 --> 00:44:55,760 +نشوف مثال جديد نبدأ + +616 +00:44:55,760 --> 00:44:57,920 +بالأمثلة الحقيقية + +617 +00:45:04,500 --> 00:45:07,760 +اللي فيها برهان طبعا هي الأمثلة الأهم بالنسبالنا + +618 +00:45:07,760 --> 00:45:13,400 +طبعا مطلوب نفهم المفاهيم البسيطة وأيضا الأهم كيف + +619 +00:45:13,400 --> 00:45:17,300 +نستخدم التعريفات في البراهين كالعادة prove that + +620 +00:45:17,300 --> 00:45:23,180 +for any relation R لأي relation domain العلاقة + +621 +00:45:23,180 --> 00:45:26,880 +بيساوي image ال inverse طبعا شيء منطقي أه واضح أنا + +622 +00:45:26,880 --> 00:45:33,320 +متوقع أن هذا الكلام صحيح هي الـA وهي الـB وهي الـR + +623 +00:45:34,170 --> 00:45:38,570 +domain الـ R هنا domain الـ R وطبعا الـ R inverse + +624 +00:45:38,570 --> 00:45:42,790 +هنا إيش بده يكون image الـ R inverse هنا بيكون على + +625 +00:45:42,790 --> 00:45:47,070 +العكس فبقول بيتساووا كمان مش بس انهم subset من الـ + +626 +00:45:47,070 --> 00:45:53,510 +A بل متساويين بالمتساويين مثال التالت المطلوب لأي + +627 +00:45:53,510 --> 00:46:00,330 +relation بدنا نثبت أن domain الـ R يساوي image الـ + +628 +00:46:00,330 --> 00:46:03,010 +R inverse solution + +629 +00:46:05,340 --> 00:46:10,520 +خلّينا نحلل السؤال خطوة خطوة طبعا إنها مُعطَعم + +630 +00:46:10,520 --> 00:46:14,620 +الـR relation أي relation ممكن ناخدها من A إلى B + +631 +00:46:14,620 --> 00:46:21,140 +فخلّينا نبدأ الحل نقول له let R be any relation + +632 +00:46:21,140 --> 00:46:32,220 +from asset A to asset B هاي relation بشكل عام، any + +633 +00:46:32,220 --> 00:46:37,070 +relation، ممتازإيش المطلوب؟ بدي أثبت domain الـR + +634 +00:46:37,070 --> 00:46:43,550 +يساوي image الـR inverse لإيش؟ لأن domain الـR + +635 +00:46:43,550 --> 00:46:47,690 +إيش؟ مجموعة إيش عناصرها؟ عناصر عادية ولا أزواج + +636 +00:46:47,690 --> 00:46:51,250 +مرتبة؟ عناصر عادية، عناصر عادية، إذا أنا إيش؟ إذا + +637 +00:46:51,250 --> 00:46:58,010 +السؤال في ظاهره الأول في حقيقته الخارجية عبارة عن + +638 +00:46:58,010 --> 00:47:01,570 +سؤال تقليدي من chapter 2 تساوي مجموعات فإذا هنبدأ + +639 +00:47:01,570 --> 00:47:05,150 +فيه ناخد عنصر من الطرف اليسارإذا مشينا تكافأة + +640 +00:47:05,150 --> 00:47:08,010 +ووصلنا اليمين، اتخلص التساوي، إذا ماقدرناش نمشي + +641 +00:47:08,010 --> 00:47:11,230 +تكافأة، بنضطر نمشي بالعكس، من اليمين لليسار، فإيش + +642 +00:47:11,230 --> 00:47:14,030 +نفس الـ «إيش» نفس السياسة، نفس المنهج، فحنبدأ + +643 +00:47:14,030 --> 00:47:22,570 +نقولّه «let X be any element such + +644 +00:47:22,570 --> 00:47:29,590 +that X تنتمي لـdomain R» + +645 +00:47:30,790 --> 00:47:34,810 +بدأنا من الطرف اليمين، فأرجو أنه طبعا احنا شوية + +646 +00:47:34,810 --> 00:47:39,370 +شوية جاهزين نتقدم، لكن بنعتمد على الأساسات، بنعتمد + +647 +00:47:39,370 --> 00:47:42,490 +على المنطق، بنعتمد على مفهوم المجموعات، لكن الأمور + +648 +00:47:42,490 --> 00:47:45,790 +تتطور، الآن مجموعات، اه مجموعات، لكن إليها تعريف + +649 +00:47:45,790 --> 00:47:49,150 +آخر، فإيش ممكن أعمل الآن؟ ممكن أستخدم تعريف ال + +650 +00:47:49,150 --> 00:47:52,710 +domain، ماذا يعني أن ال X في ال domain، هذا يكافئ + +651 +00:47:53,250 --> 00:47:58,030 +إن XY تنتمي للـ relation ماذا هو في الـ domain إذا + +652 +00:47:58,030 --> 00:48:01,250 +إن هو إحداه في أول من زوج مرتب إيش ال domain؟ + +653 +00:48:01,250 --> 00:48:05,250 +إحداه في أول و إيش ال Y؟ أي Y في ال M المهم هو زوج + +654 +00:48:05,250 --> 00:48:08,310 +مرتب، زوج مرتب مين بتكونه؟ الواحد من ال A والتاني + +655 +00:48:08,310 --> 00:48:15,190 +من ال B for .. ثواني برجعلك إلي for some Y تنتمي + +656 +00:48:15,190 --> 00:48:18,890 +لل B أه هو هيك شوف إنت كيف ناخد التعريف عشان نتعلم + +657 +00:48:18,890 --> 00:48:25,000 +مع بعض هي ال domainهو عبارة عن عنصر في الـ Capital + +658 +00:48:25,000 --> 00:48:30,560 +A بحيث ان هو إحداثي أول من زوج مرتب لمين لصم B بس + +659 +00:48:30,560 --> 00:48:33,280 +حطيت بدل A بيه حطيت XY فهنا بنقراه بهذا الشكل + +660 +00:48:33,280 --> 00:48:37,220 +فالقراة صارت بهذه الصورة اللي أمامكم تمام خلّيه + +661 +00:48:37,220 --> 00:48:40,660 +قدام للتعريف ويمكن ال image بدناياه عشان الاتجاه + +662 +00:48:40,660 --> 00:48:45,840 +التاني خلّيه تمام أه أنا إيش بدي؟ بدي أودي ال X ل + +663 +00:48:45,840 --> 00:48:49,610 +image ال R inverseإذا نبدأ أحول من R لـ R inverse + +664 +00:48:49,610 --> 00:48:53,370 +كيف بنعمل؟ بنعكس الزوج المرتب فده يمكن كتبت + +665 +00:48:53,370 --> 00:48:57,390 +العلاقة قولت A B في الـ R if and only if B A في + +666 +00:48:57,390 --> 00:49:01,250 +الـ R inverse فهذه مفتاح كثير من الأسئلة اللي + +667 +00:49:01,250 --> 00:49:03,730 +بيليها علاقة بين الـ R و الـ R inverse كيف تروح من + +668 +00:49:03,730 --> 00:49:07,010 +الـ R للـ R inverse أو العكس فالزوج المرتب و ده + +669 +00:49:07,010 --> 00:49:09,230 +يمكن أحول نفسي أشوف المفهوم الأساسي أه هي و + +670 +00:49:09,230 --> 00:49:12,790 +بينفعنا بالبرهان إذا كانت X Y في الـ R بتكون Y X + +671 +00:49:12,790 --> 00:49:16,590 +وين في الـ R inverse فعلى طول هذا يكافئ نكتب هنا + +672 +00:49:20,510 --> 00:49:25,870 +فهذا يكافئ أن YX في الـ R inverse ونخلّي هذا زي ما + +673 +00:49:25,870 --> 00:49:31,050 +هو for some Y تنتمي للـ B طبعا هذا أولا تعريف ال + +674 +00:49:31,050 --> 00:49:36,370 +domain الدليل تبعنا definition of domain وهنا + +675 +00:49:36,370 --> 00:49:42,230 +تعريف ال inverse وهنا definition of R inverse ال + +676 +00:49:42,230 --> 00:49:47,070 +domainممتاز، بدنا نوصل الـ X لمين؟ للـ H، لإميج + +677 +00:49:47,070 --> 00:49:48,890 +الـ R inverse اتطلعوا على الجملة و اتطلعوا على + +678 +00:49:48,890 --> 00:49:53,090 +التعريف الـ X أشملها إحداثي تاني من الـ R inverse + +679 +00:49:53,090 --> 00:49:55,550 +الإحداث اللي يموت بيكون في إميج الـ R inverse في + +680 +00:49:55,550 --> 00:50:00,730 +إميج الـ R inverse فده يكافئ إن X تنتمي لإميج الـ + +681 +00:50:00,730 --> 00:50:05,040 +R inverse، طبعا تعريف الـ Imageوهو المطلوب صحيح + +682 +00:50:05,040 --> 00:50:08,500 +فشفتوا كيف روحنا و كيف .. فاحنا نتطلع دايما عيننا + +683 +00:50:08,500 --> 00:50:11,920 +على المطلوب و بنحاول نفسر فشفتوا أنتوا المفهوم + +684 +00:50:11,920 --> 00:50:15,520 +البسيط اللي فهمناه أنه أنا عندي زوج في ال relation + +685 +00:50:15,520 --> 00:50:18,220 +الأحداث الأول بيكون في ال domain والتاني في ال + +686 +00:50:18,220 --> 00:50:20,720 +images استخدمناها هنا في البرهان إذا فهمناها صح + +687 +00:50:20,720 --> 00:50:24,980 +طبعا إيش؟ طبعا كل علاقاتي تكافؤ و لأنها تعريفات + +688 +00:50:24,980 --> 00:50:29,620 +فانتهى إيش الحل thus أو therefore اللي هو domain + +689 +00:50:29,620 --> 00:50:38,130 +ال Rبساوي image الار انفرس تمام + +690 +00:50:38,130 --> 00:50:43,370 +في أي سؤال تبعين اه ان شاء الله نوقفها يوم + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/sv2su8MeGKk_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/sv2su8MeGKk_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..257962ca1d447653dbacf5dd82a8b645a8d7cb3f --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/sv2su8MeGKk_postprocess.srt @@ -0,0 +1,2284 @@ +1 +00:00:20,670 --> 00:00:24,310 +بسم الله الرحمن الرحيم هنكمل مع اللي هو العائلات + +2 +00:00:24,310 --> 00:00:29,910 +المفهرة من المجموعات indexed family of sets فشوفنا + +3 +00:00:29,910 --> 00:00:34,690 +احنا النظرية الاولى في الموضوع وكانت النظرية + +4 +00:00:34,690 --> 00:00:38,710 +السابعة في الباب لان ننتقل لنظرية تانية + +5 +00:00:38,710 --> 00:00:43,530 +generalized De Morgan's theorem فطبعا احنا عارفين + +6 +00:00:43,530 --> 00:00:48,370 +ديو مورجانز تتحدث كيف اجيب مكملة التقاطع او مكملة + +7 +00:00:48,370 --> 00:00:54,640 +الاتحادفطبعا في عندنا family of six index family + +8 +00:00:54,640 --> 00:00:59,520 +of six زي ما هي قدامكوا فأول شئ مكملة الاتحاد + +9 +00:00:59,520 --> 00:01:04,360 +بتساوي تقاطع المكملات تعميم للنظرية السابقة أيضا + +10 +00:01:04,360 --> 00:01:10,650 +مكملة التقاطع تساوي اتحاد المكملاتفهذا مبدأ A عام + +11 +00:01:10,650 --> 00:01:13,650 +بغض النظر كان اللي عندنا التقاطع او الاتحاد + +12 +00:01:13,650 --> 00:01:16,850 +لمجموعتين او اكثر اي عدد من المجموعات فالكلام + +13 +00:01:16,850 --> 00:01:21,890 +دايما صحيح خلينا نشوف برهان واحدة منهم والتانية + +14 +00:01:21,890 --> 00:01:29,670 +بشكل مشابه هتركها exercise فهذه طبعا نظرية اتنين + +15 +00:01:29,670 --> 00:01:35,450 +تمانية وهذا هو البرهان عن برهن فرع ايش رأيكوا برهن + +16 +00:01:35,450 --> 00:01:41,220 +A ولا B؟B ولا ايه؟ B تمع فرع B + +17 +00:01:44,430 --> 00:01:49,030 +فطبعا زي ما مار علينا أكتر من مرة في أننا مجموعتين + +18 +00:01:49,030 --> 00:01:54,570 +متساويتين هنثبت التساوي فطبعا مافيش عننا معلومات + +19 +00:01:54,570 --> 00:01:58,450 +كتير زي ما حكيت للاتحاد والتقاط على ال family + +20 +00:01:58,450 --> 00:02:03,890 +فهنبدأ من التعريف هناخد عنصر في طرف إذا مشينا if + +21 +00:02:03,890 --> 00:02:07,790 +and only if بيكون أثبتنا التساوي إذا صار فينا اللي + +22 +00:02:07,790 --> 00:02:10,990 +هو if then بيكون احنا عملنا subset فنبدأ من الطرف + +23 +00:02:10,990 --> 00:02:14,540 +التاني و هكذا فخليني نبدأ من الطرف اليسارفنقول له + +24 +00:02:14,540 --> 00:02:24,100 +let x be any element كالعادة element and let x + +25 +00:02:24,100 --> 00:02:29,300 +تنتمي للطرف، نبدأ من إيش؟ من الطرف اللي هو اليسار، + +26 +00:02:29,300 --> 00:02:35,840 +اللي هو إيش؟ لمكملة التقاطة جامعة in capital جامعة + +27 +00:02:35,840 --> 00:02:40,810 +a sub gamma لكل برايةفهنا بداية يعتوقع بسيطة لكل + +28 +00:02:40,810 --> 00:02:44,930 +بدأي المفروض يعرف كيف يتعامل مع علاقة ال subset مع + +29 +00:02:44,930 --> 00:02:47,950 +علاقة التساوي اللي هي subset و subset ليس الا اه و + +30 +00:02:47,950 --> 00:02:51,430 +هكذا تمام ايش ممكن نعمل ان نعرّف نستخدم تعريف ال + +31 +00:02:51,430 --> 00:02:54,370 +compliment فهو اللي موجود في ال compliment هو مش + +32 +00:02:54,370 --> 00:02:58,350 +موجود في المجموعة الأصلية فهذا على طول تعريف يكافئ + +33 +00:02:59,060 --> 00:03:05,740 +فهذا يكافئ ان X لا تنتمي للتقاطع جامع ال capital + +34 +00:03:05,740 --> 00:03:09,680 +جامع a sub جامع من وين جيبت هذه الخطوة تعريف + +35 +00:03:09,680 --> 00:03:15,300 +المكملة الى prime ممكن نرمز له بها الشكل أي سؤال + +36 +00:03:16,680 --> 00:03:20,340 +مرّت علينا هذه الفكرة في السابق، قلنا احنا ماعناش + +37 +00:03:20,340 --> 00:03:24,040 +علاقة إيش معنات لا ينتمي، لكن عندنا تعريف ينتمي، + +38 +00:03:24,040 --> 00:03:27,740 +فماخو ممكن ناخد النفي برا، في أي استفسار؟ فناخد + +39 +00:03:27,740 --> 00:03:32,040 +النفي برا، فهذه مجرد notation، هذه عبارة عن not X + +40 +00:03:32,040 --> 00:03:37,260 +تنتمي لمن؟ للتقاطة، small gamma in capital gamma A + +41 +00:03:37,260 --> 00:03:42,840 +sub gamma، هذا ليس إلا notationمجرد رمز ايش معناه + +42 +00:03:42,840 --> 00:03:48,140 +تنفي اه تمام ادم النفي فالان بكتابة هذه الصورة + +43 +00:03:48,140 --> 00:03:51,300 +اصبح اندي مقدر ان اش اعمل افسر التقاطع على الفامل + +44 +00:03:51,300 --> 00:03:55,860 +افسر التقاطع على الفامل فهذه تكافئ not ايش معناه x + +45 +00:03:55,860 --> 00:03:58,680 +تنتمي للتقاطع انها موجودة في كل المجموعات اللي + +46 +00:03:58,680 --> 00:04:03,240 +احنا بنكتبها ايش for all gamma in capital gamma x + +47 +00:04:03,240 --> 00:04:08,740 +تنتمي لل a sub gamma من وينها ده تعريف تقاطع على + +48 +00:04:08,740 --> 00:04:14,410 +الفاملممكن اعمله اختصارا اللي هو موضوعنا في ال + +49 +00:04:14,410 --> 00:04:19,210 +section هذا اللي بدأنا فيه متفقين؟ امتبعين؟ تمام + +50 +00:04:19,210 --> 00:04:22,430 +الان ايش ممكن اعمل؟ ادخل النفي على ال quantifier + +51 +00:04:22,430 --> 00:04:27,110 +بهذا الشكل فهذا عبارة عن يكافئ there exists gamma + +52 +00:04:27,110 --> 00:04:33,470 +in capital gamma و X لا تنتمي لل A Gamma فشل اللي + +53 +00:04:33,470 --> 00:04:35,970 +هو ده عبارة عن مين؟ اللي هو negation او quantifier + +54 +00:04:35,970 --> 00:04:40,330 +negation quantifier + +55 +00:04:44,630 --> 00:04:47,850 +negation فهذا اللي كنا احنا بنحاول نتعلمه في + +56 +00:04:47,850 --> 00:04:51,870 +section 1-6 بتذكروا؟ هيه بنحتاجه شفتوا كيف نتعامل؟ + +57 +00:04:51,870 --> 00:04:55,430 +مع ال quantifier مع النفي و التبسيط شايفين احنا + +58 +00:04:55,430 --> 00:04:58,070 +ليش اتعلمناها؟ كنا نقول احنا بنتعلم لأن وحيانا + +59 +00:04:58,070 --> 00:05:01,590 +مجرد انك تحط النفي و بس مافيدناش، بدنا نحطها بصورة + +60 +00:05:01,590 --> 00:05:04,450 +مناسبة، بدنا تبسيط فهذا الكلام اللي احنا كنا نتحدث + +61 +00:05:04,450 --> 00:05:07,990 +عنه فاين استفدنا؟ اه اقتربنا اقتربنا لان انا بدي + +62 +00:05:07,990 --> 00:05:11,810 +احول لمين؟تقاطع للاتحاد الاتحاد هو ايش؟ there + +63 +00:05:11,810 --> 00:05:14,530 +exists و بعدين إيش بدهيها تكون في المكملة طب ما هي + +64 +00:05:14,530 --> 00:05:17,230 +إيش؟ اللي مش موجودة إيش معناتها؟ مش موجودة في الـA + +65 +00:05:17,230 --> 00:05:20,370 +Gamma موجودة وين؟ في الـA Gamma complement فده + +66 +00:05:20,370 --> 00:05:24,650 +بيكافئ طبعا بالترتيب there exists Gamma تنتمي + +67 +00:05:24,650 --> 00:05:29,450 +للـCapital Gamma والـX تنتمي للـA Gamma Pri تعريف + +68 +00:05:29,450 --> 00:05:32,710 +المكملة الـPri + +69 +00:05:34,660 --> 00:05:40,100 +فأرجو زي ما حكيت مش غلط إنه نجلد نشوف الكتاب كيف + +70 +00:05:40,100 --> 00:05:43,720 +بيحل إحنا كيف بنحل في المحاضرة والأنثى للمشابه + +71 +00:05:43,720 --> 00:05:47,480 +نمشي خطوة خطوة ما نستبقش الأحداث ما نقفزش عن بعض + +72 +00:05:47,480 --> 00:05:51,560 +الخطوات كلها خطوات ضرورية في الغالب ممكن نقتصر في + +73 +00:05:51,560 --> 00:05:55,680 +بعض الأحيان النادرة طبعا هذا يكافئ ليس إلا X تنتمي + +74 +00:05:55,680 --> 00:05:59,580 +لمين للاتحاد بتروح لتعريف اللي هو الاتحاد على ال + +75 +00:05:59,580 --> 00:06:05,320 +family A sub gamma prime definitionof اللي هو + +76 +00:06:05,320 --> 00:06:09,680 +إتحاد على الـ family وهو المطلوب بدأنا من طرف + +77 +00:06:09,680 --> 00:06:13,000 +وصلنا للطرف التاني كله تكافأت طيب متأكدين أنه كله + +78 +00:06:13,000 --> 00:06:16,560 +تكافأت؟ انشوف إيش استخدمنا؟ استخدمنا التعريف تعريف + +79 +00:06:16,560 --> 00:06:21,080 +دايما تكافأت استخدمنا notation مجرد رمز تفسير إيش + +80 +00:06:21,080 --> 00:06:25,700 +استخدمنا؟ تعريف استخدمنا quantifier negation وده + +81 +00:06:25,700 --> 00:06:28,620 +إيش معنى تكافأت لو رجعتقولها و بعضين تعريف و تعريف + +82 +00:06:28,620 --> 00:06:35,620 +فإن كله تكافأت فالبرهان انتهى فهناthus مكملة + +83 +00:06:35,620 --> 00:06:43,400 +التقاطع تساوي له اتحاد المكملات وهو المطلوب اثباته + +84 +00:06:43,400 --> 00:06:47,740 +وهو + +85 +00:06:47,740 --> 00:06:48,540 +المطلوب + +86 +00:06:52,040 --> 00:06:55,600 +في آية السفسار فجايفين احنا كل قواعد المنطق + +87 +00:06:55,600 --> 00:06:58,320 +بنستخدمها وكل اللي اتعلمناها في ال chapter الأول + +88 +00:06:58,320 --> 00:07:01,320 +اللي احنا حطينا فيه المبادئ العامة المنطق كيف + +89 +00:07:01,320 --> 00:07:05,180 +نتعامل مع الروابط كيف نتعامل مع المكملات كيف + +90 +00:07:05,180 --> 00:07:09,300 +نتعامل مع اليومل وطرق البرهان الآن بدنا نطبق في + +91 +00:07:09,300 --> 00:07:17,600 +أمثلة متعددة في أماكن متعددة تمام نشوف مثال فضل + +92 +00:07:22,750 --> 00:07:25,770 +بكون احنا عملنا subset لان لازم ارجع لانه ايش + +93 +00:07:25,770 --> 00:07:29,910 +تعريف التساوي for all x x في الأولى if and all if + +94 +00:07:29,910 --> 00:07:34,210 +x في التانى فعشان امشي لازم تكون صحيح بس بدك تعمل + +95 +00:07:34,210 --> 00:07:39,010 +two parts اه بكون انت عملت one part بدك ال part + +96 +00:07:39,010 --> 00:07:44,490 +التانى فاحنا ايش بدنالأ لأ لأ من الأول أنا بدأت + +97 +00:07:44,490 --> 00:07:47,730 +هالجيت من اليسار إذا مشيت تكافؤ ووصلت اليمين + +98 +00:07:47,730 --> 00:07:51,590 +التساوي انتهى ماشيت implies بدأ أبدأ من اليمين + +99 +00:07:51,590 --> 00:07:54,970 +الآن و أوصل لليسار لأن ممكن أعملت الأولة صبصت من + +100 +00:07:54,970 --> 00:07:59,070 +التانية إذا في implies إذا في تكافؤ تساوي إذا عملت + +101 +00:07:59,070 --> 00:08:01,310 +implies بقى ممكن أعملت أن الأولة صبصت من التانية + +102 +00:08:01,310 --> 00:08:04,170 +طب كيف تساوي و التانية كمان صبصت من الأولة لازم + +103 +00:08:04,170 --> 00:08:08,210 +أبدأ من التانيةواضحة؟ اه فهذه دايما نتذكر التعريف + +104 +00:08:08,210 --> 00:08:11,730 +ومحطوط في الملاحظة انه قلنا a تساوي b if and only + +105 +00:08:11,730 --> 00:08:15,150 +if a subset من ال b and b subset من ال a فهذا + +106 +00:08:15,150 --> 00:08:19,190 +البديل اه فهذا البديل تمام خلينا نشوف مثال ايش + +107 +00:08:19,190 --> 00:08:23,110 +فايديت هذا النظرية او احد الفوائدأنا إيش بعمل؟ + +108 +00:08:23,110 --> 00:08:28,550 +القضية إنه أنا هنا بدل ما أجيب التقاطع، بعدين بدي + +109 +00:08:28,550 --> 00:08:31,210 +أجيب المكملة، هذه طريقة، أنا ليش بقولك إيه + +110 +00:08:31,210 --> 00:08:34,550 +الترتيب، احسب التقاطع و بعدين أجيب المكملة، طب إيش + +111 +00:08:34,550 --> 00:08:39,830 +البديل؟ لأ، احسب المكملات و بعدين أخد الاتحاد، فمن + +112 +00:08:39,830 --> 00:08:42,970 +كل واحدة هتكون أحيانا أسهل من التانية، واحدة تكون + +113 +00:08:42,970 --> 00:08:45,510 +أسهل من التانية، فهذا بديل، بديني بدائل و أنا + +114 +00:08:45,510 --> 00:08:50,390 +بشيوف من الأنسب لي، عصابين المثالع سبيل المثال في + +115 +00:08:50,390 --> 00:08:56,730 +عندنا مثال أمامكم في عندنا مجموعات والمجموعات دي + +116 +00:08:56,730 --> 00:09:02,050 +شوية ممكن تكون مركبة شوية أو معقدة شوية لو أخدنا + +117 +00:09:02,050 --> 00:09:06,100 +المكملة تبعتها هيكون العملية أسهلأه solution + +118 +00:09:06,100 --> 00:09:10,140 +فالحقيقة أنا فيها عندي خمس مجموعات و التقاطع عليهم + +119 +00:09:10,140 --> 00:09:13,400 +او الاتحاد عليهم ايش المجموعات المجموعات ممكن + +120 +00:09:13,400 --> 00:09:19,140 +ارمضلها بالرمز AN تتكون من مين تتكون من جزءين من + +121 +00:09:19,140 --> 00:09:24,560 +minus infinity ل zero اتحاد من واحد على N للمانة + +122 +00:09:24,560 --> 00:09:31,460 +نهائيةكل جزء هو اتحاد من فترتين طيب لو طلعنا عليه + +123 +00:09:31,460 --> 00:09:35,320 +ممكن يتبسط ايش المكملة تبعته بالرسم ممكن تجيب + +124 +00:09:35,320 --> 00:09:41,010 +بسهولة هي الرسم هي المجموعةمن minus infinity إلى + +125 +00:09:41,010 --> 00:09:45,510 +zero وهي ال zero مفتوح ومن واحد على N اللي هو + +126 +00:09:45,510 --> 00:09:48,510 +هيكون ياش ال واحد على N ال N بيسوي ايش بيساوي واحد + +127 +00:09:48,510 --> 00:09:51,850 +اتنين تلاتة ايه للملا نهائي انا عارف بس كيف الصورة + +128 +00:09:51,850 --> 00:09:57,210 +بدت تكون بهذا الشكل فهذه ال A N من المكملة هي جزء + +129 +00:09:57,210 --> 00:10:01,630 +هذا صح بس مغلق فالمكملة ليست الا zero واحد على N + +130 +00:10:02,270 --> 00:10:05,870 +عايش الشاهد انه بدل ما اتعامل ان المجموعة الأصلية + +131 +00:10:05,870 --> 00:10:09,650 +جزئين في يوم اتحاد المكمل أبسط جزء واحد فانا ممكن + +132 +00:10:09,650 --> 00:10:12,770 +يكون الحسابات بالنسبالي أسهل يدخل الحسابات أسهل + +133 +00:10:12,770 --> 00:10:16,810 +فبدل ما انا اروح اعمل تقاطع على هدول المجموعات + +134 +00:10:16,810 --> 00:10:20,970 +اللي هم جزئين ممكن انا اجيب المكملة أولا و بعدين + +135 +00:10:20,970 --> 00:10:27,370 +اشتغل فلما يقول لي جيب الأولى هذه فانا عندين من + +136 +00:10:27,370 --> 00:10:31,070 +واحد لخمسة خلينا نبسط نيد الصياغة ليس إلا أنها دي + +137 +00:10:31,070 --> 00:10:35,650 +مظبوط إبراهيم الطرف اللي بدوياه فانا طبقا للنظرية + +138 +00:10:35,650 --> 00:10:40,730 +ده إيش بيساوي اتحاد من واحد إلى خمسة أن إبراهيم + +139 +00:10:40,730 --> 00:10:44,930 +فالان أسهل بتعامل مع هدول وفي المحاضرة الماضية + +140 +00:10:44,930 --> 00:10:48,890 +شوفنا مثال قولنا طبعا دولاش الأمثلة ال a واحد هي + +141 +00:10:48,890 --> 00:10:51,950 +من zero لواحد بعدين من zero لنص بعدين من zero لتلت + +142 +00:10:51,950 --> 00:10:54,510 +صح ل zero لخمسة طب إيش الاتحاد؟ + +143 +00:10:57,160 --> 00:11:00,300 +نزيله ل واحد بس مغلق هنا بس هاي الفرق فهي تكرار + +144 +00:11:00,300 --> 00:11:04,840 +فصار هنا الحساب أسهل لو حاولنا نجيب التاني نجيب أو + +145 +00:11:04,840 --> 00:11:08,040 +ورش التقاطع وبعدين نجيب المكملة يمكن أمور تكون + +146 +00:11:08,040 --> 00:11:11,540 +أصعب بالنسبالنا فهنا إيش استفدنا من النظرية بنفس + +147 +00:11:11,540 --> 00:11:16,720 +الأسلوب لو بده أجيب الاتحاد أو مكملة الاتحاد لل a + +148 +00:11:16,720 --> 00:11:20,380 +n الكل prime عبارة عن تقاطع المكملات + +149 +00:11:23,980 --> 00:11:27,760 +وإيش رأيكوا تقاطع المكملات هدولة نفس المثال مار + +150 +00:11:27,760 --> 00:11:33,620 +علينا Zero واحد Zero نص Zero تلت إيش تقاطعهم Zero + +151 +00:11:33,620 --> 00:11:38,100 +واحد على خمسة مار علينا بس مغلق الآن نفس الفكرة + +152 +00:11:38,100 --> 00:11:43,120 +المثال الماضي التقاطع تقاطع هدول هي المكملات هيهم + +153 +00:11:43,120 --> 00:11:48,100 +تقاطع هدول زي المثال المحاضرة السابقةنفسه بس كانت + +154 +00:11:48,100 --> 00:11:52,220 +مفتوحة بتفرجش كتير فنفس الفكرة لأن لو رسمنا هي هذه + +155 +00:11:52,220 --> 00:11:58,300 +الفترة الأولى هي رسمة من zero لواحد بعدين من zero + +156 +00:11:58,300 --> 00:12:03,260 +لنص بعدين من zero لتلت فالتقاطها بيكون المشتركة + +157 +00:12:03,260 --> 00:12:11,580 +فهنا أحد ليهاش تطبيقات النظرية نشوف كمان النظرية + +158 +00:12:14,330 --> 00:12:18,670 +Generalized distributive laws قوانين التوزيع + +159 +00:12:18,670 --> 00:12:23,230 +العامة تمام + +160 +00:12:23,230 --> 00:12:28,930 +فهنا برضه كله بعلمني كيف أتعامل مع عدد كبير من + +161 +00:12:28,930 --> 00:12:33,530 +المجموعات family of six فشوفنا دي مورجان شوفنا + +162 +00:12:33,530 --> 00:12:38,570 +اللي هو النظريات و هكذا فهذا بيخليني أتعامل مع عدد + +163 +00:12:38,570 --> 00:12:43,520 +كبير من المجموعاتطيب لت A بي a set فالـ A مجموعة + +164 +00:12:43,520 --> 00:12:48,940 +عادية و بعدين في عندي family بي سب جامع و الجامع + +165 +00:12:48,940 --> 00:12:51,780 +in capital جامع طبعا فاستخدم الحرف A لحاله مجموعة + +166 +00:12:51,780 --> 00:12:55,300 +واحدة و بده مجموعات متعددة فالـ N شغلها تستخدم رمز + +167 +00:12:55,300 --> 00:13:02,660 +جديد بي سب جامع بي any family of sixاه فهنا بده + +168 +00:13:02,660 --> 00:13:06,140 +يقاطع ال a مع اتحاد ال family .. مع اتحاد ال + +169 +00:13:06,140 --> 00:13:10,320 +family ايه صار؟ صار اتحاد على تقاطع، اتوزعت، اه + +170 +00:13:10,320 --> 00:13:13,160 +فهنا طبعا .. طبعا كيف نفهم هذه؟ ممكن لو خدت انت + +171 +00:13:13,160 --> 00:13:17,040 +هنا إيش ده يصير؟ احنا قولنا a تقاطع بي واحد اتحاد + +172 +00:13:17,040 --> 00:13:20,320 +بي اتنين، بتصير a تقاطع الأول اتحاد a تقاطع + +173 +00:13:20,320 --> 00:13:23,560 +التاني، و هكذا، هنا تكرار، فبتنكتب هذه الشكل، فهذه + +174 +00:13:23,560 --> 00:13:28,640 +بتنكتب بهذه الصورةتمام اه واتحاد مع تقاطع بيصير + +175 +00:13:28,640 --> 00:13:32,820 +ايش تقاطع الاتحادات تقاطع الاتحادات ممكن نقول اه + +176 +00:13:32,820 --> 00:13:36,340 +بتتوزع ايه بتتوزع اه فبرضه بنثبت واحدة والتانية + +177 +00:13:36,340 --> 00:13:40,040 +مشابه خلينا نثبت واحدة والتانية بشكل مشابه طبعا + +178 +00:13:40,040 --> 00:13:46,520 +بنتركها exercise فهذه نظرية اتنين + +179 +00:13:46,520 --> 00:13:52,040 +تسعة approveاختاروا واحدة والتانية هتركوا ك + +180 +00:13:52,040 --> 00:13:57,760 +exercise كل اللي بتركه exercise وهنا الأولى نعمل + +181 +00:13:57,760 --> 00:14:03,640 +الأولى حاضر فهنا طبعا من الفرص اللي بتكون مناسبة + +182 +00:14:03,640 --> 00:14:06,880 +جدا انه نعيد نفس البرهان بالتقليد وبعد اختلافات + +183 +00:14:06,880 --> 00:14:10,160 +بسيطة فهذه بتخلينا نتمرن على البرهان فهنبدأ في + +184 +00:14:10,160 --> 00:14:16,200 +اللي هو برهان Aتمام انا ابدا اشتغل على ال تعريف + +185 +00:14:16,200 --> 00:14:19,620 +نفس القضية هاخد عنصر في الطرف ووصله للطرف التاني + +186 +00:14:19,620 --> 00:14:23,460 +وإذا مشيت تكافؤ بكون انتهت وإلا هضطر أعمل للتجاه + +187 +00:14:23,460 --> 00:14:32,640 +التاني فكالعادة let x be any element such that او + +188 +00:14:32,640 --> 00:14:39,420 +and let كل واحد such that x تنتمي نيجي للطرف الأول + +189 +00:14:39,420 --> 00:14:47,420 +a تقاطعاتحاد Gamma على Gamma ب Sub Gamma + +190 +00:14:50,830 --> 00:14:58,070 +بدأنا من الطرف الأول تمام؟ أه إيش نعمل؟ ممكن بدنا + +191 +00:14:58,070 --> 00:15:02,530 +نفك مين بيقابلنا الجبل؟ التقاطع ولا الاتحاد؟ + +192 +00:15:02,530 --> 00:15:05,950 +التقاطع فده إيش؟ احنا تتذكروا كنا نتعامل مع + +193 +00:15:05,950 --> 00:15:08,630 +مجبعتين الجولد اللي كتلة واحدة؟ الآن كل ال family + +194 +00:15:08,630 --> 00:15:12,450 +كتلة واحدة فده ده إيش؟ كل كتلة تانية بتتعامل فده + +195 +00:15:12,450 --> 00:15:19,170 +عبارة عن X تنتمي لل إيه؟ and X تنتمي للاتحاد على + +196 +00:15:19,170 --> 00:15:24,660 +ال familyهذا ليس إلا تعريف التقاطع فهذا تعريف + +197 +00:15:24,660 --> 00:15:26,040 +التقاطع + +198 +00:15:29,420 --> 00:15:34,040 +تمام ايش ممكن اعمل كمان افك الاتحاد على ال family + +199 +00:15:34,040 --> 00:15:40,820 +اللي هو تعريف اه فهذه تكافئ X تنتمي لل A and ايش + +200 +00:15:40,820 --> 00:15:44,840 +معناه اتحاد يعني فيه على اقل مجموعة تحتوي ال X ليه + +201 +00:15:44,840 --> 00:15:47,880 +ايش بنقول there exist gamma in capital gamma ف + +202 +00:15:47,880 --> 00:15:52,340 +there exist small gamma in capital gamma بحيث X + +203 +00:15:52,340 --> 00:15:57,880 +تنتمي لل B gamma ايش عملت استخدام التعريف الاتحاد + +204 +00:15:57,880 --> 00:16:05,000 +على family ماعلى فهم الإيمةتمام ايش ممكن اعمل؟ + +205 +00:16:05,000 --> 00:16:07,500 +طبعا اي سؤال لما تسألي نفسك ايش بده اعمل ايش يكون + +206 +00:16:07,500 --> 00:16:12,460 +وين؟ وين عينك؟ على المطلوب بدنا نروح نحول تصير A + +207 +00:16:12,460 --> 00:16:16,520 +اتحاد الـB Gamma فانا بده اعمل عملية ايه؟ تبديل، + +208 +00:16:16,520 --> 00:16:19,700 +بده اعمل تبديل، بده اخليها X في الـA و X في الـB + +209 +00:16:19,700 --> 00:16:23,380 +Gamma ايش نعمل؟ نبدل هذه statement و هذه + +210 +00:16:23,380 --> 00:16:27,440 +statement، بدليهم مع الـand مسموح ولا مش مسموح؟ + +211 +00:16:27,440 --> 00:16:30,300 +مسموح، لأن الـand is commutative فده عبارة عن + +212 +00:16:30,300 --> 00:16:35,700 +there exists Gammain capital Gamma وال X تنتمي لل + +213 +00:16:35,700 --> 00:16:41,300 +B Gamma and X تنتمي لل A ما عملناه كله عملناه + +214 +00:16:41,300 --> 00:16:42,120 +commutative law + +215 +00:16:46,030 --> 00:16:49,910 +لأن هذه كلها statement واحدة هيها وفسرتها فهذه + +216 +00:16:49,910 --> 00:16:54,970 +statement و هذه statement ليس ال ابدال تمام؟ الآن + +217 +00:16:54,970 --> 00:16:58,170 +نقرأ مرة تانية بقول there exist gamma and gamma + +218 +00:16:58,170 --> 00:17:03,010 +ممتاز ال X في ال B جامعة وال X في ال A إيش معناته + +219 +00:17:03,010 --> 00:17:08,300 +ال X في التقاطة في التقاطة فهذهthere exists gamma + +220 +00:17:08,300 --> 00:17:12,340 +in capital gamma ال X موجودة في مجموعتين إذا وين + +221 +00:17:12,340 --> 00:17:18,060 +موجودة في تقاطعهم فال X تنتمي لل B gamma تقاطع ال + +222 +00:17:18,060 --> 00:17:22,720 +A من وين هذا بنجيبه تعريف التقاطع definition of + +223 +00:17:22,720 --> 00:17:26,560 +intersection أوصلنا للي بدنا هي نعم there exists + +224 +00:17:26,560 --> 00:17:30,180 +gamma و ال X في مجموعة ما تعتمد على الجامعة هذا + +225 +00:17:30,180 --> 00:17:34,280 +تعريف إيش الاتحاد there exists الاتحاد فده يكافئإن + +226 +00:17:34,280 --> 00:17:40,740 +ال X تنتمي اتحاد على ال family بصبجامة تقاطع ال A + +227 +00:17:40,740 --> 00:17:47,140 +تعريف الاتحاد على ال family مرة تانية هنا كان إيش + +228 +00:17:47,140 --> 00:17:53,440 +نعم برضه اتحاد على ال family كل تكافؤ لأن كل + +229 +00:17:53,440 --> 00:17:57,080 +الخطوات تكافؤ أنا استخدمت تعريفات واستخدمت اللي هو + +230 +00:17:57,080 --> 00:17:59,720 +قانون الإبدال وقانون الإبدال تكافؤ إذا أنا انتهت + +231 +00:17:59,720 --> 00:18:05,130 +المثلة انتهت البرهةفالتاني زيه تماما السؤال التاني + +232 +00:18:05,130 --> 00:18:09,750 +بأنصح انه تنعمل بنفس الخطوات بس هناك بدل ما هى + +233 +00:18:09,750 --> 00:18:16,330 +there exists هتكون for all عشان تقاضى + +234 +00:18:16,330 --> 00:18:22,010 +برضه + +235 +00:18:22,010 --> 00:18:30,570 +خلّيني أشوف مثال مثال + +236 +00:18:30,570 --> 00:18:31,330 +على النظرية + +237 +00:18:34,050 --> 00:18:38,770 +Expand العلاقة اللي أمامنا فيها أن اتحاد مجموعتين + +238 +00:18:38,770 --> 00:18:43,870 +والاتحاد كله كبير family و family into a union of + +239 +00:18:43,870 --> 00:18:48,670 +intersection فبدل ما هي تقاطع اتحادين بدخليها + +240 +00:18:48,670 --> 00:18:53,470 +لاتحاد تقاطعات بدل هي تقاطع اتحادين دخليها اتحاد + +241 +00:18:53,470 --> 00:18:58,750 +لتقاطعات union of intersection فبدنا نعمل عملية + +242 +00:18:58,750 --> 00:19:04,380 +التوزيع فهذا المثال وهي ال solutionفبدل ما هي + +243 +00:19:04,380 --> 00:19:08,720 +كتلتين و بينهم تقاطة بدي أحولها لكل اتحاد و اللي + +244 +00:19:08,720 --> 00:19:12,220 +جوا يكون تقاطة فطبعا نبدأ بال solution نبدأ باش + +245 +00:19:12,220 --> 00:19:15,820 +تقفش لوحدها بدي أعمل عمية expansion بديش أثبت إشي + +246 +00:19:15,820 --> 00:19:20,360 +بس بدي أعمل إيش بدي أفكه بدي أبسطه فانا عندي U او + +247 +00:19:20,360 --> 00:19:33,140 +اتحاد I من 1 ل M A sub Iتقاطع اتحاد J من 1 ل N بي + +248 +00:19:33,140 --> 00:19:33,720 +sub J + +249 +00:19:37,790 --> 00:19:41,870 +هنحاول نستخدم النظرية السابقة فالآن تو يمكن اللي + +250 +00:19:41,870 --> 00:19:45,910 +هو برهنها نعتبر هذه كائنها كلها A كلها A، إيش + +251 +00:19:45,910 --> 00:19:50,810 +بتصير؟ ممكن ندخلها جوا، إيش بتصير؟ بتصير اتحاد J + +252 +00:19:50,810 --> 00:19:55,890 +من 1 ل N، هذه كلها A، خليها زي ما هي، نطلع عليها + +253 +00:19:55,890 --> 00:20:03,370 +نظرة خارجية بشكل مغلق A sub I تقاطع B sub J، واحدة + +254 +00:20:03,370 --> 00:20:07,610 +من النظرية، فهذه كلها كتلة واحدةفكأنه هذه هي ال + +255 +00:20:07,610 --> 00:20:13,050 +ايه ا و ايش و دخلناها اعتبروها ايه هذه تمام اه + +256 +00:20:13,050 --> 00:20:16,430 +فطبعا نظريا بتقول ايه تقاطع الاتحاد بيصير اتحاد + +257 +00:20:16,430 --> 00:20:20,510 +ايه تقاطع اللي جوه فده ايه الان ايش ممكن اعمل الان + +258 +00:20:20,510 --> 00:20:24,450 +بالعكس هيعندي اتحاد مع تقاطع بنفس الاسلوب ادخله + +259 +00:20:24,450 --> 00:20:27,850 +جوه فهذا يساوي اه بدي اشتغل على اللي جوه الان هذا + +260 +00:20:27,850 --> 00:20:38,350 +خلناهJ من 1 ل N بتصير اتحاد I من 1 ل M AI تقاطع BJ + +261 +00:20:38,350 --> 00:20:45,670 +فعملنا ايش اتحاد لتقاطعات فده اتحاد اتحاد زي ما + +262 +00:20:45,670 --> 00:20:49,090 +ممكن تقول sigma و sigma فاتحاد اتحاد و تقاطعات + +263 +00:20:49,090 --> 00:20:54,090 +فعملنا النظرية طبقناها مرتين طبقناها مرتين على + +264 +00:20:54,090 --> 00:20:55,090 +مرحلتين + +265 +00:20:59,750 --> 00:21:06,090 +هذه هي نهاية ال section في اي سؤال قال لننتقل + +266 +00:21:08,410 --> 00:21:13,610 +اللي هنا أنا عملت هذه كانها إيه بعدين فكيتها الآن + +267 +00:21:13,610 --> 00:21:17,810 +بتطلع هنا على اللي جوا سيبك من الاتحاد الخارجي اه + +268 +00:21:17,810 --> 00:21:20,550 +طبعا النظرية مكتوبة من اليمين أو اليسار بتفرجش + +269 +00:21:20,550 --> 00:21:23,870 +لإنه إيش إبدالية الآن في عندي اتحاد مع تقاطعوش + +270 +00:21:23,870 --> 00:21:26,970 +بيصير اتحاد تقاطعات فانا إيش بدي أعمل؟ بدي أقاطع + +271 +00:21:26,970 --> 00:21:30,110 +هذه مع الأولى بعدين مع التانية، مظبوط؟ فده هي، هيك + +272 +00:21:30,110 --> 00:21:36,150 +معناها النظرية فممكن نكتب بهذه الطريقة فحولنا إلى + +273 +00:21:36,150 --> 00:21:37,750 +اتحاد تقاطعات + +274 +00:21:45,770 --> 00:21:53,050 +في ال section الأخير من هذا ال chapter section + +275 +00:21:53,050 --> 00:21:54,830 +27 + +276 +00:22:06,630 --> 00:22:12,050 +طبعاً عنوان The Russell Paradox Paradox يعني فيها + +277 +00:22:12,050 --> 00:22:17,470 +تناقض أو أيش بيفيها مشكلة للعالم Russell طبعاً هنا + +278 +00:22:17,470 --> 00:22:21,590 +احنا هنتحدث عن نقطة يمكن مرنا عليها مرور سريع وهي + +279 +00:22:21,590 --> 00:22:25,710 +ان لا يوجد حاجة اسمها universal set اللي بتحتوي كل + +280 +00:22:25,710 --> 00:22:30,370 +شيء احنا بنعتبر ان في مرحلية او جزء اللي هو مجموعة + +281 +00:22:30,370 --> 00:22:35,230 +مرجعية بتناسب دراسة معينة لكن فيش حاجة اسمهامجموعة + +282 +00:22:35,230 --> 00:22:39,570 +كونية تحتوي كل شيء فنتحدث عن هذا الموضوع ونشوفه + +283 +00:22:39,570 --> 00:22:44,050 +فطبعا في العالم باول هولموس بيقول nothing contains + +284 +00:22:44,050 --> 00:22:46,430 +everything مافيش حاجة تحتوي كل شيء مافيش حاجة + +285 +00:22:46,430 --> 00:22:49,890 +اسمها ال universal set بالمعنى الصحيح المطلق وإنما + +286 +00:22:49,890 --> 00:22:52,990 +بنشغل احنا عايش اشي نسبي انه هذه مجموعة مناسبة + +287 +00:22:52,990 --> 00:22:56,610 +لدراسة معينة مجموعة مرجعية ففيقول ليه مافيش حاجة + +288 +00:22:56,610 --> 00:23:01,920 +اسمها ال universal set الحقيقة وحكيناهافبيقول طبعا + +289 +00:23:01,920 --> 00:23:08,140 +احنا قبل قرن او اكثر كانوا علماء الرياضيات والناس + +290 +00:23:08,140 --> 00:23:14,040 +العاديين بيؤمنوا ان any set of objects could be a + +291 +00:23:14,040 --> 00:23:16,800 +set in the mathematical sense فطبعا زي ما احنا + +292 +00:23:16,800 --> 00:23:20,120 +حكينا فيه اشكالية في التعريف مافيش تعريف علمى، + +293 +00:23:20,120 --> 00:23:24,780 +صريح، جامع، مانعأه فهم كانوا بيقولك any collection + +294 +00:23:24,780 --> 00:23:28,180 +of objects ممكن يكون sets لكن هذا الكلام غير دقيق، + +295 +00:23:28,180 --> 00:23:32,360 +بده بعض الضوابط، بعض المعين، لأنه إذا أشتغلنا بهذا + +296 +00:23:32,360 --> 00:23:36,380 +الشكل أدى إلى تناقض، أدى إلى مشكلةوها دي طبعا + +297 +00:23:36,380 --> 00:23:40,500 +مستحيل تكون مشكلة لأن علم الرياضيات بكتير بيستخدم + +298 +00:23:40,500 --> 00:23:44,820 +نظرية المجموعات والمجموعات فلو كان في المجموعة دي + +299 +00:23:44,820 --> 00:23:49,160 +مش معرفة فيها خطأ كان كتير من العلوم أخطط وكل + +300 +00:23:49,160 --> 00:23:51,860 +العلوم اللي اتطبخت على الرياضيات كان مانجحتش لإن + +301 +00:23:51,860 --> 00:23:54,700 +كان في خطأ معين لكن هذا الكلام غير صحيح فكان بده + +302 +00:23:54,700 --> 00:23:58,100 +اللي هو إعادة نظر في تعريف المجموعة مين اللي بتنفع + +303 +00:23:58,100 --> 00:24:03,170 +تكون مجموعة ومين اللي ماتنفع تكون مجموعةفطبعا ع + +304 +00:24:03,170 --> 00:24:07,330 +سبيل المثال كان ممكن يتحدثوا عن set of all sets + +305 +00:24:07,330 --> 00:24:09,930 +وكانوا يتحدثوا عن مجموعة كل المجموعات اللي هي + +306 +00:24:09,930 --> 00:24:17,710 +universal set بدون ماياش يحددوا او يسألوا ايش + +307 +00:24:17,710 --> 00:24:21,590 +المقصود بالكلمة set فهذا الكلام أدى إلى تناقض + +308 +00:24:22,080 --> 00:24:26,700 +Russell Paradox arises when that makes its theory + +309 +00:24:26,700 --> 00:24:30,900 +of Frigue leads to a contradiction فالبرادوكس يعني + +310 +00:24:30,900 --> 00:24:34,380 +فيه contradiction، فيه تناقض، فيه مشكلة معينة فلو + +311 +00:24:34,380 --> 00:24:37,480 +اشتغلنا بهذه الصورة، مش هذه الصورة البسيطة، + +312 +00:24:37,480 --> 00:24:42,880 +الفطرية السادجة بالنظر للمجموعات، هذا أدى إلى + +313 +00:24:42,880 --> 00:24:48,600 +تناقض كما ذكرت قبل قليلفطبعا إيش بتقول اللي هي ال + +314 +00:24:48,600 --> 00:24:51,940 +paradox؟ the sets of all sets which are not + +315 +00:24:51,940 --> 00:24:55,160 +members of themselves contain itself فبقول + +316 +00:24:55,160 --> 00:24:59,460 +المجموعات اللي هم مجموعة كل المجموعات لازم تحتوي + +317 +00:24:59,460 --> 00:25:02,960 +نفسها ما هي التناقض اللي احنا عشان نشوف طب إذا هذه + +318 +00:25:02,960 --> 00:25:07,120 +ال universal set exist إيش مالها؟ تحتوي كل شيء طب + +319 +00:25:07,120 --> 00:25:10,130 +ما هي نفس الشيء ما هي مجموعةالمجموع هي object إذا + +320 +00:25:10,130 --> 00:25:13,170 +لازم تحتوي نفسها، فإن صار في أنا تناقض، فمنفعش أنا + +321 +00:25:13,170 --> 00:25:18,150 +تحتوي نفسها، منفعش تحتوي نفسها، فكان لابد إنه ينحل + +322 +00:25:18,150 --> 00:25:22,970 +هذا الكلامفأصبح هنا في عندي statement as that is + +323 +00:25:22,970 --> 00:25:25,230 +and its negation are true طبعا هذا هو ال + +324 +00:25:25,230 --> 00:25:28,250 +contradiction فصار عندنا فيه إشكالية حنشوف بعد + +325 +00:25:28,250 --> 00:25:30,890 +قليل كيف بيطلع ال paradox وكيف بيطلع ال + +326 +00:25:30,890 --> 00:25:34,810 +contradiction طبعا هذا زي ما حكينا نقطة مهمة جدا + +327 +00:25:34,810 --> 00:25:37,790 +لو كان هذا الكلام فعلا فيه تناقض فيه paradox كان + +328 +00:25:37,790 --> 00:25:41,290 +اللي هو ايه كتير من النظريات الرياضية انهارت وما + +329 +00:25:41,290 --> 00:25:43,690 +ترتب عليها من العلوم الأخرى كان فيها حيكون فيها + +330 +00:25:43,690 --> 00:25:48,360 +انهيارطبعًا فلمّا العالم Russell's وضّح هذا النقطة + +331 +00:25:48,360 --> 00:25:51,660 +طبعًا ويدوله حل فـRussell's paradox changed the + +332 +00:25:51,660 --> 00:25:54,820 +way mathematicians looked at mathematics فغير + +333 +00:25:54,820 --> 00:25:58,060 +النظرة وتعريف للمجموعات ومين بيصلح يكون مجموعة + +334 +00:25:58,060 --> 00:26:00,780 +ومين لا يصلح أن يكون مجموعة فطبعًا من اللي هو + +335 +00:26:00,780 --> 00:26:03,500 +الـnaive mathematicians that believed naively that + +336 +00:26:03,500 --> 00:26:07,220 +any connection could be a set فبقاشوا اتحولوا من + +337 +00:26:07,220 --> 00:26:10,220 +هذه النظرة النظرة السطحية into two more careful + +338 +00:26:10,220 --> 00:26:14,280 +creaturesصاروا بتعاملوا كمخلوقات أكثر عناية أو + +339 +00:26:14,280 --> 00:26:17,920 +أكثر ذكاء أو أكثر تحديداً في التعامل مع مفهوم + +340 +00:26:17,920 --> 00:26:23,440 +المجموعات. فالتحليل الدقيق للتناقض الموجود بهذا + +341 +00:26:23,440 --> 00:26:28,400 +الكلام، النظر السطحية، طبعاً، ما يمكن نقول إن أي + +342 +00:26:28,400 --> 00:26:32,520 +مجموعة من + +343 +00:26:32,520 --> 00:26:35,900 +المجموعات ممكن تكون مجموعة، فهذه هي النقطة التي + +344 +00:26:35,900 --> 00:26:36,800 +أدت للتناقض. + +345 +00:26:40,700 --> 00:26:43,320 +فطبعا بيقوللي the collection of all sets is + +346 +00:26:43,320 --> 00:26:50,320 +certainly something طبعا كل المجموعات هذه هو شيء + +347 +00:26:50,320 --> 00:26:54,860 +معين بس إيهش بينفعش يكون مجموعة نفسه لأنه بيصير + +348 +00:26:54,860 --> 00:26:57,520 +إيهش بيكون يحتوي نفسه لأ إذا كان في عندنا مجموعة + +349 +00:26:57,520 --> 00:27:01,860 +تحتوي لو في عندنا حاجة معينة تحتوي كل المجموعات + +350 +00:27:01,860 --> 00:27:05,860 +إذا هي مجموعة بتحتوي نفسها فده بيقدر لتناقض زي ما + +351 +00:27:05,860 --> 00:27:09,160 +حنشوف فبينفعش تكون مجموعةمنفعش يكون مجموعة اللي + +352 +00:27:09,160 --> 00:27:13,480 +بيحتوي كل شيء منفعش يكون مجموعة something that + +353 +00:27:13,480 --> 00:27:17,020 +contains all sets cannot be or should not be a set + +354 +00:27:17,020 --> 00:27:20,620 +هذه النقطة منفعش اللي بيحتوي كل شيء و كل المجموعات + +355 +00:27:20,620 --> 00:27:23,920 +يكون نفسه مجموعة لأنه هيحتوي نفسه و هذا بيقدي إلى + +356 +00:27:23,920 --> 00:27:29,570 +تناقضفهذه هي النقطة اللي احنا هنتحدث عنها بشكل + +357 +00:27:29,570 --> 00:27:37,190 +مختصر إن شاء الله طبعا، هذه النقطة إن الشيء اللي + +358 +00:27:37,190 --> 00:27:41,490 +بحتوي كل المجموعات مافعش يكون مجموعة فيه بعض اللي + +359 +00:27:41,490 --> 00:27:46,370 +هو عكسه الناس في بعض اللي هو القصص أو بعض الأمثلة + +360 +00:27:46,370 --> 00:27:51,870 +من الناحية العملية في مثال مشهور اللي هو مسألة + +361 +00:27:51,870 --> 00:27:57,990 +الحلاقفلو في احنا عندنا بلدة ما أو قرية ما، فهذا + +362 +00:27:57,990 --> 00:28:02,030 +فيها حلاج واحد، اعتبر ان في قرية صغيرة، هذا الحلاج + +363 +00:28:02,030 --> 00:28:06,070 +طبعا لمين بحلج؟ للي بحلجش لنفسه، مظبوط؟ كل واحد، + +364 +00:28:06,070 --> 00:28:08,910 +كل إنسان بقعدش يحلج لحاله في البيت، بروح للحلاج + +365 +00:28:08,910 --> 00:28:12,310 +بحلجله، طيب بالنسبة للحلاج نفسه هذا، مين بحلجله؟ + +366 +00:28:12,580 --> 00:28:16,100 +فإذا كان هو بيحلجش لنفسه، مين بيحلجله؟ الحل هذه، + +367 +00:28:16,100 --> 00:28:18,760 +يعني هو بيحلج لنفسه، وإذا بيحلج لنفسه، صار إيش؟ في + +368 +00:28:18,760 --> 00:28:21,360 +إيه المشكلة؟ فزالت تناقض، فنفسي تصير القضية، فإذا + +369 +00:28:21,360 --> 00:28:24,440 +المجموعة بتحتوي كل شيء، لازم تحتوي نفسها، فبصير + +370 +00:28:24,440 --> 00:28:28,720 +هنا فيه تناقض، فده مثال على هذا التناقض وكيف ممكن + +371 +00:28:28,720 --> 00:28:29,600 +إيه يصير + +372 +00:28:36,050 --> 00:28:39,090 +طبعا هنا هتشوف ال paradox كيف انه ممكن يكون و هي + +373 +00:28:39,090 --> 00:28:43,490 +حاجة مشابهة للمثال طبعا عشان نمهج لنظرية رئيسية في + +374 +00:28:43,490 --> 00:28:49,270 +عندنا to لما طبعا احنا في اللغة الإنجليزية نستخدم + +375 +00:28:49,270 --> 00:28:55,040 +مصطلح theoremالـ Proposition ولمّه طبعا باللغة + +376 +00:28:55,040 --> 00:28:59,480 +العربية كله بترجمه نظرية ممكن ان ترجمه او ان ترجمه + +377 +00:28:59,480 --> 00:29:03,220 +مبرهنة اه طب ايش الفرق؟ اه في الغالب لما نقول + +378 +00:29:03,220 --> 00:29:06,200 +theorem بيكون النتيجة مهمة جدا ال theorem هي الأهم + +379 +00:29:06,200 --> 00:29:11,320 +ال proposition أقل أهمية واللمّه أقل أهمية طبعا + +380 +00:29:11,320 --> 00:29:14,850 +أداء بشكل عام طبعا مش قاعدةوفي الغالب إن اللمة + +381 +00:29:14,850 --> 00:29:18,550 +بتكون أنا فيها عندي نتيجة استخدامها محدود في نظرية + +382 +00:29:18,550 --> 00:29:21,530 +ما فانا بدل ما أعمل نظرية كبيرة أو برهانة كبيرة + +383 +00:29:21,530 --> 00:29:24,650 +بروح بعض الاشئ الأيزاء أعملهم إيش لمّة مهيدة + +384 +00:29:24,650 --> 00:29:28,130 +للنظرية فاحنا هنشوف النظرية الرئيسية و هنثبت بعض + +385 +00:29:28,130 --> 00:29:32,370 +الأمور على شكل لمّةهنشوف نفس العملية اللي توقع + +386 +00:29:32,370 --> 00:29:37,630 +حكيناها فبقول suppose that there is a set U of all + +387 +00:29:37,630 --> 00:29:39,950 +sets حنظر في البرنامج مستحيل المجموعات كل + +388 +00:29:39,950 --> 00:29:45,370 +المجموعات وبنعرف مجموعة capital R هي عبارة عن + +389 +00:29:45,370 --> 00:29:48,690 +عناصرها كل المجموعات اللي بتنتمل ال U مجموعة كل + +390 +00:29:48,690 --> 00:29:52,090 +المجموعات اللي لا تنتمل نفسها فإيه المشكلة؟ + +391 +00:29:52,090 --> 00:29:54,770 +ماينفعش مجموعة تنتمل نفسها؟ قولنا لو في الحاجة + +392 +00:29:54,770 --> 00:29:57,790 +اللي تحتوي كل المجموعات هي نفسها مجموعة هتنتمل + +393 +00:29:57,790 --> 00:30:01,250 +نفسها هذا اللي عامل ال contradictionفبقول ليه إذا + +394 +00:30:01,250 --> 00:30:05,550 +كان ال R معرفة في هذا الشكل فال R لا تنتمي لنفسها + +395 +00:30:05,550 --> 00:30:10,490 +فال R لا تنتمي لنفسها إذا ال R تحتوي كل المجموعات + +396 +00:30:10,490 --> 00:30:14,970 +التي لا تنتمي لنفسها فإن ال R لا تنتمي لنفسها + +397 +00:30:14,970 --> 00:30:26,870 +خلّينا نشوف البرهار عم بتشبه قضية الحلاجة فهذه + +398 +00:30:26,870 --> 00:30:33,410 +ال proofهتلم موارد تمام اه بدي اثبت ان ال R لا + +399 +00:30:33,410 --> 00:30:39,130 +تنتمي لنفسها خلينا نعمل by contradiction اه فطبعا + +400 +00:30:39,130 --> 00:30:45,270 +كل اللي يوجد قدام ايش معطق فخلينا نقول assume R + +401 +00:30:45,270 --> 00:30:53,490 +تنتمي لل A prove او indirect prove اختصارا اي + +402 +00:30:53,490 --> 00:31:00,100 +سؤال؟طيب، الآن الـ R تنتمي للـ R، كيف معرفة الـ R؟ + +403 +00:31:00,100 --> 00:31:03,600 +معرفة في كل المجموعات اللي في الـ U والصفة المميزة + +404 +00:31:03,600 --> 00:31:07,820 +إيه؟ اللي لا تنتمي لنفسها، هيك تعريفها، آه، شوف + +405 +00:31:07,820 --> 00:31:13,190 +الـ R كيف معرفةهي كل العناصر S اللي هي مجموعات و + +406 +00:31:13,190 --> 00:31:14,970 +ايش .. ايش .. ايش .. ايش .. ايش خاصية مميزة؟ ايش + +407 +00:31:14,970 --> 00:31:18,910 +الميارات التي لا تنتمي لنفسها؟ فلجيت الـR تنتمي + +408 +00:31:18,910 --> 00:31:22,830 +للـR، بتتحقق من؟ الخاصية المميزة، فإذا من تعريف + +409 +00:31:22,830 --> 00:31:27,430 +الـR، اذا الـR لا تنتمي للـR، من وين جبتوا هذا؟ + +410 +00:31:27,430 --> 00:31:31,830 +تعريف الـR، مشاكل خاصة في المميزة؟ اه هي كل مجموعة + +411 +00:31:31,830 --> 00:31:34,050 +تنتمي لنفسها، ايش صار؟ contradiction، اه + +412 +00:31:34,050 --> 00:31:34,510 +contradiction + +413 +00:31:39,580 --> 00:31:47,260 +فالعكس هو الصحيح الان انا بقول في end U مجموعة كل + +414 +00:31:47,260 --> 00:31:50,960 +المجموعات أنصرها بتحتوي ايش كلها مجموعات عنرفت + +415 +00:31:50,960 --> 00:31:54,360 +مجموعة R بالشكل التالي هي المجموعات اللي في ال U + +416 +00:31:54,360 --> 00:31:58,100 +التي لا تحتوي نفسها التي لا تنتمي إلى نفسها اه + +417 +00:31:58,100 --> 00:32:01,140 +فبقول لي اذا ال R لا تنتمي لل R كيف بدأ بارهنها؟ + +418 +00:32:01,140 --> 00:32:04,740 +by contradiction افترضت ان العكس صحيحطيب R تنتمي + +419 +00:32:04,740 --> 00:32:08,400 +للـ R إيش معيار الـ R؟ هي المجموعات التي لا تنتمي + +420 +00:32:08,400 --> 00:32:11,060 +لنفسها مزال الـ R في الـ R إذا إيش؟ لازم تحقق + +421 +00:32:11,060 --> 00:32:14,240 +المعيار إذا الـ R لا تنتمي للـ R ر تنتمي للـ R ر + +422 +00:32:14,240 --> 00:32:18,240 +لا تنتمي للـ R بي and not be contradiction هنشوف + +423 +00:32:18,240 --> 00:32:26,400 +كمان لمبة العكس، الآن برضه الـ R تنتمي للـ R أنا + +424 +00:32:26,400 --> 00:32:29,100 +أثبتت إن الـ R لا تنتمي للـ R الآن أثبتت إن الـ R + +425 +00:32:29,100 --> 00:32:38,010 +لا تنتمي للـ R لمبة 2مرقمين عن كل ما؟ Approve ال R + +426 +00:32:38,010 --> 00:32:43,370 +نفس المتعريف بس بيقول هنا ال R تنتمي لل R تمام، + +427 +00:32:43,370 --> 00:32:47,130 +بدي أثبت أن ال R تنتمي لل R، برضه by contradiction + +428 +00:32:47,130 --> 00:32:58,060 +Assume R لا تنتمي لل R، برضه indirect proofممتازة + +429 +00:32:58,060 --> 00:33:02,340 +اشمال الار لاتنتم لار حققت المعيار اذا الار تنتم + +430 +00:33:02,340 --> 00:33:08,140 +لار من التعريف اذا الار تنتم لار من وين تعريف الار + +431 +00:33:08,140 --> 00:33:11,300 +فاياش contradiction + +432 +00:33:16,110 --> 00:33:18,770 +ما هي إيه المشكلة فماينفعش يكون مجموعة كل + +433 +00:33:18,770 --> 00:33:22,430 +المجموعات و إلا هتحتوي نفسها و هذا بيقدي ليش إنها + +434 +00:33:22,430 --> 00:33:25,450 +بتحتوي نفسها و لا تحتوي نفسها فصار إيش في + +435 +00:33:25,450 --> 00:33:29,370 +contradiction فطبعا ال نظرية + +436 +00:33:32,440 --> 00:33:36,480 +أه فهي ما هي ال paradox فبنفعش يكون المجموعة اللي + +437 +00:33:36,480 --> 00:33:39,420 +بتحتوي أو الشيء اللي بحتوي كل المجموعات يكون + +438 +00:33:39,420 --> 00:33:42,360 +مجموعة وإلا بيقدّي لهذا التناقض فطبعا هاي النظرية + +439 +00:33:42,360 --> 00:33:46,660 +الأساسية نظرية 2 عشرة there is no set of all sets + +440 +00:33:46,660 --> 00:33:51,260 +there is no set of all sets طبعا بدا تصحيح there + +441 +00:33:51,260 --> 00:33:54,280 +is no set of all sets فبنفعش يكون اللي بحتوي كل + +442 +00:33:54,280 --> 00:33:56,720 +المجموعات هو مجموعة نفسه لأنه بيقدّي له التناقض + +443 +00:33:56,720 --> 00:34:00,890 +فبقول there does not exista set of all sets ما + +444 +00:34:00,890 --> 00:34:05,130 +مفيش عادي أسمة و مجموعة تقاش لكل المجموعة تحتوي كل + +445 +00:34:05,130 --> 00:34:09,070 +شيء طبعا البرهان على اللمة على طول بتطبيق اللمة + +446 +00:34:09,070 --> 00:34:20,550 +التنتين بكون البرهان بينتهي فدي theorem اتنين + +447 +00:34:20,550 --> 00:34:22,650 +عشرة approved + +448 +00:34:26,510 --> 00:34:35,750 +طبعا هنفترض ان هناك مجموعة تحتوي كل شيء لت يو بي a + +449 +00:34:35,750 --> 00:34:40,490 +set of all sets نفترض ان هناك a set of all sets a + +450 +00:34:40,490 --> 00:34:46,470 +set of all sets طبعا هذا اسم المعلمة الابروبا in + +451 +00:34:46,470 --> 00:34:53,370 +contradiction او in direct proof تمام؟ + +452 +00:34:54,250 --> 00:34:59,130 +فطبعا طبقا ليه الكلام اللي هو إيش اللي فات بنحتاج + +453 +00:34:59,130 --> 00:35:04,710 +نعرف إشي ولا لأ؟ فهل بنحتاج نعرف زي .. احنا بن .. + +454 +00:35:04,710 --> 00:35:09,870 +طب قريبا زي اللي هو بنستخدم اللمع فهل بدنا نعرف .. + +455 +00:35:09,870 --> 00:35:18,470 +و نعرف ال R and let ال R اللي توي عرفناها هي S + +456 +00:35:18,470 --> 00:35:26,770 +تنتمي ل U such that S لا تنتميلل S فانا في عندي + +457 +00:35:26,770 --> 00:35:30,690 +مجموعة المجموعات كل شيء ف ال R فعل الكلام طبعا من + +458 +00:35:30,690 --> 00:35:39,510 +اللمة السابقة by لمة واحد ايش R تنتمي لل A لا + +459 +00:35:39,510 --> 00:35:43,850 +تنتمي مظبوط لمة واحد لا تنتمي وللعكس لمة واحد ايش + +460 +00:35:43,850 --> 00:35:50,910 +جالت لا تنتمي اه اه by لمة two ال + +461 +00:35:50,910 --> 00:35:53,350 +R تنتمي ايش صار عندنا contradiction + +462 +00:35:58,470 --> 00:36:03,150 +فطبعا إحنا بنمر على هذا الكلام عشان بس نعالج نقطين + +463 +00:36:03,150 --> 00:36:05,810 +نعالج ممررنا عنه إنه مافيش هناك حاجة اسمها + +464 +00:36:05,810 --> 00:36:10,330 +universal set تحتوي كل شيء أو أيضا كمعلومة تعرفوا + +465 +00:36:10,330 --> 00:36:13,510 +إيش ما يُعرف بيه اللي هو Russell Paradox لو احنا + +466 +00:36:13,510 --> 00:36:18,210 +اتحدثنا عن مجموعة تحتوي كل المجموعات نوصل لتنقض + +467 +00:36:18,210 --> 00:36:21,290 +فاللي بيحتوي كل المجموعات هي حاجة معينة لكن مش + +468 +00:36:21,290 --> 00:36:24,970 +مجموعة، ماينفعش يكون مجموعة لأنه بيحتوي كل + +469 +00:36:24,970 --> 00:36:28,340 +المجموعات وهو مجموعة بيحتوي نفسهو هذا يؤدي إلى + +470 +00:36:28,340 --> 00:36:34,820 +contradiction أو paradox طبعا ال chapter 3 موجود + +471 +00:36:34,820 --> 00:36:38,480 +على الموقع من بارح مش عارف إذا حد بتابع موجود ال + +472 +00:36:38,480 --> 00:36:41,120 +chapter موجود بنا نبدأ فيه ان شاء الله استغلالا + +473 +00:36:41,120 --> 00:36:46,600 +للوقت و ان شاء الله بنقدر ندرس فيه جد ما كانف + +474 +00:36:46,600 --> 00:36:50,780 +chapter تلاتة هنتحدث فيه عن relations and + +475 +00:36:50,780 --> 00:36:55,820 +functions العلاقات والدوال العلاقات والدوال فالان + +476 +00:36:55,820 --> 00:37:01,340 +هنمشي مرحلة و نتقدم خطوة للأمام نتحدث فيها عن ال + +477 +00:37:01,340 --> 00:37:06,060 +relations و ال functions طبعا هنبدأ نقطة البداية + +478 +00:37:06,060 --> 00:37:10,640 +تبعتنا هنبدأ بتعريف اللي هو Cartesian product + +479 +00:37:10,640 --> 00:37:14,340 +فطبعا + +480 +00:37:15,510 --> 00:37:20,630 +دائما إذا بنتحدث احنا عن دالة أو علاقة، علاقة أنصر + +481 +00:37:20,630 --> 00:37:24,330 +مع أنصر، فبدنا يشفي أنصرين، فبنتحدث عن أنصرين + +482 +00:37:24,330 --> 00:37:28,070 +هدولة ونكتبهم بشكل معين، أيضا إذا تتذكروا دائما من + +483 +00:37:28,070 --> 00:37:31,890 +الدوال، لما بنقول نرسم دالة Y تسوء X، نرسم إيه؟ + +484 +00:37:31,890 --> 00:37:36,330 +الزوج مرتب، النقاط في المستوى، فبنحتاج مفهوم الزوج + +485 +00:37:36,330 --> 00:37:39,990 +المرتب، وهو بالتالي بنحتاج لمفهوم ال Cartesian + +486 +00:37:39,990 --> 00:37:43,930 +product ل ال two sets أو الدرب ال Cartesian + +487 +00:37:46,800 --> 00:37:51,980 +أه طبعا احنا هندرس موضوع العلاقة المعرفة على + +488 +00:37:51,980 --> 00:37:57,760 +المجموعة بدلالة الأزواج المرتبة هندرس في علاقة بين + +489 +00:37:57,760 --> 00:38:01,880 +تجزيئ المجموعة كيف أقسمها بشكل مناسب وإيش علاقة ال + +490 +00:38:01,880 --> 00:38:05,830 +partition مصطلح ال partition اللي هو التجزيئمع + +491 +00:38:05,830 --> 00:38:09,790 +علاقات التكافؤ وهي علاقات مهمة في الرياضيات أيضا + +492 +00:38:09,790 --> 00:38:16,010 +هندرس اللي هو مفهوم الدالة وطبعا كعلاقة خاصة من + +493 +00:38:16,010 --> 00:38:19,690 +العلاقات طبعا هندرس بعض اللي هو الخواص الأساسي + +494 +00:38:19,690 --> 00:38:24,850 +للدوار في ال section الأول هنبدأ من ال Cartesian + +495 +00:38:24,850 --> 00:38:30,430 +product of two sets فطبعا + +496 +00:38:30,430 --> 00:38:36,240 +نقطة الانطلاق هي الأزواج المرتبة ordered pairsما + +497 +00:38:36,240 --> 00:38:39,840 +هو الزوج المرتب؟ طبعا الرمز تبعه زي رمز الفترة + +498 +00:38:39,840 --> 00:38:42,860 +للأسف نفس الرمز في بعض الناس بيستخدموا رمز مختلف + +499 +00:38:42,860 --> 00:38:47,720 +للفترات لكن احنا الزوج المرتب متفق عليه فبقول لي + +500 +00:38:47,720 --> 00:38:53,240 +لو انا خدت اي عنصرين A وB العنصر AB المكتوب بهذا + +501 +00:38:53,240 --> 00:38:57,080 +الشكل بيسميه زوج مرتب is called the ordered pair + +502 +00:38:57,080 --> 00:39:04,840 +AB الزوج المرتب AB تقرأ الزوج المرتب AB طبعاهنا + +503 +00:39:04,840 --> 00:39:08,780 +بالنسبة للزوج المرتب ال a بيسموها الإحداث الأول + +504 +00:39:08,780 --> 00:39:12,040 +first coordinate فهنا الترتيب مهم طبعا في المصطلح + +505 +00:39:12,040 --> 00:39:15,120 +فيه ordered pair و ال a first coordinate مش بس + +506 +00:39:15,120 --> 00:39:18,060 +coordinates الترتيب مهم و ال b بيسموها the second + +507 +00:39:18,060 --> 00:39:23,330 +coordinate فالترتيب بالنسبة لنا مهم و أساسينقطة + +508 +00:39:23,330 --> 00:39:26,250 +تالتة بدنا نعرفها من التعريف، لو في عندي زوجين + +509 +00:39:26,250 --> 00:39:30,330 +مرتبين وما بتساووا، إذا الإحداث الأول ساوى الإحداث + +510 +00:39:30,330 --> 00:39:34,110 +الأول، والإحداث التاني ساوى الإحداث التاني، فدول + +511 +00:39:34,110 --> 00:39:38,950 +أول نقاط بدنا ننطلق منها عشان نتعامل مع الأزواج + +512 +00:39:38,950 --> 00:39:45,660 +المرتبةهنا بنأكد على كلمة ordered pair زوج مرتف + +513 +00:39:45,660 --> 00:39:48,900 +فالترتيب مهم جدا مش مجموعة هادي مش زي المجموعة + +514 +00:39:48,900 --> 00:39:51,480 +الترتيب مش مهمة و التكرار مش مهم لأ زوج مرتف + +515 +00:39:51,480 --> 00:39:54,680 +فبقولي the adjective order here emphasizes يعني + +516 +00:39:54,680 --> 00:39:58,040 +بيؤكد that the order in which the objects A and B + +517 +00:39:58,040 --> 00:40:03,410 +appear in AB is essential أساسيالترتيب الظهور مهم، + +518 +00:40:03,410 --> 00:40:07,010 +فالإحداث الأول له دور، الإحداث التاني له دور، + +519 +00:40:07,010 --> 00:40:12,150 +فالترتيب مهم جدا في هذه العلاقة أو في هذا المفهوم، + +520 +00:40:12,150 --> 00:40:15,630 +فطبعا على طول واحد اتنين تختلف تماما عن الزوج + +521 +00:40:15,630 --> 00:40:20,270 +المرتب اتنين واحد، فبنتفق هذه النقطة بشكل أساسي + +522 +00:40:20,720 --> 00:40:25,400 +مثال بسيط اخر لو جالي x y كزوج مرتب بيساوي 2 و 3 + +523 +00:40:25,400 --> 00:40:29,980 +فهذه تكافئ if and only if ال x بتساوي 2 و ال y + +524 +00:40:29,980 --> 00:40:35,640 +بتساوي 3 فهنا دي أمور أساسية بدنا نعتمد عليها فيما + +525 +00:40:35,640 --> 00:40:42,640 +يليفي ISFR فهذه المقدمة الأساسية الآن هنعرف الـ + +526 +00:40:42,640 --> 00:40:48,040 +Cartesian products فهنا يمكن يكون نوع جديد من + +527 +00:40:48,040 --> 00:40:53,580 +العمليات على المجموعات احنا عرفنا الاتحاد والتقاطع + +528 +00:40:53,580 --> 00:40:57,100 +والفرق او المكملة طبعا ليش ما جالش ان هذه عملية + +529 +00:40:57,100 --> 00:41:01,800 +ضرب على المجموعات؟لأن الناتج مجموعة من نوع آخر، لو + +530 +00:41:01,800 --> 00:41:06,420 +طلعنا على الـA والاتحاد، مجموعة من نفس الجنس، نفس + +531 +00:41:06,420 --> 00:41:08,860 +العناصر، يا بتاخد العناصر المشتركة، يا بتاخد كل + +532 +00:41:08,860 --> 00:41:12,040 +العناصر، و الـminus نفس الشيء، بتاخد نفس العناصر + +533 +00:41:12,040 --> 00:41:15,580 +الموجودة، مش موجودة، في جزء من الأجزاء، لكن الآن + +534 +00:41:15,580 --> 00:41:20,190 +هنتشوف أندي مجموعتينفي ال Cartesian product بكون + +535 +00:41:20,190 --> 00:41:24,410 +مجموعة جديدة صحيح لكن عناصرها من جنس آخر من نوع + +536 +00:41:24,410 --> 00:41:30,630 +آخر أزواج مرتبة أزواج مرتبة let A and B be sits + +537 +00:41:30,630 --> 00:41:34,790 +the Cartesian product هي المفهوم of A and Bإيش + +538 +00:41:34,790 --> 00:41:38,510 +الرمز؟ a cross b هاي الرمز، هاي المفهوم، هاي + +539 +00:41:38,510 --> 00:41:42,350 +الرمز، إيش تعريفه؟ is the set of all ordered pairs + +540 +00:41:42,350 --> 00:41:45,850 +x y هي مجموعة كل الأزواج المرتبة، شفين احنا بنكون + +541 +00:41:45,850 --> 00:41:49,910 +إيش؟ نوع جديد من المجموعة، هي مجموعة صحيح الناتج، + +542 +00:41:49,910 --> 00:41:53,750 +لكن عناصرها من نوع جديد، أزواج مرتبة، أزواج مرتبة، + +543 +00:41:53,750 --> 00:41:57,570 +طبعا بشرط إن ال X في الأولى، فالترتيب مهم، و ال Y + +544 +00:41:57,570 --> 00:42:00,390 +في التانية، و ال Y في التانية، طبعا كالعادة + +545 +00:42:00,390 --> 00:42:05,230 +بالرموزA cross الـ B تساوي إيش عناصرها؟ كل الأزواج + +546 +00:42:05,230 --> 00:42:08,810 +المرتبة XY هي عناصرها على صورة أزواج مرتبة بحيث ال + +547 +00:42:08,810 --> 00:42:12,670 +X في الأول و ال Y في التانية and ال Y في التانية + +548 +00:42:12,670 --> 00:42:19,470 +فهذا هو التعريف تمام خلينا نشوف مثال نبدأ بالأمثلة + +549 +00:42:19,470 --> 00:42:23,830 +البسيطة و نحاول نتعود على هذا المفهوم + +550 +00:42:33,340 --> 00:42:38,520 +هنبدأ بمثال بسيط وهنا برضه هنلاحظ هل العملية + +551 +00:42:38,520 --> 00:42:45,380 +إبدالية ولا لأ solution فطبعا أنا عندي ال A بتساوي + +552 +00:42:45,380 --> 00:42:52,940 +واحد اتنين و تلاتة و ال B A و B الحرفين فبدنا نبدأ + +553 +00:42:52,940 --> 00:42:59,620 +A cross ال B تساويفكل العناصر أزواج مرتبة بتاخد + +554 +00:42:59,620 --> 00:43:03,240 +الإحداث الأول من ال A والإحداث التاني من ال B فانا + +555 +00:43:03,240 --> 00:43:08,300 +إيش ممكن يكون عندي؟ واحد و A، إيش كمان؟ واحد و B، + +556 +00:43:08,300 --> 00:43:11,840 +واحد و B، ليش لأ؟ لأنه بيقول ليش هي زوج مرتب، + +557 +00:43:11,840 --> 00:43:14,960 +الإحداث الأول من ال A والتاني من ال B، بنفعيت إيش؟ + +558 +00:43:14,960 --> 00:43:18,900 +طيب إيش ممكن أجيت؟ أشتغل على التنين، اتنين و A و + +559 +00:43:18,900 --> 00:43:24,640 +اتنين و B، و إيش؟ تلاتة و A و تلاتة و B، فدول كل + +560 +00:43:24,640 --> 00:43:29,200 +العناصرهنشوف إن العدد إيش بيساوي، ممكن نعرف أطول، + +561 +00:43:29,200 --> 00:43:31,740 +طبعاً العدد اللي هو الأزواج المرتبة بيساوي عدد + +562 +00:43:31,740 --> 00:43:36,580 +عناصر الـA ضرب عدد عناصر الـB، ف2×3 هي 6 عناصر، + +563 +00:43:36,580 --> 00:43:43,900 +مصبوح، فهذه ليهاش الأول، نيجي نحسب B cross الـA، + +564 +00:43:43,900 --> 00:43:53,270 +زي الأول، بس اختلف، لأ، قلت A و1 وA و2 وA و3بعدين + +565 +00:43:53,270 --> 00:43:58,310 +بي واحد أي زوج مرتب و بي مع التنين و ال بي مع + +566 +00:43:58,310 --> 00:44:02,390 +التلاتة برضه ست عناصر برضه ست عناصر لكن هل + +567 +00:44:02,390 --> 00:44:06,730 +متساويين؟ طبعا لأ مختلفين لأن هذا الزوج مانفعش هذا + +568 +00:44:06,730 --> 00:44:11,950 +يساوي هذا لأن ال a مش واحد فده ليش عملية الضرب غير + +569 +00:44:11,950 --> 00:44:15,930 +إبدالية و بنأكد على هذا الترتيب مهم فبالتالي عملية + +570 +00:44:15,930 --> 00:44:18,790 +اللي هو ال Cartesian product غير إبدالية + +571 +00:44:21,040 --> 00:44:22,900 +تمام، وقفها ان شاء الله المرة الجاية بالكملة + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/sv2su8MeGKk_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/sv2su8MeGKk_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..257962ca1d447653dbacf5dd82a8b645a8d7cb3f --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/sv2su8MeGKk_raw.srt @@ -0,0 +1,2284 @@ +1 +00:00:20,670 --> 00:00:24,310 +بسم الله الرحمن الرحيم هنكمل مع اللي هو العائلات + +2 +00:00:24,310 --> 00:00:29,910 +المفهرة من المجموعات indexed family of sets فشوفنا + +3 +00:00:29,910 --> 00:00:34,690 +احنا النظرية الاولى في الموضوع وكانت النظرية + +4 +00:00:34,690 --> 00:00:38,710 +السابعة في الباب لان ننتقل لنظرية تانية + +5 +00:00:38,710 --> 00:00:43,530 +generalized De Morgan's theorem فطبعا احنا عارفين + +6 +00:00:43,530 --> 00:00:48,370 +ديو مورجانز تتحدث كيف اجيب مكملة التقاطع او مكملة + +7 +00:00:48,370 --> 00:00:54,640 +الاتحادفطبعا في عندنا family of six index family + +8 +00:00:54,640 --> 00:00:59,520 +of six زي ما هي قدامكوا فأول شئ مكملة الاتحاد + +9 +00:00:59,520 --> 00:01:04,360 +بتساوي تقاطع المكملات تعميم للنظرية السابقة أيضا + +10 +00:01:04,360 --> 00:01:10,650 +مكملة التقاطع تساوي اتحاد المكملاتفهذا مبدأ A عام + +11 +00:01:10,650 --> 00:01:13,650 +بغض النظر كان اللي عندنا التقاطع او الاتحاد + +12 +00:01:13,650 --> 00:01:16,850 +لمجموعتين او اكثر اي عدد من المجموعات فالكلام + +13 +00:01:16,850 --> 00:01:21,890 +دايما صحيح خلينا نشوف برهان واحدة منهم والتانية + +14 +00:01:21,890 --> 00:01:29,670 +بشكل مشابه هتركها exercise فهذه طبعا نظرية اتنين + +15 +00:01:29,670 --> 00:01:35,450 +تمانية وهذا هو البرهان عن برهن فرع ايش رأيكوا برهن + +16 +00:01:35,450 --> 00:01:41,220 +A ولا B؟B ولا ايه؟ B تمع فرع B + +17 +00:01:44,430 --> 00:01:49,030 +فطبعا زي ما مار علينا أكتر من مرة في أننا مجموعتين + +18 +00:01:49,030 --> 00:01:54,570 +متساويتين هنثبت التساوي فطبعا مافيش عننا معلومات + +19 +00:01:54,570 --> 00:01:58,450 +كتير زي ما حكيت للاتحاد والتقاط على ال family + +20 +00:01:58,450 --> 00:02:03,890 +فهنبدأ من التعريف هناخد عنصر في طرف إذا مشينا if + +21 +00:02:03,890 --> 00:02:07,790 +and only if بيكون أثبتنا التساوي إذا صار فينا اللي + +22 +00:02:07,790 --> 00:02:10,990 +هو if then بيكون احنا عملنا subset فنبدأ من الطرف + +23 +00:02:10,990 --> 00:02:14,540 +التاني و هكذا فخليني نبدأ من الطرف اليسارفنقول له + +24 +00:02:14,540 --> 00:02:24,100 +let x be any element كالعادة element and let x + +25 +00:02:24,100 --> 00:02:29,300 +تنتمي للطرف، نبدأ من إيش؟ من الطرف اللي هو اليسار، + +26 +00:02:29,300 --> 00:02:35,840 +اللي هو إيش؟ لمكملة التقاطة جامعة in capital جامعة + +27 +00:02:35,840 --> 00:02:40,810 +a sub gamma لكل برايةفهنا بداية يعتوقع بسيطة لكل + +28 +00:02:40,810 --> 00:02:44,930 +بدأي المفروض يعرف كيف يتعامل مع علاقة ال subset مع + +29 +00:02:44,930 --> 00:02:47,950 +علاقة التساوي اللي هي subset و subset ليس الا اه و + +30 +00:02:47,950 --> 00:02:51,430 +هكذا تمام ايش ممكن نعمل ان نعرّف نستخدم تعريف ال + +31 +00:02:51,430 --> 00:02:54,370 +compliment فهو اللي موجود في ال compliment هو مش + +32 +00:02:54,370 --> 00:02:58,350 +موجود في المجموعة الأصلية فهذا على طول تعريف يكافئ + +33 +00:02:59,060 --> 00:03:05,740 +فهذا يكافئ ان X لا تنتمي للتقاطع جامع ال capital + +34 +00:03:05,740 --> 00:03:09,680 +جامع a sub جامع من وين جيبت هذه الخطوة تعريف + +35 +00:03:09,680 --> 00:03:15,300 +المكملة الى prime ممكن نرمز له بها الشكل أي سؤال + +36 +00:03:16,680 --> 00:03:20,340 +مرّت علينا هذه الفكرة في السابق، قلنا احنا ماعناش + +37 +00:03:20,340 --> 00:03:24,040 +علاقة إيش معنات لا ينتمي، لكن عندنا تعريف ينتمي، + +38 +00:03:24,040 --> 00:03:27,740 +فماخو ممكن ناخد النفي برا، في أي استفسار؟ فناخد + +39 +00:03:27,740 --> 00:03:32,040 +النفي برا، فهذه مجرد notation، هذه عبارة عن not X + +40 +00:03:32,040 --> 00:03:37,260 +تنتمي لمن؟ للتقاطة، small gamma in capital gamma A + +41 +00:03:37,260 --> 00:03:42,840 +sub gamma، هذا ليس إلا notationمجرد رمز ايش معناه + +42 +00:03:42,840 --> 00:03:48,140 +تنفي اه تمام ادم النفي فالان بكتابة هذه الصورة + +43 +00:03:48,140 --> 00:03:51,300 +اصبح اندي مقدر ان اش اعمل افسر التقاطع على الفامل + +44 +00:03:51,300 --> 00:03:55,860 +افسر التقاطع على الفامل فهذه تكافئ not ايش معناه x + +45 +00:03:55,860 --> 00:03:58,680 +تنتمي للتقاطع انها موجودة في كل المجموعات اللي + +46 +00:03:58,680 --> 00:04:03,240 +احنا بنكتبها ايش for all gamma in capital gamma x + +47 +00:04:03,240 --> 00:04:08,740 +تنتمي لل a sub gamma من وينها ده تعريف تقاطع على + +48 +00:04:08,740 --> 00:04:14,410 +الفاملممكن اعمله اختصارا اللي هو موضوعنا في ال + +49 +00:04:14,410 --> 00:04:19,210 +section هذا اللي بدأنا فيه متفقين؟ امتبعين؟ تمام + +50 +00:04:19,210 --> 00:04:22,430 +الان ايش ممكن اعمل؟ ادخل النفي على ال quantifier + +51 +00:04:22,430 --> 00:04:27,110 +بهذا الشكل فهذا عبارة عن يكافئ there exists gamma + +52 +00:04:27,110 --> 00:04:33,470 +in capital gamma و X لا تنتمي لل A Gamma فشل اللي + +53 +00:04:33,470 --> 00:04:35,970 +هو ده عبارة عن مين؟ اللي هو negation او quantifier + +54 +00:04:35,970 --> 00:04:40,330 +negation quantifier + +55 +00:04:44,630 --> 00:04:47,850 +negation فهذا اللي كنا احنا بنحاول نتعلمه في + +56 +00:04:47,850 --> 00:04:51,870 +section 1-6 بتذكروا؟ هيه بنحتاجه شفتوا كيف نتعامل؟ + +57 +00:04:51,870 --> 00:04:55,430 +مع ال quantifier مع النفي و التبسيط شايفين احنا + +58 +00:04:55,430 --> 00:04:58,070 +ليش اتعلمناها؟ كنا نقول احنا بنتعلم لأن وحيانا + +59 +00:04:58,070 --> 00:05:01,590 +مجرد انك تحط النفي و بس مافيدناش، بدنا نحطها بصورة + +60 +00:05:01,590 --> 00:05:04,450 +مناسبة، بدنا تبسيط فهذا الكلام اللي احنا كنا نتحدث + +61 +00:05:04,450 --> 00:05:07,990 +عنه فاين استفدنا؟ اه اقتربنا اقتربنا لان انا بدي + +62 +00:05:07,990 --> 00:05:11,810 +احول لمين؟تقاطع للاتحاد الاتحاد هو ايش؟ there + +63 +00:05:11,810 --> 00:05:14,530 +exists و بعدين إيش بدهيها تكون في المكملة طب ما هي + +64 +00:05:14,530 --> 00:05:17,230 +إيش؟ اللي مش موجودة إيش معناتها؟ مش موجودة في الـA + +65 +00:05:17,230 --> 00:05:20,370 +Gamma موجودة وين؟ في الـA Gamma complement فده + +66 +00:05:20,370 --> 00:05:24,650 +بيكافئ طبعا بالترتيب there exists Gamma تنتمي + +67 +00:05:24,650 --> 00:05:29,450 +للـCapital Gamma والـX تنتمي للـA Gamma Pri تعريف + +68 +00:05:29,450 --> 00:05:32,710 +المكملة الـPri + +69 +00:05:34,660 --> 00:05:40,100 +فأرجو زي ما حكيت مش غلط إنه نجلد نشوف الكتاب كيف + +70 +00:05:40,100 --> 00:05:43,720 +بيحل إحنا كيف بنحل في المحاضرة والأنثى للمشابه + +71 +00:05:43,720 --> 00:05:47,480 +نمشي خطوة خطوة ما نستبقش الأحداث ما نقفزش عن بعض + +72 +00:05:47,480 --> 00:05:51,560 +الخطوات كلها خطوات ضرورية في الغالب ممكن نقتصر في + +73 +00:05:51,560 --> 00:05:55,680 +بعض الأحيان النادرة طبعا هذا يكافئ ليس إلا X تنتمي + +74 +00:05:55,680 --> 00:05:59,580 +لمين للاتحاد بتروح لتعريف اللي هو الاتحاد على ال + +75 +00:05:59,580 --> 00:06:05,320 +family A sub gamma prime definitionof اللي هو + +76 +00:06:05,320 --> 00:06:09,680 +إتحاد على الـ family وهو المطلوب بدأنا من طرف + +77 +00:06:09,680 --> 00:06:13,000 +وصلنا للطرف التاني كله تكافأت طيب متأكدين أنه كله + +78 +00:06:13,000 --> 00:06:16,560 +تكافأت؟ انشوف إيش استخدمنا؟ استخدمنا التعريف تعريف + +79 +00:06:16,560 --> 00:06:21,080 +دايما تكافأت استخدمنا notation مجرد رمز تفسير إيش + +80 +00:06:21,080 --> 00:06:25,700 +استخدمنا؟ تعريف استخدمنا quantifier negation وده + +81 +00:06:25,700 --> 00:06:28,620 +إيش معنى تكافأت لو رجعتقولها و بعضين تعريف و تعريف + +82 +00:06:28,620 --> 00:06:35,620 +فإن كله تكافأت فالبرهان انتهى فهناthus مكملة + +83 +00:06:35,620 --> 00:06:43,400 +التقاطع تساوي له اتحاد المكملات وهو المطلوب اثباته + +84 +00:06:43,400 --> 00:06:47,740 +وهو + +85 +00:06:47,740 --> 00:06:48,540 +المطلوب + +86 +00:06:52,040 --> 00:06:55,600 +في آية السفسار فجايفين احنا كل قواعد المنطق + +87 +00:06:55,600 --> 00:06:58,320 +بنستخدمها وكل اللي اتعلمناها في ال chapter الأول + +88 +00:06:58,320 --> 00:07:01,320 +اللي احنا حطينا فيه المبادئ العامة المنطق كيف + +89 +00:07:01,320 --> 00:07:05,180 +نتعامل مع الروابط كيف نتعامل مع المكملات كيف + +90 +00:07:05,180 --> 00:07:09,300 +نتعامل مع اليومل وطرق البرهان الآن بدنا نطبق في + +91 +00:07:09,300 --> 00:07:17,600 +أمثلة متعددة في أماكن متعددة تمام نشوف مثال فضل + +92 +00:07:22,750 --> 00:07:25,770 +بكون احنا عملنا subset لان لازم ارجع لانه ايش + +93 +00:07:25,770 --> 00:07:29,910 +تعريف التساوي for all x x في الأولى if and all if + +94 +00:07:29,910 --> 00:07:34,210 +x في التانى فعشان امشي لازم تكون صحيح بس بدك تعمل + +95 +00:07:34,210 --> 00:07:39,010 +two parts اه بكون انت عملت one part بدك ال part + +96 +00:07:39,010 --> 00:07:44,490 +التانى فاحنا ايش بدنالأ لأ لأ من الأول أنا بدأت + +97 +00:07:44,490 --> 00:07:47,730 +هالجيت من اليسار إذا مشيت تكافؤ ووصلت اليمين + +98 +00:07:47,730 --> 00:07:51,590 +التساوي انتهى ماشيت implies بدأ أبدأ من اليمين + +99 +00:07:51,590 --> 00:07:54,970 +الآن و أوصل لليسار لأن ممكن أعملت الأولة صبصت من + +100 +00:07:54,970 --> 00:07:59,070 +التانية إذا في implies إذا في تكافؤ تساوي إذا عملت + +101 +00:07:59,070 --> 00:08:01,310 +implies بقى ممكن أعملت أن الأولة صبصت من التانية + +102 +00:08:01,310 --> 00:08:04,170 +طب كيف تساوي و التانية كمان صبصت من الأولة لازم + +103 +00:08:04,170 --> 00:08:08,210 +أبدأ من التانيةواضحة؟ اه فهذه دايما نتذكر التعريف + +104 +00:08:08,210 --> 00:08:11,730 +ومحطوط في الملاحظة انه قلنا a تساوي b if and only + +105 +00:08:11,730 --> 00:08:15,150 +if a subset من ال b and b subset من ال a فهذا + +106 +00:08:15,150 --> 00:08:19,190 +البديل اه فهذا البديل تمام خلينا نشوف مثال ايش + +107 +00:08:19,190 --> 00:08:23,110 +فايديت هذا النظرية او احد الفوائدأنا إيش بعمل؟ + +108 +00:08:23,110 --> 00:08:28,550 +القضية إنه أنا هنا بدل ما أجيب التقاطع، بعدين بدي + +109 +00:08:28,550 --> 00:08:31,210 +أجيب المكملة، هذه طريقة، أنا ليش بقولك إيه + +110 +00:08:31,210 --> 00:08:34,550 +الترتيب، احسب التقاطع و بعدين أجيب المكملة، طب إيش + +111 +00:08:34,550 --> 00:08:39,830 +البديل؟ لأ، احسب المكملات و بعدين أخد الاتحاد، فمن + +112 +00:08:39,830 --> 00:08:42,970 +كل واحدة هتكون أحيانا أسهل من التانية، واحدة تكون + +113 +00:08:42,970 --> 00:08:45,510 +أسهل من التانية، فهذا بديل، بديني بدائل و أنا + +114 +00:08:45,510 --> 00:08:50,390 +بشيوف من الأنسب لي، عصابين المثالع سبيل المثال في + +115 +00:08:50,390 --> 00:08:56,730 +عندنا مثال أمامكم في عندنا مجموعات والمجموعات دي + +116 +00:08:56,730 --> 00:09:02,050 +شوية ممكن تكون مركبة شوية أو معقدة شوية لو أخدنا + +117 +00:09:02,050 --> 00:09:06,100 +المكملة تبعتها هيكون العملية أسهلأه solution + +118 +00:09:06,100 --> 00:09:10,140 +فالحقيقة أنا فيها عندي خمس مجموعات و التقاطع عليهم + +119 +00:09:10,140 --> 00:09:13,400 +او الاتحاد عليهم ايش المجموعات المجموعات ممكن + +120 +00:09:13,400 --> 00:09:19,140 +ارمضلها بالرمز AN تتكون من مين تتكون من جزءين من + +121 +00:09:19,140 --> 00:09:24,560 +minus infinity ل zero اتحاد من واحد على N للمانة + +122 +00:09:24,560 --> 00:09:31,460 +نهائيةكل جزء هو اتحاد من فترتين طيب لو طلعنا عليه + +123 +00:09:31,460 --> 00:09:35,320 +ممكن يتبسط ايش المكملة تبعته بالرسم ممكن تجيب + +124 +00:09:35,320 --> 00:09:41,010 +بسهولة هي الرسم هي المجموعةمن minus infinity إلى + +125 +00:09:41,010 --> 00:09:45,510 +zero وهي ال zero مفتوح ومن واحد على N اللي هو + +126 +00:09:45,510 --> 00:09:48,510 +هيكون ياش ال واحد على N ال N بيسوي ايش بيساوي واحد + +127 +00:09:48,510 --> 00:09:51,850 +اتنين تلاتة ايه للملا نهائي انا عارف بس كيف الصورة + +128 +00:09:51,850 --> 00:09:57,210 +بدت تكون بهذا الشكل فهذه ال A N من المكملة هي جزء + +129 +00:09:57,210 --> 00:10:01,630 +هذا صح بس مغلق فالمكملة ليست الا zero واحد على N + +130 +00:10:02,270 --> 00:10:05,870 +عايش الشاهد انه بدل ما اتعامل ان المجموعة الأصلية + +131 +00:10:05,870 --> 00:10:09,650 +جزئين في يوم اتحاد المكمل أبسط جزء واحد فانا ممكن + +132 +00:10:09,650 --> 00:10:12,770 +يكون الحسابات بالنسبالي أسهل يدخل الحسابات أسهل + +133 +00:10:12,770 --> 00:10:16,810 +فبدل ما انا اروح اعمل تقاطع على هدول المجموعات + +134 +00:10:16,810 --> 00:10:20,970 +اللي هم جزئين ممكن انا اجيب المكملة أولا و بعدين + +135 +00:10:20,970 --> 00:10:27,370 +اشتغل فلما يقول لي جيب الأولى هذه فانا عندين من + +136 +00:10:27,370 --> 00:10:31,070 +واحد لخمسة خلينا نبسط نيد الصياغة ليس إلا أنها دي + +137 +00:10:31,070 --> 00:10:35,650 +مظبوط إبراهيم الطرف اللي بدوياه فانا طبقا للنظرية + +138 +00:10:35,650 --> 00:10:40,730 +ده إيش بيساوي اتحاد من واحد إلى خمسة أن إبراهيم + +139 +00:10:40,730 --> 00:10:44,930 +فالان أسهل بتعامل مع هدول وفي المحاضرة الماضية + +140 +00:10:44,930 --> 00:10:48,890 +شوفنا مثال قولنا طبعا دولاش الأمثلة ال a واحد هي + +141 +00:10:48,890 --> 00:10:51,950 +من zero لواحد بعدين من zero لنص بعدين من zero لتلت + +142 +00:10:51,950 --> 00:10:54,510 +صح ل zero لخمسة طب إيش الاتحاد؟ + +143 +00:10:57,160 --> 00:11:00,300 +نزيله ل واحد بس مغلق هنا بس هاي الفرق فهي تكرار + +144 +00:11:00,300 --> 00:11:04,840 +فصار هنا الحساب أسهل لو حاولنا نجيب التاني نجيب أو + +145 +00:11:04,840 --> 00:11:08,040 +ورش التقاطع وبعدين نجيب المكملة يمكن أمور تكون + +146 +00:11:08,040 --> 00:11:11,540 +أصعب بالنسبالنا فهنا إيش استفدنا من النظرية بنفس + +147 +00:11:11,540 --> 00:11:16,720 +الأسلوب لو بده أجيب الاتحاد أو مكملة الاتحاد لل a + +148 +00:11:16,720 --> 00:11:20,380 +n الكل prime عبارة عن تقاطع المكملات + +149 +00:11:23,980 --> 00:11:27,760 +وإيش رأيكوا تقاطع المكملات هدولة نفس المثال مار + +150 +00:11:27,760 --> 00:11:33,620 +علينا Zero واحد Zero نص Zero تلت إيش تقاطعهم Zero + +151 +00:11:33,620 --> 00:11:38,100 +واحد على خمسة مار علينا بس مغلق الآن نفس الفكرة + +152 +00:11:38,100 --> 00:11:43,120 +المثال الماضي التقاطع تقاطع هدول هي المكملات هيهم + +153 +00:11:43,120 --> 00:11:48,100 +تقاطع هدول زي المثال المحاضرة السابقةنفسه بس كانت + +154 +00:11:48,100 --> 00:11:52,220 +مفتوحة بتفرجش كتير فنفس الفكرة لأن لو رسمنا هي هذه + +155 +00:11:52,220 --> 00:11:58,300 +الفترة الأولى هي رسمة من zero لواحد بعدين من zero + +156 +00:11:58,300 --> 00:12:03,260 +لنص بعدين من zero لتلت فالتقاطها بيكون المشتركة + +157 +00:12:03,260 --> 00:12:11,580 +فهنا أحد ليهاش تطبيقات النظرية نشوف كمان النظرية + +158 +00:12:14,330 --> 00:12:18,670 +Generalized distributive laws قوانين التوزيع + +159 +00:12:18,670 --> 00:12:23,230 +العامة تمام + +160 +00:12:23,230 --> 00:12:28,930 +فهنا برضه كله بعلمني كيف أتعامل مع عدد كبير من + +161 +00:12:28,930 --> 00:12:33,530 +المجموعات family of six فشوفنا دي مورجان شوفنا + +162 +00:12:33,530 --> 00:12:38,570 +اللي هو النظريات و هكذا فهذا بيخليني أتعامل مع عدد + +163 +00:12:38,570 --> 00:12:43,520 +كبير من المجموعاتطيب لت A بي a set فالـ A مجموعة + +164 +00:12:43,520 --> 00:12:48,940 +عادية و بعدين في عندي family بي سب جامع و الجامع + +165 +00:12:48,940 --> 00:12:51,780 +in capital جامع طبعا فاستخدم الحرف A لحاله مجموعة + +166 +00:12:51,780 --> 00:12:55,300 +واحدة و بده مجموعات متعددة فالـ N شغلها تستخدم رمز + +167 +00:12:55,300 --> 00:13:02,660 +جديد بي سب جامع بي any family of sixاه فهنا بده + +168 +00:13:02,660 --> 00:13:06,140 +يقاطع ال a مع اتحاد ال family .. مع اتحاد ال + +169 +00:13:06,140 --> 00:13:10,320 +family ايه صار؟ صار اتحاد على تقاطع، اتوزعت، اه + +170 +00:13:10,320 --> 00:13:13,160 +فهنا طبعا .. طبعا كيف نفهم هذه؟ ممكن لو خدت انت + +171 +00:13:13,160 --> 00:13:17,040 +هنا إيش ده يصير؟ احنا قولنا a تقاطع بي واحد اتحاد + +172 +00:13:17,040 --> 00:13:20,320 +بي اتنين، بتصير a تقاطع الأول اتحاد a تقاطع + +173 +00:13:20,320 --> 00:13:23,560 +التاني، و هكذا، هنا تكرار، فبتنكتب هذه الشكل، فهذه + +174 +00:13:23,560 --> 00:13:28,640 +بتنكتب بهذه الصورةتمام اه واتحاد مع تقاطع بيصير + +175 +00:13:28,640 --> 00:13:32,820 +ايش تقاطع الاتحادات تقاطع الاتحادات ممكن نقول اه + +176 +00:13:32,820 --> 00:13:36,340 +بتتوزع ايه بتتوزع اه فبرضه بنثبت واحدة والتانية + +177 +00:13:36,340 --> 00:13:40,040 +مشابه خلينا نثبت واحدة والتانية بشكل مشابه طبعا + +178 +00:13:40,040 --> 00:13:46,520 +بنتركها exercise فهذه نظرية اتنين + +179 +00:13:46,520 --> 00:13:52,040 +تسعة approveاختاروا واحدة والتانية هتركوا ك + +180 +00:13:52,040 --> 00:13:57,760 +exercise كل اللي بتركه exercise وهنا الأولى نعمل + +181 +00:13:57,760 --> 00:14:03,640 +الأولى حاضر فهنا طبعا من الفرص اللي بتكون مناسبة + +182 +00:14:03,640 --> 00:14:06,880 +جدا انه نعيد نفس البرهان بالتقليد وبعد اختلافات + +183 +00:14:06,880 --> 00:14:10,160 +بسيطة فهذه بتخلينا نتمرن على البرهان فهنبدأ في + +184 +00:14:10,160 --> 00:14:16,200 +اللي هو برهان Aتمام انا ابدا اشتغل على ال تعريف + +185 +00:14:16,200 --> 00:14:19,620 +نفس القضية هاخد عنصر في الطرف ووصله للطرف التاني + +186 +00:14:19,620 --> 00:14:23,460 +وإذا مشيت تكافؤ بكون انتهت وإلا هضطر أعمل للتجاه + +187 +00:14:23,460 --> 00:14:32,640 +التاني فكالعادة let x be any element such that او + +188 +00:14:32,640 --> 00:14:39,420 +and let كل واحد such that x تنتمي نيجي للطرف الأول + +189 +00:14:39,420 --> 00:14:47,420 +a تقاطعاتحاد Gamma على Gamma ب Sub Gamma + +190 +00:14:50,830 --> 00:14:58,070 +بدأنا من الطرف الأول تمام؟ أه إيش نعمل؟ ممكن بدنا + +191 +00:14:58,070 --> 00:15:02,530 +نفك مين بيقابلنا الجبل؟ التقاطع ولا الاتحاد؟ + +192 +00:15:02,530 --> 00:15:05,950 +التقاطع فده إيش؟ احنا تتذكروا كنا نتعامل مع + +193 +00:15:05,950 --> 00:15:08,630 +مجبعتين الجولد اللي كتلة واحدة؟ الآن كل ال family + +194 +00:15:08,630 --> 00:15:12,450 +كتلة واحدة فده ده إيش؟ كل كتلة تانية بتتعامل فده + +195 +00:15:12,450 --> 00:15:19,170 +عبارة عن X تنتمي لل إيه؟ and X تنتمي للاتحاد على + +196 +00:15:19,170 --> 00:15:24,660 +ال familyهذا ليس إلا تعريف التقاطع فهذا تعريف + +197 +00:15:24,660 --> 00:15:26,040 +التقاطع + +198 +00:15:29,420 --> 00:15:34,040 +تمام ايش ممكن اعمل كمان افك الاتحاد على ال family + +199 +00:15:34,040 --> 00:15:40,820 +اللي هو تعريف اه فهذه تكافئ X تنتمي لل A and ايش + +200 +00:15:40,820 --> 00:15:44,840 +معناه اتحاد يعني فيه على اقل مجموعة تحتوي ال X ليه + +201 +00:15:44,840 --> 00:15:47,880 +ايش بنقول there exist gamma in capital gamma ف + +202 +00:15:47,880 --> 00:15:52,340 +there exist small gamma in capital gamma بحيث X + +203 +00:15:52,340 --> 00:15:57,880 +تنتمي لل B gamma ايش عملت استخدام التعريف الاتحاد + +204 +00:15:57,880 --> 00:16:05,000 +على family ماعلى فهم الإيمةتمام ايش ممكن اعمل؟ + +205 +00:16:05,000 --> 00:16:07,500 +طبعا اي سؤال لما تسألي نفسك ايش بده اعمل ايش يكون + +206 +00:16:07,500 --> 00:16:12,460 +وين؟ وين عينك؟ على المطلوب بدنا نروح نحول تصير A + +207 +00:16:12,460 --> 00:16:16,520 +اتحاد الـB Gamma فانا بده اعمل عملية ايه؟ تبديل، + +208 +00:16:16,520 --> 00:16:19,700 +بده اعمل تبديل، بده اخليها X في الـA و X في الـB + +209 +00:16:19,700 --> 00:16:23,380 +Gamma ايش نعمل؟ نبدل هذه statement و هذه + +210 +00:16:23,380 --> 00:16:27,440 +statement، بدليهم مع الـand مسموح ولا مش مسموح؟ + +211 +00:16:27,440 --> 00:16:30,300 +مسموح، لأن الـand is commutative فده عبارة عن + +212 +00:16:30,300 --> 00:16:35,700 +there exists Gammain capital Gamma وال X تنتمي لل + +213 +00:16:35,700 --> 00:16:41,300 +B Gamma and X تنتمي لل A ما عملناه كله عملناه + +214 +00:16:41,300 --> 00:16:42,120 +commutative law + +215 +00:16:46,030 --> 00:16:49,910 +لأن هذه كلها statement واحدة هيها وفسرتها فهذه + +216 +00:16:49,910 --> 00:16:54,970 +statement و هذه statement ليس ال ابدال تمام؟ الآن + +217 +00:16:54,970 --> 00:16:58,170 +نقرأ مرة تانية بقول there exist gamma and gamma + +218 +00:16:58,170 --> 00:17:03,010 +ممتاز ال X في ال B جامعة وال X في ال A إيش معناته + +219 +00:17:03,010 --> 00:17:08,300 +ال X في التقاطة في التقاطة فهذهthere exists gamma + +220 +00:17:08,300 --> 00:17:12,340 +in capital gamma ال X موجودة في مجموعتين إذا وين + +221 +00:17:12,340 --> 00:17:18,060 +موجودة في تقاطعهم فال X تنتمي لل B gamma تقاطع ال + +222 +00:17:18,060 --> 00:17:22,720 +A من وين هذا بنجيبه تعريف التقاطع definition of + +223 +00:17:22,720 --> 00:17:26,560 +intersection أوصلنا للي بدنا هي نعم there exists + +224 +00:17:26,560 --> 00:17:30,180 +gamma و ال X في مجموعة ما تعتمد على الجامعة هذا + +225 +00:17:30,180 --> 00:17:34,280 +تعريف إيش الاتحاد there exists الاتحاد فده يكافئإن + +226 +00:17:34,280 --> 00:17:40,740 +ال X تنتمي اتحاد على ال family بصبجامة تقاطع ال A + +227 +00:17:40,740 --> 00:17:47,140 +تعريف الاتحاد على ال family مرة تانية هنا كان إيش + +228 +00:17:47,140 --> 00:17:53,440 +نعم برضه اتحاد على ال family كل تكافؤ لأن كل + +229 +00:17:53,440 --> 00:17:57,080 +الخطوات تكافؤ أنا استخدمت تعريفات واستخدمت اللي هو + +230 +00:17:57,080 --> 00:17:59,720 +قانون الإبدال وقانون الإبدال تكافؤ إذا أنا انتهت + +231 +00:17:59,720 --> 00:18:05,130 +المثلة انتهت البرهةفالتاني زيه تماما السؤال التاني + +232 +00:18:05,130 --> 00:18:09,750 +بأنصح انه تنعمل بنفس الخطوات بس هناك بدل ما هى + +233 +00:18:09,750 --> 00:18:16,330 +there exists هتكون for all عشان تقاضى + +234 +00:18:16,330 --> 00:18:22,010 +برضه + +235 +00:18:22,010 --> 00:18:30,570 +خلّيني أشوف مثال مثال + +236 +00:18:30,570 --> 00:18:31,330 +على النظرية + +237 +00:18:34,050 --> 00:18:38,770 +Expand العلاقة اللي أمامنا فيها أن اتحاد مجموعتين + +238 +00:18:38,770 --> 00:18:43,870 +والاتحاد كله كبير family و family into a union of + +239 +00:18:43,870 --> 00:18:48,670 +intersection فبدل ما هي تقاطع اتحادين بدخليها + +240 +00:18:48,670 --> 00:18:53,470 +لاتحاد تقاطعات بدل هي تقاطع اتحادين دخليها اتحاد + +241 +00:18:53,470 --> 00:18:58,750 +لتقاطعات union of intersection فبدنا نعمل عملية + +242 +00:18:58,750 --> 00:19:04,380 +التوزيع فهذا المثال وهي ال solutionفبدل ما هي + +243 +00:19:04,380 --> 00:19:08,720 +كتلتين و بينهم تقاطة بدي أحولها لكل اتحاد و اللي + +244 +00:19:08,720 --> 00:19:12,220 +جوا يكون تقاطة فطبعا نبدأ بال solution نبدأ باش + +245 +00:19:12,220 --> 00:19:15,820 +تقفش لوحدها بدي أعمل عمية expansion بديش أثبت إشي + +246 +00:19:15,820 --> 00:19:20,360 +بس بدي أعمل إيش بدي أفكه بدي أبسطه فانا عندي U او + +247 +00:19:20,360 --> 00:19:33,140 +اتحاد I من 1 ل M A sub Iتقاطع اتحاد J من 1 ل N بي + +248 +00:19:33,140 --> 00:19:33,720 +sub J + +249 +00:19:37,790 --> 00:19:41,870 +هنحاول نستخدم النظرية السابقة فالآن تو يمكن اللي + +250 +00:19:41,870 --> 00:19:45,910 +هو برهنها نعتبر هذه كائنها كلها A كلها A، إيش + +251 +00:19:45,910 --> 00:19:50,810 +بتصير؟ ممكن ندخلها جوا، إيش بتصير؟ بتصير اتحاد J + +252 +00:19:50,810 --> 00:19:55,890 +من 1 ل N، هذه كلها A، خليها زي ما هي، نطلع عليها + +253 +00:19:55,890 --> 00:20:03,370 +نظرة خارجية بشكل مغلق A sub I تقاطع B sub J، واحدة + +254 +00:20:03,370 --> 00:20:07,610 +من النظرية، فهذه كلها كتلة واحدةفكأنه هذه هي ال + +255 +00:20:07,610 --> 00:20:13,050 +ايه ا و ايش و دخلناها اعتبروها ايه هذه تمام اه + +256 +00:20:13,050 --> 00:20:16,430 +فطبعا نظريا بتقول ايه تقاطع الاتحاد بيصير اتحاد + +257 +00:20:16,430 --> 00:20:20,510 +ايه تقاطع اللي جوه فده ايه الان ايش ممكن اعمل الان + +258 +00:20:20,510 --> 00:20:24,450 +بالعكس هيعندي اتحاد مع تقاطع بنفس الاسلوب ادخله + +259 +00:20:24,450 --> 00:20:27,850 +جوه فهذا يساوي اه بدي اشتغل على اللي جوه الان هذا + +260 +00:20:27,850 --> 00:20:38,350 +خلناهJ من 1 ل N بتصير اتحاد I من 1 ل M AI تقاطع BJ + +261 +00:20:38,350 --> 00:20:45,670 +فعملنا ايش اتحاد لتقاطعات فده اتحاد اتحاد زي ما + +262 +00:20:45,670 --> 00:20:49,090 +ممكن تقول sigma و sigma فاتحاد اتحاد و تقاطعات + +263 +00:20:49,090 --> 00:20:54,090 +فعملنا النظرية طبقناها مرتين طبقناها مرتين على + +264 +00:20:54,090 --> 00:20:55,090 +مرحلتين + +265 +00:20:59,750 --> 00:21:06,090 +هذه هي نهاية ال section في اي سؤال قال لننتقل + +266 +00:21:08,410 --> 00:21:13,610 +اللي هنا أنا عملت هذه كانها إيه بعدين فكيتها الآن + +267 +00:21:13,610 --> 00:21:17,810 +بتطلع هنا على اللي جوا سيبك من الاتحاد الخارجي اه + +268 +00:21:17,810 --> 00:21:20,550 +طبعا النظرية مكتوبة من اليمين أو اليسار بتفرجش + +269 +00:21:20,550 --> 00:21:23,870 +لإنه إيش إبدالية الآن في عندي اتحاد مع تقاطعوش + +270 +00:21:23,870 --> 00:21:26,970 +بيصير اتحاد تقاطعات فانا إيش بدي أعمل؟ بدي أقاطع + +271 +00:21:26,970 --> 00:21:30,110 +هذه مع الأولى بعدين مع التانية، مظبوط؟ فده هي، هيك + +272 +00:21:30,110 --> 00:21:36,150 +معناها النظرية فممكن نكتب بهذه الطريقة فحولنا إلى + +273 +00:21:36,150 --> 00:21:37,750 +اتحاد تقاطعات + +274 +00:21:45,770 --> 00:21:53,050 +في ال section الأخير من هذا ال chapter section + +275 +00:21:53,050 --> 00:21:54,830 +27 + +276 +00:22:06,630 --> 00:22:12,050 +طبعاً عنوان The Russell Paradox Paradox يعني فيها + +277 +00:22:12,050 --> 00:22:17,470 +تناقض أو أيش بيفيها مشكلة للعالم Russell طبعاً هنا + +278 +00:22:17,470 --> 00:22:21,590 +احنا هنتحدث عن نقطة يمكن مرنا عليها مرور سريع وهي + +279 +00:22:21,590 --> 00:22:25,710 +ان لا يوجد حاجة اسمها universal set اللي بتحتوي كل + +280 +00:22:25,710 --> 00:22:30,370 +شيء احنا بنعتبر ان في مرحلية او جزء اللي هو مجموعة + +281 +00:22:30,370 --> 00:22:35,230 +مرجعية بتناسب دراسة معينة لكن فيش حاجة اسمهامجموعة + +282 +00:22:35,230 --> 00:22:39,570 +كونية تحتوي كل شيء فنتحدث عن هذا الموضوع ونشوفه + +283 +00:22:39,570 --> 00:22:44,050 +فطبعا في العالم باول هولموس بيقول nothing contains + +284 +00:22:44,050 --> 00:22:46,430 +everything مافيش حاجة تحتوي كل شيء مافيش حاجة + +285 +00:22:46,430 --> 00:22:49,890 +اسمها ال universal set بالمعنى الصحيح المطلق وإنما + +286 +00:22:49,890 --> 00:22:52,990 +بنشغل احنا عايش اشي نسبي انه هذه مجموعة مناسبة + +287 +00:22:52,990 --> 00:22:56,610 +لدراسة معينة مجموعة مرجعية ففيقول ليه مافيش حاجة + +288 +00:22:56,610 --> 00:23:01,920 +اسمها ال universal set الحقيقة وحكيناهافبيقول طبعا + +289 +00:23:01,920 --> 00:23:08,140 +احنا قبل قرن او اكثر كانوا علماء الرياضيات والناس + +290 +00:23:08,140 --> 00:23:14,040 +العاديين بيؤمنوا ان any set of objects could be a + +291 +00:23:14,040 --> 00:23:16,800 +set in the mathematical sense فطبعا زي ما احنا + +292 +00:23:16,800 --> 00:23:20,120 +حكينا فيه اشكالية في التعريف مافيش تعريف علمى، + +293 +00:23:20,120 --> 00:23:24,780 +صريح، جامع، مانعأه فهم كانوا بيقولك any collection + +294 +00:23:24,780 --> 00:23:28,180 +of objects ممكن يكون sets لكن هذا الكلام غير دقيق، + +295 +00:23:28,180 --> 00:23:32,360 +بده بعض الضوابط، بعض المعين، لأنه إذا أشتغلنا بهذا + +296 +00:23:32,360 --> 00:23:36,380 +الشكل أدى إلى تناقض، أدى إلى مشكلةوها دي طبعا + +297 +00:23:36,380 --> 00:23:40,500 +مستحيل تكون مشكلة لأن علم الرياضيات بكتير بيستخدم + +298 +00:23:40,500 --> 00:23:44,820 +نظرية المجموعات والمجموعات فلو كان في المجموعة دي + +299 +00:23:44,820 --> 00:23:49,160 +مش معرفة فيها خطأ كان كتير من العلوم أخطط وكل + +300 +00:23:49,160 --> 00:23:51,860 +العلوم اللي اتطبخت على الرياضيات كان مانجحتش لإن + +301 +00:23:51,860 --> 00:23:54,700 +كان في خطأ معين لكن هذا الكلام غير صحيح فكان بده + +302 +00:23:54,700 --> 00:23:58,100 +اللي هو إعادة نظر في تعريف المجموعة مين اللي بتنفع + +303 +00:23:58,100 --> 00:24:03,170 +تكون مجموعة ومين اللي ماتنفع تكون مجموعةفطبعا ع + +304 +00:24:03,170 --> 00:24:07,330 +سبيل المثال كان ممكن يتحدثوا عن set of all sets + +305 +00:24:07,330 --> 00:24:09,930 +وكانوا يتحدثوا عن مجموعة كل المجموعات اللي هي + +306 +00:24:09,930 --> 00:24:17,710 +universal set بدون ماياش يحددوا او يسألوا ايش + +307 +00:24:17,710 --> 00:24:21,590 +المقصود بالكلمة set فهذا الكلام أدى إلى تناقض + +308 +00:24:22,080 --> 00:24:26,700 +Russell Paradox arises when that makes its theory + +309 +00:24:26,700 --> 00:24:30,900 +of Frigue leads to a contradiction فالبرادوكس يعني + +310 +00:24:30,900 --> 00:24:34,380 +فيه contradiction، فيه تناقض، فيه مشكلة معينة فلو + +311 +00:24:34,380 --> 00:24:37,480 +اشتغلنا بهذه الصورة، مش هذه الصورة البسيطة، + +312 +00:24:37,480 --> 00:24:42,880 +الفطرية السادجة بالنظر للمجموعات، هذا أدى إلى + +313 +00:24:42,880 --> 00:24:48,600 +تناقض كما ذكرت قبل قليلفطبعا إيش بتقول اللي هي ال + +314 +00:24:48,600 --> 00:24:51,940 +paradox؟ the sets of all sets which are not + +315 +00:24:51,940 --> 00:24:55,160 +members of themselves contain itself فبقول + +316 +00:24:55,160 --> 00:24:59,460 +المجموعات اللي هم مجموعة كل المجموعات لازم تحتوي + +317 +00:24:59,460 --> 00:25:02,960 +نفسها ما هي التناقض اللي احنا عشان نشوف طب إذا هذه + +318 +00:25:02,960 --> 00:25:07,120 +ال universal set exist إيش مالها؟ تحتوي كل شيء طب + +319 +00:25:07,120 --> 00:25:10,130 +ما هي نفس الشيء ما هي مجموعةالمجموع هي object إذا + +320 +00:25:10,130 --> 00:25:13,170 +لازم تحتوي نفسها، فإن صار في أنا تناقض، فمنفعش أنا + +321 +00:25:13,170 --> 00:25:18,150 +تحتوي نفسها، منفعش تحتوي نفسها، فكان لابد إنه ينحل + +322 +00:25:18,150 --> 00:25:22,970 +هذا الكلامفأصبح هنا في عندي statement as that is + +323 +00:25:22,970 --> 00:25:25,230 +and its negation are true طبعا هذا هو ال + +324 +00:25:25,230 --> 00:25:28,250 +contradiction فصار عندنا فيه إشكالية حنشوف بعد + +325 +00:25:28,250 --> 00:25:30,890 +قليل كيف بيطلع ال paradox وكيف بيطلع ال + +326 +00:25:30,890 --> 00:25:34,810 +contradiction طبعا هذا زي ما حكينا نقطة مهمة جدا + +327 +00:25:34,810 --> 00:25:37,790 +لو كان هذا الكلام فعلا فيه تناقض فيه paradox كان + +328 +00:25:37,790 --> 00:25:41,290 +اللي هو ايه كتير من النظريات الرياضية انهارت وما + +329 +00:25:41,290 --> 00:25:43,690 +ترتب عليها من العلوم الأخرى كان فيها حيكون فيها + +330 +00:25:43,690 --> 00:25:48,360 +انهيارطبعًا فلمّا العالم Russell's وضّح هذا النقطة + +331 +00:25:48,360 --> 00:25:51,660 +طبعًا ويدوله حل فـRussell's paradox changed the + +332 +00:25:51,660 --> 00:25:54,820 +way mathematicians looked at mathematics فغير + +333 +00:25:54,820 --> 00:25:58,060 +النظرة وتعريف للمجموعات ومين بيصلح يكون مجموعة + +334 +00:25:58,060 --> 00:26:00,780 +ومين لا يصلح أن يكون مجموعة فطبعًا من اللي هو + +335 +00:26:00,780 --> 00:26:03,500 +الـnaive mathematicians that believed naively that + +336 +00:26:03,500 --> 00:26:07,220 +any connection could be a set فبقاشوا اتحولوا من + +337 +00:26:07,220 --> 00:26:10,220 +هذه النظرة النظرة السطحية into two more careful + +338 +00:26:10,220 --> 00:26:14,280 +creaturesصاروا بتعاملوا كمخلوقات أكثر عناية أو + +339 +00:26:14,280 --> 00:26:17,920 +أكثر ذكاء أو أكثر تحديداً في التعامل مع مفهوم + +340 +00:26:17,920 --> 00:26:23,440 +المجموعات. فالتحليل الدقيق للتناقض الموجود بهذا + +341 +00:26:23,440 --> 00:26:28,400 +الكلام، النظر السطحية، طبعاً، ما يمكن نقول إن أي + +342 +00:26:28,400 --> 00:26:32,520 +مجموعة من + +343 +00:26:32,520 --> 00:26:35,900 +المجموعات ممكن تكون مجموعة، فهذه هي النقطة التي + +344 +00:26:35,900 --> 00:26:36,800 +أدت للتناقض. + +345 +00:26:40,700 --> 00:26:43,320 +فطبعا بيقوللي the collection of all sets is + +346 +00:26:43,320 --> 00:26:50,320 +certainly something طبعا كل المجموعات هذه هو شيء + +347 +00:26:50,320 --> 00:26:54,860 +معين بس إيهش بينفعش يكون مجموعة نفسه لأنه بيصير + +348 +00:26:54,860 --> 00:26:57,520 +إيهش بيكون يحتوي نفسه لأ إذا كان في عندنا مجموعة + +349 +00:26:57,520 --> 00:27:01,860 +تحتوي لو في عندنا حاجة معينة تحتوي كل المجموعات + +350 +00:27:01,860 --> 00:27:05,860 +إذا هي مجموعة بتحتوي نفسها فده بيقدر لتناقض زي ما + +351 +00:27:05,860 --> 00:27:09,160 +حنشوف فبينفعش تكون مجموعةمنفعش يكون مجموعة اللي + +352 +00:27:09,160 --> 00:27:13,480 +بيحتوي كل شيء منفعش يكون مجموعة something that + +353 +00:27:13,480 --> 00:27:17,020 +contains all sets cannot be or should not be a set + +354 +00:27:17,020 --> 00:27:20,620 +هذه النقطة منفعش اللي بيحتوي كل شيء و كل المجموعات + +355 +00:27:20,620 --> 00:27:23,920 +يكون نفسه مجموعة لأنه هيحتوي نفسه و هذا بيقدي إلى + +356 +00:27:23,920 --> 00:27:29,570 +تناقضفهذه هي النقطة اللي احنا هنتحدث عنها بشكل + +357 +00:27:29,570 --> 00:27:37,190 +مختصر إن شاء الله طبعا، هذه النقطة إن الشيء اللي + +358 +00:27:37,190 --> 00:27:41,490 +بحتوي كل المجموعات مافعش يكون مجموعة فيه بعض اللي + +359 +00:27:41,490 --> 00:27:46,370 +هو عكسه الناس في بعض اللي هو القصص أو بعض الأمثلة + +360 +00:27:46,370 --> 00:27:51,870 +من الناحية العملية في مثال مشهور اللي هو مسألة + +361 +00:27:51,870 --> 00:27:57,990 +الحلاقفلو في احنا عندنا بلدة ما أو قرية ما، فهذا + +362 +00:27:57,990 --> 00:28:02,030 +فيها حلاج واحد، اعتبر ان في قرية صغيرة، هذا الحلاج + +363 +00:28:02,030 --> 00:28:06,070 +طبعا لمين بحلج؟ للي بحلجش لنفسه، مظبوط؟ كل واحد، + +364 +00:28:06,070 --> 00:28:08,910 +كل إنسان بقعدش يحلج لحاله في البيت، بروح للحلاج + +365 +00:28:08,910 --> 00:28:12,310 +بحلجله، طيب بالنسبة للحلاج نفسه هذا، مين بحلجله؟ + +366 +00:28:12,580 --> 00:28:16,100 +فإذا كان هو بيحلجش لنفسه، مين بيحلجله؟ الحل هذه، + +367 +00:28:16,100 --> 00:28:18,760 +يعني هو بيحلج لنفسه، وإذا بيحلج لنفسه، صار إيش؟ في + +368 +00:28:18,760 --> 00:28:21,360 +إيه المشكلة؟ فزالت تناقض، فنفسي تصير القضية، فإذا + +369 +00:28:21,360 --> 00:28:24,440 +المجموعة بتحتوي كل شيء، لازم تحتوي نفسها، فبصير + +370 +00:28:24,440 --> 00:28:28,720 +هنا فيه تناقض، فده مثال على هذا التناقض وكيف ممكن + +371 +00:28:28,720 --> 00:28:29,600 +إيه يصير + +372 +00:28:36,050 --> 00:28:39,090 +طبعا هنا هتشوف ال paradox كيف انه ممكن يكون و هي + +373 +00:28:39,090 --> 00:28:43,490 +حاجة مشابهة للمثال طبعا عشان نمهج لنظرية رئيسية في + +374 +00:28:43,490 --> 00:28:49,270 +عندنا to لما طبعا احنا في اللغة الإنجليزية نستخدم + +375 +00:28:49,270 --> 00:28:55,040 +مصطلح theoremالـ Proposition ولمّه طبعا باللغة + +376 +00:28:55,040 --> 00:28:59,480 +العربية كله بترجمه نظرية ممكن ان ترجمه او ان ترجمه + +377 +00:28:59,480 --> 00:29:03,220 +مبرهنة اه طب ايش الفرق؟ اه في الغالب لما نقول + +378 +00:29:03,220 --> 00:29:06,200 +theorem بيكون النتيجة مهمة جدا ال theorem هي الأهم + +379 +00:29:06,200 --> 00:29:11,320 +ال proposition أقل أهمية واللمّه أقل أهمية طبعا + +380 +00:29:11,320 --> 00:29:14,850 +أداء بشكل عام طبعا مش قاعدةوفي الغالب إن اللمة + +381 +00:29:14,850 --> 00:29:18,550 +بتكون أنا فيها عندي نتيجة استخدامها محدود في نظرية + +382 +00:29:18,550 --> 00:29:21,530 +ما فانا بدل ما أعمل نظرية كبيرة أو برهانة كبيرة + +383 +00:29:21,530 --> 00:29:24,650 +بروح بعض الاشئ الأيزاء أعملهم إيش لمّة مهيدة + +384 +00:29:24,650 --> 00:29:28,130 +للنظرية فاحنا هنشوف النظرية الرئيسية و هنثبت بعض + +385 +00:29:28,130 --> 00:29:32,370 +الأمور على شكل لمّةهنشوف نفس العملية اللي توقع + +386 +00:29:32,370 --> 00:29:37,630 +حكيناها فبقول suppose that there is a set U of all + +387 +00:29:37,630 --> 00:29:39,950 +sets حنظر في البرنامج مستحيل المجموعات كل + +388 +00:29:39,950 --> 00:29:45,370 +المجموعات وبنعرف مجموعة capital R هي عبارة عن + +389 +00:29:45,370 --> 00:29:48,690 +عناصرها كل المجموعات اللي بتنتمل ال U مجموعة كل + +390 +00:29:48,690 --> 00:29:52,090 +المجموعات اللي لا تنتمل نفسها فإيه المشكلة؟ + +391 +00:29:52,090 --> 00:29:54,770 +ماينفعش مجموعة تنتمل نفسها؟ قولنا لو في الحاجة + +392 +00:29:54,770 --> 00:29:57,790 +اللي تحتوي كل المجموعات هي نفسها مجموعة هتنتمل + +393 +00:29:57,790 --> 00:30:01,250 +نفسها هذا اللي عامل ال contradictionفبقول ليه إذا + +394 +00:30:01,250 --> 00:30:05,550 +كان ال R معرفة في هذا الشكل فال R لا تنتمي لنفسها + +395 +00:30:05,550 --> 00:30:10,490 +فال R لا تنتمي لنفسها إذا ال R تحتوي كل المجموعات + +396 +00:30:10,490 --> 00:30:14,970 +التي لا تنتمي لنفسها فإن ال R لا تنتمي لنفسها + +397 +00:30:14,970 --> 00:30:26,870 +خلّينا نشوف البرهار عم بتشبه قضية الحلاجة فهذه + +398 +00:30:26,870 --> 00:30:33,410 +ال proofهتلم موارد تمام اه بدي اثبت ان ال R لا + +399 +00:30:33,410 --> 00:30:39,130 +تنتمي لنفسها خلينا نعمل by contradiction اه فطبعا + +400 +00:30:39,130 --> 00:30:45,270 +كل اللي يوجد قدام ايش معطق فخلينا نقول assume R + +401 +00:30:45,270 --> 00:30:53,490 +تنتمي لل A prove او indirect prove اختصارا اي + +402 +00:30:53,490 --> 00:31:00,100 +سؤال؟طيب، الآن الـ R تنتمي للـ R، كيف معرفة الـ R؟ + +403 +00:31:00,100 --> 00:31:03,600 +معرفة في كل المجموعات اللي في الـ U والصفة المميزة + +404 +00:31:03,600 --> 00:31:07,820 +إيه؟ اللي لا تنتمي لنفسها، هيك تعريفها، آه، شوف + +405 +00:31:07,820 --> 00:31:13,190 +الـ R كيف معرفةهي كل العناصر S اللي هي مجموعات و + +406 +00:31:13,190 --> 00:31:14,970 +ايش .. ايش .. ايش .. ايش .. ايش خاصية مميزة؟ ايش + +407 +00:31:14,970 --> 00:31:18,910 +الميارات التي لا تنتمي لنفسها؟ فلجيت الـR تنتمي + +408 +00:31:18,910 --> 00:31:22,830 +للـR، بتتحقق من؟ الخاصية المميزة، فإذا من تعريف + +409 +00:31:22,830 --> 00:31:27,430 +الـR، اذا الـR لا تنتمي للـR، من وين جبتوا هذا؟ + +410 +00:31:27,430 --> 00:31:31,830 +تعريف الـR، مشاكل خاصة في المميزة؟ اه هي كل مجموعة + +411 +00:31:31,830 --> 00:31:34,050 +تنتمي لنفسها، ايش صار؟ contradiction، اه + +412 +00:31:34,050 --> 00:31:34,510 +contradiction + +413 +00:31:39,580 --> 00:31:47,260 +فالعكس هو الصحيح الان انا بقول في end U مجموعة كل + +414 +00:31:47,260 --> 00:31:50,960 +المجموعات أنصرها بتحتوي ايش كلها مجموعات عنرفت + +415 +00:31:50,960 --> 00:31:54,360 +مجموعة R بالشكل التالي هي المجموعات اللي في ال U + +416 +00:31:54,360 --> 00:31:58,100 +التي لا تحتوي نفسها التي لا تنتمي إلى نفسها اه + +417 +00:31:58,100 --> 00:32:01,140 +فبقول لي اذا ال R لا تنتمي لل R كيف بدأ بارهنها؟ + +418 +00:32:01,140 --> 00:32:04,740 +by contradiction افترضت ان العكس صحيحطيب R تنتمي + +419 +00:32:04,740 --> 00:32:08,400 +للـ R إيش معيار الـ R؟ هي المجموعات التي لا تنتمي + +420 +00:32:08,400 --> 00:32:11,060 +لنفسها مزال الـ R في الـ R إذا إيش؟ لازم تحقق + +421 +00:32:11,060 --> 00:32:14,240 +المعيار إذا الـ R لا تنتمي للـ R ر تنتمي للـ R ر + +422 +00:32:14,240 --> 00:32:18,240 +لا تنتمي للـ R بي and not be contradiction هنشوف + +423 +00:32:18,240 --> 00:32:26,400 +كمان لمبة العكس، الآن برضه الـ R تنتمي للـ R أنا + +424 +00:32:26,400 --> 00:32:29,100 +أثبتت إن الـ R لا تنتمي للـ R الآن أثبتت إن الـ R + +425 +00:32:29,100 --> 00:32:38,010 +لا تنتمي للـ R لمبة 2مرقمين عن كل ما؟ Approve ال R + +426 +00:32:38,010 --> 00:32:43,370 +نفس المتعريف بس بيقول هنا ال R تنتمي لل R تمام، + +427 +00:32:43,370 --> 00:32:47,130 +بدي أثبت أن ال R تنتمي لل R، برضه by contradiction + +428 +00:32:47,130 --> 00:32:58,060 +Assume R لا تنتمي لل R، برضه indirect proofممتازة + +429 +00:32:58,060 --> 00:33:02,340 +اشمال الار لاتنتم لار حققت المعيار اذا الار تنتم + +430 +00:33:02,340 --> 00:33:08,140 +لار من التعريف اذا الار تنتم لار من وين تعريف الار + +431 +00:33:08,140 --> 00:33:11,300 +فاياش contradiction + +432 +00:33:16,110 --> 00:33:18,770 +ما هي إيه المشكلة فماينفعش يكون مجموعة كل + +433 +00:33:18,770 --> 00:33:22,430 +المجموعات و إلا هتحتوي نفسها و هذا بيقدي ليش إنها + +434 +00:33:22,430 --> 00:33:25,450 +بتحتوي نفسها و لا تحتوي نفسها فصار إيش في + +435 +00:33:25,450 --> 00:33:29,370 +contradiction فطبعا ال نظرية + +436 +00:33:32,440 --> 00:33:36,480 +أه فهي ما هي ال paradox فبنفعش يكون المجموعة اللي + +437 +00:33:36,480 --> 00:33:39,420 +بتحتوي أو الشيء اللي بحتوي كل المجموعات يكون + +438 +00:33:39,420 --> 00:33:42,360 +مجموعة وإلا بيقدّي لهذا التناقض فطبعا هاي النظرية + +439 +00:33:42,360 --> 00:33:46,660 +الأساسية نظرية 2 عشرة there is no set of all sets + +440 +00:33:46,660 --> 00:33:51,260 +there is no set of all sets طبعا بدا تصحيح there + +441 +00:33:51,260 --> 00:33:54,280 +is no set of all sets فبنفعش يكون اللي بحتوي كل + +442 +00:33:54,280 --> 00:33:56,720 +المجموعات هو مجموعة نفسه لأنه بيقدّي له التناقض + +443 +00:33:56,720 --> 00:34:00,890 +فبقول there does not exista set of all sets ما + +444 +00:34:00,890 --> 00:34:05,130 +مفيش عادي أسمة و مجموعة تقاش لكل المجموعة تحتوي كل + +445 +00:34:05,130 --> 00:34:09,070 +شيء طبعا البرهان على اللمة على طول بتطبيق اللمة + +446 +00:34:09,070 --> 00:34:20,550 +التنتين بكون البرهان بينتهي فدي theorem اتنين + +447 +00:34:20,550 --> 00:34:22,650 +عشرة approved + +448 +00:34:26,510 --> 00:34:35,750 +طبعا هنفترض ان هناك مجموعة تحتوي كل شيء لت يو بي a + +449 +00:34:35,750 --> 00:34:40,490 +set of all sets نفترض ان هناك a set of all sets a + +450 +00:34:40,490 --> 00:34:46,470 +set of all sets طبعا هذا اسم المعلمة الابروبا in + +451 +00:34:46,470 --> 00:34:53,370 +contradiction او in direct proof تمام؟ + +452 +00:34:54,250 --> 00:34:59,130 +فطبعا طبقا ليه الكلام اللي هو إيش اللي فات بنحتاج + +453 +00:34:59,130 --> 00:35:04,710 +نعرف إشي ولا لأ؟ فهل بنحتاج نعرف زي .. احنا بن .. + +454 +00:35:04,710 --> 00:35:09,870 +طب قريبا زي اللي هو بنستخدم اللمع فهل بدنا نعرف .. + +455 +00:35:09,870 --> 00:35:18,470 +و نعرف ال R and let ال R اللي توي عرفناها هي S + +456 +00:35:18,470 --> 00:35:26,770 +تنتمي ل U such that S لا تنتميلل S فانا في عندي + +457 +00:35:26,770 --> 00:35:30,690 +مجموعة المجموعات كل شيء ف ال R فعل الكلام طبعا من + +458 +00:35:30,690 --> 00:35:39,510 +اللمة السابقة by لمة واحد ايش R تنتمي لل A لا + +459 +00:35:39,510 --> 00:35:43,850 +تنتمي مظبوط لمة واحد لا تنتمي وللعكس لمة واحد ايش + +460 +00:35:43,850 --> 00:35:50,910 +جالت لا تنتمي اه اه by لمة two ال + +461 +00:35:50,910 --> 00:35:53,350 +R تنتمي ايش صار عندنا contradiction + +462 +00:35:58,470 --> 00:36:03,150 +فطبعا إحنا بنمر على هذا الكلام عشان بس نعالج نقطين + +463 +00:36:03,150 --> 00:36:05,810 +نعالج ممررنا عنه إنه مافيش هناك حاجة اسمها + +464 +00:36:05,810 --> 00:36:10,330 +universal set تحتوي كل شيء أو أيضا كمعلومة تعرفوا + +465 +00:36:10,330 --> 00:36:13,510 +إيش ما يُعرف بيه اللي هو Russell Paradox لو احنا + +466 +00:36:13,510 --> 00:36:18,210 +اتحدثنا عن مجموعة تحتوي كل المجموعات نوصل لتنقض + +467 +00:36:18,210 --> 00:36:21,290 +فاللي بيحتوي كل المجموعات هي حاجة معينة لكن مش + +468 +00:36:21,290 --> 00:36:24,970 +مجموعة، ماينفعش يكون مجموعة لأنه بيحتوي كل + +469 +00:36:24,970 --> 00:36:28,340 +المجموعات وهو مجموعة بيحتوي نفسهو هذا يؤدي إلى + +470 +00:36:28,340 --> 00:36:34,820 +contradiction أو paradox طبعا ال chapter 3 موجود + +471 +00:36:34,820 --> 00:36:38,480 +على الموقع من بارح مش عارف إذا حد بتابع موجود ال + +472 +00:36:38,480 --> 00:36:41,120 +chapter موجود بنا نبدأ فيه ان شاء الله استغلالا + +473 +00:36:41,120 --> 00:36:46,600 +للوقت و ان شاء الله بنقدر ندرس فيه جد ما كانف + +474 +00:36:46,600 --> 00:36:50,780 +chapter تلاتة هنتحدث فيه عن relations and + +475 +00:36:50,780 --> 00:36:55,820 +functions العلاقات والدوال العلاقات والدوال فالان + +476 +00:36:55,820 --> 00:37:01,340 +هنمشي مرحلة و نتقدم خطوة للأمام نتحدث فيها عن ال + +477 +00:37:01,340 --> 00:37:06,060 +relations و ال functions طبعا هنبدأ نقطة البداية + +478 +00:37:06,060 --> 00:37:10,640 +تبعتنا هنبدأ بتعريف اللي هو Cartesian product + +479 +00:37:10,640 --> 00:37:14,340 +فطبعا + +480 +00:37:15,510 --> 00:37:20,630 +دائما إذا بنتحدث احنا عن دالة أو علاقة، علاقة أنصر + +481 +00:37:20,630 --> 00:37:24,330 +مع أنصر، فبدنا يشفي أنصرين، فبنتحدث عن أنصرين + +482 +00:37:24,330 --> 00:37:28,070 +هدولة ونكتبهم بشكل معين، أيضا إذا تتذكروا دائما من + +483 +00:37:28,070 --> 00:37:31,890 +الدوال، لما بنقول نرسم دالة Y تسوء X، نرسم إيه؟ + +484 +00:37:31,890 --> 00:37:36,330 +الزوج مرتب، النقاط في المستوى، فبنحتاج مفهوم الزوج + +485 +00:37:36,330 --> 00:37:39,990 +المرتب، وهو بالتالي بنحتاج لمفهوم ال Cartesian + +486 +00:37:39,990 --> 00:37:43,930 +product ل ال two sets أو الدرب ال Cartesian + +487 +00:37:46,800 --> 00:37:51,980 +أه طبعا احنا هندرس موضوع العلاقة المعرفة على + +488 +00:37:51,980 --> 00:37:57,760 +المجموعة بدلالة الأزواج المرتبة هندرس في علاقة بين + +489 +00:37:57,760 --> 00:38:01,880 +تجزيئ المجموعة كيف أقسمها بشكل مناسب وإيش علاقة ال + +490 +00:38:01,880 --> 00:38:05,830 +partition مصطلح ال partition اللي هو التجزيئمع + +491 +00:38:05,830 --> 00:38:09,790 +علاقات التكافؤ وهي علاقات مهمة في الرياضيات أيضا + +492 +00:38:09,790 --> 00:38:16,010 +هندرس اللي هو مفهوم الدالة وطبعا كعلاقة خاصة من + +493 +00:38:16,010 --> 00:38:19,690 +العلاقات طبعا هندرس بعض اللي هو الخواص الأساسي + +494 +00:38:19,690 --> 00:38:24,850 +للدوار في ال section الأول هنبدأ من ال Cartesian + +495 +00:38:24,850 --> 00:38:30,430 +product of two sets فطبعا + +496 +00:38:30,430 --> 00:38:36,240 +نقطة الانطلاق هي الأزواج المرتبة ordered pairsما + +497 +00:38:36,240 --> 00:38:39,840 +هو الزوج المرتب؟ طبعا الرمز تبعه زي رمز الفترة + +498 +00:38:39,840 --> 00:38:42,860 +للأسف نفس الرمز في بعض الناس بيستخدموا رمز مختلف + +499 +00:38:42,860 --> 00:38:47,720 +للفترات لكن احنا الزوج المرتب متفق عليه فبقول لي + +500 +00:38:47,720 --> 00:38:53,240 +لو انا خدت اي عنصرين A وB العنصر AB المكتوب بهذا + +501 +00:38:53,240 --> 00:38:57,080 +الشكل بيسميه زوج مرتب is called the ordered pair + +502 +00:38:57,080 --> 00:39:04,840 +AB الزوج المرتب AB تقرأ الزوج المرتب AB طبعاهنا + +503 +00:39:04,840 --> 00:39:08,780 +بالنسبة للزوج المرتب ال a بيسموها الإحداث الأول + +504 +00:39:08,780 --> 00:39:12,040 +first coordinate فهنا الترتيب مهم طبعا في المصطلح + +505 +00:39:12,040 --> 00:39:15,120 +فيه ordered pair و ال a first coordinate مش بس + +506 +00:39:15,120 --> 00:39:18,060 +coordinates الترتيب مهم و ال b بيسموها the second + +507 +00:39:18,060 --> 00:39:23,330 +coordinate فالترتيب بالنسبة لنا مهم و أساسينقطة + +508 +00:39:23,330 --> 00:39:26,250 +تالتة بدنا نعرفها من التعريف، لو في عندي زوجين + +509 +00:39:26,250 --> 00:39:30,330 +مرتبين وما بتساووا، إذا الإحداث الأول ساوى الإحداث + +510 +00:39:30,330 --> 00:39:34,110 +الأول، والإحداث التاني ساوى الإحداث التاني، فدول + +511 +00:39:34,110 --> 00:39:38,950 +أول نقاط بدنا ننطلق منها عشان نتعامل مع الأزواج + +512 +00:39:38,950 --> 00:39:45,660 +المرتبةهنا بنأكد على كلمة ordered pair زوج مرتف + +513 +00:39:45,660 --> 00:39:48,900 +فالترتيب مهم جدا مش مجموعة هادي مش زي المجموعة + +514 +00:39:48,900 --> 00:39:51,480 +الترتيب مش مهمة و التكرار مش مهم لأ زوج مرتف + +515 +00:39:51,480 --> 00:39:54,680 +فبقولي the adjective order here emphasizes يعني + +516 +00:39:54,680 --> 00:39:58,040 +بيؤكد that the order in which the objects A and B + +517 +00:39:58,040 --> 00:40:03,410 +appear in AB is essential أساسيالترتيب الظهور مهم، + +518 +00:40:03,410 --> 00:40:07,010 +فالإحداث الأول له دور، الإحداث التاني له دور، + +519 +00:40:07,010 --> 00:40:12,150 +فالترتيب مهم جدا في هذه العلاقة أو في هذا المفهوم، + +520 +00:40:12,150 --> 00:40:15,630 +فطبعا على طول واحد اتنين تختلف تماما عن الزوج + +521 +00:40:15,630 --> 00:40:20,270 +المرتب اتنين واحد، فبنتفق هذه النقطة بشكل أساسي + +522 +00:40:20,720 --> 00:40:25,400 +مثال بسيط اخر لو جالي x y كزوج مرتب بيساوي 2 و 3 + +523 +00:40:25,400 --> 00:40:29,980 +فهذه تكافئ if and only if ال x بتساوي 2 و ال y + +524 +00:40:29,980 --> 00:40:35,640 +بتساوي 3 فهنا دي أمور أساسية بدنا نعتمد عليها فيما + +525 +00:40:35,640 --> 00:40:42,640 +يليفي ISFR فهذه المقدمة الأساسية الآن هنعرف الـ + +526 +00:40:42,640 --> 00:40:48,040 +Cartesian products فهنا يمكن يكون نوع جديد من + +527 +00:40:48,040 --> 00:40:53,580 +العمليات على المجموعات احنا عرفنا الاتحاد والتقاطع + +528 +00:40:53,580 --> 00:40:57,100 +والفرق او المكملة طبعا ليش ما جالش ان هذه عملية + +529 +00:40:57,100 --> 00:41:01,800 +ضرب على المجموعات؟لأن الناتج مجموعة من نوع آخر، لو + +530 +00:41:01,800 --> 00:41:06,420 +طلعنا على الـA والاتحاد، مجموعة من نفس الجنس، نفس + +531 +00:41:06,420 --> 00:41:08,860 +العناصر، يا بتاخد العناصر المشتركة، يا بتاخد كل + +532 +00:41:08,860 --> 00:41:12,040 +العناصر، و الـminus نفس الشيء، بتاخد نفس العناصر + +533 +00:41:12,040 --> 00:41:15,580 +الموجودة، مش موجودة، في جزء من الأجزاء، لكن الآن + +534 +00:41:15,580 --> 00:41:20,190 +هنتشوف أندي مجموعتينفي ال Cartesian product بكون + +535 +00:41:20,190 --> 00:41:24,410 +مجموعة جديدة صحيح لكن عناصرها من جنس آخر من نوع + +536 +00:41:24,410 --> 00:41:30,630 +آخر أزواج مرتبة أزواج مرتبة let A and B be sits + +537 +00:41:30,630 --> 00:41:34,790 +the Cartesian product هي المفهوم of A and Bإيش + +538 +00:41:34,790 --> 00:41:38,510 +الرمز؟ a cross b هاي الرمز، هاي المفهوم، هاي + +539 +00:41:38,510 --> 00:41:42,350 +الرمز، إيش تعريفه؟ is the set of all ordered pairs + +540 +00:41:42,350 --> 00:41:45,850 +x y هي مجموعة كل الأزواج المرتبة، شفين احنا بنكون + +541 +00:41:45,850 --> 00:41:49,910 +إيش؟ نوع جديد من المجموعة، هي مجموعة صحيح الناتج، + +542 +00:41:49,910 --> 00:41:53,750 +لكن عناصرها من نوع جديد، أزواج مرتبة، أزواج مرتبة، + +543 +00:41:53,750 --> 00:41:57,570 +طبعا بشرط إن ال X في الأولى، فالترتيب مهم، و ال Y + +544 +00:41:57,570 --> 00:42:00,390 +في التانية، و ال Y في التانية، طبعا كالعادة + +545 +00:42:00,390 --> 00:42:05,230 +بالرموزA cross الـ B تساوي إيش عناصرها؟ كل الأزواج + +546 +00:42:05,230 --> 00:42:08,810 +المرتبة XY هي عناصرها على صورة أزواج مرتبة بحيث ال + +547 +00:42:08,810 --> 00:42:12,670 +X في الأول و ال Y في التانية and ال Y في التانية + +548 +00:42:12,670 --> 00:42:19,470 +فهذا هو التعريف تمام خلينا نشوف مثال نبدأ بالأمثلة + +549 +00:42:19,470 --> 00:42:23,830 +البسيطة و نحاول نتعود على هذا المفهوم + +550 +00:42:33,340 --> 00:42:38,520 +هنبدأ بمثال بسيط وهنا برضه هنلاحظ هل العملية + +551 +00:42:38,520 --> 00:42:45,380 +إبدالية ولا لأ solution فطبعا أنا عندي ال A بتساوي + +552 +00:42:45,380 --> 00:42:52,940 +واحد اتنين و تلاتة و ال B A و B الحرفين فبدنا نبدأ + +553 +00:42:52,940 --> 00:42:59,620 +A cross ال B تساويفكل العناصر أزواج مرتبة بتاخد + +554 +00:42:59,620 --> 00:43:03,240 +الإحداث الأول من ال A والإحداث التاني من ال B فانا + +555 +00:43:03,240 --> 00:43:08,300 +إيش ممكن يكون عندي؟ واحد و A، إيش كمان؟ واحد و B، + +556 +00:43:08,300 --> 00:43:11,840 +واحد و B، ليش لأ؟ لأنه بيقول ليش هي زوج مرتب، + +557 +00:43:11,840 --> 00:43:14,960 +الإحداث الأول من ال A والتاني من ال B، بنفعيت إيش؟ + +558 +00:43:14,960 --> 00:43:18,900 +طيب إيش ممكن أجيت؟ أشتغل على التنين، اتنين و A و + +559 +00:43:18,900 --> 00:43:24,640 +اتنين و B، و إيش؟ تلاتة و A و تلاتة و B، فدول كل + +560 +00:43:24,640 --> 00:43:29,200 +العناصرهنشوف إن العدد إيش بيساوي، ممكن نعرف أطول، + +561 +00:43:29,200 --> 00:43:31,740 +طبعاً العدد اللي هو الأزواج المرتبة بيساوي عدد + +562 +00:43:31,740 --> 00:43:36,580 +عناصر الـA ضرب عدد عناصر الـB، ف2×3 هي 6 عناصر، + +563 +00:43:36,580 --> 00:43:43,900 +مصبوح، فهذه ليهاش الأول، نيجي نحسب B cross الـA، + +564 +00:43:43,900 --> 00:43:53,270 +زي الأول، بس اختلف، لأ، قلت A و1 وA و2 وA و3بعدين + +565 +00:43:53,270 --> 00:43:58,310 +بي واحد أي زوج مرتب و بي مع التنين و ال بي مع + +566 +00:43:58,310 --> 00:44:02,390 +التلاتة برضه ست عناصر برضه ست عناصر لكن هل + +567 +00:44:02,390 --> 00:44:06,730 +متساويين؟ طبعا لأ مختلفين لأن هذا الزوج مانفعش هذا + +568 +00:44:06,730 --> 00:44:11,950 +يساوي هذا لأن ال a مش واحد فده ليش عملية الضرب غير + +569 +00:44:11,950 --> 00:44:15,930 +إبدالية و بنأكد على هذا الترتيب مهم فبالتالي عملية + +570 +00:44:15,930 --> 00:44:18,790 +اللي هو ال Cartesian product غير إبدالية + +571 +00:44:21,040 --> 00:44:22,900 +تمام، وقفها ان شاء الله المرة الجاية بالكملة + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/t5cDWWyGX8E_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/t5cDWWyGX8E_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..6e4282ce9eedabaadf1f77a499ac42a69785591b --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/t5cDWWyGX8E_raw.srt @@ -0,0 +1,2152 @@ +1 +00:00:20,670 --> 00:00:25,530 +بسم الله الرحمن الرحيم نستكمل اليوم ان شاء الله مع + +2 +00:00:25,530 --> 00:00:30,790 +اللي هو المكممات ذكرنا في المحاضرة الماضية لما + +3 +00:00:30,790 --> 00:00:34,850 +يكون عندنا sentence تحتوي على متغير أو أكثر + +4 +00:00:34,850 --> 00:00:38,390 +سميناها open sentenceهذه ال open sentence ما + +5 +00:00:38,390 --> 00:00:42,590 +يميزها أنها بتحتوي على متغيرات ليس ذلك فقط ولكن + +6 +00:00:42,590 --> 00:00:45,490 +إذا عوضنا عن المتغيرات بقيم معينة بيصير statement + +7 +00:00:45,490 --> 00:00:49,650 +بيصير true or false فإذا أحد الطريقة عشان نحوّل ال + +8 +00:00:49,650 --> 00:00:51,990 +open sentence دا statement إنه نستبدل المتغيرات + +9 +00:00:51,990 --> 00:00:55,010 +بقيم معين لكن الطريقة الأفضل أو الطريقة الأكثر + +10 +00:00:55,010 --> 00:00:59,910 +شيوعا اللي هي استخدام المكممات for all أو there + +11 +00:00:59,910 --> 00:01:03,820 +exists بتخليها statement أيضابتخليها statement + +12 +00:01:03,820 --> 00:01:08,520 +طبعا قلنا ان ال for all هو مكمم الشمول طبعا فينا + +13 +00:01:08,520 --> 00:01:12,940 +مجموعة معينة مرجعية نسميها ال domain يعني لكل + +14 +00:01:12,940 --> 00:01:16,740 +عناصر ال domain هذه ال statement بتكون صحيحة عشان + +15 +00:01:16,740 --> 00:01:20,700 +هيك شمول يعني مافيش استثناء الكل بيحقق الخاصية أو + +16 +00:01:20,700 --> 00:01:23,820 +ال sentence P of X there exists بيقول على الأقل + +17 +00:01:23,820 --> 00:01:27,300 +موجود يعني على الأقل هناك عنصر من عناصر المجال + +18 +00:01:27,300 --> 00:01:30,920 +بيخلي ال P of X تكون اترا فهنواصل مع هذا الموضوع + +19 +00:01:30,920 --> 00:01:37,840 +فيانا الآنبعض الملاحظاتزي العادة في بعض اللي هو + +20 +00:01:37,840 --> 00:01:41,740 +الجمال اللي هي نفس المعنى أو بعض اللي هو العبارات + +21 +00:01:41,740 --> 00:01:46,500 +بتستخدم بشكل مرادف طبعا احنا العبارة الأساسية for + +22 +00:01:46,500 --> 00:01:50,380 +all طيب هل بس بتظهر بهذا الشكل لأ فبقول for every + +23 +00:01:50,380 --> 00:01:54,760 +اللي هي نفس المعنى for each اللي هي نفس المعنى و + +24 +00:01:54,760 --> 00:01:58,180 +for all طبعا هدولة التلت نفس المعنى طبعا المصالح + +25 +00:01:58,180 --> 00:02:00,840 +الأساسي for all و العبارات الأخرى اللي هي نفس + +26 +00:02:00,840 --> 00:02:04,140 +المعنى فلما نشوف في statement for each في for + +27 +00:02:04,140 --> 00:02:08,700 +everyمعناه تعيش for all معناه for allفي الرياضيات + +28 +00:02:08,700 --> 00:02:11,980 +بيستخدموا بنفس المعنى نفس القضية there exist لها + +29 +00:02:11,980 --> 00:02:17,020 +برضه مرادفات for some there is at least one وهذا + +30 +00:02:17,020 --> 00:02:18,640 +يمكن من التعبير اللي احنا قولنا انه يجب ان تكون + +31 +00:02:18,640 --> 00:02:22,740 +صحيحة اقل مرة واحدة وطبعا و there exist كلهم لهم + +32 +00:02:22,740 --> 00:02:26,900 +نفس المعنى فدولة اربع عبارات مترادفة تستخدم بنفس + +33 +00:02:26,900 --> 00:02:30,940 +المعنى في الرياضيات بنفس المعنى في الرياضيات اي + +34 +00:02:30,940 --> 00:02:34,360 +سؤال فدولة بس ملاحظة على بعض العبارات اللي هتكون + +35 +00:02:34,360 --> 00:02:40,510 +لها نفس المعنىالملاحظة التالتة في سياق آخر احنا + +36 +00:02:40,510 --> 00:02:44,670 +لما عرفنا المكممات قلنا المكمم بنحط على يسار ال + +37 +00:02:44,670 --> 00:02:51,210 +open sentence هذه هي الصورة الصحيحة الرسمية لكن في + +38 +00:02:51,210 --> 00:02:56,160 +بعض الأحيانإذا كنا بنكتب بطريقة مش رسمية أقل رسمية + +39 +00:02:56,160 --> 00:02:59,600 +بنحط المكمم على اليمين ممكن نحط المكمم على اليمين + +40 +00:02:59,600 --> 00:03:05,260 +هذا الكلام مقبول وصحيح لكنه مش هو الطريقة الأفضل + +41 +00:03:05,260 --> 00:03:09,640 +أو الطريقة الرسمية لكنه شائع جدا شائع جدا فبقول in + +42 +00:03:09,640 --> 00:03:13,080 +less formal expressions في الأمور أو التعبيرات + +43 +00:03:13,080 --> 00:03:16,760 +الأقل رسمية زي ما نقول بالعمية يعني تستخدم لكن + +44 +00:03:16,760 --> 00:03:20,720 +شائعة الاستخدام we often put the quantifier after + +45 +00:03:20,720 --> 00:03:24,910 +the sentenceبعد ال sentence مش قبل زي ما احنا + +46 +00:03:24,910 --> 00:03:31,150 +نحطينه قبل فطبعا على سبيل المثال لما نقول هنا for + +47 +00:03:31,150 --> 00:03:35,490 +all x f of x تساوى 0 هذه الصيغة الرسمية هذه الصيغة + +48 +00:03:35,490 --> 00:03:42,570 +الرسمية هذه الصيغة الاكثر استخداما او الاكثر رسمية + +49 +00:03:42,570 --> 00:03:46,550 +في الاستخدام لكن احيانا بنكتب f of x تساوى 0 for + +50 +00:03:46,550 --> 00:03:50,810 +all xنفس المعنى متكافئتين هدول إيش الفرق في اللي + +51 +00:03:50,810 --> 00:03:53,210 +علي يسار حطنا المكمم بعد ال sentence ال open + +52 +00:03:53,210 --> 00:03:56,210 +sentence F of X سواء Zero وفي التانية حطناها + +53 +00:03:56,210 --> 00:03:58,750 +بالشكل المعتاد من التعريف اللي بدأنا فيه حطنا + +54 +00:03:58,750 --> 00:04:01,730 +المكمم علي يسار ال open sentence التنتين صحيحتين + +55 +00:04:01,730 --> 00:04:06,450 +لكن هذه الصيغة الرسمية الأساسية هذه أقل رسمية أو + +56 +00:04:06,450 --> 00:04:09,430 +ممكن نسميها العامية اللي علي يسار التنتين صحيحتين + +57 +00:04:09,430 --> 00:04:13,990 +وستخدموا بشكل موسع في الرياضيات يمكن الغير رسمية + +58 +00:04:13,990 --> 00:04:19,190 +شايعة أكتر شايعة أكتر في الرياضيةنفس القضية، بشكل + +59 +00:04:19,190 --> 00:04:22,090 +رأسنا بنحط there exist أولا، لكن بعد هيك ممكن + +60 +00:04:22,090 --> 00:04:25,130 +نحطها بعد، بس إذا حطناها بعد، بيصيرش there exist، + +61 +00:04:25,130 --> 00:04:28,850 +لإن there exist بتكون مكملة الجملة، مينفعش أنهي + +62 +00:04:28,850 --> 00:04:30,990 +الجملة ب there exist، ممكن أبدأ فيها، فبنقول for + +63 +00:04:30,990 --> 00:04:33,430 +some، واتفقنا إن for some و there exist، إنهم نفس + +64 +00:04:33,430 --> 00:04:37,050 +المعنى، من الملاحظة الماضية، فبنحطها فبنقول f of x + +65 +00:04:37,050 --> 00:04:40,030 +سوا زير و for some x، يعني يوجد x يخلّي ال f أسوا + +66 +00:04:40,030 --> 00:04:43,710 +زير، يعني كأنه يوجد حل لمعادل f of x سوا زير، نفس + +67 +00:04:43,710 --> 00:04:47,860 +المعنىنفس المعرفة فهذه بس ملاحظة أنه حيانا نكتب + +68 +00:04:47,860 --> 00:04:51,980 +بيد الشكل غير الرسمي لكنه شكل شائع ومقبول ومستخدم + +69 +00:04:51,980 --> 00:04:56,720 +في الرياضية أي + +70 +00:04:56,720 --> 00:05:02,370 +سؤال؟الأن ننتقل لنقطة أخرى وهي equivalent + +71 +00:05:02,370 --> 00:05:09,350 +quantified sentences الجمال المتكافئة و التي تحتوي + +72 +00:05:09,350 --> 00:05:12,550 +على مكممات لما يكون في عندي two statements تحتوي + +73 +00:05:12,550 --> 00:05:17,640 +على مكممات و أجتاش بقول عنهم أنهم متكافئتينطبعا + +74 +00:05:17,640 --> 00:05:22,300 +المعيار الأساسي هو المعيار اللي احنا متعودين عليه + +75 +00:05:22,300 --> 00:05:25,940 +طبعا أنا عندي open sentence مع quantifier إيه + +76 +00:05:25,940 --> 00:05:29,020 +صارت؟ statement اه طبعا وقت إيش بيكون two + +77 +00:05:29,020 --> 00:05:31,640 +statements متكافئتين إذا كانوا true مع بعض أو + +78 +00:05:31,640 --> 00:05:35,240 +false مع بعض في جميع الاحتمالات الممكنة فده هو + +79 +00:05:35,240 --> 00:05:39,520 +الأساس في التكافئةلكن الآن احنا بس بدنا ندقق هو + +80 +00:05:39,520 --> 00:05:43,560 +هذا نفس الروح المعنى الأساسي هو نفس المعنى لكن مع + +81 +00:05:43,560 --> 00:05:46,960 +بعض الاختلافات هنا ممكن يكون في عندي domain of + +82 +00:05:46,960 --> 00:05:49,540 +discourse وانا بتحدث عن المكممات او اللي هو المجال + +83 +00:05:49,540 --> 00:05:53,580 +ال universe او domain of discourse فبدي بس أحدد و + +84 +00:05:53,580 --> 00:05:57,550 +أدخل المصطلح حالة في تعريف التكافئةفهعبّر على + +85 +00:05:57,550 --> 00:06:01,430 +التكافؤ على مرحلتين إذا أنا ذكرت ال domain اللي + +86 +00:06:01,430 --> 00:06:05,370 +بدرس فيه ال statements و بدي أكون بدرس التكافؤ على + +87 +00:06:05,370 --> 00:06:08,990 +ال domain نفسه أو بدي أدرس التكافؤ بشكل مطلق فبدي + +88 +00:06:08,990 --> 00:06:13,830 +أفرق بينهم نشوف التفريق كيف بيكونTwo quantified + +89 +00:06:13,830 --> 00:06:17,310 +sentences are equivalent in a given universe إذا + +90 +00:06:17,310 --> 00:06:20,810 +أنا بدأ أدرس على universe محدد بقول على two + +91 +00:06:20,810 --> 00:06:25,390 +statements تحتوي على مكممات إنهم متكافئتين فقط if + +92 +00:06:25,390 --> 00:06:29,130 +if and only if فقط وإذا فقط اشمالهم اللي هم نفس + +93 +00:06:29,130 --> 00:06:34,260 +قيمة اللي هو الصدقhave the same truth value in + +94 +00:06:34,260 --> 00:06:37,100 +that universe طبعا على ال domain طبعا في هذا ال + +95 +00:06:37,100 --> 00:06:40,040 +domain فهم يا true مع بعض على ال domain يا false + +96 +00:06:40,040 --> 00:06:43,900 +مع بعض فهذا التعريف الأول طب لو قلت equivalent من + +97 +00:06:43,900 --> 00:06:46,940 +غير محدد ال domain بدا يكونوا متكافئين على أي + +98 +00:06:46,940 --> 00:06:50,660 +domain على أي domain فبنفرق بين المصطلحين هدول + +99 +00:06:50,950 --> 00:06:54,790 +فابقوه يقول لنفس الطريقة two quantified sentences + +100 +00:06:54,790 --> 00:06:58,410 +are equivalent if and only if مجالش in محددش ال + +101 +00:06:58,410 --> 00:07:02,330 +domain if they are equivalent in every universe في + +102 +00:07:02,330 --> 00:07:05,410 +كل ال universe فده هي التكافؤ مطلق وفي تكافؤ نسبة، + +103 +00:07:05,410 --> 00:07:08,590 +نسبة لمين؟ نسبة ل domain معين أو ل universe معين + +104 +00:07:08,590 --> 00:07:12,560 +فاحنا بدنا نفرخ بينهمإذا حددت للـ Universe، أنا + +105 +00:07:12,560 --> 00:07:15,040 +بسمعني بالـ Universe، اكونوا إيه لهم true مع بعض + +106 +00:07:15,040 --> 00:07:17,420 +أو false مع بعض للـ Universe، ماحددش على كل + +107 +00:07:17,420 --> 00:07:20,160 +Universe بشكل مطلع، بدنا نكونوا دايما true مع بعض + +108 +00:07:20,160 --> 00:07:22,800 +أو false مع بعض، بغض النظر عن مين، عن الـ + +109 +00:07:22,800 --> 00:07:26,460 +Universe، بغض النظر عن الـ Universe، فهذه الفرق، + +110 +00:07:26,460 --> 00:07:29,100 +طبعا، لكن الروح واحدة، إنهم إيش، يا true مع بعض، + +111 +00:07:29,100 --> 00:07:33,100 +يا false مع بعض، بس هنا الـ domain، فيه مرجعية، + +112 +00:07:33,100 --> 00:07:36,280 +ولا بشكل مطلق، من غير مرجعية، هاي الفرق في + +113 +00:07:36,280 --> 00:07:42,570 +الحالتين، نشوف مثال،المثال الأول بيقول let the + +114 +00:07:42,570 --> 00:07:48,910 +universe be U تساوي N show that for all X X أكبر + +115 +00:07:48,910 --> 00:07:53,930 +من 0 هي statement and for all X X أكبر أو تساوي 1 + +116 +00:07:53,930 --> 00:07:58,750 +are equivalent خائط السؤال هذا يمكن ناقص in U أو N + +117 +00:07:59,720 --> 00:08:05,080 +عشان نكون دقة فدول ال two statements متكافئتين على + +118 +00:08:05,080 --> 00:08:06,780 +ال universe اللي عندنا على ال domain تبعنا اللي هو + +119 +00:08:06,780 --> 00:08:10,460 +إيش الأعداد الطبيعية أي الأعداد الصحيحة الموجبة + +120 +00:08:10,460 --> 00:08:14,360 +الأعداد الصحيحة الموجبة خلينا نحاول نحلل هذه ال + +121 +00:08:14,360 --> 00:08:20,040 +statements و نشوف إنهم متكافئتين فنبدأ + +122 +00:08:20,040 --> 00:08:25,910 +بال statement الأولى solutionfor all x, x أكبر من + +123 +00:08:25,910 --> 00:08:31,150 +0 على الكون هذي ال statement true ولا false لعداد + +124 +00:08:31,150 --> 00:08:34,210 +الصحيحة الموجة، بهاي تعريفة، هي عداد طبيعية، كلها + +125 +00:08:34,210 --> 00:08:42,650 +يشبه، فهذه true فهذه true في الكون اللي هو N خليني + +126 +00:08:42,650 --> 00:08:48,850 +أمسحها، فهذه الأولى، طيب نشوف التانية for all x, x + +127 +00:08:48,850 --> 00:08:55,860 +أكبر أو تساوي 1 true ولا falseليش؟برضه كل الاعداد + +128 +00:08:55,860 --> 00:08:58,080 +الصحيحة الموجبهية اكبر او تسوى واحد بيه الاعداد + +129 +00:08:58,080 --> 00:09:01,120 +الصحيحة الموجبهية واحد اتنين تلاتة اربع فبرضه هذه + +130 +00:09:01,120 --> 00:09:06,380 +true is it true in N واضح ان ال universe مهم لو + +131 +00:09:06,380 --> 00:09:10,580 +قلت على Z بختلف لو قلت على R ممكن يختلف لكن على ال + +132 +00:09:10,580 --> 00:09:13,100 +natural صح اذا ليش معلومة دولة متكافئة اتين تبقى + +133 +00:09:13,100 --> 00:09:18,840 +للتعريف فهذا بيقول ليه thus for all x x اكبر من + +134 +00:09:18,840 --> 00:09:23,970 +zero تكافئ for all x x اكبر او تسوى واحدوين + +135 +00:09:23,970 --> 00:09:28,570 +التكافؤ؟ in natural number فدول ال two statements + +136 +00:09:28,570 --> 00:09:32,390 +متكافئتين إذا كان المرجع تبعي ال domain تبعي مين + +137 +00:09:32,390 --> 00:09:35,210 +ال natural number فلو حطيت هذا ال statement أو + +138 +00:09:35,210 --> 00:09:38,070 +التانية نفس الشيء متكافئتين فدوله بيكافؤوا بعض + +139 +00:09:38,070 --> 00:09:41,210 +فهذا ممكن استبدالهم في كل مكان بدون أي مشاكل إذا + +140 +00:09:41,210 --> 00:09:44,790 +كان ال domain الدراسة هو ال natural number واضح؟ + +141 +00:09:44,790 --> 00:09:48,110 +أه المعنى اللي احنا حطناه أي سؤال فال domain هنا + +142 +00:09:48,110 --> 00:09:51,070 +مهم وإلا ممكن يختلف القيم فدول بالنسبة لل domain + +143 +00:09:51,070 --> 00:09:52,750 +هذا متكافئتين + +144 +00:09:54,570 --> 00:09:58,510 +نشوف كمان مثال و برضه هنا بالـ DH أكمل السؤال are + +145 +00:09:58,510 --> 00:10:05,290 +equivalent in Z أو U الكون Z يعني مجموعة الأعداد + +146 +00:10:05,290 --> 00:10:08,750 +الصحيحة كلها السالب والموجب والصفر الأعداد الصحيحة + +147 +00:10:08,750 --> 00:10:13,670 +كلها و بقول show that there exist X X تربية تساوي + +148 +00:10:13,670 --> 00:10:17,970 +2 هي statement و there exist X بحيث ان X تربية + +149 +00:10:17,970 --> 00:10:21,210 +تساوي 3 are equivalent in Z هدول ال two statements + +150 +00:10:21,210 --> 00:10:27,030 +متكافئتين على ZSolution فنبدأ بالأولى there exist + +151 +00:10:27,030 --> 00:10:30,330 +x تربية x تربية تسوى اتنين true ولا false false + +152 +00:10:30,330 --> 00:10:33,310 +فاش عدد صحيح مربع يسوى اتنين لأنه جزر التنين هو + +153 +00:10:33,310 --> 00:10:38,680 +عدد غير صحيح فاداش مانها is falseوين؟ في الـ z لكن + +154 +00:10:38,680 --> 00:10:41,720 +في الـ real true شوف مهم جدا ال domain اه واضح ان + +155 +00:10:41,720 --> 00:10:44,200 +ال domain كان بيلعب دور لو جولت على ال R بيصير + +156 +00:10:44,200 --> 00:10:48,900 +true على ال z false تمام؟ اه in R نفس القضية there + +157 +00:10:48,900 --> 00:10:53,500 +exist x تربية تسوى تلاتة اشملها برضه false نفس + +158 +00:10:53,500 --> 00:10:57,380 +القضية false in z اذا نشمل هذه ال two statements + +159 +00:10:57,380 --> 00:11:04,850 +متكافئتين ممتقيا على ال z thus there exist xX + +160 +00:11:04,850 --> 00:11:10,590 +تربيع تسوى اتنين تكافئ there exists X X تربيع تسوى + +161 +00:11:10,590 --> 00:11:16,310 +تلتة ومتكافئين انزل انزل فدولة متكافئتين على عداد + +162 +00:11:16,310 --> 00:11:20,110 +الصحيح واحد تقول دولة جمعتين مختلفتين لأ احنا من + +163 +00:11:20,110 --> 00:11:23,110 +ناحية منطقية والتعريف ايش بيقول اه بيقول ع طول + +164 +00:11:23,110 --> 00:11:25,310 +statement انهم متكافئتين if they are true مع بعض و + +165 +00:11:25,310 --> 00:11:27,750 +false مع بعض ودولة false مع بعض اذا متكافئتين + +166 +00:11:27,750 --> 00:11:33,050 +مافيش مشكلة اطلاق اي سؤالأحنا لم نفهم المعنى أن + +167 +00:11:33,050 --> 00:11:37,470 +يكون نفس المعنى المهم أنه تكافؤ منطقي صحيح تكافؤ + +168 +00:11:37,470 --> 00:11:44,650 +منطقي صحيح أي سؤال تمام + +169 +00:11:44,650 --> 00:11:55,090 +مزيد من المعاني والجمل اللي فيها مكممات هنا + +170 +00:11:55,090 --> 00:11:59,610 +بدنا نتحدث عن كيف نترجم بعض ال statements باستخدام + +171 +00:11:59,610 --> 00:12:03,510 +المكمماتفبقول لي statements of the form اللي + +172 +00:12:03,510 --> 00:12:07,110 +التقارير اللي على صورة every element of the set A + +173 +00:12:07,110 --> 00:12:13,410 +has the probability Bهذه الصيغة كثيرة الاستخدام في + +174 +00:12:13,410 --> 00:12:18,170 +الرياضيات كل عناصر مجموعة ما لها خاصية معينة زي ما + +175 +00:12:18,170 --> 00:12:21,790 +نقول كل أعداد الطبيعية أكبر من 99% كل الأعداد + +176 +00:12:21,790 --> 00:12:25,610 +الصحية مثلا لها خاصية معينة كل الأعداد الحقيقية + +177 +00:12:25,610 --> 00:12:29,390 +لها خاصية معينة هذه الجمال من هذا النوع كثيرة + +178 +00:12:29,390 --> 00:12:32,830 +الشيوع في الرياضيات لذلك تستحق أنه نعرف كيف + +179 +00:12:32,830 --> 00:12:36,490 +نترجمها بشكل صحي لأنها هتمر علينا كتير فجيد نعرف + +180 +00:12:36,490 --> 00:12:39,990 +كيف نتعامل معهافبقول ليه of course so frequently + +181 +00:12:39,990 --> 00:12:43,530 +that abbreviated symbol a symbolic form are + +182 +00:12:43,530 --> 00:12:47,850 +desirable فإن كيف نحولها لرموز مهم جدا اتعود كيف + +183 +00:12:47,850 --> 00:12:50,870 +نحولها لرمز بطريقة صحية عشان هيتعامل معها و تمروا + +184 +00:12:50,870 --> 00:12:57,130 +علينا كتير فلازم نتعامل معها بشكل الصحيحفمثلًا هذه + +185 +00:12:57,130 --> 00:12:59,610 +الـ statement كإن طبعًا فيه statement أخرى برضه + +186 +00:12:59,610 --> 00:13:02,990 +for every أو some اللي هي طبعًا every بتعنيهاش for + +187 +00:13:02,990 --> 00:13:06,070 +all with some element of the set بعض عناصر + +188 +00:13:06,070 --> 00:13:09,490 +المجموعة لأخصية معينة اللي هي there exist كيف بدنا + +189 +00:13:09,490 --> 00:13:13,050 +نترجمهم باستخدام المكممة فبقول ل every element of + +190 +00:13:13,050 --> 00:13:17,660 +the set Aكل عناصر مجموعة ما has a property بيه، + +191 +00:13:17,660 --> 00:13:22,920 +إليها خاصية معينة بيه ممكن طبعا انعيد ترجمتها أولا + +192 +00:13:22,920 --> 00:13:27,120 +بترجمة لغوية وبعدين نحويلها للرموز احنا شفنا في + +193 +00:13:27,120 --> 00:13:30,780 +السابق ان for all ممكن تتحول لجملة شرطية ان for + +194 +00:13:30,780 --> 00:13:34,600 +all ممكن تترجم بجملة شرطية فهذه ممكن نقول if x + +195 +00:13:34,600 --> 00:13:38,060 +تنتمي لل aهذه معناته for all X لأن كل عناصر الـ A + +196 +00:13:38,060 --> 00:13:42,060 +أي عنصر موجود في الـ A له الخاصية إذا هو ينتمي للـ + +197 +00:13:42,060 --> 00:13:45,100 +A إذا إيش؟ تنتمي عليه القاعدة لأن لو أقول لما أقول + +198 +00:13:45,100 --> 00:13:48,860 +إحنا جميع الإعداد الحقيقية لخاصية معينة فانا لما + +199 +00:13:48,860 --> 00:13:52,060 +أقول إذا X تنتمي لل R إذا تنتمي لأي خاصية في نفس + +200 +00:13:52,060 --> 00:13:55,900 +المعنى واضح؟ أه فإيش بنقول then كذا كذا إيش ممكن + +201 +00:13:55,900 --> 00:14:02,210 +نرمز لها؟ for all X تنتمي لل A P of Xما هو الجديد + +202 +00:14:02,210 --> 00:14:05,610 +هنا قد البعض ماينتبهش شوفنا احنا في الأول كنا + +203 +00:14:05,610 --> 00:14:10,470 +دايما بنحط ال quantifier من غير المجموعة A أو من + +204 +00:14:10,470 --> 00:14:14,810 +غير ال universe لكن في كثير من الأحوال شائع جدا في + +205 +00:14:14,810 --> 00:14:18,290 +الرياضيات انه ان تحط ال domain مع there exist مع + +206 +00:14:18,290 --> 00:14:21,590 +for all احنا بنقول ايش عناصر مجموعة ما بدا ما نقول + +207 +00:14:21,590 --> 00:14:24,270 +ال universe هو A و بعدين نقول there exist لأ + +208 +00:14:24,270 --> 00:14:27,330 +بنضمهم مع بعض فبنقول ايش there exist x in A يعني + +209 +00:14:27,330 --> 00:14:29,950 +ال domain تبعنا هو ال A و بنشتغل على ال main على + +210 +00:14:29,950 --> 00:14:34,930 +ال xو هكذا فهذا الرمز متعوي شائع جدا لما نقول ايش + +211 +00:14:34,930 --> 00:14:39,910 +every element of the set A ايش مانعه؟ كل عناصر + +212 +00:14:39,910 --> 00:14:43,250 +الـA for all X and terminal A بنترجمها for all X + +213 +00:14:43,250 --> 00:14:45,990 +and terminal A طبعا في ترجمة أخرى كيف؟ نقول the + +214 +00:14:45,990 --> 00:14:48,850 +universe U يساوي ايه؟ وبعدين اتحضت for all X بين + +215 +00:14:48,850 --> 00:14:51,950 +قصين اه هدول الطريقتين صحيحتين بس هذه الجديدة + +216 +00:14:51,950 --> 00:14:58,630 +شائعة جدا فجيد نتعود عليها جيد نتعود عليهاطيب some + +217 +00:14:58,630 --> 00:15:01,270 +نفس القضية لو في there exist بدل ما اقول ال + +218 +00:15:01,270 --> 00:15:04,050 +universe هو ايه و there exist فقط بحط there exist + +219 +00:15:04,050 --> 00:15:06,810 +x تماما من ال a بضم الجمعتين مع بعض بضم الاش + +220 +00:15:06,810 --> 00:15:09,750 +التعبيرين مع بعض بعد ما احط ان ال universe احطه و + +221 +00:15:09,750 --> 00:15:12,510 +اشرحه و احطه من الأول لحال لأ بحطه في نفس ال + +222 +00:15:12,510 --> 00:15:14,930 +statement بحطه في نفس ال statement لإن احنا كنا + +223 +00:15:14,930 --> 00:15:19,730 +لما بنقرع هنا ايش بنقرع؟there exists x هو يشيوجد + +224 +00:15:19,730 --> 00:15:23,290 +عدد صحيح لأن ال universe هو ال z فبقول there + +225 +00:15:23,290 --> 00:15:26,990 +exists x in z فهذه طريقة أخرى مختصرة و أوضحة تكون + +226 +00:15:26,990 --> 00:15:29,710 +بذكرني وين هو ال universe بدل ما أكون شوية أبطل ع + +227 +00:15:29,710 --> 00:15:32,590 +وين هو ال universe أنساء أو الذكاء لأ خلاص هي ال + +228 +00:15:32,590 --> 00:15:37,490 +universe جدامي فهذه طريقة شائعة جدا فجيد نتعود + +229 +00:15:37,490 --> 00:15:43,130 +عليها لأنه هنستخدمها في كثير من الأحيانخلّينا نشوف + +230 +00:15:43,130 --> 00:15:50,270 +بعض الأمثلة مثالنا الأول تعريف العدد النسبي في + +231 +00:15:50,270 --> 00:15:54,350 +الرياضيات ما هو العدد النسبي؟ احنا عندنا العدد + +232 +00:15:54,350 --> 00:15:57,470 +الحقيقية و العدد النسبي حالة خاصة فماكنتش بقول + +233 +00:15:57,470 --> 00:16:00,630 +العدد الحقيقي هو عدد نسبي إذا كان ممكن كتابت على + +234 +00:16:00,630 --> 00:16:04,870 +صورة بص مقام بحيث البص المقام أعداد صحيحة والمقام + +235 +00:16:04,870 --> 00:16:12,030 +ليسوء zero فهيك تعريفه عشان هيك مثلاالتنين عدد + +236 +00:16:12,030 --> 00:16:16,830 +نسبة ولا مش نسبة؟ نسبة لأنه 2 على 1 النص عدد نسبة + +237 +00:16:16,830 --> 00:16:21,230 +ولا مش نسبة؟ نسبة 1 على 2 جزر التنين غير نسبة + +238 +00:16:21,230 --> 00:16:25,110 +بقدرش أكتبه بقدرش أكتب على صورة P على Q بحس يكونوا + +239 +00:16:25,110 --> 00:16:28,460 +عدد صحيحة واحد يقول أنه 8 جزر 2 على 1بنفعش لأن جزء + +240 +00:16:28,460 --> 00:16:31,260 +اتنين مش عدد صحيح لازم يكون البص والمقام عدد صحيح + +241 +00:16:31,260 --> 00:16:34,260 +أو المقام لايساوزيه فهذه عدد غير نسبية فهذا هو + +242 +00:16:34,260 --> 00:16:37,060 +التعريف طب بنشوف كيف بدنا نكتبه بشكل اللي هو طبعا + +243 +00:16:37,060 --> 00:16:41,880 +هي التعريف the real number X is rational if and + +244 +00:16:41,880 --> 00:16:45,580 +only if there are integers there are يعني إيش؟ + +245 +00:16:45,580 --> 00:16:48,040 +there exist لأن قولنا there is يعني there exist بس + +246 +00:16:48,040 --> 00:16:50,860 +طبعا are و is يعني اللي هو إيش اللي يكون فيه جمع + +247 +00:16:50,860 --> 00:16:55,790 +أو مفرد بقدر ألاقي عدد صحيحة P and Qwith a q لا + +248 +00:16:55,790 --> 00:16:59,470 +تساوي 0 الشرط أن المقام لا يساوي صفر such that وإن + +249 +00:16:59,470 --> 00:17:02,610 +ال X أكتب على صورة مين بي أكيو بي أكيو هذا هو + +250 +00:17:02,610 --> 00:17:05,070 +التعريف طب لو بدنا نعمله بشكل مختصر بدنا نكتب + +251 +00:17:05,070 --> 00:17:08,950 +الجملة دي طويلة بدنا نكتبها بشكل رموز عشان نسهل + +252 +00:17:08,950 --> 00:17:12,460 +التعامل معهاف X is rational if and only if إيش + +253 +00:17:12,460 --> 00:17:16,020 +التعريف؟ there exist B in Z لأنه قال لي إيش؟ there + +254 +00:17:16,020 --> 00:17:20,660 +are و there exist Q in Z يوجد عددين صحيحين B and Q + +255 +00:17:20,660 --> 00:17:26,220 +إيش كمان؟ such that Q لا تسوى Zero و X عبارة عن B + +256 +00:17:26,220 --> 00:17:29,580 +على Qتساوي B على Q فانا ممكن أستخدمه بهذا الشكل + +257 +00:17:29,580 --> 00:17:32,860 +فطبعا هنا إيش الفرق؟ كان ممكن أحط ال domain أنه Z + +258 +00:17:32,860 --> 00:17:34,880 +و أكتب there exist و there exist بس هنا كتبتهم + +259 +00:17:34,880 --> 00:17:38,480 +بشكل واحد بعد ما أعمل جملة منفصلة لل universe حطيت + +260 +00:17:38,480 --> 00:17:41,460 +ال universe بنفس الوقت طبعا ده ليش مساعدنا بشكل + +261 +00:17:41,460 --> 00:17:45,400 +كمان أساسي؟ لما يكون عندي أكتر من مكمم ممكن يكون + +262 +00:17:45,400 --> 00:17:48,020 +عندي أكتر من universe فأنا إيه ده أحط ال universe + +263 +00:17:48,020 --> 00:17:50,060 +الأول و ال universe التاني؟ طب كيء لما أقول there + +264 +00:17:50,060 --> 00:17:53,110 +exist أن هو universe ترجعهيصير فيهاش؟ فيه تداخل + +265 +00:17:53,110 --> 00:17:55,610 +لكن لما أحطها هنا باعرف أن وادي من وين أن هو + +266 +00:17:55,610 --> 00:17:58,550 +universal فهذا بتكون أوضح في الكتابة خصوصا لما + +267 +00:17:58,550 --> 00:18:01,330 +يكون في عندي تعدد في المرجعية أه أنا ممكن بتداشتغل + +268 +00:18:01,330 --> 00:18:03,750 +عليها العداد الصحيح أو العداد الطبيعي مع بعض + +269 +00:18:03,750 --> 00:18:06,130 +العداد الصحيح أو العداد الحقيقية مع بعض فلما بحط + +270 +00:18:06,130 --> 00:18:08,650 +المرجع مرة واحدة فوق طب أنا لمين بده أرجع؟ في عندي + +271 +00:18:08,650 --> 00:18:11,530 +أكتر من مرجع لما أحط there exists وفي عندي أكتر من + +272 +00:18:11,530 --> 00:18:14,590 +domain لمين ترجع مش هيكون واضح فهذه الطريقة بتكون + +273 +00:18:14,590 --> 00:18:22,650 +أوضح لما في تعدد خصوصا تمام نشوف مثال آخرفي منخواص + +274 +00:18:22,650 --> 00:18:27,650 +الأعداد النسبية كل عدد نسبي بقدر ألاقي عدد صحيح + +275 +00:18:27,650 --> 00:18:33,770 +أكبر منه ادساش منخواص العدد اللي هو النسبية كل عدد + +276 +00:18:33,770 --> 00:18:36,990 +نسبي في عدد صحيح أكبر منه ولا لأ واضح هذي طبعا + +277 +00:18:36,990 --> 00:18:41,710 +ليه؟ لأن هي خط الأعدادوهي بنمثل وهي صفر وهي واحد + +278 +00:18:41,710 --> 00:18:44,850 +وهي اتنين وكل عدد نسبة بتكون على قطع الأعداد إذا + +279 +00:18:44,850 --> 00:18:48,750 +في عدد صحيح أكبر منه ولا لأ فواضحة هذا طيب فكيف هي + +280 +00:18:48,750 --> 00:18:52,170 +for every rational number there is a larger + +281 +00:18:52,170 --> 00:18:56,730 +integer فهي هيك معناها لكل عدد نسبة يوجد عدد صحيح + +282 +00:18:56,730 --> 00:19:01,230 +أكبر منه طبعا إيش ف for every for all و there is + +283 +00:19:01,230 --> 00:19:04,610 +there exist كيف ممكن نترجمها هذه ممكن نترجمها + +284 +00:19:04,610 --> 00:19:08,010 +بطريقتين الطريقة الأولى طبعا for every for all + +285 +00:19:08,460 --> 00:19:12,040 +وقلنا ما زال إيش rational number طبعا أول شي بتقول + +286 +00:19:12,040 --> 00:19:15,800 +عدد نسبي فبتقول x تنتمي ل q هذه طريقة طويلة شوف + +287 +00:19:15,800 --> 00:19:20,860 +كيف تحت مختصر إيش إذا كان ال x عدد نسبي لأنه في + +288 +00:19:20,860 --> 00:19:24,520 +rational number there exists z طب إيش مال ال z؟ z + +289 +00:19:24,520 --> 00:19:27,200 +تنتمي لل z شوف أننا بنفرق هي في أنا q و في أنا z + +290 +00:19:27,200 --> 00:19:31,460 +such that z تنتمي لل z يعني عدد صحيح و z أكبر من x + +291 +00:19:31,460 --> 00:19:35,060 +شوف طويلة جدا هنا الترجمةممكن أتأخصرها هنا بكل + +292 +00:19:35,060 --> 00:19:38,380 +بساطة for all x تنتمي إلى الـq هدول التلتين عملتوا + +293 +00:19:38,380 --> 00:19:42,420 +مع بعض لكل عدد نسبي for all x تنتمي إلى الـq إيش + +294 +00:19:42,420 --> 00:19:44,980 +مالتوا إيش بتقولوا جملة؟ يوجد عدد صحيح there + +295 +00:19:44,980 --> 00:19:48,200 +exists z تنتمي إلى الـz وشمال الـz أكبر من الـx + +296 +00:19:48,200 --> 00:19:51,980 +أكبر منه ففي الترجمة اختصرناها جدا في الطريقة + +297 +00:19:51,980 --> 00:19:54,860 +التانية التلتين صح لكن التانية مختصرة بس استخدمنا + +298 +00:19:54,860 --> 00:19:57,500 +ان وحطينا ال universe مع there exists ومع for all + +299 +00:19:57,500 --> 00:20:03,000 +أسهل كتير في التعاملفهذه الطريقة هنستخدمها وهيك + +300 +00:20:03,000 --> 00:20:09,100 +بيكون معناها أي سؤال اه طبعا في أشياء كتير احنا + +301 +00:20:09,100 --> 00:20:13,460 +بنذكرها مرة لأنه عشان تكون بس يعني ذكرت وبعد هيك + +302 +00:20:13,460 --> 00:20:16,080 +بالتطبيقات لما نطبقها بتكون واضحة معناها بس احنا + +303 +00:20:16,080 --> 00:20:18,820 +لازم نحطها على نوع موضوعها احنا بندرس ال + +304 +00:20:18,820 --> 00:20:21,400 +quantifiers فهذه المرجعية الأولى لل quantifiers + +305 +00:20:21,400 --> 00:20:24,560 +فلازم نذكر كتير من الحاجات لكن عند الاستخدام ان + +306 +00:20:24,560 --> 00:20:29,410 +شاء الله بنرجعلها مرة تانيةالان ننتقل لنقطة جديدة + +307 +00:20:29,410 --> 00:20:34,770 +rule of quantifier negation قاعدة نفي اللي هو + +308 +00:20:34,770 --> 00:20:41,760 +المكمماتذكرنا في محاضرات ماضية أن عملية النفي مهمة + +309 +00:20:41,760 --> 00:20:45,160 +جدا في البراهين لأن في بعض الأحيان أن في end + +310 +00:20:45,160 --> 00:20:49,560 +statement بحتاج أنفيها عشان للبرهانة و هنشوف هذا + +311 +00:20:49,560 --> 00:20:54,140 +الكلام و طبعا النفي فقط إن أحط قدامها نط و أسكت مش + +312 +00:20:54,140 --> 00:20:57,180 +مفيد عشان أيه كنا بتحدثنا عن ال denials اللي هو + +313 +00:20:57,180 --> 00:21:00,710 +أيش أنه محطها بشكل مكافئة يكون ماله مفيد إليعملية + +314 +00:21:00,710 --> 00:21:04,050 +النفلة عالية أحيانا بتكون غير مفيدة، بحتاج أبسط و + +315 +00:21:04,050 --> 00:21:08,170 +أحطها بصورة مكافئة، أكثر فائدة، أقدر أستخدمها طيب، + +316 +00:21:08,170 --> 00:21:11,630 +لو كان في عنا statement تحتوي على مكمم بدئا فيها، + +317 +00:21:11,630 --> 00:21:15,730 +كيف نحطها بصورة مناسبة، هذا اللي هنتحدث عنه؟عشان + +318 +00:21:15,730 --> 00:21:18,350 +نماهد لهذا الكلام و نربطها مع بعض المعلومات + +319 +00:21:18,350 --> 00:21:22,850 +السابقة عشان ما ننساش خلّينا نحاول ناخد مثال على + +320 +00:21:22,850 --> 00:21:26,950 +ال for all نفسرها بطريقة أخرى ال for all لو أخدنا + +321 +00:21:26,950 --> 00:21:30,910 +ال domain هو مجموعة منتهية من n من العناصر و ليكن + +322 +00:21:30,910 --> 00:21:36,140 +a1, a2, anماذا يعني for all احنا قلنا ما زال + +323 +00:21:36,140 --> 00:21:40,960 +الشمول ال statement لما نعود جميع العناصر تكون + +324 +00:21:40,960 --> 00:21:45,640 +true لازم تكون true فبالنسبة لنا هنا خلينا نكتب + +325 +00:21:45,640 --> 00:21:52,480 +هنا فلو + +326 +00:21:52,480 --> 00:21:58,150 +كان هذا هو ال universe فلما أقول for all xB of X + +327 +00:21:58,150 --> 00:22:04,270 +إيش تكافئ هذه لازم B of A1 تكون true مظبوط و لازم + +328 +00:22:04,270 --> 00:22:09,270 +B of A2 تكون true و هكذا و لازم B of A N كلهم + +329 +00:22:09,270 --> 00:22:12,190 +يكونوا true هيك معناه for all هذا بنأكد عليها إذا + +330 +00:22:12,190 --> 00:22:15,190 +ماكانتش واضحة بنأكد لإنه كشرمول بده تكون كله true + +331 +00:22:15,190 --> 00:22:18,650 +مافيش استثناء و اللي بيخلي وقت إيش بيكون لازم كل + +332 +00:22:18,650 --> 00:22:20,930 +العناصر تكونوا true عشان تكون الناتج كله true ال + +333 +00:22:20,930 --> 00:22:25,630 +endهي الان فإذا for all هي معنى من معاني الان بس + +334 +00:22:25,630 --> 00:22:28,430 +طبعا ال for all إذا ال domain finite عملية سهلة + +335 +00:22:28,430 --> 00:22:30,930 +مكتوبة بكتبها بس ممكن ال domain يكون infinite مثلا + +336 +00:22:30,930 --> 00:22:33,970 +زي كل real number كيف نكتبها بان؟ صعبة فال for all + +337 +00:22:33,970 --> 00:22:39,350 +هي الصورة المناسبة هي الصورة المناسبة فهذه العملية + +338 +00:22:39,350 --> 00:22:43,530 +طيب لو بدنا نيجي ننفيها طب if there exists إيش + +339 +00:22:43,530 --> 00:22:48,050 +بتكون؟ بتكون all لأنه قال لي at least one is true + +340 +00:22:49,100 --> 00:22:52,440 +أه ليش؟ فالـ R وقتاش بتكون true بيقول على الأقل + +341 +00:22:52,440 --> 00:22:54,580 +تكون واحدة صحيح لإن هي كده .. هي بتكون إذا false + +342 +00:22:54,580 --> 00:22:57,380 +false false غير هيك true إذا الواحدة true بتكون هي + +343 +00:22:57,380 --> 00:22:59,800 +true فإذا مناسب that there exists in letter game + +344 +00:22:59,800 --> 00:23:08,020 +هيش باستخدام الـ R R B of T R R B of A F إذا أول + +345 +00:23:08,020 --> 00:23:13,750 +شاهد من هذا الشرحإن الـ for all هي a and بس بقى a + +346 +00:23:13,750 --> 00:23:16,590 +and مع أكم statement مع عدد العناصر تبع ال domain + +347 +00:23:16,590 --> 00:23:19,310 +مع ال نهاية أو مع ال نهاية جد ما يكون يكون و ال + +348 +00:23:19,310 --> 00:23:23,250 +there exist كافة or مش or بس مع كل ال universe مع + +349 +00:23:23,250 --> 00:23:26,250 +كل ال universe تمام إذا فهمنا هذه النقطة خلينا + +350 +00:23:26,250 --> 00:23:31,970 +نعمل عملية negation الآن لو نيجي ننفي for all b of + +351 +00:23:31,970 --> 00:23:36,350 +x معناته بدنا ننفي هذه ال statementفي هذا المثال + +352 +00:23:36,350 --> 00:23:41,410 +طبعا لما أخدنا domain finite بتكون من عدد محدود من + +353 +00:23:41,410 --> 00:23:49,290 +العناصر B of A كيف ممكن ننفي الطرف اليمين؟ممكن + +354 +00:23:49,290 --> 00:23:53,230 +نبسط الطرف اليمين باستخدام De Morgan's اه طبعا + +355 +00:23:53,230 --> 00:23:57,970 +شوية في ناس مندهشة شوية طب De Morgan's سنتين بقى + +356 +00:23:57,970 --> 00:24:01,390 +ممكن نعمم اه ممكن انا اخدهم اجسمهم نصين هذه + +357 +00:24:01,390 --> 00:24:04,770 +capital B و هذه capital Q و بعدين ايش و النصين + +358 +00:24:04,770 --> 00:24:08,190 +اجسمهم كمان ربعين و هكذا فإذا ال De Morgan's ممكن + +359 +00:24:08,190 --> 00:24:11,530 +نعمم و هنشوف التعميم تبعه ان شاء الله فطبعا دي + +360 +00:24:11,530 --> 00:24:15,010 +معمل De Morgan's دي مورجانز إيش بيعمل بيحول ال and + +361 +00:24:15,010 --> 00:24:20,890 +ل or و بين ثمين العناصرor not b of a to .. خلّيني + +362 +00:24:20,890 --> 00:24:30,070 +أكتبها بشكل أوضح not b of a to or or not b of a + +363 +00:24:30,070 --> 00:24:33,470 +and تمام؟ + +364 +00:24:33,470 --> 00:24:37,290 +فالنفي بيحول ال and ل or و بنفي طب لل and إحنا + +365 +00:24:37,290 --> 00:24:41,830 +شوفنا من for all حولناها ل and و نفيناها صارت or + +366 +00:24:41,830 --> 00:24:45,630 +طب ال or بلغة ال quantifiers إيش هي؟ there exist + +367 +00:24:47,780 --> 00:24:51,680 +there exist طب الجملة هي نفسها ولا نفي تبعها نفي + +368 +00:24:51,680 --> 00:24:59,700 +بي اف اكس بي اف اكس فماس شاهد انه نفي ال for all + +369 +00:24:59,700 --> 00:25:03,160 +there exist و بننفي مين و بننفي ال open sentence و + +370 +00:25:03,160 --> 00:25:07,560 +بننفي ال open sentence فهذه قاعدة فهذه قاعدة فدول + +371 +00:25:07,560 --> 00:25:12,250 +شرحناهم فال quantifier نجاشفلما ننفي statement + +372 +00:25:12,250 --> 00:25:15,570 +تحتوي على for all ال for all بيصير there exist و + +373 +00:25:15,570 --> 00:25:18,950 +بننفي ال open sentence زي ما هو الاش نفي ال and or + +374 +00:25:18,950 --> 00:25:23,250 +و بننفي مين ال statements الجزئية الأعزاء بننفي كل + +375 +00:25:23,250 --> 00:25:26,350 +statement لها طبعا بنفس الطريقة لو بدنا ننفي there + +376 +00:25:26,350 --> 00:25:30,970 +exist هي or نفي ال or and و بننفي مين ال statement + +377 +00:25:30,970 --> 00:25:35,600 +اللي جوا فإذا نفي ال there exist all for allفنافي + +378 +00:25:35,600 --> 00:25:38,880 +الـ there exists for all واش و بننفي ال open + +379 +00:25:38,880 --> 00:25:42,680 +sentence فهذه قواعد كيف نتعامل مع النفي في ال + +380 +00:25:42,680 --> 00:25:45,780 +quantifiers هدول القواعد طبعا شيء منطقي لأنه نفي + +381 +00:25:45,780 --> 00:25:48,640 +النفي اثبات فلما احنا بننفي ال for all بيصير there + +382 +00:25:48,640 --> 00:25:50,980 +exists ننفي ال there exists بيصير for all ترجع + +383 +00:25:50,980 --> 00:25:55,240 +لمين للأصل و هكذا أي سؤال فهدول القواعد مهمة جدا + +384 +00:25:55,240 --> 00:25:58,860 +كيف نتعامل مع النفي في ال quantifiers فضلا دكتور + +385 +00:25:58,860 --> 00:26:02,940 +اذا ممكن انا مش فاهم قصة P of X و ايش علاقتها مع + +386 +00:26:02,940 --> 00:26:11,420 +ال for all of X و Uنعم تمام ان ايه هالجد انا عندي + +387 +00:26:11,420 --> 00:26:17,240 +universe معين اي مكان على سبيل المثال اخدنا ا واحد + +388 +00:26:17,240 --> 00:26:23,330 +ا اتنين ا اناماذا يعني for all اللي هو سميناه مكمن + +389 +00:26:23,330 --> 00:26:27,050 +مش شمول يقول إن هذه ال statement بتكون صحيحة إذا + +390 +00:26:27,050 --> 00:26:31,510 +كانت ال P of X صحيحة لجميع عناصر ال domain فلو كان + +391 +00:26:31,510 --> 00:26:34,630 +ال domain هي عناصر و إيش معناته إن P of A1 بتكون + +392 +00:26:34,630 --> 00:26:38,910 +صحيحة و P of A2 بتكون صحيحة و هكذا فإذا هذا يكافئ + +393 +00:26:38,910 --> 00:26:42,610 +هذا الكلامواضحة في الـ there exists أيش معناته؟ + +394 +00:26:42,610 --> 00:26:46,550 +يوجد على الأقل بيكون الصحيحة مرة واحدة فإذا ان دي + +395 +00:26:46,550 --> 00:26:49,990 +يا B of A one true أو B of A two true على الأقل + +396 +00:26:49,990 --> 00:26:53,450 +واحدة منهم صحيحة فإيش التعبير المناسب or أو إيش + +397 +00:26:53,450 --> 00:26:56,750 +الربط المناسب or واضحة؟ أو بعدين نفنها وشوفنا + +398 +00:26:56,750 --> 00:27:02,390 +الربط أي سؤال فإذا هذه قواعد التعامل مع النفي مع + +399 +00:27:02,390 --> 00:27:08,750 +ال quantifiers نشوف بعض الأمثلةwhich of the + +400 +00:27:08,750 --> 00:27:13,190 +following أيهما فيما يلي is equivalent to the + +401 +00:27:13,190 --> 00:27:15,230 +negation of the statement أنا في عندي statement + +402 +00:27:15,230 --> 00:27:19,550 +بدي أشوف مين بنفيها all functions are continuous + +403 +00:27:19,550 --> 00:27:24,570 +مين إنه في المناسب إلها؟ هل أقول جميع الدوال غير + +404 +00:27:24,570 --> 00:27:34,170 +متصلح؟ لأبعض الدوال متصلة لأ بعض التوال غير متصلة + +405 +00:27:34,170 --> 00:27:38,850 +C هو الحل الصحيح مين اللي بيحدد العملية مش عملية + +406 +00:27:38,850 --> 00:27:42,870 +اجتهاد او عملية نسبية كل واحد و ذوقه او عملية + +407 +00:27:42,870 --> 00:27:46,300 +ذوقية لأ فيه قواعدليه الـ C هي اللي صح؟ خلّيني + +408 +00:27:46,300 --> 00:27:49,640 +نحله بالتفصيل مع بعض فليه الـ C هو الصح؟ بينفعش + +409 +00:27:49,640 --> 00:27:53,200 +أنه الـ C for all بس أنفي ال continuous لأ أو أن + +410 +00:27:53,200 --> 00:27:56,660 +أقول some ال for all صار there exist لأ بدي أحول + +411 +00:27:56,660 --> 00:28:00,400 +ال for all ل there exist و أنفي ال open center + +412 +00:28:00,400 --> 00:28:04,860 +خلّينا نحله مع بعض بشكل كامل و نشوف ليه الـ C هي + +413 +00:28:04,860 --> 00:28:13,550 +اللي true فهذا المثال الأول وهي ال solutionأنا ال + +414 +00:28:13,550 --> 00:28:17,150 +statement المعطية الي all functions are continuous + +415 +00:28:17,150 --> 00:28:20,350 +خلينا نحولها لرموز عشان نطبق عليها القواعد فأول شي + +416 +00:28:20,350 --> 00:28:23,570 +بدي احضرليش ال domain فما هو ال domain ممكن ناخد + +417 +00:28:23,570 --> 00:28:29,370 +ال domain او universe اختصارا universe ايش ال + +418 +00:28:29,370 --> 00:28:35,850 +universe مجموع الجميع الدوال the set of all + +419 +00:28:35,850 --> 00:28:36,410 +functions + +420 +00:28:40,780 --> 00:28:45,280 +بعدين ايش بدنا كمان بدنا open sentence اه بدنا + +421 +00:28:45,280 --> 00:28:54,600 +open sentence x is continuous x is continuous فال + +422 +00:28:54,600 --> 00:29:01,090 +statement اللي معطي إلينا ال statementfor all x, b + +423 +00:29:01,090 --> 00:29:05,470 +of x، مظبوط؟ طب نقرأها، نشوف التردية ما صح و لا لأ + +424 +00:29:05,470 --> 00:29:10,330 +كل x in the universe طبعا، يعني كل x عبارة عن + +425 +00:29:10,330 --> 00:29:14,390 +دالة، b of x، x هي متصلة، فكل دالة دالة متصلة، + +426 +00:29:14,390 --> 00:29:17,670 +فالتردية ما صح يعنى، فدي أول خطوة، الآن خلينا + +427 +00:29:17,670 --> 00:29:26,420 +ننفيها، negationالـ negation not for all x b of x + +428 +00:29:26,420 --> 00:29:30,900 +هاي النافذة بتاعها بدنا انبسطه بس زي ما قلنا انحط + +429 +00:29:30,900 --> 00:29:34,980 +not خلاص مفيدناش نتعود انبسط طبقا للقواعد ده ده + +430 +00:29:34,980 --> 00:29:41,240 +ايش بيكافئ there exist x not b of x فنترجمها there + +431 +00:29:41,240 --> 00:29:45,440 +exist يعني some اه و not b of x يعني يوجد بعض + +432 +00:29:45,440 --> 00:29:52,910 +الدوال غير متصلة اللي هي c في الحال cSolution C + +433 +00:29:52,910 --> 00:29:58,010 +فالـ C هو الصح فولا واحدة بتظبط فيهم هي القواعد من + +434 +00:29:58,010 --> 00:30:02,570 +المرجعية هي القاعدة انه كيف بأنفي الـ for all أي + +435 +00:30:02,570 --> 00:30:08,250 +سؤال نشوف + +436 +00:30:08,250 --> 00:30:15,780 +مثال آخر find an equivalent statementto the + +437 +00:30:15,780 --> 00:30:19,880 +negation of the statement بدنا جملة كافئة نفي ال + +438 +00:30:19,880 --> 00:30:23,480 +statement اللي هياش ممكن نختصر denial بدنا denial + +439 +00:30:23,480 --> 00:30:25,900 +لل statement التالي ماهي ال statement some + +440 +00:30:25,900 --> 00:30:30,060 +rational numbers are integers فبدنا ننفيها و + +441 +00:30:30,060 --> 00:30:36,910 +نشوفها و نحطها بشكل أياش مناسب نجيلها denialأما + +442 +00:30:36,910 --> 00:30:41,070 +بنحوّلها لرموز أسلن طريقة عشان نطبق القواعد بعد + +443 +00:30:41,070 --> 00:30:44,510 +هيك إذا صرنا متمكنين من الموضوع ننفي مباشرة + +444 +00:30:44,510 --> 00:30:48,530 +فاشعرنا مانع فخلّيني أولشي نترجمها solution أولشي + +445 +00:30:48,530 --> 00:30:49,350 +خلّيني أحدد universe + +446 +00:30:53,360 --> 00:30:57,600 +أحنا هذه قبلها ترجمناها باستخدام universe R ممكن + +447 +00:30:57,600 --> 00:31:01,360 +او ممكن نستخدمها باستخدام universe Q زي ال + +448 +00:31:01,360 --> 00:31:05,540 +functions خلينا ناخد ال Q مجموعة العداد النسبية + +449 +00:31:05,540 --> 00:31:11,500 +طيب ال B of X إيش هي؟ X is rational ولا integer؟ + +450 +00:31:11,500 --> 00:31:15,620 +is an integer نترجم + +451 +00:31:15,620 --> 00:31:18,440 +الآن و نشوف و نراجح حالنا صح ولا لأ الترجم + +452 +00:31:19,200 --> 00:31:24,980 +statement for all x b of x نشوف التارد يعمل .. لأ + +453 +00:31:24,980 --> 00:31:31,620 +there exist واحدة واحدة there exist x some نشوف + +454 +00:31:31,620 --> 00:31:34,560 +التارد يعمل صح ولا لأ there exist x in the + +455 +00:31:34,560 --> 00:31:38,920 +universe طبعا يوجد عدد نسبة هو عدد صحيح some + +456 +00:31:38,920 --> 00:31:42,280 +rational number يعني بعض الأعداد النسبية هي أعداد + +457 +00:31:42,280 --> 00:31:45,540 +صحية التارد يعمل صحيحة ولا مش صحيحة صحيحة الآن إيش + +458 +00:31:45,540 --> 00:31:47,880 +بنعمل نجاشة ننفيها + +459 +00:31:51,270 --> 00:31:57,190 +negation not there exist x p of x نبسطها طبعا + +460 +00:31:57,190 --> 00:32:02,770 +للقواعد اشنا في there exist for all او اشنا في + +461 +00:32:02,770 --> 00:32:08,630 +اللي جوا فاذا for all x not p of x خلينا نحولها ل + +462 +00:32:08,630 --> 00:32:12,350 +words زي ما بدأنا بالكلمات نحولها ل words in words + +463 +00:32:12,350 --> 00:32:13,490 +بالكلمات + +464 +00:32:19,010 --> 00:32:30,770 +all rational numbers are not integers فهذه + +465 +00:32:30,770 --> 00:32:39,250 +الترجمة لـ denial مكافئة فهيك ترجمناها أو نفناها + +466 +00:32:39,250 --> 00:32:45,690 +بشكل دقيق و بشكل صحيح بدون ما نخطئ أطلاق أي سؤال؟ + +467 +00:32:49,410 --> 00:32:56,490 +أي سؤال؟ نشوف كمان مثال state + +468 +00:32:56,490 --> 00:33:00,770 +in words يعني زي السؤال السابق بس يمكن الصياغة + +469 +00:33:00,770 --> 00:33:07,270 +صريحة أكترthe negation of the statement فى عنا + +470 +00:33:07,270 --> 00:33:13,050 +statement for all x تنتمي لل z if x is divisible + +471 +00:33:13,050 --> 00:33:16,590 +by 6 then x is divisible by 3 فى عنا statement + +472 +00:33:16,590 --> 00:33:20,270 +فىها for all و فىها جملة شرطية if then خلّينى + +473 +00:33:20,270 --> 00:33:24,930 +نترجمها و نعملها عملية negation مثال اتقالت + +474 +00:33:24,930 --> 00:33:33,400 +solution فنبدأ بالترجمةأحنا شفنا يعني ملاعظة قبل + +475 +00:33:33,400 --> 00:33:37,040 +قليل و احنا قلنا بتمر كل عناصر العداد الطبيعي + +476 +00:33:37,040 --> 00:33:40,420 +الصحيحة لخاصية معينة طبعا احنا نقول في طريقتين + +477 +00:33:40,420 --> 00:33:43,560 +للكتابة أحط ال universe فوق و بعدين أشتغل على + +478 +00:33:43,560 --> 00:33:47,400 +المكمم مع ال statement أوماحطش ال universe وإنما + +479 +00:33:47,400 --> 00:33:50,800 +أدخل وين؟ مع المكمّم خلّينا ندخله مع المكمّم لأن + +480 +00:33:50,800 --> 00:33:54,760 +هنا في عملية خطأ شايع بدنا نتعلمه خطأ شايع بدنا + +481 +00:33:54,760 --> 00:33:59,140 +نحاول إيش؟ نتجنبه نتعلم كيف ما ننجعش فيه نتعلم كيف + +482 +00:33:59,140 --> 00:34:02,240 +ما نقعش فيه ف for all x and time ل z بتخليها زي ما + +483 +00:34:02,240 --> 00:34:06,400 +هي بتترجمها for all أو خلاص x and time ل z بتخليها + +484 +00:34:06,400 --> 00:34:09,320 +زي ما هي فال universe بتحطه مع مين؟ في ال + +485 +00:34:09,320 --> 00:34:12,200 +statement نفسه في ال statement نفسه بتاعة عندي في + +486 +00:34:12,200 --> 00:34:16,050 +جملة شرطية if x is divisible by 6ولتكن هذه P of X + +487 +00:34:16,050 --> 00:34:25,190 +X is divisible by 6 وفي عندي command لـ Q of X + +488 +00:34:25,190 --> 00:34:32,590 +وليكن X is divisible by 3 كل عدد يقبل قسم على ست + +489 +00:34:32,590 --> 00:34:36,670 +فوق وقسم على تلاتة هذه نظرية الأعداد كل عدد يقبل + +490 +00:34:36,670 --> 00:34:38,670 +قسم على ست فوق ويقبل قسم على تلاتة صح هذه نظرية + +491 +00:34:38,670 --> 00:34:42,730 +تمام فال statement عندي statement + +492 +00:34:45,110 --> 00:34:48,730 +for all x منفعش أسكت هنا و أقول بس for all x لأن + +493 +00:34:48,730 --> 00:34:52,610 +ال university مش محدد تنتمي لل z هو هيك الجملة + +494 +00:34:52,610 --> 00:34:56,110 +مدينيها واضحة بقول for all x تنتمي لل z بس هذا هي + +495 +00:34:56,110 --> 00:35:00,050 +بس عملناها بالرأس وضعت فهي طريقة جديدة الآن إيش + +496 +00:35:00,050 --> 00:35:04,990 +فيه جملة شرطية if b of x then q of x فهذه هي ال + +497 +00:35:04,990 --> 00:35:11,000 +statement أي سؤالواضح؟ فهذه طريقة أن بدل ما أضع ال + +498 +00:35:11,000 --> 00:35:13,160 +universe لحالي كل هذه الجيومة نفس القضية ممكن هنا + +499 +00:35:13,160 --> 00:35:16,420 +بدل ما أضع Q أقول there exists X تاملة Q مظبوط نفس + +500 +00:35:16,420 --> 00:35:19,160 +القضية ممكن نحلل الأمثلة كلها بهذه الطريقة فإحنا + +501 +00:35:19,160 --> 00:35:23,780 +مخيّرين إيش بنسبنا الطريقة هذه أوضح وأسهل أن أضع + +502 +00:35:23,780 --> 00:35:26,600 +خصوصا ما يكون فيه أندي أكتر من ال universe فيه + +503 +00:35:26,600 --> 00:35:32,330 +متغيرة فنعمل negation الآن ننفيnegation واحدة + +504 +00:35:32,330 --> 00:35:40,690 +واحدة فبدي أنفي for all x تنتمي لل z b of x then q + +505 +00:35:40,690 --> 00:35:49,050 +of x فهذه تكافئ أكمل هنا there exist for all there + +506 +00:35:49,050 --> 00:35:56,490 +exist و بعدين هذا هو المطاب لا تتحولش there exist + +507 +00:35:56,490 --> 00:36:02,580 +x تنتميلأن نفس الشيء احنا بس بنقول انه احنا بنشتغل + +508 +00:36:02,580 --> 00:36:07,140 +على ال domain هذه مرجعية كل عناصر ال Z بعض عناصر + +509 +00:36:07,140 --> 00:36:10,560 +ال Z ما هي هنا احنا لجيت لما نقول هنا النفي for + +510 +00:36:10,560 --> 00:36:15,130 +all x when تنتمي ل ال Q اتغيرتهي في الأصل if there + +511 +00:36:15,130 --> 00:36:18,950 +exists X أنتمي للـQ تغيرت، فتتغيرش، فهذا الانتماء + +512 +00:36:18,950 --> 00:36:21,830 +هو مش جزء من ال open sentences اللي بدها نفي، هو + +513 +00:36:21,830 --> 00:36:25,250 +جزء من المكمم، بس انكتب بطريقة مختلفة، فهذا خطأ + +514 +00:36:25,250 --> 00:36:29,450 +شائع، أرجو ما نقاش فيه، فإحنا ما نقول for all، إيش + +515 +00:36:29,450 --> 00:36:34,750 +النفي؟ إيش تنتمي بالتمعة، بتتغيش، لأن الجملة هي + +516 +00:36:34,750 --> 00:36:38,030 +بتنهد كلها، لأن المرجعية هذه الـZ، هذه المرجعية، + +517 +00:36:38,030 --> 00:36:41,950 +فإذا انهدي كلها،for all x ترجمات نلفي هاد there + +518 +00:36:41,950 --> 00:36:45,050 +exist و ال domain كان مكتوب هنا او مش مكتوب نفس + +519 +00:36:45,050 --> 00:36:50,580 +الطريقة بتغيرش بتغيرش اه طبعا لنلفي هادNot if P of + +520 +00:36:50,580 --> 00:36:57,940 +X then Q of X هذا خطوة واضح فهذا خطأ شائع ارجو ما + +521 +00:36:57,940 --> 00:37:01,340 +نقعش فيه لأن هذا هو اصلا احنا زي ما احنا عملنا هنا + +522 +00:37:01,340 --> 00:37:06,100 +ما نفناش ماصارتش X لها تم تم لل Q تمام فهذا + +523 +00:37:06,100 --> 00:37:10,430 +مابنقعش طيب ممكن ابصد اكتر من هيك؟كيف ممكن ندخل + +524 +00:37:10,430 --> 00:37:14,050 +النافي على ال F ده؟ بنحوّلها لمين ل and اللي هو H + +525 +00:37:14,050 --> 00:37:19,830 +فاحنا بنعرف إن B then Q تكافئ not B and not Q + +526 +00:37:19,830 --> 00:37:23,970 +فلمّا نحوّلها وننفيها، بروح النافي، إيش بتصير هذه + +527 +00:37:23,970 --> 00:37:30,990 +تكافئ؟ there exists X تنتمي لل Z, B of X and not Q + +528 +00:37:30,990 --> 00:37:35,150 +of X نافي النافي راحوا، النافي الخارجي راح مع + +529 +00:37:35,150 --> 00:37:38,770 +النافي فهي ال statement خلّينا نترديمها لكلمات، in + +530 +00:37:38,770 --> 00:37:39,130 +words + +531 +00:37:43,310 --> 00:37:51,390 +some x in z اشمالها are b of x are divisible by 6 + +532 +00:37:51,390 --> 00:38:00,130 +are divisible by 6 and or but ممكن نقول كله صح and + +533 +00:38:00,130 --> 00:38:07,870 +are not divisible by a tree not divisible by a + +534 +00:38:07,870 --> 00:38:13,460 +tree فهي ال statementفهيك وصلنا لنفي بشكل صحيح + +535 +00:38:13,460 --> 00:38:18,700 +وبشكل مناسب فهنتحدث عن الأعداد الصحيحة فلا + +536 +00:38:18,700 --> 00:38:23,380 +مابتتغيرش فأرجو أنه هذه النقطة ننتبه إلها وما نقعش + +537 +00:38:23,380 --> 00:38:32,380 +بهذا الخطر أي استفسار خلينا اليوم نوقف هنا ان شاء + +538 +00:38:32,380 --> 00:38:36,620 +الله ساعتين منكمل وعشان نعمل ال quiz ان شاء الله + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/vRr_TceeePg.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/vRr_TceeePg.srt new file mode 100644 index 0000000000000000000000000000000000000000..29df43b8bf75d763edbb1fd5f39267777f5db6c7 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/vRr_TceeePg.srt @@ -0,0 +1,2511 @@ +1 +00:00:19,740 --> 00:00:23,080 +بسم الله الرحمن الرحيم إن شاء الله هنواصل مع اللي + +2 +00:00:23,080 --> 00:00:27,280 +هو التكافؤ العددي للمجموعات اللي هو equivalence of + +3 +00:00:27,280 --> 00:00:31,140 +sets أو اللي هو numerically equivalent sets في + +4 +00:00:31,140 --> 00:00:34,300 +المحاضرة الماضية عرفنا أنه مجموعتين متكافئتين + +5 +00:00:34,300 --> 00:00:37,420 +عدديا وهذا هو الرمز تبعها إذا قدرنا نلاقي + +6 +00:00:37,420 --> 00:00:41,200 +bijection بين المجموعتين طبعًا واحنا بنقول بين لأن + +7 +00:00:41,200 --> 00:00:43,680 +الترتيب مش مهم مازال لجينا bijection من X لـ Y + +8 +00:00:43,680 --> 00:00:46,860 +فبتكون الـ inverse تبعه bijection من Y لـ X فالموضوع + +9 +00:00:46,860 --> 00:00:50,330 +واضح وأيضًا طبعًا شفنا بعض الأمثلة ويمكن من الأمور + +10 +00:00:50,330 --> 00:00:53,390 +اللي احنا نؤكد عليها أنه أي فترتين مفتوحتين من + +11 +00:00:53,390 --> 00:00:57,070 +الـ real numbers بيكونوا متكافئتين وأي فترة مفتوحة + +12 +00:00:57,070 --> 00:01:00,670 +تكافئ الـ R نفسها كلها وطبعًا اللي هو بواسطة الفترة + +13 +00:01:00,670 --> 00:01:03,110 +المفتوحة من سالب π على 2 لـ π على 2 لأن هذا + +14 +00:01:03,110 --> 00:01:06,110 +العلاقة هي علاقة تكافئ فهي reflexive، symmetric + +15 +00:01:06,110 --> 00:01:09,830 +وtransitive فهذه النقطة يمكن أهم شيء نشوف الآن في + +16 +00:01:09,830 --> 00:01:14,430 +نظرية مهمة وده هتمهد كيف هنتوسع في الأمور فهنا + +17 +00:01:14,430 --> 00:01:18,270 +بتقول ليه إن الـ unions of bijections are + +18 +00:01:18,270 --> 00:01:23,530 +bijections أنا عندي دالتين، الدالتين bijection، G + +19 +00:01:23,530 --> 00:01:26,630 +و F اتحادهم بيطلعوا bijection طبعًا احنا بنعرف إن + +20 +00:01:26,630 --> 00:01:30,090 +اتحاد الدالتين مش دايمًا دالة، في شروط طبعًا هو هنا + +21 +00:01:30,090 --> 00:01:33,370 +طبعًا إذا كانت دالة إذا عندنا دالتين واتحادهم دالة + +22 +00:01:33,370 --> 00:01:35,750 +فإذا كانوا الاثنين bijection فالاتحاد برضه بيطلعوا + +23 +00:01:35,750 --> 00:01:38,910 +bijection فده هو ملخص النظرية، هنشوف النص بالتفصيل + +24 +00:01:39,050 --> 00:01:47,070 +let x, y, w and v begins with x intersection w بتساوي + +25 +00:01:47,070 --> 00:01:51,310 +∅ بتساوي y intersection الـ v فهنا بده يضمن إن + +26 +00:01:51,310 --> 00:01:55,570 +الاتحاد دالة طبعًا في إن احنا حالتين لو التقاطع + +27 +00:01:55,570 --> 00:01:58,370 +ما كانش بيساوي ∅ بين الـ domains بدنا يوم يتساوي على + +28 +00:01:58,370 --> 00:02:01,290 +التقاطع طبعًا ممكن أريح حالي وآخذ التقاطع بيساوي + +29 +00:02:01,290 --> 00:02:04,750 +∅ فالشرط بتحقق automatically فهنا بنتحدث بعدي لحالة + +30 +00:02:04,750 --> 00:02:10,090 +فبقول التقاطع بده يساوي ∅ فبقولي الـ if F is a + +31 +00:02:10,090 --> 00:02:12,410 +bijection، طبعًا كتاب مش سهم، إيش معناه عن + +32 +00:02:12,410 --> 00:02:16,370 +الإشارة؟ إن الـ F بيجيكشن من X لـ Y، والـ G بيجيكشن + +33 +00:02:16,370 --> 00:02:20,810 +من W لـ V، طبعًا إيش قالي؟ X و W يتقطعوا من W في ∅، فإذا + +34 +00:02:20,810 --> 00:02:23,710 +أنا ممكن أخد الاتحاد بتاعهم دالة، صح؟ آه، على طول، + +35 +00:02:23,710 --> 00:02:28,950 +فبقولي F union G from X union W is a bijection + +36 +00:02:28,950 --> 00:02:35,210 +from Y .. من .. X union W إلى Y اتحاد الـ V، فهذه + +37 +00:02:35,210 --> 00:02:40,960 +هي النظرية، خلّيني أشوف البرهان مع بعض، فهذه نظرية + +38 +00:02:40,960 --> 00:02:49,420 +5.6 أنا في عندي الـ F bijection من X لـ Y الـ + +39 +00:02:49,420 --> 00:02:56,500 +G bijection من X لـ Y الـ G bijection من W لـ V طبعًا + +40 +00:02:56,500 --> 00:03:01,260 +تقاطع كل اثنين في ∅ فأنا بدي أثبت إنه اللي هو ممكن + +41 +00:03:01,260 --> 00:03:07,220 +أسميه H تساوي F union G is a bijection from x + +42 +00:03:07,220 --> 00:03:13,040 +union w إلى اللي هو y union اللي هي إيش طبعًا خلينا + +43 +00:03:13,040 --> 00:03:18,340 +نكتبها بنفس الطريقة bijection union الـ V فده هو + +44 +00:03:18,340 --> 00:03:25,060 +المطلوب approve اه فطبعًا كالعادة بنفترض إن شرط + +45 +00:03:25,060 --> 00:03:31,930 +الجملة شرطية صحيح فنقول له assume F is a bijection + +46 +00:03:31,930 --> 00:03:40,990 +من X لـ Y and G is a bijection from W لـ V بدي أثبت + +47 +00:03:40,990 --> 00:03:46,770 +إن H is a bijection أسهل في التعامل أسهل في + +48 +00:03:46,770 --> 00:03:52,250 +التعامل تمام فأول شيء طبعًا هي أول شيء دالة فهي دالة + +49 +00:03:52,250 --> 00:04:00,650 +نكتب بشكل مباشر since اللي هو X تقاطع W بيساوي ∅ + +50 +00:04:00,650 --> 00:04:09,810 +اه H is a function from اللي هو X union W إلى الـ Y + +51 +00:04:09,810 --> 00:04:15,890 +union V is a function هذه أول معلومة على طول نبدأ + +52 +00:04:15,890 --> 00:04:21,920 +الآن بتنهي one to one H is one to one فهنا الحقيقة + +53 +00:04:21,920 --> 00:04:26,240 +هذه مهارة H مرت علينا في السابق لأن ماذا يعني إن + +54 +00:04:26,240 --> 00:04:29,960 +الـ H هي اتحاد إن هي دالة متعددة القاعدة وهذا مرت + +55 +00:04:29,960 --> 00:04:32,520 +علينا كيف نثبت إن دالة one to one إذا كانت متعددة + +56 +00:04:32,520 --> 00:04:34,980 +القاعدة، احنا إيه دي الأمر؟ فيمكن هذا يدينا صورة + +57 +00:04:34,980 --> 00:04:42,100 +عامة، فناخد عنصرين let X1 و X2 تنتمي لـ domain الـ H + +58 +00:04:42,100 --> 00:04:47,200 +اللي هو domain X union W such that + +59 +00:04:50,000 --> 00:04:57,220 +H of X1 تساوي H of X2 تمام؟ كالعادة أخدنا عنصرين + +60 +00:04:57,220 --> 00:05:00,080 +من domain الدالة اللي بدرسها اللي هي الـ H صورهم + +61 +00:05:00,080 --> 00:05:03,600 +متساوي، إيش في عندنا الآن؟ أربع احتمالات، يعني هي + +62 +00:05:03,600 --> 00:05:06,540 +كيف الصورة لإن هو لجت هذه كأنه إيش الـ H معرفة + +63 +00:05:06,540 --> 00:05:13,260 +عندنا، ممكن أكتبها هنا H of X تساوي F of X إذا + +64 +00:05:13,260 --> 00:05:20,020 +الـ X في الـ X وتساوي G of X إذا الـ X وين في الـ W هي + +65 +00:05:20,020 --> 00:05:23,400 +هيك فهي هيك هيكمل الاتحادية تتذكروا لما عرفناها + +66 +00:05:23,400 --> 00:05:27,120 +في chapter الماضي تمام فالآن أنا هذا بتديني أربع + +67 +00:05:27,120 --> 00:05:32,560 +احتمالات لو كانوا X1 و X2 في الـ X فإيش + +68 +00:05:32,560 --> 00:05:41,420 +تعريف الـ H؟ F of X1 تساوي F of X2 ولو كانوا + +69 +00:05:41,420 --> 00:05:48,040 +الاثنين في الـ W X1 و X2 في الـ W فإيش تعريف الـ F؟ G + +70 +00:05:48,790 --> 00:05:54,820 +of x1= g of x2 هي الاحتمال الثاني or الآن في + +71 +00:05:54,820 --> 00:05:58,080 +الاحتمال إنه يكون واحد هنا وواحد هنا فلو كانت الـ + +72 +00:05:58,080 --> 00:06:03,840 +X1 في الـ X فهذا بتديني F of X1 و X2 في الـ W + +73 +00:06:03,840 --> 00:06:10,180 +بتديني G of X2 لو كانت هذه X1 في الـ X and X2 في + +74 +00:06:10,180 --> 00:06:17,620 +الـ W هنا العكس أو G of X1 تساوي F of X2 إذا كانت + +75 +00:06:17,620 --> 00:06:24,310 +X1 في الـ W لكن X2 في الـ X أربع احتمالات واضحة؟ + +76 +00:06:24,310 --> 00:06:29,830 +اه فجبت لكم مرت علينا الفكرة في صورة مشتركة متفقة + +77 +00:06:29,830 --> 00:06:33,250 +في بعض التفاصيل يكون فيها اختلافات طبعًا كالعادة + +78 +00:06:33,250 --> 00:06:36,850 +هيدّونا حالتين X1 تساوي X2 وفيها هيدينا + +79 +00:06:36,850 --> 00:06:40,150 +contradiction وفيها أمور هتدينا contradiction + +80 +00:06:40,150 --> 00:06:46,050 +implies طبعًا الأولى هتدينا X1 تساوي X2 ولا لأ لأن + +81 +00:06:46,050 --> 00:06:50,590 +الـ F one to one لأن الـ F is one to one لأنهم مدينا + +82 +00:06:50,590 --> 00:06:53,570 +إيش؟ مدينا الـ F bijection والـ G والتانية زيها + +83 +00:06:53,570 --> 00:07:01,610 +لأن الـ G one to one لأن الـ G is one to one الباقي + +84 +00:07:01,610 --> 00:07:05,810 +المفروض يكون contradiction خلينا نشوف ليش + +85 +00:07:05,810 --> 00:07:12,850 +contradiction F of X1 تساوي G of X2 ليش؟ لأن تقاطع + +86 +00:07:12,850 --> 00:07:16,550 +من الـ ∅ لأ + +87 +00:07:17,650 --> 00:07:20,130 +الثانية .. الثانية .. تقاطع الصور .. شوفوا .. + +88 +00:07:20,130 --> 00:07:23,890 +انتبهوا هنا .. شوفوا .. ممتاز .. ممتاز .. أحسنتي + +89 +00:07:23,890 --> 00:07:26,790 +.. بس شوفوا .. انتبهوا هنا .. كيف دقة الرياضيات .. + +90 +00:07:26,790 --> 00:07:30,150 +لجينا عشان يضمن إنها دالة .. إيش بدنا؟ إنه تقاطع + +91 +00:07:30,150 --> 00:07:34,130 +المجالين ليسوا ∅ بس .. لكن هو أداني كمان حاجة .. + +92 +00:07:34,130 --> 00:07:37,750 +جالنا كمان تقاطع المجالين المقابلين يساوي ∅ .. + +93 +00:07:37,750 --> 00:07:40,510 +مظبوط؟ أه .. هو أدانيها .. هل بحتاج عشان تكون H + +94 +00:07:40,510 --> 00:07:43,590 +دالة؟ لأ بحتاجش، لكن هم أدانيها عشان هذا، عشان + +95 +00:07:43,590 --> 00:07:47,290 +أحتاجها، لو كان تقاطع المجالين المقابلين مش ∅، + +96 +00:07:47,290 --> 00:07:50,190 +بتتمها دالة، لكن بإيش؟ بفقد إنها تكون one to one، + +97 +00:07:50,190 --> 00:07:53,070 +فهي مهمة جدًا، أعيد للناس اللي ما انتبهوش إيش اللي + +98 +00:07:53,070 --> 00:07:57,830 +جالته زملتهم، ماذا يعني أن F of X1، هذه وين F of + +99 +00:07:57,830 --> 00:08:03,220 +X1 بتكون؟ هذه F of X1 بتكون في وين؟ في الـ Y و G of + +100 +00:08:03,220 --> 00:08:08,620 +X2 وين بتكون في الـ V متساويين يعني مشتركين + +101 +00:08:08,620 --> 00:08:12,840 +موجودين في التقاطع وهذا ممكن مستحيل لجينا دايمًا + +102 +00:08:12,840 --> 00:08:19,120 +F of X1 وين موجودة في الـ Y و G وين بتودي على الـ + +103 +00:08:19,120 --> 00:08:22,440 +V طب هدول متساويين إذا هذا عنصر مشترك إذا موجود في + +104 +00:08:22,440 --> 00:08:26,420 +التقاطع وهذا إيش مستحيل خلينا نكتبها فده معناه + +105 +00:08:26,420 --> 00:08:35,360 +إنه F of x1 تساوي G of x2 تنتمي لتقاطع مين الـ Y + +106 +00:08:35,360 --> 00:08:39,220 +تقاطع الـ V وهو يساوي ∅ contradiction تكتبها مرة + +107 +00:08:39,220 --> 00:08:42,930 +واحدة فلو لها هذا الشرط كانت ما طلعتش إن هي one to + +108 +00:08:42,930 --> 00:08:46,470 +one هي بتتم هذه دالة لو التقاطع المجالين المقابلين + +109 +00:08:46,470 --> 00:08:49,730 +بيساويش ∅ مش مشكلة عندك ده لأ لكن كـ one to one + +110 +00:08:49,730 --> 00:08:52,950 +عمل لي خلق اه والنقطة الثانية نفس الشيء فده معناه + +111 +00:08:52,950 --> 00:08:59,910 +إنه G of X1 تساوي F of X2 تنتمي لـ Y تقاطع V وهو + +112 +00:08:59,910 --> 00:09:05,020 +يساوي ∅ Contradiction Contradiction اه طبعًا فائدة + +113 +00:09:05,020 --> 00:09:12,560 +يؤدي إن X1 تساوي X2 وبالتالي H is one to one أي + +114 +00:09:12,560 --> 00:09:16,620 +سؤال تمام؟ أه فإذا احنا الهيكلية واحدة لكن + +115 +00:09:16,620 --> 00:09:19,280 +التفاصيل وين الـ contradiction بتطلع وين بتطلع X1 + +116 +00:09:19,280 --> 00:09:22,780 +أو X2 ممكن تختلف لكن نفس إيش؟ نفس الهيكلية نفس + +117 +00:09:22,780 --> 00:09:26,260 +الهيكلية لأنه دايمًا احنا ما نحفظش بنشوف بنحلل وين + +118 +00:09:26,260 --> 00:09:28,900 +نداول الـ contradiction وليه عشان نعرف إيش الموضوع + +119 +00:09:28,900 --> 00:09:31,180 +لأنه ممكن يكون في حالة من الحالات مش متطابقة وممكن + +120 +00:09:31,180 --> 00:09:34,260 +نكتشف خلل في السؤال أو خلل في النظرية أه إذا كانت + +121 +00:09:34,260 --> 00:09:41,920 +في أي خطأ الآن اثنين H is onto تمام احنا هنستخدم + +122 +00:09:41,920 --> 00:09:44,980 +اللي هو إيش هنحسب المجال المقابل هنحسب الـ image as + +123 +00:09:44,980 --> 00:09:47,580 +if هنحسب يعني اللي هو المدى ونثبت إنه يساوي + +124 +00:09:47,580 --> 00:09:53,900 +المجال المقابل هنروح نحسب H of X union W مظبوط؟ ما + +125 +00:09:53,900 --> 00:09:58,520 +أي و أي أي دل طبعًا بنعرف إن أي دالة تتوزع الاتحاد + +126 +00:09:58,520 --> 00:10:05,500 +بدون مشاكل فها دي تساوي H of X union H of W خليناها + +127 +00:10:05,500 --> 00:10:11,140 +ده منفصل فشوفتونها الأفكار اتكررت معناها طب الآن + +128 +00:10:11,140 --> 00:10:14,260 +عملت هيك يعني هو الـ domain مكتوب اتحاده جاهز لو + +129 +00:10:14,260 --> 00:10:18,420 +ما كانش كان أنا عملته جزأته اثنين لما بعمل هيك إيش + +130 +00:10:18,420 --> 00:10:24,900 +تعريف الـ H على الـ X؟ F of X إيش تعريفها على الـ W + +131 +00:10:24,900 --> 00:10:30,620 +الـ H؟ G هيها، فتساوي G of W واضحة الفكرة اتكررت + +132 +00:10:30,620 --> 00:10:34,160 +معناها كمان وأكثر من مرة، صح؟ أه تمام، ممتاز، + +133 +00:10:34,160 --> 00:10:36,520 +الآن إيش نستخدم؟ الـ F شمالها مش بس one to one + +134 +00:10:36,520 --> 00:10:39,600 +استخدام ثانية وإنما onto إذا الـ F of X إيش + +135 +00:10:39,600 --> 00:10:45,440 +بيساوي؟ Y، أه فده يساوي Y اتحاد الـ G برضه onto، + +136 +00:10:45,440 --> 00:10:48,520 +بيساوي V، وهو المطلوب، مظبوط؟ ما هي الـ H ده من وين + +137 +00:10:48,520 --> 00:10:53,630 +لوين الـ H؟ من X هيها من X union لـ اتحاد أداني المجال + +138 +00:10:53,630 --> 00:11:00,690 +المقابل كله إذا فعلا H is onto thus H is onto وهو + +139 +00:11:00,690 --> 00:11:07,830 +المطلوب أي سؤال فإذا هنا بننتبه إنه جال الاتحاد + +140 +00:11:07,830 --> 00:11:11,650 +المجالين .. آسف تقاطعهم مساوا فيه عشان يصير دالة و + +141 +00:11:11,650 --> 00:11:14,030 +جال المجالين المقابلين تقطعهم مساواة فيه عشان يتبنن + +142 +00:11:14,030 --> 00:11:18,690 +تمها one to one فدي مهم جدا فكل حاجة دقيقة ومافيش + +143 +00:11:18,690 --> 00:11:23,570 +حاجة مُعطية .. decor لازم كله معنى لازم كله فايدة + +144 +00:11:23,570 --> 00:11:25,770 +تمام + +145 +00:11:28,170 --> 00:11:31,030 +النظرية ممكن نقرأها أو نستفيد منها حاجة ثانية، إيش + +146 +00:11:31,030 --> 00:11:35,930 +بتقول النظرية؟ في عندي أنا bijection من X لـ Y، طب + +147 +00:11:35,930 --> 00:11:38,490 +هذا إيش معناه أنه فيه bijection؟ يعني X تكافئ Y، + +148 +00:11:38,490 --> 00:11:42,270 +وفيه bijection من W لـ V، إذا W تكافئ الـ V، طب عن + +149 +00:11:42,270 --> 00:11:45,710 +تحت الشروط، الـ domain مع الـ domain تحطهم في I، و + +150 +00:11:45,710 --> 00:11:48,330 +المجال المقابل مع المجال المقابل تحطهم في I، طب + +151 +00:11:48,330 --> 00:11:51,890 +لمزال أنا قدرت ألاقي bijection من الاتحاد للاتحاد، + +152 +00:11:51,890 --> 00:11:54,660 +إذا الاتحاد يكافئ الاتحاد، إذا الاتحاد يكافئ + +153 +00:11:54,660 --> 00:11:59,240 +الاتحاد فهنا على طول معنى آخر من النظرية أنا عندي + +154 +00:11:59,240 --> 00:12:02,080 +اتحاد الـ two bijection وتم بيجيكشن تحت الشروط + +155 +00:12:02,080 --> 00:12:06,280 +اللي ذكرناها وإيش كمان بيقول النظرية خمسة ستة also + +156 +00:12:06,280 --> 00:12:11,480 +says بيقول إضافة لما سبق إنه إذا كانت X تكافئ الـ Y + +157 +00:12:11,480 --> 00:12:15,620 +وW تكافئ الـ V then الاتحاد يكافئ الاتحاد طبعا تحت + +158 +00:12:15,620 --> 00:12:18,180 +الشروط إن الأولى مع الأولى تقطعها Φ والتانية مع + +159 +00:12:18,180 --> 00:12:22,750 +التانية تقطعها Φ لأ، طب ليش لو تقاطعهم فيه بيصيرش + +160 +00:12:22,750 --> 00:12:25,910 +تكافؤ؟ ليش؟ لأن ممكن التقاطع يكون أكبر من التقاطع، + +161 +00:12:25,910 --> 00:12:29,030 +لأنه طبعا .. حتى لو أنا نظريا عندي مجموعة فيها + +162 +00:12:29,030 --> 00:12:31,890 +خمسة ومجموعة فيها عشر، الاتحاد مش ضروري يكون خمس + +163 +00:12:31,890 --> 00:12:34,710 +عشر، والتنتين خمسة وعشر، ممكن الاتحاد يكون خمسة عشر + +164 +00:12:34,710 --> 00:12:37,530 +والتنتين يكون عشرة، لأن ممكن فيه تقاطع، لكن لما + +165 +00:12:37,530 --> 00:12:41,330 +يكون التقاطع فيه، هدول خمسة عشر هدول خمسة عشر واضحة؟ + +166 +00:12:41,330 --> 00:12:44,150 +آه ف أنا بضمن حتى لو إنه مش النظرية صحيح مافيش + +167 +00:12:44,150 --> 00:12:47,170 +عناصر مشتركة إن تكون إيش مش معدودة أنا بضمن إنه هي + +168 +00:12:47,170 --> 00:12:50,630 +خمسة وعشرة مازال مافيش مشترك هي خمسة عشر وخمسة + +169 +00:12:50,630 --> 00:12:53,030 +وعشرة مافيش مشترك برضه خمسة عشر مازال مقولتيها على + +170 +00:12:53,030 --> 00:12:56,330 +المتكافئة وعلى الـ infinite نفس الصورة فده للتعامل + +171 +00:12:56,330 --> 00:13:03,950 +فدي ملاحظة مهمة نظرية فإذا إحنا شفنا إنه إذا كان في + +172 +00:13:03,950 --> 00:13:06,530 +عندنا أربع مجموعات تنتين بيكافؤوا بعض وتنتين + +173 +00:13:06,530 --> 00:13:09,710 +بيكافؤوا بعض فالاتحاد يكافئ الاتحاد بس بشرط إن + +174 +00:13:09,710 --> 00:13:13,270 +التقاطع يساوي فيه عشان إيش التكرار أكون متحكم فيه + +175 +00:13:13,270 --> 00:13:16,290 +لأنه ما أعرفش إنه لما يجي اتحاد لو إن التقاطع + +176 +00:13:16,290 --> 00:13:18,790 +ما يساويش فيه فالاتحاد ممكن يكون فيه تكرار والتكرار + +177 +00:13:18,790 --> 00:13:22,770 +بيختلف من مجموعتين لمجموعتين هنشوف نظرية مشابهة بس + +178 +00:13:22,770 --> 00:13:25,010 +بدل ما نتحدث عن الاتحاد هنتحدث عن الـ Cartesian + +179 +00:13:25,010 --> 00:13:27,960 +product برضه فيه مجموعتين متكافئتين ومتتين + +180 +00:13:27,960 --> 00:13:31,080 +متكافئتين، لو أخدت كارتيسيا مع كارتيسيا بيتموا فيه + +181 +00:13:31,080 --> 00:13:35,360 +تكافئة، فإنها طبعا هنا، بس الشرط مش هياخد الشرط + +182 +00:13:35,360 --> 00:13:41,210 +إنه التقاطع of five، بقدر أمسحه فهنا طبعا العنوان + +183 +00:13:41,210 --> 00:13:48,710 +إذا X تكافئ Y وW تكافئ V then X كارتيسرا مضادة لـ + +184 +00:13:48,710 --> 00:13:51,830 +W تكافئ Y كارتيسرا مضادة مع الـ V بدون شروط هنا + +185 +00:13:51,830 --> 00:13:54,690 +ونشوف نص النظرية بشكل صريح العنوان ده بيذكرنا + +186 +00:13:54,690 --> 00:13:57,990 +النظرية عناشي بتحكي يعني لما بحط عنوان هنا النظرية + +187 +00:13:57,990 --> 00:14:01,610 +عناشي بتحكي وبعدين بخرج التفاصيل للدقة طبعا let X + +188 +00:14:01,610 --> 00:14:05,980 +Y W V بيست زي تويبس ما قالليش تقاطع بـ Φ، مش + +189 +00:14:05,980 --> 00:14:10,340 +محتاجها هنا، مش زي الأول فبقوللي if X تكافئ الـY و + +190 +00:14:10,340 --> 00:14:14,880 +الـW تكافئ الـV، then X Cartesian W يكافئ Y + +191 +00:14:14,880 --> 00:14:19,540 +Cartesian الـV، مباشرة، بدون شروط، هنشوف ليش، + +192 +00:14:19,540 --> 00:14:24,580 +محتاجناش تقاطع بـ Φ هنالأنه في الاتحاد مهم إن + +193 +00:14:24,580 --> 00:14:28,200 +تقاطعه أساوفان لأنه في تكرار في الاتحاد لكن في الـ + +194 +00:14:28,200 --> 00:14:31,560 +Cartesian مالوش دعوة مافيش تكرار أنا عناصر مع + +195 +00:14:31,560 --> 00:14:35,080 +عناصر أنا باخد أحداثي وأنا باخد أحداثي التكرار ما + +196 +00:14:35,080 --> 00:14:40,980 +بيأثرش عليا، ما بيأثرش عليا، فهذه نظرية اللي هي + +197 +00:14:40,980 --> 00:14:49,030 +خمسة ستة سبعة طبعا إيش بتقول إذا كانت X تكافئ الـ Y + +198 +00:14:49,030 --> 00:14:57,710 +and W تكافئ الـ V مظبوط آه then X cross الـ W تكافئ + +199 +00:14:57,710 --> 00:15:03,510 +Y cross الـ V Cartesian مع الـ V طبعا Approved + +200 +00:15:03,510 --> 00:15:06,750 +Assume + +201 +00:15:08,160 --> 00:15:11,680 +خلينا نسمي الدوال بالمرة مازال متكافئة في دالة + +202 +00:15:11,680 --> 00:15:24,640 +Assume F a bijection from X لـ Y and G بيجيكشن من W + +203 +00:15:24,640 --> 00:15:31,860 +لـ V إيش المطلوب؟ We want طبعا بدنا نثبت إنه + +204 +00:15:31,860 --> 00:15:35,080 +متكافئة، بدنا ندور على دالة نسميها H We want to + +205 +00:15:35,080 --> 00:15:42,370 +find H تكون بيجيكشن من X cross الـW إلى Y cross + +206 +00:15:42,370 --> 00:15:45,890 +الـV باختصار أنا اختصرت أشياء كثيرة بس أتوقع أن + +207 +00:15:45,890 --> 00:15:48,890 +المجال يسمح ولا في أي مشكلة؟ آه طبعا أقول لك + +208 +00:15:48,890 --> 00:15:53,070 +معطيات إيش معناه إن X تكافئ الـY إذا هناك بيجيكشن + +209 +00:15:53,070 --> 00:15:55,870 +سميته F؟ وإيش معناه إن W تكافئ الـV إذا هناك + +210 +00:15:55,870 --> 00:15:59,050 +بيجيكشن سميته G؟ بدي أثبت إن المجموعة هذه وليها + +211 +00:15:59,050 --> 00:16:02,430 +كنت أسميها A اختصارا ودي بيجيكشن متكافئنا بينهم، + +212 +00:16:02,430 --> 00:16:06,490 +بدنا نسميه H، بندور على H فالسؤال كيف بنعرف الـH؟ + +213 +00:16:08,670 --> 00:16:12,030 +أول شيء أزواج مرتبة فهنا دائما أول شيء زي ما + +214 +00:16:12,030 --> 00:16:14,510 +اتعلمنا مازال المجموعات الـ X والـ Y ده مش معروف + +215 +00:16:14,510 --> 00:16:16,730 +عن أصولهم إذا انضفتر الـ Calculus حلي عشان تجيب + +216 +00:16:16,730 --> 00:16:19,290 +الـ Calculus، ما ينفعناش، بدنا نشوف على المعايش، + +217 +00:16:19,290 --> 00:16:21,430 +المعطيات، في في المعطيات ده ولا آه، كتبتهم أنا + +218 +00:16:21,430 --> 00:16:25,410 +أصلا صريح، آه، فهنعتمد عليهم، هنعتمد عليهم، آه، + +219 +00:16:25,410 --> 00:16:27,810 +فأنا بدي أعرف الـ F، خليني أرسم لكم، يمكن صورة + +220 +00:16:27,810 --> 00:16:36,860 +تساعدكم، let H from X cross W إلى y cross الـ V بـ + +221 +00:16:36,860 --> 00:16:43,920 +given by أول شيء الـ H هي أزواج مرتبة فأكتب H of X + +222 +00:16:43,920 --> 00:16:50,480 +and خليني أسميها W small w فأي عناصرها أزواج مرتبة + +223 +00:16:50,480 --> 00:16:53,700 +يعني أرجو أن الأمور تكون واضحة فهياخد زوج مرتب + +224 +00:16:53,700 --> 00:17:00,540 +ويوديه لزوج مرتب يساوي من عند اقتراح بدي أعرف الـ H + +225 +00:17:02,370 --> 00:17:08,170 +G of X ليش الـ F معرفة على مين الـ G جايه آه مين + +226 +00:17:08,170 --> 00:17:15,610 +المعرفة على الـ X F والتانية مين أحسنت + +227 +00:17:16,240 --> 00:17:21,900 +100% فحنثبت إذا الصورة مش واضحة ليش اخترنا احنا + +228 +00:17:21,900 --> 00:17:25,880 +بنحاول نتعلم كيف نفكر طبعا يعني هذا جزء هذا طبعا + +229 +00:17:25,880 --> 00:17:28,440 +هو الجزء الأصعب طبعا في جزء إنه لو اداني هاد + +230 +00:17:28,440 --> 00:17:30,160 +الدالة كيف أتعامل ما حاول ثبتنا وانتوا وانتوا + +231 +00:17:30,160 --> 00:17:33,760 +وانتوا وحنثبته طيب خلينا نشوف كيف ممكن نفكر نحاول + +232 +00:17:33,760 --> 00:17:37,600 +نعمل صورة تقريبية زي ما إحنا شفنا أكثر من مرة إن + +233 +00:17:37,600 --> 00:17:41,080 +الرسم شماله أداء مساعدة طبعا برسم مش أنا رسم دقيق + +234 +00:17:41,080 --> 00:17:45,760 +ولا رسم حقيقي وإنما رسم يقرب للصورة إيش اللي عندنا + +235 +00:17:45,760 --> 00:17:55,590 +إحنا هيعنّا X تكافئ من Y وبينهم دالة F وهيعنّا + +236 +00:17:55,590 --> 00:18:06,310 +مجموعة W تكافئ من V وبينهم دالة G عشان أنا عملت أنا + +237 +00:18:06,310 --> 00:18:12,210 +أخد زوج مرتب x w أخد x من هنا وw من هنا بدي + +238 +00:18:12,210 --> 00:18:15,390 +أوديهم على الـ y cross الـ v بدي أوديهم على زوج مرتب + +239 +00:18:15,390 --> 00:18:20,740 +ولا أسميه مثلا a وb فهيش الواضح إنه مين اللي بيودي + +240 +00:18:20,740 --> 00:18:23,720 +X على A هو الـ F فالـ A ده تساوي F of X ومين اللي + +241 +00:18:23,720 --> 00:18:28,100 +بيودي W على الـ B هو G of W واضحة عنك كيف إجت؟ فهي + +242 +00:18:28,100 --> 00:18:32,120 +الصورة الرسماء المشابهة نشوف إن هو ده فعلا .. طبعا + +243 +00:18:32,120 --> 00:18:35,740 +واضح إن هي دالة من إلى لأن هاي الـ X .. F of X وين + +244 +00:18:35,740 --> 00:18:40,300 +بتكون؟ في الـ Y وينها؟ هايها ووين الـ G of W؟ فعلا + +245 +00:18:40,300 --> 00:18:42,480 +في الـ B فبعدها تثبت إنها one to one and unto + +246 +00:18:42,480 --> 00:18:49,680 +فنبدأ one to one H is one to one خليني أعمل سطر + +247 +00:18:49,680 --> 00:18:53,320 +هنا طبعا كالبداية بدي أخد عنصرين في الـ domain إيش + +248 +00:18:53,320 --> 00:18:58,020 +أسميهم؟ X1, W1 لإنهم مزواج مرتبة من الـ domain + +249 +00:18:58,020 --> 00:19:08,360 +فعشان رأيكما X1, W1 وX2, W2 وين موجودين؟ في الـ X + +250 +00:19:08,360 --> 00:19:19,130 +cross W في الـ domain such that H X1 W1 H X2 W2 + +251 +00:19:21,440 --> 00:19:25,180 +متابعين؟ واضح ليش؟ فإن إحنا بنحكي بشكل عام فما + +252 +00:19:25,180 --> 00:19:28,100 +تسموهش X X واحد وX اتنين بديه عنصرين من الـ domain + +253 +00:19:28,100 --> 00:19:31,080 +عناصر الـ domain عناصر عادية باخدها X واحد وX + +254 +00:19:31,080 --> 00:19:33,420 +اتنين طب أزواج مرتبة أزواج مرتبة أيش ما يكون + +255 +00:19:33,420 --> 00:19:36,620 +يكونوا حتى لو كانوا عناصر الـ domain دوال أو + +256 +00:19:36,620 --> 00:19:40,220 +مجموعات بشتغل نفس الشيء ف أنا باخد عنصرين من المجال + +257 +00:19:40,220 --> 00:19:43,160 +صورهم متساوي أيش ما يكونوا العنصرين هدولة أزواج + +258 +00:19:43,160 --> 00:19:47,160 +مرتبة عناصر عادية مجموعات أي مكان فهذه هي البداية + +259 +00:19:47,590 --> 00:19:50,530 +فارجعوا إن تكون واضحة للجميع الآن إيش ممكن أعمل + +260 +00:19:50,530 --> 00:19:55,090 +استخدم التقريب لأنه معرفة ده ده فده يؤدي ماهي الـ H + +261 +00:19:55,090 --> 00:20:03,090 +قال لي F للأول G للتاني زوج مرتب ممتاز بدي أساوي + +262 +00:20:03,090 --> 00:20:10,420 +نفس القضية F الأول X2 G للتاني W2 و اين بتوصل؟ بدي + +263 +00:20:10,420 --> 00:20:14,140 +X واحد .. بدي زوج المرتب يساوي زوج المرتب و + +264 +00:20:14,140 --> 00:20:18,160 +استخدمنا في البداية .. استخدمنا في البداية وقت إيش + +265 +00:20:18,160 --> 00:20:20,100 +الأزواج المرتبة متساوي؟ إذا الأول ساوي الأول و + +266 +00:20:20,100 --> 00:20:23,460 +التاني ساوي التاني طب من هنا في عندي أزواج مرتبة + +267 +00:20:23,460 --> 00:20:25,860 +إذا لازم الأول يساوي الأول والتاني يساوي التاني + +268 +00:20:25,860 --> 00:20:26,520 +ممتاز + +269 +00:20:32,240 --> 00:20:38,620 +طبعا بس واحدة واحدة فهذا يؤدي إن F of X1 تساوي F + +270 +00:20:38,620 --> 00:20:46,220 +of X2 لأنه تساوي الأزواج and G of W1 تساوي G of W2 + +271 +00:20:46,220 --> 00:20:53,160 +من وين جبته هذا؟ ليه؟ لما A B تساوي α β if + +272 +00:20:53,160 --> 00:20:58,160 +and only if A تساوي α و β تساوي B تعريف أول + +273 +00:20:58,160 --> 00:21:01,900 +ما شغلنا في chapter 3 الأزواج يومرتب ممتاز الآن + +274 +00:21:01,900 --> 00:21:06,820 +متدال لـ F 1 to 1 فـ X1 تساوي X2 والـ G 1 to 1 يزن + +275 +00:21:06,820 --> 00:21:11,900 +W1 تساوي W2 ليش؟ لأن الـ F والـ G are one to one + +276 +00:21:11,900 --> 00:21:17,560 +أمس أوصلنا نعمل منهم أزواج مرتبة فده بيقول X1 W1 + +277 +00:21:17,560 --> 00:21:23,880 +تساوي X2 W2 وهو المطلوب تعريف الأزواج المرتبة thus + +278 +00:21:25,180 --> 00:21:32,020 +H is one to one وهو المطلوب لأ فإحنا البداية واحدة + +279 +00:21:32,020 --> 00:21:37,180 +عنصرين من الـ domain صورهم متساوية لعنصرين متساويين + +280 +00:21:37,180 --> 00:21:42,860 +أيا ما كانوا أيا ما كانوا فهذا الجزء الأول الجزء + +281 +00:21:42,860 --> 00:21:47,460 +التاني الآن بدنا نثبت أن الـ H is one to one + +282 +00:21:53,500 --> 00:21:59,960 +يعني إيش بدنا نثبت؟ بدنا نثبت إنه H of X across الـ + +283 +00:21:59,960 --> 00:22:04,520 +W تساوي اللي هو Y across الـ V هذا مطلوب + +284 +00:22:08,010 --> 00:22:11,950 +هل إحنا في عنا نظرية بتقول إن صورة المجموعات تتوزع + +285 +00:22:11,950 --> 00:22:15,150 +على الـ Cartesian؟ في عنا نظرية هيك، إحنا كانت لما + +286 +00:22:15,150 --> 00:22:19,150 +تتوزع على الاتحاد بتقاطع بس، وفي عنا الصورة + +287 +00:22:19,150 --> 00:22:21,830 +العكسية بتتوزع على الـDifference، إذا ما فيش عنا، + +288 +00:22:21,830 --> 00:22:24,170 +ما نقدرش نستخدم زي توي ما عملنا في الاتحاد، إيش + +289 +00:22:24,170 --> 00:22:27,530 +نلجأ؟ للتعريف التاني، هناخد عنصر، بس هنستفيد منها، + +290 +00:22:27,530 --> 00:22:30,830 +هنحاول نستفيد منها، فإذا أنا أبدأ بعنصر في المجال + +291 +00:22:30,830 --> 00:22:35,270 +المقابل، إيش أسميه؟ YV ما هو المعادل الأنصار من وين + +292 +00:22:35,270 --> 00:22:39,770 +المجال المقابل هي من YV أسميه مظبوط اه تنتمي ل + +293 +00:22:39,770 --> 00:22:43,610 +Capital Y cross الـ V اه إيش المطلوب خينا نعمل هامش + +294 +00:22:43,610 --> 00:22:52,850 +بدنا YV تساوي H of X and W صح؟ طيب هد إيش + +295 +00:22:52,850 --> 00:23:00,670 +بالتعريفة؟ F of X, G of W فأنا الـ Y و الـ V + +296 +00:23:00,670 --> 00:23:07,510 +معروفين بدي أختار الـ X و الـ W فواضح إن الـ X هي + +297 +00:23:07,510 --> 00:23:11,270 +الدالة اللي هي صورة الـ Y، آسف، اللي صورتها بتساوي + +298 +00:23:11,270 --> 00:23:14,610 +Y، و هكذا، آه، فعن إيه، كيف بدي أكتبها؟ خليني + +299 +00:23:14,610 --> 00:23:17,530 +أكتبها و بعدين بشرحها، يمكن صعب إن أشرحها قبل، لكن + +300 +00:23:17,530 --> 00:23:25,460 +مع الكتابة هتوضح، الآن، بدي أكتبله كتابة، since الـ + +301 +00:23:25,460 --> 00:23:30,200 +F من X إلى الـ Y is onto + +302 +00:23:30,200 --> 00:23:54,500 +‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏ + +303 +00:23:57,680 --> 00:24:02,800 +بنفس الاسلوب similarly + +304 +00:24:02,800 --> 00:24:07,560 +جي من و ل V + +305 +00:24:12,430 --> 00:24:17,390 +اه وطبعاً و الـ V تنتمي للـ V implies اللي هو إيش + +306 +00:24:17,390 --> 00:24:25,850 +V تساوي G of W for some W تنتمي للـ W فأنا لاجيته + +307 +00:24:25,850 --> 00:24:30,790 +اه بتقدر تلاقي X sub U نعم هيهم قال ليش مش mad for + +308 +00:24:30,790 --> 00:24:34,130 +some يعني there exists اه فأنا بقدر ألاقي اه اه it + +309 +00:24:34,130 --> 00:24:40,610 +follows that أو then إيش أصبح؟ أصبحت YV تساوي مين؟ + +310 +00:24:40,610 --> 00:24:43,970 +الـ Y قول الـ F في X، مظبوط؟ و اللي هو الـ V إيش + +311 +00:24:43,970 --> 00:24:49,270 +بتساوي؟ G of W و هدا إيش بيساوي؟ هدا H of X of W و + +312 +00:24:49,270 --> 00:24:52,050 +الـ X و الـ W الموجودين، الـ X موجودة في الـ X و + +313 +00:24:52,050 --> 00:24:54,070 +الـ W في الـ W فالزوج المرتبون موجود في الكارت + +314 +00:24:54,070 --> 00:24:59,770 +يسان جدك for XW تنتمي للـ X cross الـ W وهو + +315 +00:24:59,770 --> 00:25:06,810 +المطلوب فأنا فعلاً بدأت في Y,V لجهة X,W موجودة في + +316 +00:25:06,810 --> 00:25:11,270 +الكارتيسيان وصورتهم بتساوي إيش؟ Y,V فهنا ممكن ما + +317 +00:25:11,270 --> 00:25:15,210 +ساعدتنيش بشكل مباشر لكن ما دتنيش القيمة مباشرة لكن + +318 +00:25:15,210 --> 00:25:19,050 +وضحتني إيش اللي بده يعمل اه فأنا بدي بقدر ألاقي X + +319 +00:25:19,050 --> 00:25:22,850 +صورتها تحت الـF بتساوي Y نعم لأن الـF أنتو أخدت + +320 +00:25:22,850 --> 00:25:27,750 +الـY فكل Y صورة وكل V صورة لأن الـG برضه أنتو + +321 +00:25:27,750 --> 00:25:31,880 +فاحنا كتبناها وهو المطلوب فهذا يدل على أن الـDella + +322 +00:25:31,880 --> 00:25:42,080 +is onto فطبعاً + +323 +00:25:42,080 --> 00:25:46,000 +أحيانا الواحد يقدر يشوف العمر لكن كيف يكتبه؟ طبعا + +324 +00:25:46,000 --> 00:25:54,430 +نتعلم نقلد و نشوف الأمور فأنتهى البرهان تماما فهنا + +325 +00:25:54,430 --> 00:25:59,210 +طبعا بيوسعنا الأمور وهذه نظريات مهمة وممكن هنستفيد + +326 +00:25:59,210 --> 00:26:04,810 +منها فيما بعد ممكن + +327 +00:26:04,810 --> 00:26:11,470 +أمحي هنا عشان نشوف التعريف خلصته هذا؟ نمحي اللي + +328 +00:26:11,470 --> 00:26:12,110 +فوق أقل + +329 +00:26:17,410 --> 00:26:22,290 +فطبعاً هذا مفهوم التكافؤ العددي للمجموعات فهذه بعض + +330 +00:26:22,290 --> 00:26:27,250 +الأمثلة و أدينا مقدار كافي منه و هنرجعله لكن هلأ + +331 +00:26:27,250 --> 00:26:31,030 +ننتقل لمفهوم جديد مفهوم أساسي اللي هو عنوان الشابتر + +332 +00:26:31,030 --> 00:26:35,890 +هنعرف denominable sets وفي مصطلح آخر countable + +333 +00:26:35,890 --> 00:26:40,710 +sets طبعاً المصطلح يعني تقريبا تعريف نفس الشيء + +334 +00:26:40,710 --> 00:26:44,290 +countable أو denominable قابل للعدد أو قابل للترقيم + +335 +00:26:44,610 --> 00:26:47,890 +هتشوف الفرق اللي إيه؟ هذا المعنى اللغوي، المعنى + +336 +00:26:47,890 --> 00:26:51,930 +الصلاحي هنشوف، فيه فرق بينهم طبعا، فيه فرق بينهم، + +337 +00:26:51,930 --> 00:26:54,790 +نعم، فنبدأ إيش نختار من أنوا الشابتر، denimrable و + +338 +00:26:54,790 --> 00:27:01,320 +non-denimrable asset X is said to be denumerable if + +339 +00:27:01,320 --> 00:27:06,040 +X تكافئ الان المجموعة بقول عنها قابلة للعدد + +340 +00:27:06,040 --> 00:27:09,020 +denumerable إذا كانت فيها one to one + +341 +00:27:09,020 --> 00:27:11,400 +correspondence مع الـ natural number عشان هي ماعيش + +342 +00:27:11,400 --> 00:27:16,280 +بقول قابلة للترقيم لأن العداد الطبيعي هي عناصر + +343 +00:27:16,280 --> 00:27:20,880 +العدد ماعيش نقول عدد واحد اثنين ثلاثة اربعة فلمّا + +344 +00:27:20,880 --> 00:27:23,960 +أنا أقابل، أنا بدي أعد عناصر هذه المجموعة، + +345 +00:27:23,960 --> 00:27:46,860 +‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏ + +346 +00:27:49,950 --> 00:27:52,150 +ما هي الـ Countable، إيش الفرق اللي معناه + +347 +00:27:52,150 --> 00:27:54,410 +الاصطلاح، يمكن أنا ما أقدرش أميز بينهم من ناحية + +348 +00:27:54,410 --> 00:27:57,530 +لغوية باللغة العربية، لكن إيش الفرق؟ بقولّي بقول + +349 +00:27:57,530 --> 00:28:00,790 +على المجموع أنها Countable قبل العد أو الحساب، إذا + +350 +00:28:00,790 --> 00:28:04,990 +كانت Finite أو Denumerable، فFinite أو Denumerable + +351 +00:28:06,310 --> 00:28:11,650 +فالحقيقة في الحالتين بتحدث عن مجموعة صغيرة نسبيا، + +352 +00:28:11,650 --> 00:28:15,050 +مجموعة صغيرة نسبية، يعني هيك الاستلحة وحنواضحها ان + +353 +00:28:15,050 --> 00:28:18,590 +شاء الله في مقابلة، يا بتكون finite يعني صغيرة أو + +354 +00:28:18,590 --> 00:28:22,230 +infinite بس جد ياش جد الآن، والحقيقة الأن دي أصغر + +355 +00:28:22,230 --> 00:28:24,150 +مجموعة infinite الحقيقة، اللي هنشوف، هنقولها من .. + +356 +00:28:24,150 --> 00:28:26,600 +ممكن في البداية لعدل الكلام فإيه معناته؟ + +357 +00:28:26,600 --> 00:28:30,040 +denumerable أو countable مجموعة صغيرة نسبية، هيك + +358 +00:28:30,040 --> 00:28:33,940 +نفهم منها، يا إما finite واضح أنها صغيرة finite أو + +359 +00:28:33,940 --> 00:28:36,360 +infinite بس مش كبيرة كتير، بتكافئ الـ natural + +360 +00:28:36,360 --> 00:28:38,780 +number، الأعداد الصحيحة الطبيعية أو الأعداد + +361 +00:28:38,780 --> 00:28:41,380 +الصحيحة الموجودة، فهذا هو المصطلح، فهذا هو + +362 +00:28:41,380 --> 00:28:44,520 +المصطلح، فعنا الـ denumerable دايما infinite، لكن + +363 +00:28:44,520 --> 00:28:47,660 +إيش ماله تكافئ الآن؟ الـ countable يا denumerable + +364 +00:28:47,660 --> 00:28:52,380 +يا finite، يا denumerable يا finite تمام remark + +365 +00:28:55,880 --> 00:29:00,540 +هذه الملاحظة هي تعميم لملاحظة السابقة قلنا بتكون + +366 +00:29:00,540 --> 00:29:04,980 +المجموعة finite إذا كانت يا في ياته كافي N sub K + +367 +00:29:04,980 --> 00:29:08,280 +هنا بنعمم لو الـ K راحت للمالا نهاية بيصير كلها N + +368 +00:29:08,280 --> 00:29:13,640 +فبقول لي قلنا إذا كانت مش فارغة المجموعة و finite + +369 +00:29:13,640 --> 00:29:17,500 +بقدر أرقمها X واحد X K طب لو كانت بتكافئ الـ N + +370 +00:29:17,500 --> 00:29:20,960 +معناته بقدر أرقمها بس للمالا نهاية نفس المعنى لأن + +371 +00:29:20,960 --> 00:29:24,280 +قلنا إيش مجموعة الاناد مجموعة الترقيم والدالة اللي + +372 +00:29:24,280 --> 00:29:28,350 +هي الـ one to one correspondence بين أي مجموعة أو + +373 +00:29:28,350 --> 00:29:32,110 +بين الـ natural number أو subset منها هو دالة إيش + +374 +00:29:32,110 --> 00:29:34,890 +الترقيم يمكن نسميها أنا مش برقم، مظبوط لأنه بعيد + +375 +00:29:34,890 --> 00:29:37,890 +مش بعيد بقول هذا الكرسي واحد لو بدنا نحصل عدد ال + +376 +00:29:37,890 --> 00:29:40,810 +classes في القاع نقول واحد، اثنين، ثلاثة، اربعة + +377 +00:29:40,810 --> 00:29:44,210 +فإيش نستخدم؟ العداد الطبيعي فهي عياش اعداد اللي هو + +378 +00:29:44,210 --> 00:29:47,570 +عياش العد عشان هيك أنا برجح فكرة إن الصفر ليس عدد + +379 +00:29:47,570 --> 00:29:50,390 +طبيعي طبعا في بعض الوزيات النظر بيقول إنه طبيعي لأ + +380 +00:29:50,390 --> 00:29:56,460 +لأن الإنسان لما اتعلم العد اتعلم عد من واحد فعادة + +381 +00:29:56,460 --> 00:29:58,560 +لما نقول عدد طبيعية يعني ان الإنسان اتعلمها + +382 +00:29:58,560 --> 00:30:01,400 +بالفطرة هو من زمان من قديم الزمان فبدأ ياشبي يعد + +383 +00:30:01,400 --> 00:30:04,440 +واحد ما حدش بدأ يعد من صفر ويه لما اخترعوا الصفر + +384 +00:30:04,440 --> 00:30:10,030 +اللي هو مقدماء المسلمين خلينا نمحي هنا اه فهنا عندي + +385 +00:30:10,030 --> 00:30:14,610 +ملاحظة زي ما الـ finite بقدر أرقمها X1 X2 و أوقف + +386 +00:30:14,610 --> 00:30:18,510 +عند XK الـdenominable بقدر أرقمها لكن بجفش للملة + +387 +00:30:18,510 --> 00:30:22,410 +نهائية X1 X2 X3 بس للملة نهائية لأنه ما زال في one + +388 +00:30:22,410 --> 00:30:26,510 +to one correspondence صورة الواحد بسميها X1 ده ليش + +389 +00:30:26,510 --> 00:30:32,350 +العنصر الأول صورة الـ 2 بسميها X2 و هكذا فبقدر + +390 +00:30:32,350 --> 00:30:35,110 +ارقمه فهذا بيساعدنا بالتقرار فبقول if X is a + +391 +00:30:35,110 --> 00:30:38,490 +numerable set فهي اكيد infinity يعني تكافئ ال N ف + +392 +00:30:38,490 --> 00:30:41,610 +there exists F from N to X bijection هو بيقول الـ + +393 +00:30:41,610 --> 00:30:44,130 +bijection بينهم و الـ bijection من أولى لتاني و من + +394 +00:30:44,130 --> 00:30:49,340 +التاني لأولى بتفرجش في عندك السفصة ليه بتفرجش؟ ما + +395 +00:30:49,340 --> 00:30:51,540 +هو الـ bijection قولنا between لأنه إذا كانت الـ F + +396 +00:30:51,540 --> 00:30:55,020 +bijection من X لـ N فالـ F inverse bijection من N + +397 +00:30:55,020 --> 00:30:58,740 +لـ X فالترتيب مش مهم فانا بقدر أغير فيه زي ما بده + +398 +00:30:58,740 --> 00:31:01,580 +عشان ذلك أحيانا إيش بنقول between الترتيب مش مهم + +399 +00:31:01,580 --> 00:31:05,600 +يعني لأنه معروف إذا كانت في عندنا bijection من + +400 +00:31:05,600 --> 00:31:08,720 +مجموعة من X ل Y فالـ inverse للـ bijection برضه + +401 +00:31:08,720 --> 00:31:12,260 +بيجيكشن ومن إيش؟ من Y لـ X فدي دايما ملاحظة عشان + +402 +00:31:12,260 --> 00:31:14,400 +ذلك قولنا علاقة التكامل في أشمالها symmetric + +403 +00:31:14,400 --> 00:31:18,760 +تذكرين؟ اه فقولنا هي equivalence relation فبقولّي + +404 +00:31:18,760 --> 00:31:22,000 +بزال في بيشكشن فانا لو بدأ أرقم هاي عياش بسميها + +405 +00:31:22,000 --> 00:31:25,960 +دالة الترقيم، دالة العدد أفف واحد، X واحد سميها، + +406 +00:31:25,960 --> 00:31:28,540 +أفف اثنين، X اثنين، فبقدر أعط عاصر الـ X كي بها ده + +407 +00:31:28,540 --> 00:31:31,340 +الشكل، بها ده الشكل، فده بسهل التعامل معها، + +408 +00:31:31,340 --> 00:31:35,260 +التعامل مع المجموعات finite، تيجي عندي عدد بوقف + +409 +00:31:35,260 --> 00:31:38,420 +عنده K، في عشر عناصر عند العشر، هوقف، لكن ما زالها + +410 +00:31:38,420 --> 00:31:41,060 +infinite, innumerable، بتمنماشي لملا نهاية، زي + +411 +00:31:41,060 --> 00:31:44,020 +الـnatural number، فهنا بتكتمل الصورة إن شاء الله + +412 +00:31:45,370 --> 00:31:49,430 +نشوف بعض الأمثلة إذا احنا عندنا يمكن أنا بدي ألخص + +413 +00:31:49,430 --> 00:31:52,570 +في ثلاثة مصطلحات مهمة أو ثلاثة مفاهيم مهمة في هذا الـ + +414 +00:31:52,570 --> 00:31:56,970 +chapter مجموعة infinite وتعريفها بقدر ألاقي دالة + +415 +00:31:56,970 --> 00:32:00,430 +one to one من المجموعة نفسها وتكون ليست unto وفي + +416 +00:32:00,430 --> 00:32:03,770 +عندي كمان مفهوم مجموعتين متكافئتين بقدر ألاقي + +417 +00:32:03,770 --> 00:32:07,400 +bijection بينهم فيه أنا الآن مفهوم ثالث برضه مهم + +418 +00:32:07,400 --> 00:32:11,740 +المجموعة numberable اذا كدهش اشكالات بتكافئ لان + +419 +00:32:11,740 --> 00:32:13,980 +بمعنى بقدر احنا نجيب اي جيكشن بين أو بين ال + +420 +00:32:13,980 --> 00:32:16,700 +natural number فدول ثلاثة مفهوم في بينهم أشياء + +421 +00:32:16,700 --> 00:32:20,800 +مشتركة لكن هم مختلفين آه طب تمام فنشوف نتعلم + +422 +00:32:20,800 --> 00:32:27,220 +المهارة الثالثة الآن بقول لي اثبت أن N sub E مين N + +423 +00:32:27,220 --> 00:32:30,060 +sub E؟ رمز جديد اللي هي جميع الأعداد الطبيعية + +424 +00:32:30,060 --> 00:32:33,600 +الزوجية اللي بتساوي 2X بـ X تنتمي للـ N اللي يعني أنا + +425 +00:32:33,600 --> 00:32:38,360 +بسرعة 2، 4، 6 وهكذا أعداد صحيحة زوجية موجبة فقط، + +426 +00:32:38,360 --> 00:32:41,320 +من غير الصفر is denumerable is denumerable فالآن + +427 +00:32:41,320 --> 00:32:46,380 +نتعلم كيف نستخدم التعريف كيف نستخدم التعريف وإيه + +428 +00:32:46,380 --> 00:32:48,860 +اللي بدنا يشبه الـ bijection فخلينا نكتبه بالتفاصيل + +429 +00:32:48,860 --> 00:32:57,540 +لأن هو ده أول مثال هذا المثال رقم واحد فبنثبت أن + +430 +00:32:57,540 --> 00:33:01,080 +الـ N E is numerable إيش is numerable؟ يعني أنتو + +431 +00:33:01,080 --> 00:33:09,840 +كافة الـ N هذا مطلوب a proof أو solution we want to + +432 +00:33:09,840 --> 00:33:17,640 +find a bijection فإذاً أول شيء Denumerable تكافئ + +433 +00:33:17,640 --> 00:33:20,620 +الـ N فرجعنا من المصطلح إيش مهد تكافئ؟ فيه + +434 +00:33:20,620 --> 00:33:23,380 +bijection بينها وبين الـ N هاي اللي رجعنا التعريف + +435 +00:33:23,380 --> 00:33:31,400 +السابق نريد أن نجد بيجيكشن F من اللي هو N E للـ N + +436 +00:33:31,400 --> 00:33:36,000 +أو العكس، تفرجش الترتيب اللي بريحكم أو F. فبدنا + +437 +00:33:36,000 --> 00:33:41,120 +نعرف فبدور على bijection من الأعداد الصحيحة الزوجية + +438 +00:33:41,120 --> 00:33:44,440 +إلى أعداد الصحيحة الموجبة غير الزوجية فبتعرف الـ F + +439 +00:33:44,440 --> 00:33:54,320 +let F من N إلى E إلى ال N be given by خلينا نتعلم + +440 +00:33:54,320 --> 00:33:57,280 +مع بعض كيف نعرف الدالة يمكن تكون واضحة بس برضه + +441 +00:33:57,280 --> 00:34:04,110 +يمكن هي دي إيش الصورة العامة إيش عندنا احنا؟ عندنا N إيه؟ + +442 +00:34:04,110 --> 00:34:10,510 +مين عنصرها؟ إثنين، أربعة، ستة، ثمانية وهكذا بدي + +443 +00:34:10,510 --> 00:34:13,630 +أعمل one to one correspondence مع مين؟ مع الـN مين + +444 +00:34:13,630 --> 00:34:18,210 +عنصرها؟ واحد، إثنين، ثلاثة، أربعة وهكذا إذا إيش + +445 +00:34:18,210 --> 00:34:22,050 +بدي؟ من الطبيعي أودي الإثنين للواحد وأودي الأربعة + +446 +00:34:22,050 --> 00:34:28,370 +لإثنين وأودي الستة للثلاثة إذا F of X إيش بتساوي؟ + +447 +00:34:31,850 --> 00:34:34,910 +تصيروا من التعريف، طلعوا هايه صورة الـ 2 و1، + +448 +00:34:34,910 --> 00:34:37,970 +ليش جسمتها على 2؟ الأربعة 2، الثمانية 4، + +449 +00:34:37,970 --> 00:34:41,850 +إذا ليش بعمل، بأخذ العنصر بأقسمه على 2، واضحة؟ كيف + +450 +00:34:41,850 --> 00:34:44,890 +عرفنا الدالة؟ طبعاً، إذا هذه غلبتكم العكس، يمكن + +451 +00:34:44,890 --> 00:34:48,130 +أسهل، لو قلت من N لإيه؟ بيصير 2X، لو العكس، اللي + +452 +00:34:48,130 --> 00:34:50,750 +هي الـ inverse بحقها، لكن هي واضحة، فهذه الصورة + +453 +00:34:50,750 --> 00:34:53,110 +أتوقع أنها واضحة، خلّيني أتأكد إن هذه one to one + +454 +00:34:53,110 --> 00:34:57,610 +and onto طبعاً واحد يقول لي كيف قسمه طبعاً ممكن يكون + +455 +00:34:57,610 --> 00:35:00,770 +من … مش عدد صحيح ما هو كله زوجي فلما نقسم على 2 + +456 +00:35:00,770 --> 00:35:04,470 +بيطلع عدد صحيح فهي لأ ف أنا متأكد أن هي فعلاً من N E + +457 +00:35:04,470 --> 00:35:10,770 +لـ N واضحة من الصورة الـ N 1 F is one to one نثبت + +458 +00:35:10,770 --> 00:35:17,750 +نأخذ عنصرين في الـ domain let X1 وX2 تنتمي للـ N E + +459 +00:35:17,750 --> 00:35:25,350 +such that F of X1 تساوي F of X2، طبعاً هذه يخلّيه + +460 +00:35:25,350 --> 00:35:30,870 +كهنش، implies، إيش تعريف الدالة؟ تساوي X2 ÷ 2 + +461 +00:35:30,870 --> 00:35:35,090 +ويؤدي X1 تساوي X2 بضرب 2، فإذاً F is one to one + +462 +00:35:36,370 --> 00:35:40,290 +بكل سهولة طبعاً الخطوة الأساسية كيف أدل أصعب واحدة + +463 +00:35:40,290 --> 00:35:44,370 +كيف أعرف الدالة وشوفنا عدة أمثلة طبعاً في موضوع + +464 +00:35:44,370 --> 00:35:47,450 +مختلف لكن تعلمنا كيف بنفكر كيف نجيب الدالة أرجو + +465 +00:35:47,450 --> 00:35:51,370 +أن نبدأ طبعاً مع الممارسة مع التمرين هو اللي + +466 +00:35:51,370 --> 00:35:58,690 +بيعلمنا تمام 2 F is onto ممتاز + +467 +00:35:59,660 --> 00:36:02,680 +هو هأعملها بالصورة الطبيعية اللي هي هأخذ عنصر من + +468 +00:36:02,680 --> 00:36:07,260 +المجال المقابل وهذا برضه هيساعدنا let Y تنتمي من + +469 +00:36:07,260 --> 00:36:11,960 +المجال المقابل اللي هو مين؟ N آه بدي أوجد بدي Y + +470 +00:36:11,960 --> 00:36:17,260 +تساوي F في X وتساوي X ÷ 2 إذا X إيش بتساوي؟ 2Y + +471 +00:36:17,260 --> 00:36:24,990 +فهأقول له let X تساوي 2 في Y لازم أبحث حاجتين أن + +472 +00:36:24,990 --> 00:36:28,370 +أذكركم فيها أن الـ X فعلاً في الـ domain وأن صورتها + +473 +00:36:28,370 --> 00:36:31,990 +بتساوي X طيب X بتساوي 2Y في الـ domain إيش في الـ + +474 +00:36:31,990 --> 00:36:34,330 +domain؟ عدد زوجي فعلاً لأنه مضروب مضروب في 2 لأنه + +475 +00:36:34,330 --> 00:36:38,730 +عدد زوجي then الـ X تنتمي للـ N E لأنه إيش معناه + +476 +00:36:38,730 --> 00:36:42,330 +عدد زوجي؟ مضاعفات 2 ففعلاً هي مضاعفات 2 إيش + +477 +00:36:42,330 --> 00:36:49,910 +كمان؟ F of X هي F 2Y وتساوي Y لأنه بتساوي 2Y ÷ 2 + +478 +00:36:49,910 --> 00:36:55,430 +وهو المطلوب فإذاً هذا بيقول أن الـ F is onto F is one + +479 +00:36:55,430 --> 00:36:59,710 +وهو المطلوب فخلاص واحد واثنين ما زالت I get + +480 +00:36:59,710 --> 00:37:06,730 +bijection إذا فعلاً N E تكافئ الـ N Therefore N E + +481 +00:37:06,730 --> 00:37:13,980 +تكافئ الـ N أي سؤال؟ طبعاً بالمقارنة مع المحاضرة + +482 +00:37:13,980 --> 00:37:17,380 +الماضية ما فيش صدمة كتير لكن برضه هنا شفتوا إنتوا + +483 +00:37:17,380 --> 00:37:21,480 +عملنا نصف المجموعة تكافئ المجموعة لأن الأعداد + +484 +00:37:21,480 --> 00:37:24,120 +الزوجية نصفهم نصفهم والباقي جيش مش نصفهم زوج ونصفهم + +485 +00:37:24,120 --> 00:37:28,160 +فردي لكن نصف لحاله كافئ كل المجموعة لكن أمور بدينا + +486 +00:37:28,160 --> 00:37:30,600 +نتعود لأن أنتم تتعاملوا مع الـ infinite set هذا لا + +487 +00:37:30,600 --> 00:37:33,860 +يحدث بالـ finite مطلقاً لكن بالـ infinite بيحصل في + +488 +00:37:33,860 --> 00:37:38,820 +الـ infinite بيحصل نشوف + +489 +00:37:38,820 --> 00:37:44,260 +مثال مختلف أو مثال آخر آه طبعاً بس مثال عشان نوضح + +490 +00:37:44,260 --> 00:37:47,420 +إيش بقى not countable بيقول لي اثبت أن الـA من 1 + +491 +00:37:47,420 --> 00:37:49,820 +لعشرة is countable إيش بقى countable بيتثبتها يا + +492 +00:37:49,820 --> 00:37:52,000 +أنها finite يا أنها denumerable إيش رأيكم مجموعة + +493 +00:37:52,000 --> 00:38:01,410 +هذه finite آه المثال رقم 2 و solution فالـ A is + +494 +00:38:01,410 --> 00:38:05,230 +finite ليش؟ لو بدي أحط له دليل لأنها N 10 بالضبط + +495 +00:38:05,230 --> 00:38:09,910 +NK اللي هي 10 بتساوي فبقول له أن الـ A تساوي N 10 + +496 +00:38:09,910 --> 00:38:12,950 +مش بستوفيها بتساويها تماماً لأن من 1 لعشرة is + +497 +00:38:12,950 --> 00:38:19,130 +finite مثال بسيط implies A is countable + +498 +00:38:22,780 --> 00:38:26,620 +على طول مثال بسيط جداً بس عشان أوضح المفهوم + +499 +00:38:26,620 --> 00:38:30,480 +countable يا finite يا denumerable فاتعلمنا كيف + +500 +00:38:30,480 --> 00:38:34,460 +نثبت denumerable وإيش finite يا إما بتساوي N عيا K + +501 +00:38:34,460 --> 00:38:38,340 +أو 2K في NK كل واحد أو 5 فإيه واضح فالمثال + +502 +00:38:38,340 --> 00:38:43,060 +سهل طبعاً التعامل مع الـ finite دائماً أسهل نشوف كمان + +503 +00:38:43,060 --> 00:38:43,520 +مثال + +504 +00:38:48,910 --> 00:38:52,330 +denumerable أو نبدأ نثبت أن أنا countable فهذه + +505 +00:38:52,330 --> 00:38:57,910 +اللي هي كل الـ odd كل الفردية 2x-1 يعني إيش بتساوي + +506 +00:38:57,910 --> 00:39:01,070 +واحد ثلاثة هي عوضوا عوضوا أنا بتساوي واحد بتدينا + +507 +00:39:01,070 --> 00:39:04,150 +واحد أنا بتساوي 2 بتدينا 3 فالعداد الفردية + +508 +00:39:04,150 --> 00:39:06,290 +countable يعني إيش؟ بتثبت أن هي الـ finite لأ + +509 +00:39:06,290 --> 00:39:09,050 +infinite فما زالت الـ infinite بتكون countable إذا + +510 +00:39:09,050 --> 00:39:11,750 +كانت عيش denumerable احنا نثبت أن هي denumerable + +511 +00:39:11,750 --> 00:39:15,900 +فهذا المثال الثالث Solution طبعاً أول شيء أوضح لكم ن + +512 +00:39:15,900 --> 00:39:20,180 +أو وهذا من كلمة odd بتساوي 1 3 5 وهكذا + +513 +00:39:20,180 --> 00:39:23,480 +لو بدأت تعوضوا X بتساوي 1 2 بتدينا هذه + +514 +00:39:23,480 --> 00:39:27,600 +العناصر آه فطبعاً is infinite فهنثبت أن هي إيش + +515 +00:39:27,600 --> 00:39:33,380 +بتكافئ اللي هو الـ natural number كلها we will + +516 +00:39:33,380 --> 00:39:41,540 +prove that n o is denumerable + +517 +00:39:45,250 --> 00:39:52,170 +بمعنى N Zero تكافئ الـ N في + +518 +00:39:52,170 --> 00:39:58,640 +عندي طرق ثانية ممكن أثبتهم ممكن أثبتها مباشرة أجيب + +519 +00:39:58,640 --> 00:40:01,620 +دالة one to one أن أنتو من N zero للـ N وزي ما + +520 +00:40:01,620 --> 00:40:05,260 +عملنا بالـ even توة أو ممكن أثبت أن الـ N zero تكافئ + +521 +00:40:05,260 --> 00:40:09,580 +الـ N E والهدف له علاقة transitive فبتتكافئ الـ N + +522 +00:40:09,580 --> 00:40:13,060 +خليني أعمل لكم التاني عشان أؤكد على فكرة الزوجة تبع + +523 +00:40:13,060 --> 00:40:17,100 +التوة إيش العناصر؟ هاي واحد، ثلاثة، خمسة وهي عناصر + +524 +00:40:17,100 --> 00:40:21,930 +الـ N 1، 2، 3، 4 وهكذا فبدنا الواحد + +525 +00:40:21,930 --> 00:40:25,570 +تروح للواحد، بدنا الثلاثة تروح للإثنين، بدنا الخمسة + +526 +00:40:25,570 --> 00:40:30,910 +تروح للثلاثة، بدنا السابعة تروح للأربعة وكذا، ف أنا + +527 +00:40:30,910 --> 00:40:37,350 +هأعرف function عشان نأكد على المهارة، let f من n، + +528 +00:40:37,350 --> 00:40:49,040 +zero إلى ال n be given by f of x تساوي 2x نفسها لأ + +529 +00:40:49,040 --> 00:40:53,520 +الواحد واحد الثلاثة إثنين الثلاثة بتروح للإثنين + +530 +00:40:53,520 --> 00:41:07,260 +الخمسة بتروح للثلاثة X + +531 +00:41:07,260 --> 00:41:11,760 ++1 صح بس دي عشان كان زوج قسمه على إثنين، + +532 +00:41:11,760 --> 00:41:15,260 +هذه فردية، فشوف عند الواحد، واحد زي واحد 2 ÷ + +533 +00:41:15,260 --> 00:41:19,960 +2 2، 3 1، عند الثلاثة، الخمسة، 5 + +534 +00:41:19,960 --> 00:41:23,170 +زي 1 6 ÷ 2 3، صح؟ فعشان هيك بدأنا نؤكد + +535 +00:41:23,170 --> 00:41:26,350 +عليها المهارة طبعاً ممكن واحد يجرب زي ما كنا بنجيب + +536 +00:41:26,350 --> 00:41:29,170 +الصيغة العامة ل… لـ sequence ولا كذا لأس الشيء + +537 +00:41:29,170 --> 00:41:32,390 +الواحد بتعلم وبيجرب ف أنا أكد على المهارة طبعاً في + +538 +00:41:32,390 --> 00:41:37,130 +أحيان كثيرة العكس أسهل زي ما توي شفنا بقى من هنا + +539 +00:41:37,130 --> 00:41:39,810 +لهنا إيش بدأ تصير؟ ده تصير 2X ناقص 1 اللي هي + +540 +00:41:39,810 --> 00:41:43,270 +الصورة اللي بتاعي لكن ننظر لها من جانبين آه طبعاً one + +541 +00:41:43,270 --> 00:41:49,130 +to one and onto … ممكن أترك exercise؟ إيه آه من + +542 +00:41:49,130 --> 00:41:51,370 +N لأ اللي هو الـ F inverse آه ممكن تحسبيها من + +543 +00:41:51,370 --> 00:41:54,550 +تفاضل بالشيء الـ inverse آه فطبعاً هذه bijection آه + +544 +00:41:54,550 --> 00:42:07,630 +then F is a bijection آه exercise أتوقع + +545 +00:42:07,630 --> 00:42:10,990 +أن الكل قادر أنه يثبت أن هي bijection the + +546 +00:42:10,990 --> 00:42:13,430 +numerical يعني countable فإيه دي مباشرة + +547 +00:42:24,070 --> 00:42:28,010 +تمام آه الآن جاعدين احنا يمكن زي ما احنا حكينا + +548 +00:42:28,010 --> 00:42:30,730 +هدفنا من الأول بجاعدين بنشوف الـ infinite set هل + +549 +00:42:30,730 --> 00:42:34,890 +جاءت كلهم جاءت بعض ولا لأ فزي ما ذكرنا الـ natural + +550 +00:42:34,890 --> 00:42:38,170 +number اللي هي الـ denumerable هي أصغر infinite set + +551 +00:42:38,170 --> 00:42:41,030 +مطلقاً مش هألاجي أصغر منها وهنشوف هيجينا هذا الكلام + +552 +00:42:41,640 --> 00:42:44,980 +شوفنا إنه الأعداد الطبيعية denumerable طبعاً هي + +553 +00:42:44,980 --> 00:42:48,600 +الميزان هي واحدة القياس احنا كيف بنقيس إن المجموعة + +554 +00:42:48,600 --> 00:42:51,860 +denumerable لأ تكافئ N ولا ما تكافئش N زي ما + +555 +00:42:51,860 --> 00:42:55,080 +احنا كيف مثلاً بيجيسوا المتر في عندنا في المتحف + +556 +00:42:55,080 --> 00:42:59,000 +الفرنسي مظبوط في قطعة من حديد أو ملاي هي بتكون هذه + +557 +00:42:59,000 --> 00:43:02,520 +الواحدة هي الميزان لما بنيجي على زمان ما كانوش فيه + +558 +00:43:02,520 --> 00:43:04,840 +موازين إلكترونية كانوا في قطعة حديد بيقولوا هذه + +559 +00:43:04,840 --> 00:43:08,240 +kilogram واحنا من ميزاننا الـ natural number اللي + +560 +00:43:08,240 --> 00:43:12,130 +جدها denumerable واللي مش جدها مش denumerable هيك + +561 +00:43:12,130 --> 00:43:14,950 +بنعمل هي واحدة الميزان تبعها اه فالآن بدنا نشوف + +562 +00:43:14,950 --> 00:43:17,650 +فاحنا مجموعة مشهورة عندنا العداد الطبيعي + +563 +00:43:17,650 --> 00:43:21,950 +الـdenumerable هي الميزان هي القياس تبعنا طب ناخد + +564 +00:43:21,950 --> 00:43:26,130 +مجموعة أكبر شوية الـZ الـZ طبعًا أكبر من الـN جدًا + +565 +00:43:26,130 --> 00:43:29,930 +مرة وشوية وزيادة واحد الصفر لأن في كل الموجب وفي + +566 +00:43:29,930 --> 00:43:33,330 +القبل السالب والـ0 الزيادة طب هل هذه كبيرة كثير عن + +567 +00:43:33,330 --> 00:43:38,580 +الـN ولا من ناحية العدد تكافئها؟ تكافئها، بطلنا + +568 +00:43:38,580 --> 00:43:41,320 +نتفاجأ الآن إنه ضعف مش مشكلة مع الـInfinite كل + +569 +00:43:41,320 --> 00:43:45,650 +شيء جاي فبقول الـZ is denumerable الـZ كبيرة بس مش + +570 +00:43:45,650 --> 00:43:49,030 +كبيرة كثير هي صح Infinite لكن زيها زي الـN + +571 +00:43:49,030 --> 00:43:52,950 +الحقيقة عدد عناصرها زي عدد عناصر الـN فطبعًا الـ + +572 +00:43:52,950 --> 00:43:59,010 +Z of all integers is denumerable طبعًا جينا هنشوف + +573 +00:43:59,010 --> 00:44:01,650 +هنستفيد من الأمثلة السابقة ونشوف أن الأمر مش + +574 +00:44:01,650 --> 00:44:08,010 +مفاجئ، الحقيقة خليني بس أمسح مساحة معينة عشان أوضح + +575 +00:44:12,230 --> 00:44:18,890 +سأثبتها بشكل مباشر فهذا proposition 5.4 مطلوب نثبت أن الـz تكافئ الـN + +576 +00:44:18,890 --> 00:44:25,250 +prove يعني نثبت أن الـ z تكافئ الـN + +577 +00:44:25,250 --> 00:44:32,790 +فعرف دالة let f من N لـZ ولا من Z لـN + +578 +00:44:32,790 --> 00:44:38,670 +لأن تفرجش اللي بدكم يعني ما هي واحدة الدالة و + +579 +00:44:38,670 --> 00:44:40,970 +الدالة العكس تاعها be given by + +580 +00:44:45,060 --> 00:44:49,020 +نشوف إيش الفكرة، وبدأ أربط بالأمثلة السابقة في + +581 +00:44:49,020 --> 00:44:54,800 +المثال السابق أثبتنا إن الـN تكافئ الفردي لحالها و + +582 +00:44:54,800 --> 00:44:58,120 +الـN تكافئ الزوجي لحالها طب ما هي الـZ عبارة عن + +583 +00:44:58,120 --> 00:45:03,080 +مين؟ الـZ عبارة عن N وسالب N يعني كأنها نسختين + +584 +00:45:03,080 --> 00:45:06,800 +من الـN فلو أنا خليت العدادة الصحيحة الموجبة مع + +585 +00:45:06,800 --> 00:45:09,980 +الزوجي والعدادة الصحيحة السالبة مع الفردي، بكون + +586 +00:45:09,980 --> 00:45:14,720 +خلص فبقدر أغطي التنتيت لأن ما زال اللي هو الأعداد + +587 +00:45:14,720 --> 00:45:17,400 +الفردية في الـN بتغطي كل الـN إذا بتغطي كل أعداد + +588 +00:45:17,400 --> 00:45:20,360 +صحيحة الموجبة والأعداد الزوجية بتغطي الـN ما + +589 +00:45:20,360 --> 00:45:22,880 +يبقى بتغطي السالب N اللي هو السوالب ممكن تغطي كل + +590 +00:45:22,880 --> 00:45:25,800 +أعداد صحيحة السالبة وتم الصفر ما فيش مشكلة عدد + +591 +00:45:25,800 --> 00:45:30,200 +واحد مش هنزور فيه عنصر احنا إذا غطينا كلها العناصر + +592 +00:45:30,200 --> 00:45:35,420 +بيغلبنا عنصر ما بيغلبناش هنعرف الـF given by F of X + +593 +00:45:35,420 --> 00:45:44,590 +تساوي فاحنا هنجسم الموجب في جهة ومع الـzero أظن + +594 +00:45:44,590 --> 00:45:50,270 +والسالب مع بعض نشوف نبدأ هل جيت؟ أنا هودي كل السالب + +595 +00:45:50,270 --> 00:45:57,150 +للـodd مثلاً فهنا بدنا نشوف إذا كانت للـodd فإذا + +596 +00:45:57,150 --> 00:46:03,210 +كانت العداد بس نكتبهم بشكل معين فبدأ أنا أطلع كل + +597 +00:46:03,210 --> 00:46:09,380 +عدد إذا كان سالب بدي أخليه عدد صحيح وفردي طبعًا هو + +598 +00:46:09,380 --> 00:46:14,280 +سالب فلازم أخده بالـminus عشان أصير موجبة ناقص X و + +599 +00:46:14,280 --> 00:46:19,320 +بدي أخليه يكون فردي فإيش بدي يكون فسالب الـX يعني + +600 +00:46:19,320 --> 00:46:25,600 +إيش بدي أخليه .. خليني أعملها بكتير أساس يمكن بس + +601 +00:46:25,600 --> 00:46:32,000 +مش مشكلة كبيرة خليني أشوف عشان نتعلم أي صورة؟ هي + +602 +00:46:32,000 --> 00:46:37,420 +الصورة هي الصفر هي الواحد هي الاثنين هي الثلاثة + +603 +00:46:37,420 --> 00:46:42,650 +وهكذا وهي السالب واحد والسالب اثنين وهكذا إيش بده + +604 +00:46:42,650 --> 00:46:45,710 +أعمل؟ اه ممكن الـzero أضيفه في المكان فبدي هذا + +605 +00:46:45,710 --> 00:46:50,630 +الواحد إيش؟ أخليه يروح للزوجي الواحد يروح للاثنين + +606 +00:46:50,630 --> 00:46:56,750 +الاثنين تروح للأربعة الثلاثة تروح للستة وهكذا + +607 +00:46:56,750 --> 00:47:01,630 +وبده أخلي الـzero يبدأ الفردي يروح للواحد السالب + +608 +00:47:01,630 --> 00:47:03,710 +واحد يروح للثلاثة ممكن أضيف الـzero مع أي حد + +609 +00:47:03,710 --> 00:47:08,750 +ما تفرجش هذا يروح لمين؟ للخمسة وهكذا فنبدأ بالسالب + +610 +00:47:08,750 --> 00:47:13,770 +بدنا اللي هو الـzero السالب واحد يروح للثلاثة كيف + +611 +00:47:13,770 --> 00:47:17,930 +بده يصير؟ بده يصير ثلاثة إذا سالب واحد كيف بده + +612 +00:47:17,930 --> 00:47:23,630 +تصير ثلاثة؟ بده تصير سالب X بواحد نضربها في اثنين + +613 +00:47:23,630 --> 00:47:26,650 +واحد + +614 +00:47:26,650 --> 00:47:31,250 +ناقص اثنين X، بظبط؟ آه هي خذ الـX بيساوي سالب واحد + +615 +00:47:31,250 --> 00:47:35,250 +بيصير اثنين زي واحد ثلاثة خذها بتساوي اللي هو سالب + +616 +00:47:35,250 --> 00:47:39,810 +اثنين خمسة بيصير خمسة بظبط طيب الـzero واحد صح مية + +617 +00:47:39,810 --> 00:47:43,810 +لمية هذا إيش إيه إذا الـX أصغر أو يساوي + +618 +00:47:43,810 --> 00:47:50,310 +zero الـX من الـZ صح زبطت هيك العكس عكسيها، مش + +619 +00:47:50,310 --> 00:47:52,850 +مشكلة، خلينا .. أنا بدي أعمل هيك وأنت أعمليها في + +620 +00:47:52,850 --> 00:47:55,870 +البيت من الجهة الثانية، إيه أعمل الـinvoice؟ تمام؟ + +621 +00:47:55,870 --> 00:47:58,570 +آه، الآن إذا كانت موجبة بقى، بدي الواحد يروح + +622 +00:47:58,570 --> 00:48:01,990 +للإثنين سهلة، دي اثنين X إذا الـX أكبر من Zero + +623 +00:48:01,990 --> 00:48:05,090 +فنثبت + +624 +00:48:05,090 --> 00:48:08,810 +أن هذه one to one and onto فزي ما شفنا الرسماء + +625 +00:48:08,810 --> 00:48:13,750 +بتساعد كل هذه أمور مساعدة طبعًا بدي أنا أطول أكثر + +626 +00:48:13,750 --> 00:48:16,370 +من هيك هنثبت هذه الـone to one and onto إن شاء + +627 +00:48:16,370 --> 00:48:18,350 +الله المرة الجاية ويمكن تحاولوا فيها في البيت + +628 +00:48:18,350 --> 00:48:18,910 +نوقف هنا diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wQn46KUbcbM_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wQn46KUbcbM_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..493f50f3fde2e5f182f50e1ab753df78d0a5b518 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wQn46KUbcbM_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 4921, "start": 20.65, "end": 49.21, "text": "بسم الله الرحمن الرحيم بنرحب فيكوا في هذه المحاضرة الأولى طبعا في الموضوع طبعا بعض المحاضرة المقدمة اللي اتفقنا فيها على معلومات عامة عن المساق وبعض السياسات اللي هنتبعها اليوم ان شاء الله هندخل في الموضوع في 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جدا", "probability": 0.951416015625}, {"start": 1243.09, "end": 1243.19, "word": " يا", "probability": 0.84765625}, {"start": 1243.19, "end": 1243.41, "word": " أخوات", "probability": 0.7586669921875}, {"start": 1243.41, "end": 1243.53, "word": " لا", "probability": 0.6357421875}, {"start": 1243.53, "end": 1243.91, "word": " يمكنني", "probability": 0.6604817708333334}, {"start": 1243.91, "end": 1243.91, "word": " أن", "probability": 0.323486328125}, {"start": 1243.91, "end": 1244.53, "word": " أستخدم", "probability": 0.8980712890625}, {"start": 1244.53, "end": 1245.05, "word": " أي", "probability": 0.86279296875}, {"start": 1245.05, "end": 1245.33, "word": " رمز", "probability": 0.9908854166666666}, {"start": 1245.33, "end": 1245.59, "word": " ماكان", "probability": 0.562255859375}, {"start": 1245.59, "end": 1245.85, "word": " رمز", "probability": 0.9856770833333334}, {"start": 1245.85, "end": 1246.07, "word": " لأنه", "probability": 0.8019205729166666}, {"start": 1246.07, "end": 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compound true أو false نشوف القواعد اللي بتكيف بنحكم على compound statement true or false إذا عرفنا معلومات عن مركباتها true أو false فبنمر على حاجة مهمة بتساعدنا في هذا الحكم وهي truth table أو جداول الصدق جداول الصدق", "tokens": [7435, 7649, 3555, 19446, 8717, 44510, 10721, 8717, 3215, 2288, 3794, 16095, 8978, 16712, 5172, 9381, 26895, 4032, 8717, 3215, 2288, 3794, 50113, 1211, 14111, 995, 50113, 1211, 14111, 995, 8978, 16247, 2304, 12984, 37977, 45164, 12174, 1211, 2655, 5296, 8315, 5296, 10721, 8717, 3224, 7435, 1211, 8717, 5016, 24793, 15844, 2423, 5629, 2423, 14154, 2074, 34051, 7908, 8717, 8592, 38688, 25062, 14407, 22488, 13672, 1829, 39894, 4117, 33911, 44945, 5016, 24793, 15844, 14154, 5629, 2074, 420, 7908, 11933, 15730, 6225, 28480, 8315, 20449, 1211, 20498, 9307, 18871, 3714, 31747, 3555, 9307, 11296, 2074, 34051, 7908, 6156, 3555, 1863, 29973, 15844, 11331, 26108, 3660, 3714, 16095, 3660, 39894, 3794, 995, 22488, 8315, 8978, 23758, 21542, 24793, 37037, 1829, 3494, 3199, 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"temperature": 1.0}, {"id": 63, "seek": 143859, "start": 1424.47, "end": 1438.59, "text": "واضح؟ فهذه ما يُعرف بيداول الصدر طبعاً زي ما احنا قلنا مولعين بالاختصار بدل تروح نحط capital T و بدل force طبعا ممكن نستخدم هذه أو هذه و Capital AF بدل force أي سؤال", "tokens": [2407, 46958, 5016, 22807, 6156, 3224, 24192, 19446, 7251, 10859, 3615, 28480, 4724, 25708, 995, 12610, 31767, 3215, 2288, 23032, 3555, 3615, 995, 14111, 30767, 1829, 19446, 1975, 5016, 8315, 12174, 1211, 8315, 3714, 12610, 3615, 9957, 20666, 47283, 2655, 9381, 9640, 47525, 1211, 6055, 32887, 5016, 8717, 5016, 9566, 4238, 314, 4032, 47525, 1211, 3464, 23032, 3555, 3615, 995, 3714, 43020, 8717, 14851, 9778, 40448, 29538, 34051, 29538, 4032, 21502, 20389, 47525, 1211, 3464, 36632, 8608, 33604, 6027], "avg_logprob": -0.2728515602648258, "compression_ratio": 1.4754098360655739, "no_speech_prob": 0.0, "words": [{"start": 1424.47, "end": 1425.03, "word": "واضح؟", "probability": 0.69061279296875}, {"start": 1425.03, "end": 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{"start": 1430.77, "end": 1431.09, "word": " بدل", "probability": 0.9462890625}, {"start": 1431.09, "end": 1431.37, "word": " تروح", "probability": 0.67498779296875}, {"start": 1431.37, "end": 1431.65, "word": " نحط", "probability": 0.76611328125}, {"start": 1431.65, "end": 1431.93, "word": " capital", "probability": 0.51708984375}, {"start": 1431.93, "end": 1432.19, "word": " T", "probability": 0.908203125}, {"start": 1432.19, "end": 1432.29, "word": " و", "probability": 0.669921875}, {"start": 1432.29, "end": 1432.49, "word": " بدل", "probability": 0.820068359375}, {"start": 1432.49, "end": 1432.73, "word": " force", "probability": 0.6826171875}, {"start": 1432.73, "end": 1433.01, "word": " طبعا", "probability": 0.9254150390625}, {"start": 1433.01, "end": 1433.45, "word": " ممكن", "probability": 0.953857421875}, {"start": 1433.45, "end": 1433.75, "word": " نستخدم", "probability": 0.871337890625}, {"start": 1433.75, "end": 1433.89, "word": " هذه", "probability": 0.43994140625}, 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not، فإذا هي هذا المثال الأول وخلينا نحط اللي هو الحل solution وحل a فإيش الحل؟ بكل بساطة square root of two is not", "tokens": [347, 81, 1478, 12399, 37495, 22653, 6225, 3215, 3215, 32771, 13546, 8717, 35457, 3660, 12399, 11778, 3224, 11933, 1829, 8592, 28239, 35457, 3660, 22807, 8717, 5016, 9566, 4724, 9381, 4032, 3714, 4587, 10943, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 12399, 44381, 10874, 11622, 38207, 6055, 7649, 1829, 20193, 7251, 43020, 4032, 11242, 3615, 11296, 15844, 11331, 9381, 13063, 3660, 6225, 3215, 3215, 9122, 12984, 16572, 4724, 9381, 4032, 3714, 4587, 10943, 5296, 22488, 3215, 20328, 5016, 1829, 5016, 12399, 6156, 3224, 24192, 23032, 3555, 3615, 995, 9122, 33911, 8717, 1863, 41185, 11296, 22807, 4724, 28820, 4724, 3794, 41193, 3660, 12399, 47525, 8315, 8717, 14851, 9778, 40448, 406, 12399, 47525, 8315, 8717, 14851, 9778, 40448, 406, 12399, 6156, 28814, 15730, 39896, 23758, 9673, 12984, 6027, 16247, 12610, 4032, 9778, 1211, 9957, 995, 8717, 5016, 9566, 13672, 1829, 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b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wQn46KUbcbM_raw.srt @@ -0,0 +1,2228 @@ +1 +00:00:20,650 --> 00:00:25,390 +بسم الله الرحمن الرحيم بنرحب فيكوا في هذه المحاضرة + +2 +00:00:25,390 --> 00:00:29,010 +الأولى طبعا في الموضوع طبعا بعض المحاضرة المقدمة + +3 +00:00:29,010 --> 00:00:32,510 +اللي اتفقنا فيها على معلومات عامة عن المساق وبعض + +4 +00:00:32,510 --> 00:00:34,830 +السياسات اللي هنتبعها اليوم ان شاء الله هندخل في + +5 +00:00:34,830 --> 00:00:38,810 +الموضوع في هذه المحاضرة الأولى من مساق مبادئ + +6 +00:00:38,810 --> 00:00:43,010 +رياضيات ونظرية المجموعة فهنبدأ في ال chapter الأول + +7 +00:00:43,010 --> 00:00:47,630 +وهو elementary logic مبادئ المنطق أو اللي هو + +8 +00:00:47,630 --> 00:00:53,730 +الأساسيات المنطقطبعا احنا بالنسبة لنا ايش علاقة + +9 +00:00:53,730 --> 00:00:56,250 +المنطق بالرياضيات يعني هو المصداق اسمه مبادئ + +10 +00:00:56,250 --> 00:01:01,230 +الرياضيات فطبعا لابد انه نفسر ليش احنا بنبدأ + +11 +00:01:01,230 --> 00:01:07,640 +بدراسة المنطق كمدخل لدراسة الرياضياتفي هناك بشكل + +12 +00:01:07,640 --> 00:01:14,600 +عام نوعين من التفكير أو طرق الوصول للمعرفة علماء + +13 +00:01:14,600 --> 00:01:17,260 +رياضية بشكل عام أو العلماء بشكل عام لما بدرسوا أي + +14 +00:01:17,260 --> 00:01:22,240 +ظاهرة باهتموا بشوفوا شواهد متعددة أمثلة متعددة و + +15 +00:01:22,240 --> 00:01:27,060 +بيحاولوا يعملوا من هذا يستنبطوا أو يستقرؤوا علاقة + +16 +00:01:27,060 --> 00:01:31,530 +عامة أو قاعدة نظريةهذه الطريقة بيسموها طريقة + +17 +00:01:31,530 --> 00:01:36,090 +التفكير الاستقرائي أو inductive reasoning طبعا هذه + +18 +00:01:36,090 --> 00:01:40,050 +مهمة وتستخدم كثير من العلوم لكنها ليست الطريقة + +19 +00:01:40,050 --> 00:01:45,770 +المفضلة لدى علماء الرياضيات أو في الرياضياتوإنما + +20 +00:01:45,770 --> 00:01:50,790 +طريقة التفكير الأوسع انتشارا في الرياضيات هي ما + +21 +00:01:50,790 --> 00:01:55,690 +يُعرف بالتفكير الاستدلالي أو اللي هو القياسي + +22 +00:01:55,690 --> 00:01:59,790 +المنطقي اللي هو ما يُعرف ب deductive reasoning في + +23 +00:01:59,790 --> 00:02:04,570 +هذه العملية إحنا بنهتم طبعا كما قلنا في الاستقراء + +24 +00:02:04,570 --> 00:02:08,930 +بناخد من الأمثلة و بنروح للقاعدة كأنه بناخد من + +25 +00:02:08,930 --> 00:02:15,000 +القاعدة إلى القمةفي الاستقراء للتفكير الـ + +26 +00:02:15,000 --> 00:02:18,180 +Deductive Reasoning الاستدلالي بنمشي بالعكس من + +27 +00:02:18,180 --> 00:02:21,240 +القمة إلى القاع في عندنا نظرية في عندنا قاعدة و + +28 +00:02:21,240 --> 00:02:26,660 +بنحاول نطبقها على الأمثلة أو ممكن نوصفها بشكل آخر + +29 +00:02:26,660 --> 00:02:31,100 +ان احنا مهتمين ان كيفإذا كان فينا مقدمات صحيحة + +30 +00:02:31,100 --> 00:02:34,980 +نثبت إن الاستنتاج صحيح إن الاستنتاج صحيح فاحنا + +31 +00:02:34,980 --> 00:02:39,900 +بهمنا بشكل عام إنه نحكم على نتيجة ما إنها صحيحة أو + +32 +00:02:39,900 --> 00:02:44,440 +نبره إنها صحيحة باستخدام قواعد المنطق وبعض + +33 +00:02:44,440 --> 00:02:48,200 +المعلومات المُعطية والمقبول أو المتفق على إنها + +34 +00:02:48,200 --> 00:02:52,140 +صحيحة فهذه التفكير العام للرياضية طب كيف بنحكم إن + +35 +00:02:52,140 --> 00:02:55,520 +هذا الاستنتاج صحي وكذا فبنحتاج إلى علم المنطق أو + +36 +00:02:55,520 --> 00:02:57,740 +قواعد المنطق زي ما ذكرنا + +37 +00:03:02,880 --> 00:03:07,060 +فطبعا موضوعنا الرئيسي المرتبط هو موضوع البرهين في + +38 +00:03:07,060 --> 00:03:12,760 +الرياضيات فالبرهين عبارة عن جزء أساسي من التفكير + +39 +00:03:12,760 --> 00:03:16,860 +الرياضي لأنه طبعا نستدل منها على إن الاستنتاج اللي + +40 +00:03:16,860 --> 00:03:20,040 +وصلنا له صحيح أو غير صحيح إذا كان في عندنا استنتاج + +41 +00:03:20,040 --> 00:03:23,320 +فهذا اللي هو بهمنا في المنطق أن كيف نحكم على + +42 +00:03:23,320 --> 00:03:30,640 +برهيننا إنها صحيحة أو غير صحيحةفطبعا أي توضيح، أي + +43 +00:03:30,640 --> 00:03:38,120 +تفسير رياضي لا يعتمد على .. مافيش + +44 +00:03:38,120 --> 00:03:42,300 +.. في عنده برهان مقبول، هذا يعتبر غير صحيح فإحنا + +45 +00:03:42,300 --> 00:03:46,440 +عشان يكون برهاننا صحيح أو السنتاج اللي تسمعنا صحيح + +46 +00:03:46,440 --> 00:03:50,360 +أو أي معلومة نتأكد أنها صحيحة لازم تكون مدعومة + +47 +00:03:50,360 --> 00:03:55,780 +ببرهان رياضي صحيح فالبرهان بالنسبة لنا حاجة أساسية + +48 +00:03:55,780 --> 00:03:57,760 +لاغنى عنها + +49 +00:04:00,180 --> 00:04:05,720 +فدراسة المنطق اللي هو عنوان ال chapter هي دراسة + +50 +00:04:05,720 --> 00:04:11,640 +المبادئ والطرق اللي بتخلينا نقدر نميز بين برهان أو + +51 +00:04:11,640 --> 00:04:16,940 +بين حجة إنها صحيحة أو غير صحيحة وهذا هو يمكن من + +52 +00:04:16,940 --> 00:04:20,760 +أهدافنا الرئيسية فهذا اللي هو السبب اللي بيخلينا + +53 +00:04:20,760 --> 00:04:25,100 +ندرس المنطقفطبعا الهدف من هذا الـ chapter و + +54 +00:04:25,100 --> 00:04:30,880 +الانوان تبعه أنه طبعا ما ندرس المنطق بشكل عام كفرع + +55 +00:04:30,880 --> 00:04:35,480 +من فروع العلوم الفلسفية وإنما ندرس كمية كافية من + +56 +00:04:35,480 --> 00:04:38,180 +المنطق وخصوص المنطق الرياضي اللي بتساعدنا في + +57 +00:04:38,180 --> 00:04:42,080 +دراستنا في الرياضيات وإنه نقدر نكون البرهين أو + +58 +00:04:42,080 --> 00:04:46,440 +نحكم على براها إنه صح أو غير صحيح أو براهين الناس + +59 +00:04:46,440 --> 00:04:52,090 +الآخرين فطبعاsection الأول في هذا ال chapter بعد + +60 +00:04:52,090 --> 00:04:54,410 +المقدم اللي حكيناه عن ال chapter بشكل عام + +61 +00:04:54,410 --> 00:04:59,030 +statements and their connectives ال statement طبعا + +62 +00:04:59,030 --> 00:05:02,370 +احنا هناخدها بالمعنى اللي هو الاصطلاحي بيعرفوها + +63 +00:05:02,370 --> 00:05:06,430 +عنها تقرير أو قضية connectives والروابط فاحنا هنا + +64 +00:05:06,430 --> 00:05:10,470 +التقارير والروابط عنوان ال section الأول تبعنا + +65 +00:05:11,260 --> 00:05:16,320 +فنقطة البداية في دراسة المنطق هي ما يعرف بال + +66 +00:05:16,320 --> 00:05:19,900 +statement أو ال proposition زي ما في في اللغة + +67 +00:05:19,900 --> 00:05:21,740 +العربية في مصطلحين برضه وفي اللغة الإنجليزية في + +68 +00:05:21,740 --> 00:05:24,960 +مصطلحين كتابنا المعتمد باستخدام كلمة statement بعض + +69 +00:05:24,960 --> 00:05:27,620 +الكتب هتلاقيه باستخدام proposition فهي نفس المعنى + +70 +00:05:27,620 --> 00:05:31,400 +اللي احنا بنترجمها او بنعربها تقرير او قضية او + +71 +00:05:31,400 --> 00:05:34,820 +تقرية طبعا احنا هناخدها بالمعنى الاصطلاحي وليس + +72 +00:05:34,820 --> 00:05:37,580 +المعنى اللغوي طبعا المعنى الاصطلاحي هنتفق عليه او + +73 +00:05:37,580 --> 00:05:43,810 +هنوضحه في التعريف التانيفأول تعريف اللي هو بيحددنا + +74 +00:05:43,810 --> 00:05:46,230 +المعنى للصلاحي لما نشوف احنا بيجينا نحكي كلمة + +75 +00:05:46,230 --> 00:05:48,810 +statement في هذا المصاق ما هو المقصود بكلمة + +76 +00:05:48,810 --> 00:05:52,170 +statement أه فطبعا زي ما قلنا هي قضية أو تقرير + +77 +00:05:52,170 --> 00:05:56,150 +التعريب تبعها statement فما هي ال statement زي ما + +78 +00:05:56,150 --> 00:05:59,270 +بتعرفه في اللغة اللغة العربية أو اللغة التانية في + +79 +00:05:59,270 --> 00:06:03,130 +نوعين من الجمل فيما يعرف بالجمل الخبرية والجمل + +80 +00:06:03,130 --> 00:06:06,750 +الإنشائيفطبعا الجملة الخبرية بيعرفها هي الجملة + +81 +00:06:06,750 --> 00:06:09,590 +اللي بتديني خبر أو معلومة و هذه المعلومة قابلة + +82 +00:06:09,590 --> 00:06:13,630 +لواحد من اتنين يا true يا false يا صادقة يا كاذبة + +83 +00:06:13,630 --> 00:06:16,910 +يا صحيحة يا خاطئة فهذه بيسموها الجملة الخبرية هذه + +84 +00:06:16,910 --> 00:06:20,150 +هي اللي بتهمنا لإن احنا في النظريات في القوانين + +85 +00:06:20,150 --> 00:06:25,210 +ندي معلومة ندي خبر و هذا الخبرطبعا إذا كان رياضيته + +86 +00:06:25,210 --> 00:06:28,150 +و أنا ألم بيكون صحيح أو بنحكم عليه أنه خطأ و + +87 +00:06:28,150 --> 00:06:31,170 +بنصححه فهذه الشكلة فاحنا بهمنا نتعامل مع الجمال + +88 +00:06:31,170 --> 00:06:34,630 +الخبرية الجمال الإنشائية بتهم ناشت بتهم الناس اللي + +89 +00:06:34,630 --> 00:06:37,610 +بيهتموا باللغة و بالأدب و هذه الأمور فاحنا عشان + +90 +00:06:37,610 --> 00:06:40,670 +هيك بنعرف ال statement is a declarative sentence + +91 +00:06:40,670 --> 00:06:44,500 +جملة خبريةاللي هي إيش مالها، إيش بيميزها، تحتمل + +92 +00:06:44,500 --> 00:06:48,560 +واحد من الاحتمالين يا true يا false، مافيش true و + +93 +00:06:48,560 --> 00:06:52,240 +false مع بعض أو ولا واحدة فيهم، لازم يكون الاحتمال + +94 +00:06:52,240 --> 00:06:55,500 +واحد من القيمة، يا true يا false، مافيش أي احتمال + +95 +00:06:55,500 --> 00:06:58,560 +آخر، فإذا احنا بنحكي على ال statement هي جملة + +96 +00:06:58,560 --> 00:07:03,800 +خبرية، بيبقى الاحتمال واحد صحيح أو خطأطيب، هل أنا + +97 +00:07:03,800 --> 00:07:05,720 +بالضروري عشان تكون statement أنا بتعرف إن أنا صح + +98 +00:07:05,720 --> 00:07:07,700 +ولا خطأ؟ مش بالضروري، قد تكون ماعنديش أنا + +99 +00:07:07,700 --> 00:07:10,580 +المعلومات إني أحكم، لكن هي أي واحد، أنتوا + +100 +00:07:10,580 --> 00:07:13,000 +المعلومات الكافية بيقدر يقرر إن أنا صح ولا خطأ، مش + +101 +00:07:13,000 --> 00:07:16,280 +ضروري كل واحد يقدر يقرر إن أنا صحيح ولا خاطئ، لكن + +102 +00:07:16,280 --> 00:07:19,820 +هي بتدينا معلومة، هذه المعلومة يا صح يا خطأ، في + +103 +00:07:19,820 --> 00:07:22,340 +ناس بتقدر تقرر إن أنا صحيح أو في ناس مقدر تقرر إن + +104 +00:07:22,340 --> 00:07:25,440 +أنا صحيح، وفي ناس مقدرش، هذا مش موضوع تاني، لكن هي + +105 +00:07:25,440 --> 00:07:29,980 +بتديني معلومة، بتديني خبر، فهي جملة خبري، واضح؟ أي + +106 +00:07:31,790 --> 00:07:34,310 +أه فطبعا زي ما حكينا أن ال statement في بعض الناس + +107 +00:07:34,310 --> 00:07:36,930 +بيسموها a proposition أو بيستخدموا الصلاح a + +108 +00:07:36,930 --> 00:07:40,270 +proposition خلينا نشوف أمثلة عشان نوضحاش الفرق بين + +109 +00:07:40,270 --> 00:07:42,870 +الجملة الخبرية اللي هو ال statement و اللي هو + +110 +00:07:42,870 --> 00:07:46,830 +الجملة الانشئية اللي يسات statement فطبعا على سبيل + +111 +00:07:46,830 --> 00:07:50,970 +المثال ما يلي كلها عبارة عن statements و ممكن + +112 +00:07:50,970 --> 00:07:53,890 +نناقشهم مع بعض true أو false طبعا مش كلنا ممكن + +113 +00:07:53,890 --> 00:07:56,590 +يعرف لكن بعضنا بيعرف طبعا احنا حاولنا نجيب أمثلة + +114 +00:07:56,590 --> 00:08:01,010 +تكون معروفة و بسيطةفلو قلنا جازا is a palestinian + +115 +00:08:01,010 --> 00:08:05,650 +city فهذا statement لأنه دتنا خبر معلومة جغرافية و + +116 +00:08:05,650 --> 00:08:08,730 +لا لأ؟ أه طبعا كلنا .. احنا فلسطينيون عايشين في + +117 +00:08:08,730 --> 00:08:11,870 +غزة بنعرف إنها true أه طبعا أي واحد عنده معلومة + +118 +00:08:11,870 --> 00:08:14,930 +جغرافية بيعرف طب واحد في أمريكا ما .. ماعرفش مش + +119 +00:08:14,930 --> 00:08:17,230 +ضروري لكن هذا statement فهي statement عندنا و + +120 +00:08:17,230 --> 00:08:19,250 +statement في مكان ما فهذا statement لأنه دتنا + +121 +00:08:19,250 --> 00:08:21,390 +معلومة ممكن تكون صحية ممكن تكون خاطرة و احنا + +122 +00:08:21,390 --> 00:08:24,270 +عارفين إنها true لأنه عندنا المعلومات واضح؟ فهذا + +123 +00:08:24,270 --> 00:08:30,010 +مثال على statementأتنين ناقص واحد بتساوي تلاتة two + +124 +00:08:30,010 --> 00:08:33,570 +minus one equals three statement لكن اتبنى معلومة + +125 +00:08:33,570 --> 00:08:36,930 +خاطئة مش حاضية لكنها statement اه فانا statement + +126 +00:08:36,930 --> 00:08:39,430 +true or false ايش تاني لانهم تديني خبر تديني + +127 +00:08:39,430 --> 00:08:44,580 +معلومة واضح اه فدي ايش statement مثال اخرEquation + +128 +00:08:44,580 --> 00:08:49,900 +X³ plus 1 equals 0 has two real solutions هذا برضه + +129 +00:08:49,900 --> 00:08:52,960 +statement لكنها false ماشي هذه معلومة أخرى لكنها + +130 +00:08:52,960 --> 00:08:55,220 +statement لأنه دتني معلومة هذه المعادلة اللي + +131 +00:08:55,220 --> 00:08:58,660 +أحللها حقيقيا يتوقعوا الـ False، False مع أننا + +132 +00:08:58,660 --> 00:09:01,080 +معلومات طبعا احنا بنعرف ممكن واحد في ابتدائي + +133 +00:09:01,080 --> 00:09:03,180 +مايعرفش او في اعدادي لكن احنا عامة بنلاقي معلومات + +134 +00:09:03,180 --> 00:09:05,560 +لكن هذا لما .. بالنسبة لأبن الاعدادي وابتدائي هذا + +135 +00:09:05,560 --> 00:09:06,720 +statement ولا statement؟ مش ال statement .. + +136 +00:09:06,720 --> 00:09:10,420 +statementواضح؟ فأرجو أن نتميز بين إنه هي statement + +137 +00:09:10,420 --> 00:09:13,560 +وإنها true أو false وإحنا نقدر أو نقدرش هذا + +138 +00:09:13,560 --> 00:09:18,560 +الموضوع آخر إنه نعرف إنه true أو false برضه كمان + +139 +00:09:18,560 --> 00:09:21,700 +مثال AUG Islamic University of Gaza is a + +140 +00:09:21,700 --> 00:09:25,180 +palestinian university برضه statement طبعا إحنا + +141 +00:09:25,180 --> 00:09:27,480 +بنعرف يمكن لو واحد في مصر مايعرفش ولا واحد في + +142 +00:09:27,480 --> 00:09:29,900 +الصين مايعرفش لكن مش ضروري فهي statement برضه + +143 +00:09:29,900 --> 00:09:33,680 +أدتنا معلومة أدتنا معلومة قابلة للصحة أو الخطأ فدي + +144 +00:09:33,680 --> 00:09:37,260 +أمثلة على ال statement زي هيك تدينا معلومةنشوف + +145 +00:09:37,260 --> 00:09:39,740 +أمثلة غير هيك طب إيش الممكن ما تكونش statement + +146 +00:09:39,740 --> 00:09:42,860 +يعني أنت أمثلة متعددة كلها statement إيش كل الجملة + +147 +00:09:42,860 --> 00:09:46,420 +statement لأ نشوف أمثلة مختلفة فالتالي ليست + +148 +00:09:46,420 --> 00:09:51,160 +statements نشوف ليش how are youسؤال true ولا + +149 +00:09:51,160 --> 00:09:54,800 +false؟ لأ سؤال فهي ده مش statement هد هيش سؤال + +150 +00:09:54,800 --> 00:09:59,620 +جملة إنشائية نقسمها Gaza is a beautiful city غزة + +151 +00:09:59,620 --> 00:10:04,100 +مدينة جميلة هد إيه؟ وجهة نظر هد وجهة نظر إلها + +152 +00:10:04,100 --> 00:10:08,400 +مليون جواب جميلة شوية جميلة كتير أجمل مدينة في + +153 +00:10:08,400 --> 00:10:11,810 +العالم أبشع مدينة في العالم وجهة نظرفهذه ليست + +154 +00:10:11,810 --> 00:10:16,770 +statement واضح فهذه رأي وجهة نظر the sky is rich + +155 +00:10:16,770 --> 00:10:20,050 +نفس الشيء السماء غنية برضه هذه وجهة نظر ممكن تشاعر + +156 +00:10:20,050 --> 00:10:23,150 +تشوفها جميلة و تشاعر ما تشوفهاش جميلة غنية هذا مش + +157 +00:10:23,150 --> 00:10:27,790 +أيش موضوع برضه وجهة نظر أربعة زائد واحد four plus + +158 +00:10:27,790 --> 00:10:32,400 +oneهذه ولا ولا ايش مالاش معنى صحيح اه الحقيقة انه + +159 +00:10:32,400 --> 00:10:35,640 +هنا ايه انا جايب هذا المثال لأنه بنقع كتير في طلبة + +160 +00:10:35,640 --> 00:10:39,500 +بهذا الخطأ بكتب كلام ناقص اه فلازم نتأكد انه عندك + +161 +00:10:39,500 --> 00:10:42,660 +في statement كاملة و تحتمل الصح ولا الخطأ فمافي + +162 +00:10:42,660 --> 00:10:46,090 +عشان استخدم كلام اربع زايد واحد ايش يعنيفبدأ اكتب + +163 +00:10:46,090 --> 00:10:50,310 +كلام له معنى كلام له معنى و انه يديني معلومة صحيحة + +164 +00:10:50,310 --> 00:10:52,790 +او خاطئة طبعا لازم انا بدي اكتب معلومة صحيحة زي ان + +165 +00:10:52,790 --> 00:10:55,670 +انا بدي اكتب برهانة و واضح فلازم احنا نتأكد انه + +166 +00:10:55,670 --> 00:11:00,610 +نحكم على الكلام انه كلام كامل statement و هكذا I + +167 +00:11:00,610 --> 00:11:04,740 +will come to school next weekممكن ما يجيش يعني + +168 +00:11:04,740 --> 00:11:09,220 +ممكن تدنيش معلومة مثلا من شاي اه اه ممكن تدنيش + +169 +00:11:09,220 --> 00:11:15,220 +اعرفنا من حي و من مامي طلعنا فدنيش معلومة تدنيش + +170 +00:11:15,220 --> 00:11:18,240 +معلومة فدي برضه not statement would you visit us + +171 +00:11:18,240 --> 00:11:22,480 +tomorrow ممكن تتفضل تزورنا بكرا طلب او سؤال طلب + +172 +00:11:22,480 --> 00:11:26,980 +فبرضه not statement فبشكل عام يا أخواتcomments + +173 +00:11:26,980 --> 00:11:31,940 +التعليقات الأسئلة الوجهات النظر opinions كل هذه + +174 +00:11:31,940 --> 00:11:35,180 +ليست statement واضح؟ اه فطبعا فقدنا بعض الأمثلة + +175 +00:11:35,180 --> 00:11:38,420 +وحتى الأخرى فبشكل عام اللي فيها وجهة نظر فيها + +176 +00:11:38,420 --> 00:11:42,680 +تعليق فيها سؤال لا تعتبر جملة أو تقرير اللي هو + +177 +00:11:42,680 --> 00:11:49,130 +statement أي سؤالنقطة تانية، هذه هي نقطة البداية + +178 +00:11:49,130 --> 00:11:52,170 +تبعاتنا، هذه اللي هي اللبنة الرئيسية، اللتنا اللي + +179 +00:11:52,170 --> 00:11:55,910 +مستخدمها في المنطق ما يعرف بيه التقرير أو اللي هو + +180 +00:11:55,910 --> 00:11:59,910 +ال statement اللي هنتقل، compound statement، طبعا + +181 +00:11:59,910 --> 00:12:04,430 +زي كل موضوع من الموضوعات، نبدأ احنا بحجر الأساس، + +182 +00:12:04,430 --> 00:12:06,950 +الأمور البسيطة، المركبات الأساسية، الجزيئات، و + +183 +00:12:06,950 --> 00:12:10,330 +بعدين نبدأ نبني و نعنى في البنيان واحدة واحدة، فمن + +184 +00:12:10,330 --> 00:12:13,050 +هنا نمشي الجمال مش كلها بسيطة زي الأمثلة اللي + +185 +00:12:13,050 --> 00:12:16,400 +شفناهافالأمثلة في المثال الأول كل الأمثلة اللي هو + +186 +00:12:16,400 --> 00:12:18,820 +أربعة أو خمسة كلها تعتبر بسميها simple statement + +187 +00:12:18,820 --> 00:12:23,360 +لأنه دا كان معلومة واحدة بشكل عام مظبوط ففيه طبعا + +188 +00:12:23,360 --> 00:12:26,440 +احنا في الحياة نضطر نستخدم أكتر من معلومة مع بعض + +189 +00:12:26,440 --> 00:12:30,180 +ونربطهم بطريقة معينة بميز كل statement لو رجعتوا + +190 +00:12:30,180 --> 00:12:33,440 +على الأمثلة قدامكم بتلاقوا كلها statement واحدة + +191 +00:12:33,440 --> 00:12:36,690 +مافيها ولا أداة من أدوات الرابطما هي أدوات الرابط؟ + +192 +00:12:36,690 --> 00:12:39,730 +هنشوفهم، فيه خمس أدوات رابط منطقية هنشوفها، فاحنا + +193 +00:12:39,730 --> 00:12:43,670 +هنعرف أن الجملة، فهنا بقول، فكل statement في مثال + +194 +00:12:43,670 --> 00:12:46,830 +واحد are simple statements، إيش السبب؟ إنها + +195 +00:12:46,830 --> 00:12:49,390 +مابتحتويش على أداة من أداة الرابط، فهذا هو + +196 +00:12:49,390 --> 00:12:52,110 +المعيارة، يا أخي و هتنتبه إنه مش بتتكون من جزئين + +197 +00:12:52,110 --> 00:12:55,020 +أو من two statements، المعيار الأساسي وحتوىعلى + +198 +00:12:55,020 --> 00:12:58,700 +أداة رابط أو عدم احتواء على أداة رابط فما هي أداة + +199 +00:12:58,700 --> 00:13:01,820 +رابط هنشوفه مع بقى فإذا هذا هو المعيار اه فبقوللي + +200 +00:13:01,820 --> 00:13:06,880 +الـ Compound ماهي جملة مركبة أي جملة أي تقرير جملة + +201 +00:13:06,880 --> 00:13:10,720 +خبرية تحتوي على أداة من أدوات ال .. ال .. ال .. ال + +202 +00:13:10,720 --> 00:13:10,980 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +203 +00:13:10,980 --> 00:13:11,300 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +204 +00:13:11,300 --> 00:13:11,340 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +205 +00:13:11,340 --> 00:13:11,480 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +206 +00:13:11,480 --> 00:13:11,520 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +207 +00:13:11,520 --> 00:13:11,600 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +208 +00:13:11,600 --> 00:13:15,380 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +209 +00:13:15,380 --> 00:13:20,680 +ال + +210 +00:13:20,680 --> 00:13:28,860 +.. الأو أكثر نشوف أمثلة فطبعا هي فيها ان احنا + +211 +00:13:28,860 --> 00:13:31,220 +الأمثلة في المثال الأول كان ايه simple statement + +212 +00:13:31,220 --> 00:13:36,110 +نشوف كيف ممكن تكون compound statementالجملة كوك + +213 +00:13:36,110 --> 00:13:38,030 +جابليكي استخدمنا جزء منها Gaza is a Palestinian + +214 +00:13:38,030 --> 00:13:41,550 +city هاي ال statement لحالها and وهي بول جدامكوا + +215 +00:13:41,550 --> 00:13:44,130 +هذا هي رابط بيسموها هاي أحد الروابط الخامسة and + +216 +00:13:44,130 --> 00:13:47,770 +بلستان is an Arabic country فهذه إيش؟ في two + +217 +00:13:47,770 --> 00:13:51,770 +statements وفي بينهم رابط and فكل statement مع بعض + +218 +00:13:51,770 --> 00:13:54,090 +هذه الجملة اللي جدامنا بيسميها compound statement + +219 +00:13:54,090 --> 00:13:57,170 +لأنه في رابط and مش عشان الجثين الأهم إن فيها + +220 +00:13:57,170 --> 00:14:00,410 +الرابط and فده أول رابط من روابط الخمسة فهذه دي + +221 +00:14:00,410 --> 00:14:02,850 +مثال على ال compound statement لو رجعته للخمسة + +222 +00:14:02,850 --> 00:14:06,150 +مافيش أول واحد فيها andبصبوط؟ ارجع للأمثلة قدامك + +223 +00:14:06,150 --> 00:14:11,130 +المثال التاني اتنين two minus one equals three هاي + +224 +00:14:11,130 --> 00:14:15,390 +statement لحالها or أيها هاي رابط ال seven is + +225 +00:14:15,390 --> 00:14:18,690 +divisible by two السبعة تقبل قسمها اتنين هاي فيهاش + +226 +00:14:18,690 --> 00:14:21,550 +or هاي الشاهد طبعا هاي ال statement بالنسبة للأولى + +227 +00:14:21,550 --> 00:14:24,310 +ال statement للأولى true ولا false true طيب + +228 +00:14:24,310 --> 00:14:27,780 +التانيةالثانية equals to E or seven is equal to + +229 +00:14:27,780 --> 00:14:31,040 +four خالص بس هناخد كيف نحكم عليهم واحدة واحدة نأجل + +230 +00:14:31,040 --> 00:14:34,660 +هذا الكلام شوية بس هذه عايش الشهاد هنا احتواه على + +231 +00:14:34,660 --> 00:14:40,450 +R خلّيها compound هي رابط من الروابط الخامسfalse + +232 +00:14:40,450 --> 00:14:43,110 +or false false هناخدها بس أنا أجلت المعنى شوية لإن + +233 +00:14:43,110 --> 00:14:47,690 +ما أخدناش القاعدة شوية طيب هنا كمان مثال if five + +234 +00:14:47,690 --> 00:14:51,790 +is an integer then five is a real number هي هذه + +235 +00:14:51,790 --> 00:14:54,670 +تعتبر compound statement فيها رابط ما هو if then + +236 +00:14:54,670 --> 00:14:57,370 +اللي هي الجملة الشرطية أو الشرطية فهذه الرابط + +237 +00:14:57,370 --> 00:15:01,380 +التالت ففيها أنو R و if then هي تلت رابط فأي + +238 +00:15:01,380 --> 00:15:04,160 +statement تحتوي على رابط من رابط الخمسة هي أي تلت + +239 +00:15:04,160 --> 00:15:06,340 +أمثلة و هنشوف المثالين التانية تتعمل compound + +240 +00:15:06,340 --> 00:15:08,620 +statement هذي compound statement ليش compound + +241 +00:15:08,620 --> 00:15:12,790 +statement لأنها تحتوي على رابط if thenالمثال + +242 +00:15:12,790 --> 00:15:18,350 +الرابع two divides six if and only if two times + +243 +00:15:18,350 --> 00:15:23,670 +three equals six فهي الرابط الرابع فهي الـ + +244 +00:15:23,670 --> 00:15:26,290 +compound statement هذه تحتوى على الرابط if and + +245 +00:15:26,290 --> 00:15:29,870 +only if فقط و إيه ده فقط تمام؟ مرة عليكم كتير + +246 +00:15:29,870 --> 00:15:37,110 +رياضية طبعا؟ مثال أخر by is not a rational number + +247 +00:15:37,760 --> 00:15:40,320 +أه فهنا برضه الـ compound similar تحتوي على رابط + +248 +00:15:40,320 --> 00:15:45,080 +not not تعتبر برضه رابط فدول الرابط الخامسة and or + +249 +00:15:45,080 --> 00:15:49,860 +if then if and only if و not أه لو لاحظنا أيش + +250 +00:15:49,860 --> 00:15:52,520 +الفرق بين الأمثلة الأربعة الأولى و الأمثلة ايه و + +251 +00:15:52,520 --> 00:15:54,600 +الأمثلة الأخيرة بلاجئ أن الأمثلة الأربعة أولها + +252 +00:15:54,600 --> 00:15:57,180 +كانت تدينا معلومتين و مربوطين فيها تا لكن الأخيرة + +253 +00:15:57,180 --> 00:16:00,080 +أيش ما لها معلومة واحدة لكن رغم ذلك سميتها + +254 +00:16:00,080 --> 00:16:03,240 +compound الملاحظة اللي قلت ليهاش لأنه أيش تحتوي + +255 +00:16:03,240 --> 00:16:05,920 +على رابط فهي هي المعيارفي رابط أو مافيش رابط من + +256 +00:16:05,920 --> 00:16:09,500 +رابط الخمسة هم هدولة هنرسلهم بالتصيل و هنأكد عليهم + +257 +00:16:09,500 --> 00:16:12,980 +فأي statement طبعا ال statement يعني بتكون جملة + +258 +00:16:12,980 --> 00:16:16,620 +خبرية بحتمال واحدة طول أو فوس تحتوي على رابط فهي + +259 +00:16:16,620 --> 00:16:19,820 +كمبالي مافيش فيها ولا رابط نسميها simple أي سؤال + +260 +00:16:19,820 --> 00:16:27,180 +واضح تمام جبل ما نستمر خلينا نتفق على بعض اللي هو + +261 +00:16:27,180 --> 00:16:30,940 +قواعد نستخدمها و أداة مهمة في الرياضيات وهي + +262 +00:16:30,940 --> 00:16:34,720 +استخدام الرمزأه طبعا هم تعرفوا أنه احنا بنكثر من + +263 +00:16:34,720 --> 00:16:37,720 +استخدام الرموز لأنها بتوفر علينا جهد ووقت وهي + +264 +00:16:37,720 --> 00:16:40,920 +طريقة متعرف عليها زي لغة الرياضيات الرموز ولا لأ + +265 +00:16:40,920 --> 00:16:46,360 +والناس بتتفهم فيها ومعروفة وسهلة جدا بشكل عام لا + +266 +00:16:46,360 --> 00:16:51,080 +يوجد رمز خاطئ ورمز صحيح أي رمز بنستخدمه هو رمز + +267 +00:16:51,080 --> 00:16:55,900 +صحيح لكن هناك رمز أفضل من رمز هناك رمز بيدينا + +268 +00:16:55,900 --> 00:17:00,820 +أريحية وبيدينا بالتعامل أفضل من رموز ليش؟ ع سبيل + +269 +00:17:00,820 --> 00:17:04,760 +المثاللو احنا فيه عندنا في الكمبيوتر بدنا نحفظ ملف + +270 +00:17:04,760 --> 00:17:08,280 +ما لو جينا نسميه في عمليات رامزكاية تسمية ممكن + +271 +00:17:08,280 --> 00:17:12,400 +نسميه اسم عشوائي ايه ألف باه لو سميناه بهذا الشكل + +272 +00:17:12,400 --> 00:17:14,980 +طبعا الإنسان من طبيعته النسيان بعد أسبوع بعد شهر + +273 +00:17:14,980 --> 00:17:17,760 +هننسى دقيقة الملف اللي فيه عشان أعرف المحتوى بضطر + +274 +00:17:17,760 --> 00:17:21,060 +أفتحه و أعرف اللي فيهلأ، فهذا أنا سميته والكمبيوتر + +275 +00:17:21,060 --> 00:17:24,020 +قبل، هي اسم مقبول، لأنه مش خطأ، لكن لو أنا سميته + +276 +00:17:24,020 --> 00:17:26,560 +مثلا أنا بتدحفظ الملفات اللي بتتعلق بمصراح مبادئ + +277 +00:17:26,560 --> 00:17:29,800 +الرياضيات، سميته هذا مجلة مبادئ الرياضيات، أول من + +278 +00:17:29,800 --> 00:17:31,900 +العنوان بعرف أنه هذا أيش الملف، أيش اللي فيه، + +279 +00:17:31,900 --> 00:17:35,400 +فدايمًا اختيار الاسم، صحيح أنه كل أسماء صحيح، أو + +280 +00:17:35,400 --> 00:17:37,920 +الكمبيوتر بيقبل هذا وبيقبل هذا، و الرموز الرياضيات + +281 +00:17:37,920 --> 00:17:41,080 +برضه بتقبل هذا وذا، لكن في رموز أفضل من رموز، + +282 +00:17:41,080 --> 00:17:44,330 +بتساعدنا على الفهمفاختيار الرمز المناسب في + +283 +00:17:44,330 --> 00:17:48,510 +الرياضيات وده شيء من أساس تحصصنا بساعد كتير على + +284 +00:17:48,510 --> 00:17:51,470 +التعامل بدينا أريحية أحيانا طبعا احنا أي رمز بدنا + +285 +00:17:51,470 --> 00:17:54,150 +نستخدمه لازم نقوله هذا الرمز بيبقى نمزج لحاجة بيه + +286 +00:17:54,150 --> 00:17:57,330 +هو عبارة عن عدد عبارة عن statement زي ما شوفنا + +287 +00:17:57,330 --> 00:18:00,530 +عبارة عن مجموعة فبنعرفه لكن أحيانا من كتور ما احنا + +288 +00:18:00,530 --> 00:18:03,270 +متعودين أول ما نشوف رمز بنعرف أعيش بدوللأنه متعارف + +289 +00:18:03,270 --> 00:18:06,770 +عليه طبعاً في اختلافات لكن بشكل عام في عروف سائد + +290 +00:18:06,770 --> 00:18:09,990 +في الرياضيات منتشر جداً معظم الناس بتستخدمها أول + +291 +00:18:09,990 --> 00:18:12,770 +ما أشوف الرمز بعرف إنه برمز لإيه مثلا X في + +292 +00:18:12,770 --> 00:18:15,150 +الcalculus بعرف إنه real number لكن لما أشوف N + +293 +00:18:15,150 --> 00:18:18,670 +بتوقع أنها عدد صحيح و لا لأ في الغالب هيك فأي أمور + +294 +00:18:18,670 --> 00:18:21,690 +.. إختيار الرمز المناسب بيساعدنا كتير و بيسهل عليه + +295 +00:18:21,690 --> 00:18:24,570 +أه طبعاً فأحنا أول شيء بنا نبدأ أول رموز هنستخدمهم + +296 +00:18:24,570 --> 00:18:27,790 +في هذا المساق احنا إيش الوحدة تبعتنا statement + +297 +00:18:28,060 --> 00:18:31,640 +اليوم للتقريبين وفي عندنا نوعين compound واش و + +298 +00:18:31,640 --> 00:18:34,460 +simple فهنستخدم الرموز طبعا من كلمة proposition + +299 +00:18:34,460 --> 00:18:39,140 +هنبدأ بالحرف بي للرقم زي الأول فبتسميتنا نقول بدنا + +300 +00:18:39,140 --> 00:18:41,940 +نميز بين simple في الغالب هنديها small طبعا قلت + +301 +00:18:41,940 --> 00:18:44,140 +فيش قاعدة ولكن في الغالب لأنه بيساعدنا و ال + +302 +00:18:44,140 --> 00:18:47,060 +compound جيد نديها capital ولا لأ لأنه بدللما تكون + +303 +00:18:47,060 --> 00:18:49,300 +capital letter بتقول إنها كبيرة ولا لأ و small + +304 +00:18:49,300 --> 00:18:52,420 +letter إنها اسمبل طب لو استخدمتها بشكل مختلف صح مش + +305 +00:18:52,420 --> 00:18:56,580 +غلط أه لكن لما بختار بهذا الشكل أيش بيساعدني أه + +306 +00:18:56,580 --> 00:18:59,020 +فاحنا بشكل عام هنستخدم هذه القواعد لإنه بيستعلمنا + +307 +00:18:59,020 --> 00:19:04,240 +نستخدم الرموز بشكل جيد و بشكل مفيد أكتر من غير أي + +308 +00:19:04,240 --> 00:19:09,430 +سؤال؟ في أي استفسار؟أمور مدخلة إن شاء الله سهل + +309 +00:19:09,430 --> 00:19:13,110 +وسلسل الحمد لله نبدأ الآن زي ما هو في العنوان احنا + +310 +00:19:13,110 --> 00:19:16,550 +قلنا الـ statements وعرفنا إيش معنى ال statements + +311 +00:19:16,550 --> 00:19:19,710 +ونوعينهم ووجدت إيش وكان العنوان their connectives + +312 +00:19:19,710 --> 00:19:22,910 +الروابط فنتحدث عن الروابط وزي ما ذكرنا قبل قليل + +313 +00:19:22,910 --> 00:19:25,690 +فيه خمس روابط أساسية fundamental connectives + +314 +00:19:25,690 --> 00:19:29,110 +الروابط الرئيسية اللي هم ماياش خمس اللي هم خمس + +315 +00:19:29,110 --> 00:19:32,100 +فهنبدأ ندرسهم بالتفصيل على عدة مراحلفطبعا ال + +316 +00:19:32,100 --> 00:19:35,100 +fundamental connectives اللي هو الروابط المنطقية + +317 +00:19:35,100 --> 00:19:40,220 +الأساسية خمسة نبدأ بالنفي اللي هو not فيه طبعا زي + +318 +00:19:40,220 --> 00:19:43,360 +ما احنا قلنا مغرمين بالرموز فإيش هنرمزها بيها ده + +319 +00:19:43,360 --> 00:19:47,620 +الرمز كيف يقرأ not اللي هو زي عاملة عايش عاملة + +320 +00:19:47,620 --> 00:19:51,460 +اللي هو المد بس كبيرة شوية فهذا هو رمز النفي أو + +321 +00:19:51,460 --> 00:19:54,760 +not فيقرأ not لما نجيه statement محتوى جبلها يدش + +322 +00:19:54,760 --> 00:19:58,420 +نقول not كذا هنجيه بالتفصيل فهذا أول شيء هذا أول + +323 +00:19:58,420 --> 00:20:01,300 +رابطبنحددهم اللي احنا قلنا هم خمسة في الأمثلة لكن + +324 +00:20:01,300 --> 00:20:04,580 +الان بنحط القاعدة بشكل عام ان هم خمس رابط محددين + +325 +00:20:04,580 --> 00:20:07,960 +وهي الرابط الأول وهذا الرمز تبعه الرابط التاني زي + +326 +00:20:07,960 --> 00:20:11,180 +ما مر علينا أنت و هنستخدم معه الرمز هذا الرمز + +327 +00:20:11,180 --> 00:20:15,920 +الأمام كله هي V مجلوبة أو تمانية بالرموز الهندية + +328 +00:20:15,920 --> 00:20:21,740 +فهذا اللي هو الان وهذا الرمز تبعه الرابط التالت + +329 +00:20:21,740 --> 00:20:26,820 +الار و هنرمزه بالرمز V أو سبعة بالأرقام الهندية + +330 +00:20:28,290 --> 00:20:33,570 +الرابط الرابع if then هو رمز يتجه إلى اليمين سهم + +331 +00:20:33,570 --> 00:20:37,270 +إلى اليمين سهم إلى اليمين الرموز يجب أن نستخدمه + +332 +00:20:37,270 --> 00:20:40,850 +على الأقل في هذا المساق كل رمز يجب أن نستخدمه + +333 +00:20:40,850 --> 00:20:43,910 +بدلالته الرموز مهم جدا يا أخوات لا يمكنني أن + +334 +00:20:43,910 --> 00:20:47,850 +أستخدم أي رمز ماكان رمز لأنه إذا قرأ أي واحد يفهم + +335 +00:20:47,850 --> 00:20:51,250 +بشكل مختلف يجب أن أكتب لنفسي و أكتب للآخرين بشكل + +336 +00:20:51,250 --> 00:20:54,970 +عامو كطالب بقى حاجة للمدرسة و دي صح من ورايا فلازم + +337 +00:20:54,970 --> 00:20:58,150 +ان ايش نستخدم القواعد المتفق عليها و كل رمز له + +338 +00:20:58,150 --> 00:21:01,590 +أهميته أستخدمه في المكان و إيش و الزمن الصحيح فمهم + +339 +00:21:01,590 --> 00:21:04,370 +جدا طب فمافعش تقول ساهم لليمين و ساهم للشمال مكل + +340 +00:21:04,370 --> 00:21:07,650 +واحد مكل الأسهم لأ ساهم إلى اليمين لازم بدا الشكل + +341 +00:21:07,650 --> 00:21:11,170 +الرابط الخامس و الأخير if and only if و بنعمله إيش + +342 +00:21:11,170 --> 00:21:15,190 +ساهم في اتجاهين آه يمين و يساهم فهذا بيسموه if and + +343 +00:21:15,190 --> 00:21:19,220 +only ifأي سؤال فهؤلاء اللي هم الروابط الخامسة زي + +344 +00:21:19,220 --> 00:21:21,360 +ما حكينا فهؤلاء اللي هم الروابط اللي هنستخدمهم + +345 +00:21:21,360 --> 00:21:26,640 +وهذه هي الرموز تبعتهاجانب ما نبدأ ندرسهم في + +346 +00:21:26,640 --> 00:21:30,000 +التفصيل و ندرس مثلًا مثلًا في الأمثلة لو قلت لنا + +347 +00:21:30,000 --> 00:21:32,860 +لأ نهجل نحكم على ال statement ال compound true أو + +348 +00:21:32,860 --> 00:21:38,120 +false نشوف القواعد اللي بتكيف بنحكم على compound + +349 +00:21:38,120 --> 00:21:41,180 +statement true or false إذا عرفنا معلومات عن + +350 +00:21:41,180 --> 00:21:45,020 +مركباتها true أو false فبنمر على حاجة مهمة + +351 +00:21:45,020 --> 00:21:49,580 +بتساعدنا في هذا الحكم وهي truth table أو جداول + +352 +00:21:49,580 --> 00:21:54,400 +الصدق جداول الصدقزي ما اتفقنا الـ statement هي + +353 +00:21:54,400 --> 00:21:57,560 +عبارة عن جملة خبرية تحتمل احتمال واحد من اتنين يا + +354 +00:21:57,560 --> 00:22:00,360 +force يا true هذه القيمة لما بيقولها ال statement + +355 +00:22:00,360 --> 00:22:04,220 +true بيسموها قيمة الصدق لل statement بيسموها truth + +356 +00:22:04,220 --> 00:22:09,260 +value قيمة الصدق اذا احنا مهتمين ان ال statement + +357 +00:22:09,260 --> 00:22:12,040 +هذه في كثير من الحياة ان نحكم عليها true او force + +358 +00:22:12,040 --> 00:22:16,080 +يعني مهتمين ان نحدد قيمة الصدق تبعتها فما هي ال + +359 +00:22:16,080 --> 00:22:18,780 +truth table ال truth table هي عبارة عن جداول + +360 +00:22:18,780 --> 00:22:23,520 +رياضية او جداول منطقيةبنستخدمها كأداة بتساعدنا في + +361 +00:22:23,520 --> 00:22:29,710 +تحديد قيمة الصدق لل statement بشكل عامطبعا لو أنا + +362 +00:22:29,710 --> 00:22:32,590 +في عندي statement بسيطة و هي true or false بحتاج + +363 +00:22:32,590 --> 00:22:35,250 +جد ولا لأ مش بالضروري لكن احنا محتاجينها بشكل عام + +364 +00:22:35,250 --> 00:22:37,650 +على compound statement طبعا لو هي compound + +365 +00:22:37,650 --> 00:22:39,970 +statement زي الأمثل السابق اما انا بحلل و بقول + +366 +00:22:39,970 --> 00:22:44,250 +true or false لأ بشكل عام يا أخوات احنا مهتمين ان + +367 +00:22:44,250 --> 00:22:48,250 +نحط قواعد فاحنا مثلا انه على سبيل المثال compound + +368 +00:22:48,250 --> 00:22:52,070 +statement قولنا اي statement اتفقنا بنرمز بي مظبوط + +369 +00:22:52,070 --> 00:22:56,940 +و كمان statement Qو P and Q مرموظة بالرادر رامز + +370 +00:22:56,940 --> 00:23:01,120 +مظبوط فاحنا هنشوف أنه في قاعدة زي ما حكينا لو أنا + +371 +00:23:01,120 --> 00:23:03,660 +بدأ أحكم على ال compound statement اللي بتتكون من + +372 +00:23:03,660 --> 00:23:07,120 +two statements و بينهم N إنها true or false بشكل + +373 +00:23:07,120 --> 00:23:11,260 +قاعدة عشان أنا بدأ أشوف قاعدة التفكير اللي هو + +374 +00:23:11,260 --> 00:23:14,680 +الاستدلالي بدأ أقول قاعدة بدأ أروح أحللفإذا + +375 +00:23:14,680 --> 00:23:17,400 +التنتين true إيش بيكون الناتج؟ إذا التنتين false + +376 +00:23:17,400 --> 00:23:20,120 +إيش بيكون الناتج؟ الأولى true والتانية false أو + +377 +00:23:20,120 --> 00:23:22,520 +false و true إيش بيكون الناتج؟ فإذا أنا بدي أندي + +378 +00:23:22,520 --> 00:23:25,020 +احتمالات كلها عشان أحط القاعدة و أشوف الأمثلة و + +379 +00:23:25,020 --> 00:23:28,840 +أبدأ أطبق عليها فإحنا بحتاج نحط قواعد لذلك كيف بدي + +380 +00:23:28,840 --> 00:23:31,560 +أحط القواعد؟ بحتاج إن أنا أدرس جميع الاحتمالات و + +381 +00:23:31,560 --> 00:23:34,140 +أشوف الناتج تبحة كلها فبحتاج إلى ما يُعرف جداول + +382 +00:23:34,140 --> 00:23:38,220 +الصفر فالجداول هتساعدنا إن نحط القاعدة بهذه الصورة + +383 +00:23:38,220 --> 00:23:41,200 +و ندرس فيها جميع الاحتمالات المنطقية الممكنة + +384 +00:23:41,200 --> 00:23:46,330 +لمركبات أي compoundواضح؟ فهذه ما يُعرف بيداول + +385 +00:23:46,330 --> 00:23:51,090 +الصدر طبعاً زي ما احنا قلنا مولعين بالاختصار بدل + +386 +00:23:51,090 --> 00:23:53,750 +تروح نحط capital T و بدل force طبعا ممكن نستخدم + +387 +00:23:53,750 --> 00:24:00,410 +هذه أو هذه و Capital AF بدل force أي سؤالفالآن + +388 +00:24:00,410 --> 00:24:04,530 +هنبدأ بدراسة تفصيلية للروابط وقواعد كيف نتعامل + +389 +00:24:04,530 --> 00:24:10,470 +معها هنبدأ بالأبسط وهي النفي أو بالترتيب اللي احنا + +390 +00:24:10,470 --> 00:24:15,950 +متفق عليه فأول رابط بيسموه negation النفي نيجيشن + +391 +00:24:15,950 --> 00:24:19,830 +اسمه اللي هو رابط النفي أو اللي هو the negation + +392 +00:24:20,630 --> 00:24:23,570 +طبعاً إيه هو رمز؟ فهو the connective اللي هو هذا + +393 +00:24:23,570 --> 00:24:26,890 +الرمز اللي إحنا إيش نقراه؟ not إيش بيسموه؟ إيش + +394 +00:24:26,890 --> 00:24:29,730 +إسمه؟ طبعاً في إحنا أي شيء بنحطه تعريف فيه مصطلح + +395 +00:24:29,730 --> 00:24:33,130 +وفيه قواعد وكيف أستخدمه في عملية الجامعة طب إيش هي + +396 +00:24:33,130 --> 00:24:35,630 +الجامعة؟ إيش هي عملية؟ إيش هي عملية؟ إيش هي عملية؟ + +397 +00:24:35,630 --> 00:24:38,350 +وإيها اسم؟ وفي إيها رمز؟ زي في عملية الجامعة إيش + +398 +00:24:38,350 --> 00:24:41,870 +رمزها؟ ال cross هذا plus مظبوط؟ وإيش قواعدها؟ + +399 +00:24:41,870 --> 00:24:44,330 +فإحنا نفس القضية ماشيين واضح فإحنا فيه أن أول إيش + +400 +00:24:44,330 --> 00:24:45,010 +الرابط هو رابط + +401 +00:24:50,460 --> 00:24:52,960 +بدي اعمل منها compound باستخدام هذا الرابط وان + +402 +00:24:52,960 --> 00:24:58,420 +بحطها جبلفبقول إيش مالها ماب ليس ممكن تيزي وتنحط + +403 +00:24:58,420 --> 00:25:01,380 +أمام أي statement أنا عندي أي statement بدي أعمل + +404 +00:25:01,380 --> 00:25:04,440 +منها نفي بتنفيها بحط هذا الربط جدامها فصارت عندي + +405 +00:25:04,440 --> 00:25:07,320 +compound statement compound statement كيف بنقرعها + +406 +00:25:07,320 --> 00:25:11,380 +هذه not be أو the negation of be قراعتين التنتين + +407 +00:25:11,380 --> 00:25:14,920 +صح اللي بتقولها فإحنا بنقرعها not be أو the + +408 +00:25:14,920 --> 00:25:18,800 +negation of be فإذا هذه إيش بنعمل جملة compound من + +409 +00:25:18,800 --> 00:25:22,620 +جملة بسيطة باستخدام الربط اللي هو النفي اللي هو + +410 +00:25:22,620 --> 00:25:27,560 +not ال negationطيب هاي عرفنا اسم الرابط و رمزه + +411 +00:25:27,560 --> 00:25:30,720 +تمام و كيف نلفظه و كيف نتعرف طيب لو انا كيف + +412 +00:25:30,720 --> 00:25:33,360 +بتتعامل معاه؟ ايش قواعد التعامل معاه؟ لو انا عندي + +413 +00:25:33,360 --> 00:25:36,380 +compound statement و بدي اجيب قيمة الصدق تبعتها + +414 +00:25:36,380 --> 00:25:38,940 +انا عندي معلومات عن ال B كيف اجيب معلومات عن ال + +415 +00:25:38,940 --> 00:25:41,760 +compound not B؟ هاي القاعدة بتقوللي انه ايه ده؟ + +416 +00:25:41,760 --> 00:25:44,680 +النفيش بعمل بعكس قيمة الصدق إذا كانت الجملة + +417 +00:25:44,680 --> 00:25:47,860 +الأصلية true فالنفي تبعها false و إذا كانت false + +418 +00:25:47,860 --> 00:25:51,920 +فالنفي تبعها true فهنا لخصنا هذه القاعدة بيه جدول + +419 +00:25:51,920 --> 00:25:54,360 +الصدق اللي أمامناأي سؤال + +420 +00:25:56,970 --> 00:25:59,370 +فهذه هي السياسة اللي إحنا هتتبعها في دراسة إيش + +421 +00:25:59,370 --> 00:26:02,810 +الروابط الخامسة خلّينا ناخد بعض التطبيقات عشان + +422 +00:26:02,810 --> 00:26:06,350 +القاعدة تتضح وإيش كيف ممكن إحنا نكون نتمكن منها + +423 +00:26:06,350 --> 00:26:09,990 +وإيش الأسئلة اللي ممكن تواجهنا في المساق أو في أي + +424 +00:26:09,990 --> 00:26:14,850 +مكان فالمثال الأول write the negation of each of + +425 +00:26:14,850 --> 00:26:20,010 +the following اكتب نفي لل statements التالية هنشوف + +426 +00:26:20,010 --> 00:26:23,530 +كيف بننفيه لغويا و بالرموز المنطقية هتعلم اتنين + +427 +00:26:23,530 --> 00:26:27,260 +تانية لإن فينا عملية باستخدام اللغة ليس الليفعنا + +428 +00:26:27,260 --> 00:26:31,620 +أول مثال square root of two is a rational number + +429 +00:26:31,620 --> 00:26:34,420 +جزر التربيه على اتنين هو عدد نسبي هذا statement + +430 +00:26:34,420 --> 00:26:37,060 +ولا لأ؟ اه و simple مافيش فيها ولا رابط ولا فيها + +431 +00:26:37,060 --> 00:26:39,560 +رابط مافيش فيها ولا رابط طب إيش رأيكوا هي true ولا + +432 +00:26:39,560 --> 00:26:45,890 +false؟ هي عدد نسبي لجزر التنين؟irrational، يعني + +433 +00:26:45,890 --> 00:26:48,410 +عدد غير نسبة، ده إيش النسبة؟ نحط بص و مقام عدد + +434 +00:26:48,410 --> 00:26:51,290 +صحيح، لكن جزء تاني لا يمكن وضعها على حصورة عدد + +435 +00:26:51,290 --> 00:26:55,610 +كثري بص و مقام لعدد صحيح، فهذه طبعا كيف ننفيها؟ + +436 +00:26:55,610 --> 00:26:58,970 +بكل بساطة، بدنا نستخدم not، بدنا نستخدم not، فإذا + +437 +00:26:58,970 --> 00:27:04,250 +هي هذا المثال الأول وخلينا + +438 +00:27:04,250 --> 00:27:09,770 +نحط اللي هو الحل solution وحل a فإيش الحل؟ بكل + +439 +00:27:09,770 --> 00:27:15,410 +بساطة square root of two is notA rational number + +440 +00:27:19,880 --> 00:27:25,800 +أه فهنا بنميز بين حاجتين الحاجة الأولى في أن + +441 +00:27:25,800 --> 00:27:29,780 +المنطق الرمزي يعني الرموز بنحط انه في وين جاب ال + +442 +00:27:29,780 --> 00:27:33,300 +statement لكن في قواعد اللغة ما بنغيرهاش في قواعد + +443 +00:27:33,300 --> 00:27:36,440 +اللغة بنستخدم قواعد اللغة فاحنا في أن كيف نرمز لل + +444 +00:27:36,440 --> 00:27:39,520 +statement بالمنطق و كيف نتعامل مع الرموز و كيف + +445 +00:27:39,520 --> 00:27:41,580 +نتعامل من ناحية اللغوية و كيف نعكسها فاحنا بنتعلم + +446 +00:27:41,580 --> 00:27:44,980 +هذه الحاجة نحول من الرموز للغة و العكس اه فالنفي + +447 +00:27:44,980 --> 00:27:49,870 +عادي هنا في عادي قواعد اللغةأي سؤال فبكل بساطة هذا + +448 +00:27:49,870 --> 00:27:54,470 +هو الـ nothing حسب قواعد اللغة نشوف كمان مثال الـ + +449 +00:27:54,470 --> 00:28:00,090 +sine function is continuous at x equals 0 فهذا + +450 +00:28:00,090 --> 00:28:03,430 +statement يقول دالة الجهب متصلة عند الـ zero فهذا + +451 +00:28:03,430 --> 00:28:06,270 +statement صحيح من تفاضل ألف طبعا احنا مش هذا هو + +452 +00:28:06,270 --> 00:28:08,630 +هدفنا السؤال الرئيسي لكن هذا still كيف ندعم فيها + +453 +00:28:08,630 --> 00:28:14,930 +بكل بساطة بكل بساطة نفس الشيء فبنقول the sine + +454 +00:28:14,930 --> 00:28:16,270 +function + +455 +00:28:19,290 --> 00:28:29,190 +is not continuous at + +456 +00:28:29,190 --> 00:28:34,310 +x تساوي 0 فبكل بساطة حسب قواعد اللغة هذا المعروف + +457 +00:28:34,310 --> 00:28:37,810 +بالنفيه طب هو واحد يقول ممكن أنفيه أقول the tan + +458 +00:28:37,810 --> 00:28:41,810 +function is not continuous أو continuous؟ لأ، نفس + +459 +00:28:41,810 --> 00:28:44,130 +الجملة بالتانفيه، هذا داخل آيانات، مش بديش أغيرها + +460 +00:28:44,130 --> 00:28:51,210 +من عندك، واضح؟كمان مثال two divides six التنين + +461 +00:28:51,210 --> 00:28:56,150 +بتقسم الستة يعني ستة تقبل قسمها اتنين فبنحن ننفعها + +462 +00:28:56,150 --> 00:29:00,830 +وكده ندخل الـ not بحسب قواعد اللغة طبعا فبحسب + +463 +00:29:00,830 --> 00:29:09,810 +قواعد اللغة C two does not divide six فاحنا + +464 +00:29:09,810 --> 00:29:13,450 +بندخلها حسب قواعد اللغة بهذا الشكل فده هو الـ + +465 +00:29:13,450 --> 00:29:23,680 +negation للتلت أمثلة اللي أمامناأي سؤال فهذا + +466 +00:29:23,680 --> 00:29:29,140 +الرابط الأول وهو رابط النفي في مجال نكمل ولا + +467 +00:29:35,400 --> 00:29:38,800 +ماشي ندخل الان على الرابط التاني وهو رابط الان + +468 +00:29:38,800 --> 00:29:42,260 +طبعا زي ما نقول ان النط اللي هو اسم negation نفي + +469 +00:29:42,260 --> 00:29:47,980 +رابط الان اللي هو اسم conjunction أي اقتران نقرن + +470 +00:29:47,980 --> 00:29:50,820 +بين حاجتين في هذا الشكل فإذا هو العنوان + +471 +00:29:50,820 --> 00:29:53,280 +conjunction زي ما عملنا نفس السياسة بدنا نعرف + +472 +00:29:53,280 --> 00:29:56,140 +المصطلح إيش هو اللي هو اللي قال الرابط وإيش + +473 +00:29:56,140 --> 00:29:59,160 +الramens تبعه وكيف نحسب ال truth value لل + +474 +00:29:59,160 --> 00:30:03,170 +statement اللي بتحتوي على مين على الانفبقول اللي + +475 +00:30:03,170 --> 00:30:05,430 +هو ال connective اللي هو هذا هو الرمز تبعه اللي هو + +476 +00:30:05,430 --> 00:30:08,770 +and بنقرأه إيش بيسموه؟ إسمه conjunction لما نقول + +477 +00:30:08,770 --> 00:30:11,610 +هذا .. لما نقول هذا .. هذا الرمز إيش هو؟ عملية + +478 +00:30:11,610 --> 00:30:15,410 +جامعة، نفس العملية فهذا هو الرمز واسمه conjunction + +479 +00:30:16,760 --> 00:30:20,540 +it may be placed between .. طبعا لأ النافي قدام + +480 +00:30:20,540 --> 00:30:23,960 +لكن الان بيفي two statements و بينهم بديجي .. + +481 +00:30:23,960 --> 00:30:28,300 +بديجي واش؟ بينهم .. اه between two statements B + +482 +00:30:28,300 --> 00:30:30,820 +and Q و طبعا اللي هيكون compound statement اللي + +483 +00:30:30,820 --> 00:30:35,760 +هيحتوى على رابططبعا كيف بنقرأها بي و اكيو بسهولة + +484 +00:30:35,760 --> 00:30:39,720 +او في طريقة اخرى نعم the conjunction من اسم of بي + +485 +00:30:39,720 --> 00:30:44,980 +و اكيو اختران بي و اكيو طبعا كيف نحسب ال truth + +486 +00:30:44,980 --> 00:30:51,310 +value بعدين نعمل الجدولفي تعريفنا للنفي كان أن + +487 +00:30:51,310 --> 00:30:54,810 +statement واحدة ودخلت عليها النفي فعشان نحسب + +488 +00:30:54,810 --> 00:30:57,350 +الاحتمالات كان فيها احتمالين هذي ال statement + +489 +00:30:57,350 --> 00:31:00,250 +يتكونية two false الان لما يكون فيه انا two + +490 +00:31:00,250 --> 00:31:03,390 +statements الحقيقة اللي بندور فيه انا عدة احتمالات + +491 +00:31:03,390 --> 00:31:07,320 +اول احتمال تنتهي من trueو 82 false هي احتمالين طب + +492 +00:31:07,320 --> 00:31:10,120 +الأولى true والتانية false طب والأولى false + +493 +00:31:10,120 --> 00:31:13,280 +والتانية true طب الترتيب مهم؟ في الشكل عام اه مهم + +494 +00:31:13,280 --> 00:31:16,020 +في الرياضية لان تشوف انه هل هو في .. في .. في .. + +495 +00:31:16,020 --> 00:31:20,880 +يعني لكل الروابط مهم طب لكل الروابط مش مهم مش خضيع + +496 +00:31:20,880 --> 00:31:22,960 +لكن تفحص انا هذا الكلام فإذا في عندنا أربع + +497 +00:31:22,960 --> 00:31:26,040 +احتمالات فجدول الصدق اللى بده يكونه لازم يحتوي على + +498 +00:31:26,040 --> 00:31:30,440 +الأربع احتمالات فبنلاحظ من جدول الصدق انه إذا كان + +499 +00:31:30,440 --> 00:31:33,600 +في عندي compound statement فيها conjunction بتكون + +500 +00:31:33,600 --> 00:31:37,250 +ال true فقطإذا كان التنين true مع بعض، طبعا فهو + +501 +00:31:37,250 --> 00:31:41,170 +واضح إن true and true true غير هيك false بغض النظر + +502 +00:31:41,170 --> 00:31:44,090 +كان ال false التنتين مع بعض أو الأول أو التاني + +503 +00:31:44,090 --> 00:31:47,290 +false فإذا كان واحد أو اتنين false فالكل false إذا + +504 +00:31:47,290 --> 00:31:51,310 +كان التنين true فال statement كلها بتكون true فهذا + +505 +00:31:51,310 --> 00:31:56,420 +هو التعريففطبعا هو هنا في الملاحظة بنأكد على دي + +506 +00:31:56,420 --> 00:31:59,800 +المعلومة فإذا عندي compound statement تحتوي على + +507 +00:31:59,800 --> 00:32:03,840 +الـ and بتكون true فقط إذا كان كل ال components + +508 +00:32:03,840 --> 00:32:09,020 +true أو ال two components are true بس نأكد على + +509 +00:32:09,020 --> 00:32:12,590 +ملاحظة اللي هو عدد اللي هو إيش الاحتمالاتلو + +510 +00:32:12,590 --> 00:32:15,190 +باللاحظ طبعا لما كان عندنا في المثال الأول أو في + +511 +00:32:15,190 --> 00:32:17,590 +التعريف الأول one statement كان في عندي two + +512 +00:32:17,590 --> 00:32:20,850 +possibilities في احتمالين الجدول كان من صفين في + +513 +00:32:20,850 --> 00:32:23,370 +المثال التاني أو في التعريف التاني كان أربعة طب لو + +514 +00:32:23,370 --> 00:32:26,570 +كانوا تلاتة بيصيروا تمانية فالقاعدة العامة بتقول + +515 +00:32:26,570 --> 00:32:29,450 +زي ما في عندي بتطلع على المركبات الأساسية اذا كان + +516 +00:32:29,450 --> 00:32:33,190 +مركب بسيط بيكون هو بشوف عددهم N فبكون الاحتمالات + +517 +00:32:33,190 --> 00:32:36,240 +المنطقية 2 أس Nفلو كانوا تلاتة بيكونوا اتنين اقص + +518 +00:32:36,240 --> 00:32:38,600 +تلاتة تمانية لو كانوا اربعة اتنين اقص اربعة سبتاشر + +519 +00:32:38,600 --> 00:32:41,680 +وهكذا فهذه القاعدة كانت اتنين اقص واحد واحد اتنين + +520 +00:32:41,680 --> 00:32:44,700 +اقص اتنين اربعة وهكذا فهذه القاعدة العامة اللي + +521 +00:32:44,700 --> 00:32:51,330 +بتساعدنا في تكوين جداول الصورة خلينا نشوف مثالعشان + +522 +00:32:51,330 --> 00:32:55,610 +اللي هو نتمكن أو نطبق القاعدة أو التعريف اللي طوى + +523 +00:32:55,610 --> 00:33:00,090 +درسنا فبقول indicate حدد which of the following + +524 +00:33:00,090 --> 00:33:03,390 +statements is true and which is false بدنا نحدد + +525 +00:33:03,390 --> 00:33:06,190 +false أو true ونشوف تطبيق على الكلاب اللي عملنا + +526 +00:33:06,760 --> 00:33:11,280 +فأول مثال زي ما شايفين compound statement متكونة + +527 +00:33:11,280 --> 00:33:14,420 +من two statements عشان أحكم عليها كلها true or + +528 +00:33:14,420 --> 00:33:17,400 +false لإن هذي statement كمبونت يا statement كانت + +529 +00:33:17,400 --> 00:33:19,740 +simple أو كمبونت فهي statement بتكون يا true يا + +530 +00:33:19,740 --> 00:33:22,260 +false مانفعش تكون نصها true و نصها false أو كذا لأ + +531 +00:33:22,260 --> 00:33:25,940 +لازم كلها ككل أحكم عليها true or false كام بتحكم + +532 +00:33:25,940 --> 00:33:29,760 +عليها؟ بتعيش في أي زاعة ففعلنا هنا بنطلع أن في two + +533 +00:33:29,760 --> 00:33:36,440 +statements و بينهم n فالجزء الأولone and one plus + +534 +00:33:36,440 --> 00:33:41,300 +one equals two هي واحدة و هي true three ناقص one + +535 +00:33:41,300 --> 00:33:45,680 +equal to two برضه true ف true and true إذن كلها + +536 +00:33:45,680 --> 00:33:50,640 +true فهذا أول مثل فهيك بحكم فهيبقى نطبق القاعدة + +537 +00:33:50,640 --> 00:33:54,160 +واضح فانا بدأ أحكم عليها كلها مش جادر أحكم عليها + +538 +00:33:54,160 --> 00:33:57,360 +مرة واحدة بحكم على الأعزاء و بتخدم القاعدة و بحكم + +539 +00:33:57,360 --> 00:34:02,560 +على الكل و بحكم على الكل فهذا المثال الأول + +540 +00:34:05,870 --> 00:34:11,690 +المثال التاني الخمسة أو five is an integer هي + +541 +00:34:11,690 --> 00:34:18,460 +statement وهي true زي ما البعض بيحكيو one minus + +542 +00:34:18,460 --> 00:34:23,360 +three equals to one false طيب false and true true + +543 +00:34:23,360 --> 00:34:27,540 +and false false القاعدة بتقول إيش false فاحنا + +544 +00:34:27,540 --> 00:34:31,960 +استخدمنا حللنا المركبات حددنا قيمة الصدق للإعزاء + +545 +00:34:31,960 --> 00:34:35,940 +استخدمنا القاعدة التعريف و عرفنا نحدد إيش القيمة + +546 +00:34:35,940 --> 00:34:43,640 +للكل عرفنا نحدد القيمة للكل واضح تبين نشوف كمان + +547 +00:34:43,640 --> 00:34:48,340 +مثالfive minus zero to E equals four فهي statement + +548 +00:34:48,340 --> 00:34:55,480 +false اه فهنا false and and true برضه false لأنه + +549 +00:34:55,480 --> 00:34:58,000 +بغض النظر كانت ال force في الأول او في الآخر ف ال + +550 +00:34:58,000 --> 00:35:01,100 +argues of force فالكل false فإذا هذي برضه false + +551 +00:35:01,100 --> 00:35:04,840 +فهنا + +552 +00:35:04,840 --> 00:35:09,460 +بنحاول ندى أنثى على الاحتمالات الأربعة نشوف كمان + +553 +00:35:09,460 --> 00:35:16,390 +مثالfive times two equals five false five times + +554 +00:35:16,390 --> 00:35:21,430 +three equals ten false false and false false فبهيك + +555 +00:35:21,430 --> 00:35:25,830 +بنقدر نحكم عليهم و بنعرف و بنطبق القاعدة بهذه + +556 +00:35:25,830 --> 00:35:31,570 +الصورة اتوقع ان هنا مناسب ان نوقف هنا عشان الوقت + +557 +00:35:31,570 --> 00:35:33,590 +ان شاء الله ساعتين اتين بنكمل + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wUnjc84zu3o_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wUnjc84zu3o_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..28d34d8075188b1f0828021c2036431e461dbf6f --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wUnjc84zu3o_postprocess.srt @@ -0,0 +1,2484 @@ +1 +00:00:20,920 --> 00:00:25,720 +بسم الله الرحمن الرحيم في محاضرة اليوم هنستكمل + +2 +00:00:25,720 --> 00:00:29,820 +القواعد الاستدلال اللي احنا شفناها عبارة عن نظريات + +3 +00:00:29,820 --> 00:00:33,240 +متعددة يمكن مار علينا تلت نظريات فيها اكتر من + +4 +00:00:33,240 --> 00:00:36,500 +قانون الحقيقة نظرية كان فيها قانونين او اكتر تدينا + +5 +00:00:36,500 --> 00:00:39,970 +اللي هي قواعد المنطقية اللي هنعتمد عليهافي اللي هو + +6 +00:00:39,970 --> 00:00:44,210 +دراستنا و في البرهان الرياضي حتى نحكم على البرهان + +7 +00:00:44,210 --> 00:00:48,390 +تبعنا ان هو اللي هو صحيح او غير صحيح زي ما احنا + +8 +00:00:48,390 --> 00:00:51,790 +حكينا هذا هو دور المنطق في دراسة الرياضيات + +9 +00:00:51,790 --> 00:00:56,450 +بيحكملنا على البراهين تبعتنا ان هي صحيحة او غير + +10 +00:00:56,450 --> 00:01:00,560 +صحيحةجابل ما نستكمل مع بعض نظرية هنمر على مصطلح + +11 +00:01:00,560 --> 00:01:04,680 +الحقيقة بنحتاجه في بعض الأحيان وهو ما يُعرَب بالـ + +12 +00:01:04,680 --> 00:01:07,720 +Denials الـ Denials يمكن نقوله مثلا ما روحناها من + +13 +00:01:07,720 --> 00:01:11,100 +ناحية لغوية هي النفي طب ما احنا فيه ايه نقاش + +14 +00:01:11,100 --> 00:01:15,280 +النفي؟ لأ فالمعنى الاصطلاحة إيش الفرق بينهم؟ طبعا + +15 +00:01:15,280 --> 00:01:18,320 +إحنا النفي المباشر إحنا كنا عايش النفي ممكن نحط نط + +16 +00:01:18,320 --> 00:01:21,780 +نط أو نقول إن ليست هي الحالة كذا it is not the + +17 +00:01:21,780 --> 00:01:26,190 +case ممكن ننفي بهذا الشكللكن احنا بنستخدم النافذ + +18 +00:01:26,190 --> 00:01:30,530 +في الرياضيات أحيانا نحتاج ننفذ الجملة و نتعامل + +19 +00:01:30,530 --> 00:01:35,550 +معها فضروري نحطها بشكل مبسط مفيد يجعلنا نقدر + +20 +00:01:35,550 --> 00:01:38,870 +نتعامل معاه فإذا حولنا احنا بعد ما نفذنا ال + +21 +00:01:38,870 --> 00:01:42,890 +statement عملنا عليها بعض العمليات و حولناها لصورة + +22 +00:01:42,890 --> 00:01:47,410 +مكافئة بنسمي الصورة الجديدة المكافئة denialاللي هو + +23 +00:01:47,410 --> 00:01:50,450 +ممكن نسميه أيش؟ النفي المكافئ، النفي المكافئ + +24 +00:01:50,450 --> 00:01:53,270 +فالمصطلح هش بيقول ليه denial of a statement ال + +25 +00:01:53,270 --> 00:01:55,950 +denial of a statement بيه is any statement + +26 +00:01:55,950 --> 00:01:59,190 +equivalent to not be إذا إن هي تكافئ مين النفي فال + +27 +00:01:59,190 --> 00:02:03,030 +denial statement تكافئ إيش ال negation statement + +28 +00:02:03,030 --> 00:02:06,270 +تكافئ ال negation أو النفي لمين للجملة طبعا زي ما + +29 +00:02:06,270 --> 00:02:10,230 +حكيناش الهدف من ال denial إنه يحط النفي بصورة أبسط + +30 +00:02:10,230 --> 00:02:17,240 +بصورة أنسب للاستخدام، للاستخدام أي سؤال؟طبعا اللي + +31 +00:02:17,240 --> 00:02:21,500 +هو الملاحظة ال statement طبعا لها negation واحد بس + +32 +00:02:21,500 --> 00:02:24,260 +من في الجملة بقول it is not the case يمكن أبسط شيء + +33 +00:02:24,260 --> 00:02:28,080 +أو أحطله أداة انه كما هو يستخدم في قواعد اللغة + +34 +00:02:28,080 --> 00:02:31,240 +الإنجليزية اه فبقوللي ال statement has only one + +35 +00:02:31,240 --> 00:02:35,310 +negationإن فيه واضح وحيد ومعروف تبقى كام denial + +36 +00:02:35,310 --> 00:02:38,870 +isها متعددين اه لكن إيش but always has many + +37 +00:02:38,870 --> 00:02:41,130 +denials لإن في statement بحطها بصورة مكافئة في + +38 +00:02:41,130 --> 00:02:44,190 +صورة مكافئة وممكن أحطها بعدد صور مكافئة وبيعيش + +39 +00:02:44,190 --> 00:02:47,390 +دايما إن أنا من ناحية عملية بختار الصورة الأنسب + +40 +00:02:47,390 --> 00:02:51,740 +إليه الأنسب للغرض التبعي للهدف التبعيأي سؤال واضح + +41 +00:02:51,740 --> 00:02:54,700 +نشوف بعض الأمثلة و نشوف كيف .. كيف ممكن أن أحول + +42 +00:02:54,700 --> 00:02:57,180 +statement ال negation لل statement من صورة لصورة و + +43 +00:02:57,180 --> 00:03:00,280 +يكون إيش أفيد إليه أو أوضح على سبيل الأمثلة عشان + +44 +00:03:00,280 --> 00:03:05,560 +نقدر إيش نتصور إيش المقصود بصورة مكافئة إيش أنسب + +45 +00:03:05,560 --> 00:03:09,900 +أو إيش أفضل فهنا عندنا مثاليش بيقولوا give a + +46 +00:03:09,900 --> 00:03:13,900 +useful denial of each statement تديني اللي هو إيش + +47 +00:03:13,900 --> 00:03:18,820 +نفي مكافئة لكل statement من ال statements اللي هي + +48 +00:03:18,820 --> 00:03:23,470 +التاليةالجملة الأولى أو السؤال الأول فرع ايه؟ + +49 +00:03:23,470 --> 00:03:28,290 +تلاتة is greater or equal to three three is is + +50 +00:03:28,290 --> 00:03:32,150 +greater or equal to three فهذه statement صح؟ بسيطة + +51 +00:03:32,150 --> 00:03:35,370 +ولا مركبة؟ مركبة .. مركبة .. مركبة .. ايه الشيء + +52 +00:03:35,370 --> 00:03:42,950 +اللي قالت الرابط؟or or or او + +53 +00:03:42,950 --> 00:03:48,490 +او + +54 +00:03:48,490 --> 00:03:49,050 +او او او او او او او او او او او او او او او او او + +55 +00:03:49,050 --> 00:03:49,290 +او او او او او او او او او او او او او او او او او + +56 +00:03:49,290 --> 00:03:50,990 +او او او او او او او او او او او او او او او او او + +57 +00:03:50,990 --> 00:03:53,430 +او او او او او او او او او او او او او او او او او + +58 +00:03:53,430 --> 00:03:53,530 +او او او او او او او او او او او او او او او او او + +59 +00:03:53,530 --> 00:03:53,550 +او او او او او او او او او او او او او او او او او + +60 +00:03:53,550 --> 00:04:06,430 +او او او او او + +61 +00:04:06,430 --> 00:04:11,350 +او اوهي ال solution ونبدأ في إيه؟ فأول شيء نتحدث + +62 +00:04:11,350 --> 00:04:15,490 +عن ال statement statement ما هي ال statement؟ ال + +63 +00:04:15,490 --> 00:04:18,310 +tree is greater than or equal to the tree وعشان + +64 +00:04:18,310 --> 00:04:22,710 +أفسر و أتأكد أن هذه statement مركبة أقول هذه مش + +65 +00:04:22,710 --> 00:04:26,170 +تكافئة هادو كافة، زي ما بنقرعها تلاتة أكبر من + +66 +00:04:26,170 --> 00:04:32,500 +تلاتة or تلاتة تساوي تلاتةفدي جيوم لمركبة ب or مش + +67 +00:04:32,500 --> 00:04:37,620 +and فاذا بقى بنقرأها تلاتة أكبر أو مش و أكبر أو + +68 +00:04:37,620 --> 00:04:42,220 +تساوي تلاتة greater or equal to three واضح؟ فاذا + +69 +00:04:42,220 --> 00:04:44,540 +هذا ال statement الخطوة التانية اللي إحنا نعمل + +70 +00:04:44,540 --> 00:04:51,580 +ننفيها negation ال negation وحيد فإيش ال negation + +71 +00:04:51,580 --> 00:04:55,460 +اللي هو نفي تلاتة أكبر أو يساوي تلاتة بده كافة + +72 +00:04:55,460 --> 00:04:59,660 +ندخل النفي هنابدنا ننفي هذه الصورة المكافئة لأن هي + +73 +00:04:59,660 --> 00:05:03,360 +اللي بتوضح لنا أنه ممكن نبسط لأن الجملة البسيطة + +74 +00:05:03,360 --> 00:05:08,260 +مابتتبسطش لكن مين اللي بتبسط؟ المركب ولا لأ؟ فاحنا + +75 +00:05:08,260 --> 00:05:10,540 +لو أنها مش بسيطة مش بدنا نبسط فيها مافيش شيء لكنها + +76 +00:05:10,540 --> 00:05:14,690 +مركبة كيف ممكن أبسط الطرف اليمين؟باستخدام دي + +77 +00:05:14,690 --> 00:05:17,730 +مورجانز لو فهنا تبسيط و هتشوف نهي المعنى فدي + +78 +00:05:17,730 --> 00:05:21,770 +مورجانز لو بيديني قاعدة كيف اللي هو إيش أدخل + +79 +00:05:21,770 --> 00:05:25,010 +النفية على statement فيها or أو and فإيش بيقوللي + +80 +00:05:25,010 --> 00:05:29,410 +إذا كانت فيها or بتصير and وبنفيش الجزئين وبننفي + +81 +00:05:29,410 --> 00:05:34,190 +الجزئين فإذا هذه تكافئ not ال tree أكبر من ال tree + +82 +00:05:34,190 --> 00:05:39,930 +and صح ال or صارت and و بعدين not ال tree تساوي ال + +83 +00:05:39,930 --> 00:05:43,930 +treeواضح؟ بنمشي بسيطة بسيطة، بنتعلم احنا القواعد، + +84 +00:05:43,930 --> 00:05:46,610 +يمكن أشياء احنا نكون نعملها من دون ما نحط القواعد، + +85 +00:05:46,610 --> 00:05:50,110 +بس جيد إنه نقعد القواعد ونتعلم كيف بنشتغل ومن وين + +86 +00:05:50,110 --> 00:05:52,910 +الأمور اللي احنا متعودين عليها صح فعلا صحيحة ضمن + +87 +00:05:52,910 --> 00:05:55,870 +القواعد اللي بنتعلمها في المنطق، هذا خلينا نحطه + +88 +00:05:55,870 --> 00:05:58,050 +بالرموز اللي معتدين عليها، طبعا هذا متعرف عليه أنه + +89 +00:05:58,050 --> 00:06:01,370 +إيش؟ تلاتة لا تساوي تلاتة، ننفي إيش؟ إيش لا تساوي؟ + +90 +00:06:01,370 --> 00:06:04,770 +بحط هاي الرمز لا يساوي، وهذه ممكن نحطها تلاتة ليست + +91 +00:06:04,770 --> 00:06:05,190 +أكبر + +92 +00:06:11,640 --> 00:06:17,420 +السلام عليكمهل نفي الأكبر أصغر؟ لأ، هنشوف مع بعض، + +93 +00:06:17,420 --> 00:06:19,960 +شوف على الـGate احنا نشوف القواعد، أه فعلا، مين + +94 +00:06:19,960 --> 00:06:22,820 +اللي بدي يحكم إنه هل نفي الأكبر أصغر ولا لأ، هنشوف + +95 +00:06:22,820 --> 00:06:25,200 +القواعد، بدنا نشوف السند اللي بنستخدم عليه، هنشوف + +96 +00:06:25,200 --> 00:06:28,340 +مع بعض، بدنا نشوف مع بعض إيش الكلام، فهنا أنا + +97 +00:06:28,340 --> 00:06:32,840 +بسطت، وممكن هذا يبسط أكتر، بس بدي يبسط بمعلومة + +98 +00:06:32,840 --> 00:06:37,660 +إضافية، معروف إنه من خواص الإعداد الحقيقية إن أي + +99 +00:06:37,660 --> 00:06:42,230 +عددين في إيش، بينهم مقارنة واحدة من تلت حالات،يا + +100 +00:06:42,230 --> 00:06:44,950 +متساويين، يا الأول أكبر من التاني، يا أصغر منه، + +101 +00:06:44,950 --> 00:06:48,190 +مافي احتمال تالت، فانا هنا إيش نفيت، نفيت أن يكون + +102 +00:06:48,190 --> 00:06:51,050 +التلاتة أكبر من التلاتة، ونفيت التساوي، ماتامش + +103 +00:06:51,050 --> 00:06:54,490 +الاحتمال الوحيد أنه أصغر منه، أن التلاتة أصغر من + +104 +00:06:54,490 --> 00:07:00,150 +التلاتة، فإذا التلاتة أصغر من التلاتة نافي لمن؟ + +105 +00:07:00,150 --> 00:07:02,810 +نافي لهذه الجملة كلها، لتلاتة أكبر أو يساوي تلاتة، + +106 +00:07:02,810 --> 00:07:06,310 +مش نافي الأكبر بس، تلاتة أصغر من تلاتة هي مش نافي + +107 +00:07:06,310 --> 00:07:09,790 +الأكبر، وإنما نافي الأكبر مع اليساوي، واضح؟أه فإذا + +108 +00:07:09,790 --> 00:07:12,830 +لو احنا نعيش بيكون يتصرعنا بنقع في خطأ طبعا هنا + +109 +00:07:12,830 --> 00:07:15,730 +هذا هو ال denial، مظبوط؟ شوفتوا احنا بدينا من + +110 +00:07:15,730 --> 00:07:18,990 +الصورة هى النفي المباشر، النفي المباشر هيه، لما + +111 +00:07:18,990 --> 00:07:21,690 +بسطناها حصلنا على ديننا، مين أفضل أتعامل معهدي و + +112 +00:07:21,690 --> 00:07:24,990 +لا معهادي؟ معهادي، معهادي كتير لو بدي أعمل عملية + +113 +00:07:24,990 --> 00:07:27,630 +حسابية بعمل معهادي، لكن أنا بقول it is not the + +114 +00:07:27,630 --> 00:07:30,810 +case that three greater than or equal to three، + +115 +00:07:30,810 --> 00:07:35,420 +مظبوط هذا نفي، لكنه مش مفيدواضح ياه؟ واضح الصورة + +116 +00:07:35,420 --> 00:07:37,260 +اللي بتنييه؟ إيش معناه تدنييه؟ لو إيش فيديوته، + +117 +00:07:37,260 --> 00:07:40,220 +هعتنعها في صورة بسيطة جدا، بقدر أتعامل معها بكل + +118 +00:07:40,220 --> 00:07:43,500 +سهولة، اه فلمّا أقول لها الـTree الـGreat A أصغر + +119 +00:07:43,500 --> 00:07:46,300 +من تلاتة، إذا إن هي ليست أكبر وليست أكبر، طبعا + +120 +00:07:46,300 --> 00:07:49,460 +الـState False هي، لإن الـState ما بيقولهاtrue ال + +121 +00:07:49,460 --> 00:07:51,940 +statement أولى true ولا لأ تلاتة أكبر يساوي تلاتة + +122 +00:07:51,940 --> 00:07:56,060 +true ولا false true ليش لأن في واحدة منهم true صح + +123 +00:07:56,060 --> 00:07:59,540 +فجيت كل الأمور نعرف عن أيش اللي بنشتغله و ليش + +124 +00:07:59,540 --> 00:08:01,560 +بنشتغل هيك لو كنا بنشتغله من غير ما نشوف القواعد + +125 +00:08:01,560 --> 00:08:04,440 +لكن هي قواعد المنطق بتقول إن فعلا اللي كان نتعلمه + +126 +00:08:04,440 --> 00:08:08,440 +زمان صح مابتنفاش مع ليش قواعد المنطق اللي بنتعلمها + +127 +00:08:08,440 --> 00:08:11,680 +اليوم واضح إيش معناه ال denial وإيش فايديته فده هو + +128 +00:08:11,680 --> 00:08:14,220 +ال denial فإذا هنا هجيت هاي ال statement هاي ال + +129 +00:08:14,220 --> 00:08:18,460 +negation فإذا طبعا ده كله تكافح ف denialأو a + +130 +00:08:18,460 --> 00:08:21,180 +useful denial طبعا مش هو الوحيد ممكن أوقف هنا بس + +131 +00:08:21,180 --> 00:08:28,000 +هذا هو الأفضل فنقول هنا a useful denial + +132 +00:08:28,000 --> 00:08:35,440 +of a tree أكبر أو يساوي tree is a tree less than + +133 +00:08:35,440 --> 00:08:42,780 +it أي سؤال خلينا + +134 +00:08:42,780 --> 00:08:46,080 +نشوف كمان مثال + +135 +00:08:48,240 --> 00:08:54,420 +The function f of x equals sin x يعني دالة الـ sin + +136 +00:08:54,420 --> 00:09:00,980 +is odd and increasing دالة الـ sin هي دالة فردية + +137 +00:09:00,980 --> 00:09:05,760 +وتزايديةخلّيني أتعليق عن خارج السؤال ال statement + +138 +00:09:05,760 --> 00:09:08,520 +هذه مُركّبة ولا بسيطة؟ مُركّبة مُركّبة مُركّبة + +139 +00:09:08,520 --> 00:09:08,800 +مُركّبة مُركّبة مُركّبة مُركّبة مُركّبة مُركّبة + +140 +00:09:08,800 --> 00:09:08,920 +مُركّبة مُركّبة مُركّبة مُركّبة مُركّبة مُركّبة + +141 +00:09:08,920 --> 00:09:09,280 +مُركّبة مُركّبة مُركّبة مُركّبة مُركّبة مُركّبة + +142 +00:09:09,280 --> 00:09:09,340 +مُركّبة مُركّبة مُركّبة مُركّبة مُركّبة مُركّبة + +143 +00:09:09,340 --> 00:09:12,800 +مُركّبة مُركّبة مُركّبة مُركّبة مُركّبة مُركّبة + +144 +00:09:12,800 --> 00:09:16,120 +مُركّبة + +145 +00:09:16,120 --> 00:09:31,360 +مُركّبة مُركّبة مُركّبة مُركّبة + +146 +00:09:31,360 --> 00:09:34,600 +مُنحوّلها أفضل إذا كانت يعني عشانها طويلة هنا كانت + +147 +00:09:34,600 --> 00:09:36,900 +سهلة فما استخدمتش رموز لأنه سهلة ال statement + +148 +00:09:36,900 --> 00:09:41,820 +نحوّلها لرموز ننفيها نبسط النفي ونترجم النفي بنكون + +149 +00:09:41,820 --> 00:09:46,080 +حصلنا على إيش على ال denial المناسب أو denial يكون + +150 +00:09:46,080 --> 00:09:51,560 +إيش مفيد نكتب + +151 +00:09:51,560 --> 00:09:56,980 +هنا مش عارف عاد يجيب الكاميرا ولا لأ فده بيفأيجي + +152 +00:09:56,980 --> 00:09:59,860 +الأول حاجة بنحط إيش ال statement قولنا عشان ال + +153 +00:09:59,860 --> 00:10:02,620 +statement كبيرة ما نتمشي نكتبها خلّينا نعملها رموز + +154 +00:10:02,620 --> 00:10:07,540 +خلّينا نعملها رموز فخلّينا let B أو خلّيني اختصارا + +155 +00:10:07,540 --> 00:10:11,600 +B إيش تكون F of X تساوي Sine X بدي أختصر شوية في + +156 +00:10:11,600 --> 00:10:16,220 +الكلام ده function is odd هاي ال statement ال + +157 +00:10:16,220 --> 00:10:20,740 +statement التانية F of X تساوي Sine X is + +158 +00:10:20,740 --> 00:10:25,680 +increasingفدولة ايش ال two statements فال + +159 +00:10:25,680 --> 00:10:39,820 +statement بي اند اكيو بي + +160 +00:10:39,820 --> 00:10:44,060 +اند اكيو فدهي ال statement خلينا نعملها negation + +161 +00:10:44,060 --> 00:10:48,840 +الآن فال + +162 +00:10:48,840 --> 00:10:54,740 +negation not be and qفهي إيش؟ إنها ليست .. إنه ليس + +163 +00:10:54,740 --> 00:11:00,760 +صحيحاً أن ال sign فردية وتزايدية هذا نفيد نبسطه + +164 +00:11:00,760 --> 00:11:05,000 +لأنه ممكن يكون إيش صورة أوضح وصورة أفضل فبنبدأ + +165 +00:11:05,000 --> 00:11:08,340 +نبسط عشان نوصل على الدنيا لعملية إيش تبسيط طب هذي + +166 +00:11:08,340 --> 00:11:13,040 +إيش كيف ممكن أبسطها؟ من دي مرجانة فهذه طبعا تكافئ + +167 +00:11:13,040 --> 00:11:21,360 +not be or not be في أي تبسيط آخر؟أه تمام انترجمها + +168 +00:11:21,360 --> 00:11:24,480 +الـ gate خلينا نشوف انترجمها باللغة فالـ denial او + +169 +00:11:24,480 --> 00:11:31,080 +الـ denial خلينا نترجمها نط بي .. ايش نط بي؟ اللي + +170 +00:11:31,080 --> 00:11:34,760 +هي ايش؟ the function f of x is not odd the + +171 +00:11:34,760 --> 00:11:38,320 +function the + +172 +00:11:38,320 --> 00:11:47,440 +function f of x تساوي صين الـ x is not odd + +173 +00:11:50,180 --> 00:11:58,640 +or it is not increasing فهذا + +174 +00:11:58,640 --> 00:12:04,320 +denial واضح إنه إيش صار عنه الجملة إنها ليست فردية + +175 +00:12:04,320 --> 00:12:09,660 +أو ليست زوجية هي إما يا ليست فردية يا ليست زوجية + +176 +00:12:09,660 --> 00:12:13,280 +فكان الكلام طبعا إذا بدنا نحسن اللغة شوية ممكن + +177 +00:12:13,280 --> 00:12:18,760 +نقول إيش either عشان فيها or eitherإن دلر يا إما + +178 +00:12:18,760 --> 00:12:23,480 +ليست فردية، يا إما ليست تزايدية، طبعا الأول الحال + +179 +00:12:23,480 --> 00:12:27,680 +صحيح، لكن هذا من أحيان لغة يمكن يكون أفضل مع + +180 +00:12:27,680 --> 00:12:31,660 +either، لأ هذه ليست لغة أخرى، neither في النفي، في + +181 +00:12:31,660 --> 00:12:36,860 +غير، نقول either، يا إما هيك يا إما هي، it is + +182 +00:12:36,860 --> 00:12:43,960 +neither كذا أو nor، ده صير مختلف الخاطرممكن انا + +183 +00:12:43,960 --> 00:12:57,360 +اقولك التالي نشوف + +184 +00:12:57,360 --> 00:13:04,100 +كمان مثال برضه + +185 +00:13:04,100 --> 00:13:07,880 +على ال signبقول لي الـ function صيني لـ X has + +186 +00:13:07,880 --> 00:13:12,780 +positive first and second derivatives at X تساوي 0 + +187 +00:13:12,780 --> 00:13:16,360 +ده لت الصين اللي هي مشتقة أولى موجبة ومشتقة تانية + +188 +00:13:16,360 --> 00:13:18,800 +موجبة عند X تساوي 0 + +189 +00:13:28,820 --> 00:13:34,700 +فده فرق C فبرضه نبدأ بال statement نترجمها فنعمل + +190 +00:13:34,700 --> 00:13:39,440 +رموز بي في برضه هنا ال two h مركبة ومين أداة + +191 +00:13:39,440 --> 00:13:44,440 +الرابط and اه فطبعا خلينا نشوف أول شئ اللي هو sin + +192 +00:13:44,440 --> 00:13:52,100 +x اختصارا is او has positive + +193 +00:13:52,100 --> 00:13:57,220 +first derivative مشتقة أولى first derivative + +194 +00:13:59,530 --> 00:14:06,790 +at x تساوي 0 فده ال statement الاول a q sin x برضه + +195 +00:14:06,790 --> 00:14:19,230 +لان نفسها has positive second derivative at + +196 +00:14:19,230 --> 00:14:24,050 +x تساوي 0 فده ال statement فدوله ايش الجزئين اه + +197 +00:14:24,050 --> 00:14:27,290 +فال statement اللي بيبني اني انترجمها statement + +198 +00:14:29,210 --> 00:14:35,890 +B and Q فهيك أول شي أبسط و أحط رموز عشان أقدر أعيش + +199 +00:14:35,890 --> 00:14:42,150 +أبسط في ال negation الان نجيب ال negation فطبعا + +200 +00:14:42,150 --> 00:14:48,190 +ال negation not B and Q فطبعا ممكن أبسط عن طريق + +201 +00:14:48,190 --> 00:14:53,590 +ديومرجان زي المثال السابق not B or not Q هذا + +202 +00:14:53,590 --> 00:15:04,410 +التبسيط الممكنأي سؤال؟ خلّينا نترجمها، فضل حاجة + +203 +00:15:04,410 --> 00:15:11,510 +تقول إنها ليست صحيحة إن الدالة مشتقة أولى موجبة + +204 +00:15:11,510 --> 00:15:12,530 +ومشتقة تانية موجبة + +205 +00:15:15,600 --> 00:15:18,880 +يعني الأبداء دي هتحطه باللغة ليش دي قول it is not + +206 +00:15:18,880 --> 00:15:23,160 +the case و أحط ال statement بس هذا الأمر مش مفيد + +207 +00:15:23,160 --> 00:15:26,620 +هتشوف في تطبيقات في محاضرات التقلقل القادمة ان شاء + +208 +00:15:26,620 --> 00:15:32,770 +الله واضح؟لأ نطبق ان ننطق you لأ لأ بتطلعش مكافئة + +209 +00:15:32,770 --> 00:15:37,150 +منطقيا بتطلعش مكافئة منطقيا اه هنبدأ احط statement + +210 +00:15:37,150 --> 00:15:39,770 +تكون مكافئة ايش معنى مكافئة؟ يا اما هدولة true مع + +211 +00:15:39,770 --> 00:15:41,630 +بعض، اذا كانت true فهذه true، اذا كانت forced فهذه + +212 +00:15:41,630 --> 00:15:44,610 +forced، اه لكن لما اقول انا and and نفي و and + +213 +00:15:44,610 --> 00:15:49,250 +مختلفة ال statement، اه فبتظبطش، طبعا ليش تظبطش + +214 +00:15:49,250 --> 00:15:52,710 +تطلع عقول القواعد مافيش، في القواعد .. بيقول كيف + +215 +00:15:52,710 --> 00:15:54,530 +دخل النفي على ال and، هي القاعدة، وهي القاعدة + +216 +00:15:54,530 --> 00:15:59,030 +الوحيدةكيف أدخل النافع على الان؟ واضح؟ فالان اللي + +217 +00:15:59,030 --> 00:16:04,410 +هو الـ denial؟ أه بدنا ننفق برضه عشانها silent or + +218 +00:16:04,410 --> 00:16:09,150 +ممكن أحط either أو لو ماحطش كله صح either طبعا not + +219 +00:16:09,150 --> 00:16:12,310 +be اللي هو ياشه خليني بس أكتب بشكل كامل the + +220 +00:16:12,310 --> 00:16:16,350 +function sine + +221 +00:16:16,350 --> 00:16:23,050 +ال X طبعا بدام في has اذا does not have does not + +222 +00:16:23,050 --> 00:16:36,330 +havepositive first derivative or + +223 +00:16:36,330 --> 00:16:46,630 +it does not have second positive + +224 +00:16:46,630 --> 00:16:47,470 +second derivative + +225 +00:16:53,830 --> 00:17:00,970 +Second derivative of x + +226 +00:17:00,970 --> 00:17:01,590 +to the power of 0 + +227 +00:17:13,280 --> 00:17:17,520 +مقدمة وبعض الأمثلة حتى نستوعب الفكرة وبعد هيك + +228 +00:17:17,520 --> 00:17:21,680 +هنستخدمها ان شاء الله أدت مرات ونشوف كيف ال denial + +229 +00:17:21,680 --> 00:17:25,260 +لما نحول لصورة مكافئة بتكون أفيدة خليني أشوف كمان + +230 +00:17:25,260 --> 00:17:31,720 +مثال هنا في if statement جملة شرطية if the number + +231 +00:17:31,720 --> 00:17:36,930 +5.1 is an integer then it is positiveلو 5.1 هي عدد + +232 +00:17:36,930 --> 00:17:40,850 +صحيح فهي موجب فهذا statement شرطي نجيب لها denial + +233 +00:17:40,850 --> 00:17:45,570 +مناسب نشوف كيف ممكن ننفل ال if then و نبسطها و + +234 +00:17:45,570 --> 00:17:52,810 +نشوف هذا الأمور فهنا عندنا اللي هو فرع D فطبعا + +235 +00:17:52,810 --> 00:18:01,990 +خلينا نعمل رموز فال B 5.1 is an integer هذي false + +236 +00:18:01,990 --> 00:18:11,930 +ولا true؟false اكيو 5.1 is positive هذا + +237 +00:18:11,930 --> 00:18:17,930 +true ولا false true if false then true اذا ال + +238 +00:18:17,930 --> 00:18:21,090 +statement كلها true ان جيش التبع حدش حيطلع false + +239 +00:18:21,090 --> 00:18:28,350 +تمام اه فنبدأ لجيه ال statement اه if b then اكيو + +240 +00:18:28,350 --> 00:18:33,680 +بنانين فيهاشايفين الخطوات كيف نجيب ال denial؟ ال + +241 +00:18:33,680 --> 00:18:37,780 +negation ايش ال negation؟ حط نقطة قدامك، مظبوط؟ + +242 +00:18:37,780 --> 00:18:42,940 +بكل بساطة، واحدة واحدة، شوية شوية، تمام؟ اه فهذا + +243 +00:18:42,940 --> 00:18:47,480 +هو ال negationزي جميع الطالبات الخطوات واضحة + +244 +00:18:47,480 --> 00:18:51,300 +افيلهم احنا نمشي خطوة خطوة بنوصل ونقول خطوة نعرف + +245 +00:18:51,300 --> 00:18:54,880 +ايش السبب اللي بنشتغل عليه فهذا الكلام الآن السؤال + +246 +00:18:54,880 --> 00:18:57,360 +اللي زي ما سألناه في الأمثلة الماضية شوفنا احنا + +247 +00:18:57,360 --> 00:19:00,300 +لما كان تقلنا R في المثال الأول كيف دخلنا النفي + +248 +00:19:00,300 --> 00:19:04,040 +عليها الآن De Morgan's جالنا كيف ندخله عليها طب في + +249 +00:19:04,040 --> 00:19:11,240 +قانون بيعلمني كيف ادخل النفي على ال F thenلا .. + +250 +00:19:11,240 --> 00:19:13,820 +سمعنا الناس بتقولوا ال contrapositive .. لأ ال + +251 +00:19:13,820 --> 00:19:15,940 +contrapositive بتقولش أني بنفي أنا .. ال + +252 +00:19:15,940 --> 00:19:21,200 +contrapositive هي تكافئها .. تكافئها .. إذا أول شي + +253 +00:19:21,200 --> 00:19:26,080 +اللي بدنا نعرف ليست هناك قاعدة لإدخال النفي على + +254 +00:19:26,080 --> 00:19:32,210 +الإفدنلكن أول شيء فيه في التعريف ممكن أحول ال F + +255 +00:19:32,210 --> 00:19:36,210 +then باستخدام ال and و ال نفي و بعدين هنستخدم De + +256 +00:19:36,210 --> 00:19:39,790 +Morgan's إذا مافيشش طريقة مباشرة إذا نقشت اساسات + +257 +00:19:39,790 --> 00:19:43,690 +القاعدة ليست هناك قاعدة مباشرة تدخل ال نفي على ال + +258 +00:19:43,690 --> 00:19:46,990 +F then لكن أول شيء بحول ال F then إلى and من + +259 +00:19:46,990 --> 00:19:51,150 +التعريف و بعدين بدخل عليها مين؟ النفيواضح؟ اه فانا + +260 +00:19:51,150 --> 00:19:54,810 +دايما ايش .. خاطرنا انه لما ندخل النافع الآن او + +261 +00:19:54,810 --> 00:19:56,930 +على ليه .. بدأ يكون فينا قاعدة، بدأ يكون فينا + +262 +00:19:56,930 --> 00:19:59,730 +دليل، و هذا اللي هتعلمه، و هذا أهم شيء في اللي هو + +263 +00:19:59,730 --> 00:20:02,730 +البرهان الرياضي، انه ايش دليلك على ان هذا شغلك صح + +264 +00:20:02,730 --> 00:20:06,170 +او غير صح، لأنه بدنا نحكم على حل و على البرهان انه + +265 +00:20:06,170 --> 00:20:09,370 +صحيح ولا لأ، فإذا أول شيء بس نتذكر انه إيش ال .. + +266 +00:20:09,370 --> 00:20:15,530 +ال be then بعدين ننفيها، فإذا أول شيء recall that + +267 +00:20:16,650 --> 00:20:22,830 +ذكر انه be if then قلنا تكافئ not إياك أن تقعد + +268 +00:20:22,830 --> 00:20:29,150 +وتنهيش وتخلف في الوعد إياك أن تقعد وتخلف في الوعد + +269 +00:20:29,150 --> 00:20:33,050 +فبعد الصورة فإذا هي هذه ال statement إيش بدنا + +270 +00:20:33,050 --> 00:20:36,290 +نعمل؟ بدنا ننفيها فإذا اللي هو إيش ممكن نقول ال + +271 +00:20:36,290 --> 00:20:36,590 +denial + +272 +00:20:41,270 --> 00:20:49,130 +فإذا هذه صارت not B then Q أصبحت تكافئ نفي هذه نفي + +273 +00:20:49,130 --> 00:20:57,830 +افتح قص كبير وهي ال if then فيها نفي ل B and not Q + +274 +00:20:59,460 --> 00:21:03,800 +أي سؤال .. اه طبعا .. أي سؤال .. خطوة خطوة .. فإذا + +275 +00:21:03,800 --> 00:21:08,480 +احنا إيش؟ عشان نقدر نبسط اللي هو نفي اللي if then + +276 +00:21:08,480 --> 00:21:12,660 +حولناها ل and عن طريق التعريف .. اه .. الآن هل هذا + +277 +00:21:12,660 --> 00:21:15,980 +ممكن يتبسط؟ نعم، في نفي و نفي، في أنا قاعدة، أنا + +278 +00:21:15,980 --> 00:21:18,700 +في النافي إثبات، فإذا حيضيعوا بعض، فإذا هذا إيش + +279 +00:21:18,700 --> 00:21:25,520 +بيكون كافي؟B and not Q فى ديومورجانز هنا لأ لأ هنا + +280 +00:21:25,520 --> 00:21:28,380 +فى ضياء بعض و انت فى بيت تبسيط أكتر من هيك مافيش + +281 +00:21:28,380 --> 00:21:31,260 +تبسيط أكتر من هيك خلينا نترجمها خلينا نترجمها + +282 +00:21:31,260 --> 00:21:35,140 +باللغة العادية هذه لغة الرموز فخلينا نكتب ال + +283 +00:21:35,140 --> 00:21:44,660 +denial فهذا a useful denial denial + +284 +00:21:44,660 --> 00:21:52,010 +is اه بدنا نشوفهthe number + +285 +00:21:52,010 --> 00:22:03,190 +5.1 is an integer لأنه ما انتفتش and it is not + +286 +00:22:03,190 --> 00:22:03,650 +positive + +287 +00:22:09,800 --> 00:22:13,140 +نقول إن ال statement الأصلي كان true ال denial + +288 +00:22:13,140 --> 00:22:16,980 +false ليش؟ بقول إن هذه is an integer إيش؟ اللي هي + +289 +00:22:16,980 --> 00:22:20,720 +تبقى إشمال هذه false و not positive false and + +290 +00:22:20,720 --> 00:22:29,500 +false false صح مافيش مشاكة أي سؤال فهذه بعض + +291 +00:22:29,500 --> 00:22:32,420 +الأمثلة للتبسيط و نقرب الفكرة و إن شاء الله لما + +292 +00:22:32,420 --> 00:22:36,680 +نستخدمها في الرياضيات بشكل يعني حقيقي و بشكل مفيد + +293 +00:22:36,680 --> 00:22:42,790 +هنشوف هذا الكلام نرجعله فضلإنه لما انت عايز تتصيب + +294 +00:22:42,790 --> 00:22:46,570 +ال record ده إنه P نفيه و بعدين نفتح ال course و P + +295 +00:22:46,570 --> 00:22:49,970 +نفتح ال course تمام؟ اه P نفتح ال course صحيح مثلا + +296 +00:22:49,970 --> 00:22:53,370 +بيفعله مش بس هذلك مثلا إنها نفتح ال course و خلاص + +297 +00:22:53,370 --> 00:22:56,930 +بينفع بس احنا الحقيقة يمكنها تقيله بعض الفواد لأ + +298 +00:22:56,930 --> 00:23:01,310 +هي تكافئة ممكن ممكن تتبخ عليها ال demarganes و + +299 +00:23:01,310 --> 00:23:06,930 +تبصيها لأ مانع لأ مانع خلاصنا + +300 +00:23:07,560 --> 00:23:11,220 +تمام إذا نرجع الآن للقواعد مرة تانية بعد ما شوفنا + +301 +00:23:11,220 --> 00:23:15,880 +اللي هي كيف إنه نبسط النفي حتى نحصل على صيغ أكثر + +302 +00:23:15,880 --> 00:23:20,420 +فائدة أو أكتر بساطة للاستخدام نرجع للقواعد النظرية + +303 +00:23:20,420 --> 00:23:25,430 +رقم أربع في شتر واحد نشوف بعض القوانينطبعا زي ما + +304 +00:23:25,430 --> 00:23:30,890 +اتعلمنا اول statement فيها تمهيد للنظرية الهدف منه + +305 +00:23:30,890 --> 00:23:33,970 +انه يقول لي انا في هذه النظرية حسخني بعض الرموز + +306 +00:23:33,970 --> 00:23:37,670 +هذه الرموز ليهاشف ترمز على statements فبقول لي let + +307 +00:23:37,670 --> 00:23:42,070 +b, q and r be an statement اذا ايش بفهم هذا ال + +308 +00:23:42,070 --> 00:23:46,430 +statement ان اي قانون حطبه في هذه النظرية بينطبق + +309 +00:23:46,430 --> 00:23:50,030 +على اي statements b, q, r في سؤال فضل + +310 +00:23:52,740 --> 00:23:57,700 +لأن هي P and not Q فانا نفيت ال not Q وما نفيتش ال + +311 +00:23:57,700 --> 00:24:07,480 +P واضح؟ P زي ما هي و ال Q انتفت not Q واضح؟ فهي + +312 +00:24:07,480 --> 00:24:10,480 +إيش إيش ال statement وصلت في الآخر P and not Q إيش + +313 +00:24:10,480 --> 00:24:17,460 +هي ال P؟ 5.1 is an integer منفية؟ لأ طيب Q منفية + +314 +00:24:17,460 --> 00:24:21,520 +ف5.1 is positive إيش نفيها؟ is not positive لأنها + +315 +00:24:21,520 --> 00:24:26,130 +بسيطةواضحة؟ فهذه اللي فيها نافي نافي نافي ولي + +316 +00:24:26,130 --> 00:24:29,350 +مافياش نافي زي ما هي فإن هذه المقدمة كالعادية then + +317 +00:24:29,350 --> 00:24:34,010 +هيبدأ يدّينا القوانين القانون الأول associative + +318 +00:24:34,010 --> 00:24:39,470 +laws قوانين التجميع قوانين التجميع قوانين التجميع + +319 +00:24:39,470 --> 00:24:42,710 +مهمة جدا في الرياضيات و بتتطبق في كتير من العمليات + +320 +00:24:42,710 --> 00:24:48,470 +من أهمية هذه القوانين أنها بتفتح لنا الباب لعملية + +321 +00:24:48,470 --> 00:24:54,330 +ما بتتعرف علىجزئين إنها تبدأ تتعرف على تلت أيزاء و + +322 +00:24:54,330 --> 00:24:58,150 +فأكثر تلت أيزاء فأكثر فإحنا لو شفنا اتذكرنا احنا + +323 +00:24:58,150 --> 00:25:00,710 +عرفنا ال and و ال or على two statements طب لو في + +324 +00:25:00,710 --> 00:25:03,550 +عندي بدي أربط ال three statements ب and كيف بدي + +325 +00:25:03,550 --> 00:25:06,650 +أتعامل معهم فهنا بدخل إيش ال associative law لما + +326 +00:25:06,650 --> 00:25:10,050 +يكون عندي b و q و r و بدي أدخل عليهم الآن كيف + +327 +00:25:10,050 --> 00:25:14,660 +أتعامل معهمكيف أتعامل معهم فلو أنا عندي هاي B و هي + +328 +00:25:14,660 --> 00:25:18,460 +عندي Q و هي عندي R بدي أعمل بينهم and طب ده حد + +329 +00:25:18,460 --> 00:25:21,900 +أحسب إيش؟ بدي أحسب قيمة الصدق أه هو عرفنا ال and + +330 +00:25:21,900 --> 00:25:24,380 +ده اتنين طب كيف بدي أعمل على تلاتة؟ فبقول عشان + +331 +00:25:24,380 --> 00:25:27,960 +تحسب قيمة الصدق إيش ممكن تعمل؟ ممكن تاخد ال B و ال + +332 +00:25:27,960 --> 00:25:31,780 +Q مع بعض و تشوف قيمة الصدق و الناتج مع ال R أو خد + +333 +00:25:31,780 --> 00:25:34,700 +ال Q و ال R مع بعض و الناتج مع ال B إيش النتيجة؟ + +334 +00:25:34,700 --> 00:25:38,190 +في فرق؟ بقول لي مافيش فرق هذا هو التجميعهذه خاصية + +335 +00:25:38,190 --> 00:25:41,630 +التجميع فخاصية التجميع بيميزها إن أنا فيها عندي + +336 +00:25:41,630 --> 00:25:46,450 +عملية من نفس الجنس متكررة أنا عندي إيش؟ and مرتين + +337 +00:25:46,450 --> 00:25:49,870 +كيف أشتر عليها؟ بقوللي ما أنت حر ابدأ من الأول + +338 +00:25:49,870 --> 00:25:53,250 +والتاني والنتج مع التالت أو التاني مع التالت + +339 +00:25:53,250 --> 00:25:58,010 +والنتج مع الأول أي سيئة والار نفس الشيء والار نفس + +340 +00:25:58,010 --> 00:26:02,330 +الـJ الشيء أديكم مثال من الحياة ممكن يثبت العملية + +341 +00:26:02,840 --> 00:26:06,260 +لو احنا عندنا إيش؟ في عندنا جلباب الخياط عامل + +342 +00:26:06,260 --> 00:26:10,160 +الجزء الأساسي منه، خيطه، خيط لكمام، كل كم بخيطه + +343 +00:26:10,160 --> 00:26:13,620 +لحال، اللي عنده خبرة خياطة شوية، تمام؟ الآن بده + +344 +00:26:13,620 --> 00:26:17,860 +يجمحهم مع بعض، بده يجمحهم مع بعض، إذا جمع الكم + +345 +00:26:17,860 --> 00:26:21,620 +اليمين مع الجلباب، اللي هو ال body الأساسي + +346 +00:26:21,620 --> 00:26:25,760 +للجلباب، وبعدين جمع الكم الشمال أو العكس سيان، ودي + +347 +00:26:25,760 --> 00:26:29,450 +نفس الشيءفنفس الشيء فانا بدي أجمع تلات أجزاء صحراء + +348 +00:26:29,450 --> 00:26:34,990 +الجلباب فبده القم اللي هو جسم الجلباب و بعدين القم + +349 +00:26:34,990 --> 00:26:37,370 +اليمين أو الشمال كله سيام و نطلع في الآخر الجلباب + +350 +00:26:37,370 --> 00:26:41,750 +كامل فهو علينا نفس العملية فكمثال يقربلنا الصورة و + +351 +00:26:41,750 --> 00:26:45,320 +ال R و ال A نفس الشيءهدول هيش قوانين التجميل + +352 +00:26:45,320 --> 00:26:49,540 +associative laws and distributive laws أيضا ال + +353 +00:26:49,540 --> 00:26:54,100 +distributive laws فيها أكتر من عملية بس بيميزها في + +354 +00:26:54,100 --> 00:26:58,640 +ال associative كان عمليتين من نفس الجنس and مع and + +355 +00:26:59,120 --> 00:27:04,240 +و or مع or في التوزيع عمليتين بس من جنسين مختلفين + +356 +00:27:04,240 --> 00:27:07,860 +يا and مع or يا or مع and في التوزيع زي ما احنا + +357 +00:27:07,860 --> 00:27:12,000 +مشهور في الحساب بنوزع الدرب على الجمع بنوزع الدرب + +358 +00:27:12,000 --> 00:27:15,220 +على الجمع لكن بنوزع الجمع على الجمع لأ تجمع بنوزع + +359 +00:27:15,220 --> 00:27:18,640 +الدرب على الدرب لأ تجمع نفس القضية عشان هذا كمثال + +360 +00:27:18,640 --> 00:27:22,250 +متعودين عليه فهو بيقول ليهلو بدك توزع بتوزع زي + +361 +00:27:22,250 --> 00:27:26,030 +الجامعة تماما هذا أسهل شيء ان نقارنه مع الضرب مع + +362 +00:27:26,030 --> 00:27:30,210 +الجامعة هذا ليش ممكن نكتب حاجة مشابهة هي بي بدل + +363 +00:27:30,210 --> 00:27:33,570 +الان خلينا نعملها ضرب و بدل ال or خلينا نعملها + +364 +00:27:33,570 --> 00:27:41,870 +مثلا جامعةاه إيش بتساوي بي ضرب Q زائد بي ضرب R نفس + +365 +00:27:41,870 --> 00:27:46,030 +الشيء أسهل شيء للحفظ أسهل أسهل شيء للحفظ فهذا + +366 +00:27:46,030 --> 00:27:50,730 +بيسموه توزيع فإذا عمليتين من نفس الجنس تجميع + +367 +00:27:50,730 --> 00:28:00,210 +عمليتين من جنسين مختلفين توزيع فضل وين + +368 +00:28:00,210 --> 00:28:05,190 +في التوزيع ولا في ال associative في التوزيعفوق؟ أه + +369 +00:28:05,190 --> 00:28:08,670 +طبعاً بديك تعمل إبدال أنت كمان يعني جات هي إيش + +370 +00:28:08,670 --> 00:28:11,310 +بديك تعمل إبدال بيكون عملت عمليتين مع بعض فانا بحط + +371 +00:28:11,310 --> 00:28:14,310 +بس العمليات البسيطة أنا بتعرف القوانين دايما لما + +372 +00:28:14,310 --> 00:28:17,370 +نحن عارف قانون بنحطه في أبسط حالته بعدين عيني عيني + +373 +00:28:17,370 --> 00:28:20,050 +دي أكتر من قانون ممكن أستخدمهم مع بعض؟ ممكن بس أنت + +374 +00:28:20,050 --> 00:28:22,830 +عملية مركبة صرا أه لكن احنا بنحط دايما القاعدة + +375 +00:28:22,830 --> 00:28:26,050 +البسيطة و ممكن نعمل عمليتين مع بعض و تلات عمليات + +376 +00:28:26,050 --> 00:28:30,570 +هدشية مفتوح طول العمليات إيش و القواعد صحية أي + +377 +00:28:30,570 --> 00:28:36,010 +سؤال؟القانون التالت في هذه النظرية الـ Transitive + +378 +00:28:36,010 --> 00:28:40,450 +law قانون التعدى قانون التعدى بيقول إذا في عندي + +379 +00:28:40,450 --> 00:28:44,830 +two statements إيش conditional statement شرطيتين + +380 +00:28:44,830 --> 00:28:50,430 +شرط الأولى بعدين إيش الجواب الـ Q وجواب التانية هو + +381 +00:28:50,430 --> 00:28:55,720 +شرط الأولى هو .. أسفجواب الأولى شرط للتانية جواب + +382 +00:28:55,720 --> 00:29:00,560 +الأولى Q شرط للتانية Q then R فإيش النتيجة؟ بروح + +383 +00:29:00,560 --> 00:29:04,260 +من شرط الأولى إلى نتيجة التانية إلى نتيجة التانية + +384 +00:29:04,260 --> 00:29:07,700 +فهو هذا Transitive طبعا القانون هنا طبعا بدنا نحفظ + +385 +00:29:07,700 --> 00:29:10,640 +القوانين زي ما قولنا بالظبط دول كلهم تكافئوا اللي + +386 +00:29:10,640 --> 00:29:14,180 +فوق اللي تحت implications يعني اتجاه صح اتجاه + +387 +00:29:14,180 --> 00:29:17,200 +التاني بكون مش صحيح في الغالب لأنه كان حطوا تكافئ + +388 +00:29:17,200 --> 00:29:21,630 +هذا تعليقبرضه عشان خلينا نجيب برضه مثال قريب و + +389 +00:29:21,630 --> 00:29:24,850 +يمكن .. المثال يمكن بتسمعه فيه Transitive بتسمعه + +390 +00:29:24,850 --> 00:29:27,990 +اللي هو طيران ترانزيت أو سفر ترانزيت تمام؟ على إيش + +391 +00:29:27,990 --> 00:29:32,210 +ترانزيت؟ الواحد بيقول مثلا هدف و مطار اللي هو ألف + +392 +00:29:32,210 --> 00:29:36,170 +بنزل في با مؤقتا و بعدين بيكمل الألف او مثلا يمكن + +393 +00:29:36,170 --> 00:29:39,330 +هلجت موسم الحجاج الحجاج تعقبوا أنه لما طلعوا على + +394 +00:29:39,330 --> 00:29:43,150 +مكة مروا من قاهرة ترانزيت ولا لأ؟ فهي ترانزيت + +395 +00:29:43,150 --> 00:29:47,590 +راحوا من غزة B إلى القاهرة Q Cairo و بعدين من + +396 +00:29:47,590 --> 00:29:50,810 +Cairo إلى مكةمكة، فإيش هو يقولوا أصلهم؟ أيش هدفهم + +397 +00:29:50,810 --> 00:29:54,710 +الرئيسي؟ مكة، فهي من إيش؟ من بي ل آر، من غزة ل + +398 +00:29:54,710 --> 00:29:58,350 +مكة، لكن ماروح بالقاهرة transit فهي transitive + +399 +00:29:58,350 --> 00:30:04,370 +اللي ماحنقولهاش transit، قانون تعدى، إيش قاعدة + +400 +00:30:04,370 --> 00:30:08,720 +السلسلة؟ للتفاضل المختلفةمختلفة مش بالظبط هذه + +401 +00:30:08,720 --> 00:30:12,680 +خاصية التعدى هذه خاصية التعدى انه انا ايش بي تؤدي + +402 +00:30:12,680 --> 00:30:17,040 +الى Q و Q تؤدي الى R فإذا بي وصلت لمين لل R وصلت ل + +403 +00:30:17,040 --> 00:30:21,060 +R هي أسهل شيء محطة اه انت بدك تروح الى مكة بتروح + +404 +00:30:21,060 --> 00:30:23,420 +الى القاهرة أو القاهرة في طريق .. يعني في طيارات + +405 +00:30:23,420 --> 00:30:27,800 +أو في طريق من غزة لمصر وفي طريق من مصر للسعودية + +406 +00:30:27,800 --> 00:30:30,820 +فبتوصل ممكنش تروحي مباشرة كأنك بتروح عن طريق محطة + +407 +00:30:30,820 --> 00:30:34,000 +تالتة لكن الهدف الرئيسي ايش هو النهاية التالتة + +408 +00:30:34,500 --> 00:30:37,180 +خلّيني أبرهن واحدة منهم لإن ممكن ماديناش مثال على + +409 +00:30:37,180 --> 00:30:41,500 +تلاتة statements نعمل مين؟ الأخيرة .. الأخيرة + +410 +00:30:41,500 --> 00:30:45,040 +خلّيني + +411 +00:30:45,040 --> 00:30:48,880 +أحل هنا عشان بدنا أوسع .. ممكن نبدأ الحل من هنا و + +412 +00:30:48,880 --> 00:30:52,320 +بعدين نعمل جدول هناك في المكان الواسع فهذه نظرية + +413 +00:30:52,320 --> 00:31:01,260 +.. فهذه نظرية 14 proof وهذا يزوء ايش؟ C .. يزوء C + +414 +00:31:02,810 --> 00:31:06,850 +تمام ال statement اللي مطلوب اثباتها هي + +415 +00:31:06,850 --> 00:31:11,130 +implication تضمين كي بتأثبت التضمين؟ إيش معناه إيه + +416 +00:31:11,130 --> 00:31:14,090 +أثبت التضمين؟ إنه أثبت الجمهور الجملة الشرطية ناشر + +417 +00:31:14,090 --> 00:31:17,510 +إنها tautology إنها tautology إذا خدناها نكتب we + +418 +00:31:17,510 --> 00:31:24,610 +want to prove أو to show نفس الشيء that the + +419 +00:31:24,610 --> 00:31:25,210 +statement + +420 +00:31:30,540 --> 00:31:34,120 +خلّيني لأغراض أخرى أعطيها و أوضحها بتدرمز لها + +421 +00:31:34,120 --> 00:31:37,680 +بالرمز capital Q وهي تكافئ بتدرمز لهذه ال + +422 +00:31:37,680 --> 00:31:40,340 +statement أنا طويل أبدوش أتمنى أنجل كتابتها أعملها + +423 +00:31:40,340 --> 00:31:48,640 +capital Q ليمين ب and ايه أسف ب then q if b then q + +424 +00:31:48,640 --> 00:31:58,370 +andFQ then R اشمالها ايه ايه + +425 +00:31:58,370 --> 00:32:00,910 +اشمالها ايه اشمالها ايه اشمالها ايه اشمالها ايه + +426 +00:32:00,910 --> 00:32:01,130 +اشمالها ايه اشمالها ايه اشمالها ايه اشمالها + +427 +00:32:01,130 --> 00:32:01,390 +اشمالها اشمالها اشمالها اشمالها اشمالها اشمالها + +428 +00:32:01,390 --> 00:32:01,430 +اشمالها اشمالها اشمالها اشمالها اشمالها اشمالها + +429 +00:32:01,430 --> 00:32:01,890 +اشمالها اشمالها اشمالها اشمالها اشمالها اشمالها + +430 +00:32:01,890 --> 00:32:05,750 +اشمالها اشمالها اشمالها اشمالها اشمالها اشمهذا هو + +431 +00:32:05,750 --> 00:32:09,350 +المطلوب فاحنا بدنا نثبت أن هذا ال statement تتولجى + +432 +00:32:09,350 --> 00:32:11,810 +عشان مانديش اكتب عشان انا طويل ابدأ اوضع ال Q فجيت + +433 +00:32:11,810 --> 00:32:14,270 +قول مكتوبة كابتنال Q ايش ترمز لل statement هذا + +434 +00:32:14,270 --> 00:32:16,990 +نثبت ان انا تتولجى كيف؟ فاحنا ايش زي ما اتعلمنا + +435 +00:32:16,990 --> 00:32:20,130 +كيف بنحل المسائل؟ بنعيش .. بنفهم السؤال، بنعيد + +436 +00:32:20,130 --> 00:32:23,250 +صياخته، بنحطه بصورة مناسبة خطوة تانية بدنا القدرة، + +437 +00:32:23,250 --> 00:32:26,910 +طريقة، ماهي طريقة الحل؟ truth table، by truth + +438 +00:32:26,910 --> 00:32:33,840 +tableby the truth table او تقنص بتدول الصدق نبدأ + +439 +00:32:33,840 --> 00:32:39,660 +عملية الحل خلّيني أحل هنا فالآن عشان ايكون جدول + +440 +00:32:39,660 --> 00:32:44,860 +الصدق من أمور سهلة جدا باطلع أكمل statement أساسية + +441 +00:32:44,860 --> 00:32:49,040 +في الجملة تلاتة اذا بدنا جدول تلت أعمدة رئيسية وكم + +442 +00:32:49,040 --> 00:32:53,120 +احتمال تمانية اتنين او ثلاثة تمانية فخلّيني اعمل + +443 +00:32:53,120 --> 00:33:01,120 +جدول أتوقع ان شاء الله هيك بيكفيفعنا بي وعنا كيو + +444 +00:33:01,120 --> 00:33:06,320 +أساسيين وعنا ار تلت statement تلت أعمد رئيسية وفي + +445 +00:33:06,320 --> 00:33:13,090 +عنا تمان احتمالات ننصفوالنصف هنا و النصف الرابعة + +446 +00:33:13,090 --> 00:33:18,110 +نصف التاني و بعدين برضه كل جزء نصفه فهيك و نكون + +447 +00:33:18,110 --> 00:33:21,630 +حصلنا على تمان أجزاء واحد اتنين تلاتة أربعة خمسة + +448 +00:33:21,630 --> 00:33:25,550 +ستة سبعة تمانية طبعا بنبدأ .. اه .. بنبدأ دايما + +449 +00:33:25,550 --> 00:33:29,410 +العمود الأول بنجسمه نصين النص الأول true فعنا + +450 +00:33:29,410 --> 00:33:32,390 +تمانية هيكون أربعة true و بعدين التانين الأربعة + +451 +00:33:32,390 --> 00:33:36,760 +الأخرين falseيعني بعدين في العمود التاني ماببدأيش + +452 +00:33:36,760 --> 00:33:40,380 +نصف العملية بالعكس فالجيت هنا هناخد نصين كل نص + +453 +00:33:40,380 --> 00:33:44,540 +هنجسمله نصين ف true true false false و النصف + +454 +00:33:44,540 --> 00:33:48,760 +التاني بنفس الإسلوب true true false false العمود + +455 +00:33:48,760 --> 00:33:53,000 +التالت الآن بننصف عايش اللي جابله فإن true true + +456 +00:33:53,000 --> 00:33:58,260 +بيصير true false true false true false true false + +457 +00:33:58,900 --> 00:34:02,120 +أى سؤال فهذه الطريقة جد ما يكونوا تلات نين و + +458 +00:34:02,120 --> 00:34:05,340 +اتعلمنا تلاتة هيك و لو أربع نفس القضية بجسمه بيصير + +459 +00:34:05,340 --> 00:34:08,620 +ستة عشر تمانية الأول تمانية true تمانية false اللي + +460 +00:34:08,620 --> 00:34:12,800 +بعده أربعة أربعة أربعة أربع أربعات و هكذا التقسيم + +461 +00:34:12,800 --> 00:34:15,880 +بهذه الصورة فإذا احنا عايش نكون بننصف و بعدين ايش + +462 +00:34:15,880 --> 00:34:20,100 +أربع أقسام بنقسم و بعدين أيش تمان أقسام و هكذاأي + +463 +00:34:20,100 --> 00:34:24,400 +سؤال نبدأ بدنا نحسب في عندنا P then Q و Q then R و + +464 +00:34:24,400 --> 00:34:30,800 +P then R تلت جوبة شرطية بسيطة if P then Q و if Q + +465 +00:34:30,800 --> 00:34:36,760 +then R و if P then R و بعد هيك في عندنا الـQ كلها + +466 +00:34:36,760 --> 00:34:38,720 +فعشان هيك أنا حطت الرمز بدنا مكتوبة كلها مايصيحش + +467 +00:34:38,720 --> 00:34:45,810 +العمود بحط Q الآن بكون خلاصةفي N صحيح و هذا بي .. + +468 +00:34:45,810 --> 00:34:52,530 +أدعى أني أحط Q بعدين مش هتم وسع فعندي B then Q and + +469 +00:34:52,530 --> 00:34:59,990 +Q then R و بعدين Q فهذه طريقة إذا في statement + +470 +00:34:59,990 --> 00:35:03,690 +طويلة ممكن نحملها رمز عشان الوسع و نقدر نعمل + +471 +00:35:03,690 --> 00:35:07,710 +الجدول فنبدأ في العملية حساب قيام الصدق نبدأ + +472 +00:35:07,710 --> 00:35:12,670 +بالأولى هذه مع هذهtrue than true true true than + +473 +00:35:12,670 --> 00:35:16,990 +true true true than false false true than false + +474 +00:35:16,990 --> 00:35:20,190 +false الباقي كله true لأنه مافيش وعد مافيش شرط + +475 +00:35:20,190 --> 00:35:26,050 +false عطول بسهولة الآن خلصنا من الأولى نيجي + +476 +00:35:26,050 --> 00:35:32,540 +للتانية اللى هى ايش q then a هدى مع هدىالـ True ثم + +477 +00:35:32,540 --> 00:35:35,880 +الـ True، الـ True ثم الـ False، الـ False، الـ + +478 +00:35:35,880 --> 00:35:39,040 +False ثم الـ True، الـ True، الـ False ثم الـ + +479 +00:35:39,040 --> 00:35:42,800 +False، الـ True، الـ True ثم الـ True، الـ True ثم + +480 +00:35:42,800 --> 00:35:48,000 +الـ False، الـ False ثم الـ True، الـ True طبعا + +481 +00:35:48,000 --> 00:35:53,760 +عملية سهلة وبسيطة، الآن الـ B مع الـ Rأه true then + +482 +00:35:53,760 --> 00:35:58,760 +true true true false false true true true true + +483 +00:35:58,760 --> 00:36:02,800 +false false الباقى كله true لما اللي بيكون false + +484 +00:36:02,800 --> 00:36:07,860 +مافيش مشاكل أطلع أه الأن الأن بدنا mean هادي و + +485 +00:36:07,860 --> 00:36:13,380 +هادي هادي و هادي true و true true true false false + +486 +00:36:13,380 --> 00:36:18,520 +false true false false true false true true true + +487 +00:36:18,520 --> 00:36:26,060 +true false false true trueفهذا العمود قبل الأخير + +488 +00:36:26,060 --> 00:36:29,920 +لأن العمود الأخير هو الأهم بدنا اللي هو f اللي هو + +489 +00:36:29,920 --> 00:36:36,580 +ال b implies مين بيها فهذه مع هذه وسهم بالعكس بدنا + +490 +00:36:36,580 --> 00:36:42,690 +ننتبهtrue than true true false than true true + +491 +00:36:42,690 --> 00:36:47,330 +false فش مشكلة false فش مشكلة true انتبه بدنا + +492 +00:36:47,330 --> 00:36:50,750 +دايما دايما الجملة الشرطية إذا كانت الأول true + +493 +00:36:50,750 --> 00:36:53,610 +انتبهوا بدوا انتباه بدوا تدقيق إذا الأول false + +494 +00:36:53,610 --> 00:36:56,550 +خلاص على طول بنتطلعش على التاني ف true than true + +495 +00:36:56,550 --> 00:37:00,530 +true false فش مشاكل true true بنتطلع على التاني + +496 +00:37:00,530 --> 00:37:04,530 +true true true ففعلا كله true فده بيدل على ان ال Q + +497 +00:37:04,530 --> 00:37:07,630 +is datalogic وبالتالي الكلام صحي + +498 +00:37:10,500 --> 00:37:11,820 +So from the table, + +499 +00:37:16,080 --> 00:37:19,680 +we see + +500 +00:37:19,680 --> 00:37:24,960 +that if we say Q is a tautology, or if we say B + +501 +00:37:24,960 --> 00:37:36,760 +then Q and FQ then R implies FB then R. فهذا يعني + +502 +00:37:36,760 --> 00:37:44,680 +ما نريده هو F.أي سؤال فجدول الصدق فعلا سهله بهذا + +503 +00:37:44,680 --> 00:37:50,540 +الشكل إذا إتبعنا هذه الخطوات و هذه القواعد فإن شاء + +504 +00:37:50,540 --> 00:37:57,480 +الله بنقدر نعمل جدول صدق لأي استثناء نظرية + +505 +00:37:57,480 --> 00:38:02,950 +أخرى الخامسةالنظرية الخامسة في هذا الـ chapter + +506 +00:38:02,950 --> 00:38:07,650 +الآن على نفس المنهج، على نفس الطريقة، بس الآن فيه + +507 +00:38:07,650 --> 00:38:11,630 +أربع statements، هيستخدم القوانين أربع statements + +508 +00:38:11,630 --> 00:38:17,090 +بي كيو آر أس، هنرمزلهم، آه، فعنا بعض القواعد + +509 +00:38:19,050 --> 00:38:27,150 +القاعدة الأولى اسمها constructive dilemmas معضلات + +510 +00:38:27,150 --> 00:38:32,810 +بناء او معضلات + +511 +00:38:32,810 --> 00:38:37,950 +مثبتة او إيجابية بناء او إيجابي constructive + +512 +00:38:37,950 --> 00:38:46,290 +dilemma معضلات بناء او إيجابيةطبعا إيجابية لأن + +513 +00:38:46,290 --> 00:38:50,790 +فيها إثبات كله إثبات هنشوف واحدة اللي هي الهدامة + +514 +00:38:50,790 --> 00:38:53,530 +اللي فيها نفت بيادة المعنى المستخدمين المصطلح فهنا + +515 +00:38:53,530 --> 00:38:56,750 +بناها لأنه كله إثبات فطبعا اللي هنا قانون شوية + +516 +00:38:56,750 --> 00:39:02,550 +طويل في عندي جملتين شرطيتينمستقلتين عن بعض if B + +517 +00:39:02,550 --> 00:39:06,930 +then Q و if R then S تعرفوا إيش كانت؟ في حاجة + +518 +00:39:06,930 --> 00:39:10,490 +مشتركة بينهم جواب الأولى هو شرط التانية فصار + +519 +00:39:10,490 --> 00:39:13,910 +Transitive لكن الآن مستقلين عن بعض مستقلين عن + +520 +00:39:13,910 --> 00:39:17,890 +البعض الـB تؤدي للـQ و الـR تؤدي للـS إيش بقول + +521 +00:39:17,890 --> 00:39:21,890 +نتيجة؟ إذا أخدت الشرط الأول أو الشرط التاني بوصل + +522 +00:39:21,890 --> 00:39:25,670 +للنتيجة الأولى أو النتيجة التانية، هيك معناهافعندي + +523 +00:39:25,670 --> 00:39:30,390 +جملتين شرطيتين إذا الشرط الأول اتحقق بوصل لتاني أو + +524 +00:39:30,390 --> 00:39:33,570 +إذا الشرط التاني اتحقق بوصل لتاني فواحدة منهم + +525 +00:39:33,570 --> 00:39:36,770 +بيكون صحيحة فايق بالصحيحة فهي هياش بال ا فهو بيقول + +526 +00:39:36,770 --> 00:39:40,090 +ليه بيعدى الشكل implies طبعا مش تكافؤ فبقول ليه + +527 +00:39:40,090 --> 00:39:46,310 +اللي P then Q and R then S تؤدي أنه P or R تؤدي + +528 +00:39:46,310 --> 00:39:51,570 +إلى Q or S نفس القضية برضه ممكن أخد معاهم إيه and + +529 +00:39:51,570 --> 00:39:56,730 +بس أختلف الوضع هناهنا أخدت مين؟ الشرطين مع بعض + +530 +00:39:56,730 --> 00:40:01,250 +والجوابين مع بعض وبينهم or في التانية أخدت شرط + +531 +00:40:01,250 --> 00:40:04,550 +الأولى مع أيش؟ برضه الشرطين برضه الشرطين نفس الشيء + +532 +00:40:04,550 --> 00:40:08,450 +شرطين مع الجوابين بس مرة and ومرة or فدولة بيسموهم + +533 +00:40:08,450 --> 00:40:14,520 +constructive dilemmas قواعد اللي هو معضلات بناءفي + +534 +00:40:14,520 --> 00:40:19,800 +destructive dilemmas معضلات هدامة يعني إذا قولنا + +535 +00:40:19,800 --> 00:40:26,160 +بناءة أو إيجابية أو مثبتة هنا نافية لأن هنا في + +536 +00:40:26,160 --> 00:40:30,820 +نافية هنا في عملية نافية نفس الأشياءالطرف اليمين + +537 +00:40:30,820 --> 00:40:34,600 +نفسه زي اللي فوق، بس الاستنتاج فيه نفي، الاستنتاج + +538 +00:40:34,600 --> 00:40:39,760 +فيه نفي، اه فطبعا هنا الحقيقة هي عملية ليست الا + +539 +00:40:39,760 --> 00:40:43,420 +اللي هو contrapositive للي فوق، فاللي تحت هو + +540 +00:40:43,420 --> 00:40:46,100 +contrapositive للي فوق في الاستنتاج، اه فطبعا لو + +541 +00:40:46,100 --> 00:40:50,750 +بدي انا ايش ال contrapositive لهذه، نفي هذهبيقدّي + +542 +00:40:50,750 --> 00:40:54,630 +لنافية هذه طب نفلة هذه الشوة هيو ال or صارت and مع + +543 +00:40:54,630 --> 00:40:58,490 +نفلة و التانية نفس العكس بس و العكس فدولة بيسموهم + +544 +00:40:58,490 --> 00:41:02,370 +constructive dilemmas و destructive dilemmas طبعا + +545 +00:41:02,370 --> 00:41:05,690 +البرهان هنا في عندنا كام statement أساسية أربعة + +546 +00:41:05,690 --> 00:41:10,180 +نحتاج اتنين اقصى اربعة ستة عشر احتمال ستة عشرست + +547 +00:41:10,180 --> 00:41:15,300 +عشر احتمال اه طبعا مافيش حاجة جديدة فانا هتركهم + +548 +00:41:15,300 --> 00:41:19,200 +كلهم exercise لأنه بس مجرد عملية وقت يعني مش صعبة + +549 +00:41:19,200 --> 00:41:23,100 +لكن طويلة شوية لكن القواعد نفس الشيء فجيد انه + +550 +00:41:23,100 --> 00:41:26,720 +نعملها عشان نتمكن من عملية مين اللي هو ال truth + +551 +00:41:26,720 --> 00:41:29,460 +table و اللي يكون هذا اكتر شيء ممكن يكون مراهنة في + +552 +00:41:29,460 --> 00:41:34,540 +المصادر اربعة من ال statements المستقلين ف ال + +553 +00:41:34,540 --> 00:41:42,010 +proof كله هتركه exercise نظرية السادسةهنا two + +554 +00:41:42,010 --> 00:41:46,110 +statements نبيع let P and Q be any two statements، + +555 +00:41:46,110 --> 00:41:52,260 +إيش فينا قوانين؟ أه هنا فينا قانون مهممهم جدا، + +556 +00:41:52,260 --> 00:41:58,060 +هنعتمد عليه كثيرا في البراهين Modus Bonens Modus + +557 +00:41:58,060 --> 00:42:01,740 +Bonens طبعا مش English اللغة مش عارف اللي هي غالب + +558 +00:42:01,740 --> 00:42:05,440 +لاتيني او كذا المصطلح طبعا إيش ممكن نترجمها اللغة + +559 +00:42:05,440 --> 00:42:08,160 +الإنجليزية إيش تعني؟ بقول the way that affirms by + +560 +00:42:08,160 --> 00:42:12,600 +affirming الإثبات بالإثبات، الإثبات بالإثبات مر + +561 +00:42:12,600 --> 00:42:15,580 +علينا حاجة إيش اللي هو إيش؟ الإثبات بالنفي أو نفي + +562 +00:42:15,580 --> 00:42:18,420 +بالإثبات واحدة منها، فهذه إيش؟ الإثبات بالإثبات + +563 +00:42:18,710 --> 00:42:22,590 +that affirms by affirming ممكن نعمل اثبات بالاثبات + +564 +00:42:22,590 --> 00:42:25,810 +طيب نشوف احنا ده بس مجرد اسم القانون طب ايش + +565 +00:42:25,810 --> 00:42:30,850 +القانون بيقول انا في عندي جملة شرطية if b then q و + +566 +00:42:30,850 --> 00:42:36,010 +ال b صحيحة لازم ال q تكون صحيحة بمعنى اخر اذا وعدت + +567 +00:42:36,010 --> 00:42:40,400 +او في بالوعدو نفس القضية، إذا بدك توعد، بدك توفر + +568 +00:42:40,400 --> 00:42:42,500 +بقى، لازم الـQ تكون صحيحة، لازم يؤدي إلى الـQ، + +569 +00:42:42,500 --> 00:42:46,300 +فإذا كان عندي أنا، في عندي قاعدة B تؤدي إلى الـQ، + +570 +00:42:46,300 --> 00:42:48,960 +إذا الـB صحيحة، لازم الـQ تكون صحيحة، و إلا فيه + +571 +00:42:48,960 --> 00:42:51,700 +مشكلة و لا لأ؟ آه، فبقولي أنا في عندي قاعدة FB + +572 +00:42:51,700 --> 00:42:55,400 +تؤدي إلى الـQ، طب أنا الـB صح اتحققت، لازم الـQ + +573 +00:42:55,400 --> 00:43:00,090 +تتحققفده يسموه الواقعية .. طب ليش إثبات بالإثبات؟ + +574 +00:43:00,090 --> 00:43:04,210 +لأن أنا أثبتت الـQ من الـB أخدت B صحيحة لأن إذا + +575 +00:43:04,210 --> 00:43:07,770 +الـB true فالـQ لازم تكون true فإن أنا إيش؟ أثبتت + +576 +00:43:07,770 --> 00:43:10,670 +الـQ عن طريق إثبات الـB إذا أثبتت الـB بتكون إيش + +577 +00:43:10,670 --> 00:43:14,610 +الـQ صحيحة فالمعنى تبعها ليش الإسم تبعها؟ أو + +578 +00:43:14,610 --> 00:43:17,150 +القاعدة بدا الشكل ممكن أخدها فدي بسموه Modus + +579 +00:43:17,150 --> 00:43:19,910 +Boninus Modus Modus Modus Modus Modus Modus Modus + +580 +00:43:19,910 --> 00:43:20,270 +Modus Modus Modus Modus Modus Modus Modus Modus + +581 +00:43:20,270 --> 00:43:22,410 +Modus Modus Modus Modus Modus Modus Modus Modus + +582 +00:43:22,410 --> 00:43:28,690 +Modus Modus Modus Modus Modus Modus Modusthe way + +583 +00:43:28,690 --> 00:43:34,030 +that denies by denying النفي بالنفي النفي بالنفي + +584 +00:43:34,030 --> 00:43:39,370 +فنفس الشيء برضه جملة شرطية إذا بتكاس توفي بالواعد + +585 +00:43:39,370 --> 00:43:44,670 +توعدشnot the Q عشان اثبت ان ال B انها false فبتبت + +586 +00:43:44,670 --> 00:43:47,830 +بي ليه ال true فإذا ال B false not B is true ف B + +587 +00:43:47,830 --> 00:43:51,230 +is false فبتكوناش not the Q اه فإذا كانت اللي + +588 +00:43:51,230 --> 00:43:54,850 +وقعتش نفي نفينا اللي هو ال B عن طريق انه ليهاش + +589 +00:43:54,850 --> 00:43:58,610 +نفينا ال Q فإذا كانت ال Q false مش هتقدر توفي + +590 +00:43:58,610 --> 00:44:03,180 +بالوعد ماتوقعتشأه .. اه .. انت مش جادر توفي بالوعد + +591 +00:44:03,180 --> 00:44:06,680 +متوقع انك ما توفيش بالوعد not Q ال Q of A يعني ال + +592 +00:44:06,680 --> 00:44:11,520 +Q is false ماتوعدش not B .. not B فإذا ال Q false + +593 +00:44:11,520 --> 00:44:15,480 +ال B بيكون false يعني not Q هي ال true واضح فهذا + +594 +00:44:15,480 --> 00:44:19,240 +قانونيا مهمين جدا هنستخدمهم ان شاء الله في + +595 +00:44:19,240 --> 00:44:26,290 +البراهينقانون تالت reduction and absordance برضه + +596 +00:44:26,290 --> 00:44:29,830 +كل هذه مصطلحات ليست لغة انجليزية فنقد النقيد ممكن + +597 +00:44:29,830 --> 00:44:33,490 +نعرفها نقد النقيد .. نقد النقيد .. نشوف ليش نقد + +598 +00:44:33,490 --> 00:44:37,140 +النقيدأه برضه كل التلات قوانين اللي هم علاقة + +599 +00:44:37,140 --> 00:44:39,920 +بالجملة الشرطية وهي الجملة الأكثر انتشارا في + +600 +00:44:39,920 --> 00:44:42,780 +الرياضيات هلاج أن معظم القوانين هنا فيها عايش جملة + +601 +00:44:42,780 --> 00:44:45,680 +شرطية if differentiable then continuous و هكذا + +602 +00:44:45,680 --> 00:44:49,980 +فأمور زي هيك if even divisible by two كتير من + +603 +00:44:49,980 --> 00:44:52,660 +القوانين من التعريفات من النظريات فالجملة الشرطية + +604 +00:44:52,660 --> 00:44:58,140 +مهمة جدا فبقول ليهif B then Q تكافئ الآن مش + +605 +00:44:58,140 --> 00:45:03,660 +implies إذا بدك توعد و تخلف بالوعد يؤدي إلى تناقض + +606 +00:45:03,660 --> 00:45:08,360 +إنك جيبت الشيء أو ضده Q and not Q هل يجتمعان؟ + +607 +00:45:08,360 --> 00:45:11,160 +الشيء أو ضده بيجتمعوا؟ لأ، تناقض، عشان هي تناقض + +608 +00:45:11,160 --> 00:45:15,220 +النقيد، في تناقض هنا، حصلنا على تناقض، فبقولي B + +609 +00:45:15,220 --> 00:45:20,280 +and not Q تؤدي إلى جمع النقيدين مع بعض، بينفعش + +610 +00:45:20,280 --> 00:45:24,240 +نوعد و نخلف بالوعد، هذا تناقض، هذا تناقضفهذا ما + +611 +00:45:24,240 --> 00:45:28,920 +يسمى نقد النقيد، نقد النقيد، فعندك بي and not كيو، + +612 +00:45:28,920 --> 00:45:32,000 +هذا المفروض لايحدث، هذا المفروض لايحدث، لأنه يؤدي + +613 +00:45:32,000 --> 00:45:35,360 +إلى مشكلة، يؤدي إلى تناقض، يعني احنا بالمعنى العام + +614 +00:45:35,360 --> 00:45:38,900 +نقول بيؤدي إلى مشكلة، طبعا المعنى، المنطقى يؤدي + +615 +00:45:38,900 --> 00:45:41,560 +إلى تناقض، إلى إيش؟ إلى تناقض، يعني هذا عمره ما + +616 +00:45:41,560 --> 00:45:45,010 +بتكون صحيحةهذه عمرها ما بتكون صحيحة لأنه دايما + +617 +00:45:45,010 --> 00:45:49,030 +الشيء هو ضده و بينهم and إذا q true فننطق q false + +618 +00:45:49,030 --> 00:45:52,350 +فإذا نقل ال and false إذا ال q false فننطق q true + +619 +00:45:52,350 --> 00:45:56,770 +و ال and بتكون false فهذه بيسموه إيش تناقض فهذه هي + +620 +00:45:56,770 --> 00:46:03,090 +القوانين إذا حابين مافيش وقت خليني أنهي هنا إن شاء + +621 +00:46:03,090 --> 00:46:05,750 +الله المحاضرة القادمة بينكمل + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/xKzVbyXMocI.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/xKzVbyXMocI.srt new file mode 100644 index 0000000000000000000000000000000000000000..5a4b5a7785c3ab5a1b550c09c51b8949705f4fc8 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/xKzVbyXMocI.srt @@ -0,0 +1,2279 @@ +1 +00:00:21,580 --> 00:00:25,940 +بتصل مع الإنترنت 6 واخلنا في المحاضرة النارية + +2 +00:00:25,940 --> 00:00:30,620 +وزينا عند نظرية 5-3 اللي بتذكر أنه إذا كان في + +3 +00:00:30,620 --> 00:00:35,500 +عندنا مجموعة لانهائية X وحتفنا منها عنصر فتمها + +4 +00:00:35,500 --> 00:00:43,440 +لانهائية عرفنا أنه في عندنا الـ Y بتساوي X ناقص الـ + +5 +00:00:43,440 --> 00:00:48,860 +X0 والـ X0 هو عنصر من عناصر الـ X فهذه بنثبت + +6 +00:00:48,860 --> 00:00:51,840 +أنها infinite إذا كانت الـ X infinite في حالة.. من + +7 +00:00:51,840 --> 00:00:54,300 +الحالة طبعًا عشان نعرف دالة عشان إيش الـ Y infinite + +8 +00:00:54,300 --> 00:00:58,380 +إيش معناه؟ هناك دالة one to one F من Y لـ Y تكون + +9 +00:00:58,380 --> 00:01:01,780 +one to one وليست onto فاحنا كلنا لازم ناخد حالتين + +10 +00:01:01,780 --> 00:01:06,480 +لو كانت الـ X0 صورة عنصر من عناصر الـ Y فيها مشكلة + +11 +00:01:06,480 --> 00:01:10,360 +فهذه اشتغلناها لحالة ولو ما كانتش صورة ناخد الـ F + +12 +00:01:10,360 --> 00:01:13,340 +على طول بتساوي G اللي هي الدالة من ولا ويا من X لـ + +13 +00:01:13,340 --> 00:01:20,860 +X احنا في عندنا G من X لـ X الـ G 1 to 1 وليست Onto و + +14 +00:01:20,860 --> 00:01:24,880 +G of X برابر من الـ X فاحنا هنعتمد عليها عشان نعرف + +15 +00:01:24,880 --> 00:01:29,740 +الـ F فكان لابد نفرق بين حالتين لو كانت الـ X Zero + +16 +00:01:29,740 --> 00:01:33,460 +صورة عنصر بينفعش لأن الـ X Zero خارج الـ Y فلو هي + +17 +00:01:33,460 --> 00:01:37,130 +صورة بذا سير إيش خارج الـ Y بينفعش بالنسبة للـ F أه + +18 +00:01:37,130 --> 00:01:40,270 +لو كانت الصورة أخدنا F تساوي U وحلينا المثلة في + +19 +00:01:40,270 --> 00:01:44,010 +المرة الثانية إذا كانت صورة عملنا trick بسيط + +20 +00:01:44,010 --> 00:01:49,910 +وعرفنا الـ F إحنا في الحالة إن هذي X0 تنتمي للـ G of + +21 +00:01:49,910 --> 00:01:56,710 +X هذي Case 2 احنا بنشتغل هنا فعرفنا الـ F من Y لـ Y + +22 +00:01:56,710 --> 00:02:05,280 +by F of X تساوي G of X إذا الـ X لا تساوي A طبعًا + +23 +00:02:05,280 --> 00:02:09,400 +احنا عايشين هذا معناه أن X0 تساوي G of A for some A + +24 +00:02:12,800 --> 00:02:18,300 +تنتمي للـ X وإذا كانت من الـ X بتساوي A أخدناها بـ B + +25 +00:02:18,300 --> 00:02:23,880 +عنصر جديد واخترنا عنصر بـ B بعناية عشان بنفعش أخد + +26 +00:02:23,880 --> 00:02:28,420 +صورة أصلا بتكون صورة أصلا لعنصر آخر لأن لو أخدت + +27 +00:02:28,420 --> 00:02:31,180 +صورة عشوائية ممكن تدايل اتباطل one to one فمن وين + +28 +00:02:31,180 --> 00:02:36,120 +أخدت الـ B أخدت الـ B من هنا أه الـ B تنتمي لـ X + +29 +00:02:36,120 --> 00:02:39,920 +ما عدا الـ G of X صورة ليست صورة بالسابق مش من صور + +30 +00:02:39,920 --> 00:02:43,000 +الـ G الـ B فالآن تحت الـ F تصير صورة إذا كانت أول + +31 +00:02:43,000 --> 00:02:45,400 +مرة تصير صورة الـ B فبأطمنه أن دالة تمها one to + +32 +00:02:45,400 --> 00:02:48,760 +one لأن لو أخد عنصر عشوائي غير الـ B فممكن هذا + +33 +00:02:48,760 --> 00:02:51,680 +العنصر يكون صورة تحت الـ G ولمّا وديه له كمان عنصر + +34 +00:02:51,680 --> 00:02:55,020 +بيصير عنده إيش؟ بيصير صورة لعنصرين وده بيخالف الـ + +35 +00:02:55,020 --> 00:02:57,840 +one to one فاحنا اخترنا مادة شكلها طبعًا بنا نثبت أن + +36 +00:02:57,840 --> 00:03:01,940 +هذه الـ F one to one وليست unto، مظبوط؟ فاحنا أول + +37 +00:03:01,940 --> 00:03:08,240 +شيء G آسف F is one to one وصلنا هنا ولا لأ؟ أه الـ F + +38 +00:03:08,240 --> 00:03:12,940 +is one to one فكعادتنا في برهان الـ one to one ناخد + +39 +00:03:12,940 --> 00:03:20,630 +عنصرين من الـ domain تنتمي للـ Y such that F of X1 + +40 +00:03:20,630 --> 00:03:28,090 +تساوي F of X2 مطلوب أثبت أن X1 تساوي X2 مطلوب نثبت + +41 +00:03:28,090 --> 00:03:31,890 +أن X1 تساوي X2 في حد عنده مشكلة في برهان الـ one to + +42 +00:03:31,890 --> 00:03:35,910 +one بدايته على الأقل بداية بسيطة وبنتعلمها زي ما + +43 +00:03:35,910 --> 00:03:40,950 +اتعلمنا عدة مهارة بدنا نثبت أن X1 تساوي X2 واتعلمنا + +44 +00:03:40,950 --> 00:03:44,290 +أيضًا إذا الدالة معرفة هنستخدم التعريف نلاحظ إن + +45 +00:03:44,290 --> 00:03:48,550 +الدالة معرفة لكن نشملها متعددة القاعدة مرت علينا + +46 +00:03:48,550 --> 00:03:53,070 +هذه الفكرة مرة سابقة هناخدها كم احتمال؟ أربع + +47 +00:03:53,070 --> 00:03:56,770 +احتمالات لأن هنا في تجزيق إذا كان العنصرين مع بعض + +48 +00:03:56,770 --> 00:03:59,930 +في جزء أي احتمالين وإذا كان واحد في جزء وآخر في + +49 +00:03:59,930 --> 00:04:08,330 +الجزء الثاني فهذا يؤدي لو كانت X1 لا تساوي A و + +50 +00:04:08,330 --> 00:04:15,960 +X2 لا تساوي A إيش بيكون التعريف G of X1 وبرضه G of + +51 +00:04:15,960 --> 00:04:21,740 +X2 مظبوط؟ متابعين معاه؟ اه فلو كانوا لو X1 مش A + +52 +00:04:21,740 --> 00:04:25,240 +و X2 مش A وين التعريف؟ بيقول لي إذا كانت الـ X تساوي + +53 +00:04:25,240 --> 00:04:28,520 +إيش التعريف؟ G بيبقى تساوي G ناخد الثاني لو كانوا + +54 +00:04:28,520 --> 00:04:33,340 +الاثنين بيساووا إيه؟ لو كانت X1 تساوي A تساوي X2 إيش + +55 +00:04:33,340 --> 00:04:37,620 +التعريف؟ B إيش التعريف؟ B اه طبعًا إيش بينهم؟ or + +56 +00:04:37,620 --> 00:04:41,940 +لأن احتمالات الآن الاحتمالين اللي تمّوا واحد هيك و + +57 +00:04:41,940 --> 00:04:44,880 +واحد هيك هتقول اثنين من نفس الشيء وقعوا مع بعض من + +58 +00:04:44,880 --> 00:04:51,300 +نفس الجزء الآن or لو كانت X1 لا تساوي A لكن X2 + +59 +00:04:51,300 --> 00:04:56,920 +بتساوي A اللي بتساويش إيش بتكون صورتها؟ G واللي + +60 +00:04:56,920 --> 00:05:04,280 +بتساوي B احتمال الأخير B تساوي G of X2 لو كانت + +61 +00:05:04,280 --> 00:05:07,720 +X1 تساوي A و X2 لا تساوي + +62 +00:05:11,060 --> 00:05:14,740 +متابعين؟ فهدول أربعة احتمالات الحقيقة أن الاحتمال + +63 +00:05:14,740 --> 00:05:18,400 +الثالث والرابع ممكن يدمجهم في احتمال واحد ليش؟ + +64 +00:05:18,400 --> 00:05:21,860 +لأن الـ X1 والـ X2 دي الترتيب ليه مش مهم إيش اختصارهم؟ + +65 +00:05:21,860 --> 00:05:25,340 +إن واحد بيساوي A وواحد لا يساوي A فهم نفس + +66 +00:05:25,340 --> 00:05:29,580 +الاحتمال لكن هناخدهم بالتفصيل التكرار ما فيش منه + +67 +00:05:29,580 --> 00:05:33,560 +ضرر لكن أحيانًا حذف حالة بتكون أساسية ممكن يكون فيه + +68 +00:05:33,560 --> 00:05:36,620 +ضرر طبعًا لكن هم هدول لو حذفنا واحدة فيهم ما بنخسرش + +69 +00:05:36,620 --> 00:05:41,090 +شيء لكن خلينا نعمله تمام وين بدنا نوصل؟ إن X1 تساوي + +70 +00:05:41,090 --> 00:05:46,610 +X2 نبدأ نحلل الحالة الأولى إيش بتقول ليه؟ بتقول X1 + +71 +00:05:46,610 --> 00:05:51,110 +تساوي X2 ليش؟ لأن الـ G one to one لأن الـ G is one + +72 +00:05:51,110 --> 00:05:56,560 +to one والثانية بتقول B تساوي B، عدم إن هي + +73 +00:05:56,560 --> 00:06:00,840 +معروفة لكن أنا عايش بدوّك على X1 تساوي X2، ممكن + +74 +00:06:00,840 --> 00:06:04,860 +أتخلص من B تساوي B أحذفها؟ لا، لأنها دي O لكن + +75 +00:06:04,860 --> 00:06:07,720 +لو دقّقنا إيش معنى هدول، إيش معاهم؟ ما هم تساويين، + +76 +00:06:07,720 --> 00:06:12,760 +X1 تساوي X2 تساوي X2 فبرضه X1 تساوي X2 or بقدر + +77 +00:06:12,760 --> 00:06:17,520 +أستنتج طيب اللي بعده contradiction الثاني الثاني ليش + +78 +00:06:17,520 --> 00:06:22,520 +لأنه لما يقول الـ B صورة يعني الـ B وين في صور الـ G + +79 +00:06:22,520 --> 00:06:25,680 +والـ B من إيش خارج الصور مستحيل لما تقولي الـ B + +80 +00:06:25,680 --> 00:06:29,260 +صورة عنصر ما يعني بالصور والـ B من وين اخترناها + +81 +00:06:29,260 --> 00:06:31,940 +من خارج الصور عشان هيك احنا لما عرفنا الـ F كنا + +82 +00:06:31,940 --> 00:06:35,620 +دقيقين فشوفوا لما نختار صح بنسيب الأمور حتى لو + +83 +00:06:35,620 --> 00:06:38,380 +اختارنا غلط لازم نكتشف الغلط فهذا على طول بيقول الـ + +84 +00:06:38,380 --> 00:06:38,980 +H contradiction + +85 +00:06:42,600 --> 00:06:45,820 +Contradiction ليش؟ لأن الـ B تنتمي لـ X minus + +86 +00:06:45,820 --> 00:06:49,020 +الصورة هي الدليل مش الصورة والثانية برضه + +87 +00:06:49,020 --> 00:06:51,400 +Contradiction زيها ما احنا قلنا زي بعض دول + +88 +00:06:51,400 --> 00:06:55,400 +Contradiction + +89 +00:06:55,400 --> 00:07:00,340 +ليش؟ لأن الـ B برضه تنتمي لـ X ناقص G of X واضح الـ + +90 +00:07:00,340 --> 00:07:03,540 +contradiction ولا في حد مش واضح حاله؟ أه لأنه إيش + +91 +00:07:03,540 --> 00:07:08,240 +معناه أن الـ B تساوي صورة عنصر ما من مجموعة يعني + +92 +00:07:08,240 --> 00:07:13,660 +تقع في مين؟ في صور المجموعة، صورة المجموعة تعريفها + +93 +00:07:13,660 --> 00:07:17,420 +إيش معناه B تنتمي للـ G of X؟ يعني الـ B تساوي صورة + +94 +00:07:17,420 --> 00:07:20,760 +عنصر من الـ G of X أه فلو كانت الـ B تلان الـ X واحد + +95 +00:07:20,760 --> 00:07:24,100 +وين موجودة الـ X واحد دي؟ في الـ X أه B في الـ Y والـ + +96 +00:07:24,100 --> 00:07:26,160 +Y جزء من الـ X بتساويش X زيه فبتديني + +97 +00:07:26,160 --> 00:07:30,110 +contradiction طبعًا الآن B or بي بي P or + +98 +00:07:30,110 --> 00:07:33,770 +contradiction P أو P أو contradiction P فهذا يقضي + +99 +00:07:33,770 --> 00:07:37,010 +أن الـ P هي المين لـ X واحد تساوي X اثنين فهذا يقضي + +100 +00:07:37,010 --> 00:07:40,870 +أن X واحد تساوي X اثنين وهذا يقضي أن الـ F is one + +101 +00:07:40,870 --> 00:07:45,650 +to one فزي ما حكينا يمكن البداية تكون صعبة لكن + +102 +00:07:45,650 --> 00:07:49,550 +هنلاقي أنه كثير من الأفكار بتتكرر معنا فهنا فكرة + +103 +00:07:49,550 --> 00:07:53,030 +أنه ده لما متعددة القاعدة كيف نتعامل معها لما تكون + +104 +00:07:53,030 --> 00:07:56,190 +نسبتنا one to one بيصير في عيننا أربع احتمالات + +105 +00:07:56,190 --> 00:07:59,510 +بشكل تفصيلي ممكن نستغنى عن أحد الاحتمالات ويصيروا + +106 +00:07:59,510 --> 00:08:03,010 +ثلاثة ممكن لكن حتى لو كانوا أربعة طبعًا ما ينفعش + +107 +00:08:03,010 --> 00:08:05,450 +أعمل simplification لأن بينهم or فلازم تكون يا + +108 +00:08:05,450 --> 00:08:10,910 +إما المطلوب وهو X1 أو X2 أو contradiction فهذا + +109 +00:08:10,910 --> 00:08:13,110 +المطلوب الأول نشوف المطلوب الثاني أنه proper + +110 +00:08:13,110 --> 00:08:18,710 +subset ليست onto الـ F خلينا + +111 +00:08:18,710 --> 00:08:25,230 +هذه مؤقتًا إن احنا نحتاجها اثنين F الـ Y proper من + +112 +00:08:25,230 --> 00:08:31,190 +الـ Y فبدنا عنصر موجود في الـ Y وغير موجود في الـ F of + +113 +00:08:31,190 --> 00:08:35,910 +Y خلينا نحسب الـ F of Y نحسب الـ Image عشان نشوف + +114 +00:08:35,910 --> 00:08:40,650 +مين عنصر خارج الـ Image بدنا عنصر خارج الـ Image F + +115 +00:08:40,650 --> 00:08:48,360 +of Y إيش بتساوي؟ F of كيف أحسب الـ image لدالة + +116 +00:08:48,360 --> 00:08:55,200 +متعددة القاعدة كيف نحسب الـ image لدالة متعددة + +117 +00:08:55,200 --> 00:08:58,920 +القاعدة إيش متعددة القاعدة الـ domain مجسم فانا إيش + +118 +00:08:58,920 --> 00:09:03,600 +أعمل أجسم الـ domain أجسم الـ domain هذه الـ Y عبارة + +119 +00:09:03,600 --> 00:09:06,080 +عن أصلا X ناقص X Zero + +120 +00:09:09,940 --> 00:09:14,820 +واحنا التعريف إذا X لا تساوي A لها تعريف وعند الـ + +121 +00:09:14,820 --> 00:09:19,440 +A بتساوي تعريف فانا هجسم الـ domain جزء من غير A والـ + +122 +00:09:19,440 --> 00:09:23,260 +جزء اللي فيه الـ A فدي كيف ممكن أكتبها بكتبها F + +123 +00:09:23,260 --> 00:09:31,520 +of X ناقص X0 اتحاد A خليها لحالها لأن تعريفها + +124 +00:09:31,520 --> 00:09:38,120 +مختلف لأن تعريفها مختلف الآن بنعرف أن صور + +125 +00:09:38,120 --> 00:09:43,840 +المجموعات بتوزع على الاتحاد فده عبارة عن F of X ما + +126 +00:09:43,840 --> 00:09:49,760 +عدا الـ X0 والـ A اتحاد + +127 +00:09:49,760 --> 00:09:54,660 +F الـ A اللي هي على طول ممكن أكتبها مين مجموعة F + +128 +00:09:54,660 --> 00:10:01,530 +الـ A مظبوط؟ انت باين؟ ولا أعيد؟ أه الآن بدي احسب + +129 +00:10:01,530 --> 00:10:07,930 +الـ image طبعًا مين أعوض عن F؟ أعوض G ولا B؟ لا لازم + +130 +00:10:07,930 --> 00:10:11,650 +أجسم وين هي بتساوي B وين هي بتساوي G فاضطريت أجسم + +131 +00:10:11,650 --> 00:10:15,670 +الـ domain وين هي بتساوي B عند الـ A فخلت الـ A لحالها + +132 +00:10:15,670 --> 00:10:20,130 +والباقي إيش تعرفه؟ G أه فالآن من خواص الـ F تتوزع + +133 +00:10:20,130 --> 00:10:26,550 +الاتحاد الآن هذي إيش بتساوي؟ B مظبوط F of A بتساوي + +134 +00:10:26,550 --> 00:10:30,270 +B مظبوط هيك بنقرعها F of X لما الـ X بتساوي A + +135 +00:10:30,270 --> 00:10:33,690 +بتساوي B يعني F of A بتساوي B طب خارج هيك إيش + +136 +00:10:33,690 --> 00:10:43,190 +بتساوي هي G G of X ناقص X0 و A أنا جيت بقى أقدر + +137 +00:10:43,190 --> 00:10:47,110 +أمحي هذا فعشان هيك جسمت الـ domain لجزئين عشان كل + +138 +00:10:47,110 --> 00:10:51,690 +جزء له تعريف مختلف خليني أمشي كمان خطوة عشان أدور + +139 +00:10:51,690 --> 00:10:55,760 +على العنصر اللي بدي إياه معروف أتوقع في أحد التمارين + +140 +00:10:55,760 --> 00:10:59,000 +الكتاب إذا تدالة one to one الصورة بتتوزع على الـ + +141 +00:10:59,000 --> 00:11:02,340 +minus مش دائماً بتتوزع بس إذا كانت one to one إذا + +142 +00:11:02,340 --> 00:11:05,520 +اللي شافت التمارين بتلاقيها فنوزحها دي عبارة عن + +143 +00:11:05,520 --> 00:11:11,240 +مين G of X ناقص مين G العناصر دي ولا إيش بتكون G + +144 +00:11:11,240 --> 00:11:16,520 +of X zero وجيه الـA اللي هي مين اللي هي B اتحاد + +145 +00:11:16,520 --> 00:11:24,950 +الـB فهذا كله مين هذا F of Y طيب أسأل نفسي ممكن + +146 +00:11:24,950 --> 00:11:29,310 +نكون تهنا احنا عايشين بندور بدنا عنصر موجود في ال Y + +147 +00:11:29,310 --> 00:11:32,950 +مش موجود هنا طب هذا بيساوي هذا، بدي عنصر مش موجود + +148 +00:11:32,950 --> 00:11:36,670 +هنا، مين مش موجود هنا؟ إيش قدامكم مش موجود؟ ال B + +149 +00:11:36,670 --> 00:11:42,150 +بس ال B أشمالها مش موجودة أصلاً في ال Y، بدي إياها تكون + +150 +00:11:42,150 --> 00:11:45,230 +إيش؟ موجودة في ال Y مش موجودة، ال B مش موجودة، آه + +151 +00:11:45,230 --> 00:11:50,250 +لكن ال XG of X0 هذه مش موجودة في الصورة موجودة في + +152 +00:11:50,250 --> 00:11:53,250 +الـY الـB مش موجودة في الـY لكن هذه موجودة في الـY + +153 +00:11:53,250 --> 00:11:56,250 +فإذا هذا هو العنصر المناسب هنختار هذا العنصر + +154 +00:11:56,250 --> 00:12:02,530 +فهنقول له let Y تساوي G of X0 لأن هو يخرج الصورة + +155 +00:12:02,530 --> 00:12:09,490 +then الـY تنتمي للـY ليش؟ لأنه G of X0 موجودة في + +156 +00:12:09,490 --> 00:12:12,510 +الـY رغم أن الـX .. لأنه إيش؟ من العنصر بيروح على + +157 +00:12:12,510 --> 00:12:19,110 +الـX0 اللي خارج الـY الـA مش الـA and Why لا تنتمي + +158 +00:12:19,110 --> 00:12:23,270 +لمين للـF of Y؟ لأن هنا أخدناها من برة لأنه بالـ-C + +159 +00:12:23,270 --> 00:12:27,090 +طبعاً إذا حابين تتأكدوا منها إذا كانت تعتبروها هامش + +160 +00:12:27,090 --> 00:12:30,790 +ممكن ممكن تتأكدوا منها بس أنا مش هابر هنا بالتفصيل + +161 +00:12:30,790 --> 00:12:33,370 +مش هابر هنا بالتفصيل فده هو العنصر المناسب + +162 +00:12:33,370 --> 00:12:36,590 +وبالتالي هي proper subset + +163 +00:12:41,430 --> 00:12:45,170 +فحسابنا لل image بيساعدنا على اختيار العنصر اللي + +164 +00:12:45,170 --> 00:12:48,190 +.. اللي هو فيه .. اللي هو خارج ال image خارج ال + +165 +00:12:48,190 --> 00:12:50,750 +image بنعرف ال image و بنختار عنصر خارجه بهذا + +166 +00:12:50,750 --> 00:12:55,050 +الشكل خليني أشوف نتيجة طبعاً زي ما اتعلمنا النتيجة + +167 +00:12:55,050 --> 00:12:58,370 +بيكون مرتبطة مباشرة بالنظرية اه فحنشوف كيف نستخدم + +168 +00:12:58,370 --> 00:13:01,970 +النظرية عشان نبرهن الحقيقة الرياضية أو القاعدة + +169 +00:13:01,970 --> 00:13:06,150 +الرياضية التالية بقول لي لو أخدت أي عدد طبيعي يعني + +170 +00:13:06,150 --> 00:13:09,850 +عدد صحيح موجب فالمجموعة اللي بتتكون من واحد لهذا + +171 +00:13:09,850 --> 00:13:13,450 +العدد إيش بتكون؟ finite إيش معناها تبدأ الرمز لها + +172 +00:13:13,450 --> 00:13:18,830 +بالرمز؟ N sub M N واحد يمين مجموعة الواحد N اتنين + +173 +00:13:18,830 --> 00:13:23,430 +مجموعة الواحد والاتنين N عشرة مجموعة الواحد و من + +174 +00:13:23,430 --> 00:13:27,550 +واحد لعشرة وهاكذا واضحة المجموعة لانكو؟ اه N M + +175 +00:13:27,550 --> 00:13:31,950 +تعريف الـ N M خلينا نكتب بعض الأمثلة عشان تبتدح + +176 +00:13:31,950 --> 00:13:39,770 +الصورة بدنا نثبت ان هذه المجموعات finite ان واحد + +177 +00:13:39,770 --> 00:13:47,330 +ايش بتساوي مجموعة الواحد ان اتنين واحد و اتنين ان + +178 +00:13:47,330 --> 00:13:53,460 +تلاتة واحد و اتنين و تلاتة و هكذا واضح التعريف الآن + +179 +00:13:53,460 --> 00:13:58,340 +ام بيقول لخد اي ام بيكون هدهاش finite ان عشرة + +180 +00:13:58,340 --> 00:14:02,180 +finite ان الف finite ان مليون finite بدنا نثبت هذا + +181 +00:14:02,180 --> 00:14:08,320 +الكلام لأنها مهمة جدا فهدهاش corollary نتيجة خمسة + +182 +00:14:08,320 --> 00:14:14,440 +اتنين approved هنبرهنها by mathematical induction + +183 +00:14:22,550 --> 00:14:25,570 +طب ليش ال mathematical induction بنفع هنا؟ لأن في + +184 +00:14:25,570 --> 00:14:29,590 +عندنا statement بالشكل الثاني خليني أسميها PM بلاش + +185 +00:14:29,590 --> 00:14:34,570 +PM تفرجش طبعاً اسم إيش هي عبارة أن for all M تنتمي + +186 +00:14:34,570 --> 00:14:42,390 +لل N ال N M is finite واحدة + +187 +00:14:42,390 --> 00:14:48,890 +واحدة هي open sentence مع ال quantifiers for all و + +188 +00:14:48,890 --> 00:14:52,510 +ال all integer اه خنشوف تنفع induction احنا قولنا + +189 +00:14:52,510 --> 00:14:54,530 +ايش وقتاش induction لما يكون في يعني ال settlement + +190 +00:14:54,530 --> 00:14:58,230 +for all N تنتمي لـN أو من أي عدد صحيح و بتمشي بأي + +191 +00:14:58,230 --> 00:15:00,690 +درجة شكله فالuniverse بنفع نشتغل عليه induction + +192 +00:15:00,690 --> 00:15:04,880 +تمام؟ متفقين؟ فالـ universe هو الـ natural number + +193 +00:15:04,880 --> 00:15:08,280 +بينفع نشتغل عليه induction ولا بينفعش، ايه بينفع؟ + +194 +00:15:08,280 --> 00:15:10,700 +خلّيني نشوف، طبعاً ال statement أنا ليش بقول في الـ + +195 +00:15:10,700 --> 00:15:13,420 +O لأن فيه open sentence اللي بيه بيه of M، بلاش N + +196 +00:15:13,420 --> 00:15:16,520 +طبعاً، اللي هي هذه هي statement، اه open sentence + +197 +00:15:16,520 --> 00:15:19,520 +طبعاً، بدي أثبت إنه هذه إيش، دائماً finite خلّيني + +198 +00:15:19,520 --> 00:15:25,300 +نشتغل معها واحدة واحدة، نبدأ واحد بيه of one اللي + +199 +00:15:25,300 --> 00:15:31,140 +يمين، and one is finite إيش رأيكوا؟ هذي true ولا مش + +200 +00:15:31,140 --> 00:15:35,040 +true؟ ليش؟ لأن answer واحد singleton مرت علينا + +201 +00:15:35,040 --> 00:15:40,500 +فهنا n one تساوي مجموعة ال one is finite + +202 +00:15:40,500 --> 00:15:46,560 +proposition خمسة اتنين أثبتنا فيه ال five و ال + +203 +00:15:46,560 --> 00:15:50,600 +singleton six are finite خلصنا فإذا بي of one is + +204 +00:15:50,600 --> 00:15:59,710 +true thus بي of one is true أرجو إن هذا المثال يؤكد + +205 +00:15:59,710 --> 00:16:03,590 +أننا فاهمين لل induction مش كل ال induction بده + +206 +00:16:03,590 --> 00:16:08,830 +يكون جامع ولا جسمة ولا أكبر منه، لأ أي علاقة مع ال + +207 +00:16:08,830 --> 00:16:12,630 +universe مجموعة من الأعداد الصحيحة مرتبة بنفع + +208 +00:16:12,630 --> 00:16:16,210 +أشتغل عليها وطبعاً من نقطة البداية قد تكون صحيحة، + +209 +00:16:16,210 --> 00:16:20,370 +الآن بدنا mean ال induction hypothesis أو خطوة ال + +210 +00:16:20,370 --> 00:16:27,710 +induction نكتبها مع بعض، اتنينb of k is true + +211 +00:16:27,710 --> 00:16:34,790 +implies bk plus one is true تمام كله حافظ تمام + +212 +00:16:34,790 --> 00:16:45,630 +فنفترض assume b of k is true إيش يعني that is and + +213 +00:16:45,630 --> 00:16:53,800 +k is finite إيش معناه بي كي هي مكتوبة يعني أن كي is + +214 +00:16:53,800 --> 00:16:56,860 +finite هي ال statement اه فأي ما كانت ال statement + +215 +00:16:56,860 --> 00:17:01,720 +أندي هي علاقة تساوي علاقة متباينة أي ما يكون هي ال + +216 +00:17:01,720 --> 00:17:04,980 +statement not true بدي أثبت أنه بي كي plus one is + +217 +00:17:04,980 --> 00:17:07,880 +true يعني بدي أثبت أنه أن كي plus one is finite we + +218 +00:17:07,880 --> 00:17:14,300 +want to prove بي + +219 +00:17:14,300 --> 00:17:22,260 +كي plus one is true يعني that is بدنا نثبت ان NK + +220 +00:17:22,260 --> 00:17:27,940 +plus one is finite is finite statement مش true + +221 +00:17:27,940 --> 00:17:29,420 +تمام + +222 +00:17:32,290 --> 00:17:36,910 +طبعاً كتابة هنا يمكن أشياء كثيرة لكن كلها سهلة ولا + +223 +00:17:36,910 --> 00:17:40,450 +في عدى عنده صعوبة في اللي كتبناه واضح اللي كتبناه + +224 +00:17:40,450 --> 00:17:46,350 +كله أمور سابقة اه إيش مطلوب أثبت n k plus one is + +225 +00:17:46,350 --> 00:17:49,550 +finite هعملها بقى contradiction افترض إنها + +226 +00:17:49,550 --> 00:17:52,610 +infinite اتفضل في سؤال تمام هنعملها بقى + +227 +00:17:52,610 --> 00:17:55,650 +contradiction عشان بس نستخدم النظرية انتبهوا كيف + +228 +00:17:55,650 --> 00:18:02,500 +نستخدم النظرية assume and k plus one is infinite + +229 +00:18:02,500 --> 00:18:07,300 +proved by contradiction بدنا نثبت هذا اللي هو + +230 +00:18:07,300 --> 00:18:12,080 +المطلوب انها finite by contradiction proved by + +231 +00:18:12,080 --> 00:18:20,360 +contradiction طيب + +232 +00:18:20,360 --> 00:18:23,460 +مين عرفك ان اتحاد ال finite finite انت لسه عندك + +233 +00:18:23,460 --> 00:18:26,440 +معلومات قليلة لسه بدنا نثبت واحدة + +234 +00:18:30,070 --> 00:18:33,210 +احنا راح نكتبها بالخطوة السابقة، كيف ده اكتبها؟ + +235 +00:18:33,210 --> 00:18:35,890 +مافيش هنا مباشر، لكن هنا أنا بدا أستفيد، اتطلع على + +236 +00:18:35,890 --> 00:18:40,930 +البرهان، then هيعندي + +237 +00:18:40,930 --> 00:18:43,930 +k plus .. اه طيب ماشي، انتوا بتشوفوا العلاقة بين + +238 +00:18:43,930 --> 00:18:45,890 +ال .. بين هذه الخطوة و الخطوة اللي قبلها، إيش + +239 +00:18:45,890 --> 00:18:50,910 +العلاقة بينهم؟ عبارة nk ليست إلا nk plus one مطروح + +240 +00:18:50,910 --> 00:18:52,510 +من العنصر أو محظوظ من العنصر، اللي هو العنصر + +241 +00:18:52,510 --> 00:18:56,030 +الأخير، فانا هنا بدي اكتبه، هذه إيش بتساوي؟ هذه + +242 +00:18:56,030 --> 00:19:02,500 +ناقص أي عنصر ولا العنصر الأخير؟ إيش بتساوي؟ اه + +243 +00:19:02,500 --> 00:19:05,720 +فنربطها مع النظرية لو كانت الان k plus واحد + +244 +00:19:05,720 --> 00:19:08,620 +infinite فلازم تكون ناقص عنصر برضه infinite + +245 +00:19:08,620 --> 00:19:15,120 +contradiction contradiction + +246 +00:19:15,120 --> 00:19:21,820 +وانتهى البرهان وانتهى البرهن فهنا دائماً اروح من + +247 +00:19:21,820 --> 00:19:25,820 +الحالة أو الخطوة k plus one ل ال k هي العلاقة + +248 +00:19:25,820 --> 00:19:29,460 +بينهم عشان اروح من n k plus one ل n k لازم احذف + +249 +00:19:29,460 --> 00:19:32,840 +عنصر و النظرية بتقول توزفي عندي infinite set حذفنا + +250 +00:19:32,840 --> 00:19:35,220 +من عنصر بتبقى infinite فمستحيل تكونها دي infinite + +251 +00:19:35,220 --> 00:19:44,960 +وانتهى البرهن فهذه حقيقة مهمة جداً بدنا نعتمد عليها + +252 +00:19:45,640 --> 00:19:49,200 +خلّيني أشوف كمان مثال برضه على النظرية نشوف كمان + +253 +00:19:49,200 --> 00:19:59,070 +مثال مثال بقول prove that إذا كانت الـ A is a set + +254 +00:19:59,070 --> 00:20:03,770 +such that every proper super set of A is infinite، + +255 +00:20:03,770 --> 00:20:08,730 +عندنا مجموعة، كل مجموعة أكبر منها، super set منها، + +256 +00:20:08,730 --> 00:20:11,170 +proper بس، يعني أكبر منها فعلاً، مش أكبر منها و + +257 +00:20:11,170 --> 00:20:16,090 +تسويها، لو أنا في عندي مجموعة كبرتها شوية، بتصير + +258 +00:20:16,090 --> 00:20:19,430 +infinite، مجموعة ما، مش عارف عنها إيش، finite ولا + +259 +00:20:19,430 --> 00:20:22,030 +infinite، لو كبرتش، اه، بتكتسل هنا؟ + +260 +00:20:24,900 --> 00:20:30,420 +إذا كانت هذه infinite حذفنا منها عنصر بتصير infinite + +261 +00:20:30,420 --> 00:20:35,880 +طبعاً infinite contradiction لأن الان K أشمالها + +262 +00:20:35,880 --> 00:20:39,980 +finite induction hypothesis contradiction infinite + +263 +00:20:39,980 --> 00:20:42,780 +حذفنا منها عنصر بتبقى infinite لكن الاش + +264 +00:20:42,780 --> 00:20:46,960 +contradiction لأن الان الان K finite تمام فإيش + +265 +00:20:46,960 --> 00:20:56,370 +المثال بيقول؟ عنا مجموعة ما إيه؟ أول مجموعة أكبر + +266 +00:20:56,370 --> 00:20:59,990 +منها بشوية بتكون infinite يعني إيش هذه مالها؟ على + +267 +00:20:59,990 --> 00:21:04,730 +عفوة ال infinite إيش بتكون infinite؟ السؤال بيقول، + +268 +00:21:04,730 --> 00:21:08,850 +في عندنا مجموعة ما إيه؟ أي مجموعة أكبر منها إن شاء + +269 +00:21:08,850 --> 00:21:12,110 +الله بعنصر بتكون infinite إيش ده بتكون هذي؟ بتكون + +270 +00:21:12,110 --> 00:21:15,150 +infinite، بدنا نستخدم النظرية بعض نشوف أول شيء، + +271 +00:21:15,150 --> 00:21:18,890 +بقول prove that if فإيش؟ كل الشرط بتكون معطى + +272 +00:21:18,890 --> 00:21:21,230 +فهنقول له إيش؟ assume + +273 +00:21:23,780 --> 00:21:30,180 +A is a set بس مجموعة إيش معناه معلومة؟ such that + +274 +00:21:30,180 --> 00:21:37,220 +is a set such that أو and such that بقول لي every + +275 +00:21:37,220 --> 00:21:42,540 +proper subset يعني إيش every يعني for all ب ب + +276 +00:21:42,540 --> 00:21:47,460 +إشمالها تحتوي ال A و proper subset مش subset بقى + +277 +00:21:47,460 --> 00:21:52,340 +تحتوي proper subset إيش بيقدي؟ بيقدي إن ال B is + +278 +00:21:52,340 --> 00:21:56,840 +infinite لا لسه هذا المطلوب هذا كله معطى كله ده + +279 +00:21:56,840 --> 00:22:03,780 +assume is infinite اه + +280 +00:22:03,780 --> 00:22:08,860 +فبقول ليه إذا كان عندنا مجموعة ما أخدنا أي مجموعة + +281 +00:22:08,860 --> 00:22:12,800 +أكبر منها بتكون infinite أيش المطلوب أثبت منه إيه + +282 +00:22:12,800 --> 00:22:17,380 +infinite we want to prove فدي مش المطلوب اللي + +283 +00:22:17,380 --> 00:22:21,240 +implies هذا كله بالمعطيات we want to prove بس + +284 +00:22:21,240 --> 00:22:24,720 +حاولت أنا أيش أفسر أيش الشرط بعد يملة الشرطية اللي + +285 +00:22:24,720 --> 00:22:30,560 +في السؤال we want to prove that A is infinite + +286 +00:22:30,560 --> 00:22:34,400 +infinite + +287 +00:22:36,020 --> 00:22:40,460 +هستخدم النظرية بدل ما أجيب دالة و أغلب حالي هستخدم + +288 +00:22:40,460 --> 00:22:44,460 +النظرية فده نظرية تعبنا عليها نظرية طويلة في + +289 +00:22:44,460 --> 00:22:47,760 +البرهان و يمكن صعبة شوية فهنشوف كيف هنستفيد منها + +290 +00:22:47,760 --> 00:22:51,480 +دكتور ليش حطيت implies هنا يعني أيش بدنا نحطه؟ بقول + +291 +00:22:51,480 --> 00:22:56,740 +ليه every proper subset of A is infinite يعني لو + +292 +00:22:56,740 --> 00:23:01,740 +أخذنا أي proper لكل الـ B اللي هي بتحتوي A لازم ال + +293 +00:23:01,740 --> 00:23:07,400 +B تكون infinite ممكن، ممكن، بس هي بنفس المعنى، ففي + +294 +00:23:07,400 --> 00:23:12,500 +أحيان بكون أكثر من تفسير تمام، فإيش ممكن نعمل؟ أيش + +295 +00:23:12,500 --> 00:23:16,120 +ممكن نعمل؟ فاحنا مطلوب نثبت إن الـ A Infinite طبعاً + +296 +00:23:16,120 --> 00:23:19,220 +في عندنا تعريف، بدناش نستخدمه، نستخدم النظرية فأنا + +297 +00:23:19,220 --> 00:23:21,920 +كل اللي بدي إياه الآن، بدي أستفيد من المعطيات، بدي + +298 +00:23:21,920 --> 00:23:26,460 +أدور على مجموعة B بتكون أكبر من مين؟ من الـ A، و + +299 +00:23:26,460 --> 00:23:30,480 +تكون Infinite أه وإيه علاقة مع ال A؟ إيه علاقة مع + +300 +00:23:30,480 --> 00:23:34,220 +ال A؟ إذا كنت تثبت أن الـ B infinite فبقى .. آسف ال + +301 +00:23:34,220 --> 00:23:36,880 +B هتكون infinite ومنها حسن تجي أن الـ A infinite + +302 +00:23:36,880 --> 00:23:39,600 +لأنه بيقول ليه أي proper super set من الـ A + +303 +00:23:39,600 --> 00:23:43,400 +infinite بدي أثبت أن الـ A infinite أنا بعرف بدنا + +304 +00:23:43,400 --> 00:23:47,440 +علاقة نعملها زي الـ trick الماضي بدنا مجموعة ما B + +305 +00:23:47,440 --> 00:23:51,100 +نطرح منها عنصر تدينا الـ A واحنا عارفين أن الـ B + +306 +00:23:51,100 --> 00:23:53,120 +infinite لأن بقول الـ B إلى خلاص معايا بيكون + +307 +00:23:53,120 --> 00:23:56,440 +infinite والـ A عبارة عن B ناقص عنصر بيصير الـ A + +308 +00:23:56,440 --> 00:24:02,240 +infinite فكيف بنكونها؟ هنكونها مع بعض هقوله الآن + +309 +00:24:02,240 --> 00:24:09,240 +let B لا تنتمي للـ A بدي أخد عنصر خارج الـ A بدي أخد + +310 +00:24:09,240 --> 00:24:13,650 +عنصر خارج الـ A بينفع أخد عنصر خارج الـ A؟ ليش؟ لأ مش + +311 +00:24:13,650 --> 00:24:17,530 +عارف الـ B، بتكون الـ B لسه لأن مافيش إيه بتحتوي كل + +312 +00:24:17,530 --> 00:24:20,750 +شيء فقديني أي مجموعة، في مجموعة عنصر أخرج، يا + +313 +00:24:20,750 --> 00:24:23,830 +خدنا عنصر معاه الآن هنكون الـ B، انتبهوا على ال + +314 +00:24:23,830 --> 00:24:31,490 +trick اللي هنعمله أدلت B تساوي إيه اتحاد الـ A ليش + +315 +00:24:31,490 --> 00:24:35,370 +بدل الـ B بالخارج؟ عشان لما أضيفه للـ A تصير فعلا + +316 +00:24:35,370 --> 00:24:38,410 +أكبر لأن لو كان دي هو الـ A كان مع اتحاده بتعمل + +317 +00:24:38,410 --> 00:24:44,970 +إيه؟ ف أنا بديها تكون proper الآن then الـ B proper + +318 +00:24:44,970 --> 00:24:48,670 +super set من الـ A و لا لأ؟ لأنه أكبر منها بالتأكيد + +319 +00:24:48,670 --> 00:24:51,650 +لأن الـ A بي عصر الزيادة فأنا عشان أكبر هذه + +320 +00:24:51,650 --> 00:24:54,650 +المجموعة بدي أجيب طالبة من شعبة تانية و لا أجيب من + +321 +00:24:54,650 --> 00:24:59,350 +نفس الشعبة، تكبرش، تمام؟ فهي القضية، الآن أيش عندي + +322 +00:24:59,350 --> 00:25:03,190 +مقطع جالي كل proper super set إذا كانت الـ B proper + +323 +00:25:03,190 --> 00:25:05,970 +super set من أيش؟ مقلبة الـ B في infinite فهذا يؤدي + +324 +00:25:05,970 --> 00:25:12,830 +إن الـ B is infinite طيب أيش علاقة الـ B مع الـ A + +325 +00:25:12,830 --> 00:25:21,870 +بط بي ناقص الـ B تساوي A؟ ف infinite ناقص عنصر + +326 +00:25:21,870 --> 00:25:29,470 +infinite باستخدام + +327 +00:25:29,470 --> 00:25:35,390 +النظرية، النظرية خمسة تلاتة وهو المطلوب فهنا مرة + +328 +00:25:35,390 --> 00:25:37,770 +تانية كيف نستخدم النظرية فاحنا إيه المجموعة + +329 +00:25:37,770 --> 00:25:41,270 +كتبناها على صورة مجموعة ناقص عنصر إذا عرفنا + +330 +00:25:41,270 --> 00:25:44,950 +المجموعة ما infinite وطرحنا منها عنصر بتامها + +331 +00:25:44,950 --> 00:25:53,270 +infinite فهنا بنقدر نحل بهذه الطريقة أعيد + +332 +00:25:53,270 --> 00:25:56,730 +مشغلين + +333 +00:25:56,730 --> 00:26:02,250 +التكييف مش داعي احنا + +334 +00:26:02,250 --> 00:26:03,290 +شوبرين من غير تكييف + +335 +00:26:15,790 --> 00:26:25,190 +تبع .. خليني أشوف الآن نظرية جديدة الـ criterion + +336 +00:26:25,190 --> 00:26:29,840 +for finite sets أه طبعاً احنا فيها إن التعريفات + +337 +00:26:29,840 --> 00:26:33,600 +وشوفنا إنه التعريفات مش دائماً سهلة أو فيها صعوبة + +338 +00:26:33,600 --> 00:26:36,400 +فطبعاً النظرية تدينا بدائل كيف نثبت إن المجموعة + +339 +00:26:36,400 --> 00:26:39,880 +finite أو infinite شوفنا الأمثلة الماضية كنا بنثبت + +340 +00:26:39,880 --> 00:26:44,300 +infinite عن طريق نظرية معينة الآن هيدينا نظرية كيف + +341 +00:26:44,300 --> 00:26:47,850 +نثبت إن المجموعة finite كيف نثبت إن المجموعة + +342 +00:26:47,850 --> 00:26:50,950 +finite؟ الحقيقة دي نظرية مهمة جدا في بعض الكتب + +343 +00:26:50,950 --> 00:26:54,010 +تعتبر هذا هو التعريف يعني ممكن أنا أبدأ من النظرية + +344 +00:26:54,010 --> 00:26:56,890 +أن هو التعريف الـ finite وأعرف الـ infinity اللي + +345 +00:26:56,890 --> 00:27:00,210 +عبارة عن الـ negation وبعدين أوصل للي بدأت منه + +346 +00:27:00,210 --> 00:27:04,130 +التعريف كأنه ياشهصي نظرية ممكن نعكس الترتيب فهذه + +347 +00:27:04,130 --> 00:27:08,780 +مدارس وهذه آراء معينة إيش مجلد؟ وقت أيش بتكون + +348 +00:27:08,780 --> 00:27:11,780 +المجموعة finite هنشوف يدينا هنا المعيار معيار وقت + +349 +00:27:11,780 --> 00:27:15,540 +أيُش المجموعة بتكون finite بقول اللي a set X is + +350 +00:27:15,540 --> 00:27:20,560 +finite if and only if عشان هي معيار if if and + +351 +00:27:20,560 --> 00:27:26,460 +only if either X is φ يا فارغة or X is in one to + +352 +00:27:26,460 --> 00:27:29,120 +one correspondence is in one to one correspondence + +353 +00:27:29,120 --> 00:27:32,720 +with some Nk اللي تكلمنا عنها والـ Nk إيش + +354 +00:27:32,720 --> 00:27:35,780 +معناه دائماً؟ دي finite فهي إيش إيش الـ finite؟ ال + +355 +00:27:35,780 --> 00:27:40,450 +finite يا إما فارغة يعني فيها Zero من العناصر يا + +356 +00:27:40,450 --> 00:27:43,370 +فيها K من العناصر اللي يعيش عدد العناصر أشماله + +357 +00:27:43,370 --> 00:27:46,610 +finite has infinitely many فهنا بيشبه التعريف + +358 +00:27:46,610 --> 00:27:50,810 +القديم فده بتطابق مع التعريف القديم يعني يا إما + +359 +00:27:50,810 --> 00:27:54,310 +فارغة فيها Zero من العناصر أو فيها عدد محدود عشرة، + +360 +00:27:54,310 --> 00:27:58,370 +عشرين، مئة يعني بتكافئ مين؟ Nk ماودةش Nk لما بقول + +361 +00:27:58,370 --> 00:28:01,770 +أناش بعدهم واحد، اثنين، ثلاثة، K إذا رقم عناصر فيها + +362 +00:28:01,770 --> 00:28:07,210 +K من العناصر خلينا نشوف البرهان مع بعض خليني أبدأ + +363 +00:28:07,210 --> 00:28:11,690 +البرهان هنا Approve + +364 +00:28:11,690 --> 00:28:15,710 +طبعا هذه الـ statement خليني أكتبها أول شي فعنا + +365 +00:28:15,710 --> 00:28:23,070 +هنا X يمكن جاب للبرهان نكتب الـ statement X + +366 +00:28:23,070 --> 00:28:35,080 +is finite if and only if X تساوي φ أو x in one to + +367 +00:28:35,080 --> 00:28:38,520 +one correspondence يعني إيش؟ there exists a + +368 +00:28:38,520 --> 00:28:47,000 +bijection نسميه f أو g اللي بدنا إياه جي من x لمين؟ + +369 +00:28:47,000 --> 00:28:53,400 +للـ Nk for some k تمام؟ فهذه الـ statement + +370 +00:28:53,400 --> 00:28:58,180 +biconditional هنعملها علشان two parts approved + +371 +00:29:03,410 --> 00:29:06,850 +هبدأ بالاتجاه الثاني لأنه يمكن أسهل نبدأ فيه + +372 +00:29:06,850 --> 00:29:13,190 +فالاتجاه الأول اللي هو الاتجاه هذا الاتجاه إنه إذا + +373 +00:29:13,190 --> 00:29:18,910 +كانت هذه صحيحة فبتكون هذه صحيحة فهنا هقوله إيش إنه + +374 +00:29:18,910 --> 00:29:28,030 +X تساوي φ or there exist a bijection + +375 +00:29:30,440 --> 00:29:38,760 +f من X لـ Nk للـ Nk طبعا for some K تنتمي + +376 +00:29:38,760 --> 00:29:47,000 +للـ Z مظبوط for some Nk طبعا خليها واضحة مش مشكلة + +377 +00:29:47,000 --> 00:29:55,580 +implies X is finite فهذا الاتجاه الأول تمام assume + +378 +00:29:55,580 --> 00:30:03,180 +X تساوي φ Assume X تساوي φ or there exists a + +379 +00:30:03,180 --> 00:30:07,060 +bijection + +380 +00:30:07,060 --> 00:30:14,220 +f من X لـ Nk طبعا كالعادة في رد أن الشرط صحيح، + +381 +00:30:14,220 --> 00:30:19,200 +بدنا نثبت أن X إيش مالها؟ إنها finite، تمام + +382 +00:30:24,710 --> 00:30:28,850 +لأ، نفترض إن الجزء الثاني صحيح، نحن عندنا الـ + +383 +00:30:28,850 --> 00:30:33,170 +statement main الـ statement بـ if and only if Q + +384 +00:30:33,170 --> 00:30:36,530 +بدأنا نثبت main Q implies V فافترضنا إن الـ B + +385 +00:30:36,530 --> 00:30:39,670 +صحيح، عدنا نثبت الـ B، إن الـ X finite تمام، أنا + +386 +00:30:39,670 --> 00:30:42,570 +عندي الـ X، لو كانت φ، نعرف بـ Proposition + +387 +00:30:42,570 --> 00:30:47,510 +السابق إنها إيش؟ finite، فإن الاحتمال الأول، if X + +388 +00:30:47,510 --> 00:30:52,850 +تساوي φ، then X is finite + +389 +00:30:57,400 --> 00:31:00,840 +الآن بدنا نأخذ الاحتمال الثاني فهذا هو يكون + +390 +00:31:00,840 --> 00:31:05,480 +proposition خمسة اثنين أتوقع proposition خمسة + +391 +00:31:05,480 --> 00:31:09,300 +اثنين خلصنا فالآن بدنا نأخذ الاحتمال الثاني فإن + +392 +00:31:09,300 --> 00:31:16,240 +إذا ما كانت φ تكون هناك a bijection assume there + +393 +00:31:16,240 --> 00:31:24,040 +exists a bijection g + +394 +00:31:24,040 --> 00:31:35,410 +من X إلى Nk نشترك عليها مباشرة أم لا؟ أه تمام تمام + +395 +00:31:35,410 --> 00:31:40,150 +هذا برهان مر علينا قبل هيك كان فينا نظرية ونتيجة + +396 +00:31:40,150 --> 00:31:44,710 +قلنا إذا كان بيجيكشن بين two sets يا إما اثنتين finite + +397 +00:31:44,710 --> 00:31:48,010 +يا إما اثنتين infinite أنا بعرف من المثال الماضي من + +398 +00:31:48,010 --> 00:31:51,890 +النتيجة أن الـ Nk is finite إذا لازم الـ X تكون + +399 +00:31:51,890 --> 00:31:56,570 +finite أه فهنا by اللي هو الـ corollary + +400 +00:32:00,900 --> 00:32:04,200 +خمسة واحد وخمسة اثنين خمسة واحد بتقول علاش انه + +401 +00:32:04,200 --> 00:32:09,520 +مافيش بيجيكشن للاتنتين من finite and corollary + +402 +00:32:09,520 --> 00:32:17,430 +خمسة اثنين X is finite فهذا الجزء السهل خلصنا، فلو + +403 +00:32:17,430 --> 00:32:20,750 +كانت φ هي finite لأن فيها zero من العناصر، و + +404 +00:32:20,750 --> 00:32:23,710 +هذا أثبتناها قبل هيك، ولو كانت فيها bijection + +405 +00:32:23,710 --> 00:32:26,710 +بينها وبين N، Nk، ما ينفعش يكون بيجيكشن لبين + +406 +00:32:26,710 --> 00:32:29,490 +مجموعتين من نفس الجنس، بما أن Nk finite تواً + +407 +00:32:29,490 --> 00:32:32,950 +أثبتناها بالـ induction، إذا لازم الثانية تكون finite، + +408 +00:32:32,950 --> 00:32:39,120 +فأدا الاتجاه خلص، نيجي للاتجاه الثاني بدنا الآن B + +409 +00:32:39,120 --> 00:32:41,760 +implies Q بس عشانها كبيرة ما بديش أكتبها كمان مرة + +410 +00:32:41,760 --> 00:32:46,160 +مش هثبتها بشكل مباشر هثبت الـ contrapositive تبعتها + +411 +00:32:46,160 --> 00:32:50,140 +أيُش مطلوب نثبت ولا أكتب .. خليني أكتب يلا اه هل + +412 +00:32:50,140 --> 00:33:00,380 +جيش بدنا نثبت ان X is finite implies X تساوي φ + +413 +00:33:00,380 --> 00:33:05,880 +or there exists a bijection خليني أكتبها بشكل + +414 +00:33:05,880 --> 00:33:15,390 +مختصر من X لـ Nk تكون one to one and onto واضحة؟ one + +415 +00:33:15,390 --> 00:33:20,170 +to one and onto اكتبه بهذا الشكل اختصاراً أه تمام + +416 +00:33:20,170 --> 00:33:25,050 +فده مطلوب أه مش هنثبت هذه العبارة مباشرة هنثبت الـ + +417 +00:33:25,050 --> 00:33:36,930 +contrapositive تبعتها أو it's contrapositive نتذكر + +418 +00:33:38,300 --> 00:33:42,020 +chapter واحد أه بيصير not Q implies not B يعني إيه ده + +419 +00:33:42,020 --> 00:33:48,240 +تكون هذا النفي تبعتها X لا تساوي φ and their + +420 +00:33:48,240 --> 00:33:53,940 +existence هتصير هتصير for all انه .. بس هو بيقول لي + +421 +00:33:53,940 --> 00:33:56,940 +there exists يعني ما فيش ولا bijection يوجد + +422 +00:33:56,940 --> 00:34:00,280 +bijection إيش ده فيها؟ لا يوجد bijection بدنا + +423 +00:34:00,280 --> 00:34:04,200 +نكتبها بهذا الشكل .. اه هي for all .. أي دالة من x + +424 +00:34:04,200 --> 00:34:08,500 +لـ x و هتكون bijection .. اه بيصير أنه أي دالة من + +425 +00:34:08,500 --> 00:34:11,080 +x لـ و x مستحيل تكون bijection أي ده تكون فيها أو + +426 +00:34:11,080 --> 00:34:16,020 +نقول لا يوجد bijection and there is no bijection + +427 +00:34:16,020 --> 00:34:19,860 +there is no bijection + +428 +00:34:23,840 --> 00:34:30,740 +between x and mk implies + +429 +00:34:30,740 --> 00:34:40,680 +not be x is infinite صارت + +430 +00:34:40,680 --> 00:34:48,040 +هيك تكافئ بهذا الشكل فبدل ما نثبتها مرة ثانية احنا + +431 +00:34:48,040 --> 00:34:53,500 +بنعمل هذه الجملة أثبتنا Q تكافئ implies B ففي واحد + +432 +00:34:53,500 --> 00:34:58,500 +إن إيش عملنا قلنا Q implies B خلصناها الآن إيش بدنا + +433 +00:34:58,500 --> 00:35:05,220 +نثبت B implies Q أو not Q implies not B تمام؟ + +434 +00:35:05,220 --> 00:35:08,720 +متبعين باختصار شديد وده اللي عملنا تمام فالجملة + +435 +00:35:08,720 --> 00:35:11,580 +الشرطية اللي كترت بزريف هنفترض أنه ليش الشرط صحيح + +436 +00:35:11,580 --> 00:35:13,620 +فهنقوله الآن assume + +437 +00:35:15,670 --> 00:35:29,450 +X لا تساوي Φ and there is no bijection between X + +438 +00:35:29,450 --> 00:35:38,100 +and NK ولا NK مستحيل كم اتمنى البرهان شوية بده + +439 +00:35:38,100 --> 00:35:43,380 +انتباه أنا إيش مطلوب أثبت إن الـ X infinite؟ نشرح + +440 +00:35:43,380 --> 00:35:48,420 +الفكرة وبعدين نكتب أنا عندي مجموعة كبيرة بدي أثبت + +441 +00:35:48,420 --> 00:35:50,860 +إنها infinite اللي هنعمله في طريقة البرهان إن + +442 +00:35:50,860 --> 00:35:54,900 +هدول العناصر هنرتبهم فنفترض إن احنا في عندنا وعاء، + +443 +00:35:54,900 --> 00:35:59,130 +في عندنا كيس، في كرات مش عارفين عددهم هنبدأ ناخد كل + +444 +00:35:59,130 --> 00:36:01,990 +كورة ونعدها عشان نصفد إن واحدة و أنا infinite فناخد + +445 +00:36:01,990 --> 00:36:05,690 +الكورة الأولى وإيش ونقول هذه الكورة رقم واحد طيب + +446 +00:36:05,690 --> 00:36:08,250 +لو الـ K صفضي إيش بيكون اتفيلها كورة واحدة؟ إيش + +447 +00:36:08,250 --> 00:36:12,250 +بيكون؟ بناخد ما زال في كورة واحدة إذا نشمله يكافئ + +448 +00:36:12,250 --> 00:36:15,190 +عن K في عنصر واحد في one to one correspondence طيب + +449 +00:36:15,190 --> 00:36:17,630 +ما زال لا يمكن ألاقي bijection ممكن ألاقي كمان + +450 +00:36:17,630 --> 00:36:21,390 +كورة أمد إيدي واخد الكورة رقم اثنين ارقمها هي إيش + +451 +00:36:21,390 --> 00:36:26,490 +الكورة رقم اثنين طيب خلص الـ case مستحيل لو إنه خلصش + +452 +00:36:26,490 --> 00:36:30,530 +بيكون and two بينفعش فاخد إيش اخد كمان عنصر وهكذا + +453 +00:36:30,530 --> 00:36:33,570 +فدي الفكرة فدي الفكرة اللي هنعملها هنرقمها + +454 +00:36:36,520 --> 00:36:40,380 +X لا تساوي فاى، إيش معناه؟ بقدر ألاجي فيها على + +455 +00:36:40,380 --> 00:36:45,120 +أقل عنصر، implies there exists X1، أول عنصر أخدته + +456 +00:36:45,120 --> 00:36:48,420 +ارقمه، مديت إيدي في الكيس، لاجيت أول كورة، لأنه مش + +457 +00:36:48,420 --> 00:36:51,580 +فاضي، هلاجي كورة ولا مش هلاجيها؟ لأنه مش فاضي، + +458 +00:36:51,580 --> 00:36:56,560 +فهذه كورة رقم واحد، there exists X1 تنتمي للـX، + +459 +00:36:56,560 --> 00:36:58,800 +اه، اللي قاعد بالتأكيد أن الكيس ما فضيش، لو أخدت + +460 +00:36:58,800 --> 00:37:02,520 +منه كورة بفضأ، بفضاش، اه، اه، فبقى هنا بدي أقول إن + +461 +00:37:02,520 --> 00:37:11,770 +إيش، Fx تساوي x one then بقدر ألاقي bijection فهذا + +462 +00:37:11,770 --> 00:37:17,650 +مستحيل ليه؟ إيش هو الـ bijection؟ then g من n one + +463 +00:37:17,650 --> 00:37:22,880 +إلى x given by بدي أدريكيها بشكل صريح مين الـ + +464 +00:37:22,880 --> 00:37:26,160 +bijection بين N1 وبين X يلي بيساوي X1؟ الواحد + +465 +00:37:26,160 --> 00:37:33,200 +صورته X1، ديك معناته، given by G of 1 تساوي X1، G + +466 +00:37:33,200 --> 00:37:34,640 +is a bijection + +467 +00:37:38,230 --> 00:37:41,370 +لما نقول هي مجموعة الواحد والـ x واحد في بينهم one + +468 +00:37:41,370 --> 00:37:44,850 +to one correspondence ولا لأ الواحد x واحد هي + +469 +00:37:44,850 --> 00:37:47,710 +التناظر صح ولا لأ طبعا إيش مقالة ده contradiction + +470 +00:37:47,710 --> 00:37:50,630 +مستحيل اه إذا إيش مقالة اه إذا ها دي مقالة ها + +471 +00:37:50,630 --> 00:37:55,690 +مستحيل يكون بس في عنصر واحد اه فاللي هو طبعا is a + +472 +00:37:55,690 --> 00:38:00,550 +bijection طبعا impossible فهذا + +473 +00:38:00,550 --> 00:38:06,940 +بيقول إن x ناقص x one لا تساوي five بدل مكتب X + +474 +00:38:06,940 --> 00:38:13,560 +ناقص واحد تساوي نفس المعنى فما زال هذه ما خلصتش، ما + +475 +00:38:13,560 --> 00:38:16,780 +اتجافش عند X واحد، صح؟ إذاً فيها عناصر أخرى طيب، + +476 +00:38:16,780 --> 00:38:19,340 +هأقيد نفس الفكرة، زي توي ما حكيت، ما زال هذه ما + +477 +00:38:19,340 --> 00:38:22,060 +سويش five، بقدر ألاقي عنصر جديد X2، يعني أنا شيش + +478 +00:38:22,060 --> 00:38:25,720 +بعمل، أخدت الكورة الأولى، ومسحتها ورتبتها ورقمتها + +479 +00:38:25,720 --> 00:38:28,500 +وحطيتها على الدولاب، بيداردي أاخد مرة ثانية، + +480 +00:38:28,500 --> 00:38:31,280 +بيداجي عنصر جديد، لأن لو رجعت الكورة نفسها على + +481 +00:38:31,280 --> 00:38:34,380 +الكيس، بيمكن أجيها كمان مرة، بديش، واضح؟ اه، فعشان + +482 +00:38:34,380 --> 00:38:36,860 +هي كان بيدي أخدياش عنصر من X ناقص X واحدة، إن + +483 +00:38:40,230 --> 00:38:54,630 +There exists x2 تنتمي للـ x ناقص x1 بنفس + +484 +00:38:54,630 --> 00:38:59,110 +الطريقة since + +485 +00:38:59,110 --> 00:39:06,850 +there is no bijection between + +486 +00:39:09,440 --> 00:39:15,920 +X and N2 لو أنا لما أخدت العنصر الجديد خلصه كان + +487 +00:39:15,920 --> 00:39:18,800 +ياش فيه bijection مع N2 صح؟ لكن أنا بجوب أعرف أنه + +488 +00:39:18,800 --> 00:39:22,800 +ياش فيش bijection ولا مع أي NK إذن إيش؟ إذن since + +489 +00:39:22,800 --> 00:39:29,730 +فأنا عندي X ناقص X1 و X2 برضه لاتساوي 5 فبعد ما خدت + +490 +00:39:29,730 --> 00:39:34,090 +الكورتين برضه ما فضيتش الكيس ولا لأ؟ لو خلص الكيس + +491 +00:39:34,090 --> 00:39:37,110 +إيش معنى؟ هتفيه عنصر هنا بس، بس فيه كورتين، بصبتش، + +492 +00:39:37,110 --> 00:39:39,530 +اه هذه العملية ممكن أن أعملها إيش إلى مدى نهاية + +493 +00:39:39,530 --> 00:39:42,970 +لأن لكل K منفعش تكون متكافئة أن تلاتة ولا أن أربعة + +494 +00:39:42,970 --> 00:39:47,190 +ولا أن خمسة، إذا لكل عدد K بقدر ألاقي إيش عنصر + +495 +00:39:47,190 --> 00:39:52,750 +بهذا الشكل، اه continuing in + +496 +00:39:52,750 --> 00:39:53,650 +the same way + +497 +00:39:57,800 --> 00:40:05,140 +For all n تنتمي للـN، there exists xn تنتمي للـx + +498 +00:40:05,140 --> 00:40:05,920 +ناقص + +499 +00:40:10,690 --> 00:40:15,890 +نعمم الفكرة إيش اللي كدبناها تعميم لجينا X1 لو + +500 +00:40:15,890 --> 00:40:21,570 +خلصت بينفعش اتخلص لجيت X2 بعد ما X2 إيش بلاجي X3 + +501 +00:40:21,570 --> 00:40:26,490 +فكل مرة بعد ما خلص لما لاجي XN إيش بلاجي N plus + +502 +00:40:26,490 --> 00:40:29,490 +one واضحة ولا مش واضحة الـ statement ها دي اه لأنه + +503 +00:40:29,490 --> 00:40:35,370 +أنا إيش X ناقص X1 بلاجي فيها X2 طب X ناقص X1 و X2 + +504 +00:40:35,370 --> 00:40:38,770 +بلاجي فيها X3 وهذه العملية بتجاف؟ لا مابتجافش لو + +505 +00:40:38,770 --> 00:40:44,230 +وقفتلو هذا كان غلط، إيش معناه؟ إن هناك bijection + +506 +00:40:44,230 --> 00:40:48,150 +بين X و بين مين، N sub small n، صح؟ مستحيل، اه، + +507 +00:40:48,150 --> 00:40:52,350 +فالـ N تقريبا فالعملية واضح إنه إيش مش منتهية طبعا + +508 +00:40:52,350 --> 00:40:55,330 +كيف بتثبت إنها غير منتهية؟ بتستخدم يا نظرية يا + +509 +00:40:55,330 --> 00:40:58,890 +تعريف، لسه ده عملية عد، مش واضح إن هي تعريف، هنعمل + +510 +00:40:58,890 --> 00:41:07,310 +الـ trick التالي let Y تساوي X N such that N تنتمي + +511 +00:41:07,310 --> 00:41:13,230 +للـ N إيش اللي بده أعمله زي ما حكينا مرة ثانية هي + +512 +00:41:13,230 --> 00:41:17,690 +الكيس فيه كورات مخربطين ومش عارفين إيش نوعهم احنا + +513 +00:41:17,690 --> 00:41:20,790 +جاعدين كل مرة بناخد كورة بنرتبها بنمسحها بنرقمها + +514 +00:41:20,790 --> 00:41:24,050 +وحطناهم في وعاء جديد أو في دولاب جديد هذا حنسميه Y + +515 +00:41:24,050 --> 00:41:28,950 +هذا حنسميه Y اه فالآن طبعا إذا أثبت إن الـ Y + +516 +00:41:28,950 --> 00:41:32,280 +infinite كل عناصر الـ Y من أين اخذناها؟ من الـ X + +517 +00:41:32,280 --> 00:41:35,660 +فالـ Y شمالها صبصت من الـ X لأنه أنا ما أخدتش من + +518 +00:41:35,660 --> 00:41:38,460 +برا، لا إذا كثرت أثبت أن الـ Y Infinite انتهت + +519 +00:41:38,460 --> 00:41:41,900 +العملية، ليش؟ لأن إذا المجموعة Y Infinite فاللي + +520 +00:41:41,900 --> 00:41:44,540 +أكبر منها Infinite فدي فكرة البرهان، فهي فكرة + +521 +00:41:44,540 --> 00:41:48,480 +البرهان طبعا، طب ليش الـ Y التعامل معها أسهل؟ لأنها + +522 +00:41:48,480 --> 00:41:52,140 +مرتبة، مرقمة، اه كيف ممكن أثبت أن الـ Y Infinite؟ + +523 +00:41:52,140 --> 00:41:57,320 +ممكن نلاقي دالة one to one وليست onto بسهولة then + +524 +00:42:02,100 --> 00:42:11,260 +Y subset من الـ X و F من Y لـ Y مين يثبت إن الـ Y + +525 +00:42:11,260 --> 00:42:14,800 +Infinite؟ تدوني دالة one to one و ليست onto، + +526 +00:42:14,800 --> 00:42:22,330 +given by إيش نعمل؟ إيش عملنا بالـnatural number؟ + +527 +00:42:22,330 --> 00:42:26,830 +لإن احنا شبهناها 2x طب كام ممكن أعملها 2x هنا؟ + +528 +00:42:26,830 --> 00:42:31,530 +بينفعش 2 لإن x أنا ع مين الـnatural number الأن؟ + +529 +00:42:31,530 --> 00:42:35,170 +ممكن أشتغل مع الـ و ممكن أخليها 2؟ نعم ممكن أخد + +530 +00:42:35,170 --> 00:42:39,790 +كل .. يعني أنا عندي x1، x2 ممكن إيش أخد؟ x2، x4، + +531 +00:42:39,790 --> 00:42:45,860 +كل الزوجي أو في طريقة أسهل لو أنا أخدت F of X J + +532 +00:42:45,860 --> 00:42:54,540 +تساوي J plus 1 خلّي كل عنصر يروح لقى اللي بعده + +533 +00:42:54,540 --> 00:43:00,160 +فهذه one to one يعني إيش؟ X1 من صورتها X2 X3 من + +534 +00:43:00,160 --> 00:43:05,440 +صورتها X4 X50 من صورتها X51 هذه تدالة one to one + +535 +00:43:05,440 --> 00:43:08,560 +ولا مش one to one؟ one to one ليست onto + +536 +00:43:08,560 --> 00:43:15,210 +فكروا فيها أوي المكتوب and F given by is one to one + +537 +00:43:15,210 --> 00:43:21,710 +and f of y برابر من الـ y مين اللي مش صورة؟ x واحد + +538 +00:43:21,710 --> 00:43:25,230 +لأنه مش صورة حده لأنه x واحد بتروح ل x اثنين فصورة + +539 +00:43:25,230 --> 00:43:28,010 +من وين بتبدأ من x اثنين وطالع اه فأدي برابر صف صف + +540 +00:43:28,010 --> 00:43:36,490 +اه فإيش thus y is infinite اختصارا بالدكتور and + +541 +00:43:36,490 --> 00:43:40,270 +hence x + +542 +00:43:40,270 --> 00:43:40,990 +is infinite + +543 +00:43:46,740 --> 00:43:52,820 +فأنا مجموعة مش مرتبة مجموعة عشوائية أخدت منها + +544 +00:43:52,820 --> 00:43:56,740 +مجموعة مرتبة قدرت أثبت أن الجزء منها infinite فهي + +545 +00:43:56,740 --> 00:44:06,960 +لازم تكون كلها infinite فدي هي فكرة البرهان خليني + +546 +00:44:06,960 --> 00:44:13,020 +بس ننهي بملاحظة لأن ما فيش وقت كثير فالنظرية + +547 +00:44:13,020 --> 00:44:17,610 +الماضية إيش بتقول ليه؟ المجموعة الـ finite يا إما + +548 +00:44:17,610 --> 00:44:21,050 +فيها zero من العناصر يعني في أو فيها عدد محدود من + +549 +00:44:21,050 --> 00:44:25,010 +العناصر فيها بينها وبين الـ NK one to one + +550 +00:44:25,010 --> 00:44:29,250 +correspondence فهنا إيش معناه one to one + +551 +00:44:29,250 --> 00:44:32,430 +correspondence أنا بقدر أعيش مقابل الواحد في عنصر + +552 +00:44:32,430 --> 00:44:37,230 +ولا لا هي أنا عنصر مقابل الاثنين في عنصر فإذا هذه + +553 +00:44:37,230 --> 00:44:41,090 +العناصر ممكن أرقمها ممكن أرقمها فهنا الملاحظة + +554 +00:44:41,090 --> 00:44:44,630 +بتقول لي إذا الـ X is a non-empty طبعا إذا empty ما + +555 +00:44:44,630 --> 00:44:46,870 +هي معروفة نجي على الـ non-empty بنشوف إيش كيف + +556 +00:44:46,870 --> 00:44:50,830 +نتعامل معها is a non-empty finite set مجموعة + +557 +00:44:50,830 --> 00:44:55,570 +منتهية وغير فارغة إيش ده تكون؟ ده تكون فيها تناظر + +558 +00:44:55,570 --> 00:45:00,690 +مع مين؟ مع N sub M أو مع N sub K then there exists + +559 +00:45:00,690 --> 00:45:03,110 +a function هذه الـ function ممكن أسميها إيش؟ ده + +560 +00:45:03,110 --> 00:45:06,530 +اللي تتترقيم ما زالها finite مقدر أرقمهم يعني لأنه + +561 +00:45:06,530 --> 00:45:10,210 +إيش؟ فأنا إيش ممكن أعملها؟ F of واحد إيش أسميها؟ X + +562 +00:45:10,210 --> 00:45:13,930 +واحد إيش ما تكون صورة الواحد أسميها X واحد، صورة + +563 +00:45:13,930 --> 00:45:17,590 +الاثنين أسميها X اثنين، فكل عناصر الـ X ممكن إيش؟ + +564 +00:45:17,590 --> 00:45:22,540 +أرقمهم، ممكن نرقمهم، إذا أي finite set يا إما Phi + +565 +00:45:22,540 --> 00:45:26,520 +وإذا ما كانت Phi ممكن أرقمها من واحد لعدد العناصر لـ + +566 +00:45:26,520 --> 00:45:29,640 +K هذه من نظري هيك بتقول، فمن هنا وطالع هذا بيسهل + +567 +00:45:29,640 --> 00:45:33,420 +علينا، لو كل مجموعة finite ممكن أقولها إذا X تساوي + +568 +00:45:33,420 --> 00:45:36,960 +إذا مش Phi بتساوي من X واحد لـ X K for some K في + +569 +00:45:36,960 --> 00:45:40,860 +عدد K من العناصر، وهذا متفق مع التعريف القديم، نوجّه + +570 +00:45:40,860 --> 00:45:41,180 +هنا إن شاء الله diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yaE-rza0wfU.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yaE-rza0wfU.srt new file mode 100644 index 0000000000000000000000000000000000000000..4f24454670935c7b2dd9a30a93b9cdd542d46bc3 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yaE-rza0wfU.srt @@ -0,0 +1,2095 @@ +1 +00:00:19,670 --> 00:00:23,450 +بسم الله الرحمن الرحيم إن شاء الله احنا هنكمل مع + +2 +00:00:23,450 --> 00:00:28,070 +الrelations وبشكل خاص مع ال equivalence relations + +3 +00:00:28,070 --> 00:00:32,110 +وعلاقتها مع ال partition في المحاضرات الماضية + +4 +00:00:32,110 --> 00:00:37,090 +شفنا إذا في عندنا equivalence relation إبسلون + +5 +00:00:37,090 --> 00:00:42,450 +فصفوف التكافؤ اللي بتولدها هذه ال relation is a + +6 +00:00:42,450 --> 00:00:42,830 +partition + +7 +00:00:46,170 --> 00:00:50,290 +هو partition مظبوط شفنا إنه ولا صف فاضي والصفين + +8 +00:00:50,290 --> 00:00:54,910 +يا متطابقين يا تقاطع واتحاد كل الصفوف بدينا كل + +9 +00:00:54,910 --> 00:00:59,230 +ال X اليوم إن شاء الله هنشوف العكس لو بدأنا من ال + +10 +00:00:59,230 --> 00:01:05,370 +partition هل ممكن أولد علاقة التكافؤ؟ الجواب برضه + +11 +00:01:05,370 --> 00:01:08,890 +نعم. إذا بدأنا من equivalence relation وصلنا ل + +12 +00:01:08,890 --> 00:01:12,950 +partition هذا عبارة عن P partition الآن العكس نبدأ + +13 +00:01:12,950 --> 00:01:14,930 +من ال partition هل ممكن نوصل ل equivalence + +14 +00:01:14,930 --> 00:01:19,050 +relation؟ هنشوف أن الجواب نعم طبعًا هنمشي واحدة + +15 +00:01:19,050 --> 00:01:22,770 +واحدة. أولًا كيف من partition بعرف equivalence + +16 +00:01:22,770 --> 00:01:25,690 +relation؟ كيف نعرف أولًا relation وكيف تكون + +17 +00:01:25,690 --> 00:01:28,230 +equivalence relation؟ فطبعًا العنوان relations + +18 +00:01:28,230 --> 00:01:32,490 +induced by partitions. فطبعًا بقول let P be a + +19 +00:01:32,490 --> 00:01:35,930 +partition. احنا لدينا مجموعة capital X غير فارغة + +20 +00:01:35,930 --> 00:01:41,290 +مجزأة بطريقة ما مقسمة بطريقة ما ضمن شروط طبعة ال + +21 +00:01:41,290 --> 00:01:45,710 +partition ولا جزء فارغ أي جزءين يا متطابقين يا + +22 +00:01:45,710 --> 00:01:48,110 +disjoint يا مفاصلين تمامًا ما ما ما ما ما ما ما ما + +23 +00:01:48,110 --> 00:01:48,290 +ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما + +24 +00:01:48,290 --> 00:01:49,170 +ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما + +25 +00:01:49,170 --> 00:01:50,310 +ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما + +26 +00:01:50,310 --> 00:01:50,370 +ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما + +27 +00:01:50,370 --> 00:01:50,410 +ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما + +28 +00:01:50,410 --> 00:02:00,270 +ما ما ما ما ما ما ما + +29 +00:02:00,430 --> 00:02:05,470 +بيكون لهم علاقة مع بعض إذا وقعوا في نفس الجزء هاي X + +30 +00:02:05,470 --> 00:02:11,190 +وهاي Y وهاي Y وماكنتش لهم علاقة مع بعض إذا وقعوا + +31 +00:02:11,190 --> 00:02:15,510 +في نفس الجزء وهذه X طب لو أنا كان في عندي عنصر + +32 +00:02:15,510 --> 00:02:20,380 +ثالث Z هنا في جزء آخر هل الزي دي علاقة مع ال X؟ لأ + +33 +00:02:20,380 --> 00:02:24,120 +اللي علاقة مع ال Y؟ لأ فالعنصرين بيكون اللي هم + +34 +00:02:24,120 --> 00:02:27,500 +علاقة مع بعضها .. التعريف إذا وقعوا في نفس الجزء + +35 +00:02:27,500 --> 00:02:31,080 +أنا عندي partition يعني عندي أجزاء للمجموعة فكل + +36 +00:02:31,080 --> 00:02:33,960 +عنصرين إذا وقعوا في نفس الجزء اللي هم علاقة مع بعض + +37 +00:02:33,960 --> 00:02:39,010 +اختلفت الأجزاء مافيش علاقة فهي التعريف فبقول لي we + +38 +00:02:39,010 --> 00:02:42,910 +define a relation ايش .. ايش الرمز تبعها؟ X على P + +39 +00:02:42,910 --> 00:02:45,810 +زي ما دايما في عندنا مفهوم فاحنا في عندنا + +40 +00:02:45,810 --> 00:02:49,890 +partition بيولد علاقة فتسميها ايش؟ relation + +41 +00:02:49,890 --> 00:02:54,470 +induced by .. تتولد من .. induced by .. اه تعرف + +42 +00:02:54,470 --> 00:02:58,150 +بدليل ال partition ايش رمزها؟ X على P .. X على P + +43 +00:02:58,150 --> 00:03:01,690 +طيب هي relation من وين لوين؟ من X ل X لأن منصوبة إن + +44 +00:03:01,690 --> 00:03:05,600 +هي علاقة تكافؤ طيب كيف بنعرفها؟ بيقول لي الزوج + +45 +00:03:05,600 --> 00:03:09,420 +المرتب ينتمي لل relation وقت إيش؟ if and only if + +46 +00:03:09,420 --> 00:03:14,100 +there exists a set A يعني جزء تنتمي لل partition + +47 +00:03:14,100 --> 00:03:19,260 +لأنّه جزء إشماله such that X and Y are in A ال X و + +48 +00:03:19,260 --> 00:03:22,920 +Y في نفس الجزء that is بالرموز هيها ال relation + +49 +00:03:22,920 --> 00:03:27,560 +ايش عناصرها؟ أزواج مرتبة such that X في ال A والـ + +50 +00:03:27,560 --> 00:03:31,200 +Y في ال A for some A لل P فال X وال Y ليش إنهم + +51 +00:03:31,200 --> 00:03:34,540 +علاقة مع بعض؟ لأنهم وقعوا في جزء إنما لو في عندنا + +52 +00:03:34,540 --> 00:03:37,920 +هنا A و B ليش إنهم علاقة مع بعض؟ لأنهم وقعوا في + +53 +00:03:37,920 --> 00:03:41,160 +جزء معين مش دارون نفس الجزء فكل عنصرين في نفس + +54 +00:03:41,160 --> 00:03:46,020 +الجزء لكن كل جزء بيكوّن لأزواج مرتبة أزواج مرتبة + +55 +00:03:46,020 --> 00:03:48,980 +واضح التعريف؟ اه إن شاء الله هنشوف الأمثلة وإن + +56 +00:03:48,980 --> 00:03:55,700 +شاء الله الأمور بتكون أفضل نشوف المثال الأول طبعًا + +57 +00:03:55,700 --> 00:03:58,660 +دايمًا بنبدأ بالأمثلة البسيطة عشان دايمًا الإنسان + +58 +00:03:58,660 --> 00:04:02,000 +بيبدأ من المرحلة الدنيا وبيبنيه وبيطلع وبتساعد + +59 +00:04:02,000 --> 00:04:05,100 +في المفهوم نبدأ مجموعة صغيرة طبعًا هذا أسهل في + +60 +00:04:05,100 --> 00:04:09,600 +الفهم من تلت عناصر ومعوونها partition كيف ال + +61 +00:04:09,600 --> 00:04:13,440 +partition؟ ال Zero مع التانين جزء والواحد لحاله لو + +62 +00:04:13,440 --> 00:04:19,480 +رسمنا صورة هي جزء ايه فيها الواحد لحاله وال Zero + +63 +00:04:19,480 --> 00:04:23,800 +والتانين لحاله اللي مع بعض Zero واتنين والواحد + +64 +00:04:23,800 --> 00:04:27,280 +لحاله فهي partition وهي مجموعة بدنا نحسب العلاقة + +65 +00:04:27,280 --> 00:04:30,920 +اللي بيولدها هذا ال partition اللي بيش بيعرف هذا + +66 +00:04:30,920 --> 00:04:34,120 +ال partition find the relation بدنا نحسبها وبعدين + +67 +00:04:34,120 --> 00:04:38,800 +بدنا نجاوب هل العلاقة المتولدة هي علاقة تكافؤ ولا + +68 +00:04:38,800 --> 00:04:43,100 +لأ؟ فنبدأ الحل solution فطبعًا ايش الجزء الأول من + +69 +00:04:43,100 --> 00:04:48,180 +الحل؟ بدنا نحسب X على P اللي أنا ممكن اسميها Q + +70 +00:04:48,180 --> 00:04:53,740 +اختصارًا إذا حبيت نسميها Q تساوي عشان R طيب ماشي + +71 +00:04:53,740 --> 00:04:59,100 +إشماله دي من التعريف ايه فوق؟ بدنا الأزواج المرتبة + +72 +00:04:59,100 --> 00:05:02,140 +ليش يكون الأول والتاني بيقعوا بنفس الجزء + +73 +00:05:02,140 --> 00:05:07,900 +فسؤال الأول هل الواحد لعلاقة مع نفسها؟ بالتأكيد + +74 +00:05:07,900 --> 00:05:10,700 +لأنّها هي ونفسها بيقعوا في نفس الجزء إذا أول زوج + +75 +00:05:10,700 --> 00:05:14,600 +عندي الواحد وواحد بنفس الأسلوب ال Zero وال Zero + +76 +00:05:14,600 --> 00:05:18,790 +بنفس الأسلوب التنين والتنين ولا لأ؟ لازم يكون لأن + +77 +00:05:18,790 --> 00:05:22,690 +الواحد باتجاه هي في جزء ونفسها في جزء آخر، + +78 +00:05:22,690 --> 00:05:25,470 +مانفعش، وال Zero نفس الشيء وال Two نفس الجزء، + +79 +00:05:25,470 --> 00:05:29,310 +إذا حسبناها، إذا واضح على طول إنّ هذه علاقة إشماله، + +80 +00:05:29,310 --> 00:05:32,350 +علاقة انعكاس، reflexive، واضح؟ كل عنصر دي قاعمة + +81 +00:05:32,350 --> 00:05:36,190 +نفسه، تمام، طيب، ايش كمان؟ هل الواحد لعلاقة مع أي + +82 +00:05:36,190 --> 00:05:39,810 +حد آخر؟ لأ، لأنّه في جزء لحاله، إذا الواحد خلصنا، + +83 +00:05:39,810 --> 00:05:43,590 +طيب ال Zero ايه العلاقة مع حد آخر؟ مع التنين، لأنّ + +84 +00:05:43,590 --> 00:05:50,030 +هي والتنين بيقع في نفس الجزء طب والتنين و Zero و + +85 +00:05:50,030 --> 00:05:53,490 +خلصنا .. اه .. وخلصنا .. لأ .. طب ليش؟ لأنّه زي ما + +86 +00:05:53,490 --> 00:05:57,530 +تشوفين التعريف بيقول يقعوا في نفس الجزء الترتيب + +87 +00:05:57,530 --> 00:06:01,550 +مهم؟ لأ .. إذا زوج موجود عكسه لازم يكون موجود لأنّها + +88 +00:06:01,550 --> 00:06:04,030 +الـ commutative التعريف .. اه .. commutative .. + +89 +00:06:04,030 --> 00:06:07,410 +اه فيا بيكون هذه هي ال relation فعنا أجزاء عرفنا + +90 +00:06:07,410 --> 00:06:11,770 +منها relation عرفنا منها relation اه .. فاحنا هي + +91 +00:06:11,770 --> 00:06:14,070 +ال Zero مع التنين والتنين مع ال Zero وال Zero مع ال + +92 +00:06:14,070 --> 00:06:15,990 +Zero والتنين مع التنين طب هذا الجزء الأول + +93 +00:06:17,840 --> 00:06:21,220 +التكافؤ؟ لأنّ الـ reflexive واضح من أول شيء + +94 +00:06:21,220 --> 00:06:25,680 +الـ symmetric كل زوج عكسه موجود لأنّها and والـ and + +95 +00:06:25,680 --> 00:06:28,240 +دايمًا committed الترتيب مش مهم طب هل هذه + +96 +00:06:28,240 --> 00:06:30,260 +transitive؟ لو فحصنا من اللي جاها فعلًا أنّها + +97 +00:06:30,260 --> 00:06:33,980 +transitive لأنّ مين بيبدأ بواحد؟ مفيش مين بيبدأ ب + +98 +00:06:33,980 --> 00:06:37,780 +Zero؟ Zero اتنين يؤدي Zero Zero اتنين صح طيب مين + +99 +00:06:37,780 --> 00:06:40,920 +بيبدأ ب .. خلصنا مين بيبدأ باتنين؟ اتنين Zero + +100 +00:06:40,920 --> 00:06:44,740 +بيقدر اتنين Zero برضه صح مين كمان بيبدأ باتنين؟ + +101 +00:06:45,170 --> 00:06:47,890 +خلصنا، مافيش إلا Zero، خلصنا، فبنكون احنا فحصناه، + +102 +00:06:47,890 --> 00:06:51,450 +فهذه ايش فعلًا equivalence relation؟ الـ Q is an + +103 +00:06:51,450 --> 00:06:57,070 +equivalence relation relation + +104 +00:06:57,070 --> 00:07:00,530 +فلو فحصنا الشروط، بنلاقي إن كلهم متحققين، بنلاقي + +105 +00:07:00,530 --> 00:07:05,010 +هي علاقة انعكاس، علاقة تماثل، وعليها خاصية + +106 +00:07:05,010 --> 00:07:08,130 +التعدي، ففعلًا هذه علاقة تكافؤ + +107 +00:07:10,260 --> 00:07:13,840 +خلّيني أشوف كمان مثال برضه ناخد مجموعة كبيرة + +108 +00:07:40,350 --> 00:07:45,050 +هل هي علاقة تكافؤ ولا لأ؟ نبدأ بالحل نبدأ بالجزء + +109 +00:07:45,050 --> 00:07:49,550 +المباشر solution نبدأ بالفرع الأول بدنا ال + +110 +00:07:49,550 --> 00:07:55,330 +relation Q تساوي رمزها المجموعة Z على ال partition + +111 +00:07:55,330 --> 00:07:56,850 +وتساوي + +112 +00:07:58,420 --> 00:08:02,480 +طبعًا الاختلاف بين المثالين المثال الأول أنا عارف + +113 +00:08:02,480 --> 00:08:06,460 +المجموعة وبدأت أفحصهم واحد واحد ومين كل جزء ومين + +114 +00:08:06,460 --> 00:08:10,920 +عناصره واضح الأمور آه الآن عشان العناصر كتيرة يمكن + +115 +00:08:10,920 --> 00:08:14,680 +تكون حسابات شوية أطول فبدها من زاوية أخرى فإيش + +116 +00:08:14,680 --> 00:08:19,420 +نعمل؟ نفجر على التعريف الأصلي مين هذ relation؟ هي X + +117 +00:08:19,420 --> 00:08:23,760 +Y طبعًا في X cross X طبعًا لأنّ وين هي relation علي + +118 +00:08:23,760 --> 00:08:29,040 +ال X ممكن نكتبها للتأكيد هي in Z cross Z لأنّها X + +119 +00:08:29,040 --> 00:08:32,460 +cross X واضحة من الصياح المفروض تكون واضحة في + +120 +00:08:32,460 --> 00:08:35,660 +التعريف هنا X Y وين بدأ تكون في ال Cartesian + +121 +00:08:35,660 --> 00:08:39,320 +product X مع نفسها طبعًا لأنّها علاقة على ال X طبعًا + +122 +00:08:39,320 --> 00:08:45,020 +ايش التعريف؟ such that ال X تنتمي لل A and + +123 +00:08:46,890 --> 00:08:54,210 +Y تنتمي لل A for some A تنتمي لل partition اللي + +124 +00:08:54,210 --> 00:09:02,130 +في هذا السؤال هو ايه؟ هو E و D هو E و D متابعين؟ + +125 +00:09:03,680 --> 00:09:08,460 +في أي حد عنده استفسار؟ واضح تقريبًا أنا عندي علاقة + +126 +00:09:08,460 --> 00:09:13,800 +متولدة من partition ايش الزوج المرتب؟ هو كل عنصرين + +127 +00:09:13,800 --> 00:09:18,020 +موجودين في نفس الجزء في جزء ما من الأجزاء تمام؟ اه + +128 +00:09:18,020 --> 00:09:21,980 +ميزة هذا السؤال إنّ صحيح العناصر كتيرة لكن الأجزاء + +129 +00:09:21,980 --> 00:09:25,480 +قليلة جزءين لما بقوله for some A تنتمي لل + +130 +00:09:25,480 --> 00:09:29,180 +partition ايش احتمالات ال A؟ ياد E ياد D مافيش + +131 +00:09:29,180 --> 00:09:33,780 +الاحتمالين فخلينا نكتب هذا الكلام فهذا تساوي X of Y + +132 +00:09:33,780 --> 00:09:36,680 +طبعًا في ال Z cross ال Z بدي اكتب .. بديش اكتب + +133 +00:09:36,680 --> 00:09:42,140 +اختصار لإنه واضح بحيث ال X تنتمي ل E إما تنين في + +134 +00:09:42,140 --> 00:09:48,220 +ال E and Y تنتمي لل E هي الاحتمال الأول مظبوط إذا + +135 +00:09:48,220 --> 00:09:53,320 +كانت ال A تساوي E أو احتمال ثاني لإنّ هذا يمكن تكون + +136 +00:09:53,320 --> 00:09:58,380 +true أو هذا يمكن تكون true ال X في ال D and Y في + +137 +00:09:58,380 --> 00:10:02,090 +ال D ممكن اكتب بهذا الشكل هذا اليوم اللي اترجمه هيك + +138 +00:10:02,090 --> 00:10:05,050 +ولا لأ؟ لأنّ أنا بقول for some A ايش احتمالات + +139 +00:10:05,050 --> 00:10:09,430 +ال A؟ ال A يا E يا D for some ايش معناه؟ + +140 +00:10:09,430 --> 00:10:12,610 +there exist و there exist ايش تقابل؟ R شوفتوا كيف + +141 +00:10:12,610 --> 00:10:17,190 +الأمور متسايمة؟ تمام؟ تمام، نمشي كمان خطوة، بدي + +142 +00:10:17,190 --> 00:10:19,510 +أوصل الـquadration، بدي أكتبها بشكل حتى تكون أنتم + +143 +00:10:19,510 --> 00:10:26,350 +متعودين عليه، what is that? XY such that، ايش + +144 +00:10:26,350 --> 00:10:31,690 +معناة X even؟ يعني مضاعفات اثنين يعني ايش بكتبها + +145 +00:10:31,690 --> 00:10:36,290 +اثنين في N أو اثنين في M فهذا معناته أن X تساوي + +146 +00:10:36,290 --> 00:10:41,890 +اثنين N و Y تساوي اثنين M for some N و M انتجة + +147 +00:10:41,890 --> 00:10:44,970 +لأنها مضاعفات اثنين بس بدي أكتبها بالأخر بدي أجلها + +148 +00:10:44,970 --> 00:10:51,100 +شوية عشان أختصر في الكتاب orايش معنى فردي؟ 2n + +149 +00:10:51,100 --> 00:10:57,880 +زيادة 1 فال X تساوي 2n زيادة 1 and Y تساوي 2m زيادة 1 + +150 +00:10:57,880 --> 00:11:01,120 +طبعا هذول ال N و ال M ايش شمالهم؟ integers for + +151 +00:11:01,120 --> 00:11:07,040 +some N و M في ال Z اتبعين؟ + +152 +00:11:08,870 --> 00:11:13,450 +المتابعين؟ اه فاحنا قلنا تعريف العلاقة اللي بولدها + +153 +00:11:13,450 --> 00:11:17,270 +ال partition هي كل زوج مرتب بحيث أن الحدث الأول + +154 +00:11:17,270 --> 00:11:20,890 +و الثاني يقع في نفس الجزء بما أن ال partition جزءين + +155 +00:11:20,890 --> 00:11:24,090 +إذا هذول هيكون في الجزء الأول أو الجزء الثاني الآن + +156 +00:11:24,090 --> 00:11:27,690 +من معلوماتنا الجزء الأول هو الأعداد الزوجية كيف + +157 +00:11:27,690 --> 00:11:31,110 +صورتهم اثنين في N أو اثنين في M من مضاعفات الاثنين + +158 +00:11:31,110 --> 00:11:34,510 +طباشير الفردي اللي هو عيش مش زوجي يعني زائد واحد أو + +159 +00:11:34,510 --> 00:11:37,850 +ناقص واحد لأن كل أعداد اللي جابله زوجي اللي بعده + +160 +00:11:37,850 --> 00:11:41,370 +بيجي فردي اتبع ولا لأ تمام خلينا نعمل trick بسيط + +161 +00:11:41,370 --> 00:11:48,350 +الآن بس عشان أنا بدي أوصل لكل صورة مألوفة اه يساوي XY + +162 +00:11:49,560 --> 00:11:56,100 +لو طرحنا X ناقص Y في الحالتين X ناقص Y ايش بتعطيني؟ + +163 +00:11:56,100 --> 00:12:03,340 +2N ناقص M وفي الثاني برضه 2N ناقص M الواحد بتروح + +164 +00:12:03,340 --> 00:12:10,080 +مع الواحد اللي هي ايش بتساوي؟ اثنين في K for some K + +165 +00:12:10,080 --> 00:12:15,260 +from N to Z لأن ال N و ال M أعداد صحيحة فالفرق + +166 +00:12:15,260 --> 00:12:20,560 +بينهم أعداد صحيحة بدي أسميه K ال N relation لو + +167 +00:12:20,560 --> 00:12:25,230 +تخيلنا هذا مقلوبة الكل مش مقلوبة اللي سميناها Mode M + +168 +00:12:25,230 --> 00:12:28,230 +تذكروا؟ احنا أخذناها Mode 3 كمثال بالتفصيل + +169 +00:12:28,230 --> 00:12:31,850 +و قلنا لكم أي عدد صحيح غير الثلاثة بيقدر الغرض واحد + +170 +00:12:31,850 --> 00:12:35,390 +اثنين ثلاثة أربعة و هكذا و يمكن نشوف الأربعة كمثال + +171 +00:12:35,390 --> 00:12:39,250 +لما حسبنا صفوف التكافؤ و لا لأ فدياش relation فهي + +172 +00:12:39,250 --> 00:12:41,670 +شايفين أن ال relation مشهورة هي عندي بدأت بال + +173 +00:12:41,670 --> 00:12:45,050 +partition و ولدت relation و relation معروفة فهي + +174 +00:12:45,050 --> 00:12:48,880 +relation relation معروفة طبعا واحد يقول لك ضروري + +175 +00:12:48,880 --> 00:12:51,600 +نعمل كل حسابات لو المثال جاك ال relation و كده + +176 +00:12:51,600 --> 00:12:55,320 +أول تعريف يكفي عندي لكن هناكش كان الهدف أن نوصل ل + +177 +00:12:55,320 --> 00:12:58,780 +relation معروفة نوصل ل relation معروفة طبعا هلها + +178 +00:12:58,780 --> 00:13:01,400 +equivalence relation؟ طبعا متأكدين لأن احنا في + +179 +00:13:01,400 --> 00:13:06,280 +موضوع ال M فهي IH2 اللي هي IHQ is an equivalence + +180 +00:13:06,280 --> 00:13:10,060 +relation اه فالآن الحقيقة أن هو اللي صار في دول + +181 +00:13:10,060 --> 00:13:14,720 +المثالين بدأنا من partition حسبنا ال relation اللي + +182 +00:13:14,720 --> 00:13:17,800 +بيولدها ال partition طلع في المثالين اللي هذه + +183 +00:13:17,800 --> 00:13:21,620 +العلاقات هي علاقات تكافؤ فهل هذا الكلام دائما صحيح + +184 +00:13:21,620 --> 00:13:24,620 +و لا بس كانت من الصدفة المثالين الحقيقة دائما صحيح + +185 +00:13:24,620 --> 00:13:27,440 +زي ما حد شافه في النظرية فنظرية ثلاثة خمسة بيقول + +186 +00:13:27,440 --> 00:13:32,900 +دائما EQ هذي اللي هي X على B، ايش معنى X على B؟ ال + +187 +00:13:32,900 --> 00:13:36,060 +relation اللي بعرفها ال partition دائما + +188 +00:13:36,060 --> 00:13:39,800 +equivalence relation فهنا النظرية let B be a + +189 +00:13:39,800 --> 00:13:44,670 +partition of a non-empty set X then the relation X + +190 +00:13:44,670 --> 00:13:48,770 +على B is an equivalence relation on X طبعا يمكن + +191 +00:13:48,770 --> 00:13:51,710 +الرمز شوية غريب و بس احنا شايفين بيساعدنا بيقولني + +192 +00:13:51,710 --> 00:13:55,110 +the relation X على B هاد رمزها لإن معناته ايش؟ هي + +193 +00:13:55,110 --> 00:13:59,450 +العلاقة المتولدة من ال partition B على المجموعة X + +194 +00:13:59,450 --> 00:14:03,090 +على المجموعة X خليني أشوف البرهان مع بعض خليني + +195 +00:14:03,090 --> 00:14:07,750 +أشوف البرهان مع بعض طبعا كيف بنسميها الـ + +196 +00:14:07,750 --> 00:14:11,670 +equivalence relation؟ ثلاثة شروط إنها reflexive، + +197 +00:14:11,670 --> 00:14:19,310 +transitive و symmetric فهذه نظرية ثلاثة خمسة و هذه + +198 +00:14:19,310 --> 00:14:24,570 +ال proof طبعا أول شيء يجعلني أستخدم رمز أسهل لت + +199 +00:14:24,570 --> 00:14:30,800 +كيو تساوي X على B خلينا نرمز اللي احنا بالرمز Q + +200 +00:14:30,800 --> 00:14:34,000 +أسهلنا طبعا أنا ما أخد ال Q لأن زي هي واضحة علينا + +201 +00:14:34,000 --> 00:14:37,740 +زي قسمة قوشن فبدي أخد ال Q اه بدي أثبت أن ال Q + +202 +00:14:37,740 --> 00:14:40,900 +is an equivalent relation فأول شيء بدي أثبت أن الـ + +203 +00:14:40,900 --> 00:14:47,820 +Q is reflexive reflexive يعني ليش reflexive يعني + +204 +00:14:47,820 --> 00:14:53,220 +كل عنصر علاقة مع نفسه و زي ما شوفنا بالامثلة طبعا كل + +205 +00:14:53,220 --> 00:14:55,660 +عنصر زوجي ما هو بيبغى يقع مع الزوجي في المثال + +206 +00:14:55,660 --> 00:14:58,140 +الأخير و كل شوفنا أن الواحد لعقله في المثال اللي + +207 +00:14:58,140 --> 00:15:01,780 +جابله و هاكذا طب كيف بنثبت أن كل عنصر يقع مع نفسه + +208 +00:15:01,780 --> 00:15:06,820 +أنه علاقة مع نفسه أنه كل عنصر يقع بنفس الجزء من + +209 +00:15:06,820 --> 00:15:09,420 +البرتش احنا ايش عندنا معطيات؟ أن ال P partition + +210 +00:15:09,420 --> 00:15:12,460 +و هي relation و معروف كيف تعريفها ال Q بدنا نثبت إن + +211 +00:15:12,460 --> 00:15:16,760 +أنا reflexive فالآن أول شيء بدنا نثبت إنه كل .. + +212 +00:15:16,760 --> 00:15:19,640 +ايش بدنا نثبت؟ for all X، مظبوط؟ ايش تعريف + +213 +00:15:19,640 --> 00:15:24,240 +reflexive؟ for all X in capital X XX في ال Q، صح؟ + +214 +00:15:24,240 --> 00:15:27,380 +طب ما زال for all ايش كيف ده البرهان؟ let X be any + +215 +00:15:27,380 --> 00:15:32,960 +element in capital X فحنبدأ let small x in capital + +216 +00:15:32,960 --> 00:15:38,890 +X be any element any element طبعا طريقة الكتابة + +217 +00:15:38,890 --> 00:15:41,670 +و التقييم و التأخير نفس المعنى لت X be an element + +218 +00:15:41,670 --> 00:15:44,210 +such that X tend to be the capital X نفس المعنى + +219 +00:15:44,210 --> 00:15:49,090 +for all X تمام ايه؟ بدي أثبت أن ال X تقع مع نفسها + +220 +00:15:49,090 --> 00:15:55,490 +بنفس الجزء طب هل ال X بتقع بجزء أصلا؟ و ليش؟ ليش؟ + +221 +00:15:55,490 --> 00:15:59,210 +لأن ال partition بيغطي كل ال X فلازم كل عنصر يش + +222 +00:15:59,210 --> 00:16:05,160 +يكون بنفس ال X فده بيقول ليه؟ ال X تنتمي لل A for + +223 +00:16:05,160 --> 00:16:11,240 +some A تنتمي لل partition ايش دليلك أذكركم أن X + +224 +00:16:11,240 --> 00:16:15,180 +تساوي الاتحاد على ال partition تذكروا على ال A مش + +225 +00:16:15,180 --> 00:16:18,180 +هيك فيه أنا من الخاصية رقم اثنين في تعريف الـ + +226 +00:16:18,180 --> 00:16:20,760 +Partition هما عندنا فيه اللي هو خاصية رقم Zero + +227 +00:16:20,760 --> 00:16:24,160 +لضمان الكلام و خاصية رقم واحد و خاصية رقم اثنين فهذه + +228 +00:16:24,160 --> 00:16:27,640 +خاصية رقم اثنين ممتاز X تنتمي لل A إذا X اللي + +229 +00:16:27,640 --> 00:16:29,740 +علاقة مع نفسها لإننا ممكن نعمل conjunction X تنتمي + +230 +00:16:29,740 --> 00:16:33,140 +لل A و X تنتمي لل A فهي اللي بدائية فده بيقول لي إن + +231 +00:16:33,140 --> 00:16:39,240 +X X تنتمي لل Q وبالتالي and hence ال Q is + +232 +00:16:39,240 --> 00:16:44,180 +reflexive فخاصية ال reflexive أثبتت reflexive + +233 +00:16:48,110 --> 00:16:55,530 +تمام واضح تمام نجي للخاصية رقم اثنين بس خليني + +234 +00:16:55,530 --> 00:17:03,910 +أكتب ال Q is symmetric بدنا نثبت أنه أن ال Q is + +235 +00:17:03,910 --> 00:17:09,220 +symmetric و البرهان الحقيقة زي ما شرحنا من التعريف + +236 +00:17:09,220 --> 00:17:11,860 +طبعا ايش معنى symmetric إذا في زوجين ما في ال + +237 +00:17:11,860 --> 00:17:14,900 +relation عكسه بيكون موجود فحنبدأ البرهان نقول له + +238 +00:17:14,900 --> 00:17:21,880 +ايش let x,y تنتمي ل Q طيب ايش معنى ال Q إن ال x و + +239 +00:17:21,880 --> 00:17:27,220 +ال y في نفس الجزء فده implies اللي هو ايش x تنتمي + +240 +00:17:27,220 --> 00:17:33,660 +ل A و y تنتمي ل A for some a في ال partition + +241 +00:17:33,660 --> 00:17:37,620 +التعريف أنا قلت لكم تذكروا التعريفات تكون قدامنا + +242 +00:17:37,620 --> 00:17:41,760 +نعملهم بشيء ندور على كام صفحة لك تكونوا قدامنا طيب + +243 +00:17:41,760 --> 00:17:45,020 +اه الآن commutative هي القضية أنا بدي أبدل دور ال + +244 +00:17:45,020 --> 00:17:47,760 +X و دور ال Y ال X كانت إحداثي أول ده خليه إحداثي + +245 +00:17:47,760 --> 00:17:51,060 +ثاني ما هذي بتساوي هذي ايش ماله؟ أبدل لأن الآن دي + +246 +00:17:51,060 --> 00:17:55,980 +بدالية فده بيقول إن Y تنتمي لل A and X تنتمي لل A + +247 +00:17:55,980 --> 00:18:02,400 +for some A في ال partition اه الآن اتبدلت دور هذا ايه + +248 +00:18:02,400 --> 00:18:09,100 +معناته أن Y X في ال Q وهو المطلوب Thus, Q is + +249 +00:18:09,100 --> 00:18:17,180 +symmetric انتبهين + +250 +00:18:17,180 --> 00:18:24,720 +الخاصية الثالثة و الأخيرة بدنا نثبت أن ال Q is + +251 +00:18:24,720 --> 00:18:32,020 +transitive ال Q is transitive هذه ثلاثة + +252 +00:18:37,700 --> 00:18:42,020 +تمام ايه الشرط ال Transitive؟ بدنا زوجين بترتيب + +253 +00:18:42,020 --> 00:18:46,780 +معين موجودين لازم المكمل تبعهم الثالث يكون موجود + +254 +00:18:46,780 --> 00:18:53,210 +فبرضه بنبدأ ايش assume أو let let x,y في ال Q and + +255 +00:18:53,210 --> 00:18:58,470 +y,z في ال Q بدنا نثبت إنه x,z في ال Q ايش نعمل؟ + +256 +00:18:58,470 --> 00:19:02,650 +نستخدم التعريف ماذا يعني x,y في ال Q؟ يعني there + +257 +00:19:02,650 --> 00:19:05,810 +exist .. بتكتبها for some .. there exist there + +258 +00:19:05,810 --> 00:19:11,770 +exist a تنتمي لل partition بحيث x في ال A and y + +259 +00:19:11,770 --> 00:19:15,770 +في ال A هيك معناه ال x و ال y اللي ملاقة مع بعض + +260 +00:19:15,770 --> 00:19:20,360 +أنه من نفس الجزء and كفي كمان قاعدة كبيرة، ايش + +261 +00:19:20,360 --> 00:19:24,140 +معنى Y و Z في ال Q إنهم بنفس الجزء؟ طب هل ده + +262 +00:19:24,140 --> 00:19:27,160 +ضروري يكون A؟ مش عارف، تذكروا المثال اللي رسمناه؟ + +263 +00:19:27,160 --> 00:19:29,780 +اه، فانا بقول there exist .. ايش أسميها؟ A ولا + +264 +00:19:29,780 --> 00:19:32,900 +ايش؟ ولا أغير اسم؟ بنغير بيه، لأنهم مش عارفين و + +265 +00:19:32,900 --> 00:19:38,560 +متساويين، there exist B in partition بحيث أنه ايش؟ + +266 +00:19:38,560 --> 00:19:41,520 +Y في ال B و Z في ال B + +267 +00:19:44,880 --> 00:19:48,180 +تمام الآن أنا ايش مطلوب مني أثبت إن X و Z اللي هم + +268 +00:19:48,180 --> 00:19:53,100 +علاقة مع بعض يعني يقع في نفس الجزء عندي معلومات ال + +269 +00:19:53,100 --> 00:19:56,920 +X في ال A و ال Z في ال B و أنت ايش هيقع في نفس الجزء + +270 +00:19:56,920 --> 00:20:00,740 +إذا ال A و ال B تترابقها متساويين طب ليش متساويين؟ + +271 +00:20:00,740 --> 00:20:04,760 +في عناصر مشتركة و من خلاص ال partition يا كل عناصر + +272 +00:20:04,760 --> 00:20:07,580 +مشتركة يا مافيش مشتركة إذا واحدة مشتركة لازم الكل + +273 +00:20:07,580 --> 00:20:12,040 +يكون مشترك فهذا it follows ممكن أكتب بهذا الشكل it + +274 +00:20:12,040 --> 00:20:17,970 +follows that Y تنتمي ل A تقاطع ال B ال Y مشتركة + +275 +00:20:17,970 --> 00:20:25,190 +وبالتالي ال A تقاطع ال B لا يساوي فاي وبالتالي A + +276 +00:20:25,190 --> 00:20:28,210 +تساوي B لأنهم partition كل واحدة من خواص ال + +277 +00:20:28,210 --> 00:20:31,770 +partition لأن ال B partition تمام ما زال A تساوي B + +278 +00:20:31,770 --> 00:20:35,570 +ال X في ال A إذن هي في ال B و ال Z في ال A و ال B + +279 +00:20:35,570 --> 00:20:41,050 +متساوية فده بيقول ايه X و Z تنتمي ال A تساوي ال B + +280 +00:20:41,050 --> 00:20:49,090 +و هذا معناته أن X Z في ال relation وهو المطلوب is + +281 +00:20:49,090 --> 00:20:54,610 +a transit طبعاً + +282 +00:20:54,610 --> 00:20:59,950 +1 و 2 و 3 بتدل علينا علاقة تكافؤ واضح فإحنا + +283 +00:20:59,950 --> 00:21:04,870 +الأمثلة الماضية كانت مش حاجة نادرة إنما هي دائماً + +284 +00:21:04,870 --> 00:21:05,310 +صحية + +285 +00:21:08,990 --> 00:21:13,390 +نعم؟ في أي سؤال واضح؟ إذا في أي نقطة جاذب ما نمشي + +286 +00:21:13,390 --> 00:21:18,210 +عنها إذن هي ما أحنا شوفنا في النظريتين زي ما حكينا + +287 +00:21:18,210 --> 00:21:22,790 +في بداية المحاضرة كل علاقة تكافؤ بتولد partition + +288 +00:21:22,790 --> 00:21:27,610 +عبارة عن إيش؟ صفوف التكافؤ وكل partition بيولد + +289 +00:21:27,610 --> 00:21:31,110 +علاقة معرفة بدل الشكل إنه هي عبارة عن علاقة اللي + +290 +00:21:31,110 --> 00:21:34,230 +هو إيش يكونوا في نفس الجزء هي العلاقة إيش علاقة X + +291 +00:21:34,230 --> 00:21:38,880 +مع Y بيقعا في نفس الجزء. نقطة أخيرة في هذا الموضوع + +292 +00:21:38,880 --> 00:21:42,800 +احنا صار عنا ببدأ من partition بولد equivalence + +293 +00:21:42,800 --> 00:21:45,280 +relation ببدأ من equivalence relation بولد + +294 +00:21:45,280 --> 00:21:49,380 +partition طب لو أنا بدأت من نقطة ما هل برجع لنفس + +295 +00:21:49,380 --> 00:21:52,020 +النقطة ولا لأ؟ فهذا السؤال اللي احنا هنجاوب عليه + +296 +00:21:52,020 --> 00:21:59,980 +الآن فصارت عندنا الصورة التالية. بدأنا من + +297 +00:21:59,980 --> 00:22:05,780 +equivalence relation وولدنا partition عبارة عن + +298 +00:22:05,780 --> 00:22:10,160 +مين؟ صفوف التكافئة، مظبوط؟ هذه المحادرات الماضية + +299 +00:22:10,160 --> 00:22:15,360 +اليوم بدأنا من ال partition وولدنا relation Q + +300 +00:22:15,360 --> 00:22:21,240 +تساوي رمزها X على B هذه علاقة التكافئة. هل هذه + +301 +00:22:21,240 --> 00:22:24,880 +علاقة التكافئة تختلف عن الأصلية اللي بدأت منها؟ + +302 +00:22:24,880 --> 00:22:30,040 +السؤال لأ. متساويات. فدى دائرة مغلقة. بدأت من + +303 +00:22:30,040 --> 00:22:33,740 +equivalence relation بولّد partition. ال partition + +304 +00:22:33,740 --> 00:22:36,220 +بيولّد equivalence relation. ال relation الأصلية زي + +305 +00:22:36,220 --> 00:22:39,040 +ما توي شفنا في ال mod. بدأنا من ال partition وولدنا + +306 +00:22:39,040 --> 00:22:42,020 +relation ورجعنا للأصل. طب العكس. بدأت من partition + +307 +00:22:42,020 --> 00:22:46,260 +بولّد علاقة تكافؤ. علاقة التكافؤ بتولّد partition + +308 +00:22:46,260 --> 00:22:49,460 +مين هو اللى بدأت منه؟ فعشان هي زي الدائرة من أي + +309 +00:22:49,460 --> 00:22:51,720 +نقطة ابتدى بترجع لمين؟ لنفس النقطة + +310 +00:22:55,340 --> 00:22:59,740 +مش بالظبط يعني لأ. بس هي بادئة الصورة. إذا بدأنا من + +311 +00:22:59,740 --> 00:23:03,020 +partition كل partition بيولد equivalence relation + +312 +00:23:03,020 --> 00:23:06,000 +كل equivalence relation بتولد partition هل ال + +313 +00:23:06,000 --> 00:23:08,080 +partition هذا جديد ولا نفس اللي بدأت منه ونفس + +314 +00:23:08,080 --> 00:23:11,680 +اللي بدأت منه؟ فهي صورها. فطبعا عشان أوصل لعدي نظرية + +315 +00:23:11,680 --> 00:23:17,560 +بس عندي اللي هو نظرية تمهيدية لما بيقوللي إذا كان + +316 +00:23:17,560 --> 00:23:22,620 +عندي partition وال partition ايش ماله؟ وولد علاقة + +317 +00:23:22,620 --> 00:23:27,420 +تكافؤ، كل علاقة تكافؤ إيش بتعرف؟ صفوف تكافؤ، فبقول + +318 +00:23:27,420 --> 00:23:33,320 +الصف اللي بتعرفه هذه العلاقة X أنا عندي.. هي عندي + +319 +00:23:33,320 --> 00:23:38,320 +partition وهيعندي عنصر X في جزء A مثلا في هذا + +320 +00:23:38,320 --> 00:23:42,040 +الجزء طيب ال partition ولد relation اللي هي Q + +321 +00:23:42,040 --> 00:23:47,700 +واخدت عنصر X بدي احسب مين؟ X على Q صف في التكافؤ + +322 +00:23:47,700 --> 00:23:50,320 +اللي ولد وتولد relation طيب هذا ال equivalent + +323 +00:23:50,320 --> 00:23:54,360 +class عبارة عن partition إيش علاقة؟ هذا الجزء اللي + +324 +00:23:54,360 --> 00:23:58,140 +هو صف ال X مع ال A اللي إجت منها ال X متساوين.. + +325 +00:23:58,140 --> 00:24:00,220 +متساوين.. هذا اللي ما بتقول.. بقى ده الشكل و + +326 +00:24:00,220 --> 00:24:03,100 +عشان هيك بيصير تطابق لأنه كيف الصورة.. احنا قلنا + +327 +00:24:03,100 --> 00:24:07,880 +بدأنا من partition عرف علاقة التكافؤ.. علاقة + +328 +00:24:07,880 --> 00:24:11,820 +التكافؤ بتعرف partition كي بتجزه حسب صف التكافؤ.. + +329 +00:24:11,820 --> 00:24:14,760 +إيش ماله؟ ينطبق مع التجزيء السابق فهي بيجي دلوقتي + +330 +00:24:14,760 --> 00:24:17,560 +كل صف بنطبق مع اللي إيش الجزء اللي إيجي منه العنصر + +331 +00:24:17,560 --> 00:24:20,720 +.. الجزء منه العنصر.. فكان عندي العلاقة أنهصف ال + +332 +00:24:20,720 --> 00:24:23,680 +X المتولج من هذه العلاقة بيساوي الجزء اللي إتي منه + +333 +00:24:23,680 --> 00:24:28,000 +النص بشكل صريح let P be a partition of a non-empty + +334 +00:24:28,000 --> 00:24:31,440 +set X and let Q تساوي X على P الرمز اللي اتعودنا + +335 +00:24:31,440 --> 00:24:35,700 +عليه بقول if X تنتمي لل A for some A طبعاً لازم + +336 +00:24:35,700 --> 00:24:38,700 +تكون موجودة فيها then صف ال X إيش بيساوي الجزء + +337 +00:24:38,700 --> 00:24:46,040 +اللي موجود فيها إيش ال X بيساوي إيه؟ prove خلينا + +338 +00:24:46,040 --> 00:24:46,940 +نبره هنا مع بعض + +339 +00:24:50,750 --> 00:24:55,490 +لأنها تساعدنا في برهانة النظرية الجاية. proof طبعاً + +340 +00:24:55,490 --> 00:25:03,250 +هذه اللمّة تمام. فطبعاً أنا في عندي جملة شرطية X + +341 +00:25:03,250 --> 00:25:06,830 +تنتمي لل A for some A نفترض أن هذا كلام صحيح + +342 +00:25:06,830 --> 00:25:15,210 +assume X تنتمي لل A for some A in the partition + +343 +00:25:15,210 --> 00:25:22,270 +أيش بتثبت؟ أن صف ال X يسوى بهذه المجموعة A. هذه علاقة + +344 +00:25:22,270 --> 00:25:26,690 +إيش؟ تساوي مجموعات كي بدأ أثبتها؟ بدأ أبدأ عنصر من + +345 +00:25:26,690 --> 00:25:30,730 +اليمين وأصله لليسار إذا الطريق اتجاهين خلص + +346 +00:25:30,730 --> 00:25:33,590 +الإثبات إذا اتجاه واحد بدأ أرجعه إيش؟ بدي كمان + +347 +00:25:33,590 --> 00:25:38,450 +طريق تاني يتوصلني من إيه لل X على Q فهنبدأ، فهناخد + +348 +00:25:38,450 --> 00:25:42,950 +عنصر عشوائي، إيش نسميه؟ ال X مشغولة، نسمي اسم جديد + +349 +00:25:42,950 --> 00:25:47,990 +let Y be any element تنتمي لل X على Q be any + +350 +00:25:47,990 --> 00:25:51,820 +element طبعاً ممكن تلاقوا في الكتب المتقدمة ما بكتبش + +351 +00:25:51,820 --> 00:25:54,720 +N element لإنها واضحة من السياق انها عامة تمام، + +352 +00:25:54,720 --> 00:25:58,580 +بدأ أوصل ال Y لل A، الحقيقة حد مشي في اتجاهها، + +353 +00:25:58,580 --> 00:26:03,520 +ممتاز، ماذا يعني أن ال Y في صف ال X؟ ايش تعريف + +354 +00:26:03,520 --> 00:26:07,220 +الصف؟ يعني ال X وال Y لملاقا مع بعض، فهذا يؤدي أن + +355 +00:26:07,220 --> 00:26:12,180 +X و Y تنتمي ل Q، من وين جيبت هذا الكلام؟ تعريف X + +356 +00:26:12,180 --> 00:26:18,130 +على Q صحيح؟ متذكرين التعريف؟ هيك بيقول، تمام أنا + +357 +00:26:18,130 --> 00:26:20,670 +واحد من الدواصل، دواصل الـ X للـ A، طب إيش تعريف + +358 +00:26:20,670 --> 00:26:24,030 +الـ Q؟ وقت إيش بيكونوا الملاخة مع بعضيش Q، X على + +359 +00:26:24,030 --> 00:26:28,370 +B، إذا الـ X و Y وقعا في جزء ما مع بعض، فهذا يؤدي + +360 +00:26:30,470 --> 00:26:34,530 +أنه there exist طيب ال A أنا فيها عندي جزء مثبت A + +361 +00:26:34,530 --> 00:26:37,270 +لكن التعريف بيقول لي إيش ال X و ال Y قاع في جزء + +362 +00:26:37,270 --> 00:26:40,290 +ما، هل بدروا يكون إيه؟ مش عارف، لسه مش عارف، بدي + +363 +00:26:40,290 --> 00:26:43,610 +أثبت إنه إيه، فبقول لي there exist B في ال + +364 +00:26:43,610 --> 00:26:49,190 +partition بحيث X تنتمي لل B and Y تنتمي لل B، for + +365 +00:26:49,190 --> 00:26:52,510 +some كتبته في الأول، مزال X و Y له ملاقة مع بعض، + +366 +00:26:52,510 --> 00:26:55,590 +إذا لازم يقاع في نفس الجزء، هيك تعريف ال Q، طب هذا + +367 +00:26:55,590 --> 00:26:58,600 +جزء ما؟ عشان هذا الجزء بيساوي a مش عارف ال a أنا + +368 +00:26:58,600 --> 00:27:02,020 +انتقلتها من أول بقدرش أستخدمها. ممتاز إيه صار عندي + +369 +00:27:02,020 --> 00:27:05,340 +ذاتي ال trick اللي تاوي استخدمناها ال x في ال b و + +370 +00:27:05,340 --> 00:27:11,660 +ال x في ال a إذا تقاطع ال a وال b ليس في then x + +371 +00:27:11,660 --> 00:27:16,820 +تنتمي لل a تقاطع ال b ال x في ال b وال x في ال a + +372 +00:27:16,820 --> 00:27:21,760 +مظبوط إذا التقاطع لا يساوي في implies a تقاطع ال b + +373 +00:27:21,760 --> 00:27:27,600 +لا يساوي في إذا إيش ال a بتساوي بتساوي ال b إذا الـ + +374 +00:27:27,600 --> 00:27:30,880 +A بتسوى ال B إيش صار الصورة نقرأ مع بعض وده ممكن + +375 +00:27:30,880 --> 00:27:34,380 +احنا نعمله أنه خلص البوابة ولا لأ أخدت عنصر في ال + +376 +00:27:34,380 --> 00:27:38,580 +A أثبتت أنه ال إيش أنا إيش بدها أثبت أنها هي وين؟ + +377 +00:27:38,580 --> 00:27:42,940 +آسف أنا أخدت عنصر Y هاي Y في ال XQ مش هيك بدنا + +378 +00:27:42,940 --> 00:27:48,060 +نثبت أخدنا عنصر Y هنا ال Y موجودة في ال B وال B + +379 +00:27:48,060 --> 00:27:53,790 +تسوى ال A إذا ال Y وين؟ في ال A and hence Y تنتمي + +380 +00:27:53,790 --> 00:27:59,790 +للـ A فإيش وصلنا بدأنا من X على Q وصلناها للـ A إذا + +381 +00:27:59,790 --> 00:28:03,790 +الأول سبست من التاني مش ماشي تكافأ يعني لأنه ماشي + +382 +00:28:03,790 --> 00:28:08,010 +بيقيش استنتاج فإذا أثبتنا للتجاه الأول العكس الآن + +383 +00:28:08,010 --> 00:28:15,470 +نبدأ من الطرف اليمين ناخد عنصر في الـ A الآن let Y + +384 +00:28:15,470 --> 00:28:22,950 +تنتمي للـ A be any element وأرجو نتعود نقرأ صح واحد + +385 +00:28:22,950 --> 00:28:26,390 +يقولي طب ايه وأنا أ assume هدى هدى مظلة عامة تبعت + +386 +00:28:26,390 --> 00:28:29,690 +ال F then في الجملة بعدين بدينا قولنا إيش إيش + +387 +00:28:29,690 --> 00:28:33,470 +بيقول النظراء اللي ما if X تنتمي لل A for some A + +388 +00:28:33,470 --> 00:28:37,570 +فدى مثبت أخلصناها then بدي مجموعة تساوي مجموعة + +389 +00:28:37,570 --> 00:28:43,370 +عملت على إيش؟ على قسمين على 2 parts تمام ال Y تنتمي + +390 +00:28:43,370 --> 00:28:47,270 +لل A بدي اثبت ان ال Y في صف ال X طب انا عند ال + +391 +00:28:47,270 --> 00:28:51,190 +summation هذا المظلة العامة ان X في ال A و Y في ال + +392 +00:28:51,190 --> 00:28:54,430 +A موجودين في messages انهم علاقة مع بعض اه فهذا + +393 +00:28:54,430 --> 00:28:59,210 +يؤدي أن X Y تنتمي ل Q من وين جبته تعريف ال Q + +394 +00:29:02,480 --> 00:29:06,520 +أنا وين ده أوصل ال Y لصف ال X؟ طب X و Y في ال Q + +395 +00:29:06,520 --> 00:29:11,000 +إيش معناته؟ إن Y في صف ال X، هذا أسهل، Y في صف ال + +396 +00:29:11,000 --> 00:29:15,580 +X فبالتالي اللي بدأت منه إيش ماله؟ سبسط من اللي + +397 +00:29:15,580 --> 00:29:25,660 +انتهيت فيه طبعاً 1 و 2 بين هو البرهن وهو المطلوب + +398 +00:29:27,650 --> 00:29:33,170 +فأرجو أن نستخدم الرموز بشكل صحيح وعشان نكون + +399 +00:29:33,170 --> 00:29:39,590 +برهاننا كامل وصحيح فلقيا وصلنا للنظرية المطلوبة + +400 +00:29:39,590 --> 00:29:43,850 +let P be a partition of a non-empty set X بدنا من + +401 +00:29:43,850 --> 00:29:48,300 +partition then the equivalency classes induced by + +402 +00:29:48,300 --> 00:29:51,100 +the relation X على B يعني ال partitions اللي + +403 +00:29:51,100 --> 00:29:54,420 +بتولدوا هذه العلاقة التكافو X على B ليكيوسا منها + +404 +00:29:54,420 --> 00:30:00,780 +are precisely هم تماما بالظبط the sets in B بمعنى + +405 +00:30:00,780 --> 00:30:07,040 +آخر بالرموز بيقول ليه أنا عندي partition وولد + +406 +00:30:07,040 --> 00:30:11,500 +relation Q التي نسميها X على B لو جيت احسب + +407 +00:30:11,500 --> 00:30:15,880 +equivalence classes الييمين X على Q و Q هذه بتساوي + +408 +00:30:15,880 --> 00:30:20,920 +اسم تطلعوتطلع ال partition نفسه. طبعا الكتابة هنا + +409 +00:30:20,920 --> 00:30:25,500 +ممتازة. الكتابة مقلوبة عليك وإذا عملت جسمها X على X + +410 +00:30:25,500 --> 00:30:28,460 +على B مقام المقام بيصيح ال bus وال X بتروح مع ال + +411 +00:30:28,460 --> 00:30:33,540 +X فرمز موفق الحقيقة الرمز موفق لإن ما مش جسمه مجرد + +412 +00:30:33,540 --> 00:30:36,660 +رموز مجرد رموز فيمكن هذه من أعلى الأسباب اللي + +413 +00:30:36,660 --> 00:30:40,600 +اختاروا هذا الرمز إنه قسم زي القسمة واضحة فهي إيش + +414 +00:30:40,600 --> 00:30:44,800 +ال X على Q فهي نفس الكلام بدأت من partition عرفت + +415 +00:30:44,800 --> 00:30:48,700 +علاقة Q لـ Q عرفت partition نفس الـ partition اللي + +416 +00:30:48,700 --> 00:30:51,080 +بدأت منه فأنا برجع نفس النقطة دائرة بتاب ندور في + +417 +00:30:51,080 --> 00:30:58,560 +نفس الدائرة اللي حكينا عليها نشوف البرهان. البرهان + +418 +00:30:58,560 --> 00:31:01,760 +هيستخدم اللمة بشكل أساسي عشان ذلك احنا حاطناها + +419 +00:31:01,760 --> 00:31:07,160 +لأنها ساعدنا في أن البرهان يصير أقصر وبالتالي أسهل + +420 +00:31:07,160 --> 00:31:12,980 +في القراءة نظرية تلاتة ستة prove + +421 +00:31:14,270 --> 00:31:19,310 +طبعا للتسهيل خلينا نسمي الـ Q كالعادة هي X على B + +422 +00:31:19,310 --> 00:31:25,670 +تمام، إيش بدي أثبت؟ بدي أثبت إن X على Q تساوي B، + +423 +00:31:25,670 --> 00:31:33,690 +هذا هو المطلوب أكتب We want to prove اللي هو إيش؟ + +424 +00:31:33,690 --> 00:31:39,330 +X على Q تساوي الـ partition متابعين؟ + +425 +00:31:40,380 --> 00:31:45,580 +الحقيقة يمكن تكون رموز شوية كبيرة أو يعني مش + +426 +00:31:45,580 --> 00:31:50,120 +مألوفة لكن المفاهيم الرئيسية الحقيقة واحدة طيب هال + +427 +00:31:50,120 --> 00:31:55,580 +gate الـ B إيش عادي function ولا relation ولا إيش؟ + +428 +00:31:56,440 --> 00:31:59,160 +مجموعة مجموعات الـ Partition الـ Partition الـ P + +429 +00:31:59,160 --> 00:32:02,520 +Partition يعني إيش؟ مجموعة مجموعات و X على Q + +430 +00:32:02,520 --> 00:32:05,820 +مجموعة مجموعات يعني مع مجموعة صفوف في التكافؤ إذا + +431 +00:32:05,820 --> 00:32:08,680 +أنا إيش مطلوب مني أثبت؟ مجموعة تساوي مجموعة ده ما + +432 +00:32:08,680 --> 00:32:12,600 +بنبدأ إيش؟ من خارج للداخل في القراءة إذا بدأنا نثبت + +433 +00:32:12,600 --> 00:32:16,440 +مجموعة تساوي مجموعة كيف بنثبت؟ كم مرة عملناها؟ + +434 +00:32:16,440 --> 00:32:20,680 +عشرات المرات ناخد عنصر فهنبدأ من إن إيش؟ نبدأ .. + +435 +00:32:20,680 --> 00:32:24,800 +خليني أبدأ أسهل من الطرف .. صح من ورن ما بدنا + +436 +00:32:24,800 --> 00:32:30,870 +خليني أبدأ من اليسار let هاخد عنصر هان واتعلمنا انه + +437 +00:32:30,870 --> 00:32:35,110 +في الأصل اخد عنصر عشوائي صحيح طب أنا دي أنا عندي + +438 +00:32:35,110 --> 00:32:39,070 +معلومات عن المجموعة باخد عنصر بصورة المجموعات اه + +439 +00:32:39,070 --> 00:32:43,450 +أنا عندي x على q اي عنصر موجود هناك يكون صفة كافة + +440 +00:32:43,450 --> 00:32:49,450 +small x على q فهقول له let x على q be any element + +441 +00:32:49,450 --> 00:32:53,910 +تنتمي لل x على q لو عملت على مرتهم ده يقول له مثلا + +442 +00:32:53,910 --> 00:32:57,710 +let A تنتمي إيش تكون الـ A؟ لازم صفتها كافة لو أن + +443 +00:32:57,710 --> 00:33:00,630 +هذه عنصرها هيك زي ما عملنا في الأزواج المرتبة بي + +444 +00:33:00,630 --> 00:33:07,030 +any element هثبت + +445 +00:33:07,030 --> 00:33:10,970 +إنه هذه تنتمي للـ B بدي أثبت إنه هذه جزء بدي أثبت + +446 +00:33:10,970 --> 00:33:20,620 +إنه هذه عبارة عن جزء ممتاز الـ X على الـ Q تمام + +447 +00:33:20,620 --> 00:33:24,520 +بدنا نستخدم اللي ما الحقيقة هل جيت هذه الـ X small + +448 +00:33:24,520 --> 00:33:27,820 +x من وين واخدناها؟ من capital X لأنه أنا اللي بعمل + +449 +00:33:27,820 --> 00:33:34,950 +الصفر اه فالآن now small x تنتمي لل capital X وما + +450 +00:33:34,950 --> 00:33:37,730 +زال فيه partition، إذا الـ capital X عبارة عن مين؟ + +451 +00:33:37,730 --> 00:33:43,050 +اتحاد الأجزاء تساوي union على A للpartition في + +452 +00:33:43,050 --> 00:33:47,210 +مين؟ لل A، مظبوط؟ أه، هي كانت التعريفة، إذا هذه + +453 +00:33:47,210 --> 00:33:49,310 +الـ X الشمالي اللي ناجد تكون موجودة في جزء من + +454 +00:33:49,310 --> 00:33:51,810 +الأجزاء، هي موجودة في كلها، لأن X عبارة عن أجزاء + +455 +00:33:51,810 --> 00:34:00,230 +implies X تنتمي لل A for some A تنتمي للpartition + +456 +00:34:00,230 --> 00:34:03,530 +أه، هستخدم الليمة الآن + +457 +00:34:06,650 --> 00:34:11,030 +عنصر في مجموعة إذا X تنتمي للـA إذا الـH بتساوي صف + +458 +00:34:11,030 --> 00:34:16,850 +الـX توي أثبتناها by لمّا جدّاش المرقمين احنا ليه + +459 +00:34:16,850 --> 00:34:23,140 +ما جدّاش؟ ثلاثة واحد إيش في عندي ان X على Q اشملها + +460 +00:34:23,140 --> 00:34:27,920 +تساوي A و اين موجود ال A في ال partition تنتمي لل + +461 +00:34:27,920 --> 00:34:32,500 +partition إذا أول شيء بدأت من عنصر في X على Q + +462 +00:34:32,500 --> 00:34:38,620 +وصلته لل partition إذا أثبتنا ان ال capital X على + +463 +00:34:38,620 --> 00:34:44,440 +Q هي subset من ال partition فالاتجاه الأول فده هو + +464 +00:34:44,440 --> 00:34:52,400 +الاتجاه الأول نعمل اتجاه الثاني let إيش؟ بدنا ناخد + +465 +00:34:52,400 --> 00:34:56,000 +جزء من .. عنصر من الـ partition اللي صورة معينة، + +466 +00:34:56,000 --> 00:34:59,340 +مجموعة بس، لكن مش صفر، مش ضروري يكون صفر، بدي أثبت + +467 +00:34:59,340 --> 00:35:02,680 +أنه صفر، هقوله let A تنتمي للـ partition بـ an + +468 +00:35:02,680 --> 00:35:08,240 +element، بدي + +469 +00:35:08,240 --> 00:35:14,780 +أثبت أن هذا صفر تكافؤ، طيب، ممتاز، هل جيت؟ بدنا + +470 +00:35:14,780 --> 00:35:19,540 +نستخدم برضه اللي ما بدي أخد عنصر من الـ A أي عنصر + +471 +00:35:19,540 --> 00:35:22,220 +من الـ A هيكون صف هذا العنصر هو الـ A، مظبوط؟ هيك + +472 +00:35:22,220 --> 00:35:25,200 +اللي ما بتقول طب مين بيقول لي أن الـ A هيدي فيها + +473 +00:35:25,200 --> 00:35:30,400 +عنصر على الأقل؟ ولا ممكن تكون في الـ A؟ مستحيل، + +474 +00:35:30,400 --> 00:35:36,060 +لأنه partition فإذا هذا بيقول لي then A لا تساوي في + +475 +00:35:36,060 --> 00:35:41,580 +تعريف ال partition إذا there exists X تنتمي لمن؟ + +476 +00:35:41,580 --> 00:35:48,760 +للـ A بالنسبة لما إذا X تنتمي لصف X في شمال A بيساوي + +477 +00:35:48,760 --> 00:35:56,800 +الـ A بلما تلاتة واحد اللي هو إيش احنا بدنا من إيه + +478 +00:35:56,800 --> 00:36:04,330 +A تساوي صف ال X وصف ال X موجود في الصفوف ما زال الـ A + +479 +00:36:04,330 --> 00:36:07,870 +صفوف إذا هي ضمن الصفوف خلصنا بدأنا من A في ال + +480 +00:36:07,870 --> 00:36:11,010 +partition وصلنا لمجموعة الصفوف إذا صارت ال + +481 +00:36:11,010 --> 00:36:14,950 +partition جزء أو subset من الصفوف من وين من الصفوف + +482 +00:36:14,950 --> 00:36:24,790 +thus اللي هو إيش ال B subset من X على Q وهذه اثنين + +483 +00:36:24,790 --> 00:36:31,210 +طبعا واحد واثنين بيقول البرهان انتهى أي سؤال تمام؟ + +484 +00:36:34,250 --> 00:36:39,130 +خلينا ننهي الـ section بمثال توضيحي للنظرية عشان + +485 +00:36:39,130 --> 00:36:41,590 +نبقى .. إذا كان حد لسه مش واضحاه الصورة اللي بحالي + +486 +00:36:41,590 --> 00:36:46,670 +حكينا، هنبدأ من partition، هنعرف علاقة التكافؤ، + +487 +00:36:46,670 --> 00:36:49,650 +هنحسب partition متولد من علاقة التكافؤ، إيش، هنرجع + +488 +00:36:49,650 --> 00:36:52,290 +نفس النقطة، فخلينا نحسبه مع بعض، نشوف هذا الكلام + +489 +00:36:52,290 --> 00:36:53,250 +متحقق ولا لأ + +490 +00:37:04,490 --> 00:37:09,570 +مثال فهنا مديني مجموعة صغيرة من أربع عناصر و مديني + +491 +00:37:09,570 --> 00:37:13,590 +partition في عنصر لحال و الثلاثة الثانية مع بعض + +492 +00:37:13,590 --> 00:37:17,490 +حطينا طالب في شعبة و ثلاثة طلاب في شعبة جسمناهم هيك + +493 +00:37:17,490 --> 00:37:21,250 +تجسيم بيد الصورة بقول يوجد الـ partition يوجد الـ Q + +494 +00:37:21,250 --> 00:37:25,030 +ويوجد X على الـ Q بهذا المعنى عشان نوصل لبدنيا + +495 +00:37:25,030 --> 00:37:31,530 +solution فخلينا نحسب Q تساوي X على الـ partition + +496 +00:37:31,530 --> 00:37:36,150 +تمام بتتكون من أزواج مرتبة شمالها كل اللي حصلناها + +497 +00:37:36,150 --> 00:37:39,390 +في بداية المحاضرة، مش ذاكرين؟ فهي عند الـ partition + +498 +00:37:39,390 --> 00:37:42,750 +فبدأ أقول الواحد اللي علاقة مع مين؟ مع نفسها، + +499 +00:37:42,750 --> 00:37:46,690 +والاثنين مع نفسها، والثلاثة مع نفسها، والأربعة مع + +500 +00:37:46,690 --> 00:37:51,920 +نفسها، تمام، هذه النقطة السهلة هل الواحد لعلاقة مع + +501 +00:37:51,920 --> 00:37:55,260 +حد غير نفسه؟ لا لأنه موجود في جزء لحاله لكن الاثنين + +502 +00:37:55,260 --> 00:37:58,540 +لعلاقة مع الثلاثة وبالتالي الثلاثة لعلاقة مع + +503 +00:37:58,540 --> 00:38:02,180 +الاثنين لأنه symmetric مظبوط والاثنين لعلاقة مع + +504 +00:38:02,180 --> 00:38:05,620 +الأربعة والأربعة لعلاقة مع الاثنين لأنه symmetric + +505 +00:38:05,620 --> 00:38:12,590 +وثلاثة وأربعة والأربعة والثلاثة في تمشي خلصت ال + +506 +00:38:12,590 --> 00:38:15,290 +relation اه فانا في ضوء النظرية أنا عارف ان ال + +507 +00:38:15,290 --> 00:38:18,470 +relation هي Q لنا وبقدر احسب بيبقى ده الشكل تمام + +508 +00:38:18,470 --> 00:38:22,930 +فهي partition بي ده نيا وولدنا relation نشوف ال + +509 +00:38:22,930 --> 00:38:26,050 +relation ده إيش ملها بتتولد مين partition نحسبه + +510 +00:38:26,050 --> 00:38:30,430 +إيش .. إيش .. إيش رمزه X على Q مظبوط إيش بيساوي + +511 +00:38:30,430 --> 00:38:34,890 +الصفوف الـ X أكمل عنصر فيها أربع، ففيدنا يكون فيها + +512 +00:38:34,890 --> 00:38:39,330 +أربع صفوف صف الواحد، صف الاثنين، بس ممكن يكون بعضه + +513 +00:38:39,330 --> 00:38:43,830 +متساوي، صف الثلاثة وصف الأربعة، مظبوط؟ أه، الآن + +514 +00:38:43,830 --> 00:38:47,810 +انسوا أن علاقة التكافؤ، درسنا علاقات التكافؤ وكيف + +515 +00:38:47,810 --> 00:38:51,770 +نحسب صفوف التكافؤ، بس عشان ليش نوضح النظرية تمام، + +516 +00:38:51,770 --> 00:38:57,480 +بدأ جاود مباشرة، مين صف الواحد؟ في شيء للواحد لأن + +517 +00:38:57,480 --> 00:39:00,360 +الواحد بس لإنه يقول ما فيش هو صف فارغ وأول عنصر في + +518 +00:39:00,360 --> 00:39:04,300 +صف ال X هو ال X في غيره ما فيش طيب مين صف الاثنين؟ + +519 +00:39:04,300 --> 00:39:08,640 +الاثنين والثلاثة والأربعة وهو بيساوي صف الثلاثة و + +520 +00:39:08,640 --> 00:39:11,060 +بيسوي صف الأربعة لأنهم ملحقين مع بعض من خواص الصفوف + +521 +00:39:11,060 --> 00:39:12,220 +فإيش رجعنا؟ + +522 +00:39:16,490 --> 00:39:21,250 +النظرية بتقول ابدأي من partition عارفي equivalence + +523 +00:39:21,250 --> 00:39:25,630 +relation من ال partition احصي بتقع فوق ترجع لنقطة + +524 +00:39:25,630 --> 00:39:29,210 +اللي بدأتي منها أي سؤال diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yaE-rza0wfU_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yaE-rza0wfU_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..bd47f4fbad600c7ddbfe8dc9653b47c70bd7012d --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yaE-rza0wfU_raw.srt @@ -0,0 +1,2104 @@ +1 +00:00:19,670 --> 00:00:23,450 +بسم الله الرحمن الرحيم ان شاء الله احنا هنكمل مع + +2 +00:00:23,450 --> 00:00:28,070 +ال relations وبشكل خاص مع ال equivalence relations + +3 +00:00:28,070 --> 00:00:32,110 +و علاقتها مع ال partition في المحاضرات الماضية + +4 +00:00:32,110 --> 00:00:37,090 +شفنا إذا في عندنا equivalence relation أبسلون + +5 +00:00:37,090 --> 00:00:42,450 +فصفوف التكافؤ اللي بتولدها هذه ال relation is a + +6 +00:00:42,450 --> 00:00:42,830 +partition + +7 +00:00:46,170 --> 00:00:50,290 +هو partition مظبوط شفنا انه ولا صف فاضي و الصفين + +8 +00:00:50,290 --> 00:00:54,910 +يا متطابقين يا تقاط عفاي واتحاد كل الصفوف بدينا كل + +9 +00:00:54,910 --> 00:00:59,230 +ال X اليوم ان شاء الله هنشوف العكس لو بدأنا من ال + +10 +00:00:59,230 --> 00:01:05,370 +partition هل ممكن اولد علاق التكافؤ الجواب برضه + +11 +00:01:05,370 --> 00:01:08,890 +نعمفإذا بدأنا من equivalence relation وصلنا ل + +12 +00:01:08,890 --> 00:01:12,950 +partition هذا عبارة عن P partition الآن العكس نبدأ + +13 +00:01:12,950 --> 00:01:14,930 +من ال partition هل ممكن نوصل ل equivalence + +14 +00:01:14,930 --> 00:01:19,050 +relation؟ هنشوف أن الجواب نعم طبعا هنمشي واحدة + +15 +00:01:19,050 --> 00:01:22,770 +واحدة أولا كيف من partition بعرف equivalence + +16 +00:01:22,770 --> 00:01:25,690 +relation كيف نعرف أولا relation وكيف تكون + +17 +00:01:25,690 --> 00:01:28,230 +equivalence relation فطبعا العنوان relations + +18 +00:01:28,230 --> 00:01:32,490 +induced by partitionsفطبعا بقول let P be a + +19 +00:01:32,490 --> 00:01:35,930 +partition احنا لدينا مجموعة capital X غير فارغة + +20 +00:01:35,930 --> 00:01:41,290 +مجزقة بطريقة ما مقسمة بطريقة ما ضمن شروط طبعة ال + +21 +00:01:41,290 --> 00:01:45,710 +partition ولا جزء فارغ اي جزءين يا متطابقين يا + +22 +00:01:45,710 --> 00:01:48,110 +disjoint يا مفاصلين تماما ما ما ما ما ما ما ما ما + +23 +00:01:48,110 --> 00:01:48,290 +ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما + +24 +00:01:48,290 --> 00:01:49,170 +ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما + +25 +00:01:49,170 --> 00:01:50,310 +ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما + +26 +00:01:50,310 --> 00:01:50,370 +ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما + +27 +00:01:50,370 --> 00:01:50,410 +ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما + +28 +00:01:50,410 --> 00:02:00,270 +ما ما ما ما ما ما ما + +29 +00:02:00,270 --> 00:02:00,270 +ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما + +30 +00:02:00,270 --> 00:02:00,270 +ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما ما + +31 +00:02:00,430 --> 00:02:05,470 +بكون لهم علاقة مع بعض إذا وقعها في نفس الجزء هاي X + +32 +00:02:05,470 --> 00:02:11,190 +وهاي Y وهاي Y وماكنتش لهم علاقة مع بعض إذا وقعها + +33 +00:02:11,190 --> 00:02:15,510 +في نفس الجزء وهذه X طب لو أنا كان في عندي عنصر + +34 +00:02:15,510 --> 00:02:20,380 +تالت Z هنافي جزء آخر هل الزي دي علاقة مع ال X؟ لأ + +35 +00:02:20,380 --> 00:02:24,120 +اللي علاقة مع ال Y؟ لأ فالعنصرين بيكون اللي هم + +36 +00:02:24,120 --> 00:02:27,500 +علاقة مع بعضها .. التعريف إذا وقعها في نفس الجزء + +37 +00:02:27,500 --> 00:02:31,080 +أنا عندي partition يعني عندي أجزاء للمجموعة فكل + +38 +00:02:31,080 --> 00:02:33,960 +عنصرين إذا وقعوا في نفس الجزء اللي هم علاقة مع بعض + +39 +00:02:33,960 --> 00:02:39,010 +اختلفت الأجزاء مافيش علاقة فهي التعريففبقول لي we + +40 +00:02:39,010 --> 00:02:42,910 +define a relation ايش .. ايش الرمز تبعها؟ X على B + +41 +00:02:42,910 --> 00:02:45,810 +زي ما دايما في عندنا مفهوم فاحنا في عندنا + +42 +00:02:45,810 --> 00:02:49,890 +partition بيولد علاقة فتسميها ايش؟ relation + +43 +00:02:49,890 --> 00:02:54,470 +induced by .. تتولد من .. induced by .. اه تعرف + +44 +00:02:54,470 --> 00:02:58,150 +بدليل ال partition ايش رمزها؟ X على B .. X على B + +45 +00:02:58,150 --> 00:03:01,690 +طيب هي relation من وين لوين؟ من X لX لأن منصوبة ان + +46 +00:03:01,690 --> 00:03:05,600 +هي علاقة تكافأطيب كيف بنعرفها؟ بيقولّي الزوج + +47 +00:03:05,600 --> 00:03:09,420 +المرتب ينتمي لل relation وقت إيش if and only if + +48 +00:03:09,420 --> 00:03:14,100 +there exists a set A يعني جزء تنتمي لل partition + +49 +00:03:14,100 --> 00:03:19,260 +لأنه جزء إشماله such that X and Y are in A ال X و + +50 +00:03:19,260 --> 00:03:22,920 +Y في نفس الجزء that is بالرموز هيها ال relation + +51 +00:03:22,920 --> 00:03:27,560 +إيش عناصرها؟ أزواج مرتبةsuch that X في الـ A والـ + +52 +00:03:27,560 --> 00:03:31,200 +Y في الـ A for some A للـ B فالـ X والـ Y ليش انهم + +53 +00:03:31,200 --> 00:03:34,540 +علاقة مع بعض؟ لأنهم مقعوا في جزء انما لو في عندنا + +54 +00:03:34,540 --> 00:03:37,920 +هنا A و B ليش انهم علاقة مع بعض؟ لأنهم مقعوا في + +55 +00:03:37,920 --> 00:03:41,160 +جزء معين مش دارون نفس الجزء فكل أنصرين في نفس + +56 +00:03:41,160 --> 00:03:46,020 +الجزء لكن كل جزء بيكوّل لأزواج مرتبة أزواج مرتبة + +57 +00:03:46,020 --> 00:03:48,980 +واضح التعريف؟ اه ان شاء الله هنشوف الأمثلة و ان + +58 +00:03:48,980 --> 00:03:55,700 +شاء الله الأمور بتكون أفضل نشوف المثال الأولطبعا + +59 +00:03:55,700 --> 00:03:58,660 +دائما بنبدأ بالأمثلة البسيطة عشان دائما الإنسان + +60 +00:03:58,660 --> 00:04:02,000 +بيبدأ من المرحلة الدنيا و بيبنيه و بيطلع و بتساعد + +61 +00:04:02,000 --> 00:04:05,100 +في المفهوم نبدأ مجموعة صغيرة طبعا هذا أسهل في + +62 +00:04:05,100 --> 00:04:09,600 +الفهم من تلت عناصر و معوونها partition كيف ال + +63 +00:04:09,600 --> 00:04:13,440 +partition ال zero مع التانين جزء و الواحد لحاله لو + +64 +00:04:13,440 --> 00:04:19,480 +رسمنا صورة هي جزء ايه فيها الواحد لحاله و ال zero + +65 +00:04:19,480 --> 00:04:23,800 +و التانين لحاله اللي مع بعضzero و اتنين و الواحد + +66 +00:04:23,800 --> 00:04:27,280 +لحاله فهي partition وهي مجموعة بدنا نحسب العلاقة + +67 +00:04:27,280 --> 00:04:30,920 +اللي بيولدها هذا ال partition اللي بيش بيعرف هذا + +68 +00:04:30,920 --> 00:04:34,120 +ال partition find the relation بدنا نحسبها و بعدين + +69 +00:04:34,120 --> 00:04:38,800 +بدنا نجاوب هل العلاقة المتولدة هي علاقة تكافئ ولا + +70 +00:04:38,800 --> 00:04:43,100 +لأ فنبدأ الحل solution فطبعا ايش الجزء الاول من + +71 +00:04:43,100 --> 00:04:48,180 +الحل بدنا نحسب X على B اللي انا ممكن اسميها Q + +72 +00:04:48,180 --> 00:04:53,740 +اختصارا اذا حبيت نسميها Qتساوي عشان R طيب ماشي + +73 +00:04:53,740 --> 00:04:59,100 +اشملها دي من التعريف أيه فوق؟ بدنا الأزواج المرتبة + +74 +00:04:59,100 --> 00:05:02,140 +ليش يكون الأحداث الأول والتاني بيقعوا بنفس الجزء + +75 +00:05:02,140 --> 00:05:07,900 +فسؤال الأول هل الواحد لعلاقة مع نفسها؟ بالتأكيد + +76 +00:05:07,900 --> 00:05:10,700 +لأن هي و نفسها بيقعوا في نفس الجزء إذا أول زوج + +77 +00:05:10,700 --> 00:05:14,600 +عندي الواحد و واحد بنفس الأسلوب ال zero و ال zero + +78 +00:05:14,600 --> 00:05:18,790 +بنفس الأسلوب التنين و التنين ولا لأ؟لازم يكون لأن + +79 +00:05:18,790 --> 00:05:22,690 +الواحد باتجاه هي في جزء و نفسها في جزء آخر، + +80 +00:05:22,690 --> 00:05:25,470 +مانفعش، و الـ zero نفس الشياء و الـ two نفس الجزء، + +81 +00:05:25,470 --> 00:05:29,310 +إذا حسبناها، إذا واضح على طول إن هذه علاقة شمالها، + +82 +00:05:29,310 --> 00:05:32,350 +علاقة انعكاس، reflexive، واضح؟ كل أنصف دي قاعمة + +83 +00:05:32,350 --> 00:05:36,190 +نفسه، تمام، طيب، إيش كمان؟ هل الواحد لعلاقة مع أي + +84 +00:05:36,190 --> 00:05:39,810 +حد آخر؟ لأ، لأن في جزء لحالة، إذا الواحد خلصنا، + +85 +00:05:39,810 --> 00:05:43,590 +طيب الـ zero إيه العلاقة مع حد آخر؟ مع التنين، لأن + +86 +00:05:43,590 --> 00:05:50,030 +هي و التنين بيقع في نفس الجزءطب والتنين و Zero و + +87 +00:05:50,030 --> 00:05:53,490 +خلصنا .. اه .. و خلصنا .. لأ .. طب ليش؟ لأنه زي ما + +88 +00:05:53,490 --> 00:05:57,530 +تشوفين التعريف بيقول يقعاه في نفس الجزء الترتيب + +89 +00:05:57,530 --> 00:06:01,550 +مهم؟ لأ .. اذا زوج موجود عكسه لازم يكون موجود لأنه + +90 +00:06:01,550 --> 00:06:04,030 +الان commutative التعريف .. اه .. commutative .. + +91 +00:06:04,030 --> 00:06:07,410 +اه فياك بيكون هذه هي ال relation فعنا أجزاء عرفنا + +92 +00:06:07,410 --> 00:06:11,770 +منها relation عرفنا منها relation اه .. فاحنا هي + +93 +00:06:11,770 --> 00:06:14,070 +ال Zero مع التنين و التنين مع ال Zero و Zero مع ال + +94 +00:06:14,070 --> 00:06:15,990 +Zero و التنين مع التنين طب هذا الجزء الأول + +95 +00:06:17,840 --> 00:06:21,220 +التكافأة؟ لأن الـ reflexive واضح من أول شيء + +96 +00:06:21,220 --> 00:06:25,680 +الـsymmetric كل زوج عكسه موجود لأنها and والand + +97 +00:06:25,680 --> 00:06:28,240 +دائما committed الترتيب مش مهم طب هل هذه + +98 +00:06:28,240 --> 00:06:30,260 +transitive؟ لو فحصنا من اللي جاها فعلا أنها + +99 +00:06:30,260 --> 00:06:33,980 +transitive لأن مين بيبدأ بواحد؟ مفيش مين بيبدأ ب + +100 +00:06:33,980 --> 00:06:37,780 +zero؟ zero اتنين يؤدي zero zero اتنين صح طيب مين + +101 +00:06:37,780 --> 00:06:40,920 +بيبدأ ب .. خلصنا مين بيبدأ باتنين؟ اتنين zero + +102 +00:06:40,920 --> 00:06:44,740 +بيقدر اتنين zero برضه صح مين كمان بيبدأ باتنين؟ + +103 +00:06:45,170 --> 00:06:47,890 +خلصنا، مافيش إلى زيرو، خلصنا، فبنكون احنا فحصناه، + +104 +00:06:47,890 --> 00:06:51,450 +فهذه إيش فعلًا equivalence relation؟ الـ Q is an + +105 +00:06:51,450 --> 00:06:57,070 +equivalence relation relation + +106 +00:06:57,070 --> 00:07:00,530 +فلو فحصنا الشروط، بنلاقي ان كلهم متحققين، بنلاقي + +107 +00:07:00,530 --> 00:07:05,010 +هي علاقة انعكاس، علاقة تماثل، وعي فيها خاصية + +108 +00:07:05,010 --> 00:07:08,130 +التعجل، ففعلًا هذه علاقة تكافأ + +109 +00:07:10,260 --> 00:07:13,840 +خلّيني أشوف كمان مثال برضه ناخد مجموعة كبيرة + +110 +00:07:40,350 --> 00:07:45,050 +هل هي علاقة تكافؤ ولا لأ نبدأ بالحل نبدأ بالجزء + +111 +00:07:45,050 --> 00:07:49,550 +المباشر solution نبدأ بالفرع الأول بدنا ال + +112 +00:07:49,550 --> 00:07:55,330 +relation Q تساوي رمزها المجموعة Z على ال partition + +113 +00:07:55,330 --> 00:07:56,850 +وتساوي + +114 +00:07:58,420 --> 00:08:02,480 +طبعاً الاختلاف بين المثالين المثال الأول أنا عارف + +115 +00:08:02,480 --> 00:08:06,460 +المجموعة وبدأت أفحصهم واحد واحد ومين كل جزء ومين + +116 +00:08:06,460 --> 00:08:10,920 +عناصره واضح الأمور آه الآن عشان العناصر كتيرة يمكن + +117 +00:08:10,920 --> 00:08:14,680 +تكون حسابات شوية أطول فبدها من زاوية أخرى فإيش + +118 +00:08:14,680 --> 00:08:19,420 +نعمل نفجر على التعريف الأصلي مين هذ relation؟هي X + +119 +00:08:19,420 --> 00:08:23,760 +Y طبعا في X cross X طبعا لأن وين هي relation علي + +120 +00:08:23,760 --> 00:08:29,040 +ال X ممكن نكتبها للتأكيد هي in Z cross Z لأنها X + +121 +00:08:29,040 --> 00:08:32,460 +cross X واضحة من الصياح المفروض تكون واضحة في + +122 +00:08:32,460 --> 00:08:35,660 +التعريف هنا X Y وين بدأ تكون في ال Cartesian + +123 +00:08:35,660 --> 00:08:39,320 +product X مع نفسها طبعا لأنها عراقة علي ال X طبعا + +124 +00:08:39,320 --> 00:08:45,020 +ايش التعريف such that ال X تنتمي لل A and + +125 +00:08:46,890 --> 00:08:54,210 +Y تنتمي للـ A for some A تنتمي لل partition اللي + +126 +00:08:54,210 --> 00:09:02,130 +في هذا السؤال هو إيه؟ هو E و D هو E و D متابعين؟ + +127 +00:09:03,680 --> 00:09:08,460 +في أي حد عنده استفسار واضح تقريب انا عندي علاقة + +128 +00:09:08,460 --> 00:09:13,800 +متولدة من partition ايش الزوج المرتب هو كل عنصرين + +129 +00:09:13,800 --> 00:09:18,020 +موجودين في نفس الجزء في جزء ما من الأجزاء تمام؟ اه + +130 +00:09:18,020 --> 00:09:21,980 +ميزة هذا السؤال ان صحيح العناصر كتيرة لكن الأجزاء + +131 +00:09:21,980 --> 00:09:25,480 +قليلة جزءين لما بقوله for some ايه تنتمي لل + +132 +00:09:25,480 --> 00:09:29,180 +partition ايش احتمالات الـA؟ ياد E ياد D مافيش + +133 +00:09:29,180 --> 00:09:33,780 +الاحتمالين فخلينا نكتب هذا الكلام فهذا تساويX of Y + +134 +00:09:33,780 --> 00:09:36,680 +طبعا في الـ Z cross الـ Z بدي اكتب .. بديش اكتب + +135 +00:09:36,680 --> 00:09:42,140 +اختصار لإنه واضح بحيث ال X تنتمي ليا إما تنين في + +136 +00:09:42,140 --> 00:09:48,220 +ال E and Y تنتمي لل E هي الاحتمال الأول مظبوط إذا + +137 +00:09:48,220 --> 00:09:53,320 +كانت ال A تساوي E او احتمال تاني لإن هذا يمكن تكون + +138 +00:09:53,320 --> 00:09:58,380 +true أو هذا يمكن تكون true ال X في ال D and Y في + +139 +00:09:58,380 --> 00:10:02,090 +ال Dممكن اكتب بهذا الشكل هذا اليوم اللي اترجمه هيك + +140 +00:10:02,090 --> 00:10:05,050 +و لا لأ؟ لان انا بقول for some ايه؟ ايش احتمالات + +141 +00:10:05,050 --> 00:10:09,430 +الـA؟ الـA يا E يا O يا R فور some ايش معناته؟ + +142 +00:10:09,430 --> 00:10:12,610 +there exist و there exist ايش تقابل؟ R شوفتوا كيف + +143 +00:10:12,610 --> 00:10:17,190 +الأمور متسايمة؟ تمام؟ تمام، نمشي كمان خطوة، بدي + +144 +00:10:17,190 --> 00:10:19,510 +اوصل الـquadration، بدي اكتبها بشكل حتى تكون انتوا + +145 +00:10:19,510 --> 00:10:26,350 +متعودين عليه، what is that? XY such that، ايش + +146 +00:10:26,350 --> 00:10:31,690 +معناة X even؟يعني مضاعفات اتنين يعني ايش بكتوبها + +147 +00:10:31,690 --> 00:10:36,290 +اتنين في N او اتنين في M فهذا معناته ان X تساوي + +148 +00:10:36,290 --> 00:10:41,890 +اتنين N و Y تساوي اتنين M for some N و M انتجة + +149 +00:10:41,890 --> 00:10:44,970 +لانه مضاعفات اتنين بس بدي اكتوبها بالاخر بدي أجلها + +150 +00:10:44,970 --> 00:10:51,100 +شوية عشان اختصر في الكتاب orإيش معنات فردي؟ 2n + +151 +00:10:51,100 --> 00:10:57,880 +زياد 1 فال X تساوي 2n زياد 1 and Y تساوي 2m زياد 1 + +152 +00:10:57,880 --> 00:11:01,120 +طبعا هدول ال N و ال M إيه شمالهم؟ integers for + +153 +00:11:01,120 --> 00:11:07,040 +some N و M في ال Z اتبعين؟ + +154 +00:11:08,870 --> 00:11:13,450 +المتابعين؟ اه فاحنا قلنا تعريف العلاقة اللي بولدها + +155 +00:11:13,450 --> 00:11:17,270 +ال partition هي كل زوج مرتب بحيث ان الاحداث الأول + +156 +00:11:17,270 --> 00:11:20,890 +والتاني يقع في نفس الجزء بما ان ال partition جزءين + +157 +00:11:20,890 --> 00:11:24,090 +اذا هدول هيكون في الجزء الأول او الجزء التانيالان + +158 +00:11:24,090 --> 00:11:27,690 +من معلوماتنا الجزء الاول هو الاعداد الزوجية كيف + +159 +00:11:27,690 --> 00:11:31,110 +صورتهم اتنين في N او اتنين في M من ضعفات التنين + +160 +00:11:31,110 --> 00:11:34,510 +طباش الفردي اللي هو عيش مش زوجي يعني زائد واحد او + +161 +00:11:34,510 --> 00:11:37,850 +ناقص واحد لان كل اعداد اللي جابله زوجي اللي بعده + +162 +00:11:37,850 --> 00:11:41,370 +بيجي فردي اتبع ولا لأ تمام خلينا نعمل trick بسيط + +163 +00:11:41,370 --> 00:11:48,350 +الان بس عشان انا بيدوصل كل صورة مألوفة اه يساوي XY + +164 +00:11:49,560 --> 00:11:56,100 +لو طرحنا X ناقص Y في الحالتين X ناقص Y إيش بتديني؟ + +165 +00:11:56,100 --> 00:12:03,340 +2N ناقص M وفي التاني برضه 2N ناقص M الواحد بتروح + +166 +00:12:03,340 --> 00:12:10,080 +مع الواحد اللي هي إيش بتساوي؟اتنين في K for some K + +167 +00:12:10,080 --> 00:12:15,260 +from N to Z لأن الـ N و الـ M أعداد صحيحة فالفرق + +168 +00:12:15,260 --> 00:12:20,560 +بينهم أعداد صحيحة بدي أسميه K الـ N ال relation لو + +169 +00:12:20,560 --> 00:12:25,230 +تخبينا هذا مقلوفة الكل مش مقلوفةاللي سمناها Mode M + +170 +00:12:25,230 --> 00:12:28,230 +تذكروا؟ احنا أخدناها Mode 3 كمثال بالتفصيل + +171 +00:12:28,230 --> 00:12:31,850 +وقلنالكم أي عدد صحيح غير التلاتة بيقدر الغرض واحد + +172 +00:12:31,850 --> 00:12:35,390 +اتنين تلاتة اربع وهاكذا ويمكن نشوف الاربعة كمثال + +173 +00:12:35,390 --> 00:12:39,250 +لما حسبنا صفوف التكافأة و لا لأ فدياش relation فهي + +174 +00:12:39,250 --> 00:12:41,670 +شايفين ان ال relation مشهورة هي عندي بدأت بال + +175 +00:12:41,670 --> 00:12:45,050 +partition وولدت relation و relation معروفة فهي + +176 +00:12:45,050 --> 00:12:48,880 +relation relation معروفة طبعاواحد يقول لك ضروري + +177 +00:12:48,880 --> 00:12:51,600 +نعمل كل حسابات لو المثال جالك ال relation و كده + +178 +00:12:51,600 --> 00:12:55,320 +اول تعريف يكفي عندي لكن هناكش كان الهدف ان نوصل ل + +179 +00:12:55,320 --> 00:12:58,780 +relation معروفة نوصل ل relation معروفة طبعا هلها + +180 +00:12:58,780 --> 00:13:01,400 +equivalence relation؟ طبعا متأكدين لان احنا في + +181 +00:13:01,400 --> 00:13:06,280 +موضوع ال M فهي IH2 اللي هي IHQ is an equivalence + +182 +00:13:06,280 --> 00:13:10,060 +relation اه فالان الحقيقة ان هو اللي صار في دول + +183 +00:13:10,060 --> 00:13:14,720 +المثالينبدأنا من partition حسبنا ال relation اللي + +184 +00:13:14,720 --> 00:13:17,800 +بيولدها ال partition طلع في المثالين اللي هذه + +185 +00:13:17,800 --> 00:13:21,620 +العلاقات هي علاقات تكافؤ فهل هذا الكلام دايما صحيح + +186 +00:13:21,620 --> 00:13:24,620 +و لا بس كانت من الصدفة المثالين الحقيقة دايما صحيح + +187 +00:13:24,620 --> 00:13:27,440 +زي ما حد شوفه في النظرية فنظرية تلاتة خمسة بيقول + +188 +00:13:27,440 --> 00:13:32,900 +دايماEQ هذي اللي هي X على B، إيش معناه X على B؟ ال + +189 +00:13:32,900 --> 00:13:36,060 +relation اللي بعرفها ال partition دايما + +190 +00:13:36,060 --> 00:13:39,800 +equivalence relation فهنا النظرية let B be a + +191 +00:13:39,800 --> 00:13:44,670 +partition of a non-empty set Xthen the relation X + +192 +00:13:44,670 --> 00:13:48,770 +على B is an equivalence relation on X طبعا يمكن + +193 +00:13:48,770 --> 00:13:51,710 +الرمز شوية غريب و بس احنا شايفين بيساعدناش بيقولني + +194 +00:13:51,710 --> 00:13:55,110 +the relation X على B هاد رمزة لإن معناته إيش؟ هي + +195 +00:13:55,110 --> 00:13:59,450 +العلاقة المتولدة من ال partition B على المجموعة X + +196 +00:13:59,450 --> 00:14:03,090 +على المجموعة X خليني أشوف البرهان مع بعض خليني + +197 +00:14:03,090 --> 00:14:07,750 +أشوف البرهان مع بعضطبعا كيف بنسميها الـ + +198 +00:14:07,750 --> 00:14:11,670 +equivalence relation؟ تلات شروط إنها reflexive، + +199 +00:14:11,670 --> 00:14:19,310 +transitive و symmetric فهذه نظرية تلاتة خمسة وهذه + +200 +00:14:19,310 --> 00:14:24,570 +ال proof طبعا أول شيء يجعلني أستخدم رمز أسهل لت + +201 +00:14:24,570 --> 00:14:30,800 +كيو تساوي X على Bخلينا نرمز اللي احنا بالرمز Q + +202 +00:14:30,800 --> 00:14:34,000 +أسهلنا طبعا انا مااخد الـ Q لأن زي هي واضحة علينا + +203 +00:14:34,000 --> 00:14:37,740 +زي قسمة قوشن فبدي اخد الـ Q اه بدي اثبت ان الـ Q + +204 +00:14:37,740 --> 00:14:40,900 +is an equivalent relation فأول شيء بدي اثبت ان الـ + +205 +00:14:40,900 --> 00:14:47,820 +Q is reflexive reflexive يعني ليش reflexive يعني + +206 +00:14:47,820 --> 00:14:53,220 +كل عصره علاقة مع نفسهوزي ما شوفنا بالامثلة طبعا كل + +207 +00:14:53,220 --> 00:14:55,660 +عنصر زوجي ما هو بيبغى يقع مع الزوج في المثال + +208 +00:14:55,660 --> 00:14:58,140 +الأخير وكل شوفنا ان الواحد لعقله في المثال اللي + +209 +00:14:58,140 --> 00:15:01,780 +جابله وها كذا طب كيف بنثبت ان كل عنصر يقع مع نفسه + +210 +00:15:01,780 --> 00:15:06,820 +انه علاقة مع نفسه انه كل عنصر يقع بنفس الجزء من + +211 +00:15:06,820 --> 00:15:09,420 +البرتش احنا ايش عندنا معطيات؟إن الـ P partition + +212 +00:15:09,420 --> 00:15:12,460 +وهي relation ومعروف كيف تعريفها الـ Q بدنا نثبت إن + +213 +00:15:12,460 --> 00:15:16,760 +أنا reflexive فالآن أول شيء بدنا نثبت إنه كل .. + +214 +00:15:16,760 --> 00:15:19,640 +إيش بدنا نثبت؟ for all X، مظبوط؟ إيش تعريف + +215 +00:15:19,640 --> 00:15:24,240 +reflexive؟ for all X in capital X XX في الـ Q، صح؟ + +216 +00:15:24,240 --> 00:15:27,380 +طب ما زال for all إيش كيف ده البرهان؟ let X be any + +217 +00:15:27,380 --> 00:15:32,960 +element in capital X فحنبدأ let small x in capital + +218 +00:15:32,960 --> 00:15:38,890 +X be any element any elementطبعا طريقة الكتابة + +219 +00:15:38,890 --> 00:15:41,670 +والتقنيم والتأخير نفس المعنى لت X be an element + +220 +00:15:41,670 --> 00:15:44,210 +such that X tend to be the capital X نفس المعنى + +221 +00:15:44,210 --> 00:15:49,090 +for all X تمام ايه؟ بدي اثبت ان ال X تقع مع نفسها + +222 +00:15:49,090 --> 00:15:55,490 +بنفس الجزء طب هل ال X بتقع بجزء أصلا؟ وليش؟ ليش؟ + +223 +00:15:55,490 --> 00:15:59,210 +لأن ال partition بيغطي كل ال X فلازم كل عنصر يش + +224 +00:15:59,210 --> 00:16:05,160 +يكون بنفس ال X فده بيقول ليه؟ال X تنتمي لل A for + +225 +00:16:05,160 --> 00:16:11,240 +some A تنتمي لل partition ايش دليلك اذكركوا ان X + +226 +00:16:11,240 --> 00:16:15,180 +تساوي الاتحاد على ال partition تذكروا على ال A مش + +227 +00:16:15,180 --> 00:16:18,180 +هيك فيه انا من الخاصية رقم اتنينفي تعريف الـ + +228 +00:16:18,180 --> 00:16:20,760 +Partition هما عندنا فيه اللي هو خاصية رقم Zero + +229 +00:16:20,760 --> 00:16:24,160 +لضمن الكلام وخاصية رقم واحد وخاصية رقم اتنين فهذه + +230 +00:16:24,160 --> 00:16:27,640 +خاصية رقم اتنين ممتاز X تنتمي لل A إذا X اللي + +231 +00:16:27,640 --> 00:16:29,740 +علاقة مع نفسها لإننا ممكن نعمل conjunction X تنتمي + +232 +00:16:29,740 --> 00:16:33,140 +لل A و X تنتمي لل A فهي اللي بدناية فده بيقوللي إن + +233 +00:16:33,140 --> 00:16:39,240 +X X تنتمي لل Q وبالتالي and hence ال Q is + +234 +00:16:39,240 --> 00:16:44,180 +reflexive فخاصية ال reflexive أثبتت reflexive + +235 +00:16:48,110 --> 00:16:55,530 +تمام واضح تمام نيجي للخاصية رقم اتنين بس خليني + +236 +00:16:55,530 --> 00:17:03,910 +اكتف ال Q is symmetric بدنا نثبت انه ان ال Q is + +237 +00:17:03,910 --> 00:17:09,220 +symmetricوالبرهان الحقيقة زي ما شرحنا من التعريف + +238 +00:17:09,220 --> 00:17:11,860 +طبعا إيش معناه symmetric إذا في زوجين ما في ال + +239 +00:17:11,860 --> 00:17:14,900 +relation عكسه بيكون موجود فحنبدأ البرهان نقول له + +240 +00:17:14,900 --> 00:17:21,880 +إيش let x,y تنتمي لـQ طيب إيش معناه الـQ إن الـx و + +241 +00:17:21,880 --> 00:17:27,220 +الـy في نفس الجزء فده implies اللي هو إيش x تنتمي + +242 +00:17:27,220 --> 00:17:33,660 +لـA و y تنتمي لـA for some a في ال partition + +243 +00:17:33,660 --> 00:17:37,620 +التعريفأنا قلتلكم تذكروا التعريفات تكون قدامنا + +244 +00:17:37,620 --> 00:17:41,760 +نعملهم بشيء ندور على كام صفحة لك تكونوا قدامنا طيب + +245 +00:17:41,760 --> 00:17:45,020 +أه الآن commutative هي القضية أنا بدي أبدل دور ال + +246 +00:17:45,020 --> 00:17:47,760 +X و دور ال Y ال X كانت إحداثي أول ده خليه إحداثي + +247 +00:17:47,760 --> 00:17:51,060 +تاني ما هذي بتساوي هذي إيش ماله؟ أبدل لإن الآن دي + +248 +00:17:51,060 --> 00:17:55,980 +بدالية فده بيقول إن Y تنتمي لل A and X تنتمي لل A + +249 +00:17:55,980 --> 00:18:02,400 +for some A في البرتش أه الآن اتبدلت دور هذا أيه + +250 +00:18:02,400 --> 00:18:09,100 +معناته أن Y Xفي الـ Q وهو المطلوب Thus, Q is + +251 +00:18:09,100 --> 00:18:17,180 +symmetric انتبهين + +252 +00:18:17,180 --> 00:18:24,720 +الخاصية التالتة والاخيرة بدنا نثبت ان الـ Q is + +253 +00:18:24,720 --> 00:18:32,020 +transitive الـ Q is transitive هذه تلاتة + +254 +00:18:37,700 --> 00:18:42,020 +تمام ايه الشرط الـ Transitive؟ بدنا زوجين بترتيب + +255 +00:18:42,020 --> 00:18:46,780 +معين موجودين لازم المكمل تبعهم التالت يكون موجود + +256 +00:18:46,780 --> 00:18:53,210 +فبرضه بنبدأ ايش assume او letlet x,y في الـ Q and + +257 +00:18:53,210 --> 00:18:58,470 +y,z في الـ Q بدنا نثبت إنه x,z في الـ Q إيش نعمل؟ + +258 +00:18:58,470 --> 00:19:02,650 +نستخدم التعريف ماذا يعني x,y في الـ Q؟ يعني there + +259 +00:19:02,650 --> 00:19:05,810 +exist .. بتكتبها for some .. there exist there + +260 +00:19:05,810 --> 00:19:11,770 +exist a تنتمي للـ partition بحيث x في الـ A and y + +261 +00:19:11,770 --> 00:19:15,770 +في الـ A هيك معناته الـ x والـ y اللي ملاقة مع بعض + +262 +00:19:15,770 --> 00:19:20,360 +إنه من نفس الجزء andكفي كمان قاندة كبيرة، إيش + +263 +00:19:20,360 --> 00:19:24,140 +معناة Y و Z في الـQ إنهم بنفس الجزء؟ طب هل ده + +264 +00:19:24,140 --> 00:19:27,160 +ضروري يكون A؟ مش عارف، تذكروا المثال اللي رسمناه؟ + +265 +00:19:27,160 --> 00:19:29,780 +أه، فانا بقول there exist .. إيش أسميها؟ A ولا + +266 +00:19:29,780 --> 00:19:32,900 +إيش؟ ولا أغير اسم؟ بنغير بيه، لإنهم مش عارفين و + +267 +00:19:32,900 --> 00:19:38,560 +متساويين، there exist B in partition بحيث أنه إيش؟ + +268 +00:19:38,560 --> 00:19:41,520 +Y في الـB و Z في الـB + +269 +00:19:44,880 --> 00:19:48,180 +تمام الآن أنا إيش مطلوب مني أثبت إن X و Z اللي هم + +270 +00:19:48,180 --> 00:19:53,100 +علاقة مع بعض يعني يقع في نفس الجزء عندي معلومات ال + +271 +00:19:53,100 --> 00:19:56,920 +X في ال A و ال Z في ال B و أنتيش هيقع في نفس الجزء + +272 +00:19:56,920 --> 00:20:00,740 +إذا ال A و ال B تترابقها متساويين طب ليش متساويين؟ + +273 +00:20:00,740 --> 00:20:04,760 +في عناصر مشترك و من خلاص ال partition يا كل عناصر + +274 +00:20:04,760 --> 00:20:07,580 +مشتركة يا مافيش مشترك إذا واحد مشترك لازم الكل + +275 +00:20:07,580 --> 00:20:12,040 +يكون مشترك فهذا it follows ممكن أكتب بهذا الشكل it + +276 +00:20:12,040 --> 00:20:17,970 +followsthat Y تنتمي لـ A تقاطع الـ B الـ Y مشترك + +277 +00:20:17,970 --> 00:20:25,190 +وبالتالي الـ A تقاطع الـ B لا يساوي فاي وبالتالي A + +278 +00:20:25,190 --> 00:20:28,210 +تساوي B لأنهم partition كل واحدة من خواص ال + +279 +00:20:28,210 --> 00:20:31,770 +partition لأن الـ B partition تمام مازال A تساوي B + +280 +00:20:31,770 --> 00:20:35,570 +ال X في ال A إذن هي في ال B و ال Z في ال A و ال B + +281 +00:20:35,570 --> 00:20:41,050 +متساوية فده بقول إيه Xو Z تنتمي الـ A تساوي الـ B + +282 +00:20:41,050 --> 00:20:49,090 +وهذا معناته أن X Z في ال relation وهو المطلوب is + +283 +00:20:49,090 --> 00:20:54,610 +a transit طبعاً + +284 +00:20:54,610 --> 00:20:59,950 +1 و 2 و 3 بتدل علينا علاقة تكافئة واضح فإحنا + +285 +00:20:59,950 --> 00:21:04,870 +الأمثلة الماضية كانت مش حاجة نادرة إنما هي دايما + +286 +00:21:04,870 --> 00:21:05,310 +صحية + +287 +00:21:08,990 --> 00:21:13,390 +نعم؟ في أي سؤال واضح؟ إذا في أي نقطة جالب ما نمشي + +288 +00:21:13,390 --> 00:21:18,210 +عنها إذن هي ما أحنا شوفنا في النظريتين زي ما حكينا + +289 +00:21:18,210 --> 00:21:22,790 +في بداية المحاضرة كل علاقة تكافؤ بتولد partition + +290 +00:21:22,790 --> 00:21:27,610 +عبارة عن إيش؟ صفوف التكافؤ وكل partition بيولد + +291 +00:21:27,610 --> 00:21:31,110 +علاقة معرفة بدل الشكل إنه هي عبارة عن علاقة اللي + +292 +00:21:31,110 --> 00:21:34,230 +هو إيش يكونوا في نفس الجزء هي العلاقة إيش علاقة X + +293 +00:21:34,230 --> 00:21:38,880 +مع Y بيقعا في نفس الجزءنقطة أخيرة في هذا الموضوع + +294 +00:21:38,880 --> 00:21:42,800 +احنا صار عنا ببدأ من partition بولد equivalence + +295 +00:21:42,800 --> 00:21:45,280 +relation ببدأ من equivalence relation بولد + +296 +00:21:45,280 --> 00:21:49,380 +partition طب لو أنا بدأت من نقطة ما هل برجع لنفس + +297 +00:21:49,380 --> 00:21:52,020 +النقطة ولا لأ فهذا السؤال اللي احنا هنجاوب عليه + +298 +00:21:52,020 --> 00:21:59,980 +الآن فصارت عندنا الصورة التاليةبدأنا من + +299 +00:21:59,980 --> 00:22:05,780 +equivalence relation وولدنا partition عبارة عن + +300 +00:22:05,780 --> 00:22:10,160 +مين؟ صفوف التكافئة، مظبوط؟ هذه المحادرات الماضية + +301 +00:22:10,160 --> 00:22:15,360 +اليوم بدأنا من ال partition وولدنا relation Q + +302 +00:22:15,360 --> 00:22:21,240 +تساوي رمزها X على B هذه علاقة التكافئة هل هذه + +303 +00:22:21,240 --> 00:22:24,880 +علاقة التكافئة تختلف عن الأصلية اللي بدأت منها؟ + +304 +00:22:24,880 --> 00:22:30,040 +السؤال لأ متساويفدى دائرة مغلقة بدأت من + +305 +00:22:30,040 --> 00:22:33,740 +equivalence relation بولّد partition ال partition + +306 +00:22:33,740 --> 00:22:36,220 +بيولّد equivalence relation ال relation الأصلية زى + +307 +00:22:36,220 --> 00:22:39,040 +ما توي شفنا في ال mod بدأنا من ال partition وولدنا + +308 +00:22:39,040 --> 00:22:42,020 +relation ورجعنا للأصل طب العكس بدأت من partition + +309 +00:22:42,020 --> 00:22:46,260 +بولّد علاقة تكافؤ علاقة التكافؤ بتولّد partition + +310 +00:22:46,260 --> 00:22:49,460 +مين هو اللى بدأت منه فعشان هي زى الدائرة من أي + +311 +00:22:49,460 --> 00:22:51,720 +نقطة ابتدى بترجع لمين لنفس النقطة + +312 +00:22:55,340 --> 00:22:59,740 +مش بالظبط يعني لأ بس هي بادة الصورة إذا بدأنا من + +313 +00:22:59,740 --> 00:23:03,020 +partition كل partition بيولد equivalence relation + +314 +00:23:03,020 --> 00:23:06,000 +كل equivalence relation بتولد partition هل ال + +315 +00:23:06,000 --> 00:23:08,080 +partition هذا جديد و لا نفس اللي بدأت منه و نفس + +316 +00:23:08,080 --> 00:23:11,680 +اللي بدأت منه فهي صورها فطبعا عشان أوصل لعدي نظرية + +317 +00:23:11,680 --> 00:23:17,560 +بس عندي اللي هو نظرية تمهيدية لما بيقوللي إذا كان + +318 +00:23:17,560 --> 00:23:22,620 +عندي partitionوال partition ايش ماله؟ وولد علاقة + +319 +00:23:22,620 --> 00:23:27,420 +تكافؤ، كل علاقة تكافؤ إيش بتعرف؟ صفوف تكافؤ، فبقول + +320 +00:23:27,420 --> 00:23:33,320 +الصف اللي بتعرفه هذه العلاقة X أنا عندي .. هي عندي + +321 +00:23:33,320 --> 00:23:38,320 +partitionو هيعندي عنصر X في جزء A مثلا في هذا + +322 +00:23:38,320 --> 00:23:42,040 +الجزء طيب ال partition ولد relation اللي هي Q + +323 +00:23:42,040 --> 00:23:47,700 +واخدت عنصر X بدي احسب مين؟ X على Q صف في التكافأة + +324 +00:23:47,700 --> 00:23:50,320 +اللي ولد و تولد relation طيب هذا ال equivalent + +325 +00:23:50,320 --> 00:23:54,360 +class عبارة عن partition ايش علاقة؟هذا الجزء اللي + +326 +00:23:54,360 --> 00:23:58,140 +هو صف ال X مع ال A اللي إجت منها ال X متساوين .. + +327 +00:23:58,140 --> 00:24:00,220 +متساوين .. هذا اللي ما بتقول .. بقى ده الشكل و + +328 +00:24:00,220 --> 00:24:03,100 +عشان هيك بيصير تطابق لأنه كيف الصورة .. احنا قلنا + +329 +00:24:03,100 --> 00:24:07,880 +بدأنا من partition عرف علاقة التكافؤ .. علاقة + +330 +00:24:07,880 --> 00:24:11,820 +التكافؤ بتعرف partition كي بتجزه حسب صف التكافؤ .. + +331 +00:24:11,820 --> 00:24:14,760 +إيش ماله؟ ينطبق مع التجزيء السابق فهي بيجي دلوقتي + +332 +00:24:14,760 --> 00:24:17,560 +كل صف بنطبق مع اللي إيش الجزء اللي إيجي منه العنصر + +333 +00:24:17,560 --> 00:24:20,720 +.. الجزء منه العنصر .. فكان عندي العلاقة أنهصف ال + +334 +00:24:20,720 --> 00:24:23,680 +X المتولج من هذه العلاقة بيساوي الجزء اللي إتي منه + +335 +00:24:23,680 --> 00:24:28,000 +النص بشكل صريح let P be a partition of a non-empty + +336 +00:24:28,000 --> 00:24:31,440 +set X and let Q تساوي X على P الرمز اللي اتعودنا + +337 +00:24:31,440 --> 00:24:35,700 +عليه بقول if X تنتمي لل A for some A طبعا لازم + +338 +00:24:35,700 --> 00:24:38,700 +تكون موجودة فيها then صف ال X إيش بيساوي الجزء + +339 +00:24:38,700 --> 00:24:46,040 +اللي موجود فيها إيش ال X بيساوي إيه prove خلينا + +340 +00:24:46,040 --> 00:24:46,940 +نبره هنا مع بعض + +341 +00:24:50,750 --> 00:24:55,490 +لأنها تساعدنا في برهانة النظرية الجاية proof طبعاً + +342 +00:24:55,490 --> 00:25:03,250 +هذه اللمّة تمام فطبعاً أنا في عندي جملة شرطية X + +343 +00:25:03,250 --> 00:25:06,830 +تنتمي لل A for some A نفترض أن هذا كلام صحيح + +344 +00:25:06,830 --> 00:25:15,210 +assume X تنتمي لل A for some A in the partition + +345 +00:25:15,210 --> 00:25:22,270 +أيش بتثبت أن صف ال X يسوى بهذه المجموعة Aهذه علاقة + +346 +00:25:22,270 --> 00:25:26,690 +إيش؟ تساوي مجموعات كي بدأ أثبتها؟ بدأ أبدأ عنصر من + +347 +00:25:26,690 --> 00:25:30,730 +اليمين و أصله لليسار إذا الطريق اتجاهين خلص + +348 +00:25:30,730 --> 00:25:33,590 +الإثبات إذا اتجاه واحد بدأ أرجعه إيش؟ بدي كمان + +349 +00:25:33,590 --> 00:25:38,450 +طريق تاني يتوصلني من إيه لل X على Q فهنبدأ، فهناخد + +350 +00:25:38,450 --> 00:25:42,950 +عنصر عشوائي، إيش نسميه؟ ال X مشغولة، نسمي اسم جديد + +351 +00:25:42,950 --> 00:25:47,990 +let Y be any element تنتمي لل X على Q be any + +352 +00:25:47,990 --> 00:25:51,820 +elementطبعا ممكن تلاقوا في الكتب المتقدمة مابكتبش + +353 +00:25:51,820 --> 00:25:54,720 +N element لإنها واضحة من السياق انها عامة تمام، + +354 +00:25:54,720 --> 00:25:58,580 +بدأ أوصل ال Y لل A، الحقيقة حد مشي في اتجاهها، + +355 +00:25:58,580 --> 00:26:03,520 +ممتاز، ماذا يعني ان ال Y في صف ال X؟ ايش تعريف + +356 +00:26:03,520 --> 00:26:07,220 +الصف؟ يعني ال X و ال Y لملاقا مع بعض، فهذا يؤدي ان + +357 +00:26:07,220 --> 00:26:12,180 +X و Y تنتمي ل Q، من وين جيبت هذا الكلام؟ تعريف X + +358 +00:26:12,180 --> 00:26:18,130 +على Qصحيح؟ متذكرين التعريف؟ هيك بيقول، تمام أنا + +359 +00:26:18,130 --> 00:26:20,670 +واحد من الدواصل، دواصل الـ X للـ A، طب إيش تعريف + +360 +00:26:20,670 --> 00:26:24,030 +الـ Q؟ وقت إيش بيكونوا الملاخة مع بعضيش Q، X على + +361 +00:26:24,030 --> 00:26:28,370 +B، إذا الـ X و Y وقعا في جزء ما مع بعض، فهذا يؤدي + +362 +00:26:30,470 --> 00:26:34,530 +إنه there exist طيب ال A أنا فيها عندي جزء مثبت A + +363 +00:26:34,530 --> 00:26:37,270 +لكن التعريف بيقول لي إيش ال X و ال Y قاع في جزء + +364 +00:26:37,270 --> 00:26:40,290 +ما، هل بدروا يكون إيه؟ مش عارف، لسه مش عارف، بدي + +365 +00:26:40,290 --> 00:26:43,610 +أثبت إنه إيه، فبقول لي there exist B في ال + +366 +00:26:43,610 --> 00:26:49,190 +partition بحيث X تنتمي لل B and Y تنتمي لل B، for + +367 +00:26:49,190 --> 00:26:52,510 +some كتبته في الأول، مزال X و Y له ملاقة مع بعض، + +368 +00:26:52,510 --> 00:26:55,590 +إذا لازم يقاع في نفس الجزء، هيك تعريف ال Q، طب هذا + +369 +00:26:55,590 --> 00:26:58,600 +جزء ما؟عشان هذا الجزء بيساوي a مش عارف ال a أنا + +370 +00:26:58,600 --> 00:27:02,020 +انتقلتها من أول بقدرش أستخدمها ممتاز إيه صار عندي + +371 +00:27:02,020 --> 00:27:05,340 +ذاتي ال trick اللي تاوي استخدمناها ال x في ال b و + +372 +00:27:05,340 --> 00:27:11,660 +ال x في ال a إذا تقاطع ال a و ال b ليس في then x + +373 +00:27:11,660 --> 00:27:16,820 +تنتمي لل a تقاطع ال b ال x في ال b و ال x في ال a + +374 +00:27:16,820 --> 00:27:21,760 +مظبوط إذا التقاطع لا يساوي في implies a تقاطع ال b + +375 +00:27:21,760 --> 00:27:27,600 +لا يساوي في إذا إيش ال a بتساوي بتساوي ال bإذا الـ + +376 +00:27:27,600 --> 00:27:30,880 +A بتسوى ال B إيش صار الصورة نقرأ مع بعض و ده ممكن + +377 +00:27:30,880 --> 00:27:34,380 +أحنا نعمله أنه خلص البوابة ولا لأ أخدت عنصر في ال + +378 +00:27:34,380 --> 00:27:38,580 +A أثبتت أنه ال إيش أنا إيش بدها أثبت أنها هي وين؟ + +379 +00:27:38,580 --> 00:27:42,940 +آسف أنا أخدت عنصر Y هاي Y في ال XQ مش هيك بدنا + +380 +00:27:42,940 --> 00:27:48,060 +نثبت أخدنا عنصر Y هنا ال Y موجودة في ال B و ال B + +381 +00:27:48,060 --> 00:27:53,790 +تسوى ال A إذا ال Y وين؟ في ال A and henceY تنتمي + +382 +00:27:53,790 --> 00:27:59,790 +للـA فإيش وصلنا بدأنا من X على Q وصلناها للـA إذا + +383 +00:27:59,790 --> 00:28:03,790 +الأول سبست من التاني مش ماشي تكافأ يعني لأنه ماشي + +384 +00:28:03,790 --> 00:28:08,010 +بيقيش استنتاج فإذا أثبتنا للتجاه الأول العكس الآن + +385 +00:28:08,010 --> 00:28:15,470 +نبدأ من الطرف اليمين ناخد عنصر في الـA الآن let Y + +386 +00:28:15,470 --> 00:28:22,950 +تنتمي للـA be any elementو أرجو نتعود نقرأ صح واحد + +387 +00:28:22,950 --> 00:28:26,390 +يقولي طب ايه و انا ا assume هدى هدى مظلة عامة تبعت + +388 +00:28:26,390 --> 00:28:29,690 +ال F then في الجملة بعدين بدينا قولنا إيش إيش + +389 +00:28:29,690 --> 00:28:33,470 +بيقول النظراء اللي ما if X تنتمي لل A for some A + +390 +00:28:33,470 --> 00:28:37,570 +فدى مثبت أخلصناها then بدي مجموعة تساوي مجموعة + +391 +00:28:37,570 --> 00:28:43,370 +عملت على إيش على قسمين على2 parts تمام ال Y تنتمي + +392 +00:28:43,370 --> 00:28:47,270 +لل A بدي اثبت ان ال Y في صف ال X طب انا عند ال + +393 +00:28:47,270 --> 00:28:51,190 +summation هذا المظلة العامة ان X في ال A و Y في ال + +394 +00:28:51,190 --> 00:28:54,430 +A موجودين في messages انهم علاقة مع بعض اه فهذا + +395 +00:28:54,430 --> 00:28:59,210 +يؤدي ان X Y تنتمي ل Q من وين جبته تعريف ال Q + +396 +00:29:02,480 --> 00:29:06,520 +أنا وين ده أوصل ال Y لصف ال X؟ طب X و Y في ال Q + +397 +00:29:06,520 --> 00:29:11,000 +إيش معناته؟ إن Y في صف ال X، هذا أسهل، Y في صف ال + +398 +00:29:11,000 --> 00:29:15,580 +X فبالتالي اللي بدأت منه إيش ماله؟ سبسط من اللي + +399 +00:29:15,580 --> 00:29:25,660 +انتهيت فيه طبعاً 1 و 2 بين هو البرهن وهو المطلوب + +400 +00:29:27,650 --> 00:29:33,170 +فارجو أن نستخدم الرموز بشكل صحيح و عشان نكون + +401 +00:29:33,170 --> 00:29:39,590 +برهاننا كامل و صحيح فلقيا وصلنا للنظرية المطلوبة + +402 +00:29:39,590 --> 00:29:43,850 +let P be a partition of a non-empty set X بدنا من + +403 +00:29:43,850 --> 00:29:48,300 +partitionthen the equivalency classes induced by + +404 +00:29:48,300 --> 00:29:51,100 +the relation X على B يعني ال partitions اللي + +405 +00:29:51,100 --> 00:29:54,420 +بتولدوا هذه العلاقة التكافو X على B ليكيوسا منها + +406 +00:29:54,420 --> 00:30:00,780 +are precisely هم تماما بالظبط the sets in B بمعنى + +407 +00:30:00,780 --> 00:30:07,040 +آخر بالرموز بيقول ليه أنا عندي partitionوولد + +408 +00:30:07,040 --> 00:30:11,500 +relation Q التي نسميها X على B لو جيت احسب + +409 +00:30:11,500 --> 00:30:15,880 +equivalence classes الييمين X على Q و Q هذه بتساوي + +410 +00:30:15,880 --> 00:30:20,920 +اسم تطلعوتطلع ال partition نفسه طبعا الكتابة هنا + +411 +00:30:20,920 --> 00:30:25,500 +ممتازة الكتابة مقلوفة عليك وإذا عملت جسمها X على X + +412 +00:30:25,500 --> 00:30:28,460 +على B مقام المقام بيصيح ال bus و ال X بتروح مع ال + +413 +00:30:28,460 --> 00:30:33,540 +X فرمز موفق الحقيقة الرمز موفق لإن ما مش جسمه مجرد + +414 +00:30:33,540 --> 00:30:36,660 +رموز مجرد رموز فيمكن هذه من أعلى الأسباب اللي + +415 +00:30:36,660 --> 00:30:40,600 +اختاروا هذا الرمز انه قسم زي القسمة واضحة فهي إيش + +416 +00:30:40,600 --> 00:30:44,800 +ال X على Q فهي نفس الكلام بدأت من partitionعرفت + +417 +00:30:44,800 --> 00:30:48,700 +علاقة Q لـ Q عرفت partition نفس الـ partition اللي + +418 +00:30:48,700 --> 00:30:51,080 +بدأت منه فانا برجع نفس النقطة دائرة بتاب ندور في + +419 +00:30:51,080 --> 00:30:58,560 +نفس الدائرة اللي حكينا عليها نشوف البرهان البرهان + +420 +00:30:58,560 --> 00:31:01,760 +هيستخدم اللمة بشكل أساسي عشان ذلك احنا حاطناها + +421 +00:31:01,760 --> 00:31:07,160 +لانها ساعدنا في ان البرهان يصير أقصر وبالتالي أسهل + +422 +00:31:07,160 --> 00:31:12,980 +في القراءة نظرية تلاتة ستة prove + +423 +00:31:14,270 --> 00:31:19,310 +طبعا للتسهيل خلّينا نسمي الـ Q كالعادة هي X على B + +424 +00:31:19,310 --> 00:31:25,670 +تمام، إيش بدي أثبت؟ بدي أثبت إن X على Q تساوي B، + +425 +00:31:25,670 --> 00:31:33,690 +هذا هو المطلوب أكتب We want to prove اللي هو إيش؟ + +426 +00:31:33,690 --> 00:31:39,330 +X على Q تساوي الـ partition متابعين؟ + +427 +00:31:40,380 --> 00:31:45,580 +الحقيقة يمكن تكون رموز شوية كبيرة أو يعني مش + +428 +00:31:45,580 --> 00:31:50,120 +مألوفة لكن المفاهيم الرئيسية الحقيقة واحدة طيب هال + +429 +00:31:50,120 --> 00:31:55,580 +gate ال B إيش عادي function ولا relation ولا إيش؟ + +430 +00:31:56,440 --> 00:31:59,160 +مجموعة مجموعات الـ Partition الـ Partition الـ P + +431 +00:31:59,160 --> 00:32:02,520 +Partition يعني إيش؟ مجموعة مجموعات و X على Q + +432 +00:32:02,520 --> 00:32:05,820 +مجموعة مجموعات يعني مع مجموعة صفوق في التكافئة إذا + +433 +00:32:05,820 --> 00:32:08,680 +أنا إيش مطلوب مني أثبت؟ مجموعة تساوي مجموعة ده ما + +434 +00:32:08,680 --> 00:32:12,600 +بنبدأ إيش؟ من خارج للداخل في القراة إذا بدأنا نثبت + +435 +00:32:12,600 --> 00:32:16,440 +مجموعة تساوي مجموعة كيف بنثبت؟ كم مرة عملناها؟ + +436 +00:32:16,440 --> 00:32:20,680 +عشرات المرات ناخد عنصر فهنبدأ من إن إيش؟ نبدأ .. + +437 +00:32:20,680 --> 00:32:24,800 +خليني أبدأ أسهل من الطرف .. صح من ورن ما بدنا + +438 +00:32:24,800 --> 00:32:30,870 +خليني أبدأ من اليسارlet هاخد عنصر هان واتعلمنا انه + +439 +00:32:30,870 --> 00:32:35,110 +في الاصل اخد عنصر عشوائي صحيح طب انا دي انا عندي + +440 +00:32:35,110 --> 00:32:39,070 +معلومات عن المجموعة باخد عنصر بصورة المجموعات اه + +441 +00:32:39,070 --> 00:32:43,450 +انا عندي x على q اي عنصر موجود هناك يكون صفة كافة + +442 +00:32:43,450 --> 00:32:49,450 +small x على q فهقول له let x على q be any element + +443 +00:32:49,450 --> 00:32:53,910 +تنتمي لل x على q لو عملت على مرتهم ده يقول له مثلا + +444 +00:32:53,910 --> 00:32:57,710 +letA تنتمي إيش تكون الـ A؟ لازم صفتها كافة لو أن + +445 +00:32:57,710 --> 00:33:00,630 +هذه عنصرها هيك زي ما عملنا في الأزواج المرتبة بي + +446 +00:33:00,630 --> 00:33:07,030 +any element هثبت + +447 +00:33:07,030 --> 00:33:10,970 +إنه هذه تنتمي للـ B بدي أثبت إنه هذه جزء بدي أثبت + +448 +00:33:10,970 --> 00:33:20,620 +إنه هذه عبارة عن جزء ممتازالـ X على الـ Q تمام + +449 +00:33:20,620 --> 00:33:24,520 +بدنا نستخدم اللي ما الحقيقة هلجيت هذه الـ X small + +450 +00:33:24,520 --> 00:33:27,820 +x من وين واخدناها؟ من capital X لأنه أنا اللي بعمل + +451 +00:33:27,820 --> 00:33:34,950 +الصفر اه فالان now small x تنتمي لل capital Xوما + +452 +00:33:34,950 --> 00:33:37,730 +زال فيه partition، إذا الـ capital X عبارة عن مين؟ + +453 +00:33:37,730 --> 00:33:43,050 +اتحاد الأجزاء تساوي union على A للpartition في + +454 +00:33:43,050 --> 00:33:47,210 +مين؟ لل A، مظبوط؟ أه، هي كانت التعريفة، إذا هذه + +455 +00:33:47,210 --> 00:33:49,310 +الـ X الشمالي اللي ناجد تكون موجودة في جزء من + +456 +00:33:49,310 --> 00:33:51,810 +الأجزاء، هي موجودة في كلها، لأن X عبارة عن أجزاء + +457 +00:33:51,810 --> 00:34:00,230 +implies X تنتمي لل A for some A تنتمي للpartition + +458 +00:34:00,230 --> 00:34:03,530 +أه، هستخدم الليمة الآن + +459 +00:34:06,650 --> 00:34:11,030 +عنصر في مجموعة إذا X تنتمي للـA إذا الـH بتساوي صف + +460 +00:34:11,030 --> 00:34:16,850 +الـX توي أثبتناها by لمّا جدّاش المرقمين احنا ليه + +461 +00:34:16,850 --> 00:34:23,140 +ما جدّاش؟تلاتة واحد ايش في عندي ان X على Q اشملها + +462 +00:34:23,140 --> 00:34:27,920 +تساوي A و اين موجود ال A في ال partition تنتمي لل + +463 +00:34:27,920 --> 00:34:32,500 +partition اذا اول شيء بدأت من عنصر في X على Q + +464 +00:34:32,500 --> 00:34:38,620 +وصلته لل partition اذا اثبتنا ان ال capital X على + +465 +00:34:38,620 --> 00:34:44,440 +Q هي subset من ال partition فالاتجاه الاول فده هو + +466 +00:34:44,440 --> 00:34:52,400 +الاتجاه الاول نعمل اتجاه التانيlet ايش؟ بدنا ناخد + +467 +00:34:52,400 --> 00:34:56,000 +جزء من .. أنصر من الـ partition اللي صورة معينة، + +468 +00:34:56,000 --> 00:34:59,340 +مجموعة بس، لكن مش صفر، مش ضروري يكون صفر، بدي أثبت + +469 +00:34:59,340 --> 00:35:02,680 +أنه صفر، هقوله let A تنتمي للـ partition بـ an + +470 +00:35:02,680 --> 00:35:08,240 +element، بدي + +471 +00:35:08,240 --> 00:35:14,780 +أثبت أن هذا صفر تكافر، طيب، ممتاز، هل جيت؟بدنا + +472 +00:35:14,780 --> 00:35:19,540 +نستخدم برضه اللي مّا بدي أخد عنصر من الـ A أي عنصر + +473 +00:35:19,540 --> 00:35:22,220 +من الـ A هيكون صف هذا العنصر هو الـ A، مظبوط؟ هيك + +474 +00:35:22,220 --> 00:35:25,200 +اللي مابتقول طب مين بيقوللي أن الـ A هيدي فيها + +475 +00:35:25,200 --> 00:35:30,400 +عنصر على الأقل؟ ولا ممكن تكون في الـ A؟ مستحيل، + +476 +00:35:30,400 --> 00:35:36,060 +لأنه partition فإذا هذا بيقوللي then A لا تساوي في + +477 +00:35:36,060 --> 00:35:41,580 +تعريف ال partition إذا there exists X تنتمي لمن؟ + +478 +00:35:41,580 --> 00:35:48,760 +للـ Aبالنسبة لما إذا X تنتمي لصف X في شمال A بيسوء + +479 +00:35:48,760 --> 00:35:56,800 +الـ A بلما تلاتة واحد اللي هو إيش احنا بدنا من إيه + +480 +00:35:56,800 --> 00:36:04,330 +A تسوى صف ال X وصف ال X موجود في الصفوفمازال الـ A + +481 +00:36:04,330 --> 00:36:07,870 +صفف إذا هي ضمن الصفوف خلصنا بدأنا من A في ال + +482 +00:36:07,870 --> 00:36:11,010 +partition وصلنا لمجموعة الصفوف إذا صارت ال + +483 +00:36:11,010 --> 00:36:14,950 +partition جزء أو subset من الصفوف من وين من الصفوف + +484 +00:36:14,950 --> 00:36:24,790 +thus اللي هو إيش ال B subset من X على Q وهذه اتنين + +485 +00:36:24,790 --> 00:36:31,210 +طبعا واحد واتنين بيقول البرهان انتهى أي سؤال تمام؟ + +486 +00:36:34,250 --> 00:36:39,130 +خلّينا ننهي ال section بمثال توضيحي للنظرية عشان + +487 +00:36:39,130 --> 00:36:41,590 +نبقى .. إذا كان حد لسه مش واضحاه الصورة اللي بحالي + +488 +00:36:41,590 --> 00:36:46,670 +حكينا، هنبدأ من partition، هنعرف علاقة التكافؤ، + +489 +00:36:46,670 --> 00:36:49,650 +هنحسب partition متولد من علاقة التكافؤ، إيش، هنرجع + +490 +00:36:49,650 --> 00:36:52,290 +نفس النقطة، فخلّينا نحسبه مع بعض، نشوف هذا الكلام + +491 +00:36:52,290 --> 00:36:53,250 +متحقق ولا لأ + +492 +00:37:04,490 --> 00:37:09,570 +مثال فهنا مديني مجموعة صغيرة من أربع عناصر و مديني + +493 +00:37:09,570 --> 00:37:13,590 +partition في عنصر لحال و التلاتة التانية مع بعض + +494 +00:37:13,590 --> 00:37:17,490 +حطينا طالب في شعبة و تلات طلاب في شعبة جسمناهم هيك + +495 +00:37:17,490 --> 00:37:21,250 +تجسيم بيد الصورة بقول يوجد ال partition يوجد ال Q + +496 +00:37:21,250 --> 00:37:25,030 +ويوجد X على ال Q بهذا المعنى عشان نوصل لبدنيا + +497 +00:37:25,030 --> 00:37:31,530 +solution فخلينا نحسب Q تساوي X على ال partition + +498 +00:37:31,530 --> 00:37:36,150 +تمامبتتكون من أزواج مرتبة إشمالها كل اللي حصلناها + +499 +00:37:36,150 --> 00:37:39,390 +في بداية المحاضرة، مش ذاكرين؟ فهي عند ال partition + +500 +00:37:39,390 --> 00:37:42,750 +فبدأ أقول الواحد اللي علاقة مع مين؟ مع نفسها، + +501 +00:37:42,750 --> 00:37:46,690 +والتانين مع نفسها، والتلاتة مع نفسها، والاربعة مع + +502 +00:37:46,690 --> 00:37:51,920 +نفسها، تمام، هذه النقطة السهلةهل الواحد لعلاقة مع + +503 +00:37:51,920 --> 00:37:55,260 +حد غير نفسه؟ لا لأنه موجود في جزء لحاله لكن التنين + +504 +00:37:55,260 --> 00:37:58,540 +لعلاقة مع التلاتة وبالتالي التلاتة لعلاقة مع + +505 +00:37:58,540 --> 00:38:02,180 +التنين لأنه symmetric مظبوط والتنين لعلاقة مع + +506 +00:38:02,180 --> 00:38:05,620 +الأربعة والاربعة لعلاقة مع التنين لأنه symmetric + +507 +00:38:05,620 --> 00:38:12,590 +وتلاتة واربعةوالاربعة والتلاتة في تمشي خلصت ال + +508 +00:38:12,590 --> 00:38:15,290 +relation اه فانا في ضوء النظرية انا عارف ان ال + +509 +00:38:15,290 --> 00:38:18,470 +relation هي Q لنا و بقدر احسب بيبقى ده الشكل تمام + +510 +00:38:18,470 --> 00:38:22,930 +فهي partition بي ده نيا وولدنا relation انشوف ال + +511 +00:38:22,930 --> 00:38:26,050 +relation ده ايش ملها بتتولد مين partition نحسبه + +512 +00:38:26,050 --> 00:38:30,430 +ايش .. ايش .. ايش رمزه X على Q مظبوط ايش بيساوي + +513 +00:38:30,430 --> 00:38:34,890 +الصفوفالـ X أكمل عنصر فيها أربع، ففيدنا يكون فيها + +514 +00:38:34,890 --> 00:38:39,330 +أربع صفوف صف الواحد، صف التنين، بس ممكن يكون بعضه + +515 +00:38:39,330 --> 00:38:43,830 +متساوي، صف التلاتة وصف الأربع، مظبوط؟ أه، الأن + +516 +00:38:43,830 --> 00:38:47,810 +انسوا أن علاقة التكافؤ، درسنا علاقات التكافؤ وكيف + +517 +00:38:47,810 --> 00:38:51,770 +نحسب صفوف التكافؤ، بس عشان ليش نوضح النظرية تمام، + +518 +00:38:51,770 --> 00:38:57,480 +بدأ جاود مباشرة، مين صف الواحد؟ في الشيء للواحدلأن + +519 +00:38:57,480 --> 00:39:00,360 +الواحد بس لإنه يقول مافيش هو صف فاضي و أول عنصر في + +520 +00:39:00,360 --> 00:39:04,300 +صف ال X هو ال X في غيره مافيش طيب مين صف التنين؟ + +521 +00:39:04,300 --> 00:39:08,640 +التنين و التلاتة و الأربعة و هو بيسوي صف التلاتة و + +522 +00:39:08,640 --> 00:39:11,060 +بيسوي صف الأربعة لإنهم ملقا مع بعض من خواص الصفوف + +523 +00:39:11,060 --> 00:39:12,220 +فإيش رجعنا؟ + +524 +00:39:16,490 --> 00:39:21,250 +النظرية بتقول ابدأي من partition عارفي equivalence + +525 +00:39:21,250 --> 00:39:25,630 +relation من ال partition احصي بتقع فوق ترجع لنقطة + +526 +00:39:25,630 --> 00:39:29,210 +اللي بدأتي منها اي سؤال + diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yyyArAz0AFk.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yyyArAz0AFk.srt new file mode 100644 index 0000000000000000000000000000000000000000..76505a6a887c2d1ba3a2a433f620a5351152a7b9 --- /dev/null +++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yyyArAz0AFk.srt @@ -0,0 +1,2379 @@ +1 +00:00:19,660 --> 00:00:24,020 +بسم الله الرحمن الرحيم هنكمل دراستنا مع الدوال و + +2 +00:00:24,020 --> 00:00:27,700 +اليوم إن شاء الله هنتحدث عن الدوال اللي هي one to + +3 +00:00:27,700 --> 00:00:31,060 +one أو injective واللي بيسموها في اللغة العربية اللي + +4 +00:00:31,060 --> 00:00:37,080 +هو دالة متباينة أو اللي هي surjective وهي الدالة + +5 +00:00:37,080 --> 00:00:40,720 +الشاملة واللي هي الـ byjection اللي هي الدالة اللي + +6 +00:00:40,720 --> 00:00:44,300 +هي التناظرية الدالة التناظرية فهنشرح المصطلحات + +7 +00:00:44,300 --> 00:00:47,580 +الثلاثة دول بالتفصيل ونشوف كيف بنتعامل معاهم كيف + +8 +00:00:47,580 --> 00:00:51,040 +بنثبت أن الدالة تكون injection أو تكون surjection + +9 +00:00:51,040 --> 00:00:56,740 +أو تكون byjection فطبعًا هنبدأ بالمصطلح الأول وهو الـ + +10 +00:00:56,740 --> 00:01:00,820 +injection أو الـ injective function اللي هي الدالة + +11 +00:01:00,820 --> 00:01:05,020 +المتباينة طبعًا الدالة المتباينة طبعًا إحنا قلنا إن + +12 +00:01:05,020 --> 00:01:08,300 +الدالة مسموح أن تأخذ أكثر من عنصر لنفس الصورة + +13 +00:01:08,300 --> 00:01:12,120 +والممنوع من الدالة أن تأخذ عنصر لأكثر من صورة + +14 +00:01:12,120 --> 00:01:17,200 +فالأَن إذا كان في عندنا دالة وبتاخد كل عنصر لصورة + +15 +00:01:17,200 --> 00:01:20,160 +مختلفة هذه بيسميها دالة متباينة لأنها تدّي عناصر + +16 +00:01:20,160 --> 00:01:24,100 +المختلفة المتباينة بتوديها لصور متباينة فالتعريف + +17 +00:01:24,100 --> 00:01:29,080 +بالشكل التالي a function f from X to Y is said to + +18 +00:01:29,080 --> 00:01:32,580 +be injective or one to one فدول المصطلحين + +19 +00:01:32,580 --> 00:01:35,460 +المستخدمين بتقول عن دالة أنها injective function + +20 +00:01:35,460 --> 00:01:38,680 +أو one to one function إيش الشرط؟ إيش التعريف؟ + +21 +00:01:38,680 --> 00:01:43,820 +provided ده هذا الشرط لكل عنصرين في الـ domain إذا + +22 +00:01:43,820 --> 00:01:49,520 +كانت صورهم متساوية لازم يتساووا بمعنى آخر ما بتاخدش + +23 +00:01:49,520 --> 00:01:52,960 +عنصرين مختلفين لنفس الصورة آه طبعًا الدوال بشكل عام + +24 +00:01:52,960 --> 00:01:56,940 +ممكن زي الدالة التربيعية بتاخد أكثر من عنصر مختلف + +25 +00:01:56,940 --> 00:01:59,020 +إلى نفس الصورة بس تاخد الواحد وتساوي الواحد لنفس + +26 +00:01:59,020 --> 00:02:02,160 +الصورة هذه الدالة بشكل عام مسموح لكن الدالة عشان + +27 +00:02:02,160 --> 00:02:05,980 +تكون one to one لأ لازم العناصر المختلفة تروح لصور + +28 +00:02:05,980 --> 00:02:09,880 +مختلفة فده شرط إضافي طبعًا كمصطلح إحنا بنقول + +29 +00:02:09,880 --> 00:02:12,640 +injective function أو injection طبعًا قاعدة + +30 +00:02:12,640 --> 00:02:15,140 +بالنسبة لي استخدام اللغة اللي هو الـ injective عبارة + +31 +00:02:15,140 --> 00:02:19,860 +عن صفة والـ injection هي الـ noun هي الاسم تمام قبل + +32 +00:02:19,860 --> 00:02:24,520 +ما نبدأ في التطبيق نشوف اللي هو ملاحظة مهمة جدًا كيف + +33 +00:02:24,520 --> 00:02:29,180 +بدنا نتعامل.. نحول التعريف بلغة الرموز لأن هذا + +34 +00:02:29,180 --> 00:02:31,660 +مهم جدًا.. إحنا كيف نتعامل.. زي ما شوفنا إيش معنى + +35 +00:02:31,660 --> 00:02:35,880 +subset وكيف بنحوله بلغة الرموز وهذا بيساعدنا في + +36 +00:02:35,880 --> 00:02:38,920 +البرهان.. إيش نعمل في البرهان؟ فلو بدنا نثبت إن ده + +37 +00:02:38,920 --> 00:02:42,220 +injective.. إيش معنى injective.. بدنا نفسر هذا + +38 +00:02:42,220 --> 00:02:46,230 +الكلام فبيقول لي إذا كانت X واحد وX اتنين تنتمي لـ X + +39 +00:02:46,230 --> 00:02:51,010 +صورهم متساوية لازم العناصر تكون متساوية كيف بنعبر + +40 +00:02:51,010 --> 00:02:54,870 +عنها؟ أنه لجميع العناصر في الـ domain هذا الشرط + +41 +00:02:54,870 --> 00:02:57,710 +لازم يكون طبق على جميع عناصر الـ domain فبيقول لي + +42 +00:02:57,710 --> 00:03:00,490 +for all X one طبعًا وين X one؟ في الـ Capital X في + +43 +00:03:00,490 --> 00:03:03,070 +الـ domain بس هنا لو أندي الـ domain of discourse هو + +44 +00:03:03,070 --> 00:03:07,630 +الـ domain لكل X اتنين لكل X one لكل X اتنين إذا + +45 +00:03:07,630 --> 00:03:12,710 +الصور تساوت لازم العناصر تتساوى طبعًا ممكن أنا إيش + +46 +00:03:12,710 --> 00:03:15,570 +هاد أكتبه على صورة اللي هو الـ..الـ..الـ + +47 +00:03:15,570 --> 00:03:18,730 +contrapositive أعملها أحولها طبعًا الـ contrapositive + +48 +00:03:18,730 --> 00:03:21,530 +إليها علاقة بمين؟ بجملة الشرطية ما عليها علاقة بالـ + +49 +00:03:21,530 --> 00:03:24,490 +quantifiers for all x1 for all x2 لكن الجملة + +50 +00:03:24,490 --> 00:03:29,250 +الشرطية بتصير إيش؟ مبت Q يعني x1 لا تساوي x2 تؤدي + +51 +00:03:29,250 --> 00:03:32,950 +إلى إيش؟ f of x1 لا تساوي x2 طبعًا الصورة الثانية هي + +52 +00:03:32,950 --> 00:03:36,630 +الصورة الأوضح في التعريف، إيش one to one؟ العناصر + +53 +00:03:36,630 --> 00:03:40,610 +المختلفة بتروح لصور مختلفة، بتؤدي إلى صور مختلفة، + +54 +00:03:40,610 --> 00:03:45,150 +هذا المعنى، لكن من ناحية رياضيات التعامل مع هذه + +55 +00:03:45,150 --> 00:03:48,830 +الصورة صعب، لأن إيش معنى لا يساوي؟ ما فيش قواعد + +56 +00:03:48,830 --> 00:03:52,490 +كيف أتعامل معها، هل هي أصغر ولا أكبر؟ فلذلك ذاك + +57 +00:03:52,490 --> 00:03:56,310 +الصورة هي الأنسب للتعامل الرياضية لكن الصورة + +58 +00:03:56,310 --> 00:03:59,770 +الثانية أوضح من ناحية المعنى أن العناصر المختلفة + +59 +00:03:59,770 --> 00:04:04,750 +بتنتقل إلى صور مختلفة فاثنتين صحيحتين إحنا بنتعامل + +60 +00:04:04,750 --> 00:04:09,410 +معها دي كـ answer بصورة answer فإذا هذا هو التعريف + +61 +00:04:09,410 --> 00:04:12,570 +أنه لجميع عناصر الـ domain لأي أخدت أي عنصرين في الـ + +62 +00:04:12,570 --> 00:04:16,090 +domain إذا صورهم متساوية لازم دول عنصرين يتساوي + +63 +00:04:16,090 --> 00:04:19,440 +لازم دول عنصرين يتساوي فالأَن اعتمادًا على هذه + +64 +00:04:19,440 --> 00:04:22,540 +الملاحظة أو هذا التعريف والكتابة هنبدأ نشتغل كيف + +65 +00:04:22,540 --> 00:04:27,540 +نثبت أنه دالة ما one to one فإذن إحنا عرفنا إيش + +66 +00:04:27,540 --> 00:04:30,940 +معناه injective function أو one to one الآن بدنا + +67 +00:04:30,940 --> 00:04:35,200 +نشوف كيف بنطبق التعريف في البراهين لو داني دالة ما + +68 +00:04:35,200 --> 00:04:38,600 +كيف بدي أثبت إنها one to one أو injective فهذه هي + +69 +00:04:38,600 --> 00:04:42,620 +المهارة اللي بدنا نتعلمها هنبدأ بمثال بسيط جدًا + +70 +00:04:42,620 --> 00:04:46,270 +عشان نحط الهيكلية العامة زي ما اتعلمنا كيف بنثبت + +71 +00:04:46,270 --> 00:04:49,990 +subset؟ بنقول let x be any element في الـ..في الـ + +72 +00:04:49,990 --> 00:04:52,250 +..في الـ.. يقعد على اليسار ونوصل لليمين فبنشوف + +73 +00:04:52,250 --> 00:04:55,430 +الهيكلية العامة طبعًا التفاصيل بتختلف من مثال لمثال + +74 +00:04:55,430 --> 00:04:58,250 +زي ما اتعلمنا لكن في اللي هو structure معين في + +75 +00:04:58,250 --> 00:05:02,030 +تركيبة معينة للبرهان كيف أبدأ؟ وين بعرف إن إيش + +76 +00:05:02,030 --> 00:05:04,930 +البرهان انتهى؟ فنحن هنتعلم نفس الشيء بالنسبة لمين؟ + +77 +00:05:04,930 --> 00:05:07,430 +للـ injective function أو الـ one to one فنبدأ + +78 +00:05:07,430 --> 00:05:14,240 +بالمثال المثال بقول ليه؟ let X be a subset of Y وF + +79 +00:05:14,240 --> 00:05:18,080 +دالة من X لـ Y اشترطت أن الـ domain يكون مجموعة جزئية + +80 +00:05:18,080 --> 00:05:22,100 +من المجال المقابل اشترطت أن المجال X يكون مجموعة + +81 +00:05:22,100 --> 00:05:25,760 +جزئية من المجال المقابل be a function given by.. + +82 +00:05:25,760 --> 00:05:29,060 +بدي أعرفها.. إيش أعرفها؟ هي الدالة المحايدة.. هي + +83 +00:05:29,060 --> 00:05:31,540 +الدالة المحايدة يعني العنصر X يشمل.. ما بتغيروش.. + +84 +00:05:31,540 --> 00:05:35,690 +ما بتخليه زي ما X.. عشان هيك لازم الـ X تكون subset + +85 +00:05:35,690 --> 00:05:39,150 +من الـ Y لأن الـ X مش هتتغير فأنا باخد X من Capital + +86 +00:05:39,150 --> 00:05:42,230 +X بوديها لـ Y، بينفع الـ Y تكون مختلفة؟ لأ، لأنها + +87 +00:05:42,230 --> 00:05:44,410 +بتكون نفس العنصر، مش هتصير عليه تغيير، فعشان إيه + +88 +00:05:44,410 --> 00:05:48,070 +جالي لازم تكون الـ X ما لها subset من الـ Y تمام، + +89 +00:05:48,070 --> 00:05:52,310 +إيش المطلوب؟ show that، يعني prove that F is an + +90 +00:05:52,310 --> 00:05:55,610 +injective function فهذا أول مثل، نتعلم كيف بنثبت + +91 +00:05:55,610 --> 00:06:00,290 +إن الدالة injective أو إنها one to one فهذا المثال + +92 +00:06:00,290 --> 00:06:02,790 +الأول solution + +93 +00:06:05,360 --> 00:06:08,140 +آه زي ما اتعلمنا بنشوف إيش معنى injective إحنا + +94 +00:06:08,140 --> 00:06:12,200 +ندفنها injective كتبناها إيش بتساوي؟ جال إيش؟ for + +95 +00:06:12,200 --> 00:06:17,680 +all x one خليني أكتبها نكتبها كمان مرة F is + +96 +00:06:18,250 --> 00:06:22,710 +injection أو injective function تكافئ التعريف اللي + +97 +00:06:22,710 --> 00:06:27,690 +حطيناه في الملاحظة For all X1 وإذا بدنا نكون أكثر + +98 +00:06:27,690 --> 00:06:33,170 +دقة في الـ Capital X في الـ domain For all X2 في الـ + +99 +00:06:33,170 --> 00:06:40,610 +domain إذا كانت F of X1 تساوي F of X2 لازم X1 + +100 +00:06:40,610 --> 00:06:45,420 +تساوي X2 إذاً هذه هي الـ stem هذا هو التعريف هذا هو + +101 +00:06:45,420 --> 00:06:49,140 +التعريف جال لي أثبت أن F injection يعني أثبت هذا + +102 +00:06:49,140 --> 00:06:51,700 +الكلام، مظبوط؟ آه، هذا ده هو الرموز وهذا المجال + +103 +00:06:51,700 --> 00:06:54,860 +اللي أتعامل معاه رياضيًا فبتبدأ البرهان آه، زي ما + +104 +00:06:54,860 --> 00:06:58,300 +اتعلمنا، إيش؟ for all كيب على الجهة، باخد عنصر + +105 +00:06:58,300 --> 00:07:02,940 +عشوائي وكم for all ما عندي؟ اثنين فلازم لازم آخذ + +106 +00:07:02,940 --> 00:07:06,320 +X1 any element in Capital X وX2 any element in + +107 +00:07:06,320 --> 00:07:11,240 +Capital X لأن for all for all فحقوله البرهان let X1 + +108 +00:07:11,240 --> 00:07:20,000 +وX2 تنتمي للـ Capital X بـ Any Element لو ما كتبتش + +109 +00:07:20,000 --> 00:07:22,340 +أنا إيه اللي ما اسمه مش موجودش قضية Assume.. آه + +110 +00:07:22,340 --> 00:07:26,060 +تمام.. آه فإذا هذه علاجنا لمين؟ ليش بدينا هيك؟ + +111 +00:07:26,060 --> 00:07:29,260 +عشان for all وfor all واضحة؟ لما كانت مرة for all + +112 +00:07:29,260 --> 00:07:32,040 +واحدة كنا بنقول X واحدة عشان هم اثنتين سميناهم X + +113 +00:07:32,040 --> 00:07:34,400 +واحد وX اثنين ممكن يسميهم X وY ممكن بس عشان هم + +114 +00:07:34,400 --> 00:07:38,200 +عناصر في الـ domain الأنسب الـ X تمام، الآن بعد ما + +115 +00:07:38,200 --> 00:07:40,500 +خلصنا علاجنا للـ for all ده أنا أعالج الجملة، جملة + +116 +00:07:40,500 --> 00:07:43,840 +شرطية كيف أبدأ أثبتها؟ أبدأ أفترض أن الشرط صحيح، آه + +117 +00:07:43,840 --> 00:07:45,800 +فهنقوله الآن Assume + +118 +00:07:48,350 --> 00:07:55,180 +F of X1 تساوي F of X2 آه إيش المطلوب؟ مطلوب أثبت إن + +119 +00:07:55,180 --> 00:07:58,420 +X1 تساوي X2 فإذا هذه هي كالية البرهان إذا البرهان + +120 +00:07:58,420 --> 00:08:01,660 +الـ one-to-one ببدأ إنه باخد عنصرين عشوائيين من + +121 +00:08:01,660 --> 00:08:05,700 +الـ domain صورهم متساوية آه زي ما بنقول كيب نثبت إنه + +122 +00:08:05,700 --> 00:08:09,240 +subset بناخد عنصر عشوائي في المجموعة الأولى و + +123 +00:08:09,240 --> 00:08:11,700 +بنوصل للمجموعة الثانية إذا إن أنا باخد عنصرين + +124 +00:08:11,700 --> 00:08:16,340 +عشوائيين صورتهم متساوية وأثبت إنهم هم متساويين إن + +125 +00:08:16,340 --> 00:08:19,400 +هم متساويين آه كيب نثبت إنهم متساويين بيختلف من + +126 +00:08:19,400 --> 00:08:24,030 +مثال لمثال طبعًا مفتاح أساسي أستخدم تعريف الدالة هنا من + +127 +00:08:24,030 --> 00:08:28,370 +تعريف الـ function f of x1 إيش بتساوي؟ x1 f of x2 + +128 +00:08:28,370 --> 00:08:31,530 +بتساوي x2 من وين جبته؟ لأن تعريف الدالة في هذا + +129 +00:08:31,530 --> 00:08:35,510 +المثال هي الدالة المحايدة وصلت للي بديها نعم انتهى + +130 +00:08:35,510 --> 00:08:39,950 +البرهان x1 تساوي x2 إذا انتهى البرهان فإذا خلاص + +131 +00:08:39,950 --> 00:08:47,840 +thus f is injection and injection فعلاً هي + +132 +00:08:47,840 --> 00:08:52,500 +injective function أو injection فهذه طريقة كيف + +133 +00:08:52,500 --> 00:08:55,240 +نبرهن الـ one to one كيف البداية وكيف النهاية + +134 +00:08:55,240 --> 00:08:59,740 +التفاصيل هتختلف من مثال لمثال واضح فإحنا زي نفس + +135 +00:08:59,740 --> 00:09:05,110 +السياسة كيف نتعلم نثبت الـ subset كيف اتعلمنا نثبت + +136 +00:09:05,110 --> 00:09:08,270 +التساوي للمجموعات وهكذا فنفس القضية بنتعلم هذه + +137 +00:09:08,270 --> 00:09:11,710 +المهارة بنتعلم هذه المهارة فإذا عشان أثبت أن + +138 +00:09:11,710 --> 00:09:15,070 +الدالة تكون one to one أو injective ببدأ بهذه + +139 +00:09:15,070 --> 00:09:18,850 +البداية باخد عنصرين من الـ domain عشوائيين وبقول أن + +140 +00:09:18,850 --> 00:09:22,650 +صورهم متساوية وبثبت أن هما العناصر نفسهم متساوية + +141 +00:09:22,650 --> 00:09:27,890 +نشوف مثال آخر، طب العكس لو بدأت بتقول دالة ليست one + +142 +00:09:27,890 --> 00:09:31,590 +to one، بت DM فيها، فإذا بدل for all لو أديت مثال + +143 +00:09:31,590 --> 00:09:35,870 +عكسي عنصرين مختلفين صورهم متساوية، بتبطل one to one + +144 +00:09:35,870 --> 00:09:40,010 +لأن مش one to one، جميع العناصر المختلفة بتتطابق إلى + +145 +00:09:40,010 --> 00:09:43,070 +صور مختلفة، طب لما تكون not one to one في عنصرين + +146 +00:09:43,070 --> 00:09:46,490 +مختلفين صورهم متساوية، بنديله مثال عكسي بس على هذا + +147 +00:09:46,490 --> 00:09:50,500 +الكلام، فهنا مثلا هيدينا دالة، بقولي اثبت أن الدالة + +148 +00:09:50,500 --> 00:09:54,780 +not injection، الدالة التربيعية، لو أديت عنصرين + +149 +00:09:54,780 --> 00:09:58,760 +مختلفين من ال domain، صورهم متساوية، خلصت بكون إيش + +150 +00:09:58,760 --> 00:10:03,880 +خلصت، فهنا في المثال رقم 2، عشان نثبت أنها ليست one + +151 +00:10:03,880 --> 00:10:09,120 +to one، بدنا عنصرين مختلفين، مين ناخد؟ الواحد والسالب + +152 +00:10:09,120 --> 00:10:14,800 +واحد، إن الدالة التربيعية، فبقوله let x1 تساوي واحد + +153 +00:10:14,800 --> 00:10:22,370 +and x2 تساوي سالب واحد، then، طبعا x1 بتساوي x2؟ لأ، + +154 +00:10:22,370 --> 00:10:29,610 +غير متساويين، لكن صورهم f of x1 اللي هي f of 1 + +155 +00:10:29,610 --> 00:10:35,070 +بتساوي 1، بتساوي f of سالب 1 اللي هي f of x2، فإن + +156 +00:10:35,070 --> 00:10:40,530 +أديت مثال، إذا الدالة ليست one to one، thus f is + +157 +00:10:40,530 --> 00:10:45,370 +not injective، injective، + +158 +00:10:45,370 --> 00:10:51,170 +an injective function أو uninjection، تمام؟ واضح؟ فإذا + +159 +00:10:51,170 --> 00:10:55,730 +هنا إيش هدول المثالين؟ بسيطين، أو المثالين نتعلم إيش + +160 +00:10:55,730 --> 00:10:58,670 +طريقة إثبات الدالة one to one زي ما شرحنا في + +161 +00:10:58,670 --> 00:11:01,790 +المثال الأول، وكيف نثبت الدالة ليست one to one زي + +162 +00:11:01,790 --> 00:11:03,890 +ما شرحنا في المثال الثاني، طبعا هاختلف إيه إيش + +163 +00:11:03,890 --> 00:11:10,370 +التفاصيل بتختلف، واضح؟ ننتقل مثال آخر، نشوف مثال + +164 +00:11:10,370 --> 00:11:11,890 +متقدم بعض الشيء + +165 +00:11:21,090 --> 00:11:25,570 +فهنا هذه مهارات أساسية، زي ما تعلمنا في المواضيع + +166 +00:11:25,570 --> 00:11:28,990 +الماضية أيضًا، بدنا نتعلم كيف نتعامل مع الدالة و + +167 +00:11:28,990 --> 00:11:33,950 +هذه المفاهيم، let f from X to Y be a function and + +168 +00:11:33,950 --> 00:11:39,070 +let A subset من X، هذه كلها مواضيع متقدمة، السؤال + +169 +00:11:39,070 --> 00:11:47,500 +prove that، إيش المطلوب؟ إذا كانت ال F is injective، + +170 +00:11:47,500 --> 00:11:55,580 +implies F inverse لل F of A تساوي A، هذا هو المقلوب، + +171 +00:11:55,580 --> 00:12:01,640 +السؤال، solution، طبعا تعليق حد يقولي طب ما هذه إيه + +172 +00:12:01,640 --> 00:12:04,920 +بديهية، ما هي ال F inverse وال F بضيعوا بعض؟ لأ، هذا + +173 +00:12:04,920 --> 00:12:07,780 +في الـ إيش؟ في الدالة العكسية، في الدالة العكسية، + +174 +00:12:07,780 --> 00:12:10,300 +لكن هذا مش دالة عكسية، هذه إيش؟ اللي هو عبارة عن + +175 +00:12:10,300 --> 00:12:14,400 +صورة وصورة عكسية، مختلفين، مختلفين، هدول مش دالة + +176 +00:12:14,400 --> 00:12:17,480 +عكسية، هزمش أحكينا الملاحظة؟ آه، بالنسبة إلينا، + +177 +00:12:17,480 --> 00:12:20,920 +الـF inverse هذه إيش؟ هي دي إيش؟ أول شيء، F of A + +178 +00:12:20,920 --> 00:12:24,260 +مجموعة، والـF inverse هي إيش؟ الصورة العكسية، لأن + +179 +00:12:24,260 --> 00:12:27,780 +الـinverse ماشي، مش دوال عكس بعض، يضيعوا بعض، آه، + +180 +00:12:27,780 --> 00:12:30,760 +فهذه مختلفة، بدنا نثبتها، مش دائما صحيحة هذه العلاقة، + +181 +00:12:30,760 --> 00:12:36,870 +فبدفده، أول تعليق، آه، الآن جملة شرطية، كالعادة، هنبدأ + +182 +00:12:36,870 --> 00:12:44,490 +نفترض أن الشرط صحيح، فهنبدأ نقول له assume F + +183 +00:12:44,490 --> 00:12:46,770 +is injective، + +184 +00:12:53,090 --> 00:12:57,230 +بدي أثبت هذا الكلام، هذا عبارة عن إيش؟ تساوي + +185 +00:12:57,230 --> 00:13:01,170 +مجموعات، فعندنا بدي اخذ عنصر من طرف ونوصله لطرف + +186 +00:13:01,170 --> 00:13:03,910 +الثاني، إذا مشينا تكافؤ وانتهت، ما مشيناش هنضطر + +187 +00:13:03,910 --> 00:13:07,090 +ناخد في الاتجاه الثاني، فنحاول نمشي، طبعا ال F + +188 +00:13:07,090 --> 00:13:10,670 +inverse وال A، ال A subset من ال X، فعناصرها X + +189 +00:13:10,670 --> 00:13:14,150 +المفروض تكون، لإن أنا في ال domain، فناخد عنصر let + +190 +00:13:14,150 --> 00:13:20,610 +اللي هو إيش؟ X تنتمي لل F inverse F of A، + +191 +00:13:23,450 --> 00:13:27,210 +طبعا مرت علينا أكثر من مرة، هذه طبعا دائما حاولوا + +192 +00:13:27,210 --> 00:13:30,710 +لما تكون الأمر مركب، تاخدوا ببساطة، أنا في عندي F + +193 +00:13:30,710 --> 00:13:34,550 +inverse لمجموعة ما، وعندنا إن ال X بتنتمي ل F inverse + +194 +00:13:34,550 --> 00:13:38,030 +of B if and only if صورتها في ال B، فإذا هذا ما له + +195 +00:13:38,030 --> 00:13:43,370 +if and only if F of X تنتمي لل B اللي هي F of A في + +196 +00:13:43,370 --> 00:13:48,920 +هذا المثال، تمام؟ آه، واضح؟ متابعين؟ ممتاز، الآن هنا + +197 +00:13:48,920 --> 00:13:52,640 +المفتاح، وهنا اللي احنا حذرنا منه قبل هيك، وبنكرره + +198 +00:13:52,640 --> 00:13:56,640 +هل جئت أنا عندي الصورة في ال F of A ضروري إيش تكون + +199 +00:13:56,640 --> 00:14:00,300 +في ال A؟ لأ، مش في الضروري، أنا حكاية عبرنا عنها + +200 +00:14:00,300 --> 00:14:04,140 +بالماضي، آه، فهنا إيش؟ هي الصورة، طبعا كما قلت، دالة + +201 +00:14:04,140 --> 00:14:08,220 +تربيعية، ال F of Tof سلب اتنين بتساوي اربع موجودة في + +202 +00:14:08,220 --> 00:14:10,280 +المثال المرة اللي فاتت، لكن السلب اتنين نفسها مش + +203 +00:14:10,280 --> 00:14:13,020 +موجودة، لأن اربع من وين اجت؟ من عنصر آخر، مش من السلب + +204 +00:14:13,020 --> 00:14:17,340 +اتنين، فانا إيش ممكن اكتب هنا؟ ممكن أكتب هنا إن هذا + +205 +00:14:17,340 --> 00:14:23,220 +يؤدي إن ال F of X اللي هي Y بتساوي إيش؟ مزال ال F + +206 +00:14:23,220 --> 00:14:31,820 +في إيش عناصرها سوا بتساوي F of A for some A تنتمي + +207 +00:14:31,820 --> 00:14:36,500 +للـ A، هيك التعريف طبعاً، هنا هذا تعريف ال F inverse، + +208 +00:14:36,500 --> 00:14:44,760 +F inverse لل B، وهذا تعريف إيش اللي هو definition + +209 +00:14:44,760 --> 00:14:50,770 +لل F of A، طبعا ممكن أنا احطها نقاش AF واقول F بس + +210 +00:14:50,770 --> 00:14:53,550 +مش ضروري، مش هقدر أمشي بيها بالسهولة، فهنا النقطة، + +211 +00:14:53,550 --> 00:14:56,970 +هنا المفتاح الأساسي، بأنفعش أقول على طول X في + +212 +00:14:56,970 --> 00:15:01,950 +الـA، آه، الآن هنستفيد F of X تساوي F of A، و + +213 +00:15:01,950 --> 00:15:05,430 +الدالة one to one، الصور تساوت، لازم العناصر + +214 +00:15:05,430 --> 00:15:08,530 +تتساوى، فلو لأن الدالة one to one، كان مقدرش + +215 +00:15:08,530 --> 00:15:14,770 +أستنتج، فهنا يؤدي إن X تساوي A، ليش؟ لأن الـF is + +216 +00:15:14,770 --> 00:15:17,450 +one to one، اختصارا، ده بتوبة Injective أو one to + +217 +00:15:17,450 --> 00:15:22,040 +one، ممتاز، إذا نقش ال X تساوي A، وال A تنتمي لل A + +218 +00:15:22,040 --> 00:15:26,280 +خلصنا، إذا نادي مالها؟ تنتمي لل A، إذا بدأت من عنصر + +219 +00:15:26,280 --> 00:15:32,040 +هنا وصلت لل A، إذا الأولى subset من الثاني، thus F + +220 +00:15:32,040 --> 00:15:38,520 +inverse ال F of A تنقش subset من ال A، فده واحد مش + +221 +00:15:38,520 --> 00:15:45,330 +هقدر أمشي تكافؤ لأن الأمور مش بهذه السهولة، فهنا + +222 +00:15:45,330 --> 00:15:50,190 +مهمة جدا ملاحظة كتبناها، وهي هنا بنطبقها بشكل عام، + +223 +00:15:50,190 --> 00:15:54,150 +فلما تكون الصورة في ال F في A مش ضروري تكون عنصر + +224 +00:15:54,150 --> 00:15:56,950 +نفسه، ممكن تكون جاية من عنصر آخر، لكن عشان الدالة one + +225 +00:15:56,950 --> 00:16:02,070 +to one، نجي لاتجاه العكسي، لت X تنتمي لمن؟ لل A + +226 +00:16:02,070 --> 00:16:05,750 +نوصلها لهذا الكلام، الحقيقة لهذا الأمر أسهل إن شاء + +227 +00:16:05,750 --> 00:16:10,010 +الله، طيب، إذا كان العنصر موجود، صورته وين بتكون؟ في + +228 +00:16:10,010 --> 00:16:14,370 +صورة الدالة، المجموعة على طول، فهذا على طول يكافئ F + +229 +00:16:14,370 --> 00:16:18,090 +of X تنتمي لل F of A، بس اتجاه واحد، اتجاه الثاني + +230 +00:16:18,090 --> 00:16:22,870 +عكس، عشان هيك احنا لازم ناخدها بشكل منفصل، تمام؟ آه + +231 +00:16:22,870 --> 00:16:26,950 +لو هذه هي B، أنا بدي أتحدث عن X، أنا بقول بيهم إنه + +232 +00:16:26,950 --> 00:16:29,990 +اوصل X لمين؟ لطرف الثاني، اللي هو هذا، F inverse + +233 +00:16:29,990 --> 00:16:33,330 +F of X، إذا كانت هذه B، لما تكون الصورة في الـB، + +234 +00:16:33,330 --> 00:16:36,490 +وين بتكون الـX؟ في الصورة العكسية للـB، فهنا ممكن + +235 +00:16:36,490 --> 00:16:42,460 +أبدأ أتودى إن X تنتقل لمين؟ للـF inverse F of X، لأ، + +236 +00:16:42,460 --> 00:16:45,720 +فإذا خلاص، وبدنا من عنصر ووصلنا لطرف، إذا الطرف + +237 +00:16:45,720 --> 00:16:50,980 +الأول subset من الطرف الثاني، thus ال A، هرجع بس + +238 +00:16:50,980 --> 00:16:54,780 +خليني اكتب وهرجع أي استفسار، فهذا الاتجاه أسهل + +239 +00:16:54,780 --> 00:16:59,600 +الحقيقة، فهذا الاتجاه دائما صحيح، ما استخدمناه إنّه + +240 +00:16:59,600 --> 00:17:01,700 +one to one في هذا الاتجاه، لكن استخدمناه في + +241 +00:17:01,700 --> 00:17:05,320 +الاتجاه الثاني، في أي استفسار، في أي نقطة مش + +242 +00:17:05,320 --> 00:17:10,580 +واضحة، فإذا واحد واثنين يقدر إنه يشفي تسعة، 1 و2 + +243 +00:17:10,580 --> 00:17:17,540 +implies ال A تساوي F inverse ال F، أفضل، فهذا بيؤكد + +244 +00:17:17,540 --> 00:17:20,440 +إن هدول مش عملية بديهية إنهم بضيعوا بعض، لأ، لو + +245 +00:17:20,440 --> 00:17:26,340 +لدالة one to one كان هذه العلاقة غير صحيحة، واضح؟ أي + +246 +00:17:26,340 --> 00:17:29,380 +سؤال؟ تمام + +247 +00:17:32,860 --> 00:17:36,740 +ننتقل للمفهوم الثاني، طبعا احنا هذا الأمثلة بس مجرد + +248 +00:17:36,740 --> 00:17:41,060 +يعني كأول أمثلة، هيمر علينا الموضوع أكثر من اتجاه، + +249 +00:17:41,060 --> 00:17:46,860 +Surjection اللي هي بيسموها إيش؟ اللي هو الاقتران + +250 +00:17:46,860 --> 00:17:50,120 +الشامل أو الدالة الشاملة، طبعا من وين اتجاه معنى + +251 +00:17:50,120 --> 00:17:53,820 +شامل؟ شامل لمين؟ إنه بيغطي كل المجال المقابل، + +252 +00:17:53,820 --> 00:17:56,960 +هنشوف التعريف، فاحنا بنقول إن إذا المدى غطى كل + +253 +00:17:56,960 --> 00:18:00,160 +المجال المقابل، بيسميها إيش؟ Surjection، هاي التعريف + +254 +00:18:00,160 --> 00:18:07,110 +الحقيقي، A function F from X to Y is said to be surjective + +255 +00:18:07,110 --> 00:18:11,150 +or onto، في .. زي هناك قلنا injection one to one + +256 +00:18:11,150 --> 00:18:14,350 +في مصطلحين، وغالبا أن المصطلح one to one كان + +257 +00:18:14,350 --> 00:18:17,250 +القديم، المصطلح الجديد اللي هو إيش؟ ال injective وال + +258 +00:18:17,250 --> 00:18:20,890 +surjective، surjective or onto، provided that + +259 +00:18:20,890 --> 00:18:26,270 +يعني هي الشرط تبعها إيش؟ for all Y تنتمي ل Y إيش + +260 +00:18:26,270 --> 00:18:30,710 +there exists at least one X in X such that F of X + +261 +00:18:30,710 --> 00:18:34,330 +تساوي Y، بمعنى آخر احنا إيش قلنا؟ بدنا المجال + +262 +00:18:34,330 --> 00:18:37,650 +المقابل إيش يكون؟ كله صورة ما فيش فيه زيادة، هو على + +263 +00:18:37,650 --> 00:18:41,530 +قدر المدى بالظبط، آه، فاحنا أنا إذا بنحاول نعمل صورة + +264 +00:18:41,530 --> 00:18:48,350 +تقريبية، هي ال X وهي ال Y، فجميع عناصر ال Y إيش جاي + +265 +00:18:48,350 --> 00:18:52,420 +عليها سهم، من كل إيش؟ جاي فيه سهم، لأن كلها صورة + +266 +00:18:52,420 --> 00:18:57,760 +فبيعبروا عنه إنه لكل Y في الـY، الـY صورة عنصر من + +267 +00:18:57,760 --> 00:19:00,560 +الـX، لازم تكون صورة، فإيش إيش إذا الصورة اسمالها + +268 +00:19:00,560 --> 00:19:05,420 +غطت كل الـX شملت كل عناصر الـX، فغطت كل الـY شملت + +269 +00:19:05,420 --> 00:19:08,720 +عناصر كل الـY، فعشان هي الشيء اسمها دالة شاملة أو + +270 +00:19:08,720 --> 00:19:13,130 +اقتران تطبيق شامل، بيعرضه بيسموه تبع in other words + +271 +00:19:13,130 --> 00:19:18,050 +معنى آخر، هيوش بيقول ليه إن ال Y بتساوي المدى، ال Y + +272 +00:19:18,050 --> 00:19:22,330 +بتساوي المدى، اللي هو F of X، بتساوي ال Y اللي هو كل + +273 +00:19:22,330 --> 00:19:24,990 +المدى، احنا بشكل عام ال F of X بتساوي المدى، دائما + +274 +00:19:24,990 --> 00:19:30,010 +بتساوي المجال المقابل اللي هو ال Y، فإذن زي ما احنا + +275 +00:19:30,010 --> 00:19:34,170 +شايفين بالنسبة للدوال بشكل عام ليس بالضروري إن + +276 +00:19:34,170 --> 00:19:37,370 +العناصر المختلفة تذهب إلى صور مختلفة، إذا صارت بيها + +277 +00:19:37,370 --> 00:19:41,150 +اسم آخر، مش ده، لا سمينها one to one أو injection، آه + +278 +00:19:41,150 --> 00:19:44,770 +ليس بالضروري إن المدى يكون كل المجال المقابل، إذا + +279 +00:19:44,770 --> 00:19:48,190 +صار بيساوي له، اسم نسميها surjective أو ده لا شاملة + +280 +00:19:48,190 --> 00:19:52,290 +إذن هذا هو شرط إضافي مش متوفر في كل الدوال، الدوال + +281 +00:19:52,290 --> 00:19:56,790 +اللي لها اسم خاص لحالة خاصة بتكون تمام فهذه + +282 +00:19:56,790 --> 00:20:00,310 +الملاحظة الأولى أو التعريف الثاني طبعا زي ما نقول + +283 +00:20:00,310 --> 00:20:04,470 +إن احنا surjective function أو surjection بسموها + +284 +00:20:04,470 --> 00:20:07,050 +كأدبس مجرد اللي هو اللغة كيف الاستخدام + +285 +00:20:07,050 --> 00:20:13,890 +surjection تمام نشوف كيف بدنا نثبت إن الدالة إنّها + +286 +00:20:13,890 --> 00:20:18,850 +surjective أو ليست surjective نتعلم كيف الصيغة أو + +287 +00:20:18,850 --> 00:20:24,830 +كيف بنبرهن هذه الأمور كيف بنبرهن هذه الأمور فإحنا + +288 +00:20:24,830 --> 00:20:29,510 +زي ما إحنا بنحاول بناخد المفهوم و بنعرفه و بنحط + +289 +00:20:29,510 --> 00:20:33,810 +كيف معناه بلغة الرموز بالمنطق و كيف نتعامل معاه + +290 +00:20:33,810 --> 00:20:39,430 +فهنا أول مثال اثبت إنّه دالة ما اسمها surjective + +291 +00:20:39,430 --> 00:20:44,310 +مدينا الدالة التربيعية معرفة من R لـ 0 infinity show + +292 +00:20:44,310 --> 00:20:47,650 +that F is a surjective function a surjective + +293 +00:20:47,650 --> 00:20:50,590 +function خلينا نحط التعريف و نشوف كيف بدنا نتعامل + +294 +00:20:50,590 --> 00:20:59,470 +معاه فإحنا بدنا f is surjective if and only if إيش + +295 +00:20:59,470 --> 00:21:06,730 +جهة للتعريف for all y in capital Y there exist x + +296 +00:21:06,730 --> 00:21:11,590 +in X such that y تساوي f of x، مظبوط؟ لو رجعتوا + +297 +00:21:11,590 --> 00:21:15,650 +للتعريف بتلاقوا هيك معناته أرجعلكوا إياها شوية، + +298 +00:21:15,650 --> 00:21:20,570 +طيب for all y in y there exists at least one x + +299 +00:21:20,570 --> 00:21:24,990 +there exists x معناة at least such that y to the + +300 +00:21:24,990 --> 00:21:27,730 +power of x واضحة التعريف بلغة الرموز فده هو + +301 +00:21:27,730 --> 00:21:31,620 +المعنى فنبدأ يا شكيب نتعامل معاه بالبرهان تمام + +302 +00:21:31,620 --> 00:21:34,920 +ماذا for all كيف نتعلم ماذا for all؟ بناخد عنصر + +303 +00:21:34,920 --> 00:21:38,420 +عشوائي، شفت السياسة؟ نفس السياسة حكيناها من 6 إلى + +304 +00:21:38,420 --> 00:21:43,720 +Y على 7 وهنا بنطبقها، فهنبدأ نقول له let small y + +305 +00:21:43,720 --> 00:21:47,740 +تنتمي لكابيتال Y، في هذا المثال، كم هي كابيتال Y؟ الفترة + +306 +00:21:47,740 --> 00:21:50,940 +من 0 إلى infinity، هذه هي المجموعة الـY، مظبوط؟ + +307 +00:21:50,940 --> 00:21:54,660 +أه، فهي مظبوط، إيش المطلوب؟ بدنا نثبت إنّ هناك + +308 +00:21:54,660 --> 00:21:58,060 +there exists X في الـX اللي هي R بحيث إنّ Y تساوي + +309 +00:21:58,060 --> 00:22:07,750 +F of X، خليني أكتب We want to prove that there + +310 +00:22:07,750 --> 00:22:11,550 +exists X in capital X اللي في هذا المثال بتساوي R + +311 +00:22:11,550 --> 00:22:18,110 +such that Y تساوي F of X اللي هي إيش؟ X تربيع، صح؟ + +312 +00:22:18,110 --> 00:22:21,630 +هيك تعرف الدالة، فأنا بكتب بشكل عام و بخصص في هذا + +313 +00:22:21,630 --> 00:22:26,870 +المثال، فممتاز طيب، مطلوب نثبت there exists، في + +314 +00:22:26,870 --> 00:22:31,090 +طريقة عامة أن نثبت there exists؟ لا، ما اتعلمناش، + +315 +00:22:31,090 --> 00:22:34,750 +قلنا فيه يا إمّا بحاول أجيب أعطيله إياها بطريقة + +316 +00:22:34,750 --> 00:22:38,090 +معينة أو أثبت إنها فعلا موجودة، في هذا المثال إيش + +317 +00:22:38,090 --> 00:22:42,370 +هنعمل؟ هنروح نعمل هامش عشان الكتابة مختلفة، بدي + +318 +00:22:42,370 --> 00:22:44,230 +أنه أدلّه على الـ X، هو بيقول لي there exists X، + +319 +00:22:44,230 --> 00:22:47,330 +بدي أحسبه له إياها، بدي أدلّه على الـ X، أنا إيش بدي + +320 +00:22:47,330 --> 00:22:53,310 +X؟ بدي X تحقق إنّ Y تساوي F of X، يعني بدي Y X + +321 +00:22:53,310 --> 00:22:57,110 +تربيع فالسؤال أنا الـ Y معطية لي، مظبوط؟ قال لي + +322 +00:22:57,110 --> 00:23:00,590 +إيش؟ let Y أخذتها إذا الـ Y بتساوي X تربيع إذا الـ X + +323 +00:23:00,590 --> 00:23:04,890 +إيش بتساوي؟ جذر الـ Y، زائد أو ناقص جذر الـ Y فده + +324 +00:23:04,890 --> 00:23:09,690 +بيقول له إنّ X ساوي زائد أو ناقص جذر الـ Y، بنفع + +325 +00:23:09,690 --> 00:23:15,050 +ولا لأ؟ طيب السؤال إذا كانت الـ Y معطية، هل X هذه + +326 +00:23:15,050 --> 00:23:19,470 +موجودة في الـ R؟ هل جذر الـ Y أو ثالث جذر الـ Y هو + +327 +00:23:19,470 --> 00:23:25,980 +real number؟ دائما الجذر؟ ليش؟ في جذر صمم إذا كانت + +328 +00:23:25,980 --> 00:23:29,900 +مين اللي تحتها نيجاتيف طب هل الـ Y ممكن تكون نيجاتيف + +329 +00:23:29,900 --> 00:23:43,820 +لا لا + +330 +00:23:43,820 --> 00:23:45,240 +لا لا لا لا لا لا لا لا لا لا لا لا لا لا لا لا لا + +331 +00:23:45,240 --> 00:23:45,260 +لا لا لا لا لا لا لا لا لا لا لا لا لا لا لا لا لا + +332 +00:23:45,260 --> 00:23:54,600 +لا لا لا لا لا لا لا + +333 +00:23:55,180 --> 00:23:58,960 +هل جيت إيش بيقول له؟ الـ Y أخدت الـ Y يعني إيش Y + +334 +00:23:58,960 --> 00:24:02,580 +ممكن تكون؟ لو Y صفر إيش الـ X؟ صفر، لو الـ Y بتساوي + +335 +00:24:02,580 --> 00:24:05,680 +14، إيش الـ X؟ اثنين، وهاكذا، إذا أنا أديني أي Y + +336 +00:24:05,680 --> 00:24:08,600 +بقدر ألاقي الـ X، قدرت ولا ما قدرت؟ لكل Y there + +337 +00:24:08,600 --> 00:24:14,280 +exists X، لقيت Y تساوي just then الـ X تنتمي للـ R، + +338 +00:24:14,280 --> 00:24:18,940 +ليش؟ شرحنا، لأن الـ Y أكبر أو يساوي Zero، مظبوط؟ + +339 +00:24:18,940 --> 00:24:22,260 +عملناها، مظبوط؟ الـ X يعني ما جاءت إيش، ممكن يكون + +340 +00:24:22,260 --> 00:24:26,840 +التخيل لا، لأن الـ Y positive، and هذه طريقة + +341 +00:24:26,840 --> 00:24:29,480 +الكتابة، هنا تقريبا 90% من الحالة، لكن الكتابة + +342 +00:24:29,480 --> 00:24:34,580 +البرهانية، إيش بنثبت؟ F of X بتساوي F جذر الـ Y + +343 +00:24:34,580 --> 00:24:39,080 +تساوي جذر الـ Y لكل تربيع وتساوي 1، وهو المطلوب + +344 +00:24:40,190 --> 00:24:46,070 +لدى أي Y أقدر ألاقي X المقابلة المناسبة وفعلا F الـ + +345 +00:24:46,070 --> 00:24:48,490 +X بتساوي Y ولا بتساويش بتساوي Y فهذه طريقة + +346 +00:24:48,490 --> 00:24:52,010 +الكتابة فإحنا عن الهامش عشان كيف نختار الـ X الهامش + +347 +00:24:52,010 --> 00:24:55,590 +بنشوف كيف بنحسب الـ X المناسبة وبعدين بنتأكد إنها + +348 +00:24:55,590 --> 00:24:58,350 +بتحقق الشروط إنها موجودة فعلا في الـ domain و + +349 +00:24:58,350 --> 00:25:01,930 +صورتها هي الـ Y المطلوب صورتها Y المطلوب فبهذه + +350 +00:25:01,930 --> 00:25:06,870 +الطريقة بنثبت أن الدالة Onto أو surjective فهذه هي + +351 +00:25:06,870 --> 00:25:11,960 +الطريقة في ضوء التعريف وفي ضوء المهارات اللي + +352 +00:25:11,960 --> 00:25:12,580 +اتعلمناها + +353 +00:25:15,050 --> 00:25:18,510 +أه كيف نثبت إن الدالة ليست one to one؟ إذا قدرت + +354 +00:25:18,510 --> 00:25:22,410 +تلاقي عنصر في المجال المقابل ليس صورة لأحد، ليس + +355 +00:25:22,410 --> 00:25:24,910 +صورة لأحد، هيك بتقول القرية، اللي أنا مش بقول لي + +356 +00:25:24,910 --> 00:25:28,270 +إيش معناه subjective؟ إن جميع المجال المقابل كله + +357 +00:25:28,270 --> 00:25:32,210 +صورة، كل عناصره صورة، إذا في عنصر مش صورة، انتهت + +358 +00:25:32,210 --> 00:25:35,430 +العملية، فهنا طبعا مثال مباشر من غير مطلوب، لو + +359 +00:25:35,430 --> 00:25:40,070 +أخذنا الدالة التربيعية، من R لـ R، هل هذه الدالة on + +360 +00:25:40,070 --> 00:25:43,790 +to؟ لا، لأنه سالب واحد مش صورة حد، أو بمعنى آخر، + +361 +00:25:43,790 --> 00:25:48,220 +إذا حابين كمان، أه لو طلعنا مين الـ image تبع الدالة + +362 +00:25:48,220 --> 00:25:53,720 +ها دي طب بس تعالى مين الـ image ها دي الدالة من صفر + +363 +00:25:53,720 --> 00:25:56,820 +لما لا نهاية من صفر لما لا نهاية هل هذا يساوي R لا + +364 +00:25:56,820 --> 00:26:02,530 +يساوي Y اللي هي Y تبعنا في هذا المثال أو طبعا هي + +365 +00:26:02,530 --> 00:26:06,530 +كمان مثال في عندي سالب واحد في الـ R لكنها مش صورة + +366 +00:26:06,530 --> 00:26:09,070 +حد في الـ Y طبعا اه فمن الـ A دي مش .. مش + +367 +00:26:09,070 --> 00:26:11,870 +surjective في R دي ليش نديله مثال عكسي أو نحسب هذا + +368 +00:26:11,870 --> 00:26:14,510 +الشكل كله صح فلو قدرنا نلاقي عنصر في المجال + +369 +00:26:14,510 --> 00:26:18,250 +المقابل لا يمكن يكون صورة انتهت العملية انتهت + +370 +00:26:18,250 --> 00:26:20,930 +العملية لأن ما زال جالي for all Y لو قدرتي تلاقي Y + +371 +00:26:20,930 --> 00:26:25,490 +بتخلي هذا الشرط انتهت العملية انتهت العملية فده + +372 +00:26:25,490 --> 00:26:30,090 +مثلا كيف الطريقة العامة نثبت إنّها surjective أو + +373 +00:26:30,090 --> 00:26:38,410 +إنّها ليست surjective نشوف مثال مختلف مثال ثالث Prove + +374 +00:26:38,410 --> 00:26:43,190 +that the X projection function دالة معرفة من X + +375 +00:26:43,190 --> 00:26:46,170 +cross الـ Y للـ X اللي هي دالة إيش الإسقاط اللي + +376 +00:26:46,170 --> 00:26:49,330 +بتجيب المسقط الصيني اللي هو إيش الصيني about إيش + +377 +00:26:49,330 --> 00:26:54,210 +مالها إنّها surjective دالة الإسقاط هي دالة شاملة + +378 +00:26:54,210 --> 00:26:59,630 +هي دالة شاملة المثال الثالث هنشغل عليها واحدة + +379 +00:26:59,630 --> 00:27:02,770 +واحدة زي ما اتعلمنا نطبق اللي اتعلمنا بسمع مثال + +380 +00:27:02,770 --> 00:27:08,190 +جديد فإذا إيش نبدأ بالـ solution فمن وين البداية؟ + +381 +00:27:08,190 --> 00:27:11,810 +هاخد عنصر عشوائي من المجال المقابل من المجال + +382 +00:27:11,810 --> 00:27:17,710 +المقابل فحقول له let X تنتمي لكابيتال X في هذه + +383 +00:27:17,710 --> 00:27:20,990 +الدالة منين المجال المقابل؟ كابيتال X فواضح هي + +384 +00:27:20,990 --> 00:27:24,390 +الدالة من وين لوين من X cross الـ Y للـ X فبدي أخد + +385 +00:27:24,390 --> 00:27:27,990 +عنصر من X اسمه small x واضح؟ طبعا فإحنا نشكوا إنّ + +386 +00:27:27,990 --> 00:27:32,270 +أفق واسعة كيف نتعامل تمام ايه في المطلوب؟ خلينا + +387 +00:27:32,270 --> 00:27:35,650 +نعمل هامش ممكن أكتب we want to find + +388 +00:27:40,580 --> 00:27:46,160 +to find لأنه yes there exist يعني ما يضايقش هناك يوجد + +389 +00:27:46,160 --> 00:27:49,580 +إيش بدنا؟ عنصر في الـ domain كيف عناصر الـ domain؟ + +390 +00:27:49,580 --> 00:27:55,620 +زوج مرتب بدنا زوج مرتب A B تنتمي لمن؟ للـ X across + +391 +00:27:55,620 --> 00:28:01,900 +Y بحيث such that صورة هذا العنصر على الـ domain إيش + +392 +00:28:01,900 --> 00:28:05,560 +بيساوي؟ بيساوي الـ Y اللي أخذتها اللي إيه X سميتها + +393 +00:28:05,560 --> 00:28:10,580 +واضح؟ مش هيك بتبقى إيه الترجمة تبعها؟ متفقين إنّ + +394 +00:28:10,580 --> 00:28:13,600 +هذه الترجمة مميزة مناسبة ولا في صعوبة؟ في نقطة مش + +395 +00:28:13,600 --> 00:28:16,040 +واضحة، بس هنا بننتبه، مين الصعوبة شوية اللي + +396 +00:28:16,040 --> 00:28:19,200 +متغلبنا؟ إنّ الـ domain عناصر و أزواج مرتبة، في + +397 +00:28:19,200 --> 00:28:21,980 +مشكلة، ما فيش مشكلة، لأن الدالة تتعرف من أي مجموعة + +398 +00:28:21,980 --> 00:28:24,840 +لأي مجموعة، إيش عناصر المجموعة، أزواج مرتبة، عناصر + +399 +00:28:24,840 --> 00:28:27,500 +عادية، إيش ما يكون يكون، كلّه صح، فإذا أنا أخدت + +400 +00:28:27,500 --> 00:28:30,560 +عنصر من المجال المقابل، بدي يا يكون صورة عنصر من + +401 +00:28:30,560 --> 00:28:34,620 +وين، من الـ domain، خلينا نشوف كيف نختار من الـ A و + +402 +00:28:34,620 --> 00:28:41,290 +الـ B، كيف نختار الـ A و الـ B، أنا بدي of A and B + +403 +00:28:41,290 --> 00:28:46,690 +تساوي X نعمل الهامش بمين بس مش F هي X بي سب إكس + +404 +00:28:46,690 --> 00:28:55,390 +معلش اسم الدالة بي سب إكس بي سب إكس مظبوط طيب الـ + +405 +00:28:55,390 --> 00:28:58,990 +بي سب إكس هتاش تعمل تعمل إسقاط يعني إيش تعريف الـ + +406 +00:28:58,990 --> 00:29:04,670 +بي إكس للـ A و الـ B إيه بديها تساوي X بديها تساوي X + +407 +00:29:08,290 --> 00:29:12,030 +هذه الدالة هي المدينه يعني هي الدالة من الإسقاط + +408 +00:29:12,030 --> 00:29:15,290 +المسقط الـ projection بتاخد الزوج المرتب بالنسبة + +409 +00:29:15,290 --> 00:29:17,770 +لتعمل إسقاطه على إحدى على الـ C كيف إسقاطه على الـ + +410 +00:29:17,770 --> 00:29:20,170 +C؟ إحدى في الأول فإسقاطه على الـ Y إحدى في + +411 +00:29:20,170 --> 00:29:24,610 +الثاني واضحة تمام فإذا هنا الداني إذا كيف ممكن + +412 +00:29:24,610 --> 00:29:29,020 +أختار الـ A و الـ B؟ لازم الـ A تساوي X و الـ B حرة + +413 +00:29:29,020 --> 00:29:31,440 +خذيها اللي بدك إياها خذيها اللي بدك إياها زي طوب + +414 +00:29:31,440 --> 00:29:34,620 +مش كان فرقانا خيارين هنا أنا ما للّنهاية من الخيارات + +415 +00:29:34,620 --> 00:29:38,020 +بس المهم إنّ الحدث الأول يكون X فبدأ أجي أبرهن .. + +416 +00:29:38,020 --> 00:29:40,880 +بدأ أكتبه له الآن بدأ أعكس هذا الكلام زي شوف نفس + +417 +00:29:40,880 --> 00:29:44,360 +الخطوات واضحة؟ شايف الهيكلية العامة؟ هقول له إيش + +418 +00:29:44,360 --> 00:29:50,340 +هنا؟ We want to find let A, B تساوي X و بدنا أي + +419 +00:29:50,340 --> 00:29:57,410 +عنصر في مين في الـ Y أي عنصر X ومين و أي B for some + +420 +00:29:57,410 --> 00:30:05,970 +B تنتمي للـ Y أي عنصر في الـ Y طبعا then واضح إنّ + +421 +00:30:05,970 --> 00:30:11,850 +اللي هو الـ XB تنتمي للـ X cross الـ Y وإيش كمان + +422 +00:30:11,850 --> 00:30:18,130 +وصورتها projection X للـ XB إيش بيساوي؟ بيساوي X وهو + +423 +00:30:18,130 --> 00:30:22,000 +المطلوب أهو، فهذه هي الهيكلية العامة، وهذول مثالين + +424 +00:30:22,000 --> 00:30:25,780 +أرجو اللي طبعًا هتشوف أمثلة أخرى تكون الأمور واضحة + +425 +00:30:25,780 --> 00:30:28,660 +هنا في شوية صعوبة عشان الـ domain عناصر وأزواج + +426 +00:30:28,660 --> 00:30:32,200 +مرتبة لكن نفس الطريقة نفس الطريقة + +427 +00:30:36,070 --> 00:30:40,690 +أه فطبعًا احنا اللي هو إيش أخذنا؟ عرفنا كيف نحسب + +428 +00:30:40,690 --> 00:30:44,730 +الزوج المرتب، شوفنا كيف حسبنا الزوج المرتب، فإحنا + +429 +00:30:44,730 --> 00:30:47,790 +إيش اخترنا؟ اللي يقول الزوج المرتب يكون على صورة X + +430 +00:30:47,790 --> 00:30:52,950 +وأي عنصر آخر فعلاً بنتمي للـ domain وصورته فعلاً + +431 +00:30:52,950 --> 00:30:56,230 +بتساوي X، اتحقق، فانا الـ haمش بساعدني كيف بدي أختار + +432 +00:30:56,230 --> 00:30:59,150 +لأنه there exist، فانا هاختاره بشكل صريح، فانا + +433 +00:30:59,150 --> 00:31:03,430 +بالـ haمش بحسب وبعرف أختار العنصر زي ما عملنا هنا و + +434 +00:31:03,430 --> 00:31:07,460 +عملنا هنا نفس الطريقة، واضح؟ وبنتأكد أنه فعلاً الـ.. + +435 +00:31:07,460 --> 00:31:10,040 +الـ .. الزوج اللي .. العنصر اللي اخترته فيه من ضمن الـ + +436 +00:31:10,040 --> 00:31:14,120 +domain فيه شرطين وإيش كمان؟ وصورته بتساوي من الـ Y + +437 +00:31:14,120 --> 00:31:16,560 +اللي اخترتها أو الـ X اللي بدأت منها في هذا المثال + +438 +00:31:16,560 --> 00:31:20,100 +نشوف + +439 +00:31:20,100 --> 00:31:22,640 +كمان مثال جيد، في كمان مثال + +440 +00:31:27,340 --> 00:31:31,900 +فبنتعود على هذا المفهوم وكيف نتعامل وكيف نثبت أن + +441 +00:31:31,900 --> 00:31:35,240 +الدالة surjective وكيف نثبت أنها ليست surjective + +442 +00:31:35,240 --> 00:31:40,910 +وكل الأمور هذه، مثال الرابع، let f a function from x + +443 +00:31:40,910 --> 00:31:44,570 +to y be a function and let b subset من الـ y prove + +444 +00:31:44,570 --> 00:31:49,750 +that if f is surjective then اه هالجيت f f inverse + +445 +00:31:49,750 --> 00:31:52,190 +لـ الـ b بيساوي بيه برضه، مش زي طويل بيطيعوش بعض دول + +446 +00:31:52,190 --> 00:31:54,890 +مش automatic العملية لإنه مش دول عكسية، هنشوف إن + +447 +00:31:54,890 --> 00:31:59,390 +هذا الكلام صحيح، فده المثال الرابع، إيش المطلوب إذا + +448 +00:31:59,390 --> 00:32:10,130 +كانت f is surjective اه implies f f inverse للـ B + +449 +00:32:10,130 --> 00:32:18,430 +تساوي B بالمقلوب، فطبعًا solution assume F is + +450 +00:32:18,430 --> 00:32:26,070 +surjective بدنا نثبت هذا الكلام أيضًا، تساوي مجموعات + +451 +00:32:26,070 --> 00:32:31,410 +فخلينا نبدأ من طرف الـ B subset من الـ Y، فمناسب إن + +452 +00:32:31,410 --> 00:32:38,390 +أنا آخد اسمه عنصر Y، let Y تنتمي للـ F F inverse الـ + +453 +00:32:38,390 --> 00:32:44,520 +B، تمام، يمكن مرّت علينا في المحاضرة الماضية، إيش + +454 +00:32:44,520 --> 00:32:48,920 +معناه أن Y في الـ F of A، أن الـ Y صورة عنصر من الـ A + +455 +00:32:48,920 --> 00:32:57,060 +فهذا على طول يؤدي أن Y تساوي F of X for some X + +456 +00:32:57,060 --> 00:33:02,880 +تنتمي للـ A اللي هي مين؟ F inverse الـ B، F inverse الـ + +457 +00:33:02,880 --> 00:33:09,720 +B، ممكن نمشي بالاتجاهين غالبًا لأ غالبًا لأ، فهذا + +458 +00:33:09,720 --> 00:33:13,820 +الاتجاه الأول تمام، أعيد الكتابة، إيش ممكن أعمل؟ ممكن + +459 +00:33:13,820 --> 00:33:17,820 +هذه أفسرها، فخلّينا نعيد الكلام، قعدبنا عشان نغيره، Y + +460 +00:33:17,820 --> 00:33:26,860 +تساوي F of X for some X وإيش كمان؟ such that F of X + +461 +00:33:26,860 --> 00:33:31,650 +تنتمي للـ B، such that f of x تنتمي للـ b، هيك معناته + +462 +00:33:31,650 --> 00:33:35,510 +في أين بقدر ألاجي وانصر x هو موجود في الـ f inverse + +463 +00:33:35,510 --> 00:33:38,950 +of b، يعني صورته وين في الـ b، هيك معناته التعريف + +464 +00:33:38,950 --> 00:33:43,810 +ممتاز، إذا أصبح من عندي y تساوي f of x والـ f of x + +465 +00:33:43,810 --> 00:33:49,070 +للـ b، يعني y وين في الـ b، فإذا هذا يؤدي إنه y تنتمي + +466 +00:33:49,070 --> 00:33:53,510 +للـ b، إذا بدأنا في مجموعة وصلنا للمجموعة، إذا الأولى + +467 +00:33:53,510 --> 00:34:03,030 +subset من التانية، thus F F inverse الـ B subset من الـ + +468 +00:34:03,030 --> 00:34:07,570 +B، هذا واحد، ملاحظة + +469 +00:34:07,570 --> 00:34:11,740 +مهمة جدًا زي ما أنتم شايفين، هل استخدمنا احنا اللي + +470 +00:34:11,740 --> 00:34:16,100 +هو الفرضية إن الدالة subjective؟ لأ، فهذا بتدل على + +471 +00:34:16,100 --> 00:34:19,340 +إن هذا حالنا ناقص لسه، مش كامل، هو نص الحالة، أه هذا + +472 +00:34:19,340 --> 00:34:22,840 +باكد إنه مافيش تكافئة، هنبدأ نشوف اتجاه التاني اللي + +473 +00:34:22,840 --> 00:34:27,680 +هنحتاج فيه هذا الشرط، هنحتاج فيه هذا الشرط، فمهم جدا + +474 +00:34:27,680 --> 00:34:31,140 +دايمًا الأمور اللي بتساعدنا على إن نحكم حالنا صح + +475 +00:34:31,140 --> 00:34:34,440 +ولا لأ، لازم نستخدم كل المواطيع، اتجاه التاني الآن + +476 +00:34:34,440 --> 00:34:45,180 +let Y تنتمي للـ B، let Y تنتمي للـ B، بدي أوصل إن الـ Y + +477 +00:34:45,180 --> 00:34:49,900 +في الـ F F inverse of P، أه يمكن هذا السؤال بيشبه + +478 +00:34:49,900 --> 00:34:54,260 +سؤال سابق لما في مثال حلنا، قولنا إذا كانت أظن الـ + +479 +00:34:54,260 --> 00:34:57,880 +.. الـ B subset من الـ C في الـ F inverse لـ الـ B subset + +480 +00:34:57,880 --> 00:35:00,540 +من الـ F inverse of C، بيشبهوا كثير، فعشان أقدر + +481 +00:35:00,540 --> 00:35:04,980 +أتعامل مع الصورة والصورة العكسية، بد الـ Y تكون صورة + +482 +00:35:04,980 --> 00:35:10,840 +.. بد الـ Y تكون صورة، هل جميع عناصر الـ B صور؟ عشان + +483 +00:35:10,840 --> 00:35:13,880 +I'm surjective، فهذه المرة أداني إياها، وهذه المرة + +484 +00:35:13,880 --> 00:35:18,920 +أداني إياها، فطبعًا أول شيء أبدأ أكتب له then Y تنتمي + +485 +00:35:18,920 --> 00:35:23,240 +للـ Y لأن الـ B subset من الـ Y، والـ Y إيش معناته + +486 +00:35:23,240 --> 00:35:26,500 +surjective؟ إن الـ Y بيساوي F of X، هذه مدينيش إياها + +487 +00:35:26,500 --> 00:35:29,580 +بشكل صريح، نفس المثال المرة اللي فاتت أدانيها بشكل + +488 +00:35:29,580 --> 00:35:32,580 +صريح لإنه ما كانش شارح أو مديني إيش معناته + +489 +00:35:32,580 --> 00:35:39,560 +surjective، الآن إيش أقدر أكتب لها؟ بط Y تساوي F of X + +490 +00:35:39,560 --> 00:35:44,020 +هي معنى الـ surjective، ليش؟ لأن الـ F is onto أو + +491 +00:35:44,020 --> 00:35:48,920 +surjective، طبعًا، فهذا مهم جدًا، مدينيش إياها، طيب ما زال الـ + +492 +00:35:48,920 --> 00:35:52,640 +Y في الـ F of X، إذا ناشية صورة عنصر من الـ X، فهذا + +493 +00:35:52,640 --> 00:35:59,940 +يؤدي أن Y تساوي F of X for some X تنتمي لـ capital X + +494 +00:35:59,940 --> 00:36:06,390 +فهذا مهم جدًا، فانا بشكل عام عناصر الـ capital Y المجال + +495 +00:36:06,390 --> 00:36:09,710 +المقابل، مش كلها صور إلا إذا كانت Onto إلا إذا كانت + +496 +00:36:09,710 --> 00:36:15,750 +surjective، الآن أقدر أشتغل، فالآن Now نرجع لهذه Y تساوي + +497 +00:36:15,750 --> 00:36:21,490 +F of X تنتمي لـ B، إيش معناها؟ F and all if الـ X + +498 +00:36:21,490 --> 00:36:27,030 +موجودة في الـ F inverse of B، معروف، وإذا كانت الـ X + +499 +00:36:27,030 --> 00:36:29,610 +في الـ F inverse of B، وين تكون صورتها؟ في صورة + +500 +00:36:29,610 --> 00:36:36,370 +المجموعة، فهذا يؤدي إن F of X تنتمي للـ F F inverse + +501 +00:36:36,370 --> 00:36:41,170 +of B اللي طبعًا بتساوي Y وهو المطلوب، فإذا بدأنا من Y + +502 +00:36:41,170 --> 00:36:46,070 +في الـ B وصلناها للطرف التاني، إذا الطرف الأول Thus + +503 +00:36:46,070 --> 00:36:53,870 +B هي subset من F F inverse الـ B، وهذه اتنين واحد واتنين + +504 +00:36:53,870 --> 00:37:03,070 +بيخلصوا البرهان، عرفنا واحد واتنين implies B + +505 +00:37:03,070 --> 00:37:07,450 +تساوي F F inverse الـ B + +506 +00:37:11,570 --> 00:37:14,650 +فمهم جدًا كيف نستخدم .. طبعًا احنا استخدمنا التعريف + +507 +00:37:14,650 --> 00:37:17,950 +الـ surjective التاني إنه لازم المجال المقابل يساوي + +508 +00:37:17,950 --> 00:37:21,910 +المدى، فهذه اللي استفدنا منها، فإذا جميع عناصر + +509 +00:37:21,910 --> 00:37:26,370 +المجال المقابل هي صور، فلو لا هيك كان الكلام غير + +510 +00:37:26,370 --> 00:37:32,070 +صحي، المصطلح التالت والأخير bijection + +511 +00:37:33,980 --> 00:37:37,760 +المقطع by مرة علينا قبل هيك زي by conditional وby + +512 +00:37:37,760 --> 00:37:41,560 +nominal ثنائي فهو by injection بيكون إنه injective + +513 +00:37:41,560 --> 00:37:44,960 +أو injection وsurjection من هنا، فإذا by injection + +514 +00:37:44,960 --> 00:37:48,080 +يعني التنتين مع بعض إذا تكون one to one and one to + +515 +00:37:48,080 --> 00:37:54,560 +injection وsurjection بكل اختصار، ف a function from + +516 +00:37:54,560 --> 00:37:58,040 +X to Y is said to be bijective if it is both + +517 +00:37:58,040 --> 00:38:02,800 +injective and surjective، فدي بكل سهولة والمقطع + +518 +00:38:02,800 --> 00:38:06,860 +بيساعدنا علشان المعرفة، طبعًا في اسم آخر بيسموها + +519 +00:38:06,860 --> 00:38:10,520 +تناظري، ده التناظري أو اقتران تناظري بيسموها one + +520 +00:38:10,520 --> 00:38:13,850 +to one correspondence واحد لواحد، لأن كل عنصر له + +521 +00:38:13,850 --> 00:38:17,590 +صورة وحيدة، وكل عنصر في المجال المقابل هو صورة عنصر + +522 +00:38:17,590 --> 00:38:21,270 +فهي فيها تناظر لكل عنصر في الـ domain في المجال + +523 +00:38:21,270 --> 00:38:24,530 +هناك صورة في المجال المقابل، ولكل صورة في المجال + +524 +00:38:24,530 --> 00:38:27,830 +المقابل جاي فيه عنصر، جاية منه فيه مصدر جاية منه + +525 +00:38:27,830 --> 00:38:33,270 +فهذه بيسموها اللي هو يشدالة تناظري أو one to one + +526 +00:38:33,270 --> 00:38:33,690 +correspondence + +527 +00:38:37,320 --> 00:38:41,740 +واضح؟ في أي تعليق؟ تمام، نشوف الأمثلة الآن طبعًا + +528 +00:38:41,740 --> 00:38:46,560 +فإذا مافيش شيء جديد، أنا لو جالي أثبت إنها bijection + +529 +00:38:46,560 --> 00:38:49,760 +بدي أثبت إنها one to one وأنها surjective مع بعض، فاحنا هنعيد + +530 +00:38:49,760 --> 00:38:54,540 +نفس اللي هو المهارات بس هنجمع بين التنتين، فنبدأ + +531 +00:38:54,540 --> 00:38:55,440 +بالمثال الأول + +532 +00:39:03,600 --> 00:39:07,820 +المثال الأول، في عندنا دالة من الـ real للـ real + +533 +00:39:07,820 --> 00:39:17,900 +تُعرف أن f of x من R إلى R مُعرفة على صورة 2x زائد + +534 +00:39:17,900 --> 00:39:23,680 +3، أثبت إنها bijection، solution فمطلوب إن أثبت + +535 +00:39:23,680 --> 00:39:28,160 +إنها injective وsurjective، فنبدأ نجسم البرهان أول + +536 +00:39:28,160 --> 00:39:32,340 +شيء f is injective + +537 +00:39:34,510 --> 00:39:36,510 +فبيحطنا هيدية عشان هيك أنا لما شرحنا قولنا إيش + +538 +00:39:36,510 --> 00:39:39,970 +هنشوف أمثلة أخرى، فالآن نبدأ كيف نثبت أنها + +539 +00:39:39,970 --> 00:39:43,630 +injective؟ هناخد عنصرين في الـ domain صورهم متساوية + +540 +00:39:43,630 --> 00:39:46,730 +هناخد عنصرين في الـ domain صورهم متساوية، فأقول له + +541 +00:39:46,730 --> 00:39:52,550 +let X1 وX2 تنتمي للـ R اللي هو الـ domain اللي هو + +542 +00:39:52,550 --> 00:39:55,450 +الـ X تبعتنا، and assume أو أقوله such that نفس + +543 +00:39:55,450 --> 00:40:02,710 +المعنى، صورهم متساوية such that F of X1 تساوي F of + +544 +00:40:02,710 --> 00:40:09,700 +X2، من هنا نثبت هذا الكلام، فإذا بنتعلم من هذا المثال + +545 +00:40:09,700 --> 00:40:14,080 +والمثال الماضي، عشان أثبت إنه دالة one to one بداية + +546 +00:40:14,080 --> 00:40:17,380 +البرهان بناخد عنصرين عشوائين في الـ domain صورهم + +547 +00:40:17,380 --> 00:40:20,100 +متساوية، ووقت إشبنتها البرهان نستطيع أن نثبت أن + +548 +00:40:20,100 --> 00:40:23,260 +العناصر نفسهم إيش متساوية؟ إيش ممكن نعمل؟ نستخدم + +549 +00:40:23,260 --> 00:40:28,640 +تعريف الدالة، إيش معناته؟ F of X1، اتنين X1 زائد + +550 +00:40:28,640 --> 00:40:32,720 +تلاتة، وهذا اتنين X2 زائد تلاتة، هذا من تعريف الدالة + +551 +00:40:33,890 --> 00:40:38,150 +مظبوط، يعني هي بقى ده الشكل طبعًا فالآن بنحاول نثبت + +552 +00:40:38,150 --> 0:40:45,050 +نطرح التلاتة من الطرفين، 2 X 2 ونجسمها، 2 X 1 تساوي + +553 +00:40:45,050 --> 00:40:48,790 +X 2 وهو المطلوب، خلصنا، فالنهاية زي ما حكينا + +554 +00:40:48,790 --> 00:40:52,630 +البرهان بنبدأ البداية وهي النهاية، واضحة؟ أه فهذا + +555 +00:40:52,630 --> 00:40:56,610 +مثال الماضي كان بديهي جدًا، الآن في شوية شغل مش صعب + +556 +00:40:56,610 --> 00:41:02,890 +لكن في شوية شغل، F is injective، طبعًا مع تكرار + +557 +00:41:02,890 --> 00:41:07,650 +الأمثلة هنعيد ونكرر لحد ما تصير الأمور ثابتة + +558 +00:41:07,650 --> 00:41:11,970 +ومهارة أساسية زي مهارة الـ subset أو غيرها، فهذا + +559 +00:41:11,970 --> 00:41:15,410 +الشيء المطلوب الأول، المطلوب التاني بيضالي يثبت إن + +560 +00:41:15,410 --> 00:41:22,010 +الـ F is surjective، surjective تمام الشيء، فنبدأ بناخد + +561 +00:41:22,010 --> 00:41:27,060 +عنصر من المجال المقابل فبنقوله let small y تنتمي + +562 +00:41:27,060 --> 00:41:31,200 +المجال المقابل R بدنا ندور على x بحيث أن y تساوي f + +563 +00:41:31,200 --> 00:41:43,590 +of x we have to find x تنتمي لل R such that f of x + +564 +00:41:43,590 --> 00:41:47,990 +تساوي Y ونعمل الهامش كالعادى فده أنا بعلمكوا فيه + +565 +00:41:47,990 --> 00:41:52,890 +طرق يعني تكرار يعني ما فيش فيه تركات كتير وفيه + +566 +00:41:52,890 --> 00:41:56,270 +قالية معينة واضحة بنها ده المثال فانا ايش بدنا + +567 +00:41:56,270 --> 00:42:02,960 +بدنا f of x تساوي Y يعني بدنا 2X زائد 3 تساوي Y ايش + +568 +00:42:02,960 --> 00:42:06,500 +بنعمل؟ بنحل لل X بدل ال Y زي ما عملنا في اليادة + +569 +00:42:06,500 --> 00:42:12,600 +بنحل لل X بدل ال Y فدي X تتساوي Y ناقص 3 ع 2 طيب + +570 +00:42:12,600 --> 00:42:16,500 +ممكن كل المعادلة تنحل أو يقدرنا نحل أو ما نحلش بس + +571 +00:42:16,500 --> 00:42:20,380 +في سؤال مهم هل ال X بتنتمي في R أنا بدي حاجتين بعد + +572 +00:42:20,380 --> 00:42:24,460 +ما حل بدي ال X تنتمي في R وصورتها تساوي Y بتنتمي في + +573 +00:42:24,460 --> 00:42:27,780 +R ليش؟ لأن ال Y في R طرحنا منها 3 بتنتمي في + +574 +00:42:27,780 --> 00:42:31,560 +R قسمناها ع 2 في R إذا فعلا X في R كيف بدّه أكتب؟ + +575 +00:42:31,560 --> 00:42:34,340 +لجيت؟ فهذا الحل هده هامش كيف بدّه أكتب؟ من وين ببدأ + +576 +00:42:34,340 --> 00:42:37,420 +الكتاب؟ بقوله let X تساوي فإن بعد ما أكتب هنا إيش + +577 +00:42:37,420 --> 00:42:40,740 +بقوله جلب وي want to find لجيت ولا ما لجيتش؟ لجيت + +578 +00:42:40,740 --> 00:42:46,380 +بدي أسمله ياه بقوله let X تساوي Y ناقص 3 ع 2 then + +579 +00:42:47,580 --> 00:42:53,340 +ال X تنتمي لل R بالتأكيد، ايش كمان؟ و أقيم في X، + +580 +00:42:53,340 --> 00:42:58,100 +ايش بتساوي؟ بدي أتأكد إن حساباتي صحيحة و هذه مهمة، + +581 +00:42:58,100 --> 00:43:00,980 +طبعا ممكن أكتب و أخلص، لكن إذا خفت إنه يكون في + +582 +00:43:00,980 --> 00:43:03,540 +عندي خطأ أكتشفه، بكتشفه، طيب ايش بتساوي؟ إيش + +583 +00:43:03,540 --> 00:43:07,020 +الدالة تعريفها؟ بضرب، اللي متغير ب 2، بجمع له + +584 +00:43:07,020 --> 00:43:11,020 +3، ايش بتساوي هذه؟ بتساوي Y، بس بدي أتأكد منها + +585 +00:43:11,980 --> 00:43:15,620 +زائد 3 أو تساوي Y صح حتى لو كان في عندي خطأ في + +586 +00:43:15,620 --> 00:43:19,320 +الهامش أكتشفه ممكن أكتشفه فايش تعمل الدالة تضرب + +587 +00:43:19,320 --> 00:43:22,220 +اللي جواها ب 2 و تجمع له 3 ففعلا لو ضربنا + +588 +00:43:22,220 --> 00:43:24,220 +ب 2 و جمعنا 3 بيطلع Y فيقع فعلا حسب بقى + +589 +00:43:24,220 --> 00:43:27,160 +الصحيحة و انتهت العمل فهذه هي الطريقة واضحة هي + +590 +00:43:27,160 --> 00:43:30,300 +ثالث مثال هي ثالث مثال طبعا هذا يمكن أول مرة طلعت + +591 +00:43:30,300 --> 00:43:35,260 +ال X وحيدة ما فيش خيارين لل X ما فيش لخيار واحد فهذه + +592 +00:43:35,260 --> 00:43:38,920 +طريقة إثبات اللي هي ال onto طبعا 1 و 2 بتدل + +593 +00:43:38,920 --> 00:43:50,460 +على أن ال function فف 1 و 2 implies F is bijective + +594 +00:43:50,460 --> 00:43:59,100 +أي سؤال؟ تمام؟ اه تمام في هنا ايش مكان مناسب نوقف + +595 +00:43:59,100 --> 00:44:01,200 +ان شاء الله المرة الجاية بنكمل diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/zP0kNk_tTIE_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/zP0kNk_tTIE_raw.json new file mode 100644 index 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0.83746337890625}, {"start": 41.78, "end": 42.12, "word": " الـ", "probability": 0.781982421875}, {"start": 42.12, "end": 42.4, "word": " function", "probability": 0.69140625}, {"start": 42.4, "end": 43.12, "word": " كمفهوم", "probability": 0.98193359375}, {"start": 43.12, "end": 43.6, "word": " رياضي", "probability": 0.9884033203125}, {"start": 43.6, "end": 44.18, "word": " مفهوم", "probability": 0.9285888671875}, {"start": 44.18, "end": 44.84, "word": " أساسي", "probability": 0.9615478515625}, {"start": 44.84, "end": 45.98, "word": " صعب", "probability": 0.990234375}, {"start": 45.98, "end": 46.24, "word": " إنه", "probability": 0.5843505859375}, {"start": 46.24, "end": 46.5, "word": " نلاقي", "probability": 0.8203125}, {"start": 46.5, "end": 46.98, "word": " فيه", "probability": 0.881591796875}, {"start": 46.98, "end": 47.36, "word": " فرع", "probability": 0.9783528645833334}, {"start": 47.36, "end": 47.52, "word": " من", "probability": 0.9912109375}, {"start": 47.52, "end": 47.68, "word": " فروع", "probability": 0.6419270833333334}, {"start": 47.68, "end": 48.22, "word": " الرياضيات", "probability": 0.96005859375}, {"start": 48.22, "end": 48.36, "word": " لا", "probability": 0.73974609375}, {"start": 48.36, "end": 48.84, "word": " يستخدم", "probability": 0.9852294921875}, {"start": 48.84, "end": 49.22, "word": " مفهوم", "probability": 0.9840087890625}, {"start": 49.22, "end": 49.86, "word": " الدالة", "probability": 0.9801432291666666}, {"start": 49.86, "end": 50.3, "word": " أو", "probability": 0.9482421875}, {"start": 50.3, "end": 51.0, "word": " الاقتراح", "probability": 0.65972900390625}, {"start": 51.0, "end": 52.2, "word": " فمفهوم", "probability": 0.96669921875}, {"start": 52.2, "end": 52.42, "word": " الـ", "probability": 0.915771484375}, {"start": 52.42, "end": 52.66, "word": " function", "probability": 0.88232421875}, {"start": 52.66, "end": 52.9, "word": " is", "probability": 0.83056640625}, {"start": 52.9, "end": 53.1, "word": " one", "probability": 0.94189453125}, {"start": 53.1, "end": 53.24, "word": " of", "probability": 0.98291015625}, {"start": 53.24, "end": 53.38, "word": " the", "probability": 0.91748046875}, {"start": 53.38, "end": 53.6, "word": " most", "probability": 0.93017578125}, {"start": 53.6, "end": 54.04, "word": " basic", "probability": 0.97705078125}, {"start": 54.04, "end": 54.54, "word": " ideas", "probability": 0.87548828125}, {"start": 54.54, "end": 54.78, "word": " in", "probability": 0.92724609375}, {"start": 54.78, "end": 55.32, "word": " every", "probability": 0.8017578125}, {"start": 55.32, "end": 56.3, "word": " branch", "probability": 0.84619140625}, {"start": 56.3, "end": 56.5, "word": " of", "probability": 0.96337890625}, {"start": 56.5, "end": 56.94, "word": " mathematics", "probability": 0.650390625}, {"start": 56.94, "end": 57.22, "word": " فهذا", "probability": 0.677978515625}, {"start": 57.22, "end": 57.7, "word": " المفاهيم", "probability": 0.9510498046875}, {"start": 57.7, "end": 58.36, "word": " الأساسية", "probability": 0.9892578125}, {"start": 58.36, "end": 59.14, "word": " اللي", "probability": 0.92236328125}, {"start": 59.14, "end": 60.52, "word": " بتقابلنا", "probability": 0.96572265625}, {"start": 60.52, "end": 60.74, "word": " في", "probability": 0.98876953125}, {"start": 60.74, "end": 61.04, "word": " أي", "probability": 0.84912109375}, {"start": 61.04, "end": 61.84, "word": " تخصص", "probability": 0.9920654296875}, {"start": 61.84, "end": 62.0, "word": " أو", "probability": 0.93505859375}, {"start": 62.0, "end": 62.14, "word": " في", "probability": 0.96630859375}, {"start": 62.14, "end": 62.32, "word": " أي", "probability": 0.90966796875}, {"start": 62.32, "end": 62.56, "word": " فرع", "probability": 0.9842122395833334}, {"start": 62.56, "end": 62.7, "word": " من", "probability": 0.998046875}, {"start": 62.7, "end": 62.92, "word": " فروع", "probability": 0.7976888020833334}, {"start": 62.92, "end": 63.4, "word": " الرياضية", "probability": 0.9195556640625}, {"start": 63.4, "end": 64.88, "word": " التعريف", "probability": 0.953857421875}], "temperature": 1.0}, {"id": 3, "seek": 8548, "start": 65.68, "end": 85.48, "text": "نشوف كيف التعريف اه طبعا احنا متحدث عن function بين مجموعتين كما هو معروف يعني ده مفهوم مرة علينا لكن بدنا نشوف احنا كيف بدنا ندرسه بشكل عام و بشكل مجرد فاحنا في عندنا مجموعتين let x and y be sets فدي هي نقطة البداية عشان نعرف اللي هو ال function", "tokens": [1863, 8592, 38688, 9122, 33911, 16712, 3615, 16572, 5172, 1975, 3224, 23032, 3555, 3615, 995, 1975, 5016, 8315, 44650, 24401, 12984, 18871, 2445, 49374, 3714, 7435, 2304, 45367, 2655, 9957, 9122, 15042, 31439, 20449, 32887, 5172, 37495, 22653, 11778, 3224, 3714, 5172, 3224, 20498, 3714, 25720, 25894, 8315, 44381, 47525, 8315, 8717, 8592, 38688, 1975, 5016, 8315, 9122, 33911, 47525, 8315, 8717, 3215, 2288, 3794, 3224, 4724, 8592, 28820, 6225, 10943, 4032, 4724, 8592, 28820, 3714, 7435, 2288, 3215, 6156, 39319, 8315, 8978, 43242, 8315, 3714, 7435, 2304, 45367, 2655, 9957, 718, 2031, 293, 288, 312, 6352, 6156, 16254, 39896, 8717, 47432, 3660, 29739, 28259, 10632, 6225, 8592, 7649, 8717, 3615, 28480, 13672, 1829, 31439, 2423, 2445], "avg_logprob": -0.12129236934548718, "compression_ratio": 1.8070175438596492, "no_speech_prob": 0.0, "words": [{"start": 65.68, "end": 66.02, "word": "نشوف", "probability": 0.6907552083333334}, {"start": 66.02, "end": 66.22, "word": " كيف", "probability": 0.9716796875}, {"start": 66.22, "end": 66.82, "word": " التعريف", "probability": 0.9622802734375}, {"start": 66.82, "end": 67.64, "word": " اه", "probability": 0.301422119140625}, {"start": 67.64, "end": 67.94, "word": " طبعا", "probability": 0.9638671875}, {"start": 67.94, "end": 68.08, "word": " احنا", "probability": 0.8982747395833334}, {"start": 68.08, "end": 68.52, "word": " متحدث", "probability": 0.75830078125}, {"start": 68.52, "end": 68.66, "word": " عن", "probability": 0.96923828125}, {"start": 68.66, "end": 69.04, "word": " function", "probability": 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نشوف", "probability": 0.9952799479166666}, {"start": 74.14, "end": 74.44, "word": " احنا", "probability": 0.9695638020833334}, {"start": 74.44, "end": 75.26, "word": " كيف", "probability": 0.96337890625}, {"start": 75.26, "end": 75.66, "word": " بدنا", "probability": 0.974853515625}, {"start": 75.66, "end": 76.16, "word": " ندرسه", "probability": 0.99619140625}, {"start": 76.16, "end": 76.56, "word": " بشكل", "probability": 0.9892578125}, {"start": 76.56, "end": 77.02, "word": " عام", "probability": 0.99853515625}, {"start": 77.02, "end": 77.22, "word": " و", "probability": 0.501953125}, {"start": 77.22, "end": 77.52, "word": " بشكل", "probability": 0.8795572916666666}, {"start": 77.52, "end": 78.12, "word": " مجرد", "probability": 0.9921875}, {"start": 78.12, "end": 78.78, "word": " فاحنا", "probability": 0.9539388020833334}, {"start": 78.78, "end": 78.88, "word": " في", "probability": 0.93896484375}, {"start": 78.88, "end": 79.14, "word": " عندنا", "probability": 0.84716796875}, {"start": 79.14, "end": 79.86, "word": " مجموعتين", "probability": 0.9651692708333334}, {"start": 79.86, "end": 80.14, "word": " let", "probability": 0.80810546875}, {"start": 80.14, "end": 80.52, "word": " x", "probability": 0.66650390625}, {"start": 80.52, "end": 80.86, "word": " and", "probability": 0.90771484375}, {"start": 80.86, "end": 81.18, "word": " y", "probability": 0.9951171875}, {"start": 81.18, "end": 81.5, "word": " be", "probability": 0.92138671875}, {"start": 81.5, "end": 81.78, "word": " sets", "probability": 0.86279296875}, {"start": 81.78, "end": 82.38, "word": " فدي", "probability": 0.6121826171875}, {"start": 82.38, "end": 82.54, "word": " هي", "probability": 0.68896484375}, {"start": 82.54, "end": 82.82, "word": " نقطة", "probability": 0.9833984375}, {"start": 82.82, "end": 83.42, "word": " البداية", "probability": 0.982421875}, {"start": 83.42, "end": 83.88, "word": " عشان", "probability": 0.9842122395833334}, {"start": 83.88, "end": 84.38, "word": " نعرف", "probability": 0.93896484375}, {"start": 84.38, "end": 84.78, "word": " اللي", "probability": 0.961181640625}, {"start": 84.78, "end": 84.92, "word": " هو", "probability": 0.98291015625}, {"start": 84.92, "end": 85.12, "word": " ال", "probability": 0.9794921875}, {"start": 85.12, "end": 85.48, "word": " function", "probability": 0.91357421875}], "temperature": 1.0}, {"id": 4, "seek": 10898, "start": 85.96, "end": 108.98, "text": "تمام ما هي ال function اللي هي الدالة أو الاقتران a function from X to Y فالان احنا هنا الترتيب مهم من الى فهم نتحدث عن function اللي يحمل مظلة بالرمز F من X ل Y ما هي ال function بيقول عبارة عن ال triple من تلت أشياء يعني ال triple يعني الثلاثة مما تتكون ال function من تلت أشياء إيش هما؟", "tokens": [39237, 10943, 19446, 39896, 2423, 2445, 13672, 1829, 39896, 32748, 6027, 3660, 34051, 42963, 38149, 2288, 7649, 257, 2445, 490, 1783, 281, 398, 6156, 6027, 7649, 1975, 5016, 8315, 34105, 16712, 2288, 31371, 3555, 3714, 16095, 9154, 2423, 7578, 6156, 3224, 2304, 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"end": 88.2, "word": " اللي", "probability": 0.641357421875}, {"start": 88.2, "end": 88.34, "word": " هي", "probability": 0.818359375}, {"start": 88.34, "end": 88.8, "word": " الدالة", "probability": 0.83740234375}, {"start": 88.8, "end": 88.96, "word": " أو", "probability": 0.3154296875}, {"start": 88.96, "end": 89.5, "word": " الاقتران", "probability": 0.8428955078125}, {"start": 89.5, "end": 89.96, "word": " a", "probability": 0.59130859375}, {"start": 89.96, "end": 90.34, "word": " function", "probability": 0.96826171875}, {"start": 90.34, "end": 90.66, "word": " from", "probability": 0.92041015625}, {"start": 90.66, "end": 91.02, "word": " X", "probability": 0.66259765625}, {"start": 91.02, "end": 91.26, "word": " to", "probability": 0.96826171875}, {"start": 91.26, "end": 91.56, "word": " Y", "probability": 0.99169921875}, {"start": 91.56, "end": 91.94, "word": " فالان", "probability": 0.8011067708333334}, {"start": 91.94, "end": 92.14, "word": " احنا", "probability": 0.8976236979166666}, {"start": 92.14, "end": 92.3, "word": " هنا", "probability": 0.75634765625}, {"start": 92.3, "end": 92.76, "word": " الترتيب", "probability": 0.9783935546875}, {"start": 92.76, "end": 93.12, "word": " مهم", "probability": 0.98681640625}, {"start": 93.12, "end": 93.74, "word": " من", "probability": 0.96630859375}, {"start": 93.74, "end": 94.28, "word": " الى", "probability": 0.7098388671875}, {"start": 94.28, "end": 94.74, "word": " فهم", "probability": 0.4813639322916667}, {"start": 94.74, "end": 95.08, "word": " نتحدث", "probability": 0.92529296875}, {"start": 95.08, "end": 95.26, "word": " عن", "probability": 0.98779296875}, {"start": 95.26, "end": 95.8, "word": " function", "probability": 0.93505859375}, {"start": 95.8, "end": 96.66, "word": " اللي", "probability": 0.9267578125}, {"start": 96.66, "end": 96.86, "word": " يحمل", "probability": 0.5756022135416666}, {"start": 96.86, "end": 97.12, "word": " مظلة", "probability": 0.6705729166666666}, {"start": 97.12, "end": 97.58, "word": " بالرمز", "probability": 0.9566650390625}, {"start": 97.58, "end": 97.92, "word": " F", "probability": 0.91162109375}, {"start": 97.92, "end": 98.4, "word": " من", "probability": 0.9775390625}, {"start": 98.4, "end": 98.72, "word": " X", "probability": 0.98779296875}, {"start": 98.72, "end": 98.9, "word": " ل", "probability": 0.658203125}, {"start": 98.9, "end": 99.18, "word": " Y", "probability": 0.8671875}, {"start": 99.18, "end": 99.94, "word": " ما", "probability": 0.49609375}, {"start": 99.94, "end": 100.18, "word": " هي", "probability": 0.9443359375}, {"start": 100.18, "end": 100.34, "word": " ال", "probability": 0.98095703125}, {"start": 100.34, "end": 100.68, "word": " function", "probability": 0.955078125}, {"start": 100.68, "end": 101.02, "word": " بيقول", "probability": 0.6761881510416666}, {"start": 101.02, "end": 101.44, "word": " عبارة", "probability": 0.81268310546875}, {"start": 101.44, "end": 101.72, "word": " عن", "probability": 0.99462890625}, {"start": 101.72, "end": 101.94, "word": " ال", "probability": 0.81689453125}, {"start": 101.94, "end": 102.34, "word": " triple", "probability": 0.89501953125}, {"start": 102.34, "end": 103.36, "word": " من", "probability": 0.94873046875}, {"start": 103.36, "end": 103.64, "word": " تلت", "probability": 0.8271484375}, {"start": 103.64, "end": 104.0, "word": " أشياء", "probability": 0.9615478515625}, {"start": 104.0, "end": 104.18, "word": " يعني", "probability": 0.847900390625}, {"start": 104.18, "end": 104.28, "word": " ال", "probability": 0.798828125}, {"start": 104.28, "end": 104.42, "word": " triple", "probability": 0.81884765625}, {"start": 104.42, "end": 104.64, "word": " يعني", "probability": 0.968017578125}, {"start": 104.64, "end": 105.56, "word": " الثلاثة", "probability": 0.9322102864583334}, {"start": 105.56, "end": 105.9, "word": " مما", "probability": 0.93212890625}, {"start": 105.9, "end": 106.32, "word": " تتكون", "probability": 0.9254557291666666}, {"start": 106.32, "end": 106.48, "word": " ال", "probability": 0.91015625}, {"start": 106.48, "end": 106.76, "word": " function", "probability": 0.96484375}, {"start": 106.76, "end": 106.94, "word": " من", "probability": 0.9921875}, {"start": 106.94, "end": 107.22, "word": " تلت", "probability": 0.9912109375}, {"start": 107.22, "end": 107.78, "word": " أشياء", "probability": 0.98974609375}, {"start": 107.78, "end": 108.38, "word": " إيش", "probability": 0.7776692708333334}, {"start": 108.38, "end": 108.98, "word": " هما؟", "probability": 0.84765625}], "temperature": 1.0}, {"id": 5, "seek": 13501, "start": 109.43, "end": 135.01, "text": "مجموعة أولى مجموعة تانية و relation و relation فهي triple اه ال relation اللى هتكون function طبعا هنشوف الشروط اللى عليها و مجموعتين مجموعة ابتداء و مجموعة انتهاء X و Y where F is a relation from X to Y فال F عبارة عن relation ايش معنى relation يعني ال F هي subset من X across ال Y هذا ايه ايش هذا مبدأيا", "tokens": [2304, 7435, 2304, 2407, 27884, 5551, 12610, 7578, 3714, 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"end": 153.49, "text": "الكلام ممكن يجي سؤال يتبادل للذهن هل ال correlation function طبعا لا فهي ال relation عليها شروط إضافية عليها شروط إضافية أول شرط بدنا ال domain لهذه ال relation يكون بيغطي كل المجموعة الأولى X", "tokens": [6027, 28820, 10943, 3714, 43020, 7251, 7435, 1829, 8608, 33604, 6027, 7251, 2655, 3555, 18513, 1211, 24976, 8848, 3224, 1863, 8032, 1211, 2423, 20009, 2445, 23032, 3555, 3615, 995, 20193, 6156, 3224, 1829, 2423, 9721, 25894, 11296, 13412, 32887, 9566, 11933, 11242, 31845, 10632, 25894, 11296, 13412, 32887, 9566, 11933, 11242, 31845, 10632, 5551, 12610, 13412, 2288, 9566, 47525, 8315, 2423, 9274, 46740, 24192, 2423, 9721, 7251, 30544, 4724, 1829, 17082, 9566, 1829, 28242, 9673, 7435, 2304, 2407, 27884, 16247, 12610, 7578, 1783], "avg_logprob": -0.23530506076557295, "compression_ratio": 1.6559139784946237, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 136.69, "end": 137.61, "word": "الكلام", "probability": 0.5458577473958334}, {"start": 137.61, 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المهم يكون subset ال relation كلها تعريفها بسيط جدا فأي subset من الكارتيسة هي relation لكن الآن ال functions هي ال relation عليها شروط أول شرط بدنا ال domain يغطي كل المجموعة الأولى الشرط التاني", "tokens": [44510, 8315, 2423, 9274, 7251, 17082, 9566, 1829, 28242, 9673, 7435, 2304, 2407, 27884, 16247, 12610, 7578, 23032, 3555, 3615, 995, 2423, 9721, 9122, 8315, 6225, 28480, 8315, 11296, 39896, 36632, 25993, 9154, 2423, 1783, 3278, 2423, 398, 34051, 2423, 316, 3278, 2423, 363, 44381, 19446, 41185, 8592, 13412, 2288, 9566, 14739, 3224, 3714, 9957, 7251, 17082, 9566, 1829, 9673, 16095, 7251, 30544, 25993, 2423, 9721, 28242, 11296, 37279, 16572, 5172, 11296, 4724, 3794, 1829, 9566, 10874, 28259, 6156, 10721, 1829, 25993, 9154, 33251, 9640, 31371, 3794, 3660, 39896, 9721, 44381, 6024, 48506, 2423, 6828, 39896, 2423, 9721, 25894, 11296, 13412, 32887, 9566, 5551, 12610, 13412, 2288, 9566, 47525, 8315, 2423, 9274, 7251, 17082, 9566, 1829, 28242, 9673, 7435, 2304, 2407, 27884, 16247, 12610, 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"probability": 0.8611653645833334}, {"start": 1007.76, "end": 1008.12, "word": " ال", "probability": 0.724609375}, {"start": 1008.12, "end": 1008.38, "word": " X", "probability": 0.9912109375}, {"start": 1008.38, "end": 1008.9, "word": " واقع", "probability": 0.9523111979166666}, {"start": 1008.9, "end": 1009.2, "word": " هان", "probability": 0.915283203125}, {"start": 1009.2, "end": 1009.94, "word": " الواحد", "probability": 0.9337565104166666}, {"start": 1009.94, "end": 1010.18, "word": " وها", "probability": 0.73583984375}, {"start": 1010.18, "end": 1010.44, "word": " كذا", "probability": 0.926025390625}, {"start": 1010.44, "end": 1010.98, "word": " تاخد", "probability": 0.8753255208333334}, {"start": 1010.98, "end": 1011.3, "word": " أول", "probability": 0.979248046875}, {"start": 1011.3, "end": 1011.54, "word": " عدد", "probability": 0.97998046875}, {"start": 1011.54, "end": 1011.74, "word": " صحيح", "probability": 0.994384765625}, {"start": 1011.74, "end": 1012.2, "word": " بيقابلك", "probability": 0.9591796875}, {"start": 1012.2, "end": 1012.34, "word": " من", "probability": 0.99609375}, {"start": 1012.34, "end": 1012.78, "word": " اليسار", "probability": 0.9903971354166666}, {"start": 1012.78, "end": 1013.42, "word": " أول", "probability": 0.6961669921875}, {"start": 1013.42, "end": 1013.64, "word": " عدد", "probability": 0.9951171875}, {"start": 1013.64, "end": 1013.92, "word": " صحيح", "probability": 0.9945068359375}, {"start": 1013.92, "end": 1014.24, "word": " بيقابلك", "probability": 0.9876953125}, {"start": 1014.24, "end": 1014.34, "word": " من", "probability": 0.98583984375}, {"start": 1014.34, "end": 1014.56, "word": " اليسار", "probability": 0.9983723958333334}, {"start": 1014.56, "end": 1014.86, "word": " طب", "probability": 0.7841796875}, {"start": 1014.86, "end": 1015.16, "word": " العدد", "probability": 0.9676106770833334}, {"start": 1015.16, "end": 1015.44, "word": " الصحيح", "probability": 0.9595947265625}, {"start": 1015.44, "end": 1015.64, "word": " بيطلع", "probability": 0.89091796875}, {"start": 1015.64, "end": 1015.8, "word": " زي", "probability": 0.988037109375}, {"start": 1015.8, "end": 1015.88, "word": " ما", "probability": 0.97705078125}, {"start": 1015.88, "end": 1016.08, "word": " هو", "probability": 0.99609375}, {"start": 1016.08, "end": 1016.74, "word": " بيطلع", "probability": 0.847705078125}, {"start": 1016.74, "end": 1016.92, "word": " زي", "probability": 0.996826171875}, {"start": 1016.92, "end": 1017.02, "word": " ما", "probability": 0.9833984375}, {"start": 1017.02, "end": 1017.24, "word": " هو", "probability": 0.99609375}, {"start": 1017.24, "end": 1017.76, "word": " تمام", "probability": 0.849365234375}, {"start": 1017.76, "end": 1018.26, "word": " فدي", "probability": 0.6312255859375}, {"start": 1018.26, "end": 1018.4, "word": " هي", "probability": 0.7919921875}, {"start": 1018.4, "end": 1018.78, "word": " الدالة", "probability": 0.9690755208333334}], "temperature": 1.0}, {"id": 46, "seek": 105168, "start": 1022.78, "end": 1051.68, "text": "في هذه نظرية، نظرية 3-6 بدي أتأكد على معلومة أو الحقيقة إن المجال المقابل ليس إلا وعاء يحتوي الصور، بدنا وعاء يكون كبير بشكل كافي يحتوي الصور، فإيه بتقول each set containing the image can be arranged يعني إحنا إيش دور المجال المقابل؟ بدنا مجموعة تقدر تحتوي كل إيش المدى، تكون جد المدى بالظبط يؤدي، لو كبرتها زيادة، فإيش عندي مشكلة", "tokens": [41185, 29538, 8717, 19913, 2288, 10632, 12399, 8717, 19913, 2288, 10632, 805, 12, 21, 4724, 16254, 5551, 2655, 10721, 4117, 3215, 15844, 20449, 1211, 20498, 3660, 34051, 21542, 38436, 28671, 36145, 9673, 7435, 6027, 9673, 4587, 16758, 1211, 32239, 3794, 11933, 15040, 4032, 3615, 16606, 7251, 33753, 45865, 31767, 13063, 12399, 47525, 8315, 4032, 3615, 16606, 7251, 30544, 9122, 3555, 13546, 4724, 8592, 28820, 9122, 31845, 1829, 7251, 33753, 45865, 31767, 13063, 12399, 6156, 28814, 1829, 3224, 39894, 39648, 1184, 992, 19273, 264, 3256, 393, 312, 18721, 37495, 22653, 11933, 5016, 8315, 11933, 1829, 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1038.38, "word": " بتقول", "probability": 0.9580078125}, {"start": 1038.38, "end": 1038.74, "word": " each", "probability": 0.049774169921875}, {"start": 1038.74, "end": 1039.14, "word": " set", "probability": 0.93701171875}, {"start": 1039.14, "end": 1040.24, "word": " containing", "probability": 0.88330078125}, {"start": 1040.24, "end": 1040.54, "word": " the", "probability": 0.8974609375}, {"start": 1040.54, "end": 1040.94, "word": " image", "probability": 0.958984375}, {"start": 1040.94, "end": 1041.3, "word": " can", "probability": 0.94384765625}, {"start": 1041.3, "end": 1041.54, "word": " be", "probability": 0.95849609375}, {"start": 1041.54, "end": 1042.0, "word": " arranged", "probability": 0.89404296875}, {"start": 1042.0, "end": 1042.52, "word": " يعني", "probability": 0.707275390625}, {"start": 1042.52, "end": 1042.74, "word": " إحنا", "probability": 0.8785807291666666}, {"start": 1042.74, "end": 1042.94, "word": " إيش", "probability": 0.97119140625}, {"start": 1042.94, "end": 1043.2, "word": " دور", "probability": 0.975830078125}, {"start": 1043.2, "end": 1043.7, "word": " المجال", "probability": 0.9947916666666666}, {"start": 1043.7, "end": 1044.58, "word": " المقابل؟", "probability": 0.94619140625}, {"start": 1044.58, "end": 1044.92, "word": " بدنا", "probability": 0.9736328125}, {"start": 1044.92, "end": 1045.52, "word": " مجموعة", "probability": 0.96806640625}, {"start": 1045.52, "end": 1046.02, "word": " تقدر", "probability": 0.9853515625}, {"start": 1046.02, "end": 1046.44, "word": " تحتوي", "probability": 0.99169921875}, {"start": 1046.44, "end": 1046.76, "word": " كل", "probability": 0.97021484375}, {"start": 1046.76, "end": 1047.06, "word": " إيش", "probability": 0.7932942708333334}, {"start": 1047.06, "end": 1047.78, "word": " المدى،", "probability": 0.888671875}, {"start": 1047.78, "end": 1048.12, "word": " تكون", "probability": 0.958984375}, {"start": 1048.12, "end": 1048.36, "word": " جد", "probability": 0.95361328125}, {"start": 1048.36, "end": 1048.66, "word": " المدى", "probability": 0.95263671875}, {"start": 1048.66, "end": 1049.04, "word": " بالظبط", "probability": 0.9927978515625}, {"start": 1049.04, "end": 1049.72, "word": " يؤدي،", "probability": 0.6859130859375}, {"start": 1049.72, "end": 1049.88, "word": " لو", "probability": 0.9755859375}, {"start": 1049.88, "end": 1050.42, "word": " كبرتها", "probability": 0.8333740234375}, {"start": 1050.42, "end": 1050.92, "word": " زيادة،", "probability": 0.84658203125}, {"start": 1050.92, "end": 1051.04, "word": " فإيش", "probability": 0.692626953125}, {"start": 1051.04, "end": 1051.26, "word": " عندي", "probability": 0.674560546875}, {"start": 1051.26, "end": 1051.68, "word": " مشكلة", "probability": 0.982421875}], "temperature": 1.0}, {"id": 47, "seek": 106842, "start": 1051.78, "end": 1068.42, "text": "أه فهي النظرية بتقولي انا لو استبدلت المجال المقابل بأي مجموعة كبيرة تحتوي المهم ايش الشرط تحتوي الاش المدى تحتوي المدى فبتتمها دالة دالة بتتغيرش بتتمها دالة فبقولي let f from x y be a function", "tokens": [10721, 3224, 6156, 3224, 1829, 28239, 19913, 2288, 10632, 39894, 39648, 1829, 1975, 8315, 45164, 44713, 44510, 1211, 2655, 9673, 7435, 6027, 9673, 4587, 16758, 1211, 4724, 10721, 1829, 3714, 7435, 2304, 2407, 27884, 9122, 3555, 48923, 6055, 33753, 45865, 9673, 16095, 1975, 1829, 8592, 25124, 2288, 9566, 6055, 33753, 45865, 2423, 33599, 9673, 3215, 7578, 6055, 33753, 45865, 9673, 3215, 7578, 6156, 3555, 2655, 39237, 11296, 11778, 6027, 3660, 11778, 6027, 3660, 39894, 2655, 17082, 13546, 8592, 39894, 39237, 11296, 11778, 6027, 3660, 6156, 3555, 39648, 1829, 718, 283, 490, 2031, 288, 312, 257, 2445], "avg_logprob": -0.23501933481275422, "compression_ratio": 1.7741935483870968, "no_speech_prob": 0.0, "words": [{"start": 1051.78, "end": 1052.06, "word": "أه", "probability": 0.3873291015625}, {"start": 1052.06, "end": 1052.3, "word": " فهي", "probability": 0.7252604166666666}, {"start": 1052.3, "end": 1052.68, "word": " النظرية", 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حاجة لأ جلي أي مجموعات أي عناصر تمام ننتقل لنقطة أخرى unions of functions اتحاد الدولة يمكن المصطلح يكون غريب", "tokens": [2304, 2655, 3615, 10943, 1211, 9957, 25894, 11296, 4032, 2304, 2655, 3615, 28480, 9957, 25894, 11296, 9154, 2423, 33400, 4724, 9957, 5172, 3615, 8592, 5551, 3615, 28480, 16095, 15844, 36632, 3714, 7435, 2304, 2407, 27884, 44381, 8032, 3215, 12610, 32748, 12610, 4724, 9957, 5172, 3615, 5551, 3615, 28480, 16095, 15844, 36632, 3714, 7435, 2304, 45367, 9307, 19446, 10874, 20292, 8592, 2423, 1783, 4032, 2423, 398, 11778, 12610, 3660, 3547, 49429, 6352, 49429, 4386, 49429, 36632, 11331, 26108, 3660, 5296, 10721, 10874, 20292, 36632, 3714, 7435, 2304, 45367, 9307, 36632, 18871, 33546, 2288, 46811, 10943, 8717, 29399, 4587, 1211, 5296, 1863, 47432, 3660, 5551, 34740, 7578, 24914, 295, 6828, 1975, 2655, 5016, 18513, 32748, 12610, 3660, 7251, 43020, 9673, 9381, 9566, 1211, 5016, 7251, 30544, 32771, 16572, 3555], "avg_logprob": -0.19091796642169356, "compression_ratio": 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relation، فالمصطلح أولا مش غريب، واحد أحداش مش غريب؟", "tokens": [14407, 24401, 7251, 39648, 9122, 33911, 32748, 12610, 13672, 1829, 4724, 1829, 25957, 1211, 14407, 25894, 16095, 1975, 2655, 5016, 18513, 22807, 6225, 8592, 7649, 8717, 11622, 26895, 23758, 2423, 24971, 8717, 2655, 8848, 37983, 2423, 2445, 39896, 11933, 1829, 8592, 22807, 39896, 2423, 9721, 16070, 9721, 25993, 3714, 7435, 2304, 2407, 27884, 9154, 5551, 11622, 2407, 26108, 3714, 43500, 49401, 12399, 11933, 15730, 4724, 28543, 2288, 5551, 2655, 24401, 12984, 18871, 1975, 2655, 5016, 18513, 2423, 2299, 12399, 18871, 6055, 4587, 41193, 3615, 2423, 2299, 12399, 18871, 2423, 2649, 24976, 9721, 12399, 18871, 2423, 17103, 24976, 9721, 12399, 6156, 45340, 9381, 9566, 1211, 5016, 5551, 12610, 995, 37893, 32771, 16572, 3555, 12399, 36764, 24401, 5551, 24401, 33599, 37893, 32771, 16572, 3555, 22807], "avg_logprob": -0.21358367259944638, "compression_ratio": 1.8202247191011236, "no_speech_prob": 0.0, "words": [{"start": 2453.44, 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2495.73, "word": " بعض", "probability": 0.951416015625}, {"start": 2495.73, "end": 2496.09, "word": " الأمثلة", "probability": 0.976318359375}, {"start": 2496.09, "end": 2496.81, "word": " التمهيدية", "probability": 0.966796875}], "temperature": 1.0}, {"id": 114, "seek": 251212, "start": 2498.44, "end": 2512.12, "text": "الأنفلة التمهيدية الحقيقة الموضوع أقرب شيء احنا طبعا مر علينا ال university جاب ال هيك في دراستكوا اتحاد الدول مر عليكم جاب ال هيك في الدراسة مر عليكم بس بشكل مختلف", "tokens": [6027, 33456, 5172, 37977, 16712, 2304, 3224, 25708, 10632, 21542, 38436, 28671, 9673, 2407, 11242, 45367, 5551, 4587, 25513, 44049, 38207, 1975, 5016, 8315, 23032, 3555, 3615, 995, 3714, 2288, 25894, 8315, 2423, 5454, 10874, 16758, 2423, 39896, 4117, 8978, 11778, 23557, 14851, 4117, 14407, 1975, 2655, 5016, 18513, 32748, 12610, 3714, 2288, 25894, 24793, 10874, 16758, 2423, 39896, 4117, 8978, 32748, 23557, 3794, 3660, 3714, 2288, 25894, 24793, 4724, 3794, 4724, 8592, 28820, 3714, 46456, 46538], "avg_logprob": -0.20793268944208437, "compression_ratio": 1.7245508982035929, "no_speech_prob": 0.0, "words": [{"start": 2498.4400000000005, "end": 2499.1600000000003, "word": "الأنفلة", "probability": 0.6741943359375}, {"start": 2499.1600000000003, "end": 2499.88, "word": " التمهيدية", "probability": 0.8193359375}, {"start": 2499.88, "end": 2500.4, "word": " الحقيقة", "probability": 0.8430989583333334}, {"start": 2500.4, "end": 2500.92, "word": " الموضوع", "probability": 0.9942626953125}, {"start": 2500.92, "end": 2501.36, "word": " أقرب", "probability": 0.900390625}, {"start": 2501.36, "end": 2501.6, "word": " شيء", "probability": 0.749267578125}, {"start": 2501.6, "end": 2501.74, "word": " احنا", "probability": 0.830810546875}, {"start": 2501.74, "end": 2502.44, "word": " طبعا", "probability": 0.96484375}, {"start": 2502.44, "end": 2503.2, "word": " مر", "probability": 0.861328125}, {"start": 2503.2, "end": 2503.5, "word": " علينا", "probability": 0.935546875}, {"start": 2503.5, 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دو طول بفصيلة بواحد فهي أقرب شيء له تعدد الدالة بالتجزيئة نشوف مثال، خدي نشوف مثال let f from one two to zero", "tokens": [1211, 10721, 12399, 39896, 6225, 3555, 9640, 3660, 18871, 32748, 6027, 3660, 9673, 3615, 28480, 3660, 20666, 2655, 7435, 11622, 1829, 19986, 3660, 39896, 5551, 4587, 25513, 44049, 38207, 5296, 11296, 5296, 3215, 6027, 3660, 19446, 7251, 30544, 32748, 6027, 3660, 20449, 28480, 3660, 20666, 2655, 7435, 11622, 1829, 19986, 3660, 30767, 1829, 2423, 8236, 2158, 2423, 8236, 2158, 6225, 3555, 9640, 3660, 18871, 1975, 2655, 5016, 18513, 11778, 6027, 2655, 9957, 32748, 6027, 3660, 9673, 5016, 995, 25708, 3660, 16070, 3215, 6027, 3660, 11778, 2407, 23032, 12610, 4724, 5172, 9381, 26895, 3660, 4724, 14407, 24401, 6156, 3224, 1829, 5551, 4587, 25513, 44049, 38207, 5296, 3224, 6055, 22488, 3215, 32748, 6027, 3660, 20666, 2655, 7435, 11622, 1829, 19986, 3660, 8717, 8592, 38688, 50113, 6027, 12399, 16490, 16254, 8717, 8592, 38688, 50113, 6027, 718, 283, 490, 472, 732, 281, 4018], 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"probability": 0.9212239583333334}, {"start": 2530.45, "end": 2530.91, "word": " مثال", "probability": 0.967529296875}, {"start": 2530.91, "end": 2531.73, "word": " let", "probability": 0.463134765625}, {"start": 2531.73, "end": 2532.09, "word": " f", "probability": 0.50439453125}, {"start": 2532.09, "end": 2532.49, "word": " from", "probability": 0.87451171875}, {"start": 2532.49, "end": 2532.79, "word": " one", "probability": 0.57177734375}, {"start": 2532.79, "end": 2533.11, "word": " two", "probability": 0.451904296875}, {"start": 2533.11, "end": 2533.31, "word": " to", "probability": 0.96435546875}, {"start": 2533.31, "end": 2533.61, "word": " zero", "probability": 0.8994140625}], "temperature": 1.0}, {"id": 116, "seek": 255476, "start": 2534.64, "end": 2554.76, "text": "from one to zero اه صحيح هو الدوال المتعددة القاعدة الدالة المعرفة بالتيزيه او الاقتران او الدالة المتعددة القاعدة صحيح فهذا اقرب موضوعله او يمكن هو بالظبط يعني الدالة متعددة القاعدة", "tokens": [20579, 472, 281, 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بعدين بقولي هل هو function ولا لأ طبعا الاتحاد مش أسهل من هيك ايش عليا احطهم مع بعض اجمحهم فطبعا بالدبدة 01", "tokens": [17, 4032, 1958, 4032, 2423, 460, 568, 4032, 1025, 4032, 805, 4032, 1025, 23032, 3555, 3615, 995, 4724, 39648, 10874, 1829, 3555, 2423, 9307, 5016, 18513, 4724, 39648, 1829, 915, 264, 11671, 4032, 39182, 9957, 4724, 39648, 1829, 8032, 1211, 31439, 2445, 49429, 5296, 10721, 23032, 3555, 3615, 995, 2423, 9307, 5016, 18513, 37893, 5551, 3794, 3224, 1211, 9154, 39896, 4117, 1975, 1829, 8592, 11203, 25528, 1975, 5016, 9566, 16095, 20449, 45030, 11242, 1975, 7435, 2304, 5016, 16095, 6156, 9566, 3555, 3615, 995, 20666, 3215, 3555, 41891, 23185], "avg_logprob": -0.24473314472798552, "compression_ratio": 1.6627906976744187, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2587.97, "end": 2588.27, "word": "2", "probability": 0.2327880859375}, {"start": 2588.27, "end": 2588.55, "word": " و", "probability": 0.36474609375}, {"start": 2588.55, "end": 2588.85, "word": " 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الله", "probability": 0.95849609375}, {"start": 2928.42, "end": 2928.62, "word": " المرة", "probability": 0.87744140625}, {"start": 2928.62, "end": 2928.8, "word": " الجاية", "probability": 0.61083984375}, {"start": 2928.8, "end": 2929.22, "word": " بنكمل", "probability": 0.8826497395833334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2929.4526875, "duration_after_vad": 2812.4399999999873} \ No newline at end of file diff --git a/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/7VkFVIFSEiE_postprocess.srt b/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/7VkFVIFSEiE_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..47afdc2bfbc9292018cfe71fed61e900ed7d8583 --- /dev/null +++ b/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/7VkFVIFSEiE_postprocess.srt @@ -0,0 +1,2928 @@ +1 +00:00:20,480 --> 00:00:24,700 +طيب اليوم هنبدأ في المادة ب chapter واحد chapter + +2 +00:00:24,700 --> 00:00:29,320 +واحد بتكلم على ال definitions و ال properties ل + +3 +00:00:29,320 --> 00:00:34,360 +digital integrated circuits او اللي حكيناها سابقا + +4 +00:00:34,360 --> 00:00:40,360 +اللي هي ال matrix ل ال digital logics ال digital + +5 +00:00:40,360 --> 00:00:45,320 +gates ايش ال matrix اللي انا بدي أجيس فيها؟اليوم + +6 +00:00:45,320 --> 00:00:51,520 +هنتكلم نبدأ بال ideal inverter نعرف أبسط قطعة + +7 +00:00:51,520 --> 00:00:57,300 +logic أو أبسط logic gate اللي هي الاش ال inverter + +8 +00:00:57,300 --> 00:01:01,560 +هنبدأ بال inverter ال symbol تبعت ال inverter + +9 +00:01:01,560 --> 00:01:07,890 +نتكلم عن ال ideal inverter و بعدهانتكلم على الـ + +10 +00:01:07,890 --> 00:01:12,190 +Typical Inverter أو الـ Commercial Inverter هنحاول + +11 +00:01:12,190 --> 00:01:17,850 +نعرف كيف نتعامل مع أو كيف نعمل derivation نرسم ال + +12 +00:01:17,850 --> 00:01:20,950 +voltage transfer characteristics أو كيف نعمل + +13 +00:01:20,950 --> 00:01:26,730 +relation بين ال output و ال input هنتطرق بعد هيكة + +14 +00:01:26,730 --> 00:01:31,550 +لحاجة بنسميها noise margin قداش ال system يعني how + +15 +00:01:31,550 --> 00:01:36,320 +much can the system tolerateالـ term of noise يعني + +16 +00:01:36,320 --> 00:01:40,400 +كده بدخل على ال system noise بظل عندي ال system + +17 +00:01:40,400 --> 00:01:46,280 +act as a digital gate يعني في عندي input low input + +18 +00:01:46,280 --> 00:01:50,300 +high و في عندي output low output high بعد هيك + +19 +00:01:50,300 --> 00:01:55,760 +هنتكلم عن ال fan in و ال fan out بعدهاهنتكلم على + +20 +00:01:55,760 --> 00:01:59,860 +ال transient behavior لل system اللى بنتكلم فيه عن + +21 +00:01:59,860 --> 00:02:03,740 +ال rise time و ال fall time بنتكلم على ال + +22 +00:02:03,740 --> 00:02:07,120 +propagation delay كده بيصير delay و أخر اشي + +23 +00:02:07,120 --> 00:02:12,830 +بنتكلمه في المحاضرة عن ال power dissipationكل ال + +24 +00:02:12,830 --> 00:02:15,570 +chapters اللي هتتكلم عنهم من هنا او ال logic + +25 +00:02:15,570 --> 00:02:18,690 +family اللي هتتكلم عليهم من هنا لآخر ال system تلت + +26 +00:02:18,690 --> 00:02:22,230 +شغلات هتضالها مساحبالنا على طول ايش هي احفظوها ال + +27 +00:02:22,230 --> 00:02:28,130 +VTC ال fan out و ال power dissipation هنقولك خلصنا + +28 +00:02:28,130 --> 00:02:32,710 +واحد ايش التاني هتقولي ال fan out او ال power + +29 +00:02:32,710 --> 00:02:35,270 +dissipation التالتة و ال power dissipation نشتغل + +30 +00:02:35,270 --> 00:02:40,490 +عليهم كويس هيك؟أول ما ببدأ بحطلكم اليوم عشان + +31 +00:02:40,490 --> 00:02:42,990 +تتنشطوا معي و تضالكم تابعين ال homework تبع ال + +32 +00:02:42,990 --> 00:02:50,410 +chapter الموجود هنا كويس؟ + +33 +00:02:50,410 --> 00:03:03,250 +هذا + +34 +00:03:03,250 --> 00:03:09,550 +عشان تضلك ماشي معاهومتبع بلزمش تضيع أي وقت من هنا + +35 +00:03:09,550 --> 00:03:15,090 +لآخر الفصل يعني ضالك معي شغال المادة بسيطة وسهلة + +36 +00:03:15,090 --> 00:03:19,070 +ومافيش فيها اي اشكالية الان ال inverter بشكل عام + +37 +00:03:19,070 --> 00:03:22,990 +لما نتكلم عنه ال symbol تبعه يا اما بنحط ال bubble + +38 +00:03:22,990 --> 00:03:27,490 +ع شجة ال output او ال bubble ع شجة ال input + +39 +00:03:31,310 --> 00:03:35,010 +هي ال inverter ال non inverter اللي هو بنسميه ال + +40 +00:03:35,010 --> 00:03:43,050 +buffer تبقى عندى يا اما two bubbles يا + +41 +00:03:43,050 --> 00:03:48,690 +اما no bubbles at all هاي ال inverter لل inverter + +42 +00:03:48,690 --> 00:03:54,470 +typical inverter عندى هاي + +43 +00:03:54,470 --> 00:04:01,520 +ال inputوهنا ال output وهنا مشبوك ويبقى مشبوك + +44 +00:04:01,520 --> 00:04:10,340 +ويبقى مشبوك ويبقى مشبوك ويبقى مشبوك ويبقى + +45 +00:04:10,340 --> 00:04:14,320 +مشبوك ويبقى مشبوك ويبقى مشبوك ويبقى مشبوك ويبقى + +46 +00:04:14,320 --> 00:04:15,160 +مشبوك ويبقى مشبوك ويبقى مشبوك ويبقى مشبوك ويبقى + +47 +00:04:15,160 --> 00:04:16,100 +مشبوك ويبقى مشبوك ويبقى مشبوك ويبقى مشبوك ويبقى + +48 +00:04:16,100 --> 00:04:16,880 +مشبوك ويبقى مشبوك ويبقى مشبوك ويبقى مشبوك ويبقى + +49 +00:04:16,880 --> 00:04:23,500 +مشبوك ويبقى مشبوك ويبقى + +50 +00:04:23,500 --> 00:04:36,250 +مشبوك ويبقى مشT شغل ال output نفس الشغل هاي T هاي + +51 +00:04:36,250 --> 00:04:46,430 +V out لل inverter عكس الموجود هنا هيكون وهكذا + +52 +00:04:46,430 --> 00:04:52,550 +هذه ال V in و ال V out كده بنحصل على معلومات هنا + +53 +00:04:52,550 --> 00:04:59,550 +مش كتيرأو الرسمة تعني ليش كثير إذا بتلاحظوا احنا + +54 +00:04:59,550 --> 00:05:03,810 +كنا يمكن في مادة ال signals لما ناخدته كنا لما + +55 +00:05:03,810 --> 00:05:07,710 +نجيب يعني نتعرف على ال characteristics تبع اي + +56 +00:05:07,710 --> 00:05:11,290 +system ايش كنا نتطلع على ايش على المواضل لل system + +57 +00:05:11,290 --> 00:05:15,710 +مظبوط المواضل ايش بيعمل ليه بوربط ال input و ال + +58 +00:05:15,710 --> 00:05:19,170 +output يا إما على شكل differential equation أو على + +59 +00:05:19,170 --> 00:05:22,450 +شكل ال state space model أو على شكل ال transfer + +60 +00:05:22,450 --> 00:05:27,310 +function مظبوطكنا من بعد هي كان نقدر نتكلم على ال + +61 +00:05:27,310 --> 00:05:31,090 +system هل هو stable نتكلم على ال stability + +62 +00:05:31,090 --> 00:05:35,430 +property نتكلم على أي property حتى لاحقا في سنة + +63 +00:05:35,430 --> 00:05:37,110 +رابعة في ال control هتتكلموا على ال + +64 +00:05:37,110 --> 00:05:39,670 +controllability behavior و ال observability + +65 +00:05:39,670 --> 00:05:45,270 +behavior تتكلموا علىحاجات تانية مثل الـ casualty + +66 +00:05:45,270 --> 00:05:50,090 +تتكلموا عن ال variance وعلى ال time variance shift + +67 +00:05:50,090 --> 00:05:53,410 +in variance كل هذه العلاقات كنا نتكلم عليها بس + +68 +00:05:53,410 --> 00:05:57,990 +لازم تكون عندي علاقة بتحدد ال input مع ال output + +69 +00:05:57,990 --> 00:06:02,810 +نفس الشأن هنا عندنا في ال digital circuit لازم نجد + +70 +00:06:02,810 --> 00:06:08,670 +علاقة تربطلي ال input versus ال output أسهل حاجة + +71 +00:06:08,670 --> 00:06:13,850 +نحط التنتين على نفسالرسمة وهذا لما نحط التنتين على + +72 +00:06:13,850 --> 00:06:17,650 +نفس الرسمة ايش بنتكلم بنتكلم على ال voltage + +73 +00:06:17,650 --> 00:06:23,110 +transfer characteristics اللي بنسميها بالمختصر VTC + +74 +00:06:23,110 --> 00:06:29,810 +voltage + +75 +00:06:29,810 --> 00:06:34,490 +transfer + +76 +00:06:34,490 --> 00:06:38,650 +characteristics + +77 +00:06:43,280 --> 00:06:52,640 +وبهايهم شايفهم ال VTC الان لو عند ال input في شاجة + +78 +00:06:52,640 --> 00:07:01,520 +ال input VCC في ال ideal بالدرجة لنقطة النص VCC + +79 +00:07:01,520 --> 00:07:07,540 +على اتنين و + +80 +00:07:07,540 --> 00:07:15,330 +اقول هاديالـ high اللى عندى اللى هى VCC الان اللى + +81 +00:07:15,330 --> 00:07:20,170 +بدي اعمله التالي لو قبل هذه الرسمة خلّينا نقول بدي + +82 +00:07:20,170 --> 00:07:26,770 +احدد بدي اجعل شجة هذه قلت هذه شجة ال output وهذه + +83 +00:07:26,770 --> 00:07:35,380 +شجة الال input يعني عمود x و عمود y و خط المستقيم + +84 +00:07:35,380 --> 00:07:41,880 +تبع x ع ال x axis هذا بمثل المين ال input ال y + +85 +00:07:41,880 --> 00:07:48,260 +axis بمثل ال output الآن زي ما بنعرف لو بدي اتكلم + +86 +00:07:48,260 --> 00:07:51,280 +عن ال input ال input في ال digital يا اما بدي يكون + +87 +00:07:51,280 --> 00:07:55,500 +high يا اما بدي يكون low في حالة ال ideal + +88 +00:08:00,160 --> 00:08:04,320 +انفيرتر ايش بيصير عندى النقطة اللى بتحدد ال .. ال + +89 +00:08:04,320 --> 00:08:07,740 +.. ال .. وين بيصير اللى هي نقطة ال ash المنتصف + +90 +00:08:07,740 --> 00:08:12,580 +يعني هذا المنطقة يعتبر ال input فيها low و هذا + +91 +00:08:12,580 --> 00:08:17,640 +المنطقة يعتبر ال input فيها ashو النقطة اللي فيها + +92 +00:08:17,640 --> 00:08:24,040 +discontinuity تعتبر نقطة ال VCC على 2 يعني انا جيت + +93 +00:08:24,040 --> 00:08:29,200 +للدائرة او جيت لل range تبع ال input لو عندي 5 من + +94 +00:08:29,200 --> 00:08:34,460 +0 ل 2.5بقول عنه low من اتنين و نص لخمسة باعتبره + +95 +00:08:34,460 --> 00:08:40,120 +ايش high فانا قسمت ال input عندى لمنطقتين منطقة + +96 +00:08:40,120 --> 00:08:43,480 +low ومنطقة high بالنسبة لل inverter لو كان ال + +97 +00:08:43,480 --> 00:08:48,420 +input عندى zero ال output كده بيكون one يعني لو + +98 +00:08:48,420 --> 00:08:52,280 +كان ال input low ال output بيكون high لو قلت ال + +99 +00:08:52,280 --> 00:08:58,280 +VCC بتساوى خمسة يبقى هذا 2.2 2.5 لو هنا حطيت zero + +100 +00:08:58,280 --> 00:09:05,400 +volt كده ال outputالان ال output عنده حالتين high + +101 +00:09:05,400 --> 00:09:09,760 +بيساوي خمسة low بيساوي كام؟ zero فهنا عنده + +102 +00:09:09,760 --> 00:09:16,200 +بالنسبالي هي هذه المنطقة هي ال high وهذا الخط هو + +103 +00:09:16,200 --> 00:09:21,160 +ال low وهذا يمثل خط ال high الخمسة هذا على طول وخط + +104 +00:09:21,160 --> 00:09:27,080 +ال low يمثل إيه؟ سفرفانا من ناحية شكة ال y axis + +105 +00:09:27,080 --> 00:09:31,500 +عندى هى خط بمثل ال high وهى خط بمثل ال low شكة ال + +106 +00:09:31,500 --> 00:09:37,520 +input عندى region مش خط عندى من 0 ل 2.5 او ل VCC + +107 +00:09:37,520 --> 00:09:43,320 +على 2 هذا بمثل ال low و من VCC على 2 ل VCC بمثل ال + +108 +00:09:43,320 --> 00:09:48,990 +high واضحة هذهطالما ال input له ال output إيش لازم + +109 +00:09:48,990 --> 00:09:53,110 +يطلع؟ لو دخلت عندي هنا سفر قولت بيعطيني خمسة لو + +110 +00:09:53,110 --> 00:09:59,550 +دخلت واحد بيعطيني كام؟ بيعطيني خمسةلو دخلت اتنين + +111 +00:09:59,550 --> 00:10:03,190 +بدي اعطيني كام؟ خمسة النقطة اتنين و نص اللي هي + +112 +00:10:03,190 --> 00:10:07,650 +نقطة المنتصف هي اللي بيصير فيها discontinuity ممكن + +113 +00:10:07,650 --> 00:10:11,870 +تعطيني اتنين اتنين و خمسة و ممكن تعطيني ايش؟ Zero + +114 +00:10:11,870 --> 00:10:15,330 +في نفس الوقت في هذا اللي بسميها فهذا طالما انا ال + +115 +00:10:15,330 --> 00:10:19,960 +input في هذا المنطقةو انا باعتبر ال output ايش + +116 +00:10:19,960 --> 00:10:23,860 +اللي بيعطيني هاي جيت على المنطقة هاي ال output + +117 +00:10:23,860 --> 00:10:28,260 +قديش بيصير low يعني هذه لو بترسمها هاي الخط اللي + +118 +00:10:28,260 --> 00:10:28,800 +بالأحمر + +119 +00:10:35,260 --> 00:10:39,520 +الخط اللي بالأحمر هذا مثله نقطة ال high هذا لما ال + +120 +00:10:39,520 --> 00:10:42,920 +input كان عندى فى هذه المنطقة تانى output هذا ال + +121 +00:10:42,920 --> 00:10:47,320 +input صار فى منطقة ال high ال output صار فى منطقة + +122 +00:10:47,320 --> 00:10:54,400 +ال low الآن هذا رسمتلى الخارطة تبع الدائرة اللى + +123 +00:10:54,400 --> 00:10:58,880 +عندى الآن فى الحالة اللى عندنا حالة ال ideal ايش + +124 +00:10:58,880 --> 00:11:03,750 +عندي طلعة الخط هذا عموديفي الـ commercial أو الـ + +125 +00:11:03,750 --> 00:11:09,270 +typical خط هذا مش هيكون عمودي هيكون مائل الان ال + +126 +00:11:09,270 --> 00:11:14,210 +voltage اللي عندي هان اعطاني VCC و اعطاني zero + +127 +00:11:14,210 --> 00:11:20,550 +هدولة ممكن اوصل هن مش لا اوصل ل VCC ولا انزل ل + +128 +00:11:20,550 --> 00:11:24,490 +zero الان هذه النقطة زي ما حكينا فيه نقطة فيها + +129 +00:11:24,490 --> 00:11:30,520 +discontinuity اذا الخط صار مائل صار عندي slopeو + +130 +00:11:30,520 --> 00:11:37,260 +هنتكلم عنه الحين هذي ال typical VTC لل ideal طب لو + +131 +00:11:37,260 --> 00:11:44,000 +بتكلم عن حاجة مش ideal typical ايش بتدرسوه بتدرسو + +132 +00:11:44,000 --> 00:11:53,260 +من ال VTC هعطيكوا رسمة و بنق عليها V in و V out و + +133 +00:11:53,260 --> 00:11:56,100 +نحدد ايش ال characteristic + +134 +00:12:05,440 --> 00:12:14,400 +هي عندي هذه سميها VOH هذه VOL هذه VIL وهنا VIH وفي + +135 +00:12:14,400 --> 00:12:21,580 +حاجة نسميها في النصVM الان نعرف ايش هذه المناطق + +136 +00:12:21,580 --> 00:12:28,120 +ايش اللي بنقصد فيه ال VOH و ال VIH و ال VM و هدول + +137 +00:12:28,120 --> 00:12:32,920 +الحاجات بس عشان تتعرفها هاد بنتكلم ع شكة ال ايش ال + +138 +00:12:32,920 --> 00:12:37,360 +output هذا بنقول عنه output high ال voltage في + +139 +00:12:37,360 --> 00:12:41,250 +حالة output highهذا ال voltage في حالة ال output + +140 +00:12:41,250 --> 00:12:45,990 +low هنا بشجة ال input بقول ال voltage لل input low + +141 +00:12:45,990 --> 00:12:50,430 +وهنا ال voltage لل input high هذا ال midpoint اللي + +142 +00:12:50,430 --> 00:12:56,850 +هي بنحددها بنسميها VM كويس هيك ال midpoint كانت + +143 +00:12:56,850 --> 00:13:02,090 +هنا عندى بتساوي VCC على اتنين الموجودة هنا اللي + +144 +00:13:02,090 --> 00:13:07,770 +عندى الان هنا VIL و VIH هان ايش انضغطوا في نقطة + +145 +00:13:07,770 --> 00:13:13,860 +واحدةاللي هي ال midpoint اللي موجودة عندى هان ال + +146 +00:13:13,860 --> 00:13:20,240 +VCC هان ممكن تكون ال VOH بس ال VOL هان زيرو هان + +147 +00:13:20,240 --> 00:13:28,650 +عندى مش زيروواضحة؟ طيب في عندى حاجتين بدك تعرفهم + +148 +00:13:28,650 --> 00:13:34,050 +يعني مش .. بغلبنش وفي حاجتين تانيات بغلبن شوية شجة + +149 +00:13:34,050 --> 00:13:38,310 +ال input بتغلب شوية شجة ال output أبسط نيجي نتكلم + +150 +00:13:38,310 --> 00:13:42,630 +على شجة ال output اللي هي ال VOH وال VOL ايش بتعني + +151 +00:13:42,630 --> 00:13:50,310 +ال VOH؟ حد بدي يعمل guess أو بدي يعني يعلق عليها؟ + +152 +00:13:51,310 --> 00:13:58,150 +أيش بنعنى بال VOH؟ اعلى + +153 +00:13:58,150 --> 00:14:03,170 +قيمة voltage ممكن ال output يصلها هذه بسميها VOH + +154 +00:14:03,170 --> 00:14:08,850 +واضحة هي ايش هي؟أعلى قيمة voltage ممكن يصلها ال + +155 +00:14:08,850 --> 00:14:14,390 +output عادة أعلى voltage في الدائرة VCC ممكن توصل + +156 +00:14:14,390 --> 00:14:19,590 +VCC وممكن توصل أقل من + +157 +00:14:19,590 --> 00:14:30,690 +هذه القيمة ال VOL عكسها أقل قيمة ممكن يوصلها ال + +158 +00:14:30,690 --> 00:14:36,770 +voltageالان هذه ممكن تكون zero وممكن ماتكونش zero + +159 +00:14:36,770 --> 00:14:44,050 +في دوائر كتير بحطها لكم عشان ماتكونش zero و بقولك + +160 +00:14:44,050 --> 00:14:49,430 +قداش ال VOL الدائرة لو طلعت عليها وشفتها by + +161 +00:14:49,430 --> 00:14:54,450 +inspection تقدر تقولي جواباللي أنا شايفه بقول by + +162 +00:14:54,450 --> 00:14:58,890 +inspection بتقوللي إيه الجواب بعض منكوا بنص صفحة + +163 +00:14:58,890 --> 00:15:02,810 +بيعمل تحليل analysis في الآخر بيوصل ليه بيوصللي + +164 +00:15:02,810 --> 00:15:07,910 +جواب zero طبعا إذا أنا بدى أطلع لل saturated + +165 +00:15:07,910 --> 00:15:18,210 +transistor قداش ال VCE تبعته ال VCE ال typical + +166 +00:15:18,210 --> 00:15:23,270 +اللي احنا بنتعامل معاه point اتنين صح؟ال VBE في + +167 +00:15:23,270 --> 00:15:25,850 +حالة ال forward active اللي انتوا بتعرفوه point 7 + +168 +00:15:25,850 --> 00:15:30,610 +و ال VBE في حالة ال saturation point 8 لان انا + +169 +00:15:30,610 --> 00:15:35,350 +بتكلم على point 2 كويس ال point 2 يعني لو انا حطيت + +170 +00:15:35,350 --> 00:15:40,710 +شبكت ال emitter مع ال ground و ال collector مع ال + +171 +00:15:40,710 --> 00:15:44,170 +output و قلت ال transistor في حالة ال saturation + +172 +00:15:44,170 --> 00:15:46,590 +قداش ال output تبعته ال low + +173 +00:15:54,120 --> 00:15:58,060 +لأن أقل قيمة ممكن يوصلها ال output point 2 مش ممكن + +174 +00:15:58,060 --> 00:16:01,980 +يوصل ل zero وهذا كنتوا إيش في ال saturation دايما + +175 +00:16:01,980 --> 00:16:07,300 +تنزلوها بال minus أحيانا ال VCE تطلع عندكمصح؟ او + +176 +00:16:07,300 --> 00:16:12,220 +لو انت مااخدتش بالك تيجي تحسب التيارة بتحسب كل إش + +177 +00:16:12,220 --> 00:16:15,180 +بتلاقي فيه عندك حاجة بتطلع بال minus بتقنع حالك + +178 +00:16:15,180 --> 00:16:18,380 +أنها plus و تقلب الإشارة اللي طلعت معاك و تقول هي + +179 +00:16:18,380 --> 00:16:24,260 +الجواب هذا حاجة طبيعية تيجي لأن في عالمنا نحنا + +180 +00:16:24,260 --> 00:16:29,150 +منطقة ال saturation بتحب نشتغل فيهافانت هتصير فيها + +181 +00:16:29,150 --> 00:16:31,990 +ايش زي ما بيقولها معلم في الشغل في هذه المنطقة + +182 +00:16:31,990 --> 00:16:38,070 +ماعاد تتخربط في وضع ال saturation ونقولك هذا بدك + +183 +00:16:38,070 --> 00:16:43,430 +تكون بصحصة عندك فهذا بتخليك تصحصة فمعناته ايش اقل + +184 +00:16:43,430 --> 00:16:50,810 +قيمة ممكن يصلها ال output هتكون ال VOL مش هينزل + +185 +00:16:50,810 --> 00:16:56,680 +اقل من هيك نفس الشيء اعلى قيمة ممكن يصلهاال output + +186 +00:16:56,680 --> 00:17:04,260 +بنسميها VOH كويسك؟ طيب الآن هذا الجزء السهل إيش + +187 +00:17:04,260 --> 00:17:10,180 +الجزء الأصعب؟ ال VIL و ال VIH إيش بنقصد فيه؟ حد + +188 +00:17:10,180 --> 00:17:15,380 +بدي أخد يحذر إيش .. إيش بنقصد فيه؟ ال VIL ناخد؟ + +189 +00:17:15,380 --> 00:17:20,040 +مين يقول إيش ال VIL؟ + +190 +00:17:20,040 --> 00:17:25,870 +أعلى قيمة بيصلها ال input و بيضالب نحس belowيعني + +191 +00:17:25,870 --> 00:17:30,810 +بعد القيمة high ال input ماعادى نسميه low دخل على + +192 +00:17:30,810 --> 00:17:37,350 +منطقة مجهولة الهوية undetermined region لا هي high + +193 +00:17:37,350 --> 00:17:44,010 +ولا هي low في ال ideal إذا عدى هذا النقطة بنقول + +194 +00:17:44,010 --> 00:17:47,950 +دخل ال high قبل النقطة high في إيش؟ في ال low هنا + +195 +00:17:47,950 --> 00:17:54,420 +إذا عدى هذا النقطة دخل منطقة مجهولة مش highهذه + +196 +00:17:54,420 --> 00:17:59,160 +المنطقة فهي أخر نقطة في ال input يعد ال input فيها + +197 +00:17:59,160 --> 00:18:04,360 +low يعني في هذه المنطقة ال input عنده يعتبر low + +198 +00:18:04,360 --> 00:18:15,220 +بعدها علامة استفهام فهي خط النهاية لنقطة لإيش + +199 +00:18:15,220 --> 00:18:19,720 +لمنطق ال low في شجة ال input هذه بدي أسميها last + +200 +00:18:21,400 --> 00:18:25,420 +Last point في ال input يعتبر ال input عندي low + +201 +00:18:25,420 --> 00:18:32,120 +خلّيكي مركز معايا فيها هذه لأن هذه أول نقطة ستخربط + +202 +00:18:32,120 --> 00:18:39,040 +فيهاأنا قاعد بقول بعني هي أخر نقطة في ال input + +203 +00:18:39,040 --> 00:18:44,600 +يعتبر ال input فيها low و أي digital gate او + +204 +00:18:44,600 --> 00:18:48,360 +digital circuit لازم تعطيني شكة ال input low و + +205 +00:18:48,360 --> 00:18:52,920 +high و شكة ال output low و high لو اعطتني واحدة من + +206 +00:18:52,920 --> 00:18:57,880 +التنتين ال circuit high او ال gate بطلت تشتغل ك + +207 +00:18:57,880 --> 00:19:03,950 +digital circuit يعني هتعطيني خطيا إما ها يا إما لو + +208 +00:19:03,950 --> 00:19:08,190 +في منطقة ال output ها يا إما ال output له و تظل + +209 +00:19:08,190 --> 00:19:11,890 +هتابت عليه إيش ما تغير في ال input مش هيصير أي + +210 +00:19:11,890 --> 00:19:18,030 +تغير معه في ال output هل هذه digital circuit ؟ هذه + +211 +00:19:18,030 --> 00:19:22,810 +المشكلة لما أدخل على هذه المناطق طيب ال VIH إيش + +212 +00:19:22,810 --> 00:19:32,250 +بنقصد فيها؟ أقل نقطةأو أصغر نقطة في ال input عشان + +213 +00:19:32,250 --> 00:19:39,970 +نعتبره high او أول نقطة في ال input تعتبر في منطقة + +214 +00:19:39,970 --> 00:19:48,010 +ال high فهذه بعدها بنقول عنها high + +215 +00:19:48,010 --> 00:19:53,110 +وهذه بنقول عنها first عشان انت تميزها ال first + +216 +00:19:53,110 --> 00:20:02,520 +point في ال region high اللي بتعتبرHi طب سؤال تاني + +217 +00:20:02,520 --> 00:20:07,700 +ممكن هذه .. هذه كويسة مين بتتوقع أكبر ال VIL ولا + +218 +00:20:07,700 --> 00:20:10,920 +ال VOL؟ + +219 +00:20:10,920 --> 00:20:20,900 +اه ال VIL .. انا بتكلم عن .. ال IL ولا ال OL؟ ال + +220 +00:20:20,900 --> 00:20:25,900 +IL .. ليش؟ مش فاكر ان هو أفضل قيمة + +221 +00:20:29,860 --> 00:20:35,400 +الـ VIL لازم + +222 +00:20:35,400 --> 00:20:41,120 +تكون أكبر من ال OL ليش؟ لو ال OL أكبر خلّيني أقول + +223 +00:20:41,120 --> 00:20:45,000 +هاي ال stage هذا و هاي ال stage اللي بعده هذا + +224 +00:20:45,000 --> 00:20:50,080 +بتعطيني output low إذا كان أكبر من input low يبقى + +225 +00:20:50,080 --> 00:20:53,940 +هذا ال output تبقى هذا مش هيتغير مظبوط؟ هيظل زي ما + +226 +00:20:53,940 --> 00:20:59,330 +هوأنا بتكلم high stages هذا بيعطيني low بس ال low + +227 +00:20:59,330 --> 00:21:03,610 +تبقى هذا أكبر من ال low ال input لهذا معناته هذا + +228 +00:21:03,610 --> 00:21:07,330 +هيعطيني ال inverter بتكلم من دوائر inverter هذا + +229 +00:21:07,330 --> 00:21:12,670 +قلت low ال low تبقى أكبر هذا يعني الأصل لما يدخل + +230 +00:21:12,670 --> 00:21:16,510 +ال low يعطيني high هذا هيعطيني باعتبر الإشارة اللي + +231 +00:21:16,510 --> 00:21:20,470 +كانت هنا undetermined و إيش ما بدي يطلع بدي يعطيني + +232 +00:21:20,470 --> 00:21:23,290 +حاجة في منطقة ال undetermined مش هيعطيني شيء + +233 +00:21:23,710 --> 00:21:28,370 +باعتباره high هنا فانا الإشارة اللى بتدخل عندى مش + +234 +00:21:28,370 --> 00:21:33,350 +هتأثر على ال output هنا منطقة ال high مش حصلها من + +235 +00:21:33,350 --> 00:21:36,470 +هذا ال stage لإيش لأن ال low اللى دخلها مش معترف + +236 +00:21:36,470 --> 00:21:42,270 +فيه low هو برا ال range تبع ال low فالأصل فيه في + +237 +00:21:42,270 --> 00:21:46,230 +هذه المنطقة لما اتكلم عنها بتكلم عن حاجة واحدة انا + +238 +00:21:46,230 --> 00:21:53,520 +بدي ال VIL دايما يبقى أكبر من ال VOLطب هاذي إيش + +239 +00:21:53,520 --> 00:22:00,740 +بترتب عليها لو ماكانتش زي هيك؟ في الدوائر اللي جاي + +240 +00:22:00,740 --> 00:22:04,380 +اللاحقة قولنا بنتكلم عن تلت شغلات لكل .. لكل + +241 +00:22:04,380 --> 00:22:09,320 +family logic إيش هم اللي حكيناهم؟ أيوة و ال fan + +242 +00:22:09,320 --> 00:22:14,520 +out و ال power dissipation فمعناته هتنسقل سؤال + +243 +00:22:14,520 --> 00:22:18,980 +دايما عن ال fan outفي حالة لما يكون عندى ال VOL + +244 +00:22:18,980 --> 00:22:24,060 +أكبر من ال VIL في مشكلة بال fan out فانت بتقول لى + +245 +00:22:24,060 --> 00:22:29,560 +بما انه في مشكلة هذا الوضع ان ال VOL أكبر من ال + +246 +00:22:29,560 --> 00:22:33,480 +VIL يبقى عندى المشكلة التالية ان ال fan out لازم + +247 +00:22:33,480 --> 00:22:39,300 +يساوي zero بقدرش أبنى stages إذا أنا في عندى مشكلة + +248 +00:22:39,300 --> 00:22:45,080 +في ال logic تبع ال output لل first stageيعني ال + +249 +00:22:45,080 --> 00:22:49,160 +driver تبعي في مشكلة فيه بقدرش أحمل عليها أي load + +250 +00:22:49,160 --> 00:22:54,220 +فبتقول لي ال fan out equal zero نهاية المطاف لا + +251 +00:22:54,220 --> 00:22:57,680 +بتعملي تحليل ولا بتعملي derivation للدائرة ولا + +252 +00:22:57,680 --> 00:23:03,240 +حاجة واضحة هذه؟ إيش اللي بنحكي؟ حاجة واحدة لازم + +253 +00:23:03,240 --> 00:23:09,540 +تظل ثابتة اللي هي ال VIL لازم تبقى أكبر من ال VOL + +254 +00:23:09,540 --> 00:23:13,100 +على طول طب هذي إيش برضه اللي دخل؟ اللي دخل بحاجة + +255 +00:23:13,100 --> 00:23:22,280 +تانيةفرضا انا قلت ال VIL بتساوي عندى 1.5 كويس و ال + +256 +00:23:22,280 --> 00:23:34,300 +VOL 0.5 كويس هذه قلت عندى ال VOL بتساوي 0.5 و ال + +257 +00:23:34,300 --> 00:23:36,620 +VIL بتساوي 1.5 + +258 +00:23:43,080 --> 00:23:51,920 +تحكي للتالي انه لو انا دخلت input من point five ل + +259 +00:23:51,920 --> 00:23:57,720 +one point five هذا يعتبر ايش low تعرف ايش ال noise + +260 +00:23:57,720 --> 00:24:02,140 +تعريف ال noise unwanted + +261 +00:24:02,140 --> 00:24:08,000 +signal forced on the desired signal or joined the + +262 +00:24:08,000 --> 00:24:16,280 +desired signal فيعني unwantedفهي إشارة دخلت على + +263 +00:24:16,280 --> 00:24:20,960 +الإشارة اللي أنا بدي إياها غصب عني هاي ال noise مش + +264 +00:24:20,960 --> 00:24:25,580 +قادر أقولها أعزلها طالما هذا الإشارة في حدود + +265 +00:24:25,580 --> 00:24:32,920 +المعقول وانا إيش ال input لساته عنده low مظبوط؟ + +266 +00:24:32,920 --> 00:24:38,050 +إيش حدود المعقول هذا اللي بتكلم عليها؟انا اتكلمت + +267 +00:24:38,050 --> 00:24:42,750 +كلمة فاضي عامة حدود المعقول حدود المعقول في لغة + +268 +00:24:42,750 --> 00:24:47,310 +المهندسية تقول مش عارفها هذه انك ماتخليش ال اوة + +269 +00:24:47,310 --> 00:24:52,910 +تتزيد عن الامر لأ شايف هذه هذي انت قداشي الفرق + +270 +00:24:52,910 --> 00:24:59,150 +بينهم واحد طالما ال noise حجمها واحد او اقل وانا + +271 +00:24:59,150 --> 00:25:04,690 +في السليم لأن ايش بيصير عندى لسات ال low هذا اللي + +272 +00:25:04,690 --> 00:25:11,150 +طلع عندى زائد ال noiseلساته اقل او بساوي هذا اذا + +273 +00:25:11,150 --> 00:25:15,270 +هذا موجود يبقى انا ال system عندي can tolerate هذا + +274 +00:25:15,270 --> 00:25:19,050 +ال noise بدون مشكلة بلاحظ حاجة واحدة يمكن كل هيتكم + +275 +00:25:19,050 --> 00:25:23,670 +بتشوفوها لو اجت زنانة و انت بتتفرج على التلفزيون + +276 +00:25:23,670 --> 00:25:30,990 +ايش بحصل؟ بتجمد الصورة، مظبوط؟ حد منكم عنده analog + +277 +00:25:30,990 --> 00:25:40,270 +TV تلفزيون analog من الإقدام؟بصيرش فيه تأثير كبير؟ + +278 +00:25:40,270 --> 00:25:46,490 +ليش؟ طيب طب ليش؟ مين أحسن ال digital ولا ال + +279 +00:25:46,490 --> 00:25:55,410 +analog؟ طب لو الدنيا شتت إيش بحصل؟ نفس الشغل زي ما + +280 +00:25:55,410 --> 00:25:58,950 +بقول طب إيش تفسيرك العلمي للي بحصل؟ + +281 +00:26:04,340 --> 00:26:08,460 +الان هذه code ال input signal code عندك بيصيرها as + +282 +00:26:08,460 --> 00:26:13,160 +ones and zeros مظبوط الان لو أنا كانت عندي zero و + +283 +00:26:13,160 --> 00:26:16,900 +أجت ال noise بال positive ممكن ترفحها لإياش لواحد + +284 +00:26:16,900 --> 00:26:21,240 +و الواحد أجت على ال negative ممكن تنزل لإياش ل + +285 +00:26:21,240 --> 00:26:26,240 +zero كل شي انت زي ما بتعرف الكلمات بتعملها coding + +286 +00:26:26,240 --> 00:26:30,600 +ask code لكل حرف مظبوطنفس الشي الكلمة زي هيك و + +287 +00:26:30,600 --> 00:26:35,640 +ببدأك تمثلها bits و bytes و words و هكذا، الآن هذه + +288 +00:26:35,640 --> 00:26:41,660 +لما أجي تيجي عندى أعملها هذه أجت عندى مش هي اللى + +289 +00:26:41,660 --> 00:26:46,000 +دخلتها لتطلع صورة، إيش بيصيرلها؟ distortionدخل + +290 +00:26:46,000 --> 00:26:49,080 +عندى ال noise غير المحتوى هذا لما اجى اطلعوا + +291 +00:26:49,080 --> 00:26:53,040 +بلقوهوش هو نفسه صار محتوى تانى المحتوى التانى + +292 +00:26:53,040 --> 00:26:57,180 +بيرمزليش لأى حاجة فى ال digital إذا بيرمزليش لأى + +293 +00:26:57,180 --> 00:27:01,500 +حاجة مش زى ال analog بطلعلك حاجة يعني الوجه ممكن + +294 +00:27:01,500 --> 00:27:05,560 +يطلعلك يمده يسوي هذه لأ هذه بتطلعك إشارة unknown + +295 +00:27:05,560 --> 00:27:10,440 +فبتطلع عندك unknown signal وبتطلع عندك lost signal + +296 +00:27:12,320 --> 00:27:17,400 +لأن الـ low اللي عندك اللي داخل على ال system hand + +297 +00:27:17,400 --> 00:27:21,880 +بطل low او ال high اللي داخل عندك على ال system + +298 +00:27:21,880 --> 00:27:27,260 +بطل high واضح هذي؟ هذا في عالم ال digital هذا اللي + +299 +00:27:27,260 --> 00:27:32,560 +بحصل فيه لان نفس الشيء مين بتتوقع أكبر ال VIH ولا + +300 +00:27:32,560 --> 00:27:41,170 +ال VOH؟الـ VOH أكبر لازم يظلوا دايما أكبر من الـ + +301 +00:27:41,170 --> 00:27:46,650 +VIH هدول الكلام اللي حكيناه بيقودنا لحاجة اللي هي + +302 +00:27:46,650 --> 00:27:50,810 +بنسميها noise margin ال noise margin لناس اللي + +303 +00:27:50,810 --> 00:27:56,710 +أخدوا ال signals أو أخدوا بداية ال control في حاجة + +304 +00:27:56,710 --> 00:28:00,770 +بنسميها لما نرسم ال body plot ال phase margin و ال + +305 +00:28:00,770 --> 00:28:04,790 +gain margin مرت عليكوا؟ مرت عليكوا بالدوائر اتنين + +306 +00:28:06,820 --> 00:28:13,960 +صح؟ والله انسيتوها حاسوب طيب خدت ال signals؟ + +307 +00:28:13,960 --> 00:28:20,000 +مومرتش عليكوا ال body plot؟ بقى ال control يات + +308 +00:28:20,000 --> 00:28:24,520 +اتنين طيب تاخدوها في ال control لاتقلقوش السنة + +309 +00:28:24,520 --> 00:28:29,680 +الجاية تاخدوها في control واحد او الفصل هذا الفصل + +310 +00:28:29,680 --> 00:28:33,580 +هذا تاخدوها control واحد اخر control واحد تاخدوا + +311 +00:28:33,580 --> 00:28:37,440 +ال body plotالـ body plot في حاجة بيسميها ال gain + +312 +00:28:37,440 --> 00:28:40,880 +margin و ال phase margin هدول بيحددوا قداش عندى + +313 +00:28:40,880 --> 00:28:44,580 +مجال في ال gain يتغير او في ال phase يتغير و ال + +314 +00:28:44,580 --> 00:28:47,720 +system يظل في حدود ال stable لو ال system كان عندى + +315 +00:28:47,720 --> 00:28:51,460 +stable قداش ممكن ندخل عليه gain او phase و ال + +316 +00:28:51,460 --> 00:28:56,070 +system يظلStable هذا نفس الشي ال noise margin كده + +317 +00:28:56,070 --> 00:29:02,230 +يدخل على ال system noise ويبقى ال behavior of ال + +318 +00:29:02,230 --> 00:29:04,530 +system stable ايش يعني ال behavior stable يعني + +319 +00:29:04,530 --> 00:29:08,770 +اشارة ال input ال low بتظهر low و اشارة ال input + +320 +00:29:08,770 --> 00:29:14,010 +ال high بتظهر high فهذا بنسميه noise margin اللي + +321 +00:29:14,010 --> 00:29:14,410 +عندي + +322 +00:29:22,250 --> 00:29:27,270 +يعني بنعرفه mathematically إيش هو عشان نبني عليه + +323 +00:29:27,270 --> 00:29:43,330 +نقول + +324 +00:29:43,330 --> 00:29:50,170 +عنه في noise و margin في لل low و في noise margin + +325 +00:29:51,420 --> 00:29:55,320 +بعض الأحيان هتلاقيني اعمل drop لل V ويبقى لدي + +326 +00:29:55,320 --> 00:29:58,820 +noise margin low وnoise margin high نقصد فيه ال + +327 +00:29:58,820 --> 00:30:02,060 +voltage في حالة noise margin low و ال voltage في + +328 +00:30:02,060 --> 00:30:04,980 +حالة noise margin high في حالة ال low زي ما + +329 +00:30:04,980 --> 00:30:07,780 +اتكلمنا عنها عندي ال VIL + +330 +00:30:10,660 --> 00:30:16,200 +-Vol هذه لازم تكون اكبر او بتساوي 0 فانا ال Voh + +331 +00:30:16,200 --> 00:30:22,200 +-Vih بيكون اكبر او بيساوي 0 ايش بنقصد منه فيهم + +332 +00:30:22,200 --> 00:30:27,620 +فرضا انا قاعد بقولك لو في عندى مشكلة كان طلع ال + +333 +00:30:27,620 --> 00:30:32,840 +Vih اكبر من ال Voh بدك تقولي automatic الفان out + +334 +00:30:32,840 --> 00:30:38,510 +بيساوي 0لو طلع ال VOL أكبر من ال VIL بدك تقولي + +335 +00:30:38,510 --> 00:30:42,390 +automatic بدون ما تعمللي أي شغل ال fan out بيساوي + +336 +00:30:42,390 --> 00:30:47,470 +ايش؟ Zero احنا في عهد مهندس المهندس ايش بدي يكون + +337 +00:30:47,470 --> 00:30:55,390 +فيه تدريبه ان الفطن عنده عالية بيحطش مجهود بدون + +338 +00:30:55,390 --> 00:31:03,220 +ضرورةأو بدفعش فلوس على حاجة بتستاهلش نفس المفهوم + +339 +00:31:03,220 --> 00:31:07,040 +هذا اللي بدنا نصله يعني انت متحطش energy أو متحطش + +340 +00:31:07,040 --> 00:31:13,460 +effort على حاجة محلولة لحالها صح؟ خمس سنين عندنا + +341 +00:31:13,460 --> 00:31:19,280 +لازم هذا الفكرة تتبت عندنا كيف بدي أصير من خلال + +342 +00:31:19,280 --> 00:31:22,820 +بعض التدريبات اللي بنقودك فيها أنا قاعد بقول هنا + +343 +00:31:22,820 --> 00:31:27,780 +عندي بالنسبة للي بحكيه ال noise marginقاعد بقول + +344 +00:31:27,780 --> 00:31:31,880 +طيب ال input بدك تذكرها دايما ال input low لازم + +345 +00:31:31,880 --> 00:31:38,860 +يكون اعلى من ال output low طب فرضا انا مش ذاكرها + +346 +00:31:38,860 --> 00:31:49,940 +كيف بدي اعرف فرضا صراحت انسيت كل هذا ممكن هذه لازم + +347 +00:31:49,940 --> 00:31:55,520 +ترجعك لوين للذاكرة تبعتك اذا انطلعتهم طلعت عندك + +348 +00:31:55,520 --> 00:32:00,310 +بال negativeهذه لازم تذكرك على طول تقول اه انا هذه + +349 +00:32:00,310 --> 00:32:04,090 +الدكتور وصاد اذا كان اللي دير فعلك لو انسيت هذه + +350 +00:32:04,090 --> 00:32:07,870 +لازم تردك اذا هذه طلعت عندك بال negative او هذه + +351 +00:32:07,870 --> 00:32:11,550 +بال negative معناته على طول بتقول الفان out في + +352 +00:32:11,550 --> 00:32:22,050 +مشكلة واضح؟ هذه اللي بتخليك ترجع تاني تتذكر فاحنا + +353 +00:32:22,050 --> 00:32:26,450 +بنوصي و بنوصي و بنوصي بس برضه لازم نحط checkin + +354 +00:32:26,450 --> 00:32:30,870 +case هدول كل اللي حكيناها مالقطش في حاجة تانية + +355 +00:32:30,870 --> 00:32:34,670 +لازم تلقط و توقفك هذا إشارة يعني دايما لما تطلع + +356 +00:32:34,670 --> 00:32:40,710 +عندك الإشارة عكس ماتتوقع ماتطنش هاش تقول أنا .. + +357 +00:32:40,710 --> 00:32:45,470 +هذا بتقولك في حاجة غلط إيش الغلط عندك؟ بدك تشوف + +358 +00:32:45,470 --> 00:32:52,540 +إيش اللي كان حاصل موجود هذا واضحة هذه؟طيب إيش ممكن + +359 +00:32:52,540 --> 00:32:57,240 +تاني هاد ال noise margin ماشي الحال هاد بنستخدمها + +360 +00:32:57,240 --> 00:33:01,100 +بشكل كبير و good technique دايما لما أسألك على ال + +361 +00:33:01,100 --> 00:33:05,540 +find out تطلع عن noise margin كويس؟ طلع عليها و + +362 +00:33:05,540 --> 00:33:09,700 +خليها بالك الآن في .. في metric تاني بنسميه noise + +363 +00:33:09,700 --> 00:33:13,280 +sensitivity قداش ال system sensitive لل noise + +364 +00:33:23,330 --> 00:33:27,610 +Noise Sensitivity هي نفس اللي هنا في عندى noise + +365 +00:33:27,610 --> 00:33:31,410 +sensitivity في noise sensitivity في حالة ال low + +366 +00:33:31,410 --> 00:33:37,610 +وفي noise sensitivity في حالة ال high إيش هذه بدها + +367 +00:33:37,610 --> 00:33:45,130 +تساوي هذه بدها تساوي ال VOH minus VM وهذه بدها + +368 +00:33:45,130 --> 00:33:51,790 +تساوي هذه بالنسبة ال high مغير هذا وهذه في حالة ال + +369 +00:33:51,790 --> 00:33:58,390 +lowبيدها تساوي VM-VOL + +370 +00:33:58,390 --> 00:34:05,690 +كويسة الآن اتطلع عندى انا ايش اللى بدياه بدي هذه + +371 +00:34:05,690 --> 00:34:09,850 +المسافة تبقى اكبر اشي ممكن اذا اكبر اشي ممكن + +372 +00:34:09,850 --> 00:34:16,170 +معناته ال tolerance عندى hand بيبقى ايش عالى انا + +373 +00:34:16,170 --> 00:34:24,120 +حكيت في ال logic swing اللى عندىفي هاي هذه بسميها + +374 +00:34:24,120 --> 00:34:29,240 +كتبناها و لا كتبناها V logic swing و هذه بسميها + +375 +00:34:29,240 --> 00:34:35,400 +المسافة Vtr ايش ال logic swing يعني ال logic من + +376 +00:34:35,400 --> 00:34:40,600 +قداش لقداش بيصير له swing يعني قداش ال high و قداش + +377 +00:34:40,600 --> 00:34:44,440 +ال low في حالة ال ideal كانت هذه بتساوي VCC وهذه + +378 +00:34:44,440 --> 00:34:45,260 +بتساوي ايش + +379 +00:34:51,640 --> 00:34:58,140 +أو من السكة للسكة تعبير من السكة للسكة بديش أخلي + +380 +00:34:58,140 --> 00:35:04,460 +مسافة تروح حدر فهذا بسميها V voltage أو logic + +381 +00:35:04,460 --> 00:35:05,440 +swing voltage + +382 +00:35:12,120 --> 00:35:16,320 +اللي هي في شقة ال output قداش المنطقة هذه كل ما + +383 +00:35:16,320 --> 00:35:20,780 +بديها desired هذه تبقى أكبر اشي ممكن هذه المنطقة + +384 +00:35:20,780 --> 00:35:32,020 +بسميها transition width voltage + +385 +00:35:32,020 --> 00:35:35,060 +ولاحظنا + +386 +00:35:35,060 --> 00:35:40,620 +في حالة ال ideal قداش هذه كانت صفرفهذه كل ما فيه + +387 +00:35:40,620 --> 00:35:45,180 +دياهة بديها ايش اصغر ما كده هذه بدي اقللها و هذه + +388 +00:35:45,180 --> 00:35:49,800 +ايش بدي اوسعها الان في ال noise sensitivity في + +389 +00:35:49,800 --> 00:35:54,020 +حالة ال high او ال low هدول ايش بدي اساوي فيهم بدي + +390 +00:35:54,020 --> 00:35:59,100 +اوسعهم الان هدول بيعطوني قيم بإيش ال term of + +391 +00:35:59,100 --> 00:36:03,400 +voltages الان في noise immunity هدول بيعطيني قيم + +392 +00:36:03,400 --> 00:36:08,960 +على شكل percentage يعني هذا بيسميها noise immunity + +393 +00:36:17,650 --> 00:36:24,490 +عندي ال V noise immunity low وفي ال V noise + +394 +00:36:24,490 --> 00:36:30,270 +immunity high فهذا يتساوي V noise sensitivity low + +395 +00:36:30,270 --> 00:36:35,930 +على V logic swing وهذا يتساوي V noise sensitivity + +396 +00:36:35,930 --> 00:36:40,290 +high على V logic swing + +397 +00:36:43,480 --> 00:36:49,620 +هذه الـ maximum ستعطي 50% و هذه الـ maximum 50% + +398 +00:36:49,620 --> 00:36:57,280 +بشكل عام لو هذه الـ maximum و هذه الـ maximum 50% + +399 +00:36:57,280 --> 00:37:00,540 +و هذه الـ maximum 50% و هذه الـ maximum 50% بشكل + +400 +00:37:00,540 --> 00:37:05,540 +عام لو هذه الـ maximum 50% و هذه الـ maximum 50% و + +401 +00:37:05,540 --> 00:37:07,220 +هذه الـ maximum 50% و هذه الـ maximum 50% و هذه + +402 +00:37:07,220 --> 00:37:07,940 +الـ maximum 50% و هذه الـ maximum 50% و هذه الـ + +403 +00:37:07,940 --> 00:37:08,060 +maximum 50% و هذه الـ maximum 50% و هذه الـ + +404 +00:37:08,060 --> 00:37:08,640 +maximum 50% و هذه الـ maximum 50% و هذه الـ + +405 +00:37:08,640 --> 00:37:10,280 +maximum 50% و هذه الـ maximum 50% و هذه الـ + +406 +00:37:10,280 --> 00:37:10,360 +maximum 50% و هذه الـ maximum 50% و هذه الـ + +407 +00:37:10,360 --> 00:37:10,380 +maximum 50% و هذه الـ maximum 50% و هذه الـ + +408 +00:37:10,380 --> 00:37:12,200 +maximum 50% و هذه الـ maximum 50% وكل ما كان ال + +409 +00:37:12,200 --> 00:37:15,900 +sensitivity ايش بتقولي لو هذه كانت صغيرة جدا اقل + +410 +00:37:15,900 --> 00:37:19,280 +noise بتيجي على ال system ايش هتسوى فيه هتغير + +411 +00:37:19,280 --> 00:37:24,260 +الإشارة تبعته فانا بدي ال noise sensitivity تبقى + +412 +00:37:24,260 --> 00:37:27,680 +في عندي margin عالي فيها بحيث لو دخلت إشارة + +413 +00:37:27,680 --> 00:37:31,780 +ماتغيرش ال output تبعي او ماتغيرش هذا في حالة ال + +414 +00:37:31,780 --> 00:37:34,760 +output ماتغيروش لا من high ل low ولا من low ل high + +415 +00:37:34,760 --> 00:37:41,560 +يعني لو كانت هذه الجريبة لل VM مثلا ال VM كانت2.5 + +416 +00:37:41,560 --> 00:37:46,540 +و هذه كانت 2.4 لو أجت point one volt as a noise + +417 +00:37:46,540 --> 00:37:52,900 +بتغيرلي ال output اللي عندى فانا بدي شيها زي هيكا + +418 +00:37:52,900 --> 00:37:59,880 +بدي تكون هذهأكبر قيمة ممكنة بحيث انه انا يصير عندى + +419 +00:37:59,880 --> 00:38:03,440 +ال system بقدر يستوعب ال noise و ال output تبعى + +420 +00:38:03,440 --> 00:38:07,640 +مايتغيرش فهذه بسميها noise sensitivity هذه بتعطينا + +421 +00:38:07,640 --> 00:38:10,580 +إياها term of what؟ voltages ال noise immunity + +422 +00:38:10,580 --> 00:38:13,180 +بتعطينا إياها على شكل percentage لأن إيش أنا + +423 +00:38:13,180 --> 00:38:17,940 +بعمللها؟ بعملها normalization بالظبط هذا واضحة؟ + +424 +00:38:19,860 --> 00:38:24,160 +طيب الآن هنتكلم بعد هيك على ال fan in هيك بنكون + +425 +00:38:24,160 --> 00:38:28,940 +انهينا ال VTC نتكلم على ال fan in و ال fan out + +426 +00:38:28,940 --> 00:38:39,420 +اتفضى ال mid point نص نقطة المنتصف ال VCC + +427 +00:38:39,420 --> 00:38:48,200 +ع اتنين يعني انا اقول لك في هذا بشكل عام كويس؟ اي + +428 +00:38:48,200 --> 00:38:49,160 +سؤال تاني؟ + +429 +00:38:58,080 --> 00:39:03,580 +طيب هنعمل حاجة تانية لان نتكلم على ال fan in و ال + +430 +00:39:03,580 --> 00:39:09,080 +fan out ناخد ال fan in ايش بنقصد فيه هاي عندي + +431 +00:39:09,080 --> 00:39:19,120 +inverter وهي inverter تاني وهي تالت رابع هدول + +432 +00:39:19,120 --> 00:39:27,320 +كلهم كل واحد له تيار مظبوطهي I O I O I O هدولة + +433 +00:39:27,320 --> 00:39:33,200 +كلهم بدهم يدخلوا على ال stage تاني هي I I prime + +434 +00:39:33,200 --> 00:39:40,300 +كويس هيك؟ الان مجموعة هدول بدي ساومين اللي هى + +435 +00:39:40,300 --> 00:39:44,100 +ضربنا example في المحاضرة اللى فاتت لو هى بدي + +436 +00:39:44,100 --> 00:39:51,020 +اتكلم عندى شارع وعندي قداش خمس ست شوارع بتصب في + +437 +00:39:51,020 --> 00:39:55,590 +هذا الشارعالان في وقت الزحمة كل هذه سيارات مليانة + +438 +00:39:55,590 --> 00:39:58,990 +وداخلة على هذا الشارع الشارع هذا هيستوعب كل هذه + +439 +00:39:58,990 --> 00:40:04,270 +السيارات لو كان حجمه كبير جدا عامله مصمم صح الأصل + +440 +00:40:04,270 --> 00:40:08,570 +يستوعب كل هذه السيارات ماكانش مصمم صح مش هيستوعب + +441 +00:40:08,570 --> 00:40:12,850 +هذه السيارات ايش هيصير؟ زحمة delay زي احنا يوم + +442 +00:40:12,850 --> 00:40:16,430 +الجمعة في الجامعة لان نجي كل هيتنا نخلص الصلاة و + +443 +00:40:16,430 --> 00:40:20,970 +نجي كل هيتنا نطلع من الباب ايش بيحصل؟ بيصير queue + +444 +00:40:21,440 --> 00:40:27,100 +وبنستنى لناخد جيل الدور لطلع صح؟ ليش؟ لأن حجم + +445 +00:40:27,100 --> 00:40:33,340 +الباب بساناش كله نطلع مرة واحدة لو مافيش حطاة + +446 +00:40:33,340 --> 00:40:38,100 +وكلها يعني زي ما بيقولوها ساحة ومغطية كله بيطلع + +447 +00:40:38,100 --> 00:40:42,380 +بدون أي مشكلة لاحظت فيه مشكلة؟ لو صليت بساحة كبيرة + +448 +00:40:42,380 --> 00:40:46,100 +بتخلص الصلاة وكله بيضلوا رايح مافيش اي اشكالية بس + +449 +00:40:46,100 --> 00:40:50,140 +مع أنه صار بوابة البوابة لها كباسة معينة اللي بقدر + +450 +00:40:50,140 --> 00:40:55,720 +يطلع منهاكويس؟ هذا نفس الشي احنا ايش بحصل يمكن بعض + +451 +00:40:55,720 --> 00:41:00,000 +منكم في اللي بتسمع ايام الحج النفق في نفق زمان كان + +452 +00:41:00,000 --> 00:41:04,240 +بين .. موجود هو للحق للآن بس الحركة عليه خفيفة بين + +453 +00:41:04,240 --> 00:41:10,020 +منا و مكةالان هذا النفق زمان كان هو الطريق الرئيسي + +454 +00:41:10,020 --> 00:41:14,480 +اللي بتحركوا فيه الحجاج فبتلاقيهم بيطلعوا منه و + +455 +00:41:14,480 --> 00:41:18,980 +بيروحوا ع مكة الان هذا ايه القدرة زي اي شارع هالجد + +456 +00:41:18,980 --> 00:41:22,960 +بيستوعب ناسه الان عادة في الأوضاع اللي مافيش فيها + +457 +00:41:22,960 --> 00:41:26,960 +مشاكل ماتحصلش اشي كل بدخل و بيضل يطلع حصلت اي + +458 +00:41:26,960 --> 00:41:32,220 +مشكلة ايش بيصير بيسموها في اللغة استنبيد استنبيد + +459 +00:41:32,220 --> 00:41:40,450 +يعنيفي إيش صار اندفاع كبير بيقدّي يعني لحوادث + +460 +00:41:40,450 --> 00:41:45,350 +للسنبي فالآن بندفع الكل بيصير اللي بجع ايش بيصير + +461 +00:41:45,350 --> 00:41:49,190 +فيه؟ بيخبطوا عليه و بيبقوا ماشيين بيصير فيه ضحايا + +462 +00:41:49,190 --> 00:41:53,730 +صح؟ الآن نفس الشيء بالنسبة إلنا احنا إيش ضحية لما + +463 +00:41:53,730 --> 00:41:59,340 +ال gate هذه يدخل عليها تيار أكتر منهاتنحرك .. هذا + +464 +00:41:59,340 --> 00:42:03,260 +اللي بنقول .. تنحرك ليش؟ لأنه تقدرش تستوعب اللي + +465 +00:42:03,260 --> 00:42:11,460 +جاي إلها .. كويس؟ هذه .. اللي .. عندي لو هذه قناة + +466 +00:42:11,460 --> 00:42:15,760 +و بتجي منها الميه و هذا الميه كلهيتها بدت تيجي .. + +467 +00:42:15,760 --> 00:42:18,360 +و هذه مش قادرة تستوعب الميه اللي بتجي إلها .. إيش + +468 +00:42:18,360 --> 00:42:22,660 +بيصيرها؟ طوف .. بتطوف .. بتغرق المناطق المحيطة + +469 +00:42:22,660 --> 00:42:28,120 +فيها .. الأنهار بتسير .. الأنهار إلو ..يعني انهار + +470 +00:42:28,120 --> 00:42:32,660 +فرعية او شلالات بتوصل له، لان هذه لما تيجي في وقت + +471 +00:42:32,660 --> 00:42:38,700 +ال .. يعني الوقت اللي خليني اقول اللي فيه التغذية + +472 +00:42:38,700 --> 00:42:46,310 +الرئيسية، فإيش بيحصل؟بطف النهر عن مجراه وبغرق + +473 +00:42:46,310 --> 00:42:50,710 +المناطق اللي حوالها لهذا السبب بيكون انت إذا مصمم + +474 +00:42:50,710 --> 00:42:55,770 +الأمور صح انها بتجه هذا الممر بيقدر يستوعب أكبر + +475 +00:42:55,770 --> 00:43:00,950 +كمية ممكن تحصل فيها worst case scenario كويس وهذا + +476 +00:43:00,950 --> 00:43:05,310 +نفس الشي بالنسبة لها الان اللي بيهمنا أكتر من ال + +477 +00:43:05,310 --> 00:43:08,690 +fan in ال fan out هذا ال fan in ال fan out + +478 +00:43:13,150 --> 00:43:17,770 +أيش بحصل فيها هاي عندى ال gate اللى موجودة هنا + +479 +00:43:17,770 --> 00:43:28,350 +هادى بدها توزع على gate تانية هادى + +480 +00:43:28,350 --> 00:43:39,790 +I N Prime I N Prime I N Prime هنا I Out كويس هادى + +481 +00:43:39,790 --> 00:43:40,790 +بنسميه driver + +482 +00:43:44,480 --> 00:43:49,480 +هذا بنسميه ال load في الكتاب تبعنا ال prime هذه + +483 +00:43:49,480 --> 00:43:54,320 +مقصود فيها ايش ال load هذا بالكتاب ال textbook + +484 +00:43:54,320 --> 00:44:01,280 +تبعنا ال load هي بنحطلها prime الاد اللي عندي + +485 +00:44:01,280 --> 00:44:05,700 +طبيعي هذا زي ما حكينا ان هذا ال gate بتتغدى gates + +486 +00:44:05,700 --> 00:44:12,650 +تانية كام واحدة منهم بتقدر تتغدى مش عارفيعني ممكن + +487 +00:44:12,650 --> 00:44:17,690 +ت .. خلّيني أقول حاجة بنحسها في حياتنا حينا مع + +488 +00:44:17,690 --> 00:44:22,770 +جطعة الكهربا بنحسها بشكل كبير، الآن أنت في البيت + +489 +00:44:22,770 --> 00:44:29,050 +كل إشي بتستنى تشغله، بدك تغسل، بدك تطبخ، بدك تخبص، + +490 +00:44:29,050 --> 00:44:33,550 +بدك .. التلاجة، كل الأجهزة الكهربائية عندك، + +491 +00:44:33,550 --> 00:44:37,910 +الكمبيوتر، التلفاز، كل حاجة بيشتغل وقت إيش، أول ما + +492 +00:44:37,910 --> 00:44:42,310 +تيجي الكهربا كله بيشغل كل إشي، صح؟لأن بدي خلص اللي + +493 +00:44:42,310 --> 00:44:45,750 +عليه أبنك بدي تخلص الغسيلة بدي تخلص كل شي انت في + +494 +00:44:45,750 --> 00:44:48,810 +عندك قراية بدي تخلصها أخوك الصغير بدي يتفرج على + +495 +00:44:48,810 --> 00:44:52,690 +التلفزيون اللي بيستنى فترة فكل الأجهزة بتشتغل مرة + +496 +00:44:52,690 --> 00:44:55,930 +واحدة وده في كوي بيلاحقوها في الكوي كل واحد بدي + +497 +00:44:55,930 --> 00:45:01,190 +خلص اللي عليه ايش اللي بحصل؟ شوية اللي الكهربا + +498 +00:45:01,190 --> 00:45:07,410 +قطعت طب حد فكر ليش قطعت؟ ايش بتقوله؟ + +499 +00:45:09,470 --> 00:45:13,930 +و أنا شغالت كل إشي في بيتي و جاري نفسه و اللي بعده + +500 +00:45:13,930 --> 00:45:18,030 +و اللي بعده و اللي بعده هذا لما اتصمم ال .. ال + +501 +00:45:18,030 --> 00:45:22,850 +Trans صمم يغدي عدد معين من البيوت معروف جديش كل + +502 +00:45:22,850 --> 00:45:27,450 +بيت جديش لازم ياخد انت بتصممه هذا كمهندس كهربا + +503 +00:45:27,450 --> 00:45:28,550 +الأصل مصمم + +504 +00:45:30,800 --> 00:45:35,220 +إذا أنا مصمم صح و حاطة ال Trans هذا صح حتى لو انت + +505 +00:45:35,220 --> 00:45:38,320 +شغالت كل ما عندك ما انت معروف جديش داخلك البيت + +506 +00:45:38,320 --> 00:45:42,000 +بيقدر جديش ياخد بتبقى مصمم على أيش و ما مصممين + +507 +00:45:42,000 --> 00:45:46,600 +بتلاقي بزيادة هذا ال Trans بيستخدم ممكن يغدي خمسين + +508 +00:45:46,600 --> 00:45:51,100 +بيت بروح حاطة سبعين بيت بقول مش معجول كل شكل كل + +509 +00:45:51,100 --> 00:45:55,320 +إشي يعني ياخد ال maximum المتاح له لكل واحد فيهم + +510 +00:45:55,800 --> 00:46:00,580 +فإيش بيحصل في هذا اللحظة لأ الكل اتسخدم كل إشي فهو + +511 +00:46:00,580 --> 00:46:05,060 +ماقدرش انا زي القاعة عنده هذا بتسع سبعين نفر بقول + +512 +00:46:05,060 --> 00:46:10,000 +في عشرة في المية دايما غياب كويس و بنسجل تمانين + +513 +00:46:10,000 --> 00:46:15,100 +طالب فيها أجوا التمانين إيش بيحصل بتسعاش القاعة + +514 +00:46:15,100 --> 00:46:20,000 +مظبوط أو خلي أقوله القاعة بتسع متين و بسجل متين و + +515 +00:46:20,000 --> 00:46:23,220 +خمسين طبعا ضرب يوم من الأيام أجوا المتين و خمسين + +516 +00:46:23,220 --> 00:46:28,150 +بتصير فوضةوهذا اللي محصل عندنا فيها فانا بدا صمم + +517 +00:46:28,150 --> 00:46:33,450 +القاعة مش على أساس اللي بيغيبه او بقول ده مجهش ولا + +518 +00:46:33,450 --> 00:46:38,730 +واحد القاعة مش بتسعة متين وخمسين بتسعة ألف مظبوط؟ + +519 +00:46:38,730 --> 00:46:44,330 +الان اللي بدا تشتغل عليه في التصميم تشتغل انا بسجل + +520 +00:46:44,330 --> 00:46:49,330 +عندى خمسين القاعة بدي تكون فيها خمسين صح؟ هذا ال + +521 +00:46:49,330 --> 00:46:52,970 +Trans بيغدي خمسين بيت صار عندى واحد وخمسين بدي + +522 +00:46:52,970 --> 00:46:58,140 +أركب Trans جديدنفس الشي بالنسبة لهاد .. هاد بنتطلع + +523 +00:46:58,140 --> 00:47:02,820 +عليه كام واحد بيقدر يغزى لأنه انت هناك الأمان تبعه + +524 +00:47:02,820 --> 00:47:05,960 +بنزل ايش .. ايش .. ليش بنزل؟ اذا لاحظت حاجة واحدة + +525 +00:47:05,960 --> 00:47:13,660 +لو في عندك نيون و بدك تضويه او طفا و بدك تضويه لما + +526 +00:47:13,660 --> 00:47:16,960 +تكون الكهربا خلينا نقول الكل مشغل كله بضوي عندك + +527 +00:47:16,960 --> 00:47:22,020 +ليش؟ لو قص ال voltage عندك قداش في البيت بتلاقيه؟ + +528 +00:47:23,420 --> 00:47:28,000 +180 .. 170 .. كل ما زادت البيوت ايش فيه بيصير drop + +529 +00:47:28,000 --> 00:47:32,340 +طب كيف ال voltage drop و الأجهزة شغالة؟ ايش اللي + +530 +00:47:32,340 --> 00:47:39,220 +بيحصل؟ ال power بتنقص؟ الجهاز اللي بده عشرين watt + +531 +00:47:39,220 --> 00:47:43,950 +ليه يشتغل؟ بده يظل عشرين watt ليه يشتغل؟واط يشتغل + +532 +00:47:43,950 --> 00:47:47,950 +بدون 200 اللي بزيد الطيار فانت ال output الطيار + +533 +00:47:47,950 --> 00:47:51,830 +اللي طالع عندى من هنا ال voltage حلاقي ايش بيصيرله + +534 +00:47:51,830 --> 00:47:56,070 +ال drop و الطيار اللي هنا بزيد وانا بزود على هدول + +535 +00:47:56,070 --> 00:48:00,150 +فإيش اللي بيصير عندى انا اتذكر عندى حاجة واحدة ال + +536 +00:48:00,150 --> 00:48:04,900 +output highو لو مظبوط اذا ال .. ال .. ال .. انا + +537 +00:48:04,900 --> 00:48:09,560 +بدأت بمتين و عشرين و عماله كل ما مزود ايش؟ مية + +538 +00:48:09,560 --> 00:48:12,880 +وتسعين، مية وتمانين، مية وخمسين، مية وارفين، لحد + +539 +00:48:12,880 --> 00:48:16,760 +ات منطقة مبطل ايش عندي؟ ايش تغير؟ ايش مبطل عندي + +540 +00:48:16,760 --> 00:48:20,440 +هذا؟ في لغة ال .. ال logic عندي انا بتكلم على high + +541 +00:48:20,440 --> 00:48:25,300 +بضل ينزل من output high لحد ات ما يصير اقل من ال I + +542 +00:48:25,300 --> 00:48:30,460 +ال V I H مظبوط؟ اذا صار اقل من ال V I H صار عندي + +543 +00:48:30,460 --> 00:48:36,510 +high؟بطل عندى high فصار انه انا ال high اللى بدى + +544 +00:48:36,510 --> 00:48:42,850 +هيه مش موصله فمعناته انا حطيت حاجة اكتر او غديت + +545 +00:48:42,850 --> 00:48:47,190 +حاجة اكتر من ما هو مسموحي انا بضل نغذف هدول لحد + +546 +00:48:47,190 --> 00:48:51,770 +ديت ما .. و ال voltage ينزل اخر نقطة عندى ال Vih + +547 +00:48:51,770 --> 00:48:56,230 +لو نزل اقل من ال Vih بيصير عندى ايش هنا مشكلة + +548 +00:48:56,230 --> 00:49:02,720 +معناته هنا بدي اقول ال I outبدي أسوي مجموع الـ I + +549 +00:49:02,720 --> 00:49:08,900 +in prime أو لو قلت ال I in prime هدول المتساويات + +550 +00:49:08,900 --> 00:49:15,480 +بدي أسوي N في I in prime أو بعبارة تانية N بدي + +551 +00:49:15,480 --> 00:49:22,260 +أسوي I outعلى I N Prime هذا المعادلة بتحسبلي قداش + +552 +00:49:22,260 --> 00:49:29,220 +ال .. قداش ال N المسموح فيها زي ما حكيت المرة اللي + +553 +00:49:29,220 --> 00:49:33,840 +فاتت لو كان عندي خط ميه واحد انش و كل واحد .. مرة + +554 +00:49:33,840 --> 00:49:37,760 +روع المدينة تغزى كلها هذا ال inch .. خط ال inch + +555 +00:49:37,760 --> 00:49:45,280 +هذا و كله مسكر حنافيته مش هيوصل لكل البيوتلأن الكل + +556 +00:49:45,280 --> 00:49:51,720 +ايش؟ مسكر لو عشرة فتحوا حنافيتهم راحت الميه و بطل + +557 +00:49:51,720 --> 00:49:58,460 +اتوصل لحاجة فالان بغيث انا الاساس المسموح فيه على + +558 +00:49:58,460 --> 00:50:01,420 +الكل مسكر حنافيته ولا كان واحد فاتح حنافيته و + +559 +00:50:01,420 --> 00:50:05,960 +الميه بتصله الكل + +560 +00:50:05,960 --> 00:50:09,960 +فاتح هذا اللي بقرر فيه فانا اللي بدي اتكلم عليه في + +561 +00:50:09,960 --> 00:50:18,030 +انديهان ان في حالة ال outputhigh و في end في حالة + +562 +00:50:18,030 --> 00:50:22,750 +ال output ايش low في حالة ال output high هنا بتطلع + +563 +00:50:22,750 --> 00:50:29,610 +على ايش ال I out في حالة ال output high على I end + +564 +00:50:29,610 --> 00:50:34,670 +prime في حالة ال output high وهنا بتطلع على I out + +565 +00:50:34,670 --> 00:50:41,310 +في حالة ال output low على I end prime في حالة ال + +566 +00:50:41,310 --> 00:50:47,320 +output lowو من هذه و هذه بدي اختار مين الأكبر ولا + +567 +00:50:47,320 --> 00:50:58,760 +الأصغر ان ماكس بدها تساوي ال minimum ده ايش NOL و + +568 +00:50:58,760 --> 00:51:05,040 +N OH انت زي ما حكيت انت فاكر فيها الكل مسكر + +569 +00:51:05,040 --> 00:51:10,980 +حنافيته العدد جديش infinite الكل فاتحالعدد صار + +570 +00:51:10,980 --> 00:51:16,100 +finite ال finite هو اللي بيحددلي مش ال infinite صح + +571 +00:51:16,100 --> 00:51:23,420 +فهد بيطلع عليهم لو طلعت هد مية و هد عشرين باخد ال + +572 +00:51:23,420 --> 00:51:24,640 +a العشرين + +573 +00:51:27,130 --> 00:51:33,650 +كويس هيك؟ طيب ايش فيه كمان؟ هذا بالنسبة لل fan in + +574 +00:51:33,650 --> 00:51:40,550 +و ال fan out واضحة هذه؟ هذه هندخل فيها كتير يعني + +575 +00:51:40,550 --> 00:51:45,350 +مش مرة ولا تنتين هنظلنا فيها بشكل كبير لحد دي ما + +576 +00:51:45,350 --> 00:51:51,750 +نشوف في الأول و في الآخر إلى وين نوصل فيها الآن + +577 +00:51:51,750 --> 00:51:58,140 +هروح على حاجةبنسميها .. هدولة هنشوفهن بشكل كبير بس + +578 +00:51:58,140 --> 00:52:01,180 +اللي هنتكلم عنه اللي هو ال transient behavior + +579 +00:52:01,180 --> 00:52:04,740 +هنشوفه في جزء المادة، هنركز عليه في الجزء التاني + +580 +00:52:04,740 --> 00:52:08,140 +من المادة لما نتكلم عن ال mosfets ليش؟ لأنه في + +581 +00:52:08,140 --> 00:52:13,800 +علاقة مباشرة يعني بالنسبة لل fan out بهذه ال + +582 +00:52:13,800 --> 00:52:17,960 +property فاحنا بنتكلم على ال transient behavior + +583 +00:52:27,510 --> 00:52:32,990 +أو الـ Transient Characteristics الآن هاي ال input + +584 +00:52:32,990 --> 00:52:36,010 +T + +585 +00:52:36,010 --> 00:52:51,450 +in nanoseconds و هاي V in هاي + +586 +00:52:51,450 --> 00:52:58,470 +T in nanoseconds و هنا V outللـ inverter لما ال + +587 +00:52:58,470 --> 00:53:03,050 +input يبقى high ال output ايش بدي يكون low فهبدأ ب + +588 +00:53:03,050 --> 00:53:09,130 +low فحتى هنعمل sketch هنا عشان نضل احنا تبعين هاي + +589 +00:53:09,130 --> 00:53:14,570 +بدأت ب low الان ال input ايش تغير تغير في ال + +590 +00:53:14,570 --> 00:53:18,350 +output بيصيرش على طول بالظبط بيصير فيه شوية delay + +591 +00:53:18,350 --> 00:53:24,550 +هاي ال delay اللي عنديوبعده بيبدأ يصحب التغير هنا + +592 +00:53:24,550 --> 00:53:29,130 +وصلنا لل maximum ايش هنا بيحصل ال input جلب ال + +593 +00:53:29,130 --> 00:53:36,310 +output هيجلب بس بعد شوية delay هيبدأ يسوي ليه + +594 +00:53:36,310 --> 00:53:41,890 +يتغير الآن اللي بتدرسه هو التالي هنا عندى بالزمن + +595 +00:53:41,890 --> 00:53:50,180 +هاي ال VOH وهذه ال VOLالان بدي اخد عشرة في المية + +596 +00:53:50,180 --> 00:53:57,520 +وتسعين في المية هاي العشرة في المية وهاي التسعين + +597 +00:53:57,520 --> 00:54:05,260 +نايني percent وهاي ال ten percent الان وين بتقاطع + +598 +00:54:05,260 --> 00:54:09,600 +التقاطعات بدي نزل أخطوط + +599 +00:54:23,890 --> 00:54:30,010 +هذه أول جزئية لما نتغير ال input لحد 10% بسميها T + +600 +00:54:30,010 --> 00:54:40,650 +D و بسميها دي delay time كويسة هذا ال delay لحد ما + +601 +00:54:40,650 --> 00:54:47,070 +ال system عرف انه صار تغيير في ال input وهنا + +602 +00:54:47,070 --> 00:54:53,410 +الإشارة لما تروح من 10% ل 90% بسميها ال rise time + +603 +00:54:54,720 --> 00:55:05,060 +تر هي ال rise time كويس هيك؟ الان ال output هان + +604 +00:55:05,060 --> 00:55:10,820 +ايش حصله ال input اتغير بس ال output لسه ماحسش انه + +605 +00:55:10,820 --> 00:55:15,180 +اتغير لحد ديت ما يشعر ان التغير هي بسميها TS هي + +606 +00:55:15,180 --> 00:55:21,020 +نفس مفهوم ال delay بس هان عشان في عند مخزن high او + +607 +00:55:21,020 --> 00:55:26,990 +واحد بقول storage timeالاسم بس اختلف اما هو delay + +608 +00:55:26,990 --> 00:55:30,930 +storage + +609 +00:55:30,930 --> 00:55:35,650 +type + +610 +00:55:35,650 --> 00:55:41,250 +هذا اللي عندي بسميه TF اللي هي من 90% ل 10% بسميه + +611 +00:55:41,250 --> 00:55:43,610 +full type + +612 +00:55:47,440 --> 00:55:52,920 +90% هدولة properties اللي بيهمن فيهم ال TR وال TF + +613 +00:55:52,920 --> 00:55:58,320 +بشكل أساسي ال TR وال TF في نص التانية في المادة + +614 +00:55:58,320 --> 00:56:02,680 +هنشوف كيف نعمله derivation وكيف نجيبه فهذا في له + +615 +00:56:02,680 --> 00:56:07,520 +شغل كتير يعني و هنفرجلكوا إياه بالنسبة لها بس هدق + +616 +00:56:07,520 --> 00:56:12,420 +بها ال TR وال TD او ال TR وال TF مش بالضرورة + +617 +00:56:12,420 --> 00:56:16,380 +يكونوا متساويينبكونوا متساوين في حالة لما تكون + +618 +00:56:16,380 --> 00:56:21,420 +الدائرة عندى ال symmetric بكونوا متساوين نفس الشي + +619 +00:56:21,420 --> 00:56:28,980 +بالنسبة لل Td و Ts واضحة؟ فى حاجة تانية اللى علاقة + +620 +00:56:28,980 --> 00:56:33,140 +بال delay اللى بنتكلم ال propagation delay اللى هى + +621 +00:56:33,140 --> 00:56:34,940 +ال delay من ال stage للتانى + +622 +00:56:39,430 --> 00:56:45,370 +هي اللى عندى من اى stage للتانى هى T ال + +623 +00:56:45,370 --> 00:57:01,850 +nanoseconds هى V in هى T ال nanoseconds هى + +624 +00:57:01,850 --> 00:57:11,350 +V out هذا بحط خط الخمسين في الميةوهنا خط الخمسين + +625 +00:57:11,350 --> 00:57:27,430 +في المية و بنزل من هذه و هذه وين التقاطع هذي + +626 +00:57:27,430 --> 00:57:32,390 +بسميه تي بي تي بي ال propaganda طب كيف ادميز واحدة + +627 +00:57:32,390 --> 00:57:37,020 +فيهم عن إيش التانية؟بطلع ال output ال output هذا + +628 +00:57:37,020 --> 00:57:43,220 +ايش حصل له رايح من وين من low ل high فهذا بقول low + +629 +00:57:43,220 --> 00:57:49,820 +to high هذا اللي عنده رايح من وين من high ل low من + +630 +00:57:49,820 --> 00:57:53,900 +high ل low هاي ال propagation delay هنا من low to + +631 +00:57:53,900 --> 00:57:57,180 +high و من high ل low فى حاجة property بتلزمني + +632 +00:57:57,180 --> 00:58:02,990 +بسميها ال average تبعهم TB averageاللي عندى + +633 +00:58:02,990 --> 00:58:08,630 +بتتساوي TB from low to high زي ال TB from high to + +634 +00:58:08,630 --> 00:58:24,150 +low على اتنين هذا ال propagation delay + +635 +00:58:24,150 --> 00:58:27,770 +time propagation delay time اللي عندى او ال + +636 +00:58:27,770 --> 00:58:31,630 +average propagation delay time كويسك؟ + +637 +00:58:33,900 --> 00:58:38,760 +الان غطينا وضلت عندنا جزئية معينة ايش هي مين + +638 +00:58:38,760 --> 00:58:43,220 +مذكرها power dissipation ايوة ال power dissipation + +639 +00:58:43,220 --> 00:58:47,500 +اللي ضلت عندنا ال power dissipation لما بدي اتكلم + +640 +00:58:47,500 --> 00:58:51,940 +عليه بدي اقول هاي + +641 +00:58:51,940 --> 00:58:58,960 +ال power ال + +642 +00:58:58,960 --> 00:59:05,320 +بالزمني ال average BCC averageاللي هي بديها تساوي + +643 +00:59:05,320 --> 00:59:13,420 +PCC output low زائد PCC output high طب ال power + +644 +00:59:13,420 --> 00:59:20,240 +إيش بتساوي ال volt على الطيار ولا في الطيار بديها + +645 +00:59:20,240 --> 00:59:30,850 +تساوي ICC output low VCC زائد ICC outputoutput + +646 +00:59:30,850 --> 00:59:35,590 +high في ال VCC هذا على اتنين نسيت احطها هي على + +647 +00:59:35,590 --> 00:59:43,150 +اتنين و بدها تساوي ICC output low زائد ICC output + +648 +00:59:43,150 --> 00:59:54,350 +high على اتنين VCC ايش بنقصد بال ICC حد عارف احنا + +649 +00:59:54,350 --> 00:59:58,290 +هنا بنتكلم على ICC ICC ايش بنقصد فيها + +650 +01:00:06,700 --> 01:00:17,160 +هذه النقطة هي VCC وهذه النقطة هي ground الان كل ال + +651 +01:00:17,160 --> 01:00:21,620 +paths اللي بتوصل من VCC + +652 +01:00:27,600 --> 01:00:34,740 +للـ ground هاي بدي اسميه I1 I2 I3 IN كل هدول اللي + +653 +01:00:34,740 --> 01:00:42,320 +بوصلوا من VCC لل ground بسميهم ICC ف ICC بدي ساوي + +654 +01:00:42,320 --> 01:00:50,920 +I1 زائد I2 زائد ربع لحد ديتin اللي عندك كل هدولة + +655 +01:00:50,920 --> 01:00:56,460 +اي path بنزل لو عند واحد جاي من هنا VCC prime لهان + +656 +01:00:56,460 --> 01:01:00,840 +هذا لا يأخد بس لو واحد من هنا رايح لل ground عبر + +657 +01:01:00,840 --> 01:01:07,020 +ال stage تاني ايش بتحسب احسبه هاي ال VCC من VCC لل + +658 +01:01:07,020 --> 01:01:15,260 +ground كل هدول بيعتبروا ايش ICC واضحة هذه؟ عليك + +659 +01:01:15,260 --> 01:01:15,780 +سؤال؟ + +660 +01:01:18,510 --> 01:01:22,430 +طيب ايش ضال عندنا؟ ضال عندنا metric واحد بنسميه ال + +661 +01:01:22,430 --> 01:01:34,210 +power PD اللي هو power delay product اللي بسميه هي + +662 +01:01:34,210 --> 01:01:47,050 +PD بدي ساوي BCC average مضروب في I في T B average + +663 +01:01:50,100 --> 01:01:56,160 +كويسة هاي ال power delay اللي موجود عندى لان اتطلع + +664 +01:01:56,160 --> 01:02:04,320 +ان احنا هنا ايش غطينا اليوم اتكلمنا + +665 +01:02:04,320 --> 01:02:09,680 +في البداية عن ال inverter ID ال inverter اتكلمنا + +666 +01:02:09,680 --> 01:02:15,700 +عنالـ VTC للـ Ideal Inverter واتكلمنا عن الـ VTC + +667 +01:02:15,700 --> 01:02:20,040 +للـ Typical Inverter حددنا الـ Typical Voltages أو + +668 +01:02:20,040 --> 01:02:23,540 +الـ Critical Voltages اللي هي ال input low و ال + +669 +01:02:23,540 --> 01:02:27,780 +input high ال output low و ال output high الآن + +670 +01:02:27,780 --> 01:02:32,640 +قلنا حاجة واحدة تظلنا نتذكرها ان ال VIL لازم تكون + +671 +01:02:32,640 --> 01:02:41,210 +أكبر من ال VOL و الVOH أكبر من VIH عساس انه يظل + +672 +01:02:41,210 --> 01:02:46,830 +عندى الدائرة تشتغل as a digital circuit لو في أي + +673 +01:02:46,830 --> 01:02:51,230 +خلل بيصير عندى مشكلة في ال fan out لان اتحقق من + +674 +01:02:51,230 --> 01:02:55,930 +هاي ولا لو انسيت طلع ال noise margin سواء في حالة + +675 +01:02:55,930 --> 01:03:00,410 +ال low او ال high لازم تبقى positive لو ماكنتش + +676 +01:03:00,410 --> 01:03:05,700 +positive معناته فاش عندىفان اوت اتكلمنا على ال fan + +677 +01:03:05,700 --> 01:03:09,680 +in و ال fan out وقداشى ال maximum fan out اللى + +678 +01:03:09,680 --> 01:03:14,500 +بنتكلم عليه او ال maximum fan in اللى بنتكلم عليه + +679 +01:03:14,500 --> 01:03:20,900 +اتكلمنا بعد هيك على ال transient characteristics + +680 +01:03:20,900 --> 01:03:25,520 +اتكلمنا على ال TF و TR ال rise و ال fall time + +681 +01:03:25,520 --> 01:03:30,690 +اتكلمنا على ال propagation delay time في حالةgoing + +682 +01:03:30,690 --> 01:03:33,430 +from low to high او high to low و اتكلمنا عن ال + +683 +01:03:33,430 --> 01:03:36,870 +average اتكلمنا على ال power dissipation as a + +684 +01:03:36,870 --> 01:03:42,090 +whole و ختمنا في اخر اشي اللي هي ال power delay + +685 +01:03:42,090 --> 01:03:46,630 +product في هذا المجال هيك بيبقى خلصنا chapter واحد + +686 +01:03:46,630 --> 01:03:50,070 +في الكتاب كويس؟ + +687 +01:03:52,110 --> 01:03:57,210 +احنا في .. إذا بتلاحظ كل فكرة chapter فاحنا عندنا + +688 +01:03:57,210 --> 01:04:03,710 +بنوصل ل chapter تلاتة وتلاتين في المادة فماتعدش + +689 +01:04:03,710 --> 01:04:09,370 +ال chapter عد أفكار ال + +690 +01:04:09,370 --> 01:04:13,590 +homework هذا معاكم أسبوع لاتحلوه بتحلوه بتسلموه + +691 +01:04:13,590 --> 01:04:19,850 +يعني كويس؟ في أي تساؤل لكم؟ تفضل + +692 +01:04:23,610 --> 01:04:28,430 +مش fifty ال maximum you can get is fifty تكون أقل + +693 +01:04:28,430 --> 01:04:35,250 +في العشاء هذا اه تفضل انت + +694 +01:04:35,250 --> 01:04:40,750 +ال N max انا في حالة الضروة بقدر ازود عشرة بيوت + +695 +01:04:40,750 --> 01:04:44,670 +كهربا من ال transport و في حالة الاسترخاء بزود + +696 +01:04:44,670 --> 01:04:51,130 +خمسين بحسب حسابي على عشرة ولا خمسينلأو خمسين وكل + +697 +01:04:51,130 --> 01:04:55,850 +شغل اللي عنده في أي لحظة، إيش هيحصل؟ ال Trans + +698 +01:04:55,850 --> 01:05:00,090 +هيفصل، مظبوط؟ مش هتيجي عندك كهربا، انت بدك .. احنا + +699 +01:05:00,090 --> 01:05:04,670 +عندنا هذا لما .. معناه يفصل ان ال gate اللي عندنا + +700 +01:05:04,670 --> 01:05:09,270 +هتنحرج، هل أنا بدي هتنحرج؟ أصمم؟ ولا بصمم على + +701 +01:05:09,270 --> 01:05:10,830 +السيف؟ + +702 +01:05:14,490 --> 01:05:17,870 +الان انا في حال .. لما انا بده احسب عندى، انا + +703 +01:05:17,870 --> 01:05:22,850 +خليني اجيبها على حاجة انت بتحسها، انا في حالة + +704 +01:05:22,850 --> 01:05:28,210 +الدروة عندى كل بيت بده يسحب 16 امبير، كويس؟ انا + +705 +01:05:28,210 --> 01:05:32,410 +اللي طالع من ال trans بده اقول عندى 160 امبير، + +706 +01:05:32,410 --> 01:05:38,260 +كويس؟ معناته كام بيت بيقدر يزود، فهم؟مية و ستين + +707 +01:05:38,260 --> 01:05:42,640 +على .. على ستاش بيعطيني عشرة هذا لو الكل أخد + +708 +01:05:42,640 --> 01:05:49,380 +الستاش فرضه في حالة مش الكل أخد ستاش الكل أخد خمسة + +709 +01:05:49,380 --> 01:05:53,360 +أو تمانية خلينا نقول الرقم أسهل مية و ستين على + +710 +01:05:53,360 --> 01:05:57,640 +تمانية هيعطينا عشرين أنا بصمم على .. أزود عشرة ولا + +711 +01:05:57,640 --> 01:06:04,150 +أزود عشرين؟لأنه لو بتزود على عشرين افرض الكل أخد + +712 +01:06:04,150 --> 01:06:09,390 +الستاش تبعته، إيش محصل؟ في مشكلة زي ما أنا أقول + +713 +01:06:09,390 --> 01:06:14,010 +هنا القاع عندى بتستوعب سبعين كرسى، كويس؟ أنا + +714 +01:06:14,010 --> 01:06:18,470 +بصممها لسبعين طالب ولا مية و أربعين طالب؟ يعني بخل + +715 +01:06:18,470 --> 01:06:22,070 +الشعب أسجل فيها مسموح تسجيل لسبعين ولا مية و + +716 +01:06:22,070 --> 01:06:27,270 +أربعين؟بس بصممهاش بصممها قداش ال maximum اللي بقدر + +717 +01:06:27,270 --> 01:06:31,870 +مش قداش الشعب التقليدية الشعب التقليدية عندى ممكن + +718 +01:06:31,870 --> 01:06:37,250 +توصل في التخصص اقول بتوصل عندى مية بس انا الغرفة + +719 +01:06:37,250 --> 01:06:42,370 +هذه بتسع سبعين ب .. ب .. بحطش انا انه سبعين بقى + +720 +01:06:42,370 --> 01:06:46,050 +اسمح لأكتر من سبعين طالب يسجل اذا انا بدي اشتغل صح + +721 +01:06:46,050 --> 01:06:51,310 +اذا انا بدي اوقفهمو أصبح فيه ناس في الممرات بحط + +722 +01:06:51,310 --> 01:06:55,770 +العدد الكبير بصمم .. بصمم قداش اللي أنا بشوفه + +723 +01:06:55,770 --> 01:07:01,690 +منطقي مش قداش استيعاب الغرفة فانا نفس الشي بالنسبة + +724 +01:07:01,690 --> 01:07:05,730 +لال .. ال .. ال fan out بتطلع على ال maximum اللي + +725 +01:07:05,730 --> 01:07:10,570 +بقدر يزوده في وقت الضروة يعني قداش لو الكل أخد + +726 +01:07:10,570 --> 01:07:15,630 +maximum يعني التيار أخد حصته من التيار قداش بقدر + +727 +01:07:15,630 --> 01:07:23,180 +أوزق عنديكويس؟ اتفضى ال noise immunity هي metric + +728 +01:07:23,180 --> 01:07:28,540 +بيعطيني percentage ال noise نفس ال metric تبع ال + +729 +01:07:28,540 --> 01:07:32,140 +sensitivity بس ال sensitivity بتعطيني voltage ال + +730 +01:07:32,140 --> 01:07:35,940 +immunity بتعطيني percentage لإن بعملها + +731 +01:07:35,940 --> 01:07:41,280 +normalization أيه التفسير تاني؟ طيب بيعطيكوا + +732 +01:07:41,280 --> 01:07:44,840 +العافية و بنشوفكم يوم الأحد ان شاء الله + diff --git a/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/7g_oRcp8Jco_postprocess.srt b/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/7g_oRcp8Jco_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..01be36e17ec25ecc9fecd246f4a71d06d1027093 --- /dev/null +++ b/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/7g_oRcp8Jco_postprocess.srt @@ -0,0 +1,2220 @@ +1 +00:00:20,860 --> 00:00:25,460 +طيب اليوم اللى هنعمله هنكمل في ال chapter 18 المرة + +2 +00:00:25,460 --> 00:00:30,260 +اللى فات تكلمنا على ال VTC وكنا من خلال ال VTC لما + +3 +00:00:30,260 --> 00:00:34,780 +نجيب ال output هو high او ال output low او ال + +4 +00:00:34,780 --> 00:00:38,420 +input high و ال input low و ال midpoint كنا نعمل + +5 +00:00:38,420 --> 00:00:39,940 +ال voltage + +6 +00:00:41,790 --> 00:00:48,350 +في RL نشوف إيش بيساوي اللي هو VDD minus Vout على + +7 +00:00:48,350 --> 00:00:55,230 +RL ونقول ال I RL بدي ساوي ال ID فكنا إذا هذه حلت + +8 +00:00:55,230 --> 00:00:59,190 +جابت لنا المطلوب فكنا نقول كافي ما جابتش كنا ناخد + +9 +00:00:59,190 --> 00:01:04,190 +ال derivative تبع ال ID و ال derivative تبع ال IL + +10 +00:01:04,190 --> 00:01:08,970 +و نسويهم فبصير عندنا معادلتينفي الغالب عندنا ده + +11 +00:01:08,970 --> 00:01:13,670 +فيه مجهول أو اتنين بنقدر نحلهم عبر هذه المعادلتين + +12 +00:01:13,670 --> 00:01:18,390 +الموجودة الآن اليوم بنكمل على شغلتين تانيات + +13 +00:01:18,390 --> 00:01:23,710 +الشغلتين التانيات لأي logic قلنا بلزم نعرف ال VTC + +14 +00:01:23,710 --> 00:01:29,390 +و ال power dissipationو ال fan-out الان نغطي ال + +15 +00:01:29,390 --> 00:01:34,090 +power dissipation و بعدها نغطي ال fan-out اليوم + +16 +00:01:34,090 --> 00:01:41,330 +سنعمل سلسلة derivation للمعادلة كيف نوصل ل .. نربط + +17 +00:01:41,330 --> 00:01:47,790 +ال fan-out مع ال load مع ال capacitors CL تبعتنا + +18 +00:01:47,790 --> 00:01:51,610 +الان لما نطلق لل power dissipation ال power + +19 +00:01:51,610 --> 00:01:53,550 +dissipation انه نوعين نوع ال static + +20 +00:01:56,990 --> 00:02:05,870 +اللي هو بيسمينها BDD average اللي هو بيساوي VDD في + +21 +00:02:05,870 --> 00:02:15,710 +IDD output high زائد ال IDD output low على اتنين + +22 +00:02:15,710 --> 00:02:22,010 +اللي هي نفس الشيء قولنا لل dynamic عند + +23 +00:02:22,010 --> 00:02:24,350 +ال BD9 + +24 +00:02:25,980 --> 00:02:31,300 +بساوي CL اللي هي load capacitor مضروبة ب switching + +25 +00:02:31,300 --> 00:02:38,280 +frequency مضروبة Vdd² الآن ايش بعد هبنا نجيب ال + +26 +00:02:38,280 --> 00:02:45,290 +IDD في حالة output highفي حالة output-high يتساوي + +27 +00:02:45,290 --> 00:02:50,370 +ال ID فال output-high يعني ان ال input بيبقى low + +28 +00:02:50,370 --> 00:02:54,970 +ال input low يعني Vgs أقل من Vt يبقى ال device + +29 +00:02:54,970 --> 00:03:03,410 +بيكون off وال ID off كم بيساويالان لما يقول ال IDD + +30 +00:03:03,410 --> 00:03:11,950 +في وضع ال output low بيساوي ال ID في وضع ال + +31 +00:03:11,950 --> 00:03:19,170 +saturation ال output + +32 +00:03:19,170 --> 00:03:25,530 +low معناه ان input high بيساوي كام VDD ال output + +33 +00:03:25,530 --> 00:03:41,880 +low بيساوي كامVDD VGS-VT أكبر من VDS لما + +34 +00:03:41,880 --> 00:03:49,000 +VGS-VT أكبر من VDS بيكون ال output بيكون ال mode + +35 +00:03:49,000 --> 00:03:53,380 +of operation في وضع linear يبقى هنا بدي أضع linear + +36 +00:03:53,380 --> 00:03:55,480 +مش saturation + +37 +00:03:57,400 --> 00:04:04,560 +وفي وضع اللينير ايش بدى يساوي K Vgs + +38 +00:04:04,560 --> 00:04:15,300 +minus Vt Vds minus one half Vds squared ال Vgs + +39 +00:04:15,300 --> 00:04:24,790 +بتساوي Vdd و Vds بتساوي Volالـ VOL² ومعادلة الـ + +40 +00:04:24,790 --> 00:04:29,710 +VOL موجودة عندك بتطبقها بتبعتيك ال ID Linear وال + +41 +00:04:29,710 --> 00:04:35,610 +ID of I0 يعني ال ID Linear بضربه في نص و بضربه VV + +42 +00:04:35,610 --> 00:04:40,170 +ال VDD بيعطيني ال power dissipation الان نقطة + +43 +00:04:40,170 --> 00:04:47,450 +تانية اللي هنتكلم فيها بعد هيك Dynamic Response + +44 +00:04:49,540 --> 00:04:58,280 +ماذا بنقصد فيها الان عندى هاي ال VDD هاي + +45 +00:04:58,280 --> 00:05:09,320 +ال resistor هاي + +46 +00:05:09,320 --> 00:05:16,740 +عندى ال NO ال transistor هاي VIN وهنا هاي ال Vout + +47 +00:05:17,350 --> 00:05:22,410 +هذه ال R L الان هذه بتبقى مشبوكة مع ايش مع عدة + +48 +00:05:22,410 --> 00:05:31,990 +دوائر ال load بدي ادخلها على هاي + +49 +00:05:31,990 --> 00:05:40,310 +load VDD prime هاي R L prime N O prime الان نفس + +50 +00:05:40,310 --> 00:05:44,250 +الشيء لل load التاني نفس الشيء لل load الاش + +51 +00:05:44,250 --> 00:05:48,990 +التالتةالان كل واحدة من هذه ال load لها gate + +52 +00:05:48,990 --> 00:05:57,930 +capacitors مظبوط CG one prime هنا CG + +53 +00:05:57,930 --> 00:06:02,970 +two prime هاي + +54 +00:06:02,970 --> 00:06:07,210 +ال CG الان هدولة كلها هي ال capacitors واضحهم ايش + +55 +00:06:07,210 --> 00:06:11,550 +parallel صح ال capacitors لما يكونوا واضحهم + +56 +00:06:11,550 --> 00:06:18,630 +parallel نجمحهم جمعفالان بقدر اقول عندى هاي ال VDD + +57 +00:06:18,630 --> 00:06:28,130 +هاي ال load هاي + +58 +00:06:28,130 --> 00:06:35,110 +ال VIN هاي ال Vout هاي ال load capacitor بسميها CL + +59 +00:06:35,110 --> 00:06:42,010 +اللي عندى هاي ال NO هاي ال Vout اللي عندى و ال RL + +60 +00:06:42,010 --> 00:06:43,750 +هاي IL + +61 +00:06:49,010 --> 00:06:57,430 +ICID وعندي ال CL بدها تساوي ال summation لل CG + +62 +00:06:57,430 --> 00:07:01,970 +prime يعني مجموع ال gate capacitance و ال gate + +63 +00:07:01,970 --> 00:07:07,850 +capacitance ايش بتساوي ال W في L في COX prime اللي + +64 +00:07:07,850 --> 00:07:11,490 +موجود عندك الان لما قاعد اتطلعت على هدول ايش بده + +65 +00:07:11,490 --> 00:07:18,150 +اشتغل بعدهاطلع عندى لما يكون ال input وضعه low ايش + +66 +00:07:18,150 --> 00:07:23,650 +بدي يحصل هنا لما يكون ال input low هذا هذا هيكون + +67 +00:07:23,650 --> 00:07:30,650 +وضعه off مظبوط vgs 0 خلينا نقول vgs 0 معناته هذا + +68 +00:07:30,650 --> 00:07:35,750 +هيصير له off عندى capacitor ايش ال capacitor هذا + +69 +00:07:35,750 --> 00:07:42,720 +بدي يصير لها هتصير charging لحد ات ما توصل vddالان + +70 +00:07:42,720 --> 00:07:48,920 +بعد هيك هذا حول من low ل high فهذا صار يشتغل صار + +71 +00:07:48,920 --> 00:07:52,580 +شغال ال capacitor مشحونة في VDD ايش بدي يصير لها؟ + +72 +00:07:54,370 --> 00:07:58,650 +discharging فصارت عملية الهاي charging و + +73 +00:07:58,650 --> 00:08:03,710 +discharging بتعرف ال charging بتاخد وقت مظبوط لحد + +74 +00:08:03,710 --> 00:08:07,490 +ما توصل ل VDD بتاخد في عندي propagate delay و في + +75 +00:08:07,490 --> 00:08:11,250 +عندي rise time لتوصل من عشرة في المية لتسعين في + +76 +00:08:11,250 --> 00:08:15,010 +المية و في حالة التفريغ في عندي propagation delay + +77 +00:08:15,010 --> 00:08:20,930 +و في عندي fall time فانا اليوم شغلتي احسب قداش ال + +78 +00:08:20,930 --> 00:08:25,790 +rise time و قداش ال fall timeواربطه مع ال fan out + +79 +00:08:25,790 --> 00:08:30,430 +كويسك؟ فال derivation تبعاتنا هتم على هذا الأساس + +80 +00:08:30,430 --> 00:08:34,910 +طب لما نيجي نطلع يمكن ال output بدأ اقول عندى لما + +81 +00:08:34,910 --> 00:08:46,590 +كان عندى V in low او high خليني اقول كويس؟ + +82 +00:08:46,590 --> 00:08:51,490 +ايش صار عندى؟ ال + +83 +00:08:51,490 --> 00:09:00,310 +N O كان onمظبوط الان ال VIN و ال GO لإيش ل low ف + +84 +00:09:00,310 --> 00:09:10,130 +ال NO هتصير واضحة off الان هنا ال output كان لما + +85 +00:09:10,130 --> 00:09:18,730 +هدي وضعه شغال وصل لإيش low او VOL الان عندى لما + +86 +00:09:18,730 --> 00:09:21,150 +هدي صارت low بدى يصير عندى ال output + +87 +00:09:24,340 --> 00:09:29,520 +Hi كويس يعني بعبارة تانية لو بتدرسم الرسمة هاي + +88 +00:09:29,520 --> 00:09:38,400 +الرسمة اللي عندى هاي T in nanoseconds هاي VIN هو + +89 +00:09:38,400 --> 00:09:48,280 +راح من high ل low هاي ال VOL وهنا ال VOH ايش اللي + +90 +00:09:48,280 --> 00:09:49,400 +بدى يترتب عليها + +91 +00:09:52,970 --> 00:10:08,190 +شك تاني تي نانو ساكنتس ال output سيروح من low الى + +92 +00:10:08,190 --> 00:10:11,990 +high الان + +93 +00:10:11,990 --> 00:10:18,270 +بهمني ال property التالية هذا في عندي rise time هي + +94 +00:10:18,270 --> 00:10:26,090 +عشرة في المية خلينا نضع بصة الخطوطهذا الـ 10% هذا + +95 +00:10:26,090 --> 00:10:36,410 +الـ 90% وهذا الـ 50% خط الأن انا بدي اخد المسافات + +96 +00:10:36,410 --> 00:10:43,910 +من هنا لهان هذي بسميها TB ال propagation delay هنا + +97 +00:10:43,910 --> 00:10:52,640 +رايح من low ليش ل high او خلينا نحطها هكذاهذا اللي + +98 +00:10:52,640 --> 00:11:04,900 +هنا من عشرة في المية لتسعين في المية هذا بسميه TR + +99 +00:11:04,900 --> 00:11:10,480 +ال rise time كويس فال rise time راح من عشرة في + +100 +00:11:10,480 --> 00:11:14,480 +المية لتسعين في المية ال propagation delay راح من + +101 +00:11:14,480 --> 00:11:25,940 +ال low لحد دي خمسين في الميةهذه بسميها T واحد + +102 +00:11:27,440 --> 00:11:34,900 +هذه لها T2 لهذه وهذه T1' لهذه وهذه T2' لهذه بس + +103 +00:11:34,900 --> 00:11:38,760 +عشان اميز ان كل واحدة لها نقطة بداية في الوقت + +104 +00:11:38,760 --> 00:11:42,920 +ونقطة نهاية في الوقت فانا كل اللي بعمله اذا طلعت + +105 +00:11:42,920 --> 00:11:47,840 +على ال IRL ايش بيساوي في هذا الحالة انا عندي ككل + +106 +00:11:47,840 --> 00:11:56,540 +هان عندي IRL بدي ساوي ID plus ايشICL الان ال ID + +107 +00:11:56,540 --> 00:12:03,220 +لما ال device هذه off ال ID ايش هو Zero فعندي في + +108 +00:12:03,220 --> 00:12:07,580 +هذه الحالة ال device صارت هنا كانت شغالة صارت off + +109 +00:12:07,580 --> 00:12:13,680 +معناته ال ID اللي عندي بدي ساوي Zero معناته IRL + +110 +00:12:13,680 --> 00:12:20,760 +بدي ساوي ICL طب ال IRL ايش بيساوي VDD minus Vout + +111 +00:12:20,760 --> 00:12:30,260 +علىالـ RL هذي بدي ساوي CL في ال DV out على DT كويس + +112 +00:12:30,260 --> 00:12:35,260 +هيك الآن بدي اعمل شوية اللي بنعملها بال math شغلب + +113 +00:12:35,260 --> 00:12:41,240 +هدول هنا شوية math بدي أصير عند ال DT بدي ساوي ال + +114 +00:12:41,240 --> 00:12:48,780 +integral أو قبل ال integral بدي ساوي هي ال CL + +115 +00:13:02,110 --> 00:13:08,830 +الان ناخد ال integration ل both sides من + +116 +00:13:08,830 --> 00:13:17,470 +T1 ل T2 وهذا من V1 ل V2 الان لما ناخد ال + +117 +00:13:17,470 --> 00:13:22,270 +integration ايش بدي يطلع عندىهذه بدي أسميها delta + +118 +00:13:22,270 --> 00:13:40,190 +T التي هي تساوي T2 ناقص T1 تساوي CR في RL خليني + +119 +00:13:40,190 --> 00:13:48,050 +أعوض مباشرة هذا تساوي minus CLRL ال VDD ال natural + +120 +00:13:48,050 --> 00:13:48,630 +log + +121 +00:13:54,150 --> 00:14:02,950 +VDD-V2 VDD-V1 V2 + +122 +00:14:02,950 --> 00:14:03,290 +V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 + +123 +00:14:03,290 --> 00:14:04,330 +V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 + +124 +00:14:04,330 --> 00:14:04,970 +V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 + +125 +00:14:04,970 --> 00:14:05,010 +V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 + +126 +00:14:05,010 --> 00:14:05,050 +V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 V2 + +127 +00:14:05,050 --> 00:14:07,390 +V2 V2 V2 V2 + +128 +00:14:16,170 --> 00:14:26,350 +للـ VDD-V1 على ال VDD-V2 لان نجي نترجمها هذه لحتى + +129 +00:14:26,350 --> 00:14:30,390 +الآن وصلت لل T هذا ال T هذا ال delta T ممكن تكون + +130 +00:14:30,390 --> 00:14:34,430 +ال propagation delay وممكن تكون ال rise time لو + +131 +00:14:34,430 --> 00:14:42,040 +أخدت ال rise time ايش عندي؟V1 V1 هتساوى التالي + +132 +00:14:42,040 --> 00:14:47,200 +كويس انا V1 رايح من VOL لهات يعني زي انا الحين لما + +133 +00:14:47,200 --> 00:14:51,940 +نطلع من الطابق .. كام طابق في المبنى هات؟ ست زيادة + +134 +00:14:51,940 --> 00:14:57,390 +ال bedroom مظبوط؟7 الأن لو قلت لك انت طلعت من + +135 +00:14:57,390 --> 00:15:01,110 +الأرض تنزل تنزل على الأرض و تبقى طالع لا تنزل على + +136 +00:15:01,110 --> 00:15:07,070 +البدرف صح فكل حركتك كام طابق طلعت هتقولي ست طوابق + +137 +00:15:07,070 --> 00:15:12,290 +اللي طلعتهم من الأرض لها مظبوط فالقضية فيها يعني + +138 +00:15:12,290 --> 00:15:15,910 +انه انا بدأ ابدأ من ال rise time لما اقول عشرة + +139 +00:15:15,910 --> 00:15:20,550 +لتسعين فالمئة الحد الأدنى عند VOL مش Zero فانا + +140 +00:15:20,550 --> 00:15:26,430 +ببدأ من VOLV1 تستوي VOL زائد العشرة في المية + +141 +00:15:26,430 --> 00:15:33,290 +العشرة في المية لإيش ل VOH minus VOL زائد عشرة في + +142 +00:15:33,290 --> 00:15:41,730 +المية في VOH minus VOL VOH عبارة عن VDD يعني تستوي + +143 +00:15:41,730 --> 00:15:57,210 +VOL0.1 VDD ناقص 0.1 VOL 0.1 VDD ناقص 0.9 VOL نفس + +144 +00:15:57,210 --> 00:16:08,110 +الشيء ل V2 VOL ناقص 90%فى ال VDD ناقص ال VOL اللى + +145 +00:16:08,110 --> 00:16:16,630 +بدى تساوي عندى 0.9 VDD plus 0.1 VOL الان هدولة بدى + +146 +00:16:16,630 --> 00:16:23,990 +اعوض فيهم ويهان فبدي استخدم ال TR بدى تساوي هى CL + +147 +00:16:23,990 --> 00:16:34,650 +هى RL هى ال natural log ل VDD كلها ناقص 0.1VDD + +148 +00:16:34,650 --> 00:16:47,930 +ناقص point nine VOL على VDD ناقص point nine VDD + +149 +00:16:47,930 --> 00:16:57,850 +ناقص point nine VOL كويس الان او point one هنا ال + +150 +00:16:57,850 --> 00:17:01,190 +VOL الان تطلع عليهم كده تساوي + +151 +00:17:04,230 --> 00:17:09,810 +بتساوي ال CL في ال RL في ال natural log ال VDD قد + +152 +00:17:09,810 --> 00:17:15,630 +يش point واحد هتساوي point تسعة VDD ناقص point + +153 +00:17:15,630 --> 00:17:24,170 +تسعة VOL على point واحد ال VDD ناقص point واحد ال + +154 +00:17:24,170 --> 00:17:31,070 +VOL او بدي ساوي عندى ال CL و ال RL في ال natural + +155 +00:17:31,070 --> 00:17:39,000 +log لقد يش لتسعةده دي اه ال derivation تبعتنا مش + +156 +00:17:39,000 --> 00:17:54,600 +هالصعبة في ال charging العملية مش صعبة ال + +157 +00:17:54,600 --> 00:17:57,780 +TB + +158 +00:17:57,780 --> 00:18:02,320 +من بدي + +159 +00:18:02,320 --> 00:18:03,380 +اعمل فيها ال TB + +160 +00:18:06,310 --> 00:18:14,130 +من low ل high ايش هي عند V1 تساوي VOL V2 تساوي VOL + +161 +00:18:14,130 --> 00:18:25,890 +plus نص VDD minus VOH VOH minus VOL اللي هو عندى + +162 +00:18:25,890 --> 00:18:32,170 +بتساوي نص VDD plus نص VOL + +163 +00:18:35,060 --> 00:18:39,980 +كويس هيك الان دي اعوض فيها فعندي اتصال ال TB from + +164 +00:18:39,980 --> 00:18:46,980 +low to high بدي ساوي هي CL في ال RL في ال natural + +165 +00:18:46,980 --> 00:18:59,400 +log ال VDD minus VOL على VDD minus نص VDD ناقص نص + +166 +00:18:59,400 --> 00:19:07,060 +VOL اللي عندي بدي ساويالـ CLRL في الـ natural log + +167 +00:19:07,060 --> 00:19:17,480 +ل VDD minus VOL على نص VDD ناقص نص VOL اللي هو + +168 +00:19:17,480 --> 00:19:24,760 +ساوي الـ CL في الـ RL في الـ natural log لكده ايش؟ + +169 +00:19:24,760 --> 00:19:29,220 +لتنين لان اتطلع عندي ايش موجود هنا + +170 +00:19:35,530 --> 00:19:41,330 +وين موجودات هدول العلاقة + +171 +00:19:41,330 --> 00:19:48,290 +الموجودة هنا علاقة ايش proportional proportionally + +172 +00:19:48,290 --> 00:19:54,790 +directly ترضي مظبوط كل ما زادت CL بزيد ال rise + +173 +00:19:54,790 --> 00:20:01,350 +time و بزيد ال delay time الان قداش من هدول بقدر + +174 +00:20:01,350 --> 00:20:09,350 +اضيفالـ CL هي عبارة عن مجموع الـ Gate Capacity كده + +175 +00:20:09,350 --> 00:20:13,850 +من هذول المسموح بحيث ان يظلوا عنده الـ TR و ال T + +176 +00:20:13,850 --> 00:20:19,610 +.. خلّيني أقول و ال TA و ال TB from low to high + +177 +00:20:19,610 --> 00:20:26,130 +مقبول يعني لو قلتلك عندك جهاز سرعته عشرة جيجاهرتز + +178 +00:20:26,130 --> 00:20:28,530 +كام second بياخدوا ليعمل ال operation؟ + +179 +00:20:34,670 --> 00:20:47,150 +0.1 نانو ثانية نصبوت 0.1 نانو ثانية نصبوت 0.1 نانو + +180 +00:20:47,150 --> 00:20:53,090 +ثانية نصبوت 0.1 نانو ثانية نصبوتشايف ايش اللي عندى + +181 +00:20:53,090 --> 00:20:58,630 +فهذا اذا بدى احطه ال propagation delay او ال rise + +182 +00:20:58,630 --> 00:21:02,890 +time بدوا يكون اقل من ال fraction تبعه يعني اقل + +183 +00:21:02,890 --> 00:21:07,590 +اذا اتجسم على اربعة اقل من الربع تبع ال point one + +184 +00:21:07,590 --> 00:21:12,260 +nanosecondهذا بيضع لي ال limit على كمية load يكون + +185 +00:21:12,260 --> 00:21:17,360 +لديه لأن كل مزودة load بيزيد عند مين زي ما قلنا ال + +186 +00:21:17,360 --> 00:21:20,660 +capacitance اللي هي ال CL اللي بيساوي مجموع ال + +187 +00:21:20,660 --> 00:21:24,480 +gate capacitance تبعات ال load فلهذا السبب هذا + +188 +00:21:24,480 --> 00:21:30,350 +اللي بربطلي العلاقة بين ال fan outوالـ Capacitors + +189 +00:21:30,350 --> 00:21:35,370 +الموجودة هنا هذا الكلام اللي حكيناه في عملية الشحن + +190 +00:21:35,370 --> 00:21:39,650 +طيب لو صار عملية الان هذا اللي عندى ال output كان + +191 +00:21:39,650 --> 00:21:44,130 +going from low to high طب لو ال input بدل ما هو + +192 +00:21:44,130 --> 00:21:49,220 +high صار إيه؟يعني هنا كان .. بدل ما هو هنا اللون + +193 +00:21:49,220 --> 00:21:53,480 +عكست ال input اللي كان له اللي كان اللي كان اللي + +194 +00:21:53,480 --> 00:21:53,960 +كان اللي اللي كان اللي اللي اللي اللي اللي اللي + +195 +00:21:53,960 --> 00:21:56,240 +اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي + +196 +00:21:56,240 --> 00:21:56,440 +اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي + +197 +00:21:56,440 --> 00:21:56,540 +اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي + +198 +00:21:56,540 --> 00:21:56,900 +اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي + +199 +00:21:56,900 --> 00:22:04,360 +اللي اللي اللي + +200 +00:22:04,360 --> 00:22:10,980 +اللي اللي اللي اللي + +201 +00:22:24,510 --> 00:22:31,370 +عندي هذا ال input كان + +202 +00:22:31,370 --> 00:22:40,670 +عندي low بدي أروح لإيش؟ ل high فال output اللي + +203 +00:22:40,670 --> 00:22:48,870 +هو عندي high بدي أروح لإيش؟ ل low يعني بعبارة + +204 +00:22:48,870 --> 00:22:58,640 +تانية ال NO هذاكان وضعه إذا بنطلع عليه off هيروح + +205 +00:22:58,640 --> 00:23:07,740 +لإيش ل on و ال capacitor هنا ال CL كانت بتعمل + +206 +00:23:07,740 --> 00:23:17,400 +charging هيصيرها إيش يعني + +207 +00:23:17,400 --> 00:23:21,620 +بعبارة تانية التيار اللي بدي يجي بدي يصير إيش في + +208 +00:23:21,620 --> 00:23:29,200 +المعاكسطيب فى هذه الحالة زى ما عملتها انا بدى اعمل + +209 +00:23:29,200 --> 00:23:37,700 +هناك ايش اللى عندى هذه بطلت zero صار عندى ال ID + +210 +00:23:37,700 --> 00:23:46,540 +بدي ساوي IRL ناقص ICL ال IRL بالمقارنة فى هذه + +211 +00:23:46,540 --> 00:23:50,980 +الحالة صغيرة كتير مقارنة مع ايش مع هدول فبقول ايش + +212 +00:23:50,980 --> 00:23:58,260 +هذا اعمله neglectبتهمله بيصير عندي ال ID تقريبا + +213 +00:23:58,260 --> 00:24:08,060 +بيساوي سالب ال ICL طب ال ID في وضع ال on هذا بدي + +214 +00:24:08,060 --> 00:24:17,160 +ساوي minus CL في ال DV out على ال DT او زي ما + +215 +00:24:17,160 --> 00:24:24,200 +عملنا هناك ال DT بيبقى تساوي سالب CL في ال DV out + +216 +00:24:24,770 --> 00:24:34,810 +على ال ID on الان طلع عندى ايش اللى بحصل انا عندى + +217 +00:24:34,810 --> 00:24:43,930 +بديت بحاجة بديت ب VIN يدوب اكبر من مين من ال VT + +218 +00:24:43,930 --> 00:24:50,730 +كويس لما يدوب كان هو off هذا الكباسور شحنة ل VDD + +219 +00:24:50,730 --> 00:24:56,980 +الكباسور هنا موجودة فيها كده تشارجVDD او بعبارة + +220 +00:24:56,980 --> 00:25:05,440 +تانية VDS هنا بتساوي VDD الان VGS كانت low و + +221 +00:25:05,440 --> 00:25:10,280 +يدوبها اشتغلت يعني يدوبها اكبر من VT يعني بعبارة + +222 +00:25:10,280 --> 00:25:17,660 +تانية VGS minus VT يدوبها اكبر من Zero و قلت VDS + +223 +00:25:17,660 --> 00:25:24,180 +هو حوالين ال VDDيعني احنا ال device اشتغلت في اي + +224 +00:25:24,180 --> 00:25:28,700 +mode of operation صارت اذا عندي Vgs minus Vt يدوب + +225 +00:25:28,700 --> 00:25:37,060 +اكبر من zero و Vds تقريبا حوالين Vdd يعني Vds اكبر + +226 +00:25:37,060 --> 00:25:41,800 +من Vgs minus Vt في اي mode of operation + +227 +00:25:46,540 --> 00:25:53,260 +Vgs أكبر من Vt فال device is on بس Vgs minus Vt + +228 +00:25:53,260 --> 00:26:00,040 +يدوبها أكبر من zero و Vds Vds هي أكبر منهم وهي + +229 +00:26:00,040 --> 00:26:05,920 +اللي بتساوي تقريبا Vdd يعني Vdd أكبر من ال zero + +230 +00:26:05,920 --> 00:26:11,490 +مظبوط طيب الآن فأي mode هذههاتول من الشغلات + +231 +00:26:11,490 --> 00:26:16,390 +الضرورية تاخدهم من chapter 16 و 17 و 18 و 19 و 20 + +232 +00:26:16,390 --> 00:26:20,670 +كيف بيشتغلوا ال mode of operations لازم تاخدهم و + +233 +00:26:20,670 --> 00:26:24,930 +تحفظهم و المعادلات تبعات ال linear و ال saturation + +234 +00:26:24,930 --> 00:26:31,070 +الان احنا قولنا لما VDS اكبر من VGS minus VT بنقول + +235 +00:26:31,070 --> 00:26:35,570 +ال device وضعه saturation الان انا ببدأ في ال + +236 +00:26:35,570 --> 00:26:40,390 +device و بوضع saturation الان هذه هتصير فيها ايش + +237 +00:26:41,640 --> 00:26:47,780 +هتصير discharge هتنزل و ال VIN هيوصل ل VDD لما ال + +238 +00:26:47,780 --> 00:26:53,000 +VIN بيساوي VDD و هذه عمالها بتنزل طلع لعند ال VIN + +239 +00:26:53,000 --> 00:27:00,360 +VIN بيساوي VDD يعني VIN minus VT بيساوي كام VDD + +240 +00:27:00,360 --> 00:27:08,830 +minusبتنزل مجرد ما هيتصير اصغر من vdd minus vtn + +241 +00:27:08,830 --> 00:27:14,410 +هيتحول ال mode لأن هذا ايش صارت ال vgs minus vt + +242 +00:27:14,410 --> 00:27:21,150 +صارت اكبر من ال vds اذا اكبر من ال vds معناته + +243 +00:27:21,150 --> 00:27:25,310 +هتحول ل linear فمعناته هنا عندى two modes of + +244 +00:27:25,310 --> 00:27:30,900 +operation هيصير عندى واحدسأبدأ بالـ Saturation ثم + +245 +00:27:30,900 --> 00:27:34,900 +أحول بالـ Linear يعني لاخد ال integration ل both + +246 +00:27:34,900 --> 00:27:48,060 +sides من T3 ل T4 T3 ل T4 ل T4 + +247 +00:27:48,060 --> 00:27:49,420 +ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 + +248 +00:27:49,420 --> 00:27:52,060 +ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 + +249 +00:27:52,060 --> 00:27:56,860 +ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 + +250 +00:27:56,860 --> 00:27:57,160 +ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 ل T4 + +251 +00:27:57,160 --> 00:28:09,240 +ل T4من T3 ل VDD minus VT هي ال minus CL DV out على + +252 +00:28:09,240 --> 00:28:19,420 +ID saturation ناقص هي ال integral من VDD minus VT + +253 +00:28:19,420 --> 00:28:32,550 +ل V4 وهي ال CL في ال DV outعلى ال ID Linear او + +254 +00:28:32,550 --> 00:28:36,850 +بعبارة تانية بقدر اقول عندى ال Delta T صارت بتساوي + +255 +00:28:36,850 --> 00:28:46,510 +Delta T Sat زائد Delta T لمية لل Linear ده انا + +256 +00:28:46,510 --> 00:28:49,290 +بتكلم عن ال saturation و ال linear بهذه الشغله + +257 +00:28:49,290 --> 00:28:54,770 +بتاخد كل جزئية لحالة الان الجزئية هذه لحالة ال + +258 +00:28:54,770 --> 00:29:07,020 +Delta Tدلتا تي سات تساوي سالب CL انتجرال من T3 ل + +259 +00:29:07,020 --> 00:29:19,600 +VDD-VT دي V out المعادلة تبعت IDSAT نص + +260 +00:29:19,600 --> 00:29:21,740 +K + +261 +00:29:23,270 --> 00:29:34,330 +Vgs-Vt² Vgs-Vt² Vgs-Vt² Vgs-Vt² Vgs-Vt² Vgs-Vt² + +262 +00:29:34,330 --> 00:29:34,410 +Vgs-Vt² Vgs-Vt² Vgs-Vt² Vgs-Vt² Vgs-Vt² Vgs-Vt² + +263 +00:29:34,410 --> 00:29:34,510 +Vgs-Vt² Vgs-Vt² Vgs-Vt² Vgs-Vt² Vgs-Vt² Vgs-Vt² + +264 +00:29:34,510 --> 00:29:44,970 +Vgs-Vt² Vgs-Vt² Vgs-Vt² Vgs-Vt² Vgs-Vt² Vgs-Vt² + +265 +00:29:44,970 --> 00:29:59,750 +Vgs-Vt² VgsVDD-VT VDD + +266 +00:29:59,750 --> 00:30:09,870 +-VT VOUT VDD + +267 +00:30:09,870 --> 00:30:12,570 +-VT + +268 +00:30:19,340 --> 00:30:28,340 +هي عبارة عن V out evaluated at VDD minus VT و V3 + +269 +00:30:28,340 --> 00:30:35,620 +كويس هيك؟ هذا الجزء السهل اللي حليته في المعادلة + +270 +00:30:35,620 --> 00:30:42,200 +هنا في تربيع هنا، مظبوط في هنا عند التربيع + +271 +00:30:45,530 --> 00:30:49,310 +كويس هي تظل جزء التاني اللي هو تبع من ال linear + +272 +00:30:49,310 --> 00:30:57,330 +فجزء ال linear هي delta T في + +273 +00:30:57,330 --> 00:31:03,970 +ال linear ايش بدها تساوي بدها تساوي هاي السالب CL + +274 +00:31:03,970 --> 00:31:13,490 +ال integral من VDD minus VT ل V4 عندي ال DV outعلى + +275 +00:31:13,490 --> 00:31:27,190 +ال ID Linear ايش بيساوي K Vgs-Vt Vds-1.5 Vds2 طيب + +276 +00:31:27,190 --> 00:31:37,610 +ايش عندي ال Vgs بتساوي Vdd هنا وهذه بتساوي Vout + +277 +00:31:37,610 --> 00:31:40,570 +وهذه Vout + +278 +00:31:48,250 --> 00:31:53,030 +DVout DVout DVout DVout DVout DVout DVout DVout + +279 +00:31:53,030 --> 00:31:57,170 +DVout DVout DVout DVout DVout DVout DVout DVout + +280 +00:31:57,170 --> 00:31:58,390 +DVout DVout DVout DVout DVout DVout DVout DVout + +281 +00:31:58,390 --> 00:31:58,410 +DVout DVout DVout DVout DVout DVout DVout DVout + +282 +00:31:58,410 --> 00:31:58,470 +DVout DVout DVout DVout DVout DVout DVout DVout + +283 +00:31:58,470 --> 00:31:58,490 +DVout DVout DVout DVout DVout DVout DVout DVout + +284 +00:31:58,490 --> 00:31:58,510 +DVout DVout DVout DVout DVout DVout DVout DVout + +285 +00:31:58,510 --> 00:32:02,790 +DVout DVout DVout DVout DVout DVout DVout DV + +286 +00:32:06,570 --> 00:32:10,530 +فلو طلع ال natural log هتعطيني هذا بالظبط التالي + +287 +00:32:10,530 --> 00:32:17,430 +عشان أنصيه لكم إياها بدها تساوي سالب + +288 +00:32:17,430 --> 00:32:22,230 +CL على + +289 +00:32:22,230 --> 00:32:32,350 +K VDD minus VT في ال natural log لل V out على + +290 +00:32:34,280 --> 00:32:43,740 +الـ VDD-VT- نص Vout اللي + +291 +00:32:43,740 --> 00:32:56,800 +عندي evaluated at V2 VDD- VT كويسيك؟ + +292 +00:32:57,830 --> 00:33:03,670 +الان هذه بدها تساوي لما نعملها evaluation minus CL + +293 +00:33:03,670 --> 00:33:12,730 +على K VDD minus VT هاي أفتح جوس هاي ال natural log + +294 +00:33:12,730 --> 00:33:20,350 +لل V أو التعوض عنها في أول حاجة V2 على VDD minus + +295 +00:33:20,350 --> 00:33:24,370 +VT minus نص V2 + +296 +00:33:27,950 --> 00:33:40,710 +هيناقص ال natural log ل Vdd minus Vt على Vdd minus + +297 +00:33:40,710 --> 00:33:53,050 +Vt minus نص Vdd minus نص أو زائد نص Vt إيش هذا + +298 +00:33:53,050 --> 00:33:58,760 +بتعطيني؟نص ال quantity اللي فوق معناته هذا الرقم + +299 +00:33:58,760 --> 00:34:05,620 +بتعطينا ال natural log ل 2 الان + +300 +00:34:05,620 --> 00:34:10,220 +اي حاجة اقسمها بال natural log ل 2 ايش هتعطيني؟ + +301 +00:34:10,220 --> 00:34:15,760 +بدي اقسم هذا ال natural على 2 فهذه بتتساوي سالب CL + +302 +00:34:15,760 --> 00:34:23,480 +على K VDD minus VT في ال natural log + +303 +00:34:32,000 --> 00:34:44,420 +VDD-2VT-V2 VDD-2VT-V2 VDD-2VT-V2 VDD-2VT + +304 +00:34:44,420 --> 00:34:51,160 +-V2 VDD-2VT-V2 VDD-2VT-V2 VDD-2VT-V2 VDD-2VT-V2 + +305 +00:34:51,160 --> 00:34:51,180 +VDD-2VT-V2 VDD-2VT-V2 VDD-2VT-V2 VDD-2VT-V2 VDD + +306 +00:34:51,180 --> 00:34:52,700 +VDD-2VT-V2 VDD-2VT-V2 VDD-2VT-V2 VDD-2VT-Vبرضه ال + +307 +00:34:52,700 --> 00:34:57,740 +CL هيها موجودة مع علاقة هنا ال CL وال CL موجودين + +308 +00:34:57,740 --> 00:35:00,040 +هذول اللي هم علاقة إيش تفضل + +309 +00:35:02,240 --> 00:35:06,800 +اللي هان الان هذه ال natural ناقص ال natural على + +310 +00:35:06,800 --> 00:35:10,100 +اتنين ال natural على اتنين لما ناخد ال natural اغ + +311 +00:35:10,100 --> 00:35:13,540 +على اتنين ايش معناته؟ بدي اقسم بممكن ادخلها جوا + +312 +00:35:13,540 --> 00:35:17,940 +هان كيف بدخلها جوا هان ال natural ناقص ال natural + +313 +00:35:17,940 --> 00:35:23,760 +عملية ال natural القيمة هاد بقسمها على ال هاد لو + +314 +00:35:23,760 --> 00:35:28,150 +كانت plus بضربفالقسمة بنزل القسمة بدها تصير إيش + +315 +00:35:28,150 --> 00:35:31,430 +بدها تيجي في هان هاي اتنين هان اتنين هان و اتنين + +316 +00:35:31,430 --> 00:35:39,710 +فى النص ده هتعطينا إيش واحد هان كويس هيك طيب الآن + +317 +00:35:39,710 --> 00:35:43,330 +زى ما عملت قبل شوية بدي أعمل لهدول برضه بنفس + +318 +00:35:43,330 --> 00:35:47,450 +الطريقة الآن عندي أنا هان ده بتطلع على الرسمة + +319 +00:35:47,450 --> 00:35:52,570 +تبعتى إيش موجود موجود + +320 +00:35:52,570 --> 00:35:53,870 +هاي input + +321 +00:35:59,530 --> 00:36:06,250 +هي T in nanoseconds هاي VIN مظبوط هو ال VIN going + +322 +00:36:06,250 --> 00:36:17,410 +from low to high هاي ال VOH هاي ال VOL ال output + +323 +00:36:17,410 --> 00:36:22,510 +هيروح + +324 +00:36:22,510 --> 00:36:26,030 +هو هنا وضعه هاي ال Vout + +325 +00:36:29,760 --> 00:36:36,800 +الانبوت هيه من low رايح ل high ال output بده يروح + +326 +00:36:36,800 --> 00:36:43,320 +من high ل low فال output شكله بده يبدأ من high و + +327 +00:36:43,320 --> 00:36:45,740 +بعد هيك عند هذا النقطة بده يروح + +328 +00:36:48,330 --> 00:36:54,810 +لو هاي ال VOL اللي عندى هاي ال VOH اللى موجود عندى + +329 +00:36:54,810 --> 00:36:58,570 +زى ما عملت قبل شوية بدي اعمل الخطوط تبعته العشرة + +330 +00:36:58,570 --> 00:37:03,250 +في المية والتسعين هاي + +331 +00:37:03,250 --> 00:37:08,150 +ال nine percent هاي + +332 +00:37:08,150 --> 00:37:18,830 +العشرة ten percent هاي الخمسين50% الان بدي اجيال + +333 +00:37:18,830 --> 00:37:24,750 +ال T هاي عندي هاي + +334 +00:37:24,750 --> 00:37:33,250 +قيمة هاي التانية هاي التالتة هاي الرابعة الان هذه + +335 +00:37:33,250 --> 00:37:39,890 +منهذا النقطة لخمسين فلمية سميتها TB from high to + +336 +00:37:39,890 --> 00:37:46,530 +low هذا النقطة من هذه لهذه سميتها TF من عشرة فلمية + +337 +00:37:46,530 --> 00:37:51,530 +من تسعين فلمية لعشرة فلمية يعني بعبارة تانية اللي + +338 +00:37:51,530 --> 00:37:56,870 +بدي أجيبه بدي أقول هاي عندي ال TF إيش بدها تساوي + +339 +00:37:56,870 --> 00:38:03,730 +في عندها حاجتين V تلاتة و V أربعة طب إيش V تلاتة + +340 +00:38:03,730 --> 00:38:12,000 +بتساويبتساوي ال VOL زائد point nine في قداش ال VOH + +341 +00:38:12,000 --> 00:38:18,720 +minus ال VOL وال VOH هي عبارة عن ال VDD فابدها + +342 +00:38:18,720 --> 00:38:31,560 +تعطيني هنا point واحد او point nine VDD هنا زائد + +343 +00:38:31,560 --> 00:38:39,210 +point onevol نفس الشي هان بديها تساوي vol زائد + +344 +00:38:39,210 --> 00:38:44,290 +point واحد vdd + +345 +00:38:44,290 --> 00:38:52,550 +minus vol بدي ساوي point واحد vdd plus point nine + +346 +00:38:52,550 --> 00:39:01,230 +الvol هذه النقاط بالنسبة لل fold time بالنسبة لل + +347 +00:39:01,230 --> 00:39:05,220 +propagation delayعن طريق الوصول الى الـ Tb from + +348 +00:39:05,220 --> 00:39:11,960 +high to low عن طريق الوصول + +349 +00:39:11,960 --> 00:39:16,640 +الى Tb + +350 +00:39:16,640 --> 00:39:19,700 +from high to low عن طريق الوصول الى Tb from high + +351 +00:39:19,700 --> 00:39:20,820 +to low عن طريق الوصول الى Tb from high to low عن + +352 +00:39:20,820 --> 00:39:23,040 +طريق الوصول الى Tb from high to low عن طريق الوصول + +353 +00:39:23,040 --> 00:39:23,100 +الى Tb from high to low عن طريق الوصول الى Tb from + +354 +00:39:23,100 --> 00:39:23,460 +high to low عن طريق الوصول الى Tb from high to low + +355 +00:39:23,460 --> 00:39:23,660 +عن طريق الوصول الى Tb from high to low عن طريق + +356 +00:39:23,660 --> 00:39:24,040 +Tb from high to low عن طريق الوصول الى Tb from + +357 +00:39:24,040 --> 00:39:27,720 +high to low عن طريق الوصول الى Tb from high to low + +358 +00:39:27,720 --> 00:39:31,460 +عن طريق الوصول الى Tb fromVol الان بدى اعوض في + +359 +00:39:31,460 --> 00:39:33,960 +المعادلات هذا اللي لك هو اشوف كده ايش بيطلع عندى + +360 +00:39:33,960 --> 00:39:38,140 +اعوض في هدول هذه الجزء و هذا الجزء هدول اللي + +361 +00:39:38,140 --> 00:39:42,340 +بيكونوني هدى و هدى بتكون لي ال delta T بدى اعوض في + +362 +00:39:42,340 --> 00:39:47,920 +ال delta T لحالة ال TF و حالة ال حالة التانية + +363 +00:39:47,920 --> 00:39:49,360 +دعونا نشوف ايش بيطلع عندى + +364 +00:39:53,730 --> 00:40:02,670 +شكل المعادلات هنا كبير عشان هي كده فال TF بدها + +365 +00:40:02,670 --> 00:40:07,210 +تساوي الجزء الأولاني لما نعوض فيه هنا بدعوض بدل + +366 +00:40:07,210 --> 00:40:13,980 +مينبدي اعوض بدل V3 هاي V3 اللي عندي لهادي بدي اعوض + +367 +00:40:13,980 --> 00:40:17,860 +في القيم هذا انا هعطيك ال forum جاهز لان انا + +368 +00:40:17,860 --> 00:40:22,020 +مابديش اظل نشايل ال package هذه كلها و اناقل فيها + +369 +00:40:22,020 --> 00:40:34,440 +بس بنقشها يعني ف ال TF بتساوي CL على K مضروبة + +370 +00:40:38,740 --> 00:40:49,980 +تو VT plus point one VOL minus + +371 +00:40:49,980 --> 00:40:54,740 +point + +372 +00:40:54,740 --> 00:41:06,520 +one VDD على VDD minus VT squared زائد + +373 +00:41:10,600 --> 00:41:20,060 +1 على VDD minus VT الـ Natural Log للـ 1.9 VDD + +374 +00:41:20,060 --> 00:41:33,740 +minus 2 VT minus 0.9 VOL على 0.1 VDD plus 0.9 VOL + +375 +00:41:35,600 --> 00:41:42,920 +هذه جزئية الـ TF نفس الشيء يعمل للـ propagation + +376 +00:41:42,920 --> 00:41:50,990 +delay timetb from high to low بدي ساوي two cl vt + +377 +00:41:50,990 --> 00:42:05,250 +على k vdd minus vt square plus cl على k vdd minus + +378 +00:42:05,250 --> 00:42:24,670 +vt في ال natural log ل one point five-2VDD-2VT-1 + +379 +00:42:24,670 --> 00:42:26,370 +.5VOL + +380 +00:42:37,350 --> 00:42:41,790 +الرسمة المعادلة .. معادلة هان أكبر معادلة هتشوف + +381 +00:42:41,790 --> 00:42:48,110 +تمشي فيها بس هذه من الشغلات الهينة ليش؟ لإن ان انت + +382 +00:42:48,110 --> 00:42:54,070 +خد K وخد CL و VT و VDD تصير عملية استخدم ال + +383 +00:42:54,070 --> 00:42:54,990 +calculator عدل + +384 +00:43:01,050 --> 00:43:05,310 +فالقصد منها أهم نقطة اللى بدك تشوفها هي عند ال CL + +385 +00:43:05,310 --> 00:43:10,890 +وعند ال CL الموجودة يعنى كل ما بزود قيمة CL كل ما + +386 +00:43:10,890 --> 00:43:15,250 +إلها تأثير على ال fan out في ال chapters الجاية + +387 +00:43:15,250 --> 00:43:21,510 +هفرجيكوا بشكل عام كيف نعمل التصميماليوم ال .. ال + +388 +00:43:21,510 --> 00:43:24,630 +.. ال .. حتى الآن اللي عملنا ايش هو في هذه في ال + +389 +00:43:24,630 --> 00:43:29,410 +dynamic response احنا بدنا نجيب قيمة ال .. سواء ال + +390 +00:43:29,410 --> 00:43:33,070 +TF او TR او ال propagation delay سواء من ال high + +391 +00:43:33,070 --> 00:43:37,690 +او من ال low هو مربوط بعملية شحن وتفريغ ال + +392 +00:43:37,690 --> 00:43:40,770 +capacitor اللي موجودة عندنا وعملنا شوية math + +393 +00:43:40,770 --> 00:43:44,570 +derivation وصلنا لهذه طب الآن لو في الدائرة اللي + +394 +00:43:44,570 --> 00:43:47,630 +عندي حصلت تالي خليني بس + +395 +00:44:06,570 --> 00:44:10,130 +عشان في كل الرسمات اللي بنرسمها في عندنا هالشغلة + +396 +00:44:10,130 --> 00:44:16,990 +هاي عندي ال + +397 +00:44:16,990 --> 00:44:17,550 +VDD + +398 +00:44:43,160 --> 00:44:48,280 +إيش اختلف؟ نقش + +399 +00:44:48,280 --> 00:44:55,040 +هذا، إيش .. إيش اللي اختلف عندي؟ طب إيش هاد هتعمل؟ + +400 +00:44:55,040 --> 00:44:59,140 +هت + +401 +00:44:59,140 --> 00:45:01,100 +.. هتأثر على حاجة هاد؟ + +402 +00:45:05,850 --> 00:45:11,510 +انت الان عندي ايش هنا الموجود؟ Vborg صح؟ ال Vborg + +403 +00:45:11,510 --> 00:45:19,870 +عبارة عن ايش؟ بيأثر في اي حاجة؟ تكلمنا عنها؟ + +404 +00:45:19,870 --> 00:45:23,070 +الان السؤال اللي ماحكناش عنه، السؤال اللي ماحكناش + +405 +00:45:23,070 --> 00:45:30,130 +عن ال Vborg الان انا عندي خلينا نقول قطب مغناطيسي، + +406 +00:45:30,130 --> 00:45:34,290 +هذا قطب جنوبيالان لو حطيت على الشجرة التانية قطب + +407 +00:45:34,290 --> 00:45:38,830 +شمال ايش بيسوي؟ بشدب، لو حطيت قطب جنوبي ايش بدي + +408 +00:45:38,830 --> 00:45:42,870 +اعمل؟ هينافر فيها، هيبعدهم، الان انا في ال + +409 +00:45:42,870 --> 00:45:47,390 +substrate في ال most fits ال majority career ايش + +410 +00:45:47,390 --> 00:45:47,810 +هي؟ + +411 +00:45:50,740 --> 00:45:54,380 +خلينا نقول ايش نوع ال material تبعات ال substrate + +412 +00:45:54,380 --> 00:45:58,440 +بيه material ف ال majority holes و ال minority ايش + +413 +00:45:58,440 --> 00:46:03,480 +electrons الان لو انا حطيت على ال bulk ع شقة ال + +414 +00:46:03,480 --> 00:46:08,960 +bulk حطيت negative source ايش هيعملي؟ هيشدب كل ال + +415 +00:46:08,960 --> 00:46:13,280 +holes و يعملي تنافر لمين ال electrons هيبعتهم فوق + +416 +00:46:13,280 --> 00:46:17,300 +اذا راحوا ال electrons لفوق يعني راحوا ع شقة ال + +417 +00:46:17,300 --> 00:46:21,730 +channel صح؟فانا زوّدت ال electrons اللي رايحة على + +418 +00:46:21,730 --> 00:46:23,990 +ال channel كل ما زوّدت ال voltage ال negative + +419 +00:46:23,990 --> 00:46:28,610 +voltage هناك كل ما زادت ايوة الان لو حطيت positive + +420 +00:46:28,610 --> 00:46:33,650 +voltage ايش هيعمله ال holes هتطلع على فوق و هيشدف + +421 +00:46:33,650 --> 00:46:39,030 +ال electrons فانا بأثر على اللي هاي الان في معادلة + +422 +00:46:39,030 --> 00:46:43,250 +احنا قولنا ال threshold voltage ايش بتساوي في + +423 +00:46:43,250 --> 00:46:48,790 +معادلة ال threshold voltage بتساوي التالت Vtبتساوي + +424 +00:46:48,790 --> 00:46:59,590 +VT0 plus Gamma L في ال square root ل2VF plus VPS + +425 +00:46:59,590 --> 00:47:03,730 +minus square root ل2VF + +426 +00:47:05,620 --> 00:47:10,640 +هذه المعادلة الان لو كانت vps بتساوي زيرو يعني + +427 +00:47:10,640 --> 00:47:15,080 +الاتنين ال bulk و ال source مشبوكين مع بعض احنا كل + +428 +00:47:15,080 --> 00:47:18,960 +اللي شفناه كنا ال bulk و ال source مشبوكين مع بعض + +429 +00:47:18,960 --> 00:47:23,320 +بتساوي زيرو معناته عند ال vt بتساوي ال vt zero + +430 +00:47:23,320 --> 00:47:27,340 +اللي هي threshold under zero biasing الان لو انا + +431 +00:47:27,340 --> 00:47:32,060 +بده اغير في المعادلة هذه بطلت تساوي زيرو يقول ال + +432 +00:47:32,060 --> 00:47:36,310 +threshold voltage صار بعتمد على مين؟is a function + +433 +00:47:36,310 --> 00:47:42,310 +of vps و ال vps في هذا الحال ايش بتساوي ال vp + +434 +00:47:42,310 --> 00:47:47,770 +بتساوي v out و ال vs بتساوي ايش بتساوي zero يعني + +435 +00:47:47,770 --> 00:47:54,030 +هذا صار عبارة عن a function of v out طب ايش هذا + +436 +00:47:54,030 --> 00:47:58,710 +بتأثر عليا اذا + +437 +00:47:58,710 --> 00:48:03,470 +هذا function of v out حد بقدر يقولي ايش بتأثر على + +438 +00:48:03,470 --> 00:48:12,520 +ايشع ال time هذه واضحة ليش؟ هي + +439 +00:48:12,520 --> 00:48:21,460 +قدامك المعادلة لأ بدهاش مش عارف، لأ بدك تعرف بس + +440 +00:48:21,460 --> 00:48:28,820 +ال VT كنت بعتبره إيش؟ بعتبره constant صح؟ و أنا + +441 +00:48:28,820 --> 00:48:34,440 +كنت أخد ال DV out with respect لمن؟ال Vt كنت أقول + +442 +00:48:34,440 --> 00:48:38,080 +هذا مش موجود هذا constant و اطلع برا و مالوش دخل + +443 +00:48:38,080 --> 00:48:41,740 +بالمعادلة الآن ال Vt هذا اللي كنت باعتبره مالوش + +444 +00:48:41,740 --> 00:48:46,260 +دخل صار صار إله دخل لإنه بده أحسب حسابه لما نعمل + +445 +00:48:46,260 --> 00:48:51,940 +ال integration الآن نفس الشيء ارجعه تاني مش بس + +446 +00:48:51,940 --> 00:48:58,000 +لهدول أنا كنت أقول قبل عند ال ID بيساوي في ال VTC + +447 +00:48:58,000 --> 00:49:04,560 +ال ID بيساوي ال IL صح؟وكنت اقول لما .. هذا ماتحلش + +448 +00:49:04,560 --> 00:49:07,640 +اقول ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +449 +00:49:07,640 --> 00:49:10,780 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +450 +00:49:10,780 --> 00:49:12,060 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +451 +00:49:12,060 --> 00:49:12,080 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +452 +00:49:12,080 --> 00:49:12,620 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +453 +00:49:12,620 --> 00:49:12,680 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +454 +00:49:12,680 --> 00:49:13,780 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +455 +00:49:13,780 --> 00:49:13,800 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +456 +00:49:13,800 --> 00:49:14,440 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +457 +00:49:14,440 --> 00:49:15,480 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +458 +00:49:15,480 --> 00:49:20,680 +ال .. + +459 +00:49:20,680 --> 00:49:24,440 +ال .. ال .. + +460 +00:49:28,110 --> 00:49:31,690 +وعمل iteration بحيث يغيرها هي approximation أنا + +461 +00:49:31,690 --> 00:49:36,670 +بقولك بس بالنسبة لهذه المادة اعرف ان كل القوانين + +462 +00:49:36,670 --> 00:49:42,830 +اللي كانت عندنا are not valid anymore كويس؟هذا + +463 +00:49:42,830 --> 00:49:47,710 +اللي بديك تعرف فيه انه هذه حد ما عملت هذا الحركة + +464 +00:49:47,710 --> 00:49:51,930 +صار ال V بي اس is a function of V out فكل ال + +465 +00:49:51,930 --> 00:49:55,290 +derivation تبعها تبدأ أعيد حسابها و أحط في الحسبان + +466 +00:49:55,290 --> 00:50:00,930 +عندي ال Vt صارت a function of V out و لو بدك + +467 +00:50:00,930 --> 00:50:05,050 +تعملها يدويكنت أطلبها محيطا من بعض اللي هي قولت + +468 +00:50:05,050 --> 00:50:09,650 +اللي بيجيبها و ماحدش جابها صح اللي بيجيبها .. + +469 +00:50:09,650 --> 00:50:14,130 +فماحدش بيجيبها صح فانا بطلت أطلب من أي حد يعمل ال + +470 +00:50:14,130 --> 00:50:17,890 +derivation بقولك be aware من هذه الشغلات أنا مش + +471 +00:50:17,890 --> 00:50:25,350 +هتطرقلها أكتر من هذه الجزية كويس هيك؟ طيب اللي أنا + +472 +00:50:25,350 --> 00:50:30,290 +بدي أعمله حاجة تانيةلأن في المحاضرات الجاية هذه زي + +473 +00:50:30,290 --> 00:50:36,290 +ما حكيناها هذه بتأثر فاحنا على طول بنعمل في هذه في + +474 +00:50:36,290 --> 00:50:43,030 +ال chapter 19 ايش بتعمل باجي لهذه ال load بغيرها + +475 +00:50:43,030 --> 00:50:55,410 +بحط التالف طلع + +476 +00:50:55,410 --> 00:50:57,170 +هذه ايش مش .. ايش معمول فيها + +477 +00:51:02,270 --> 00:51:05,870 +ماذا حصل عندك؟ بدل ال load ماذا حطيت هنا؟ + +478 +00:51:05,870 --> 00:51:16,950 +ترانزوستر ترانزوستر هنا ال Vgs تبعه كم بتساوي؟ ال + +479 +00:51:16,950 --> 00:51:25,910 +Vg مربوط مع مين؟ مربوط مع ال Vdd، مظبوط؟ فال Vdd + +480 +00:51:25,910 --> 00:51:32,830 +أكبر من ال Vout يعني Vgs هذهإذا أنا بدأ امشي عليها + +481 +00:51:32,830 --> 00:51:38,330 +هذه دايما هتكون شغالة ليش لأن ال VG minus ال Vout + +482 +00:51:38,330 --> 00:51:43,410 +هذي أكبر من ال threshold فهذه دايما شغالة طب الآن + +483 +00:51:43,410 --> 00:51:54,690 +اتطلع عندى VGS و VDS ايش واضحهم متساوين صح VGS و + +484 +00:51:54,690 --> 00:51:59,930 +VDS لأن هاي ال gate هاي ال gateو هاي ال drill + +485 +00:51:59,930 --> 00:52:05,210 +اتنين مشبكين على نفس النقطة صح فاتنين لازم يكونوا + +486 +00:52:05,210 --> 00:52:10,150 +انا بالحاجة بقول بدي Vgs و Vds فاتنين متساوين + +487 +00:52:10,150 --> 00:52:19,110 +كويسين ايش في حاجة تانية الان عندي Vgs minus Vt + +488 +00:52:19,110 --> 00:52:26,090 +هيكون دايما اصغر من Vds صح ده اتنين متساوين و واحد + +489 +00:52:26,090 --> 00:52:30,920 +باخد منه بطرح منه voltageيبقى هداك حيكون البطرح + +490 +00:52:30,920 --> 00:52:35,420 +منه حيكون أصغر، معناته vgs minus vt دايما أصغر من + +491 +00:52:35,420 --> 00:52:40,880 +vds، يبقى في أي mode of operation؟ لأ، أنا قلت ال + +492 +00:52:40,880 --> 00:52:45,560 +.. ال .. ال .. ال vds مالهاش .. مالهاش دخل بالإيش؟ + +493 +00:52:45,560 --> 00:52:49,950 +بال on و ال offالـ VDS لما أجي أحطه بقول هذا إيه + +494 +00:52:49,950 --> 00:52:54,690 +دخل بال saturation أو linear بس ال VGS إيه اللي + +495 +00:52:54,690 --> 00:52:59,670 +دخل أنا قاعد بقول VGS هذا أكبر من VT على طول فهذا + +496 +00:52:59,670 --> 00:53:03,430 +ال transistor اللي عندي ال load transistor أو + +497 +00:53:03,430 --> 00:53:06,950 +خلينا نقول ال pull-up transistor اللي موجودها + +498 +00:53:06,950 --> 00:53:12,680 +دايما شغال و دايما شغال في وضع ال saturationفهنا + +499 +00:53:12,680 --> 00:53:17,000 +لما بدي اجيب و بدي اقول هان اللي عندى صار عندى ال + +500 +00:53:17,000 --> 00:53:30,100 +ID SAT IDL SAT بدي ساوي ال ID N هنا في الأوضاع + +501 +00:53:30,100 --> 00:53:38,040 +التالتة حسب ال VIN كويس؟لما يكون off يعني ال IDL + +502 +00:53:38,040 --> 00:53:42,540 +بدي ساوي في وضع ال saturation بدي ساوي ال ايش ال + +503 +00:53:42,540 --> 00:53:46,860 +ID off يعني بدي اقول عندى معادلة ال ID set اللى + +504 +00:53:46,860 --> 00:53:52,980 +بتساوي نص في K في Vgs minus Vt بدي ساوي ال ID off + +505 +00:53:52,980 --> 00:54:00,390 +اللى هى Zero ومنه بدي اشتغل قديش عندى ال Vgsال Vgs + +506 +00:54:00,390 --> 00:54:06,230 +هتطلع بتساوي ال Vt لما يكون واضحهم لإن إيش اللي + +507 +00:54:06,230 --> 00:54:13,410 +عندي في هذا الحالة هذا إيش معادلته بدي ساوي نص + +508 +00:54:13,410 --> 00:54:23,010 +في ك Vgs minus Vt squared طب Vgs هي عبارة عن إيش + +509 +00:54:23,010 --> 00:54:26,950 +Vdd minus Vout صح؟ + +510 +00:54:29,920 --> 00:54:35,740 +هذا بدي ساوي هذا لما يكون V in low بدي ساوي zero I + +511 +00:54:35,740 --> 00:54:45,420 +D L بدي ساوي I D N صح يبقى هذا بدي تساوي Zero النص + +512 +00:54:45,420 --> 00:54:48,920 +بتساوي Zero و ال K بتساوي Zero مين اللي ممكن يساوي + +513 +00:54:48,920 --> 00:54:53,980 +Zero هذه اللي جوا ال goals V D D minus V out minus + +514 +00:54:53,980 --> 00:54:58,300 +V T يعني بعبارة تانية V out ايش بدي تساوي + +515 +00:55:04,340 --> 00:55:09,200 +هذا متساوى 0 يعني عندى ايش هذا من هذه متساوى 0 + +516 +00:55:09,200 --> 00:55:16,500 +متساوى عندى vdd minus vout minus vt متساوى 0 او + +517 +00:55:16,500 --> 00:55:25,080 +vout متساوى vdd minus vt كويس + +518 +00:55:25,080 --> 00:55:29,100 +يعني دايما بقى اقل حاجة بطلع عليه لأن انا بقول + +519 +00:55:29,100 --> 00:55:37,430 +شغال هو صح معناته vgs متساوىVT VT هي نقطة الفصل + +520 +00:55:37,430 --> 00:55:43,050 +VDS + +521 +00:55:43,050 --> 00:55:48,210 +يعني drop يعني VGS او VT + +522 +00:55:54,190 --> 00:55:58,830 +يعني خلّيني أقول صار قديش بده أجيب ال VIL و بقول + +523 +00:55:58,830 --> 00:56:01,890 +عنده ال ID hand بيساوي ال ID hand و نفس الشيء في + +524 +00:56:01,890 --> 00:56:05,150 +الخطوات اللي قمت فيها قبل في ال chapter 18 بده + +525 +00:56:05,150 --> 00:56:09,790 +أعملها و باخد ال derivative لهذا و هذا function of + +526 +00:56:09,790 --> 00:56:13,330 +V out و هذا function of VIL و هذا function of V + +527 +00:56:13,330 --> 00:56:17,510 +out و function of VIH و أعمل يصير عنده معادلتين + +528 +00:56:17,510 --> 00:56:21,310 +derivative و هذا الشيء بعد هيك في ال chapter عشرين + +529 +00:56:21,310 --> 00:56:27,000 +ايش هعمل؟بدل ما هو هذا الترانزستور في هذا الشكل + +530 +00:56:27,000 --> 00:56:34,000 +بتاخد نفس الترانزستور واشبكوا + +531 +00:56:34,000 --> 00:56:44,420 +مع VGG ايش VGG هذا VGG هذا بيضمن للترانزستور يبقى + +532 +00:56:44,420 --> 00:56:49,960 +وضعه الترانزستور هذا بيكون وضعه دايما في حالة + +533 +00:56:53,300 --> 00:56:58,900 +linear كويس و اجيب ال ID في حالة ال linear بدي + +534 +00:56:58,900 --> 00:57:04,500 +ساوي ال ID اللي ها و اعمل خطوات تانية بعد هيك ال + +535 +00:57:04,500 --> 00:57:09,460 +chapter هذا chapter كام هذا قولنا تسعتاش هذا عشرين + +536 +00:57:09,460 --> 00:57:13,600 +واحد و عشرين بدي امسك اللي عند ال transistor اللي + +537 +00:57:13,600 --> 00:57:20,820 +ها وضعه شوية بختلف هذا اللي ها هيكون enhancement + +538 +00:57:20,820 --> 00:57:21,620 +depletion + +539 +00:57:24,440 --> 00:57:29,000 +Enhancement Depletion فالـ gate و ال source + +540 +00:57:29,000 --> 00:57:35,440 +مشبوكين مع بعض مش ال gate و ال drain يعني هاناش + +541 +00:57:35,440 --> 00:57:39,600 +هيطلع عندك Vgs + +542 +00:57:39,600 --> 00:57:47,700 +بتساوي كم؟ Zero Vgs + +543 +00:57:47,700 --> 00:57:50,820 +بتساوي Zero الان Vds + +544 +00:57:53,510 --> 00:58:00,310 +اللي بيساوي بيساوي VDD-Vout الان بناء عليه هو ايش + +545 +00:58:00,310 --> 00:58:03,470 +بتساوي بس انتبهي عندي ال enhancement depletion ايش + +546 +00:58:03,470 --> 00:58:15,010 +وضعه قداش VT فيه حد + +547 +00:58:15,010 --> 00:58:20,450 +ذاكر؟ chapter 16 ال enhancement depletion ال VT + +548 +00:58:20,450 --> 00:58:28,030 +بالنجативكويس فإذا ال Vt بالنجاتف معناته هذا بيبقى + +549 +00:58:28,030 --> 00:58:33,670 +شغال فلما ال Vgs بيساو Zero يبقى إيش؟ شغال الآن + +550 +00:58:33,670 --> 00:58:37,090 +بتبحث فيه هذا إيش ال mode of operation تبعته لما + +551 +00:58:37,090 --> 00:58:43,070 +نشتغل هذا بيعتمد على مين؟ على V out بيعتمد على + +552 +00:58:43,070 --> 00:58:48,390 +قيمة V out وهذا اللي هتناقشه المحاضرة جاي لكل + +553 +00:58:48,390 --> 00:58:49,430 +التلاتة هذول + +554 +00:58:52,670 --> 00:58:55,630 +هنقولك لما يكون هنا إيش فيه و هنا إيش فيه و هنا + +555 +00:58:55,630 --> 00:59:01,430 +إيش فيه، كويس هيك؟ فيه تساؤل؟ + diff --git a/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/DRRdNqB0WX8_raw.json b/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/DRRdNqB0WX8_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..39148320bfb183c3152b0e5f2be1bffd7de025c9 --- /dev/null +++ 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بيحول ال input تبعته من saturated دوية ل Linear ففي هذا النقطة صار عندك ال NN وضعه saturated و ال NO وضعه Linear الان بجيب ال ID Linear بتبعدها وال ID Linear تبعد", "tokens": [6027, 7649, 4724, 11622, 23328, 8978, 2423, 4846, 8032, 2407, 36520, 46740, 15730, 28239, 47432, 3660, 23758, 28239, 47432, 3660, 1975, 1829, 8592, 43242, 4117, 23758, 2423, 34750, 4724, 1829, 5016, 12610, 2423, 4846, 6055, 3555, 34268, 3224, 9154, 25408, 11778, 2407, 10632, 5296, 14670, 289, 6156, 41185, 23758, 28239, 47432, 3660, 20328, 9640, 43242, 4117, 2423, 426, 45, 4032, 11242, 3615, 3224, 25408, 4032, 2423, 9146, 4032, 11242, 3615, 3224, 14670, 289, 2423, 7649, 4724, 7435, 1829, 3555, 2423, 7348, 14670, 289, 39894, 3555, 22488, 11296, 16070, 7348, 14670, 289, 6055, 3555, 22488], "avg_logprob": -0.39638158145703767, "compression_ratio": 1.8608247422680413, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 688.08, "end": 688.48, "word": "الان", "probability": 0.489013671875}, {"start": 688.48, 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Vim إذا المعادلة فيها أشكال unknown اللي هي Vih و Vim مقدرش أخلها فليش بعملها أخلها بجيب ال derivative يعني منها انا عندي ال ID", "tokens": [6027, 1211, 11536, 13672, 1829, 39896, 2423, 2235, 493, 4032, 4724, 25957, 1211, 16095, 44650, 3794, 995, 20498, 9957, 6156, 6027, 43761, 8032, 2655, 4587, 1211, 22653, 11331, 26108, 3660, 9673, 3615, 18513, 37977, 36764, 24401, 3660, 8978, 11296, 732, 46048, 1975, 1829, 8592, 8032, 2304, 2423, 691, 4247, 4032, 691, 332, 11933, 15730, 9673, 3615, 18513, 37977, 8978, 11296, 5551, 8592, 4117, 6027, 9841, 13672, 1829, 39896, 691, 4247, 4032, 691, 332, 3714, 28543, 2288, 8592, 5551, 9778, 1211, 11296, 6156, 20292, 8592, 4724, 25957, 1211, 11296, 5551, 9778, 1211, 11296, 4724, 7435, 1829, 3555, 2423, 13760, 37495, 22653, 9154, 11296, 1975, 8315, 18871, 16254, 2423, 7348], "avg_logprob": -0.3285550327476012, "compression_ratio": 1.7194570135746607, "no_speech_prob": 2.384185791015625e-06, "words": [{"start": 714.96, "end": 715.6, "word": "اللون", 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cancellation لـ DT فبصير عندك V واحدة منهم بعمل فيها partial rule بصير عندك هاي معادلة و هاي معادلة معادلتين و اللي عندك انه Vih و Vout فانا منهم بحلل", "tokens": [3555, 6027, 1863, 35457, 3660, 5296, 39184, 413, 51, 4724, 4587, 2407, 9566, 8032, 2655, 3794, 995, 45865, 2423, 39184, 11953, 4032, 2423, 39184, 10699, 4032, 20666, 1863, 35457, 3660, 5296, 39184, 413, 51, 4032, 44945, 3615, 28480, 16472, 2423, 691, 346, 307, 257, 2445, 295, 565, 6156, 1211, 3224, 15730, 21136, 3555, 3555, 4724, 47283, 3215, 1975, 1829, 8592, 22807, 4724, 9566, 3555, 4587, 2423, 5021, 4978, 4032, 39182, 3224, 4724, 25957, 1211, 45867, 5296, 39184, 413, 51, 6156, 3555, 9381, 13546, 43242, 4117, 691, 36764, 24401, 3660, 9154, 16095, 4724, 25957, 1211, 8978, 11296, 14641, 4978, 4724, 9381, 13546, 43242, 4117, 8032, 47302, 20449, 18513, 37977, 4032, 8032, 47302, 20449, 18513, 37977, 20449, 18513, 1211, 2655, 9957, 4032, 13672, 1829, 43242, 4117, 16472, 3224, 691, 4247, 4032, 691, 346, 6156, 7649, 995, 9154, 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1085.04, "word": " كانت", "probability": 0.946533203125}, {"start": 1085.04, "end": 1085.44, "word": " تساوي", "probability": 0.8028564453125}, {"start": 1085.44, "end": 1085.82, "word": " Zero", "probability": 0.91064453125}, {"start": 1085.82, "end": 1087.64, "word": " هاي", "probability": 0.646484375}, {"start": 1087.64, "end": 1088.12, "word": " شرط", "probability": 0.5998128255208334}, {"start": 1088.12, "end": 1089.3, "word": " VIN", "probability": 0.625732421875}], "temperature": 1.0}, {"id": 36, "seek": 111456, "start": 1089.7, "end": 1114.56, "text": "بتساوي Zero ال N هو وضع O وال IDO بتساوي Zero اللي هو بيساوي IDN وضع الليلة اللي بيساوي ال IDO بيساوي Zero اللي هو بيساوي KM", "tokens": [3555, 2655, 3794, 995, 45865, 17182, 2423, 426, 31439, 4032, 11242, 3615, 422, 16070, 7348, 46, 4724, 2655, 3794, 995, 45865, 17182, 13672, 1829, 31439, 4724, 1829, 3794, 995, 45865, 7348, 45, 4032, 11242, 3615, 13672, 26895, 3660, 13672, 1829, 4724, 1829, 3794, 995, 45865, 2423, 7348, 46, 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"word": " بتساوي", "probability": 0.781103515625}, {"start": 1100.76, "end": 1101.08, "word": " Zero", "probability": 0.9267578125}, {"start": 1101.08, "end": 1101.38, "word": " اللي", "probability": 0.83056640625}, {"start": 1101.38, "end": 1101.48, "word": " هو", "probability": 0.98291015625}, {"start": 1101.48, "end": 1102.1, "word": " بيساوي", "probability": 0.90439453125}, {"start": 1102.1, "end": 1104.48, "word": " IDN", "probability": 0.795654296875}, {"start": 1104.48, "end": 1105.04, "word": " وضع", "probability": 0.8927408854166666}, {"start": 1105.04, "end": 1105.9, "word": " الليلة", "probability": 0.532958984375}, {"start": 1105.9, "end": 1106.48, "word": " اللي", "probability": 0.650390625}, {"start": 1106.48, "end": 1107.1, "word": " بيساوي", "probability": 0.955078125}, {"start": 1107.1, "end": 1107.74, "word": " ال", "probability": 0.28515625}, {"start": 1107.74, "end": 1108.74, "word": " IDO", "probability": 0.911376953125}, {"start": 1108.74, "end": 1111.92, "word": " بيساوي", "probability": 0.8000732421875}, {"start": 1111.92, "end": 1112.22, "word": " Zero", "probability": 0.94970703125}, {"start": 1112.22, "end": 1112.42, "word": " اللي", "probability": 0.977294921875}, {"start": 1112.42, "end": 1112.52, "word": " هو", "probability": 0.99267578125}, {"start": 1112.52, "end": 1113.04, "word": " بيساوي", "probability": 0.95302734375}, {"start": 1113.04, "end": 1114.56, "word": " KM", "probability": 0.583251953125}], "temperature": 1.0}, {"id": 37, "seek": 113852, "start": 1121.24, "end": 1138.52, "text": "بطولة BDL بطولة BDSL بطولة BDSL بطولة BDSL", "tokens": [3555, 9566, 12610, 3660, 363, 35, 43, 4724, 9566, 12610, 3660, 363, 35, 47012, 4724, 9566, 12610, 3660, 363, 35, 47012, 4724, 9566, 12610, 3660, 363, 11844, 43], "avg_logprob": -0.7332974220144337, "compression_ratio": 2.066666666666667, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1121.24, "end": 1122.64, "word": "بطولة", "probability": 0.4028778076171875}, {"start": 1122.64, "end": 1123.72, "word": " BDL", "probability": 0.5561726888020834}, {"start": 1123.72, "end": 1124.32, "word": " بطولة", "probability": 0.7255020141601562}, {"start": 1124.32, "end": 1125.08, "word": " BDSL", "probability": 0.4676920572916667}, {"start": 1125.08, "end": 1126.14, "word": " بطولة", "probability": 0.81976318359375}, {"start": 1126.14, "end": 1128.72, "word": " BDSL", "probability": 0.537841796875}, {"start": 1128.72, "end": 1137.88, "word": " بطولة", "probability": 0.797271728515625}, {"start": 1137.88, "end": 1138.52, "word": " BDSL", "probability": 0.737060546875}], "temperature": 1.0}, {"id": 38, "seek": 116863, "start": 1151.53, "end": 1168.63, "text": "لو أخدت هذه جوجلينه هتساوي زيرو، إيش هتعطينا؟ هتعطينا ال VDSM بدي ساوي اتنين VGSM minus VDE هل هذا الكلام مظلوم؟", "tokens": [1211, 2407, 5551, 9778, 3215, 2655, 8032, 8848, 3224, 10874, 29245, 1211, 9957, 3224, 8032, 2655, 3794, 995, 45865, 30767, 13546, 2407, 12399, 11933, 1829, 8592, 8032, 2655, 3615, 9566, 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"end": 1167.97, "word": " الكلام", "probability": 0.91162109375}, {"start": 1167.97, "end": 1168.63, "word": " مظلوم؟", "probability": 0.771533203125}], "temperature": 1.0}, {"id": 39, "seek": 119133, "start": 1172.61, "end": 1191.33, "text": "هذا اللي عملته متساوز يبقى عشان يطلع من الناس يطلع من الناس بهذه الجهة يعملها متساوز يبقى عشان يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس يطلع من الناس", "tokens": [3224, 15730, 13672, 1829, 6225, 42213, 47395, 44650, 3794, 995, 2407, 11622, 7251, 3555, 4587, 7578, 6225, 8592, 7649, 7251, 9566, 1211, 3615, 9154, 2423, 8315, 3794, 7251, 9566, 1211, 3615, 9154, 2423, 8315, 3794, 39627, 24192, 25724, 3224, 3660, 7251, 25957, 1211, 11296, 44650, 3794, 995, 2407, 11622, 7251, 3555, 4587, 7578, 6225, 8592, 7649, 7251, 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--> 00:00:32,640 +diodes بيشتغلوا، هذه حاجة عامة، بعد هيك هنتكلم على + +4 +00:00:32,640 --> 00:00:37,280 +الـ operations، الـ mode of operations للـ diodes، بعد + +5 +00:00:37,280 --> 00:00:40,760 +ذلك سأتكلم عن الـ diode resistor logic، نبدأ بـ two + +6 +00:00:40,760 --> 00:00:45,500 +circuits من الـ logic family هذه، بعد ذلك سنعدل في + +7 +00:00:45,500 --> 00:00:48,760 +هذه الـ two circuits لكي تكون في بعض ال + +8 +00:00:48,760 --> 00:00:52,420 +characteristics التي سنشاهدها ليست كما يجب، فلازم + +9 +00:00:52,420 --> 00:00:57,980 +يتم التعديل عليهم، الآن الـ diode هي أبسط قطعة + +10 +00:00:57,980 --> 00:01:06,260 +إلكترونية نتعامل معها، فيها requirement، هذه عبارة عن + +11 +00:01:06,260 --> 00:01:11,980 +بي ماتيريال أو بي دوب ماتيريال connected with ان + +12 +00:01:11,980 --> 00:01:21,880 +دوب ماتيريال، يعني بشكل عام لو بنتكلم عليه، هاي + +13 +00:01:21,880 --> 00:01:28,540 +الآن ماتيريال، وهنا البي دوب ماتيريال، هاي شحنة ال + +14 +00:01:28,540 --> 00:01:31,940 +positive، هاي شحنة الـ negative، الـ symbol تبعته + +15 +00:01:34,550 --> 00:01:39,530 +plus minus، هنا عندي هذا بسميه الـ VD، و هذا التيار + +16 +00:01:39,530 --> 00:01:45,530 +الـ ID، لأن هذا بشكل عام الـ diet ف الـ B material و + +17 +00:01:45,530 --> 00:01:48,390 +الـ N material، هنا الـ majority carriers ايش هما في + +18 +00:01:48,390 --> 00:01:53,750 +الـ B material، الـ holes، و هنا الـ majority carriers + +19 +00:01:53,750 --> 00:01:59,700 +الـ electrons، في في النص هنا هيصير عندي اللى إيه، إيش + +20 +00:01:59,700 --> 00:02:03,420 +بنسميها الـ depletion junction، الـ depletion + +21 +00:02:03,420 --> 00:02:08,240 +junction هذه لها خصائص، الخصائص التالية under zero + +22 +00:02:08,240 --> 00:02:14,620 +biasing، لها width، لها يعني عرض هذه، قد إيش بيصير ال + +23 +00:02:14,620 --> 00:02:19,160 +depletion، عادة لما تحط حاجة موجب و حاجة سالبة جنب + +24 +00:02:19,160 --> 00:02:24,580 +بعض إيش بيصير، بيصير تجاذب، وبعدها بيصير في منطقة في + +25 +00:02:24,580 --> 00:02:28,340 +النص ع الشحنة هذه، في تجمع ع الشحنة هذه، في تجمع حد + +26 +00:02:28,340 --> 00:02:33,080 +بتعمله التجاذب هذا اللي بيتحد بيسوي الـ depletion + +27 +00:02:33,080 --> 00:02:36,500 +area، الآن الـ depletion area، بدك تفكر فيها زي + +28 +00:02:36,500 --> 00:02:44,180 +خندق، كويس؟ الخندق هذا لو خلينا نقول عرضه متر، في + +29 +00:02:44,180 --> 00:02:47,320 +ناس بتعديه و في ناس بتعدهوش، مظبوط؟ اللي زيكم + +30 +00:02:47,320 --> 00:02:48,800 +معظمكم لازم يعديه + +31 +00:02:51,630 --> 00:02:56,990 +خلّيني أقول لو جفزت بتعديه بشوية مجهود بتعديه، الآن + +32 +00:02:56,990 --> 00:03:00,750 +لو جيبت لحد أكبر في السن بيقدروش يعدوه، لو جيت + +33 +00:03:00,750 --> 00:03:04,770 +لصغار في السن بيقدروش يعدوه، بس بالنسبة لإن في نسبة + +34 +00:03:04,770 --> 00:03:08,550 +من الناس بتقدر تعديه، اللي هي الشباب اللي زيكم، هذا + +35 +00:03:08,550 --> 00:03:14,070 +under zero biasing، الآن في وضع الـ forward bias ايش + +36 +00:03:14,070 --> 00:03:19,210 +بيصير؟ هذا الخندق بديجبصير زي عشرة سم، العشرة + +37 +00:03:19,210 --> 00:03:24,010 +سم كام واحد مقدرش يعديه؟ الغالبية الناس بتعديه، + +38 +00:03:24,010 --> 00:03:28,170 +و لو سويت له الـ bias إن كان perfect، هاد بيصير عبارة + +39 +00:03:28,170 --> 00:03:33,750 +عن صفر سم، صفر سم، كل high asphalt مبدود الكل + +40 +00:03:33,750 --> 00:03:37,410 +بيعديه، الآن في وضع الـ reverse bias بيصير كيف؟ + +41 +00:03:37,410 --> 00:03:41,170 +بيصير عرضه زي اثنين متر، اثنين متر كام واحد مقدر + +42 +00:03:41,170 --> 00:03:46,180 +يعديه؟ فالقصد من هنا الناس اللي بتعديه بتبقى قليلة، + +43 +00:03:46,180 --> 00:03:51,620 +لو صارت ثلاثة متر إيش بنقول؟ بنوقف الآن، بنقول حد + +44 +00:03:51,620 --> 00:03:55,120 +من .. يمكن حد على مستوى العالم واحد يقدر يعديه، + +45 +00:03:55,120 --> 00:04:00,560 +يمكن ما فيش، ف الـ reverse هي .. الـ region في وضع ال + +46 +00:04:00,560 --> 00:04:05,640 +reverse بيصير خندق كبير، مش أي electron بيقدر يعديه، + +47 +00:04:05,640 --> 00:04:10,210 +الـ electron اللي عنده very very high Energy هو اللي + +48 +00:04:10,210 --> 00:04:14,870 +بيقدر يعديه، وهذا نسبته عادة بتبقى قليلة جدا، قليلة + +49 +00:04:14,870 --> 00:04:18,430 +جدا، يعني لما تقول واحد من عشرة أُس ناقص تلاتاش ولا + +50 +00:04:18,430 --> 00:04:22,990 +أربعتاش ولا خمستاش، هذا ايش يعني؟ زي ما تقول شبه + +51 +00:04:22,990 --> 00:04:27,370 +مستحيل يعديه، بتلاقيه صغير جدا، هذه خصائص ال + +52 +00:04:27,370 --> 00:04:31,440 +depletion region، القادر اللي عندي أنا حاجتين هنا في + +53 +00:04:31,440 --> 00:04:36,340 +عندي VD و في عندي ID، دايما كويس نربطهم مع بعض من + +54 +00:04:36,340 --> 00:04:40,780 +الـ characteristics لهذا الدوائر، بنربط الـ output أو + +55 +00:04:40,780 --> 00:04:45,740 +بنربط التيار مع الـ voltage اللي موجود، هذا الربط + +56 +00:04:45,740 --> 00:04:50,540 +بنسميه Shockley voltage current expression أو + +57 +00:04:50,540 --> 00:04:56,340 +بنقول عنه Shockley equation، كويس، اللي هو بيمثل ال + +58 +00:04:56,340 --> 00:04:57,220 +diode modeling + +59 +00:05:05,450 --> 00:05:13,550 +نتكلم على الشاقلي expression + +60 +00:05:13,550 --> 00:05:17,230 +اللي + +61 +00:05:17,230 --> 00:05:28,030 +عندي هي ID بدي أساوي IS E to the VD على V of T ناقص + +62 +00:05:28,030 --> 00:05:33,500 +واحد، الآن بدي أعرف، هي يقول لنا الـ ID اللي هو تيار تبع + +63 +00:05:33,500 --> 00:05:37,140 +الدايود اللي بيمر من خلال الدايود، الـ VD اللي هو تيار + +64 +00:05:37,140 --> 00:05:44,760 +الـ voltage across الدايود، الـ VD، الـ VD، الـ VD، الـ VD + +65 +00:05:44,760 --> 00:05:49,340 +الـ VD، الـ VD + +66 +00:05:49,340 --> 00:05:50,100 +VD، الـ VD، الـ VD، الـ VD، الـ VD، الـ VD، الـ VD، الـ VD، الـ VD + +67 +00:05:50,100 --> 00:05:51,600 +الـ VD، الـ VD، الـ VD، الـ VD، الـ VD، الـ VD، الـ VD، الـ VD، ال + +68 +00:05:58,360 --> 00:06:02,820 +في وضع الـ .. الـ .. الـ .. عندي الـ diode وضع + +69 +00:06:02,820 --> 00:06:07,340 +reverse bias، إذا هو كان هو في وضع reverse bias + +70 +00:06:07,340 --> 00:06:11,900 +فمعناته إيش، بتتذكر الخندق هاد ال analogy دايما + +71 +00:06:11,900 --> 00:06:15,180 +خليها و خبيها، خبيها in the back of your head يعني + +72 +00:06:15,180 --> 00:06:18,580 +في الخلفية تبعتك دايما خبيها، ايش معناته؟ معناته + +73 +00:06:18,580 --> 00:06:23,320 +هذا خندق كبير صار، كام electron بيقدر يعدي؟ هذا هو + +74 +00:06:23,320 --> 00:06:30,840 +التيار، فعادة هذا الـ range تبعه بين 10⁻¹² لـ 10⁻¹⁵ + +75 +00:06:30,840 --> 00:06:41,100 +أمبير، الآن الـ V of T بسميه الـ thermal voltage + +76 +00:06:41,100 --> 00:06:44,580 +وهذا + +77 +00:06:44,580 --> 00:06:48,760 +بيساوي التالي، بدي + +78 +00:06:48,760 --> 00:06:57,100 +أساويه بـ K T على Q، طيب إيش هذا الـ K، الـ K بنسميه + +79 +00:06:57,100 --> 00:07:12,360 +Boltzmann constant، وهذا + +80 +00:07:12,360 --> 00:07:19,460 +بيساوي 1.38 × 10⁻²³ + +81 +00:07:20,600 --> 00:07:27,040 +بـ degree Kelvin، و الـ T عبارة عن الـ temperature + +82 +00:07:27,040 --> 00:07:31,920 +و + +83 +00:07:31,920 --> 00:07:35,540 +الـ temperature عادة تبقى مُعطى in degrees Kelvin + +84 +00:07:35,540 --> 00:07:45,640 +و الـ Kelvin بتساوي 273 زائد الـ degree in Celsius، ال + +85 +00:07:45,640 --> 00:07:48,120 +Q اللي هي الـ charge للإلكترون + +86 +00:07:56,630 --> 00:08:02,330 +و هذه بتساوي 1.6 times 10 to the minus 19 كولون + +87 +00:08:02,330 --> 00:08:08,390 +هذه بشكل عام الموجودة عندي، طيب لو بدي أشوف هذه + +88 +00:08:08,390 --> 00:08:11,170 +القوانين اللي عندي، لو بدي أشوف طبيعة العلاقة ايش + +89 +00:08:11,170 --> 00:08:15,810 +لازم أعمل، لازم أشوف كده ايش بيطلع عندي، أشوف example + +90 +00:08:15,810 --> 00:08:21,270 +حيّ الـ example حيّ بنقعه على هاي، بدي أقول هيه given + +91 +00:08:21,270 --> 00:08:25,830 +ايش بدي أقول عنه given اللي عندي + +92 +00:08:28,980 --> 00:08:36,120 +IS equal one times ten to the minus fourteen + +93 +00:08:36,120 --> 00:08:42,200 +ampere، وعندي room temperature، الـ room temperature + +94 +00:08:42,200 --> 00:08:51,620 +قديش عادة 25، بس 25 زائد 273 قديش بتطلع؟ 298، ف أنا + +95 +00:08:51,620 --> 00:08:55,380 +تجاوزًا بقول عشان الأرقام سهلة الحسب الحسبة بعملها + +96 +00:08:55,380 --> 00:09:03,530 +قديش 300، بقول هذه تقريبًا 300 degree Kelvin، الآن بدي + +97 +00:09:03,530 --> 00:09:14,710 +أحسب VT لها، VT بدي أحسب 1.38 × 10⁻²³ × 300 + +98 +00:09:14,710 --> 00:09:28,350 +على 1.6 × 10⁻¹⁹، بيطلع تقريبًا 25.9 ملي فولت، الآن + +99 +00:09:28,350 --> 00:09:32,570 +بناءً عليها المطلوب مني أجيب إيش من هذه المعطيات؟ + +100 +00:09:32,570 --> 00:09:38,290 +بقول لي compute ID + +101 +00:09:38,290 --> 00:09:57,260 +given for VD 0.1، 0.2، 0.5، 0.7، 0.8، 1، و 2.3 فولت، لهذا + +102 +00:09:57,260 --> 00:10:03,440 +القيم كلها احسب القيمة ال + +103 +00:10:03,440 --> 00:10:07,760 +ID و شوف كيف الشكل يطلع تبعها، فهذا أول خطوة بدي + +104 +00:10:07,760 --> 00:10:16,080 +أقول الـ ID هذه المعادلة بدي أساوي IS في E to the VD + +105 +00:10:16,080 --> 00:10:24,810 +على 25.9 ناقص 1، اللي بدي أساوي عشرة أُس ناقص أربعتاش على + +106 +00:10:24,810 --> 00:10:31,030 +ايه بتاخذ واحد على هذه اللي بتطلع تقريبًا 25.9 VD + +107 +00:10:31,030 --> 00:10:37,890 +ناقص واحد، اللي هي عشانها بتاخذ واحد، VD على 25.9 + +108 +00:10:37,890 --> 00:10:42,010 +ملي، اللي بتساوي بتاخذها مجلوب + +109 +00:10:42,010 --> 00:10:46,370 +تساوي تقريبًا 40، الآن بتعوض عنهم بتقول عندي هي + +110 +00:10:46,370 --> 00:10:58,040 +ID point one Volt، ID الـ ID لـ 0.2 Volt، ID لـ 0.5 + +111 +00:10:58,040 --> 00:11:07,520 +Volt، ID لـ 0.7 Volt، الـ ID لـ 0.8 Volt، و الـ ID لـ + +112 +00:11:07,520 --> 00:11:16,860 +1 Volt، و الـ ID لـ 2.3 Volt، هاد + +113 +00:11:16,860 --> 00:11:21,280 +ده يصير عندها عشرة أُس ناقص أربعتاش ضرب بتضرب point + +114 +00:11:21,280 --> 00:11:26,500 +واحد يعطيني هاد قد ايش؟ لما اضربها بـ point واحد هذا + +115 +00:11:26,500 --> 00:11:30,680 +بتعطيني أربعة ولا 40؟ أربعة، أربعة بتعطيني، أتوقع + +116 +00:11:30,680 --> 00:11:36,140 +إذا ذاكر الرقم أربعة + +117 +00:11:36,140 --> 00:11:40,980 +VD، مش 40، اهو بدي أطلع زي هيك، فلما بدي أخذها + +118 +00:11:40,980 --> 00:11:45,220 +بدي أقول عندها أربعة كده بدي أطلع عندها بدي أقول + +119 +00:11:45,220 --> 00:11:53,170 +هنا اي على four point واحد -1، ده حسب هاد بدي تطلع + +120 +00:11:53,170 --> 00:12:01,130 +عند الرقم، إذا ذاكر هنا 536 + +121 +00:12:01,130 --> 00:12:09,070 +فهمتوا، أمبير، هاي عشرة أُس ناقص أربعتاش فإيه أربعة و + +122 +00:12:09,070 --> 00:12:14,330 +point اثنين ناقص واحد يساوي عندي 9.8 + +123 +00:12:14,330 --> 00:12:17,650 +point 8 Pico Ampere + +124 +00:12:29,790 --> 00:12:39,030 +بدها تساوي 4.85 micro ampere + +125 +00:12:39,030 --> 00:12:42,910 +في + +126 +00:12:42,910 --> 00:12:50,110 +أربعة في point سبعة ناقص واحد بدي يعطينا 14.5 + +127 +00:12:50,110 --> 00:12:56,390 +point 5 milli ampere، هي عشرة أُس ناقص أربعتاش في + +128 +00:12:56,390 --> 00:13:02,440 +أربعة point ثمانية ناقص واحد بدي يعطيني 790 + +129 +00:13:02,440 --> 00:13:08,440 +و 90 ملي أمبير، ناقص واحد بدي يعطيني عشرة أُس ناقص + +130 +00:13:08,440 --> 00:13:18,300 +أربعتاش في أربعة point point point أو ناقص واحد + +131 +00:13:18,300 --> 00:13:21,820 +بدي أساوي 253 + +132 +00:13:26,210 --> 00:13:33,050 +عشرة أُس ناقص أربعتاش في أربعة في أربعة في أربعة + +133 +00:13:33,050 --> 00:13:33,350 +أربعة في أربعة في أربعة في أربعة في أربعة في أربعة + +134 +00:13:33,350 --> 00:13:35,790 +في أربعة في أربعة في أربعة في أربعة في أربعة في + +135 +00:13:35,790 --> 00:13:36,490 +أربعة في أربعة في أربعة في أربعة في أربعة في أربعة + +136 +00:13:36,490 --> 00:13:39,170 +في أربعة في أربعة في أربعة في أربعة في أربعة في + +137 +00:13:39,170 --> 00:13:39,650 +أربعة في أربعة في أربعة في أربعة في أربعة في أربعة + +138 +00:13:39,650 --> 00:13:40,450 +في أربعة في أربعة في أربعة في أربعة في أربعة في + +139 +00:13:40,450 --> 00:13:41,650 +أربعة في أربعة في أربعة في أربعة في أربعة في أربعة + +140 +00:13:41,650 --> 00:13:42,710 +في أربعة في أربعة في أربعة في أربعة في أربعة في أ + +141 +00:13:44,580 --> 00:13:48,940 +طلعت الأرقام اللي بتطلع عندك في هذا المجال هذه بيت + +142 +00:13:48,940 --> 00:13:55,520 +القصيد لما كان عند ال voltage أقل من point 7 قد إيش؟ + +143 +00:13:55,520 --> 00:13:59,200 +الأرقام ضعيفة + +144 +00:13:59,200 --> 00:14:03,360 +جدا، طلع ال voltage لما صار أكثر من point 8 + +145 +00:14:03,360 --> 00:14:14,450 +أرقام مخيفة الآن، هل هذا معقول؟ هذا بنعتبره zero، هذا + +146 +00:14:14,450 --> 00:14:18,850 +اللي بنعتبره on، هذا اللي بنعتبره في وضع saturation + +147 +00:14:18,850 --> 00:14:22,870 +لأنه مش معقول يعطيني تيارات في هذا المجال بيت + +148 +00:14:22,870 --> 00:14:28,290 +القصيد من هذا لو بدأت أرسم زي ما برسم دائمًا هي VD + +149 +00:14:28,290 --> 00:14:33,470 +وهنا ال ID هيطلع الشكل تبعه هي ك exponential رسمة + +150 +00:14:33,470 --> 00:14:38,730 +ال exponential هذا اللي عندي من هنا بتبدأ ال point + +151 +00:14:38,730 --> 00:14:45,870 +7 وبعده هنا ال point ثمانية اللي بطلع عندي اللي + +152 +00:14:45,870 --> 00:14:51,270 +بدي يعني من كلها حاجتين اتوصلنا، اتوصلنا لل mode of + +153 +00:14:51,270 --> 00:14:54,450 +operation تبع ال diode، ال diode، ال mode of operation + +154 +00:14:54,450 --> 00:14:59,750 +اللي قد إيش؟ كام واحدة؟ اثنتين، اثنتين، هي ال mode of + +155 +00:14:59,750 --> 00:15:06,450 +operation اثنتين، إيش هم؟ في حالة ال on وفي حالة ال + +156 +00:15:06,450 --> 00:15:13,520 +off، في حالة ... لما نقول ال on إيش المعروف عندي؟ + +157 +00:15:13,520 --> 00:15:17,400 +المعروف + +158 +00:15:17,400 --> 00:15:22,460 +عندي في حالة ال on حاجتين، point seven، point سبعة + +159 +00:15:22,460 --> 00:15:27,720 +اللي هي ال Vd، الثانية هي اللي بدي أحسبها من + +160 +00:15:27,720 --> 00:15:34,160 +الدائرة هي الآن، ال bias هي ال mode of operation + +161 +00:15:40,700 --> 00:15:45,780 +هنا بقدر ال mode of operation اللي عندي وهنا vd + +162 +00:15:45,780 --> 00:15:53,000 +وهنا id، هنا إيش اللي بدأ أتكلم عليه؟ forward bias + +163 +00:15:53,000 --> 00:16:00,620 +كويس، ال forward bias اللي عندي، ال mode of + +164 +00:16:00,620 --> 00:16:05,780 +operation تبعه on، ال id قد إيش في حالة ال on + +165 +00:16:05,780 --> 00:16:15,020 +بيعطينا ال vd on اللي هو بقول عنه كام؟ .7 تقريبًا و + +166 +00:16:15,020 --> 00:16:19,420 +ال ID بتحسبه حسب الدائرة الموجودة، فهو مش معروف + +167 +00:16:19,420 --> 00:16:27,060 +عندي الآن في وضع ال reverse bias + +168 +00:16:27,060 --> 00:16:32,580 +إيش اللي عندي؟ ال mode of operation cut off، ال Vd + +169 +00:16:32,580 --> 00:16:38,860 +أقل من ال point 7 وال ID بيساوي كم؟ Zero + +170 +00:16:41,800 --> 00:16:48,560 +الآن بيهمني حاجتين في هذه ال VD + +171 +00:16:48,560 --> 00:16:51,860 +VD VD + +172 +00:16:51,860 --> 00:16:52,000 +VD VD VD VD VD VD VD VD VD VD VD VD VD VD VD VD VD + +173 +00:16:52,000 --> 00:16:52,380 +VD VD VD VD VD VD VD VD VD VD VD VD VD VD VD VD + +174 +00:16:52,380 --> 00:16:53,400 +VD VD VD VD VD VD VD VD VD VD VD VD VD VD VD VD + +175 +00:16:53,400 --> 00:16:56,720 +VD VD VD VD VD VD VD VD VD VD VD VD VD + +176 +00:16:56,720 --> 00:16:56,740 +VD VD VD VD VD VD VD VD VD VD VD VD VD VD VD VD + +177 +00:16:56,740 --> 00:16:58,240 +VD VD VD + +178 +00:17:07,310 --> 00:17:11,590 +إذا مش شغال وأنا أعطيتك ال voltage one، قد إيش ال + +179 +00:17:11,590 --> 00:17:17,810 +voltage هذا بدي يكون؟ هذا مش شغال، أقل + +180 +00:17:17,810 --> 00:17:22,510 +من 1، point سبعة، لو حاطط لي 1.6 بقول لك + +181 +00:17:22,510 --> 00:17:27,330 +صح، 1.5، واحد بس ما تحط لي 1.7 + +182 +00:17:27,330 --> 00:17:35,620 +أكثر هأقول لك الإجابة مش مظبوطة، في حالة إنه شغال، لو ال + +183 +00:17:35,620 --> 00:17:45,260 +voltage هنا واحد، 1.3، 1.3، + +184 +00:17:45,260 --> 00:17:50,800 +1.3، 1.3، 1.3، + +185 +00:17:50,800 --> 00:17:51,460 +1.3، 1.3، 1.3، + +186 +00:17:51,460 --> 00:17:51,580 +1.3، 1.3، 1.3، + +187 +00:17:51,580 --> 00:17:54,020 +1.3، 1.3، 1.3، + +188 +00:17:54,020 --> 00:18:01,930 +1.3، 1.3، لأ ده ... ده + +189 +00:18:01,930 --> 00:18:04,930 +أعطيتك هذا ال voltage واحد، وقولت لك شغال، قد إيش ال + +190 +00:18:04,930 --> 00:18:08,290 +voltage هذا؟ 1.7، شايفين ال difficulty + +191 +00:18:08,290 --> 00:18:13,110 +صارت إيش؟ أعلى شوية، لأن إيش؟ أنا متعود أن أشوفها + +192 +00:18:13,110 --> 00:18:15,610 +من ال positive لل negative، مش متعود أشوفها من ال + +193 +00:18:15,610 --> 00:18:22,550 +negative لل positive، واضحة هذه؟ طيب، أبسط حاجة الآن + +194 +00:18:22,550 --> 00:18:27,090 +يعني أتكلمنا على هدول، بنتكلم على شغل ثاني بنسميه + +195 +00:18:27,090 --> 00:18:31,310 +ال diode capacitance، ال diode capacitance بتيجي من + +196 +00:18:31,310 --> 00:18:35,490 +إيش؟ لو كان عندي في charge هنا وفي charge ثاني + +197 +00:18:35,490 --> 00:18:39,070 +هنا وفي فرق بينهم، يعني في فرق جهد بيصير عندي + +198 +00:18:39,070 --> 00:18:43,760 +capacitance effect، مظبوط؟ أنا بأتكلم عندي في ال + +199 +00:18:43,760 --> 00:18:48,160 +region depletion، في عندي حشوة positive ion على + +200 +00:18:48,160 --> 00:18:51,880 +الشحنة هذه وفي عندي negative ion على الشحنة الثانية + +201 +00:18:51,880 --> 00:18:58,240 +حيصير إيش؟ two charges في بينهم إيش اللي بيحصل؟ في + +202 +00:18:58,240 --> 00:19:02,910 +عندي صار capacitance effect بينهم، حاجة ثانية يمكن + +203 +00:19:02,910 --> 00:19:07,050 +ال example ده بنقول لو جئت أنت وولعت، طفينا الغرفة + +204 +00:19:07,050 --> 00:19:12,250 +هاي وولعت حاجة بتدخن، الدخان هيمشي في الغرفة بشكل + +205 +00:19:12,250 --> 00:19:20,910 +متوازن، كيف هيمشي؟ عشوائي، بناء على إيش؟ بناء على + +206 +00:19:20,910 --> 00:19:24,810 +الضغط الموجود وقد إيش الفراغات الموجودة في الهواء، في + +207 +00:19:24,810 --> 00:19:28,350 +النقطة هتلاقيها مش ماشية عدل ولا ماشية باتجاهها + +208 +00:19:28,350 --> 00:19:31,950 +نفس الشيء لو جئت كبيت شوية ماء على الأرض هتلاقيها + +209 +00:19:31,950 --> 00:19:36,730 +تمشي مشي على شكل خط مستقيم إذا كان شوية شوية حسب + +210 +00:19:36,730 --> 00:19:41,550 +التعروجات الموجودة في الأرض، وين بتلاقيها؟ هتلاقيها + +211 +00:19:41,550 --> 00:19:46,830 +ماشية فيها، معناته إيش؟ في أي حاجة في عندي ... هذا + +212 +00:19:46,830 --> 00:19:49,830 +بيسميه ال ... ال ... في capacitance within ال + +213 +00:19:49,830 --> 00:19:54,070 +material نفسها، هذا طبيعي يبقى هذا فأنا لما بدي + +214 +00:19:54,070 --> 00:20:06,790 +أحسب ال diode capacitance بدي أحكي على التالي، و + +215 +00:20:06,790 --> 00:20:13,850 +هأسميها Cd اللي بتعتمد على ال Vd، بديها تساوي Tau of + +216 +00:20:13,850 --> 00:20:28,070 +T IS على P of T E لل VD على P of T plus CD0 على 1 + +217 +00:20:28,070 --> 00:20:36,850 +plus VD على P of 0 للM، في عندي جزئيتين، جزئية هات + +218 +00:20:36,850 --> 00:20:40,810 +اللي دخلت بال depletion + +219 +00:20:45,900 --> 00:20:53,420 +region charge وهذه الجزئية لها دخل بال storage + +220 +00:20:53,420 --> 00:20:57,060 +minority + +221 +00:20:57,060 --> 00:21:00,600 +charge + +222 +00:21:00,600 --> 00:21:03,920 +فهذه + +223 +00:21:03,920 --> 00:21:04,740 +الجزئية الثانية + +224 +00:21:07,480 --> 00:21:12,120 +ال VD عرفناها، ال C D، ال C اللي هي ال capacitance و + +225 +00:21:12,120 --> 00:21:16,020 +ال P of T عرفناها قبل، وال IS عرفناها قبل، إيش ده + +226 +00:21:16,020 --> 00:21:22,900 +اللي عندي؟ حاجتين، ال tau of T اللي حقًا بنسميه + +227 +00:21:22,900 --> 00:21:27,820 +minority carrier + +228 +00:21:27,820 --> 00:21:31,240 +transit + +229 +00:21:35,730 --> 00:21:42,950 +وفي عندي ضالة هنا، ال Cdo اللي هاد بقول capacitance + +230 +00:21:42,950 --> 00:21:46,690 +للد diode + +231 +00:21:46,690 --> 00:21:56,370 +under zero bias، وفي عندي ال phi of zero اللي بسميه + +232 +00:21:56,370 --> 00:22:01,690 +ال junction potential + +233 +00:22:05,660 --> 00:22:09,060 +under zero bias اللي هي بيسميها دي بالضبط، typical + +234 +00:22:09,060 --> 00:22:15,020 +point seven volt إلى point nine volt وفي عندي ال m + +235 +00:22:15,020 --> 00:22:21,600 +بيسميه grading coefficient + +236 +00:22:21,600 --> 00:22:29,730 +وهذا يا إما ثلث يا إما نصف، معرفة هذه وهذه وهذه + +237 +00:22:29,730 --> 00:22:34,390 +اللي بيقررها مين؟ ال manufacturing، يعني لما نفتح ال + +238 +00:22:34,390 --> 00:22:38,150 +grade ال specification sheet بنلاقيها ونفس الشيء + +239 +00:22:38,150 --> 00:22:43,790 +هذه بنلاقيها في ال specification sheet تبعات مين؟ ال + +240 +00:22:43,790 --> 00:22:48,070 +diode موجودة، لأن هذا ال capacitance under zero + +241 +00:22:48,070 --> 00:22:51,890 +bias لما أنا ما شيكتش ال diode ولا بأشي، قد إيش ال + +242 +00:22:51,890 --> 00:22:55,830 +capacitance الموجودة فيه، ال junction potential + +243 +00:22:55,830 --> 00:22:59,370 +قد إيش ال potential اللي جاي لما يصير عندي في under + +244 +00:22:59,370 --> 00:23:06,820 +zero bias بين ال both sides للدايود اللي عندي هذا + +245 +00:23:06,820 --> 00:23:11,100 +دولة إيش؟ لل junction اللي عندنا، بنقول عنها ال + +246 +00:23:11,100 --> 00:23:14,360 +depletion region اللي موجودة عندنا، ال grading هذا + +247 +00:23:14,360 --> 00:23:19,040 +نسبة كده، نسبة ال doping اللي موجود لل system الآن + +248 +00:23:19,040 --> 00:23:24,940 +ال minority charge، كده أنا عندي الوقت اللي بتاخده + +249 +00:23:24,940 --> 00:23:29,720 +للثواني بال B material، ال minority إيش عندي؟ + +250 +00:23:29,720 --> 00:23:35,970 +electrodes اللي بتأخذ ال electrons لترجع لمين؟ ل ال + +251 +00:23:35,970 --> 00:23:39,990 +N material، كده بتأخذ وقت لتعمل ال transit من هذه + +252 +00:23:39,990 --> 00:23:43,890 +ال region ل region الثانية، هذا بنسميه إيش؟ لما + +253 +00:23:43,890 --> 00:23:47,890 +يصير عندي switching من on ل off كده بتأخذ وقت + +254 +00:23:47,890 --> 00:23:51,950 +لترجع هناك، لأ، بعبارة ثانية، تتذكرين احنا لما فتحنا + +255 +00:23:51,950 --> 00:23:55,650 +الحدود بيننا وبين المصريين، كل أهل غزة، اين راحوا؟ + +256 +00:23:56,500 --> 00:23:59,080 +راحوا على المنطقة اللي هناك وبعدين كل المصريين + +257 +00:23:59,080 --> 00:24:03,280 +أجوا عندنا، لما قالوا سكرت الكل، صار إيه؟ بده يرجع + +258 +00:24:03,280 --> 00:24:06,680 +على المكان اللي هو فيه، نفس ال analogy بتقدر + +259 +00:24:06,680 --> 00:24:12,260 +تستخدمها أنت هناك، مش أصلي، مش majority أنت majority + +260 +00:24:12,260 --> 00:24:16,160 +فأنت بدك ترجع ل majority تبعتك في غزة، نفس الشيء + +261 +00:24:16,160 --> 00:24:20,120 +اللي بنتكلم عنه في هذه الحالة إن ال electrodes as + +262 +00:24:20,120 --> 00:24:24,300 +a majority مكانها في ال N material وال hose as a + +263 +00:24:24,300 --> 00:24:27,720 +majority مكانها في ال P material، فهذا على طول + +264 +00:24:27,720 --> 00:24:33,300 +بيرجعوا للثانية، هذه سوف نستخدمها ليس الآن، لو كنا + +265 +00:24:33,300 --> 00:24:38,880 +نتكلم عن ال dynamic بتلزمنا نعرف قد إيش ال + +266 +00:24:38,880 --> 00:24:43,600 +capacitance، لأنه قد إيش بتأخذ وقت لتعمل charging و + +267 +00:24:43,600 --> 00:24:49,340 +discharging لهذه ال capacitor، الآن الدائرة اللي + +268 +00:24:49,340 --> 00:24:55,000 +بتهمنا أكثر شيء اللي هي دائرة بسيطة هتطبقها + +269 +00:24:55,000 --> 00:25:01,150 +بالمختبر وتشوف كيف بيطلع عندنا الفرق بينهم، إيش هي + +270 +00:25:01,150 --> 00:25:06,310 +اللي بنتكلم عنها؟ بنتكلم على ال diode resistor + +271 +00:25:06,310 --> 00:25:13,330 +logic + +272 +00:25:13,330 --> 00:25:21,250 +وبنسميه DRL، هذه أول عائلة من عائلات ال logic ده + +273 +00:25:21,250 --> 00:25:26,070 +أول عائلة من عائلات ال logic، الشكل تبعها شوية أنت + +274 +00:25:26,070 --> 00:25:37,600 +مش متعود عليه، هي Vout، هاي ال A، هاي ال Vdc، هاي + +275 +00:25:37,600 --> 00:25:45,960 +two diodes على شحنة ال input، Vna، Vnb، هاي Da وهاي + +276 +00:25:45,960 --> 00:25:57,050 +Db، الآن بتطلع على هدول ال diodes، الخيارات اللي + +277 +00:25:57,050 --> 00:26:01,730 +عندي، يا إما هدول الدايود بدهم يكونوا on يا off يا + +278 +00:26:01,730 --> 00:26:06,170 +واحد منهم on وواحد off، مظبوط؟ نيجي نطلع على التلت + +279 +00:26:06,170 --> 00:26:14,110 +خيارات اللي عندي، دي دي أي دي اي + +280 +00:26:14,110 --> 00:26:18,910 +دي اي دي اي دي اي دي اي دي اي دي اي دي اي دي اي دي + +281 +00:26:18,910 --> 00:26:21,320 +اي دي اي دي اي دي اي دي اي دي اي دي اي أو دي بي بدي + +282 +00:26:21,320 --> 00:26:25,820 +يكون on على سبيل المثال أو أي واحد منهم معكوسة + +283 +00:26:25,820 --> 00:26:31,140 +العكس شبه لهذا يعني الثانية لما نقول ال دي بي off و + +284 +00:26:31,140 --> 00:26:37,740 +دي ايه on نفس الفكرة طيب لو كانوا هدول off ايش ال + +285 +00:26:37,740 --> 00:26:41,400 +output؟ + +286 +00:26:41,400 --> 00:26:42,840 +بدي يساوي كام؟ + +287 +00:26:47,700 --> 00:26:53,940 +أي drop أنت مشبوك فيه حاجة عندك يبقى هذا عبارة عن + +288 +00:26:53,940 --> 00:26:59,980 +كله صار wire فالفي أوت بدي يساوي ال في دي سي في حالة مين + +289 +00:26:59,980 --> 00:27:08,160 +يعني في حالة في هذه الحالة عندي في أوت equal في دي سي + +290 +00:27:08,160 --> 00:27:11,720 +كويس السؤال الآخر اللي بيطرح نفسه ووقتيش هدولة + +291 +00:27:11,720 --> 00:27:12,920 +بيكونوا off + +292 +00:27:19,350 --> 00:27:23,950 +خليني أقول هذه عشان أسهل عليكم هذه بدي أحطها five + +293 +00:27:23,950 --> 00:27:28,950 +volt هنا بقول إن عندي صار five volt وقتيش هدولة + +294 +00:27:28,950 --> 00:27:34,310 +بيكونوا off طيب + +295 +00:27:34,310 --> 00:27:38,390 +في عندي واحد جواب بيقول لما ال في إن يكون أكبر من 4 + +296 +00:27:38,390 --> 00:27:41,690 +.3 في جواب ثاني + +297 +00:27:45,290 --> 00:27:50,450 +أقل من أربعة point تلاتة هذه الجواب جوابين طيب لما + +298 +00:27:50,450 --> 00:27:56,790 +نقول أكبر من أربعة ليش؟ طيب + +299 +00:27:56,790 --> 00:28:04,470 +ولما نقول أقل من أربعة point تلاتة ليش؟ احنا + +300 +00:28:04,470 --> 00:28:12,760 +بدئين؟معناته off بيكون ال في دي أقل من 0.7 إذا + +301 +00:28:12,760 --> 00:28:17,960 +بيكون أقل من 0.7 يبقى الشجة هذه بيكون أكبر من 4.3 + +302 +00:28:17,960 --> 00:28:28,420 +مظبوط يعني هنا أنا بيقول في إن بيكون أكبر من في دي سي + +303 +00:28:28,420 --> 00:28:36,280 +ناقص في دي on اللي هي ال 4.3 بس هذه symbolically + +304 +00:28:36,280 --> 00:28:40,620 +كتبناها زي كده، معناته في هذه الحالة بعطيني ال في + +305 +00:28:40,620 --> 00:28:46,400 +أوت بدي يساوي هدول off ال في أوت بدي يساوي في دي سي اللي + +306 +00:28:46,400 --> 00:28:52,750 +عندي، اتفقنا عليها هذه؟ فش طالما مش مشبوكة على أي + +307 +00:28:52,750 --> 00:28:57,950 +حاجة فش أي drop مظبوط؟ ايش ال أوت بدي يساوي؟ بدي + +308 +00:28:57,950 --> 00:29:03,770 +يساوي في دي سي ناقص أي في ار إذا أي بيساوي Zero يبقى بدي + +309 +00:29:03,770 --> 00:29:09,450 +يساوي بس في دي سي لو حطيت ال ground بدي تصير سيارة رايحة + +310 +00:29:09,450 --> 00:29:13,990 +إن تيار اه بطل بيساوي زي هيك فاحنا بنحطه في ال + +311 +00:29:13,990 --> 00:29:17,390 +logic بنقول لك عود حالك تبرمج في هذه الطريقة اللي + +312 +00:29:17,390 --> 00:29:23,540 +احنا بنبرمجك عليها واضح الجواب اللي عندي؟ حد بيختلف + +313 +00:29:23,540 --> 00:29:27,860 +معايا في هذه الشغلة؟ الكل فاهمها كيف اجت؟ انا اللي + +314 +00:29:27,860 --> 00:29:33,720 +بدي اياه بدي ال في دي ال في دي يكون أقل من ال point 7 + +315 +00:29:33,720 --> 00:29:38,160 +اللي حكيناها في ال mode of operation عندي هذا طيب + +316 +00:29:38,160 --> 00:29:46,660 +الحل اللي بعدها هدولة on إذا هدولة on كويس؟ ايش + +317 +00:29:46,660 --> 00:29:51,380 +اللي بدي يحصل عندي؟ هذا حطيت zero أول خطوة + +318 +00:29:51,380 --> 00:30:00,080 +ما عملناهاش ايش هي لأي دايت تحط ال priority تبعته + +319 +00:30:00,080 --> 00:30:03,120 +هي positive negative positive negative عشان ما أضيعش + +320 +00:30:03,120 --> 00:30:10,920 +الأقل وهذا صفر قداش ال voltage هذا point 7 يعني لو + +321 +00:30:10,920 --> 00:30:16,860 +جيت أدرسه من ال في تي سي تبعته هوب هذه ال في إن وهنا ايش + +322 +00:30:17,370 --> 00:30:24,250 +في أوت هنا قلت صفر ال في إن اعطتني كم point 7 كانت + +323 +00:30:24,250 --> 00:30:38,410 +point 7 كم بتعطيني 1.4 كانت 2 point 7 كانت 2 2 + +324 +00:30:38,410 --> 00:30:45,970 +point 7 بتزود 7 بضل أزود فيه يعني علاقة واحد زي + +325 +00:30:45,970 --> 00:30:51,370 +هيكا لقد ايش لحد ما يصير هدول ايش off هدول off + +326 +00:30:51,370 --> 00:30:57,190 +ما كانت بيصيروا لما ال في إن لما + +327 +00:30:57,190 --> 00:31:03,010 +تصير ال في إن عندي بتساوي في دي سي ناقص في دي on إذا أنا + +328 +00:31:03,010 --> 00:31:06,810 +حاطيتها على الخمسة بدها تكون أربعة point تلاتة بعدها + +329 +00:31:06,810 --> 00:31:11,890 +ال output بيصير ايش straight line كل ما أزود في ال + +330 +00:31:11,890 --> 00:31:20,010 +input ال output بيظله على ال في دي سي اللي موجود عندي + +331 +00:31:20,010 --> 00:31:24,110 +فأنا بديت من point سبعة وظلت نطالع ايش اللي حصل + +332 +00:31:24,110 --> 00:31:32,330 +هنا هذا بيصير off يعني ال دي أي وضعه off وهنا ال دي أي + +333 +00:31:32,330 --> 00:31:38,090 +كله ايش on مظبوط هنا ال دي أي off هدولة صاروا off على + +334 +00:31:38,840 --> 00:31:43,740 +لما من أربعة point تلاتة وطالع الموجود عندي هدولة + +335 +00:31:43,740 --> 00:31:49,640 +صاروا off الآن حلت هذه حلتها أنا هنا قلت ال في أوت + +336 +00:31:49,640 --> 00:31:57,540 +بدي يساوي اللي عندي في إن زائد في دي on الموجود عندي + +337 +00:31:57,540 --> 00:32:03,040 +في هذه الحالة ظلت الحالة الثالثة الحالة + +338 +00:32:03,040 --> 00:32:08,320 +الثالثة ايش بدي احط عندي هذا عندي صفر وهذا خمسة + +339 +00:32:09,220 --> 00:32:18,060 +مديش ال output بدي يطلع الجواب + +340 +00:32:18,060 --> 00:32:25,280 +عنده يا هيطلع حاجتين مظبوط يا هيطلع خمسة يا إما + +341 +00:32:25,280 --> 00:32:30,920 +هيطلع point 7 مين اللي هيطلع فيهم فيه جواب point 7 + +342 +00:32:30,920 --> 00:32:37,460 +ايش الثاني كم واحد بيقول point 7 يرفع يده كم واحد + +343 +00:32:37,460 --> 00:32:46,060 +بيقول خمسة والباقي ولاوش قرار الآن + +344 +00:32:46,060 --> 00:32:50,140 +لو هذا ما اشتغلش ايش بدو يعملوا؟ بدو يشيله من + +345 +00:32:50,140 --> 00:32:55,220 +الدائرة مظبوط الدائرة بتشتغل ولا لأ؟ إذا بتشتغل + +346 +00:32:55,220 --> 00:32:59,940 +بتعطيني كام؟ point 7 طالما اشتغلت هتعطيني point 7 + +347 +00:32:59,940 --> 00:33:05,580 +يبقى هذه مش هتأثر على الدائرة صح؟ ايش أعطتنها؟ + +348 +00:33:05,580 --> 00:33:15,800 +بدأت هنا ب high و hi عطتني ايش؟ hi مظبوط بدأت هنا + +349 +00:33:15,800 --> 00:33:24,560 +بإيش؟ low و low عطتني ايش؟ low بدأت هنا ب low و + +350 +00:33:24,560 --> 00:33:33,280 +high عطتني ايش؟ low ولو عكستها هذه high و low + +351 +00:33:33,280 --> 00:33:39,370 +هتعطيني low ايش هذه ال gate؟ أيوة شايفين مثلها إذا + +352 +00:33:39,370 --> 00:33:43,990 +أنت بتشتغلها صح بتطلع + +353 +00:33:43,990 --> 00:33:47,970 +عندك الجواب سهل أنا ما رضيتش أكتب اسم ال gate عشان + +354 +00:33:47,970 --> 00:33:57,270 +تصور الاستنتاج هذا هذا بنقول عنها دي ار ال and gate + +355 +00:33:57,270 --> 00:34:02,290 +الدائرة الموجودة عندي لأن أنا هنا لما حطيت الحالات + +356 +00:34:02,290 --> 00:34:06,900 +الموجودة عندي التلات حالات أو الأربع حالات ايش اللي + +357 +00:34:06,900 --> 00:34:11,120 +أعطاني هنا وقت ايش ال دي أي بدها تكون off وقت ايش + +358 +00:34:11,120 --> 00:34:14,580 +بدها تكون شغالة لما الواحدة شغالة وواحدة مش + +359 +00:34:14,580 --> 00:34:19,480 +شغالة ايش وضع الدائرة الموجودة عندي قدرت اخذ اللي + +360 +00:34:19,480 --> 00:34:24,300 +هاته هنا طلع عندي لساتها ال في أوت بدها تساوي في إن + +361 +00:34:24,300 --> 00:34:32,240 +plus في دي on الموجود عندي نعيدها + +362 +00:34:34,850 --> 00:34:39,990 +طيب أنا ايش اللي عملته هان أول خطوة طلعت فيها لو + +363 +00:34:39,990 --> 00:34:43,370 +كانت ال input اللي عندي high ايش بدو يصير ال + +364 +00:34:43,370 --> 00:34:47,510 +diodes هدول بدها تصيروا off إذا off يبقى ال output + +365 +00:34:47,510 --> 00:34:55,470 +بدو يساوي في دي سي هدولة شغالين يبقى ال input بدو يكون + +366 +00:34:55,470 --> 00:35:02,280 +عندي لو بدأت من low من صفر بدي أزود point 7 عليهم و + +367 +00:35:02,280 --> 00:35:05,100 +ال في أوت بيعطيني قداش ال input زائد point 7 + +368 +00:35:05,100 --> 00:35:10,360 +بيعطيني ال في أوت هي طبيعة الدائرة عندي الآن لو + +369 +00:35:10,360 --> 00:35:15,480 +واحدة منهم شغالة وواحدة مش شغالة المش شغالة هتروح + +370 +00:35:15,480 --> 00:35:20,060 +مش هيكون لها تأثير الشغالة هي اللي هتأثر على شجة + +371 +00:35:20,060 --> 00:35:24,060 +مين ال output هذا طبيعته في التحليل تبعته هذا + +372 +00:35:24,060 --> 00:35:30,980 +بتطلع and gate اللي موجود عندنا واضحة + +373 +00:35:30,980 --> 00:35:37,230 +هذا هتشتغلوها بالمختبر الدائرة نفسها عشان تتأكد أن + +374 +00:35:37,230 --> 00:35:44,650 +الأجوبة اللي بتطلع عندكم هي مقنعة بهذه الطريقة في + +375 +00:35:44,650 --> 00:35:48,990 +الكوية سؤال عليها؟ هذه اتكلمنا على الاد، بدنا نروح + +376 +00:35:48,990 --> 00:35:53,150 +على مين الحين؟ على الار، زي ما بنسوي الار جيت، + +377 +00:35:53,150 --> 00:35:59,710 +هتشوفها أبسط كتير من مين؟ من الاد، ليش؟ لأ مش عشان + +378 +00:35:59,710 --> 00:36:06,340 +هفهمين ال orientation تبعتها، متعودين على شكلها الـ + +379 +00:36:06,340 --> 00:36:20,120 +Orientation للـ R في الاتجاه اللي بتعود عليه هذه + +380 +00:36:20,120 --> 00:36:33,450 +في إن ايه في إن بي هذه دي ايه دي بي في أوت وهنا الـ R الآن أول + +381 +00:36:33,450 --> 00:36:36,950 +خطوة بدي اعملها زي ما بعمل دائما اللي هي أحدد ال + +382 +00:36:36,950 --> 00:36:43,610 +positive و ال negative طلع عندي ايش اللي بدي يطلع + +383 +00:36:43,610 --> 00:36:48,130 +لو كان خليني أقول هدول هدولة بدنا نحط زي هناك ايش + +384 +00:36:48,130 --> 00:36:58,670 +بدي يكون الحالات هدولة واضحة ال دي أي off ال دي أي on دي + +385 +00:36:58,670 --> 00:37:08,660 +ايه offdv out كويسة هدول لو off ايش معناتهم ال + +386 +00:37:08,660 --> 00:37:13,940 +output كده يساوي؟ zero أنا بدي أقول ال في أوت هنا + +387 +00:37:13,940 --> 00:37:23,060 +equal zero طب وقت ايش هدول بيكونوا off؟ بدي ال + +388 +00:37:23,060 --> 00:37:28,080 +voltage drop يكون ايش؟ أقل من point 7 الشجة هذه + +389 +00:37:28,080 --> 00:37:32,080 +عندي كام ال output الحين؟ zero لو هذا كان عندي zero + +390 +00:37:32,080 --> 00:37:37,660 +كده الفرق؟ off يعني حبدأ فيه طب لو كان point اتنين + +391 +00:37:37,660 --> 00:37:43,780 +point تلاتة لحد دي point سبعة يعني هذا حيضل off + +392 +00:37:43,780 --> 00:37:48,240 +لحد دي point سبعة يعني لو بتدرسوا من ال في تي سي تبعته + +393 +00:37:48,240 --> 00:37:56,280 +هي في إن وهنا في أوت حبدأ من zero zero لحد دي موصل + +394 +00:37:56,280 --> 00:38:02,510 +وين؟ ال point 7 اللي هي ال video on وبعدها ال + +395 +00:38:02,510 --> 00:38:08,010 +video on وبعدها لو هذه point 8 كده ال output + +396 +00:38:08,010 --> 00:38:15,930 +point واحد واحد point تلاتة اتنين واحد point تلاتة + +397 +00:38:15,930 --> 00:38:21,820 +شايفين هذه مثلها شكلها ايش بسيط ليش؟ لأنه على طول + +398 +00:38:21,820 --> 00:38:25,400 +أنا بتعود للاتجاه اللي أنا بتعود عليه طول حياتي + +399 +00:38:25,400 --> 00:38:29,620 +بشوف ال diode رايح في هذا الاتجاه، بشوفوش رايح زيها + +400 +00:38:29,620 --> 00:38:34,920 +في الاتجاه الاخر المعاكس، هذا جديد عليا الرسمة، هذا + +401 +00:38:34,920 --> 00:38:41,200 +رسمة بتعود عليها بلاقيش غلب فيها الآن هذه عملناها و + +402 +00:38:41,200 --> 00:38:45,560 +هذه عملناها وقلنا هذا ال في أوت بدي يساوي في إن + +403 +00:38:45,560 --> 00:38:52,820 +ناقص في دي on ضلت الحالة الثالثة لو هذه off وهذه + +404 +00:38:52,820 --> 00:38:57,300 +شغالة مين اللي بيحكم؟ الشغالة هذا اللي بتحكم وهذه + +405 +00:38:57,300 --> 00:39:02,000 +مالها أي تأثير عندي يعني إذا الشغالة بدها تمشي + +406 +00:39:02,000 --> 00:39:06,620 +معها المعادلة مين هذه بدها تبقى ماشية معها ال في + +407 +00:39:06,620 --> 00:39:12,160 +أوت بيساوي في إن ناقص في دي on ال في إن تبعت مين + +408 +00:39:12,160 --> 00:39:18,320 +المتغيرة تبعت ايه؟ تبعت ال بي هذا تبعت ال بي اللي + +409 +00:39:18,320 --> 00:39:24,820 +بدها تمشي معها أي سؤال على هذه الدائرة طلع هنا ايش + +410 +00:39:24,820 --> 00:39:31,360 +حصل عندي وين بدأت هنا بدأت هنا مظبوط و ال في أوت + +411 +00:39:31,360 --> 00:39:36,900 +فيه إلو ايش shift أو ال في أوت هنا إلو shift وهنا + +412 +00:39:36,900 --> 00:39:43,360 +ال في أوت اللي عندي بدأت منه بإيش point سبعة فيه + +413 +00:39:43,360 --> 00:39:47,800 +shift عندي هنا shift شجة ال output وهنا shift شجة + +414 +00:39:47,800 --> 00:39:54,200 +ال input طب أنا ممكن بشوية تعديل في الدائرة أشيل ال + +415 +00:39:54,200 --> 00:39:58,060 +shift هات يعني يصير عند ال في إن بيساوي ال في أوت لما + +416 +00:39:58,060 --> 00:40:02,380 +أحط zero بيعطيني ال output zero أحط واحد بيعطيني + +417 +00:40:02,380 --> 00:40:06,240 +واحد القيمة اللي بحطها بتطلع عندي فبتصير العلاقة + +418 +00:40:06,240 --> 00:40:11,870 +ايش طبيعتها linear هذه بسميها level shifted Logic + +419 +00:40:11,870 --> 00:40:19,190 +DRL Gates أنا بعملهم shifting طب كيف بعمله خليني + +420 +00:40:19,190 --> 00:40:25,290 +أشوف example على الموجودين هنا ناخد الدائرتين و + +421 +00:40:25,290 --> 00:40:29,510 +نشوف كيف ممكن نعمل ال shifting الموجود عندنا + +422 +00:41:09,740 --> 00:41:11,220 +العزيزة يا ربي + +423 +00:41:37,030 --> 00:41:42,170 +نظري إلى هذه الدائرة ماذا أضافته الجزء الموجود هنا + +424 +00:41:42,170 --> 00:41:48,290 +أضافته الأعمال shifting لهذه الدائرة طيب في هذه + +425 +00:41:48,290 --> 00:41:53,090 +الحالة دعنا نرى كيف نتعامل معها أو ايش الحالات + +426 +00:41:53,090 --> 00:41:57,090 +اللي عندي طبعاً الحالات اللي عندي عندي أربع حالات + +427 +00:41:57,090 --> 00:42:01,050 +بدهم يطلعوا ايش هما هذولة بسميها شجرة ال input ايش + +428 +00:42:01,050 --> 00:42:05,130 +ال input فهذولة بقول عنهم ال d eyes يا إما بيكون + +429 +00:42:05,130 --> 00:42:14,640 +عندي ال d eyes on و ال dial on هي حالة عندي ال di's + +430 +00:42:14,640 --> 00:42:25,820 +on و ال dial off عندي ال di's off و ال dial on + +431 +00:42:25,820 --> 00:42:35,450 +عندي الحالة الرابعة ال di's off و ال dial شايفين + +432 +00:42:35,450 --> 00:42:39,270 +اللي عندي هذول أربع حالات لأن الاربع حالات بدي + +433 +00:42:39,270 --> 00:42:43,350 +أشوف لما أدخل عند ال input ايش بيطلع output وأرسم + +434 +00:42:43,350 --> 00:42:53,530 +ال VTC لهذا الدائرة عشان أشوف كيف بيطلع شكلها هاي + +435 +00:42:53,530 --> 00:42:54,210 +ال VTC + +436 +00:43:07,070 --> 00:43:13,610 +هذا أنزل في هذه الأن هتشوف مش بس عند السفر هتبدأ + +437 +00:43:13,610 --> 00:43:17,490 +من عند السفر على shift هذا صار بالنسبة إلى لهذه + +438 +00:43:17,490 --> 00:43:21,670 +الشجرة أو من هنا في هذا الحالة بدي أعمله الشيء + +439 +00:43:21,670 --> 00:43:27,490 +السفر بدي أبدأ كله من عند السفر اللي عندي هذا بقول + +440 +00:43:27,490 --> 00:43:33,350 +هذول بديهم يكونوا on وهذا بيكون on مظبوط الآن هذا + +441 +00:43:33,350 --> 00:43:38,150 +بدي أسميه نقطة X وهاي ال positive negative + +442 +00:43:38,150 --> 00:43:42,770 +positive negative positive negative الآن ال + +443 +00:43:42,770 --> 00:43:47,290 +voltage الموجود هنا ايش بده اعمله لوصله هنا لما + +444 +00:43:47,290 --> 00:43:56,010 +هذول شغالين يعني ال VX هنا ايش بده يساوي VN زائد + +445 +00:43:56,010 --> 00:44:02,290 +VD on مظبوط الآن لوصل لهذا الشجرة ايش بده أعمل فيه + +446 +00:44:03,970 --> 00:44:12,450 +الـ Vout بدي يساوي Vx ناقص Vd on مظبوط اللي هو بدي + +447 +00:44:12,450 --> 00:44:24,970 +يعطيني Vx Vn ناقص زائد Vd on ناقص Vd on هيعطيني Vn + +448 +00:44:24,970 --> 00:44:32,840 +يعني ال Vout بساوي كم ال Vn الآن لو بدأت من صفر ال + +449 +00:44:32,840 --> 00:44:36,840 +output صفر ال input واحد ال output واحد ال input + +450 +00:44:36,840 --> 00:44:40,420 +اثنين ال output اثنين ال input ناقص واحد ال output + +451 +00:44:40,420 --> 00:44:44,600 +ناقص واحد ال input ناقص اثنين ال output ناقص اثنين + +452 +00:44:44,600 --> 00:44:50,980 +يعني بدي أكون عندي خط زي هي clean يعني + +453 +00:44:50,980 --> 00:44:54,480 +هاي + +454 +00:44:54,480 --> 00:44:59,750 +اللي عندي الاسلوب تبعنا ايش واحد الموجود هنا الآن + +455 +00:44:59,750 --> 00:45:06,570 +زي ما بتعرفوا أوصل لمنطقة حاجة تحصل على الشجرة هاد + +456 +00:45:06,570 --> 00:45:11,930 +تعمله مستقيم وحاجة تصل هاد تعمل ليها مستقيم مظبوط + +457 +00:45:11,930 --> 00:45:16,810 +الآن هذه الحالة أبسط حاجة قداش ال input قداش ال + +458 +00:45:16,810 --> 00:45:21,570 +output يعني في هذه طلع عندي v in equal v out + +459 +00:45:21,570 --> 00:45:29,320 +وخلصنا كل شايفها هذه؟ هنا بضيف point 7 وهذا بطرح ال + +460 +00:45:29,320 --> 00:45:36,220 +point 7 بيطلع المحصلة zero الآن نجي الحالة هنا + +461 +00:45:36,220 --> 00:45:42,660 +هذول شغالين وهذول off إذا هذا مش شغال قداش ال + +462 +00:45:42,660 --> 00:45:49,370 +voltage هنا؟ لأ طلع عندي هذا مش شغال مش zero أنا + +463 +00:45:49,370 --> 00:45:53,950 +شابكوه مع minus VE لو هذا قلته بدي يساوي سالب أربعة + +464 +00:45:53,950 --> 00:45:58,570 +volt وهذا بدي اسميه زائد خمسة volt بس عشان يصير + +465 +00:45:58,570 --> 00:46:03,570 +reference لك هذا قداش بديكون عندي سالب أربعة volt + +466 +00:46:03,570 --> 00:46:10,050 +يعني هذا مجرد ما يكون off هذا بديكون V out بديساوي + +467 +00:46:10,050 --> 00:46:17,830 +minus VE يعني هنا بديصل لها ال V out عندي في هذه + +468 +00:46:17,830 --> 00:46:26,370 +المنطقة هاي الـ minus VEE بدي يعطيني ال V out و + +469 +00:46:26,370 --> 00:46:35,030 +بعده هيعطيني هنا قلت ال DI و اضغط ال DL هنا off و + +470 +00:46:35,030 --> 00:46:47,380 +هنا ال DI on ال DI هنا ال DI on و ال DL في هذه + +471 +00:46:47,380 --> 00:46:53,300 +المنطقة اللي .. فيش .. فيش drop عليها، فيش drop + +472 +00:46:53,300 --> 00:46:59,160 +لأن هذا فيش أي تيار ماشي فيها، فعندي هذا off يبقى + +473 +00:46:59,160 --> 00:47:05,720 +هذا ايش بدي أساوي؟ ليش؟ + +474 +00:47:05,720 --> 00:47:12,020 +لأن اللي عندي أنا ايش قاعد بضيفه؟ هذا يعني جهد + +475 +00:47:12,020 --> 00:47:16,140 +مطلوب، إن حطوا هذا جهد بدي أشيله، في عندي أي شيء + +476 +00:47:16,140 --> 00:47:21,680 +من هذه النقطة لهاذه النقطة، أي مقاومة؟ أنا أحسب + +477 +00:47:21,680 --> 00:47:26,260 +الجزئيات هذول في ال digital، أنت بتقدر تحسبها في ال + +478 +00:47:26,260 --> 00:47:30,260 +... يعني و تجيب النتيجة و تشوف كمية drop across كل + +479 +00:47:30,260 --> 00:47:33,900 +resistor، بس هل هتفيدني؟ أنا في عالم ال digital + +480 +00:47:33,900 --> 00:47:38,340 +بلزمني قد ايش input و قد ايش output مش على طول في حالة + +481 +00:47:38,340 --> 00:47:42,160 +ال high و في حالة ال low بشكل عام الآن أنا قاعد + +482 +00:47:42,160 --> 00:47:45,700 +بقول هاي اللي بختار الحالات عندي في هذه الحالة لما + +483 +00:47:45,700 --> 00:47:50,740 +هذه يبقى شغالة قد ايش ال input و قد ايش ال output في + +484 +00:47:50,740 --> 00:47:57,840 +حالة هذه ماهي ال di شغالة و ال dl مش شغالة قد ايش ال + +485 +00:47:57,840 --> 00:48:01,900 +output تعرفته الآن بدي أعرف قد ايش ليهاش ال input + +486 +00:48:02,820 --> 00:48:06,000 +قداش ال input بدها تجي أطلع عليه drop هنا إذا هذا مش + +487 +00:48:06,000 --> 00:48:09,920 +شغال كده أقل + +488 +00:48:09,920 --> 00:48:14,700 +من point 7 مظبوط يعني أقل من point 7 يعني اللي هنا + +489 +00:48:14,700 --> 00:48:20,160 +لو هذه كانت ناقص أربعة بديكون هذه بالناقص أكثر من + +490 +00:48:20,160 --> 00:48:24,260 +ناقص ثلاثة point ثلاثة أكثر من هذا القيمة بالناقص + +491 +00:48:24,260 --> 00:48:29,420 +إذا أكثر من .. لو شغال أي رقم أكبر من الرقم اللي + +492 +00:48:29,420 --> 00:48:33,820 +هنا بس .. بس خليك معاه أنت أنا جايبك لنقطة اللي + +493 +00:48:33,820 --> 00:48:37,360 +بدك تجيه اتصلها الآن خليك معاه في هذه الشغلة الآن + +494 +00:48:37,360 --> 00:48:40,580 +هذه اللي عندي لو كانت ثلاثة point أربعة بالسالم + +495 +00:48:40,580 --> 00:48:46,640 +قداش هذه ال فارق point ستة ال point ستة أقل من ال + +496 +00:48:46,640 --> 00:48:51,320 +point سبعة أقل يبقى هذا off الآن بدي أجي لهنا ايش + +497 +00:48:51,320 --> 00:48:55,880 +بدي هذه بال positive بتطرح منها كم ناقص من هذه + +498 +00:48:55,880 --> 00:48:59,800 +point سبعة مش هذه شغال ناقص point سبعة قداش بدي + +499 +00:48:59,800 --> 00:49:08,410 +أطلع عندي ناقص point 7 و ناقص 3 point 4 ناقص 4 + +500 +00:49:08,410 --> 00:49:15,810 +point 1 ناقص 4 point 1 ناقص 4 point 3 ناقص 4 ناقص + +501 +00:49:15,810 --> 00:49:24,970 +4 ناقص 4 ناقص 4 ناقص 4 ناقص 4 ناقص 4 ناقص 4 ناقص 4 + +502 +00:49:25,270 --> 00:49:29,910 +بعد هيك لو هذه بالنقص اجت أكثر من ناقص أربعة هذا + +503 +00:49:29,910 --> 00:49:34,070 +بيعطيني ايش off طلع الرسمة عندي مع أنه slope واحد + +504 +00:49:34,070 --> 00:49:39,690 +هذا النقطة اللي عندي ايش minus VEE آخر نقطة بشتغل + +505 +00:49:39,690 --> 00:49:44,570 +فيها الآن اللي دخل بال Resistors في الحسبة هذه اجت + +506 +00:49:44,570 --> 00:49:49,330 +هذه موجودة وفي تيار بيروح عليها بتاخده drop بس + +507 +00:49:49,330 --> 00:49:55,150 +بتلزمني مش هي ده جدوى في حسبتي أنا حسبتي وين بيجي + +508 +00:49:55,150 --> 00:49:58,910 +أنا لما بأخذ ال loop هذا في ال loop هذا في أي + +509 +00:49:58,910 --> 00:50:04,750 +resistor فش عندي هي zero زائد point سبعة ناقص + +510 +00:50:04,750 --> 00:50:09,210 +point سبعة بدي يعطيني ال voltage اللي هذا هذا ال + +511 +00:50:09,210 --> 00:50:14,190 +loop تبعي فأنا عادة في ال digital world بأخذ ال + +512 +00:50:14,190 --> 00:50:18,990 +loop اللي بفيدني الآن لاحقا عندما نتكلم في chapter + +513 +00:50:18,990 --> 00:50:24,890 +4 و 5 سأتكلم عن حاجتين تيجي على ال ending سأتكلم + +514 +00:50:24,890 --> 00:50:29,690 +عن ال fan out سأتكلم عن ال power dissipation ساتر + +515 +00:50:29,690 --> 00:50:37,210 +أروح على كل هذه الدوائر أحللها بس لل VTC تلزمش للـ + +516 +00:50:37,210 --> 00:50:42,610 +VTC بلزمش أحلل كل الدائرة وهذا في عالم ال digital + +517 +00:50:42,610 --> 00:50:49,070 +لما نقول لك ما تضيعش وقتك على معلومة مش مطلوبة عشان + +518 +00:50:49,070 --> 00:50:56,570 +ايش تعمل optimization الآن هذه واضحة الحالة + +519 +00:50:56,570 --> 00:51:02,380 +هذه الأخيرة جايلها هنقول لك ايش التعليق عليها فهنا + +520 +00:51:02,380 --> 00:51:08,840 +عندي صار VIN هتكون أقل من ناقص أقل أو بساوي ناقص + +521 +00:51:08,840 --> 00:51:13,560 +VEE بالناقص يعني بال نيجاتيف طالما هي أقل من هذا + +522 +00:51:13,560 --> 00:51:17,940 +القيمة و هاد الحالة موجودة طب هاد الحالة ايش بيحصل + +523 +00:51:17,940 --> 00:51:23,780 +فيها هنا عندي ال DIs off و هاد ايش شغال يعني + +524 +00:51:23,780 --> 00:51:29,310 +بعبارة ثانية هذه المحايا هذول off ايش off؟ مش + +525 +00:51:29,310 --> 00:51:34,610 +موجودين إذا هذول مش موجودين ايش ال output بدي + +526 +00:51:34,610 --> 00:51:40,270 +يساوي؟ بدك + +527 +00:51:40,270 --> 00:51:47,930 +تاخد ال loop هاي ال loop تبعي و أجيب الطيار الآن و + +528 +00:51:47,930 --> 00:51:50,890 +أجيب ال condition drop across ال resistor الآن ال + +529 +00:51:50,890 --> 00:51:52,130 +loop هذا ايش بيقولي؟ + +530 +00:51:55,460 --> 00:52:00,420 +VDC-IRH-VDLON + +531 +00:52:00,420 --> 00:52:03,640 +-IRL + +532 +00:52:03,640 --> 00:52:11,840 +-1.5 Plus VEE بدي يساوي ايه؟ Zero اللي عندي لأنه + +533 +00:52:11,840 --> 00:52:17,520 +الآن أنا في عندي صار ال loop تبع اللي بمور بمور + +534 +00:52:17,520 --> 00:52:21,540 +عبر الموجود هنا لو بدي أجيب ال V out لازم أعرف + +535 +00:52:21,540 --> 00:52:25,620 +قداش drop هنالو بدي أجيب ال Vout من هذه الشكلة + +536 +00:52:25,620 --> 00:52:29,520 +بدي أعرف كده دروبها فلازم أعرف الآن معلومة كده + +537 +00:52:29,520 --> 00:52:33,080 +دروب across ال resistor لأن ال path اللي كنت باخده + +538 +00:52:33,080 --> 00:52:40,180 +انقطع هنا لما قلت هذول off يبقى هذول مش موجودة إذا + +539 +00:52:40,180 --> 00:52:44,340 +مش موجودة يعني ما أقدر أخد ال path هذا و أقول قداش + +540 +00:52:44,340 --> 00:52:48,260 +ال هذا مش موجود بدا أروح عليها على في الاتجاه + +541 +00:52:48,260 --> 00:52:51,460 +الموجود هنا في الاتجاه هذا ايش معناه بدي أخد ال + +542 +00:52:51,460 --> 00:52:55,080 +loop هذا اللي موجود عندي الآن بدي أجيب I قداش I + +543 +00:52:55,080 --> 00:53:02,240 +بدي يساوي I اللي بدي أجيبه بدي يساوي VDC plus VEE + +544 +00:53:02,240 --> 00:53:06,320 +ناقص VDL on على + +545 +00:53:11,920 --> 00:53:15,300 +التيار اللي هنا بيساوي ال voltage head زائد ال + +546 +00:53:15,300 --> 00:53:18,360 +voltage head ناقص ال voltage drop across ال diode + +547 +00:53:18,360 --> 00:53:23,340 +على قيمتين ال R L و ال RH طب لو بدي أجيب ال V out + +548 +00:53:23,340 --> 00:53:29,880 +هنا ايش بدي أساوي؟ Vout بدي يساوي يا إما بدي أجيبه + +549 +00:53:29,880 --> 00:53:37,140 +من هذا الاتجاه minus VEE زائد I في RL اللي عندي يا + +550 +00:53:37,140 --> 00:53:40,920 +إما بدي أجيبه في الاتجاه الثاني من فوق Vout بدي + +551 +00:53:40,920 --> 00:53:48,480 +يساوي VDC ناقص I في RH ناقص VD on اللي موجودة + +552 +00:53:48,480 --> 00:53:53,470 +عندي فأنا جبته يا إما بده أجيبه من هنا يا إما بده أجيبه + +553 +00:53:53,470 --> 00:53:57,730 +من هنا فش طريقة أخرى أجيبه لأوصل لها طب هاد ال + +554 +00:53:57,730 --> 00:54:03,650 +output قداش ال input بدو يكون لو + +555 +00:54:03,650 --> 00:54:08,190 +zero اشتغل بدو يهان off يبقى ايش ال drop قداش بدو + +556 +00:54:08,190 --> 00:54:08,510 +يكون + +557 +00:54:12,930 --> 00:54:17,930 +الآن هذه لل voltage اللي هنا بدي أضيف له point 7 + +558 +00:54:17,930 --> 00:54:23,750 +والفرق بين هذه و هذه أقل من point 7 يعني لو رسمتهم + +559 +00:54:23,750 --> 00:54:29,110 +بدي أطلع عليهم بهذه الطريقة هنجيب اللون غريب عشان + +560 +00:54:29,110 --> 00:54:36,870 +نوصل هذا هتكون هذا مستقيم هذا عندي أعطتني ال VOH + +561 +00:54:36,870 --> 00:54:38,210 +اللي هي أعطتني إياها هنا + +562 +00:54:42,680 --> 00:54:47,900 +يبقى هذا هو نفس الـ VOH الموجود هنا عندي الـ DI + +563 +00:54:47,900 --> 00:54:55,620 +وضعهم off والـ DL وضعهم on اللي موجود عندي في هاد + +564 +00:54:55,620 --> 00:54:59,220 +قداش الـ voltage اللي بيطلع عندي هاد أي voltage + +565 +00:54:59,220 --> 00:55:05,910 +موجود من هذا أو أكبر بيعطيني إيش بيعطيني DI's of + +566 +00:55:05,910 --> 00:55:10,310 +وهذا بده حسبة مش given number زي هذا لأن مضطر أعرف + +567 +00:55:10,310 --> 00:55:13,290 +قداش قيمة الـ + +568 +00:55:13,290 --> 00:55:13,990 +الـ + +569 +00:55:13,990 --> 00:55:15,670 +الـ + +570 +00:55:15,670 --> 00:55:18,150 +الـ + +571 +00:55:18,150 --> 00:55:22,270 +الـ + +572 +00:55:22,270 --> 00:55:23,590 +الـ + +573 +00:55:23,590 --> 00:55:24,270 +الـ + +574 +00:55:31,880 --> 00:55:36,840 +على اثنين كيلو، بدي يعطينا مثلًا أربعة خلينا نقول + +575 +00:55:36,840 --> 00:55:41,520 +ثمانية point ثلاثة على اثنين كيلو، بدي يعطينا + +576 +00:55:41,520 --> 00:55:47,850 +قداش الأربع واحد point هي يعني بتعطينا أربعة point + +577 +00:55:47,850 --> 00:55:54,490 +واحد خمسة milli-amp هاي بدأ أجيبهم ناقص أربعة زائد + +578 +00:55:54,490 --> 00:56:00,370 +واحد كيلو في أربعة point واحد خمسة يعني هذه + +579 +00:56:00,370 --> 00:56:07,640 +بتعطينا واحد point 0.15 volt اللي بيعطيني إيه سواء + +580 +00:56:07,640 --> 00:56:12,400 +الـ output high اللي هو بيعطيني إيه يعني بعبارة + +581 +00:56:12,400 --> 00:56:16,760 +ثانية خليني أقول لو كان عندي رح بدي أحط لك الأرقام + +582 +00:56:16,760 --> 00:56:23,300 +هنا لو كان عندي RL بدي أساوي بدي أساوي RH بدي أساوي + +583 +00:56:23,300 --> 00:56:29,380 +واحد كيلو أم إيش بدي يحصل عندي الـ I بدي يطلع عندي + +584 +00:56:29,380 --> 00:56:32,420 +اللي هنا خمسة + +585 +00:56:32,870 --> 00:56:38,030 +زائد أربعة ناقص point سبعة على two K بدي يعطيني + +586 +00:56:38,030 --> 00:56:43,850 +أربعة point واحد خمسة ملي أمبير يبقى الـ VOH إيش + +587 +00:56:43,850 --> 00:56:50,370 +بدي أساوي عندي بدي أساوي ناقص أربعة زائد أربعة + +588 +00:56:50,370 --> 00:56:55,650 +point واحد خمسة ملي ضرب واحد K بدي يعطيني zero + +589 +00:56:55,650 --> 00:57:02,550 +point واحد خمسة volt يعني هذه عند أي قيمة في الـ + +590 +00:57:02,550 --> 00:57:10,590 +input أكبر من 0.15 volt هتعطيني كم؟ + +591 +00:57:10,590 --> 00:57:16,090 +0.15 volt على طول وفي هذه الحالة هيكون عند هذول + +592 +00:57:16,090 --> 00:57:20,710 +off هذا الرسم بتلاحظ أنها مش symmetric زي ما أنت + +593 +00:57:20,710 --> 00:57:26,600 +بدك إذا أنا بقول هذا الخط أنا مادة لفوق هذا الخط + +594 +00:57:26,600 --> 00:57:31,640 +لازم يكون على جبال هذه النقطة اللي عندي مش بالشكل + +595 +00:57:31,640 --> 00:57:36,980 +اللي موجود عندي بس هذا حسب حسب قيمة RL و RH اللي + +596 +00:57:36,980 --> 00:57:42,120 +موجودة عندي لو غيرت قيمة RL و RH هيتغير المجال + +597 +00:57:42,120 --> 00:57:49,320 +اللي عندي كويس هيك الحالة + +598 +00:57:49,320 --> 00:57:56,310 +الرابعة حالة مش موجودة ليش؟ بدي هذا وهذا off + +599 +00:57:56,310 --> 00:58:02,290 +مطلوبات هذا أن يكون off تنطبخش اثنين عليهم تنطبخش + +600 +00:58:02,290 --> 00:58:10,490 +على أي voltage موجود فهذه غير + +601 +00:58:10,490 --> 00:58:15,350 +قابلة عندي ثلاث حالات الموجودة هنا فهنا بيعطيني الـ + +602 +00:58:15,350 --> 00:58:16,030 +Vout + +603 +00:58:34,240 --> 00:58:39,310 +الـ analysis اللي عملناه في هذه الدائرة عملنا لها تحليل من + +604 +00:58:39,310 --> 00:58:43,570 +ناحية معينة إيش هي الناحية لها لما حطيت الحالات + +605 +00:58:43,570 --> 00:58:47,750 +لها أنا ممكن أشتغل الدائرة هاي بدون هذه الحالات + +606 +00:58:47,750 --> 00:58:52,450 +اللي هنا بس إيش بيبقى شغلي مش systematic مرتب + +607 +00:58:52,450 --> 00:58:56,830 +بوصل reach لنفس النقطة يعني أنت هتصل لنفس الجواب بس + +608 +00:58:56,830 --> 00:59:01,590 +هتحس حالك شوية هيك مضايق في الوصول لها هنا إيش + +609 +00:59:01,590 --> 00:59:06,310 +سهلت العملية لما يكونوا اثنين شغلة الـ input وشغلة الـ + +610 +00:59:06,310 --> 00:59:10,810 +output الـ diodes فيهم شغالة إيش بيحصل؟ هنا يكونوا + +611 +00:59:10,810 --> 00:59:14,650 +شغلة الـ input شغالة وشغلة الـ output مش شغالة؟ هنا + +612 +00:59:14,650 --> 00:59:18,150 +شغلة الـ output شغالة وشغلة الـ input مش شغالة؟ إيش + +613 +00:59:18,150 --> 00:59:23,130 +اللي بيحصل؟ قداش الـ Vout وقداش الـ Vin المطلوب الآن + +614 +00:59:23,130 --> 00:59:28,190 +لكل الـ VTC دائمًا بنسأل قداش الـ Vout وقداش الـ Vin + +615 +00:59:28,190 --> 00:59:34,930 +الموجود هذا المطلوب منا بشكل عام واضح هذا؟ الآن + +616 +00:59:34,930 --> 00:59:40,890 +هنا عملنا shifting لمن؟ + +617 +00:59:40,890 --> 00:59:46,070 +للـ OR في نفس الطريقة اللي بنعملها هنا + +618 +01:00:04,230 --> 01:00:05,950 +عشان أشوف إيه دي + +619 +01:01:03,010 --> 01:01:05,210 +إيش اللي أضفت أنا عندها؟ + +620 +01:01:09,690 --> 01:01:13,390 +أضفت الجزئية زي ما أضفت هناك أضفت هذه الجزئية اللي + +621 +01:01:13,390 --> 01:01:17,010 +عندي كويس + +622 +01:01:17,010 --> 01:01:23,770 +لأعمل هذا plus زي ما عملت هنا minus plus minus أضفت + +623 +01:01:23,770 --> 01:01:29,870 +الجزئية هذه عشان أعدل أعمل الـ shifting المطلوب مني + +624 +01:01:29,870 --> 01:01:33,810 +الآن نفس الـ scenarios اللي عملناها هناك بدنا + +625 +01:01:33,810 --> 01:01:34,370 +نعملها + +626 +01:01:54,910 --> 01:02:09,570 +بدي أرسم الـ VTC لها في + +627 +01:02:09,570 --> 01:02:17,030 +عندي الـ DI on والـ DL on هاي نفس السيناريو بدي + +628 +01:02:17,030 --> 01:02:29,320 +أقول عندي هاي الـ DI's on الـ DL on هي الـ di's of الـ + +629 +01:02:29,320 --> 01:02:40,660 +dl on هي الـ di's on الـ dl off اللي موجودة عندي نفس + +630 +01:02:40,660 --> 01:02:46,280 +السيناريو اللي عملته قبل شوية لما يكون هدول نفسهم + +631 +01:02:46,280 --> 01:02:54,390 +هذا وهدول on إيش بيحصل عندي الـ input بدي يساوي الـ + +632 +01:02:54,390 --> 01:03:00,650 +output صح؟ الـ input بدي يساوي الـ output هنا عندي + +633 +01:03:00,650 --> 01:03:05,690 +بدي أطرح point 7 وهنا بدي أضيف فهذه مقلوبة الأصل + +634 +01:03:05,690 --> 01:03:12,270 +الرسم اللي هنا plus + +635 +01:03:12,270 --> 01:03:22,350 +minus هذه بدي إيش أعملها؟ بدي أطرح point 7 وهنا بدي + +636 +01:03:22,350 --> 01:03:29,220 +أضيف الـ point 7 بيساووا بعض وبلغوا بعض في هذه + +637 +01:03:29,220 --> 01:03:34,940 +الطريقة كويسة؟ الآن هذه اثنين متساويتين اثنين شغالين + +638 +01:03:34,940 --> 01:03:38,300 +مافيش مشكلة الـ input بدي يساوي الـ output اللي هي + +639 +01:03:38,300 --> 01:03:42,200 +الرسمة اللي عندي هنا الخط المستقيم اللي موجود هنا + +640 +01:03:42,200 --> 01:03:47,540 +الحالة الثانية هدول off وهذا إيش شغال إذا هدول + +641 +01:03:47,540 --> 01:03:53,280 +off إيش بده أعمل زي ما عملت قبل شوية هدول بدأ + +642 +01:03:53,280 --> 01:03:58,580 +أشيلها صح بدي آخد اللوب اللي موجود عندي في اللوب + +643 +01:03:58,580 --> 01:04:01,800 +اللي موجود عندي هذا إيش بدي يصير عنده بدي آخد نفس + +644 +01:04:01,800 --> 01:04:13,820 +اللوب اللي عملته قبل شوية VCC-IRL-VD on- I في R H + +645 +01:04:13,820 --> 01:04:17,480 +زائد VEE + +646 +01:04:17,480 --> 01:04:21,060 +زائد VEE + +647 +01:04:21,060 --> 01:04:24,980 +زائد VEE + +648 +01:04:24,980 --> 01:04:25,080 +زائد VEE + +649 +01:04:25,080 --> 01:04:25,240 +زائد VEE + +650 +01:04:25,240 --> 01:04:32,600 +زائد VEE + +651 +01:04:32,600 --> 01:04:34,480 +زائد + +652 +01:04:57,770 --> 01:05:03,070 +هذه الطريقة وهذه الثانية تختار اللي برايحك فيهم + +653 +01:05:07,270 --> 01:05:14,450 +هذه بتعطينا الـ output low هناك كانت بتعطينا 100 + +654 +01:05:14,450 --> 01:05:20,290 +فهذه + +655 +01:05:20,290 --> 01:05:25,450 +بتعطينا الـ output low وده بدأ أرسمها زي قبل هنا + +656 +01:05:25,450 --> 01:05:31,490 +هذا + +657 +01:05:31,490 --> 01:05:39,390 +عندي الـ DI's إيش أوضحهم هنا قلنا الـ DI's off والـ DI + +658 +01:05:39,390 --> 01:05:45,230 +الـ on طلع عند الحالة الثالثة الحالة الثالثة إيش + +659 +01:05:45,230 --> 01:05:49,870 +بتقولي هذا + +660 +01:05:49,870 --> 01:05:57,790 +الـ off وهدول إيش شغالين في هذه الحالة إيش الـ + +661 +01:05:57,790 --> 01:06:01,290 +output أيوة في هذا عندي + +662 +01:06:03,750 --> 01:06:10,690 +الـ VOH بدي يساوي الـ VCC وهنا هاي الـ VCC يعني لما + +663 +01:06:10,690 --> 01:06:14,910 +الـ input يبقى VCC أو أكبر الـ output بدي يعطيني هذا + +664 +01:06:14,910 --> 01:06:24,350 +وهذا عندي الـ DL off والـ DI و أوضحهم إيش on وسهل + +665 +01:06:24,350 --> 01:06:29,290 +الحالة هي تعرف لما الـ input يبقى عندي VCC أو أكبر + +666 +01:06:29,290 --> 01:06:35,870 +بيعطيني إيش الـ output بيساوي VCC على طول بالنسبة لي + +667 +01:06:35,870 --> 01:06:39,890 +هذا الحالة اللي بدها الحسبة اللي هي حالة تحديد الـ + +668 +01:06:39,890 --> 01:06:45,350 +VOL لما الـ VOL يبقى عندي أو الـ input voltage يبقى + +669 +01:06:45,350 --> 01:06:52,560 +أقل من الـ VOL أو VOL أقل الـ DI's هيصير واضح هم off + +670 +01:06:52,560 --> 01:06:57,620 +if the di is off فهي الدائرة الموجودة فهذا بتطلب + +671 +01:06:57,620 --> 01:07:02,680 +مني أحسب مين أحسب التيار اللي بيمر على عبرها عشان + +672 +01:07:02,680 --> 01:07:09,580 +أجيب الـ output اللي موجود عندي فالدائرة الموجودة + +673 +01:07:09,580 --> 01:07:14,620 +عند الـ OR gate بكل بساطة إيش المطلوب مني فيها لما + +674 +01:07:14,620 --> 01:07:17,760 +الـ input بيساوي الـ output بيصير عندي level + +675 +01:07:17,760 --> 01:07:24,190 +shifting بيصير يعني لما الـ DI والـ DL ON الـ input + +676 +01:07:24,190 --> 01:07:31,430 +بيساوي الـ output لما عندي الـ DI وضعهم OFF و DL ON + +677 +01:07:31,430 --> 01:07:37,890 +هذا بتطلب مني أحسب الـ I في الـ loop من VCC لـ VEE و + +678 +01:07:37,890 --> 01:07:43,110 +إذا حسبت التيار في هذا الـ loop بقدر أحسب قيمة الـ V + +679 +01:07:43,110 --> 01:07:49,790 +out عن طريق بيساوي VCC-I في الـ RH أوالـ minus الـ + +680 +01:07:49,790 --> 01:07:56,230 +Vout بيساوي minus VE زائد I في الـ RL زائد VD on + +681 +01:07:56,230 --> 01:08:02,830 +اللي هو across الـ DL الآن الحالة الثالثة لما يكون + +682 +01:08:02,830 --> 01:08:10,170 +الـ DL وضعه off الـ output بيساوي VCC وفي هذه الحالة + +683 +01:08:10,170 --> 01:08:16,110 +الـ input لما بيبدأ تبعه بيكون VCC أو أكبر من هنا + +684 +01:08:16,110 --> 01:08:21,520 +واضح هذا؟ هي اليوم إيش إحنا عملنا للخلاصة عملنا + +685 +01:08:21,520 --> 01:08:25,680 +التالي طلعنا على الـ diode as a diode جبنا العلاقة + +686 +01:08:25,680 --> 01:08:30,740 +بين الـ ID والـ VD طلعنا على الـ mode of operation + +687 +01:08:30,740 --> 01:08:38,460 +بنينا الـ AND gate والـ OR gate باستخدام الـ basic + +688 +01:08:38,460 --> 01:08:44,460 +diodes two input عملنا two input AND و two input + +689 +01:08:45,550 --> 01:08:51,150 +لقينا في عندنا في حالة الـ AND في shift في شغلة الـ + +690 +01:08:51,150 --> 01:08:57,630 +output 0.7 لقينا عندنا في حالة الـ OR في shift في شغلة + +691 +01:08:57,630 --> 01:09:02,290 +الـ input 0.7 لنتخلص من هذا الـ shift قلنا بنعمل + +692 +01:09:02,290 --> 01:09:06,720 +level shifting أو level shifted AND gate و level + +693 +01:09:06,720 --> 01:09:10,260 +shifted OR gate في حالة الـ level shifting إيش + +694 +01:09:10,260 --> 01:09:14,280 +نلقينا الـ input بيساوي الـ output في حالة الـ DI's والـ + +695 +01:09:14,280 --> 01:09:20,800 +DL شغالين في حالة الـ input diode شغلت والـ + +696 +01:09:20,800 --> 01:09:26,210 +output diode مش شغال كان في الـ AND إلها وضع وفي الـ + +697 +01:09:26,210 --> 01:09:31,170 +OR اللي هيوضعه في حالة الـ AND كنا بنقول إذا الـ DL + +698 +01:09:31,170 --> 01:09:37,270 +مش شغال معناته الـ output بدي يساوي كام بدي يساوي + +699 +01:09:37,270 --> 01:09:42,590 +minus VEE في حالة الـ OR gate لما الـ DL مش شغال + +700 +01:09:42,590 --> 01:09:49,890 +output بدي يساوي VCC في حالة الـ input مش شغال الـ + +701 +01:09:49,890 --> 01:09:55,830 +input diode مش شغالين في الـ OR والآن كنا لازم نجيب + +702 +01:09:55,830 --> 01:10:02,050 +التيار ونطلع الـ loop من VCC لـ minus VEE ونجيب منه + +703 +01:10:02,050 --> 01:10:07,420 +تيار وبعد هيك نجيب الـ output بناء على الـ voltage + +704 +01:10:07,420 --> 01:10:13,380 +drop عبر الـ Resistors ونتبعه للـ output الآن الـ + +705 +01:10:13,380 --> 01:10:21,900 +input اللي بيوصلي أحد سواء الـ DIs ما يشتغلش بدي نطلع + +706 +01:10:21,900 --> 01:10:27,570 +عليه بدي أكبر في هذه الحالة اللي بدي أطلع عليه في + +707 +01:10:27,570 --> 01:10:32,330 +حالة الـ OR بتختلف شوية عنه في حالة الـ AND الـ AND في + +708 +01:10:32,330 --> 01:10:35,970 +حالة الـ OR إيش اللي جيت عندي؟ هدول بيشتغلوش + +709 +01:10:35,970 --> 01:10:41,650 +معناته هذا الـ output عنده يكون high طب الـ output + +710 +01:10:41,650 --> 01:10:45,130 +هنا وقت إيش هدول بيصير عنده بيشتغلوش لما نـ drop + +711 +01:10:45,130 --> 01:10:49,130 +اللي عنده هنا يبقى أقل من 0.7 أو بعبارة ثانية + +712 +01:10:49,130 --> 01:10:54,930 +الـ V in أكبر من Vcc اللي موجود عنده لما يكون أكبر + +713 +01:10:54,930 --> 01:10:59,070 +من Vcc بيعطيني هذه الحالة فأنت بدك تتطلع عليها + +714 +01:10:59,070 --> 01:11:04,290 +بالمُلخّص الـ diode لما يكون مش شغال يبقى الـ Vd بتاعه + +715 +01:11:04,290 --> 01:11:09,410 +بيكون أقل من 0.7 يكون شغال الـ Vd بدي يساوي كم؟ + +716 +01:11:09,410 --> 01:11:14,210 +0.7 في حالة الـ diode off الـ ID بدي يساوي 0 في حالة + +717 +01:11:14,210 --> 01:11:17,430 +الـ diode on بدي أشوف قد إيش الـ ID حسب الـ circuit + +718 +01:11:17,430 --> 01:11:20,750 +اللي موجود عندها فيلقوا أي سؤال اليوم؟ diff --git a/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/JwnM_vjAHGc_raw.json b/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/JwnM_vjAHGc_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..a1fb583ee2665bedf5ccc8377d079ecf93700bf0 --- /dev/null +++ b/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/JwnM_vjAHGc_raw.json @@ -0,0 +1 @@ +{"segments": [{"id": 1, "seek": 3626, "start": 20.38, "end": 36.26, "text": "طيب اليوم هنبدأ ب chapter اتنين chapter اتنين بتكلم على ال diodes ايش هنعرف في ال diodes كيف ال diodes بيشتغلوا هذه حاجة عامة بعد هيك هنتكلم على ال operations ال mode of operations لل diodes", "tokens": [9566, 1829, 3555, 45595, 20498, 8032, 1863, 44510, 10721, 4724, 7187, 1975, 2655, 1863, 9957, 7187, 1975, 2655, 1863, 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بيسميه grading coefficient وهذا يا إما تلت يا إما نص معرفة", "tokens": [6617, 4018, 12577, 13672, 1829, 39896, 4724, 1829, 38251, 1829, 11296, 11778, 1829, 20666, 19913, 3555, 9566, 7476, 935, 3407, 5962, 30731, 935, 4949, 5962, 4032, 41185, 18871, 16254, 2423, 275, 4724, 1829, 38251, 1829, 3224, 35540, 17619, 37037, 15730, 35186, 11933, 15042, 6055, 1211, 2655, 35186, 11933, 15042, 8717, 9381, 20449, 28480, 3660], "avg_logprob": -0.33721591017462993, "compression_ratio": 1.3962264150943395, "no_speech_prob": 0.0, "words": [{"start": 1325.66, "end": 1326.16, "word": "under", "probability": 0.2415771484375}, {"start": 1326.16, "end": 1326.6, "word": " zero", "probability": 0.4638671875}, {"start": 1326.6, "end": 1327.1, "word": " bias", "probability": 0.88134765625}, {"start": 1327.1, "end": 1327.34, "word": " اللي", "probability": 0.45831298828125}, {"start": 1327.34, "end": 1327.5, "word": " هي", "probability": 0.61865234375}, {"start": 1327.5, "end": 1328.1, "word": " بيسميها", 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" و", "probability": 0.6591796875}, {"start": 1349.33, "end": 1349.73, "word": " هذه", "probability": 0.96923828125}, {"start": 1349.73, "end": 1350.11, "word": " اللي", "probability": 0.5931396484375}, {"start": 1350.11, "end": 1350.85, "word": " بيقررهم", "probability": 0.8536783854166666}, {"start": 1350.85, "end": 1351.19, "word": " مين", "probability": 0.5589599609375}, {"start": 1351.19, "end": 1351.41, "word": " ال", "probability": 0.5693359375}, {"start": 1351.41, "end": 1351.99, "word": " manufacturing", "probability": 0.2822265625}, {"start": 1351.99, "end": 1352.67, "word": " يعني", "probability": 0.59906005859375}, {"start": 1352.67, "end": 1352.87, "word": " لما", "probability": 0.899658203125}, {"start": 1352.87, "end": 1353.69, "word": " نفتح", "probability": 0.8623046875}, {"start": 1353.69, "end": 1354.39, "word": " ال", "probability": 0.425048828125}, {"start": 1354.39, "end": 1354.95, "word": " grade", "probability": 0.8544921875}, {"start": 1354.95, "end": 1355.49, 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0.780517578125}, {"start": 3969.99, "end": 3970.69, "word": " لما", "probability": 0.8798828125}, {"start": 3970.69, "end": 3970.85, "word": " ال", "probability": 0.953125}, {"start": 3970.85, "end": 3971.09, "word": " input", "probability": 0.6279296875}, {"start": 3971.09, "end": 3971.55, "word": " يبقى", "probability": 0.93505859375}, {"start": 3971.55, "end": 3972.19, "word": " VCC", "probability": 0.966064453125}, {"start": 3972.19, "end": 3972.51, "word": " او", "probability": 0.821044921875}, {"start": 3972.51, "end": 3972.97, "word": " اكبر", "probability": 0.8551432291666666}, {"start": 3972.97, "end": 3973.45, "word": " ال", "probability": 0.875}, {"start": 3973.45, "end": 3973.83, "word": " output", "probability": 0.986328125}, {"start": 3973.83, "end": 3974.17, "word": " بدي", "probability": 0.85546875}, {"start": 3974.17, "end": 3974.61, "word": " يعطيني", "probability": 0.8218994140625}, {"start": 3974.61, "end": 3974.91, "word": " هذا", "probability": 0.34521484375}, {"start": 3974.91, "end": 3975.25, "word": " وهذا", "probability": 0.6317138671875}, {"start": 3975.25, "end": 3975.67, "word": " عندي", "probability": 0.6881103515625}, {"start": 3975.67, "end": 3976.45, "word": " ال", "probability": 0.94091796875}, {"start": 3976.45, "end": 3977.19, "word": " DL", "probability": 0.5064697265625}, {"start": 3977.19, "end": 3978.19, "word": " off", "probability": 0.311279296875}, {"start": 3978.19, "end": 3979.39, "word": " و", "probability": 0.6259765625}, {"start": 3979.39, "end": 3979.53, "word": " ال", "probability": 0.5732421875}, {"start": 3979.53, "end": 3980.21, "word": " DI", "probability": 0.80615234375}, {"start": 3980.21, "end": 3982.11, "word": " و", "probability": 0.55322265625}, {"start": 3982.11, "end": 3982.65, "word": " اضحهم", "probability": 0.77032470703125}, {"start": 3982.65, "end": 3983.05, "word": " ايش", "probability": 0.6780598958333334}, {"start": 3983.05, "end": 3983.55, "word": " on", "probability": 0.84423828125}, {"start": 3983.55, "end": 3984.35, "word": " وسهل", "probability": 0.9244791666666666}, {"start": 3984.35, "end": 3984.79, "word": " الحالة", "probability": 0.9666341145833334}, {"start": 3984.79, "end": 3984.95, "word": " هي", "probability": 0.39892578125}, {"start": 3984.95, "end": 3985.45, "word": " تعرف", "probability": 0.97802734375}, {"start": 3985.45, "end": 3985.81, "word": " لما", "probability": 0.9287109375}, {"start": 3985.81, "end": 3986.47, "word": " ال", "probability": 0.9677734375}, {"start": 3986.47, "end": 3987.13, "word": " input", "probability": 0.9755859375}, {"start": 3987.13, "end": 3987.55, "word": " يبقى", "probability": 0.9373779296875}, {"start": 3987.55, "end": 3987.87, "word": " عندى", "probability": 0.525146484375}, {"start": 3987.87, "end": 3988.41, "word": " VCC", "probability": 0.98388671875}, {"start": 3988.41, "end": 3988.77, "word": " او", "probability": 0.967041015625}, {"start": 3988.77, "end": 3989.29, "word": " اكبر", "probability": 0.9309895833333334}, {"start": 3989.29, "end": 3989.89, "word": " بيعطيني", "probability": 0.83330078125}, {"start": 3989.89, "end": 3990.29, "word": " ايش", "probability": 0.9283854166666666}], "temperature": 1.0}, {"id": 152, "seek": 401169, "start": 3990.85, "end": 4011.69, "text": "الـ output بيساوي VCC على طول بالنسبالي هذا الحالة اللي بدها الحسبة اللي هي حالة تميين ال VOL لما ال VOL يبقى عندى او ال input voltage يبقى اقل من ال VOL او VOL اقل ال DIs هيصير واضح هم", "tokens": [6027, 39184, 5598, 4724, 1829, 3794, 995, 45865, 691, 11717, 15844, 23032, 12610, 20666, 1863, 35457, 6027, 1829, 23758, 21542, 6027, 3660, 13672, 1829, 47525, 11296, 21542, 35457, 3660, 13672, 1829, 39896, 11331, 6027, 3660, 46811, 1829, 9957, 2423, 691, 5046, 5296, 15042, 2423, 691, 5046, 7251, 3555, 4587, 7578, 43242, 7578, 1975, 2407, 2423, 4846, 8352, 7251, 3555, 4587, 7578, 1975, 4587, 1211, 9154, 2423, 691, 5046, 1975, 2407, 691, 5046, 1975, 4587, 1211, 2423, 413, 6802, 8032, 1829, 9381, 13546, 4032, 46958, 5016, 8032, 2304], "avg_logprob": -0.2677556916394017, "compression_ratio": 1.6666666666666667, "no_speech_prob": 0.0, "words": [{"start": 3990.85, "end": 3991.19, "word": "الـ", "probability": 0.3701171875}, {"start": 3991.19, "end": 3991.57, "word": " output", "probability": 0.80810546875}, {"start": 3991.57, "end": 3992.37, "word": " بيساوي", "probability": 0.73330078125}, {"start": 3992.37, "end": 3993.91, "word": " VCC", "probability": 0.64013671875}, {"start": 3993.91, "end": 3994.63, "word": " على", "probability": 0.68603515625}, {"start": 3994.63, "end": 3995.39, "word": " طول", "probability": 0.947998046875}, {"start": 3995.39, "end": 3995.87, "word": " بالنسبالي", "probability": 0.776513671875}, {"start": 3995.87, "end": 3996.13, "word": " هذا", "probability": 0.8115234375}, {"start": 3996.13, "end": 3997.55, "word": " الحالة", "probability": 0.725341796875}, {"start": 3997.55, "end": 3997.61, "word": " اللي", "probability": 0.74462890625}, {"start": 3997.61, "end": 3997.85, "word": " بدها", "probability": 0.7919921875}, {"start": 3997.85, "end": 3998.35, "word": " الحسبة", "probability": 0.76904296875}, {"start": 3998.35, "end": 3998.51, "word": " اللي", "probability": 0.612548828125}, {"start": 3998.51, "end": 3998.63, "word": " هي", "probability": 0.8701171875}, {"start": 3998.63, "end": 3998.99, "word": " حالة", "probability": 0.9768880208333334}, {"start": 3998.99, "end": 3999.39, "word": " تميين", "probability": 0.474853515625}, {"start": 3999.39, "end": 3999.89, "word": " ال", "probability": 0.70849609375}, {"start": 3999.89, "end": 4000.75, "word": " VOL", "probability": 0.732177734375}, {"start": 4000.75, "end": 4001.15, "word": " لما", "probability": 0.791748046875}, {"start": 4001.15, "end": 4001.31, "word": " ال", "probability": 0.59326171875}, {"start": 4001.31, "end": 4001.71, "word": " VOL", "probability": 0.6712646484375}, {"start": 4001.71, "end": 4002.05, "word": " يبقى", "probability": 0.9654541015625}, {"start": 4002.05, "end": 4002.53, "word": " عندى", "probability": 0.73046875}, {"start": 4002.53, "end": 4003.43, "word": " او", "probability": 0.833740234375}, {"start": 4003.43, "end": 4003.79, "word": " ال", "probability": 0.83154296875}, {"start": 4003.79, "end": 4004.55, "word": " input", "probability": 0.9365234375}, {"start": 4004.55, "end": 4005.03, "word": " voltage", "probability": 0.8779296875}, {"start": 4005.03, "end": 4005.35, "word": " يبقى", "probability": 0.9639892578125}, {"start": 4005.35, "end": 4005.83, "word": " اقل", "probability": 0.9132486979166666}, {"start": 4005.83, "end": 4006.21, "word": " من", "probability": 0.978515625}, {"start": 4006.21, "end": 4006.41, "word": " ال", "probability": 0.84716796875}, {"start": 4006.41, "end": 4006.97, "word": " VOL", "probability": 0.947265625}, {"start": 4006.97, "end": 4007.55, "word": " او", "probability": 0.916015625}, {"start": 4007.55, "end": 4008.01, "word": " VOL", "probability": 0.83349609375}, {"start": 4008.01, "end": 4008.63, "word": " اقل", "probability": 0.94384765625}, {"start": 4008.63, "end": 4010.11, "word": " ال", "probability": 0.93994140625}, {"start": 4010.11, "end": 4010.65, "word": " DIs", "probability": 0.4893798828125}, {"start": 4010.65, "end": 4011.05, "word": " هيصير", "probability": 0.8692626953125}, {"start": 4011.05, "end": 4011.41, "word": " واضح", "probability": 0.9767252604166666}, {"start": 4011.41, "end": 4011.69, "word": " هم", "probability": 0.60986328125}], "temperature": 1.0}, {"id": 153, "seek": 404140, "start": 4012.08, "end": 4041.4, "text": "off if the di is off فهي الدائرة الموجودة فهذا بتطلب مني احسب مين احسب التيارة اللي بيمر على عبرها عشان اجيب ال output اللي موجود عندى فالدائرة الموجودة عند ال or gate بكل بساطة ايش المطلوب مني فيها لما ال input بيساوي ال output بيصير عندى level shifting بيصير يعني لما ال di", "tokens": [4506, 498, 264, 1026, 307, 766, 6156, 3224, 1829, 32748, 16373, 25720, 9673, 29245, 23328, 3660, 6156, 3224, 15730, 39894, 9566, 46152, 9154, 1829, 1975, 5016, 35457, 3714, 9957, 1975, 5016, 35457, 16712, 1829, 9640, 3660, 13672, 1829, 4724, 32640, 2288, 15844, 6225, 26890, 11296, 6225, 8592, 7649, 1975, 7435, 1829, 3555, 2423, 5598, 13672, 1829, 3714, 29245, 23328, 43242, 7578, 6156, 6027, 3215, 16373, 25720, 9673, 29245, 23328, 3660, 43242, 2423, 420, 8539, 4724, 28820, 4724, 3794, 41193, 3660, 1975, 1829, 8592, 9673, 9566, 1211, 37746, 9154, 1829, 8978, 11296, 5296, 15042, 2423, 4846, 4724, 1829, 3794, 995, 45865, 2423, 5598, 4724, 1829, 9381, 13546, 43242, 7578, 1496, 17573, 4724, 1829, 9381, 13546, 37495, 22653, 5296, 15042, 2423, 1026], "avg_logprob": -0.2874483352850291, "compression_ratio": 1.9646017699115044, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 4012.08, "end": 4012.56, "word": "off", "probability": 0.07379150390625}, {"start": 4012.56, "end": 4012.86, "word": " if", "probability": 0.1319580078125}, {"start": 4012.86, "end": 4012.98, "word": " the", "probability": 0.340576171875}, {"start": 4012.98, "end": 4013.28, "word": " di", "probability": 0.367919921875}, {"start": 4013.28, "end": 4013.5, "word": " is", "probability": 0.7529296875}, {"start": 4013.5, "end": 4013.8, "word": " off", "probability": 0.8798828125}, {"start": 4013.8, "end": 4015.22, "word": " فهي", "probability": 0.4137369791666667}, {"start": 4015.22, "end": 4015.76, "word": " الدائرة", "probability": 0.7765299479166666}, {"start": 4015.76, "end": 4016.62, "word": " الموجودة", "probability": 0.9296875}, {"start": 4016.62, "end": 4017.12, "word": " فهذا", "probability": 0.64404296875}, {"start": 4017.12, "end": 4017.62, "word": " بتطلب", "probability": 0.8247884114583334}, {"start": 4017.62, "end": 4017.9, "word": " مني", "probability": 0.927978515625}, {"start": 4017.9, "end": 4018.28, "word": " احسب", "probability": 0.8522135416666666}, {"start": 4018.28, "end": 4018.66, "word": " مين", "probability": 0.59033203125}, {"start": 4018.66, "end": 4019.74, "word": " احسب", "probability": 0.9241536458333334}, {"start": 4019.74, "end": 4021.1, "word": " التيارة", "probability": 0.69775390625}, {"start": 4021.1, "end": 4021.16, "word": " اللي", "probability": 0.4591064453125}, {"start": 4021.16, "end": 4021.44, "word": " بيمر", "probability": 0.7449544270833334}, {"start": 4021.44, "end": 4021.68, "word": " على", "probability": 0.427978515625}, {"start": 4021.68, "end": 4022.36, "word": " عبرها", "probability": 0.7185872395833334}, {"start": 4022.36, "end": 4022.68, "word": " عشان", "probability": 0.9345703125}, {"start": 4022.68, "end": 4023.06, "word": " اجيب", "probability": 0.9388427734375}, {"start": 4023.06, "end": 4023.2, "word": " ال", "probability": 0.373291015625}, {"start": 4023.2, "end": 4024.66, "word": " output", "probability": 0.90380859375}, {"start": 4024.66, "end": 4025.44, "word": " اللي", "probability": 0.883056640625}, {"start": 4025.44, "end": 4025.82, "word": " موجود", "probability": 0.9625651041666666}, {"start": 4025.82, "end": 4026.26, "word": " عندى", "probability": 0.81298828125}, {"start": 4026.26, "end": 4029.02, "word": " فالدائرة", "probability": 0.85185546875}, {"start": 4029.02, "end": 4029.58, "word": " الموجودة", "probability": 0.88818359375}, {"start": 4029.58, "end": 4029.8, "word": " عند", "probability": 0.947265625}, {"start": 4029.8, "end": 4029.98, "word": " ال", "probability": 0.71435546875}, {"start": 4029.98, "end": 4030.28, "word": " or", "probability": 0.2626953125}, {"start": 4030.28, "end": 4030.7, "word": " gate", "probability": 0.96240234375}, {"start": 4030.7, "end": 4031.98, "word": " بكل", "probability": 0.906005859375}, {"start": 4031.98, "end": 4032.48, "word": " بساطة", "probability": 0.9857177734375}, {"start": 4032.48, "end": 4032.7, "word": " ايش", "probability": 0.7965494791666666}, {"start": 4032.7, "end": 4033.14, "word": " المطلوب", "probability": 0.9608154296875}, {"start": 4033.14, "end": 4033.44, "word": " مني", "probability": 0.794189453125}, {"start": 4033.44, "end": 4033.82, "word": " فيها", "probability": 0.974365234375}, {"start": 4033.82, "end": 4034.62, "word": " لما", "probability": 0.870361328125}, {"start": 4034.62, "end": 4035.08, "word": " ال", "probability": 0.9111328125}, {"start": 4035.08, "end": 4035.52, "word": " input", "probability": 0.99267578125}, {"start": 4035.52, "end": 4036.02, "word": " بيساوي", "probability": 0.766650390625}, {"start": 4036.02, "end": 4036.2, "word": " ال", "probability": 0.8935546875}, {"start": 4036.2, "end": 4036.66, "word": " output", "probability": 0.99365234375}, {"start": 4036.66, "end": 4037.06, "word": " بيصير", "probability": 0.8978271484375}, {"start": 4037.06, "end": 4037.46, "word": " عندى", "probability": 0.821533203125}, {"start": 4037.46, "end": 4037.76, "word": " level", "probability": 0.95703125}, {"start": 4037.76, "end": 4038.38, "word": " shifting", "probability": 0.86083984375}, {"start": 4038.38, "end": 4039.32, "word": " بيصير", "probability": 0.8785400390625}, {"start": 4039.32, "end": 4039.9, "word": " يعني", "probability": 0.880126953125}, {"start": 4039.9, "end": 4040.96, "word": " لما", "probability": 0.93408203125}, {"start": 4040.96, "end": 4041.12, "word": " ال", "probability": 0.94384765625}, {"start": 4041.12, "end": 4041.4, "word": " di", "probability": 0.7607421875}], "temperature": 1.0}, {"id": 154, "seek": 406795, "start": 4042.17, "end": 4067.95, "text": "و ال DL ON ال input بيساوي ال output لما عندي ال DI وضعهم OFF و DL ON هذا بتطلب مني أحسب ال I في ال loop من VCC ل- VEE و إذا حسبت التيار في هذا ال loop بقدر أحسب قيمة ال V out عن طريق بيساوي VCC-I في ال RH أو", "tokens": [2407, 2423, 413, 43, 9299, 2423, 4846, 4724, 1829, 3794, 995, 45865, 2423, 5598, 5296, 15042, 18871, 16254, 2423, 11953, 4032, 11242, 3615, 16095, 24115, 4032, 413, 43, 9299, 23758, 39894, 9566, 46152, 9154, 1829, 5551, 5016, 35457, 2423, 286, 8978, 2423, 6367, 9154, 691, 11717, 5296, 12, 691, 7258, 4032, 11933, 15730, 11331, 35457, 2655, 38392, 9640, 8978, 23758, 2423, 6367, 4724, 28543, 2288, 5551, 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00:00:25,510 +اليوم مش اللي هنعمله احنا غطينا سابقا بدينا بال + +2 +00:00:25,510 --> 00:00:29,910 +RDL + +3 +00:00:29,910 --> 00:00:33,230 +RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL + +4 +00:00:33,230 --> 00:00:37,890 +RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL + +5 +00:00:37,890 --> 00:00:39,010 +RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL + +6 +00:00:39,010 --> 00:00:42,130 +RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL + +7 +00:00:42,130 --> 00:00:42,190 +RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL + +8 +00:00:42,190 --> 00:00:42,710 +RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL RDL + +9 +00:00:42,710 --> 00:00:50,130 +RDL + +10 +00:00:50,130 --> 00:00:54,190 +RDL RDالان هنروح على عائلة اخرى نسميها ال emitter + +11 +00:00:54,190 --> 00:00:58,030 +coupled logic ال emitter coupled logic فيها ميزة + +12 +00:00:58,030 --> 00:01:03,890 +ايش هي الحاجة و its complement يعني ال signal and + +13 +00:01:03,890 --> 00:01:08,250 +its inverse متاحين في نفس الوجه يعني انا بتكلم على + +14 +00:01:08,250 --> 00:01:13,130 +ال inverter الدائرة فيها inverter و bufferوال + +15 +00:01:13,130 --> 00:01:16,490 +output متاح في نفس الوقت يعني في نفس ال time + +16 +00:01:16,490 --> 00:01:20,250 +ماعندى propagation delay لأنه قبل لو عندى inverter + +17 +00:01:20,250 --> 00:01:24,610 +و بدى buffer ايش بعمل بحط two inverters بطلعوليه + +18 +00:01:24,610 --> 00:01:31,770 +buffer صح؟ الان نفس الشيء لو بدى ore وعندي nor بحط + +19 +00:01:31,770 --> 00:01:35,370 +inverter بطلعلها هان عندى ال ore و ال nor متاحين + +20 +00:01:35,370 --> 00:01:41,430 +في نفس الوقتفهذه ميزة لهذه العقلة طبيعة الدائرة زي + +21 +00:01:41,430 --> 00:01:48,950 +ما هنشوف لاحقا في ال modified one انه موجود عند ال + +22 +00:01:48,950 --> 00:01:53,730 +current spike عادة لما نغير من low to high او high + +23 +00:01:53,730 --> 00:01:57,230 +to low بيصير عنده spike يمكن هذا بتلاحظوها حتى في + +24 +00:01:57,230 --> 00:02:03,500 +البيت لما تقطع الكهربا اول ما تيجي ايش بتلاحظبتبقى + +25 +00:02:03,500 --> 00:02:07,000 +جوية و احيانا بتحرر كل الموجود لان ال spike اللى + +26 +00:02:07,000 --> 00:02:11,300 +عندى بتبقى عالى هذا ال logic بتعملى القصد فيها ان + +27 +00:02:11,300 --> 00:02:18,080 +on off او يعني low high هذا بتعملى spike فانا هذا + +28 +00:02:18,080 --> 00:02:21,500 +بعمل elimination لان بشتغل في ال negative region + +29 +00:02:21,500 --> 00:02:27,720 +ال propagation delay time هنا عندى صغير جدا تقريبا + +30 +00:02:27,720 --> 00:02:32,280 +one nanoseconds العين في هذه الدائرةpower + +31 +00:02:32,280 --> 00:02:36,860 +dissipation تبعها عالي ليش لأن ال transistors احنا + +32 +00:02:36,860 --> 00:02:41,200 +كنا بنحكي في كل ال logic اللي فات انا بحب اشتغل في + +33 +00:02:41,200 --> 00:02:46,440 +ال cut-off و ال saturationهذا الـ saturation ليس + +34 +00:02:46,440 --> 00:02:50,280 +كثير لها مفعولة أنا بشتغل بال cut-off و بال + +35 +00:02:50,280 --> 00:02:53,880 +forward active forward active متى ما أشتغل فيه + +36 +00:02:53,880 --> 00:02:59,540 +دائما بيقولي التيار عندي عالي فلازم يعطيني power + +37 +00:02:59,540 --> 00:03:03,580 +dissipation عالي هذا ال power dissipation للسل + +38 +00:03:03,580 --> 00:03:11,420 +تقريبا بيعطينا 25 ملي وات 25 ملي وات عالي مقارنة + +39 +00:03:11,420 --> 00:03:17,220 +بال standard المعروفةهذه الشركة اللى اشتغل عليها + +40 +00:03:17,220 --> 00:03:21,220 +بيسميها Motorola emitter coupled logic لأن شركة + +41 +00:03:21,220 --> 00:03:25,760 +موتوريلا اشتغلت فيها في ال 1962 في ستنات القرن + +42 +00:03:25,760 --> 00:03:37,660 +الماضي الان شكل الدائرة كالتالي VCC two + +43 +00:03:37,660 --> 00:03:40,220 +resistors two transistors + +44 +00:03:45,360 --> 00:03:52,060 +وهذا بنقول عنه dependent current source minus VEE + +45 +00:03:52,060 --> 00:03:58,800 +هنا بسميها VE هنا VBB اللي هو reference وهنا QR + +46 +00:03:58,800 --> 00:04:09,240 +وهنا RCR وهي V NONE INVERSEوهنا عندي ال V Inverse + +47 +00:04:09,240 --> 00:04:17,500 +وهنا ال V In وهنا ال RCI و ال QI هذا ال V Inverse + +48 +00:04:17,500 --> 00:04:24,160 +يعني بتقدر تقول عبارة عن V Out وهذه ال V Out ايش؟ + +49 +00:04:24,160 --> 00:04:29,380 +complement سبعتها هي هذه اللي بتطلع عليها الدائرة + +50 +00:04:29,380 --> 00:04:34,700 +هذه هتطلع عليها من ناحيتين من ناحية التيار و من + +51 +00:04:34,700 --> 00:04:40,770 +ناحيةالـ voltage كدائرة و هنشوف كيف نتطلع عليها + +52 +00:04:40,770 --> 00:04:47,850 +الان خليني اقول هذا ايش عندها two identical + +53 +00:04:47,850 --> 00:04:52,710 +transistors واحد في اليمين و واحد في الشمال هنا لو + +54 +00:04:52,710 --> 00:04:56,370 +أخدت هذا الشجة لحالها هذه عبارة عن ال inverter + +55 +00:04:56,370 --> 00:05:01,810 +circuit لو أخدت هذه هذه inverter اتنين مع بعض ايش + +56 +00:05:01,810 --> 00:05:07,820 +بيعملولي two inverters كانوا يعملولي بفرالان هاي + +57 +00:05:07,820 --> 00:05:12,140 +ال output و هاي ال output complement او ال output + +58 +00:05:12,140 --> 00:05:15,320 +لل buffer فهذا بيقول لي انه حيكون عندى لما ارسم ال + +59 +00:05:15,320 --> 00:05:21,460 +VTC to VTC مظبوط تنتين مع بعض يعني لما ارسمها + +60 +00:05:21,460 --> 00:05:28,040 +هتكون واحدة + +61 +00:05:28,040 --> 00:05:31,420 +طبيعى + +62 +00:05:35,570 --> 00:05:41,810 +هذه تبعت الـ buffer أو + +63 +00:05:41,810 --> 00:05:47,890 +بيسميه الـ VNone Inverse والتانية الـ V Inverse + +64 +00:05:47,890 --> 00:05:58,090 +هذه + +65 +00:05:58,090 --> 00:06:05,730 +الـ VOL وهذه الـ Vout هذه V Inverseللـ inverter + +66 +00:06:05,730 --> 00:06:10,590 +هذي ال + +67 +00:06:10,590 --> 00:06:18,950 +VIL هنا ال VIH هذي بسميها VS اللي عندى QI بيصيرله + +68 +00:06:18,950 --> 00:06:26,070 +saturated وهذه النقطة اللي في النص اللي بسميها VBB + +69 +00:06:30,330 --> 00:06:33,050 +اللي هي ال reference voltage ال reference voltage + +70 +00:06:33,050 --> 00:06:37,470 +هذا fixed value يعني انا بعطيك مثلا هنا بقول هو + +71 +00:06:37,470 --> 00:06:41,790 +اتنين volt هذا القيمة هي ايش؟ fixed الان اللي + +72 +00:06:41,790 --> 00:06:46,970 +بيصير فيه تغيير مين؟ ال VIN اللي هنا الان نطلع + +73 +00:06:46,970 --> 00:06:51,710 +عليها لو قولنا if VIN + +74 +00:06:51,710 --> 00:06:58,150 +is less than VBB كويس؟أنا قاعد بقول قيمة ال VIN + +75 +00:06:58,150 --> 00:07:07,410 +أقل من قيمة ال VBB يعني بعبارة تانية VIN ناقص VBB + +76 +00:07:07,410 --> 00:07:14,090 +بتبقى في ال negative، مظبوط؟ إذا هذي أكبر من هذي، + +77 +00:07:14,090 --> 00:07:18,750 +هذي جيبتها هذي، بدى يكون القيمة هذي بال-، بالسالم، + +78 +00:07:18,750 --> 00:07:25,780 +صح؟يعني لو عندى VBB زى ما حكيت اتنين و VIN واحد + +79 +00:07:25,780 --> 00:07:32,940 +point كسعة كويس؟ مش بعيد عنك، مظبوط؟ الان VIN ناقص + +80 +00:07:32,940 --> 00:07:38,140 +VBB جديش بدى يعطينى؟ minus point one صح؟ يعني + +81 +00:07:38,140 --> 00:07:42,320 +القيمة عندى اقل من zero بالminus الان لو بدى اجيب + +82 +00:07:42,320 --> 00:07:48,160 +قيمة VE ايش بدها تساوي؟ هذا هقول عنه شغال بال + +83 +00:07:48,160 --> 00:07:54,000 +forward active ال assumptionكويس؟ و ممكن قبل ما + +84 +00:07:54,000 --> 00:08:00,160 +هاي اروح لك لخطوة شوية أسهل لو VIN بتساوي VBB ايش + +85 +00:08:00,160 --> 00:08:07,280 +بدي يحصل؟ هاي هنا VIN equal + +86 +00:08:07,280 --> 00:08:14,240 +VBB اللي يحصل التالي QI و QR هيكونوا بال forward + +87 +00:08:14,240 --> 00:08:21,760 +active كويس؟الان اذا هدول متساوين و هذا عندى ايش + +88 +00:08:21,760 --> 00:08:28,820 +بدى يصير عندى ال VOL VE VBB + +89 +00:08:28,820 --> 00:08:42,600 +-VBE VBE VBB-VBE VBE VBE VBE VBE + +90 +00:08:42,600 --> 00:08:43,240 +VBE VBE VBE VBE VBE VBE VBE VBE VBE VBE VBE VBE + +91 +00:08:43,240 --> 00:08:43,260 +VBE VBE VBE VBE VBE VBE VBE VBE VBE VBE VBE VBE + +92 +00:08:43,260 --> 00:08:50,950 +VBE VBE Vبإي إي سي أل عشان أميزها وهذه بتساوي 0.75 + +93 +00:08:50,950 --> 00:08:55,030 +فورت نوعية الترانزستور بختلف عن الترانزستور + +94 +00:08:55,030 --> 00:09:01,950 +التانين شوية هذه الآن عندي ال ال بي اي فورورد اكت + +95 +00:09:01,950 --> 00:09:06,410 +بتساوي 0.75 كويس احنا قبل كنا تبكي اللي جديش عندنا + +96 +00:09:06,410 --> 00:09:18,020 +0.7اللي نجي اطلعها هي ال VE بدها تساوي VBB-VBE ECL + +97 +00:09:18,020 --> 00:09:23,500 +اللي موجودة عندى طيب هذه لو قلت هي عبارة عن + +98 +00:09:23,500 --> 00:09:28,560 +resistor RE هذه عندى dependent current source لو + +99 +00:09:28,560 --> 00:09:36,660 +حطيت RE هي نفس الشيء فال RE ها او ال Ire ايش بدي + +100 +00:09:36,660 --> 00:09:46,580 +ساوي بدي ساوي ve minus minus ve يعني i re بدي + +101 +00:09:46,580 --> 00:09:54,220 +ساوي ve minus minus ve على ال re او بدي ساوي vbb + +102 +00:09:54,220 --> 00:10:05,560 +ناقص vbe acl plus ve على ال re صح؟ + +103 +00:10:07,580 --> 00:10:10,220 +التيار اللي هان جبته طب هذا كيف من وين دي ييجي + +104 +00:10:10,220 --> 00:10:14,800 +التيار نصه بدي ييجي من هان و نصه بدي ييجي من هان + +105 +00:10:14,800 --> 00:10:19,820 +يعني IRE بدي + +106 +00:10:19,820 --> 00:10:29,620 +ساوي IRCI زائد IRCR وهو تقريبا بعبارة تانية IRCR + +107 +00:10:30,890 --> 00:10:40,810 +بدي ساوى IRCI بدي ساوى نص IRE لأن هدولة التنتين + +108 +00:10:40,810 --> 00:10:44,730 +identical و ال registers اللي هان matched معناته + +109 +00:10:44,730 --> 00:10:48,070 +النص اللي هان بدي أجي مع نص منها + +110 +00:10:50,830 --> 00:10:55,650 +الان اللي بحكيه هان اختلف شويه هان كان ال voltages + +111 +00:10:55,650 --> 00:11:01,390 +VIN و VBB ايش متساويات هان بقول ال VIN اقل من مين + +112 +00:11:01,390 --> 00:11:06,370 +من ال VBB اذا اقل من ال VBB طيب جبته من هذا + +113 +00:11:06,370 --> 00:11:13,030 +الاتجاه وهذا قلت عنه forward active اللي هان طب + +114 +00:11:13,030 --> 00:11:19,330 +هذا ايش وضعه مش عارف مش عارف انا بدي اشوفه ايش هو + +115 +00:11:19,990 --> 00:11:26,430 +لو عرف بجاوب طب هذا اذا بدأ افحص ايش افحص ال + +116 +00:11:26,430 --> 00:11:31,230 +junction اللي هان قداش بتساوي ال junction اللي هان + +117 +00:11:31,230 --> 00:11:37,630 +الان انا بقول VE ايش بتساوي VE من هذا الطرف ال + +118 +00:11:37,630 --> 00:11:45,030 +forward كانت بتساوي VBB minus VBE على ال R خليني + +119 +00:11:45,030 --> 00:11:50,910 +اقول فضل ECL اللي هى قداش قلنا عنهاpoint seven + +120 +00:11:50,910 --> 00:11:56,210 +five لو جيت في الاتجاه هذا و قولت هذا خليني أشوف + +121 +00:11:56,210 --> 00:11:59,630 +هذا assume انه forward active فاشوف كده ايش بدي + +122 +00:11:59,630 --> 00:12:06,210 +يطلع عندي بدي اقول هنا هي VE بده تساوي VIN ناقص + +123 +00:12:06,210 --> 00:12:10,710 +VBE لل I ومش هقول عنه forward active ولا I بدي + +124 +00:12:10,710 --> 00:12:15,830 +اشوف هذا كده يطلع عندي هذول اتنين هم نفسهم مظبوط + +125 +00:12:15,830 --> 00:12:22,360 +بدي اقول يعني هذه بتساوي هذه الاتجاهطيب هاي عندي + +126 +00:12:22,360 --> 00:12:33,100 +VIN minus VBE لل I بدي ساوي VBB minus VBE هي ECL + +127 +00:12:33,100 --> 00:12:37,140 +هادي معروفة و هادي معروفة و هادي إيش اللي عندي + +128 +00:12:37,140 --> 00:12:42,180 +معرفات هادي أصغر من هان و هادي كابتة و هادي fixed + +129 +00:12:42,180 --> 00:12:52,540 +يبقى VBE لل I إيش بدها تساوي بدها تساوي VIN-VBP + +130 +00:12:52,540 --> 00:13:02,920 +-VBP-VBP-VBP-VBP-VBP-VBP-VBP-VBP-VBP-VBP-VBP + +131 +00:13:02,920 --> 00:13:08,560 +-VBP-VBP + +132 +00:13:12,900 --> 00:13:16,880 +هذا اللي عنده القيمة هي بتكون زي قبل شوية لما قلت + +133 +00:13:16,880 --> 00:13:21,360 +لو هذه عندى اتنين وهذه one point nine كده الفرق + +134 +00:13:21,360 --> 00:13:26,220 +عندى هنا point واحد بالسالب مظبوط ال point واحد ده + +135 +00:13:26,220 --> 00:13:31,460 +حط على ال point seven five كده يعطيني point six + +136 +00:13:31,460 --> 00:13:36,240 +five صح ال point six five هتشغلي هذا ال transistor + +137 +00:13:36,240 --> 00:13:39,580 +يبقى هذا بدي يصير ايه ايش off + +138 +00:13:44,220 --> 00:13:51,980 +يعني هذا مجرد انه هذا ال Vbb أكبر من Vin حسبت هنا + +139 +00:13:51,980 --> 00:13:56,020 +جيت أخدت الاتجاه اللي هنا و حسبت الطيار بلقيت هذا + +140 +00:13:56,020 --> 00:13:59,980 +اللي عندي خلنا نقول ال voltage drop هذا point + +141 +00:13:59,980 --> 00:14:03,920 +seven five لما جيت أطلع على هذه لقيت ال voltage + +142 +00:14:03,920 --> 00:14:08,920 +drop اللي هنا أقل من ال Vbe forward active معناته + +143 +00:14:08,920 --> 00:14:13,890 +هذه مش هيكون في forward active هيكون وضعه offيعني + +144 +00:14:13,890 --> 00:14:18,810 +هذا اللي عندي صار off يعني هذا برا الدائرة وهذا + +145 +00:14:18,810 --> 00:14:23,150 +شغال forward active يبقى كل التيار اللي هان جاي من + +146 +00:14:23,150 --> 00:14:29,210 +وين؟ من هان هان جاي حاجة؟ مافيش مش جاي ولا إشي + +147 +00:14:29,210 --> 00:14:34,490 +بهذا الإتجار يعني كل التيار جاي باتجاه اللي موجود + +148 +00:14:34,490 --> 00:14:39,110 +عندي هان طيب في هذه الحالة كداش ال output اللي + +149 +00:14:39,110 --> 00:14:48,220 +هان؟ كل شايفها؟إذا بقول هذا off ال output هنا بدي + +150 +00:14:48,220 --> 00:14:53,640 +ساوي ال VCC يعني هنا بقول عندي V inverse بدي ساوي + +151 +00:14:53,640 --> 00:15:02,800 +VCC وهذا بسميته ال VOH طيب + +152 +00:15:02,800 --> 00:15:09,360 +اللي هنا إيش بدك تسوي؟ مش عكسه، بدي أمشي في + +153 +00:15:09,360 --> 00:15:13,080 +الطيار، اتجاه الطيار الطيار اللي هنا إيش بدي أسوي؟ + +154 +00:15:14,440 --> 00:15:20,580 +هي اللي عندى هان هان يساوي عندى I RE بدي ساوي بدي + +155 +00:15:20,580 --> 00:15:28,280 +امشي من هان VBB-VBEECL + +156 +00:15:28,280 --> 00:15:36,880 +plus VEE على ال RE كويس الان بقول التيار اللي هان + +157 +00:15:36,880 --> 00:15:40,980 +تقريبا بدي ساوي التيار اللي هان يبقى ال V non + +158 +00:15:40,980 --> 00:15:42,240 +inverse ايش بدي اساوي + +159 +00:15:45,840 --> 00:15:59,600 +بدي ساوي VCC minus IRC في RC RCR و IRCR هذا تقريبا + +160 +00:15:59,600 --> 00:16:12,520 +بيساوي IRE فصار عندي V none inverse بدي ساويvcc + +161 +00:16:12,520 --> 00:16:20,720 +-vbb-vbeecl + +162 +00:16:20,720 --> 00:16:32,920 +plus vee على re مضروبة في ال RCR فلاحظ + +163 +00:16:32,920 --> 00:16:41,070 +هذه طلعت ال V inverse وطلعت ال V non inverseطيب + +164 +00:16:41,070 --> 00:16:45,730 +انا لما اجي بدي اطلع عليها من زاوية تانية لو + +165 +00:16:45,730 --> 00:16:52,850 +اتكلمت تيار انا كده قلت ال voltage اللي عندى ايوة + +166 +00:16:52,850 --> 00:16:56,590 +الان بدي اشوفها من ناحية تيار هنا عبارة ايش عندى + +167 +00:16:56,590 --> 00:17:03,170 +دايت مظبوط وهنا + +168 +00:17:03,170 --> 00:17:03,610 +دايت + +169 +00:17:06,590 --> 00:17:10,250 +بدي اشوف هذا قول تانى اللى عندى ايش معادلة الدايد + +170 +00:17:10,250 --> 00:17:17,350 +I D اللى هانا ايش بدي ساوي I S في E to the VD على + +171 +00:17:17,350 --> 00:17:24,430 +25 ملي مظبوط او بعبارة تانى اللى هتساوي I S في E + +172 +00:17:24,430 --> 00:17:29,190 +to the 40 VD + +173 +00:17:33,190 --> 00:17:36,830 +ألف عالى خمسة وعشرين مية عالى خمسة واربعين مظبوط + +174 +00:17:36,830 --> 00:17:45,230 +هيك و هذا ايش بدي ساوي ID بدي ساوي IS في E اربعين + +175 +00:17:45,230 --> 00:17:53,090 +VD كويس هيك حتى assume ال IS زي ما أخدناه سابقا + +176 +00:17:53,090 --> 00:17:59,430 +واحد في عشر أقصى ناقص اربعتاشوهذا ال VD اللي عندي + +177 +00:17:59,430 --> 00:18:11,570 +هنا هذا بيساوي 0.75 وهذا بيساوي 0.65 مين يحسب اللي + +178 +00:18:11,570 --> 00:18:12,470 +قداش هدول؟ + +179 +00:18:25,280 --> 00:18:40,140 +و هذه عشرة واحد فعشرة minus fourteen اربعين + +180 +00:18:40,140 --> 00:18:48,100 +و خمسة و سبعين يعني هنا تلاتين مية و ستة + +181 +00:18:48,100 --> 00:18:51,260 +طيب + +182 +00:18:51,260 --> 00:18:52,300 +و هذه + +183 +00:18:56,680 --> 00:19:13,700 +هذه لأ point six five هنا واحد + +184 +00:19:13,700 --> 00:19:23,160 +point تسعة خمسة ميلي شوف هذه لهذه ايش يعد ايش + +185 +00:19:25,840 --> 00:19:32,860 +هذا يعني اتنين ميلي وهذا مائة ميلي سيظهر انه ستجد + +186 +00:19:32,860 --> 00:19:38,440 +مثل شخص يمشي بسرعة مائة وشخص يركب سيارة يمشي بسرعة + +187 +00:19:38,440 --> 00:19:43,580 +مائة وشخص يمشي باتنين متر في التانية وهذا شخص يمشي + +188 +00:19:43,580 --> 00:19:48,000 +بمائة متر في التانية او هذا اتنين كيلو بالساعة + +189 +00:19:48,000 --> 00:19:54,550 +وهذا اتنين كيلو بالساعة سيشعر انه واقفوانت بتشوف + +190 +00:19:54,550 --> 00:19:58,490 +احيانا بتشوف حدا ماشي وانت هاي بتشوفه واقف اذا + +191 +00:19:58,490 --> 00:20:02,890 +راكب طيارة وماشية وسيارة تحت ماشية بتشوف السيارة + +192 +00:20:02,890 --> 00:20:08,510 +واقفة ليش؟ لأن سرعتها لا تتكر جنب السرعة اللي انت + +193 +00:20:08,510 --> 00:20:15,230 +ماشي فيها فهذا نفس الشي هنا عندي هنا 106 هشوفناها + +194 +00:20:15,230 --> 00:20:19,850 +من ناحية التيار ان هذا مبين off وهذا اللي شغال ومن + +195 +00:20:19,850 --> 00:20:25,130 +ناحية ال voltage أثبتناها ان هذا لازم يكون ايشفانت + +196 +00:20:25,130 --> 00:20:30,210 +شفتها من زاوية ايه؟ وشفنا ال output هنا كيف وضعه + +197 +00:20:30,210 --> 00:20:33,270 +وال output اللي هنا ايش وضعه؟ ايش اللي عملناه؟ بس + +198 +00:20:33,270 --> 00:20:37,030 +خلنا نستذكر انا جيت في الأول واطلعت على الدائرة + +199 +00:20:37,030 --> 00:20:40,710 +هذه قلت اللي عند ال input اللي هنا بيساوي ال + +200 +00:20:40,710 --> 00:20:44,640 +reference voltage اللي هنالما نفرص الهان متساوي + +201 +00:20:44,640 --> 00:20:51,140 +التيار هذا ال transistor Qi و Qi هدول اتنين + +202 +00:20:51,140 --> 00:20:55,620 +forward active forward active نص الطيار اللي هان + +203 +00:20:55,620 --> 00:20:58,920 +بدي يجي من هذا الطرف و النص بدي يكونمن هذا الطرف + +204 +00:20:58,920 --> 00:21:03,060 +في هذا الحالة طيب ال IE ال IRE هذا بقدر اجيب و هو + +205 +00:21:03,060 --> 00:21:07,280 +بيساوي عندى VBB minus ال drop ال point seven five + +206 +00:21:07,280 --> 00:21:11,860 +ال drop اللى عندى اللى هنا زائد ال VE على ال RE + +207 +00:21:11,860 --> 00:21:15,720 +اعطانى التيار اللى هنا نصه بدي اخد نصه هذا التيار + +208 +00:21:15,720 --> 00:21:21,370 +على اتنين بقدر اجيب ال V out اللى عندىنص في VCC + +209 +00:21:21,370 --> 00:21:28,250 +minus half IRE في RCR بيعطيني ال V non inverse و + +210 +00:21:28,250 --> 00:21:34,450 +لو طبقت على الشك هذه بتعطيني ال V inverse الآن + +211 +00:21:34,450 --> 00:21:40,330 +اللي قلت if VN is less than VBBالـ VIN اللي هان + +212 +00:21:40,330 --> 00:21:46,130 +هذا ال VBE ال VBB أكبر من ال VIN أو هذا زيبته أقل + +213 +00:21:46,130 --> 00:21:49,750 +من القيمة اللي هان لقيت ايش ال drop اللي هان هذا + +214 +00:21:49,750 --> 00:21:56,280 +بيكون forward active حسبت ال VE اللي هانبتساوي VBB + +215 +00:21:56,280 --> 00:22:00,640 +-0.75 اللي هنا طب لما جيت بدي اشوف ايش وضع + +216 +00:22:00,640 --> 00:22:03,320 +الترانزستور هنا بدي اشوف قداش ال voltage اللي هنا + +217 +00:22:03,320 --> 00:22:07,760 +لو جيته 0.75 معناته هذا forward active جيت حسبته + +218 +00:22:07,760 --> 00:22:11,840 +وجيت بيطلع عنده هنا ال voltage اللي هنا بدي ساوي + +219 +00:22:11,840 --> 00:22:18,290 +VIN ناقصالـ VBE اللي هات جيت حسبت ما ان هذا ال VE + +220 +00:22:18,290 --> 00:22:21,450 +هي نقطة مشتركة فال voltage من كل الطرفين الأصلي + +221 +00:22:21,450 --> 00:22:26,850 +يعطيني نفس القيمة لو اتنين شغالين فجيت حسبت قلت + +222 +00:22:26,850 --> 00:22:30,530 +اتنين متساويين حسبت ال VBE اللي هات وجيت ال VBE + +223 +00:22:30,530 --> 00:22:35,870 +اللي هات بتطلع أقل من قيمةالـ 0.75 اللي انا + +224 +00:22:35,870 --> 00:22:39,930 +ماتعطيها لأن عندي هيطلع VIN minus VBP وهذا القيمة + +225 +00:22:39,930 --> 00:22:44,870 +بالنجاتف فهتقول لي ان هذا الترانزستور اللي عندي مع + +226 +00:22:44,870 --> 00:22:50,690 +ان ال VBE له أقل من 0.75 فهيكون ايه اش off هذا off + +227 +00:22:50,690 --> 00:22:54,910 +وهذا forward active هذا ال output اللي عندي مع انه + +228 +00:22:54,910 --> 00:22:59,130 +off بدي ساوي VCC لأن ال drop اللي عندي سفر since + +229 +00:22:59,130 --> 00:23:04,300 +مافيش اي load هذا اللي عندي كل التيار اللي هنافي + +230 +00:23:04,300 --> 00:23:08,080 +ال IRE جاي من هذا الترانزستور وهذا ال assumption + +231 +00:23:08,080 --> 00:23:12,780 +اللي عملته قلت ال IE بدي ساوي ال IC اللي هان اللي + +232 +00:23:12,780 --> 00:23:17,800 +هو بساوي IRE وال IRE بدي ساوي ال VBB minus ال + +233 +00:23:17,800 --> 00:23:23,080 +point seven five زائد ال VE على ال RE عطتني التيار + +234 +00:23:23,080 --> 00:23:26,380 +اللي هان و هذا التيار ضربته فات وطرحته من ال VCC + +235 +00:23:26,380 --> 00:23:31,980 +عطاني ال V non inverse طيب الان + +236 +00:23:33,430 --> 00:23:39,370 +هذه جيبته طلع عندى بيساوي كام VCC وهذه بقدر اجيبه + +237 +00:23:39,370 --> 00:23:44,470 +من الطرفين هذه لو طبقت هذه المعادلة بتعطينى ال VOL + +238 +00:23:44,470 --> 00:23:49,790 +ال VIL ايش بيساوي هذه بالنسبة للدائرة السهلة ال + +239 +00:23:49,790 --> 00:23:58,430 +VIL بيساوي VBB-0.05 V و ال VIH بيساوي + +240 +00:24:06,250 --> 00:24:09,910 +الرقم هذا احيانا بتلاقيه هالجدوة احيانا بتلاقيه + +241 +00:24:09,910 --> 00:24:14,530 +حوالينه شوية بزيادة بس البيت القصيد لو عندي + +242 +00:24:14,530 --> 00:24:22,350 +seventy five millivolt تعملي فرق كبير بين الأداء + +243 +00:24:22,350 --> 00:24:28,650 +تبع ال transistors اللي هيأي هدول تبتدل هدول ده + +244 +00:24:28,650 --> 00:24:33,490 +أسهل حاجة هدول لما أسألك أقولك إيش ال V .. ال VTC + +245 +00:24:33,490 --> 00:24:42,290 +هدول من بدون شغل ايوة هدول بسهولة + +246 +00:24:42,290 --> 00:24:48,150 +هاد الان لو عكست اتفضى هو أطلع معلومة هاد و VDO ده + +247 +00:24:48,150 --> 00:24:51,730 +هي point سبعة خمسة ولا ايه؟ لأ هي هاد بالنسبة لل + +248 +00:24:51,730 --> 00:24:56,450 +ACL هي point سبعة خمسةأيوة ال specification تبعت + +249 +00:24:56,450 --> 00:25:01,690 +ال transistor هاي بتقولك ال VBE بيساوي point seven + +250 +00:25:01,690 --> 00:25:09,450 +five كويس؟ الآن بدي أعكس هاي بدل ما أقول هذه + +251 +00:25:09,450 --> 00:25:17,230 +الأصغر بدي أقول هذه أكبر و هذه تابتة هذه بدل ما هي + +252 +00:25:17,230 --> 00:25:20,970 +كانت .. عملت هذه one point nine وهذه اتنين وهذه + +253 +00:25:20,970 --> 00:25:26,180 +اتنين point oneفي هذه الحالة ماذا سيحصل عندك؟ هذا + +254 +00:25:26,180 --> 00:25:31,760 +سيصبح forward active وهذا off الoff يعني ال V non + +255 +00:25:31,760 --> 00:25:36,680 +inverse تساوي VCC و بدي أعمل زي نفس ما عملتها ال V + +256 +00:25:36,680 --> 00:25:40,840 +inverse بدي أجيب ال I كله اللي هان هو نفسه اللي + +257 +00:25:40,840 --> 00:25:46,480 +هان معناته بدي أقول عند V in ناقص ال point seven + +258 +00:25:46,480 --> 00:25:51,980 +five زائد ال V E على ال R E بدي أعطيني التياراللي + +259 +00:25:51,980 --> 00:25:56,680 +هان و ال output اللي عنده ايش بدي ساوي VCC مضروب + +260 +00:25:56,680 --> 00:26:02,280 +مناقصة ال RCI في ال IRE اللي هان بدي اعطيني ال V + +261 +00:26:02,280 --> 00:26:05,880 +inverse و هذا اللي بقول عنها الحالة التانية + +262 +00:26:22,780 --> 00:26:32,780 +when v in greater than v bb معناته qr off وqi + +263 +00:26:32,780 --> 00:26:38,880 +forward active في هذا الحالة ايش بدى يحصل عندى بدى + +264 +00:26:38,880 --> 00:26:45,660 +اقول عندى v none inverse بدى يساوي v cc وبدى اجيب + +265 +00:26:45,660 --> 00:26:50,480 +ال v inverse اللى عندى بدى احسبها هان عندى ال IRE + +266 +00:26:51,560 --> 00:27:02,860 +بدي ساوي ال IE لل I بدي ساوي ال ICI تقريبا assume + +267 +00:27:02,860 --> 00:27:07,940 +انها beta much much greater beta forward than one + +268 +00:27:07,940 --> 00:27:18,160 +فاللي عندى ال IRE بدي ساوي VN minus VBE ECL plus + +269 +00:27:18,160 --> 00:27:30,270 +VEE علىالـ RE وعندي ال V inverse VCC minus VIN + +270 +00:27:30,270 --> 00:27:39,210 +وهنا هاي خلّيني أقول عنه minus + +271 +00:27:39,210 --> 00:27:49,930 +VBE ACL plus VEE على ال RE مضروبة في RCI + +272 +00:27:53,270 --> 00:27:56,730 +طيب لو ضليتني ازود في ال input ايش هيحصل في + +273 +00:27:56,730 --> 00:28:02,070 +الترانزستور اللي هذا ايوة + +274 +00:28:02,070 --> 00:28:06,050 +هذا + +275 +00:28:06,050 --> 00:28:13,550 +الترانزستور اذا ضليتنيه هذي ازود فيه هلاحظ هذا + +276 +00:28:13,550 --> 00:28:19,270 +المنطقة هيصير له saturation يعني هذا ايش مقدر اقول + +277 +00:28:19,270 --> 00:28:22,030 +هنا as + +278 +00:28:33,560 --> 00:28:39,400 +في حالة الـ saturated يعني + +279 +00:28:39,400 --> 00:28:43,960 +انت بده تشوف قداش قيمة v in اللي بتعمل ل qi + +280 +00:28:43,960 --> 00:28:48,260 +saturated حد عرفها قداش هي + +281 +00:28:51,860 --> 00:28:57,720 +انا مش عارف بدي أشوفها هذا بدي أسميها vs شايف هذا + +282 +00:28:57,720 --> 00:29:02,580 +بدل ما بقي نقول vn بتعمل qi saturated بدي أسميها + +283 +00:29:02,580 --> 00:29:07,960 +vs و أصير اش .. انا ديها بعد هيك ايه ايه؟ vs أسهل + +284 +00:29:07,960 --> 00:29:13,580 +من ما بقي نسويها الان عندي هذا وضعه قلت ايه ايش + +285 +00:29:13,580 --> 00:29:18,740 +saturated هاي + +286 +00:29:18,740 --> 00:29:24,150 +plus minus plus minusالليهان مقدر اجيب ال voltage + +287 +00:29:24,150 --> 00:29:30,370 +الليهان مظبوط هذا ايش بده يساوي VIN اللي هو بعملي + +288 +00:29:30,370 --> 00:29:34,590 +هذا بتسميه VIN اللي بعمليها بعدين بعوض عنه minus + +289 +00:29:34,590 --> 00:29:44,570 +ال VBESAT الليهان و ال VIN هذه سميتها ايش VS طيار + +290 +00:29:44,570 --> 00:29:48,810 +الليهان ايش بده يساوي IRE + +291 +00:29:49,320 --> 00:29:57,920 +واضع الـ SATA RATED بدي ساوي VS-VBE SATA plus VEE + +292 +00:29:57,920 --> 00:30:07,800 +على RE كويس ال output اللي هنا ايش بدي ساوي VIN + +293 +00:30:07,800 --> 00:30:18,920 +بدي ساوي VCC minus اللي هو اللي هنا VS minus VBE + +294 +00:30:30,980 --> 00:30:37,960 +مظبوط ايش عند المجاهيل هنا في عندى تنتين هذا مش + +295 +00:30:37,960 --> 00:30:44,980 +عارفه و هذا مش عارفه صح عارفهم هدول لا انا عارف + +296 +00:30:44,980 --> 00:30:49,580 +قداش ال V انفرس ولا عارفالـ VIN اللي بيعمل ليهان + +297 +00:30:49,580 --> 00:30:52,720 +طب فى حاجة فى طريقة تانية ممكن اجيب الـ V Inverse + +298 +00:30:52,720 --> 00:30:57,580 +أسهل لو + +299 +00:30:57,580 --> 00:31:04,180 +روحت اللوب اللي هنا مظبوط طلع عندى ايش الفرق ب .. + +300 +00:31:04,180 --> 00:31:09,940 +هى ال V Inverse هنا صح هى ال VIN ال VS اللي عندى + +301 +00:31:09,940 --> 00:31:15,650 +هنا هى دى بدها تكون أعلى من اللي هنا بقداشبال بي + +302 +00:31:15,650 --> 00:31:17,830 +بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي + +303 +00:31:17,830 --> 00:31:21,230 +بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي + +304 +00:31:21,230 --> 00:31:22,910 +بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي + +305 +00:31:22,910 --> 00:31:30,990 +بي بي بي بي بي بي بي بي بي بي بي بي بي + +306 +00:31:30,990 --> 00:31:32,530 +بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي + +307 +00:31:32,530 --> 00:31:36,250 +بي بي بي بي بي بي بي بي بي بي + +308 +00:31:36,250 --> 00:31:41,950 +بي + +309 +00:31:41,950 --> 00:31:42,770 +بي + +310 +00:31:46,480 --> 00:31:52,780 +معادلة فيها one unknown صح فصار عندى ال vs minus + +311 +00:31:52,780 --> 00:32:07,780 +vbc set بدي ساوي vcc minus vs minus + +312 +00:32:07,780 --> 00:32:21,210 +vbe set plus veeعلى الـ RE مضروبة في RCI صح؟ هذي + +313 +00:32:21,210 --> 00:32:25,450 +بدي أقسمها بدي أفتفتها اللي هي بحيث يصير عندى هذا + +314 +00:32:25,450 --> 00:32:29,370 +الـ VS لحال هو أجيبها عوين على الشق هذه إذا عملتها + +315 +00:32:29,370 --> 00:32:38,790 +بهذه الطريقة إيش بدي يطلع عندى؟ VS minus VBCSATبدي + +316 +00:32:38,790 --> 00:32:43,910 +ساوي VCC هاي ال minus بدي اضرب في هذه وهاي بدي اخد + +317 +00:32:43,910 --> 00:32:51,750 +VS minus VS في RCI على RE ال minus بدي ادخله على + +318 +00:32:51,750 --> 00:32:56,750 +تنتين التانيات هاي بدي اعمل plus هيصير عندي ايش + +319 +00:32:56,750 --> 00:33:03,010 +هنا هاي VBE set + +320 +00:33:03,010 --> 00:33:14,620 +ناقص VEEفي الـ RCI على الـ RE طيب الآن الـ VS بدي + +321 +00:33:14,620 --> 00:33:16,800 +أجيبها على الشجة هذه و هذي تجيبها على الشجة + +322 +00:33:16,800 --> 00:33:27,840 +التانية إيش بدي يصير عندك واحد زائد RCI على RE في + +323 +00:33:27,840 --> 00:33:33,280 +VS بدي ساوي VCC plus + +324 +00:33:35,190 --> 00:33:40,610 +vbc set زائد + +325 +00:33:40,610 --> 00:33:55,670 +vbe saturated minus vee في rci على re الان هادي + +326 +00:33:55,670 --> 00:34:03,410 +ممكن اعمل solving لل vs إذا عملته بيصير عند ال vs + +327 +00:34:03,410 --> 00:34:16,010 +بدها تساويهي VCC plus VBCSAT plus VBESAT + +328 +00:34:16,010 --> 00:34:31,090 +ناقص VEE في RCI على RE على 1 زائد RCI على RE + +329 +00:34:34,460 --> 00:34:38,300 +الان انا جبت كل ال voltage اللي عندي ال critical + +330 +00:34:38,300 --> 00:34:45,840 +voltage اللي موجود ليش؟ انا كان هذه ال VOH جبته و + +331 +00:34:45,840 --> 00:34:50,900 +ال VOL جبته و ال VIL و ال VIH هان ضال عند الحاجة + +332 +00:34:50,900 --> 00:34:56,040 +اللي كانت مجهولة ايش ال VS و هين جبت ال VS ال VS + +333 +00:34:56,040 --> 00:35:01,430 +ايش بدي ساوي؟بدي ساوي انا لما جيت من هذا الاتجاه + +334 +00:35:01,430 --> 00:35:07,030 +قولت ال Vs اللي عندي هان بدي ساوي ال V inverse + +335 +00:35:07,030 --> 00:35:12,390 +ناقص او زائد اللي عند ال V inverse زائد ال point + +336 +00:35:12,390 --> 00:35:16,110 +seven five اللي هان لإن هادي بال negative وهنا بال + +337 +00:35:16,110 --> 00:35:21,720 +positive او ال V inverse بدي ساوي Vsناقص ال point + +338 +00:35:21,720 --> 00:35:28,600 +seven five جبت ال V inverse عبرت الطريقة التقليدية + +339 +00:35:28,600 --> 00:35:34,440 +فالتقليدية لإن قلت V in اللي عندي اللي هي Vs minus + +340 +00:35:34,440 --> 00:35:38,600 +point seven five زائد VE على RE اعطتنا التيار هاد + +341 +00:35:38,600 --> 00:35:44,170 +والتيار اللي هادبدي اخد ال RC اضربها فيها و اطلع + +342 +00:35:44,170 --> 00:35:47,990 +هذا drop من VCC يعطينا V Inverse لقيت في هذا + +343 +00:35:47,990 --> 00:35:52,550 +المعادلة في عندى V Inverse مش عارفه و Vsh مش عارفه + +344 +00:35:52,550 --> 00:35:56,350 +في المعادلة التانية اللي روحتها البسيطة هاي Vs مش + +345 +00:35:56,350 --> 00:35:59,950 +عارفها و V Inverse مش عارفها صار عندى معادلتين و + +346 +00:35:59,950 --> 00:36:04,460 +ال two unknown بعمل eliminationللـ V inverse بقدر + +347 +00:36:04,460 --> 00:36:08,140 +اجيب بعد هيك بيصير عندى معادلة فيها ال Vs unknown + +348 +00:36:08,140 --> 00:36:12,800 +وهي اعطانى ال Vs اعطانى اللى بتعمل الترانزستور هذا + +349 +00:36:12,800 --> 00:36:17,880 +وضعه saturated فالان ال critical voltages ككل + +350 +00:36:17,880 --> 00:36:19,360 +جبتهم فيك سؤال + +351 +00:36:25,870 --> 00:36:29,370 +هي مش هتأثر بس هي احنا ال critical voltage ايش + +352 +00:36:29,370 --> 00:36:33,970 +عندى بحصل لأن هذا بيصير الهدب اكتر شوية من ال + +353 +00:36:33,970 --> 00:36:40,570 +output low عرفت يعني هذا بتنزل عندى شوية اقل من ال + +354 +00:36:40,570 --> 00:36:46,170 +output low بس في عندي صار تغيير في الشكل تبع ال + +355 +00:36:46,170 --> 00:36:49,630 +transistor تغيير في حالة ال transistor تغيير في + +356 +00:36:49,630 --> 00:36:52,730 +حالة ال transistor انا عادة كل ما بزود ال input + +357 +00:36:52,730 --> 00:36:58,390 +ايش بيصير عندىيعني كل ما زود ال input بيصير فيه + +358 +00:36:58,390 --> 00:37:02,890 +تغير بيزيد عندي ال IC مظبوط في هذه الحالة او + +359 +00:37:02,890 --> 00:37:07,930 +العلاقة اللي عندي ال IBكل ما بزيد ال IP ال IC ايش + +360 +00:37:07,930 --> 00:37:11,750 +بزيد لحد ات لما وصلت و اضع ال saturation بس هنا + +361 +00:37:11,750 --> 00:37:16,870 +زود في ال IP ال IC ايش بوصل ال saturation ببطل + +362 +00:37:16,870 --> 00:37:20,210 +بيصير قيمته ال beta .. الدرب في ال beta forward + +363 +00:37:20,210 --> 00:37:24,850 +بطلت ايش تشتغل صار بدي اضرب في ال sigma كمان و ال + +364 +00:37:24,850 --> 00:37:29,380 +sigmaكل ما فيها بتنزل لتحت اقل من واحد ببدأ بواحد + +365 +00:37:29,380 --> 00:37:32,560 +at the edge of saturation و بضل لكل ما اتعمق في ال + +366 +00:37:32,560 --> 00:37:36,460 +saturation بتنزل عندى فروحت انا لل non linear + +367 +00:37:36,460 --> 00:37:45,620 +region ال VBB تابت انت بتغيروه كيف يعني؟ لأ انت + +368 +00:37:45,620 --> 00:37:51,340 +ممكن تقلبه بس عادة في ال standard اللي عندى VBB + +369 +00:37:51,340 --> 00:37:55,430 +بحطه as a referenceالـ reference دائما بجيسه على + +370 +00:37:55,430 --> 00:38:00,770 +هواحي مظموم؟ هي لأ في ال standard gate جايين لكمان + +371 +00:38:00,770 --> 00:38:06,370 +دقيقتين هنقولك قداش القيمة تبعته وهذا ال standard + +372 +00:38:06,370 --> 00:38:09,710 +gate هتلاقيه بال negative و الشغل اللي موجود عندك + +373 +00:38:09,710 --> 00:38:14,490 +لحد تلان واضحة إيش اللي عملناه؟ عملنا بالنسبة لل + +374 +00:38:14,490 --> 00:38:20,750 +VTC الدائرة هذه الأداء تبحها مش المعقد يعني اتطلع + +375 +00:38:20,750 --> 00:38:26,750 +عليهاو اتجاه واحد في الوقت يعني هاي سكت غطي على + +376 +00:38:26,750 --> 00:38:30,590 +هاي و اتكلم على هذه الجهة و بعدها تعالي على الجهة + +377 +00:38:30,590 --> 00:38:36,090 +التانية ببين الأداء اللي عندك طب لما بدى اعمل ore + +378 +00:38:36,090 --> 00:38:42,470 +و النور ايش بعمل بجيب هذه الشجة و بضيف ال + +379 +00:38:42,470 --> 00:38:46,610 +transistor يعني هذا اللي بمده شوية و بضيف + +380 +00:38:50,640 --> 00:38:55,880 +الترانزيستور تاني وهذا بسميه QA وهذا VNA وهذا + +381 +00:38:55,880 --> 00:39:01,280 +بسميه QIB وهذا + +382 +00:39:01,280 --> 00:39:15,320 +بسميه VNB الان هذه شقة VNOR وهذه شقة VR أسهل + +383 +00:39:15,320 --> 00:39:22,640 +عمل ال OR والنور هناترانزيستر واحد حطيته اعطاني ال + +384 +00:39:22,640 --> 00:39:31,720 +VOR و VNOR بنفس الوقت طيب الان انتوا زي ما بتلاحظ + +385 +00:39:31,720 --> 00:39:36,860 +هادئ لو شبكت عليه load كويس؟ + +386 +00:39:42,780 --> 00:39:46,760 +أيش هلاحظ اللي عندي؟ كل ما بزيد هدول ال branches + +387 +00:39:46,760 --> 00:39:55,080 +كل ما هذا بصير ال drop عندي أكتر هذه بتسويلي شوية + +388 +00:39:55,080 --> 00:39:58,860 +ضغط على ال fan out فلحل المشكلة هذا ناشي عملت في + +389 +00:39:58,860 --> 00:39:59,600 +السابق؟ + +390 +00:40:03,860 --> 00:40:08,600 +قولت دايما لما نيجي انا اللي عندي يعني الفكرة في + +391 +00:40:08,600 --> 00:40:13,640 +البيت خط الميه دي بوصلنيش ميه كافي ايش بعمل؟ بركب + +392 +00:40:13,640 --> 00:40:18,020 +motor و ال motor عندنا هنا ايش هو؟ transistor ايش + +393 +00:40:18,020 --> 00:40:23,000 +بسميه؟ emitter follower ال emitter follower هو ال + +394 +00:40:23,000 --> 00:40:26,480 +motor تبعنا ال gain ال voltage gain تبعه هذا كده + +395 +00:40:26,480 --> 00:40:31,700 +ايش؟ واحد فهو بيعمل amplification لإيش؟ للتيار لل + +396 +00:40:31,700 --> 00:40:38,440 +currentفانا دايما ال motor ربطها هذه عندك ال motor + +397 +00:40:38,440 --> 00:40:42,220 +دايما ايش هو ال emitter follower اللي عندنا اللي + +398 +00:40:42,220 --> 00:40:47,520 +بيعمل generation بيعمل amplification للتيار الآن + +399 +00:40:47,520 --> 00:40:52,120 +ال motor هذا اللي بدي اسميه بدي اطلع عليه بطريقة + +400 +00:40:52,120 --> 00:40:53,500 +أخرى + +401 +00:40:56,760 --> 00:41:01,440 +هو ال motor بيعمل لي حاجته ال emitter follower act + +402 +00:41:01,440 --> 00:41:04,780 +as يعني amplification في نفس الوقت هو buffer + +403 +00:41:04,780 --> 00:41:10,040 +بيعزلي ال resistance اللي هان او ال impedance اللي + +404 +00:41:10,040 --> 00:41:14,340 +هان عند ال load التاني اللي موجود عندى فالشكل + +405 +00:41:14,340 --> 00:41:17,740 +تبعها هيختلف شوية عند الدائرة + +406 +00:41:37,930 --> 00:41:42,370 +هرسم الدائرة الجديدة وجديد فيها + +407 +00:42:14,420 --> 00:42:17,820 +السلام عليكم ورحمة الله وبركاته + +408 +00:42:58,210 --> 00:43:03,770 +هذا اللي كنا عارفينه سابقا مظبوط الان ايش اللي + +409 +00:43:03,770 --> 00:43:17,730 +ضفتها حطيت buffer فهذه + +410 +00:43:17,730 --> 00:43:24,410 +سميتها RDO two kilo ohm فع الشجة هذه برضه حطيت + +411 +00:43:24,410 --> 00:43:25,110 +كمان buffer + +412 +00:43:36,100 --> 00:43:39,560 +ر دي ان ر دي ان ر دي ان ر دي ان ر دي ان ر دي ان ر + +413 +00:43:39,560 --> 00:43:42,480 +دي ان ر دي ان ر دي ان ر دي ان ر دي ان ر دي ان ر دي + +414 +00:43:42,480 --> 00:43:42,620 +ان ر دي ان ر دي ان ر دي ان ر دي ان ر دي ان ر دي ان + +415 +00:43:42,620 --> 00:43:43,020 +ر دي ان ر دي ان ر دي ان ر دي ان ر دي ان ر دي ان ر + +416 +00:43:43,020 --> 00:43:45,140 +دي ان ر دي ان ر دي ان ر دي ان ر دي ان ر دي ان ر دي + +417 +00:43:45,140 --> 00:43:47,460 +ان ر دي ان ر دي ان ر دي ان ر دي ان ر دي ان ر دي ان + +418 +00:43:47,460 --> 00:43:55,300 +ر ديان ر ديان ر ديان ر ديان ر ديان + +419 +00:43:58,000 --> 00:44:04,860 +بو و VR وهذه + +420 +00:44:04,860 --> 00:44:11,940 +اللي هي شبكتها على ال ground هذا + +421 +00:44:11,940 --> 00:44:15,700 +الاختلاف اللي عملته في هذه الدائرة الدائرة الزرقه + +422 +00:44:15,700 --> 00:44:19,480 +اللي بالازرقه هي اللي احنا كنا نشتغل عليها قبل + +423 +00:44:19,480 --> 00:44:23,460 +شوية الأحمر هدوله اللي ضفناه اللي هو ال emitter + +424 +00:44:23,460 --> 00:44:26,700 +follower هذا بنسميها MCL1 + +425 +00:44:30,890 --> 00:44:41,550 +متر كابل دازج مي سي أل وان كيد + +426 +00:44:41,550 --> 00:44:50,810 +ويد بابر output + +427 +00:44:58,330 --> 00:45:03,670 +أو عشان نحط ال technical term تبعتها بالظبط خلّينا + +428 +00:45:03,670 --> 00:45:17,650 +نكتب or nor لأن هذا mcl or nor gate with output + +429 +00:45:17,650 --> 00:45:22,950 +buffers الأن + +430 +00:45:22,950 --> 00:45:30,260 +هذه output buffersكويس هاي ال ore اللي ها و هاي + +431 +00:45:30,260 --> 00:45:35,160 +النور و ال emitter coupled logic type one و هاد ال + +432 +00:45:35,160 --> 00:45:39,840 +M4 Motorola Motorola بتعرفوا شركة اللي هي ال + +433 +00:45:39,840 --> 00:45:44,280 +semiconductor لتصنيع ال semiconductors فهي ال + +434 +00:45:44,280 --> 00:45:47,560 +Motorola اللي موجودة هنا أشهر أشي بتعرفوا عن + +435 +00:45:47,560 --> 00:45:51,280 +Motorola إيش الجوالات بس هي قبل ما تشتغل في + +436 +00:45:51,280 --> 00:45:58,040 +الجوالات هي شركة تصنيع ICsطيب مافيش حد فضله تابعت + +437 +00:45:58,040 --> 00:46:05,140 +الان ال هنا ال voltage اللي هنا ال VCC صار بيساوي + +438 +00:46:05,140 --> 00:46:08,520 +ايش؟ Zero كل الشغل عندي في ال negative voltage + +439 +00:46:08,520 --> 00:46:15,220 +يعني لو بدى اطلع على هذه هذه ايش صارت؟ تتذكروا لما + +440 +00:46:15,220 --> 00:46:22,320 +تعمل على هذه copy و move بدك تجيبها لهنا شايفين + +441 +00:46:22,320 --> 00:46:27,520 +هذه؟ بدى امسكها زي ما هيو أعملها slide و أجيبها في + +442 +00:46:27,520 --> 00:46:32,240 +هذه الشجرة فأصبح كل شغل في أي quadrant الموجود هنا + +443 +00:46:32,240 --> 00:46:36,400 +يعني نفس الدائرة اللي هنا وهذا شويه بتعملكوا شويه + +444 +00:46:36,400 --> 00:46:46,280 +confusion ليش؟ + +445 +00:46:46,280 --> 00:46:50,520 +بتضايفوا + +446 +00:46:50,520 --> 00:46:57,760 +هنا هذا صار ال VOH عندي و أنا ال VOLوهنا ال Vs و + +447 +00:46:57,760 --> 00:47:05,620 +Vil و Vih هدولة شوية انتوا ايش بتصير فيها زي ما + +448 +00:47:05,620 --> 00:47:09,140 +قلت هاد اللي هاندك تعملها زي ايه اش تسحبها و تحطها + +449 +00:47:09,140 --> 00:47:14,810 +هادبنفس الأرقام لأ القيم هتصير بالسالم بس نفس اللي + +450 +00:47:14,810 --> 00:47:18,450 +هان يعني ال VOH اللي هي العالية ال VON اللي ساتها + +451 +00:47:18,450 --> 00:47:23,210 +اللي هان ال VIL على الشجهات ال VIH على الشجهات هذه + +452 +00:47:23,210 --> 00:47:29,710 +هدول أحيانا بتشجلموا فيهم كتير يعني بيجيلك سؤال + +453 +00:47:29,710 --> 00:47:33,790 +مثلا في الامتحان ايش بقول ارسملي ال VTC لدائرة زي + +454 +00:47:33,790 --> 00:47:39,810 +هذه هذه الأصل فيهايعني هذه علامات في الجيبة لأنه + +455 +00:47:39,810 --> 00:47:44,790 +فيش فيها حاجة يعني القوانين اللي عندك حاططها بتشيط + +456 +00:47:44,790 --> 00:47:50,210 +شيط بتطلحها و بتطبرها و بتقول هي القوانين لسبب أو + +457 +00:47:50,210 --> 00:47:55,070 +لآخر بتقلبوا ال VIL و ال VIH و ال VOL و ال VOH + +458 +00:47:55,070 --> 00:48:00,730 +بيصيروا بالمقلبة انت + +459 +00:48:00,730 --> 00:48:05,460 +بتطلع ان عندك الأرقام بس بتعرفش مين فيهم مينأيوة + +460 +00:48:05,460 --> 00:48:10,240 +كيف الصفر؟ فانت أسهل حاجة الرسمة اللي هنا حركها + +461 +00:48:10,240 --> 00:48:15,960 +هيك لهاد و اللي عندك هدول الرقام حطهم زي ما هم ما + +462 +00:48:15,960 --> 00:48:22,600 +تلعبش فيهم كويسك؟ اما انت بدك تحركها زي هيك يعني + +463 +00:48:22,600 --> 00:48:30,450 +مسكها سويلها select all و أسحبها لهاد الشجرةو هديك + +464 +00:48:30,450 --> 00:48:34,050 +بتلغيها هديك خلصت الحين في هذه الدقرة احنا مافيش + +465 +00:48:34,050 --> 00:48:38,890 +عندنا حاجة في ال positive كويس + +466 +00:48:38,890 --> 00:48:43,830 +فصرنا في هذه الحارة مش في الحارة هديك صرنا في هذه + +467 +00:48:43,830 --> 00:48:48,670 +المنطقة واضح + +468 +00:48:48,670 --> 00:48:52,670 +ايش .. ايش .. ايش اللي عملناها فانت بتعمل select + +469 +00:48:52,670 --> 00:48:57,650 +هناك بتعمله select all و drag لها و اعمله moving + +470 +00:48:57,650 --> 00:49:05,580 +في هذه المنطقةفهذه بتريحك من عناء أنك تفكر كتير، + +471 +00:49:05,580 --> 00:49:10,440 +يعني بتخفف عليك كمية التفكير في هذه المنطقةلأنه + +472 +00:49:10,440 --> 00:49:16,520 +عشان دايما مبدأ اللي بريح حاله في التفكير أي حاجة + +473 +00:49:16,520 --> 00:49:21,920 +بتاخدش مجهود عملها بيصير سهل، أي أشي في الدنيا، + +474 +00:49:21,920 --> 00:49:25,260 +ماتحطش فيه مجهود بيصير .. يعني تعمل بدون مجهود + +475 +00:49:25,260 --> 00:49:30,220 +معناته أنت وصلت لمرحلات المهنية العالية، أي أشي + +476 +00:49:30,220 --> 00:49:35,690 +بتعمله بمجهود معناته أنت لساتك مش بتعود عليهيعني + +477 +00:49:35,690 --> 00:49:41,250 +انت بقولها أبسط إشي اطلع إجري أول يوم أبو كيلو + +478 +00:49:41,250 --> 00:49:45,650 +هتلاقي حالك تعبان و فيه مجهود تاني يوم تالت يوم + +479 +00:49:45,650 --> 00:49:51,170 +ضلك بسوي عليها بسبوع زمان بتحس بعد هيك أنه إيش؟ + +480 +00:49:51,170 --> 00:49:56,880 +مافيش حاجة .. حاجة .. حاجة مريحة جدابديش أقول بعد + +481 +00:49:56,880 --> 00:50:01,000 +أسبوع خليني أقول بعد شهر، بس بتصير إيش أنك مابتحسش + +482 +00:50:01,000 --> 00:50:05,120 +أنك بتبدأ المجهود، خصوصا إذا بتعملها حسب الأصول، + +483 +00:50:05,120 --> 00:50:10,700 +يعني حسب التمرين الصحي فبتحس أنه مابتعطيهاش مجهود، + +484 +00:50:10,700 --> 00:50:16,000 +أي إشي بتعطهوش مجهود بتقدر تداوم عليه بشكل دائم، + +485 +00:50:16,000 --> 00:50:19,280 +يعني انت الحين لو حد قالك أول أيام احنا صغار احفظ + +486 +00:50:19,280 --> 00:50:24,370 +جدور الضرب، إيش كانت؟بس بعد هيك تقوله ايه جدول + +487 +00:50:24,370 --> 00:50:31,610 +الضرب بتصير ايش؟ انت .. انت جيل ال calculator صحيح + +488 +00:50:31,610 --> 00:50:37,970 +زمان + +489 +00:50:37,970 --> 00:50:41,030 +.. زمان كان عندنا حاجة جيلنا احنا كان ال + +490 +00:50:41,030 --> 00:50:44,830 +calculator موجودة بس مش .. يعني قليلة .. قليلة و + +491 +00:50:44,830 --> 00:50:46,690 +مش مسموح لك تدخلها الامتحانات + +492 +00:50:49,900 --> 00:50:54,340 +مش الجدول اللي تضرب ال calculator ككل كان مش مسموح + +493 +00:50:54,340 --> 00:50:58,780 +تدخلها الامتحانات فانت عندك اي ارقام بدك تضربهم + +494 +00:50:58,780 --> 00:51:04,320 +كبيرة ايش بتعمل كان؟ الورق الورق بيظبطش كثير كان + +495 +00:51:04,320 --> 00:51:08,380 +في حاجة بيسميها ال log table بتعرفوهم جداول ال + +496 +00:51:08,380 --> 00:51:15,400 +logs لغر ترميليات كان عندنا كتاب صغير فيه كل جداول + +497 +00:51:15,400 --> 00:51:19,880 +زي هيك فانت بتيجي تضرب حسب هدوليعني فيه قالية + +498 +00:51:19,880 --> 00:51:22,880 +اتعلمناها و بنيجي نضرب فيها طب ما أنت بتيجي تضربها + +499 +00:51:22,880 --> 00:51:25,840 +على ال calculator اللي بتقعد فيها ربع ساعة بتاخدك + +500 +00:51:25,840 --> 00:51:32,380 +ثوانىفكانت على هذه الأصول فإيش كنا بيت القصيد أي + +501 +00:51:32,380 --> 00:51:35,980 +رقمين تضربهم انت عارف كده في أي حارة هيطلع الرقم + +502 +00:51:35,980 --> 00:51:38,660 +فانت بتيجي تدخل على ال calculator بتطلع عندك بتقول + +503 +00:51:38,660 --> 00:51:41,960 +مصدق و بتاخدها احنا عندنا بنضرب على ال calculator + +504 +00:51:41,960 --> 00:51:45,880 +لأ في حاجة داخلة غلطة يعني ليش لأنه لازم يطلع في + +505 +00:51:45,880 --> 00:51:49,740 +هذه المنطقة طلع عندك حاجة تانية على طول بنفكر فيها + +506 +00:51:49,740 --> 00:51:54,290 +فهذهمن ال advantages انا مابقولكوا شو بدنا نروح + +507 +00:51:54,290 --> 00:51:57,730 +عليها بس دايما بقول لازم تعرف في اي منطقة انت + +508 +00:51:57,730 --> 00:52:03,670 +موجود الان انا عندها فش عندى VCC فلازم كل ال + +509 +00:52:03,670 --> 00:52:06,630 +voltage اللي عندى بال negative ال input و ال + +510 +00:52:06,630 --> 00:52:11,410 +output في ال negative وين بيكون في هذا المنطقة في + +511 +00:52:11,410 --> 00:52:15,510 +المربع التالت لو اي رقم طلع عندى في اي مربع غير + +512 +00:52:15,510 --> 00:52:20,420 +التالتمعناته في عندي خلل في العمل ماتقوليش + +513 +00:52:20,420 --> 00:52:24,820 +المعادلة طلعتلي هيك لو المعادلة طلعتلك رقم في أي + +514 +00:52:24,820 --> 00:52:27,280 +منطقة تانية يبقى المعادلة اللي انت بتشتغل عليها مش + +515 +00:52:27,280 --> 00:52:34,520 +صح هذا الفكر اللي بديها الان القالية اللي بنشتغل + +516 +00:52:34,520 --> 00:52:40,100 +عليها ماختلفتش عن اللي قبل بداشي أطلع عليه زي ما + +517 +00:52:40,100 --> 00:52:48,170 +حكينا قبل لو ال input أقل من VPP VPP هيقدش-1.75 + +518 +00:52:48,170 --> 00:52:55,530 +يعني + +519 +00:52:55,530 --> 00:53:02,450 +انا بدأ اطرح من هذه يعني ممكن يكون 1.2 اقل + +520 +00:53:03,320 --> 00:53:08,020 +فهذا لو هو اقل من هذه المنطقة ايش بدي يطلع عندى او + +521 +00:53:08,020 --> 00:53:12,920 +minus one point three يعني في الاش في السالب انا + +522 +00:53:12,920 --> 00:53:16,540 +بروح في الاتجاه هذا في ال minus فهذا هيصير عندى + +523 +00:53:16,540 --> 00:53:23,380 +forward active وهدول ايش بدي يصير off هى خلينا بس + +524 +00:53:23,380 --> 00:53:28,000 +نكتبها if VIN + +525 +00:53:28,000 --> 00:53:34,750 +is less than VBB less than minusVBB عشان تكون تظلك + +526 +00:53:34,750 --> 00:53:40,710 +سوى يعني بهذه أقل من هذه هذا هيصير forward active + +527 +00:53:40,710 --> 00:53:46,790 +و هذا هيصير ايش اوف هدول طب ال output اللي هان ايش + +528 +00:53:46,790 --> 00:53:53,770 +بدي ساوي هذا بداش تطلع عليه زي ما عملت سابقا هجيب + +529 +00:53:53,770 --> 00:53:58,290 +ال I اللي هان اللي بدي ساوي minus VBB minus ال + +530 +00:53:58,290 --> 00:54:06,630 +point seven five--plus الـ 5.2 على ال 1.24 اللي + +531 +00:54:06,630 --> 00:54:12,690 +عندي هنا مظبوط يعني هنا لما بتقول عندي هذا بتقول + +532 +00:54:12,690 --> 00:54:19,950 +ليه QR وضعه forward active و QI وضعه off إذا QI + +533 +00:54:19,950 --> 00:54:26,910 +هنا عندي ال IRE بدي ساوي ال IRCRاللي هو هذا بدي + +534 +00:54:26,910 --> 00:54:37,430 +ساوي minus VBB minus VBE ECL plus VEE على ال R + +535 +00:54:37,430 --> 00:54:46,450 +الآن ال V هذا ساميه VCR بدي ساوي التالي VCC minus + +536 +00:54:46,450 --> 00:54:51,230 +I RCI + +537 +00:54:53,070 --> 00:54:59,170 +في RCR اللي هو بيساوي عندي Zero انا بحط هذا ليش + +538 +00:54:59,170 --> 00:55:06,050 +عشان ما تنساش اشارة ال negative Zero minus هي عندي + +539 +00:55:06,050 --> 00:55:20,390 +هنا minus تانية VBB minus VBE ECL plus VEE علىالـ + +540 +00:55:20,390 --> 00:55:25,770 +RE مضروبة في RCI الـ Negative هذه ممكن ادخلها جوا + +541 +00:55:25,770 --> 00:55:40,170 +هتصير ايش هذه VBB زائد VBE ECL minus VEE على الـ + +542 +00:55:40,170 --> 00:55:50,720 +RE مضروبة في الـ RCR اللي عندنا هانا اعططنىالـ VCR + +543 +00:55:50,720 --> 00:55:57,580 +صح اللي هي ال voltage وين عند هذا النقطة طب ال + +544 +00:55:57,580 --> 00:56:02,240 +voltage هنا إيش بدي ساوي؟ + +545 +00:56:02,240 --> 00:56:08,640 +بدي أطرح ال point seven five و بس فهنا + +546 +00:56:08,640 --> 00:56:17,880 +ال VOR في هذا الحالة بديها تساوي VCR minus VBEECL + +547 +00:56:17,880 --> 00:56:23,600 +اللي عندي هان واضح + +548 +00:56:23,600 --> 00:56:29,400 +ايش اللي عملته هان انا قلت هذا هذا من الدائرة + +549 +00:56:29,400 --> 00:56:34,100 +السابقة ماانه هذا ال voltage اللي هان اكبر من ال + +550 +00:56:34,100 --> 00:56:39,180 +VIN يبقى هدول off و هذا ايش شغال الان جبت التيار + +551 +00:56:39,180 --> 00:56:42,620 +اللي هان اللي هو بدي ساوي ال voltage اللي هان ناقص + +552 +00:56:42,620 --> 00:56:48,240 +ال point7.5 زائد ال voltage اللي هنا لأن هذا + +553 +00:56:48,240 --> 00:56:54,420 +بالنجاتف على ال 1.24k أتتني ال IRE ال IRE بدي ساوي + +554 +00:56:54,420 --> 00:56:57,260 +اللي عندى ال voltage اللي هنا طب ال voltage اللي + +555 +00:56:57,260 --> 00:57:03,460 +هنا إيش بدي ساوي؟ Zero لتنساش ال zero سالبالـ I في + +556 +00:57:03,460 --> 00:57:08,740 +ال RCR هذا هيطلع عندى بالنجاتف للعلم ال voltage + +557 +00:57:08,740 --> 00:57:12,260 +اللى هات الان هذا بدى اطرح منه كمان point seven + +558 +00:57:12,260 --> 00:57:20,560 +five هيعطينا ال V or اللى هيطلع عندى هنا طيب + +559 +00:57:20,560 --> 00:57:25,520 +للشكة التانية ايش بدي احصل بقدر اعمل بنفس الطريقة + +560 +00:57:29,670 --> 00:57:36,070 +بدا امشي في ال loop هذا مافيش + +561 +00:57:36,070 --> 00:57:39,970 +عندى حاجة جاهزة بظبط هنا في عندى حاجة جاهزة و + +562 +00:57:39,970 --> 00:57:43,370 +اشتغلت عليها هناك مافيش حاجة جاهزة ايش بدى اشتغل + +563 +00:57:43,370 --> 00:57:51,130 +بدا امشي ال loop ايش ال loop عندى بقول zero ناقص I + +564 +00:57:51,130 --> 00:58:11,150 +RCI في RCI ناقص VBE لل N QNECL ناقص I RDN RDN زائد + +565 +00:58:11,150 --> 00:58:22,350 +VEE بدي ساوي Zero مظبوط ايش عندي مجهيل هنا هذا + +566 +00:58:22,350 --> 00:58:26,670 +التيار والتيار اللي هنا في علاقة بينهم + +567 +00:58:32,820 --> 00:58:38,480 +طلع عندى وين هما؟ هى التيار اللى هان و هى التيار + +568 +00:58:38,480 --> 00:58:45,500 +اللى هان ايش فى علاقة بينهم؟ فى عندى Beta هذا IB + +569 +00:58:45,500 --> 00:58:51,720 +وهذا IE، مظبوط؟ يعنى هنا بقدر اقول عنه هذا اللى + +570 +00:58:51,720 --> 00:59:00,860 +عندى بيساوى IB للبيئة و هذا عندى IE للبيئةمظبوط + +571 +00:59:00,860 --> 00:59:07,800 +ايش العلاقة بين IE و IB ل forward active ايوة + +572 +00:59:07,800 --> 00:59:13,580 +فهذا بدي اقول عنه beta forward plus واحد في ال + +573 +00:59:13,580 --> 00:59:20,860 +IBPN او لو كانت beta كبيرة مقارنة بالواحد much + +574 +00:59:20,860 --> 00:59:24,420 +much greater فكان واحد بقول في beta forward بس + +575 +00:59:24,420 --> 00:59:27,840 +خليني على ال standard الموجود لان صارت عندى معادلة + +576 +00:59:27,840 --> 00:59:36,350 +فيها لأنهوحد فهنا ايش بده اقول فهي I P P N بده + +577 +00:59:36,350 --> 00:59:48,090 +يساوي فهي V E E minus V B E E C L على ال R C I + +578 +00:59:48,090 --> 00:59:56,070 +plus beta forward plus واحد في ال R E اللي عندك ال + +579 +00:59:56,070 --> 00:59:56,830 +R D N + +580 +01:00:05,220 --> 01:00:09,400 +جبت الان التيار اللي هاد في هذه المنطقة طب ال + +581 +01:00:09,400 --> 01:00:13,280 +output ايش بدي ساوي بدي ساوي zero ممكن اجيبه في + +582 +01:00:13,280 --> 01:00:18,900 +الاتجاه هنا ناقص ال IBM في ال RCI ناقص ال point + +583 +01:00:18,900 --> 01:00:22,380 +seven five او بدي اجيبه في الاتجاه المعاكس بدي + +584 +01:00:22,380 --> 01:00:34,230 +ساوي minus ال VE زائد ليش ال IEالـ IEPN في ال RDN + +585 +01:00:34,230 --> 01:00:37,110 +اللي هي اللي بيساوي هذا Beta Forward زائد واحد + +586 +01:00:37,110 --> 01:00:41,370 +فيها بدي cash بجيبها انا عادة بحب اجيب الاتجاه هذا + +587 +01:00:41,370 --> 01:00:45,850 +ليش عشان ماتنساش ال Beta Forward زائد واحد في + +588 +01:00:45,850 --> 01:00:49,510 +الضرب فيها فلو بدك تجيبها هنا بدي اقول التالي + +589 +01:00:59,040 --> 01:01:03,780 +بتصير عندى vnor + +590 +01:01:03,780 --> 01:01:13,880 +بدي ساوي zero minus ibbn في rci minus zero point + +591 +01:01:13,880 --> 01:01:22,400 +او خلينا ناخد هنا vbe للecl اللى عندى وهنا بعوض + +592 +01:01:22,400 --> 01:01:27,020 +بداله مباشرة بتكاشف جيب زي هيك اش بتقول عندى برضه + +593 +01:01:28,590 --> 01:01:35,350 +بتساوي سالب VEE plus beta forward زائد واحد في ال + +594 +01:01:35,350 --> 01:01:40,350 +IPN في + +595 +01:01:40,350 --> 01:01:45,850 +RDN هاي طريقة و هاي طريقة اختار اللي بدك إياها + +596 +01:01:45,850 --> 01:01:54,650 +توصل فيها هاد + +597 +01:01:54,650 --> 01:01:55,910 +الشجاليش + +598 +01:01:58,690 --> 01:02:02,210 +الطيار اللي هنا انا عارفه وهنا الطيار عارفه هذا + +599 +01:02:02,210 --> 01:02:07,570 +فيه ششة مش مربوط مع حاجة الطيار .. هذا اللي هنا + +600 +01:02:07,570 --> 01:02:12,850 +ماهذا .. هاي ال I .. I .. I B ايش هذا بدي ساوي I C + +601 +01:02:12,850 --> 01:02:18,490 +ال I C ايش بيساوي beta forward في ال I B ال I C + +602 +01:02:18,490 --> 01:02:23,250 +أنا مش عارفه عارفه VCE انت عارفها لل forward + +603 +01:02:23,250 --> 01:02:28,830 +active لأ لو عارفها بروح ال path هذابمشي في هذا + +604 +01:02:28,830 --> 01:02:33,910 +الاتجاه بس في هان بوقف عند هذا النقطة هاد مجهولة + +605 +01:02:33,910 --> 01:02:41,570 +انا مش بدي اضيف unknowns انا بدي حلفه فعشان هيك + +606 +01:02:41,570 --> 01:02:44,910 +روحت الاتجاه هاد لإن هان في علاقة بتربط two + +607 +01:02:44,910 --> 01:02:51,130 +unknowns اللي هان بينما لو روحت هان عند ال VCE + +608 +01:02:51,130 --> 01:02:55,090 +اللي هان مش عارفها وال IE او ال IC اللي هان مش + +609 +01:02:55,090 --> 01:03:01,160 +عارفه فماستفدتش اشي من هذهمن هذا الاتجاه هنا + +610 +01:03:01,160 --> 01:03:05,900 +الطيار اللي عندي عارفه هو بيساوي الطيار اللي هنا + +611 +01:03:05,900 --> 01:03:11,480 +فجبت الطيار اللي هنا و جبت ال drop اللي هنا و طرحت + +612 +01:03:11,480 --> 01:03:17,240 +منه ال point seven five فأسهل من الطريقة التانية + +613 +01:03:17,240 --> 01:03:24,120 +بينما الاتجاه هذا أصعب الآن لو غلبتها و قلت هذا + +614 +01:03:24,120 --> 01:03:28,130 +اللي عندي إيشأكبر .. هذا أكبر من هذا .. ايش بدي + +615 +01:03:28,130 --> 01:03:33,130 +يصير عندك؟ هذا بدي يصير forward active هذا الشجة و + +616 +01:03:33,130 --> 01:03:38,890 +هذا بدي هتصير اياش؟ off .. اذا off ال V out تبعيها + +617 +01:03:38,890 --> 01:03:43,090 +سهل اجيبههأ من هذا الاتجاه هاد بدي أجيب التيار + +618 +01:03:43,090 --> 01:03:46,270 +اللي هاد يساوي التيار اللي هاد بدي أخد V in minus + +619 +01:03:46,270 --> 01:03:50,670 +point seven five زائد ال V E على ال R E بيعطيني ال + +620 +01:03:50,670 --> 01:03:53,930 +voltage هاد أطرح منه point seven five بيعطيني ال V + +621 +01:03:53,930 --> 01:03:57,490 +نوع لهاد أش بدي أروح بدي أخد ال loop زي ما أخدته + +622 +01:03:57,490 --> 01:04:04,160 +هناك و أعيد نفس الطريقة الموجودة عندكلأ نفس الشي + +623 +01:04:04,160 --> 01:04:07,860 +حتى في ال VS المعادلة اللى بتطلع عندك نفس المعادلة + +624 +01:04:07,860 --> 01:04:12,460 +اللى فاتت لأن بطلعش برا بوقف لحد ديتها بدي ال VC + +625 +01:04:12,460 --> 01:04:16,520 +اللى هان فى حالة ال saturation و بسويها اللى هى + +626 +01:04:16,520 --> 01:04:20,960 +نفسها اللى هان ف VS ال formula تبعت VS اللى طلعت + +627 +01:04:20,960 --> 01:04:25,500 +عندنا قبل شوية هى نفسها بتنطبق على اللى موجود هنا + +628 +01:04:25,500 --> 01:04:30,760 +السؤال بيسأل اقحاله حاجتين ضالوا عندنا اللى هم ايش + +629 +01:04:30,760 --> 01:04:34,610 +احنا دايما بنشتغلالفان اوت وال power dissipation + +630 +01:04:34,610 --> 01:04:38,470 +ال power dissipation في هذه الوضع حاجة .. حاجة + +631 +01:04:38,470 --> 01:04:43,470 +سهلة و كويسة ليش؟ لأنه في معادلات بتتكرر دايما + +632 +01:04:43,470 --> 01:04:47,170 +عندي أي اشي بتكرر او زي ما شرحت قبل شوية اللي + +633 +01:04:47,170 --> 01:04:51,910 +بنطبق على هاي بنطبق على هاي هذه بتريحني يعني لما + +634 +01:04:51,910 --> 01:04:55,770 +ابدأ اتكلم عنه في ال average power dissipation + +635 +01:04:55,770 --> 01:05:00,070 +عندي اكتر من شغلة في ال power dissipation كام + +636 +01:05:00,070 --> 01:05:01,010 +source عندي؟ + +637 +01:05:17,970 --> 01:05:23,410 +عندي اكتر من sources موجود هنا طبعا طلع اللي عندك + +638 +01:05:23,410 --> 01:05:32,550 +عند VBB عند VCC و VEE مظبوط الان VCC كده بيساوي + +639 +01:05:32,550 --> 01:05:39,430 +يعني هذا اللي بتطلع عليها بدي اشوف ال VCC و VEE و + +640 +01:05:39,430 --> 01:05:41,010 +VEE + +641 +01:05:43,310 --> 01:05:46,910 +الان هاذي ما انه VCC عندى بيساوي Zero يبقى هاذي + +642 +01:05:46,910 --> 01:05:53,610 +ايش راحت ايش اللى ضال عندى ال VBB و VEE طلع لما + +643 +01:05:53,610 --> 01:05:59,510 +اصفر هاذ ايش بدي اصوى ال VBB من هان لل ground ايش + +644 +01:05:59,510 --> 01:06:04,290 +بدروها هاذ بلاقيها صغيرة جدا مقارنة مع مين مع ال + +645 +01:06:04,290 --> 01:06:12,490 +VEE فهاذي بقدر اعملها Neglect ايش اللى ضال عندىبدي + +646 +01:06:12,490 --> 01:06:20,650 +ال BEE AVERAGE وال BEE AVERAGE بدها تساوى IEE في + +647 +01:06:20,650 --> 01:06:26,570 +حالة ال output high زائد ال IEE في حالة ال output + +648 +01:06:26,570 --> 01:06:31,430 +low على اتنين ال VEE ودايما ال average power + +649 +01:06:31,430 --> 01:06:34,090 +dissipation بتطلع بال positive بتطلعش بال negative + +650 +01:06:36,980 --> 01:06:40,740 +فلما أجى أطلع عليها على هذا المثال بدي أجيب ال IE + +651 +01:06:40,740 --> 01:06:43,940 +في حالة ال output low ال output low اللي هي الشجة + +652 +01:06:43,940 --> 01:06:51,300 +هذه هي low VOL هذا اللي هتساوي وهذا هتساوي VOH في + +653 +01:06:51,300 --> 01:06:57,460 +حالة ال output low مين + +654 +01:06:57,460 --> 01:06:58,500 +بيكون شغال؟ + +655 +01:07:05,950 --> 01:07:10,930 +هذه inverter فإذا بتكلم على ال low هذولة بيبقوا + +656 +01:07:10,930 --> 01:07:18,110 +شغالين وهذا بيبقى اللي عنده ايش off يبقى لما بدي + +657 +01:07:18,110 --> 01:07:23,350 +أجيب اللي عنده IEE اللي هو التيار اللي هان والتيار + +658 +01:07:23,350 --> 01:07:26,930 +اللي هان والتيار اللي هان يعني IEE + +659 +01:07:29,440 --> 01:07:42,060 +بدي ساوي IRE زائد IRDN زائد IRDO هدول سهلين أجيبها + +660 +01:07:42,060 --> 01:07:51,460 +في حالة output low VOL أو IEE في حالة output low + +661 +01:07:51,460 --> 01:07:59,200 +بدي ساوي IRE في حالة output low زائد IRDO في حالة + +662 +01:07:59,200 --> 01:08:05,260 +الـ output low زائد الـ IRDNفي حالة ال output low + +663 +01:08:05,260 --> 01:08:13,180 +نفس الشيء IEE في حالة ال output high IRE في حالة + +664 +01:08:13,180 --> 01:08:17,920 +ال output high IRDO + +665 +01:08:17,920 --> 01:08:23,900 +في حالة ال output high IRDN في حالة ال output high + +666 +01:08:23,900 --> 01:08:30,300 +هدولة اتنين الأربعة هدولة سهلات الأرقام هي نفسها + +667 +01:08:30,300 --> 01:08:35,880 +2K 2Kففي حالة ال output type بدي أقول هنا هاي عند + +668 +01:08:35,880 --> 01:08:41,040 +إيش هنا؟ هاي ال output هذي شجة اللي بعتبرها ال + +669 +01:08:41,040 --> 01:08:48,520 +output فهذه عند إيش؟ ال IRDO في حالة خلينا نقول + +670 +01:08:48,520 --> 01:08:55,340 +output low اللي هنا هذي إيش بدها تساوي؟ هذي ال RDO + +671 +01:08:55,340 --> 01:09:00,080 +في هذا الحالة جاي مع مين هذا؟ إيش عندها؟ بدها + +672 +01:09:00,080 --> 01:09:09,600 +تساوي VOHplus VEE على RDO VOL + +673 +01:09:09,600 --> 01:09:13,900 +plus VEE على RDO VOL plus VEE على RDO VOL plus VEE + +674 +01:09:13,900 --> 01:09:15,020 +على RDO VOL plus VEE على RDO RDO VOL plus VEE على + +675 +01:09:15,020 --> 01:09:15,900 +RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO + +676 +01:09:15,900 --> 01:09:17,080 +RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO + +677 +01:09:17,080 --> 01:09:17,260 +RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO + +678 +01:09:17,260 --> 01:09:17,360 +RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO + +679 +01:09:17,360 --> 01:09:18,900 +RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO + +680 +01:09:18,900 --> 01:09:20,900 +RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO + +681 +01:09:20,900 --> 01:09:20,920 +RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO RDO + +682 +01:09:20,920 --> 01:09:21,260 +RDO RDO RDO RDO RDO + +683 +01:09:33,080 --> 01:09:42,380 +اللي عندى هنا VEE على RE وهنا عندى لأن ال output + +684 +01:09:42,380 --> 01:09:50,180 +low هذا بتكون ايش بتساوي high مظبوط ال input بتكون + +685 +01:09:50,180 --> 01:09:52,680 +high عشان تعطيني output low مش هذا inverter + +686 +01:09:55,930 --> 01:09:59,910 +أنا لما أتكلم على هذه إذا هذه low يبقى هنا high + +687 +01:09:59,910 --> 01:10:06,030 +إذا هذه high هذه low فأنا لما أتكلم على شكل ال + +688 +01:10:06,030 --> 01:10:11,470 +output ال VIN هي اللي بتتحكم لي فيها وده VIN high + +689 +01:10:11,470 --> 01:10:14,950 +معناته بدي أمشي في هذا الاتجاه ده VIN low بدي أمشي + +690 +01:10:14,950 --> 01:10:19,550 +في إيش؟ في الاتجاه المعاكس اللي موجود هنا الان هذه + +691 +01:10:19,550 --> 01:10:24,090 +إيش بدي أعمل لهدول؟ هدول بدي أعكسهم هنا ال output + +692 +01:10:24,090 --> 01:10:32,350 +إيش؟هذا الوصف هاي هنا فإيش بده يصير عندى VOH plus + +693 +01:10:32,350 --> 01:10:42,710 +VEE على ال RDN هذي نفسها VOL + +694 +01:10:42,710 --> 01:10:51,730 +plus VEE على ال RDO طلع هذول إيش موجود فيها هذي + +695 +01:10:51,730 --> 01:10:54,510 +عكس هذول و هذول متساويين + +696 +01:10:56,870 --> 01:11:02,610 +و هدولة و هدول متساويين التنتين اللي صار عندى مين + +697 +01:11:02,610 --> 01:11:07,310 +اللي بختلف عندى هدى + +698 +01:11:07,310 --> 01:11:23,550 +بتساوي VBB minus VBE ECL plus VEE على ال R على ال + +699 +01:11:23,550 --> 01:11:29,680 +REالاختلاف عندي ايش هنا هنا بحط ممكن احط ال VIH + +700 +01:11:29,680 --> 01:11:35,780 +وهنا بحط ال VBB الفرق بيني قد ياش point oh five + +701 +01:11:35,780 --> 01:11:41,920 +الأرقام اللي عندك مش هتأثر كتير هتلاقيها جريبة + +702 +01:11:41,920 --> 01:11:47,180 +لبعضها الآن ضال عندنا ال fan out بنغطيه المحاضرة + +703 +01:11:47,180 --> 01:11:50,480 +الجاية المحاضرة الجاية ايش مطلوب منكم في عندكم + +704 +01:11:50,480 --> 01:11:55,450 +quiz بال chapter 6 والمحاضرة اللي بعدهاال quiz في + +705 +01:11:55,450 --> 01:11:58,490 +ال chapter عشرة و سبعة + diff --git a/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/VV2WqNTCOZc_postprocess.srt b/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/VV2WqNTCOZc_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..4e187588cc528471eac3ce800babaa3772c1c391 --- /dev/null +++ b/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/VV2WqNTCOZc_postprocess.srt @@ -0,0 +1,2748 @@ +1 +00:00:21,090 --> 00:00:24,230 +طيب اليوم إيش اللي هنعمل هنغطي chapter عشرة + +2 +00:00:24,230 --> 00:00:30,730 +chapter عشرة بتكلم عن TTL NAND Gates احنا غطينا ال + +3 +00:00:30,730 --> 00:00:36,510 +basically ال NAND Gate بنغطي الآن اليوم ال and + +4 +00:00:36,510 --> 00:00:42,570 +ونغطي ال or و النورالان جزء كبير منه هتلاقي هو نفس + +5 +00:00:42,570 --> 00:00:48,710 +اللي بنتكلم عنه يعني ال .. ال critical voltage ال + +6 +00:00:48,710 --> 00:00:52,930 +VTC هو نفسه ال fan out هي نفس التقنية ال power + +7 +00:00:52,930 --> 00:00:57,190 +dissipation في عندى في ال ore و النور بختلف شوية و + +8 +00:00:57,190 --> 00:01:02,890 +هذا اللي هنغطيه جزئية منه بشكل مفصل اكتر بس اليوم + +9 +00:01:02,890 --> 00:01:08,450 +هنبدأ بال and و بعدها هروح على ال nor و بعدين على + +10 +00:01:08,800 --> 00:01:14,600 +ال or لنغطي كل المحتويات الموجودة عندك هلاحظ ان + +11 +00:01:14,600 --> 00:01:18,800 +التالي فيها لما هسأل أسئلة هتلاقيها repeat من + +12 +00:01:18,800 --> 00:01:22,660 +المحاضرة السابقة او المحاضرتين السابقة مثلا على + +13 +00:01:22,660 --> 00:01:29,240 +سبيل مثال نرسم الرسمة تبعت ال end تبعت ال end و ال + +14 +00:01:29,240 --> 00:01:31,200 +none تشوف ايش الفرق بينهم + +15 +00:02:20,330 --> 00:02:23,810 +مش عارف انا اتكلم عن الـ + +16 +00:02:34,560 --> 00:02:38,460 +مش حاسسش ان انا اشوف اشوف اشوف اشوف اشوف اشوف اشوف + +17 +00:02:38,460 --> 00:02:41,920 +اشوف + +18 +00:04:12,990 --> 00:04:17,250 +إذا شيلنا هذه الجزئية اللي في النص هي عبارة عن + +19 +00:04:17,250 --> 00:04:20,570 +إيش؟ + +20 +00:04:20,570 --> 00:04:27,330 +لو شيلت هذه الـ none + +21 +00:04:27,330 --> 00:04:33,130 +جيت اللي أخدتها، مظبوط؟ هذه الجزئية اللي جلبتليها + +22 +00:04:33,130 --> 00:04:38,870 +لإيش؟ ل end أما + +23 +00:04:38,870 --> 00:04:42,890 +بجيتها هيالـ NAND gate اللي عندك السؤال اللي + +24 +00:04:42,890 --> 00:04:48,110 +بنسأله دايما By inspection هدول لازم تعرفوهم ال + +25 +00:04:48,110 --> 00:04:57,630 +VOL و VOH مظبوط ايش ال VOL بيساوي كلكم + +26 +00:04:57,630 --> 00:05:01,350 +شايفينها هذا ال transistor اللي عندى في وضع ال + +27 +00:05:01,350 --> 00:05:06,030 +saturation بدي يعطيني VCE SAT + +28 +00:05:11,070 --> 00:05:14,870 +طيب اللي عندي هذا لما هو هذا فوضع ال saturation + +29 +00:05:14,870 --> 00:05:21,890 +فوضع ال cut-off جداش بساوي؟ من + +30 +00:05:21,890 --> 00:05:25,850 +أي + +31 +00:05:25,850 --> 00:05:32,130 +اتجاه بدك إياها، جداش بساوي؟ جداش؟ هي فيه خمسة او + +32 +00:05:32,130 --> 00:05:32,710 +.. + +33 +00:05:44,170 --> 00:05:47,990 +طيب خلّيني .. خلّيني نبدأ من حاجة .. من حاجة بسيطة + +34 +00:05:47,990 --> 00:05:53,250 +لو كان عند ال input zero كويس قداش ال voltage هات + +35 +00:05:53,250 --> 00:05:59,470 +في هذه المنطقة؟ zero + +36 +00:06:02,710 --> 00:06:07,250 +هذا اتفاقنا عليه اعتبر ال two input مشبكين مع بعض + +37 +00:06:07,250 --> 00:06:12,390 +هنا zero يبقى هذا بيكون saturated مش اتفاقنا عليه + +38 +00:06:12,390 --> 00:06:19,070 +هي plus minus هيبقوا اتنين هذا off إذا هذا off هذا + +39 +00:06:19,070 --> 00:06:25,190 +off صح؟ هذا ال off قطعنا الطريق بينهم الآن هذا + +40 +00:06:25,190 --> 00:06:28,410 +هشغاله هذا وشغاله هدول هدول اتنين هيكون وضعهم + +41 +00:06:28,410 --> 00:06:35,000 +saturatedهذا عندى point 8 او point 8 او point 7 + +42 +00:06:35,000 --> 00:06:39,040 +اذا بدى اجيب التيار اللى عندى فالان وصلنا لهذا + +43 +00:06:39,040 --> 00:06:44,960 +saturated saturated قداش عندى point 2 هتفرق عندى + +44 +00:06:44,960 --> 00:06:48,560 +لو هدوله احنا قاعد بقول لو هذا لأ طب لو واحد منهم + +45 +00:06:48,560 --> 00:06:56,020 +high واحد low ايش بدي يحصل لو + +46 +00:06:56,020 --> 00:07:01,750 +هذا high هذا ايش هيكون وضعهالـ junction هذه + +47 +00:07:01,750 --> 00:07:08,470 +reversed وهذا saturated الـ saturated اللي هو اللي + +48 +00:07:08,470 --> 00:07:12,210 +هيغلب، مظبوط؟ فيعني في ال end إيش اللي عندي؟ ال + +49 +00:07:12,210 --> 00:07:21,010 +VTC تبعتها؟ هل عندي V in؟ لأ مش مشكلة، هي ال V out + +50 +00:07:21,010 --> 00:07:24,670 +لما كان لو إيش عندي طلع ال output؟ + +51 +00:07:28,100 --> 00:07:30,940 +قلنا هات saturated و هات saturated طلع عندى point + +52 +00:07:30,940 --> 00:07:35,160 +اتنين يعني ببدأ فيها من وين من هان هيك في هذا + +53 +00:07:35,160 --> 00:07:40,020 +الاتجاه عادة ببدأ من وين كنت قبل من هان فهذا عندى + +54 +00:07:40,020 --> 00:07:44,600 +ال VOL بيساوي zero point اتنين ايش اللى كان عندى + +55 +00:07:44,600 --> 00:07:51,140 +في هذا الحالة كان التالي عندى QI وضعه saturated + +56 +00:07:51,140 --> 00:08:03,690 +QS2 and QSD هدولة offQS و QO كان واضح و مستراتد و + +57 +00:08:03,690 --> 00:08:13,130 +QP ايش وضعه طلع عندي قداش ال voltage هان هاي point + +58 +00:08:13,130 --> 00:08:18,070 +تمانية وهنا قداش point اتنين point اتنين هان قداش + +59 +00:08:18,070 --> 00:08:23,650 +بتطلع عندي point اتنين و واحد مطلوب point point + +60 +00:08:23,650 --> 00:08:25,750 +four اللي متاعي عندي point eight يبقى هدول اللي + +61 +00:08:25,750 --> 00:08:27,770 +بدهم يكونوا QP بدي يكون + +62 +00:08:32,020 --> 00:08:41,920 +off كويس هذا فضع ال VOL طيب احنا لاحظنا حاجة واحدة + +63 +00:08:41,920 --> 00:08:46,940 +بال NAND طلع عندي حاجة بسميها ال input break point + +64 +00:08:46,940 --> 00:08:53,840 +صح؟ الآن لما بتكلم عن ال critical voltages اللي + +65 +00:08:53,840 --> 00:08:58,060 +سميتها ال VIL و VIH و VOL و VOH ايش .. ايش بحصل + +66 +00:08:58,060 --> 00:08:59,020 +فيها؟ + +67 +00:09:01,470 --> 00:09:04,490 +في تغير في الاتجاه اللى بيمشي عندى ان انا ماشي + +68 +00:09:04,490 --> 00:09:08,890 +مستقيم فى تغير فى عندى slope صار تغير فى ال slope + +69 +00:09:08,890 --> 00:09:12,970 +بيصير فى عندى critical voltage مظبوط فىش تغير + +70 +00:09:12,970 --> 00:09:17,930 +مافيش اشي طلع عندى هان لو زودتها ل point five ايش + +71 +00:09:17,930 --> 00:09:24,150 +اللى بيحصل عندى هان قداش ال voltage هان point + +72 +00:09:24,150 --> 00:09:24,450 +seven + +73 +00:09:28,670 --> 00:09:32,930 +الـ 0.7 ايش هتعمل بالترانزستور هات؟ هتشغله هذا + +74 +00:09:32,930 --> 00:09:39,430 +هيصير forward active قداش ال voltage هان؟ Zero ال + +75 +00:09:39,430 --> 00:09:44,650 +zero هيأثر على هات؟ يبقى هذه ال point five هل هي + +76 +00:09:44,650 --> 00:09:50,510 +ال critical volt؟ مش هيأثر مش ال critical voltage + +77 +00:09:50,510 --> 00:09:53,530 +يبقى بتزود في ال voltage لو صار عندي هنا point + +78 +00:09:53,530 --> 00:10:00,840 +سبعة قداش ال voltage هات؟0.9 هنا كم؟ 0.2 هتأثر على + +79 +00:10:00,840 --> 00:10:07,060 +هذه الشجة؟ مش هتأثر حاجة معناته مش هتأثر على ال + +80 +00:10:07,060 --> 00:10:12,700 +output يبقى هنا وقت ايش بيصير بتأثر؟ 1.2 هتعطيني + +81 +00:10:12,700 --> 00:10:19,280 +هذه 1.4 هنا هتعطيني 0.7 هذا forward active هنا + +82 +00:10:19,280 --> 00:10:23,060 +هيصير عندى forward active هيصير يشتغل يبقى اول + +83 +00:10:23,060 --> 00:10:29,930 +critical voltage عندى هناالـ VAL بدي ساوي 1.2 V + +84 +00:10:29,930 --> 00:10:36,530 +بعده الآن الحالة التانية اللي بيصير تغيير فيها + +85 +00:10:36,530 --> 00:10:41,410 +الآن إيش اللي بيحصل بيصير عندي drop hand هذه عندى + +86 +00:10:41,410 --> 00:10:46,890 +0.7 هذا بيشغال forward active بيصير عندي drop hand + +87 +00:10:46,890 --> 00:10:51,470 +بيأثر على ال output اللي موجود في هذا الإتجار طيب + +88 +00:10:51,470 --> 00:10:56,290 +الآن لو زودت ل 1.4 إيش بيحصل عندى + +89 +00:11:00,000 --> 00:11:08,960 +هنا هذا بيصير كام هذا شو بيصيره saturated هنا + +90 +00:11:08,960 --> 00:11:16,560 +point تمانية هنا what saturated مظبوط إذا هذا + +91 +00:11:16,560 --> 00:11:20,660 +saturated و هذا saturated كده ال voltage هذا point + +92 +00:11:20,660 --> 00:11:25,520 +اتنين point اتنين ايش هيحصل في هذا + +93 +00:11:29,220 --> 00:11:35,040 +off و هاد ايش بدي يصير جداش + +94 +00:11:35,040 --> 00:11:35,520 +ال output + +95 +00:11:42,830 --> 00:11:48,990 +لأ ليش GCC هاي ال Vih بيساوي one point four volt + +96 +00:11:48,990 --> 00:11:57,070 +وهنا عندى ال Voh قداش بيساوي ليش هاي امشي معايا في + +97 +00:11:57,070 --> 00:12:02,970 +الاتجاه هذا شغال وهذا شغال قداش هدول واحد point + +98 +00:12:02,970 --> 00:12:07,390 +أربعة هانا في عندى تيار ماشيفهذا ماعتبر فش drop + +99 +00:12:07,390 --> 00:12:10,970 +خمسة minus ال one point four كدهش بيعطينا تلاتة + +100 +00:12:10,970 --> 00:12:17,530 +ستة ازيد عليكم هذا الرقم ال + +101 +00:12:17,530 --> 00:12:23,010 +VOL و ال VOH لأي TTL gate point اتنين تلاتة point + +102 +00:12:23,010 --> 00:12:23,870 +ستة و نقطة + +103 +00:12:27,310 --> 00:12:30,290 +بتقعدش تجهد فيها ولا تقول أي حاجة هذا و أنت مغمض + +104 +00:12:30,290 --> 00:12:35,230 +زيك أجتلك دائرة TTL تكتب هذه بدون ما تفكر في أي + +105 +00:12:35,230 --> 00:12:40,550 +حاجة VOL 0.2 VOH 3.6 بتغمض عينك وبعدها بتقول إيش + +106 +00:12:40,550 --> 00:12:44,210 +.. إيش المطلوب قبل ما تقول للدائرة إيش أنت بتقول + +107 +00:12:44,210 --> 00:12:48,710 +إيش المطلوب هدول بتحطهم و بعدين بتبدأ تقول إيش + +108 +00:12:48,710 --> 00:12:49,290 +المطلوب + +109 +00:12:52,000 --> 00:12:55,680 +لأن ال TTL مش يتغير في ال output low و لا ال + +110 +00:12:55,680 --> 00:13:02,100 +output high تفضل الآن + +111 +00:13:02,100 --> 00:13:07,260 +هذا قداش بلزمه لا يصير saturated بقى 8 volts إذا + +112 +00:13:07,260 --> 00:13:12,080 +عندي هذا متاح 1.6 هذا هياخد 1.8 ويصير saturated + +113 +00:13:12,080 --> 00:13:17,140 +قداش ده اللي عندي 1.8 هتعملي هذا saturatedأنا + +114 +00:13:17,140 --> 00:13:22,180 +مطلوب زي حكاية هذه بدي أروح من هنا لرفح أو لمنطقة + +115 +00:13:22,180 --> 00:13:26,400 +معينة بدي أوقف في المحطة تانية إذا وصلت المحطة + +116 +00:13:26,400 --> 00:13:29,880 +الأولى و معي ال .. معي الإيجار من هنا ل .. هذه + +117 +00:13:29,880 --> 00:13:33,120 +المحطة .. المحطة تانية يعني في الوقفة باجي بنزل + +118 +00:13:33,120 --> 00:13:36,580 +بدفع لكل واحد الأجرة الأولى و بعدين بدفع للتانية + +119 +00:13:36,580 --> 00:13:40,220 +إذا معي أقل معناته بضلني واقف في ال .. في النقطة + +120 +00:13:40,220 --> 00:13:43,800 +اللي قبل معي أكتر بدفع .. هاي زي الأجرة بتركب + +121 +00:13:43,800 --> 00:13:47,670 +السيارة الأجرة هالقدةو بعدين هدول بيحسبوا قبل + +122 +00:13:47,670 --> 00:13:55,570 +مافيش واحدة تمشي اتفضل + +123 +00:13:55,570 --> 00:14:06,070 +اتفضل + +124 +00:14:06,070 --> 00:14:07,550 +اتفضل اتفضل اتفضل اتفضل اتفضل اتفضل اتفضل اتفضل + +125 +00:14:07,550 --> 00:14:07,790 +اتفضل اتفضل اتفضل اتفضل اتفضل اتفضل اتفضل اتفضل + +126 +00:14:07,790 --> 00:14:14,650 +اتفضل اتفضل اتفضل اتفضل اتفضل اتفضل اتلأ ال + +127 +00:14:14,650 --> 00:14:18,930 +transistor بحسب أنه هذا صار له forward bias و هذا + +128 +00:14:18,930 --> 00:14:23,010 +شغال ال + +129 +00:14:23,010 --> 00:14:28,390 +5 volts هذه تقدر تعطي هذا و تعطي هذا يعني بعبارة + +130 +00:14:28,390 --> 00:14:33,990 +تانية أنا معايا 5 شكل و الأجار عندى شكل و شكل بقدر + +131 +00:14:33,990 --> 00:14:38,290 +أركب من هنا لأى مكان تانى بقدر في الطريق ممكن + +132 +00:14:38,290 --> 00:14:43,150 +تقولي بدي ساندوش بدي حاجةلو الطريقة بعيدة هتقولي + +133 +00:14:43,150 --> 00:14:46,930 +بدي ساندويش او بدي علبة كولة أشربها بقولك اه معايا + +134 +00:14:46,930 --> 00:14:50,570 +أدفع بس الان مش مطلوب مني .. مطلوب مني لصل النقطة + +135 +00:14:50,570 --> 00:14:55,290 +الأخيرة قداش أجرة الطريق بس و هذا اللي بنحكي فيه + +136 +00:14:55,290 --> 00:15:00,210 +مش .. هذا المصروف اللي هو ليش الآية تبعت اللي .. + +137 +00:15:00,210 --> 00:15:03,650 +زي الساندويش زي جنيه الكولة زي غيره إذا أنت مركز + +138 +00:15:03,650 --> 00:15:07,790 +في منطقة صعبة فيها درجة حرارة عالية بدك ميه بدك + +139 +00:15:07,790 --> 00:15:13,550 +سواجو هذا مش محسوبة في الحسابات، بس كحد أدنى إيش + +140 +00:15:13,550 --> 00:15:18,670 +بقولك؟ مضطوب منك القدر، أجرة الطريق، واضحة دي إيش + +141 +00:15:18,670 --> 00:15:25,110 +هي؟ تفضل حدث + +142 +00:15:25,110 --> 00:15:27,610 +بتناها في أول ما بدأنا في ال chapter خمسة + +143 +00:15:31,860 --> 00:15:37,820 +حجم التيار I اللي طالع من هنا من IP عالي جدا الان + +144 +00:15:37,820 --> 00:15:41,480 +لو بده اضرب في Beta Forward هيعطينا ال IC ال IC + +145 +00:15:41,480 --> 00:15:46,320 +هساوة ال IP اللي هاد اللي هو هدف وضع cut-off لما + +146 +00:15:46,320 --> 00:15:51,780 +يكون cut-off و ال IP تبعته بالملي في مشكلة مظبوط؟ + +147 +00:15:52,370 --> 00:15:57,150 +مستحيل يكون هذا cut off هتقول لي لأ الحاجة اللي هي + +148 +00:15:57,150 --> 00:16:00,190 +بتجبطش عندى لأن هذا انا عارف مافيش عندى voltage + +149 +00:16:00,190 --> 00:16:06,030 +يخليه يشتغل forward active فال IC اللي هنا لازم + +150 +00:16:06,030 --> 00:16:08,430 +يكون مضروب في سيجما سيجما لما .. ايش .. ايش + +151 +00:16:08,430 --> 00:16:15,050 +وظيفتها بتنزل قيمة ال IC فالان هذا الحل الاستنتاج + +152 +00:16:15,050 --> 00:16:18,330 +الوحيد هذا ليشتغل لما يكون ال input عندى zero low + +153 +00:16:18,330 --> 00:16:23,440 +ان هذا لازم يكون forward active مشيكون saturation + +154 +00:16:23,440 --> 00:16:29,920 +مش forward active لأن في حالة ال forward active + +155 +00:16:29,920 --> 00:16:34,400 +إيش ال IC بيساوي Beta forward في ال IP بس في حالة + +156 +00:16:34,400 --> 00:16:37,860 +ال saturation ال IC بيساوي Sigma في Beta forward + +157 +00:16:37,860 --> 00:16:42,280 +في ال IP يعني القيمة تبعت ال IC بتنزل بتصير معقولة + +158 +00:16:42,280 --> 00:16:44,380 +أن يكون leakage اتفضل + +159 +00:16:48,580 --> 00:16:57,140 +فورورد فورورد فورورد فورورد فورورد فورورد فورورد + +160 +00:16:57,140 --> 00:17:03,580 +فورورد فورورد فورورد فورورد + +161 +00:17:15,310 --> 00:17:19,290 +تأخد تبقى متناسب يعني هذا تعطيني point اللي عندي + +162 +00:17:19,290 --> 00:17:24,110 +انا بدي اياه هذا point one point volt فال biasing + +163 +00:17:24,110 --> 00:17:29,010 +اللي عندنا انا بدي اياه زي هيك لو ماشيت في الاتجاه + +164 +00:17:29,010 --> 00:17:33,050 +اللي هذا مش هذا بدي اياه plus minus الان لو انا + +165 +00:17:33,050 --> 00:17:39,510 +قلت هذا الاتجاه بتظبط معي لو هدولة شغالين؟ مازبوت + +166 +00:17:42,040 --> 00:17:45,120 +بتطلع اكتر بس انا لما اقول هذا saturation و هذا + +167 +00:17:45,120 --> 00:17:48,800 +saturation ال voltage اللي عندي ايش point اتنين + +168 +00:17:48,800 --> 00:17:51,900 +هنا مظبوط و بتظبط معايا ال voltage اللي هنا قداش + +169 +00:17:51,900 --> 00:17:56,120 +هذه بدها تصير point اتنين زائد point سبعة point + +170 +00:17:56,120 --> 00:17:59,220 +تسعة قداش الفرق هنا one point six ناقص point تسعة + +171 +00:17:59,220 --> 00:18:03,820 +قداش point سبعة معناه انت بتعمليها ايش saturation + +172 +00:18:03,820 --> 00:18:10,120 +فال biasing اللي انت بتشتغل معاه بيعملك الجزئية + +173 +00:18:11,990 --> 00:18:16,310 +الان عملنا في الدائرة إيش هذه؟ جبنا ال input low + +174 +00:18:16,310 --> 00:18:20,450 +وجبنا ال input high وجبنا ال output low وجبنا ال + +175 +00:18:20,450 --> 00:18:24,090 +output high، في اختلاف عندها؟ مافيش break point + +176 +00:18:24,090 --> 00:18:30,480 +لهذه الدائرة، طلعهذه الدائرة خلصنا منها فى الشكل + +177 +00:18:30,480 --> 00:18:33,520 +اللى هى الان لما انا اطلع على هذا اقول لو زوّات ال + +178 +00:18:33,520 --> 00:18:37,680 +input هذا هيصير reverse وهذا forward وهذا reverse + +179 +00:18:37,680 --> 00:18:41,400 +biased لما تكون او reverse active وهذا عندي + +180 +00:18:41,400 --> 00:18:45,940 +saturation وهذا off او off اللى موجودة عندى + +181 +00:18:45,940 --> 00:18:51,720 +الدائرة هذه مش فيها اي شيء جديد علينا شكل الدائرة + +182 +00:18:51,720 --> 00:18:57,550 +بختلف هذه انعملت عشان تعملىالـ ANDING بدل ال + +183 +00:18:57,550 --> 00:19:00,670 +NANDING هذه لو مش موجودة الجزئية هذه اللي علمت + +184 +00:19:00,670 --> 00:19:03,810 +عليها بالأخضر بيصير هذه عندي ال NAND gate اللي + +185 +00:19:03,810 --> 00:19:09,550 +احنا شفناها بتاعي الان اللي هنعمله هنفرجيكم ال OR + +186 +00:19:09,550 --> 00:19:14,410 +gate و بعدها هنفرجيكم NOR gate ال OR gate تختلفش + +187 +00:19:14,410 --> 00:19:20,030 +عن هذه الان هتقولي طيب بعد شوية بس خلينا نحكيلكوا + +188 +00:19:20,030 --> 00:19:24,510 +إياها وبعدها هنفرجيكوا تقولي مين فيهم مينفي الدواء + +189 +00:19:24,510 --> 00:19:31,690 +او انا ايش اللي هشوفه بعد هيكا + +190 +00:19:31,690 --> 00:19:40,730 +طيب + +191 +00:19:40,730 --> 00:19:49,270 +بالنسبة لنا بتكلم على TTL OR + +192 +00:19:49,270 --> 00:19:58,690 +gateالنمبر تبعها seven four three two الشكل تبعها + +193 +00:19:58,690 --> 00:20:02,070 +ده هذا خايف منها اتنى لو ما تشوف هذه + +194 +00:20:50,820 --> 00:20:55,920 +مش عارف كده + +195 +00:21:30,100 --> 00:21:32,180 +سهل يا عزيزي + +196 +00:22:16,650 --> 00:22:23,170 +تنتهى يا عزيزي؟ خلاص يا عزيزي، و بعد الوقت بدأت + +197 +00:22:23,170 --> 00:22:23,550 +أبقى نهار + +198 +00:23:31,530 --> 00:23:36,570 +أنت اللي بتستخدمه في المقتبرات ال basic اللي + +199 +00:23:36,570 --> 00:23:40,870 +بتشتغل عليه في كلها هدول هم الأور والنور اللي عندك + +200 +00:23:40,870 --> 00:23:42,070 +في المقتبر هم هدول + +201 +00:23:46,580 --> 00:23:56,640 +بتتعرف على ال digital هن كيف مصممات اه + +202 +00:23:56,640 --> 00:23:59,880 +بس انت عرفت هدول بتعرف تشتغل على غيرها اه بس انت + +203 +00:23:59,880 --> 00:24:05,820 +عرفت كيف تشتغل على غيرها لأ + +204 +00:24:05,820 --> 00:24:09,240 +انت مهندس الان مهندس كهربا مش مهندس .. + +205 +00:24:12,480 --> 00:24:17,340 +عشان تقضي برصايا؟ ايوة بكرا بدك تصمم انت المبري + +206 +00:24:17,340 --> 00:24:20,720 +اذا انت مش عارف هدول كيف بيشتغلوا او بدك تصمم + +207 +00:24:20,720 --> 00:24:24,200 +latch gate او بدك تصمم switchage بدك تصمم .. انت + +208 +00:24:24,200 --> 00:24:28,340 +مش عارف ال structure تبعهم انت بتمشي وانت مغمط + +209 +00:24:28,340 --> 00:24:33,540 +بتصير انا عارف اشتغل برصايا + +210 +00:24:33,540 --> 00:24:36,400 +.. انا عارف اشتغل برصايا + +211 +00:24:46,110 --> 00:24:50,670 +لو اجتلك زي هيك هدولة من ال giveaway points يعني + +212 +00:24:50,670 --> 00:24:56,710 +انا بعطيكيها عشان تاخد علامات يعني + +213 +00:24:56,710 --> 00:25:01,090 +انا قلتلكوا كل ما كبرت الدارة كل ما كانت أسهل، + +214 +00:25:01,090 --> 00:25:05,070 +الآن لو سألتوا السؤال ال VOL و ال VH لها دي قديش؟ + +215 +00:25:08,610 --> 00:25:13,890 +و هاي هدول هخلصوا كيف؟ هذا في وضع ال saturated هاي + +216 +00:25:13,890 --> 00:25:17,450 +اللي هان وضع ال cut-off هذا off هذا off نفس هذا ال + +217 +00:25:17,450 --> 00:25:20,950 +structure شوفت في كل واحدة فيهم، مظبوط؟ هذه + +218 +00:25:20,950 --> 00:25:26,870 +الجزئية اللي قلتلك بتتكرر في وضع إيش؟ ال R و ال N + +219 +00:25:26,870 --> 00:25:32,070 +هذي، الآن ده تيجي تبدأ في البداية نفس اللي بدناها، + +220 +00:25:32,070 --> 00:25:35,430 +الآن ده بيقولك خد اتجاه واحد التاني اعتبره مش + +221 +00:25:35,430 --> 00:25:40,510 +موجود، لو هذي zero قديش ال voltage هان؟هذا point + +222 +00:25:40,510 --> 00:25:44,810 +اتنين ايش هتعمل في هذا point اف اف اف اف اف اف اف + +223 +00:25:44,810 --> 00:25:45,930 +اف اف اف اف اف اف اف اف اف اف اف اف اف اف اف اف اف + +224 +00:25:45,930 --> 00:25:52,250 +اف اف اف اف اف اف اف اف اف اف اف اف اف اف اف اف اف + +225 +00:25:52,250 --> 00:25:53,890 +اف اف اف اف اف اف اف اف اف اف اف اف اف اف اف اف اف + +226 +00:25:53,890 --> 00:25:53,910 +اف اف اف اف اف اف اف اف اف اف اف اف اف اف اف اف اف + +227 +00:25:53,910 --> 00:26:08,130 +اف اف اف اف اف اف اف اف اف اف اف + +228 +00:26:08,130 --> 00:26:14,230 +اأفناش نضل الحاجات اللي .. خلّيني أقول اللي فيها + +229 +00:26:14,230 --> 00:26:19,590 +قطنها بدل مرة أربع خمس مرات نرجعلها نقول لأ هاد مش + +230 +00:26:19,590 --> 00:26:27,930 +عارفينها انتهينا منها فال VOL بدها تساوي VCE SAT + +231 +00:26:27,930 --> 00:26:32,870 +اللي هي بتساوي point اتنين وال VOH اللي قولنا + +232 +00:26:32,870 --> 00:26:35,510 +بتساوي VCC minus + +233 +00:26:37,810 --> 00:26:44,330 +VBE لل .. خلّيني أقول .. بدي أطلع عليها VBB لل B + +234 +00:26:44,330 --> 00:26:50,970 +Forward Active minus VDL on اللي هي بتساوي 3.6 + +235 +00:26:50,970 --> 00:26:59,150 +Volt كويس؟ الآن بدأت بـ Zero بدي أزود هذه بدل Zero + +236 +00:26:59,150 --> 00:27:04,960 +لقداش .. لـ 0.5 قداش ال voltage اللي هيبوينت سبعة + +237 +00:27:04,960 --> 00:27:10,020 +هشغل هذا ايش حيحصل لهذا اف حيأثر على ال output + +238 +00:27:10,020 --> 00:27:14,940 +يبقى مش هو ال critical voltage بدي ازود هذه يعني + +239 +00:27:14,940 --> 00:27:19,380 +ال critical voltages هنا one point اتنين بعطيني ال + +240 +00:27:19,380 --> 00:27:23,820 +VIL بساوي one point اتنين ايش بعطيني هذا saturated + +241 +00:27:23,820 --> 00:27:31,530 +هذا اللي عندى one point fourهذا بياخد point 7 وهذا + +242 +00:27:31,530 --> 00:27:35,070 +بياخد point 7 هذا بيصير forward active وهذا + +243 +00:27:35,070 --> 00:27:37,150 +forward active اللي عندى + +244 +00:27:44,510 --> 00:27:48,830 +مظبوط ايش بدي اخد هذا بدي يصير point تمانية ال VPE + +245 +00:27:48,830 --> 00:27:53,130 +لهذه point تمانية ال VPE لهذه ناقص ال point اتنين + +246 +00:27:53,130 --> 00:27:58,450 +ال VCE ال VCE لهذه بدي اعطيني one point اربعة + +247 +00:27:58,450 --> 00:28:07,830 +الموجود عندى هدول + +248 +00:28:07,830 --> 00:28:12,670 +اختلفن عن الدائرة اللى قبل شويةنفس ال .. نفس + +249 +00:28:12,670 --> 00:28:17,770 +الألية طلع عد إيش اللي بدي أحصل نفس الشي هات لما + +250 +00:28:17,770 --> 00:28:22,550 +هدا saturated قديش ال voltage اللي هان؟ هذا off + +251 +00:28:22,550 --> 00:28:28,790 +هذا off ال output واضح كويس؟ + +252 +00:28:28,790 --> 00:28:32,030 +الآن بدي أخد هذه أطلع على .. بدل هذه أطلع على + +253 +00:28:32,030 --> 00:28:37,650 +الجزئية هان واعتبر هذه إيش؟ مش موجودة كويس؟ إيش + +254 +00:28:37,650 --> 00:28:43,850 +اللي هيحصل؟ لو هذه zeroهذا اللي عندي point 2 هذا + +255 +00:28:43,850 --> 00:28:48,470 +off هذا هيكون saturated saturated نفس الخطوات اللي + +256 +00:28:48,470 --> 00:28:51,950 +قمت فيها هذا عندي one point اتنين هذا هيصير + +257 +00:28:51,950 --> 00:28:57,450 +forward active هذا هيصير forward active السؤال هذي + +258 +00:28:57,450 --> 00:29:02,030 +high high هذا reverse active reverse active هذا + +259 +00:29:02,030 --> 00:29:06,210 +saturated saturated اللي عندي saturated هذا off + +260 +00:29:06,210 --> 00:29:11,230 +هذا offالخدولة خلصنا ال break point بس انا بفرجيك + +261 +00:29:11,230 --> 00:29:14,870 +كيف بيشتغل ك or الان السؤال لو واحد high و واحد + +262 +00:29:14,870 --> 00:29:21,590 +low ايش اللي بيحصل؟ هذي عندى 1.4 و هذي عندى ايش؟ + +263 +00:29:21,590 --> 00:29:27,230 +zero هذي صارت high و هذي low هذا اللي عندى هيكون + +264 +00:29:27,230 --> 00:29:32,810 +saturated هذا اللي عندى هي point two ايش هذا وضعه؟ + +265 +00:29:32,810 --> 00:29:38,960 +off هذا اللي عندى هيتأثر بهذاإذا عنده ال point 8 + +266 +00:29:38,960 --> 00:29:44,560 +من هذا الاتجاه هتأثر عليه هذا مش هيأثر فهيظل شغال + +267 +00:29:44,560 --> 00:29:48,480 +هذا عندى يعطيني ال point 2 يعطيني ال low لهذا + +268 +00:29:48,480 --> 00:29:54,620 +السبب لما يكون عندى في ال or high و low بيعطيني ال + +269 +00:29:54,620 --> 00:29:58,420 +output اللى هو إيه ال high اللى موجود عندى لأن هذا + +270 +00:29:58,420 --> 00:30:01,700 +هيكون عندى في هذا الحالة اللى هنا وقولت هذا + +271 +00:30:01,700 --> 00:30:09,140 +saturated هذا off وهذا offو هذا عندى forward + +272 +00:30:09,140 --> 00:30:15,300 +action القليل صارت يعني وصلت لمرحلات انهم مش مش + +273 +00:30:15,300 --> 00:30:21,980 +هال excitement العادي الموجودة اه + +274 +00:30:21,980 --> 00:30:32,020 +اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه + +275 +00:30:32,020 --> 00:30:32,280 +اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه + +276 +00:30:32,280 --> 00:30:34,810 +اه اه اه اه اه اه اه اهأه بس انا لو قلتلك تبقى لي + +277 +00:30:34,810 --> 00:30:40,110 +حركة ال q ال transistors بدك تعرف ايش بيصير انت في + +278 +00:30:40,110 --> 00:30:44,170 +الأول و في الآخر انت مهندس كهربا مش technician + +279 +00:30:44,170 --> 00:30:48,510 +الفرق بين ال technician و المهندس انك انت بتعرف + +280 +00:30:48,510 --> 00:30:52,750 +التصميم تبعها و بهمك انت ممكن يعني خلينا نقول في + +281 +00:30:52,750 --> 00:30:57,850 +المستقبل لو فاتحيل اتيحت اليك الفرصة انك تصمم gate + +282 +00:30:57,850 --> 00:31:04,990 +زي هيكوالحاسوب .. شوف .. انت .. الكهربا و الحاسوب + +283 +00:31:04,990 --> 00:31:08,770 +فيش اللي عندكم في المسمة بختلف في أي اعلان وظيفة + +284 +00:31:08,770 --> 00:31:13,430 +لكهربا ولا حاسوب في العالم بطلب اتنين بطلبوش يقول + +285 +00:31:13,430 --> 00:31:18,290 +بدي بس شهادة حاسوب او بدي شهادة كهربا بطلب التخصص + +286 +00:31:18,290 --> 00:31:21,790 +كهربا او حاسوب و بيجيوا بيعملوا مقابلة و بناء + +287 +00:31:21,790 --> 00:31:24,130 +عليها بختار مين الأفضل + +288 +00:31:31,290 --> 00:31:40,690 +simplified gates او او gate او او او او او او او + +289 +00:31:40,690 --> 00:31:40,830 +او او او او او او او او او او او او او او او او او + +290 +00:31:40,830 --> 00:31:41,890 +او او او او او او او او او او او او او او او او او + +291 +00:31:41,890 --> 00:31:42,050 +او او او او او او او او او او او او او او او او او + +292 +00:31:42,050 --> 00:31:42,210 +او او او او او او او او او او او او او او او او او + +293 +00:31:42,210 --> 00:31:46,770 +او او او او او او او او + +294 +00:31:54,230 --> 00:31:57,810 +الان انت هتشوف بعد هيك لسه في عندنا family تاني + +295 +00:31:57,810 --> 00:32:01,130 +مخلصاش المحاضرة الجاية هتشوف ال emitter coupled + +296 +00:32:01,130 --> 00:32:05,590 +logic فيه transistor هيختلف بعد هيك هندخل على ال + +297 +00:32:05,590 --> 00:32:13,670 +mosfets في ال mosfets عالم تاني هتتوسع + +298 +00:32:13,670 --> 00:32:19,270 +أكتر لا تخافي بس + +299 +00:32:19,270 --> 00:32:22,290 +لازم تفهمها عشان تصير عندك appreciation للتاني + +300 +00:32:27,850 --> 00:32:33,490 +أه بس .. الأن اللي انت بت .. بس حاجة واحدة بدك + +301 +00:32:33,490 --> 00:32:37,910 +تفهمها، الآن ليش احنا بنتعلم هذا العلم؟ لأنه انت + +302 +00:32:37,910 --> 00:32:42,270 +لما تيجي تبقى بدك تعمل، تصنع، مابتيجيش تصنع قطعة + +303 +00:32:42,270 --> 00:32:46,830 +قطعة و تجمحهم لبعض، يعني انت لو الان بدك تشتغل على + +304 +00:32:46,830 --> 00:32:52,990 +أي .. حاليا بدك تبرمج مثلا ال Bic، بدك تبرمج غيره، + +305 +00:32:52,990 --> 00:32:57,360 +انت بتشتغل برمج و مش عارف أيش اللي بتعملهالان اللى + +306 +00:32:57,360 --> 00:33:01,660 +.. اللى بدك تفهمه التالت، الان اللى احنا بنعملهان، + +307 +00:33:01,660 --> 00:33:05,590 +انا قاعد بدى ..اعمل controller ال controller هذا + +308 +00:33:05,590 --> 00:33:10,750 +له transfer function مظبوط او له قالية معينة او + +309 +00:33:10,750 --> 00:33:14,850 +انا بدي اعمل ممري اخزن فيها استخدم ممري او بدي + +310 +00:33:14,850 --> 00:33:18,270 +استخدم switch ال switch له components انا في + +311 +00:33:18,270 --> 00:33:21,470 +البرمجة اللي عندى في اللغة انا قاعد بقوله بدى + +312 +00:33:21,470 --> 00:33:26,230 +التصميم تبع التالي و بحمله عليه فبتخزن بعملى + +313 +00:33:26,230 --> 00:33:31,720 +التخزين هذهاللي هي شكل الدائرة هانا بدى Transistor + +314 +00:33:31,720 --> 00:33:34,340 +هانا بدى أغيره هانا بدى أسوأه هاي بعملها انت + +315 +00:33:34,340 --> 00:33:37,480 +بتفكرش فيها من هذه الناحية انت بتفكر ان انا عندي + +316 +00:33:37,480 --> 00:33:40,960 +code و بدي استخدم هذا ال code و أعمل البرمجة هذه + +317 +00:33:40,960 --> 00:33:46,260 +لو بتاخد الدائرة كاملة حين انت بتبطل انت بتشتغل في + +318 +00:33:46,260 --> 00:33:51,040 +منطقة اللي هو و تروح لمنطقة المحترفين المحترفين + +319 +00:33:51,040 --> 00:33:54,260 +انا كيف حتى لو مابدي أعمل حاجة كيف بدي أحسن في + +320 +00:33:54,260 --> 00:33:59,680 +أدائها؟كداش بتهتكلفني هذه الوقت لإن احنا بنطلع على + +321 +00:33:59,680 --> 00:34:03,700 +ال propagation delay عندى لما نروح من stage ل + +322 +00:34:03,700 --> 00:34:07,580 +stage فى delay عندى بدنا نقصه ال propagation delay + +323 +00:34:07,580 --> 00:34:10,440 +فى نفس الوقت بدنا نقصه ال power dissipation انا + +324 +00:34:10,440 --> 00:34:16,520 +لما احط مليون او اتنين مليون transistor في في في + +325 +00:34:16,520 --> 00:34:22,130 +هى بده احسب كده بتاخدpower dissipation و اضربها في + +326 +00:34:22,130 --> 00:34:27,670 +هذا العدد هلاجيها ايش تفرق فانتهاء هي tools ممكن + +327 +00:34:27,670 --> 00:34:32,050 +ما تستخدموها لو بدك تعمل اور و نور مش هتستخدمها بس + +328 +00:34:32,050 --> 00:34:38,270 +إذا بدك تعمل حاجة أكبر تلزمك هذه الان لو بدك تشغل + +329 +00:34:38,270 --> 00:34:43,330 +على ال VHDL تقدرش تروح هناك بدون هذه لازم تبقى + +330 +00:34:43,330 --> 00:34:46,670 +فاهم هذه عشان تقدر تعمل برمجة اللي هناك + +331 +00:34:51,490 --> 00:34:55,410 +الان عادة انت بتبنيها .. هذي بقى .. هذي الان انت + +332 +00:34:55,410 --> 00:34:59,070 +عندك يعني في ال .. في الغالبش اللي بيجيلك عندك + +333 +00:34:59,070 --> 00:35:04,520 +disk جاهز انت بتصنعش واحدة واحدةوبتبقى فيه الحجم + +334 +00:35:04,520 --> 00:35:07,620 +تبقى هالقدر ال disk هذي زي ما حكينا في البداية إيش + +335 +00:35:07,620 --> 00:35:12,500 +هي أنا بقى في عندي خلطة بعملها من السيليكون في + +336 +00:35:12,500 --> 00:35:15,600 +عندي .. في .. في material و in material و .. و + +337 +00:35:15,600 --> 00:35:20,660 +توزعت زي كده، لأن بعد هيك بصيرعملت لهدولة الحجم + +338 +00:35:20,660 --> 00:35:24,120 +هذا بصير اقصقص فيها القطع الصغيرة اللي بتجيلكم هذا + +339 +00:35:24,120 --> 00:35:28,060 +بس هذه صار إلها إيش fabrication انت الآن لما تخزن + +340 +00:35:28,060 --> 00:35:32,200 +على ال CD على سبيل المثال ال CD اللي بتشتريها إيش + +341 +00:35:32,200 --> 00:35:37,400 +بتسوي باجي بخزن عليها مرة و خلصنا مظبوط؟ إيش أنت + +342 +00:35:37,400 --> 00:35:43,300 +عملت فيها؟أنا عملت fabrication للموجود للمبرئ اللى + +343 +00:35:43,300 --> 00:35:46,120 +عندي انا بدي هاد يكون فيها واحد هاد بدي يكون فيها + +344 +00:35:46,120 --> 00:35:50,480 +zero بدي يكون زي كده لان كل اشي coded الكلام عندي + +345 +00:35:50,480 --> 00:35:57,170 +coded انا اللى بعمل فيهعملية واحد application انا + +346 +00:35:57,170 --> 00:36:00,250 +بدأ اخزنه بس مادخلنيش وين بتروح او ايش بيصير فيها + +347 +00:36:00,250 --> 00:36:05,190 +او كيف هي بتنعمل بس انت في اخر المادة بتشوف انا لو + +348 +00:36:05,190 --> 00:36:10,270 +بداش أبني خلية رام ايش بلزمني؟ لو بدأ ابني خلية + +349 +00:36:10,270 --> 00:36:14,490 +رام read only memory ايش بلزمني؟ وكيف بدأ احطهم؟ + +350 +00:36:14,490 --> 00:36:17,790 +وكيف بدأ اسويهم؟ هاد بتقدرش تفطلها من اول course + +351 +00:36:17,790 --> 00:36:22,300 +اروحله هناك و اقولك اشرحلكم هدول لإن بلزم ايش؟تفهم + +352 +00:36:22,300 --> 00:36:26,660 +الحاجات .. الحاجات الأبسط لنصل لهديك النقطة جيب + +353 +00:36:26,660 --> 00:36:30,680 +الشغل و استخدمها ماليش داخل كيف هي لأ بدك .. بدك + +354 +00:36:30,680 --> 00:36:34,860 +تعرف كيف هي لأن أحيانا انا بدي شي .. يعني بدي .. + +355 +00:36:34,860 --> 00:36:40,080 +بديها .. بدي أعملها custom made custom made إلي مش + +356 +00:36:40,080 --> 00:36:43,680 +لغيري أو بديش أخد ال .. of the shell + +357 +00:36:53,040 --> 00:36:59,000 +لازم تفهم فعلا الان الدائرة اللى جاية احنا اتكلمنا + +358 +00:36:59,000 --> 00:37:02,480 +عن ال and و اتكلمنا عن ال or و اتكلمنا عن ال ند + +359 +00:37:02,480 --> 00:37:10,890 +بنتكلم عن مين ضال النور نفس الطريقةمااختلفتش على + +360 +00:37:10,890 --> 00:37:15,570 +حاجة الحاجة الوحيدة اللي هتختلف عند الدائرة هذه + +361 +00:37:15,570 --> 00:37:19,670 +والدائرة اللي جاية في ال power dissipation فهأشرح + +362 +00:37:19,670 --> 00:37:23,410 +على الدائرة الجاية اللي هي ال نور بالنسبة إلينا ال + +363 +00:37:23,410 --> 00:37:26,250 +power dissipation إلها وبعد هيك + +364 +00:37:31,900 --> 00:37:35,200 +و بعد هيك بتبقى خلصناها ال power dissipation في + +365 +00:37:35,200 --> 00:37:40,320 +الحالها يعني هتختلف شوية فاحنا بنتكلم الآن على ال + +366 +00:37:40,320 --> 00:37:50,980 +TTL NOR GATE اللي هي الرقم تبعها 7402 + +367 +00:38:16,350 --> 00:38:19,090 +السلام عليكم ورحمة الله وبركاته + +368 +00:38:35,470 --> 00:38:41,510 +أيوة .. أب ولا أب؟ أب + +369 +00:38:41,510 --> 00:38:54,530 +.. أب .. أب .. أب .. أب .. أب .. أب .. أب .. أب .. + +370 +00:38:54,530 --> 00:38:57,970 +أب .. أب .. + +371 +00:39:01,320 --> 00:39:05,400 +أنا مش عارف أكتر .. أكتر .. أكتر .. أكتر .. أكتر + +372 +00:39:05,400 --> 00:39:08,440 +.. أكتر .. أكتر .. أكتر .. أكتر .. أكتر .. أكتر .. + +373 +00:39:08,440 --> 00:39:09,360 +أكتر .. أكتر .. أكتر .. أكتر .. أكتر .. أكتر .. + +374 +00:39:09,360 --> 00:39:11,640 +أكتر .. أكتر .. أكتر .. أكتر .. أكتر .. أكتر .. + +375 +00:39:11,640 --> 00:39:13,080 +أكتر .. أكتر .. أكتر .. أكتر .. أكتر .. أكتر .. + +376 +00:39:13,080 --> 00:39:13,180 +أكتر .. أكتر .. أكتر .. أكتر .. أكتر .. أكتر .. + +377 +00:39:13,180 --> 00:39:14,700 +أكتر .. أكتر .. أكتر .. أكتر .. أكتر .. أكتر .. + +378 +00:39:14,700 --> 00:39:17,600 +أكتر .. أكتر .. أكت + +379 +00:39:48,640 --> 00:39:57,060 +أتمنى أن تكون حلوة + +380 +00:40:33,240 --> 00:40:39,300 +الدائرة اللى موجودة ده إذا بنشيل الجزئية اللى هان + +381 +00:40:39,300 --> 00:40:47,440 +هي نفسها نوعا ما، مظبوط؟ + +382 +00:40:47,440 --> 00:40:54,540 +يعني شيل هذه بس خلّي هذه الجزئية بتلاقيها نفس اللى + +383 +00:40:54,540 --> 00:41:01,520 +موجود عندى، يعني هذه اللى هان دمجتهم في هذه بسطلع + +384 +00:41:01,520 --> 00:41:08,360 +عندى بناحية نور و ناند النور و الناند اللي هم + +385 +00:41:08,360 --> 00:41:13,460 +structure معين الجزء اللي فى النص هذا مش موجود + +386 +00:41:13,460 --> 00:41:18,220 +فيهم مظبوط الاند + +387 +00:41:18,220 --> 00:41:23,480 +و الأور فيهم ال para .. ال .. ال .. ال .. ال .. ال + +388 +00:41:23,480 --> 00:41:23,740 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +389 +00:41:23,740 --> 00:41:24,040 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +390 +00:41:24,040 --> 00:41:24,360 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +391 +00:41:24,360 --> 00:41:24,460 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +392 +00:41:24,460 --> 00:41:25,220 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +393 +00:41:25,220 --> 00:41:26,120 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +394 +00:41:26,120 --> 00:41:26,460 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +395 +00:41:26,460 --> 00:41:26,600 +ال .. ال + +396 +00:41:31,010 --> 00:41:36,150 +الاند والناند ليس فيهم بررستركشر يعني لو حاطيتك + +397 +00:41:36,150 --> 00:41:43,090 +الدائرة هذه بتقدر تعرفها أي نوعها؟ الاصل تعرف + +398 +00:41:43,090 --> 00:41:50,010 +بررستركشر في عنده or أو nor القلب هذا موجود معناته + +399 +00:41:50,010 --> 00:41:56,830 +ايش؟ or نفس الشي هناك ليس عند بررستركشر يعني اند + +400 +00:41:56,830 --> 00:42:01,530 +او ناندفي عنده جزئية اللى موجودة اللى زى hand + +401 +00:42:01,530 --> 00:42:05,870 +الدايد hand والتراكسسر اللى هاد معناه هذا ايش بدها + +402 +00:42:05,870 --> 00:42:10,290 +تكون بدها تكون and مافيش فيها الدايد اللى فى النص + +403 +00:42:10,290 --> 00:42:15,470 +يبقى بدها تكون none هذا ال basic structure الأول + +404 +00:42:15,470 --> 00:42:19,190 +السؤال اللى بنسأله على طول ال output high و output + +405 +00:42:19,190 --> 00:42:33,840 +low point 2 و point 3 و 6مظبوط 3.6 كويس الان اللى + +406 +00:42:33,840 --> 00:42:38,760 +عندى لو حطيت ال input هنا zero بدى اخد one path و + +407 +00:42:38,760 --> 00:42:42,740 +امشي معاه و بعدين بحط معمل على التانى هذا zero + +408 +00:42:42,740 --> 00:42:49,580 +قداش ال voltage هات ايش هتعمل بترانزوستر هات هذا + +409 +00:42:49,580 --> 00:42:53,080 +off هذا off يبقى هذا ايش اللى عند ال output ايش + +410 +00:42:53,080 --> 00:43:00,770 +بدى يصيرأيوة تلاتة point ستة طيب عملته point five + +411 +00:43:00,770 --> 00:43:07,970 +ايش هيحصل عندى point سبعة ايش هيحصل عندى في هذه + +412 +00:43:07,970 --> 00:43:16,190 +هذا هيسوي هذا الان صار عندى point ستة ايش هيطلع + +413 +00:43:19,310 --> 00:43:26,170 +هي point تمانية جداش هنا point واحد هذا هيغير على + +414 +00:43:26,170 --> 00:43:31,790 +ال output ولا لأ؟ ليش؟ + +415 +00:43:31,790 --> 00:43:37,890 +لأن هذا هي drop هنا و رافقه drop هنا هتغير قيمة + +416 +00:43:37,890 --> 00:43:43,610 +من؟ ال output فعند معناته ال VAL جداش بدي ساوي؟ + +417 +00:43:48,480 --> 00:43:53,820 +هي هدول لساتهم زي ما هما ال VOL بدي ساوي عندهم + +418 +00:43:53,820 --> 00:44:01,960 +point 2 ال VOH بدي ساوي 3.6 ال VIL بدي ساوي 0.5 + +419 +00:44:01,960 --> 00:44:09,420 +اتفضل ال QSV + +420 +00:44:09,420 --> 00:44:15,320 +اللي هذا إذا هذي point 8 هذا بياخد gamma 7 قداشي + +421 +00:44:15,320 --> 00:44:21,730 +بيظل عندهاpoint واحد فهذا forward لأنه مش كافي .. + +422 +00:44:21,730 --> 00:44:26,690 +مش كافي هي اعطيها انت + +423 +00:44:26,690 --> 00:44:29,930 +بعد ما هذا .. انت مين بدك تاخد؟ هذا بدك تاخد ال + +424 +00:44:29,930 --> 00:44:32,690 +point سبعة بعدين بتاخد لغيره + +425 +00:44:35,570 --> 00:44:39,970 +بهو .. الان شوف يعني زي .. زي كيف هدى، انت عندك + +426 +00:44:39,970 --> 00:44:43,830 +حاجة بتعتمد على حاجة، الان وقتش .. وقتش هدى بتاخد + +427 +00:44:43,830 --> 00:44:48,770 +.. بتتشبع، بعد ما اللي التاني ياخد الحصة تبعته، + +428 +00:44:48,770 --> 00:44:53,290 +يعني هدى لازم في الأول تشتغل قبل ما هدى ت .. توصل + +429 +00:44:53,290 --> 00:44:59,080 +لمرحلة تشبعمن الفعش هذه زي أنت و أخوك قاعدين جنبها + +430 +00:44:59,080 --> 00:45:03,360 +فعش أنت تشبع و هو قاعد جنبك لازم هو يأكل أقل شيء + +431 +00:45:03,360 --> 00:45:08,600 +يصير فيه عنده طاقة و بعدين أنت بتوصل لمرحلات أنك + +432 +00:45:08,600 --> 00:45:14,380 +أنا ممكن أأكل أشبع أو أمزمز قبل ما هو إيش قبل ما + +433 +00:45:14,380 --> 00:45:19,420 +هو يأكل من الفعشفهذا نفس الشيء يعني فيه ترابط + +434 +00:45:19,420 --> 00:45:23,740 +بينهم التاني لازم يشتغل قبل ما يوصل الأولاني + +435 +00:45:23,740 --> 00:45:30,160 +لمرحلات ال saturation كويسة؟ فالان هذا كلها .. فال + +436 +00:45:30,160 --> 00:45:35,420 +.. اللي عند ال .. ال VIL معناته بدي ساوي كام؟ طيب + +437 +00:45:35,420 --> 00:45:42,480 +هذا مقدش ملزمه ليشتغل يصير forward active؟ طيب و + +438 +00:45:42,480 --> 00:45:53,860 +هذا مقدش ملزمه؟يبقى ال IP اللي عندي قداش ال output + +439 +00:45:53,860 --> 00:45:58,700 +هنا إذا هذه point 7 قداش هنا بدي يصير عندي الطيار + +440 +00:45:58,700 --> 00:46:03,200 +point 7 ملي وقولنا الطيار اللي هنا بساوي تقريبا + +441 +00:46:03,200 --> 00:46:10,790 +اللي هنا drop هنا قداش بدي يطلع 1.12 مظبوطوهنا + +442 +00:46:10,790 --> 00:46:14,490 +عندى واحد point كام واحد point أربعة واحد point + +443 +00:46:14,490 --> 00:46:19,330 +أربعة واحد point واحد point واحد point واحد point + +444 +00:46:19,330 --> 00:46:19,670 +واحد point واحد point واحد point واحد point واحد + +445 +00:46:19,670 --> 00:46:19,890 +point واحد point واحد point واحد point واحد point + +446 +00:46:19,890 --> 00:46:20,130 +واحد point واحد point واحد point واحد point واحد + +447 +00:46:20,130 --> 00:46:20,230 +واحد point واحد point واحد point واحد point واحد + +448 +00:46:20,230 --> 00:46:20,530 +point واحد point واحد point واحد point واحد point + +449 +00:46:20,530 --> 00:46:20,690 +واحد point واحد point واحد point واحد point واحد + +450 +00:46:20,690 --> 00:46:28,170 +point واحد point واحد point واحد point واحد + +451 +00:46:28,170 --> 00:46:32,550 +point + +452 +00:46:32,550 --> 00:46:39,290 +وا + +453 +00:46:42,020 --> 00:46:47,160 +هذه point 8 point 8 point 6 point 1 point 6 point + +454 +00:46:47,160 --> 00:46:47,640 +6 point 6 point 6 point 6 point 6 point 6 point 6 + +455 +00:46:47,640 --> 00:46:49,260 +point 6 point 6 point 6 point 6 point 6 point 6 + +456 +00:46:49,260 --> 00:46:49,280 +point 6 point 6 point 6 point 6 point 6 point 6 + +457 +00:46:49,280 --> 00:46:49,300 +point 6 point 6 point 6 point 6 point 6 point 6 + +458 +00:46:49,300 --> 00:46:50,060 +point 6 point 6 point 6 point 6 point 6 point 6 + +459 +00:46:50,060 --> 00:46:50,180 +point 6 point 6 point 6 point 6 point 6 point 6 + +460 +00:46:50,180 --> 00:46:55,260 +point 6 point 6 point 6 point 6 point 6 point 6 + +461 +00:46:55,260 --> 00:47:02,660 +point 6 point 6 point 6 + +462 +00:47:12,420 --> 00:47:16,360 +فهذا بتقولك هذا العائلة واحدة انها من عائلة واحدة + +463 +00:47:16,360 --> 00:47:22,560 +في هذا الدائرة مش هذا بيت القصيد هذا صارت من + +464 +00:47:22,560 --> 00:47:28,720 +المسلمات بيت القصيد اللي عندى التالي لهذا الدائرة + +465 +00:47:28,720 --> 00:47:36,980 +اللى + +466 +00:47:36,980 --> 00:47:42,980 +بتطلع عليها اللى هى حالة ال power dissipationو هذا + +467 +00:47:42,980 --> 00:47:48,620 +السؤال أجى في امتحانات سابقة تالتة اربع مرات نفس + +468 +00:47:48,620 --> 00:47:55,180 +السؤال حتى ال example اللي بنشرحه هو هذا جبته و + +469 +00:47:55,180 --> 00:48:00,900 +على الرغم من هيك أحيانا كان يقولولي هذا السؤال على + +470 +00:48:00,900 --> 00:48:03,200 +الرغم من أنه شايف example و بشرحه و بقولهم هذا + +471 +00:48:03,200 --> 00:48:07,620 +الكلام بلاقي نسبة الخطأ فيه أكتر من خمسين في المية + +472 +00:48:09,500 --> 00:48:12,640 +ولا مرة إلا بقولهم هذا السؤال أجى في امتحانات + +473 +00:48:12,640 --> 00:48:20,100 +سابقة و هو نفسه زي بهو و + +474 +00:48:20,100 --> 00:48:25,020 +هيمسجل الآن عشان يلكل الأجيال التانية احنا قاعدين + +475 +00:48:25,020 --> 00:48:29,400 +و على الرغم من هيك أخر مرة جبته نسبة الخطأ أكتر من + +476 +00:48:29,400 --> 00:48:33,340 +50% و هذا بيقوللي أصعب سؤال قلتله مفتح الكتاب و + +477 +00:48:33,340 --> 00:48:33,980 +تطلع عليه + +478 +00:48:38,340 --> 00:48:41,980 +أنا كل حاجة قاعد بقولك إيه هجيبلك زي هيك صار عندك + +479 +00:48:41,980 --> 00:48:47,160 +عينة معروفة إيش اللي بدي جيلك إذا أنت بتركز عليه + +480 +00:48:47,160 --> 00:48:51,600 +اللي بتساوي صحتين بدك تجيب مية تجيب مية مش هتخل + +481 +00:48:51,600 --> 00:48:57,860 +عليك فيها جابوا ميات السنة اللي فاتت في ناس جابت + +482 +00:48:57,860 --> 00:49:03,340 +طيب نرجع لهذا اللي عندك الآن عندك ده بنتطلع هذا + +483 +00:49:03,340 --> 00:49:08,800 +ليش عندك؟عندي اربع حالات هنا مظبوط عند حالة ال + +484 +00:49:08,800 --> 00:49:17,360 +input low و low فعندي low و high وعندي high و low + +485 +00:49:17,360 --> 00:49:25,920 +وعندي high و high مظبوط الآن ال ICC اللي عندى لهذا + +486 +00:49:25,920 --> 00:49:33,070 +الدائرة ايش بيساوي هاي عندى واحد هاي اتنينهذه + +487 +00:49:33,070 --> 00:49:41,670 +تلاتة وهذه أربعة هنا عندي I R + +488 +00:49:41,670 --> 00:49:49,250 +C B I R + +489 +00:49:49,250 --> 00:49:49,710 +B + +490 +00:49:54,520 --> 00:49:58,580 +الان بدي اطلع عليهم في حالة لما ال input اللي عندي + +491 +00:49:58,580 --> 00:50:03,500 +هنا يبقى low low قداش بيساون و التغيرات الأربعة + +492 +00:50:03,500 --> 00:50:08,040 +هدول ال combination الأربعة قداش بديساو فيهم ناخد + +493 +00:50:08,040 --> 00:50:17,980 +أول حالة ايش هي هاي بتكلم على ال power dissipation + +494 +00:50:17,980 --> 00:50:21,380 +اللي + +495 +00:50:21,380 --> 00:50:28,660 +عندي PCC averageهتساوي التالي و هتخليها عندك ICC + +496 +00:50:28,660 --> 00:50:35,900 +في حالة low low زائد ICC في حالة low high زائد ICC + +497 +00:50:35,900 --> 00:50:43,360 +في حالة high low زائد ICC في حالة high high على + +498 +00:50:44,180 --> 00:50:48,740 +اربع كام واحدة هدول؟ اربع فبتجسم على اربع مضروبة + +499 +00:50:48,740 --> 00:50:53,420 +في ال VCC الان بعضكم بيشتغل كل الشغل صح و بيجي ع + +500 +00:50:53,420 --> 00:50:57,620 +بدل ما يجسم على اربع بيجسم ع كده؟ ع اتنين بعضكم + +501 +00:50:57,620 --> 00:51:02,080 +بيشتغل بس النصين هذه و هذه و اللي في النص هدول ال + +502 +00:51:02,080 --> 00:51:05,940 +combination بيشتغل هنا هذا الأخطاء الشائعة بعض + +503 +00:51:05,940 --> 00:51:13,150 +منكم بيصرح بزيادة بيبقى عشو المربع هذا كلهانا + +504 +00:51:13,150 --> 00:51:16,650 +بقولكوا ايش اللي بخطأ الان بدي اطلع عليهم لما اول + +505 +00:51:16,650 --> 00:51:23,850 +حالة بدي اطلع عليها ال ICC في حالة ال low low بدي + +506 +00:51:23,850 --> 00:51:31,430 +ساوي IRBA في حالة انه موجود عند low زائد IRBB في + +507 +00:51:31,430 --> 00:51:41,310 +حالة ال low زائد IRC زائد IRCB كويس؟عشان تطلع عندى + +508 +00:51:41,310 --> 00:51:46,210 +لما ال input اللى عندي هذا low يعني هنا zero point + +509 +00:51:46,210 --> 00:51:50,270 +اتنين بدي اخدها وهنا point اتنين قداش ال voltage + +510 +00:51:50,270 --> 00:51:55,410 +هنا point اربعة point اربعة point اربعة ايش هيحصل + +511 +00:51:55,410 --> 00:52:00,110 +بالترانزستورات هذول اتنين هاي بدي اشيلها هذا هاي + +512 +00:52:00,110 --> 00:52:07,110 +ال off و هاي هذا ال off كويس و هذا ايش off الآن + +513 +00:52:07,110 --> 00:52:19,220 +عندى قداش IRCزيرو و اشبك معاشي قداش IRCB هيتنتين ع + +514 +00:52:19,220 --> 00:52:28,000 +السريع خلصنا منهم زيرو زيرو ايش اللي ضال عندى هذي + +515 +00:52:28,000 --> 00:52:33,940 +بدي اجعل ال loop في هذا الاتجاه و احسبه و هذا بدي + +516 +00:52:33,940 --> 00:52:39,740 +احسبه اتنين نفس الشي مظبوطتنين نفس الشي هاي عندى + +517 +00:52:39,740 --> 00:52:43,860 +VCC minus ال point تمانية و minus ال point اتنين + +518 +00:52:43,860 --> 00:52:53,100 +على اربعة كيلو صح فعندي ها انا بدي اقول ال I R B A + +519 +00:52:53,100 --> 00:52:58,720 +في وضع ال low بدي ساوي ال I R B B في وضع ال low + +520 +00:52:58,720 --> 00:53:05,740 +بدي ساوي VCC minus VBE لل I في وضع ال saturation + +521 +00:53:08,840 --> 00:53:16,160 +-v input في وضع اللوغ اللي اعطيته هذه point 2 صار + +522 +00:53:16,160 --> 00:53:20,860 +عندى خمسة ناقص point تمانية ناقص point اتنين على + +523 +00:53:20,860 --> 00:53:30,220 +four k اعطتنى كام واحد ميلي ام الان عندى يبقى ال + +524 +00:53:30,220 --> 00:53:36,510 +ICCهذا عندى one milli و هذا عندى one milli كده اش + +525 +00:53:36,510 --> 00:53:45,590 +صار مجموعه two milli M كل شايفها هذه اللي عندى + +526 +00:53:45,590 --> 00:53:49,110 +اللي هان هذا ال path الوحيد اللي موجود الان بتداجي + +527 +00:53:49,110 --> 00:53:57,560 +للوضع التاني اتنين بتطلع على ال ICCهي high low + +528 +00:53:57,560 --> 00:54:03,380 +عشان بداخلكوا بالتدريج عشان ماحدش يتعود ايش يفط + +529 +00:54:03,380 --> 00:54:11,620 +الخطوات دي ساوة IRBA في وضع ال high زائد IRBB في + +530 +00:54:11,620 --> 00:54:20,540 +وضع ال low زائد IRC زائد IRCB كويس؟ الآن اشوف اللي + +531 +00:54:20,540 --> 00:54:27,890 +عندى هذا لما تكون high معناته هنا عندى قداش3.6 + +532 +00:54:27,890 --> 00:54:35,570 +مظبوط هذا اللي عندي ايش صار فيها هذا reverse وهذا + +533 +00:54:35,570 --> 00:54:43,470 +forward فصارت ايش هذا reverse active هذا كان + +534 +00:54:43,470 --> 00:54:47,210 +saturated وهذا + +535 +00:54:47,210 --> 00:54:53,090 +كان saturated وهذا اللي عندي اللي قلنا عنه بالنسبة + +536 +00:54:53,090 --> 00:54:59,840 +لنا هذا الهذا ايش بدى يحصل فيه؟ ان هذا saturated + +537 +00:54:59,840 --> 00:55:07,160 +قداش ال voltage هذا؟ قداش ال voltage هذا؟ + +538 +00:55:07,160 --> 00:55:10,640 +point تمانية زي point اتنين واحد هذه automatic + +539 +00:55:10,640 --> 00:55:15,260 +لازم تحفظها لأنه مرت علينا الحين براحة ست سبعة و + +540 +00:55:15,260 --> 00:55:19,500 +تمان مرات فهذا عندى واحد هذا saturated هذا + +541 +00:55:19,500 --> 00:55:23,420 +saturated هذا automatic اللى بتقولي off بدهاش + +542 +00:55:23,420 --> 00:55:31,020 +تفكير سارةفهذا off عندى هذا ال IRCP كده بتساوي هاي + +543 +00:55:31,020 --> 00:55:41,460 +هذا عملناها zero هذا اللى عندى كده هي ال low هاي + +544 +00:55:41,460 --> 00:55:45,900 +point اتنين وهذا saturated point تمانية لسه في وضع + +545 +00:55:45,900 --> 00:55:50,640 +ال low ماتغيرش هيعطينا خمسة ناقص point تمانية او + +546 +00:55:50,640 --> 00:55:55,060 +ناقص point اتنين على اربع ويعطينا one milliهذا + +547 +00:55:55,060 --> 00:56:00,300 +يبقى الـ 1 ميلي انا بحسبهم هذه و هذه ايش صار فيهم + +548 +00:56:00,300 --> 00:56:05,100 +ال voltage عندي قداش هنا هذا saturated قداش هنا + +549 +00:56:05,100 --> 00:56:09,940 +point 8 point 8 هذا saturated قداش ال voltage هنا + +550 +00:56:09,940 --> 00:56:14,460 +point 2 point 2 مجموع ال point 8 و point 2 ايش + +551 +00:56:14,460 --> 00:56:19,500 +واحد خمسة ناقص واحد على one point six هيعطينا كام + +552 +00:56:19,500 --> 00:56:26,450 +two point five milli ampere فعندي ال IRC هنابدي + +553 +00:56:26,450 --> 00:56:32,970 +ساوى VCC minus VBE لل O ووضع ال saturated minus + +554 +00:56:32,970 --> 00:56:41,990 +VCE لل S ووضع ال saturated على ال RC بدي ساوى خمسة + +555 +00:56:41,990 --> 00:56:46,110 +ناقص point تمانية ناقص point اتنين على one point + +556 +00:56:46,110 --> 00:56:50,590 +six K بدي اعطيني two point five milli amp يعني هذه + +557 +00:56:50,590 --> 00:56:51,590 +اللي عندي صارت + +558 +00:56:54,590 --> 00:57:00,050 +2.5 ملي امبير دل عندى مين هذى طلع عندى هنا ايش + +559 +00:57:00,050 --> 00:57:06,450 +الوضع ها saturated قداش ال voltage ها point تمانية + +560 +00:57:06,450 --> 00:57:10,170 +هذا اللى عندى ايش وضعه هاي بدى امشي على هذا اللوب + +561 +00:57:10,170 --> 00:57:13,890 +هذا اللوب مقطوع اللى عندى هذا لأن هذا ايش وضعه off + +562 +00:57:13,890 --> 00:57:19,710 +بس على اللوب هذا ايش عندى ها لهذا الاتجاه اللى + +563 +00:57:19,710 --> 00:57:26,930 +بمشي فيه انا1.6 هذا ايش وضعه reverse active بتضيف + +564 +00:57:26,930 --> 00:57:32,230 +هذا قداش عندى 0.7 يعني صار عندى هنا 2.3 خمسة ناقص + +565 +00:57:32,230 --> 00:57:40,390 +2.3 على ال 4K في هذا ال I RBA + +566 +00:57:40,390 --> 00:57:46,090 +في حالة ال high صار عندى بساوة VCC minus اللي عندى + +567 +00:57:46,090 --> 00:57:52,330 +VBC لل I في وضع ال reverse active minus VB + +568 +00:58:07,710 --> 00:58:13,690 +اللي عندي صار خمسة ناقص ناقص ناقص ناقص ناقص ناقص + +569 +00:58:13,690 --> 00:58:14,330 +ناقص ناقص ناقص ناقص ناقص ناقص ناقص ناقص ناقص ناقص + +570 +00:58:14,330 --> 00:58:15,530 +ناقص ناقص ناقص ناقص ناقص ناقص ناقص ناقص ناقص ناقص + +571 +00:58:15,530 --> 00:58:17,110 +ناقص ناقص ناقص ناقص ناقص ناقص ناقص ناقص ناقص ناقص + +572 +00:58:17,110 --> 00:58:19,250 +ناقص ناقص ناقص ناقص ناقص ناقص ناقص ناقص ناقص ناقص + +573 +00:58:19,250 --> 00:58:23,060 +ناقص ناقص ناقص ناقص ناقص ناقص ناقص نااللي عندي + +574 +00:58:23,060 --> 00:58:29,160 +الآن هذه بحطها 0.675 + +575 +00:58:29,160 --> 00:58:36,560 +ميلي امبير نجمحهم مع بعض هي عندي كام هنا 3.5 زائد + +576 +00:58:36,560 --> 00:58:42,160 +هاي 4.175 + +577 +00:58:42,160 --> 00:58:48,060 +ميلي امبير الآن لما نعكسها خطوة رقم ترية ايش اللي + +578 +00:58:48,060 --> 00:58:55,910 +بدي اياهاICC في حالة low high بدي ساوي اللي عندى + +579 +00:58:55,910 --> 00:59:03,830 +نفس الشي IRBA في وضع ال low زائد IRBV في وضع ال + +580 +00:59:03,830 --> 00:59:14,190 +high زائد IRC زائد IRCP هذا اللي عندى بدي هتساوي1 + +581 +00:59:14,190 --> 00:59:19,370 +ملي زي ما عملناها هذا اللي عندي بدها تساوي 675 + +582 +00:59:19,370 --> 00:59:25,990 +micro هذا اللي عندي بدها تساوي 2.5 ملي هذا تساوي 0 + +583 +00:59:25,990 --> 00:59:35,230 +ملي بده يعطينا هنا برضه 4.175 ملي ام هاي + +584 +00:59:35,230 --> 00:59:38,110 +اللي عندي كويس + +585 +00:59:39,910 --> 00:59:44,390 +نفس اللي هي بس اللي صار انعكسا القيام ايش اللي ضال + +586 +00:59:44,390 --> 00:59:46,010 +عند الحالة الرابعة؟ + +587 +00:59:49,680 --> 00:59:59,400 +حالة الرابعة ICC في حالة الـ I I R B + +588 +00:59:59,400 --> 01:00:08,320 +A I R B A I R B A I R B A I R B A I R B A I R B A + +589 +01:00:08,320 --> 01:00:08,500 +I R B A I R B A I R B A I R B A I R B A I R B A I + +590 +01:00:08,500 --> 01:00:11,320 +R B A I R B A I R B A I R B A I R B A I R B A I R + +591 +01:00:11,320 --> 01:00:11,980 +B A I R B A I R B A I R B A I R B A I R B A I R B + +592 +01:00:11,980 --> 01:00:12,400 +A I R B A I R B A I R B A I R B A I R B A I R B A + +593 +01:00:12,400 --> 01:00:13,060 +I R B A I R B A I R B A I R B A I R B A I R B A I + +594 +01:00:13,060 --> 01:00:13,080 +R B A I R B A I R B A I R B A I R B A I R B A I R + +595 +01:00:13,080 --> 01:00:15,360 +B A I R B A I R B A I R B A I R B A I R B A I R B + +596 +01:00:15,360 --> 01:00:34,090 +A I R B A Ireverse active هذا saturated هذا + +597 +01:00:34,090 --> 01:00:41,590 +qsb saturated ال a هذا مش هغير على ال IRC ولا هغير + +598 +01:00:41,590 --> 01:00:49,120 +عالمياعلى ال IRCB هذه لأنه saturated هذا عنده off + +599 +01:00:49,120 --> 01:00:53,840 +وهذا اللي عنده ال voltage اللي موجود هنا لسه كام + +600 +01:00:53,840 --> 01:00:58,260 +one oh اللي عنده وهذا point two اللي موجودة عندى + +601 +01:00:58,260 --> 01:01:02,720 +يعني مش هيغير فيهم فمعناته ايش اللي عنده كده عنده + +602 +01:01:02,720 --> 01:01:06,360 +اللي في حالة ال high كان هنا او في حالة ال high + +603 +01:01:06,360 --> 01:01:19,760 +هنا0.675 ميلي او 0.675 ميلي او 0.675 + +604 +01:01:19,760 --> 01:01:24,560 +ميلي او 0.675 ميلي او 0.675 ميلي او + +605 +01:01:27,300 --> 01:01:32,160 +الخطوات اللي عندى بعد ما خلصت هذه و الواحد و اتنين + +606 +01:01:32,160 --> 01:01:36,560 +تلاتة و اربعة صرت اخد من الأرقام الاش السابقة لإن + +607 +01:01:36,560 --> 01:01:41,040 +انا حليتهم مافيش ذاعضام لحل فيهم على طول باجي + +608 +01:01:41,040 --> 01:01:44,120 +بتطلع عليهم في هاد الحالة إيش بحصل و هاد الحالة + +609 +01:01:44,120 --> 01:01:50,740 +إيش بحصللما كان عند ال output high كان عند ال IRC + +610 +01:01:50,740 --> 01:01:57,220 +و IRCB هدول اتنين بيساوي 0 في حالة ال output low + +611 +01:01:57,220 --> 01:02:04,630 +هد بيساوي 0 و هد بيساوي 2.5 مليهذه في حالة ال low + +612 +01:02:04,630 --> 01:02:08,630 +بيساوي عندى 1 ميلي في حالة ال high بيساوي 675 + +613 +01:02:08,630 --> 01:02:15,710 +مايكرو امبير الان لما جمعتهم بدأت اقول اطبق ال BCC + +614 +01:02:15,710 --> 01:02:20,950 +average ايش بدها تساوي بدها + +615 +01:02:20,950 --> 01:02:26,830 +تساوي زى ما حكينا هناك ICC low low 2 ميلي زائد 4 + +616 +01:02:26,830 --> 01:02:42,090 +.125 او 75 زائد1.7 ولا 1.2 1.25 7 + +617 +01:02:42,090 --> 01:02:55,890 +.5 زائد ملي زائد 4.175 ملي زائد 3.85 + +618 +01:02:55,890 --> 01:03:08,910 +ملي على 4مضروبة في خمسة هتعطيني هذه تقريبا 17.75 + +619 +01:03:08,910 --> 01:03:14,110 +ملي + +620 +01:03:14,110 --> 01:03:22,380 +واتفلاحظ هذه اعطت ناس تقريبا 70% higher than ال + +621 +01:03:22,380 --> 01:03:25,560 +inverter power dissipation يعني لو استخدمت .. لما + +622 +01:03:25,560 --> 01:03:31,380 +كنت استخدم ال inverter كانت اقل من هيكا ب 70 .. ب + +623 +01:03:31,380 --> 01:03:37,980 +.. ب ت .. يعني ب 70% طيب + +624 +01:03:37,980 --> 01:03:44,900 +تفضل اولا دلوقت نحسس ال ICC output low وال ICC + +625 +01:03:44,900 --> 01:03:48,930 +output highتمام؟ و بيجسم .. لأن احنا بدنا ال + +626 +01:03:48,930 --> 01:03:51,650 +average، كمش بطلع قوة distribution مظبوط طب انت + +627 +01:03:51,650 --> 01:03:54,430 +انا حاسبت في الأربع حالات، طب انا بحسب حتين لل + +628 +01:03:54,430 --> 01:03:57,570 +output high و لل output low، ليش انت حاسبت واحد، + +629 +01:03:57,570 --> 01:04:01,550 +اتنين، تلات، اربع؟ ليش هذه الحالة؟ لأن اللي عندي + +630 +01:04:01,550 --> 01:04:05,510 +هدول ال output high و ال output low مابتاخدش بس + +631 +01:04:05,510 --> 01:04:08,630 +بحالة واحدة، طلع عندي ايه ال .. ال .. ال .. هذه + +632 +01:04:08,630 --> 01:04:12,370 +عبارة عن إيش؟ عن نور، النور إيش ال structure + +633 +01:04:12,370 --> 01:04:17,130 +تبعها؟لما يكون input low و low إيش بيعطيني ال + +634 +01:04:17,130 --> 01:04:21,550 +output؟ high لما يكون input low و high إيش + +635 +01:04:21,550 --> 01:04:27,690 +بيعطيني؟ low low high و low بيعطيني low high و + +636 +01:04:27,690 --> 01:04:34,110 +high بيعطيني low فعندي تلت حالات تعطيني output low + +637 +01:04:34,110 --> 01:04:35,790 +أي واحدة بدك تاخد + +638 +01:04:38,460 --> 01:04:43,040 +ال average تبع مين؟ اي واحدة منك بقى لأ كل واحدة + +639 +01:04:43,040 --> 01:04:48,580 +اعطتك رقم بختلف، مظبوط؟ في حالة ال high اعطتنك + +640 +01:04:48,580 --> 01:04:55,280 +جديش؟ اتنين مليص، صح؟ في حالة هذه وهذا رقم واحد، + +641 +01:04:55,280 --> 01:04:58,720 +في حالة التالتة هنا الرقم اختلف فانت بدك تاخد ال + +642 +01:04:58,720 --> 01:05:02,680 +average تبع هدول و تعمل ال average مع هدول، مع حدي + +643 +01:05:02,680 --> 01:05:07,200 +عشان تجيب ال average power، مظبوط؟ما هو .. ماكانش + +644 +01:05:07,200 --> 01:05:10,760 +عندي أربع حالات بيختلفوا زي هيكا، اللي بيختلفوا + +645 +01:05:10,760 --> 01:05:13,820 +هذا بس في حالة .. في حالة مين؟ ال ore و النور، + +646 +01:05:13,820 --> 01:05:17,740 +الاختلاف، لإنه صار عندي برا ال restructure، هناك + +647 +01:05:17,740 --> 01:05:24,620 +لأ، حالتين، أه بس ال output إذا بتطلع عليه فيه مش + +648 +01:05:24,620 --> 01:05:31,180 +هيختلفمش هيختلف عندى في من جهة ال ايش يعنى + +649 +01:05:31,180 --> 01:05:33,340 +الخيارات اللى عندى الأرقام اللى عندى لما انت + +650 +01:05:33,340 --> 01:05:37,740 +حاسبها للحالات الأربعة مش هتلاقيها مختلفة زى هانا + +651 +01:05:37,740 --> 01:05:41,820 +هانا اللى عندى الأختلفة ليش صار عندى أربع حالات + +652 +01:05:41,820 --> 01:05:47,930 +لأن كل حالة أعطتني ICC بختلففي قبل لما كنا نتبع + +653 +01:05:47,930 --> 01:05:52,490 +الأربع حالات ماكانش يعطوننا .. الحالتين ال output + +654 +01:05:52,490 --> 01:05:55,790 +high و ال output low ماكانش يعطوننا أرقام باختلاف + +655 +01:05:55,790 --> 01:06:01,030 +.. كان الأرقام هي نفسها عرفت + +656 +01:06:01,030 --> 01:06:04,970 +نتاجي انت بعد ما حدد؟ ماركب ال .. ماركب ال .. + +657 +01:06:04,970 --> 01:06:05,090 +ماركب ال .. ماركب ال .. ماركب ال .. ماركب ال .. + +658 +01:06:05,090 --> 01:06:05,450 +ماركب ال .. ماركب ال .. ماركب ال .. ماركب ال .. + +659 +01:06:05,450 --> 01:06:05,610 +ماركب ال .. ماركب ال .. ماركب ال .. ماركب ال .. + +660 +01:06:05,610 --> 01:06:06,090 +ماركب ال .. ماركب ال .. ماركب ال .. ماركب ال .. + +661 +01:06:06,090 --> 01:06:07,930 +ماركب ال .. ماركب ال .. ماركب ال .. ماركب ال .. + +662 +01:06:07,930 --> 01:06:13,300 +ماركب ال .. ماركب ال .. مارعشان بقولك هذه الدائرة + +663 +01:06:13,300 --> 01:06:17,900 +بتختلف عن إيه غيرها، الآن بتاخد هي .. يعني تطلع + +664 +01:06:17,900 --> 01:06:22,380 +عندك، هذه لما كانت low كانت high، اختلفت النتيجة، + +665 +01:06:22,380 --> 01:06:26,520 +مضمون؟ في الدائرة .. في الدائرة هي ودائرة ال .. + +666 +01:06:26,520 --> 01:06:30,460 +الدائرة اللي كانت تانية ال or اللي عندك، في + +667 +01:06:30,460 --> 01:06:35,920 +التنتيجة هذول بتحسب الأربع حلالة، الباقي لأ بتضلوا + +668 +01:06:35,920 --> 01:06:41,000 +زي ما هملأن دا لاحظة مختلفةش كتير ال structure + +669 +01:06:52,670 --> 01:07:03,850 +الـ DTL لساتها أعلى احسبها انت بتتطلع + +670 +01:07:03,850 --> 01:07:09,370 +عندك حاجتين تتطلع عليهم تتطلع عندي قداش عندي ال + +671 +01:07:09,370 --> 01:07:15,650 +propagation delay و قداش عنديال power dissipation + +672 +01:07:15,650 --> 01:07:21,930 +هدولة مهماتما انت في الآخر عندك بدكتيش تطلع انا + +673 +01:07:21,930 --> 01:07:26,590 +عندى منطقة فيها تهوية شوية power dissipation بسعر + +674 +01:07:26,590 --> 01:07:29,770 +أرخص ماجبلها حتى كمهندس الحين بدك تسخدم ال + +675 +01:07:29,770 --> 01:07:33,530 +application تطلع عليها انا بدى حاسين اطلع عليهم + +676 +01:07:33,530 --> 01:07:40,230 +بدى ال power احيانا السرعة مهمة و ال .. يعني اللى + +677 +01:07:40,230 --> 01:07:42,810 +هى السرعة اللى عندى ال delay اللى بيصير في اللى + +678 +01:07:42,810 --> 01:07:46,330 +عندى ال power dissipation مهم الحاجة التالتة السعر + +679 +01:07:47,920 --> 01:07:52,740 +هدول كمهندش بدك توازن بينهم إذا قدرت توازن بينهم + +680 +01:07:52,740 --> 01:07:59,680 +معناه توصلت للنقطة يعني لل optimal decision حتى لو + +681 +01:07:59,680 --> 01:08:02,380 +بدك تستخدم ال application بدك تعرف توازن بينهم + +682 +01:08:02,380 --> 01:08:07,150 +الآن العلم التالياليوم إيش اللي عملنا؟ عملنا ال + +683 +01:08:07,150 --> 01:08:13,470 +TTL كملنا باقية ال gate الأربعة section 10.4 مش + +684 +01:08:13,470 --> 01:08:17,070 +مطلوب منكم فيها اللي هو بتكلم عن ال exclusive or و + +685 +01:08:17,070 --> 01:08:21,410 +ال exclusive not مش مطلوب بهذه الآن إيش اللي + +686 +01:08:21,410 --> 01:08:27,090 +هنغطيه المرحلة الجاية؟ هنغطي المحاضرة الجاية ال + +687 +01:08:27,090 --> 01:08:29,850 +ECL ال emitter coupled logic + diff --git a/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/hdSEyo60vi8_postprocess.srt b/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/hdSEyo60vi8_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..d398bc0b1c822d97bf04c112a0515185f4e433a9 --- /dev/null +++ b/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/hdSEyo60vi8_postprocess.srt @@ -0,0 +1,2204 @@ +1 +00:00:21,160 --> 00:00:27,060 +اليوم مش اللي هنعمله هنكمل + +2 +00:00:27,060 --> 00:00:32,480 +على chapter 7 ندخل شوية في chapter 10 هنعمل .. + +3 +00:00:32,480 --> 00:00:38,100 +هتاخد quiz طبعا في chapter 5 الآن هنعمل شوية + +4 +00:00:38,100 --> 00:00:43,660 +review للي أخدناه في chapter 7 لما نبدأ في chapter + +5 +00:00:43,660 --> 00:00:49,580 +7 احنا اتكلمنا على ال VTC و اتكلمنا على ال fan out + +6 +00:00:50,010 --> 00:00:54,630 +هنشوف ايش ذاكرين من ال VTC و من ال fan out و بعدها + +7 +00:00:54,630 --> 00:00:59,710 +هنغطي ال power dissipation و بعدها هنروح للنور و + +8 +00:00:59,710 --> 00:01:02,890 +ال ore و ال and gates اللي هم موجودة في ال chapter + +9 +00:01:02,890 --> 00:01:10,830 +عشرة هاي عندي ال V in و ال V out لو طلعت عندي ال + +10 +00:01:10,830 --> 00:01:11,410 +VTC + +11 +00:01:27,020 --> 00:01:31,240 +في كل منطقة بدطها أسهل أشياء أبدأ من شقة ال output + +12 +00:01:31,240 --> 00:01:41,040 +في ال output عندي المطلوب VOL و VOH وعندي هنا ال + +13 +00:01:41,040 --> 00:01:51,080 +intermediate point VOP هنا عندي I VIL VIH وهنا VIB + +14 +00:01:52,980 --> 00:01:58,300 +لو جينا تطلعنا على ال output اللي عندي هان عندي + +15 +00:01:58,300 --> 00:02:01,340 +حالتين بتطلع على QS لما يكون وضعوا saturation + +16 +00:02:01,340 --> 00:02:06,720 +ويكونوا وضعوا cut-off في وضع ال saturation قداش ال + +17 +00:02:06,720 --> 00:02:12,680 +output كل شايفها point 2 هذا هيكون وضعوا ال + +18 +00:02:12,680 --> 00:02:17,220 +saturation ال voltage هان هو بساوي ال VCE ووضع ال + +19 +00:02:17,220 --> 00:02:20,340 +saturation اللي هي ال point 2 فهنا automatically + +20 +00:02:20,340 --> 00:02:31,140 +بقول هذا بتساويvce set point two volt الان في وضع + +21 +00:02:31,140 --> 00:02:38,560 +cut off ايش اللي عندي ال V out ساوي VCC + +22 +00:02:38,560 --> 00:02:46,140 +minus IRC في ال RC minus VBE لل P في وضع forward + +23 +00:02:46,140 --> 00:02:55,030 +active minus VDL onالان ال IRC هو وضع في الشلود + +24 +00:02:55,030 --> 00:03:00,890 +عندى هذا off و هذا off في الشلود ايش بدى يساوي؟ ال + +25 +00:03:00,890 --> 00:03:08,970 +I يعني بعبارة تانية لما هذا مفصول و هذا مفصول قداش + +26 +00:03:08,970 --> 00:03:15,680 +قيمة ال I اللى هات و في الشلود؟ Zeroفإذا I بتساوي + +27 +00:03:15,680 --> 00:03:21,380 +Zero معناته IRC بتساوي Zero إيش ضال عندي خمسة ناقص + +28 +00:03:21,380 --> 00:03:27,620 +VBE forward active minus VDL on اللي هي خمسة minus + +29 +00:03:27,620 --> 00:03:32,080 +point seven minus point seven بيعطيني إيش three + +30 +00:03:32,080 --> 00:03:38,540 +point six في + +31 +00:03:38,540 --> 00:03:43,640 +هذا الحالة إيش عندي؟عندي qi كانت في حالة output + +32 +00:03:43,640 --> 00:03:53,260 +high qi وضعه saturation qs و qo وضعهم off وعندي ال + +33 +00:03:53,260 --> 00:04:03,000 +qp وضعه forward active فهي الملخص لهذا المنطقة في + +34 +00:04:03,000 --> 00:04:08,920 +هذا المنطقة ايش عندي الملخص لهذا عندي + +35 +00:04:09,500 --> 00:04:16,040 +الـ QI وضعه reverse active الـ QS و الـ QO وضعهم + +36 +00:04:16,040 --> 00:04:23,900 +saturation و الـ QP وضعه off احنا بدنا نعرف في + +37 +00:04:23,900 --> 00:04:26,720 +hand و في hand ايش اللي بحصل او ال critical point + +38 +00:04:26,720 --> 00:04:30,880 +ايش اللي بحصل فيهم كل واحدة بنغطيها و بنطلعها هذا + +39 +00:04:30,880 --> 00:04:35,340 +هسيبها للاخر لان هذه مربوطة في هذه المنطقة طيب ال + +40 +00:04:35,340 --> 00:04:41,000 +VIL ايش هوهو ال voltage اللي بيعمل لهذا ال QS وضعه + +41 +00:04:41,000 --> 00:04:48,240 +forward active يعني بيعمله on قداش ال voltage اللي + +42 +00:04:48,240 --> 00:04:53,260 +بلزم لهذا يكون ال QS on قداش + +43 +00:04:53,260 --> 00:04:57,160 +ال voltage اللي بلزم ليعمل لهذا ال QS forward + +44 +00:04:57,160 --> 00:05:03,700 +activeهنا بالزمن اللي بيبقى point 7 هاي plus minus + +45 +00:05:03,700 --> 00:05:08,080 +plus minus طب لو بدى اروح هنا عندى بالزمن point 7 + +46 +00:05:08,080 --> 00:05:15,280 +هانا قداش بتكون عندى بده اطرح منها point 2 مصبوط + +47 +00:05:15,280 --> 00:05:20,820 +هتعطيني هنا كمش بدأ ازود بدأ اطرح هذا بزاد و هذا + +48 +00:05:20,820 --> 00:05:25,040 +ناقص بدأ تعطيني point خمسة فهذا عندى بالساوى zero + +49 +00:05:25,040 --> 00:05:30,440 +point five و هذا النقطة عندى ايش بحصل هذا بيصير + +50 +00:05:30,440 --> 00:05:37,340 +عندى لساته QS وضعوا saturation Qi وضعوا saturation + +51 +00:05:37,340 --> 00:05:47,240 +QS وضعوا forward active QO وضعوا off و ال QBواضع + +52 +00:05:47,240 --> 00:05:54,320 +forward active في هذا النقطة هذا اللي عنده النقطة + +53 +00:05:54,320 --> 00:06:01,760 +هي بس عملت لمين هذا forward active طيب الآن لما + +54 +00:06:01,760 --> 00:06:06,360 +بدي اشوف النقطة الأخيرة هنا انا في الvih ايش + +55 +00:06:06,360 --> 00:06:12,370 +بتعملي؟تعمل الـ QO Saturation مظبوط إذا هذا + +56 +00:06:12,370 --> 00:06:15,490 +Saturation هذا بيكون Saturation و هذا لساته + +57 +00:06:15,490 --> 00:06:19,450 +Saturation يعني في هذه النقطة اللي عندي خلّيني + +58 +00:06:19,450 --> 00:06:29,930 +أجيبها لجاي عند التالي QI و QS و QO هدول وضحهم إيه + +59 +00:06:29,930 --> 00:06:33,150 +Saturation و ال QP وضحهم Off + +60 +00:06:37,720 --> 00:06:41,420 +النقطة اللي هنا طب دي هذا saturation قداش ال input + +61 +00:06:41,420 --> 00:06:44,700 +هذا قداش ال voltage اللي عندي point تمانية point + +62 +00:06:44,700 --> 00:06:48,200 +تمانية point تمانية point تمانية point تمانية + +63 +00:06:48,200 --> 00:06:49,040 +point تمانية point تمانية point تمانية point + +64 +00:06:49,040 --> 00:06:50,340 +تمانية point تمانية point تمانية point تمانية + +65 +00:06:50,340 --> 00:06:50,880 +point تمانية point تمانية point تمانية point + +66 +00:06:50,880 --> 00:06:52,180 +تمانية point تمانية point تمانية point تمانية + +67 +00:06:52,180 --> 00:06:54,080 +point تمانية point تمانية point تمانية point + +68 +00:06:54,080 --> 00:06:57,400 +تمانية point تمانية point تمانية point تمانية + +69 +00:06:57,400 --> 00:06:58,020 +point تمانية point تمانية point تمانية point + +70 +00:06:58,020 --> 00:06:58,060 +تمانية point تمانية point تمانية point تمانية + +71 +00:06:58,060 --> 00:07:01,980 +point + +72 +00:07:01,980 --> 00:07:10,750 +تمانية point تمانيةكلكوا فاهمين هادى؟ مين مش عارف + +73 +00:07:10,750 --> 00:07:16,850 +حاجة؟ يرفع ايده مافيش .. مافيش فيها خجل ها تفضل + +74 +00:07:16,850 --> 00:07:24,970 +طيب + +75 +00:07:24,970 --> 00:07:30,040 +انت لما تيجي تطلع حاجةهذا الوضع في ال VTC لما + +76 +00:07:30,040 --> 00:07:35,360 +حسبنا ال voltage اللي هنا لقنا هذا الطيار اللي هنا + +77 +00:07:35,360 --> 00:07:40,300 +too much لهذا يكون forward + +78 +00:07:40,300 --> 00:07:44,000 +active لان في ال forward activation اللي عندى ال I + +79 +00:07:44,000 --> 00:07:46,900 +C بده يساوي beta forward + +80 +00:07:52,400 --> 00:07:57,680 +التيار اللي هنا بيكون + +81 +00:07:57,680 --> 00:08:03,180 +عالي كتير فصعب هذا يصير له وضع فبقول أسهل أشي أشي + +82 +00:08:03,180 --> 00:08:07,240 +يكون عندي أخده على شكل saturation فهذا qi وضعه + +83 +00:08:07,240 --> 00:08:09,860 +saturation لما ال input كان عندي low + +84 +00:08:12,900 --> 00:08:15,340 +اللي هو ليش؟ لأن هذا الـ junction اللي عندى + +85 +00:08:15,340 --> 00:08:19,040 +forward active صارت او forward bias ففي حالة ال + +86 +00:08:19,040 --> 00:08:22,540 +forward bias هذا اللي عندى يامده هتكون reverse + +87 +00:08:22,540 --> 00:08:26,700 +bias ال junction هذا او forward bias لو كانت + +88 +00:08:26,700 --> 00:08:29,420 +reverse bias هتكون عندى هذا ال transistor في وضع + +89 +00:08:29,420 --> 00:08:32,020 +forward active forward active يقولنا ايش اللي عندى + +90 +00:08:32,020 --> 00:08:36,450 +هذا يعطينا تيار كتير لل Cفلازم يكون وضعه + +91 +00:08:36,450 --> 00:08:41,550 +saturation عشان حجم التيار اللهان يتناسب مع اللهان + +92 +00:08:41,550 --> 00:08:47,210 +لان ال IC بيساوي سيجما و سيجما في beta forward في + +93 +00:08:47,210 --> 00:08:52,490 +ال IP و سيجما هاي أصغر من واحد فالان هذا قلت + +94 +00:08:52,490 --> 00:08:54,850 +saturation ده هذا ال saturation لو ال voltage هنا + +95 +00:08:54,850 --> 00:08:59,190 +point اتنين كده اش بدي احط عليهايجب ان اجمعه في + +96 +00:08:59,190 --> 00:09:03,110 +وضع ال saturation ال point اتنين ايش بتعمله في ال + +97 +00:09:03,110 --> 00:09:08,110 +transistor هذا يشغله يبقى هذا off يبقى هذا اتاني + +98 +00:09:08,110 --> 00:09:12,510 +ايش off هدولة off الان اللي عندي انا لساتني في هذا + +99 +00:09:12,510 --> 00:09:16,930 +المنطقة ال output قديش بدي ساوي هذا off و هذا off + +100 +00:09:16,930 --> 00:09:21,580 +هذا بديكون forwardباياس اللي هي طبيعته اللي هان + +101 +00:09:21,580 --> 00:09:24,880 +قولنا هذا emitter follower دايما بيبقى forward + +102 +00:09:24,880 --> 00:09:29,060 +bias او off فهذا forward bias اللي عندك تياه ال + +103 +00:09:29,060 --> 00:09:32,380 +output بدي ساوة حسب المعادلة هاي بدي امشي في هذا + +104 +00:09:32,380 --> 00:09:37,500 +الخط وهين امشي لك في هذا عشان تشوف اي خط اللي ماشي + +105 +00:09:37,500 --> 00:09:37,800 +فيه + +106 +00:09:40,720 --> 00:09:44,820 +فهذا الان لان مافيش عندى اي load قلت هذا بيساوي 0 + +107 +00:09:44,820 --> 00:09:48,920 +الان بيدزود في ال voltage اللى هاد بضل ازود هذا من + +108 +00:09:48,920 --> 00:09:53,500 +point 2 point 3 point 4 point 5 لحد ايه point 5 + +109 +00:09:53,500 --> 00:09:57,480 +هذا بيصير عندى point ايه 7 ال point 7 بتشغللي هذا + +110 +00:09:57,480 --> 00:10:02,600 +الشجة بعد هذا ال voltage هذا كام Zeroالـ point 7 + +111 +00:10:02,600 --> 00:10:07,280 +هاي بقول اللي هي حطيتها أنا قلت هاد بسميها ال VIN + +112 +00:10:07,280 --> 00:10:11,460 +لأن point 7 ناقص ال point 2 أعطتني ال point 5 اللي + +113 +00:10:11,460 --> 00:10:16,960 +هي عملتلي أول تغيير صار ال QS وضعه forward active + +114 +00:10:16,960 --> 00:10:21,370 +الحين بضلني أزود في ال inputهذا saturation وهذا + +115 +00:10:21,370 --> 00:10:25,630 +forward active لو انا وصلت لهنا 1 volt هذا بيكون 1 + +116 +00:10:25,630 --> 00:10:30,910 +.2 هذا بياخد 0.7 بيبقى 0.5 بتشغليش هذا الان لما + +117 +00:10:30,910 --> 00:10:36,090 +انا وصل ل 1.2 هذا بيصير عندى 1.4 هذا saturation + +118 +00:10:36,090 --> 00:10:40,510 +هذا بيصار forward active بياخد 0.7 هذا بيصار ايش + +119 +00:10:41,910 --> 00:10:45,650 +فورورد اكتف بياخد ال point سبعة التانية هذا ال + +120 +00:10:45,650 --> 00:10:49,210 +next critical point اللي سميتها ايش ال IB اللي + +121 +00:10:49,210 --> 00:10:53,330 +عنده بيساوي one point two volt في هذا الحالة ايش + +122 +00:10:53,330 --> 00:10:59,150 +عند ال voltage اللي ها point سبعة وهي النقطة اللي + +123 +00:10:59,150 --> 00:11:06,420 +هاهي عندى ال QP و ال QS و ال QO هدولة صاروا + +124 +00:11:06,420 --> 00:11:10,800 +forward active و عندى ال QI هو ال saturation + +125 +00:11:10,800 --> 00:11:14,500 +الوحيد اللى هى فى هذا النقطة الان ده شوف قداش ال + +126 +00:11:14,500 --> 00:11:18,360 +output اللى أنا شوفش كيف التدرج فى ال ها ال output + +127 +00:11:18,360 --> 00:11:22,520 +اللى عندى بداجي أطلع عليه اذا هنا point 7 يبقى ال + +128 +00:11:22,520 --> 00:11:27,720 +volt التيار اللى ها قداش بيساوي0.7 ملي انا بقول + +129 +00:11:27,720 --> 00:11:32,040 +التيار الليهان تقريبا بيساوي الليهان هذا الليهان 0 + +130 +00:11:32,040 --> 00:11:41,080 +.7 ضرب 1.6 بيعطيني 1.12 volt ال 1.12 volt بنزودلهم + +131 +00:11:41,080 --> 00:11:48,820 +0.7 و 0.7 بيعطوني هناك 2.52 ال 2.52 ال V out + +132 +00:11:48,820 --> 00:11:53,120 +بيساوي خمسة ناقص ال drop هذا بيعطيني 2.48 + +133 +00:11:57,790 --> 00:12:02,430 +اللي هو بدي ساوي ال voltage اللي هان زائد ال + +134 +00:12:02,430 --> 00:12:05,610 +voltage اللي هان زائد ال voltage drop اللي هان و + +135 +00:12:05,610 --> 00:12:07,690 +ال voltage drop اللي هان قولنا الطيار اللي هان + +136 +00:12:07,690 --> 00:12:10,630 +تقريبا بدي ساوي الطيار اللي هان و الطيار اللي هان + +137 +00:12:10,630 --> 00:12:17,070 +بقدر اجيبه كويس ايه الان لما ازود ل 1.3 ايش حيصير؟ + +138 +00:12:17,070 --> 00:12:21,230 +حيصير head saturation بس هذامش saturation لما نزود + +139 +00:12:21,230 --> 00:12:25,230 +ل 1.4 هذا بيصيح saturation هذا satu .. هذا بيصيح + +140 +00:12:25,230 --> 00:12:29,470 +ان عندي 1.6 هذا saturation و هذا saturation يبقى + +141 +00:12:29,470 --> 00:12:34,050 +ال VIH اللي عندي اللي هو بيساوي 1.4 اللي عمللي هذا + +142 +00:12:34,050 --> 00:12:36,350 +saturation و هذا saturation و هذا saturation و اذا + +143 +00:12:36,350 --> 00:12:41,550 +طلعت عندي ال voltage هان قداش؟ point 2 في هذا + +144 +00:12:41,550 --> 00:12:46,840 +الحالة لما نكون saturation هان point 8هنا يكون 1.0 + +145 +00:12:46,840 --> 00:12:55,220 +ليشتغلوا هدول قديش بالزمن؟ 1.4 فاللي عندي قديش؟ 1 + +146 +00:12:55,220 --> 00:13:00,020 +.8 فهي واحد ناقص هم مش هتشغلهم فهذا ما أقول عنه في + +147 +00:13:00,020 --> 00:13:05,100 +هذا الحالة of اللي حكيتها هنا في هذا الحالة الأخر + +148 +00:13:05,100 --> 00:13:08,480 +لما أظل أزود في input إيش اللي حيحصل عندي؟ هذه + +149 +00:13:08,480 --> 00:13:13,310 +هتصير reverseوهذا forward صار عندى ايش ال reverse + +150 +00:13:13,310 --> 00:13:16,770 +active اللى اعطانى هذه الخانة و هذا off و هدول + +151 +00:13:16,770 --> 00:13:20,170 +لساتهم اتنين saturation شوفت كيف ال mode of + +152 +00:13:20,170 --> 00:13:23,490 +operation اللى بتمشي فيه طب تمشي من اتجاهه بيقول + +153 +00:13:23,490 --> 00:13:26,370 +من اتجاه ال input بدي ازود ال input و اشوف ايش + +154 +00:13:26,370 --> 00:13:30,050 +التغير البطرق سواء على كل transistor من ال + +155 +00:13:30,050 --> 00:13:37,390 +transistors اللى موجودة هنا واضحة هذه حداله تساؤل + +156 +00:13:37,390 --> 00:13:42,610 +فيهاقبل ما نروح ل .. احنا لساتنا فى مرحلة مراجعة + +157 +00:13:42,610 --> 00:13:48,010 +المحاضرة اللى فاتت قبل ما نعدى ع اللى بعدها كله + +158 +00:13:48,010 --> 00:13:53,110 +كويس ؟ طيب روحنا ل اللى بعدها قولنا انا بيدطلع على + +159 +00:13:53,110 --> 00:13:56,910 +ايش ال fan out بالنسبة للدائرة هاى ال fan out ايش + +160 +00:13:56,910 --> 00:14:03,610 +بيدطلعها هاد جايلى من ال loads عندى ال load اللى + +161 +00:14:03,610 --> 00:14:07,830 +موجود عنده ايش طبيعته هحطه بلون تانى عشان تشوفوا + +162 +00:14:13,370 --> 00:14:21,290 +هذا VCC' وهذا RB' وهذا QI' الآن لو كان عند ال + +163 +00:14:21,290 --> 00:14:27,870 +output high ايش بدي يحصل له دول ال output high هذي + +164 +00:14:27,870 --> 00:14:29,970 +high وهنا high ايش هذي + +165 +00:14:34,240 --> 00:14:37,660 +هذا الـ junction reverse بغض النظر عن التاني لما + +166 +00:14:37,660 --> 00:14:42,480 +تكون reverse معناه تفشي تيار بمشي صح؟ التيار اللي + +167 +00:14:42,480 --> 00:14:45,680 +موجود عنده هو ال leakage ال IS وال IS بتعرفوا ال + +168 +00:14:45,680 --> 00:14:53,660 +range تبعه؟بيعني عشرة minus اتناش لاربعتاش لخمساش + +169 +00:14:53,660 --> 00:14:58,860 +جليل جدا فمعناته بلا يذكر فهذا لو كان عند ال loads + +170 +00:14:58,860 --> 00:15:03,680 +واحد والله مليون مش هتفرق فلهذا السبب بنقول في + +171 +00:15:03,680 --> 00:15:07,560 +حالة ال output high ال N عندي دايما بتساوي هنا ايش + +172 +00:15:07,560 --> 00:15:12,820 +لل TTL بتساوي infinityالحاجة الوحيدة اللى بتعمل + +173 +00:15:12,820 --> 00:15:15,800 +determine للـ fan out مش في وضع ال output high فى + +174 +00:15:15,800 --> 00:15:19,800 +وضع ال output low لما يكون هذا عندي بيساوي VOL + +175 +00:15:19,800 --> 00:15:25,680 +اللى عندي معناته ايش اللى بقدر اتبع بيجيلى طيار من + +176 +00:15:25,680 --> 00:15:31,240 +هنا فى هذا الاتجاه هذا اللى سميته I N prime وهنا + +177 +00:15:31,240 --> 00:15:36,790 +عندي I Nprime و هكذا اللي موجود عندى فالتيار اللي + +178 +00:15:36,790 --> 00:15:42,570 +بيجي عندى هان بسميه IOL في حالة ال output هي في + +179 +00:15:42,570 --> 00:15:46,990 +حالة ال output اللي هو ايش اللي عنده المواصفات QI + +180 +00:15:46,990 --> 00:15:54,850 +وضع reverse active QB وضع off ال Q يعني عبارة عن + +181 +00:15:54,850 --> 00:16:03,590 +هذه المنطقة مش موجودة بتقدر تقولالان ال QS و ال QO + +182 +00:16:03,590 --> 00:16:08,030 +وضحهم saturation في هذه الحالة في الحالة هاي ايش + +183 +00:16:08,030 --> 00:16:14,330 +قلت التيار اللي جاي منها هدول بيعطوني + +184 +00:16:14,330 --> 00:16:22,660 +IOL مظبوط او IOL بدي ساوي N في I N primeطيب يعني N + +185 +00:16:22,660 --> 00:16:28,940 +بدي ساوي IOL على IN' يعني + +186 +00:16:28,940 --> 00:16:33,260 +N بدي تساوي الطيار اللي هان على واحد من هدول طيب + +187 +00:16:33,260 --> 00:16:37,640 +الطيار اللي هان إيش بدي ساوي بدي ساوي VCC ناقص ال + +188 +00:16:37,640 --> 00:16:41,420 +point 8 اللي بعملي هذا saturation ناقص ال output + +189 +00:16:41,420 --> 00:16:47,970 +low على ال RBجيبت منهم هذول ايش ال IN برايب من + +190 +00:16:47,970 --> 00:16:51,650 +هذول كل هيتو الآن بدي اجي الى الخطوة طب ال IOL + +191 +00:16:51,650 --> 00:16:56,890 +عبارة عن ايش عن ال IC تبع حياتك تفضل بيشيل ال BC + +192 +00:16:56,890 --> 00:17:02,270 +نقص و ال VBD و VBZ نقص و V output low على ال RB + +193 +00:17:02,270 --> 00:17:02,870 +بساوي ال IB + +194 +00:17:10,320 --> 00:17:15,500 +هي اللي بتحكي technically مظبوط بس لأنه احنا بنقول + +195 +00:17:15,500 --> 00:17:21,180 +هذا هيكون في وضع تشبع كتير فبقول تلقائيا بدي ساوي + +196 +00:17:21,180 --> 00:17:27,160 +تقريبا ال I N اللي عندىفهي approximation يعني زي + +197 +00:17:27,160 --> 00:17:31,620 +.. اتكلمنا على حاجة بنسميها ال hand waving ال hand + +198 +00:17:31,620 --> 00:17:35,660 +waving انت عادة لما تسلم على واحد ايش بتسوي؟ الإيد + +199 +00:17:35,660 --> 00:17:39,940 +بتلمس الإيد، بيصير إيش؟ هذا .. يعني انت فيه إحساس، + +200 +00:17:39,940 --> 00:17:43,920 +الأقل من بعيد تشوحله و تكون قريب تشوحه، بس هو في + +201 +00:17:43,920 --> 00:17:46,760 +شجة و أنت في شجة تشوحله، فانتوا هذا سلام على + +202 +00:17:46,760 --> 00:17:53,070 +الطايرأه فاحنا هذا اللي بنعملها hand waving هذا + +203 +00:17:53,070 --> 00:17:59,710 +يعني مش الكلام جوي يعني لو بدك جوي الكلام اللي + +204 +00:17:59,710 --> 00:18:05,930 +بتحكيه مظبوط بدك تضرب في beta forward plus واحد و + +205 +00:18:05,930 --> 00:18:10,770 +تضرب بال sigma يعني ساعة واحد زائد sigma في beta + +206 +00:18:10,770 --> 00:18:14,630 +forward و هذا الكلام بعد شوية بعملها more + +207 +00:18:14,630 --> 00:18:19,470 +complicated فاحنا بندور علىالأسهل لكم عشان ما + +208 +00:18:19,470 --> 00:18:23,730 +نعقدهاش بزيادة على اللازم أسهل بس technically + +209 +00:18:23,730 --> 00:18:29,670 +لساتنا بتتكلم نوعا ما valid فهذه اللي بقولها دايما + +210 +00:18:29,670 --> 00:18:33,690 +ان ال hand waving إيش هي عبارة عن حاجة بتتكلم فيها + +211 +00:18:33,690 --> 00:18:39,510 +technically مش بعيدة عن الصواب بس بتسهل الشغليعني + +212 +00:18:39,510 --> 00:18:45,070 +زي انت الحين احيانا لو بدك تحل مسألة و بتكشف تخدم + +213 +00:18:45,070 --> 00:18:49,210 +ال calculator بتصيرش تقرب الأرقام يعني لو عندى two + +214 +00:18:49,210 --> 00:18:53,090 +point seven بتقسمها على سبعة بتقول هي عبارة عن two + +215 +00:18:53,090 --> 00:18:56,290 +point eight على سبعة بيعطيني point four و خلصنا + +216 +00:18:57,320 --> 00:19:02,220 +فيعني الحل ايش بسهل حالي في الآخر الرقم اللي هطلع + +217 +00:19:02,220 --> 00:19:06,940 +فيه في neighborhood في نفس الحارة الرقم اللي هيطلع + +218 +00:19:06,940 --> 00:19:12,900 +عنده بس مش بالظبط نفسه بدون استخدام calculators او + +219 +00:19:12,900 --> 00:19:16,300 +اي حاجة فانت نفس الطريقة اللي احنا بنتكلم فيها + +220 +00:19:16,300 --> 00:19:21,800 +فيهاالان اللى بنحكيه ال I N Prime اللى بدي ساوي + +221 +00:19:21,800 --> 00:19:25,460 +خمسة ناقص ال drop هنا ناقص ال point اللى هنا على + +222 +00:19:25,460 --> 00:19:31,840 +ال R B اللى موجودة هنا و هذا قولنا بدي ساوي N اللى + +223 +00:19:31,840 --> 00:19:36,420 +هنا هذا في N بدي ساوي ال IOL ال IOL بدي ساوي ال IC + +224 +00:19:36,420 --> 00:19:39,940 +في وضع ال saturation اللى هنا طب ال IC في وضع ال + +225 +00:19:39,940 --> 00:19:41,380 +saturation من وين بدي أجيبه + +226 +00:19:45,620 --> 00:19:52,260 +يعني ال IC اللى هاناش قولت N بدي ساوي IOL على IN + +227 +00:19:52,260 --> 00:19:58,940 +prime وقلت ال IN prime بدي ساوي اللى هى إيش عندى + +228 +00:19:58,940 --> 00:20:09,640 +VCC minus VBE SAT minus VCE SAT على ال RB كويس + +229 +00:20:09,640 --> 00:20:15,080 +الآن أنا بقول ال IOL اللى عندى هانا بدي ساوي ال IC + +230 +00:20:16,670 --> 00:20:21,530 +SAT تبعت ال O اللي هو بيساوي هذا طب ال IC SAT ايش + +231 +00:20:21,530 --> 00:20:25,470 +بدي ساوي ايوة + +232 +00:20:25,470 --> 00:20:33,910 +ال IC O SAT بدي ساوي Sigma في Beta Forward في ال + +233 +00:20:33,910 --> 00:20:38,330 +IBO اللي هي التيار اللي جاي من وين من هات في وضع + +234 +00:20:38,330 --> 00:20:42,890 +ال saturation طيب ال IBO هذا بقدر اجيبه + +235 +00:20:48,770 --> 00:20:54,910 +ماذا يفعل؟ هذا وصلت لهنا وهذا اللي هنا وهذا اللي + +236 +00:20:54,910 --> 00:20:58,150 +بتابعه هنا طب هذا ايش عندي؟ لو جبت التيار اللي هنا + +237 +00:20:58,150 --> 00:21:03,270 +وطرحت منه هات بجيب هات يعني بعبارة تانية هان اللي + +238 +00:21:03,270 --> 00:21:11,010 +بدي أقوله هي ال IBO بدي ساوي ال IES minus ال IRD + +239 +00:21:11,010 --> 00:21:20,620 +طب ال IRD اللي هنا ممكن نجيبه؟ هي IRDال IRD بدي + +240 +00:21:20,620 --> 00:21:27,120 +ساوي VBE تبعت ال O في وضع ال saturation على ال RD + +241 +00:21:27,120 --> 00:21:33,000 +مظبوط؟ ماعرفي + +242 +00:21:33,000 --> 00:21:40,480 +هذا ولا لو حد وقف شايف فيه صمت شوية نرجع + +243 +00:21:40,480 --> 00:21:46,600 +تاني الان نيجي عند هذا ال KCL لهذا ايش بتحكي؟ + +244 +00:21:47,900 --> 00:21:51,240 +التيار اللي هان بدي ساوي مجموع التيارات اللي جاي + +245 +00:21:51,240 --> 00:22:00,320 +منها هد متفقين عليها طيب هي كويس اسمعنا صوت طيب + +246 +00:22:00,320 --> 00:22:03,940 +التيار اللي جاي هان بتاخد واحد منه ال assumption + +247 +00:22:03,940 --> 00:22:08,500 +ان كل ال cues اللي هان ايش identical فمعناته لو + +248 +00:22:08,500 --> 00:22:12,740 +جبت تيار واحد فيهم وضربته في عددهم بدي اعطيهم + +249 +00:22:12,740 --> 00:22:17,540 +المجموع كويس هيك؟طيب الآن الطيارة اللي هان قديش + +250 +00:22:17,540 --> 00:22:23,700 +بدي ساوي اللي جاي منها بدي ساوي التالي VCC ناقص ال + +251 +00:22:23,700 --> 00:22:28,100 +point 8 هذا لأن ال input لوه تبعه بدي يكون وضعه + +252 +00:22:28,100 --> 00:22:32,720 +saturation ال voltage هان قديش point 8 و ال + +253 +00:22:32,720 --> 00:22:38,260 +voltage هان كام point 2 بدي أقول خمسة ناقص ال + +254 +00:22:38,260 --> 00:22:42,940 +point 8 ناقص ال point 2 على ال RB بيعطينا ال I هذا + +255 +00:22:42,940 --> 00:22:49,060 +اللي أنا بحكي عنهمتفقين عليها هذه؟ طيب فهاتين تاني + +256 +00:22:49,060 --> 00:22:52,600 +الأولة هاتي جيبناها و التانية جيبناها لان نيجي + +257 +00:22:52,600 --> 00:22:57,220 +لإيش؟ لتالتة التالتة هذه ايش بتقولي؟ التيار هذا هو + +258 +00:22:57,220 --> 00:23:03,360 +نفسها لأن مافيش حاجة جاية من هناالتيار هذا هو نفسه + +259 +00:23:03,360 --> 00:23:07,160 +ال IC ال IC في ال transistor اللي عندي هنا وضعه + +260 +00:23:07,160 --> 00:23:12,560 +إيش saturation فال IOL بيساوي ال IC لل output ال + +261 +00:23:12,560 --> 00:23:15,620 +transistor في وضع ال saturation هذه برضه واضحة + +262 +00:23:15,620 --> 00:23:22,440 +نروح للبعد ال IC في وضع ال saturation بجيبه بأي + +263 +00:23:22,440 --> 00:23:26,300 +طريقة مافيش حاجة بتجيبه إلا عن طريق مين ال IB فهو + +264 +00:23:26,300 --> 00:23:30,640 +بيساوي ال IB مضروب في Sigma مضروب في Beta Forward + +265 +00:23:32,000 --> 00:23:39,920 +طيب لحد تلان ما تبعنا يعني هدول وصلنا لهان ال KCL + +266 +00:23:39,920 --> 00:23:45,340 +لهذا النقطة ايش بدي ساوي؟ التيار اللي هان بدي روح + +267 +00:23:45,340 --> 00:23:49,380 +جزء منه هان و جزءهان الجزء اللي هان سميته IB و + +268 +00:23:49,380 --> 00:23:56,730 +الجزء اللي هان سميته IRD متفقين على هذه؟طيب اللي + +269 +00:23:56,730 --> 00:24:03,810 +صار عندي هنا يبقى ال ip اللي هان بدي ساوي ال IES + +270 +00:24:03,810 --> 00:24:10,390 +تبعت هذا ال transistor ناقص ال IRD كويس؟ يعني عملت + +271 +00:24:10,390 --> 00:24:15,510 +solving لمين؟ لل IBO اللي هان طيب هذا كده ايش + +272 +00:24:15,510 --> 00:24:18,730 +بيساوي؟ هذا ال voltage اللي عندي عارفه point + +273 +00:24:18,730 --> 00:24:23,650 +تمانية point تمانية على ال one k بعطيني ال IRD ضال + +274 +00:24:23,650 --> 00:24:29,470 +بدي مين؟ال IES ال IES هو عبارة عن ايش بتعرف في ال + +275 +00:24:29,470 --> 00:24:36,170 +transistor ايش بيساوي بيساوي ال ICS زائد ال IBS + +276 +00:24:36,170 --> 00:24:43,050 +مظبوط يعني ها بهدنا نكتبه هاي ال IES هده جبناها + +277 +00:24:43,050 --> 00:24:46,750 +هاي ال I ال IES + +278 +00:24:49,860 --> 00:24:56,060 +بدي ساوى IBS زائد ICS طب ال ICS اللي هو عبارة عن + +279 +00:24:56,060 --> 00:25:02,480 +إيش IRC مظبوط لأنه هنا مافيش حاجة فالتيار اللي هنا + +280 +00:25:02,480 --> 00:25:09,660 +هو نفسه اللي هنا لحد الآن هذي ماشيين معايا ولا طيب + +281 +00:25:09,660 --> 00:25:15,860 +ال voltage هنا قداش هذا وضعه saturation بيجينا + +282 +00:25:15,860 --> 00:25:22,550 +قداش فوقهpoint 2 صار مجموع كام هنا واحد خمسة ناقص + +283 +00:25:22,550 --> 00:25:27,530 +واحد على ال RC بيعطينا ال what ال IRC اللي هو جاي + +284 +00:25:27,530 --> 00:25:31,650 +هان فهذا ايش بدأ اقول عندك هو بهايات بيساوي VCC + +285 +00:25:31,650 --> 00:25:39,870 +minus VBE لل O في وضع ال saturation ناقص VCE لل S + +286 +00:25:39,870 --> 00:25:44,870 +في وضع ال saturation على ال RC + +287 +00:25:47,840 --> 00:25:52,300 +الان ضال اللي عندي يعني هذا جبته ضال عندي مين ال + +288 +00:25:52,300 --> 00:25:58,300 +IBS ال IBS اللي هو التيار اللي هان التيار + +289 +00:25:58,300 --> 00:26:04,760 +اللي هان ايش بيساوي هذا اللي عندي سميته ال ICI هذا + +290 +00:26:04,760 --> 00:26:09,500 +الترانزستو وضعه reverse active هذا و هذا بتساويين + +291 +00:26:09,500 --> 00:26:15,540 +بس بيختلفوا في ال إيش في الإشارة مظبوط يعني لما + +292 +00:26:15,540 --> 00:26:24,010 +بدي أقول عندي هانبدأش أقول عندي ال I B S بدي ساوي + +293 +00:26:24,010 --> 00:26:33,770 +سالم I C I طب ال I C I إيش بيساوي خليني + +294 +00:26:33,770 --> 00:26:36,930 +أذكر في وضع ال forward active عشان أذكركم في ال + +295 +00:26:36,930 --> 00:26:42,790 +forward active ال I E إيش بيساوي Beta forward زائد + +296 +00:26:42,790 --> 00:26:49,220 +واحدفي ال I B مظبوط في وضع ال reverse active بدك + +297 +00:26:49,220 --> 00:26:56,840 +تطلع على ال I C هو بمثابة I E حاجتين بدك تغير بدل + +298 +00:26:56,840 --> 00:27:00,440 +beta forward تحط beta reverse وتحط إشارة negative + +299 +00:27:00,440 --> 00:27:07,260 +قدامها قدام ال I B فبدي أصير عندي يعني ال I C I + +300 +00:27:07,260 --> 00:27:15,320 +هذا بدي ساوي عشان I C I بدي ساوي سالببيتا ريفيرس + +301 +00:27:15,320 --> 00:27:21,480 +بلس واحد في ال IP هذا الان بدى اعوض هواية هنا ايش + +302 +00:27:21,480 --> 00:27:26,760 +حيصير عندى؟ هاي نيجاتيب و نيجاتيب ايش هتعطيني؟ + +303 +00:27:26,760 --> 00:27:31,800 +positive فهذا هتصير عندى بيتا ريفيرس زائد واحد في + +304 +00:27:31,800 --> 00:27:39,120 +ال IP I اللي عندىهذا شفتكوا وقفته حد ما جيبنا سيرة + +305 +00:27:39,120 --> 00:27:47,000 +ال reverse active ال chapter تلاتة إيش اللي أخدنا + +306 +00:27:47,000 --> 00:27:54,340 +منهم؟أخدنا ال mode of operations بس في ال chapter + +307 +00:27:54,340 --> 00:28:00,600 +3 قولنا في ال chapter 3 خلينا نراجع شوية لكم فى + +308 +00:28:00,600 --> 00:28:06,080 +حالة ال cut-off mode إيش عندي عند ال IB بيساوي ال + +309 +00:28:06,080 --> 00:28:10,980 +IC بيساوي ال IE بيساوي 0 فى ال forward active إيش + +310 +00:28:10,980 --> 00:28:16,640 +عندي عند ال VBE بيساوي point تمانية وعند ال IC + +311 +00:28:16,640 --> 00:28:22,810 +بيساوي beta forwardمظبوط في IB في حالة ال + +312 +00:28:22,810 --> 00:28:29,830 +saturation ايش عندى؟عندي VBE بيساوي 0.8 VCE بيساوي + +313 +00:28:29,830 --> 00:28:36,790 +0.2 VBC بيساوي 0.6 كويس هدول التلاتة وعندي ال IC + +314 +00:28:36,790 --> 00:28:42,590 +بيساوي Sigma في Beta Forward في ال IP في حالة ال + +315 +00:28:42,590 --> 00:28:46,870 +reverse active عندي معلومتين ايش هما عندي VBC + +316 +00:28:46,870 --> 00:28:54,190 +بيساوي 0.7وعندي ال I E بيساوي negative beta + +317 +00:28:54,190 --> 00:28:56,710 +reverse في ال I B + +318 +00:29:00,280 --> 00:29:03,520 +الـ IE ما هو إيش عبارة .. ال IC عبارة عن إيش؟ + +319 +00:29:03,520 --> 00:29:08,780 +مجموع ال IP زائد إيش؟ ال I .. ال IE في حالة إيش + +320 +00:29:08,780 --> 00:29:13,080 +اسمه؟ ال reverse بس الإشارة كل هدول يعني هو + +321 +00:29:13,080 --> 00:29:18,980 +الإشارة عكس رايح من التيار رايح يعني كان عندنا من + +322 +00:29:18,980 --> 00:29:23,580 +ال emitter في اتجاه ال إيش؟ ال collector رايح مضاد + +323 +00:29:23,580 --> 00:29:29,060 +معاكس لإنت اللي بتعرفهواضحة لها فالحاجة الوحيدة + +324 +00:29:29,060 --> 00:29:33,140 +اللي جبت عندى انا لو ماكنت احكيها في حالة ال + +325 +00:29:33,140 --> 00:29:41,030 +reverse active عندىVBC بيساوي point سبعة عندي ال + +326 +00:29:41,030 --> 00:29:50,150 +IC بدي ساوي سالب ال IB سالب ال .. او .. لأ ال IB + +327 +00:29:50,150 --> 00:29:55,990 +اللي عندى سالب واحدة ال IB زائد ال IC زائد ال IE + +328 +00:29:55,990 --> 00:30:03,870 +بالسالب اللي عندى وعندي ال IE بدي ساوي سالب beta + +329 +00:30:03,870 --> 00:30:13,770 +reverse في ال Iب إيه اللي عندي؟ كويس هيك؟ إذا بدي + +330 +00:30:13,770 --> 00:30:17,590 +أضعها هنا بدي أضع السالب لبرا هنا عندي سالب تصبح + +331 +00:30:17,590 --> 00:30:23,830 +الإشارة مية لمية هيك هذا اللي عندي ككل هذا اللي + +332 +00:30:23,830 --> 00:30:28,730 +موجود عندي هذا لما أجمعها بدي أضعها هنا ال beta + +333 +00:30:28,730 --> 00:30:33,830 +reverse في ال IP إيش هتعطيني؟ هاي بالسالب هتعطيني + +334 +00:30:35,120 --> 00:30:41,400 +ككل ال IC بيتساوى سالم واحد زائد beta reverse في + +335 +00:30:41,400 --> 00:30:46,200 +ال IP اللي عندي زي ما كان عندي في حالة ال forward + +336 +00:30:46,200 --> 00:30:50,580 +active ال IE بيساوى beta forward plus واحد في ال + +337 +00:30:50,580 --> 00:30:56,590 +IPالان انا طبقته في هذه الحالة اللى عندي قولت عندي + +338 +00:30:56,590 --> 00:31:00,910 +هذا بدي ساوي هاي و هاي و جيتها لفورملة اللى موجودة + +339 +00:31:00,910 --> 00:31:09,640 +عندي هذا طب ال IBA ايش بدي ساوي ال IBI بدي ساويVCC + +340 +00:31:09,640 --> 00:31:18,720 +minus VBC لل I في وضع ال reverse active minus VBE + +341 +00:31:18,720 --> 00:31:26,240 +لل S في وضع ال saturation minus VBE لل O في وضع ال + +342 +00:31:26,240 --> 00:31:29,800 +saturation على ال RB + +343 +00:31:33,160 --> 00:31:37,280 +الان انت بتقول المعادلة شكلها طويلة طب مانا ب .. ب + +344 +00:31:37,280 --> 00:31:41,740 +.. بعملها بشكل أسهل كيف؟ بتقول هي عندي point + +345 +00:31:41,740 --> 00:31:47,980 +تمانية و point تمانية هي قداش؟1.6 زي 0.7 هي 2.3 + +346 +00:31:47,980 --> 00:31:52,420 +بديش اكتب معدلتك بديش اقول خمسة ناقص ال 2.3 على + +347 +00:31:52,420 --> 00:31:59,500 +الأربعة كيلو وهي بيعطيني ال IP في وضع ال reverse + +348 +00:31:59,500 --> 00:32:05,240 +active وأسهل المجود أحفظ بالمعادلة و BPE وغيره أنا + +349 +00:32:05,240 --> 00:32:09,300 +فاهم أيش اللي بعمل بقولك صحتي انا لما بشرح بشرح + +350 +00:32:09,300 --> 00:32:14,400 +لمينلكل واحد فيكوا في حياته انه ي .. انتبه مانتبهش + +351 +00:32:14,400 --> 00:32:18,020 +أقل اشي ميبقى شايف من وين جاية انت لو مابتحل بتحل + +352 +00:32:18,020 --> 00:32:23,080 +لمين؟ لحالك فانت ايش بترتاح و بتمشي معاه انا ما .. + +353 +00:32:23,080 --> 00:32:26,560 +مافيش مشكلة فيا كويس هيك؟ + +354 +00:32:33,410 --> 00:32:39,110 +أه لأنك إنت لما تدخل أول حاجة مش بدي أدخل ال input + +355 +00:32:39,110 --> 00:32:44,170 +بإيش بدي أساوي فيه بدي أدخل لما يكون low هيعطيني + +356 +00:32:44,170 --> 00:32:47,770 +ال saturation صح؟ لما أظل أزود في ال input هل س .. + +357 +00:32:47,770 --> 00:32:54,010 +هل هال داله saturation؟ لما + +358 +00:32:54,010 --> 00:33:00,780 +أوصل لدرجة معينة في ال input أكتر من ال vihيعني + +359 +00:33:00,780 --> 00:33:04,320 +هيحول ليش؟ لإن انت تطلع عندى، عند ال range خمسة + +360 +00:33:04,320 --> 00:33:10,240 +volt ال Vih قداشر؟ one point four طب أنا لو وصلت + +361 +00:33:10,240 --> 00:33:14,600 +اتنين اتنين و نص، هل هيظلوا ال saturation هات؟ لأ + +362 +00:33:40,140 --> 00:33:45,460 +رقميا مش هتفرق كتيرليش؟ لأن ال point 7 و ال point + +363 +00:33:45,460 --> 00:33:52,280 +6 grab لبعض، بس من ناحية المفهوم اختلفت كتير و + +364 +00:33:52,280 --> 00:33:58,100 +اختلفت ال I لإنك انت بدك الان جيب علاقة بين .. بدك + +365 +00:33:58,100 --> 00:34:03,140 +تجيب ال I C اللي هي .. بدك تعرف قداش sigma، مظبوط؟ + +366 +00:34:03,140 --> 00:34:06,860 +بدك تفرض sigma من عندك، و في حاجات كتير صارت في + +367 +00:34:06,860 --> 00:34:13,810 +حدود ال unknownفأسهل .. أسهل في .. انك تمشي على ال + +368 +00:34:13,810 --> 00:34:17,010 +.. من ناحية .. من ناحية ال concept تبقى مشيها صح + +369 +00:34:17,010 --> 00:34:22,130 +لأنه طبيعي انا لما نزود ال input في وضع ال high مش + +370 +00:34:22,130 --> 00:34:25,650 +هيكون .. هيكون بختلف عنه في ال .. ال transistor في + +371 +00:34:25,650 --> 00:34:30,370 +وضع اللوة وإلا لما نتكلم عن ال fan out الفكرة + +372 +00:34:30,370 --> 00:34:35,510 +تبعتي مش هتظبط ان اقول output في وضع ال high عندي + +373 +00:34:35,510 --> 00:34:38,270 +N بتساوي infinity هتبطل N تساوي infinity + +374 +00:34:41,450 --> 00:34:47,610 +ماشي؟ طيب الآن احنا غطينا راجعنا ال VTC و راجعنا + +375 +00:34:47,610 --> 00:34:51,810 +ال fan out ايش رقم تلاتة اللي بديها؟ بدي ال power + +376 +00:34:51,810 --> 00:34:55,330 +dissipation ال average power dissipation فلما + +377 +00:34:55,330 --> 00:35:00,730 +اتكلم عن ال average power dissipation بدي اتكلم في + +378 +00:35:00,730 --> 00:35:03,670 +وضع ال high و وضع ال low ايش عندي؟ + +379 +00:35:21,460 --> 00:35:28,120 +عشان ارجع الدائرة زي مكانها ونشوف ايش بطلع عندى اي + +380 +00:35:28,120 --> 00:35:28,880 +جزئية + +381 +00:35:53,500 --> 00:36:00,680 +عندي ال power dissipation PCC average بده تساوي + +382 +00:36:00,680 --> 00:36:07,400 +ICC في حالة ال output high زائد ال ICC في حالة ال + +383 +00:36:07,400 --> 00:36:16,780 +output low على اتنين مضروبة في VCC طيب هذا بقول + +384 +00:36:16,780 --> 00:36:23,760 +التاليال ICC ايش وضعه ال ICC بدي ساوي التيارات + +385 +00:36:23,760 --> 00:36:27,640 +التلاتة اللي جايات عندها هاي واحد اتنين تلاتة بدي + +386 +00:36:27,640 --> 00:36:37,600 +ساوي ICC او بدي ساوي IRB زائد + +387 +00:36:37,600 --> 00:36:43,400 +IRC زائد IRCB + +388 +00:36:43,400 --> 00:36:50,450 +هاي التيارات واحدهاو واحد ها و واحد ها في حالة ال + +389 +00:36:50,450 --> 00:36:55,710 +power dissipation طيب كيف بدي اجيب ال ها بدي اطلع + +390 +00:36:55,710 --> 00:36:59,830 +في حالة اللي كتبناها هنا اللي شيلناها هنا في حالة + +391 +00:36:59,830 --> 00:37:03,550 +ال output low و في حالة ال output high ناخد في + +392 +00:37:03,550 --> 00:37:09,860 +حالة ال output low ايش بدي يطلع عندك هاي ICCفي + +393 +00:37:09,860 --> 00:37:15,820 +حالة output low بدي ساوي IRB في حالة output low + +394 +00:37:15,820 --> 00:37:23,860 +زائد IRC في حالة output low زائد IRCB في حالة + +395 +00:37:23,860 --> 00:37:24,780 +output low + +396 +00:37:34,730 --> 00:37:38,610 +الـ power dissipation لأ مدك تاخد حاجة واحدة تحط + +397 +00:37:38,610 --> 00:37:44,570 +ال VCC بيساوي Zero وتشوف من هات لوين رايحة الاتجاه + +398 +00:37:44,570 --> 00:37:48,610 +انت بتتذكر اخدته بالدوائر واحد ايش ال + +399 +00:37:48,610 --> 00:37:52,330 +superposition فانت لما تجيب ال power dissipation + +400 +00:37:52,330 --> 00:37:56,950 +ال power dissipation لدائرة ككل مدك تجيب ال VCC و + +401 +00:37:56,950 --> 00:38:01,450 +ال VEE تبعات ال source اللي مدك تحطه هات و أي + +402 +00:38:01,450 --> 00:38:06,290 +source تاني موجودأيوة و تشوف ايش الاتجاهات اللي + +403 +00:38:06,290 --> 00:38:13,850 +بتمشي فيها كل source لوحدها طيب الان لما نتكلم في + +404 +00:38:13,850 --> 00:38:17,030 +ال hype ده تطلع عندك في وضع ال saturation ال + +405 +00:38:17,030 --> 00:38:21,290 +output له ايش قولنا هذا هذا اللي هنوضعه خليني حتى + +406 +00:38:21,290 --> 00:38:28,370 +هنعلم بالأحمر هنوضعه off هذا + +407 +00:38:28,370 --> 00:38:35,170 +وضعه saturation هنوضعه saturationهنا وضعه في + +408 +00:38:35,170 --> 00:38:39,550 +reverse active فنشوف ايش التيارات اللي عندي اول + +409 +00:38:39,550 --> 00:38:44,310 +تيار اللي جبته هنا ابدا من اخر اشي عملناها تيار + +410 +00:38:44,310 --> 00:38:51,730 +اللي هنا ايش بدي اساوي طيب + +411 +00:38:51,730 --> 00:38:55,030 +بدي امشي من هنا هاي اللي عندي بدي اجيب ال voltage + +412 +00:38:55,030 --> 00:38:59,410 +هنا ال voltage هنا ايش بدي اساويبدي ساوي point 7 + +413 +00:38:59,410 --> 00:39:03,430 +اللي هان زائد point 8 اللي هان زائد point 8 اللي + +414 +00:39:03,430 --> 00:39:08,450 +هان اعطاني ال 2.3 بدي اقول الخمسة ناقص ال 2.3 اللي + +415 +00:39:08,450 --> 00:39:15,490 +هان على ال RB اللي موجود عندى يعني بدي اقول هى IRB + +416 +00:39:15,490 --> 00:39:21,930 +في حالة ال output low بدي ساوي VCC minus VBC في ال + +417 +00:39:21,930 --> 00:39:28,710 +reverse activeلل I عشان تشوفوها minus VBE لل S + +418 +00:39:28,710 --> 00:39:39,010 +saturation minus VBE لل O في ال saturation على ال + +419 +00:39:39,010 --> 00:39:44,910 +Rb كويس ايه؟ شايفين هذه ولا في حد ماشوفتهاش؟ هذه + +420 +00:39:44,910 --> 00:39:50,780 +اللي عملناها لسه قبل شويةالتيار اللي هان بدي ساوي + +421 +00:39:50,780 --> 00:39:54,240 +إذا جبت ال voltage اللي هان بدي أقول خمسة ناقص ال + +422 +00:39:54,240 --> 00:39:57,760 +voltage اللي هان على ال RB بيعطيني التيار اللي هان + +423 +00:39:57,760 --> 00:40:00,940 +طب ال voltage اللي هان إيش بدي ساوي ال point سبعة + +424 +00:40:00,940 --> 00:40:04,920 +تبعت ال reverse active زائد ال point تمانية تبعت + +425 +00:40:04,920 --> 00:40:07,400 +ال saturation هاد زائد ال point تمانية تبعت ال + +426 +00:40:07,400 --> 00:40:13,900 +saturation هاد أعطتني التيار اللي هان واضحة هذهطيب + +427 +00:40:13,900 --> 00:40:18,160 +الليهان ايش عندى ال VCC نقص الليهان الليهان ايش هو + +428 +00:40:18,160 --> 00:40:24,060 +ال point 8 للليهان زاد ال point 2 على ال RC هذا هي + +429 +00:40:24,060 --> 00:40:30,460 +ال IRC في حالة ال output له ايش بدها تساوي VCC + +430 +00:40:30,460 --> 00:40:39,880 +minus VBE لل O في وضع ال saturation minus VCE لل S + +431 +00:40:39,880 --> 00:40:42,420 +هو حالة ال saturation على + +432 +00:40:46,880 --> 00:40:56,860 +التالتة ايش بتساوي؟ Zero لأن هذا وضعه off IRC + +433 +00:40:56,860 --> 00:41:04,140 +B equal output low equal zero لأنه نعمل التاني + +434 +00:41:04,140 --> 00:41:08,440 +لحالة مين؟الـ output high في حالة ال output high + +435 +00:41:08,440 --> 00:41:15,260 +هاي ICC output high بدي ساوي IRB في حالة ال output + +436 +00:41:15,260 --> 00:41:23,380 +high زائد IRC في حالة ال output high زائد IRCB في + +437 +00:41:23,380 --> 00:41:27,140 +حالة ال output high يعني لما يكون عند ال output + +438 +00:41:27,140 --> 00:41:32,660 +هنا high ايش بدي يكون وضع الترانزستور هذا هذول + +439 +00:41:32,660 --> 00:41:33,340 +هيغيروا + +440 +00:41:36,640 --> 00:41:40,620 +الـ output هنا هي high بدي اعتبره هذا ايش بدي يكون + +441 +00:41:40,620 --> 00:41:46,840 +low في ال low هذا ايش بدي يصير saturation ال + +442 +00:41:46,840 --> 00:41:55,040 +saturation هذا ايش وضعه هذا off وهذا ايش off وهذا + +443 +00:41:55,040 --> 00:42:04,180 +forward active ووضع ال off ايش بقدر اقول كويس؟ + +444 +00:42:04,970 --> 00:42:09,750 +شكل الدائرة صار لطيف قداش + +445 +00:42:09,750 --> 00:42:14,590 +اللي عندي هذي بساوي ال I اللي هذ و ال I اللي هذ + +446 +00:42:14,590 --> 00:42:20,070 +شايف محسنها ايش + +447 +00:42:20,070 --> 00:42:26,070 +صار اللي بديها اللي هذ اللي هذ وين الاتجاه تبعه + +448 +00:42:26,070 --> 00:42:31,410 +مظبوط هذ بدي ساوي هذ I + +449 +00:42:34,540 --> 00:42:42,180 +Rb في حالة output type دي ساوي Vcc minus Vbe لل I + +450 +00:42:42,180 --> 00:42:49,360 +في حالة saturation minus Vin low وحط اللي بدك يجيه + +451 +00:42:49,360 --> 00:42:56,100 +على ال Rb وخلصت + +452 +00:42:56,100 --> 00:42:57,000 +المسألة + +453 +00:43:04,220 --> 00:43:11,340 +صعبة هذه؟ الخطوات هنا بنعيد هنا بشكل كبير ماضالش + +454 +00:43:11,340 --> 00:43:17,020 +اشي مش يعني مجهول هنا في هذا ال .. في اللي بنشرحه + +455 +00:43:17,020 --> 00:43:22,880 +الخطوات واحدة واحدة واحدة واحدة بنمشي فيها ايش + +456 +00:43:22,880 --> 00:43:32,680 +رأيكم؟ فاهمينها؟ طيب نيجي لحاجة تانية يعني هي انا + +457 +00:43:32,680 --> 00:43:33,480 +بدا .. + +458 +00:43:36,620 --> 00:43:42,300 +لأ مش هدخل يوملكم على عشرة هنخلّيه بس لأن .. لأن + +459 +00:43:42,300 --> 00:43:47,760 +اللي بدنا يهاشي التالي المطلوب منكم انه قبل ما نصل + +460 +00:43:47,760 --> 00:43:52,540 +عشرة تبقوا فاهمين سبعة كويس لإن انت فاهمها معناته + +461 +00:43:52,540 --> 00:43:58,440 +عشرة بتصير مش .. مش هالغلبة اللي بنتغلبها في هذا + +462 +00:43:58,440 --> 00:44:04,460 +المجال طيب السؤال اللي بدي أسأله في الدائرة اللي + +463 +00:44:04,460 --> 00:44:11,760 +عندي هناال VTC عرفناها و ال fan out عرفناها و ال + +464 +00:44:11,760 --> 00:44:17,600 +power dissipation يعني اتحدد بشكل كبير وين ممكن + +465 +00:44:17,600 --> 00:44:22,820 +اغلط هذا السؤال و المعادلات مسموح ادخلها على + +466 +00:44:22,820 --> 00:44:27,400 +الامتحان ايش هذي انت بدك تعرف تستخدم ال calculator + +467 +00:44:27,400 --> 00:44:32,880 +و القوانين عندك مابديها الشطارةفالأسئلة اللي زيك + +468 +00:44:32,880 --> 00:44:36,020 +انت كل اللي بدك هي تعرف ان هذا ال gate اللي قدامك + +469 +00:44:36,020 --> 00:44:41,560 +هي ال non gate اللي انت عارفها لختها وعارف تطبقها + +470 +00:44:41,560 --> 00:44:46,060 +بشكل عارف تطبق القوانين بشكل مباشر لأ بقولك أعملها + +471 +00:44:46,060 --> 00:44:50,000 +derivation ولا بقول أي إشي في الامتحان بس الأصل + +472 +00:44:50,000 --> 00:44:55,520 +أنا ببقى فاهم إيش اللي بعمل يعني في هذه القضية ومش + +473 +00:44:55,520 --> 00:45:00,440 +صعبة أوصل لهاعادة الأسئلة اللي زي هيكها دي زي + +474 +00:45:00,440 --> 00:45:05,240 +الاسم تباحة يقولك cookbook، cookbook عندي كل إشي + +475 +00:45:05,240 --> 00:45:11,020 +بتباحة بوصل للأسئلة عادة الوقت بحها fixed الأسئلة + +476 +00:45:11,020 --> 00:45:16,950 +اللي بدها تفكير إجابتها قصيرةالإجابة تبعتك اللى + +477 +00:45:16,950 --> 00:45:22,190 +بتاخدها مش طويلة يعني انت زى ما لاحظنا سابقا لما + +478 +00:45:22,190 --> 00:45:27,130 +حطينا علك و قولتلك هى مسألة على سبيل المثال قبل + +479 +00:45:27,130 --> 00:45:30,990 +شوية عطيتك quiz لعند البنات على chapter 4 و + +480 +00:45:30,990 --> 00:45:35,910 +قولتلهم هى السؤال و انت شوفوه انتقدت ل quiz + +481 +00:45:45,240 --> 00:45:49,340 +مش فاهم شوية + +482 +00:45:49,340 --> 00:45:50,740 +المدرسة اللي بيعملها + +483 +00:46:21,290 --> 00:46:28,970 +طلع هاي السؤال اللي أخدوه، إيش السؤال اللي بيسأل؟ + +484 +00:46:28,970 --> 00:46:34,150 +هاي ال base ما هي مش مارو شبوكة على إشي السؤال + +485 +00:46:34,150 --> 00:46:39,590 +اللي بيسأل بهذه الطريقة، بدي ال Vb و ال Ve لكل + +486 +00:46:39,590 --> 00:46:46,700 +واحدة من هدولهذا السؤال بده ايش؟ بده تفكير، هذا + +487 +00:46:46,700 --> 00:46:52,680 +السؤال اللي بقول عادة نغلبش معاكم فيه، هو سؤال + +488 +00:46:52,680 --> 00:46:55,660 +موجود وعالمك شوف من مين أحكيلكوا إياه، هيجيلكوا + +489 +00:46:55,660 --> 00:46:59,940 +سؤال من هذا القبيل، مافيش أشي مخبأ في هذا العمل، + +490 +00:46:59,940 --> 00:47:01,180 +القاعد + +491 +00:47:03,150 --> 00:47:07,470 +هو ليش بيقولك هذا علمك شوف هذا بدياك تظل تحاول في + +492 +00:47:07,470 --> 00:47:10,730 +كل الأسئلة اللي بتشوفه من هذا القبيل بتصير عندك + +493 +00:47:10,730 --> 00:47:16,330 +القدرة انك بعد هيك اي سؤال اجالك او هو بركز على ال + +494 +00:47:16,330 --> 00:47:19,430 +chapter تلاتة بقولنا ال mode of operation اذا انت + +495 +00:47:19,430 --> 00:47:22,470 +عارف ال mode of operation اللي راجعناه انا اليوم + +496 +00:47:22,470 --> 00:47:28,450 +معناته هذا السؤال تحصيل حصل بيصير الان هذا ايش + +497 +00:47:28,450 --> 00:47:30,290 +بنبدأ فيه اول خطوة + +498 +00:47:33,940 --> 00:47:40,280 +بحدد الإشارات التابعاتي plus minus plus minus plus + +499 +00:47:40,280 --> 00:47:49,140 +minus plus minus plus minus plus minus plus minus + +500 +00:47:49,140 --> 00:47:53,320 +plus minus plus minus plus minus plus minus plus + +501 +00:47:53,320 --> 00:47:58,020 +minus plus minus plus minus plus minus plus minus + +502 +00:47:58,020 --> 00:48:00,800 +plus minus plus minus plus minus plus minus plus + +503 +00:48:00,800 --> 00:48:00,900 +minus plus minus plus minus plus minus plus minus + +504 +00:48:00,900 --> 00:48:00,940 +plus minus plus minus plus minus plus minus plus + +505 +00:48:00,940 --> 00:48:00,980 +minus plus minus plus minus plus minus plus minus + +506 +00:48:00,980 --> 00:48:02,040 +minus plus minus plus minus plus minus plusعندى + +507 +00:48:02,040 --> 00:48:06,920 +هنا ال voltage كان zero هذه قداش اللى عندى point + +508 +00:48:06,920 --> 00:48:11,260 +تمانية point تمانية زائد zero هى point تمانية هى + +509 +00:48:11,260 --> 00:48:18,000 +خلصت واحد اتنين تبعت هذه صح الان هنا قداش point + +510 +00:48:18,000 --> 00:48:21,920 +اتنين point اتنين هى النقطة التالتة اللى هنا قداشه + +511 +00:48:21,920 --> 00:48:25,840 +بدى يكون هذا ايش وضعه reverse + +512 +00:48:28,620 --> 00:48:33,400 +هذا ال reverse جدّيش بده يكون عندى .. ال junction + +513 +00:48:33,400 --> 00:48:37,380 +هذي إيش بدها تكون ال junction هذي إيش بدها تكون + +514 +00:48:37,380 --> 00:48:42,460 +بدها تكون reverse bias reverse bias يعني اللي عندى + +515 +00:48:42,460 --> 00:48:47,720 +drop هذا أقل من point 7 إذا هذه point 2 و هذي بدها + +516 +00:48:47,720 --> 00:48:55,140 +تكون بالسلب صح سلب جدّيش هذه طب سلب 3 و زاد 2 + +517 +00:48:55,140 --> 00:49:00,040 +جدّيش عندىسالب point خمسة جوابك صحيح technically + +518 +00:49:00,040 --> 00:49:04,600 +بس لو بدى اخد هاي القيمة اللى بدها تكون عندى اكبر + +519 +00:49:04,600 --> 00:49:12,140 +يعني هنا VE بدها تكون اكبر من سالب ايش point خمسة + +520 +00:49:12,140 --> 00:49:20,280 +point ستة point سالب نص الان نص و اتنين جداش.7 + +521 +00:49:20,280 --> 00:49:24,340 +يعني القيمة اللي عندي هنا ل VE واحد اللي هتكون + +522 +00:49:24,340 --> 00:49:28,160 +أكبر من هذه القيمة لو كانت أكبر بتصير عندي هذه + +523 +00:49:28,160 --> 00:49:32,580 +reverse يبقى وصلت لل reverse active الآن ال + +524 +00:49:32,580 --> 00:49:38,180 +voltage اللي هنا قداشي بدي يكون؟ هاي point اتنين + +525 +00:49:38,180 --> 00:49:41,100 +اللي عندي وهذه الإشارة بال positive ولا ال + +526 +00:49:41,100 --> 00:49:47,000 +negative؟ بال negative ده اترح من هذه ايش بده يعني + +527 +00:49:47,000 --> 00:49:53,880 +تصير عندي؟هذه سالب نص طيب هذه سالب نص هذه قداش؟ + +528 +00:49:53,880 --> 00:49:57,040 +سالب واحد و سبعة و نص و نص و نص و نص و نص و نص و + +529 +00:49:57,040 --> 00:49:58,120 +نص و نص و نص و نص و نص و نص و نص و نص و نص و نص و + +530 +00:49:58,120 --> 00:49:59,800 +نص و نص و نص و نص و نص و نص و نص و نص و نص و نص و + +531 +00:49:59,800 --> 00:50:02,680 +نص و نص و نص و نص و نص و نص و نص و نص و نص و نص و + +532 +00:50:02,680 --> 00:50:14,820 +نص و نص و نص و نص و نص و نص و نص و نص و + +533 +00:50:14,820 --> 00:50:19,610 +نبال positive هنا بال إيش بال negative يبقى هذه + +534 +00:50:19,610 --> 00:50:24,490 +الفرق عندي عارفه point 7 بس هذه بدها تكون أعلى من + +535 +00:50:24,490 --> 00:50:30,030 +هذه ال point 7 الحين لو ضفت لل point 5 point 7 كده + +536 +00:50:30,030 --> 00:50:34,930 +هتعطيك point 2 هذا ال negative دايما بيكون الأكتر + +537 +00:50:34,930 --> 00:50:41,170 +هذا خزنها في الداكرة عندك إذا خزنتها في الداكرة + +538 +00:50:42,310 --> 00:50:45,810 +بتعرف انا اول حاجة قولتلكوا في المساقى ايش عندك + +539 +00:50:45,810 --> 00:50:52,730 +حاجتين دايما بدك تتذكرهم الدايود و اي اشي حط + +540 +00:50:52,730 --> 00:50:56,370 +الاشارات + +541 +00:50:56,370 --> 00:51:04,770 +عشان ال frame of reference يبقى تبعك وين واضح الان + +542 +00:51:04,770 --> 00:51:09,730 +انا عندى ككل في ال reverse active ايش بدى يكون + +543 +00:51:09,730 --> 00:51:14,810 +عندىووضع الـ Reverse Active هذه بدها تكون reverse + +544 +00:51:14,810 --> 00:51:24,130 +biased وهذه بدها تكون forward biased + +545 +00:51:24,130 --> 00:51:27,490 +الـ forward biased هذه بدها تكون عندها drop point + +546 +00:51:27,490 --> 00:51:32,170 +7 هذه أكبر من هذه في ال reverse هذه بدها تكون أقل + +547 +00:51:32,170 --> 00:51:36,870 +من point 7 هذه + +548 +00:51:36,870 --> 00:51:42,580 +positive وهذه negative معناته ان هذه بدها تكوناللي + 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{"id": 26, "seek": 72893, "start": 716.27, "end": 728.93, "text": "الان ال output عندي بطلع على ال bitline و ال bitline complement فبطلع لي حاجتين هذه ال bitline و ال bitline complement هذا في ال S رقم", "tokens": [6027, 7649, 2423, 5598, 18871, 16254, 4724, 9566, 1211, 3615, 15844, 2423, 857, 1889, 4032, 2423, 857, 1889, 17103, 6156, 3555, 9566, 1211, 3615, 32239, 11331, 26108, 2655, 9957, 29538, 2423, 857, 1889, 4032, 2423, 857, 1889, 17103, 23758, 8978, 2423, 318, 12602, 4587, 2304], "avg_logprob": -0.4582201041605162, "compression_ratio": 1.5327868852459017, "no_speech_prob": 1.4901161193847656e-06, "words": [{"start": 716.2700000000001, "end": 717.19, "word": "الان", "probability": 0.5250244140625}, {"start": 717.19, "end": 717.35, "word": " ال", "probability": 0.2890625}, {"start": 717.35, "end": 717.87, "word": " output", "probability": 0.869140625}, {"start": 717.87, "end": 718.35, "word": " عندي", "probability": 0.6239013671875}, {"start": 718.35, "end": 718.79, "word": " 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ال bit line و ال compliments بتاعتها على ال bit line compliments كويس هيك؟ طيب ايش فيه ممكن؟ الان لو انا بده اخزن اي حاجة هنا هذه لازم يكون ايش عندى high يعني لو انا جيت رسمت هذه ال bit line", "tokens": [6027, 9952, 13672, 1829, 47525, 3224, 1975, 9778, 11622, 1863, 3224, 8978, 21136, 1211, 4032, 2423, 35468, 6055, 3555, 3615, 3224, 4032, 4724, 9566, 1211, 3615, 2423, 9952, 9673, 9778, 11622, 1863, 43242, 7578, 15844, 2423, 857, 1622, 4032, 2423, 35468, 39894, 995, 34268, 11296, 15844, 2423, 857, 1622, 35468, 9122, 45865, 3794, 39896, 4117, 22807, 23032, 1829, 3555, 1975, 1829, 8592, 8978, 3224, 3714, 43020, 22807, 2423, 7649, 45164, 1975, 8315, 47525, 3224, 1975, 9778, 11622, 1863, 1975, 1829, 11331, 26108, 3660, 34105, 29538, 5296, 31377, 2304, 7251, 30544, 1975, 1829, 8592, 43242, 7578, 1090, 37495, 22653, 45164, 1975, 8315, 10874, 36081, 12602, 38251, 2655, 29538, 2423, 857, 1622], "avg_logprob": -0.25126688115231627, "compression_ratio": 1.9631336405529953, "no_speech_prob": 0.0, 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لو بدي اجي ارسمهم ايه كيف بدي ارسمهم؟ بدي اجي اطلعها", "tokens": [6027, 39184, 1349, 1622, 6225, 3555, 9640, 3660, 18871, 7830, 13672, 1829, 39896, 13672, 1829, 1975, 8315, 5296, 15042, 4724, 16254, 1975, 39648, 8032, 47302, 2423, 499, 8032, 47302, 2423, 499, 35468, 8032, 47302, 2423, 261, 287, 13672, 1829, 3714, 9566, 1211, 37746, 9154, 3224, 1975, 1829, 3224, 2423, 1225, 4032, 2423, 1225, 35468, 2423, 4675, 8032, 47302, 2423, 4675, 4032, 2423, 1225, 35468, 13672, 1829, 3714, 9778, 11622, 1863, 8978, 6225, 4117, 3794, 11296, 13672, 1829, 1975, 8315, 45164, 4724, 16254, 1975, 7435, 1829, 1975, 2288, 38251, 16095, 1975, 1829, 3224, 9122, 33911, 4724, 16254, 1975, 2288, 38251, 16095, 22807, 4724, 16254, 1975, 7435, 1829, 1975, 9566, 1211, 3615, 11296], "avg_logprob": -0.38616072040583405, "compression_ratio": 2.155440414507772, "no_speech_prob": 0.0, "words": [{"start": 801.97, "end": 802.29, "word": "الـ", "probability": 0.4542236328125}, {"start": 802.29, "end": 802.53, "word": " word", "probability": 0.8798828125}, {"start": 802.53, "end": 802.83, "word": " line", "probability": 0.6875}, {"start": 802.83, "end": 803.27, "word": " عبارة", "probability": 0.985595703125}, {"start": 803.27, "end": 803.57, "word": " عن", "probability": 0.9970703125}, {"start": 803.57, "end": 804.17, "word": " clock", "probability": 0.1993408203125}, {"start": 804.17, "end": 805.01, "word": " اللي", "probability": 0.57098388671875}, {"start": 805.01, "end": 805.27, "word": " هي", "probability": 0.261474609375}, {"start": 805.27, "end": 805.97, "word": " اللي", "probability": 0.59161376953125}, {"start": 805.97, "end": 806.17, "word": " انا", "probability": 0.5257568359375}, {"start": 806.17, "end": 806.35, "word": " لما", "probability": 0.644775390625}, {"start": 806.35, "end": 806.55, "word": " بدي", "probability": 0.333984375}, {"start": 806.55, "end": 806.81, "word": " اقول", "probability": 0.836669921875}, {"start": 806.81, "end": 807.57, "word": " هاي", "probability": 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memory", "probability": 0.2130126953125}, {"start": 820.41, "end": 821.43, "word": " و", "probability": 0.77587890625}, {"start": 821.43, "end": 821.57, "word": " ال", "probability": 0.8291015625}, {"start": 821.57, "end": 821.77, "word": " mom", "probability": 0.96630859375}, {"start": 821.77, "end": 822.57, "word": " compliments", "probability": 0.93310546875}, {"start": 822.57, "end": 824.47, "word": " اللي", "probability": 0.898193359375}, {"start": 824.47, "end": 825.07, "word": " مخزن", "probability": 0.9830322265625}, {"start": 825.07, "end": 825.23, "word": " في", "probability": 0.93212890625}, {"start": 825.23, "end": 825.79, "word": " عكسها", "probability": 0.9813232421875}, {"start": 825.79, "end": 826.25, "word": " اللي", "probability": 0.7064208984375}, {"start": 826.25, "end": 826.49, "word": " انا", "probability": 0.8525390625}, {"start": 826.49, "end": 826.59, "word": " لو", "probability": 0.59765625}, {"start": 826.59, "end": 826.79, "word": " بدي", "probability": 0.7061767578125}, {"start": 826.79, "end": 827.13, "word": " اجي", "probability": 0.615966796875}, {"start": 827.13, "end": 827.73, "word": " ارسمهم", "probability": 0.901611328125}, {"start": 827.73, "end": 828.03, "word": " ايه", "probability": 0.783203125}, {"start": 828.03, "end": 828.21, "word": " كيف", "probability": 0.77099609375}, {"start": 828.21, "end": 828.39, "word": " بدي", "probability": 0.779541015625}, {"start": 828.39, "end": 828.95, "word": " ارسمهم؟", "probability": 0.84892578125}, {"start": 828.95, "end": 829.09, "word": " بدي", "probability": 0.909912109375}, {"start": 829.09, "end": 829.25, "word": " اجي", "probability": 0.9314778645833334}, {"start": 829.25, "end": 829.85, "word": " اطلعها", "probability": 0.8505859375}], "temperature": 1.0}, {"id": 30, "seek": 85850, "start": 830.64, "end": 858.5, "text": "بدي ابدأ ب initial value ال initial اللي بدكوا ابدأ فيه high ولا low للممory اختاروا واحدة ايش بدكوا يا high يا low low high اللي في النص high و اللي هيه طيب خلينا ناخد الأصعب ال high هي ال high اللي انا اتطلع عندى و هي هنا low", "tokens": [3555, 16254, 1975, 44510, 10721, 4724, 5883, 2158, 2423, 5883, 13672, 1829, 47525, 4117, 14407, 1975, 44510, 10721, 8978, 3224, 1090, 49429, 2295, 5296, 19528, 2304, 827, 1975, 46456, 9640, 14407, 36764, 24401, 3660, 1975, 1829, 8592, 47525, 4117, 14407, 35186, 1090, 35186, 2295, 2295, 1090, 13672, 1829, 8978, 28239, 9381, 1090, 4032, 13672, 1829, 39896, 3224, 23032, 1829, 3555, 16490, 20292, 8315, 8717, 47283, 3215, 16247, 9381, 3615, 3555, 2423, 1090, 39896, 2423, 1090, 13672, 1829, 1975, 8315, 1975, 2655, 9566, 1211, 3615, 43242, 7578, 4032, 39896, 34105, 2295], "avg_logprob": -0.35920328818834746, "compression_ratio": 1.8125, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 830.64, "end": 830.96, "word": "بدي", "probability": 0.374267578125}, {"start": 830.96, "end": 831.22, "word": " ابدأ", "probability": 0.7556966145833334}, {"start": 831.22, "end": 831.32, "word": " ب", "probability": 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النص", "probability": 0.879638671875}, {"start": 847.76, "end": 848.0, "word": " high", "probability": 0.91943359375}, {"start": 848.0, "end": 848.18, "word": " و", "probability": 0.62353515625}, {"start": 848.18, "end": 848.22, "word": " اللي", "probability": 0.6343994140625}, {"start": 848.22, "end": 848.56, "word": " هيه", "probability": 0.300537109375}, {"start": 848.56, "end": 849.04, "word": " طيب", "probability": 0.8429361979166666}, {"start": 849.04, "end": 849.74, "word": " خلينا", "probability": 0.786376953125}, {"start": 849.74, "end": 850.0, "word": " ناخد", "probability": 0.9861653645833334}, {"start": 850.0, "end": 850.58, "word": " الأصعب", "probability": 0.7347412109375}, {"start": 850.58, "end": 851.0, "word": " ال", "probability": 0.943359375}, {"start": 851.0, "end": 851.32, "word": " high", "probability": 0.92724609375}, {"start": 851.32, "end": 853.98, "word": " هي", "probability": 0.335693359375}, {"start": 853.98, "end": 854.14, "word": " ال", "probability": 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"tokens": [9566, 1211, 3615, 43242, 7578, 11933, 1829, 8592, 13672, 7578, 4724, 1829, 9381, 13546, 8032, 7578, 8032, 3215, 7578, 20328, 9640, 8978, 3224, 6055, 17082, 1829, 13546, 8978, 33688, 8592, 9640, 3660, 3714, 19913, 3555, 2407, 9566, 4724, 3794, 8032, 3215, 7578, 5296, 3794, 3224, 1975, 2655, 1863, 4587, 8592, 45164, 4724, 15040, 5016, 4587, 3224, 33599, 4724, 7435, 7578, 5551, 15040, 5016, 4587, 4032, 9957, 8978, 8032, 3215, 7578, 9673, 1863, 9566, 28671, 6024, 48506, 34105, 20328, 9640, 6055, 17082, 1829, 13546, 34105, 6055, 17082, 1829, 13546, 34105, 13672, 7578, 43242, 7578, 8978, 3224, 6055, 17082, 1829, 13546, 34105], "avg_logprob": -0.20792078558761296, "compression_ratio": 1.9506172839506173, "no_speech_prob": 0.0, "words": [{"start": 860.72, "end": 861.14, "word": "طلع", "probability": 0.82373046875}, {"start": 861.14, "end": 861.42, "word": " عندى", "probability": 0.7373046875}, {"start": 861.42, "end": 861.58, "word": " إيش", "probability": 0.7645670572916666}, 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"word": " صار", "probability": 0.981689453125}, {"start": 876.32, "end": 876.98, "word": " تغيير", "probability": 0.925537109375}, {"start": 876.98, "end": 880.82, "word": " هنا", "probability": 0.86767578125}, {"start": 880.82, "end": 881.5, "word": " تغيير", "probability": 0.9423828125}, {"start": 881.5, "end": 883.84, "word": " هنا", "probability": 0.91650390625}, {"start": 883.84, "end": 884.02, "word": " اللى", "probability": 0.94873046875}, {"start": 884.02, "end": 884.58, "word": " عندى", "probability": 0.8232421875}, {"start": 884.58, "end": 885.78, "word": " فيه", "probability": 0.763916015625}, {"start": 885.78, "end": 886.4, "word": " تغيير", "probability": 0.982177734375}, {"start": 886.4, "end": 888.38, "word": " هنا", "probability": 0.96435546875}], "temperature": 1.0}, {"id": 32, "seek": 91670, "start": 889.72, "end": 916.7, "text": "التغيير في الإشارة طلع عندى هنا بما أن التغيير موجود بس ال wordline ايش وضعه لو بلاحقش حاجة بضلنى ماشي على ما أنا عليه لحد ديت ايش ال wordline لما يصير اين هاي ال wordline هاي ايش بطلع عندى هنا ال output اللى عندى ايش وضعه ال pl هاي بضلنى ماشي معاه اللى أنا ماشيت معاه", "tokens": [6027, 2655, 17082, 1829, 13546, 8978, 33688, 8592, 9640, 3660, 23032, 1211, 3615, 43242, 7578, 34105, 4724, 15042, 14739, 16712, 17082, 1829, 13546, 3714, 29245, 23328, 4724, 3794, 2423, 1349, 1889, 1975, 1829, 8592, 4032, 11242, 3615, 3224, 45164, 4724, 15040, 5016, 4587, 8592, 11331, 26108, 3660, 4724, 11242, 1211, 1863, 7578, 3714, 33599, 1829, 15844, 19446, 41850, 47356, 5296, 24401, 11778, 36081, 1975, 1829, 8592, 2423, 1349, 1889, 5296, 15042, 7251, 9381, 13546, 1975, 9957, 8032, 47302, 2423, 1349, 1889, 8032, 47302, 1975, 1829, 8592, 4724, 9566, 1211, 3615, 43242, 7578, 34105, 2423, 5598, 13672, 7578, 43242, 7578, 1975, 1829, 8592, 4032, 11242, 3615, 3224, 2423, 499, 8032, 47302, 4724, 11242, 1211, 1863, 7578, 3714, 33599, 1829, 20449, 40294, 13672, 7578, 41850, 3714, 33599, 36081, 20449, 40294], "avg_logprob": -0.26308139534883723, 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{"start": 934.62, "end": 936.72, "word": " طلع", "probability": 0.7467447916666666}, {"start": 936.72, "end": 937.0, "word": " عندي", "probability": 0.733154296875}, {"start": 937.0, "end": 937.2, "word": " ايش", "probability": 0.8216145833333334}, {"start": 937.2, "end": 937.52, "word": " هذه", "probability": 0.484130859375}, {"start": 937.52, "end": 937.78, "word": " هنا", "probability": 0.214935302734375}, {"start": 937.78, "end": 938.04, "word": " صار", "probability": 0.718017578125}, {"start": 938.04, "end": 938.36, "word": " عندي", "probability": 0.81298828125}, {"start": 938.36, "end": 938.98, "word": " low", "probability": 0.44287109375}, {"start": 938.98, "end": 939.78, "word": " ال", "probability": 0.478271484375}, {"start": 939.78, "end": 940.0, "word": " low", "probability": 0.96630859375}, {"start": 940.0, "end": 940.24, "word": " هنا", "probability": 0.74951171875}, {"start": 940.24, "end": 940.5, "word": " مفيه", "probability": 0.6585286458333334}, {"start": 940.5, 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تغيير", "probability": 0.9686279296875}, {"start": 955.81, "end": 956.23, "word": " عندى", "probability": 0.942138671875}, {"start": 956.23, "end": 956.67, "word": " هنا", "probability": 0.8896484375}, {"start": 956.67, "end": 956.91, "word": " بدي", "probability": 0.822998046875}, {"start": 956.91, "end": 957.23, "word": " أصبح", "probability": 0.654541015625}, {"start": 957.23, "end": 957.61, "word": " high", "probability": 0.94189453125}, {"start": 957.61, "end": 958.47, "word": " بدي", "probability": 0.6746826171875}, {"start": 958.47, "end": 958.73, "word": " امشي", "probability": 0.894287109375}, {"start": 958.73, "end": 958.97, "word": " معاه", "probability": 0.8994140625}, {"start": 958.97, "end": 959.31, "word": " high", "probability": 0.95166015625}, {"start": 959.31, "end": 959.75, "word": " وهذا", "probability": 0.545654296875}, {"start": 959.75, "end": 960.11, "word": " تصبح", "probability": 0.7727864583333334}, {"start": 960.11, "end": 960.49, "word": " low", 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1545.6399999999958} \ No newline at end of file diff --git a/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/tQ46RIraKCI.srt b/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/tQ46RIraKCI.srt new file mode 100644 index 0000000000000000000000000000000000000000..70699eea94fae985b6a0166a6026c9f87b09c82b --- /dev/null +++ b/PL9fwy3NUQKwaZgUE02hmS5fI0wHk77Q86/tQ46RIraKCI.srt @@ -0,0 +1,2815 @@ +1 +00:00:20,550 --> 00:00:26,180 +طيب ..اليوم احنا هنتكلم على الـ transistor و + +2 +00:00:26,180 --> 00:00:30,500 +الـ transistor و transistor logic + +3 +00:00:30,500 --> 00:00:36,020 +اللي هو باختصار TTL، إذا بتلاحظوا في المختبرات معظم + +4 +00:00:36,020 --> 00:00:40,240 +القطع اللي بتستخدموها إيش من نوعية؟ إيش الـ TTL + +5 +00:00:40,240 --> 00:00:49,080 +families؟ سواء الـ OR، الـ NAND، الـ NOR، الـ inverter، الـ + +6 +00:00:49,080 --> 00:00:54,130 +AND، الـ NAND، كلها هتلاقيها من هذه النوعية، السبب إنها + +7 +00:00:54,130 --> 00:00:59,290 +عاشت فترات طويلة، في عندنا نوعين منها: نوع تجاري + +8 +00:00:59,290 --> 00:01:01,490 +والتجاري + +9 +00:01:01,490 --> 00:01:04,070 +والتجاري + +10 +00:01:04,070 --> 00:01:09,170 +والتجاري + +11 +00:01:09,170 --> 00:01:10,370 +والتجاري + +12 +00:01:10,370 --> 00:01:12,370 +والتجاري + +13 +00:01:12,370 --> 00:01:13,070 +والتجاري + +14 +00:01:13,070 --> 00:01:13,310 +والتجاري + +15 +00:01:13,310 --> 00:01:14,930 +والتجاري + +16 +00:01:14,930 --> 00:01:24,870 +والتجاري + +17 +00:01:24,870 --> 00:01:32,170 +التجاري 120 درجة مئوية، الآن اللي بيميز الـ TTL family + +18 +00:01:32,170 --> 00:01:37,290 +في عندي active pull up وبعدين مصممة بشوية + +19 +00:01:37,290 --> 00:01:42,750 +protection عشان لو الطلاب مثلًا أو الـ amateur user + +20 +00:01:42,750 --> 00:01:49,370 +يقدر يستخدموها بدون أي إشكالية، هنبدأ بحاجة بسيطة + +21 +00:01:49,370 --> 00:01:52,830 +اللي هي نوصل الفكرة، بعد هيك هروح يعني اليوم + +22 +00:01:52,830 --> 00:01:57,490 +في المحاضرة، هنبدأ بالـ basic TTL inverter ودائرة بسيطة، + +23 +00:01:57,490 --> 00:02:04,560 +وده فهمتها بكون أسهل لفهم الـ standard TTL gate اليوم. + +24 +00:02:04,560 --> 00:02:11,360 +هنغطي جزئيًا حسب النشاط تبعنا، جزئيًا هنغطي الـ TTL + +25 +00:02:11,360 --> 00:02:18,740 +VTC، الـ VTC، إلها، هنغطي كمان الـ fan out والـ + +26 +00:02:18,740 --> 00:02:22,280 +power dissipation، يعني + +27 +00:02:23,250 --> 00:02:29,150 +من اليوم لليوم الثاني هندخل على، يعني اليوم الأحد + +28 +00:02:29,150 --> 00:02:34,390 +هندخل على الـ NOR والـ NAND والـ OR، فانت هتغطي الـ + +29 +00:02:34,390 --> 00:02:40,390 +inverter، هنغطي الـ NAND والـ NOR والـ OR والـ AND، هدول + +30 +00:02:40,390 --> 00:02:45,250 +هنغطيهم بشكل كامل خلال أسبوع هذا، يعني محاضرة اليوم + +31 +00:02:45,250 --> 00:02:49,730 +أسبوع الجاي، شكل الدوائر أحيانًا بتشوف شكلها كبير + +32 +00:02:49,730 --> 00:02:54,950 +ومزعج، لما تتكلم على الـ standard gate فش فيها أنت + +33 +00:02:54,950 --> 00:02:59,490 +بتغيرش فيها الـ input معروف، الـ output معروف، الـ + +34 +00:02:59,490 --> 00:03:02,950 +break points أو الـ critical voltages فيها معروفة، + +35 +00:03:02,950 --> 00:03:07,150 +أنت بتغيرش فيها، أنت كل اللي مطلوب منك تفهم كيف + +36 +00:03:07,150 --> 00:03:15,250 +بتشتغل بينما في الـ chapter اللي فات، الشكل الـ input + +37 +00:03:15,250 --> 00:03:23,330 +والـ output بتتغير بشكل كامل حسب كيف نشبك الـ VCC والـ + +38 +00:03:23,330 --> 00:03:27,130 +الله بدك تشبك مع الـ ground، والله بدك تشبك الـ + +39 +00:03:27,130 --> 00:03:30,130 +ground بدل الـ VTC، وnegative voltage، كل هذه + +40 +00:03:30,130 --> 00:03:33,270 +العوامل كانت في عندنا في الـ chapter + +41 +00:03:33,270 --> 00:03:37,850 +اللي فاتت، في الـ standard gate لأ، الشكل واضح، فهنبدأ + +42 +00:03:37,850 --> 00:03:39,470 +اليوم إن شاء الله بالـ basic + +43 +00:03:43,150 --> 00:03:48,810 +TTL inverter والـ + +44 +00:03:48,810 --> 00:03:57,730 +basic هاي عند الـ VCC، عند الـ resistor، وهذه + +45 +00:03:57,730 --> 00:04:02,830 +الشيجة اللي احنا معتمدينها، Vout، وهي الـ Q0 وهنا الـ + +46 +00:04:02,830 --> 00:04:10,850 +RC، في الشجيجة هذه هنا كان في DTL إيش عندي موجود؟ + +47 +00:04:10,850 --> 00:04:14,710 +دايود مظبوط، واحد بالشيجة هذه، واحد بالشيجة الثانية، + +48 +00:04:14,710 --> 00:04:22,770 +هنا هنستعيض منه بداله بالترانزستور، هذا بسميه QI وهذا + +49 +00:04:22,770 --> 00:04:30,970 +الـ RP وهذا الـ VN اللي عندي، شكل تبعها بيختلف عن + +50 +00:04:30,970 --> 00:04:36,210 +الأشكال اللي أنتووا متعرفين عليها، هاي عندي عشان + +51 +00:04:36,210 --> 00:04:38,990 +برضه أظل دايمًا بصحح، هاي positive negative، + +52 +00:04:38,990 --> 00:04:43,330 +positive negative positive negative، عشان أظل نقاش + +53 +00:04:43,330 --> 00:04:50,850 +الصورة متكاملة عندي ما أضيعش شيء في الطريق، الآن لو + +54 +00:04:50,850 --> 00:04:56,550 +جينا طلعنا لو كان الـ input عندي بيساوي zero، كويس؟ + +55 +00:04:56,550 --> 00:05:02,630 +هاي الـ input عندي zero، إيش وضع الترانزستور اللي + +56 +00:05:02,630 --> 00:05:05,830 +هنا؟ + +57 +00:05:05,830 --> 00:05:13,150 +شغال؟ forward؟ لأ، نيجي نتطلع عليه خطوة خطوة، كويس + +58 +00:05:13,150 --> 00:05:16,770 +هذه ليش؟ بدها شوية صبر عشان تستوعب هذه، لأن هنا + +59 +00:05:16,770 --> 00:05:21,030 +عليها بتركب two chapters فبدها تستوعب معاه شوية + +60 +00:05:21,030 --> 00:05:26,040 +شوية، طلع على هذه الـ junction، كويس؟ هاي الـ junction + +61 +00:05:26,040 --> 00:05:31,280 +اللي موجود عندي، إيش اللي موجود هنا؟ zero، إيش موجود + +62 +00:05:31,280 --> 00:05:37,160 +في الشجيجة هذه؟ جاي من الـ high، الـ VCC، فهذه هتكون + +63 +00:05:37,160 --> 00:05:41,240 +forward bias، الـ junction عندي، يعني هنا بقول عندي + +64 +00:05:41,240 --> 00:05:49,520 +الـ B E للـ I junction هنا forward bias، + +65 +00:05:57,230 --> 00:06:03,230 +كويس، الآن هذه الاحتمالين اللي موجودة هي إيش هما يا + +66 +00:06:03,230 --> 00:06:07,630 +reverse يا إما forward، يعني لو كانت هذه reverse، هذه + +67 +00:06:07,630 --> 00:06:14,150 +forward وهذه reverse، إيش الوضع؟ forward active، ولو + +68 +00:06:14,150 --> 00:06:16,650 +كانت هذه forward وهذه forward، الاحتمال هي + +69 +00:06:16,650 --> 00:06:20,870 +saturation، يعني عندي الاحتمالين لهذا الـ transistor، + +70 +00:06:20,870 --> 00:06:24,960 +يا إما يبقى في forward active mode، يا إما يبقى في + +71 +00:06:24,960 --> 00:06:30,100 +الـ saturation mode، طيب نيجي ناخد الاحتمال الأول، + +72 +00:06:30,100 --> 00:06:36,660 +أنا فيه، يعني ممكن أثبت حاجة بنفي شيء، مظبوط؟ بتاخد + +73 +00:06:36,660 --> 00:06:42,040 +الاحتمال الأول أقول هذا forward active، let's + +74 +00:06:42,040 --> 00:06:42,640 +assume، + +75 +00:06:45,660 --> 00:06:50,920 +QI وضعه forward active، في حالة الـ forward active، + +76 +00:06:50,920 --> 00:06:59,160 +قديش الـ VCC بدي أساوي الطيار اللي هان I تبعه؟ IB للـ I، + +77 +00:06:59,160 --> 00:07:06,120 +بدي أساوي الـ VCC minus VBE للـ I، فوضع الـ forward active، + +78 +00:07:06,120 --> 00:07:11,780 +على الـ RB، مظبوط؟ الطيار هذا الـ range تبعه بالقديش؟ + +79 +00:07:11,780 --> 00:07:23,030 +عادة بيطلع بالملي، مظبوط؟ الـ IP بعرفه بالـ micro أو مش + +80 +00:07:23,030 --> 00:07:28,290 +بالـ ملي زي هذا، فلما أضرب بـ beta forward عشان أجيب + +81 +00:07:28,290 --> 00:07:34,130 +الـ IC هتلاقي beta forward عالي كثير، صح؟ إذا عالي + +82 +00:07:34,130 --> 00:07:39,340 +كثير معناته هذا مش لازم يكون بالـ forward active، هذا + +83 +00:07:39,340 --> 00:07:42,200 +بيقول إنه لازم يكون في وضع الـ saturation، حال أتيت + +84 +00:07:42,200 --> 00:07:46,980 +جاوز الـ specification تبع الـ transistor اللي هنا، + +85 +00:07:46,980 --> 00:07:52,180 +فلازم يكون، وهذا بدي يشتغل على طول، لازم يكون هذا + +86 +00:07:52,180 --> 00:07:55,260 +الـ transistor في وضع الـ saturation، فمعناته هنا + +87 +00:07:55,260 --> 00:08:00,480 +حكاية الـ forward active اللي أنا عملته مش مظبوط، + +88 +00:08:00,480 --> 00:08:08,400 +لهذا السبب لازم يكون عندي الـ QI must be saturated، + +89 +00:08:10,910 --> 00:08:16,930 +كويس، هيك يعني هذا جينا طلعنا على حجم التيار اللي + +90 +00:08:16,930 --> 00:08:21,550 +هان، لقيته لازم يكون عنده هان التيار الـ IP عالي، + +91 +00:08:21,550 --> 00:08:25,610 +بتقدر الـ beta forward مش هتظبط المعادلة تبعتي، فـ QI + +92 +00:08:25,610 --> 00:08:30,230 +لازم يكون وضعه saturation، إذا QI وضعه saturation، و + +93 +00:08:30,230 --> 00:08:35,550 +هذه zero، الـ voltage اللي هان قد ايش؟ point 2، كل + +94 +00:08:35,550 --> 00:08:40,760 +شيء افه هذه، فهنا عندي point 2، الـ point 2 إيش + +95 +00:08:40,760 --> 00:08:46,460 +هتقول لكيو نوت off، إذا اف الـ V out إيش بدي أساوي؟ + +96 +00:08:46,460 --> 00:08:52,920 +VCC، VCC، شايفين كيف تتدرج؟ يعني هنا عندي بتبسم الـ + +97 +00:08:52,920 --> 00:09:03,320 +VTC، هي الـ V in، هي الـ V out، هي + +98 +00:09:03,320 --> 00:09:09,580 +عندي الـ Q not off، والـ QI وضعه saturated، وهذا + +99 +00:09:09,580 --> 00:09:17,920 +أعطاني الـ VOH اللي هو بيساوي VCC، طب + +100 +00:09:17,920 --> 00:09:24,620 +لو كانت point 1، قد ايش الـ voltage هنا؟ point 3، + +101 +00:09:24,620 --> 00:09:31,520 +هتشغل هذه، point 2، point 4 هتشغل point + +102 +00:09:31,520 --> 00:09:40,530 +4، هتشغل point 5، point 7 هتشغل اللي ها يعني + +103 +00:09:40,530 --> 00:09:44,170 +هيشتغل عند كيو نوت هيصير forward active، يعني الـ + +104 +00:09:44,170 --> 00:09:49,350 +voltage اللي عندي ها + +105 +00:09:49,350 --> 00:09:53,450 +الـ VIL عندي بدي أساوي اللي هو عندي، إذا بدي أطلع + +106 +00:09:53,450 --> 00:09:59,430 +عليه بيساوي VBE، يعني as Vin increases، + +107 +00:10:03,670 --> 00:10:08,990 +الـ q not will become forward active، وعندي الـ VIL + +108 +00:10:08,990 --> 00:10:14,530 +في هذه الحالة تساوي VBE للـ O forward active minus + +109 +00:10:14,530 --> 00:10:21,170 +VCE للـ I في وضع الـ saturation اللي طلعت عندي point + +110 +00:10:21,170 --> 00:10:31,350 +خمسة volt اللي عملتها، فعطتني الـ VIL، وهذا سميتها الـ + +111 +00:10:31,350 --> 00:10:38,080 +edge، الآن بعد هيك ازود لـ point 6 إيش بدها تعطيني هنا؟ + +112 +00:10:38,080 --> 00:10:43,920 +point 8، إيش بدها يحصل في الترانزستور هذا؟ saturation، + +113 +00:10:43,920 --> 00:10:47,740 +فهذه اللي بدها ينزل عندي، يعني هنا + +114 +00:10:54,820 --> 00:10:59,000 +هذه الـ vi-edge اللي هو بدي أساوي point 6 عندي، + +115 +00:10:59,000 --> 00:11:04,240 +هنا الـ edge of saturation، وهنا الـ q not لسه توضع + +116 +00:11:04,240 --> 00:11:10,000 +صار saturation، هنا الـ q not forward active والـ qi + +117 +00:11:10,000 --> 00:11:19,820 +saturated، والـ qi saturated في هذا + +118 +00:11:19,820 --> 00:11:32,410 +الحالة كده الـ output لما يصير saturated، مظبوط؟ + +119 +00:11:36,410 --> 00:11:39,790 +saturation، لأن الـ drop اللي عندي هنا كان point + +120 +00:11:39,790 --> 00:11:46,330 +2، فالآن هي الـ VIL، الـ VIH اختلف عندي، صار عندي + +121 +00:11:46,330 --> 00:11:54,430 +VBE للـ O وضع الـ saturated minus VCE للـ I saturated، + +122 +00:11:54,430 --> 00:11:59,730 +اللي طلعت عندنا zero point 6، وهنا طلع الـ VOL بدي + +123 +00:11:59,730 --> 00:12:07,650 +أساوي VCE للـ O saturated، الآن هذه سهلة العملية و + +124 +00:12:07,650 --> 00:12:12,130 +smooth، لحد الآن أنا عندي الـ transistor هان بدأت من + +125 +00:12:12,130 --> 00:12:18,410 +zero وصلتها لـ point 6، مر هذا في forward active، + +126 +00:12:18,410 --> 00:12:22,710 +عملية at point 5 أو point 6، وصلت لـ saturated، + +127 +00:12:22,710 --> 00:12:28,410 +طيب لو ضليتني ازود في الـ voltage اللي هان، إيش هيحصل + +128 +00:12:28,410 --> 00:12:31,970 +في الـ transistor هذا؟ هل هيضلوا saturated؟ + +129 +00:12:36,280 --> 00:12:43,060 +سيصبح الـ transistor reverse active، الـ transistor + +130 +00:12:43,060 --> 00:12:47,920 +سيصبح عالق عالق عالق عالق عالق عالق عالق عالق عالق + +131 +00:12:47,920 --> 00:12:48,200 +عالق عالق عالق عالق عالق عالق عالق عالق عالق عالق + +132 +00:12:48,200 --> 00:12:48,520 +عالق عالق عالق عالق عالق عالق عالق عالق عالق عالق + +133 +00:12:48,520 --> 00:12:49,040 +عالق عالق عالق عالق عالق عالق عالق عالق عالق عالق + +134 +00:12:49,040 --> 00:13:05,900 +عالق عالق عالق عالق عالق عالق عالق عالق عالق عال + +135 +00:13:07,520 --> 00:13:11,720 +لـ reverse active at one port، بضل شغال في الـ + +136 +00:13:11,720 --> 00:13:15,020 +reverse active mode، طالما أنا هنا عندي الـ input + +137 +00:13:15,020 --> 00:13:24,720 +وضع إيش؟ high، كويس، كل صندوق شكلي اتكلمت حاجة مش + +138 +00:13:24,720 --> 00:13:28,720 +واضحة، خليني اتكلم على حاجتين، الـ transistor لحدد الـ + +139 +00:13:28,720 --> 00:13:33,440 +mode of operation، إيش ملزم نعرفه؟ حاجتين، + +140 +00:13:34,390 --> 00:13:38,010 +لازم أعرف الـ BE Junction والـ BC Junction إيش + +141 +00:13:38,010 --> 00:13:41,610 +وضحوه مش هيك في الـ chapter 3 الحاجة الوحيدة اللي + +142 +00:13:41,610 --> 00:13:46,150 +اخدناها منه ايش هي الـ mode of operations و الـ mode + +143 +00:13:46,150 --> 00:13:49,690 +of operations اللي بنتكلم عنها بنتكلم على ايش وضع + +144 +00:13:49,690 --> 00:13:54,650 +الـ junctions اللي موجودة هنا أنا الـ junction شغالة + +145 +00:13:54,650 --> 00:14:02,470 +الـ voltage VBE عبارة عن VB-VE إذا VE عندي قاعدة + +146 +00:14:02,470 --> 00:14:08,170 +بتزيد at one point هتصير الـ junction عندي بالنيجاتيف + +147 +00:14:08,170 --> 00:14:13,870 +مظبوط أو هتصير الـ voltage drop أقل من الـ point 7 + +148 +00:14:13,870 --> 00:14:20,050 +المطلوبة يعني الفرق بين VB و VE هيصير أقل من 0.7 في + +149 +00:14:20,050 --> 00:14:23,450 +هذه الحالة هتنقلب الـ mode of operation بدل ما هي + +150 +00:14:23,450 --> 00:14:28,190 +صار هذه صارت الـ junction عندي reverse الـ BE و الـ + +151 +00:14:28,190 --> 00:14:32,810 +BC لساتها forward هذه بتقول لإنه الترانزستور اتحول + +152 +00:14:32,810 --> 00:14:37,150 +للـ mode of operation اللي هي الـ reverse active في + +153 +00:14:37,150 --> 00:14:39,310 +الـ reverse active ايش المعروف عندي؟ + +154 +00:14:45,080 --> 00:14:51,600 +معروف عندي الـ VBC الـ VBC كده ايه بتساوي؟ point 7 + +155 +00:14:51,600 --> 00:14:54,480 +وعندي الـ IE ايه ايه بتساوي؟ + +156 +00:15:00,010 --> 00:15:04,610 +بساوي واحد واحد زائد beta reverse مظبوط أو beta + +157 +00:15:04,610 --> 00:15:13,690 +reverse مضروبة العلاقة بين I C و I B أو I E و I B + +158 +00:15:13,690 --> 00:15:17,530 +اللي هي الـ beta reverse اللي موجود عندي ف أنا بدي + +159 +00:15:17,530 --> 00:15:22,550 +اجيب الـ beta reverse في هذه الحالة طيب اللي هي + +160 +00:15:22,550 --> 00:15:27,730 +عندي I E بساوي beta reverse في I B بالسالب طبعا + +161 +00:15:30,960 --> 00:15:36,480 +اتفقنا على هذه الشيء؟ طيب نرجع تاني للجزء يعني هذا + +162 +00:15:36,480 --> 00:15:42,600 +بيبدأ عندي وضع saturation بتتحول مع زيادة ال + +163 +00:15:42,600 --> 00:15:49,540 +voltage إلى reverse active اتفقنا على هذه النقطة + +164 +00:15:49,540 --> 00:15:57,220 +الـ QO بيبدأ cut off بيصير forward active وبعدين + +165 +00:15:57,220 --> 00:16:03,220 +بيصير saturation كويسك؟ الآن قبل ما نعدي عن هان أنا + +166 +00:16:03,220 --> 00:16:06,400 +بتذكر في الـ chapter خمسة ايش عملنا لما عملنا nand + +167 +00:16:06,400 --> 00:16:10,240 +gate حطينا + +168 +00:16:10,240 --> 00:16:17,120 +ايش؟ حطينا diodes in parallel مع بعض، مظبوط؟ طب + +169 +00:16:17,120 --> 00:16:20,700 +هان بدي اعمل حاجة in parallel، ايش بعمل؟ باجي لل + +170 +00:16:20,700 --> 00:16:26,170 +emitter head، بضيف كمان emitter head بتصير عندي ال + +171 +00:16:26,170 --> 00:16:29,930 +basic NAND gate بزود emitter في هذه بنسميه multi + +172 +00:16:29,930 --> 00:16:37,510 +emitter diode multi emitter diode بعملي الـ NAND في + +173 +00:16:37,510 --> 00:16:43,430 +الـ structure هات بيقدر يعملي الـ NAND gate طيب الآن + +174 +00:16:43,430 --> 00:16:52,170 +هنا الـ input ايش عندي وضعه صار هاي صح VIN high + +175 +00:16:56,640 --> 00:17:02,280 +الـ output اللي عندي ايش كان وضعه الـ saturation + +176 +00:17:02,280 --> 00:17:09,700 +بدي إياها يروح لإيش هي q not بدي أخليه q not يروح لمين + +177 +00:17:09,700 --> 00:17:14,180 +ل off صح؟ + +178 +00:17:14,180 --> 00:17:21,500 +مظبوط ولا لأ هذه الـ saturation بدي روح ل off يعني + +179 +00:17:21,500 --> 00:17:25,320 +الـ VIN من high ل low إذا بتطلع عليه هذا + +180 +00:17:25,320 --> 00:17:30,020 +الترانزستور كان وضعه في الـ reverse active mode صح؟ + +181 +00:17:30,020 --> 00:17:37,140 +يعني هنا كان عندي Qi وضع reverse active بده يروح ل + +182 +00:17:37,140 --> 00:17:44,240 +mode معين ايش هذا الـ mode؟ بده أعرفها كويس بهذه + +183 +00:17:44,240 --> 00:17:51,240 +الطريقة؟ أنا الـ output كان عندي هذه بسميها الـ + +184 +00:17:51,240 --> 00:17:56,260 +voltage هان كده اللي موجود هنا لما كان saturation + +185 +00:17:56,260 --> 00:17:59,700 +ال + +186 +00:17:59,700 --> 00:18:04,360 +voltage هان point 2 ولا point 8 الـ voltage اللي + +187 +00:18:04,360 --> 00:18:08,840 +هان كان بيساوي point 8 volt بعبارة تانية هاي اللي + +188 +00:18:08,840 --> 00:18:13,780 +موجود عندي هاي الـ base و هاي الـ emitter و هاي الـ + +189 +00:18:13,780 --> 00:18:18,680 +collector هذا الـ junction ليصير هذا الـ high بدأت + +190 +00:18:18,680 --> 00:18:23,710 +تكون reverse و هاد الـ junction بيديها ايش؟ reverse + +191 +00:18:23,710 --> 00:18:28,690 +مظبوط؟ و الـ point 8 قاعدة هان إذا الـ point 8 هاد + +192 +00:18:28,690 --> 00:18:34,690 +ما راحتش مش حأقدر أعمل للـ junction بيه reverse صح؟ + +193 +00:18:34,690 --> 00:18:42,730 +صح الكلام هاد؟ لازم الـ point 8 أرفعها طب الـ point + +194 +00:18:42,730 --> 00:18:44,570 +8 و من و كيف بتروح؟ + +195 +00:18:47,100 --> 00:18:51,320 +على الدائرة هاي بدها تروح عبر الترانزستور اللي هنا + +196 +00:18:51,320 --> 00:18:56,860 +صح؟ يعني وضع الترانزستور هذا بده يختلف من reverse + +197 +00:18:56,860 --> 00:19:03,120 +active طيب إذا الـ input صار عندي هنا zero وضع هذه + +198 +00:19:03,120 --> 00:19:07,000 +ايش هو؟ + +199 +00:19:07,000 --> 00:19:13,660 +بده يصير forward bias صح؟ يعني إذا بده أطلع عليها + +200 +00:19:13,660 --> 00:19:22,380 +في هذه الحالة عندي الـ B E junction لهذا forward + +201 +00:19:22,380 --> 00:19:25,860 +biased + +202 +00:19:25,860 --> 00:19:29,100 +مظبوط + +203 +00:19:29,100 --> 00:19:33,060 +هذا + +204 +00:19:33,060 --> 00:19:36,680 +اللي عندي forward biased الاحتمال اللي موجود عندي + +205 +00:19:36,680 --> 00:19:42,160 +يا هذه بتكون forward يا هذه بتكون reverse صح؟ يعني + +206 +00:19:42,160 --> 00:19:45,700 +هذا الترانزوسير يكون إما forward active أو + +207 +00:19:45,700 --> 00:19:51,840 +saturation طب نيجي نطلع عليه الـ voltage اللي هان + +208 +00:19:51,840 --> 00:19:57,820 +قلت سارة عندي كام؟ Zero كويس؟ أو low الـ low يا + +209 +00:19:57,820 --> 00:20:02,580 +بحطه point اتنين يا بحطه zero صح؟ لو حطيته هنا + +210 +00:20:02,580 --> 00:20:07,660 +zero كده ايش الـ voltage هان؟ أنا بقول هاد forward + +211 +00:20:07,660 --> 00:20:09,540 +biased سارة point سبعة + +212 +00:20:16,430 --> 00:20:21,650 +قداش الـ voltage هنا أنا قاعد بقول point ثمانيه ايش + +213 +00:20:21,650 --> 00:20:28,790 +وضع الـ junction هذي reverse مظبوط مش مصدقين حالكم + +214 +00:20:28,790 --> 00:20:34,110 +كيف .. كيف .. كيف هذي reverse الآن أنا قاعد بقول + +215 +00:20:34,110 --> 00:20:38,770 +بتحسبها حسابات يعني ما فيش في العلم تبعنا ال + +216 +00:20:38,770 --> 00:20:42,070 +guessing game مش موجودة أنا بتحذر ايش بتطلع + +217 +00:20:42,070 --> 00:20:48,140 +بتحسبها الآن أنا اللي بحكي التالي حصل عندي عادةً + +218 +00:20:48,140 --> 00:20:53,340 +عندما أغيّر الـ input سأرافقه هذا inverter صح؟ أي + +219 +00:20:53,340 --> 00:20:57,440 +تغيير على الـ input سيحب تغييره في شغل الـ output + +220 +00:20:57,440 --> 00:21:03,400 +عندما كان الـ input high الـ output low الـ input + +221 +00:21:03,400 --> 00:21:08,300 +سيصبح low والـ output يجب أن يذهب high إذا كنت تذهب + +222 +00:21:08,300 --> 00:21:11,500 +high يعني أن تتحول الترانزوسور الذي لدي من وضع ال + +223 +00:21:11,500 --> 00:21:16,960 +output من وضع الـ saturation لوضع cut off طب طالما + +224 +00:21:16,960 --> 00:21:21,160 +عندي فيه charge point تمانية موجودة مخزنة مش هيغيّر + +225 +00:21:21,160 --> 00:21:31,420 +إلا هذا charge تروح هذا بنسميها charge removal + +226 +00:21:31,420 --> 00:21:36,140 +current + +227 +00:21:36,140 --> 00:21:41,320 +الـ I أو هذا بنسميها stored + +228 +00:21:47,060 --> 00:21:54,020 +ASCR التيار اللي عندي هذا كم هو الآن أنا لو عندي + +229 +00:21:54,020 --> 00:22:00,200 +برميل مية فيه خلينا نقول كوب + +230 +00:22:00,200 --> 00:22:06,460 +و بده تفريغ هي لما اجيب بربيش نص انش أو الفتحة + +231 +00:22:06,460 --> 00:22:12,440 +تبعته في بربيش نص انش وافتحه بياخد وقت صح؟ لو جبت + +232 +00:22:12,440 --> 00:22:18,460 +بدل النص انش اتنين انش ايش بيصير؟ بيصير أسرع بقل + +233 +00:22:18,460 --> 00:22:27,880 +الوقت و لو ركبت motor أسرع بكثير صح؟ مظبوط؟ طيب، + +234 +00:22:27,880 --> 00:22:30,620 +الآن اللي عند الـ transistor تبعنا في ال + +235 +00:22:30,620 --> 00:22:36,640 +electronics هو بعد الـ ايش؟ motor، مظبوط؟ الآن في + +236 +00:22:36,640 --> 00:22:43,130 +وضع الـ saturation التيار بيبقى العلاقة بينه وبين ال + +237 +00:22:43,130 --> 00:22:49,740 +IP كيف فيه sigma مظبوط و الـ sigma دايما بتكون أقل + +238 +00:22:49,740 --> 00:22:54,100 +من ايش؟ من واحد بينما في وضع الـ forward active + +239 +00:22:54,100 --> 00:22:59,660 +بتبقى ايش؟ الـ sigma بتساوي واحد يعني معناته احسن + +240 +00:22:59,660 --> 00:23:04,500 +شيء للتفريغ أن يكون عندي motor ي هذا شغال على + +241 +00:23:04,500 --> 00:23:08,180 +forward active طب احنا نشوف الـ junction اللي عندي + +242 +00:23:08,180 --> 00:23:11,880 +أنا قاعد بقول في عندي هنا قاعد point ثمانيه volt + +243 +00:23:11,880 --> 00:23:17,370 +اللي موجود عندي هنا الآن عندما أصبح الهدف low أصبح + +244 +00:23:17,370 --> 00:23:21,110 +وضع الـ junction الـ BE اللي عندي هذا forward + +245 +00:23:21,110 --> 00:23:26,810 +bias في حالة الـ forward bias اللي عندي بقدر اجيب + +246 +00:23:26,810 --> 00:23:33,310 +الـ Ip اللي هنا صح؟ لهذه هذه ستمر في عبر اللوب اللي + +247 +00:23:33,310 --> 00:23:37,450 +هنا الآن هذه الـ junction بتعرف ايش واضحة لما جيت + +248 +00:23:37,450 --> 00:23:41,030 +احسبها موجود هنا point 8 وهنا موجود عندي zero زائد + +249 +00:23:41,030 --> 00:23:45,770 +point 7 أعطتني point 7 بتكاشي point 2 زائد point 7 + +250 +00:23:45,770 --> 00:23:50,410 +أعطتني point 9 point 9 ناقص point 8 point 1 غير + +251 +00:23:50,410 --> 00:23:54,110 +كافية تشغلي الـ junction اللي هنا فالـ junction اللي + +252 +00:23:54,110 --> 00:23:57,350 +هنا هتكون reverse bias وهذه forward bias + +253 +00:23:57,350 --> 00:24:03,390 +الترانزوسر صار في وضع ايش؟ forward active ف في هذه + +254 +00:24:03,390 --> 00:24:10,290 +الحالة أقول لأ الـ B C junction reverse + +255 +00:24:10,290 --> 00:24:14,070 +bias + +256 +00:24:14,070 --> 00:24:22,290 +لأن هنا اللي عندي ايش عندي VBE أو VB لل I بتساوي + +257 +00:24:22,290 --> 00:24:25,890 +له VE + +258 +00:24:25,890 --> 00:24:38,800 +لل I بتساوي له وعندي الـ VBE بيبقى + +259 +00:24:38,800 --> 00:24:46,600 +VBE بيبقى VBE بيبقى VBE بيبقى VBE بيبقى VBE بيبقى + +260 +00:24:46,600 --> 00:24:46,740 +VBE بيبقى VBE بيبقى VBE بيبقى VBE بيبقى VBE بيبقى + +261 +00:24:46,740 --> 00:24:46,960 +VBE بيبقى VBE بيبقى VBE بيبقى VBE بيبقى VBE بيبقى + +262 +00:24:46,960 --> 00:24:50,060 +VBE بيبقى VBE بيبقى VBE بيبقى VBE بيبقى VBE بيبقى + +263 +00:24:50,060 --> 00:24:54,460 +VBE + +264 +00:24:54,460 --> 00:24:56,800 +بيب + +265 +00:25:05,840 --> 00:25:15,820 +عندي من هنا السبب أن vbc بدي أساوي 0.9-0.8 بدي أساوي + +266 +00:25:15,820 --> 00:25:21,540 +0.14 لهذا السبب بقول أنا عندي الاستنتاج اللي وصلت له + +267 +00:25:21,540 --> 00:25:27,120 +أن هذي لازم تكون في وضع الـ reverse bias إذا هذول + +268 +00:25:27,120 --> 00:25:31,900 +reverse bias يبقى عندي الـ Q من هذي حسب هذول + +269 +00:25:31,900 --> 00:25:37,880 +هيقدوني أن الـ QI must be forward active بس الـ QI + +270 +00:25:37,880 --> 00:25:45,340 +forward active لقداشي مش كتير لأن هذا عندي طيار + +271 +00:25:45,340 --> 00:25:52,110 +بفضي بسرعة هائلة مقارنة مع ايش مع charge موجودة + +272 +00:25:52,110 --> 00:25:56,550 +point 8 فهي نتكلم عن حاجة بال nano second بقعد في + +273 +00:25:56,550 --> 00:26:02,450 +وضع forward axis بعدها بيحول مجرد ما هيصير عند + +274 +00:26:02,450 --> 00:26:08,170 +الفرق اللي عندي هنا point 6 بروح لإيش لل + +275 +00:26:08,170 --> 00:26:15,400 +saturation mode فانتهينا من اللحظية الآن اللي بتكلم + +276 +00:26:15,400 --> 00:26:20,300 +عنه في هذه الشغلة charge remover يعني forward + +277 +00:26:20,300 --> 00:26:26,520 +active معناته الـ ICI بدي أساوي beta forward في ال + +278 +00:26:26,520 --> 00:26:31,320 +IBI اللي + +279 +00:26:31,320 --> 00:26:36,880 +هو بدي أساوي beta forward الـ IBI ايش بتساوي بتساوي + +280 +00:26:36,880 --> 00:26:48,290 +VCC minus VBE للـ I forward active minus Vin وضع ال + +281 +00:26:48,290 --> 00:26:54,890 +low على الـ RB وهذه عادة باخدها عشان زي ما حكيت VCE + +282 +00:26:54,890 --> 00:27:03,690 +SAT الرقم اللي باخده طيب لو كان عندي التالي VCC + +283 +00:27:03,690 --> 00:27:05,570 +بساوي خمسة فولت + +284 +00:27:08,490 --> 00:27:19,630 +هذا يتساوى 2K وهذا يتساوى 1K كداش الـ ICI الذي + +285 +00:27:19,630 --> 00:27:25,030 +سميتها ICR + +286 +00:27:25,030 --> 00:27:32,010 +هذا يتساوى و Beta عندي خد Beta لهذه forward equal + +287 +00:27:32,010 --> 00:27:32,590 +50 + +288 +00:27:35,200 --> 00:27:42,160 +بتساوي عندي خمسين ضرب خمسة ناقص 0.7 minus + +289 +00:27:42,160 --> 00:27:47,040 +0.2 على RB2K + +290 +00:27:47,040 --> 00:27:53,420 +إذا حسبتها بتطلع عندي تقريبا 102.5 milli amp نتذكر هذا في الـ DTL كده كان الرقم + +291 +00:27:53,420 --> 00:28:01,300 +هذا عندي هل حد ذاكر الـ example اللي عملناه كان عندي + +292 +00:28:01,300 --> 00:28:06,600 +الـ RD في الـ DTL كان عندي الـ RD بدها تساوي 5K وقلنا + +293 +00:28:06,600 --> 00:28:14,360 +الـ I stored charge removal بدها تساوي IRD اللي هو + +294 +00:28:14,360 --> 00:28:19,900 +بيساوي VBE بالـ saturation على الـ RD اللي هو كان + +295 +00:28:19,900 --> 00:28:26,110 +عندي 0.8 على 5 K اللي قولنا 160 + +296 +00:28:26,110 --> 00:28:31,970 +micro amp طلع عندي هنا قداش وهنا قداش هنا 1 + +297 +00:28:31,970 --> 00:28:38,950 +sixty micro amp هنا ايش 102.5 يعني + +298 +00:28:38,950 --> 00:28:44,150 +لو جبت نسبة الـ TTL هذا الـ TTL الـ TTL على الـ DTL بدي + +299 +00:28:44,150 --> 00:28:53,710 +أُتساوى عندي 102.5 على 160 micro amp بدي اعطيه + +300 +00:28:53,710 --> 00:28:59,930 +تقريبا 640.9 حاجة زي هي 640.6 + +301 +00:28:59,930 --> 00:29:15,410 +فهذه + +302 +00:29:15,410 --> 00:29:21,210 +أفضل الـ TTL أفضل من الـ DTL بـ 640 مرة يعني هذي بتعمل + +303 +00:29:21,210 --> 00:29:28,710 +switching سريع بشكل أسرع بـ 640 مرة من الـ DTL هذي + +304 +00:29:28,710 --> 00:29:41,910 +مركب موتور وحاطط خط كبير ومشغل على طول أيوة فهذه + +305 +00:29:41,910 --> 00:29:48,330 +بتشيلها بسرعة كبيرة جدا طيب إذا الأداء تبح لها درجة + +306 +00:29:48,330 --> 00:29:56,100 +كويس، طب كيف ممكن .. ايش .. ايش اللي ممكن نتكلم + +307 +00:29:56,100 --> 00:29:59,440 +فيه لن .. لن .. يعني نعملها الـ standard؟ لأن هاي + +308 +00:29:59,440 --> 00:30:04,720 +الـ NAND structure وهاي الـ basic idea الـ basic + +309 +00:30:04,720 --> 00:30:08,840 +idea أنا بركز على هذا، هذا عندي ايش بيشتغل؟ هذا هو + +310 +00:30:08,840 --> 00:30:14,420 +وضع الـ saturation اللي ببدأ فيه لما الـ input low + +311 +00:30:14,420 --> 00:30:17,920 +وهذا بكون up لإن أنا عندي 0.2 لإن كل ما بزود + +312 +00:30:17,920 --> 00:30:24,160 +بالـ voltage اللي أنا بزوده لـ 0.5 بعطيني + +313 +00:30:24,160 --> 00:30:27,380 +0.7 هان بشغللي الـ Q نقطة في حالة ما اشتغل + +314 +00:30:27,380 --> 00:30:32,360 +بشوف ايش اللي بيطلع عندي بعد هيك بزود فيها لـ 0.6 + +315 +00:30:32,940 --> 00:30:37,500 +بلاحظ هذا 0.8 هذا بيصير saturation في حالة + +316 +00:30:37,500 --> 00:30:40,880 +الـ saturation الـ Q الـ V out بيساوي VOL في حالة الـ + +317 +00:30:40,880 --> 00:30:45,500 +off الـ V out بيساوي VCC اللي عندي هذا الـ transistor + +318 +00:30:45,500 --> 00:30:50,940 +اشتغل من off لـ forward active لـ saturation + +319 +00:30:50,940 --> 00:30:54,220 +الـ transistor هذا بدأ بـ saturation على طول لما أزود + +320 +00:31:01,140 --> 00:31:03,840 +في الـ input هذا الـ transistor بيروح في آخر في + +321 +00:31:03,840 --> 00:31:08,760 +reverse active mode الآن لما نغير الـ input من high + +322 +00:31:08,760 --> 00:31:14,700 +لـ low هذا لحظيا بيصير في الـ forward active بعدين + +323 +00:31:14,700 --> 00:31:20,960 +بيحول لـ saturation هذه الفكرة الموجودة عندي ككل + +324 +00:31:20,960 --> 00:31:27,340 +هنا واضحة؟ الآن هروح على circuit اعقد شوية ايش الـ + +325 +00:31:27,340 --> 00:31:45,160 +circuit بنسميها الـ standard TTL NAND gate ايه + +326 +00:31:45,160 --> 00:31:52,120 +هذا سهل لحتى الآن هذا الدائرة إذا بتلاحظ عندي very + +327 +00:31:52,120 --> 00:31:57,080 +standard الآن أطلع الـ ... أطلع الدائرة اللي بعدها + +328 +00:31:57,080 --> 00:32:02,240 +يعني زي ما بيقولوها أنت أي شيء مافيش فيه اجتهاد + +329 +00:32:02,240 --> 00:32:08,060 +فهو سهل، يعني هاد الخطوات اللي عندي، الـ V out لو + +330 +00:32:08,060 --> 00:32:10,880 +سألتك عليهم إن شاء الله حجم الدائرة حاطط قدامها هل + +331 +00:32:10,880 --> 00:32:15,900 +جد؟ جدش الـ V out؟ الأصل عرفت الـ output high والـ + +332 +00:32:15,900 --> 00:32:22,420 +output low بدك تقولي على طول VCC و VCE سات انتهينا + +333 +00:32:22,420 --> 00:32:26,400 +منها الآن في الـ input بدك تجمع يعني مافيش فيها + +334 +00:32:26,400 --> 00:32:29,900 +حاجة بدك تجمع حاجة عندي هذا لايشتغل الـ VIL بدي + +335 +00:32:29,900 --> 00:32:34,880 +0.7 بده أطرح منها 0.2 الـ V .. ده بده أطلع + +336 +00:32:34,880 --> 00:32:39,400 +على الشغل الثاني الـ VIH 0.8 بده أطرح منها + +337 +00:32:39,400 --> 00:32:46,110 +0.2 هدول صعبات؟ الـ VTC هو أنت مغمض تكتبهم قبل + +338 +00:32:46,110 --> 00:32:50,470 +ما تقولي المسألة كيف أنت تكتبهم وتحطهم هضل على + +339 +00:32:50,470 --> 00:32:54,690 +الجامعة قبل ما أفكر ايش بدها المسألة الآن الحاجة + +340 +00:32:54,690 --> 00:32:58,970 +اللي بدها تفكيري ليش قلناها اللي هي بدنا الـ I + +341 +00:32:58,970 --> 00:33:02,650 +charge removal وأنت عارفه الآن عرفتها إنه صار في الـ + +342 +00:33:02,650 --> 00:33:06,930 +forward active mode انتهينا من هذا الشغل يعني في + +343 +00:33:06,930 --> 00:33:10,630 +هذا القانون عندك تدقه وتشتغل عليه مافيش فيها + +344 +00:33:10,630 --> 00:33:15,910 +اجتهادات القادة الدائرة اللي هنعطيها الحيط شكلها + +345 +00:33:15,910 --> 00:33:20,330 +شوية مزعج بس نفس الشيء مافيش فيها ولا إجتهاد اللي + +346 +00:33:20,330 --> 00:33:29,070 +بنسميها الـ standard TTL + +347 +00:33:29,070 --> 00:33:38,810 +NAND GATE ونقول عنها الـ series 7400 + +348 +00:33:40,790 --> 00:33:47,370 +5400 ايش الشكل اللي عندي هاي VCC في عندي three + +349 +00:33:47,370 --> 00:33:55,250 +branches أو + +350 +00:33:55,250 --> 00:33:56,730 +خلينا نطولها شوية + +352 +00:34:38,110 --> 00:34:42,390 +أشهد أن الناس اللي بيبقى عايزة تتعامل مع بعضها مع + +353 +00:34:42,390 --> 00:34:45,090 +بعضها + +354 +00:35:34,620 --> 00:35:39,480 +هذه مش أكبر دائرة هتشوفها هتشوفها أكبر منها في + +355 +00:35:39,480 --> 00:35:40,160 +الكثير + +356 +00:36:11,170 --> 00:36:15,690 +بس لما أنت فاهمها بيضلش عليها شيء + +357 +00:36:19,830 --> 00:36:24,990 +يعني الغلبة فيها قبل ما تفهم كيف بتشتغل إذا فهمت + +358 +00:36:24,990 --> 00:36:30,170 +كيف بتشتغل بتقول هذه مافيش فيها أولاً الـ diodes + +359 +00:36:30,170 --> 00:36:35,410 +الموجودين هدول بنسموهم clamping diodes الهدف منهم + +360 +00:36:35,410 --> 00:36:40,270 +يعملوا الـ protection لهذه الـ gate ليش؟ لو شبك + +361 +00:36:40,270 --> 00:36:44,610 +عليها negative voltage ايش بيحصل فيهم؟ هي بتشتغل + +362 +00:36:44,610 --> 00:36:49,250 +هدول بيشتغلوا الدائرة مافيش لها يعني بيصير حاش أي + +363 +00:36:49,250 --> 00:36:52,610 +شيء بتعمل protection يعني هذا الغرض .. الغرض .. + +364 +00:36:52,610 --> 00:36:57,410 +الغرض من هدول اتنين يعمل protection لباقي الدائرة + +365 +00:36:57,410 --> 00:37:02,510 +لأن هذا وقتيش هدول بيشتغلوا لما هدول يبقى الـ + +366 +00:37:02,510 --> 00:37:05,770 +voltage عنده بالـ negative يعني بيصير التيار كله + +367 +00:37:05,770 --> 00:37:09,510 +بيمشي من عبر هدول الـ two diodes وماليش داخل باقي + +368 +00:37:09,510 --> 00:37:17,630 +الدائرة هذا حساس إن أنت في المختبر لو شطحت لك شطحة + +369 +00:37:17,630 --> 00:37:25,070 +ما تحرق لنش حد في code اتعامل مع الـ CMOS أو الـ + +370 +00:37:25,070 --> 00:37:32,870 +MOSFET بالمختبر ما حدش مساكه الـ MOSFET من الشغلات + +371 +00:37:32,870 --> 00:37:37,520 +اللي بتنحرقه بسرعة يعني ممكن أنت بدون ما تمسكها + +372 +00:37:37,520 --> 00:37:41,300 +تيجي .. إذا مش مخزنة صح تلاقيها محروقة شاريها + +373 +00:37:41,300 --> 00:37:44,760 +جديدة بالكرتونة وحاططها .. وحاطيتها رميتها في + +374 +00:37:44,760 --> 00:37:48,660 +الدورة و تيجي تفتح الدورة و تلاقيها محروقة طريقة + +375 +00:37:48,660 --> 00:37:54,100 +التخزين هنعلمكم إياها في chapter 16 ايش هدول؟ في + +376 +00:37:54,100 --> 00:37:57,040 +.. في مشاكل فيهم أحيان بيعمل conductance .. + +377 +00:37:57,040 --> 00:38:02,320 +conductance و هن قاعدين لأ هي طبيعة التصنيع تبعهم، + +378 +00:38:02,320 --> 00:38:06,560 +فقالية التخزين لهم قليلة محددة، فإنما الـ TTL + +379 +00:38:06,560 --> 00:38:09,420 +موجودة بالمختبرات والكل بيشتغل فيها وبيرم فيها + +380 +00:38:09,420 --> 00:38:13,520 +بوين ما جاء ما بيحصل لها أيش، أي شيء، ففيها + +381 +00:38:13,520 --> 00:38:18,800 +protection نوعا ما، أيام مدرست كان احنا الدكتور + +382 +00:38:18,800 --> 00:38:21,780 +كان دائما في Jeep to capture diffusers في المختبرات + +383 +00:38:21,780 --> 00:38:29,080 +الـ voltmeter اللي عندنا أي كان طريقة شبك غلط + +384 +00:38:29,080 --> 00:38:33,000 +بنحرق الـ fuse فهو حاطط الـ fuse وبيغير الـ fuse أنت + +385 +00:38:33,000 --> 00:38:35,380 +الـ voltmeter اللي بتتعامل فيها ما بيحصلش فيها + +386 +00:38:35,380 --> 00:38:40,720 +الإشكالية هذه صح؟ هو عملولها حماية بعد التجارب على + +387 +00:38:40,720 --> 00:38:47,030 +الأجيال اللي قبلكم وصلت لكم جاهزة فالآن نجي نتطلع + +388 +00:38:47,030 --> 00:38:51,310 +لها فهدولة بتعتبرهم ايش مش موجودين في جزء الـ + +389 +00:38:51,310 --> 00:38:56,690 +analysis الآن هذه الجزئية مرت علينا سابقا قبل شوية + +390 +00:38:56,690 --> 00:39:01,050 +هذه وهذه صح؟ الآن أنا قلت لو الـ input عندي zero + +391 +00:39:01,050 --> 00:39:08,670 +بعتبر هذا ايش saturation صح؟ ليش؟ لأن حجم التيار + +392 +00:39:08,670 --> 00:39:14,710 +اللي جاي هنا كبير جدا مقارنة يكون في وضع forward + +393 +00:39:14,710 --> 00:39:18,050 +active فلازم يكون saturation إذا saturation يبقى + +394 +00:39:18,050 --> 00:39:21,570 +هذه negative وهذه positive فهذه بتعطينا ايش 0.2 + +395 +00:39:21,570 --> 00:39:25,030 +الـ 0.2 حد ايش هتعمل اللي بالـ transistor + +396 +00:39:25,030 --> 00:39:34,250 +اللي هي الـ QS هيكون off مش هيشتغل off بده أشيل ايش + +397 +00:39:34,250 --> 00:39:40,890 +أشيله من الدائرة قداش الـ I اللي هي في وضع حد cut + +398 +00:39:40,890 --> 00:39:41,190 +off + +399 +00:39:44,840 --> 00:39:47,840 +ده ده 0.2 0.2 هتشغللي هذا الـ + +400 +00:39:47,840 --> 00:39:52,600 +junction يبقى هيكون off الـ I اللي هان قداش؟ Zero + +401 +00:39:52,600 --> 00:39:57,960 +يبقى قداش الـ voltage هان؟ Zero هذا ايش بديكون؟ هاي + +402 +00:39:57,960 --> 00:40:03,340 +off هاي اتنين off كويس؟ اتنين off قداش الـ V out + +403 +00:40:03,340 --> 00:40:03,940 +هنا؟ + +404 +00:40:10,420 --> 00:40:13,860 +للعلم هذا هو ايش emitter follower الـ emitter + +405 +00:40:13,860 --> 00:40:17,760 +follower قلنا دائما بيبقى ايش يا إما forward يا + +406 +00:40:17,760 --> 00:40:23,480 +إما off ما بدخلش الـ saturation فهنا عندي forward هذا + +407 +00:40:23,480 --> 00:40:27,500 +اللي بيكون يا forward يا .. الآن طلع عندك الـ V out + +408 +00:40:27,500 --> 00:40:34,660 +ايش بده يساوي تساوي VCC ناقص IRC في الـ RC ناقص + +409 +00:40:38,110 --> 00:40:46,130 +VBE للـ B في حالة forward active ناقص VDL on هذا + +410 +00:40:46,130 --> 00:40:51,670 +مشبوك مع أي حاجة الآن + +411 +00:40:51,670 --> 00:40:54,270 +الـ assumption اللي عندك اللي هي الـ biasing تبعك + +412 +00:40:54,270 --> 00:41:00,150 +هذا مشبوك مع ايش مع VCC ومشبوك مع مين الشكتين هذا + +413 +00:41:00,150 --> 00:41:05,050 +مشبوك مع الـ VCC الـ voltage اللي موجود هنا مش هيكون + +414 +00:41:06,130 --> 00:41:11,390 +أقل من الـ voltage هذا لأن المقاومة 120 أقل فالـ + +415 +00:41:11,390 --> 00:41:15,650 +drop اللي هنا أقل من الـ drop اللي هنا فهذه بتكون + +416 +00:41:15,650 --> 00:41:19,990 +reverse الـ voltage اللي هنا أعلى من هذا لأنه هذا + +417 +00:41:19,990 --> 00:41:24,910 +مشموك مع ولا أي شيء مع الـ ground يعني باعتباره الآن + +418 +00:41:24,910 --> 00:41:28,820 +الـ voltage اللي هنا هذا بتكون forward bias forward + +419 +00:41:28,820 --> 00:41:32,720 +bias و reverse bias بيكون ككل في الـ forward active + +420 +00:41:32,720 --> 00:41:36,460 +forward active اللي في عنده drop 0.7 وهذا + +421 +00:41:36,460 --> 00:41:40,140 +بيكون شغال point سبعة point سبعة point سبعة point + +422 +00:41:40,140 --> 00:41:43,800 +سبعة واحد point أربعة الـ draw الطيار اللي هان قداش + +423 +00:41:43,800 --> 00:41:47,400 +بيساوي الآن + +424 +00:41:47,400 --> 00:41:51,820 +مشبوك معاشر ما تحطليش معادلات تفكر zero مش مشبوك + +425 +00:41:51,820 --> 00:41:57,440 +ولا حاجة مظبوطو يبقى zero الـ voltage اللي هان قداش + +426 +00:41:57,440 --> 00:42:05,760 +بدي أساوي VCC اللي هو بيساوي خمسة volt ناقص + +427 +00:42:05,760 --> 00:42:11,900 +الـ 1.4 يعني قداش 3.6 يعني لو برسم الـ VTC اللي هاد + +428 +00:42:11,900 --> 00:42:20,760 +بدي أطلع كالتالي هاي Vin وهنا Vout هاي الـ VCC بدي + +429 +00:42:20,760 --> 00:42:27,370 +أجي على 3.6 واعمل خط زي هيك هذا عندي التالي عندي + +430 +00:42:27,370 --> 00:42:37,150 +qi saturated qo and qs off و الـ qp forward active + +431 +00:42:37,150 --> 00:42:44,050 +كويس هيك و هذا الـ voltage طالع عندي كم 3.6 volt + +432 +00:42:44,050 --> 00:42:48,510 +أنا بكتب الـ volt بليش بالرقم ليش لأن هذا ال + +433 +00:42:48,510 --> 00:42:56,120 +standard اللي عندي هي و هد بيصير يساوي Zero يبقى + +434 +00:42:56,120 --> 00:43:03,840 +عندي الـ Vout اللي سميته VOH بيساوي VCC-VBE Forward + +435 +00:43:03,840 --> 00:43:13,340 +Active-VDL On طيب لو هد الـ voltage صار point 2 قداش + +436 +00:43:13,340 --> 00:43:18,900 +الـ voltage اللي هد point 4 هشغل هديبقى الوضع على + +437 +00:43:18,900 --> 00:43:25,800 +ما هو عليها هنا point 5 ايش بدي يحصل عندي point 5 + +438 +00:43:25,800 --> 00:43:31,500 +قداش الـ voltage هذا point 7 point 7 ايش هيعمله + +439 +00:43:31,500 --> 00:43:37,020 +هيشغل هذا يبقى هذا باش يبقى تاني قداش الـ voltage + +440 +00:43:37,020 --> 00:43:43,240 +هذا zero هيشغل هذا يبقى أول نقطة بتغير فيها اللي + +441 +00:43:43,240 --> 00:43:44,240 +هي النقطة هذه + +442 +00:43:49,760 --> 00:43:54,220 +في هذه النقطة ايش حصل عندي؟ الـ QS صار وضعه + +443 +00:43:54,220 --> 00:44:00,160 +forward active وعندي الـ QP لسه forward active + +444 +00:44:00,160 --> 00:44:07,600 +وعندي الـ QO وضعه off والـ QI وضعه saturation هي + +445 +00:44:07,600 --> 00:44:12,460 +ملخص النقطة هذه هي ملخص النقطة هذه هيدلوا ماشي + +446 +00:44:12,460 --> 00:44:21,190 +عندي لما point 6 ايش حيصير عندها؟ point 8 هنا point + +447 +00:44:21,190 --> 00:44:27,390 +.. لأ سترحل point 7 لسه ودي يطلع عندي ايش point 1 + +448 +00:44:27,390 --> 00:44:32,930 +هذا لسه off هضل أزود لحد لو هذا واحد قداش ال + +449 +00:44:32,930 --> 00:44:43,210 +voltage هات واحد point اتنين هنا لسه يعني هذا لما + +450 +00:44:43,210 --> 00:44:50,990 +نوصل هنا one point two قداش حيصير عندي هنا 1.4 1.4 + +451 +00:44:50,990 --> 00:44:58,530 +مظبوط هنا قداش مدي يصير 0.7 هذا ايش حيصير فيه؟ + +452 +00:44:58,530 --> 00:45:04,710 +هيشتغل يعني عندي اشتغل لما صار عندي هنا الـ voltage + +453 +00:45:04,710 --> 00:45:08,510 +هذا + +454 +00:45:08,510 --> 00:45:14,290 +سميته الـ VIL اللي عندي الـ VIL ايش قلنا بيساوي؟ + +455 +00:45:16,270 --> 00:45:22,590 +اللي هو بيساوي VBE للـ S Forward Active minus VCE + +456 +00:45:22,590 --> 00:45:32,290 +للـ I Saturation وقلت اللي بيساوي عندي 0.54 هذا + +457 +00:45:32,290 --> 00:45:39,870 +اللي عندي بسميه الـ VIB اللي هو بيساوي 1.2 Volt و + +458 +00:45:39,870 --> 00:45:46,400 +الـ VIB هنعرفه ايش هو بدي أساوي two او بدي أساوي .. + +459 +00:45:46,400 --> 00:45:51,680 +خلّيني أكتب المعادلة كاملة VBE للـ O forward active + +460 +00:45:51,680 --> 00:46:00,000 +زائد VBE للـ S forward active ناقص VCE للـ I + +461 +00:46:00,000 --> 00:46:05,940 +saturated او بقول عنه ايش بدي أساوي two VBE forward + +462 +00:46:05,940 --> 00:46:12,760 +active ناقص VCE للـ I saturated اللي عندي اللي هي + +463 +00:46:12,760 --> 00:46:20,320 +منها one point two volt وهذا بنسميه الـ break point + +464 +00:46:20,320 --> 00:46:25,900 +input break + +465 +00:46:25,900 --> 00:46:30,460 +point الـ input break point اللي عندي هنا اللي at + +466 +00:46:30,460 --> 00:46:34,380 +one point two في الـ one point two ايش اللي عندي + +467 +00:46:34,380 --> 00:46:42,870 +صار الـ QO و الـ QS واضحهم في الـ forward active طيب + +468 +00:46:42,870 --> 00:46:49,010 +وضع الـ output كده في هذه الحالة طلع عندي ايش بتطلع + +469 +00:46:49,010 --> 00:46:55,210 +عليه هذا الآن صار عندي forward active هذا forward + +470 +00:46:55,210 --> 00:47:00,970 +active وهذا forward active وهذا saturation اللي + +471 +00:47:00,970 --> 00:47:08,710 +عندي الآن التيار اللي هنا هذا بسميه IRD تقريبا بدي + +472 +00:47:08,710 --> 00:47:10,610 +أقول بدي أساوي I + +473 +00:47:13,050 --> 00:47:17,530 +IRC جزء منه سيذهب إلى الـ IC و جزء منه سيذهب إلى + +474 +00:47:17,530 --> 00:47:24,790 +الـ Hand نفس الشيء هنا الـ IE سيحصل على مجموع الـ + +475 +00:47:24,790 --> 00:47:29,810 +IP و الـ IC و جزء منه سيذهب إلى الـ IP الخاص بالـ + +476 +00:47:29,810 --> 00:47:34,070 +output فأنا تقريبا بنعمل هذا بسميها الـ hand + +477 +00:47:34,070 --> 00:47:40,230 +waving تقريبا الطيارة هذه ستصبح الطيارة هذه عند ال + +478 +00:47:40,230 --> 00:47:44,250 +IRC بدي + +479 +00:47:44,250 --> 00:47:52,290 +أقول بدي أساوي الـ IRD طب الـ IRD ايش بيساوي؟ + +480 +00:47:52,290 --> 00:47:58,470 +ما أقدر أحسبه؟ + +481 +00:48:01,150 --> 00:48:06,910 +طيب هي بسهولة هدى بدي أساوي عندي VBE للـ O في حالة + +482 +00:48:06,910 --> 00:48:11,030 +الـ forward active على الـ RD اللي هي بدي أساوي عندي + +483 +00:48:11,030 --> 00:48:17,950 +0.7 على 1K بدي أعطينا 0.7 milli amp يبقى drop اللي + +484 +00:48:17,950 --> 00:48:26,070 +عندي هنا قداشي بدي أساوي طيب + +485 +00:48:26,070 --> 00:48:31,410 +اللي بدي أطلع تقريبا 1.12 volt مظبوط يعني تقريبا + +486 +00:48:31,410 --> 00:48:36,350 +هذه بدها ضرب في ضرب point seven من اللي بدي يعطيني + +487 +00:48:36,350 --> 00:48:42,630 +one point one two four الـ output ايش بدي أساوي؟ بدي + +488 +00:48:42,630 --> 00:48:46,710 +أساوي خمسة ناقص الـ one point one two ناقص الـ one + +489 +00:48:46,710 --> 00:48:49,290 +point four الـ point سبعة و الـ point سبعة بدي + +490 +00:48:49,290 --> 00:48:52,250 +يعطيني الـ payout اللي بيعطيني تقريبا two point + +491 +00:48:52,250 --> 00:48:58,500 +four eight اللي موجود عندي هذا بسميه VOP اللي هو + +492 +00:48:58,500 --> 00:49:02,880 +بدي أساوي 2.48 واِيش بدي أساوي بالضبط هذا بسميه + +493 +00:49:02,880 --> 00:49:12,380 +output break point الـ VOP بدي أساوي عندي + +494 +00:49:14,860 --> 00:49:21,760 +VCC-IRC-VBE + +495 +00:49:21,760 --> 00:49:26,440 +-VDL + +496 +00:49:26,440 --> 00:49:27,580 +ON + +497 +00:49:40,380 --> 00:49:48,300 +في الـ 1 plus RC على RD minus VDL on هذه الفورمولة + +498 +00:49:48,300 --> 00:49:55,300 +اللي عندي فالآن أنا جبت الـ voltage في حالة الـ + +499 +00:49:55,300 --> 00:49:58,940 +break point اللي هذي اللي اجت في النص عندي لما هذا + +500 +00:49:58,940 --> 00:50:02,920 +و هذا اشتغل طيب لما أزود الـ voltage هنا بدل ما هي + +501 +00:50:02,920 --> 00:50:07,000 +one point two صار one point three ايش بدي يحصل كده + +502 +00:50:07,000 --> 00:50:13,120 +الـ voltage هنا 1.5 ايش بدي يحصل في الترانزيستور هذا + +503 +00:50:13,120 --> 00:50:21,420 +هذا هيصير saturated كداش هنا هنا بدي آخذ 1.8 من 1 + +504 +00:50:21,420 --> 00:50:26,780 +.5 أنا بدي آخذ 1.7 هذا هيظل forward active لما هذا + +505 +00:50:26,780 --> 00:50:35,500 +يصير عندي 1.4 هذا بدي يصير عندي 1.6 هنا 1.8 هذا + +506 +00:50:35,500 --> 00:50:43,640 +هيصير وضعه Saturated و هذا Saturated مظبوط في وضع + +507 +00:50:43,640 --> 00:50:47,100 +الـ Saturate يعني هذا طب الـ voltage اللي مطلوب هنا + +508 +00:50:47,100 --> 00:50:52,560 +ايش بدي أساوي هذا بسميها النقطة اللي بعدها اللي + +509 +00:50:52,560 --> 00:50:59,260 +عندي هذه او بدي أعطيها Sharper + +510 +00:51:09,120 --> 00:51:13,960 +هذه النقطة اللي هنا بسميها الـ VIH في الـ VIH + +511 +00:51:13,960 --> 00:51:21,160 +ايش اللي عندي هنا الـ QI و الـ QS و الـ Q ايش أو + +512 +00:51:21,160 --> 00:51:25,480 +هدولة saturated دل عند الـ QP بدّه أشوف ايش وضع + +513 +00:51:25,480 --> 00:51:26,800 +كويس؟ + +514 +00:51:30,520 --> 00:51:34,340 +الآن هذا مش بدي آخذ .. عندي one point ستة الـ one + +515 +00:51:34,340 --> 00:51:36,760 +point ستة هذا لا يصير saturated بدي آخذ point + +516 +00:51:36,760 --> 00:51:43,600 +ثمانية متاح له point ثمانية هنا الآن + +517 +00:51:43,600 --> 00:51:47,340 +هو بياخد جزئية بياخد لو أخذ point سبعة قداش + +518 +00:51:47,340 --> 00:51:52,500 +متظالها point تسعة الـ point تسعة أكثر من حاجة هذا + +519 +00:51:52,500 --> 00:51:58,790 +الآن لو أخذ point ثمانية بدي أبقى عندي point 8 + +520 +00:51:58,790 --> 00:52:02,690 +بتكفي بتعمل هذا saturation و بتعمل هذا saturation + +521 +00:52:02,690 --> 00:52:10,550 +ماحنا جايين لك لسه بس حبة حبة الآن واضحة هذه فهذا + +522 +00:52:10,550 --> 00:52:14,450 +بياخد ليكون saturated بياخد point 8 و point 8 و + +523 +00:52:14,450 --> 00:52:21,230 +بيدطرح منه point 2 بيعطين الـ VIL فالـ VIL اللي عندي + +524 +00:52:21,230 --> 00:52:24,950 +ايش بدي أساوي VBE + +525 +00:52:26,480 --> 00:52:30,880 +2vbe-vbe + +526 +00:52:30,880 --> 00:52:37,180 +-vce + +527 +00:52:47,980 --> 00:52:55,940 +سات ناطس VCE سات اللي هو بدي أساوي one point four volt + +528 +00:52:55,940 --> 00:53:03,000 +اللي عندي كويس + +529 +00:53:03,000 --> 00:53:09,020 +هيك الـ voltage هنا قداش قلت أنا عنه هاي هنا point + +530 +00:53:09,020 --> 00:53:15,800 +اثنين الـ voltage هنا قداش point ثمانية وقداش هنا + +531 +00:53:15,800 --> 00:53:23,790 +بجيلها 0.2 جديش الـ voltage هنا؟ جديش الفرق بين النقطتين + +532 +00:53:23,790 --> 00:53:33,230 +هدول؟ 0.8 جديش مطلوب للتنين يشتغلوا؟ 1.4 يبقى + +533 +00:53:33,230 --> 00:53:38,450 +الترانزيستور هذا هيشتغل يبقى هذا مش reverse هذا + +534 +00:53:38,450 --> 00:53:45,510 +بيكون off مش + +535 +00:53:45,510 --> 00:53:46,090 +هيشتغل + +536 +00:53:49,160 --> 00:53:53,580 +لايش؟ لأن الـ voltage اللي عندي 1 وهذا point 2 لو + +537 +00:53:53,580 --> 00:53:59,480 +حطيت point 7 هيصير عندي هنا كام؟ point 9 وهنا 1 + +538 +00:53:59,480 --> 00:54:02,980 +الـ point هي .. واحد مش هتشغل الـ transistor لها + +539 +00:54:02,980 --> 00:54:10,660 +فهذا لازم يكون وضعه off في هذه الحالة فعندي الـ VOL + +540 +00:54:10,660 --> 00:54:16,160 +بدي أساوي VCE للـ off و وضع الـ saturated اللي موجود + +541 +00:54:16,160 --> 00:54:17,440 +عندي فهذا + +542 +00:54:22,270 --> 00:54:25,850 +الآن كل ما أزود في الـ voltage اللي هنا at one + +543 +00:54:25,850 --> 00:54:30,630 +point هيصير هذا وضع ايش reverse active اللي موجود + +544 +00:54:30,630 --> 00:54:34,010 +هنا لأن + +545 +00:54:34,010 --> 00:54:38,030 +لما أزيد هذا الـ junction ايش بدي يحصل فيها reverse + +546 +00:54:38,030 --> 00:54:43,850 +هتدخل الـ reverse active mode اللي احنا شوفناها قبل + +547 +00:54:43,850 --> 00:54:48,450 +شوية في الـ metal طيب احنا ايش عملنا اليوم هنا نيجي + +548 +00:54:48,450 --> 00:54:56,270 +نختصرها أنا بدأت في شغلة معينة بدأت في الـ .. في لما + +549 +00:54:56,270 --> 00:55:00,710 +الـ input كان بيساوي zero قلت الـ qi لازم يكون وضعه + +550 +00:55:00,710 --> 00:55:05,550 +saturation الـ vc تبع الـ qi كان بيساوي point 2 الـ + +551 +00:55:05,550 --> 00:55:11,710 +point 2 غير كافية تشغل الـ qs و ده qs off و qo + +552 +00:55:11,710 --> 00:55:16,150 +بيكون off الـ qp اللي جيتة forward active الـ v out + +553 +00:55:16,150 --> 00:55:20,830 +في هذه الحالة بيبقى يساوي vcc minus الـ drop across + +554 +00:55:20,830 --> 00:55:25,850 +الـ VBE للـ QP زائد الـ drop across الـ DL الموجود + +555 +00:55:25,850 --> 00:55:30,570 +عندي طلع عندي بيساوي 3.6 زودت الـ input لحد ما + +556 +00:55:30,570 --> 00:55:35,390 +شغلت الـ QS الـ QS صار بـ forward active mode وهذا + +557 +00:55:35,390 --> 00:55:39,130 +قلت الـ voltage اللي بيشغله بسميه VIL قداش الـ + +558 +00:55:39,130 --> 00:55:43,990 +voltage اللي بيشغله 0.7 ناقص الـ 0.2 أعطاني الـ 0.5 + +559 +00:55:43,990 --> 00:55:49,570 +volt لأن الخطوة اللي بعدها روحت بدي أشغّل مش بس الـ + +560 +00:55:49,570 --> 00:55:55,270 +QS بدي أشغل الـ QO و الـ QS صار عند الـ QO شغال و + +561 +00:55:55,270 --> 00:55:59,630 +الـ QS شغال، الـ voltage المطلوب لشغلهم سميته الـ + +562 +00:55:59,630 --> 00:56:03,070 +break point، ال input break point اللي هو بيساوي 1. + +563 +00:56:03,070 --> 00:56:07,670 +2 اللي هو بيساوي إيه؟ قلنا الـ VBE forward للـ QO + +564 +00:56:07,670 --> 00:56:16,070 +زائد الـ VBE forward للـ QS ناقص الـ VCE SAT للـ QI. + +565 +00:56:17,530 --> 00:56:22,090 +فطلعت هذه لما نجمعها 1.2، طيب نسبة لل output في + +566 +00:56:22,090 --> 00:56:26,650 +حالة ال break point كده إيش بيساوي؟ قولنا التيار + +567 +00:56:26,650 --> 00:56:31,430 +عبر الـ RD بيساوي تقريبا التيار عبر الـ RC، طب التيار + +568 +00:56:31,430 --> 00:56:36,230 +عبر الـ ID إيش بيساوي؟ بيساوي الـ 0.7 على الـ RD اللي + +569 +00:56:36,230 --> 00:56:41,320 +هي 1K بيعطينا 0.7، الآن لما بدي اجي اشوف الـ Vout في + +570 +00:56:41,320 --> 00:56:45,120 +هذه الحالة، بدي اشوف كده، اضرب الـ IRC اللي هو بيساوي + +571 +00:56:45,120 --> 00:56:51,840 +IRD في الـ RC، طلع الحالة بيساوي 1.12 زائد اللي عندي + +572 +00:56:51,840 --> 00:56:56,720 +الـ 1.4 اللي موجودة من الـ DL و الـ QP اللي هي 1.4 + +573 +00:56:56,720 --> 00:57:02,860 +صار مجموعهم 2.52، بدي أطرح منها الخمسة، بتعطيني الـ 2.48 + +574 +00:57:02,860 --> 00:57:07,000 +لأن قلت بتزود الـ voltage، ال next critical voltage + +575 +00:57:07,000 --> 00:57:11,260 +اللي هي لما يصير عندي ال saturation الـ QS و الـ QO + +576 +00:57:11,260 --> 00:57:16,400 +saturated، بلاقي هذا بيساوي 1.4، ليش؟ لأن عندي بداخل + +577 +00:57:16,400 --> 00:57:25,740 +في الحساب QP، الـ VBE للـ QO و الـ VBE للـ QS هدول في + +578 +00:57:25,740 --> 00:57:29,800 +وضع ال saturation بيعطيني 1.6، بضع طرح منهم الـ 0 + +579 +00:57:29,800 --> 00:57:36,420 +.2 اللي هو تبعت الـ VCE للـ Qi بيعطيني 1.4، الأهم في + +580 +00:57:36,420 --> 00:57:39,640 +هذا الحالة قد إيش ال output بيساوي؟ بيساوي الـ VCE، طيب + +581 +00:57:39,640 --> 00:57:44,690 +الـ QB قلت إيش وضعه؟ بدي أشوفه، لقيت أنه على شجة + +582 +00:57:44,690 --> 00:57:49,010 +الدايود، يعني ال output تبع الدايود اللي جاته قد إيش + +583 +00:57:49,010 --> 00:57:53,170 +بتطلع عندي، في عندي point two، إذا تبعت الخط في شجة + +584 +00:57:53,170 --> 00:58:00,610 +ال base تبعت الـ QP اللي جيت عندي one volt بالظبط + +585 +00:58:00,610 --> 00:58:04,970 +اللي شغل الـ QP و شغل الـ DL one point four اللي + +586 +00:58:04,970 --> 00:58:09,470 +موجود عندي point eight، معناته الـ QP لازم يكون وضعه + +587 +00:58:09,470 --> 00:58:14,240 +off، الآن لما نكمل الدائرة أنا إيش قاعد بقول؟ بقول + +588 +00:58:14,240 --> 00:58:21,540 +عند الـ QS أو الـ QP، الـ QI، هزود ال input voltage + +589 +00:58:21,540 --> 00:58:25,620 +هيصير عند الـ PE junction تبعتها اللي هي موجودة هنا + +590 +00:58:25,620 --> 00:58:31,160 +هتصير reverse bias، هذا عند forward bias، معناته هذا + +591 +00:58:31,160 --> 00:58:36,540 +هيتحول لوضع ال reverse active mode، واضحة هذه لحد + +592 +00:58:36,540 --> 00:58:42,770 +تلاقوها؟ طيب، الخطوة التالية اللي بنتكلم عنها الـ fan + +593 +00:58:42,770 --> 00:58:46,910 +out و الـ fan out، شفت المحاضرة اللي فاتت لما اتبعنا + +594 +00:58:46,910 --> 00:58:52,810 +الـ fan out كيف كان؟ كان cookbook، و هنا بنتكلم عنه + +595 +00:58:52,810 --> 00:58:56,700 +cookbook again، لأن هذه standard gate، أنت بتمسك + +596 +00:58:56,700 --> 00:58:59,940 +المعادلات هاي، المعادلات اللي عندك أو هاي الـ VTC + +597 +00:58:59,940 --> 00:59:03,800 +بتقولي هاي الـ VTC و خلصت لهذه الدائرة بهذه الشطارة + +598 +00:59:03,800 --> 00:59:09,560 +يعني هذه عملية الحفظ بتظبط معك فيها أو عملية كيف + +599 +00:59:09,560 --> 00:59:13,940 +تشغل هاي بتظبط، الآن اللي عندي بالـ fan out إيش + +600 +00:59:13,940 --> 00:59:18,000 +بتطلع عندي على هذه الشجة + +601 +00:59:37,280 --> 00:59:50,860 +شكل الـ fan out، في عندي هنا جاي هاي + +602 +00:59:50,860 --> 00:59:56,360 +VCC prime، هاي الـ RB prime، هاي الـ QI prime + +603 +01:00:00,210 --> 01:00:06,030 +هنا بيجي عندي in prime، هاي الـ in prime، هاي الـ in + +604 +01:00:06,030 --> 01:00:12,230 +prime، ال output عندي اللي هاد، بديه VOL، ال low اللي + +605 +01:00:12,230 --> 01:00:17,210 +موجود عندي، ليش؟ لأن في حالة ال high إيش وضع هاد الـ + +606 +01:00:17,210 --> 01:00:24,350 +junctions اللي هاد؟ Reverse bias، يعني هذا معزول عن + +607 +01:00:24,350 --> 01:00:29,910 +دائرة ال driver اللي عندي الآن، اللي عندي هي عندي + +608 +01:00:29,910 --> 01:00:37,170 +الـ IOL يعني الـ IJH، و هذا عندي IOL مظبوط، عندي الـ + +609 +01:00:37,170 --> 01:00:41,010 +IOL إيش بده يساوي؟ هذا الـ fan out بده ياخد القوانين + +610 +01:00:41,010 --> 01:00:49,250 +الـ IOL بده يساوي I N Prime، و I يعني بعبارة ثانية + +611 +01:00:49,250 --> 01:00:57,110 +N بدها تساوي I OL على I N Prime، تيار اللي هان + +612 +01:00:57,110 --> 01:00:59,930 +مجموعة تيارات اللي جاي من هان، طب التيار اللي هان + +613 +01:00:59,930 --> 01:01:07,070 +إيش بده يساوي؟ الـ I هذا خط اتنين، الـ I N Prime إيش + +614 +01:01:07,070 --> 01:01:18,330 +بده يساوي؟ VCC minus VOL + +615 +01:01:18,330 --> 01:01:25,210 +على RB، VCC + +616 +01:01:25,210 --> 01:01:30,170 +minus VBE + +617 +01:01:30,170 --> 01:01:37,310 +SAT minus VCE SAT + +618 +01:01:38,410 --> 01:01:46,470 +على الـ RB، كويس؟ ليش؟ لأن هي التيار اللي عندي اللي + +619 +01:01:46,470 --> 01:01:51,570 +داخل هذه، ناقص الـ drop هنا، ناقص الـ voltage اللي هنا + +620 +01:01:51,570 --> 01:01:55,950 +على الـ RB بيعطيني التيار اللي جاي في هذا الاتجاه + +621 +01:01:55,950 --> 01:02:02,250 +طيب إيش في غيره؟ طلع عندي اللي هنا هذا، قلت وضعه + +622 +01:02:02,250 --> 01:02:08,300 +إيش؟ saturation، هذا وضعه off، يعني هذا بقدر أشيله من + +623 +01:02:08,300 --> 01:02:14,640 +الدائرة ككل، طلع + +624 +01:02:14,640 --> 01:02:21,140 +عندي إيش اللي هان؟ التيار اللي هان إيش بدي أساوي الـ + +625 +01:02:21,140 --> 01:02:30,640 +ION تلاتة، بدي أساوي الـ ICO SAT اللي هو بدي أساوي كام؟ + +626 +01:02:30,640 --> 01:02:36,760 +هذا بدي أساوي التيار اللي هان، بدي أساوي سيجما في beta + +627 +01:02:36,760 --> 01:02:41,600 +forward في الـ IBO اللي عندي في وضع ال saturation + +628 +01:02:41,600 --> 01:02:45,080 +لها، طب + +629 +01:02:45,080 --> 01:02:51,560 +الـ IBO إيش بدي يساوي؟ هذا التيار اللي هان، IBO إيش + +630 +01:02:51,560 --> 01:02:59,280 +هذا بدي يساوي، بدي يساوي التيار اللي هان أربعة، الـ + +631 +01:02:59,280 --> 01:03:09,740 +IBO بدي يساوي I E لل S- IRD، مظبوط هاي، هذا هي الـ + +632 +01:03:09,740 --> 01:03:20,700 +IBO وهنا هي الـ IES وهنا هي الـ IRD، طيب خمسة، الـ IRD + +633 +01:03:20,700 --> 01:03:30,820 +بدي أساوي VBESET على الـ RD، طيب الآن بندمن هنا الـ + +634 +01:03:30,820 --> 01:03:35,460 +IES، الـ IES إيش بدي أساوي؟ التيار اللي هاد زائد التيار + +635 +01:03:35,460 --> 01:03:48,200 +اللي هي، مظبوط هي 6، IES بدي أساوي ICS ناقص I زائد + +636 +01:03:48,200 --> 01:03:54,920 +IVS، طب الـ ICS إيش بديها تساوي؟ موجودة عندي، هذا بقدر + +637 +01:03:54,920 --> 01:03:57,280 +أجيبه هي الـ ICS + +638 +01:04:04,060 --> 01:04:12,420 +عشان سابعة، الـ ICS بدي أساوي الـ IRC بدي أساوي VBE أو + +639 +01:04:12,420 --> 01:04:26,780 +VCC minus VBE لل O set ناقص VCE لل S set على الـ RC + +640 +01:04:26,780 --> 01:04:33,840 +هذا اللي عندي واحد خمسة ناقص واحد على هذه صح؟ + +641 +01:04:34,140 --> 01:04:37,020 +بيعطينا التيار لها، طب التيار لها أنا إيش بدي أساوي + +642 +01:04:37,020 --> 01:04:47,300 +هذا الـ I، هي سبعة تمانية، هي عندي الـ I بي اس بديها + +643 +01:04:47,300 --> 01:04:53,780 +تساوي سالب ICI، مظبوط + +644 +01:04:53,780 --> 01:04:59,880 +لأن هي الـ ICI صح؟ + +645 +01:05:00,980 --> 01:05:06,000 +هذه إيش بدها تساوي؟ بدها يجي هذه في هذه، هذه الآن + +646 +01:05:06,000 --> 01:05:12,760 +بدها تساوي الـ ICI اللي هي بدها تساوي minus واحد + +647 +01:05:12,760 --> 01:05:21,280 +زائد beta reverse في الـ IPI صح؟ + +648 +01:05:21,280 --> 01:05:25,640 +هاي اللي .. اللي هاد، هاد مربوط في هذه، طب هاد إيش + +649 +01:05:25,640 --> 01:05:29,780 +بدها تساوي؟ الـ voltage اللي هاد قد إيش؟ point تمانية + +650 +01:05:30,150 --> 01:05:34,890 +و point تمانية، واحد point ستة زائد الـ point سبعة + +651 +01:05:34,890 --> 01:05:40,170 +لأن هذا reverse active اللي عندي صار إيش؟ two point + +652 +01:05:40,170 --> 01:05:45,110 +three، خمسة ناقص two point three على ال Rb بيعطينا + +653 +01:05:45,110 --> 01:05:51,950 +الـ I اللي هات، فـ تسعة IBI + +654 +01:05:51,950 --> 01:05:59,250 +بتتساوى VCC minus two VBE set + +655 +01:06:01,830 --> 01:06:12,990 +-vbc reverse active على الـ RB، هي تسع خطوات بتؤدي + +656 +01:06:12,990 --> 01:06:19,930 +للجواب اللي عندي، الـ fan out و لما أنا أقول + +657 +01:06:19,930 --> 01:06:24,690 +cookbook cookbook، فش فيها اختراع جديد، يعني الخطوات + +658 +01:06:24,690 --> 01:06:30,070 +هدول بتمشي عليهم بالعكس، بتصل للجواب، بس شغل الـ + +659 +01:06:30,070 --> 01:06:34,870 +calculator تبعتك و اعرف كيف تشغلها صح، مافيش فيها + +660 +01:06:34,870 --> 01:06:41,450 +أي شطارة، لو جينا للدائرة هاي و طبقنا عليها قد إيش الـ + +661 +01:06:41,450 --> 01:06:48,390 +fan افضل + +662 +01:06:48,390 --> 01:06:54,210 +خليني + +663 +01:06:54,210 --> 01:06:57,510 +ناخد الأرقام التالية لنشوف قد إيش بيطلع عندي + +664 +01:07:07,080 --> 01:07:15,000 +عندي sigma، خد sigma هنا بتساوي 0.85، وعندي beta + +665 +01:07:15,000 --> 01:07:23,480 +forward equal 25 و beta reverse equal 0.1، المطلوب + +666 +01:07:23,480 --> 01:07:33,420 +n max، إذا + +667 +01:07:33,420 --> 01:07:41,820 +بتشتغل عليهم هذول، مش هطبقلك الخطوات يعني بس هقولك + +668 +01:07:41,820 --> 01:07:48,360 +إيش بدك تبدأ؟ بدك تبدأ من هذه، أيوه هي خمسة ناقص two + +669 +01:07:48,360 --> 01:07:53,380 +point three على الـ R P اللي هي four K، خمسة ناقص + +670 +01:07:53,380 --> 01:07:58,660 +هاي بدي يطلع عندك الرقم هان، هاي رقم تسعة، اخد من + +671 +01:07:58,660 --> 01:08:03,740 +الأرقام، بدي يطلع الجواب عندك six seven five micro + +672 +01:08:03,740 --> 01:08:10,050 +ampere، تمانية بدي .. بدي أجيب هاي تمانية و سبعة هي + +673 +01:08:10,050 --> 01:08:16,050 +بتقدر تقول عنهم واحد، الآن تمانية بدي أطلع عندي الـ + +674 +01:08:16,050 --> 01:08:23,530 +IBS تقريبا هي one زائد point one في six seven five + +675 +01:08:23,530 --> 01:08:31,710 +micro، بدي أطلع عندي seven four three micro، M سبعة + +676 +01:08:33,230 --> 01:08:42,550 +عملية، بدي أجيب الـ IRC، الـ IRC بتطلع عندي 2.5، 2.5 + +677 +01:08:42,550 --> 01:08:51,390 +ميلي امبير، 6 عملية الجمع بدي أطلع عندي هنا 3.24 + +678 +01:08:51,390 --> 01:08:59,070 +ميلي امبير، 5 بدي أطلع عندي اللي هان، الـ IRD بيساوي + +679 +01:08:59,070 --> 01:09:14,170 +0.8 ميلي امبير، بناخد لون تاني، أربعة + +680 +01:09:14,170 --> 01:09:23,170 +بيطلع عندي two point four four milli-amp، تلاتة + +681 +01:09:23,170 --> 01:09:28,810 +بيطلع عندي fifty one point nine milli-amp، اتنين + +682 +01:09:28,810 --> 01:09:40,890 +بيطلع عندي one point one milli-amp، و إذا كتبت 51.9 + +683 +01:09:40,890 --> 01:09:44,250 +يبقى منها Nmax + +684 +01:09:48,170 --> 01:09:54,710 +الخطوات مش كتير يعني لما .. زي ما بقولوها مش كتير + +685 +01:09:54,710 --> 01:10:03,230 +مشوقة لنوصل لجواب يعني متى عرفت إيش ال steps بعد + +686 +01:10:03,230 --> 01:10:09,790 +هيك، تمسك الـ calculator بيبقى شغال عليها الـ fan out + +687 +01:10:09,790 --> 01:10:14,470 +very .. يعني very systematic، لها الدائرة هي اللي + +688 +01:10:14,470 --> 01:10:19,400 +اليوم شفتها مش هتشوف غيرها، يعني الخطوات تبعتنا + +689 +01:10:19,400 --> 01:10:24,340 +محسومة، الدائرة الأولى ممكن تلعب فيها الواحد اللي + +690 +01:10:24,340 --> 01:10:30,400 +هي تعكس ال voltages يعني تعمل بقى VCC بساوية ground + +691 +01:10:30,400 --> 01:10:34,380 +و ال ground تعمله بال negative، مادون ذلك بالنسبة + +692 +01:10:34,380 --> 01:10:37,820 +للدائرة الكبيرة مافيش تغيير عليها إذا بتفهم كيف + +693 +01:10:37,820 --> 01:10:41,760 +تشتغل، و عرفت ال formulas اللي بتحطهم في ال cheat + +694 +01:10:41,760 --> 01:10:45,440 +sheet مافيش عليك خوف، أنت مافيش عليك + +695 +01:10:49,930 --> 01:10:56,110 +أما بدون ذلك، شكل الدائرة صح كبير بس المطلوب منك + +696 +01:10:56,110 --> 01:10:59,850 +تفهمها و تشوف كيف تستخدم ال formulas، اليوم مش اللي + +697 +01:10:59,850 --> 01:11:07,350 +عملناه، طلعنا على ال TTL inverter، يعني شرحنا كيه الـ + +698 +01:11:07,350 --> 01:11:13,050 +basic TTL inverter، كيف بنعمل منه NAND gate، بعد هيك + +699 +01:11:13,050 --> 01:11:17,850 +غطينا ال standard TTLNand gate اللي هي الـ series + +700 +01:11:17,850 --> 01:11:22,830 +عندي ال family تبعت الـ seven thousand four hundred + +701 +01:11:22,830 --> 01:11:26,650 +أو الـ five thousand four hundred طلعنا على الـ VTC + +702 +01:11:26,650 --> 01:11:30,870 +تقيلها طلعنا على الـ fan out ضال عندنا شغلة تانية + +703 +01:11:30,870 --> 01:11:34,550 +بنتطلع عليها اللى هى الـ power dissipation المحاضرة + +704 +01:11:34,550 --> 01:11:41,410 +الجاية هنتكلمنا اليوم علياش على الـ nand هنتكلم على + +705 +01:11:41,410 --> 01:11:44,110 +الـ and و الـ nor و الـ or diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/6qhuIEc1m54_raw.json b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/6qhuIEc1m54_raw.json new file mode 100644 index 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لا يمكن قطعها يعني المادة تتكون من مكونات صغيرة للغاية لا تنقسم", "tokens": [6027, 5172, 15040, 3794, 5172, 3660, 50239, 14407, 16472, 3224, 5296, 16758, 3215, 42963, 16472, 9673, 18513, 3660, 6055, 2655, 30544, 9154, 29910, 2288, 9307, 20328, 17082, 48923, 10874, 28259, 20193, 6055, 1863, 4587, 38251, 1975, 2407, 20193, 7251, 43020, 12174, 9566, 3615, 11296, 37495, 22653, 9673, 18513, 3660, 6055, 2655, 30544, 9154, 3714, 4117, 2407, 8315, 2655, 20328, 17082, 48923, 24976, 17082, 995, 10632, 20193, 6055, 1863, 4587, 38251], "avg_logprob": -0.11905809838167379, "compression_ratio": 1.952755905511811, "no_speech_prob": 0.0, "words": [{"start": 70.12, "end": 71.04, "word": "الفلاسفة", "probability": 0.8806966145833334}, {"start": 71.04, "end": 71.42, "word": " قالوا", "probability": 0.837158203125}, {"start": 71.42, "end": 71.62, "word": " انه", "probability": 0.477783203125}, {"start": 71.62, "end": 72.02, "word": " لابد", "probability": 0.9049479166666666}, {"start": 72.02, "end": 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0.86376953125}], "temperature": 1.0}, {"id": 25, "seek": 59695, "start": 573.43, "end": 596.95, "text": "كل تمانية جرام من الأكسجين بيتحدوا مع واحد جرام من الهيدروجين كل تمانية جرام من الأكسجين بيتحدوا مع واحد جرام من الهيدروجين عشان يكون الـH2O لكن في مركب زي الـH2O2 هلاقي كل ستة عشر جرام أكسجين بتحدوا مع واحد جرام من الهيدروجين إذا الـH2O2 يحتوي على ضعف عدد ذرات الأكسجين", "tokens": [28820, 46811, 7649, 10632, 10874, 2288, 10943, 9154, 16247, 4117, 3794, 7435, 9957, 4724, 36081, 24401, 14407, 20449, 36764, 24401, 10874, 2288, 10943, 9154, 2423, 3224, 25708, 2288, 29245, 9957, 28242, 46811, 7649, 10632, 10874, 2288, 10943, 9154, 16247, 4117, 3794, 7435, 9957, 4724, 36081, 24401, 14407, 20449, 36764, 24401, 10874, 2288, 10943, 9154, 2423, 3224, 25708, 2288, 29245, 9957, 6225, 8592, 7649, 7251, 30544, 2423, 39184, 39, 17, 46, 44381, 8978, 3714, 31747, 3555, 30767, 1829, 2423, 39184, 39, 17, 46, 17, 8032, 15040, 38436, 28242, 8608, 2655, 3660, 6225, 46309, 10874, 2288, 10943, 5551, 4117, 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"probability": 0.9701334635416666}, {"start": 593.37, "end": 593.81, "word": " يحتوي", "probability": 0.96826171875}, {"start": 593.81, "end": 594.19, "word": " على", "probability": 0.9072265625}, {"start": 594.19, "end": 595.63, "word": " ضعف", "probability": 0.9158528645833334}, {"start": 595.63, "end": 595.95, "word": " عدد", "probability": 0.9689127604166666}, {"start": 595.95, "end": 596.31, "word": " ذرات", "probability": 0.802734375}, {"start": 596.31, "end": 596.95, "word": " الأكسجين", "probability": 0.9775390625}], "temperature": 1.0}, {"id": 26, "seek": 62361, "start": 597.73, "end": 623.61, "text": "حسب الـ law of multiple proportions فالـ H2O2 هنلاقي انه بيحتوي على ضعيف عدد ذرات الأكسجين than الميّه نفس الكلام مثال بسيط بيقول الـ compound A contains 1.333 gram of oxygen per gram of carbon حلو يعني كل gram من الكربون يقابل 1.333 gram of oxygen", "tokens": [5016, 35457, 2423, 39184, 2101, 295, 3866, 32482, 6156, 6027, 39184, 389, 17, 46, 17, 8032, 1863, 15040, 38436, 16472, 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{"start": 614.63, "end": 614.95, "word": " gram", "probability": 0.62841796875}, {"start": 614.95, "end": 615.97, "word": " of", "probability": 0.51513671875}, {"start": 615.97, "end": 616.47, "word": " oxygen", "probability": 0.83154296875}, {"start": 616.47, "end": 616.81, "word": " per", "probability": 0.943359375}, {"start": 616.81, "end": 617.21, "word": " gram", "probability": 0.947265625}, {"start": 617.21, "end": 617.43, "word": " of", "probability": 0.9775390625}, {"start": 617.43, "end": 617.91, "word": " carbon", "probability": 0.93701171875}, {"start": 617.91, "end": 618.89, "word": " حلو", "probability": 0.9524739583333334}, {"start": 618.89, "end": 619.65, "word": " يعني", "probability": 0.9541015625}, {"start": 619.65, "end": 619.89, "word": " كل", "probability": 0.98388671875}, {"start": 619.89, "end": 620.17, "word": " gram", "probability": 0.625}, {"start": 620.17, "end": 620.31, "word": " من", "probability": 0.98974609375}, {"start": 620.31, "end": 620.73, "word": " 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{"start": 3271.3, "end": 3271.74, "word": " weights", "probability": 0.72412109375}, {"start": 3271.74, "end": 3272.3, "word": " لمين", "probability": 0.680908203125}, {"start": 3272.3, "end": 3273.42, "word": " للisotopes", "probability": 0.74639892578125}, {"start": 3273.42, "end": 3274.6, "word": " فعلشان", "probability": 0.916259765625}, {"start": 3274.6, "end": 3274.96, "word": " أحسب", "probability": 0.9251302083333334}, {"start": 3274.96, "end": 3275.1, "word": " ال", "probability": 0.98486328125}, {"start": 3275.1, "end": 3275.42, "word": " average", "probability": 0.81494140625}, {"start": 3275.42, "end": 3275.78, "word": " atomic", "probability": 0.96484375}, {"start": 3275.78, "end": 3276.24, "word": " weight", "probability": 0.9384765625}, {"start": 3276.24, "end": 3276.82, "word": " بقول", "probability": 0.976318359375}, {"start": 3276.82, "end": 3277.0, "word": " ال", "probability": 0.75732421875}, {"start": 3277.0, "end": 3277.6, "word": " summation", "probability": 0.953125}, {"start": 3277.6, "end": 3278.62, "word": " isotope", "probability": 0.948486328125}, {"start": 3278.62, "end": 3279.24, "word": " mass", "probability": 0.86376953125}, {"start": 3279.24, "end": 3281.06, "word": " كويس", "probability": 0.9013671875}, {"start": 3281.06, "end": 3281.54, "word": " اللي", "probability": 0.87158203125}, {"start": 3281.54, "end": 3281.88, "word": " هي", "probability": 0.83056640625}, {"start": 3281.88, "end": 3282.6, "word": " كتلة", "probability": 0.98486328125}, {"start": 3282.6, "end": 3282.88, "word": " ال", "probability": 0.4677734375}, {"start": 3282.88, "end": 3283.32, "word": " protons", "probability": 0.95361328125}, {"start": 3283.32, "end": 3284.24, "word": " و", "probability": 0.54541015625}, {"start": 3284.24, "end": 3284.52, "word": " ال", "probability": 0.83203125}, {"start": 3284.52, "end": 3285.3, "word": " neutrons", "probability": 0.97412109375}, {"start": 3285.3, "end": 3286.04, "word": " و", "probability": 0.96142578125}, {"start": 3286.04, "end": 3286.14, "word": " ال", "probability": 0.8369140625}, {"start": 3286.14, "end": 3286.56, "word": " electrons", "probability": 0.395263671875}], "temperature": 1.0}, {"id": 140, "seek": 331502, "start": 3287.72, "end": 3315.02, "text": "بالـ AMU مضروبة في الـ fraction للإيزوتوب، نسبة الماوية مضروبة في الـ fraction للإيزوتوب والنسبة الماوية، طبعا النسبة الماوية في الآخر بيتكمل لـ 100% فمثلا، لو قال لي Naturally occurring carbon is composed of 98.93% carbon 12 and 1.07% carbon 13 حلو، بيتكون من carbon 12 و carbon 13، هاي لعب أقولي بس", "tokens": [3555, 6027, 39184, 6475, 52, 3714, 11242, 32887, 49401, 8978, 2423, 39184, 14135, 24976, 28814, 1829, 11622, 35473, 37746, 12399, 8717, 35457, 3660, 9673, 995, 2407, 10632, 3714, 11242, 32887, 49401, 8978, 2423, 39184, 14135, 24976, 28814, 1829, 11622, 35473, 37746, 16070, 1863, 35457, 3660, 9673, 995, 2407, 10632, 12399, 23032, 3555, 3615, 995, 28239, 35457, 3660, 9673, 995, 2407, 10632, 8978, 6024, 95, 34740, 4724, 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3308.78, "end": 3309.48, "word": ".07", "probability": 0.98876953125}, {"start": 3309.48, "end": 3310.2, "word": "%", "probability": 0.97021484375}, {"start": 3310.2, "end": 3310.6, "word": " carbon", "probability": 0.9404296875}, {"start": 3310.6, "end": 3311.24, "word": " 13", "probability": 0.97314453125}, {"start": 3311.24, "end": 3312.18, "word": " حلو،", "probability": 0.73321533203125}, {"start": 3312.18, "end": 3312.5, "word": " بيتكون", "probability": 0.7848307291666666}, {"start": 3312.5, "end": 3312.7, "word": " من", "probability": 0.97900390625}, {"start": 3312.7, "end": 3312.96, "word": " carbon", "probability": 0.93115234375}, {"start": 3312.96, "end": 3313.32, "word": " 12", "probability": 0.943359375}, {"start": 3313.32, "end": 3313.44, "word": " و", "probability": 0.98779296875}, {"start": 3313.44, "end": 3313.68, "word": " carbon", "probability": 0.697265625}, {"start": 3313.68, "end": 3314.14, "word": " 13،", "probability": 0.896728515625}, {"start": 3314.14, "end": 3314.26, "word": " هاي", "probability": 0.5894775390625}, {"start": 3314.26, "end": 3314.48, "word": " لعب", "probability": 0.7698567708333334}, {"start": 3314.48, "end": 3314.76, "word": " أقولي", "probability": 0.5882161458333334}, {"start": 3314.76, "end": 3315.02, "word": " بس", "probability": 0.991943359375}], "temperature": 1.0}, {"id": 141, "seek": 334097, "start": 3316.39, "end": 3340.97, "text": "بقول the masses of these isotopes are 12 AMU exactly and 13.00335 AMU respectively يعني الكربون 12 12 AMU بينما الكربون 13 13.0035 بيقول يحسب ال average atomic weight", "tokens": [3555, 39648, 264, 23935, 295, 613, 38018, 30545, 366, 2272, 6475, 52, 2293, 293, 3705, 13, 628, 18, 8794, 6475, 52, 25009, 37495, 22653, 33251, 25513, 11536, 2272, 2272, 6475, 52, 49374, 15042, 33251, 25513, 11536, 3705, 3705, 13, 628, 8794, 4724, 1829, 39648, 7251, 5016, 35457, 2423, 4274, 22275, 3364], "avg_logprob": -0.270282449057469, "compression_ratio": 1.275, "no_speech_prob": 0.0, "words": [{"start": 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3323.69, "end": 3325.41, "word": ".00335", "probability": 0.9193115234375}, {"start": 3325.41, "end": 3325.95, "word": " AMU", "probability": 0.925048828125}, {"start": 3325.95, "end": 3326.65, "word": " respectively", "probability": 0.81298828125}, {"start": 3326.65, "end": 3327.39, "word": " يعني", "probability": 0.825439453125}, {"start": 3327.39, "end": 3328.85, "word": " الكربون", "probability": 0.84228515625}, {"start": 3328.85, "end": 3329.73, "word": " 12", "probability": 0.74951171875}, {"start": 3329.73, "end": 3331.23, "word": " 12", "probability": 0.16650390625}, {"start": 3331.23, "end": 3332.33, "word": " AMU", "probability": 0.956787109375}, {"start": 3332.33, "end": 3333.49, "word": " بينما", "probability": 0.982666015625}, {"start": 3333.49, "end": 3334.43, "word": " الكربون", "probability": 0.9640299479166666}, {"start": 3334.43, "end": 3335.01, "word": " 13", "probability": 0.96142578125}, {"start": 3335.01, "end": 3336.09, "word": " 13", "probability": 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"word": " Weight", "probability": 0.966796875}, {"start": 3344.52, "end": 3344.86, "word": " سوى", "probability": 0.715576171875}, {"start": 3344.86, "end": 3345.32, "word": " الـ", "probability": 0.607666015625}, {"start": 3345.32, "end": 3346.0, "word": " Summation", "probability": 0.6353352864583334}, {"start": 3346.0, "end": 3346.76, "word": " مجموعة", "probability": 0.8755859375}, {"start": 3346.76, "end": 3347.16, "word": " الـ", "probability": 0.575439453125}, {"start": 3347.16, "end": 3347.6, "word": " Isotope", "probability": 0.8094075520833334}, {"start": 3347.6, "end": 3348.12, "word": " Mass", "probability": 0.7333984375}, {"start": 3348.12, "end": 3348.78, "word": " AMU", "probability": 0.759033203125}, {"start": 3348.78, "end": 3348.92, "word": " في", "probability": 0.74853515625}, {"start": 3348.92, "end": 3349.44, "word": " الفريقشن", "probability": 0.667529296875}, {"start": 3349.44, "end": 3350.26, "word": " يعني", "probability": 0.78076171875}, {"start": 3350.26, 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"temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3429.332, "duration_after_vad": 3305.981249999986} \ No newline at end of file diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/7MCoQnDYoSk.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/7MCoQnDYoSk.srt new file mode 100644 index 0000000000000000000000000000000000000000..28c0169bc4daa0c8a0edd03cc400dd4db1b8320a --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/7MCoQnDYoSk.srt @@ -0,0 +1,4063 @@ +1 +00:00:21,310 --> 00:00:25,130 +بسم الله الرحمن الرحيم، إذا الله رد اليوم بنكمل في + +2 +00:00:25,130 --> 00:00:30,010 +chapter reactions in aqueous solutions شوفنا في المرة + +3 +00:00:30,010 --> 00:00:34,350 +الماضية إيش يعني solution؟ إيش يعني solvent؟ إيش + +4 +00:00:34,350 --> 00:00:42,200 +يعني solute؟ إيش يعني electrolytic solution؟ و أيضا + +5 +00:00:42,200 --> 00:00:47,520 +شفنا إيش يعني solvation إيش يعني hydration على وجه + +6 +00:00:47,520 --> 00:00:50,780 +الخصوص لأن كل شغلنا هيكون في الـ solutions يعني في + +7 +00:00:50,780 --> 00:00:55,540 +المحاليل المائية، فإذا الله رد اليوم بنكمل في نفس + +8 +00:00:55,540 --> 00:00:59,280 +الموضوع، في الحقيقة كتير طبعا من الـ molecular + +9 +00:00:59,280 --> 00:01:06,420 +compounds بتدوب في الميه، يعني مثلا لو حاولنا ندوب + +10 +00:01:06,420 --> 00:01:10,440 +سكر في الميه بيدوب بسهولة ما فيش مشكلة فيه، لو + +11 +00:01:10,440 --> 00:01:13,440 +حاولنا ندوب كحول في الميه بيدوب بسهولة، مع أنه + +12 +00:01:13,440 --> 00:01:16,760 +molecular compound مش ionic، فمش بس الـ ionic + +13 +00:01:16,760 --> 00:01:22,840 +compounds هي اللي بتدوب في الميه لأ، كمان الكثير من + +14 +00:01:22,840 --> 00:01:25,820 +الـ molecular compounds بتدوب في الميه، لكن الـ + +15 +00:01:25,820 --> 00:01:31,280 +molecular compounds عادة Non-electrolytes، ممكن تكون + +16 +00:01:31,280 --> 00:01:35,120 +زي ما هنشوف بعد شوية weak electrolytes، لكن في أغلب + +17 +00:01:35,120 --> 00:01:38,740 +الأحيان هي عبارة عن non-electrolytes لأن الـ + +18 +00:01:38,740 --> 00:01:41,860 +molecular compounds لا تتفكك إلى أيونات، واحنا شفنا + +19 +00:01:41,860 --> 00:01:46,000 +سابقا إنه التوصيل الكهربي أو الـ conductivity + +20 +00:01:46,000 --> 00:01:49,440 +للمحلول بتتوقف على الأيونات اللي موجودة فيه، لأن هي + +21 +00:01:49,440 --> 00:01:53,380 +اللي بتحمل الشحنة، فبالتالي محلول مثلًا زي الـ + +22 +00:01:53,380 --> 00:01:56,720 +Sucrose اللي هو السكر العادي، أو محلول زي الـ + +23 +00:01:56,720 --> 00:02:01,540 +Methanol اللي هو الكحول، هدول لا يوصلوا المفروض + +24 +00:02:01,540 --> 00:02:04,520 +للكهرباء، محليلهم لا توصل للكهرباء لأن ما فيشوا + +25 +00:02:04,520 --> 00:02:09,480 +أيونات، فهذا يعني يعتبر وضع طبيعي، لكن في بعض + +26 +00:02:09,480 --> 00:02:15,840 +المركبات الموليكولية، الجزيئية، محليلها توصل للكهرباء، + +27 +00:02:15,840 --> 00:02:22,720 +هذه يعني تحديدًا هي محليل الـ Acids زي مثلا الـ HCl + +28 +00:02:22,720 --> 00:02:34,260 +الـ HNO3، الـ H2SO4، الـ HI، الـ HBr، الـ HClO4، هذه + +29 +00:02:34,260 --> 00:02:40,960 +كلها عبارة عن يعني مركبات تساهمية في + +30 +00:02:40,960 --> 00:02:45,400 +الأصل، لكن في المحلول الميه قادر على إنها تنتزع + +31 +00:02:45,400 --> 00:02:49,460 +لبروتون أو تنتزع الـ H+ من الـ acid وبالتالي + +32 +00:02:49,460 --> 00:02:54,360 +بيصير المحلول في أيونات، فهو المادة بحد ذاتها في الـ + +33 +00:02:54,360 --> 00:02:59,190 +gas form في الشكل الغازي بتكون molecular، لكن في + +34 +00:02:59,190 --> 00:03:03,510 +الميّه لأ مش molecular، في الميه إذا كانت مولكيول + +35 +00:03:03,510 --> 00:03:07,150 +ما فيش عندي أيونات، ما فيش توصيل، لكن الـ acids تحديدا في + +36 +00:03:07,150 --> 00:03:11,610 +الميّه بنلاحظ إنها بسهولة جدا بتتفكك وبتعطيني + +37 +00:03:11,610 --> 00:03:15,450 +الأيونات تبعها، وبالتالي محاليل الـ acids مع أنها + +38 +00:03:15,450 --> 00:03:20,070 +molecular compounds تعتبر محاليل Electrolytic. + +39 +00:03:21,710 --> 00:03:25,590 +بنتكلم الآن عن الـ strong و الـ weak electrolytes. + +40 +00:03:25,590 --> 00:03:29,710 +الـ strong electrolytes، يمكن من المفيد إنه في الأول + +41 +00:03:29,710 --> 00:03:35,130 +نفّرج بين الـ solubility و خليني أقول الـ electrical + +42 +00:03:35,130 --> 00:03:38,330 +conductivity، الـ solubility مواد كتير بتدوب في + +43 +00:03:38,330 --> 00:03:43,430 +الميه ما فيش مشكلة، لكن هذا ما لهوش دعوة بتوصيلية + +44 +00:03:43,430 --> 00:03:46,430 +التوصيلية تعتمد على الأيونات، Solubility تعتمد على + +45 +00:03:46,430 --> 00:03:49,570 +طبيعة المركبات، فمركبات كتير عندي بتدوب في الميه زي + +46 +00:03:49,570 --> 00:03:52,510 +ما شوفنا السكروز زي ما شوفنا الميثانول الإيثانول + +47 +00:03:52,510 --> 00:03:57,250 +وغيرهم، الأمونيا بتدوب في الميه، لكن توصيلية ما فيش + +48 +00:03:57,250 --> 00:04:03,290 +توصيلية، فما لهاش دعوة توصيلية لحد كبير يعني بالإيه، + +49 +00:04:03,290 --> 00:04:08,390 +بهل المادة free of soluble في الميه ولا لأ، ما لهاش + +50 +00:04:08,390 --> 00:04:13,550 +دعوة، فبالتالي يمكن من المفيد إنه نطلع على + +51 +00:04:13,550 --> 00:04:16,430 +الـStrong و الـWeak Electrolytes على أساس إنه هل + +52 +00:04:16,430 --> 00:04:21,010 +المادة بتتفكك للأيونات بشكل كبير ولا بشكل قليل + +53 +00:04:21,010 --> 00:04:25,050 +للغاية، إذا تفككت إلى أيوناتها بشكل كبير في الميه + +54 +00:04:25,050 --> 00:04:28,270 +معناته هي strong electrolyte، لكن إذا كانت تفكك + +55 +00:04:28,270 --> 00:04:33,550 +بشكل قليل فتعتبر weak electrolyte، فمثلا لو شفنا + +56 +00:04:33,550 --> 00:04:38,190 +حاجة زي الـHCl حمض معروف، وقلنا هو في الـ gas form + +57 +00:04:38,190 --> 00:04:42,130 +هو molecular لكن في الميه فورا بتفكك بيعطي H+ + +58 +00:04:42,130 --> 00:04:46,650 +و الـCl− لكن لو إجينا في الميه هل بنلاقي HCl + +59 +00:04:46,650 --> 00:04:51,830 +molecules، بنقول لأ، بنقول لأ، فهو يبقى محلول الـHCl + +60 +00:04:51,830 --> 00:04:56,150 +بما إنه بتفكك تفكك كامل في الميه إلى أيوناته، بنقول + +61 +00:04:56,150 --> 00:04:59,950 +والله هو strong electrolyte، يتفكك تفكك كامل في + +62 +00:04:59,950 --> 00:05:05,150 +الميه، فهو strong electrolyte، كل المحاليل الناتجة + +63 +00:05:05,150 --> 00:05:08,480 +عن خليني أقول الـ ionic compounds هي strong + +64 +00:05:08,480 --> 00:05:12,100 +electrolytes وبين جسين عندما تكون ذائبة، لأن في بعض + +65 +00:05:12,100 --> 00:05:15,880 +الأحيان بعض الـ ionic compounds بتدوبش في الميه + +66 +00:05:15,880 --> 00:05:20,420 +بشكل يعني كويس، بتكون شحيحة الذوبان جدا في الميه + +67 +00:05:20,960 --> 00:05:25,380 +مثلًا الـ Mercuric Sulphide شحيح جدا، ده باين في + +68 +00:05:25,380 --> 00:05:30,620 +الميه قليل خالص، لو بنتطلع على مثلًا الـ Aluminum + +69 +00:05:30,620 --> 00:05:34,000 +Hydroxide برضه شحيح جدا، الـ Iron Hydroxide شحيح + +70 +00:05:34,000 --> 00:05:38,040 +جدا، فكمية الأيونات لا يُعتبر Strong Electrolyte + +71 +00:05:38,040 --> 00:05:42,080 +عشان يكون Strong Electrolyte لازم يكون يعني إله + +72 +00:05:42,080 --> 00:05:44,940 +Solubility زي ما هنشوف بعد شوية، Solubility تبعته + +73 +00:05:44,940 --> 00:05:49,660 +تتجاوز 1 من 100 مولر، يعني أكثر من 1 من 100 مولر + +74 +00:05:50,090 --> 00:05:54,150 +عشان نقول والله إنه soluble، فبالتالي يعني حتى + +75 +00:05:54,150 --> 00:06:00,490 +المركبات الأيونية مش كلها بنقدر نقول إنه تعطينا + +76 +00:06:00,490 --> 00:06:04,410 +strong electrolytes إلا إذا كانت ذائبة بشكل معقول + +77 +00:06:04,410 --> 00:06:07,410 +لأن أنا في النهاية عشان يكون الـ electrolyte قوي + +78 +00:06:07,410 --> 00:06:11,550 +بدي يكون في عندي كمية محترمة من الأيونات، فإذا كانت + +79 +00:06:11,550 --> 00:06:18,590 +بتفككش مشكلة أو هنشوف ليش بعد شوية، لكن بشكل عام + +80 +00:06:18,590 --> 00:06:22,570 +بقدر أقول كل الـ alkaline metals، salts، اللي هي + +81 +00:06:22,570 --> 00:06:27,250 +المجموعة الأولى، مهما اتحدت بأي شيء، هي عبارة عن + +82 +00:06:27,250 --> 00:06:29,450 +strong electrolytes، بسهولة بتتفكك، strong + +83 +00:06:29,450 --> 00:06:35,350 +electrolytes، بسهولة بتتفكك، كل محاليل الـ ammonium + +84 +00:06:35,350 --> 00:06:39,800 +على سبيل المثال برضه بسهولة بسهولة جدا بتتفكك، فـأولا + +85 +00:06:39,800 --> 00:06:43,200 +ما بنلاقي أمونيوم، أمونيوم كربونيت، أمونيوم بروميد + +86 +00:06:43,200 --> 00:06:47,320 +أمونيوم كلوريد، أمونيوم نايترايت، كل أملاح الأمونيوم + +87 +00:06:47,320 --> 00:06:52,300 +بتتفكك تفكك كامل في الميه فورا، بتدوب بسهولة و + +88 +00:06:52,300 --> 00:06:58,940 +بتتفكك تفكك كامل، وهنشوف ذوبانيتها بعد شوية الـ + +89 +00:06:58,940 --> 00:07:02,280 +Strong Electrolyte هو الـ Electrolyte اللي بيتفكك + +90 +00:07:02,280 --> 00:07:06,940 +تفكك كامل في الميه، والـ Ionic Compounds مثال عليه، + +91 +00:07:06,940 --> 00:07:09,820 +لكن الـ Ionic Compounds بدي آخد بالنا إنه يجب أن + +92 +00:07:09,820 --> 00:07:14,320 +تكون ذائبة أصلا بنسبة معقولة علشان نقول والله إنها + +93 +00:07:14,320 --> 00:07:18,860 +Strong Electrolytes، لكن المجموعة الأولى كلها ذائبة + +94 +00:07:18,860 --> 00:07:23,240 +إذا بتعطيني Strong Electrolytes، الـ Acids المجموعة + +95 +00:07:23,240 --> 00:07:29,880 +الأخيرة، HCl، HBr، HI، كلها strong electrolytes، بينما + +96 +00:07:29,880 --> 00:07:35,620 +الـ HF لأ ضعيف لأن الرابطة التساهمية تبعته قوية كتير + +97 +00:07:35,620 --> 00:07:40,060 +الـ H مربوطة بالـ F برابطة قوية جدا، الميه لا + +98 +00:07:40,060 --> 00:07:45,760 +تستطيع أن تنتزع الـ H من الـHF، وبالتالي الـHCl + +99 +00:07:45,760 --> 00:07:51,680 +الـHBr، الـHI كلها تعتبر إلكتروليتات قوية، strong + +100 +00:07:51,680 --> 00:07:56,400 +electrolytes، خلينا الآن نتطلع على الـ weak + +101 +00:07:56,400 --> 00:07:59,460 +electrolytes، الـ weak electrolytes جال والله هي + +102 +00:07:59,460 --> 00:08:04,840 +التي لا تتفكك في الميه بشكل كامل، من أشهر أمثلتها + +103 +00:08:04,840 --> 00:08:09,700 +اللي هي الـ weak acids والـ weak acids هي عبارة عن + +104 +00:08:09,700 --> 00:08:13,380 +الـ acids ما عدا الـ strong، هنشوف بعد شوية إيش هي + +105 +00:08:13,380 --> 00:08:18,360 +الـ strong acids وخلافها كله يعتبر weak، من أمثلته + +106 +00:08:18,360 --> 00:08:22,380 +أي شيء بيحتوي على المجموعة اللي بنقولها كربوكسيلات + +107 +00:08:22,380 --> 00:08:26,740 +COOH، مش معاكم إنكم بتعرفوا اسم الكربوكسيلات؟ لكن + +108 +00:08:26,740 --> 00:08:31,220 +اسم الكربوكسيلات وإن بنلاقي COOH، هذه الـ H تعتبر + +109 +00:08:31,220 --> 00:08:38,870 +إيه؟ acidic فهي بتتفكك بتعطينا CH3COO− زائد H+ + +110 +00:08:38,870 --> 00:08:44,950 +لكن تفكك هذا الحمض اللي قدامي، أي مادة تحتوي + +111 +00:08:44,950 --> 00:08:50,670 +على COOH تسمى حمض، لكن في نفس الوقت حمض إيه؟ ضعيف + +112 +00:08:50,670 --> 00:08:54,690 +إيش يعني ضعيف؟ يعني لا تتفكك بشكل معقول في الميه + +113 +00:08:54,690 --> 00:08:59,210 +مثلًا هذا اسمه Acetic acid بيتفكك تقريبا نسبة واحد + +114 +00:08:59,210 --> 00:09:02,650 +في المية في المياه، كمية الأيونات مش كافية يعتبر + +115 +00:09:02,650 --> 00:09:06,730 +weak electrolyte، weak electrolyte لا يتفكك تفكك + +116 +00:09:06,730 --> 00:09:11,650 +كمية في المياه، هل نستطيع أن نجد CH3COOH molecules + +117 +00:09:11,650 --> 00:09:19,080 +نعم، بوفرة، بوفرة، أغلب المحلول بيكون CH3COOH بدون + +118 +00:09:19,080 --> 00:09:22,980 +تفكك، لكن اللي متفكك منه قليل تقريبا واحد في المية + +119 +00:09:22,980 --> 00:09:26,620 +لكن في الـ strong electrolytes لا نستطيع أن نجد الـ + +120 +00:09:26,620 --> 00:09:30,340 +molecular compound، مش ممكن بنلاقيش الـ molecular + +121 +00:09:30,340 --> 00:09:36,700 +compound، ماشي يا جماعة، نفس الكلام الـ ammonia الـ + +122 +00:09:36,700 --> 00:09:40,720 +ammonia أيضا تعتبر weak electrolyte، لأن لما نضيف + +123 +00:09:40,720 --> 00:09:44,220 +الـ ammonia للميه بتاخد H+ من الميه وبتصير + +124 +00:09:44,220 --> 00:09:50,680 +ammonium، لكن قليل بتاخد حوالي واحد في المية واحد في المية + +125 +00:09:50,680 --> 00:09:54,540 +بس من الأمونيا بيتحول للأمونيوم، يعني بيعطينا + +126 +00:09:54,540 --> 00:09:59,620 +أيونات واحد في المية، لكن معظم المحلول أمونيا معظمه + +127 +00:09:59,620 --> 00:10:04,100 +أمونيا molecular وبالتالي تعتبر الأمونيا weak + +128 +00:10:04,100 --> 00:10:09,620 +electrolyte، الكالسيوم هيدروكسايد والباريوم + +129 +00:10:09,620 --> 00:10:13,960 +هيدروكسايد والاسترانشيوم + +130 +00:10:13,960 --> 00:10:17,100 +هيدروكسايد هدول في المجموعة الثانية ما قلتش + +131 +00:10:17,100 --> 00:10:21,460 +المغنيزيوم، المغنيزيوم لأ قوي، يعني بيضله solid، لكن هدول + +132 +00:10:21,460 --> 00:10:25,600 +كالسيوم، باريوم، استرانشيوم هيدروكسايد، هذه + +133 +00:10:25,600 --> 00:10:31,850 +الهيدروكسايد يعني تذوب في الماء نسبيا، تذوب في الماء + +134 +00:10:31,850 --> 00:10:35,470 +نسبيا فهي تعتبر strong electrolytes يعني أكثر من + +135 +00:10:35,470 --> 00:10:39,890 +واحد في المية حسب يعني تحليل لإيش هو الـ strong + +136 +00:10:39,890 --> 00:10:42,870 +electrolyte بدي يكون دايب في الميه نسبة أكثر من + +137 +00:10:42,870 --> 00:10:47,170 +واحد في المية حسب الكاتب ما بده يعني، فبنقول هنا الـ + +138 +00:10:47,170 --> 00:10:51,030 +calcium hydroxide، الفكرة إن strong electrolyte ليه + +139 +00:10:51,030 --> 00:10:54,210 +لأنه لو إجينا لمحلول الـ calcium hydroxide مع أنه + +140 +00:10:54,210 --> 00:10:58,080 +بيدوبش كامل في الميه، لكن لو إجينا للمحلول هل نجد + +141 +00:10:58,080 --> 00:11:03,440 +كالسيوم هايدروكسايد اثنين هذا كله على هيئة مولكيل + +142 +00:11:03,440 --> 00:11:08,580 +في الماء؟ لا بنلاقيهش، مدام ذاب، إذا كالسيوم اثنين + +143 +00:11:08,580 --> 00:11:12,760 +plus و اثنين هايدروكسايد، لكن بدنا نتذكر أن + +144 +00:11:12,760 --> 00:11:15,080 +الكالسيوم هايدروكسايد والباريوم هايدروكسايد + +145 +00:11:15,080 --> 00:11:19,240 +والسترانشيوم هايدروكسايد هذه المواد يعني ذوبانها + +146 +00:11:19,240 --> 00:11:22,920 +في الماء مش freely، مش freely، لكن مثلاً Sodium + +147 +00:11:22,920 --> 00:11:27,760 +Hydroxide، Potassium Hydroxide، Lithium Hydroxide، + +148 +00:11:27,760 --> 00:11:31,400 +هذه المواد بتدوب في الماء بشكل كامل ومحاليلها لا + +149 +00:11:31,400 --> 00:11:34,300 +تحتوي على أي solid زي اللي بتدوب freely في الماء + +150 +00:11:34,300 --> 00:11:39,520 +المغنيزيوم ذوبانيته قليلة جداً، فلذلك لا نقدرش نعتبره + +151 +00:11:39,520 --> 00:11:44,240 +strong electrolyte نعم المغنيزيوم Hydroxide weak + +152 +00:11:44,240 --> 00:11:47,300 +زي الألمنيوم Hydroxide لأنه كمية الأيونات يعني + +153 +00:11:47,300 --> 00:11:51,000 +اللي بدها تدوب منه كمية قليلة خالص، كمية لا تكاد + +154 +00:11:51,000 --> 00:11:54,980 +تذكر، فنعتبره weak electrolyte ما جبناش سيرته هنا + +155 +00:11:54,980 --> 00:11:59,340 +يعني إحنا في هذا الـ chapter بنحاول أنه نعطي + +156 +00:11:59,340 --> 00:12:03,760 +المفاهيم العامة بحيث أنه لو مر علينا أي شيء في + +157 +00:12:03,760 --> 00:12:08,660 +الحياة العملية أو في أي سؤال نفهم يعني الاتجاه وين + +158 +00:12:08,660 --> 00:12:12,760 +رايح لكن مش بالتفصيل المهمين لأنه بالنسبة لي أنا + +159 +00:12:12,760 --> 00:12:15,400 +أنا بعتبر الـ calcium hydroxide هذا لا يذوب في + +160 +00:12:15,400 --> 00:12:18,420 +الماء بعتبره non electrolyte أنا بالنسبة ليه؟ هو + +161 +00:12:18,420 --> 00:12:20,640 +كأستاذ بيعتبره non electrolyte، هو الكاتب لا جال + +162 +00:12:20,640 --> 00:12:23,940 +لا أنا بيعتبره non electrolyte، عفواً يعني، بيعتبر + +163 +00:12:23,940 --> 00:12:26,360 +الـ electrolyte هو اللي بدوب أيونياً اه، لكن بدوب + +164 +00:12:26,360 --> 00:12:31,320 +بإيه، يعني أكثر من واحد في المئة مولار، هذا + +165 +00:12:31,320 --> 00:12:34,860 +تعريفه، لكن أنا في إسبائيلي لا، تعريفي والله لا، + +166 +00:12:34,860 --> 00:12:37,040 +هو إذا كان بدوب شفريلي في الماء، فهو لا يعتبر + +167 +00:12:37,040 --> 00:12:41,880 +strong electrolyte، فهي يعني اللي بدنا نوصله إحنا + +168 +00:12:41,880 --> 00:12:46,600 +في هذا المساء أنه نشوف الاتجاه العام للأمور لأنه + +169 +00:12:46,600 --> 00:12:51,620 +التفاصيل كثيرة فإحنا بدنا نحاول بس ناخد فكرة يعني + +170 +00:12:51,620 --> 00:12:57,460 +جيدة وقوية و أساس متين للحكم على الأمور لكن مش + +171 +00:12:57,460 --> 00:13:02,400 +بالتفاصيل الدقيقة خاصة في هذه الأمور لأنه بتتفاوت + +172 +00:13:02,400 --> 00:13:07,460 +آراء الناس فيها يعني، بنجي الآن بنتطلع على موضوع + +173 +00:13:07,460 --> 00:13:11,700 +كثير مهم اللي هو الاتزان، طب إحنا بنقول أن الـ + +174 +00:13:11,700 --> 00:13:16,100 +acetic acid لما نحط جثين ونحط aqueous يعني دايب + +175 +00:13:16,100 --> 00:13:19,560 +في الماء في الماء aqueous الـ acetic acid في الماء + +176 +00:13:19,560 --> 00:13:22,660 +وهي موجود في الماء على هيئة ايه؟ مولكيول لأنه كانت + +177 +00:13:22,660 --> 00:13:26,700 +بـ aqueous، جاي بيتفكك جزئياً وبيعطينا الـ Acetate + +178 +00:13:26,700 --> 00:13:30,380 +والـ H Plus حوالي 1% منه، الـ Acetate بتكون أكواث + +179 +00:13:30,380 --> 00:13:33,200 +والـ H Plus أكواث، ايش يعني لما نقول أكواث؟ يعني + +180 +00:13:33,200 --> 00:13:38,740 +Hydrated، يعني في جزيئات ماء حواليها، Solvated قلنا + +181 +00:13:38,740 --> 00:13:43,160 +أن الـ H2O، الـ H عليها partial positive والـ O + +182 +00:13:43,160 --> 00:13:47,480 +عليها partial negative، فهنًّا مثلاً بتجرب الـ H من + +183 +00:13:47,480 --> 00:13:52,340 +الـ H2O أكثر من H، أكثر من يعني مولكيول من الـ H2O + +184 +00:13:52,340 --> 00:13:56,840 +بيجوا بيصيروا أنصفير حوالين الأسيتات فهذا يعني + +185 +00:13:56,840 --> 00:14:01,420 +اسمه hydration ولو كان solvent غير الماء بنقول + +186 +00:14:01,420 --> 00:14:04,700 +اسمه solvation لكن إحنا بنشتغل في الماء وبنقول هذا + +187 +00:14:04,700 --> 00:14:08,740 +ايه hydration بنقولها water of hydration، هنًّا الـ H + +188 +00:14:08,740 --> 00:14:12,900 +بلس كمان التاني بيحصل له hydration بتجرب عليه الـ O + +189 +00:14:12,900 --> 00:14:17,000 +سالب partial negative O partial negative O partial + +190 +00:14:17,000 --> 00:14:19,980 +negative O partial negative بعمله حوالي أسفير + +191 +00:14:19,980 --> 00:14:23,920 +فبيصير كمان الـ H بلس hydrated لكن ما يهمني في هذه + +192 +00:14:23,920 --> 00:14:27,920 +المعادلة أن الـ acetic acid بتفكك لـ acetate والـ H + +193 +00:14:27,920 --> 00:14:33,900 +بلس لغاية مرحلة معينة، طب وبعدين خلاص وقف 1% وقف + +194 +00:14:33,900 --> 00:14:39,980 +التفكك بنقول في الحقيقة الـ Equilibrium Dynamic + +195 +00:14:39,980 --> 00:14:43,520 +يعني بمعنى آخر بيضلوا الـ Acetic Acid يتفكك و + +196 +00:14:43,520 --> 00:14:47,260 +يعطيني Acetate و H Plus لكن في نفس الوجه وبنفس + +197 +00:14:47,260 --> 00:14:50,320 +المعدل يعني بنفس السرعة، الـ H Plus بتتحد بالـ + +198 +00:14:50,320 --> 00:14:54,280 +Acetate وبتعطيني Acetic Acid لكن في أي مرحلة في + +199 +00:14:54,280 --> 00:14:58,600 +أي وقت من الأوقات بعد الاتزان بعد الاتزان في أي + +200 +00:14:58,600 --> 00:15:03,900 +وقت لو اجيت عديت عدد أيونات الـ Acetate أو الـ H + +201 +00:15:03,900 --> 00:15:06,980 +plus مالجهة ثابتة في المحلول، لها تتغير، لكن مش + +202 +00:15:06,980 --> 00:15:10,360 +معناه كلام أن الـ acetic acid مش عامله يتفكك ولا + +203 +00:15:10,360 --> 00:15:12,840 +الـ acetate والـ H plus مش عاملين يحصل لهم + +204 +00:15:12,840 --> 00:15:16,180 +combination ويكونوا الـ acetic acid، لا الـ acetic + +205 +00:15:16,180 --> 00:15:20,080 +acid باستمرار رايح لليمين بيكون نواتج والنواتج + +206 +00:15:20,080 --> 00:15:24,220 +باستمرار رايح لليسار بتكون متفاعلات اللي هو يعني + +207 +00:15:24,220 --> 00:15:27,480 +الـ acetic acid، هذه النقطة اللي عندها بيتساوى معدل + +208 +00:15:27,480 --> 00:15:30,460 +التفاعل في الاتجاه الأمامي مع معدل التفاعل في + +209 +00:15:30,460 --> 00:15:33,680 +الاتجاه الخلفي أو العكسي اسمها point of + +210 +00:15:33,680 --> 00:15:38,550 +equilibrium نقطة الاتزان يعني وصلنا للاتزان ممكن + +211 +00:15:38,550 --> 00:15:42,910 +نحصل الاتزان على الاتزان يعني بسرعة وممكن نحصل + +212 +00:15:42,910 --> 00:15:46,750 +عليه ببطء ممكن ياخد أوقات طويلة جداً وممكن ياخد + +213 +00:15:46,750 --> 00:15:49,610 +أوقات قصيرة جداً، ما لناش دعوة في هذا الكلام اللي + +214 +00:15:49,610 --> 00:15:53,550 +قالنا دعوة فيه أنه مجرد ما يتساوى معدلي التفاعل في + +215 +00:15:53,550 --> 00:15:56,570 +الاتجاه الأمامي والاتجاه العكسي معناه كلام هذه + +216 +00:15:56,570 --> 00:16:01,350 +اسمها نقطة الاتزان، ما فيش عندي نقطة اتزان للـ strong + +217 +00:16:01,350 --> 00:16:04,900 +electrolytes ما فيش عندي، ليه؟ لأن الـ strong + +218 +00:16:04,900 --> 00:16:09,280 +electrolyte بحطش سهمين متعاكسين، سهم في اتجاه واحد + +219 +00:16:09,280 --> 00:16:13,700 +لأنه ممنوع الـ strong electrolyte يكون موجود يعني + +220 +00:16:13,700 --> 00:16:15,640 +على هيئة molecule، لا يكون موجود على هيئة + +221 +00:16:15,640 --> 00:16:19,560 +molecule، ما فيش، كله بده يخلص يروح لإيه؟ لليمين، كله + +222 +00:16:19,560 --> 00:16:26,820 +لازم ينتهي ويروح للنواتج، فهي مثلاً الـ HCl كله بده + +223 +00:16:26,820 --> 00:16:30,780 +يروح للنواتج، ممنوع يظل عند HCl في المحلول فهذا لا + +224 +00:16:30,780 --> 00:16:36,060 +مش اتزان، الاتزان فقط للـ weak electrolytes، الاتزان + +225 +00:16:36,060 --> 00:16:40,280 +بنكتبه فقط للـ weak electrolytes، تعالوا نتطلع على + +226 +00:16:40,280 --> 00:16:44,340 +أشياء بسيطة جداً، بيقول لي مثلاً which solute has a + +227 +00:16:44,340 --> 00:16:51,890 +strong electrolytic solution، عايش بدي أدور انه جزء + +228 +00:16:51,890 --> 00:16:55,870 +بيعطيني أيونات أكثر؟ أنه مادة بتعطيني أيونات أكثر؟ + +229 +00:16:55,870 --> 00:16:59,790 +لما نقول لك which solute has a strong electrolytic + +230 +00:16:59,790 --> 00:17:04,290 +solution، معناته أن solute بيعطيني أيونات أكثر لأن + +231 +00:17:04,290 --> 00:17:07,250 +إذا كان عطاني أيونات أكثر بيكون ايه؟ a stronger + +232 +00:17:07,250 --> 00:17:11,950 +electrolytic solution، فتعالى نشوف الميثانول، هل هذا + +233 +00:17:11,950 --> 00:17:15,770 +أيوني compound؟ وهذا حكمنا على الأمور بندور على + +234 +00:17:15,770 --> 00:17:19,640 +أيوني compound، هل هو أيوني compound من أصله؟ لا، الـ + +235 +00:17:19,640 --> 00:17:22,780 +Ionic compound بتكون من Metal و Non-metal، لا والله هذا مش Metal و Non-metal، هذا Molecular + +236 +00:17:22,780 --> 00:17:24,940 +compound، إذا لا مش هذا، Sodium Hydroxide طبعاً هاي + +237 +00:17:24,940 --> 00:17:30,110 +معدن والجروبس اللي اتكلمنا عنها، فهي هيدروكسيد + +238 +00:17:30,110 --> 00:17:36,070 +وصوديان، اه مدام عندي معدن من المجموعة الأولى إذا اه + +239 +00:17:39,670 --> 00:17:44,590 +هذا بيتفكك تفكك كامل لـ N A Plus والـ O H سالب إذا + +240 +00:17:44,590 --> 00:17:48,330 +اه هذا محلوله strong electrolyte، طب نيجي لقى + +241 +00:17:48,330 --> 00:17:53,480 +الـ acetic acid، قال اه الـ acetic acid ايش فيه؟ فيه CO + +242 +00:17:53,480 --> 00:17:57,840 +ايش فيه فيه ايه؟ فيه Carboxylic Acid، هو عبارة عن + +243 +00:17:57,840 --> 00:18:00,140 +Carboxylic Acid يعني في عندهم Carboxylatic group + +244 +00:18:00,140 --> 00:18:03,540 +هذا weak electrolyte weak acid مش strong acid + +245 +00:18:03,540 --> 00:18:08,000 +مدامه weak acid إذا ما هو strong electrolyte إذا + +246 +00:18:08,000 --> 00:18:11,620 +بس محلول الـ sodium hydroxide هو اللي بيعطيني strong + +247 +00:18:11,620 --> 00:18:16,600 +electrolyte، مثلاً بيقول دي diagram below represents + +248 +00:18:16,600 --> 00:18:21,840 +an aqueous solution of either مغنيزيوم كلوريد أو + +249 +00:18:21,840 --> 00:18:26,260 +KCl أو K2SO4، بدنا نعرف هذا المحلول هل هو مغنيزيوم + +250 +00:18:26,260 --> 00:18:30,220 +كلوريد ولا KCl ولا K2SO4، طبعاً أنا باجي بطلع + +251 +00:18:30,220 --> 00:18:34,200 +بأجي أول حاجة متفكك تفكك كامل، هدول كلهم عبارة عن + +252 +00:18:34,200 --> 00:18:37,360 +أصلًا كلهم عبارة عن اه strong electrolytes لأن كلهم + +253 +00:18:37,360 --> 00:18:41,200 +عبارة عن ionic compounds لكن بأجي مثلاً السالب + +254 +00:18:41,200 --> 00:18:45,590 +جديش عنده اثنين، فبشوف والله هذه السالب جديش + +255 +00:18:45,590 --> 00:18:48,870 +الكلوريد سالب واحد، هذه الكلوريد سالب واحد هذه + +256 +00:18:48,870 --> 00:18:54,030 +سالب اثنين، إذا هذا سلفيت مثلاً باجي بطلع، بأجي اطلع هنًّا + +257 +00:18:54,030 --> 00:18:58,710 +اه الـ potassium واحد potassium سلفيت، لأنه كل واحدة + +258 +00:18:58,710 --> 00:19:01,870 +من السالب اثنين سالب، هدول بتاخد اثنين موجب عشان + +259 +00:19:01,870 --> 00:19:06,130 +تعمل فهذا K2SO4، حكي يعني مش كثير ما عاصر يعني يجيلنا + +260 +00:19:06,130 --> 00:19:09,150 +حاجة زي هيك في الامتحان لكن الكتاب صاير ذاكره + +261 +00:19:09,150 --> 00:19:15,010 +فبندكره زي ما هو، لعله يعني يكون مفيدًا، الآن بدي اطلع + +262 +00:19:15,010 --> 00:19:18,350 +على نتكلم عن الـ reactions in aqueous solutions + +263 +00:19:18,350 --> 00:19:23,010 +فبدي اطلع على تلات أنواع من أنواع الـ reactions هذا + +264 +00:19:23,010 --> 00:19:29,470 +هو جوهر أو الجزء المهم من هذا الـ chapter، حاول اطلع + +265 +00:19:29,470 --> 00:19:32,450 +على التفاعلات المختلفة اللي بتحصل في الـ aqueous + +266 +00:19:32,450 --> 00:19:36,110 +solutions بتتكلم عن تفاعلات الترسيب اللي هي + +267 +00:19:36,110 --> 00:19:40,170 +precipitation reactions بدي أتكلم عن تفاعلات الـ + +268 +00:19:40,170 --> 00:19:44,730 +acids والـ bases الأحماض والقواعد وبدي أتكلم عن + +269 +00:19:44,730 --> 00:19:49,630 +تفاعلات الأكسدة والاختزال، بعدين الجزء الأخير من + +270 +00:19:49,630 --> 00:19:54,530 +الشابتر بتحدث عن الحسابات تبعتهم، لكن الآن بس بدي + +271 +00:19:54,530 --> 00:19:57,870 +أتحدث عن ايش هو الـ precipitation reaction بقول في + +272 +00:19:57,870 --> 00:20:01,010 +بعض الأحيان بكون في عندي محلولين، مادة ذائبة هنًّا + +273 +00:20:01,010 --> 00:20:05,250 +ومادة ذائبة هنًّا، بأجي بحط المحلولين على بعض بطلع + +274 +00:20:05,250 --> 00:20:11,070 +لراسب اه، فالراسب أو يعني مقدر أقول أنا الـ + +275 +00:20:11,070 --> 00:20:16,650 +precipitation reaction هو الـ reaction اللي بيعطيني + +276 +00:20:16,650 --> 00:20:21,370 +راسب نتيجة خلق مادتين ذائبتين في الماء هو التفاعل + +277 +00:20:21,370 --> 00:20:25,170 +اللي بيعطيني راسب نتيجة خلق مادتين ذائبتين في + +278 +00:20:25,170 --> 00:20:29,350 +الماء، فإني مادتين ذائبتين خلقتهم يعطاني ايه؟ راسب + +279 +00:20:29,350 --> 00:20:33,450 +فمثلاً الـ potassium iodide، الـ K I بدور في الماء + +281 +00:20:33,450 --> 00:20:38,450 +طبعا لأنه أيوني lead nitrate برضه دائما في الميه + +282 +00:20:38,450 --> 00:20:44,410 +لأنها أيونية lead و nitrate أيونية حلو كثير الآن + +283 +00:20:44,410 --> 00:20:51,630 +خلطناهم جاب أعطتني النتيجة راسب أصفر ايش اللي حصل + +284 +00:20:51,630 --> 00:20:57,530 +في الحقيقة lead nitrate اتفاعل مع ال ki و أعطاني lead + +285 +00:20:57,530 --> 00:21:03,310 +iodide الـ lead iodide هو عبارة عن راسب أصفر أو طبعا + +286 +00:21:03,310 --> 00:21:11,250 +KNO3 أي تفاعل بينتج عنه insoluble product نتيجة + +287 +00:21:11,250 --> 00:21:14,250 +خلق مادتين دائمتين بنقول له هذا عبارة عن + +288 +00:21:14,250 --> 00:21:20,080 +precipitation reaction شفنا سابقا الـ Combination + +289 +00:21:20,080 --> 00:21:24,580 +Reaction، الـ Decomposition Reaction، الـ + +290 +00:21:24,580 --> 00:21:28,900 +Combustion Reaction، يعني بإجمال فهنا مر عليّ + +291 +00:21:28,900 --> 00:21:31,100 +ايه؟ حاجة جديدة بتقول لي الـ Precipitation + +292 +00:21:31,100 --> 00:21:37,840 +Reaction، يعني تفاعل بيتم فيه تكون راسب في المحلول + +293 +00:21:38,480 --> 00:21:42,480 +هي اللي بيحصل معايا هي الـ lead nitrate مثلا وهي الـ + +294 +00:21:42,480 --> 00:21:47,740 +KI هذا هي clear وهذا هي clear بدأت أضيف فإيش + +295 +00:21:47,740 --> 00:21:51,040 +اتكون راسب أصفر جميل جدا بعد فترة لون أصفر طبعا + +296 +00:21:51,040 --> 00:21:55,240 +بينزل في القاع فهذا عبارة عن الـ precipitation + +297 +00:21:55,240 --> 00:22:01,900 +reaction لكن لو سألت نفسي السؤال كيف بدي أعرف إذا + +298 +00:22:01,900 --> 00:22:05,470 +كان هيتكون عندي precipitate ولا لأ؟ جاب إذا كان + +299 +00:22:05,470 --> 00:22:08,730 +بدي أعرف هل بتكون عندي precipitate ولا لأ لازم + +300 +00:22:08,730 --> 00:22:12,830 +أعرف ايش المواد الذائبة وايت المواد غير الذائبة + +301 +00:22:12,830 --> 00:22:16,930 +ايش المواد اللي بتكون ذائبة في المحلول وايت المواد + +302 +00:22:16,930 --> 00:22:22,470 +اللي عامة ما بتكونش ذائبة في المحلول لكن بشكل عام + +303 +00:22:22,470 --> 00:22:29,270 +يعني هو الكاتب هيعتبر + +304 +00:22:29,270 --> 00:22:36,880 +أنه أي مادة أي مادة ذوبانيتها أقل من 0.01 مولار بده + +305 +00:22:36,880 --> 00:22:39,700 +يعتبرها insoluble يعني إذا كانت ذوبانية أكثر من 0 + +306 +00:22:39,700 --> 00:22:42,640 +.01 مولار بده يعتبرها soluble زي ما قلنا سابقا + +307 +00:22:42,640 --> 00:22:45,460 +أكثر من 0.01 مولار بده يعتبرها soluble لكن أقل من + +308 +00:22:45,460 --> 00:22:51,500 +0.01 مولار بده يعتبرها insoluble فبالتالي لو اجينا + +309 +00:22:51,500 --> 00:22:55,820 +سؤال لحالة سؤال قلنا ايش هي المواد اللي والله ممكن + +310 +00:22:55,820 --> 00:23:03,190 +نعتبرها insoluble بنقول بشكل عام تعالوا نتذكر .. + +311 +00:23:03,190 --> 00:23:06,470 +هأعطيكم جدول بعد شوية لكن تقلقت يعني بس خلينا نتذكر + +312 +00:23:06,470 --> 00:23:11,690 +هالحاجة وإذا كانت ذكرناها بتخدمنا كثير بدنا نتذكر + +313 +00:23:11,690 --> 00:23:17,170 +أنه عناصر المجموعة الأولى كل مركباتها soluble وين + +314 +00:23:17,170 --> 00:23:21,330 +ما لاقيها المركب اللي ما هي على طول soluble كويس + +315 +00:23:21,330 --> 00:23:25,990 +هذه أول حاجة بدي أتذكرها تاني حاجة بدي أتذكر أنه + +316 +00:23:25,990 --> 00:23:32,540 +أي ملح لنيترات أو الأسيتات soluble يبقى وين ما + +317 +00:23:32,540 --> 00:23:35,880 +معايا نيترات أو اسيتات ايش بده يعتبرها soluble + +318 +00:23:37,180 --> 00:23:41,800 +الحاجة الثالثة جاب أي ملح موجود فيه نيتريت اي عفوا + +319 +00:23:41,800 --> 00:23:46,180 +امونيوم جول نان نيتريت امونيوم بده يعتبرها soluble + +320 +00:23:46,180 --> 00:23:48,660 +يعني وين ما لاقي امونيوم على طول الملح ايه soluble + +321 +00:23:48,660 --> 00:23:51,040 +مثل امونيوم كلوريد soluble امونيوم كربونات + +322 +00:23:51,040 --> 00:23:54,600 +soluble امونيوم صلفية soluble امونيوم فلوريد + +323 +00:23:54,600 --> 00:23:59,840 +soluble على طول طيب نيترات لب نيترات soluble كبير + +324 +00:23:59,840 --> 00:24:04,620 +نيترات soluble Iron Nitrate Soluble Zinc Nitrate + +325 +00:24:04,620 --> 00:24:07,200 +Soluble كل ايش فيه نيترات ايه على طول من غير مفكر + +326 +00:24:07,200 --> 00:24:11,900 +Soluble طب عناصر المجموعة الأولى Sodium Hydroxide + +327 +00:24:11,900 --> 00:24:13,660 +Soluble Sodium Hydroxide Soluble Sodium Hydroxide + +328 +00:24:13,660 --> 00:24:14,880 +Soluble Sodium Sodium Sodium Sodium Sodium Sodium + +329 +00:24:14,880 --> 00:24:15,520 +Sodium Sodium Sodium Sodium Sodium Sodium Sodium + +330 +00:24:15,520 --> 00:24:17,780 +Sodium Sodium Sodium Sodium Sodium Sodium Sodium + +331 +00:24:17,780 --> 00:24:19,260 +Sodium Sodium Sodium Sodium Sodium Sodium Sodium + +332 +00:24:19,260 --> 00:24:19,660 +Sodium Sodium Sodium Sodium Sodium Sodium Sodium + +333 +00:24:19,660 --> 00:24:28,260 +Sodium Sodium Sodium Sodium + +334 +00:24:28,260 --> 00:24:31,230 +Sodium أي مادة فيها نيترات، أي Salt فيها نيترات، + +335 +00:24:31,230 --> 00:24:35,470 +أي Salt فيها Ammonium، هيك بنرتاح من معظم المواد + +336 +00:24:35,470 --> 00:24:38,910 +تبعنا وبصير الحكم على الأمور بمجرد النظر لو + +337 +00:24:38,910 --> 00:24:42,930 +اذكرنا هذه الحاجات البسيطة هذه يبقى على رأس + +338 +00:24:42,930 --> 00:24:48,550 +المجموعة الأولى، كل أملاحها Soluble، أي .. أي ملح + +339 +00:24:48,550 --> 00:24:54,430 +فيه نيترات أو Acetate Soluble أي ملح فيه أمونيوم + +340 +00:24:54,430 --> 00:24:58,030 +برضه soluble والباقي تعالوا نشوفه .. والباقي + +341 +00:24:58,030 --> 00:25:05,450 +تعالوا نشوفه .. هدول قلناهم الـ chloride الـ + +342 +00:25:05,450 --> 00:25:10,130 +bromide و الـ iodide كويس كل أملاحة soluble هدول + +343 +00:25:10,130 --> 00:25:14,290 +soluble .. soluble إلا ما .. و الثلاث زي بعض + +344 +00:25:15,150 --> 00:25:18,690 +الثلاث زي بعض إلا إذا كان عندي silver او mercurous + +345 +00:25:18,690 --> 00:25:21,870 +او lead نفس الكلاب نفس الكلاب يبقى الثلاث دول + +346 +00:25:21,870 --> 00:25:27,690 +دائما soluble إلا بدي أذكر إذا كان معهم مع أي واحد + +347 +00:25:27,690 --> 00:25:31,470 +فيهم silver ببطل soluble silver chloride مش + +348 +00:25:31,470 --> 00:25:36,290 +soluble silver bromide مش soluble silver iodide مش + +349 +00:25:36,290 --> 00:25:43,560 +soluble إذا كان معهم silver او mercurous Hg2 موجب أو + +350 +00:25:43,560 --> 00:25:50,460 +lead بس الآن الصلفات كل أملاحها soluble إلا إذا كان + +351 +00:25:50,460 --> 00:25:53,340 +المجموعة الأولى .. المجموعة الثانية عفوا + +352 +00:25:53,340 --> 00:25:57,600 +strontium mercurous و الـ lead strontium + +353 +00:25:57,600 --> 00:26:00,880 +mercurous و الـ lead فهدول بكونوا insoluble + +354 +00:26:03,330 --> 00:26:07,770 +اذكرنا الـ anions هدول اللي هم ايش أصلهم soluble + +355 +00:26:07,770 --> 00:26:12,030 +كلهم soluble إلا الـ exceptions هدول و لو طلعتوا + +356 +00:26:12,030 --> 00:26:18,610 +عليهم يعني بسيطة مش كثيرة طب نيجي لن الـ anions + +357 +00:26:18,610 --> 00:26:23,030 +اللي اصلها insoluble أصلهم ايش يعني دائما بيكونوا + +358 +00:26:23,030 --> 00:26:27,940 +insoluble الا الا وفي شغلات بدها الشطارة يعني لما + +359 +00:26:27,940 --> 00:26:31,560 +ييجي يقول لي مثلا compose of ammonium طب أنا عارف + +360 +00:26:31,560 --> 00:26:34,600 +أنه كل الـ compounds امونيوم بقيت معايش مكان يعني هي + +361 +00:26:34,600 --> 00:26:37,940 +تعتبر soluble فالـ sulfide مثلا الـ alkylamides طب + +362 +00:26:37,940 --> 00:26:40,880 +ماحنا عارفين أن الـ alkylamides دائما يعني soluble + +363 +00:26:40,880 --> 00:26:44,240 +مش ضروري نحطها كـ exception ماحنا عارفينها لكنها + +364 +00:26:44,240 --> 00:26:49,140 +اضاف calcium strontium barium calcium strontium + +365 +00:26:49,140 --> 00:26:54,730 +barium مع الـ sulfide لأ، هذا exception، هي بتكون + +366 +00:26:54,730 --> 00:26:57,950 +soluble، الاصل تبعها insoluble، لكن لو كانت مع + +367 +00:26:57,950 --> 00:27:01,450 +هدول، بتكون soluble، ايه كويس؟ الآن الكربونات + +368 +00:27:01,450 --> 00:27:05,350 +و الفسفيت، لاحظوا ايشي مش مفروض ينذكر، ليه؟ لأنه + +369 +00:27:05,350 --> 00:27:07,850 +يقول Compounds of Ammonium و الـ Alkalinity، طب + +370 +00:27:07,850 --> 00:27:11,010 +احنا عارفين ان كل الـ Compounds هيفهم هدول ارفعوهم + +371 +00:27:11,010 --> 00:27:17,220 +نهائيا، مابلزموناش الـ hydroxide دائما insoluble + +372 +00:27:17,220 --> 00:27:21,940 +إلا لو كان مع الـ NH4 مثلا طب احنا عارفين لو كان + +373 +00:27:21,940 --> 00:27:24,640 +الـ Alkyl و طب احنا عارفين لكن لأ بس ايه؟ Calcium is + +374 +00:27:24,640 --> 00:27:29,000 +a transient barium هذا هي زيها نفس الشيء فهذه هي + +375 +00:27:29,000 --> 00:27:34,700 +القواعد اللي احنا بنعتبرها في ايش المادة اللي + +376 +00:27:34,700 --> 00:27:37,080 +بتكون soluble وايت المادة اللي بتكون مش soluble + +377 +00:27:37,080 --> 00:27:40,580 +فكمان مرة لو اجينا بتلخصنا كل أملاح الـ nitrate و + +378 +00:27:40,580 --> 00:27:44,420 +الـ acetate soluble مفهوم، زي ما قلنا سابقا، + +379 +00:27:44,420 --> 00:27:47,000 +الكلوريد و البروميد و الايوديد، في الـ exceptions + +380 +00:27:47,000 --> 00:27:51,320 +الثلاثة، silver, mercurous, lead الصلفية كلها + +381 +00:27:51,320 --> 00:27:55,920 +soluble، إلا مع المركبات strontium, barium, Hg2, + +382 +00:27:56,160 --> 00:28:00,680 +2+, و lead الآن نيجي نطلع على المواد اللي اصلها + +383 +00:28:00,680 --> 00:28:06,500 +insoluble و بنلاحظ أن معظم الحاجات اللي موجودة هنا، + +384 +00:28:06,500 --> 00:28:09,840 +إذا كنتم ملاحظين هذا المربع كله، هو عبارة عن + +385 +00:28:09,840 --> 00:28:12,520 +Compounds of Ammonium و الـ Alkaline Metals، يعني + +386 +00:28:12,520 --> 00:28:15,960 +طبعا هيكون كلها Soluble، مافي مشكلة فيها، لكن ان + +387 +00:28:15,960 --> 00:28:19,300 +الـ Sulphide، Calcium, Strontium, Barium، Calcium + +388 +00:28:19,300 --> 00:28:23,230 +يعني المجموعة الثانية، المجموعة الثانية أما + +389 +00:28:23,230 --> 00:28:25,010 +الهيدروكسيد فالكالسيوم و السترونشيوم الباريوم زي + +390 +00:28:25,010 --> 00:28:29,010 +المجموعة الثانية يبقى لو اذكرنا هذا وهذا كالسيوم و + +391 +00:28:29,010 --> 00:28:34,670 +سترونشيوم الباريوم انتهت كل قوانين الـ solubility + +392 +00:28:34,670 --> 00:28:39,970 +فبالتالي لو اعتمدنا الثلاث مجموعات اللي ذكرناها + +393 +00:28:39,970 --> 00:28:44,890 +مجموعة الاليكالي ميتالز مجموعة الامونيوم و الاسيتات + +394 +00:28:44,890 --> 00:28:50,750 +والحاجة الثالثة الـ nitrates هذه كلها soluble هذا + +395 +00:28:50,750 --> 00:28:55,190 +الكلام بيهون علينا بشكل كبير يعني كمية المادة اللي + +396 +00:28:55,190 --> 00:28:59,030 +بدنا نحفظها هنا بتكون كمية أو ناخذ بالنا منها كمية + +397 +00:28:59,030 --> 00:29:04,830 +قليلة جدا وبتيجي مع التدريب شوية شوية الان بيقول + +398 +00:29:04,830 --> 00:29:09,790 +ليه ا classify these ionic compounds as soluble or + +399 +00:29:09,790 --> 00:29:14,770 +insoluble in water صوديوم كربونات على طول فيها صوديوم + +400 +00:29:14,770 --> 00:29:20,730 +فيها صوديوم soluble طيب ماشي ليد صلفيت اه الصلفيت + +401 +00:29:20,730 --> 00:29:23,930 +اه + +402 +00:29:23,930 --> 00:29:29,450 +الصلفيت ده ايش هاد ايه الصلفيت الاصل انها ايه في + +403 +00:29:29,450 --> 00:29:33,050 +soluble كل مرة لكن مع الـ lead اه انا اتذكر مع الـ + +404 +00:29:33,050 --> 00:29:34,890 +lead insoluble طيب + +405 +00:29:37,610 --> 00:29:40,270 +بقول classify the following compounds as soluble + +406 +00:29:40,270 --> 00:29:45,070 +or insoluble in water cobalt hydroxide مر معنا .. + +407 +00:29:45,070 --> 00:29:49,550 +مر معنا الـ .. الـ cobalt كـ exception ما مر معنا + +408 +00:29:49,550 --> 00:29:52,330 +معروف الـ exceptions طبعا كالسيوم سترونشيوم باريوم + +409 +00:29:52,330 --> 00:29:54,790 +كالسيوم سترونشيوم باريوم هاي الـ exceptions في الـ + +410 +00:29:54,790 --> 00:29:58,770 +hydroxide و الـ sulphide فطبعا هذا على طول ايه + +411 +00:29:58,770 --> 00:30:02,770 +insoluble باريوم نيترات اه نيترات + +412 +00:30:08,440 --> 00:30:15,720 +معظم الأسئلة بتكون مبينة إذا كانت اتبعتوا القوانين + +413 +00:30:15,720 --> 00:30:18,300 +اللي أنا قلت لكم في الأول الثلاث هدول الـ + +414 +00:30:18,300 --> 00:30:21,060 +exceptions ما معك حاجة تغلط فيها مرات لأنه لسه أنت + +415 +00:30:21,060 --> 00:30:24,660 +جديد على الكيمياء يعني لكن معك يعني مش غلط إنك تغلط + +416 +00:30:24,660 --> 00:30:32,480 +فيها عادي بدها يعني شوية تركيز وحفظ مع الخبرة يعني + +417 +00:30:32,480 --> 00:30:36,640 +في حل المسائل لكن بشكل عام معذورة إنك تغلط فيها + +418 +00:30:36,640 --> 00:30:41,020 +لكن مش معذورة إنك تغلط المجموعة الأولى نيترات و + +419 +00:30:41,020 --> 00:30:46,220 +امونيوم نيترات و اسيتات و الامونيوم هدول لأ هدول + +420 +00:30:46,220 --> 00:30:48,540 +المعروفين ومعظم المواد هتجهم زي هيك حتى في + +421 +00:30:48,540 --> 00:30:53,810 +الامتحان ممكن يجيك شيء مباشر زي هيك طيب بدنا نركز + +422 +00:30:53,810 --> 00:30:56,750 +على ال solubility لأنه لازم يجيك منها سؤال في + +423 +00:30:56,750 --> 00:31:00,290 +الامتحان يعني زي هيك لازم يجيك منها سؤال اللي + +424 +00:31:00,290 --> 00:31:03,830 +نعرف هل بتعرف المادة ذائبة ولا مش ذائبة خاصة أن في + +425 +00:31:03,830 --> 00:31:08,870 +عليها تطبيقات بعد شوية ماشي يا جماعة الآن بدنا نجيء + +426 +00:31:08,870 --> 00:31:13,370 +نتكلم عن نوع من أنواع ال reactions بنسميه + +427 +00:31:13,370 --> 00:31:17,330 +metathesis reaction أو exchange reaction metathesis + +428 +00:31:17,330 --> 00:31:25,470 +يعني switch استبدال ماشي في عندي أنا مادة تتفاعل + +429 +00:31:25,470 --> 00:31:29,170 +مع مادة أخرى كل مادة عبارة عن مثلًا كتاين وأناين + +430 +00:31:29,170 --> 00:31:33,170 +والمادة الثانية كتاين وأناين بقصد بالاستبدال + +431 +00:31:33,170 --> 00:31:37,030 +الكتاين للأولى بياخد الأنّايون للتانية والأنّايون + +432 +00:31:37,030 --> 00:31:40,810 +للتانية بياخد الكتاين للأولى هذا هي النواتج هذا هو + +433 +00:31:40,810 --> 00:31:46,770 +التفاعل اللي بنسميه metathesis reaction هذا التفاعل + +434 +00:31:46,770 --> 00:31:51,910 +بيتم فعلًا؟ ماتتش بيتم فعلًا؟ يعني المتفاعلات + +435 +00:31:51,910 --> 00:31:56,370 +بيعطوني نواتج قال إذا كان كانت نتيجة التفاعل أحد + +436 +00:31:56,370 --> 00:32:01,350 +ثلاث حاجات، يا إما precipitate، لو كان نتيجة + +437 +00:32:01,350 --> 00:32:05,870 +precipitate، اه التفاعل بيتم، لو كان النتيجة gas، + +438 +00:32:05,870 --> 00:32:10,190 +يعني بتصعد غاز، التفاعل بيتم أو لو كانت النتيجة + +439 +00:32:10,190 --> 00:32:13,810 +weak electrolyte والمية بدي أذكركم أنها weak + +440 +00:32:13,810 --> 00:32:18,730 +electrolyte يعني لأنه بتتفكك بشكل قليل جدًا فهي non + +441 +00:32:18,730 --> 00:32:21,790 +electrolyte أو يعني ممكن نسميها weak electrolyte + +442 +00:32:21,790 --> 00:32:26,730 +أو المية واحد منهم يعني إذا كان حصلت على مية برضه + +443 +00:32:26,730 --> 00:32:33,370 +هذا التفاعل بيتم برضه ال metathesis reaction إيه + +444 +00:32:33,370 --> 00:32:37,690 +له اسم ثاني بيقول double replacement استبدال ثنائي + +445 +00:32:37,690 --> 00:32:40,330 +لأن هذا بيستبدل من هذا وهذا بيستبدل من هذا bubble + +446 +00:32:40,330 --> 00:32:44,950 +replacement فهو bubble replacement reaction فمثلًا + +447 +00:32:44,950 --> 00:32:53,920 +لو عندي ax زائد by a بتاخد b وx بتاخد y A بتاخد Y + +448 +00:32:53,920 --> 00:32:58,520 +لأنها دي الأنيون و X بتاخد B فهي بيطلع عندي AY + +449 +00:32:58,520 --> 00:33:04,520 +زائد ال BX فمثلًا AGNO3 Aqueous دايبة في الميه KCl + +450 +00:33:04,520 --> 00:33:09,880 +أيضًا دايب في الميه بيعطيني ال AG هياخد ال CL AGCL + +451 +00:33:09,880 --> 00:33:16,520 +آه كل أملاح الكلورايت دائبة مع ده مع ال AG و ال + +452 +00:33:16,520 --> 00:33:23,100 +Mercurus ولت صحيح إذا هذا إيه راسب زائد KNO ثلاثة + +453 +00:33:23,100 --> 00:33:27,320 +معنى أن حصلت على راسب إذا نعم التفاعل بيتم هنا + +454 +00:33:27,320 --> 00:33:31,120 +لازم النتيجة تكون يا إما راسب يا إما غاز يا إما + +455 +00:33:31,120 --> 00:33:34,480 +weak electrolyte لو ما حصلش واحد من هدول التفاعل + +456 +00:33:34,480 --> 00:33:38,320 +بيتمش حاجة أنه بس التفاعل بيكون عبارة عن خليط بين + +457 +00:33:38,320 --> 00:33:42,120 +المادتين بيتمش تفاعل فيش تفاعل يعني المتفاعلات هي + +458 +00:33:42,120 --> 00:33:46,000 +نفسها النواتج طيب + +459 +00:33:49,000 --> 00:33:53,240 +الـ Acids و الـ Bases برضه مثال على الـ Metathesis + +460 +00:33:53,240 --> 00:33:57,860 +Reaction HCl بتفاعل مع ال Sodium Hydroxide فالـ H + +461 +00:33:57,860 --> 00:34:02,080 +بياخد ال OH من ال Hydroxide تصير مية اه يتم + +462 +00:34:02,080 --> 00:34:06,440 +التفاعل اه و ال NA بتروح مع ال CL بيعطينا NACL + +463 +00:34:06,440 --> 00:34:10,680 +فهذا يعتبر أيضًا Metathesis Reaction أو Double + +464 +00:34:10,680 --> 00:34:16,590 +Replacement Reaction في يعني قوانين بسيطة جدًا احنا + +465 +00:34:16,590 --> 00:34:23,590 +عادة بنستخدمها علشان نكتب المعادلة لـ + +466 +00:34:23,590 --> 00:34:26,950 +Metatase reaction يعني نوصل للمعادلة الحقيقية ك + +467 +00:34:26,950 --> 00:34:31,170 +product يعني فبنقول في البداية use the chemical + +468 +00:34:31,170 --> 00:34:34,530 +formula of the reactants to determine which ions + +469 +00:34:34,530 --> 00:34:37,870 +are represented يعني بنكتب المتفاعلات الأول + +470 +00:34:37,870 --> 00:34:41,370 +والتاني ال chemical formulas بنحدد أيش الأيونات و + +471 +00:34:41,370 --> 00:34:44,560 +أيش الكاتيونات والأن بنقول write the chemical + +472 +00:34:44,560 --> 00:34:47,820 +formulas of the products يعني بدنا ناخد الكاتيون + +473 +00:34:47,820 --> 00:34:51,260 +من ال او الأول مع الانيون من التاني طب حلو كتير by + +474 +00:34:51,260 --> 00:34:54,040 +combining the cation from one reactant with the + +475 +00:34:54,040 --> 00:34:58,180 +anion of the other using the ionic charges إيش + +476 +00:34:58,180 --> 00:35:01,760 +فيها ال ionic charges عشان نظبط عليه الدرات فإذا + +477 +00:35:01,760 --> 00:35:05,830 +كان مثلًا كالسيان بده اتنين أكلورايد كالسيام بتتفعل + +478 +00:35:05,830 --> 00:35:08,290 +مع الكلورايد لكن بده اتنين كلورايد، هنشوف الـGET + +479 +00:35:08,290 --> 00:35:12,630 +هذا الكلام بعد شوية فلازم نظبط عدد الذرات باستخدام + +480 +00:35:12,630 --> 00:35:15,790 +الشحنات اللي على الأيونات بيقول اتشيك the nature + +481 +00:35:15,790 --> 00:35:19,530 +of the products هل هو غاز أو weak electrolyte أو + +482 +00:35:19,530 --> 00:35:22,110 +precipitate لأن إذا ماكنش فيش تفاعل + +483 +00:35:25,110 --> 00:35:28,450 +عشان تشوف أنه هل هو precipitate أو لا، we have to + +484 +00:35:28,450 --> 00:35:31,630 +check the solubility rules، we have to check the + +485 +00:35:31,630 --> 00:35:35,070 +solubility rules، بعدين في الآخر بنوزان المعادلة، + +486 +00:35:35,070 --> 00:35:39,650 +خلينا نتطلع مثلًا على المثال التالي، بقول a + +487 +00:35:39,650 --> 00:35:42,690 +predicting a metathesis reaction، هل هذا التفاعل + +488 +00:35:42,690 --> 00:35:46,340 +الاستبدالي بيحصل ولا لأ يعني؟ فبنقول predict the + +489 +00:35:46,340 --> 00:35:52,380 +identity of the precipitate that forms when أكبر + +490 +00:35:52,380 --> 00:35:55,840 +solutions of barium chloride and K2SO4 are mixed + +491 +00:35:55,840 --> 00:36:04,870 +في الأول باريوم كبريتات الكبريتات كل أملاحها ذائبة إلا مع + +492 +00:36:04,870 --> 00:36:10,510 +مين؟ أربع حاجات من ضمنها .. من ضمنها .. من ضمنها + +493 +00:36:10,510 --> 00:36:14,450 +.. من ضمنها البريوم، إذا الباريوم كبريتات هو عبارة عن + +494 +00:36:14,450 --> 00:36:17,330 +الراسب الباريوم كبريتات هو عبارة عن الراسب اللي بي + +495 +00:36:17,330 --> 00:36:19,930 +write the balanced chemical equation for the + +496 +00:36:19,930 --> 00:36:25,760 +reaction بقول عشان أكتب المعادلة الموزونة في الأول + +497 +00:36:25,760 --> 00:36:29,160 +بدي أشوف ال barium أكتب ال barium وهي ال chloride + +498 +00:36:29,160 --> 00:36:32,920 +و ال potassium وهي ال sulfate بتاخد ال barium مع + +499 +00:36:32,920 --> 00:36:36,840 +ال sulfate الكاتيون من الأول مع الأنيون من + +500 +00:36:36,840 --> 00:36:40,260 +التاني ال barium ال sulfate وهذا راسب خلصت منه طب + +501 +00:36:40,260 --> 00:36:45,400 +خلينا نتطلع هنا ال chloride و ال k plus زي بعض إذا + +502 +00:36:45,400 --> 00:36:49,080 +kcl إذا kcl لأن هذا واحد وهذا واحد ما فيش عندي + +503 +00:36:49,080 --> 00:36:54,780 +coefficients كويس كتير، إذا المحصلة بدها تكون والله + +504 +00:36:54,780 --> 00:37:00,320 +barium chloride زائد K2SO4 تعطيني بالي صلفية زائد + +505 +00:37:00,320 --> 00:37:07,220 +KCl لكن بدي أجي أوزن المعادلة لو إجيت عند باريام، + +506 +00:37:07,220 --> 00:37:12,460 +هاي باريام، كلورايد اتنين، هاي ضربت half اتنين، + +507 +00:37:12,460 --> 00:37:16,780 +بوتاسيوم اتنين، هاي هاتنين، كبريتات هاي كبريتات، إذا + +508 +00:37:16,780 --> 00:37:21,230 +المعادلة موزونة عندي، بوتاسيوم، كبريتات طب نيجي نطلع + +509 +00:37:21,230 --> 00:37:27,190 +و نستخدم ال .. إيش بيسموها ال charges يعني عشان + +510 +00:37:27,190 --> 00:37:32,590 +نعرف عدد الذرات فبيقول مثال ثاني what compound + +511 +00:37:32,590 --> 00:37:35,670 +precipitates when aqueous solutions of iron + +512 +00:37:35,670 --> 00:37:39,690 +sulfate and lithium hydroxide are mixed حلو كتير + +513 +00:37:39,690 --> 00:37:44,940 +أنا قلت سابقًا إنه هذا مثلًا ال iron هياخد + +514 +00:37:44,940 --> 00:37:47,940 +الهيدروكسيد والليثيوم هياخد الكبريتات طبعًا ليثيوم + +515 +00:37:47,940 --> 00:37:52,920 +وكبريتات مش راسب مش راسب لأنه مجموعة أولى ليثيوم + +516 +00:37:52,920 --> 00:37:56,820 +مجموعة أولى إذا ال iron هيدروكسيد هل هو راسب نعم + +517 +00:37:56,820 --> 00:38:02,100 +راسب ليه لأنه كل الهيدروكسيد عبارة عن رواسب إلا + +518 +00:38:03,000 --> 00:38:08,560 +الكالي متالز أمونيوم كالسمسترانشانباريام زي .. اه + +519 +00:38:08,560 --> 00:38:12,100 +إذا .. إذا .. اه هاي الراسب iron هيدروكسايد لكن + +520 +00:38:12,100 --> 00:38:15,760 +ال iron ثلاثة الهيدروكسيد واحد فكيف بدي أقول + +521 +00:38:15,760 --> 00:38:19,240 +iron هيدروكسيد بتكون iron ثلاثة بتنزل تحت + +522 +00:38:19,240 --> 00:38:24,200 +الهيدروكسيد بتيجي هنا زي ما تعلمنا سابقًا يعني لو + +523 +00:38:24,200 --> 00:38:30,390 +أجي هنا قلنا هيها Iron ثلاثة وهي Hydroxide سالب هذه + +524 +00:38:30,390 --> 00:38:35,110 +بتيجي واحد هنا وهذه بتيجي هنا يبقى Iron OH ثلاثة + +525 +00:38:35,110 --> 00:38:38,690 +لأن الواحد ما بنكتبهاش ايه يا بنات متذكرين أن هذا + +526 +00:38:38,690 --> 00:38:46,090 +الكلام عملناه سابقًا طيب إيش بيقول لك أيضًا will a + +527 +00:38:46,090 --> 00:38:50,870 +precipitate form when solutions of calcium nitrate + +528 +00:38:50,870 --> 00:38:55,350 +and sodium carbonate are mixed طب نيجي نتطلع + +529 +00:38:55,350 --> 00:38:59,710 +calcium .. وين ال calcium؟ calcium nitrate هاي + +530 +00:38:59,710 --> 00:39:05,230 +calcium و هاي nitrate هذا الأول و عندي كمان hand + +531 +00:39:05,230 --> 00:39:10,090 +sodium و هاي carbonate هذا الثاني لو إجيت أنا قلت + +532 +00:39:10,090 --> 00:39:13,730 +والله ال sodium مع ال nitrate هذا لأ هذا soluble + +533 +00:39:13,730 --> 00:39:16,910 +لأنه مش معقولة طب و ال carbonate مع ال calcium + +534 +00:39:16,910 --> 00:39:23,120 +نيجي بنسأل حالنا نسأل ال carbonate كل أملاحها غير + +535 +00:39:23,120 --> 00:39:29,700 +ذائبة إلا مع أمونيوم والمجموعة الأولى، بس أمونيوم + +536 +00:39:29,700 --> 00:39:33,080 +والمجموعة الأولى، إذا الكربونات مع الكالسيام هذا + +537 +00:39:33,080 --> 00:39:40,220 +insoluble، متذكرين؟ هايو، هايو، هايو، هايو، هايو، + +538 +00:39:40,220 --> 00:39:40,560 +هايو، هايو، هايو، هايو، هايو، هايو، هايو، هايو، + +539 +00:39:40,560 --> 00:39:43,360 +هايو، هايو، هايو، هايو، هايو، هايو، هايو، هايو، + +540 +00:39:43,360 --> 00:39:43,940 +هايو، هايو، هايو، هايو، هايو، هايو، هايو، هايو، + +541 +00:39:43,940 --> 00:39:47,060 +هايو، هايو، هايو، هايو، هايو، هايو، هايو، هايو، + +542 +00:39:47,060 --> 00:39:52,150 +هايو، هايبس فبالتالي كلها تعتبر إيه؟ insoluble + +543 +00:39:52,150 --> 00:39:55,910 +فهذا وضع طبيعي أنه insoluble يبقى ال calcium + +544 +00:39:55,910 --> 00:40:01,480 +carbonate insoluble على فكرة كانت المسألة calcium + +545 +00:40:01,480 --> 00:40:04,860 +hydroxide بس أنا يعني مش مقتنع في الحقيقة في نفسي + +546 +00:40:04,860 --> 00:40:08,640 +أن أقول عنه أن هو ال hydro .. هو بيقول عنه soluble + +547 +00:40:08,640 --> 00:40:13,480 +يعني أو يعني مش كتير المثال مش حلو لأنه في مجلة + +548 +00:40:13,480 --> 00:40:17,640 +الجدل فيه يعني فأنا لا بجبهلك في الامتحان ولا حتى + +549 +00:40:17,640 --> 00:40:20,080 +حاولت أن أرفعه من هنا كان المفروض أقول لك calcium + +550 +00:40:20,080 --> 00:40:26,460 +hydroxide calcium nitrate مع sodium hydroxide عشان + +551 +00:40:26,460 --> 00:40:33,000 +تتكون عندي calcium أو شيء زي هيك .. شيء زي هيك بس + +552 +00:40:33,000 --> 00:40:35,700 +أنا مش حابب المثال على أي حال + +553 +00:40:39,620 --> 00:40:43,000 +نيجي نتطلع على ال equations فبنقول an equation like + +554 +00:40:43,000 --> 00:40:46,200 +the following is called a molecular equation مثلًا + +555 +00:40:46,200 --> 00:40:50,280 +زي باريوم الكلوريد زي K2SO4 وهي مرسومة بالشكل هذا + +556 +00:40:50,280 --> 00:40:56,160 +باريوم كبريتات زي KCl كل formula مكتوبة مع بعضها + +557 +00:40:56,160 --> 00:40:59,780 +البعض هذه بنسميها molecular equation ليه؟ لأنها + +558 +00:40:59,780 --> 00:41:04,180 +مكتوبة وكأنها هذه molecules مش مفككة مكتوب ما فيش + +559 +00:41:04,180 --> 00:41:08,810 +عليها أي شحنات فبنقولها molecular equations ممكن + +560 +00:41:08,810 --> 00:41:11,690 +نكتب منها الـ Ionic equation كيف ال Ionic + +561 +00:41:11,690 --> 00:41:14,090 +equation؟ جال ال باريوم؟ اه باريوم two plus + +562 +00:41:14,090 --> 00:41:18,010 +كلوريد اتنين يعني اتنين Cl سالب يعني أخدنا + +563 +00:41:18,010 --> 00:41:20,790 +الايونات منها وكل واحد aqueous زي ما هو هذا + +564 +00:41:20,790 --> 00:41:25,510 +البوتاسيوم اتنين يعني اتنين K plus الصلفية صلفية + +565 +00:41:25,510 --> 00:41:29,410 +اتنين سالب لازم نعرف شحنات ال ايه؟ الايونات + +566 +00:41:29,410 --> 00:41:33,480 +المختلفة بتعطيني باريوم صلفية مقدرش اقول هذا أيونات + +567 +00:41:33,480 --> 00:41:38,420 +لأن هذا insoluble اتفاجنا أنه علشان يكون المركب .. + +568 +00:41:38,420 --> 00:41:43,720 +خلنا نقول electrolyte يعني بتفكك لازم يكون soluble + +569 +00:41:43,720 --> 00:41:47,900 +بداية فهذا لأ insoluble بنخليه زي ما هو و الجاز + +570 +00:41:47,900 --> 00:41:50,720 +بنخليه زي ما هو و ال weak electrolyte بنخليه زي ما + +571 +00:41:50,720 --> 00:41:57,100 +هو لأن هو ناتج التفاعل الـ K اتنين K Plus والـ CL + +572 +00:41:57,100 --> 00:42:03,080 +اتنين CL Minus بديكم تلاحظوا هنا الـ CL وهنا زيها + +573 +00:42:03,080 --> 00:42:06,440 +الـ CL وهنا اتنين K Plus وهنا زيها اتنين K Plus + +574 +00:42:06,440 --> 00:42:12,500 +هذه بنسميها spectator ions أيونات متفرجة داخلة في + +575 +00:42:12,500 --> 00:42:15,860 +التفاعل وهي نفسها تطالع من التفاعل، مالش إشي، + +576 +00:42:15,860 --> 00:42:19,620 +أيونات إيش مالها؟ متفرجة، مالهاش أي قيمة، وجودها + +577 +00:42:19,620 --> 00:42:22,560 +مالوش قيمة، لا على اليمين ولا على اليسار، لدرجة إن + +578 +00:42:22,560 --> 00:42:27,160 +ممكن إيه؟ نشطبهم، لو شطبداهم من المعادلة الأيونية + +579 +00:42:28,090 --> 00:42:32,910 +بصير عندي ال net ionic equation بصير عندي حاجة + +580 +00:42:32,910 --> 00:42:38,470 +بنقولها net ionic equation فلمّا نرفعهم بيظل عندي + +581 +00:42:38,470 --> 00:42:43,230 +barium زائد sulfate بتعطيني barium sulfate solid + +582 +00:42:43,230 --> 00:42:50,850 +فهذه بنقولها net ionic equation ده + +583 +00:42:50,850 --> 00:42:53,830 +بتطلع بيقول لي which ions are spectator ions in the + +584 +00:42:53,830 --> 00:42:58,050 +reaction بدنا .. بدنا .. بدنا نجيب الـ Ionic + +585 +00:42:58,050 --> 00:43:01,050 +equation من هنا و نشوف إيش اللي ع اليمين و اليسار + +586 +00:43:01,050 --> 00:43:04,690 +نفس الشيء فبقول A,G,N,O تلاتة aqueous N,A,C,L + +587 +00:43:04,690 --> 00:43:08,510 +aqueous A,G,C,L solid ليش solid؟ جال لأن كل + +588 +00:43:08,510 --> 00:43:15,030 +chloride معدي الـ silver والمركورس وال LED فهذا + +589 +00:43:15,030 --> 00:43:19,390 +ايه؟ اه ال silver بيكون راسب زائد NA NO تلاتة حلو + +590 +00:43:19,390 --> 00:43:22,990 +كتير أنا بجيب ال Ionic equation ال AG اه AG plus + +591 +00:43:22,990 --> 00:43:28,890 +NO تلاتة سالب NA plus Cl سالب هذا طبعا solid لأنه + +592 +00:43:28,890 --> 00:43:34,090 +متفككش مش Electrolyte NA NA plus NO تلاتة اه هدا + +593 +00:43:34,090 --> 00:43:40,850 +هي هي NA plus و NO اه هدول هدهم أذن بيبقى عندي ag + +594 +00:43:40,850 --> 00:43:44,690 +plus زائد cl minus بتعطينا ag cl هدى هي ال net + +595 +00:43:44,690 --> 00:43:49,350 +ionic equation إذا ال spectator ions ال nitrate + +596 +00:43:49,350 --> 00:43:53,730 +والسودانيون بيبينوا ايه؟ عليسار و عليمين عليسار و + +597 +00:43:53,730 --> 00:43:57,010 +عليمين فهدى هي ال spectator ions + +598 +00:43:59,350 --> 00:44:03,090 +نتكلم عن ال acids و ال bases الآن بنقدر نقول أن ال + +599 +00:44:03,090 --> 00:44:06,550 +precipitation reactions يعني أنه جافهان لحظة و + +600 +00:44:06,550 --> 00:44:10,890 +نتطلع على ال acids و ال bases إيش هو ال acid جال + +601 +00:44:10,890 --> 00:44:17,370 +ال acid هو المادة اللي اللي بتتفكك في المياه كويس + +602 +00:44:17,370 --> 00:44:22,010 +و بتعطي hydrogen ions و في أحيان كثير بنقول بتعطي + +603 +00:44:22,010 --> 00:44:26,370 +proton طب إيش هو البروتون؟ ليش بنقول عنه بروتون؟ + +604 +00:44:26,370 --> 00:44:30,650 +قال لأن ال H فيش فيها إلا بروتون و إلكترون فإذا + +605 +00:44:30,650 --> 00:44:36,050 +كان فقد الإلكترون لأن ال H واحد بس فيها بروتون و + +606 +00:44:36,050 --> 00:44:40,450 +إلكترون طب لو فقد الإلكترون إيش بيضل؟ إذا عشان هيك + +607 +00:44:40,450 --> 00:44:45,330 +بنسميه بروتون فال acid بيعطي hydrogen ions أو + +608 +00:44:45,330 --> 00:44:53,110 +بيعطي بروتون عشان هيك بنسمي ال acids بروتون donors + +609 +00:44:54,210 --> 00:44:57,590 +البروتونز في الـ aqua solutions عادة بتكون + +610 +00:44:57,590 --> 00:45:00,130 +solvated بالمية يعني hydrated + +611 +00:45:13,890 --> 00:45:18,010 +لو طلعنا على ال acids عموما بنقول والله ال acids + +612 +00:45:18,010 --> 00:45:22,790 +تتفكك في الميه ممكن ال acid يعني يعطيني one proton + +613 +00:45:22,790 --> 00:45:25,690 +أو يعطيني two protons أو يعطيني تلاتة protons + +614 +00:45:25,690 --> 00:45:28,710 +فمثلا HCl ما فيش فيها إلا proton واحد بتعطيني + +615 +00:45:28,710 --> 00:45:31,810 +proton HNO3 بتعطيني proton ما فيش فيها إلا proton + +616 +00:45:31,810 --> 00:45:36,250 +واحد لكن حاجة زي مثلا ال sulfuric acid فيها اتنين + +617 +00:45:36,250 --> 00:45:40,290 +فال ال acids اللي فيها واحد proton بنقول عنها + +618 +00:45:40,290 --> 00:45:45,630 +monoprotic acids بينما اللي فيها اتنين زي الـ + +619 +00:45:45,630 --> 00:45:50,070 +Sulfuric Acid بنقولها Diprotic Acids، Diprotic + +620 +00:45:50,070 --> 00:45:52,290 +يعني فيها ايه اتنين؟ وإذا فيها تلاتة زي الـ + +621 +00:45:52,290 --> 00:45:56,330 +Phosphoric Acid، H3PO4، بيقولها Triprotic Acids أو + +622 +00:45:56,330 --> 00:46:02,030 +بمعنى يعني أوسع Polyprotic، Poly متعددة ال .. اه + +623 +00:46:02,030 --> 00:46:07,250 +فعنا الـ H2SO4 التفكك الأول قوي فكك كامل بيعطيني H + +624 +00:46:07,250 --> 00:46:11,010 +plus و HSO4 بينما الثاني بيكون weak هيوها ساهمين + +625 +00:46:11,010 --> 00:46:16,050 +رايح راجع لكن محلول ال sulfuric acid بيكون موجود + +626 +00:46:16,050 --> 00:46:21,670 +في ال H plus و ال HSO4 و ال SO4 لكن هل في H2SO4 لأ + +627 +00:46:21,670 --> 00:46:27,010 +ليه لأن ال H2SO4 ساهم واحد خلص كله خلص كله من أول + +628 +00:46:27,010 --> 00:46:31,370 +خطوة خلص كله لكن ببقى اللي عندي H plus و HSO4 و + +629 +00:46:31,370 --> 00:46:32,350 +SO42 + +630 +00:46:34,940 --> 00:46:40,360 +ال acids يا جماعة يا اما بتكون mineral acids زي + +631 +00:46:40,360 --> 00:46:44,680 +اللي شوفناها يعني وحنشوفها بعد شوية strong acids + +632 +00:46:44,680 --> 00:46:47,940 +يا بتكون weak acids ال weak acids هي اللي بتحتوي + +633 +00:46:47,940 --> 00:46:51,280 +على جمعة الكربوكسليات فهذا اسمه acidic acid الخل + +634 +00:46:51,280 --> 00:46:55,660 +اللي موجود في الخل الخل واللي اندهان جداش فيه + +635 +00:46:55,660 --> 00:47:00,000 +تلاتة هي واحد هي تنين هي تلاتة try protect try + +636 +00:47:00,000 --> 00:47:04,500 +protect هذا اللي موجود في عصير الليمون Citric Acid + +637 +00:47:04,500 --> 00:47:09,120 +Citric Acid كويس فيمكن يكون فيه بروتون واحد ويمكن + +638 +00:47:09,120 --> 00:47:13,580 +يكون فيه أكثر من بروتون لكن علشان ال H تكون acidic + +639 +00:47:13,580 --> 00:47:17,480 +لازم تكون مربوطة في ايه؟ في Carboxylate مش مثلا و + +640 +00:47:17,480 --> 00:47:21,580 +الله هذه ال H .. لا مش .. بتعطيش H plus ولا هذه + +641 +00:47:21,580 --> 00:47:26,580 +علشان تعطي H plus وين بدها تكون؟ في مجموعة ال + +642 +00:47:26,580 --> 00:47:31,700 +Carboxylate بسيبقى هذا بيعطيني تلاتة H plus كتفكك + +643 +00:47:31,700 --> 00:47:35,480 +تفكك كامل أو لو اتفاعل مع ال base تفاعل تم بتفاعل + +644 +00:47:35,480 --> 00:47:38,840 +مع تلاتة من ال base ليه؟ لأنه في تلاتة بروتون + +645 +00:47:38,840 --> 00:47:41,120 +تفاعل مع تلاتة هيدروكسيد لأنه في تلاتة بروتون + +646 +00:47:41,120 --> 00:47:45,000 +بينما ال acetic acid هي هي هادي بس ال ايه ال acidic + +647 +00:47:45,000 --> 00:47:49,340 +proton بينما هدول لأ ما لهو مش دعوة لأن ال proton + +648 +00:47:49,340 --> 00:47:53,140 +عشان يكون acidic لازم يكون ضمن الكربوكسيلات بتشوف + +649 +00:47:53,140 --> 00:47:57,310 +أكم كربوكسيلات في عندي بنعرف أكثر من برواتون بيكون + +650 +00:47:57,310 --> 00:48:02,370 +أسيدي بالنسبة لي ال bases هنعرفنا ال acids ال acids + +651 +00:48:02,370 --> 00:48:07,970 +اللي هي المشهورة زي ال HCl ال HNO3 ال H2SO4 وحنشوف + +652 +00:48:07,970 --> 00:48:13,150 +بعد شوية يعني acids ثاني لكن الآن ال bases بنقول + +653 +00:48:13,150 --> 00:48:17,430 +ال bases أي إشي فيه هيدروكسيد وأنا بضيف oscillable + +654 +00:48:17,430 --> 00:48:20,850 +هيدروكسيد لأن قلنا المغنيزيوم هيدروكسيد الألوانم + +655 +00:48:20,850 --> 00:48:24,010 +هيدروكسيد لا يعتبر يعني base قوي هو base لكن مش + +656 +00:48:24,010 --> 00:48:28,070 +base قوي عشان يكون الـBase قوي، بدو يكون دايم + +657 +00:48:28,070 --> 00:48:32,930 +فهدول الـAluminum Hydroxide والمغنيزيوم Hydroxide + +658 +00:48:32,930 --> 00:48:38,470 +لأ مابيدوش فعندي مثلا المجموعة الأولى Sodium + +659 +00:48:38,470 --> 00:48:41,190 +Hydroxide, Potassium Hydroxide, Lithium Hydroxide, + +660 +00:48:42,530 --> 00:48:46,930 +Rubidium Hydroxide, Cesium Hydroxide، كل هذا عبارة + +661 +00:48:46,930 --> 00:48:53,150 +عن قواعد قوية، كويس؟ ليه؟ لأنه بتعطي Hydroxide أو + +662 +00:48:53,150 --> 00:48:58,210 +ممكن نقول والله هي قواعد لأنها بتاخد بروتون من + +663 +00:48:58,210 --> 00:49:04,070 +المية فمثلا الأمونيا برضه كمان ايه قاعدة ليش قاعدة + +664 +00:49:04,070 --> 00:49:07,170 +المهم انها قاعدة ليش قاعدة لأنها بتاخد بروتون من + +665 +00:49:07,170 --> 00:49:12,010 +المية هي الأمونيا فيها ايه فيها تلاتة H وهي + +666 +00:49:12,010 --> 00:49:14,830 +النيتروجين وهي المية فيها تنين H وهي الأكسجين + +667 +00:49:14,830 --> 00:49:19,190 +بتاخد H من المية فبتصير NH أربع عموم جابه + +668 +00:49:19,190 --> 00:49:24,070 +Hydroxide فهي a base لأنها بتاخد الـ H plus من + +669 +00:49:24,070 --> 00:49:27,250 +الميّه فال base هو اللي بيحتوي على ال hydroxide أو + +670 +00:49:27,250 --> 00:49:30,670 +يعني بيعطينا hydroxide أو قادر على أنه ياخد H plus + +671 +00:49:30,670 --> 00:49:35,590 +من الميّه ال acid هو اللي بيعطينا بروتون كويس اه + +672 +00:49:35,590 --> 00:49:40,450 +proton donor هو اللي بيعطي بروتون باستمرار طيب + +673 +00:49:40,450 --> 00:49:43,890 +نطلع على ال strong acids و ال weak acids ال strong + +674 +00:49:43,890 --> 00:49:49,570 +acids و ال weak acids بنقول في البداية قوة ال .. أو + +675 +00:49:49,570 --> 00:49:54,010 +خلّيني أقول نشاط .. نشاط الحمض لا يتوقف فقط على + +676 +00:49:54,010 --> 00:49:58,530 +الـH plus، لأ بيتوقف على الـH plus وعلى نوعية + +677 +00:49:58,530 --> 00:50:02,250 +الانيون المرتبط معاها، بنعرف هذا الكلام من وين، بس + +678 +00:50:02,250 --> 00:50:09,290 +للمعلومات، من الـHF الـ HF يعتبر حمض ضعيف، ليش حمض + +679 +00:50:09,290 --> 00:50:13,650 +ضعيف؟ لأنه لا يتفكك تفكك كامل في المية، لأن الرابط + +680 +00:50:13,650 --> 00:50:19,530 +بين الـ F والـ H قوية، فالمية لا تستطيع أن تنتزع H + +681 +00:50:19,530 --> 00:50:27,830 +Plus من الـ HF لكن مع إنه حمض ضعيف إلا إنه يعني + +682 +00:50:27,830 --> 00:50:31,590 +يعتبر very reactive ال reactivity تبعته مش بس من + +683 +00:50:31,590 --> 00:50:36,390 +ال H جاية لأ لأن ال HCl غير ال HCl مش زيه لأ جاي + +684 +00:50:36,390 --> 00:50:40,870 +من ال H و من ال F من ال H plus و ال F سالب لدرجة + +685 +00:50:40,870 --> 00:50:48,300 +إن ال HF يستطيع يعني يأكل الزجاج حاطه في زجاج تلاقي + +686 +00:50:48,300 --> 00:50:52,060 +أنه زجاج بدوب عمال منه قوى جدا جدا من ناحية ايه؟ + +687 +00:50:52,060 --> 00:50:54,840 +reactive خليني أقول مش قوي هو مش قوي فهو reactive + +688 +00:50:54,840 --> 00:50:57,820 +خليني أقول نشاطيته، نشاطيته اللي بقوله أنا + +689 +00:50:57,820 --> 00:51:02,260 +النشاطية تبعته بتتوقف على مش بس ال H plus لأ وكمان + +690 +00:51:02,260 --> 00:51:07,020 +بتعتمد على ال anion اللي هو في هذه الحالة ال F + +691 +00:51:07,020 --> 00:51:11,990 +سالب الـ strong electrolytes هي الـ strong acids هي + +692 +00:51:11,990 --> 00:51:15,850 +الـ acids اللي بتتفكك تفكك كامل في المحلول بينما + +693 +00:51:15,850 --> 00:51:20,050 +ال weak acids و ال bases برضه هي عبارة عن ال + +694 +00:51:20,050 --> 00:51:22,990 +acids و ال bases اللي لا تتفكك تفكك كامل في + +695 +00:51:22,990 --> 00:51:29,150 +المحلول يعني تتفكك بشكل جزئي في المحلول ال acids + +696 +00:51:29,150 --> 00:51:36,130 +لازم نحفظها لأنها بسيطة أول حاجة مدام الـ HF مش + +697 +00:51:36,130 --> 00:51:41,430 +strong نجي لـ HCl و الـ HBr و الـ HI اللي هو في + +698 +00:51:41,430 --> 00:51:48,210 +المجموعة الأخيرة هدول كلهم strong بالإضافة لـ HNO3 + +699 +00:51:48,210 --> 00:52:00,070 +و HClO3 و HClO4 الـ HClO3 والـ HClO4 والنيتريك أسيد + +700 +00:52:00,070 --> 00:52:05,530 +أما السلفوريك أسيد فهو بس التفكك الأول بس التفكك + +701 +00:52:05,530 --> 00:52:09,990 +الأول أنا لازم أعرف هدول هيها الهيدروكلوريك أسيد + +702 +00:52:09,990 --> 00:52:14,790 +يمكن تلاتة فيهم ClCl وClO3 وClO4 تلاتة strong + +703 +00:52:23,490 --> 00:52:28,760 +لازم نعرف هذول عارفين ليه؟ لأن ما عداهم weak بعدها + +704 +00:52:28,760 --> 00:52:31,140 +weak أنا إذا أنا عرفت هدول بأعرف كل الباقي إيه + +705 +00:52:31,140 --> 00:52:37,340 +weak فلازم أعرف هدول و زي ما قلت HCl HBr HI بعدين + +706 +00:52:37,340 --> 00:52:43,040 +بضل في المجموعة الهالوجينات HClO3 HClO4 خلصتهم دلوقت + +707 +00:52:43,040 --> 00:52:50,420 +عندي HNO3 وH2SO4 ماشي طب الـ basis الـ basis جال + +708 +00:52:50,420 --> 00:52:54,440 +والله الـ المجموعة الأولى و الـ calcium و الـ potassium + +709 +00:52:54,440 --> 00:52:58,320 +و الـ barium المجموعة الثانية و برضه يعني مع تحفظ لكن + +710 +00:52:58,320 --> 00:53:02,840 +بالنسبة لهذه لكن يعني إحنا هناخد نِتابع أسلوب + +711 +00:53:02,840 --> 00:53:08,020 +الكاتب يعني في الموضوع فخلاص نحفظ هدول بس يعني و + +712 +00:53:08,020 --> 00:53:12,750 +ما عداهم كل ما عداهم weak انتهينا يبقى إحنا لو + +713 +00:53:12,750 --> 00:53:17,110 +عرفنا هدول كـ strong acids و bases بنعرف إنه كل + +714 +00:53:17,110 --> 00:53:21,630 +الباقي weak بيقول لي أنه أقوى من هذه الأحماض، أنه + +715 +00:53:21,630 --> 00:53:28,010 +أقوى، كل حمض موجود منه ثمانية species فهذه + +716 +00:53:28,010 --> 00:53:33,490 +الثمانية كلهم متفككين، تفكك كامل، إذا هذا حمض قوي، + +717 +00:53:33,490 --> 00:53:37,880 +طب هانقد إيش قد من الثمانية متفكك؟ بس اتنين طب هنقد إيش + +718 +00:53:37,880 --> 00:53:42,540 +تلاتة هيفجأ هذا أقوى واحد هذا الثاني بعدين هذا أقل + +719 +00:53:42,540 --> 00:53:50,080 +واحد سهل خالص طيب بدي + +720 +00:53:50,080 --> 00:53:55,760 +ألخص بدي أقول أنه يجب أن نتذكر أن الـ strong acids + +721 +00:53:55,760 --> 00:54:00,480 +هي الـ acids اللي توي ذكرتها أنا و ما عداها يعتبر + +722 +00:54:00,480 --> 00:54:03,860 +weak الـ strong bases هي اللي ما ذكرتها برضه قبل + +723 +00:54:03,860 --> 00:54:08,960 +شوية الـ .. الـ .. الـ hydroxides للمجموعة الأولى + +724 +00:54:08,960 --> 00:54:12,900 +زائد strontium, barium, calcium، strontium, + +725 +00:54:13,000 --> 00:54:16,100 +barium, calcium أو calcium, barium, strontium، + +726 +00:54:16,100 --> 00:54:19,360 +كويس هدول التلاتة هدول strong و ما عداهم كله weak + +727 +00:54:19,360 --> 00:54:24,690 +الـ molecular compounds ممكن تكون strong electrolytes زي + +728 +00:54:24,690 --> 00:54:28,950 +مثلًا الـ Acids الـ Acids كلها اللي بتدوب في المية + +729 +00:54:28,950 --> 00:54:34,510 +أو weak electrolytes زي الـ Acetic Acid و الـ + +730 +00:54:34,510 --> 00:54:36,930 +Citric Acid اللي فيها مجموعة الـ Carboxylate و + +731 +00:54:36,930 --> 00:54:41,130 +الـ ammonia أو non electrolytes زي الـ sucrose و + +732 +00:54:41,130 --> 00:54:45,410 +الـ methanol إلى أخرها الـ ammonia و الـ Amine + +733 +00:54:45,410 --> 00:54:50,730 +Containing Compounds ammonia يعني in H تلاتة لو + +734 +00:54:50,730 --> 00:54:52,330 +غيرنا واحدة H بـ R + +735 +00:54:55,250 --> 00:55:01,270 +هذه اسمها Amine أو R2NH برضه هذه امين أو R3N هذه + +736 +00:55:01,270 --> 00:55:07,830 +برضه امين اسمها فالأمونيا أو أي امين يعني هذه كلها + +737 +00:55:07,830 --> 00:55:11,110 +عبارة عن weak electrolytes لأنها weak bases weak + +738 +00:55:11,110 --> 00:55:15,670 +electrolytes فهذا تلخيص تقريبًا للكلام اللي إحنا + +739 +00:55:15,670 --> 00:55:20,380 +شفناه سابقًا بيقول classify these dissolved + +740 +00:55:20,380 --> 00:55:24,640 +substances as strong, weak or non-electrolytes لو + +741 +00:55:24,640 --> 00:55:30,060 +طلعنا على الـ calcium chloride strong لأنه ionic + +742 +00:55:30,060 --> 00:55:34,220 +compound و soluble ionic compound و إيه؟ و soluble طب + +743 +00:55:34,220 --> 00:55:40,300 +الـ HNO3 هذا strong لأنه أسيد في المياه في المياه أو + +744 +00:55:40,300 --> 00:55:43,300 +أعطيني H plus و NO تلاتة سالب تفكه كامل لأنه + +745 +00:55:43,300 --> 00:55:48,740 +strong acid الـ ethanol non electrolyte الـ formic + +746 +00:55:48,740 --> 00:55:52,060 +acid هاي و ها طلعوا هيك بديكوا تتذكروا ها ده هي + +747 +00:55:52,060 --> 00:55:56,840 +كاربوكسيلات في واحدة كويس واحدة إذا اه هذا عبارة + +748 +00:55:56,840 --> 00:56:00,060 +عن weak weak acid يعني weak electrolyte الـ KOH + +749 +00:56:00,060 --> 00:56:04,480 +طبعًا strong electrolyte كل strong acids و bases + +750 +00:56:04,480 --> 00:56:08,750 +strong electrolytes مدعم strong acid أو بيز متفكك + +751 +00:56:08,750 --> 00:56:17,950 +بنسبة 100% إذا هو strong electrolyte طيب كمان مثال + +752 +00:56:17,950 --> 00:56:21,110 +يعني كبير بس على الفاضي يعني consider solutions in + +753 +00:56:21,110 --> 00:56:23,870 +which point one mole of each of the following + +754 +00:56:23,870 --> 00:56:27,230 +compounds is dissolved in one liter of water + +755 +00:56:27,230 --> 00:56:33,430 +كالسوميترات حطيناه في لتر من المية جلوكوز حطيناه + +756 +00:56:33,430 --> 00:56:35,190 +في لتر من المية واحد من عشر مول + +757 +00:56:40,180 --> 00:56:45,460 +Sodium Acetate حطيناه في المية Astic Acid حطيناه + +758 +00:56:45,460 --> 00:56:50,680 +في المية فإيش بيقول لي؟ بيقول لي والله rank the + +759 +00:56:50,680 --> 00:56:53,520 +solutions in order of increasing electrical + +760 +00:56:53,520 --> 00:57:00,440 +conductivity إيش يعني؟ مين بيوصل الكهربا أكثر؟ إيش + +761 +00:57:00,440 --> 00:57:02,360 +معناته دا كله؟ مع أيش بدي أدور؟ + +762 +00:57:05,170 --> 00:57:09,690 +مين بده يعطينا أيونات أكثر في المية؟ اه مين بده + +763 +00:57:09,690 --> 00:57:12,470 +يعطينا أيونات أكثر؟ طب مين نتطلع على هذا؟ هذا + +764 +00:57:12,470 --> 00:57:17,190 +بيعطينا أيونات؟ هذا أضحى اللي بيعطي شيء طيب اسيتك + +765 +00:57:17,190 --> 00:57:21,510 +أسيد ضعيف تفكك ضعيف الـ Sodium Acetate بيعطي أيون + +766 +00:57:21,510 --> 00:57:24,730 +Sodium و أيون إيه؟ Acetate بينما الـ Calcium + +767 +00:57:24,730 --> 00:57:29,580 +Nitrate بيعطي واحد Calcium و اتنين تلاتة يعني هذا + +768 +00:57:29,580 --> 00:57:32,680 +عدد أيوناته أكثر في المية فهذا more conductive + +769 +00:57:32,680 --> 00:57:36,740 +يبقى هذا أكثر شيء هذا بعده هذا بعده طبعًا اللي جوه + +770 +00:57:36,740 --> 00:57:45,560 +كوز بيكون أقل شيء من خصائص الـ الـ acidic solutions + +771 +00:57:45,560 --> 00:57:52,560 +أنه يعني الـ acidic solutions حمضية سورية يعني + +772 +00:57:52,560 --> 00:57:58,100 +حامضة حامضة يعني طعمها حامض عشانيك اسمها أحماض + +773 +00:57:58,100 --> 00:58:05,460 +طعمها متصور كمان لو إجينا جبنا صبغة زي صبغة عباد + +774 +00:58:05,460 --> 00:58:10,220 +الشمس بيقولوا لها أه و حطينا بتحمر ورقة عباد الشمس + +775 +00:58:10,220 --> 00:58:13,920 +يعني تأثيرها على الصبغة تأثير معين بينما الـ base + +776 +00:58:13,920 --> 00:58:21,300 +طعمه bitter اه مر قابض مر ولو حطينا نفس الصبغة + +777 +00:58:21,300 --> 00:58:27,310 +حطينا ورقة فيها نفس الصبغة بلاحظ أنها بتزرق الخصائص + +778 +00:58:27,310 --> 00:58:33,090 +يعني متباينة في الحقيقة يعني للغاية ما يميز الـ + +779 +00:58:33,090 --> 00:58:36,530 +acids و الـ bases أن الـ acids بتتفاعل مع الـ bases و + +780 +00:58:36,530 --> 00:58:41,230 +بتعطيني salt و water بنسمي التفاعل الـ + +781 +00:58:41,230 --> 00:58:45,270 +neutralization reaction الـ neutralization reaction + +782 +00:58:45,270 --> 00:58:49,870 +فمثلًا الـ HCl بيتفاعل مع الـ sodium hydroxide + +783 +00:58:49,870 --> 00:58:54,490 +بيعطيني NaCl زائد مية طب هل هذا التفاعل بيتم؟ + +784 +00:58:54,490 --> 00:58:59,330 +بنقول نعم لأنه النتيجة مية و هذا عبارة عن acid و + +785 +00:58:59,330 --> 00:59:03,150 +base فالـ acid و الـ base بتفاعل و بيعطوني salt و + +786 +00:59:03,150 --> 00:59:07,500 +مية في الحقيقة الـ salt خصائصه تختلف كلية عن خصائص + +787 +00:59:07,500 --> 00:59:12,280 +الـ acid و عن خصائص الـ base يعني الـ salt له خصائص + +788 +00:59:12,280 --> 00:59:17,460 +منفصلة ليس لها علاقة بخصائص الـ acid ولا خصائص الـ + +789 +00:59:17,460 --> 00:59:20,920 +base لكن مجرد تفاعل الـ acid مع الـ base يبقى يعطينا + +790 +00:59:20,920 --> 00:59:26,180 +نتيجة عبارة عن salt و مياه + +791 +00:59:29,930 --> 00:59:33,690 +مثلًا ممكن نقول يعني التفاعل الماضي لو بدنا نكتبه + +792 +00:59:33,690 --> 00:59:37,830 +على هيئة Ionic equation فبقول H plus زائد Cl minus + +793 +00:59:37,830 --> 00:59:41,550 +Na plus زائد Hydroxide تعطينا Na plus أكويوس زائد + +794 +00:59:41,550 --> 00:59:46,150 +Cl سالب أكويوس H2O أكويوس لكن الـ H2O هي عبارة عن + +795 +00:59:46,150 --> 00:59:52,810 +إيه؟ عبارة عن مادة تعتبر weak electrolyte إذاً هاي + +796 +00:59:52,810 --> 00:59:56,430 +الـ Cl- و الـ Na+, الـ Cl-, و الـ Na، بهذا الـ Spectator + +797 +00:59:56,430 --> 01:00:00,530 +Ions معناه كلها في الحقيقة التفاعل وكأنه أساسًا هو + +798 +01:00:00,530 --> 01:00:03,370 +عبارة عن الـ H Plus اللي هو الـ Acid زائد + +799 +01:00:03,370 --> 01:00:07,510 +الـ Hydroxide اللي هو الـ Base عشان يعطيني مية ليه؟ + +800 +01:00:07,510 --> 01:00:13,170 +لأنه الـ NaCl هو عبارة عن salt بيكون دايب ذوبان تام + +801 +01:00:13,170 --> 01:00:15,750 +في المية و Ionic compound + +802 +01:00:17,630 --> 01:00:21,050 +نطلع على المثال التالي يقول write the molecular + +803 +01:00:21,050 --> 01:00:23,810 +ionic and net ionic equations for the reaction + +804 +01:00:23,810 --> 01:00:27,010 +between hydrochloric acid and water insoluble + +805 +01:00:27,010 --> 01:00:30,450 +magnesium hydroxide نفس الكلام اللي شفناه يعني + +806 +01:00:30,450 --> 01:00:34,150 +سابقا فيما يتعلق بالمعادلات لكن hand acid و base + +807 +01:00:34,150 --> 01:00:37,970 +هذا يعتبر base magnesium hydroxide insoluble و مع + +808 +01:00:37,970 --> 01:00:43,170 +ذلك طبعًا الـ H بتفعل مع الهيدروكسيد فالمغنيزيوم + +809 +01:00:43,170 --> 01:00:46,930 +الهيدروكسيد solid اتنين HCl مغنيزيوم كلوريد زائد + +810 +01:00:46,930 --> 01:00:51,290 +اتنين H2O لو بدك تب المعادلة الايونية هذا لانه + +811 +01:00:51,290 --> 01:00:56,050 +solid بسيبه زي ما هو ممنوع يتأين مابتفككش اتنين H + +812 +01:00:56,050 --> 01:00:59,250 +plus اتنين Cl minus مغنيزيوم اتنين H plus اتنين Cl + +813 +01:00:59,250 --> 01:01:07,750 +minus H2O بلاحظ أنا انه هاي بس هذا و هذا هما بس الـ + +814 +01:01:07,750 --> 01:01:10,930 +chloride هو الـ spectator ion و الباقيين لأ + +815 +01:01:10,930 --> 01:01:15,170 +magnesium hydroxide زائد اتنين H plus يعطي + +816 +01:01:15,170 --> 01:01:19,730 +magnesium two plus زائد two H two O فبس الـ + +817 +01:01:19,730 --> 01:01:23,070 +chloride هو الايه الـ spectator ion + +818 +01:01:26,540 --> 01:01:31,140 +هذا يعني بيقول إنه الـ Magnesium Hydroxide يستخدم + +819 +01:01:31,140 --> 01:01:36,160 +في المحاليل اللي الناس بتاخدها علشان حرقة المعدة + +820 +01:01:36,160 --> 01:01:39,900 +بتعرفوا المحاليل اللي بيستخدم لحرقة المعدة يعني + +821 +01:01:39,900 --> 01:01:42,380 +فالـ Magnesium Hydroxide إيش اللي بيعمل هاي الـ + +822 +01:01:42,380 --> 01:01:45,440 +Magnesium Hydroxide و هي الـ HCl اللي في المعدة + +823 +01:01:45,440 --> 01:01:51,680 +بنلاحظ إنه الـ H Plus اللي في المعدة بتاخد الـ + +824 +01:01:51,680 --> 01:01:54,140 +Hydroxide من الـ Magnesium Hydroxide بتخليه مية + +825 +01:01:54,140 --> 01:01:58,940 +هيه و بالتالي الـ H plus بتقل لأن الـ H plus هي الأبيض + +826 +01:01:58,940 --> 01:02:02,640 +بياخد الهيدروكسيد و بيحاولوا لاقيه لمية، هذا كان + +827 +01:02:02,640 --> 01:02:04,960 +هيدروكسيد و هذا كان هيدروكسيد و هذا كان هيدروكسيد + +828 +01:02:04,960 --> 01:02:07,980 +و هذا كان هيدروكسيد اتفاعلوا مع الـ H plus اللي + +829 +01:02:07,980 --> 01:02:13,440 +هانو اتحولوا لمية فحرقة المعدة بتقل فيها إنها كمان + +830 +01:02:13,440 --> 01:02:17,160 +يعني ليست كبيرة من المستحضرات اللي بتستخدم كـ + +831 +01:02:17,160 --> 01:02:22,160 +antacids يعني ضد حرقة المعدة فمش المفروض نحفظها + +832 +01:02:22,160 --> 01:02:27,200 +يعني بس أنه يعني هذه أسماء تجارية إلها الـ مالوكسيدا + +833 +01:02:27,200 --> 01:02:30,660 +مشهور و الـ روليدز و الـ تمز هدول مشهورين في غزة يعني + +834 +01:02:30,660 --> 01:02:37,200 +فهذه كلها مواد تستخدم كيميائية طبعًا تستخدم للتخفيف + +835 +01:02:37,200 --> 01:02:43,170 +من حرقة المعدة نطلع على مثال بيقول for the + +836 +01:02:43,170 --> 01:02:46,210 +reaction between aqueous solutions of acetic acid + +837 +01:02:46,210 --> 01:02:50,270 +and barium hydroxide أنا أكتب لكم بالبصيرة dilute + +838 +01:02:50,270 --> 01:02:52,550 +barium hydroxide لأنه أصلاً الـ barium hydroxide لا + +839 +01:02:52,550 --> 01:02:55,670 +يدوب يعني ذوبان كامل ما علينا من هذا الكلام write + +840 +01:02:55,670 --> 01:02:58,570 +إيه the balanced molecular equation the complete + +841 +01:02:58,570 --> 01:03:02,970 +ionic equation والـ net ionic equation طبعًا مباشرة + +842 +01:03:02,970 --> 01:03:07,930 +الـ molecular equation تحتوي على المكونات على + +843 +01:03:07,930 --> 01:03:10,630 +هيئة وكأنها molecules يعني سواء كانت أيونية أو مش + +844 +01:03:10,630 --> 01:03:14,150 +أيونية فهذا weak electrolyte زي ما هو barium + +845 +01:03:14,150 --> 01:03:18,050 +hydroxide aqueous باريوم أسيتات لأنه exchange + +846 +01:03:18,050 --> 01:03:22,890 +reaction هو metathesis reaction ومية الآن بدك تكتب + +847 +01:03:22,890 --> 01:03:27,650 +ionic compound هذا بسيبه زي ما هو لأن أسيتيك أسيد لو + +848 +01:03:27,650 --> 01:03:30,630 +أنه كان بتفكك تفكك كامل كان كتابته أيونات لكن لا + +849 +01:03:30,630 --> 01:03:34,150 +بكتبوش أيونات الباريوم هيدروكسيد آه باريوم اتنين + +850 +01:03:34,150 --> 01:03:38,010 +هيدروكسيد باريوم أسيتات آه لأن كل أملاح الأسيتات + +851 +01:03:38,010 --> 01:03:42,690 +دائمًا نتذكر باريوم واتنين أسيتات والـ H2O بيضل لها + +852 +01:03:42,690 --> 01:03:48,490 +زي ما هي فلو جيت طلعت الباريوم من هنا والباريوم من + +853 +01:03:48,490 --> 01:03:53,420 +هنا بس هذا هو الـ spectator ion والباقيين لأ مش + +854 +01:03:53,420 --> 01:03:58,240 +spectator فبعطينا 2 CH3COOH زي 2 Hydroxide بعطينا + +855 +01:03:58,240 --> 01:04:03,080 +2 CH3COO زي 2 ميه بنعرفش.. نختم القوانين بالازدواج + +856 +01:04:03,080 --> 01:04:06,740 +.. بنعرفش أنه يكون في المعادلة مضروبة في factor + +857 +01:04:06,740 --> 01:04:10,640 +يجب أن النسبة بين عدد المولات تكون أبسط ما يمكن + +858 +01:04:10,640 --> 01:04:13,460 +مش اتنين لا اتنين لا اتنين لا اتنين لأ بيكون واحد + +859 +01:04:13,460 --> 01:04:16,700 +آه فبنقول والله أسيتيك.. بنقسم على اتنين أسيتيك أسيد + +860 +01:04:16,700 --> 01:04:19,800 +Hydroxide بعطينا أسيتات ومية + +861 +01:04:24,930 --> 01:04:27,850 +كمان مثال بيقول for the reaction of phosphorus + +862 +01:04:27,850 --> 01:04:33,110 +acid H3PO3 لأن الفسفور موجود في المجموعة اللي في + +863 +01:04:33,110 --> 01:04:35,970 +النص هذه اللي حطيناه قلنا أنه الـ reference + +864 +01:04:35,970 --> 01:04:44,190 +oxyanion هو الـ 8 في 4 فأه الـ P O أربعة هو الـ + +865 +01:04:44,190 --> 01:04:48,570 +reference زي S O أربعة زي سلينيوم أربعة كل هدول + +866 +01:04:48,570 --> 01:04:52,410 +تيلوريوم أربعة فهذا الـ reference أربعة فما أنه أقل + +867 +01:04:52,410 --> 01:04:56,910 +بواحد فصار إيه فوسفوراس كان فوسفايت فالـ فوسفايت + +868 +01:04:56,910 --> 01:05:02,340 +بيصير لما بنقوله acid فوسفوراسكويس فـ for the + +869 +01:05:02,340 --> 01:05:05,740 +reaction of phosphorus acid H3PO3 and potassium + +870 +01:05:05,740 --> 01:05:09,900 +hydroxide write a balanced molecular equation and + +871 +01:05:09,900 --> 01:05:13,800 +be the net ionic equation طب بنكتب المعادلة + +872 +01:05:13,800 --> 01:05:22,220 +phosphorus acid و KOH K3PO3 و 3H2O طبعًا بنعرف يعني + +873 +01:05:26,070 --> 01:05:29,870 +نكتبها على هيئة Ionic compound وبعدين بنرفع الـ + +874 +01:05:29,870 --> 01:05:32,950 +spectator ions فبيضل لعيننا phosphorus acid و + +875 +01:05:32,950 --> 01:05:43,770 +hydroxide بيعطينا phosphite و H2 ومية خلينا + +876 +01:05:43,770 --> 01:05:47,990 +الآن ننتقل لنوع + +877 +01:05:47,990 --> 01:05:51,710 +مهم كثير من أنواع التفاعلات هي الـ neutralization + +878 +01:05:51,710 --> 01:05:56,500 +reactions اللي بتعطيني غازات يعني أسيد بيز لكن + +879 +01:05:56,500 --> 01:05:59,540 +النتيجة عبارة عن غاز هذا الكلام في الحقيقة بشوفه + +880 +01:05:59,540 --> 01:06:05,560 +أنا مع الـ two anions بشوفه مع الـ sulphide وبشوفه + +881 +01:06:05,560 --> 01:06:08,260 +مع الكربونيت والبيكربونيت طبعًا الكربونيت والـ + +882 +01:06:08,260 --> 01:06:13,400 +بيكربونيت فالنتيجة مثلًا HCl مع الـ sulphide إيش ما + +883 +01:06:13,400 --> 01:06:17,600 +كان مع الـ sulphide بعطيني H2S الـ H2S هذا عبارة عن + +884 +01:06:17,600 --> 01:06:21,380 +غاز أو الـ solubility قليلة جدًا في المية أو الـ + +885 +01:06:21,380 --> 01:06:23,640 +solubility قليلة جدًا في المية اللي هو بيقولوله + +886 +01:06:23,640 --> 01:06:27,680 +يمكن في المدارس علموكوا أن هذا الغاز هو ورائحة + +887 +01:06:27,680 --> 01:06:33,020 +البيض الفاسد زي ريحة المجاري يعني سيء رائحة البيض + +888 +01:06:33,020 --> 01:06:39,300 +الفاسد كويس فهذا الـ H2S فعندنا احنا لو كتبنا الـ HCl + +889 +01:06:39,300 --> 01:06:44,660 +H plus و Cl minus الـ NA2S Na plus و S2 minus لأن + +890 +01:06:44,660 --> 01:06:51,590 +هذا ذائب الذائب الذائب بيكون aqueous ذائب وهو عبارة + +891 +01:06:51,590 --> 01:06:54,850 +عن ionic compound وهو عبارة عن strong electrolyte + +892 +01:06:54,850 --> 01:06:59,410 +لأنه Sodium Sulphide H2S هدرسيبه زي ما هو فككش + +893 +01:06:59,410 --> 01:07:04,330 +molecular gas Na Cl كذلك Na و Na Plus Cl سالب + +894 +01:07:04,330 --> 01:07:07,270 +بيكون الـ net equation اتنين H Plus زائد S اتنين + +895 +01:07:07,270 --> 01:07:11,290 +سالب تعطينا H2S gas فالـ neutralization reactions + +896 +01:07:11,290 --> 01:07:18,800 +مع الـ formation of gases أحد الـ Anions اللي + +897 +01:07:18,800 --> 01:07:22,480 +بتعطيني غاز وأيضًا الكربونيت أو الـ بيكربونيت + +898 +01:07:22,480 --> 01:07:26,820 +الكربونيت أو الـ بيكربونيت بتعطي عادة CO2 فمثلًا لو + +899 +01:07:26,820 --> 01:07:30,380 +كان في عندي HCl زائد Sodium بيكربونيت هعطيني NaCl + +900 +01:07:30,380 --> 01:07:34,220 +زائد CO2 زائد H2O في بعض الأحيان الناس بكتبوها + +901 +01:07:34,220 --> 01:07:40,540 +H2CO3 ماشي لكن هو الـ H2CO3 بنتذكر أنه CO2 زائد H2O + +902 +01:07:40,980 --> 01:07:49,960 +الـ H2CO3 هو عبارة عن CO2 زائد H2O فبرضه لو كتبنا + +903 +01:07:49,960 --> 01:07:54,260 +الـ H بلس و CL ماينوس NA بلس و HCO تلاتة سالب + +904 +01:07:54,260 --> 01:07:56,000 +بيكربونيت + +905 +01:07:57,280 --> 01:08:01,580 +N A Plus C L سالب طبعًا CO2 زي ما هي H2O Liquid زي ما + +906 +01:08:01,580 --> 01:08:06,700 +هي لأنها بتتفككش فبيطلع عندي H Plus و B Carbonate + +907 +01:08:06,700 --> 01:08:15,200 +بتعطيلي الـ CO2 و H2O والـ CO2 عبارة عن غاز الآن + +908 +01:08:15,200 --> 01:08:19,020 +يمكن وصلنا + +909 +01:08:19,020 --> 01:08:22,480 +للـ oxidation reduction reactions من أهم أنواع الـ + +910 +01:08:22,480 --> 01:08:24,920 +reactions اللي بنطلع عليها وتطبيقاتها في الحياة + +911 +01:08:24,920 --> 01:08:29,770 +العمليّة بالنسبة لكم يمكن تكون أحسن كثير من الـ + +912 +01:08:29,770 --> 01:08:32,610 +precipitation أو حتى الـ neutralization reactions + +913 +01:08:32,610 --> 01:08:36,490 +وإن كان بعضكم هيستفيد من الـ neutralization + +914 +01:08:36,490 --> 01:08:44,410 +reactions لكن الـ oxidation reaction كتفاعلات + +915 +01:08:44,410 --> 01:08:48,350 +بتهتم بالـ.. زي ما هندرسها احنا تحديدًا في هذا + +916 +01:08:48,350 --> 01:08:55,310 +المثال بس في نوع واحد من الـ.. الـ Substances اللي + +917 +01:08:55,310 --> 01:08:58,750 +هي الـ Metals فبتكون مهمة بالنسبة لكم لأن هندرس + +918 +01:08:58,750 --> 01:09:03,550 +التفاعلات الأكسدة والاختزال التي تتضمن Metal-Ion + +919 +01:09:03,550 --> 01:09:07,510 +Metal يعني Metal تتضمن إيه؟ Metal والـ Metals طبعًا + +920 +01:09:07,510 --> 01:09:12,090 +المهندسين المفروض إنهم بيهتموا فيها لأنها مكون + +921 +01:09:12,090 --> 01:09:16,250 +أساسي من المكونات شغلات كثير بيستخدموها إيش هي + +922 +01:09:16,250 --> 01:09:18,650 +تفاعلات الأكسدة والاختزال؟ + +923 +01:09:21,440 --> 01:09:25,300 +إيش هي تفاعلات الأكسدة والاختزال؟ قال تفاعلات + +924 +01:09:25,300 --> 01:09:27,940 +الأكسدة والاختزال الـ Oxidation Reduction Reactions + +925 +01:09:27,940 --> 01:09:32,460 +وفي بعض الأحيان بيقولها Redox Reactions Oxidation + +926 +01:09:32,460 --> 01:09:37,500 +Reduction أو Redox Reactions هذه التفاعلات هي + +927 +01:09:37,500 --> 01:09:41,820 +التفاعلات التي يتم خلالها انتقال إلكترونات هي + +928 +01:09:41,820 --> 01:09:45,760 +التفاعلات اللي بيتم خلالها انتقال إلكترونات يعني + +929 +01:09:45,760 --> 01:09:49,280 +مثلًا تفاعلات الـ Precipitation كانت بتكون عن دراسة + +930 +01:09:50,400 --> 01:09:52,980 +بحط مادة تانية على بعض بتكون الراسب الـ + +931 +01:09:52,980 --> 01:09:56,600 +neutralization أو الـ acid base كان.. كان بيتكون + +932 +01:09:56,600 --> 01:10:00,020 +عندي ملح ومال التفاعلات الأكسدة والاختزال لأ + +933 +01:10:00,020 --> 01:10:03,720 +التفاعلات الأكسدة والاختزال بده يعني ينتقل مش H بلس + +934 +01:10:03,720 --> 01:10:07,360 +أو هيدروكسيل لأ بده ينتقل إلكترونات فالتفاعلات + +935 +01:10:07,360 --> 01:10:11,220 +اللي بيتم خلالها انتقال إلكترونات هي عبارة عن + +936 +01:10:11,220 --> 01:10:15,480 +oxidation reduction reactions + +937 +01:10:17,970 --> 01:10:21,730 +وزي ما قلت احنا هنركز بس على الـ Redox Reactions + +938 +01:10:21,730 --> 01:10:26,170 +اللي بيكون الـ Metal أحد مكونات التفاعل ليه؟ لأن + +939 +01:10:26,170 --> 01:10:31,890 +الـ Oxidation Reduction Reactions يعني واسعة جدًا + +940 +01:10:31,890 --> 01:10:35,270 +فاحنا بس هنركز على هذا النوع من أنواع الـ Oxidation + +941 +01:10:35,270 --> 01:10:42,670 +Reduction Reactions طبعًا اللي فيه Metal تمام؟ إيش + +942 +01:10:42,670 --> 01:10:48,130 +تعريف الـ X ده؟ تعريف الـ X ده قال هيفقد إلكترونات + +943 +01:10:48,130 --> 01:10:53,090 +الأكسدة loss of electrons يعني أي species عندي + +944 +01:10:53,090 --> 01:10:59,190 +مثلًا الـ metal ذرة أيون بيفقد إلكترونات يعني بيصير + +945 +01:10:59,190 --> 01:11:02,830 +more positive فهذه عبارة عن عملية أكسدة يبقى + +946 +01:11:02,830 --> 01:11:07,730 +الأكسدة oxidation is a process of loss of + +947 +01:11:07,730 --> 01:11:12,290 +electrons loss of electrons فعندنا الأكسدة loss of + +948 +01:11:12,290 --> 01:11:17,980 +electrons عكسها الـ reduction Gain of Electrons Gain + +949 +01:11:17,980 --> 01:11:26,020 +of Electrons اكتسب إلكترونات يعني يمكن تسمية + +950 +01:11:26,020 --> 01:11:30,020 +ليه سموها أكسدة قال لأنه أول ما يعني لاحظوها + +951 +01:11:30,020 --> 01:11:36,380 +لاحظوها مواد نتجت عن التفاعل مع الأكسجين فسموها + +952 +01:11:36,380 --> 01:11:43,930 +إيه أكسدة في يعني غالبًا يعني بدايتها أنه لاحظوها مع + +953 +01:11:43,930 --> 01:11:50,530 +الـ oxygen فسموها أكسدة من أكثر الشيء ملاحظة احنا + +954 +01:11:50,530 --> 01:11:54,230 +في الحياة العملية بنشوفه مثلًا لو عندنا شمبيك حماية + +955 +01:11:54,230 --> 01:12:00,530 +في البيت من الحديد أو درابزين حديد بنلاحظ أن في + +956 +01:12:00,530 --> 01:12:04,810 +عليه صدأ، بنلاحظ أن في عليه صدأ الصدأ هذا هو عبارة + +957 +01:12:04,810 --> 01:12:11,980 +عن عملية أكسدة فيها الـ iron الـ iron بيفقد إلكترونات + +958 +01:12:11,980 --> 01:12:16,520 +ويصير iron تلاتة والـ oxygen اللي في الهواء + +959 +01:12:16,520 --> 01:12:22,600 +بيكتسب إلكترونات ويصير oxide O2 سالب O2 سالب فالـ + +960 +01:12:22,600 --> 01:12:26,320 +iron تلاتة + +961 +01:12:26,320 --> 01:12:30,220 +مع الـ O2 سالب قال والله هذه بتيجي هنا وبتيجي هنا + +962 +01:12:30,220 --> 01:12:35,720 +يعني iron 2 O3 هذا هو الصدأ هذا هو الصدأ أو الـ + +963 +01:12:35,720 --> 01:12:38,200 +corrosion اللي بيحصل فـ.. + +964 +01:12:43,820 --> 01:12:49,440 +فعادة يعني الـ.. الـ metals مش بس الـ iron لأ الـ + +965 +01:12:49,440 --> 01:12:54,960 +iron الـ copper الـ.. الـ cobalt الـ nickel الـ zinc + +966 +01:12:54,960 --> 01:13:00,460 +تقريبًا كل المعادن تقريبًا يعني كل المعادن بيحصلها + +967 +01:13:00,460 --> 01:13:04,700 +corrosion بنسبة متفاوتة أقلها اللي هي الـ coinage + +968 +01:13:04,700 --> 01:13:08,440 +metals يعني الدهب مثلًا نستخدمه لفترة زمنية طويلة + +969 +01:13:08,440 --> 01:13:12,400 +مايحصلش له كيروجين مايتأكسدش الـ silver يعنيها أقل منه + +970 +01:13:12,400 --> 01:13:16,780 +البلاتين أحسن منه مثلًا يعني فبنلاحظ أن الـ coinage + +971 +01:13:16,780 --> 01:13:20,420 +metals + +972 +01:13:20,420 --> 01:13:26,660 +يعني أكثر صمودًا ضد العوامل الجوية لأنه العملية + +973 +01:13:26,660 --> 01:13:31,130 +الأكسدة والاختزال اللي بتتم في البيئة هذه تتطلب + +974 +01:13:31,130 --> 01:13:34,670 +وجود الهواء مع الـ metal ion فعناصر اللي.. + +975 +01:13:34,670 --> 01:13:37,690 +العناصر اللي بنصنع منها العملات المعدنية اللي هي + +976 +01:13:37,690 --> 01:13:43,010 +الـ coinage metals تعتبر أكثر مقاومة للظروف + +977 +01:13:43,010 --> 01:13:50,950 +البيئية اللي هي موجودة فيها فعلى سبيل المثال يعني + +978 +01:13:50,950 --> 01:13:59,010 +ممكن تقول هذه شوكة silver مثلًا في عليها شوية شوية + +979 +01:13:59,010 --> 01:14:05,050 +إيش بيسموه يعني صدأ على السطح الصدأ الخارجي لكن و + +980 +01:14:05,050 --> 01:14:07,950 +أغلب المعادن ممكن يصير فعلًا صدأ على السطح الخارجي + +981 +01:14:07,950 --> 01:14:14,770 +لكن بعض المعادن زي مثلا السفن والـ يعني المراكب + +982 +01:14:14,770 --> 01:14:21,690 +الصيد وغيره بنلاحظ أنه ممكن يصل الصدى إلى أعماق + +983 +01:14:21,690 --> 01:14:27,040 +المعدن لدرجة أنه يسبب holes في الـ skeleton أو الـ + +984 +01:14:27,040 --> 01:14:35,260 +body للسفينة على سبيل المثال فيعتبر يعني هذه + +985 +01:14:35,260 --> 01:14:39,900 +الظواهر تعتبر يعني خليني أقول دلالة واضحة على + +986 +01:14:39,900 --> 01:14:44,490 +عمليات الأكسدة والاختزال واحنا لو فهمنا عمليات + +987 +01:14:44,490 --> 01:14:48,130 +الأكسدة والاختزال بشكل سليم ممكن نوفر على حالنا + +988 +01:14:48,130 --> 01:14:52,410 +جهد كبير جدا يعني هذا كلمة وكذا أنه يعني نتلافى + +989 +01:14:52,410 --> 01:14:55,350 +هذا الـ .. أو هذه الـ hole اللي موجودة في السفينة + +990 +01:14:55,350 --> 01:14:59,030 +كان ممكن نتلافها وفي الحقيقة بسهولة يعني مش يعني + +991 +01:14:59,030 --> 01:15:03,310 +صعوبة كثير ممكن نتلافها عن طريق إضافة بعض المعادن + +992 +01:15:03,310 --> 01:15:09,450 +للـ iron اللي موجود عندها بتخلي الصدأ ما يحصلش + +993 +01:15:09,450 --> 01:15:15,520 +أصلا عناصر المجموعة الأولى ممكن أنها تتآكل تآكل تام + +994 +01:15:15,520 --> 01:15:19,780 +والمجموعة الثانية عموما تتآكل تآكل تام لو حاطناها + +995 +01:15:19,780 --> 01:15:26,380 +في الهواء لأنه فورا هي بتفقد إلكترونات و بتتأكسد + +996 +01:15:26,380 --> 01:15:30,360 +بتصير مثلا Sodium Sodium موجب والـ Oxygen O2 سالب + +997 +01:15:30,360 --> 01:15:36,130 +وبتكون مركب فبعد فترة بنلاحظ أنه المواد هذه أو الـ + +998 +01:15:36,130 --> 01:15:40,330 +metals هذه كلها اتحولت لما يشبه يعني الـ spongy + +999 +01:15:40,330 --> 01:15:47,090 +salt أو material يعني التخلخل اللي هو الصدأ الداخل + +1000 +01:15:47,090 --> 01:15:51,610 +أو الأكسد التخلخل للداخل وصار ممكن أنه والله بإيده + +1001 +01:15:51,610 --> 01:15:56,580 +هيك نحسه نلاقيه عبارة عن زي salt حواليه بعد + +1002 +01:15:56,580 --> 01:16:00,720 +فترة بيبطل موجود الـmetal من أصله الكالسيوم يعتبر + +1003 +01:16:00,720 --> 01:16:05,040 +من العناصر يعني سهلة جدا إنها تتأكسد فالكالسيوم + +1004 +01:16:05,040 --> 01:16:08,240 +برضه بيفقد اثنين إلكترون والأكسجين بياخد اثنين + +1005 +01:16:08,240 --> 01:16:13,010 +إلكترون فبالتالي كالسيوم اثنين موجب وهذا أو اثنين + +1006 +01:16:13,010 --> 01:16:20,190 +سالب وبعدين بيصير اثنين كالسيوم أكسيد فالاكسوجين + +1007 +01:16:20,190 --> 01:16:26,370 +بياخد إلكترونات يعني بيتم اختزاله والكالسيوم بيفقد + +1008 +01:16:26,370 --> 01:16:30,510 +إلكترونات يعني بيتأكسد فالكالسيوم عملية أكسدة + +1009 +01:16:30,510 --> 01:16:33,290 +والأكسوجين عملية اختزال + +1010 +01:16:34,980 --> 01:16:38,740 +وين في عندي في التفاعل عملية أكسدة يجب أن تصاحبها + +1011 +01:16:38,740 --> 01:16:43,180 +عملية اختزال وين في عندي في أي تفاعل عملية أكسدة + +1012 +01:16:43,180 --> 01:16:49,520 +يجب أن تصاحبها عملية اختزال عدد الإلكترونات اللى + +1013 +01:16:49,520 --> 01:16:55,480 +بيتم إنفاقها في عملية الأكسدة يجب يجب أن تساوي عدد + +1014 +01:16:55,480 --> 01:16:59,120 +الإلكترونات اللى بيتم اكتسابها من المادة الأخرى + +1015 +01:16:59,120 --> 01:17:03,850 +إذا الله رد الحصة الجاية بنحاول نفصل فيها الأكسدة + +1016 +01:17:03,850 --> 01:17:09,670 +والاختزال ويمكن يكون بإمكاننا أن نخلص الـ chapter + +1017 +01:17:09,670 --> 01:17:11,630 +إذا الله راض فبنشوفكم الحصة الجاية diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/BZEbgk4AhLo_raw.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/BZEbgk4AhLo_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..b6c698971fb60da7f4e4efc23b1c4318e6d22c30 --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/BZEbgk4AhLo_raw.srt @@ -0,0 +1,3820 @@ +1 +00:00:21,720 --> 00:00:25,260 +بسم الله الرحمن الرحيم إذا الله راضي اليوم بنكمل + +2 +00:00:25,260 --> 00:00:27,560 +في ال chapter اللي بتحدث عن ال properties of + +3 +00:00:27,560 --> 00:00:34,420 +solutions اليوم إذا الله راضي هنبدأ ببعض الحسابات + +4 +00:00:34,420 --> 00:00:39,140 +اللي كنا بدناها الحصة الماضية و هحاول أني أفصل + +5 +00:00:39,140 --> 00:00:44,790 +فيها لأنه هي عبارة عن أجزاء صغيرةممكن نسئل فيها في + +6 +00:00:44,790 --> 00:00:48,670 +الامتحان بالاضافة لأنه بتلزمنا بعد شوية لما نتكلم + +7 +00:00:48,670 --> 00:00:52,790 +عن حاجة بنقولها Collegative Properties فهيلزمنا + +8 +00:00:52,790 --> 00:00:57,230 +كيف نعمل التحويلات الحسابية اللي هتكلم عنها الآن + +9 +00:00:57,230 --> 00:01:04,720 +فباختصار شديد جدا و من واقع خليني اقولتسائل الطلبة + +10 +00:01:04,720 --> 00:01:09,220 +سابقا بقول يمكن انا حطيت بعض القوانين السهلة لإنه + +11 +00:01:09,220 --> 00:01:15,000 +نحاول نعمل تحويلات في التركيز لو عندى مثلا + +12 +00:01:15,000 --> 00:01:18,240 +molarity اقدر احول ل molality لو عندى percentage + +13 +00:01:18,240 --> 00:01:22,020 +اقدر احول ل molarity او ل molality و العكس + +14 +00:01:29,190 --> 00:01:34,790 +الكلام اللى شوفناه الحصة الماضية باختصار لكن هحاول + +15 +00:01:34,790 --> 00:01:39,890 +انه اطلع على كل نوع من أنواع المسائل على حده فبقول + +16 +00:01:39,890 --> 00:01:45,450 +اذا كان بدنا نبسط الحسابات نعتبر التالي دائما اذا + +17 +00:01:45,450 --> 00:01:51,180 +كان معطيني الفبدي افرض ان اللي عندى الف جرام من ال + +18 +00:01:51,180 --> 00:01:54,880 +solvent لان تعريف ال molality ال molality بسوء + +19 +00:01:54,880 --> 00:01:59,280 +number of moles على ال kilogram solvent يعني الف + +20 +00:01:59,280 --> 00:02:01,140 +جرام من ال solvent فبدي اعتبر دايما ان عندى والله + +21 +00:02:01,140 --> 00:02:04,780 +الف جرام من ال solvent لو اعطانى ال molality بدي + +22 +00:02:04,780 --> 00:02:10,500 +اعتبر انه عندى الف جرام من ال solvent لو اعطانى ال + +23 +00:02:10,500 --> 00:02:14,480 +molarity بدي اعتبر انه عندى الف مل من ال solution + +24 +00:02:14,480 --> 00:02:19,290 +لان تعريف ال molarityمولاريتي بتساوي ال number of + +25 +00:02:19,290 --> 00:02:23,490 +moles of solute على ال letter of solution أو + +26 +00:02:23,490 --> 00:02:26,170 +الموجودة في ال letter of solution فال letter هو + +27 +00:02:26,170 --> 00:02:30,930 +عبارة عن الف من ال solution لو أعطاني التركيز معبر + +28 +00:02:30,930 --> 00:02:36,010 +عنه بال percentage مثلا عشرة في المية ميتريك أسد + +29 +00:02:37,510 --> 00:02:41,770 +بقول بدي اعتبر ان عندي دائما 100 جرام solution لان + +30 +00:02:41,770 --> 00:02:47,570 +10% نيترك اسد يعني 10 جرام في كل 100 جرام 10 جرام + +31 +00:02:47,570 --> 00:02:52,030 +في كل 100 جرام فبدي اعتبر هدول التلاتة قدامك لما + +32 +00:02:52,030 --> 00:02:57,310 +يعني اتواجهني اي مثلة بده اشوف هل هي molarity ولا + +33 +00:02:57,310 --> 00:03:02,630 +percentage وكمان يمكن حاجة رابعة لو اعطاني ال mol + +34 +00:03:02,630 --> 00:03:09,390 +fraction لأى component من المحلول بدي اتذكر ان ال + +35 +00:03:09,390 --> 00:03:13,130 +total number ال total value للمولي fraction او ال + +36 +00:03:13,130 --> 00:03:17,870 +total mole fraction لكل ال components و هتصحيح بدي + +37 +00:03:17,870 --> 00:03:20,750 +اتذكر هذا الكلام مفيد جدا جدا في حل المسائل + +38 +00:03:23,330 --> 00:03:27,470 +بعطيني ال density في كثير من الأحيان تلزمني في + +39 +00:03:27,470 --> 00:03:31,130 +كثير من الأحيان فبدى اقول انا اشهد ال density بدى + +40 +00:03:31,130 --> 00:03:33,890 +اذكر انه عبارة عن اجرام solution على ال mill + +41 +00:03:33,890 --> 00:03:37,290 +solution مهم جدا مش اقول اجرام على ال mill طب من + +42 +00:03:37,290 --> 00:03:41,330 +ايش اجرام solution ال density لل solution هي عبارة + +43 +00:03:41,330 --> 00:03:45,570 +عن اجرام solution على ال mill solution ومنها بدر + +44 +00:03:45,570 --> 00:03:48,670 +اجيب ال mill solution اجرام solution على ال + +45 +00:03:48,670 --> 00:03:53,450 +density ومنهابقدر اجيب لـ Grand solution مليف + +46 +00:03:53,450 --> 00:03:59,390 +ساليوشن في الـ density هذه تقريبا يعني خليني اقول + +47 +00:03:59,390 --> 00:04:05,270 +معظم العلاقات اللي بتفيد في حل المسائل الان بدي + +48 +00:04:05,270 --> 00:04:11,190 +اخد حاجة حاجة و اشوف كيف بطبق هذه الأمور على حل + +49 +00:04:11,190 --> 00:04:18,070 +المسائل المختلفة في البداية نتطلع بس على كيفية + +50 +00:04:18,070 --> 00:04:21,120 +حساب الـ mole fractionاقفل وقول ايه؟ solution + +51 +00:04:21,120 --> 00:04:25,100 +having one mole of acetone, two moles of ethanol, + +52 +00:04:25,600 --> 00:04:28,720 +three moles of methanol and fourteen moles of + +53 +00:04:28,720 --> 00:04:32,800 +water حلو هذا المحلول بتكون من هدول find the mole + +54 +00:04:32,800 --> 00:04:37,460 +fraction of each component بقول عادي جدا ال mole + +55 +00:04:37,460 --> 00:04:40,620 +fraction هي عبارة عن للمادة ايه؟ عبارة عن ال moles + +56 +00:04:40,620 --> 00:04:43,440 +من ايه؟ عدد مولات ايه؟ على ال total number of + +57 +00:04:43,440 --> 00:04:46,900 +moles هاي ال mole fraction عبارة عن كثيركسر + +58 +00:04:46,900 --> 00:04:51,600 +المولات المول من a على total number of moles فمثلا + +59 +00:04:51,600 --> 00:04:56,360 +بدي x للأسيتون يعني مول فراشن للأسيتون المول فراشن + +60 +00:04:56,360 --> 00:05:01,540 +مرضه بالرمز xبتساوي الاسيتون واحد مول على ال total + +61 +00:05:01,540 --> 00:05:04,700 +number of moles طبعا يا بنات كان بيمكنه يقول + +62 +00:05:04,700 --> 00:05:10,480 +يعطيني اجرامات الاسيتون اجرامات الاثانول اجرامات + +63 +00:05:10,480 --> 00:05:14,260 +الميثانول اجرامات الميه اه لو اعطاني الاجرامات و + +64 +00:05:14,260 --> 00:05:17,720 +جالي بدي المول fraction بدي اجسم كل عدد اجرامات + +65 +00:05:17,720 --> 00:05:21,080 +على من مادة معينة على ال formula وايت تبعها عشان + +66 +00:05:21,080 --> 00:05:23,760 +اجيب ال number of moles بس ان هو ايه معطيني ال + +67 +00:05:23,760 --> 00:05:28,680 +number of moles مباشرةX للإيثانول اتنين مول على ال + +68 +00:05:28,680 --> 00:05:32,560 +total number of moles X للميثانول تلاتة مول على ال + +69 +00:05:32,560 --> 00:05:37,520 +total number of moles X للميه اربعتاشر مول على ال + +70 +00:05:37,520 --> 00:05:42,880 +total number of moles لاحظوا ان مجموع ال poly + +71 +00:05:42,880 --> 00:05:48,240 +fractions واحد صحيح لازم مدام عندي محلول فيه قدت + +72 +00:05:48,240 --> 00:05:51,760 +components كل component له poly fraction فمجموع ال + +73 +00:05:51,760 --> 00:05:57,840 +poly fractions لازم sum up to oneنتطلع على مسألة + +74 +00:05:57,840 --> 00:06:01,140 +كتير بسيطة بيقول فيها ا solution made by + +75 +00:06:01,140 --> 00:06:06,520 +dissolving 13.5 gram of glucose in 0.1 kilogram of + +76 +00:06:06,520 --> 00:06:10,200 +water what is the mole fraction of glucose and + +77 +00:06:10,200 --> 00:06:14,260 +water in this solution دوبنا وزن معين من ال + +78 +00:06:14,260 --> 00:06:20,240 +glucose في كمية معينة من الميه انا لو جبت number + +79 +00:06:20,240 --> 00:06:22,700 +of moles of glucose وnumber of moles of water + +80 +00:06:22,700 --> 00:06:26,550 +انتهت المسألةلأنه بقول والله المول الفريكسي عبارة + +81 +00:06:26,550 --> 00:06:29,510 +عن number of moles على total number of moles فبقول + +82 +00:06:29,510 --> 00:06:31,970 +المول للجلوكوز هي عبارة عن جرام جلوكوز على ال + +83 +00:06:31,970 --> 00:06:35,010 +formula weight للجلوكوز تلتاشر نص على مية و تمانية + +84 +00:06:35,010 --> 00:06:38,490 +بيطلع point oh seven five طب الميه الميه جالي + +85 +00:06:38,490 --> 00:06:41,850 +point one kilogram انا عندي ايه يعني أميت جرام + +86 +00:06:41,850 --> 00:06:45,810 +المول للميه جرام للميه على ال formula weight للميه + +87 +00:06:45,810 --> 00:06:52,310 +مية على تمانتاش pointلأ خمسة point مش point خمسة + +88 +00:06:52,310 --> 00:06:57,210 +point خمسة ستة ماشي خمسة point خمسة ستة point one + +89 +00:06:57,210 --> 00:07:01,210 +kilogram يعني مية gram هي دي خمسة point خمس ستة + +90 +00:07:01,210 --> 00:07:04,630 +خلاص اعتبروها point O one حطوا point O one تصير + +91 +00:07:04,630 --> 00:07:07,970 +عشرة gram عشرة gram على تمتعش point five five six + +92 +00:07:07,970 --> 00:07:12,710 +يمكن أسهلنا في التصحيحإذا مولي جلوكوز على ال total + +93 +00:07:12,710 --> 00:07:15,350 +number of moles هو اللي بيعطينا X للجلوكوز أو ال + +94 +00:07:15,350 --> 00:07:20,270 +mole fraction للجلوكوز 0.075 على 0.075 زي 0.556 + +95 +00:07:20,270 --> 00:07:25,290 +بيعطينا 0.12 إذا الميه 0.556 على المجموع بيعطينا 0 + +96 +00:07:25,290 --> 00:07:29,290 +.88 لو جمعناهم برضه هيطلع لنا واحد مفيد جدا لأنه + +97 +00:07:29,290 --> 00:07:32,650 +في بعض الأحيان بيعطينا ال mole fraction و بسيبني + +98 +00:07:32,650 --> 00:07:36,990 +لازم أعرف كمية ال component الآخر من قيمة ال mole + +99 +00:07:36,990 --> 00:07:43,720 +fractionفمهم جدا نعرف هذه المعلومة طب الآن بيقول + +100 +00:07:43,720 --> 00:07:47,720 +لي ايه certain aqueous solution contains seven + +101 +00:07:47,720 --> 00:07:51,040 +percent ethanol by mass calculate the mole + +102 +00:07:51,040 --> 00:07:54,940 +fraction of ethanol and water اتفجنا احنا جالي + +103 +00:07:54,940 --> 00:07:59,100 +percent ايش على طول بقول assume 100 gram solution + +104 +00:08:00,410 --> 00:08:04,270 +السليوشن 100 جرام فانا عندي الاثانول جالي 7 في + +105 +00:08:04,270 --> 00:08:09,430 +المية اذا 7 جرام يبقى الميه قداش 93 انتهينا خلاص + +106 +00:08:09,430 --> 00:08:13,510 +يبقى بجرد اني جيب الملات 7 على 46 و 1 اعطاني ملات + +107 +00:08:13,510 --> 00:08:19,430 +الاثانول 93 على 18 5 17 اللي هي ملات الميه مادام + +108 +00:08:19,430 --> 00:08:24,790 +جيبت الملات اذا X للاثانول point 152 على ال total + +109 +00:08:25,960 --> 00:08:29,600 +.152 على الـ total والمية 5.17 على الـ total + +110 +00:08:29,600 --> 00:08:34,960 +ومجموعهم لازم يكون واحد صحيح اذا هذا اول تطبيق على + +111 +00:08:34,960 --> 00:08:39,140 +الكلام اللي قلنا والله بدنا نبسط الحسابات اتبعتنا + +112 +00:08:39,140 --> 00:08:44,120 +يفجأة اعطاني 7% إيثانول ما تسأليش طب ايش الوزنة + +113 +00:08:44,120 --> 00:08:48,320 +تسأليش خلاص سبعة جرام في المية جرام اذا كان سبعة + +114 +00:08:48,320 --> 00:08:54,400 +جرام إيثانول اذا تلاتة وتسعين جرام مية انتهيناطيب + +115 +00:08:54,400 --> 00:08:57,800 +بيقول لي ايه كالسوميكلورايد ال foreign ولا تقولوا + +116 +00:08:57,800 --> 00:09:03,840 +101 جرام ع المول اكوا ال solution is 4.57 molal ام + +117 +00:09:03,840 --> 00:09:09,140 +صغيرة ام صغيرة يعني ايه molality يعني molal find + +118 +00:09:09,140 --> 00:09:12,080 +the mole fraction of calcium chloride and water in + +119 +00:09:12,080 --> 00:09:16,980 +solution بقول حلو كتير لمن يعطيني ال molality + +120 +00:09:16,980 --> 00:09:18,400 +معناته ايش بدى افترض + +121 +00:09:24,000 --> 00:09:27,660 +الماية أكم جرام ألف جرام على طول + +122 +00:09:37,020 --> 00:09:40,100 +عند الملات تبع الكالسيوم الكلورايد بجيب الملات + +123 +00:09:40,100 --> 00:09:43,080 +للميه 1000 على 18 لأن عندي 1000 جرام ميه هي ال + +124 +00:09:43,080 --> 00:09:47,660 +assumption تبعها دائما 55.6 إذا أنا على طول X + +125 +00:09:47,660 --> 00:09:50,260 +لكالسيوم الكلورايد ملات الكالسيوم الكلورايد اللي + +126 +00:09:50,260 --> 00:09:53,520 +هي نفس ال morality لأنه اعتبرتها ايه ال morality + +127 +00:09:53,520 --> 00:09:57,280 +four point ايش هي ال morality جال عدد الملات في ال + +128 +00:09:57,280 --> 00:10:02,300 +1000 جراملو قلت 100 جرام فهذا سيكون 0.457 لكن لأ + +129 +00:10:02,300 --> 00:10:04,860 +انا بقول ال assumption تبعي أسهل ليه مادام + +130 +00:10:04,860 --> 00:10:08,060 +molality على طول اللي بقول في عندي جداش ألف جرام + +131 +00:10:08,060 --> 00:10:13,840 +بحل على هذا الأساس 4.57 على مجموعهم 0.076 طب و + +132 +00:10:13,840 --> 00:10:19,940 +المياه قال والله 55.6 على 4.57 زائد 55.6 على 0.9 + +133 +00:10:20,730 --> 00:10:24,530 +توفر مجموعهم اكيد لازم يكون واحد طبعا انا طلعت + +134 +00:10:24,530 --> 00:10:27,550 +هنلي جرامات مش بحاجة اليها بس مجرد ان انا بقولكم + +135 +00:10:27,550 --> 00:10:30,930 +لو بطلع جرامات مضرب هدف ايه في ال formula weight + +136 +00:10:30,930 --> 00:10:37,350 +طيب الان خلينا نحول من percentage to molality + +137 +00:10:37,350 --> 00:10:43,470 +percentage to molalityبقول عشان احول من ال + +138 +00:10:43,470 --> 00:10:47,690 +percentage ل ال morality بقول ال assumption تبعي + +139 +00:10:47,690 --> 00:10:51,110 +الموجود دائما when percentage is given ايش بده + +140 +00:10:51,110 --> 00:10:56,510 +افترض 100 gram solution from this we know ان ال + +141 +00:10:56,510 --> 00:10:59,680 +mass of solute هو عبارة عن ال percentageالـ mass + +142 +00:10:59,680 --> 00:11:01,880 +of solute هو عبارة عن .. لما أقول سبعة في المية + +143 +00:11:01,880 --> 00:11:05,660 +إيثانول، إذا سبعة جرام إيثانول يبقى ال .. ال mass + +144 +00:11:05,660 --> 00:11:08,640 +of solute هي عبارة عن إيه؟ هي ال percentage، قيمة + +145 +00:11:08,640 --> 00:11:13,040 +ال percentage ال mass of solution مائة جرام طيب ال + +146 +00:11:13,040 --> 00:11:16,600 +mass of solvent جال مية minus ال mass of solute + +147 +00:11:16,600 --> 00:11:20,500 +مية minus ال mass of solute هاي ال .. أنا عندي ال + +148 +00:11:20,500 --> 00:11:26,420 +solution جداش مائة جرام، إذا طب أنا عندي ال solute + +149 +00:11:26,420 --> 00:11:32,490 +معروفوال .. و ال solution معروف إذا بقدر أجيب ال + +150 +00:11:32,490 --> 00:11:35,830 +mass of solvent يبجى 100 اللي هي ال metagram of + +151 +00:11:35,830 --> 00:11:39,870 +solution minus ال mass of solvent بتعطيني ال mass + +152 +00:11:39,870 --> 00:11:43,750 +of solvent طب المول لل solute جال ال mass لل + +153 +00:11:43,750 --> 00:11:46,550 +solute على الفورمولويت يبجى جبت المول لل solute + +154 +00:11:46,550 --> 00:11:50,700 +وجبت ال mass لمن؟ لل solvent هي ال molalityيبقى + +155 +00:11:50,700 --> 00:11:54,480 +المولاريتي بساوي المول الهيني جيبتها والكيلوجرام + +156 +00:11:54,480 --> 00:12:00,620 +نتذكر ان السولفان بعوض عنه بالكيلوجرام والمولاريتي + +157 +00:12:00,620 --> 00:12:07,460 +بالليتر طب خلينا نشوف تطبيق بيقول ليهأيه certain + +158 +00:12:07,460 --> 00:12:11,380 +aqueous solution contains 7% إيثانول by mass؟ + +159 +00:12:11,380 --> 00:12:15,440 +Calculate the molality of solution بقول على طول + +160 +00:12:15,440 --> 00:12:19,580 +Assume مدام أعطاني ال percentage إذا إيه Assume + +161 +00:12:19,580 --> 00:12:22,620 +100 gram solution يبقى ال 100 gram solution حلو + +162 +00:12:22,620 --> 00:12:25,300 +كتير يبقى في عند ال substance اللي هو الإيثانول 7 + +163 +00:12:25,300 --> 00:12:31,020 +gram يبقى كدهش الميه 93 93 حلو كتير إذا عدد + +164 +00:12:31,020 --> 00:12:40,120 +المولات7 على 46.152 الميه ما علينا يعني انا بدي ال + +165 +00:12:40,120 --> 00:12:44,400 +morality يعني بلزمنيش بلزمنيش اي اش يعني يعني الا + +166 +00:12:44,400 --> 00:12:49,640 +بس اللي هي حجم ال solvent وزن ال solvent عفوا فال + +167 +00:12:49,640 --> 00:12:53,240 +morality عبارة عن M بتساوي ال mole solute على ال + +168 +00:12:53,240 --> 00:12:57,660 +kilogram solvent ال mole solute 0.152 اكم كيلو + +169 +00:12:57,660 --> 00:13:03,060 +جرام ال 93 جرام.093 مش بحاجة نقول على الف نسمع + +170 +00:13:03,060 --> 00:13:06,080 +عنها الف مباشرة يعني بدل ما هي التلاتة وتسعين + +171 +00:13:06,080 --> 00:13:09,760 +بتكون point oh nine three بدك تسمعها في عشرة أقل + +172 +00:13:09,760 --> 00:13:12,280 +سالب تلاتة عملها في عشرة أقل سالب تلاتة مش بس + +173 +00:13:12,280 --> 00:13:18,800 +بمجرد النظر اللي بتناعمله طيب نتطلع على هذه + +174 +00:13:18,800 --> 00:13:22,880 +المسألة مسألة حلوة بيقول لي an aqueous solution of + +175 +00:13:22,880 --> 00:13:31,120 +HCl contains 36% HCl by weightCalculate the mole + +176 +00:13:31,120 --> 00:13:35,240 +fraction and molality of HCl وقول نفس الكلام + +177 +00:13:35,240 --> 00:13:38,680 +أعطاني ال percentage ال assumption تبقى جاهز بقول + +178 +00:13:38,680 --> 00:13:41,940 +assume 100 gram of solution 100 gram of solution + +179 +00:13:41,940 --> 00:13:49,000 +معناته أقل 36% يبقى 36 gram HCl إذا نجدش ميه إذا + +180 +00:13:49,000 --> 00:13:53,880 +كان عندي 100مئة اربعة وستين يبقى انتهت المسألة + +181 +00:13:53,880 --> 00:13:57,420 +بجيب ملات ال HCl ستة و تلاتين على ستة و تلاتين و + +182 +00:13:57,420 --> 00:14:00,800 +نص بعطيني ال point nine nine بجيب ملات المية اربعة + +183 +00:14:00,800 --> 00:14:04,720 +و ستين على تمانتاش بعطيني تلاتة و ستة و خمسين اذا + +184 +00:14:04,720 --> 00:14:09,160 +ال modifaction لل HCl ان ال HCl على المجموع point + +185 +00:14:09,160 --> 00:14:11,400 +nine nine على point nine nine زائد تلاتة point + +186 +00:14:11,400 --> 00:14:16,180 +five ستة بعطيني ال point two twoطيب لو حبينا ال + +187 +00:14:16,180 --> 00:14:20,800 +مول فركشن للميهو مش طالبه على طول بدل ال hcl الميه + +188 +00:14:20,800 --> 00:14:24,720 +على المجموع بدها تكمل او نقول واحد ناقص point two + +189 +00:14:24,720 --> 00:14:28,400 +two بطلع عندنا point seven eight سيال طب ايه ال + +190 +00:14:28,400 --> 00:14:33,320 +molality اه المول solute اللي طلعته على ال + +191 +00:14:33,320 --> 00:14:40,760 +kilogram solvent اذا على point oh six four0.0.0.0 + +192 +00:14:40,760 --> 00:14:41,720 +.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0 + +193 +00:14:41,720 --> 00:14:43,880 +.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0 + +194 +00:14:43,880 --> 00:14:46,560 +.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0 + +195 +00:14:46,560 --> 00:14:56,160 +.0.0.0.0.0.0.0 + +196 +00:14:56,160 --> 00:14:56,180 +.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0 + +197 +00:14:56,180 --> 00:14:59,360 +.0. + +198 +00:15:08,530 --> 00:15:11,450 +بيدوا الـ molality لازم يعطيني ال density لأنه + +199 +00:15:11,450 --> 00:15:15,810 +لازم احول الحجم الى gram بدي ال density فبيقول اه + +200 +00:15:15,810 --> 00:15:18,290 +اعطاني hand mill of water at 25 degree c بيقول + +201 +00:15:18,290 --> 00:15:21,110 +calculate the molality of glucose provided that + +202 +00:15:21,110 --> 00:15:25,670 +the density of water at 25 degree c is 1 gram على + +203 +00:15:25,670 --> 00:15:30,750 +المل اذا انا بدي اجيب وزن الميه فبتطلع 25 في 1 + +204 +00:15:30,750 --> 00:15:34,890 +يعني 25 مختلف لاش لكن لو كان اي solvent تاني ممكن + +205 +00:15:34,890 --> 00:15:42,160 +تختلفأذا على طول انا عندي لجلوكوز الوزنة 4.35 بقدر + +206 +00:15:42,160 --> 00:15:44,420 +اجيب ال number of moles باقسم على الفورمولوهات + +207 +00:15:44,420 --> 00:15:50,020 +اللي هي 180 باطيني اللي هو number of moles طيب + +208 +00:15:50,020 --> 00:15:56,690 +الميه جداش وزنتها جال 25 جرام؟أذا الـ molality الـ + +209 +00:15:56,690 --> 00:16:02,570 +moles point oh two four two على point oh two five + +210 +00:16:02,570 --> 00:16:07,070 +كيلو جرام point oh two five لأنه إيه خمسة و عشرين + +211 +00:16:07,070 --> 00:16:12,010 +جرام خمسة و عشرين أنا بديها بالكيلو جرام إذا خمسة + +212 +00:16:12,010 --> 00:16:14,810 +و عشرين في عشر أقل ثالث تلاتة أو يعني point oh two + +213 +00:16:14,810 --> 00:16:18,650 +five بيطلع عندنا point nine seven molal + +214 +00:16:23,470 --> 00:16:28,250 +طيب نتطلع على فكرة ال notes كان فيها غلطة هذه كانت + +215 +00:16:28,250 --> 00:16:32,450 +مكتوبة تسعة أو تمانية فبدأ تصحيح عموما ال notes + +216 +00:16:32,450 --> 00:16:36,110 +دايما بعد ما نخلص ال chapter بناخد ال notes + +217 +00:16:36,110 --> 00:16:41,630 +المصححة من الصفحة يعني على أي حال نتطلع على المثال + +218 +00:16:41,630 --> 00:16:46,890 +هان a magnesium sulfate aqueous solution has a + +219 +00:16:46,890 --> 00:16:50,680 +moly fraction of 0.2What is the molality of the + +220 +00:16:50,680 --> 00:16:53,780 +solution؟ اعطاني بس ال mol fraction للمجنيزة و + +221 +00:16:53,780 --> 00:16:58,560 +الصلفية قال لي اه بدي افترض هان ان ال number of + +222 +00:16:58,560 --> 00:17:03,440 +moles جديش كل ال .. يعني ال total number ال mol + +223 +00:17:03,440 --> 00:17:08,700 +fraction كلها جديش بدي افترض واحد اه اذا اذا كان + +224 +00:17:08,700 --> 00:17:13,560 +هادي point two بفترض انه ال mol fraction point two + +225 +00:17:13,560 --> 00:17:17,120 +اذا انا على طول هادي ايه point eight لان مجموعهم + +226 +00:17:17,120 --> 00:17:23,440 +واحدعلى طول بقول والله لجرامات 24.1 لو حبيت + +227 +00:17:23,440 --> 00:17:30,780 +لجرامات 24.1 هان جرامات الميه لما نكون point eight + +228 +00:17:30,780 --> 00:17:36,280 +moles من الميه هدى على طول point two moles بتعطينى + +229 +00:17:36,280 --> 00:17:39,920 +هلجان point eight moles بتعطينى point eight في + +230 +00:17:39,920 --> 00:17:44,120 +تمانتاش اربعتاش واربعة من عشرة اذا صارت عندى وزنة + +231 +00:17:44,120 --> 00:17:51,110 +الميه معروفةوعدد مولات المجنيزيوم صلفيت معروف + +232 +00:17:51,110 --> 00:17:54,250 +فبقول والله المولات point two على point one four + +233 +00:17:54,250 --> 00:18:05,610 +four kilogram فبيعطي 13.9 مولل مظبوط + +234 +00:18:05,610 --> 00:18:09,150 +هي نفسها لو عملتيها كيف ما عملتيها ال mole + +235 +00:18:09,150 --> 00:18:15,910 +fraction اللي هي X لمثل المجنيزيوم صلفيتبتساوى + +236 +00:18:15,910 --> 00:18:20,390 +point two يعني ايش بتساوى اذا كان هي point two على + +237 +00:18:20,390 --> 00:18:24,230 +point two زائد point eight لو اعتبرتيها number of + +238 +00:18:24,230 --> 00:18:28,110 +moles فما هي صارت point two لو اعتبرتها اتنين على + +239 +00:18:28,110 --> 00:18:31,630 +اتنين زائد تمانية برضه point two كيف ما اعتبرتيها + +240 +00:18:31,630 --> 00:18:34,990 +هيطلع معاكي نفس القيمة يعني هذه لو اعتبرتيها مثلا + +241 +00:18:34,990 --> 00:18:40,590 +اتنين هتكون هذه تمانية اذا تمانية في تمنتاشمية + +242 +00:18:40,590 --> 00:18:45,320 +اربعة واربعين دائما النسبة بتظلها واحدةمعاها فلأ + +243 +00:18:45,320 --> 00:18:50,840 +انت تعتبر ان ال total number of يعني بتعتبر ان ال + +244 +00:18:50,840 --> 00:18:53,240 +mole fraction عبارة عن number of moles و ال total + +245 +00:18:53,240 --> 00:18:58,040 +mole fraction عبارة عن واحد هدأ أسألك فيك انك + +246 +00:18:58,040 --> 00:19:02,920 +تعتبر هذه اتنين وهذه تمانية اعتبر ان هذه عشرين + +247 +00:19:02,920 --> 00:19:10,060 +وهذه تمانين سيئا نفس النتيجة ما بتتغيرماشي؟ الكل + +248 +00:19:10,060 --> 00:19:14,280 +متفقيني، لإيه؟ لإن هذا عبارة عن ratio في الآخر، + +249 +00:19:14,280 --> 00:19:16,360 +هذا عبارة عن ratio، إذا كنت قلت هذه اتنين، هذه + +250 +00:19:16,360 --> 00:19:20,300 +ترفع من هذه سفر، قلت هذه عشرين، بتحطي .. تضرب هذه + +251 +00:19:20,300 --> 00:19:23,420 +في مية، عشرين تضرب هذه في مية، و هكذا، فدائما + +252 +00:19:23,420 --> 00:19:25,880 +النسبة عندي واحدة + +253 +00:19:30,060 --> 00:19:35,060 +هذه فكرة ان المول فراكشن هي عبارة عن number of + +254 +00:19:35,060 --> 00:19:37,000 +moles على total number of moles + +255 +00:19:40,440 --> 00:19:44,360 +انتهينا اذا ال moles هي ال mole fraction عبارة عن + +256 +00:19:44,360 --> 00:19:49,400 +عدد المولات وانتهت المسألة طيب نتطلع الآن على + +257 +00:19:49,400 --> 00:19:53,320 +التحويل من molality ل molarity وانا كاتب شوية + +258 +00:19:53,320 --> 00:19:57,220 +حاجات هنا نتطلع عليها بقول انا بدى احول من + +259 +00:19:57,220 --> 00:20:00,680 +molality فبقول if molality is given ايش بدى افترض؟ + +260 +00:20:01,430 --> 00:20:05,330 +ألف جرام سولفان، من هناك تعرفين أن المولالية هي + +261 +00:20:05,330 --> 00:20:08,830 +عدد الموالات، لما نقول كذا مولال، بعتبرها عدد + +262 +00:20:08,830 --> 00:20:13,130 +الموالات، الmass of solute هي مولة السوليوت في + +263 +00:20:13,130 --> 00:20:17,210 +الفورمولا ويت، لأن مولة السوليوت هي عبارة عن ال + +264 +00:20:17,210 --> 00:20:20,170 +mass of solute على الفورمولا ويت، فبنقدر نقول ال + +265 +00:20:20,170 --> 00:20:22,490 +mass of solute عبارة عن مولة السوليوت في الفورمولا + +266 +00:20:22,490 --> 00:20:27,190 +ويت، إذا بقدر نعرف ال mass of soluteوانا عارف ان + +267 +00:20:27,190 --> 00:20:30,470 +ال mass of solution جداش الف اذا ال mass of + +268 +00:20:30,470 --> 00:20:34,930 +solution الف زائد mass of solute الف اللي هي ال + +269 +00:20:34,930 --> 00:20:38,130 +mass of solvent الف ال mass of solution الف زائد + +270 +00:20:38,130 --> 00:20:42,810 +اللي هي ال solvent زائد ال soluteالـ mass of + +271 +00:20:42,810 --> 00:20:46,550 +solution هي عضار على الـ solvent زائد الـ solute + +272 +00:20:46,550 --> 00:20:49,330 +الـ solute هي اللي جيبناه، اذا بجبعه على الـ mass + +273 +00:20:49,330 --> 00:20:53,990 +of solution طيب من ال density، اه مدام عندي ال + +274 +00:20:53,990 --> 00:20:58,770 +mass of solution بقدر اجيب ال mill of solution، ال + +275 +00:20:58,770 --> 00:21:00,890 +gram solution اللي هي ال mass of solution على ال + +276 +00:21:00,890 --> 00:21:03,170 +density بجيب ال mill of solution، مدام جيبنا ال + +277 +00:21:03,170 --> 00:21:05,970 +mill of solution انتهت ال mass اللي عنده ال moles + +278 +00:21:05,970 --> 00:21:08,270 +number of moles اللي هي ال molality number of + +279 +00:21:08,270 --> 00:21:10,890 +moles على ال mill of solution على ال liter of + +280 +00:21:10,890 --> 00:21:16,280 +solutionعال letter solution ماشي يا جماعة هذه يفجح + +281 +00:21:16,280 --> 00:21:20,740 +نلاقيها زي هيك عال letter solution نصلح حالكم ان + +282 +00:21:20,740 --> 00:21:22,740 +شاء الله في ال notes + +283 +00:21:30,400 --> 00:21:33,180 +بيقول لي calculate .. تطبيق بباشر .. بيقول لي + +284 +00:21:33,180 --> 00:21:36,920 +calculate the molarity of a point three nine six + +285 +00:21:36,920 --> 00:21:40,700 +molal glucose لما يقول لي molal glucose معناته + +286 +00:21:40,700 --> 00:21:45,300 +عنده point three nine six mol glucose في أكم مية + +287 +00:21:45,300 --> 00:21:50,950 +في الف جرام مية solventطيب ايش بيقول ليه؟ if the + +288 +00:21:50,950 --> 00:21:54,970 +density of the solution is 1.16 ml فبدي احسب ال + +289 +00:21:54,970 --> 00:22:00,310 +modality لو كانت ال density 1.16 gram ع المل بقول + +290 +00:22:00,310 --> 00:22:05,470 +انا ال glucose 0.396 moles اذا 0.396 مليون و + +291 +00:22:05,470 --> 00:22:08,350 +تمانين و واحد و سبعين و تلاتة من عشرة و انا عندي + +292 +00:22:08,350 --> 00:22:12,410 +الميه الف اذا الف و واحد و سبعين و تلاتة هذه وزنتي + +293 +00:22:12,410 --> 00:22:16,580 +المحلولما دام عندي وزنة المحلول ال mill solution + +294 +00:22:16,580 --> 00:22:19,780 +هي عبارة عن جرام solution ألف واحد السبب ما طلعت + +295 +00:22:19,780 --> 00:22:24,640 +على ال density إذا طلعت ال mill solution ما دام + +296 +00:22:24,640 --> 00:22:27,540 +طلعت ال mill solution عندي number of balls point + +297 +00:22:27,540 --> 00:22:32,320 +three nine six على ال mill اللي هي letter يعني + +298 +00:22:32,320 --> 00:22:36,740 +بيقول point nine two three five بيقسم هذه على الف + +299 +00:22:37,220 --> 00:22:42,260 +تصير point nine two three five لتر لأنه ال + +300 +00:22:42,260 --> 00:22:46,060 +modularity المولز على ال volume بال ايه بال لتر + +301 +00:22:46,060 --> 00:22:53,700 +طيب كمان مثلا بيقول a solution with a density of + +302 +00:22:53,700 --> 00:22:57,980 +point eight seven six gram ع المل contains five + +303 +00:22:57,980 --> 00:23:03,680 +gram toluene and 225 gram of بنزين calculate the + +304 +00:23:03,680 --> 00:23:08,260 +molarity of the solution حلو كتيرأنا عندى وزنة + +305 +00:23:08,260 --> 00:23:13,160 +الطلوين 5 جرام ووزنة البنزين 225 اذا وزنة ال + +306 +00:23:13,160 --> 00:23:19,720 +solution 230 طيب حلو فبقول اكمل طلوين 5 على 92 + +307 +00:23:19,720 --> 00:23:25,790 +فورميلة ويتطيب طب المولاريتي .. اه بدنا نجيب ال + +308 +00:23:25,790 --> 00:23:28,350 +mil solution انا عندى وزنة ال .. اه وزنة ال + +309 +00:23:28,350 --> 00:23:33,630 +solution معايا نجيب ال mil solution 230 على 0.876 + +310 +00:23:33,630 --> 00:23:36,590 +تلتين متين اتنين وستين وستة من عشرة هذا حجم + +311 +00:23:36,590 --> 00:23:41,650 +المحلول اذا المولاريتي عدد المولات 0.054 اللى هى + +312 +00:23:41,650 --> 00:23:46,610 +خمسة على تنين وتسعين على الحجم بالليتير 0.2626 + +313 +00:23:48,350 --> 00:23:53,670 +فالمسألة انحلت بارجو انه يعني تكونوا ماشيين معايا + +314 +00:23:53,670 --> 00:23:58,770 +في هذا الكلام لأنه هو سهل لكن في نفس الوقت دقيق + +315 +00:23:58,770 --> 00:24:02,630 +يعني المهم انك تحلي المسألة بالسرعة الكافية + +316 +00:24:03,350 --> 00:24:06,530 +بالاستماع انه في الامتحان بيكونش فيه معنى وجد يعني + +317 +00:24:06,530 --> 00:24:10,650 +انه ان يعني ناخد وقت كافي جدا في التفكير في + +318 +00:24:10,650 --> 00:24:14,470 +المسألة لأ فبدك على طول كنعافى الطريقة فالطريقة + +319 +00:24:14,470 --> 00:24:18,670 +سهلة جدا جدا الطريقة بسيطة للغاية ففي البداية + +320 +00:24:18,670 --> 00:24:24,010 +بنجيب وزن المحلول من وزن المحلول بنجيب حجم المحلول + +321 +00:24:25,000 --> 00:24:28,120 +باستخدام ال density بعدين عندنا number of moles + +322 +00:24:28,120 --> 00:24:32,800 +سهلة نجسب number of moles على الحجم بالليتر طب + +323 +00:24:32,800 --> 00:24:38,780 +كمان نشوف طب العكس من molarity ل molalityكيف بدنا + +324 +00:24:38,780 --> 00:24:42,840 +نحول من molarity ل molality بقول if molarity is + +325 +00:24:42,840 --> 00:24:48,800 +given ايش بدى افترض الف من ال solution تمام كل نوع + +326 +00:24:48,800 --> 00:24:53,160 +من أنواع المسائل لاحظوا مفتاح حلو اشي بسيط لازم + +327 +00:24:53,160 --> 00:24:58,790 +نتذكره لازم نتذكره فال percentage اه عندى100 gram + +328 +00:24:58,790 --> 00:25:03,610 +solution المولاريتي 1000 gram solvent المولاريتي + +329 +00:25:03,610 --> 00:25:07,210 +1000 mil solution من هذا الكلام ايش بنعرف ان + +330 +00:25:07,210 --> 00:25:10,090 +المولاريتي هي عدد المولات number of moles انا + +331 +00:25:10,090 --> 00:25:14,110 +بتفترض انه 1000 mil solution عندي فالمولاريتي + +332 +00:25:14,110 --> 00:25:18,470 +قيمته هي عبارة عن عدد المولات مباشرة يبقى ال mass + +333 +00:25:18,470 --> 00:25:22,810 +solute انا عندي عدد المولات معروف ال mass solute + +334 +00:25:22,810 --> 00:25:26,190 +هي ال mole solute في ال formula weightيبقى انعرف + +335 +00:25:26,190 --> 00:25:30,670 +عند ال mass solute ال mass solution اه ال density + +336 +00:25:30,670 --> 00:25:35,750 +في الف لان انا عندي الف mill solution وكل mill كذا + +337 +00:25:35,750 --> 00:25:39,590 +اجرعها فعندي الف في ال density بتعطيني ال mass of + +338 +00:25:39,590 --> 00:25:42,930 +solution ال mass of solvent طلعت ال mass of + +339 +00:25:42,930 --> 00:25:46,850 +solution وعندي ال mass of solute بنطلع فيه هاي ال + +340 +00:25:46,850 --> 00:25:50,870 +mass of solvent الان سهل خالص ان نقول والله ال mol + +341 +00:25:50,870 --> 00:25:55,290 +of solute له قيمة ال molarity اصلاعلى الـ kilogram + +342 +00:25:55,290 --> 00:26:00,090 +of solvent اللي حسبناها فرق ال solution minus ال + +343 +00:26:00,090 --> 00:26:05,850 +solute ماشي يا جماعة طيب ناخد تطبيق على هذا الكلام + +344 +00:26:05,850 --> 00:26:14,750 +بيقول لي what's the molality of a 0.586 molar + +345 +00:26:15,870 --> 00:26:26,350 +مولارتي ايه؟ مولارتي ايه؟ مولارتي ايه؟ مولارتي + +346 +00:26:26,350 --> 00:26:30,170 +ايه؟ + +347 +00:26:30,170 --> 00:26:36,360 +مولارتي ايه؟ مولارتي ايه؟2.7 جرام على الميل فبيقول + +348 +00:26:36,360 --> 00:26:44,020 +ايه على طول الاثانول معناته 5.86 مول لجرامات نضرب + +349 +00:26:44,020 --> 00:26:50,520 +في الفورمولا ويطلع 269.6 انا عندي لجرام solution + +350 +00:26:50,520 --> 00:26:54,380 +سهل جدا احصل عليه هو عبارة عن ال density في ال + +351 +00:26:54,380 --> 00:26:57,840 +volume لل solution ال volume لل solution الف هذا + +352 +00:26:57,840 --> 00:27:01,350 +مفتاح للحلمدى افتراض النهاردة على المولات اذا انا + +353 +00:27:01,350 --> 00:27:04,530 +على طول عندي الف مل solution ف point nine two + +354 +00:27:04,530 --> 00:27:07,090 +seven في الف تسعة مية سبعة عشرين هذا لجرام + +355 +00:27:07,090 --> 00:27:11,510 +solution اذا لجرام solvent لجرام solution تسعة مية + +356 +00:27:11,510 --> 00:27:14,670 +سبعة عشرين ناقص لجرام solute ستمية سبعة وخمسين + +357 +00:27:14,670 --> 00:27:18,010 +واربعة من عشرة انتهت المسألة ليه لأنه الآن بقول + +358 +00:27:18,010 --> 00:27:22,020 +مدارتي هي المول على الكيلوجرامwater او يعني + +359 +00:27:22,020 --> 00:27:25,920 +solvent five point eight six اللي هي عدد المولات + +360 +00:27:25,920 --> 00:27:31,820 +على وزن المياه بالكيلوجرام يعني point six five + +361 +00:27:31,820 --> 00:27:35,800 +seven four فبيعطيني eight point nine one mole + +362 +00:27:44,090 --> 00:27:48,450 +هذا ما عطيني السؤال التالي بيقول the density of a + +363 +00:27:48,450 --> 00:27:55,800 +2.45 molar aqueous methanolSolution is 0.976 Gram + +364 +00:27:55,800 --> 00:28:00,640 +علمي الـ what is the molality of this solution نفس + +365 +00:28:00,640 --> 00:28:03,700 +الحاجة طبعا يعني لأن هذا مثال على التحويل من + +366 +00:28:03,700 --> 00:28:08,020 +molality ل molality فبقول بما أنه أعطاني molality + +367 +00:28:08,020 --> 00:28:12,120 +فبعتبر أنه عندي ألف من ال solution قيمة ال + +368 +00:28:12,120 --> 00:28:15,620 +molality هي ال number of moles لو ضربته في ال + +369 +00:28:15,620 --> 00:28:18,760 +formula weight بعطيني ال mass of solute اللي هو + +370 +00:28:18,760 --> 00:28:23,410 +الميثانولمدام هيك انا بطلع ال gram solution ال + +371 +00:28:23,410 --> 00:28:25,990 +gram solution هو عبارة عن الف ال density تسعمية + +372 +00:28:25,990 --> 00:28:29,890 +ستة و سبعين طب ال gram solvent جال لجرام solution + +373 +00:28:29,890 --> 00:28:33,610 +minus لجرام solute بقى لجرام solvent اللي هو + +374 +00:28:33,610 --> 00:28:37,310 +تمانية سبعة وتسعين و ستة من عشرة المسألة خلصت لأن + +375 +00:28:37,310 --> 00:28:40,070 +المول بتاعة عبارة عن مول كيلو جرام + +376 +00:28:45,980 --> 00:28:55,940 +بتعطيل الـ 2.73 مولال يمكن + +377 +00:28:55,940 --> 00:29:00,840 +هذه أخر حاجة ان شاء اللهبتقول ايش؟ from percentage + +378 +00:29:00,840 --> 00:29:03,300 +to molarity شوفنا في البداية percentage to + +379 +00:29:03,300 --> 00:29:06,740 +molarity الـ get percentage to ايه؟ to molarity + +380 +00:29:06,740 --> 00:29:11,480 +بقول when percentage is given ايش؟ دائما، دائما، + +381 +00:29:11,480 --> 00:29:16,200 +دائما، مئتي جرام solution، دائما طيب from this you + +382 +00:29:16,200 --> 00:29:19,000 +know الmass of solute هو عبارة عن ال percentage، + +383 +00:29:19,000 --> 00:29:22,940 +مافي خلاف ممكن نطلع المول of solute هي الmass of + +384 +00:29:22,940 --> 00:29:28,530 +soluteعالفورمولويت طب الماس لل solution دائما هيها + +385 +00:29:28,530 --> 00:29:32,870 +100 جرام الماس لل solution 100 جرام اذا المل + +386 +00:29:32,870 --> 00:29:37,890 +solution اجرام solution اللي هي 100 على ال density + +387 +00:29:37,890 --> 00:29:43,910 +معانا ال density بتكون يبقى الان طلعت ال mole of + +388 +00:29:43,910 --> 00:29:47,390 +solute وطلعت ال letter of solution + +389 +00:29:51,110 --> 00:29:55,650 +فبطلع الـ molarity هي عند ال mill solution بحوله ل + +390 +00:29:55,650 --> 00:29:59,510 +letter ف ال molarity عبارة عن number of moles اللي + +391 +00:29:59,510 --> 00:30:05,970 +حسبناها على ال letter of solutionنتطلع على المسألة + +392 +00:30:05,970 --> 00:30:12,190 +التالية بيقول what's the molarity of a 0.95% + +393 +00:30:12,190 --> 00:30:17,230 +acetic acid solution ال density 1.049 جرام على + +394 +00:30:17,230 --> 00:30:20,310 +المل بما أنه أعطاني ال percentage على طول assume + +395 +00:30:20,310 --> 00:30:25,360 +100 gram solutionميت اجرام صليوشين حلو كتير طب اكم + +396 +00:30:25,360 --> 00:30:33,940 +اجرام صليوت انا بعرف انه 95 95 اجرام صليوت على 61 + +397 +00:30:33,940 --> 00:30:41,510 +.5833 طيب حلو كتيرالان بقدر اجيب ال mil solution + +398 +00:30:41,510 --> 00:30:46,250 +ال mil solution انا عند ال gram solution على ال + +399 +00:30:46,250 --> 00:30:50,990 +density 95.33 جبت ال mil solution طبعا عند ال + +400 +00:30:50,990 --> 00:30:56,650 +number of balls وعندي الحجم بس هان بال mil بده + +401 +00:30:56,650 --> 00:31:02,170 +احوال ال liter اذا بقى احصل على ال molarity 1.5833 + +402 +00:31:02,170 --> 00:31:07,630 +على 0.09533 بتعطيني molarity 16 و 6 من 10 + +403 +00:31:12,360 --> 00:31:18,760 +انا اخد نفس الكلام بس لل HCL بيقول + +404 +00:31:18,760 --> 00:31:24,720 +لي an aqueous solution of HCL contains 36% HCL by + +405 +00:31:24,720 --> 00:31:29,460 +weight if the density of solution is 1.21 gram ع + +406 +00:31:29,460 --> 00:31:33,460 +الميل calculate the molarity and molality of HCL + +407 +00:31:34,670 --> 00:31:38,130 +بدوا الـMolarity والـMolarity بقول مفتاح الحل + +408 +00:31:38,130 --> 00:31:41,890 +تبعنا ان والله عندي percentage زي 100 جرام + +409 +00:31:41,890 --> 00:31:49,710 +solution طيب ال HCL أكم جرام 36 لو حبنا ال gram + +410 +00:31:49,710 --> 00:31:55,470 +solution 100 إذا نجداش 100 او 64 هذا على طول مجرد + +411 +00:31:55,470 --> 00:32:00,070 +النظر اللي بنعمله بدي أجيب المل HCL لجرام HCL على + +412 +00:32:00,070 --> 00:32:05,980 +ال formula weight 0.99 طب المل solutionليه جرعان + +413 +00:32:05,980 --> 00:32:12,540 +على ال density؟ 100 على 1.21 بيعطيني 82.64 طيب حلو + +414 +00:32:12,540 --> 00:32:16,680 +بتقول الآن ال molarity جال والله more solute على + +415 +00:32:16,680 --> 00:32:20,660 +ال letter solution ال more solute 0.99 ال letter + +416 +00:32:20,660 --> 00:32:26,980 +solution 0.08264 0.08264 لإن أنا مضروف في العخرة + +417 +00:32:26,980 --> 00:32:30,130 +أسالب تلاتة بال letter ها دي ملأنا بدي letter + +418 +00:32:30,130 --> 00:32:36,770 +فبطلع 11 و 98 طيب ال molalty بقول ال mol solute + +419 +00:32:36,770 --> 00:32:40,550 +اللي هو 0.99 على ال kilogram solvent السولفان اللي + +420 +00:32:40,550 --> 00:32:50,330 +عندي 64 جرام اذا 0.064 kilogramماشي يا جماعة طبعا + +421 +00:32:50,330 --> 00:32:55,590 +انا يعني حرست على اني اجيب هذا الكمل كبير من + +422 +00:32:55,590 --> 00:32:59,190 +المسائل لأنه يمكن لاحظته في الامتحان الأول كتير من + +423 +00:32:59,190 --> 00:33:05,720 +الأسئلة بتيجي على صورة مسائل وهذه شغلاتيعني الناس + +424 +00:33:05,720 --> 00:33:09,660 +اللي بدرسوا كيميا بحبوا أنهم يسألوا فيها لأنها + +425 +00:33:09,660 --> 00:33:14,440 +يعني من أكتر من جانب هي شغلات مفيدة ومهمة وفي نفس + +426 +00:33:14,440 --> 00:33:19,400 +الوقت بتفرجينا مدى قدرة الطالب على أنه يعني يشغل + +427 +00:33:19,400 --> 00:33:24,410 +عجله يربط بين المفاهيم المختلفةاللي اتعلمها فانا + +428 +00:33:24,410 --> 00:33:28,970 +بارجو انه يعني لما نتراوحه اتراجعوا كل المسائل و + +429 +00:33:28,970 --> 00:33:32,550 +تشوفوا اذا كانت بتحلوها بشكل منهجي زي ما احنا + +430 +00:33:32,550 --> 00:33:35,970 +طلعنا عليها هان و بتطلعوا نفس الإجابات دائما + +431 +00:33:35,970 --> 00:33:40,730 +اوصلوا لإجابة نهائية لأنه الإجابة النهائية مهمة + +432 +00:33:41,400 --> 00:33:50,240 +الان خلينا نتطلع على خصائص المحلين فبدي اتكلم عن + +433 +00:33:50,240 --> 00:33:58,000 +حاجة بنقولها colligative properties ايش هي ال + +434 +00:33:58,000 --> 00:34:00,860 +colligative properties لأ انا ماعرفش ايش ممكن + +435 +00:34:00,860 --> 00:34:04,560 +اترجمها باللغة العربيةلكن هي عبارة عن الـ + +436 +00:34:04,560 --> 00:34:07,880 +Collegative Properties اللي هي التالي الـ + +437 +00:34:07,880 --> 00:34:12,440 +Collegative Properties هي عبارة عن الخصائص اللي + +438 +00:34:12,440 --> 00:34:17,000 +التغير فيها لما تتغير يعني التغير فيها لا يتوقف + +439 +00:34:17,000 --> 00:34:22,280 +على نوع الصليوت ولكن يتوقف على كمية الصليوت أو + +440 +00:34:22,280 --> 00:34:27,940 +يعني عدد ال species من الصليوت في المحلولعدد الـ + +441 +00:34:27,940 --> 00:34:31,560 +Species أو تركيز الصليوت في المحلول، لكن لا يتوقف + +442 +00:34:31,560 --> 00:34:36,080 +على إيش هو الصليوت، يعني ممكن الصليوت يكون مثلا + +443 +00:34:36,080 --> 00:34:44,280 +Methanol أو Ethanol، ماشي، ممكن الصليوت يكون مثلا + +444 +00:34:44,280 --> 00:34:47,060 +Sucrose أو Glucose + +445 +00:34:50,240 --> 00:34:54,280 +الـ Collegative Properties هي عبارة عن الـ + +446 +00:34:54,280 --> 00:34:59,560 +properties اللي التغير فيه قيمتها، قيمة الخاصية + +447 +00:34:59,560 --> 00:35:04,660 +هذه، التغير فيها، لا يتوقف علىنوع الـ solute ولكن + +448 +00:35:04,660 --> 00:35:09,060 +يتوقف على عدد ال species من ال solute الموجودة في + +449 +00:35:09,060 --> 00:35:12,880 +المحلول يعني بمعنى أو باخر تركيز المحلول أو خلينا + +450 +00:35:12,880 --> 00:35:17,620 +نقول بمعنى أدق ال molality للمحلول إلى حد كبير + +451 +00:35:17,620 --> 00:35:23,860 +يعني في أغلب الأحيانكويس زي ما هنشوف فهي التركيز + +452 +00:35:23,860 --> 00:35:26,700 +تركيز ما ممكن التركيز يكون molality ممكن بعض + +453 +00:35:26,700 --> 00:35:30,480 +الاحيان يكون molarity زي ما هنشوف في ال osmotic + +454 +00:35:30,480 --> 00:35:34,060 +pressure على سبيل المثال فهذه الخصائص اللي هي ال + +455 +00:35:34,060 --> 00:35:38,620 +colligative properties هي عبارة عن اربع خصائص اللي + +456 +00:35:38,620 --> 00:35:42,060 +هندرسها هي عبارة عن ايه اربع خصائص راحين اللاجئ + +457 +00:35:42,060 --> 00:35:45,460 +ايه انه والله اذا كان في عندى + +458 +00:35:48,460 --> 00:35:53,020 +Non volatile solute وبتكلم دائما عن ال non + +459 +00:35:53,020 --> 00:35:58,300 +volatile solutes في هذا المساق بتكلم عن ال non + +460 +00:35:58,300 --> 00:36:02,400 +volatile solutes يعني ال solutes مالهاش vapor + +461 +00:36:02,400 --> 00:36:08,000 +pressure غير متطايرة فبقول إيه إذا كانت موجودة هذه + +462 +00:36:08,000 --> 00:36:11,480 +ال non volatile solutes فبلاحظ إن ال vapor + +463 +00:36:11,480 --> 00:36:14,360 +pressure للمحلول بيقل عشان ذلك أول خاصية بقول + +464 +00:36:14,360 --> 00:36:17,400 +vapor pressure lowering ال vapor pressure للمحلول + +465 +00:36:17,400 --> 00:36:22,930 +أشمالهبيقل تاني حاجة ال boiling point للمحلول + +466 +00:36:22,930 --> 00:36:26,710 +بتزيد ال boiling point للمحلول بزيد عشان يقول + +467 +00:36:26,710 --> 00:36:30,230 +boiling point elevation يبقى ال boiling point + +468 +00:36:30,230 --> 00:36:33,930 +للمحلول الشمال بزيد هذه خاصية تانية طب ال melting + +469 +00:36:33,930 --> 00:36:37,570 +point او ال freezing point جال a freezing point + +470 +00:36:37,570 --> 00:36:43,810 +depression بتقلالـ osmotic pressure هنتطلع عليه .. + +471 +00:36:43,810 --> 00:36:48,030 +هنتطلع كيف يعني بيتغير بتغير عدد ال species أو + +472 +00:36:48,030 --> 00:36:57,110 +التركيز هو طبعا ال .. هذا الكلام هنشوفه بالتفصيل + +473 +00:36:57,110 --> 00:37:02,880 +فهنبدأ نتكلم عن خاصية خاصية من هذه الخصائصخاصية + +474 +00:37:02,880 --> 00:37:05,760 +خاصية من هذه الخصائص و نشوف الله ايه كيف التغير + +475 +00:37:05,760 --> 00:37:10,800 +فيها بيتم و ايش نتيجة التغير و ليش التغير هذا + +476 +00:37:10,800 --> 00:37:17,780 +دائما بيكون مثلا اقل او زيادة لكن في النهاية كل + +477 +00:37:17,780 --> 00:37:24,800 +هذه الخصائص التغير فيها لا يتوقف على نوع ال ال + +478 +00:37:24,800 --> 00:37:28,820 +solute ولكن يتوقف على عدد جزيئات خليني اقول بين + +479 +00:37:28,820 --> 00:37:33,280 +جثين ال solute في المحلولفنتكلم عن الـ Vapor + +480 +00:37:33,280 --> 00:37:38,400 +Pressure في البداية فبقول انه يعني عملية الذوبان + +481 +00:37:38,400 --> 00:37:40,840 +عملية محبة بس كان لجينا حاجة بتدوب في حاجة فهي + +482 +00:37:40,840 --> 00:37:44,260 +حاجة محبة زي ما ندوّب بجلوكوز أو سكروس في الميه + +483 +00:37:44,260 --> 00:37:47,380 +شيء محبب لإيه؟ لأن في عندنا solute solvent + +484 +00:37:47,380 --> 00:37:51,560 +interactions قوية solute solvent interactions ايه + +485 +00:37:51,560 --> 00:37:54,820 +اشمالها؟ قوية وبالتالي + +486 +00:37:56,510 --> 00:38:00,970 +لما نكون في عيننا non volatile solutes بتخلي + +487 +00:38:00,970 --> 00:38:06,770 +جزيئات ال solvent يعني أصعب عليها انه تترك السطح + +488 +00:38:06,770 --> 00:38:10,770 +ليه؟ لأنه هي مرتبطة معها بقوة، الأصل هيك، إذا كانت + +489 +00:38:10,770 --> 00:38:14,630 +قوة محلول، فعيننا ال solute وال solvent molecules + +490 +00:38:14,630 --> 00:38:18,570 +بيكون ال intermolecular forces بينهم إشمالهم قوية، + +491 +00:38:18,570 --> 00:38:26,360 +فلا يميل ال solvent لأنهيطلع على هيئة vapor يعني + +492 +00:38:26,360 --> 00:38:30,100 +يتخلص او escape from the surface لا يميل انه يغرب + +493 +00:38:30,100 --> 00:38:35,140 +من السطح و ايه و يغادر السطح و يعطيني ال vapor + +494 +00:38:35,140 --> 00:38:43,360 +يمكن هذا لو كان في عنا solvent لوحده فبيحصل على + +495 +00:38:43,360 --> 00:38:46,640 +اتزان بعد فترة وبيكون ال vapor pressure اللي موجود + +496 +00:38:46,640 --> 00:38:48,700 +فيه عبارة عن ال vapor pressure اللي pure solvent + +497 +00:38:53,740 --> 00:38:58,680 +لكن لو كان في عندي non-polar .. non-electrolytic + +498 +00:38:58,680 --> 00:39:03,900 +.. non volatile solute اللي هو الأحمر على سبيل + +499 +00:39:03,900 --> 00:39:11,100 +المثال فبلاحظ أنه عدد الجزيئات من ال solvent اللي + +500 +00:39:11,100 --> 00:39:14,480 +هو الأزراج بتقل يعني هي العدد أكبر هي العدد أقل + +501 +00:39:15,330 --> 00:39:21,250 +وبالتالي ال vapor pressure المفروض انه بيقل لغاية + +502 +00:39:21,250 --> 00:39:24,850 +ما نوصل للاتزان لغاية ما نوصل للاتزان بيكون ال + +503 +00:39:24,850 --> 00:39:29,330 +vapor pressure اقل يعني عدد هدول مثلا عندي سبعة + +504 +00:39:29,330 --> 00:39:33,130 +تمانية هدول بيكونوا اكتر واحد تمانية و تلاتة + +505 +00:39:33,130 --> 00:39:37,450 +احداشر السبب الرئيسي ممكن نتخيله احنا كالتالي + +506 +00:39:37,450 --> 00:39:42,530 +السبب الرئيسي كالتاليهي عندى هذا pure solvent + +507 +00:39:42,530 --> 00:39:50,270 +شايفين و الله بيحصل عندى escape او هروب لبعض + +508 +00:39:50,270 --> 00:39:55,270 +الجزايات من السطح الى اعلى يعني في ال vicinity في + +509 +00:39:55,270 --> 00:39:58,110 +ال space اللى فوق المحلول لغاية ما يحصل عندى + +510 +00:39:58,110 --> 00:40:02,330 +equilibrium او اتزان فش عندي مشكلة لكن لو كان في + +511 +00:40:02,330 --> 00:40:06,660 +عندى soluteوالـ Solute هذا non-volatile فلاحظوا ان + +512 +00:40:06,660 --> 00:40:10,220 +الـ Solute على السطح هو طبعا بيكون موزع بالتساوي + +513 +00:40:10,220 --> 00:40:14,880 +لأنه دايب لكن على السطح اذا كانتم لاحظين في كمية + +514 +00:40:14,880 --> 00:40:20,540 +من ايه؟ من الـ non-volatile solute معناته السطح مش + +515 +00:40:20,540 --> 00:40:25,640 +كله solventعشان هيك لما يكون في عنا fraction مثلا + +516 +00:40:25,640 --> 00:40:33,220 +نصه سوليوت نص السطح سوليوت و النص التاني solvent + +517 +00:40:33,220 --> 00:40:37,080 +طب ال solvent اه ممكن يهرب طب و السوليوت لأ فمعناه + +518 +00:40:37,080 --> 00:40:39,280 +كله ان السطح المتيح صار النص + +519 +00:40:42,220 --> 00:40:47,100 +فالضغط طبيعي انه يقل ففي وجود ال non volatile + +520 +00:40:47,100 --> 00:40:52,280 +solute ال vapor pressure ل المحلول ايش بده؟ بده + +521 +00:40:52,280 --> 00:40:57,120 +يقلتمام؟ لأنه بالاضافة لأنه طبعا الـ + +522 +00:40:57,120 --> 00:41:01,100 +Intermolecular forces بتكون قوية أقوى من ال + +523 +00:41:01,100 --> 00:41:08,360 +solvent solvent فبرضه كمان ال solute بيشغل حيز مهم + +524 +00:41:08,360 --> 00:41:12,560 +من أو مساحة مهمة من السطح فبالتالي عدد الجزيئات + +525 +00:41:12,560 --> 00:41:16,720 +اللي ممكن انها تغادر من ال solvent بتجلد وهذا + +526 +00:41:16,720 --> 00:41:20,160 +موضوع طبيعي ولا هيك بيكون ال vapor pressure عندنا + +527 +00:41:20,160 --> 00:41:27,400 +أقلتعالوا نتطلع على هال تلت حاجات هذه، بنقول الـ + +528 +00:41:27,400 --> 00:41:30,320 +dissolving a non volatile solute will result in a + +529 +00:41:30,320 --> 00:41:32,740 +decrease in the vapor pressure زي ما شفنا of the + +530 +00:41:32,740 --> 00:41:37,580 +solution، هذا كل ما شفناه واستوعبنا ليشطيب when + +531 +00:41:37,580 --> 00:41:40,260 +the vapor pressure of the solute هذا اذا كان بس + +532 +00:41:40,260 --> 00:41:43,300 +احنا مش هاندرسه when the vapor pressure of the + +533 +00:41:43,300 --> 00:41:46,060 +solute equals the vapor pressure of the solvent + +534 +00:41:46,060 --> 00:41:51,800 +يعني لو كان في عنا solute او solvent في solution + +535 +00:41:51,800 --> 00:41:54,600 +لكن ال vapor pressure لهذا بيساوي ال vapor + +536 +00:41:54,600 --> 00:41:57,080 +pressure لهذا ال vapor pressure لل solute بيساوي + +537 +00:41:57,080 --> 00:42:01,180 +ال vapor pressure لل solvent راح نلاقي ان ال total + +538 +00:42:01,180 --> 00:42:06,430 +vapor pressure واحد ماتغيرش وضع طبيعيوالعكس لو كان + +539 +00:42:06,430 --> 00:42:09,550 +ال vapor pressure للسوليوت اعلى من ال vapor + +540 +00:42:09,550 --> 00:42:11,490 +pressure للسوليوت فانت راح تلاقي ال vapor pressure + +541 +00:42:11,490 --> 00:42:15,510 +زاد .. ليه؟ لأن ال vapor pressure للسوليوت اعلى .. + +542 +00:42:15,510 --> 00:42:19,670 +لكن احنا فقط مهتمين في ما لو كان عندنا non + +543 +00:42:19,670 --> 00:42:24,050 +volatile solute .. ايش اللي بيحصل بنقول والله + +544 +00:42:24,050 --> 00:42:29,390 +بيحصل lowering في ال vapor pressure .. lowering في + +545 +00:42:29,390 --> 00:42:34,750 +ال vapor pressureهذا كلام quantitatively من ناحية + +546 +00:42:34,750 --> 00:42:46,710 +كمية عالج السيد رؤونرأوزلو بيقول P A اللي هو ال + +547 +00:42:46,710 --> 00:42:52,690 +vapor pressure ل A للمادة A او لل solvent A بيسوى + +548 +00:42:52,690 --> 00:42:58,930 +XA زائد P not A XA اللي هي الموليفكشن ل A P not A + +549 +00:42:58,930 --> 00:43:02,730 +قال هي ال vapor pressure ل ال pure A ال vapor + +550 +00:43:02,730 --> 00:43:09,100 +pressure ل ال pure A فإذا كان ال XA واحديعني + +551 +00:43:09,100 --> 00:43:14,520 +ماعندى اي non volatile solute فال P A عبارة عن P + +552 +00:43:14,520 --> 00:43:17,900 +نقطة لل A نفس ال vapor pressure هو هو ماتغيرش لكن + +553 +00:43:17,900 --> 00:43:22,020 +كل ما انا زودت ال non volatile solute معناته XA + +554 +00:43:22,020 --> 00:43:29,780 +بتجل ليه؟ لأن ال XA زاد ال XB بدها تساوي واحد فإذا + +555 +00:43:29,780 --> 00:43:33,740 +كان XB أنا عمال بزودها ال XA ايش بتسوي؟ بتجل يبقى + +556 +00:43:33,740 --> 00:43:38,110 +ال vapor pressure بده يجلتمام لأنه انا افترضت انه + +557 +00:43:38,110 --> 00:43:43,830 +عندي non volatile solute فال XA هي المولي fraction + +558 +00:43:43,830 --> 00:43:48,870 +لل component A او ال compound A وال P0A هي ال + +559 +00:43:48,870 --> 00:43:52,050 +normal vapor pressure of pure A ال solvent ل pure + +560 +00:43:52,050 --> 00:43:55,170 +at that temperature فبقول لو كان عندي two + +561 +00:43:55,170 --> 00:44:00,690 +components solution بتكون من two components solute + +562 +00:44:00,690 --> 00:44:06,490 +او solventفبقول P للسوليوتش مستوي X للسوليوت في P0 + +563 +00:44:06,490 --> 00:44:11,590 +للسوليوت زائد X للسوليفت في P0 للسوليفت و لو في + +564 +00:44:11,590 --> 00:44:15,870 +عندي اكتر من اتنين يعني اكتر من اتنين يعني اكتر من + +565 +00:44:15,870 --> 00:44:15,870 +اتنين يعني اكتر من اتنين يعني اكتر من اتنين يعني + +566 +00:44:15,870 --> 00:44:15,870 +اكتر من اتنين يعني اكتر من اتنين يعني اكتر من + +567 +00:44:15,870 --> 00:44:16,030 +اتنين يعني اكتر من اتنين يعني اكتر من اتنين يعني + +568 +00:44:16,030 --> 00:44:16,070 +اكتر من اتنين يعني اكتر من اتنين يعني اكتر من + +569 +00:44:16,070 --> 00:44:22,310 +اتنين يعني اكتر من اتنين يعني اكتر من اتنين يعني + +570 +00:44:22,310 --> 00:44:26,410 +اكتر من اتنين يع + +571 +00:44:30,230 --> 00:44:35,710 +إذا كان السوليوت non-volatile فال P نقطه إيه جداش؟ + +572 +00:44:35,710 --> 00:44:38,250 +ال vapor pressure إيه جداش إذا كانه non-volatile؟ + +573 +00:44:38,250 --> 00:44:43,870 +ال vapor pressure إيه جداش؟ non + +574 +00:44:43,870 --> 00:44:47,910 +-volatile، non-volatile، بطرش خالص، ال vapor + +575 +00:44:47,910 --> 00:44:51,550 +pressure إيه جداش؟ صفر، non-volatile معناته ال P + +576 +00:44:51,550 --> 00:44:55,430 +نقطه إيه؟ صفر، إذا كانه non-volatile فال P نقطه + +577 +00:44:55,430 --> 00:44:59,840 +إيه؟ صفرطيب إذا هد ال X سوليوت في ال P نوت سوليوت + +578 +00:44:59,840 --> 00:45:03,640 +هنلاقيها بتساوي صفر يبقى ال P لل solution بتساوي X + +579 +00:45:03,640 --> 00:45:07,840 +لل solvent في ال P نوت لل solvent بس هد هي الحالة + +580 +00:45:07,840 --> 00:45:11,720 +اللي احنا كمان مرة بقول بنعالجها في هذا المساق في + +581 +00:45:11,720 --> 00:45:14,640 +مساقات أخرى أه بنعالج و الله لو كان في عندنا أكتر + +582 +00:45:14,640 --> 00:45:18,260 +من سوليوت أو كان السوليوت فئل و فئر بشرة لكن هلأ + +583 +00:45:18,260 --> 00:45:23,360 +بنقول السوليوت اللي عندي non volatile تمام فبقول + +584 +00:45:23,360 --> 00:45:25,900 +والله ال P لل solution إذا كان هدي بالصفر + +585 +00:45:29,080 --> 00:45:33,060 +أذا X سوليوت في P نوت سوليوت بصفر يبقى P لا + +586 +00:45:33,060 --> 00:45:37,960 +سوليوتش ناشو بتساوي X solvent في P نوت solvent نفس + +587 +00:45:37,960 --> 00:45:44,770 +قانون رقولطيب يبقى ال P solution بتساوي هي ايش ال + +588 +00:45:44,770 --> 00:45:49,250 +.. ايش ال X للسوليفنت؟ جال واحد minus X للسوليوت + +589 +00:45:49,250 --> 00:45:52,670 +صح ولا لأ؟ واحد minus X للسوليوت طب تعالوا نقوم + +590 +00:45:52,670 --> 00:45:56,970 +إذا P للسوليوت ساوي X solvent في P not للسوليفنت + +591 +00:45:56,970 --> 00:46:00,190 +أو يعني واحد minus X للسوليوت في P not للسوليوت + +592 +00:46:00,190 --> 00:46:05,720 +نضرب P not للسوليفنت هانP0 للسولفانت نضرب P0 + +593 +00:46:05,720 --> 00:46:09,620 +للسولفانت في واحد P0 للسولفانت minus X للسوليوت في + +594 +00:46:09,620 --> 00:46:17,440 +P0 للسولفانت X للسوليوت في P0 للسولفانت هذا هو ال + +595 +00:46:17,440 --> 00:46:22,200 +vapor pressure لل pure solvent طب و هذه القيمة جال + +596 +00:46:22,200 --> 00:46:25,970 +هذه القيمة هي عبارة عنX لصولت المولي فركشن لصولت + +597 +00:46:25,970 --> 00:46:31,390 +في ال P نوت لصولفت وكأنها بتعبر عن يعني ال vapor + +598 +00:46:31,390 --> 00:46:37,470 +pressure lowering نقص لأنه كل ما زابت هذه كل ما + +599 +00:46:37,470 --> 00:46:44,070 +الفرق الفرق يعني خليني + +600 +00:46:44,070 --> 00:46:51,230 +أقولالفرق عندى بيزيد الفرق عندى بيزيد فال P + +601 +00:46:51,230 --> 00:46:56,970 +Nautilus solvent يعني هلاحظ انه لما بدي اجي اطرح + +602 +00:46:56,970 --> 00:47:01,290 +منها هذه الكمية هذه الكمية بتعبر عن ال vapor + +603 +00:47:01,290 --> 00:47:06,460 +pressure lowering النقص في ال vapor pressureفمعنى + +604 +00:47:06,460 --> 00:47:11,760 +كلام الـ delta P أو النقص في ال .. ال .. ال vapor + +605 +00:47:11,760 --> 00:47:14,680 +pressure هو عبارة عن X للسوليوت في ال peanut + +606 +00:47:14,680 --> 00:47:18,400 +للسوليوت، لأن هي ال peanut للسولفان، بديجل، بديجل + +607 +00:47:18,400 --> 00:47:21,180 +بمقدار إيه؟ X للسوليوت في ال peanut للسولفان، يعني + +608 +00:47:21,180 --> 00:47:25,120 +هذه هي ال pressure أو ال vapor pressure lowering، + +609 +00:47:25,120 --> 00:47:30,370 +هذا هو النقص، لأن هي الأصل، بديجل بمقدار كميةاكس + +610 +00:47:30,370 --> 00:47:34,330 +للسوليوت في P نوت للسوليفان، هذا عبارة عن ايه؟ عن + +611 +00:47:34,330 --> 00:47:37,570 +الـVapour pressure lowering أو الـDelta P بدها + +612 +00:47:37,570 --> 00:47:42,230 +تساوي X للسوليوت في P نوت للسوليفان، هذا عبارة عن + +613 +00:47:42,230 --> 00:47:47,170 +النقص في الـVapour pressure نتيجة وجود الـNon + +614 +00:47:47,170 --> 00:47:51,520 +volatile soluteفانا اذا كان عندى X للسوليوت اللى + +615 +00:47:51,520 --> 00:47:54,460 +هى ال mol fraction للسوليوت و عندى طبعا ال P0 + +616 +00:47:54,460 --> 00:48:00,540 +للسولفان بقدر احسب جداش ال decrease in vapor + +617 +00:48:00,540 --> 00:48:07,780 +pressure بدي اعطيكم يعنى مثال بسيط على هذا الكلام + +618 +00:48:07,780 --> 00:48:12,280 +بيقول لى the vapor pressure of pure water at 20 + +619 +00:48:12,280 --> 00:48:17,040 +degrees C ال 17.5 دور عند 20 درجة ال vapor + +620 +00:48:17,040 --> 00:48:22,520 +pressure للميهللـ pure water سبعتاشر و نص طور + +621 +00:48:22,520 --> 00:48:26,120 +بيقول if glucose أو بنجوسين a non volatile solute + +622 +00:48:26,120 --> 00:48:31,640 +is added to water at constant temperature يعني عند + +623 +00:48:31,640 --> 00:48:35,060 +عشرين ديجري سي so that the moly fraction of water + +624 +00:48:35,060 --> 00:48:40,560 +is point eight المولي فراكشن للميه point eight هان + +625 +00:48:40,560 --> 00:48:45,220 +كان pure water المولي فراكشن واحدبس هاني أعطاني + +626 +00:48:45,220 --> 00:48:48,820 +الموالي fraction للمي للمي قداش point ات calculate + +627 +00:48:48,820 --> 00:48:52,960 +the pressure of water above solution بقول فيش أبسط + +628 +00:48:52,960 --> 00:48:59,080 +منها رأي وصله P لل H2O لل solution خليني أقول هذه + +629 +00:48:59,080 --> 00:49:05,580 +الأحسن يعني P لل solution X لل H2O في P note لل + +630 +00:49:05,580 --> 00:49:11,210 +H2O يبقى ال P لل solutionبدو يساوي X اللي هي + +631 +00:49:11,210 --> 00:49:14,930 +تمانية من عشرة المولي فركشن للميه في سبعتاشر و نص + +632 +00:49:14,930 --> 00:49:18,770 +بتلع اربعتاشر تور طيب ال lowering in vapor + +633 +00:49:18,770 --> 00:49:22,770 +pressure كان سبعتاشر و نص صار اربعتاشر اذا سبعتاشر + +634 +00:49:22,770 --> 00:49:27,010 +و نص minus اربعتاشر تلاتة و نص تور جلت بقدر احسب + +635 +00:49:27,010 --> 00:49:31,130 +الكل ينتبه بقدر احسب هذا الكلام بالظبط لو قلت + +636 +00:49:31,130 --> 00:49:36,460 +والله ال delta P بتساوي X للسولد في P0 للسولفانX + +637 +00:49:36,460 --> 00:49:40,940 +للسوليوت جديش السوليوت جال اتنين من عشرة اذا كان + +638 +00:49:40,940 --> 00:49:44,620 +هذه المية تمانية من عشرة المولي فراكشن اذا المولي + +639 +00:49:44,620 --> 00:49:48,060 +فراكشن للسوليوت اللي هو الجليكوز اتنين من عشرة في + +640 +00:49:48,060 --> 00:49:52,940 +السبعتاشر و نص تلاتة و نص تورية هيطبعا فانا انه + +641 +00:49:52,940 --> 00:49:56,340 +نحسب ال depression او ال lowering in vapor + +642 +00:49:56,340 --> 00:49:59,780 +pressure باستخدام Raoult's law او ال delta P + +643 +00:49:59,780 --> 00:50:04,740 +مباشرة سيان راولتس لاو بده احسب ال vapor pressure + +644 +00:50:04,740 --> 00:50:09,120 +النهائي في وجود ال ايه في وجود الصليوت وبعدين اطرح + +645 +00:50:09,120 --> 00:50:11,980 +هذا ال vapor pressure من ال vapor pressure في غياب + +646 +00:50:11,980 --> 00:50:16,310 +او في عدم وجود الصليوتأما الـ Vapor Pressure + +647 +00:50:16,310 --> 00:50:19,490 +Lowering بقدر أحسبه على طول بإني أحسب الـ X + +648 +00:50:19,490 --> 00:50:23,170 +للسوليوت في الـ P0 للسوليوت جداش فهذا كلام + +649 +00:50:23,170 --> 00:50:27,290 +للسولفان P0 للسوليوت طبعا السوليوت صفر P0 للسوليوت + +650 +00:50:27,290 --> 00:50:30,830 +صفر P0 للسولفان هيك هذا اللي اشتقنها قبل شوية + +651 +00:50:30,830 --> 00:50:35,110 +فبيطلع ان التلاتة و نص هي نفس التلاتة و نص مافيش + +652 +00:50:35,110 --> 00:50:40,930 +إشكاليةإذن في وجود من هذا الكلام اللي نقول في وجود + +653 +00:50:40,930 --> 00:50:44,750 +ال non volatile solute ال vapor pressure ل ال + +654 +00:50:44,750 --> 00:50:49,090 +solution بيقل بقدر أحسب هذا الكلام نعم باستخدام + +655 +00:50:49,090 --> 00:50:53,770 +Raoult's law بقدر أعرف ال vapor pressure الجديد + +656 +00:50:53,770 --> 00:50:57,560 +باستخدام Raoult's lawفانا عندي ال vapor pressure + +657 +00:50:57,560 --> 00:51:00,460 +لل pure solvent و فيها عندي ال vapor pressure لل + +658 +00:51:00,460 --> 00:51:04,440 +solution بقدر اطرحهم من بعض بجيب ال lowering او ان + +659 +00:51:04,440 --> 00:51:08,980 +استخدم ال delta P بتسوي X لل solute في P0 لل + +660 +00:51:08,980 --> 00:51:14,920 +solvent و انتهينا بجيب لل lowering على طول طيب هذا + +661 +00:51:14,920 --> 00:51:16,380 +سؤال كويس يعني + +662 +00:51:19,330 --> 00:51:23,330 +بيفرجينا جداش ال lowering in vapor pressure المفيد + +663 +00:51:23,330 --> 00:51:27,690 +في الكيميا فبيقول at 25 degree c the vapor + +664 +00:51:27,690 --> 00:51:32,950 +pressure of pure water is 23.76 millimeters إقبق + +665 +00:51:32,950 --> 00:51:37,390 +طور يعني and that of a urea non volatile solute + +666 +00:51:39,310 --> 00:51:44,330 +that of a urea solution يعني في عندنا solution + +667 +00:51:44,330 --> 00:51:48,070 +موجود في urea is اتنين وعشرين واتمانة وتسعين + +668 +00:51:48,070 --> 00:51:53,130 +مليمتر ذئبق يعني Tor find the molality of solution + +669 +00:51:53,130 --> 00:51:59,150 +بده يحسب ال molality تمام؟ ايش اللي احنا بنقوله؟ + +670 +00:51:59,150 --> 00:52:03,380 +واللهبس كان حبيته يعني على طول مباشرة نقول الـ + +671 +00:52:03,380 --> 00:52:06,860 +Delta P بتسوي X للسوليوت اللي هو الـ Non-volatile + +672 +00:52:06,860 --> 00:52:12,000 +شفناها في ال P نوت لسولفان اللي هو الميه منها + +673 +00:52:12,000 --> 00:52:16,000 +بتجيب ال Delta P معروفة كان تلاتة و عشرين و ستة و + +674 +00:52:16,000 --> 00:52:19,320 +سبعين صار اتنين و عشرين و تمانية و تسعين فبنقدر + +675 +00:52:19,320 --> 00:52:20,040 +نقول والله + +676 +00:52:22,800 --> 00:52:27,480 +X لليوريا هي عبارة عن Delta P على P Note للواتر + +677 +00:52:27,480 --> 00:52:30,700 +Delta P هي تلاتة و عشرين و ستة و سبعين minus تانية + +678 +00:52:30,700 --> 00:52:34,280 +و عشرين و تمانية وتسعين على تلاتة و عشرين و ستة و + +679 +00:52:34,280 --> 00:52:36,800 +سبعين اللي هي ال P Note للواتر بيطلع point O33 + +680 +00:52:36,800 --> 00:52:44,520 +يبقى ال fraction لليوريا بتساوي point O33 + +681 +00:52:46,970 --> 00:52:49,730 +لو اعتبرنا .. لو يعني عشان بدي أجيب الـ molality + +682 +00:52:49,730 --> 00:52:53,870 +يعني لو اعتبرنا .. assume الف جرام of water بقول + +683 +00:52:53,870 --> 00:52:56,710 +number of moles of water in واحد كيلوجرام سوى خمسة + +684 +00:52:56,710 --> 00:53:00,630 +خمسين ستة من عشرة we can find the number of moles + +685 +00:53:00,630 --> 00:53:04,970 +of urea يعني انا عندي ال mol fraction لليوريا + +686 +00:53:04,970 --> 00:53:09,350 +معروف point O33 اعتبرت انه عندي الف جرام .. انا + +687 +00:53:09,350 --> 00:53:11,630 +بدي أجيب ال molality و ال molality هي عبارة عن + +688 +00:53:14,530 --> 00:53:21,390 +مول يوريا على كيلو جرام water اللي هو ال solvent + +689 +00:53:21,390 --> 00:53:25,830 +فاعتبرت انه عندي كيلو جرام water اكم مول في الكيلو + +690 +00:53:25,830 --> 00:53:30,230 +جرام جالي خمسة و خمسين وستة من عشرة الان هاي ال X + +691 +00:53:30,230 --> 00:53:34,430 +لليوريا بسوء N لليوريا N لليوريا زاد N للwater X + +692 +00:53:34,430 --> 00:53:40,120 +لليوريا معروفة point O three threeان لاليوريا + +693 +00:53:40,120 --> 00:53:47,920 +بدياها على ان لاليوريا زائد fifty five point six + +694 +00:53:47,920 --> 00:53:52,240 +اللي هي الميه فصار عندي بس مجهول واحد اللي هو ان + +695 +00:53:52,240 --> 00:53:56,380 +لاليوريا فبلاحظ ان الان لاليوريا هي عبارة عن واحد + +696 +00:53:56,380 --> 00:54:00,580 +وتسعة من عشرة في الف جرام اللي هو اعتبرنا ان الميه + +697 +00:54:00,580 --> 00:54:04,720 +عبارة عن الف جرام يبقى معنا الكلام واحد وتسعة على + +698 +00:54:04,720 --> 00:54:08,900 +واحد kilogram يعني واحد وتسعة مولالواحد و تسعة من + +699 +00:54:08,900 --> 00:54:19,260 +العشرة مولال كمان مرة بقول في عندى ميه ال vapor + +700 +00:54:19,260 --> 00:54:22,220 +pressure تبعها عند خمسة و عشرين degree c تلاتة و + +701 +00:54:22,220 --> 00:54:28,720 +عشرين و ستة و سبعين tor انا حطيت عملت محلول حطيت + +702 +00:54:28,720 --> 00:54:34,250 +شوية yuri عليهابحيث انه لما اجهت جيسة الفيب هذا + +703 +00:54:34,250 --> 00:54:38,210 +عشان لجته 22.98 فبده احسب ال molality بده احسب + +704 +00:54:38,210 --> 00:54:41,690 +تركيز المحلول حلو كتير السؤال حلو كتير بده احسب + +705 +00:54:41,690 --> 00:54:45,630 +تركيز المحلول فبقول يمكن حساب تركيز المحلول ببساطة + +706 +00:54:46,080 --> 00:54:50,060 +لأن أنا عند المولي فراكشن لليوريا بقدر أجيبه من + +707 +00:54:50,060 --> 00:54:52,700 +الـ Delta P ال Delta P بيساوي المولي فراكشن + +708 +00:54:52,700 --> 00:54:55,980 +لليوريا في ال P not للwater ال P not للwater معايا + +709 +00:54:55,980 --> 00:55:00,520 +و ال Delta P معايا بقدر أحسب المولي فراكشن المولي + +710 +00:55:00,520 --> 00:55:04,600 +فراكشن طالع عند 0.033 الآن لو بدأ أقول والله + +711 +00:55:04,600 --> 00:55:10,400 +المولي فراكشن عبارة عن 0.033 بيبقى تساوي N لليوريا + +712 +00:55:10,400 --> 00:55:17,090 +على N لليوريا زائد N للwaterكويس فانا لازم افترض + +713 +00:55:17,090 --> 00:55:21,630 +حاجة هيك ماقدرش احلي المسألة فالان انا بفترض انه + +714 +00:55:21,630 --> 00:55:26,670 +عندي الف جرام water لان ال molality اللي بدو + +715 +00:55:26,670 --> 00:55:31,450 +يحسبها هي عبارة عن ال molality هي عبارة عن mol + +716 +00:55:31,450 --> 00:55:38,330 +urea على kilogram water فانا خليني اخد kilogram + +717 +00:55:38,330 --> 00:55:42,210 +water فهنا kilogram water حولوا in لل water على + +718 +00:55:42,210 --> 00:55:48,260 +جداش 18إذا صرت in للميه معايا بقدر أحسب ال in + +719 +00:55:48,260 --> 00:55:51,740 +لليوريا عدد ملات اليوريا اللي هتكون موجودة في الف + +720 +00:55:51,740 --> 00:55:55,920 +kilogram في الف gram يعني في ال kilogram فمع هذا + +721 +00:55:55,920 --> 00:55:59,460 +الكلام بيطلع + +722 +00:55:59,460 --> 00:56:02,900 +عند ال in لليوريا واحد وتسعة من عشرة معناته واحد + +723 +00:56:02,900 --> 00:56:06,800 +وتسعة من عشرة على واحد kilogram يبقى هذه هي ال + +724 +00:56:06,800 --> 00:56:10,020 +morality سؤال في الحقيقة كتير حلو من ناحية كيمية + +725 +00:56:10,020 --> 00:56:10,800 +كويسة كتير + +726 +00:56:29,240 --> 00:56:33,100 +برضه حاجة كتير مهمة بالنسبة لنا بيقول الاجليسريين + +727 +00:56:33,100 --> 00:56:37,060 +ال form اللي بيبقى له 92 و 1 من 10 gram ع المول is + +728 +00:56:37,060 --> 00:56:40,960 +a non volatile non electrolyte non volatile و non + +729 +00:56:40,960 --> 00:56:44,400 +electrolyte هنلاحظ انه كمان non electrolyte لها + +730 +00:56:44,400 --> 00:56:48,870 +معنى مهمبس مش هناخدوا الحصة هذه يعني الـ Non + +731 +00:56:48,870 --> 00:56:51,470 +-volatile فهمنا ليش لأن مافيش ايه الفهم .. كمان + +732 +00:56:51,470 --> 00:56:55,690 +Non-electrolyte مهم جدا Non-electrolyte مهم جدا + +733 +00:56:55,690 --> 00:56:59,870 +فحنشوف أهميته الحصة الجاهزة الله رضي الله فبيقول + +734 +00:56:59,870 --> 00:57:03,730 +لي كمان مرة Glycerin formula weight 92.1 gram ع + +735 +00:57:03,730 --> 00:57:08,750 +المول is a non-volatile non-electrolyte with a + +736 +00:57:08,750 --> 00:57:11,630 +density of 1.26 gram ع المل + +737 +00:57:18,600 --> 00:57:31,220 +خمسين مل إجلسريين لخمسمية + +738 +00:57:31,220 --> 00:57:36,410 +مل من الماءبرضه انا بتهمنيش المل مية بتهمني جرام + +739 +00:57:36,410 --> 00:57:41,850 +مية في أغلب الأحيان at 25 degrees C the vapor + +740 +00:57:41,850 --> 00:57:45,410 +pressure of pure water is 23.8 Torr and its + +741 +00:57:45,410 --> 00:57:48,890 +density is 1 gram على المل فهو ايش بده يحسب + +742 +00:57:48,890 --> 00:57:52,130 +calculate the vapor pressure of solution ال vapor + +743 +00:57:52,130 --> 00:58:00,410 +pressure of solution P لل solution حسب رؤوس له X X + +744 +00:58:00,410 --> 00:58:09,410 +لل waterفي P Note للـ Water فيبقى أنا بدي أجيبالـ + +745 +00:58:09,410 --> 00:58:13,970 +X للـ Water لأن الـ Peanut للـ Water معايا 23.8 + +746 +00:58:13,970 --> 00:58:15,070 +مليون عشرة مليون عشرة مليون عشرة مليون عشرة مليون + +747 +00:58:15,070 --> 00:58:16,370 +عشرة مليون عشرة مليون عشرة مليون عشرة مليون عشرة + +748 +00:58:16,370 --> 00:58:16,890 +مليون عشرة مليون عشرة مليون عشرة مليون عشرة مليون + +749 +00:58:16,890 --> 00:58:18,650 +عشرة مليون عشرة مليون عشرة مليون عشرة مليون عشرة + +750 +00:58:18,650 --> 00:58:22,930 +مليون عشرة مليون عشرة مليون عشرة مليون عشرة مليون + +751 +00:58:22,930 --> 00:58:26,070 +عشرة مليون عشرة مليون عشرة مليون عشرة مليون عشرة + +752 +00:58:26,070 --> 00:58:30,170 +مليون عشرة مليون عشرة مليون عشرة مليون عشرة + +753 +00:58:30,170 --> 00:58:37,070 +مليون عشرة مليون عشرة + +754 +00:58:37,070 --> 00:58:40,530 +مليون عشرةإيجليسرين طب جداش وزن المياه؟ جالي + +755 +00:58:40,530 --> 00:58:43,350 +خمسمية مل طب جداش ال density اللي هي واحد؟ دي + +756 +00:58:43,350 --> 00:58:48,930 +بيبقى خمسمية في واحد خمسمية إجرام أنا هاي عندي هاد + +757 +00:58:48,930 --> 00:58:53,590 +إجرام سيافوج موجودة خمسمية إجرام مادام جيب ال + +758 +00:58:53,590 --> 00:58:59,110 +إجرامات بقدر أحولها لمولات إذا ال moles 63 على 92 + +759 +00:58:59,110 --> 00:59:04,680 +و 1بطلع point eight six four والمياه خمسمية على + +760 +00:59:04,680 --> 00:59:07,840 +تمانتاش سبعة و عشرين و تمانية من عشرة المول ال + +761 +00:59:07,840 --> 00:59:11,020 +fraction للمياه in لل water على in لل إجرسرين زائد + +762 +00:59:11,020 --> 00:59:14,200 +in لل water سبعة و عشرين و تمانية على point eight + +763 +00:59:14,200 --> 00:59:15,780 +six four زائد سبعة و عشرين و تمانية بطلع point + +764 +00:59:15,780 --> 00:59:21,080 +nine sevenالان هذه هي ال X لل water وعند ال P نقطة + +765 +00:59:21,080 --> 00:59:24,860 +لل water معناه ال كلام ال P لل solution بتساوي X + +766 +00:59:24,860 --> 00:59:27,280 +لل water point nine seven في تلاتة و عشرين و + +767 +00:59:27,280 --> 00:59:31,540 +تمانية طلعة تلاتة و عشرين و واحد Tor يبقى حصل + +768 +00:59:31,540 --> 00:59:36,000 +lowering لل vapor pressure بمقدار سبعة من عشرة Tor + +769 +00:59:36,000 --> 00:59:39,620 +نتيجة إضافة لجليسرين + +770 +00:59:49,890 --> 00:59:54,010 +طيب خلينا نتطلع الآن على خاصية أخرى شفنا في + +771 +00:59:54,010 --> 00:59:59,070 +البداية ال vapor pressure lowering وشفنا بالفعل + +772 +00:59:59,070 --> 01:00:04,290 +بيحصل lowering ولاجينا رؤولز logo قدامنا بيقول P + +773 +01:00:04,290 --> 01:00:09,270 +لل solution بساوي X لل solvent في P0 لل solvent + +774 +01:00:09,270 --> 01:00:15,820 +على اعتبار ان ال solute non volatileتمام وشوفنا + +775 +01:00:15,820 --> 01:00:19,420 +كمان حاجة مهمة كتير ال lowering in vapor pressure + +776 +01:00:19,420 --> 01:00:24,820 +بقدر احسبه delta P بتسوي X لل solute في ال P note + +777 +01:00:24,820 --> 01:00:31,200 +لل solvent اذا خلصنا من ال vapor pressure lowering + +778 +01:00:31,200 --> 01:00:35,860 +اول خاصية من ال colligative properties الان نتطلع + +779 +01:00:35,860 --> 01:00:40,240 +على خاصية اخرىبتكلم عن الـ boiling point elevation + +780 +01:00:40,240 --> 01:00:43,580 +وبعدين خاصية تالتة ال freezing point depression + +781 +01:00:43,580 --> 01:00:48,900 +مرتبطين مع بعض هفرجيكم كيف احنا + +782 +01:00:48,900 --> 01:00:51,920 +شفنا ان الـ non volatile solute solvent + +783 +01:00:51,920 --> 01:00:54,820 +interactions cause the vapor pressure of solution + +784 +01:00:54,820 --> 01:00:59,440 +to decrease ايش معناة هذا الكلام؟هفرجيكم اليف + +785 +01:00:59,440 --> 01:01:03,460 +ثواني لكن بنلاقي ان هذا التصرف بما ان ال vapor + +786 +01:01:03,460 --> 01:01:08,920 +pressure للمحلول صار اقل معناته ال boiling point + +787 +01:01:08,920 --> 01:01:12,900 +لازم تزيد و ال freezing point لازم تجلد كيف هذا + +788 +01:01:12,900 --> 01:01:18,440 +الكلام جالب نتطلع على ال face diagram اللي أخدناه + +789 +01:01:18,440 --> 01:01:24,060 +ال chapter الماضي هاي ال vapor هاي ال liquid وهاي + +790 +01:01:24,060 --> 01:01:28,580 +ال vapor هاي ال equilibriumفبقول إنه إيش .. إيش + +791 +01:01:28,580 --> 01:01:33,540 +معنى إنه ال .. ال vapor pressure بيقل، معناته هادة + +792 +01:01:33,540 --> 01:01:38,860 +بدل ما هو الآن الخط اللي خليني أقول المستمر، صار + +793 +01:01:38,860 --> 01:01:43,910 +أقل، فان هو الخط المتقطعجل ال vapor pressure عند + +794 +01:01:43,910 --> 01:01:47,710 +اي نقطة جل ال vapor pressure تمام؟ عند اي نقطة جل + +795 +01:01:47,710 --> 01:01:52,070 +ال vapor pressure فبالتالي انا عند واحد atmosphere + +796 +01:01:52,070 --> 01:01:56,410 +ال boiling point تبعتي هي عبارة عن درجة الحرارة + +797 +01:01:56,410 --> 01:02:02,790 +اللي ال vapor pressure لالمحلول اللي عندي بيساوي + +798 +01:02:02,790 --> 01:02:06,470 +ال atmospheric pressure يعني واحد atmosphere فهي + +799 +01:02:06,470 --> 01:02:09,870 +بتطلعها ان كان هاي ال boiling point هدهي ال normal + +800 +01:02:09,870 --> 01:02:10,650 +boiling point + +801 +01:02:13,810 --> 01:02:17,870 +هذا الشكل ليس عنده أي صليوت طب لو في عند الصليوت + +802 +01:02:17,870 --> 01:02:21,670 +ال vapor pressure حيصير هنا طب عشان نطلع كيف + +803 +01:02:21,670 --> 01:02:24,430 +بتتغير ال boiling point او كيف ال boiling point + +804 +01:02:24,430 --> 01:02:30,950 +بترتفع بالفعل في وجود الانفلة الصليوت تعالوا نطلع + +805 +01:02:30,950 --> 01:02:35,290 +على ال face diagram بقول ال face diagram بيقوللي + +806 +01:02:35,290 --> 01:02:39,170 +والله هذا شكل ال face diagram للميهفبقول ال + +807 +01:02:39,170 --> 01:02:43,430 +boiling point الاصل انه لما ال vapor pressure له + +808 +01:02:43,430 --> 01:02:52,570 +الميه يساوي 760 تور او 1 اتمسفير الميه بتغلي كويس + +809 +01:02:52,570 --> 01:02:58,180 +تتحول من liquidبتتحول من liquid الى vapor فعند هذه + +810 +01:02:58,180 --> 01:03:02,280 +النقطة الان في وجود منفرة ال solute بلاحظ ان طبعا + +811 +01:03:02,280 --> 01:03:04,820 +ال vapor pressure بده يقل اذا عند هذه النقطة + +812 +01:03:04,820 --> 01:03:08,100 +تحديدا مش غليان للميه لان ال vapor pressure + +813 +01:03:08,100 --> 01:03:15,360 +للمحلول مش واحد atmosphere اقل اذا بده اكمل هان + +814 +01:03:15,360 --> 01:03:21,350 +راح تغلي الميه عند واحد atmosphere يعنيالميّه راح + +815 +01:03:21,350 --> 01:03:24,690 +تبدأ تغلي هان هان احنا نلاحظ ان هذه ال boiling + +816 +01:03:24,690 --> 01:03:29,490 +point الجديدة للميّه كانت هان ال boiling point + +817 +01:03:29,490 --> 01:03:34,370 +صارت هان معناته ايش حصل زادت ال boiling point زادت + +818 +01:03:34,370 --> 01:03:40,770 +هذا بنقوله boiling point elevation زيادة دائما بما + +819 +01:03:40,770 --> 01:03:45,530 +ان ال vapor pressure قل فمعناته في عندي زيادة في + +820 +01:03:45,530 --> 01:03:52,080 +ال boiling pointفي quantitatively يعني هذا الكلب + +821 +01:03:52,080 --> 01:04:03,140 +ممكن يترجم للتالي بقول ال delta T بيه الزيادة في + +822 +01:04:03,140 --> 01:04:07,000 +ال boiling point أو ال elevation في ال boiling + +823 +01:04:07,000 --> 01:04:12,630 +point بساوي ثابت KB في ال molalityثابت اسمه Kb في + +824 +01:04:12,630 --> 01:04:16,550 +الـMolarity الثابت هذا الـKb بنقوله الـMolar + +825 +01:04:16,550 --> 01:04:20,310 +Boiling Point Elevation Constant وهذا خاص + +826 +01:04:20,310 --> 01:04:26,390 +بالـSolvent كل Solvent فيه إله Molar Boiling Point + +827 +01:04:26,390 --> 01:04:30,350 +Elevation Constant يعني هذا الـBoiling Point + +828 +01:04:30,350 --> 01:04:33,150 +Elevation Constant هو عبارة عن الـProperty of + +829 +01:04:33,150 --> 01:04:38,470 +Solvent الآن جيبنا الـDelta Tb طب جداش درجة غليان + +830 +01:04:38,730 --> 01:04:44,650 +المحلول قال اه درجة غليان المحلول هي عبارة عن ال + +831 +01:04:44,650 --> 01:04:52,170 +normal boiling point Tb زادة ال delta Tb زادت هاي + +832 +01:04:52,170 --> 01:04:58,990 +ال T boiling لل solution هاد ال normal boiling + +833 +01:04:58,990 --> 01:04:59,410 +point + +834 +01:05:03,390 --> 01:05:08,030 +هذا النوع زائد وانضفلها term الـ Delta Tb اذا واضح + +835 +01:05:08,030 --> 01:05:12,730 +بالنسبة لنا انه دائما ال boiling point بدها تزيد + +836 +01:05:12,730 --> 01:05:15,910 +ال boiling point بدها تزيد في وجود ال non volatile + +837 +01:05:15,910 --> 01:05:20,450 +solute عندي بعض ال solvents زي ال acetic acid مثلا + +838 +01:05:20,450 --> 01:05:24,790 +ماليش دعوة في هذا ال term مش مهم بالنسبة ليه ال Kb + +839 +01:05:24,790 --> 01:05:28,530 +له تلاتة و اتنين و عشرين البنزين اتنين و اربعة و + +840 +01:05:28,530 --> 01:05:33,780 +ستين ال camphor اربعة و واحد وتسعينالنيترو بنزين + +841 +01:05:33,780 --> 01:05:38,900 +خمسة وأربعة وأشرين ال water point five one يعني + +842 +01:05:38,900 --> 01:05:43,480 +بلاحظش الزيادة في الميه بشكل كبير ممكن تلاحظها + +843 +01:05:43,480 --> 01:05:47,300 +أكتر في النيترو بنزين مثلا الزيادة في ال boiling + +844 +01:05:47,300 --> 01:05:49,400 +point ممكن تلاحظها أكتر في النيترو بنزين أو أكتر + +845 +01:05:49,400 --> 01:05:53,380 +في ال camphor أو أكتر في البنزين لكن الميه جليلة + +846 +01:05:53,380 --> 01:05:57,240 +الزيادة في ال boiling point تعتبر إيه شمالها قليلة + +847 +01:05:57,240 --> 01:06:02,480 +نسبيالكن بدي أذكر القانون delta Tb بتساوي ال Kb في + +848 +01:06:02,480 --> 01:06:06,800 +ال M نتطلع + +849 +01:06:06,800 --> 01:06:10,120 +على ال freezing point بنفس الصورة نتطلع على ال + +850 +01:06:10,120 --> 01:06:12,860 +freezing point بنفس الصورة بنقول the change in + +851 +01:06:12,860 --> 01:06:16,400 +freezing point can be found similarly delta Tf + +852 +01:06:16,400 --> 01:06:20,500 +بتساوي ال Kf في ال M حيث ال delta Tf اللي هي + +853 +01:06:20,500 --> 01:06:24,060 +depression in freezing point احفرجيكم ليش هي + +854 +01:06:24,060 --> 01:06:30,320 +depressiondepression النقص ال decrease KF المولال + +855 +01:06:30,320 --> 01:06:34,880 +freezing point depression constant of the solvent + +856 +01:06:34,880 --> 01:06:40,080 +لأن كل solvent فيه KF زي الكبير KF مختلف وال M هي + +857 +01:06:40,080 --> 01:06:45,620 +ال molality للمحلول فبنقول ال T freezing لل + +858 +01:06:45,620 --> 01:06:54,940 +solution بدها تساوي ال T normal T freezing normal + +859 +01:06:56,550 --> 01:07:06,030 +الدلتا تي اف بدنا نترحها + +860 +01:07:06,030 --> 01:07:11,790 +من ال + +861 +01:07:11,790 --> 01:07:19,910 +normal freezing point طيب الان هذا برضه بعض ال + +862 +01:07:19,910 --> 01:07:24,810 +solastic acid تلاتة و تلاتة و ستينالبرنامج البنزين + +863 +01:07:24,810 --> 01:07:32,610 +الـ KF Indy 5 و 7 و بدي اتقارنه يعني بين هذه القيم + +864 +01:07:32,610 --> 01:07:38,400 +اللي جابلها الكنفور 37 و 8 من 10يعني ال freezing + +865 +01:07:38,400 --> 01:07:41,320 +point depression ايش بيكون كتير كبير هذه اللي هو + +866 +01:07:41,320 --> 01:07:44,040 +انعكاس مهم لأنه هنستخدم ال freezing point + +867 +01:07:44,040 --> 01:07:46,940 +depression و ال boiling point elevation عشان نعمل + +868 +01:07:46,940 --> 01:07:50,920 +تحديد للموليكولار mass بعد شوية فبالتالي هذه القيم + +869 +01:07:50,920 --> 01:07:54,200 +كتير مهمة يعني لما نكون فيه عندي ايش زي الكفر بقدر + +870 +01:07:54,200 --> 01:07:57,490 +احصل علىالـ freezing point depression عالي جدا + +871 +01:07:57,490 --> 01:08:01,830 +وبالتالي بقدر أعين ال mass ال molecular mass بدقة + +872 +01:08:01,830 --> 01:08:07,410 +أكبر ال nitro benzene 6.78 ال water 1.86 لكن كلهم + +873 +01:08:07,410 --> 01:08:14,010 +أكبر من ال Kb كلهم يعني دائما ال freezing point + +874 +01:08:14,010 --> 01:08:18,350 +depression كقيمة أعلى من قيمة ال boiling point + +875 +01:08:18,350 --> 01:08:22,630 +elevation لكل ال solvents بقدر أشوف هذا الكلام + +876 +01:08:22,630 --> 01:08:23,950 +بالشكل التالي + +877 +01:08:26,920 --> 01:08:36,400 +أنا عندى هذا الشكل اللى هو ال freezing point هان + +878 +01:08:36,400 --> 01:08:40,160 +موجودة فى هذى المنطقة هذى ال normal freezing point + +879 +01:08:40,160 --> 01:08:43,660 +طبعا مادام هدى جلق وصارت هان ل triple point هدى + +880 +01:08:43,660 --> 01:08:48,100 +بدى يكمل بنفس الصورة فبلاحظ أنه عند واحد + +881 +01:08:48,100 --> 01:08:52,940 +atmosphere ال freezing point صارت فى المنطقة هادي + +882 +01:08:52,940 --> 01:08:57,170 +هانهذه الـ freezing point الجديدة معنى الكلام + +883 +01:08:57,170 --> 01:09:01,950 +انتقلت ال freezing point من هذه الحرارة إلى هذه + +884 +01:09:01,950 --> 01:09:06,130 +الحرارة يبقى صار في عندي decrease في ال freezing + +885 +01:09:06,130 --> 01:09:10,470 +point او بنقول عنه freezing point depression + +886 +01:09:10,470 --> 01:09:14,310 +freezing point depression ال delta TF بدها تساوي + +887 +01:09:15,990 --> 01:09:22,710 +الـ KF في المولالية طب نتطلع على يعني أمثلة سريعة + +888 +01:09:22,710 --> 01:09:26,670 +بيقول List the following aqueous solutions in + +889 +01:09:26,670 --> 01:09:30,210 +terms of their expected freezing point حاجة عندي + +890 +01:09:30,210 --> 01:09:34,290 +محليل مختلفة طب وين كل محلول أو بدنا نرتبهم بحسب + +891 +01:09:34,290 --> 01:09:37,850 +ال freezing point عندي 0.05 مولال كالسيوم الكلوريد + +892 +01:09:37,850 --> 01:09:40,390 +ليش قلت مولال لإن ال freezing point إيه دعوة + +893 +01:09:40,390 --> 01:09:46,310 +بالمولالية KF في إيش؟في الـMolality فـ 0.15 مولل + +894 +01:09:46,310 --> 01:09:52,430 +NaCl، 0.1 مولل HCl، 0.05 مولل Acetic Acid و 0.1 + +895 +01:09:52,430 --> 01:09:58,090 +مولل سوكروز بقول أنا بهمني في الـ freezing point + +896 +01:09:58,090 --> 01:10:00,870 +depression و elevation وكل الـcollegiate + +897 +01:10:00,870 --> 01:10:05,450 +properties عدد او الـ molality للمحلول الـ + +898 +01:10:05,450 --> 01:10:12,290 +molality هي عبارة عنلا تتوقف على نوع المادة بيهمني + +899 +01:10:12,290 --> 01:10:16,030 +عدد ال species عشان هيك مثلا ال calcium chloride + +900 +01:10:16,030 --> 01:10:20,770 +اه في calcium و 2 chloride تلاتة يبقى تلاتة في 0 + +901 +01:10:20,770 --> 01:10:26,330 +.15 أو 0.05 molar calcium او 0.1 molar chloride + +902 +01:10:26,330 --> 01:10:32,530 +يعني 0.15 ال NaCl 0.15 molar Na plus 0.15 molar اه + +903 +01:10:32,530 --> 01:10:40,850 +0.3الـ HCl 0.1 و 0.1 و 0.2 الاستكاسيد 0.05 لأنه + +904 +01:10:40,850 --> 01:10:46,490 +أسهل الإلكتروليت 0.05 السكراز لا يتفكك أصلا 0.1 زي + +905 +01:10:46,490 --> 01:10:51,750 +ما هو فبنلاحظ ببساطة كل ما بتزيد الـ morality الـ + +906 +01:10:51,750 --> 01:10:57,490 +delta TF بتزيد يعني الـ depression بيزيدفعشان هيك + +907 +01:10:57,490 --> 01:11:02,090 +مقدر اقول ان ال NACL هيكون فيه له ال lowest + +908 +01:11:02,090 --> 01:11:08,610 +freezing point بعده ال HCL لأنه تلاتة من عشرة ال + +909 +01:11:08,610 --> 01:11:14,390 +HCL اتنين من عشرة ال calcium chloride point one + +910 +01:11:14,390 --> 01:11:18,090 +five السكروز واحد من عشرة واخيرا ال acetic acid + +911 +01:11:18,090 --> 01:11:24,130 +point oh fiveطيب بيقول لي what's the freezing + +912 +01:11:24,130 --> 01:11:28,010 +point of a solution containing 478 gram of + +913 +01:11:28,010 --> 01:11:31,790 +ethylene glycolبستخدمهم في السيارات يقولون انها + +914 +01:11:31,790 --> 01:11:40,270 +كانتفريز in 3202 gram of water يعني دوبنا 478 gram + +915 +01:11:40,270 --> 01:11:44,750 +إترينيجلايكل في تلاتة كيلو شوية من الميه the molar + +916 +01:11:44,750 --> 01:11:48,150 +mass of ethylene glycol is 62.1 gram بقول على طول + +917 +01:11:48,150 --> 01:11:53,050 +delta TF بتساوي ال KF في ال M ال KF لل water 1.860 + +918 +01:11:53,050 --> 01:12:00,900 +.. عفوا 1.86 degree C per moleمول التي هي مول + +919 +01:12:00,900 --> 01:12:05,280 +التي؟ جال والله المول صليت على ال mass of solvent + +920 +01:12:05,280 --> 01:12:12,460 +بالكيلوجرام المول صليت 478 على الفورمولا ويت لال + +921 +01:12:12,460 --> 01:12:19,350 +إترينيجلايكلعلى كيلو جرام سولفان هو 241 دلتا TF KF + +922 +01:12:19,350 --> 01:12:25,170 +M 1.86 ديجري C يعني في 241 مطلع 48 مطلع 48 معناه + +923 +01:12:25,170 --> 01:12:30,790 +كلام الـ Delta TF TF Note minus TF أو بنجرده للـ + +924 +01:12:30,790 --> 01:12:34,190 +TF للمحلول TF Note اللي هي ال Normal minus Delta + +925 +01:12:34,190 --> 01:12:36,470 +TF يعني صفر اللي هو أصلا الميه + +926 +01:12:40,760 --> 01:12:46,060 +-4.48 يعني انت تقريبا سالب اربعة و نص ديجري سي راح + +927 +01:12:46,060 --> 01:12:51,320 +تتجمد الميه اخر مثال ناخده اليوم بتقول + +928 +01:12:51,320 --> 01:12:57,110 +الاثرينيجلايكل is a non volatile liquidUsed in + +929 +01:12:57,110 --> 01:13:01,250 +antifreeze water preparations الميه لازم تتجمد و + +930 +01:13:01,250 --> 01:13:04,590 +نحط عليها شوية إترانيجليكون بيقول calculate the + +931 +01:13:04,590 --> 01:13:08,810 +boiling point and freezing point of a 25 mass + +932 +01:13:08,810 --> 01:13:10,050 +percent solution + +933 +01:13:18,170 --> 01:13:23,270 +على طول 100 gram of solution نفس المنهج بقول 25 + +934 +01:13:23,270 --> 01:13:27,890 +gram of glycol and 75 gram ميه فورا لأن المحلول + +935 +01:13:27,890 --> 01:13:33,550 +كله 100 gramهو جل 25% إثرينيجلايكول، إذاً 25 جرام + +936 +01:13:33,550 --> 01:13:38,050 +إثرينيجلايكول و 75 جرام ماء، إذاً على طول مول + +937 +01:13:38,050 --> 01:13:42,690 +إثرينيجلايكول point four اللي هو الوزنة على ال + +938 +01:13:42,690 --> 01:13:46,950 +formula weight و الملالة للمحلول اللي هو ال moles + +939 +01:13:46,950 --> 01:13:51,210 +على ال kilogram solvent اللي هو الميه، بتطلع عندي + +940 +01:13:51,210 --> 01:13:56,520 +five point three seven ال delta TFكيف في ام الكيف + +941 +01:13:56,520 --> 01:14:00,340 +one point eight six في ام حسبناها five point three + +942 +01:14:00,340 --> 01:14:04,620 +seven بتطلع عشر درجات اذا معنى الكلام الميه راح + +943 +01:14:04,620 --> 01:14:10,280 +تتجمد in سالم عشرة صفر minus عشرة يعني minus عشرة + +944 +01:14:10,280 --> 01:14:14,020 +degree c therefore the freezing point of solution + +945 +01:14:14,020 --> 01:14:18,160 +is صفر minus عشرة minus عشرة degree c ال delta Tb + +946 +01:14:18,160 --> 01:14:23,880 +طيبنفس الطريقة الـ KB في الـ M الـ M حسبناها 5.37 + +947 +01:14:23,880 --> 01:14:29,360 +و الـ KB من الجدول 0.51 إذا ال boiling point + +948 +01:14:29,360 --> 01:14:35,740 +elevation 2.7 يبقى وقتاش الميه راح تغلي جال 100 ال + +949 +01:14:35,740 --> 01:14:41,700 +normal boiling point زائد 2 و 7 من 10 بطلع 102 و 7 + +950 +01:14:41,700 --> 01:14:43,820 +من 10 degrees C + +951 +01:14:46,690 --> 01:14:52,230 +بتهيأ لإنه كفاية اليوم ماعليش كانت الحسابات عندنا + +952 +01:14:52,230 --> 01:14:57,470 +كتيرة خالص ويعني بتفتح الرأس إلى حد ما وبدها + +953 +01:14:57,470 --> 01:15:02,110 +انتباه لكن الحصة الجاية فيها شرح أكتر فيها شوية + +954 +01:15:02,110 --> 01:15:05,930 +أمثل لكن فيها شرح أكتر فإذا الله رغبت بنشوفكم + +955 +01:15:05,930 --> 01:15:06,850 +الحصة الجاية + diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/K46ofvPrXxU_raw.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/K46ofvPrXxU_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..be5a3ea645d550c248b207b85acf365bbca8114a --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/K46ofvPrXxU_raw.srt @@ -0,0 +1,4232 @@ +1 +00:00:21,480 --> 00:00:24,500 +بسم الله الرحمن الرحيم إذا الله راضي اليوم بنبدأ + +2 +00:00:24,500 --> 00:00:28,680 +نتكلم عن chapter جديد بتحدث عن ال liquids و ال + +3 +00:00:28,680 --> 00:00:33,880 +intermolecular forces هنشوف بشكل أساسي في هذا ال + +4 +00:00:33,880 --> 00:00:39,100 +chapter إيش أنواع ال intermolecular forces و كيف + +5 +00:00:39,100 --> 00:00:44,220 +ال intermolecular forces بتأثر على خصائص ال + +6 +00:00:44,220 --> 00:00:49,250 +liquids تحديداً طبعاً هي كمان بتأثر على خصائصالـ + +7 +00:00:49,250 --> 00:00:52,690 +solids بشكل كبير لكن احنا هنتكلم فقط عن تأثيرها + +8 +00:00:52,690 --> 00:00:57,860 +على قصائص ال liquids اذا الله رادفي البداية خلاص + +9 +00:00:57,860 --> 00:01:03,380 +بس مراجعة سريعة يعني كنا بنتكلم عن three states of + +10 +00:01:03,380 --> 00:01:07,000 +matter كنا بنتكلم عن ال gases و عن ال liquids و عن + +11 +00:01:07,000 --> 00:01:12,900 +ال solids فال gases قلنا إنه هي اسيوم يعني بتاخد + +12 +00:01:12,900 --> 00:01:16,220 +both volume and shape of its container يعني الغاز + +13 +00:01:16,220 --> 00:01:21,640 +بيملي الوعى اللي هو موجود فيه مهما كان أيضا ال + +14 +00:01:21,640 --> 00:01:27,370 +gases expand to fill the containerإذا كان حطينا + +15 +00:01:27,370 --> 00:01:30,550 +غاز في container فهو راح يتمدد علشان لازم يمل ال + +16 +00:01:30,550 --> 00:01:34,390 +container لأنه في البداية قلنا assumes both volume + +17 +00:01:34,390 --> 00:01:38,570 +and shape of its container الغاز compressible + +18 +00:01:38,570 --> 00:01:45,290 +بينضغط flows readily diffusion within a gas occurs + +19 +00:01:45,290 --> 00:01:48,770 +rapidly يعني الغازات ال diffusion من خلالها بيحدث + +20 +00:01:48,770 --> 00:01:54,050 +بسرعة لأنه المسافات بينها واسعة كتيربالنسبة للـ + +21 +00:01:54,050 --> 00:01:57,230 +liquids طبعا assume shape of portion of container + +22 +00:01:57,230 --> 00:02:01,370 +it occupies بس فقط الحجم اللي هي موجودة فيه لكن + +23 +00:02:01,370 --> 00:02:06,510 +فوق يعني مافيش حاجة doesn't expand to fill its + +24 +00:02:06,510 --> 00:02:11,410 +container طبيعي بضالها جاعدة محلها ماتتمددش علشان + +25 +00:02:11,410 --> 00:02:16,310 +تشغل كل الحيز اللي موجود في ال container بشكل يعني + +26 +00:02:16,310 --> 00:02:21,210 +عام بنقولincompressible لا تنضغط يعني ان ضغطها + +27 +00:02:21,210 --> 00:02:25,010 +يكاد يكون معدوم او مهمل كمية قليلة جدا جدا لدرجة + +28 +00:02:25,010 --> 00:02:27,810 +نقول والله هي incompressible if it flows readily + +29 +00:02:27,810 --> 00:02:31,090 +نعم if it flows readily we can pour it ممكن انه + +30 +00:02:31,090 --> 00:02:35,710 +نصبها او كذا فبتنزل ف if it flows readily ال + +31 +00:02:35,710 --> 00:02:39,430 +diffusion من خلالها بيحدث لكنه بيحدث slowly يعني + +32 +00:02:39,430 --> 00:02:45,980 +لو انه في عندي مثلا ماءالكمية من الماء مثلا بحيرة + +33 +00:02:45,980 --> 00:02:49,000 +وكبّينا فيها اي pollutant نلاحظ ان ال pollutant + +34 +00:02:49,000 --> 00:02:53,520 +هذا نعم بينتقل لكن بده وقت طويل بينما لو اخد نفس + +35 +00:02:53,520 --> 00:02:57,340 +الكمية من غاز وحطينا فيها غاز اخر فبنلاحظ ان ال + +36 +00:02:57,340 --> 00:03:02,080 +diffusion بكون اسرع بكتيرالـ solids مش هنتكلم عنها + +37 +00:03:02,080 --> 00:03:05,300 +طبعا هي إلها شكلها الخاص بنحط ال solid بظله زي ما + +38 +00:03:05,300 --> 00:03:08,520 +هو مابياخدش حجم ال container اللي هو موجود فيه فهو + +39 +00:03:08,520 --> 00:03:13,340 +حجمه هو و شكله هو مش حجم شكل ال container لأ تمدد + +40 +00:03:13,340 --> 00:03:17,140 +طبعا incompressible بشكل أساسي does not flow لأ + +41 +00:03:17,140 --> 00:03:21,020 +كله بيوجع مرة واحدة يعني diffusion within a solid + +42 +00:03:21,020 --> 00:03:25,940 +occurs extremely slowly فهذه فرقات أساسية بين ال + +43 +00:03:25,940 --> 00:03:31,200 +states of matterأحنا بشكل أساسي متتمين بالـ liquid + +44 +00:03:31,200 --> 00:03:35,440 +state لأنه احنا اتكلمنا عن ال gases في المحاضرات + +45 +00:03:35,440 --> 00:03:38,900 +الماضية و ال solids ده لأسف كان فيها chapter لكن + +46 +00:03:38,900 --> 00:03:42,720 +عشان طبيعة المساق مش هنتكلم عنها فبس هنتكلم في هذا + +47 +00:03:42,720 --> 00:03:48,620 +ال chapter عن ال liquids بنقول + +48 +00:03:48,620 --> 00:03:52,160 +الفرق الأساسي بين ال states of matter التلاتة هو + +49 +00:03:52,160 --> 00:03:55,700 +المسافة بين الجزيئاتالمسافة بين الجزيئات، بنلاحظ + +50 +00:03:55,700 --> 00:04:00,260 +أن المسافة بين جزيئات الغاز كبيرة جدا وبنلاحظ + +51 +00:04:00,260 --> 00:04:03,860 +المسافة بين جزيئات ال liquid أقل كتير بشكل ملحوظ + +52 +00:04:03,860 --> 00:04:08,140 +والمسافة بين جزيئات ال solids بتكون يعني أقل ما + +53 +00:04:08,140 --> 00:04:13,060 +يمكن قليلة جدا جدا وبالتالي هذا هو اللي بيحدد إيش + +54 +00:04:13,060 --> 00:04:16,320 +يعني إيش المادة تكون عندي هل تكون gas أو تكون + +55 +00:04:16,320 --> 00:04:22,960 +liquid أو تكون solidفال distance between particles + +56 +00:04:22,960 --> 00:04:27,360 +decreases بتقل when going from gas to liquid to + +57 +00:04:27,360 --> 00:04:31,720 +solid طبعا ال gas زي ما شوفنا بيملأ حجم ال + +58 +00:04:31,720 --> 00:04:35,520 +container اللي هو موجود فيه ال liquid بس بياخد + +59 +00:04:35,520 --> 00:04:39,420 +الجزء فقط اللي بيشغله بدون حاجة ال solid بيكون + +60 +00:04:39,420 --> 00:04:44,360 +intact solid والمسافات واضحة بالنسبة لنا هذا gas + +61 +00:04:44,360 --> 00:04:46,600 +هذا liquid هذا solid مثلا يعني + +62 +00:04:49,320 --> 00:04:53,840 +بنلاحظ كمان أنه الغازات يعني ال disorder بيكون + +63 +00:04:53,840 --> 00:04:58,170 +فيها عالي جداليه؟ لأن الغازات جزيئات تتحرك بسرعة + +64 +00:04:58,170 --> 00:05:01,610 +كبيرة خالص واتكلمنا عن الـ mean free path الأعمال + +65 +00:05:01,610 --> 00:05:06,770 +بتتحرك يعني بشكل عشوائي random motion فبنلاحظ أن + +66 +00:05:06,770 --> 00:05:10,110 +ال disorder بيكون عنا كبير ال liquids ال disorder + +67 +00:05:10,110 --> 00:05:14,990 +موجود لكنه مش جد ال gases بينما ال crystalline + +68 +00:05:14,990 --> 00:05:21,210 +solids عادة بتكون خليني أقول ال arrangements أو ال + +69 +00:05:21,210 --> 00:05:27,440 +order بيكون highly orderedطلعوا كيف يعني انتظام + +70 +00:05:27,440 --> 00:05:33,620 +بشكل كبير للغاية فهذا برضه مقش منلحظه ايضا في + +71 +00:05:33,620 --> 00:05:41,140 +خاصية لل .. لل liquids عموما بنقول انه اذا كان + +72 +00:05:41,140 --> 00:05:44,640 +يعني و هذا كلام منلحظه كتير يعني لو كان في وعى + +73 +00:05:44,640 --> 00:05:48,720 +موجود فيه wax او زيت اتره يعني وحطينا فيه ميه + +74 +00:05:48,720 --> 00:05:53,460 +باللحظة ان الميه ايه بتتكور بتفردشتتكوّر وتفرج + +75 +00:05:53,460 --> 00:05:57,540 +يعني في عندنا قوة + +76 +00:05:57,540 --> 00:06:02,140 +تجاذب بين جزيئات الميّه أكبر من قوة التجاذب مع + +77 +00:06:02,140 --> 00:06:04,500 +السطح اللي هي موجودة عليه بالذات لما يكون السطح + +78 +00:06:04,500 --> 00:06:13,340 +waxed يعني في عليه شوية wax احنا + +79 +00:06:13,340 --> 00:06:19,370 +عموما هنقول ان ال liquids وال solidsبدنا نقول لأن + +80 +00:06:19,370 --> 00:06:23,430 +جزيئتها متقاربة جدا من بعضها البعض بدنا نقول عنها + +81 +00:06:23,430 --> 00:06:28,590 +condensed phases، condensed phases، كويس؟ phase هو + +82 +00:06:28,590 --> 00:06:32,130 +عبارة عن يعني جزء من ال system homogeneous، جزء + +83 +00:06:32,130 --> 00:06:37,890 +homogeneous من ال systemبيتميز بخصائص معينة فهذه + +84 +00:06:37,890 --> 00:06:41,550 +لأن الجزيئات متقاربة جدا بدنا نسميها condensed + +85 +00:06:41,550 --> 00:06:46,430 +فإذا كان عندي liquid phase فهو condensed liquid + +86 +00:06:46,430 --> 00:06:49,110 +phase وإذا كان عندي solid برضه condensed solid + +87 +00:06:49,110 --> 00:06:52,050 +phase ماقراش الصورة اللي حوالها هذه droplets من + +88 +00:06:52,050 --> 00:06:57,030 +الميه مثلا بنلاحظ أنها كلها بتتكور وهذه أيضا اللي + +89 +00:06:57,030 --> 00:07:01,530 +شفناها سابقا هذه droplet من الميهعلى ورقة نبات + +90 +00:07:01,530 --> 00:07:05,810 +معين كاره للماء الورقة نفسها سطحها كاره للماء + +91 +00:07:05,810 --> 00:07:12,250 +فبنلاحظ انها ايه تاخد الشكل الكراوي اه .. يمكن اه + +92 +00:07:12,250 --> 00:07:16,870 +هذه هيك مبينةأكتر بالنسبة لنا و يمكن هذا بنلاحظه + +93 +00:07:16,870 --> 00:07:22,070 +إذا كان بنغسل سيارة أو بنغسل بعض الأطباق يعني إذا + +94 +00:07:22,070 --> 00:07:26,870 +اللي قاترها مثلا زيت بنلاحظ أنه النقاط بتكون عليها + +95 +00:07:26,870 --> 00:07:30,270 +مكورة بينما تغسل بالصبون و تكون ممتازة اه مافيش + +96 +00:07:30,270 --> 00:07:33,310 +ميه بتلزج عليها بتكون سهل جدا طيب + +97 +00:07:36,570 --> 00:07:40,930 +الـ states of matter برضه كمان لها علاقة بخاصيتين + +98 +00:07:40,930 --> 00:07:46,930 +متضادتين، هل المادة liquid ولا المادة solid؟ ولّا + +99 +00:07:46,930 --> 00:07:52,330 +جاز؟ لها علاقة بخاصيتين متضادتين، بنقولهم + +100 +00:07:52,330 --> 00:07:53,810 +antagonistic + +101 +00:08:00,960 --> 00:08:03,720 +العامل الأول هو الـ kinetic energy of the + +102 +00:08:03,720 --> 00:08:07,160 +particles المكونة له الجاز أو الليكود أو الصليد + +103 +00:08:07,160 --> 00:08:10,320 +طبعا كل ما كانت ال kinetic energy كبيرة بروح ناحية + +104 +00:08:10,320 --> 00:08:10,800 +الجاز + +105 +00:08:14,950 --> 00:08:22,310 +الحاجة التانية هي قوة + +106 +00:08:22,310 --> 00:08:26,050 +قوة التجاذب بين الجزيئات، كل ما كانت قوة التجاذب + +107 +00:08:26,050 --> 00:08:30,740 +كبيرةأه بيبطل غاز بيروح من غاز ده liquid من liquid + +108 +00:08:30,740 --> 00:08:35,840 +ل solid فهذا بيعتمد على خاصيتين متضادتين أو عاملين + +109 +00:08:35,840 --> 00:08:40,280 +متضادين ال kinetic energy وأيضا في نفس الوقت جداش + +110 +00:08:40,280 --> 00:08:44,140 +قوة الترابط بين الجزئة طبعا بالنسبة للغازات + +111 +00:08:44,140 --> 00:08:50,190 +المثالية اعتبرنا حسب الال .. ال molecular .. ال + +112 +00:08:50,190 --> 00:08:52,930 +kinetic molecular theory عندي اعتبرنا انه ال + +113 +00:08:52,930 --> 00:08:57,010 +attractions between gas molecules negligible مش + +114 +00:08:57,010 --> 00:09:00,950 +موجودة عشان نتخيل انه الغازات فيش عندي attractions + +115 +00:09:00,950 --> 00:09:04,330 +لو في عندي attractions كتير كان كانت liquids و لو + +116 +00:09:04,330 --> 00:09:07,310 +كان attractions أكتر كانت solids فاحنا في النظرية + +117 +00:09:07,310 --> 00:09:11,310 +الحركية للغازات اعتبرنا انه ال .. اه ال attraction + +118 +00:09:11,310 --> 00:09:16,380 +forces between gas molecules are negligibleالان + +119 +00:09:16,380 --> 00:09:19,520 +علشان نستوعب الكلام اللى بدنا نقوله في الـ + +120 +00:09:19,520 --> 00:09:24,500 +Intermolecular forces بشكل كويس لابد الا انه نتحدث + +121 +00:09:24,500 --> 00:09:33,000 +يعني خليني اقول بنوع من التبسيط عن خاصية من خصائص + +122 +00:09:33,000 --> 00:09:38,550 +الذراتهذه الخاصية الـ Electronegativity للأسف كانت + +123 +00:09:38,550 --> 00:09:44,190 +مشروحة أن في chapter منفصل هي وحصائص أخرى عشان + +124 +00:09:44,190 --> 00:09:48,010 +نبين حصائص العناصر في الجدول الدوري لكن احنا + +125 +00:09:48,010 --> 00:09:50,590 +ماخدناش هذا ال chapter أو هذا ال chapter مش من + +126 +00:09:50,590 --> 00:09:54,070 +الشباتل المحررة معانا فيههذا الفصل علشان هيك بس + +127 +00:09:54,070 --> 00:09:58,110 +انا هقول ما يهمنا بشكل عام فيما يتعلق بالـ + +128 +00:09:58,110 --> 00:10:01,270 +Intermolecular Forces فهتكلم عن مفهوم الـ + +129 +00:10:01,270 --> 00:10:05,870 +Electronegativity خليني اقول ببساطة شديدة جدا ال + +130 +00:10:05,870 --> 00:10:09,990 +.. ال Electronegativity ما هي اللي يعني تعبير عن + +131 +00:10:09,990 --> 00:10:14,910 +ال .. يعني ال sharing of electrons تعبير عن ال + +132 +00:10:14,910 --> 00:10:18,090 +sharing of electrons رايح جهة مين في ال chemical + +133 +00:10:18,090 --> 00:10:21,760 +bond في عنده إلكتروناتالكميكال بوند هي عبارة عن + +134 +00:10:21,760 --> 00:10:25,200 +إلكترونات، مش هيك؟ الكميكال بوند الرابطة هي عبارة + +135 +00:10:25,200 --> 00:10:29,380 +عن إلكترونات، إلكترونين، ماشي؟ إلكترونين، طب هدول + +136 +00:10:29,380 --> 00:10:33,540 +الإلكترونين هل بيكونوا shared equally between + +137 +00:10:33,540 --> 00:10:38,480 +atoms؟ في عندى two atoms مربطين بإيه؟ برابطة، هل + +138 +00:10:38,480 --> 00:10:44,820 +الإلكترونات هذه بتكون shared؟ مشاركة؟ متشاركة؟بشكل + +139 +00:10:44,820 --> 00:10:48,820 +متساوى بين الذرتين ولا لا؟ ولا في ذرة مثلا بتحب + +140 +00:10:48,820 --> 00:10:51,140 +الإلكترونات أكتر من الأخرى فبتاخد .. بتشد + +141 +00:10:51,140 --> 00:10:55,780 +الإلكترونات ناحيتها شوية؟ ال .. ال .. الـ + +142 +00:10:55,780 --> 00:10:59,840 +electronegativity للـ atoms هي عبارة أو يعني ممكن + +143 +00:10:59,840 --> 00:11:06,560 +نقول هي مدى رغبة الذرة في جاذب الإلكترونات ناحيتها + +144 +00:11:07,250 --> 00:11:10,490 +Electronegativity هي عبارة عن رغبة الذرّة في جذب + +145 +00:11:10,490 --> 00:11:13,470 +الإلكترونات نحوها، يعني تصير more negative، يعني + +146 +00:11:13,470 --> 00:11:16,230 +على سبيل المثال في الجدول الدوري، كلنا بنعرف إن + +147 +00:11:16,230 --> 00:11:19,510 +مجموعة الهالوجينات بتحب تاخد إلكترون عشان إيش + +148 +00:11:19,510 --> 00:11:22,370 +تسوي؟ أه تروح للـ noble gas structure، وها نفس + +149 +00:11:22,370 --> 00:11:26,190 +الكلام، يعني إنها رغبتها في إنها تاخد إلكترون مدى + +150 +00:11:26,190 --> 00:11:29,470 +رغبتها في اكتساب إلكترونات، هذا بعبر عن + +151 +00:11:29,470 --> 00:11:33,330 +الـElectronegativity، لا إلاتمام؟ إذا لما نكون في + +152 +00:11:33,330 --> 00:11:36,770 +عندي ذرّة بترغب في اكتساب الإلكترونات أكتر من + +153 +00:11:36,770 --> 00:11:41,630 +الأخرى، الإلكترونات وين هتكون؟ هتكون أقرب إلى + +154 +00:11:41,630 --> 00:11:47,230 +الذرّة المحبة للاكتساب الإلكترونات، بنقول في هذه + +155 +00:11:47,230 --> 00:11:51,850 +الحالة الـ electronegativity لهذه الذرّةأعلى ال + +156 +00:11:51,850 --> 00:11:54,550 +electronegativity لهذه الذراع لكلورين لبرومين + +157 +00:11:54,550 --> 00:11:57,770 +لفلورين الايودين هذه الذراعات موجودة مثلا في آخر + +158 +00:11:57,770 --> 00:12:00,590 +الجدول الدوري بتحب تكتسب إلكترونات فالها high + +159 +00:12:00,590 --> 00:12:05,150 +electronegativity عكسها مثلا عكسها خالص وبنتكلم مش + +160 +00:12:05,150 --> 00:12:08,470 +عنه هان كتير اللي هو لو كان من المجموعة الأولى + +161 +00:12:08,470 --> 00:12:12,730 +المجموعة الأولى بتحب تكتسب إلكترونات لأ إذابنقدر + +162 +00:12:12,730 --> 00:12:16,730 +نقول إن الـ Electronegativity إلها قليلة جدا، الـ + +163 +00:12:16,730 --> 00:12:18,590 +Electronegativity إلها قليلة، بالعكس هي + +164 +00:12:18,590 --> 00:12:21,910 +Electropositive مش Electronegative، آه، يعني لو + +165 +00:12:21,910 --> 00:12:24,490 +كان فيها إلينا إلكترونات، مش هتحب تاخد إلكترونة، + +166 +00:12:24,490 --> 00:12:27,550 +هتحب إنها تعطي إلكترونة، إلكترونة positive، بينما + +167 +00:12:27,550 --> 00:12:31,810 +المجموعات أو العناصر اللي على يمين الجدول الدوري، + +168 +00:12:31,810 --> 00:12:34,750 +اللي هي الـnon-metals تحديدًا، بتحب تكتسب + +169 +00:12:34,750 --> 00:12:39,570 +إلكترونات، وبالتالي إلها Electronegativity أعلىفلو + +170 +00:12:39,570 --> 00:12:45,050 +طلعنا مثلا على ال HCl هي الـ H ذرة فيها بس إلكترون + +171 +00:12:45,050 --> 00:12:50,650 +واحد والـ Cl ذرة فيها سبع إلكترونات بعملوا رابطة H + +172 +00:12:50,650 --> 00:12:54,350 +وهي إلكترونين وهي Cl صار حوالين الـ Cl تمانية + +173 +00:12:54,350 --> 00:12:59,510 +حوالين الـ H تين تين طيب بنقول هل هدول الإلكترونين + +174 +00:12:59,990 --> 00:13:04,030 +هيكون متواجدين في النص بالظبط يعني معنى الكلام ان + +175 +00:13:04,030 --> 00:13:09,210 +الهيدروجين بيستمتع بالاتنين الالكترون او نصهم و ال + +176 +00:13:09,210 --> 00:13:13,690 +CL بتستمتع بالاتنين الالكترون او نصهم تماما بشكل + +177 +00:13:13,690 --> 00:13:17,050 +متساوي بنقول في الحقيقة لأ لإيه لأن الchlorine + +178 +00:13:17,050 --> 00:13:20,890 +بتحب الالكترونات بتحب تكتسب الالكترونات وبالتالي + +179 +00:13:20,890 --> 00:13:26,090 +بتكون جاذبها للالكترونات اكتر جاذبها للالكترونات + +180 +00:13:26,090 --> 00:13:28,770 +اكتر ومعنى الكلام هيصير عليها partial negative + +181 +00:13:30,490 --> 00:13:34,310 +بينما في نفس الوقت مدام الإلكترونيات ابتعدوا عن + +182 +00:13:34,310 --> 00:13:37,770 +الهيدروجين الهيدروجين حيصير عليه ايه partial + +183 +00:13:37,770 --> 00:13:43,850 +partial positive جزء positive جزء بنسمي هذا الشكل + +184 +00:13:43,850 --> 00:13:48,970 +بنقوله dipole دايبول لإنه صار عنده موجة بسالب هذا + +185 +00:13:48,970 --> 00:13:53,370 +بنسميه دايبول واحنا بنرمزه يعني بالرمز يعني حاجة + +186 +00:13:53,370 --> 00:14:01,600 +زي هيك و الوحدة تبعته ديبايكداش قيمة الـ dipole دي + +187 +00:14:01,600 --> 00:14:04,920 +باي كل ما زاد الـ dipole كل ما كان الـ unequal + +188 +00:14:04,920 --> 00:14:09,800 +sharing أكتر كل ما كان الـ unequal واحدة أه واحدة + +189 +00:14:09,800 --> 00:14:14,760 +قياس الـ dipole أنا بقول مدام في عندي polarization + +190 +00:14:14,760 --> 00:14:19,540 +يعني خليني أقول أو يعني صار في عندي جذب للإلكرونات + +191 +00:14:19,540 --> 00:14:23,920 +أكتر بوسط ال more electronegative أتم معنى كلام + +192 +00:14:23,920 --> 00:14:27,020 +بتكون عند الـ dipole الـ dipole هذا الوحدة تبعته + +193 +00:14:27,020 --> 00:14:33,250 +دي باي أو Dهذا الـ D كل ما زادت معناته في عندي + +194 +00:14:33,250 --> 00:14:37,170 +unequal sharing أكبر في عندي ال partial negative و + +195 +00:14:37,170 --> 00:14:42,130 +ال partial positive أكبر كل ما زادت قيمة ال D + +196 +00:14:48,250 --> 00:14:51,930 +يبقى أنا بشكل أساسي بدي أطلع على ال bond يعني عشان + +197 +00:14:51,930 --> 00:14:54,670 +أطلع على ال bond بدي أطلع على ال two atoms + +198 +00:14:54,670 --> 00:14:59,430 +المرتبطين بال bond هذه يبقى حددت تقريبا إيش يعني + +199 +00:14:59,430 --> 00:15:03,690 +مفهوم ال electronegativity الآن من الجدول الدوري + +200 +00:15:03,690 --> 00:15:07,230 +بدنا نعرف إنه ال electronegativity بتزيد بهذا + +201 +00:15:07,230 --> 00:15:10,450 +الشكل يعني هنا شايفين مثلا اتنين اتنين و نص تلاتة + +202 +00:15:10,450 --> 00:15:12,850 +تلاتة و نص اربعة هذه القيمة الفلورين بياخد أعلى + +203 +00:15:12,850 --> 00:15:17,730 +قيمةكويس؟ لاحظوا معايا و احنا ماشيين خلال ال + +204 +00:15:17,730 --> 00:15:21,430 +period رايحين ناحية ال ايه؟ ناحية ال noble gases + +205 +00:15:21,430 --> 00:15:25,290 +ايش بحصل لل electronegativity لل atoms؟ قال بتزيد + +206 +00:15:25,290 --> 00:15:30,150 +طيب و احنا طالعين من تحت لفوق قال برضه بتزيد بس + +207 +00:15:30,150 --> 00:15:34,160 +بنذكر هذا المفهومبتنذكر هذا المفهوم يعني و احنا + +208 +00:15:34,160 --> 00:15:37,700 +ماشيين في ال group في ال period a بتزيد لليمين و + +209 +00:15:37,700 --> 00:15:41,260 +احنا ماشيين في ال group جال بتزيد لأعلى يعني + +210 +00:15:41,260 --> 00:15:44,280 +التنتين بيودوا اين؟ على الفلورين اذا كانوا انتوا + +211 +00:15:44,280 --> 00:15:47,780 +ملاحظين التنتين بيودوا على الفلورين الان برضه كمان + +212 +00:15:47,780 --> 00:15:51,480 +ما يهمني كل ما ابعاد يتياه اللي في عند رابط بين ال + +213 +00:15:51,480 --> 00:16:00,760 +F و ال C ال F و ال N ال O و ال C ال C و ال Nكل ما + +214 +00:16:00,760 --> 00:16:06,260 +بعدنا في + +215 +00:16:06,260 --> 00:16:11,080 +العناصر فرق الـ electronegativity أشماله بيزيد فرق + +216 +00:16:11,080 --> 00:16:14,740 +ال electronegativity مثلا ال F لل C واحد و نص + +217 +00:16:14,740 --> 00:16:22,100 +بينما ال F لل O نص كل ما زاد معناته ال bold + +218 +00:16:22,100 --> 00:16:27,840 +polarity بتزيديبقى الـD بيزيد لأن الـCharges بتزيد + +219 +00:16:27,840 --> 00:16:32,020 +كل ما زادت المسافة أو الفرق يعني ابتعاد العناصر عن + +220 +00:16:32,020 --> 00:16:35,740 +بعضها البعض ونفس الكلام لو اجينا وقولنا والله هدول + +221 +00:16:35,740 --> 00:16:46,300 +اتنين تكون رابطة FI او IF ومثلا هذا وهذا ال F ال + +222 +00:16:46,300 --> 00:16:50,990 +CLFبنلاحظ أنه كل ما ابتعدوا عن بعض في نفس الـ A في + +223 +00:16:50,990 --> 00:16:54,210 +نفس ال group كل ما ابتعدوا عن بعض كل ما كان ال + +224 +00:16:54,210 --> 00:16:58,470 +bond polarity أكبر يعني فرق ال electronegatives + +225 +00:16:58,470 --> 00:17:02,910 +بدو يكون أكبرلو أخدنا هذا الكلام بحين الاعتبار + +226 +00:17:02,910 --> 00:17:06,650 +بحلللي مشاكل كتير في الحقيقة أثناء شغلي في هذا ال + +227 +00:17:06,650 --> 00:17:10,010 +chapter و لازم أحذركم أنه مش زي الشباتر الماضية + +228 +00:17:10,010 --> 00:17:14,050 +كتير من المسائل متعلقة بهذا الكلام مش هنقدر نحلها + +229 +00:17:14,050 --> 00:17:16,870 +من آخر ال chapter فما نداجش من هذا الكلام ليه؟ + +230 +00:17:16,870 --> 00:17:19,950 +لأنه تعتمد على مثلا شكل الجزيئة وغيره مش هنتكلم + +231 +00:17:19,950 --> 00:17:23,610 +عنه لأنه هذا موضوع طويل و مغطب بشباتر ماضية ما + +232 +00:17:23,610 --> 00:17:27,500 +اتحدثناش عنهافاحنا بس بدنا ناخد معايا هم فيما + +233 +00:17:27,500 --> 00:17:32,300 +يتعلق بالـ Intermolecular forces بشكل عام طيب نيجي + +234 +00:17:32,300 --> 00:17:35,620 +نطلع بنقول الـ Electronegativity value as + +235 +00:17:35,620 --> 00:17:39,040 +pertinent to scope discussed here بس فيما يتعلق + +236 +00:17:39,040 --> 00:17:41,860 +بطبيعة الموضوع اللي حنتكلم عنه هان إيه اللي + +237 +00:17:41,860 --> 00:17:46,400 +هالخصائص التالية ال Electronegativity إيش بالسوقال + +238 +00:17:46,400 --> 00:17:49,340 +indicates the attraction of an atom for shared + +239 +00:17:49,340 --> 00:17:57,660 +electrons بتعبر عن جذب الاتم لإيه؟للإلكترونات اللي + +240 +00:17:57,660 --> 00:18:01,120 +في الرابطة جداش جذب الإلكترون الإلكترون ده + +241 +00:18:01,120 --> 00:18:04,200 +الإلكترون اللي في الرابط بقول ال electronegativity + +242 +00:18:04,200 --> 00:18:08,600 +increases from left to right going across a period + +243 +00:18:08,600 --> 00:18:13,780 +on the periodic table وطبعا كمان from bottom to + +244 +00:18:13,780 --> 00:18:18,330 +topis low for the metals طب الأولى electropositive + +245 +00:18:18,330 --> 00:18:21,610 +metals بتحبش الإلكترونات metals are usually + +246 +00:18:21,610 --> 00:18:25,870 +electropositive and form ionic bonds بداش ننسى ال + +247 +00:18:25,870 --> 00:18:29,730 +metals إيش بتكون مهما كان وين بنشوف metal إيش + +248 +00:18:29,730 --> 00:18:33,470 +الرابطة تبعته Ionic انتهينا وين بنشوف metal إيش + +249 +00:18:33,470 --> 00:18:39,870 +رابطته Ionic طيب through a period bond polarity + +250 +00:18:39,870 --> 00:18:43,230 +increases towards right نفس الكوافق من اللي فوق ال + +251 +00:18:43,230 --> 00:18:48,700 +bond polarityبتزيد و احنا رايحين على اليمين + +252 +00:18:48,700 --> 00:18:53,940 +towards right nonmetal الى ال nonmetal اللي على + +253 +00:18:53,940 --> 00:18:57,580 +اليمين as the distance between nonmetals increases + +254 +00:18:57,580 --> 00:19:01,280 +كل ما زادت المسافة between ال nonmetals بتروح ال + +255 +00:19:01,280 --> 00:19:04,880 +bond بولارة ناحية مين ال nonmetal اللي على اليمين + +256 +00:19:04,880 --> 00:19:09,370 +..قولنا هذا الكلام طيب through a groupBond + +257 +00:19:09,370 --> 00:19:13,470 +polarity increases towards upper nonmetal خلال + +258 +00:19:13,470 --> 00:19:17,830 +الجروب كويس؟ أه بتروح الـ bond polarity لحجة المتل + +259 +00:19:17,830 --> 00:19:22,830 +الأعلى as distance between the two nonmetals + +260 +00:19:22,830 --> 00:19:26,730 +المكونين للرابطة increases هذه خصائص + +261 +00:19:26,730 --> 00:19:30,430 +الالكترونيكتفة حلوة كتير لو عرفناها بتساعدنا بشكل + +262 +00:19:30,430 --> 00:19:36,710 +كبير خالص في حل المسائلبنقول مثلا في عندي خلّيني + +263 +00:19:36,710 --> 00:19:40,670 +أقول بشكل أساسي نوعين من أنواع الروابط التساهمية + +264 +00:19:40,670 --> 00:19:44,550 +لأنه أنا عندي الـnon-metals اللي بتكلم عنهم الرابط + +265 +00:19:44,550 --> 00:19:47,680 +بينهم التساهمية وهذه اللي بتكلم عنهاالرابط + +266 +00:19:47,680 --> 00:19:50,640 +الساهمية فبقول فيه نوعين يا اما بتكون non polar + +267 +00:19:50,640 --> 00:19:54,740 +covalent يا بتكون polar covalent و اگتش بتكون non + +268 +00:19:54,740 --> 00:19:58,180 +polar covalent لمن يكون فيش عنده فرق في ال ايه في + +269 +00:19:58,180 --> 00:20:00,840 +ال electronegativity non polar طب و اگتش بتكون + +270 +00:20:00,840 --> 00:20:03,140 +polar covalent لمن يكون عنده فرق في ال + +271 +00:20:03,140 --> 00:20:06,900 +electronegativities الفرق هذا تقريبا بنقول اكتر من + +272 +00:20:06,900 --> 00:20:10,100 +اربعة من عشرة ماعلينا بدناش نحفظه بدناش نحفظه + +273 +00:20:10,100 --> 00:20:15,800 +فبقول ال non polar covalent هي عبارةOccurs between + +274 +00:20:15,800 --> 00:20:18,360 +non-metals؟ طبعاً، باتكلمش عن الـmetals، الـmetals + +275 +00:20:18,360 --> 00:20:21,580 +ايونيك بونز، باتكلمش عنها، فبتكلم بس عن الـnon + +276 +00:20:21,580 --> 00:20:24,440 +-metals، بقول occurs between non-metals؟ طبعا، + +277 +00:20:24,440 --> 00:20:27,680 +between non-metals، لأنه الـnon-metals هي اللي + +278 +00:20:27,680 --> 00:20:32,800 +بتعطيني covalent bondsis an equal or almost equal + +279 +00:20:32,800 --> 00:20:36,380 +sharing of electrons اه عشان هيك نان بولر فاش عندى + +280 +00:20:36,380 --> 00:20:39,680 +dipole فى اتجاه معين نان بولر يعنى ال + +281 +00:20:39,680 --> 00:20:43,160 +electronegative للذرة الأولى تقريبا بتساوي ال + +282 +00:20:43,160 --> 00:20:46,160 +electronegative للذرة التانية إجراب على بعض كتير + +283 +00:20:46,160 --> 00:20:52,360 +هيكونه مش هيكون بعاد تمام فممكن يكون من نفس النوع + +284 +00:20:52,360 --> 00:21:02,970 +زى ايش مثلا CL وCL CL2 هذه هي CLوCL H2 H OH نون + +285 +00:21:02,970 --> 00:21:09,770 +بولر نون بولر كوفيلاند زي بعض بالظبط طيب has + +286 +00:21:09,770 --> 00:21:14,510 +almost no electronegativity difference بقى بيقولنا + +287 +00:21:14,510 --> 00:21:20,470 +بداش نحفظ هذا الكلام أمثل عليها NN N2 طبعاالـ CLPR + +288 +00:21:20,470 --> 00:21:24,310 +إجراب على بعض إذا كنتم لاحظين إجراب على بعض الـ CL + +289 +00:21:24,310 --> 00:21:27,930 +فوق الـ PR على طول إجراب على بعض الـ C و الـ H + +290 +00:21:27,930 --> 00:21:30,310 +لازم نعرفها هذا الـ C و الـ H هي الـ non polar على + +291 +00:21:30,310 --> 00:21:34,990 +طول الـ C و الـ H كل ال carbon hydrogen atoms + +292 +00:21:34,990 --> 00:21:42,440 +bonds هي عبارة عن non polar covalent bondsفإذا كان + +293 +00:21:42,440 --> 00:21:48,340 +الجزيء والله هو المتكون homonuclear diatomic يعني + +294 +00:21:48,340 --> 00:21:55,140 +نفس العنصر فهذا طبعا يعني non polar covalentإذا + +295 +00:21:55,140 --> 00:21:59,280 +كان العنصر .. إذا كان الـ bond هي عبارة عن C و H، + +296 +00:21:59,280 --> 00:22:02,820 +non-polar covalent، أي اتنين اجراب جدا على بعض، + +297 +00:22:02,820 --> 00:22:07,740 +ممكن يعني .. بشكل عام يعني معرفتي في الـ + +298 +00:22:07,740 --> 00:22:10,580 +electronegativity values بتساعدني لأنه ممكن يكون + +299 +00:22:10,580 --> 00:22:12,840 +في بعض الأحيان polar، في بعض الأحيان non-polar + +300 +00:22:13,700 --> 00:22:17,600 +نتكلم عن النوع التاني لل .. لل covalent bonds + +301 +00:22:17,600 --> 00:22:21,220 +فبقول والله polar covalent bond .. polar covalent + +302 +00:22:21,220 --> 00:22:24,360 +bond ال polar covalent bond that occurs between + +303 +00:22:24,360 --> 00:22:27,820 +nonmetal .. طبعا لازم nonmetal atoms لأن covalent + +304 +00:22:27,820 --> 00:22:33,600 +is an equal .. is an unequal sharing of electrons + +305 +00:22:33,600 --> 00:22:36,600 +آه عدم تساوي في مشاركة الإلكترونات + +306 +00:22:40,800 --> 00:22:43,900 +الذرّة اللي بتكون more electronegative بتجذب + +307 +00:22:43,900 --> 00:22:47,600 +الإلكترونات ناحيتها وبالتالي بتعمل dipole وبالتالي + +308 +00:22:47,600 --> 00:22:51,980 +بتعمل dipole بتعمل bond polarity الإلكترونات بتروح + +309 +00:22:51,980 --> 00:22:55,540 +عليها على ناحية has moderate electronegativity + +310 +00:22:55,540 --> 00:22:58,700 +difference من 5 إلى 11 مش هيتكلم عن ال values لإن + +311 +00:22:58,700 --> 00:23:03,370 +هذا بتطلب أن يكون عندي جدول وإحنا بدناش نحفظهفعلى + +312 +00:23:03,370 --> 00:23:08,970 +سبيل المثال لو قلنا ال P و ال CL يعني بس عشان + +313 +00:23:08,970 --> 00:23:13,650 +افرجيكم اياه يعني هاي ال P و هاي ال CL في period + +314 +00:23:13,650 --> 00:23:21,490 +اه بعيدة هذه polar ال .. ال C و ال F ابعاد polar + +315 +00:23:21,490 --> 00:23:29,630 +لحيط ال F مثلا ال .. ال .. ال .. قلنا ال I و ال F + +316 +00:23:30,460 --> 00:23:36,800 +الـ I و ال F بولر، ال PR و ال F حلوة برضه، بولر و + +317 +00:23:36,800 --> 00:23:41,660 +هكذافبدي العناصر تكون بعيدة شوية عن بعضها البعض + +318 +00:23:41,660 --> 00:23:46,260 +سواء في الدورة أو في المجموعة ساعتها بكون متأكد + +319 +00:23:46,260 --> 00:23:53,440 +انه ال .. ال .. ال .. خليني أقول ال bond polar + +320 +00:23:53,440 --> 00:23:59,600 +ليه؟ لأن ال electronegativity للذرة الأبعد يكوين + +321 +00:23:59,600 --> 00:24:03,200 +سواء up ولا على اليمين بتكون ال electronegativity + +322 +00:24:03,200 --> 00:24:07,040 +لها أعلى وبالتاني ال bond polarity بتكون موجودة + +323 +00:24:09,430 --> 00:24:16,310 +فهذه الـ XH الـ H لما نكون مربوطة ب F أو مربوطة ب + +324 +00:24:16,310 --> 00:24:21,290 +CL لأن الـ H بنعتبرها يعني هي الـ Electrodynamics + +325 +00:24:21,290 --> 00:24:25,230 +بتاعتها يعني almost nothing يعني، كويس؟ اه هي + +326 +00:24:25,230 --> 00:24:28,330 +اتنين، واحد من العشرة تقريبا، ماعلينا كقيمة يعني + +327 +00:24:28,510 --> 00:24:31,230 +لكن ما اعتبرها يعني فرق كبير بينها و بين + +328 +00:24:31,230 --> 00:24:34,370 +الهالوجينات لأن الهالوجينات دائما أي اشي برتبط + +329 +00:24:34,370 --> 00:24:38,030 +معاها بعيد عنها بتكون polar ناحية الهالوجينات لأن + +330 +00:24:38,030 --> 00:24:41,890 +الهالوجينات بتحب تاخد ال .. تكتسب الالكترونات + +331 +00:24:41,890 --> 00:24:48,330 +وبالتالي ال bond بتكون polar فأي X .. X يعني F أو + +332 +00:24:48,330 --> 00:24:54,580 +CL أو PR أو I مدام في عندي Fمدام اندي اكس يعني + +333 +00:24:54,580 --> 00:24:56,640 +هالوجين ماعليه اتش عارف تاني بنقول والله هادي + +334 +00:24:56,640 --> 00:24:59,000 +polar covalent + +335 +00:25:06,660 --> 00:25:11,200 +فهي مثلا ال H مع ال H طبعا يعني فيش اي داعي ان ال + +336 +00:25:11,200 --> 00:25:14,560 +Electronic هدول ينجذبوا ناحية ال H هذه اكتر من ال + +337 +00:25:14,560 --> 00:25:19,080 +H التانية فهذه non polar covalent بينما ال HCL + +338 +00:25:19,080 --> 00:25:21,920 +اللي شفناها اه في داعي لإنهم ينجذبوا ناحية ال CL + +339 +00:25:21,920 --> 00:25:29,860 +وبالتالي هذه polar covalent وبتكون ال polarity او + +340 +00:25:29,860 --> 00:25:33,700 +ال dipole يتجه نحو ال CL اه لأنه more + +341 +00:25:33,700 --> 00:25:35,260 +electronegative + +342 +00:25:37,880 --> 00:25:43,060 +بسرعة لو قلنا الـH2 طبعا shared equally فهي non + +343 +00:25:43,060 --> 00:25:47,820 +polar covalent، هلأ نسيبنا من الأرقام يعني، الـCl2 + +344 +00:25:47,820 --> 00:25:52,800 +طبعا non polar covalent لأن هم زي بعضHBr هذي HX + +345 +00:25:52,800 --> 00:25:57,720 +يعني اه Polar Covalent HCl طبعا Polar Covalent + +346 +00:25:57,720 --> 00:26:04,240 +لأنه الـCl Electronegative NaCl Ionic MgO Ionic + +347 +00:26:04,240 --> 00:26:08,120 +مالناش داعوا نتكلمش عنهم نتكلمش عنهم في ال bond + +348 +00:26:08,120 --> 00:26:15,540 +polarity لأنهم Ionic فش عندي اي مركب + +349 +00:26:15,540 --> 00:26:19,500 +بيحتوي على metal ion metal ion compound هذا معناته + +350 +00:26:19,500 --> 00:26:27,930 +IonicCompound الان هذه كانت مقدمة عن خليني اقول ال + +351 +00:26:27,930 --> 00:26:30,410 +Electronegativity الان بدى اشوف ايش علاقة هذا + +352 +00:26:30,410 --> 00:26:36,250 +الكلام بال Intermolecular forces وبقول في عندى + +353 +00:26:36,250 --> 00:26:41,990 +نوعين من ال forces بتكون موجودة عادة في الجزيئات + +354 +00:26:41,990 --> 00:26:46,750 +مجتمعة الجزيئ الواحد فيه covalent bonds مش هيك فيه + +355 +00:26:46,750 --> 00:26:49,690 +covalent bonds زى ما نقول H2O + +356 +00:26:51,860 --> 00:26:57,780 +هي عداد عبارة عن O OH OH بنسمي الروابط هذه اللي هي + +357 +00:26:57,780 --> 00:27:00,940 +روابط أساسية في الجزيق في الجزيق نفسه + +358 +00:27:00,940 --> 00:27:05,440 +Intramolecular Forces Intramolecular سميها + +359 +00:27:05,440 --> 00:27:10,340 +Intramolecular يعني كل الـ Covalent Bonds هي عبارة + +360 +00:27:10,340 --> 00:27:14,240 +عن Intramolecular Intra يعني داخل الجزيق نفسه + +361 +00:27:14,240 --> 00:27:19,470 +Inter يعني بين الجزيقاتلكن بنسمي الروابط بين + +362 +00:27:19,470 --> 00:27:23,850 +جزيئات الميه ككل جزيئ ميه وجزيئ ميه اخر في روابط + +363 +00:27:23,850 --> 00:27:29,030 +بينهم مهما كانت بنسميها Intermolecular forces فانا + +364 +00:27:29,030 --> 00:27:32,370 +في هذا ال chapter بتحدثش عن الـ Intramolecular + +365 +00:27:32,370 --> 00:27:36,630 +تكوين الـ Covalent bonds بتحدثش عنهبتتحدث عن + +366 +00:27:36,630 --> 00:27:41,070 +الروابط اللي بتحصل بين الجزيئات المختلفة وبالتالي + +367 +00:27:41,070 --> 00:27:44,070 +بتكلم عن الـ Intermolecular forces + +368 +00:27:49,130 --> 00:27:53,270 +يبقى الـ Intermolecular forces ممكن ألاقيها والله + +369 +00:27:53,270 --> 00:27:57,710 +في الجزيئات المختلفة، أي جزيئ سواء كان neutral أو + +370 +00:27:57,710 --> 00:28:04,750 +كان charged أو كان polyatomic ion، نيتريت غيره ما + +371 +00:28:04,750 --> 00:28:10,850 +فيها إيه، فيها روابطعندما أتكلم عن الـ Intra + +372 +00:28:10,850 --> 00:28:14,950 +بأتكلم عن الروابط اللي بتربط بين الذرات بعضها مع + +373 +00:28:14,950 --> 00:28:18,050 +بعض في نفس الجزيئة لكن عندما أتكلم عن الـ + +374 +00:28:18,050 --> 00:28:21,570 +Intermolecular forces بأتكلم عن الـ Species + +375 +00:28:21,570 --> 00:28:25,670 +المختلفة، كويس؟ إيش الروابط اللي بينها؟ الجزيئات + +376 +00:28:25,670 --> 00:28:29,550 +المختلفة إيش الروابط اللي بينها؟ وهذه ليست روابط + +377 +00:28:29,550 --> 00:28:32,590 +Covalent، لو كانت روابط Covalent، كان هذا الجزيئة + +378 +00:28:32,590 --> 00:28:42,500 +أكبر، لأ ليست Covalentفبقول في عندى عادة الرابطة + +379 +00:28:42,500 --> 00:28:46,460 +الـ covalent أقوى كتير من الرابطة اللى بتكون بين + +380 +00:28:46,460 --> 00:28:49,720 +الجزيئاتيعني الرابط بين الجزيئات ممكن تكون + +381 +00:28:49,720 --> 00:28:57,380 +electrostatic attraction يعني جزيئات موجودة يعني + +382 +00:28:57,380 --> 00:29:00,380 +الرابط اللي بالها عادة بتكون ضعيفة نسبيا لكن + +383 +00:29:00,380 --> 00:29:04,500 +الرابط ال covalent بتكون اشمالها قوية للغاية لأن + +384 +00:29:04,500 --> 00:29:08,600 +هي اللي تمسك الذرات مع بعضها البعض علشان هيك ممكن + +385 +00:29:08,600 --> 00:29:12,340 +احنا نشوف مثلا بد حوالي تسعمائة و تلاتين كيلو جول + +386 +00:29:12,340 --> 00:29:19,040 +عشان اكسرالـ OH هذه الرابطة وهذه الرابطة بدي 930 + +387 +00:29:19,040 --> 00:29:23,900 +كيلو جول عشان اكسر روابط في الميه هذه الرابطة ايش + +388 +00:29:23,900 --> 00:29:28,480 +نوعها انترا انترا مليكورية انترا مليكورية انترا + +389 +00:29:28,480 --> 00:29:31,320 +مليكورية انترا مليكورية فبدي كمية هائلة من الطاقة + +390 +00:29:31,320 --> 00:29:37,320 +علشان اكسرهم لكن لو انا بدي احول الميه + +391 +00:29:41,270 --> 00:29:49,270 +من liquid water ل vapor عند 100 degree C يعني + +392 +00:29:49,270 --> 00:29:55,990 +من ميه عند 100 درجة ميه عند 100 درجة الى vapor عند + +393 +00:29:55,990 --> 00:30:00,290 +100 درجة قال باعوز بس يعني ايش بده اسوي يعني بده + +394 +00:30:00,290 --> 00:30:03,830 +افرق جزيئات الميه على بعض انا في ال .. في ال + +395 +00:30:03,830 --> 00:30:07,000 +liquid .. في ال condensed stateأو في الـ condensed + +396 +00:30:07,000 --> 00:30:10,480 +phase الميّه جزيئاتها متقاربة وفي attraction + +397 +00:30:10,480 --> 00:30:14,860 +forces بينها انا بدى احاول ايه اتغلب علي هذه ال + +398 +00:30:14,860 --> 00:30:17,820 +attraction forces اللي هي ال intermolecular forces + +399 +00:30:17,820 --> 00:30:22,680 +واخلي كل جزيئه يطلع لوحده يصير vapor جداش بدى طاقة + +400 +00:30:22,680 --> 00:30:30,070 +جال بس 41 كيلوجول بينما عشان اكسرالـ ال ال ال ال + +401 +00:30:30,070 --> 00:30:30,550 +ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال + +402 +00:30:30,550 --> 00:30:31,030 +ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال + +403 +00:30:31,030 --> 00:30:31,830 +ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال + +404 +00:30:31,830 --> 00:30:32,170 +ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال + +405 +00:30:32,170 --> 00:30:34,110 +ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال + +406 +00:30:34,110 --> 00:30:40,550 +ال ال ال ال ال + +407 +00:30:40,550 --> 00:30:41,430 +ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال + +408 +00:30:41,430 --> 00:30:41,450 +ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال + +409 +00:30:41,450 --> 00:30:41,450 +ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال + +410 +00:30:41,450 --> 00:30:41,450 +ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال + +411 +00:30:41,450 --> 00:30:41,690 +ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال + +412 +00:30:41,690 --> 00:30:41,770 +ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال + +413 +00:30:41,770 --> 00:30:44,430 +ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال + +414 +00:30:44,430 --> 00:30:45,970 +ال ال ال ال ال ال ال ال ال + +415 +00:30:54,310 --> 00:30:58,470 +خلّيني أطلع هنا بس جملة صغيرة هي الجملة التحتانية + +416 +00:30:58,470 --> 00:31:03,850 +في عندي هاي ال HCl والله في عندي رابطة هادي + +417 +00:31:03,850 --> 00:31:07,550 +covalent bond طبعا هي polar covalent ورايحة ناحية + +418 +00:31:07,550 --> 00:31:11,510 +ال chlorine ووضع يعني أكيد ال dipole ناحية ال + +419 +00:31:11,510 --> 00:31:16,450 +chlorine لكن قوة الرابطة قوة عظيمة جدا very strong + +420 +00:31:17,460 --> 00:31:23,620 +فهذه عشانها إيه؟ Intramolecular attraction force + +421 +00:31:23,620 --> 00:31:27,900 +اللي هي bond فبقول هذه والله تعتبر very strong + +422 +00:31:27,900 --> 00:31:34,890 +bondبينما الرابط بين جزء HCl و جزء HCl آخر هذي + +423 +00:31:34,890 --> 00:31:38,570 +بتكون weak intermolecular attraction فال + +424 +00:31:38,570 --> 00:31:42,750 +attractions between molecules are much weaker than + +425 +00:31:42,750 --> 00:31:47,110 +the intramolecular attraction that hold compounds + +426 +00:31:47,110 --> 00:31:51,810 +together طيب + +427 +00:31:51,810 --> 00:31:57,600 +خلينا نطلع هان برضهنفس المنطق، بتكلم عن الـ + +428 +00:31:57,600 --> 00:32:03,100 +intermolecular forces، بقول these intermolecular + +429 +00:32:03,100 --> 00:32:09,240 +attractions are however strong enough to control + +430 +00:32:09,240 --> 00:32:13,720 +physical properties، يبقى الروابط هذه اللي هي بين + +431 +00:32:13,720 --> 00:32:18,440 +الجزيئاتاللي هي الـ Intermolecular forces مهمة جدا + +432 +00:32:18,440 --> 00:32:25,980 +و قادرة و إلها القوة اللي تتحكم في ال physical + +433 +00:32:25,980 --> 00:32:30,420 +properties زي إيه؟ زي ال boiling point و ال + +434 +00:32:30,420 --> 00:32:33,980 +melting point وين يحصل للمادة boiling عند أي درجة؟ + +435 +00:32:33,980 --> 00:32:36,800 +طب وين يحصل المادة melting عند أي درجة؟ ال vapor + +436 +00:32:36,800 --> 00:32:41,580 +pressure جداش ال vapor pressure لإلها ال viscosity + +437 +00:32:41,580 --> 00:32:47,310 +ال surface tensionكل هذه الشغلات لها علاقة فقط + +438 +00:32:47,310 --> 00:32:52,970 +بالـ Intermolecular forces، كل ما زادت، آه تأثيرها + +439 +00:32:52,970 --> 00:32:56,250 +على ال physical properties بيزيد، يعني خلّيني أقول + +440 +00:32:56,250 --> 00:33:03,530 +حاجة، زادت ال Intermolecular forces لمادة معينةهل + +441 +00:33:03,530 --> 00:33:08,750 +من السهل اني اخليها تغلي + +442 +00:33:08,750 --> 00:33:12,450 +او خليها تكون صلبة؟ هل من السهل اني اعملها + +443 +00:33:12,450 --> 00:33:15,970 +melting؟ لأ مش من السهل لان الروابط اللي بين + +444 +00:33:15,970 --> 00:33:19,850 +الجزيئات قوية بدي احط طاقة عالية و نفس الكلام لو + +445 +00:33:19,850 --> 00:33:26,090 +كانت liquid هل من السهل اني اخليها تحول ل vapor؟ + +446 +00:33:26,090 --> 00:33:30,410 +ابدا مش سهل عشانك ال boiling point بتكون غالية + +447 +00:33:30,410 --> 00:33:36,530 +عاليةالـ .. الـ vapor pressure بدي يكون قليل مش + +448 +00:33:36,530 --> 00:33:40,050 +بسهولة بيطلع جزيق بسيب السطح بقى و بيطلع فوق لأنه + +449 +00:33:40,050 --> 00:33:43,610 +روابط إشمالة إلى حد ما بين الجزيقات بتكلم روابط + +450 +00:33:43,610 --> 00:33:48,530 +إيه إلى حد ما قوية إلى حد ما هي طبعا ليست أكيد + +451 +00:33:48,530 --> 00:33:52,730 +بقوة ال covalent bonds لكن هي وجودهاقوته النسبة + +452 +00:33:52,730 --> 00:33:58,030 +بيحدد ال physical properties للمواد فيما يتعلق بال + +453 +00:33:58,030 --> 00:34:01,650 +liquids يعني حاجة زي ال boiling point وال melting + +454 +00:34:01,650 --> 00:34:04,930 +point لما الليكويد انجمد ونعود نرجع الليكويد تاني + +455 +00:34:04,930 --> 00:34:08,190 +ال vapor pressure ال surface tension ال viscosity + +456 +00:34:08,190 --> 00:34:14,070 +الاخرين فحنلاقي انهالـ Intermolecular forces هي + +457 +00:34:14,070 --> 00:34:16,930 +السبب الأساسي اللي هنحاول أو العامل الأساسي اللي + +458 +00:34:16,930 --> 00:34:20,430 +هنستخدمه عشان نفسر ليش بعض المواد الـ boiling + +459 +00:34:20,430 --> 00:34:22,730 +point تبعتها عالية وبعضها ال boiling point تبعتها + +460 +00:34:22,730 --> 00:34:28,050 +قليلة؟ ليش بعض المواد مثلا الفسكوستي إليها عالية + +461 +00:34:28,050 --> 00:34:30,730 +بينما بعض المواد الأخرى الفسكوستي إليها منخفضة؟ و + +462 +00:34:30,730 --> 00:34:38,000 +هكذا الفسكوستي إيش؟ لزوجةطيب هذه الـ + +463 +00:34:38,000 --> 00:34:44,840 +Intermolecular forces كويس بدنا نسميها Vanderwaal + +464 +00:34:44,840 --> 00:34:48,160 +forces هي تلت أنواع ال Vanderwaal forces و في نوع + +465 +00:34:48,160 --> 00:34:54,960 +يعني رابع هنقوله بس مش جزء منها يعني فال + +466 +00:34:54,960 --> 00:34:59,240 +Vanderwaal forces هتكون هي عبارة عن اجروب من ال + +467 +00:34:59,240 --> 00:35:03,330 +Intermolecular forces هي التاليفالـ Intermolecular + +468 +00:35:03,330 --> 00:35:08,290 +forces بشكل أساسي اللي بنسميها Vanderwaal forces + +469 +00:35:08,290 --> 00:35:14,250 +هي تلت أنواع و طبعا بدنا نتذكر إنه هي بتحدث + +470 +00:35:14,250 --> 00:35:21,410 +between ال neutral molecules عادة بأول + +471 +00:35:21,410 --> 00:35:26,750 +نوع منها اللي هو ال ..الـ London forces أو London + +472 +00:35:26,750 --> 00:35:28,990 +dispersion forces و تاني نوع اللي هو الـ dipole + +473 +00:35:28,990 --> 00:35:31,690 +-dipole interactions و تالت نوع اللي هو الـ + +474 +00:35:31,690 --> 00:35:34,970 +hydrogen bonding فهذه تلت أنواع من أنواع الـ + +475 +00:35:34,970 --> 00:35:37,730 +intermolecular forces هندرسها و نعرف أيش هي بالظبط + +476 +00:35:37,730 --> 00:35:44,510 +و كيف بتأثر على خصائص المحاليل بشكل عام يبقى هذه + +477 +00:35:44,510 --> 00:35:47,250 +تلت أنواع من أنواع الـ intermolecular forces بتحدث + +478 +00:35:47,250 --> 00:35:49,990 +بين الـ neutral molecules يعني هذه ال forces بتجمع + +479 +00:35:49,990 --> 00:35:57,440 +لـ neutral moleculesويلها تأثير مهم على خصائص + +480 +00:35:57,440 --> 00:35:58,520 +المحليل + +481 +00:36:00,460 --> 00:36:04,560 +السوائل .. السائل حاجة نقية المحلول حاجة ضايبة فيه + +482 +00:36:04,560 --> 00:36:11,080 +أو يعني مش نقية بقول لكن في عندى قوة تانية مش + +483 +00:36:11,080 --> 00:36:14,280 +تابعة ل vendor valve forces عادة هي بنقولها ion + +484 +00:36:14,280 --> 00:36:17,240 +-dipole forces وال ionic bonding هذا مش حيتكلم + +485 +00:36:17,240 --> 00:36:20,540 +عنهم ال ion-dipole حنتكلم عنه شوية ال ionic + +486 +00:36:20,540 --> 00:36:23,740 +bonding لأ شفناها سابقا + +487 +00:36:25,630 --> 00:36:32,410 +فهنتكلم بداية عن الـ London Dispersion Forces أحد + +488 +00:36:32,410 --> 00:36:38,090 +أنواع الـ Intermolecular Forces + +489 +00:36:38,090 --> 00:36:41,250 +منشأها + +490 +00:36:41,250 --> 00:36:48,130 +بشكل عام قد يعني يكون غريب شوية بالنسبة لبعضكم لكن + +491 +00:36:48,130 --> 00:36:55,680 +احنا هنحاول أن نبينه لأن مفهومه بسيطفمثلا بنلاحظ + +492 +00:36:55,680 --> 00:37:01,680 +انه في جزائيات عندى non polar زى البرومين والبنزين + +493 +00:37:01,680 --> 00:37:04,260 +والهجزين هذه عبارة عن liquids at room temperature + +494 +00:37:04,260 --> 00:37:08,820 +طب ايش اللى خلها liquids؟ طيب و بعض الحاجات + +495 +00:37:08,820 --> 00:37:11,520 +التانية زى ال IOD جنب البرومين تحته على طول + +496 +00:37:11,520 --> 00:37:18,460 +النفتلين ال solids كلها كلها عبارة عن non polarnon + +497 +00:37:18,460 --> 00:37:22,200 +-polar molecules بمعنى أخر الـ bonds اللي فيه non + +498 +00:37:22,200 --> 00:37:25,160 +-polar، مافيش عند الـ dipole، كله non-polar. إيش + +499 +00:37:25,160 --> 00:37:28,020 +معنى بعض الحاجات بتكون liquids، a true + +500 +00:37:28,020 --> 00:37:31,960 +temperature، وبعض الحاجات بتكون solids؟ هذا الكلام + +501 +00:37:31,960 --> 00:37:37,750 +أو هذا السؤالاللي هو ببساطة خالص إيش أنواع ال + +502 +00:37:37,750 --> 00:37:41,030 +attractive forces اللي ممكن تكون موجودة بين ال non + +503 +00:37:41,030 --> 00:37:44,570 +polar molecules لإنها non polar طب إيش أنواع ال + +504 +00:37:44,570 --> 00:37:47,910 +attractive forces اللي ممكن تكون موجودة بينها؟ هذا + +505 +00:37:47,910 --> 00:37:53,670 +السؤال تحديدا جاب عليه السيد Fritz London في 1930، + +506 +00:37:53,670 --> 00:37:58,350 +ببساطة خالص، إيش اللي جاله؟ جال إنه عادة + +507 +00:37:58,350 --> 00:38:03,170 +الإلكترونات في الذرةفي الذرات المختلفة الإلكترونات + +508 +00:38:03,170 --> 00:38:06,770 +بتكون electronic clouds distributed equally + +509 +00:38:06,770 --> 00:38:11,050 +المفروض في الذرة distributed equally فهنا + +510 +00:38:11,050 --> 00:38:12,790 +الإلكترونات distributed equally وهنا الإلكترونات + +511 +00:38:12,790 --> 00:38:17,250 +distributed equally هذه ذرات heliumحلو؟ بيقول هو + +512 +00:38:17,250 --> 00:38:21,590 +إيه؟ بيقول إنه صح الوضع الطبيعي إنه الالكترونات + +513 +00:38:21,590 --> 00:38:26,330 +distributed إيه؟ equal لكن في بعض الأحيان بيحصل + +514 +00:38:26,330 --> 00:38:32,590 +عند instantaneous dipole أو induced dipole كيف؟ + +515 +00:38:32,590 --> 00:38:38,640 +يعني في لحظة معينة كانوا الالكترونات أقربالى جهة + +516 +00:38:38,640 --> 00:38:44,720 +معينة من الجهة الأخرى فى لحظة هم صح يعني موجودين + +517 +00:38:44,720 --> 00:38:47,980 +بس مش ثابتين يعني هو متحركين باستمرار الإلكترونات + +518 +00:38:47,980 --> 00:38:53,580 +بتمشي بسرعات عالية جدا فبالتالي فى لحظة ما كان + +519 +00:38:53,580 --> 00:39:00,220 +تركيز الإلكترونات فى جزء من أو على جزء من الذرّة + +520 +00:39:00,220 --> 00:39:04,680 +أكثر من غيرها هذا بيخلى ان هو exposed فى الجزء + +521 +00:39:04,680 --> 00:39:08,560 +الفعيد بس يعني هان هى الإلكترونات وين؟كانت موجودة + +522 +00:39:08,560 --> 00:39:12,160 +هان أكتر، طيب هان الألكترونات أحنا بتروزها + +523 +00:39:12,160 --> 00:39:16,440 +بالأحمر؟ ماعشان الحال، هان موجودة أكتر، إذا صار في + +524 +00:39:16,440 --> 00:39:21,510 +عندى partial positive و partial negativeطب حلو + +525 +00:39:21,510 --> 00:39:26,910 +كتير، ذرة تانية، ذرة تانية، كويس، برضه الإلكترونات + +526 +00:39:26,910 --> 00:39:33,650 +اللي عندها كانت إيه؟ في لحظة ما موجودة في منطقة + +527 +00:39:33,650 --> 00:39:36,650 +أكبر من منطقة تانية، إذا partial positive و + +528 +00:39:36,650 --> 00:39:41,330 +partial negative، إذا صار في عندي تجاذب بين ال + +529 +00:39:41,330 --> 00:39:44,030 +partial negative و partial positive للذرتين هدول + +530 +00:39:45,230 --> 00:39:49,230 +ممكن نقول حاجة تانية احنا، ممكن نقول انه طب حصل في + +531 +00:39:49,230 --> 00:39:52,650 +ذرة واحدة هذا الكلام، يبقى صار في اندهانه partial + +532 +00:39:52,650 --> 00:39:55,170 +negative اكتر، ال partial negative ايه حسب + +533 +00:39:55,170 --> 00:39:59,070 +الإلكترونات اللي جانبه؟ لأ ال partial negative + +534 +00:39:59,070 --> 00:40:03,550 +هيبعدهمأه هيبعدهم فهيروحوا الإلكترونات بعيد اذا + +535 +00:40:03,550 --> 00:40:08,030 +برضه هيعمل induced dipole هو عمل دايبول هو اخترعت + +536 +00:40:08,030 --> 00:40:12,350 +دايبول ليه؟ لأنه الإلكترونات في لحظة ما على ذرع ما + +537 +00:40:12,350 --> 00:40:17,050 +اتركزت في مكان معين في جهة معينة ثابت الجهة + +538 +00:40:17,050 --> 00:40:18,010 +التانية اشمالها + +539 +00:40:25,300 --> 00:40:28,100 +الصحابة الإلكترونية كانت اكسبوز من الناحية + +540 +00:40:28,100 --> 00:40:32,680 +التانية، في درجة ان صحابة الإلكترونية متساوية + +541 +00:40:32,680 --> 00:40:36,400 +عليها، ايش بتاع الصحابة الإلكترونية؟ بتشدها عليها + +542 +00:40:36,400 --> 00:40:39,000 +اذا صار في عندي induced dipole + +543 +00:40:46,970 --> 00:40:51,670 +هذا هو أساس .. طبعا هذا بيحصل في كل الذرات، بيحصل + +544 +00:40:51,670 --> 00:40:56,150 +في كل الجزيئات، مافي جزيئات بيحصل فيها يعني London + +545 +00:40:56,150 --> 00:40:58,930 +Forces جزيئات، لأ كل الجزيئات فيها London Forces، + +546 +00:40:58,930 --> 00:41:02,230 +كلها، ليه؟ لأن هذه الإلكترونات بتلوف، ممكن يحصل في + +547 +00:41:02,230 --> 00:41:07,560 +لحظة مالحظة ما أن الألكترونات كانت وجودها على جزء + +548 +00:41:07,560 --> 00:41:12,180 +من الذرّة أكتر من الجزء الآخر الجزء الآخر بيعمل + +549 +00:41:12,180 --> 00:41:15,520 +induced dipole في ذرّة أخرى قريبة عليه وبالتالي + +550 +00:41:15,520 --> 00:41:21,640 +بيحصل نوع من ال attraction ما بين الألكترونات وال + +551 +00:41:21,640 --> 00:41:27,360 +partial positive اللي موجود على الذرّة الأولى على + +552 +00:41:27,360 --> 00:41:29,100 +سبيل المثال هذا بشكل عام + +553 +00:41:31,880 --> 00:41:37,220 +هو اللي بيحصل في الـ London Forces، لو جينا + +554 +00:41:37,220 --> 00:41:42,220 +اطلعناه، نفس المنطقة بالظبط يعني، هذا الشكل هو ال + +555 +00:41:42,220 --> 00:41:46,300 +polarization of view بنقوله، هذه partial negative، + +556 +00:41:46,300 --> 00:41:49,020 +هذه partial positive، ال partial positive تشذب + +557 +00:41:49,020 --> 00:41:53,090 +حواليهاتجذب الإلكترونات وبالتالي بتخلي هذه partial + +558 +00:41:53,090 --> 00:41:56,210 +نيجاتيف صارت هذه partial positive partial positive + +559 +00:41:56,210 --> 00:41:59,450 +بتجذب الإلكترونات اللي حواليها فبتخلي ايه partial + +560 +00:41:59,450 --> 00:42:01,630 +negative partial positive هذا بنقوله induced + +561 +00:42:01,630 --> 00:42:05,850 +dipole induced + +562 +00:42:05,850 --> 00:42:08,490 +dipole يبقى فيه عنده كمية هائلة من ال induced + +563 +00:42:08,490 --> 00:42:12,630 +dipoles عادة بتكون موجودة في الجزيئات ووضع طبيعي + +564 +00:42:12,630 --> 00:42:17,070 +انهالـ Induced Dipoles هذه بتزيد كل ما زاد عدد + +565 +00:42:17,070 --> 00:42:22,090 +الذرات أو بمعنى كل ما زاد عدد الإلكترونات كل ما + +566 +00:42:22,090 --> 00:42:26,110 +زاد ال molecular weight كل ما زاد ال molecular + +567 +00:42:26,110 --> 00:42:29,710 +size يعني و عدد ال .. ال size إيه اللي علاقة بعدد + +568 +00:42:29,710 --> 00:42:36,430 +الذرات، دي كويس فبالتالي يعني ممكن نتكلم عن عدة + +569 +00:42:36,430 --> 00:42:42,970 +عوامل بتأثر على مدى قوة ال London Forcesفبقول بشكل + +570 +00:42:42,970 --> 00:42:45,890 +عام، these forces اللي هي لندن forces are present + +571 +00:42:45,890 --> 00:42:49,770 +in ايه؟ All molecules، مافيش جزيق مافيش فيه لندن + +572 +00:42:49,770 --> 00:42:52,910 +forces، لازم يكون فيه لندن forces، whether they + +573 +00:42:52,910 --> 00:42:56,750 +are polar or non-polar، بهمنيش، ليه؟ لأنه مدام فيه + +574 +00:42:56,750 --> 00:43:00,050 +ذراء إذا و عليها .. فيها إلكترونات، إذا محتمل إن + +575 +00:43:00,050 --> 00:43:03,070 +الإلكترونات تتركز في منطقة معينة أكتر من منطقة + +576 +00:43:03,070 --> 00:43:06,850 +أخرة وبالتالي بحصل عندي induced dipole، ماشي؟ إذا + +577 +00:43:06,850 --> 00:43:14,040 +كل الجزيقاتبغض النظر عن هل هي polar ولا non-polar + +578 +00:43:14,040 --> 00:43:20,260 +ما بيهمنيش قابلية إن الـ electronic cloud يحصلها + +579 +00:43:20,260 --> 00:43:24,720 +distortion يعني تصير أعلى في منطقة وعلى حساب منطقة + +580 +00:43:24,720 --> 00:43:30,020 +أخرى هذا مصطلح بنسميه polarizabilityPolarizability + +581 +00:43:30,020 --> 00:43:33,480 +مالوش دعوة في ال light polarization الاستقطاب + +582 +00:43:33,480 --> 00:43:36,580 +الضوء يمكن نسمع عنه استقطاب الضوء لأ مالوش دعوة + +583 +00:43:36,580 --> 00:43:40,060 +هذا اسمه polarizability يبقى هذا عبارة عن مصطلح + +584 +00:43:40,060 --> 00:43:43,520 +بنعبر عنه بنقول عنه هو عبارة عن ال polarizability + +585 +00:43:44,420 --> 00:43:49,940 +طيب يبقى إيش هي ال polarizability؟ هي سهولة حدوث + +586 +00:43:49,940 --> 00:43:56,560 +distortion لل electronic cloud distortion يعني عدم + +587 +00:43:56,560 --> 00:44:00,360 +انتظام، تشوّه، تشوّه، إيش يعني تشوّه؟ يعني + +588 +00:44:00,360 --> 00:44:03,420 +الإلكترونات بتتركز في منطقة على حساب منطقة تانية، + +589 +00:44:03,420 --> 00:44:06,080 +منطقة تكون فقيرة بالإلكترونات ومنطقة تكون أغنى + +590 +00:44:06,080 --> 00:44:09,980 +بالإلكترونات، هذا اسمه polarizabilityطيب ال + +591 +00:44:09,980 --> 00:44:13,220 +polarizability هذه بتتوقف على إيه؟ جاء ال + +592 +00:44:13,220 --> 00:44:18,400 +polarizability increases سهولة حدوث التشوهات، + +593 +00:44:18,400 --> 00:44:22,960 +سهولة حدوث London forces، سهولة حدوث ال + +594 +00:44:22,960 --> 00:44:25,400 +polarizability بيقول polarizability increases at + +595 +00:44:25,400 --> 00:44:30,440 +the number of electrons in an atom increasesيبقى + +596 +00:44:30,440 --> 00:44:33,980 +أول حاجة إذا زاد عدد الإلكترونات or increasing + +597 +00:44:33,980 --> 00:44:37,580 +molecular weight طبعا وقتاش بزيد عدد الإلكترونات + +598 +00:44:37,580 --> 00:44:42,800 +إذا كان عندي ال molecular weight أعلى، دي لأنه كل + +599 +00:44:42,800 --> 00:44:47,660 +ما زاد عدد الإلكترونات معناته عندي نيوترونات جدها + +600 +00:44:47,660 --> 00:44:52,040 +بالظبط لأنه عندنا بروتونات جدها بالظبط لأنه عندنا + +601 +00:44:52,040 --> 00:44:54,940 +ال neutral molecules وبالتالي يعني ال molecular + +602 +00:44:54,940 --> 00:44:58,740 +weight يكون أكبرفكل ما زاد عدد الإلكترونات أو زاد + +603 +00:44:58,740 --> 00:45:03,900 +ال micro mass بنقدر نقول إن ال polarizability + +604 +00:45:03,900 --> 00:45:08,820 +بتزيد، إيش يعني بتزيد؟ يعني بيسهل إن الإلكترونات + +605 +00:45:08,820 --> 00:45:13,680 +تتركز في منطقة على حسب منطقة أخرى، يسهل حدوث ال + +606 +00:45:13,680 --> 00:45:21,770 +induced dipole في الذرات المختلفةما هي العوامل + +607 +00:45:21,770 --> 00:45:24,510 +اللي بتأثر على الـ London forces مهم جدا عشان نقدر + +608 +00:45:24,510 --> 00:45:27,930 +نعمل prediction ما هي العوامل اللي بتأثر على + +609 +00:45:27,930 --> 00:45:38,050 +London forces بقول في البداية ال shape و ال .. و + +610 +00:45:38,050 --> 00:45:42,210 +ال size ال shape و ال size بقول the shape of the + +611 +00:45:42,210 --> 00:45:45,030 +molecule affects the strength of the dispersion + +612 +00:45:45,030 --> 00:45:51,320 +forces فمثلا في عندى جزء شايفينه linearفي عندي + +613 +00:45:51,320 --> 00:45:55,680 +جزائي branched هذا عامل زي الكورة بدي أفرجيكم شكله + +614 +00:45:55,680 --> 00:46:06,040 +وهذا طويل بنقوله linear skinnyوهذا ال .. ايش + +615 +00:46:06,040 --> 00:46:10,040 +بيسموه الجزيء + +616 +00:46:10,040 --> 00:46:16,060 +بيكون عادة زي .. زي ما نقول spherical إلى حد كبير + +617 +00:46:16,060 --> 00:46:19,080 +يعني شكله و تتراهيدر لكن الشكل الأهم له spherical + +618 +00:46:19,080 --> 00:46:24,580 +فتطلعوا على ال inputين هم شكله طويل هذا عامل زي + +619 +00:46:24,580 --> 00:46:29,570 +الكرة لو طلعنا على ال areaتبعته من هناك هذا فيها + +620 +00:46:29,570 --> 00:46:34,130 +نفس العدد تخدوا بالكم من ال c5 اتش يطلع ال c5 نفسه + +621 +00:46:34,130 --> 00:46:40,630 +فبالتالي بنلاحظ ان هذا المساحة السطحية أكبر من هذا + +622 +00:46:40,630 --> 00:46:44,390 +جال عشان هيك بما ان المساحة السطحية أكبر يعني ال + +623 +00:46:44,390 --> 00:46:49,350 +contact ما بين الجزيئات المختلفة أكبر اذا ال + +624 +00:46:49,350 --> 00:46:52,970 +London forces في هذا أكبر وبالتالي بنتوقع انه يكون + +625 +00:46:52,970 --> 00:46:58,980 +ال boiling point تبعته أعلىلأنه لأنه ال London + +626 +00:46:58,980 --> 00:47:01,700 +forces أعلى وهان مافيش عندنا London forces لأنه + +627 +00:47:01,700 --> 00:47:05,620 +non polar بينما هان هذا spherical المساحة السطحية + +628 +00:47:05,620 --> 00:47:10,600 +أقل ال contact area ال contact area مع الجزيئات + +629 +00:47:10,600 --> 00:47:15,440 +الأخرى أقل معناه الكلام بلاحظ أن ال boiling point + +630 +00:47:15,440 --> 00:47:21,840 +له أقل 282 هان 309 يبقى أول حاجة ال shape هل هو + +631 +00:47:21,840 --> 00:47:29,050 +long ولا skinnyهل هو long skinny ولا هو مثلا إلى + +632 +00:47:29,050 --> 00:47:33,010 +حد ما spherical و branched فالـ long و ال skinny + +633 +00:47:33,010 --> 00:47:39,210 +بيكونوا ايه فيهم London forces اقوى ليه ببساطة + +634 +00:47:39,210 --> 00:47:43,930 +خالص لأن ال contact area بتكون اعلى، يبقى هذا اول + +635 +00:47:43,930 --> 00:47:51,830 +حاجةالـ London forces يعني إلها دور مهم أو يعني + +636 +00:47:51,830 --> 00:47:58,470 +إنأكاس مهم لإلها من ناحية الـ size of atoms، كلام + +637 +00:47:58,470 --> 00:48:03,130 +نتكلم عن ال atoms فمثلا إحنا لما ننزل في الجدول + +638 +00:48:03,130 --> 00:48:09,490 +الدوري، ال size بيزيدالـ size بيزيد في الـ groups + +639 +00:48:09,490 --> 00:48:13,510 +فانا عندي مثلا لو أخدنا مجموعة الغازات الخاملة هذه + +640 +00:48:13,510 --> 00:48:19,270 +نيون و لو حبينا تحتها هن ممكن نحط هليوم اذا حبينا + +641 +00:48:19,270 --> 00:48:23,490 +هليوم نيون ارغن اكريبتون زينون لاحظوا ال boiling + +642 +00:48:23,490 --> 00:48:26,130 +point ايش بجرالها هن ال boiling point عمال بتزيد + +643 +00:48:26,130 --> 00:48:29,810 +هن اقل هن اكتر هن اكتر طب ايش اللي حصل؟ ما كلهم + +644 +00:48:29,810 --> 00:48:35,100 +عبارة عن ذرات فقطجال اه درنات فقط صحيح لكن ال + +645 +00:48:35,100 --> 00:48:38,980 +polarizability مدى سهولة عمل distortion لل + +646 +00:48:38,980 --> 00:48:45,860 +electronic cloud بيتوقف على ال atomic size فكل ما + +647 +00:48:45,860 --> 00:48:49,110 +زاد ال atomic sizeوهي نفس الكلام حتى كمان ال + +648 +00:48:49,110 --> 00:48:51,650 +electrons لو حبيته، هين عدد ال electrons أقل، هين + +649 +00:48:51,650 --> 00:48:54,950 +أكتر، هين أكتر، هين أكتر، برضه لو حبيته، فال + +650 +00:48:54,950 --> 00:48:58,450 +polarizability بتزيد، معنى الكلام ال dispersion + +651 +00:48:58,450 --> 00:49:03,270 +forces أيضا بتزيد وبالتالي ال boiling point بتزيد + +652 +00:49:03,940 --> 00:49:09,780 +نفس الكلام هذا يعني ممكن نطبقه على حاجة في مجموعة + +653 +00:49:09,780 --> 00:49:13,800 +الـC تحته + +654 +00:49:13,800 --> 00:49:17,900 +الـSilicone تحته الـGermanium تحته الـTin لو أجينا + +655 +00:49:17,900 --> 00:49:19,900 +نتطلع على الـmolecular weight هيك عامة + +656 +00:49:19,900 --> 00:49:26,290 +الـmolecular weight بيزيديعني ال CH4 18، ال SIH4 + +657 +00:49:26,290 --> 00:49:31,070 +يعني يمكن تلاتين اش و تلاتين، تلاتة و تلاتين، + +658 +00:49:31,070 --> 00:49:36,770 +الجيرمانيوم 677، ال 10H4 هيوهان، نحظوا إيش بيحصل ل + +659 +00:49:36,770 --> 00:49:39,530 +ال molecular weight عمال أو ال molecular mass؟ + +660 +00:49:39,530 --> 00:49:43,370 +بيزيد ال molecular mass هيكجال مادام زاد ال + +661 +00:49:43,370 --> 00:49:47,190 +molecular mass إذا ال dispersion forces بتزيد يبقى + +662 +00:49:47,190 --> 00:49:50,710 +ال boiling point بدها تزيد في هذا الاتجاه مافيش + +663 +00:49:50,710 --> 00:49:55,030 +مشكلة عندنا لو أخدنا كل المجموعات خلينا ناخد بس + +664 +00:49:55,030 --> 00:49:58,470 +هدول فيهم جزء صح هنتكلم عنها في المستقبل من هنا + +665 +00:49:58,470 --> 00:50:03,930 +يعني كله بيزيدجروب تانية هي كلها بتزيد، جروب تالتة + +666 +00:50:03,930 --> 00:50:07,350 +هي كلها بتزيد، إذا كل ما زاد ال molecular mass أو + +667 +00:50:07,350 --> 00:50:10,550 +ال molecular weight معناته ال dispersion forces + +668 +00:50:10,550 --> 00:50:17,090 +بتزيد، يبقى ال boiling point بتزيد، نفس الكلام إذا + +669 +00:50:17,090 --> 00:50:20,330 +كان بدنا نطلع على الخصائص الأخرى، إنه بتتكلم عن ال + +670 +00:50:20,330 --> 00:50:24,730 +boiling point فال boiling points increase as the + +671 +00:50:24,730 --> 00:50:27,810 +formula weight أو يعني molecular weight is + +672 +00:50:27,810 --> 00:50:31,480 +increased due to stronger dispersion forcesهذا + +673 +00:50:31,480 --> 00:50:37,200 +واضح للغاية نتطلع على كمان حاجة فيما يتعلق بال + +674 +00:50:37,200 --> 00:50:42,240 +molecular weight لو طلعنا على الفلورين F2 هاي ال + +675 +00:50:42,240 --> 00:50:43,640 +molecular weight تبعه + +676 +00:50:46,790 --> 00:50:50,770 +عندي ال boiling point موليكار ويت قليل الكلورين + +677 +00:50:50,770 --> 00:50:54,530 +موليكار ويت أكبر البرومين موليكار ويت أكبر + +678 +00:50:54,530 --> 00:50:58,470 +الايودين موليكار ويت أكبر لو طلعنا على ال boiling + +679 +00:50:58,470 --> 00:51:06,110 +point بنلاحظ 85,239,333,458 يعني عندي برضه زيادة + +680 +00:51:06,110 --> 00:51:08,490 +في ال boiling point مع ال + +681 +00:51:11,320 --> 00:51:13,580 +زيادة مع الـ molecular mass أو الـ molecular + +682 +00:51:13,580 --> 00:51:17,440 +weight وهذا الكلام برضه يعني واضح بالنسبة لنا شفنا + +683 +00:51:17,440 --> 00:51:24,000 +بالنسبة للذرات شفنا في واحد سابق يبقى هذا أول نوع + +684 +00:51:24,000 --> 00:51:31,110 +من أنواعالانتر موليكولار فورسيز اللي هي vanderwaal + +685 +00:51:31,110 --> 00:51:35,090 +forces أول نوع من vanderwaal forces النوع التاني + +686 +00:51:35,090 --> 00:51:38,210 +قولنا vanderwaal forces تلت أنواع أو تلت أشكال + +687 +00:51:38,210 --> 00:51:42,250 +لندن فورسيز هذه أول واحدة والتانية دايبول دايبول + +688 +00:51:42,250 --> 00:51:48,960 +ففي الدايبول دايبول interactionsباتكلمش عن الـ non + +689 +00:51:48,960 --> 00:51:51,980 +-polar covalent لأ بتتكلم عن الـ polar covalent + +690 +00:51:51,980 --> 00:51:55,240 +الجزائيات اللي فيها الـ dipole من وين بتجي ال + +691 +00:51:55,240 --> 00:51:59,320 +dipole؟ لازم ال bond تكون ايه؟ polar covalent + +692 +00:51:59,320 --> 00:52:03,820 +بمعنى اخر لازم ذرة من الذرتين المرتبطات مع بعضهم + +693 +00:52:03,820 --> 00:52:08,020 +البعض تكون more electronegative يعني اقرب لليمين و + +694 +00:52:08,020 --> 00:52:13,500 +اعلىأعلى في ال group و أقرب لليمين اللي هو على + +695 +00:52:13,500 --> 00:52:17,480 +يمين الجدول الدوري لازم تكون واحدة منهم زي هي أنا + +696 +00:52:17,480 --> 00:52:23,700 +عندي الرابط equivalentcovalent معناته non-metals + +697 +00:52:23,700 --> 00:52:27,620 +مرتبطة مع بعض البعض هذه الرابطة يجب أن تكون + +698 +00:52:27,620 --> 00:52:31,780 +unequally shared electrons فيها unequally + +699 +00:52:31,780 --> 00:52:36,940 +unequally مش متساويات واحدة من الذرتين بتجذب + +700 +00:52:36,940 --> 00:52:42,520 +الإلكترونات أكتر هذا بيعمل بايبول شفناه زي ال HCl + +701 +00:52:42,520 --> 00:52:51,320 +هذا هو في هذا الاتجاه هذا بايبولفالنوع الـ + +702 +00:52:51,320 --> 00:52:53,920 +interaction اللي بتكلم عنه هو الـ dipole-dipole + +703 +00:52:53,920 --> 00:53:00,060 +interaction يعني في عنده dipole moments في عنده + +704 +00:53:00,060 --> 00:53:03,660 +bond polarization فهذا بينشعنها dipole فبيحصل عنده + +705 +00:53:03,660 --> 00:53:07,720 +dipole-dipole interaction فبنقول as a result of + +706 +00:53:07,720 --> 00:53:10,420 +differences of electronegativities of atoms + +707 +00:53:10,420 --> 00:53:15,870 +connected by covalent bonds a dipole is formedأذا + +708 +00:53:15,870 --> 00:53:18,470 +ناشع عن الـDifferences في الـElectronegativities + +709 +00:53:18,470 --> 00:53:25,470 +بتكون عندي ايه؟ Dipole نتطلع + +710 +00:53:25,470 --> 00:53:28,270 +عليهم شوية، بيقول الـMolecules that have permanent + +711 +00:53:28,270 --> 00:53:31,670 +dipoles are attracted to each other يعني مثلا + +712 +00:53:31,670 --> 00:53:35,930 +الـHCl مع HCl تاني، يعني هاد صارت partial positive + +713 +00:53:35,930 --> 00:53:41,730 +و هاد partial negative و لا مع HCl تانية، هاي HCl، + +714 +00:53:41,730 --> 00:53:45,640 +إذا هدا هيهالأن هذه partial positive وهذه partial + +715 +00:53:45,640 --> 00:53:47,320 +negative، ال partial positive مع ال partial + +716 +00:53:47,320 --> 00:53:50,260 +negative، هذه الرابطة، هذه الرابطة ال + +717 +00:53:50,260 --> 00:53:54,320 +intermolecular force بنقولها dipole-dipole لإن + +718 +00:53:54,320 --> 00:54:00,620 +حصلت between two dipoles، dipole-dipole طيب بقول + +719 +00:54:00,620 --> 00:54:03,700 +the positive end of one dipole is connected أو + +720 +00:54:03,700 --> 00:54:06,560 +attracted to the negative end of the other and + +721 +00:54:06,560 --> 00:54:11,510 +vice versaطيب، these forces are only important + +722 +00:54:11,510 --> 00:54:16,730 +when the molecules are close to each other، يعني + +723 +00:54:16,730 --> 00:54:20,250 +هاد مهم كتير لما ايه يكون الجزيئات ي grow up جدا + +724 +00:54:20,250 --> 00:54:24,410 +على بعض، يعني في ال condensed state، في ال liquid + +725 +00:54:24,410 --> 00:54:35,970 +أو ال solidوبالتالي في عندى جزء او رابطة هى + +726 +00:54:35,970 --> 00:54:38,710 +partially positive partially negative ال partial + +727 +00:54:38,710 --> 00:54:40,410 +negative مع ال partial positive وال partial + +728 +00:54:40,410 --> 00:54:43,040 +positive مع ال partial negative اوممكن نقول حاجة + +729 +00:54:43,040 --> 00:54:45,620 +زي هيك ال partial negative مع ال partial positive + +730 +00:54:45,620 --> 00:54:51,160 +سيئان زي ما بدنا يعني نرسم نرسم في عن نهاية طبعا + +731 +00:54:51,160 --> 00:54:53,300 +ال negative مع ال negative هذا repulsion و ال + +732 +00:54:53,300 --> 00:54:55,000 +negative مع ال negative أو ال positive مع ال + +733 +00:54:55,000 --> 00:54:57,320 +positive برضه repulsion ففي الحقيقة هو بيحصل + +734 +00:54:57,320 --> 00:55:00,000 +attractions و repulsions لكن ال attractions بتكون + +735 +00:55:00,000 --> 00:55:04,360 +أكبر كتير من ال repulsions فهي يعني ال molecules + +736 +00:55:04,360 --> 00:55:11,270 +بيحصلهم orientation بحيث انهالـ Positive بيجرب على + +737 +00:55:11,270 --> 00:55:14,070 +الـ Negative غالبا والـ Negative بيبتعد عن الـ + +738 +00:55:14,070 --> 00:55:17,470 +Negative والـ Positive بيبتعد عن الـ Positive + +739 +00:55:17,470 --> 00:55:21,150 +وبالتالي بيكون عندي الـ Net يعني هذا كله Negative + +740 +00:55:21,150 --> 00:55:24,350 +مع Positive كل الأخضر عبارة عن Attractions والأسود + +741 +00:55:24,350 --> 00:55:26,790 +عبارة عن Repulsions + +742 +00:55:28,320 --> 00:55:31,760 +فبتكون في الحقيقة يعني شغلة معقدة جدا داخل المحلول + +743 +00:55:31,760 --> 00:55:37,580 +لكنها سهلة الفهم للغاية فمثلا بقول في ال solid CH3 + +744 +00:55:37,580 --> 00:55:42,480 +in the solid ماشي في ال solid form CH3CN بنقول له + +745 +00:55:42,480 --> 00:55:47,910 +Acetonitrile molecules are arrangedبترتب حالها في + +746 +00:55:47,910 --> 00:55:53,190 +الصليدها فالجزيقات + +747 +00:55:53,190 --> 00:55:56,550 +الاسيتونيترال بترتب حالها are arranged with the + +748 +00:55:56,550 --> 00:56:00,350 +negatively charged nitrogen end of each molecule + +749 +00:56:00,350 --> 00:56:05,210 +close to the positively charged CH3 أنا عندي هي + +750 +00:56:05,210 --> 00:56:08,330 +CH3CN + +751 +00:56:08,520 --> 00:56:11,140 +هذه more electronegative يعني في عندك دايبول في + +752 +00:56:11,140 --> 00:56:14,940 +هذا الاتجاه فهذه بتاخد ككل partial positive وهذه + +753 +00:56:14,940 --> 00:56:21,820 +بتاخد partial negative مثلا فبترتب حالها بحيث انه + +754 +00:56:21,820 --> 00:56:27,360 +هاي ال nitrogen اللي هي partial negative وهي ال + +755 +00:56:27,360 --> 00:56:31,240 +CH3 اللي هي partial positive هي partial negative + +756 +00:56:31,240 --> 00:56:36,990 +partialPositive نجاتيف مع نجاتيف نجاتيف نجاتيف + +757 +00:56:36,990 --> 00:56:43,810 +نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف + +758 +00:56:43,810 --> 00:56:45,070 +نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف + +759 +00:56:45,070 --> 00:56:45,070 +نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف + +760 +00:56:45,070 --> 00:56:45,910 +نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف + +761 +00:56:45,910 --> 00:56:46,150 +نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف + +762 +00:56:46,150 --> 00:56:46,430 +نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف + +763 +00:56:46,430 --> 00:56:47,210 +نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف نجاتيف + +764 +00:56:47,210 --> 00:56:53,280 +نجاتيف نجاتيففي الـ Liquid بيكون يعني مش بها + +765 +00:56:53,280 --> 00:56:56,560 +الصراعمة هذه اللي قدامي لأ بيكون فيها نوع من + +766 +00:56:56,560 --> 00:56:59,920 +المرونة flexibility ففيه تحقق لإيه لأن الجزيئات + +767 +00:56:59,920 --> 00:57:04,740 +بتتحرك وبالتالي ممكن يكون في أنها نهيه نوع من + +768 +00:57:04,740 --> 00:57:08,500 +التجاذب لكن ممكن يكون في أن بعض التنافرات طبعا في + +769 +00:57:08,500 --> 00:57:13,000 +المحلول بيحاولوا يركبوا حالهمبحيث أن التجاذبات + +770 +00:57:13,000 --> 00:57:17,220 +تكون أكتر من التنافرات، وضع طبيعي، لأن اتنين + +771 +00:57:17,220 --> 00:57:20,280 +بتجاذب وبيعدوا عن بعض، وبالتالي بيصير في عندنا نوع + +772 +00:57:20,280 --> 00:57:24,180 +من التقارب + +773 +00:57:24,180 --> 00:57:28,070 +بشحنتين مختلفتين، فبيكون تجاذب بينهمفبيكون في + +774 +00:57:28,070 --> 00:57:32,330 +عيننا لا شك بيكون في عيننا في .. يعني في مناطق أو + +775 +00:57:32,330 --> 00:57:34,590 +جزيئات .. بعض الجزيئات المعينة بيكون في عيننا + +776 +00:57:34,590 --> 00:57:37,530 +تنافر وبعضها بيكون في عيننا تجاذب لكن التجاذب هو + +777 +00:57:37,530 --> 00:57:41,810 +اللي بيكون أكبر شيء ممكن ليه؟ لأنه الجزيئ حر + +778 +00:57:41,810 --> 00:57:46,070 +الحركة فمضايق من حياته جانبه فيه تنافر إيش بيسوي؟ + +779 +00:57:46,070 --> 00:57:52,390 +بيجلب مش مشكلة وبالتالي هدف ال liquid stateو هذا + +780 +00:57:52,390 --> 00:57:54,350 +في ال solid state و لاحظوا في ال liquid state + +781 +00:57:54,350 --> 00:57:57,890 +اتطلعوا على طول الرابطة بنلاقيها أطول يعني هانلاقي + +782 +00:57:57,890 --> 00:58:07,710 +الرابطة أكثر هناك أطول دكتور + +783 +00:58:07,710 --> 00:58:11,850 +كيف عرفنا إننا سيالين ال electronegativity أعلى؟ + +784 +00:58:11,850 --> 00:58:17,730 +هو احنا لما نقول والله ال nitrogen لو رجعنا للجدول + +785 +00:58:17,730 --> 00:58:22,600 +ال nitrogen رح يجذب الإلكترونات نوحيهالنيتروجين رح + +786 +00:58:22,600 --> 00:58:27,800 +يجذب الإلكترونات نوحيه لأن النيتروجين هيها في عنده + +787 +00:58:27,800 --> 00:58:34,020 +بورون كاربون نيتروجين اكسجين فالنيتروجين هو + +788 +00:58:34,020 --> 00:58:38,160 +النيتروجين والأكسجين والفلور electronegative + +789 +00:58:38,160 --> 00:58:43,320 +فالكربون زي الهيدروجين تقريبا الكربون زي + +790 +00:58:43,320 --> 00:58:48,450 +الهيدروجينالهيدروجين يعني ارتبط بأي واحد من هدول + +791 +00:58:48,450 --> 00:58:53,550 +فهذا polar الكربون نفس الكلام فهو الكربون نيتروجين + +792 +00:58:53,550 --> 00:58:57,990 +هياخد الإكترونة التنوحية فهيعمل هذا partial + +793 +00:58:57,990 --> 00:59:00,970 +positive واللي ورا ال CH تلاتة هتكون partial + +794 +00:59:00,970 --> 00:59:02,270 +positive ككل يعني + +795 +00:59:06,170 --> 00:59:09,010 +مفيد جدا الجدول الدوري في حالات زي هذه يعني + +796 +00:59:09,010 --> 00:59:11,410 +بالنسبة لنا لما نطلع الجدول الدوري نعرف وان + +797 +00:59:11,410 --> 00:59:14,630 +العناصر بس يكوينسي نذكر انه الكربون و الهيدروجين + +798 +00:59:14,630 --> 00:59:19,070 +زي بعضه وعشان هيك أنا قلت انه الـC و الـH CH دائما + +799 +00:59:19,070 --> 00:59:23,470 +non polar covalent نطلع على الجزيئات التالية مثلا + +800 +00:59:23,470 --> 00:59:29,770 +عندي هانا بروبينالـ Boiling Point تبعته 231، عند + +801 +00:59:29,770 --> 00:59:33,050 +هنا Dye مثل الـ Ether، الـ Boiling Point تبعته + +802 +00:59:33,050 --> 00:59:38,110 +248، أعلى، طب عند هنا Acetaldehyde، الـ Boiling + +803 +00:59:38,110 --> 00:59:43,150 +Point تبعته 294، أعلى، طب عند هنا Acetonitrile، + +804 +00:59:43,150 --> 00:59:45,530 +الـ Boiling Point تبعته 350، هل بنستطيع أن نفسر + +805 +00:59:45,530 --> 00:59:50,800 +هذا الكلام؟ هل بنستطيع أن نفسر هذا الكلام؟لو جانا + +806 +00:59:50,800 --> 00:59:53,520 +تطلعنا على اذا كان اعطاني قيمة الـ dipole هدول + +807 +00:59:53,520 --> 00:59:56,980 +كلهم لهم تقريبا نفس ال molecular mass عشان هيك لهم + +808 +00:59:56,980 --> 00:59:59,620 +نفس ال dispersion forces لأن احنا قلنا ال + +809 +00:59:59,620 --> 01:00:02,660 +dispersion forces ده هو بال molecular mass فهنا + +810 +01:00:02,660 --> 01:00:05,560 +نفس ال molecular mass اذا تقريبا نفس ال ايه نفس ال + +811 +01:00:05,560 --> 01:00:10,340 +dispersion forces تقريبا يعني فبنطلع لو طلعنا على + +812 +01:00:10,340 --> 01:00:13,820 +ال dipole moment + +813 +01:00:15,150 --> 01:00:18,130 +هنجدش قيمة الـ Dipole هنجدش قيمة الـ Dipole واحد + +814 +01:00:18,130 --> 01:00:21,950 +من عشر لأن فيه فرق لكن قليل هن واحد و تلاتة هن + +815 +01:00:21,950 --> 01:00:25,290 +اتنين و سبعة هن تلاتة و تسعة فبما انه ال Dipole + +816 +01:00:25,290 --> 01:00:29,410 +بزيد يعني ال bond polarity بتزيد يبقى ال Dipole + +817 +01:00:29,410 --> 01:00:33,190 +Dipole interactions بتزيد في هذا الاتجاه اذا اه + +818 +01:00:33,190 --> 01:00:36,770 +يبقى ال boiling point هتزيد في هذا الاتجاهماشي يا + +819 +01:00:36,770 --> 01:00:40,130 +جماعة يبقى اذا كان عندى قيمة الـdipole moment سهل + +820 +01:00:40,130 --> 01:00:46,170 +جدا اكتشف انه ال boiling point في هذا الاتجاه + +821 +01:00:46,170 --> 01:00:49,730 +هتزيد طب لو فاش عندى ممكن يجيني سؤال يقولي والله + +822 +01:00:49,730 --> 01:00:58,010 +يعني انه واحد من هدول له lowest boiling pointلأ هو + +823 +01:00:58,010 --> 01:01:00,770 +هلجيت هدول كلها بتقريبا زي بعض كانت ملاحظة يعنى + +824 +01:01:00,770 --> 01:01:05,310 +نفس الحاجة هي واحد اتنين تلاتة واحد اتنين تلاتة + +825 +01:01:05,310 --> 01:01:08,630 +واحد اتنين تلاتة الذرات الأساسية واحد اتنين تلاتة + +826 +01:01:08,630 --> 01:01:12,050 +هو نفسه هو جابها بالذات زي هيك علشان نفهم بقول + +827 +01:01:12,050 --> 01:01:16,090 +السؤال ممكن يجي كتالة طب احنا مافيش عنا قيم دى مش + +828 +01:01:16,090 --> 01:01:20,110 +عارفين ال popularity جديش كويس طب إيه أش ممكن + +829 +01:01:20,110 --> 01:01:24,840 +نعمل؟قال ممكن يسألني سؤال يقول لي أن هو واحد من + +830 +01:01:24,840 --> 01:01:29,120 +هدول اللي له lowest boiling point اللي له lowest + +831 +01:01:29,120 --> 01:01:34,280 +boiling point هو ال إيه؟ هو المركب اللي ال + +832 +01:01:34,280 --> 01:01:38,160 +international forces بعته أقل ما يمكن، هان هذا فيه + +833 +01:01:38,160 --> 01:01:43,790 +بس لندن forces، هذا فيه لندن forces زيها كمان،لأنه + +834 +01:01:43,790 --> 01:01:46,730 +polar هذا دايبول دايبول لـ London forces، هذا + +835 +01:01:46,730 --> 01:01:51,210 +دايبول دايبول لـ London forces، إذاً، يكون هذا أقل + +836 +01:01:51,210 --> 01:01:55,890 +جزء من الجزيئات فيما يتعلق بالـ boiling point، + +837 +01:01:55,890 --> 01:01:58,650 +لماذا؟ لأنه ليس فيه بس إلا غير dispersion forces، + +838 +01:01:58,650 --> 01:02:01,470 +بينما هذا في نفس ال dispersion اللي هان زائد + +839 +01:02:01,470 --> 01:02:02,790 +دايبول دايبول + +840 +01:02:10,200 --> 01:02:14,760 +مثلا قال لي which has a higher boiling point اثل + +841 +01:02:14,760 --> 01:02:24,280 +مثل اثر او تومثل بروبين ان هو واحد اللي هو higher + +842 +01:02:24,280 --> 01:02:28,160 +boiling point طبعا هذا فيه dispersion forces وهذا + +843 +01:02:28,160 --> 01:02:32,950 +فيه dispersion forces مش خلافمش عارف قيمتهم بالظبط + +844 +01:02:32,950 --> 01:02:37,610 +انا لكن يعني يبدو ليه جراب على بعض مش مش مش هالاشي + +845 +01:02:37,610 --> 01:02:40,650 +اللي كتير لإن هن في عندي أربع أساسيات و هن في عندي + +846 +01:02:40,650 --> 01:02:43,610 +أربع أساسيات مافيش عندي مشكلة فتقريبا ال + +847 +01:02:43,610 --> 01:02:47,680 +experience فلس قريبة لكن بلاحظ أن هذا إيش مالهمدن + +848 +01:02:47,680 --> 01:02:52,240 +فيه CO إذاً هذا فيه دايبول دايبول فيه دايبول + +849 +01:02:52,240 --> 01:02:55,660 +دايبول بينما هذا ايه مافيش فيه دايبول دايبول + +850 +01:02:55,660 --> 01:02:59,120 +فبلاحظ أنا أنه اللي له higher boiling point هيكون + +851 +01:02:59,120 --> 01:03:06,520 +هذا بسهولة يعني بدي أحاول أني لو أفهمت إيش يعني + +852 +01:03:06,520 --> 01:03:09,800 +دايبول دايبول وإيش يعني the spanish forces سهل أنه + +853 +01:03:09,800 --> 01:03:15,880 +أفرق بين الجزيئات بناء علىهل عندي فقط dispersion + +854 +01:03:15,880 --> 01:03:19,260 +forces او دايبول دايبول زائد dispersion forces + +855 +01:03:19,260 --> 01:03:23,580 +مثلا بيقول ال relationship between the dipole + +856 +01:03:23,580 --> 01:03:25,720 +moment and the boiling point of organic compounds + +857 +01:03:25,720 --> 01:03:28,980 +of similar molar mass لما بيقول similar molar mass + +858 +01:03:28,980 --> 01:03:32,460 +معناته ال dispersion forces متقاربة هى يعني + +859 +01:03:32,460 --> 01:03:38,420 +similar اه طيب ال C3H6 هى ال molar mass 42% يعني + +860 +01:03:38,420 --> 01:03:42,140 +اقرب على بعضبلاحظ أن ال boiling point 240 Kelvin + +861 +01:03:42,140 --> 01:03:46,080 +هان إيش في عندي؟ إيش أنواع الروابط الموجودة اللي + +862 +01:03:46,080 --> 01:03:49,780 +هي intermolecular forces بس dispersion forces هان + +863 +01:03:49,780 --> 01:03:54,980 +في عندي دايبول دايبول زائد dispersion كويس؟ آه + +864 +01:03:54,980 --> 01:03:59,810 +زادت 248الاسيتو نيترال تلات و خمس و خمسين لان عندي + +865 +01:03:59,810 --> 01:04:06,650 +برضه dispersion forces و عندي كمان dipole-dipole و + +866 +01:04:06,650 --> 01:04:11,010 +لاحظوا ان ال dipole لهذا اكبر تلاتة و تسعة يعني في + +867 +01:04:11,010 --> 01:04:15,270 +عندي قوة ال dipole-dipole بتكون اعلى كتير من ال + +868 +01:04:15,270 --> 01:04:17,210 +die مثل ال ether + +869 +01:04:22,670 --> 01:04:25,950 +هذه في الحقيقة يعني Controversial يعني بدها شوية + +870 +01:04:25,950 --> 01:04:31,630 +يعني تركيز عشان نقدر نقرأ فيها جيدا أو نفهمها جيدا + +871 +01:04:31,630 --> 01:04:35,550 +بتقول which have a greater effect أنهي إلها تأثير + +872 +01:04:35,550 --> 01:04:38,770 +أعلى دايبول دايبول interactions ولا dispersion + +873 +01:04:38,770 --> 01:04:46,390 +forces يعني لو جزء فيه دايبول دايبول وجزء تاني فيه + +874 +01:04:46,390 --> 01:04:49,770 +dispersion طب أنه هل ممكن نقارن بينهم؟ بنقول بده + +875 +01:04:49,770 --> 01:04:53,880 +ننتبه لهدول الجملتينبقول if two molecules are of + +876 +01:04:53,880 --> 01:04:57,800 +comparable size إذا كانت الاتنين لهم comparable + +877 +01:04:57,800 --> 01:05:00,660 +size، إيش يعني comparable size؟ إيش معناتها بالـ + +878 +01:05:00,660 --> 01:05:03,300 +intermolecular forces؟ يعني ال dispersion forces + +879 +01:05:03,300 --> 01:05:08,260 +تقريبا مثل .. آه ساعتها إيش بيكون؟Dipole-dipole + +880 +01:05:08,260 --> 01:05:11,080 +interactions are likely to be the dominating + +881 +01:05:11,080 --> 01:05:14,900 +force، يعني الـDipole-Dipole هيكون أعلى، أكبر، + +882 +01:05:14,900 --> 01:05:18,060 +تأثيره أكبر، ليه؟ الجزء اللي فيه الـDipole-Dipole + +883 +01:05:18,060 --> 01:05:20,860 +هيكون تأثيره أكتر، ليه؟ لأن الأثنين لهم نفس + +884 +01:05:20,860 --> 01:05:24,580 +الـmolecular mass، واحد بس dispersion forces + +885 +01:05:24,580 --> 01:05:28,670 +والتانيبايبول بايبول إذا التاني هيكون عندي بايبول + +886 +01:05:28,670 --> 01:05:31,090 +بايبول زائد dispersion forces الأول بس dispersion + +887 +01:05:31,090 --> 01:05:33,510 +forces فال بايبول بايبول هيكون هو ال dominating + +888 +01:05:33,510 --> 01:05:37,390 +force على الناحية الأخرى if one molecule is much + +889 +01:05:37,390 --> 01:05:47,010 +larger than the other واحد جزء كبير كتير مثلا CH3 + +890 +01:05:47,010 --> 01:05:59,810 +CH2 خلاني أقول تمانية CH3جزائي كبير وعندي مثلا CH3 + +891 +01:05:59,810 --> 01:06:03,630 +فهذا + +892 +01:06:03,630 --> 01:06:06,530 +جزائي أشماله كبير يعني ال London force استبعته + +893 +01:06:06,530 --> 01:06:10,350 +أشمالها عالية جدا و هان في عندي London force لكن + +894 +01:06:10,350 --> 01:06:13,170 +في عندي أيه كمان دايبول دايبول بقول إذا كان + +895 +01:06:13,170 --> 01:06:17,380 +الجزائي كبيرخالص أكبر كتير من التاني is much + +896 +01:06:17,380 --> 01:06:21,280 +larger than the other is much larger مش larger is + +897 +01:06:21,280 --> 01:06:24,280 +much larger than اه ساعتها ال dispersion forces + +898 +01:06:24,280 --> 01:06:27,580 +will likely to determine its physical properties + +899 +01:06:27,580 --> 01:06:31,360 +بتكون ال dispersion forces أكبر يعني أعلى وهي اللي + +900 +01:06:31,360 --> 01:06:36,680 +بتحدد خصائصه بشكل أكبر فهي يعني حاجة للأمانة يعني + +901 +01:06:36,680 --> 01:06:38,640 +بدها حذر في استخدامها + +902 +01:06:42,500 --> 01:06:45,360 +الان لو اجينا تاني للرسمة هذه اللي مرت معناها + +903 +01:06:45,360 --> 01:06:52,080 +سابقا نحاول نفهم منها فكرة جديدة بقول انا لو اطلعت + +904 +01:06:52,080 --> 01:06:58,400 +CH4, SIH4, Germanium H4, Tin H4 بلاحظ في عندى + +905 +01:06:58,400 --> 01:07:02,120 +اتجاه انه اه والله كل ما زاد ال molecular mass + +906 +01:07:02,120 --> 01:07:09,580 +بزيد ال boiling point هان ببدأ يعني هذا لأهذا لأ + +907 +01:07:09,580 --> 01:07:14,640 +بقول والله لو بدأت من هنا اه لما نزيد المكتر ماسك + +908 +01:07:14,640 --> 01:07:18,400 +بتزيد ال boiling point طب من هنا برضه نفس الكلام + +909 +01:07:18,400 --> 01:07:21,500 +الا ان ال H2 و ال HF و ال H3 لأ + +910 +01:07:24,750 --> 01:07:28,950 +الـ H2O لأ والله حتى ال boiling point تبعته أعلى + +911 +01:07:28,950 --> 01:07:32,790 +كتير، مع أن ال formula الواقعية لها أقل، و ال HF + +912 +01:07:32,790 --> 01:07:36,990 +ال formula الواقعية لها أقل من هذا، لكن ال boiling + +913 +01:07:36,990 --> 01:07:40,710 +point تبعته أعلى، الأبونيا يعني formula الواقعية + +914 +01:07:40,710 --> 01:07:44,090 +قليلة، هي المفروض تكون هنا، كلهم يكونوا هنا تحتإيش + +915 +01:07:44,090 --> 01:07:48,390 +معنى هدول التلاتة بالذات بيعطوني very high boiling + +916 +01:07:48,390 --> 01:07:52,150 +points؟ بنقول السبب في هذا الكلام في الحقيقة هو + +917 +01:07:52,150 --> 01:07:57,790 +نوع آخر من أنواع ال intermolecular forces ال van + +918 +01:07:57,790 --> 01:08:02,990 +der Waals forces بنسميه hydrogen bonding ليه؟ لأن + +919 +01:08:02,990 --> 01:08:06,450 +هدول التلاتة تحديدا فيهم نوع من أنواع ال + +920 +01:08:06,450 --> 01:08:11,430 +intermolecular forces القوية بشكل استثنائيبشكل + +921 +01:08:11,430 --> 01:08:14,190 +استثنائي هو ليش هدول بيعطوني high boiling point + +922 +01:08:14,190 --> 01:08:18,330 +لأن الـ Intermolecular forces ايش مالهم قوية جدا + +923 +01:08:18,330 --> 01:08:21,570 +.. قوية جدا ال Intermolecular forces طب ليش قوية + +924 +01:08:21,570 --> 01:08:24,490 +طبعا مش زي صغير ال molecular mass بقته قليلة قال + +925 +01:08:24,490 --> 01:08:29,230 +اه نوع ال Intermolecular force اللي بتتكون قوية + +926 +01:08:29,230 --> 01:08:33,790 +ايش هي قال اسمها hydrogen bonding hydrogen bonding + +927 +01:08:33,790 --> 01:08:38,890 +ايش هي ال hydrogen bonding قال ال hydrogen bonding + +928 +01:08:38,890 --> 01:08:49,370 +بتحصلبين ال H المرتبطة ب O أو ال H المرتبطة ب N أو + +929 +01:08:49,370 --> 01:08:59,630 +ال H المرتبطة ب F هذه مع O أو N أو F وهذه نفس + +930 +01:08:59,630 --> 01:09:08,290 +الكلام هذه الرابطةبنقولها hydrogen bonding اذا انا + +931 +01:09:08,290 --> 01:09:15,790 +في عندي تلت عناصر فقط النيتروجين والاكسوجين + +932 +01:09:15,790 --> 01:09:19,570 +والفلورين وهدول تحديدا لان ممكن الالكتروناكيف + +933 +01:09:19,570 --> 01:09:23,070 +تباعتهم عالية المهم هدول التلاتة اذا كان مطبق + +934 +01:09:23,070 --> 01:09:26,990 +معاهم H كإنتر موليكولير + +935 +01:09:36,500 --> 01:09:46,600 +هذا الـ H مربوطة مع + +936 +01:09:46,600 --> 01:09:49,580 +الـ O ممكن تكون هذه الـ O + +937 +01:09:57,490 --> 01:10:06,830 +الـ F أو ممكن تكون كمان هذه الـ O مع + +938 +01:10:06,830 --> 01:10:13,310 +ال N فهذه الرابطة إيش بنسميها؟ Hydrogen bond هذه + +939 +01:10:13,310 --> 01:10:20,650 +الرابطة exceptionally strong يعني أقوى يعني من + +940 +01:10:20,650 --> 01:10:24,930 +الروابط الأخرى بشكل استثنائيبشكل استثنائي وهذا + +941 +01:10:24,930 --> 01:10:29,670 +اللي بيخلّي ال boiling point للميّه وال boiling + +942 +01:10:29,670 --> 01:10:33,990 +point للـHF وال boiling point للأمونيا أعلى مما هو + +943 +01:10:33,990 --> 01:10:38,230 +متوقع من الجدوة من ال curves المفروض يكونوا ايه + +944 +01:10:38,230 --> 01:10:42,530 +لتحتهان لكن لأ لجناهم عالين كتير هذا الكلام ناشئ + +945 +01:10:42,530 --> 01:10:47,560 +عن ال hydrogen bondingهذه الـ hydrogen bonding هي + +946 +01:10:47,560 --> 01:10:50,420 +نوع من أنواع الـ dipole-dipole interaction في + +947 +01:10:50,420 --> 01:10:56,320 +الحقيقة لكن بيحصل between ايه؟ between ال H من + +948 +01:10:56,320 --> 01:11:02,240 +جزيء مع ال O أو ال F أو ال N من جزيء آخر، ماشي؟ + +949 +01:11:02,240 --> 01:11:05,860 +فهي عبارة عن dipole-dipole interaction لكن الـ + +950 +01:11:05,860 --> 01:11:10,020 +dipole-dipole هذا interaction قوي بشكل استثنائي + +951 +01:11:10,840 --> 01:11:14,200 +وهذا النوع من الـ dipole-dipole اللي بيكون عبارة + +952 +01:11:14,200 --> 01:11:18,060 +عن رابط بين الـH و الـO أو الـH و الـF أو الـH و + +953 +01:11:18,060 --> 01:11:22,980 +الـN هذا بنقوله hydrogen bond و هو زي ما قلت + +954 +01:11:22,980 --> 01:11:27,580 +unusually أو exceptionally strong + +955 +01:11:29,720 --> 01:11:33,680 +في الحقيقة يعني لو قلنا هذا جزء ميّه وهذا جزء ميّه + +956 +01:11:33,680 --> 01:11:39,800 +فهي ال H مرتبطة بال O هذا شكل الميّه لما تكون يعني + +957 +01:11:39,800 --> 01:11:44,700 +at very low temperatures يعني تكون تلج عادة بيكون + +958 +01:11:44,700 --> 01:11:47,900 +في بينها فراغات لما تتنظم في بينها فراغات وعشان + +959 +01:11:47,900 --> 01:11:52,060 +هيك الحجم تبعها بيزيد مش موضوعنا يعني مش موضوعنا + +960 +01:11:52,060 --> 01:11:55,960 +لو + +961 +01:11:55,960 --> 01:12:01,540 +أجينا لمثلًا ال acetic acidالـ Acetic Acid هذا هو + +962 +01:12:01,540 --> 01:12:09,340 +CH3COOH + +963 +01:12:09,340 --> 01:12:20,160 +وممكن نقول والله أو أو نقول هيك أحسن HOCOCH3 + +964 +01:12:20,160 --> 01:12:24,120 +فنقول هان الـ H هذه مرتبطة بـ O و هذه O لحالها + +965 +01:12:24,120 --> 01:12:28,800 +هيها إذا ممكن يكون في عندي إيه hydrogen bond و هان + +966 +01:12:28,800 --> 01:12:33,570 +هذه الـ Oممكن الـ H هاد إيه؟ هاي Hydrogen bond + +967 +01:12:33,570 --> 01:12:39,530 +يبقى أكم رابطة الـ Acetic acid بيكوّن قال رابطتين + +968 +01:12:39,530 --> 01:12:44,430 +Hydrogen bonds رابطتين طب لو جينا اتطلعنا على حاجة + +969 +01:12:44,430 --> 01:12:48,470 +فيها عدد ذرات زيه تقريبا يعني الموليكورامات 60 + +970 +01:12:48,470 --> 01:12:54,030 +وهدا موليكورامات 60 اللي هو one-propanol هاي CH3 + +971 +01:12:54,030 --> 01:13:07,270 +CH2 CH2 OHوهي H وهي O وهي CH2 وهي CH2 وهي .. هان + +972 +01:13:07,270 --> 01:13:11,310 +هذا ممكن و الله انه يكون رابطة hydrogen bond هان + +973 +01:13:11,310 --> 01:13:15,970 +أكام رابطة hydrogen bond؟ واحدة هان تنتين فبنلاقي + +974 +01:13:15,970 --> 01:13:20,570 +انه التنتين أكبر من واحدة معنى الكلام الترابط بين + +975 +01:13:20,570 --> 01:13:25,330 +جزيئات ال acetic acid هيكون ايه أقوى ولا أضعف من + +976 +01:13:25,330 --> 01:13:33,080 +الترابط بين جزيئات الأنه أقوى في الترابط .. أحلو + +977 +01:13:33,080 --> 01:13:36,240 +يعني ال .. أستيك أسد على شرح البلاجة أنه ال + +978 +01:13:36,240 --> 01:13:39,720 +boiling point له تلت مية و واحد وتسعين بينما ال + +979 +01:13:39,720 --> 01:13:45,520 +boiling point للإيه؟ ل .. ال .. بروبانول تلت مية و + +980 +01:13:45,520 --> 01:13:49,840 +سبعين لا + +981 +01:13:49,840 --> 01:13:53,260 +هو بس بيحاول يعلمنا يعني مديش .. مديش هيك ترسميهم + +982 +01:13:53,260 --> 01:13:58,940 +يعني هو بحاول بس يعلمنا يعني مش أكتروإذا مارمعك + +983 +01:13:58,940 --> 01:14:02,120 +تتذكر إن الاستيك أسد فيه رابطات إن إذا مارمعك + +984 +01:14:02,120 --> 01:14:08,540 +هاتروس ماهمش لأ يعني ممكن إنه ال .. هيك خلصنا + +985 +01:14:08,540 --> 01:14:13,040 +Vanderwaal forces اللي هم قلنا تلت أنواع London + +986 +01:14:13,040 --> 01:14:16,840 +forces وDipole-Dipole و Hydrogen bonding الآن + +987 +01:14:16,840 --> 01:14:22,700 +بنيجي لنوع آخر من ال Intermolecular forces بنقوله + +988 +01:14:22,700 --> 01:14:26,840 +Ion-Dipole interactions Ion-Dipole interactions + +989 +01:14:28,550 --> 01:14:32,810 +بقول الـ ion-dipole interactions هذي مهمة فقط في + +990 +01:14:32,810 --> 01:14:38,970 +المحليل ليه؟ لأنه أنا عند الـ liquid يعني .. يعني + +991 +01:14:38,970 --> 01:14:44,730 +خليني أقول مافيش فيه أيونات فأنا بضيف عليه أيون + +992 +01:14:44,730 --> 01:14:48,250 +يعني بتدوب مثلا فيه Sodium chloride فصار محلول مش + +993 +01:14:48,250 --> 01:14:52,670 +liquid صار solution هي مهمة فقط في ال إيه؟ في + +994 +01:14:52,670 --> 01:14:56,240 +المحليل بقول أناالكلورايت يمكن شوفنا هذا الكلام + +995 +01:14:56,240 --> 01:14:59,920 +سابقا الميه partial positive و partial negative + +996 +01:14:59,920 --> 01:15:03,560 +صح؟ الأكسجين partial negative و ال H partial + +997 +01:15:03,560 --> 01:15:06,400 +positiveفالـ partial positive مع ال chloride + +998 +01:15:06,400 --> 01:15:09,800 +partial negative بيعمله زي سفير يعني سمناها زمان + +999 +01:15:09,800 --> 01:15:13,800 +water of solvation أو water of hydration إذا كانوا + +1000 +01:15:13,800 --> 01:15:18,380 +متذكرين أخدناها عمار معنى والصوديا نفس الكلام موجب + +1001 +01:15:18,380 --> 01:15:23,160 +إذا الطرف السالب من الميه بده يجرب ال solvent بده + +1002 +01:15:23,160 --> 01:15:26,840 +يجرب عليه بده يعطيني برضه water of hydration أو + +1003 +01:15:26,840 --> 01:15:32,000 +water of solvation بنقول إحنا ال ion-dipole + +1004 +01:15:32,000 --> 01:15:37,180 +interactionsكويس هذا هيو دايبول عشان هيك وهذا ايون + +1005 +01:15:37,180 --> 01:15:41,690 +فهذا ايون دايبولالـ Ion-dipole interactions هي + +1006 +01:15:41,690 --> 01:15:49,410 +السبب الرئيسي في قدرة + +1007 +01:15:49,410 --> 01:15:54,610 +بعض الأملاح على الدوبان في الميّه، لو تريدين تدوب + +1008 +01:15:54,610 --> 01:15:58,230 +ملح، ليش بحب يدوب؟ لأنه في عندنا Ion-dipole + +1009 +01:15:58,230 --> 01:16:01,130 +interactions ليش الملح بدوب في الميه؟ ليش الأملاح + +1010 +01:16:01,130 --> 01:16:05,850 +بدوب في الميه؟ لأنه عندنا بشكل أساسي Ion-dipole + +1011 +01:16:05,850 --> 01:16:11,220 +interactionsفهذا برضه أحد أنواع الـ Intermolecular + +1012 +01:16:11,220 --> 01:16:18,600 +Forces هذا كتايون الموجب بنسميه كتايون والسالب + +1013 +01:16:18,600 --> 01:16:22,920 +بالأيون السالب بنقوله أنايون فهذا كتايون Dipole + +1014 +01:16:22,920 --> 01:16:28,000 +Attraction زي ما أحنا شايفينها بينما هذا أنايون + +1015 +01:16:28,000 --> 01:16:33,140 +Dipole Attraction ماعنش كتير بنتكلم عنه الآن بس + +1016 +01:16:33,140 --> 01:16:38,700 +بدي أعطي فكرةيعني سرعوك تطلع عليهم برضه في البيت + +1017 +01:16:38,700 --> 01:16:44,440 +يعني which of the following pairs has a higher + +1018 +01:16:44,440 --> 01:16:49,580 +boiling point هذا ولا هذا؟ أنه بده يكون له higher + +1019 +01:16:49,580 --> 01:16:51,680 +boiling point؟ إيش اللي إله higher boiling point + +1020 +01:16:51,680 --> 01:16:56,860 +في البداية؟ اللي فيه stronger intermolecular + +1021 +01:16:56,860 --> 01:16:59,960 +forces فإيش أنواع ال intermolecular forces اللي + +1022 +01:16:59,960 --> 01:17:02,380 +هين موجودين؟ + +1023 +01:17:04,960 --> 01:17:08,440 +Dipole اه لكن برضه كمان في عندي ال hydrogen + +1024 +01:17:08,440 --> 01:17:12,320 +bonding هذا مابدناش ننساه اللي انه OH معناه ان في + +1025 +01:17:12,320 --> 01:17:18,280 +عندي hydrogen bonding طب و هذا ايش فيه نفس الاشي + +1026 +01:17:18,280 --> 01:17:22,620 +طب انه بدي يكون له higher boiling point ال + +1027 +01:17:22,620 --> 01:17:26,300 +hydrogen واحدة و hydrogen واحدة فش فيه dipole و + +1028 +01:17:26,300 --> 01:17:30,580 +هذا dipole dispersion forces ان هو اللي dispersion + +1029 +01:17:30,580 --> 01:17:35,960 +forces أكبراه هذا هو ليه؟ لأنه إله higher + +1030 +01:17:35,960 --> 01:17:42,340 +molecular mass HF ولا HBR؟ + +1031 +01:17:42,340 --> 01:17:45,560 +هو خدوا بالكم، هذي أنا بقول .. أنا بده أقول هذي + +1032 +01:17:45,560 --> 01:17:51,480 +هيك، ليش؟ مش عارف أنا، ليش؟ لأن ال HBR عادة .. + +1033 +01:17:51,480 --> 01:17:58,540 +عادة ال HBR إيش ماله؟الـ HPR الو الو high + +1034 +01:17:58,540 --> 01:18:01,400 +molecular mass فالمفروض ان يكون فيه high + +1035 +01:18:01,400 --> 01:18:05,900 +dispersion force لكن الـ HF ايش الو في hydrogen + +1036 +01:18:05,900 --> 01:18:10,080 +bonding فهي تعتمد تعتمد تعتمد مش عارف يعني هو طبعا + +1037 +01:18:10,080 --> 01:18:16,440 +من الجدول اللي معانا اللي يعني مشكوك + +1038 +01:18:16,440 --> 01:18:23,290 +فيه ماعرفش بالظبط يعني طب H2O ولا H2S؟الـH تقول + +1039 +01:18:23,290 --> 01:18:31,470 +أنه فيها إيه؟ Hydrogen bonding أكتر PR2 ولا ICL؟ + +1040 +01:18:31,470 --> 01:18:38,710 +ليش مش ال PR2؟ لأ، ما تتكلماش عن مسافات، ما + +1041 +01:18:38,710 --> 01:18:41,390 +تتكلماش عن مسافات، قولنا إنه هذه بس dispersion + +1042 +01:18:41,390 --> 01:18:45,270 +forces، هذه dispersion forces زائد + +1043 +01:18:47,650 --> 01:19:00,990 +أه ICL-Dipole طيب CH-CL تلاتة ولا CH-PR تلاتة؟ لأ + +1044 +01:19:00,990 --> 01:19:04,070 +مش الـCL تلاتة CH-PR تلاتة ليه؟ لأن هذي إلها + +1045 +01:19:04,070 --> 01:19:07,730 +higher molecular mass higher molecular mass PR + +1046 +01:19:07,730 --> 01:19:10,570 +أكبر من الـPR أكبر من الـPR أكبر من الـPR أكبر من + +1047 +01:19:10,570 --> 01:19:10,730 +الـPR أكبر من الـPR أكبر من الـPR أكبر من الـPR + +1048 +01:19:10,730 --> 01:19:10,750 +أكبر من الـPR أكبر من الـPR أكبر من الـPR أكبر من + +1049 +01:19:10,750 --> 01:19:10,830 +الـPR أكبر من الـPR أكبر من الـPR أكبر من الـPR + +1050 +01:19:10,830 --> 01:19:10,970 +أكبر من الـPR أكبر من الـPR أكبر من الـPR أكبر من + +1051 +01:19:10,970 --> 01:19:10,970 +الـPR أكبر من الـPR أكبر من الـPR أكبر من الـPR + +1052 +01:19:10,970 --> 01:19:11,630 +أكبر من الـPR أكبر من الـPR أ + +1053 +01:19:18,500 --> 01:19:29,020 +ethanol ولا CH2 CH CH2 برضه هذه التانية OH فيها + +1054 +01:19:29,020 --> 01:19:33,100 +تنتين hydrogen bonds اه قويات كتير يبقى يعني كلام + +1055 +01:19:33,100 --> 01:19:37,300 +زي هيك بيكون سهل احطلكم بعض ال slides هنا حاولوا + +1056 +01:19:37,300 --> 01:19:41,620 +انكم تتطلعوا عليهم يمكن الحصة الجاية نرجعها مافيش + +1057 +01:19:41,620 --> 01:19:44,740 +مشكلة طب خيانه جفان وإذا الله راضي الحصة الجاية + +1058 +01:19:44,740 --> 01:19:45,320 +بنكمل + diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/M9PaeSfPGKw_raw.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/M9PaeSfPGKw_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..8fe847feaec68bd6be4b4a92988a0ac05db6b03f --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/M9PaeSfPGKw_raw.srt @@ -0,0 +1,3804 @@ +1 +00:00:21,190 --> 00:00:24,170 +بسم الله الرحمن الرحيم إذا الله راضي اليوم بنكمل + +2 +00:00:24,170 --> 00:00:28,690 +في ال chapter اللي بتحدث عن ال thermochemistry أو + +3 +00:00:28,690 --> 00:00:34,170 +الكيميا الحرارية شوفنا في الحصة الماضية دالة جديدة + +4 +00:00:34,170 --> 00:00:40,950 +سمنها ال enthalpy فال enthalpy هي عبارة عن دالة + +5 +00:00:40,950 --> 00:00:44,370 +بتقيس ال heat flow أو ال heat content لل reaction + +6 +00:00:47,690 --> 00:00:50,750 +فلو افترضنا يعني انه في عنديا as confined في + +7 +00:00:50,750 --> 00:00:54,550 +container فبنقول انه هذا ال system عندي + +8 +00:00:54,550 --> 00:00:59,210 +characterized by several properties اللي هي غالبا + +9 +00:00:59,210 --> 00:01:06,250 +ممكن نتحدث عن ال pressure وال volume واحنا بنعرف + +10 +00:01:06,250 --> 00:01:12,810 +انه ال internal energy كانت ان هي عبارة عن state + +11 +00:01:12,810 --> 00:01:19,340 +function بمعنى انهقيمتها فقط تعتمد على الحالة + +12 +00:01:19,340 --> 00:01:22,100 +الأولية الها ال initial state والحالة النهائية ال + +13 +00:01:22,100 --> 00:01:26,400 +final state بحيث ان ال delta E كان سوى E final + +14 +00:01:26,400 --> 00:01:27,460 +minus E initial + +15 +00:01:38,240 --> 00:01:42,820 +الدلتا P هي P final minus P initial والدلتا V هي V + +16 +00:01:42,820 --> 00:01:45,840 +final minus V initial + +17 +00:01:47,530 --> 00:01:51,750 +تحدثنا أيضًا عن إنه بإمكاننا إن نعمل combination + +18 +00:01:51,750 --> 00:01:55,350 +ما بين التلاتة state functions الـE والـP والـV + +19 +00:01:55,350 --> 00:01:58,830 +بحيث إنه نحصل على state function جديدة سمنها + +20 +00:01:58,830 --> 00:02:05,610 +الـEnthalpy بحيث إنه الـH بدها تساوي E زائد الـPV + +21 +00:02:06,340 --> 00:02:11,200 +زي ما هنشوف هذه الدالة الجديدة اللي هي الـ H كويس + +22 +00:02:11,200 --> 00:02:15,300 +احنا مهتمين فيها at constant pressure يعني ال + +23 +00:02:15,300 --> 00:02:19,880 +condition اللي هنشتغل عنده غالبا هو ال condition + +24 +00:02:19,880 --> 00:02:25,240 +اللي بيكون فيه الضغط ثابت يعني الضغط الجوي لأن + +25 +00:02:25,240 --> 00:02:29,800 +معظم تفاعلاتنا اللي بتتم في المختبرات بتتم عند ضغط + +26 +00:02:29,800 --> 00:02:35,100 +جوي مش تحت ضغوط مختلفة على أي حال الـ H عرفناها + +27 +00:02:35,100 --> 00:02:40,490 +دالة جديدةسمناها enthalpy عرفناها على أنها تساوي E + +28 +00:02:40,490 --> 00:02:46,550 +زائد PV وبما أن ال E دالة حالة و ال P و ال V أيضا + +29 +00:02:46,550 --> 00:02:50,110 +دوايا الحالة state functions فال H بالضرورة تعتبر + +30 +00:02:50,110 --> 00:02:58,480 +state functionخلينا نتطلع على كيف بدنا نستخدم الـ + +31 +00:02:58,480 --> 00:03:03,960 +H ليش الـ H حاجة مهمة فخلينا نتطلع على ال pressure + +32 +00:03:03,960 --> 00:03:10,260 +volume work فمثلا في عندي تفاعل زينك مع الـ HCl أو + +33 +00:03:10,260 --> 00:03:16,260 +أي حمض بعطينا زينك 2 plus و هيدروجينهن معنى الكلام + +34 +00:03:16,260 --> 00:03:18,640 +هذا ال system لو اعتبرنا هذا هو ال system تبعي + +35 +00:03:18,640 --> 00:03:22,320 +معنى كلام ال system إيش بيعطيني جاز يبقى ال volume + +36 +00:03:22,320 --> 00:03:26,460 +للجاز إيش بده يجعله بده يزيد بده يزيد معناته إن ال + +37 +00:03:26,460 --> 00:03:28,900 +system هذا بيعمل PV work + +38 +00:03:31,620 --> 00:03:35,980 +الحجم الغاز بدو يزيد اذا انا عندي ال work P delta + +39 +00:03:35,980 --> 00:03:40,740 +V فبقول والله ال work الغاز هذا بيعمل work او ال + +40 +00:03:40,740 --> 00:03:44,980 +system بيعمل work زي ما هنشوف في الشكل اللي قدامي + +41 +00:03:44,980 --> 00:03:49,180 +هاي هنا شوية زينك وهي انا عندي HCL وهي لحظة ال + +42 +00:03:49,180 --> 00:03:56,680 +piston له خليني اقول يعني height معين فلو بس لفنا + +43 +00:03:56,680 --> 00:04:01,780 +هذه القطعة الزجاج اللى موجود فيها الـ Zinc من + +44 +00:04:01,780 --> 00:04:05,200 +اللحظة ان الـ Zinc بينزل على الـ HC اللى بيتفاعل + +45 +00:04:05,200 --> 00:04:09,540 +فال Piston اشماله بيرتفع الارتفاع هذا عبارة عن + +46 +00:04:09,540 --> 00:04:14,700 +خليني اقول اذا كان اعتبرنا انه هان عند ال V V1 و + +47 +00:04:14,700 --> 00:04:18,640 +هاد V أو V initial و V final هاد ال Delta V او هاد + +48 +00:04:18,640 --> 00:04:24,180 +عبارة عن حجم الغاز اللى بهمنيش كتير الحجم بهمني + +49 +00:04:24,180 --> 00:04:27,900 +اناالـ Delta V على المهنوش الارتفاع بالظبط بيهم + +50 +00:04:27,900 --> 00:04:33,180 +الـ Delta V فالـ Delta V هي عبارة عن كمية تستخدم + +51 +00:04:33,180 --> 00:04:38,060 +في قياس ال work يبقى الغاز بيعمل work الغاز بيعمل + +52 +00:04:38,060 --> 00:04:42,140 +work على ال environment فهذا الشيء المهم بالنسبالي + +53 +00:04:42,140 --> 00:04:47,520 +ال work اللي طوى شفناه هذا عبارة عن expansion work + +54 +00:04:48,310 --> 00:04:52,030 +Expansion work يعني ال system نفسه هو اللي بيعمل + +55 +00:04:52,030 --> 00:04:55,110 +ال work على ال surroundings و احنا افهمنا سابقا + +56 +00:04:55,110 --> 00:04:58,130 +انه لما ال system هو اللي يعمل work على ال + +57 +00:04:58,130 --> 00:05:03,660 +surroundings معناته ال work هذا negativeبينما لو + +58 +00:05:03,660 --> 00:05:06,100 +ان عمل لو ال surroundings هي اللي عملت work على ال + +59 +00:05:06,100 --> 00:05:09,080 +system فبكون عندنا ال convention ان ال work + +60 +00:05:09,080 --> 00:05:13,160 +positive فعندي ال expansion work هو عبارة عن + +61 +00:05:13,160 --> 00:05:15,580 +negative value في ال W سواء minus P دلتا V لل + +62 +00:05:15,580 --> 00:05:18,380 +system اللي ايه اللي ذكرناها سابقا لكن لو كان في + +63 +00:05:18,380 --> 00:05:22,940 +عندي system اخر مثلا مادتين بتفاعلوا عشان يعطوني + +64 +00:05:22,940 --> 00:05:28,540 +ال solid فالحجم بيقلأه إذا ال volume عندي صار أقل + +65 +00:05:28,540 --> 00:05:34,460 +لمعنى الكلام أو بيكون عندي الشغل معمول على ال + +66 +00:05:34,460 --> 00:05:36,640 +system مش ال system هو اللي بيعمل الشغل على + +67 +00:05:36,640 --> 00:05:41,820 +surroundings فمعنى الكلام بيكون ال P Delta V قيمة + +68 +00:05:41,820 --> 00:05:46,980 +أو الورق قيمة موجة بقى طبعا احنا ذكرنا ال sign + +69 +00:05:46,980 --> 00:05:50,520 +conventions الحصة الماضية ومش هنعيد هذا الكلام + +70 +00:05:54,580 --> 00:06:03,660 +خلّيني أقول إن الـ H تساوي E زائد PV لأن الـ H + +71 +00:06:03,660 --> 00:06:10,220 +تساوي E زائد PV لأن الـ H تساوي E زائد PV لأن الـ + +72 +00:06:10,220 --> 00:06:14,160 +H تساوي E زائد PV لأن الـ H تساوي E زائد PV لأن + +73 +00:06:14,160 --> 00:06:15,540 +الـ H تساوي E زائد PV لأن الـ H تساوي E زائد PV + +74 +00:06:15,540 --> 00:06:17,900 +لأن الـ H تساوي E زائد PV لأن الـ H تساوي E زائد + +75 +00:06:17,900 --> 00:06:18,700 +PV لأن الـ H تساوي E زائد PV لأن الـ H تساوي E + +76 +00:06:18,700 --> 00:06:19,300 +زائد PV لأن الـ H تساوي E زائد PV لأن الـ H تساوي + +77 +00:06:19,300 --> 00:06:20,160 +E زائد PV لأن الـ H تساوي E زائد PV لأن الـ H + +78 +00:06:20,160 --> 00:06:22,380 +تساوي E زائد PV لأن الـ H تسافالـ Delta S سوى الـ + +79 +00:06:22,380 --> 00:06:26,160 +Delta للـ E زائد الـ PV أو الـ Delta S سوى Delta E + +80 +00:06:26,160 --> 00:06:31,200 +زائد P Delta V زائد V Delta P لكن أنا ذكرت سابقا + +81 +00:06:31,200 --> 00:06:34,240 +أننا مهتمين بالـ Enthalpy at A الـ Constant + +82 +00:06:34,240 --> 00:06:38,280 +Pressure لأن معظم العمليات اللي بتتم سواء ذوبان .. + +83 +00:06:38,280 --> 00:06:45,500 +خليني أقول ثلج .. يعني أي مادة ذوبانها ال melting + +84 +00:06:45,500 --> 00:06:52,240 +ال boiling أي تفاعل كيميائيconstant pressure في + +85 +00:06:52,240 --> 00:06:57,120 +الجو العادي عند واحد أتموسفير فبما أنه احنا بنتكلم + +86 +00:06:57,120 --> 00:07:00,160 +عن ال H at constant pressure فمعنى الكلام ال V + +87 +00:07:00,160 --> 00:07:04,860 +Delta P راح تسوى صفر لإن ال Delta P a constant + +88 +00:07:04,860 --> 00:07:08,380 +pressure لإن P final يسوى P initial يبقى ال V + +89 +00:07:08,380 --> 00:07:13,700 +Delta P بتسوى صفر معنى الكلام ال Delta H كإنثال P + +90 +00:07:13,700 --> 00:07:18,380 +بدها تسوى ال Delta E زائد ال P Delta V كمان يسهد + +91 +00:07:18,380 --> 00:07:23,710 +الكلام؟هذا ما حكيناه الحصة الماضية لكن دعنا نكمل + +92 +00:07:23,710 --> 00:07:29,050 +خطوة إضافية على هذا الكلام فبقول تعالوا نتطلع على + +93 +00:07:29,050 --> 00:07:32,210 +ال expansion work يعني نفس ال system اللي ذكرناها + +94 +00:07:32,210 --> 00:07:36,950 +قبل شوية وبقول هايه بالخط الأحمر ان work is done + +95 +00:07:36,950 --> 00:07:40,690 +by the system لأنه expansion ال system بتمدد كويس؟ + +96 +00:07:40,690 --> 00:07:44,730 +يذن عند ال work negative لأن ال system هو اللي + +97 +00:07:44,730 --> 00:07:48,810 +بيعمل work ال system هو اللي بيعمل workفبنقول W + +98 +00:07:48,810 --> 00:07:53,930 +سوى minus P delta V يعني ال Delta E بتساوي Q انا + +99 +00:07:53,930 --> 00:07:56,690 +قلت Q زي ال W هاي ال Delta E اذا كان متذكره من + +100 +00:07:56,690 --> 00:08:01,330 +الحص الماضية ال Delta E بتساوي Q زي ال W لكن ال W + +101 +00:08:01,330 --> 00:08:05,310 +هي هنأيه بما انه expansion work minus P delta V + +102 +00:08:05,310 --> 00:08:10,450 +اذا ال Delta E بتساوي Q minus P delta V طيب تعالوا + +103 +00:08:10,450 --> 00:08:16,230 +نشوف ايش نتيجة هذه المعادلة اذا كانت اشتغلت at + +104 +00:08:16,230 --> 00:08:21,520 +constant volumeالـ constant volume معناته الـ Vi + +105 +00:08:21,520 --> 00:08:25,600 +بتساوي Vf أو الـ V initial بتساوي V final معناته + +106 +00:08:25,600 --> 00:08:29,600 +الـ Delta V جداش سفر يبقى Delta E بتساوي QV بس + +107 +00:08:29,600 --> 00:08:33,340 +وقتاش اه لما ال Delta V اللي هو وقتاش يعني ال + +108 +00:08:33,340 --> 00:08:36,860 +constant volume يبقى ال constant volume ممكن انا + +109 +00:08:36,860 --> 00:08:42,590 +اعرف ال Delta E عليها والله ال Q ال heatflow at + +110 +00:08:42,590 --> 00:08:47,850 +constant volume الهي تفلو at constant volume او + +111 +00:08:47,850 --> 00:08:52,050 +الهي تتشيج at constant volume تمام؟ يبجي هذه + +112 +00:08:52,050 --> 00:08:59,090 +معادلة كتير حلوة طيب تعالوا ايش بحصل لو اشتغلنا at + +113 +00:08:59,090 --> 00:09:03,760 +constant pressure مش at constant volumeبقول ال + +114 +00:09:03,760 --> 00:09:06,560 +constant pressure delta E بتساوي Q at constant + +115 +00:09:06,560 --> 00:09:10,900 +pressure minus P delta V يعني هي ال delta E بتساوي + +116 +00:09:10,900 --> 00:09:13,500 +نفس ال system بدي أدرس بس ايه مش at constant + +117 +00:09:13,500 --> 00:09:15,900 +volume ال constant volume درسناه اللي جينا ال + +118 +00:09:15,900 --> 00:09:19,800 +delta E بتساوي QV مافيش مشكلة طب ال constant + +119 +00:09:19,800 --> 00:09:24,160 +pressure قال ال delta E بتساوي QP minus P delta V + +120 +00:09:24,870 --> 00:09:29,990 +يعني Delta E بتساوي Q at constant pressure minus + +121 +00:09:29,990 --> 00:09:33,070 +ال P Delta V زي ما هي، مالغنهاش لأن Delta V لها + +122 +00:09:33,070 --> 00:09:35,750 +قيمة at constant pressure إذا كان في عندي + +123 +00:09:35,750 --> 00:09:39,550 +expansion work طيب تعالي و ارتب، تعالي ناخد ال QP + +124 +00:09:39,550 --> 00:09:43,790 +برا و ارتب، و ال QP بتساوي Delta E زائد P Delta V + +125 +00:09:43,790 --> 00:09:48,710 +حلو؟ طب أنا عندي بعادلة Delta H بتساوي Delta E + +126 +00:09:48,710 --> 00:09:54,150 +زائد P Delta Vمعايا طب و لسه قلتها اذا ال delta H + +127 +00:09:54,150 --> 00:09:58,470 +ايش بتكون تساوي ال QP يبقى ال delta H هي عبارة عن + +128 +00:09:58,470 --> 00:10:02,930 +ال heat flow في ال system ال heat flow at constant + +129 +00:10:02,930 --> 00:10:08,250 +pressure بينما ال delta E هي عبارة عن ال heat flow + +130 +00:10:08,250 --> 00:10:13,950 +at constant volume اذا في عندي حاجتين كمان مرة ال + +131 +00:10:13,950 --> 00:10:19,120 +delta E بتساوي Q زائد W لكنللـ Expansion Work الـ + +132 +00:10:19,120 --> 00:10:23,400 +W بدي تسوي minus P Delta V إذا الـ Delta A بتسوي Q + +133 +00:10:23,400 --> 00:10:27,160 +minus P Delta V at constant volume Delta A هتسوي + +134 +00:10:27,160 --> 00:10:31,940 +QV لو عملنا نفس العملية .. نفس العملية السابقة + +135 +00:10:31,940 --> 00:10:36,080 +وقلنا والله الـ Delta A بديها تسوي Q زائد W يعني Q + +136 +00:10:36,080 --> 00:10:39,400 +minus P Delta V لكن هنشتغل at constant pressure + +137 +00:10:39,400 --> 00:10:42,740 +معناته الـ Delta A هتسوي QP minus P Delta V + +138 +00:10:42,740 --> 00:10:47,320 +رتبناها الـ QP هتسوي Delta E زائد P Delta Vلكن الـ + +139 +00:10:47,320 --> 00:10:51,660 +Delta H هي أصلا بتساوي Delta E زائد P Delta V اذا + +140 +00:10:51,660 --> 00:10:57,820 +ال Delta H هتساوي QP معنى الكلام Delta E تساوي Q + +141 +00:10:57,820 --> 00:11:00,680 +at constant volume او ال heat flow at constant + +142 +00:11:00,680 --> 00:11:07,220 +volume وال Delta H بتساوي QP او ال heat flow at + +143 +00:11:07,220 --> 00:11:12,560 +constant pressure تمام؟ هذا كتير مهم ليه؟ لأنه في + +144 +00:11:12,560 --> 00:11:19,290 +الحقيقةالـ QP هذه يمكن بسهولة تجريبيا أني أقيصها + +145 +00:11:19,290 --> 00:11:24,190 +الـ QP تجريبيا بسهولة ممكن أقيصها وإذا كان مابديش + +146 +00:11:24,190 --> 00:11:28,230 +أقيصها تجريبيا بقدر أحسبها حسابا سهل كتير هنشوف + +147 +00:11:28,230 --> 00:11:32,570 +أمثلة سهل كتير يبقى يا إما بعينها تجريبيا يا إما + +148 +00:11:32,570 --> 00:11:37,770 +بعينها حسابا الـ QP سهل جدا أني أوصله لكن الـ + +149 +00:11:37,770 --> 00:11:42,250 +Delta E مش سهلالـ delta E مش سهل لكن الـ QP سهل + +150 +00:11:42,250 --> 00:11:45,690 +جدا، عشان هيك يعتبر الـ enthalpy قيمة + +151 +00:11:45,690 --> 00:11:50,650 +thermodynamic value مفيدة جدا بالنسبالنا، ليه؟ + +152 +00:11:50,650 --> 00:11:53,550 +لأنها بتساوي زي ما احنا شايفين الـ QP، و الـ QP + +153 +00:11:53,550 --> 00:11:58,510 +سهل جدا ان احسبها، اذا يبقى بقدر احسب delta H لأي + +154 +00:11:58,510 --> 00:11:59,410 +reaction + +155 +00:12:02,200 --> 00:12:06,460 +طبعا يعني بعضكم متذكر انه احنا قلنا انه الـQ + +156 +00:12:06,460 --> 00:12:09,700 +ماهياش state function فكيف الـDelta H هي state + +157 +00:12:09,700 --> 00:12:13,220 +function بينما صارت تساوي QP مش state function او + +158 +00:12:13,220 --> 00:12:18,560 +الـDelta A هي state function بينما صارت تساوي QV + +159 +00:12:18,560 --> 00:12:21,820 +اللي هي مش state function لـQ لأن شفنا في الحصة + +160 +00:12:21,820 --> 00:12:26,090 +الماضية ان الـQ و الـW ماهماش state functionsليه؟ + +161 +00:12:26,090 --> 00:12:29,650 +لأنه زي ما شفناه ممكن افرغ بطارية بس عن طريق work + +162 +00:12:29,650 --> 00:12:36,230 +او ممكن افرغ بطارية عن طريق work و heat او يعني + +163 +00:12:36,230 --> 00:12:38,810 +ممكن افرغ بطارية عن طريق work اذا كان لجيت فيه + +164 +00:12:38,810 --> 00:12:46,130 +system يعني باسخنش لما افرغ البطارية فبما ان ال Q + +165 +00:12:46,130 --> 00:12:51,890 +و ال W بتعتمد على المسارإذن هي ليست الـ State + +166 +00:12:51,890 --> 00:12:53,970 +Function بينما الـ Delta E هي الـ State Function + +167 +00:12:53,970 --> 00:12:57,670 +فكيف هان بنقول إن الـ Delta E بتساوي الـ QV؟ الـ + +168 +00:12:57,670 --> 00:12:59,610 +Delta E هي الـ State Function طب و الـ QV هي مش + +169 +00:12:59,610 --> 00:13:02,430 +الـ State Function؟ و الـ Delta E عبارة عن State + +170 +00:13:02,430 --> 00:13:04,750 +Function من الـ QP مش الـ State Function؟ كيف؟ هذا + +171 +00:13:04,750 --> 00:13:09,290 +يعتبر فيه تناقض، بنقول لأ لأن الـ QV و الـ QP + +172 +00:13:09,290 --> 00:13:14,230 +معرفة عند .. يعني هان الـ QV معرفة عند constant + +173 +00:13:14,230 --> 00:13:18,060 +volume، لازم ال volume يكون constantلازم يكون ال + +174 +00:13:18,060 --> 00:13:23,220 +volume عندى constant و لازم يكون ال pressure عندى + +175 +00:13:23,220 --> 00:13:28,440 +constant و طبعا ال temperature هي معرفة at some + +176 +00:13:28,440 --> 00:13:32,220 +set of conditions فهي هذه تساوي هذه فقط عند شروط + +177 +00:13:32,220 --> 00:13:36,550 +معينةوالـ delta H تساوي QV فقط عند شروط معينة، لكن + +178 +00:13:36,550 --> 00:13:39,530 +في الحقيقة الـ Q ما هيش ال set function، الـ Q ما + +179 +00:13:39,530 --> 00:13:42,590 +هي ال set function، لا، لكن ليش هذا كلام حصل؟ جال + +180 +00:13:42,590 --> 00:13:46,750 +لأنه هذا التعريف تحت ايه؟ تحت ظروف معينة، اه + +181 +00:13:46,750 --> 00:13:50,490 +تساويها، بس اذا كان اختلفت هذه الشروط، لا تساويها، + +182 +00:13:50,490 --> 00:13:55,840 +مش دائما بتساويها، الا تحت الشروط هذهفبس يعني عشان + +183 +00:13:55,840 --> 00:14:00,320 +بعضكم ممكن يعني يشوف انه كيف public U ما هي state + +184 +00:14:00,320 --> 00:14:03,940 +function وهن تساوي حاجة تعتبر state function + +185 +00:14:03,940 --> 00:14:09,960 +بالنسبة لقيم الـ delta E والـ delta H بنلاحظ انه + +186 +00:14:09,960 --> 00:14:14,020 +الـ delta H تساوي delta E زائد P delta V مفهومة + +187 +00:14:14,020 --> 00:14:18,900 +اذا لو رفعنا ال P delta V الـ delta H تساوي الـ + +188 +00:14:18,900 --> 00:14:25,090 +delta E لو كان هذا القيمة قليلة جداكويس ايش + +189 +00:14:25,090 --> 00:14:27,510 +بنلاحظ؟ بنلاحظ ان ال delta E بتساوي ال delta H + +190 +00:14:27,510 --> 00:14:31,330 +بنلاحظ ان ال delta E لو رفعنا ال P delta V اللي هو + +191 +00:14:31,330 --> 00:14:37,030 +ال work بنلاحظ ان ال delta H تساوي ال delta E طب + +192 +00:14:37,030 --> 00:14:40,930 +هل هذا ال work قيمة كبيرة؟ بنقول للتفاعلات اللي + +193 +00:14:40,930 --> 00:14:45,110 +بتتم في المحاليل زي معظم التفاعلات تبعتنا كويس + +194 +00:14:45,110 --> 00:14:47,130 +للتفاعلات اللي بتتم في المحاليل at constant + +195 +00:14:47,130 --> 00:14:50,970 +pressure عادة و .. و .. يعني constant pressure + +196 +00:14:50,970 --> 00:14:57,220 +بنقول واللهجدّاش الـ Delta V عندك مثلا محلول بيحصل + +197 +00:14:57,220 --> 00:15:01,320 +فيه تفاعل يعني كما إذا حطينا Sodium Hydroxide على + +198 +00:15:01,320 --> 00:15:07,680 +HCl حصل تفاعل طب جدّاش الحجم يتغير؟ بيتغيرش الحجم + +199 +00:15:07,680 --> 00:15:12,240 +بيتغيرش الحجم مهم بس للتفاعلات اللي فيها غازات عدد + +200 +00:15:12,240 --> 00:15:17,260 +مولاتها مختلف لكن في المحاليلالكل ينتبه في + +201 +00:15:17,260 --> 00:15:22,080 +المحاليل مافيش عنده تغير في الحجم ففي أغلب الأحيان + +202 +00:15:22,080 --> 00:15:27,120 +ال P Delta V قيمة قليلة جدا جدا ال P Delta V قيمة + +203 +00:15:27,120 --> 00:15:32,080 +قليلة جدا جدا علشان هيك بقدر اقول انه تقريبا ال + +204 +00:15:32,080 --> 00:15:35,300 +Delta H سوى Delta E الفرق بينهم هيكون بسيط كتير هو + +205 +00:15:35,300 --> 00:15:38,820 +عبارة عن ال P Delta V وللمحاليل للشغل في المحاليل + +206 +00:15:40,370 --> 00:15:43,930 +الشغل في المحليل تقريباً ال .. ال .. ال .. الـ + +207 +00:15:43,930 --> 00:15:47,710 +changes in volume تقريباً Zero إذا الفرق في ال + +208 +00:15:47,710 --> 00:15:52,180 +value ما بين ال Delta E و Delta Hمش zero small + +209 +00:15:52,180 --> 00:15:56,980 +very small حلو يبقى معنا الكلام انا بقدر استخدم ال + +210 +00:15:56,980 --> 00:16:00,820 +delta H عشان اعبر عن ال delta E عن ال internal + +211 +00:16:00,820 --> 00:16:04,720 +energy بقدر اعبر عن ال internal energy باستخدام ال + +212 +00:16:04,720 --> 00:16:09,700 +delta H لأنه اجراب جدا على بعض ال delta H سهل جدا + +213 +00:16:09,700 --> 00:16:13,560 +احسبها ال delta E لأزي ما حنشوف في الـ Delta H + +214 +00:16:13,560 --> 00:16:16,440 +هلجيتها الحاسوبها بسهولة الـ Delta E لأ مش زيها مش + +215 +00:16:16,440 --> 00:16:21,660 +سهلة زيها وبالتالي هذه نتيجة مهمة جدا بالنسبة ليه + +216 +00:16:21,660 --> 00:16:26,420 +ان والله اه ال Delta H قيمتها قريبة جدا من قيمة ال + +217 +00:16:26,420 --> 00:16:31,860 +Delta E بالذات لما يكون التفاعل عندي في ال + +218 +00:16:31,860 --> 00:16:36,240 +solution يعني + +219 +00:16:36,240 --> 00:16:42,870 +لا يتضمن volume changeأو لا يتضمن حاليًا أقول + +220 +00:16:42,870 --> 00:16:46,510 +volume change إيه له معنى يعني مش volume change + +221 +00:16:46,510 --> 00:16:51,190 +يعني محسوس مش كتير لما يكون ال delta V قليلة جدا + +222 +00:16:51,190 --> 00:16:55,810 +جدا تقترب من الصفر فال delta E تقريبًا بتساوي ال + +223 +00:16:55,810 --> 00:16:59,750 +delta H ال sign لل delta H نفس الكلام أنا عندي + +224 +00:16:59,750 --> 00:17:02,630 +system delta H و ده قاسفها ال heat flow في ال + +225 +00:17:02,630 --> 00:17:05,250 +system يا إما ال heat flow داخل ال system يا إما + +226 +00:17:05,250 --> 00:17:07,970 +ال heat flow out of the system heat flow بتجيس ال + +227 +00:17:07,970 --> 00:17:12,330 +heat flowزي الـ Internal Energy، كنا بنجيس الـ + +228 +00:17:12,330 --> 00:17:16,990 +Flow للـ Work والـ Heat، + +229 +00:17:16,990 --> 00:17:20,910 +كويس، يا إما to the system، يا إما out of the + +230 +00:17:20,910 --> 00:17:24,310 +system، وكلنا بنقول، والله، إذا كان الـ Heat، الـ + +231 +00:17:24,310 --> 00:17:27,610 +Flow كان رايح على الـ System، معناته الـ Delta E + +232 +00:17:27,610 --> 00:17:32,710 +موجباالـ Q والـ E يعني إذا كان الـ heat و ال work + +233 +00:17:32,710 --> 00:17:35,590 +رايحين على ال system و لجينا الخزنة ايه شمالها + +234 +00:17:35,590 --> 00:17:39,450 +تكبر اه ال deposit ال bank account بزيد لأنه ايه + +235 +00:17:39,450 --> 00:17:44,010 +حاجات داخل ال system بينما لو ال system بده يعطي + +236 +00:17:44,010 --> 00:17:48,210 +حرارة exothermic او لو بده يعطيه يعمل هو شغل + +237 +00:17:48,210 --> 00:17:52,430 +معناته فيه نقص وبالتالي ال delta E بتكون سالب هذا + +238 +00:17:52,430 --> 00:17:56,690 +نفس الكلام لكن مانحكيش عن ال work و ال A و ال Q بس + +239 +00:17:56,690 --> 00:18:01,360 +عن ال QP ال heat flowفإذا كان الـ system عندى + +240 +00:18:01,360 --> 00:18:07,140 +بياخد حرارة معناته الـ delta H موجبة طب وقتاش + +241 +00:18:07,140 --> 00:18:10,720 +بياخد حرارة جال لما يكون هو endothermic وقتاش الـ + +242 +00:18:10,720 --> 00:18:14,440 +system بياخد حرارة جال لما يكون هو endothermic ولو + +243 +00:18:14,440 --> 00:18:17,340 +أعطانى حرارة يبقى الـ delta H سالبة طب وقتاش الـ + +244 +00:18:17,340 --> 00:18:21,640 +delta H سالبة جال لما التفاعل يكون exothermic + +245 +00:18:21,640 --> 00:18:24,240 +بيعطى حرارة الحرارة أول ما تروح تطلع من الـ system + +246 +00:18:24,240 --> 00:18:26,820 +لل surroundings لأنه أنا عندى system و + +247 +00:18:26,820 --> 00:18:29,820 +surroundingsإذا كان هناك حرارة زيادة في الـ system + +248 +00:18:29,820 --> 00:18:32,260 +تذهب إلى الـ surroundings إذا كان هناك حرارة زيادة + +249 +00:18:32,260 --> 00:18:34,420 +في الـ surroundings تذهب إلى الـ system ما فيش غير + +250 +00:18:34,420 --> 00:18:40,200 +هيك مجموعه بيكون واحد energy is conserved الـ heat + +251 +00:18:40,200 --> 00:18:47,060 +flow النهائي كمجموع ال surroundings زائد ال system + +252 +00:18:47,060 --> 00:18:50,120 +بيكون صفر أو ال Q لل surroundings معنى ال Q لل + +253 +00:18:50,120 --> 00:18:52,940 +system ال Q لل surroundings معنى ال Q لل system + +254 +00:18:52,940 --> 00:18:59,800 +والعكس إذا بقدر أقول أنا إذا كان ال heatالـ system + +255 +00:18:59,800 --> 00:19:04,520 +أخد heat دخلت الـ أيش بده يجرى قال والله الـ delta + +256 +00:19:04,520 --> 00:19:07,960 +H تبعته بالها تكبر طب وقتاش ال system بياخد heat + +257 +00:19:07,960 --> 00:19:13,260 +لما نكون endothermic ال delta H أكبر من صفر طيب ال + +258 +00:19:13,260 --> 00:19:16,780 +delta H أكبر من صفر طيب وإذا كان ال system فقد + +259 +00:19:16,780 --> 00:19:23,000 +حرارةمعناته عند هذا اكسو ثرميك ليش بده يفقد حرارة؟ + +260 +00:19:23,000 --> 00:19:25,780 +ليش بده يعطي الصينيونات حرارة؟ جاه لأن حرارته أعلى + +261 +00:19:25,780 --> 00:19:31,380 +لأن حرارته أعلى معنى الكلام الـ Delta H هتكون أقل + +262 +00:19:31,380 --> 00:19:36,000 +من صفر negative يبقى Delta H positive endothermic + +263 +00:19:36,000 --> 00:19:47,700 +reaction Q in طيب Delta H أقل من صفر معناته اكسو + +264 +00:19:47,700 --> 00:19:55,130 +ثرميك reactionEQ out هذا الـ sign convention نفس + +265 +00:19:55,130 --> 00:19:58,270 +الأشياء زي الـ Delta E لكن الـ Delta E كل ما اتكلم + +266 +00:19:58,270 --> 00:20:01,510 +عن two factors الـ Q بالضبط ليهان فش عنه غير الـ + +267 +00:20:01,510 --> 00:20:07,010 +QP فش عنه غير فقط الـ Q فالـ Q إذا كان فيه عند Q + +268 +00:20:07,010 --> 00:20:10,270 +رايح على الـ system يبقى الـ system بارد بدو ياخد + +269 +00:20:10,270 --> 00:20:13,710 +حرارة من ال surroundings هذا endothermic Delta H + +270 +00:20:13,710 --> 00:20:20,680 +أخد إذن زاد البنك accountأخد heat gain انتفخ ال + +271 +00:20:20,680 --> 00:20:25,080 +bank account اعطى heat loss جل ال bank account + +272 +00:20:25,080 --> 00:20:28,640 +لأنه بدي يعطي منه و دائما زي ما قلت ال Q لل + +273 +00:20:28,640 --> 00:20:31,920 +systems و مناسبة Q لل surroundings فيما يتعلق بال + +274 +00:20:31,920 --> 00:20:37,010 +delta Hتعالى نتطلع على كيف ممكن نعين الـSin + +275 +00:20:37,010 --> 00:20:42,110 +لـDelta H لبعض العمليات فبقول indicate the sign of + +276 +00:20:42,110 --> 00:20:45,270 +the enthalpy change Delta H in these processes + +277 +00:20:45,270 --> 00:20:48,530 +carried out under atmospheric pressure عشان يقولي + +278 +00:20:48,530 --> 00:20:50,230 +الـDelta H سوى QP + +279 +00:20:52,760 --> 00:20:59,120 +وانتج اذا كل البروكيز اندو ثرمي او اكسو ثرمي او + +280 +00:20:59,120 --> 00:21:01,840 +اكسو ثرمي او اندو ثرمي او اكسو ثرمي او اندو ثرمي + +281 +00:21:01,840 --> 00:21:03,100 +او اكسو ثرمي او اندو ثرمي او اكسو ثرمي او اندو + +282 +00:21:03,100 --> 00:21:04,360 +ثرمي او اندو ثرمي او اندو ثرمي او اندو ثرمي او + +283 +00:21:04,360 --> 00:21:04,960 +اندو ثرمي او اندو ثرمي او اندو ثرمي او اندو ثرمي + +284 +00:21:04,960 --> 00:21:05,000 +او اندو ثرمي او اندو ثرمي او اندو ثرمي او اندو + +285 +00:21:05,000 --> 00:21:10,780 +ثرمي او اندو ثرمي او اندو ثرمي اطيب الهواء اللي + +286 +00:21:10,780 --> 00:21:15,200 +حواليه حرارته أعلى من ال ice cube ولا أقل؟ أعلى + +287 +00:21:15,200 --> 00:21:19,420 +إذا الحرارة الموجة بتروح من ال surroundings إلى ال + +288 +00:21:19,420 --> 00:21:23,700 +ice cube لل system إذا ال delta H موجة لأن ال + +289 +00:21:23,700 --> 00:21:30,370 +system كسبإذا كان دلتا H موجبة هل هذا البرنامج + +290 +00:21:30,370 --> 00:21:34,810 +اندوهيرميك او اكسوهيرميك؟ طبعا اندوهيرميك لأنه + +291 +00:21:34,810 --> 00:21:40,230 +لايعطي كسب حرارة فهو اندوهيرميك بي واحد جرام + +292 +00:21:40,230 --> 00:21:43,150 +بيوتين مخلص بالكمبسطين باستخدام الكمبسطين باستخدام + +293 +00:21:43,150 --> 00:21:45,590 +الكمبسطين باستخدام الكمبسطين باستخدام الكمبسطين + +294 +00:21:45,590 --> 00:21:47,350 +باستخدام الكمبسطين باستخدام الكمبسطين باستخدام + +295 +00:21:47,350 --> 00:21:50,050 +الكمبسطين باستخدام الكمبسطين باستخدام الكمبسطين + +296 +00:21:50,050 --> 00:21:53,540 +باستخدام الكمبسطين باستخدام الكبتعطينا حرارة لأنها + +297 +00:21:53,540 --> 00:21:58,620 +احتراق في ال system لما يحترق ايش بالنسبة لل + +298 +00:21:58,620 --> 00:22:01,820 +surroundings كيف حرارته اعلى اذا بده يعطي + +299 +00:22:01,820 --> 00:22:05,440 +surroundings يبقى هيفقد يبقى ال delta H سالبة ومع + +300 +00:22:05,440 --> 00:22:09,980 +انه بيعطي حرارة مش بياخد بيعطي فهذا اكسو thermic + +301 +00:22:09,980 --> 00:22:15,280 +الحرارة الخارجة منه بس فسهل جدا انه نعرف ال sign + +302 +00:22:15,280 --> 00:22:23,730 +لل delta Hبقول لي كمان مثال مولتن جولد يعني دهب + +303 +00:22:23,730 --> 00:22:29,690 +منصهر is poured into a mold صبناه في جالب عشان + +304 +00:22:29,690 --> 00:22:31,930 +ياخد شكل حلو وينباع يعني + +305 +00:22:38,820 --> 00:22:48,240 +هذا الدهب المصهور حطناه في جالب علشان يتجمد يصير + +306 +00:22:48,240 --> 00:22:53,840 +صلب at constant pressureفهو لما يكون molten بتكون + +307 +00:22:53,840 --> 00:22:57,600 +حرارته جداش عالية جدا جدا طب والهواء اللي حواليه + +308 +00:22:57,600 --> 00:23:01,080 +كيف بيكون؟ اه طيب خلينا نشوف ايش بيقولنا with the + +309 +00:23:01,080 --> 00:23:04,520 +gold defined as the system يبقى ال gold هو ال + +310 +00:23:04,520 --> 00:23:08,720 +system تبعناه is the solidification an exothermic + +311 +00:23:08,720 --> 00:23:14,460 +or an endothermic process؟Exothermic لأنه راح + +312 +00:23:14,460 --> 00:23:18,200 +تعطينا إيه؟ راح تعطي حرارة للـsurroundings، فأه طب + +313 +00:23:18,200 --> 00:23:21,940 +و الـDelta H كيف وضعها؟ سالبة، سالبة، هذا أكيد، + +314 +00:23:21,940 --> 00:23:25,200 +لاحظوا إن ال solidification عكس ال melting، يعني + +315 +00:23:25,200 --> 00:23:28,680 +لو في عملية عكسية، لو إجينا يقولنا والله في عندنا + +316 +00:23:28,680 --> 00:23:33,660 +جالب دهببدنا نسهره فعشان اه هذا endothermic لانه + +317 +00:23:33,660 --> 00:23:37,360 +بده حرارة فهذا endothermic و ال delta H بيكون + +318 +00:23:37,360 --> 00:23:43,000 +موجبة لانه بدنا نحط فيه حرارة نعطيله حرارة heat + +319 +00:23:43,000 --> 00:23:49,000 +وبالتالي سهل جدا انه نعرف إشارة ال delta H و هل ال + +320 +00:23:49,000 --> 00:23:53,080 +process اللي عندي endothermic ولا exothermic + +321 +00:23:54,760 --> 00:23:58,020 +نتطلع الآن على أهم يعني كل هذا مقدمة في الحقيقة + +322 +00:23:58,020 --> 00:24:02,080 +عشان نوصل الـ Delta H لل reaction كل هذا مقدمة + +323 +00:24:02,080 --> 00:24:05,340 +علشان نقدر نوصل ال Delta H لل reaction علشان أنا + +324 +00:24:05,340 --> 00:24:10,840 +أقدر أحسب ال Delta H لل reaction و أشوف يعني كل + +325 +00:24:10,840 --> 00:24:14,440 +reaction جديش المحتوى الحراري أو ال heat flow لإله + +326 +00:24:14,440 --> 00:24:19,480 +إما heat flow in أو heat flow outفبنطلع ونقول الـ + +327 +00:24:19,480 --> 00:24:24,600 +Δ H سوى الـ H final minus الـ H initial وفي .. + +328 +00:24:24,600 --> 00:24:28,740 +للتفاعل الكيميائي الـ final هي ال products و ال + +329 +00:24:28,740 --> 00:24:32,100 +initial هي ال reactants، إذا لأي تفاعل Delta H + +330 +00:24:32,100 --> 00:24:35,400 +reaction بتساوي الـ H لال products لأنه هي الـ H + +331 +00:24:35,400 --> 00:24:40,420 +final minus الـ H لال reactants زي على فكرة زي ال + +332 +00:24:40,420 --> 00:24:46,040 +E، ال E بنقدرش نعرف قيمتها ك Eبنعرف الـ Change + +333 +00:24:46,040 --> 00:24:49,000 +وهذا نفس الكلام الـ H بناعرفش قيمتها ولا الـ H + +334 +00:24:49,000 --> 00:24:53,340 +بناعرف قيمتها أما نعرف الـ Delta H اللي هي الـ QP + +335 +00:24:53,340 --> 00:24:56,620 +نعرفها لكن كل H اللي واحدة H جديش ال initial وجدش + +336 +00:24:56,620 --> 00:24:59,680 +ولا لأ ومش مهتمين فيه في الحقيقة يعني مش مهم + +337 +00:24:59,680 --> 00:25:03,680 +بالنسبة إلنا حلو نعرفه لكن انه مابيعوجناش احنا + +338 +00:25:03,680 --> 00:25:05,400 +بدنا نعرف ايه ال Change + +339 +00:25:11,360 --> 00:25:15,820 +هن الـ delta HRXN يعني reaction هذي اختصار لإيه + +340 +00:25:15,820 --> 00:25:19,820 +لأبدا مكتوب كل مرة reaction مكتوبها RXN reaction + +341 +00:25:19,820 --> 00:25:24,980 +وخلاص بس بس نعرف هذه الشغله فتعالوا نتطلع + +342 +00:25:32,320 --> 00:25:36,540 +على تفاعل زي هذا بيقول اتنين اتش اتنين gas زائد او + +343 +00:25:36,540 --> 00:25:40,220 +اتنين gas بيعطينا اتنين اتش او اتنين gas دلتا اتش + +344 +00:25:40,220 --> 00:25:44,600 +لل reaction minus اربعمية و تلاتة و تمانين وستة من + +345 +00:25:44,600 --> 00:25:50,550 +عشرة كيلوجولاللي بدأ اقوله انا انه لابد لما بدي + +346 +00:25:50,550 --> 00:25:55,550 +اشتغل او احسب ال heat flow ال delta H لابد الا انه + +347 +00:25:55,550 --> 00:26:01,670 +تكون عندى معادلة التفاعل موجودة و موزونة هذه اول + +348 +00:26:01,670 --> 00:26:07,470 +نقطة موجودة و موزونة ليه؟ لأن ال delta H هي عبارة + +349 +00:26:07,470 --> 00:26:13,030 +عن ممكن نقولها extensive property + +350 +00:26:14,350 --> 00:26:17,270 +في ال properties نوعين يا intensive property يا + +351 +00:26:17,270 --> 00:26:20,710 +extensive property ال extensive تعتمد على كمية + +352 +00:26:20,710 --> 00:26:24,670 +المادة ف ال delta H تعتمد على كمية المادة يعني اذا + +353 +00:26:24,670 --> 00:26:27,810 +كانت حطيت مول واحد في عندي delta H محتوى حدد او + +354 +00:26:27,810 --> 00:26:32,390 +heat flow حسب المول لو حطيت واحد جرام يعني heat + +355 +00:26:32,390 --> 00:26:35,210 +flow معينة لو حطيت واحد من عشر جرام heat flow + +356 +00:26:35,210 --> 00:26:40,190 +معينة فبالتالي لازم اكتب المعادلة موزونة عشان هذا + +357 +00:26:40,190 --> 00:26:45,680 +الرقم اللي علاقة بمين بعدد المولاتليه؟ لأنه لو عدد + +358 +00:26:45,680 --> 00:26:48,600 +المولات جال، هذا الرقم هيجيل، هنشوف ده الكلام بعد + +359 +00:26:48,600 --> 00:26:53,940 +شوية، اذا علشان انا اشتغل، لابد الا انه .. لابد + +360 +00:26:53,940 --> 00:26:57,680 +الا انه اكتب المعادلة موزونة، هذه اول نقطة، + +361 +00:26:57,680 --> 00:27:01,760 +والنقطة التانية، لابد الا ان ال states تبعت + +362 +00:27:01,760 --> 00:27:05,940 +المتفاعلات والنواتج تكون موجودة ايضا، لأن الـ + +363 +00:27:05,940 --> 00:27:09,780 +delta H بتعتمد عليها، قيمة الـ delta H، يعني هنا + +364 +00:27:09,780 --> 00:27:14,180 +لو بتحصل على H2O liquid، بتلاقي الـ delta H مختلفة + +365 +00:27:15,370 --> 00:27:19,130 +يبقى لازم اعمل حاجتين لازم يعني احط المعادلة او + +366 +00:27:19,130 --> 00:27:25,430 +اكتب المعادلة موزونة و اكتب من ضمن المعادلة ال + +367 +00:27:25,430 --> 00:27:30,530 +states لكل متفاعل او ناتج من النواتج لازم اكتب ال + +368 +00:27:30,530 --> 00:27:34,810 +states هل هو liquid ولا solid ولا gas ليه؟ لأن ال + +369 +00:27:34,810 --> 00:27:38,270 +delta H راح تتوقف على هذه الحاجات على المعادلة + +370 +00:27:38,270 --> 00:27:41,930 +الموزونة اكمل مستخدم يعني ها لو بده اضرب مثلا في + +371 +00:27:41,930 --> 00:27:45,210 +اتنين بده اضرب هذه في اتنينلو بدك تضرب هذا في + +372 +00:27:45,210 --> 00:27:48,710 +أربعة بدك تضرب delta H في أربعة لو بدك تسمها على + +373 +00:27:48,710 --> 00:27:52,590 +خمسة بدك تسم delta H على خمسة ماشي يا جماعة و لو + +374 +00:27:52,590 --> 00:27:57,630 +كان اي واحد من هدول مختلف ال state يعني برضه كمان + +375 +00:27:57,630 --> 00:28:01,930 +ال delta H راح تختلف و حاججكم أمثلة بعد شوية + +376 +00:28:01,930 --> 00:28:06,030 +المعادلة المكتوبة بالشكل هذا بما في ذلك جدش ال + +377 +00:28:06,030 --> 00:28:10,390 +delta H لل reactionبسميها thermochemical equation + +378 +00:28:10,390 --> 00:28:14,990 +بسميها thermochemical equation ليه؟ لأن ال heat + +379 +00:28:14,990 --> 00:28:18,750 +flow موجود من ضمن المعادلة بقول هاشي chemical + +380 +00:28:18,750 --> 00:28:22,150 +equation لأ عشان ال heat flow موجود بسميها ايه؟ + +381 +00:28:22,150 --> 00:28:26,050 +thermochemical equation لحظة ال delta H سالبة، إيش + +382 +00:28:26,050 --> 00:28:30,730 +معناته؟ معناته التفاعل exothermic معناته التفاعل + +383 +00:28:30,730 --> 00:28:34,830 +exothermic يعني ال system بيعطي حرارة لل + +384 +00:28:34,830 --> 00:28:35,390 +surroundings + +385 +00:28:38,640 --> 00:28:42,880 +المثال اللى شفناه سابقا هو عبارة عن مثلا هذا فيه + +386 +00:28:42,880 --> 00:28:50,860 +H2 وهي الهواء عندى فيه Oxygen كويس فلو اجيت انا سخ + +387 +00:28:50,860 --> 00:28:56,120 +.. يعني سخنت البلون يعني هتجربت عليه ولعة فإيش بده + +388 +00:28:56,120 --> 00:29:00,260 +يحصل؟ هذا راح يفجع اللى هو البلون فهيطلع ال + +389 +00:29:00,260 --> 00:29:03,870 +hydrogen إيش هيلاقي جانبه؟الأكسجين سيتفاعل مع + +390 +00:29:03,870 --> 00:29:10,170 +هيدروجين وأكسجين ويعطينا H2O كويس الـ2H2 زائد + +391 +00:29:10,170 --> 00:29:13,530 +الـO2 واضح أنه يعطينا حرارة هائلة يعني أعلى من + +392 +00:29:13,530 --> 00:29:15,710 +الـsurroundings وهو اللي هيعطيه يعني هيتفاعل + +393 +00:29:15,710 --> 00:29:23,300 +اكسوثرميك واضحفالـ 2H2G زائد O2G هتعطيلنا 2H2O، + +394 +00:29:23,300 --> 00:29:29,920 +لوحظوا أن الـ H2O الجاز النواتج الـ الـ H تبعتها + +395 +00:29:29,920 --> 00:29:35,530 +أقل، ليه؟ لأن هذا تفاعل Exothermicيبقى فقط جزء من + +396 +00:29:35,530 --> 00:29:40,290 +طاقته لمن؟ للـSurroundings فعنا الـ Delta H سالبة + +397 +00:29:40,290 --> 00:29:44,590 +Delta H أقل من صفر لأنه Exothermic يعني هان ال E + +398 +00:29:44,590 --> 00:29:51,500 +final أقل ال F ال H final أقل من ال Hانشال او الـH + +399 +00:29:51,500 --> 00:29:56,760 +للـproducts اقل من الـH للـreacts لأنه تفاعل اكسو + +400 +00:29:56,760 --> 00:30:01,620 +ثيرميك لكن لو عكسته لو عكسته قولت اتنين H2O بدي + +401 +00:30:01,620 --> 00:30:05,320 +احولهم لاتنين H2 زائد O2 ايش بدي اسوي؟ قال بدي + +402 +00:30:05,320 --> 00:30:11,210 +اسخنالـ H2O هذه بدي أسخنها يعني بدي أضع فيها حرارة + +403 +00:30:11,210 --> 00:30:15,890 +عشان تتكسر تعطيني 2H2 زائد O2 لما أسخن يبجي هذا + +404 +00:30:15,890 --> 00:30:19,570 +التفاعل بدي أضع حرارة يبجي Delta H موجبة و التفاعل + +405 +00:30:19,570 --> 00:30:24,330 +Endothermic لكن لاحظوا أنه عشان هدول يعطوني H2O أو + +406 +00:30:24,330 --> 00:30:29,070 +عشان الـ H2O تعطيني هدول نفس كمية الطاقة بالظبط + +407 +00:30:29,070 --> 00:30:35,780 +لكن الإشارة فقط مختلفةالإشارة فقط مختلفة ليش هذا + +408 +00:30:35,780 --> 00:30:39,780 +الكلام؟ جال هذا الكلام لأن الـ H هي عبارة عن state + +409 +00:30:39,780 --> 00:30:43,340 +function مش مهم كيف أحصل عليها، مش مهم الوسيلة، مش + +410 +00:30:43,340 --> 00:30:48,660 +مهم .. المهم أنه دائما إذا + +411 +00:30:48,660 --> 00:30:53,560 +عكست التفاعل، معناه كله بس بعكس الإشارة بدل ما هي + +412 +00:30:53,560 --> 00:30:56,400 +التفاعل الـ exothermic بده يصير تفاعل الـ + +413 +00:30:56,400 --> 00:31:01,880 +endothermic لكن نفس كمية الطاقة بإشارة مختلفةكيف + +414 +00:31:01,880 --> 00:31:05,400 +بدي استخدم او بعض الحاجات المهمة بالنسبالي عشان + +415 +00:31:05,400 --> 00:31:08,400 +افهم كيف استخدم الـ Thermochemical Equations بقول + +416 +00:31:08,400 --> 00:31:15,660 +في البداية الـ SCAN ضربت مثلا لو عندي CH4 2 O2 + +417 +00:31:21,430 --> 00:31:24,290 +الدلتا اتش سالب تمانية وتسعين ايش معناه سالب + +418 +00:31:24,290 --> 00:31:27,410 +تمانية وتسعين اكسو ثرميك تفاعل اكسو ثرميك طارد + +419 +00:31:27,410 --> 00:31:31,750 +الحرار حلو كتير بقول لو بدي اتنين مول من ال CH4 + +420 +00:31:31,750 --> 00:31:35,990 +اربع مول من ال O2 اتنين CO2 اربع مية liquid جال + +421 +00:31:35,990 --> 00:31:39,170 +بدرب هذه في اتنين يعني على طول هيها ضربت في اتنين + +422 +00:31:39,170 --> 00:31:43,600 +كيف صارت ال Delta Hنتذكر هذا الكلام لماذا؟ قال لأن + +423 +00:31:43,600 --> 00:31:48,160 +الـ Delta H أو الـ Enthalpy is an extensive + +424 +00:31:48,160 --> 00:31:52,720 +property يعني يتوقف على كمية المادة بيتوقف على + +425 +00:31:52,720 --> 00:31:56,320 +كمية المادة فالمول الواحد بيعطي 890 طب الاتنين مول + +426 +00:31:56,320 --> 00:32:03,180 +قال بيعطي 2 في 890 تمام هذه أول حاجة نتذكرها تاني + +427 +00:32:03,180 --> 00:32:07,660 +حاجة بيقول إذا كانت شوفناها قبل شوية إذا كان عندي + +428 +00:32:07,660 --> 00:32:08,340 +CH + +429 +00:32:11,620 --> 00:32:17,920 +عند .. طب ماشي عند CH4 و 2 O2 حرجناهم يعطينا CO2 و + +430 +00:32:17,920 --> 00:32:23,520 +H2O طبعا هذا الفاعل combustion علشان هيك النواتج + +431 +00:32:23,520 --> 00:32:28,080 +يلهم H أقل لأنه جزء من الطاقة هذا exothermic + +432 +00:32:28,080 --> 00:32:31,560 +reaction فالـ delta H negative هي هذه طب نقول لو + +433 +00:32:31,560 --> 00:32:36,480 +بدنا نمشي نتحول ال CO2 و 2H2O إلى هذا .. جال هذا + +434 +00:32:36,480 --> 00:32:42,910 +endothermic و بده طاقةتمنمية عكس هذه بالظبط فإذا + +435 +00:32:42,910 --> 00:32:47,370 +كان عكسنا يعني بدل ما هي CH4 زي اتنين O2 بتعطينا + +436 +00:32:47,370 --> 00:32:52,210 +CO2 زي اتنين H2O لو جولنا CO2 زي اتنين H2O Liquid + +437 +00:32:52,210 --> 00:32:56,310 +بتعطينا CH4 جايز و اتنين O2 جايز جال الدلتا H نفس + +438 +00:32:56,310 --> 00:32:58,810 +القيمة لكنها ايه موجة بعدين لإن إذا كان بدي أعكس + +439 +00:32:58,810 --> 00:33:05,170 +معادلة بدي أعكس الإشارة لل Delta Hالحاجة التالتة + +440 +00:33:05,170 --> 00:33:10,290 +اللى برضه ذكرتها انا مثلًا التفاعل CH4G زائد 2 O2G + +441 +00:33:10,290 --> 00:33:14,330 +بيعطينا CO2G زائد 2H2O ليكود الـ Δ H ثالث نفسنا + +442 +00:33:14,330 --> 00:33:17,590 +شفناها سابقًا في ال slide اللى جابلها لكن تعالوا + +443 +00:33:17,590 --> 00:33:23,090 +نتطلع لو كان CH4G زائد 2O2G بتعطينا CO2G زائد + +444 +00:33:23,090 --> 00:33:28,130 +2H2OAجاز مش liquid قال بنلحظ دلت H سلب تمانية و + +445 +00:33:28,130 --> 00:33:32,510 +اتنين طب ليش قال لأنه عشان احول ال H2O liquid ل + +446 +00:33:32,510 --> 00:33:37,090 +H2O gas انا بحاجة ان اعطي طاقة جداش قال الاتنين + +447 +00:33:37,090 --> 00:33:41,210 +مول بتعطي تمانية و تمانين كيلوجول هيها اتنين H2O + +448 +00:33:41,210 --> 00:33:47,020 +liquid اتحول لاتنين H2O gasبدها الـ ΔH كده؟ 88 هذا + +449 +00:33:47,020 --> 00:33:50,400 +للإتنين مول زي هذه إتنين مول زي هذه إتنين مول إذا + +450 +00:33:50,400 --> 00:33:55,040 +أنا لازم أحط 88 كيلوجول يبقى بدي أحط موجة بـ 88 + +451 +00:33:55,040 --> 00:33:58,560 +كيلوجول إذا بيبقى عندي الحرارة اللي ناتجة عن + +452 +00:33:58,560 --> 00:34:03,920 +التفاعل لما الـ H2O بيكون جاذ هي ΔH سالب 882 سالب + +453 +00:34:03,920 --> 00:34:08,560 +882 ليه؟ طرحنا 88 من الـ 882 أو يعني + +454 +00:34:12,270 --> 00:34:18,310 +كقيمة موجبة 88 يعني جمعنا التين تين مع بعض علشان + +455 +00:34:18,310 --> 00:34:24,830 +انحول هذه الفكرة انه بدى احول ال H2O لهذه + +456 +00:34:24,830 --> 00:34:32,490 +بيهادمتها زائد 88 كيلو جول معنى الكلام هان اذا كان + +457 +00:34:32,490 --> 00:34:35,610 +liquid اه بحصل على 890 كيلو جول لكن لما نحولها + +458 +00:34:35,610 --> 00:34:41,170 +لجاس انا فقدت 88 منهم وين؟في تحويلها للجاز بال + +459 +00:34:41,170 --> 00:34:45,050 +liquid للجاز اذا البجد الرقص حالي فعليا هو عبارة + +460 +00:34:45,050 --> 00:34:56,310 +عن 802 كج طبعا سالب لأنه التفاعل اكسو ثرميك يبقى + +461 +00:34:56,310 --> 00:35:04,030 +اللي بدي استنتجهان انه لابد الا انأحافظ على ال + +462 +00:35:04,030 --> 00:35:09,770 +states للمتفاعلات والنواتج مكتوبة لأنه مافيش معنى + +463 +00:35:09,770 --> 00:35:12,630 +لل thermochemical equation إذا كان ال states مش + +464 +00:35:12,630 --> 00:35:17,870 +موجودة ال liquid بده يتحول ل solid بده يعطي طاقة + +465 +00:35:17,870 --> 00:35:22,110 +ال liquid بتحول ل gas بده ياخد طاقة مثلا فلازم + +466 +00:35:22,110 --> 00:35:25,650 +تكون هذه ال states إشمالها منصوص عليها في المعادلة + +467 +00:35:25,650 --> 00:35:31,570 +نتذكر هذا الكلام طيب + +468 +00:35:32,580 --> 00:35:38,680 +خلّينا نحاول نحسب الـ Δلتا H أو الـ heat released + +469 +00:35:38,680 --> 00:35:43,720 +للتفاعلات المختلفة نفرجكم بس الطريقة يعني بقول in + +470 +00:35:43,720 --> 00:35:46,680 +the following reaction how much heat is released + +471 +00:35:46,680 --> 00:35:50,980 +when أربعة و نصف جرام of مثين released يعني يعني + +472 +00:35:50,980 --> 00:35:53,780 +هو التفاعل اكسو ثرميك لأنه زي ما هنشوفه التفاعل + +473 +00:35:53,780 --> 00:35:58,000 +combustion released يعني أيه متحرر يعني أو بحصل + +474 +00:35:58,000 --> 00:36:03,940 +عليهاعندما يتم بناء 4.5 جرام من ميثاين جاز في نظام + +475 +00:36:03,940 --> 00:36:09,180 +درجة مباشرة يعني حطناه في وعى درجة مباشرة وانا وعى + +476 +00:36:09,180 --> 00:36:14,880 +عادي وحرك ده تمام فعايز احسب جداش ال heat flow او + +477 +00:36:14,880 --> 00:36:19,600 +ال heat release خدوا بالكم انا عند المول من + +478 +00:36:19,600 --> 00:36:24,660 +الميثاين جداش بعطيني 890 + +479 +00:36:26,410 --> 00:36:29,970 +كل شغل بال مولات يعني انا هو يقولي انا والله + +480 +00:36:29,970 --> 00:36:32,310 +بيقولي وين اربع مول استاجرام او ماثين بده اشوف + +481 +00:36:32,310 --> 00:36:35,710 +هدول اربع مول استاجرام اكم مول لان المول الواحد + +482 +00:36:35,710 --> 00:36:41,210 +بيعطيني 890 هي واحد مول في المعادلة CH4 بس انا + +483 +00:36:41,210 --> 00:36:45,210 +ماتكبش الواحد فهي الواحد مول من ال CH4 ايش + +484 +00:36:45,210 --> 00:36:50,190 +بيعطيني؟890 انا بس بديش واحد مول بده اربع .. بده + +485 +00:36:50,190 --> 00:36:54,190 +اربع و نص جرام فبقول والله عدد مولات الميثين اربع + +486 +00:36:54,190 --> 00:36:57,930 +و نص جرام على ال formula ويتلى الميثين اذا عدد + +487 +00:36:57,930 --> 00:37:00,870 +مولات الميثين point two eight one يبقى ال heat + +488 +00:37:00,870 --> 00:37:04,190 +released من هذه الكمية ال number of moles في ال + +489 +00:37:04,190 --> 00:37:07,270 +heat .. في ال heat released per mole ال number of + +490 +00:37:07,270 --> 00:37:11,370 +moles اللي انا حسبتها مضروبة في الحرارة اللي بحصل + +491 +00:37:11,370 --> 00:37:15,140 +عليها من المولفلو كان عندى مول واحد بحصل على + +492 +00:37:15,140 --> 00:37:17,860 +تمانية وتسعين انا ماعنديش مول انا عندى point two + +493 +00:37:17,860 --> 00:37:21,380 +eight one فبضرب point two eight one مول فيه سالب + +494 +00:37:21,380 --> 00:37:24,200 +تمانية وتسعين kilo joule per mole بطلع عندى سالب + +495 +00:37:24,200 --> 00:37:26,760 +متين وخمسين kilo joule يبقى الأربعة و نص الجرام + +496 +00:37:26,760 --> 00:37:29,440 +هيعطونى متين وخمسين kilo joule او هيعطوا ال + +497 +00:37:29,440 --> 00:37:33,960 +surroundings في الحقيقة متين وخمسين kilo joule طيب + +498 +00:37:35,130 --> 00:37:38,690 +الهيدروجين بيروكسايد يمكن أن يتنقص إلى الماء + +499 +00:37:38,690 --> 00:37:43,310 +والأكسجون من خلال التطبيقات اتنين اتش تو او ليكود + +500 +00:37:43,310 --> 00:37:49,550 +اتحول لاتنين اتش تو او ليكود زائد او اتو جازجداش + +501 +00:37:49,550 --> 00:37:53,250 +سالب مية و ستة وتسعين كيلوجول يعني هذا التفاعل ايش + +502 +00:37:53,250 --> 00:37:57,510 +ماله اكسو ثيرمك هذا التفاعل اكسو ثيرمك طارد + +503 +00:37:57,510 --> 00:38:02,450 +للحرارة لحظة انه الاتنين مول ايش بعطوني مية و ستة + +504 +00:38:02,450 --> 00:38:06,750 +وتسعين الاتنين مول مش المول الاتنين مول بعطوني مية + +505 +00:38:06,750 --> 00:38:09,690 +ستة وتسعين اذا المول الواحد بده يعطي مية و ستة + +506 +00:38:09,690 --> 00:38:13,980 +وتسعين على اتنينالمواد الواحد دلوقتي 196 طيب ماعلي + +507 +00:38:13,980 --> 00:38:17,780 +هنا احنا بنقول والله هو بده يقول calculate the + +508 +00:38:17,780 --> 00:38:21,540 +quantity of heat released when خمسة جرام of H2O2 + +509 +00:38:21,540 --> 00:38:24,940 +decomposes at constant pressure لو عندى اتنين مول + +510 +00:38:24,940 --> 00:38:28,940 +كان اه حصلت على 196 لو عندى مول واحد كان حصلت على + +511 +00:38:28,940 --> 00:38:31,740 +196 على 2 لكن لأ هو قال دى بس خمسة جرام اللى عندي + +512 +00:38:31,740 --> 00:38:36,240 +فبدي اجيب عدد مولات ال H2O2 عدد المولات اللى هو + +513 +00:38:36,240 --> 00:38:37,780 +number of moles بده ساوي + +514 +00:38:41,930 --> 00:38:44,890 +أو إذا كان عندي عنصر جرام على الاتوميك weight + +515 +00:38:44,890 --> 00:38:49,510 +فجرام عندي خمسة جرام الفورمولا weight لل H2O2 + +516 +00:38:49,510 --> 00:38:52,530 +أربعة و تلاتي لذا بيعطيين point one four seven + +517 +00:38:52,530 --> 00:38:56,430 +moles ال quantity of heat released هي عبارة عن + +518 +00:38:56,430 --> 00:39:00,390 +المول عدد المولات يعني مضروع في ال delta H للمول + +519 +00:39:01,470 --> 00:39:04,250 +فانا بقول والله point one four seven مضروبة فيه + +520 +00:39:04,250 --> 00:39:07,830 +سالب مية ستة وتسعين على اتنين مول ليه؟ لأنه هاد + +521 +00:39:07,830 --> 00:39:14,890 +الميه ناشع عن ايه؟ ناشع عن اتنين مول يبقى مية ستة + +522 +00:39:14,890 --> 00:39:19,910 +وتسعين على اتنين ماشي يا جماعة بيطلع عندى سالب + +523 +00:39:19,910 --> 00:39:26,430 +اربعة عشر او اربعة من عشرة كيلوجول كمان مسألة بقول + +524 +00:39:26,430 --> 00:39:31,370 +given the thermochemical equationس او تو جاس زائد + +525 +00:39:31,370 --> 00:39:36,690 +نص او تو جاس بتعطينا س او ثري جاس دلتا اتش بتساوي + +526 +00:39:36,690 --> 00:39:39,930 +سالب تسعة وتسعين واحد من عشر كيلوجول طيب بيقول لي + +527 +00:39:39,930 --> 00:39:43,330 +find the heat evolved يعني ال heat released هي هي + +528 +00:39:43,330 --> 00:39:44,650 +when + +529 +00:39:48,200 --> 00:39:54,920 +الفورميل الواتر 74.67 جرام SO2 جاز هو تحويل لـ SO3 + +530 +00:40:03,490 --> 00:40:08,290 +نفس الجثة بيدحول الـ 74 جرام لعدد مولات فبيدجسم + +531 +00:40:08,290 --> 00:40:14,690 +الـ 74 جرام على ال formula weight للـ S O2 64.7×1 + +532 +00:40:14,690 --> 00:40:19,930 +.155 هذا عدد مولات الـ S O2 بيدقول والله عدد مولات + +533 +00:40:19,930 --> 00:40:26,930 +الـ S O2 هي المول في الـ Delta H لكل مول 1.155 + +534 +00:40:26,930 --> 00:40:33,480 +مضروبة فيه سالب 99 و 1 من 10 على جداش على 1كان + +535 +00:40:33,480 --> 00:40:37,880 +ممكن انا اكتب هذه المعادلة زي هيك اتنين SO2 جاهز + +536 +00:40:37,880 --> 00:40:43,780 +مش غلط زائد O2 جاهز تعطينا اتنين SO3 جاهز و في هذه + +537 +00:40:43,780 --> 00:40:50,020 +الحالة الـ Delta H تساوي one nine eight point two + +538 +00:40:50,020 --> 00:40:54,410 +بالسالب kilo jouleأه ممكن اكتفها زي هيك لكن في هذه + +539 +00:40:54,410 --> 00:40:58,230 +الحالة لما بدي عوض delta H على البرمول بدي أقول + +540 +00:40:58,230 --> 00:41:04,090 +سالب 192 على 2 لأن عدد ملاتل SO2A اتنين فبدي انا + +541 +00:41:04,090 --> 00:41:10,930 +انتباه يعني طيب + +542 +00:41:10,930 --> 00:41:17,690 +طيب الآن اخر مثال هذا اه اخر مثال بيقول find the + +543 +00:41:17,690 --> 00:41:20,710 +heat evolved when 206 كلهم exothermic اللي زار + +544 +00:41:20,710 --> 00:41:26,570 +الأمثلةطيب وين 266 جرام solid P4 P4 هذا عنصر + +545 +00:41:26,570 --> 00:41:29,830 +الفوسفور موجود على هيئة بيقولوله white phosphorus + +546 +00:41:29,830 --> 00:41:33,270 +عادة is burnt in oxygen according to the + +547 +00:41:33,270 --> 00:41:39,610 +thermochemical equation P4 زائد خمسة O2 gas P4 + +548 +00:41:39,610 --> 00:41:44,590 +solid زائد خمسة O2 gas تعطينا P4 عشرة gas إيش ممكن + +549 +00:41:44,590 --> 00:41:51,240 +نسميها دهبانات؟ إيش ممكن نسميها؟هذا binary + +550 +00:41:51,240 --> 00:41:58,600 +compound لـ non-metals عند تسميته لأنه هي فسفور و + +551 +00:41:58,600 --> 00:42:01,480 +أكسجين مش metal و non-metal لأ فهذا binary + +552 +00:42:01,480 --> 00:42:05,860 +compound نستخدم فيه أيه؟ نستخدم فيه ال prefixes + +553 +00:42:05,860 --> 00:42:11,200 +mono-, di- و tri- فبنعدهن أربعة فسفور تترا فسفورس + +554 +00:42:11,200 --> 00:42:14,220 +ديكوكسيد + +555 +00:42:14,220 --> 00:42:21,910 +ديكوكسيد عشرة دقيقة العشرة ديكوكسيدماشي تترا + +556 +00:42:21,910 --> 00:42:29,330 +فوسفورس ديكوكسايد طيب ما علينا بقول عايز يحسب كمية + +557 +00:42:29,330 --> 00:42:35,470 +الحرارة المتساعدة او الخارجة when 256 gram of + +558 +00:42:35,470 --> 00:42:40,410 +solid P4 is burnt in oxygen حسب المعادلة بقول حلو + +559 +00:42:40,410 --> 00:42:49,860 +كتير بدنا نعرف هدول اكم مولفبقول والله 266 على 124 + +560 +00:42:49,860 --> 00:42:56,020 +هذا ال formula هي تلال ال phosphorus P4 يعني أربعة + +561 +00:42:56,020 --> 00:42:59,200 +في ال P بتعطيني 2.145 + +562 +00:43:02,410 --> 00:43:06,670 +عرفت عرض الملات الآن بدى اقول الـ delta H per mol + +563 +00:43:06,670 --> 00:43:11,430 +دلتا H سالب تلات تلاف و تلات عشر على اكمل عندى + +564 +00:43:11,430 --> 00:43:14,990 +واحد اذا انا على واحد يعني بس سالب تلات تلاف و + +565 +00:43:14,990 --> 00:43:18,950 +تلات عشر بطلع عندى سالب ست لاف و اربعمية و تلاتة و + +566 +00:43:18,950 --> 00:43:25,690 +ستين كيلو جولالحسابات طبعتها بسيطة لأن عندي عدد + +567 +00:43:25,690 --> 00:43:30,530 +مولات معين بيعطي delta H معينة فإذا كان عندي + +568 +00:43:30,530 --> 00:43:34,530 +جرامات بس مجرد أن أحوّله لمول بقى و بضرب في ال + +569 +00:43:34,530 --> 00:43:39,970 +delta H per mole وخلاص سهل جدا الحسابات من هذا + +570 +00:43:39,970 --> 00:43:48,070 +النوع الآن نتطلع علىالـ heat capacity وانا كل غرضي + +571 +00:43:48,070 --> 00:43:54,770 +ان اوصل للنقطة اللي بقدر احسب فيها تجريبيا جداش + +572 +00:43:54,770 --> 00:43:59,790 +الـ delta H فبقول + +573 +00:43:59,790 --> 00:44:04,270 +ال heat capacity يمكن + +574 +00:44:04,270 --> 00:44:10,530 +تعريفها على ان هي كمية الحرارةamount of heat + +575 +00:44:10,530 --> 00:44:14,830 +required to raise the temperature of an object by + +576 +00:44:14,830 --> 00:44:22,230 +one degrees C أو one degrees Kelvin كويس؟ one + +577 +00:44:22,230 --> 00:44:30,350 +degrees C أو one degrees Kelvin مش كل المواد بحاجة + +578 +00:44:30,350 --> 00:44:36,130 +لنفس كمية الحرارة علشان ترتفع نفس العدد من + +579 +00:44:36,130 --> 00:44:41,920 +الدرجات، لأكل مادة إلها طبيعة مختلفة فبنلاحظ مثلا + +580 +00:44:41,920 --> 00:44:46,680 +الميّه بحاجة لكمية حرارة أكبر عشان ترتفع عدد درجات + +581 +00:44:46,680 --> 00:44:52,440 +معينة أو درجة واحدة مثلا بينما الحديد أقل فهذا + +582 +00:44:52,440 --> 00:45:00,560 +بتوقف على طبيعة المادة في + +583 +00:45:00,560 --> 00:45:05,980 +كثير من الأحيان في كثير من الأحيان يعني يمكن من + +584 +00:45:05,980 --> 00:45:11,000 +المفيد أنه أعرف حاجة جنبهابقولها specific heat + +585 +00:45:11,000 --> 00:45:16,200 +بقولها specific heat ايش ال specific heat قال هي + +586 +00:45:16,200 --> 00:45:22,560 +كمية الحرارة اللازمة لرفع درجة حرارة واحد جرام مش + +587 +00:45:22,560 --> 00:45:26,140 +الجسم اللي مش عارف انا كده اش هو واحد جرام من + +588 +00:45:26,140 --> 00:45:32,720 +المادة درجة واحدة فقطكويس يبقى ال specific heat هي + +589 +00:45:32,720 --> 00:45:36,840 +عبارة عن كمية الحرارة لكيو اللازمة لرفع درجة حرارة + +590 +00:45:36,840 --> 00:45:43,160 +ايه واحد جرام من المادة درجة واحدة مئوية او Kelvin + +591 +00:45:43,160 --> 00:45:48,360 +في عندي كمان حاجة بقولها molar heat capacity كويس + +592 +00:45:48,360 --> 00:45:54,120 +نعرفها ال molar heat capacity هي عبارة عن كمية + +593 +00:45:54,120 --> 00:46:01,020 +الحرارة اللازمة لرفعدرجة حرارة واحد مول من المادة + +594 +00:46:01,020 --> 00:46:07,580 +درجة واحدة مئوية كويس كمية الحرارة اللازمة لرفع + +595 +00:46:07,580 --> 00:46:11,960 +درجة حرارة واحد مول من المادة درجة واحدة مئوية + +596 +00:46:11,960 --> 00:46:21,180 +درجة واحدة مئوية درجة واحدة مئوية درجة واحدة مئوية + +597 +00:46:21,180 --> 00:46:22,920 +درجة واحدة مئوية درجة واحدة مئوية درجة واحدة مئوية + +598 +00:46:22,920 --> 00:46:24,260 +درجة واحدة مئوية درجة واحدة مئوية درجة واحدة مئوية + +599 +00:46:24,260 --> 00:46:27,800 +درجة واحدة مئوية درجة واحدة مئوية درجة واحدة مئوية + +600 +00:46:27,800 --> 00:46:27,880 +درجة واحدة مئوية درجة واحدة مئوية درجة واحدة مئوية + +601 +00:46:27,880 --> 00:46:31,240 +درجة واحدة مئمن المادة ده واحد مول درجة واحدة + +602 +00:46:31,240 --> 00:46:33,760 +مئوية والها molar heat capacity طب ال specific + +603 +00:46:33,760 --> 00:46:37,280 +heat لا لأ ال specific heat هي كمية الحرارة اللي + +604 +00:46:37,280 --> 00:46:41,620 +لازم يرفع درجة حرارة واحد gram من المادة درجة + +605 +00:46:41,620 --> 00:46:50,480 +واحدة مئوية يعني + +606 +00:46:50,480 --> 00:46:54,420 +في الحقيقة ال specific heat هي عبارة عن ال heat + +607 +00:46:54,420 --> 00:46:57,680 +capacity للواحد gramمن المادة هي الـ heat capacity + +608 +00:46:57,680 --> 00:47:00,020 +اللي واحد يجرام من المادة بقدر أقول أنا ال + +609 +00:47:00,020 --> 00:47:03,480 +specific heat هذا لازم نحفظه بيجعله أسئلة في + +610 +00:47:03,480 --> 00:47:07,540 +الامتحانات بشكل يعني كويس ال specific heat عبارة + +611 +00:47:07,540 --> 00:47:11,660 +عن ال quantity of heat transferred ال quantity of + +612 +00:47:11,660 --> 00:47:15,800 +heat مقسومة على ال grams of substance في ال + +613 +00:47:15,800 --> 00:47:22,000 +temperature change يعني ال C اسمه يتساوى ال Qعلى M + +614 +00:47:22,000 --> 00:47:26,340 +في الـ Delta T أو ممكن نقول لك U بتساوي ال CS في + +615 +00:47:26,340 --> 00:47:30,720 +ال M في ال Delta T ال CS في ال M في ال Delta T + +616 +00:47:30,720 --> 00:47:36,760 +فتعالوا نتطلع على كيف ممكن نستخدم هذا القانون في + +617 +00:47:36,760 --> 00:47:42,500 +الحسابة بقول Assume على فرض 209 Joule is required + +618 +00:47:42,500 --> 00:47:45,520 +to increase the temperature of 50 grams of water + +619 +00:47:45,520 --> 00:47:51,470 +by 1 KelvinCalculate the specific heat بقول + +620 +00:47:51,470 --> 00:47:55,670 +specific heat of water حلو بقول ال specific heat + +621 +00:47:55,670 --> 00:47:58,890 +ساوي ال quantity of heat transferred in grams of + +622 +00:47:58,890 --> 00:48:02,430 +substance in temperature change فال specific heat + +623 +00:48:02,430 --> 00:48:07,650 +ال CS فيها ساوي انا حطيت 209 جول طب 209 جول على 50 + +624 +00:48:07,650 --> 00:48:14,030 +جرام كمية المادة 50 جرام او كتتها 50 جرام في ال + +625 +00:48:14,030 --> 00:48:19,410 +delta T جال بس واحد Kelvin فبيطلعالـ Specification + +626 +00:48:19,410 --> 00:48:24,990 +اللي هو 4.18 هذا رقم معروف لازم نحفظه حتى لأن هو + +627 +00:48:24,990 --> 00:48:29,910 +exact value يعني 4.184 جول هذا عبارة عن exact + +628 +00:48:29,910 --> 00:48:33,750 +value لازم نحفظه زي إنه المتر ميت صنطي وخلافه يعني + +629 +00:48:35,830 --> 00:48:42,270 +يبقى احنا بحاجة لاربعة و تمانتاش و مية جول لكل + +630 +00:48:42,270 --> 00:48:46,690 +جرام احنا بحاجة لاربعة ليه لان كل الخمسين اخدوا + +631 +00:48:46,690 --> 00:48:49,870 +متين وتسعة فاحنا بحاجة لكل جرام four point one + +632 +00:48:49,870 --> 00:48:51,850 +eight joules + +633 +00:48:56,880 --> 00:48:59,880 +الـ specific heat عادة زي ما قلتلكم في الحصة + +634 +00:48:59,880 --> 00:49:05,840 +الماضية بتعتمد قليلا جدا على درجة الحرارة اللي + +635 +00:49:05,840 --> 00:49:10,280 +بتنجس عندها بتعتمد قليلا جدا عشان هيك ال specific + +636 +00:49:10,280 --> 00:49:16,060 +heat للميهأتعرفت في التعريف تبعها إنه هي كمية + +637 +00:49:16,060 --> 00:49:20,280 +الحرارة اللازمة لرفع واحد جرام لرفع درجة حرارة + +638 +00:49:20,280 --> 00:49:24,140 +واحد جرام من الميه Initially موجودة عند اربعة عشر + +639 +00:49:24,140 --> 00:49:27,700 +و نص إلى خمستاشر و نص ديجري سي ليش عملها هيك جال + +640 +00:49:27,700 --> 00:49:31,460 +لأن ال specific heat في الحقيقة بتعتمد على درجة + +641 +00:49:31,460 --> 00:49:35,280 +الحرارة لكن اعتمادها على درجة الحرارة جديش قليل + +642 +00:49:35,280 --> 00:49:42,680 +جدا فعشان احنا نعرف صحالصح انه نذكر درجة الحرارة + +643 +00:49:42,680 --> 00:49:46,580 +اللى عندها ال heat capacity مقاسة ليه؟ لأن ال heat + +644 +00:49:46,580 --> 00:49:50,820 +capacity بتعتمد على درجة الحرارة وإن كان بكمية + +645 +00:49:50,820 --> 00:49:57,780 +يعني قليلة للغاية طب نتطلع على ال heat capacities + +646 +00:49:57,780 --> 00:50:05,940 +لبعض المواد ال nitrogen مثلا 1.04الـ Aluminum 0.9 + +647 +00:50:05,940 --> 00:50:13,460 +الـ Iron 0.45 الـ Mercury 0.14 الـ H2O 4.18 لحظة + +648 +00:50:13,460 --> 00:50:20,120 +CH4 2.2 الـ CO2 0.84 الـ Calcium Carbonate 0.82 + +649 +00:50:20,120 --> 00:50:23,860 +الـ Solid A ما هو معنى هذا الكلام؟ معنى هذا الكلام + +650 +00:50:23,860 --> 00:50:29,540 +أن مثلا الـ Iron 0.45 يعني لو أعطيت نفس كمية + +651 +00:50:29,540 --> 00:50:34,150 +الحرارةلو اعطيت نفس كمية الحرارة لواحد جرام من + +652 +00:50:34,150 --> 00:50:37,330 +الميه و واحد جرام من ال ايرون ال ايرون درجة حرارته + +653 +00:50:37,330 --> 00:50:42,790 +بترتفع اكتر لو اعطيت نفس كمية الحرارة لواحد جرام + +654 +00:50:42,790 --> 00:50:45,650 +من الميه و واحد جرام من ال ايرون بلاحظ ان ال ايرون + +655 +00:50:45,650 --> 00:50:49,750 +بترتفع درجة حرارته ايه اكتر لو اعطيت واحد جرام لو + +656 +00:50:49,750 --> 00:50:58,570 +اعطيت كمية حرارة ل مثلا واحد جرام ميركوري و واحد + +657 +00:50:58,570 --> 00:51:04,590 +جرامميثين بلاحظ انه لأن الميثين ال specific heat + +658 +00:51:04,590 --> 00:51:08,130 +له أعلى يعني بده حرارة أعلى اه حرارة ال mercury + +659 +00:51:08,130 --> 00:51:12,550 +بترفع أكتر فهذا هو مفهوم ال specific heat اللي + +660 +00:51:12,550 --> 00:51:16,670 +قدامي فمثلا هال بيقول لي which substance in the + +661 +00:51:16,670 --> 00:51:19,550 +table undergoes the greatest temperature change + +662 +00:51:19,550 --> 00:51:23,810 +with the same mass نفترض اسمه 1 جرام a same mass + +663 +00:51:23,810 --> 00:51:27,430 +of each substance absorbs the same quantity of + +664 +00:51:27,430 --> 00:51:31,800 +heat يعني أعطينا نفس كمية الطاقةنفس كمية الحرارة + +665 +00:51:31,800 --> 00:51:38,160 +عفواً لواحد فقط لإعتمادها لكل واحد من هدول نفس + +666 +00:51:38,160 --> 00:51:43,440 +الوزن نفس الكتلة أنه أو أنهي مادة من هدول راح + +667 +00:51:43,440 --> 00:51:47,040 +ترتفع درج حررتها أكتر طبعا اللي إلها lower + +668 +00:51:47,040 --> 00:51:50,400 +specific heat هترتفع درج حررتها أعلى ال lowest + +669 +00:51:50,400 --> 00:51:53,290 +specific heat اللي عندهاهي لـ Mercury إذا الـ + +670 +00:51:53,290 --> 00:51:57,690 +Mercury هيرتفع لو أعطناها نفس كمية الحرارة و نفس + +671 +00:51:57,690 --> 00:52:01,330 +الوزنة كويسة هنلاحظ الـ Mercury درجة Delta T تبعته + +672 +00:52:01,330 --> 00:52:08,310 +هتكون أعلى أو أكبر طب نطلع برضه على بعض الأمثلة + +673 +00:52:08,310 --> 00:52:12,590 +اللي جيس فيها الـ heat flow أو ال heat capacity + +674 +00:52:12,590 --> 00:52:19,210 +يعني بيقول how much heat is needed to warm 250 + +675 +00:52:19,210 --> 00:52:24,890 +gram of waterبقول يعني تقريبا كوب يعني كوبية from + +676 +00:52:24,890 --> 00:52:28,290 +اتنين و عشرين degree C to تمانية وتسعين degree C + +677 +00:52:28,970 --> 00:52:33,250 +ناخد واحدة واحدة how much heat انا بدي ال CS + +678 +00:52:33,250 --> 00:52:37,310 +بتساوي Q على ال M في ال Delta T او ال Q بتساوي ال + +679 +00:52:37,310 --> 00:52:41,170 +CS في ال M في ال Delta T نفس القانون هو هو فانا + +680 +00:52:41,170 --> 00:52:44,850 +عنده بدي ال Q قال والله ال CS للمياء اربعة و + +681 +00:52:44,850 --> 00:52:49,290 +تمانتاش الماس لل water متين و خمسين ال Delta T + +682 +00:52:49,290 --> 00:52:52,710 +تمانية وتسعين ناقص اتنين و عشرين بيطلع عنده سبعة و + +683 +00:52:52,710 --> 00:52:56,230 +تسعة في عشر عقص اربعة جول او تسعة و سبعين كيلو جول + +684 +00:52:56,840 --> 00:52:59,880 +طب نتطلع عليه بيقول what's the molar heat capacity + +685 +00:52:59,880 --> 00:53:07,300 +of water؟بيدوا الـ heat capacity للمول فبنقول + +686 +00:53:07,300 --> 00:53:11,180 +بسيطة خالص ال molar heat capacity CM هي عبارة عن + +687 +00:53:11,180 --> 00:53:18,220 +CS في الفورمولا ويت ال CM بتساوي 4.18 في 18 فبيطلع + +688 +00:53:18,220 --> 00:53:21,620 +عند ال .. لإن ال gram الواحد 4.18 بيده انا + +689 +00:53:21,620 --> 00:53:25,160 +الفورمولا ويت عند ال 18 ال gram الميه فبيطلع في 18 + +690 +00:53:25,160 --> 00:53:31,840 +بيطلع 75.2 kilo jouleكمان مثال زي هيك بيقول the + +691 +00:53:31,840 --> 00:53:38,300 +specific heat of some rocks is 0.82 joule gram + +692 +00:53:38,300 --> 00:53:41,880 +Kelvin يعني calcium carbonate solid بيقول + +693 +00:53:41,880 --> 00:53:45,660 +calculate the quantity of heat absorbed by fifty + +694 +00:53:45,660 --> 00:53:50,330 +kilograms of rocksعندي خمسين كيلو جرام من الصخور + +695 +00:53:50,330 --> 00:53:53,530 +if their temperature increases by اتناشر دجري ال C + +696 +00:53:53,530 --> 00:53:57,230 +ايش يعني ال delta T اتناشر لان لما اقول ان الحرارة + +697 +00:53:57,230 --> 00:54:00,670 +زادت اتناشر درجة يعني دلتا T اتناشر ناخد هذه + +698 +00:54:00,670 --> 00:54:03,970 +وبعدين نروح ل B بقول ال Q بتساوي ال C is point + +699 +00:54:03,970 --> 00:54:08,890 +eight two ال M بالجرام دائما لان ال C is للجرام + +700 +00:54:08,890 --> 00:54:14,090 +فمنفعش هذه يكون جرام وهنا كيلو جرام لأأجرام فبنذكر + +701 +00:54:14,090 --> 00:54:19,350 +ال M إيه شمالها إجرام زي ال C S فخمسة في عشر أقصى + +702 +00:54:19,350 --> 00:54:23,490 +أربعة جرام خمسين كيلو جرام في ال Delta T بطلع + +703 +00:54:23,490 --> 00:54:30,390 +أربعة وتسعة في عشر أقصى خمسة جول هذه كمية الحرارة + +704 +00:54:30,390 --> 00:54:34,710 +اللي بتمتصها خمسين كيلو جرام من ال rocks بيقول بيه + +705 +00:54:34,710 --> 00:54:37,590 +what temperature change would these rocks undergo + +706 +00:54:37,590 --> 00:54:43,110 +if they emit 450 kilo joule of heatأه إذا كانت هي + +707 +00:54:43,110 --> 00:54:47,470 +بتعطيني 450 kilo joule of heat فالـ Q موجودة معايا + +708 +00:54:47,470 --> 00:54:53,170 +فبس بدي أعرف الـ Delta T الـ Delta T من القانون + +709 +00:54:53,170 --> 00:54:57,730 +Delta T هي لها حاطين هدول تحت صرت Delta T بيتساوي + +710 +00:54:57,730 --> 00:55:01,390 +Q على ال CS في ال M Delta TQ على ال CS في ال M + +711 +00:55:01,390 --> 00:55:08,060 +فDelta TQ معايا أربعة و نص فعشرة أس خمسة jouleكويس + +712 +00:55:08,060 --> 00:55:12,700 +450 kilojoule يعني أربعة و نص والكيلو في مية يعني + +713 +00:55:12,700 --> 00:55:15,600 +والكيلو عشر أقصرات أربعة و نص في عشر أقصر خمسة + +714 +00:55:15,600 --> 00:55:21,640 +kilojoule of heat على CS point eight two ال mass + +715 +00:55:21,640 --> 00:55:25,000 +خمسة في عشر أقصر أربعة جرام بتطلع أحد عشر Kelvin + +716 +00:55:25,000 --> 00:55:30,720 +إذا حرارة ال rocks هتزيد بمقدار أحد عشر Kelvin + +717 +00:55:33,650 --> 00:55:37,310 +5 جرام من الكبار كان محرر من 20 إلى 80 درجة، انظر + +718 +00:55:37,310 --> 00:55:42,110 +إلى كم طاقة استخدمت لحرر الكباركمان مرة كيو بيستوى + +719 +00:55:42,110 --> 00:55:45,830 +CSM في الـ Delta T ال specific heat للكبار point + +720 +00:55:45,830 --> 00:55:49,910 +three eight بسهولة بيسخن لأن ال specific heat بعته + +721 +00:55:49,910 --> 00:55:54,070 +جليلة خمسة gram في تمانين ناقص عشرين بيطلع مية + +722 +00:55:54,070 --> 00:55:58,130 +وأربعة عشر joule كمية قليلة في الحقيقة لتساخدوا + +723 +00:55:58,130 --> 00:56:02,710 +لستين درجة يعني لو مية بدها كمية يعني كبيرة خالص + +724 +00:56:02,710 --> 00:56:09,350 +على الأقل عشر أضعاف هذه الكمية يعنيبقول if if هذا + +725 +00:56:09,350 --> 00:56:13,210 +مهم اسمها if a three point one gram ring is heated + +726 +00:56:13,210 --> 00:56:19,930 +using عشرة جول حطينا عشرة جول سخننا خاتم كويس its + +727 +00:56:19,930 --> 00:56:23,370 +temperature rises by سبعتاشر تسعة و عشرة ديجري سي + +728 +00:56:23,370 --> 00:56:28,490 +كويس لما اعطيناه عشرة جول حرارته ايه ارتفعت + +729 +00:56:28,490 --> 00:56:31,130 +سبعتاشر تسعة و عشرة يعني ال delta T عند سبعتاشر + +730 +00:56:31,130 --> 00:56:33,950 +تسعة و عشرة ديجري سي بقول calculate the specific + +731 +00:56:33,950 --> 00:56:39,030 +heat of ringبس في الأول ال specific heat والله Q + +732 +00:56:39,030 --> 00:56:42,750 +اللي هي العشرة اللي حطناها على وزن طول M الماس + +733 +00:56:42,750 --> 00:56:46,090 +تلاتة و واحد في ال Delta T بطلع point one eight + +734 +00:56:46,090 --> 00:56:51,770 +Joule per gram ديجري سين فبسأل السؤال is the ring + +735 +00:56:51,770 --> 00:56:56,510 +pure gold أنا عندي هان إيش اللي حسبته ال specific + +736 +00:56:56,510 --> 00:57:00,030 +heat لل ring بروح للجداول بقول طب جدش ال specific + +737 +00:57:00,030 --> 00:57:05,760 +heat لل gold بلاجيها point one threeأذن هذا طلع + +738 +00:57:05,760 --> 00:57:08,700 +عندى point one eight يبقى هذا لا يمكن يكون دهب + +739 +00:57:08,700 --> 00:57:14,200 +خالص وسيلة سهلة جدا لمعرفة نقاوة المعدن او الماعدن + +740 +00:57:14,200 --> 00:57:18,160 +هذا يعني ايش نوع المعدن على سبيل المثال حلو جدا + +741 +00:57:18,160 --> 00:57:23,180 +وسهلة خالص معايا انا طلعت specific heat لل ring و + +742 +00:57:23,180 --> 00:57:25,500 +بسأل ان هل هو دهب ولا ولا بدور على المادة تبعته + +743 +00:57:25,500 --> 00:57:29,500 +بروح بدور والله اطلعت لجيت الدهب لأ point one + +744 +00:57:29,500 --> 00:57:32,540 +three اذا لأ والله هذا مش دهب لأن لو دهب بده point + +745 +00:57:32,540 --> 00:57:37,930 +one eightكويس؟ زي .. زي بالظبط يعني ال specificية + +746 +00:57:37,930 --> 00:57:40,370 +الدهب بيكون point one eight لكن لأ هي point one + +747 +00:57:40,370 --> 00:57:49,190 +three اذا هو مش دهبالان احنا جاهزين نحسب الـ Delta + +748 +00:57:49,190 --> 00:57:55,150 +H عمليا فبدأ + +749 +00:57:55,150 --> 00:58:00,830 +اطلع على الـ Calorimetry Calorimetry يعني الـ + +750 +00:58:00,830 --> 00:58:04,790 +Calorimetry هي عبارة عن مجرم of heat flow مجرم of + +751 +00:58:04,790 --> 00:58:07,670 +heat flow ايش يعني heat flow؟ يعني عندي reaction + +752 +00:58:07,670 --> 00:58:12,010 +بعطيباعطي heat للـ surroundings وبالتالي في عندي + +753 +00:58:12,010 --> 00:58:14,870 +flow لل heat من ال system لل surroundings أو العكس + +754 +00:58:14,870 --> 00:58:18,830 +ال surroundings بتعطي heat لإيه؟ لل system فهذا + +755 +00:58:18,830 --> 00:58:24,810 +اسمه heat flow فال calorie meter هي عبارة عن ال + +756 +00:58:24,810 --> 00:58:27,990 +measurement of heat flow ال measurement of heat + +757 +00:58:27,990 --> 00:58:33,630 +flow احنا بنجيزها باستخدام calorie meter استخدام + +758 +00:58:33,630 --> 00:58:37,950 +أداة قياس ال heat flow اللي هو ال calorie meter + +759 +00:58:40,220 --> 00:58:44,920 +فاحنا بدنا نحاول نحسب الـ delta H عمليًا by + +760 +00:58:44,920 --> 00:58:47,680 +measuring heat flow accompanying a chemical + +761 +00:58:47,680 --> 00:58:51,200 +reaction أو chemical process at constant pressure + +762 +00:58:51,200 --> 00:58:58,140 +زي ما عرفنا الـ delta H at constant pressure كيف + +763 +00:58:58,140 --> 00:59:02,900 +بدنا نعمل هذا الكلام؟ بدنا نحاول نجيس يعني التغير + +764 +00:59:02,900 --> 00:59:05,280 +في درجة الحالة الـ delta T بدنا نحاول نجيس الـ + +765 +00:59:05,280 --> 00:59:09,290 +delta T للسيستمبدنا نحاول نجيس الـ Delta T للـ + +766 +00:59:09,290 --> 00:59:12,510 +system اللي عندنا عشان نعمل هذا الكلام في عندى + +767 +00:59:12,510 --> 00:59:17,190 +نوعين من أنواع الـ calorie meter أجهزة قياس الـ + +768 +00:59:17,190 --> 00:59:21,640 +heat flowفي عندى جهاز بسيط كتير بنقوله constant + +769 +00:59:21,640 --> 00:59:26,480 +pressure calorimeter او تقنيكي يعني calorimetry + +770 +00:59:26,480 --> 00:59:30,880 +اللى هو coffee cup calorimeter coffee cup يعني + +771 +00:59:30,880 --> 00:59:35,360 +فنجار اللى هو كباية الجهوة تعرفوا لما تشتريوا + +772 +00:59:35,360 --> 00:59:40,580 +كباية جهوة من المكينة بيعطيكوا كباية ورق يعني + +773 +00:59:40,580 --> 00:59:48,730 +ورقية فى كبايات styrofoamمن هذا النوع الأبيض + +774 +00:59:48,730 --> 00:59:53,650 +المنفوخ اللي بيتكسر بتعرفوا هذا اسمه Styrofoam زي + +775 +00:59:53,650 --> 00:59:57,590 +الفلين زي ما تشتريوا بعض الصحون برضه ببيعوهم + +776 +00:59:57,590 --> 01:00:02,210 +بتكسروا على طول هذا اسمه Styrofoamما يميزه انه + +777 +01:00:02,210 --> 01:00:06,610 +يعني ممكن تمسك الكباية من غير ما ايه ما ايديك تسخن + +778 +01:00:06,610 --> 01:00:10,470 +لأن اه هو عازل إلى حد ما فاحنا بدنا نحاول نعزل ال + +779 +01:00:10,470 --> 01:00:15,050 +system عن الجو الخارج وبنستخدم ال styrofoam كويس + +780 +01:00:15,050 --> 01:00:19,770 +هدف ال coffee cup calorie meter والفي الحقيقة هو + +781 +01:00:19,770 --> 01:00:23,910 +في أجهزة من هذا النوع دقيقة جدا لكن احنا بدنا + +782 +01:00:23,910 --> 01:00:27,540 +نحاول في المختبرات تبعتنابنستخدم ال coffee cup + +783 +01:00:27,540 --> 01:00:32,120 +calorie meter لأنه سهل ومتوفر ورخيص وبيعطي نفس + +784 +01:00:32,120 --> 01:00:36,960 +الفكرة العامة وإن كان القراءات مش يعني مية في + +785 +01:00:36,960 --> 01:00:43,160 +المية صحيح طيب + +786 +01:00:43,160 --> 01:00:49,800 +هذا هو ال ..هذا هو ال .. لاحظوا هذه الكباية تبعتي + +787 +01:00:49,800 --> 01:00:52,620 +اللي أنا حطيت فيها حطت تنتين في بعض عشان العزل + +788 +01:00:52,620 --> 01:00:57,520 +يكون ايه؟ احسن وفي غطاية وفي هنا stirer غطاية و + +789 +01:00:57,520 --> 01:01:02,440 +stirer و ترمومتر كويس فهنا انا بحط المتفاعلات + +790 +01:01:03,210 --> 01:01:08,530 +والتكن مثلا HCl و Sodium Hydroxide مثلا خمسين مل + +791 +01:01:08,530 --> 01:01:11,770 +HCl و خمسين مل Sodium Hydroxide هذا تركيز و واحد + +792 +01:01:11,770 --> 01:01:15,570 +مولر وهذا تركيز و واحد مولر حطيتهم و سكرت و انا + +793 +01:01:15,570 --> 01:01:19,590 +ايه و بقى يعني اول حاجة عارف انا درج حرارتهم + +794 +01:01:19,590 --> 01:01:22,870 +الاصلية اللي هي درج حرارة الجو فلما انحطيتهم بدي + +795 +01:01:22,870 --> 01:01:29,330 +اقرأ الزيادةأنا عندى .. بدنا نفهم كويس ال system + +796 +01:01:29,330 --> 01:01:35,290 +اللى عندى هو فقط ال HCL المولاد تبعته و ال sodium + +797 +01:01:35,290 --> 01:01:38,770 +hydroxide المولاد تبعته لكن الميه تعتبر + +798 +01:01:38,770 --> 01:01:42,870 +surroundings بالنسباله معايا نفهم كويس الميه هي + +799 +01:01:42,870 --> 01:01:46,750 +ايه ال surroundings ابحث انه لو التفاعل اعطانى + +800 +01:01:46,750 --> 01:01:50,430 +حرارة لمن بدي اعطيها للميه اذا لو جسد حرارة الميه + +801 +01:01:50,430 --> 01:01:54,410 +انا بعرف ال surroundings جداش اخدتتمام؟ و لو كان + +802 +01:01:54,410 --> 01:01:58,090 +التفاعل ماصد الحرارة الميّه راح تعطيه فحشيه في + +803 +01:01:58,090 --> 01:02:03,090 +النقص معاه اذا بعتبر انا كل شيء ما عدا التفاعل هو + +804 +01:02:03,090 --> 01:02:06,230 +عبارة عن سرّانة مما في ذلك الميّه اللي هي ال + +805 +01:02:06,230 --> 01:02:10,570 +solvent يعني ضروري نفهم هذا الكلام الان انا و الله + +806 +01:02:10,570 --> 01:02:15,150 +لو عارف كمية الميّه اللي هي M الماسلة إيها و ال C + +807 +01:02:15,150 --> 01:02:20,410 +اسمها معروفة للميّه جديش و ال delta T هي نجستها + +808 +01:02:20,410 --> 01:02:27,500 +اذا بجيب لك Uيا فنات ماشي انا ايش بقول هيها ال Q + +809 +01:02:27,500 --> 01:02:35,360 +بتساوي CS M في ال Delta T صح فهي ال CS معايا للميه + +810 +01:02:35,360 --> 01:02:39,720 +و الم S معايا للميه فانا حطيت خمسين مل و خمسين مل + +811 +01:02:39,720 --> 01:02:43,720 +مثلا واحد المل واحد جرام يعني مائة جرام و Delta T + +812 +01:02:43,720 --> 01:02:50,250 +مانا بجيسها اذا ايش مقدر اجيب ال Q لل solutionاللي + +813 +01:02:50,250 --> 01:02:54,750 +هو ال surroundings، إذاً ال Q لل reaction سوى + +814 +01:02:54,750 --> 01:02:59,110 +minus Q لل solution، ليه؟ لأنه عكسه، إذا كان ال + +815 +01:02:59,110 --> 01:03:03,490 +solution زادت حرارته، معناته ال system هو اللي + +816 +01:03:03,490 --> 01:03:08,530 +يعطى، فدائما ال Q لل reaction minus Q لل solution + +817 +01:03:09,380 --> 01:03:15,880 +طب خلّينا نتطلع هذا هو مفهومه يعني الـ Q للـ + +818 +01:03:15,880 --> 01:03:18,140 +solution من الـ secular reaction الصحيح لـ Q للـ + +819 +01:03:18,140 --> 01:03:23,740 +solution 100% مافيش مشكلة تيبجي نتطلع على أمثلة و + +820 +01:03:23,740 --> 01:03:28,420 +خلاص تيبجي هذه فكرته من الناحية النظرية فكرة كتير + +821 +01:03:28,420 --> 01:03:32,360 +كتير بسيطة فكرة كتير كتير بسيطة نتطلع على المثال + +822 +01:03:32,360 --> 01:03:37,750 +التالي بيقول when a studentmixes 50ml of 1 molar + +823 +01:03:37,750 --> 01:03:43,110 +HCl مع 50ml of 1 molar sodium hydroxide in a + +824 +01:03:43,110 --> 01:03:47,030 +coffee cup calorimeter، شفناه؟ the temperature of + +825 +01:03:47,030 --> 01:03:50,910 +the resultant solution increases from 21 degrees C + +826 +01:03:50,910 --> 01:03:55,650 +to 27.5 degrees C لما خلطهم حصلت تفاعل، بنسميه + +827 +01:03:55,650 --> 01:03:59,350 +بالمناسبة يا بنات a neutralization reaction، تفاعل + +828 +01:03:59,350 --> 01:04:03,830 +الأسد مع ال base، بنسميه neutralizationالمهم بيقول + +829 +01:04:03,830 --> 01:04:06,610 +calculate the enthalpy change for the reaction + +830 +01:04:06,610 --> 01:04:11,070 +ولاحظوا أنه التفاعل بيتم at constant pressure لأنه + +831 +01:04:11,070 --> 01:04:16,950 +يعني ال .. احنا مش عاملين حسابنا أنه نعزل .. يعني + +832 +01:04:16,950 --> 01:04:19,430 +نحطه في closed system، لأ مش في closed system، at + +833 +01:04:19,430 --> 01:04:22,910 +constant pressure فعايز يحسب ال enthalpy change in + +834 +01:04:22,910 --> 01:04:28,190 +kilo joule per mole HClPer mole HCl Assuming that + +835 +01:04:28,190 --> 01:04:31,850 +the calorimeter loses only a negligible quantity + +836 +01:04:31,850 --> 01:04:35,010 +of it يعني اللي راح يطلع برا احنا حطناه في ايه؟ في + +837 +01:04:35,010 --> 01:04:38,010 +two cups اللي راح يطلع برا للهواء Negligible يعني + +838 +01:04:38,010 --> 01:04:41,290 +وين كل الحرارة هتتمها؟ بس في الميه، في المحلول + +839 +01:04:41,290 --> 01:04:46,110 +يعني عند ال calorimeter موجود فيه ال HCl وال + +840 +01:04:46,110 --> 01:04:49,390 +Sodium hydroxide ترتفع الحرارة طب الحرارة ممكن + +841 +01:04:49,390 --> 01:04:55,400 +تطلع من ال calorimeter لوين؟ كمان للهواءبنقول لأ + +842 +01:04:55,400 --> 01:04:58,760 +على فرض أن هذه الكمية اللي بيطلع الهواء مهملة يعني + +843 +01:04:58,760 --> 01:05:02,740 +وين كل الحرارة اللي طلعت من ال reaction جال تمت + +844 +01:05:02,740 --> 01:05:05,880 +وين في ال calorie meter يعني ال surroundings اللي + +845 +01:05:05,880 --> 01:05:11,940 +هي المي اللي هي اللي أخدتها، كويس؟ that the volume + +846 +01:05:11,940 --> 01:05:15,280 +of the solution is hundred ml خمسين مل وخمسين مل + +847 +01:05:15,280 --> 01:05:18,860 +يعني ال volume hundred ml that its density is واحد + +848 +01:05:18,860 --> 01:05:23,140 +gram per ml عشان أجيب ال mathالـ volume 100 و ال + +849 +01:05:23,140 --> 01:05:27,340 +density 1 جرام يعني عندي 100 جرام and that the + +850 +01:05:27,340 --> 01:05:32,380 +specific heat of water is 4.18 Joule per gram per + +851 +01:05:32,380 --> 01:05:36,180 +Kelvin زي ما نقول Joule per gram per degree C لأن + +852 +01:05:36,180 --> 01:05:40,500 +المقدار لـ Kelvin هو عبارة عن نفسه المقدار لل + +853 +01:05:40,500 --> 01:05:44,960 +degree C هذا هو التفاعل 1 mol HCl بنشوف إيش + +854 +01:05:44,960 --> 01:05:49,520 +بيعطيلنا mass of solution meat meal في ال density + +855 +01:05:49,520 --> 01:05:54,370 +100 جرامتمام الـ Q للسليوشن لـ specific heat + +856 +01:05:54,370 --> 01:05:58,370 +للسليوشن في الـ grams للسليوشن في الـ Delta T و + +857 +01:05:58,370 --> 01:06:03,870 +بتساوي minus Q لل reaction طيب الـ Delta H بتساوي + +858 +01:06:03,870 --> 01:06:09,500 +الـ Q لل reactionدلتا الان هي Q P Q at constant + +859 +01:06:09,500 --> 01:06:11,940 +pressure وانا بشتغل at constant pressure بساوية Q + +860 +01:06:11,940 --> 01:06:15,020 +P بساوية minus Q لل solution اذا ان ال delta H + +861 +01:06:15,020 --> 01:06:18,920 +بدها تساوي ممكن اعوض عنها delta H بدها تساوي minus + +862 +01:06:18,920 --> 01:06:22,980 +لان التفاعل ايش ماله الحرارة زادت minus four point + +863 +01:06:22,980 --> 01:06:27,060 +one eight اللي هي ال specific heat في مائة جرام في + +864 +01:06:27,060 --> 01:06:32,830 +ال delta T بطلع-2.71 KJ يبقى Delta H لهذا التفاعل + +865 +01:06:32,830 --> 01:06:43,510 +بقدر اقول Delta H هنا حسبتها سالب 2.71 KJ لأ مش + +866 +01:06:43,510 --> 01:06:49,610 +للتفاعل هذا لسههذا لإيه؟ لعدد مولات معين مش لكل + +867 +01:06:49,610 --> 01:06:54,270 +التفاعل انا اللي حصلت عليه جديشي عند المولات تبع + +868 +01:06:54,270 --> 01:07:01,950 +ال HCL خمسين ميل في عشرة أسالب تلاتة اللي هي + +869 +01:07:01,950 --> 01:07:06,250 +surliter ضربتها في واحد صارت moles فبقى أنا بقول + +870 +01:07:06,250 --> 01:07:10,950 +هذه الكمية اللي حصلت عليها هي من الخمسين ميل من ال + +871 +01:07:10,950 --> 01:07:18,050 +HCLيعني الـ HCl الكمية هذه أعطتني 2.71 كيلوجولز هو + +872 +01:07:18,050 --> 01:07:26,110 +طالب ال إيه ال kilojoules per mole HCl مش بس + +873 +01:07:26,110 --> 01:07:29,410 +الكمية اللي حطها هو الكمية اللي حطها هي عبارة عن + +874 +01:07:29,410 --> 01:07:33,750 +عدد مولات الـ HCl واحد في خمسة من مية الحجم خمسة + +875 +01:07:33,750 --> 01:07:37,890 +من مية لتر يعني point oh five هذه ال point oh five + +876 +01:07:37,890 --> 01:07:44,920 +mole ال point oh five moleالشركة HCL اعطتنا 2.71 + +877 +01:07:44,920 --> 01:07:45,700 +كيلوجول + +878 +01:07:51,630 --> 01:07:56,130 +أنا بدّي الـ 1 مول فبقول انا الـ Δ H بتساوي 2.71 + +879 +01:07:56,130 --> 01:08:00,990 +كيلوجول على عدد الملات 0.05 مول H سيرة بتعطيني 54 + +880 +01:08:00,990 --> 01:08:05,810 +.3 كيلوجول، اذا عدد الملاء عدد ال .. او كمية + +881 +01:08:05,810 --> 01:08:13,190 +الحرارة الناتجة عن 1 مول كامل هي عبارة عن 54.3 + +882 +01:08:13,190 --> 01:08:14,510 +كيلوجول + +883 +01:08:17,040 --> 01:08:21,700 +خلّيني أخد كمان مثال وبرضه نحسب الكلوجول per mole + +884 +01:08:21,700 --> 01:08:25,880 +بيقول when خمسين mil of point one molar silver + +885 +01:08:25,880 --> 01:08:30,420 +nitrate and خمسين mil of point one molar HCl are + +886 +01:08:30,420 --> 01:08:34,420 +mixed in a constant pressure calorimeter, the + +887 +01:08:34,420 --> 01:08:36,740 +temperature of the mixture increases from إتنين و + +888 +01:08:36,740 --> 01:08:39,400 +عشرين و تلاتة لتلاتة و عشرين و أحد عشر The + +889 +01:08:39,400 --> 01:08:42,220 +temperature increase is used by the following + +890 +01:08:42,220 --> 01:08:49,050 +reactionهذا هو التفاعل اللي بيتم طب حلو كتير بيقول + +891 +01:08:49,050 --> 01:08:52,410 +calculate delta H for this reaction in kilojoule + +892 +01:08:52,410 --> 01:08:56,450 +per mole silver nitrate انا لاحظوا ان انا ماحطيتش + +893 +01:08:56,450 --> 01:08:59,890 +مول انا حطيت شوية بشوف شوية هذي جداش بتعطيني + +894 +01:08:59,890 --> 01:09:03,930 +وبعدين بشوف المول جداش بتعطينيفانا بقول والله على + +895 +01:09:03,930 --> 01:09:05,970 +طول الـ Q solution هي عبارة عن معنى secure + +896 +01:09:05,970 --> 01:09:10,550 +reaction يعني الـ Delta H ببساطة اللي هي الـ CS + +897 +01:09:10,550 --> 01:09:14,950 +مضروبة في 100 مضروبة في الـ Delta T بتعطيني 339 + +898 +01:09:14,950 --> 01:09:20,950 +جول طب هذه الـ 339 جول كيف حصلت عليها انا اللي هي + +899 +01:09:20,950 --> 01:09:24,330 +يعني 0.339 كيلوجول كيف حصلت عليها جالة حصلت عليها + +900 +01:09:24,330 --> 01:09:28,190 +من عدد ملات معين من أيه؟ من الـ silver nitrate طب + +901 +01:09:28,190 --> 01:09:33,020 +جديش عدد ملات الـ silver nitrate جال pointone مول + +902 +01:09:33,020 --> 01:09:38,040 +كويس مول ع ال letter هي ال molarity مضروبة في ال + +903 +01:09:38,040 --> 01:09:43,600 +volume بالمل لأن هي ال molarity بتساوي عدد المولات + +904 +01:09:43,600 --> 01:09:49,400 +ع ال volume بالletter فالمول بده يساوي عدد المولات + +905 +01:09:49,400 --> 01:09:53,340 +ساوي ال molarity في ال volume بالletter جدش ال + +906 +01:09:53,340 --> 01:09:59,010 +molarity واحد من عشرة جدش ال volume بالletterخمسة + +907 +01:09:59,010 --> 01:10:03,870 +من مائة اذا بتساوي point o o five mole يبجى عدد + +908 +01:10:03,870 --> 01:10:08,150 +مولات ال silver nitrate point o o five mole طيب + +909 +01:10:08,150 --> 01:10:13,090 +هذه انا حصلت عليها من point o o five mole طب المول + +910 +01:10:13,090 --> 01:10:16,870 +ايش بيعطيني جالب اقول الرقم point three three nine + +911 +01:10:16,870 --> 01:10:21,110 +kilo joule على point o o five بتعطينا sixty seven + +912 +01:10:21,110 --> 01:10:26,050 +point eight kilo joule per mole يبجى هان بقدر اقول + +913 +01:10:26,050 --> 01:10:37,210 +ال delta Hبالفعل سالب 66.8 كيلو جول لماذا؟ لأنه + +914 +01:10:37,210 --> 01:10:40,250 +اكمل عندي هنا واحد يبقى لواحد مول اه يبقى هذه pair + +915 +01:10:40,250 --> 01:10:42,250 +مول ماشي يا جماعة + +916 +01:10:50,460 --> 01:10:54,660 +بنطلع على كمان مسألة بيقول واحد و نص جرام of + +917 +01:10:54,660 --> 01:11:00,780 +magnesium was combined with 125 ml of 1 molar HCL + +918 +01:11:00,780 --> 01:11:06,420 +in a coffee cup calorie meter يعني حطينا واحد و نص + +919 +01:11:06,420 --> 01:11:11,460 +جرام من المجنيزيوم الصليد على 125 مل من one molar + +920 +01:11:11,460 --> 01:11:14,240 +HCL وحنا عارفين ان المجنيزيوم فوق الهيدروجين يعني + +921 +01:11:14,240 --> 01:11:19,920 +بتفاعل مع ال HCLطيب بيقول the initial temperature + +922 +01:11:19,920 --> 01:11:22,440 +was خمسة و عشرين degree c and the final + +923 +01:11:22,440 --> 01:11:25,100 +temperature was اتنين و سبعين و تلاتة من عشرة + +924 +01:11:25,100 --> 01:11:29,680 +degree c calculate ايه ال heat involved in the + +925 +01:11:29,680 --> 01:11:34,300 +reaction بده ال Q على طول ال Q يعني ال delta H ال + +926 +01:11:34,300 --> 01:11:40,760 +Q اللي هي ال delta H بس ايهالـ Q بتساوي minus Q + +927 +01:11:40,760 --> 01:11:43,720 +reaction والـ Q reaction بتساوي Delta H إذا الـ + +928 +01:11:43,720 --> 01:11:48,520 +Delta H بتساوي minus CS للميّه في وزن الميّه في + +929 +01:11:48,520 --> 01:11:53,420 +الـ Delta T بتطلع 24.7 كيلوجول يبقى هذه عبارة عن + +930 +01:11:53,420 --> 01:11:56,120 +الخطوة الأولى الـ heat involved in the reaction + +931 +01:11:56,120 --> 01:11:59,180 +مجلّيش per mole بس الـ heat involved in الهدف هي + +932 +01:11:59,180 --> 01:12:05,150 +124.7 كيلوجولبعدين بيقول ايه؟ the enthalpy of + +933 +01:12:05,150 --> 01:12:08,350 +reaction in terms of the number of moles of + +934 +01:12:08,350 --> 01:12:14,830 +magnesium used يعني بده ال delta H لل reaction ال + +935 +01:12:14,830 --> 01:12:18,970 +delta H لل reaction per mole يعني فبالتالي بده + +936 +01:12:18,970 --> 01:12:22,170 +اقسم على عرض الملات انا عندي واحد و نص جرام + +937 +01:12:22,170 --> 01:12:25,490 +ماجنيزيام واحد و نص جرام على ال atomic weight + +938 +01:12:25,490 --> 01:12:28,130 +للماجنيزيام اربعة و شنتلات بيعطيني point O six one + +939 +01:12:28,130 --> 01:12:32,030 +seven عندي اربع عشر و سبعمل عشر على point O six + +940 +01:12:32,030 --> 01:12:36,870 +one sevenبيعطينا حوالي 400 كيلوجول per mole ماشي + +941 +01:12:36,870 --> 01:12:42,730 +يا جماعة فيعني واضح أن الأمثلة بسيطة للغاية ويعني + +942 +01:12:42,730 --> 01:12:47,370 +بتشكلش أي نوع من أنواع الصعوبة + +943 +01:12:52,330 --> 01:12:56,230 +طيب يعني للأسف اليوم من رأيكم بتجيج تاني تلاتة + +944 +01:12:56,230 --> 01:13:03,630 +يعني بقى الجزء بسيط من هذا الموضوع اللي بتحدث عن + +945 +01:13:03,630 --> 01:13:09,250 +ال bomb calorimetry اللي هو قياس ال heat flow at + +946 +01:13:09,250 --> 01:13:14,590 +constant volume بالذات فقط لل combustion reactions + +947 +01:13:14,590 --> 01:13:21,940 +هذه يعني reactions معينة بيتم خلالهااحتراق هيدرو + +948 +01:13:21,940 --> 01:13:26,920 +كاربون وبحصل منه على حرارة لكن بتكون كل هذه + +949 +01:13:26,920 --> 01:13:33,020 +العملية بتتم at constant volume في وعى مغلق في وعى + +950 +01:13:33,020 --> 01:13:36,100 +مغلق تماما فحنشوف هذا الكلام إذا الله راد الحصة + +951 +01:13:36,100 --> 01:13:36,460 +الجاية + diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/MdYlKYcQfdg_postprocess.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/MdYlKYcQfdg_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..55aff49ccef2642a6224a22854c3b757e34dc96c --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/MdYlKYcQfdg_postprocess.srt @@ -0,0 +1,4012 @@ +1 +00:00:21,020 --> 00:00:23,980 +بسم الله الرحمن الرحيم إذا الله راضي اليوم برضه + +2 +00:00:23,980 --> 00:00:27,720 +بنكمل ب chapter ال thermochemistry الكيميا + +3 +00:00:27,720 --> 00:00:32,320 +الحرارية كنا بدأنا نتكلم من الحصة الماضية عن تعيين + +4 +00:00:32,320 --> 00:00:37,840 +ال delta H لل reaction فاتكلمنا عن ال calorimetry + +5 +00:00:37,840 --> 00:00:42,360 +واتكلمنا في البداية عن ال coffee cup + +6 +00:00:51,110 --> 00:00:54,990 +النوع التاني من الـ Calorimeters بتحدث عن الـ + +7 +00:00:54,990 --> 00:00:58,750 +Constant Volume Calorimetry أو ما يسمى بالـ Bomb + +8 +00:00:58,750 --> 00:01:02,530 +Calorimetry هنشوف ايش هو ال Constant Volume + +9 +00:01:02,530 --> 00:01:06,930 +Calorimeterبس فى البداية بدى أقول أن هذا النوع من + +10 +00:01:06,930 --> 00:01:11,630 +الـ Calorimetry أو الـ Calorimeters يستخدم بشكل + +11 +00:01:11,630 --> 00:01:17,170 +أساسى لتعيين الـ Delta H لل combustion reactions + +12 +00:01:17,170 --> 00:01:21,190 +لل combustion reactions فال reactants عادة اللى هى + +13 +00:01:21,190 --> 00:01:27,010 +عبارة عن Hydrocarbon أو ممكن نقول Fuel Hydrocarbon + +14 +00:01:27,010 --> 00:01:32,150 +أو Fuel و Oxygen موجودين مع بعض فى وعاء بنسميه + +15 +00:01:32,150 --> 00:01:38,920 +Bombكويس هنشوفه بعد شوية فهدول والله يعني اذا كان + +16 +00:01:38,920 --> 00:01:43,900 +.. كان في عندى شرارة كهربية في هذا الوعاء + +17 +00:01:43,900 --> 00:01:48,700 +فهيتفاعلوا هيتفاعلوا فهيحترق ال hydrocarbon بال + +18 +00:01:48,700 --> 00:01:53,570 +oxygen ويكون CO2 وميه عادةونتيجة التفاعل طبعا راح + +19 +00:01:53,570 --> 00:01:57,990 +يطلع حرارة البومب هيكون محط بكمية من الماء الماء + +20 +00:01:57,990 --> 00:02:02,030 +هذا راح يسخن والبومب نفسه راح تسخن فممكن بمعلومية + +21 +00:02:02,030 --> 00:02:07,550 +ال heat capacity لل calorie meter ممكن نعرف والله + +22 +00:02:07,550 --> 00:02:12,910 +جداش كمية ال heat evolved وبالتالي بنقدر نعين ال + +23 +00:02:12,910 --> 00:02:18,590 +heat flow فنشوف هذه + +24 +00:02:18,590 --> 00:02:19,870 +هي البومب + +25 +00:02:22,090 --> 00:02:27,190 +و واضح ان فيها وعاء صغير جوا بنحط فيه ال reactants + +26 +00:02:27,190 --> 00:02:32,730 +سواء كان liquid او solid و بيتم ضخ كمية من ال + +27 +00:02:32,730 --> 00:02:38,910 +oxygen علشان تكون كافية لاتفاعل يتم بشكل تمو في + +28 +00:02:38,910 --> 00:02:42,190 +عندى سلكين كهرباء هان بيقدروا يعطوا فيه زى + +29 +00:02:42,190 --> 00:02:46,750 +filament صغيرة تسخن فلمّا توصل لحد معين يعني + +30 +00:02:46,750 --> 00:02:50,310 +بيحترق ال fuel و ال oxidant و هان في عندى زى ما + +31 +00:02:50,310 --> 00:02:55,150 +احنا شايفين ميّه و هذا شيء عازل فبنقدر نقول احنا + +32 +00:02:55,150 --> 00:02:58,390 +بشكل عام وهذا طبعا ال tiller عشان يخلى الحرارة + +33 +00:02:58,390 --> 00:03:03,830 +داخل الميّه كلها تجربة تاخد نفس الحرارة و طبعا ال + +34 +00:03:03,830 --> 00:03:08,390 +thermometer عشان يجس لفرق درجات الحرارةواضح + +35 +00:03:08,390 --> 00:03:12,170 +بالنسبة لي انه اذا كان هذا عازل تماما يعني مش راح + +36 +00:03:12,170 --> 00:03:16,550 +لا يعطي حرارة ولا يمتص حرارة فحرارة فانا عندي + +37 +00:03:16,550 --> 00:03:23,810 +الحرارة الناشعة عن ال reaction هتسخن ال bomb و + +38 +00:03:23,810 --> 00:03:28,010 +هتسخن ايضا الميه فعادة اتكون يعني ممكن اقول انا ان + +39 +00:03:28,010 --> 00:03:35,890 +ال Q لل reaction هتساويالـ Q أو minus Q لأن طبعا + +40 +00:03:35,890 --> 00:03:41,050 +هي هتعطي minus Q لبوم زائد ال calorie meter اللي + +41 +00:03:41,050 --> 00:03:44,710 +هو عبارة عن الميه اللي في ال calorie meterفي بقى + +42 +00:03:44,710 --> 00:03:47,810 +في كثير من الأحيان بنقول إذا كان حطينا كمية معينة + +43 +00:03:47,810 --> 00:03:50,790 +في calorie meter معين و ال bomb تبعته معروفة + +44 +00:03:50,790 --> 00:03:53,390 +فبتكون ال heat capacity لل calorie meter ككل + +45 +00:03:53,390 --> 00:03:56,630 +معروفة اللي هي عبارة عن ال bomb زائد ال ايه؟ الميه + +46 +00:03:56,630 --> 00:03:59,390 +فممكن نلاقي بعض الأسئلة بتقولنا والله ال heat + +47 +00:03:59,390 --> 00:04:02,670 +capacity للميه هل جد أو هل جد في عيننا ميه؟ و ال + +48 +00:04:02,670 --> 00:04:05,890 +bomb ال heat capacity لها يعني قيمة معينة و في بعض + +49 +00:04:05,890 --> 00:04:08,550 +الأسئلة الأخرى ممكن تقولنا والله ال heat capacity + +50 +00:04:08,550 --> 00:04:12,450 +لل calorie meter ككل هل جد فتعني يعني أن والله ال + +51 +00:04:12,450 --> 00:04:18,500 +bombزائد الميّه اللي موجودة فهذه الفكرة العامة + +52 +00:04:18,500 --> 00:04:26,200 +للجهاز فكرة كتير بسيطة و فكرة كتير سهلة و أفضل + +53 +00:04:26,200 --> 00:04:29,460 +طريقة في الحقيقة لتعيين ال heat flow لمثل هذه ال + +54 +00:04:29,460 --> 00:04:34,700 +reactions هي أن نعملها bomb calorimeterالكلولة ال + +55 +00:04:34,700 --> 00:04:38,620 +reaction هتساوي minus طبعا بالسلب لأنه انا عندي + +56 +00:04:38,620 --> 00:04:42,200 +exothermic + +57 +00:04:42,200 --> 00:04:46,860 +reaction ف C للكالوريمتر اللي هي عبارة عن ال heat + +58 +00:04:46,860 --> 00:04:53,920 +capacity للميه في كتلة الميههذا الـ heat .. هذا + +59 +00:04:53,920 --> 00:04:58,600 +عبارة عن الـ C للميّه وكمان ال bomb ال heat + +60 +00:04:58,600 --> 00:05:01,920 +capacity لل bomb و ال C لل .. و ال heat capacity + +61 +00:05:01,920 --> 00:05:06,920 +لل .. CS لل bomb مضروبة في ال mass لل bomb بأي + +62 +00:05:06,920 --> 00:05:10,360 +material معمولة يعني و ال delta T طبعا للاتنين + +63 +00:05:10,360 --> 00:05:13,420 +بتعطين ال C .. لل .. ال C calorie meter ككل ال + +64 +00:05:13,420 --> 00:05:15,980 +heat capacity لل calorie meter ككل في ال delta T + +65 +00:05:15,980 --> 00:05:20,670 +اللي هو ال change in temperatureفخلينا نطلع على + +66 +00:05:20,670 --> 00:05:28,370 +مثال كتير بسيط كيف نعين الـ Q لل reaction بيقول + +67 +00:05:28,370 --> 00:05:32,810 +the combustion of methylhydrazine a liquid rocket + +68 +00:05:32,810 --> 00:05:37,130 +fuel يعني وقود بيستخدم .. وقود سائل بيستخدم + +69 +00:05:37,130 --> 00:05:43,190 +للصواريخ produces nitrogen, carbon dioxide and H2O + +70 +00:05:43,190 --> 00:05:47,100 +هي المعادلة اللي عنديكويس كتير بيقول when أربعة + +71 +00:05:47,100 --> 00:05:50,080 +جرام of methylhydrazine is combusted in a bomb + +72 +00:05:50,080 --> 00:05:55,080 +calorimeter يعني حطيناها والله هان أربعة جرام من + +73 +00:05:55,080 --> 00:06:00,260 +ال methylhydrazine the temperature of the + +74 +00:06:00,260 --> 00:06:03,660 +calorimeter increases from خمسة و عشرين تتسعة و + +75 +00:06:03,660 --> 00:06:08,160 +تلاتين point five degrees c حلو بيقول in a + +76 +00:06:08,160 --> 00:06:12,130 +separate experiment في تجربة منفصلة تماماThe heat + +77 +00:06:12,130 --> 00:06:15,170 +capacity of the calorimeter is measured to be 7 + +78 +00:06:15,170 --> 00:06:18,810 +.794 kilojoules per degree c يعني ال heat capacity + +79 +00:06:18,810 --> 00:06:24,410 +للكالوريمتر ككل معروفة 7.794 kilojoules per degree + +80 +00:06:24,410 --> 00:06:27,510 +c بيقول calculate the heat of reaction for the + +81 +00:06:27,510 --> 00:06:32,810 +combustion of one mole of methylhydrazine بدوش + +82 +00:06:32,810 --> 00:06:36,670 +الأربعة جرام بدوا إيه؟ لل one moleبقول حلو كتير + +83 +00:06:36,670 --> 00:06:39,270 +خلينا نشوف في الأول ال heat evolved من الأربعة + +84 +00:06:39,270 --> 00:06:43,270 +جرام و بعدين بنحوّل الأربعة جرام لمول فبقول أنا ال + +85 +00:06:43,270 --> 00:06:48,210 +Q لل reaction بتساوي minus Q للميه زائد Q للبوم + +86 +00:06:48,210 --> 00:06:53,110 +بالتان تان مع بعض ل Q ككل بتساوي minus Q بتساوي + +87 +00:06:53,110 --> 00:06:56,730 +minus Q لكالوريمتر يعني minus C لكالوريمتر في ال + +88 +00:06:56,730 --> 00:07:00,380 +Delta Tالـ C للكالوريمتر هي عبارة عن الـ C للـ + +89 +00:07:00,380 --> 00:07:03,460 +Water زائد الـ C للـ Bomb شفنا هذا الكلام قبل شوية + +90 +00:07:03,460 --> 00:07:06,060 +الـ Q للـ reaction يعني بتساوي minus الـ Q + +91 +00:07:06,060 --> 00:07:09,120 +للكالوريمتر بتساوي minus C للكالوريمتر في الـ + +92 +00:07:09,120 --> 00:07:13,400 +Delta T بس هذه يعني تفصيل مني أنا علشان أترجم + +93 +00:07:13,400 --> 00:07:17,320 +الكلام اللي قلته سابقا يعني بشكل مفصل معنى الكلام + +94 +00:07:17,320 --> 00:07:21,520 +الـ Q لل reaction بتساوي سالب الـ C للكالوريمتر + +95 +00:07:21,520 --> 00:07:29,540 +معايا 7.794 في الـ Delta Tاللي هي هي 7.794 في 39.5 + +96 +00:07:29,540 --> 00:07:35,260 +minus 25 تعطيني سالب 113 kilojoule بس هذا ال .. او + +97 +00:07:35,260 --> 00:07:39,640 +هذه القيمة resulting from ايه؟ الاربعة جرام انا + +98 +00:07:39,640 --> 00:07:43,560 +الآن لو بدي ل مول بدي احوّل الاربعة جرام لمول عدد + +99 +00:07:43,560 --> 00:07:46,940 +ملاتل مثل الهيدرزين جال والله ال mass على ال + +100 +00:07:46,940 --> 00:07:49,920 +formula weightبعطينا عدد المولات وهي عدد المولات + +101 +00:07:49,920 --> 00:07:55,020 +اذا والله انا بدي ال Q لل reaction للمول اذا بدي + +102 +00:07:55,020 --> 00:07:58,520 +اجسم هذه على عدد المولات فبتعطيني one point three + +103 +00:07:58,520 --> 00:08:02,120 +فعشرة اقصى تلاتة one point three فعشرة اقصى تلاتة + +104 +00:08:02,120 --> 00:08:07,150 +يعني حوالي الف و تلاتمية kilo joule per moleالـ + +105 +00:08:07,150 --> 00:08:11,270 +heat flow أو الـ heat of reaction اللي عندي، كويس؟ + +106 +00:08:11,270 --> 00:08:15,110 +وطبعا هي يعني هن بالسالب، لازم يكون عندي هن سالب + +107 +00:08:15,110 --> 00:08:19,810 +لأنها exothermic reaction، exothermic reaction طيب + +108 +00:08:19,810 --> 00:08:26,210 +احنا عملنا التجربة هذه at constant ايه؟ at + +109 +00:08:26,210 --> 00:08:29,760 +constant volume، لكن احنا بنعرف ان الـ delta HAt + +110 +00:08:29,760 --> 00:08:33,180 +constant pressure ايش اللي at constant volume دلتا + +111 +00:08:33,180 --> 00:08:36,680 +E فانا معناه كده ان بجيسي ال delta E هان مش ال + +112 +00:08:36,680 --> 00:08:40,450 +delta Hوصحيح انا بجيث الـ Delta E at constant + +113 +00:08:40,450 --> 00:08:44,030 +volume لكن يا بنات احنا ايش قلنا؟ قلنا ان الفرق + +114 +00:08:44,030 --> 00:08:47,490 +بين ال Delta E و Delta H قليل جدا هو ال PDV اللي + +115 +00:08:47,490 --> 00:08:51,370 +هو ال Expansion Work وهذا قليل جدا يعني لو اجينا + +116 +00:08:51,370 --> 00:08:55,310 +شوفنا في الواقع جداش الفرق بين ال Delta H و Delta + +117 +00:08:55,310 --> 00:09:00,750 +E بنلاقي تقريبا واحد كيلوجول الفرق بينهم واقعيا + +118 +00:09:00,750 --> 00:09:04,550 +علميا يعني واقعيا واحد كيلوجول يعني نسبة خطأ عندى + +119 +00:09:04,550 --> 00:09:08,260 +لو بدى اقول ان انا اللى حسبته هذا Delta Hنسبة خطأ + +120 +00:09:08,260 --> 00:09:12,500 +point one percent تقريبا ولا إشي فممكن نعبر عن ال + +121 +00:09:12,500 --> 00:09:17,040 +delta E at constant volume اللي هي QV اللي توي أنا + +122 +00:09:17,040 --> 00:09:19,680 +حسبتها أقول والله هذه هي ال delta H لل reaction + +123 +00:09:19,680 --> 00:09:23,480 +على أي حال في كتب ال thermodynamics والجداو اللي + +124 +00:09:23,480 --> 00:09:28,020 +احنا بنحطها ال delta H مصححة يعني عند ال delta E + +125 +00:09:28,020 --> 00:09:31,780 +بنحصل على ال delta E at constant volume وبنصححها + +126 +00:09:31,780 --> 00:09:36,630 +عشان نحصل على ال delta H at constant pressureلكن + +127 +00:09:36,630 --> 00:09:42,850 +التصحيح اشمله مقداره ضئيل للغاية، مقداره ضئيل + +128 +00:09:42,850 --> 00:09:47,670 +للغاية، مش كتير وبالتالي احنا بالنسبالنا for all + +129 +00:09:47,670 --> 00:09:50,790 +practical purposes يعني زي ما بنقول ممكن اعتبار + +130 +00:09:50,790 --> 00:09:53,970 +القيمة اللي بنحصل عليها من ال bomb calorimeter ك + +131 +00:09:53,970 --> 00:09:59,670 +heat of reaction ممكن نعتبرها delta Hتمام فهنا + +132 +00:09:59,670 --> 00:10:03,450 +بنقول delta H لل reaction بتساوي one point three + +133 +00:10:03,450 --> 00:10:07,810 +فعشرة عقل ثلاثة kilojoule بس طبعا بالسالب لأنها + +134 +00:10:07,810 --> 00:10:15,830 +exothermic يعني هنا في عندي إشارة سالبة نطلع + +135 +00:10:15,830 --> 00:10:21,150 +على كمان تفاعل حلو كتير بيقول أخدت point five + +136 +00:10:21,150 --> 00:10:25,270 +eight six five gram من ال lactic acid وحرجناه في + +137 +00:10:25,270 --> 00:10:30,930 +bomb calorimeterهو heat capacity is 4.812 + +138 +00:10:30,930 --> 00:10:33,450 +kilojoules per degree c برضه ال heat capacity + +139 +00:10:33,450 --> 00:10:39,630 +للبوم كله معروفة يعني الميه زائد البوم كله معروف + +140 +00:10:39,630 --> 00:10:45,290 +قيمته كله 4.812 kilojoules per degree c بيقول ال + +141 +00:10:45,290 --> 00:10:49,850 +temperature increases from 23.1 degree c to 24.95 + +142 +00:10:49,850 --> 00:10:53,490 +degree c calculate the heat of combustion of + +143 +00:10:53,490 --> 00:11:00,500 +lactic acid a per gramحلو كتير وبعدين بده per mole + +144 +00:11:00,500 --> 00:11:05,440 +بقول الـ Q للكالوريمتر بتساوي minus Q لكيو ل ال + +145 +00:11:05,440 --> 00:11:08,820 +reaction عفوا بتساوي minus Q لكالوريمتر في ال + +146 +00:11:08,820 --> 00:11:13,260 +delta T يعني هادي لل reaction Q لل reaction هادي + +147 +00:11:13,260 --> 00:11:20,290 +هادي Q لل reaction بتساوي minus Q لكالوريمترالـ Q + +148 +00:11:20,290 --> 00:11:23,190 +للكالوريمتر صحيح Q للكالوريمتر بقى تساوي بس هذه + +149 +00:11:23,190 --> 00:11:26,990 +بالموجب يعني C للكالوريمتر في الـ Delta T هذه + +150 +00:11:26,990 --> 00:11:32,030 +الموجبة Q للكالوريمتر C للكالوريمتر و Delta T is + +151 +00:11:32,030 --> 00:11:34,990 +an equivalent reaction minus Q لكالوريمتر بتساوي + +152 +00:11:34,990 --> 00:11:39,670 +minus C لكالوريمتر في ال Delta T طيب بدنا نعوض عن + +153 +00:11:39,670 --> 00:11:44,230 +الـ C لكالوريمتروالـ Delta T برضه معايا فمعنى + +154 +00:11:44,230 --> 00:11:48,770 +الكلام ال reaction in G في الأول per gram بنقول + +155 +00:11:48,770 --> 00:11:53,730 +سالب 4.812 kilo joule per degree c في ال Delta T + +156 +00:11:53,730 --> 00:11:58,410 +بيطلع سالب 8.902 kilo joules لكن هذه ال kilo + +157 +00:11:58,410 --> 00:12:02,210 +joules او هذه مقدار الطاقة او ال heat evolved من + +158 +00:12:02,210 --> 00:12:08,730 +ايه؟ من 0.5865 gram طب انا بدي من ال gram كله بدي + +159 +00:12:08,730 --> 00:12:13,880 +اقسم عليهاكويس فبتطلع + +160 +00:12:13,880 --> 00:12:17,360 +عندى سالب fifteen point one eight kilo joule per + +161 +00:12:17,360 --> 00:12:25,040 +gram لو بدى اجيب ال ال heat evolved او ال heat of + +162 +00:12:25,040 --> 00:12:28,780 +combustion يعنى per mole معناته بدى احول هذه + +163 +00:12:28,780 --> 00:12:36,660 +القيمة لمole و بعدين بدى اقول والله بدى اجسم على + +164 +00:12:36,660 --> 00:12:42,710 +عدد المولات فبيطلع عندىالـ 8.902 KJ اللي هي point + +165 +00:12:42,710 --> 00:12:45,930 +eight five بتنقسمها على عدد الملات فبتطلع عندي six + +166 +00:12:45,930 --> 00:12:48,210 +point five two فعشرة أقصى سالب تلاتة اللي هي عدد + +167 +00:12:48,210 --> 00:12:50,810 +الملات بتطلع عندي سالب one point three seven فعشرة + +168 +00:12:50,810 --> 00:12:54,170 +أقصى تلاتة لإنه عندي عدد الملات اللي هي ال mass + +169 +00:12:54,170 --> 00:13:05,830 +على ال formula ويتمفهم هذا الكلام نفس الطريقة طيب + +170 +00:13:09,610 --> 00:13:15,290 +خلّيني أطلع على المثال التالي بيقول calculate the + +171 +00:13:15,290 --> 00:13:19,970 +heat of combustion of one gram of octane ال octane + +172 +00:13:19,970 --> 00:13:23,290 +هو عبارة عن هيدرو كاربون بيقول in a bomb + +173 +00:13:23,290 --> 00:13:27,130 +calorimeter if the temperature rises from 25 + +174 +00:13:27,130 --> 00:13:32,240 +degree c to 33.2 degree cالكالوريمتر يحتوي على + +175 +00:13:32,240 --> 00:13:35,720 +1200 جرام ميلاد ميلاد ميلاد ميلاد ميلاد ميلاد + +176 +00:13:35,720 --> 00:13:37,320 +ميلاد ميلاد ميلاد ميلاد ميلاد ميلاد ميلاد ميلاد + +177 +00:13:37,320 --> 00:13:40,640 +ميلاد ميلاد ميلاد ميلاد ميلاد ميلاد ميلاد ميلاد + +178 +00:13:40,640 --> 00:13:46,240 +ميلاديعني اعطاني ال heat capacity ل البومب و + +179 +00:13:46,240 --> 00:13:51,100 +اعطاني ال mass للميه من ال mass للميه و من ال + +180 +00:13:51,100 --> 00:13:55,580 +specific heat للميه اللي هي معروفة 4.18 كويس و ال + +181 +00:13:55,580 --> 00:14:00,760 +delta T بقدر اجيب ال Q للميه اذا كان انا حبيت طب + +182 +00:14:00,760 --> 00:14:05,500 +على اي حال هي عندي التفاعلأنا عندي q لل reaction + +183 +00:14:05,500 --> 00:14:11,040 +بتساوي minus q لل calorie meter ال calorie meter + +184 +00:14:11,040 --> 00:14:12,880 +ال heat capacity لل calorie meter عبارة عن ال heat + +185 +00:14:12,880 --> 00:14:17,360 +capacity للميه زاد ال heat capacity لل pump فال q + +186 +00:14:17,360 --> 00:14:23,810 +لل water هي عبارة عن ال heat capacityلل water في + +187 +00:14:23,810 --> 00:14:26,870 +ال mass لل water في ال delta T مفهومة شوفناها + +188 +00:14:26,870 --> 00:14:32,070 +الحادثة الماضية كتير فبتطلع 41.170 طب ال Q لل bomb + +189 +00:14:32,070 --> 00:14:36,210 +قال والله ال heat capacity لل bomb مضروبة في ال + +190 +00:14:36,210 --> 00:14:39,070 +delta T لأن هذه ال heat capacity هي ال CS لل bomb + +191 +00:14:39,070 --> 00:14:42,810 +في ال mass لل bomb طبعا مضروبة في ال delta T + +192 +00:14:42,810 --> 00:14:46,930 +بتعطيني اللي هي ال heat capacity هان مضروبة في ال + +193 +00:14:46,930 --> 00:14:51,930 +delta T بتعطيني ال Q لل bombأذا الـ Q للـ water + +194 +00:14:51,930 --> 00:14:55,290 +زائد الـ Q للبوم بجموعهم حلو كتير الـ Q لل + +195 +00:14:55,290 --> 00:15:00,520 +reaction minus Q للcalorimeterأنا التفاعل بيعطي + +196 +00:15:00,520 --> 00:15:05,480 +حرارة فبالتالي ال sign convention بتقول إنه ال Q + +197 +00:15:05,480 --> 00:15:09,720 +التفاعل اكسو ثيرميك ال Q اللي هو بالسالم إذا ال + +198 +00:15:09,720 --> 00:15:13,280 +heat of combustion of one gram of octane بتساوي + +199 +00:15:13,280 --> 00:15:16,840 +هذه القيمة تمانية وأربعين تقريبا كيلوجول تمانية + +200 +00:15:16,840 --> 00:15:20,240 +وأربعين كيلوجول يعني التفاعل طالد للحرارة بيعطي + +201 +00:15:20,240 --> 00:15:22,240 +تمانية وأربعين كيلوجول + +202 +00:15:24,930 --> 00:15:28,450 +لأنه طالب بس الـ heat of combustion of one gram of + +203 +00:15:28,450 --> 00:15:33,350 +octane مش طالب per mole وانا عندي هاي النتيجة ال + +204 +00:15:33,350 --> 00:15:38,550 +one gram ان الحرارة تفاعت من 25 ل 33.2 من 10 طيب + +205 +00:15:38,550 --> 00:15:44,090 +الآن يبقى صار بإمكاني ان احسب ال delta H باستخدام + +206 +00:15:44,810 --> 00:15:49,250 +اما coffee cup calorimeter او bomb calorimeter + +207 +00:15:49,250 --> 00:15:53,790 +بالطبع ال bomb calorimeter يعني far more precise + +208 +00:15:53,790 --> 00:15:58,850 +او accurate than اللي هو ال coffee cup calorimeter + +209 +00:15:58,850 --> 00:16:01,330 +ال precision عالية جدا في ال bomb calorimeter + +210 +00:16:01,330 --> 00:16:05,250 +لوعتبر من افضل الأجهزة اللي ممكن نستخدمها لحساب ال + +211 +00:16:05,250 --> 00:16:06,130 +heat flow + +212 +00:16:11,490 --> 00:16:15,770 +طبعا مش معناه كلام مافيش precision coffee cup لا + +213 +00:16:15,770 --> 00:16:20,730 +فيه precision coffee cup كالوريمتر بس مش هيك اسمه + +214 +00:16:20,730 --> 00:16:24,090 +constant pressure calorimeter مش coffee cup كويسه + +215 +00:16:24,090 --> 00:16:27,750 +بشبهه لكن هو constant pressure calorimeter موجود + +216 +00:16:27,750 --> 00:16:31,650 +precision instruments لكن بيضل انه لل combustion + +217 +00:16:31,650 --> 00:16:36,290 +reactions افضل كالوريمتر او افضل طريقة لحساب ال + +218 +00:16:36,290 --> 00:16:40,700 +delta H لإلها هي استخدام ال bomb calorimeterللـ + +219 +00:16:40,700 --> 00:16:44,220 +Combustion Reactions تحديدًا الآن دعوني أتطلع على + +220 +00:16:44,220 --> 00:16:52,140 +قانون السيد Hess في الحقيقة يعني هو قانون رائع + +221 +00:16:52,140 --> 00:16:57,300 +جدًا ومفيد جدًا لنا في الكيميا لأنه بيقول كلام + +222 +00:16:57,300 --> 00:17:02,780 +كتير بسيط بيقول احنا مش مضطرين انه نحسب ال heat of + +223 +00:17:02,780 --> 00:17:06,410 +reaction تجريبيًاممكن نحسب ال heat of reaction + +224 +00:17:06,410 --> 00:17:09,990 +ايه؟ نظريا من ال heat of reactions ل other + +225 +00:17:09,990 --> 00:17:14,130 +reactions ليش هذا الكلام؟ جال لأن ال delta H هي + +226 +00:17:14,130 --> 00:17:18,110 +عبارة عن state function يعني بتعتمد على ال initial + +227 +00:17:18,110 --> 00:17:21,550 +state و ال final state مدام بدأت من ال initial + +228 +00:17:21,550 --> 00:17:24,910 +state و بدأ اروح لل final state اذا انا بحاجة + +229 +00:17:24,910 --> 00:17:28,570 +لكمية من الطاقة او انا بحاجة لاني اخد كمية من + +230 +00:17:28,570 --> 00:17:32,650 +الطاقة اما ان التفاعل يحرر او اما التفاعل يستلزم + +231 +00:17:32,650 --> 00:17:37,390 +ياخدبغض النظر عن ال route بغض النظر عن ايه عن + +232 +00:17:37,390 --> 00:17:44,190 +الطريق حولت مثلا عندي انا حولت بدي اروح من A ل D + +233 +00:17:44,190 --> 00:17:50,390 +قال والله انا A ل D بدي اجيب ال hot delta H فقول + +234 +00:17:50,390 --> 00:17:55,850 +حلو كتير خليني ادور على اي route اي طريق اي طريق + +235 +00:17:55,850 --> 00:18:00,790 +بوصلني من A ل D فمثلا قلت والله اه من A بدي اروح ل + +236 +00:18:00,790 --> 00:18:05,770 +Bهذا معروف الـ delta H تبعته في ال literature، + +237 +00:18:05,770 --> 00:18:10,310 +معروفة في الجداول، معروف جداش، طب من B ل C، معروف + +238 +00:18:10,310 --> 00:18:15,230 +جداش، delta H تبعته، طب من C ل D، معروف جداش، انا + +239 +00:18:15,230 --> 00:18:20,030 +وصلت، اذا انا روحت من A ل E ل D، معنى الكلام ال + +240 +00:18:20,030 --> 00:18:22,390 +delta H، انا ساوي ال delta H هذه، زائد هذه، زائد + +241 +00:18:22,390 --> 00:18:26,190 +هذهليه؟ لأن هذا state function، لا يمكن أن يكون + +242 +00:18:26,190 --> 00:18:30,970 +أكتر أو أجل، عارفين لو كان أكتر أو أجل، يعني ممكن + +243 +00:18:30,970 --> 00:18:35,170 +نقول إن الكون بيختل، ليه؟ لأنه أنا باخد تفاعل معين + +244 +00:18:35,170 --> 00:18:41,450 +و بقدر أوصله بطريقة معينة بإيه؟ بطاقة أقل، كويس؟ و + +245 +00:18:41,450 --> 00:18:44,630 +لو أصلتله، إذا بخليه يتحول لتاني و يعطينا طاقة + +246 +00:18:44,630 --> 00:18:49,380 +أكتربقى بوصل له طاقة أقل و باخد منه طاقة أكتر .. + +247 +00:18:49,380 --> 00:18:51,980 +بوصل له طاقة أقل .. إذا أنا صار في عندي حاجة + +248 +00:18:51,980 --> 00:18:54,460 +بنقولها perpetualitual motion machine يعني .. يعني + +249 +00:18:54,460 --> 00:18:57,720 +شغل بتطلع طاقة ببلاش .. مستحيل هذا الكلام .. + +250 +00:18:57,720 --> 00:19:01,260 +مابينفعش .. مابينفع .. ال thermodynamics ليه؟ لأن + +251 +00:19:01,260 --> 00:19:05,740 +ال energy is conservedالإنيرجي هي مفهوم القانون + +252 +00:19:05,740 --> 00:19:10,260 +الأول للـ Thermodynamics فانا لأ مابقدرش مدام + +253 +00:19:10,260 --> 00:19:13,900 +أوصلت من A ل D بروت معين اذا الـ Delta H هتسوى + +254 +00:19:13,900 --> 00:19:18,660 +مجموع الـ Delta H values هذا كلام كتير مفيد لأن A + +255 +00:19:18,660 --> 00:19:24,460 +ل D بده تجربة عملية لكن A ل B معمول و B ل C معمول + +256 +00:19:24,460 --> 00:19:27,780 +في ال literature موجود و C ل D معمول اذا بعرف جديش + +257 +00:19:27,780 --> 00:19:32,660 +A ل Dهذا كلام السيد اسم مش بس هيك في أحيان .. في + +258 +00:19:32,660 --> 00:19:36,600 +بعض الأحيان بعض التفاعلات بقدرش أعملها مباشرة + +259 +00:19:36,600 --> 00:19:41,760 +بقدرش أعملها لأسباب مختلفة هنشوف بعضها يعني لأسباب + +260 +00:19:41,760 --> 00:19:45,860 +مختلفة طيب هذه إيش بدي أعمل فيها بقدرش أحسب إيه + +261 +00:19:45,860 --> 00:19:51,940 +لدي مباشرة مستحيل إذا أسهل كتير إن إيش أسوي أدور + +262 +00:19:51,940 --> 00:19:56,870 +على routeممكن هذا بدل ما ان هيك هعمل ممكن والله a + +263 +00:19:56,870 --> 00:20:03,070 +ل a prime بعدين a ل b prime بعدين b prime ل b ممكن + +264 +00:20:03,070 --> 00:20:07,190 +جدا اكتر من هيك او اقل من هيك يعني عرض الخطوات مش + +265 +00:20:07,190 --> 00:20:11,290 +مهم المهم في النهاية مدان بديت من a ال initial + +266 +00:20:11,290 --> 00:20:18,430 +ووصلت ل bd ال finalيبقى ال route هذا نفس الطاقة، + +267 +00:20:18,430 --> 00:20:23,250 +بغض النظر عن الطريق اللي أنا اتبعته، هذا شيء ممتاز + +268 +00:20:23,250 --> 00:20:29,390 +جدا، شيء عظيم جدا في العلم، يعني يعتبر اختراق حلو + +269 +00:20:29,390 --> 00:20:33,490 +خالص و فهم عظيم لل thermodynamics عموما + +270 +00:20:38,740 --> 00:20:43,740 +Hesse's law states that if a reaction is carried + +271 +00:20:43,740 --> 00:20:50,620 +out in a series of steps في خطوات متتالية أو + +272 +00:20:50,620 --> 00:20:56,870 +متتابعة Δ H for the overall reactionequals the sum + +273 +00:20:56,870 --> 00:21:00,190 +of the enthalpy changes for the individual steps + +274 +00:21:00,190 --> 00:21:05,270 +نفس الكلام اللي قلناه لو عملنا أي تفاعل كويس + +275 +00:21:05,270 --> 00:21:10,890 +بخطوات متعددة بدل خطوة واحدة يعني دورنا على route + +276 +00:21:10,890 --> 00:21:16,030 +يحولني من المتفاعلات إلى أيه؟ إلى النواتج فأخدني + +277 +00:21:16,030 --> 00:21:21,820 +هذه عدة خطوات جالت Delta H للتفاعلالخطوة الواحدة + +278 +00:21:21,820 --> 00:21:26,600 +الـ Over all reaction بساوي ال sum للخطوات + +279 +00:21:26,600 --> 00:21:37,860 +المختلفة دلتا H دلتا + +280 +00:21:37,860 --> 00:21:41,260 +H دلتا H دلتا H دلتا H دلتا H دلتا H دلتا H دلتا H + +281 +00:21:41,260 --> 00:21:44,440 +دلتا H دلتا H دلتا H دلتا H دلتا H دلتا H دلتا H + +282 +00:21:44,440 --> 00:21:52,050 +دلتا H دلتا Hاسكان معادلة بيبين فيها ال states + +283 +00:21:52,050 --> 00:21:57,130 +طبعا التفاهم يكون موزون بداية بعدين ال states هل + +284 +00:21:57,130 --> 00:22:03,180 +هي كل مادة gas او liquid او solidلازم تكون مبينة + +285 +00:22:03,180 --> 00:22:07,720 +لأن هذا كله مهم و بعدين كمان الـ ΔH بنسمي هذه الـ + +286 +00:22:07,720 --> 00:22:13,340 +Thermochemical equation فعلشان نشتغل احنا و نطبق + +287 +00:22:13,340 --> 00:22:18,900 +قانون السيد Hess بشكل جيد و بطريق مختصر كتير بنقول + +288 +00:22:18,900 --> 00:22:23,160 +في البداية لازم نطلع على ال target equation + +289 +00:22:23,160 --> 00:22:27,380 +التفاعل اللي انا بده أحسبله الـ ΔH طبعاً بتكون من + +290 +00:22:27,380 --> 00:22:35,220 +متفاعلات و نواتج بمسك واحدة واحدةو بشوف ايش او كيف + +291 +00:22:35,220 --> 00:22:39,480 +بدي احصل عليها من التفاعلات او ال steps المختلف + +292 +00:22:39,480 --> 00:22:43,280 +اللي برضه موطع معايا و موجودة في ال literature لكن + +293 +00:22:43,280 --> 00:22:47,040 +اذا كان في عندي مكون من المكونات بتكرر في اكتر من + +294 +00:22:47,040 --> 00:22:53,160 +معادلة بسيبه بتعاملش معاها بسيبه للاخرهفرجيكم إيش + +295 +00:22:53,160 --> 00:22:56,660 +معنى هذا الكلام يبقى هذه أول نقطة يبقى بدي أعمل + +296 +00:22:56,660 --> 00:23:00,880 +check للمعادلة target equation و أشوف إيش مكوناتها + +297 +00:23:00,880 --> 00:23:05,140 +و بدي أطلع إذا كان في عندي شغلات بتتكرر في + +298 +00:23:05,140 --> 00:23:08,300 +المعادلات أخرى بدي أقول لأ هذا والله بديش أستخدمها + +299 +00:23:08,300 --> 00:23:12,880 +أنا بدي أحاول أحصل على كل مكون من هذه المكونات + +300 +00:23:12,880 --> 00:23:16,440 +سواء في النواتج أو المتفاعلات من واحدة من + +301 +00:23:16,440 --> 00:23:20,960 +المعادلات المعطاعة معاياانشوف كيف بقول start + +302 +00:23:20,960 --> 00:23:23,940 +performing mathematical operations so that each + +303 +00:23:23,940 --> 00:23:28,180 +operation results in one component of the target + +304 +00:23:28,180 --> 00:23:31,880 +equation يعني بده اشوف اي معادلة بده احصل منها على + +305 +00:23:31,880 --> 00:23:35,020 +اما واحد من المتفاعلات و اما واحد من النواتج بما + +306 +00:23:35,020 --> 00:23:39,640 +في ذلك عدد المولات يعني اذا كان في المتفاعلات + +307 +00:23:39,640 --> 00:23:43,040 +اتنين مول وانا عندى في ال target equation واحد مول + +308 +00:23:43,040 --> 00:23:46,730 +بده اضرب ال target equation في اتنينأذا كان الـ + +309 +00:23:46,730 --> 00:23:51,170 +target equation المادة هادة في النواتج بينما الـ + +310 +00:23:51,170 --> 00:23:54,150 +target equation في النواتج المادة بينما المعطاعة + +311 +00:23:54,150 --> 00:23:57,030 +في المتفاعلات في أحد المعادلات بدي أجلب المعادلة + +312 +00:23:57,030 --> 00:24:00,910 +أخليها في النواتج هفرجيكم تطبيق عملي على هذا + +313 +00:24:00,910 --> 00:24:07,350 +الكلامبعد ما نعمل و نطلع كل المواد اللي موجودة في + +314 +00:24:07,350 --> 00:24:10,630 +المعادلة target equation بنكون جاهزين انه نجمع + +315 +00:24:10,630 --> 00:24:13,950 +المعادلات و نطلع قيمة الـ Δ H لل reaction خلينا + +316 +00:24:13,950 --> 00:24:19,370 +نشوف شغل كتير بسيطة as an example combustion of + +317 +00:24:19,370 --> 00:24:25,030 +methane gas CH4 to form CO2 ومياه can be thought + +318 +00:24:25,030 --> 00:24:32,530 +of as occurring in one step هي CH4 زاد 2 O2 هذا هو + +319 +00:24:33,150 --> 00:24:36,990 +بيعطينا CO2 زي اتنين مياد دلتا H تبعته مجهولة مش + +320 +00:24:36,990 --> 00:24:45,570 +عارفينها طيب or ممكن نفكر فيه زي هيك or in two + +321 +00:24:45,570 --> 00:24:50,670 +steps ال CH4 زي اتنين O2 بتعطينا CO2 زي ان اتنين + +322 +00:24:50,670 --> 00:24:54,330 +H2O جاهز هنقش ايه عشان اللي عندي انا اتنين H2O + +323 +00:24:54,330 --> 00:24:58,040 +liquid اذا هذه المعادلة مش هي هذهوكمان معادلة + +324 +00:24:58,040 --> 00:25:02,920 +اتنين H2O جاز تتحول لاتنين H2O liquid الـ delta H + +325 +00:25:02,920 --> 00:25:06,260 +الها سالب تمانية و تمانية كيلوجول مثلا يعني هي + +326 +00:25:06,260 --> 00:25:10,660 +عندي هدول المعادلتين هدول المعادلتين كيف بدي احصل + +327 +00:25:10,660 --> 00:25:15,760 +منهم على هاد المعادلة بقول CH4 هاد CH4 حلو يبجي + +328 +00:25:15,760 --> 00:25:22,000 +هاد خلصنا منه خلصنا منه باجي ل مثلا ال H2O + +329 +00:25:23,910 --> 00:25:28,810 +هذا البرنامج موجود زي ما هي H2O gas بتحول ل H2O + +330 +00:25:28,810 --> 00:25:32,510 +liquid زي ما هي في النواتج + +331 +00:25:38,830 --> 00:25:44,850 +فبجمع هذه المعادلتين الـ2H2O راحت مع الـ2H2O نتيجة + +332 +00:25:44,850 --> 00:25:48,670 +الجمع ايش اعطتني؟ الـTarget Equation بالظبط اذا + +333 +00:25:48,670 --> 00:25:52,810 +الـDelta H لهذا التفاعل هاي مخبيها تساوي الـDelta + +334 +00:25:52,810 --> 00:25:56,470 +H هذه زائد هذه ليه؟ لأنه لما جمعنا التفاعلين + +335 +00:25:56,470 --> 00:26:02,850 +اعطالني زي هدا هي هاي يعني هفرجيكم في عندي slide + +336 +00:26:02,850 --> 00:26:07,040 +اللي اقلهالما جمعنا المعادلتين اعطتني المعادلة الـ + +337 +00:26:07,040 --> 00:26:09,720 +target اذا الـ delta H للمعادلة الـ target الـ + +338 +00:26:09,720 --> 00:26:12,460 +over all reaction يسبب مجموعة delta H values + +339 +00:26:12,460 --> 00:26:16,240 +للمعادلتين فانا عندي سالب تمانية و اتنين زائد سالب + +340 +00:26:16,240 --> 00:26:18,660 +تمانية و تمانين يبقى سالب تمانية و تسعين kilo + +341 +00:26:18,660 --> 00:26:27,440 +joules هذا يعني consequence ل ال law of energy + +342 +00:26:27,440 --> 00:26:31,360 +conservation طيب + +343 +00:26:32,580 --> 00:26:36,500 +خلينا نطلع على هذه نفس الحاجة أنا كان بإمكاني أن + +344 +00:26:36,500 --> 00:26:43,940 +أروح من المتفاعلات هي CH4G2O2 إلى CH4G2O2 + +345 +00:26:43,940 --> 00:26:46,080 +إلى CH4G2O2 إلى CH4G2O2 إلى CH4G2O2 إلى CH4G2O2 + +346 +00:26:46,080 --> 00:26:48,180 +إلى CH4G2O2 إلى CH4G2O2 إلى CH4G2O2 إلى CH4G2O2 + +347 +00:26:48,180 --> 00:26:50,940 +إلى CH4G2O2 إلى CH4G2O2 إلى CH4G2O2 إلى CH4G2O2 + +348 +00:26:50,940 --> 00:26:51,520 +إلى CH4G2O2 إلى CH4G2O2 إلى CH4G2O2 إلى CH4G2O2 + +349 +00:26:51,520 --> 00:26:51,540 +إلى CH4G2O2 إلى CH4G2O2 إلى CH4G2O2 إلى CH4G2O2 + +350 +00:26:51,540 --> 00:26:54,560 +إلى CH4G2O2 إلى CH4G2O2 إلى CH4G2O2 إلى CH4G2O2 + +351 +00:26:54,560 --> 00:27:00,610 +إلى CH4G2O2 إلى CH4بعدين روحت من CO2 و 2 H2O gas + +352 +00:27:00,610 --> 00:27:06,110 +إلى CO2 gas و 2 H2O liquid هذا إيش أعطاني؟ جالع + +353 +00:27:06,110 --> 00:27:09,730 +أعطاني 88 كيلوجول بما أنه أنا روحت من المتفاعلات، + +354 +00:27:09,730 --> 00:27:13,170 +لأ نواتش، يعني هذا كلها أيها السهم الأزراج، إذا + +355 +00:27:13,170 --> 00:27:16,370 +السهم الأزراج هو الـ delta H هتساوي هذه زائد هذه، + +356 +00:27:16,370 --> 00:27:19,610 +مافيش فايدة، وكان بإمكاني أن أروح لحاجة وساطية هان + +357 +00:27:19,610 --> 00:27:23,940 +يعني، إذا كان حبيته، يعني حاجة تالتة مثلاو اقول + +358 +00:27:23,940 --> 00:27:28,520 +تلاتة او اربعة او خمسة مافيش عندي مشكلة ممكن اروح + +359 +00:27:28,520 --> 00:27:34,760 +لهنا و اعود ارجع تاني مثلا يعني المهم في النهاية + +360 +00:27:34,760 --> 00:27:39,440 +في النهاية لابد الا ان احصل على ال target equation + +361 +00:27:39,440 --> 00:27:45,000 +من عدد من المعادلات هات من جلها ال steps الخطوات + +362 +00:27:45,000 --> 00:27:49,000 +ممكن ادور على route تاني هذا another route انتبهوا + +363 +00:27:49,000 --> 00:27:53,980 +شويةتبه شوية CH4 زائد 2 O2 كان بإمكاني أروح للـ + +364 +00:27:53,980 --> 00:27:58,480 +CO2 Gas زائد 2 H2O Liquid 890 كل جول heat of + +365 +00:27:58,480 --> 00:28:03,560 +reaction negative قال ممكن أروح من الـ CH4 على 2 و + +366 +00:28:03,560 --> 00:28:08,100 +2 O2 إلى حاجة Delta H2 اللي هي CO زائد .. بتعطينها + +367 +00:28:08,100 --> 00:28:14,800 +CO زائد 2 H2O Liquid زائد نص O2 Gas هذا تفاعل من + +368 +00:28:14,800 --> 00:28:20,620 +hand ل hand هيوCH4 زي 2O2 بيعطيني CO جاز 2H2O + +369 +00:28:20,620 --> 00:28:25,260 +liquid نص O2 جاز الـ Delta H سالف 607 في ال + +370 +00:28:25,260 --> 00:28:30,600 +literature موجود بعدين أحول هذا، هذا بيعطيني هذا + +371 +00:28:30,600 --> 00:28:33,580 +برضه تفاعل موجود في ال literature الـ CO جاز زي + +372 +00:28:33,580 --> 00:28:38,800 +2H2O liquid زي نص O2 بيعطيني CO2 زي 2H2O liquid + +373 +00:28:38,800 --> 00:28:45,070 +Delta Hسالب 283 KJ المهم روحنا من هنا لهنا اذا الـ + +374 +00:28:45,070 --> 00:28:48,890 +delta H هذه زاد الـ delta H هذه لازم يطلع 890 + +375 +00:28:48,890 --> 00:28:52,680 +negative لازمالتفاعلين المختلفين خالص اللي + +376 +00:28:52,680 --> 00:28:57,060 +استخدمناهم، لكن ما ينفعش يعطينا حاجة تانية، + +377 +00:28:57,060 --> 00:29:00,840 +مابينفعش، لأ مدام إجينا من الحالة الأولية للحالة + +378 +00:29:00,840 --> 00:29:04,300 +النهائية، انتهينا، خلاص، يبقى نفس الكمية من + +379 +00:29:04,300 --> 00:29:08,360 +الطاقة، وإلا زي ما قلتلكم سابقا، ممكن أستخدم تفاعل + +380 +00:29:08,360 --> 00:29:11,800 +مرارا وتكرارا عشان أتمني إيه، أخليه يولد الطاقة + +381 +00:29:11,800 --> 00:29:17,490 +وهذا الكلام، مستحيل، مابينفعش يعنيطيب نتطلع على + +382 +00:29:17,490 --> 00:29:23,270 +حاجة يعني كتير جميلة في his law قولت انا انه his + +383 +00:29:23,270 --> 00:29:28,750 +law في بعض الأحيان الذهاب من ال reactants إلى ال + +384 +00:29:28,750 --> 00:29:32,890 +products بكون شبه مستحيل فمثلا لو انا بدي اجيب ال + +385 +00:29:32,890 --> 00:29:38,690 +heat of combustion لل carbon to CO مش CO to CO + +386 +00:29:38,690 --> 00:29:41,070 +فماجي بحط والله carbon solid + +387 +00:29:44,850 --> 00:29:50,390 +زائد نص O2 تعطيلنا CO، بقول هذا التفاعل بحصلش، + +388 +00:29:50,390 --> 00:29:58,710 +بحصلش هيك، هذا التفاعل هيعطيلنا COA و هيعطي CO2 و + +389 +00:29:58,710 --> 00:30:05,890 +هيزيد هنا شوية C solid، مش هيتحول الكربون للـCO بس + +390 +00:30:06,790 --> 00:30:11,910 +مجرد وجود Oxygen هيتحول جزء منه للـCO2 وجزء منه + +391 +00:30:11,910 --> 00:30:17,230 +للـCO وحيزيد شوية ايه؟ حيزيد شوية C solid طب انا + +392 +00:30:17,230 --> 00:30:21,170 +بدي اجيب ال Delta H للتفاعل هذا انا بدي اجيب ال + +393 +00:30:21,170 --> 00:30:24,930 +Delta H لهذا التفاعل يا جماعة ايش ال Delta H له؟ + +394 +00:30:24,930 --> 00:30:32,310 +قال بقدرش اوصله بشكل مباشر لازم ادورلي على لفةأه + +395 +00:30:32,310 --> 00:30:36,690 +لازم أدور على لفة أدور على steps أخرى ممكن جدا إنه + +396 +00:30:36,690 --> 00:30:41,250 +تعطيني في نهاية delta H لهذا التفاعل وهذا يعني شيء + +397 +00:30:41,250 --> 00:30:50,290 +عظيم في فوائد الشغل باستخدام his law شيء عظيم جدا + +398 +00:30:50,290 --> 00:30:50,930 +في الحقيقة + +399 +00:30:55,020 --> 00:30:58,780 +طيب تتطلع كيف ممكن نعملها؟ جال والله مثلا بيقول + +400 +00:30:58,780 --> 00:31:01,040 +الـthe enthalpy of reaction for the combustion of + +401 +00:31:01,040 --> 00:31:07,160 +C is to CO2 is .. هذا معروف معروف احتراك كامل للـC + +402 +00:31:07,160 --> 00:31:11,380 +للـCO2 معروف excess oxygen كل الكربون بحترق للـCO2 + +403 +00:31:11,380 --> 00:31:17,690 +سالب 393.5 kilojoule per mole degrees Kelvinطيب، + +404 +00:31:17,690 --> 00:31:21,990 +and the enthalpy of the composition of CO to CO2 + +405 +00:31:21,990 --> 00:31:26,030 +برضه معروف، لو جيبت CO وحطيت عليها Oxygen، هيتحول + +406 +00:31:26,030 --> 00:31:30,870 +لـCO2؟ طبعا، هذا برضه تفاعل معروف، جداش باطين يجال + +407 +00:31:30,870 --> 00:31:33,510 +سالب مائتين تلاتة و تمانين كيلو جول برمول، أنا مش + +408 +00:31:33,510 --> 00:31:35,890 +مهتم فيهم، لأن هدول معروفين في ال literature، أنا + +409 +00:31:35,890 --> 00:31:41,530 +مهتم بالـCS زائد نص O2، بده يتحول للـCO، اللي قلنا + +410 +00:31:41,530 --> 00:31:45,930 +مباشرة، بينفعش ينعملمباشرة منفعش نعمل طب تعالوا + +411 +00:31:45,930 --> 00:31:49,650 +نطلع CS هي .. هي بتطلع على هذه المعادلة target + +412 +00:31:49,650 --> 00:31:53,370 +equation CS في المتفاعلات هي CS في المتفاعلات يبقى + +413 +00:31:53,370 --> 00:31:59,890 +فيش مشكلة COMهان في النواتج هان وين اذا واحد مول + +414 +00:31:59,890 --> 00:32:03,510 +بدي اجلبها لما اجلبها ايش باجلب على طول الاشارة + +415 +00:32:03,510 --> 00:32:06,630 +اذا انهيتها المعادلة الأولى خليناها زي ما هي + +416 +00:32:06,630 --> 00:32:10,990 +المعادلة التانية ايش عملناها reverse ف delta H ايش + +417 +00:32:10,990 --> 00:32:15,050 +صارت موجب لكن لما اجيت لغاية الـCO2 وسيقفت عند ال + +418 +00:32:15,050 --> 00:32:19,390 +CS زائد هان نص O2 في النواتج هان O2 في المتفاعلات + +419 +00:32:19,390 --> 00:32:23,090 +اذا نص O2 بيعطينا CO هي المعادلة اللي انا كنت + +420 +00:32:23,090 --> 00:32:26,580 +بديها و مش عارف اوصل لهاجداشل دلتاشل ال reaction + +421 +00:32:26,580 --> 00:32:37,120 +قال والله مجموع التنتين ماشي يا جماعة طيب نطلع + +422 +00:32:37,120 --> 00:32:42,960 +أيضا على هذا التفاعلبيقول given the thermochemical + +423 +00:32:42,960 --> 00:32:49,260 +equations بيعطيني هذه الـ C2H2 gas و 5 O2 بتعطيني + +424 +00:32:49,260 --> 00:32:56,940 +4 CO2 H2O liquid C2H6 7 O2 4 CO2 6 H2O كل واحدة + +425 +00:32:56,940 --> 00:33:01,980 +إلهم Delta H والـ H2 gas نص O2 بتعطيني H2O liquid + +426 +00:33:01,980 --> 00:33:07,940 +أنا بدي أوجد Delta H لهذا التفاعل بمعلوميةهذه الـ + +427 +00:33:07,940 --> 00:33:12,260 +steps أو هذه التفاعلات اللي عندي فبقول C2H2 زي 2H2 + +428 +00:33:12,260 --> 00:33:17,080 +تعطينا C2H6 كم بده أسوي؟ بمسك مادة مادة C2H2 وين + +429 +00:33:17,080 --> 00:33:23,020 +موجودة؟ هن .. هن أكمل هن جدش، إذاً بدك سيل المعادل + +430 +00:33:23,020 --> 00:33:28,000 +الأولى على 2 عشان + +431 +00:33:28,000 --> 00:33:29,240 +إيه؟ أنا بدي بس واحد + +432 +00:33:35,030 --> 00:33:41,910 +خلّيني أقول H2 هى هى وين؟ H2 هى هى هى بتنضرب فى + +433 +00:33:41,910 --> 00:33:48,210 +اتنين اذا هدى فى اتنين طب C2H6 هدى موجودة وين؟ + +434 +00:33:48,810 --> 00:33:56,030 +نجلبها بس نجلبها و نجسم على اتنين معايا يا بنات + +435 +00:33:56,030 --> 00:34:00,130 +كمان مرة نقولهم ابصرها بقول كيف بفكر انا في حل + +436 +00:34:00,130 --> 00:34:03,270 +المسألة باستخدام Mrs Law بمسك ال target equation + +437 +00:34:03,270 --> 00:34:06,170 +على فكرة هذا كله بتنسقله فيه كتير في الامتحان يعني + +438 +00:34:06,170 --> 00:34:12,050 +بيجي دائما سؤال على Mrs Law فإيش بنقول؟طلع معايا + +439 +00:34:12,050 --> 00:34:16,430 +بقول بتطلع على ال target equation ايش اول تجه فيها + +440 +00:34:16,430 --> 00:34:21,210 +C2H2 هيني بلجيه هين في اول معادلة اذا هان واحد هان + +441 +00:34:21,210 --> 00:34:24,050 +اتنين بدي اجسم المعادلة على اتنين و ال delta H + +442 +00:34:24,050 --> 00:34:27,150 +بقتين اجسم على اتنين مش بس المعادلة المعادلة و ال + +443 +00:34:27,150 --> 00:34:34,650 +delta H هان عندي H2 اتنين H2 هان H2 واحدة بس one + +444 +00:34:34,650 --> 00:34:37,250 +more اذا بدي اضرب هذه المعادلة في اتنين و ال delta + +445 +00:34:37,250 --> 00:34:41,230 +H بدي اضربها في اتنينطيب الـ C2H6 جال هدف + +446 +00:34:41,230 --> 00:34:45,590 +النواتيجي هنوى ظاهرة اذا بدي اجلب المعادلة و + +447 +00:34:45,590 --> 00:34:50,690 +اكسبها اتنين و ماانساش اجلب الإشارة لما نعمل هيك + +448 +00:34:50,690 --> 00:34:54,650 +بقى لاحظ انه لما نجمع بحث على ال target equation + +449 +00:34:54,650 --> 00:34:58,590 +عن طريق جمعة delta H1, delta H2 و delta H3 اللي + +450 +00:34:58,590 --> 00:35:03,630 +هنعملهم delta H4, delta H5, delta H6ماشي يا جماعة + +451 +00:35:03,630 --> 00:35:07,150 +هو انا عاملكم هذا نفس اللون في المعادلة السابقة + +452 +00:35:07,150 --> 00:35:09,170 +يعني لو جيتوا و طلعتوا المعادلة السابقة نفس + +453 +00:35:09,170 --> 00:35:12,010 +الألوان عاملها على أساس انه تعرفوا ايش عملناها في + +454 +00:35:12,010 --> 00:35:17,530 +المعادلة طيب كمان مثال بيقول calculate the delta H + +455 +00:35:17,530 --> 00:35:22,320 +for the reactionتنين FE Solid زي التلاتة على اتنين + +456 +00:35:22,320 --> 00:35:27,360 +O2 Gas بتعطينا FE تنين O تلاتة Solid Given هاي + +457 +00:35:27,360 --> 00:35:30,340 +اعطاني المعادلة اللي هستخدمها FE تنين O تلاتة + +458 +00:35:30,340 --> 00:35:33,960 +Solid زي التلاتة CO Gas بتعطينا تنين FE Solid زي + +459 +00:35:33,960 --> 00:35:38,600 +التلاتة CO2 Gas واللي عندنا دلتة H دلتة H معينة + +460 +00:35:38,600 --> 00:35:43,400 +الـCO زي نص O2 بتعطينا CO2 برضه دلتة H معينة باجي + +461 +00:35:43,400 --> 00:35:48,390 +انا لل target equation اتنين FE Solidطب إذا هذه + +462 +00:35:48,390 --> 00:35:52,610 +وين مش ده في النواتج؟ بدي أجلبها و بدي ايه؟ أغير + +463 +00:35:52,610 --> 00:35:58,910 +الإشارة طب حلو كتير طب ال F E اتنين او تلاتة؟ اه + +464 +00:35:58,910 --> 00:36:02,450 +هي انجلبت already يعني انجلبت already طب خليني + +465 +00:36:02,450 --> 00:36:06,090 +أشوف .. خليني أشوف الآن هذه انجلبت لما انجلبتها + +466 +00:36:06,090 --> 00:36:09,430 +صار في عندي تلاتة CO يعني هذه المعادلة مافيش منها + +467 +00:36:09,430 --> 00:36:12,910 +فايدة كبيرة هالجيت إلا بس عشان أضايق ال CO لأن هذا + +468 +00:36:13,770 --> 00:36:18,330 +وهذا صاروا موجودين هنا يعني هذا صار موجود وهذا صار + +469 +00:36:18,330 --> 00:36:22,150 +موجود الآن هذه المعادلة لو جيب طلعت عليها بلاجأ + +470 +00:36:22,150 --> 00:36:25,850 +انه لازم ال CO تروح مع ال CO فبتضرب هذه في تلاتة + +471 +00:36:25,850 --> 00:36:30,590 +أزر الدلتة H بيتضرب في تلاتة في النهايةفي النهاية + +472 +00:36:30,590 --> 00:36:37,910 +بيلاقي ان الـ + +473 +00:36:37,910 --> 00:36:41,530 +delta H لل reaction هتساوي مجموع الـ delta H + +474 +00:36:41,530 --> 00:36:48,560 +values للمعادلتين اللي عنديطيب برضه نبطلع هان يعني + +475 +00:36:48,560 --> 00:36:51,880 +على المعادلة اللي موجودة بقول لي calculate the + +476 +00:36:51,880 --> 00:36:55,800 +delta H for the reaction اتنين N O two بتحولت N + +477 +00:36:55,800 --> 00:36:59,240 +two O أربعة جاز اتنين N O two جاز تحولت N two O + +478 +00:36:59,240 --> 00:37:05,720 +أربعة جاز حد بيقدر يسميلي هذا المركب binary + +479 +00:37:05,720 --> 00:37:11,370 +compound بنفع نقول mono nitrogen ولا مينفعش؟بنفعش + +480 +00:37:11,370 --> 00:37:15,410 +نحط mono في أول الطريقة لأ لأ لأ لأ لأ لأ نيترايت + +481 +00:37:15,410 --> 00:37:20,310 +لما نكون عليه سالب لأ هذا nitrogen dioxide بنفعش + +482 +00:37:20,310 --> 00:37:23,430 +نقول mono nitrogen هان dinitrogen tetroxide + +483 +00:37:23,430 --> 00:37:27,290 +dinitrogen tetroxide مش لازم ننسيها، انا لسه في + +484 +00:37:27,290 --> 00:37:31,690 +بداية الفصل طيب على أي حال على أي حال هاي ال + +485 +00:37:31,690 --> 00:37:34,010 +target equation و انا عندي هدول ال two equations + +486 +00:37:34,010 --> 00:37:40,250 +باشي بقول ال N O two بدي يا وينأه بدي يا على + +487 +00:37:40,250 --> 00:37:45,310 +اليسار بجيب أطلع وين هو وهي موجودة هان ال N O2 ال + +488 +00:37:45,310 --> 00:37:48,910 +N O2 موجودة هان اتنين و اتنين اه حلو كتير بس بدي + +489 +00:37:48,910 --> 00:37:52,530 +إيش أسوي أجلب المعادلة بدي أجلب المعادلة و أغير + +490 +00:37:52,530 --> 00:37:56,550 +الشحن ليه لأن ال N O2 هان وين ال reactants هان + +491 +00:37:56,550 --> 00:38:01,910 +النواتج لأ بدي أجلبها طيب ال N2O4 مظبوطة هي مول + +492 +00:38:01,910 --> 00:38:05,010 +واحد مول واحد و في النواتج حلو كتير إذا بس أني + +493 +00:38:05,010 --> 00:38:07,930 +أجمع المعادلتين بعد هيك سهل خالص + +494 +00:38:13,480 --> 00:38:20,220 +أيش رأيكم .. طيب .. ناخد لنا كمان أكمل مثال مش + +495 +00:38:20,220 --> 00:38:23,840 +مشكلة بقول الـ carbon occurs in two forms graphite + +496 +00:38:23,840 --> 00:38:27,780 +and diamond ال graphite تعرفه الكربون و ال diamond + +497 +00:38:27,780 --> 00:38:31,800 +اللي هو ال mass، الأثنين كربون، الأثنين كربون ال + +498 +00:38:31,800 --> 00:38:35,960 +enthalpy of the combustion of graphite is سالب 393 + +499 +00:38:35,960 --> 00:38:40,200 +.5 kilo joules per mole and that of diamond is 394 + +500 +00:38:40,200 --> 00:38:44,770 +.10 kilo joules per moleالمعادلة C ديامون زائد O2 + +501 +00:38:44,770 --> 00:38:48,210 +بتعطينا CO2 ديلتا اتش معروفة لها والـ C غرافيت + +502 +00:38:48,210 --> 00:38:51,850 +زائد O2 بتعطينا CO2 طبعا لأنه تلاني كاربون ديلتا + +503 +00:38:51,850 --> 00:38:55,830 +اتش سالب تلاتمية جريبة كتير منها كيلو جول بيرمون + +504 +00:38:55,830 --> 00:38:58,930 +بيقول calculate ديلتا اتش for the conversion of + +505 +00:38:58,930 --> 00:39:02,690 +graphite to diamond C graphite هتروح للـ CA + +506 +00:39:02,690 --> 00:39:07,310 +diamond ماشي يا جماعة ايش الـ delta H لها؟بنفس + +507 +00:39:07,310 --> 00:39:11,490 +الطريقة بنفس الطريقة بدي ادريغرافيت على اليسار ف C + +508 +00:39:11,490 --> 00:39:15,890 +graphite اه زي ما هي بينما هنا بدنا نجلب ال + +509 +00:39:15,890 --> 00:39:19,670 +diamond CO2 بيأت كل عن ناحية التانية فحصلنا C + +510 +00:39:19,670 --> 00:39:22,830 +graphite تروح لل C diamond بدنا نجمع التانتين + +511 +00:39:22,830 --> 00:39:31,010 +لاحظوا ال delta H جديش جليلة جليلة والتفاعل + +512 +00:39:31,010 --> 00:39:36,880 +endothermic يعني التفاعل يعني endothermicلكن بدنا + +513 +00:39:36,880 --> 00:39:41,220 +يعني .. يعني هل سهل نحول لـ Graphite للـ Diamonds + +514 +00:39:41,220 --> 00:39:46,020 +بقى عن الكلام؟ مالهاش دعوة، مالهاش دعوة عادة يا + +515 +00:39:46,020 --> 00:39:49,820 +فنات الـ Thermodynamics مش هان اللي هندرسه + +516 +00:39:49,820 --> 00:39:54,780 +بالتفصيل في الشبتل الأخير بعطيني فكرة عن ال + +517 +00:39:54,780 --> 00:39:58,000 +spontaneity للتفاعل التفاعل هل بيتم بصورة تلقائية + +518 +00:39:58,000 --> 00:40:04,160 +ولا إيه؟ ولا بده يعني مساعدات عشان يتم؟كويس لكن + +519 +00:40:04,160 --> 00:40:08,960 +بيعطينيش فكرة عن ال rate المعدل كدهش السرعة + +520 +00:40:08,960 --> 00:40:11,960 +مابيعطيني فكرة السرعة بندرسها في حاجة اسمها + +521 +00:40:11,960 --> 00:40:16,920 +chemical kinetics فيعني مش شرط انه والله اعطاني + +522 +00:40:16,920 --> 00:40:20,440 +delta H يعني التغير قليل معناته اه والله بسهولة + +523 +00:40:20,440 --> 00:40:24,420 +بيتحول لأ صعب جدا و الا كان ال mass لجنائه سعر + +524 +00:40:24,420 --> 00:40:29,270 +الفحم يعني وده مستحيلكالكوليت دلتا H for the + +525 +00:40:29,270 --> 00:40:36,190 +reaction اتنين CS زائد H2 بتعطينا C2H2 gas ومعطيني + +526 +00:40:36,190 --> 00:40:41,430 +المعادلات التالية تلت + +527 +00:40:41,430 --> 00:40:44,070 +معادلات بقول كيف بدي افكر في حد المثال اهم + +528 +00:40:44,070 --> 00:40:47,630 +بالنسبالي carbon solid بدور وين موجودة هي موجودة + +529 +00:40:47,630 --> 00:40:52,290 +هنا لكن ايه اش مالها؟بنغربها في اتنين صحيح طيب H2 + +530 +00:40:52,290 --> 00:41:00,210 +وين موجودة الـH2؟ تحتها زي ما هي طيب C2H2 C2H2 هاي + +531 +00:41:00,210 --> 00:41:05,590 +هالـ C .. اه بدها جلب بنجلبها بس إذا ال .. المجموع + +532 +00:41:05,590 --> 00:41:11,890 +هيعطيني Delta H لل reaction بتهيألي معين يعني + +533 +00:41:11,890 --> 00:41:16,610 +أسئلة بتشوفوا الأسئلة الفاضلة ممكن تطلعوا عليها + +534 +00:41:19,320 --> 00:41:22,140 +في ال notes يعني ممكن تطلعوا عليها و تحلوا حلوة + +535 +00:41:22,140 --> 00:41:25,020 +حالكم في ال notes أنا حابب أن أعطي أمثلة كتير يعني + +536 +00:41:25,020 --> 00:41:28,300 +قليل اللي موجود في الكتاب لكن لأنه الموضوع ممكن + +537 +00:41:28,300 --> 00:41:32,200 +تنسقلي فيه ويعني وفيه varieties في الحقيقة يعني في + +538 +00:41:32,200 --> 00:41:35,860 +عنا أسئلة كتير ممكن أن الواحد يتعرض لها في هذا + +539 +00:41:35,860 --> 00:41:38,200 +الباب فانا حابب أن أعطي أمثلة بالزيادة في هذا + +540 +00:41:38,200 --> 00:41:42,000 +الموضوع الآن خليني أتكلم عن ال enthalpy of + +541 +00:41:42,000 --> 00:41:48,160 +formationالـ enthalpy of formation أو الـ heat of + +542 +00:41:48,160 --> 00:41:53,980 +formation حرارة التكوين enthalpy of formation أو + +543 +00:41:53,980 --> 00:42:00,320 +ال heat of formationفي البداية يعني لازم نعرف انه + +544 +00:42:00,320 --> 00:42:09,920 +في عندنا كمية هائلة من ال ال constants لتغيرات + +545 +00:42:09,920 --> 00:42:13,600 +متعددة في ال thermodynamics فممكن نلاقي مثلا + +546 +00:42:13,600 --> 00:42:17,870 +تقريباعدد هائل من الـ tables لـ Delta H + +547 +00:42:17,870 --> 00:42:23,710 +Vaporization يعني Delta H لتحويل الليكود إلى جاز + +548 +00:42:23,710 --> 00:42:34,270 +Delta H لرفيوجين أو ال melting للصليد للليكود ممكن + +549 +00:42:34,270 --> 00:42:39,580 +Delta H Sublimation تحول الصليد إلى جازفحنلاقي + +550 +00:42:39,580 --> 00:42:44,640 +جداول كثيرة جدا في الحقيقة موجودة عندنا في الـ + +551 +00:42:44,640 --> 00:42:49,880 +Literature اللي بدي أتكلم عنه أنا اليوم هو عبارة + +552 +00:42:49,880 --> 00:42:53,620 +عن الـ Enthalpy of Formation أنا بدي أكوّن مادة، + +553 +00:42:53,620 --> 00:43:01,130 +بدي أكوّن مادةفالمادة هذه بدي أكونها من .. بديش + +554 +00:43:01,130 --> 00:43:03,770 +تطلعها من تفاعل زي this is law ممكن أني أعمل هذا + +555 +00:43:03,770 --> 00:43:07,410 +الكلام لكن بشكل أساس أنا مهتم أني أكونها من + +556 +00:43:07,410 --> 00:43:13,410 +عناصرها الأولية من عناصرها الأولية يعني مثلا لو + +557 +00:43:13,410 --> 00:43:19,950 +بدي أطلع على CO2 + +558 +00:43:19,950 --> 00:43:23,850 +بقول بدي أكونه gas بقول بدي أكونه طب من إيش بتكون؟ + +559 +00:43:23,850 --> 00:43:29,910 +جال من الـCGraphite زائد + +560 +00:43:29,910 --> 00:43:36,490 +Oxygen Gas فانا بده اكون المادة من ايه؟ من عناصرها + +561 +00:43:36,490 --> 00:43:40,750 +الأساسية اللي انا بده اتكلم عنه هو تكوين المادة من + +562 +00:43:40,750 --> 00:43:46,550 +عناصرها الأساسيةمش بس هيك انا مهتم اكتر في ان اكون + +563 +00:43:46,550 --> 00:43:53,910 +المادة في حالتها العادية في حالتها العادية + +564 +00:43:53,910 --> 00:43:57,810 +القياسية في حالتها القياسية يعني الـCO2 بده يكون + +565 +00:43:57,810 --> 00:44:01,430 +هو جاز مش liquid لان عادة الـCO2 ايش بيكون؟ جاز + +566 +00:44:01,430 --> 00:44:07,250 +بده يكون من عناصره الأولية في حالتها القياسية ايش + +567 +00:44:07,250 --> 00:44:10,150 +هي الحالة القياسية اللي انا بتكلم عنها الحالة + +568 +00:44:10,150 --> 00:44:14,250 +القياسية اللي انا بتكلم عنهاهي الـ State في + +569 +00:44:14,250 --> 00:44:19,790 +البداية يعني الـ State at 25 degrees C و 1 + +570 +00:44:19,790 --> 00:44:25,770 +atmosphere يعني هي درجة الحرارة العادية والضغط + +571 +00:44:25,770 --> 00:44:30,570 +العادي فمثلا الميه بتكون liquid فانا بتكوينها من + +572 +00:44:30,570 --> 00:44:35,350 +H2 Gas أصله Gas عند حرارة 25 درجة و 1 atmosphere + +573 +00:44:35,350 --> 00:44:40,800 +هو Gas O2 برضه هو Gasلكن الميه اللى بدى احصل عليها + +574 +00:44:40,800 --> 00:44:45,380 +ايه؟ Liquid لإيه؟ لأن حالتها العادية هي عبارة عن + +575 +00:44:45,380 --> 00:44:53,020 +ال liquid فبنسمي ال delta H of formation delta Hf + +576 +00:44:53,020 --> 00:44:59,720 +وإذا كان بشتغل at standard state بحط دائرة صغيرة + +577 +00:44:59,720 --> 00:45:03,420 +فوق يعني standard state وقولنا ل standard state + +578 +00:45:06,160 --> 00:45:10,440 +أنا بشتغل عند حرارة خمسة و عشرين ديجري سي او 298 + +579 +00:45:10,440 --> 00:45:15,950 +كيلوفر وبشتغل اه وبشتغل عند ايه؟و بشتغل واحد + +580 +00:45:15,950 --> 00:45:19,710 +أتموسفير و لازم المادة تكون ايه؟ في حالتها + +581 +00:45:19,710 --> 00:45:23,930 +الطبيعية و لما يكون في عندى اكتر من حالة طبيعية + +582 +00:45:23,930 --> 00:45:29,150 +للمادة بقول باخد الحالة اللى بتكون most stable + +583 +00:45:29,150 --> 00:45:32,750 +فمثلا ال oxygen ممكن يكون موجود على هيئة oxygen 2 + +584 +00:45:32,750 --> 00:45:36,630 +O2 هذا هو المشهور لكن ممكن يكون موجود ozone فوق + +585 +00:45:36,630 --> 00:45:41,350 +فبرضه هذا ozone برضه كمان جاز طب ozone ولا oxygen؟ + +586 +00:45:41,350 --> 00:45:45,820 +قال لأ ال oxygen هو الحالة الطبيعيةليه؟ لأنه أكثر + +587 +00:45:45,820 --> 00:45:49,500 +استقرارا فباخد الحالة المستقرة أكثر استقرارا + +588 +00:45:49,500 --> 00:45:53,740 +فالحالة المستقرة أكثر الحالة عندي حاجة لازم الأكثر + +589 +00:45:53,740 --> 00:45:57,520 +استقرارا بعدين واحد أتمسفير بعدين خمسة و عشرين + +590 +00:45:57,520 --> 00:46:02,060 +degrees عارفينها + +591 +00:46:02,060 --> 00:46:08,160 +بنعرفها اه بنعرفها اه احنا بنعرفها من خلال خبرتنا + +592 +00:46:08,160 --> 00:46:10,660 +العملية و من خلال القراءات ناس كان مشوفناش الأنصار + +593 +00:46:10,660 --> 00:46:14,760 +قبل هيكفلأ احنا لازم نكون عارفين العناصر في حالتها + +594 +00:46:14,760 --> 00:46:17,520 +الطبيعية، يعني الحاجات اللي احنا متعودين عليها + +595 +00:46:17,520 --> 00:46:21,780 +مثلا الـ O2، بنقولش والله احنا يعني ال ozone مثلا + +596 +00:46:21,780 --> 00:46:23,680 +الـ O3 على حالة طبيعية، لأ مش حالة طبيعية + +597 +00:46:23,680 --> 00:46:27,680 +للأكسجين، مش حالته الطبيعية العادية، لأ حالته + +598 +00:46:27,680 --> 00:46:32,320 +العادية O2، الأكثر استقراراالكربون اي graphite ولا + +599 +00:46:32,320 --> 00:46:35,880 +diamond؟ لأ والله graphite مثلا يعني هو الموجود + +600 +00:46:35,880 --> 00:46:39,540 +الفوسفور + +601 +00:46:39,540 --> 00:46:46,160 +مثلا يعني حلجي مثلا P4 مثلا ال sulfur رومبك سالفر + +602 +00:46:46,160 --> 00:46:50,120 +مثلا يعني فهي شغلات بتيجي بالخبرة وبرضه بالقراءة + +603 +00:46:50,120 --> 00:46:58,710 +بالمعرفة يعني فخلينا نشوفكيف ممكن نستخدم ال heat + +604 +00:46:58,710 --> 00:47:05,530 +of formation و بالفعل نحصل على فوائد عظيمة جدا + +605 +00:47:05,530 --> 00:47:10,650 +بالذات يعني كمان في بعض الأحيان ممكن نستخدم ال + +606 +00:47:10,650 --> 00:47:14,630 +heat of formation في أحيان كتيرة في الحقيقة لحساب + +607 +00:47:14,630 --> 00:47:17,800 +ال heat of reaction إذا كنت أنا عارفالـ heat of + +608 +00:47:17,800 --> 00:47:20,560 +formation للمواد المختلفة إذا بقدر أعرف الـ heat + +609 +00:47:20,560 --> 00:47:24,280 +of reaction ليه؟ لأن عندي المواد متفاعلات و نواتج + +610 +00:47:24,280 --> 00:47:28,040 +و دائما الـ ΔH لل reaction هي عبارة عن إن الـ H + +611 +00:47:28,040 --> 00:47:31,020 +للنواتج مانصر الـ H للمتفاعلات هي الـ ΔH لل + +612 +00:47:31,020 --> 00:47:35,920 +reaction و بما إن الـ ΔH لل reaction واحدة إذا أنا + +613 +00:47:35,920 --> 00:47:38,560 +عندي المتفاعلات و النواتج لو أنا عارف الـ ΔH F + +614 +00:47:38,560 --> 00:47:41,900 +لإلهم إذا لل formation لكل واحد في الوضع إذا بقدر + +615 +00:47:41,900 --> 00:47:44,780 +أعرف الـ ΔH لل reaction هنشوف هذا الكلام هنلاقي + +616 +00:47:44,780 --> 00:47:48,070 +جداول كتير زي هيكهذه الـ Standard enthalpes of + +617 +00:47:48,070 --> 00:47:55,810 +formation ΔH0F للعديد من ايه؟ من المواد عند 298 + +618 +00:47:55,810 --> 00:48:02,050 +Kelvin هنلاقي مثلا ال .. ال Acetylene C2H2 Gas لأن + +619 +00:48:02,050 --> 00:48:07,450 +ال Acetylene Gas حالته الطبيعية طيب حلو كتيربتكون + +620 +00:48:07,450 --> 00:48:12,710 +من ايش؟ جال C Graphite زائد H .. اتنين C Solid + +621 +00:48:12,710 --> 00:48:17,170 +Graphite زائد مثلا H2 بيعطينا C2H2 هذا هو .. هذه + +622 +00:48:17,170 --> 00:48:20,990 +معادلة التكوين عندى .. يبقى معادلة التكوين دائما + +623 +00:48:21,820 --> 00:48:28,680 +عناصر في حالتها القياسية عن ضغط جوه واحد + +624 +00:48:28,680 --> 00:48:34,900 +atmosphere او temperature 298 Kelvin او 25 degrees + +625 +00:48:34,900 --> 00:48:40,090 +Celsiusفحنلاقي جداول زي هيك كتيرة خالص و بنستفيد + +626 +00:48:40,090 --> 00:48:43,870 +منها في الحقيقة في حل الأسئلة و إذا كان مالاجناهش + +627 +00:48:43,870 --> 00:48:46,650 +المادة اللي بدناها بنرجع في آخر الكتاب برا و + +628 +00:48:46,650 --> 00:48:51,010 +بنلاقي جداول يعني مفصلة بشكل كبير فيها الـ delta H + +629 +00:48:51,010 --> 00:48:56,590 +not F للمواد + +630 +00:48:56,590 --> 00:49:00,910 +المختلفة قبل ما أبدأ أفصل في أمثلة و غيره بس بدي + +631 +00:49:00,910 --> 00:49:05,770 +ألفت انتباهكمأنا بجيب ال delta او يعني مهتم بال + +632 +00:49:05,770 --> 00:49:12,510 +delta H not F للمواد المختلفة طب ايش بيحصل من + +633 +00:49:12,510 --> 00:49:17,010 +عناصرها الأولية ال standard state طب حلو طب ايش + +634 +00:49:17,010 --> 00:49:22,420 +بيحصل لو بدي اجيب ال delta H not F لأي عنصر؟في + +635 +00:49:22,420 --> 00:49:25,520 +حالته العادية حالته القياسية بقول هي عبارة عن + +636 +00:49:25,520 --> 00:49:30,500 +Delta H لل reaction لتحويل هذا العنصر من حالته + +637 +00:49:30,500 --> 00:49:36,320 +العنصرية القياسية إلى حالته العنصرية القياسية طب + +638 +00:49:36,320 --> 00:49:41,310 +هو موجود فيهاأي عنصر من العناصر موجود في حالته + +639 +00:49:41,310 --> 00:49:45,530 +الطبيعية عند خمسة و عشرين degree c و واحد + +640 +00:49:45,530 --> 00:49:50,410 +atmosphere كيف بده يحوله لعنصر موجود في حالته + +641 +00:49:50,410 --> 00:49:53,310 +القياسية عند خمسة و عشرين degree c و واحد + +642 +00:49:53,310 --> 00:49:57,690 +atmosphere؟ جداش ماعوز طاقة؟ zero ماعوزش شيء عشان + +643 +00:49:57,690 --> 00:50:02,690 +هيك دائما بنقول ان العناصراللي بتكون في الـ + +644 +00:50:02,690 --> 00:50:07,050 +standard state في حالتها الطبيعية الـ delta H0FL + +645 +00:50:07,050 --> 00:50:11,110 +هدائمة صفر فمثلا الأكسجين الـ delta H0FL هو جداش + +646 +00:50:11,110 --> 00:50:14,490 +صفر لأنه بده يكون أكسجين من نفسه في حالته الطبيعية + +647 +00:50:14,490 --> 00:50:17,070 +و هو أصلا موجود في حالته الطبيعية، لذا إيش بده + +648 +00:50:17,070 --> 00:50:21,670 +طاقة؟ و لا إيش، مابديش حاجة، مابدي نتذكر إنه أي + +649 +00:50:21,670 --> 00:50:26,710 +عنصر من العناصرموجود في حالته الطبيعية بقولش مثلا + +650 +00:50:26,710 --> 00:50:32,350 +H2O .. O2 liquid لأ O2 gas O2 .. الحالة الطبيعية + +651 +00:50:32,350 --> 00:50:39,810 +gas عند واحد أتمسفير و 298 degrees .. عفوا 298 + +652 +00:50:39,810 --> 00:50:43,950 +Kelvin بقول والله الـ Delta H0 تبعت Delta H0 F له + +653 +00:50:43,950 --> 00:50:47,110 +صفر لأنه اللي بده كونه من ذاته عند نفس ظروفه لأنه + +654 +00:50:47,110 --> 00:50:50,140 +في الحاجة القياسية واصلا موجود فما بده طاقةفي + +655 +00:50:50,140 --> 00:50:53,440 +حالته الطبيعية والله بتفرض علي ان اقول delta H not + +656 +00:50:53,440 --> 00:51:02,720 +F لاله هي عبارة عن صفر ال H2 نفس الكلام ال H2 نفس + +657 +00:51:02,720 --> 00:51:08,550 +الكلامصفر الـC Graphite صفر بدا كونه من نفسه الـC + +658 +00:51:08,550 --> 00:51:11,050 +Graphite بدا كونه من الـC Graphite عند خمسة و + +659 +00:51:11,050 --> 00:51:14,830 +عشرين ديجريات C و عند واحد اتنسيت بحجر طاقة جداش + +660 +00:51:14,830 --> 00:51:19,270 +صفر وبالتالي كل العناصر هذا الكلام بريحني بشكل + +661 +00:51:19,270 --> 00:51:23,350 +كبير وماحدش يسأل عن ايش الـDelta H Note F العنصر + +662 +00:51:23,350 --> 00:51:28,030 +معين في الامتحانلما نجيك معادلة طبعا المناطقية الـ + +663 +00:51:28,030 --> 00:51:30,490 +delta H not F لعنصر ما إنها بتساوي صفر لإنها + +664 +00:51:30,490 --> 00:51:35,130 +معروفة تعريف معروفة وبالتالي بدك تتذكر أنه تفهم + +665 +00:51:35,130 --> 00:51:40,390 +هذا الكلام وما تسألي عنه نهائيا بيقول for which of + +666 +00:51:40,390 --> 00:51:44,070 +these reactions at 25 degrees C does the enthalpy + +667 +00:51:44,070 --> 00:51:47,390 +change represent a standard enthalpy of formation + +668 +00:51:47,390 --> 00:51:52,090 +هذه معادلات أنهي واحدة من هدول هي عبارة عن + +669 +00:51:52,090 --> 00:51:53,710 +standard enthalpy of formation + +670 +00:51:57,640 --> 00:52:01,000 +بقول for each that does not اللي مش هي standard + +671 +00:52:01,000 --> 00:52:04,440 +enthalpy of formation what changes are needed to + +672 +00:52:04,440 --> 00:52:08,360 +make it an equation whose delta H is enthalpy of + +673 +00:52:08,360 --> 00:52:12,820 +formation ماشي في البداية اتنين NA solid زائد نص + +674 +00:52:12,820 --> 00:52:20,760 +O2 gas تعطينا NA2O solid هل هذه standard + +675 +00:52:20,760 --> 00:52:25,740 +enthalpy of formation equation بشوف في البداية هل + +676 +00:52:25,740 --> 00:52:32,180 +هدولالمتفاعلات هي عبارة عن elements في حالتها + +677 +00:52:32,180 --> 00:52:38,260 +القياسية كويس ولا لأ ف ال NA solid صحيح ال O2 gas + +678 +00:52:38,260 --> 00:52:45,760 +صحيحكمان NA2O هذا ملح صليد صحيح إذا نعم بما أن هذه + +679 +00:52:45,760 --> 00:52:49,920 +عبارة عن elements في حالتها القياسية تتحول إلى + +680 +00:52:49,920 --> 00:52:54,440 +مادة NA2O فهذه عبارة عن standard enthalpy of + +681 +00:52:54,440 --> 00:53:01,090 +formation لل NA2O صليديبقى أول معادلة نعم هي عبارة + +682 +00:53:01,090 --> 00:53:05,130 +عن معادلة يعني standard enthalpy of formation لـ + +683 +00:53:05,130 --> 00:53:10,850 +Na2O طيب المعادلة التانية 2K liquid زائد Cl2 gas + +684 +00:53:10,850 --> 00:53:15,490 +2K Cl solid نيجيهان البوتاسيوم كيف بيكون في حالته + +685 +00:53:15,490 --> 00:53:19,830 +الطبيعية solid solid اذا اه لأ هذه مش على طول هذه + +686 +00:53:19,830 --> 00:53:23,510 +ماهياش standard enthalpy of formationلأن عشان تكون + +687 +00:53:23,510 --> 00:53:30,090 +طب ال CL2 جاهز طبيعي ال KCL solid صحيح ملح طبيعي + +688 +00:53:30,090 --> 00:53:34,190 +اذا بس هذه عشان يكون enthalpy standard enthalpy of + +689 +00:53:34,190 --> 00:53:38,550 +formation لازم الكائش تكون solid بعدين هذه حاجة + +690 +00:53:38,550 --> 00:53:45,600 +والحاجة التانية ال delta HF دائما بتكونالمول واحد + +691 +00:53:45,600 --> 00:53:50,240 +مش لتنين مول او لتلاتة مول او لنص مول معنى الكلام + +692 +00:53:50,240 --> 00:53:54,780 +لازم المعادلة هذه كمان تنجسم على اتنين لازم + +693 +00:53:54,780 --> 00:53:58,800 +المعادلة هذه تنجسم على اتنين لانه لازم النتيجة ايش + +694 +00:53:58,800 --> 00:54:05,900 +تكون ال delta H not F هي عبارة عن تكوين واحد مول + +695 +00:54:05,900 --> 00:54:11,980 +من المادة من علاصرها الأساسيةفي الحاجة القياسية + +696 +00:54:11,980 --> 00:54:16,780 +واحد مول مش اكتر اذا هان لأ بنفعش اتنين بنفعش هد + +697 +00:54:16,780 --> 00:54:20,120 +على اتنين هد على اتنين هد على اتنين هيك بتصير + +698 +00:54:20,120 --> 00:54:28,990 +صحيحةطب C6H12O6 صليد بتحول ل C6C6H2G3O2G + +699 +00:54:28,990 --> 00:54:32,450 +هل هذه standard enthalpy of formation equation لأ + +700 +00:54:32,450 --> 00:54:36,330 +هذه بالعكس لو جلبناها كان صارت standard enthalpy + +701 +00:54:36,330 --> 00:54:39,590 +of formation لأن واحد منهم هذا diamond لأ ال + +702 +00:54:39,590 --> 00:54:42,630 +diamond مش diamond بدنا يكون graphite بدنا يكون + +703 +00:54:42,630 --> 00:54:46,570 +graphite لازم يكون graphite وهذا حالته طبيعي هذا + +704 +00:54:46,570 --> 00:54:50,920 +حالته طبيعي صحيحيعني بدها نجلبها و الـ C بدها تكون + +705 +00:54:50,920 --> 00:54:55,160 +مش دايمون بدها تكون إجرافي طيب if the following + +706 +00:54:55,160 --> 00:54:58,380 +equation is standard enthalpy of formation + +707 +00:54:58,380 --> 00:55:04,640 +equation S solid زائد S O زائد O2 gas بتعطينا S O2 + +708 +00:55:04,640 --> 00:55:11,880 +gas أعطتني واحد مول هي شرط اتحقق هذا ال sulfur هل + +709 +00:55:11,880 --> 00:55:16,670 +هو solid في حالته الطبيعية ولا لأ اه ال O2Gas اذا + +710 +00:55:16,670 --> 00:55:19,810 +وهذا الـ S O2 برضه كمان Gas يبقى اه هذه عبارة عن + +711 +00:55:19,810 --> 00:55:22,270 +standard enthalpy of formation equation يعني الـ + +712 +00:55:22,270 --> 00:55:25,490 +delta H ليلة هي عبارة عن delta H not F بقول if the + +713 +00:55:25,490 --> 00:55:28,830 +following equation standard enthalpy of formation + +714 +00:55:28,830 --> 00:55:34,110 +equation هي S solid زايد O2 liquid بتعطينا S O2 + +715 +00:55:34,110 --> 00:55:38,730 +liquid بنقول لا ماهياش هذه لازم تكون Gas وهذه لازم + +716 +00:55:38,730 --> 00:55:41,530 +تكون Gas طب if the following equation standard + +717 +00:55:41,530 --> 00:55:44,970 +enthalpy of formation equationأتنين H2 زائد O2 + +718 +00:55:44,970 --> 00:55:51,490 +بتعدر اتنين H2 .. لا .. لا مش صحيح أول حاجة هذه + +719 +00:55:51,490 --> 00:55:56,130 +لازم واحد mole وكمان liquid .. اه liquid ماشي يا + +720 +00:55:56,130 --> 00:55:59,590 +جماعة واضحة بالنسبالنا إيش يعني delta H0 if إذا + +721 +00:55:59,590 --> 00:56:04,230 +بقول كيف بدي استخدم ال enthalpy of formation عشان + +722 +00:56:04,230 --> 00:56:08,450 +أحسب ال enthalpy of reaction بقول ال delta H0 لل + +723 +00:56:08,450 --> 00:56:13,600 +reaction بتسوي ال summationن اللي هي عدد ملات كل + +724 +00:56:13,600 --> 00:56:17,200 +واحدة فيهم عدد الملات Delta H not F لـproducts + +725 +00:56:17,200 --> 00:56:21,280 +minus summation M برضه عدد الملات Delta H not F لل + +726 +00:56:21,280 --> 00:56:27,060 +reactantsكويس؟ ليه؟ لأنه كمان مرة الـ delta H note + +727 +00:56:27,060 --> 00:56:30,480 +لل reaction هي عبارة عن ال products minus ال + +728 +00:56:30,480 --> 00:56:33,560 +reactants و أنا ال products عندي ال delta H note F + +729 +00:56:33,560 --> 00:56:36,360 +values و ال reactants عندي ال delta H note F + +730 +00:56:36,360 --> 00:56:41,280 +values معناه يكلم بقدر أطرحهم من بعض و أحصل على ال + +731 +00:56:41,280 --> 00:56:44,940 +delta H note لل reaction دكتور يا عزيزي سمحت لل + +732 +00:56:44,940 --> 00:56:49,360 +reactants دايما تكون سمحت؟ لل reactants إذا كان ال + +733 +00:56:49,360 --> 00:56:54,010 +reactant أو ال productعنصر في its standard state + +734 +00:56:54,010 --> 00:57:00,610 +اه بس انصر هالجيل هنشوف امثلة بيقول مثلا consider + +735 +00:57:00,610 --> 00:57:08,570 +the combustion of propane والله انا يعني طيب + +736 +00:57:08,570 --> 00:57:14,930 +بدي ارجع لهدا بعد شوية اه بدي اقول هذا in the + +737 +00:57:14,930 --> 00:57:23,490 +reaction2C6H6 Liquid زائد 15 O2 Gas تعطينا 12 CO2 + +738 +00:57:23,490 --> 00:57:31,970 +Gas زائد 6 H2O Liquid ماشي الـ Delta H0 minus 6542 + +739 +00:57:31,970 --> 00:57:40,030 +KJ نقول F Delta H0 F للميه معايا Delta H0 F للـCO2 + +740 +00:57:40,030 --> 00:57:43,890 +معايا Find Delta H0 F للـC6H6 + +741 +00:57:45,630 --> 00:57:48,830 +بقول انا الـ ΔH نوت F لل reaction معايا هي سالب + +742 +00:57:48,830 --> 00:57:54,650 +6542 بقول ايش بتساوي N ΔH نوت F لل products minus + +743 +00:57:54,650 --> 00:57:57,250 +summation N ΔH نوت F لل reactions طب ماشي لل + +744 +00:57:57,250 --> 00:58:00,730 +products ها هاي ال .. هاي ال .. هاي ال N لل + +745 +00:58:00,730 --> 00:58:06,350 +products ايش فيه عندى؟ اتناش CO2 يبقى اتناش خلينا + +746 +00:58:06,350 --> 00:58:09,970 +ناخد ستة مية في الأول ماشي ستة مية ستة في ΔH نوت F + +747 +00:58:09,970 --> 00:58:14,490 +للمية زاد اتناشفي الـ delta H نقطة F لـ C minus + +748 +00:58:14,490 --> 00:58:21,090 +summation ايش بيقوللي اتنين في في ال delta H نقطة + +749 +00:58:21,090 --> 00:58:28,690 +F لبنزين زائد صفر خمستاشر صفر ليه؟ لأنه هذا عنصر + +750 +00:58:28,690 --> 00:58:33,030 +فانا معايا ال delta H نقطة F لكن ماعيشي ال C6H6 + +751 +00:58:33,030 --> 00:58:40,210 +liquid فبقدر اني اجيبها مباشرة هتطلع + +752 +00:58:40,210 --> 00:58:43,120 +علىممم + +753 +00:58:46,940 --> 00:58:50,740 +طيب نمشي معناه الكلام نبدأ في السؤال من أوله يعني + +754 +00:58:50,740 --> 00:58:54,180 +هو عبارة عن هذا .. هذا الشيء السهل خالص يعني إنه + +755 +00:58:54,180 --> 00:58:58,220 +يعطيني الـ delta H not if ل ال products و ال + +756 +00:58:58,220 --> 00:59:01,480 +reactants و يقوللي هات .. هات ال إيه ال delta H لل + +757 +00:59:01,480 --> 00:59:04,380 +reaction delta H not لل reaction هذا سهل جداً بدي + +758 +00:59:04,380 --> 00:59:08,220 +أقول والله على طول summation N delta H not if ل ال + +759 +00:59:08,220 --> 00:59:11,280 +products minus summation M في ال delta H not if لل + +760 +00:59:11,280 --> 00:59:15,510 +reactants لكن في بعض الأحيان أنا باجي بعمل خلطما + +761 +00:59:15,510 --> 00:59:19,990 +بين this is law و هذا القانون ففي عندي يعني + +762 +00:59:19,990 --> 00:59:23,090 +flexibility مرونة عظيمة جدا في الحقيقة بقول + +763 +00:59:23,090 --> 00:59:26,750 +consider the combustion of propane هاي ال propane + +764 +00:59:26,750 --> 00:59:33,570 +هذا حصل له combustion delta H نوت لل reaction مش + +765 +00:59:33,570 --> 00:59:37,030 +معروف find delta H نوت لل reaction انا والله + +766 +00:59:44,130 --> 00:59:47,570 +بقدر أني أجيب الـ delta H0 بيعطيني هو يعني هذه + +767 +00:59:47,570 --> 00:59:54,030 +المعادلات فانا بقدر أني أقول على طول بكون منها هذه + +768 +00:59:54,030 --> 01:00:02,430 +هي موجودة في اليسار مش مشكلة طيب الـCO2 بيكون + +769 +01:00:02,430 --> 01:00:06,830 +موجودة على اليمين هذه اللي اتحولت للـCO2 مضروبة في + +770 +01:00:06,830 --> 01:00:11,570 +تلاتةهذه الميّه اربعة ميّه liquid هي موجودة لو + +771 +01:00:11,570 --> 01:00:15,190 +جمعتهم بيعطينا الـ Delta H naught لل reaction ممكن + +772 +01:00:15,190 --> 01:00:20,230 +لكن برضه برضه بقدر ايش اقول انا ال Delta H naught + +773 +01:00:20,230 --> 01:00:24,810 +لل reaction ممكن اجمعهم عادي جدا Delta H naught لل + +774 +01:00:24,810 --> 01:00:28,850 +reaction ايش بتساوي جال خليني اقول لل products + +775 +01:00:28,850 --> 01:00:33,580 +دلتا H naught لل reaction بتساويالبرودكس ايش عند + +776 +01:00:33,580 --> 01:00:38,620 +الـ تلاتة في الـ delta H naught F للـ CO2 صحيح + +777 +01:00:38,620 --> 01:00:45,840 +زائد أربعة في الـ delta H naught F للمية minus + +778 +01:00:45,840 --> 01:00:56,320 +واحد يعني الـ delta H naught F للـ C3H8 بس زائد + +779 +01:00:56,320 --> 01:01:00,440 +صفر خلنا نقول زائد صفر حاضر زائد صفر يعني لأقل صفر + +780 +01:01:00,440 --> 01:01:05,740 +لأن هذه كلها يعنيطب هيها هيك خلاص زائد صفر صفر + +781 +01:01:05,740 --> 01:01:09,910 +طبعا ال auto فممكن نعملها زي هيك وخلاصمعايا او + +782 +01:01:09,910 --> 01:01:12,830 +ممكن نعملها الطريقة اللي اتعلمناها قبل شوية اللي + +783 +01:01:12,830 --> 01:01:15,650 +هي زي هيك هذا لو اجمع التلاتة و اعملهم برضه نفس + +784 +01:01:15,650 --> 01:01:19,290 +الجثة يعني بغض النظر انا هان ممكن ماعرفش ان هذه + +785 +01:01:19,290 --> 01:01:22,590 +اسمها delta H not F لكن هي delta H لل reaction + +786 +01:01:22,590 --> 01:01:26,170 +delta H not F هي delta H لل reaction هذا نفسه يعني + +787 +01:01:26,170 --> 01:01:30,870 +مثلا ال C graphite لو خدنا واحد واحد واحد هذه + +788 +01:01:30,870 --> 01:01:34,230 +بتكون يعني على تلاتة اه هي تلاتة لها تلاتة في ال + +789 +01:01:34,230 --> 01:01:38,080 +delta H not Fهي عبارة عن Delta H للتحول هذا أو للـ + +790 +01:01:38,080 --> 01:01:42,740 +Change هذا فممكن أن اشتغل هيك أو ان اشتغل باستخدام + +791 +01:01:42,740 --> 01:01:48,330 +Hesse's law زي ما اتعلمتإيش اللي بحتّم عليها كيف + +792 +01:01:48,330 --> 01:01:52,750 +أشتغل؟ قال والله إذا كان ال .. ال .. المتفاعلات + +793 +01:01:52,750 --> 01:01:56,070 +والنواتج موجودة معادلات الـ Formation أو قيمة الـ + +794 +01:01:56,070 --> 01:01:59,710 +Delta H0 F لهم أسهللي أشتغل بالسطر، سطر واحد + +795 +01:01:59,710 --> 01:02:02,970 +وخلاص، بدل ما أني أشوف المعادلات و أكون المعادلة + +796 +01:02:02,970 --> 01:02:05,450 +الـ Target Equation المعادلة الأصلية، لأ مش ضروري + +797 +01:02:05,450 --> 01:02:12,850 +كتير طيب، هذا شوفناه أظنني، ولا لأ؟ طيب، انشوف هذا + +798 +01:02:12,850 --> 01:02:17,050 +مثلابيقول ليه؟ given the following equations H2 + +799 +01:02:17,050 --> 01:02:20,810 +gas نص O2 وعطينا H2O liquid هذا دلتا H not F أصلا + +800 +01:02:20,810 --> 01:02:28,260 +حلو طيب H2 gas نص O2H2O Gas Delta H Note هذي + +801 +01:02:28,260 --> 01:02:33,880 +ماهياشي Liquid Delta H Note بده H2O Liquid للـ H2O + +802 +01:02:33,880 --> 01:02:38,580 +Gas أنا متبرهن ان اشتغل ايش بيسموها Hesis Law + +803 +01:02:38,580 --> 01:02:43,360 +فبقول والله H2O Liquid وين موجودة هي هانا بتجلب + +804 +01:02:43,360 --> 01:02:48,760 +هذه المعادلة H2O Gas زي ما هي طب حلو كتير لو + +805 +01:02:48,760 --> 01:02:53,890 +جمعناهم بطلع ان على طول النتجبديك تدبر حالك في إنه + +806 +01:02:53,890 --> 01:02:57,570 +يعني تستخدم المتاحة جدامك الأسهل إليك، هذا واضح + +807 +01:02:57,570 --> 01:03:02,770 +جدا بالنسبة لنا طيب بيقول fine delta H0 if for C + +808 +01:03:02,770 --> 01:03:05,830 +is too liquid carbon disulfide آه هنا سميته لكم، + +809 +01:03:05,830 --> 01:03:09,750 +بدي أسالكم عن اسمه carbon disulfide ليه؟ لأنه هذا + +810 +01:03:09,750 --> 01:03:16,010 +binary non-metallic compoundبنفعش نقول مونو سلفان + +811 +01:03:16,010 --> 01:03:20,750 +مونو كاربون داي سلفان لأ مونو بتنحطش في الأول + +812 +01:03:20,750 --> 01:03:24,210 +والكاربون داي سلفان طيب بده ال delta H نوت F له + +813 +01:03:24,210 --> 01:03:29,350 +ماعطيني سيلة لجرافيت او حلو كتير هذه delta H نوت + +814 +01:03:29,350 --> 01:03:34,630 +لهذا التفاعل اللي هو delta H نوت F كمان هو delta H + +815 +01:03:34,630 --> 01:03:42,010 +لهذا التفاعل اه لكن هي نفسها delta H نوت F لل + +816 +01:03:42,010 --> 01:03:47,090 +CO2 هي نفسهابس هي طبعاً لاتفاعل كمان مافيش مشكلة S + +817 +01:03:47,090 --> 01:03:53,630 +Rhombic زائد O2 اتنين S O2 لأ S O2 Gas طب C S2 + +818 +01:03:53,630 --> 01:03:58,490 +Liquid تلاتة O2 اتنين S O2 Gas زائد C O2 انا بدي + +819 +01:03:58,490 --> 01:04:07,570 +ال Delta H Note F لـ C S2 طب كيف بدي اكونه C S2؟ + +820 +01:04:07,570 --> 01:04:15,410 +جال والله C للجرافيت زائد اتنين Sسلفر رومبك وهذا + +821 +01:04:15,410 --> 01:04:21,690 +يعني stable form CS2 liquid يعني بدي أحصل علي هذه + +822 +01:04:21,690 --> 01:04:25,150 +المعادلة هذه المعادلة طب كيف بدي أحصل عليها؟ بدي + +823 +01:04:25,150 --> 01:04:30,440 +أحاول أن أجيب هدول على اليسار وهذا على اليمينلأنه + +824 +01:04:30,440 --> 01:04:34,400 +يعني انا لو كنت عارف لو كان هذه القيمة و هذه + +825 +01:04:34,400 --> 01:04:37,080 +القيمة و أجيبها على طول مثلا يعني و هذه معروفة + +826 +01:04:37,080 --> 01:04:40,180 +أجيبها على طول لكن لا انا عندي هذا هو صفر و هذه + +827 +01:04:40,180 --> 01:04:43,780 +صفر مهيأ يا بنات؟ اذا بدنا نرجع هان و نقول والله + +828 +01:04:43,780 --> 01:04:46,540 +بد ال C graphite تكون على اليسار هاي C graphite + +829 +01:04:46,540 --> 01:04:49,980 +اذا هذه خليها زي ما هي بد ال S rhombic على اليسار + +830 +01:04:49,980 --> 01:04:53,200 +و مضروها في اتنين بتقول انه في اتنين و هذه كمان في + +831 +01:04:53,200 --> 01:04:59,670 +اتنين C is to liquid بدنا نجلبها اهممكن تتصير + +832 +01:04:59,670 --> 01:05:05,810 +موجبان، ماشي خلاص ابنش معاهم يطلع لنا الـDH0 F هي + +833 +01:05:05,810 --> 01:05:09,870 +الـDelta H لل reaction أصلا هي الـDelta H هي نفسها + +834 +01:05:09,870 --> 01:05:14,550 +الـDelta H لل reaction هذا اللي هو باعتبار هو صح + +835 +01:05:14,550 --> 01:05:18,330 +لهذا التفاعل، لكن هذا التفاعل هو تفاعل تكوين، ليه؟ + +836 +01:05:18,330 --> 01:05:27,740 +لأنهالمادة هيها تتكون من العناصر الأساسية الـ + +837 +01:05:27,740 --> 01:05:28,720 +Standard State + +838 +01:05:34,510 --> 01:05:46,670 +لهذا التفاعل يا بنتي هي مش دلتا H نوت F دلتا + +839 +01:05:46,670 --> 01:05:50,870 +H نوت F دلتا H نوت F دلتا H نوت F دلتا H نوت F + +840 +01:05:50,870 --> 01:05:51,830 +دلتا H نوت F دلتا H نوت F دلتا H نوت F دلتا H نوت + +841 +01:05:51,830 --> 01:05:52,490 +F دلتا H نوت F دلتا H نوت F دلتا H نوت F دلتا H + +842 +01:05:52,490 --> 01:05:54,690 +دلتا H نوت F دلتا H نوت F دلتا H نوت F دلتا H نوت + +843 +01:05:54,690 --> 01:06:00,900 +F دلتا H نوت F دلتا H نوت F دلتفهي طبعا هي نفسها + +844 +01:06:00,900 --> 01:06:04,800 +لهذا التفعل وبرضه كمان تسمى delta H note لو كانت + +845 +01:06:04,800 --> 01:06:10,040 +المعادلة مقلوبة لأ طبيعي طبيعي لو كانت المعادلة + +846 +01:06:10,040 --> 01:06:11,420 +مقلوبة ماتبطل formation + +847 +01:06:16,790 --> 01:06:19,590 +نتطلع على هذا التفاعل الحلو كتير وبسيط بس برضه + +848 +01:06:19,590 --> 01:06:22,050 +بيعطيك الفكرة اللي انا بدي اياها بيقول in the + +849 +01:06:22,050 --> 01:06:27,670 +reaction اتنين Sodium Bicarbonate تتحول ل Sodium + +850 +01:06:27,670 --> 01:06:31,010 +Solid تتحول ل Sodium Carbonate Solid زائد H2O Gas + +851 +01:06:31,010 --> 01:06:35,290 +زائد CO2 Gas بيقول find delta H not لل reaction if + +852 +01:06:36,880 --> 01:06:40,720 +Delta Hnot F للصوديوم كربونيت هل جد Delta Hnot F + +853 +01:06:40,720 --> 01:06:44,800 +للصوديوم باي كربونيت هل جد Delta Hnot F لل H2O + +854 +01:06:44,800 --> 01:06:49,760 +برضه معايا Delta Hnot F لل CO2 معايا طب خلاص يفجأت + +855 +01:06:49,760 --> 01:06:53,320 +Delta Hnot F لل reaction هي عبارة ايش نقول مع بعض + +856 +01:06:53,320 --> 01:06:56,220 +Delta Hnot F لل reaction ايش بتسوي ال products + +857 +01:06:56,220 --> 01:07:02,980 +يللا هذا هي ال products 1 في Delta Hnot F للصوديوم + +858 +01:07:02,980 --> 01:07:14,000 +كربونيت زائدDelta H0 F واحد بس لل H2O جاز زائد + +859 +01:07:14,000 --> 01:07:24,280 +Delta H0 F لل CO2 جاز هذا كله ناطس اتنين فيه Delta + +860 +01:07:24,280 --> 01:07:31,170 +H0 F لل Sodium Bicarbonateخلاص و كلهم معايا بس + +861 +01:07:31,170 --> 01:07:35,350 +بنعوض تعويض مباشر بيطلع عندى موجة بـ 128 دولار و + +862 +01:07:35,350 --> 01:07:38,350 +طبيعى لأنه ال sodium b carbonate بيبقى تنحرج عشان + +863 +01:07:38,350 --> 01:07:44,050 +تتحول ل Sodium carbonate و CO2 gas و ميه يبقى + +864 +01:07:44,050 --> 01:07:47,270 +بيدها حرارة عشان هيك التفاعل اندو thermic يبقى + +865 +01:07:47,270 --> 01:07:55,130 +لازم ال delta H ايش تكون موجة بقى اقول + +866 +01:07:55,130 --> 01:07:57,230 +هذا يعني مثلا اخر مثال معايا + +867 +01:08:01,010 --> 01:08:06,750 +بقول calculate delta H0 لل reaction اتنين NA2 O2 + +868 +01:08:06,750 --> 01:08:13,310 +solid هذا Sodium Peroxide Sodium Peroxide بنات ال + +869 +01:08:13,310 --> 01:08:18,820 +O2 قولنا هذه Sodium Peroxideمراكب ايوني طبعا زائد + +870 +01:08:18,820 --> 01:08:23,400 +اتنين H2O liquid تعطينا اربع NAOH solid زائد O2 + +871 +01:08:23,400 --> 01:08:27,020 +gas بيقول بده يحسب ال Delta H لل reaction provided + +872 +01:08:27,020 --> 01:08:35,140 +that Delta H not if لل NA2O2 معايا Delta H not if + +873 +01:08:35,140 --> 01:08:39,920 +لل Sodium Hydroxide معايا Delta H not if للميه + +874 +01:08:39,920 --> 01:08:44,870 +معاياطب الأكسجين ماتهليش لأنها لأنها نصفة طب خلاص + +875 +01:08:44,870 --> 01:08:50,170 +يفجر المسألة المحلولة لأن هي ال delta H نوت لل + +876 +01:08:50,170 --> 01:08:54,590 +reaction إيش بدها تساوي بسرعة بدها تساوي أربعة في + +877 +01:08:54,590 --> 01:09:01,350 +ال delta H نوت F لل Sodium Hydroxide ناقص هي فتحنا + +878 +01:09:01,350 --> 01:09:10,420 +جوس كبير اتنين في delta H نوت F لل NA2O2 زائدتنين + +879 +01:09:10,420 --> 01:09:17,380 +في دلتا H نوت F الـH2O اللي هي الـ liquid و خلاص و + +880 +01:09:17,380 --> 01:09:20,180 +لاحظوا أن الأكسجين ماحطناهاش ولا اعطاناها اي + +881 +01:09:20,180 --> 01:09:23,100 +اهتمام لأنه طبعا هي بتساوي صفر + +882 +01:09:27,300 --> 01:09:30,680 +المسألة هذه زي المثال اللي جابلها بالظبط the + +883 +01:09:30,680 --> 01:09:33,580 +standard enthalpy change for the reaction هذا + +884 +01:09:33,580 --> 01:09:39,300 +مجهول لأ ماتين أيام 178 و 11 كيلوجود بقول use the + +885 +01:09:39,300 --> 01:09:41,620 +tabulated standard enthalpies of formation to + +886 +01:09:41,620 --> 01:09:44,760 +calculate the standard enthalpy of formation of + +887 +01:09:44,760 --> 01:09:49,040 +calcium carbonate انا بقول هذا معايا اللي هو الـ + +888 +01:09:49,040 --> 01:09:55,800 +delta H0 لل reaction 178.1 بدها تساوي النواتجالـ + +889 +01:09:55,800 --> 01:10:03,200 +Delta H0F للـ Calcium Oxide زائد Delta H0F للـ CO2 + +890 +01:10:03,200 --> 01:10:11,160 +Gas، هذا الصليد، هدول ناقص Delta H0F للـ Calcium + +891 +01:10:11,160 --> 01:10:15,440 +Carbonateهو طالب الـ ΔH نوت F للكالسيوم + +892 +01:10:15,440 --> 01:10:18,400 +الكاروينسيكا وبدأ أبحث في الجداول على الـ Calcium + +893 +01:10:18,400 --> 01:10:22,000 +Oxide و الـ CO2 الجداول موجود فيها كل هذه + +894 +01:10:22,000 --> 01:10:27,360 +المراكبات فهي الـ Calcium Oxide وهي الـ CO2 هذه + +895 +01:10:27,360 --> 01:10:31,570 +مجهولة بقدر أحسبها مباشرة فسواء جلد Delta Hللـ + +896 +01:10:31,570 --> 01:10:35,250 +reaction أو جالي اعطاني ال reaction و جالي بده + +897 +01:10:35,250 --> 01:10:40,510 +والله delta H not F لمادة من المواد سهل جدا ان + +898 +01:10:40,510 --> 01:10:46,230 +اوصل لها ليه؟ لأنه السطر هذا او المعادلة المعادلة + +899 +01:10:46,230 --> 01:10:50,770 +سهلة بسيطة خالص وجدامي موجودة ال delta H not لل + +900 +01:10:50,770 --> 01:10:54,430 +reaction بساوي summation delta H not F لل products + +901 +01:10:54,430 --> 01:10:58,320 +minus reactantsوبالتالي كله موجود، بس واحدة بتكون + +902 +01:10:58,320 --> 01:11:02,060 +مجهولة بقدر أجيبها، فهو لازم يعطيني كل شيء معدى، + +903 +01:11:02,060 --> 01:11:05,280 +مادة واحدة يعني، الآن بنيجي لآخر جزئية في هذا ال + +904 +01:11:05,280 --> 01:11:10,080 +chapter نتكلم عن Caloric Value أو يعني القيمة + +905 +01:11:10,080 --> 01:11:15,180 +الغذائية لل food و ال fuels عموما، القيمة الغذائية + +906 +01:11:15,180 --> 01:11:20,520 +لل food ك energy، ك energy، ولل fuel برضه قيمة ال + +907 +01:11:20,520 --> 01:11:25,480 +energy اللي موجودة فيهفبنقول بشكل أساسي يمكن ال + +908 +01:11:25,480 --> 01:11:29,960 +energy في أجسامنا بتيجي من حاجتين ال carbohydrates + +909 +01:11:29,960 --> 01:11:31,300 +و ال fats + +910 +01:11:34,470 --> 01:11:38,490 +الـ carbohydrates أساسا يعني بتكون موجود على هيئة + +911 +01:11:38,490 --> 01:11:43,850 +سكريات و starches وهذه بتتكسر في ال intestines في + +912 +01:11:43,850 --> 01:11:47,390 +الأمعاء يعني بتتحول ل glucose، اللي هو اللي احنا + +913 +01:11:47,390 --> 01:11:53,720 +بنستفيد منه كمصدر للطاقة لأنه بيتحول ل CO2 وH2Oيا + +914 +01:11:53,720 --> 01:11:58,220 +سلام، بتحول لـCO2 وH2؟ آه، زي ما نحرج في الحياة + +915 +01:11:58,220 --> 01:12:02,320 +العملية، أي هيدرو كاربون، بنزين، سولار، كذا، بتحول + +916 +01:12:02,320 --> 01:12:05,720 +لـCO2 ومياه، نفس الكلام، طاقة طاقة، كله طاقة، + +917 +01:12:05,720 --> 01:12:11,630 +فالجسم برضه لما يحرج لجلوكوز، بتحول لـCO2وH2O + +918 +01:12:11,630 --> 01:12:15,830 +طلعوا كمية طاقة فظيعة المول من ال 180 جرام يعني + +919 +01:12:15,830 --> 01:12:22,810 +المول من ال glucose بيعطيني 2803 kilo joules اشي + +920 +01:12:22,810 --> 01:12:27,350 +كتير خالص يعني كمية رهيبة جدا من الطاقة + +921 +01:12:28,770 --> 01:12:31,810 +على أي حال، اللي بدنا نعرفه شغلات بسيطة كتير، اللي + +922 +01:12:31,810 --> 01:12:36,750 +بدنا نعرفه كيف ممكن نحسب كمية الـcaloric content + +923 +01:12:36,750 --> 01:12:41,970 +في أي كمية من الـfood، هذا بداية، فبنقول إنه كل + +924 +01:12:41,970 --> 01:12:46,610 +gram من الـcarbohydrates موجود في 17 أو بقدر + +925 +01:12:46,610 --> 01:12:50,990 +يعطينا 17 kilojouleكل إجراب carbohydrate بيعطينا + +926 +01:12:50,990 --> 01:12:55,630 +السبعتاشر كيلو جول أو يعني تقريبا أربعة كيلو + +927 +01:12:55,630 --> 01:13:00,930 +كالوري لأنه احنا بنعرف أنه يعني + +928 +01:13:00,930 --> 01:13:06,330 +العلاقة بين الجول والكلوري 4.18 شفناها سابقا + +929 +01:13:06,890 --> 01:13:11,310 +بالنسبة للـ Fats يعني من أشهر الـ Fats أو أغلبها + +930 +01:13:11,310 --> 01:13:14,750 +يعني بيكون عليها Triestrine و حاجة فظيعة يعني + +931 +01:13:14,750 --> 01:13:18,530 +تصوروا كيف بده يكون التركيب وهذا فظيع جدا هذا كيف + +932 +01:13:18,530 --> 01:13:24,470 +الجسم بيتعامل معاه فظيع كتير فالـ Fats هذا بيعطيني + +933 +01:13:24,470 --> 01:13:29,430 +كمية أكبر من الطاقة كمية أكبر فكل جرام بيعطيني + +934 +01:13:29,430 --> 01:13:33,550 +حوالي تمانية و تلاتين كيلوجول ضعف السكر تمانية و + +935 +01:13:33,550 --> 01:13:38,710 +تلاتين كيلوجول تقريبا يعنيو هاي التفاعل هو يالله + +936 +01:13:38,710 --> 01:13:44,830 +جد إيه؟ 75-520 KJ إيش إيه فظيعة خالص، كمية الطاقة + +937 +01:13:44,830 --> 01:13:49,310 +فظيعة للغاية يعني فاحنا اللي بدنا نعرفه التالي، + +938 +01:13:49,310 --> 01:13:55,050 +بدنا نعرف إنه مثلًا الـ Carbohydrates يقولنا 17 KJ + +939 +01:13:55,050 --> 01:14:00,330 +per gram الفات 38 KJ طبعًا بدنا مش نحفظه، يعني + +940 +01:14:00,330 --> 01:14:03,370 +بدنا نكون معانا يعني، لكن بدنا نقدر نحسبه، + +941 +01:14:03,370 --> 01:14:08,620 +البروتين حوالي 17برضو كيلو زي تقريبا زي ال + +942 +01:14:08,620 --> 01:14:14,220 +carbohydrates ال .. ال apples موجود فيها + +943 +01:14:14,220 --> 01:14:17,300 +carbohydrates وموجود فيها fat وموجود فيها protein + +944 +01:14:17,300 --> 01:14:20,700 +لما نيجي نحسبها تطلع تقريبا اتنين و نص kilo joule + +945 +01:14:20,700 --> 01:14:25,460 +per gram ال bread طبعا موجود فيه كمية كبيرة من ال + +946 +01:14:25,460 --> 01:14:29,060 +carbohydrates كمية من الفات كمية .. بتحول اتناش + +947 +01:14:29,060 --> 01:14:35,890 +kilo joule per gram فهذه بتعبرلي عن ال ..الـ Fuel + +948 +01:14:35,890 --> 01:14:41,970 +Value للـ Food بشكل عام الـ Fuel Value للـ Food + +949 +01:14:41,970 --> 01:14:49,250 +بشكل عام فخلّيني أخد مثال نحسب فيه جداش مثلا الـ + +950 +01:14:49,250 --> 01:14:54,550 +Caloric Content ل One Serving ففيه عندي 28 جرام، 1 + +951 +01:14:54,550 --> 01:14:59,910 +أنص، أنصة يعني طبعا الأنصة دي بستخدمها في بريطانيا + +952 +01:14:59,910 --> 01:15:03,680 +أو في أمريكا يعنيالبلاد اللي استخدم ال foot و ال + +953 +01:15:03,680 --> 01:15:08,000 +inch برضه استخدموا الانص اللي لهم نظام خاص يعني اه + +954 +01:15:08,000 --> 01:15:13,520 +تبانية و عشرين جرام تقريبا واحد انص تقريبا واحد + +955 +01:15:13,520 --> 01:15:16,520 +انص يعني تبانية و عشرين جرام serving of a popular + +956 +01:15:16,520 --> 01:15:19,540 +breakfast cereal تعرفوه ال cornflakes يعني على + +957 +01:15:19,540 --> 01:15:23,680 +سبيل المثال بيقولوله برا cereal served with ميه و + +958 +01:15:23,680 --> 01:15:27,900 +عشرين مل و skim milk skim milk يعني حليب من زوعة + +959 +01:15:27,900 --> 01:15:33,610 +دسم ميه و عشرين ملprovides 8 gram يعني هادي في هذه + +960 +01:15:33,610 --> 01:15:39,250 +الوجبة كويس اللي هي 28 gram breakfast cereal مع + +961 +01:15:39,250 --> 01:15:45,010 +120 ml من ال skim milk موجود فيها 8 gram protein و + +962 +01:15:45,010 --> 01:15:49,430 +26 gram carbohydrates و 2 gram fats فبدنا نستخدم + +963 +01:15:49,430 --> 01:15:54,390 +الجدولاللي شفناها قبل شويه عشان نحسب جداش ال + +964 +01:15:54,390 --> 01:15:59,730 +calorie content لهذا الواجبه نقول energy 8 gram + +965 +01:15:59,730 --> 01:16:04,510 +protein كل gram 17 kilo joule 26 gram carbohydrate + +966 +01:16:04,510 --> 01:16:09,170 +برضه كل gram 17 kilo joule 2 gram fat كل gram 38 + +967 +01:16:09,170 --> 01:16:13,590 +kilo joule فمعنى الكلام 650 kilo joule ولو بدنا + +968 +01:16:13,590 --> 01:16:18,150 +نحويلها ل calorie نقسمها ل 4.18 ميه بطلع حوالي 156 + +969 +01:16:18,150 --> 01:16:23,720 +kilo calorieمافي او ارا كتابة calorie C كبيرة C + +970 +01:16:23,720 --> 01:16:25,420 +كبيرة يعني ايه كيلو كالوري + +971 +01:16:29,820 --> 01:16:36,500 +الوقود بشكل عام برضه مش كله فيه له نفس يعني القدرة + +972 +01:16:36,500 --> 01:16:41,100 +على مدنة بالطاقة، فيه وقود بيكون الطاقة المختزنة + +973 +01:16:41,100 --> 01:16:46,540 +فيه طاقة كبيرة جدا، طبعا الكاتب بيذكر انه يعني هال + +974 +01:16:46,540 --> 01:16:48,860 +petrol اللي احنا بنستخدمه اللي هو ال fossil fuels + +975 +01:16:48,860 --> 01:16:53,910 +هذا تكون خلال ملايين السنين الله أعلم يعنيلكن احنا + +976 +01:16:53,910 --> 01:16:57,710 +يعني .. يعني هل الله عز وجل خلق وما ما خلق ولا هو + +977 +01:16:57,710 --> 01:17:02,970 +بالفعل يعني تكون نتيجة وجود كائنات ونباتات + +978 +01:17:02,970 --> 01:17:07,110 +وحيوانات وخلافه خلال ملايين السنين صحيح الله أعلم + +979 +01:17:07,110 --> 01:17:11,030 +المهم أنه موجود هو بالفعل لو بده يتكون بده يعني + +980 +01:17:11,030 --> 01:17:14,250 +سنوات طويلة جدا يعني عشان .. وظروف كمان صعبة جدا + +981 +01:17:14,250 --> 01:17:19,970 +عشان يتكون خاصة بالكميات هذهفهو بيقول يعني ان هذه + +982 +01:17:19,970 --> 01:17:25,350 +كلها يعني بتختلف في قدرتها على مادنا بالطاقة فمثلا + +983 +01:17:25,350 --> 01:17:28,130 +يعني ال natural gas اللي هو بتكون أساسا من ال + +984 +01:17:28,130 --> 01:17:32,070 +methane لكن مخلوط معاه طبعا ethane و probane و + +985 +01:17:32,070 --> 01:17:37,770 +butane كميات متفاوتة مش زي ال hydrogen ولا زي + +986 +01:17:37,770 --> 01:17:41,770 +البنزين اللي احنا بنستخدمه في السياراتولا زي الـ + +987 +01:17:41,770 --> 01:17:46,550 +Solar لأ كل واحد منهم فيه إله يعني إمكانية إنه + +988 +01:17:46,550 --> 01:17:51,770 +يمدنب بقدرة معينة فمثلا ال wood ال fuel value إله + +989 +01:17:51,770 --> 01:17:59,010 +18 kilo joule per gram ال wood ال coal حسب مصدره + +990 +01:17:59,010 --> 01:18:04,210 +31-32 kilo joule per gram الفحم 34 kilo joule per + +991 +01:18:04,210 --> 01:18:11,250 +gram لو جنرال الجازولين 48natural gas 49 جريب منه + +992 +01:18:11,250 --> 01:18:15,470 +الهيدروجين او كتير خالص per gram ليه؟ لأن اذا كانت + +993 +01:18:15,470 --> 01:18:18,570 +تلاحظوا الهيدروجين ال gram تبعه عبارة عن نص مول + +994 +01:18:18,570 --> 01:18:22,350 +كمية هائلة ال gram تبع الهيدروجين عبارة عن ايه؟ + +995 +01:18:22,350 --> 01:18:26,670 +عبارة عن نص مول فبيعطيني 142 اجرام مش المفروض مني + +996 +01:18:26,670 --> 01:18:29,930 +ان احفظ هذا الكلام لكن المفروض انه اذا كان اعتالنا + +997 +01:18:30,420 --> 01:18:37,180 +قيم ال .. يعني ال fuel value لبعض ال .. ال + +998 +01:18:37,180 --> 01:18:40,620 +components من مثلا واجبة غذائية او غير وممكن انه + +999 +01:18:40,620 --> 01:18:44,080 +والله اه لازم نقدر نحسب كداش ال calorie content + +1000 +01:18:44,080 --> 01:18:51,570 +لإلها بس مش اكتر بتمنى انه يعني نكونإن كون يعني + +1001 +01:18:51,570 --> 01:18:54,410 +استفدنا من هذا ال chapter و بتمنى أنه ترجعوه كويس + +1002 +01:18:54,410 --> 01:18:58,630 +كتير لأنه مجال الأسئلة فيه متعدد و كتير خالص + +1003 +01:18:58,630 --> 01:19:00,930 +فبنشوفكم إذا الله راهد الحصة الجاية + diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/OTv5mpM3an4_raw.json b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/OTv5mpM3an4_raw.json new file mode 100644 index 0000000000000000000000000000000000000000..81a450eedae255a4fac042b125696b6e7eace628 --- /dev/null +++ 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عندي solvent هو المادة اللى موجودة بكمية أكبر", "tokens": [5172, 3555, 1863, 39648, 16585, 3827, 6156, 7578, 18871, 16254, 11331, 26108, 2655, 9957, 6156, 7578, 18871, 16254, 1404, 1169, 31439, 9673, 18513, 3660, 13672, 7578, 3714, 29245, 23328, 3660, 4724, 24793, 10632, 12174, 20292, 37977, 4032, 6156, 7578, 18871, 16254, 33575, 31439, 9673, 18513, 3660, 13672, 7578, 3714, 29245, 23328, 3660, 4724, 24793, 10632, 5551, 4117, 26890], "avg_logprob": -0.16234110775640456, "compression_ratio": 1.7380952380952381, "no_speech_prob": 0.0, "words": [{"start": 154.56, "end": 155.34, "word": "فبنقول", "probability": 0.69696044921875}, {"start": 155.34, "end": 155.62, "word": " NA", "probability": 0.39697265625}, {"start": 155.62, "end": 156.3, "word": " solution", "probability": 0.6591796875}, {"start": 156.3, "end": 156.56, "word": " فى", "probability": 0.5728759765625}, {"start": 156.56, "end": 156.76, "word": " عندي", "probability": 0.7352294921875}, {"start": 156.76, "end": 157.3, "word": " 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1975, 3224, 16070, 43761, 5296, 15042, 2423, 1404, 1169, 7251, 7435, 1829, 20449, 2423, 33575, 23758, 39896, 3615, 9566, 9957, 1829, 23032, 995, 28671], "avg_logprob": -0.24703663793103448, "compression_ratio": 1.1444444444444444, "no_speech_prob": 0.0, "words": [{"start": 302.45, "end": 302.99, "word": "ساعتها", "probability": 0.9110107421875}, {"start": 302.99, "end": 303.21, "word": " اه", "probability": 0.657958984375}, {"start": 303.21, "end": 303.47, "word": " والله", "probability": 0.5931396484375}, {"start": 303.47, "end": 303.69, "word": " لما", "probability": 0.948974609375}, {"start": 303.69, "end": 303.87, "word": " ال", "probability": 0.82177734375}, {"start": 303.87, "end": 304.51, "word": " solute", "probability": 0.7396240234375}, {"start": 304.51, "end": 306.61, "word": " يجي", "probability": 0.7962239583333334}, {"start": 306.61, "end": 306.77, "word": " مع", "probability": 0.98486328125}, {"start": 306.77, "end": 306.93, "word": " ال", "probability": 0.82275390625}, 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نتفة ال bipolar", "tokens": [9566, 3555, 3615, 995, 14111, 2423, 39184, 24631, 313, 4032, 11242, 3615, 3224, 6156, 19913, 40228, 10874, 28259, 14111, 6156, 3224, 15730, 44945, 15040, 38436, 3224, 37495, 22653, 2107, 12367, 12399, 4724, 1829, 3215, 20498, 8592, 11933, 15040, 8978, 2423, 39184, 2107, 12367, 30767, 1829, 2423, 5954, 717, 5757, 482, 12399, 2423, 5954, 23319, 81, 608, 6746, 482, 12399, 2423, 3224, 1829, 7435, 11622, 9957, 12399, 41950, 12610, 2407, 9957, 30731, 19753, 34740, 10632, 12399, 4032, 41193, 1211, 3615, 14407, 13412, 28820, 3224, 28242, 23758, 2423, 24631, 313, 5874, 28242, 11296, 12399, 8032, 47302, 16247, 5016, 29973, 12399, 8032, 47302, 8717, 2655, 5172, 3660, 2423, 42469], "avg_logprob": -0.34608643968528674, "compression_ratio": 1.6347826086956523, "no_speech_prob": 0.0, "words": [{"start": 1444.75, "end": 1445.23, "word": "طبعاً", "probability": 0.6697265625}, {"start": 1445.23, "end": 1445.37, "word": " الـ", "probability": 0.760009765625}, {"start": 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Sulphur مشبوكين في رنج طيب، هذا إيش أنواع الـ Intermolecular forces اللي بتجمع الـ Elemental Sulphur مع بعض البعض؟ إيش نوع ال forces؟", "tokens": [1211, 3615, 45340, 24793, 2423, 39184, 318, 23, 31439, 2423, 39184, 20900, 304, 35897, 950, 374, 37495, 22653, 14739, 9381, 2288, 2423, 39184, 35897, 950, 374, 3714, 29245, 23328, 8978, 41950, 21292, 27884, 13672, 1829, 39896, 2423, 39184, 318, 23, 39896, 4117, 13412, 28820, 3224, 4724, 1829, 30544, 46811, 10943, 11778, 2288, 9307, 35897, 950, 374, 37893, 3555, 2407, 4117, 9957, 8978, 12602, 1863, 7435, 23032, 1829, 3555, 12399, 23758, 11933, 1829, 8592, 14739, 14407, 3615, 2423, 39184, 5751, 3280, 306, 17792, 5874, 13672, 1829, 39894, 7435, 2304, 3615, 2423, 39184, 20900, 304, 35897, 950, 374, 20449, 45030, 11242, 29739, 3615, 11242, 22807, 11933, 1829, 8592, 8717, 45367, 2423, 5874, 22807], "avg_logprob": -0.28515626463506905, "compression_ratio": 1.658008658008658, "no_speech_prob": 0.0, "words": [{"start": 1490.65, "end": 1491.51, 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"word": " ال", "probability": 0.9423828125}, {"start": 2205.61, "end": 2205.95, "word": " acetic", "probability": 0.61865234375}, {"start": 2205.95, "end": 2206.53, "word": " acid؟", "probability": 0.89697265625}], "temperature": 1.0}, {"id": 96, "seek": 223315, "start": 2207.35, "end": 2233.15, "text": "ليش الاستيك أسيد؟ لأن الدايبول الدايبول هو هيدروجين بوني قوي جدا و تنتين هيدروجين بوني حاجة ممتازة فهيكون free لصلبول يمكن في الميه، هذا لأ هذا non polar يعني في polarity ضعيفة يعني طيب ال carbon تترا كلورايد ولا التترا هيدروفيوران؟ التترا هيدروفيوران يا جماعة هذا هو طبعا انتوا شايفين ال O فيعني بتصد هي لكن هذا هو", "tokens": [20292, 8592, 2423, 32277, 31371, 4117, 5551, 3794, 25708, 22807, 5296, 33456, 2423, 28259, 1829, 3555, 12610, 2423, 28259, 1829, 3555, 12610, 31439, 8032, 25708, 2288, 29245, 9957, 4724, 11536, 1829, 12174, 45865, 10874, 28259, 4032, 6055, 29399, 9957, 8032, 25708, 2288, 29245, 9957, 4724, 11536, 1829, 11331, 26108, 3660, 3714, 2304, 2655, 31377, 3660, 6156, 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"probability": 0.6552734375}, {"start": 2217.59, "end": 2218.01, "word": " polar", "probability": 0.68408203125}, {"start": 2218.01, "end": 2218.65, "word": " يعني", "probability": 0.8095703125}, {"start": 2218.65, "end": 2219.01, "word": " في", "probability": 0.82861328125}, {"start": 2219.01, "end": 2219.45, "word": " polarity", "probability": 0.829345703125}, {"start": 2219.45, "end": 2219.91, "word": " ضعيفة", "probability": 0.98388671875}, {"start": 2219.91, "end": 2221.33, "word": " يعني", "probability": 0.639892578125}, {"start": 2221.33, "end": 2222.25, "word": " طيب", "probability": 0.9235026041666666}, {"start": 2222.25, "end": 2222.43, "word": " ال", "probability": 0.66552734375}, {"start": 2222.43, "end": 2222.79, "word": " carbon", "probability": 0.75732421875}, {"start": 2222.79, "end": 2223.13, "word": " تترا", "probability": 0.7469075520833334}, {"start": 2223.13, "end": 2223.79, "word": " كلورايد", "probability": 0.80244140625}, {"start": 2223.79, "end": 2224.55, "word": " ولا", "probability": 0.60009765625}, {"start": 2224.55, "end": 2224.97, "word": " التترا", "probability": 0.88232421875}, {"start": 2224.97, "end": 2225.83, "word": " هيدروفيوران؟", "probability": 0.77081298828125}, {"start": 2225.83, "end": 2226.23, "word": " التترا", "probability": 0.9659830729166666}, {"start": 2226.23, "end": 2226.87, "word": " هيدروفيوران", "probability": 0.9363141741071429}, {"start": 2226.87, "end": 2226.97, "word": " يا", "probability": 0.515625}, {"start": 2226.97, "end": 2227.23, "word": " جماعة", "probability": 0.9957682291666666}, {"start": 2227.23, "end": 2227.41, "word": " هذا", "probability": 0.64404296875}, {"start": 2227.41, "end": 2227.65, "word": " هو", "probability": 0.99462890625}, {"start": 2227.65, "end": 2228.39, "word": " طبعا", "probability": 0.87225341796875}, {"start": 2228.39, "end": 2228.55, "word": " انتوا", "probability": 0.7328287760416666}, {"start": 2228.55, "end": 2228.89, "word": " شايفين", "probability": 0.9864501953125}, {"start": 2228.89, "end": 2229.05, "word": " ال", "probability": 0.9853515625}, {"start": 2229.05, "end": 2229.31, "word": " O", "probability": 0.462646484375}, {"start": 2229.31, "end": 2230.99, "word": " فيعني", "probability": 0.7572428385416666}, {"start": 2230.99, "end": 2231.55, "word": " بتصد", "probability": 0.9646809895833334}, {"start": 2231.55, "end": 2231.83, "word": " هي", "probability": 0.72265625}, {"start": 2231.83, "end": 2232.53, "word": " لكن", "probability": 0.64404296875}, {"start": 2232.53, "end": 2232.87, "word": " هذا", "probability": 0.94287109375}, {"start": 2232.87, "end": 2233.15, "word": " هو", "probability": 0.99755859375}], "temperature": 1.0}, {"id": 97, "seek": 225346, "start": 2235.68, "end": 2253.46, "text": "هذه تتراهيدروفيوران فانا مانجي أطلع هذا ولا ال carbon tetrachloride اه ال THF اللي هو التتراهيدروفيوران اكتر ليه؟ لأنه ال carbon tetrachloride non polar ككل هو non polar", "tokens": [3224, 24192, 6055, 2655, 23557, 3224, 25708, 32887, 5172, 1829, 13063, 7649, 6156, 7649, 995, 3714, 7649, 7435, 1829, 5551, 9566, 1211, 3615, 23758, 49429, 2423, 5954, 23319, 81, 608, 6746, 482, 1975, 3224, 2423, 3578, 37, 13672, 1829, 31439, 16712, 2655, 23557, 3224, 25708, 32887, 5172, 1829, 13063, 7649, 1975, 4117, 2655, 2288, 32239, 3224, 22807, 5296, 33456, 3224, 2423, 5954, 23319, 81, 608, 6746, 482, 2107, 12367, 9122, 28820, 31439, 2107, 12367], "avg_logprob": -0.3752083237965902, "compression_ratio": 1.6387096774193548, "no_speech_prob": 0.0, "words": [{"start": 2235.68, "end": 2236.0, "word": "هذه", "probability": 0.66015625}, {"start": 2236.0, "end": 2237.06, "word": " تتراهيدروفيوران", "probability": 0.6791015625}, {"start": 2237.06, "end": 2237.92, "word": " فانا", "probability": 0.3127034505208333}, {"start": 2237.92, "end": 2238.14, "word": " مانجي", "probability": 0.458251953125}, {"start": 2238.14, "end": 2238.64, "word": " أطلع", "probability": 0.78125}, {"start": 2238.64, "end": 2239.04, "word": " هذا", "probability": 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"probability": 0.6276041666666666}, {"start": 2248.88, "end": 2249.36, "word": " لأنه", "probability": 0.70751953125}, {"start": 2249.36, "end": 2249.8, "word": " ال", "probability": 0.88623046875}, {"start": 2249.8, "end": 2250.12, "word": " carbon", "probability": 0.93994140625}, {"start": 2250.12, "end": 2251.04, "word": " tetrachloride", "probability": 0.9466796875}, {"start": 2251.04, "end": 2251.48, "word": " non", "probability": 0.52587890625}, {"start": 2251.48, "end": 2252.04, "word": " polar", "probability": 0.693359375}, {"start": 2252.04, "end": 2252.62, "word": " ككل", "probability": 0.93310546875}, {"start": 2252.62, "end": 2252.8, "word": " هو", "probability": 0.78369140625}, {"start": 2252.8, "end": 2253.06, "word": " non", "probability": 0.8779296875}, {"start": 2253.06, "end": 2253.46, "word": " polar", "probability": 0.88916015625}], "temperature": 1.0}, {"id": 98, "seek": 227813, "start": 2254.99, "end": 2278.13, "text": "طيب نيجي نتطلع على السؤال نفس السؤال لكن بيسأل بيقول which compound in each pair will be more soluble in بنزين البنزين بتعرفوه هذا هو هذا منبولر طيب ايش اللي هيكون ضايق في البنزين اكتر ال cyclohexane ولا ال methanol هاي ال cyclohexane", "tokens": [9566, 1829, 3555, 8717, 1829, 7435, 1829, 8717, 2655, 9566, 1211, 3615, 15844, 21136, 33604, 6027, 8717, 36178, 21136, 33604, 6027, 44381, 4724, 1829, 3794, 10721, 1211, 4724, 1829, 39648, 597, 14154, 294, 1184, 6119, 486, 312, 544, 24807, 638, 294, 44945, 11622, 9957, 29739, 1863, 11622, 9957, 39894, 3615, 28480, 2407, 3224, 23758, 31439, 23758, 9154, 3555, 12610, 2288, 23032, 1829, 3555, 1975, 1829, 8592, 13672, 1829, 39896, 30544, 48812, 47302, 4587, 8978, 29739, 1863, 11622, 9957, 1975, 4117, 2655, 2288, 2423, 38154, 752, 675, 87, 1929, 49429, 2423, 1131, 35735, 8032, 47302, 2423, 38154, 752, 675, 87, 1929], "avg_logprob": -0.19368812589362117, "compression_ratio": 1.6090909090909091, "no_speech_prob": 0.0, "words": [{"start": 2254.99, "end": 2255.43, "word": "طيب", 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ليه؟ لأنه ايش اللي بيخلي ال solid solid؟", "tokens": [1211, 10721, 1975, 3224, 1975, 3224, 1975, 3224, 4724, 3794, 2423, 44422, 533, 33251, 2655, 37977, 9673, 20292, 19986, 3660, 6055, 3555, 34268, 3224, 1975, 4117, 26890, 1975, 3224, 2423, 50134, 533, 6055, 3794, 27884, 4032, 8608, 3555, 3615, 9957, 4032, 2423, 44422, 533, 3714, 10632, 4032, 8608, 3555, 27884, 4032, 6225, 46309, 9957, 6055, 4587, 16572, 3555, 995, 6156, 6027, 44422, 533, 1975, 4117, 2655, 2288, 1975, 1829, 8592, 20449, 1863, 7578, 22807, 4724, 16254, 1975, 2655, 15040, 5016, 19913, 14407, 11331, 26108, 3660, 4724, 16254, 1975, 2655, 15040, 5016, 19913, 14407, 11331, 26108, 3660, 11778, 16373, 15042, 2423, 6553, 544, 24807, 638, 813, 5100, 2423, 6553, 32239, 3224, 22807, 5296, 33456, 3224, 1975, 1829, 8592, 13672, 1829, 4724, 1829, 9778, 20292, 2423, 5100, 5100, 22807], "avg_logprob": -0.17529297387227416, "compression_ratio": 1.908256880733945, "no_speech_prob": 0.0, "words": [{"start": 2433.68, "end": 2434.6, "word": 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"text": "Solid بينما في الـ PR الـ dispersion force أقل وبالتالي صار Liquid الـ Liquid خلّيني أقول بسهولة بيدوب في الـ Liquid لأنه أنا بدي بعيد من الجزيئات ماقدرش ال Solid أنزع ال Solid يعني نفس ال energy أو نفس الطاقة اللي أنا بحتاجها للـ Liquid لأ ال Solid بده طاقة أكبر كتير علشان هيك بلاحظ أنه دائما في ال non polar solvents البرومين بدوب", "tokens": [50, 401, 327, 49374, 15042, 8978, 2423, 39184, 11568, 2423, 39184, 24631, 313, 3464, 5551, 4587, 1211, 46599, 6027, 2655, 6027, 1829, 20328, 9640, 38943, 2423, 39184, 38943, 16490, 1211, 11703, 9957, 1829, 5551, 39648, 4724, 3794, 3224, 12610, 3660, 4724, 25708, 37746, 8978, 2423, 39184, 38943, 5296, 33456, 3224, 41850, 4724, 16254, 45030, 25708, 9154, 25724, 11622, 1829, 19986, 9307, 19446, 28543, 2288, 8592, 2423, 26664, 14739, 11622, 3615, 2423, 26664, 37495, 22653, 8717, 36178, 2423, 2281, 34051, 8717, 36178, 41950, 995, 28671, 13672, 1829, 41850, 4724, 33753, 26108, 11296, 24976, 39184, 38943, 5296, 10721, 2423, 26664, 47525, 3224, 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"seek": 268774, "start": 2675.12, "end": 2687.74, "text": "فلجينا المتبقي مش ال nickel هذا اللي كان موجود حبيبات لأ لجيناه salt يعني ال nickel راح اتفاعل مع ال HCl و اعطان ال nickel كلورايد", "tokens": [5172, 1211, 7435, 1829, 8315, 9673, 2655, 3555, 38436, 37893, 2423, 30542, 23758, 13672, 1829, 25961, 3714, 29245, 23328, 11331, 21292, 3555, 9307, 5296, 10721, 5296, 7435, 1829, 8315, 3224, 5139, 37495, 22653, 2423, 30542, 12602, 39319, 1975, 2655, 5172, 995, 30241, 20449, 2423, 389, 9966, 4032, 1975, 3615, 9566, 7649, 2423, 30542, 9122, 1211, 13063, 995, 25708], "avg_logprob": -0.21610170097674353, "compression_ratio": 1.4482758620689655, "no_speech_prob": 0.0, "words": [{"start": 2675.12, "end": 2675.82, "word": "فلجينا", "probability": 0.7359375}, {"start": 2675.82, "end": 2676.64, "word": " المتبقي", "probability": 0.8763427734375}, {"start": 2676.64, "end": 2677.26, "word": " مش", "probability": 0.81591796875}, {"start": 2677.26, "end": 2677.88, "word": " ال", "probability": 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بيطلع أنها H2 هذا تفاعل في فرق بين التفاعل و ال solubility احنا في ال solubility بنتحدث عن physical process بنتكلمش عن تفاعلات فالذوبانية مش تفاعل", "tokens": [2407, 9566, 3555, 3615, 995, 5551, 12984, 1863, 16606, 16712, 5172, 995, 30241, 39894, 15040, 5016, 19913, 14739, 8978, 32771, 31377, 4724, 1829, 9566, 1211, 3615, 30767, 1829, 2423, 29062, 5296, 15042, 7251, 2655, 5172, 995, 30241, 20449, 2423, 389, 9966, 4724, 1829, 9566, 1211, 3615, 14739, 11296, 389, 17, 23758, 6055, 5172, 995, 30241, 8978, 6156, 2288, 4587, 49374, 16712, 5172, 995, 30241, 4032, 2423, 1404, 836, 1140, 1975, 5016, 8315, 8978, 2423, 1404, 836, 1140, 44945, 2655, 24401, 12984, 18871, 4001, 1399, 44945, 2655, 4117, 19528, 8592, 18871, 6055, 5172, 995, 30241, 9307, 6156, 6027, 8848, 37746, 7649, 10632, 37893, 6055, 5172, 995, 30241], "avg_logprob": -0.17917640465442267, "compression_ratio": 1.6839622641509433, "no_speech_prob": 0.0, "words": [{"start": 2688.3, "end": 2688.94, "word": "وطبعا", "probability": 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اكتر علشان هيك لما نيجوا يعملوا soft drink كولا مثلا", "tokens": [1211, 1211, 7435, 31377, 2423, 14641, 3321, 24976, 7435, 31377, 6156, 30543, 9673, 5016, 1211, 12610, 39894, 11622, 25708, 32545, 37746, 7649, 37495, 22653, 4724, 7435, 26890, 6024, 118, 31377, 16472, 3224, 7251, 3215, 37746, 1975, 4117, 2655, 2288, 4724, 7435, 26890, 6024, 118, 31377, 16472, 3224, 7251, 3215, 37746, 1975, 4117, 2655, 2288, 11203, 8592, 7649, 39896, 4117, 5296, 15042, 8717, 1829, 7435, 14407, 7251, 25957, 1211, 14407, 2787, 2822, 9122, 12610, 995, 50113, 15040], "avg_logprob": -0.17796266001540345, "compression_ratio": 1.6962025316455696, "no_speech_prob": 0.0, "words": [{"start": 2801.32, "end": 2802.06, "word": "للجاز", "probability": 0.623626708984375}, {"start": 2802.06, "end": 2802.48, "word": " ال", "probability": 0.3349609375}, {"start": 2802.48, "end": 2802.86, "word": " partial", "probability": 0.49609375}, {"start": 2802.86, "end": 2803.3, "word": " pressure", "probability": 0.94287109375}, 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"word": " لو", "probability": 0.89501953125}, {"start": 2869.89, "end": 2870.11, "word": " اجيت", "probability": 0.7262369791666666}, {"start": 2870.11, "end": 2870.63, "word": " اخدت", "probability": 0.840576171875}, {"start": 2870.63, "end": 2871.15, "word": " قلبة", "probability": 0.8468424479166666}, {"start": 2871.15, "end": 2871.59, "word": " الكولة", "probability": 0.88671875}], "temperature": 1.0}, {"id": 126, "seek": 289120, "start": 2872.34, "end": 2891.2, "text": "أو سخنتها انت كمان بيضل فيها الصودة؟ لأ بيضلش فيها كله بيهرب نعم صحيح ال solids و ال liquids لما بدنا نسخن بتدوب اكتر زي ما هنشوف بعد شوية طيب نتطلع على solubility of gases in solution بشكل اكبر شوية", "tokens": [10721, 2407, 8608, 9778, 29399, 11296, 16472, 2655, 9122, 2304, 7649, 4724, 1829, 11242, 1211, 8978, 11296, 31767, 23328, 3660, 22807, 5296, 10721, 4724, 1829, 11242, 1211, 8592, 8978, 11296, 28242, 3224, 4724, 1829, 3224, 25513, 8717, 25957, 20328, 5016, 1829, 5016, 2423, 38536, 4032, 2423, 38960, 5296, 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{"start": 2901.58, "end": 2901.74, "word": " the", "probability": 0.88818359375}, {"start": 2901.74, "end": 2902.02, "word": " gas", "probability": 0.90625}, {"start": 2902.02, "end": 2902.58, "word": " ليه؟", "probability": 0.708984375}, {"start": 2902.58, "end": 2902.72, "word": " يعني", "probability": 0.9013671875}, {"start": 2902.72, "end": 2903.06, "word": " ..", "probability": 0.47509765625}, {"start": 2903.06, "end": 2905.42, "word": " يعني", "probability": 0.864013671875}, {"start": 2905.42, "end": 2905.64, "word": " هذه", "probability": 0.65283203125}, {"start": 2905.64, "end": 2906.56, "word": " ملاحظة", "probability": 0.9890625}, {"start": 2906.56, "end": 2907.68, "word": " بالنسبة", "probability": 0.979248046875}, {"start": 2907.68, "end": 2908.38, "word": " إلينا", "probability": 0.74072265625}, {"start": 2908.38, "end": 2908.8, "word": " أن", "probability": 0.375}, {"start": 2908.8, "end": 2909.04, "word": " ال", "probability": 0.607421875}, {"start": 2909.04, "end": 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الارجون 40 واحد و نص الكريبتون 84 اتنين و تسعة و سبعين فلاحظنا انه كل ما كان ال molecular mass للغاز اكبر كل ما زادت ال solubility دي اول ملاحظة الملاحظة التانية طب هدول اتنين لهم نفس ال", "tokens": [9778, 20292, 8315, 9154, 2423, 39184, 3002, 2423, 39184, 422, 17, 2423, 39184, 19046, 2758, 8858, 20193, 5016, 19913, 8315, 16472, 3224, 6055, 4587, 16572, 3555, 995, 48812, 25513, 2655, 8978, 568, 502, 13, 12625, 37550, 3279, 43516, 119, 18, 2423, 9640, 7435, 11536, 3356, 36764, 24401, 4032, 8717, 9381, 33251, 16572, 3555, 2655, 11536, 29018, 1975, 2655, 1863, 9957, 4032, 6055, 3794, 27884, 4032, 8608, 3555, 3615, 9957, 6156, 15040, 5016, 19913, 8315, 16472, 3224, 28242, 19446, 25961, 2423, 19046, 2758, 24976, 17082, 31377, 1975, 4117, 26890, 28242, 19446, 30767, 18513, 2655, 2423, 1404, 836, 1140, 11778, 1829, 1975, 12610, 3714, 15040, 5016, 19913, 3660, 9673, 15040, 5016, 19913, 3660, 16712, 7649, 10632, 23032, 3555, 8032, 3215, 12610, 1975, 2655, 1863, 9957, 5296, 16095, 8717, 36178, 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solubility .. أغيرت الضغط بقدر أشوف ال solubility مثلا عندي solubility معينة عن ضغط معين طبعا ضغط جديد جديش ال solubility بقدر أحسبها هذا المقصود من هذا القانون الحرارة لأ", "tokens": [38, 13672, 1829, 31439, 48812, 17082, 9566, 6024, 118, 31377, 412, 4188, 502, 15844, 48812, 17082, 9566, 6024, 118, 31377, 412, 4188, 568, 37495, 22653, 45164, 32771, 13546, 2655, 50113, 15040, 11778, 47341, 3660, 21542, 2288, 9640, 3660, 4724, 28543, 2288, 16070, 43761, 5551, 8592, 38688, 2423, 1404, 836, 1140, 4386, 5551, 17082, 13546, 2655, 6024, 114, 17082, 9566, 4724, 28543, 2288, 5551, 8592, 38688, 2423, 1404, 836, 1140, 50113, 15040, 18871, 16254, 1404, 836, 1140, 20449, 9957, 3660, 18871, 48812, 17082, 9566, 20449, 9957, 23032, 3555, 3615, 995, 48812, 17082, 9566, 10874, 16254, 3215, 10874, 16254, 8592, 2423, 1404, 836, 1140, 4724, 28543, 2288, 5551, 5016, 35457, 11296, 23758, 9673, 4587, 9381, 23328, 9154, 23758, 25062, 7649, 11536, 21542, 2288, 9640, 3660, 5296, 10721], "avg_logprob": 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"probability": 0.8065185546875}, {"start": 3603.69, "end": 3604.17, "word": " الجوي", "probability": 0.882568359375}], "temperature": 1.0}, {"id": 157, "seek": 362928, "start": 3605.68, "end": 3629.28, "text": "هذا شكله يبين الـ ozone solubility مع الحرارة، لاحظوا at high temperature في عندى شوية جزيئات ozone بينما at low temperature عدد الجزيئات بيزيد بشكل كبير وهذا كلام احنا يعني لازم نتوقعه الآن هذا ما يتعلق بال solubility", "tokens": [3224, 15730, 13412, 28820, 3224, 7251, 3555, 9957, 2423, 39184, 46769, 1404, 836, 1140, 20449, 21542, 2288, 9640, 3660, 12399, 20193, 5016, 19913, 14407, 412, 1090, 4292, 8978, 43242, 7578, 13412, 2407, 10632, 10874, 11622, 1829, 19986, 9307, 46769, 49374, 15042, 412, 2295, 4292, 6225, 3215, 3215, 25724, 11622, 1829, 19986, 9307, 4724, 1829, 11622, 25708, 4724, 8592, 28820, 9122, 3555, 13546, 37037, 15730, 28242, 10943, 1975, 5016, 8315, 37495, 22653, 5296, 31377, 2304, 8717, 2655, 30543, 3615, 3224, 6024, 48506, 23758, 19446, 7251, 2655, 30241, 4587, 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"end": 3802.18, "word": " أربعين", "probability": 0.93896484375}, {"start": 3802.18, "end": 3802.32, "word": " في", "probability": 0.8828125}, {"start": 3802.32, "end": 3802.58, "word": " مية", "probability": 0.92626953125}, {"start": 3802.58, "end": 3803.38, "word": " خمسة", "probability": 0.9571533203125}, {"start": 3803.38, "end": 3803.64, "word": " و", "probability": 0.9267578125}, {"start": 3803.64, "end": 3803.9, "word": " واحد", "probability": 0.951171875}, {"start": 3803.9, "end": 3804.04, "word": " من", "probability": 0.97802734375}, {"start": 3804.04, "end": 3804.32, "word": " عشرة", "probability": 0.8963216145833334}, {"start": 3804.32, "end": 3804.48, "word": " في", "probability": 0.921875}, {"start": 3804.48, "end": 3805.0, "word": " المية", "probability": 0.94921875}, {"start": 3805.0, "end": 3805.24, "word": " هذا", "probability": 0.78857421875}, {"start": 3805.24, "end": 3805.64, "word": " بنقوله", "probability": 0.64013671875}, {"start": 3805.64, "end": 3805.94, "word": " mass", "probability": 0.86572265625}, {"start": 3805.94, "end": 3806.6, "word": " Pearson", "probability": 0.97216796875}, {"start": 3806.6, "end": 3807.7, "word": " طيب", "probability": 0.9459635416666666}], "temperature": 1.0}, {"id": 165, "seek": 381709, "start": 3809.83, "end": 3817.09, "text": "في حاجة بيقولها Mass Fraction الـ Mass Fraction هي عبارة عن .. يعني زي ال mass person، ال person مش بدروه في مية", "tokens": [41185, 11331, 26108, 3660, 4724, 1829, 39648, 11296, 10482, 1526, 2894, 2423, 39184, 10482, 1526, 2894, 39896, 6225, 3555, 9640, 3660, 18871, 4386, 37495, 22653, 30767, 1829, 2423, 2758, 954, 12399, 2423, 954, 37893, 47525, 32887, 3224, 8978, 3714, 10632], "avg_logprob": -0.4569359814248434, "compression_ratio": 1.2403100775193798, "no_speech_prob": 0.0, "words": [{"start": 3809.83, "end": 3810.03, "word": "في", "probability": 0.2432861328125}, {"start": 3810.03, "end": 3810.25, "word": " حاجة", "probability": 0.9490559895833334}, {"start": 3810.25, "end": 3810.57, "word": " بيقولها", "probability": 0.733734130859375}, {"start": 3810.57, "end": 3810.77, "word": " Mass", "probability": 0.27734375}, {"start": 3810.77, "end": 3811.37, "word": " Fraction", "probability": 0.651611328125}, {"start": 3811.37, "end": 3812.53, "word": " الـ", "probability": 0.4312744140625}, {"start": 3812.53, "end": 3812.69, "word": " Mass", "probability": 0.783203125}, {"start": 3812.69, "end": 3813.27, "word": " Fraction", "probability": 0.900146484375}, {"start": 3813.27, "end": 3813.81, "word": " هي", "probability": 0.91552734375}, {"start": 3813.81, "end": 3814.29, "word": " عبارة", "probability": 0.992431640625}, {"start": 3814.29, "end": 3814.61, "word": " عن", "probability": 0.994140625}, {"start": 3814.61, "end": 3815.03, "word": " ..", "probability": 0.2247314453125}, {"start": 3815.03, "end": 3815.37, "word": " يعني", "probability": 0.70068359375}, {"start": 3815.37, "end": 3815.53, "word": " زي", "probability": 0.98583984375}, {"start": 3815.53, "end": 3815.63, "word": " ال", "probability": 0.9599609375}, {"start": 3815.63, "end": 3815.79, "word": " mass", "probability": 0.2861328125}, {"start": 3815.79, "end": 3816.19, "word": " person،", "probability": 0.32977294921875}, {"start": 3816.19, "end": 3816.27, "word": " ال", "probability": 0.55419921875}, {"start": 3816.27, "end": 3816.31, "word": " person", "probability": 0.4228515625}, {"start": 3816.31, "end": 3816.47, "word": " مش", "probability": 0.88037109375}, {"start": 3816.47, "end": 3816.73, "word": " بدروه", "probability": 0.51953125}, {"start": 3816.73, "end": 3816.81, "word": " في", "probability": 0.9228515625}, {"start": 3816.81, "end": 3817.09, "word": " مية", "probability": 0.69677734375}], "temperature": 1.0}, {"id": 166, "seek": 384818, "start": 3818.64, "end": 3848.18, "text": "mass fraction لماس يعني عبارة عن fraction مش percent فبنقول ال mass fraction لإيه؟ هي عبارة عن اجرام من إيه على الإجرام solution وهذا عبارة عن كسر هذا هو ال fraction fraction يعني كسر fraction كسر فبقول for example a solution containing 12 gram methanol and 38 gram water has الmass fraction من الميثانول 12 على المحلول كله 50.24", "tokens": [47386, 14135, 5296, 15042, 3794, 37495, 22653, 6225, 3555, 9640, 3660, 18871, 14135, 37893, 3043, 6156, 3555, 1863, 39648, 2423, 2758, 14135, 5296, 28814, 1829, 3224, 22807, 39896, 6225, 3555, 9640, 3660, 18871, 1975, 7435, 2288, 10943, 9154, 11933, 1829, 3224, 15844, 33688, 7435, 2288, 10943, 3827, 37037, 15730, 6225, 3555, 9640, 3660, 18871, 9122, 3794, 2288, 23758, 31439, 2423, 14135, 14135, 37495, 22653, 9122, 3794, 2288, 14135, 9122, 3794, 2288, 6156, 3555, 39648, 337, 1365, 257, 3827, 19273, 2272, 21353, 1131, 35735, 293, 12843, 21353, 1281, 575, 2423, 47386, 14135, 9154, 9673, 1829, 12984, 7649, 12610, 2272, 15844, 9673, 5016, 1211, 12610, 28242, 3224, 2625, 13, 7911], "avg_logprob": -0.32396789428290973, "compression_ratio": 1.792828685258964, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 3818.64, "end": 3818.94, "word": "mass", "probability": 0.3837890625}, {"start": 3818.94, "end": 3819.52, "word": " fraction", "probability": 0.50927734375}, {"start": 3819.52, "end": 3820.32, "word": " لماس", "probability": 0.54583740234375}, {"start": 3820.32, "end": 3820.74, "word": " يعني", "probability": 0.512908935546875}, {"start": 3820.74, "end": 3821.02, "word": " عبارة", "probability": 0.7303314208984375}, {"start": 3821.02, "end": 3821.18, "word": " عن", "probability": 0.99609375}, {"start": 3821.18, "end": 3821.62, "word": " fraction", "probability": 0.39404296875}, {"start": 3821.62, "end": 3822.14, "word": " مش", "probability": 0.227294921875}, {"start": 3822.14, "end": 3822.7, "word": " percent", "probability": 0.82080078125}, {"start": 3822.7, "end": 3823.48, "word": " فبنقول", "probability": 0.7684326171875}, {"start": 3823.48, "end": 3823.62, "word": " ال", "probability": 0.7578125}, {"start": 3823.62, "end": 3823.8, "word": " mass", "probability": 0.5322265625}, {"start": 3823.8, "end": 3824.38, "word": " fraction", "probability": 0.87158203125}, {"start": 3824.38, "end": 3825.44, "word": " لإيه؟", "probability": 0.789111328125}, {"start": 3825.44, "end": 3825.56, "word": " هي", "probability": 0.292236328125}, {"start": 3825.56, "end": 3825.84, "word": " عبارة", "probability": 0.992431640625}, {"start": 3825.84, "end": 3826.06, "word": " عن", "probability": 0.978515625}, {"start": 3826.06, "end": 3826.64, "word": " اجرام", "probability": 0.88330078125}, {"start": 3826.64, "end": 3827.1, "word": " من", "probability": 0.9072265625}, {"start": 3827.1, "end": 3827.68, "word": " إيه", "probability": 0.7989908854166666}, {"start": 3827.68, "end": 3827.94, "word": " على", "probability": 0.498291015625}, {"start": 3827.94, "end": 3828.4, "word": " الإجرام", "probability": 0.82635498046875}, {"start": 3828.4, "end": 3829.02, "word": " solution", "probability": 0.5341796875}, {"start": 3829.02, "end": 3829.62, "word": " وهذا", "probability": 0.69580078125}, {"start": 3829.62, "end": 3829.94, "word": " عبارة", "probability": 0.9888916015625}, {"start": 3829.94, "end": 3830.4, "word": " عن", "probability": 0.99267578125}, {"start": 3830.4, "end": 3830.94, "word": " كسر", "probability": 0.6066080729166666}, {"start": 3830.94, "end": 3831.54, "word": " هذا", "probability": 0.403076171875}, {"start": 3831.54, "end": 3831.68, "word": " هو", "probability": 0.8916015625}, {"start": 3831.68, "end": 3831.78, "word": " ال", "probability": 0.479248046875}, {"start": 3831.78, "end": 3832.26, "word": " fraction", "probability": 0.93798828125}, {"start": 3832.26, "end": 3833.02, "word": " fraction", "probability": 0.33251953125}, {"start": 3833.02, "end": 3833.3, "word": " يعني", "probability": 0.98046875}, {"start": 3833.3, "end": 3834.04, "word": " كسر", "probability": 0.9788411458333334}, {"start": 3834.04, "end": 3834.96, "word": " fraction", "probability": 0.4814453125}, {"start": 3834.96, "end": 3835.46, "word": " كسر", "probability": 0.9091796875}, {"start": 3835.46, "end": 3836.0, "word": " فبقول", "probability": 0.9143880208333334}, {"start": 3836.0, "end": 3836.2, "word": " for", "probability": 0.42138671875}, {"start": 3836.2, "end": 3836.62, "word": " example", "probability": 0.96435546875}, {"start": 3836.62, "end": 3836.8, "word": " a", "probability": 0.2335205078125}, {"start": 3836.8, "end": 3837.16, "word": " solution", "probability": 0.9599609375}, {"start": 3837.16, "end": 3838.0, "word": " containing", "probability": 0.8994140625}, {"start": 3838.0, "end": 3838.66, "word": " 12", "probability": 0.62890625}, {"start": 3838.66, "end": 3839.0, "word": " gram", "probability": 0.62158203125}, {"start": 3839.0, "end": 3839.42, "word": " methanol", "probability": 0.81787109375}, {"start": 3839.42, "end": 3839.68, "word": " and", "probability": 0.87841796875}, {"start": 3839.68, "end": 3840.16, "word": " 38", "probability": 0.978515625}, {"start": 3840.16, "end": 3840.68, "word": " gram", "probability": 0.88037109375}, {"start": 3840.68, "end": 3841.44, "word": " water", "probability": 0.900390625}, {"start": 3841.44, "end": 3842.12, "word": " has", "probability": 0.8623046875}, {"start": 3842.12, "end": 3842.74, "word": " الmass", "probability": 0.596435546875}, {"start": 3842.74, "end": 3843.2, "word": " fraction", "probability": 0.87548828125}, {"start": 3843.2, "end": 3843.46, "word": " من", "probability": 0.9912109375}, {"start": 3843.46, "end": 3844.1, "word": " الميثانول", "probability": 0.89111328125}, {"start": 3844.1, "end": 3844.94, "word": " 12", "probability": 0.63037109375}, {"start": 3844.94, "end": 3845.38, "word": " على", "probability": 0.6748046875}, {"start": 3845.38, "end": 3846.02, "word": " المحلول", "probability": 0.975830078125}, {"start": 3846.02, "end": 3846.48, "word": " كله", "probability": 0.9677734375}, {"start": 3846.48, "end": 3847.24, "word": " 50", "probability": 0.8984375}, {"start": 3847.24, "end": 3848.18, "word": ".24", "probability": 0.919921875}], "temperature": 1.0}, {"id": 167, "seek": 387266, "start": 3849.84, "end": 3872.66, "text": "كويس طب ال mass fraction للمياه جال تمانية وتلاتين جرام مياه على ال total solution grams او ال mass يعني فبيعطيني point seven six لحظة ان ال fractions دائما بتكمل لواحد مجموعة ال fractions دائما هي عبارة عن واحد صحية", "tokens": [4117, 45865, 3794, 23032, 3555, 2423, 2758, 14135, 5296, 19528, 1829, 40294, 10874, 6027, 6055, 2304, 7649, 10632, 34683, 1211, 9307, 9957, 10874, 2288, 10943, 3714, 1829, 40294, 15844, 2423, 3217, 3827, 11899, 1975, 2407, 2423, 2758, 37495, 22653, 6156, 21292, 3615, 9566, 9957, 1829, 935, 3407, 2309, 5296, 5016, 19913, 3660, 16472, 2423, 36058, 11778, 16373, 15042, 39894, 24793, 1211, 5296, 14407, 24401, 3714, 7435, 2304, 2407, 27884, 2423, 36058, 11778, 16373, 15042, 39896, 6225, 3555, 9640, 3660, 18871, 36764, 24401, 20328, 5016, 10632], "avg_logprob": -0.24563952760640964, "compression_ratio": 1.6237623762376239, "no_speech_prob": 0.0, "words": [{"start": 3849.84, "end": 3850.38, "word": "كويس", "probability": 0.65533447265625}, {"start": 3850.38, "end": 3851.26, "word": " طب", "probability": 0.5509033203125}, {"start": 3851.26, "end": 3851.44, "word": " ال", "probability": 0.2012939453125}, {"start": 3851.44, "end": 3851.66, "word": " mass", "probability": 0.5576171875}, {"start": 3851.66, "end": 3852.24, "word": " fraction", "probability": 0.7763671875}, {"start": 3852.24, "end": 3853.04, "word": " للمياه", "probability": 0.730224609375}, {"start": 3853.04, "end": 3853.38, "word": " جال", "probability": 0.882080078125}, {"start": 3853.38, "end": 3853.78, "word": " تمانية", "probability": 0.8289794921875}, {"start": 3853.78, "end": 3854.28, "word": " وتلاتين", "probability": 0.8736572265625}, {"start": 3854.28, "end": 3854.58, "word": " جرام", "probability": 0.8611653645833334}, {"start": 3854.58, "end": 3854.98, "word": " مياه", "probability": 0.7921549479166666}, {"start": 3854.98, "end": 3855.46, "word": " على", "probability": 0.7998046875}, {"start": 3855.46, "end": 3856.5, "word": " ال", "probability": 0.93310546875}, {"start": 3856.5, "end": 3856.88, "word": " total", "probability": 0.857421875}, {"start": 3856.88, "end": 3858.04, "word": " solution", "probability": 0.884765625}, {"start": 3858.04, "end": 3859.24, "word": " grams", "probability": 0.55029296875}, {"start": 3859.24, "end": 3859.44, "word": " او", "probability": 0.83837890625}, {"start": 3859.44, "end": 3859.58, "word": " ال", "probability": 0.9326171875}, {"start": 3859.58, "end": 3859.88, "word": " mass", "probability": 0.6513671875}, {"start": 3859.88, "end": 3860.3, "word": " يعني", "probability": 0.89599609375}, {"start": 3860.3, "end": 3861.52, "word": " فبيعطيني", "probability": 0.7750244140625}, {"start": 3861.52, "end": 3862.4, "word": " point", "probability": 0.9189453125}, {"start": 3862.4, "end": 3862.7, "word": " seven", "probability": 0.767578125}, {"start": 3862.7, "end": 3863.08, "word": " six", "probability": 0.94873046875}, {"start": 3863.08, "end": 3863.64, "word": " لحظة", "probability": 0.8695068359375}, {"start": 3863.64, "end": 3863.76, "word": " ان", "probability": 0.75927734375}, {"start": 3863.76, "end": 3863.88, "word": " ال", "probability": 0.8330078125}, {"start": 3863.88, "end": 3864.38, "word": " fractions", "probability": 0.87548828125}, {"start": 3864.38, "end": 3864.96, "word": " دائما", "probability": 0.9099934895833334}, {"start": 3864.96, "end": 3866.32, "word": " بتكمل", "probability": 0.96728515625}, {"start": 3866.32, "end": 3867.18, "word": " لواحد", "probability": 0.8517252604166666}, {"start": 3867.18, "end": 3868.36, "word": " مجموعة", "probability": 0.87724609375}, {"start": 3868.36, "end": 3868.48, "word": " ال", "probability": 0.8916015625}, {"start": 3868.48, "end": 3869.04, "word": " fractions", "probability": 0.89892578125}, {"start": 3869.04, "end": 3869.82, "word": " دائما", "probability": 0.7718912760416666}, {"start": 3869.82, "end": 3870.14, "word": " هي", "probability": 0.61181640625}, {"start": 3870.14, "end": 3870.46, "word": " عبارة", "probability": 0.985107421875}, {"start": 3870.46, "end": 3870.74, "word": " عن", "probability": 0.99169921875}, {"start": 3870.74, "end": 3871.64, "word": " واحد", "probability": 0.990478515625}, {"start": 3871.64, "end": 3872.66, "word": " صحية", "probability": 0.9462890625}], "temperature": 1.0}, {"id": 168, "seek": 390428, "start": 3876.66, "end": 3904.28, "text": "لو قال لي نفس السؤال الماضي ايه ال solution بين 12 gram methanol او 38 gram water؟ find the mass percent of each بسيطة كتير ال mass percent methanol 12 على 50 اللي هو ال total في 100 من 100 24 و ال mass percent من 100 38 على 50 في 100 بس ضربنا في 100 76 و طبعا مجموع ال mass percentage دائما 100 في 100 لمجموع ال fractions واحد فضربناها في 100 يعني صارت 100", "tokens": [1211, 2407, 50239, 32239, 8717, 36178, 21136, 33604, 6027, 9673, 46958, 1829, 1975, 1829, 3224, 2423, 3827, 49374, 2272, 21353, 1131, 35735, 1975, 2407, 12843, 21353, 1281, 22807, 915, 264, 2758, 3043, 295, 1184, 4724, 3794, 1829, 9566, 3660, 9122, 2655, 13546, 2423, 2758, 3043, 1131, 35735, 2272, 15844, 2625, 13672, 1829, 31439, 2423, 3217, 8978, 2319, 9154, 2319, 4022, 4032, 2423, 2758, 3043, 9154, 2319, 12843, 15844, 2625, 8978, 2319, 4724, 3794, 48812, 25513, 8315, 8978, 2319, 24733, 4032, 23032, 3555, 3615, 995, 3714, 7435, 2304, 45367, 2423, 2758, 9668, 11778, 16373, 15042, 2319, 8978, 2319, 5296, 2304, 7435, 2304, 45367, 2423, 36058, 36764, 24401, 6156, 11242, 25513, 8315, 11296, 8978, 2319, 37495, 22653, 20328, 9640, 2655, 2319], "avg_logprob": -0.2524739479025205, "compression_ratio": 1.76, "no_speech_prob": 0.0, "words": [{"start": 3876.66, "end": 3877.0, "word": "لو", "probability": 0.6602783203125}, {"start": 3877.0, "end": 3877.2, "word": " قال", "probability": 0.916015625}, {"start": 3877.2, "end": 3877.44, "word": " لي", "probability": 0.45166015625}, {"start": 3877.44, "end": 3877.78, "word": " نفس", "probability": 0.9501953125}, {"start": 3877.78, "end": 3878.16, "word": " السؤال", "probability": 0.9962565104166666}, {"start": 3878.16, "end": 3878.72, "word": " الماضي", "probability": 0.9075520833333334}, {"start": 3878.72, "end": 3879.1, "word": " ايه", "probability": 0.6894938151041666}, {"start": 3879.1, "end": 3879.14, "word": " ال", "probability": 0.6376953125}, {"start": 3879.14, "end": 3879.4, "word": " solution", "probability": 0.82421875}, {"start": 3879.4, "end": 3879.6, "word": " بين", "probability": 0.1541748046875}, {"start": 3879.6, "end": 3879.9, "word": " 12", "probability": 0.60693359375}, {"start": 3879.9, "end": 3880.16, "word": " gram", "probability": 0.5224609375}, {"start": 3880.16, "end": 3880.56, "word": " methanol", "probability": 0.7349853515625}, {"start": 3880.56, "end": 3880.68, "word": " او", "probability": 0.655517578125}, {"start": 3880.68, "end": 3881.06, "word": " 38", "probability": 0.9384765625}, {"start": 3881.06, "end": 3881.54, "word": " gram", "probability": 0.955078125}, {"start": 3881.54, "end": 3882.3, "word": " water؟", "probability": 0.71630859375}, {"start": 3882.3, "end": 3882.46, "word": " find", "probability": 0.5048828125}, {"start": 3882.46, "end": 3882.64, "word": " the", "probability": 0.91357421875}, {"start": 3882.64, "end": 3882.8, "word": " mass", "probability": 0.9111328125}, {"start": 3882.8, "end": 3883.3, "word": " percent", "probability": 0.896484375}, {"start": 3883.3, "end": 3883.5, "word": " of", "probability": 0.97509765625}, {"start": 3883.5, "end": 3883.9, "word": " each", "probability": 0.9638671875}, {"start": 3883.9, "end": 3885.16, "word": " بسيطة", "probability": 0.92734375}, {"start": 3885.16, "end": 3885.38, "word": " كتير", "probability": 0.9510091145833334}, {"start": 3885.38, "end": 3885.6, "word": " ال", "probability": 0.72998046875}, {"start": 3885.6, "end": 3885.86, "word": " mass", "probability": 0.7861328125}, {"start": 3885.86, "end": 3886.32, "word": " percent", "probability": 0.970703125}, {"start": 3886.32, "end": 3886.8, "word": " methanol", "probability": 0.666748046875}, {"start": 3886.8, "end": 3887.36, "word": " 12", "probability": 0.7197265625}, {"start": 3887.36, "end": 3887.76, "word": " على", "probability": 0.438720703125}, {"start": 3887.76, "end": 3888.28, "word": " 50", "probability": 0.912109375}, {"start": 3888.28, "end": 3888.56, "word": " اللي", "probability": 0.915771484375}, {"start": 3888.56, "end": 3888.66, "word": " هو", "probability": 0.49951171875}, {"start": 3888.66, "end": 3888.76, "word": " ال", "probability": 0.95458984375}, {"start": 3888.76, "end": 3889.12, "word": " total", "probability": 0.818359375}, {"start": 3889.12, "end": 3889.54, "word": " في", "probability": 0.7998046875}, {"start": 3889.54, "end": 3889.72, "word": " 100", "probability": 0.7841796875}, {"start": 3889.72, "end": 3889.9, "word": " من", "probability": 0.97998046875}, {"start": 3889.9, "end": 3890.28, "word": " 100", "probability": 0.8505859375}, {"start": 3890.28, "end": 3890.94, "word": " 24", 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{"start": 3895.3, "end": 3895.68, "word": " ضربنا", "probability": 0.970703125}, {"start": 3895.68, "end": 3895.8, "word": " في", "probability": 0.9111328125}, {"start": 3895.8, "end": 3896.1, "word": " 100", "probability": 0.7880859375}, {"start": 3896.1, "end": 3897.14, "word": " 76", "probability": 0.385498046875}, {"start": 3897.14, "end": 3897.62, "word": " و", "probability": 0.9140625}, {"start": 3897.62, "end": 3897.94, "word": " طبعا", "probability": 0.90380859375}, {"start": 3897.94, "end": 3898.42, "word": " مجموع", "probability": 0.8519287109375}, {"start": 3898.42, "end": 3898.56, "word": " ال", "probability": 0.94775390625}, {"start": 3898.56, "end": 3898.76, "word": " mass", "probability": 0.91162109375}, {"start": 3898.76, "end": 3899.32, "word": " percentage", "probability": 0.79931640625}, {"start": 3899.32, "end": 3899.84, "word": " دائما", "probability": 0.8990885416666666}, {"start": 3899.84, "end": 3900.38, "word": " 100", "probability": 0.82666015625}, {"start": 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{"id": 169, "seek": 393261, "start": 3905.31, "end": 3932.61, "text": "في عندي كمان مصطلحين للتعبير عن التركيز مصطلح بنقوله part per million و مصطلح بنقوله part per billion واحد في المليون و واحد في الألف مليون بليون يعني فال part per million ppm من مادة a هو عبارة عن ال mass ل a باليجرام على ال mass solution باليجرام مضروبة في عشر أقل ستة", "tokens": [41185, 18871, 16254, 9122, 2304, 7649, 3714, 9381, 9566, 1211, 5016, 9957, 24976, 2655, 3615, 3555, 13546, 18871, 16712, 31747, 1829, 11622, 3714, 9381, 9566, 1211, 5016, 44945, 39648, 3224, 644, 680, 2459, 4032, 3714, 9381, 9566, 1211, 5016, 44945, 39648, 3224, 644, 680, 5218, 36764, 24401, 8978, 9673, 20292, 11536, 4032, 36764, 24401, 8978, 16247, 46538, 3714, 20292, 11536, 4724, 20292, 11536, 37495, 22653, 6156, 6027, 644, 680, 2459, 280, 14395, 9154, 3714, 18513, 3660, 257, 31439, 6225, 3555, 9640, 3660, 18871, 2423, 2758, 5296, 257, 20666, 1829, 7435, 2288, 10943, 15844, 2423, 2758, 3827, 20666, 1829, 7435, 2288, 10943, 3714, 11242, 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"word": " PPP", "probability": 0.963623046875}, {"start": 4064.0, "end": 4064.34, "word": " مافيش", "probability": 0.8372395833333334}, {"start": 4064.34, "end": 4064.7, "word": " أبسط", "probability": 0.9805908203125}, {"start": 4064.7, "end": 4064.86, "word": " من", "probability": 0.994140625}, {"start": 4064.86, "end": 4065.22, "word": " هيك", "probability": 0.916748046875}, {"start": 4065.22, "end": 4065.72, "word": " بسيط", "probability": 0.9854736328125}, {"start": 4065.72, "end": 4066.48, "word": " للغاية", "probability": 0.95263671875}, {"start": 4066.48, "end": 4067.66, "word": " طيب", "probability": 0.9640299479166666}], "temperature": 1.0}, {"id": 177, "seek": 409384, "start": 4068.24, "end": 4093.84, "text": "زي ما شوفنا ال mass per cent بدنا نشوف ال mass fraction بدنا نشوف حياتنا و نقولها المولي fraction المولي fraction برضه fraction معناته كسر طيب المولي fraction من ايه جال عدد مولات ايه على ال total number of moles عدد مولات ايه على ال total number هذا بيعطينا الكسر تبع ايه", "tokens": [11622, 1829, 19446, 13412, 38688, 8315, 2423, 2758, 680, 1489, 47525, 8315, 8717, 8592, 38688, 2423, 2758, 14135, 47525, 8315, 8717, 8592, 38688, 11331, 1829, 9307, 8315, 4032, 8717, 39648, 11296, 9673, 12610, 1829, 14135, 9673, 12610, 1829, 14135, 4724, 43042, 3224, 14135, 20449, 8315, 47395, 9122, 3794, 2288, 23032, 1829, 3555, 9673, 12610, 1829, 14135, 9154, 1975, 1829, 3224, 10874, 6027, 6225, 3215, 3215, 3714, 12610, 9307, 1975, 1829, 3224, 15844, 2423, 3217, 1230, 295, 34286, 6225, 3215, 3215, 3714, 12610, 9307, 1975, 1829, 3224, 15844, 2423, 3217, 1230, 23758, 4724, 1829, 3615, 9566, 1829, 8315, 33251, 3794, 2288, 6055, 3555, 3615, 1975, 1829, 3224], "avg_logprob": -0.21626751862953755, "compression_ratio": 2.1191709844559585, "no_speech_prob": 0.0, "words": [{"start": 4068.24, "end": 4068.6, "word": "زي", "probability": 0.783447265625}, {"start": 4068.6, "end": 4068.7, "word": " ما", "probability": 0.9482421875}, {"start": 4068.7, "end": 4069.16, "word": " 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"end": 4294.34, "word": " ان", "probability": 0.406005859375}, {"start": 4294.34, "end": 4295.16, "word": " يعني", "probability": 0.748046875}], "temperature": 1.0}, {"id": 187, "seek": 432370, "start": 4297.88, "end": 4323.7, "text": "فاطبقات كتيرة في هذا ال chapter جبت لكم انا هذا من كتاب يعني بيقول عندي ماس سبعة و تمانية سوديوم صلفية الماس عندي سبعة و تمانية جرام و الحجم متين و خمسة و عشرين عايز يحسب ال molarity انا بعرف ال molarity بتساوي ال mol على ال letter من ال solution حلو كتير قدر المولات سبعة و تمانية", "tokens": [5172, 41193, 3555, 4587, 9307, 9122, 2655, 48923, 8978, 23758, 2423, 7187, 10874, 3555, 2655, 5296, 24793, 1975, 8315, 23758, 9154, 9122, 2655, 16758, 37495, 22653, 4724, 1829, 39648, 18871, 16254, 3714, 32277, 8608, 3555, 27884, 4032, 46811, 7649, 10632, 8608, 23328, 1829, 20498, 20328, 46538, 10632, 9673, 32277, 18871, 16254, 8608, 3555, 27884, 4032, 46811, 7649, 10632, 10874, 2288, 10943, 4032, 21542, 7435, 2304, 44650, 9957, 4032, 16490, 2304, 3794, 3660, 4032, 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0.9051513671875}, {"start": 4317.02, "end": 4317.48, "word": " ال", "probability": 0.6025390625}, {"start": 4317.48, "end": 4317.88, "word": " mol", "probability": 0.79931640625}, {"start": 4317.88, "end": 4318.8, "word": " على", "probability": 0.57177734375}, {"start": 4318.8, "end": 4319.32, "word": " ال", "probability": 0.908203125}, {"start": 4319.32, "end": 4319.6, "word": " letter", "probability": 0.4296875}, {"start": 4319.6, "end": 4319.88, "word": " من", "probability": 0.99560546875}, {"start": 4319.88, "end": 4320.04, "word": " ال", "probability": 0.83154296875}, {"start": 4320.04, "end": 4320.6, "word": " solution", "probability": 0.9853515625}, {"start": 4320.6, "end": 4321.24, "word": " حلو", "probability": 0.9871419270833334}, {"start": 4321.24, "end": 4321.54, "word": " كتير", "probability": 0.9816080729166666}, {"start": 4321.54, "end": 4321.96, "word": " قدر", "probability": 0.8759765625}, {"start": 4321.96, "end": 4322.52, "word": " المولات", "probability": 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20666, 9566, 3555, 3615, 37495, 22653, 4032, 44945, 7435, 1829, 3555, 2423, 2758], "avg_logprob": -0.24255951937465442, "compression_ratio": 1.5405405405405406, "no_speech_prob": 0.0, "words": [{"start": 4326.09, "end": 4326.47, "word": "على", "probability": 0.760009765625}, {"start": 4326.47, "end": 4327.61, "word": " 142", "probability": 0.84814453125}, {"start": 4327.61, "end": 4328.27, "word": " طيب", "probability": 0.7473958333333334}, {"start": 4328.27, "end": 4328.59, "word": " و", "probability": 0.5712890625}, {"start": 4328.59, "end": 4328.67, "word": " ال", "probability": 0.716796875}, {"start": 4328.67, "end": 4328.87, "word": " letter", "probability": 0.892578125}, {"start": 4328.87, "end": 4329.59, "word": " solution", "probability": 0.91943359375}, {"start": 4329.59, "end": 4330.95, "word": " 0", "probability": 0.132568359375}, {"start": 4330.95, "end": 4331.95, "word": ".225", "probability": 0.9602864583333334}, {"start": 4331.95, "end": 4332.37, "word": " بطلع", 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"probability": 0.99072265625}, {"start": 4340.11, "end": 4340.71, "word": " بنجيبها", "probability": 0.786328125}, {"start": 4340.71, "end": 4341.39, "word": " بطبيعي", "probability": 0.7919921875}, {"start": 4341.39, "end": 4341.63, "word": " يعني", "probability": 0.831298828125}, {"start": 4341.63, "end": 4341.95, "word": " ممكن", "probability": 0.891357421875}, {"start": 4341.95, "end": 4342.39, "word": " نجيب", "probability": 0.935546875}, {"start": 4342.39, "end": 4342.69, "word": " عدد", "probability": 0.8992513020833334}, {"start": 4342.69, "end": 4343.27, "word": " المولات", "probability": 0.650390625}, {"start": 4343.27, "end": 4343.69, "word": " و", "probability": 0.97314453125}, {"start": 4343.69, "end": 4344.11, "word": " منها", "probability": 0.750244140625}, {"start": 4344.11, "end": 4344.77, "word": " بالطبع", "probability": 0.9320068359375}, {"start": 4344.77, "end": 4345.01, "word": " يعني", "probability": 0.90234375}, {"start": 4345.01, "end": 4345.13, "word": " و", "probability": 0.78173828125}, {"start": 4345.13, "end": 4345.63, "word": " بنجيب", "probability": 0.9375}, {"start": 4345.63, "end": 4345.83, "word": " ال", "probability": 0.82177734375}, {"start": 4345.83, "end": 4346.13, "word": " mass", "probability": 0.80615234375}], "temperature": 1.0}, {"id": 189, "seek": 436172, "start": 4346.64, "end": 4361.72, "text": "و لو عنده كمان هنا Sodium acetate عنده ال mass بقدر أجيب منها ال moles وهي ال molarity معايا بقدر أجيب ال volume of solution برضه حاجة مباشرة للغاية", "tokens": [2407, 45164, 43242, 3224, 9122, 2304, 7649, 34105, 42059, 2197, 37848, 473, 43242, 3224, 2423, 2758, 4724, 28543, 2288, 5551, 7435, 1829, 3555, 9154, 11296, 2423, 34286, 37037, 1829, 2423, 8015, 17409, 20449, 995, 25528, 4724, 28543, 2288, 5551, 7435, 1829, 3555, 2423, 5523, 295, 3827, 4724, 43042, 3224, 11331, 26108, 3660, 3714, 3555, 33599, 25720, 24976, 17082, 995, 10632], "avg_logprob": -0.23245389344262296, "compression_ratio": 1.3962264150943395, 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"probability": 0.8896484375}, {"start": 4353.6, "end": 4353.84, "word": " منها", "probability": 0.9794921875}, {"start": 4353.84, "end": 4353.94, "word": " ال", "probability": 0.7177734375}, {"start": 4353.94, "end": 4354.32, "word": " moles", "probability": 0.7744140625}, {"start": 4354.32, "end": 4354.68, "word": " وهي", "probability": 0.6817626953125}, {"start": 4354.68, "end": 4354.78, "word": " ال", "probability": 0.83544921875}, {"start": 4354.78, "end": 4355.24, "word": " molarity", "probability": 0.5391845703125}, {"start": 4355.24, "end": 4356.26, "word": " معايا", "probability": 0.9645182291666666}, {"start": 4356.26, "end": 4356.66, "word": " بقدر", "probability": 0.9617513020833334}, {"start": 4356.66, "end": 4357.02, "word": " أجيب", "probability": 0.9600830078125}, {"start": 4357.02, "end": 4357.14, "word": " ال", "probability": 0.77978515625}, {"start": 4357.14, "end": 4357.64, "word": " volume", "probability": 0.98681640625}, {"start": 4357.64, "end": 4358.5, "word": " 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"وهذا كلام بحصله من ال N لأن ال N اللي هي number of moles ساوي ال mass باليجرام على ال formula weight أو ال molecular mass تمام؟", "tokens": [2407, 3224, 15730, 28242, 10943, 4724, 5016, 36520, 3224, 9154, 2423, 426, 5296, 33456, 2423, 426, 13672, 1829, 39896, 1230, 295, 34286, 8608, 995, 45865, 2423, 2758, 20666, 1829, 7435, 2288, 10943, 15844, 2423, 8513, 3364, 34051, 2423, 19046, 2758, 46811, 10943, 22807], "avg_logprob": -0.38352273540063336, "compression_ratio": 1.3071428571428572, "no_speech_prob": 0.0, "words": [{"start": 166.32, "end": 166.72, "word": "وهذا", "probability": 0.6099039713541666}, {"start": 166.72, "end": 166.96, "word": " كلام", "probability": 0.6317138671875}, {"start": 166.96, "end": 167.34, "word": " بحصله", "probability": 0.7926025390625}, {"start": 167.34, "end": 167.44, "word": " من", "probability": 0.9521484375}, {"start": 167.44, "end": 167.56, "word": " ال", "probability": 0.86865234375}, {"start": 167.56, "end": 167.74, "word": " N", "probability": 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الوزنة", "probability": 0.92890625}, {"start": 1697.73, "end": 1698.03, "word": " و", "probability": 0.701171875}, {"start": 1698.03, "end": 1698.25, "word": " هذه", "probability": 0.7197265625}, {"start": 1698.25, "end": 1698.99, "word": " الوزنة", "probability": 0.9833984375}, {"start": 1698.99, "end": 1699.35, "word": " بقدر", "probability": 0.9650065104166666}, {"start": 1699.35, "end": 1699.63, "word": " اجيب", "probability": 0.8974609375}, {"start": 1699.63, "end": 1700.09, "word": " وزنة", "probability": 0.96630859375}, {"start": 1700.09, "end": 1700.67, "word": " الغاز", "probability": 0.9820963541666666}, {"start": 1700.67, "end": 1701.31, "word": " اللي", "probability": 0.80078125}, {"start": 1701.31, "end": 1701.69, "word": " موجود", "probability": 0.990234375}, {"start": 1701.69, "end": 1701.79, "word": " في", "probability": 0.8984375}, {"start": 1701.79, "end": 1701.89, "word": " ال", "probability": 0.8955078125}, {"start": 1701.89, "end": 1702.25, "word": " flask", "probability": 0.94970703125}, {"start": 1702.25, "end": 1702.81, "word": " طيب", "probability": 0.95849609375}, {"start": 1702.81, "end": 1703.35, "word": " بقول", "probability": 0.862060546875}, {"start": 1703.35, "end": 1703.55, "word": " if", "probability": 0.7890625}, {"start": 1703.55, "end": 1703.73, "word": " the", "probability": 0.90576171875}, {"start": 1703.73, "end": 1704.05, "word": " flask", "probability": 0.979248046875}, {"start": 1704.05, "end": 1704.29, "word": " has", "probability": 0.91943359375}, {"start": 1704.29, "end": 1704.47, "word": " a", "probability": 0.9296875}, {"start": 1704.47, "end": 1704.81, "word": " volume", "probability": 0.9560546875}, {"start": 1704.81, "end": 1704.97, "word": " of", "probability": 0.974609375}, {"start": 1704.97, "end": 1706.13, "word": " 936", "probability": 0.868408203125}, {"start": 1706.13, "end": 1706.55, "word": " ml", "probability": 0.465087890625}, {"start": 1706.55, "end": 1707.95, "word": " حجم", "probability": 0.9837239583333334}, {"start": 1707.95, "end": 1708.45, "word": " ال", "probability": 0.9111328125}, {"start": 1708.45, "end": 1709.07, "word": " flask", "probability": 0.966796875}, {"start": 1709.07, "end": 1709.53, "word": " 900", "probability": 0.70654296875}], "temperature": 1.0}, {"id": 78, "seek": 173347, "start": 1710.03, "end": 1733.47, "text": "و 36 ميل بيقول calculate the molar mass of the gas حلو كتير فى البداية PV مادام بيدومورم PV بتساوي لجرام ع ال formula weight فى الارض تمام ال P هي 735 على 760 ال volume point nine three six liter point nine three six liter", "tokens": [2407, 8652, 3714, 26895, 4724, 1829, 39648, 8873, 264, 45712, 2758, 295, 264, 4211, 11331, 1211, 2407, 9122, 2655, 13546, 6156, 7578, 29739, 28259, 10632, 23035, 3714, 18513, 10943, 4724, 25708, 20498, 13063, 2304, 23035, 39894, 3794, 995, 45865, 5296, 7435, 2288, 10943, 6225, 2423, 8513, 3364, 6156, 7578, 2423, 9640, 11242, 46811, 10943, 2423, 430, 39896, 1614, 8794, 15844, 1614, 4550, 2423, 5523, 935, 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1713.33, "end": 1713.61, "word": " gas", "probability": 0.912109375}, {"start": 1713.61, "end": 1714.17, "word": " حلو", "probability": 0.9573567708333334}, {"start": 1714.17, "end": 1714.45, "word": " كتير", "probability": 0.9733072916666666}, {"start": 1714.45, "end": 1714.87, "word": " فى", "probability": 0.518310546875}, {"start": 1714.87, "end": 1715.39, "word": " البداية", "probability": 0.9900716145833334}, {"start": 1715.39, "end": 1715.89, "word": " PV", "probability": 0.6591796875}, {"start": 1715.89, "end": 1716.25, "word": " مادام", "probability": 0.67431640625}, {"start": 1716.25, "end": 1716.73, "word": " بيدومورم", "probability": 0.6595703125}, {"start": 1716.73, "end": 1717.17, "word": " PV", "probability": 0.69775390625}, {"start": 1717.17, "end": 1718.63, "word": " بتساوي", "probability": 0.8829345703125}, {"start": 1718.63, "end": 1719.19, "word": " لجرام", "probability": 0.684814453125}, {"start": 1719.19, "end": 1719.33, "word": " ع", "probability": 0.302978515625}, {"start": 1719.33, "end": 1719.45, "word": " ال", "probability": 0.406005859375}, {"start": 1719.45, "end": 1719.71, "word": " formula", "probability": 0.473876953125}, {"start": 1719.71, "end": 1719.97, "word": " weight", "probability": 0.17431640625}, {"start": 1719.97, "end": 1720.11, "word": " فى", "probability": 0.9453125}, {"start": 1720.11, "end": 1720.47, "word": " الارض", "probability": 0.7527669270833334}, {"start": 1720.47, "end": 1721.83, "word": " تمام", "probability": 0.8935546875}, {"start": 1721.83, "end": 1722.45, "word": " ال", "probability": 0.9560546875}, {"start": 1722.45, "end": 1722.77, "word": " P", "probability": 0.970703125}, {"start": 1722.77, "end": 1723.23, "word": " هي", "probability": 0.6142578125}, {"start": 1723.23, "end": 1724.11, "word": " 735", "probability": 0.852294921875}, {"start": 1724.11, "end": 1724.81, "word": " على", "probability": 0.5107421875}, {"start": 1724.81, "end": 1725.91, "word": " 760", "probability": 0.927734375}, {"start": 1725.91, "end": 1726.57, "word": " ال", "probability": 0.65283203125}, {"start": 1726.57, "end": 1727.01, "word": " volume", "probability": 0.974609375}, {"start": 1727.01, "end": 1727.63, "word": " point", "probability": 0.61865234375}, {"start": 1727.63, "end": 1728.91, "word": " nine", "probability": 0.6435546875}, {"start": 1728.91, "end": 1729.37, "word": " three", "probability": 0.8154296875}, {"start": 1729.37, "end": 1729.95, "word": " six", "probability": 0.94677734375}, {"start": 1729.95, "end": 1730.37, "word": " liter", "probability": 0.642578125}, {"start": 1730.37, "end": 1731.09, "word": " point", "probability": 0.888671875}, {"start": 1731.09, "end": 1731.71, "word": " nine", "probability": 0.93505859375}, {"start": 1731.71, "end": 1732.11, "word": " three", "probability": 0.9453125}, {"start": 1732.11, "end": 1732.71, "word": " six", "probability": 0.96435546875}, {"start": 1732.71, "end": 1733.47, "word": " liter", "probability": 0.9375}], "temperature": 1.0}, {"id": 79, "seek": 176087, "start": 1734.17, "end": 1760.87, "text": "ليجرام بتدي أطرح مية أربعة و تلاتين خمسة ستة سبعة من مية سبعة و تلاتين point four five six اذا هذه ليجرام ال R.O821 ال temperature واحد و تلاتين و متين و ثلاثة و سبعين اذا تعويض مباشر يا جماعة بيعطينا الفورمولوية تسعة و سبعين و سبعة من عشرة يمكن اخر مثال معانا اه", "tokens": [20292, 7435, 2288, 10943, 39894, 16254, 5551, 9566, 2288, 5016, 3714, 10632, 5551, 25513, 27884, 4032, 6055, 1211, 9307, 9957, 16490, 2304, 3794, 3660, 8608, 2655, 3660, 8608, 3555, 27884, 9154, 3714, 10632, 8608, 3555, 27884, 4032, 6055, 1211, 9307, 9957, 935, 1451, 1732, 2309, 1975, 15730, 29538, 32239, 7435, 2288, 10943, 2423, 497, 13, 46, 23, 4436, 2423, 4292, 36764, 24401, 4032, 6055, 1211, 9307, 9957, 4032, 44650, 9957, 4032, 38637, 1211, 5718, 104, 3660, 4032, 8608, 3555, 3615, 9957, 1975, 15730, 37279, 45865, 11242, 3714, 3555, 33599, 2288, 35186, 10874, 15042, 27884, 4724, 40228, 9566, 1829, 8315, 27188, 13063, 2304, 12610, 2407, 10632, 6055, 3794, 27884, 4032, 8608, 3555, 3615, 9957, 4032, 8608, 3555, 27884, 9154, 6225, 8592, 25720, 7251, 43020, 1975, 34740, 50113, 6027, 20449, 7649, 995, 1975, 3224], "avg_logprob": -0.23566729771463493, "compression_ratio": 1.8032786885245902, "no_speech_prob": 0.0, "words": [{"start": 1734.17, "end": 1734.87, "word": "ليجرام", "probability": 0.6551513671875}, {"start": 1734.87, "end": 1735.55, "word": " بتدي", "probability": 0.3883056640625}, {"start": 1735.55, "end": 1736.13, "word": " أطرح", "probability": 0.8162841796875}, {"start": 1736.13, "end": 1736.49, "word": " مية", "probability": 0.583740234375}, {"start": 1736.49, "end": 1736.81, "word": " أربعة", "probability": 0.84912109375}, {"start": 1736.81, "end": 1736.95, "word": " و", "probability": 0.6982421875}, {"start": 1736.95, "end": 1737.33, "word": " تلاتين", "probability": 0.9306640625}, {"start": 1737.33, "end": 1737.67, "word": " خمسة", "probability": 0.8824462890625}, {"start": 1737.67, "end": 1737.95, "word": " ستة", "probability": 0.8924153645833334}, {"start": 1737.95, "end": 1738.23, "word": " سبعة", "probability": 0.8790690104166666}, {"start": 1738.23, "end": 1738.51, "word": " من", "probability": 0.943359375}, {"start": 1738.51, "end": 1739.23, "word": " مية", "probability": 0.890869140625}, {"start": 1739.23, "end": 1739.51, "word": " سبعة", "probability": 0.9630533854166666}, {"start": 1739.51, "end": 1739.61, "word": " و", "probability": 0.71728515625}, {"start": 1739.61, "end": 1740.03, "word": " تلاتين", "probability": 0.9873046875}, {"start": 1740.03, "end": 1740.35, "word": " point", "probability": 0.91845703125}, {"start": 1740.35, "end": 1740.85, "word": " four", "probability": 0.86328125}, {"start": 1740.85, "end": 1741.41, "word": " five", "probability": 0.91064453125}, {"start": 1741.41, "end": 1741.97, "word": " six", "probability": 0.962890625}, {"start": 1741.97, "end": 1742.97, "word": " اذا", "probability": 0.607421875}, {"start": 1742.97, "end": 1743.27, "word": " 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"word": " و", "probability": 0.986328125}, {"start": 1753.71, "end": 1754.33, "word": " سبعين", "probability": 0.938232421875}, {"start": 1754.33, "end": 1755.09, "word": " و", "probability": 0.98095703125}, {"start": 1755.09, "end": 1755.63, "word": " سبعة", "probability": 0.8123372395833334}, {"start": 1755.63, "end": 1755.97, "word": " من", "probability": 0.97900390625}, {"start": 1755.97, "end": 1756.75, "word": " عشرة", "probability": 0.8113606770833334}, {"start": 1756.75, "end": 1759.55, "word": " يمكن", "probability": 0.8662109375}, {"start": 1759.55, "end": 1759.89, "word": " اخر", "probability": 0.863525390625}, {"start": 1759.89, "end": 1760.25, "word": " مثال", "probability": 0.93994140625}, {"start": 1760.25, "end": 1760.61, "word": " معانا", "probability": 0.85791015625}, {"start": 1760.61, "end": 1760.87, "word": " اه", "probability": 0.9248046875}], "temperature": 1.0}, {"id": 80, "seek": 178039, "start": 1761.75, "end": 1780.39, "text": "بيقول calculate the average molar mass of a dry air ليش بيقول ال average molar mass لأن ال air مش مكون واحد يعني هو بده ياخد وزن ال liter كويس مثلا و يعطيها ال density يعني و بده ال average molar mass", "tokens": [3555, 1829, 39648, 8873, 264, 4274, 45712, 2758, 295, 257, 4016, 1988, 32239, 8592, 4724, 1829, 39648, 2423, 4274, 45712, 2758, 5296, 33456, 2423, 1988, 37893, 3714, 30544, 36764, 24401, 37495, 22653, 31439, 47525, 3224, 7251, 47283, 3215, 4032, 11622, 1863, 2423, 2733, 9122, 45865, 3794, 50113, 15040, 4032, 37495, 9566, 1829, 11296, 2423, 10305, 37495, 22653, 4032, 47525, 3224, 2423, 4274, 45712, 2758], "avg_logprob": -0.25745192307692305, "compression_ratio": 1.6176470588235294, "no_speech_prob": 0.0, "words": [{"start": 1761.75, "end": 1762.07, "word": "بيقول", "probability": 0.5096435546875}, {"start": 1762.07, "end": 1762.49, "word": " calculate", "probability": 0.78515625}, {"start": 1762.49, "end": 1762.87, "word": " the", "probability": 0.83203125}, {"start": 1762.87, "end": 1763.43, "word": " 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"probability": 0.84619140625}, {"start": 1766.57, "end": 1767.39, "word": " لأن", "probability": 0.712890625}, {"start": 1767.39, "end": 1768.01, "word": " ال", "probability": 0.6826171875}, {"start": 1768.01, "end": 1768.29, "word": " air", "probability": 0.8857421875}, {"start": 1768.29, "end": 1768.63, "word": " مش", "probability": 0.97119140625}, {"start": 1768.63, "end": 1769.03, "word": " مكون", "probability": 0.84814453125}, {"start": 1769.03, "end": 1769.47, "word": " واحد", "probability": 0.9892578125}, {"start": 1769.47, "end": 1770.67, "word": " يعني", "probability": 0.766845703125}, {"start": 1770.67, "end": 1771.27, "word": " هو", "probability": 0.95703125}, {"start": 1771.27, "end": 1771.53, "word": " بده", "probability": 0.685302734375}, {"start": 1771.53, "end": 1771.87, "word": " ياخد", "probability": 0.9830729166666666}, {"start": 1771.87, "end": 1772.93, "word": " وزن", "probability": 0.9825846354166666}, {"start": 1772.93, "end": 1773.23, "word": " ال", 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"probability": 0.86767578125}, {"start": 1779.67, "end": 1779.95, "word": " molar", "probability": 0.97802734375}, {"start": 1779.95, "end": 1780.39, "word": " mass", "probability": 0.83447265625}], "temperature": 1.0}, {"id": 81, "seek": 180843, "start": 1780.95, "end": 1808.43, "text": "مالهاش معنى كبير لكن يعني خلاص زي ما بده Calculate the average molar mass of dry air if it has a density of 1.17 gram per liter and 21 degrees C and 740 Torr بقول بطبق المعادلة ممكن جدا يعني ان اقول P بتساوي D RT على ال FW ال P 740 اذا 740 على 760 لأنه أتمسفير", "tokens": [2304, 6027, 3224, 33599, 20449, 1863, 7578, 9122, 3555, 13546, 44381, 37495, 22653, 16490, 1211, 33546, 30767, 1829, 19446, 47525, 3224, 3511, 2444, 473, 264, 4274, 45712, 2758, 295, 4016, 1988, 498, 309, 575, 257, 10305, 295, 502, 13, 7773, 21353, 680, 2733, 293, 5080, 5310, 383, 293, 1614, 5254, 7160, 81, 4724, 39648, 4724, 9566, 3555, 4587, 9673, 3615, 18513, 37977, 3714, 43020, 10874, 28259, 37495, 22653, 16472, 1975, 39648, 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2360.88, "word": " المول", "probability": 0.970458984375}, {"start": 2360.88, "end": 2361.3, "word": " أكسجين", "probability": 0.97236328125}, {"start": 2361.3, "end": 2361.76, "word": " معايا", "probability": 0.9638671875}, {"start": 2361.76, "end": 2362.08, "word": " يبقى", "probability": 0.8358154296875}, {"start": 2362.08, "end": 2362.34, "word": " أربعة", "probability": 0.6943359375}, {"start": 2362.34, "end": 2362.72, "word": " تلاتة", "probability": 0.9630126953125}, {"start": 2362.72, "end": 2363.12, "word": " فيه", "probability": 0.740234375}, {"start": 2363.12, "end": 2363.5, "word": " point", "probability": 0.8212890625}, {"start": 2363.5, "end": 2363.9, "word": " five", "probability": 0.73828125}, {"start": 2363.9, "end": 2364.38, "word": " nine", "probability": 0.94287109375}, {"start": 2364.38, "end": 2364.86, "word": " seven", "probability": 0.9375}], "temperature": 1.0}, {"id": 106, "seek": 238542, "start": 2371.22, "end": 2385.42, "text": "معنى الكلام في أي مسألة Stoichiometric reaction موجود في غاز أول شغلة بجيبها عدد ملات الغاز", "tokens": [2304, 3615, 1863, 7578, 2423, 28820, 10943, 8978, 36632, 47524, 10721, 37977, 745, 78, 18543, 29470, 5480, 3714, 29245, 23328, 8978, 32771, 31377, 5551, 12610, 13412, 17082, 37977, 4724, 7435, 1829, 3555, 11296, 6225, 3215, 3215, 3714, 1211, 9307, 6024, 118, 31377], "avg_logprob": -0.2627180107804232, "compression_ratio": 1.1788617886178863, "no_speech_prob": 0.0, "words": [{"start": 2371.22, "end": 2372.5, "word": "معنى", "probability": 0.53369140625}, {"start": 2372.5, "end": 2372.96, "word": " الكلام", "probability": 0.8592122395833334}, {"start": 2372.96, "end": 2373.68, "word": " في", "probability": 0.5517578125}, {"start": 2373.68, "end": 2373.92, "word": " أي", "probability": 0.72314453125}, {"start": 2373.92, "end": 2374.48, "word": " مسألة", "probability": 0.921875}, {"start": 2374.48, "end": 2375.92, "word": " Stoichiometric", "probability": 0.7149658203125}, {"start": 2375.92, "end": 2379.28, "word": " reaction", "probability": 0.80126953125}, {"start": 2379.28, "end": 2380.88, "word": " موجود", "probability": 0.9791666666666666}, {"start": 2380.88, "end": 2381.04, "word": " في", "probability": 0.9580078125}, {"start": 2381.04, "end": 2381.58, "word": " غاز", "probability": 0.98095703125}, {"start": 2381.58, "end": 2382.6, "word": " أول", "probability": 0.75634765625}, {"start": 2382.6, "end": 2382.94, "word": " شغلة", "probability": 0.78125}, {"start": 2382.94, "end": 2383.52, "word": " بجيبها", "probability": 0.9248046875}, {"start": 2383.52, "end": 2384.3, "word": " عدد", "probability": 0.9651692708333334}, {"start": 2384.3, "end": 2384.72, "word": " ملات", "probability": 0.81201171875}, {"start": 2384.72, "end": 2385.42, "word": " الغاز", "probability": 0.8815104166666666}], "temperature": 1.0}, {"id": 107, "seek": 240517, "start": 2386.34, "end": 2405.18, "text": "من ايه؟ من الـ PV بتساوي NRT بعد ما اجيب عدد مولات الغاز بعدين بروح بعمل relation ما بينها و عدد مولات المادة اللي انا بدي احسبها لكن اول خطوة دائما ايه عدد مولات الغاز انتهينا يبقى عدد مولات الغاز اولان بعدين منها بروح ل", "tokens": [27842, 1975, 1829, 3224, 22807, 9154, 2423, 39184, 23035, 39894, 3794, 995, 45865, 426, 49, 51, 39182, 19446, 1975, 7435, 1829, 3555, 6225, 3215, 3215, 3714, 12610, 9307, 6024, 118, 31377, 39182, 9957, 4724, 32887, 5016, 4724, 25957, 1211, 9721, 19446, 49374, 11296, 4032, 6225, 3215, 3215, 3714, 12610, 9307, 9673, 18513, 3660, 13672, 1829, 1975, 8315, 4724, 16254, 1975, 5016, 35457, 11296, 44381, 1975, 12610, 16490, 9566, 2407, 3660, 11778, 16373, 15042, 1975, 1829, 3224, 6225, 3215, 3215, 3714, 12610, 9307, 6024, 118, 31377, 16472, 47395, 1829, 8315, 7251, 3555, 4587, 7578, 6225, 3215, 3215, 3714, 12610, 9307, 6024, 118, 31377, 1975, 12610, 7649, 39182, 9957, 9154, 11296, 4724, 32887, 5016, 5296], "avg_logprob": -0.18941885559705265, "compression_ratio": 2.0157068062827226, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2386.34, "end": 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برضه الـ P للنيتروجين عدد ملاته في ال R في ال T على الحجم والهيدروجين برضه عدد ملاته في ال R في ال T على الحجم ال total pressure عبارة عن مجموعة ال partial pressures بقدر أعمل نفس الجثة لو جمعت 0.215 و 0.0118 بطلع 0.227 برضه باخدين نفس الحجم تماما نفس ال pressure تماما", "tokens": [6027, 39184, 3321, 294, 264, 18098, 8717, 36178, 2423, 28820, 10943, 4724, 43042, 3224, 2423, 39184, 430, 5296, 1211, 1863, 36081, 2288, 29245, 9957, 6225, 3215, 3215, 3714, 1211, 9307, 3224, 8978, 2423, 497, 8978, 2423, 314, 15844, 21542, 7435, 2304, 16070, 3224, 25708, 2288, 29245, 9957, 4724, 43042, 3224, 6225, 3215, 3215, 3714, 1211, 9307, 3224, 8978, 2423, 497, 8978, 2423, 314, 15844, 21542, 7435, 2304, 2423, 3217, 3321, 6225, 3555, 9640, 3660, 18871, 3714, 7435, 2304, 2407, 27884, 2423, 14641, 23573, 4724, 28543, 2288, 5551, 25957, 1211, 8717, 36178, 25724, 12984, 3660, 45164, 10874, 2304, 34268, 1958, 13, 4436, 20, 4032, 1958, 13, 15, 5348, 23, 4724, 9566, 1211, 3615, 1958, 13, 7490, 22, 4724, 43042, 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{"start": 2926.19, "end": 2926.37, "word": " من", "probability": 0.99169921875}, {"start": 2926.37, "end": 2926.87, "word": " حاجة", "probability": 0.9947916666666666}, {"start": 2926.87, "end": 2927.57, "word": " خلطت", "probability": 0.97607421875}, {"start": 2927.57, "end": 2927.85, "word": " صار", "probability": 0.8642578125}, {"start": 2927.85, "end": 2927.97, "word": " في", "probability": 0.92236328125}, {"start": 2927.97, "end": 2928.35, "word": " عندي", "probability": 0.964111328125}, {"start": 2928.35, "end": 2929.03, "word": " volume", "probability": 0.93212890625}, {"start": 2929.03, "end": 2929.41, "word": " نهائي", "probability": 0.9769287109375}, {"start": 2929.41, "end": 2930.09, "word": " 300ml", "probability": 0.84814453125}, {"start": 2930.09, "end": 2930.67, "word": " what", "probability": 0.62353515625}, {"start": 2930.67, "end": 2931.11, "word": " would", "probability": 0.97705078125}, {"start": 2931.11, "end": 2931.65, "word": " be", "probability": 0.96435546875}, 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grams O2 and 9 grams CH4 is placed in 15 liter vessel at 0 degree C", "tokens": [2304, 43020, 7251, 1829, 7435, 1829, 37495, 9566, 1829, 22653, 6225, 3215, 3215, 5296, 7435, 2288, 10943, 9307, 9154, 6024, 118, 31377, 9307, 37893, 6225, 3215, 3215, 9673, 12610, 18513, 20666, 19913, 3555, 9566, 6156, 21292, 39648, 32239, 257, 9925, 295, 1386, 11899, 422, 17, 293, 1722, 11899, 5995, 19, 307, 7074, 294, 2119, 2733, 18098, 412, 1958, 4314, 383], "avg_logprob": -0.2574282786885246, "compression_ratio": 1.2529411764705882, "no_speech_prob": 0.0, "words": [{"start": 3069.21, "end": 3069.59, "word": "ممكن", "probability": 0.899658203125}, {"start": 3069.59, "end": 3069.87, "word": " ييجي", "probability": 0.782958984375}, {"start": 3069.87, "end": 3070.45, "word": " يعطيني", "probability": 0.7613525390625}, {"start": 3070.45, "end": 3071.29, "word": " عدد", "probability": 0.978515625}, {"start": 3071.29, "end": 3072.23, "word": " لجرامات", "probability": 0.841015625}, {"start": 3072.23, "end": 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{"start": 4145.26, "end": 4145.42, "word": " ال", "probability": 0.2127685546875}, {"start": 4145.42, "end": 4145.72, "word": " V", "probability": 0.74267578125}, {"start": 4145.72, "end": 4146.2, "word": " ربع", "probability": 0.6590983072916666}, {"start": 4146.2, "end": 4146.44, "word": " لتر", "probability": 0.8680013020833334}, {"start": 4146.44, "end": 4146.58, "word": " هي", "probability": 0.62744140625}, {"start": 4146.58, "end": 4147.24, "word": " الحجم", "probability": 0.8649088541666666}, {"start": 4147.24, "end": 4147.62, "word": " تبع", "probability": 0.81591796875}, {"start": 4147.62, "end": 4148.12, "word": " الغاز", "probability": 0.966796875}, {"start": 4148.12, "end": 4149.12, "word": " بدي", "probability": 0.62744140625}, {"start": 4149.12, "end": 4149.58, "word": " ساوي", "probability": 0.7770182291666666}, {"start": 4149.58, "end": 4150.06, "word": " N", "probability": 0.87744140625}, {"start": 4150.06, "end": 4150.46, "word": " عدد", "probability": 0.9612630208333334}, {"start": 4150.46, "end": 4150.8, "word": " المولات", "probability": 0.8468424479166666}, {"start": 4150.8, "end": 4150.94, "word": " انا", "probability": 0.7469482421875}, {"start": 4150.94, "end": 4151.54, "word": " بديها", "probability": 0.9189453125}, {"start": 4151.54, "end": 4152.74, "word": " R", "probability": 0.876953125}, {"start": 4152.74, "end": 4153.44, "word": " constant", "probability": 0.78857421875}, {"start": 4153.44, "end": 4153.7, "word": " و", "probability": 0.673828125}, {"start": 4153.7, "end": 4154.04, "word": " T", "probability": 0.75244140625}, {"start": 4154.04, "end": 4154.48, "word": " متين", "probability": 0.4705403645833333}, {"start": 4154.48, "end": 4154.78, "word": " تسعة", "probability": 0.96630859375}, {"start": 4154.78, "end": 4155.22, "word": " وتسعين", "probability": 0.9268798828125}, {"start": 4155.22, "end": 4155.44, "word": " اذا", "probability": 0.8134765625}, {"start": 4155.44, "end": 4155.8, "word": " جبت", "probability": 0.93115234375}, {"start": 4155.8, "end": 4155.94, "word": " ال", "probability": 0.84765625}, {"start": 4155.94, "end": 4156.24, "word": " N", "probability": 0.96044921875}, {"start": 4156.24, "end": 4157.12, "word": " ال", "probability": 0.84326171875}, {"start": 4157.12, "end": 4157.32, "word": " N", "probability": 0.9306640625}, {"start": 4157.32, "end": 4157.5, "word": " لل", "probability": 0.73193359375}, {"start": 4157.5, "end": 4157.88, "word": " Oxygen", "probability": 0.64892578125}, {"start": 4157.88, "end": 4158.16, "word": " تسعة", "probability": 0.9705403645833334}, {"start": 4158.16, "end": 4158.42, "word": " وتسعة", "probability": 0.91943359375}, {"start": 4158.42, "end": 4158.56, "word": " في", "probability": 0.27783203125}, {"start": 4158.56, "end": 4158.76, "word": " عشرة", "probability": 0.8875325520833334}, {"start": 4158.76, "end": 4158.94, "word": " او", "probability": 0.4151611328125}, {"start": 4158.94, "end": 4159.16, "word": " سالت", "probability": 0.6495768229166666}, {"start": 4159.16, "end": 4159.58, "word": " تلاتة", "probability": 0.912109375}, {"start": 4159.58, "end": 4160.02, "word": " مول", "probability": 0.68896484375}, {"start": 4160.02, "end": 4161.2, "word": " طب", "probability": 0.77685546875}, {"start": 4161.2, "end": 4161.4, "word": " انا", "probability": 0.941162109375}, {"start": 4161.4, "end": 4161.76, "word": " بدي", "probability": 0.789794921875}, {"start": 4161.76, "end": 4162.72, "word": " يعني", "probability": 0.760498046875}, {"start": 4162.72, "end": 4163.64, "word": " لو", "probability": 0.90087890625}, {"start": 4163.64, "end": 4163.84, "word": " جلي", "probability": 0.754638671875}, {"start": 4163.84, "end": 4164.36, "word": " بدي", "probability": 0.750244140625}, {"start": 4164.36, "end": 4165.14, "word": " اجرامات", "probability": 0.884375}, {"start": 4165.14, "end": 4165.74, "word": " Oxygen", "probability": 0.97900390625}, {"start": 4165.74, "end": 4166.88, "word": " بضرب", "probability": 0.8216145833333334}, {"start": 4166.88, "end": 4167.02, "word": " في", "probability": 0.88671875}, {"start": 4167.02, "end": 4167.22, "word": " اتنين", "probability": 0.84130859375}, {"start": 4167.22, "end": 4167.36, "word": " و", "probability": 0.76025390625}, {"start": 4167.36, "end": 4167.74, "word": " تلاتين", "probability": 0.956787109375}, {"start": 4167.74, "end": 4167.88, "word": " في", "probability": 0.90380859375}, {"start": 4167.88, "end": 4167.98, "word": " ال", "probability": 0.90478515625}, {"start": 4167.98, "end": 4168.26, "word": " formula", "probability": 0.494384765625}, {"start": 4168.26, "end": 4168.52, "word": " وقت", "probability": 0.478515625}, {"start": 4168.52, "end": 4169.02, "word": " بس", "probability": 0.807373046875}, {"start": 4169.02, "end": 4169.16, "word": " هو", "probability": 0.83642578125}, {"start": 4169.16, "end": 4169.46, "word": " هنقاش", "probability": 0.551666259765625}, {"start": 4169.46, "end": 4169.8, "word": " جلي", "probability": 0.921630859375}, {"start": 4169.8, "end": 4170.5, "word": " جلي", "probability": 0.695556640625}, {"start": 4170.5, "end": 4170.68, "word": " how", "probability": 0.6552734375}, {"start": 4170.68, "end": 4170.92, "word": " many", "probability": 0.91845703125}, {"start": 4170.92, "end": 4171.34, "word": " grams", "probability": 0.77783203125}, {"start": 4171.34, "end": 4171.68, "word": " of", "probability": 0.9765625}, {"start": 4171.68, "end": 4172.52, "word": " KClO", "probability": 0.7621256510416666}, {"start": 4172.52, "end": 4173.02, "word": " تلاتة", "probability": 0.9385986328125}, {"start": 4173.02, "end": 4173.4, "word": " اذا", "probability": 0.89453125}, {"start": 4173.4, "end": 4173.66, "word": " بدي", "probability": 0.875732421875}, {"start": 4173.66, "end": 4174.2, "word": " اجيب", "probability": 0.86376953125}], "temperature": 1.0}, {"id": 181, "seek": 420343, "start": 4175.26, "end": 4203.44, "text": "بدي اجيب المول KClO3 بتساوي 2 على 3 مول اكسجين فانا عند المول اكسجين هيها اذا تسعة و تسعة فعشرة اقصر ضرب اتنين على تلاتة بيعطيني عدد مولات ال KClO3 مدام جيبنا عدد مولاتها بضربها في ال formula weight مية و اتنين و عشرين و ستة من عشرة بيعطينا عدد اجرامتها جميل جدا تجربة جميلة جدا بتعرفني بالظبط", "tokens": [3555, 16254, 1975, 7435, 1829, 3555, 9673, 12610, 591, 9966, 46, 18, 39894, 3794, 995, 45865, 568, 15844, 805, 3714, 12610, 1975, 4117, 3794, 7435, 9957, 6156, 7649, 995, 43242, 9673, 12610, 1975, 4117, 3794, 7435, 9957, 39896, 11296, 1975, 15730, 6055, 3794, 27884, 4032, 6055, 3794, 27884, 6156, 3615, 8592, 25720, 1975, 4587, 9381, 2288, 48812, 25513, 1975, 2655, 1863, 9957, 15844, 6055, 1211, 9307, 3660, 4724, 40228, 9566, 1829, 22653, 6225, 3215, 3215, 3714, 12610, 9307, 2423, 591, 9966, 46, 18, 3714, 3215, 10943, 10874, 1829, 3555, 8315, 6225, 3215, 3215, 3714, 12610, 9307, 11296, 4724, 11242, 25513, 11296, 8978, 2423, 8513, 3364, 3714, 10632, 4032, 1975, 2655, 1863, 9957, 4032, 6225, 46309, 9957, 4032, 8608, 2655, 3660, 9154, 6225, 8592, 25720, 4724, 40228, 9566, 1829, 8315, 6225, 3215, 3215, 1975, 7435, 2288, 10943, 2655, 11296, 10874, 2304, 26895, 10874, 28259, 6055, 7435, 25513, 3660, 10874, 2304, 26895, 3660, 10874, 28259, 39894, 3615, 28480, 22653, 20666, 19913, 3555, 9566], "avg_logprob": -0.19502314078955002, "compression_ratio": 1.96875, "no_speech_prob": 0.0, "words": [{"start": 4175.26, "end": 4175.56, "word": "بدي", "probability": 0.22076416015625}, {"start": 4175.56, "end": 4175.8, "word": " اجيب", "probability": 0.8629150390625}, {"start": 4175.8, "end": 4176.56, "word": " المول", "probability": 0.665771484375}, {"start": 4176.56, "end": 4179.34, "word": " KClO3", "probability": 0.711669921875}, {"start": 4179.34, "end": 4179.84, "word": " بتساوي", "probability": 0.70001220703125}, {"start": 4179.84, "end": 4180.26, "word": " 2", "probability": 0.86083984375}, {"start": 4180.26, "end": 4180.58, "word": " على", "probability": 0.53369140625}, {"start": 4180.58, "end": 4181.2, "word": " 3", "probability": 0.95947265625}, {"start": 4181.2, "end": 4182.28, "word": " مول", "probability": 0.83984375}, {"start": 4182.28, "end": 4182.94, "word": " اكسجين", "probability": 0.766552734375}, {"start": 4182.94, "end": 4183.2, "word": " فانا", "probability": 0.7223307291666666}, {"start": 4183.2, "end": 4183.4, "word": " عند", "probability": 0.966796875}, {"start": 4183.4, "end": 4183.74, "word": " المول", "probability": 0.916015625}, {"start": 4183.74, "end": 4184.34, "word": " اكسجين", "probability": 0.98046875}, {"start": 4184.34, "end": 4185.12, "word": " هيها", "probability": 0.753173828125}, {"start": 4185.12, "end": 4185.8, "word": " اذا", "probability": 0.626708984375}, {"start": 4185.8, "end": 4186.4, "word": " تسعة", "probability": 0.78955078125}, {"start": 4186.4, "end": 4186.54, "word": " و", "probability": 0.5966796875}, {"start": 4186.54, "end": 4187.0, "word": " تسعة", "probability": 0.9171549479166666}, {"start": 4187.0, "end": 4188.66, "word": " فعشرة", "probability": 0.815673828125}, {"start": 4188.66, "end": 4188.92, "word": " اقصر", "probability": 0.67279052734375}, {"start": 4188.92, "end": 4189.48, "word": " ضرب", "probability": 0.6048583984375}, {"start": 4189.48, "end": 4189.84, "word": " اتنين", "probability": 0.8138427734375}, {"start": 4189.84, "end": 4190.0, "word": " على", "probability": 0.83544921875}, {"start": 4190.0, "end": 4190.42, "word": " تلاتة", "probability": 0.9522705078125}, {"start": 4190.42, "end": 4191.1, "word": " بيعطيني", "probability": 0.8294921875}, {"start": 4191.1, "end": 4191.5, "word": " عدد", "probability": 0.96044921875}, {"start": 4191.5, "end": 4191.92, "word": " مولات", "probability": 0.9708658854166666}, {"start": 4191.92, "end": 4192.06, "word": " ال", "probability": 0.689453125}, {"start": 4192.06, "end": 4193.1, "word": " KClO3", "probability": 0.8756103515625}, {"start": 4193.1, "end": 4193.86, "word": " مدام", "probability": 0.75927734375}, {"start": 4193.86, "end": 4194.12, "word": " جيبنا", "probability": 0.912353515625}, {"start": 4194.12, "end": 4194.38, "word": " عدد", "probability": 0.9930013020833334}, {"start": 4194.38, "end": 4194.98, "word": " مولاتها", "probability": 0.9853515625}, {"start": 4194.98, "end": 4195.78, "word": " بضربها", "probability": 0.78662109375}, {"start": 4195.78, "end": 4195.9, "word": " في", "probability": 0.798828125}, {"start": 4195.9, "end": 4196.02, "word": " ال", "probability": 0.85888671875}, {"start": 4196.02, "end": 4196.32, "word": " formula", "probability": 0.70361328125}, {"start": 4196.32, "end": 4196.68, "word": " weight", "probability": 0.89697265625}, {"start": 4196.68, "end": 4196.94, "word": " مية", "probability": 0.80126953125}, {"start": 4196.94, "end": 4197.04, "word": " و", "probability": 0.93994140625}, {"start": 4197.04, "end": 4197.22, "word": " اتنين", "probability": 0.9102783203125}, {"start": 4197.22, "end": 4197.32, "word": " و", "probability": 0.91259765625}, {"start": 4197.32, "end": 4197.64, "word": " عشرين", "probability": 0.93212890625}, {"start": 4197.64, "end": 4198.02, "word": " و", "probability": 0.9443359375}, {"start": 4198.02, "end": 4198.32, "word": " ستة", "probability": 0.8416341145833334}, {"start": 4198.32, "end": 4198.42, "word": " من", "probability": 0.9736328125}, {"start": 4198.42, "end": 4198.68, "word": " عشرة", "probability": 0.9612630208333334}, {"start": 4198.68, "end": 4199.08, "word": " بيعطينا", "probability": 0.80927734375}, {"start": 4199.08, "end": 4199.52, "word": " عدد", "probability": 0.9912109375}, {"start": 4199.52, "end": 4200.3, "word": " اجرامتها", "probability": 0.8745930989583334}, {"start": 4200.3, "end": 4200.62, "word": " جميل", "probability": 0.9778645833333334}, {"start": 4200.62, "end": 4200.96, "word": " جدا", "probability": 0.9892578125}, {"start": 4200.96, "end": 4201.42, "word": " تجربة", "probability": 0.8828125}, {"start": 4201.42, "end": 4201.78, "word": " جميلة", "probability": 0.978271484375}, {"start": 4201.78, "end": 4202.12, "word": " جدا", "probability": 0.9970703125}, {"start": 4202.12, "end": 4202.9, "word": " بتعرفني", "probability": 0.8896484375}, {"start": 4202.9, "end": 4203.44, "word": " بالظبط", "probability": 0.990478515625}], "temperature": 1.0}, {"id": 182, "seek": 423216, "start": 4204.1, "end": 4232.16, "text": "كيف اعرف كمية الغاز اللى تكون كيف اعرف جداش التفكك من المادة جداش التفاعل من المادة تجربة جميلة للغاية يعني كتير مفيدة و بنستخدمها عادة فى المختبر بشكل فعال و ممكن تستخدم كتجربة عملية نتطلع على كمان مثال بيقول in an experiment conducted at 25 degrees C", "tokens": [4117, 33911, 1975, 3615, 28480, 9122, 2304, 10632, 6024, 118, 31377, 13672, 7578, 6055, 30544, 9122, 33911, 1975, 3615, 28480, 10874, 3215, 33599, 16712, 5172, 4117, 4117, 9154, 9673, 18513, 3660, 10874, 3215, 33599, 16712, 5172, 995, 30241, 9154, 9673, 18513, 3660, 6055, 7435, 25513, 3660, 10874, 2304, 26895, 3660, 24976, 17082, 995, 10632, 37495, 22653, 9122, 2655, 13546, 3714, 5172, 25708, 3660, 4032, 44945, 14851, 9778, 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4462.87, "word": " total", "probability": 0.62158203125}, {"start": 4462.87, "end": 4463.31, "word": " pressure", "probability": 0.927734375}, {"start": 4463.31, "end": 4463.95, "word": " how", "probability": 0.452392578125}, {"start": 4463.95, "end": 4464.19, "word": " many", "probability": 0.91845703125}, {"start": 4464.19, "end": 4464.51, "word": " grams", "probability": 0.70654296875}, {"start": 4464.51, "end": 4464.71, "word": " of", "probability": 0.9658203125}, {"start": 4464.71, "end": 4465.21, "word": " ammonium", "probability": 0.937744140625}, {"start": 4465.21, "end": 4466.45, "word": " nitrate", "probability": 0.82080078125}, {"start": 4466.45, "end": 4467.21, "word": " were", "probability": 0.7021484375}, {"start": 4467.21, "end": 4468.03, "word": " decomposed", "probability": 0.927490234375}, {"start": 4468.03, "end": 4468.69, "word": " عشان", "probability": 0.93896484375}, {"start": 4468.69, "end": 4469.01, "word": " اجيب", "probability": 0.8912353515625}, {"start": 4469.01, "end": 4469.35, "word": " هذا", "probability": 0.908203125}, {"start": 4469.35, "end": 4470.29, "word": " لازم", "probability": 0.95849609375}, {"start": 4470.29, "end": 4470.45, "word": " في", "probability": 0.916015625}, {"start": 4470.45, "end": 4470.89, "word": " البداية", "probability": 0.98388671875}, {"start": 4470.89, "end": 4471.19, "word": " اجيب", "probability": 0.9708251953125}, {"start": 4471.19, "end": 4471.47, "word": " عدد", "probability": 0.9856770833333334}, {"start": 4471.47, "end": 4472.01, "word": " الملات", "probability": 0.7779134114583334}], "temperature": 1.0}, {"id": 193, "seek": 448781, "start": 4472.45, "end": 4487.81, "text": "بعدد ملات الجاز لازم لان هذا عبارة عن تفاعل بيعطيني غاز فلازم بعدد ملات الغاز ومنه بقدر اجيب جداش كمية المادة المتفككة فبقول get in لل nitrogen and use it to find in لل ammonium nitrate", "tokens": [3555, 22488, 3215, 3714, 1211, 9307, 25724, 31377, 5296, 31377, 2304, 5296, 7649, 23758, 6225, 3555, 9640, 3660, 18871, 6055, 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"word": " اجيب", "probability": 0.9141845703125}, {"start": 4480.99, "end": 4481.45, "word": " جداش", "probability": 0.7535807291666666}, {"start": 4481.45, "end": 4481.79, "word": " كمية", "probability": 0.9788411458333334}, {"start": 4481.79, "end": 4482.17, "word": " المادة", "probability": 0.9814453125}, {"start": 4482.17, "end": 4482.97, "word": " المتفككة", "probability": 0.9625651041666666}, {"start": 4482.97, "end": 4483.77, "word": " فبقول", "probability": 0.9078776041666666}, {"start": 4483.77, "end": 4484.07, "word": " get", "probability": 0.50732421875}, {"start": 4484.07, "end": 4484.43, "word": " in", "probability": 0.76123046875}, {"start": 4484.43, "end": 4484.59, "word": " لل", "probability": 0.783203125}, {"start": 4484.59, "end": 4485.01, "word": " nitrogen", "probability": 0.3994140625}, {"start": 4485.01, "end": 4485.27, "word": " and", "probability": 0.9052734375}, {"start": 4485.27, "end": 4485.51, "word": " use", "probability": 0.83154296875}, {"start": 4485.51, 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a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/Sp8Q6FPQZTc.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/Sp8Q6FPQZTc.srt new file mode 100644 index 0000000000000000000000000000000000000000..bf203608e52ea3f7249c8496f833543426babc45 --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/Sp8Q6FPQZTc.srt @@ -0,0 +1,3831 @@ +1 +00:00:20,670 --> 00:00:23,910 +بسم الله الرحمن الرحيم، الاخوة إن شاء الله اليوم + +2 +00:00:23,910 --> 00:00:29,430 +بنكمل في الشابتر الثاني elements, molecules and + +3 +00:00:29,430 --> 00:00:36,890 +ions. اتكلمنا في الحصة الماضية عن الذرات ومنشأها + +4 +00:00:36,890 --> 00:00:43,970 +وكيف تعرّفوا على الجسيمات اللي بتكونها وإيش النظر + +5 +00:00:43,970 --> 00:00:47,770 +الحديثة للذرة؟ فقلنا إن الذرة بتتكون من + +6 +00:00:50,510 --> 00:00:55,790 +نواة وإلكترونات بتدور حول النواة. النواة موجود + +7 +00:00:55,790 --> 00:01:01,810 +فيها الـ protons والـ neutrons والكتلة الذرية + +8 +00:01:01,810 --> 00:01:07,530 +تتركز في النواة، يعني معظم كتلة الذرة هي + +9 +00:01:07,530 --> 00:01:12,550 +عبارة عن النواة، وكتلة الإلكترونات تعتبر قليلة جداً + +10 +00:01:12,550 --> 00:01:18,590 +بالنسبة لكتلة النواة، لدرجة إنه تقريباً كل proton + +11 +00:01:21,690 --> 00:01:26,110 +بيزن حوالي ألف وثمانية وتزيد عن ألف وثمانية وستة + +12 +00:01:26,110 --> 00:01:29,590 +وثلاثين electron. فلما نكون في عندي عدد من ال + +13 +00:01:29,590 --> 00:01:34,630 +protons وعدد من ال neutrons معناته الذرة بالفعل + +14 +00:01:34,630 --> 00:01:43,010 +تتركز كتلتها في النواة. أيضاً عرفنا أنه في عندنا + +15 +00:01:43,010 --> 00:01:50,510 +الذرات لكل عنصر من العناصر متشابهة، بمعنى أن كل + +16 +00:01:50,510 --> 00:01:57,590 +عنصر من العناصر بيحتوي على نفس العدد من الـ protons + +17 +00:01:57,590 --> 00:02:01,470 +لأن الـ protons هو اللي بيحدد هوية العنصر. عدد الـ protons هو + +18 +00:02:01,470 --> 00:02:06,290 +اللي بيحدد هوية العنصر. فعناصر أو ذرات العنصر + +19 +00:02:06,290 --> 00:02:09,810 +الواحد متشابهة، وإن كان فيه عندي زي ما شفنا + +20 +00:02:09,810 --> 00:02:15,450 +isotopes. فالـ isotopes بتتشابه في العدد الذري لها + +21 +00:02:15,450 --> 00:02:20,770 +اللي هو number of protons. سمّيناها atomic number و + +22 +00:02:20,770 --> 00:02:23,530 +فهي بتتشابه في الـ atomic number. فبنلاحظ أن الكربون + +23 +00:02:23,530 --> 00:02:29,030 +مثلاً كل الكربون مهما كان نوعه، هنلاحظ أن ال + +24 +00:02:29,030 --> 00:02:33,350 +synthetic أو حتى كمان naturally occurring، هنلاحظ + +25 +00:02:33,350 --> 00:02:39,220 +أن كل ذرة من ذراتها حوالي 6 بروتونات. لكن عدد + +26 +00:02:39,220 --> 00:02:42,500 +النيوترونات ممكن يختلف، وهذا اللي بيعطينا النظائر + +27 +00:02:42,500 --> 00:02:48,300 +فمجموع عدد الـ protons والـ neutrons سمّيناها الـ mass + +28 +00:02:48,300 --> 00:02:53,340 +number. ففي عندي كل عنصر من العناصر فيه له أو كل + +29 +00:02:53,340 --> 00:03:00,410 +ذرة من ذرات العنصر موجود فيها لها atomic number + +30 +00:03:00,410 --> 00:03:04,630 +اللي هو عدد الـ protons، وموجود لها أيضاً mass number + +31 +00:03:04,630 --> 00:03:08,890 +اللي هو مجموع عدد الـ protons والـ neutrons. ولأنه + +32 +00:03:08,890 --> 00:03:12,230 +دائماً العنصر الواحد الـ atomic number اللي هو واحد + +33 +00:03:12,230 --> 00:03:15,510 +فعادة ما بنكتبش الـ atomic number، بنكتب الـ mass + +34 +00:03:15,510 --> 00:03:20,490 +number. فبنقول مثلاً الـ carbon اللي بيحتوي على ستة + +35 +00:03:20,490 --> 00:03:26,360 +بروتونات وستة نيوترونات، بنقول له carbon 12 فقط. مش + +36 +00:03:26,360 --> 00:03:30,040 +carbon 612. ممكن نكتبه carbon 612 لكن هو carbon 12. + +37 +00:03:30,040 --> 00:03:34,440 +بيقال لو كان بيحتوي على سبعة نيوترونات ولازم + +38 +00:03:34,440 --> 00:03:37,740 +بالضرورة يحتوي على ستة protons. فمعناته ده carbon + +39 +00:03:37,740 --> 00:03:44,780 +13، سبعة وستة ثلاثة عشر. ولو كان بيحتوي على ثمانية الـ + +40 +00:03:44,780 --> 00:03:49,060 +neutrons، وطبعاً ستة الـ protons فبنسميه carbon 14. + +41 +00:03:49,060 --> 00:03:56,040 +وهذه كلها الـ carbon 12 و 13 و 14 تعتبر isotopes أو + +42 +00:03:56,040 --> 00:03:56,580 +نظائر. + +43 +00:03:59,180 --> 00:04:04,840 +طبعاً عدد الإلكترونات في الذرة المتعادلة دائماً + +44 +00:04:04,840 --> 00:04:08,260 +بيساوي عدد الـ protons. الـ protons بيساوي عدد + +45 +00:04:08,260 --> 00:04:11,320 +الإلكترونات، وهيك بتكون الذرة متعادلة، لإن الإلكترونات + +46 +00:04:11,320 --> 00:04:18,200 +شفنا إن الشحنة تبعها minus one، أما الـ protons فهو + +47 +00:04:18,200 --> 00:04:21,860 +plus one. الإلكترونات minus one، فبيداروا البروتونات + +48 +00:04:21,860 --> 00:04:27,250 +شفنا إنه plus one، وطبعاً هذا بوحدات المفروض إنه + +49 +00:04:27,250 --> 00:04:32,530 +مضروبة في شحنة الإلكترون الحقيقية اللي هي 1 + +50 +00:04:32,530 --> 00:04:40,170 +.602×10¹⁹. كلهم الآن من الـ isotopes والـ abundance + +51 +00:04:40,170 --> 00:04:43,030 +تبعها، يعني جدّاش النسبة المئوية لها في الطبيعة؟ + +52 +00:04:43,030 --> 00:04:46,590 +اقدرنا نحسب الـ average atomic weight أو atomic + +53 +00:04:46,590 --> 00:04:52,050 +mass للعناصر المختلفة، للذرات المختلفة. فشوفنا الحصة + +54 +00:04:52,050 --> 00:04:55,660 +الماضية أيضاً إن الـ Atomic Weight أو الـ Average + +55 +00:04:55,660 --> 00:04:59,160 +Atomic Weight هو عبارة عن summation للـ Isotope + +56 +00:04:59,160 --> 00:05:04,500 +Mass معبر عنها بالـ AMU في الـ fraction للـ Isotope + +57 +00:05:04,500 --> 00:05:08,220 +Abundance، يعني النسبة المئوية لوجوده في الطبيعة. + +58 +00:05:08,220 --> 00:05:13,040 +وحلّينا هذا المثال، فقلنا إنه الـ Carbon اللي موجود + +59 +00:05:13,040 --> 00:05:18,460 +في الطبيعة عادةً هو Carbon 12 و Carbon 13، لكن الـ + +60 +00:05:18,460 --> 00:05:24,420 +Carbon 12 بيمثل 98.93%، بينما الـ Carbon 13 بيمثل + +61 +00:05:24,420 --> 00:05:31,500 +فقط 1.07%، فكيف نحسب الـ Atomic weight للـ Carbon + +62 +00:05:31,500 --> 00:05:34,660 +اللي بدنا نحطه في الجدول الدوري بعد شويّة؟ بنقول + +63 +00:05:34,660 --> 00:05:39,660 +لازم ناخد بعين الاعتبار الـ two isotopes. فكل واحد + +64 +00:05:39,660 --> 00:05:48,680 +حسب ال... جدّاش الـ mass الـ atomic mass له. فمثلاً + +65 +00:05:48,680 --> 00:05:53,360 +الـ carbon 12 الـ atomic mass له 12 amu بالضبط، 12 + +66 +00:05:53,360 --> 00:06:02,180 +.000 amu، بينما الـ carbon 13 13.00335 amu. فقلنا إن + +67 +00:06:02,180 --> 00:06:07,180 +والله الـ atomic weight بيساوي 12 amu مضروبة في + +68 +00:06:07,180 --> 00:06:11,600 +النسبة المئوية طبعاً كثيراً fraction، ما حدا يضرب في + +69 +00:06:11,600 --> 00:06:15,900 +98، لإن هيك بيصير الـ atomic weight يعني عالي جداً + +70 +00:06:15,900 --> 00:06:19,760 +جداً، غلط، مش هيك، فاحنا بنقول ايه في النسبة المئوية + +71 +00:06:19,760 --> 00:06:25,440 +طبعاً كثيراً fraction، كثر فـ point nine eight nine + +72 +00:06:25,440 --> 00:06:32,610 +three. مجموع لها الـ isotope الثاني 13.00335 AMU + +73 +00:06:32,610 --> 00:06:35,530 +اللي هو الكربون 13 في النسبة المئوية تبعته ك + +74 +00:06:35,530 --> 00:06:39,630 +fraction بيطلع عندي 12.01، عشان هيك لما نيجي نقول + +75 +00:06:39,630 --> 00:06:44,010 +والله جدّاش الـ atomic weight للكربون اللي موجود في + +76 +00:06:44,010 --> 00:06:49,140 +الجدول الدوري، بنقول 12.01. ليه؟ لأن الـ two isotopes + +77 +00:06:49,140 --> 00:06:51,980 +بيشاركوا في تحديد الـ atomic weight أو الـ average + +78 +00:06:51,980 --> 00:06:55,720 +atomic weight للعنصر اللي في حالتنا هذه هو الكربون. + +79 +00:06:55,720 --> 00:07:00,160 +كمان مثال أو مثالين، بقول Naturally occurring + +80 +00:07:00,160 --> 00:07:05,700 +chlorine is 75.78% chlorine 35. + +81 +00:07:10,160 --> 00:07:15,080 +جدّاش الـ Atomic Master لكلورين 35 جاله والله 34 + +82 +00:07:15,080 --> 00:07:24,300 +.969 AMU، ولاحظوا الأصل إنه لكلورين 35 يعني معناته + +83 +00:07:24,300 --> 00:07:28,780 +بيحتوي على 35 بروتون ونيوترون، هو في الحقيقة بيحتوي + +84 +00:07:28,780 --> 00:07:35,320 +على 17 بروتون و 18 نيوترون. طب لِبروتونا لِنيوترون + +85 +00:07:36,150 --> 00:07:41,650 +الـ Atomic Mass له أكثر من واحد، 1.000 كسر، شفنا + +86 +00:07:41,650 --> 00:07:46,170 +الحصة الماضية، طيب، الأصل إن الـ Atomic Mass تبعته + +87 +00:07:46,170 --> 00:07:51,790 +إيش تكون؟ أكثر من 35 مش 34، هنعلّق على هذا الكلام + +88 +00:07:51,790 --> 00:08:00,450 +بعد شويّة. الكلورين 37 النسبة المئوية له 24.22%، والـ + +89 +00:08:00,450 --> 00:08:10,550 +atomic mass 36.966، برضه أقل شويّة من 37، مع إنه + +90 +00:08:10,550 --> 00:08:15,570 +مفروض تكون أكثر شويّة من 37. على أي حال خليني الآن + +91 +00:08:15,570 --> 00:08:17,610 +نحسب الـ atomic weight وبعدين بنعلّق على هذا + +92 +00:08:17,610 --> 00:08:20,390 +الكلام في الـ slide اللي جاية. بقول calculate the + +93 +00:08:20,390 --> 00:08:22,350 +atomic weight of the chlorine. إيش هو الـ atomic + +94 +00:08:22,350 --> 00:08:24,670 +weight اللي احنا بدنا نحطه في الجدول الدوري؟ قال + +95 +00:08:24,670 --> 00:08:28,370 +بقدرش أقول والله الـ atomic weight فقط هو عبارة عن + +96 +00:08:28,370 --> 00:08:33,290 +34.969، لإن هيك بكون أهمل وجود الـ carbon 37. ولا + +97 +00:08:33,290 --> 00:08:38,030 +بقدر أقول إنه والله هو 36 point 966، لإن هيك بكون + +98 +00:08:38,030 --> 00:08:43,210 +أهمل لـ chlorine 35، فلازم الاتنين يشاركوا. فالقانون + +99 +00:08:43,210 --> 00:08:49,450 +اللي عندنا الـ summation، بدي مجموع الحاصل + +100 +00:08:49,450 --> 00:08:54,430 +ضرب الـ amu لكل isotope في نسبة المئوية تبعته ك + +101 +00:08:54,430 --> 00:09:02,790 +fraction. فعندي الـ carb الـ chlorine 35 الـ amu 34.969 + +102 +00:09:02,790 --> 00:09:08,570 +مضروبة في النسبة المئوية كـ fraction زائد 36.966 في + +103 +00:09:08,570 --> 00:09:12,810 +0.2422 اللي هي الـ fraction من نسبة المئوية، بيطلع لي + +104 +00:09:12,810 --> 00:09:15,970 +35.45، اه هذا هو الـ atomic weight اللي أنا بحطه في + +105 +00:09:15,970 --> 00:09:21,780 +الجدول الدوري تمام. كمان مثال، بيقول الـ three + +106 +00:09:21,780 --> 00:09:25,100 +isotopes of silicone occur in nature. في عندي + +107 +00:09:25,100 --> 00:09:27,960 +ثلاثة isotopes للسيليكون موجودة في الطبيعة. + +108 +00:09:27,960 --> 00:09:31,180 +السيليكون 28 نسبته 92.23%، + +109 +00:09:31,180 --> 00:09:35,880 +هذا هو يعني أعلى نسبة، زي مثلاً لما + +110 +00:09:35,880 --> 00:09:40,720 +شفنا الكربون 98 وشويّة، الكلورين 35 هو + +111 +00:09:40,720 --> 00:09:45,520 +75 وشويّة. ففيه دائماً ايزوتوب من الـ isotopes إيش بيكون + +112 +00:09:45,520 --> 00:09:50,020 +بيكون يعني highly abundant، بيكون موجود بشكل كبير + +113 +00:09:50,020 --> 00:09:53,260 +للغاية، أكثر بكثير من غيره، وفيه isotopes تكون موجودة + +114 +00:09:53,260 --> 00:09:58,020 +marginal، هامشية، يعني وجودها قليل جداً. فالسيليكون + +115 +00:09:58,020 --> 00:10:08,750 +28 النسبة المئوية له 92.23%. الـ AMU 27.97693 + +116 +00:10:08,750 --> 00:10:13,650 +وكمان مرة السيليكون 28، لكن الـ atomic mass له أقل + +117 +00:10:13,650 --> 00:10:21,000 +طيب السيليكون 29، قال موجود 4.68% فقط. طب جدّاش + +118 +00:10:21,000 --> 00:10:28,580 +الـ atomic mass؟ جاله 28.97649 + +119 +00:10:28,580 --> 00:10:33,340 +AMU. والسيليكون 30 كمان أقل، 3.09%، + +120 +00:10:33,340 --> 00:10:37,400 +وتلاتة وواحد من عشرة تقريباً في المائة، طب الـ AMU + +121 +00:10:37,400 --> 00:10:44,090 +جاله 29.9737. هدول الثلاثة isotopes لازم يشاركوا + +122 +00:10:44,090 --> 00:10:48,230 +كلهم في تحديد الـ atomic weight للعنصر اللي المفروض + +123 +00:10:48,230 --> 00:10:52,190 +احنا نكون معناه في الجدول الدولي. لو عندنا أيّ + +124 +00:10:52,190 --> 00:10:58,130 +حسابات بدنا نجريها على يعني أيّ مادة فيها سيليكون + +125 +00:10:58,130 --> 00:11:00,610 +فالأصل أن نستخدم هذا الـ atomic weight في الحساب + +126 +00:11:00,610 --> 00:11:04,520 +تبعنا، مش لأن السيليكون بيكون في كل شيء، لكن نسبة + +127 +00:11:04,520 --> 00:11:07,880 +بينهم بتكون متفاوتة، زي ما احنا شايفين قدامنا. + +128 +00:11:07,880 --> 00:11:14,040 +فبنقول والله الـ AMU لسيليكون 28 في النسبة تبعته كـ + +129 +00:11:14,040 --> 00:11:19,660 +fraction، الـ AMU لسيليكون 29 في النسبة المئوية له + +130 +00:11:19,660 --> 00:11:25,090 +كـ fraction، زائد الـ AMU للسيليكون 30 في النسبة + +131 +00:11:25,090 --> 00:11:31,490 +المئوية له كـ fraction، بيطلع عندي 28.09 AMU. هذه هي + +132 +00:11:31,490 --> 00:11:35,490 +القيمة اللي بتكون reported أو موجودة في الجدول + +133 +00:11:35,490 --> 00:11:36,150 +الدوري. + +134 +00:11:38,710 --> 00:11:43,530 +طيب، الآن نيجي لسؤال اللي طرحناه قبل شويّة، بنقول الـ + +135 +00:11:43,530 --> 00:11:50,750 +mass لبروتون 1.0073 amu، والـ mass لنيوترون 1.0087 + +136 +00:11:50,750 --> 00:11:56,470 +amu. فكيف مثلاً الـ chlorine 35، وقس على ذلك كل الـ + +137 +00:11:56,470 --> 00:12:01,120 +isotopes اللي شفناهم في الـ slide الماضية؟ الـ + +138 +00:12:01,120 --> 00:12:06,500 +atomic mass له 34.969، الأصل أنه 35، يعني بدي يكون + +139 +00:12:06,500 --> 00:12:11,480 +35 من هذا وهذا، بدي يكون 35 في... يعني خليني أقول + +140 +00:12:11,480 --> 00:12:15,560 +مجموهم على اثنين مثلاً يعني، فبدي يكون أكثر من 35. + +141 +00:12:15,560 --> 00:12:22,240 +فليش هو أعطاني 34.969 قال آه قال لأنه جزء من هذه + +142 +00:12:22,240 --> 00:12:27,080 +الـmass تحولت إلى binding energy هدول ال neutrons و + +143 +00:12:27,080 --> 00:12:30,420 +ال protons موجودين في النواة فبدهم يحافظوا على بعض + +144 +00:12:30,420 --> 00:12:34,880 +يعني في النواة مترابطين بشكل جيد يكونوا النواة + +145 +00:12:34,880 --> 00:12:38,260 +فبيفقدوا جزء من الـmass تبعتهم تتحول إلى طاقة + +146 +00:12:38,260 --> 00:12:43,860 +ترابط يبقى النقص في الـatomic mass unit هذا وين + +147 +00:12:43,860 --> 00:12:50,490 +راح؟ راح نتيجة تحوله إلى طاقة ترابط ماشي يا جماعة + +148 +00:12:50,490 --> 00:12:56,870 +برضه كمان يمكن بيمر معنا أثناء شغلنا مسألة زي هذه + +149 +00:12:56,870 --> 00:13:00,650 +بيقول الـparticular atom of the chromium has a + +150 +00:13:00,650 --> 00:13:06,610 +mass of 52.94 amu ذرة معينة من ذرات الـchromium + +151 +00:13:06,610 --> 00:13:12,610 +الها mass 52.94 amu بيقول لكن الـatomic weight + +152 +00:13:12,610 --> 00:13:15,090 +where is the atomic weight of the chromium is 51 + +153 +00:13:15,090 --> 00:13:21,460 +.99 ليش فيه فرق هيك يعني؟ ليش فيه فرق؟ الفرق واضح + +154 +00:13:21,460 --> 00:13:25,040 +طبعا أو السؤال إجابته واضحة لأنه عندي نظائر ويبدو + +155 +00:13:25,040 --> 00:13:30,140 +أن الذرة اللي أنا بتكلم عنها ذرة معينة 52.94 هذا + +156 +00:13:30,140 --> 00:13:35,660 +عبارة عن أحد ذرات النظير، نظير معين من نظائر + +157 +00:13:35,790 --> 00:13:40,410 +الكروميام وهذا النظير واضح أنه موجود بنسبة مئوية + +158 +00:13:40,410 --> 00:13:44,210 +قليلة لأنه لو كان هو المتغلب لكتير كان لجينا الـ + +159 +00:13:44,210 --> 00:13:48,570 +atomic mass تقريبا زيه لكن لأ لأن نسبته بتكون + +160 +00:13:48,570 --> 00:13:53,070 +قليلة فبيأثرش كتير على الـatomic mass ل الكروميام + +161 +00:13:53,070 --> 00:13:55,970 +فبنلاحظ اه ممكن الـatomic mass ل الكروميام يكون + +162 +00:13:55,970 --> 00:14:00,730 +fifty one point nine أو حتى أقل يعني إذا كان عنصر + +163 +00:14:00,730 --> 00:14:04,590 +آخر ممكن يكون الفرق بينهم أكبر ليه؟ لأنه إذا كان + +164 +00:14:04,590 --> 00:14:09,490 +النظير وجوده بكمية قليلة جداً لا تؤثر تأثير كبير + +165 +00:14:09,490 --> 00:14:11,850 +على قيمة الـAtomic Weight وهذا الكلام ممكن زي ما + +166 +00:14:11,850 --> 00:14:16,310 +شفنا في طريقة الحساب فأكيد مش راح ينعكس وجود ذرات + +167 +00:14:16,310 --> 00:14:20,930 +إلها Atomic Masses عالية أو منخفضة كتير على + +168 +00:14:20,930 --> 00:14:24,310 +الـAtomic Weight إذا كان الـabundance لإلها قليل + +169 +00:14:24,310 --> 00:14:29,590 +للغاية فبرضه هذا من اللي يعني في بعض الأحيان شغلات + +170 +00:14:29,590 --> 00:14:32,790 +بتمر علينا ولازم ناخد بالنا منها الآن + +171 +00:14:34,870 --> 00:14:39,630 +كيف احنا بنحدد الـatomic masses؟ أنا في عندي مثلا + +172 +00:14:39,630 --> 00:14:44,250 +الـsilicon 28 و الـsilicon 29 و الـsilicon 30 + +173 +00:14:44,250 --> 00:14:50,170 +عندي carbon 11 و carbon 12 و carbon 13 و carbon 14 + +174 +00:14:50,170 --> 00:14:57,130 +عندي chlorine 35 و chlorine 37 طب كيف هذه نظائر؟ + +175 +00:14:57,130 --> 00:15:02,530 +طب كيف أنا بحدد الـatomic mass لكل نظير عشان أعرف + +176 +00:15:03,600 --> 00:15:07,040 +أحسب الـatomic weight كيف بحدد الـatomic mass لكل + +177 +00:15:07,040 --> 00:15:10,220 +نظير قال في عندنا جهاز اسمه mass spectrometer + +178 +00:15:10,220 --> 00:15:15,280 +مطياف الكتلة مطياف الكتلة هذا المطياف هو الشكل + +179 +00:15:15,280 --> 00:15:18,640 +اللي قدامي هذا أحد أشكاله في الحقيقة مش الشكل + +180 +00:15:18,640 --> 00:15:24,920 +الدائم لإله لأ في عندنا أشكال عديدة جدا من مطياف + +181 +00:15:24,920 --> 00:15:27,640 +الكتلة جهاز مطياف الكتلة أو الـmass spectrometers + +182 +00:15:27,640 --> 00:15:33,440 +فهذا أحد الأشكال اللي قدامي مثلا لو في عندي + +183 +00:15:33,440 --> 00:15:39,300 +كلورين 35 أو 37 بقول المطياف بشكل عام بيتكون من + +184 +00:15:39,300 --> 00:15:45,820 +التالي بيتكون من في البداية غرفة التأين يعني أي + +185 +00:15:45,820 --> 00:15:51,400 +ذرة بتعدي جوا إيش بيحصلها تتحول إلى أيون أنا بهمني + +186 +00:15:51,400 --> 00:15:54,240 +طبعا أيونات سالبة أيونات موجبة إلا أنا بهمني بس + +187 +00:15:54,240 --> 00:15:58,900 +الايونات الموجبة ففي عندي اتحولت لأيون بتعدي على + +188 +00:15:58,900 --> 00:16:04,300 +حاجة بقولها accelerator مسرع + +189 +00:16:04,300 --> 00:16:11,460 +مسرع إيش المسرع أنا عندي أيون موجب وعندي بده يمشي + +190 +00:16:11,460 --> 00:16:16,380 +فبده يسرعه فبقول لو كان هذا سالب وهذا سالب أكثر + +191 +00:16:16,380 --> 00:16:20,740 +منه قطبين واحد سالب والتاني سالب أكثر منه والموجب + +192 +00:16:20,740 --> 00:16:23,960 +دخل من عند السالب راح لجه سالب أكثر منه إيش بيعمل + +193 +00:16:24,910 --> 00:16:30,250 +بتسرع سرعته أكبر فبيتسرع هذا بنقولها accelerator + +194 +00:16:30,250 --> 00:16:39,930 +برضه ممكن نسميها focusing lens lens يعني إيه؟ عدسة + +195 +00:16:39,930 --> 00:16:44,190 +بس هي مش عدسة المقصودة مش عدسة optical بصرية لأ + +196 +00:16:44,190 --> 00:16:48,530 +عدسة يعني electrode electrodes قطب بس بنسميه + +197 +00:16:48,530 --> 00:16:54,870 +focusing lens لأنه بيعمل يعني خليني أقول تركيز أو + +198 +00:16:54,870 --> 00:16:59,550 +تسريع لال أيونات تبعتي فبعد ما حولت الايونات + +199 +00:16:59,550 --> 00:17:04,690 +لchlorine 35 وchlorine 37 لchlorine 35 موجب + +200 +00:17:04,690 --> 00:17:09,710 +وchlorine 37 موجب دخلوا على إيه؟ دخلوا على الـ + +201 +00:17:09,710 --> 00:17:12,090 +focusing lens أو على الـaccelerator فصاروا سريعين + +202 +00:17:12,090 --> 00:17:16,060 +كتير فمشيين بسرعة إذا كانت بتلاحظوا الأصل أنه + +203 +00:17:16,060 --> 00:17:20,520 +ماشيين بسرعة فظيعة جدا يدور جوانه لأنه بقى مستقيم + +204 +00:17:20,520 --> 00:17:24,220 +ماشيين بسرعة رهيبة كتير لكن لأ في في الطريق إيه + +205 +00:17:24,220 --> 00:17:33,180 +مغناطيس وقلنا سابقا أنه أي شحنة متحركة أي شحنة متحركة + +206 +00:17:33,180 --> 00:17:37,060 +بتعمل مجال مغناطيسي وبالتالي بتتأثر بالمجالات + +207 +00:17:37,060 --> 00:17:41,680 +المغناطيسية فهنا حسب المجال المغناطيسي حسب شدته + +208 +00:17:41,680 --> 00:17:48,160 +هنلاحظ أنه حصل deflection للشحنة وبالتالي خدوا + +209 +00:17:48,160 --> 00:17:51,040 +بالكم حسب قيمة المجال المغناطيسي أنا ممكن أظبطه + +210 +00:17:51,040 --> 00:17:55,800 +بحيث أنه بس الـ35 هي اللي تعدي لأن كل واحدة حسب + +211 +00:17:55,800 --> 00:18:00,800 +كتلتها بيقولها mass to charge حسب الكتلة والشحنة + +212 +00:18:00,800 --> 00:18:06,960 +تبعتها والـ37 ما عدتش فالـdetector أو الكاشف + +213 +00:18:06,960 --> 00:18:12,520 +هيعطيني اه peak لـ35 غيرت في المجال المغناطيسي C + +214 +00:18:12,520 --> 00:18:21,130 +طلعت الـ37 هي 37 لحظة كبر الـPeak تبعتي بتعبر عن + +215 +00:18:21,130 --> 00:18:25,510 +إيه؟ بتعبر عن الـabundance الشدة بتعبر عن التركيز + +216 +00:18:25,510 --> 00:18:30,510 +فهان يعني في عند الـchlorine 35 كتير بينما الـ + +217 +00:18:30,510 --> 00:18:34,370 +chlorine 37 أشمال وأقل وبالفعل الـchlorine 35 كان + +218 +00:18:34,370 --> 00:18:40,330 +حوالي 75% بينما الـchlorine 37 كان حوالي 25% واضح + +219 +00:18:40,330 --> 00:18:43,750 +جدا في الـmass spectrometer يبقى استخدمنا الـmass + +220 +00:18:43,750 --> 00:18:47,210 +spectrometer هو نوع معين من الـMass Spectrometer + +221 +00:18:47,210 --> 00:18:50,510 +بنقوله High Resolution Mass Spectrometer علشان + +222 +00:18:50,510 --> 00:18:56,290 +يعطيني الـatomic mass units لمين؟ للـisotopes + +223 +00:18:56,290 --> 00:19:01,280 +المختلفة من كل عنصر وبالتالي أقدر أتعرف كل عنصر + +224 +00:19:01,280 --> 00:19:04,300 +جدّاش الـabundance لإله النسبة المئوية لإله و + +225 +00:19:04,300 --> 00:19:09,820 +جدّاش الـAMU بالظبط تبعته فمن هذه المعلومات أقدرت + +226 +00:19:09,820 --> 00:19:16,220 +أستخدم أجد الـisotopes و الـabundance تبعهم علشان + +227 +00:19:16,220 --> 00:19:21,250 +أحسب الـatomic weight لكل عنصر اللي قبل شوية احنا + +228 +00:19:21,250 --> 00:19:26,450 +حسبناه بس فرجيتكم الآن كيف بنعمله من ناحية عملية + +229 +00:19:26,450 --> 00:19:31,470 +فسهل جدا نعرف الـatomic mass unit لكل isotope كل + +230 +00:19:31,470 --> 00:19:35,690 +نوع من أنواع الذرات لكن العنصر بيتكون من أكثر من + +231 +00:19:35,690 --> 00:19:38,670 +نوع واحد أغلب العناصر في الحقيقة مش عنصر أو عنصرين + +232 +00:19:38,670 --> 00:19:42,830 +أغلب عناصر الجدول الدوري فيها isotopes أغلبها يعني + +233 +00:19:42,830 --> 00:19:45,910 +نادر نلاقي عنصر بس والله ما فيش إلا نوع واحد من + +234 +00:19:45,910 --> 00:19:49,580 +الذرات فيه لأ أغلبها في إيه؟ أكثر من الـisotope + +235 +00:19:49,580 --> 00:19:53,260 +طبعا هو نفس النوع العنصر نفس النوع من الذرات لكن + +236 +00:19:53,260 --> 00:19:56,400 +الـatomic mass unit لأ بيختلف لأنه عدد الـ + +237 +00:19:56,400 --> 00:19:59,860 +neutrons ممكن أن تكون تختلف الـprotons صح ثابتة لكن + +238 +00:19:59,860 --> 00:20:03,920 +الـneutrons ممكن تختلف وبالتالي بقدر أعين الـ + +239 +00:20:03,920 --> 00:20:09,370 +atomic mass لكل isotope من الـisotopes وكمان مش بس + +240 +00:20:09,370 --> 00:20:12,530 +الـmass ولا وكمان الـrelative abundance اللي هي + +241 +00:20:12,530 --> 00:20:16,930 +عبارة عن الـsignal intensity بتعطيني فكرة عن الـ + +242 +00:20:16,930 --> 00:20:20,290 +abundance وبالتالي بقدر أعرف الـatomic masses + +243 +00:20:20,290 --> 00:20:26,160 +لل عناصر المختلفة الآن عرفنا أنه كل عنصر له atomic + +244 +00:20:26,160 --> 00:20:32,660 +number عدد للـprotons كل عنصر له atomic weight تمام + +245 +00:20:32,660 --> 00:20:36,680 +العلماء حاولوا أنهم يستفيدوا من هذه المعلومات فبعد + +246 +00:20:36,680 --> 00:20:42,580 +جهد كبير جدا استطاعوا أنهم يعني يجدوا نوع من الـ + +247 +00:20:42,580 --> 00:20:48,690 +periodicity يعني التكرارية كيف؟ قالوا والله إذا كان + +248 +00:20:48,690 --> 00:20:53,630 +احنا رتبنا العناصر بناء على عدد الـprotons اللي + +249 +00:20:53,630 --> 00:20:57,970 +موجودة فيها يعني الـatomic number، كويس، هذه أول + +250 +00:20:57,970 --> 00:21:01,830 +حاجة، يبقى بنرتب العناصر حسب إيه؟ حسب الـatomic + +251 +00:21:01,830 --> 00:21:06,910 +number وكمان حاجة قال وكمان بدنا نحاول نحط العناصر + +252 +00:21:06,910 --> 00:21:12,150 +المتشابهة تحت بعضها يعني لو أثناء ترتيبنا للعناصر + +253 +00:21:12,150 --> 00:21:18,890 +حسب الـatomic number وصلنا لعنصر معين بعدين العنصر + +254 +00:21:18,890 --> 00:21:23,110 +اللي بعده الـatomic number أعلى بواحد لكن هنلاحظ + +255 +00:21:23,110 --> 00:21:27,470 +أنه مثلا كان مشابه في خصائصه لأول عنصر حنطلع تحت + +256 +00:21:27,470 --> 00:21:30,680 +أول عنصر ونبدأ من أول وجديد مع هذا كمان مرة أقول + +257 +00:21:30,680 --> 00:21:33,700 +لا كمان مرة احنا بدأنا نقول atomic number واحد + +258 +00:21:33,700 --> 00:21:38,500 +اتنين تلاتة أربعة خمسة ستة سبعة ثمانية لجينا انه + +259 +00:21:38,500 --> 00:21:43,720 +تسعة تسعة عشر لجينا أنه حد عاشر زي واحد إن كمل حد + +260 +00:21:43,720 --> 00:21:46,940 +عاشر تماما مش هي سطر واحد لأ زي واحد حطه تحت واحد + +261 +00:21:46,940 --> 00:21:51,320 +اثنا عشر ثلاثة عشر أربعة عشر خمسة عشر وهكذا فعلنا + +262 +00:21:51,320 --> 00:21:54,520 +حاجة شبيهة بالجدول الدوري ولجينا فيها periodicity + +263 +00:21:54,520 --> 00:22:01,400 +يعني نوع من التكرارية فمثلا واحد اثنين تلاتة أربعة + +264 +00:22:01,400 --> 00:22:06,640 +إلى آخره تسعة عشر اللي جينا نيون الصوديوم أحد عشر + +265 +00:22:06,640 --> 00:22:10,300 +أحد عشر أكملنا هيك لكن اللي جينا إن الصوديوم + +266 +00:22:10,300 --> 00:22:15,160 +بالظبط زي الليثيوم إذا نحطه تحته البوتاسيوم بالظبط + +267 +00:22:15,160 --> 00:22:18,780 +زي الصوديوم زي الصوديوم و زي الليثيوم إذا نحطه تحت + +268 +00:22:18,780 --> 00:22:26,640 +الصوديوم فعلنا periods دورات horizontal وعملنا + +269 +00:22:26,640 --> 00:22:33,610 +مجموعات vertical تمام فلجينا أنه يعني زي إيش مثلا + +270 +00:22:33,610 --> 00:22:38,710 +هان على سبيل المثال العنصر الهيليوم لجيناه non + +271 +00:22:38,710 --> 00:22:45,010 +-reactive inert gas هان non-reactive inert gas هان + +272 +00:22:45,010 --> 00:22:47,610 +non-reactive inert gas فيه periodicity في العناصر + +273 +00:22:47,610 --> 00:22:52,770 +لما نرتبه حسب الـإيه؟ حسب الـatomic number طب نيجي + +274 +00:22:52,770 --> 00:22:56,530 +نطلع على الـlithium soft و very reactive metal + +275 +00:22:57,130 --> 00:23:02,430 +الصوديوم صغير ومحرك جدًا، البوتاسيوم صغير ومحرك + +276 +00:23:02,430 --> 00:23:07,190 +جدا، زي بعض، نفس الخصائص، فقدرنا نعمل أو نستفيد + +277 +00:23:07,190 --> 00:23:10,630 +من هذا الكلام في بناء الجدول الدوري ومش هنتكلم عن + +278 +00:23:10,630 --> 00:23:16,080 +كيف وصلنا للجدول الدوري الحديث لأن هذا موضوع ثاني + +279 +00:23:16,080 --> 00:23:21,060 +هو جزء من المادة لتخصصات ثانية لكن احنا هنبص ناخد + +280 +00:23:21,060 --> 00:23:24,400 +الفكرة العامة عن إيش يعني جدول دوري كيف تم بنائه + +281 +00:23:24,400 --> 00:23:30,420 +وكيف نستفيد منه فقط لكن مش هنيجي لإيش المشاكل اللي + +282 +00:23:30,420 --> 00:23:36,080 +واجهتهم أثناء ترتيبه كيف وصلوا له مش هنتكلم عن هذا + +283 +00:23:36,080 --> 00:23:38,960 +الكلام اللي الشكل العام اللي شفناه سابقا فالآن في + +284 +00:23:38,960 --> 00:23:43,280 +الجدول الدوري هنلاحظ أن رمز العنصر بين قوسين عادة + +285 +00:23:43,940 --> 00:23:47,660 +فوقه بينحط الـ atomic number لأننا رتبنا حسب الـ + +286 +00:23:47,660 --> 00:23:51,540 +atomic number، تحت بنحط الـ atomic + +287 +00:23:51,540 --> 00:23:57,140 +weight اللي هو الوزن الذري اللي حسبناه اللي حسبناه من + +288 +00:23:57,140 --> 00:24:00,560 +كل النظائر الـ atomic weight اللي حسبناه من كل + +289 +00:24:00,560 --> 00:24:01,820 +النظائر + +290 +00:24:05,880 --> 00:24:09,360 +بيجي قدامنا الجدول الدوري التالي إذا عملنا هيك + +291 +00:24:09,360 --> 00:24:14,820 +بيجي قدامنا الجدول الدوري التالي الـ .. بنسمي + +292 +00:24:14,820 --> 00:24:19,800 +العناصر في الشكل الأفقي بنسميه period دورة + +293 +00:24:19,800 --> 00:24:24,480 +وبنسمي العناصر في الـ vertical lines أو الـ vertical + +294 +00:24:24,480 --> 00:24:29,700 +groups هذه بنسميها groups تمام؟ يبقى الجدول الدوري + +295 +00:24:29,700 --> 00:24:33,520 +عبارة عن periods و groups بدنا نفهم هذا الكلام هن + +296 +00:24:33,520 --> 00:24:34,480 +بشكل كويس كثير + +297 +00:24:38,220 --> 00:24:43,980 +عندي العناصر مقسمة إلى قسمين قسم شايفين الـ scan + +298 +00:24:43,980 --> 00:24:49,880 +شايفين هذا الخط قسم جاب للخط المتعرج على يساره و + +299 +00:24:49,880 --> 00:24:53,860 +قسم على يمينه مهم جدا نفهم هذا الكلام القسم اللي + +300 +00:24:53,860 --> 00:24:57,920 +على يساره بنقول هذه metals والقسم اللي على يمينه + +301 +00:24:57,920 --> 00:25:03,700 +بنقول هذه non metals هدول معادن وهدول غير معادن + +302 +00:25:04,560 --> 00:25:09,140 +كويس المعادن لها خصائص وغير المعادن لها خصائص + +303 +00:25:09,140 --> 00:25:13,400 +طيب يبقى هدول معادن وهدول غير معادن اللي قريبة + +304 +00:25:13,400 --> 00:25:19,200 +على الخط هذا لو جينا وحطينا هي القطر هذه عبارة عن + +305 +00:25:19,200 --> 00:25:23,740 +أشبه .. يعني خلينا نقول ماشي semi metals يعني بين + +306 +00:25:23,740 --> 00:25:27,940 +المعادن وأشباه المعادن بين المعادن وأشباه .. بين + +307 +00:25:27,940 --> 00:25:33,690 +المعادن وغير المعادن بين المعادن وغير المعادن هذه + +308 +00:25:33,690 --> 00:25:40,050 +المجموعة هي مجموعة الغازات الخاملة أو في بعض اللي + +309 +00:25:40,050 --> 00:25:43,010 +احنا نقول غازات نادرة لأن في الكيمياء احنا يعني + +310 +00:25:43,010 --> 00:25:46,850 +عموما ما مافيش عندنا شيء خامل هو خامل ضمن الظروف + +311 +00:25:46,850 --> 00:25:49,990 +اللي احنا بنعيشها لكن ضمن ظروف ثانية ممكن أنه + +312 +00:25:49,990 --> 00:25:53,770 +يتفاعل فهو ليش نقول عنه خامل برضه بالعقل يعني + +313 +00:25:53,770 --> 00:25:59,170 +فاحنا ممكن نسميها rare gases إيش يعني؟ آه نادرة لكن + +314 +00:25:59,170 --> 00:26:03,670 +هي برضه يطلق عليها غازات خاملة لا شك لكن احنا + +315 +00:26:03,670 --> 00:26:08,390 +ككيميائيين بنحب نسميها نادرة مش خاملة لأنها خاملة + +316 +00:26:08,390 --> 00:26:11,850 +ضمن الظروف العادية اللي احنا بنعيشها لكن تحت ظروف + +317 +00:26:11,850 --> 00:26:16,190 +ثانية لأ ممكن انها تتفاعل طيب إيش في عندنا كمان + +318 +00:26:16,190 --> 00:26:22,640 +حاجات يبقى هذه مجموعة إيش؟ الغازات الخاملة أو + +319 +00:26:22,640 --> 00:26:26,440 +النادرة اللي جانبها على طول فلورين كلورين برومين + +320 +00:26:26,440 --> 00:26:30,920 +يودين هذه جماعة مجموعة الهالوجينات + +321 +00:26:32,040 --> 00:26:36,320 +هالوجينات لازم نتذكرها لأنها جزء من شغلنا و + +322 +00:26:36,320 --> 00:26:40,120 +هنستفيد منها كثير في حل المسائل وكنا بنسأل عنها + +323 +00:26:40,120 --> 00:26:43,340 +كثير لأنها مهمة أنا بعطيكم أهم شيء في الجدول الدوري + +324 +00:26:43,340 --> 00:26:47,220 +وهذه إيش بنسميها؟ مجموعة الهالوجينات أبني جاهان في + +325 +00:26:47,220 --> 00:26:52,620 +عندي أول مجموعة ما عدا الهيدروجين أول مجموعة قال + +326 +00:26:52,620 --> 00:27:00,050 +هذه الـ alkali metals الـ alkali metals والجموعة اللي + +327 +00:27:00,050 --> 00:27:06,230 +جانبها على طول alkaline earth metals مفصلة لكم أنا + +328 +00:27:06,230 --> 00:27:09,890 +في جدول آخر alkaline earth metals طب واللي بينهم + +329 +00:27:09,890 --> 00:27:14,810 +هن في هدول الكسرة هادي جالها من هن لهن هدول + +330 +00:27:14,810 --> 00:27:19,370 +اسمهم الـ transition metals transition metals + +331 +00:27:19,370 --> 00:27:24,430 +العناصر الانتقالية العناصر الانتقالية باختصار + +332 +00:27:24,430 --> 00:27:30,200 +بالنسبة لنا إحنا هي عناصر قد تأخذ أكثر من Valency + +333 +00:27:30,200 --> 00:27:33,860 +يعني ممكن يكون العنصر موجب باتنين أو موجب بتلاتة + +334 +00:27:33,860 --> 00:27:38,000 +أو موجب بأربعة بخلاف العناصر الأخرى اللي هي مش + +335 +00:27:38,000 --> 00:27:41,160 +Transition اللي مش Transition عادي تنقلها نفس الـ + +336 +00:27:41,160 --> 00:27:45,500 +Valency لكن الـ Transition elements ممكن تأخذ + +337 +00:27:45,980 --> 00:27:51,320 +تكافؤات أكثر من تكافؤ واحد يعني ممكن نلاقي عنصر + +338 +00:27:51,320 --> 00:27:55,260 +موجب اثنين زي ما قلت موجب ثلاثة موجب أربعة موجب + +339 +00:27:55,260 --> 00:27:59,080 +خمسة موجب ستة موجب سبعة ممكن نلاقي كل هذا الكلام + +340 +00:27:59,080 --> 00:28:04,020 +فهذا عبارة عن إيش؟ الـ transition elements طبعا فيها + +341 +00:28:04,020 --> 00:28:08,180 +شايفين فراغ صغير هدول الـ two groups موجودين في + +342 +00:28:08,180 --> 00:28:13,000 +الفراغ هذا لو بدنا نحطهم هنا ونكمل بإمكاننا لكن + +343 +00:28:13,000 --> 00:28:16,280 +بتصير الـ group where راح اللي عند البابيعني + +344 +00:28:16,280 --> 00:28:18,980 +الصف الثاني اللي جد وجهره ما استعملوش الصفحة فأخذناهم + +345 +00:28:18,980 --> 00:28:23,180 +من هنا وحطناهم في إيش؟ أربعة عشر عنصر أربعة عشر + +346 +00:28:23,180 --> 00:28:27,080 +عنصر في إيش؟ في two periods لحالهم هذه الـ period + +347 +00:28:27,080 --> 00:28:30,480 +الأولانية بنقولها بعد الـ lanthanum بنقولها + +348 +00:28:30,480 --> 00:28:35,060 +lanthanides وهذه بعد الـ actinium بنقولها actinides + +349 +00:28:35,950 --> 00:28:41,430 +كويس الـ .. مش بحاجة لأنكم بتعرفوا إنه الـ + +350 +00:28:41,430 --> 00:28:45,050 +transition elements بنقولها D block elements والـ + +351 +00:28:45,050 --> 00:28:48,230 +.. وهذه الـ elements بنقولها F block elements مش + +352 +00:28:48,230 --> 00:28:53,250 +هيمر معنا أثناء المساق هذا لأ يعني عشان هيك بنفصلش + +353 +00:28:53,250 --> 00:28:58,790 +في هذا الكلام لما طلعنا على التسميات هذه شايفين الـ + +354 +00:28:58,790 --> 00:29:04,610 +groups في عندي عدة أنواع من أنواع الـ criteria أو + +355 +00:29:04,610 --> 00:29:10,010 +خليني أقول الوصف لهذه الـ groups فالوصف اللي قدامنا + +356 +00:29:10,010 --> 00:29:13,550 +اللي إحنا معتمدينه إن الأولى one a والثانية two a + +357 +00:29:13,550 --> 00:29:19,410 +نيجي إيش هن على بدنا نش نكمل بتقول تلاتة بيه عشان + +358 +00:29:19,410 --> 00:29:23,350 +تمشي مع هذه بتقول تلاتة بيه أربعة بيه خمسة بيه ستة + +359 +00:29:23,350 --> 00:29:28,840 +بيه سبعة بيه هدول التلاتة ثمانية بيه واحد بي واثنين + +360 +00:29:28,840 --> 00:29:33,720 +بي هيهم هن واحد بي واثنين بي هيهم هن في أسباب + +361 +00:29:33,720 --> 00:29:38,980 +طبعا لهذا الكلام مش شغلنا إحنا في هذا المساء بعدين + +362 +00:29:38,980 --> 00:29:42,600 +بنكمل اثنين إيش تلاتة إيش أربعة إيش خمسة إيش ستة + +363 +00:29:42,600 --> 00:29:47,500 +إيش سبعة إيش كل الـ a هذه كل الـ groups اللي فيها a هذه + +364 +00:29:47,500 --> 00:29:51,800 +بنقولها يعني هي الـ .. + +365 +00:29:55,720 --> 00:29:58,560 +الجدول .. يعني خليني أقول الجدول الدوري المبسط + +366 +00:29:58,560 --> 00:30:03,240 +الجدول الدوري المبسط يعني هنشوفه برضه يعني بعد + +367 +00:30:03,240 --> 00:30:07,100 +شوية جدول دوري مبسط ما .. ما فيه أي transition + +368 +00:30:07,100 --> 00:30:12,400 +elements ولا inner transition elements اللي هي الـ + +369 +00:30:12,400 --> 00:30:17,320 +Actinides والـ Lanthanides فهنشوفه بعد شوية طيب + +370 +00:30:17,320 --> 00:30:22,560 +خليني أشوف + +371 +00:30:22,560 --> 00:30:22,880 +هذا + +372 +00:30:25,920 --> 00:30:31,360 +نرجع بس مع بعض الكلام اللي إحنا شفناه خدوا بالكم + +373 +00:30:31,360 --> 00:30:36,320 +قلت المجموعة الأولى اسمها alkaline metals حلو؟ + +374 +00:30:36,320 --> 00:30:41,200 +المجموعة الثانية alkaline earth metals هذه + +375 +00:30:41,200 --> 00:30:45,910 +المجموعتين ملونة لكم كويس إيش اسمها؟ الـ + +376 +00:30:45,910 --> 00:30:51,570 +Transition metals هذه المجموعة إيش سميناها؟ الـ + +377 +00:30:51,570 --> 00:30:55,150 +halogens هذه المجموعة طالعة من الـ rare gas كل الـ + +378 +00:30:55,150 --> 00:30:59,710 +A هو عبارة عن الجدول الرئيسي الجدول الدوري الرئيسي + +379 +00:30:59,710 --> 00:31:03,250 +بنقوله main group elements main group elements + +380 +00:31:03,250 --> 00:31:07,110 +الجدول الرئيسي أو بنقوله main group elements اللي + +381 +00:31:07,110 --> 00:31:13,230 +هو كل الـ A لو جينا في تحت الـ .. أو يعني هي جانب + +382 +00:31:13,230 --> 00:31:15,830 +الـ one a في عندي واحد، اثنين، ثلاثة، أربعة، خمسة، + +383 +00:31:15,830 --> 00:31:19,890 +ستة، سبعة، ثمانية، تسعة، عشرة لغاية ثمانية عشر هذه + +384 +00:31:19,890 --> 00:31:22,830 +برضه تسمية أخرى بإمكانك تستخدم من الـ a أو التسمية + +385 +00:31:22,830 --> 00:31:25,830 +اللي إحنا ذكرناها تستخدم من a وb أو التسمية اللي + +386 +00:31:25,830 --> 00:31:28,870 +إحنا ذكرناها واحد، اثنين، ثلاثة، أربعة لغاية + +387 +00:31:28,870 --> 00:31:33,230 +ثمانية عشر الواحد لغاية ثمانية عشر هي تسمية الـ IUPAC + +388 +00:31:33,230 --> 00:31:38,550 +تسمية الـ .. يعني الاتحاد + +389 +00:31:38,550 --> 00:31:47,980 +الـ .. الدولي للكيمياء IUPAC كويس فهذا هو سماها خروجا + +390 +00:31:47,980 --> 00:31:55,540 +من التناقضات أو التعدد في تسمية إيش هي الـ groups + +391 +00:31:55,540 --> 00:31:59,840 +المختلفة اللي عندي فجأة بدل ما نسميها مثلا A وB + +392 +00:31:59,840 --> 00:32:03,560 +وبدل ما نسميها برضه هذه Arabic numerals ممكن + +393 +00:32:03,560 --> 00:32:08,440 +يسموها Roman يحطوا مثلا الـ .. بتعرفوا واحد يعني I + +394 +00:32:08,440 --> 00:32:12,320 +اثنين يعني اثنين I جنب بعض الخمسة يعني V العشرة + +395 +00:32:12,320 --> 00:32:15,400 +يعني X فكل هذه التسميات موجودة فجاء القسم بواحدة + +396 +00:32:15,400 --> 00:32:20,000 +ثمانية عشر خلاص لكن إحنا هنعتمد الـ A والـ B زي ما هو + +397 +00:32:20,000 --> 00:32:25,240 +موجود قدامنا وإن كان مش هنستخدمه برضه كثير في + +398 +00:32:25,240 --> 00:32:31,420 +شغلنا إلا إنه هنستفيد من شكل الجدول الدوري في إنه + +399 +00:32:31,420 --> 00:32:35,660 +نقدر نحل مسائل عليه هذا ما عرفنا أن هذه مجموعة + +400 +00:32:35,660 --> 00:32:38,340 +أولى وهذه مجموعة ثانية وهذه Transition Metals وهذه + +401 +00:32:38,340 --> 00:32:43,000 +Actinides وLanthanides وهذه Halogens هدول Non + +402 +00:32:43,000 --> 00:32:46,600 +-metals اللي بعد الخط هيك هذا Non-metals وهدول + +403 +00:32:46,600 --> 00:32:50,960 +اللي قبل الخط Metals واللي على جانبي الخط هيك + +404 +00:32:50,960 --> 00:32:57,360 +يعني لو أخذنا قطر بنقول هدول يعني ما بين الـ + +405 +00:32:57,360 --> 00:33:00,940 +Metals والـ Non-metals + +406 +00:33:04,130 --> 00:33:07,050 +يبقى هذا الجدول الدوري تبعنا لازم نعرف كل + +407 +00:33:07,050 --> 00:33:09,610 +المصطلحات اللي موجودة هنا لأنها مهمة يعني إيش في + +408 +00:33:09,610 --> 00:33:12,830 +عندي حاجة مسجلة أنا هن بالإضافة للـ rare gases أو + +409 +00:33:12,830 --> 00:33:15,670 +للـ noble gases لازم نعرفها إيش هي؟ نعرف المجموعة + +410 +00:33:15,670 --> 00:33:18,690 +الأولى، الثانية، الثالثة، الرابعة، إيش في عندنا الـ + +411 +00:33:18,690 --> 00:33:23,610 +main group elements لازم نعرف هذا الكلام بشكل كويس + +412 +00:33:23,610 --> 00:33:27,530 +هذه الـ noble gases صارت موجودة طيب + +413 +00:33:35,360 --> 00:33:38,320 +اللي لو طلعنا بس على الـ .. مثلا على الـ atomic + +414 +00:33:38,320 --> 00:33:40,920 +number تسعة عشر عشرين واحد عشرين اثنين عشرين ثلاثة + +415 +00:33:40,920 --> 00:33:42,680 +عشرين أربعة عشرين خمسة عشرين ستة عشرين ستة عشرين + +416 +00:33:42,680 --> 00:33:45,220 +اثنين عشرين ثلاثة عشرين الباقين شوف سبحان الله + +417 +00:33:45,220 --> 00:33:48,020 +يعني لما نرتبهم بالترتيب زي ذلك حسب الـ protons + +418 +00:33:48,020 --> 00:33:52,400 +بنلاقي دائما اللي تحتهم شيء متشابه هذا شيء عجيب + +419 +00:33:52,400 --> 00:33:55,420 +هذا في نفس الـ .. يعني في حد ذاته يعتبر آية عظيمة + +420 +00:33:55,420 --> 00:33:59,850 +يعني، آية عظيمة جدا يعني كل ما مشينا سطر نلاحظ اللي + +421 +00:33:59,850 --> 00:34:03,730 +تحت زيه بالظبط، شيء عجيب، يعني شيء ما بتوقعهش + +422 +00:34:03,730 --> 00:34:07,970 +العقل أنه جاي والله هيك صدفة يعني، طيب + +423 +00:34:10,970 --> 00:34:16,990 +هذا بعبّرني شوية عن يعني مكونات الجدول الدوري + +424 +00:34:16,990 --> 00:34:21,130 +وحكينا هذا الكلام بشكل واضح وهي الـ groups تبعتي + +425 +00:34:21,130 --> 00:34:24,310 +برضه حكينا عنها بشكل واضح في الـ coinage metals + +426 +00:34:24,310 --> 00:34:26,930 +coinage يعني ما عاملها الـ coins الـ coins اللي هي + +427 +00:34:26,930 --> 00:34:33,730 +العملة الحديد يعني هذه كوينز زي الشواكل يعني اه فهي + +428 +00:34:33,730 --> 00:34:38,710 +كبر و silver و gold لو شفناهم هما في نفس الـ group + +429 +00:34:38,710 --> 00:34:44,330 +هيكونوا هاي كبر و silver و gold نفس الخصائص مش سهل + +430 +00:34:44,330 --> 00:34:51,290 +أنهم يعني خليني أقول يتغيروا بالعوامل الجوية خاصة + +431 +00:34:51,290 --> 00:34:54,770 +في وجود alloys منهم مش سهل يعني بيحافظوا على حالهم + +432 +00:34:54,770 --> 00:34:58,450 +هم مش متغيرين لفترات زمنية طويلة جدا عشان هي الناس + +433 +00:34:58,450 --> 00:35:02,610 +بتحب تستخدمهم في ايه؟ في العملات المعدنية الـ coins + +434 +00:35:02,610 --> 00:35:09,230 +بس يعني كمعلومة أن هذه هي الـ coinage metals بتنتمي + +435 +00:35:09,230 --> 00:35:15,680 +للـ 1B group فالآن المهم أنه بده يعرفنا كيف عملنا + +436 +00:35:15,680 --> 00:35:19,040 +الجدول الدوري فبدنا نحاول أنه نستفيد من الجدول + +437 +00:35:19,040 --> 00:35:21,980 +الدوري كيف بنستخدمه عشان نستفيد هذا المهم بالنسبة + +438 +00:35:21,980 --> 00:35:26,880 +لي أنا يعني كيف بدنا نستفيد من الجدول الدوري فمثلا + +439 +00:35:26,880 --> 00:35:32,720 +مثلا لو طلعنا على حد بيسأل which two of these + +440 +00:35:32,720 --> 00:35:36,000 +elements would you expect to show the greatest + +441 +00:35:36,000 --> 00:35:40,020 +similarity in chemical and physical properties أي + +442 +00:35:40,020 --> 00:35:46,420 +اتنين من هدول الـ elements اللي بيفرجينه يعني أكتر + +443 +00:35:46,420 --> 00:35:51,640 +تشابه في خصائصه عموما الكيميائية والفيزيائية لو + +444 +00:35:51,640 --> 00:35:55,160 +سألها سؤال زي هيك بتقول إيش هي العناصر اللي راح + +445 +00:35:55,160 --> 00:35:58,300 +تتشابه في خصائصها الكيميائية وفيزيائية الجانب اللي + +446 +00:35:58,300 --> 00:36:02,500 +موجودة في نفس الـ group لازم لأن احنا قلنا خلص الـ + +447 +00:36:02,500 --> 00:36:06,260 +period بنبدأ لما نلاقي ايه عنصر مشابه لعنصر يبقى + +448 +00:36:06,260 --> 00:36:08,780 +العناصر اللي في نفس الـ group هي اللي متشابهة نشوف + +449 +00:36:08,780 --> 00:36:12,790 +أن هو اللي في نفس الـ group فبنجيب نطلع اه والله + +450 +00:36:12,790 --> 00:36:15,610 +المغنيسيوم والكالسيوم هايهم تحت بعض لفظ الجلوب إذا + +451 +00:36:15,610 --> 00:36:20,330 +هدول هيعطوني أكبر تشابه بين الخصائص الكيميائية + +452 +00:36:20,330 --> 00:36:23,230 +والفيزيائية لهذول اثنين إذا نعم الكالسيوم + +453 +00:36:23,230 --> 00:36:27,430 +والمغنيسيوم بينما لو جينا طلعنا الـ boron و الـ + +454 +00:36:27,430 --> 00:36:30,630 +fluor هاي الـ boron هان وهي الـ fluor عايش بعيد عن + +455 +00:36:30,630 --> 00:36:34,310 +بعض خالص لو كان تحته كان ممكن فبالتالي لأ بس الـ + +456 +00:36:34,310 --> 00:36:35,610 +calcium والمغنيسيوم + +457 +00:36:39,080 --> 00:36:43,140 +طيب، كل شغل الـ gate هو محاولة لاستفادة من الجدول + +458 +00:36:43,140 --> 00:36:46,760 +الدوري، يعني مش بس هذا السؤال، كل شغل الحصة هذه + +459 +00:36:46,760 --> 00:36:51,220 +محاولة لاستفادة من الجدول الدوري فخليني أتكلم عن + +460 +00:36:51,220 --> 00:36:56,020 +الـ molecules و الـ molecular compounds الـ + +461 +00:36:56,020 --> 00:36:59,880 +molecules طبعا بتختلف عن الـ elements الـ elements + +462 +00:36:59,880 --> 00:37:03,580 +تتكون من نفس النوع من العناصر حتى لو كان طبعا و + +463 +00:37:03,580 --> 00:37:08,040 +ضروري أنه يكون فيها different isotopes لما بقول + +464 +00:37:08,040 --> 00:37:11,340 +والله في عندي سيليكون الـ silicon موجود فيه سيليكون + +465 +00:37:11,340 --> 00:37:14,860 +ثمانية وعشرين وتسعة وعشرين وثلاثين في عند مثلا + +466 +00:37:14,860 --> 00:37:19,560 +كاربون هيكون فيه اه كاربون ثلاثة عشر وكاربون اثنا عشر + +467 +00:37:19,560 --> 00:37:24,360 +لازم فلما أتكلم عن العنصر بقول هو عبارة عن ايه نفس + +468 +00:37:24,360 --> 00:37:27,680 +النوع من الذرات ونفس النوع معناته مش مانع + +469 +00:37:27,680 --> 00:37:31,260 +different isotopes نعم مش مشكلة فهذا عنصر يبقى + +470 +00:37:31,260 --> 00:37:36,130 +العنصر بتكون من نوع واحد من الذرات نوع واحد من + +471 +00:37:36,130 --> 00:37:40,490 +الذرات ومعنى كلام نوع واحد مش معناته isotope واحد + +472 +00:37:40,490 --> 00:37:47,450 +لأ كل الـ isotopes من العنصر اه فش مشكلة فالعنصر + +473 +00:37:47,450 --> 00:37:56,010 +بيحتوي على نفس النوع من الذرات طيب + +474 +00:37:57,750 --> 00:38:02,090 +خليني أتكلم عن الـ molecules ايش هي الـ molecules + +475 +00:38:02,090 --> 00:38:10,630 +أو ايش هي الجزيئات يعني هي عبارة عن مجموعة من + +476 +00:38:10,630 --> 00:38:15,470 +ذرتين أو أكثر نفس العنصر أو أو مختلفة مافيش مشكلة + +477 +00:38:15,470 --> 00:38:19,270 +مدام ذرتين أو أكثر فهو molecule مدام ذرتين أو أكثر + +478 +00:38:19,270 --> 00:38:23,230 +فهو molecule نوع واحد من الذرات هو عنصر نوع واحد + +479 +00:38:23,230 --> 00:38:27,230 +من الذرات هو ايه عنصر يعني الفوسفور + +480 +00:38:29,870 --> 00:38:37,570 +P هذا عنصر لكن الـ P أربعة هو عنصر لكن .. لكن ايه؟ + +481 +00:38:37,570 --> 00:38:42,670 +جزيء في نفس الوجود لكن جزيء هو عنصر لكنه جزيء زي الـ + +482 +00:38:42,670 --> 00:38:48,750 +S هذا سلفر طب والـ S ثمانية برضه سلفر هو عنصر لكن + +483 +00:38:48,750 --> 00:38:51,950 +عنصر جزيء يعني نسميه جزيء ليه؟ لأنه أكثر من ذرة + +484 +00:38:51,950 --> 00:38:55,410 +فإذا كان في عندي أكثر من ذرة معناته + +485 +00:38:59,700 --> 00:39:02,960 +إذا عندي أكثر من ذرة يبقى صار فيه عندي جزيء + +486 +00:39:02,960 --> 00:39:10,600 +الجزيئات يا جماعة ممكن تكون جزيء عنصري زي ما شوفنا + +487 +00:39:10,600 --> 00:39:16,540 +جزيء بيتكون من نفس النوع من الذرات وممكن يكون جزيء + +488 +00:39:16,540 --> 00:39:20,320 +بيتكون من أكثر من نوع من الذرات إذا كان يتكون من + +489 +00:39:20,320 --> 00:39:23,560 +نفس النوع من الذرات بنقوله molecular element + +490 +00:39:23,560 --> 00:39:28,910 +molecular element لكن لو اختلف نوع الذرات بنقوله + +491 +00:39:28,910 --> 00:39:35,530 +compound مركب صار compound مركب إذا إذا كان في + +492 +00:39:35,530 --> 00:39:39,430 +عندي نوعين من أنواع الذرات أو أكثر كونوا جزيء + +493 +00:39:39,430 --> 00:39:44,590 +فهذا ايش اسمه compound molecular compound مش + +494 +00:39:44,590 --> 00:39:50,910 +element الـ molecular elements قلنا مثلا زي الـ + +495 +00:39:50,910 --> 00:39:55,690 +oxygen O2 هذا molecular element الـ O هي عبارة عن + +496 +00:39:55,690 --> 00:39:59,990 +الـ O2 هي element لكنه بما أنه أكثر من ذرة فهو جزء + +497 +00:39:59,990 --> 00:40:08,330 +لذا هذا molecular element الـ O2 الـ N2 الـ Cl2 Br2 + +498 +00:40:08,330 --> 00:40:15,300 +F2 I2 هذه كلها عبارة عن molecular Elements و الـ P4 + +499 +00:40:15,300 --> 00:40:18,620 +و الـ S8 هذي كلها molecular elements ليه؟ لأنه + +500 +00:40:18,620 --> 00:40:23,580 +بتتكون من نوع واحد من الذرات وهي في نفس الوجود أكثر + +501 +00:40:23,580 --> 00:40:28,340 +من ذرة، مدام أكثر من ذرة، إذا molecular element + +502 +00:40:30,550 --> 00:40:36,050 +لاحظوا أنه كل مجموعة الـ .. ايش بيسموها الهالوجينات + +503 +00:40:36,050 --> 00:40:40,310 +هي عبارة عن هذا غاز وهذا غاز الـ Br2 Liquid في + +504 +00:40:40,310 --> 00:40:45,030 +الحقيقة الـ I2 يعني الـ solid و الـ sub-limes يعني + +505 +00:40:45,030 --> 00:40:51,810 +بيتبخر بتحول لغاز مباشرة الـ hydrogen طبعا برضه + +506 +00:40:51,810 --> 00:40:57,170 +molecular element يبقى هيها الـ hydrogen و هذه + +507 +00:40:57,170 --> 00:41:02,410 +المجموعة هيك هذه كلها بتعطيني molecular elements + +508 +00:41:02,410 --> 00:41:08,150 +عادة وطبعا قلت لكم الـ P4 و الـ S8 برضه بتعطيني + +509 +00:41:08,150 --> 00:41:14,810 +molecular elements هل + +510 +00:41:14,810 --> 00:41:24,400 +ضروري أنه إذا كان ذرة معينة بتعطيني أو ذرات معينة + +511 +00:41:24,400 --> 00:41:28,640 +من نفس النوع بتعطيني molecular element هل ضروري أن + +512 +00:41:28,640 --> 00:41:33,740 +الـ molecular elements هذه تكون + +513 +00:41:33,740 --> 00:41:36,900 +متشابهة في الخصائص مثلا يعني في عند الـ oxygen ممكن + +514 +00:41:36,900 --> 00:41:43,040 +يكون O2 بنسميه oxygen و O3 ozone هل خصائصهم متشابهة + +515 +00:41:43,040 --> 00:41:47,980 +لأنه بيتكونوا من الـ oxygen فقط بنقول أبدا أبدا + +516 +00:41:48,690 --> 00:41:52,990 +المركب خصائصه .. أفوان .. يعني الـ molecule + +517 +00:41:52,990 --> 00:41:57,770 +خصائصه بتتوقف على طبيعة الذرات وهي نفس النوع لكن + +518 +00:41:57,770 --> 00:42:01,890 +طبيعة بتربطها بتعطيني خصائص مختلفة للغاية فبنلاحظ + +519 +00:42:01,890 --> 00:42:05,450 +أن الـ Oxygen ممتاز جدا، بنتنفسه، مقدرش نعيش من + +520 +00:42:05,450 --> 00:42:10,560 +غيره، ضروري للنبات والحيوان والحياة بشكل عام لكن + +521 +00:42:10,560 --> 00:42:16,400 +الـ O3 هذا ايه؟ الأوزون يعتبر سام إذا كان بدنا + +522 +00:42:16,400 --> 00:42:21,360 +نستنشقه، طبعا هو مش سام هو يعتبر disinfectant، + +523 +00:42:21,360 --> 00:42:25,480 +مطهر، ممكن يضعف بدل لكلور على المية مافيش مشكلة، + +524 +00:42:25,480 --> 00:42:28,840 +بنشرب ويكون في جزء مافيش مشكلة، لكن إذا كان بدنا + +525 +00:42:28,840 --> 00:42:35,870 +نتنفسه زي الأكسجين فهو سام تمام؟ إذا كان فيه عندي + +526 +00:42:35,870 --> 00:42:41,370 +أكثر من شكل من أشكال الـ molecular element بنسمي + +527 +00:42:41,370 --> 00:42:45,050 +هذه الأشكال allotropes ليه بيجيء اسم allotropes؟ + +528 +00:42:45,050 --> 00:42:47,310 +الـ allotropes هو عبارة عن .. الـ allotropes هي + +529 +00:42:47,310 --> 00:42:52,810 +عبارة عن .. يعني أشكال مختلفة من نفس الـ molecular + +530 +00:42:52,810 --> 00:42:58,660 +elements تمام؟ يعني مثلا S2 و S8 بيقول والله هدول + +531 +00:42:58,660 --> 00:43:03,720 +Allotropes S2 في عندي بس عنصر molecular element + +532 +00:43:03,720 --> 00:43:08,020 +بتكون من عنصر .. ذرتين من الـ sulfur و S8 بتكون من + +533 +00:43:08,020 --> 00:43:11,280 +ثمانية من الـ sulfur بيقول هذا عبارة عن Allotropes + +534 +00:43:11,280 --> 00:43:15,440 +وهذا نفس الكلام الـ O2 و الـ O3 عبارة عن Allotropes + +535 +00:43:15,440 --> 00:43:20,980 +يبقى الـ Allotropes نفس نوع الذرات لكن different + +536 +00:43:20,980 --> 00:43:28,470 +molecules نفس نوع الذرات لكن different molecules طب + +537 +00:43:28,470 --> 00:43:31,070 +شوفنا الـ molecular elements شوفنا نفس النوع من + +538 +00:43:31,070 --> 00:43:33,790 +الذرات الي هنتكلم عن الـ molecular compounds طبعا + +539 +00:43:33,790 --> 00:43:37,730 +الـ molecular compounds في عندي نوعين أو أكثر من + +540 +00:43:37,730 --> 00:43:42,330 +الذرات نوعين أو أكثر من الذرات فمثلا الكربون بتتحد + +541 +00:43:42,330 --> 00:43:48,090 +مع الهيدروجين بيعطيني CH4 اللي هو الميثين أو + +542 +00:43:48,090 --> 00:43:54,460 +الكربون بيتحد مع O2 الأكسجين بيعطيني الـ CO2 Carbon + +543 +00:43:54,460 --> 00:43:59,340 +Dioxide هذا Molecular Compound الأكسجين بتتحد مع + +544 +00:43:59,340 --> 00:44:05,060 +H2 بيعطيني H2O مركب المية اللي احنا بنعرفه إذا + +545 +00:44:05,060 --> 00:44:11,840 +الـ molecular compound هو عبارة عن مركب بيحتوي على + +546 +00:44:11,840 --> 00:44:18,160 +نوعين أو أكثر من الذرات نوعين أو أكثر إذا احتوى + +547 +00:44:18,160 --> 00:44:22,280 +بس على نوعين بنقوله binary باينري، بتعرفوا الـ + +548 +00:44:22,280 --> 00:44:26,360 +binary system؟ باينري، بس نوعين، لكن scan أكثر، + +549 +00:44:26,360 --> 00:44:30,060 +خلاص، ممكن نقوله poly أو بنسميهوش poly، أما الـ + +550 +00:44:30,060 --> 00:44:33,100 +scan اثنين، بس تحديدا بنقوله binary، binary + +551 +00:44:33,100 --> 00:44:34,140 +molecular compound + +552 +00:44:43,630 --> 00:44:46,310 +الـ Molecular Compounds اللي احنا هنواجهها في + +553 +00:44:46,310 --> 00:44:53,050 +الحقيقة أغلبها بتوجع في منطقة الـ Non-metals يعني + +554 +00:44:53,050 --> 00:44:58,790 +الـ Non-metals مع بعضها لبعض بتكون مركبات عادة + +555 +00:44:58,790 --> 00:45:02,280 +Molecular Compounds يبقى الـ molecular compounds + +556 +00:45:02,280 --> 00:45:07,100 +وين هنلاقيها؟ شفتوا الخط المتعرج اللي على يمينه، + +557 +00:45:07,100 --> 00:45:10,940 +ايش بتتحد مع بعض، هيعطوني ايه؟ Molecular + +558 +00:45:10,940 --> 00:45:15,600 +compound، لكن في عندي حاجة ثانية Ionic، هنشوفها + +559 +00:45:15,600 --> 00:45:19,540 +كيف بتتكون في المستقبل، فعندي مثلا الـ hydrogen، + +560 +00:45:19,540 --> 00:45:26,150 +oxygen، هذه عبارة عن Elements فهذه يعني molecular + +561 +00:45:26,150 --> 00:45:31,750 +elements بينما عندي الـ carbon monoxide مثلا الـ + +562 +00:45:31,750 --> 00:45:36,870 +hydrogen peroxide الميثين والـ + +563 +00:45:36,870 --> 00:45:41,190 +الإيثيلين هذه عبارة عن جزيئات فبنقولها molecular + +564 +00:45:41,190 --> 00:45:45,550 +compounds لأنها تحتوي على أكثر من نوع من أنواع + +565 +00:45:45,550 --> 00:45:52,010 +الذرات،أيضا في عندي حاجة بنقولها molecular formula + +566 +00:45:52,010 --> 00:45:56,150 +و empirical formula، الـ molecular formula هي عبارة + +567 +00:45:56,150 --> 00:46:02,210 +عن الجزيء اللي عندي من كم ذرة من كل نوع بيتكون + +568 +00:46:02,210 --> 00:46:07,510 +مثلا الماء H2O هذه molecular formula ذرتين من + +569 +00:46:07,510 --> 00:46:15,670 +الـ H وذرة من الـ O، تمام، الـ H2O2 هيدروجين بيروكسايد + +570 +00:46:15,670 --> 00:46:20,290 +ذرتين من الـ H وذرتين من الـ O فهذه عبارة عن + +571 +00:46:20,290 --> 00:46:26,570 +molecular formula، صيغة الجزيء الحقيقية، تعطينا عدد + +572 +00:46:26,570 --> 00:46:30,950 +الذرات الحقيقية من كل نوع من أنواع الذرات، يبقى الـ + +573 +00:46:30,950 --> 00:46:36,850 +molecular formula بتعطيني عدد الذرات الحقيقي من كل + +574 +00:46:36,850 --> 00:46:40,670 +نوع من أنواع الذرات الموجودة في الجزيء أو في + +575 +00:46:40,670 --> 00:46:44,970 +المركب، بتعطيني عدد الذرات الحقيقي، طب الـ empirical + +576 +00:46:44,970 --> 00:46:49,330 +من اسمها أولية، قالت بتعطيني + +577 +00:46:51,930 --> 00:46:57,030 +النسبة بين الذرات، النسبة بين الذرات على أساس + +578 +00:46:57,030 --> 00:47:02,250 +integer، يعني النسبة الأولية، النسبة الأولية بين + +579 +00:47:02,250 --> 00:47:08,630 +عدد الذرات، مثلا H2O2 هذه formula molecular، هان + +580 +00:47:08,630 --> 00:47:11,530 +اتنين وهان اتنين، طب لو قسمت على اتنين يصير HO + +581 +00:47:12,920 --> 00:47:17,780 +جايز القسمة تصير HO، هادي empirical formula، الماء + +582 +00:47:17,780 --> 00:47:22,940 +H2O، هادي molecular formula، طب الـ empirical + +583 +00:47:22,940 --> 00:47:27,560 +formula بتطلع على إيش العامل المشترك بينهم، واحد، دلتا + +584 +00:47:27,560 --> 00:47:31,200 +زي ماء H2O، الـ empirical formula هان زي الـ + +585 +00:47:31,200 --> 00:47:34,700 +molecular formula، ليه؟ لأنه بتتبسطش، الاتنين والـ + +586 +00:47:34,700 --> 00:47:40,720 +واحد بتتبسطش أبسط من هيك معايا، فهي قولنا الـ H2O2 + +587 +00:47:40,720 --> 00:47:46,000 +الـ empirical تبعته HO، الـ C2H4 اللي هو الإيثيلين + +588 +00:47:46,810 --> 00:47:52,210 +والله تجسم على 2، عامل مشترك تصبح CH2، هذه الـ + +589 +00:47:52,210 --> 00:47:55,890 +empirical formula من الإيثيلين بينما C2H4 + +590 +00:47:55,890 --> 00:48:02,710 +الـ molecular formula للاثيلين، المهم + +591 +00:48:02,710 --> 00:48:06,350 +أنه في فرق بين الـ molecular formula، هي اللي احنا + +592 +00:48:06,350 --> 00:48:09,880 +بنستفيد منها في الحقيقة، مش معنى إن الـ Empirical + +593 +00:48:09,880 --> 00:48:14,780 +formula مش فيه دا، لأ، بعض المركبات بنفعش بنعرفش الـ + +594 +00:48:14,780 --> 00:48:17,260 +molecular formula، لإنها مش molecules، فبالتالي الـ + +595 +00:48:17,260 --> 00:48:20,660 +empirical formula بتعبر تعبير حقيقي عن طبيعة + +596 +00:48:20,660 --> 00:48:23,820 +الذرات المرتبطة مع بعض البعض، لكن بالنسبة لي إذا + +597 +00:48:23,820 --> 00:48:27,700 +كان عندي جزيئات، ففي عندي molecular formula بتعبر + +598 +00:48:27,700 --> 00:48:32,180 +تعبير صحيح عن عدد الذرات الموجودة من كل نوع من + +599 +00:48:32,180 --> 00:48:35,320 +أنواع الذرات، عدد الذرات الموجودة في الجزيء من كل + +600 +00:48:35,320 --> 00:48:39,480 +نوع من أنواع الذرات، هية في عندي ذرتين كربون، أربعة + +601 +00:48:39,480 --> 00:48:42,700 +هيدروجين، هذه molecular formula، هيك المركب بيحتوي + +602 +00:48:42,700 --> 00:48:46,880 +كل مركب لو مسكناها واحد واحد، كل واحد في حاله + +603 +00:48:46,880 --> 00:48:52,140 +بيحتوي على C2H4، لكن الـ empirical formula الأولية + +604 +00:48:52,140 --> 00:48:58,290 +اللي هي بنجسم على العامل المشترك، فبتعطيني CH2، اتنين + +605 +00:48:58,290 --> 00:49:04,150 +هذه empirical formula، و + +606 +00:49:04,150 --> 00:49:07,410 +زي ما قلنا مثلا في حالة زي الماء الـ empirical + +607 +00:49:07,410 --> 00:49:12,310 +formula هي الـ الـ الـ الـ molecular formula هي الـ + +608 +00:49:12,310 --> 00:49:16,630 +empirical formula، طب الـ CO2، الـ CO2 هذي molecular + +609 +00:49:16,630 --> 00:49:19,750 +formula، carbon dioxide، ثاني أكسيد الكربون، طب إيش الـ + +610 +00:49:19,750 --> 00:49:24,960 +empirical formula اللي له؟ نفسها لأن ما فيش بتتبسطش + +611 +00:49:24,960 --> 00:49:29,180 +أكثر من هيك، طيب هنشوفه بعد شوية، مثال لجلوكوز C6 + +612 +00:49:29,180 --> 00:49:35,340 +H12O6، هي الموليكولار formula، CH2O + +613 +00:49:35,340 --> 00:49:39,140 +آه، سهل جدا، سهل جدا، طيب + +614 +00:49:42,350 --> 00:49:47,550 +ليه احنا مهتمين بالـ empirical formula في الحقيقة؟ + +615 +00:49:47,550 --> 00:49:51,590 +احنا مهتمين في الـ empirical formula لسببها رئيسيا + +616 +00:49:51,590 --> 00:49:58,110 +أنه في كثير من الأحيان علشان أقدر أعين الـ + +617 +00:49:58,110 --> 00:50:01,830 +molecular formula لازم أكون عارف الـ empirical + +618 +00:50:01,830 --> 00:50:08,030 +formula، فأنا بعين الـ empirical formula وبأعمل تجارب + +619 +00:50:08,030 --> 00:50:12,230 +أخرى بتخلي في علاقة بين الـ empirical والـ + +620 +00:50:12,230 --> 00:50:15,470 +molecular، فمن العلاقة هذه بقدر أوصل لـ molecular + +621 +00:50:15,470 --> 00:50:20,170 +formula، يبقى في عندي طرق ممتازة لتعينها، أو كثير من + +622 +00:50:20,170 --> 00:50:23,430 +الطرق الكيميائية بتعطيني بس الـ empirical formula لكن + +623 +00:50:23,430 --> 00:50:27,010 +في تجارب أخرى بتعمل علاقة بين الـ empirical formula + +624 +00:50:27,010 --> 00:50:30,530 +و الـ molecular formula، فبستخدم هذه العلاقة عشان + +625 +00:50:30,530 --> 00:50:34,310 +أقدر أوصل من الـ empirical للـ molecular، لأنه أنا + +626 +00:50:34,310 --> 00:50:38,210 +بتهمني الـ molecular formula علشان هي اللي بدي + +627 +00:50:38,210 --> 00:50:41,170 +أستخدمها في الحسابات، بعد شوية لازم أكون عارف + +628 +00:50:41,170 --> 00:50:45,030 +المركب من إيش بيتكون عشان لو بدي أجيب له مثلا الـ + +629 +00:50:45,030 --> 00:50:49,820 +formula weight من الـ atomic weights للعناصر + +630 +00:50:49,820 --> 00:50:52,280 +المختلفة أو الذرات المختلفة أو المركبة أقدر أجيبها + +631 +00:50:52,280 --> 00:50:56,420 +فلازم أكون عارف إيش هي الـ molecular formula عشان + +632 +00:50:56,420 --> 00:50:59,260 +إيه؟ كان مهتم في الـ empirical formula لأن منها بدي + +633 +00:50:59,260 --> 00:51:02,160 +أقدر أجيب الـ إيه؟ الـ molecular formula، هذه حاجة + +634 +00:51:02,160 --> 00:51:07,000 +والحاجة الثانية أو السبب الثاني زي ما قلت إنه كثير + +635 +00:51:07,000 --> 00:51:11,140 +من المركبات ماهيّش مركبات molecular، مركبات + +636 +00:51:11,140 --> 00:51:15,660 +أيونية، ومعنى إنه مركب أيوني معناته مش جزيئات، كل + +637 +00:51:15,660 --> 00:51:19,600 +جزيء منفصل لوحده، بقدر نأي سي إيه، المركبات الأيونية، + +638 +00:51:19,600 --> 00:51:23,720 +كويس؟ بس ماقللوش مركبات يعني خليني أقول تجاوز + +639 +00:51:23,720 --> 00:51:27,120 +المركبات الأيونية مركبات لأنه بيحتوي على نوعين من أنواع + +640 +00:51:27,120 --> 00:51:33,000 +الذرات في المركبات الأيونية، بقدرش آخد واحد NaCl وكمان + +641 +00:51:33,000 --> 00:51:37,240 +واحد NaCl وكمان واحد ... لا المركبات الأيونية + +642 +00:51:37,240 --> 00:51:44,260 +بتتكون في شبكة بلورية بحيث إنه كل مثلا الـ chloride + +643 +00:51:44,260 --> 00:51:49,060 +بتكون مرتبطة بعدد من + +644 +00:51:49,060 --> 00:51:53,180 +الـ sodium atoms وكل sodium atom مرتبطة بعدد من الـ + +645 +00:51:53,180 --> 00:51:56,740 +chloride، فبقدرش إن أفصل حاجة منهم أقول والله هذا + +646 +00:51:56,740 --> 00:52:02,250 +جزء NaCl لأ ما بيحصلش هذا الكلام، فأنا ... أنا ضروري + +647 +00:52:02,250 --> 00:52:06,330 +أعرف الـ empirical formula لأنه بتعبر ليه عن الـ + +648 +00:52:06,330 --> 00:52:10,250 +formula في المركبات الأيونية، بتعبر عن الـ formula + +649 +00:52:10,250 --> 00:52:13,910 +في المركبات الأيونية، شوفنا هذا الكلام قبل شوية + +650 +00:52:13,910 --> 00:52:19,590 +لجلوكوز C6H12O6 هذه molecular formula، إيش الـ + +651 +00:52:19,590 --> 00:52:24,130 +empirical formula؟ قلنا CH2O + +652 +00:52:24,130 --> 00:52:31,720 +CH2O، طيب الـ nitrous oxide، الـ كاتب اللي كنا نستخدمه ك + +653 +00:52:31,720 --> 00:52:36,080 +مخدر، ناثيتك يعني مخدر، وعادة يطلق عليه laughing + +654 +00:52:36,080 --> 00:52:41,420 +gas، غاز الضحك، الـ molecular formula له N2O، طيب إيش + +655 +00:52:41,420 --> 00:52:45,360 +الـ empirical formula؟ نفسه لأنه ما بتبسط أكثر من + +656 +00:52:45,360 --> 00:52:49,760 +هيك، كلام كثير كثير سهل، كيف نتطلع على الـ molecules + +657 +00:52:49,760 --> 00:52:53,400 +كيف نتطلع على الـ molecules؟ فبنقول في عدة + +658 +00:52:53,400 --> 00:52:56,360 +approaches + +659 +00:52:57,720 --> 00:53:02,320 +الكيميائيين ممكن ينظروا إلى الجزيئات من خلالها + +660 +00:53:02,320 --> 00:53:05,340 +فممكن يستخدموا molecular formula اللي بنعرفها احنا + +661 +00:53:05,340 --> 00:53:10,000 +مثلا الميثين، هاي الميثين CH4، molecular formula اسمها + +662 +00:53:10,640 --> 00:53:15,140 +وممكن هذه يعني نفسها بتعرفنا بس إيش نوع الذرات + +663 +00:53:15,140 --> 00:53:18,100 +المرتبطة مع بعض، وفي عندي والله آه كربون مرتبطة + +664 +00:53:18,100 --> 00:53:22,060 +بأربعة من الـ H، لكن كيف مرتبطين؟ بتبينش الـ molecular + +665 +00:53:22,060 --> 00:53:26,280 +formula، بس بتقول لي والله آه عندك في الجزيء، جزيء + +666 +00:53:26,280 --> 00:53:32,880 +الميثين ذرة كربون وأربعة H فقط، لكن ما بتعرفنا كيف + +667 +00:53:32,880 --> 00:53:37,980 +مرتبطين مع بعض من بعض، بنيجي نوع ثاني من الـ + +668 +00:53:37,980 --> 00:53:43,400 +Picturing أو التصور الجزيء أو النظر للجزيء، بنقول + +669 +00:53:43,400 --> 00:53:45,460 +في عندي حاجة نسميها Structural Formula + +670 +00:53:48,350 --> 00:53:52,050 +بترسم لي كيف كل ذرة من الذرات مرتبطة بالذرة + +671 +00:53:52,050 --> 00:53:56,490 +الأخرى، ففي الـ CH4 بأعرف إن الـ H مرتبطة بالـ C، الـ H + +672 +00:53:56,490 --> 00:53:58,550 +مرتبطة بالـ C، الـ H مرتبطة بالـ C، الـ H مرتبطة بالـ C، الـ H + +673 +00:53:58,550 --> 00:54:03,630 +مرتبطة بالـ C، الـ H مرتبطة بالـ C، الـ H مرتبطة بالـ C، الـ H + +674 +00:54:03,630 --> 00:54:07,730 +مرتبطة بالـ C، الـ H مرتبطة بالـ C، الـ H مرتبطة بالـ C، الـ H + +675 +00:54:07,730 --> 00:54:08,110 +مرتبطة بالـ C، الـ H مرتبطة بالـ C، الـ H مرتبطة بالـ C، الـ H + +676 +00:54:08,110 --> 00:54:08,130 +مرتبطة بالـ C، الـ H مرتبطة بالـ C، الـ H مرتبطة بالـ C، الـ H + +677 +00:54:08,130 --> 00:54:11,110 +مرتبطة بالـ C، الـ H مرتبطة + +678 +00:54:13,550 --> 00:54:17,270 +في عندي حاجة بيقولها perspective drawing، هذا + +679 +00:54:17,270 --> 00:54:22,150 +بعرفني إلى حد ما الزوايا، بيعرفني الزوايا لكن بيبقى + +680 +00:54:22,150 --> 00:54:26,210 +شكل بيكون في three dimensional، بنقوله perspective + +681 +00:54:26,210 --> 00:54:31,530 +drawing، كويس شايفين؟ هذه الخط المتقطع معناته هذه + +682 +00:54:31,530 --> 00:54:36,610 +الـ edge لورا، الخط الـ solid هذه يعني الـ edge لقدام + +683 +00:54:36,610 --> 00:54:42,450 +الخط نفسه اللي زي هذا في نفس مستوى السبورة، ماشي يا + +684 +00:54:42,450 --> 00:54:46,270 +جماعة؟ فهذا three dimensional، برضه من الأشكال اللي + +685 +00:54:46,270 --> 00:54:50,770 +احنا بنستخدمها كثير وبنحاول نفرجها للطلبة لكن + +686 +00:54:50,770 --> 00:54:56,530 +أنا للأسف يعني مش جايب معايا models اللي هو بنقوله + +687 +00:54:56,530 --> 00:55:00,870 +الـ ball and stick، ball and stick يعني كل ذرة هي + +688 +00:55:00,870 --> 00:55:08,010 +عبارة عن إيه؟ عن كرة، والروابط عبارة عن عصية صغيرة + +689 +00:55:08,010 --> 00:55:15,510 +يعني فالكل مثلا الـ carbon هتلاقي فيها أربع فتحات والـ + +690 +00:55:15,510 --> 00:55:20,350 +فتحات هذه بزوايا معينة بتمثل فعلا الـ carbon في + +691 +00:55:20,350 --> 00:55:26,040 +الـ CH4 وكل فتحة بعدي فيها عصا، فهذا الشكل بنقوله + +692 +00:55:26,040 --> 00:55:29,460 +ball and stick، والعصا طبعا تربط هي ذرة هيدروجين + +693 +00:55:29,460 --> 00:55:32,780 +هيدروجين، هيدروجين، هيدروجين، والـ Carbon في بعض الأحيان + +694 +00:55:32,780 --> 00:55:38,420 +كمان هان بيكون مكتوب إن هذه C وهذه H في بعض + +695 +00:55:38,420 --> 00:55:41,960 +الأحيان لكن في أغلب الأحيان اللون هو اللي بيحدد + +696 +00:55:41,960 --> 00:55:46,240 +يعني مثلا معروف الأكسجين أحمر، مثلا معروف دائما + +697 +00:55:46,240 --> 00:55:53,600 +يعني الـ carbon أسود غالبا، كويسة يعني فممكن اللون + +698 +00:55:53,600 --> 00:55:57,000 +يميز للناس اللي بتشتغل في هذا المجال كثير، أخر شكل + +699 +00:55:57,000 --> 00:55:58,940 +اللي بدنا نطلع عليه حاجة بقولها space filling + +700 +00:55:58,940 --> 00:56:03,260 +model، برضه هذا model زي هيك بتركب تركيب هاي ذرة + +701 +00:56:03,260 --> 00:56:06,200 +الكربون هذه ذرة الهيدروجين الهيدروجين الهيدروجين + +702 +00:56:06,200 --> 00:56:09,900 +الهيدروجين لكن واضح إن الزوايا بتكونش واضحة + +703 +00:56:09,900 --> 00:56:14,600 +كتير كل واحد منهم بيبين يخليني أقول مفهوم في مجال + +704 +00:56:14,600 --> 00:56:18,160 +من مجالات الكيميا بشكل أفضل إن واضح جدا الزوايا + +705 +00:56:19,180 --> 00:56:21,080 +تتراهيدرال الشكل على طول بتطلع اللي بيقول هي + +706 +00:56:21,080 --> 00:56:26,260 +تتراهيدرال رباع الأوجه الزاوية تبعته معروفة كويس + +707 +00:56:26,260 --> 00:56:29,600 +فكل شكل من هذه الأشكال بتقدر نقول إنه فيه فايدة + +708 +00:56:29,600 --> 00:56:35,040 +كل هذه الأشكال مهمة لكن الـ molecular formula بقى + +709 +00:56:35,040 --> 00:56:38,950 +شفتش الـ molecule و أنا في هذا الفصل مش بحاجة لإني + +710 +00:56:38,950 --> 00:56:42,370 +أشوف الـ molecules، يعني غالبا هستخدم بس الـ + +711 +00:56:42,370 --> 00:56:45,110 +molecular formula، وإن كنا لازم نعرف إن في عندنا + +712 +00:56:45,110 --> 00:56:47,210 +molecular formula، وعندنا structural formula، + +713 +00:56:47,210 --> 00:56:50,370 +structural formula ما فيش عندي معرفة بالزوايا ولا + +714 +00:56:50,370 --> 00:56:53,590 +الريضة، كلهم نفس المستوى، لكن معروف كل ذرة في إيش + +715 +00:56:53,590 --> 00:56:59,870 +مرتبطة، الـ Perspective Drawing 3D، الـ Ball and + +716 +00:56:59,870 --> 00:57:03,130 +Stick طبعا هو موديل يعني 3D وموديل يعني شغلات + +717 +00:57:03,130 --> 00:57:07,530 +نمسكها بإيدينا، والـ Space Filling برضه موديل ذرات + +718 +00:57:07,530 --> 00:57:10,890 +نمسكها بإيدينا ونركبها بإيدينا أيضا + +719 +00:57:18,790 --> 00:57:23,690 +طيب الآن نتطلع على إيش يعني أيونات وإيش يعني + +720 +00:57:23,690 --> 00:57:30,530 +مركبات لازم + +721 +00:57:30,530 --> 00:57:35,470 +نفهم في البداية إن شغلنا كله يتعلق بالإلكترونات + +722 +00:57:35,470 --> 00:57:40,530 +مالوش دعوة بالـ nucleus إن .. إنه بتحتوي على الـ + +723 +00:57:40,530 --> 00:57:44,570 +protons و الـ neutrons لكن هي قاعدة في المركز + +724 +00:57:44,570 --> 00:57:49,460 +وملهاش دعوة في أي تفاعلات بتحصل برة، طب ها التفاعلات + +725 +00:57:49,460 --> 00:57:52,900 +اللي بتحصل .. بتحصل نتيجة إيش؟ جال نتيجة + +726 +00:57:52,900 --> 00:57:55,660 +الإلكترونات اللي موجودة في المدارات الخارجية فقط + +727 +00:57:55,660 --> 00:58:02,580 +أما النواة فهي قاعدة بحالها تمام؟ فالنواة مالناش + +728 +00:58:02,580 --> 00:58:07,100 +دعوة أو مايلها أي دخل في التفاعلات اللي بتحصل .. + +729 +00:58:07,100 --> 00:58:09,420 +التفاعلات الكيميا اللي بتحصل لنا عادة طب ها إيش + +730 +00:58:09,420 --> 00:58:13,760 +اللي إله دخل؟ جال بس إلكترونات التكافؤ، فهد مهمتنا + +731 +00:58:13,760 --> 00:58:19,080 +إحنا بنطلع بس على المدار الأخر إيش فيه؟ وبناء عليه + +732 +00:58:19,080 --> 00:58:24,440 +بنتطلع على التفاعل، إيش هو التفاعل اللي ممكن يحصل، + +733 +00:58:24,440 --> 00:58:30,460 +ففي عندي نوعين من أنواع الذرات، في عندي الذرات بعد + +734 +00:58:30,460 --> 00:58:34,080 +الخط المتعرج، وقولنا هذه دائما بتكون molecules + +735 +00:58:34,080 --> 00:58:40,440 +بينما مع بعضها البعض طبعا، وفي نفس الوقت هذه اللي + +736 +00:58:40,440 --> 00:58:46,390 +بعد الخط المتعرج بتعطيني أيونات سالبة، هي كمان + +737 +00:58:46,390 --> 00:58:52,890 +حاجة قولنا مع بعضها لبعض إيش بتكون مركبات، زي الـ O2، + +738 +00:58:52,890 --> 00:59:01,690 +F2، ICl مثلاً، P2O5، كلها مع بعضها بتكون molecules + +739 +00:59:01,690 --> 00:59:07,630 +لكن لحالها كل ذرة لوحدها هل ممكن تكون أيون سالب + +740 +00:59:07,630 --> 00:59:10,730 +ولا أيون موجب؟ جال أيونات سالبة، يبقى بعد الخط + +741 +00:59:10,730 --> 00:59:14,770 +المتعرج أيونات، A على يمينها أيونات سالبة وعلى يسار + +742 +00:59:14,770 --> 00:59:20,860 +الخط المتعرج أيونات موجبة، إيش السبب اللي بيخلي؟ إيش + +743 +00:59:20,860 --> 00:59:26,860 +السالب بيخلي ذرة معينة عنصر معين يكون أيون سالب أو + +744 +00:59:26,860 --> 00:59:33,660 +يكون أيون موجب؟ قال .. قال علشان يقدر يوصل لحالة + +745 +00:59:33,660 --> 00:59:37,800 +مستقرة، إيش هي الحالة المستقرة؟ قال أقرب غاز خامل له + +746 +00:59:37,800 --> 00:59:44,720 +أقرب غاز خامل له، فمثلا هي الـ Fluorine بده Electron واحد علشان يصير عشرة مثلا + +747 +00:59:44,720 --> 00:59:51,690 +اللي هو يعني يوصل بغض النظر، يوصل لغاز الخامل + +748 +00:59:51,690 --> 00:59:53,910 +Electron واحد، يبقى F سالب بحب إنه ياخد Electron + +749 +00:59:53,910 --> 00:59:58,650 +الـ Oxygen بده Electron عشان يوصل، مش معروف يقول الـ + +750 +00:59:58,650 --> 01:00:01,450 +Oxygen تعالي يوصل هنا، فهيط، طب الـ Nitrogen بده + +751 +01:00:01,450 --> 01:00:06,090 +ثلاثة، إذا ثلاثة، سالب هي المجموعة السابعة دائما + +752 +01:00:06,090 --> 01:00:11,480 +سالب واحد، المجموعة السادسة سالب اثنين، المجموعة + +753 +01:00:11,480 --> 01:00:14,740 +الخامسة سالب ثلاثة، معايا يا بنات؟ هذا ببساطة خالص + +754 +01:00:14,740 --> 01:00:21,700 +طب و مدون ذلك كان الـ Sodium بده يفقد واحد عشان + +755 +01:00:21,700 --> 01:00:27,100 +يوصل هنا لأنه كان بعيد .. إذا كنتم مذكرين كان بعيد + +756 +01:00:27,100 --> 01:00:33,090 +الغاز الخاملي بواحد، لأن خصائصه متشابهة مع الـ + +757 +01:00:33,090 --> 01:00:38,970 +Lithium، إي جينا جبناها هنا، فحو ولا لأ؟ فهو بده يفقد + +758 +01:00:38,970 --> 01:00:42,790 +إلكترون واحد هنا، بيفقد إلكترون بيفقد .. كل هدول + +759 +01:00:42,790 --> 01:00:45,630 +بيفقدوا إلكترون، يبقى كل هدول موجب واحد، موجب + +760 +01:00:45,630 --> 01:00:48,630 +باتنين، هلاحظ الـ Transition elements مش هحكي عنها + +761 +01:00:48,630 --> 01:00:52,790 +هلاّجيت، يعني المهم إن هذه المجموعة كويس هو كل هدول + +762 +01:00:52,790 --> 01:00:57,090 +موجبين، كلهم موجبين، الـ transition elements بتاخد + +763 +01:00:57,090 --> 01:01:01,990 +أكثر من تكافؤ، مش كلها يعني معظمها في عدد قليل + +764 +01:01:01,990 --> 01:01:06,750 +بياخد تكافؤات أقل أو تكافؤات ثابتة يعني، لكن أغلب + +765 +01:01:06,750 --> 01:01:15,090 +العناصر الانتقالية في لها أكثر من تكافؤ، المهم + +766 +01:01:15,090 --> 01:01:19,330 +المجموعة الأولى دائما إيه؟ موجب واحد لأنه بقى يفقد + +767 +01:01:19,330 --> 01:01:23,770 +إلكترون عشان تاخد الـ Nobel gas structure، المجموعة + +768 +01:01:23,770 --> 01:01:27,820 +الثانية موجب اثنين لأنه فقدت two electrons لتصل + +769 +01:01:27,820 --> 01:01:31,140 +لـ Nobel gas structure، المجموعة السابعة بدها + +770 +01:01:31,140 --> 01:01:33,780 +electron إذا سالب واحد عشان توصل لـ Nobel gas + +771 +01:01:33,780 --> 01:01:36,700 +structure، المجموعة السادسة سالب اثنين عشان توصل لـ Nobel gas + +772 +01:01:36,700 --> 01:01:39,400 +structure، المجموعة الخامسة سالب ثلاثة، هذا الكلام لو ذكرناه + +773 +01:01:39,400 --> 01:01:43,880 +أبنه نرتاح كثير، وكمان لو فيه ذرتين منهم تفاعلوا + +774 +01:01:43,880 --> 01:01:48,040 +مع بعض، إذا ما عندي سالب وموجب لأ عندي مركب + +775 +01:01:48,040 --> 01:01:56,100 +Molecular compound مركب جزئي، ما هوش أيوني، في الشحنات ممنوع + +776 +01:01:56,100 --> 01:02:00,680 +الشحنات، المركب الجزئي مش ما فيش عنده شحنات، تمام؟ في + +777 +01:02:00,680 --> 01:02:06,700 +عندي حاجة بتقولها تساهمية تساهمية، طيب، فمثلا الـ + +778 +01:02:06,700 --> 01:02:14,440 +Sodium في 11 بروتون، يعني إيش في 11 إلكترون بيفقد + +779 +01:02:14,440 --> 01:02:21,650 +إلكترون بيصير عنده عشر إلكترونات، بيوصل الـ Sodium + +780 +01:02:21,650 --> 01:02:26,850 +Ion، هذا العشر إلكترونات هذا التركيب هو تركيب الـ + +781 +01:02:26,850 --> 01:02:30,730 +Neon، تركيب النيون لكن طبعا نيون غاز خامل فبنلاحظ + +782 +01:02:30,730 --> 01:02:38,080 +أنه كمان يعني الـ Ion صغير، ما علينا يعني احنا + +783 +01:02:38,080 --> 01:02:43,060 +بنتكلم في كيميا عامة على تفاصيل هذا الكلام، لكن مش + +784 +01:02:43,060 --> 01:02:48,620 +معانا في هذا المساق، الـ Chlorine + +785 +01:02:48,620 --> 01:02:53,740 +17 بروتون يعني كم إلكترون؟ 17، لأنه لازم تكون الذرة + +786 +01:02:53,740 --> 01:02:59,710 +متعادلة، الذرات متعادلة كهربياً، فبيروح بياخد إلكترون + +787 +01:02:59,710 --> 01:03:04,170 +علشان يوصل تركيب الغاز الخامل الارجون اللي جانبه + +788 +01:03:04,170 --> 01:03:08,750 +على طول، فبيصير 18 إلكترون طبعاً 17 صار سالب لأن عدد + +789 +01:03:08,750 --> 01:03:14,970 +الإلكترونات أكثر بواحد يبقى صار سالب واحد، طيب + +790 +01:03:14,970 --> 01:03:26,710 +عادة الشحنات يعني بنقولها موجب يعني موجب واحد + +791 +01:03:28,200 --> 01:03:32,740 +اثنين موجب، مش زائد اثنين، اثنين موجب يعني شحنتين + +792 +01:03:32,740 --> 01:03:37,700 +موجبتين، اثنين موجب أو ثلاثة موجب نفس الكلام، السالب + +793 +01:03:37,700 --> 01:03:41,900 +سالب يعني سالب واحد مش واحد سالب، واحد نكتب سالب + +794 +01:03:41,900 --> 01:03:46,080 +اثنين سالب أو ثلاثة سالب زي هيك بتنكتب، مش سالب + +795 +01:03:46,080 --> 01:03:51,240 +ثلاثة، لأ، ثلاثة سالب يعني ثلاث شحنات سالبة وهكذا + +796 +01:03:51,240 --> 01:03:56,700 +خلينا ناخذ مثال صغير تطبيق بيقول give the chemical + +797 +01:03:58,150 --> 01:04:03,770 +symbol including superscript indicating mass + +798 +01:04:03,770 --> 01:04:07,670 +number 4A the ion with 22 protons with 26 neutrons + +799 +01:04:07,670 --> 01:04:13,770 +and 19 electron، لو طلعتوا هنا 22 بروتون وكم + +800 +01:04:13,770 --> 01:04:18,230 +إلكترون إذا إيش هو إيش الشحنة اللي عليه؟ بمجرد + +801 +01:04:18,230 --> 01:04:23,130 +النظر فورا؟ غلط + +802 +01:04:23,130 --> 01:04:26,070 +موجب ثلاثة يا فنتي، اثنين وعشرين بروتون اثنين + +803 +01:04:27,560 --> 01:04:30,260 +وعشرين موجب وتسعة عشر سالب معها، اثنين وعشرين موجب + +804 +01:04:30,260 --> 01:04:35,420 +اثنين وعشرين بروتون وتسعة عشر سالب معناته ثلاثة + +805 +01:04:35,420 --> 01:04:40,240 +موجب، هذا بغض النظر احنا هتشوف الـ answer بندور أول + +806 +01:04:40,240 --> 01:04:43,980 +حاجة على الـ answer من الجدول الدوري، طيب ناخد واحد + +807 +01:04:43,980 --> 01:04:48,300 +واحد، هي اثنين وعشرين طلع الـ Titanium، إذا بدي أكتب + +808 +01:04:48,300 --> 01:04:55,180 +هنا Titanium بدي أحط الـ superscript إيش هالـ super + +809 +01:04:55,180 --> 01:04:59,380 +script؟ جالي الـ mass number اللي هو إيه؟ عدد + +810 +01:04:59,380 --> 01:05:05,400 +البرتون زائد عدد النيوترون، 26 و 22، 48، 48، طب الشحنة + +811 +01:05:05,400 --> 01:05:13,220 +اللي عليه قلناها قبل شوية موجب ثلاثة، طيب، بي the + +812 +01:05:13,220 --> 01:05:18,040 +ion of sulfur جالي هو الـ Sulfur that has 16 نيوترون + +813 +01:05:18,040 --> 01:05:22,900 +and 18 إلكترون نشوف الـ Sulfur عشان نشوف شحنته الـ Sulfur + +814 +01:05:22,900 --> 01:05:28,580 +هي هنا كم بروتون فيه + +815 +01:05:28,580 --> 01:05:31,660 +الـ Sulfur؟ + +816 +01:05:34,520 --> 01:05:42,920 +الـ Sulfur 16 كم البروتون فيه؟ الـ Sulfur يا بنتي إيش + +817 +01:05:42,920 --> 01:05:45,580 +اللي هنا اللي مكتوب فوق؟ إيش اللي بنكتب فوق في + +818 +01:05:45,580 --> 01:05:48,740 +الجدول الدوري؟ فوقه مش superscript إيش اللي بيكون + +819 +01:05:48,740 --> 01:05:53,700 +مكتوب فوق؟ أنا مرتب الجدول بناء على إيه؟ لأ واحد و + +820 +01:05:53,700 --> 01:05:55,260 +ثلاثة واثنين واثنين واثنين وأربع واثنين وخمس واثنين + +821 +01:05:55,260 --> 01:05:58,860 +بناء على إيش هذا؟ الـ Atomic number عدد البروتون، ده + +822 +01:05:58,860 --> 01:06:04,200 +نتذكره، اه عدد البروتون، هان الجدول الدوري مبني على + +823 +01:06:04,200 --> 01:06:08,660 +أساس عدد البروتون ليه؟ لأن لو بدنا نقول والله عدد + +824 +01:06:08,660 --> 01:06:11,800 +الكتلي، هو عدد الكتلي هو عدد الكتلي عدد الكتلي هو + +825 +01:06:11,800 --> 01:06:13,040 +عدد الكتلي عدد الكتلي عدد الكتلي عدد الكتلي عدد + +826 +01:06:13,040 --> 01:06:13,120 +الكتلي عدد الكتلي عدد الكتلي عدد الكتلي عدد الكتلي + +827 +01:06:13,120 --> 01:06:14,020 +عدد الكتلي عدد الكتلي عدد الكتلي عدد الكتلي عدد + +828 +01:06:14,020 --> 01:06:21,460 +الكتلي عدد الكتلي عدد الكتلي عدد الكتلي عدد الكتلي + +829 +01:06:21,460 --> 01:06:28,060 +عدد الكتلي عدد الكتلي عدد الكتلي عدد الكتلي عدد + +830 +01:06:28,060 --> 01:06:29,520 +الكتلي عدد الكتلي عدد الكتلي عدد الـ Sulfur وين + +831 +01:06:29,520 --> 01:06:37,900 +الـ Sulfur؟ Sulfur 16 هي S 16 16، طيب 16 + +832 +01:06:37,900 --> 01:06:42,200 +وكم برو كم نيوترون في الـ Sulfur جالي كمان 16 + +833 +01:06:42,200 --> 01:06:48,170 +إذا Sulfur 32 البروتونز زائد النيوترونز 16 + +834 +01:06:48,170 --> 01:06:50,810 +بروتونز من الجدول الدوري جبنا الـ Sulfur الـ Atomic + +835 +01:06:50,810 --> 01:06:55,330 +number هو 16 ومن السؤال كم النيوترون جالي 16 زي + +836 +01:06:55,330 --> 01:07:00,690 +32، طب هنا قال لي في عندي 18 إلكترون لكن الـ Sulfur + +837 +01:07:00,690 --> 01:07:08,910 +كم البروتون فيه شفناه 16، اه 16 بروتون صار 18 + +838 +01:07:08,910 --> 01:07:17,300 +إلكترون يعني إيه شحنته؟ اثنين سالب، اثنين سالب إذا + +839 +01:07:17,300 --> 01:07:25,080 +Sulfur 32 اثنين سالب، هذه واضحة + +840 +01:07:25,080 --> 01:07:31,040 +إذا بستفيد من الجدول الدوري بشكل مباشر + +841 +01:07:43,520 --> 01:07:47,040 +طيب كمان مثال بيقول لي how many protons and + +842 +01:07:47,040 --> 01:07:54,060 +neutrons and electrons does the selenium 79 2 سالب + +843 +01:07:54,060 --> 01:07:57,840 +possess بيحتوي على كدهش يعني كم بيمتلك .. كم بيحتوي + +844 +01:07:57,840 --> 01:08:00,480 +على .. اه بدي اشوف عدد الـ neutrons و الـ electrons + +845 +01:08:00,480 --> 01:08:04,960 +ايش بدي اعمل؟ لازم اروح للجدول الدوري علشان منه + +846 +01:08:04,960 --> 01:08:09,840 +بعرف عدد الـ protons فبروح للجدول الدوري + +847 +01:08:09,840 --> 01:08:14,500 +السيلينيوم كم بروتون فيه؟ أربعة و ثلاثين برجع فوق + +848 +01:08:14,500 --> 01:08:18,100 +بقول تسعة وسبعين ناقص أربعة و ثلاثين خمسة و + +849 +01:08:18,100 --> 01:08:22,940 +أربعين نيوترون إذا عرفت عدد النيوترونات طب عدد + +850 +01:08:22,940 --> 01:08:29,120 +الإلكترونات لحظة لحظة شوية لحظة شوية أنا عندي الـ + +851 +01:08:29,120 --> 01:08:33,730 +atomic number أربعة و ثلاثين وهان يعني أربعة و + +852 +01:08:33,730 --> 01:08:38,710 +ثلاثين المتعادل أربعة و ثلاثين إلكترون لكن هان في + +853 +01:08:38,710 --> 01:08:43,210 +عنده كمان اثنين إلكترون ستة و ثلاثين إلكترون إذا + +854 +01:08:43,210 --> 01:08:47,470 +عدد الإلكترون هو ستة و ثلاثين ليه؟ لأن المتعادل + +855 +01:08:47,470 --> 01:08:49,230 +السيلينيوم + +856 +01:08:51,370 --> 01:08:57,050 +قلنا جدّاش الـ 34 تسعة + +857 +01:08:57,050 --> 01:09:03,030 +و سبعين هذا متعادل طب لما يكون سيلينيوم اثنين سالب + +858 +01:09:03,030 --> 01:09:07,910 +إذا بدي يكون عندي هنا ستة و ثلاثين ليش؟ لأن هن في + +859 +01:09:07,910 --> 01:09:10,730 +عندي أربعة و ثلاثين إلكترون و كان متعادل حطيت عليه + +860 +01:09:10,730 --> 01:09:13,670 +كمان هذه بتبقى طبعا أربعة و ثلاثين الـ atomic + +861 +01:09:13,670 --> 01:09:18,660 +number عدد البروتونات لكن اثنين سالب معناته بيصير + +862 +01:09:18,660 --> 01:09:23,620 +ستة و ثلاثين إلكترون وهذا طبعا زي ما هي تسعة وسبعين + +863 +01:09:40,890 --> 01:09:45,690 +خلّيني أطلع على كيف الأيونات تتكون كيف الأيونات + +864 +01:09:45,690 --> 01:09:54,090 +بتتكون ف أنا أطلع على picturing ionic charges مثلا + +865 +01:09:54,090 --> 01:09:57,790 +كل هذا اشتقاق من الجدول من غير ما نعرف الجدول دلوقت ما + +866 +01:09:57,790 --> 01:10:02,340 +نعرفوش لازم ناخد بعين الاعتبار دائما ايش هو الجدول + +867 +01:10:02,340 --> 01:10:04,460 +الدوري؟ وبنتاش نحفظ عادة الجدول الدوري اللي + +868 +01:10:04,460 --> 01:10:07,800 +بتاخدوه في الامتحان أو بنكتبلكم المعلومات اللي + +869 +01:10:07,800 --> 01:10:13,900 +لازمكم كتابة فبقول predict the charge expected for + +870 +01:10:13,900 --> 01:10:18,720 +the most stable ion of barium and the most stable + +871 +01:10:18,720 --> 01:10:26,560 +ion of oxygen ايش أكثر أيون مستقر للباريوم و ايش + +872 +01:10:26,560 --> 01:10:29,160 +أكثر أيون مستقر للأكسجين لو بدنا نجاوب على هذا + +873 +01:10:29,160 --> 01:10:34,540 +السؤال بشكل عام بنقول هو أيون اللي بيعطيني تركيب + +874 +01:10:34,540 --> 01:10:41,110 +النوبل جاز القريب منه تركيب أقرب نوبل جاز له يعني + +875 +01:10:41,110 --> 01:10:46,610 +يبدو يفقد الإلكترون بحيث أنه ايه يوصل النوبل جاز + +876 +01:10:46,610 --> 01:10:52,530 +الـ structure فلو طلعنا على الأكسجين علشان يوصل + +877 +01:10:52,530 --> 01:10:57,030 +النوبل جاز الـ structure اه بده يكتسب اثنين + +878 +01:10:57,030 --> 01:11:01,270 +الإلكترون ايش اللي بيصير؟ أو اثنين سالب الـ باريوم + +879 +01:11:01,270 --> 01:11:04,990 +هيهان بدي يفقد اثنين ايه؟ طبعا في المجموعة الثانية + +880 +01:11:04,990 --> 01:11:07,030 +لازم اثنين Electronic كل هذا اثنين Electronic لازم + +881 +01:11:07,030 --> 01:11:09,790 +تحفظوه على طول يعني مش بحاجة إنك تبطلها تقول والله + +882 +01:11:09,790 --> 01:11:12,790 +نوبل جاز مش لأ المجموعة بيقول الموجة بواحد المجموعة + +883 +01:11:12,790 --> 01:11:16,830 +الثانية موجبة باثنين وانسوا وبعدين hand سالب واحد + +884 +01:11:16,830 --> 01:11:20,070 +سالب اثنين سالب ثلاثة هذه لازم نكون عارفينها زي + +885 +01:11:20,070 --> 01:11:25,420 +أسمنا ماشي بدهاشي يعني لا نطلع على جدول الدوري ولا + +886 +01:11:25,420 --> 01:11:29,520 +غيره على طول مجرد معرفتنا وين بيوجع الأنصار إذا + +887 +01:11:29,520 --> 01:11:34,200 +بيوجع في الأولى أو الثانية أو على اليمين الجدول + +888 +01:11:34,200 --> 01:11:37,700 +الدوري فيه المجموعة السابعة أو السادسة أو الثالثة + +889 +01:11:37,700 --> 01:11:42,760 +معروف جدّاش يعني + +890 +01:11:42,760 --> 01:11:48,020 +الـ .. الـ Valency تبعه أو جدّاش لازم يكون عليه + +891 +01:11:48,020 --> 01:11:51,200 +charges بهال اللي بده يفقد أو يكتسب بيقول predict + +892 +01:11:51,200 --> 01:11:54,340 +the charge expected for the most stable ion of a + +893 +01:11:54,340 --> 01:11:59,700 +aluminum and fluorine طيب خلينا نطلع تاني aluminum + +894 +01:11:59,700 --> 01:12:06,040 +هاي الـ aluminum هان كويس أسهل يروح هان ولا بس + +895 +01:12:06,040 --> 01:12:08,980 +اثنين هان ثلاثة هان اللي بده هان؟ لأ الـ aluminum + +896 +01:12:08,980 --> 01:12:13,930 +بيفقد بعدين خدوا بالكم ما فيش حد يقول ليه في عنصر + +897 +01:12:13,930 --> 01:12:18,110 +هان بده يكتسب Electronic ممنوع اللي بيكتسب بعد + +898 +01:12:18,110 --> 01:12:24,190 +الـ ايه؟ بعد الخط المتعرج لكن هان كلها ايه؟ Metals + +899 +01:12:24,190 --> 01:12:29,270 +الـ metals دائما بتعطينا أيونات موجبة الـ non-metals + +900 +01:12:29,270 --> 01:12:32,750 +بتعطينا أيونات سالبة فمن دا قبل الخط المتعرج اه + +901 +01:12:32,750 --> 01:12:37,330 +بده يفقد ثلاثة إلكترونات واحد، اثنين، ثلاثة عشان يوصل + +902 +01:12:37,330 --> 01:12:42,270 +للـ Nobel gas structure is an aluminum ثلاثة موجب + +903 +01:12:42,270 --> 01:12:50,500 +يبقى الـ .. ايش في عنا؟الفلورين يكون سالب واحد لأنه + +904 +01:12:50,500 --> 01:12:53,960 +في المجموعة السابعة أو لأنه بحاجة لإلكترون واحد + +905 +01:12:53,960 --> 01:12:56,860 +عشان يوصل الـ Nobel gas structure + +906 +01:13:01,040 --> 01:13:05,440 +يفقد إلكترون عشان يصير صوديوم موجب و لما يكتسب + +907 +01:13:05,440 --> 01:13:10,520 +الكلورين إلكترون عشان يصير سالب واحد طبعا بيصير + +908 +01:13:10,520 --> 01:13:13,400 +فيه interaction الكتروستاتيكية ما بين الاثنين لو + +909 +01:13:13,400 --> 01:13:16,200 +كانوا الاثنين مع بعض، يعني لو في عندي صوديوم وكلورين + +910 +01:13:16,590 --> 01:13:20,170 +الصوديوم سيحب أن يعطي إلكترون من إلكتروناته + +911 +01:13:20,170 --> 01:13:24,050 +للـ كلورين لأن الكلورين يحب أن يأخذ إلكترون الصوديوم + +912 +01:13:24,050 --> 01:13:26,530 +يحب أن يعطي إلكترون لأنه يريد أن يصل إلى نوبة + +913 +01:13:26,530 --> 01:13:30,390 +الـ Gas Structure و الكلور يحب أن يأخذ إلكترون لأنه + +914 +01:13:30,390 --> 01:13:32,170 +يريد أن يصل إلى نوبة الـ Gas Structure هذه شغلة + +915 +01:13:32,170 --> 01:13:37,730 +محببة كثير فبنلاحظ أن الصوديوم سيعطي إلكترون + +916 +01:13:37,730 --> 01:13:40,650 +للـ كلورين الصوديوم سيحصل إلى صوديوم موجب والكلورين + +917 +01:13:40,650 --> 01:13:43,630 +سالب للكلورين والثانية سيحصل إلى Electrostatic + +918 +01:13:43,630 --> 01:13:49,410 +Interaction أو Attraction تجاذب وطبعا لأنه عندي عدد + +919 +01:13:49,410 --> 01:13:53,630 +مهول جدا من ذرات الصوديوم والكلورين فهيتكون عندي + +920 +01:13:53,630 --> 01:13:59,630 +حاجة زي هيك crystal structure من الصوديوم كلوريد + +921 +01:13:59,630 --> 01:14:02,890 +الـ crystal structure من الصوديوم كلوريد بقدرش + +922 +01:14:02,890 --> 01:14:07,230 +أقول والله أن هذه الكلورين مرتبطة بهذه الصوديوم + +923 +01:14:07,230 --> 01:14:10,610 +فقط لأ الكلورين هذه مرتبطة بالصوديوم هذه والصوديوم + +924 +01:14:10,610 --> 01:14:12,990 +هذه والصوديوم هذه والصوديوم هذه وفي كمان صوديوم + +925 +01:14:12,990 --> 01:14:15,750 +تحتها وصوديوم تحتها وصوديوم فوقها وصوديوم فوقها + +926 +01:14:15,750 --> 01:14:20,430 +مثلا يعني فبالتالي ما كنتش أقول في عندي جزء صوديوم + +927 +01:14:20,430 --> 01:14:26,410 +كلورية زي ما قلت ولهيك كل المركبات الأيونية الـ + +928 +01:14:26,410 --> 01:14:31,770 +Formula اللي الها هي عبارة عن Ionic Formula + +929 +01:14:31,770 --> 01:14:36,810 +Empirical Formula مش Molecular Formula دائما الـ N + +930 +01:14:36,810 --> 01:14:44,210 +.. بنفعش أقول N2Cl2 أو N3Cl .. لأ باخد بس الـ + +931 +01:14:44,210 --> 01:14:48,350 +Empirical Formula لأي مركب أيوني يبقى أي مركب + +932 +01:14:48,350 --> 01:14:53,330 +أيوني دائما .. لو جيت طلعت على عدد الذرات المكونة + +933 +01:14:53,330 --> 01:14:55,730 +له مش صارت تكون اثنين مثلا Sodium Carbonate ن + +934 +01:14:55,730 --> 01:15:02,490 +اثنين CO ثلاثة تعال أطلع ثلاثة الـ Oxygen الكربون + +935 +01:15:02,490 --> 01:15:07,930 +واحد Sodium اثنين دائما بحلجيها ايه؟ Empirical + +936 +01:15:07,930 --> 01:15:12,750 +تجسمش على حاجة على common factor فدائما Empirical + +937 +01:15:12,750 --> 01:15:20,010 +فالـ ionic compounds دائما الـ formula إليها عادة + +938 +01:15:20,010 --> 01:15:29,110 +بتكون Empirical Formula مثلا + +939 +01:15:29,110 --> 01:15:33,730 +برضه عندي آخر حاجة اليوم بنقولها مثلا عندي + +940 +01:15:33,730 --> 01:15:41,530 +Magnesium و في عندي نيتروجين نيتروجين لو شوفناه + +941 +01:15:41,530 --> 01:15:46,630 +برضه بحب ياخد ثلاث إلكترونات علشان يكون الـ Nitride + +942 +01:15:46,630 --> 01:15:50,870 +ويوصل لتركيب الغاز الخامل حلو والـ Magnesium + +943 +01:15:50,870 --> 01:15:53,670 +اثنين طب هله لو نقول Magnesium Nitride هذا فيه + +944 +01:15:53,670 --> 01:15:57,710 +اثنين موجب وهذا فيه ثلاثة سالب شطرين أنتو كيف + +945 +01:15:57,710 --> 01:16:00,690 +أخلق دائما المركبات متعادلة كهربيا، لا يمكن أن + +946 +01:16:00,690 --> 01:16:06,530 +يكون المركب سالب أو موجب، المركبات متعادلة + +947 +01:16:06,530 --> 01:16:11,800 +كهربيا، فكيف أعمل؟ بقول هذا شحنتين إذا لازم أضرب + +948 +01:16:11,800 --> 01:16:14,540 +هذا في ثلاثة هذا ثلاثة إذا لازم أضربه في اثنين + +949 +01:16:14,540 --> 01:16:18,940 +عشان يصير الست شحنات سالبة والست شحنات موجبة فمعنى + +950 +01:16:18,940 --> 01:16:22,440 +الكلام Magnesium بتنكتب Magnesium ثلاثه N ضربته + +951 +01:16:22,440 --> 01:16:26,360 +في اثنين صار N2 ليه؟ لأنه لما يكون N2 + +952 +01:16:26,360 --> 01:16:31,140 +يعني ست شحنات سالبة مجنيزيام ثلاثة يعني ست شحنات + +953 +01:16:31,140 --> 01:16:35,560 +موجبة فبيكون دائما مجنيزيام ثلاثه N2 ومدام + +954 +01:16:35,560 --> 01:16:40,160 +مركب أيوني يعني أنا فعلت أيونات إذا الـ formula line + +955 +01:16:40,160 --> 01:16:43,680 +دي ايش منها تكون Empirical Formula لا يمكن أن تكون + +956 +01:16:43,680 --> 01:16:51,020 +Formula جزيئية لأنها أبسط Ratio ما بين الذرات + +957 +01:16:51,020 --> 01:16:56,840 +المختلفة إذا الله راد بنكتفي اليوم و الحصة الجاية + +958 +01:16:56,840 --> 01:17:00,110 +بنكملها يعطيكم العافية diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/aGHocnXKcM0.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/aGHocnXKcM0.srt new file mode 100644 index 0000000000000000000000000000000000000000..93073d4cfba7bff406c15f055989a79999eaecfd --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/aGHocnXKcM0.srt @@ -0,0 +1,3543 @@ +1 +00:00:20,670 --> 00:00:24,070 +بسم الله الرحمن الرحيم إذا الله راضي اليوم بنتكلم + +2 +00:00:24,070 --> 00:00:27,610 +عن Chapter جديد بيتحدث عن الـ Chemistry of the + +3 +00:00:27,610 --> 00:00:32,430 +Environment في هذا الـ Chapter يعني بنتحدث عن بعض + +4 +00:00:32,430 --> 00:00:38,070 +المفاهيم الأساسية فيما يتعلق بعلاقة الكيمياء + +5 +00:00:38,070 --> 00:00:41,950 +بالبيئة اللي بتحيط فينا وعشان نتكلم عن هذا الكلام + +6 +00:00:41,950 --> 00:00:48,460 +لازم في البداية يمكن نتكلم عن الـ Atmosphere ليه؟ + +7 +00:00:48,460 --> 00:00:51,700 +لأن نتكلم عن البيئة يعني أقرب شيء لنا يمكن + +8 +00:00:51,700 --> 00:00:57,080 +الـ Atmosphere اللي هو يعني عبارة عن الهواء اللي + +9 +00:00:57,080 --> 00:01:01,200 +بيحيط فينا ودائماً + +10 +00:01:01,200 --> 00:01:08,040 +هو موجود فبالطبع الكرة الأرضية ككل محاطة بغطاء + +11 +00:01:08,040 --> 00:01:12,820 +Blanket أو غطاء من الهواء احنا بنسميه + +12 +00:01:12,820 --> 00:01:18,690 +الـ Atmosphere طبعاً الـ Atmosphere يعني كبير جداً جداً + +13 +00:01:18,690 --> 00:01:27,130 +يعني الـ Altitude تبعه واسع خالص فبنقدر نقول أنه + +14 +00:01:27,130 --> 00:01:32,330 +والله يزيد عن خمسمئة وستين كيلومتر وإن كان مش كله + +15 +00:01:32,330 --> 00:01:36,950 +منطقة واحدة يعني في عبارة عن هو عبارة عن عدة مناطق + +16 +00:01:37,380 --> 00:01:43,360 +في الحقيقة في حوالي خمسمئة وستين كيلومتر هذا اللي + +17 +00:01:43,360 --> 00:01:48,940 +يمكن بيوصل لألف ومئتين وثمانين كيلومتر إذا كانت + +18 +00:01:48,940 --> 00:01:51,440 +بدنا نقول والله بدنا نتجاوز الـ Atmosphere ونروح على + +19 +00:01:51,440 --> 00:01:55,120 +الـ Space الفضاء فبدنا نتجاوز حوالي ألف ومئتين و + +20 +00:01:55,120 --> 00:01:58,920 +ثمانين كيلومتر في الحقيقة فهو حوالي يعني خلينا نقول + +21 +00:01:58,920 --> 00:02:02,340 +وكل هذا تقريبي يعني خمسمئة وستين كيلومتر from + +22 +00:02:02,340 --> 00:02:04,340 +the surface of the earth + +23 +00:02:07,990 --> 00:02:12,010 +طبعاً احنا يمكن أكثر ما نشعر به هو الـ Atmosphere + +24 +00:02:12,010 --> 00:02:15,830 +اللي حوالينا مش كل الـ Atmosphere مش هالـ 560 + +25 +00:02:15,830 --> 00:02:20,470 +كيلومتر أو أكثر في الهواء الجوية لأ الـ Atmosphere + +26 +00:02:20,470 --> 00:02:25,270 +اللي بيأثر على حياتنا بشكل واضح جداً فيما يتعلق + +27 +00:02:25,270 --> 00:02:29,440 +مثلاً بالمناخ بدرجة الحرارة هذا هو الـ Atmosphere + +28 +00:02:29,440 --> 00:02:33,360 +القريب علينا أو اللي بنقوله الـ Troposphere يعني زي + +29 +00:02:33,360 --> 00:02:38,820 +ما هنشوف بعد شوية فاحنا بنقدر نشوف بس ايش اللي + +30 +00:02:38,820 --> 00:02:43,100 +بيحصل very close to the earth very close يعني في + +31 +00:02:43,100 --> 00:02:48,260 +حدود الـ 20 كيلومتر وأقل من هيك أقل من 20 كيلومتر + +32 +00:02:49,630 --> 00:02:53,090 +الـ Blanket أو الغطاء هذا اللي هو بيتكون من الهواء + +33 +00:02:53,090 --> 00:02:56,530 +Moderates Temperature يعدل الحرارة بيخلي الحرارة + +34 +00:02:56,530 --> 00:03:02,590 +مقبولة Protects us from harmful radiation أيضاً + +35 +00:03:02,590 --> 00:03:06,470 +بيقضي على كل الـ Radiation الضارة اللي بتيجي من + +36 +00:03:06,470 --> 00:03:11,680 +الشمس لأنه في Radiation ضارة جداً بتيجي من الشمس + +37 +00:03:11,680 --> 00:03:16,080 +فلابد من مرشحات لها أو Filter لها بحيث أنه تقضي + +38 +00:03:16,080 --> 00:03:19,760 +عليها فوظيفة الـ Blanket أو الـ Atmosphere اللي + +39 +00:03:19,760 --> 00:03:24,050 +حولنا أنه أيضاً يخلصنا من الـ Harm from Radiation and + +40 +00:03:24,050 --> 00:03:28,610 +Supports Life يعني يحافظ عليه الحياة دورة الحياة + +41 +00:03:28,610 --> 00:03:34,090 +وجود مثلاً الـ Oxygen وجود الميه باستمرار الـ Cycling + +42 +00:03:34,090 --> 00:03:39,050 +لهذه المكونات بشكل دائم + +43 +00:03:41,060 --> 00:03:46,820 +بنقول أنه الـ Troposphere والـ Stratosphere تقريباً فيهم + +44 +00:03:46,820 --> 00:03:50,380 +تسعة وتسعون في المئة من الـ Mass للأتموسفير يعني + +45 +00:03:50,380 --> 00:03:54,740 +معظم الغازات اللي بتكون موجودة بتكون موجودة في + +46 +00:03:54,740 --> 00:04:01,420 +جزئين من الأتموسفير مهمات جداً هما الـ Troposphere هذا + +47 +00:04:01,420 --> 00:04:05,460 +القريب علينا والـ Stratosphere اللي بعده على طول هذا + +48 +00:04:05,460 --> 00:04:08,660 +بيشكل تسعة وتسعين في المئة من كتلة الـ ايه الـ + +49 +00:04:08,660 --> 00:04:13,180 +Atmosphere يعني كتلة الهواء اللي موجودة في الفضاء + +50 +00:04:13,180 --> 00:04:18,560 +حولنا يعني خمسة وسبعين في المئة من هذه الـ Mass في الـ + +51 +00:04:18,560 --> 00:04:25,650 +Troposphere لأنه في الحقيقة يعني الجاذبية الأرضية + +52 +00:04:25,650 --> 00:04:30,890 +بتجذب الـ Atmosphere هذا اللي هو عبارة عن جزيئات و + +53 +00:04:30,890 --> 00:04:35,350 +Particles وغيرها بتجذبه إليها فبالتالي بنلاحظ أن + +54 +00:04:35,350 --> 00:04:41,410 +الـ Molecules والذرات الخفيفة بتطلع لفوق يعني + +55 +00:04:41,410 --> 00:04:45,790 +بتنجذبش كثير بينما اللي أثقل بتنجذب لتحت وبالتالي + +56 +00:04:45,790 --> 00:04:50,130 +في عندنا معظم الـ Mass للـ Atmosphere موجود وين؟ في الـ + +57 +00:04:50,130 --> 00:04:53,870 +Troposphere حوالينا يعني أقرب ما يكون إلى الأرض + +58 +00:04:53,870 --> 00:04:58,170 +من سطح الأرض ولفوق حوالي Maximum 17 كيلومتر + +59 +00:04:58,170 --> 00:05:04,090 +تقريباً عشر أميال تقريباً بقول 75% of which is the + +60 +00:05:04,090 --> 00:05:07,370 +Mass of the Mass in the Troposphere اللي هي Mass + +61 +00:05:07,370 --> 00:05:11,750 +للـ Atmosphere في الـ Troposphere Consequently, most of + +62 +00:05:11,750 --> 00:05:15,770 +the Chemistry that follows اللي هندرسها بتتعلق في + +63 +00:05:15,770 --> 00:05:19,490 +التروبوسفير والاستراتوسفير، يعني مش هندرس مثلاً + +64 +00:05:19,490 --> 00:05:23,450 +الميزوسفير بعدهم، الـ Thermosphere بالتفصيل، مش + +65 +00:05:23,450 --> 00:05:27,870 +هندرسهم، هنذكرهم اه، لكن مش رايحين ندرسهم بنوع من + +66 +00:05:27,870 --> 00:05:34,110 +التفصيل فصح الـ Atmosphere ينقسم لعدة أقسام لكن المهم + +67 +00:05:34,110 --> 00:05:37,370 +بالنسبة لنا هو الـ Troposphere والـ Stratosphere هنشوف + +68 +00:05:37,370 --> 00:05:42,430 +ليه لأن هم اللي بيأثروا على حياتنا بشكل كبير خالص + +69 +00:05:42,430 --> 00:05:49,230 +إذا كان اطلعنا على الحرارة وكيف بتتغير مع الـ + +70 +00:05:49,230 --> 00:05:57,720 +Altitude الارتفاع ممكن أن نجسم الـ ..الـ Atmosphere + +71 +00:05:57,720 --> 00:06:02,260 +لأربع أقسام بناء على الحرارة وكيف الحرارة هذه + +72 +00:06:02,260 --> 00:06:05,940 +تتغير كل ما ارتفعنا إلى أعلى ممكن تقسيم الـ + +73 +00:06:05,940 --> 00:06:10,400 +Atmosphere إلى أربع أقسام القريب علينا جداً هو + +74 +00:06:10,400 --> 00:06:16,120 +التروبوسفير بعده الستراتوسفير بعده الميزوسفير + +75 +00:06:16,120 --> 00:06:20,680 +وبعده الـ Thermosphere هذه الأربع أجسام طبعاً + +76 +00:06:20,680 --> 00:06:24,780 +الحرارة يعني هفرجيكوا إنها بتتغير بتتغير بشكل يعني + +77 +00:06:24,780 --> 00:06:30,180 +غير متوقع في الحقيقة لكن هذا هو تغير الحرارة كل + +78 +00:06:30,180 --> 00:06:35,150 +ما ارتفعنا أو يعني اطلعنا أكثر في الـ Altitude فبنلاحظ + +79 +00:06:35,150 --> 00:06:39,330 +أن الحرارة ممكن إنها لها Profile معين وممكن + +80 +00:06:39,330 --> 00:06:44,010 +تحديد كل منطقة من هذا الـ Profile يعني الحرارة + +81 +00:06:44,010 --> 00:06:47,570 +ماشية عمال بتزيد بدأت تنزل اه إذا بدنا نقول والله + +82 +00:06:47,570 --> 00:06:51,770 +هذه منطقة نزلت نزلت نزلت طب ماشي بدأت تزيد إذا هذه + +83 +00:06:51,770 --> 00:06:56,730 +كمان منطقة بعدين زادت ماشي الحال بعدين بدأت تنزل + +84 +00:06:56,730 --> 00:07:00,370 +هذه كمان وهكذا وين في عندي Inflection في التغير + +85 +00:07:00,370 --> 00:07:05,260 +في درجة الحرارة سمينا هذه المنطقة Pause Pause زي ما + +86 +00:07:05,260 --> 00:07:11,480 +هنشوف بعد شوية وبعدين يعني على أساس هذا الكلام + +87 +00:07:11,480 --> 00:07:14,740 +قلنا والله ممكن تقسيم الـ Atmosphere للأربع + +88 +00:07:14,740 --> 00:07:21,650 +أقسام اللي اتكلمنا عنها فـ Just above the surface في + +89 +00:07:21,650 --> 00:07:27,710 +التروبوسفير تقريباً + +90 +00:07:27,710 --> 00:07:35,510 +تتقل الحرارة لغاية ما توصل تقريباً 215 كلفن يعني + +91 +00:07:35,510 --> 00:07:41,470 +حوالي ماينص خمسة وخمسين سبع وخمسين درجة سي + +92 +00:07:41,470 --> 00:07:47,550 +عند حوالي عشرة كيلومتر وبالمناسبة العشرة كيلومتر + +93 +00:07:47,550 --> 00:07:55,550 +هادية هي الحد اللي تقريباً الطائرات اللي بتنقل + +94 +00:07:55,550 --> 00:08:00,150 +المسافرين بتطير عنده يعني الطائرة التجارية اللي + +95 +00:08:00,150 --> 00:08:05,290 +بتنقل المسافرين بتطير عند حوالي عشر كيلومتر طبعاً + +96 +00:08:05,290 --> 00:08:09,010 +هي لما نطير عند حوالي عشر كيلومتر بتكون تقريباً + +97 +00:08:09,010 --> 00:08:12,630 +عامة اللي بتنتقل يعني في آخر الـ Troposphere إذا زي + +98 +00:08:12,630 --> 00:08:18,070 +ما قلنا يعني كل ما ارتقينا أكثر في الارتفاع درجة + +99 +00:08:18,070 --> 00:08:21,310 +الحرارة بتقل في ما يتعلق بالـ Troposphere لأن انتقل + +100 +00:08:21,310 --> 00:08:25,950 +لمكان ثاني لأ ممكن الوضع يتغير فبتقل درجة الحرارة + +101 +00:08:25,950 --> 00:08:30,070 +لغاية ما توصل حوالي 215 كيلومتر عند حوالي عشر + +102 +00:08:30,070 --> 00:08:35,230 +كيلومتر في الحقيقة منطقة الـ Troposphere اللي + +103 +00:08:35,230 --> 00:08:38,770 +حوالين العشرة كيلومتر أقل من عشرة كيلومتر تقريباً + +104 +00:08:38,770 --> 00:08:43,550 +يعني بنلاحظ أنه يعني كل الظواهر اللي بنشوفها عادة + +105 +00:08:43,550 --> 00:08:47,990 +في الطبيعة في الـ Environment فيما يتعلق بالأتمسفير + +106 +00:08:47,990 --> 00:08:51,710 +بتحصل فيها يعني مثلاً في عندنا الرياح العاتية اللي + +107 +00:08:51,710 --> 00:08:57,650 +بنشوفها العواصف وغيرها الـ Soft Breezes يعني + +108 +00:08:57,650 --> 00:09:03,780 +خليني أقول النسمات الخفيفة اللي احنا ممكن نحس فيها + +109 +00:09:03,780 --> 00:09:08,940 +الـ .. الـ Rain المطر الـ Sunny Skies كل هذا بيحصل في + +110 +00:09:08,940 --> 00:09:12,820 +هذه المنطقة يعني الـ Troposphere اللي هو المكان + +111 +00:09:12,820 --> 00:09:16,240 +الملاصق للأرض كل الظواهر اللي احنا متعودين + +112 +00:09:16,240 --> 00:09:20,940 +عليها واللي بنعرفها بتحصل فيها مش في عالي الـ + +113 +00:09:20,940 --> 00:09:24,320 +Atmosphere فوق لأ في المنطقة القريبة جداً من الأرض + +114 +00:09:24,320 --> 00:09:30,620 +مش بس الحرارة هي اللي بتتغير إذا كان طلعنا في الـ + +115 +00:09:30,620 --> 00:09:34,920 +Altitude أو ارتفاعاً يعني في الـ Atmosphere لأ الـ + +116 +00:09:34,920 --> 00:09:37,560 +Pressure بينخفض أيضاً كل ما طلعنا لفوق لكن الـ + +117 +00:09:37,560 --> 00:09:43,920 +Pressure مافيش له خليني أقول الـ Profile متنوع زي + +118 +00:09:43,920 --> 00:09:47,920 +الحرارة الحرارة قلنا بتتغير سلباً وإيجاباً اه + +119 +00:09:47,920 --> 00:09:50,880 +بتنزل تنزل وبعدين بتزيد وبعدين بتنزل وبعدين بتزيد + +120 +00:09:50,880 --> 00:09:55,580 +كويس لكن الضغط لأ كل ما طلعنا لفوق الضغط بيقل وهذا + +121 +00:09:55,580 --> 00:10:03,260 +وضع طبيعي ليه؟ ارتفاع عمود الهواء بيقل لأن كمية الـ + +122 +00:10:03,260 --> 00:10:07,720 +Atoms والـ Molecules ومكونات الهواء بتقل كل ما + +123 +00:10:07,720 --> 00:10:12,520 +طلعنا لفوق لدرجة أنه يعني قلنا أن معظم الـ Mass + +124 +00:10:12,520 --> 00:10:15,880 +موجودة في الـ Troposphere وبتبدأ طبعاً تقل كل ما + +125 +00:10:15,880 --> 00:10:19,320 +طلعنا لأعلى لكن فوق خالص بنلاقي أنه لأ الـ Pressure + +126 +00:10:19,320 --> 00:10:23,480 +بيكون قليل جداً جداً جداً لأن عمود الهواء مش له + +127 +00:10:23,480 --> 00:10:29,950 +تقريباً هذا الوزن في ما يتعلق بالضغط خلينا نبدأ + +128 +00:10:29,950 --> 00:10:33,890 +بالضغط اه كل ما طلعنا هذا هو الـ Altitude ارتفاعاً + +129 +00:10:33,890 --> 00:10:38,370 +كل ما طلعنا لفوق الضغط عمال شمال بيقل هذا .. هذا + +130 +00:10:38,370 --> 00:10:43,830 +مافيش فيه أي تفصيل هو هذا وضع طبيعي لأنه عندنا الـ + +131 +00:10:43,830 --> 00:10:50,080 +Mass لعمود الهواء بيقل لأن كمية الهواء فيه بتقل و + +132 +00:10:50,080 --> 00:10:54,540 +كل ما طلعنا لفوق بتقل بشكل كبير خالص لتعرف نطلع + +133 +00:10:54,540 --> 00:10:58,640 +على الحرارة الحرارة هي احنا عند Altitude صفر يعني + +134 +00:10:58,640 --> 00:11:04,580 +على سطح الأرض مثلاً 290 درجة 25 Degree C 23 Degree + +135 +00:11:04,580 --> 00:11:10,620 +C ماشي طيب بدينا نطلع لفوق ارتفاعاً الحرارة ايه + +136 +00:11:10,620 --> 00:11:13,900 +شمالها عمال بتقل بتقل بتقل لغاية ما نوصل تقريباً + +137 +00:11:13,900 --> 00:11:19,220 +215 Kelvin بعدين ايه بتبدأ تزيد ما دام بدأت تزيد هنا + +138 +00:11:19,220 --> 00:11:22,600 +في هذه المنطقة المنطقة اللي حصل فيها الـ Inflection + +139 +00:11:22,600 --> 00:11:27,080 +أو التغير من النقص إلى الزيادة هذه اسمها Pause + +140 +00:11:27,080 --> 00:11:34,120 +فعندي Troposphere في عندي Tropopause توقفت درجة + +141 +00:11:34,120 --> 00:11:39,190 +الحرارة عن النقص وبدأت إيش تزيد، الستراتوسفير بدأت + +142 +00:11:39,190 --> 00:11:43,090 +تزيد تزيد تزيد تزيد لغاية ما وصلت حرارة معينة + +143 +00:11:43,090 --> 00:11:46,770 +بعدين بدت بدها تنقص تاني اه، هذه المنطقة هي + +144 +00:11:46,770 --> 00:11:52,570 +الستراتوسفير، مدام اتغير الـ temperature profile من + +145 +00:11:52,570 --> 00:12:01,970 +سلبا إلى إيجابا مثلا، فعندي اتغير الجزء من الـ + +146 +00:12:01,970 --> 00:12:06,070 +atmosphere نوعه اتغير هنا، الـ Troposphere كان فيه نقص + +147 +00:12:06,650 --> 00:12:10,470 +بدأت الزيادة صار اسمه stratosphere، بدأ النقص صار + +148 +00:12:10,470 --> 00:12:13,790 +اسمه mesosphere، بدأت الزيادة صار اسمه + +149 +00:12:13,790 --> 00:12:17,710 +thermosphere، إذا كل هذا بتوقف على الـ temperature + +150 +00:12:17,710 --> 00:12:21,150 +profiles، يعني هذه التقسيمات موجودة بناء على الـ + +151 +00:12:21,150 --> 00:12:22,770 +temperature profiles + +152 +00:12:25,990 --> 00:12:30,150 +هذا باختصار، ما يعني نتدقق كتير على هذه الأرقام + +153 +00:12:30,150 --> 00:12:36,490 +عموما لأنها أرقام بحسب المصادر المختلفة متاحة من + +154 +00:12:36,490 --> 00:12:40,710 +المصادر المختلفة، ففي تفاوت بسيط بينها، فبنلاحظ إن + +155 +00:12:40,710 --> 00:12:45,950 +إذا كان هذا هو سطح الأرض حوالي أنه سبعة عشر كيلومتر، + +156 +00:12:45,950 --> 00:12:51,410 +ثمانية عشر كيلومتر، هذا هو الـ Troposphere المنطقة + +157 +00:12:51,410 --> 00:12:54,630 +هذه الـ Tropopause اللي هي إيش عاملينها احنا يعني + +158 +00:12:54,630 --> 00:12:58,490 +بخط مختلف شوي، من أربعة عشر لتمانية عشر تقريبا، + +159 +00:12:58,490 --> 00:13:01,230 +هي الـ Tropopause اللي عندها الحرارة بتصير + +160 +00:13:01,230 --> 00:13:06,470 +ثابتة، بعدين بنيجي للالألوان الأغمق، هذا + +161 +00:13:06,470 --> 00:13:11,160 +الغامق، هذا هو عبارة عن الـ Stratosphere وارتفاعه + +162 +00:13:11,160 --> 00:13:16,640 +حوالي خمسين كيلومتر، والأحمر هذا هو طبقة الأوزون + +163 +00:13:16,640 --> 00:13:21,380 +اللي احنا بنسمع عنها دائما، فطبقة الأوزون في آخر أو + +164 +00:13:21,380 --> 00:13:26,180 +آخر الـ stratosphere، آخر الـ stratosphere، وبعدين + +165 +00:13:26,180 --> 00:13:29,900 +عندنا الـ stratopause لأن الحرارة هتتغير هي هذه + +166 +00:13:29,900 --> 00:13:34,760 +المنطقة زي هذه بالظبط، الـ stratopause، بعدين بيجينا الـ + +167 +00:13:34,760 --> 00:13:40,210 +mesosphere، وبعدين اللي هو الـ thermosphere + +168 +00:13:40,210 --> 00:13:48,230 +اللي هو بتكون من منطقتين زي ما هنشوف بعد شوية، فإذا + +169 +00:13:48,230 --> 00:13:54,850 +كان هذه هي الكرة الأرضية، الـ troposphere كويس، هو + +170 +00:13:54,850 --> 00:14:01,010 +عبارة عن من سطح إلى حوالي سبعة عشر كيلومتر، الـ + +171 +00:14:01,010 --> 00:14:06,620 +stratosphere من حوالي سبعة عشر لخمسين كيلومتر، هدول + +172 +00:14:06,620 --> 00:14:09,360 +قلنا المناطقين، هما المنطقتين اللي بيأثروا على + +173 +00:14:09,360 --> 00:14:17,920 +الأرض والـ environment فيها بشكل أساسي، في + +174 +00:14:17,920 --> 00:14:21,880 +الـ .. إيش بيسموه؟ يعني هذا الخط تروبوبوز هو عبارة + +175 +00:14:21,880 --> 00:14:26,980 +عن ارتفاع معظم السحب، يعني معظم السحب وين موجودة؟ + +176 +00:14:26,980 --> 00:14:32,140 +موجودة داخل الطبيعة .. داخل الـ troposphere، داخل الـ + +177 +00:14:32,140 --> 00:14:38,210 +troposphere، فنتكلم بس باختصار شديد عن كل واحد من + +178 +00:14:38,210 --> 00:14:43,590 +هدول الأجزاء المكونة للأتمسفير، فبنقول الـ + +179 +00:14:43,590 --> 00:14:46,030 +troposphere is the lowest region in the atmosphere + +180 +00:14:46,030 --> 00:14:51,930 +on the earth, it goes from ground أو يعني sea level + +181 +00:14:51,930 --> 00:14:57,130 +الماء يعني، أو sea level up to about 11 mile أو 17 + +182 +00:14:57,130 --> 00:15:01,910 +kilometer تقريبا تقريبا about يعني تقريبا طيب + +183 +00:15:01,910 --> 00:15:04,950 +weather and clouds occur in the troposphere، يبقى + +184 +00:15:04,950 --> 00:15:11,530 +كل الـ climate تبعنا جاي من الـ troposphere, in the + +185 +00:15:11,530 --> 00:15:14,710 +troposphere the temperature generally decreases as + +186 +00:15:14,710 --> 00:15:19,700 +altitude increases، يعني لو جينا طلعنا هي الـ + +187 +00:15:19,700 --> 00:15:24,700 +Troposphere دي واطلعنا على الـ altitude مثلا اه + +188 +00:15:24,700 --> 00:15:31,100 +كل ما ارتفعنا في الـ altitude، الـ altitude صفر وصلنا + +189 +00:15:31,100 --> 00:15:34,580 +لعشرين لاحظوا الحرارة كانت حوالي سالب خمسين سالب + +190 +00:15:34,580 --> 00:15:39,720 +ثلاثة زي ما شوفناها قبل شوية، فالحرارة طبعا بتقل كل + +191 +00:15:39,720 --> 00:15:45,620 +ما ارتفعنا فيها في الـ altitude، الـ Stratosphere طيب من + +192 +00:15:45,620 --> 00:15:48,920 +حوالي السبعة عشر لخمسين كيلومتر، شفنا هذا كلام + +193 +00:15:48,920 --> 00:15:52,940 +above the earth's surface أو water، الـ earth's + +194 +00:15:52,940 --> 00:15:56,200 +ozone layer is located in the stratosphere، فالـ + +195 +00:15:56,200 --> 00:15:58,920 +ozone لما نتكلم عن الـ ozone بنقول والله هو وين + +196 +00:15:58,920 --> 00:16:03,780 +موجود في الـ stratosphere، إيش هو الـ ozone؟ ده الـ + +197 +00:16:03,780 --> 00:16:06,740 +ozone is a form of oxygen، هو O ثلاثة بدل ما هو O + +198 +00:16:06,740 --> 00:16:10,220 +اثنين، الـ oxygen ملك للـ oxygen O اثنين هو O ثلاثة + +199 +00:16:10,900 --> 00:16:17,280 +كويس طبعا، ليش مهم جدا بالنسبة لنا؟ جال لأنه بيمتص + +200 +00:16:17,280 --> 00:16:22,940 +الأشعة من حوالي 240 ل 310 نانومتر، وهذه الأشعة + +201 +00:16:22,940 --> 00:16:26,800 +بتوجع في منطقة الـ UV لو ما كانش الـ ozone موجود + +202 +00:16:26,800 --> 00:16:31,140 +معناته هذه الأشعة راح توصل للأرض وراح يعني نعيش + +203 +00:16:31,140 --> 00:16:36,440 +في وجودها، وهذا ضرر جدا على الصحة بتقدر تكسر الروابط + +204 +00:16:36,820 --> 00:16:41,440 +بتقدر تسبب سرطانات للبشر والكائنات الحية، يعني + +205 +00:16:41,440 --> 00:16:45,180 +بشكل عام، فبالتالي هي خطيرة للغاية، ووجودها يعتبر + +206 +00:16:45,180 --> 00:16:53,140 +حيوي بشكل كبير، وهنرجع لها، فكل يعني الأشعة اللي + +207 +00:16:53,140 --> 00:16:58,420 +صادرة من الشمس تقريبا في الـ range من 240 لـ 310، طبقة + +208 +00:16:58,420 --> 00:17:02,060 +الأوزون بتصفيها وبتخلي كمية الأشعة هذه اللي وصلت + +209 +00:17:02,060 --> 00:17:04,740 +للأرض مهملة، كمية قليلة للغاية + +210 +00:17:07,040 --> 00:17:10,040 +بقول only the highest clouds are in the lower + +211 +00:17:10,040 --> 00:17:13,900 +stratosphere، يعني بالا هي في الـ troposphere أو في + +212 +00:17:13,900 --> 00:17:19,160 +أدنى الـ stratosphere، هذه اللي خلينا نقول الـ clouds أو + +213 +00:17:19,160 --> 00:17:25,620 +الصحوب العالية جدا، هاي الـ stratosphere واحنا هي + +214 +00:17:25,620 --> 00:17:28,700 +ممكن هاد الـ stratopause لأن الحرارة ما تتغيرش من + +215 +00:17:28,700 --> 00:17:34,300 +هان لهان، هاد الـ stratopause، كويس، بعدين تبدأ الحرارة + +216 +00:17:34,300 --> 00:17:40,140 +تزيد، إذا هذا هو الـ stratosphere تمام، بعده طبعا + +217 +00:17:40,140 --> 00:17:45,240 +هييجي عندنا الـ mesosphere، الـ mesosphere من خمسين لـ + +218 +00:17:45,240 --> 00:17:49,660 +ثمانين، خمسة وثمانين كيلومتر، من خمسين لـ ثمانين + +219 +00:17:49,660 --> 00:17:54,100 +خمسة وثمانين كيلومتر أعلى من طبعا فوق سطح الأرض + +220 +00:17:54,100 --> 00:17:59,440 +يعني الـ temperature بتنعكس، temperature in the + +221 +00:17:59,440 --> 00:18:00,440 +mesosphere drop + +222 +00:18:05,840 --> 00:18:13,560 +بتنزل الحرارة بشكل كبير لحوالي سالب مية وتسعين، مية + +223 +00:18:13,560 --> 00:18:20,620 +كويس، فالحرارة بتنزل بشكل كبير، طيب بنقول in the + +224 +00:18:20,620 --> 00:18:23,200 +mesosphere temperature quickly decreases as + +225 +00:18:23,200 --> 00:18:27,640 +height increases، هذا كلام واضح من الشكل + +226 +00:18:31,050 --> 00:18:34,430 +بيقول الـ Mesosphere is also the layer in which a + +227 +00:18:34,430 --> 00:18:39,370 +lot of meteors burn up while entering the earth's + +228 +00:18:39,370 --> 00:18:43,010 +atmosphere، بنعرف النيازك مرات بنشوفها زي السهم + +229 +00:18:43,010 --> 00:18:48,290 +السريع جدا جدا ومولع نار زي النجم بيكون، هذه + +230 +00:18:48,290 --> 00:18:52,850 +عبارة عن نيازك بتحترق لما توصل لمنطقة الـ + +231 +00:18:52,850 --> 00:18:56,880 +Mesosphere، في الـ Mesosphere، ففي منطقة الميزوسفير + +232 +00:18:56,880 --> 00:19:02,140 +هذه النيازك كثير منها بيحترق بينما يدخل للأرض + +233 +00:19:02,140 --> 00:19:10,960 +الجو من الأرض، يسمونها شُهب شُهب نجوم، نجوم كأنها + +234 +00:19:10,960 --> 00:19:18,740 +نجوم سريعة جدا جدا زي السهم يعني، بتكون طيب الـ + +235 +00:19:18,740 --> 00:19:23,580 +thermosphere هو آخر منطقة في الـ atmosphere تبعنا + +236 +00:19:24,360 --> 00:19:28,780 +الـ temperature بتعود تزيد مع الارتفاع لدرجة إنه + +237 +00:19:28,780 --> 00:19:34,680 +ممكن توصل لـ 1700 درجة، لكن خليني أقول إنه تأثير + +238 +00:19:34,680 --> 00:19:38,340 +الحرارة فوق مش كتير مهم، لأنه عدد الجزيئات اللي + +239 +00:19:38,340 --> 00:19:42,060 +حاملة الحرارة هذه نادر قليل جدا، صح الجزيئات بتكون + +240 +00:19:42,060 --> 00:19:47,080 +very hot لكن جداً عددها، فعددها لا يكاد يذكر قليل + +241 +00:19:47,080 --> 00:19:49,860 +جدا، علشان التأثير الحرارة مش كتير كبير في هذه + +242 +00:19:49,860 --> 00:19:53,180 +المنطقة، لكن هذه المنطقة تلاحظ إن هي قريبة من الشمس + +243 +00:19:53,700 --> 00:19:56,680 +التي أقرب ما يكون إلى الشمس، فالطبيعة هي إن حرارتها + +244 +00:19:56,680 --> 00:20:04,080 +تكون عالية، الـ thermosphere هتنقسم لقسمين، تنقسم لـ + +245 +00:20:04,080 --> 00:20:09,260 +الـ ionosphere والـ exosphere، الـ ionosphere والـ + +246 +00:20:09,260 --> 00:20:13,780 +exosphere، إذا منطقة الـ thermosphere تنقسم لقسمين + +247 +00:20:15,880 --> 00:20:20,560 +Ionosphere و Exosphere، لحظة الحرارة تزيد بشكل مهول + +248 +00:20:20,560 --> 00:20:25,460 +وتبقى تزيد، لأنه بعد ذلك سنصل للشمس، لـ 28 نطلع من + +249 +00:20:25,460 --> 00:20:31,960 +الـ atmosphere ونصل للشمس، فالحرارة تزيد زيادة مهولة + +250 +00:20:31,960 --> 00:20:36,820 +للغاية، بنتكلم عن الـ .. باختصار برضه عن الـ + +251 +00:20:36,820 --> 00:20:41,260 +ionosphere وبنقول والـ exosphere، الـ thermosphere + +252 +00:20:41,260 --> 00:20:45,100 +كان بيقولنا identified in two parts، الـ ionosphere + +253 +00:20:45,100 --> 00:20:48,500 +والـ exosphere، الـ ionosphere من خمسة وثمانين + +254 +00:20:48,500 --> 00:20:51,200 +كيلومتر، يعني من نهاية الـ stratosphere إلى حوالي + +255 +00:20:51,200 --> 00:20:54,980 +ستماية وأربعين كيلومتر، it contains many ions and + +256 +00:20:54,980 --> 00:20:58,750 +free electrons plasma، الـ plasma هي عبارة عن + +257 +00:20:58,750 --> 00:21:02,670 +mixture من الـ atoms والـ ions والـ electrons + +258 +00:21:02,670 --> 00:21:06,670 +موجودة at very high temperature، هذا هو تعريف الـ + +259 +00:21:06,670 --> 00:21:10,430 +plasma فهي عبارة عن mixture homogeneous mixture من + +260 +00:21:10,430 --> 00:21:14,390 +atoms و ions و electrons موجودة at very high + +261 +00:21:14,390 --> 00:21:18,570 +temperature، فعندي plasma موجودة وين؟ في الـ + +262 +00:21:18,570 --> 00:21:23,650 +ionosphere، يعني موجودة عند كم هائل من الـ ions والـ + +263 +00:21:23,650 --> 00:21:28,390 +free electrons، Aruras occur in the ionosphere، + +264 +00:21:28,390 --> 00:21:34,670 +الـ Aruras هي عبارة عن أضواء معروفة في شمال القارة + +265 +00:21:34,670 --> 00:21:40,110 +بالأضواء الشمالية عند القطب الشمالي بتكون، هفرجيكم + +266 +00:21:40,110 --> 00:21:44,710 +إياها وإيش سببها، وعند القطب الجنوبي أيضا موجودة، + +267 +00:21:44,710 --> 00:21:48,550 +واسمها الأضواء الجنوبية، فبنقولها الثانية ثانية، + +268 +00:21:48,550 --> 00:21:54,350 +بقولها Aruras، الواحدة Aurora، فهذا عبارة عن أضواء + +269 +00:21:55,460 --> 00:22:00,060 +لا ضوء ضوء ضوء، هفرجيكي ايه إيش هو من وين جاي + +270 +00:22:00,060 --> 00:22:03,640 +بالظبط، the aurora or northern lights المدخل + +271 +00:22:03,640 --> 00:22:06,760 +الشمالي are a result of particles from the sun + +272 +00:22:06,760 --> 00:22:10,020 +coming into contact with the earth's atmosphere + +273 +00:22:10,020 --> 00:22:15,620 +هذا عبارة عن خلينا نقول particles جاية من الشمس + +274 +00:22:15,620 --> 00:22:20,580 +بتوصل لـ earth's atmosphere فوق في الـ ionosphere + +275 +00:22:21,310 --> 00:22:25,550 +وفي الـ .. في الـ ionosphere تحديدا يعني، فبتعمل + +276 +00:22:25,550 --> 00:22:31,990 +interaction مع الـ electrons، وهنشوف يعني بعد شوية + +277 +00:22:31,990 --> 00:22:35,550 +هنفرجيكم بعض الـ mechanism يعني من وين هذه الأضواء + +278 +00:22:35,550 --> 00:22:40,040 +بتيجي وإيش هي هذه الأضواء، الـ Exosphere اللي هو آخر + +279 +00:22:40,040 --> 00:22:43,400 +جزء، عشان بس نخلص هذا الجزء الخاص بمكونات الـ + +280 +00:22:43,400 --> 00:22:47,240 +Atmosphere هو الـ Outermost Layer of the Earth's + +281 +00:22:47,240 --> 00:22:50,800 +Atmosphere أعلى منطقة في الـ Earth's Atmosphere + +282 +00:22:50,800 --> 00:22:55,980 +اللي بعدها لو إشي تجاوزها بيكون طلع على الفضاء + +283 +00:22:55,980 --> 00:23:01,280 +الخارجي بقلّ في الاتمسفير للأرض، بعد الـ Exosphere، + +284 +00:23:01,280 --> 00:23:04,900 +لو أي إشي هرب من الـ Exosphere، أي جزيه، أي ذرة، + +285 +00:23:04,900 --> 00:23:09,840 +أي إلكترون هرب من الـ Exosphere، وين بده يروح؟ خلاص + +286 +00:23:09,840 --> 00:23:13,600 +صار في الفضاء الخارجي انتهينا بده يظل يلف الفضاء + +287 +00:23:13,600 --> 00:23:20,920 +الخارجي كجثيم يعني بقول from about 400 miles to 640 + +288 +00:23:20,920 --> 00:23:25,740 +800 mile يعني 1180 كيلومتر هذه تقريبا حدود ال + +289 +00:23:25,740 --> 00:23:29,160 +exosphere بعد ال 1180 خلاص دهانا على الفضاء + +290 +00:23:29,160 --> 00:23:32,360 +الخارجي the lower boundary of the exosphere is + +291 +00:23:32,360 --> 00:23:35,780 +called the critical level of escape الـ Critical + +292 +00:23:35,780 --> 00:23:40,660 +Level of Escape هو يعني الحد اللي بعده، يعني + +293 +00:23:40,660 --> 00:23:44,960 +بسهولة بنلاحظ أن الجزيء أو الذرّة أو الإلكترون + +294 +00:23:44,960 --> 00:23:52,290 +بيهرب من الـ atmosphere where the where atmospheric + +295 +00:23:52,290 --> 00:23:56,490 +pressure is very low بيوصل لعشرة أس سالب ستة عشر + +296 +00:23:56,490 --> 00:24:00,670 +أس سالب سبعة Torr يعني زي أحسن مفرغة بنعملها عندنا في + +297 +00:24:00,670 --> 00:24:04,870 +الأرض عشان تعملنا تفريغ فوق زي هيك ليه؟ لأن ما فيش + +298 +00:24:04,870 --> 00:24:09,670 +جزيئات ما فيش جزيئات ما فيش ذرات قليل جدا الضغط قليل + +299 +00:24:09,670 --> 00:24:14,370 +للغاية and the temperature is very low في ال + +300 +00:24:14,370 --> 00:24:19,890 +exosphere مش very low في الـ exosphere ال + +301 +00:24:19,890 --> 00:24:23,470 +temperature مش very low الـ temperature high يعني In + +302 +00:24:23,470 --> 00:24:26,730 +this region, atoms and molecules escape into this + +303 +00:24:26,730 --> 00:24:29,630 +space خلينا هذه ليست الـ Low لأن هذه + +304 +00:24:29,630 --> 00:24:33,230 +الـ Thermosphere + +305 +00:24:33,230 --> 00:24:37,390 +اللي قلنا بتكون من الـ Ionosphere و الـ Exosphere + +306 +00:24:37,390 --> 00:24:42,030 +و الـ Exosphere كمان لفوق يعني الحرارة بيكون عالية + +307 +00:24:42,030 --> 00:24:43,210 +المفروض للغاية + +308 +00:24:45,940 --> 00:24:49,040 +طيب لكن في هذه المنطقة يقولنا الـ atoms و الـ + +309 +00:24:49,040 --> 00:24:51,820 +molecules escape into this space يعني بتسيب الفضاء + +310 +00:24:51,820 --> 00:24:55,240 +تبعنا و بتروح على الـ space نتكلم شوية بس عن + +311 +00:24:55,240 --> 00:25:00,360 +القرورة الأرورا قلنا هي عبارة عن natural light + +312 +00:25:00,360 --> 00:25:07,580 +display عبارة عن ضوء طبيعي بنشوفه في الفضاء + +313 +00:25:07,580 --> 00:25:12,060 +particularly in the high altitudes في الفضاء يعني + +314 +00:25:12,060 --> 00:25:16,540 +فوق خالص في أي منطقة في الـ Arctic و الـ Antarctic + +315 +00:25:16,540 --> 00:25:21,140 +regions في منطقة القطب الشمالي والجنوبي يعني تعرفوا + +316 +00:25:21,140 --> 00:25:24,600 +الأرض فيها قطب شمال و قطب جنوب في هذه المناطق caused + +317 +00:25:24,600 --> 00:25:27,460 +by the collision of energetic charged particles + +318 +00:25:27,460 --> 00:25:31,880 +اللي بتيجي عاوزة من الشمس with atoms in the high + +319 +00:25:31,880 --> 00:25:37,360 +altitude atmosphere يعني الـ ionosphere ما هو + +320 +00:25:37,360 --> 00:25:41,520 +جزء من الـ thermosphere the charged particles are + +321 +00:25:41,520 --> 00:25:46,160 +directed by earth's magnetic field into the + +322 +00:25:46,160 --> 00:25:50,660 +atmosphere كيف يعني؟ أنا عندي الأرض طبعا إيش في + +323 +00:25:50,660 --> 00:25:56,440 +إلها؟ في الها magnetic field صح في magnetic field و + +324 +00:25:56,440 --> 00:25:59,780 +كلنا بنعرف البوصلة ليش البوصلة في magnetic field + +325 +00:26:00,380 --> 00:26:05,400 +طيب لما نكون في عندنا charge particle جاية أي + +326 +00:26:05,400 --> 00:26:10,340 +charge particle بتتحرك في magnetic field هنلاحظ + +327 +00:26:10,340 --> 00:26:14,500 +أنه بيلف عمودي على الـ magnetic field فهذا اللي + +328 +00:26:14,500 --> 00:26:18,380 +بيحصل طب الـ magnetic field مثلا هاي الأرض هاي الـ + +329 +00:26:18,380 --> 00:26:21,460 +magnetic field تبع الأرض okay نقول والله هذا هو + +330 +00:26:21,460 --> 00:26:24,580 +بهذا الشكل الأحمر هذا إذا هاي الـ magnetic field في + +331 +00:26:24,580 --> 00:26:28,140 +هذا الاتجاه مثلا إذا الـ charge particles كده بدأت + +332 +00:26:28,140 --> 00:26:32,520 +تللف و هان حوالين القطبين الشمالي والجنوبي هاي + +333 +00:26:32,520 --> 00:26:38,900 +اللي تشارج particles طب هذه لما تصطدم فيها الأشعة + +334 +00:26:38,900 --> 00:26:43,700 +اللي جاءت من الشمس إيش اللي راح يعني يحصل عندي + +335 +00:26:43,700 --> 00:26:47,040 +excitation اللي بتعطيني emission excitation يعني + +336 +00:26:47,040 --> 00:26:51,620 +إثارة فرح تعطي emission لضوء هذا الضوء اللي أنا + +337 +00:26:51,620 --> 00:26:56,740 +عادة بحصل عليه بنقوله الـ Aurora خلاني أقول وين + +338 +00:26:56,740 --> 00:27:02,510 +بنتوقع أنه نحصل على الـ Aurora؟ جال والله عند القطب + +339 +00:27:02,510 --> 00:27:06,170 +الشمالي في المنطقة الشمالية والمنطقة الجنوبية ليه؟ + +340 +00:27:06,170 --> 00:27:11,050 +لأن الـ charge particles بدها يعني تلف عمودي على الـ + +341 +00:27:11,050 --> 00:27:15,310 +magnetic field و الـ magnetic field بتركز في الـ + +342 +00:27:15,310 --> 00:27:20,130 +south pole و الـ north pole فحواليهم بدوا يكون في + +343 +00:27:20,130 --> 00:27:24,210 +عندي .. لحظة و هاي الـ charge particles بتلف و بدي + +344 +00:27:24,210 --> 00:27:28,530 +يكون فيه عند الـ Aurora نتيجة التصادم مع الجسيمات + +345 +00:27:28,530 --> 00:27:35,410 +و الأشعة اللي جاية من الشمس تحديدا فالـ .. في اسمين + +346 +00:27:35,410 --> 00:27:41,550 +للـ Aurora في Aurora Borealis هذه يعني الـ .. نقول + +347 +00:27:41,550 --> 00:27:47,150 +الأضواء الشمالية و في Aurora Australis هذه الأضواء + +348 +00:27:47,150 --> 00:27:51,530 +الجنوبية كويس؟ حسب منطقة الـ Aurora هل هي في الشمال + +349 +00:27:51,530 --> 00:27:57,420 +ولا هي في الجنوب قلنا الـ mechanism يعني حكينا عنها + +350 +00:27:58,310 --> 00:28:03,030 +تصوروا يعني هذه إحنا بنشوفهاش عندنا في مناطقنا يعني + +351 +00:28:03,030 --> 00:28:08,050 +دائما يعني نادرة جدا إذا كان شفنا بعضها بس غريب + +352 +00:28:08,050 --> 00:28:10,830 +أنه نشوف بعضها يعني أما أن هي في شمال الكوكب + +353 +00:28:10,830 --> 00:28:13,690 +الأرضية و الناس بتروح خصوصا عشان تتفرج على هذه + +354 +00:28:13,690 --> 00:28:18,250 +الأضواء فتطلعوا شغلات جميلة يعني للغاية تطلعوا + +355 +00:28:18,250 --> 00:28:23,070 +يعني تخيلوا أنكم تشوفوا حاجة زي هيك في مكان ما + +356 +00:28:23,070 --> 00:28:30,420 +يعني هذه برضه Aurora ألوان عجيبة يعني تطلعوا الـ أصفر + +357 +00:28:30,420 --> 00:28:35,840 +على الأحمر على الـ violet على الأزرق هذه حاجات تطلعوا + +358 +00:28:35,840 --> 00:28:39,280 +أحمر و أخر اشي غريب يعني اشي غريب كثير ألوان يعني + +359 +00:28:39,280 --> 00:28:47,010 +بالفعل جذابة للغاية هذه برضه أشكال تانية اللي بحاول + +360 +00:28:47,010 --> 00:28:52,230 +اللي بحب ممكن أنه يتطلع على الـ net على سبيل المثال + +361 +00:28:52,230 --> 00:28:57,210 +تكتبوا Aurora مثلا و تشوفوا مناظر جميلة للغاية يعني + +362 +00:28:57,210 --> 00:29:01,320 +إذا كان الـ resolution عندكم عالية هتلاقوا ناس كثير + +363 +00:29:01,320 --> 00:29:05,540 +مهتمة بإنها تنزل الصور اللي صورتها و مناظر في + +364 +00:29:05,540 --> 00:29:10,340 +الحقيقة يعني عجيبة للغاية مناظر جميلة جدا جدا كل + +365 +00:29:10,340 --> 00:29:14,940 +هذا الكلام ينشأ عن الـ interaction أو الـ collisions + +366 +00:29:14,940 --> 00:29:21,360 +للـ very energetic particles اللي جاءت من الشمس لما + +367 +00:29:21,360 --> 00:29:26,600 +تتصادم مع الـ ionized الـ ions و الـ electrons اللي + +368 +00:29:26,600 --> 00:29:34,150 +موجودة في الـ Arctic و الـ Antarctic regions فبينشأ + +369 +00:29:34,150 --> 00:29:37,990 +عنها هذه الأضواء التي تجد الإثارة أو الـ + +370 +00:29:37,990 --> 00:29:41,670 +Excitation لهذه الأيونات و إنها لما تنزل على الـ + +371 +00:29:41,670 --> 00:29:44,370 +ground state مرة تانية بتعطيني photons اللي هو + +372 +00:29:44,370 --> 00:29:48,590 +عبارة عن ضوء أضواء بكل الألوان يعني أحمر أخضر أزرق + +373 +00:29:48,590 --> 00:29:55,610 +كل الألوان بنشوفها بوضوح طيب الآن نرجع ثاني لل + +374 +00:29:55,610 --> 00:30:02,050 +atmosphere و بنقول أنه الـ pressure عندي واضح أن + +375 +00:30:02,050 --> 00:30:07,610 +معظم الـ pressure في الـ .. يعني at low altitude + +376 +00:30:07,610 --> 00:30:10,050 +يعني إحنا موجودين على الأرض تخيلوا كده الـ pressure + +377 +00:30:10,050 --> 00:30:13,650 +سبعماية و ستين Torr على الأرض الفرشة سبعماية و ستين + +378 +00:30:13,650 --> 00:30:17,490 +Torr لكن تعالوا نطلع شوية بس شوية شوية يعني عند + +379 +00:30:17,490 --> 00:30:21,940 +عشرة كيلو في مكان ما بتطير الطائرات التجارية الـ + +380 +00:30:21,940 --> 00:30:27,380 +pressure قليل جدا، يعني حوالي 230، 250 Torr قليل + +381 +00:30:27,380 --> 00:30:32,160 +كثير، لكن تعالوا كمان نطلع على ارتفاعات عالية، آه + +382 +00:30:32,160 --> 00:30:35,740 +الـ pressure خلاص، يعني قل بشكل كبير جدا و هذا كله + +383 +00:30:35,740 --> 00:30:42,170 +ناشئ عن أن عمود الهواء المحمول قليل يعني ما إستبعته + +384 +00:30:42,170 --> 00:30:46,490 +قليل جدا لأنه لا يحتوي على عدد محترم على عدد يعني + +385 +00:30:46,490 --> 00:30:52,030 +كبير من الذرات و الجزيئات ليه؟ لأنه زي ما ذكرت + +386 +00:30:52,030 --> 00:30:56,550 +الجاذبية الأرضية بتحاول أنها تجذب كل هذه الجزيئات + +387 +00:30:56,550 --> 00:31:01,330 +إليها و بالتالي هذه الجزيئات و الـ atoms بتتركز وين؟ + +388 +00:31:01,330 --> 00:31:07,280 +بالقرب من سطح الأرض لدرجة أنه أكثر من تسعة و تسعين + +389 +00:31:07,280 --> 00:31:13,040 +في المئة من الـ mass ده الـ atmosphere اللي بتتوجع في + +390 +00:31:13,040 --> 00:31:19,600 +منطقة الـ troposphere و الـ stratosphere لكن هذا هو + +391 +00:31:19,600 --> 00:31:23,460 +الشكل للـ pressure ما فيش فيه أي profiles تانية + +392 +00:31:23,460 --> 00:31:27,940 +دائما بيقل كل ما إرتفعنا لأعلى + +393 +00:31:32,880 --> 00:31:37,280 +ما هي الـ composition للأتمسفير؟ من إيش بيتكون + +394 +00:31:37,280 --> 00:31:43,800 +الأتمسفير؟ في البداية بنقول والله لأنه في عندي + +395 +00:31:43,800 --> 00:31:47,540 +تغيرات كبيرة في الأتمسفير زي ما شفنا في الـ + +396 +00:31:47,540 --> 00:31:51,360 +atmospheric conditions زي ما شفنا بنتوقع أنه الـ + +397 +00:31:51,360 --> 00:31:56,380 +composition للجازز في الأتمسفير ما يكونش uniform أو + +398 +00:31:56,380 --> 00:32:00,370 +homogeneous إحنا عاملين بنقول أنه بالقرب من الأرض في + +399 +00:32:00,370 --> 00:32:06,110 +عندي كمية هائلة من الـ atoms و الـ molecules بينما + +400 +00:32:06,110 --> 00:32:09,410 +كل ما طلعنا لفوق بتقلّ، إذا هل هو homogeneous، هل + +401 +00:32:09,410 --> 00:32:12,450 +هو uniform؟ لأ ما هو uniform، هذا يجب نكون + +402 +00:32:12,450 --> 00:32:16,710 +متأكدين منه، معظم الـ atmosphere هو عبارة عن + +403 +00:32:16,710 --> 00:32:21,380 +nitrogen و oxygen نيتروجين و أكسجين طبعا بنعرف إحنا + +404 +00:32:21,380 --> 00:32:28,460 +أنه حوالي يمكن ثمانية و سبعين في المئة نيتروجين و + +405 +00:32:28,460 --> 00:32:31,420 +واحد و عشرين في المئة أكسجين هي تسعة و تسعين في + +406 +00:32:31,420 --> 00:32:35,550 +المئة تسعة وتسعون هي فقط نيتروجين و أكسجين و برضه بدنا + +407 +00:32:35,550 --> 00:32:41,930 +ناخد بالنا عشان نفهم إيش تأثير هذه الغازات على الـ + +408 +00:32:41,930 --> 00:32:45,170 +environment بشكل عام و إيش تأثير الـ chemistry على + +409 +00:32:45,170 --> 00:32:48,690 +الـ environment مهم نعرف أن الـ oxygen is more + +410 +00:32:48,690 --> 00:32:52,340 +reactive than nitrogen الـ Oxygen is more reactive + +411 +00:32:52,340 --> 00:32:57,740 +لأ يعني بسببين أساسيين ممكن أقول أنا في البداية + +412 +00:32:57,740 --> 00:33:02,080 +يعني بنلاحظ أن الـ nitrogen في عندي تلت روابط بتربط + +413 +00:33:02,080 --> 00:33:07,940 +ذرتين الـ nitrogen الـ N2 في عندي تلت روابط صحيح؟ + +414 +00:33:07,940 --> 00:33:12,420 +بينما الـ O2 في عندي بس إيه؟ إثنتين الـ bond energy + +415 +00:33:12,420 --> 00:33:15,920 +للـ nitrogen حوالي تسعمية و واحد و أربعين كيلوجول + +416 +00:33:15,920 --> 00:33:19,490 +per mole تسعمية و واحد و أربعين كيلوجول بيرمول + +417 +00:33:19,490 --> 00:33:25,250 +بينما الـ bond energy للـ oxygen حوالي أربع مئة و + +418 +00:33:25,250 --> 00:33:29,770 +خمسين كيلوجول بيرمول أربع مئة و خمسين يعني أقل من + +419 +00:33:29,770 --> 00:33:36,010 +النصف لو طلعنا على المعادن بشكل عام عندنا في البيئة + +420 +00:33:36,010 --> 00:33:40,850 +بنلاحظ أن معظم المعادن متكونة أكاسيد لكن متكونش + +421 +00:33:40,850 --> 00:33:46,060 +نيتروجين المعظم المعادل ليه؟ لأن الـ Oxygen is more + +422 +00:33:46,060 --> 00:33:51,280 +reactive وهذا له impact كبير جدا على البيئة عندنا + +423 +00:33:51,280 --> 00:33:58,180 +زي ما هنشوف ال major components للـ dry air near + +424 +00:33:58,180 --> 00:34:08,020 +sea level بنقول إن النيتروجين حوالي 78.78% هذا + +425 +00:34:08,020 --> 00:34:10,200 +المولي فراكشن اللي له يعني 78% + +426 +00:34:10,200 --> 00:34:14,780 +الأكسجين حوالي 21% الأرجون حوالي + +427 +00:34:14,780 --> 00:34:19,460 +1% وبعدين كاربون دايوكسايد نيون + +428 +00:34:19,460 --> 00:34:24,400 +هيليوم ميثان كريبتون شغلات قليلة جدا جدا جدا فمعظم + +429 +00:34:25,090 --> 00:34:29,510 +معظم الأتموسفير هو عبارة عن نيتروجين أو أكسجين + +430 +00:34:29,510 --> 00:34:33,050 +وشوية قليلة من الأرجون شوية قليلة من الأرجون لو + +431 +00:34:33,050 --> 00:34:37,250 +طلعنا على الهيليوم آه قليل جدا جدا الهيليوم قليل + +432 +00:34:37,250 --> 00:34:41,710 +للغاية طبعا هذا غاز كامل وهذا غاز كامل فالأرجون لأ + +433 +00:34:41,710 --> 00:34:47,330 +الأرجون موجود إلى حد ما بكمية معقولة تسمح لنا + +434 +00:34:47,330 --> 00:34:54,000 +بتسييله زي ما بنسيل الـ oxygen يعني ممكن نسيله و + +435 +00:34:54,000 --> 00:34:58,680 +نجمعه من الطبيعة ونستخدمه زي ما بنسيل الـ oxygen و + +436 +00:34:58,680 --> 00:35:02,460 +النيتروجين ممكن أننا نسيل أيضا الأرجون لأنه + +437 +00:35:02,460 --> 00:35:06,240 +كميته 1% مش سيئة كثير مش زي مثلا + +438 +00:35:06,240 --> 00:35:11,920 +لو جينا نتطلع على الهيليوم أصعب كثير لأنه كميته + +439 +00:35:11,920 --> 00:35:17,780 +قليلة جدا في الـ atmosphere فببساطة خالص معظم الـ + +440 +00:35:17,780 --> 00:35:24,280 +atmosphere هو عبارة عن نيتروجين وأكسجين وفي عندي + +441 +00:35:24,280 --> 00:35:28,620 +هذا اللي في النصها هذا عبارة عن أرجون في شوية + +442 +00:35:28,620 --> 00:35:32,900 +كربون دايوكسايد أقل كثير منه وفي الـ all other + +443 +00:35:32,900 --> 00:35:36,100 +gases تقريبا جدا الكربون دايوكسايد أقل كثير من + +444 +00:35:36,100 --> 00:35:40,640 +الأرجون حتى أقل كثير من الأرجون + +445 +00:35:42,970 --> 00:35:46,190 +يعني معنى الكلام الـ Oxygen والـ Nitrogen هم اللي + +446 +00:35:46,190 --> 00:35:51,210 +هيأثروا تأثير مباشر على البيئة تبعتنا هم اللي + +447 +00:35:51,210 --> 00:35:57,790 +هيأثروا تأثير مباشر على البيئة تبعتنا الآن احنا + +448 +00:35:57,790 --> 00:36:05,670 +بنعرف إنه بنحسب الـ PPM في السوائل على أساس إنه + +449 +00:36:05,670 --> 00:36:08,430 +كم جرام صليوت لكل + +450 +00:36:11,320 --> 00:36:19,240 +مليون جرام من الـ solution واحد في المليون كل جرام + +451 +00:36:19,240 --> 00:36:26,640 +لمليون جرام كويس في الحقيقة فيما يتعلق بالغازات + +452 +00:36:26,640 --> 00:36:30,000 +الوضع قد يختلف لأن الغازات احنا بنجيزها بالـ volume + +453 +00:36:30,000 --> 00:36:36,860 +فبدنا نقول آه الـ volume من الغاز للمليون volume من + +454 +00:36:36,860 --> 00:36:43,120 +الغاز هيك بدنا نقول volume من الغاز للمليون volume + +455 +00:36:43,120 --> 00:36:48,820 +من الغاز لكن احنا بنعرف إن الـ volume بيتناسب مع N + +456 +00:36:48,820 --> 00:36:54,580 +من PV بتساوي NRT إذا بدل ما أقول volume ممكن أن + +457 +00:36:54,580 --> 00:37:01,960 +أقول إيه N number of moles كويس فإذا والله بيبقى + +458 +00:37:01,960 --> 00:37:05,520 +إنه الـ volume متناسب مع الـ number of moles فال .. بدي + +459 +00:37:05,520 --> 00:37:08,420 +أقول الـ volume من الغاز إذا الـ number of moles من + +460 +00:37:08,420 --> 00:37:15,060 +الغاز على الـ volume من الكل فبقول معناه كلام الـ + +461 +00:37:15,060 --> 00:37:17,420 +total number of moles طب الـ number of mole على الـ + +462 +00:37:17,420 --> 00:37:20,280 +total number of moles هذا عبارة عن الـ X اللي هي الـ + +463 +00:37:20,280 --> 00:37:20,920 +mole fraction + +464 +00:37:23,450 --> 00:37:27,890 +معنى الكلام الـ PPM من الغاز هي عبارة عن مولي + +465 +00:37:27,890 --> 00:37:31,090 +فراكشن اللي هي هي بالظبط الـ volume fraction هي هي + +466 +00:37:31,090 --> 00:37:34,210 +نفس القيمة الـ volume fraction بس بتعوض عنها بالـ + +467 +00:37:34,210 --> 00:37:38,050 +مولي فراكشن لأن المول أسهل المولي فراكشن مضروبة في + +468 +00:37:38,050 --> 00:37:42,150 +عشرة أس سالب ستة المولي فراكشن مضروبة في عشرة أس سالب ستة + +469 +00:37:42,150 --> 00:37:47,730 +إذا بقدر أقول الـ PPM للغاز هي عبارة عن كمان مرة الـ + +470 +00:37:47,730 --> 00:37:52,200 +volume للغاز على الـ total volume لكن أنا بعرف إن الـ + +471 +00:37:52,200 --> 00:37:59,220 +volume بيتناسب مع الـ n إذا ممكن أقول الـ n للغاز + +472 +00:37:59,220 --> 00:38:03,260 +على الـ total number of moles طب إيش الـ n للغاز على + +473 +00:38:03,260 --> 00:38:04,760 +الـ total number of moles؟ قالها دي الـ mole + +474 +00:38:04,760 --> 00:38:10,490 +fraction للغاز، إذا الـ PPM بتساوي المولي فراكشن + +475 +00:38:10,490 --> 00:38:13,550 +مضروبة في عشرة أس سالب ستة المولي فراكشن مضروبة في عشرة + +476 +00:38:13,550 --> 00:38:16,490 +أس سالب ستة لماذا أقول هذا كلام الجهة اللي قالت بما إنه + +477 +00:38:16,490 --> 00:38:21,370 +اتكلمنا عن الـ composition للأتموسفير وعرفنا كل غاز + +478 +00:38:21,370 --> 00:38:26,610 +قد إيش موجود منه إذا ممكن نحسب قد إيش PPM من كل غاز + +479 +00:38:27,860 --> 00:38:33,500 +فمثلا لو طلعنا على الـ carbon dioxide بنلاحظ من + +480 +00:38:33,500 --> 00:38:37,280 +العلاقة السابقة إن الـ mol fraction للـ carbon + +481 +00:38:37,280 --> 00:38:42,560 +dioxide 0.000382 هذا الـ mol fraction للـ carbon + +482 +00:38:42,560 --> 00:38:47,820 +dioxide في الـ إيه؟ في الـ atmosphere طب قد إيش الـ part + +483 +00:38:47,820 --> 00:38:50,500 +per million carbon dioxide اللي موجود في الهواء؟ + +484 +00:38:50,500 --> 00:38:53,900 +قالب نأخذ الـ mol fraction وبنضربها في عشرة أس سالب ستة + +485 +00:38:54,420 --> 00:38:59,360 +هذه المولي فراكشن 0.000382 في عشرة أس سالب ستة + +486 +00:38:59,360 --> 00:39:06,760 +بيطلع 382 إذا الـ PPM أو تركيز + +487 +00:39:06,760 --> 00:39:11,700 +الـ carbon dioxide في الـ atmosphere 382 + +488 +00:39:11,700 --> 00:39:14,380 +و80 هي عبارة عن إيه؟ عبارة عن المولي فراكشن + +489 +00:39:14,380 --> 00:39:18,340 +للـ carbon dioxide مضروبة في عشرة أس سالب ستة نفس الكلام + +490 +00:39:18,340 --> 00:39:26,180 +ممكن نتطلع لحساب الـ moly fraction للمية وأيضا + +491 +00:39:26,180 --> 00:39:32,640 +منها نأخذ الـ .. نعرف قد إيش الـ water vapor قد إيش الـ + +492 +00:39:32,640 --> 00:39:36,780 +PPM لإله أو تركيزه بالـ PPM فنتطلع على هذا المثال، + +493 +00:39:36,780 --> 00:39:41,320 +المثال بيقول what is the concentration in parts + +494 +00:39:41,320 --> 00:39:45,740 +per million of water vapor؟ في مجموعة الهواء إذا + +495 +00:39:45,740 --> 00:39:52,240 +كانت مقدمة الماء 810 طور ومقدمة الهواء 735 طور + +496 +00:39:52,240 --> 00:39:56,820 +فأنا عندي الـ vapor pressure لإيه؟ للمية وعندي الـ + +497 +00:39:56,820 --> 00:40:03,840 +total pressure للهواء 735 طور بقول أنا بعرف إن الـ + +498 +00:40:03,840 --> 00:40:09,520 +P للـ H2O مقدمة المية هو عبارة عن الـ X للـ H2O مرة + +499 +00:40:09,520 --> 00:40:12,880 +ما علا في الغازات المول الـ fractional H2O مضروبة + +500 +00:40:12,880 --> 00:40:17,020 +في الـ A في الـ total pressure يعني عند الـ الـ + +501 +00:40:17,020 --> 00:40:22,070 +partial pressure هي جزء من الـ total pressure فبقدر + +502 +00:40:22,070 --> 00:40:27,170 +أحسب الـ X H2O الـ X للـ H2O بتساوي الـ P للـ H2O على + +503 +00:40:27,170 --> 00:40:31,970 +الـ Pt يعني 810 تور على 735 و + +504 +00:40:31,970 --> 00:40:35,770 +30 بيعطيني 0.0011 هذه المولي فراكشن + +505 +00:40:35,770 --> 00:40:39,610 +للمية مدام عرفت المولي فراكشن للمية بقدر أقول + +506 +00:40:39,610 --> 00:40:44,570 +مباشرة الـ PPM عبارة عن المولي فراكشن مضروبة في + +507 +00:40:44,570 --> 00:40:51,090 +عشرة أس سالب ستة فالمولي فراكشن 0.0011 في عشرة أس سالب + +508 +00:40:51,090 --> 00:40:57,490 +ستة بيعطينا 1100 PPM بهذه الطريقة بنقدر نحسب + +509 +00:40:57,490 --> 00:41:03,250 +التركيز أي غاز موجود في الأتموسفير معبر عنه بالإيه + +510 +00:41:03,250 --> 00:41:09,870 +بالـ PPM لأن الغازات عادة بنعبر عن تركيزاتها بـ PPM + +511 +00:41:09,870 --> 00:41:10,610 +أو ppb + +512 +00:41:16,270 --> 00:41:20,410 +اتكلمنا عن الـ Molecular Nitrogen والـ Molecular + +513 +00:41:20,410 --> 00:41:25,670 +Oxygen Reactivity وشوفنا إن الـ Oxygen is far more + +514 +00:41:25,670 --> 00:41:29,830 +reactive than النيتروجين بشكل أساسي لأن الـ bond + +515 +00:41:29,830 --> 00:41:33,250 +energy في النيتروجين حوالي 941 كيلوجول per mole + +516 +00:41:33,250 --> 00:41:38,430 +بينما الأكسجين حوالي 495 كيلوجول per mole وهذا + +517 +00:41:38,430 --> 00:41:43,940 +يجعل الأكسجين much more reactive than النيتروجين كلنا + +518 +00:41:43,940 --> 00:41:48,880 +بنعرف كدلالة على هذه الـ reactivity إن الـ oxygen + +519 +00:41:48,880 --> 00:41:53,960 +reacts with many substances to form oxides فمثلا + +520 +00:41:53,960 --> 00:41:57,720 +بتفاعل مع الـ sulfur وبيكون sulfur dioxide + +521 +00:42:06,570 --> 00:42:10,630 +الـ combustion engines يعني اللي هي محركات + +522 +00:42:10,630 --> 00:42:18,270 +الاحتراق زي مثلا محركات السيارات محركات مولدات + +523 +00:42:18,270 --> 00:42:24,270 +الكهربا الشركة الكهربا المولدات تبعتها عندنا الـ + +524 +00:42:24,270 --> 00:42:30,720 +oil اللي هو الـ fuel بيحترق الـ fuel فيه شوية إيه؟ فيه + +525 +00:42:30,720 --> 00:42:34,600 +شوية سلفر فهو بيحترق في وجود أكسجين فالسلفرفورا + +526 +00:42:34,600 --> 00:42:38,700 +بيكون سلفر دايوكسايد مع الأكسجين وهذا سبب أساسي + +527 +00:42:38,700 --> 00:42:46,290 +للأمطار الحمضية ليه؟ لأن الـ SO2 اللي تكون بسهولة أيضا + +528 +00:42:46,290 --> 00:42:52,030 +بيتفاعل مع مور أكسجين وبعطيني SO3 والـ SO3 في + +529 +00:42:52,030 --> 00:42:56,650 +المية هو عبارة عن sulfuric acid فالـ SO3 بيطلع + +530 +00:42:56,650 --> 00:43:01,530 +فوق على طبقات الهواء في الـ تروبوسفير وهناك بيدوب + +531 +00:43:01,530 --> 00:43:07,050 +في البخار المية ولما الدنيا تشتي بينزل acid rain + +532 +00:43:07,050 --> 00:43:14,210 +بيخرب الأشجار بيقتل الكائنات المائية الأسماك + +533 +00:43:14,210 --> 00:43:17,930 + وغيرها إذا كان فيها بحيرات صغيرة أو ما شابه طبعا + +534 +00:43:17,930 --> 00:43:21,510 +تأثيره على المحاطات بيكون أقل كثير لكن تأثيره على + +535 +00:43:21,510 --> 00:43:27,930 +البيئة البسيطة زي مثلا بحيرة صغيرة أو ما شابه + +536 +00:43:27,930 --> 00:43:31,260 +تأثيره فظيع تأثيره على الغابات بنلاحظ إنه برضه + +537 +00:43:31,260 --> 00:43:34,600 +بيحرق الغابات حرق لأنه عبارة عن acid بيقتل + +538 +00:43:34,600 --> 00:43:40,160 +النباتات فهذا الـ CO2 ممكن + +539 +00:43:40,160 --> 00:43:46,070 +نلاحظ إنه مع active metal زي الكالسيوم فورا بيكون + +540 +00:43:46,070 --> 00:43:49,610 +calcium oxide لو حطينا شوية صوديوم في الهواء ثواني + +541 +00:43:49,610 --> 00:43:53,510 +اللي هو تكون عليه طبقة من الـ sodium oxide وها كده + +542 +00:43:53,510 --> 00:43:58,290 +فالـ oxygen is very reactive بينما النيتروجين + +543 +00:43:58,290 --> 00:44:01,950 +ملاحظش إنه فيه الـ reactivity بالعكس يعني الـ + +544 +00:44:01,950 --> 00:44:07,730 +reactivity تبعته قليل للغاية كمان من حديثنا عن الـ + +545 +00:44:07,730 --> 00:44:11,030 +atmosphere متحدث عن الـ radiation اللي جاية من + +546 +00:44:11,030 --> 00:44:16,950 +الشمس الرادياشن اللي جاية من الشمس فبنقول إن الـ + +547 +00:44:16,950 --> 00:44:22,630 +atmosphere is the first line of defense against + +548 +00:44:22,630 --> 00:44:26,610 +harmful radiation from the sun هو أول خطوط الدفاع + +549 +00:44:26,610 --> 00:44:32,470 +عن طبعا البيئة تبعتنا أو عننا كبشر وعن الأرض كـ + +550 +00:44:32,470 --> 00:44:39,760 +living system يعني أول خطوة الدفاع ضد الـ .. ضد الـ + +551 +00:44:39,760 --> 00:44:44,340 +Harmful Radiation from the Sun The Sun emits a + +552 +00:44:44,340 --> 00:44:48,440 +wide range of wavelengths of radiation مش بس من + +553 +00:44:48,440 --> 00:44:53,240 +240 ل 310 أو ما شبه لأ وكمان أقل من هيك كثير فيه + +554 +00:44:53,240 --> 00:44:56,540 +عندي very energetic radiation أقل من 100 نانومتر + +555 +00:44:56,540 --> 00:45:00,000 +أقل من 100 .. احنا كيف بنعبر عن الـ radiation + +556 +00:45:00,000 --> 00:45:07,820 +energy بنقول E بتساوي Hν أي اللي هي الـ energy H + +557 +00:45:07,820 --> 00:45:11,620 +Planck's constant والـ ν هي الـ frequency أو ممكن + +558 +00:45:11,620 --> 00:45:16,960 +نقول E بتساوي HC over lambda لأن الـ ν بتساوي C + +559 +00:45:16,960 --> 00:45:21,160 +over lambda فالـ energy تتناسب عكسيا مع الـ lambda + +560 +00:45:22,050 --> 00:45:24,930 +فلما يكون فيه عنده very high energy، معناته اللحمة + +561 +00:45:24,930 --> 00:45:30,210 +تبعتها أطوالها قليلة، ففيه عنده أطوال موجية قليلة + +562 +00:45:30,210 --> 00:45:33,510 +جدا بتصدر من الشمس ولابد أن هتلاقي حاجة في + +563 +00:45:33,510 --> 00:45:39,830 +الطريق يعني تتغلب عليها، وإلا إذا كان وسط الأرض + +564 +00:45:39,830 --> 00:45:41,690 +بتكون مشكلة كبيرة للغاية + +565 +00:45:45,160 --> 00:45:50,820 +هن بس بنذكركم أن الضوء اللي جاي أو ال radiation + +566 +00:45:50,820 --> 00:46:00,020 +اللي جاية من الشمس كويس في منطقة الـ UV قادرة أن تكسر ال chemical bond لما تكون قادرة أن تكسر ال + +567 +00:46:00,020 --> 00:46:03,260 +chemical bond معناته كل الحياة اللي على الأرض + +568 +00:46:03,260 --> 00:46:06,540 +بتكون مهددة + +569 +00:46:06,540 --> 00:46:07,440 +بتكون مهددة + +570 +00:46:14,210 --> 00:46:25,950 +الـ UV radiation عموما + +571 +00:46:25,950 --> 00:46:34,090 +عند أي molecule علشان نقول والله أن ممكن يتأثر + +572 +00:46:34,090 --> 00:46:37,470 +بالضوء اللي ساقط عليه لابد أن هذا الـ molecule + +573 +00:46:37,470 --> 00:46:43,340 +يمتص الضوء، لما ينتصر الضوء ممكن هذا الضوء يكون كافي + +574 +00:46:43,340 --> 00:46:45,900 +لأنه يحصل عندي photo dissociation، photo + +575 +00:46:45,900 --> 00:46:49,600 +dissociation يعني آه الضوء اللي ساقط لأنه ضوء + +576 +00:46:49,600 --> 00:46:53,560 +بنقوله photo لأن الضوء عبارة عن photons فبنقول + +577 +00:46:53,560 --> 00:46:55,940 +photo dissociation يعني هذا الضوء اللي ساقط عليه + +578 +00:46:55,940 --> 00:47:00,360 +الـ photons قادر إنه يكسر الرابطة، لكن وقت إشهاد + +579 +00:47:00,360 --> 00:47:04,600 +الكلام لابد أن المادة تقدر تمتص الضوء، فإذا + +580 +00:47:04,600 --> 00:47:08,240 +كان امتصت الضوء، آه ساعتها والله بنقول أن ممكن + +581 +00:47:08,240 --> 00:47:10,520 +يحصل photo dissociation، إذا كان كمية الضوء أو الـ + +582 +00:47:10,520 --> 00:47:14,420 +energy للضوء اللي امتصته أكبر من الـ bond energy + +583 +00:47:15,170 --> 00:47:20,790 +يعني الـ energy والـ bond اللي امتصته أكبر من الـ bond ال + +584 +00:47:20,790 --> 00:47:24,250 +energy ساعتها والله آه بيكون في احتمال كبير أن الـ + +585 +00:47:24,250 --> 00:47:30,450 +bond تنكسر مباشرة، الضوء اللي جينا أو الـ spectrum + +586 +00:47:30,450 --> 00:47:34,530 +اللي جاي من الشمس تقريبا هيك شكله outside the + +587 +00:47:34,530 --> 00:47:38,310 +atmosphere، هذا هو الشكل، هذا الـ solar spectrum at + +588 +00:47:38,310 --> 00:47:42,150 +sea level، هذا هو اللي at sea level عندنا هذه المنطقة + +589 +00:47:42,150 --> 00:47:47,130 +الـ visible ممتاز جدا للحياة البشرية، منطقة الـ + +590 +00:47:47,130 --> 00:47:52,290 +Infrared اللي بتجعل الأجسام + +591 +00:47:52,290 --> 00:47:56,570 +تسخن بشكل عام برضه يعني موجودة substantial في + +592 +00:47:56,570 --> 00:48:00,690 +الحقيقة، لكن في منطقة أقل من الـ visible اللي هي + +593 +00:48:00,690 --> 00:48:06,770 +منطقة الـ ultraviolet وطبعا قبل الـ ultraviolet أو + +594 +00:48:06,770 --> 00:48:11,710 +أقل طول موجي منها اللي شايفينه احنا هنا خليني أقول + +595 +00:48:11,710 --> 00:48:17,760 +الـ ultraviolet العادية، حاجة بنقولها vacuum UV كمان + +596 +00:48:17,760 --> 00:48:21,060 +الـ vacuum UV لأ من حوالي مائة وعشرين نانومتر مش + +597 +00:48:21,060 --> 00:48:25,580 +مبينة هنا من هنا مائة وعشرين نانومتر لكن أقل من + +598 +00:48:25,580 --> 00:48:30,100 +هيك بيصير X-ray يعني الـ UV هي أقرب ما يكون إلى الـ + +599 +00:48:30,100 --> 00:48:33,400 +X-ray طب الـ X-ray لما نيجي نروح مستشفى أو غيره + +600 +00:48:33,400 --> 00:48:38,120 +بناخد احتياطات فظيعة علشان مثلا ناخد صورة، وبالتالي + +601 +00:48:38,120 --> 00:48:42,100 +يعني الـ UV لا تقل خطورة يعني هي خطورة كبيرة صح مش + +602 +00:48:42,100 --> 00:48:46,020 +جد الـ Excel لكنها خطيرة أيضا بدرجة عالية جدا من + +603 +00:48:46,020 --> 00:48:49,240 +من منطقة الـ visible لاحظوا هذه المنطقة المهمة بالنسبة + +604 +00:48:49,240 --> 00:48:55,040 +لنا للحياة على يعني الأرض + +605 +00:48:56,870 --> 00:49:00,370 +نتيجة الـ radiation اللي بتسقط من الشمس ممكن يحصل + +606 +00:49:00,370 --> 00:49:05,430 +أحد حاجتين يا اما photo dissociation إذا كان الـ + +607 +00:49:05,430 --> 00:49:10,530 +molecule امتص طاقة، الطاقة هذه أكبر من طاقة + +608 +00:49:10,530 --> 00:49:13,870 +الترابط فبتنكس الرابطة إذا اسمه photo dissociation + +609 +00:49:13,870 --> 00:49:16,970 +شافناه وبرضه جال ممكن يحصل حاجة تانية جال ممكن + +610 +00:49:16,970 --> 00:49:21,800 +يحصل photo ionization، الـ photo ionization جال آه + +611 +00:49:21,800 --> 00:49:25,760 +الفوتون اللي جاي من الشمس فيه طاقة كافية أن يعمل + +612 +00:49:25,760 --> 00:49:30,540 +ejection لإلكترون، ضرب في إلكترون موجود في ذرة أو + +613 +00:49:30,540 --> 00:49:35,340 +في جزيء، فإيش عمل؟ طلع الإلكترون برا الجزيء أو برا + +614 +00:49:35,340 --> 00:49:39,200 +الذرعة، فالذرعة صارت ionized والإلكترون أو المولكول + +615 +00:49:39,200 --> 00:49:43,730 +صار ionized والإلكترون صار free طلع برا الذرعة خالص + +616 +00:49:43,730 --> 00:49:47,110 +فهذول الحاجتين الـ photo dissociation والـ photo + +617 +00:49:47,110 --> 00:49:54,110 +ionization بيحصلوا نتيجة الطاقة تصادم الأشعة مع + +618 +00:49:54,110 --> 00:49:59,350 +الذرات والجزيئات، والطاقة اللي بتحتويها هذه الأشعة + +619 +00:49:59,350 --> 00:50:03,070 +طاقة عالية كافية أن تعمل photo dissociation أو + +620 +00:50:03,070 --> 00:50:09,790 +photo ionization، الـ photo dissociation بيفرج عن الـ + +621 +00:50:09,790 --> 00:50:13,590 +photo ionization، الـ photo dissociation بيكون الكسر + +622 +00:50:13,590 --> 00:50:18,570 +homolytic homolytic homolytic يعني متجانس بالنص + +623 +00:50:18,570 --> 00:50:24,950 +بالظبط، فإنها هي الرابطة انكسرت وانكسرت H and U + +624 +00:50:24,950 --> 00:50:29,650 +هذا جاي من الشمس طاقة كافية حلو طب انكسرت الرابطة + +625 +00:50:29,650 --> 00:50:32,490 +قال آه هذه بتاخد ست إلكترون، هذي بتاخد ست إلكترونات + +626 +00:50:32,490 --> 00:50:37,310 +يعني مافيش عندي أي أيونات فهذا بنقوله homolytic + +627 +00:50:38,120 --> 00:50:47,480 +fission أو homolytic dissociation فالـ O2 بتاخد H and + +628 +00:50:47,480 --> 00:50:51,800 +U وبتعطيني اتنين O زي بعض بالظبط، هذا photo + +629 +00:50:51,800 --> 00:50:57,800 +dissociation، الـ photo dissociation للـ oxygen طبعا + +630 +00:50:57,800 --> 00:51:05,660 +بحاجة لـ 495 كجول برمول، شفنا هذا الكلام طيب نشوف + +631 +00:51:05,660 --> 00:51:11,340 +وين الـ oxygen بالظبط بيحصل له photo dissociation + +632 +00:51:11,340 --> 00:51:16,060 +إيش الطاقة اللي لازمها؟ إيش طول الموجي اللي لازمه + +633 +00:51:16,060 --> 00:51:19,600 +عشان يحصل له photo dissociation؟ فبقول what's the + +634 +00:51:19,600 --> 00:51:23,680 +maximum wavelength of light in nanometers that has + +635 +00:51:23,680 --> 00:51:28,490 +enough energy per photon to dissociate هو الـ + +636 +00:51:28,490 --> 00:51:33,870 +Oxygen Molecule كويس، بقول حلو كتير عندي أنا + +637 +00:51:33,870 --> 00:51:38,030 +أربعمائة + +638 +00:51:38,030 --> 00:51:42,770 +وخمسين وخمسين كيلو جول per mole وعندي الـ mole في + +639 +00:51:42,770 --> 00:51:46,650 +6.022 في عشرة أس ستة وعشرين، الـ molecule تطلع عندي + +640 +00:51:46,650 --> 00:51:52,370 +الطاقة لكل molecule 8.22 في عشرة أس ستة وعشرين + +641 +00:51:52,370 --> 00:51:57,060 +الجول لكل molecule لـ NU التي تساوي E على H لأن E + +642 +00:51:57,060 --> 00:52:01,940 +تساوي H نيو قال والله هي الطاقة اللي حسبتها على + +643 +00:52:01,940 --> 00:52:08,040 +ثابت بلانك بيعطيني 1.24 في 10 أس 15، طيب يا جماعة + +644 +00:52:08,040 --> 00:52:13,820 +كنا بنقول أن حسبنا الـ energy اللازمة per mole + +645 +00:52:13,820 --> 00:52:21,130 +فطلعت 8.22 في 10 أس 19 جول لكل molecule ليه؟ هذه + +646 +00:52:21,130 --> 00:52:27,170 +جاية من 495×10³ جول ع المول لأن 495 kilo joule + +647 +00:52:27,170 --> 00:52:33,250 +per mole فـ 10³ joule ع المول، كل mole 6.022×10³ يعني + +648 +00:52:33,250 --> 00:52:38,530 +بيعطيني 8.22×10³ 19 joule لكل molecule الآن بنحسب + +649 +00:52:38,530 --> 00:52:43,130 +لـ new بتساوي E على H لأن عندنا E بتساوي H new + +650 +00:52:43,740 --> 00:52:46,680 +بنعوض عن الـ energy اللي حسبناها على Plank's + +651 +00:52:46,680 --> 00:52:51,940 +constant بيعطينا 1.24×10√15 per second، الآن الـ + +652 +00:52:51,940 --> 00:52:57,830 +lambda هي عبارة عن c speed of light على الـ new فالـ + +653 +00:52:57,830 --> 00:53:00,130 +speed of light تلاتة في عشرة أس تمانية متر على + +654 +00:53:00,130 --> 00:53:05,730 +الثانية على الـ new one point two four المحسوبة في + +655 +00:53:05,730 --> 00:53:09,130 +عشرة أس خمس عشرة على الثانية في عشرة أس تسعة نانو + +656 +00:53:09,130 --> 00:53:13,410 +متر لكل متر ليه؟ لأن المتر عشرة أس تسعة نانو متر + +657 +00:53:13,410 --> 00:53:17,210 +بيطلع عندي 242 ممتاز جدا، لما الـ + +658 +00:53:17,210 --> 00:53:18,670 +oxygen يكون بانقص + +659 +00:53:21,150 --> 00:53:25,730 +الـ energy عند حوالي 240 نانومتر، طب عندي كمية كبيرة + +660 +00:53:25,730 --> 00:53:29,150 +من الـ oxygen عشرين في المية، واحدة وعشرين في المية + +661 +00:53:29,150 --> 00:53:35,650 +من المكونات الهواء عندي oxygen فمعنى الكلام هذا الـ + +662 +00:53:35,650 --> 00:53:41,890 +oxygen راح ينطس كمية كبيرة جدا جدا من الـ UV + +663 +00:53:41,890 --> 00:53:45,790 +radiation عند 240 وهذا شيء يعتبر ممتاز جدا حيوي خالص + +664 +00:53:45,790 --> 00:53:50,980 +بالنسبة لنا في ما يتعلق بالـ Oxygen + +665 +00:53:50,980 --> 00:53:56,480 +Photodissociation، عادة الـ dissociation للأكسجين + +666 +00:53:56,480 --> 00:54:01,420 +مستمر جدا في أعماق أعماق أعظم، يعني الأكسجين O2 + +667 +00:54:01,420 --> 00:54:06,860 +ينقسم إلى O و O هذا بيتم عند حوالي يعني فوق خالص + +668 +00:54:06,860 --> 00:54:10,560 +عند حوالي يعني في الـ higher atmosphere يعني فوق + +669 +00:54:10,560 --> 00:54:16,240 +الـ 130، 150، 200 كيلومتر، فيقول at 400 كيلومتر for + +670 +00:54:16,240 --> 00:54:21,880 +example تقريبا فقط 1% من الأكسجين في شكل الـ O2 + +671 +00:54:21,880 --> 00:54:27,700 +و 400 كيلو فقط حوالي 1% من الأكسجين تقريبا فقط فقط + +672 +00:54:27,700 --> 00:54:29,240 +1% من الأكسجين تقريبا فقط 1% من الأكسجين تقريبا + +673 +00:54:29,240 --> 00:54:34,380 +99% من الأكسجين + +674 +00:54:34,380 --> 00:54:37,160 +هو الأكسجين الذري، 99% من الأكسجين هو الأكسجين + +675 +00:54:37,160 --> 00:54:40,760 +الذري، 99% من الأكسجين هو الأكسجين الذري، 99% + +676 +00:54:40,760 --> 00:54:41,800 +من الأكسجين الذري، 99% من الأكسجين الذري، 99% + +677 +00:54:41,800 --> 00:54:44,120 +من الأكسجين الذري، 99% من الأكسجين الذري، 99% + +678 +00:54:44,120 --> 00:54:46,980 +من الأكسجين الذري، 99% من الأكسجين الذري + +679 +00:54:47,700 --> 00:54:54,440 +abundant عند 130 آه كمية الـ O2 زي كمية الـ OO الـ O + +680 +00:54:54,440 --> 00:54:58,260 +لحالة الـ atoms آه لكن طب أجل من هيك لا عندنا + +681 +00:54:58,260 --> 00:55:02,720 +بالقرب من سطح الأرض مافيش عندنا oxygen atoms قليل + +682 +00:55:02,720 --> 00:55:06,360 +جدا جدا يمكن بتتناسب واحد لتسعة وتسعين في المية + +683 +00:55:06,360 --> 00:55:12,400 +تمام، فعمال كل ما طلعنا لفوق نسبة ذرات الـ oxygen + +684 +00:55:12,400 --> 00:55:17,100 +لأن حصل Photodissociation للأكسجين، نسبة ذرات + +685 +00:55:17,100 --> 00:55:21,900 +الأكسجين إلى جزيئات الأكسجين كل ما طلعنا لأعلى كل + +686 +00:55:21,900 --> 00:55:26,520 +ما زادت نسبة الذرات إلى الـ O2 كل ما نزلنا لأسفل لأ + +687 +00:55:26,520 --> 00:55:31,280 +العكس صحيح كل ما زاد الـ O2 بالنسبة للـ O فبالـ O + +688 +00:55:31,280 --> 00:55:35,710 +130 كيلومتر Oxygen is more abundant than atomic + +689 +00:55:35,710 --> 00:55:39,130 +oxygen because most of the solar energy has been + +690 +00:55:39,130 --> 00:55:42,550 +absorbed in the upper atmosphere، معظم الـ solar + +691 +00:55:42,550 --> 00:55:47,690 +energy خلصت ليه؟ لأن فوق موجود solar energy كتير + +692 +00:55:47,690 --> 00:55:52,890 +فراح تكسر الـ oxygen إلى OO مافيش مشكلة، لكن كل ما + +693 +00:55:52,890 --> 00:55:58,750 +نزلنا لتحت هذه بتضعف لغاية ما تقريبا تتلاشى لما نوصل + +694 +00:55:58,750 --> 00:56:04,550 +احنا لتروبوسفير ما عندي أشعة هذه الأطوال الموجية + +695 +00:56:04,550 --> 00:56:10,990 +جاية من الشمس تمام؟ لكن لو اتطلع على الـ + +696 +00:56:10,990 --> 00:56:14,430 +dissociation energy اللي أنتو is very high + +697 +00:56:14,430 --> 00:56:18,730 +تسعمائة وحدة من كيلو جول per mole، only photons + +698 +00:56:18,730 --> 00:56:22,670 +having a wavelength shorter than 127 وهذه اللي + +699 +00:56:22,670 --> 00:56:29,140 +shorter than 127 تقريبا يعني في الـ low level من الـ + +700 +00:56:29,140 --> 00:56:33,340 +vacuum UV أو قريب على الـ X-ray لكن احنا لو حسبنا + +701 +00:56:33,340 --> 00:56:39,040 +جدّاش الطاقة اللازمة لتفكيك الـ nitrogen هنلاحظ أنه + +702 +00:56:39,040 --> 00:56:43,900 +بتعبر عنها طول الموجة 127 نانومتر بيعبر عنه طول + +703 +00:56:43,900 --> 00:56:46,700 +الموجة.. هذا طول الموجة قليل جدا جدا يعني طاقة + +704 +00:56:46,700 --> 00:56:53,890 +عالية للغاية فالـ dissociation للـ nitrogen gas + +705 +00:56:53,890 --> 00:56:58,110 +into atomic نيتروجين يكون قليل للغاية لأنه بحاجة + +706 +00:56:58,110 --> 00:57:01,610 +لطاقة عالية وإذا كان بده يحصل بيحصل في الـ very + +707 +00:57:01,610 --> 00:57:06,490 +high atmosphere ليه؟ لأنه في الـ very high + +708 +00:57:06,490 --> 00:57:11,200 +atmosphere نعم بيكون جاي من الشمس أشعة لها أطوال + +709 +00:57:11,200 --> 00:57:14,160 +موجية قليلة خلاص وبيخلصنا منها يعني برضه نفس + +710 +00:57:14,160 --> 00:57:17,520 +الكلام هنتطلع على ذرات الـ nitrogen هلاحظ إنه والله + +711 +00:57:17,520 --> 00:57:20,580 +الـ nitrogen أه ممكن يكون موجود فيه كذرات ممكن يكون + +712 +00:57:20,580 --> 00:57:28,180 +موجود فيها عالي الـ atmosphere مش بالقرب من الأرض + +713 +00:57:28,180 --> 00:57:32,960 +يعني فالـ nitrogen h nu بيعطيني N2 plus أه حصل + +714 +00:57:32,960 --> 00:57:40,480 +لفوتو ايه؟ Ionization الجدّاش أخد طول موجي 81.1 هذا + +715 +00:57:40,480 --> 00:57:48,800 +X-ray 81.1 نانومتر X-ray الأكسجين زائد HNO2 plus + +716 +00:57:48,800 --> 00:57:53,660 +زائد إلكترونتسعة وتسعين و تلاتة من عشرة برضه كمان + +717 +00:57:53,660 --> 00:57:58,480 +X-ray أقل من الـ vacuum UV O زائد HNU ionization + +718 +00:57:58,480 --> 00:58:03,780 +واحد وتسعين و اتنين من عشرة NO زائد HNU NO plus + +719 +00:58:03,780 --> 00:58:08,500 +زائد إلكترون مية أربعة و تلاتين vacuum UV فلاحظوا + +720 +00:58:08,500 --> 00:58:11,860 +أن عمليات الـ ionization اللي بده أقوله في الـ + +721 +00:58:11,860 --> 00:58:16,500 +ionosphere في الـ ionosphere اللي هي بعد الـ + +722 +00:58:16,500 --> 00:58:20,900 +stratosphere عمليات الـ ionization هذه هي اللي + +723 +00:58:20,900 --> 00:58:27,760 +بتخلصني من كميات هائلة من الـ الـ solar radiation الـ + +724 +00:58:27,760 --> 00:58:31,740 +harmful Solar Radiation لأن هدى غير هيك لو هدول مش + +725 +00:58:31,740 --> 00:58:34,720 +لو هدى العمليات مش موجودة هدى الأطواق الموجية + +726 +00:58:34,720 --> 00:58:39,460 +المفروض أنه بذاته جينيه على الأرض مثلا فهذا الكلام + +727 +00:58:39,460 --> 00:58:44,420 +يعتبر ضار جدا لو هدى الأشعة بالفعل بيوصل لكن مجرد + +728 +00:58:44,420 --> 00:58:48,020 +وجود الـ photo dissociation و الـ photo ionization + +729 +00:58:48,020 --> 00:58:54,400 +بيخلصني من معظم الأشعة اللي يعني ضارة بالحياة على + +730 +00:58:54,400 --> 00:58:56,640 +سطح الأرض + +731 +00:59:00,490 --> 00:59:08,050 +بالمناسبة وجود هذه الايونات في الـ ionosphere مهم + +732 +00:59:08,050 --> 00:59:12,250 +جدا للاتصالات اللي احنا حاليا بنعملها و بنلاقي + +733 +00:59:12,250 --> 00:59:17,090 +مافيش أي صعوبة فيها ليه؟ لأنه كان زمان في فكرة + +734 +00:59:17,090 --> 00:59:24,010 +سائدة أن الأشعة بتسير في خطوط ايش؟ مستقيمة فمعنى + +735 +00:59:24,010 --> 00:59:30,350 +الكلام بما أن الأرض كروية فإذا كان بعتنا شعيع عشان + +736 +00:59:30,350 --> 00:59:34,770 +يوصل من مثلا لو قلنا هذه هي الكورة الأرضية يوصل من + +737 +00:59:34,770 --> 00:59:38,410 +المنطقة هنا للمنطقة هنا بده يعمل curvature فلما + +738 +00:59:38,410 --> 00:59:42,210 +نبعت شعيع هيطلع فوق مش هيوصل هنا وبالتالي الـ long + +739 +00:59:42,210 --> 00:59:47,110 +range communication مستحيلة كان في فكرهم زمان يعني + +740 +00:59:48,080 --> 00:59:53,200 +لكن لا هي مش مستحيلة هي ممكنة بفضل أو جزء مهم من + +741 +00:59:53,200 --> 00:59:57,020 +الموضوع هي وجود الايونات في الايونسفير وجود + +742 +00:59:57,020 --> 01:00:01,420 +الايونات والالكترونات في الايونسفير يعني هذه بتسهل + +743 +01:00:01,420 --> 01:00:07,020 +الـ bending للاشعة وبالتالي بتعود رجعها الأرض كمان + +744 +01:00:07,020 --> 01:00:11,920 +مرة وإلا كان الشعاع طلع و تم طلع فوق خط مستقيم + +745 +01:00:11,920 --> 01:00:19,390 +يعني لكن هذا الكلام مش صحيح فهذه الايونسفيرو هي + +746 +01:00:19,390 --> 01:00:25,030 +عندنا.. هي خط إرسال كويس فلاحظوا إنه هي الخط + +747 +01:00:25,030 --> 01:00:29,190 +الإرسال أو يعني محطة الإرسال أرسلت موجة مستقيمة + +748 +01:00:29,190 --> 01:00:35,670 +صحيح فضربت في أو اصطدمت في الـ ions فوق فرجعت ثاني + +749 +01:00:35,670 --> 01:00:40,370 +على الأرض الأرض انعكست ثاني للـ ionosphere وهكذا + +750 +01:00:40,370 --> 01:00:45,430 +لغاية ما إنه والله يقدر حد يتلقى الإشارة بالرغم من + +751 +01:00:46,400 --> 01:00:50,380 +الـ curvature طبعا هذه تجربة عملها أحد الأشخاص + +752 +01:00:50,380 --> 01:00:56,390 +بداية الف وتسعمائة تقريبًا فأرسل رسالة من بريطانيا + +753 +01:00:56,390 --> 01:01:00,970 + لمنطقة أخرى حوالي ألفين وتسعمائة كيلومتر بعيدة + +754 +01:01:00,970 --> 01:01:04,310 +وكانوا بتوقعوا أن هذه اللي عمرا راح توصل لأن الأرض + +755 +01:01:04,310 --> 01:01:09,050 +كروية والأشعة تسير في خطوط مستقيمة فكان طبعا يعني + +756 +01:01:09,050 --> 01:01:15,510 +اتفاجأوا أنه لأ وصلت فالسبب في هذا الكلام هو وجود + +757 +01:01:15,510 --> 01:01:21,630 +الـ ions في منطقة الـ ionosphere و الـ electrons طيب + +758 +01:01:21,630 --> 01:01:32,280 +الآن كمان حاجة تأثير مهم جدا لوجود الهواء في الـ + +759 +01:01:32,280 --> 01:01:34,860 +Troposphere أو في منطقة الاتموسفير القريبة من + +760 +01:01:34,860 --> 01:01:41,540 +الأرض بنقول إن الـ Oxygen جزء منه بتحول للـ Ozone + +761 +01:01:41,540 --> 01:01:45,560 +و الـ Ozone هذا بتحول أو هذا الجزء بتحول في منطقة + +762 +01:01:45,560 --> 01:01:51,210 +الـ Stratosphere الستراتوسفير طبعا في الستراتو + +763 +01:01:51,210 --> 01:01:54,790 +سفير اللي هي حوالي تمتد لحوالي خمسين كيلومتر عن + +764 +01:01:54,790 --> 01:01:58,190 +سطح الأرض في آخر الستراتوسفير تقريبًا بتكون عنده + +765 +01:01:58,190 --> 01:02:08,070 +طبقة من الأوزون فالأوزون + +766 +01:02:08,070 --> 01:02:12,430 +هو عبارة عن تفاعل بين الـ oxygen الـ molecular + +767 +01:02:12,430 --> 01:02:17,980 +oxygen و ذرة oxygen وهذا التفاعل في الحقيقة يعني + +768 +01:02:17,980 --> 01:02:22,220 +spontaneous، التفاعل بيتم بدرجة معقولة زي ما + +769 +01:02:22,220 --> 01:02:27,780 +هنشوف، وبالتالي بيعطيني أوزون، والأوزون هل بيصير + +770 +01:02:27,780 --> 01:02:32,400 +excited، ممكن جدا أنه يتفكك ثاني ويعطيني O و O2، + +771 +01:02:32,400 --> 01:02:36,700 +لكن نظرا لتصادم مع جزيئات أخرى، وبالأخص اللي موجود + +772 +01:02:36,700 --> 01:02:39,780 +كتير هو الـ Nitrogen مثلا يعني إذا اتصادم مع الـ + +773 +01:02:39,780 --> 01:02:42,220 +نيتروجين بيعطي طاقته للنيتروجين فتصبح الـ O تلاتة + +774 +01:02:42,220 --> 01:02:46,080 +ثابت خلاص مبتبقاش excited فبتتفككش ثاني يعني ليه؟ + +775 +01:02:46,080 --> 01:02:53,520 +لأنه عندي نيتروجين كمية كبيرة الـ Ozon بيمتص + +776 +01:02:53,520 --> 01:02:58,640 +الأطوال الموجية من 240 اللي ما بيمتصهاش الـ O2 من + +777 +01:02:58,640 --> 01:03:05,490 +240 إلى 310 وهذا شيء ممتاز جدا لأن هذه أشعة ضارة + +778 +01:03:05,490 --> 01:03:16,870 +جدا بالحياة على سطح الأرض فالـ Ozon بيكون shield أو + +779 +01:03:16,870 --> 01:03:17,410 +واق + +780 +01:03:25,940 --> 01:03:31,660 +فاحنا بنعرف إنه يعني بمجرد ما إنه الـ radiation + +781 +01:03:31,660 --> 01:03:36,980 +للشمس اللي جاي من الشمس توصل altitude أو ارتفاع + +782 +01:03:36,980 --> 01:03:41,160 +حوالي تسعين كيلومتر above earth surface بتكون معظم + +783 +01:03:41,160 --> 01:03:45,610 +الأشعة Wavelength راحت في الـ Ionosphere تحديدا + +784 +01:03:45,610 --> 01:03:51,310 +يعني، ليه؟ لأ يا إما حصل photo dissociation، يا + +785 +01:03:51,310 --> 01:03:55,850 +إما حصل photo ionization، فمعظمها خلصت، فبيبقى بعد + +786 +01:03:55,850 --> 01:04:01,980 +هيك الأشعة اللي هي من يعني أطول من 240 فمن 240 لـ + +787 +01:04:01,980 --> 01:04:06,120 +310 المفروض أن الأوزون هالجت يشتغل شغله ويحاول أن + +788 +01:04:06,120 --> 01:04:12,620 +يخلصني من هذه الأشعة فلهذا السبب ممكن نطلق على + +789 +01:04:12,620 --> 01:04:18,150 +الأوزون أن هو ozone shield واقي أو حامي طبقة واقية + +790 +01:04:18,150 --> 01:04:24,450 +أو طبقة حامية ليه؟ لأنه هي اللي هتخلصني من الأشعة + +791 +01:04:24,450 --> 01:04:30,750 +اللي هي من 240 لحوالي 310 ومن هذا المنطلق بنقول إنه + +792 +01:04:30,750 --> 01:04:36,770 +لا بد من حماية طبقة الأوزون من التقلص أو الاختفاء + +793 +01:04:36,770 --> 01:04:41,010 +فأي شيء بيأثر سلبا على طبقة الأوزون المفروض إنه + +794 +01:04:41,520 --> 01:04:46,920 +نحاول أن احنا نقلل الويلة راح بعد فترة هذه الأشعة + +795 +01:04:46,920 --> 01:04:53,180 +اللي هي من 240 ل 310 تنفذ إلى الأرض يعني تنفذ إلى + +796 +01:04:53,180 --> 01:05:00,000 +الأرض وبالتالي تأثيرها الضار راح تكون موجودة بشكل + +797 +01:05:00,000 --> 01:05:04,100 +كبير في + +798 +01:05:04,100 --> 01:05:06,800 +الحقيقة الشغلات اللي بتأثر على طبقة الأوزون كثيرة + +799 +01:05:07,710 --> 01:05:13,970 +لكن خليني أقول ممكن تقسيمها إلى قسمين ممكن + +800 +01:05:13,970 --> 01:05:19,470 +تقسيمها يعني حاجات طبيعية زي البراكين تحديدا وما + +801 +01:05:19,470 --> 01:05:25,660 +بتنفثه في الهواء الجوي من particulates وممكن نقول + +802 +01:05:25,660 --> 01:05:30,360 +في حاجة anthropogenic يعني شغلات man-caused أو + +803 +01:05:30,360 --> 01:05:35,460 +human-caused يعني شغلات سببها الإنسان فالحاجات + +804 +01:05:35,460 --> 01:05:39,960 +الطبيعية مثلا كلنا بنتذكر يمكن أنتو لا يمكن + +805 +01:05:39,960 --> 01:05:47,560 +تتذكروش في الـ 91 بعتقد في الـ.. بركان في الفلبين + +806 +01:05:47,560 --> 01:05:55,910 +آه في الـ 91 بركان في الفلبين كان يعني تأثير وضار + +807 +01:05:55,910 --> 01:06:00,010 +جدا على البيئة بحيث أنه نفث في الهواء الجوي حوالي + +808 +01:06:00,010 --> 01:06:06,490 +عشرة كيلومتر مكعب من المواد في الهواء فهذه انتقلت + +809 +01:06:06,490 --> 01:06:12,210 +إلى الـ troposphere والستراتوسفير جلست هناك تقريبًا + +810 +01:06:12,210 --> 01:06:22,010 +حوالي سنتين لثلاث سنين وهي موجودة هذه الجسيمات + +811 +01:06:22,010 --> 01:06:26,690 +قللت كمية الأشعة اللي واصلة من الشمس تقريبًا بـ 10% + +812 +01:06:26,690 --> 01:06:32,590 +ورفعت درجة الحرارة حوالي نصف درجة + +813 +01:06:40,050 --> 01:06:46,590 +في براكين أخرى أيضا لكن مش بكثافة الكميات اللي + +814 +01:06:46,590 --> 01:06:50,610 +أصدرها هذا البركان برضه نفس الكلام أثرت سلبًا على + +815 +01:06:50,610 --> 01:06:55,250 +البيئة أو على الجو على الـ climate بشكل عام لغاية + +816 +01:06:55,250 --> 01:06:59,170 +ما زالت لأنه في الحقيقة بتاخد وقت طويل جدا لما + +817 +01:06:59,170 --> 01:07:01,250 +نتلاشاها + +818 +01:07:02,770 --> 01:07:06,090 +فهذه شغلات طبيعية اللي ما نستطيع التحكم فيها لكن + +819 +01:07:06,090 --> 01:07:09,550 +اللي نستطيع التحكم فيه هو الحاجات اللي صادرة عن + +820 +01:07:09,550 --> 01:07:15,830 +النشاطات الإنسانية النشاطات الإنسانية فمثلا هذا + +821 +01:07:15,830 --> 01:07:21,070 +صورة للبركان يعني ايش نفث فوق في الـ.. في الهواء + +822 +01:07:21,070 --> 01:07:28,040 +يعني فمثلًا بنلاحظ إنه في بعض المواد إحنا بننتجها + +823 +01:07:28,040 --> 01:07:32,960 +وهذه المواد بتأثر سلبًا على طبقة الأوزون من أهم + +824 +01:07:32,960 --> 01:07:39,040 +هذه المواد اللي هي الـ Chlorofluorocarbons + +825 +01:07:39,090 --> 01:07:42,830 +الـ Chlorofluorocarbons هي عبارة عن مواد احنا + +826 +01:07:42,830 --> 01:07:49,150 +حضرناها وعملنا منها ملايين الأطنان ملايين الايه؟ + +827 +01:07:49,150 --> 01:07:52,330 +الأطنان مش طن ولا اثنين ولا تلاتة لأن نقول مشكلة + +828 +01:07:52,330 --> 01:07:55,950 +محلولة لا ملايين الأطنان و ليش حبيناها وعملنا منها + +829 +01:07:55,950 --> 01:08:00,450 +كثير؟ تستخدم كـ refrigerant وبتستخدم في غازات الـ.. + +830 +01:08:00,450 --> 01:08:05,350 +الـ conditioner الـ air conditioners وشغلات زي هيك + +831 +01:08:05,350 --> 01:08:13,560 +يعني وأحببنا فيها بشكل كبير إنها مواد خاملة مواد + +832 +01:08:13,560 --> 01:08:19,100 +خاملة يعني بتتكسرش بتعيش فترة زمنية طويلة بتخربش + +833 +01:08:19,100 --> 01:08:24,920 +inert بتتفاعلش مع أي حاجة فعشان هي أكلجناها وبتنفع + +834 +01:08:24,920 --> 01:08:27,980 +كـ refrigerant فاشتغلنا منها ملايين الأطنان وصار كل + +835 +01:08:27,980 --> 01:08:37,030 +العالم قائم عليه للأسف تبين في 1974 اثنين من + +836 +01:08:37,030 --> 01:08:43,110 +العلماء رولاند و مولينا لاقوا أن الكلورين بيحطم + +837 +01:08:43,110 --> 01:08:47,670 +طبقة الأوزون الكلورين وجدوا أنه يحطم طبقة الأوزون + +838 +01:08:47,670 --> 01:08:54,730 +والـ chlorofluorocarbons طبعا يعني هي الـ CF2 + +839 +01:08:54,730 --> 01:09:01,990 +أغلبها CCL وCL طب هذه الـ CCL بسهولة بتنكسر في + +840 +01:09:01,990 --> 01:09:05,870 +الطبقات الهوائية العليا photo dissociation photo + +841 +01:09:05,870 --> 01:09:11,510 +dissociation بتنكسر فبتطلع عند الـ CL جاز ذرة هذه الـ + +842 +01:09:11,510 --> 01:09:17,410 +الـ CL جاز بتحطم الأوزون فجوا هذا الكلام فالناس + +843 +01:09:17,410 --> 01:09:24,310 +انتبهت أنه والله آه قد يكون فيه تأثير سلبي لهذه + +844 +01:09:24,310 --> 01:09:28,670 +المركبات على الأوزون ولو طلعتوا هنا اللون مش واضح + +845 +01:09:28,670 --> 01:09:36,120 +هتلاحظوا أن في عندي منطقة الأوزون فيها قليل حاولوا + +846 +01:09:36,120 --> 01:09:42,440 +.. حاولوا أنه يعني يدرسوا هذا الكلام أكثر فجوا + +847 +01:09:42,440 --> 01:09:49,980 +بالفعل أن الـ CF2CCL2 مع الـ HNU بتتحول لـ CF2CCL + +848 +01:09:49,980 --> 01:09:54,950 +وCLGAS فووتو ديسوشياش عادي بيحصل بسهولة من مية + +849 +01:09:54,950 --> 01:09:58,570 +وتسعين لمتين وخمس وعشرين نانومتر الـ scan في + +850 +01:09:58,570 --> 01:10:02,030 +الأندويفليكس زي هيك فورا بتنكسر الرابطة طب والـ CL + +851 +01:10:02,030 --> 01:10:04,950 +جاز تتفاعل مع الـ O تلاتة جاز اللي هو الأوزون + +852 +01:10:04,950 --> 01:10:10,520 +تعطينا الـ CLOO2 والـ CLO المصيبة الأكبر أن الـ CLO + +853 +01:10:10,520 --> 01:10:16,000 +بسهولة بتنكسر تتحول لـ O gas و CL gas والـ CL gas + +854 +01:10:16,000 --> 01:10:21,180 +هذه مرة ثانية بالـ .. مع الأوزون صارت catalyst صارت + +855 +01:10:21,180 --> 01:10:24,340 +عامل مساعد يعني عامل إيه؟ بتعيد الـ cycle مرة و + +856 +01:10:24,340 --> 01:10:27,620 +مرتين وثلاث وميت ألف مرة ومليون مرة نفس الذرة + +857 +01:10:27,620 --> 01:10:32,420 +جاعدة بتكسر في الأوزون طبعا عند ملايين الأطنان + +858 +01:10:34,140 --> 01:10:39,480 +فاتفقوا عالميا على أنه يلاجوا بدائل + +859 +01:10:39,480 --> 01:10:42,720 +للـ Chlorofluorocarbons طبعا إلا للأغراض الضرورية + +860 +01:10:42,720 --> 01:10:46,320 +جدا يعني ممنوع تصنيعها حاليا إلا للأغراض الضرورية + +861 +01:10:46,320 --> 01:10:54,020 +جدا جدا وحاليا بالفعل يعني صار في عندنا X أو + +862 +01:10:54,020 --> 01:10:57,720 +تشريعات + +863 +01:10:59,030 --> 01:11:03,330 +بتمنع تصنيع الـ Chlorofluorocarbons، لكن للأسف هذه + +864 +01:11:03,330 --> 01:11:05,470 +الـ Chlorofluorocarbons اللي في الهواء واللي + +865 +01:11:05,470 --> 01:11:10,270 +موجودة في البيئة راحت عايش كمان يعني يمكن آلاف + +866 +01:11:10,270 --> 01:11:15,960 +السنين، إذا ما كانش أكثر من هيك ويتم حلقة الـ + +867 +01:11:15,960 --> 01:11:21,600 +Ozone هذه والـ Depletion لإله شغالة لكن في نفس + +868 +01:11:21,600 --> 01:11:26,620 +الوقت برضه الـ Ozone عامل بيتكون فحاليا يعني الـ + +869 +01:11:26,620 --> 01:11:31,960 +NASA في عندها مرصد بس بيرصد طبقة + +870 +01:11:31,960 --> 01:11:36,560 +الأوزون وبيعطي معلومات يومية عن يعني online عن + +871 +01:11:36,560 --> 01:11:40,400 +طبقة الأوزون كيف هي فحصل الآن استقرار بعد ما + +872 +01:11:41,680 --> 01:11:45,460 +أوقفوا استخدام الـ chlorofluorocarbons حصل استقرار + +873 +01:11:45,460 --> 01:11:50,480 +فيها لكن هذا الكلام يعني قد يتأثر بأي مؤثرات + +874 +01:11:50,480 --> 01:11:54,980 +خارجية أخرى .. قد يتأثر بأي مؤثرات خارجية أخرى .. + +875 +01:11:54,980 --> 01:12:00,820 +بعض الناس يمكن تقول والله طيب ما هو يعني مثلا الـ + +876 +01:12:00,820 --> 01:12:06,100 +HCL بيطلع على الـ .. على الهواء الجو وبرضه بيعطي + +877 +01:12:06,100 --> 01:12:10,150 +بنحصل بيعطي الـ CL gas تقول لأ أوقفوا شوية الـ + +878 +01:12:10,150 --> 01:12:13,030 +chlorofluorocarbons المشكلة الأساسية تبعته أنها لا + +879 +01:12:13,030 --> 01:12:17,570 +تتدوب في الماء فلما تتكون فوق ويأتي الشتاء لا + +880 +01:12:17,570 --> 01:12:22,570 +تتدوب عشان تنزل تبقى هوا فوق لكن الـ HCl ما شبه + +881 +01:12:22,570 --> 01:12:26,570 +مركبات الكلورين الأخرى بسهولة تتدوب فلما تتدوب آه + +882 +01:12:26,570 --> 01:12:30,490 +تأتي على الأرض من عليجها ليس خلاف يعني لكن لا تبقى + +883 +01:12:30,490 --> 01:12:33,670 +في طبقات الهواء العليا اللي تعمل تكسير لطبقة + +884 +01:12:33,670 --> 01:12:35,530 +الأوزون + +885 +01:12:38,270 --> 01:12:47,370 +طيب يعني اليوم كان في عندنا عدة توقفات معينة لغاية + +886 +01:12:47,370 --> 01:12:50,010 +الآن وإذا الله راضي الحصة الجاية بنكمل diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/fbLNdOQVMfA_raw.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/fbLNdOQVMfA_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..692c7150e44f5e173dd7cc2db1541b11a381538e --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/fbLNdOQVMfA_raw.srt @@ -0,0 +1,4156 @@ +1 +00:00:20,810 --> 00:00:24,250 +بسم الله الرحمن الرحيم إذا الله راضي اليوم بنكمل + +2 +00:00:24,250 --> 00:00:26,650 +في ال chapter اللي بتحدث عن ال chemistry of the + +3 +00:00:26,650 --> 00:00:31,410 +environment شوفنا في الحصة الماضية تركيب ال + +4 +00:00:31,410 --> 00:00:37,490 +atmosphere و الأجزاء اللي بيتكون منها و الغازات + +5 +00:00:37,490 --> 00:00:43,100 +اللي بيحتويها، الآنبنطلع في غازات في الحقيقة يعني + +6 +00:00:43,100 --> 00:00:47,440 +موجودة بكميات قليلة لكنها تأثير مهم فبنطلع على ال + +7 +00:00:47,440 --> 00:00:50,420 +gases in the troposphere لكن مش كل ال gases لأ ال + +8 +00:00:50,420 --> 00:00:53,800 +gases اللي كنا ذكرناها سابقا لكن كانت موجودة + +9 +00:00:53,800 --> 00:00:59,220 +بكميات قليلة فمنها مثلا ال carbon monoxide حوالي + +10 +00:00:59,220 --> 00:01:03,260 +عشرة PPM ال hydrocarbons تلاتة PPM ال sulfur + +11 +00:01:03,260 --> 00:01:08,450 +dioxide point 08PPM نيتروجين أكسايز 0.05 + +12 +00:01:08,450 --> 00:01:14,990 +والأكسيدنت حوالي 0.02 فمعنى الكلام يعني كمية غازات + +13 +00:01:14,990 --> 00:01:20,350 +قليلة مش كتير كبيرة لكن بنلاحظ أنه في إلها أهمية + +14 +00:01:20,350 --> 00:01:25,870 +كبيرة نظرا لو وجودها في التروبوسفير فحنحاول نطلع + +15 +00:01:25,870 --> 00:01:30,090 +على بعض هذه الغازات فعلى سبيل المثال ال carbon + +16 +00:01:30,090 --> 00:01:32,050 +monoxide هو pollutant + +17 +00:01:34,690 --> 00:01:39,770 +very toxic في الحقيقة، toxic كتير، بشكل أساسي + +18 +00:01:39,770 --> 00:01:46,510 +بينتج عن احتراق غير كامل في كل آلات الاحتراق زي + +19 +00:01:46,510 --> 00:01:52,250 +مثلا مواطير السيارات، شركة الكهربا والتوربينات + +20 +00:01:52,250 --> 00:01:56,950 +تبعتها، مولدات الطاقة اللي موجودة في البيوت + +21 +00:01:56,950 --> 00:02:00,910 +وموجودة في العمارات المختلفة مثلا في بيئتنا في غزة + +22 +00:02:00,910 --> 00:02:10,430 +هانففي عدة مصادر بتعطيني احتراق غير كامل لال fuel + +23 +00:02:10,430 --> 00:02:15,470 +وبالتالي بينتج عنها بعض ال CO ال .. بنقول a + +24 +00:02:15,470 --> 00:02:20,070 +typical engine سيارة without an emission control + +25 +00:02:20,070 --> 00:02:23,230 +system emits about عشر او خمس عشر جرامof + +26 +00:02:23,230 --> 00:02:27,710 +hydrocarbons per mile يعني عشان السيارة تمشي مثلا + +27 +00:02:27,710 --> 00:02:34,030 +ميل واحد كيلو ستة من عشرة تقريبا عشان تمشي هذه + +28 +00:02:34,030 --> 00:02:38,590 +المسافة بينتج عنها عشرة و خمساشر gram of + +29 +00:02:38,590 --> 00:02:42,870 +hydrocarbons يعني هذه مش محترقة لسه بدها كمان + +30 +00:02:42,870 --> 00:02:46,530 +احتلاق من عشرة و خمساشر gram هذه ضرر للغاية يعني + +31 +00:02:46,530 --> 00:02:51,370 +لأن تراكمها بسبب مشاكل بيئية كبيرة + +32 +00:02:54,570 --> 00:02:58,850 +القيمة القياسية اللى احنا بدنا نوصل لها حاليا يعنى + +33 +00:02:58,850 --> 00:03:05,890 +هي 0.075 جرام لكل ميل يعني بد ال engine مش يتطلع + +34 +00:03:05,890 --> 00:03:11,550 +10 الى 15 جرام لكل ميل لأ بده يتطلع 0.075 يعني + +35 +00:03:11,550 --> 00:03:17,230 +كمية تعتبر قليلة جدا بالمقارنة مع هذه الكمية طبعا + +36 +00:03:19,880 --> 00:03:24,800 +يعني عشان اوصل لهذا الغرض بدي اطور كتير في ال + +37 +00:03:24,800 --> 00:03:29,740 +engines مثلا خليها كفائتها عالية اكتر بتحرق ال + +38 +00:03:29,740 --> 00:03:33,980 +hydrocarbons بشكل افضل ممكن نقول والله يعني + +39 +00:03:33,980 --> 00:03:38,380 +بتستخدم ميكانيزمات تانية لانه تحول ال fuel لطاقة + +40 +00:03:38,380 --> 00:03:42,080 +على سبيل المثال وهذا كله مشغول عليه او بيحاولوا + +41 +00:03:42,080 --> 00:03:43,360 +يعملوا عليه دراسات + +42 +00:03:45,790 --> 00:03:50,970 +طبعا ال .. خلّيني أقول المصانع الضخمة اللي بتستخدم + +43 +00:03:50,970 --> 00:03:55,350 +كميات كبيرة من الوقود هذه عرضة لإنه تطلع لكميات + +44 +00:03:55,350 --> 00:03:59,430 +أيضا كبيرة من ال carbon monoxide خلّيني أقول + +45 +00:03:59,430 --> 00:04:05,150 +بيولوجيا ال carbon monoxide بيتحد مع ال iron اللي + +46 +00:04:05,150 --> 00:04:10,570 +موجود في خلايا الدم الحمراء بدل ال oxygenوبالتالي + +47 +00:04:10,570 --> 00:04:16,090 +يعني في بيات مثلا في مدفأة على الفحم كلنا بنسمع + +48 +00:04:16,090 --> 00:04:20,450 +هذا كلام دائما، مسكرين البواب والشوابك عشان + +49 +00:04:20,450 --> 00:04:24,010 +الحرارة التنغة موجودة، فمش عارفين أن عمال ال + +50 +00:04:24,010 --> 00:04:28,590 +oxygen بيستهلك في ال إيه؟ في عملية الاحتراق، طيب + +51 +00:04:28,590 --> 00:04:31,590 +ال oxygen قال بيبطل يطلع عند ال co2 بيبطل يطلع عند + +52 +00:04:31,590 --> 00:04:37,620 +ال co، ال coالانسان بيستنشقه و الخلايا الدم + +53 +00:04:37,620 --> 00:04:40,580 +الحمراء تحتوي على طبعا ايرون الايرون بيرتبط مع + +54 +00:04:40,580 --> 00:04:44,060 +الاكسجين فالان مافيش اكسجين كفاية مافيش بيرتبط مع + +55 +00:04:44,060 --> 00:04:48,520 +ال CO معناه كلام حصل عندي اختناق و بلاحظ ان + +56 +00:04:48,520 --> 00:04:56,860 +الانسان عرض لانه يموت فورا في ناس كتير بيموتوا + +57 +00:04:56,860 --> 00:05:01,360 +نظرا لانهم بيستنشقوا كمية كبيرة من ال CO ال CO + +58 +00:05:01,360 --> 00:05:04,680 +بالظبط زيه زي ال اوتو بيمسك فيه الايرونفي خلاية دم + +59 +00:05:04,680 --> 00:05:08,700 +الحمراء و بينتقله بدل ال oxygen لكن هل يستعيد عن + +60 +00:05:08,700 --> 00:05:13,960 +الجسم؟ بالطبع لأ، يعني لا يستخدم الجسم كما يستخدم + +61 +00:05:13,960 --> 00:05:18,120 +ال oxygen فبالتالي بنلاحظ أنه الإنسان بيختنق، + +62 +00:05:18,120 --> 00:05:23,360 +بيفقد الوعي في البداية و بيموت بدون ما يشعر غالبا، + +63 +00:05:23,360 --> 00:05:25,640 +الناس كتير بيكونوا هم و أطفالهم + +64 +00:05:28,470 --> 00:05:33,090 +يعني موجودين في جو محصور فبنلاحظ انه يفتقدوا لل + +65 +00:05:33,090 --> 00:05:37,010 +Oxygen فال Carbon Monoxide على قلته يعتبر Toxic + +66 +00:05:37,010 --> 00:05:41,890 +Pollutant صح قليل حوالي عشرة PPM لكنه يعتبر من + +67 +00:05:41,890 --> 00:05:48,750 +الغازات المهمةأيضا السلفر بيعطينا سلفر ديوكسيد + +68 +00:05:48,750 --> 00:05:52,730 +والسلفر ديوكسيد من ال pollutants المهمة جدا جدا + +69 +00:05:52,730 --> 00:05:58,130 +سلفر ديوكسيد من ال pollutants المهمة جدا جدا بشكل + +70 +00:05:58,130 --> 00:06:02,630 +أساسي السلفر + +71 +00:06:02,630 --> 00:06:06,650 +موجود في الفحم بالذات الفحم الحجري بكميات كبيرة + +72 +00:06:06,650 --> 00:06:10,310 +السلفر موجود في الفحم بالذات الفحم الحجري بكميات + +73 +00:06:10,310 --> 00:06:16,840 +كبيرة وأيضا موجود في البترولبالذات ال solarالسولر + +74 +00:06:16,840 --> 00:06:20,760 +اللى بنستخدمه طبعا في المركبات العمومية كلها + +75 +00:06:20,760 --> 00:06:28,140 +تقريبا فموجود فيه كمية من السلفر مش كل السولر او + +76 +00:06:28,140 --> 00:06:31,860 +كل البترول في نفس الكمية من السلفر فيه high sulfur + +77 +00:06:31,860 --> 00:06:35,480 +content و فيه low sulfur content و بنسمع غاز .. + +78 +00:06:35,480 --> 00:06:39,140 +بنسمع يعني petrol خفيف و petrol ثقيل و petrol فيه + +79 +00:06:39,140 --> 00:06:42,220 +sulfur كتير و petrol فيه sulfur اقل طبعا كل ما + +80 +00:06:42,220 --> 00:06:46,210 +زادت كمية السلفر في البترول كل ما قلت قيمتهكل ما + +81 +00:06:46,210 --> 00:06:50,230 +قلت قيمة البترول فليش هذا كلام جاهز لإن السلفر لما + +82 +00:06:50,230 --> 00:06:55,150 +يحترق بيعطيني SO2 في ال engine في هواء في ال + +83 +00:06:55,150 --> 00:06:59,230 +engine كيف أنا بحرق البترول بدخل هواء ال هواء عند + +84 +00:06:59,230 --> 00:07:03,270 +حرارة عالية بيتفاعل مع السلفر بيعطيني SO2 و ال SO2 + +85 +00:07:03,270 --> 00:07:08,850 +مع نصه بلاش نقول O3 مع الأكسجين الجوي بيعطيني SO3 + +86 +00:07:10,600 --> 00:07:14,820 +كويس؟ هذا بتنفج فى الغلاف الجوى فوق يعنى فى أعلى + +87 +00:07:14,820 --> 00:07:18,180 +التروبوسفير جريم على ال استراتوسفير لأنه ال ozone + +88 +00:07:18,180 --> 00:07:22,360 +بتكون متوفر كتير فوق فبعطينا ال S O تلاتة طيب اوش + +89 +00:07:22,360 --> 00:07:26,160 +يعنى جال ال S O تلاتة مع الميه بيعطينى sulfuric + +90 +00:07:26,160 --> 00:07:30,380 +acid تخيلوا ان ال S O تلاتة غازي بتطلع فوق بتطلع + +91 +00:07:30,380 --> 00:07:34,520 +على مع الغازات اللى فى الهواء الجوي طيب الغازات + +92 +00:07:34,520 --> 00:07:37,480 +اللى فى الهواء الجوي لما الدنيا تنطرايش اللي + +93 +00:07:37,480 --> 00:07:41,900 +بيحصل؟ بتدوب و بتنزل على الأرض معناه الكلام المطر + +94 +00:07:41,900 --> 00:07:47,480 +ايش بيحتوي على ايش عندي؟ H2SO4 فظيع حمض فظيع قوي + +95 +00:07:47,480 --> 00:07:53,040 +جدا مخرب هذا اللي بنقوله او هو السبب الأساسي لل + +96 +00:07:53,040 --> 00:07:56,440 +acid rain السبب الأساسي لل acid rain طبعا هذه + +97 +00:07:56,440 --> 00:07:59,940 +مشكلة عويصة بتعاني منها او بيعاني منها العالم كله + +98 +00:07:59,940 --> 00:08:06,800 +لأنه يعني الجو عموماهو عبارة عن وحدة واحدة وإن كان + +99 +00:08:06,800 --> 00:08:10,580 +بعض الدول طبعا يعني بتعاني أكتر من غيرها الدول + +100 +00:08:10,580 --> 00:08:13,980 +الصناعية بالذات لأنه على فرض أن الغاز عمال بيطلع + +101 +00:08:13,980 --> 00:08:17,840 +والدنيا بتشتي فهينزل عليهم إيه أمطار حمضية بينما + +102 +00:08:17,840 --> 00:08:22,120 +احنا هان في غزة مثلا قليل مش عنا سافر كتير فيه + +103 +00:08:22,120 --> 00:08:25,500 +طبعا لكن مش زي الدول الصناعية خاصة لو تكون دول + +104 +00:08:25,500 --> 00:08:30,220 +ممتدة زي مثلا الولايات المتحدة شايفينها هانلحظوا + +105 +00:08:30,220 --> 00:08:35,960 +هان ال pH كويسة الأخضر هذا، لكن هان في المنطقة + +106 +00:08:35,960 --> 00:08:39,880 +الشرقية اللي هي منطقة صناعات فظيعة، لحظوا ال pH + +107 +00:08:39,880 --> 00:08:43,280 +هان كل ما نزلنا بتجل ال pH، يعني هان في عندي acid + +108 +00:08:43,280 --> 00:08:48,680 +rain كتيرacid rain بشكل يعني كفير خالص، إيش؟ يعني + +109 +00:08:48,680 --> 00:08:52,720 +بنقول والله ال acid rain بيأثر على ال إيه؟ بيأثر + +110 +00:08:52,720 --> 00:08:55,520 +على الأشجار و بيأثر أيضا على المياه لإنه بيخلي + +111 +00:08:55,520 --> 00:09:00,220 +البحيرات و المياه الراكدة بيخلي ال pH تبعيتها + +112 +00:09:00,220 --> 00:09:05,480 +قليلة وهذا قد يمنع ال aquatic life قد يمنع الحياة + +113 +00:09:05,480 --> 00:09:10,200 +المائيةتمام؟ فهي ال S اللي جاي من ال coal بيحترم + +114 +00:09:10,200 --> 00:09:15,200 +ويعطينا S O2 ال S O2 مع شوية أكسجين بيعطينا S .. + +115 +00:09:15,200 --> 00:09:19,600 +بيعطيه .. وميه بيعطينا H2 S O4 ال H2 S O4 مع المطر + +116 +00:09:19,600 --> 00:09:21,760 +إيه؟ شو ساوي بيجي على الأشدار؟ طب إيه إيش اللي + +117 +00:09:21,760 --> 00:09:25,560 +بيحصل؟ طلعوا الأشدار كيف صارت؟ في أماكن كتير .. + +118 +00:09:25,560 --> 00:09:28,160 +أماكن كتير في العالم، بالذات في .. في الصين على + +119 +00:09:28,160 --> 00:09:32,740 +سبيل المثال، في أمريكا تحديدًا، في بريطانيا بنلاحظ + +120 +00:09:32,740 --> 00:09:39,020 +غابات كاملة تسحرتغابات مش جلة ميا لأ في مطر كتير + +121 +00:09:39,020 --> 00:09:43,060 +لكن المطر اللي موجود هو عبارة عن مطر بيحتوي على + +122 +00:09:43,060 --> 00:09:49,240 +SO2 يعني sulfuric acid تحول إلى sulfuric acid أيضا + +123 +00:09:49,240 --> 00:09:53,820 +البحيرات كاملة كانت زاخرة بالسمك هذا سمك شايفينه + +124 +00:09:53,820 --> 00:09:58,700 +يعني واضح الصورة سمك هذا بحيرة مليانة سمك لكن نظرا + +125 +00:09:58,700 --> 00:10:03,660 +لإنه في عندي acid rain ال pH قلت بشكل كبير في + +126 +00:10:03,660 --> 00:10:09,600 +السمك ماتفبنلاحظ انه بعد ما يموتوا بيطفوا بيطلعوا + +127 +00:10:09,600 --> 00:10:13,580 +على الشواطئ .. طلعوا شواطئ مليانة أطنان مئات + +128 +00:10:13,580 --> 00:10:16,940 +الأطنان من الأسماك وبحيرات فقدت الحياة المائية + +129 +00:10:16,940 --> 00:10:22,140 +اللي فيها فطبعا هذا اشي خطير للغاية مش بس هيك ال + +130 +00:10:22,140 --> 00:10:27,090 +acid rain أيضا بيأثر على البيئة الحجريةمش بس + +131 +00:10:27,090 --> 00:10:31,170 +البيئة المائية و الأشجار لأ حتى البيئة الحجرية + +132 +00:10:31,170 --> 00:10:37,770 +فبيطلع هذا المنظر هو منظر لتاج محل بتسمعوا فيه في + +133 +00:10:37,770 --> 00:10:43,390 +الهند تاج محل كان أبيض من الرخام الأبيض الجميل جدا + +134 +00:10:43,390 --> 00:10:47,730 +مع ال acid rain اتحول العمال بتحول للون الأصفر زي + +135 +00:10:47,730 --> 00:10:52,380 +هيك بصيركان أبيض جميل جدا، بياض و ناصح، بياض جميل + +136 +00:10:52,380 --> 00:10:55,180 +جدا جدا، لان مع الوقت و مع التورة الصناعية اللى + +137 +00:10:55,180 --> 00:10:59,500 +موجودة غاد و مع كمية ال acid rain اللى صارت الأرض + +138 +00:10:59,500 --> 00:11:03,960 +تستقبلها فهدك المنطقة، اللان صار اللون يميل إلى + +139 +00:11:03,960 --> 00:11:09,870 +اللون الأصفر، صار ال marble يتآكلأيضا لو جينا + +140 +00:11:09,870 --> 00:11:15,330 +نطلعنا مباني كتير قديمة مباني كتير قديمة برضه فيها + +141 +00:11:15,330 --> 00:11:19,710 +تآكل طبعا الماء بيعمل تآكل لكن ال acid rain بيعمل + +142 +00:11:19,710 --> 00:11:26,690 +تآكل ايه؟ أسرع بشكل كبير نتخيل هذا عبارة عن يعني + +143 +00:11:26,690 --> 00:11:32,010 +منطقة عالية جدا صخرية عالية جدا وكان هذا الجزء كان + +144 +00:11:32,010 --> 00:11:34,850 +خلينا اقول يعني + +145 +00:11:36,970 --> 00:11:41,670 +جزء من هذا الجبل لكن نظرا لل acid rain لاحظنا انه + +146 +00:11:41,670 --> 00:11:47,130 +في تسرب في منطقة ماهان فلاحظنا انه بقى قادر يحمل + +147 +00:11:47,130 --> 00:11:52,970 +هذا الثقل فنزل نفس الكلام انهار كانت تجري قريب من + +148 +00:11:52,970 --> 00:11:58,310 +السطح صارت تجري وين؟يعني في أعماق كبيرة جدا نظرا + +149 +00:11:58,310 --> 00:12:03,690 +برضه لل acid rain وقلنا نتذكر شكل الكهوف اللي + +150 +00:12:03,690 --> 00:12:07,050 +موجودة في الجبال طبعا الميه بتعمل هذا الشيء ما + +151 +00:12:07,050 --> 00:12:10,350 +بنقولش الميه بتعملش لكن إذا كان الميه موجود فيها + +152 +00:12:10,350 --> 00:12:15,730 +acids فال acids بتدوب ال carbonates بشكل كبير لأن + +153 +00:12:15,730 --> 00:12:21,470 +معظم هذه الصخور و ال marble و غيره من ال calcium + +154 +00:12:21,470 --> 00:12:26,530 +carbonateفال Carbonate مع ال Acid على طول بتعطيني + +155 +00:12:26,530 --> 00:12:32,070 +CO2 و H2O بتدوبها فورا ال Acid مع ال Carbonate على + +156 +00:12:32,070 --> 00:12:36,510 +طول بيعطيني CO2 فمعنى الكلام هيكون في عندي تطور + +157 +00:12:36,510 --> 00:12:42,090 +سريع جدا جدا جدا في البيئة الحجرية أيضا نظرا للإيه + +158 +00:12:42,090 --> 00:12:47,690 +لوجود ال Acid Rain وفي مناظر في الحقيقة يعني كتيرة + +159 +00:12:47,690 --> 00:12:51,170 +خالص ممكن الإنسان يطلع عليها ويدلع علي تأثير ال + +160 +00:12:51,170 --> 00:12:59,740 +Acid Rainالعالم الغربي حاول انه يقلل من تأثير وجود + +161 +00:12:59,740 --> 00:13:04,960 +السلفر، فحاول انه يتخلص من السلفر قبل ما يطلع على + +162 +00:13:04,960 --> 00:13:07,560 +الهواء الجوي، لانه طلع على الهواء الجوي ك S O2 + +163 +00:13:07,560 --> 00:13:13,810 +معناته plus acid rain، فحاول يتخلص منهقبل تكون + +164 +00:13:13,810 --> 00:13:18,950 +الاس او تلاتة يعني لو جرى تكون الاس او توا يحاول + +165 +00:13:18,950 --> 00:13:23,070 +انه يتخلص منه .. كيف بده يتخلص منه؟ قال والله لازم + +166 +00:13:23,070 --> 00:13:29,680 +نعالج الوقود اللي هو عبارة عن ال oilالبترول وايضا + +167 +00:13:29,680 --> 00:13:36,620 +ال coal قبل ما انه نحرقه لكن صعب جدا نستخرج ال + +168 +00:13:36,620 --> 00:13:41,900 +sulfur تحديدا من ال coal او من البترول قبل حرقه + +169 +00:13:41,900 --> 00:13:46,280 +عمليات مكلفة للغاية نقدرش عليها قال طب اذا ايش + +170 +00:13:46,280 --> 00:13:50,560 +ممكن نعمل قال في عندنا طريقة فبنقول one method is + +171 +00:13:50,560 --> 00:13:53,880 +powdered calcium carbonate بنحرجها تتحول ال + +172 +00:13:53,880 --> 00:13:57,950 +calcium oxide بنحرجها مع البترول بنحرجها معالـ + +173 +00:13:57,950 --> 00:14:02,150 +coal يعني بندخلها مع البترول أو بندخلها مع ال coal + +174 +00:14:02,150 --> 00:14:07,230 +مع الفحم في الفرن فبتتحول ال calcium carbonate ل + +175 +00:14:07,230 --> 00:14:12,090 +calcium oxide لما يتكون ال SO2 جال والله ال + +176 +00:14:12,090 --> 00:14:15,010 +calcium oxide بتفاعل مع ال SO2 بعطيني صلب calcium + +177 +00:14:15,010 --> 00:14:21,270 +sulfite calcium sulfiteالكالسيوم سالفايت هذا solid + +178 +00:14:21,270 --> 00:14:26,730 +يمكن ازالته تمام؟ مش هيطلع على الهواء الجوي لكن + +179 +00:14:26,730 --> 00:14:31,390 +بالطبع يعني يتبقى كمية كبيرة من ال S.O.2 يعني + +180 +00:14:31,390 --> 00:14:34,850 +بياخد شوية من ال S.O.2 صحيح لكن يتبقى كمية كبيرة + +181 +00:14:34,850 --> 00:14:40,290 +من ال S.O.2 علشان هيك عادة بيدخله الكالسيوم + +182 +00:14:40,290 --> 00:14:44,550 +سالفايت والزيادة من ال S.O.2 على اكواس كالسيوم + +183 +00:14:44,550 --> 00:14:49,210 +اكسايداكواس كالسوم اكسايد يعني كالسوم اكسايد دايب + +184 +00:14:49,210 --> 00:14:54,890 +في المياه هو بيكون slurry بيكون يعني مش دايب تماما + +185 +00:14:54,890 --> 00:14:59,510 +slurry فنتيجة هذا الكلام برضه بيترسب ال calcium + +186 +00:14:59,510 --> 00:15:04,530 +بترسب ال calcium sulfite يعني ال S O2 بقدر ان + +187 +00:15:04,530 --> 00:15:07,750 +اتخلص منه فهنا زي ما احنا شايفين في الرسم هادي + +188 +00:15:07,750 --> 00:15:15,730 +عندي هذه الفحمهاي سلفر كول وانا بضيف هنا كالسيوم + +189 +00:15:15,730 --> 00:15:19,790 +كربونيت الهاي سلفر كول عند السلفر بتفاعل مع ال + +190 +00:15:19,790 --> 00:15:23,550 +oxygen و بتحول ال S O2 الكالسيوم كربونيت تفكك + +191 +00:15:23,550 --> 00:15:30,810 +لكالسيوم أكسيد الكالسيوم أكسيد بيتفاعل مع السلفر + +192 +00:15:30,810 --> 00:15:36,210 +بيوكسيد وبعطيني كالسام سالفايت الكالسام سالفايت مع + +193 +00:15:36,930 --> 00:15:41,790 +الاس او تولي زيادة بندخله على ال towers موجود فيها + +194 +00:15:41,790 --> 00:15:49,530 +calcium oxide aqueous فهذا بيرسبلي بجيهة الاس او + +195 +00:15:49,530 --> 00:15:53,670 +تولي الموجود على هيئة calcium sulfite وفي الآخر + +196 +00:15:53,670 --> 00:15:57,990 +الهواء الخارجي بيكون أنقى بشكل كبير لكن بالطبع + +197 +00:15:57,990 --> 00:16:01,390 +يعني مش ممكن انه نجبر العالم كله يعمل .. هذا عملية + +198 +00:16:01,390 --> 00:16:05,670 +صعبة مش عملية سهلةإذا كان مثلا يعني طب .. طب + +199 +00:16:05,670 --> 00:16:09,250 +المواطين الكهربا اللي بتشتغل والسيارات إيش نسوا + +200 +00:16:09,250 --> 00:16:14,250 +فيها؟ حطيلها كمان محارق كالسيم كاربونيت؟ مستحيل + +201 +00:16:14,250 --> 00:16:19,430 +هذا الكلام، لكن هم بيحاولوا يعملوا إشي بحيث أنه + +202 +00:16:19,430 --> 00:16:24,630 +يكون أضاف للبيئة، لكن هذا محدود للغايةو مش مضطرين + +203 +00:16:24,630 --> 00:16:28,530 +انهم يعملوه لأنه يعني لما يكون في حد بيخرب و حد + +204 +00:16:28,530 --> 00:16:31,470 +بيعمر و اللي بيخربه كتار اللي بيعمر يعني ميده يقول + +205 +00:16:31,470 --> 00:16:34,190 +على الفعض يعني، اذا كان في دولة بتعمل زي هيك، طب + +206 +00:16:34,190 --> 00:16:38,590 +ما هو الهواء اللي تباعها؟ ما هو جارتها، ممكن ييجي + +207 +00:16:38,590 --> 00:16:42,070 +الهواء من جارتها، حركة الهواء متنقلة، فمشكلة عوي + +208 +00:16:42,070 --> 00:16:46,000 +صوف بالذات انه مكلفة للغاية، مش حاجة سهلةو برضه + +209 +00:16:46,000 --> 00:16:49,920 +كفائتها يعني مش عاطلة لكن انها .. يعني مش لل large + +210 +00:16:49,920 --> 00:16:53,220 +scale بشكل كبير لإنه هنحتاج كميات مهولة من ال + +211 +00:16:53,220 --> 00:17:00,670 +calcium carbonateفالـ SO2 عنصر أساسي من عناصر ال + +212 +00:17:00,670 --> 00:17:04,510 +pollution في هذا الكون عنصر أساسي السبب الرئيسي + +213 +00:17:04,510 --> 00:17:07,970 +انه يعطينا ال acid rain الان ال nitrogen oxides + +214 +00:17:07,970 --> 00:17:12,850 +برضه كمية قليلة كمية قليلة كتير ال SO2 بتتكلم عن + +215 +00:17:12,850 --> 00:17:15,950 +الغازات اللي كمية قليلة ال SO2 صح كمية قليلة لكن + +216 +00:17:15,950 --> 00:17:20,650 +تأثيره كبير ال N nitrogen oxides برضه كمية قليلة + +217 +00:17:20,650 --> 00:17:22,630 +جدا لكن تأثيرها برضه فظيعة + +218 +00:17:26,180 --> 00:17:31,820 +هي المسئولة عن الـ Brownish جاز او لونه هو الـ + +219 +00:17:31,820 --> 00:17:35,420 +Brownish يعني على بنة بنتطلع على بعض المدن + +220 +00:17:35,420 --> 00:17:39,720 +الصناعية زي كاتبها Los Angeles هفرجيكم منظر بنلاحظ + +221 +00:17:39,720 --> 00:17:46,440 +ان في عليها فوق المباني غلاف بنة غلاف غاز خفيف بنة + +222 +00:17:46,440 --> 00:17:50,660 +هذا عبارة عن الـ NO2 من وين بيجي؟ من وين بيجي الـ + +223 +00:17:50,660 --> 00:17:58,050 +NO2؟ قال واللهفي نفس الكلام، آلات الاحتراق اللي هي + +224 +00:17:58,050 --> 00:18:02,390 +مثلا مواتير السيارات و برضه ال power plants و + +225 +00:18:02,390 --> 00:18:08,430 +خلافه، هان بحترق البترول في وجود الهواء، معنى + +226 +00:18:08,430 --> 00:18:13,030 +الكلام، عندي حرارة عالية جدا، فالنيتروجين مع + +227 +00:18:13,030 --> 00:18:16,490 +الأكسجين بيعطيني نو و أكسيد متعدد، نو إكس خليني + +228 +00:18:16,490 --> 00:18:22,070 +أقولباعطيني NO او NOX ال NO مع اكسجين زي ال NO2 + +229 +00:18:22,070 --> 00:18:28,050 +هذا ال NO2 هو اللي لونه بنى ال NO2 هذا هو اللي + +230 +00:18:28,050 --> 00:18:32,970 +لونه ايه لونه بنى فحنلاحظ ان البلاد الصناعية لحظوا + +231 +00:18:32,970 --> 00:18:38,250 +هذا بده حرارة صح لأن ال nitrogen خامل بتفعل مع + +232 +00:18:38,250 --> 00:18:41,530 +الاكسجين في الهواء الجوية بتفعلوش ولا كان مالجيناش + +233 +00:18:41,530 --> 00:18:44,810 +اكسجين لأن ال nitrogen كتير لكن عند حرارة حالية + +234 +00:18:44,810 --> 00:18:49,790 +حرارة الاحتراك بتفعلوافهذه العملية بدها طاقة دلتا + +235 +00:18:49,790 --> 00:18:52,750 +اتش مية و تمانين مية واحد و تمانين كيلوجول لكن + +236 +00:18:52,750 --> 00:18:56,890 +الان او مع ال او اتو بتعطيني طاقة سهل جدا يعني + +237 +00:18:56,890 --> 00:19:00,610 +الان او مجرد ما يتكون بيعطيني ان او اتو والان او + +238 +00:19:00,610 --> 00:19:04,610 +لعالمكم كمان الان او الان او pollutant مهم لأنه في + +239 +00:19:04,610 --> 00:19:06,250 +النهاية برضه بيدل الان او اتو + +240 +00:19:09,110 --> 00:19:14,270 +كويس طيب عادة .. عادة جداش ال typical engine + +241 +00:19:14,270 --> 00:19:22,070 +بتعطيني لكل ميل من ال NO جال بتعطيني حوالي أربعة + +242 +00:19:22,070 --> 00:19:27,550 +جرام لكل ميل أربعة جرام لكل ميل بحصل على NO حوالي + +243 +00:19:27,550 --> 00:19:32,270 +أربعة جرام لكل ميل طب الآن ايش ال standard؟ جال ال + +244 +00:19:32,270 --> 00:19:37,950 +standard point او سفني جرام لكل ميلعشان هيك اي + +245 +00:19:37,950 --> 00:19:42,170 +سيارة حاليا بيصنعوها لازم يكون فيها emission + +246 +00:19:42,170 --> 00:19:45,790 +control system emission control ال emission يعني + +247 +00:19:45,790 --> 00:19:48,050 +الحاجات اللي تطلع منها من ال exhaust emission + +248 +00:19:48,050 --> 00:19:51,090 +control اه في عندك control على ال emissions بحيث + +249 +00:19:51,090 --> 00:19:55,000 +انه ماتزيدش عن هذا ال standardطبعاً في ناس كتير + +250 +00:19:55,000 --> 00:19:58,760 +مثلا بتهتمش بال standards فبتستورد السيارات كيف ما + +251 +00:19:58,760 --> 00:20:01,760 +كان مش مشكلة بعض البلاد اللي بتهتم بهذه ال + +252 +00:20:01,760 --> 00:20:05,000 +standards لأن هذا بيأثر على ال P-Line ده اه بتقول + +253 +00:20:05,000 --> 00:20:07,300 +لأ انا بدي السيارة يكون فيها emission control + +254 +00:20:07,300 --> 00:20:11,500 +system طبعا هذا بيرفع سعيرهاوكمان بده متابعة يعني + +255 +00:20:11,500 --> 00:20:14,780 +كل فترة لازم يعملوا inspection او فحص لهذا ال + +256 +00:20:14,780 --> 00:20:18,020 +emission control system بده تغيير يتغير بده تصحيح + +257 +00:20:18,020 --> 00:20:23,440 +يصححوه فالمهم انه ال targeted value اللي هي 0.07 + +258 +00:20:23,440 --> 00:20:26,940 +gram للميل أقل كتير من الأربعة جرام هذا كان أربعة + +259 +00:20:26,940 --> 00:20:30,960 +جرام كان مسبوحي قبل 2004 بعد 2004 قال لأ مبنوق بس + +260 +00:20:30,960 --> 00:20:36,020 +0.07 gram ليش؟ لأنه تأثيره على البيئة كبير خاصة + +261 +00:20:36,020 --> 00:20:41,490 +انه بيكون حجم نقولها ال smogتصوروا، ماعرفش، يعني + +262 +00:20:41,490 --> 00:20:46,050 +هي السماء الصافية وهي ال .. يعني هذا نهار، تطلعوا + +263 +00:20:46,050 --> 00:20:51,770 +الولد هان، هذا اللون البني كله، هذه Los Angeles، + +264 +00:20:51,770 --> 00:20:54,750 +اللون البني هذا اللي احنا شايفينه في ال + +265 +00:20:54,750 --> 00:20:57,790 +background، تطلعوا الأزمد، في فرق واضح من و بينها، + +266 +00:20:57,790 --> 00:21:03,120 +هذه عبارة عن بنقوله nitrogen oxide spongeنيتروجين + +267 +00:21:03,120 --> 00:21:08,400 +أكسيد مثل الفونج الفونج هو الضباب بينما ال .. ال + +268 +00:21:08,400 --> 00:21:13,120 +smoke هو عبارة عن غازات مش .. مش .. مش ميه مش + +269 +00:21:13,120 --> 00:21:16,460 +water vapor الفونج عادة water vapor في أغلبه لكن + +270 +00:21:16,460 --> 00:21:19,760 +هان هذا عبارة عن نيترس أكسيد تعالوا نطلع هاي + +271 +00:21:19,760 --> 00:21:22,620 +سيارات جاء في هذا الاتجاه بس عشان نشوف الفرق يعني + +272 +00:21:23,050 --> 00:21:27,990 +هذا في الصين، هذا صيني يعني، في الصين، لكن لو جينا + +273 +00:21:27,990 --> 00:21:32,150 +نطلعنا على الناحية التانية لنشوف ال background، + +274 +00:21:32,150 --> 00:21:35,630 +هذه نفس الصورة، نفس الصورة، بنلاحظ هذه الألوان + +275 +00:21:35,630 --> 00:21:41,330 +الفظيعة جدا، هذا عبارة عن NO2NO2 Nitrogen Oxides + +276 +00:21:41,330 --> 00:21:46,590 +Nitrogen Dioxide فهذا عبارة عن إسماج بيتكون و + +277 +00:21:46,590 --> 00:21:50,170 +بيغطي البلد تقريبا كلها بالذات المدن الصناعية + +278 +00:21:50,170 --> 00:21:54,010 +نادرا ما يشوفوا أو يعني يقدروا يشوفوا الشمس بشكل + +279 +00:21:54,010 --> 00:21:58,290 +واضح فدائما سبحان الله في غطاء من ال nitrogen + +280 +00:21:58,290 --> 00:22:03,190 +dioxide هاي برضه هذا شكل تاني ممكن هذا برضه واضح + +281 +00:22:03,190 --> 00:22:07,930 +جدا تخيلوا يعني هان جريب من الكاميرا أه شايفه منيح + +282 +00:22:08,330 --> 00:22:12,250 +جريب من الكاميرا شايفه نحو و وضوح كويس لكن اطلعوا + +283 +00:22:12,250 --> 00:22:16,970 +ال nitrogen dioxide هذه المدن الصناعية هذه المدن + +284 +00:22:16,970 --> 00:22:21,490 +الصناعية تصوروا كيف حجم ال pollution اللي بيكون + +285 +00:22:21,490 --> 00:22:27,830 +موجود فيها فقط من غازات جداش موجودة في البيئة يعني + +286 +00:22:27,830 --> 00:22:32,430 +ولا اشي قليل جدا جدا قليل للغاية يعني point O حاجة + +287 +00:22:32,430 --> 00:22:40,660 +من ال PPM طيب الآن خلينا نطلع علىحاجة بنسمعها + +288 +00:22:40,660 --> 00:22:44,980 +دايما ال greenhouse phenomena، ظاهرة ال greenhouse + +289 +00:22:44,980 --> 00:22:49,200 +أو ال effect، ال greenhouse effect، بنقول إنه + +290 +00:22:49,200 --> 00:22:58,100 +الأرض يعني الله عز وجل لما فصل الكون خلّى الأرض + +291 +00:22:58,100 --> 00:23:03,660 +محاطة بالأتمسفيرو في ال атмосفير بعض الغازات + +292 +00:23:03,660 --> 00:23:06,140 +البسيطة اللي احنا بنتكلم عنها ال gate بدنا نتكلم + +293 +00:23:06,140 --> 00:23:08,900 +عنها لغاية الحصة لها ال gate بعض الغازات اللي + +294 +00:23:08,900 --> 00:23:16,320 +موجودة كميات قليلة زي مثلا ال CO2 زي مثلا الميثين + +295 +00:23:16,320 --> 00:23:23,460 +زي مثلا ال nitrous oxide N2O زي الميه بخار الميه + +296 +00:23:23,460 --> 00:23:29,300 +هذه عاملة زي إطار blanket زي ما تجيب الحاف و تغطى + +297 +00:23:29,300 --> 00:23:33,610 +فيه حاجةإيش بتسوي ال blanket هذه؟ جال بتحافظ على + +298 +00:23:33,610 --> 00:23:39,090 +ال thermal consistency للأرض، تخلي الأرض دائما + +299 +00:23:39,090 --> 00:23:46,390 +الحرارة تبعتها حرارة يعني جيدة، مناسبة، فزي ما + +300 +00:23:46,390 --> 00:23:50,510 +اتغطي حاجة عشان تحافظ عليها، ما تبردش أو ما تصيرش + +301 +00:23:50,510 --> 00:23:55,450 +حامية، ففي عند ال blanket إيش هي حامة زيادة بترده + +302 +00:23:56,250 --> 00:24:00,130 +الأرض بيجيها تبرد بزيادة؟ لأ بتغطيها ايه؟ بتدفيها + +303 +00:24:00,130 --> 00:24:07,530 +ففي عندي الأرض في thermal consistency يعني حررتها + +304 +00:24:07,530 --> 00:24:13,570 +تقريبا يعني إلى حد كبير اللي داخل عليها كمية + +305 +00:24:13,570 --> 00:24:17,870 +الحرارة اللي ساقطة على الأرض تساوي كمية الحرارة + +306 +00:24:17,870 --> 00:24:21,650 +اللي خارجة من الأرض و بالتالي في عندي thermal + +307 +00:24:21,650 --> 00:24:26,670 +equilibrium او thermal consistencyفهذه اللي + +308 +00:24:26,670 --> 00:24:30,150 +بنقولها ظهرت الـ greenhouse effect يعني في عندي + +309 +00:24:30,150 --> 00:24:36,370 +غطاء من هذه الغازات هنفرجيكم كيف بتحافظ على حرارة + +310 +00:24:36,370 --> 00:24:39,690 +الأرض يعني هنفرجيكم بعد شوية ففي عندي غطاء هذا + +311 +00:24:39,690 --> 00:24:49,450 +الغطاء بيخلي معدل استقبال الأرض للطاقة أو للحرارة + +312 +00:24:49,450 --> 00:24:54,900 +بساوي معدل فقدان الأرضللطاقة و هذا ما اقوله الـ + +313 +00:24:54,900 --> 00:25:00,340 +Thermal Equilibrium او الـ Thermal Consistency ال + +314 +00:25:00,340 --> 00:25:07,000 +Solar Energy من الشمس طبعا بتسقط على الأرض لما + +315 +00:25:07,000 --> 00:25:10,660 +تسقط على الأرض ممكن و الله تواجه قيوم بتنعكس مش + +316 +00:25:10,660 --> 00:25:14,040 +مشكلة جزء منها لكن الجزء اللي بوصل الأرض بوصل + +317 +00:25:14,040 --> 00:25:23,440 +الأرض برضه كمان بينعكس لو انه مافيش اي غطاءلو فيش + +318 +00:25:23,440 --> 00:25:28,780 +اي غطاء كان مثلا يعني في الشتاء او في الليل الأرض + +319 +00:25:28,780 --> 00:25:33,340 +بتصير باردة جدا جدا لأنه فيش ايه؟ في الشمس فتصير + +320 +00:25:33,340 --> 00:25:36,480 +باردة خالص هي بقى تفقد طاقة بس و الطاقة على طول + +321 +00:25:36,480 --> 00:25:41,080 +بتطلع لأنه برد وبالتالي الأرض بتتلج لكن لأ اللي + +322 +00:25:41,080 --> 00:25:42,140 +بحصل مش هيك + +323 +00:25:45,310 --> 00:25:48,970 +بنقول إنه اللي بيحصل إنه في عندى هذه ال blanket + +324 +00:25:48,970 --> 00:25:52,970 +اللي عبارة عن مجموعة من الغازات اللي موجودة بكميات + +325 +00:25:52,970 --> 00:25:57,870 +بسيطة زي ما شوفنا مش موجودة بكميات كبيرة خالص فبدى + +326 +00:25:57,870 --> 00:26:01,630 +أشوف الآن إيش علاقة ل greenhouse effect وجود هذه + +327 +00:26:01,630 --> 00:26:06,920 +ال blanketبشغلة بنقولها global warming اللى برضه + +328 +00:26:06,920 --> 00:26:11,740 +بنسمع عنها اللى هو ايه ال .. الانحباس الحرارى او + +329 +00:26:11,740 --> 00:26:14,560 +الاحتباس الحرارى اللى القرض والله حررتها عن مال + +330 +00:26:14,560 --> 00:26:19,520 +اشمالها بتزيد و تشوف ليش بتزيد و كيف بتزيد فبنقول + +331 +00:26:19,520 --> 00:26:22,740 +ان + +332 +00:26:22,740 --> 00:26:27,460 +وجود ال atmosphere مش بس بيقينة من ال harmful + +333 +00:26:27,460 --> 00:26:30,780 +radiation لأ كمان + +334 +00:26:32,290 --> 00:26:36,410 +بيخلّي ال climate على وجه الأرض، الجو على وجه + +335 +00:26:36,410 --> 00:26:41,190 +الأرض، المناخ على وجه الأرض، له temperature range + +336 +00:26:41,190 --> 00:26:45,690 +معقول، يعني هذا ال atmosphere اللي حوالينا، اللي + +337 +00:26:45,690 --> 00:26:50,650 +أنا بعتبر انه ال greenhouse effect جزء منه، مش + +338 +00:26:50,650 --> 00:26:53,930 +كله، جزء منه، ال greenhouse effect جزء من ال + +339 +00:26:53,930 --> 00:26:59,690 +atmosphere، فال atmosphere نعم بمنع الأشعة الضارة + +340 +00:26:59,690 --> 00:27:03,870 +انها توصلنالكن الـ greenhouse effect هي موجودة في + +341 +00:27:03,870 --> 00:27:12,330 +التروبوسفيركويس هذه خليني اقول بتخلي درجة حرارة + +342 +00:27:12,330 --> 00:27:17,990 +الأرض درجة حرارة معقولة ففي فائدتين مهمات من ال + +343 +00:27:17,990 --> 00:27:22,030 +атмосفير اللي بنقول green house effect جزء منه + +344 +00:27:22,030 --> 00:27:25,450 +علشان هيك بنقول الأرض is said to be in thermal + +345 +00:27:25,450 --> 00:27:29,270 +balance بمعنى ان كمية الطاقة اللي وصلها زي كمية + +346 +00:27:29,270 --> 00:27:32,330 +الطاقة اللي بتفقدها فهي in thermal balance with + +347 +00:27:32,330 --> 00:27:36,460 +the universe ال universe بيعطيها طاقةماشي هي بتعطي + +348 +00:27:36,460 --> 00:27:39,780 +ال universe طاقة هدول الطاقتين اللي داخلة و + +349 +00:27:39,780 --> 00:27:43,880 +الخارجة متساويت ففي عند ايه thermal balance او + +350 +00:27:43,880 --> 00:27:44,320 +equilibrium + +351 +00:27:47,180 --> 00:27:54,720 +طيب ال .. اهم .. اهم ال greenhouse gases هم ال CO2 + +352 +00:27:54,720 --> 00:27:58,500 +و ال H2O فيه gases تانية اه شفناها و هنشوفها بعد + +353 +00:27:58,500 --> 00:28:04,800 +شوية بس أهمهم ال CO2 و ال H2O ليه؟ بشكل أساسي لأن + +354 +00:28:04,800 --> 00:28:10,320 +امتصاصهم ل ال infrared اللي هي بتاعة الحرارة يعني + +355 +00:28:10,840 --> 00:28:15,720 +الطاقة اللى بتعطى الحرارة للأرض أو بترقل الحرارة + +356 +00:28:15,720 --> 00:28:21,080 +امتصاصهم ممتاز امتصاصهم في ال infrared ممتاز + +357 +00:28:25,780 --> 00:28:29,700 +الماية الـ water vapor طبعا بيشارك مشاركة فعالة + +358 +00:28:29,700 --> 00:28:33,120 +جدا يمكن يكون أكتر من غيره، ليه؟ لأن كميته بالقرب + +359 +00:28:33,120 --> 00:28:39,480 +من سطح الأرض عالية، في عندي تبخر بخار مياه من + +360 +00:28:39,480 --> 00:28:44,160 +المحيطات اللي بتشكل حوالي أكتر من 97% من مساحة + +361 +00:28:44,160 --> 00:28:49,330 +الأرضمن .. اعفوا من الميه يعنى .. سبعة أصول في + +362 +00:28:49,330 --> 00:28:53,090 +الميه من الميه الموجودة ففي عندي تبخر من المحيطات + +363 +00:28:53,090 --> 00:28:56,630 +و البحار و الأنهار و أيضا من ال respiration من ال + +364 +00:28:56,630 --> 00:29:02,370 +.. من خليني أقول البشر و ال respiration من + +365 +00:29:02,370 --> 00:29:07,650 +النباتات فكلها بتطلع بخار ميه فبخار الميه يعتبر + +366 +00:29:07,650 --> 00:29:10,930 +يعني من أهم ال .. + +367 +00:29:14,570 --> 00:29:20,550 +لأن انتاجه بالقرب من سطح الأرض يعتبر كبير للغاية، + +368 +00:29:20,550 --> 00:29:26,220 +لكن المشكلة في الـ CO2ما احنا قولنا الـCO2 والمية + +369 +00:29:26,220 --> 00:29:31,240 +أهم نازين المية صح كتيرة ومتوفرة و بالذات + +370 +00:29:31,240 --> 00:29:34,500 +بالقرمصات الأرض وهذا ايش احنا ماتتحكمش فيه؟ + +371 +00:29:34,500 --> 00:29:38,080 +ماتقولش لالمحيط والله لأ ماتتبخرش تعطيليش بخار مية + +372 +00:29:38,080 --> 00:29:41,720 +جلل بخار المية تبعك لأنه عمللي مشكلة نقدرش نعمل + +373 +00:29:41,720 --> 00:29:46,540 +هذا الكلام هذا ايش طبيعي لكن الـCO2 الـCO2 احنا + +374 +00:29:46,540 --> 00:29:51,070 +بننتجه بكميات فظيعة جدا وهذا human activityإنتاج + +375 +00:29:51,070 --> 00:29:55,350 +الـCO2 هو عبارة عن human activity يعني عندنا + +376 +00:29:55,350 --> 00:30:01,310 +المصانع كلها، بتلاحظ، المداخن، هاي مثلا، طلعوا، + +377 +00:30:01,310 --> 00:30:05,470 +بلد زي هذه، حرام، بلد زي هذه، طلعوا، يعني حاجة + +378 +00:30:05,470 --> 00:30:08,690 +مرتبة، حاجة جميلة جدا، الصورة جميلة جدا، الصورة + +379 +00:30:08,690 --> 00:30:11,750 +جميلة جدا، تصوروا إنه هيك، يعني هذه المداخن كلها + +380 +00:30:11,750 --> 00:30:15,930 +في البلد، إيش بتعمل؟ هذه الدخان كله CO2، أغلب + +381 +00:30:15,930 --> 00:30:20,030 +الـCO2 تسعة .. تسعين .. تسعة وتسعين في المية CO2طب + +382 +00:30:20,030 --> 00:30:23,030 +وين هذا بيروحوا؟ كل بلاد زي هيك، حتى عندنا في غزة، + +383 +00:30:23,030 --> 00:30:26,870 +نفس الكلام، كل مداخن السيارات والموتير وشركة + +384 +00:30:26,870 --> 00:30:31,370 +الكهربا وخلافه، كلها CO2 عمال بيطلع، ملايين + +385 +00:30:31,370 --> 00:30:38,320 +الأقنان بتطلع يوميا CO2، طيب هذه وين بتروح؟بتروح + +386 +00:30:38,320 --> 00:30:43,540 +في الجو الخارجي طب حلو كتير بس اشي بسيط بقول ال + +387 +00:30:43,540 --> 00:30:47,060 +greenhouse gases هاي مثلا ال carbon dioxide المثين + +388 +00:30:47,060 --> 00:30:50,380 +الأوزون طبعا الأوزون مش موجود بكميات في + +389 +00:30:50,380 --> 00:30:54,500 +الأتروبوسفير وبالمناسبة الأوزون في الأتروبوسفير أو + +390 +00:30:54,500 --> 00:30:59,080 +في الجو العادي ضار لكن في الأعالي كويس لأن الأوزون + +391 +00:30:59,080 --> 00:31:03,500 +لو استنشقناه pollutant لو استنشقناه ممنوع نستنشقه + +392 +00:31:04,060 --> 00:31:08,740 +دهر .. هنشوف انه بنعمل فيه disinfection للميه .. + +393 +00:31:08,740 --> 00:31:12,980 +اه في الميه مش مشكلة .. لكن تنفسه لأ .. كتنفس لأ + +394 +00:31:12,980 --> 00:31:17,100 +.. لكن في ال .. في ال stratosphere اه مهم جدا لأنه + +395 +00:31:17,100 --> 00:31:22,540 +بياخد ال UV radiation من 240 ل 810 فهو كويس هو .. + +396 +00:31:22,540 --> 00:31:25,980 +لكن تحت لأ .. لأنه اعتبر من ضمن ال .. هو موجود + +397 +00:31:25,980 --> 00:31:29,990 +بكميات قليلة في ال troposphere يعنيالميه طبعاً و + +398 +00:31:29,990 --> 00:31:35,750 +الـ nitrous oxide هذه أهم .. هذه أهم ال إيه؟ أهم + +399 +00:31:35,750 --> 00:31:40,450 +لـ greenhouse gases، لكن على رأسها بيجي الـ CO2 + +400 +00:31:40,450 --> 00:31:46,700 +والميه، على رأسهاطيب فال .. لو قلنا هذا ال + +401 +00:31:46,700 --> 00:31:50,780 +spectrum ال IR spectrum بنلاحظ إنه الميه بتمتص في + +402 +00:31:50,780 --> 00:31:53,520 +هذا الجزء ال CO2 بمتص في هذا الجزء و الميه بتمتص + +403 +00:31:53,520 --> 00:31:57,260 +في هذه الأجزاء ال CO2 بمتص يعني تقريبا كل المنطق + +404 +00:31:57,260 --> 00:32:01,620 +هذه فيه أهم المنطق هذه فيها انت متصلا إيه لل IR من + +405 +00:32:01,620 --> 00:32:07,230 +ال CO2 و ال H2O تمام؟يعني إذا كنا نقول إن هذا هو + +406 +00:32:07,230 --> 00:32:10,190 +الـ spectrum فهي امتصاد الـ CO2 في هذا الـ range + +407 +00:32:10,190 --> 00:32:14,570 +الـ H2O في هذا الـ range الـ CO2 في هذا الـ range + +408 +00:32:14,570 --> 00:32:18,150 +الميّه في هذا الـ range الـ CO2 في هذه الـ ranges + +409 +00:32:18,150 --> 00:32:23,270 +طبعاً الميثان و غيره بمتص برضه في أماكن أخرى تمام؟ + +410 +00:32:23,270 --> 00:32:27,690 +لكن المهم إن الـ CO2 و الـ H2O بمتصوا الـ IR رديشن + +411 +00:32:27,690 --> 00:32:32,210 +بشكل ممتاز طب نذكر هذه الحقيقة + +412 +00:32:34,610 --> 00:32:40,570 +بنقول طب تعالى نتطلع على الـ CO2 ومدى خلّيني أقول + +413 +00:32:40,570 --> 00:32:45,530 +تكوّنه أو تركيزه في الهواء في السنوات الأخيرة من + +414 +00:32:45,530 --> 00:32:52,450 +1969 ل 2010 في 1960 كان أقل من 320 PPM طبعا لما + +415 +00:32:52,450 --> 00:32:57,850 +اتكلم عن الكون ككل هذه تعتبر يعني فروقات فظيعة أقل + +416 +00:32:57,850 --> 00:33:03,700 +من 320 PPM طب في 2010صار اكتر من تلاتمية وتسعين + +417 +00:33:03,700 --> 00:33:07,660 +PPM زاد + +418 +00:33:07,660 --> 00:33:13,960 +بشكل كبير زاد حوالي سبعين PPM خلال خمسين سنةزاد + +419 +00:33:13,960 --> 00:33:17,740 +حوالي سبعين PPM خلال خمسين سنة، إيش بعمل هذا + +420 +00:33:17,740 --> 00:33:21,660 +الكلام؟ إيش بعمل هذا الكلام؟ شوفوا عادة أو قديما + +421 +00:33:21,660 --> 00:33:26,020 +كيف كان، هاي الأرض وهي الأطرقو، ال sphere تبعنا، + +422 +00:33:26,020 --> 00:33:30,040 +ال atmosphere تبع الأرض، وهي عندي في آخره إيش فيه + +423 +00:33:30,040 --> 00:33:32,700 +عندي؟ طبعا في البداية اللي هو الغازات العادية اللي + +424 +00:33:32,700 --> 00:33:38,620 +إحنا بنتنفسها، ال CO2 اللي بطلع على فوق، فعندي + +425 +00:33:38,620 --> 00:33:43,040 +hand ل greenhouse gasesتصوروا عامة زي blanket زي + +426 +00:33:43,040 --> 00:33:49,320 +غطاء لكن هذا الغطاء شوفوا جديش ثمكه تمام؟ الآن ال + +427 +00:33:49,320 --> 00:33:54,860 +radiation اللي جاء من الشمس تسقط على الأرض طبعا ال + +428 +00:33:54,860 --> 00:33:59,040 +.. تسقط على الأرض بتنعكس جزء منها، بينعكس ايش + +429 +00:33:59,040 --> 00:34:06,780 +بيلاقي؟ بيلاقي الغازات هذه ففي حاجتين بيحصلفي عندى + +430 +00:34:06,780 --> 00:34:10,020 +الغازات اللى بتمطص لإنها بتمطص ال IR و أنا بتتكلم + +431 +00:34:10,020 --> 00:34:14,300 +عن ال IR تمطص ال IR فهى نفسها اللى بتاخد طاقة كويس + +432 +00:34:14,300 --> 00:34:19,220 +بعدين بتعمل re emission بتودد طاقة على الأرض لكن + +433 +00:34:19,220 --> 00:34:25,000 +جزء من هذا الطاقة بيطلعmore heat into space بيطلع + +434 +00:34:25,000 --> 00:34:30,680 +من خلال ال greenhouse gases، ليه؟ لأنه يعني ال CO2 + +435 +00:34:30,680 --> 00:34:34,460 +والماء مابتمطسش كل شيء أو ال greenhouse gases + +436 +00:34:34,460 --> 00:34:38,520 +تمطسش كل شيء، لأ تمطس كمية، لكن طلع كمية محترمة + +437 +00:34:39,390 --> 00:34:44,090 +المهم انه اللى داخل المفروض انه في النهاية فيه + +438 +00:34:44,090 --> 00:34:46,970 +عندى thermal equilibrium يعني اللى أخدته الأرض + +439 +00:34:46,970 --> 00:34:51,610 +بالظبط زى اللى أعطته بالظبط طيب، الآن إيش بحصل + +440 +00:34:51,610 --> 00:34:56,550 +نتيجة تراكم الـCO2؟ لأن احنا عمال بنضخ CO2، كل + +441 +00:34:56,550 --> 00:35:01,070 +مصانع العالم بندخ ملايين أطنان الـCO2 يوميا، إيش + +442 +00:35:01,070 --> 00:35:06,350 +بحصل؟ جال هذا الطبقة عمال إيه؟ شمالها؟هذه الطبقة + +443 +00:35:06,350 --> 00:35:11,910 +بتتسع، ال thickness بتزيد بشكل كبير، اذا هاي الشمس + +444 +00:35:11,910 --> 00:35:18,530 +دخلت والله طاقة + +445 +00:35:18,530 --> 00:35:25,190 +solar radiation، الآن في عندى انعكاس، انعكستحلو + +446 +00:35:25,190 --> 00:35:30,610 +كتير، طب re-emitted تاني للأرض، طب إيش كمية اللي + +447 +00:35:30,610 --> 00:35:36,690 +طالع؟ بيقدرش يخترق كل هذا الاتساع و يطلع برا، كمية + +448 +00:35:36,690 --> 00:35:40,150 +طالعة قليلة كتير، إذا عماد الحرارة إيش بتسوي؟ + +449 +00:35:40,150 --> 00:35:45,750 +بتتراكم في جو الأرضاللي بتعطيه الأرض أقل من اللي + +450 +00:35:45,750 --> 00:35:48,610 +بتاخده، اللي بتاخده أكتر، يبقى عمال إيش الحرارة دا + +451 +00:35:48,610 --> 00:35:52,710 +أقصى؟ لا، تبتتراكم في الأرض، مع أن هالكلام، بنتوقع + +452 +00:35:52,710 --> 00:35:56,950 +أن حرارة الأرض ترتفع وهذا طبعاً له ناكسات مهمة، + +453 +00:35:56,950 --> 00:36:00,470 +لأنه في عندي زي ما هنشوف water balance، في عندي + +454 +00:36:00,470 --> 00:36:05,330 +جزء من المي على هيئة مية، في جزء بحار ومحيطات، في + +455 +00:36:05,330 --> 00:36:10,770 +جزء مية على هيئة snow و ice، فهذه إيش بده يجرالها؟ + +456 +00:36:10,770 --> 00:36:15,420 +هذه ال snow و ال ice بده يدوبسكان داب الميه حجمها + +457 +00:36:15,420 --> 00:36:22,320 +هيزيد لأنه جبال فظيعة يعني مناطق يعني شاسعة جدا + +458 +00:36:22,320 --> 00:36:28,440 +كلها عبارة عن snow فوق الجبال وغيره مش يعني على + +459 +00:36:28,440 --> 00:36:33,220 +الأرض وكذا فلما نهدد دوب كلها راح تعمل imbalance + +460 +00:36:33,220 --> 00:36:37,520 +في تواجد الميه على سطح الأرض ماعلينا احنا اللي + +461 +00:36:37,520 --> 00:36:40,860 +بيهمنا هنا ان نتيجة ال human activities اللي هي + +462 +00:36:40,860 --> 00:36:47,170 +إنتاج كمياتها إلى منكل .. مش بس الـCO2، كل + +463 +00:36:47,170 --> 00:36:50,310 +greenhouse effect وعلى رأسها الـCO2 .. كل + +464 +00:36:50,310 --> 00:36:53,990 +greenhouse gases وعلى رأسها الـCO2 بنلاحظ أنه ال + +465 +00:36:53,990 --> 00:37:00,990 +blanket لل greenhouse phenomena أو effect بتتسع، + +466 +00:37:00,990 --> 00:37:08,490 +معنى إنها بتتسع معناته صارت حرارة الأرضأو زادت عن + +467 +00:37:08,490 --> 00:37:13,670 +اللازم و هتزيد باستمرار كل ما تسعت هذه الطبقة أو + +468 +00:37:13,670 --> 00:37:18,810 +هذه ال blanket وهذه اللي بنقولها ال global warming + +469 +00:37:18,810 --> 00:37:24,110 +هذا هو السبب الرئيسي لل global warmingفيما يتعلق + +470 +00:37:24,110 --> 00:37:28,470 +بالـ greenhouse gases تحديدًا في الولايات المتحدة + +471 +00:37:28,470 --> 00:37:33,090 +سنة 2014 بيعملوا دائمًا يعني إحصاءات فال carbon + +472 +00:37:33,090 --> 00:37:37,590 +dioxide كان بشكل 81% من هذه الغازات اللي اللي + +473 +00:37:37,590 --> 00:37:40,690 +بيحصلها Emission فقط في الولايات المتحدة الأمريكية + +474 +00:37:41,250 --> 00:37:47,430 +الميثان 11% النايتس أكسيد 6% والجازات الفلورينية + +475 +00:37:47,430 --> 00:37:56,130 +حوالي 3% طبعا هذه كلها من الجازات الجزائية اللي + +476 +00:37:56,130 --> 00:37:59,790 +طبعا تراكمها بيؤدي لجلوبال وارمينج ويمكن انتوا + +477 +00:37:59,790 --> 00:38:04,390 +بتسمعوا ان دول كتير صارت حاليا منتبهة لهذا الأمر + +478 +00:38:04,390 --> 00:38:07,770 +وصاروا يحاولوا انهم يعني يقننوا + +479 +00:38:11,170 --> 00:38:19,110 +كميات الـ CO2 اللي يعني ممكن انه اي دولة يعني + +480 +00:38:19,110 --> 00:38:22,430 +مسبوح لها انه تطلعها في الهواء الجو لكن هذا كلام + +481 +00:38:22,430 --> 00:38:27,110 +بعيد عن التطبيق لأن العالم ككل هو عالم مادي يعني + +482 +00:38:27,110 --> 00:38:34,030 +في النهاية بتهمه مصلحته و بتهمه جداش هو يعني اقول + +483 +00:38:34,030 --> 00:38:42,770 +ينتج خليني اقولمواد و يبيعها و يحصل على أرباح و + +484 +00:38:42,770 --> 00:38:48,430 +يرفع الشعب تبعه و يخل في عنده داخل كويس فبعتقد ان + +485 +00:38:48,430 --> 00:38:53,710 +انتاج ال CO2 راح يستمر في يعني على الأقل يعني و + +486 +00:38:53,710 --> 00:38:57,720 +بأو الحال يعنيوبالتالي متوقع ان ال global warming + +487 +00:38:57,720 --> 00:39:04,420 +يزيد بشكل كبير من الناحية خليني اقول النظرية لكن + +488 +00:39:04,420 --> 00:39:11,600 +عمليا يعني قد يكون في يعني في الكون ميكانيزمات انه + +489 +00:39:11,600 --> 00:39:15,440 +يعني تعمل نوع من ال balance ماعرفش يعني بس .. بس + +490 +00:39:15,440 --> 00:39:19,040 +من ناحية نظرية نعم راح يتراكم ال CO2 والحرارة لا + +491 +00:39:19,040 --> 00:39:22,740 +شك انها راح تزيد وراح نلاجي تقلبات مناخية فظيعة + +492 +00:39:23,310 --> 00:39:29,250 +نتيجة ال global warming لكن هل في في الكون يعني + +493 +00:39:29,250 --> 00:39:34,330 +أشياء مضادة عند حد معين مثلا انه مازدش عنه سيبنعمل + +494 +00:39:34,330 --> 00:39:37,470 +ال equilibrium في حاجة تانية هذا كلام لسه ماحدش + +495 +00:39:37,470 --> 00:39:44,750 +بيعرفه طيب الآن ننتقل من الغازات و من ال + +496 +00:39:44,750 --> 00:39:46,490 +atmosphere بشكل عام للميه + +497 +00:39:49,670 --> 00:39:55,710 +بنقول المياه طبعا يعني بتشكل حوالي 72% من الارض + +498 +00:39:55,710 --> 00:40:05,910 +يعني سطح الأرض 72% منه مياه و 28% يابسة كويس كل + +499 +00:40:05,910 --> 00:40:11,030 +المياه عادة مرتبطة بما يسمى global water cycle + +500 +00:40:11,030 --> 00:40:18,220 +دورة المياه العالمية أو globalكويس فكلها مرتبطة مع + +501 +00:40:18,220 --> 00:40:23,520 +بعض يعني بمعنى أخر في عند نوع من ال circulation + +502 +00:40:23,520 --> 00:40:28,500 +للميه من شكل لشكل أخر، من مكان لمكان أخر فهذا كلام + +503 +00:40:28,500 --> 00:40:32,820 +كله مرتبط في بعضه مهما كانت الميه أينما كانت، + +504 +00:40:32,820 --> 00:40:38,410 +كيفما كانتفالميه الوضع الطبيعي لما اتكلم عن ال + +505 +00:40:38,410 --> 00:40:42,830 +global water cycle يعني بنقول والله الميه تتبخر من + +506 +00:40:42,830 --> 00:40:47,170 +المحيطات و البحار و ال rivers و ال lakes و ال + +507 +00:40:47,170 --> 00:40:51,350 +streams و وين فيه ميه فيه عنده تبخرthus converted + +508 +00:40:51,350 --> 00:40:54,950 +to vapor و ال water vapors accumulated and come + +509 +00:40:54,950 --> 00:40:57,750 +back يعني deposit onto the surface as rain and + +510 +00:40:57,750 --> 00:41:01,310 +snow يعني في عند ميه بتتبخر و بعد ما تتبخر الميه + +511 +00:41:01,310 --> 00:41:11,010 +راح تنزل على هيئة مطر أو ثلج يعني snow كويس في + +512 +00:41:11,010 --> 00:41:16,490 +البحار و المحيطاتعادةً الـ salinity للميّه + +513 +00:41:16,490 --> 00:41:22,470 +وبالتالي ال density بتتوقف على الدبف .. بتتوقف على + +514 +00:41:22,470 --> 00:41:28,250 +الدبف هذه معلومة ال sunlight ضوء الشمس لا يستطيع + +515 +00:41:28,250 --> 00:41:34,910 +ان يخترق في ال ocean أو في الميه لأعماق كبيرة جدا + +516 +00:41:34,910 --> 00:41:41,760 +يعني مثلا ممكن يخترق لحوالي 200 متريعني نشوف بوضوح + +517 +00:41:41,760 --> 00:41:44,740 +.. يعني يمكن حوالي 200 متر، لكن بعد هيك لما نوصل + +518 +00:41:44,740 --> 00:41:49,540 +حوالي مثلا ألف متر، راحين نلاجى البحر من تحت black + +519 +00:41:49,540 --> 00:41:53,880 +وكمان very cold، يعني حرارته حوالي أربع درجات، + +520 +00:41:53,880 --> 00:41:57,880 +cold، very cold، فهيكون black، مش هنشوف إشيو أكبر + +521 +00:41:57,880 --> 00:42:02,300 +فرصة وجدت إيه؟ لأن أشعة الشمس لا تستطيع أن تخترق + +522 +00:42:02,300 --> 00:42:07,760 +كل هذه المسافة في الميه فعند حوالي كيلو خلاص البحر + +523 +00:42:07,760 --> 00:42:11,580 +من تحت أو المحيط من تحت بيكون black و cold حوالي + +524 +00:42:11,580 --> 00:42:18,180 +أربع درجاتما يهمنا برضه هان ان ال .. ال waters في + +525 +00:42:18,180 --> 00:42:22,100 +ال seas و ال ocean absorb CO2 يعني لازم .. يعني + +526 +00:42:22,100 --> 00:42:24,980 +مادام فيه CO2 و احنا بنعرف انه لازم يكون فيه نوع + +527 +00:42:24,980 --> 00:42:29,580 +من ال equilibrium حسب Henry's law يعني في عند حسب + +528 +00:42:29,580 --> 00:42:33,280 +ضغط ال CO2 في الهواء الجوي بنلاحظ انه لازم يكون + +529 +00:42:33,280 --> 00:42:38,310 +دايم في المحلولفهو بيدوب في الميه وبالتالي يعني + +530 +00:42:38,310 --> 00:42:41,870 +مدام إذا كان زاد ال carbon dioxide فإيش بده يحصل + +531 +00:42:41,870 --> 00:42:46,190 +كمية ال carbon dioxide في الميه راح تزيد فيمكن هذا + +532 +00:42:46,190 --> 00:42:49,310 +بيعمل نوع من ال balance بس لأ balance جليل يعني مش + +533 +00:42:49,310 --> 00:42:53,690 +كافي balance جليل مش كافي ليه؟ لأنه احنا بنشهد نوع + +534 +00:42:53,690 --> 00:42:58,770 +من ال global warming فال water cycle تبعتنا هاي + +535 +00:42:58,770 --> 00:43:01,090 +والله الميه من بحار ومحيطات + +536 +00:43:05,720 --> 00:43:11,580 +و أيضا الميه بتطلع من ال respiration للنباتات + +537 +00:43:11,580 --> 00:43:15,960 +المختلفة فبيطلع عند بخار ميه و طبعا بخار الميه + +538 +00:43:15,960 --> 00:43:22,100 +بيصير clouds و ال clouds بترتفع ارتفع اكتر و + +539 +00:43:22,100 --> 00:43:25,220 +بتنتقل لاماكن اخرى و بعدين بحصل عندى precipitation + +540 +00:43:25,220 --> 00:43:30,860 +بتنزل او deposition بتنزل هذه الامطار او ال water + +541 +00:43:30,860 --> 00:43:37,040 +vapor بينزل على هيئة امطار او snowو جزء منه طبعا + +542 +00:43:37,040 --> 00:43:40,900 +ينزل و ينزل تاني على المحيطات و البحار و طبعا جزء + +543 +00:43:40,900 --> 00:43:44,440 +تاني منه بيروح على ال ground water ال ground water + +544 +00:43:44,440 --> 00:43:47,560 +هي المياه اللى بنعتبرها نوع من ال freshwater ال + +545 +00:43:47,560 --> 00:43:56,000 +ground water هي عبارة عن مياه مجزونة داخل الطبقات + +546 +00:43:56,000 --> 00:43:59,300 +من الأرض طبقات مسامية من الأرض + +547 +00:44:02,240 --> 00:44:05,900 +ال salt water طبعا موجودة عادة في ال oceans و ال + +548 +00:44:05,900 --> 00:44:10,620 +seas موجودة في ال oceans و ال seas و يمكن + +549 +00:44:15,450 --> 00:44:18,970 +يمكن بعض الناس اللي هم يعني oceanographers + +550 +00:44:18,970 --> 00:44:21,370 +بنسميهم، الناس اللي بيشتغلوا في علوم المحيطات + +551 +00:44:21,370 --> 00:44:26,150 +كويس، بيعتبروا أن المحيطات هذه مش محيطات، بيعتبرها + +552 +00:44:26,150 --> 00:44:29,050 +كلها محيط واحد، يعني عشان كما اتكلم عنها، بيتكلم + +553 +00:44:29,050 --> 00:44:32,310 +عن ocean مش oceans، احنا بنعرف المحيط الهادي و + +554 +00:44:32,310 --> 00:44:35,960 +الهندي و الاطلاندي و الاطلسي و غيرهلكن لأ هم لما + +555 +00:44:35,960 --> 00:44:39,520 +اتكلموا عن المحيطات لما اتكلموا عن محيط واحد وكأنه + +556 +00:44:39,520 --> 00:44:44,040 +كل المحيطات هذه عبارة عن محيط واحد الميه في + +557 +00:44:44,040 --> 00:44:49,180 +المحيطات هذه و البحر حوالي 97.2% من ال earth water + +558 +00:44:49,180 --> 00:44:54,200 +يعني كل خرش water تبعتنا حوالي 82 من 10 فالكم هذه + +559 +00:44:54,200 --> 00:45:00,180 +من الميه موجودة وين؟موجودة في البحار والمحيطات + +560 +00:45:00,180 --> 00:45:03,900 +عشان هيك إذا كان الميه اللي عندنا جلت مافيش قدامنا + +561 +00:45:03,900 --> 00:45:07,640 +إلا أن نروح للمحيطات و البحار عشان ناخد الميه منها + +562 +00:45:07,640 --> 00:45:11,800 +لكن للأسف البحار و المحيطات الميه تبعتها مالحة و + +563 +00:45:11,800 --> 00:45:15,360 +مالحة ملوحة يعني شديدة زي ما هنشوف فهذا بيشكل + +564 +00:45:15,360 --> 00:45:18,740 +عندنا مشكلة كبيرة جدا لأن تقريبا ال salinity لل + +565 +00:45:18,740 --> 00:45:23,170 +sea water خمسة و تلاتين جرام ملحفي كل كيلو جرام، + +566 +00:45:23,170 --> 00:45:26,290 +خمسة وتلاتين جرام، ملح في كل كيلو جرام، كل كيلو + +567 +00:45:26,290 --> 00:45:29,110 +موجود في خمسة وتلاتين جرام، كمية هائلة جدا، إيش + +568 +00:45:29,110 --> 00:45:32,710 +يطلع هذه الخمسة وتلاتين جرام؟ كمية هائلة جدا جدا، + +569 +00:45:32,710 --> 00:45:36,170 +يعني المسموح فيه أقل من خمسمية PPM، نص جرام + +570 +00:45:38,780 --> 00:45:43,300 +فهذه خمسة و ثلاثين جرام يعتبر كثير كثير من أهم ال + +571 +00:45:43,300 --> 00:45:47,080 +ions اللي موجودة في البحار اللي هو ال chloride وال + +572 +00:45:47,080 --> 00:45:49,720 +sodium طبعا كلنا بنعرف انه الملح هو ال sodium و ال + +573 +00:45:49,720 --> 00:45:51,540 +chloride أغلب ميط الملح هو ال sodium و ال chloride + +574 +00:45:51,540 --> 00:45:58,340 +فلاحظوا ال concentration خليني أقول هذه من الجرام + +575 +00:45:58,340 --> 00:46:01,280 +لو قلنا من الجرام تستخدم عشرة جرام عشر جرام و نص + +576 +00:46:01,280 --> 00:46:05,780 +اتنين جرام و ستة من عشرة صلفيتمجنيزيوم اجرام وخمس + +577 +00:46:05,780 --> 00:46:09,580 +وثلاثين من مائة هذا في كل ايه في كل لتر فكميات + +578 +00:46:09,580 --> 00:46:13,940 +هائلة جدا بس لحظة دولالصوديوم الكلوريد حوالي + +579 +00:46:13,940 --> 00:46:17,860 +تلاتين لحاله تقريبا تلاتين جرام صوديوم الكلوريد + +580 +00:46:17,860 --> 00:46:22,000 +لحاله بس تلاتين جرام في كل لتر فكمية مهولة للغاية + +581 +00:46:22,000 --> 00:46:26,420 +طبعا في كالسيوم بوتاسيوم كربونات بروميد بوريت + +582 +00:46:26,420 --> 00:46:30,240 +سيليكيت استرانشام وفلوريد طب في حاجات تانية لكن + +583 +00:46:30,240 --> 00:46:35,640 +اقل من واحد PPM ماجبتاش في الجدول يعني بس هان + +584 +00:46:35,640 --> 00:46:39,100 +الجدول للي اكتر من واحد PPM + +585 +00:46:46,410 --> 00:46:52,450 +فكمية المذاب من الايونات يعتبر كمية كبيرة جدا، مش + +586 +00:46:52,450 --> 00:46:57,750 +كل البحار والمحيطات لها نفس التركيب بالظبط، لأ، + +587 +00:46:57,750 --> 00:47:00,490 +بنلاحظ في اختلاف هائل جدا، طبعا عندنا في فلسطين + +588 +00:47:00,490 --> 00:47:04,530 +يعني البحر الميت أكبر مثال، لأن كمية الأملح اللي + +589 +00:47:04,530 --> 00:47:09,620 +فيه عالية مش كتبه دهانيعني ماوجدتش مصدر منيح يعني + +590 +00:47:09,620 --> 00:47:15,380 +اللي اقدر اقارنه، لكن مثلا الشرق + +591 +00:47:15,380 --> 00:47:19,120 +المتوسط يعني احنا يعني على سبيل المثال ال chloride + +592 +00:47:19,120 --> 00:47:25,940 +واحد وعشرين جرام كويس، احداشر وتمانية الصوديوم، + +593 +00:47:25,940 --> 00:47:27,520 +الصلفيت كتير + +594 +00:47:40,930 --> 00:47:44,870 +الخليجي العربي مثلا هادى من مش واحد و عشرين لأ + +595 +00:47:44,870 --> 00:47:49,070 +تلاتة و عشرين مش احد عاشر خمس عشر او ست عشر تقريبا + +596 +00:47:49,610 --> 00:47:54,650 +هذه قريبة تلاتة و اتنين من عشرة و واحد و سبعة من + +597 +00:47:54,650 --> 00:47:59,690 +عشرة كتير شوية المجنيزيا متقاربات ال red sea + +598 +00:47:59,690 --> 00:48:05,390 +متوسطة اتنين و عشرين اربعتاش تلاتة point seven + +599 +00:48:05,390 --> 00:48:09,030 +point two الاخرين فبنلاحظ ان مش كل البحار مش كل + +600 +00:48:09,030 --> 00:48:14,560 +المحيطات لهمنفس التركيب من الأيونات، لأ في عندنا + +601 +00:48:14,560 --> 00:48:19,100 +اختلافات و ممكن الاختلافات تكون كبيرة و حتى لما + +602 +00:48:19,100 --> 00:48:23,660 +نيجي لبحار مثلا أصغر في بعض الأحيان ممكن نلاقي + +603 +00:48:23,660 --> 00:48:27,860 +الاختلافات بتصير كبيرة جدا، ليه؟ لأن كمية المتبخر + +604 +00:48:27,860 --> 00:48:33,280 +له أثر كبير على كمية المتبقيفبالتالي المتبقى حسب + +605 +00:48:33,280 --> 00:48:37,120 +نوعية الصقور اللى موجودة تحته و اللى بتأثر على + +606 +00:48:37,120 --> 00:48:41,560 +كمية الأيونات فممكن كمية الأيونات تتغير تغير كبير + +607 +00:48:41,560 --> 00:48:45,920 +فيها فانا احنا مابنحكيش كتير عن ال oceans و البحار + +608 +00:48:45,920 --> 00:48:48,920 +يعني مش قضيتنا اللى بيهمنا اكتر اللى هو ال + +609 +00:48:48,920 --> 00:48:51,960 +freshwater و ال groundwaterالـ fresh water اللي هي + +610 +00:48:51,960 --> 00:48:54,880 +ال ground water جزء من ال fresh water بتقول احنا + +611 +00:48:54,880 --> 00:49:00,460 +ال fresh water هو term بنعبر عنه عن ال natural + +612 +00:49:00,460 --> 00:49:03,040 +water اللي لها low concentration of dissolved + +613 +00:49:03,040 --> 00:49:06,660 +solids يعني الميه اللي فيها تركيزات قليلة من ال + +614 +00:49:06,660 --> 00:49:10,320 +dissolved solids بحيث انه نقدر نشربها هاي يعني هاي + +615 +00:49:10,320 --> 00:49:19,130 +المقصد يعنيالتركيز للدزاوصل أقل من 500 PPM وهذا + +616 +00:49:19,130 --> 00:49:22,570 +النوع من ال water اللي هو ال fresh water includes + +617 +00:49:22,570 --> 00:49:26,770 +ال rivers و ال lakes و ال streams و ال stream + +618 +00:49:26,770 --> 00:49:29,410 +waters and the like بما فيها ال ground water + +619 +00:49:32,070 --> 00:49:35,770 +كمية الـ freshwater على الأرض كمية متواضعة جدا + +620 +00:49:35,770 --> 00:49:41,790 +شفنا انه 97.2 من الميه كلها مالحة فكمية ال + +621 +00:49:41,790 --> 00:49:46,390 +freshwater كمية ضئيلة جدا كلها الأنهار والبحيرات + +622 +00:49:46,390 --> 00:49:51,270 +وكذا تعتبر كمية لا تكاد تذكر بجانبالـ Oceans والـ + +623 +00:49:51,270 --> 00:49:55,990 +Seas أو المي المالحة، فهي تعتبر كمية قليلة للغاية، + +624 +00:49:55,990 --> 00:49:59,850 +حوالي عشرين في المية من الـ freshwater موجودة على + +625 +00:49:59,850 --> 00:50:02,290 +هيئة الـ underground water، طبعا في غزة احنا مش + +626 +00:50:02,290 --> 00:50:04,750 +عيننا انهار، مش عيننا انهار underground water وميط + +627 +00:50:04,750 --> 00:50:08,100 +المطرUnderground و الـ Underground طبعاً في تآكل + +628 +00:50:08,100 --> 00:50:11,160 +مستمر لأن ال population عامل بيزيد بشكل كبير + +629 +00:50:11,160 --> 00:50:15,080 +والاستخدامات بتزيد ومتطلبات الناس بتزيد يعني + +630 +00:50:15,080 --> 00:50:19,700 +..يعني زمان كان استهلاك نهر الميه أقل كتير لأنه + +631 +00:50:19,700 --> 00:50:24,420 +كان مثلا ال ..استهلاك الميّه الا استدعى ان الواحد + +632 +00:50:24,420 --> 00:50:27,960 +يروح يحمل الميّه من مكان لمكان هالجهة تلاقى بيفتح + +633 +00:50:27,960 --> 00:50:30,900 +الحنفية وكما مش بس بيفتح الحنفية بيجيب ماتور و + +634 +00:50:30,900 --> 00:50:34,140 +بيصير يشفط من البلدية كما يصير يفتح الحنفية او + +635 +00:50:34,140 --> 00:50:38,320 +عنده حتى بير ميه في جلب البيت يعني او في جلب + +636 +00:50:38,320 --> 00:50:43,160 +العمارة وبالتالي صار سهل جدا الوصول للماءفزادت + +637 +00:50:43,160 --> 00:50:46,960 +متطلبات البشر من على سبيل المثال استهلاك نظافة + +638 +00:50:46,960 --> 00:50:52,740 +شخصية، نظافة بيوت، نظافة سيارات، نظافة يعني مداخل + +639 +00:50:52,740 --> 00:50:55,880 +البيوت، حدائق في بيوت على سبيل المثال، وهذا + +640 +00:50:55,880 --> 00:51:01,200 +بيستهلك مياه كتيرة خالص و بيحط قيود فظيعة على ال + +641 +00:51:01,200 --> 00:51:02,460 +fresh water supplies + +642 +00:51:05,170 --> 00:51:09,290 +في مصطلح مهم انه نفهمه بنقول الـ groundwater وين + +643 +00:51:09,290 --> 00:51:14,790 +موجودة؟ جال موجودة في طبقات من الصخور المسامية + +644 +00:51:14,790 --> 00:51:19,030 +طبقات من الصخور المسامية layers of porous rocks + +645 +00:51:19,030 --> 00:51:22,930 +هذه ال layers من ال porous rocks اللي بتحتوي على + +646 +00:51:22,930 --> 00:51:27,270 +الميه ال fresh under ground اللي هي ال groundwater + +647 +00:51:27,270 --> 00:51:32,350 +بنقولها aquifers هذه ال layers ايش بنسميها؟ + +648 +00:51:32,350 --> 00:51:35,750 +aquifers الميه بتكون داخلهاوبتكون هذه ال aquifers + +649 +00:51:35,750 --> 00:51:39,030 +قريبة على سطح الأرض بحيث انه لو حفرنا بير على طول + +650 +00:51:39,030 --> 00:51:43,650 +باللاجة ايه؟ باللاجة مية تحت ال aquifers هذه في + +651 +00:51:43,650 --> 00:51:51,830 +عندي solid dense rocks مافيش فيها مسامات يفجأ راح + +652 +00:51:51,830 --> 00:51:54,590 +تحفظ الميه هذه اللي موجودة ايه في الصخور اللي + +653 +00:51:54,590 --> 00:51:58,410 +فوقها بحيث انه ماتنزلش تحت وبالتالي بتقعد الميه + +654 +00:51:58,410 --> 00:52:04,820 +آلاف السنينطبعا في الكتب ملايين السنين محفوظة في + +655 +00:52:04,820 --> 00:52:07,940 +ال underground تستنى لما البشر يحتجوها علشان + +656 +00:52:07,940 --> 00:52:11,820 +ياخدوها ويعملوا فيه ميه زي البترول مثلا قعدت فترات + +657 +00:52:11,820 --> 00:52:15,660 +زمنية طويلة لما الناس عرفت ان فيه petrol واستخرجته + +658 +00:52:15,660 --> 00:52:21,660 +نفس الكلام ال ground water يعني موجودة للاستخدام + +659 +00:52:21,660 --> 00:52:29,550 +لكن في بلاد زي بلادنا مثلا بعتقد انا انهيعني عامة + +660 +00:52:29,550 --> 00:52:33,770 +المياه الجوفية بتستنفد لأنه الأمطار شحيحة فبالتالي + +661 +00:52:33,770 --> 00:52:38,570 +بتقدرش تغذي دورة هذه المياه بشكل عام + +662 +00:52:44,810 --> 00:52:49,950 +النشاطات البشرية لها تأثير يعني ضار جدا على الميه + +663 +00:52:49,950 --> 00:52:54,550 +اللى موجودة فبنستخدم حاليا احنا كميات كبيرة من ال + +664 +00:52:54,550 --> 00:52:58,670 +fertilizers ليش؟ لأنه والله بدنا ننتج كميات وفيرة + +665 +00:52:58,670 --> 00:53:02,550 +بالمحاصيل لأن عرض السكان كبير مثلا يعني فبنستخدم + +666 +00:53:02,550 --> 00:53:06,670 +fertilizers صناعية بالذات كبيرة جدا .. كثيرة جدا + +667 +00:53:06,670 --> 00:53:10,650 +جدا كميات .. كميات هائلة برضه عشان نحافظ على + +668 +00:53:10,650 --> 00:53:16,960 +النباتننتج أكبر قدر من النبات الصالح للاستهلاك + +669 +00:53:16,960 --> 00:53:22,760 +نستخدم كميات وافرة من ال pesticides المبيدات + +670 +00:53:22,760 --> 00:53:26,880 +الحشرية علشان نقضى على الأمراض ايضا نستخدم + +671 +00:53:26,880 --> 00:53:34,400 +synthetic chemicals كتيرة خالص مثلا البويات وطلاء + +672 +00:53:34,400 --> 00:53:36,920 +المعادن ومش عارف يعني + +673 +00:53:40,020 --> 00:53:46,280 +الكيميا الصناعية كلها بولمرات و plastics ومخلفات + +674 +00:53:46,280 --> 00:53:52,160 +مصانع الملابس وغيرها والدباغة كميات هائلة جدا من + +675 +00:53:52,160 --> 00:53:56,000 +ال synthetic chemicals كل هذا بيأثر على ال water + +676 +00:53:56,000 --> 00:53:59,180 +quality لا شك في هذا الكلام لا شك لأن وين في + +677 +00:53:59,180 --> 00:54:01,320 +النهاية كل هذه بدها تروح؟ في المياه + +678 +00:54:05,630 --> 00:54:09,050 +هذا كلام مهم اكتر اذا ما طلعنا على الميه من ناحية + +679 +00:54:09,050 --> 00:54:12,810 +استهلاك بشري لل domestic use يعني لانه بدنا نشرب + +680 +00:54:12,810 --> 00:54:19,650 +بدنا نطبخ بدنا .. يعني استهلاك طبيعي فبدنا يعني + +681 +00:54:19,650 --> 00:54:23,530 +الميه اللى على الأقل بنستخدمها تكون safe لكن مع + +682 +00:54:23,530 --> 00:54:28,190 +استخدامنا لكل هذه الحاجات وبكميات مهولة جدا يعني + +683 +00:54:28,190 --> 00:54:35,210 +ال safety بتكون قليلةطيب هذا بشكل عام، بنقول عادة + +684 +00:54:35,210 --> 00:54:40,850 +كمان يعني الميه ال dissolved oxygen اللي فيها مهم + +685 +00:54:40,850 --> 00:54:45,130 +جدا للحياة المائية بشكل عام، ال dissolved oxygen + +686 +00:54:45,130 --> 00:54:46,610 +مهم جدا للقيا المائية + +687 +00:54:50,860 --> 00:54:54,920 +الـ Aerobic Bacteria بتستخدم الـ Dissolved Oxygen + +688 +00:54:54,920 --> 00:55:01,060 +عشان تحول أجزاء مهمة من هذه المواد إلى أجزاء أخرى + +689 +00:55:01,060 --> 00:55:06,080 +مثلًا مثلًا الكربون بتحوله لـ B-Carbonate مش ضار + +690 +00:55:06,080 --> 00:55:14,420 +ممكن تخلصه بس مش ضار الـ H2O بتحوله لميهالـ N2 + +691 +00:55:14,420 --> 00:55:19,500 +بتحويل لـ NO3 مثلا الـ Sulfur بتحويل لـ SO4 + +692 +00:55:19,500 --> 00:55:24,820 +الفسفور بتحويل لـ PO4 طيب وهذه بعضها مهم لل + +693 +00:55:24,820 --> 00:55:30,830 +aquatic lifeلكن في غياب الأكسجين، ليس عنده أكسجين، + +694 +00:55:30,830 --> 00:55:34,010 +الأوروبيك بكتيريا لا تعمل، اللي تعمل هي الأوروبيك + +695 +00:55:34,010 --> 00:55:36,950 +بكتيريا، الأوروبيك بتعمل في أيه؟ أو بتعمل + +696 +00:55:36,950 --> 00:55:41,890 +متابوليزم في غياب الأكسجين، فبنلاحظ أنه بتحول + +697 +00:55:41,890 --> 00:55:46,430 +الكربون لميثان، طب الميثان ما هو يعتبر ايه؟ يعتبر + +698 +00:55:46,430 --> 00:55:54,230 +من الـ greenhouse gases مثلابتحول ال نيتروجين + +699 +00:55:54,230 --> 00:56:00,510 +لأمونيا ترفع ال pH مثلا للميه والأمونيا غاز مش + +700 +00:56:00,510 --> 00:56:06,690 +يعني ماهواش طيب كتير يعني ال sulfur بتحول ال H2S + +701 +00:56:07,560 --> 00:56:16,660 +الـ H2S ريحته كريهة يعني مش كويس فوسفين الفوسفون + +702 +00:56:16,660 --> 00:56:20,520 +الفوسفين برضه ضار فمعنى الكلام و other products + +703 +00:56:20,520 --> 00:56:24,620 +فمعنى الكلام غياب الأكسجين في الميه بيقدي لمشاكل + +704 +00:56:24,620 --> 00:56:29,700 +عويصة ليه؟ لأن ال anaerobic bacteria بتطلع مكونات + +705 +00:56:29,700 --> 00:56:37,480 +ماهياش يعني جيدة بالعكس هي ضارة بالبيئة بشكل كبير + +706 +00:56:38,620 --> 00:56:44,320 +الأهم مصدر من مصادر الفوسفور والنيتروجين هو عبارة + +707 +00:56:44,320 --> 00:56:47,720 +عن ال domestic sewage اللي هو بالذات من ال + +708 +00:56:47,720 --> 00:56:51,220 +detergents على سبيل المثال وال fertilizers وال + +709 +00:56:51,220 --> 00:56:54,360 +animal wastes فهذه بتعطيني كميات وافرة من + +710 +00:56:54,360 --> 00:57:00,500 +الفوسفورات والنيتروجين ما يهمني هان انه قد يصل + +711 +00:57:00,500 --> 00:57:01,800 +الحال في + +712 +00:57:04,540 --> 00:57:08,640 +مصادر المياه لـ Fresh زي ال Lakes مثلا البحيرات + +713 +00:57:08,640 --> 00:57:13,000 +انه الحياة المائية عدم تماما فيها، نظرا ليش، نظرا + +714 +00:57:13,000 --> 00:57:15,980 +لقلة ال Oxygen، من وين يجي قلة ال Oxygen؟ قلة ال + +715 +00:57:15,980 --> 00:57:21,980 +Oxygen ممكن تيجي والله من توفر ال Phosphorus + +716 +00:57:24,240 --> 00:57:27,920 +الفوسفوراس والنيتروجين بشكل كبير، بقول ده من وين؟ + +717 +00:57:27,920 --> 00:57:31,140 +من عدة مصادر الـdomestic sewage، ال fertilizers + +718 +00:57:31,140 --> 00:57:33,880 +والأيوالويس، طب إيش بيعملوا النيتروجين + +719 +00:57:33,880 --> 00:57:36,580 +والفوسفوراس؟ قال إن النيتروجين والفوسفوراس يعتبروا + +720 +00:57:36,580 --> 00:57:42,490 +غذاء أساسي للتحالبده أساسي للتحالب التحالب لما + +721 +00:57:42,490 --> 00:57:47,070 +تلاقي كمية وافرة من الفوسفورس والنيتروجين نيتريتز + +722 +00:57:47,070 --> 00:57:52,210 +بتنمو نمو كبير للغاية لدرجة انه ممكن هاي بحيرة + +723 +00:57:52,210 --> 00:57:57,790 +تغطى كل وجهها بالتحالب طب ايش بيحصل التحالب تستهلي + +724 +00:57:57,790 --> 00:58:01,810 +كمية كبيرة من الأكسجين تاخدوا الأكسجين اللي في + +725 +00:58:01,810 --> 00:58:08,690 +الميه معناه كلام صار في عندي نقص في الأكسجين مصطلح + +726 +00:58:10,320 --> 00:58:15,240 +Eutrophication بنقوله عبارة عن يعني نمو كبير + +727 +00:58:15,240 --> 00:58:24,820 +للتحالب، هذه حاجة، نتيجة نقص الأكسجين، هذه حاجة، + +728 +00:58:24,820 --> 00:58:30,860 +نمو التحالب نتيجة وجود الفسفور والنيتروجين، أيضا + +729 +00:58:30,860 --> 00:58:39,150 +القاءالقاء كميات كبيرة من الأشجار الميتة ويعني + +730 +00:58:39,150 --> 00:58:43,250 +الحاجات اللي ممكن انه organic material القاها في + +731 +00:58:43,250 --> 00:58:47,730 +الميه هذه طيب علشان تتأكسد بدها أكسجين وبالتالي + +732 +00:58:47,730 --> 00:58:56,270 +الأكسجين عاملا بيستنفذ فهذا بيقدر لنقص في الأكسجين + +733 +00:58:56,270 --> 00:59:00,400 +اللي موجود في الميهو ممكن النقص هيدا يكون شديد + +734 +00:59:00,400 --> 00:59:07,540 +للغاية لدرجة انه ال aquatic life تتوقف يعني خلاص + +735 +00:59:07,540 --> 00:59:14,080 +مافيش oxygen لأ مثلا السمك انه يعيش سبب اللاحظ انه + +736 +00:59:14,080 --> 00:59:18,880 +في هذه المناطق اللي كثرت فيها التحالي بشكل كبير و + +737 +00:59:18,880 --> 00:59:25,280 +تم استنفاذ ال oxygen السمك بدأ برضه نفس الكلام بدأ + +738 +00:59:25,280 --> 00:59:32,750 +يموتهذه حاجة ناتجة ناتجة مباشرة عن نقص كمية ال + +739 +00:59:32,750 --> 00:59:39,270 +oxygen في المياه فيمكن + +740 +00:59:39,270 --> 00:59:48,050 +لهذا السبب دوما كثير حاليا بتحط regulations مثلا + +741 +00:59:48,050 --> 00:59:53,130 +ايش الشغلات اللي ممكن يتم + +742 +00:59:56,400 --> 01:00:01,720 +أو صبها في الـ lakes أو الأنهار أو ما شابه، أي + +743 +01:00:01,720 --> 01:00:03,240 +شغلات ممكن تأثر على + +744 +01:00:06,460 --> 01:00:12,060 +أى شغلات ممكن تأثر على ال water quality المفروض + +745 +01:00:12,060 --> 01:00:16,140 +انه يتم منعها ايضا بالاضافة لا مش بس ال oxygen + +746 +01:00:16,140 --> 01:00:20,800 +ممكن يصير فيه تسمم من المعادن الثقيلة اللى يتم + +747 +01:00:20,800 --> 01:00:27,800 +ضخها ايضا للبحيرات والانهار لان مثلا مصانع التعدين + +748 +01:00:27,800 --> 01:00:34,180 +مصانع الطلاق الكهربي كلها مصانع بتضخ كميات وافرة + +749 +01:00:34,180 --> 01:00:39,160 +جدا منالمعادن الثقيلة اللى بتكون عادة ضارة جدا + +750 +01:00:39,160 --> 01:00:42,600 +بالبيئة و بالبيئة المائية بشكل عام + +751 +01:00:49,370 --> 01:00:55,450 +بقول كيف بدي ارفع ال salt من الميه عشان احول ال + +752 +01:00:55,450 --> 01:01:00,630 +salt water الى مياه fresh نستطيع استخدامها قال + +753 +01:01:00,630 --> 01:01:03,070 +بقول والله في البداية في ال natural desalination + +754 +01:01:03,070 --> 01:01:07,450 +افضل طريقة ان والله اه هذه طريقة لا بتتعب ولا اللي + +755 +01:01:07,450 --> 01:01:10,630 +لدور فيها اللي هي عملية تبخر المياه من البحار و + +756 +01:01:10,630 --> 01:01:16,240 +المحيطاتو ارتف طبعا بخرا هي water vapor فلما تنزل + +757 +01:01:16,240 --> 01:01:20,580 +تنزل مطر يعني سائر الشرب ممتاز جدا مش فيه أملاح + +758 +01:01:20,580 --> 01:01:25,380 +المفروض فهذه تعتبر يعني من أهم الطرق اللي موجودة + +759 +01:01:25,380 --> 01:01:29,920 +في ال global water cycle يعني عموما فأه جزء مهم من + +760 +01:01:29,920 --> 01:01:34,640 +الميه بس كيف نقدر نحصل عليها و نحافظ عليها هذا + +761 +01:01:34,640 --> 01:01:39,120 +المهم فهذا عبارة عن natural desalination الحاجة + +762 +01:01:39,120 --> 01:01:42,760 +التانية جال والله ممكن بال distillationممكن بال + +763 +01:01:42,760 --> 01:01:46,600 +distillation، يعني أجيب الميه اللي هي مالحة و + +764 +01:01:46,600 --> 01:01:51,560 +أسخنها، لما تغلي ال water vapor بيطلع و الأملح + +765 +01:01:51,560 --> 01:01:54,820 +بتظلها مركزة، وهذا اللي بنقوله distillation، + +766 +01:01:54,820 --> 01:01:59,420 +تقطير، كويس؟ وهذا طبعا بيستهلك طاقة كبيرة للأسف + +767 +01:01:59,420 --> 01:02:05,890 +يعنيمش كل الناس بتقدر تعمله اكتر شئ حاليا من + +768 +01:02:05,890 --> 01:02:08,670 +الشغلات الدرجة اللي هو ال diesel ignition using RO + +769 +01:02:08,670 --> 01:02:12,710 +او reverse osmosis شوفنا ال reverse osmosis سابقا + +770 +01:02:12,710 --> 01:02:16,690 +يعني هو عبارة عن انه والله ظاهرة يعني في ال + +771 +01:02:16,690 --> 01:02:20,390 +reverse osmosis انا بطبق ضغط اكبر من ال osmotic + +772 +01:02:20,390 --> 01:02:20,830 +pressure + +773 +01:02:23,580 --> 01:02:31,160 +على الميّه اللي موجودة يعني بمحاذات غشاء شبه منفذ + +774 +01:02:31,160 --> 01:02:35,560 +فبلاحظ انه الميّه تمتقل من المحلول المركز إلى + +775 +01:02:35,560 --> 01:02:40,880 +المحلول المخفف طبعا هذا إذا كان طبقت ضغط أكبر من + +776 +01:02:40,880 --> 01:02:44,460 +ضغط الأوزموزي يعني الأوزموزي يعني ال pressure يعني + +777 +01:02:44,460 --> 01:02:46,680 +ماعنى كلام أنا بشغل reverse osmosis عكسية + +778 +01:02:46,680 --> 01:02:51,140 +الأوزموزيفهذا الكلام اللي يعني مثلا لو كان هذا + +779 +01:02:51,140 --> 01:02:57,180 +عندي غشاء شبه منفذ وهنا المحلول الخارجي هو عبارة + +780 +01:02:57,180 --> 01:03:01,800 +عن محلول مركز وهنا شايفين هي فيه analytes فلو طبقت + +781 +01:03:01,800 --> 01:03:07,910 +ضغط بلاحظ ان بس الميه هي اللي بتعدي داخلالتيوب + +782 +01:03:07,910 --> 01:03:10,490 +واحدة من التيوب سادوا وبالتالي بيكون في عندي + +783 +01:03:10,490 --> 01:03:18,150 +desalination فباخد بس الميه بدون الأملح طبعا ال + +784 +01:03:18,150 --> 01:03:25,430 +desalination plants ممكن تكون على مستوى عمارة او + +785 +01:03:25,430 --> 01:03:30,450 +تكون على مستوى بلد ممكن تكون كبيرة جدا وممكن تكون + +786 +01:03:30,450 --> 01:03:35,410 +يعني صغيرة للغاية على مستوى بيتممكن شفتوا هذه + +787 +01:03:35,410 --> 01:03:39,390 +الأشكال في بعض البيوت يعني اه هذا .. هذا عبارة عن + +788 +01:03:39,390 --> 01:03:46,270 +خدنا نقول filter واحد منهم بيكون عبارة عن filter + +789 +01:03:46,270 --> 01:03:50,070 +بياخد ال sediments بياخد ال particles و اتنين + +790 +01:03:50,070 --> 01:03:54,910 +بيكون عادة coal او فحم بياخدوا برضه ال organics + +791 +01:03:54,910 --> 01:03:58,390 +اللي بتكون عالقة و بياخدوا ايضا الروائح اذا كان في + +792 +01:03:58,390 --> 01:04:05,760 +اي روائح مش طيبة لكن القرء موجود يعنيهذا اللي هو + +793 +01:04:05,760 --> 01:04:11,640 +اللي بيحتوي على الـ reverse osmotic membranes + +794 +01:04:11,640 --> 01:04:16,640 +فبيتم تنقية الميه بهذه الطريقة + +795 +01:04:19,980 --> 01:04:23,520 +الـ water purification for public بشكل عام يعني + +796 +01:04:23,520 --> 01:04:31,240 +كيف مثلا البلدية بتنقل ميه وبتعطيها للبلد كلها + +797 +01:04:31,240 --> 01:04:36,770 +طبعا مهم جدا أن الميه تكون safe و clean لازمفكيف + +798 +01:04:36,770 --> 01:04:41,950 +البلدية بتعمل هذا الكلام؟ بنقول بشكل عام يعني، هذه + +799 +01:04:41,950 --> 01:04:47,910 +العملية بتتم عبر خطوات، خطوات واضحة عندي، هي عندي + +800 +01:04:47,910 --> 01:04:54,850 +مثلا ال beer أو المكان يعني، بحيرة أو ما شابهففي + +801 +01:04:54,850 --> 01:04:59,050 +عندى filtration system بيطلع بياخدش الطين او + +802 +01:04:59,050 --> 01:05:04,390 +الحجار او خلافه وبيضخ الميه لتور هان بنضيف calcium + +803 +01:05:04,390 --> 01:05:10,230 +oxide و aluminum sulfate علشان يرسبولي اي + +804 +01:05:10,230 --> 01:05:15,310 +particulates موجودة في او جزيئات موجودة في الميه + +805 +01:05:15,310 --> 01:05:19,530 +فهدى وبرضه بظبط ال pH للميه ال calcium oxide بظبط + +806 +01:05:19,530 --> 01:05:24,720 +ال pH للميه فبيحصل عندى sedimentation يعنىفلما + +807 +01:05:24,720 --> 01:05:28,280 +بدخلها على sand filter فكل ال sediments بتتكون + +808 +01:05:28,280 --> 01:05:31,280 +ميان في اللي بتعديش على ال .. بتعديش مع الميه + +809 +01:05:31,280 --> 01:05:36,540 +يعنى، كل الشغلات اللي حصلها sedimentation بتعديش + +810 +01:05:36,540 --> 01:05:40,660 +مع الميه اللي بعدي بس الميه، بنعمل aeration، بنحط + +811 +01:05:40,660 --> 01:05:45,220 +يعني فيها oxygenIrration يعني بندخل هوا فيها عشان + +812 +01:05:45,220 --> 01:05:50,980 +يصير فيها كمية من الأكسجين والأكسجين كويس لأنه بي + +813 +01:05:50,980 --> 01:05:55,580 +oxid ال organic materials اللي موجودة وبعدين بعد + +814 +01:05:55,580 --> 01:06:00,600 +هيك بدنا نضيف عليها disinfectant زي الchlor + +815 +01:06:01,510 --> 01:06:10,450 +Chlorine Cl2 أو أوزون بحيث انه نعمل disinfection + +816 +01:06:10,450 --> 01:06:13,210 +للمياه نقضع على البكتيريا و الميكروبات اللي فيها + +817 +01:06:13,210 --> 01:06:18,730 +وبعدين والله بتتجمع في طور عالي جدا حووز بنقوله + +818 +01:06:18,730 --> 01:06:22,470 +احنا حاجة عالية زمان كان موجود بصلجات مش موجود + +819 +01:06:22,470 --> 01:06:26,230 +بضخم مباشر كويس وبعدين ال users اللي بياخدوا + +820 +01:06:26,230 --> 01:06:29,450 +الميكروبات فهذه الدورة اللي بتعملها عادة من + +821 +01:06:29,450 --> 01:06:35,330 +البلدياتلكن يمكن زمان كان عندنا اشي زي هيك لكن + +822 +01:06:35,330 --> 01:06:40,010 +يعني حاليا بعتقد انا انه بياخدوا مباشر من القبار + +823 +01:06:40,010 --> 01:06:47,650 +بيشوفوا في البداية اللي هو المكونات + +824 +01:06:47,650 --> 01:06:51,270 +الميه في ال ..أبار المختلفة و بيشوفوا الأبار + +825 +01:06:51,270 --> 01:06:55,090 +الصالح على الشرب و بيقدروا يعني يفحصوا هذا الكلام + +826 +01:06:55,090 --> 01:06:59,550 +كل فترة لكن بيضخوا مباشر من ال beer بعد ما يحطوا + +827 +01:06:59,550 --> 01:07:04,730 +كميات معينة من ليكلور لأنه ليكلور يعني يعتبر رخيص + +828 +01:07:04,730 --> 01:07:09,810 +نسبيا .. نسبيا و .. و كفوء كويس يعني مش سيئ وإن + +829 +01:07:09,810 --> 01:07:15,550 +كان فيه بعض السلبيات ممكن نطلع عليها الآن يعني + +830 +01:07:17,090 --> 01:07:19,710 +فعادةً الليكلورين هو اللي يستخدم للـ disinfection + +831 +01:07:19,710 --> 01:07:22,790 +الليكلورين في الميه بيتحول للـhypochlorite + +832 +01:07:22,790 --> 01:07:24,810 +والـhypochlorite is a very good oxidizing agent + +833 +01:07:24,810 --> 01:07:28,250 +يعني بيأكسد ال organic material بيقتل البكتيريا + +834 +01:07:28,250 --> 01:07:32,510 +فهو disinfectant كويس كتير لكن في السنوات الأخيرة + +835 +01:07:32,510 --> 01:07:40,270 +ظهر إلنا إنه في وجود الليكلورين في بعض المركبات + +836 +01:07:40,270 --> 01:07:47,420 +بنقولها Trihalomethanesزي الـ CHCl3, CHClBr2, + +837 +01:07:47,640 --> 01:07:56,080 +CHCl2Br و CHBr3 هذي Carcinogens Suspected بتنشأ + +838 +01:07:56,080 --> 01:07:59,460 +نتيجة أكسرة الـ Organic Material بالـ HClO + +839 +01:08:05,320 --> 01:08:11,440 +فبالتالي الـ World Health Organization الحطت الـ + +840 +01:08:11,440 --> 01:08:16,780 +Standards جالت إن الـTHM مفروض ما تزيدش عن 80 PPP + +841 +01:08:16,780 --> 01:08:23,020 +مفروض ما تزيدش في الميه عن 80 part per billion80 + +842 +01:08:23,020 --> 01:08:26,500 +part per billion بس ليه؟ لأنه suspected + +843 +01:08:26,500 --> 01:08:32,980 +carcinogens طبعا البعض اقترح انه طب خلاص نستخدم + +844 +01:08:32,980 --> 01:08:37,480 +الأوزوان، الأوزوان غالي، أغلى يعنيو الكلورين دا + +845 +01:08:37,480 --> 01:08:41,900 +يوكسايد برضه بدل الكلورين لأن الكلورين بيعطيني HCl + +846 +01:08:41,900 --> 01:08:45,060 +و الكلورين دا يوكسايد مباشر يعني هو نفسه يستخدم + +847 +01:08:45,060 --> 01:08:50,480 +كدس إنفكتانت فهدول بيطلعوا less harmful byproducts + +848 +01:08:50,480 --> 01:08:57,800 +لكن وجدنا إنه في وجود البروميد إذا كان موجود في + +849 +01:08:57,800 --> 01:09:02,760 +الميه بروميد أصلا فالبروميد في وجود الأوزون أو ال + +850 +01:09:02,760 --> 01:09:08,730 +CLO2 بتحول لبروميتو البروميت برضه للأسف cancer + +851 +01:09:08,730 --> 01:09:15,590 +causing chemical فيعني من وين بدنا نشرد منها؟ بعض + +852 +01:09:15,590 --> 01:09:19,350 +الناس طبعا بيحاولوا إنهم يستخدموا ال UV فقط يعني + +853 +01:09:19,350 --> 01:09:25,490 +ال UV لكن مش كافية أو برضه مش كفوة لل plants + +854 +01:09:25,490 --> 01:09:34,190 +الكبيرة خالصفي عندنا طريقة بنستخدمها ايضا لتحسين + +855 +01:09:34,190 --> 01:09:37,890 +جودة الميه بنقولها water softening ال water + +856 +01:09:37,890 --> 01:09:44,310 +softening يعني soft عكس hard الميه اللى بتحتوي على + +857 +01:09:44,310 --> 01:09:48,350 +كميات من الكالسيوم والمجنيزيوم بنقولها hard water + +858 +01:09:48,350 --> 01:09:51,520 +هذا termHard water بتحتوي على كمية من الكالسيوم + +859 +01:09:51,520 --> 01:09:56,020 +والمجنيزيوم اسمها hard الان لو بدى انا اجلي كمية + +860 +01:09:56,020 --> 01:09:59,740 +الكالسيوم والمجنيزيوم بقول والله اذا كان جلالتهم + +861 +01:09:59,740 --> 01:10:03,980 +بتصير الميه softer ف ال soft water هي عبارة عن + +862 +01:10:03,980 --> 01:10:06,640 +الميه اللى بتحتوي على كمية اقل من الكالسيوم + +863 +01:10:06,640 --> 01:10:11,200 +والمجنيزيومفالـ water softening هو تقليل كمية + +864 +01:10:11,200 --> 01:10:15,360 +الكالسيوم والمجنيزيوم في الميه طب ليش؟ يعني + +865 +01:10:15,360 --> 01:10:19,300 +الكالسيوم كويس يعني للعضاوب ناخده في حبوب مثلا + +866 +01:10:19,300 --> 01:10:21,780 +الناس اللي بتاخد حبوب كالسيوم والمجنيزيوم كمان جيد + +867 +01:10:21,780 --> 01:10:26,500 +جال لأ احنا مش معترضين عليهم لأنهم والله كيمويات + +868 +01:10:26,500 --> 01:10:30,660 +ضارة أو مسبب لأمراض او غيره لأ احنا معترضين عليهم + +869 +01:10:30,660 --> 01:10:34,440 +لأن جودة الميه بتكون قليلة من أي ناحية؟ جال في عند + +870 +01:10:34,440 --> 01:10:43,570 +ناحيتين اول ناحيةإنه يعني لما نيجي بدنا نستخدم ال + +871 +01:10:43,570 --> 01:10:48,640 +detergentsقال الـ detergents بتترسب في وجود + +872 +01:10:48,640 --> 01:10:51,160 +الكالسيوم والمجنيزيوم انا بتستخدم الدرجة عشان + +873 +01:10:51,160 --> 01:10:55,460 +والله اه نظف الهدوم مثلا الملابس طيب لما يكون فيه + +874 +01:10:55,460 --> 01:10:59,020 +في الميه كالسيوم ومجنيزيوم لأ ال detergent بترسب + +875 +01:10:59,020 --> 01:11:04,100 +بدل ما نظف بوثق لأنه راسب صار فحيه ترسب على سطح + +876 +01:11:04,100 --> 01:11:08,200 +الملابس بدل ما نظفه هو هيفقد قدرته على التنظيف + +877 +01:11:08,200 --> 01:11:13,020 +عشان ينظف لازم يدوب فهو بطل دايمالحاجة التانية + +878 +01:11:13,020 --> 01:11:19,180 +الكالسيوم والمجنيزيوم بيسببه scales بيسببه ترصبات + +879 +01:11:19,180 --> 01:11:23,720 +داخل الأنابيب بالذات أنابيب المياه الساخنة وعشان + +880 +01:11:23,720 --> 01:11:28,900 +هيك كل فترة مثلا بنلاحظ أنه والله السخان ال boiler + +881 +01:11:28,900 --> 01:11:34,550 +اللي عندنا في البيت لازم يتغير ال ..خلّيني أقول + +882 +01:11:34,550 --> 01:11:38,990 +يتنظف من جوا ويتغير ال .. ال heater اللي فيه ليه؟ + +883 +01:11:38,990 --> 01:11:42,330 +لأنه في عندنا ترسبات كبيرة جدا من الكالسوم + +884 +01:11:42,330 --> 01:11:47,490 +والمغنيزيوم وهذه ابتنع الكهربا والحرارة انها تنتقل + +885 +01:11:47,490 --> 01:11:52,160 +بشكل جيدفبتفقد ال boilers كفاءة كبيرة جدا فليه ده + +886 +01:11:52,160 --> 01:11:56,720 +للسببين يعني بنقول انه لأ جملة الميه تقتضي + +887 +01:11:56,720 --> 01:12:00,840 +للاستخدام ال .. ال .. بيتي تقتضي انه اتخلص منه و + +888 +01:12:00,840 --> 01:12:06,020 +اعمل softening لل water كيف بعمل softening؟جال + +889 +01:12:06,020 --> 01:12:09,100 +والله ممكن ان ارسم هذه القيونات عن طريق اضافة + +890 +01:12:09,100 --> 01:12:14,060 +Sodium Carbonate و Calcium Hydroxide هذه اسمها الـ + +891 +01:12:14,060 --> 01:12:19,720 +Sodolime Process يعني البلديات بتضيف Sodium + +892 +01:12:19,720 --> 01:12:25,700 +Carbonate و Calcium Hydroxide على الميه عشان تحسن + +893 +01:12:25,700 --> 01:12:30,600 +جودتها ايش اللي بيحصل؟ اللي بيحصل انه تترسب ال + +894 +01:12:30,600 --> 01:12:36,010 +calcium و ال magnesium من الميهالحاجة التانية جال + +895 +01:12:36,010 --> 01:12:39,490 +والله نستخدم حاجة بنقولها ion exchange reasons + +896 +01:12:39,490 --> 01:12:44,710 +يعني نستخدم مواد بتستبدل ال .. بتاخد ال calcium و + +897 +01:12:44,710 --> 01:12:48,010 +المجنيزيوم و بتعطيني ايونات دائمة بدالها + +898 +01:12:48,010 --> 01:12:53,950 +فبيستخدموا ال sodium ion exchange reason عادة يعني + +899 +01:12:53,950 --> 01:12:59,870 +فهذا بيخلصني من ال calcium و المجنيزيومفعنا في ال + +900 +01:12:59,870 --> 01:13:03,590 +iron exchange technique احنا بنضيف ال hard water + +901 +01:13:03,590 --> 01:13:06,930 +بتطلع عندنا soft water ليه؟ لأن ال iron exchange + +902 +01:13:06,930 --> 01:13:10,710 +أخد ال calcium و المجنيزيوم و أعطاني بدالهم أيه؟ + +903 +01:13:10,710 --> 01:13:14,630 +أيونات ذائبة زي ال sodium أو ال hydrogen H plus + +904 +01:13:14,630 --> 01:13:21,880 +فأعطاني أيونات ذائبةهذه شكل .. هي شوف الحديد على + +905 +01:13:21,880 --> 01:13:25,060 +سبيل المثال وهي ال skills اللى جوا ال skills اللى + +906 +01:13:25,060 --> 01:13:29,880 +عبارة عن الترثبات هي نفس الكلام الحديد هذه عبارة + +907 +01:13:29,880 --> 01:13:34,640 +عن .. بالذات مهمة في وجود المياه السخنة في وجود + +908 +01:13:34,640 --> 01:13:37,720 +المياه الساخنة ال boilers و الأنابيب اللى بتنقل + +909 +01:13:37,720 --> 01:13:40,680 +المياه الساخنة فورا بتكون فيها skills كبيرة خالص + +910 +01:13:40,680 --> 01:13:45,220 +إذا كان عند المياه hard يعني فيها كميات وافرة من + +911 +01:13:45,220 --> 01:13:51,410 +ال calcium و ال magnesiumكيف تشتغل شغلة ال water + +912 +01:13:51,410 --> 01:13:54,170 +softening بقول فى البداية هذا هو عبارة عن ال ion + +913 +01:13:54,170 --> 01:14:00,030 +exchange ريزين فى sodium plus فى عندى هنا كل واحدة + +914 +01:14:00,030 --> 01:14:04,130 +من هدول مربوط فيها اكتر من ال sodium plus انا بضيف + +915 +01:14:04,130 --> 01:14:07,710 +ال hard water اللى هي عبارة عن فيها كالسيوم و + +916 +01:14:07,710 --> 01:14:11,210 +مجنيزيوم الكالسيوم و المجنيزيوم بحلوا محل الصوديوم + +917 +01:14:11,210 --> 01:14:16,980 +اللى موجود هان و بطلع هنا ايه الصوديومطبعا فكل ما + +918 +01:14:16,980 --> 01:14:22,060 +حطيت ازيادة من المي اللي hard ايش بيحصل بتاعة + +919 +01:14:22,060 --> 01:14:25,900 +تستبدل ال calcium وال magnesium بيبقى في ال .. في + +920 +01:14:25,900 --> 01:14:30,180 +ال resin المادة الصلبة و بيطلع بدله ايه ال sodium + +921 +01:14:30,180 --> 01:14:34,160 +خلص انت لصار هذا كله ايه ان يعني بطل ياخد اي + +922 +01:14:34,160 --> 01:14:39,320 +ازيادة من ال hard water طب ايش بده نعمل بعد هيك + +923 +01:14:39,320 --> 01:14:44,550 +خلاص هذا بطل ينفعالريزين انتهى، دوره انتهى، قدرته + +924 +01:14:44,550 --> 01:14:50,110 +على الاحتفاظ بالكالسوم والمجنيزيوم انعدمت، جالب + +925 +01:14:50,110 --> 01:14:56,780 +بدي أعمله regenerationعكسي بضخ هنا محلول صوديوم و + +926 +01:14:56,780 --> 01:15:00,360 +محلول صوديوم مخصت كتير ميه البحر يعني بضخ ميه + +927 +01:15:00,360 --> 01:15:04,200 +البحر فدهش اللي بيحصل الصوديوم بيستبدل الكالسيوم و + +928 +01:15:04,200 --> 01:15:06,900 +الماجنيزيوم فالصوديوم بحل محل الكالسيوم و + +929 +01:15:06,900 --> 01:15:09,060 +الماجنيزيوم يبقى الميه اللي طالعة منها إيش فيها + +930 +01:15:09,060 --> 01:15:14,040 +كالسيوم و ماجنيزيوم هي أنا بضخ من هنا صوديوم بطلع + +931 +01:15:14,040 --> 01:15:16,680 +الكالسيوم و الماجنيزيوم بتمني أضخ صوديوم بطلع + +932 +01:15:16,680 --> 01:15:20,120 +الكالسيوم و تمني أضخ صوديومالصوديوم من ايه؟ مية + +933 +01:15:20,120 --> 01:15:25,420 +محر يعني فبطلع لغاية نحصل على ايه؟ على بس الرزن + +934 +01:15:25,420 --> 01:15:30,100 +بالصوديوم يعني زي ما كان سابقا هيه وبالتالي بكون + +935 +01:15:30,100 --> 01:15:36,900 +عملتله regeneration في بعض البلاد يعني ممكن انه + +936 +01:15:36,900 --> 01:15:42,900 +نلاقي حاجة زي هيك هذه عبارة عن water purification + +937 +01:15:42,900 --> 01:15:46,180 +technology بيسموها + +938 +01:15:50,210 --> 01:15:57,430 +Life Straw فهي عبارة عن ايش بالظبط؟ هي بدخل ميه من + +939 +01:15:57,430 --> 01:16:01,450 +هنا ففي عنده فلاتر اول حاجة فلتر ل الحاجات الكبيرة + +940 +01:16:01,450 --> 01:16:04,990 +ثاني حاجة ميت مايكرون فلتر ل الحاجات الأصغر خمس + +941 +01:16:04,990 --> 01:16:10,190 +عشر مايكرون بعدين بعد على ايودين بيدزهذا عبارة عن + +942 +01:16:10,190 --> 01:16:15,250 +حبيبات تحتوي على الايودين الايودين بيقتل البكتيريا + +943 +01:16:15,250 --> 01:16:20,870 +و خلافه يعني اي حاجات ضارة بيقتلها بعدين يبني جهان + +944 +01:16:20,870 --> 01:16:24,910 +على كربون الكربون بياخد الايودين لزيادة الريحة + +945 +01:16:24,910 --> 01:16:28,090 +العاطلة تبع الايودين و الطعم العاطل و بيطلع مياه + +946 +01:16:28,090 --> 01:16:31,590 +نقية فلو يعني زي ما انتوا شايفين ممكن المياه مهما + +947 +01:16:31,590 --> 01:16:39,610 +كان مصدرها ملوثة ممكن جدا انه تكون مناسبة للشربأخر + +948 +01:16:39,610 --> 01:16:43,630 +نقطة في هذا ال chapter يعني معلش تلت اربعة دقايق + +949 +01:16:43,630 --> 01:16:50,150 +نتكلم عن انه الآن احنا يعني + +950 +01:16:50,150 --> 01:16:55,470 +المفروض نتطلع على الكيميا من جانب انه والله بدنا + +951 +01:16:55,470 --> 01:17:01,570 +كل العمليات الكيميائية و ايضا المنتجات الكيميائية + +952 +01:17:01,570 --> 01:17:05,870 +تكون safer للأشخاص اللي بيشتغلوا للبناء الأدمين + +953 +01:17:05,870 --> 01:17:13,210 +العاشرين لل environmentبالإضافة للتكلفة القليلة + +954 +01:17:13,210 --> 01:17:20,270 +فمن حوالي تلاتين اربعين سنة صار في عنا واعي + +955 +01:17:20,270 --> 01:17:24,110 +واستيعاب اكتر لأهمية انه احنا نحافظ على البيئة + +956 +01:17:24,110 --> 01:17:28,450 +تبعتنا ونحافظ على السلامة العامة تبعتنا ونحاول + +957 +01:17:28,450 --> 01:17:34,050 +نوجه التصنيع الكيميائي كله في هذا الاتجاه فأي + +958 +01:17:34,050 --> 01:17:40,690 +عمليات بتحافظ علىالصحة والبيئة كويس وأيضا الحاجة + +959 +01:17:40,690 --> 01:17:44,170 +اللي نقولها sustainability يعني انه تم انلاج + +960 +01:17:44,170 --> 01:17:48,330 +المواد تستخدم باستمرار Renewable يعني استخدم ال + +961 +01:17:48,330 --> 01:17:54,250 +resources Sustainability فهذا شيء جيد سمنا هذا + +962 +01:17:54,250 --> 01:17:57,870 +المفهوم ال green chemistry فال green chemistry + +963 +01:17:57,870 --> 01:18:03,230 +takes in consideration environmental effects as + +964 +01:18:03,230 --> 01:18:06,420 +well as health effectsIn addition to + +965 +01:18:06,420 --> 01:18:10,120 +sustainability فال + +966 +01:18:10,120 --> 01:18:14,020 +green chemistry لما بدهش احضر اي مادة لازم اخد في + +967 +01:18:14,020 --> 01:18:20,740 +بالي هل هي مثلا environmentally friendly ولا لأ؟ + +968 +01:18:20,740 --> 01:18:23,700 +هل هي ضارة في البيئة ولا مش ضارة في البيئة؟ هل هي + +969 +01:18:23,700 --> 01:18:26,740 +صحيه اكويسر اللي بده يحضرها ولا اللي بده يستخدمها + +970 +01:18:26,740 --> 01:18:31,380 +ولا لأ؟وكمان هل مصادر التحضير هذه sustainable يعني + +971 +01:18:31,380 --> 01:18:35,380 +ممكن انه renewable ولا لأ فصار في عندنا initiative + +972 +01:18:35,380 --> 01:18:42,540 +صار في عندنا initiative عملت هذه المبادرة يعني من + +973 +01:18:42,540 --> 01:18:49,160 +ناس حطوا principles ل ال chemistry عشان تكون green + +974 +01:18:49,160 --> 01:18:52,720 +حطوا principles ل ال chemistry عشان تكون green + +975 +01:18:52,720 --> 01:18:55,880 +بمعنى تاخد بالها من ال environment وال health + +976 +01:18:55,880 --> 01:18:56,660 +وايضا + +977 +01:18:59,920 --> 01:19:05,620 +أول حاجة جالة prevention حط 12 نبدأ بيقول it is + +978 +01:19:05,620 --> 01:19:10,260 +better to prevent wastethan to clean it up يعني + +979 +01:19:10,260 --> 01:19:16,400 +أني أمنع تكوين ال waste أفضل من أني أنظفه لأنه إذا + +980 +01:19:16,400 --> 01:19:19,260 +كانت صار فيه waste مافيش تنظيف خلاص ماقدرش أن أنظف + +981 +01:19:19,260 --> 01:19:23,700 +هذا أول مبدأ المبادئ التانية atom economy بحب كتير + +982 +01:19:23,700 --> 01:19:26,680 +أنه كل ال atoms اللي دخلت في التفاعل تكون في ال + +983 +01:19:26,680 --> 01:19:33,290 +product مايكونش في عندي حاجات زائدةless hazard as + +984 +01:19:33,290 --> 01:19:39,910 +chemical synthesis أي شيء بيعطيني hazard بيعطيني + +985 +01:19:39,910 --> 01:19:45,490 +خطر أثناء التصنيع بدي أستثنيه design of safer + +986 +01:19:45,490 --> 01:19:49,630 +chemicals بدي ال chemicals اللي أنا ب .. أستخدمها + +987 +01:19:49,630 --> 01:19:54,690 +أو بدي أحضرها لازم تكون ماهياش toxic safe فبدي ال + +988 +01:19:54,690 --> 01:19:58,370 +chemicals تكون safe لكن في نفس الوقت طبعا تحتفظ + +989 +01:19:58,370 --> 01:20:03,420 +بالخصائص المطلوبةسافر solvents بدي ال solvents + +990 +01:20:03,420 --> 01:20:06,920 +اللي بدي استخدمها تكون safe وال auxiliaries إذا + +991 +01:20:06,920 --> 01:20:10,260 +كان فيه حاجات إضافية أنا بستخدمها و بقدر استجنع + +992 +01:20:10,260 --> 01:20:12,560 +عنها لأ بدي استجنع عنها مديش auxiliaries + +993 +01:20:15,230 --> 01:20:19,270 +Energy efficient بدي يكون التحضير عندي مستهليكش + +994 +01:20:19,270 --> 01:20:23,950 +طاقة كبيرة إلى آخره اقرأوا هذا الكلام في ال .. في + +995 +01:20:23,950 --> 01:20:27,770 +البيت عشان بس الوقت اللي بدي اقوله انا انه من افضل + +996 +01:20:27,770 --> 01:20:31,090 +ال solvents بس امثلة بسيطة جيجا واحدة ال solvents + +997 +01:20:31,090 --> 01:20:34,690 +من افضلها ان يكون super critical ومن افضل ال super + +998 +01:20:34,690 --> 01:20:38,150 +critical solvents اللي هو الميه وايضا ال carbon + +999 +01:20:38,150 --> 01:20:41,610 +dioxide شفنا هذا الكلام سابقا + +1000 +01:20:42,950 --> 01:20:48,510 +فمثلا عندنا ال chlorofluorocarbons كانت تستخدم + +1001 +01:20:48,510 --> 01:20:54,990 +كsolvent لتحضير التفلون CF2CF2 لكن احنا عارفين ان + +1002 +01:20:54,990 --> 01:20:59,820 +ال chlorofluorocarbons مضرر بالغزونفجال لهذا السبب + +1003 +01:20:59,820 --> 01:21:03,500 +سبب نستخدم ال super critical CO2 يعني روحنا ل + +1004 +01:21:03,500 --> 01:21:06,780 +greener chemistry لأن ال CO2 بنستخدمه بيطلع هو هو + +1005 +01:21:06,780 --> 01:21:11,220 +مابيتغيرش فهذا يعتبر greener chemistry ففي عندي + +1006 +01:21:11,220 --> 01:21:17,800 +هذه ال process كانت بتستخدم تحويل ال Parazilin إلى + +1007 +01:21:17,800 --> 01:21:21,620 +Terephthalic Acid كان بيستخدم حرارة عالية وضغط + +1008 +01:21:21,620 --> 01:21:29,170 +عالي في وجود ال Acetic Acid فاحنا استبدلناالـ + +1009 +01:21:29,170 --> 01:21:32,810 +Acetic Acid بالـ Supercritical Water فهذا طبعاً + +1010 +01:21:32,810 --> 01:21:38,230 +أعطاني شيء ممتاز جداً و بدل ال Oxidizing Agent + +1011 +01:21:38,230 --> 01:21:44,310 +استخدمنا Hydrogen Peroxide H2O2 هذا لما يتسخن + +1012 +01:21:44,310 --> 01:21:50,570 +بتحول لمي ولا أكسجين يعني ولا إشي لو اطلعنا على + +1013 +01:21:50,570 --> 01:21:58,750 +المركب COCl2 هذا فسجين هذا سامهذا المراكب سام قال + +1014 +01:21:58,750 --> 01:22:02,950 +ممكن نستبدله بهذا المراكب شبيه فيه جدا COClCl شبيه + +1015 +01:22:02,950 --> 01:22:05,590 +فيه جدا فبدل ما نستخدم هذا المراكب نستخدم هذا + +1016 +01:22:05,590 --> 01:22:08,270 +المراكب فهذا يعتبر greener chemistry + +1017 +01:22:14,500 --> 01:22:18,720 +طب بدل ما نستخدم البنزين اللى هو بس حلقة البنزين + +1018 +01:22:18,720 --> 01:22:22,940 +عارفينها و هذا سام و carcinogen قال نستخدم طلوين + +1019 +01:22:22,940 --> 01:22:26,440 +أحسن منه قال والله هو أدل ضرر منه بس فى إشياء أهم + +1020 +01:22:26,440 --> 01:22:34,450 +أن الطلوين لزيادة هذا الطلوين بقدر سهولة أحاولمثلا + +1021 +01:22:34,450 --> 01:22:38,730 +بنزيويك أسد مش ضار بقدر بسهولة احاول .. اه يفضل .. + +1022 +01:22:38,730 --> 01:22:42,310 +اذا هو نفسه حتى لو كان هو ضار شوية لكن بقدر في + +1023 +01:22:42,310 --> 01:22:45,510 +النهاية احاوله لايش ايه ماهواش ضار بينما البنزين + +1024 +01:22:45,510 --> 01:22:51,930 +كبنزين لأ ماقدرش احاوله حاجة مش سهل طالعوا + +1025 +01:22:51,930 --> 01:22:54,830 +قال هذا التفاعل كل المواد الداخلة في التفاعل + +1026 +01:22:54,830 --> 01:22:59,030 +اعطتني ناتج مافيش ايش زاد حلو جدا هذا greener + +1027 +01:22:59,030 --> 01:23:05,380 +chemistryهنا في عندي تفاعل بدحضر ال quinone او ال + +1028 +01:23:05,380 --> 01:23:10,640 +hydroquinone ففي عندي مواد زائدة .. في عندي مواد + +1029 +01:23:10,640 --> 01:23:15,060 +زائدة .. هذا مش كويس لأنه هذه waste طب ايش ممكن + +1030 +01:23:15,060 --> 01:23:19,000 +اعمل؟ يمكن ادور على route تانيفحاليا انا حضرته + +1031 +01:23:19,000 --> 01:23:22,680 +بهذه الطريقة هي الكوينون او الهيدروكوينون ايش زاد + +1032 +01:23:22,680 --> 01:23:27,800 +عندي هذا وهذا لكن هدول اتنين اللي بالاخضر يمكن + +1033 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1349.74, "end": 1350.14, "word": " زغبق", "probability": 0.6929931640625}, {"start": 1350.14, "end": 1350.54, "word": " هي", "probability": 0.77587890625}, {"start": 1350.54, "end": 1350.82, "word": " عبارة", "probability": 0.9698486328125}, {"start": 1350.82, "end": 1350.96, "word": " عن", "probability": 0.98388671875}, {"start": 1350.96, "end": 1351.24, "word": " 14", "probability": 0.8193359375}, {"start": 1351.24, "end": 1351.78, "word": ".7", "probability": 0.98974609375}, {"start": 1351.78, "end": 1352.48, "word": " PSI", "probability": 0.723876953125}, {"start": 1352.48, "end": 1353.18, "word": " 14", "probability": 0.295166015625}, {"start": 1353.18, "end": 1354.22, "word": ".7", "probability": 0.987060546875}, {"start": 1354.22, "end": 1356.54, "word": " PSI", "probability": 0.915283203125}, {"start": 1356.54, "end": 1358.36, "word": " فلازم", "probability": 0.950927734375}, {"start": 1358.36, "end": 1358.68, "word": " نعرف", "probability": 0.9913736979166666}, {"start": 1358.68, "end": 1358.94, "word": " هدول", "probability": 0.9422200520833334}, {"start": 1358.94, "end": 1359.24, "word": " علشان", "probability": 0.9739583333333334}, {"start": 1359.24, "end": 1359.5, "word": " نقدر", "probability": 0.8904622395833334}, {"start": 1359.5, "end": 1359.86, "word": " نحول", "probability": 0.7669270833333334}, {"start": 1359.86, "end": 1360.14, "word": " بين", "probability": 0.9609375}, {"start": 1360.14, "end": 1360.56, "word": " الوحدات", "probability": 0.969482421875}, {"start": 1360.56, "end": 1361.0, "word": " المختلفة", "probability": 0.9835205078125}, {"start": 1361.0, "end": 1361.08, "word": " و", "probability": 0.78955078125}, {"start": 1361.08, "end": 1361.3, "word": " ناخد", "probability": 0.78759765625}, {"start": 1361.3, "end": 1361.46, "word": " لنا", "probability": 0.643310546875}, {"start": 1361.46, "end": 1361.74, "word": " شوية", "probability": 0.91455078125}, {"start": 1361.74, "end": 1362.4, "word": " تحويلات", "probability": 0.8828125}, {"start": 1362.4, "end": 1363.5, "word": " بيقول", "probability": 0.869140625}, {"start": 1363.5, "end": 1364.12, "word": " convert", "probability": 0.79345703125}, {"start": 1364.12, "end": 1364.44, "word": " 0", "probability": 0.458251953125}, {"start": 1364.44, "end": 1365.4, "word": ".357", "probability": 0.9490559895833334}, {"start": 1365.4, "end": 1365.96, "word": " atmosphere", "probability": 0.76904296875}, {"start": 1365.96, "end": 1366.36, "word": " to", "probability": 0.939453125}, {"start": 1366.36, "end": 1366.74, "word": " torque", "probability": 0.29052734375}], "temperature": 1.0}, {"id": 56, "seek": 138343, "start": 1367.67, "end": 1383.43, "text": "والله لو عندى الـ Tor بده يساوي 0.357 أتمسفير، ايش ال Tor؟ 760 Tor، هذا عبارة عن واحد أتمسفير، 760 Tor من العلاقة الواحد أتمسفير 760 Tor", "tokens": [2407, 6027, 43761, 45164, 43242, 7578, 2423, 39184, 7160, 47525, 3224, 7251, 3794, 995, 45865, 1958, 13, 8794, 22, 5551, 39237, 3794, 5172, 13546, 12399, 1975, 1829, 8592, 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ستين Tor سهل جدا طب convert مية سبعة واربعين و اتنين و عشرة kilo Pascal to Tor", "tokens": [2304, 33599, 1829, 35186, 10874, 15042, 27884, 6156, 21292, 9566, 1211, 3615, 43242, 3224, 15844, 23032, 12610, 23032, 1829, 3555, 7620, 8608, 2655, 3660, 4032, 8608, 2655, 3660, 8978, 6225, 8592, 25720, 5551, 3794, 6027, 1829, 4724, 9307, 1863, 9957, 7160, 281, 8018, 8717, 36178, 2423, 28820, 10943, 2423, 8018, 8608, 2655, 3660, 4032, 8608, 2655, 3660, 8978, 6225, 8592, 25720, 5551, 3794, 6027, 1829, 4724, 9307, 1863, 9957, 7160, 47525, 8315, 8717, 2655, 9778, 1211, 9381, 9154, 2423, 7160, 4032, 8717, 5016, 9566, 2423, 14407, 24401, 8018, 8608, 3555, 27884, 3714, 10632, 4032, 8608, 2655, 9957, 7160, 8608, 3224, 1211, 10874, 28259, 23032, 3555, 7620, 3714, 10632, 8608, 3555, 27884, 4032, 9640, 3555, 3615, 9957, 4032, 1975, 2655, 1863, 9957, 4032, 6225, 8592, 25720, 21112, 41723, 281, 7160], "avg_logprob": -0.2275240360544278, "compression_ratio": 1.9391304347826086, "no_speech_prob": 0.0, 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"probability": 0.93896484375}], "temperature": 1.0}, {"id": 58, "seek": 142675, "start": 1404.13, "end": 1426.75, "text": "حلو كتير، مية سبعة و إتنين و أشعة كيلو باسكال في سبعمية و ستين طور على مية و واحد يعني تكافئ اللي هي الضغط الجوي، سبعمية و ستين طور، مية و واحد point three two five كيلو باسكال زي ما احنا شوفنا قبل شوية، فبسهولة التحويل يعني قضية سهلة للغاية convert a pressure of 745 tor to kilopascal", "tokens": [5016, 1211, 2407, 9122, 2655, 13546, 12399, 3714, 10632, 8608, 3555, 27884, 4032, 11933, 2655, 1863, 9957, 4032, 5551, 8592, 27884, 9122, 26895, 2407, 4724, 32277, 4117, 6027, 8978, 8608, 3555, 25957, 10632, 4032, 8608, 2655, 9957, 23032, 13063, 15844, 3714, 10632, 4032, 36764, 24401, 37495, 22653, 6055, 4117, 31845, 19986, 13672, 1829, 39896, 6024, 114, 17082, 9566, 25724, 45865, 12399, 8608, 3555, 25957, 10632, 4032, 8608, 2655, 9957, 23032, 13063, 12399, 3714, 10632, 4032, 36764, 24401, 935, 1045, 732, 1732, 9122, 26895, 2407, 4724, 32277, 4117, 6027, 30767, 1829, 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zero atmosphere في ال closed end لو كانت ضغط zero atmosphere جال هدول والله زي بعض لأن هانفش عندى اي ضغط هدى زي هدى فهدى بيقرألي هدول هد زي بعض تماما زي بعض تماما لو كان عندى", "tokens": [1829, 3555, 4587, 7578, 9673, 7649, 2407, 3714, 36081, 2288, 8717, 45367, 9957, 35186, 1975, 15042, 5395, 917, 35186, 1975, 15042, 1269, 917, 6225, 2304, 2407, 15042, 45164, 25961, 2655, 48812, 17082, 9566, 4018, 8018, 8978, 2423, 5395, 917, 45164, 25961, 2655, 48812, 17082, 9566, 4018, 8018, 10874, 6027, 8032, 3215, 12610, 16070, 43761, 30767, 1829, 45030, 11242, 5296, 33456, 8032, 7649, 5172, 8592, 43242, 7578, 1975, 1829, 48812, 17082, 9566, 8032, 3215, 7578, 30767, 1829, 8032, 3215, 7578, 6156, 3224, 3215, 7578, 4724, 1829, 4587, 2288, 10721, 20292, 8032, 3215, 12610, 8032, 3215, 30767, 1829, 45030, 11242, 46811, 10943, 995, 30767, 1829, 45030, 11242, 46811, 10943, 995, 45164, 25961, 43242, 7578], "avg_logprob": -0.22815264853755984, "compression_ratio": 1.9748743718592965, "no_speech_prob": 0.0, 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"end": 1867.03, "word": " gas", "probability": 0.94775390625}, {"start": 1867.03, "end": 1867.33, "word": " laws", "probability": 0.8681640625}, {"start": 1867.33, "end": 1867.45, "word": " اللي", "probability": 0.857666015625}, {"start": 1867.45, "end": 1867.59, "word": " هي", "probability": 0.8603515625}, {"start": 1867.59, "end": 1868.21, "word": " قوانين", "probability": 0.9901123046875}, {"start": 1868.21, "end": 1868.97, "word": " الغازات", "probability": 0.9906005859375}, {"start": 1868.97, "end": 1870.07, "word": " في", "probability": 0.80029296875}, {"start": 1870.07, "end": 1870.67, "word": " الواقع", "probability": 0.9898681640625}], "temperature": 1.0}, {"id": 77, "seek": 188760, "start": 1871.6, "end": 1887.6, "text": "بنقدر احنا نحدد خصائص الخصائص الفيزيائية لأي غاز إذا كان عرفنا أربع حاجات ال pressure للغاز وال volume وال temperature والكمية", "tokens": [3555, 1863, 28543, 2288, 1975, 5016, 8315, 8717, 24401, 3215, 16490, 9381, 16373, 9381, 33962, 9381, 16373, 9381, 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{"start": 1923.58, "end": 1923.78, "word": " بين", "probability": 0.91015625}, {"start": 1923.78, "end": 1924.08, "word": " اتنين", "probability": 0.920654296875}, {"start": 1924.08, "end": 1924.22, "word": " من", "probability": 0.994140625}, {"start": 1924.22, "end": 1924.7, "word": " هدول", "probability": 0.9420572916666666}, {"start": 1924.7, "end": 1925.44, "word": " او", "probability": 0.7093505859375}, {"start": 1925.44, "end": 1926.0, "word": " تلاتة", "probability": 0.946533203125}, {"start": 1926.0, "end": 1926.26, "word": " او", "probability": 0.947509765625}, {"start": 1926.26, "end": 1926.7, "word": " الأربعة", "probability": 0.7939453125}, {"start": 1926.7, "end": 1926.92, "word": " هذه", "probability": 0.27783203125}, {"start": 1926.92, "end": 1927.1, "word": " ايه", "probability": 0.88330078125}, {"start": 1927.1, "end": 1927.62, "word": " كلها", "probability": 0.95703125}, {"start": 1927.62, "end": 1928.16, "word": " gas", "probability": 0.4833984375}, {"start": 1928.16, "end": 1928.44, "word": " laws", "probability": 0.853515625}, {"start": 1928.44, "end": 1928.66, "word": " هذه", "probability": 0.73583984375}, {"start": 1928.66, "end": 1929.06, "word": " قوانين", "probability": 0.99072265625}, {"start": 1929.06, "end": 1929.64, "word": " غازات", "probability": 0.9837239583333334}], "temperature": 1.0}, {"id": 80, "seek": 195274, "start": 1930.3, "end": 1952.74, "text": "يعني علاقة بين ال pressure و ال volume هذا قانون غاز ال pressure و ال temperature قانون غاز ال volume و ال temperature قانون غاز ال pressure و ال in قانون غاز ال volume و ال in قانون غاز ال pressure و ال volume و ال in قانون غاز أي combination من هدول الأربعة أي combination سواء كانت من اتنين من تلاتة من الأربعة كل واحد من هدول يسمى قانون من قوانين الغاز", "tokens": [40228, 22653, 11203, 995, 28671, 49374, 2423, 3321, 4032, 2423, 5523, 23758, 12174, 7649, 11536, 32771, 31377, 2423, 3321, 4032, 2423, 4292, 12174, 7649, 11536, 32771, 31377, 2423, 5523, 4032, 2423, 4292, 12174, 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molecules اذا زي لعد انه moles فهي نفس ال mole relationship يعني", "tokens": [39237, 10943, 22807, 6156, 39319, 8315, 8032, 6027, 1412, 47525, 15040, 9154, 8717, 2655, 9566, 1211, 3615, 15844, 2423, 34286, 3714, 43020, 8717, 2655, 9566, 1211, 3615, 15844, 2423, 22219, 8978, 11331, 1211, 9673, 3794, 16373, 1211, 30767, 1829, 19446, 8032, 1863, 8592, 38688, 8978, 9673, 14851, 4587, 36150, 32239, 3224, 22807, 5296, 33456, 3224, 37495, 22653, 28242, 5523, 4724, 33753, 2407, 7578, 15844, 8717, 36178, 18863, 3215, 3215, 9154, 2423, 13093, 1975, 15730, 30767, 1829, 5296, 22488, 16472, 3224, 34286, 6156, 3224, 1829, 8717, 36178, 2423, 6353, 2480, 37495, 22653], "avg_logprob": -0.22860055011899574, "compression_ratio": 1.733009708737864, "no_speech_prob": 0.0, "words": [{"start": 2778.42, "end": 2778.92, "word": "تمام؟", "probability": 0.5105387369791666}, {"start": 2778.92, "end": 2779.2, "word": " فاحنا", "probability": 0.92578125}, {"start": 2779.2, "end": 2779.38, "word": " هال", 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" لنا", "probability": 0.79248046875}, {"start": 2909.59, "end": 2910.15, "word": " بس", "probability": 0.958251953125}, {"start": 2910.15, "end": 2910.29, "word": " هو", "probability": 0.96826171875}, {"start": 2910.29, "end": 2910.55, "word": " بده", "probability": 0.832763671875}, {"start": 2910.55, "end": 2911.15, "word": " يفرجينا", "probability": 0.96396484375}, {"start": 2911.15, "end": 2911.73, "word": " كيف", "probability": 0.9794921875}, {"start": 2911.73, "end": 2912.23, "word": " تغيير", "probability": 0.955322265625}, {"start": 2912.23, "end": 2912.43, "word": " ال", "probability": 0.9580078125}, {"start": 2912.43, "end": 2912.79, "word": " in", "probability": 0.3095703125}, {"start": 2912.79, "end": 2914.73, "word": " بيغير", "probability": 0.885498046875}, {"start": 2914.73, "end": 2915.29, "word": " يعني", "probability": 0.84765625}, {"start": 2915.29, "end": 2916.83, "word": " المتغيرات", "probability": 0.9806640625}, {"start": 2916.83, "end": 2917.11, "word": " زي", "probability": 0.951171875}, {"start": 2917.11, "end": 2917.25, "word": " ال", "probability": 0.95361328125}, {"start": 2917.25, "end": 2917.53, "word": " volume", "probability": 0.98876953125}, {"start": 2917.53, "end": 2917.73, "word": " أو", "probability": 0.5166015625}, {"start": 2917.73, "end": 2917.81, "word": " ال", "probability": 0.91796875}, {"start": 2917.81, "end": 2918.09, "word": " pressure", "probability": 0.98291015625}, {"start": 2918.09, "end": 2918.29, "word": " أو", "probability": 0.62255859375}, {"start": 2918.29, "end": 2918.59, "word": " غيره", "probability": 0.97412109375}], "temperature": 1.0}, {"id": 124, "seek": 293463, "start": 2919.05, "end": 2934.63, "text": "فبقول what happens to the density of a gas as the gas is heated in a constant volume container ماعملاش حاجة نفس الغاز بس خنها في constant volume بزيدش الحجم لإنه جالي constant volume", "tokens": [5172, 3555, 39648, 437, 2314, 281, 264, 10305, 295, 257, 4211, 382, 264, 4211, 307, 18806, 294, 257, 5754, 5523, 10129, 19446, 25957, 1211, 33599, 11331, 26108, 3660, 8717, 36178, 6024, 118, 31377, 4724, 3794, 16490, 1863, 11296, 8978, 5754, 5523, 4724, 11622, 25708, 8592, 21542, 7435, 2304, 5296, 28814, 1863, 3224, 10874, 6027, 1829, 5754, 5523], "avg_logprob": -0.19450431522624245, "compression_ratio": 1.4683544303797469, "no_speech_prob": 0.0, "words": [{"start": 2919.05, "end": 2919.59, "word": "فبقول", "probability": 0.7003580729166666}, {"start": 2919.59, "end": 2919.87, "word": " what", "probability": 0.62255859375}, {"start": 2919.87, "end": 2920.37, "word": " happens", "probability": 0.904296875}, {"start": 2920.37, "end": 2920.55, "word": " to", "probability": 0.97607421875}, {"start": 2920.55, "end": 2920.95, "word": " the", "probability": 0.8232421875}, {"start": 2920.95, "end": 2921.41, "word": " density", "probability": 0.92236328125}, {"start": 2921.41, "end": 2921.65, "word": " of", "probability": 0.9814453125}, {"start": 2921.65, "end": 2921.83, "word": " a", "probability": 0.97119140625}, {"start": 2921.83, "end": 2922.09, "word": " gas", "probability": 0.92138671875}, {"start": 2922.09, "end": 2922.49, "word": " as", "probability": 0.82373046875}, {"start": 2922.49, "end": 2923.23, "word": " the", "probability": 0.84619140625}, {"start": 2923.23, "end": 2923.57, "word": " gas", "probability": 0.93701171875}, {"start": 2923.57, "end": 2923.85, "word": " is", "probability": 0.96240234375}, {"start": 2923.85, "end": 2924.37, "word": " heated", "probability": 0.94921875}, {"start": 2924.37, "end": 2924.71, "word": " in", "probability": 0.96728515625}, {"start": 2924.71, "end": 2924.97, "word": " a", "probability": 0.978515625}, {"start": 2924.97, "end": 2925.43, "word": " constant", "probability": 0.89892578125}, {"start": 2925.43, "end": 2925.85, "word": " volume", "probability": 0.93017578125}, {"start": 2925.85, "end": 2926.37, "word": " container", "probability": 0.89599609375}, {"start": 2926.37, "end": 2927.05, "word": " ماعملاش", "probability": 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"word": " جالي", "probability": 0.7604166666666666}, {"start": 2933.81, "end": 2934.17, "word": " constant", "probability": 0.94091796875}, {"start": 2934.17, "end": 2934.63, "word": " volume", "probability": 0.96533203125}], "temperature": 1.0}, {"id": 125, "seek": 296584, "start": 2936.52, "end": 2965.84, "text": "بس الحجم بسخن اه لكن ايه قال الحجم بيضله ثابت هو قال لي هيك الحجم بيضله ثابت يبقى لا لا اتغيرت الكتلة ولا اتغير الحجم فاه فقال لي can not change لا اتغيرت الكتلة ولا اتغير الحجم اذا not change طيب ال gas is compressed at constant temperature اه الحجم اشمله قل بدها تزيد الكثافة بدها تزيد", "tokens": [3555, 3794, 21542, 7435, 2304, 4724, 3794, 9778, 1863, 1975, 3224, 44381, 1975, 1829, 3224, 50239, 21542, 7435, 2304, 4724, 1829, 11242, 43761, 38637, 16758, 2655, 31439, 50239, 32239, 39896, 4117, 21542, 7435, 2304, 4724, 1829, 11242, 43761, 38637, 16758, 2655, 7251, 3555, 4587, 7578, 20193, 20193, 1975, 2655, 17082, 13546, 2655, 33251, 2655, 37977, 49429, 1975, 2655, 17082, 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"end": 2948.8, "word": " not", "probability": 0.88525390625}, {"start": 2948.8, "end": 2949.38, "word": " change", "probability": 0.833984375}, {"start": 2949.38, "end": 2950.42, "word": " لا", "probability": 0.4462890625}, {"start": 2950.42, "end": 2950.88, "word": " اتغيرت", "probability": 0.96337890625}, {"start": 2950.88, "end": 2951.32, "word": " الكتلة", "probability": 0.9920247395833334}, {"start": 2951.32, "end": 2952.18, "word": " ولا", "probability": 0.97412109375}, {"start": 2952.18, "end": 2952.54, "word": " اتغير", "probability": 0.971435546875}, {"start": 2952.54, "end": 2952.94, "word": " الحجم", "probability": 0.9894205729166666}, {"start": 2952.94, "end": 2953.28, "word": " اذا", "probability": 0.77294921875}, {"start": 2953.28, "end": 2953.58, "word": " not", "probability": 0.5126953125}, {"start": 2953.58, "end": 2953.98, "word": " change", "probability": 0.75048828125}, {"start": 2953.98, "end": 2955.26, "word": " طيب", "probability": 0.9513346354166666}, {"start": 2955.26, "end": 2955.82, "word": " ال", "probability": 0.67041015625}, {"start": 2955.82, "end": 2956.18, "word": " gas", "probability": 0.78564453125}, {"start": 2956.18, "end": 2956.46, "word": " is", "probability": 0.94580078125}, {"start": 2956.46, "end": 2957.26, "word": " compressed", "probability": 0.865234375}, {"start": 2957.26, "end": 2958.34, "word": " at", "probability": 0.9462890625}, {"start": 2958.34, "end": 2959.04, "word": " constant", "probability": 0.90234375}, {"start": 2959.04, "end": 2959.8, "word": " temperature", "probability": 0.93994140625}, {"start": 2959.8, "end": 2960.66, "word": " اه", "probability": 0.84814453125}, {"start": 2960.66, "end": 2961.72, "word": " الحجم", "probability": 0.98974609375}, {"start": 2961.72, "end": 2962.12, "word": " اشمله", "probability": 0.6796875}, {"start": 2962.12, "end": 2962.44, "word": " قل", "probability": 0.968505859375}, {"start": 2962.44, "end": 2963.54, "word": " بدها", "probability": 0.71728515625}, {"start": 2963.54, "end": 2964.04, "word": " تزيد", "probability": 0.9775390625}, {"start": 2964.04, "end": 2965.38, "word": " الكثافة", "probability": 0.9085693359375}, {"start": 2965.38, "end": 2965.56, "word": " بدها", "probability": 0.9580078125}, {"start": 2965.56, "end": 2965.84, "word": " تزيد", "probability": 0.99609375}], "temperature": 1.0}, {"id": 126, "seek": 298602, "start": 2966.08, "end": 2986.02, "text": "طيب التالتة additional gas is added to a constant volume container حطينا كمان كمية الحجم بيزيدش constant volume constant volume container بس حطينا n زيادة حطينا كتلة زيادة كيف؟", "tokens": [9566, 1829, 3555, 16712, 6027, 2655, 3660, 4497, 4211, 307, 3869, 281, 257, 5754, 5523, 10129, 11331, 9566, 1829, 8315, 9122, 2304, 7649, 9122, 2304, 10632, 21542, 7435, 2304, 4724, 1829, 11622, 25708, 8592, 5754, 5523, 5754, 5523, 10129, 4724, 3794, 11331, 9566, 1829, 8315, 297, 30767, 1829, 18513, 3660, 11331, 9566, 1829, 8315, 9122, 2655, 37977, 30767, 1829, 18513, 3660, 9122, 33911, 22807], "avg_logprob": -0.13581730769230768, "compression_ratio": 1.6551724137931034, "no_speech_prob": 0.0, "words": [{"start": 2966.08, "end": 2966.62, "word": "طيب", "probability": 0.9484049479166666}, {"start": 2966.62, "end": 2967.98, "word": " التالتة", "probability": 0.889892578125}, {"start": 2967.98, "end": 2968.76, "word": " additional", "probability": 0.439208984375}, {"start": 2968.76, "end": 2969.88, "word": " gas", "probability": 0.63525390625}, {"start": 2969.88, "end": 2970.1, "word": " is", "probability": 0.923828125}, {"start": 2970.1, "end": 2970.52, "word": " added", "probability": 0.8916015625}, {"start": 2970.52, "end": 2970.86, "word": " to", "probability": 0.95751953125}, {"start": 2970.86, "end": 2971.1, "word": " a", "probability": 0.95361328125}, {"start": 2971.1, "end": 2971.6, "word": " constant", "probability": 0.87890625}, {"start": 2971.6, "end": 2972.12, "word": " volume", "probability": 0.92822265625}, {"start": 2972.12, "end": 2972.68, "word": " container", "probability": 0.94091796875}, {"start": 2972.68, "end": 2973.34, "word": " حطينا", "probability": 0.8310546875}, {"start": 2973.34, "end": 2973.88, "word": " كمان", "probability": 0.98974609375}, {"start": 2973.88, "end": 2974.5, "word": " كمية", "probability": 0.994140625}, {"start": 2974.5, "end": 2975.16, "word": " الحجم", "probability": 0.9622395833333334}, {"start": 2975.16, "end": 2975.58, "word": " بيزيدش", "probability": 0.80224609375}, {"start": 2975.58, "end": 2975.86, "word": " constant", "probability": 0.8466796875}, {"start": 2975.86, "end": 2976.4, "word": " volume", "probability": 0.982421875}, {"start": 2976.4, "end": 2977.78, "word": " constant", "probability": 0.2098388671875}, {"start": 2977.78, "end": 2978.48, "word": " volume", "probability": 0.978515625}, {"start": 2978.48, "end": 2979.08, "word": " container", "probability": 0.91796875}, {"start": 2979.08, "end": 2979.52, "word": " بس", "probability": 0.971923828125}, {"start": 2979.52, "end": 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جدا ان يكون فيه عندك كمية كبيرة من الجاز و + +25 +00:02:11,150 --> 00:02:14,970 +تحطها فيه حجم صغير جدا أبسط مثال على هذا الكلام + +26 +00:02:14,970 --> 00:02:17,990 +مثلا ال cylinder تبع الناس للجاز اللي بيكون عندنا + +27 +00:02:17,990 --> 00:02:22,150 +في البيوت هذا كمية هائلة من الجاز لكن ضغطينه و + +28 +00:02:22,150 --> 00:02:26,740 +حطينه في ايه؟ في وعاء ضيق فال gasesبتنضغط بينما + +29 +00:02:26,740 --> 00:02:30,420 +الـ liquids والـ solids practically incompressible + +30 +00:02:30,420 --> 00:02:34,440 +practically طبعا ممكن نقول انها بتنضغط يعني قليل + +31 +00:02:34,440 --> 00:02:37,040 +جدا جدا مش هنتكلم عن هذا الكلام بنقول من ناحية + +32 +00:02:37,040 --> 00:02:40,540 +عملية بالنسبالنا في هذا المساء من ناحية عملية هي + +33 +00:02:40,540 --> 00:02:44,940 +لا تنضغط أما الغازات فانضغطها سهل للغاية ال + +34 +00:02:44,940 --> 00:02:48,480 +densities للغاز قليلة جدا إذا ما كورنت بال + +35 +00:02:48,480 --> 00:02:53,210 +densities لل liquids وال solids لدرجة انهالـ + +36 +00:02:53,210 --> 00:02:58,850 +Density مثلاً للـ Liquid بنجيسها جرام على المل أو + +37 +00:02:58,850 --> 00:03:03,690 +جرام على السنتمتر مكعب بينما بالنسبة للجازيز + +38 +00:03:03,690 --> 00:03:07,790 +بنجيسها جرام على اللتر لأن كمية قليلة فبدنا نتذكر + +39 +00:03:07,790 --> 00:03:14,110 +أن ال density للجاز بنجيسها جرام على اللتر الجازيز + +40 +00:03:14,110 --> 00:03:18,450 +وين حطينا مجموعة من الجازيز فورا بتكون homogenous + +41 +00:03:18,450 --> 00:03:23,070 +mixtureبحيث انه كل غاز بيكون بيملأ ال container + +42 +00:03:23,070 --> 00:03:27,150 +اللي هو موجود فيه وين في أي منطقة اي جزء من ال + +43 +00:03:27,150 --> 00:03:30,710 +container هأخدنا منه عينة بنلاقي فيها الغازات + +44 +00:03:30,710 --> 00:03:38,570 +الموجودة كلها بحسب ال mole fractions لإلها فو كأنه + +45 +00:03:38,570 --> 00:03:43,450 +جزيئات الغاز بتتصرف و كأنه كل جزء موجود لوحده في + +46 +00:03:43,450 --> 00:03:47,530 +الوعاء والاخرين غير موجودين ليه؟ لأنه في الحقيقة + +47 +00:03:48,050 --> 00:03:53,410 +المسافات بين جزيئات الغاز واسعة جدا جدا كبيرة خالص + +48 +00:03:53,410 --> 00:03:57,930 +إذا ما قورنت ب .. خلانا نقول الحجم الحقيقي لـ + +49 +00:03:57,930 --> 00:04:04,190 +molecule أو جزيئ الغاز ال molecular gases عادة + +50 +00:04:05,270 --> 00:04:11,370 +مجموعات نوبل جازيز مخصصة نوبل جازيز مخصصة نوبل + +51 +00:04:11,370 --> 00:04:16,890 +جازيز مخصصة نوبل جازيز مخصصة نوبل جازيز مخصصة نوبل + +52 +00:04:16,890 --> 00:04:18,970 +جازيز مخصصة نوبل جازيز مخصصة نوبل جازيز مخصصة نوبل + +53 +00:04:18,970 --> 00:04:19,050 +جازيز مخصصة نوبل جازيز مخصصة نوبل جازيز مخصصة نوبل + +54 +00:04:19,050 --> 00:04:22,090 +جازيز مخصصة نوبل جازيز مخصصة نوبل جازيز مخصصة نوبل + +55 +00:04:22,090 --> 00:04:27,370 +جازيز مخصصة نوبل جازيز مخصصة نوبل جازيز مخصصة نوبل + +56 +00:04:27,370 --> 00:04:33,550 +جازيز مخصصة نوبلاللي في F2 و CL2 فهذه موليكولار + +57 +00:04:33,550 --> 00:04:37,350 +جازي و نيتروجين و اكسوجين موليكولار جازي و ايضا + +58 +00:04:37,350 --> 00:04:40,710 +خلط من مثلا كاربون هيدروجين كاربون اكسوجين + +59 +00:04:40,710 --> 00:04:46,150 +نيتروجين اكسوجين كلور اكسوجين مثلا يعني هذه كلها + +60 +00:04:46,150 --> 00:04:51,010 +اقارة عن جازي فهي بتكون ايه؟ non-metallic elements + +61 +00:04:51,010 --> 00:04:56,110 +ملاقيش مثلا جاز بتكون من متل و non-metalal؟ لأ + +62 +00:04:56,660 --> 00:05:00,280 +الهيدروجين كان نان ميتال برضه و الهيدروجين H2 برضه + +63 +00:05:00,280 --> 00:05:08,120 +بيعطيني نان ميتاليك كمباون اللي هو عبارة عن جاز + +64 +00:05:08,120 --> 00:05:12,300 +بنقول جاز هف very similar physical properties + +65 +00:05:12,300 --> 00:05:16,180 +بالرغم من ان ال chemical properties ممكن انه + +66 +00:05:16,180 --> 00:05:20,580 +تتفاوت لكن ال physical properties تقريبا نفس ال + +67 +00:05:20,580 --> 00:05:23,420 +physical properties بقصد بال chemical properties + +68 +00:05:23,420 --> 00:05:27,630 +يعني مثلا ال نيتروجين خاملبينما الـ Oxygen مو + +69 +00:05:27,630 --> 00:05:31,570 +أكسيد الـ Oxygen ضروري للحياة الـ Nitrogen لأ مثلا + +70 +00:05:31,570 --> 00:05:37,570 +بالنسبالنا احنا كبشر يعني او ككائنات حية مثلا الـ + +71 +00:05:37,570 --> 00:05:42,050 +Carbon Dioxide غاز ينشأ عن الاحتراق بنقدر نقول انه + +72 +00:05:42,050 --> 00:05:48,630 +مش سام بينما الـ CO يعتبر سام فيعني تتفاوت الخصائص + +73 +00:05:48,630 --> 00:05:52,330 +الكيمية بينما الفيزيائية لأ هلاحظ انه ممكن انه + +74 +00:05:52,330 --> 00:05:57,580 +نتعامل مع الغازات كلهابنفس الصورة من الناحية + +75 +00:05:57,580 --> 00:06:04,280 +الفيزيائية طبعا موجود عندها هذه المجموعة اللي هي + +76 +00:06:04,280 --> 00:06:09,060 +مجموعة النوبل جازيز هذه عبارة من مونو أتميك مونو + +77 +00:06:09,060 --> 00:06:14,360 +أتميك جازيز مونو أتميك يعني الهيليوم لحاله ني + +78 +00:06:14,360 --> 00:06:21,440 +لحاله ذره وهي غاز الارجون ذره وهي غاز و هكذا رينون + +79 +00:06:21,440 --> 00:06:29,260 +هذا زينون هذا رينون زينونزينون مشهور كتير في + +80 +00:06:29,260 --> 00:06:35,440 +العلوم يعني بيستخدم في عمل لمبات و بيستخدم برضه في + +81 +00:06:35,440 --> 00:06:39,260 +ال lasers فهو بي .. excitement lasers فهو مشهور + +82 +00:06:39,260 --> 00:06:45,340 +كتير على أي حال ال N هذا بتاخد N2 ال O O2 ال F F2 + +83 +00:06:45,340 --> 00:06:52,240 +بس هدول مونو أتوميك ال Cl Cl2 ال brom و ال mercury + +84 +00:06:52,240 --> 00:06:59,600 +هدول liquidsبر2 و HG هدول liquids طبعا الهيدروجين + +85 +00:06:59,600 --> 00:07:02,780 +هو عبارة عن جاز بس مايكونش مونو اتوميك او داي + +86 +00:07:02,780 --> 00:07:10,440 +اتوميك H2 بعض الغازات مثلا هيدروجين سايانايد هذا + +87 +00:07:10,440 --> 00:07:15,100 +هو غاز بينما لو كان موجود في الميه هيدرو سايانك + +88 +00:07:15,100 --> 00:07:20,170 +أسدبنتذكر هذا الكلام هيدرو سيانك أسد وهذا بنتكلم + +89 +00:07:20,170 --> 00:07:24,490 +عن الغازات فبنقراها كغازات H2S هيدروجين سالفايت + +90 +00:07:24,490 --> 00:07:28,130 +وقولنا انه طب هذه عبارة عن non metallic compound + +91 +00:07:28,130 --> 00:07:34,070 +حلو كتير لكن احنا عموما يعني الهيدروجين بنقولش + +92 +00:07:34,070 --> 00:07:36,810 +مثلا dye hydrogen لأن الهيدروجين معروف انه واحد + +93 +00:07:36,810 --> 00:07:40,870 +بنقولش dye hydrogenالـ CO كاربون مونوكسايد كاربون + +94 +00:07:40,870 --> 00:07:45,690 +دايوكسايد كاربون دايوكسايد كاربون + +95 +00:07:45,690 --> 00:07:52,090 +دايوكسايد كاربون دايوكسايد كاربون دايوكسايد كاربون + +96 +00:07:52,090 --> 00:07:53,710 +دايوكسايد كاربون دايوكسايد كاربون دايوكسايد كاربون + +97 +00:07:53,710 --> 00:07:54,010 +دايوكسايد كاربون دايوكسايد كاربون دايوكسايد كاربون + +98 +00:07:54,010 --> 00:07:54,010 +دايوكسايد كاربون دايوكسايد كاربون دايوكسايد كاربون + +99 +00:07:54,010 --> 00:07:59,210 +دايوكسايد كاربون دايوكسايد + +100 +00:07:59,210 --> 00:08:03,850 +كاربون دايوكسايد كاربون داالـ NO2 نيتروجين + +101 +00:08:03,850 --> 00:08:09,210 +دايوكسايد نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه + +102 +00:08:09,210 --> 00:08:09,350 +نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه + +103 +00:08:09,350 --> 00:08:17,170 +نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه + +104 +00:08:17,170 --> 00:08:27,190 +نفسه نفسه نفسه نفسه نفسه + +105 +00:08:28,610 --> 00:08:32,150 +رائحته يعني مميزة، نفاذة للغاية، يعني مش سهل أنه + +106 +00:08:32,150 --> 00:08:37,830 +هيتنفس في وجودها الـ Sulphur dioxide ال .. ال .. + +107 +00:08:37,830 --> 00:08:43,550 +ال .. acidic rain فتتفاوت في خصائصها الكيميا، لكن + +108 +00:08:43,550 --> 00:08:46,210 +إذا كانوا حاطينها مع بعض في mixture فيزيائيا + +109 +00:08:46,210 --> 00:08:51,750 +كخصائص فيزيائية بنلاحظ إنه نفس الكلام و كأنها غاز + +110 +00:08:51,750 --> 00:08:58,880 +واحد طيب، الآن نتكلم عن الـ atmospheric pressureفي + +111 +00:08:58,880 --> 00:09:03,280 +الحقيقة من يعني قديم الزمان كانوا الناس بيعتقدوا + +112 +00:09:03,280 --> 00:09:08,660 +ان ال atmosphere مافيش له ضغط الجو عموما مافيش له + +113 +00:09:08,660 --> 00:09:14,000 +ضغط على الأرض يعني مافيه له ضغط لكن + +114 +00:09:14,000 --> 00:09:20,560 +حقيقة حقيقة بنقول ان وين في عندي غازات فهذه + +115 +00:09:20,560 --> 00:09:26,420 +الغازات بتعطيني ضغط على ال surfaces اللي هي in + +116 +00:09:26,420 --> 00:09:30,350 +contact معاهاكويس وين فيه غاز in contact مع + +117 +00:09:30,350 --> 00:09:34,830 +surface معينة بلاحظ انه هذا الغاز بيبذل او يعني + +118 +00:09:34,830 --> 00:09:40,790 +بيعطي ضغط على هذه ال surface وهذا الكلام يعني بديه + +119 +00:09:40,790 --> 00:09:44,410 +جدا ممكن نلاحظه في الحياة العملية بشكل كبير + +120 +00:09:44,410 --> 00:09:52,190 +وحفرجيكم مثال يعني بعد شوية فال gas في بلون ال gas + +121 +00:09:52,190 --> 00:09:57,930 +اللي داخل البلون بيتغط على السطح الداخل للبلونحلو + +122 +00:09:57,930 --> 00:10:01,550 +كتير و الغاز اللى برا البالون بيبط على السطح + +123 +00:10:01,550 --> 00:10:04,570 +الداخل للبالون لو كانت ضغط الخارجي أكبر من ضغط + +124 +00:10:04,570 --> 00:10:09,650 +الداخل مش هنقدر ننفق البالون معاها نتخيل هذا + +125 +00:10:09,650 --> 00:10:13,610 +الكلام لو كان الضغط الخارجي قوى جدا مش هنقدر ننفق + +126 +00:10:13,610 --> 00:10:18,770 +البالون يعنى و لو كان الضغط الخارجي خفيف بسهولة + +127 +00:10:18,770 --> 00:10:22,390 +طفل صغير ممكن ننفق البالون هذا كلام بالنسبة لنا + +128 +00:10:22,390 --> 00:10:31,350 +واضح كتيرعموما في عندنا الجزيئات الغاز طبعاً إلها + +129 +00:10:31,350 --> 00:10:36,430 +كتل، كل غاز يعني جزيئاته إلها كتلة معينة، وأيضا + +130 +00:10:36,430 --> 00:10:40,190 +بيبتد تحرك جزيئات الغاز بسرعة كبيرة جدا، فلجزيئات + +131 +00:10:40,190 --> 00:10:45,190 +الغاز kinetic energy، أي غاز في لجزيئاته kinetic + +132 +00:10:45,190 --> 00:10:49,080 +energyهذه الـ kinetic energy أعلى من الـ + +133 +00:10:49,080 --> 00:10:54,920 +gravitational attraction للأرض وإلا لو كانت الـ + +134 +00:10:54,920 --> 00:10:58,640 +gravitational attraction أكبر من الـ kinetic + +135 +00:10:58,640 --> 00:11:02,060 +energy كان لجينا كل الهواء اللي في الجو متجمع على + +136 +00:11:02,060 --> 00:11:05,400 +الأرض زي و زي أي جبل زي و زي أي .. لكن لا الـ + +137 +00:11:05,400 --> 00:11:08,800 +kinetic energy عندنا أكبرمن الـ gravitational + +138 +00:11:08,800 --> 00:11:12,980 +attraction وبالتالي جزيئات الغاز من الجهاش في + +139 +00:11:12,980 --> 00:11:20,620 +الحقيقة متجمعة على سطح الأرض بتامها في الهواءإلا + +140 +00:11:20,620 --> 00:11:24,020 +إنه مش معناة كلام إن الـ gravity ما لهاش تأثير، لأ + +141 +00:11:24,020 --> 00:11:27,820 +الـ gravity إلها تأثير وهي السبب في الضغط الجو + +142 +00:11:27,820 --> 00:11:33,680 +اللي احنا بنلاحظه، ببساطة ممكن نثبت إنه في ضغط جوي + +143 +00:11:33,680 --> 00:11:39,260 +كشيء عام، بإنه مثلا لو أخدنا علبة كولة فاضية، مش + +144 +00:11:39,260 --> 00:11:43,660 +علبة، اللي هي جنية كولة فاضية، plastic، و حاولنا + +145 +00:11:43,660 --> 00:11:48,690 +نشفط الغاز اللي فيهافإيش بيحصل لل .. of time كمش + +146 +00:11:48,690 --> 00:11:53,590 +اه يعني بتعدي لجوة cave in تمام طب ليش cave in؟ + +147 +00:11:53,590 --> 00:11:58,650 +جال لأنه ضغط الغاز أو الضغط الجوي صار أكبر من ضغط + +148 +00:11:58,650 --> 00:12:03,290 +الغاز داخل ال إيه؟ داخل ال .. البطل وبالتالي ضغط + +149 +00:12:03,290 --> 00:12:08,360 +على البطل فخلاها يحصلها caving inببساطة لأنه عدد + +150 +00:12:08,360 --> 00:12:13,260 +الجزيئات لما انا شفطت الغاز اللي في ال bottle ايش + +151 +00:12:13,260 --> 00:12:16,180 +اللي حصل؟ عدد الجزيئات اللي موجودة في هذه ال + +152 +00:12:16,180 --> 00:12:20,500 +bottle جال فبالتالي ضغط الجزيئات على السطح الداخلي + +153 +00:12:20,500 --> 00:12:27,640 +لل bottle طبعا جال وبالتالي اه cave inالضغط + +154 +00:12:27,640 --> 00:12:30,240 +الخارجي أكبر من الضغط الداخلي فهي تبساطة خالص + +155 +00:12:30,240 --> 00:12:35,640 +بيخلي .. بيخلي أنا أعتقد أنه في للضغط .. في لل .. + +156 +00:12:35,640 --> 00:12:39,760 +يعني في عندي حاجة اسمها ضغط جوي، في عندي إشي اسمه + +157 +00:12:39,760 --> 00:12:44,500 +ضغط جوي وإلا إيش بده يخلي ال .. ال .. الـvotal + +158 +00:12:44,500 --> 00:12:50,240 +يعني تنكمش على سبيل المثال، فلأ في عندي ضغط جوي، + +159 +00:12:50,240 --> 00:12:53,890 +ال pressureممكن يعرفوا P is defined as the force + +160 +00:12:53,890 --> 00:12:57,530 +that acts on a given area A فال P اللي هو ال + +161 +00:12:57,530 --> 00:13:00,630 +pressure بيساوي ال F على ال A ال F هي ال force وال + +162 +00:13:00,630 --> 00:13:04,790 +A هي ال area هذا الكلام مفهوم وال force كمان ممكن + +163 +00:13:04,790 --> 00:13:08,210 +تعريفها زي ما احنا عارفين بإنها MA برضه هذا الكلام + +164 +00:13:08,210 --> 00:13:11,810 +معروف من ال simple physics يعني ال F اللي هي ال + +165 +00:13:11,810 --> 00:13:17,150 +force ساوي ال mass في ال acceleration حلو كتير لو + +166 +00:13:17,150 --> 00:13:26,040 +اجينا قولنا انهفي عندى مساحة مقدارها متر مربع على + +167 +00:13:26,040 --> 00:13:32,110 +الأرض عند سطح البحر وبدي اشوف والله جداشجدّاش ال + +168 +00:13:32,110 --> 00:13:37,430 +force اللي موجود على هذه المساحة جدّاش ال force + +169 +00:13:37,430 --> 00:13:43,690 +اللي موجود على هذه المساحة فبقول هذه المساحة بتشكل + +170 +00:13:43,690 --> 00:13:49,870 +عمود مقداره يعني مساحته ال يعني واحد متر مربع + +171 +00:13:49,870 --> 00:13:53,210 +وارتفاعه ارتفاع ال atmosphere كله حوالي 200 + +172 +00:13:53,210 --> 00:13:57,170 +كيلومتر 200 كيلومتر جالوزن هذا العمود حوالي عشر + +173 +00:13:57,170 --> 00:14:00,440 +تلاف كيلو جرامالـ 200 كيلومتر من الهواء في واحد + +174 +00:14:00,440 --> 00:14:03,500 +متر مربع جالسة حوالي عشر تلف كيلو جرام طبعاً دي ال + +175 +00:14:03,500 --> 00:14:07,650 +accelerationتسعة وتميرة واحد فى عشرة أسخلصة كيلو + +176 +00:14:07,650 --> 00:14:12,330 +جرام متر على ثانية تربيهة طبعا فى علاقة بين ال .. + +177 +00:14:12,330 --> 00:14:16,250 +نيوتن + +178 +00:14:16,250 --> 00:14:19,130 +اللى هو نيوتن واحد فى عشر أسخلصة نيوتن يعنى كيلو + +179 +00:14:19,130 --> 00:14:22,710 +.. أفوا كيلو جرام متر على ثانية تربيهة عبارة عن + +180 +00:14:22,710 --> 00:14:27,610 +النيوتن ال unit للنيوتن النيوتن طبعا هو ال ايه ال + +181 +00:14:27,610 --> 00:14:31,600 +SI unit لقياسالـ Force هذا المفهوم الـ SI unit كل + +182 +00:14:31,600 --> 00:14:38,000 +ما عدا يعتبر ما هواش SI unit فعنا ال force على ال + +183 +00:14:38,000 --> 00:14:44,900 +.. اللي موجود على المتر المربع حوالي عشر تلاف كيلو + +184 +00:14:44,900 --> 00:14:48,020 +جرام في تسعة تمانية متر عتانية تربيع بتعطينا حوالي + +185 +00:14:48,020 --> 00:14:54,320 +واحد في عشر أقصى خمسة نيوتون طيب الان لو احنا ال + +186 +00:14:54,320 --> 00:14:57,840 +force .. ال force .. هذا ال force فقط على المتر + +187 +00:14:57,840 --> 00:15:02,620 +المربع بيصير pressureطبعا دي واحد متر مربع اذا + +188 +00:15:02,620 --> 00:15:08,500 +هتبقى واحد في عشر أقص خمسة اه بس ايش هيكون ان واحد + +189 +00:15:08,500 --> 00:15:12,600 +في عشر أقص خمسة بس هياخد على المتر المربع صارت ان + +190 +00:15:12,600 --> 00:15:17,300 +دي pressure بدنا نقول عنه Pascal بعد شوية ليه؟ لأن + +191 +00:15:17,300 --> 00:15:20,740 +الواحد نيوتون هو أبارح الواحد كيلو جرام متر على + +192 +00:15:20,740 --> 00:15:24,100 +ثانية الكربيا ال Pascal عرفنا عليه واحد نيوتون على + +193 +00:15:24,100 --> 00:15:28,960 +المتر المربع واحد نيوتون فلما نيجي يقول لي هانإنه + +194 +00:15:28,960 --> 00:15:33,300 +واحد فى عشرة أس خمسة نيوتون معناته والله واحد فى + +195 +00:15:33,300 --> 00:15:38,840 +عشرة أس خمسة Pascal كويس فال Pascal هو عبارة عن + +196 +00:15:38,840 --> 00:15:43,640 +النيوتون على المتر مربع ال Pascal هو الوحدة ال SI + +197 +00:15:43,640 --> 00:15:47,500 +unit لقياس ال pressure الوحدة اللى هى ال SI unit + +198 +00:15:47,500 --> 00:15:51,280 +لقياس ال pressure واحنا عارفين سابقا كمان النيوتون + +199 +00:15:51,280 --> 00:15:55,720 +عبارة عن واحد kilogram متر على الثانيةتربيع فهذا + +200 +00:15:55,720 --> 00:15:59,360 +الشكل بيننا هي ال .. واحد المتر المربع بس طبعا من + +201 +00:15:59,360 --> 00:16:01,920 +هنا يعني لو طلعنا عليه من فوق ماببينش من هنا 200 + +202 +00:16:01,920 --> 00:16:06,460 +كيلومتر ف .. لكن هو لأ هو عبارة عن حاجة عدلة خالص + +203 +00:16:06,460 --> 00:16:09,780 +يعني فهذا عبارة عن ال pressure في الحقيقة ضخم جدا + +204 +00:16:09,780 --> 00:16:14,740 +لكن العلماء قديما ماكانوش مقتنعين او الناس ماكانوش + +205 +00:16:14,740 --> 00:16:18,280 +مقتنعين ان في عنا ضغط جوة ليه؟ جال لأنه احنا + +206 +00:16:18,280 --> 00:16:21,400 +عايشين فيه فاحنا مابنحسش فيه لأنه عايشين داخله + +207 +00:16:21,400 --> 00:16:27,660 +فاحنا مابنحس فيهلكن كان في واحد اسمه تورشيل، + +208 +00:16:27,660 --> 00:16:33,380 +بتعرفوا يعني؟ كان من الناس اللي ما آمنش انه والله + +209 +00:16:33,380 --> 00:16:39,180 +فاش ضبط جوي، ما آمن فعمل barometer، الbarometer + +210 +00:16:39,180 --> 00:16:46,150 +هذا بساطة خالصقال ايه والله وعاء في ميركوري + +211 +00:16:46,150 --> 00:16:51,690 +وانبوبة طويلة ايضا ملاها ميركوري وروح جلبها في + +212 +00:16:51,690 --> 00:16:58,350 +الوعاء هان ففي الانبوبة ضال عنده ايه عمود من + +213 +00:16:58,350 --> 00:17:02,450 +الميركوري فجال هذا العمود موجود لسبب ايش السبب جال + +214 +00:17:02,450 --> 00:17:09,690 +انه ضغط الجو هان على الايهعلى الميركوري بيمنع + +215 +00:17:09,690 --> 00:17:12,530 +الميركوري هذا انه ينزل فهنا فيه ضغط و هنا فيه ضغط + +216 +00:17:12,530 --> 00:17:16,110 +لكن الدغطين متساويين و اجتيش جال لما كان هذا حوالي + +217 +00:17:16,110 --> 00:17:22,290 +760 ملي متر ذئبك مثلا 76 ساطي 760 ملي متر ذئبك هذا + +218 +00:17:22,290 --> 00:17:25,590 +ببساطة خالص فجال لأ فيه ضغط جوي طبعا الناس + +219 +00:17:25,590 --> 00:17:30,830 +ماعجبهمش برضه و يعني تفكيره او تفسيره لهذه الظاهرة + +220 +00:17:30,830 --> 00:17:40,120 +قبل برفض فظيعفيعني في احد العلماء اللي هو Pascal + +221 +00:17:40,120 --> 00:17:44,800 +قال طب احنا ليش نختلف يعني انا بدي اخد two + +222 +00:17:44,800 --> 00:17:52,220 +parameters واحد خليه عند سطح الأرض كويس والتاني + +223 +00:17:52,220 --> 00:17:57,900 +بدي اخده فوق جبل اذا كان خدناه فوق جبل عالي فمعناه + +224 +00:17:57,900 --> 00:18:01,700 +كلام ضغط الجو اللي عليه هان ايش بده يكون اقل + +225 +00:18:01,700 --> 00:18:07,280 +فالمفروض انه هانهيجيل نفس الكلام الدغط هيجيل + +226 +00:18:07,280 --> 00:18:12,760 +فبالفعل حط واحد تحت وصعد الجبل كل ما صعد لجأ انه + +227 +00:18:12,760 --> 00:18:15,520 +والله العمود بيجيل بيجيل بيجيل جالف جالف اه كيف + +228 +00:18:15,520 --> 00:18:17,980 +فيه دغط جوي؟ ليه؟ لأنه ايش اللي بيبنع العمود ينزل؟ + +229 +00:18:17,980 --> 00:18:21,280 +دغط الجوي فكل ما جالد دغط الجوي لقى العمود بينزل + +230 +00:18:21,280 --> 00:18:25,360 +ولو طلعنا دغط جوي مافيش دغط جوي هيكون والله ايه + +231 +00:18:25,360 --> 00:18:31,280 +مافيش عندى اي عمود نهائيافهذا أثبت أنه في عندنا + +232 +00:18:31,280 --> 00:18:39,180 +ضغط جوي والضغط الجوي يمكن قياسه في الحقيقة زي ما + +233 +00:18:39,180 --> 00:18:46,630 +هنشوف بعد شوية كيف ممكن نجيسهلكن هذه التجربة أثبتت + +234 +00:18:46,630 --> 00:18:50,890 +بما لا يدعم مجالا للشك أنه والله في عندنا ضغط جوء + +235 +00:18:50,890 --> 00:18:54,070 +لأنه إذا كان فيش ضغط جوء معناه الكلام لابد إلا إن + +236 +00:18:54,070 --> 00:18:59,610 +العمود هذا يبقى إما خلانا نقول ثابت أو إنه يعني ما + +237 +00:18:59,610 --> 00:19:04,090 +.. ماينزلش لأنه ضغط الجو جال فلأ كل ما طلعنا لفوق + +238 +00:19:04,090 --> 00:19:10,480 +بينزل معناه الكلام بالفعل موجود عند ضغط جوءالـ SI + +239 +00:19:10,480 --> 00:19:17,580 +unit للـ pressure قلنا إنها الـ Pascal فالـ + +240 +00:19:17,580 --> 00:19:21,320 +atmospheric pressure الـ atmospheric pressure اللي + +241 +00:19:21,320 --> 00:19:27,440 +هو الـ 760 ميلي متر ذئبق كويس هذه عبارة عن الـ + +242 +00:19:27,440 --> 00:19:32,180 +atmospheric pressure هي عبارة عن 1.01325 في عشر + +243 +00:19:32,180 --> 00:19:41,610 +أقصى خمسة Pascal أو 101.325 كيلو Pascal101.325 + +244 +00:19:41,610 --> 00:19:48,650 +كيلو باسكال طبعا قيمة ال pressure بتتوقف على + +245 +00:19:48,650 --> 00:19:52,150 +الأحوال الجوية في الحقيقة و أيضا كمان درجة الحرارة + +246 +00:19:52,150 --> 00:19:56,910 +لأن هذا كلام يتوقف عليه قداش ثقل العمود إذا كانت + +247 +00:19:56,910 --> 00:20:00,670 +مثلا رطوبة عالية عمود ثقيل مثلا يعني فتتوقف على + +248 +00:20:00,670 --> 00:20:05,930 +الأحوال الجوية وتتوقف أيضا على درجة الحرارةلكن في + +249 +00:20:05,930 --> 00:20:08,870 +عندى وحدات تانية احنا بنستخدمها كتير وحدات شائعة + +250 +00:20:08,870 --> 00:20:13,150 +في الحقيقة للتعبير عن ال pressure فمثلا اشهر الشيء + +251 +00:20:13,150 --> 00:20:19,290 +اللى هو ال atmosphere ال atmosphere 760 mm زئبق او + +252 +00:20:19,290 --> 00:20:24,120 +يعني 760 Tor يعني ال Tor عبارة عن مليمتر زئبقنمشي + +253 +00:20:24,120 --> 00:20:27,760 +خطوة، طب قلنا ال atmosphere هيك، طب إيش ال + +254 +00:20:27,760 --> 00:20:31,100 +atmosphere؟ جاها ضغط جوة، إذا one point oh one + +255 +00:20:31,100 --> 00:20:35,040 +three two five عشر أقصى خمس باسكال أو يعني مية و + +256 +00:20:35,040 --> 00:20:39,780 +واحد point three two five كيلو باسكال جال برضه هذه + +257 +00:20:39,780 --> 00:20:43,280 +بالثانية one point oh one three two five bar، + +258 +00:20:43,280 --> 00:20:50,700 +كويس؟ one point يعني ال atmosphere مش بالظبط bar، + +259 +00:20:50,700 --> 00:20:54,780 +لأبار وشوية ال atmosphere one point oh one three + +260 +00:20:54,780 --> 00:20:59,800 +two five bar فال bar .. ال bar عندى بالظبط عشرة + +261 +00:20:59,800 --> 00:21:02,940 +أقصى خمسة Pascal هذا تعريفه ال bar عشرة أقصى خمسة + +262 +00:21:02,940 --> 00:21:07,240 +Pascal لكن ال atmosphere أكتر شوية ال atmosphere + +263 +00:21:07,240 --> 00:21:11,380 +أكتر شوية فبالتالي اه ال bar عشرة أقصى خمسة Pascal + +264 +00:21:11,380 --> 00:21:16,620 +صحيح هذه الحاجات بقول أنا مهم أنه نعرفها يعني بدنا + +265 +00:21:16,620 --> 00:21:21,920 +نحفظها للأسف يعنيمش صعبة، مش صعبة، لكن بتيجي أسئلة + +266 +00:21:21,920 --> 00:21:26,200 +عليها قضية تحويل من واحدة لواحدة تانية قد نضطر إنه + +267 +00:21:26,200 --> 00:21:31,280 +نحوّل، فلازم نعرف هذه ال factors اللي موجودة، إيش + +268 +00:21:31,280 --> 00:21:34,960 +كل واحدة من وحدات ال pressure بتعني بالنسبالنا، زي + +269 +00:21:34,960 --> 00:21:39,140 +ما قلنا في ال chapter الماضي مثلا ال jewel و ال + +270 +00:21:39,140 --> 00:21:49,720 +calorieوالـ Joule مثلا عرفناه بشكل و الـ BTU مثلا + +271 +00:21:49,720 --> 00:21:54,820 +فالعلاقات بينهم مهمة في الحقيقة ابتجينا بعض + +272 +00:21:54,820 --> 00:22:00,030 +الأسئلة لازم يمكننستخدم هذه العلاقات في حالها في + +273 +00:22:00,030 --> 00:22:05,470 +عندى في امريكا والبريطانيا والدول المشتقة من هدول + +274 +00:22:05,470 --> 00:22:10,010 +البلدين تحديدا بيستخدموا واحدة تانية للتعبير عن ال + +275 +00:22:10,010 --> 00:22:14,010 +pressure بيقولوا ال PSI pound per square inch + +276 +00:22:14,010 --> 00:22:17,210 +pound per square inch لأنهم بيستخدموا ال inch + +277 +00:22:17,210 --> 00:22:21,250 +لغاية بيستخدموا ال inch فعندي انا ال atmospheric + +278 +00:22:21,250 --> 00:22:23,950 +pressure عندهم اربعتاش وسبعة من عشرة PSI + +279 +00:22:25,240 --> 00:22:28,000 +Atmospheric pressure برضه بنعرف ان الـ Atmospheric + +280 +00:22:28,000 --> 00:22:32,480 +pressure الـ 760 ملي متر زغبق هي عبارة عن 14.7 PSI + +281 +00:22:32,480 --> 00:22:40,140 +14.7 PSI فلازم نعرف هدول علشان نقدر نحول بين + +282 +00:22:40,140 --> 00:22:43,500 +الوحدات المختلفة و ناخد لنا شوية تحويلات بيقول + +283 +00:22:43,500 --> 00:22:48,470 +convert 0.357 atmosphere to torqueوالله لو عندى + +284 +00:22:48,470 --> 00:22:52,170 +الـ Tor بده يساوي 0.357 أتمسفير، ايش ال Tor؟ 760 + +285 +00:22:52,170 --> 00:22:59,870 +Tor، هذا عبارة عن واحد أتمسفير، 760 Tor من العلاقة + +286 +00:22:59,870 --> 00:23:07,040 +الواحد أتمسفير 760 Torماشي يا جماعة فبيطلع عنده + +287 +00:23:07,040 --> 00:23:09,900 +على طول طيب convert ستة و ستة في عشرة أسالي باتنين + +288 +00:23:09,900 --> 00:23:13,220 +Tor to atmosphere نفس الكلام ال atmosphere ستة و + +289 +00:23:13,220 --> 00:23:16,380 +ستة في عشرة أسالي باتنين Tor بدنا نتخلص من ال Tor + +290 +00:23:16,380 --> 00:23:19,480 +و نحط الواحد atmosphere سبعة مية و ستين Tor سهل + +291 +00:23:19,480 --> 00:23:22,380 +جدا طب convert مية سبعة واربعين و اتنين و عشرة + +292 +00:23:22,380 --> 00:23:25,850 +kilo Pascal to Torحلو كتير، مية سبعة و إتنين و + +293 +00:23:25,850 --> 00:23:30,090 +أشعة كيلو باسكال في سبعمية و ستين طور على مية و + +294 +00:23:30,090 --> 00:23:34,410 +واحد يعني تكافئ اللي هي الضغط الجوي، سبعمية و ستين + +295 +00:23:34,410 --> 00:23:37,130 +طور، مية و واحد point three two five كيلو باسكال + +296 +00:23:37,130 --> 00:23:40,670 +زي ما احنا شوفنا قبل شوية، فبسهولة التحويل يعني + +297 +00:23:40,670 --> 00:23:45,850 +قضية سهلة للغاية convert a pressure of 745 tor to + +298 +00:23:45,850 --> 00:23:51,000 +kilopascalناخد .. ناخد في البداية هذه حلو كتير 745 + +299 +00:23:51,000 --> 00:23:57,300 +تور انا عندي 101.325 كيلو باسكال على 760 تور اللي + +300 +00:23:57,300 --> 00:24:01,780 +هي ملي متر زيبق يعني تمام فسهل جدا طب بيه the + +301 +00:24:01,780 --> 00:24:05,080 +pressure at the center of hurricane Katrina سمعته + +302 +00:24:05,080 --> 00:24:10,780 +فيه طبعا يعني هذا اللي دمر الجزء الجنوب من امريكا + +303 +00:24:10,780 --> 00:24:14,670 +قبل سنوات عديدة يعنيفبيقول ان ال pressure at the + +304 +00:24:14,670 --> 00:24:17,870 +center of hurricane Katrina was 902 millibar + +305 +00:24:17,870 --> 00:24:22,470 +millibar يعني عشرة أس سالب تلاتة bar الملي عشرة أس + +306 +00:24:22,470 --> 00:24:26,570 +سالب تلاتة convert this pressure to atmosphere طيب + +307 +00:24:26,570 --> 00:24:29,610 +902 في عشرة أس سالب تلاتة bar الواحد atmosphere + +308 +00:24:29,610 --> 00:24:34,230 +أكم bar جال one point oh one three two five bar + +309 +00:24:34,230 --> 00:24:38,990 +فمعنى الكلام برضه التحويل سهل للغاية الآن نيجي + +310 +00:24:38,990 --> 00:24:44,600 +نتطلع على ال manometer كيف بدنا نجيسالبراشر للغاز + +311 +00:24:44,600 --> 00:24:51,440 +البراشر للأتمسفير بنجيسه بالبروميتر اللى شفناه + +312 +00:24:51,440 --> 00:24:55,600 +للأتمسفير بنجيسه بالبروميتر في عندى وعى فيه + +313 +00:24:55,600 --> 00:25:00,320 +ميركوري وفي عندى عمود مليان ميركوري بقى أجلبه في + +314 +00:25:00,320 --> 00:25:06,960 +هذا الوعى و بقرأ أكم مليمتر ذئبق فوق سطح الميركوري + +315 +00:25:06,960 --> 00:25:11,360 +هذا اسمه باروميتربجيس ايه؟ بجيس الـ atmospheric + +316 +00:25:11,360 --> 00:25:14,720 +pressure لكن انا لو في عندى غاز محصور فى وعاء و + +317 +00:25:14,720 --> 00:25:18,960 +بدى اعرف جداش ضغطه جال بستخدم الـ manometer بستخدم + +318 +00:25:18,960 --> 00:25:23,780 +ال manometer ال manometers نوعين يا اما manometer + +319 +00:25:23,780 --> 00:25:33,760 +closed end closed end هذه مسكرة يا اما open end + +320 +00:25:34,510 --> 00:25:38,390 +يبقى المانو ميتر نوعين يا اما closed end يا اما + +321 +00:25:38,390 --> 00:25:44,190 +open end عموما + +322 +00:25:44,190 --> 00:25:47,570 +لو كانت ضغط zero atmosphere في ال closed end لو + +323 +00:25:47,570 --> 00:25:51,450 +كانت ضغط zero atmosphere جال هدول والله زي بعض لأن + +324 +00:25:51,450 --> 00:25:56,350 +هانفش عندى اي ضغط هدى زي هدى فهدى بيقرألي هدول هد + +325 +00:25:56,350 --> 00:26:02,640 +زي بعض تماما زي بعض تماما لو كان عندىالضغط .. ضغط + +326 +00:26:02,640 --> 00:26:07,360 +الغاز واحد أتمسفير فبتكون هدولهان جت بعض بالظبط + +327 +00:26:07,360 --> 00:26:12,900 +زائد ستة و سبعين .. يعني سبعمية و ستين ملي متر زي + +328 +00:26:12,900 --> 00:26:16,580 +بقى .. سبعمية و ستين طوار .. تمام؟ طيب .. هذا + +329 +00:26:16,580 --> 00:26:22,420 +بالنسبة لإيه؟ للي closed .. للي closed system طب + +330 +00:26:22,420 --> 00:26:26,180 +لل open-end manometer جال .. هذا بيكون .. إذا كان + +331 +00:26:26,180 --> 00:26:29,340 +هذا واحد أتمسفير و هذا واحد .. هيكونوا جت بعض .. + +332 +00:26:29,340 --> 00:26:33,650 +تختلف عن هذاإذا كانت تنين إذا كان هذا مفتوح فالضغط + +333 +00:26:33,650 --> 00:26:35,830 +اللي هنا واحد أتمسفير والضغط اللي هنا واحد أتمسفير + +334 +00:26:35,830 --> 00:26:38,930 +هيخلّي هدول إيه؟ زي بعض بالظبط كمان مرة مفتوح + +335 +00:26:38,930 --> 00:26:41,670 +الضغط اللي هنا واحد أتمسفير طب والضغط اللي هنا + +336 +00:26:41,670 --> 00:26:46,210 +واحد أتمسفير إذا؟ هيكون وجد بعض بالظبط طيب لو كان + +337 +00:26:46,210 --> 00:26:50,130 +عندي الضغط هنا اتنين أتمسفير معناه كلمة الضغط اللي + +338 +00:26:50,130 --> 00:26:53,110 +هنا اتنين هيعمل pushing لـ Mercury فالـ Mercury + +339 +00:26:53,110 --> 00:26:56,790 +هيطلع هنا ليه؟ لأن الضغط هنا أكبر من هنا إيش الفرق + +340 +00:26:56,790 --> 00:27:03,290 +بينهم؟ الـ760تمام يا جماعة فهك مهما كان الضغط اللي + +341 +00:27:03,290 --> 00:27:08,050 +جوا اذا كان احنا روحنا وصلنا هذه الأنبوبة اللي + +342 +00:27:08,050 --> 00:27:10,830 +طالعة من ال flask اللي موجود في الغاز اللي بدأ جيس + +343 +00:27:10,830 --> 00:27:15,920 +ضغطه ب ال youtube اللي موجودة قدامي هانوفتحت ال + +344 +00:27:15,920 --> 00:27:21,480 +ايه؟ فتحت ال .. خدوا بالك وفي البداية اليوتيوب هذي + +345 +00:27:21,480 --> 00:27:27,980 +بيكون فيه هذا يعني نفسه متساوي فانا عندي لما + +346 +00:27:27,980 --> 00:27:32,820 +اوصلها وافتح ال note تبعها بلاحظ انه صار في عندي + +347 +00:27:32,820 --> 00:27:39,500 +فرق الفرق هذي بيعبرلي عن جداش الضغط الجوي فقررنا + +348 +00:27:39,500 --> 00:27:45,640 +نطلع على حاجة عمليةبيقول on a certain day a + +349 +00:27:45,640 --> 00:27:48,700 +laboratory barometer indicates that the + +350 +00:27:48,700 --> 00:27:54,240 +atmospheric pressure is 764.7 Torr يعني أجينا + +351 +00:27:54,240 --> 00:27:58,420 +جيبنا وع ال mercury و جيبنا لتيوب طبعة ال mercury + +352 +00:27:58,420 --> 00:28:02,600 +طويلة ملناها mercury و جلبناهاوانتظرنا شوية + +353 +00:28:02,600 --> 00:28:06,980 +فلاجينا ان الفرق بين سطح ال mercury و اعلى نقطة في + +354 +00:28:06,980 --> 00:28:12,080 +ال mercury اللى موجود فى ال tube لاجينا انه سبعمية + +355 +00:28:12,080 --> 00:28:16,860 +و اربعة و ستين و سبعة من عشرة ملي متر ذئبق يعني + +356 +00:28:16,860 --> 00:28:20,860 +التور هذا ال parameter خيله جسدنا الضغط الجو بال + +357 +00:28:20,860 --> 00:28:25,960 +parameter الان بيقول ليه a sample of gas is placed + +358 +00:28:25,960 --> 00:28:30,140 +in a flaskattached to an open-end mercury + +359 +00:28:30,140 --> 00:28:36,400 +manometer and a meter stick عشان بدنا نجيس المسافة + +360 +00:28:36,400 --> 00:28:40,240 +ارتفاع ال mercury is used to measure the height of + +361 +00:28:40,240 --> 00:28:45,240 +the mercury in the two arms of the u-tube the + +362 +00:28:45,240 --> 00:28:50,220 +height of the mercury in the open-end arm is 136 + +363 +00:28:50,220 --> 00:28:54,650 +و4 من 10 ملي مترand the height of .. and the + +364 +00:28:54,650 --> 00:28:58,610 +height in the arm in contact with the gas in the + +365 +00:28:58,610 --> 00:29:02,810 +flask is 103 millimeter هفرجيكم أيها بالظبط على + +366 +00:29:02,810 --> 00:29:05,750 +الرسمة هالجيت what is the pressure of the gas in + +367 +00:29:05,750 --> 00:29:11,070 +the flask in atmospheres وكمان in kilopascals + +368 +00:29:11,070 --> 00:29:14,390 +أفرجيكم في الأول إيش الكلام اللي إحنا قلناه هذا + +369 +00:29:14,390 --> 00:29:16,430 +open end manometer + +370 +00:29:18,680 --> 00:29:25,100 +وصلنا بالجاس فالميكو يرتفع بنعرف على طول أن ضغط + +371 +00:29:25,100 --> 00:29:29,580 +الغاز أعلى من الضغط الجوي لأن لو كان أقل كان رتفع + +372 +00:29:29,580 --> 00:29:33,640 +هان فهو أعلى من الضغط الجوي يعني أكتر من واحد + +373 +00:29:33,640 --> 00:29:37,340 +حيكون طيب على أي حال بيقول الارتفاع من هان لهان + +374 +00:29:37,340 --> 00:29:40,540 +مية ستة وتلاتين وأربعة من عشرة الارتفاع من هان + +375 +00:29:40,540 --> 00:29:45,700 +لهانمية و تلاتة و تمانية من عشرة ملي متر، إذا الـH + +376 +00:29:45,700 --> 00:29:49,600 +الارتفاع من هان لهان هو الفرق بينهم، الفرق بينهم، + +377 +00:29:49,600 --> 00:29:52,480 +فاحنا بنقول الـP للجاز سواء الـP أتمسفير، الـP + +378 +00:29:52,480 --> 00:30:00,200 +للجاز، الـP أتمسفير زائد الـP للـH، الـP للأتمسفير + +379 +00:30:00,200 --> 00:30:06,730 +زائد الـP للـHفبيطلع عندى ال P أتمسفير سبعمية و + +380 +00:30:06,730 --> 00:30:09,490 +أربعة و ستين و سبعة من عشرة Tor زائد مية ستة و + +381 +00:30:09,490 --> 00:30:11,810 +تلاتين و أربعة مناس مية و تلاتة و تمانية من عشرة + +382 +00:30:11,810 --> 00:30:15,710 +طبعا هذه millimeters يعني Tor فبيطلع سبعمية و سبعة + +383 +00:30:15,710 --> 00:30:20,860 +و تسعين و تلاتة من عشرة Torالـ P للجاز بالأتمسفير + +384 +00:30:20,860 --> 00:30:24,580 +بقول هذا الـ Tor عند الواحد أتمسفير سبعمية و ستين + +385 +00:30:24,580 --> 00:30:27,880 +Tor اذا one point zero four nine أتمسفير الـ P + +386 +00:30:27,880 --> 00:30:32,840 +للجاز كيلو Pascal قال اه الاتمسفير طبعا عند الكيلو + +387 +00:30:32,840 --> 00:30:35,860 +Pascal one oh one point three two five كيلو Pascal + +388 +00:30:35,860 --> 00:30:39,740 +لكل واحد أتمسفير فبيطلع عند مية و ستة و تلاتة من + +389 +00:30:39,740 --> 00:30:46,700 +عشرة كيلو Pascal هذه هي الاستخدامات البروميتر + +390 +00:30:46,700 --> 00:30:51,670 +والمانوميتربروميتر بيجيس الضغط الجوي المانوميتر + +391 +00:30:51,670 --> 00:30:56,830 +بيجيس الضغط للجاز داخل أي container باستخدام اما + +392 +00:30:56,830 --> 00:31:02,390 +open-end manometer او closed-end manometer الان + +393 +00:31:02,390 --> 00:31:07,450 +نتطلع على ال gas laws نتطلع على ال gas laws اللي + +394 +00:31:07,450 --> 00:31:14,000 +هي قوانين الغازات في الواقعبنقدر احنا نحدد خصائص + +395 +00:31:14,000 --> 00:31:19,860 +الخصائص الفيزيائية لأي غاز إذا كان عرفنا أربع + +396 +00:31:19,860 --> 00:31:26,060 +حاجات ال pressure للغاز وال volume وال temperature + +397 +00:31:26,060 --> 00:31:32,510 +والكميةوالكمية باعتبار الكمية عبارة عن number of + +398 +00:31:32,510 --> 00:31:37,730 +moles فهذه الأربع حاجات هي اللي بتحدد خصائص الغاز + +399 +00:31:37,730 --> 00:31:44,090 +هي اللي بتحدد الخصائص الأساسية للغاز بنقول the + +400 +00:31:44,090 --> 00:31:48,680 +equation that expresses the relationshipsThe + +401 +00:31:48,680 --> 00:31:52,700 +equations that express the relationships among + +402 +00:31:52,700 --> 00:31:56,320 +these four variables اللي اللي قلتها pressure + +403 +00:31:56,320 --> 00:32:01,500 +volume T و A و N اللي هي number one are known as + +404 +00:32:01,500 --> 00:32:06,000 +the gas laws أي علاقة بين اتنين من هدول او تلاتة + +405 +00:32:06,000 --> 00:32:09,640 +او الأربعة هذه ايه كلها gas laws هذه قوانين غازات + +406 +00:32:10,300 --> 00:32:12,480 +يعني علاقة بين ال pressure و ال volume هذا قانون + +407 +00:32:12,480 --> 00:32:15,340 +غاز ال pressure و ال temperature قانون غاز ال + +408 +00:32:15,340 --> 00:32:17,880 +volume و ال temperature قانون غاز ال pressure و ال + +409 +00:32:17,880 --> 00:32:20,420 +in قانون غاز ال volume و ال in قانون غاز ال + +410 +00:32:20,420 --> 00:32:22,780 +pressure و ال volume و ال in قانون غاز أي + +411 +00:32:22,780 --> 00:32:26,500 +combination من هدول الأربعة أي combination سواء + +412 +00:32:26,500 --> 00:32:29,920 +كانت من اتنين من تلاتة من الأربعة كل واحد من هدول + +413 +00:32:29,920 --> 00:32:34,280 +يسمى قانون من قوانين الغازليه؟ لأنه إيش هو + +414 +00:32:34,280 --> 00:32:40,000 +القانون؟ هو كيفية اعتماد متغير على خلّيني أقول + +415 +00:32:40,000 --> 00:32:46,270 +متغير آخركيف بتغير واحد بالنسبة للآخر فهذا الكلام + +416 +00:32:46,270 --> 00:32:51,550 +بيعطينا قوانين متعددة ولكن في الحقيقة يعني سهلة + +417 +00:32:51,550 --> 00:32:55,230 +جدا وانا لقصتلكم في يعني كلمتين صغار بعد شوية + +418 +00:32:55,230 --> 00:32:59,570 +هنشوفهم ففي البداية خلينا نطلع على القوانين + +419 +00:32:59,570 --> 00:33:03,730 +الأساسية للغاز اللي أعطتنا المعادلة أو القانون + +420 +00:33:03,730 --> 00:33:09,650 +الكليللغازات نتطلع على القوانين الجزئية اللى نتج + +421 +00:33:09,650 --> 00:33:12,710 +عنها القانون الكل للغازات القانون الكل اللى بده + +422 +00:33:12,710 --> 00:33:17,030 +يجمع بين ال ايه الاربعة variables طيب بنقول فى + +423 +00:33:17,030 --> 00:33:22,930 +البداية boils law boils law جال كلام بسيط كتير جال + +424 +00:33:22,930 --> 00:33:30,090 +والله ال pressure بيتناسب عكسيا مع ال volume بمعنى + +425 +00:33:30,090 --> 00:33:34,730 +اخرإذا كان أنا والله عندى volume معين، عندى + +426 +00:33:34,730 --> 00:33:39,570 +pressure معين، لو إجيتطبقت pressure أعلى، إيش بده + +427 +00:33:39,570 --> 00:33:43,730 +يحصل ال volume؟ بده يقول هذا كلام بسيط جدا، كلام + +428 +00:33:43,730 --> 00:33:47,050 +بديهي و كلام بسيط، لكن هو طبعا كمان فرجانا كيف بجل + +429 +00:33:47,050 --> 00:33:52,210 +يعني عشان نكون امناع مع الراجل يعني، اه بعدين + +430 +00:33:52,210 --> 00:33:56,770 +الحاجة التانية، بتهيألي ان هو يعني قدم للبشرية + +431 +00:33:56,770 --> 00:33:59,910 +حاجات ممتازة جدا بإنه يعني + +432 +00:34:02,450 --> 00:34:06,490 +من ناحية علمية يعني كيف أنه ممكن يثبت حاجة ويغير + +433 +00:34:06,490 --> 00:34:09,190 +حاجة عشان يشوف تأثيرها، يمكن هو من أوائل الناس + +434 +00:34:09,190 --> 00:34:13,470 +اللي عملوا هذا الشيء قديمًا وهذا منهج علمي محترم، + +435 +00:34:13,470 --> 00:34:16,110 +أنه بالله بدي أشوف تأثير حاجة على حاجة تانية، طب + +436 +00:34:16,110 --> 00:34:20,250 +بنثبت المتغيرات وبنغير متغير واحد بس عشان نشوف إيش + +437 +00:34:20,250 --> 00:34:23,350 +تأثيره، فهذا إشي يعتبر جوهري في الحقيقة + +438 +00:34:25,980 --> 00:34:29,400 +فعلى سبيل المثال لو في عندى بالون والبالون هذا + +439 +00:34:29,400 --> 00:34:33,980 +ارتفع فى الفضاء بلاحظة ان البالون يعني بيكبر لدرجة + +440 +00:34:33,980 --> 00:34:37,440 +انه يعني لو احنا طلعنا عليه منيح بعد فترة وراقبنا + +441 +00:34:37,440 --> 00:34:40,780 +بلاحظة انه ممكن ينبعض فوق، ليه؟ لأن الضغط الجو + +442 +00:34:40,780 --> 00:34:44,970 +اللى فوق بيكون قليلطب و اللى جوا ضغط اكبر فبضلوا + +443 +00:34:44,970 --> 00:34:50,510 +ينتفخ اكتر و اكتر طبعا جسم البالون بتحملاش فبينفجر + +444 +00:34:50,510 --> 00:34:55,630 +يعنى فهذا وضع طبيعى جدا فجال انه ال gas volume + +445 +00:34:55,630 --> 00:34:58,830 +increases as the pressure decreases as the + +446 +00:34:58,830 --> 00:35:01,610 +pressure exerted on the gas decreases هذا وضع + +447 +00:35:01,610 --> 00:35:09,690 +طبيعى للغايةبويلز إكسبيريمنت كانت كالتالي هان في + +448 +00:35:09,690 --> 00:35:15,050 +عندى يوتيوب هدي closed end وفيها كمية من الغاز + +449 +00:35:15,050 --> 00:35:18,610 +كويس؟ حاط فيها كمية من الغاز وحاط فيها شوية + +450 +00:35:18,610 --> 00:35:24,430 +ميركوري فطبعا يعني ات ايش بيسموه في الضغط الجوي + +451 +00:35:24,430 --> 00:35:29,440 +هدول متساوي يعني ضغط جوي طب ايش ايش اعمل؟دغط الجو + +452 +00:35:29,440 --> 00:35:32,220 +حط عليه كمان سبعمية و ستين تمه يزيد يزيد دي لما + +453 +00:35:32,220 --> 00:35:34,840 +صار الفرق ايه سبعمية و ستين دي بقى صارت دغط الجو + +454 +00:35:34,840 --> 00:35:39,380 +زائد صار اتنين دغط جوي بدل ماكان الحجم عنده هان + +455 +00:35:39,380 --> 00:35:46,140 +ستين اشلجا تلاتين اذا اه بجل الحجم و بجل للنص و + +456 +00:35:46,140 --> 00:35:50,600 +بجل ايه اذا كان ضعفنا الضغط فالحجم بجل للنص طب + +457 +00:35:50,600 --> 00:35:56,780 +اكتر من هيك كمانهي نفس التجربة نشتغلها تلاتة هان + +458 +00:35:56,780 --> 00:36:01,180 +في عندي ال atmospheric pressure بساوي ال pressure + +459 +00:36:01,180 --> 00:36:07,640 +للجاس هان في عندي ايش الحجم عندي هنا الحجم عندي V + +460 +00:36:07,640 --> 00:36:13,620 +مثلا لو اجينا طبقنا حطينا mercury بزيادة لما صار + +461 +00:36:13,620 --> 00:36:18,560 +فرق فرق الارتفاع سبعمية وستين يعني حطينا ايه + +462 +00:36:18,560 --> 00:36:23,010 +باعتبار واحد أتمسفير إضافيفهن صار عنده اتنين + +463 +00:36:23,010 --> 00:36:26,170 +أتموسفير يعني ال P الجاز الف و خمسمائية و عشرين + +464 +00:36:26,170 --> 00:36:29,930 +ملي متر زئبق مش سبعمية و ستين فلاحظ ان ال volume + +465 +00:36:29,930 --> 00:36:35,030 +الجاز ايش صار له V على اتنين اناص طيب كمان حط كمان + +466 +00:36:35,030 --> 00:36:37,530 +مركوري كمان لما صار الارتفاع انه الف و خمسمائية و + +467 +00:36:37,530 --> 00:36:41,960 +عشرين يعني هناك مجوهأتنين و واحد تلاتة تلاتة جوة + +468 +00:36:41,960 --> 00:36:46,260 +إذا ال V إيش جرالها انجسمت على تلاتة بجانب ال 100% + +469 +00:36:46,260 --> 00:36:51,640 +هذه العلاقة P تتناسب مع واحد على V تاهينا P تتناسب + +470 +00:36:51,640 --> 00:36:55,260 +مع واحد على V و العلاقة طبعا A عكسية + +471 +00:36:59,910 --> 00:37:05,030 +لو بنجي لنص القانون نص القانون بيقول the volume of + +472 +00:37:05,030 --> 00:37:08,510 +a fixed quantity of gas maintained at constant + +473 +00:37:08,510 --> 00:37:12,090 +temperature مهم بالنسباله وهي كمان ايه اذا كنتوا + +474 +00:37:12,090 --> 00:37:17,310 +ملاحظين fixed quantity of gas يعني وثبت الانوثبت + +475 +00:37:17,310 --> 00:37:21,830 +ايه؟ الحرارة وغير بس متغير واحد علشان يدرسه + +476 +00:37:21,830 --> 00:37:26,970 +المتغير الاخر بيقول فاشلة جال the volume of a + +477 +00:37:26,970 --> 00:37:29,970 +fixed quantity of gas maintained at constant + +478 +00:37:29,970 --> 00:37:33,630 +temperature is inversely proportional to the + +479 +00:37:33,630 --> 00:37:38,470 +pressure هذا هو النص النص القوية او V بتساوي + +480 +00:37:38,470 --> 00:37:43,830 +constant في واحد على P constant في واحد على P او + +481 +00:37:43,830 --> 00:37:48,620 +ان ال PV بتساوي constantالـ PV حاصل الدرد بده + +482 +00:37:48,620 --> 00:37:52,220 +يساوي دائما constant لأن إذا كان ال V صارت على 2 + +483 +00:37:52,220 --> 00:37:56,560 +ال P بيكون في 2 فالـ PV دائما ايه إذا كان ال P + +484 +00:37:56,560 --> 00:38:00,720 +صارت في تلاتة يبقى ال V على تلاتة تلاتة مع تلاتة + +485 +00:38:00,720 --> 00:38:05,120 +تمت ال PV إيش عنده constant فالـ PV constant هذا + +486 +00:38:05,120 --> 00:38:11,010 +يعتبر قانون من قوانين الغازات هذا gaz lowهذا عندى + +487 +00:38:11,010 --> 00:38:15,830 +gas law لكن ال value of the constant طبعا depends + +488 +00:38:15,830 --> 00:38:19,750 +on the temperature and the amount of gas اللى هو + +489 +00:38:19,750 --> 00:38:23,690 +ثبتهم لأنه لو غير ال amount of gas او لو غير ال + +490 +00:38:23,690 --> 00:38:26,730 +temperature اكيد ال result بتبعته هتتغير تعالى + +491 +00:38:26,730 --> 00:38:30,860 +نشوف ايش اللى رسمه السيد Boyleرسم ال V مع ال P في + +492 +00:38:30,860 --> 00:38:34,680 +الجانب العامل زي هيك exponential طبيعي طبيعي + +493 +00:38:34,680 --> 00:38:38,520 +للتناسب العكسي لكن رسم ال V مع ال 1 على P خط + +494 +00:38:38,520 --> 00:38:44,240 +مستقيم أكيدطب رسم ال V مع واحد على P طب رسم ال P + +495 +00:38:44,240 --> 00:38:49,660 +مع واحد على V نفس الكلام خط مستقيم فاستنتج من هذا + +496 +00:38:49,660 --> 00:38:53,180 +الكلام طبعا ان ال PV هي constant و طبيعة ال + +497 +00:38:53,180 --> 00:38:59,540 +constant هذا بتتوقف على ال amount of gas و ايضا ال + +498 +00:38:59,540 --> 00:39:00,080 +temperature + +499 +00:39:02,560 --> 00:39:05,680 +فيبنيجي نسأل بيقول what happens to the pressure of + +500 +00:39:05,680 --> 00:39:10,300 +a gas مش مهم إيش هو الجاز مش مهم كل الغازات واحد + +501 +00:39:10,300 --> 00:39:14,380 +وهذا ما يميز يعني الغازات و هيك بتكون من أسهل ما + +502 +00:39:14,380 --> 00:39:18,100 +يكون لإنه كل الغازات واحد مسميش إيش هو الغاز + +503 +00:39:18,100 --> 00:39:22,140 +مهمنيش كلهم نفس التصرف و هفرجيكم بعض الصيدات جميلة + +504 +00:39:22,140 --> 00:39:25,520 +جدا لكل الغازات بيقول what happens to the pressure + +505 +00:39:25,520 --> 00:39:29,720 +of a gas if you double its volume while its + +506 +00:39:29,720 --> 00:39:34,640 +temperature is held constantThe pressure is + +507 +00:39:34,640 --> 00:39:38,520 +reduced to one half its initial value لإي لأن + +508 +00:39:38,520 --> 00:39:41,880 +الحجم تضعف يبقى ال pressure بده يقل و احنا عرفنا + +509 +00:39:41,880 --> 00:39:47,960 +هذا الكلام مؤكد من شغل السيد Boyle بنيجي الآن لشغل + +510 +00:39:47,960 --> 00:39:49,880 +السيد Charles + +511 +00:39:52,050 --> 00:39:57,970 +شغل السيدة شارز بيعمل relation ما بين ال volume + +512 +00:39:57,970 --> 00:40:04,470 +والحرارة ال volume والحرارة فبطبيعي يعني انه لجأ + +513 +00:40:04,470 --> 00:40:07,750 +ان ال volume increases at the temperature of the + +514 +00:40:07,750 --> 00:40:10,610 +gas increases and decreases at the temperature of + +515 +00:40:10,610 --> 00:40:14,370 +the gas decreases وضع طبيعي لو سخلنا غاز بيتمدد + +516 +00:40:14,370 --> 00:40:18,930 +بسرعة بيكبر كويس فال volume بيزيد الحرارة تتناسب + +517 +00:40:18,930 --> 00:40:24,980 +تتناسب مباشر معالـ Volume والحرارة تتناسب تناسب + +518 +00:40:24,980 --> 00:40:29,390 +مباشرة مع ال pressureبرضه كل ما زودت الحرارة اتضغط + +519 +00:40:29,390 --> 00:40:35,150 +اه انا عندى في cylinder gas اللى هو حطيت تحته + +520 +00:40:35,150 --> 00:40:38,650 +حرارة عالية ايش بيسوي بعد شوية الغاز بنفجر ال + +521 +00:40:38,650 --> 00:40:42,190 +cylinder بنفجر ليه لأن الضغط بيزيد كتير فطبعا + +522 +00:40:42,190 --> 00:40:49,030 +الضغط كمان بيزيد بزيادة درجة الحرارة هولى الأمانة + +523 +00:40:49,030 --> 00:40:54,940 +شغل السيدة شارز كان مكمل شغل السيدةمش بنقول جايل و + +524 +00:40:54,940 --> 00:40:59,340 +ساك يعني .. يمكن .. ولا جايل و ساك .. لأ هو + +525 +00:40:59,340 --> 00:41:03,200 +vocadero اللي كمل شغل جايل و ساك على أي حال .. + +526 +00:41:03,200 --> 00:41:10,140 +بنطلع هنا ال .. ال مثلا بالون .. روحنا بردناه فإيش + +527 +00:41:10,140 --> 00:41:15,860 +حصل؟ اه طبعا لأنه .. لأنه الحرارة خلت الحجم الداخل + +528 +00:41:15,860 --> 00:41:22,220 +يزيجل طب لو سخلناهبزيد هذا وضع طبيعي جدا وكمان لو + +529 +00:41:22,220 --> 00:41:25,240 +حطينا على بلون حلو كتير لو حطينا عليه liquid + +530 +00:41:25,240 --> 00:41:28,620 +nitrogen مش شايفينه طبعا انتوا وماحدش طبعا ممسك ال + +531 +00:41:28,620 --> 00:41:31,940 +liquid nitrogen بيده بس اكيد هذه مصفحة ومعزولة + +532 +00:41:31,940 --> 00:41:36,680 +تماما لان ال liquid nitrogen حرارته سلب يعني 87 + +533 +00:41:36,680 --> 00:41:41,880 +degree c تقريبا يعنيف .. تمنية و سبعين درجة C + +534 +00:41:41,880 --> 00:41:46,980 +تقريبا يعني فبالتالي .. ولا أجل من هيك المهم قليلة + +535 +00:41:46,980 --> 00:41:51,140 +جدا باردة جدا فالمهم لما أضافوا على ال balloon إيش + +536 +00:41:51,140 --> 00:41:56,200 +حصل؟ انكمش جدا من جوا .. انكمش جدا جدا من جوا + +537 +00:41:56,200 --> 00:42:01,540 +وبالتالي صحيح إن ال temperature إلها علاقة بال + +538 +00:42:01,540 --> 00:42:04,160 +volume لل gas + +539 +00:42:07,740 --> 00:42:14,200 +السيد Charles لجأ شغلات يعني جميلة جدا لجأ انه + +540 +00:42:14,200 --> 00:42:17,840 +والله لو عمل chart ما بين ال volume و ال + +541 +00:42:17,840 --> 00:42:20,500 +temperature فلجأ ان ال volume بيزيد بزيادة ال + +542 +00:42:20,500 --> 00:42:25,740 +temperature بيزيد بيزيد طب لو اجا مد هذا الخط + +543 +00:42:25,740 --> 00:42:29,320 +المستقيم جالب يقطع ال X axis اللي هو ال X تبع ال + +544 +00:42:29,320 --> 00:42:36,100 +temperature عند حرارة تقريبا 273 بالسالب273 + +545 +00:42:36,100 --> 00:42:41,100 +بالسالب وكمان اكتر من هيك شاف جاب غازات .. الغازات + +546 +00:42:41,100 --> 00:42:47,200 +هذه عند ضغوط مختلفة يعني استخدم تغيير في الضغط + +547 +00:42:47,200 --> 00:42:52,460 +كمانفوجد انه .. غير ال .. ال .. ال .. يعني الحرارة + +548 +00:42:52,460 --> 00:42:55,940 +مع ال volume فوجد ان كل الغازات ه .. طلعوا كلها + +549 +00:42:55,940 --> 00:43:00,380 +بتلتقي وين؟ في نفس النقطة مش غريب طب غير ال amount + +550 +00:43:00,380 --> 00:43:03,540 +of gas اللي هو المتغير ال ايه؟ الرابع غير ال + +551 +00:43:03,540 --> 00:43:07,560 +amount of gas لأ هذي اللي بعدها فهن point O one + +552 +00:43:07,560 --> 00:43:12,820 +point O eight point O six point O four مثلا يعنيو + +553 +00:43:12,820 --> 00:43:17,540 +غزات مختلفة غير ال amount point 002 فلجأ انه برضه + +554 +00:43:17,540 --> 00:43:22,860 +كلهم ايه بيلتقوا عند نقطة واحدة متين تلاتة و سبعين + +555 +00:43:22,860 --> 00:43:29,320 +point one five degrees c بالسالب بالسالب كويس + +556 +00:43:29,320 --> 00:43:34,520 +فبيجي بعده طبعا الخط اللي هان بيجي بعده السيد + +557 +00:43:34,520 --> 00:43:38,570 +Kelvin و بيقول هذه ال absolute temperatureهد ال + +558 +00:43:38,570 --> 00:43:42,230 +absolute temperature فجال انه معنى الكلام ال V + +559 +00:43:42,230 --> 00:43:46,930 +تتناسب مع ال absolute temperature مع ال T لأن كلهم + +560 +00:43:46,930 --> 00:43:50,430 +بلتقيوين في ال absolute temperature فجال انه يبجى + +561 +00:43:50,430 --> 00:43:53,770 +ال V تتناسب مع T اللي هي إيش هي ال T جال ال + +562 +00:43:53,770 --> 00:43:58,650 +absolute temperature اللي هي 273 زائد ال degrees C + +563 +00:43:58,650 --> 00:44:04,050 +جد ما كانت 273 زائد ال degrees C لأن هي الصفر عنده + +564 +00:44:04,050 --> 00:44:06,390 +273 Kelvin + +565 +00:44:10,400 --> 00:44:13,760 +بنتكلم الآن عن الـ Quantity اللي هو المتغير إذا + +566 +00:44:13,760 --> 00:44:17,560 +شفنا ال P و شفنا ال V و تناسب ال V مع ال T و ال P + +567 +00:44:17,560 --> 00:44:24,360 +مع ال T فالمتغير اللي بعد هيك اللي هو ال amount فـ + +568 +00:44:24,360 --> 00:44:27,800 +Avogadro's hypothesis بيقول equal volumes of gases + +569 +00:44:27,800 --> 00:44:31,240 +at the same temperature and pressure contain equal + +570 +00:44:31,240 --> 00:44:35,520 +number of molecules حلو كتير equal number .. equal + +571 +00:44:35,520 --> 00:44:39,210 +volumes of gasesAt the same temperature and + +572 +00:44:39,210 --> 00:44:42,670 +pressure contain equal number of molecules يعني لو + +573 +00:44:42,670 --> 00:44:49,230 +أخدنا أي غاز و أخدنا حجم معين منه و ليكن مثلا هذا + +574 +00:44:49,230 --> 00:44:53,050 +إلها سبب اتنين و عشرين و أربعمان عشر لليتر كويس at + +575 +00:44:53,050 --> 00:44:57,770 +one atmosphere or zero degrees c مثلا كويس و هنقول + +576 +00:44:57,770 --> 00:45:00,370 +لكم ليش one atmosphere or zero degrees c بعد شوية + +577 +00:45:01,920 --> 00:45:08,780 +الهيليوم 4 جرام مثلا يعني 4 جرام لكن عدد الجزيئات + +578 +00:45:08,780 --> 00:45:12,560 +اللي موجودة هان عدد الجزيئات في 22 و 4 من 10 + +579 +00:45:12,560 --> 00:45:18,170 +لليتير 6.02 في 10 أقصى 23 Avogadro numberطيب نيجي + +580 +00:45:18,170 --> 00:45:23,390 +للنيتروجين 22 و 4 من 10 لتر أخدنا منه طيب at one + +581 +00:45:23,390 --> 00:45:27,510 +atmosphere و 0 degree c جداش ال formula ويتقيله 28 + +582 +00:45:27,510 --> 00:45:31,210 +يعني المول الواحد أكم جرام 28 جرام هنا المول + +583 +00:45:31,210 --> 00:45:36,110 +الواحد 4 جرام هنا المول 28 جرام طيب أكم جزء + +584 +00:45:36,110 --> 00:45:40,290 +نيتروجين موجود فيه جال عدد avogadro طيب نيجي هى + +585 +00:45:40,290 --> 00:45:46,990 +200 أخدنا 22 و 4 من 10 لتر نفس الحجم كويس؟ + +586 +00:45:49,850 --> 00:45:53,930 +عند واحد أتمسفير و Zero degrees C طب جداش المول + +587 +00:45:53,930 --> 00:45:57,770 +منه أكم جرام جال ستة عشر جرام؟ تفاوت كبير بينهم، + +588 +00:45:57,770 --> 00:46:00,090 +هذا أربع، هذا تمانية وعشرين، هذا ستة عشر، طب أكم + +589 +00:46:00,090 --> 00:46:04,090 +مولكول CH4 موجود هان؟ عدد الـ Avogadro 6.02 في عشر + +590 +00:46:04,090 --> 00:46:09,830 +وعشرة وعشرين، فهذا ال hypothesis لسيد Avogadro جال + +591 +00:46:09,830 --> 00:46:13,690 +equal volumes of gases at the same temperature and + +592 +00:46:13,690 --> 00:46:18,920 +pressure contain equal number of moleculesتمام؟ + +593 +00:46:18,920 --> 00:46:22,240 +فاحنا هال data بدلا من نتطلع على ال moles ممكن + +594 +00:46:22,240 --> 00:46:26,280 +نتطلع على ال volumes في حل المسائل زي ما هنشوف في + +595 +00:46:26,280 --> 00:46:30,820 +المستقبل ليه؟ لأنه يعني كل volume بحتوى على نفس + +596 +00:46:30,820 --> 00:46:35,980 +العدد من ال molecules اذا زي لعد انه moles فهي نفس + +597 +00:46:35,980 --> 00:46:37,640 +ال mole relationship يعني + +598 +00:46:44,860 --> 00:46:49,100 +المحتوى يعني الـ hypothesis للسيد Avogadro بيقول + +599 +00:46:49,100 --> 00:46:52,880 +يعني التالي بيقول الـ volume of a gas maintained + +600 +00:46:52,880 --> 00:46:56,760 +at constant temperature and pressure is directly + +601 +00:46:56,760 --> 00:46:58,920 +proportional to the number of moles of the gas + +602 +00:46:58,920 --> 00:47:03,940 +يعني إذا كان جيبنا أي غاز at constant temperature + +603 +00:47:03,940 --> 00:47:10,450 +and pressureفالـ volume هيكون بيتناسب مع in عدد + +604 +00:47:10,450 --> 00:47:14,210 +المولات in اللي هي number of moles فال volume + +605 +00:47:14,210 --> 00:47:18,590 +هيتناسب مع in يعني ال V بتساوي constant في in + +606 +00:47:18,590 --> 00:47:23,650 +وممكن .. ممكن كمان احنا بالنسبالنا بنفس الطريقة + +607 +00:47:23,650 --> 00:47:28,130 +نقول the pressure of gas maintained at constant + +608 +00:47:28,130 --> 00:47:32,590 +temperature and volume is directly proportional to + +609 +00:47:32,590 --> 00:47:37,810 +in إذا كان حبينافهي ال V constant في N + +610 +00:47:42,100 --> 00:47:47,160 +عيننا ان ال equal volumes من ال من اي غاز at + +611 +00:47:47,160 --> 00:47:51,700 +constant temperature يعني + +612 +00:47:51,700 --> 00:48:01,060 +at constant temperature حيكون عدد ال و pressure + +613 +00:48:01,060 --> 00:48:04,320 +حيكون عدد ال molecules اللي موجود في هذا ال volume + +614 +00:48:04,320 --> 00:48:08,380 +مساوي لأي غاز اخر عن نفس الظروف في نفس ال volume + +615 +00:48:08,380 --> 00:48:12,690 +في نفس الظروففخلّيني نتطلع على مثلا بعض الأمثلة + +616 +00:48:12,690 --> 00:48:16,650 +ترجمة للكلام هذا بالظبط بيقول what happens to the + +617 +00:48:16,650 --> 00:48:22,250 +density of a gas as طبعا ال density عبارة عن ايه؟ + +618 +00:48:22,250 --> 00:48:26,770 +اه جرام كتلة على الحجم بس قلنا بالنسبة للغازات + +619 +00:48:26,770 --> 00:48:30,550 +الحجم بالليتر مش خلاف بالنسبة لنا بس هو بده + +620 +00:48:30,550 --> 00:48:37,250 +يفرجينا كيف تغيير ال in بيغير يعني المتغيرات زي ال + +621 +00:48:37,250 --> 00:48:40,550 +volume أو ال pressure أو غيرهفبقول what happens to + +622 +00:48:40,550 --> 00:48:44,970 +the density of a gas as the gas is heated in a + +623 +00:48:44,970 --> 00:48:47,790 +constant volume container ماعملاش حاجة نفس الغاز + +624 +00:48:47,790 --> 00:48:53,810 +بس خنها في constant volume بزيدش الحجم لإنه جالي + +625 +00:48:53,810 --> 00:48:59,980 +constant volumeبس الحجم بسخن اه لكن ايه قال الحجم + +626 +00:48:59,980 --> 00:49:04,180 +بيضله ثابت هو قال لي هيك الحجم بيضله ثابت يبقى لا + +627 +00:49:04,180 --> 00:49:08,560 +لا اتغيرت الكتلة ولا اتغير الحجم فاه فقال لي can + +628 +00:49:08,560 --> 00:49:13,280 +not change لا اتغيرت الكتلة ولا اتغير الحجم اذا + +629 +00:49:13,280 --> 00:49:19,040 +not change طيب ال gas is compressed at constant + +630 +00:49:19,040 --> 00:49:25,380 +temperature اه الحجم اشمله قل بدها تزيد الكثافة + +631 +00:49:25,380 --> 00:49:31,100 +بدها تزيدطيب التالتة additional gas is added to a + +632 +00:49:31,100 --> 00:49:35,160 +constant volume container حطينا كمان كمية الحجم + +633 +00:49:35,160 --> 00:49:39,080 +بيزيدش constant volume constant volume container + +634 +00:49:39,080 --> 00:49:46,020 +بس حطينا n زيادة حطينا كتلة زيادة كيف؟ + +635 +00:49:46,650 --> 00:49:49,950 +طبعا بتزود عدد الملات ليش؟ لأن الغاز هو عبارة عن + +636 +00:49:49,950 --> 00:49:53,690 +ملات فالكتلة بتزيد بعد كلام ال density راح تزيد + +637 +00:49:53,690 --> 00:49:58,430 +لأن الكتلة زيادة الحجم ثابت بسيط يعني مش عارف أنا + +638 +00:49:58,430 --> 00:50:03,390 +ليش بسأل أسئلة زيادة يعني بسيطة كتير طيب بيقول + +639 +00:50:03,390 --> 00:50:06,610 +كمان indicate how each of the following changes + +640 +00:50:06,610 --> 00:50:11,410 +affects the average distance between molecules + +641 +00:50:13,320 --> 00:50:16,340 +وكمان the pressure of the gas and the number of + +642 +00:50:16,340 --> 00:50:20,700 +moles of the gas confined يعني موجودة او محصورة في + +643 +00:50:20,700 --> 00:50:24,360 +سيلندر with a movable piston ال piston بيتحرك + +644 +00:50:24,360 --> 00:50:31,060 +بيقول اول حاجة heat the gas from 298 ل360 ايش ال + +645 +00:50:31,060 --> 00:50:35,940 +constant pressure ايش بيحصل لل volume بزيد طب عدد + +646 +00:50:35,940 --> 00:50:39,990 +الملات بتزيدمن ورا من هتزيد؟ من ورا من هتزيد؟ من + +647 +00:50:39,990 --> 00:50:43,390 +ورا من هتزيد؟ المادة mass conservation يعني العيون + +648 +00:50:43,390 --> 00:50:47,590 +المالية ما بتزيد بس ال volume بيزيد لأنه عندنا + +649 +00:50:47,590 --> 00:50:50,890 +الحرارة زادت و ال piston movable فطبعا ال piston + +650 +00:50:50,890 --> 00:50:55,170 +بيتمدد على سبيل المثال بيقول reduce the volume + +651 +00:50:55,170 --> 00:50:58,850 +from one liter to half liter at constant + +652 +00:50:58,850 --> 00:51:04,610 +temperature ايش بيحصل لل pressure؟ اذا كاناسكان + +653 +00:51:04,610 --> 00:51:08,390 +يعني خلّين الحجم من واحد لتر لنصف لتر، ايش بيحصل + +654 +00:51:08,390 --> 00:51:11,690 +ال pressure؟ بتضعف ال pressure، هذا كلام صحيح ال + +655 +00:51:11,690 --> 00:51:16,770 +pressure بيتضعف، Boy's law طب inject additional + +656 +00:51:16,770 --> 00:51:20,570 +gas keeping the temperature and volume constant، + +657 +00:51:20,570 --> 00:51:26,770 +اه ال pressure ايش بيحصل؟ زودنا على دلمولات، خدي + +658 +00:51:26,770 --> 00:51:30,220 +بالكهن بيقولك inject at keeping the temperature + +659 +00:51:30,220 --> 00:51:34,680 +and volume constant يعني بس حطيت .. اه ال pressure + +660 +00:51:34,680 --> 00:51:38,500 +بده يزيد لإن حطيت more material more moles + +661 +00:51:38,500 --> 00:51:43,920 +وبالتالي ال pressure بيزيد تمام لإن ال P تتناسب مع + +662 +00:51:43,920 --> 00:51:55,060 +N طيب بيقول if we combineلو حطينا تلاتة لتر من ال + +663 +00:51:55,060 --> 00:52:00,660 +NO جاز مع واحد و نص لتر من ال O2 and they react + +664 +00:52:00,660 --> 00:52:03,760 +according to the balanced equation يعطون اتنين NO2 + +665 +00:52:03,760 --> 00:52:09,460 +جاز بقول what volume of NO2 will be produced what + +666 +00:52:09,460 --> 00:52:14,160 +volume of NO2 will be produced ناخد واحدة واحدة من + +667 +00:52:14,160 --> 00:52:20,460 +هدول والله الاتنين مول ايش بتعطيني اتنين مول اذا + +668 +00:52:21,030 --> 00:52:24,770 +هذه الاتنين مول هو الحاجة هذه stoichiometric يعني + +669 +00:52:24,770 --> 00:52:28,990 +مافي فيهم هذه واحد و نص وهذه اتنين يعني خلينا نقول + +670 +00:52:28,990 --> 00:52:34,510 +انه لو كان في عندي لو كان في عندي limiting + +671 +00:52:34,510 --> 00:52:39,170 +reactant فهو هذا تلاتة liter لأ والله مافي + +672 +00:52:39,170 --> 00:52:41,470 +limiting reactant الاتنين زي بعض الاتنين زي بعض + +673 +00:52:41,470 --> 00:52:44,510 +بالظبط ماعندي مشكلة فيهم فبقول التلاتة liter + +674 +00:52:44,510 --> 00:52:49,560 +هيعطوني اكم literالتنين مول بيعطي تنين مول يبقى + +675 +00:52:49,560 --> 00:52:53,920 +تلاتة لتر لما هي الفكرة الفكرة في الـ Avogadro's + +676 +00:52:53,920 --> 00:53:00,900 +law انه جال equal volumes من الغازات المختلفة عند + +677 +00:53:00,900 --> 00:53:05,900 +ظروف معينة تحتوي على نفس العدد من الجزائقات وممكن + +678 +00:53:05,900 --> 00:53:09,540 +نقول تحتوي على نفس العدد من المولات اذا كان حبينا + +679 +00:53:09,540 --> 00:53:13,580 +فهي نفس الكلام تلاتة لتر يبقى هدف تعطيني تلاتة لتر + +680 +00:53:13,580 --> 00:53:20,190 +من ال N O2ماشي يا جماعة يبقى بنستخدم ال volumes و + +681 +00:53:20,190 --> 00:53:26,550 +كأنها moles ال volumes و كأنها moles طيب بيقول + +682 +00:53:26,550 --> 00:53:30,670 +what volume in liters of water vapor will be + +683 +00:53:30,670 --> 00:53:36,270 +produced when 34 لتر من ال H2 و 17 لتر من ال O2 + +684 +00:53:36,270 --> 00:53:39,980 +برضه stoichiometric هي دي يعني بيخلصوا كلهمبيعطوني + +685 +00:53:39,980 --> 00:53:44,920 +اتنين H2O واضح جدا يا بده اقول والله السبعة عشر + +686 +00:53:44,920 --> 00:53:47,800 +بتعطي السبعة عشر يا بده اقول الاربعة و تلاتين + +687 +00:53:47,800 --> 00:53:51,240 +بتعطي اربعة و تلاتين السبعة عشر بتعطي اربعة و + +688 +00:53:51,240 --> 00:53:54,840 +تلاتين الواحد بيعطي اتنين يا بده اقول الاربعة و + +689 +00:53:54,840 --> 00:53:59,500 +تلاتين اللي هو الاتنين بيعطي اتنين سيان هي هي كيف + +690 +00:53:59,500 --> 00:54:02,280 +بده اقولها سيان زي ما هي بالظبط فهذا الاربعة و + +691 +00:54:02,280 --> 00:54:05,980 +تلاتين لتر H2O بتعطي نفس الكمية لهذا اتنين اربعة و + +692 +00:54:05,980 --> 00:54:10,100 +تلاتين طب لو قلنا السبعة عشر لتر O2الواحد ايش + +693 +00:54:10,100 --> 00:54:13,400 +بيعطيه اتنين و السبعة عشر ايش بتعطيه اربع ضعفها + +694 +00:54:13,400 --> 00:54:16,960 +اربع و تلاتين الواحد بيعطي ضعفه طب السبعة عشر + +695 +00:54:16,960 --> 00:54:20,640 +بتعطي ضعفها يعني اربع و تلاتين فسيان سواء جولنا H2 + +696 +00:54:20,640 --> 00:54:27,500 +او جولنا O2 دائما النتيجة هي اربع و تلاتين لتر من + +697 +00:54:27,500 --> 00:54:34,080 +الميه ك summary فيما يتعلق بال gas laws ك summary + +698 +00:54:34,080 --> 00:54:37,160 +يعني الملخص العام + +699 +00:54:40,210 --> 00:54:45,870 +إيش بيحصل لما أجلل ال pressure، هان جللت ال + +700 +00:54:45,870 --> 00:54:51,870 +pressure؟ الحجم ذاتي، الحجم ذاتي، في علاقة بين ال + +701 +00:54:51,870 --> 00:54:55,910 +volume و ال pressure، هذا boys low، هذا boys low، + +702 +00:54:55,910 --> 00:55:00,910 +عكس طبعا، إيش بيحصل؟ هاي ال pressure ثابت، إذا + +703 +00:55:00,910 --> 00:55:05,460 +كنتوا ملاحظين هدولدرجة الحرارة لأ هي نزوّتها هان + +704 +00:55:05,460 --> 00:55:09,620 +ايش بيحصل؟ جال ال volume زاد طبيعي يعني و ايه هان + +705 +00:55:09,620 --> 00:55:13,400 +برضه ال pressure ايش ماله؟ ثابت ثابت و الحرارة ايش + +706 +00:55:13,400 --> 00:55:18,740 +مالها؟ ثابت ثابت فلما نزود عدد الجزيئات ايش بيحصل؟ + +707 +00:55:18,740 --> 00:55:23,340 +زيد الحجم زيد الحجم لما نزود عدد الجزيئات ايش حصل + +708 +00:55:23,340 --> 00:55:27,120 +للحجم؟ زاد هذا هي القوانين التلاتة اللي احنا + +709 +00:55:27,120 --> 00:55:30,280 +اتحدثنا عنها هذه هي القوانين التلاتة اللي احنا + +710 +00:55:30,280 --> 00:55:36,460 +اتحدثنا عنهاالان بالنسبة لل .. ال ideal gas + +711 +00:55:36,460 --> 00:55:42,640 +equation اللي هو ال general gas law ال overall gas + +712 +00:55:42,640 --> 00:55:47,060 +equation بقول كان عند ال V تتناسب مع 1 على P اللي + +713 +00:55:47,060 --> 00:55:50,260 +هو Boy's law وكان عند ال V تتناسب مع T charge law + +714 +00:55:50,260 --> 00:55:54,680 +وكان V تتناسب مع N Avogadro's law يعني ال V تتناسب + +715 +00:55:54,680 --> 00:56:02,050 +مع N في T على P او يعني ال V بتساوي R constantنت + +716 +00:56:02,050 --> 00:56:07,730 +على P أو لو رتبتها PV بتساوي nRT PV بتساوي nRT هدى + +717 +00:56:07,730 --> 00:56:12,410 +عبارة عن ايه الجازلو ايديال جازلو ايديال ليه؟ ليش + +718 +00:56:12,410 --> 00:56:15,370 +قلنا عنه ايديال؟ جال لأنه في الآخر هنجي ونقول ان + +719 +00:56:15,370 --> 00:56:19,770 +هذه المعادلة تقريباهذه المقليه هنتبتلكم انها + +720 +00:56:19,770 --> 00:56:24,210 +تقريبية ونفرجيكم ليش هي تقريبية لكن تقريبية بشكل + +721 +00:56:24,210 --> 00:56:30,010 +يعني مش سيء بالذات at low pressures يعني فهي جيدة + +722 +00:56:30,010 --> 00:56:32,510 +at low pressures لكن at high pressures ممكن يصير + +723 +00:56:32,510 --> 00:56:35,760 +فيها عنده يعنيبعض المشاكل سنريكم ما هي أصل هذه + +724 +00:56:35,760 --> 00:56:41,240 +المشاكل لكن في المستقبل فعند الـ gas الـ ideal gas + +725 +00:56:41,240 --> 00:56:45,160 +law او الـ ideal gas equation هي PV بتساوي nRT الـ + +726 +00:56:45,160 --> 00:56:47,960 +P ال pressure و V ال volume و ال N number of moles + +727 +00:56:47,960 --> 00:56:51,440 +و ال R هي الثابت اللي هال gas هنفرجيكم إيش هي و ال + +728 +00:56:51,440 --> 00:56:54,520 +T هي ال absolute temperature هذي بنقولها ال ideal + +729 +00:56:54,520 --> 00:56:57,360 +gas law وهي اللي بتستخدم في حال كل مسائل تقريبا + +730 +00:56:57,360 --> 00:57:02,700 +يعني ال gasesبشكل او باخر هفرجيكم ايش المتغيرات + +731 +00:57:02,700 --> 00:57:04,460 +اللي ممكن تحصل عليها عشان نحل اي مسألة + +732 +00:57:10,460 --> 00:57:17,340 +يبقى هذا هو الـ Ideal Gas Law هذا الـ Ideal Gas هو + +733 +00:57:17,340 --> 00:57:22,120 +عبارة عن Hypothetical Gas لأنه زي ما هنشوف انه + +734 +00:57:22,120 --> 00:57:26,340 +والله في أسباب حيوية بتخليني اقول ان هذا المعادلة + +735 +00:57:26,340 --> 00:57:31,740 +لابد من تعديلها لكن مش هالجيت وقتها ال .. ال .. + +736 +00:57:31,740 --> 00:57:35,460 +الثابت اللي هو R لو احنا حبنا نقول PV + +737 +00:57:38,510 --> 00:57:48,110 +بتساوي N R T يبقى ال R بتساوي P V على ال R T P بال + +738 +00:57:48,110 --> 00:57:56,350 +لتر بالاتмосفير و V بال لتر على ال N T و ال N اللي + +739 +00:57:56,350 --> 00:58:00,210 +هي mole و T Kelvin هاي ال .. هاي ال .. هاي ال .. + +740 +00:58:00,210 --> 00:58:07,150 +ال unit هد هي على طول ال V لتر ال P اتمسفيرالـ T + +741 +00:58:07,150 --> 00:58:11,410 +كلفن ال N مول يبقى هذه الوحدات المستخدمة يبقى لما + +742 +00:58:11,410 --> 00:58:16,390 +تستخدم R بهذه القيمة يبقى لازم ال P إيش تكون؟ + +743 +00:58:16,390 --> 00:58:25,390 +أتمسفير ال V لتر ال N مول ال T R يبقى لازم تستخدم + +744 +00:58:25,390 --> 00:58:30,930 +هذه القيمة و بدنا نحفظها بدنا نحفظها 0.0821 + +745 +00:58:34,540 --> 00:58:40,080 +طيب انا بس بتعطيكم واحدة تانية نحفظها و خلاص جال + +746 +00:58:40,080 --> 00:58:44,440 +ممكن جدا وهذا هنستخدمها في آخر chapter ال + +747 +00:58:44,440 --> 00:58:52,900 +thermodynamics ممكن ال R يكون قيمتها 8.314 8.314 + +748 +00:58:52,900 --> 00:58:56,440 +هو + +749 +00:58:56,440 --> 00:59:03,200 +بديش اقول هذه هيك بدي اقول عنها جول per Kelvin per + +750 +00:59:03,200 --> 00:59:05,820 +mole8.314 Joule per Kelvin per mole + +751 +00:59:21,270 --> 00:59:28,250 +كلفن مول جول على الكلفن مول يبقى أنهي قيمة من هذه + +752 +00:59:28,250 --> 00:59:32,170 +القيم بدي أستخدم جال حسب الوحدات اللي أنا بستخدمها + +753 +00:59:32,170 --> 00:59:37,410 +في الـA في المعادلة في الـgas law حسب يعني كيف بدي + +754 +00:59:37,410 --> 00:59:40,190 +أعبر عن ال pressure كيف بدي أعبر عن ال volume كيف + +755 +00:59:40,190 --> 00:59:43,710 +بدي أعبر عن ال degree C الحرارة هل هي degree C ولا + +756 +00:59:43,710 --> 00:59:48,030 +Kelvin مثلا يعني هل بدي أستخدم Tor ولا أطبوسفير + +757 +00:59:48,520 --> 00:59:52,740 +مثلا فهذا الكلام اللى هنستخدمه دائما و هنحول كل + +758 +00:59:52,740 --> 00:59:56,160 +شيء له علشان ما نتغلبش بدنا نحفظ هدول التنتين بس + +759 +00:59:56,160 --> 01:00:00,860 +بدنا نعرف ايش الوحدات تبعتهم يبقى point 0821 + +760 +01:00:00,860 --> 01:00:08,140 +معناته letter atmosphere على Kelvin mole8.314 + +761 +01:00:08,140 --> 01:00:12,500 +جلجول على مول كيلفين وانتهينا بس هدول التنتين + +762 +01:00:12,500 --> 01:00:16,120 +هحلوا كل المسائل إذا كانت طالت أني أحول من unit ل + +763 +01:00:16,120 --> 01:00:19,140 +unit تاني بحول بس ال R اللي بده أستخدمها واحدة من + +764 +01:00:19,140 --> 01:00:23,360 +هدول التنتين و طبعا في ال gas laws كلها بس هذه لكن + +765 +01:00:23,360 --> 01:00:29,780 +هذه الواحدة وين بيستخدمها في ال thermodynamics و + +766 +01:00:29,780 --> 01:00:32,640 +لسه هذا الكلام في آخر chapter يبقى هذه الراجعة مش + +767 +01:00:32,640 --> 01:00:36,440 +حاسبة بس بدنا نحفظ ايه؟ هذه هي اللي بدنا نحفظهافي + +768 +01:00:36,440 --> 01:00:41,700 +هذا الـ chapter بس عندنا ال R.0821 و الوحدات + +769 +01:00:41,700 --> 01:00:47,060 +letter لل volume atmosphere لل pressure على N عدد + +770 +01:00:47,060 --> 01:00:53,060 +الملات T Kelvin و انتهينا ماشي فلما نيجي نعوض بدنا + +771 +01:00:53,060 --> 01:00:54,640 +نعوض بهذا الشكل + +772 +01:01:05,570 --> 01:01:09,030 +نعود الآن لنريكم من أين جاءت الـ 22 و 4 من 10 أو + +773 +01:01:09,030 --> 01:01:14,150 +إيش يعني STP فبقول أنا ال volume of one mole of + +774 +01:01:14,150 --> 01:01:19,790 +gas at STP STP يعني standard temperature and + +775 +01:01:19,790 --> 01:01:25,330 +pressure standardtemperature and pressure وللأسف + +776 +01:01:25,330 --> 01:01:30,190 +كل نظام علمي فيه له standards فيه له standard + +777 +01:01:30,190 --> 01:01:33,990 +conditions يعني مثلا لما شوفنا احنا ال delta H + +778 +01:01:33,990 --> 01:01:40,410 +naught F في ال chapter الماضي قلنا ال standard + +779 +01:01:40,410 --> 01:01:46,490 +conditions واحد أتمسفير وعنا بالنسبة لنا بالنسبة + +780 +01:01:46,490 --> 01:01:53,510 +للحرارة 298 Kelvin او 25 degree Cهن لأ هن عندي انا + +781 +01:01:53,510 --> 01:02:00,510 +ال STP بتقوللي بتقوللي ايه؟ بتقوللي الحرارة zero + +782 +01:02:00,510 --> 01:02:05,470 +degree c يعني متين تلاتة وسبعين وخمستاشر مش خمسة + +783 +01:02:05,470 --> 01:02:08,750 +وعشرين degree c يعني متين وتمانية وتسعين وخمستاشر + +784 +01:02:08,750 --> 01:02:12,930 +فبدنا نتذكر هذا الكلام ال STP بالنسبة علنا بالنسبة + +785 +01:02:12,930 --> 01:02:18,960 +إلنا احنا هن الحرارة متين تلاتة وسبعين0.15 Kelvin + +786 +01:02:18,960 --> 01:02:26,280 +واختصارا 273 مابيأثرش يعني ايه كويس مش 298 زي ما + +787 +01:02:26,280 --> 01:02:30,820 +كنا بنقول في ال Delta H0 F كل نظام فيه له ال + +788 +01:02:30,820 --> 01:02:35,540 +standards تبعته فانا بدي اجيب الحجم اللي ناتج عن + +789 +01:02:35,540 --> 01:02:40,460 +one mole من ال ideal gas فبقول والله ال V ال P V + +790 +01:02:40,460 --> 01:02:46,790 +بتسوى N RT يعني ال V بتسوى N RT على POne mole in + +791 +01:02:46,790 --> 01:02:52,670 +واحد مول حلو فيه R.08206 liter atmosphere عالمول + +792 +01:02:52,670 --> 01:02:57,410 +Kelvin اذا اخترت هدف ثابت بتبقى متعود عن ال P + +793 +01:02:57,410 --> 01:03:01,290 +بالاتمسفير واحد اتمسفير والواحد اتمسفير هو بجيت ال + +794 +01:03:01,290 --> 01:03:08,190 +STP عند واحد اتمسفير و 293 Kelvin طيب و ال Kelvin + +795 +01:03:08,190 --> 01:03:14,270 +273 عوضت بطلع عندي 22.4 من 10إذن الـ 22 و 4 من 10 + +796 +01:03:14,270 --> 01:03:20,450 +هي عبارة عن حجم 1 مول من الجاز at STP لأنه لو أنا + +797 +01:03:20,450 --> 01:03:23,290 +مابديش أشغل at STP، بدي أشغل at 25 degrees C، + +798 +01:03:23,290 --> 01:03:27,610 +حيزيد، أكتر هيكون الحجم، لو بدي أشغل عند pressure + +799 +01:03:27,610 --> 01:03:32,990 +تاني، هيختلف، فانا بقول لأ، لما هذه تكون ثابتة، + +800 +01:03:32,990 --> 01:03:37,650 +وهذه تكون ثابتة، فانا عند الـ 1 مول من أي جاز، + +801 +01:03:37,650 --> 01:03:44,320 +هيعطيه 22 و 4 من 10 لترماشي يا جماعة يبقى بقدر + +802 +01:03:44,320 --> 01:03:48,260 +اقول انا زي ما كنت بقول سابقا .. زي ما كنت بقول + +803 +01:03:48,260 --> 01:03:53,760 +سابقا انه ال mall هو عبارة عن ال formula weight + +804 +01:03:53,760 --> 01:03:57,200 +معبرة عنها بال إجرامات أو إجرام formula weight + +805 +01:03:57,200 --> 01:04:03,040 +بقول والله ال mall بساوة 22.4 متر اه بقولها هد قصة + +806 +01:04:03,040 --> 01:04:05,780 +جديدة لل mall كنت بقول ال mall عدد أفجادره من + +807 +01:04:05,780 --> 01:04:11,140 +الأشياء صح؟هذه واحدة و ال mall اجرام فرمولويت صح + +808 +01:04:11,140 --> 01:04:15,620 +اجرام فرمولويت صح و كمان ال mall ايش طول المعنى + +809 +01:04:15,620 --> 01:04:21,680 +اتنين و عشرين و اربع من عشرة بس ايه at stp at stp + +810 +01:04:21,680 --> 01:04:24,740 +اللي هي standard temperature and pressure + +811 +01:04:28,040 --> 01:04:31,960 +فهيوهان بيقولكم ان ال conditions 0 degree c اللي + +812 +01:04:31,960 --> 01:04:36,840 +هو يعني 273.15 Kelvin and one atmosphere are + +813 +01:04:36,840 --> 01:04:40,220 +referred to as standard temperature and pressure + +814 +01:04:40,220 --> 01:04:47,600 +وين هذا في الجازز ماشي في الجاززفمعنى الكلام ال + +815 +01:04:47,600 --> 01:04:51,240 +volume occupied by one mole of an ideal gas at STP + +816 +01:04:51,240 --> 01:04:58,000 +22.4 عادة بيدعى molar volume of an ideal gas at + +817 +01:04:58,000 --> 01:05:03,420 +STP، ليش molar volume؟ لأن هو حجم المولحجم المول + +818 +01:05:03,420 --> 01:05:08,440 +زي ما كنا بنقول delta H not F اللي هي molar heat + +819 +01:05:08,440 --> 01:05:12,660 +of formation لأنه ال delta H not F بتعبر عن ايه؟ + +820 +01:05:12,660 --> 01:05:16,920 +عن تكوين واحد مول فبتسمى برضه molar heat of + +821 +01:05:16,920 --> 01:05:22,120 +formation فهان ايش بنقدر نقول؟ بنقول 22.4 is known + +822 +01:05:22,120 --> 01:05:28,930 +as the molar volume of an ideal gas at aSTP فقط + +823 +01:05:28,930 --> 01:05:33,170 +how many molecules are in 22 أربعة من عشرة letter + +824 +01:05:33,170 --> 01:05:36,610 +of an ideal gas at STP طبعا avogadro's number لأنه + +825 +01:05:36,610 --> 01:05:40,830 +واحد مول واحد مول موجود فيها واحد هذا حجم واحد مول + +826 +01:05:40,830 --> 01:05:44,190 +الواحد مول six point oh two في عشر أقصى تلاتة + +827 +01:05:44,190 --> 01:05:51,470 +وعشرين طيب + +828 +01:05:51,470 --> 01:05:55,110 +هي ده الجول اللي هنتكلم عنه في المستقبل ناخد شوية + +829 +01:05:55,110 --> 01:06:03,340 +أمثلةبيقول ال calcium carbonate solid decomposes + +830 +01:06:03,340 --> 01:06:09,700 +يعني بيتفكك upon heating لما نسخنه ل calcium oxide + +831 +01:06:09,700 --> 01:06:14,360 +solid and CO2 gas طيب a sample of calcium + +832 +01:06:14,360 --> 01:06:17,760 +carbonate اللي هو ال solid is decomposed and the + +833 +01:06:17,760 --> 01:06:22,820 +carbon dioxide is collected in a 250 milli flask + +834 +01:06:23,730 --> 01:06:28,310 +عندما ينتهي الانتقال عندما ينتهي الانتقال عندما + +835 +01:06:28,310 --> 01:06:29,090 +ينتهي الانتقال عندما ينتهي الانتقال عندما ينتهي + +836 +01:06:29,090 --> 01:06:30,490 +الانتقال عندما ينتهي الانتقال عندما ينتهي الانتقال + +837 +01:06:30,490 --> 01:06:31,170 +عندما ينتهي الانتقال عندما ينتهي الانتقال عندما + +838 +01:06:31,170 --> 01:06:31,950 +ينتهي الانتقال عندما ينتهي الانتقال عندما ينتهي + +839 +01:06:31,950 --> 01:06:32,250 +الانتقال عندما ينتهي الانتقال عندما ينتهي الانتقال + +840 +01:06:32,250 --> 01:06:36,870 +عندما ينتهي الانتقال عندما ينتهي الانتقال عندما + +841 +01:06:36,870 --> 01:06:37,570 +ينتهي الانتقال عندما ينتهي الانتقال عندما ينتهي + +842 +01:06:37,570 --> 01:06:41,410 +الانتقال عندما + +843 +01:06:41,410 --> 01:06:50,090 +ينتهي الانتقال عندما + +844 +01:06:50,090 --> 01:06:51,380 +يكانوا مجتمعين وكانوا مجتمعين وكانوا مجتمعين + +845 +01:06:51,380 --> 01:06:54,960 +وكانوا مجتمعين وكانوا مجتمعين وكانوا مجتمعين + +846 +01:06:54,960 --> 01:07:02,980 +وكانوا مجتمعين وكانوا مجتمعين وكانوا مجتمعين + +847 +01:07:02,980 --> 01:07:07,800 +وكانوا مجتمعين + +848 +01:07:07,820 --> 01:07:13,220 +إذن point two five zero على الف لأنها letter ال N + +849 +01:07:13,220 --> 01:07:17,220 +أكم مول بدهياها بده ال number how many moles بده + +850 +01:07:17,220 --> 01:07:24,900 +ال N ال R point O eight one ال T جال والله متين + +851 +01:07:24,900 --> 01:07:29,000 +تلاتة و سبعين زائد واحد و تلاتين انتهينا نفس + +852 +01:07:29,000 --> 01:07:33,160 +الكلام بالظبط بس يعني هان حل طويل بطلع عندي point + +853 +01:07:33,160 --> 01:07:37,000 +O one three mole من ال CO2 بديهاش كلامشابتر + +854 +01:07:37,000 --> 01:07:41,580 +الغازات هذا من الشباتر المضمونة فهما واستيعابا + +855 +01:07:41,580 --> 01:07:45,720 +وايضا المفروض درجات سهل جدا مافي مجال للخطأ فيه + +856 +01:07:52,910 --> 01:07:55,650 +بيقول ال tennis balls are usually filled with + +857 +01:07:55,650 --> 01:08:00,310 +either air or nitrogen تعرفوا أكولات التنس؟ يا + +858 +01:08:00,310 --> 01:08:05,050 +بعبوها هوا يا بعبوها نيترجن لإن لازم يكون فيها هوا + +859 +01:08:05,050 --> 01:08:12,230 +أو غاز يول إيه وإلا راح الضغط الضغط الجو حيكسرها + +860 +01:08:12,230 --> 01:08:16,590 +حيخليها cave in يعنيفلازم يكون فيها غاز او هتكون + +861 +01:08:16,590 --> 01:08:20,410 +صلبة كلها يعني مش ممكن تكون صلبة كلها تقيلة فبتكون + +862 +01:08:20,410 --> 01:08:23,790 +فيها غاز فحطوا فيها هوا او نيتروجين جاز to a + +863 +01:08:23,790 --> 01:08:27,590 +pressure above atmospheric pressure لازم above ولا + +864 +01:08:27,590 --> 01:08:32,250 +راح تنطني من جهات معينة بسهولة لازم يكون اعلى a + +865 +01:08:32,250 --> 01:08:36,950 +tennis ball has a volume of 144 cm مكعب هي ال V + +866 +01:08:36,950 --> 01:08:43,590 +and contains 0.33 gram of nitrogen هي كمية + +867 +01:08:43,590 --> 01:08:48,800 +النيتروجينWhat is the pressure inside the ball at + +868 +01:08:48,800 --> 01:08:56,260 +24 degrees C؟ هاي الحرارة بقول PV بتساوي nRT ال P + +869 +01:08:56,260 --> 01:09:03,220 +قداش؟ بتدوياها ال V قداش؟ point one four four ال N + +870 +01:09:03,220 --> 01:09:07,420 +اللي هي عدد المولات جال هاي هاليجرامات point three + +871 +01:09:07,420 --> 01:09:12,120 +three على تمانية و عشرين ال R point O eight two + +872 +01:09:12,120 --> 01:09:18,230 +one ال Tمتين تلاتة سبعين زائد واحد وعشرين كأنه + +873 +01:09:18,230 --> 01:09:23,970 +جالي اربع اربع وعشرين خلاص اتحت ضايل بس ال P بقاش + +874 +01:09:23,970 --> 01:09:29,150 +بطلع معايا ال P بقاش بال atmosphere سهل للغاية + +875 +01:09:29,150 --> 01:09:39,330 +بيجي + +876 +01:09:39,330 --> 01:09:43,450 +يعني النوع التاني من المسائل ايش بيجي بيقول ليه؟ + +877 +01:09:43,630 --> 01:09:47,730 +ممكن يقول لي والله يعني في عندي غاز، عندي ظروف + +878 +01:09:47,730 --> 01:09:51,690 +معينة، كويس، إله حجم، إله ضغط، إله عدد ملات، إله + +879 +01:09:51,690 --> 01:09:55,710 +مش عارف حرارة، لكن أنا بدي أشوف متغير من هذه + +880 +01:09:55,710 --> 01:10:01,970 +المتغيرات، إيش بجراله لما نغير الظروفيعني مثلا كان + +881 +01:10:01,970 --> 01:10:08,510 +عند ..يعني إله ضغط وحجم وعدد مولات عند temperature + +882 +01:10:08,510 --> 01:10:12,110 +معينة، طب إيش بيحصل مثلا للي pressure لما ال + +883 +01:10:12,110 --> 01:10:16,150 +temperature تزيد؟ مثلا عشرين درجة ولا تلاتين درجة؟ + +884 +01:10:16,150 --> 01:10:22,030 +إيش بده أعمل؟أو ممكن يقول والله عند حرارة معينة + +885 +01:10:22,030 --> 01:10:25,870 +والحرارة ثابتة طب إيش حصلها الحجم؟ يعني في عندي + +886 +01:10:25,870 --> 01:10:30,990 +حاجة فقط بده أشوف إيش تأثير التغير عليها، بس حاجة + +887 +01:10:30,990 --> 01:10:37,950 +واحدة، بقول عادة أنا بهمني أني أعمل التالي، بهمني + +888 +01:10:37,950 --> 01:10:42,460 +أني أقولانه بتحدث عن غازات والغازات كلها واحد + +889 +01:10:42,460 --> 01:10:46,380 +عموما يعني وانا بتكلم عن الغاز نفسه يعني بتكلم عن + +890 +01:10:46,380 --> 01:10:50,600 +في بعض الأحيان نفس عدد المولات إلا إذا كان هو جال + +891 +01:10:50,600 --> 01:10:55,300 +إنها تغيرت بتكلم عن R هي نفسها يعني مثلا P V + +892 +01:10:55,300 --> 01:11:00,660 +بتساوي N R T يعني ممكن أقول P V واحد P واحد V واحد + +893 +01:11:00,660 --> 01:11:05,240 +N واحد R ما هي ثابت T واحد و أقول P اتنين V اتنين + +894 +01:11:05,240 --> 01:11:10,820 +بتساوي N اتنين R T اتنينغيرت الظروف، طب إيش بيحصل + +895 +01:11:10,820 --> 01:11:14,120 +إذا أقسم 1 على 2؟ بقول سهل جدا، هذا على هذا وهذا + +896 +01:11:14,120 --> 01:11:19,060 +على هذا، تساوي، معايا؟ وبما أن ال R ثابتة، هي ال R + +897 +01:11:19,060 --> 01:11:23,660 +راحت، لأن ال R ثابتة هي نفس ال R، تتغيرش، فصار في + +898 +01:11:23,660 --> 01:11:28,200 +أن دي معادلة جديدة، لحظة دائما، ممكن لو جالي أن ال + +899 +01:11:28,200 --> 01:11:31,700 +N هو أو أنا فهمت من السؤال إن ال N ماتغيرتش، إذن + +900 +01:11:31,700 --> 01:11:36,420 +هدول راحوا إن 1 بتساوي أن 2معايا؟ لو قال إنه عند + +901 +01:11:36,420 --> 01:11:40,160 +نفس درجة الحرارة كمان هدوا و راحوا، يبقى صار P1 V1 + +902 +01:11:40,160 --> 01:11:44,140 +على P2 V2 متساوية واحدة أو إن ال P1 V1 ساوية P2 V2 + +903 +01:11:44,140 --> 01:11:53,100 +إذا كان إحنا بنقرأ السؤال صح إيجاد المتغير عند + +904 +01:11:53,100 --> 01:11:58,680 +تغيير الظروف بيكون سهل للغايةإذا أنا قرأت السؤال + +905 +01:11:58,680 --> 01:12:02,660 +صح لأن عندي أصلا كل هدول موجودين ماشي الحال بحل + +906 +01:12:02,660 --> 01:12:05,460 +إذا كان والله أه عدد الملات اتغير و ال temperature + +907 +01:12:05,460 --> 01:12:08,680 +اتغيرت ماشي الحال و ال volume اتغير بقدر أجيب ال P + +908 +01:12:08,680 --> 01:12:13,920 +مثلا لكن إذا قال لي إنه ما جابليش سيرة ال N قال لي + +909 +01:12:13,920 --> 01:12:17,420 +لأ هو نفسه بس غيرنا الظروف فال N نفسها طب لو قالوا + +910 +01:12:17,420 --> 01:12:19,960 +عملنا هذا الكلام at constant temperature يبقى ال T + +911 +01:12:19,960 --> 01:12:24,440 +نفسها ف .. لكن هذا أصل المعادلة هذا أصل المعادلة + +912 +01:12:24,440 --> 01:12:29,920 +منها بدي أوجد النتيجةأنا عملتلكم هذه الـ equations + +913 +01:12:29,920 --> 01:12:35,000 +مش بس لهان و كمان لمستقبل الأسئلة تبعتنا بقول + +914 +01:12:35,000 --> 01:12:39,120 +بنستخدم هذه ال equations في الحلما هي الـ equation + +915 +01:12:39,120 --> 01:12:42,500 +اللي بتستخدمها؟ جال الـPV بتساوي NRT لما يعطيني + +916 +01:12:42,500 --> 01:12:47,120 +يعني تلت متغيرات و بدوا رابع لأن الـR دي اتتت تلت + +917 +01:12:47,120 --> 01:12:50,120 +متغيرات و بدوا رابع هذه مباشرة مافيش فيها اي مشكلة + +918 +01:12:50,120 --> 01:12:55,200 +الحاجة التانية زي ما حكيتكم قبل شوية P1V1 بتساوي + +919 +01:12:55,200 --> 01:13:01,600 +N1RT1 و P2V2 بتساوي N2RT2 و بنروح الـR مع الـR و + +920 +01:13:01,600 --> 01:13:05,840 +هدول ايه؟ بنسويهموبالتالي اذا كان جالي at constant + +921 +01:13:05,840 --> 01:13:09,540 +temperature راحوا ال temperature ماجاليش انه لإن + +922 +01:13:09,540 --> 01:13:13,360 +اتغيرت راحه ممكن يقول at constant volume واحسب ال + +923 +01:13:13,360 --> 01:13:18,180 +temperature كل يعني هذه المعادلة العامة اللي لو + +924 +01:13:18,180 --> 01:13:23,690 +يعني غير كل شيء بستخدمهامن وين إجت تحفظهاش هيها زي + +925 +01:13:23,690 --> 01:13:28,850 +ما قلت PV بتساوي N RT يبقى P1 V1 بتساوي N1 RT1 و + +926 +01:13:28,850 --> 01:13:33,410 +P2 V2 بتساوي N2 RT2 بكسبهم على بعض و انتهينا ما + +927 +01:13:33,410 --> 01:13:39,070 +تحفظيها بدك بس تعرف ان ال N هي عدد المولات طيب ال + +928 +01:13:39,070 --> 01:13:45,990 +N عندي ممكن ييجي يطلب مني ممكن يعطيني إجرام و أنا + +929 +01:13:45,990 --> 01:13:50,420 +طب بدي ال N جال بكسب على الفورمولواتممكن .. ممكن + +930 +01:13:50,420 --> 01:13:56,740 +يطلب مني ال formulawet ويعطيني كل شيء اه خدوا + +931 +01:13:56,740 --> 01:13:59,440 +بالكم بيعطيني ال gram هو لكن بطلب من ال formulawet + +932 +01:13:59,440 --> 01:14:02,800 +بقدر اجيب ال formulawet يعني هذه ال n ممكن تخلي + +933 +01:14:02,800 --> 01:14:06,660 +احسب ال gram او تخلي احسب ال formulawet ال n ممكن + +934 +01:14:06,660 --> 01:14:10,820 +تخلي احسب ال gram او تخلي احسب ال formulawet كمان + +935 +01:14:10,820 --> 01:14:14,370 +في عندي حاجة تانية في الأسئلةغير هيك يبقى ممكن + +936 +01:14:14,370 --> 01:14:17,970 +أحصل على N أو عدد الإجرامات أو الفورمولوات و جاله + +937 +01:14:17,970 --> 01:14:22,290 +كمان على ال density ليه؟ لأن ال density هي عبارة + +938 +01:14:22,290 --> 01:14:25,810 +عن إجرام على ال volume بالمل طب أنا عند ال PV + +939 +01:14:25,810 --> 01:14:32,190 +بتساوي N RT طب هذه ال N هي عبارة عن إيش؟ + +940 +01:14:53,430 --> 01:14:58,110 +المهم ان هذه كل الأسئلة اللى ممكن تجيلنا يا بدى + +941 +01:14:58,110 --> 01:15:02,320 +يحسب جرام يا بدى يحسب formula weightيا بده يحسب + +942 +01:15:02,320 --> 01:15:04,860 +Density فبنشوفكم إذا الله راضي الحدث اللي جاي + diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ouZhgFHnb0w.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ouZhgFHnb0w.srt new file mode 100644 index 0000000000000000000000000000000000000000..515dd5a1e9a8d5b654230db428411830909d47b0 --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ouZhgFHnb0w.srt @@ -0,0 +1,3749 @@ +1 +00:00:21,210 --> 00:00:24,110 +بسم الله الرحمن الرحيم بسم الله الرحمن الرحيم + +2 +00:00:24,110 --> 00:00:29,150 +اليوم بنكمل في ال chemical thermodynamics تحدثنا + +3 +00:00:29,150 --> 00:00:34,890 +في الحصة الماضية بشكل أساسي عن كيفية حساب ال + +4 +00:00:34,890 --> 00:00:42,750 +delta S ل reaction ما و تحدثنا أيضًا عن الـ phase + +5 +00:00:42,750 --> 00:00:48,470 +transition أو بشكل مقتضب يعني إيش بيحصل لو كان في + +6 +00:00:48,470 --> 00:00:56,530 +عندي equilibrium بين gas و liquid أو liquid أو + +7 +00:00:56,530 --> 00:00:57,090 +solid + +8 +00:01:01,640 --> 00:01:05,420 +أو حتى sublimation فاتحدثنا أيضًا عن ال effect of + +9 +00:01:05,420 --> 00:01:10,180 +temperature على ال delta S أو على ال entropy بشكل + +10 +00:01:10,180 --> 00:01:15,100 +عام اليوم بنطلع على معلومات كثير بسيطة بنطلع على + +11 +00:01:15,100 --> 00:01:18,200 +ال free energy و علاقتها بال phase transition + +12 +00:01:18,200 --> 00:01:23,280 +temperature شفنا هذا الكلام سابقًا لكن ما عملناش ال + +13 +00:01:23,280 --> 00:01:28,240 +relation من ال free energy و بالمناسبة free energy + +14 +00:01:28,240 --> 00:01:32,900 +مش معناتها أنها يعني زي بعض الناس ما بتعتقد أنها + +15 +00:01:32,900 --> 00:01:38,980 +عبارة عن طاقة خليني أقول مجانية free لأ مش المقصود + +16 +00:01:38,980 --> 00:01:44,220 +أنها طاقة مجانية لأ free energy يعني أقرب ما تكون + +17 +00:01:44,220 --> 00:01:47,800 +ال available energy ال available energy ال energy + +18 +00:01:47,800 --> 00:01:51,560 +اللي ممكن تعمل شغل فيزيائي يعني ال energy موجودة ممكن + +19 +00:01:51,560 --> 00:01:55,600 +تعمل شغل لكن مش free energy يعني إيه يعني طاقة + +20 +00:01:55,600 --> 00:02:00,800 +مجانية لأ هذا تعبير أو يعني تفسير خاطئ لمعنى ال + +21 +00:02:00,800 --> 00:02:05,560 +term فبنبدأ نطلع على ال phase transition temperature + +22 +00:02:05,560 --> 00:02:10,450 +من واقع أو من ال free energy فبقول في البداية أنا + +23 +00:02:10,450 --> 00:02:14,330 +عندي الـ delta G not at standard conditions يعني + +24 +00:02:14,330 --> 00:02:17,510 +نسوي delta H not minus T delta S not لو مش + +25 +00:02:17,510 --> 00:02:20,670 +standard conditions طبعًا بنرفع ال note تصير عادي + +26 +00:02:20,670 --> 00:02:25,030 +delta G بتساوي delta H minus T delta S لكن أنا بعرف + +27 +00:02:25,030 --> 00:02:28,950 +أن ال delta G not بتساوي 0 for a phase transfer + +28 +00:02:28,950 --> 00:02:32,170 +لأنه عندي equilibrium reversible process فمعنى + +29 +00:02:32,170 --> 00:02:37,470 +الكلام ال delta H هتساوي T delta S أو بمعنى آخر ال + +30 +00:02:37,470 --> 00:02:41,270 +temperature هتساوي delta H على delta S فإذا كان + +31 +00:02:41,270 --> 00:02:46,050 +بتكلم عن fusion أو يعني ذوبان delta H fusion على + +32 +00:02:46,050 --> 00:02:51,370 +delta S fusion إذا بتكلم عن Vaporization ليكود مع + +33 +00:02:51,370 --> 00:02:55,730 +فيبر بقول والله ال tea boiling بتصير لأنها boiling + +34 +00:02:55,730 --> 00:02:58,890 +ف delta H vaporization على delta S vaporization + +35 +00:02:58,890 --> 00:03:01,370 +إذا كنت بتكلم عن ال sublimation فال tea لل + +36 +00:03:01,370 --> 00:03:04,650 +sublimation تساوي delta H sublimation على delta S + +37 +00:03:04,650 --> 00:03:08,110 +لل sublimation وفي الواقع مش شرط أن يكون في عندي + +38 +00:03:08,110 --> 00:03:16,590 +حتى phase a transition يعني خلّيني أقول بالصورة + +39 +00:03:16,590 --> 00:03:22,050 +اللي أنا ذكرتها هذه المعهودة لأ ممكن والله مثلًا زي + +40 +00:03:22,050 --> 00:03:26,350 +ما ذكرت سابقًا orthorhombic + +41 +00:03:26,350 --> 00:03:31,030 +sulfur يتحول ل monoclonic sulfur أو العكس يعني + +42 +00:03:31,030 --> 00:03:35,510 +فهذا يعتبر أيضًا phase transition فانا بقول ال T + +43 +00:03:35,510 --> 00:03:42,330 +بشكل عام لل phase change هتساوي الـ delta H للتشينج + +44 +00:03:42,330 --> 00:03:45,730 +على ال delta S للتشينج، بغض النظر عن الاسم، هل هي + +45 +00:03:45,730 --> 00:03:51,010 +هذه أو هذه أو هذه، وحتى two solid phases مع بعض في + +46 +00:03:51,010 --> 00:03:57,010 +phase أثبت من phase آخر، فهذا الكلام كله ممكن نجمعه + +47 +00:03:57,010 --> 00:03:59,150 +ونقول والله ال T لل phase change ده ال delta H + +48 +00:03:59,150 --> 00:04:03,940 +للتشينج على ال delta S هذا كله من أين جاء ببساطة من + +49 +00:04:03,940 --> 00:04:06,780 +أنه والله قلنا في ال phase change في عندي + +50 +00:04:06,780 --> 00:04:10,060 +equilibrium ما بين ال two phases أو في عندي a + +51 +00:04:10,060 --> 00:04:13,400 +transition temperature هذه ال temperature اللي + +52 +00:04:13,400 --> 00:04:17,640 +قبلها بيكون عندي phase معين بعدها بيصير عندي phase + +53 +00:04:17,640 --> 00:04:20,810 +آخر هذه هي الـ Transition Temperature اللي أنا + +54 +00:04:20,810 --> 00:04:24,790 +بتكلم عنها و زي ما احنا شايفين هذا الكلام قدرنا + +55 +00:04:24,790 --> 00:04:28,370 +نحصل عليه لأنه افترضنا أن ال Delta G بتساوي صفر + +56 +00:04:28,370 --> 00:04:32,410 +و هذا الكلام صحيح لأن في عندي equilibrium ما بين ال + +57 +00:04:32,410 --> 00:04:37,400 +two phases أو التغير بيكون reversible فعلى سبيل + +58 +00:04:37,400 --> 00:04:42,100 +المثال هذا الـ T Delta S هي تغيرها مع الحرارة و + +59 +00:04:42,100 --> 00:04:47,020 +احنا في هذا المساء هنعتبر أنه يعني في كثير من + +60 +00:04:47,020 --> 00:04:50,740 +الأحيان إذا كان قلنا لك أنه والله تتغيرش فبنعتبر أن + +61 +00:04:50,740 --> 00:04:54,300 +هذا التغير مش موجود و كأنها خط و كأنها خط أفق + +62 +00:04:54,300 --> 00:04:58,280 +تمامًا يعني ما فيش عندي تغير مع الحرارة وهي ال Delta + +63 +00:04:58,280 --> 00:05:03,140 +H على سبيل المثال التغير إليها مع الحرارة وكذلك في + +64 +00:05:03,140 --> 00:05:06,960 +كثير من الأحيان الـ delta H لا تتغير مع الحرارة، + +65 +00:05:06,960 --> 00:05:10,380 +طبعًا هذا يتوقف على ال system مرات التغير كبير و + +66 +00:05:10,380 --> 00:05:16,160 +مرات التغير قليل فلما نقول لا تتغير ال delta S أو + +67 +00:05:16,160 --> 00:05:19,520 +ال delta H مع الحرارة فمعنى الكلام حسبتنا تقريبية + +68 +00:05:19,520 --> 00:05:26,000 +يعني القيم اللي بنحصل عليها هي قيم تقريبية مش + +69 +00:05:26,000 --> 00:05:30,190 +حقيقية لكن احنا بنستخدم هذا المفهوم ببساطة نقول + +70 +00:05:30,190 --> 00:05:34,070 +والله لا تتغيرش مع الحرارة عشان نبسط الحل بحيث أن + +71 +00:05:34,070 --> 00:05:38,450 +نروح ناخد القيم الموجودة في الجداول فبشتغل + +72 +00:05:38,450 --> 00:05:41,450 +باستخدام ال delta H أو ال delta S at the standard + +73 +00:05:41,450 --> 00:05:45,150 +state اللي هي قيمها موجودة في الجداول فما أضطرّش أن + +74 +00:05:45,150 --> 00:05:47,930 +أنا أدور على قيم ال delta H و delta S عند الحرارة + +75 +00:05:47,930 --> 00:05:51,810 +اللي أنا بدي إياها بالظبط لكن هذا الشكل بيبين أن + +76 +00:05:51,810 --> 00:05:55,330 +أنا اتغير ال delta S و delta H مع الحرارة لاحظوا + +77 +00:05:55,330 --> 00:05:59,980 +أنهم بتتقاطعوا في نقطة عند هذه النقطة بالظبط الـ delta + +78 +00:05:59,980 --> 00:06:05,280 +H بتساوي يعني الحرارة، عند الحرارة هذه، في عندي + +79 +00:06:05,280 --> 00:06:09,080 +ال delta H ساوية T delta S عند الحرارة هذه + +80 +00:06:09,080 --> 00:06:12,600 +بالظبط، لأن التقاطع ال delta أو عند ال delta G + +81 +00:06:12,600 --> 00:06:16,310 +بتساوي zero فهذه ال transition temperature لاحظوا + +82 +00:06:16,310 --> 00:06:20,930 +قبلها ممكن يكون spontaneous بعدها spontaneous أو + +83 +00:06:20,930 --> 00:06:23,890 +العكس ممكن يكون قبلها spontaneous بعدها non + +84 +00:06:23,890 --> 00:06:29,310 +spontaneous تمام؟ لكن هذه عبارة عن ال transition + +85 +00:06:29,310 --> 00:06:32,210 +temperature اللي عندها ال delta H بالساوية T delta + +86 +00:06:32,210 --> 00:06:37,670 +S وعندها بيكون ال delta G عبارة عن Zero لأن هذا + +87 +00:06:37,670 --> 00:06:42,080 +عبارة عن equilibrium معنى الكلام الـ two phases أو + +88 +00:06:42,080 --> 00:06:46,180 +الـ change بدي يكون reversible في هذه المنطقة عند + +89 +00:06:46,180 --> 00:06:49,500 +هذه الحرارة بالظبط بيكون reversible فلو في عندي + +90 +00:06:49,500 --> 00:06:54,740 +غليان يعني أقل من مائة درجة للمية، non spontaneous + +91 +00:06:54,740 --> 00:06:59,160 +أكثر من مائة درجة، spontaneous أو عند مائة درجة + +92 +00:06:59,160 --> 00:07:03,340 +equilibrium دلتة جيب تساوي صفر تمام؟ فهذا المفهوم + +93 +00:07:03,340 --> 00:07:07,960 +يعني ال transition temperature اللي أنا بتكلم عنه + +94 +00:07:08,740 --> 00:07:14,880 +خلّيني أخد بعض الأمثلة التوضيحية بقول مثلًا بيحكي + +95 +00:07:14,880 --> 00:07:20,320 +at 25 degrees c يعني 298 Kelvin the reduction of + +96 +00:07:20,320 --> 00:07:25,240 +copper one oxide is non spontaneous حلو، بدنا نعمل + +97 +00:07:25,240 --> 00:07:27,700 +reduction لل copper one oxide، هذه non spontaneous + +98 +00:07:27,700 --> 00:07:32,380 +ال delta G positive 8.9 كيلوجول طبعًا لو كان + +99 +00:07:32,380 --> 00:07:35,940 +spontaneous ال delta G بدها تكون سالبة لأن ال + +100 +00:07:35,940 --> 00:07:40,100 +delta G سالبة لل spontaneous processes بقول + +101 +00:07:40,100 --> 00:07:42,760 +calculate the temperature at which the reaction + +102 +00:07:42,760 --> 00:07:47,160 +becomes spontaneous إيش هي الحاجة هو هان non + +103 +00:07:47,160 --> 00:07:51,400 +spontaneous شفنا المربع تبعه قبل شوية ع اليسار طب + +104 +00:07:51,400 --> 00:07:55,040 +إيش الحرارة اللي عندها هذا هو يعني هان هو هان non + +105 +00:07:55,040 --> 00:07:59,720 +spontaneous عند خمسة و عشرين ديجري ال سي عند حرارة + +106 +00:07:59,720 --> 00:08:02,580 +معينة non spontaneous بده الحرارة اللي عندها بيصير + +107 +00:08:02,580 --> 00:08:07,730 +spontaneous هان بالظبط بيصير spontaneous يعني هان + +108 +00:08:07,730 --> 00:08:10,830 +بالظبط بيبدأ يصير spontaneous لأنه بعد على طول بعد + +109 +00:08:10,830 --> 00:08:15,270 +شيء قليل جدا بيصير spontaneous فلازم يعني نحسب إيه + +110 +00:08:15,270 --> 00:08:19,830 +لل transition temperature فبيقول ليه أكمل السؤال + +111 +00:08:19,830 --> 00:08:22,570 +بيقول ليه calculate the temperature at which the + +112 +00:08:22,570 --> 00:08:28,210 +reaction becomes spontaneous ΔH and ΔS are 58.1 + +113 +00:08:28,210 --> 00:08:34,060 +kilo joule and 165 joule per Kelvin باعطين قيمة الـ + +114 +00:08:34,060 --> 00:08:38,560 +ΔH والـ ΔS لتاعة المثالة الـ T بتساوي ΔH على ΔS + +115 +00:08:39,460 --> 00:08:41,820 +معنى الكلام ليه؟ لأن ليش هذا الكلام؟ أنا بدي أجيب + +116 +00:08:41,820 --> 00:08:43,880 +الـTransition Temperature اللي بعد الـTransition + +117 +00:08:43,880 --> 00:08:47,140 +Temperature بده يصير عندي الـChange اللي أنا بديه + +118 +00:08:47,140 --> 00:08:49,440 +يعني فبدي أجيب الـTransition Temperature بالظبط + +119 +00:08:49,440 --> 00:08:52,740 +وين .. وين هي الـTemperature اللي بعدها على طول + +120 +00:08:52,740 --> 00:08:55,240 +بيحصل عندي الـChange اللي بيقول الـT بيساوي + +121 +00:08:55,240 --> 00:08:58,620 +الـDelta S على الـDelta S fifty eight point one في + +122 +00:08:58,620 --> 00:09:03,900 +عشرة قصة ثلاثة لأنه الانتروبي بالجول أنا عندي هذه + +123 +00:09:03,900 --> 00:09:07,800 +kilo Joule فحولتهم لجول بيطلع عندي تلت مية اتنين + +124 +00:09:07,800 --> 00:09:13,610 +وخمسين Kelvin إذا بعد ال 352 كيلوفر خلاص التفاعل + +125 +00:09:13,610 --> 00:09:18,870 +بيصير عندي إيه؟ spontaneous عند 352 اه في عندي + +126 +00:09:18,870 --> 00:09:24,530 +equilibrium أقل من 352 ما نِ spontaneous فمش بس عند + +127 +00:09:24,530 --> 00:09:30,230 +25 degree c لأ عند أقل من 352 بيظل هو non + +128 +00:09:30,230 --> 00:09:35,280 +spontaneous ما دام أقل من 352 إذا من spontaneous + +129 +00:09:35,280 --> 00:09:41,640 +هان أقل من 352 من spontaneous 352 بالظبط اترازشن + +130 +00:09:41,640 --> 00:09:47,380 +temperature بعد 352 بشحته صار spontaneous فهي + +131 +00:09:47,380 --> 00:09:51,940 +مفهوم المسألة نيجي نتطلع على مسألة ثانية بتقول if + +132 +00:09:51,940 --> 00:09:55,660 +the reaction below spontaneous at room temperature + +133 +00:09:55,660 --> 00:10:00,270 +15 degree c If not, at what temperature will it + +134 +00:10:00,270 --> 00:10:03,350 +start to be spontaneous؟ هل هذا التفاعل + +135 +00:10:03,350 --> 00:10:09,810 +spontaneous عند خمسة أو عشرين degrees C؟ والله، هي + +136 +00:10:09,810 --> 00:10:12,530 +بدنا نجاوب على هذا السؤال، بدنا نجاوب على هذا + +137 +00:10:12,530 --> 00:10:17,610 +السؤال إذا ما كانش spontaneous، إيش الحرارة اللي + +138 +00:10:17,610 --> 00:10:19,310 +عندها بده يصير spontaneous؟ بدنا ندورها على عالي + +139 +00:10:19,310 --> 00:10:22,230 +ترازشين temperature، لازم نفهم السؤال بالظبط إيش + +140 +00:10:22,230 --> 00:10:25,750 +اللي بده ياه فانا بشوف والله عند خمسة و عشرين ديجري + +141 +00:10:25,750 --> 00:10:29,490 +سي دلتا جي نوت بتساوي دلتا H نوت ماينص تي دلتا S + +142 +00:10:29,490 --> 00:10:32,890 +نوت فبنعوض في المعادلة one seventy seven point eight + +143 +00:10:32,890 --> 00:10:36,130 +ماينص two ninety eight في مائة و ستين point five + +144 +00:10:36,130 --> 00:10:38,810 +فعشرة أسئلة بتانية حوالي الكيلو جول، بيطلع عند + +145 +00:10:38,810 --> 00:10:43,020 +مائة و ثلاثين point zero كيلو جول بير مول هذه الـ + +146 +00:10:43,020 --> 00:10:48,320 +دلتا جي نوت موجبة أم سالبة؟ موجبة إذن وليس + +147 +00:10:48,320 --> 00:10:53,660 +سبونتانيوس لأن شرط ال spontaneity أن تكون ال + +148 +00:10:53,660 --> 00:10:57,880 +دلتا جي سالبة شرط ال spontaneity أن تكون ال دلتا + +149 +00:10:57,880 --> 00:11:00,920 +جي سالبة أم موجبة موجبة suggesting a non + +150 +00:11:00,920 --> 00:11:04,680 +spontaneous process at 25 degrees C + +151 +00:11:09,110 --> 00:11:13,470 +طبعا لو عوضنا بها بالـ Transition Temperature، + +152 +00:11:13,470 --> 00:11:15,910 +عارفين إيش اللي بيحصل؟ الـ Delta G Note بيتساوى + +153 +00:11:15,910 --> 00:11:20,710 +صفر، لو .. آه لو إنه .. لو إنه أعطاني قيمة مثلا هل + +154 +00:11:20,710 --> 00:11:27,510 +هي .. هل ال .. يعني هل التفاعل spontaneous at 1108 + +155 +00:11:29,470 --> 00:11:33,370 +كيلفن لو أجيت أنا ب 1108 Kelvin راح أجيب + +156 +00:11:33,370 --> 00:11:38,410 +النتيجة قد إيش؟ صفر ليه؟ لأن دلتا جي بتساوي صفر دلتا جي + +157 +00:11:38,410 --> 00:11:41,850 +نوت بتساوي صفر لازم يطلع عندي صفر تعالوا نحسب الآن + +158 +00:11:41,850 --> 00:11:45,510 +إيش هي ال transition temperature اللي عندها يعني + +159 +00:11:45,510 --> 00:11:50,150 +أو بعدها ال change بيصير spontaneous بقول to + +160 +00:11:50,150 --> 00:11:52,230 +calculate the temperature at which the reaction + +161 +00:11:52,230 --> 00:11:55,130 +starts to be spontaneous we should assume the + +162 +00:11:55,130 --> 00:11:59,290 +equilibrium state where دلتا جي نوت بتساوي صفر الـ T + +163 +00:11:59,290 --> 00:12:03,430 +ΔH على ΔS والله عوضنا عنها دول هتطلع 1108 يعني + +164 +00:12:03,430 --> 00:12:06,670 +التفاعل بيكون و non spontaneous لغاية ما نوصل لل + +165 +00:12:06,670 --> 00:12:11,190 +transition temperature اللي هي 1108 أقل منها non + +166 +00:12:11,190 --> 00:12:16,230 +spontaneous أكثر منها spontaneous لو عوضنا بأكثر + +167 +00:12:16,230 --> 00:12:23,620 +من 1108 هان إشارة الـ Δجينوت هتكون سالبة خلاص عند + +168 +00:12:23,620 --> 00:12:29,460 +ما نعوض من 1108 هتكون صفر أقل من 1108 هتكون موجبة + +169 +00:12:29,460 --> 00:12:32,860 +يعني non spontaneous جميل جدا جميل جدا إذا اللي + +170 +00:12:32,860 --> 00:12:35,520 +بنعرف الحرارة اللي عندها بيصير عندي ال change + +171 +00:12:35,520 --> 00:12:40,580 +spontaneous أم non spontaneous هذا شيء كثير مفيد + +172 +00:12:40,580 --> 00:12:44,960 +بيقول لي if the reaction below spontaneous or non + +173 +00:12:44,960 --> 00:12:48,740 +spontaneous at 25 degrees c at what temperature + +174 +00:12:48,740 --> 00:12:52,300 +will this reaction reverse direction إذا كانوا + +175 +00:12:52,300 --> 00:12:54,840 +spontaneous فتصبح non spontaneous، إذا كانوا non + +176 +00:12:54,840 --> 00:12:57,860 +spontaneous فتصبح spontaneous، إذا كانوا non + +177 +00:12:57,860 --> 00:12:58,080 +spontaneous فتصبح non spontaneous، إذا كانوا non + +178 +00:12:58,080 --> 00:13:00,300 +spontaneous فتصبح non spontaneous، إذا كانوا non + +179 +00:13:00,300 --> 00:13:02,800 +spontaneous فتصبح non spontaneous، إذا كانوا non + +180 +00:13:02,800 --> 00:13:05,160 +spontaneous فتصبح non spontaneous، إذا فبقول + +181 +00:13:05,160 --> 00:13:08,900 +تعالوا نطلع دلتا H0 ماينص تي دلتا S0 هذا عبارة عن + +182 +00:13:08,900 --> 00:13:13,280 +دلتا G0 بنعوض عنهم At 25 degrees C دلتا G0 + +183 +00:13:13,280 --> 00:13:19,400 +هيعطيني في مسألة ثانية أنا بعرفها اللي هو دلتا H0 + +184 +00:13:19,400 --> 00:13:22,460 +ماينص 92.38 للتفاعل هذا + +185 +00:13:25,940 --> 00:13:30,720 +الحرارة خمسة و عشرين ديجري سي بده دلتا اس برضه هذا + +186 +00:13:30,720 --> 00:13:34,740 +هي معايا سالب سالب مائة و ثمانية و تسعين و ثلاثة من + +187 +00:13:34,740 --> 00:13:37,700 +عشرة بيطلع عندي سالب ثلاثة و ثلاثين و ثلاثة من + +188 +00:13:37,700 --> 00:13:42,600 +عشرة كيلوجول آه يبقى التفاعل spontaneous at room + +189 +00:13:42,600 --> 00:13:46,900 +temperature وهذا سؤال مهم هأرجع له عدة مرات لإيش؟ + +190 +00:13:46,900 --> 00:13:50,140 +لأن هذا الـ Haber process اللي هي طريقة تحضير + +191 +00:13:50,140 --> 00:13:53,000 +الأمونيا من الـ nitrogen والهيدروجين عملية صناعية + +192 +00:13:53,000 --> 00:13:57,340 +ممتازة وفعالة ومفيدة جدا بالنسبة لنا وبنستخدمها + +193 +00:13:57,340 --> 00:14:01,160 +بشكل كبير عشان هيك إلها زيارات متعددة زرنا إياها بهيك + +194 +00:14:01,160 --> 00:14:05,190 +لكن برضه كمان إلها زيارات متعددة لأنه مهم طب تعالوا + +195 +00:14:05,190 --> 00:14:08,070 +نشوف ال Transition temperature هو اللي أنا عارفه لإنه + +196 +00:14:08,070 --> 00:14:12,650 +spontaneous طب وقتش بيصير non spontaneous إذا بدي + +197 +00:14:12,650 --> 00:14:15,630 +أجيب ال Transition temperature لحد الفاصل ال Transition + +198 +00:14:15,630 --> 00:14:18,210 +temperature فيقول ال T بتساوي دلتا H على ال + +199 +00:14:18,210 --> 00:14:24,850 +دلتا S هي دلتا S دلتا H سالب 92 380 يعني + +200 +00:14:24,850 --> 00:14:30,530 +نضربها في الألف عشان تصير جول وهي ال S أو دلتا + +201 +00:14:30,530 --> 00:14:35,790 +S سالب 198 و ثلاثة من عشرة جول بير كيلفن فبيطلع + +202 +00:14:35,790 --> 00:14:40,940 +عندي أربعمائة وخمسة وستون وتسعة من عشرة حلو كثير هذه + +203 +00:14:40,940 --> 00:14:45,360 +الحرارة يا جماعة قبلها التفاعل هذا بيكون + +204 +00:14:45,360 --> 00:14:50,300 +spontaneous بعدها بيصير not spontaneous عندها + +205 +00:14:50,300 --> 00:14:53,240 +بالضبط بيكون في عنده equilibrium عندها بالضبط + +206 +00:14:53,240 --> 00:14:55,280 +بيكون في عنده equilibrium + +207 +00:14:59,980 --> 00:15:03,920 +طيب هذا السؤال بيعطيني لما نكون فيه عندي + +208 +00:15:03,920 --> 00:15:07,980 +equilibrium بيقول لي write the chemical equation + +209 +00:15:07,980 --> 00:15:11,720 +that defines the normal boiling point of liquid + +210 +00:15:11,720 --> 00:15:17,660 +carbon tetrachloride CCL4 بقول المعادلة اللي + +211 +00:15:17,660 --> 00:15:21,220 +بتعطيني ال normal boiling point إن يكون ال CCL4 ال + +212 +00:15:21,220 --> 00:15:29,420 +liquid in equilibrium مع ال CCL4 gas هذه المعادلة + +213 +00:15:29,420 --> 00:15:35,640 +CCL4 liquid يتحول إلى CCL4 gas reversibly فهذه هي + +214 +00:15:35,640 --> 00:15:40,240 +المعادلة طيب بيقول لي what is the value of delta G + +215 +00:15:40,240 --> 00:15:43,680 +note for the equilibrium in part A؟ إيش قيمة ال + +216 +00:15:43,680 --> 00:15:50,520 +دلتا جي نوت لهذا ال equilibrium؟ هتكون صفر طبعا، + +217 +00:15:50,520 --> 00:15:58,280 +ليه؟ آه لأن at equilibrium دلتا جي نوت بدها + +218 +00:15:58,280 --> 00:16:03,810 +تساوي صفر في عندي reversible change ما بين ال + +219 +00:16:03,810 --> 00:16:09,310 +liquid و ال vapor فبالتالي بدها تكون صفر هذا سابق + +220 +00:16:09,310 --> 00:16:13,810 +لأوانا شوية هيجي لنا بعدين مفهوم ال Q reaction + +221 +00:16:13,810 --> 00:16:19,280 +quotient بيقول NFC بيقول estimate the normal + +222 +00:16:19,280 --> 00:16:25,680 +boiling point of CCL4 provided that ΔH0 F4 CCL4 و + +223 +00:16:25,680 --> 00:16:30,840 +CCL4 gas و liquid are minus 106.7 kilojoule per + +224 +00:16:30,840 --> 00:16:36,500 +mole و minus 139 kilojoule per mole Also it's not + +225 +00:16:36,500 --> 00:16:43,800 +for CCL4 and CCL4 gas and liquid are 309.4 and 214 + +226 +00:16:43,800 --> 00:16:47,800 +.4 respectively Assume ΔH and ΔS do not change + +227 +00:16:47,800 --> 00:16:50,900 +with temperature طبعا هذا مش حقيقي اتفاجأنا على هذا + +228 +00:16:50,900 --> 00:16:54,340 +الكلام هو فيه تغير بيعتمد على ال system مدى التغير + +229 +00:16:54,340 --> 00:16:58,020 +بيعتمد على ال system HU لكن إحنا لسهولة الحسابات + +230 +00:16:58,020 --> 00:17:06,240 +عشان نحصل على خليني أقول نستخدم دلتا H عند أي حرارة + +231 +00:17:06,240 --> 00:17:09,160 +بقيمتها عند خمسة وعشرين ديجري سي لل standard + +232 +00:17:09,160 --> 00:17:13,220 +state لازم نفترض هذا الافتراض يمكن مش كثير أنتم + +233 +00:17:13,220 --> 00:17:16,500 +يعني بتحسوا بأهمية الموضوع لكن الموضوع كثير مهم + +234 +00:17:16,500 --> 00:17:21,140 +الموضوع كثير كثير مهم فخلينا نركز مع بعض شوية بقول + +235 +00:17:21,140 --> 00:17:23,340 +أنا ما دام في عندي + +236 +00:17:27,060 --> 00:17:31,100 +بعدين بده ال normal boiling point كويس إذا أنا بدي + +237 +00:17:31,100 --> 00:17:34,360 +أشتغل عند ال إيش؟ عند ال equilibrium أو بدلي + +238 +00:17:34,360 --> 00:17:38,350 +transition temperature فبالتالي بقول دلتا جي 0 + +239 +00:17:38,350 --> 00:17:43,110 +بيساوي صفر أو ال T بيساوي دلتا S أو الـ T بيساوي + +240 +00:17:43,110 --> 00:17:49,230 +دلتا H نوت على دلتا S نوت دلتا H على دلتا S دلتا H + +241 +00:17:49,230 --> 00:17:53,310 +نوت على دلتا S دلتا H نوت على دلتا S دلتا H نوت + +242 +00:17:53,310 --> 00:17:59,210 +على دلتا S دلتا H نوت على دلتا S دلتا H نوت على + +243 +00:17:59,210 --> 00:18:00,030 +دلتا S دلتا H نوت على دلتا S دلتا H نوت على دلتا S + +244 +00:18:00,030 --> 00:18:01,310 +دلتا H نوت على دلتا S دلتا H نوت على دلتا S دلتا H + +245 +00:18:01,310 --> 00:18:04,650 +نوت على دلتا S دلتا H نوت على دلتا S دلتا H نوت + +246 +00:18:04,650 --> 00:18:08,970 +على دلتا معنى الكلام بده أشوف والله دلتا H + +247 +00:18:08,970 --> 00:18:13,090 +نوت واحد مول فيه ماينص one oh six point seven + +248 +00:18:13,090 --> 00:18:18,370 +كيلو جول بير مول ماينص بنعوض تعويض يعني عن دلتا + +249 +00:18:18,370 --> 00:18:25,330 +H نوت if لهذا و للآخر يعني للجاز و + +250 +00:18:25,330 --> 00:18:29,230 +لليكويد وهنا دلتا S نوت بنقول والله S + +251 +00:18:29,230 --> 00:18:34,250 +نوت للجاز ماينص S نوت لليكويد فبحصل على + +252 +00:18:34,250 --> 00:18:39,850 +القيمة دي هي دلتا H نوت وهي دلتا S نوت فبقول + +253 +00:18:39,850 --> 00:18:44,170 +والله ال T بيساوي دلتا H نوت على دلتا S نوت + +254 +00:18:44,170 --> 00:18:50,370 +ثلاثةلاف و متون و ستين اللي هو اللي عبارة عن دلتا + +255 +00:18:50,370 --> 00:18:55,670 +H اللي حسبتها على خمسة وتسعين جول بير كيلفن + +256 +00:18:55,670 --> 00:19:01,150 +اللي بيعطيني ألف و ثلاثة و أربعين كيلفن يعني + +257 +00:19:01,150 --> 00:19:05,370 +بيقول لي إن ال boiling point ل CCL4 قد إيش؟ + +258 +00:19:14,460 --> 00:19:21,840 +تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً + +259 +00:19:21,840 --> 00:19:22,660 +تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً + +260 +00:19:22,660 --> 00:19:22,700 +تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً + +261 +00:19:22,700 --> 00:19:22,820 +تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً + +262 +00:19:22,820 --> 00:19:23,020 +تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً + +263 +00:19:23,020 --> 00:19:25,370 +تقريباً تقريباً تقريباً طيب ليش الفرق هذا؟ جاء لأنه + +264 +00:19:25,370 --> 00:19:28,890 +إحنا اعتبرنا أو افترضنا إن دلتا H ودلتا S + +265 +00:19:28,890 --> 00:19:33,030 +لا تتغيروا بالنسبة للحرارة لكنهم في الحقيقة لأ في الحقيقة + +266 +00:19:33,030 --> 00:19:37,550 +بيتأثروا بالحرارة لكن هذه الفرضية بتسهل علينا + +267 +00:19:37,550 --> 00:19:42,510 +شغلنا لأن على طول بدي أحسب بأنه جاء هذا الكلام بروح + +268 +00:19:42,510 --> 00:19:44,890 +فورا بجيب دلتا لو ما أعطانيش هدول بجيب دلتا H + +269 +00:19:44,890 --> 00:19:49,630 +not F و دلتا H not F at standard state و ال S not + +270 +00:19:49,630 --> 00:19:53,010 +و ال S not at standard state واللي أنا بفترض إن + +271 +00:19:53,010 --> 00:19:55,950 +هدول هم قد ال standard state هم نفسهم عند أي + +272 +00:19:55,950 --> 00:19:59,750 +حرارة، لأنهم لا يتأثروا بالحرارة، لكن هذا كلام إيش؟ + +273 +00:19:59,750 --> 00:20:04,670 +مش صحيح على الإطلاق، وكمان بيتوقف على ال system + +274 +00:20:09,530 --> 00:20:14,950 +طبعا نفس السؤال خلينا نتطلع عليه بشكل آخر هذه ال + +275 +00:20:14,950 --> 00:20:18,350 +process for the production of ammonia involves the + +276 +00:20:18,350 --> 00:20:23,850 +equilibrium in N2 زائد 3H2 بعطينا 2NH3 assume that + +277 +00:20:23,850 --> 00:20:29,330 +ΔH0 و ΔS0 for this reaction do not change with + +278 +00:20:29,330 --> 00:20:29,830 +temperature + +279 +00:20:32,820 --> 00:20:36,860 +تقريباً تقريباً predict the direction in which delta + +280 +00:20:36,860 --> 00:20:39,700 +G naught for the reaction it changes with + +281 +00:20:39,700 --> 00:20:41,060 +increasing temperature + +282 +00:20:48,630 --> 00:20:56,170 +فبدنا نشوف وقت إيش الـ Delta G not بتتغير إشارتها + +283 +00:20:56,170 --> 00:21:00,570 +بتتغير إذا بدي أشوف الـ Delta G not عند الصفر لما + +284 +00:21:00,570 --> 00:21:03,290 +الصفر بتكون بصفر، صفر اه قبله بتكون موجبة وبعده + +285 +00:21:03,290 --> 00:21:07,010 +بتكون إيه سالبة، هذا مفهوم السؤال، هذا مفهوم السؤال + +286 +00:21:07,010 --> 00:21:09,750 +لما نيجي يقول predict the direction in which Delta + +287 +00:21:09,750 --> 00:21:14,250 +G not for the reaction it changes with increasing + +288 +00:21:14,250 --> 00:21:16,710 +temperature يعني وقت يحول من سالبة لموجبة لموجبة + +289 +00:21:16,710 --> 00:21:17,990 +لسالبة، إذا بدي أجيب + +290 +00:21:26,950 --> 00:21:32,670 +بعدين يحسب قيمة الـ Delta G عند 25 و 500 على فرض + +291 +00:21:32,670 --> 00:21:40,070 +أن Delta H و Delta S لا تتغيران بالحرارة لأن لو كانت + +292 +00:21:40,070 --> 00:21:46,310 +تتغيران بالحرارة يعني لازم نجيب قيمهم عند 25 و 500 + +293 +00:21:47,410 --> 00:21:51,250 +عند 25 هم المعروفون لأنهم من الجداول، طب عند 500 + +294 +00:21:51,250 --> 00:21:56,410 +لازم نشوف جداول عند 500 أو أنه يعني نقدرهم عند + +295 +00:21:56,410 --> 00:22:00,310 +500، لكن لا، احنا هنستخدم اللي عند 25 كمان عند 500 + +296 +00:22:00,310 --> 00:22:07,970 +هي نفس القيمة لـ Delta H و لـ Delta S أو للـ S يعني + +297 +00:22:07,970 --> 00:22:16,890 +تعالوا نتطلع عموما، لو جينا نتطلع هنلاقي انتروبي + +298 +00:22:16,890 --> 00:22:23,210 +بيزيد ولا بيقل؟ المفروض التفاعل هذا،الانتروبي بيقل + +299 +00:22:23,210 --> 00:22:28,270 +لأن هنا عندي أربعة مولات غازية وهنا عندي بس اثنين + +300 +00:22:28,270 --> 00:22:32,430 +إذا النتيجة عدد مولات غازية أقل يبقى الـ Delta S + +301 +00:22:32,430 --> 00:22:38,790 +قيمة إيه؟ قيمة سالبة، معناه الكلام في العلاقة Delta + +302 +00:22:38,790 --> 00:22:43,050 +H not minus T Delta S not، الـ minus T Delta S not + +303 +00:22:43,050 --> 00:22:47,210 +هذا إيش هتكون؟ هتكون positive and increases with a + +304 +00:22:47,210 --> 00:22:52,710 +increasing temperature. As a result ΔG0 becomes more + +305 +00:22:52,710 --> 00:22:58,890 +positive with increasing temperature لأن ΔG0، ΔH0 + +306 +00:22:58,890 --> 00:23:08,050 +minus T ΔS0 هذه موجبة لأن ΔS سالبة في سالب صارت + +307 +00:23:08,050 --> 00:23:14,290 +موجبة، إذا as a result ΔG0 becomes more positive + +308 +00:23:14,290 --> 00:23:19,830 +لأن عمال احنا بنزود الإيجابية، بنزود قيمة الـ T + +309 +00:23:19,830 --> 00:23:23,010 +Delta S وبالتالي الـ Delta G not تصير أكثر + +310 +00:23:23,010 --> 00:23:27,750 +positive with increasing temperature. Thus, the + +311 +00:23:27,750 --> 00:23:30,230 +driving force for the production of ammonia + +312 +00:23:30,230 --> 00:23:34,310 +becomes smaller with increasing temperature. مدام + +313 +00:23:34,310 --> 00:23:36,750 +الـ Delta G not تصير أكثر positive مش أكثر + +314 +00:23:36,750 --> 00:23:40,170 +negative، إذن الـ driving force لأنه يتكون عند + +315 +00:23:40,170 --> 00:23:45,420 +الأمونيا بيقل مع زيادة درجة الحرارة، الـ driving force + +316 +00:23:45,420 --> 00:23:49,200 +لإيه؟ لأنه كل ما زادت درجة الحرارة، إيش بيحصل لـ + +317 +00:23:49,200 --> 00:23:55,180 +دلتا G نقطة هذه؟ more positive، بتزيد الـ + +318 +00:23:55,180 --> 00:23:58,540 +positivity تبعتها، يعني بيقل احتمال أن يحصل + +319 +00:23:58,540 --> 00:24:03,680 +التفاعل، عشان يحصل، بيصير negative، تمام؟ لكن لا، + +320 +00:24:03,680 --> 00:24:07,660 +احنا كل ما زودنا الحرارة عامة، إيش بيحصل؟ تتجه لـ + +321 +00:24:07,660 --> 00:24:10,740 +more positive، معناه الكلام، الـ driving force بتقل + +322 +00:24:18,940 --> 00:24:26,680 +طيب خليني أطلع على الحسابات تبعتي عند خمسة و عشرين + +323 +00:24:26,680 --> 00:24:28,680 +درجة الـ C وعند + +324 +00:24:31,750 --> 00:24:36,210 +500 درجة سي، يعني 25 درجة سي يعني 298 كيلو فهرنهايت، دلتا + +325 +00:24:36,210 --> 00:24:40,230 +جي نوت تساوي دلتا H معروفة للتفاعل وحسبناها قبل + +326 +00:24:40,230 --> 00:24:48,990 +هيك minus 92.38 كيلوجول minus T 298 في الـ Delta S + +327 +00:24:49,720 --> 00:24:56,180 +-183.10 J per Kelvin، طبعا بدي أحول الـ J لـ KJ + +328 +00:24:56,180 --> 00:25:00,060 +فبقى أضرب واحد على ألف فتطلع عندي سالب ثلاثة و + +329 +00:25:00,060 --> 00:25:02,720 +ثلاثين وثلاثة وعشرة KJ، إذا أنا عند خمسة وعشرين + +330 +00:25:02,720 --> 00:25:08,240 +درجة الـ C كانت إيه؟ كانت spontaneous، طيب عند خمس + +331 +00:25:08,240 --> 00:25:13,480 +مئة يعني 730 كيلو فهرنهايت، من عوض هذه نفس + +332 +00:25:13,480 --> 00:25:16,100 +القيمة لحظة معايا، لازم تعوض بـ 500 يعني عوض بالـ + +333 +00:25:16,100 --> 00:25:18,920 +Delta H تبعت الـ 500 و Delta S تبعت الـ 500 لكن + +334 +00:25:18,920 --> 00:25:23,080 +لا، هو إيش قال؟ قال إنه لا تتغيروا بالحرارة، إذا أعوض + +335 +00:25:23,080 --> 00:25:27,100 +بالـ Delta H و Delta S بس هنغير درجة الحرارة، قال + +336 +00:25:27,100 --> 00:25:31,060 +صارت 160 كيلوجول موجبة بقى، إذن لما رفعنا + +337 +00:25:31,060 --> 00:25:35,760 +لـ 500 درجة سي، التفاعل تحول من spontaneous إلى + +338 +00:25:35,760 --> 00:25:43,870 +non spontaneous، الـ equilibrium temperature هي + +339 +00:25:43,870 --> 00:25:50,170 +Delta H على Delta S حسبناها 465 قبل شوية + +340 +00:25:58,610 --> 00:26:03,370 +هذه هي الـ T حسبناها قبل قليل، كم تتراوح الـ + +341 +00:26:03,370 --> 00:26:09,690 +temperature قبلها تكون سالبة وبعدها تكون موجبة بدل + +342 +00:26:09,690 --> 00:26:12,870 +جي نوت وبالتالي قبلها تكون spontaneous قبل هذه + +343 +00:26:12,870 --> 00:26:15,930 +الحرارة وبعدها تكون non spontaneous + +344 +00:26:22,220 --> 00:26:26,660 +بسألني كمان سؤال يعني جميل احنا بنحاول نرسخ مفهوم + +345 +00:26:26,660 --> 00:26:31,200 +إيش يعني transition temperature، وقت إيش التفاعل + +346 +00:26:31,200 --> 00:26:33,240 +بيكون spontaneous، وقت إيش التفاعل بيكون non + +347 +00:26:33,240 --> 00:26:37,460 +spontaneous، فخلينا نطلع على حاجة بنشوفها كل يوم و + +348 +00:26:37,460 --> 00:26:41,220 +بنعرفها كويس، فالسؤال if the conversion of liquid + +349 +00:26:41,220 --> 00:26:44,960 +water to water vapor at one atmosphere and mid + +350 +00:26:44,960 --> 00:26:48,040 +degree c، يعني الـ normal boiling point، spontaneous + +351 +00:26:48,040 --> 00:26:50,860 +ولا non spontaneous ولا reversible؟ إيش بنجيب على + +352 +00:26:50,860 --> 00:26:53,800 +هذا السؤال؟ لحظة، درجة ما نحسب؟ إيش بنجيب على إيه؟ + +353 +00:26:53,800 --> 00:26:58,640 +هل تحول الـ liquid water إلى water vapor عند واحد + +354 +00:26:58,640 --> 00:27:02,820 +أتموسفير و mid degree c؟ هل هو spontaneous ولا non + +355 +00:27:02,820 --> 00:27:05,060 +spontaneous ولا reversible؟ + +356 +00:27:07,320 --> 00:27:11,700 +إيش رأي الجماعة يعني؟ طبعا reversible لأنه + +357 +00:27:11,700 --> 00:27:13,940 +equilibrium عند 100 درجة، هذه الـ normal boiling + +358 +00:27:13,940 --> 00:27:19,660 +point، ففي عندي equilibrium أكيد هو reversible يعني + +359 +00:27:19,660 --> 00:27:23,760 +احنا، طيب خلينا نقول إن احنا يعني مش عارفين لكن هو + +360 +00:27:23,760 --> 00:27:28,860 +أعطانا الـ Delta H VAP 40.657 وطبعا الـ Delta H VAP + +361 +00:27:28,860 --> 00:27:32,100 +موجبة، ليه؟ لأنه بدها .. اه كيف؟ + +362 +00:27:34,670 --> 00:27:42,470 +بنقدر نحسبها، فهذه موجبة، Delta S VAP طبعا يعني لما + +363 +00:27:42,470 --> 00:27:48,370 +نزيد درجة الحرارة، فمعناه الكلام 108.96 هذه برضه + +364 +00:27:48,370 --> 00:27:52,250 +موجبة، فبقول الـ Delta G at mid degree C والله إذا + +365 +00:27:52,250 --> 00:27:55,950 +كانت سالبة يبقى spontaneous، موجبة يبقى non spontaneous + +366 +00:27:55,950 --> 00:28:01,520 +صفر عن طريق التعويض، دلتا جي ات ميت ديجري سي تساوي + +367 +00:28:01,520 --> 00:28:08,300 +40.657 جول minus عند 100 يعني 373.15 كيلوفن في 108 + +368 +00:28:08,300 --> 00:28:11,560 +.96 جول per Kelvin، اه بتحطين الصفر يعني + +369 +00:28:11,560 --> 00:28:15,300 +كلام reversible، بس هو اصلا .. يعني لازم نعرف إنه + +370 +00:28:15,300 --> 00:28:18,840 +reversible بدون ما نعمل كل هذه العملية، هذه لأن + +371 +00:28:18,840 --> 00:28:21,000 +الماء احنا متعاملين معاه جدا وبنعرف إنه normal + +372 +00:28:21,000 --> 00:28:24,440 +boiling point لإنها عند واحد أتموسفير 100 درجة + +373 +00:28:24,440 --> 00:28:28,500 +الـC، فعند 100 درجة الـC طبعا الـ liquid water + +374 +00:28:28,500 --> 00:28:31,460 +بيكون in equilibrium مع الـ water vapor فلازم نعرف + +375 +00:28:31,460 --> 00:28:36,580 +إنه reversible لكن على أي حال حسبنا ووجدنا أيضا + +376 +00:28:36,580 --> 00:28:40,060 +صفر، مدام صفر فهو الـ conversion reversible، طيب نفسه + +377 +00:28:40,060 --> 00:28:48,440 +بيقول is heating one mole of liquid water to one + +378 +00:28:48,440 --> 00:28:51,620 +hundred and ten degrees c will converted to water + +379 +00:28:51,620 --> 00:28:55,300 +vapor spontaneously or not؟ برضه اخذنا السؤال أنجبنا + +380 +00:28:55,300 --> 00:28:59,420 +عليه بدون ما نعمل المثال يعني بدون ما نعمل المثال + +381 +00:28:59,420 --> 00:29:02,440 +طبعا، فهل تحويل واحد مول من الـ liquid water إذا + +382 +00:29:02,440 --> 00:29:11,080 +كان سخنناه لـ 110 degree c هل تحوله لـ water vapor + +383 +00:29:11,080 --> 00:29:15,760 +spontaneous ولا non spontaneous، إذا كان سخننا الماء + +384 +00:29:15,760 --> 00:29:20,760 +لـ 110 degree c، spontaneous ولا مش spontaneous بتحول + +385 +00:29:20,760 --> 00:29:26,280 +لـ vapor، الماء بتحول لـ vapor طبعا spontaneous طبعا + +386 +00:29:26,280 --> 00:29:32,300 +spontaneous، أكيد أقل من 100 ماهو spontaneous، فوق + +387 +00:29:32,300 --> 00:29:36,200 +الـ .. بتلاقي water .. بتلاقي liquid water at 110 و + +388 +00:29:36,200 --> 00:29:39,280 +عشرة degree c، هل .. هل بنلاقي الـ liquid water at + +389 +00:29:39,280 --> 00:29:42,700 +110 degree c لحد الأقصى الـ 100 بس الـ water + +390 +00:29:42,700 --> 00:29:46,720 +vapor، إذا الـ conversion للـ liquid water إلى water + +391 +00:29:46,720 --> 00:29:49,480 +vapor عند 110 هذا spontaneous الـ process + +392 +00:29:49,480 --> 00:29:51,820 +عند 110 spontaneous، أكثر من 100 spontaneous، + +393 +00:29:51,820 --> 00:29:55,580 +أقل من 100 لا ولا بنلاقي الماء 100 Liquid water + +394 +00:30:00,110 --> 00:30:03,190 +liquid water، لا جهاز جاز لا تتحول إلى جاز + +395 +00:30:03,190 --> 00:30:07,210 +spontaneously، هذا كلام بسيط كثير، هذا كلام كثير + +396 +00:30:07,210 --> 00:30:11,250 +بسيط، is heating one mole of liquid water to 110 + +397 +00:30:11,250 --> 00:30:14,990 +degrees C will convert يعني حصل على الماء 110 + +398 +00:30:14,990 --> 00:30:20,170 +degrees C، هل هذا هيحولها لـ water vapor ولا لا؟ سخنها + +399 +00:30:20,170 --> 00:30:23,450 +لأكثر من الـ normal boiling point، هل هتحولها لـ water + +400 +00:30:23,450 --> 00:30:26,730 +vapor ولا لا؟ طبعا هيتحول لـ water vapor spontaneously + +401 +00:30:26,730 --> 00:30:33,330 +انتهينا، استخدام دلتا H ودلتا S لا يتغيرا بشكل كبير + +402 +00:30:33,330 --> 00:30:37,490 +مع التمبراتور، طيب ما اعطينا دلتا H VAP وما اعطينا + +403 +00:30:37,490 --> 00:30:42,650 +دلتا S VAP تعالوا نحسب دلتا G at 110 degree C، دلتا + +404 +00:30:42,650 --> 00:30:47,070 +H minus T دلتا S، هناخد القيم عن 110 هي نفسها عند + +405 +00:30:47,070 --> 00:30:53,920 +25 degree C، دلتا اتش 40.657 + +406 +00:30:53,920 --> 00:30:58,380 +جول يعني اجربناها في الف minus اه 110 مش + +407 +00:30:58,380 --> 00:31:01,260 +373.15، 373.18 + +408 +00:31:01,260 --> 00:31:07,260 +صارت في 108.63 دلتا اصبحت سالبة، إيش معناه انها + +409 +00:31:07,260 --> 00:31:09,960 +سالبة؟ يعني نعم التفاعل spontaneous او التغير مش + +410 +00:31:09,960 --> 00:31:14,820 +تفاعل، التغير spontaneous طبعا لما سخننا الماء عند + +411 +00:31:14,820 --> 00:31:18,760 +أكثر من 100 فهذا التغير spontaneous، طب إيش بيحصل + +412 +00:31:18,760 --> 00:31:23,420 +لو is heating one mole of liquid water to 90 + +413 +00:31:23,420 --> 00:31:28,190 +degrees will convert water to vapor spontaneously + +414 +00:31:28,190 --> 00:31:32,310 +or not، طبعا لا، مش ممكن لأنه أقل من الـ boiling + +415 +00:31:32,310 --> 00:31:36,110 +point، أقل من الـ boiling point، بس لو ما بعرفش حنلّن + +416 +00:31:36,110 --> 00:31:39,810 +عليها الحسابات، لو ما بعرفش هذا الكلام حنلّن علي + +417 +00:31:39,810 --> 00:31:42,810 +الحسابات، برضه تقول لي assume الـ Delta H والـ Delta + +418 +00:31:42,810 --> 00:31:45,890 +S do not change significantly، والـ temperature عشان + +419 +00:31:45,890 --> 00:31:49,430 +أستخدم الـ Delta H قيمتها عند 25 degree C والـ Delta S + + + +421 +00:31:49,430 --> 00:31:53,380 +س برضه قيمتها عند 25 ديجري C لإن أنا متوفرة متوفرة و + +422 +00:31:53,380 --> 00:31:56,560 +معايا في المسألة بيقول الـ delta G عن تسعين دجري + +423 +00:31:56,560 --> 00:31:59,620 +ال C بيساوي ال delta H minus T delta S ال delta G + +424 +00:31:59,620 --> 00:32:03,400 +عن تسعين دجري ال C بدها تساوي قيمة ال delta H + +425 +00:32:03,400 --> 00:32:07,620 +بالجول minus A تسعين يعني تلاتمية تلاتة و ستين + +426 +00:32:07,620 --> 00:32:11,500 +Kelvin مضروبة في مية و تمانية point nine six طبعا + +427 +00:32:11,500 --> 00:32:15,920 +الف و تمانية و تمانية جول positive معناته لأ و الله + +428 +00:32:15,920 --> 00:32:21,140 +مانفعش مش راح يتحول ال liquid water الى water + +429 +00:32:21,140 --> 00:32:26,300 +vapor مباشرة spontaneous دي عن 90 degree c لأ ده + +430 +00:32:26,300 --> 00:32:29,260 +كله مابحصلش هو هتبقى وضع طبيعي أقل من ال boiling + +431 +00:32:29,260 --> 00:32:33,500 +point ال liquid بتعمل liquid مابتحول كله لغاز فورا + +432 +00:32:33,500 --> 00:32:37,260 +أكبر من ال boiling point لأ و الله خلاص ال boiling + +433 +00:32:37,260 --> 00:32:39,900 +point فيه equilibrium بعد ال boiling point انتهينا + +434 +00:32:39,900 --> 00:32:44,420 +كله gas steam بخار water vapor + +435 +00:32:49,290 --> 00:32:52,390 +طب at what temperature will liquid water be at + +436 +00:32:52,390 --> 00:32:55,790 +equilibrium with water vapor؟ نعرف هذا الكلام، + +437 +00:32:55,790 --> 00:32:57,730 +liquid water بقى ال water vapor، عند أي + +438 +00:32:57,730 --> 00:33:03,190 +temperature؟ الهي 100، أكيد، أكيد هذا الكلام، بقول + +439 +00:33:03,190 --> 00:33:07,690 +inserting the values of delta H and delta S into + +440 +00:33:07,690 --> 00:33:11,310 +the definition of delta G لأنها بتدل equilibrium، + +441 +00:33:11,310 --> 00:33:16,030 +يفجأة ال delta G إيش هي تساوي؟ صفر، يفجأة ال delta + +442 +00:33:16,030 --> 00:33:21,400 +S هي تساوي ال T الـ T تطلع تلات مئة و تلات سبعين و + +443 +00:33:21,400 --> 00:33:24,980 +خمس عشر اللي هي ايه؟ الـ Normal boiling point of + +444 +00:33:24,980 --> 00:33:29,700 +water one hundred degrees C تمام؟ طبعا هذا مضع + +445 +00:33:29,700 --> 00:33:35,880 +طبيعي لأن الـ Delta G بتسوء صفر الـ T بتسوء تلات + +446 +00:33:35,880 --> 00:33:38,040 +مئة و تلات سبعين و خمس عشر لإنها Normal boiling + +447 +00:33:38,040 --> 00:33:44,500 +point يعني عند واحد أتمسفير طب عن temperature أكتر + +448 +00:33:44,500 --> 00:33:48,290 +من تلات مئة و تلات سبعينجال ديلتا جيب تصير + +449 +00:33:48,290 --> 00:33:52,930 +negative لأنه أكتر من ال boiling point طب عند أجل + +450 +00:33:52,930 --> 00:33:57,590 +من 38 و 79 جال دلتا جيب تصير positive يعني أقل من + +451 +00:33:57,590 --> 00:34:00,630 +100 وأكتر من 100 كويس؟ زي ما شوفناها الأمثلة اللي + +452 +00:34:00,630 --> 00:34:05,500 +شوفناها هذه بالظبط هي الكلام اللى بيحصل فوق المية + +453 +00:34:05,500 --> 00:34:08,800 +هاي المية هي ال transition temperature اللى هى ال + +454 +00:34:08,800 --> 00:34:11,860 +normal boiling point اللى هى ال equilibrium اللى + +455 +00:34:11,860 --> 00:34:19,720 +هى ال reversible conversion كويس اكتر منها اه ال + +456 +00:34:19,720 --> 00:34:23,640 +liquid ال water بتروح ل water vapor spontaneously + +457 +00:34:23,640 --> 00:34:27,600 +اقل منها لا والله ال liquid water لا يتحول الى + +458 +00:34:27,600 --> 00:34:35,100 +water vapor spontaneously طيب نتطلع على يمكن أخر + +459 +00:34:35,100 --> 00:34:44,440 +جزئية في هذا ال chapter تتعلق بال delta G تحديدا + +460 +00:34:44,440 --> 00:34:47,100 +يعني نتطلع على ال free energy و علاقتها بال + +461 +00:34:47,100 --> 00:34:49,960 +equilibrium ال free energy و علاقتها بال + +462 +00:34:49,960 --> 00:34:52,650 +equilibrium الـ Free Energy التي هي الـ Delta G + +463 +00:34:52,650 --> 00:34:57,950 +بتساوي الـ Delta G نوت زائد الـ RT لن لـ Q RT لن ل + +464 +00:34:57,950 --> 00:35:01,650 +Q إيش الـ Q هذه؟ الـ Q هي ال reaction quotient إيش + +465 +00:35:01,650 --> 00:35:07,270 +يعني ال reaction quotient؟ يعني لو عندي A NA زائد + +466 +00:35:07,270 --> 00:35:10,830 +MB + +467 +00:35:10,830 --> 00:35:13,350 +بتعطيلنا + +468 +00:35:18,030 --> 00:35:26,670 +xc زائد yd جالي q بتساوي زي ال equilibrium + +469 +00:35:26,670 --> 00:35:36,650 +constant مش بيفرق بينهم يعني حط c النواتج قص xd قص + +470 +00:35:36,650 --> 00:35:46,610 +y ع ال a قص n ال b قص am طب هذه يا أستاذ هي نفسها + +471 +00:35:46,610 --> 00:35:49,030 +ال equilibrium constant يا لأ ال equilibrium + +472 +00:35:49,030 --> 00:35:52,290 +constant هذه التركيزات بتكون هي التركيزات ال + +473 +00:35:52,290 --> 00:35:57,350 +equilibrium كويس ال Q ممكن تكون اكبر او تساوي او + +474 +00:35:57,350 --> 00:36:01,290 +اقل من ال K ال K هو ال equilibrium constant فعند + +475 +00:36:01,290 --> 00:36:10,000 +التركيزات وعند الاتزان اه هذه K لكن اي تركيزات اخرى + +476 +00:36:10,000 --> 00:36:14,740 +اذا كانت مش عند الافادة بيقولها reaction quotient + +477 +00:36:14,740 --> 00:36:19,500 +يعني بس ال Q بتساوي K عند ايه؟ عند الاتزان يعني + +478 +00:36:19,500 --> 00:36:23,560 +بتساوي ال equilibrium constant فقط وقتاش جال عند + +479 +00:36:23,560 --> 00:36:29,560 +الاتزان فبس هذه الفكرة بدنا نعرف إن الـ delta G + +480 +00:36:29,560 --> 00:36:35,260 +بتساوي الـ delta G note زائد ال RT لـ Q في حالة ما + +481 +00:36:35,260 --> 00:36:41,010 +إنه نستخدم الـ standard state الـStandard State + +482 +00:36:41,010 --> 00:36:44,650 +Concentrations كلها هي عبارة عن واحد مولار شوفنا + +483 +00:36:44,650 --> 00:36:48,510 +هذا في حصة سابقة الـStandard State بالنسبة للتركيز + +484 +00:36:48,510 --> 00:36:51,790 +هو ايه؟ واحد مولار لما يكون واحد مولار اوسع اش + +485 +00:36:51,790 --> 00:36:55,490 +مكان بيضلوا واحد في واحد على واحد في واحد يعني + +486 +00:36:55,490 --> 00:36:59,410 +واحد لـQ بتساوي واحد لإن الواحد جال صفر إذا + +487 +00:36:59,410 --> 00:37:02,250 +الـDelta G بتساوي الـDelta G Note يفجأت + +488 +00:37:02,250 --> 00:37:05,070 +الـStandard State الـDelta G بتساوي الـDelta G + +489 +00:37:05,070 --> 00:37:09,270 +Note لكن عند أي State غير الـStandard State الـ ΔG + +490 +00:37:09,270 --> 00:37:13,270 +بتساوي ΔG نوت زائد الـ RT لين الـ Q لكن عند الـ + +491 +00:37:13,270 --> 00:37:16,090 +Standard State لما كل التركيزات كانوا واحد معناته + +492 +00:37:16,090 --> 00:37:22,550 +لين الـ Q بصفر لأن الـ Q بتساوي واحد لكن إذا كان + +493 +00:37:22,550 --> 00:37:25,590 +عندي Standard State فالـ ΔG بتساوي الـ ΔG نوت + +494 +00:37:25,590 --> 00:37:28,870 +تعالوا نتطلع أيش اللي بيحصل بالظبط في أي تفاعل + +495 +00:37:28,870 --> 00:37:34,270 +كيميائي جال في عندي Reactants وفي عندي إبرادات + +496 +00:37:34,270 --> 00:37:41,220 +دائما في بينهم زي ال valley بحيث انه لو سقط مثلا + +497 +00:37:41,220 --> 00:37:45,500 +حجر من الكرة نعتبر + +498 +00:37:45,500 --> 00:37:49,440 +وهي عمال نازلة لما توصل هنا خدوا بالكم ايش بتبتحك + +499 +00:37:49,440 --> 00:37:54,280 +تعمل؟ اه بتبتحرك حوالي ال ايه؟ ال valley هذا مكينه + +500 +00:37:54,280 --> 00:37:59,020 +equilibrium اتزان اتزان reversible اه Delta X + +501 +00:37:59,020 --> 00:38:02,540 +رايحة Delta X جاية reversible فهنا عندي + +502 +00:38:02,540 --> 00:38:08,770 +equilibrium هنا ال products وهنا ال reactants وهنا + +503 +00:38:08,770 --> 00:38:15,430 +طبعا يعني خليني اقول ال free energy فانا بقدر اقول + +504 +00:38:15,430 --> 00:38:19,810 +ان ال free energy دلتا جي بتسوي دلتا جي لل product + +505 +00:38:19,810 --> 00:38:23,620 +minus ال delta جي لل reactants وبعدين بقول والله هل + +506 +00:38:23,620 --> 00:38:30,540 +هذا الكلام يعتبر موجب ولا سالب، إذا كان سالب فهو + +507 +00:38:30,540 --> 00:38:34,020 +spontaneous إذا كان .. يعني بيمشي في الاتجاه اللي + +508 +00:38:34,020 --> 00:38:37,800 +مكتوب، إذا كان موجب فلأ والله الاتجاه العكسي هو + +509 +00:38:37,800 --> 00:38:40,300 +اللي بيمشي فيه أو يعني بيكون spontaneous في + +510 +00:38:40,300 --> 00:38:48,200 +الاتجاه اللي مكتوب، مثلا عندي ال .. الأمونيا أي + +511 +00:38:48,200 --> 00:38:51,540 +اتفاعل يعني مش شرط الأمونيا فهي نفس الكلام هي + +512 +00:38:51,540 --> 00:38:54,920 +الفعل هدا ممكن تيجي هان يعني ممكن ييجي هيك والله + +513 +00:38:54,920 --> 00:38:58,080 +مثلا + +514 +00:38:58,080 --> 00:39:01,260 +هنا ال equilibrium يعني ممكن ييجي هيك هنا ال + +515 +00:39:01,260 --> 00:39:04,880 +equilibrium يعني مش شرط يعني انه دايما لا يعني ال + +516 +00:39:04,880 --> 00:39:07,940 +equilibrium ممكن وين مكان ييجي حسب المسألة اللي + +517 +00:39:07,940 --> 00:39:15,210 +عندي هلأ التوضيح موجود بالشكل اللي قدامي هالفال .. + +518 +00:39:15,210 --> 00:39:20,750 +في عندي هان عموما ال reactance معناته هي على سبيل + +519 +00:39:20,750 --> 00:39:27,510 +المثال ال nitrogen و ال oxygen و ال nitrogen مثلا + +520 +00:39:27,510 --> 00:39:31,830 +يعني هذه هي ان هذا هو ال nitrogen و هذا هو ال + +521 +00:39:31,830 --> 00:39:36,350 +hydrogen هذا هو ال hydrogen و هذا هو ال nitrogen + +522 +00:39:36,350 --> 00:39:40,730 +فهذه متفاعلة فشولاش هان عندي بس متفاعلة nitrogen و + +523 +00:39:40,730 --> 00:39:46,240 +hydrogen هن في عندى product معناته products أمونيا، + +524 +00:39:46,240 --> 00:39:50,600 +فالنص هن إيش في عندى؟ خلط اللي هو ال equilibrium، + +525 +00:39:50,600 --> 00:39:54,600 +خلط اللي هو ال equilibrium، بقول هن ال Q أقل من ال + +526 +00:39:54,600 --> 00:40:01,590 +K، هن ال Q أكبر من ال K، هن ال Q بتساوي ال K يبقى + +527 +00:40:01,590 --> 00:40:08,010 +H9D ع جهة ال products ال Q أكبر من ال K إيش يعني + +528 +00:40:08,010 --> 00:40:14,770 +ال Q أكبر من ال K؟ يعني البست عندي أكبر من المقام، + +529 +00:40:14,770 --> 00:40:19,930 +أكبر من المقام، إذا؟ والله أه، بده يعني ال Q عندي + +530 +00:40:19,930 --> 00:40:24,110 +أكبر من ال K، البست أكبر من المقام، ال Q أقل من ال + +531 +00:40:24,110 --> 00:40:30,690 +K الـ Q .. اه عندي انا ال ايه .. ال .. ال Q أقل من + +532 +00:40:30,690 --> 00:40:35,410 +ال K يعني عندي المقام أكبر من .. أكبر من ال bus طب + +533 +00:40:35,410 --> 00:40:38,930 +هو إيش المقام هان؟ المتفاعلات .. المتفاعلات عشان + +534 +00:40:38,930 --> 00:40:42,250 +هيك .. اه مدان المتفاعلات أكبر إذن بدها تروح ناحية + +535 +00:40:42,250 --> 00:40:45,990 +النواتج لإن هو عندي كمية كبيرة منها إذن هي التفاعل + +536 +00:40:45,990 --> 00:40:49,390 +رايح ناحية ال A رايح ناحية النواتج .. هان بالعكس + +537 +00:40:50,330 --> 00:40:55,670 +النواتج أكبر بتروح لحيط المتفاعلات spontaneously + +538 +00:40:55,670 --> 00:40:59,410 +فمعنى + +539 +00:40:59,410 --> 00:41:04,850 +الكلام سهل أنه نتوقع إيش اللي بيحصل عنا من الشكل + +540 +00:41:04,850 --> 00:41:09,550 +اللي جداميبقول تعالى نطلع على الأشكال التلاتة لما + +541 +00:41:09,550 --> 00:41:15,690 +يكون في عندنا ال Q أكبر من K و أقل من K و ال Q + +542 +00:41:15,690 --> 00:41:21,590 +بتساوي ال K فناخد جزء من العصابي مثلا ال + +543 +00:41:21,590 --> 00:41:26,450 +equilibrium اللي عندي فبقول لما ال delta G لل + +544 +00:41:26,450 --> 00:41:30,150 +products تكون أقل كتير من ال delta G لل reactants + +545 +00:41:30,150 --> 00:41:33,810 +هي delta G لل reactants هي delta G لل products أقل + +546 +00:41:33,810 --> 00:41:35,470 +كتير واضح انه + +547 +00:41:39,230 --> 00:41:43,130 +الـ Delta G Note هتكون Large Negative ليه؟ لأن الـ + +548 +00:41:43,130 --> 00:41:46,710 +Delta G Note هتكون لـ Products اللي هي القليلة، + +549 +00:41:46,710 --> 00:41:51,590 +قليلة كتير، minus ال reactants اللي هي كبيرة فمع + +550 +00:41:51,590 --> 00:41:54,430 +هذا الكلام Large Negative الـ Delta G Note is a + +551 +00:41:54,430 --> 00:41:58,810 +Large Negative Quantity and equilibrium is very + +552 +00:41:58,810 --> 00:42:01,730 +far to the right towards products يعني ال + +553 +00:42:01,730 --> 00:42:06,440 +equilibrium .. هلاحظ أنكم مش شايفين هذا يعني هذا + +554 +00:42:06,440 --> 00:42:11,860 +عامل هيك، ماشي؟ فال equilibrium ايش ماله؟ احنا + +555 +00:42:11,860 --> 00:42:15,460 +قولنا .. شفتوا هذا الشكل؟ قولنا مش دايما بكون هيك، + +556 +00:42:15,460 --> 00:42:19,880 +ممكن يكون مشدود ناحية .. اه إذا كان .. إذا كان ال + +557 +00:42:19,880 --> 00:42:25,720 +delta G كانت very large negative value، معناته ال + +558 +00:42:25,720 --> 00:42:28,930 +equilibrium بيجرب ناحية ال products الـ Equilibrium + +559 +00:42:28,930 --> 00:42:32,050 +بيجرب ناحية الـ Probats فالـ Δ G لـ Probats أقل + +560 +00:42:32,050 --> 00:42:37,210 +كتير من الـ Δ G لل Reactants إذاً الـ Δ G نوت هي + +561 +00:42:37,210 --> 00:42:43,310 +عبارة عن Large Negative Value، معناتها وين الـ + +562 +00:42:43,310 --> 00:42:45,810 +Equilibrium قريب على ال Products، لأنها Large + +563 +00:42:45,810 --> 00:42:49,010 +Negative، عكس هذا الكلام، وهذا الكلام طبعًا احنا + +564 +00:42:49,010 --> 00:42:53,190 +ممكن نتخيله، بنقول وين الـ Q أقل من K، this means + +565 +00:42:53,190 --> 00:42:57,050 +that الـ Q أقل، معناته Reactants concentrations + +566 +00:42:57,050 --> 00:43:05,900 +are large مدام كبير مدام كبير مدام كبير مدام كبير + +567 +00:43:05,900 --> 00:43:14,100 +مدام + +568 +00:43:14,100 --> 00:43:21,760 +كبير مدام + +569 +00:43:21,760 --> 00:43:28,100 +كبير مدام + +570 +00:43:28,100 --> 00:43:33,590 +كبير هي هذا الشكل الـ Equilibrium وين هو؟ قريب على + +571 +00:43:33,590 --> 00:43:37,170 +الـ Reactants فهنا هاي الـ Reactants وهاي الـ + +572 +00:43:37,170 --> 00:43:41,690 +Products الـ Delta G لـ Products الكمية كبيرة minus + +573 +00:43:41,690 --> 00:43:46,770 +الـ Reactants كمية قليلة إذا Large Positive Delta G + +574 +00:43:46,770 --> 00:43:51,410 +is not a large positive quantity and Equilibrium + +575 +00:43:51,410 --> 00:43:56,020 +is very far to the left يعني towards Reactants جنب + +576 +00:43:56,020 --> 00:43:59,500 +الـ Reactants حلو هذا الكلام طبعًا هذا لما Delta G + +577 +00:43:59,500 --> 00:44:02,420 +لـ Products تكون أكبر كثير من Delta G للـ Reactants + +578 +00:44:02,420 --> 00:44:07,060 +وهنا نفس المنطقة بنقول when Q أكبر من K this means + +579 +00:44:07,060 --> 00:44:12,260 +that Products' concentrations are large and thus + +580 +00:44:12,260 --> 00:44:16,660 +reaction proceeds towards Reactants formation عشان + +581 +00:44:16,660 --> 00:44:20,780 +هيك الـ Equilibrium بيكون قريب جدا من الـ Reactants + +582 +00:44:23,450 --> 00:44:27,530 +الحالة الأخيرة أن يكون حاجة هيك في النص زي اللي + +583 +00:44:27,530 --> 00:44:32,690 +شفناها سابقا يعني ها عندنا الـ Q بتساوي الـ K والـ + +584 +00:44:32,690 --> 00:44:37,130 +Delta G ساعتها بدها تساوي صفر والـ Delta G بدها + +585 +00:44:37,130 --> 00:44:40,890 +تساوي صفر الـ Delta G لـ Products بتساوي تقريبًا الـ + +586 +00:44:40,890 --> 00:44:45,990 +Delta G للـ Reactants يعني بلاش الرسم هاتي ما فيش + +587 +00:44:45,990 --> 00:44:48,410 +عندي رسمة لها ما فيش عندي رسمة لها يعني بيكون إشي + +588 +00:44:48,410 --> 00:44:48,870 +زي هيك + +589 +00:44:54,450 --> 00:44:59,010 +حاجة زي هيك هي الـ Reactants قريبين على بعض كثير ف + +590 +00:44:59,010 --> 00:45:03,210 +الـ Delta G تقريبًا تقريبًا صفر الـ Delta G لـ الـ + +591 +00:45:03,210 --> 00:45:06,050 +Products تقريبًا صفر الـ Delta G للـ Reactants علشان + +592 +00:45:06,050 --> 00:45:11,230 +هيك بيقول الـ Equilibrium more towards the center في + +593 +00:45:11,230 --> 00:45:15,890 +النص الـ Center of the Reaction Profile when Q is + +594 +00:45:15,890 --> 00:45:20,510 +equal to K this means that Delta G بتساوي صفر and + +595 +00:45:20,510 --> 00:45:25,530 +Delta G not بتساوي Minus RT لإن الـ K إذا كان الـ + +596 +00:45:25,530 --> 00:45:30,730 +Delta G بتساوي صفر فالـ Delta G not من المعادلة + +597 +00:45:30,730 --> 00:45:36,790 +اللي بتقول Delta G بتساوي Delta G not minus RT + +598 +00:45:38,040 --> 00:45:44,260 +زائد RT ln Q فإذا كان الـ Q هادي هي K ساعتها + +599 +00:45:44,260 --> 00:45:49,200 +بتكون هادي صفر Delta G not بدها تساوي زائد RT + +600 +00:45:49,200 --> 00:45:54,190 +ln K إذا كان هذا صفر فالـ ΔG not تساوي Minus + +601 +00:45:54,190 --> 00:45:59,870 +RT ln K وبهذه الطريقة ممكن طبعًا Delta G not + +602 +00:45:59,870 --> 00:46:04,530 +نعرف نحسبها كويس من Delta G not من الـ Delta H + +603 +00:46:04,530 --> 00:46:08,550 +minus T Delta F عدة طرق لحساب الـ Delta G إذا + +604 +00:46:08,550 --> 00:46:11,450 +مدين باعرف أحسب Delta G not إذا إيش مقدر أعرف + +605 +00:46:11,450 --> 00:46:15,130 +أحسب؟ بقدر أحسب الـ Equilibrium Constant للتفاعل + +606 +00:46:15,130 --> 00:46:19,290 +وهذا إشي يعتبر جوهري جدا في الكيمياء يعني يعتبر + +607 +00:46:19,290 --> 00:46:24,630 +حاجة جوهرية جدا كيف نعرف نحسب الـ Equilibrium + +608 +00:46:24,630 --> 00:46:33,900 +Constant هذه بعض قيم الـ Delta G not والإيقاليبريام + +609 +00:46:33,900 --> 00:46:39,420 +Constants 298 لحظة إذا كان الـ Equilibrium Constants + +610 +00:46:39,420 --> 00:46:43,060 +يجب أن يكون واحد فـ Delta G not على طول بس هو صفر + +611 +00:46:43,060 --> 00:46:50,320 +لأنه Minus RT ln K لما الـ K يساوي واحد Delta G + +612 +00:46:50,320 --> 00:46:56,970 +not تساوي Minus RT ln K لما الـ K يساوي واحد + +613 +00:46:56,970 --> 00:47:00,330 +معناته الـ Delta G not على طول هتساوى الصفر لكن + +614 +00:47:00,330 --> 00:47:06,060 +لاحظوا كل ما زاد الـ K اه لما نزيد الـ K، الـ Delta G + +615 +00:47:06,060 --> 00:47:09,360 +إيش بيجرالها؟ بتقل، يعني بتصير تفاعل More + +616 +00:47:09,360 --> 00:47:13,800 +Spontaneous، تفاعل يعني بيمشي لليمين بشكل أكبر، + +617 +00:47:13,800 --> 00:47:17,260 +ليش؟ لأنه عندنا Minus RT ln K لما هذا يكون + +618 +00:47:17,260 --> 00:47:20,860 +كبير، يعني وهذا سالب، بعد كل هذا قيمة أكبر + +619 +00:47:20,860 --> 00:47:24,960 +بالسالب، قيمة أكبر بالسالب، عكس هذا الكلام، لو كان + +620 +00:47:24,960 --> 00:47:30,190 +أقل من واحد كان صفر زودنا عن + +621 +00:47:30,190 --> 00:47:34,890 +الواحد اه قلت كثير الـ Delta G not طب قللنا عن + +622 +00:47:34,890 --> 00:47:40,850 +واحد بنلاحظ أنه بتتحول لإيه لقيمة موجبة بيصير أنه + +623 +00:47:40,850 --> 00:47:45,470 +التفاعل والله مش Spontaneous صعب جدا يمشي لليمين + +624 +00:47:51,110 --> 00:47:55,910 +نفس المنطقي يعني هنا الـ K أكبر من واحد لإن الـ K + +625 +00:47:55,910 --> 00:47:58,950 +Positive Delta G not Negative الـ Products are + +626 +00:47:58,950 --> 00:48:04,870 +favored K بتساوي واحد لإن الـ K صفر Delta G not صفر + +627 +00:48:04,870 --> 00:48:09,430 +الـ Products and Reactants في Equilibrium أقل من + +628 +00:48:09,430 --> 00:48:15,830 +واحد لإن الـ K Negative Delta G not Positive الـ + +629 +00:48:15,830 --> 00:48:20,870 +Reactants are favored برضه كلام مفهوم جدا الآن + +630 +00:48:20,870 --> 00:48:26,730 +إجمالًا بقول الـ Criteria for the Spontaneity of a + +631 +00:48:26,730 --> 00:48:30,630 +Process as Written يعني التفاعل زي ما هو مكتوب أو + +632 +00:48:30,630 --> 00:48:35,150 +التغير زي ما هو مكتوب إيش الـ Criteria المعايير أنه + +633 +00:48:35,150 --> 00:48:37,950 +والله يكون هل هو Spontaneous ولا لأ؟ بنقول إذا + +634 +00:48:37,950 --> 00:48:41,830 +كانوا Spontaneous الـ Delta S للـ Universe لازم تكون + +635 +00:48:41,830 --> 00:48:46,430 +أكبر من صفر وهذا نص القانون الثاني للـ + +636 +00:48:46,430 --> 00:48:49,310 +Thermodynamics إذا كان التفاعل Spontaneous أو + +637 +00:48:49,310 --> 00:48:54,730 +الـ Process Spontaneous لازم الـ Delta S للكون تكون + +638 +00:48:54,730 --> 00:48:59,630 +أكبر من صفر أو إن الـ Delta G للـ System للتفاعل + +639 +00:48:59,630 --> 00:49:07,170 +تكون سالبة أقل من صفر أو حاجة جديدة الـ Q تكون أقل + +640 +00:49:07,170 --> 00:49:12,750 +من K أقل من K يعني High Reactants Concentration + +641 +00:49:12,750 --> 00:49:15,930 +يعني هتروح ناحية الـ Products is Spontaneous أي + +642 +00:49:15,930 --> 00:49:21,270 +واحدة من هدول بتخلي التفاعل Spontaneous أي واحدة + +643 +00:49:21,270 --> 00:49:23,470 +منهم بتخلي التفاعل Spontaneous هاي الـ Criteria هاي + +644 +00:49:23,470 --> 00:49:26,550 +المعايير الـ Equilibrium إيش معايير وجال والله بـ + +645 +00:49:26,550 --> 00:49:30,290 +Delta S للـ Universe تكون صفر حلو إذا كانت Delta S + +646 +00:49:30,290 --> 00:49:34,570 +للـ Universe لأي System لأي System يعني في النهاية + +647 +00:49:34,570 --> 00:49:40,500 +لأي تغير صفر معناته عندي Equilibrium إذا كان الـ + +648 +00:49:40,500 --> 00:49:45,040 +Delta G للـ System صفر، طبعًا أيضًا إيقاليبريان، إذا + +649 +00:49:45,040 --> 00:49:48,960 +كان الـ Q بتساوي الـ K، أكيد إيقاليبريان، ماشي يا + +650 +00:49:48,960 --> 00:49:51,420 +جماعة، طب الـ Non Spontaneity أو الـ Non + +651 +00:49:51,420 --> 00:49:54,160 +Spontaneous Change، بقول إذا كان الـ Delta S في + +652 +00:49:54,160 --> 00:49:58,390 +الـ Universe أقل من صفر، هذا Non Spontaneous إذا كان + +653 +00:49:58,390 --> 00:50:02,130 +الـ Delta G للـ System أكبر من صفر موجبة، Non + +654 +00:50:02,130 --> 00:50:04,890 +Spontaneous، إذا كان الـ Q أكبر من الـ K، يعني + +655 +00:50:04,890 --> 00:50:07,210 +الـ High Product Concentration، يبقى لازم تذهب ناحية + +656 +00:50:07,210 --> 00:50:11,310 +الـ Reactants، فهذا Non Spontaneous، as what? as + +657 +00:50:11,310 --> 00:50:16,010 +written، كما هو مكتوب، يعني زي ما هو التفاعل مكتوب + +658 +00:50:16,010 --> 00:50:20,230 +عندي، فهذه حاجات أساسية بتلخص الكلام اللي قلناه + +659 +00:50:20,230 --> 00:50:24,330 +تقريبًا من بداية الـ Chapter هذا فيما يتعلق بالـ + +660 +00:50:24,330 --> 00:50:28,840 +Spontaneity بقول what is the criteria for + +661 +00:50:28,840 --> 00:50:33,160 +Spontaneity in terms of Entropy and in terms of + +662 +00:50:33,160 --> 00:50:38,240 +Free Energy وما عطينا خيارات نقرأهم من تحت The + +663 +00:50:38,240 --> 00:50:43,920 +Entropy of the Universe Decreases Violation مخالفة + +664 +00:50:43,920 --> 00:50:49,720 +ممكن يعني The Entropy of the Universe Decreases لأ + +665 +00:50:49,720 --> 00:50:52,880 +هذا مش Spontaneous إذا أول واحدة عرفها المجرمة كان + +666 +00:50:52,880 --> 00:50:57,740 +بالغلط غلط لإيه؟ لأن الـ Spontaneity .. هذا إيه؟ إيش + +667 +00:50:57,740 --> 00:51:00,960 +الـ Entropy للـ Universe؟ آه لازم يكون أكبر من صفر + +668 +00:51:00,960 --> 00:51:06,000 +.. Decreases لأ .. طيب قال لي قبلها .. The Entropy + +669 +00:51:06,000 --> 00:51:10,300 +of the System Increases .. ما لهوش دعوة الـ System .. + +670 +00:51:10,300 --> 00:51:13,540 +أنا بدي إيه؟ الـ Universe .. إذا برضه ما لهوش دعوة + +671 +00:51:13,540 --> 00:51:17,300 +فيها .. The Entropy of the System Decreases .. + +672 +00:51:17,300 --> 00:51:20,160 +ما لهوش دعوة فيها .. الأصل ما لهوش دعوة فيها .. أنا بدي + +673 +00:51:20,160 --> 00:51:21,320 +الـ Universe .. + +674 +00:51:32,440 --> 00:51:42,040 +الخيار الأول هو الخيار الصحيح لو كملته ستجد حل في + +675 +00:51:42,040 --> 00:51:45,560 +الـ Free Energy + +676 +00:51:49,380 --> 00:51:53,240 +بإنتروبي الإنتروبي لازم يقول إن الإنتروبي للكون + +677 +00:51:53,240 --> 00:51:56,880 +بتزيد عشان التفاعل يكون Spontaneous ما قالليش إنها + +678 +00:51:56,880 --> 00:52:01,160 +بتزيد خلاص ما أقدرش أحكم لأن الإنتروبي للـ System قالت + +679 +00:52:01,160 --> 00:52:04,020 +ولا لأ ما يهمنيش لأن الـ Surroundings حاجة تانية خلاص + +680 +00:52:04,020 --> 00:52:07,860 +ما جابليش Threat أنا ما أنفعش لازم مجموعهم هو المهم + +681 +00:52:07,860 --> 00:52:11,560 +اللي هو الـ Delta S للـ Universe لازم يكون أكثر من + +682 +00:52:11,560 --> 00:52:16,920 +واحد يعني قيمة موجبة أكثر من صفر قيمة موجبة + +683 +00:52:19,690 --> 00:52:23,670 +بنطلع على المثال التالي بيقول The Normal Boiling + +684 +00:52:23,670 --> 00:52:29,000 +Point of Benzene is 80 Degrees C نقطة وهنا بقى + +685 +00:52:29,000 --> 00:52:33,260 +أقول لكم إنه كان في خطأ في الـ Notes اللي معاكم اللي + +686 +00:52:33,260 --> 00:52:36,840 +موجودة على الصفحة أنا هغيرها يعني فاطلعوا على الـ + +687 +00:52:36,840 --> 00:52:39,800 +Notes اللي هنزلها اليوم إذا الله راد معاكي Notes + +688 +00:52:39,800 --> 00:52:43,760 +بس راجعي وصححي الأخطاء وقدمت وقرأت بعض الـ + +689 +00:52:43,760 --> 00:52:47,400 +Slides اللي جيتها أفضل يعني فأنا بفضل دائما إنه + +690 +00:52:47,400 --> 00:52:51,300 +تأخذ الـ Slides بعد ما أخلص أنا شريحة كل الـ Slides + +691 +00:52:51,300 --> 00:52:54,800 +اللي عندك على الصفحة الآن مناسبة وكويسة كثير + +692 +00:52:54,800 --> 00:52:58,580 +للدراسة لو عندك حاجة قديمة ممكن تتخلص منها ويمكن + +693 +00:52:58,580 --> 00:53:02,260 +تكون أفضل على أي حال بيقول طب At One Hundred + +694 +00:53:02,260 --> 00:53:06,720 +Degrees C and One Atmosphere which is greater in + +695 +00:53:06,720 --> 00:53:11,420 +Magnitude for the Vaporization of Benzene Delta H + +696 +00:53:11,420 --> 00:53:17,920 +ولا T Delta S أنهي أكبر في القيمة Delta H ولا T Delta + +697 +00:53:17,920 --> 00:53:21,420 +S خذوا بالكم هو اين بيغلي البنزين الـ Boiling Point + +698 +00:53:21,420 --> 00:53:30,800 +اين؟ عند 80 فهو بيسأل عند 100 أن هو أكبر Delta H + +699 +00:53:30,800 --> 00:53:38,000 +ولا Delta S ومعطيني خيارات بقول Delta H بتساوي T + +700 +00:53:38,000 --> 00:53:39,560 +Delta S هدول At Equilibrium + +701 +00:53:42,560 --> 00:53:46,540 +يا هادي يا هادي يا ماء الأخيرة ايش اللي أنا بقوله + +702 +00:53:46,540 --> 00:53:50,380 +أنا بقوله because at one hundred degree C the + +703 +00:53:50,380 --> 00:53:53,840 +vaporization of benzene is spontaneous وهذا وضع + +704 +00:53:53,840 --> 00:53:56,540 +طبيعي لأنه عند 80 كان عند 80 ال boiling + +705 +00:53:56,540 --> 00:54:00,660 +point فعند 100 الأصل أنه spontaneous بتحول + +706 +00:54:00,660 --> 00:54:07,280 +spontaneous للغاز بقول the term -TΔS + +707 +00:54:07,280 --> 00:54:13,140 +should have a more negative value عشان هو بيتحول + +708 +00:54:13,140 --> 00:54:17,580 +للغاز هذا ال term لازم ي... لأنه ال ΔS موجبة + +709 +00:54:19,090 --> 00:54:26,350 +كويس فبي بده يتحول إيه ل more negative value -T + +710 +00:54:26,350 --> 00:54:29,830 +ΔS the term -TΔS should have a + +711 +00:54:29,830 --> 00:54:33,330 +more negative value than the positive ΔHVAP + +712 +00:54:33,330 --> 00:54:37,490 +ليه؟ لأن التحويل من liquid إلى vapor معناه ال + +713 +00:54:37,490 --> 00:54:40,950 +ΔH هذه VAP اللي هي positive positive value + +714 +00:54:40,950 --> 00:54:45,630 +فهنا عندنا لأنه spontaneous فال ΔG يجب أن + +715 +00:54:45,630 --> 00:54:48,960 +تكون negative طب ما بتكون negative إلا لما إنّ + +716 +00:54:48,960 --> 00:54:52,340 +ده السالب يكون أكبر، يبقى ال TΔS هي اللي + +717 +00:54:52,340 --> 00:54:57,260 +أكبر من ال ΔH عشان النتيجة ايش تكون؟ سالبة، + +718 +00:54:57,260 --> 00:55:01,000 +آه يبقى الخيار الثاني هو اللي صح الخيار هذا أكيد + +719 +00:55:01,000 --> 00:55:01,500 +خطأ + +720 +00:55:04,160 --> 00:55:07,780 +شفنا يعني هذا الكلام شوفنا إنّ الـ ΔG بتساوي + +721 +00:55:07,780 --> 00:55:13,600 +الـ ΔG° زائد ال RT لن ال Q وشفنا إن وقت + +722 +00:55:13,600 --> 00:55:17,880 +الإيكويليبريوم Q بتساوي K و ΔG بتساوي صفر و ال + +723 +00:55:17,880 --> 00:55:21,120 +equation بتتحول لـ ΔG° بتساوي -RT لن + +724 +00:55:21,120 --> 00:55:27,580 +ال K أو ال K بتساوي E أس -ΔG°/RT + +725 +00:55:27,580 --> 00:55:33,990 +و هنا ممكن نحسب ال K فخلينا نحسب ال K خليني + +726 +00:55:33,990 --> 00:55:38,150 +أحسب الـK لأ بدّوش أحسب الـK هون بعد بشوية بحسب + +727 +00:55:38,150 --> 00:55:42,230 +الـK مش مشكلة بيقول calculate ΔG at 298 Kelvin for + +728 +00:55:42,230 --> 00:55:46,630 +the reaction below where one atmosphere nitrogen + +729 +00:55:46,630 --> 00:55:51,830 +ثلاثة atmosphere H2 and one atmosphere NH3 are + +730 +00:55:51,830 --> 00:55:56,870 +present in the mixture ΔG° at 298 Kelvin متساوي + +731 +00:55:56,870 --> 00:56:01,330 +سالب 33.3 كيلوجول اللي متعودين عليها شفناها كثير + +732 +00:56:01,330 --> 00:56:05,320 +شفنا الرقم هذا بشكل كبير ال Q بتساوي تركيزات + +733 +00:56:05,320 --> 00:56:08,920 +النواتج على تركيزات المتفاعلات، كل تركيز مرفوع + +734 +00:56:08,920 --> 00:56:15,020 +لقوة عدد المولات، لكن لما تكون في عندي غازات فقط + +735 +00:56:15,020 --> 00:56:18,610 +بدل التركيز بحط ال pressure فال pressure للأمونيا + +736 +00:56:18,610 --> 00:56:21,970 +تربيع على pressure للهيدروجين قوّة ثلاثة ل + +737 +00:56:21,970 --> 00:56:24,990 +pressure للنيتروجين قوّة واحد يبقى إذا كان عندي + +738 +00:56:24,990 --> 00:56:31,970 +pressures فبقى أحط ال pressures بدل التركيزات ال Q + +739 +00:56:31,970 --> 00:56:35,170 +بتطلع عندي 3.7 × 10-2 ال Δ + +740 +00:56:35,170 --> 00:56:40,290 +G بتساوي ΔG° زائد ال RT لن لQ + +741 +00:56:46,070 --> 00:56:48,570 +بعطينا الـ ΔG° سالب 33.3 + +742 +00:56:48,570 --> 00:56:50,490 +من عشرة وبعوّض عنها بسالب 33.3 من + +743 +00:56:50,490 --> 00:56:55,410 +عشرة زائد ال R هنا يا جماعة لازم نعوض عنها بالجول + +744 +00:56:55,410 --> 00:57:00,550 +لأن هذه بالجول في معناه كلام 8.314 مش 0.81 + +745 +00:57:00,550 --> 00:57:04,370 +فاحنا قلنا لما نكون وحدات طاقة بنعوض عن + +746 +00:57:04,370 --> 00:57:09,070 +ال R بـ 8.314 في 298 لن لQ + +747 +00:57:11,770 --> 00:57:17,090 +بينطلع عند ΔG سالب 44.5 يعني عند + +748 +00:57:17,090 --> 00:57:20,710 +هذه التركيزات برضه عند ΔG سالب يعني التفاعل + +749 +00:57:20,710 --> 00:57:28,350 +spontaneous لليمين يعني راح يتكون عندي أمونيا بقول + +750 +00:57:28,350 --> 00:57:31,390 +لهون تطبيق على الكلام اللي ذكرته في ال slide + +751 +00:57:31,390 --> 00:57:35,190 +الماضية بقول calculate the equilibrium constant Kp + +752 +00:57:35,190 --> 00:57:40,010 +at 25 degree C for the reaction 2H2O(l) + +753 +00:57:40,010 --> 00:57:45,930 +بتحول لـ 2H2(g) زائد O2(g) هل عمرنا شفنا إنّ + +754 +00:57:45,930 --> 00:57:49,030 +الماء بتتحول لـ H2O2؟ + +755 +00:57:52,160 --> 00:57:56,600 +ولا كان فيش ماء، فيش liquid water، بتتحولش يعني، + +756 +00:57:56,600 --> 00:57:59,380 +بتتحولش، عشان هيك هالاجي إنّ ال equilibrium + +757 +00:57:59,380 --> 00:58:03,900 +constant تتوقع يكون قيمة كبيرة ولا قيمة قليلة جدا، + +758 +00:58:03,900 --> 00:58:08,880 +إذا كانت بتتحولش، فنتوقع إنّ النواتج تكون كبيرة ولا + +759 +00:58:08,880 --> 00:58:14,200 +مهمة؟ لا هتكون قليلة كثير ال equilibrium constant + +760 +00:58:14,200 --> 00:58:17,740 +هتكون قليلة جدا ال equilibrium constant هتكون قليلة + +761 +00:58:17,740 --> 00:58:22,940 +جدا فال ΔG° لل reaction معطينا هو ΔG + +762 +00:58:22,940 --> 00:58:27,720 +°f لل H2O(l) ΔG°f لل H2 و ΔG° + +763 +00:58:27,720 --> 00:58:31,040 +f لل O2 وفي الامتحان ما عطينيش هدول التلاتة لا لل + +764 +00:58:31,040 --> 00:58:34,820 +O2 ولا لل H2ولأنهم معروفين إنّه أصفر ΔG° + +765 +00:58:34,820 --> 00:58:40,170 +f ΔH°f لكن ال S° لأ الـ S° بتكون + +766 +00:58:40,170 --> 00:58:46,910 +بتكون صفر بس at 0 Kelvin للـ Pure Crystalline .. + +767 +00:58:46,910 --> 00:58:50,730 +Perfectly Crystalline Substances لكن هنا ΔG° + +768 +00:58:50,730 --> 00:58:54,370 +f و ΔH°f على طول أصفار هدول فالـ ΔG° لل + +769 +00:58:54,370 --> 00:58:59,730 +reaction بتساوي N نواتج أصفار - 2 فبتطلع + +770 +00:58:59,730 --> 00:59:02,910 +474.4 من عشرة ال ΔG° لل + +771 +00:59:02,910 --> 00:59:07,960 +reaction -RT لن ال K إذا بنعود تعويض مباشر + +772 +00:59:07,960 --> 00:59:13,340 +بيطلع عند ال K 7 × 10-84 اللي بتطلع عليه + +773 +00:59:13,340 --> 00:59:15,720 +و اللي بيعرف شوية كيميا بيعرف إنّ هذا يعني شبه + +774 +00:59:15,720 --> 00:59:19,260 +مستحيل حتى ال calculator ده بيعرف يحسبه ما بيحصلش + +775 +00:59:19,260 --> 00:59:27,260 +يعني ما بيحصل نهائيا قليل جدا جدا نطلع على أيضا مثال + +776 +00:59:27,260 --> 00:59:30,940 +آخر لحساب الـ K بيقول الـ standard free energy + +777 +00:59:30,940 --> 00:59:34,820 +change for the Haber process is سالب 33.3 + +778 +00:59:34,820 --> 00:59:37,660 +كيلوجول لكل مول ΔG° + +779 +00:59:37,660 --> 00:59:40,760 +سالب 33.3 كيلوجول لكل + +780 +00:59:40,760 --> 00:59:43,780 +مول نفس السؤال اللي مانعناه سابقا لكن هون بده + +781 +00:59:43,780 --> 00:59:47,940 +يحسب قيمة ال equilibrium constant بيقول use this + +782 +00:59:47,940 --> 00:59:51,140 +value of ΔG° to calculate the equilibrium + +783 +00:59:51,140 --> 00:59:56,580 +constant for the process فال K بعرف بتساوي E أس - + +784 +00:59:56,580 --> 01:00:01,660 +ΔG°/RT بعوض K بتساوي E أس -ΔG° + +785 +01:00:01,660 --> 01:00:06,270 +هذا هيسالب 33.3 كيلوجول أو 33300 جول لكل + +786 +01:00:06,270 --> 01:00:09,110 +مول على ال R 8.314 جول لكل + +787 +01:00:09,110 --> 01:00:15,690 +مول لكل كلفن مضروبة في RT مضروبة في 298 بيطلع + +788 +01:00:15,690 --> 01:00:20,750 +7 × 105 7 × 105 بدي اكم + +789 +01:00:20,750 --> 01:00:26,170 +اتلاحظوا لهذا التفاعل ايش عمال بيحصل في ال + +790 +01:00:26,170 --> 01:00:31,330 +equilibrium constant؟ عند 300 كان 10-3 + +791 +01:00:31,330 --> 01:00:34,490 +، عند 400 كان 10-4، عند 450 10-5 + +792 +01:00:34,490 --> 01:00:39,250 +، عند 550 10-5 أقل، عند + +793 +01:00:39,250 --> 01:00:42,950 +550 10-6، عند 600 10-6 + +794 +01:00:42,950 --> 01:00:46,550 +أقل، ايش بيحصل؟ عمال كل ما رفعنا درجة الحرارة، ايش + +795 +01:00:50,290 --> 01:00:54,460 +بيحصل ال equilibrium constant؟ بيقل يعني تكون + +796 +01:00:54,460 --> 01:01:00,800 +النواتج بيقل يعني التفاعل non spontaneous بعد + +797 +01:01:00,800 --> 01:01:08,020 +الـ 450 بيصير non spontaneous فهو + +798 +01:01:08,020 --> 01:01:11,620 +كل ما رفعنا الحرارة بيصير more non spontaneous + +799 +01:01:11,620 --> 01:01:13,980 +يعني ال equilibrium constant بيروح ناحية + +800 +01:01:13,980 --> 01:01:18,060 +المتفاعلات مش النواتج لكن زي ما ذكرت يعني هذه مش + +801 +01:01:18,060 --> 01:01:24,000 +كل القصة يعني احنا بنستخدم في الحقيقة لـ Haber process + +802 +01:01:24,000 --> 01:01:30,300 +بنستخدم high temperature حوالي يمكن فوق الـ 400 + +803 +01:01:30,300 --> 01:01:34,360 +درجة وبنستخدم very high pressures وقول ده ليش ال + +804 +01:01:34,360 --> 01:01:38,420 +very high pressures بتجبر المتفاعلات تتحول إلى + +805 +01:01:38,420 --> 01:01:41,720 +نواتج لأنّ ال pressure تبع النواتج أقل من + +806 +01:01:41,720 --> 01:01:47,160 +المتفاعلات وبرضه ممكن يعني الناس تفكر بطرق ثانية + +807 +01:01:47,700 --> 01:01:52,940 +يعني حتى لو كان التفاعل ما بيمشي للأمام كثير، لكن + +808 +01:01:52,940 --> 01:01:58,220 +يعني حسب قاعدة لوشاتليه احنا ما ذكرناهاش، يعني لو + +809 +01:01:58,220 --> 01:02:03,240 +باستمرار أخذنا النواتج، فبنحجبر التفاعل يمشي برضه + +810 +01:02:03,240 --> 01:02:09,760 +للأمام، فمش كل القصة، بس جدّاش الحرارة بتأثر على ال + +811 +01:02:09,760 --> 01:02:14,500 +equilibrium constant، لا في عوامل ثانية يعني مهمة + +812 +01:02:15,300 --> 01:02:20,920 +ولكن ك calculations وكاستفادة من تأثير الحرارة على + +813 +01:02:20,920 --> 01:02:25,620 +ال spontaneity أو ΔG فهذا شيء واضح، يعني لا + +814 +01:02:25,620 --> 01:02:31,660 +يستطيع أن ينكره أي إنسان ممكن تبعا نحسب الـ ΔG + +815 +01:02:31,660 --> 01:02:36,160 +under non-standard conditions بس كان ما عنديش + +816 +01:02:36,160 --> 01:02:40,240 +standard conditions فبيقول ال calculate ΔG at + +817 +01:02:40,240 --> 01:02:45,780 +298 Kelvin for a mixture of مش K لأ أي قيم أي قيم + +818 +01:02:45,780 --> 01:02:49,300 +زي المثال اللي أخذناه أول مثال mixture of واحد + +819 +01:02:49,300 --> 01:02:55,000 +أتموسفير نيتروجين ثلاثة أتموسفير H2 نصف أتموسفير أو + +820 +01:02:55,000 --> 01:02:57,440 +غيّروا هدول زي ما بدكم هذه اسمها non standard + +821 +01:02:57,440 --> 01:03:01,080 +conditions غيروا هذه ال pressure زي ما بدكم هذه + +822 +01:03:01,080 --> 01:03:05,420 +اسمها non standard conditions being used in the + +823 +01:03:05,420 --> 01:03:08,520 +Haber process provided ده ΔG° سالب 33.3 + +824 +01:03:08,520 --> 01:03:10,680 +و 3 و 10 كيلوجول لكل مول و Q + +825 +01:03:10,680 --> 01:03:13,760 +بتساوي 9.3 × 10-3 هو حسب ال + +826 +01:03:13,760 --> 01:03:19,800 +Q لهدول أمونيا تربيع على ال H23 في ال + +827 +01:03:19,800 --> 01:03:23,280 +نيتروجين ال Pressures تبعتهم فبيقول الـ ΔG + +828 +01:03:23,280 --> 01:03:27,580 +تساوى ΔG° زائد الـ RT لن الـ Q - 37.3 + +829 +01:03:27,580 --> 01:03:35,280 +كيلوجول لكل مول زائد الـ R في الـ T حولنا الـ R + +830 +01:03:35,280 --> 01:03:41,080 +من جول لكيلوجول لأن الـ Q تمام فبيطلع عندي سالب 44 + +831 +01:03:41,080 --> 01:03:51,410 +.9 هو نفس القيمة لأ هذه كانت واحد أتموسفير خلينها + +832 +01:03:51,410 --> 01:03:54,570 +نصف اللي هي ال ammonia فتغير طبعا تغيرت القيمة لكن + +833 +01:03:54,570 --> 01:03:57,710 +إذا كان شفت كيف اتغيرت؟ اتغيرت الأمور negative + +834 +01:03:57,710 --> 01:04:05,350 +سالب مثلا 1.4 فتغير ال ... خليني أقول الظروف بتغير + +835 +01:04:05,350 --> 01:04:07,870 +قيمة ال ΔG أيضا + +836 +01:04:15,090 --> 01:04:18,390 +يعني الـ Larger value للـ ΔG بتقول والله ال + +837 +01:04:18,390 --> 01:04:22,190 +driving force لتكوين الأمونيا بتزيد + +839 +01:04:24,460 --> 01:04:27,460 +يبقى هذه هي الـ ΔG equations ممكن نقول والله + +840 +01:04:27,460 --> 01:04:31,540 +الـ ΔG° -RT لن ال Q طبعا لأنّ ال K at + +841 +01:04:31,540 --> 01:04:36,140 +equilibrium لأن الـ Q بتساوي الـ K أو بتساوي delta H + +842 +01:04:36,140 --> 01:04:40,220 +not minus T delta S not أو بتساوي الـ delta G minus + +843 +01:04:40,220 --> 01:04:43,860 +RT لن الـ Q لأن الـ delta G بتساوي delta G not زائد + +844 +01:04:43,860 --> 01:04:47,940 +الـ RT لن الـ Q فأنا ببني المعادلة أو بتساوي + +845 +01:04:47,940 --> 01:04:52,490 +summation M delta G notF لـ products minus + +846 +01:04:52,490 --> 01:04:57,590 +summation دلتا G أو إذا كان في عندي delta G نقطة + +847 +01:04:57,590 --> 01:05:01,090 +لـ reactants و لـ products برضه هذا الكلام صحيح يعني + +848 +01:05:01,090 --> 01:05:06,070 +ففي عندي عدة علاقات بتحكم الـ delta G وممكن أن + +849 +01:05:06,070 --> 01:05:09,810 +أستخدم أي واحدة فيهم في حل المسائل ابتداءً الآن + +850 +01:05:09,810 --> 01:05:13,690 +نقطة صغيرة بقول في بعض الأحيان في عندي تفاعل الـ + +851 +01:05:13,690 --> 01:05:18,560 +delta G له موجبة هل معنى الكلام أنه خلاص فش إيه + +852 +01:05:18,560 --> 01:05:22,160 +الحيلة فهذا التفاعل مش راح يمشي إلى اليمين؟ قال لأ + +853 +01:05:22,160 --> 01:05:29,040 +ممكن أنا إذا كان لجيت التفاعل الآخر الـ delta G له + +854 +01:05:29,040 --> 01:05:34,520 +سالبة وهذا التفاعل بتفاعل مع أحد نواتج التفاعل + +855 +01:05:34,520 --> 01:05:41,470 +الأول ممكن التفاعل الأول يصير spontaneous ففي عندي + +856 +01:05:41,470 --> 01:05:44,730 +تفاعل non spontaneous زي .. زي الـ zinc sulfide + +857 +01:05:44,730 --> 01:05:48,030 +يتحول لـ zinc solid زائد sulfur الـ delta G له + +858 +01:05:48,030 --> 01:05:51,310 +مية وتمانين كيلوجول positive very + +859 +01:05:51,310 --> 01:05:55,890 +يعني ما تحصلش non spontaneous .. non + +860 +01:05:55,890 --> 01:06:01,460 +spontaneous لكن في عندي تفاعل ثاني الـ S Solid زائد + +861 +01:06:01,460 --> 01:06:06,380 +الـ O2 Gas بيعطيني S O2 Gas الـ Delta Genot تبعته + +862 +01:06:06,380 --> 01:06:10,700 +very negative سالب تلاتمية طب هذا الـ S هل ممكن + +863 +01:06:10,700 --> 01:06:15,520 +يتفاعل مع الـ Oxygen اه وبالتالي يعطيني S O2 فلو + +864 +01:06:15,520 --> 01:06:19,800 +جيت جمعت المعادلتين هدول مع بعض لو جيت جمعت + +865 +01:06:19,800 --> 01:06:24,260 +المعادلتين بقول coupling the two reactions gives + +866 +01:06:24,260 --> 01:06:35,230 +Zinc Sulphide زائد أكسجين اه من هذا رح يطلع هذا إذا + +867 +01:06:35,230 --> 01:06:39,890 +زنك سالفايد زائد أكسجين زنك صلب اللي هو هايه + +868 +01:06:39,890 --> 01:06:44,910 +النتج اللي أنا بديّه زائد SO2 جاز جداش الدل تجي + +869 +01:06:44,910 --> 01:06:48,550 +لهذا التفاعل قال احنا جمعنا هدول و بنجمعهم لأنه + +870 +01:06:48,550 --> 01:06:53,250 +هذا state function بنجمعهم delta g note مية وتمانين + +871 +01:06:53,250 --> 01:07:03,870 +وتسعين سالب تلاتمية فبيطلع عندي سالب مية واثنا عشر + +872 +01:07:07,150 --> 01:07:13,110 +زائد سالب هذه هذه يعني زائد مية وتمانين وتسعين + +873 +01:07:13,110 --> 01:07:16,430 +يعني هي مجموعة ما نهان جمعهم زائد مية وتمانين + +874 +01:07:16,430 --> 01:07:20,710 +وتسعين بتعطيني سالب مية واثنا عشر لأنه حصلت على هذا + +875 +01:07:20,710 --> 01:07:24,930 +التفاعل من مجموع الأثنين فإبدا أجمع الـ delta G زي + +876 +01:07:24,930 --> 01:07:29,910 +ما كنا بنجمع الـ delta H فمجموعهم سالب 112 يعني + +877 +01:07:29,910 --> 01:07:34,230 +التفاعل ايش صار؟ التفاعل صار spontaneous هذا + +878 +01:07:34,230 --> 01:07:42,830 +بنقوله coupling يعني عملية جمع two reactions واحد + +879 +01:07:42,830 --> 01:07:48,210 +بيكون non spontaneous والتاني spontaneous فالنتيجة + +880 +01:07:48,210 --> 01:07:53,670 +طبعاً أن التفاعل الـ non spontaneous صار ممكن صار + +881 +01:07:53,670 --> 01:08:00,510 +spontaneous الآن ببساطة خالص يعني فكرة صغيرة بنقول + +882 +01:08:00,510 --> 01:08:05,670 +أنه شغلة الـ coupling of reactions يعني هادي كتير + +883 +01:08:05,670 --> 01:08:10,310 +مشهورة في الـ living organisms يعني عموم تفاعلات + +884 +01:08:10,310 --> 01:08:13,390 +كتير تُعتبر منها spontaneous ممكن إنه نعملها + +885 +01:08:13,390 --> 01:08:19,950 +coupling لتفاعل spontaneous أحصل على spontaneous + +886 +01:08:19,950 --> 01:08:23,750 +process لمن spontaneous process أصلاً فمثلاً في + +887 +01:08:23,750 --> 01:08:28,590 +الجسم الجلوكوز بيتأكسد لـ CO2 و water و بيعطينا + +888 +01:08:28,590 --> 01:08:32,150 +طاقة يعني الـ delta G تبعته negative spontaneous + +889 +01:08:32,150 --> 01:08:37,150 +and the energy released convert ADP هذا low free + +890 +01:08:37,150 --> 01:08:46,710 +energy molecule أنتو ATP يعني يتفاعل ADP إلى ATP + +891 +01:08:46,710 --> 01:08:48,310 +هذا non spontaneous + +892 +01:08:50,960 --> 01:08:53,440 +فبده طاقة عشان يصير spontaneous بده نعملوا + +893 +01:08:53,440 --> 01:08:57,140 +coupling مع حاجة ثانية فهذا لما نعمل ناخد الطاقة + +894 +01:08:57,140 --> 01:09:01,220 +اللي .. لأن هذا low energy وهذا high energy، + +895 +01:09:01,220 --> 01:09:04,700 +فمعنى الكلام الـ Delta G positive لهذا التفاعل، + +896 +01:09:04,700 --> 01:09:09,080 +لكن آه فإيش اللي بنقوله احنا؟ ناخد الطاقة الـ free + +897 +01:09:09,080 --> 01:09:15,320 +energy من الـ glucose، و بتحول هذه الطاقة الـ ADP لـ + +898 +01:09:15,320 --> 01:09:19,860 +الـ ATP high free energy content، والـ ATP اللي + +899 +01:09:19,860 --> 01:09:25,150 +هالجهة يصير يعني ATP، الـ ADP اللي صار ATP، هذا + +900 +01:09:25,150 --> 01:09:30,770 +بيعطي الطاقة تبعته لبناء مكونات أبسط في الجسم + +901 +01:09:30,770 --> 01:09:35,310 +وبيعمل منها خلايا، بيعمل منها membranes كل + +902 +01:09:35,310 --> 01:09:39,800 +المشاطات الحيوية تبع الجسم وبرجع تاني للـ ADP، الـ + +903 +01:09:39,800 --> 01:09:43,720 +ADP بده طاقة عشان يتحول تاني للـ ATP بياخدها من الـ + +904 +01:09:43,720 --> 01:09:48,460 +glucose، because بيصير ATP، الـ ATP بيعطي ..بالتالي + +905 +01:09:48,460 --> 01:09:53,060 +الطاقة تبعته لـ .. يعني أو بيستخدم الطاقة تبعته + +906 +01:09:53,060 --> 01:10:00,210 +لعمل عمليات حيوية أخرى هذا الـ ATP أدينين تراي + +907 +01:10:00,210 --> 01:10:03,510 +فوسفات يعني في تلاتة فوسفات هذا أدينين تراي فوسفات + +908 +01:10:03,510 --> 01:10:06,350 +واحد فوسفات تلاتة فوسفات تلاتة أدينين تراي فوسفات + +909 +01:10:06,350 --> 01:10:10,970 +الـ ATP أدينين داي فوسفات هي فوسفات هي فوسفات داي + +910 +01:10:10,970 --> 01:10:17,770 +يعني بس اثنين فهن بنعطيله energy للـ ATP بتحول للـ + +911 +01:10:17,770 --> 01:10:25,160 +ATP الـ ATP بيعطي الـ energy تبعته للجسم يعني بيعمل + +912 +01:10:25,160 --> 01:10:29,680 +عمليات حيوية مختلفة بتحول جزيئات بسيطة لجزيئات + +913 +01:10:29,680 --> 01:10:33,820 +أكثر تعقيداً إلى آخره فبيتحول تاني للـ ADP وهكذا + +914 +01:10:33,820 --> 01:10:39,790 +دورة مستمرة فهذا الشكل اللي برضه هتشوفوه في الكتاب + +915 +01:10:39,790 --> 01:10:43,470 +الـ Glucose Oxidation بيعطينا CO2 و H2O و High + +916 +01:10:43,470 --> 01:10:49,170 +Energy الـ High Energy بتحول الـ ADP للـ ATP الـ ATP + +917 +01:10:49,170 --> 01:10:54,350 +بتعمل Cellular Development Cell Constituents بتحول + +918 +01:10:54,350 --> 01:10:58,570 +الـ Simpler Molecules لأشياء ثانية وبرجع تاني للـ + +919 +01:10:58,570 --> 01:11:04,680 +ADP وهكذا وهذه الرسمة جميلة مثل المكان اللي + +920 +01:11:04,680 --> 01:11:08,940 +متعودين عليه يعني فهي الـ food مع الـ oxygen بيعطينا + +921 +01:11:08,940 --> 01:11:14,020 +CO2 H2O يعني glucose food مع oxygen هذا أعطاني + +922 +01:11:14,020 --> 01:11:19,820 +طاقة الآن الطاقة الزايدة هذه شغلت هذا الـ terce + +923 +01:11:19,820 --> 01:11:25,760 +يعني الـ terce هذا حول الـ ATP لـ ADP دهر للطاقة + +924 +01:11:25,760 --> 01:11:29,140 +الزيادة حولت الـ simpler molecules لـ more complex + +925 +01:11:29,140 --> 01:11:36,100 +molecules وهكذا فاستفدت + +926 +01:11:36,100 --> 01:11:40,920 +من التفاعلات المختلفة + +927 +01:11:40,920 --> 01:11:45,540 +اللي عادة بتعطيني more energy علشان أشغل تفاعلات + +928 +01:11:45,540 --> 01:11:51,820 +أخرى بحاجة إلى energy طبعاً جسم الإنسان بيستخدم هذه + +929 +01:11:51,820 --> 01:12:00,510 +العمليات بكفاءة عالية للغاية احنا يعني هيك بنكون + +930 +01:12:00,510 --> 01:12:09,350 +خلصنا المساق بتمنى إن شاء الله أنه نكون استفدنا + +931 +01:12:15,460 --> 01:12:20,640 +التواجد دي هكون موجود كل يوم من الساعة عشرة لصلاة + +932 +01:12:20,640 --> 01:12:26,960 +الظهر فأي حد عنده سؤال ممكن يسأل في عندنا واجب + +933 +01:12:26,960 --> 01:12:33,640 +موعده يعني كمان يومين بتهيألي في عندنا واجب على + +934 +01:12:33,640 --> 01:12:39,880 +الصفحة موجود فبتجيبوه للواجب في أي وقت يعني في + +935 +01:12:39,880 --> 01:12:45,570 +موعده المحدد على الصفحة يعني وهيك بنقول لكم يعني + +936 +01:12:45,570 --> 01:12:49,090 +أعطيكم العافية وإن شاء الله بنتمنالكم التوفيق و + +937 +01:12:49,090 --> 01:12:53,430 +لعلي طبعاً ما أشوفكمش في مساقات ثانية لأنه طبعاً أنتو + +938 +01:12:53,430 --> 01:12:57,290 +مهندسات يعني فما أقدرش .. ما ألقاكمش إلا في هذا المساق + +939 +01:12:57,290 --> 01:13:00,990 +في الكيميا فبتمنالكم التوفيق و بارك الله فيكم diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ouZhgFHnb0w_postprocess.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ouZhgFHnb0w_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..e0540eefc221c71237a95e454ab0d08dfd3f4d34 --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ouZhgFHnb0w_postprocess.srt @@ -0,0 +1,3756 @@ +1 +00:00:21,210 --> 00:00:24,110 +بسم الله الرحمن الرحيم أزياء الله الرحمن الرحيم + +2 +00:00:24,110 --> 00:00:29,150 +اليوم بنكمل في ال chemical thermodynamics اتحدثنا + +3 +00:00:29,150 --> 00:00:34,890 +في الحصة الماضية بشكل أساسي عن كيفية حساب ال ال + +4 +00:00:34,890 --> 00:00:42,750 +delta S ل reaction ما و اتحدثنا أيضا عنالـ phase + +5 +00:00:42,750 --> 00:00:48,470 +transition أو بشكل مقتصري يعني إيش بيحصل لو كان في + +6 +00:00:48,470 --> 00:00:56,530 +عندى equilibrium بين gas و liquid أو liquid أو + +7 +00:00:56,530 --> 00:00:57,090 +solid + +8 +00:01:01,640 --> 00:01:05,420 +أو حتى sublimation فاتحدثنا أيضا عن ال effect of + +9 +00:01:05,420 --> 00:01:10,180 +temperature على ال delta S أو على ال entropy بشكل + +10 +00:01:10,180 --> 00:01:15,100 +عام اليوم بنطلع على معلومات كتير بسيطة بنطلع على + +11 +00:01:15,100 --> 00:01:18,200 +ال free energy و علاقتها بال phase transition + +12 +00:01:18,200 --> 00:01:23,280 +temperature شفنا هذا الكلام سابقا لكن ماعملناش ال + +13 +00:01:23,280 --> 00:01:28,240 +relation من ال free energyو بالمناسبة free energy + +14 +00:01:28,240 --> 00:01:32,900 +مش معناتها انها يعني زي بعض الناس مابتعتقد انها + +15 +00:01:32,900 --> 00:01:38,980 +عبارة عن طاقة خليني اقول مجانية free لأ مش المقصود + +16 +00:01:38,980 --> 00:01:44,220 +انها طاقة مجانية لأ free energy يعني اقرب ما تكون + +17 +00:01:44,220 --> 00:01:47,800 +ال available energy ال available energy ال energy + +18 +00:01:47,800 --> 00:01:51,560 +اللي ممكن تعمل شغلخيص يعني ال energy موجودة ممكن + +19 +00:01:51,560 --> 00:01:55,600 +تعمل شغل لكن مش free energy يعني إيه يعني طاقة + +20 +00:01:55,600 --> 00:02:00,800 +مجانية لأ هذا تعبير أو يعني تفسير خاطئ لمعنى ال + +21 +00:02:00,800 --> 00:02:05,560 +term فبدأ أطلع على ال phase transition temperature + +22 +00:02:05,560 --> 00:02:10,450 +من واقع أو من ال free energyفبقول في البداية انا + +23 +00:02:10,450 --> 00:02:14,330 +عندى الـ delta G not at standard conditions يعني + +24 +00:02:14,330 --> 00:02:17,510 +نسوي delta H not minus T delta S not لو مش + +25 +00:02:17,510 --> 00:02:20,670 +standard conditions طبعا بنرفع ال note تصير عادي + +26 +00:02:20,670 --> 00:02:25,030 +delta G بتسوي delta H minus T delta S لكن انا بعرف + +27 +00:02:25,030 --> 00:02:28,950 +ان ال delta G not بتساوي0 for a phase transfer + +28 +00:02:28,950 --> 00:02:32,170 +لأنه عندي equilibrium reversible process فمعنى + +29 +00:02:32,170 --> 00:02:37,470 +الكلام ال delta H هتساوي T delta S او بمعنى اخر ال + +30 +00:02:37,470 --> 00:02:41,270 +temperature هتساوي delta H على delta S فإذا كان + +31 +00:02:41,270 --> 00:02:46,050 +بتكلم عن fusion او يعني ذوبان delta H fusion على + +32 +00:02:46,050 --> 00:02:51,370 +delta S fusionإذا بتكلم عن Vaporization ليكود مع + +33 +00:02:51,370 --> 00:02:55,730 +فيبر بقول والله ال tea boiling بتصير لأنه boiling + +34 +00:02:55,730 --> 00:02:58,890 +ف delta H vaporization على delta S vaporization + +35 +00:02:58,890 --> 00:03:01,370 +إذا كنت بتكلم عن ال sublimation فال tea لل + +36 +00:03:01,370 --> 00:03:04,650 +sublimation تساوي delta H sublimation على delta S + +37 +00:03:04,650 --> 00:03:08,110 +لل sublimation وفي الواقع مش شرط أن يكون في عندي + +38 +00:03:08,110 --> 00:03:16,590 +حتى phase a transitionيعني خلّيني أقول بالصورة + +39 +00:03:16,590 --> 00:03:22,050 +اللي أنا ذكرتها هذه المعهودة لأ ممكن والله مثلا زي + +40 +00:03:22,050 --> 00:03:26,350 +ما ذكرت سابقا orthorhombic + +41 +00:03:26,350 --> 00:03:31,030 +sulfur يتحول ل monoclonic sulfur أو العكس يعني + +42 +00:03:31,030 --> 00:03:35,510 +فهذا يعتبر أيضا phase transition فانا بقول ال T + +43 +00:03:35,510 --> 00:03:42,330 +بشكل عام لل phase changeهتساوى الـ delta H للتشينج + +44 +00:03:42,330 --> 00:03:45,730 +على ال delta S للتشينج، بغض النظر عن الاسم، هل هي + +45 +00:03:45,730 --> 00:03:51,010 +هذه أو هذه أو هذه، وحتى two solid phases مع بعض في + +46 +00:03:51,010 --> 00:03:57,010 +phase أثبت من phase آخر، فهذا كلام كله ممكن نجمعه + +47 +00:03:57,010 --> 00:03:59,150 +ونقول والله ال T لل phase change ده ال delta H + +48 +00:03:59,150 --> 00:04:03,940 +للتشينج على ال delta Sهذا كله من اين جاء ببساطة من + +49 +00:04:03,940 --> 00:04:06,780 +انه والله قلنا في ال phase change في عندي + +50 +00:04:06,780 --> 00:04:10,060 +equilibrium ما بين ال two phases او في عندي a + +51 +00:04:10,060 --> 00:04:13,400 +transition temperature هذه ال temperature اللي + +52 +00:04:13,400 --> 00:04:17,640 +قبلها بيكون عندي phase معين بعدها بيصير عندي phase + +53 +00:04:17,640 --> 00:04:20,810 +اخرهذه هي الـ Transition Temperature اللي أنا + +54 +00:04:20,810 --> 00:04:24,790 +بتكلم عنها و زي ما احنا شايفين هذا الكلام اقدرنا + +55 +00:04:24,790 --> 00:04:28,370 +نحصل عليه لأنه افترضنا ان ال Delta G بتساوي صفر + +56 +00:04:28,370 --> 00:04:32,410 +وهذا كلام صحيح لإن في عندي equilibrium ما بين ال + +57 +00:04:32,410 --> 00:04:37,400 +two phases او التغير بيكون reversibleفعلى سبيل + +58 +00:04:37,400 --> 00:04:42,100 +المثال هذا الـ T Delta S هي تغيرها مع الحرارة و + +59 +00:04:42,100 --> 00:04:47,020 +احنا في هذا المساء هنعتبر انه يعني في كثير من + +60 +00:04:47,020 --> 00:04:50,740 +الأحيان اذا كان قلنالك انه والله تتغيرش فبنعتبر ان + +61 +00:04:50,740 --> 00:04:54,300 +هذا التغير مش موجود و كأنها خط و كأنها خط أفق + +62 +00:04:54,300 --> 00:04:58,280 +تماما يعني مافيش عندى تغير مع الحرارة وهي ال Delta + +63 +00:04:58,280 --> 00:05:03,140 +H على سبيل المثال التغير إليها مع الحرارةوكذلك في + +64 +00:05:03,140 --> 00:05:06,960 +كثير من الأحيان الـ delta H لا تتغير مع الحرارة، + +65 +00:05:06,960 --> 00:05:10,380 +طبعا هذا يتوقف على ال system مرات التغير كبير و + +66 +00:05:10,380 --> 00:05:16,160 +مرات التغير قليل فلما نقول لا تتغير ال delta S أو + +67 +00:05:16,160 --> 00:05:19,520 +ال delta H مع الحرارة فمعنى الكلام حسبتنا تقريبية + +68 +00:05:19,520 --> 00:05:26,000 +يعني القيم اللي بنحصل عليها هي قيم تقريبية مش + +69 +00:05:26,000 --> 00:05:30,190 +حقيقيةلكن احنا بنستخدم هذا المفهوم ببساطة نقول + +70 +00:05:30,190 --> 00:05:34,070 +والله لأ تتغيرش مع الحرارة عشان نبسط الحل بحيث ان + +71 +00:05:34,070 --> 00:05:38,450 +نروح ناخد القيم الموجودة في الجداول فبشتغل + +72 +00:05:38,450 --> 00:05:41,450 +باستخدام ال delta H او ال delta S at the standard + +73 +00:05:41,450 --> 00:05:45,150 +state اللي هي قيمها موجودة في الجداول فماضطرش ان + +74 +00:05:45,150 --> 00:05:47,930 +انا ادور على قيم ال delta H و delta S عند الحرارة + +75 +00:05:47,930 --> 00:05:51,810 +اللي انا بدي اياها بالظبط لكن هذا الشكل بيبين ان + +76 +00:05:51,810 --> 00:05:55,330 +انا اتغير ال delta S و delta H مع الحرارة لاحظوا + +77 +00:05:55,330 --> 00:05:59,980 +انهم بتقيوا في نقطةعند هذه النقطة بالظبط الـ delta + +78 +00:05:59,980 --> 00:06:05,280 +H بتساوي يعني الحرارة، عند الحرارة هادى، في عندي + +79 +00:06:05,280 --> 00:06:09,080 +ال delta H ساوية T delta S عند الحرارة هادى + +80 +00:06:09,080 --> 00:06:12,600 +بالظبط، لأن التقاطة ال delta أو عند ال delta G + +81 +00:06:12,600 --> 00:06:16,310 +بتساوي zero فهذه ال transition temperatureلحظوا + +82 +00:06:16,310 --> 00:06:20,930 +قبلها ممكن يكون spontaneous بعدها spontaneous أو + +83 +00:06:20,930 --> 00:06:23,890 +العكس ممكن يكون قبلها spontaneous بعدها non + +84 +00:06:23,890 --> 00:06:29,310 +spontaneous تمام؟ لكن هذه عبارة عن ال transition + +85 +00:06:29,310 --> 00:06:32,210 +temperature اللي عندها ال delta H بالساوية T delta + +86 +00:06:32,210 --> 00:06:37,670 +S وعندها بيكون ال delta G عبارة عن Zero لأن هذا + +87 +00:06:37,670 --> 00:06:42,080 +عبارة عن equilibriumمعنى الكلام الـ two phases او + +88 +00:06:42,080 --> 00:06:46,180 +الـ change بدي يكون reversible في هذه المنطقة عند + +89 +00:06:46,180 --> 00:06:49,500 +هذه الحرارة بالظبط بيكون reversible فلو في عندي + +90 +00:06:49,500 --> 00:06:54,740 +غلية يعني اقل من مائة درجة للميه، non spontaneous + +91 +00:06:54,740 --> 00:06:59,160 +اكتر من مائة درجة، spontaneous او عند مائة درجة + +92 +00:06:59,160 --> 00:07:03,340 +equilibrium دلتة جيب تساوي صفر تمام؟ فهذا المفهوم + +93 +00:07:03,340 --> 00:07:07,960 +يعني ال transition temperature اللي انا بتكلم عنه + +94 +00:07:08,740 --> 00:07:14,880 +خلّيني أخد بعض الأمثلة التوضيحية بقول مثلًا بيحكي + +95 +00:07:14,880 --> 00:07:20,320 +at 25 degrees c يعني 298 Kelvin the reduction of + +96 +00:07:20,320 --> 00:07:25,240 +copper one oxide is non spontaneous حلو، بدنا نعمل + +97 +00:07:25,240 --> 00:07:27,700 +reduction لل copper one oxide، هذه non spontaneous + +98 +00:07:27,700 --> 00:07:32,380 +ال delta G positive 8.9 كيلوجول طبعًا لو كان + +99 +00:07:32,380 --> 00:07:35,940 +spontaneous ال delta G بدها تكون سالبة لأن ال + +100 +00:07:35,940 --> 00:07:40,100 +delta G سالبة لل spontaneous processesبقول + +101 +00:07:40,100 --> 00:07:42,760 +calculate the temperature at which the reaction + +102 +00:07:42,760 --> 00:07:47,160 +becomes spontaneous ايش هي الحاجة هو هان non + +103 +00:07:47,160 --> 00:07:51,400 +spontaneous شوفنا المربع تبعه قبل شوية ع اليسار طب + +104 +00:07:51,400 --> 00:07:55,040 +ايش الحرارة اللي عندها هذا هو يعني هان هو هان non + +105 +00:07:55,040 --> 00:07:59,720 +spontaneous عند خمسة و عشرين ديجري ال سي عند حرارة + +106 +00:07:59,720 --> 00:08:02,580 +معينة non spontaneous بده الحرارة اللي عندها بيصير + +107 +00:08:02,580 --> 00:08:07,730 +spontaneous هان بالظبط بيصير spontaneousيعني هان + +108 +00:08:07,730 --> 00:08:10,830 +بالظبط بيبدأ يصير spontaneous لأنه بعد على طول بعد + +109 +00:08:10,830 --> 00:08:15,270 +شي قليل جدا بيصير spontaneous فلازم يعني نحسب ايه + +110 +00:08:15,270 --> 00:08:19,830 +ل transition temperature فبيقول ليه اكمل السؤال + +111 +00:08:19,830 --> 00:08:22,570 +بيقول ليه calculate the temperature at which the + +112 +00:08:22,570 --> 00:08:28,210 +reaction becomes spontaneous ΔH and ΔS are 58.1 + +113 +00:08:28,210 --> 00:08:34,060 +kilo joule and 165 joule per Kelvinباعتين قيمة الـ + +114 +00:08:34,060 --> 00:08:38,560 +ΔH والـ ΔS لتاعة المثالة الـ T بتساوى ΔH على ΔS + +115 +00:08:39,460 --> 00:08:41,820 +معنى الكلام ليه؟ لأن ليش هذا الكلام؟ أنا بدي أجيب + +116 +00:08:41,820 --> 00:08:43,880 +الـTransition Temperature اللي بعد الـTransition + +117 +00:08:43,880 --> 00:08:47,140 +Temperature بده يصير عندي الـChange اللي أنا بديه + +118 +00:08:47,140 --> 00:08:49,440 +يعني فبدي أجيب الـTransition Temperature بالظبط + +119 +00:08:49,440 --> 00:08:52,740 +وين .. وين هي الـTemperature اللي بعدها على طول + +120 +00:08:52,740 --> 00:08:55,240 +بيحصل عندي الـChange اللي بيقول الـT بيساوي + +121 +00:08:55,240 --> 00:08:58,620 +الـDelta S على الـDelta S fifty eight point one في + +122 +00:08:58,620 --> 00:09:03,900 +عشرة قصة ثلاثة لأنه الانتروبي بالجول أنا عندي هذه + +123 +00:09:03,900 --> 00:09:07,800 +kilo Joule فحولتهم لجول بيطلع عندي تلت مية اتنين + +124 +00:09:07,800 --> 00:09:13,610 +وخمسين Kelvinأذا بعد ال 352 كيلوفر خلاص التفاعل + +125 +00:09:13,610 --> 00:09:18,870 +بيصير عندي إيه؟ spontaneous عند 352 اه في عندي + +126 +00:09:18,870 --> 00:09:24,530 +equilibrium أقل من 352 ماني spontaneous فمش بس عند + +127 +00:09:24,530 --> 00:09:30,230 +25 degree c لأ عند أقل من 352 بيظل هو non + +128 +00:09:30,230 --> 00:09:35,280 +spontaneousما دام اقل من 352 اذا من spontaneous + +129 +00:09:35,280 --> 00:09:41,640 +هان اقل من 352 من spontaneous 352 بالظبط اترازشن + +130 +00:09:41,640 --> 00:09:47,380 +temperature بعد 352 بشحته صار spontaneous فهي + +131 +00:09:47,380 --> 00:09:51,940 +مفهوم المسألة نيجي نتطلع على مسألة تانية بتقول if + +132 +00:09:51,940 --> 00:09:55,660 +the reaction below spontaneous at room temperature + +133 +00:09:55,660 --> 00:10:00,270 +15 degree cIf not, at what temperature will it + +134 +00:10:00,270 --> 00:10:03,350 +start to be spontaneous؟ هل هذا التفاعل + +135 +00:10:03,350 --> 00:10:09,810 +spontaneous عند خمسة أو عشرين degrees C؟ والله، هى + +136 +00:10:09,810 --> 00:10:12,530 +بدنا نجاوب على هذا السؤال، بدنا نجاوب على هذا + +137 +00:10:12,530 --> 00:10:17,610 +السؤالإذا ماكانش spontaneous، إيش الحرارة اللي + +138 +00:10:17,610 --> 00:10:19,310 +عندها بده يصير spontaneous؟ بدنا ندورها على عالي + +139 +00:10:19,310 --> 00:10:22,230 +ترازشين temperature، لازم نفهم السؤال بالظبط إيش + +140 +00:10:22,230 --> 00:10:25,750 +اللي بده ياه فانا بشوف الله عند خمسة و عشرين ديجري + +141 +00:10:25,750 --> 00:10:29,490 +سي ديرتا جي نوت بتساوي ديرتا H نوت minus T ديرتا S + +142 +00:10:29,490 --> 00:10:32,890 +نوت فابعوض في المثلة one seventy seven point eight + +143 +00:10:32,890 --> 00:10:36,130 +minus two ninety eight في مية و ستين point five + +144 +00:10:36,130 --> 00:10:38,810 +فعشرة أسالة بتانية حوالي الا كيلو جول، بطلع عند + +145 +00:10:38,810 --> 00:10:43,020 +مية و تلاتين point zero kilo joule per moleهذه الـ + +146 +00:10:43,020 --> 00:10:48,320 +delta G note موجبة و لا سالبة؟ موجبة إذا و ليس + +147 +00:10:48,320 --> 00:10:53,660 +spontaneous لأن شرط ال spontaneity أن تكون ال + +148 +00:10:53,660 --> 00:10:57,880 +delta G سالبة شرط ال spontaneity أن تكون ال delta + +149 +00:10:57,880 --> 00:11:00,920 +G سالبة و لا سالبة موجبة suggesting a non + +150 +00:11:00,920 --> 00:11:04,680 +spontaneous process at 25 degrees C + +151 +00:11:09,110 --> 00:11:13,470 +طبعا لو عوض مهام بالـ Transition Temperature، + +152 +00:11:13,470 --> 00:11:15,910 +عارفين ايش اللي بيحصل؟ الـ Delta G Note بيتساوى + +153 +00:11:15,910 --> 00:11:20,710 +صفر، لو .. اه لو انه .. لو انه اعطاني جلي مثلا هل + +154 +00:11:20,710 --> 00:11:27,510 +هي .. هل ال .. يعني هل التفاعل spontaneous at 1108 + +155 +00:11:29,470 --> 00:11:33,370 +هلجيتها لو اقعد انا ب 1108 Kelvin راح الاجي + +156 +00:11:33,370 --> 00:11:38,410 +النتيجة قداش صفر ليه لأن دلتاجي بتساوي صفر دلتاجي + +157 +00:11:38,410 --> 00:11:41,850 +نوت بتساوي صفر لازم اطلع عنده صفر تعالوا نحسب الآن + +158 +00:11:41,850 --> 00:11:45,510 +ايش هي ال transition temperature اللي عندها يعني + +159 +00:11:45,510 --> 00:11:50,150 +او بعدها ال change بيصير spontaneous بقول to + +160 +00:11:50,150 --> 00:11:52,230 +calculate the temperature at which the reaction + +161 +00:11:52,230 --> 00:11:55,130 +starts to be spontaneous we should assume the + +162 +00:11:55,130 --> 00:11:59,290 +equilibrium state where دلتاجي نوت بتساوي صفرالـ T + +163 +00:11:59,290 --> 00:12:03,430 +ΔH على ΔS و الله عوضنا عنها دول هتطي 1108 يعني + +164 +00:12:03,430 --> 00:12:06,670 +التفاعل بتام و non spontaneous لغاية ما نوصل لل + +165 +00:12:06,670 --> 00:12:11,190 +transition temperature اللي هي 1108 أقل منها non + +166 +00:12:11,190 --> 00:12:16,230 +spontaneous أكتر منها spontaneous لو عوضنا بأكتر + +167 +00:12:16,230 --> 00:12:23,620 +من 1108 هان إشارة الـ Δجينوت هتكون سالبة خلاصعند + +168 +00:12:23,620 --> 00:12:29,460 +ما نعوض من 1108 هتكون صفر أقل من 1108 هتكون موجبا + +169 +00:12:29,460 --> 00:12:32,860 +يعني non spontaneous جميل جدا جميل جدا إذا اللي + +170 +00:12:32,860 --> 00:12:35,520 +بنعرف الحرارة اللي عندها بيصير عندي ال change + +171 +00:12:35,520 --> 00:12:40,580 +spontaneous ولا non spontaneous هذا إشي كتير مفيد + +172 +00:12:40,580 --> 00:12:44,960 +بيقول لي if the reaction below spontaneous or non + +173 +00:12:44,960 --> 00:12:48,740 +spontaneous at 25 degrees c at what temperature + +174 +00:12:48,740 --> 00:12:52,300 +will this reaction reverse directionإذا كانوا + +175 +00:12:52,300 --> 00:12:54,840 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +176 +00:12:54,840 --> 00:12:57,860 +spontaneous فتصبحوا spontaneous، إذا كانوا non + +177 +00:12:57,860 --> 00:12:58,080 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +178 +00:12:58,080 --> 00:13:00,300 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +179 +00:13:00,300 --> 00:13:02,800 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +180 +00:13:02,800 --> 00:13:05,160 +spontaneous فتصبحوا non spontaneous، إذافبقول + +181 +00:13:05,160 --> 00:13:08,900 +تعالي نطلع Delta H0 minus T Delta S0 هذا عبارة عن + +182 +00:13:08,900 --> 00:13:13,280 +Delta G0 بعوض عنهم At 25 degrees C Delta G0 + +183 +00:13:13,280 --> 00:13:19,400 +همعطيني في مسألة تانية أنا بعرفها اللي هو Delta H0 + +184 +00:13:19,400 --> 00:13:22,460 +minus 92.38 للتفاعل هذا + +185 +00:13:25,940 --> 00:13:30,720 +الحرارة خمسة و عشرين ديجري سي بده دلتا اس برضه هدا + +186 +00:13:30,720 --> 00:13:34,740 +هي معايا سالب سالب مية تمانية تسعين و تلاتة من + +187 +00:13:34,740 --> 00:13:37,700 +عشرة بيطلع عندى سالب تلاتة و تلاتين و تلاتة من + +188 +00:13:37,700 --> 00:13:42,600 +عشرة كيلوجولأه يبقى التفاعل spontaneous at room + +189 +00:13:42,600 --> 00:13:46,900 +temperature وهذا سؤال مهم حدرجعله عدة مرات لإيه؟ + +190 +00:13:46,900 --> 00:13:50,140 +لأن هذا الـ hyper process اللي هي طريقة تحضير + +191 +00:13:50,140 --> 00:13:53,000 +الأمونيا من الـ nitrogen والهيدروجين عملية صناعية + +192 +00:13:53,000 --> 00:13:57,340 +ممتازة وفعالة ومفيدة جدا بالنسبالنا وبنستخدمها + +193 +00:13:57,340 --> 00:14:01,160 +بشكل كبير عشان هيك إله زيارات متعددة زرناجة بالهيك + +194 +00:14:01,160 --> 00:14:05,190 +لكن برضه كمان إله زيارات متعددة لأنه مهمطب تعالى + +195 +00:14:05,190 --> 00:14:08,070 +نشوف لترازشن temperature هو اللى أنا عارفه لإنه + +196 +00:14:08,070 --> 00:14:12,650 +spontaneous طب وقتش بيصير non spontaneousأذا بدي + +197 +00:14:12,650 --> 00:14:15,630 +أجيب لترازيش ال temperature لحد الفاصل لترازيش ال + +198 +00:14:15,630 --> 00:14:18,210 +temperature فيقول ال T بتساوي ال delta H على ال + +199 +00:14:18,210 --> 00:14:24,850 +delta S هي ال delta S ال delta H سالب 92 380 يعني + +200 +00:14:24,850 --> 00:14:30,530 +نضربينها في الف عشان تصير جول وهي ال S أو ال delta + +201 +00:14:30,530 --> 00:14:35,790 +S سالب 198 و تلاتة من عشرة جول per Kelvin فبيطلع + +202 +00:14:35,790 --> 00:14:40,940 +عندي أربعمية خمسة ستين وتسعة من عشرةحلو كتير هذه + +203 +00:14:40,940 --> 00:14:45,360 +الحرارة يا جماعة قبلها التفاعل هذا بيكون + +204 +00:14:45,360 --> 00:14:50,300 +spontaneous بعدها بيصير not spontaneous عندها + +205 +00:14:50,300 --> 00:14:53,240 +بالظبط بيكون في عنده equilibrium عندها بالظبط + +206 +00:14:53,240 --> 00:14:55,280 +بيكون في عنده equilibrium + +207 +00:14:59,980 --> 00:15:03,920 +طيب هذا السؤال بيعطيني لما نكون فيه عندي + +208 +00:15:03,920 --> 00:15:07,980 +equilibrium بيقول لي write the chemical equation + +209 +00:15:07,980 --> 00:15:11,720 +that defines the normal boiling point of liquid + +210 +00:15:11,720 --> 00:15:17,660 +carbon tetrachloride CCL4بقول ال equation اللى + +211 +00:15:17,660 --> 00:15:21,220 +بتعطينه ال normal boiling point ان يكون ال CCL4 ال + +212 +00:15:21,220 --> 00:15:29,420 +liquid in equilibrium مع ال CCL4 gas هذه المعادلة + +213 +00:15:29,420 --> 00:15:35,640 +CCL4 liquid يتحول ال CCL4 gas reversiblyفهذه هي + +214 +00:15:35,640 --> 00:15:40,240 +المعادلة طيب بيقول لي what is the value of delta G + +215 +00:15:40,240 --> 00:15:43,680 +note for the equilibrium in part A؟ ايش قيمة ال + +216 +00:15:43,680 --> 00:15:50,520 +delta G note لهذا ال equilibrium؟ هتكون صفر طبعا، + +217 +00:15:50,520 --> 00:15:58,280 +ليش؟ اه لأن at equilibrium ال delta G note بدها + +218 +00:15:58,280 --> 00:16:03,810 +تساوي صفرفي عندي reversible change ما بين ال + +219 +00:16:03,810 --> 00:16:09,310 +liquid و ال vapor فبالتالي بدها تكون صفر هذا سابق + +220 +00:16:09,310 --> 00:16:13,810 +لأوانا شوية حيجيلناه بعدين مفهوم ال Q reaction + +221 +00:16:13,810 --> 00:16:19,280 +quotientبيقول NFC بيقول estimate the normal + +222 +00:16:19,280 --> 00:16:25,680 +boiling point of CCL4 provided that ΔH0 F4 CCL4 و + +223 +00:16:25,680 --> 00:16:30,840 +CCL4 gas و liquid are minus 106.7 kilojoule per + +224 +00:16:30,840 --> 00:16:36,500 +mole و minus 139 kilojoule per moleAlso it's not + +225 +00:16:36,500 --> 00:16:43,800 +for CCL4 and CCL4 gas and liquid are 309.4 and 214 + +226 +00:16:43,800 --> 00:16:47,800 +.4 respectively Assume ΔH and ΔS do not change + +227 +00:16:47,800 --> 00:16:50,900 +with temperature طبعا هذا مش حقيقي اتفاجنا على هذا + +228 +00:16:50,900 --> 00:16:54,340 +الكلام هو فيه تغير بيعتمد على ال system مدى التغير + +229 +00:16:54,340 --> 00:16:58,020 +بيعتمد على ال system HU لكن احنا لسهولة الحسابات + +230 +00:16:58,020 --> 00:17:06,240 +عشان نحصل على خليني اقول نستخدم ال ΔHعند أي حرارة + +231 +00:17:06,240 --> 00:17:09,160 +بقيمتها عند خمسة و عشرين ديجري سي لل standard + +232 +00:17:09,160 --> 00:17:13,220 +state لازم نفترض هذا الافتراض يمكن مش كتير انتوا + +233 +00:17:13,220 --> 00:17:16,500 +يعني بتحسوا بأهمية الموضوع لكن الموضوع كتير مهم + +234 +00:17:16,500 --> 00:17:21,140 +الموضوع كتير كتير مهم فخلينا نركز مع بعض شوية بقول + +235 +00:17:21,140 --> 00:17:23,340 +انا مادام في عند + +236 +00:17:27,060 --> 00:17:31,100 +بعدين بده ال normal boiling point كويس اذا انا بده + +237 +00:17:31,100 --> 00:17:34,360 +اشتغل عند ال ايه؟ عند ال equilibrium او بدلي + +238 +00:17:34,360 --> 00:17:38,350 +transition temperatureفبالتالي بقول الـ delta G0 + +239 +00:17:38,350 --> 00:17:43,110 +يتساوي صفر أو الـ T يتساوي دلتة S أو الـ T يتساوي + +240 +00:17:43,110 --> 00:17:49,230 +دلتة H نوت على دلتة S نوت دلتة H على دلتة S دلتة H + +241 +00:17:49,230 --> 00:17:53,310 +نوت على دلتة S دلتة H نوت على دلتة S دلتة H نوت + +242 +00:17:53,310 --> 00:17:59,210 +على دلتة S دلتة H نوت على دلتة S دلتة H نوت على + +243 +00:17:59,210 --> 00:18:00,030 +دلتة S دلتة H نوت على دلتة S دلتة H نوت على دلتة S + +244 +00:18:00,030 --> 00:18:01,310 +دلتة H نوت على دلتة S دلتة H نوت على دلتة S دلتة H + +245 +00:18:01,310 --> 00:18:04,650 +نوت على دلتة S دلتة H نوت على دلتة S دلتة H نوت + +246 +00:18:04,650 --> 00:18:08,970 +على دلتفمعنى الكلام بده اشوف والله الـ delta H + +247 +00:18:08,970 --> 00:18:13,090 +naught واحد مول فيه minus one oh six point seven + +248 +00:18:13,090 --> 00:18:18,370 +kilo joule per mole minus بنعوض تعويض يعني عن ال + +249 +00:18:18,370 --> 00:18:25,330 +delta H naught if لهذا و للآخر يعني للجاز و + +250 +00:18:25,330 --> 00:18:29,230 +للليكويد وهنا ال delta S naught بنقول والله S + +251 +00:18:29,230 --> 00:18:34,250 +naught للجاز minus S naught للليكويد فبحصل على + +252 +00:18:34,250 --> 00:18:39,850 +القيمة دي هي delta Hنوت وهي Delta S نوت فبقول + +253 +00:18:39,850 --> 00:18:44,170 +والله ال T بيبتساو Delta H نوت على Delta S نوت + +254 +00:18:44,170 --> 00:18:50,370 +تلتلاف و متون و ستين اللي هو اللي عبارة عن ال + +255 +00:18:50,370 --> 00:18:55,670 +Delta H اللي حسبتها على خمسة وتسعين جول per Kelvin + +256 +00:18:55,670 --> 00:19:01,150 +اللي بيعطيني تلتمية و تلاتة و أربعين Kelvin يعني + +257 +00:19:01,150 --> 00:19:05,370 +بيقول لي ان ال pointing point لل CCL4 جداش + +258 +00:19:14,460 --> 00:19:21,840 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +259 +00:19:21,840 --> 00:19:22,660 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +260 +00:19:22,660 --> 00:19:22,700 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +261 +00:19:22,700 --> 00:19:22,820 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +262 +00:19:22,820 --> 00:19:23,020 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +263 +00:19:23,020 --> 00:19:25,370 +تقريبا تقريبا تقريبطيب ليش الفرق هذا؟ جال لأنه + +264 +00:19:25,370 --> 00:19:28,890 +احنا اعتبرنا او افترضنا ان ال delta H و ال delta S + +265 +00:19:28,890 --> 00:19:33,030 +لا تتغيروا بالنسبة لكنهم في الحقيقة لأ في الحقيقة + +266 +00:19:33,030 --> 00:19:37,550 +بيتأثروا بالحرارة لكن هذه الفرضية بتسهل علينا + +267 +00:19:37,550 --> 00:19:42,510 +شغلنا لأنه على طول بدي احسب بأنه جال هذا كلب بروح + +268 +00:19:42,510 --> 00:19:44,890 +فورا بجيب ال delta لو ماعطانيش هدول بجيب delta H + +269 +00:19:44,890 --> 00:19:49,630 +not F و delta H not F at standard state و ال S not + +270 +00:19:49,630 --> 00:19:53,010 +و ال S not at standard stateواللي أنا بفترض أن + +271 +00:19:53,010 --> 00:19:55,950 +هدول هم قد ال standard state هم نفسهم عند أي + +272 +00:19:55,950 --> 00:19:59,750 +حرارة، لأنه لا يتأثروا بالحرارة، لكن هذا كلام إيه؟ + +273 +00:19:59,750 --> 00:20:04,670 +مش صحيح على إطلاق، وكمان بتوقف على ال system + +274 +00:20:09,530 --> 00:20:14,950 +طبعا نفس السؤال خلينا نتطلع عليه بشكل آخر هذه ال + +275 +00:20:14,950 --> 00:20:18,350 +process for the production of ammonia involves the + +276 +00:20:18,350 --> 00:20:23,850 +equilibrium in 2 زائد 3H2 بعطينا 2MH3 assume that + +277 +00:20:23,850 --> 00:20:29,330 +ΔH0 و ΔS0 for this reaction do not change with + +278 +00:20:29,330 --> 00:20:29,830 +temperature + +279 +00:20:32,820 --> 00:20:36,860 +تقريبا تقريبا predict the direction in which delta + +280 +00:20:36,860 --> 00:20:39,700 +G naught for the reaction it changes with + +281 +00:20:39,700 --> 00:20:41,060 +increasing temperature + +282 +00:20:48,630 --> 00:20:56,170 +فبدنا نشوف وقت إيش ال delta G not بتتغير إشارتها + +283 +00:20:56,170 --> 00:21:00,570 +بتغير إذا بدي أشوف ال delta G not عند الصفر لما + +284 +00:21:00,570 --> 00:21:03,290 +الصفر بتكون بصفر صفر اه قبله بتكون موجب وبعده + +285 +00:21:03,290 --> 00:21:07,010 +بتكون إيه سالب هذا مفهوم السؤال هذا مفهوم السؤال + +286 +00:21:07,010 --> 00:21:09,750 +لما نيجي يقول predict the direction in which delta + +287 +00:21:09,750 --> 00:21:14,250 +G not for the reaction it changes with increasing + +288 +00:21:14,250 --> 00:21:16,710 +temperature يعني وقت يحول من سالب لموجب لموجب + +289 +00:21:16,710 --> 00:21:17,990 +لسالب إذا بدي أجيب + +290 +00:21:26,950 --> 00:21:32,670 +بعدين يحسب قيمة الـ Delta G عند 25 و 500 على فرض + +291 +00:21:32,670 --> 00:21:40,070 +ان Delta H و Delta S لا تتغير بالحرارة لأن لو كانت + +292 +00:21:40,070 --> 00:21:46,310 +تتغير بالحرارة يعني لازم نجيب قيمهم عند 25 و 500 + +293 +00:21:47,410 --> 00:21:51,250 +عيند 25 هم المعروفين لأنهم من الجداول طب عيند 500 + +294 +00:21:51,250 --> 00:21:56,410 +لازم نشوف جداول عيند 500 او انه يعني نقدرهم عيند + +295 +00:21:56,410 --> 00:22:00,310 +500 لكن لا احنا هنستخدم اللي عيند 25 كمان عيند 500 + +296 +00:22:00,310 --> 00:22:07,970 +هي نفس القيمة لدلتا H و لدلتا S او لل S يعني + +297 +00:22:07,970 --> 00:22:16,890 +تعالوا نتطلع عموما لو جينا نتطلع هنابنلاقي انتروبي + +298 +00:22:16,890 --> 00:22:23,210 +بيزيد ولا بيجل المفروض التفاعل هدئالانتروبيا بيقل + +299 +00:22:23,210 --> 00:22:28,270 +لأن هنا عندى اربعة مولز غازي وهنا عندى بس اتنين + +300 +00:22:28,270 --> 00:22:32,430 +اذا النتيجة عدد مولات غازية اقل يبقى ال delta S + +301 +00:22:32,430 --> 00:22:38,790 +قيمة ايه؟ قيمة سالبة معناه الكلام في العلاقة delta + +302 +00:22:38,790 --> 00:22:43,050 +H not minus T delta S not ال minus T delta S not + +303 +00:22:43,050 --> 00:22:47,210 +هدى ايش هتكون؟ هتكون positive and increases with a + +304 +00:22:47,210 --> 00:22:52,710 +increasing temperatureAs a result ΔG0 becomes more + +305 +00:22:52,710 --> 00:22:58,890 +positive with increasing temperature لأن ΔG0 ΔH0 + +306 +00:22:58,890 --> 00:23:08,050 +minus T ΔS0 هذي موجبة لأن ΔS سالبة في سالب صارت + +307 +00:23:08,050 --> 00:23:14,290 +موجبة اذا as a result ΔG0 becomes more positive + +308 +00:23:14,290 --> 00:23:19,830 +لان عمال احنا بنزود الإيجابية بنزود قيمةالـ T + +309 +00:23:19,830 --> 00:23:23,010 +Delta S وبالتالي الـ Delta Genote تصير أكتر + +310 +00:23:23,010 --> 00:23:27,750 +positive with increasing temperature. Thus, the + +311 +00:23:27,750 --> 00:23:30,230 +driving force for the production of ammonia + +312 +00:23:30,230 --> 00:23:34,310 +becomes smaller with increasing temperature. مدام + +313 +00:23:34,310 --> 00:23:36,750 +الـ Delta Genote تصير أكتر positive مش أكتر + +314 +00:23:36,750 --> 00:23:40,170 +negative، إذن ال driving force لأنه يتكون عند + +315 +00:23:40,170 --> 00:23:45,420 +أمانيابيقل مع زيادة درجة الحرارة ل driving force + +316 +00:23:45,420 --> 00:23:49,200 +لإيه؟ لأنه كل ما زوّات درجة الحرارة، إيش بيحصل لك + +317 +00:23:49,200 --> 00:23:55,180 +دلتا G نقطة هادي؟ more positive، بتزيد ال + +318 +00:23:55,180 --> 00:23:58,540 +positivity تبعتها، يعني بيقل احتمالية أن يحصل + +319 +00:23:58,540 --> 00:24:03,680 +التفاعل، عشان يحصل، بيصير negative، تمام؟ لكن لا، + +320 +00:24:03,680 --> 00:24:07,660 +احنا كل ما زوّد الحرارة عامة، إيش بيحصل؟ تتجه ل + +321 +00:24:07,660 --> 00:24:10,740 +more positive، معناه كلام، ال driving force بتقل + +322 +00:24:18,940 --> 00:24:26,680 +طيب خليني اطلع على الحسابات تبعتي عند خمسة و عشرين + +323 +00:24:26,680 --> 00:24:28,680 +ديجري ال C و عند + +324 +00:24:31,750 --> 00:24:36,210 +500 ديجري سي يعني 25 ديجري سي يعني 298 كيلوفر دلتا + +325 +00:24:36,210 --> 00:24:40,230 +جي نوت ساوية دلتا H معروفة للاتفاعل وحسبناها قبل + +326 +00:24:40,230 --> 00:24:48,990 +هيك minus 92.38 كيلوجول minus T 298 في ال Delta S + +327 +00:24:49,720 --> 00:24:56,180 +-183.10 J per Kelvin طبعاً بدي أحول ال J ل K J + +328 +00:24:56,180 --> 00:25:00,060 +فبقى أضرف واحد على ألف فتطلع عندي سالب تلاتة و + +329 +00:25:00,060 --> 00:25:02,720 +تلاتين و تلاتة و عشرة K J إذا أنا عند خمسة و عشرين + +330 +00:25:02,720 --> 00:25:08,240 +ديجري ال C كانت إيه؟ كانت spontaneous طيب عند خمس + +331 +00:25:08,240 --> 00:25:13,480 +ميةيعني سبعمية تلاتة سبعين كيلوفير من عوض هذه نفس + +332 +00:25:13,480 --> 00:25:16,100 +القيمة لحظة معايا لازم أنت خمسمية يعني عوض بال + +333 +00:25:16,100 --> 00:25:18,920 +Delta H تبعت الخمسمية و Delta S تبعت الخمسمية لكن + +334 +00:25:18,920 --> 00:25:23,080 +لا هو إيش جال جال إنه لأ تغيروا بالحرارة إذا أعوض + +335 +00:25:23,080 --> 00:25:27,100 +بال Delta H و Delta S بس هنغير درجة الحرارة جال + +336 +00:25:27,100 --> 00:25:31,060 +صارت واحد ستين كيلوجول موجة بقى إذن لما رفعنا + +337 +00:25:31,060 --> 00:25:35,760 +لخمسمية ديجريل C التفاعل اتحول من spontaneous إلى + +338 +00:25:35,760 --> 00:25:43,870 +non spontaneousالـ equilibrium temperature هي + +339 +00:25:43,870 --> 00:25:50,170 +Delta H على Delta S حسبناها 465 قبل شوية + +340 +00:25:58,610 --> 00:26:03,370 +هذه هي ال T حسبناها قبل قليل كمه تترازش ال + +341 +00:26:03,370 --> 00:26:09,690 +temperature قبلها تكون سالبة وبعدها تكون موجة بدل + +342 +00:26:09,690 --> 00:26:12,870 +جيوة وبالتالي قبلها تكون spontaneous قبل هذه + +343 +00:26:12,870 --> 00:26:15,930 +الحرارة وبعدها تكون non spontaneous + +344 +00:26:22,220 --> 00:26:26,660 +بسألنى كمان سؤال يعنى جميل احنا بنحاول نرسخ مفهوم + +345 +00:26:26,660 --> 00:26:31,200 +ايش يعنى transition temperature وقت ايش التفاعل + +346 +00:26:31,200 --> 00:26:33,240 +بيكون spontaneous وقت ايش التفاعل بيكون non + +347 +00:26:33,240 --> 00:26:37,460 +spontaneous فخلينى نطلع على حاجة بنشوفها كل يوم و + +348 +00:26:37,460 --> 00:26:41,220 +بنعرفها كويسفالسؤال if the conversion of liquid + +349 +00:26:41,220 --> 00:26:44,960 +water to water vapor at one atmosphere and mid + +350 +00:26:44,960 --> 00:26:48,040 +degree c يعني ال normal boiling point spontaneous + +351 +00:26:48,040 --> 00:26:50,860 +ولا non spontaneous ولا reversible؟ إيش بنجيب على + +352 +00:26:50,860 --> 00:26:53,800 +هذا السؤال لحظة درجة ما نحسب؟ إيش بنجيب على إيه؟ + +353 +00:26:53,800 --> 00:26:58,640 +هل تحول ال liquid water إلى water vapor عند واحد + +354 +00:26:58,640 --> 00:27:02,820 +أتمسفير و mid degree c؟ هل هو spontaneous ولا non + +355 +00:27:02,820 --> 00:27:05,060 +spontaneous ولا reversible؟ + +356 +00:27:07,320 --> 00:27:11,700 +أيش رأي الجماعة يعني؟ طبعا reversible لأنه + +357 +00:27:11,700 --> 00:27:13,940 +equilibrium عند 100 درجة هذه ال normal boiling + +358 +00:27:13,940 --> 00:27:19,660 +point ففي عندي equilibrium أكيد هو reversible يعني + +359 +00:27:19,660 --> 00:27:23,760 +احنا طيب خلينا نقول ان احنا يعني مش عارفين لكن هو + +360 +00:27:23,760 --> 00:27:28,860 +أعطانا ال delta HVAB 40.657 وطبعا ال delta HVAB + +361 +00:27:28,860 --> 00:27:32,100 +موجبة ليه؟ لأنه بدها .. اه كيف؟ + +362 +00:27:34,670 --> 00:27:42,470 +بنقدر نحسبها فهذه موجبة Delta S VAB طبعا يعني لما + +363 +00:27:42,470 --> 00:27:48,370 +نزيد درجة الحرارة فمعناه الكلام 108.96 هذي برضه + +364 +00:27:48,370 --> 00:27:52,250 +موجبة فبقول ال Delta G at mid degree C والله إذا + +365 +00:27:52,250 --> 00:27:55,950 +كانت سالبة يبقى spontaneous موجبة مانا spontaneous + +366 +00:27:55,950 --> 00:28:01,520 +صفرعن طريق الانعواض دلتا جي ات ميت ديجري سي تساوي + +367 +00:28:01,520 --> 00:28:08,300 +اربعين سيكس فايف سبن جول minus عند مية يعني تلت + +368 +00:28:08,300 --> 00:28:11,560 +مية تلت سبعين وخمس تعاش كيلوفين في one oh eight + +369 +00:28:11,560 --> 00:28:15,300 +point nine six جول per Kelvin اه بتحطين الصفر يعني + +370 +00:28:15,300 --> 00:28:18,840 +كلام reversibleبس هو اصلا .. يعني لازم نعرف انه + +371 +00:28:18,840 --> 00:28:21,000 +reversible بدون ما نعمل كل هذه العملية هذه لان + +372 +00:28:21,000 --> 00:28:24,440 +المي احنا متخلفين معاها جدا و بنعرف انه normal + +373 +00:28:24,440 --> 00:28:28,500 +boiling point لإنها عند واحد أتمسفير 100 ديجري + +374 +00:28:28,500 --> 00:28:31,460 +الـC فعند 100 ديجري الـC طبعا ال liquid water + +375 +00:28:31,460 --> 00:28:36,580 +بيكون in equilibrium مع ال water vaporفلازم نعرف + +376 +00:28:36,580 --> 00:28:40,060 +إنه reversible لكن على أي حال حسبنا و لجناه أيضا + +377 +00:28:40,060 --> 00:28:48,440 +صفر مدام صفر فهو ال conversion reversible طيب نفسه + +378 +00:28:48,440 --> 00:28:51,620 +بيقول is heating one mole of liquid water to one + +379 +00:28:51,620 --> 00:28:55,300 +hundred and ten degrees c will converted to water + +380 +00:28:55,300 --> 00:28:59,420 +vapor spontaneously or not؟برضه خدت السؤال انجاب + +381 +00:28:59,420 --> 00:29:02,440 +عليه بدون ما نعمل المثلة يعنى بدون ما نعمل المثلة + +382 +00:29:02,440 --> 00:29:11,080 +طبعا فهل تحويل واحد مول من ال liquid water اذا + +383 +00:29:11,080 --> 00:29:15,760 +كان سخناه ل110 degree c هل تحوله ل water vapor + +384 +00:29:15,760 --> 00:29:20,760 +spontaneous ولا non spontaneous اذا كان سخنا الميه + +385 +00:29:20,760 --> 00:29:26,280 +ل110 degree c spontaneous ولا مش spontaneous بتحول + +386 +00:29:26,280 --> 00:29:32,300 +ل vapor الميه بتحول ل vaporطبعا spontaneous طبعا + +387 +00:29:32,300 --> 00:29:36,200 +spontaneous أكيد أقل من مية ماهواش spontaneous فوق + +388 +00:29:36,200 --> 00:29:39,280 +ال .. بتلاقي water .. بتلاقي liquid water at مية و + +389 +00:29:39,280 --> 00:29:42,700 +عشرة degree c هل .. هل بنلاقي ال liquid water at + +390 +00:29:42,700 --> 00:29:46,720 +مية و عشرة degree c لحد الأقصى الهمية بس ال water + +391 +00:29:46,720 --> 00:29:49,480 +vapor اذا ال conversion لل liquid water إلى water + +392 +00:29:49,480 --> 00:29:51,820 +vapor عند مية و عشرة هذا spontaneous ال process + +393 +00:29:51,820 --> 00:29:55,580 +عند مية و عشرة spontaneous أكتر من مية spontaneous + +394 +00:29:55,580 --> 00:30:00,110 +أقل من مية لا ولا بنلاقي المية ميةLiquid water + +395 +00:30:00,110 --> 00:30:03,190 +liquid water لا جهاز جاز لا تتحول إلى جاز + +396 +00:30:03,190 --> 00:30:07,210 +spontaneously هذا كلام بسيط كتير هذا كلام كتير + +397 +00:30:07,210 --> 00:30:11,250 +بسيط is heating one mole of liquid water to 110 + +398 +00:30:11,250 --> 00:30:14,990 +degrees C will convert يعني حصل على الميه 110 + +399 +00:30:14,990 --> 00:30:20,170 +degrees C هل هذا هيحولها لواتر فيبر ولا لا سخنها + +400 +00:30:20,170 --> 00:30:23,450 +لأكتر من ال normal boiling point هل هتحولها لواتر + +401 +00:30:23,450 --> 00:30:26,730 +فيبر ولا لا طبعا هيتحول لواتر فيبر spontaneously + +402 +00:30:26,730 --> 00:30:33,330 +انتهينااستخدام دلتا H ودلتا S لا يتغيروا بشكل كبير + +403 +00:30:33,330 --> 00:30:37,490 +مع التمبراتور طيب ماعطينا دلتا H VAP و ماعطينا + +404 +00:30:37,490 --> 00:30:42,650 +دلتا S VAP تعالوا نحسب دلتا G at 110 degree C دلتا + +405 +00:30:42,650 --> 00:30:47,070 +H minus T دلتا S هناخد القيم عن 110 هي نفسها عند + +406 +00:30:47,070 --> 00:30:53,920 +25 degree Cدلتا اتش اربعين اربعين سيكس فايف سبن + +407 +00:30:53,920 --> 00:30:58,380 +جول يعني اجربناها في الف minus اه مية و عشرة مش + +408 +00:30:58,380 --> 00:31:01,260 +تلات مية و تلاتة و سبعين تلات مية و تلاتة و تمانين + +409 +00:31:01,260 --> 00:31:07,260 +صارتفى 108.63 ديلتا اصبحت سالبة ايش معناه انها + +410 +00:31:07,260 --> 00:31:09,960 +سالبة؟ يعني نعم التفاعل spontaneous او التغير مش + +411 +00:31:09,960 --> 00:31:14,820 +تفاعل التغير spontaneous طبعا لما ساخد الميه عند + +412 +00:31:14,820 --> 00:31:18,760 +اكتر من مية فهذا التغير spontaneous طب ايش بيحصل + +413 +00:31:18,760 --> 00:31:23,420 +لو is heating one mole of liquid water to 90 + +414 +00:31:23,420 --> 00:31:28,190 +degrees will convert water toVapor spontaneously + +415 +00:31:28,190 --> 00:31:32,310 +or not طبعا لا مش ممكن لأنه أقل من ال boiling + +416 +00:31:32,310 --> 00:31:36,110 +point أقل من ال boiling point بس لو مابعرفش حدّلنا + +417 +00:31:36,110 --> 00:31:39,810 +عليها الحسابات لو ماعرفش هذا الكلام حدّلنا علي + +418 +00:31:39,810 --> 00:31:42,810 +الحسابات برضه تقول لي assume ال delta H و ال delta + +419 +00:31:42,810 --> 00:31:45,890 +S do not change significantly وال temperature عشان + +420 +00:31:45,890 --> 00:31:49,430 +أستخدم ال delta H قيمتها عند 25 ديجري C و ال delta + +421 +00:31:49,430 --> 00:31:53,380 +S برضه قيمتها عند 25 ديجري C لإن أنا متوفرمتوفرة و + +422 +00:31:53,380 --> 00:31:56,560 +معايا في المسألة بيقول الـ delta G عن تسعين دجري + +423 +00:31:56,560 --> 00:31:59,620 +ال C بيساوي ال delta H minus T delta S ال delta G + +424 +00:31:59,620 --> 00:32:03,400 +عن تسعين دجري ال C بدها تساوي قيمة ال delta H + +425 +00:32:03,400 --> 00:32:07,620 +بالجول minus A تسعين يعني تلاتمية تلاتة و ستين + +426 +00:32:07,620 --> 00:32:11,500 +Kelvin مضروبة في مية و تمانية point nine six طبعا + +427 +00:32:11,500 --> 00:32:15,920 +الف و تمانية و تمانية جول positiveمعناته لأ و الله + +428 +00:32:15,920 --> 00:32:21,140 +مانفعش مش راح يتحول ال liquid water الى water + +429 +00:32:21,140 --> 00:32:26,300 +vapor مباشرة spontaneous دي عن 90 degree c لأ ده + +430 +00:32:26,300 --> 00:32:29,260 +كله مابحصلش هو هتبقى وضع طبيعي أقل من ال boiling + +431 +00:32:29,260 --> 00:32:33,500 +point ال liquid بتعمل liquid مابتحول كله لغاز فورا + +432 +00:32:33,500 --> 00:32:37,260 +أكبر من ال boiling point لأ و الله خلاص ال boiling + +433 +00:32:37,260 --> 00:32:39,900 +point فيه equilibrium بعد ال boiling point انتهينا + +434 +00:32:39,900 --> 00:32:44,420 +كله gas steam بخار water vapor + +435 +00:32:49,290 --> 00:32:52,390 +طب at what temperature will liquid water be at + +436 +00:32:52,390 --> 00:32:55,790 +equilibrium with water vapor؟ نعرف هذا الكلام، + +437 +00:32:55,790 --> 00:32:57,730 +liquid water بقى ال water vapor، عند أي + +438 +00:32:57,730 --> 00:33:03,190 +temperature؟ الهي 100، أكيد، أكيد هذا الكلام، بقول + +439 +00:33:03,190 --> 00:33:07,690 +inserting the values of delta H and delta S into + +440 +00:33:07,690 --> 00:33:11,310 +the definition of delta G لأنها بتدل equilibrium، + +441 +00:33:11,310 --> 00:33:16,030 +يفجأة ال delta G إيش هي تساوي؟ صفر، يفجأة ال delta + +442 +00:33:16,030 --> 00:33:21,400 +S هي تساوي ال Tالـ T تطلع تلات مئة و تلات سبعين و + +443 +00:33:21,400 --> 00:33:24,980 +خمس عشر اللي هي ايه؟ الـ Normal boiling point of + +444 +00:33:24,980 --> 00:33:29,700 +water one hundred degrees C تمام؟ طبعا هذا مضع + +445 +00:33:29,700 --> 00:33:35,880 +طبيعي لأن الـ Delta G بتسوء صفر الـ T بتسوء تلات + +446 +00:33:35,880 --> 00:33:38,040 +مئة و تلات سبعين و خمس عشر لإنها Normal boiling + +447 +00:33:38,040 --> 00:33:44,500 +point يعني عند واحد أتمسفير طب عن temperature أكتر + +448 +00:33:44,500 --> 00:33:48,290 +من تلات مئة و تلات سبعينجال ديلتا جيب تصير + +449 +00:33:48,290 --> 00:33:52,930 +negative لأنه أكتر من ال boiling point طب عند أجل + +450 +00:33:52,930 --> 00:33:57,590 +من 38 و 79 جال دلتا جيب تصير positive يعني أقل من + +451 +00:33:57,590 --> 00:34:00,630 +100 وأكتر من 100 كويس؟ زي ما شوفناها الأمثلة اللي + +452 +00:34:00,630 --> 00:34:05,500 +شوفناهاهذه بالظبط هي الكلام اللى بيحصل فوق المية + +453 +00:34:05,500 --> 00:34:08,800 +هاي المية هي ال transition temperature اللى هى ال + +454 +00:34:08,800 --> 00:34:11,860 +normal boiling point اللى هى ال equilibrium اللى + +455 +00:34:11,860 --> 00:34:19,720 +هى ال reversible conversion كويس اكتر منها اه ال + +456 +00:34:19,720 --> 00:34:23,640 +liquid ال water بتروح ل water vapor spontaneously + +457 +00:34:23,640 --> 00:34:27,600 +اقل منها لا والله ال liquid water لا يتحول الى + +458 +00:34:27,600 --> 00:34:35,100 +water vapor spontaneouslyطيب نتطلع على يمكن أخر + +459 +00:34:35,100 --> 00:34:44,440 +جزئية في هذا ال chapter تتعلق بال delta G تحديدا + +460 +00:34:44,440 --> 00:34:47,100 +يعني نتطلع على ال free energy و علاقتها بال + +461 +00:34:47,100 --> 00:34:49,960 +equilibrium ال free energy و علاقتها بال + +462 +00:34:49,960 --> 00:34:52,650 +equilibriumالـ Free Energy التي هي الـ Delta G + +463 +00:34:52,650 --> 00:34:57,950 +بتساوي الـ Delta G نوت زائد الـ RT لن لـ Q RT لن ل + +464 +00:34:57,950 --> 00:35:01,650 +Q إيش الـ Q هذه؟ الـ Q هي ال reaction quotient إيش + +465 +00:35:01,650 --> 00:35:07,270 +يعني ال reaction quotient؟ يعني لو عندي A NA زائد + +466 +00:35:07,270 --> 00:35:10,830 +MB + +467 +00:35:10,830 --> 00:35:13,350 +بتعطيلنا + +468 +00:35:18,030 --> 00:35:26,670 +xc زائد yd جالي q بتساوي زي ال equilibrium + +469 +00:35:26,670 --> 00:35:36,650 +constant مش بيفرق بينهم يعني حط c النواتج قص xd قص + +470 +00:35:36,650 --> 00:35:46,610 +y ع ال a قص n ال b قص amطب هذه يا أستاذ هي نفسها + +471 +00:35:46,610 --> 00:35:49,030 +ال equilibrium constant يا لأ ال equilibrium + +472 +00:35:49,030 --> 00:35:52,290 +constant هذه التركيزات بتكون هي التركيزات ال + +473 +00:35:52,290 --> 00:35:57,350 +equilibrium كويس ال Q ممكن تكون اكبر او تساوي او + +474 +00:35:57,350 --> 00:36:01,290 +اقل من ال K ال K هو ال equilibrium constant فعند + +475 +00:36:01,290 --> 00:36:10,000 +التركيزات وعند الاتزان اه هذه Kلكن اي تركيزات اخرى + +476 +00:36:10,000 --> 00:36:14,740 +اذا كانت مش عند الافادة بيقولها reaction quotient + +477 +00:36:14,740 --> 00:36:19,500 +يعني بس ال Q بتساوي K عند ايه؟ عند الاتزان يعني + +478 +00:36:19,500 --> 00:36:23,560 +بتساوي ال equilibrium constant فقط وقتاش جال عند + +479 +00:36:23,560 --> 00:36:29,560 +الاتزان فبس هذه الفكرةبدنا نعرف إن الـ delta G + +480 +00:36:29,560 --> 00:36:35,260 +بتساوي الـ delta G note زائد ال RT لـ Q في حالة ما + +481 +00:36:35,260 --> 00:36:41,010 +إنه نستخدم الـ standard stateالـStandard State + +482 +00:36:41,010 --> 00:36:44,650 +Concentrations كلها هي عبارة عن واحد مولار شوفنا + +483 +00:36:44,650 --> 00:36:48,510 +هذا في حصة سابقة الـStandard State بالنسبة للتركيز + +484 +00:36:48,510 --> 00:36:51,790 +هو ايه؟ واحد مولار لما يكون واحد مولار اوسع اش + +485 +00:36:51,790 --> 00:36:55,490 +مكان بيضلوا واحد في واحد على واحد في واحد يعني + +486 +00:36:55,490 --> 00:36:59,410 +واحد لـQ بتساوي واحد لإن الواحد جال صفر إذا + +487 +00:36:59,410 --> 00:37:02,250 +الـDelta G بتساوي الـDelta G Note يفجأت + +488 +00:37:02,250 --> 00:37:05,070 +الـStandard State الـDelta G بتساوي الـDelta G + +489 +00:37:05,070 --> 00:37:09,270 +Note لكن عند أي State غير الـStandard Stateالـ ΔG + +490 +00:37:09,270 --> 00:37:13,270 +بتساوي ΔG نوت زائد الـ RT لين الـ Q لكن عند الـ + +491 +00:37:13,270 --> 00:37:16,090 +Standard State لما كل التركيزات كانوا واحد معناته + +492 +00:37:16,090 --> 00:37:22,550 +لين الـ Q بصفر لأن الـ Q بتساوي واحد لكن إذا كان + +493 +00:37:22,550 --> 00:37:25,590 +عندي Standard State فالـ ΔG بتساوي الـ ΔG نوت + +494 +00:37:25,590 --> 00:37:28,870 +تعالوا نتطلع أيش اللي بيحصل بالظبط في أي تفاعل + +495 +00:37:28,870 --> 00:37:34,270 +كيميائي جال في عندي Reactants وفي عندي إبرادات + +496 +00:37:34,270 --> 00:37:41,220 +دائما في بينهم زي ال valleyبحيث انه لو سقط مثلا + +497 +00:37:41,220 --> 00:37:45,500 +حجر من الكرة نعتبر + +498 +00:37:45,500 --> 00:37:49,440 +وهي عمال نازلة لما توصل هنا خدوا بالكم ايش بتبتحك + +499 +00:37:49,440 --> 00:37:54,280 +تعمل؟ اه بتبتحرك حوالي ال ايه؟ ال valley هذا مكينه + +500 +00:37:54,280 --> 00:37:59,020 +equilibrium اتزان اتزان reversible اه Delta X + +501 +00:37:59,020 --> 00:38:02,540 +رايحة Delta X جاية reversible فهنا عندي + +502 +00:38:02,540 --> 00:38:08,770 +equilibriumهنا ال products وهنا ال reactants وهنا + +503 +00:38:08,770 --> 00:38:15,430 +طبعا يعني خليني اقول ال free energy فانا بقدر اقول + +504 +00:38:15,430 --> 00:38:19,810 +ان ال free energy دلتا جي بتسوي دلتا جي لل product + +505 +00:38:19,810 --> 00:38:23,620 +minus ال delta جي لل reactantsوبعدين بقول والله هل + +506 +00:38:23,620 --> 00:38:30,540 +هذا الكلام يعتبر موجب ولا سالب، إذا كان سالب فهو + +507 +00:38:30,540 --> 00:38:34,020 +spontaneous إذا كان .. يعني بيمشي في الاتجاه اللي + +508 +00:38:34,020 --> 00:38:37,800 +مكتوب، إذا كان موجب فلأ والله الاتجاه العكسي هو + +509 +00:38:37,800 --> 00:38:40,300 +اللي بيمشي فيه أو يعني بيكون spontaneous في + +510 +00:38:40,300 --> 00:38:48,200 +الاتجاه اللي مكتوب، مثلا عندي ال ..الأمونيا أي + +511 +00:38:48,200 --> 00:38:51,540 +اتفاعل يعني مش شرط الأمونيا فهي نفس الكلام هي + +512 +00:38:51,540 --> 00:38:54,920 +الفعل هدا ممكن تيجي هان يعني ممكن ييجي هيك والله + +513 +00:38:54,920 --> 00:38:58,080 +مثلا + +514 +00:38:58,080 --> 00:39:01,260 +هنا ال equilibrium يعني ممكن ييجي هيك هنا ال + +515 +00:39:01,260 --> 00:39:04,880 +equilibrium يعني مش شرط يعني انه دايما لا يعني ال + +516 +00:39:04,880 --> 00:39:07,940 +equilibrium ممكن وين مكان ييجي حسب المسألة اللي + +517 +00:39:07,940 --> 00:39:15,210 +عندي هلأ التوضيح موجود بالشكل اللي قدامي هالفال .. + +518 +00:39:15,210 --> 00:39:20,750 +في عندي هان عموما ال reactance معناته هي على سبيل + +519 +00:39:20,750 --> 00:39:27,510 +المثال ال nitrogen و ال oxygen و ال nitrogen مثلا + +520 +00:39:27,510 --> 00:39:31,830 +يعني هذه هي ان هذا هو ال nitrogen و هذا هو ال + +521 +00:39:31,830 --> 00:39:36,350 +hydrogen هذا هو ال hydrogen و هذا هو ال nitrogen + +522 +00:39:36,350 --> 00:39:40,730 +فهذه متفاعلة فشولاش هان عندي بس متفاعلة nitrogen و + +523 +00:39:40,730 --> 00:39:46,240 +hydrogenهن في عندى product معناته products أمونيا، + +524 +00:39:46,240 --> 00:39:50,600 +فالنص هن إيش في عندى؟ خلط اللي هو ال equilibrium، + +525 +00:39:50,600 --> 00:39:54,600 +خلط اللي هو ال equilibrium، بقول هن ال Q أقل من ال + +526 +00:39:54,600 --> 00:40:01,590 +K، هن ال Q أكبر من ال K، هن ال Q بتساوي ال Kيبقى + +527 +00:40:01,590 --> 00:40:08,010 +H9D ع جهة ال products ال Q أكبر من ال K إيش يعني + +528 +00:40:08,010 --> 00:40:14,770 +ال Q أكبر من ال K؟ يعني البست عندي أكبر من المقام، + +529 +00:40:14,770 --> 00:40:19,930 +أكبر من المقام، إذا؟ والله أه، بده يعني ال Q عندي + +530 +00:40:19,930 --> 00:40:24,110 +أكبر من ال K، البست أكبر من المقام، ال Q أقل من ال + +531 +00:40:24,110 --> 00:40:30,690 +Kالـ Q .. اه عندي انا ال ايه .. ال .. ال Q أقل من + +532 +00:40:30,690 --> 00:40:35,410 +ال K يعني عندي المقام أكبر من .. أكبر من ال bus طب + +533 +00:40:35,410 --> 00:40:38,930 +هو إيش المقام هان؟ المتفاعلات .. المتفاعلات عشان + +534 +00:40:38,930 --> 00:40:42,250 +هيك .. اه مدان المتفاعلات أكبر إذن بدها تروح ناحية + +535 +00:40:42,250 --> 00:40:45,990 +النواتج لإن هو عندي كمية كبيرة منها إذن هي التفاعل + +536 +00:40:45,990 --> 00:40:49,390 +رايح ناحية ال A رايح ناحية النواتج .. هان بالعكس + +537 +00:40:50,330 --> 00:40:55,670 +النواتج أكبر بتروح لحيط المتفاعلات spontaneously + +538 +00:40:55,670 --> 00:40:59,410 +فمعنى + +539 +00:40:59,410 --> 00:41:04,850 +الكلام سهل أنه نتوقع إيش اللي بيحصل عنا من الشكل + +540 +00:41:04,850 --> 00:41:09,550 +اللي جداميبقول تعالى نطلع على الأشكال التلاتة لما + +541 +00:41:09,550 --> 00:41:15,690 +يكون في عندنا ال Q أكبر من K و أقل من K و ال Q + +542 +00:41:15,690 --> 00:41:21,590 +بتساوي ال K فناخد جزء من العصابي مثلا ال + +543 +00:41:21,590 --> 00:41:26,450 +equilibrium اللي عندي فبقول لما ال delta G لل + +544 +00:41:26,450 --> 00:41:30,150 +products تكون أقل كتير من ال delta G لل reactants + +545 +00:41:30,150 --> 00:41:33,810 +هي delta G لل reactants هي delta G لل products أقل + +546 +00:41:33,810 --> 00:41:35,470 +كتير واضح انه + +547 +00:41:39,230 --> 00:41:43,130 +الـ Delta G Note هتكون Large Negative ليه؟ لأن الـ + +548 +00:41:43,130 --> 00:41:46,710 +Delta G Note هتكون لـ Products اللي هي القليلة، + +549 +00:41:46,710 --> 00:41:51,590 +قليلة كتير، minus ال reactants اللي هي كبيرة فمع + +550 +00:41:51,590 --> 00:41:54,430 +هذا الكلام Large Negative الـ Delta G Note is a + +551 +00:41:54,430 --> 00:41:58,810 +Large Negative Quantity and equilibrium is very + +552 +00:41:58,810 --> 00:42:01,730 +far to the right towards products يعني ال + +553 +00:42:01,730 --> 00:42:06,440 +equilibrium .. هلاحظ أنكم مش شايفين هذايعني هذا + +554 +00:42:06,440 --> 00:42:11,860 +عامل هيك، ماشي؟ فال equilibrium ايش ماله؟ احنا + +555 +00:42:11,860 --> 00:42:15,460 +قولنا .. شفتوا هذا الشكل؟ قولنا مش دايما بكون هيك، + +556 +00:42:15,460 --> 00:42:19,880 +ممكن يكون مشدود ناحية .. اه إذا كان .. إذا كان ال + +557 +00:42:19,880 --> 00:42:25,720 +delta G كانت very large negative value، معناته ال + +558 +00:42:25,720 --> 00:42:28,930 +equilibrium بيجرب ناحية ال productsالـ Equilibrium + +559 +00:42:28,930 --> 00:42:32,050 +بيجرب ناحية الـ Probats فالـ Δ G لـ Probats أقل + +560 +00:42:32,050 --> 00:42:37,210 +كتير من الـ Δ G لل Reactants إذاً الـ Δ G نوت هي + +561 +00:42:37,210 --> 00:42:43,310 +عبارة عن Large Negative Value، معناة وين الـ + +562 +00:42:43,310 --> 00:42:45,810 +Equilibrium جريب على ال Probats، لأنها Large + +563 +00:42:45,810 --> 00:42:49,010 +Negative، عكس هذا الكلام، و هذا الكلام طبعا احنا + +564 +00:42:49,010 --> 00:42:53,190 +ممكن نتخيله، بنقول وين الـ Q أقل من K، this means + +565 +00:42:53,190 --> 00:42:57,050 +that الـ Q أقل، معناته Reactants concentrations + +566 +00:42:57,050 --> 00:43:05,900 +are largeمدام كبير مدام كبير مدام كبير مدام كبير + +567 +00:43:05,900 --> 00:43:14,100 +مدام + +568 +00:43:14,100 --> 00:43:21,760 +كبير مدام + +569 +00:43:21,760 --> 00:43:28,100 +كبير مدام + +570 +00:43:28,100 --> 00:43:33,590 +كبيرهي هذا الشكل ال equilibrium وين هو؟ جريب على + +571 +00:43:33,590 --> 00:43:37,170 +ال reactance فهنر هاي ال reactance و هاي ال + +572 +00:43:37,170 --> 00:43:41,690 +products ال delta G ل products الكمية كبيرة minus + +573 +00:43:41,690 --> 00:43:46,770 +ال reactance كمية قليلة اذا large positive delta G + +574 +00:43:46,770 --> 00:43:51,410 +not is a large positive quantity and equilibrium + +575 +00:43:51,410 --> 00:43:56,020 +is very far to the leftيعني towards reactants جنب + +576 +00:43:56,020 --> 00:43:59,500 +ال reactants حلو هذا كلام طبعا هذا لما delta G + +577 +00:43:59,500 --> 00:44:02,420 +لproducts تكون أكبر كتير من delta G لل reactants + +578 +00:44:02,420 --> 00:44:07,060 +وهنا نفس المنطقة بنقول when Q أكبر من K this means + +579 +00:44:07,060 --> 00:44:12,260 +that product's concentrations are large and thus + +580 +00:44:12,260 --> 00:44:16,660 +reaction proceeds towards reactants formation عشان + +581 +00:44:16,660 --> 00:44:20,780 +هيك ال equilibrium بيكون قريب جدا من ال reactants + +582 +00:44:23,450 --> 00:44:27,530 +الحالة الأخيرة ان يكون حاجة هيك في النص زي اللي + +583 +00:44:27,530 --> 00:44:32,690 +شفناها سابقا يعني ها عندنا ال Q بتساوي ال K و ال + +584 +00:44:32,690 --> 00:44:37,130 +delta G ساعتها بدها تساوي صفر و ال delta G بدها + +585 +00:44:37,130 --> 00:44:40,890 +تساوي صفر ال delta G لل products بتساوي تقريبا ال + +586 +00:44:40,890 --> 00:44:45,990 +delta G لل reactants يعني بلاش الرسم هاتي مافيش + +587 +00:44:45,990 --> 00:44:48,410 +عندي رسمة لها مافيش عندي رسمة لها يعني بيكون اشي + +588 +00:44:48,410 --> 00:44:48,870 +زي هيك + +589 +00:44:54,450 --> 00:44:59,010 +حاجة زي هيك هي ال reactance إجراب على بعض كتير ف + +590 +00:44:59,010 --> 00:45:03,210 +ال delta G تقريبا تقريبا صفر ال delta G ل ال + +591 +00:45:03,210 --> 00:45:06,050 +product تقريبا صفر ال delta G لل reactance علشان + +592 +00:45:06,050 --> 00:45:11,230 +هيك بيقول ال equilibrium more towards the centerفى + +593 +00:45:11,230 --> 00:45:15,890 +النُص الـ center of the reaction profile when q is + +594 +00:45:15,890 --> 00:45:20,510 +equal to k this means that delta g بتساوي صفر and + +595 +00:45:20,510 --> 00:45:25,530 +delta g not بتساوي minus ال RT لإن ال K إذا كان ال + +596 +00:45:25,530 --> 00:45:30,730 +delta g بتساوي صفر فال delta g not من المعادلة + +597 +00:45:30,730 --> 00:45:36,790 +اللى بتقول delta g بتساوي delta g not minus ال RT + +598 +00:45:38,040 --> 00:45:44,260 +زائد ال RT لين ال Q فإذا كان ال Q هادى هي K ساعتها + +599 +00:45:44,260 --> 00:45:49,200 +بتكون هادة صفر Delta G not بدها تساوي زائد ال RT + +600 +00:45:49,200 --> 00:45:54,190 +لينالـ K إذا كان هذا صفر فالـ Δ G نوت تسوى minus + +601 +00:45:54,190 --> 00:45:59,870 +ال RT لإن ال K وبهذه الطريقة ممكن طبعا Delta G نوت + +602 +00:45:59,870 --> 00:46:04,530 +نعرف نحسبها كويس من Delta G نوت F من ال Delta H + +603 +00:46:04,530 --> 00:46:08,550 +minus Delta T Delta F عدة طرق لحساب ال Delta G إذا + +604 +00:46:08,550 --> 00:46:11,450 +مدين باعرف أحسب Delta G نوت إذا إيش مقدر أعرف + +605 +00:46:11,450 --> 00:46:15,130 +أحسب؟بقدر احسب الكائن equilibrium constant للتفاعل + +606 +00:46:15,130 --> 00:46:19,290 +وهذا اشي يعتبر جوهري جدا في الكيميا يعني يعتبر + +607 +00:46:19,290 --> 00:46:24,630 +حاجة جوهرية جدا كيف نعرف نحسب ال equilibrium + +608 +00:46:24,630 --> 00:46:33,900 +constant هذه بعض قيم الدلتا جي نوت والإيقاليبريام + +609 +00:46:33,900 --> 00:46:39,420 +constants 298 لحظة إذا كان الإيقاليبريام constants + +610 +00:46:39,420 --> 00:46:43,060 +يجب أن يكون واحد فدلتا جي نوت على طول بس هو صفر + +611 +00:46:43,060 --> 00:46:50,320 +لأنه minus RT لن ال K لما ال K سوى واحد دلتا جي + +612 +00:46:50,320 --> 00:46:56,970 +نوتتساوى minus ال R T لن ال K لما ال K ساوى واحد + +613 +00:46:56,970 --> 00:47:00,330 +معناته الدلتاجينوتر على طول هتساوى الصفر لكن + +614 +00:47:00,330 --> 00:47:06,060 +لاحظوا كل ما زاد ال Kأه لما نزيد ال K، ال delta G + +615 +00:47:06,060 --> 00:47:09,360 +ايش بيجرالها؟ بتقلل، يعني بتصير اتفاعل more + +616 +00:47:09,360 --> 00:47:13,800 +spontaneous، اتفاعل يعني بيمشي لليمين بشكل أكبر، + +617 +00:47:13,800 --> 00:47:17,260 +ليش؟ لأنه عندنا minus RT لإن ال K لما هذا يكون + +618 +00:47:17,260 --> 00:47:20,860 +كبير، يعني وهذا سالب، بعد كل هذا قيمة أكبر + +619 +00:47:20,860 --> 00:47:24,960 +بالسالب، قيمة أكبر بالسالب، عكس هذا الكلام، لو كان + +620 +00:47:24,960 --> 00:47:30,190 +أقل من واحدهن واحد زود واحد كان صفر زودنا عن + +621 +00:47:30,190 --> 00:47:34,890 +الواحد اه قلت كتير ال delta G Note طب قللنا عن + +622 +00:47:34,890 --> 00:47:40,850 +واحد بنلاحظ انه بتتحول لايه لقيمة موجبة بيصير انه + +623 +00:47:40,850 --> 00:47:45,470 +التفاعل والله مش spontaneous صعب جدا يمشي لليامين + +624 +00:47:51,110 --> 00:47:55,910 +نفس المنطقي يعني هان ال K أكبر من واحد لإن ال K + +625 +00:47:55,910 --> 00:47:58,950 +Positive Delta G Not Negative ال products are + +626 +00:47:58,950 --> 00:48:04,870 +favored K بتساوى واحد لإن ال K صفر Delta G Not صفر + +627 +00:48:04,870 --> 00:48:09,430 +ال products and reactants في equilibrium أقل من + +628 +00:48:09,430 --> 00:48:15,830 +واحد لإن ال K Negative Delta G Not Positiveالـ + +629 +00:48:15,830 --> 00:48:20,870 +Reactance are favored برضه كلام مفهوم جدا.الان + +630 +00:48:20,870 --> 00:48:26,730 +اجمالا بقول ال criteria for the spontaneity of a + +631 +00:48:26,730 --> 00:48:30,630 +process as written يعني التفاعل زي ما هو مكتوب أو + +632 +00:48:30,630 --> 00:48:35,150 +التغير زي ما هو مكتوب ايش ال criteria المعايير انه + +633 +00:48:35,150 --> 00:48:37,950 +والله يكون هل هو spontaneous ولا لأ؟بنقول اذا + +634 +00:48:37,950 --> 00:48:41,830 +كانوا spontaneous ال delta S لل universe لازم تكون + +635 +00:48:41,830 --> 00:48:46,430 +اكبر من صفروهذا نص القانون التاني للـ + +636 +00:48:46,430 --> 00:48:49,310 +Thermodynamics إذا كان التفاعل spontaneous أو + +637 +00:48:49,310 --> 00:48:54,730 +البروسيس spontaneous لازم الـ delta S للكون تكون + +638 +00:48:54,730 --> 00:48:59,630 +أكبر من صفر أو إن الـ delta G للsystem للتفاعل + +639 +00:48:59,630 --> 00:49:07,170 +تكون سالبة أقل من صفر أو حاجة جديدة الـ Q تكون أقل + +640 +00:49:07,170 --> 00:49:12,750 +من Kأقل من K يعني high reactance concentration + +641 +00:49:12,750 --> 00:49:15,930 +يعني هتروح لحيط ال products is spontaneous أي + +642 +00:49:15,930 --> 00:49:21,270 +واحدة من هدول بتخلي التفاعل spontaneous أي واحدة + +643 +00:49:21,270 --> 00:49:23,470 +منهم بتخلي التفاعل spontaneous هاي ال criteria هاي + +644 +00:49:23,470 --> 00:49:26,550 +المعايير ال equilibrium ايش معاير و جال والله ب + +645 +00:49:26,550 --> 00:49:30,290 +delta S للuniversة تكون صفر حلو إذا كانت delta S + +646 +00:49:30,290 --> 00:49:34,570 +للuniversة لأي system لأي system يعني في النهاية + +647 +00:49:34,570 --> 00:49:40,500 +لأي تغير صفر معناته عندي equilibriumإذا كان الـ + +648 +00:49:40,500 --> 00:49:45,040 +Delta G للـ system صفر، طبعا أيضا إيقاليبريان، إذا + +649 +00:49:45,040 --> 00:49:48,960 +كان الـ Q بتساوي الـ K، أكيد إيقاليبريان، ماشي يا + +650 +00:49:48,960 --> 00:49:51,420 +جماعة، طب الـ non spontaneity أو الـ non + +651 +00:49:51,420 --> 00:49:54,160 +spontaneous change، بقول إذا كان الـ Delta S في + +652 +00:49:54,160 --> 00:49:58,390 +الunivers أقل من صفر، هذا non spontaneousإذا كان + +653 +00:49:58,390 --> 00:50:02,130 +الـDelta G للـsystem أكبر من صفر موجبة، non + +654 +00:50:02,130 --> 00:50:04,890 +spontaneous، إذا كان الـQ أكبر من الـK، يعني + +655 +00:50:04,890 --> 00:50:07,210 +الـhigh product concentration، يبقى لازم تذهب حياة + +656 +00:50:07,210 --> 00:50:11,310 +الـreactants، فهذا non spontaneous، as what؟ as + +657 +00:50:11,310 --> 00:50:16,010 +written، كما هو مكتوب، يعني زي ما هو التفاعل مكتوب + +658 +00:50:16,010 --> 00:50:20,230 +عندي، فهذه حاجات أساسية بتلخص الكلام اللي قلناه + +659 +00:50:20,230 --> 00:50:24,330 +تقريبا من بداية ال chapter هذا فيما يتعلق بال + +660 +00:50:24,330 --> 00:50:28,840 +spontaneityبقول what is the criteria for + +661 +00:50:28,840 --> 00:50:33,160 +spontaneity in terms of entropy and in terms of + +662 +00:50:33,160 --> 00:50:38,240 +free energy وماعطينا خيارات نقرأهم من تحت the + +663 +00:50:38,240 --> 00:50:43,920 +entropy of the universe decreases violation مخالفة + +664 +00:50:43,920 --> 00:50:49,720 +ممكن يعني ال entropy of the universe decreases لأ + +665 +00:50:49,720 --> 00:50:52,880 +هذا مش spontaneous إذا أول واحدة عرفه المجرمة كان + +666 +00:50:52,880 --> 00:50:57,740 +بالغلطغلط لإيه؟ لأن ال spontaneity .. هذا إيه؟ إيش + +667 +00:50:57,740 --> 00:51:00,960 +ال entropy لل universe؟ آه لازم يكون الأكبر من صفر + +668 +00:51:00,960 --> 00:51:06,000 +.. decreases لأ .. طيب قال لي قبلها .. the entropy + +669 +00:51:06,000 --> 00:51:10,300 +of the system increases .. مالوش دعوة ال system .. + +670 +00:51:10,300 --> 00:51:13,540 +أنا بد إيه؟ ال universe .. إذا برضه مالوش دعوة + +671 +00:51:13,540 --> 00:51:17,300 +فيها .. the entropy of the system decreases .. + +672 +00:51:17,300 --> 00:51:20,160 +مالوش دعوة فيها .. الأصل مالوش دعوة فيها .. أنا بد + +673 +00:51:20,160 --> 00:51:21,320 +ال universe .. + +674 +00:51:32,440 --> 00:51:42,040 +الخيار الأول هو الخيار الصحيح لو كملته ستجد حلل في + +675 +00:51:42,040 --> 00:51:45,560 +الـ free energy + +676 +00:51:49,380 --> 00:51:53,240 +بال انتروبي الانتروبي لازم يقول ان الانتروبي للكون + +677 +00:51:53,240 --> 00:51:56,880 +بتزيد عشان التفاعل يكون spontaneous مجلليش انها + +678 +00:51:56,880 --> 00:52:01,160 +بتزيد خلاص مقدرش احكم لان الانتروبي لل system جلت + +679 +00:52:01,160 --> 00:52:04,020 +ولا لأ بهمنيش لان ال surroundings حاجة تانية خلاص + +680 +00:52:04,020 --> 00:52:07,860 +مجبليش threat انا مانفعش لازم مجموعهم هو المهم + +681 +00:52:07,860 --> 00:52:11,560 +اللي هو ال delta S لل universe لازم يكون اكتر من + +682 +00:52:11,560 --> 00:52:16,920 +واحد يعني قيمة موجبة اكتر من صفر قيمة موجبة + +683 +00:52:19,690 --> 00:52:23,670 +بنطلع على المثال التالي بيقول the normal boiling + +684 +00:52:23,670 --> 00:52:29,000 +point of benzene is 80 degrees c نقطةو هان بقى + +685 +00:52:29,000 --> 00:52:33,260 +اقولكم انه كان في خطأ في ال notes اللى معاكم اللى + +686 +00:52:33,260 --> 00:52:36,840 +موجودة على الصفحه انا هغيرها يعنى فاطلعوا على ال + +687 +00:52:36,840 --> 00:52:39,800 +notes اللى هنزلها اليوم اذا الله راد معاكي notes + +688 +00:52:39,800 --> 00:52:43,760 +بس راجعي و صلح الأخطاء و قدامت و اقرت بعض ال + +689 +00:52:43,760 --> 00:52:47,400 +slides اللى جيتها افضل يعنى فانا بفضل دائما انه + +690 +00:52:47,400 --> 00:52:51,300 +تاخد ال slides بعد ما اخلص انا شريحفكل ال slides + +691 +00:52:51,300 --> 00:52:54,800 +اللي عندك على الصفحة الان مناسبة وكويسة كتير + +692 +00:52:54,800 --> 00:52:58,580 +للدراسة لو عندك حاجة قديمة ممكن تتخلص منها ويمكن + +693 +00:52:58,580 --> 00:53:02,260 +تكون أفضل على أي حال بيقول طب at one hundred + +694 +00:53:02,260 --> 00:53:06,720 +degrees c and واحد atmosphere which is greater in + +695 +00:53:06,720 --> 00:53:11,420 +magnitude for the vaporization of benzene دلتا H + +696 +00:53:11,420 --> 00:53:17,920 +ولا T دلتا S أنهي أكبر في القيمة دلتا H ولا T دلتا + +697 +00:53:17,920 --> 00:53:21,420 +Sخدوا بالكم هو اين بيغلي النورة الـ boiling point + +698 +00:53:21,420 --> 00:53:30,800 +اين؟ عند 80 فهو بيسأل عند 100 ان هو اكبر delta H + +699 +00:53:30,800 --> 00:53:38,000 +ولا delta S ومعطيني خيارات بقول delta H بالساوية T + +700 +00:53:38,000 --> 00:53:39,560 +delta S هدولة at equilibrium + +701 +00:53:42,560 --> 00:53:46,540 +يا هادي يا هادي يا ماء الأخيرة ايش اللي انا بقوله + +702 +00:53:46,540 --> 00:53:50,380 +انا بقوله because at one hundred degree c the + +703 +00:53:50,380 --> 00:53:53,840 +vaporization of benzene is spontaneous و هذا وضع + +704 +00:53:53,840 --> 00:53:56,540 +طبيعي لأنه عند مقاس كان عند تمانين ال boiling + +705 +00:53:56,540 --> 00:54:00,660 +point فعند مية الاصل انه spontaneous بتحول + +706 +00:54:00,660 --> 00:54:07,280 +spontaneous للجاز بقول the term minus T delta S + +707 +00:54:07,280 --> 00:54:13,140 +should have a more negative valueعشان هو بتحول + +708 +00:54:13,140 --> 00:54:17,580 +لناس فهذا ال term لازم ي .. لأنه ال delta S موجبة + +709 +00:54:19,090 --> 00:54:26,350 +كويس فبده يتحول ايه ل more negative value minus T + +710 +00:54:26,350 --> 00:54:29,830 +delta S the term minus T delta S should have a + +711 +00:54:29,830 --> 00:54:33,330 +more negative value than the positive delta H VAP + +712 +00:54:33,330 --> 00:54:37,490 +ليه؟ لأن التحويل من liquid إلى vapor معناته ال + +713 +00:54:37,490 --> 00:54:40,950 +delta H هذي VAP اللي هي positive positive value + +714 +00:54:40,950 --> 00:54:45,630 +فهنا عندنا لأنه spontaneous فال delta G يجب أن + +715 +00:54:45,630 --> 00:54:48,960 +تكون negativeطب مقتش بتكون negative جال لما انها + +716 +00:54:48,960 --> 00:54:52,340 +ده السالب يكون اكبر، يبقى ال T Delta S هي اللي + +717 +00:54:52,340 --> 00:54:57,260 +اكبر من ال Delta H عشان النتيجة ايش تكون؟ سالبة، + +718 +00:54:57,260 --> 00:55:01,000 +اه يبقى الخيار التاني هو اللي صح الخيار هذا أكيد + +719 +00:55:01,000 --> 00:55:01,500 +خطأ + +720 +00:55:04,160 --> 00:55:07,780 +شوفنا يعني هذا الكلام شوفنا ان الـ delta G بتساوي + +721 +00:55:07,780 --> 00:55:13,600 +الـ delta G not زاد ال RT لن ال Q وشوفنا ان وقت + +722 +00:55:13,600 --> 00:55:17,880 +ايقاليبرام Q بتساوي K و Delta G بتساوي صفر و ال + +723 +00:55:17,880 --> 00:55:21,120 +equation بتتحول ل delta G not بتساوي minus RT لن + +724 +00:55:21,120 --> 00:55:27,580 +ال K او ال K بتساوي E أس سالب delta G not على ال + +725 +00:55:27,580 --> 00:55:33,990 +RT و هان ممكن نحسب ال K فخلينا نحسب ال Kخلّيني + +726 +00:55:33,990 --> 00:55:38,150 +أحسب الـK لأ بدّوش أحسب الـK هن بعد بشوية بحسب + +727 +00:55:38,150 --> 00:55:42,230 +الـK مش مشكلة بيقول calculate ΔG at 298 Kelvin for + +728 +00:55:42,230 --> 00:55:46,630 +the reaction below where one atmosphere nitrogen + +729 +00:55:46,630 --> 00:55:51,830 +تلاتة atmosphere H2 and one atmosphere in H3 are + +730 +00:55:51,830 --> 00:55:56,870 +present in the mixture ΔG نوت at 298 Kelvin متساوي + +731 +00:55:56,870 --> 00:56:01,330 +سالم 33.3 كيلوجول اللي متعودين عليها شفناها كتير + +732 +00:56:01,330 --> 00:56:05,320 +شفنا الرقم هذا بشكل كبيرالـ Q بتساوي تركيزات + +733 +00:56:05,320 --> 00:56:08,920 +النواتج على تركيزات المتفاعلات، كل تركيز مرفوع + +734 +00:56:08,920 --> 00:56:15,020 +لقصم عرض الملات، لكن لما تكون في عندي غازات فعارة + +735 +00:56:15,020 --> 00:56:18,610 +بدل التركيز بحط ال pressureفال pressure للأمونيا + +736 +00:56:18,610 --> 00:56:21,970 +تربيع على ال pressure للهيدروجين قص تلاتة ل + +737 +00:56:21,970 --> 00:56:24,990 +pressure للهيدروجين قص واحد يبقى اذا كان عندي + +738 +00:56:24,990 --> 00:56:31,970 +pressures فبقى احط ال pressures بدل التركيزات ال Q + +739 +00:56:31,970 --> 00:56:35,170 +بتطلع عندي تلاتة سبعة فعشرة قص سالب اتنين ال delta + +740 +00:56:35,170 --> 00:56:40,290 +G بتساوي delta G not زاد ال RT لن لQ + +741 +00:56:46,070 --> 00:56:48,570 +بعطينا الـ delta Gnot سالب تلاتة و تلاتين و تلاتة + +742 +00:56:48,570 --> 00:56:50,490 +من عشرة و بعوض عنها سالب تلاتة و تلاتين و تلاتة من + +743 +00:56:50,490 --> 00:56:55,410 +عشرة زائد ال R هنا يا جماعة لازم نعوض عنها بالجول + +744 +00:56:55,410 --> 00:57:00,550 +لأن هذه بالجول في معناه كلام 8.314 مش point O + +745 +00:57:00,550 --> 00:57:04,370 +eight one فاحنا جولنا لما نكون وحدات طاقة بنعوض عن + +746 +00:57:04,370 --> 00:57:09,070 +ال R ب 8.314 في 288 لين ل Q + +747 +00:57:11,770 --> 00:57:17,090 +بينطلع عند دلتا جي سالب واحد واربعين ونص يعني عند + +748 +00:57:17,090 --> 00:57:20,710 +هذه التركيزات برضه عند دلتا جي سالب يعني التفاعل + +749 +00:57:20,710 --> 00:57:28,350 +spontaneous لليمين يعني راح يتكون عند أمونيابقول + +750 +00:57:28,350 --> 00:57:31,390 +لهان تطبيق على الكلام اللي ذكرته في ال slide + +751 +00:57:31,390 --> 00:57:35,190 +الماضية بقول calculate the equilibrium constant Kp + +752 +00:57:35,190 --> 00:57:40,010 +at 25 degree C for the reaction اتنين H2O liquid + +753 +00:57:40,010 --> 00:57:45,930 +بتحول لاتنين H2 gas زائد O2 gas هل عمرنا شفنا انه + +754 +00:57:45,930 --> 00:57:49,030 +الميه بتتحول لH2O2؟ + +755 +00:57:52,160 --> 00:57:56,600 +ولا كان فيش ميه، فيش liquid water، بتتحولش يعني، + +756 +00:57:56,600 --> 00:57:59,380 +بتتحولش، عشان هيك هالاجى ان ال equilibrium + +757 +00:57:59,380 --> 00:58:03,900 +constant تتوقع يكون قيمة كبيرة ولا قيمة قليلة جدا، + +758 +00:58:03,900 --> 00:58:08,880 +اذا كانت بتتحولش، فنتوقع ان النواتج تكون كبيرة ولا + +759 +00:58:08,880 --> 00:58:14,200 +مهمة لاهتكون قليلة كتير ال equilibrium constant + +760 +00:58:14,200 --> 00:58:17,740 +هتكون قليل جدا ال equilibrium constant هتكون قليل + +761 +00:58:17,740 --> 00:58:22,940 +جدا فال delta G not لل reaction معطينه هو delta G + +762 +00:58:22,940 --> 00:58:27,720 +not F لل H2O liquid دلتا G not F لل H2و دلتا G not + +763 +00:58:27,720 --> 00:58:31,040 +F لل O2و في الامتحان ماعطينيش هدول التنتين لا لل + +764 +00:58:31,040 --> 00:58:34,820 +O2 ولا لل H2و لأنهم معروفين ان هو أصفر Delta G not + +765 +00:58:34,820 --> 00:58:40,170 +F Delta H not F لكن ال S not لأالـ S0 بتكون A + +766 +00:58:40,170 --> 00:58:46,910 +بتكون صفر بس at 0 Kelvin للـ Pure Crystalline .. + +767 +00:58:46,910 --> 00:58:50,730 +Perfectly Crystalline Substances لكن هنا Delta G0 + +768 +00:58:50,730 --> 00:58:54,370 +F و Delta H0 F على طول أصفار هدول فالـ Delta G0 لل + +769 +00:58:54,370 --> 00:58:59,730 +reaction بتساوي N نواتج أصفار minus اتنين فبتطلع + +770 +00:58:59,730 --> 00:59:02,910 +أربعمية أربعة سبعين وأربعة من عشرة ال Delta G0 لل + +771 +00:59:02,910 --> 00:59:07,960 +reaction minus RT لإن ال Kأذا بنعود تعويض مباشر + +772 +00:59:07,960 --> 00:59:13,340 +بيطلع عند ال K 7 في 10 أقل سالب 84 اللي بتطلع عليه + +773 +00:59:13,340 --> 00:59:15,720 +و اللي بعرف شوية كيميا بيعرف أن هذا يعني شبه + +774 +00:59:15,720 --> 00:59:19,260 +مستحيل حتى ال calculator ده بيعرف يحسبه مابيحصلش + +775 +00:59:19,260 --> 00:59:27,260 +يعني مابيحصل نهائيا قليل جدا جدانطلع على أيضا مثال + +776 +00:59:27,260 --> 00:59:30,940 +آخر لحساب الـ K بيقول الـ standard free energy + +777 +00:59:30,940 --> 00:59:34,820 +change for the hyper process is سالب تلاتة و + +778 +00:59:34,820 --> 00:59:37,660 +تلاتين point three kilo joule per mole دلتا جي نوت + +779 +00:59:37,660 --> 00:59:40,760 +سالب تلاتة و تلاتين point three kilo joule per + +780 +00:59:40,760 --> 00:59:43,780 +mole نفس السؤال اللي مانعناه سابقا لكن هان بده + +781 +00:59:43,780 --> 00:59:47,940 +يحسبقيمة ال equilibrium constant بيقول use this + +782 +00:59:47,940 --> 00:59:51,140 +value of delta G not to calculate the equilibrium + +783 +00:59:51,140 --> 00:59:56,580 +constant for the process فال K بعرف بتسوي E أسالب + +784 +00:59:56,580 --> 01:00:01,660 +delta G not على ال RT بعوض K بتسوي E أسالب delta G + +785 +01:00:01,660 --> 01:00:06,270 +not هذا هيسالب تلاتة و تلاتين point three kilo + +786 +01:00:06,270 --> 01:00:09,110 +joule او تلاتة و تلاتين الف و تلات مية joule per + +787 +01:00:09,110 --> 01:00:15,690 +mole على ال R eight point three one four joule per + +788 +01:00:15,690 --> 01:00:20,750 +mole per Kelvin مضروبة في RT مضروبة في 298 بطلع + +789 +01:00:20,750 --> 01:00:26,170 +سبعة في عشر أقص خمسة سبعة في عشر أقص خمسة بدي اكم + +790 +01:00:26,170 --> 01:00:31,330 +اتلاحظوا لهذا التفاعلأيش عمال بيحصل في ال + +791 +01:00:31,330 --> 01:00:34,490 +equilibrium constant؟ عند 300 كان عشر أقل سالب + +792 +01:00:34,490 --> 01:00:39,250 +تلاتة، عند 400 كان عشر أقل سالب أربعة، عند 450 عشر + +793 +01:00:39,250 --> 01:00:42,950 +أقل سالب خمسة، عند 550 عشر أقل سالب خمسة أقل، عند + +794 +01:00:42,950 --> 01:00:46,550 +550 عشر أقل سالب ستة، عند 600 عشر أقل سالب ستة + +795 +01:00:46,550 --> 01:00:50,290 +أقل، أيش بيحصل؟ عمال كل ما رفعنا درجة الحرارة، أيش + +796 +01:00:50,290 --> 01:00:54,460 +بيحصل ال equilibrium constant؟ بيقل يعنيتكون + +797 +01:00:54,460 --> 01:01:00,800 +النواتج بيقل يعني التفاعل non spontaneous بعد + +798 +01:01:00,800 --> 01:01:08,020 +الاربعمية و خمسة و ستين بيصير non spontaneous فهو + +799 +01:01:08,020 --> 01:01:11,620 +كل ما رفعنا الحرارة بيصير more non spontaneous + +800 +01:01:11,620 --> 01:01:13,980 +يعني ال equilibrium constant بيروح ناحية + +801 +01:01:13,980 --> 01:01:18,060 +المتفاعلات مش النواتج لكن زي ما ذكرت يعني هذي مش + +802 +01:01:18,060 --> 01:01:24,000 +كل الجثة يعنياحنا بنستخدم فى الحقيقة للهبر process + +803 +01:01:24,000 --> 01:01:30,300 +بنستخدم high temperature حوالى يمكن فوق ال 400 + +804 +01:01:30,300 --> 01:01:34,360 +درجة وبنستخدم very high pressures وقول ده ليش ال + +805 +01:01:34,360 --> 01:01:38,420 +very high pressures بتجبر المتفاعلات تتحول إلى + +806 +01:01:38,420 --> 01:01:41,720 +نواتج لأنه ال pressure تبع النواتج أقل من + +807 +01:01:41,720 --> 01:01:47,160 +المتفاعلات وبرضه ممكن يعنى الناس تفكر بطرق تانية + +808 +01:01:47,700 --> 01:01:52,940 +يعني حتى لو كان التفاعل بمشيش للأمام كتير، لكن + +809 +01:01:52,940 --> 01:01:58,220 +يعني حسب قاعدة لوتشاتليه احنا ما ذكرناهاش، يعني لو + +810 +01:01:58,220 --> 01:02:03,240 +باستمرار أخدنا النواتج، فبنجبر التفاعل يمشي برضه + +811 +01:02:03,240 --> 01:02:09,760 +للأمام، فمش كل الجثة، بس جداش الحرارة بتأثر على ال + +812 +01:02:09,760 --> 01:02:14,500 +equilibrium constant، لأ في عوامل تانية يعني مهمة + +813 +01:02:15,300 --> 01:02:20,920 +ولكن كcalculations وكاستفادة من تأثير الحرارة على + +814 +01:02:20,920 --> 01:02:25,620 +ال spontaneity أو delta G فهذا شيء واضح، يعني لا + +815 +01:02:25,620 --> 01:02:31,660 +يستطيع انكاره أي إنسانممكن تبعا نحسب الـ Delta G + +816 +01:02:31,660 --> 01:02:36,160 +under non-standard conditions بس كان ماعنديش + +817 +01:02:36,160 --> 01:02:40,240 +standard conditions فبيقول ال calculate Delta G at + +818 +01:02:40,240 --> 01:02:45,780 +298 Kelvin for a mixture of مش K لأ أي قيم أي قيم + +819 +01:02:45,780 --> 01:02:49,300 +زي المثال اللي أخدناه أول مثال mixture of واحد + +820 +01:02:49,300 --> 01:02:55,000 +أتمسفير ناتروجين تلاتة أتمسفير H2 نص أتمسفيرأو + +821 +01:02:55,000 --> 01:02:57,440 +غيروا هدول زي ما بدكم هدى اسمها non standard + +822 +01:02:57,440 --> 01:03:01,080 +conditions غيروا هدى ال pressure زي ما بدكم هدى + +823 +01:03:01,080 --> 01:03:05,420 +اسمها non standard conditions being used in the + +824 +01:03:05,420 --> 01:03:08,520 +hyper process provided ده delta G not سالب تلاتة و + +825 +01:03:08,520 --> 01:03:10,680 +تلاتين و تلاتة و عشرة كيلوجول per mole and Q + +826 +01:03:10,680 --> 01:03:13,760 +بتساوي تسعة و تلاتة فعشرة او سالب تلاتة هو حسب ال + +827 +01:03:13,760 --> 01:03:19,800 +Q لهدول أمونيا تربية على ال H أُس تلاتة في ال + +828 +01:03:19,800 --> 01:03:23,280 +نيتروجينالـ Pressures تبعتهم فبيقول الـ Delta U + +829 +01:03:23,280 --> 01:03:27,580 +سوى Delta G Note زائد الـ RT لإن الـ Q minus 37.3 + +830 +01:03:27,580 --> 01:03:35,280 +kilojoule per mole زائد الـ R في الـ T حولنا الـ R + +831 +01:03:35,280 --> 01:03:41,080 +من جول لكيلوجول لإن الـ Q تمام فبيطلع عندى سالب 44 + +832 +01:03:41,080 --> 01:03:51,410 +.9 هو نفس القيمة لأ هذه كانت واحد أتمسفيرخلّينها + +833 +01:03:51,410 --> 01:03:54,570 +نص اللي هي ال ammonia فتغير طبعا تغيرت القيمة لكن + +834 +01:03:54,570 --> 01:03:57,710 +إذا كان شفته كيف اتغيرت؟ اتغيرت الأمور negative + +835 +01:03:57,710 --> 01:04:05,350 +سالم مثلا 1.4 فتغير ال .. خلّيني أقول الظروف بتغير + +836 +01:04:05,350 --> 01:04:07,870 +قيمة ال delta G أيضا + +837 +01:04:15,090 --> 01:04:18,390 +يعني الـ Larger value للـ Delta G بتقول والله ال + +838 +01:04:18,390 --> 01:04:22,190 +driving force لتكوين الأمونيا بتزيد + +839 +01:04:24,460 --> 01:04:27,460 +يبقى هذه هي الـ delta G equations ممكن نقول والله + +840 +01:04:27,460 --> 01:04:31,540 +الـ delta G not minus RT لن ال Q طبعا لأن ال K at + +841 +01:04:31,540 --> 01:04:36,140 +equilibrium لأن ال Q بتساوي ال K او بتساوي delta H + +842 +01:04:36,140 --> 01:04:40,220 +not minus T delta S not او بتساوي ال delta G minus + +843 +01:04:40,220 --> 01:04:43,860 +RT لن ال Q لأن ال delta G بتساوي delta G not زاد + +844 +01:04:43,860 --> 01:04:47,940 +ال RT لن ال Q فأنا بتبني المعادلة او بتساوي + +845 +01:04:47,940 --> 01:04:52,490 +summation M delta G notF لـproducts minus + +846 +01:04:52,490 --> 01:04:57,590 +summation دلتا G او اذا كان في عندى delta G نقطة + +847 +01:04:57,590 --> 01:05:01,090 +لـreactants و لـproducts برضه هذا كلام صحيح يعنى + +848 +01:05:01,090 --> 01:05:06,070 +ففي عندى عدة علاقات بتحكم ال delta G وممكن ان + +849 +01:05:06,070 --> 01:05:09,810 +استخدم اي واحدة فيهم فى حل المسائل ابتجين الان + +850 +01:05:09,810 --> 01:05:13,690 +نقطة صغيرة بقول فى بعض الأحيان في عندى تفاعل ال + +851 +01:05:13,690 --> 01:05:18,560 +delta G الو موجبةهل معنى الكلام انه خلاص فش إيه + +852 +01:05:18,560 --> 01:05:22,160 +الحيلة فهذا التفاعل مش راح يمشي إلى اليمين؟ قال لأ + +853 +01:05:22,160 --> 01:05:29,040 +ممكن انا اذا كان لجيت التفاعل آخر ال delta G له + +854 +01:05:29,040 --> 01:05:34,520 +سالبة وهذا التفاعل بتفاعل مع أحد نواتج التفاعل + +855 +01:05:34,520 --> 01:05:41,470 +الأولفممكن التفاعل الأول يصير spontaneous ففي عندى + +856 +01:05:41,470 --> 01:05:44,730 +تفاعل non spontaneous زي .. زي ال zinc sulfide + +857 +01:05:44,730 --> 01:05:48,030 +يتحول ل zinc solid زائد sulfur ال delta G نور + +858 +01:05:48,030 --> 01:05:51,310 +تبعته مية تمانية تسعين كالوجول purple very + +859 +01:05:51,310 --> 01:05:55,890 +positive يعني ماتحصلش non spontaneous .. non + +860 +01:05:55,890 --> 01:06:01,460 +spontaneousلكن في عندى تفاعل تانى ال S Solid زائد + +861 +01:06:01,460 --> 01:06:06,380 +ال O2 Gas بيعطينى S O2 Gas ال Delta Genot تبعته + +862 +01:06:06,380 --> 01:06:10,700 +very negative سالب تلت مية طب هذا ال S هيه ممكن + +863 +01:06:10,700 --> 01:06:15,520 +يتفاعل مع ال Oxygen اه وبالتالي يعطينى S O2 فلو + +864 +01:06:15,520 --> 01:06:19,800 +جيت جماعة المعادلتين هدول مع بعض لو جيت جماعة + +865 +01:06:19,800 --> 01:06:24,260 +المعادلتين بقول coupling the two reactions gives + +866 +01:06:24,260 --> 01:06:35,230 +Zinc Sulphideزائد اكسجين اه من هذا رحمة هذا اذا + +867 +01:06:35,230 --> 01:06:39,890 +زنك سالفايت زائد اكسجين زنك صليب اللي هو هايه + +868 +01:06:39,890 --> 01:06:44,910 +النتج اللي انا بديه زائد SO2 جاز جداش الدل تجي + +869 +01:06:44,910 --> 01:06:48,550 +لهذا التفاعل قال احنا جمعنا هدول و بنجمعهم لأنه + +870 +01:06:48,550 --> 01:06:53,250 +هذا state functionبنجمعهم delta g note مية تمانية + +871 +01:06:53,250 --> 01:07:03,870 +وتسعين سالب تلت مية فبيطلع عنده سالب مية واتناش + +872 +01:07:07,150 --> 01:07:13,110 +زائد سالب هذه هذه يعني زائد مية وتمانية وتسعين + +873 +01:07:13,110 --> 01:07:16,430 +يعني هي مجموعة ما نهان جماعتهم زائد مية وتمانية + +874 +01:07:16,430 --> 01:07:20,710 +وتسعين بتعطيني سالب مية واطن عاش لأنه حصلت على هذا + +875 +01:07:20,710 --> 01:07:24,930 +التفاعل من مجموع الأتنين فابد أجمع ال delta G زي + +876 +01:07:24,930 --> 01:07:29,910 +ما كنا بنجمع ال delta Hفمجموعهم سالب 112 يعني + +877 +01:07:29,910 --> 01:07:34,230 +التفاعل ايش صار؟ التفاعل صار spontaneous هذا + +878 +01:07:34,230 --> 01:07:42,830 +بنقوله coupling يعني عملية جمع two reactions واحد + +879 +01:07:42,830 --> 01:07:48,210 +بيكون non spontaneous والتاني spontaneous فالنتيجة + +880 +01:07:48,210 --> 01:07:53,670 +طبعا ان التفاعل ال non spontaneous صار ممكن صار + +881 +01:07:53,670 --> 01:08:00,510 +spontaneousالان ببساطة خالص يعني فكرة صغيرة بنقول + +882 +01:08:00,510 --> 01:08:05,670 +انه شغلة ال coupling of reactions يعني هادي كتير + +883 +01:08:05,670 --> 01:08:10,310 +مشهورة في ال living organisms يعني عموماتفاعلات + +884 +01:08:10,310 --> 01:08:13,390 +كتير تُعتبر منها spontaneous ممكن إنه نعملها + +885 +01:08:13,390 --> 01:08:19,950 +coupling لتفاعل spontaneous أحصل على spontaneous + +886 +01:08:19,950 --> 01:08:23,750 +process لمن spontaneous process أصلا فمثلا في + +887 +01:08:23,750 --> 01:08:28,590 +الجسم الجلوكوز بيتأكسد ل CO2 و water و بيعطينا + +888 +01:08:28,590 --> 01:08:32,150 +طاقة يعني ال delta G تبعته negative spontaneous + +889 +01:08:32,150 --> 01:08:37,150 +and the energy released convert ADP هذا low free + +890 +01:08:37,150 --> 01:08:46,710 +energy moleculeانتوا ATP يعني اتفاعل ADP إلى ATP + +891 +01:08:46,710 --> 01:08:48,310 +هذا non spontaneous + +892 +01:08:50,960 --> 01:08:53,440 +فبدوا طاقة عشان يصبحوا spontaneous، بدوا نعملوا + +893 +01:08:53,440 --> 01:08:57,140 +coupling مع حاجة تانية، فهذا لما نعمل ناخد الطاقة + +894 +01:08:57,140 --> 01:09:01,220 +اللي .. لأن هذا low energy و هذا high energy، + +895 +01:09:01,220 --> 01:09:04,700 +فمعنى الكلام الـ Delta G positive لهذا التفاعل، + +896 +01:09:04,700 --> 01:09:09,080 +لكن اه، فإيش اللي بنقوله احنا؟ ناخد الطاقة ال free + +897 +01:09:09,080 --> 01:09:15,320 +energy من ال glucose، و بتحول هذه الطاقة ال ADP ل + +898 +01:09:15,320 --> 01:09:19,860 +ال ATP high free energy content، و ال ATP اللي + +899 +01:09:19,860 --> 01:09:25,150 +هالجهة اتصاريعني ATP، الـ ADP اللي صار ATP، هذا + +900 +01:09:25,150 --> 01:09:30,770 +بيعطي الطاقة تبعته مرتين لها مكونات أبسط في الجسم + +901 +01:09:30,770 --> 01:09:35,310 +و بيعمل منها خلايا، بيعمل منها membranes، كل + +902 +01:09:35,310 --> 01:09:39,800 +المشاطات الحيوية تبعت الجسموبيرجع تاني لل ADP، ال + +903 +01:09:39,800 --> 01:09:43,720 +ADP بده طاقة عشان يتحول تاني لل ATP، بياخدها من ال + +904 +01:09:43,720 --> 01:09:48,460 +glucose، because بيصير ATP، ال ATP بيعطي ..بالتالي + +905 +01:09:48,460 --> 01:09:53,060 +الطاقة تبعته ل .. يعني أو بيستخدم الطاقة تبعته + +906 +01:09:53,060 --> 01:10:00,210 +لعمل عمليات حيوية أخرىهذا ال ATP ادينين تراي + +907 +01:10:00,210 --> 01:10:03,510 +فوسفات يعني في تلاتة فوسفات هذا ادينين تراي فوسفات + +908 +01:10:03,510 --> 01:10:06,350 +واحد فوسفات تلاتة فوسفات تلاتة ادينين تراي فوسفات + +909 +01:10:06,350 --> 01:10:10,970 +ال ATP ادينين داي فوسفات هي فوسفات هي فوسفات داي + +910 +01:10:10,970 --> 01:10:17,770 +يعني بس اتنين فهن بنعطيله energy لل ATP بتحول لل + +911 +01:10:17,770 --> 01:10:25,160 +ATP ال ATP بيعطي ال energy تبعتهللجسم يعني بيعمل + +912 +01:10:25,160 --> 01:10:29,680 +عمليات حيوية مختلفة بتحول جزيئات بسيطة لجزيئات + +913 +01:10:29,680 --> 01:10:33,820 +اكتر تعقيدا الى اخره فبيتحول تاني لل ADP و هكذا + +914 +01:10:33,820 --> 01:10:39,790 +دورة مستمرةفهذا الشكل اللي برضه هتشوفوه في الكتاب + +915 +01:10:39,790 --> 01:10:43,470 +الـ Glucose Oxidation بيعطينا CO2 و H2O و High + +916 +01:10:43,470 --> 01:10:49,170 +Energy ال High Energy بتحول ال ADP لل ATP ال ATP + +917 +01:10:49,170 --> 01:10:54,350 +بتعمل Cellular Development Cell Constituents بتحول + +918 +01:10:54,350 --> 01:10:58,570 +ال Simpler Molecules لأشياء تانية و بترجع تاني لل + +919 +01:10:58,570 --> 01:11:04,680 +ADP و هكذاوهذه الرسمة جميلة مثل المكان اللي + +920 +01:11:04,680 --> 01:11:08,940 +متعودين عليه يعني فهي ال food مع ال oxygen بيعطينا + +921 +01:11:08,940 --> 01:11:14,020 +CO2 H2O يعني glucose food مع oxygen هذا أعطاني + +922 +01:11:14,020 --> 01:11:19,820 +طاقة الآن الطاقة الزايدة هذه شغلت هذا ال terce + +923 +01:11:19,820 --> 01:11:25,760 +يعني ال terce هذا حول ال ATP ل ADP دهر للطاقة + +924 +01:11:25,760 --> 01:11:29,140 +الزيادة حولت ال simpler molecules ل more complex + +925 +01:11:29,140 --> 01:11:36,100 +moleculesو هكذا فا استفدت + +926 +01:11:36,100 --> 01:11:40,920 +من التفاعلات المختلفة + +927 +01:11:40,920 --> 01:11:45,540 +اللي عادة بتعطيني more energy علشان أشغل تفاعلات + +928 +01:11:45,540 --> 01:11:51,820 +أخرى بحاجة إلى energy طبعا جسم الإنسان بيستخدم هذه + +929 +01:11:51,820 --> 01:12:00,510 +العمليات بكفاءة عالية للغايةاحنا يعني هيك بنكون + +930 +01:12:00,510 --> 01:12:09,350 +خلصنا المساق بتمنى ان شاء الله انه نكون استفدنا + +931 +01:12:15,460 --> 01:12:20,640 +التواجد دي هكون موجود كل يوم من الساعة عشرة لصلاة + +932 +01:12:20,640 --> 01:12:26,960 +الظهر فأي حد عنده سؤال ممكن يسأل في عندنا واجب + +933 +01:12:26,960 --> 01:12:33,640 +موعده يعني كمان يومين بتهيألي في عندنا واجب على + +934 +01:12:33,640 --> 01:12:39,880 +الصفحة موجود فبتجيبوه للواجب في أي وقت يعني في + +935 +01:12:39,880 --> 01:12:45,570 +موعده المحدد على الصفحة يعنيو هيك بنقولكم يعني + +936 +01:12:45,570 --> 01:12:49,090 +اعطيكم العافية و ان شاء الله بنتمنالكم التوفيق و + +937 +01:12:49,090 --> 01:12:53,430 +لعلي طبعا ما اشوفكمش مساقات تانية لأنه طبعا انتوا + +938 +01:12:53,430 --> 01:12:57,290 +مهندسات يعني فماقدر .. ماالكمش اللي غير هذا المساق + +939 +01:12:57,290 --> 01:13:00,990 +في الكيميا فبتمنالكم التوفيق و برك الله فيكم + diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ouZhgFHnb0w_raw.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ouZhgFHnb0w_raw.srt new file mode 100644 index 0000000000000000000000000000000000000000..506b2f18bb28533d5f4c14523d5a9e6bb00f2046 --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ouZhgFHnb0w_raw.srt @@ -0,0 +1,3800 @@ +1 +00:00:21,210 --> 00:00:24,110 +بسم الله الرحمن الرحيم أزياء الله الرحمن الرحيم + +2 +00:00:24,110 --> 00:00:29,150 +اليوم بنكمل في ال chemical thermodynamics اتحدثنا + +3 +00:00:29,150 --> 00:00:34,890 +في الحصة الماضية بشكل أساسي عن كيفية حساب ال ال + +4 +00:00:34,890 --> 00:00:42,750 +delta S ل reaction ما و اتحدثنا أيضا عنالـ phase + +5 +00:00:42,750 --> 00:00:48,470 +transition أو بشكل مقتصري يعني إيش بيحصل لو كان في + +6 +00:00:48,470 --> 00:00:56,530 +عندى equilibrium بين gas و liquid أو liquid أو + +7 +00:00:56,530 --> 00:00:57,090 +solid + +8 +00:01:01,640 --> 00:01:05,420 +أو حتى sublimation فاتحدثنا أيضا عن ال effect of + +9 +00:01:05,420 --> 00:01:10,180 +temperature على ال delta S أو على ال entropy بشكل + +10 +00:01:10,180 --> 00:01:15,100 +عام اليوم بنطلع على معلومات كتير بسيطة بنطلع على + +11 +00:01:15,100 --> 00:01:18,200 +ال free energy و علاقتها بال phase transition + +12 +00:01:18,200 --> 00:01:23,280 +temperature شفنا هذا الكلام سابقا لكن ماعملناش ال + +13 +00:01:23,280 --> 00:01:28,240 +relation من ال free energyو بالمناسبة free energy + +14 +00:01:28,240 --> 00:01:32,900 +مش معناتها انها يعني زي بعض الناس مابتعتقد انها + +15 +00:01:32,900 --> 00:01:38,980 +عبارة عن طاقة خليني اقول مجانية free لأ مش المقصود + +16 +00:01:38,980 --> 00:01:44,220 +انها طاقة مجانية لأ free energy يعني اقرب ما تكون + +17 +00:01:44,220 --> 00:01:47,800 +ال available energy ال available energy ال energy + +18 +00:01:47,800 --> 00:01:51,560 +اللي ممكن تعمل شغلخيص يعني ال energy موجودة ممكن + +19 +00:01:51,560 --> 00:01:55,600 +تعمل شغل لكن مش free energy يعني إيه يعني طاقة + +20 +00:01:55,600 --> 00:02:00,800 +مجانية لأ هذا تعبير أو يعني تفسير خاطئ لمعنى ال + +21 +00:02:00,800 --> 00:02:05,560 +term فبدأ أطلع على ال phase transition temperature + +22 +00:02:05,560 --> 00:02:10,450 +من واقع أو من ال free energyفبقول في البداية انا + +23 +00:02:10,450 --> 00:02:14,330 +عندى الـ delta G not at standard conditions يعني + +24 +00:02:14,330 --> 00:02:17,510 +نسوي delta H not minus T delta S not لو مش + +25 +00:02:17,510 --> 00:02:20,670 +standard conditions طبعا بنرفع ال note تصير عادي + +26 +00:02:20,670 --> 00:02:25,030 +delta G بتسوي delta H minus T delta S لكن انا بعرف + +27 +00:02:25,030 --> 00:02:28,950 +ان ال delta G not بتساوي0 for a phase transfer + +28 +00:02:28,950 --> 00:02:32,170 +لأنه عندي equilibrium reversible process فمعنى + +29 +00:02:32,170 --> 00:02:37,470 +الكلام ال delta H هتساوي T delta S او بمعنى اخر ال + +30 +00:02:37,470 --> 00:02:41,270 +temperature هتساوي delta H على delta S فإذا كان + +31 +00:02:41,270 --> 00:02:46,050 +بتكلم عن fusion او يعني ذوبان delta H fusion على + +32 +00:02:46,050 --> 00:02:51,370 +delta S fusionإذا بتكلم عن Vaporization ليكود مع + +33 +00:02:51,370 --> 00:02:55,730 +فيبر بقول والله ال tea boiling بتصير لأنه boiling + +34 +00:02:55,730 --> 00:02:58,890 +ف delta H vaporization على delta S vaporization + +35 +00:02:58,890 --> 00:03:01,370 +إذا كنت بتكلم عن ال sublimation فال tea لل + +36 +00:03:01,370 --> 00:03:04,650 +sublimation تساوي delta H sublimation على delta S + +37 +00:03:04,650 --> 00:03:08,110 +لل sublimation وفي الواقع مش شرط أن يكون في عندي + +38 +00:03:08,110 --> 00:03:16,590 +حتى phase a transitionيعني خلّيني أقول بالصورة + +39 +00:03:16,590 --> 00:03:22,050 +اللي أنا ذكرتها هذه المعهودة لأ ممكن والله مثلا زي + +40 +00:03:22,050 --> 00:03:26,350 +ما ذكرت سابقا orthorhombic + +41 +00:03:26,350 --> 00:03:31,030 +sulfur يتحول ل monoclonic sulfur أو العكس يعني + +42 +00:03:31,030 --> 00:03:35,510 +فهذا يعتبر أيضا phase transition فانا بقول ال T + +43 +00:03:35,510 --> 00:03:42,330 +بشكل عام لل phase changeهتساوى الـ delta H للتشينج + +44 +00:03:42,330 --> 00:03:45,730 +على ال delta S للتشينج، بغض النظر عن الاسم، هل هي + +45 +00:03:45,730 --> 00:03:51,010 +هذه أو هذه أو هذه، وحتى two solid phases مع بعض في + +46 +00:03:51,010 --> 00:03:57,010 +phase أثبت من phase آخر، فهذا كلام كله ممكن نجمعه + +47 +00:03:57,010 --> 00:03:59,150 +ونقول والله ال T لل phase change ده ال delta H + +48 +00:03:59,150 --> 00:04:03,940 +للتشينج على ال delta Sهذا كله من اين جاء ببساطة من + +49 +00:04:03,940 --> 00:04:06,780 +انه والله قلنا في ال phase change في عندي + +50 +00:04:06,780 --> 00:04:10,060 +equilibrium ما بين ال two phases او في عندي a + +51 +00:04:10,060 --> 00:04:13,400 +transition temperature هذه ال temperature اللي + +52 +00:04:13,400 --> 00:04:17,640 +قبلها بيكون عندي phase معين بعدها بيصير عندي phase + +53 +00:04:17,640 --> 00:04:20,810 +اخرهذه هي الـ Transition Temperature اللي أنا + +54 +00:04:20,810 --> 00:04:24,790 +بتكلم عنها و زي ما احنا شايفين هذا الكلام اقدرنا + +55 +00:04:24,790 --> 00:04:28,370 +نحصل عليه لأنه افترضنا ان ال Delta G بتساوي صفر + +56 +00:04:28,370 --> 00:04:32,410 +وهذا كلام صحيح لإن في عندي equilibrium ما بين ال + +57 +00:04:32,410 --> 00:04:37,400 +two phases او التغير بيكون reversibleفعلى سبيل + +58 +00:04:37,400 --> 00:04:42,100 +المثال هذا الـ T Delta S هي تغيرها مع الحرارة و + +59 +00:04:42,100 --> 00:04:47,020 +احنا في هذا المساء هنعتبر انه يعني في كثير من + +60 +00:04:47,020 --> 00:04:50,740 +الأحيان اذا كان قلنالك انه والله تتغيرش فبنعتبر ان + +61 +00:04:50,740 --> 00:04:54,300 +هذا التغير مش موجود و كأنها خط و كأنها خط أفق + +62 +00:04:54,300 --> 00:04:58,280 +تماما يعني مافيش عندى تغير مع الحرارة وهي ال Delta + +63 +00:04:58,280 --> 00:05:03,140 +H على سبيل المثال التغير إليها مع الحرارةوكذلك في + +64 +00:05:03,140 --> 00:05:06,960 +كثير من الأحيان الـ delta H لا تتغير مع الحرارة، + +65 +00:05:06,960 --> 00:05:10,380 +طبعا هذا يتوقف على ال system مرات التغير كبير و + +66 +00:05:10,380 --> 00:05:16,160 +مرات التغير قليل فلما نقول لا تتغير ال delta S أو + +67 +00:05:16,160 --> 00:05:19,520 +ال delta H مع الحرارة فمعنى الكلام حسبتنا تقريبية + +68 +00:05:19,520 --> 00:05:26,000 +يعني القيم اللي بنحصل عليها هي قيم تقريبية مش + +69 +00:05:26,000 --> 00:05:30,190 +حقيقيةلكن احنا بنستخدم هذا المفهوم ببساطة نقول + +70 +00:05:30,190 --> 00:05:34,070 +والله لأ تتغيرش مع الحرارة عشان نبسط الحل بحيث ان + +71 +00:05:34,070 --> 00:05:38,450 +نروح ناخد القيم الموجودة في الجداول فبشتغل + +72 +00:05:38,450 --> 00:05:41,450 +باستخدام ال delta H او ال delta S at the standard + +73 +00:05:41,450 --> 00:05:45,150 +state اللي هي قيمها موجودة في الجداول فماضطرش ان + +74 +00:05:45,150 --> 00:05:47,930 +انا ادور على قيم ال delta H و delta S عند الحرارة + +75 +00:05:47,930 --> 00:05:51,810 +اللي انا بدي اياها بالظبط لكن هذا الشكل بيبين ان + +76 +00:05:51,810 --> 00:05:55,330 +انا اتغير ال delta S و delta H مع الحرارة لاحظوا + +77 +00:05:55,330 --> 00:05:59,980 +انهم بتقيوا في نقطةعند هذه النقطة بالظبط الـ delta + +78 +00:05:59,980 --> 00:06:05,280 +H بتساوي يعني الحرارة، عند الحرارة هادى، في عندي + +79 +00:06:05,280 --> 00:06:09,080 +ال delta H ساوية T delta S عند الحرارة هادى + +80 +00:06:09,080 --> 00:06:12,600 +بالظبط، لأن التقاطة ال delta أو عند ال delta G + +81 +00:06:12,600 --> 00:06:16,310 +بتساوي zero فهذه ال transition temperatureلحظوا + +82 +00:06:16,310 --> 00:06:20,930 +قبلها ممكن يكون spontaneous بعدها spontaneous أو + +83 +00:06:20,930 --> 00:06:23,890 +العكس ممكن يكون قبلها spontaneous بعدها non + +84 +00:06:23,890 --> 00:06:29,310 +spontaneous تمام؟ لكن هذه عبارة عن ال transition + +85 +00:06:29,310 --> 00:06:32,210 +temperature اللي عندها ال delta H بالساوية T delta + +86 +00:06:32,210 --> 00:06:37,670 +S وعندها بيكون ال delta G عبارة عن Zero لأن هذا + +87 +00:06:37,670 --> 00:06:42,080 +عبارة عن equilibriumمعنى الكلام الـ two phases او + +88 +00:06:42,080 --> 00:06:46,180 +الـ change بدي يكون reversible في هذه المنطقة عند + +89 +00:06:46,180 --> 00:06:49,500 +هذه الحرارة بالظبط بيكون reversible فلو في عندي + +90 +00:06:49,500 --> 00:06:54,740 +غلية يعني اقل من مائة درجة للميه، non spontaneous + +91 +00:06:54,740 --> 00:06:59,160 +اكتر من مائة درجة، spontaneous او عند مائة درجة + +92 +00:06:59,160 --> 00:07:03,340 +equilibrium دلتة جيب تساوي صفر تمام؟ فهذا المفهوم + +93 +00:07:03,340 --> 00:07:07,960 +يعني ال transition temperature اللي انا بتكلم عنه + +94 +00:07:08,740 --> 00:07:14,880 +خلّيني أخد بعض الأمثلة التوضيحية بقول مثلًا بيحكي + +95 +00:07:14,880 --> 00:07:20,320 +at 25 degrees c يعني 298 Kelvin the reduction of + +96 +00:07:20,320 --> 00:07:25,240 +copper one oxide is non spontaneous حلو، بدنا نعمل + +97 +00:07:25,240 --> 00:07:27,700 +reduction لل copper one oxide، هذه non spontaneous + +98 +00:07:27,700 --> 00:07:32,380 +ال delta G positive 8.9 كيلوجول طبعًا لو كان + +99 +00:07:32,380 --> 00:07:35,940 +spontaneous ال delta G بدها تكون سالبة لأن ال + +100 +00:07:35,940 --> 00:07:40,100 +delta G سالبة لل spontaneous processesبقول + +101 +00:07:40,100 --> 00:07:42,760 +calculate the temperature at which the reaction + +102 +00:07:42,760 --> 00:07:47,160 +becomes spontaneous ايش هي الحاجة هو هان non + +103 +00:07:47,160 --> 00:07:51,400 +spontaneous شوفنا المربع تبعه قبل شوية ع اليسار طب + +104 +00:07:51,400 --> 00:07:55,040 +ايش الحرارة اللي عندها هذا هو يعني هان هو هان non + +105 +00:07:55,040 --> 00:07:59,720 +spontaneous عند خمسة و عشرين ديجري ال سي عند حرارة + +106 +00:07:59,720 --> 00:08:02,580 +معينة non spontaneous بده الحرارة اللي عندها بيصير + +107 +00:08:02,580 --> 00:08:07,730 +spontaneous هان بالظبط بيصير spontaneousيعني هان + +108 +00:08:07,730 --> 00:08:10,830 +بالظبط بيبدأ يصير spontaneous لأنه بعد على طول بعد + +109 +00:08:10,830 --> 00:08:15,270 +شي قليل جدا بيصير spontaneous فلازم يعني نحسب ايه + +110 +00:08:15,270 --> 00:08:19,830 +ل transition temperature فبيقول ليه اكمل السؤال + +111 +00:08:19,830 --> 00:08:22,570 +بيقول ليه calculate the temperature at which the + +112 +00:08:22,570 --> 00:08:28,210 +reaction becomes spontaneous ΔH and ΔS are 58.1 + +113 +00:08:28,210 --> 00:08:34,060 +kilo joule and 165 joule per Kelvinباعتين قيمة الـ + +114 +00:08:34,060 --> 00:08:38,560 +ΔH والـ ΔS لتاعة المثالة الـ T بتساوى ΔH على ΔS + +115 +00:08:39,460 --> 00:08:41,820 +معنى الكلام ليه؟ لأن ليش هذا الكلام؟ أنا بدي أجيب + +116 +00:08:41,820 --> 00:08:43,880 +الـTransition Temperature اللي بعد الـTransition + +117 +00:08:43,880 --> 00:08:47,140 +Temperature بده يصير عندي الـChange اللي أنا بديه + +118 +00:08:47,140 --> 00:08:49,440 +يعني فبدي أجيب الـTransition Temperature بالظبط + +119 +00:08:49,440 --> 00:08:52,740 +وين .. وين هي الـTemperature اللي بعدها على طول + +120 +00:08:52,740 --> 00:08:55,240 +بيحصل عندي الـChange اللي بيقول الـT بيساوي + +121 +00:08:55,240 --> 00:08:58,620 +الـDelta S على الـDelta S fifty eight point one في + +122 +00:08:58,620 --> 00:09:03,900 +عشرة قصة ثلاثة لأنه الانتروبي بالجول أنا عندي هذه + +123 +00:09:03,900 --> 00:09:07,800 +kilo Joule فحولتهم لجول بيطلع عندي تلت مية اتنين + +124 +00:09:07,800 --> 00:09:13,610 +وخمسين Kelvinأذا بعد ال 352 كيلوفر خلاص التفاعل + +125 +00:09:13,610 --> 00:09:18,870 +بيصير عندي إيه؟ spontaneous عند 352 اه في عندي + +126 +00:09:18,870 --> 00:09:24,530 +equilibrium أقل من 352 ماني spontaneous فمش بس عند + +127 +00:09:24,530 --> 00:09:30,230 +25 degree c لأ عند أقل من 352 بيظل هو non + +128 +00:09:30,230 --> 00:09:35,280 +spontaneousما دام اقل من 352 اذا من spontaneous + +129 +00:09:35,280 --> 00:09:41,640 +هان اقل من 352 من spontaneous 352 بالظبط اترازشن + +130 +00:09:41,640 --> 00:09:47,380 +temperature بعد 352 بشحته صار spontaneous فهي + +131 +00:09:47,380 --> 00:09:51,940 +مفهوم المسألة نيجي نتطلع على مسألة تانية بتقول if + +132 +00:09:51,940 --> 00:09:55,660 +the reaction below spontaneous at room temperature + +133 +00:09:55,660 --> 00:10:00,270 +15 degree cIf not, at what temperature will it + +134 +00:10:00,270 --> 00:10:03,350 +start to be spontaneous؟ هل هذا التفاعل + +135 +00:10:03,350 --> 00:10:09,810 +spontaneous عند خمسة أو عشرين degrees C؟ والله، هى + +136 +00:10:09,810 --> 00:10:12,530 +بدنا نجاوب على هذا السؤال، بدنا نجاوب على هذا + +137 +00:10:12,530 --> 00:10:17,610 +السؤالإذا ماكانش spontaneous، إيش الحرارة اللي + +138 +00:10:17,610 --> 00:10:19,310 +عندها بده يصير spontaneous؟ بدنا ندورها على عالي + +139 +00:10:19,310 --> 00:10:22,230 +ترازشين temperature، لازم نفهم السؤال بالظبط إيش + +140 +00:10:22,230 --> 00:10:25,750 +اللي بده ياه فانا بشوف الله عند خمسة و عشرين ديجري + +141 +00:10:25,750 --> 00:10:29,490 +سي ديرتا جي نوت بتساوي ديرتا H نوت minus T ديرتا S + +142 +00:10:29,490 --> 00:10:32,890 +نوت فابعوض في المثلة one seventy seven point eight + +143 +00:10:32,890 --> 00:10:36,130 +minus two ninety eight في مية و ستين point five + +144 +00:10:36,130 --> 00:10:38,810 +فعشرة أسالة بتانية حوالي الا كيلو جول، بطلع عند + +145 +00:10:38,810 --> 00:10:43,020 +مية و تلاتين point zero kilo joule per moleهذه الـ + +146 +00:10:43,020 --> 00:10:48,320 +delta G note موجبة و لا سالبة؟ موجبة إذا و ليس + +147 +00:10:48,320 --> 00:10:53,660 +spontaneous لأن شرط ال spontaneity أن تكون ال + +148 +00:10:53,660 --> 00:10:57,880 +delta G سالبة شرط ال spontaneity أن تكون ال delta + +149 +00:10:57,880 --> 00:11:00,920 +G سالبة و لا سالبة موجبة suggesting a non + +150 +00:11:00,920 --> 00:11:04,680 +spontaneous process at 25 degrees C + +151 +00:11:09,110 --> 00:11:13,470 +طبعا لو عوض مهام بالـ Transition Temperature، + +152 +00:11:13,470 --> 00:11:15,910 +عارفين ايش اللي بيحصل؟ الـ Delta G Note بيتساوى + +153 +00:11:15,910 --> 00:11:20,710 +صفر، لو .. اه لو انه .. لو انه اعطاني جلي مثلا هل + +154 +00:11:20,710 --> 00:11:27,510 +هي .. هل ال .. يعني هل التفاعل spontaneous at 1108 + +155 +00:11:29,470 --> 00:11:33,370 +هلجيتها لو اقعد انا ب 1108 Kelvin راح الاجي + +156 +00:11:33,370 --> 00:11:38,410 +النتيجة قداش صفر ليه لأن دلتاجي بتساوي صفر دلتاجي + +157 +00:11:38,410 --> 00:11:41,850 +نوت بتساوي صفر لازم اطلع عنده صفر تعالوا نحسب الآن + +158 +00:11:41,850 --> 00:11:45,510 +ايش هي ال transition temperature اللي عندها يعني + +159 +00:11:45,510 --> 00:11:50,150 +او بعدها ال change بيصير spontaneous بقول to + +160 +00:11:50,150 --> 00:11:52,230 +calculate the temperature at which the reaction + +161 +00:11:52,230 --> 00:11:55,130 +starts to be spontaneous we should assume the + +162 +00:11:55,130 --> 00:11:59,290 +equilibrium state where دلتاجي نوت بتساوي صفرالـ T + +163 +00:11:59,290 --> 00:12:03,430 +ΔH على ΔS و الله عوضنا عنها دول هتطي 1108 يعني + +164 +00:12:03,430 --> 00:12:06,670 +التفاعل بتام و non spontaneous لغاية ما نوصل لل + +165 +00:12:06,670 --> 00:12:11,190 +transition temperature اللي هي 1108 أقل منها non + +166 +00:12:11,190 --> 00:12:16,230 +spontaneous أكتر منها spontaneous لو عوضنا بأكتر + +167 +00:12:16,230 --> 00:12:23,620 +من 1108 هان إشارة الـ Δجينوت هتكون سالبة خلاصعند + +168 +00:12:23,620 --> 00:12:29,460 +ما نعوض من 1108 هتكون صفر أقل من 1108 هتكون موجبا + +169 +00:12:29,460 --> 00:12:32,860 +يعني non spontaneous جميل جدا جميل جدا إذا اللي + +170 +00:12:32,860 --> 00:12:35,520 +بنعرف الحرارة اللي عندها بيصير عندي ال change + +171 +00:12:35,520 --> 00:12:40,580 +spontaneous ولا non spontaneous هذا إشي كتير مفيد + +172 +00:12:40,580 --> 00:12:44,960 +بيقول لي if the reaction below spontaneous or non + +173 +00:12:44,960 --> 00:12:48,740 +spontaneous at 25 degrees c at what temperature + +174 +00:12:48,740 --> 00:12:52,300 +will this reaction reverse directionإذا كانوا + +175 +00:12:52,300 --> 00:12:54,840 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +176 +00:12:54,840 --> 00:12:57,860 +spontaneous فتصبحوا spontaneous، إذا كانوا non + +177 +00:12:57,860 --> 00:12:57,860 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +178 +00:12:57,860 --> 00:12:57,860 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +179 +00:12:57,860 --> 00:12:57,860 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +180 +00:12:57,860 --> 00:12:57,860 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +181 +00:12:57,860 --> 00:12:57,860 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +182 +00:12:57,860 --> 00:12:57,860 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +183 +00:12:57,860 --> 00:12:57,860 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +184 +00:12:57,860 --> 00:12:57,860 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +185 +00:12:57,860 --> 00:12:57,860 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +186 +00:12:57,860 --> 00:12:57,860 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +187 +00:12:57,860 --> 00:12:58,080 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +188 +00:12:58,080 --> 00:13:00,300 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +189 +00:13:00,300 --> 00:13:02,800 +spontaneous فتصبحوا non spontaneous، إذا كانوا non + +190 +00:13:02,800 --> 00:13:05,160 +spontaneous فتصبحوا non spontaneous، إذافبقول + +191 +00:13:05,160 --> 00:13:08,900 +تعالي نطلع Delta H0 minus T Delta S0 هذا عبارة عن + +192 +00:13:08,900 --> 00:13:13,280 +Delta G0 بعوض عنهم At 25 degrees C Delta G0 + +193 +00:13:13,280 --> 00:13:19,400 +همعطيني في مسألة تانية أنا بعرفها اللي هو Delta H0 + +194 +00:13:19,400 --> 00:13:22,460 +minus 92.38 للتفاعل هذا + +195 +00:13:25,940 --> 00:13:30,720 +الحرارة خمسة و عشرين ديجري سي بده دلتا اس برضه هدا + +196 +00:13:30,720 --> 00:13:34,740 +هي معايا سالب سالب مية تمانية تسعين و تلاتة من + +197 +00:13:34,740 --> 00:13:37,700 +عشرة بيطلع عندى سالب تلاتة و تلاتين و تلاتة من + +198 +00:13:37,700 --> 00:13:42,600 +عشرة كيلوجولأه يبقى التفاعل spontaneous at room + +199 +00:13:42,600 --> 00:13:46,900 +temperature وهذا سؤال مهم حدرجعله عدة مرات لإيه؟ + +200 +00:13:46,900 --> 00:13:50,140 +لأن هذا الـ hyper process اللي هي طريقة تحضير + +201 +00:13:50,140 --> 00:13:53,000 +الأمونيا من الـ nitrogen والهيدروجين عملية صناعية + +202 +00:13:53,000 --> 00:13:57,340 +ممتازة وفعالة ومفيدة جدا بالنسبالنا وبنستخدمها + +203 +00:13:57,340 --> 00:14:01,160 +بشكل كبير عشان هيك إله زيارات متعددة زرناجة بالهيك + +204 +00:14:01,160 --> 00:14:05,190 +لكن برضه كمان إله زيارات متعددة لأنه مهمطب تعالى + +205 +00:14:05,190 --> 00:14:08,070 +نشوف لترازشن temperature هو اللى أنا عارفه لإنه + +206 +00:14:08,070 --> 00:14:12,650 +spontaneous طب وقتش بيصير non spontaneousأذا بدي + +207 +00:14:12,650 --> 00:14:15,630 +أجيب لترازيش ال temperature لحد الفاصل لترازيش ال + +208 +00:14:15,630 --> 00:14:18,210 +temperature فيقول ال T بتساوي ال delta H على ال + +209 +00:14:18,210 --> 00:14:24,850 +delta S هي ال delta S ال delta H سالب 92 380 يعني + +210 +00:14:24,850 --> 00:14:30,530 +نضربينها في الف عشان تصير جول وهي ال S أو ال delta + +211 +00:14:30,530 --> 00:14:35,790 +S سالب 198 و تلاتة من عشرة جول per Kelvin فبيطلع + +212 +00:14:35,790 --> 00:14:40,940 +عندي أربعمية خمسة ستين وتسعة من عشرةحلو كتير هذه + +213 +00:14:40,940 --> 00:14:45,360 +الحرارة يا جماعة قبلها التفاعل هذا بيكون + +214 +00:14:45,360 --> 00:14:50,300 +spontaneous بعدها بيصير not spontaneous عندها + +215 +00:14:50,300 --> 00:14:53,240 +بالظبط بيكون في عنده equilibrium عندها بالظبط + +216 +00:14:53,240 --> 00:14:55,280 +بيكون في عنده equilibrium + +217 +00:14:59,980 --> 00:15:03,920 +طيب هذا السؤال بيعطيني لما نكون فيه عندي + +218 +00:15:03,920 --> 00:15:07,980 +equilibrium بيقول لي write the chemical equation + +219 +00:15:07,980 --> 00:15:11,720 +that defines the normal boiling point of liquid + +220 +00:15:11,720 --> 00:15:17,660 +carbon tetrachloride CCL4بقول ال equation اللى + +221 +00:15:17,660 --> 00:15:21,220 +بتعطينه ال normal boiling point ان يكون ال CCL4 ال + +222 +00:15:21,220 --> 00:15:29,420 +liquid in equilibrium مع ال CCL4 gas هذه المعادلة + +223 +00:15:29,420 --> 00:15:35,640 +CCL4 liquid يتحول ال CCL4 gas reversiblyفهذه هي + +224 +00:15:35,640 --> 00:15:40,240 +المعادلة طيب بيقول لي what is the value of delta G + +225 +00:15:40,240 --> 00:15:43,680 +note for the equilibrium in part A؟ ايش قيمة ال + +226 +00:15:43,680 --> 00:15:50,520 +delta G note لهذا ال equilibrium؟ هتكون صفر طبعا، + +227 +00:15:50,520 --> 00:15:58,280 +ليش؟ اه لأن at equilibrium ال delta G note بدها + +228 +00:15:58,280 --> 00:16:03,810 +تساوي صفرفي عندي reversible change ما بين ال + +229 +00:16:03,810 --> 00:16:09,310 +liquid و ال vapor فبالتالي بدها تكون صفر هذا سابق + +230 +00:16:09,310 --> 00:16:13,810 +لأوانا شوية حيجيلناه بعدين مفهوم ال Q reaction + +231 +00:16:13,810 --> 00:16:19,280 +quotientبيقول NFC بيقول estimate the normal + +232 +00:16:19,280 --> 00:16:25,680 +boiling point of CCL4 provided that ΔH0 F4 CCL4 و + +233 +00:16:25,680 --> 00:16:30,840 +CCL4 gas و liquid are minus 106.7 kilojoule per + +234 +00:16:30,840 --> 00:16:36,500 +mole و minus 139 kilojoule per moleAlso it's not + +235 +00:16:36,500 --> 00:16:43,800 +for CCL4 and CCL4 gas and liquid are 309.4 and 214 + +236 +00:16:43,800 --> 00:16:47,800 +.4 respectively Assume ΔH and ΔS do not change + +237 +00:16:47,800 --> 00:16:50,900 +with temperature طبعا هذا مش حقيقي اتفاجنا على هذا + +238 +00:16:50,900 --> 00:16:54,340 +الكلام هو فيه تغير بيعتمد على ال system مدى التغير + +239 +00:16:54,340 --> 00:16:58,020 +بيعتمد على ال system HU لكن احنا لسهولة الحسابات + +240 +00:16:58,020 --> 00:17:06,240 +عشان نحصل على خليني اقول نستخدم ال ΔHعند أي حرارة + +241 +00:17:06,240 --> 00:17:09,160 +بقيمتها عند خمسة و عشرين ديجري سي لل standard + +242 +00:17:09,160 --> 00:17:13,220 +state لازم نفترض هذا الافتراض يمكن مش كتير انتوا + +243 +00:17:13,220 --> 00:17:16,500 +يعني بتحسوا بأهمية الموضوع لكن الموضوع كتير مهم + +244 +00:17:16,500 --> 00:17:21,140 +الموضوع كتير كتير مهم فخلينا نركز مع بعض شوية بقول + +245 +00:17:21,140 --> 00:17:23,340 +انا مادام في عند + +246 +00:17:27,060 --> 00:17:31,100 +بعدين بده ال normal boiling point كويس اذا انا بده + +247 +00:17:31,100 --> 00:17:34,360 +اشتغل عند ال ايه؟ عند ال equilibrium او بدلي + +248 +00:17:34,360 --> 00:17:38,350 +transition temperatureفبالتالي بقول الـ delta G0 + +249 +00:17:38,350 --> 00:17:43,110 +يتساوي صفر أو الـ T يتساوي دلتة S أو الـ T يتساوي + +250 +00:17:43,110 --> 00:17:49,230 +دلتة H نوت على دلتة S نوت دلتة H على دلتة S دلتة H + +251 +00:17:49,230 --> 00:17:53,310 +نوت على دلتة S دلتة H نوت على دلتة S دلتة H نوت + +252 +00:17:53,310 --> 00:17:59,210 +على دلتة S دلتة H نوت على دلتة S دلتة H نوت على + +253 +00:17:59,210 --> 00:18:00,030 +دلتة S دلتة H نوت على دلتة S دلتة H نوت على دلتة S + +254 +00:18:00,030 --> 00:18:01,310 +دلتة H نوت على دلتة S دلتة H نوت على دلتة S دلتة H + +255 +00:18:01,310 --> 00:18:04,650 +نوت على دلتة S دلتة H نوت على دلتة S دلتة H نوت + +256 +00:18:04,650 --> 00:18:08,970 +على دلتفمعنى الكلام بده اشوف والله الـ delta H + +257 +00:18:08,970 --> 00:18:13,090 +naught واحد مول فيه minus one oh six point seven + +258 +00:18:13,090 --> 00:18:18,370 +kilo joule per mole minus بنعوض تعويض يعني عن ال + +259 +00:18:18,370 --> 00:18:25,330 +delta H naught if لهذا و للآخر يعني للجاز و + +260 +00:18:25,330 --> 00:18:29,230 +للليكويد وهنا ال delta S naught بنقول والله S + +261 +00:18:29,230 --> 00:18:34,250 +naught للجاز minus S naught للليكويد فبحصل على + +262 +00:18:34,250 --> 00:18:39,850 +القيمة دي هي delta Hنوت وهي Delta S نوت فبقول + +263 +00:18:39,850 --> 00:18:44,170 +والله ال T بيبتساو Delta H نوت على Delta S نوت + +264 +00:18:44,170 --> 00:18:50,370 +تلتلاف و متون و ستين اللي هو اللي عبارة عن ال + +265 +00:18:50,370 --> 00:18:55,670 +Delta H اللي حسبتها على خمسة وتسعين جول per Kelvin + +266 +00:18:55,670 --> 00:19:01,150 +اللي بيعطيني تلتمية و تلاتة و أربعين Kelvin يعني + +267 +00:19:01,150 --> 00:19:05,370 +بيقول لي ان ال pointing point لل CCL4 جداش + +268 +00:19:14,460 --> 00:19:21,840 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +269 +00:19:21,840 --> 00:19:22,660 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +270 +00:19:22,660 --> 00:19:22,700 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +271 +00:19:22,700 --> 00:19:22,820 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +272 +00:19:22,820 --> 00:19:22,820 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +273 +00:19:22,820 --> 00:19:23,020 +تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا + +274 +00:19:23,020 --> 00:19:25,370 +تقريبا تقريبا تقريبطيب ليش الفرق هذا؟ جال لأنه + +275 +00:19:25,370 --> 00:19:28,890 +احنا اعتبرنا او افترضنا ان ال delta H و ال delta S + +276 +00:19:28,890 --> 00:19:33,030 +لا تتغيروا بالنسبة لكنهم في الحقيقة لأ في الحقيقة + +277 +00:19:33,030 --> 00:19:37,550 +بيتأثروا بالحرارة لكن هذه الفرضية بتسهل علينا + +278 +00:19:37,550 --> 00:19:42,510 +شغلنا لأنه على طول بدي احسب بأنه جال هذا كلب بروح + +279 +00:19:42,510 --> 00:19:44,890 +فورا بجيب ال delta لو ماعطانيش هدول بجيب delta H + +280 +00:19:44,890 --> 00:19:49,630 +not F و delta H not F at standard state و ال S not + +281 +00:19:49,630 --> 00:19:53,010 +و ال S not at standard stateواللي أنا بفترض أن + +282 +00:19:53,010 --> 00:19:55,950 +هدول هم قد ال standard state هم نفسهم عند أي + +283 +00:19:55,950 --> 00:19:59,750 +حرارة، لأنه لا يتأثروا بالحرارة، لكن هذا كلام إيه؟ + +284 +00:19:59,750 --> 00:20:04,670 +مش صحيح على إطلاق، وكمان بتوقف على ال system + +285 +00:20:09,530 --> 00:20:14,950 +طبعا نفس السؤال خلينا نتطلع عليه بشكل آخر هذه ال + +286 +00:20:14,950 --> 00:20:18,350 +process for the production of ammonia involves the + +287 +00:20:18,350 --> 00:20:23,850 +equilibrium in 2 زائد 3H2 بعطينا 2MH3 assume that + +288 +00:20:23,850 --> 00:20:29,330 +ΔH0 و ΔS0 for this reaction do not change with + +289 +00:20:29,330 --> 00:20:29,830 +temperature + +290 +00:20:32,820 --> 00:20:36,860 +تقريبا تقريبا predict the direction in which delta + +291 +00:20:36,860 --> 00:20:39,700 +G naught for the reaction it changes with + +292 +00:20:39,700 --> 00:20:41,060 +increasing temperature + +293 +00:20:48,630 --> 00:20:56,170 +فبدنا نشوف وقت إيش ال delta G not بتتغير إشارتها + +294 +00:20:56,170 --> 00:21:00,570 +بتغير إذا بدي أشوف ال delta G not عند الصفر لما + +295 +00:21:00,570 --> 00:21:03,290 +الصفر بتكون بصفر صفر اه قبله بتكون موجب وبعده + +296 +00:21:03,290 --> 00:21:07,010 +بتكون إيه سالب هذا مفهوم السؤال هذا مفهوم السؤال + +297 +00:21:07,010 --> 00:21:09,750 +لما نيجي يقول predict the direction in which delta + +298 +00:21:09,750 --> 00:21:14,250 +G not for the reaction it changes with increasing + +299 +00:21:14,250 --> 00:21:16,710 +temperature يعني وقت يحول من سالب لموجب لموجب + +300 +00:21:16,710 --> 00:21:17,990 +لسالب إذا بدي أجيب + +301 +00:21:26,950 --> 00:21:32,670 +بعدين يحسب قيمة الـ Delta G عند 25 و 500 على فرض + +302 +00:21:32,670 --> 00:21:40,070 +ان Delta H و Delta S لا تتغير بالحرارة لأن لو كانت + +303 +00:21:40,070 --> 00:21:46,310 +تتغير بالحرارة يعني لازم نجيب قيمهم عند 25 و 500 + +304 +00:21:47,410 --> 00:21:51,250 +عيند 25 هم المعروفين لأنهم من الجداول طب عيند 500 + +305 +00:21:51,250 --> 00:21:56,410 +لازم نشوف جداول عيند 500 او انه يعني نقدرهم عيند + +306 +00:21:56,410 --> 00:22:00,310 +500 لكن لا احنا هنستخدم اللي عيند 25 كمان عيند 500 + +307 +00:22:00,310 --> 00:22:07,970 +هي نفس القيمة لدلتا H و لدلتا S او لل S يعني + +308 +00:22:07,970 --> 00:22:16,890 +تعالوا نتطلع عموما لو جينا نتطلع هنابنلاقي انتروبي + +309 +00:22:16,890 --> 00:22:23,210 +بيزيد ولا بيجل المفروض التفاعل هدئالانتروبيا بيقل + +310 +00:22:23,210 --> 00:22:28,270 +لأن هنا عندى اربعة مولز غازي وهنا عندى بس اتنين + +311 +00:22:28,270 --> 00:22:32,430 +اذا النتيجة عدد مولات غازية اقل يبقى ال delta S + +312 +00:22:32,430 --> 00:22:38,790 +قيمة ايه؟ قيمة سالبة معناه الكلام في العلاقة delta + +313 +00:22:38,790 --> 00:22:43,050 +H not minus T delta S not ال minus T delta S not + +314 +00:22:43,050 --> 00:22:47,210 +هدى ايش هتكون؟ هتكون positive and increases with a + +315 +00:22:47,210 --> 00:22:52,710 +increasing temperatureAs a result ΔG0 becomes more + +316 +00:22:52,710 --> 00:22:58,890 +positive with increasing temperature لأن ΔG0 ΔH0 + +317 +00:22:58,890 --> 00:23:08,050 +minus T ΔS0 هذي موجبة لأن ΔS سالبة في سالب صارت + +318 +00:23:08,050 --> 00:23:14,290 +موجبة اذا as a result ΔG0 becomes more positive + +319 +00:23:14,290 --> 00:23:19,830 +لان عمال احنا بنزود الإيجابية بنزود قيمةالـ T + +320 +00:23:19,830 --> 00:23:23,010 +Delta S وبالتالي الـ Delta Genote تصير أكتر + +321 +00:23:23,010 --> 00:23:27,750 +positive with increasing temperature. Thus, the + +322 +00:23:27,750 --> 00:23:30,230 +driving force for the production of ammonia + +323 +00:23:30,230 --> 00:23:34,310 +becomes smaller with increasing temperature. مدام + +324 +00:23:34,310 --> 00:23:36,750 +الـ Delta Genote تصير أكتر positive مش أكتر + +325 +00:23:36,750 --> 00:23:40,170 +negative، إذن ال driving force لأنه يتكون عند + +326 +00:23:40,170 --> 00:23:45,420 +أمانيابيقل مع زيادة درجة الحرارة ل driving force + +327 +00:23:45,420 --> 00:23:49,200 +لإيه؟ لأنه كل ما زوّات درجة الحرارة، إيش بيحصل لك + +328 +00:23:49,200 --> 00:23:55,180 +دلتا G نقطة هادي؟ more positive، بتزيد ال + +329 +00:23:55,180 --> 00:23:58,540 +positivity تبعتها، يعني بيقل احتمالية أن يحصل + +330 +00:23:58,540 --> 00:24:03,680 +التفاعل، عشان يحصل، بيصير negative، تمام؟ لكن لا، + +331 +00:24:03,680 --> 00:24:07,660 +احنا كل ما زوّد الحرارة عامة، إيش بيحصل؟ تتجه ل + +332 +00:24:07,660 --> 00:24:10,740 +more positive، معناه كلام، ال driving force بتقل + +333 +00:24:18,940 --> 00:24:26,680 +طيب خليني اطلع على الحسابات تبعتي عند خمسة و عشرين + +334 +00:24:26,680 --> 00:24:28,680 +ديجري ال C و عند + +335 +00:24:31,750 --> 00:24:36,210 +500 ديجري سي يعني 25 ديجري سي يعني 298 كيلوفر دلتا + +336 +00:24:36,210 --> 00:24:40,230 +جي نوت ساوية دلتا H معروفة للاتفاعل وحسبناها قبل + +337 +00:24:40,230 --> 00:24:48,990 +هيك minus 92.38 كيلوجول minus T 298 في ال Delta S + +338 +00:24:49,720 --> 00:24:56,180 +-183.10 J per Kelvin طبعاً بدي أحول ال J ل K J + +339 +00:24:56,180 --> 00:25:00,060 +فبقى أضرف واحد على ألف فتطلع عندي سالب تلاتة و + +340 +00:25:00,060 --> 00:25:02,720 +تلاتين و تلاتة و عشرة K J إذا أنا عند خمسة و عشرين + +341 +00:25:02,720 --> 00:25:08,240 +ديجري ال C كانت إيه؟ كانت spontaneous طيب عند خمس + +342 +00:25:08,240 --> 00:25:13,480 +ميةيعني سبعمية تلاتة سبعين كيلوفير من عوض هذه نفس + +343 +00:25:13,480 --> 00:25:16,100 +القيمة لحظة معايا لازم أنت خمسمية يعني عوض بال + +344 +00:25:16,100 --> 00:25:18,920 +Delta H تبعت الخمسمية و Delta S تبعت الخمسمية لكن + +345 +00:25:18,920 --> 00:25:23,080 +لا هو إيش جال جال إنه لأ تغيروا بالحرارة إذا أعوض + +346 +00:25:23,080 --> 00:25:27,100 +بال Delta H و Delta S بس هنغير درجة الحرارة جال + +347 +00:25:27,100 --> 00:25:31,060 +صارت واحد ستين كيلوجول موجة بقى إذن لما رفعنا + +348 +00:25:31,060 --> 00:25:35,760 +لخمسمية ديجريل C التفاعل اتحول من spontaneous إلى + +349 +00:25:35,760 --> 00:25:43,870 +non spontaneousالـ equilibrium temperature هي + +350 +00:25:43,870 --> 00:25:50,170 +Delta H على Delta S حسبناها 465 قبل شوية + +351 +00:25:58,610 --> 00:26:03,370 +هذه هي ال T حسبناها قبل قليل كمه تترازش ال + +352 +00:26:03,370 --> 00:26:09,690 +temperature قبلها تكون سالبة وبعدها تكون موجة بدل + +353 +00:26:09,690 --> 00:26:12,870 +جيوة وبالتالي قبلها تكون spontaneous قبل هذه + +354 +00:26:12,870 --> 00:26:15,930 +الحرارة وبعدها تكون non spontaneous + +355 +00:26:22,220 --> 00:26:26,660 +بسألنى كمان سؤال يعنى جميل احنا بنحاول نرسخ مفهوم + +356 +00:26:26,660 --> 00:26:31,200 +ايش يعنى transition temperature وقت ايش التفاعل + +357 +00:26:31,200 --> 00:26:33,240 +بيكون spontaneous وقت ايش التفاعل بيكون non + +358 +00:26:33,240 --> 00:26:37,460 +spontaneous فخلينى نطلع على حاجة بنشوفها كل يوم و + +359 +00:26:37,460 --> 00:26:41,220 +بنعرفها كويسفالسؤال if the conversion of liquid + +360 +00:26:41,220 --> 00:26:44,960 +water to water vapor at one atmosphere and mid + +361 +00:26:44,960 --> 00:26:48,040 +degree c يعني ال normal boiling point spontaneous + +362 +00:26:48,040 --> 00:26:50,860 +ولا non spontaneous ولا reversible؟ إيش بنجيب على + +363 +00:26:50,860 --> 00:26:53,800 +هذا السؤال لحظة درجة ما نحسب؟ إيش بنجيب على إيه؟ + +364 +00:26:53,800 --> 00:26:58,640 +هل تحول ال liquid water إلى water vapor عند واحد + +365 +00:26:58,640 --> 00:27:02,820 +أتمسفير و mid degree c؟ هل هو spontaneous ولا non + +366 +00:27:02,820 --> 00:27:05,060 +spontaneous ولا reversible؟ + +367 +00:27:07,320 --> 00:27:11,700 +أيش رأي الجماعة يعني؟ طبعا reversible لأنه + +368 +00:27:11,700 --> 00:27:13,940 +equilibrium عند 100 درجة هذه ال normal boiling + +369 +00:27:13,940 --> 00:27:19,660 +point ففي عندي equilibrium أكيد هو reversible يعني + +370 +00:27:19,660 --> 00:27:23,760 +احنا طيب خلينا نقول ان احنا يعني مش عارفين لكن هو + +371 +00:27:23,760 --> 00:27:28,860 +أعطانا ال delta HVAB 40.657 وطبعا ال delta HVAB + +372 +00:27:28,860 --> 00:27:32,100 +موجبة ليه؟ لأنه بدها .. اه كيف؟ + +373 +00:27:34,670 --> 00:27:42,470 +بنقدر نحسبها فهذه موجبة Delta S VAB طبعا يعني لما + +374 +00:27:42,470 --> 00:27:48,370 +نزيد درجة الحرارة فمعناه الكلام 108.96 هذي برضه + +375 +00:27:48,370 --> 00:27:52,250 +موجبة فبقول ال Delta G at mid degree C والله إذا + +376 +00:27:52,250 --> 00:27:55,950 +كانت سالبة يبقى spontaneous موجبة مانا spontaneous + +377 +00:27:55,950 --> 00:28:01,520 +صفرعن طريق الانعواض دلتا جي ات ميت ديجري سي تساوي + +378 +00:28:01,520 --> 00:28:08,300 +اربعين سيكس فايف سبن جول minus عند مية يعني تلت + +379 +00:28:08,300 --> 00:28:11,560 +مية تلت سبعين وخمس تعاش كيلوفين في one oh eight + +380 +00:28:11,560 --> 00:28:15,300 +point nine six جول per Kelvin اه بتحطين الصفر يعني + +381 +00:28:15,300 --> 00:28:18,840 +كلام reversibleبس هو اصلا .. يعني لازم نعرف انه + +382 +00:28:18,840 --> 00:28:21,000 +reversible بدون ما نعمل كل هذه العملية هذه لان + +383 +00:28:21,000 --> 00:28:24,440 +المي احنا متخلفين معاها جدا و بنعرف انه normal + +384 +00:28:24,440 --> 00:28:28,500 +boiling point لإنها عند واحد أتمسفير 100 ديجري + +385 +00:28:28,500 --> 00:28:31,460 +الـC فعند 100 ديجري الـC طبعا ال liquid water + +386 +00:28:31,460 --> 00:28:36,580 +بيكون in equilibrium مع ال water vaporفلازم نعرف + +387 +00:28:36,580 --> 00:28:40,060 +إنه reversible لكن على أي حال حسبنا و لجناه أيضا + +388 +00:28:40,060 --> 00:28:48,440 +صفر مدام صفر فهو ال conversion reversible طيب نفسه + +389 +00:28:48,440 --> 00:28:51,620 +بيقول is heating one mole of liquid water to one + +390 +00:28:51,620 --> 00:28:55,300 +hundred and ten degrees c will converted to water + +391 +00:28:55,300 --> 00:28:59,420 +vapor spontaneously or not؟برضه خدت السؤال انجاب + +392 +00:28:59,420 --> 00:29:02,440 +عليه بدون ما نعمل المثلة يعنى بدون ما نعمل المثلة + +393 +00:29:02,440 --> 00:29:11,080 +طبعا فهل تحويل واحد مول من ال liquid water اذا + +394 +00:29:11,080 --> 00:29:15,760 +كان سخناه ل110 degree c هل تحوله ل water vapor + +395 +00:29:15,760 --> 00:29:20,760 +spontaneous ولا non spontaneous اذا كان سخنا الميه + +396 +00:29:20,760 --> 00:29:26,280 +ل110 degree c spontaneous ولا مش spontaneous بتحول + +397 +00:29:26,280 --> 00:29:32,300 +ل vapor الميه بتحول ل vaporطبعا spontaneous طبعا + +398 +00:29:32,300 --> 00:29:36,200 +spontaneous أكيد أقل من مية ماهواش spontaneous فوق + +399 +00:29:36,200 --> 00:29:39,280 +ال .. بتلاقي water .. بتلاقي liquid water at مية و + +400 +00:29:39,280 --> 00:29:42,700 +عشرة degree c هل .. هل بنلاقي ال liquid water at + +401 +00:29:42,700 --> 00:29:46,720 +مية و عشرة degree c لحد الأقصى الهمية بس ال water + +402 +00:29:46,720 --> 00:29:49,480 +vapor اذا ال conversion لل liquid water إلى water + +403 +00:29:49,480 --> 00:29:51,820 +vapor عند مية و عشرة هذا spontaneous ال process + +404 +00:29:51,820 --> 00:29:55,580 +عند مية و عشرة spontaneous أكتر من مية spontaneous + +405 +00:29:55,580 --> 00:30:00,110 +أقل من مية لا ولا بنلاقي المية ميةLiquid water + +406 +00:30:00,110 --> 00:30:03,190 +liquid water لا جهاز جاز لا تتحول إلى جاز + +407 +00:30:03,190 --> 00:30:07,210 +spontaneously هذا كلام بسيط كتير هذا كلام كتير + +408 +00:30:07,210 --> 00:30:11,250 +بسيط is heating one mole of liquid water to 110 + +409 +00:30:11,250 --> 00:30:14,990 +degrees C will convert يعني حصل على الميه 110 + +410 +00:30:14,990 --> 00:30:20,170 +degrees C هل هذا هيحولها لواتر فيبر ولا لا سخنها + +411 +00:30:20,170 --> 00:30:23,450 +لأكتر من ال normal boiling point هل هتحولها لواتر + +412 +00:30:23,450 --> 00:30:26,730 +فيبر ولا لا طبعا هيتحول لواتر فيبر spontaneously + +413 +00:30:26,730 --> 00:30:33,330 +انتهينااستخدام دلتا H ودلتا S لا يتغيروا بشكل كبير + +414 +00:30:33,330 --> 00:30:37,490 +مع التمبراتور طيب ماعطينا دلتا H VAP و ماعطينا + +415 +00:30:37,490 --> 00:30:42,650 +دلتا S VAP تعالوا نحسب دلتا G at 110 degree C دلتا + +416 +00:30:42,650 --> 00:30:47,070 +H minus T دلتا S هناخد القيم عن 110 هي نفسها عند + +417 +00:30:47,070 --> 00:30:53,920 +25 degree Cدلتا اتش اربعين اربعين سيكس فايف سبن + +418 +00:30:53,920 --> 00:30:58,380 +جول يعني اجربناها في الف minus اه مية و عشرة مش + +419 +00:30:58,380 --> 00:31:01,260 +تلات مية و تلاتة و سبعين تلات مية و تلاتة و تمانين + +420 +00:31:01,260 --> 00:31:07,260 +صارتفى 108.63 ديلتا اصبحت سالبة ايش معناه انها + +421 +00:31:07,260 --> 00:31:09,960 +سالبة؟ يعني نعم التفاعل spontaneous او التغير مش + +422 +00:31:09,960 --> 00:31:14,820 +تفاعل التغير spontaneous طبعا لما ساخد الميه عند + +423 +00:31:14,820 --> 00:31:18,760 +اكتر من مية فهذا التغير spontaneous طب ايش بيحصل + +424 +00:31:18,760 --> 00:31:23,420 +لو is heating one mole of liquid water to 90 + +425 +00:31:23,420 --> 00:31:28,190 +degrees will convert water toVapor spontaneously + +426 +00:31:28,190 --> 00:31:32,310 +or not طبعا لا مش ممكن لأنه أقل من ال boiling + +427 +00:31:32,310 --> 00:31:36,110 +point أقل من ال boiling point بس لو مابعرفش حدّلنا + +428 +00:31:36,110 --> 00:31:39,810 +عليها الحسابات لو ماعرفش هذا الكلام حدّلنا علي + +429 +00:31:39,810 --> 00:31:42,810 +الحسابات برضه تقول لي assume ال delta H و ال delta + +430 +00:31:42,810 --> 00:31:45,890 +S do not change significantly وال temperature عشان + +431 +00:31:45,890 --> 00:31:49,430 +أستخدم ال delta H قيمتها عند 25 ديجري C و ال delta + +432 +00:31:49,430 --> 00:31:53,380 +S برضه قيمتها عند 25 ديجري C لإن أنا متوفرمتوفرة و + +433 +00:31:53,380 --> 00:31:56,560 +معايا في المسألة بيقول الـ delta G عن تسعين دجري + +434 +00:31:56,560 --> 00:31:59,620 +ال C بيساوي ال delta H minus T delta S ال delta G + +435 +00:31:59,620 --> 00:32:03,400 +عن تسعين دجري ال C بدها تساوي قيمة ال delta H + +436 +00:32:03,400 --> 00:32:07,620 +بالجول minus A تسعين يعني تلاتمية تلاتة و ستين + +437 +00:32:07,620 --> 00:32:11,500 +Kelvin مضروبة في مية و تمانية point nine six طبعا + +438 +00:32:11,500 --> 00:32:15,920 +الف و تمانية و تمانية جول positiveمعناته لأ و الله + +439 +00:32:15,920 --> 00:32:21,140 +مانفعش مش راح يتحول ال liquid water الى water + +440 +00:32:21,140 --> 00:32:26,300 +vapor مباشرة spontaneous دي عن 90 degree c لأ ده + +441 +00:32:26,300 --> 00:32:29,260 +كله مابحصلش هو هتبقى وضع طبيعي أقل من ال boiling + +442 +00:32:29,260 --> 00:32:33,500 +point ال liquid بتعمل liquid مابتحول كله لغاز فورا + +443 +00:32:33,500 --> 00:32:37,260 +أكبر من ال boiling point لأ و الله خلاص ال boiling + +444 +00:32:37,260 --> 00:32:39,900 +point فيه equilibrium بعد ال boiling point انتهينا + +445 +00:32:39,900 --> 00:32:44,420 +كله gas steam بخار water vapor + +446 +00:32:49,290 --> 00:32:52,390 +طب at what temperature will liquid water be at + +447 +00:32:52,390 --> 00:32:55,790 +equilibrium with water vapor؟ نعرف هذا الكلام، + +448 +00:32:55,790 --> 00:32:57,730 +liquid water بقى ال water vapor، عند أي + +449 +00:32:57,730 --> 00:33:03,190 +temperature؟ الهي 100، أكيد، أكيد هذا الكلام، بقول + +450 +00:33:03,190 --> 00:33:07,690 +inserting the values of delta H and delta S into + +451 +00:33:07,690 --> 00:33:11,310 +the definition of delta G لأنها بتدل equilibrium، + +452 +00:33:11,310 --> 00:33:16,030 +يفجأة ال delta G إيش هي تساوي؟ صفر، يفجأة ال delta + +453 +00:33:16,030 --> 00:33:21,400 +S هي تساوي ال Tالـ T تطلع تلات مئة و تلات سبعين و + +454 +00:33:21,400 --> 00:33:24,980 +خمس عشر اللي هي ايه؟ الـ Normal boiling point of + +455 +00:33:24,980 --> 00:33:29,700 +water one hundred degrees C تمام؟ طبعا هذا مضع + +456 +00:33:29,700 --> 00:33:35,880 +طبيعي لأن الـ Delta G بتسوء صفر الـ T بتسوء تلات + +457 +00:33:35,880 --> 00:33:38,040 +مئة و تلات سبعين و خمس عشر لإنها Normal boiling + +458 +00:33:38,040 --> 00:33:44,500 +point يعني عند واحد أتمسفير طب عن temperature أكتر + +459 +00:33:44,500 --> 00:33:48,290 +من تلات مئة و تلات سبعينجال ديلتا جيب تصير + +460 +00:33:48,290 --> 00:33:52,930 +negative لأنه أكتر من ال boiling point طب عند أجل + +461 +00:33:52,930 --> 00:33:57,590 +من 38 و 79 جال دلتا جيب تصير positive يعني أقل من + +462 +00:33:57,590 --> 00:34:00,630 +100 وأكتر من 100 كويس؟ زي ما شوفناها الأمثلة اللي + +463 +00:34:00,630 --> 00:34:05,500 +شوفناهاهذه بالظبط هي الكلام اللى بيحصل فوق المية + +464 +00:34:05,500 --> 00:34:08,800 +هاي المية هي ال transition temperature اللى هى ال + +465 +00:34:08,800 --> 00:34:11,860 +normal boiling point اللى هى ال equilibrium اللى + +466 +00:34:11,860 --> 00:34:19,720 +هى ال reversible conversion كويس اكتر منها اه ال + +467 +00:34:19,720 --> 00:34:23,640 +liquid ال water بتروح ل water vapor spontaneously + +468 +00:34:23,640 --> 00:34:27,600 +اقل منها لا والله ال liquid water لا يتحول الى + +469 +00:34:27,600 --> 00:34:35,100 +water vapor spontaneouslyطيب نتطلع على يمكن أخر + +470 +00:34:35,100 --> 00:34:44,440 +جزئية في هذا ال chapter تتعلق بال delta G تحديدا + +471 +00:34:44,440 --> 00:34:47,100 +يعني نتطلع على ال free energy و علاقتها بال + +472 +00:34:47,100 --> 00:34:49,960 +equilibrium ال free energy و علاقتها بال + +473 +00:34:49,960 --> 00:34:52,650 +equilibriumالـ Free Energy التي هي الـ Delta G + +474 +00:34:52,650 --> 00:34:57,950 +بتساوي الـ Delta G نوت زائد الـ RT لن لـ Q RT لن ل + +475 +00:34:57,950 --> 00:35:01,650 +Q إيش الـ Q هذه؟ الـ Q هي ال reaction quotient إيش + +476 +00:35:01,650 --> 00:35:07,270 +يعني ال reaction quotient؟ يعني لو عندي A NA زائد + +477 +00:35:07,270 --> 00:35:10,830 +MB + +478 +00:35:10,830 --> 00:35:13,350 +بتعطيلنا + +479 +00:35:18,030 --> 00:35:26,670 +xc زائد yd جالي q بتساوي زي ال equilibrium + +480 +00:35:26,670 --> 00:35:36,650 +constant مش بيفرق بينهم يعني حط c النواتج قص xd قص + +481 +00:35:36,650 --> 00:35:46,610 +y ع ال a قص n ال b قص amطب هذه يا أستاذ هي نفسها + +482 +00:35:46,610 --> 00:35:49,030 +ال equilibrium constant يا لأ ال equilibrium + +483 +00:35:49,030 --> 00:35:52,290 +constant هذه التركيزات بتكون هي التركيزات ال + +484 +00:35:52,290 --> 00:35:57,350 +equilibrium كويس ال Q ممكن تكون اكبر او تساوي او + +485 +00:35:57,350 --> 00:36:01,290 +اقل من ال K ال K هو ال equilibrium constant فعند + +486 +00:36:01,290 --> 00:36:10,000 +التركيزات وعند الاتزان اه هذه Kلكن اي تركيزات اخرى + +487 +00:36:10,000 --> 00:36:14,740 +اذا كانت مش عند الافادة بيقولها reaction quotient + +488 +00:36:14,740 --> 00:36:19,500 +يعني بس ال Q بتساوي K عند ايه؟ عند الاتزان يعني + +489 +00:36:19,500 --> 00:36:23,560 +بتساوي ال equilibrium constant فقط وقتاش جال عند + +490 +00:36:23,560 --> 00:36:29,560 +الاتزان فبس هذه الفكرةبدنا نعرف إن الـ delta G + +491 +00:36:29,560 --> 00:36:35,260 +بتساوي الـ delta G note زائد ال RT لـ Q في حالة ما + +492 +00:36:35,260 --> 00:36:41,010 +إنه نستخدم الـ standard stateالـStandard State + +493 +00:36:41,010 --> 00:36:44,650 +Concentrations كلها هي عبارة عن واحد مولار شوفنا + +494 +00:36:44,650 --> 00:36:48,510 +هذا في حصة سابقة الـStandard State بالنسبة للتركيز + +495 +00:36:48,510 --> 00:36:51,790 +هو ايه؟ واحد مولار لما يكون واحد مولار اوسع اش + +496 +00:36:51,790 --> 00:36:55,490 +مكان بيضلوا واحد في واحد على واحد في واحد يعني + +497 +00:36:55,490 --> 00:36:59,410 +واحد لـQ بتساوي واحد لإن الواحد جال صفر إذا + +498 +00:36:59,410 --> 00:37:02,250 +الـDelta G بتساوي الـDelta G Note يفجأت + +499 +00:37:02,250 --> 00:37:05,070 +الـStandard State الـDelta G بتساوي الـDelta G + +500 +00:37:05,070 --> 00:37:09,270 +Note لكن عند أي State غير الـStandard Stateالـ ΔG + +501 +00:37:09,270 --> 00:37:13,270 +بتساوي ΔG نوت زائد الـ RT لين الـ Q لكن عند الـ + +502 +00:37:13,270 --> 00:37:16,090 +Standard State لما كل التركيزات كانوا واحد معناته + +503 +00:37:16,090 --> 00:37:22,550 +لين الـ Q بصفر لأن الـ Q بتساوي واحد لكن إذا كان + +504 +00:37:22,550 --> 00:37:25,590 +عندي Standard State فالـ ΔG بتساوي الـ ΔG نوت + +505 +00:37:25,590 --> 00:37:28,870 +تعالوا نتطلع أيش اللي بيحصل بالظبط في أي تفاعل + +506 +00:37:28,870 --> 00:37:34,270 +كيميائي جال في عندي Reactants وفي عندي إبرادات + +507 +00:37:34,270 --> 00:37:41,220 +دائما في بينهم زي ال valleyبحيث انه لو سقط مثلا + +508 +00:37:41,220 --> 00:37:45,500 +حجر من الكرة نعتبر + +509 +00:37:45,500 --> 00:37:49,440 +وهي عمال نازلة لما توصل هنا خدوا بالكم ايش بتبتحك + +510 +00:37:49,440 --> 00:37:54,280 +تعمل؟ اه بتبتحرك حوالي ال ايه؟ ال valley هذا مكينه + +511 +00:37:54,280 --> 00:37:59,020 +equilibrium اتزان اتزان reversible اه Delta X + +512 +00:37:59,020 --> 00:38:02,540 +رايحة Delta X جاية reversible فهنا عندي + +513 +00:38:02,540 --> 00:38:08,770 +equilibriumهنا ال products وهنا ال reactants وهنا + +514 +00:38:08,770 --> 00:38:15,430 +طبعا يعني خليني اقول ال free energy فانا بقدر اقول + +515 +00:38:15,430 --> 00:38:19,810 +ان ال free energy دلتا جي بتسوي دلتا جي لل product + +516 +00:38:19,810 --> 00:38:23,620 +minus ال delta جي لل reactantsوبعدين بقول والله هل + +517 +00:38:23,620 --> 00:38:30,540 +هذا الكلام يعتبر موجب ولا سالب، إذا كان سالب فهو + +518 +00:38:30,540 --> 00:38:34,020 +spontaneous إذا كان .. يعني بيمشي في الاتجاه اللي + +519 +00:38:34,020 --> 00:38:37,800 +مكتوب، إذا كان موجب فلأ والله الاتجاه العكسي هو + +520 +00:38:37,800 --> 00:38:40,300 +اللي بيمشي فيه أو يعني بيكون spontaneous في + +521 +00:38:40,300 --> 00:38:48,200 +الاتجاه اللي مكتوب، مثلا عندي ال ..الأمونيا أي + +522 +00:38:48,200 --> 00:38:51,540 +اتفاعل يعني مش شرط الأمونيا فهي نفس الكلام هي + +523 +00:38:51,540 --> 00:38:54,920 +الفعل هدا ممكن تيجي هان يعني ممكن ييجي هيك والله + +524 +00:38:54,920 --> 00:38:58,080 +مثلا + +525 +00:38:58,080 --> 00:39:01,260 +هنا ال equilibrium يعني ممكن ييجي هيك هنا ال + +526 +00:39:01,260 --> 00:39:04,880 +equilibrium يعني مش شرط يعني انه دايما لا يعني ال + +527 +00:39:04,880 --> 00:39:07,940 +equilibrium ممكن وين مكان ييجي حسب المسألة اللي + +528 +00:39:07,940 --> 00:39:15,210 +عندي هلأ التوضيح موجود بالشكل اللي قدامي هالفال .. + +529 +00:39:15,210 --> 00:39:20,750 +في عندي هان عموما ال reactance معناته هي على سبيل + +530 +00:39:20,750 --> 00:39:27,510 +المثال ال nitrogen و ال oxygen و ال nitrogen مثلا + +531 +00:39:27,510 --> 00:39:31,830 +يعني هذه هي ان هذا هو ال nitrogen و هذا هو ال + +532 +00:39:31,830 --> 00:39:36,350 +hydrogen هذا هو ال hydrogen و هذا هو ال nitrogen + +533 +00:39:36,350 --> 00:39:40,730 +فهذه متفاعلة فشولاش هان عندي بس متفاعلة nitrogen و + +534 +00:39:40,730 --> 00:39:46,240 +hydrogenهن في عندى product معناته products أمونيا، + +535 +00:39:46,240 --> 00:39:50,600 +فالنص هن إيش في عندى؟ خلط اللي هو ال equilibrium، + +536 +00:39:50,600 --> 00:39:54,600 +خلط اللي هو ال equilibrium، بقول هن ال Q أقل من ال + +537 +00:39:54,600 --> 00:40:01,590 +K، هن ال Q أكبر من ال K، هن ال Q بتساوي ال Kيبقى + +538 +00:40:01,590 --> 00:40:08,010 +H9D ع جهة ال products ال Q أكبر من ال K إيش يعني + +539 +00:40:08,010 --> 00:40:14,770 +ال Q أكبر من ال K؟ يعني البست عندي أكبر من المقام، + +540 +00:40:14,770 --> 00:40:19,930 +أكبر من المقام، إذا؟ والله أه، بده يعني ال Q عندي + +541 +00:40:19,930 --> 00:40:24,110 +أكبر من ال K، البست أكبر من المقام، ال Q أقل من ال + +542 +00:40:24,110 --> 00:40:30,690 +Kالـ Q .. اه عندي انا ال ايه .. ال .. ال Q أقل من + +543 +00:40:30,690 --> 00:40:35,410 +ال K يعني عندي المقام أكبر من .. أكبر من ال bus طب + +544 +00:40:35,410 --> 00:40:38,930 +هو إيش المقام هان؟ المتفاعلات .. المتفاعلات عشان + +545 +00:40:38,930 --> 00:40:42,250 +هيك .. اه مدان المتفاعلات أكبر إذن بدها تروح ناحية + +546 +00:40:42,250 --> 00:40:45,990 +النواتج لإن هو عندي كمية كبيرة منها إذن هي التفاعل + +547 +00:40:45,990 --> 00:40:49,390 +رايح ناحية ال A رايح ناحية النواتج .. هان بالعكس + +548 +00:40:50,330 --> 00:40:55,670 +النواتج أكبر بتروح لحيط المتفاعلات spontaneously + +549 +00:40:55,670 --> 00:40:59,410 +فمعنى + +550 +00:40:59,410 --> 00:41:04,850 +الكلام سهل أنه نتوقع إيش اللي بيحصل عنا من الشكل + +551 +00:41:04,850 --> 00:41:09,550 +اللي جداميبقول تعالى نطلع على الأشكال التلاتة لما + +552 +00:41:09,550 --> 00:41:15,690 +يكون في عندنا ال Q أكبر من K و أقل من K و ال Q + +553 +00:41:15,690 --> 00:41:21,590 +بتساوي ال K فناخد جزء من العصابي مثلا ال + +554 +00:41:21,590 --> 00:41:26,450 +equilibrium اللي عندي فبقول لما ال delta G لل + +555 +00:41:26,450 --> 00:41:30,150 +products تكون أقل كتير من ال delta G لل reactants + +556 +00:41:30,150 --> 00:41:33,810 +هي delta G لل reactants هي delta G لل products أقل + +557 +00:41:33,810 --> 00:41:35,470 +كتير واضح انه + +558 +00:41:39,230 --> 00:41:43,130 +الـ Delta G Note هتكون Large Negative ليه؟ لأن الـ + +559 +00:41:43,130 --> 00:41:46,710 +Delta G Note هتكون لـ Products اللي هي القليلة، + +560 +00:41:46,710 --> 00:41:51,590 +قليلة كتير، minus ال reactants اللي هي كبيرة فمع + +561 +00:41:51,590 --> 00:41:54,430 +هذا الكلام Large Negative الـ Delta G Note is a + +562 +00:41:54,430 --> 00:41:58,810 +Large Negative Quantity and equilibrium is very + +563 +00:41:58,810 --> 00:42:01,730 +far to the right towards products يعني ال + +564 +00:42:01,730 --> 00:42:06,440 +equilibrium .. هلاحظ أنكم مش شايفين هذايعني هذا + +565 +00:42:06,440 --> 00:42:11,860 +عامل هيك، ماشي؟ فال equilibrium ايش ماله؟ احنا + +566 +00:42:11,860 --> 00:42:15,460 +قولنا .. شفتوا هذا الشكل؟ قولنا مش دايما بكون هيك، + +567 +00:42:15,460 --> 00:42:19,880 +ممكن يكون مشدود ناحية .. اه إذا كان .. إذا كان ال + +568 +00:42:19,880 --> 00:42:25,720 +delta G كانت very large negative value، معناته ال + +569 +00:42:25,720 --> 00:42:28,930 +equilibrium بيجرب ناحية ال productsالـ Equilibrium + +570 +00:42:28,930 --> 00:42:32,050 +بيجرب ناحية الـ Probats فالـ Δ G لـ Probats أقل + +571 +00:42:32,050 --> 00:42:37,210 +كتير من الـ Δ G لل Reactants إذاً الـ Δ G نوت هي + +572 +00:42:37,210 --> 00:42:43,310 +عبارة عن Large Negative Value، معناة وين الـ + +573 +00:42:43,310 --> 00:42:45,810 +Equilibrium جريب على ال Probats، لأنها Large + +574 +00:42:45,810 --> 00:42:49,010 +Negative، عكس هذا الكلام، و هذا الكلام طبعا احنا + +575 +00:42:49,010 --> 00:42:53,190 +ممكن نتخيله، بنقول وين الـ Q أقل من K، this means + +576 +00:42:53,190 --> 00:42:57,050 +that الـ Q أقل، معناته Reactants concentrations + +577 +00:42:57,050 --> 00:43:05,900 +are largeمدام كبير مدام كبير مدام كبير مدام كبير + +578 +00:43:05,900 --> 00:43:14,100 +مدام + +579 +00:43:14,100 --> 00:43:21,760 +كبير مدام + +580 +00:43:21,760 --> 00:43:28,100 +كبير مدام + +581 +00:43:28,100 --> 00:43:33,590 +كبيرهي هذا الشكل ال equilibrium وين هو؟ جريب على + +582 +00:43:33,590 --> 00:43:37,170 +ال reactance فهنر هاي ال reactance و هاي ال + +583 +00:43:37,170 --> 00:43:41,690 +products ال delta G ل products الكمية كبيرة minus + +584 +00:43:41,690 --> 00:43:46,770 +ال reactance كمية قليلة اذا large positive delta G + +585 +00:43:46,770 --> 00:43:51,410 +not is a large positive quantity and equilibrium + +586 +00:43:51,410 --> 00:43:56,020 +is very far to the leftيعني towards reactants جنب + +587 +00:43:56,020 --> 00:43:59,500 +ال reactants حلو هذا كلام طبعا هذا لما delta G + +588 +00:43:59,500 --> 00:44:02,420 +لproducts تكون أكبر كتير من delta G لل reactants + +589 +00:44:02,420 --> 00:44:07,060 +وهنا نفس المنطقة بنقول when Q أكبر من K this means + +590 +00:44:07,060 --> 00:44:12,260 +that product's concentrations are large and thus + +591 +00:44:12,260 --> 00:44:16,660 +reaction proceeds towards reactants formation عشان + +592 +00:44:16,660 --> 00:44:20,780 +هيك ال equilibrium بيكون قريب جدا من ال reactants + +593 +00:44:23,450 --> 00:44:27,530 +الحالة الأخيرة ان يكون حاجة هيك في النص زي اللي + +594 +00:44:27,530 --> 00:44:32,690 +شفناها سابقا يعني ها عندنا ال Q بتساوي ال K و ال + +595 +00:44:32,690 --> 00:44:37,130 +delta G ساعتها بدها تساوي صفر و ال delta G بدها + +596 +00:44:37,130 --> 00:44:40,890 +تساوي صفر ال delta G لل products بتساوي تقريبا ال + +597 +00:44:40,890 --> 00:44:45,990 +delta G لل reactants يعني بلاش الرسم هاتي مافيش + +598 +00:44:45,990 --> 00:44:48,410 +عندي رسمة لها مافيش عندي رسمة لها يعني بيكون اشي + +599 +00:44:48,410 --> 00:44:48,870 +زي هيك + +600 +00:44:54,450 --> 00:44:59,010 +حاجة زي هيك هي ال reactance إجراب على بعض كتير ف + +601 +00:44:59,010 --> 00:45:03,210 +ال delta G تقريبا تقريبا صفر ال delta G ل ال + +602 +00:45:03,210 --> 00:45:06,050 +product تقريبا صفر ال delta G لل reactance علشان + +603 +00:45:06,050 --> 00:45:11,230 +هيك بيقول ال equilibrium more towards the centerفى + +604 +00:45:11,230 --> 00:45:15,890 +النُص الـ center of the reaction profile when q is + +605 +00:45:15,890 --> 00:45:20,510 +equal to k this means that delta g بتساوي صفر and + +606 +00:45:20,510 --> 00:45:25,530 +delta g not بتساوي minus ال RT لإن ال K إذا كان ال + +607 +00:45:25,530 --> 00:45:30,730 +delta g بتساوي صفر فال delta g not من المعادلة + +608 +00:45:30,730 --> 00:45:36,790 +اللى بتقول delta g بتساوي delta g not minus ال RT + +609 +00:45:38,040 --> 00:45:44,260 +زائد ال RT لين ال Q فإذا كان ال Q هادى هي K ساعتها + +610 +00:45:44,260 --> 00:45:49,200 +بتكون هادة صفر Delta G not بدها تساوي زائد ال RT + +611 +00:45:49,200 --> 00:45:54,190 +لينالـ K إذا كان هذا صفر فالـ Δ G نوت تسوى minus + +612 +00:45:54,190 --> 00:45:59,870 +ال RT لإن ال K وبهذه الطريقة ممكن طبعا Delta G نوت + +613 +00:45:59,870 --> 00:46:04,530 +نعرف نحسبها كويس من Delta G نوت F من ال Delta H + +614 +00:46:04,530 --> 00:46:08,550 +minus Delta T Delta F عدة طرق لحساب ال Delta G إذا + +615 +00:46:08,550 --> 00:46:11,450 +مدين باعرف أحسب Delta G نوت إذا إيش مقدر أعرف + +616 +00:46:11,450 --> 00:46:15,130 +أحسب؟بقدر احسب الكائن equilibrium constant للتفاعل + +617 +00:46:15,130 --> 00:46:19,290 +وهذا اشي يعتبر جوهري جدا في الكيميا يعني يعتبر + +618 +00:46:19,290 --> 00:46:24,630 +حاجة جوهرية جدا كيف نعرف نحسب ال equilibrium + +619 +00:46:24,630 --> 00:46:33,900 +constant هذه بعض قيم الدلتا جي نوت والإيقاليبريام + +620 +00:46:33,900 --> 00:46:39,420 +constants 298 لحظة إذا كان الإيقاليبريام constants + +621 +00:46:39,420 --> 00:46:43,060 +يجب أن يكون واحد فدلتا جي نوت على طول بس هو صفر + +622 +00:46:43,060 --> 00:46:50,320 +لأنه minus RT لن ال K لما ال K سوى واحد دلتا جي + +623 +00:46:50,320 --> 00:46:56,970 +نوتتساوى minus ال R T لن ال K لما ال K ساوى واحد + +624 +00:46:56,970 --> 00:47:00,330 +معناته الدلتاجينوتر على طول هتساوى الصفر لكن + +625 +00:47:00,330 --> 00:47:06,060 +لاحظوا كل ما زاد ال Kأه لما نزيد ال K، ال delta G + +626 +00:47:06,060 --> 00:47:09,360 +ايش بيجرالها؟ بتقلل، يعني بتصير اتفاعل more + +627 +00:47:09,360 --> 00:47:13,800 +spontaneous، اتفاعل يعني بيمشي لليمين بشكل أكبر، + +628 +00:47:13,800 --> 00:47:17,260 +ليش؟ لأنه عندنا minus RT لإن ال K لما هذا يكون + +629 +00:47:17,260 --> 00:47:20,860 +كبير، يعني وهذا سالب، بعد كل هذا قيمة أكبر + +630 +00:47:20,860 --> 00:47:24,960 +بالسالب، قيمة أكبر بالسالب، عكس هذا الكلام، لو كان + +631 +00:47:24,960 --> 00:47:30,190 +أقل من واحدهن واحد زود واحد كان صفر زودنا عن + +632 +00:47:30,190 --> 00:47:34,890 +الواحد اه قلت كتير ال delta G Note طب قللنا عن + +633 +00:47:34,890 --> 00:47:40,850 +واحد بنلاحظ انه بتتحول لايه لقيمة موجبة بيصير انه + +634 +00:47:40,850 --> 00:47:45,470 +التفاعل والله مش spontaneous صعب جدا يمشي لليامين + +635 +00:47:51,110 --> 00:47:55,910 +نفس المنطقي يعني هان ال K أكبر من واحد لإن ال K + +636 +00:47:55,910 --> 00:47:58,950 +Positive Delta G Not Negative ال products are + +637 +00:47:58,950 --> 00:48:04,870 +favored K بتساوى واحد لإن ال K صفر Delta G Not صفر + +638 +00:48:04,870 --> 00:48:09,430 +ال products and reactants في equilibrium أقل من + +639 +00:48:09,430 --> 00:48:15,830 +واحد لإن ال K Negative Delta G Not Positiveالـ + +640 +00:48:15,830 --> 00:48:20,870 +Reactance are favored برضه كلام مفهوم جدا.الان + +641 +00:48:20,870 --> 00:48:26,730 +اجمالا بقول ال criteria for the spontaneity of a + +642 +00:48:26,730 --> 00:48:30,630 +process as written يعني التفاعل زي ما هو مكتوب أو + +643 +00:48:30,630 --> 00:48:35,150 +التغير زي ما هو مكتوب ايش ال criteria المعايير انه + +644 +00:48:35,150 --> 00:48:37,950 +والله يكون هل هو spontaneous ولا لأ؟بنقول اذا + +645 +00:48:37,950 --> 00:48:41,830 +كانوا spontaneous ال delta S لل universe لازم تكون + +646 +00:48:41,830 --> 00:48:46,430 +اكبر من صفروهذا نص القانون التاني للـ + +647 +00:48:46,430 --> 00:48:49,310 +Thermodynamics إذا كان التفاعل spontaneous أو + +648 +00:48:49,310 --> 00:48:54,730 +البروسيس spontaneous لازم الـ delta S للكون تكون + +649 +00:48:54,730 --> 00:48:59,630 +أكبر من صفر أو إن الـ delta G للsystem للتفاعل + +650 +00:48:59,630 --> 00:49:07,170 +تكون سالبة أقل من صفر أو حاجة جديدة الـ Q تكون أقل + +651 +00:49:07,170 --> 00:49:12,750 +من Kأقل من K يعني high reactance concentration + +652 +00:49:12,750 --> 00:49:15,930 +يعني هتروح لحيط ال products is spontaneous أي + +653 +00:49:15,930 --> 00:49:21,270 +واحدة من هدول بتخلي التفاعل spontaneous أي واحدة + +654 +00:49:21,270 --> 00:49:23,470 +منهم بتخلي التفاعل spontaneous هاي ال criteria هاي + +655 +00:49:23,470 --> 00:49:26,550 +المعايير ال equilibrium ايش معاير و جال والله ب + +656 +00:49:26,550 --> 00:49:30,290 +delta S للuniversة تكون صفر حلو إذا كانت delta S + +657 +00:49:30,290 --> 00:49:34,570 +للuniversة لأي system لأي system يعني في النهاية + +658 +00:49:34,570 --> 00:49:40,500 +لأي تغير صفر معناته عندي equilibriumإذا كان الـ + +659 +00:49:40,500 --> 00:49:45,040 +Delta G للـ system صفر، طبعا أيضا إيقاليبريان، إذا + +660 +00:49:45,040 --> 00:49:48,960 +كان الـ Q بتساوي الـ K، أكيد إيقاليبريان، ماشي يا + +661 +00:49:48,960 --> 00:49:51,420 +جماعة، طب الـ non spontaneity أو الـ non + +662 +00:49:51,420 --> 00:49:54,160 +spontaneous change، بقول إذا كان الـ Delta S في + +663 +00:49:54,160 --> 00:49:58,390 +الunivers أقل من صفر، هذا non spontaneousإذا كان + +664 +00:49:58,390 --> 00:50:02,130 +الـDelta G للـsystem أكبر من صفر موجبة، non + +665 +00:50:02,130 --> 00:50:04,890 +spontaneous، إذا كان الـQ أكبر من الـK، يعني + +666 +00:50:04,890 --> 00:50:07,210 +الـhigh product concentration، يبقى لازم تذهب حياة + +667 +00:50:07,210 --> 00:50:11,310 +الـreactants، فهذا non spontaneous، as what؟ as + +668 +00:50:11,310 --> 00:50:16,010 +written، كما هو مكتوب، يعني زي ما هو التفاعل مكتوب + +669 +00:50:16,010 --> 00:50:20,230 +عندي، فهذه حاجات أساسية بتلخص الكلام اللي قلناه + +670 +00:50:20,230 --> 00:50:24,330 +تقريبا من بداية ال chapter هذا فيما يتعلق بال + +671 +00:50:24,330 --> 00:50:28,840 +spontaneityبقول what is the criteria for + +672 +00:50:28,840 --> 00:50:33,160 +spontaneity in terms of entropy and in terms of + +673 +00:50:33,160 --> 00:50:38,240 +free energy وماعطينا خيارات نقرأهم من تحت the + +674 +00:50:38,240 --> 00:50:43,920 +entropy of the universe decreases violation مخالفة + +675 +00:50:43,920 --> 00:50:49,720 +ممكن يعني ال entropy of the universe decreases لأ + +676 +00:50:49,720 --> 00:50:52,880 +هذا مش spontaneous إذا أول واحدة عرفه المجرمة كان + +677 +00:50:52,880 --> 00:50:57,740 +بالغلطغلط لإيه؟ لأن ال spontaneity .. هذا إيه؟ إيش + +678 +00:50:57,740 --> 00:51:00,960 +ال entropy لل universe؟ آه لازم يكون الأكبر من صفر + +679 +00:51:00,960 --> 00:51:06,000 +.. decreases لأ .. طيب قال لي قبلها .. the entropy + +680 +00:51:06,000 --> 00:51:10,300 +of the system increases .. مالوش دعوة ال system .. + +681 +00:51:10,300 --> 00:51:13,540 +أنا بد إيه؟ ال universe .. إذا برضه مالوش دعوة + +682 +00:51:13,540 --> 00:51:17,300 +فيها .. the entropy of the system decreases .. + +683 +00:51:17,300 --> 00:51:20,160 +مالوش دعوة فيها .. الأصل مالوش دعوة فيها .. أنا بد + +684 +00:51:20,160 --> 00:51:21,320 +ال universe .. + +685 +00:51:32,440 --> 00:51:42,040 +الخيار الأول هو الخيار الصحيح لو كملته ستجد حلل في + +686 +00:51:42,040 --> 00:51:45,560 +الـ free energy + +687 +00:51:49,380 --> 00:51:53,240 +بال انتروبي الانتروبي لازم يقول ان الانتروبي للكون + +688 +00:51:53,240 --> 00:51:56,880 +بتزيد عشان التفاعل يكون spontaneous مجلليش انها + +689 +00:51:56,880 --> 00:52:01,160 +بتزيد خلاص مقدرش احكم لان الانتروبي لل system جلت + +690 +00:52:01,160 --> 00:52:04,020 +ولا لأ بهمنيش لان ال surroundings حاجة تانية خلاص + +691 +00:52:04,020 --> 00:52:07,860 +مجبليش threat انا مانفعش لازم مجموعهم هو المهم + +692 +00:52:07,860 --> 00:52:11,560 +اللي هو ال delta S لل universe لازم يكون اكتر من + +693 +00:52:11,560 --> 00:52:16,920 +واحد يعني قيمة موجبة اكتر من صفر قيمة موجبة + +694 +00:52:19,690 --> 00:52:23,670 +بنطلع على المثال التالي بيقول the normal boiling + +695 +00:52:23,670 --> 00:52:29,000 +point of benzene is 80 degrees c نقطةو هان بقى + +696 +00:52:29,000 --> 00:52:33,260 +اقولكم انه كان في خطأ في ال notes اللى معاكم اللى + +697 +00:52:33,260 --> 00:52:36,840 +موجودة على الصفحه انا هغيرها يعنى فاطلعوا على ال + +698 +00:52:36,840 --> 00:52:39,800 +notes اللى هنزلها اليوم اذا الله راد معاكي notes + +699 +00:52:39,800 --> 00:52:43,760 +بس راجعي و صلح الأخطاء و قدامت و اقرت بعض ال + +700 +00:52:43,760 --> 00:52:47,400 +slides اللى جيتها افضل يعنى فانا بفضل دائما انه + +701 +00:52:47,400 --> 00:52:51,300 +تاخد ال slides بعد ما اخلص انا شريحفكل ال slides + +702 +00:52:51,300 --> 00:52:54,800 +اللي عندك على الصفحة الان مناسبة وكويسة كتير + +703 +00:52:54,800 --> 00:52:58,580 +للدراسة لو عندك حاجة قديمة ممكن تتخلص منها ويمكن + +704 +00:52:58,580 --> 00:53:02,260 +تكون أفضل على أي حال بيقول طب at one hundred + +705 +00:53:02,260 --> 00:53:06,720 +degrees c and واحد atmosphere which is greater in + +706 +00:53:06,720 --> 00:53:11,420 +magnitude for the vaporization of benzene دلتا H + +707 +00:53:11,420 --> 00:53:17,920 +ولا T دلتا S أنهي أكبر في القيمة دلتا H ولا T دلتا + +708 +00:53:17,920 --> 00:53:21,420 +Sخدوا بالكم هو اين بيغلي النورة الـ boiling point + +709 +00:53:21,420 --> 00:53:30,800 +اين؟ عند 80 فهو بيسأل عند 100 ان هو اكبر delta H + +710 +00:53:30,800 --> 00:53:38,000 +ولا delta S ومعطيني خيارات بقول delta H بالساوية T + +711 +00:53:38,000 --> 00:53:39,560 +delta S هدولة at equilibrium + +712 +00:53:42,560 --> 00:53:46,540 +يا هادي يا هادي يا ماء الأخيرة ايش اللي انا بقوله + +713 +00:53:46,540 --> 00:53:50,380 +انا بقوله because at one hundred degree c the + +714 +00:53:50,380 --> 00:53:53,840 +vaporization of benzene is spontaneous و هذا وضع + +715 +00:53:53,840 --> 00:53:56,540 +طبيعي لأنه عند مقاس كان عند تمانين ال boiling + +716 +00:53:56,540 --> 00:54:00,660 +point فعند مية الاصل انه spontaneous بتحول + +717 +00:54:00,660 --> 00:54:07,280 +spontaneous للجاز بقول the term minus T delta S + +718 +00:54:07,280 --> 00:54:13,140 +should have a more negative valueعشان هو بتحول + +719 +00:54:13,140 --> 00:54:17,580 +لناس فهذا ال term لازم ي .. لأنه ال delta S موجبة + +720 +00:54:19,090 --> 00:54:26,350 +كويس فبده يتحول ايه ل more negative value minus T + +721 +00:54:26,350 --> 00:54:29,830 +delta S the term minus T delta S should have a + +722 +00:54:29,830 --> 00:54:33,330 +more negative value than the positive delta H VAP + +723 +00:54:33,330 --> 00:54:37,490 +ليه؟ لأن التحويل من liquid إلى vapor معناته ال + +724 +00:54:37,490 --> 00:54:40,950 +delta H هذي VAP اللي هي positive positive value + +725 +00:54:40,950 --> 00:54:45,630 +فهنا عندنا لأنه spontaneous فال delta G يجب أن + +726 +00:54:45,630 --> 00:54:48,960 +تكون negativeطب مقتش بتكون negative جال لما انها + +727 +00:54:48,960 --> 00:54:52,340 +ده السالب يكون اكبر، يبقى ال T Delta S هي اللي + +728 +00:54:52,340 --> 00:54:57,260 +اكبر من ال Delta H عشان النتيجة ايش تكون؟ سالبة، + +729 +00:54:57,260 --> 00:55:01,000 +اه يبقى الخيار التاني هو اللي صح الخيار هذا أكيد + +730 +00:55:01,000 --> 00:55:01,500 +خطأ + +731 +00:55:04,160 --> 00:55:07,780 +شوفنا يعني هذا الكلام شوفنا ان الـ delta G بتساوي + +732 +00:55:07,780 --> 00:55:13,600 +الـ delta G not زاد ال RT لن ال Q وشوفنا ان وقت + +733 +00:55:13,600 --> 00:55:17,880 +ايقاليبرام Q بتساوي K و Delta G بتساوي صفر و ال + +734 +00:55:17,880 --> 00:55:21,120 +equation بتتحول ل delta G not بتساوي minus RT لن + +735 +00:55:21,120 --> 00:55:27,580 +ال K او ال K بتساوي E أس سالب delta G not على ال + +736 +00:55:27,580 --> 00:55:33,990 +RT و هان ممكن نحسب ال K فخلينا نحسب ال Kخلّيني + +737 +00:55:33,990 --> 00:55:38,150 +أحسب الـK لأ بدّوش أحسب الـK هن بعد بشوية بحسب + +738 +00:55:38,150 --> 00:55:42,230 +الـK مش مشكلة بيقول calculate ΔG at 298 Kelvin for + +739 +00:55:42,230 --> 00:55:46,630 +the reaction below where one atmosphere nitrogen + +740 +00:55:46,630 --> 00:55:51,830 +تلاتة atmosphere H2 and one atmosphere in H3 are + +741 +00:55:51,830 --> 00:55:56,870 +present in the mixture ΔG نوت at 298 Kelvin متساوي + +742 +00:55:56,870 --> 00:56:01,330 +سالم 33.3 كيلوجول اللي متعودين عليها شفناها كتير + +743 +00:56:01,330 --> 00:56:05,320 +شفنا الرقم هذا بشكل كبيرالـ Q بتساوي تركيزات + +744 +00:56:05,320 --> 00:56:08,920 +النواتج على تركيزات المتفاعلات، كل تركيز مرفوع + +745 +00:56:08,920 --> 00:56:15,020 +لقصم عرض الملات، لكن لما تكون في عندي غازات فعارة + +746 +00:56:15,020 --> 00:56:18,610 +بدل التركيز بحط ال pressureفال pressure للأمونيا + +747 +00:56:18,610 --> 00:56:21,970 +تربيع على ال pressure للهيدروجين قص تلاتة ل + +748 +00:56:21,970 --> 00:56:24,990 +pressure للهيدروجين قص واحد يبقى اذا كان عندي + +749 +00:56:24,990 --> 00:56:31,970 +pressures فبقى احط ال pressures بدل التركيزات ال Q + +750 +00:56:31,970 --> 00:56:35,170 +بتطلع عندي تلاتة سبعة فعشرة قص سالب اتنين ال delta + +751 +00:56:35,170 --> 00:56:40,290 +G بتساوي delta G not زاد ال RT لن لQ + +752 +00:56:46,070 --> 00:56:48,570 +بعطينا الـ delta Gnot سالب تلاتة و تلاتين و تلاتة + +753 +00:56:48,570 --> 00:56:50,490 +من عشرة و بعوض عنها سالب تلاتة و تلاتين و تلاتة من + +754 +00:56:50,490 --> 00:56:55,410 +عشرة زائد ال R هنا يا جماعة لازم نعوض عنها بالجول + +755 +00:56:55,410 --> 00:57:00,550 +لأن هذه بالجول في معناه كلام 8.314 مش point O + +756 +00:57:00,550 --> 00:57:04,370 +eight one فاحنا جولنا لما نكون وحدات طاقة بنعوض عن + +757 +00:57:04,370 --> 00:57:09,070 +ال R ب 8.314 في 288 لين ل Q + +758 +00:57:11,770 --> 00:57:17,090 +بينطلع عند دلتا جي سالب واحد واربعين ونص يعني عند + +759 +00:57:17,090 --> 00:57:20,710 +هذه التركيزات برضه عند دلتا جي سالب يعني التفاعل + +760 +00:57:20,710 --> 00:57:28,350 +spontaneous لليمين يعني راح يتكون عند أمونيابقول + +761 +00:57:28,350 --> 00:57:31,390 +لهان تطبيق على الكلام اللي ذكرته في ال slide + +762 +00:57:31,390 --> 00:57:35,190 +الماضية بقول calculate the equilibrium constant Kp + +763 +00:57:35,190 --> 00:57:40,010 +at 25 degree C for the reaction اتنين H2O liquid + +764 +00:57:40,010 --> 00:57:45,930 +بتحول لاتنين H2 gas زائد O2 gas هل عمرنا شفنا انه + +765 +00:57:45,930 --> 00:57:49,030 +الميه بتتحول لH2O2؟ + +766 +00:57:52,160 --> 00:57:56,600 +ولا كان فيش ميه، فيش liquid water، بتتحولش يعني، + +767 +00:57:56,600 --> 00:57:59,380 +بتتحولش، عشان هيك هالاجى ان ال equilibrium + +768 +00:57:59,380 --> 00:58:03,900 +constant تتوقع يكون قيمة كبيرة ولا قيمة قليلة جدا، + +769 +00:58:03,900 --> 00:58:08,880 +اذا كانت بتتحولش، فنتوقع ان النواتج تكون كبيرة ولا + +770 +00:58:08,880 --> 00:58:14,200 +مهمة لاهتكون قليلة كتير ال equilibrium constant + +771 +00:58:14,200 --> 00:58:17,740 +هتكون قليل جدا ال equilibrium constant هتكون قليل + +772 +00:58:17,740 --> 00:58:22,940 +جدا فال delta G not لل reaction معطينه هو delta G + +773 +00:58:22,940 --> 00:58:27,720 +not F لل H2O liquid دلتا G not F لل H2و دلتا G not + +774 +00:58:27,720 --> 00:58:31,040 +F لل O2و في الامتحان ماعطينيش هدول التنتين لا لل + +775 +00:58:31,040 --> 00:58:34,820 +O2 ولا لل H2و لأنهم معروفين ان هو أصفر Delta G not + +776 +00:58:34,820 --> 00:58:40,170 +F Delta H not F لكن ال S not لأالـ S0 بتكون A + +777 +00:58:40,170 --> 00:58:46,910 +بتكون صفر بس at 0 Kelvin للـ Pure Crystalline .. + +778 +00:58:46,910 --> 00:58:50,730 +Perfectly Crystalline Substances لكن هنا Delta G0 + +779 +00:58:50,730 --> 00:58:54,370 +F و Delta H0 F على طول أصفار هدول فالـ Delta G0 لل + +780 +00:58:54,370 --> 00:58:59,730 +reaction بتساوي N نواتج أصفار minus اتنين فبتطلع + +781 +00:58:59,730 --> 00:59:02,910 +أربعمية أربعة سبعين وأربعة من عشرة ال Delta G0 لل + +782 +00:59:02,910 --> 00:59:07,960 +reaction minus RT لإن ال Kأذا بنعود تعويض مباشر + +783 +00:59:07,960 --> 00:59:13,340 +بيطلع عند ال K 7 في 10 أقل سالب 84 اللي بتطلع عليه + +784 +00:59:13,340 --> 00:59:15,720 +و اللي بعرف شوية كيميا بيعرف أن هذا يعني شبه + +785 +00:59:15,720 --> 00:59:19,260 +مستحيل حتى ال calculator ده بيعرف يحسبه مابيحصلش + +786 +00:59:19,260 --> 00:59:27,260 +يعني مابيحصل نهائيا قليل جدا جدانطلع على أيضا مثال + +787 +00:59:27,260 --> 00:59:30,940 +آخر لحساب الـ K بيقول الـ standard free energy + +788 +00:59:30,940 --> 00:59:34,820 +change for the hyper process is سالب تلاتة و + +789 +00:59:34,820 --> 00:59:37,660 +تلاتين point three kilo joule per mole دلتا جي نوت + +790 +00:59:37,660 --> 00:59:40,760 +سالب تلاتة و تلاتين point three kilo joule per + +791 +00:59:40,760 --> 00:59:43,780 +mole نفس السؤال اللي مانعناه سابقا لكن هان بده + +792 +00:59:43,780 --> 00:59:47,940 +يحسبقيمة ال equilibrium constant بيقول use this + +793 +00:59:47,940 --> 00:59:51,140 +value of delta G not to calculate the equilibrium + +794 +00:59:51,140 --> 00:59:56,580 +constant for the process فال K بعرف بتسوي E أسالب + +795 +00:59:56,580 --> 01:00:01,660 +delta G not على ال RT بعوض K بتسوي E أسالب delta G + +796 +01:00:01,660 --> 01:00:06,270 +not هذا هيسالب تلاتة و تلاتين point three kilo + +797 +01:00:06,270 --> 01:00:09,110 +joule او تلاتة و تلاتين الف و تلات مية joule per + +798 +01:00:09,110 --> 01:00:15,690 +mole على ال R eight point three one four joule per + +799 +01:00:15,690 --> 01:00:20,750 +mole per Kelvin مضروبة في RT مضروبة في 298 بطلع + +800 +01:00:20,750 --> 01:00:26,170 +سبعة في عشر أقص خمسة سبعة في عشر أقص خمسة بدي اكم + +801 +01:00:26,170 --> 01:00:31,330 +اتلاحظوا لهذا التفاعلأيش عمال بيحصل في ال + +802 +01:00:31,330 --> 01:00:34,490 +equilibrium constant؟ عند 300 كان عشر أقل سالب + +803 +01:00:34,490 --> 01:00:39,250 +تلاتة، عند 400 كان عشر أقل سالب أربعة، عند 450 عشر + +804 +01:00:39,250 --> 01:00:42,950 +أقل سالب خمسة، عند 550 عشر أقل سالب خمسة أقل، عند + +805 +01:00:42,950 --> 01:00:46,550 +550 عشر أقل سالب ستة، عند 600 عشر أقل سالب ستة + +806 +01:00:46,550 --> 01:00:50,290 +أقل، أيش بيحصل؟ عمال كل ما رفعنا درجة الحرارة، أيش + +807 +01:00:50,290 --> 01:00:54,460 +بيحصل ال equilibrium constant؟ بيقل يعنيتكون + +808 +01:00:54,460 --> 01:01:00,800 +النواتج بيقل يعني التفاعل non spontaneous بعد + +809 +01:01:00,800 --> 01:01:08,020 +الاربعمية و خمسة و ستين بيصير non spontaneous فهو + +810 +01:01:08,020 --> 01:01:11,620 +كل ما رفعنا الحرارة بيصير more non spontaneous + +811 +01:01:11,620 --> 01:01:13,980 +يعني ال equilibrium constant بيروح ناحية + +812 +01:01:13,980 --> 01:01:18,060 +المتفاعلات مش النواتج لكن زي ما ذكرت يعني هذي مش + +813 +01:01:18,060 --> 01:01:24,000 +كل الجثة يعنياحنا بنستخدم فى الحقيقة للهبر process + +814 +01:01:24,000 --> 01:01:30,300 +بنستخدم high temperature حوالى يمكن فوق ال 400 + +815 +01:01:30,300 --> 01:01:34,360 +درجة وبنستخدم very high pressures وقول ده ليش ال + +816 +01:01:34,360 --> 01:01:38,420 +very high pressures بتجبر المتفاعلات تتحول إلى + +817 +01:01:38,420 --> 01:01:41,720 +نواتج لأنه ال pressure تبع النواتج أقل من + +818 +01:01:41,720 --> 01:01:47,160 +المتفاعلات وبرضه ممكن يعنى الناس تفكر بطرق تانية + +819 +01:01:47,700 --> 01:01:52,940 +يعني حتى لو كان التفاعل بمشيش للأمام كتير، لكن + +820 +01:01:52,940 --> 01:01:58,220 +يعني حسب قاعدة لوتشاتليه احنا ما ذكرناهاش، يعني لو + +821 +01:01:58,220 --> 01:02:03,240 +باستمرار أخدنا النواتج، فبنجبر التفاعل يمشي برضه + +822 +01:02:03,240 --> 01:02:09,760 +للأمام، فمش كل الجثة، بس جداش الحرارة بتأثر على ال + +823 +01:02:09,760 --> 01:02:14,500 +equilibrium constant، لأ في عوامل تانية يعني مهمة + +824 +01:02:15,300 --> 01:02:20,920 +ولكن كcalculations وكاستفادة من تأثير الحرارة على + +825 +01:02:20,920 --> 01:02:25,620 +ال spontaneity أو delta G فهذا شيء واضح، يعني لا + +826 +01:02:25,620 --> 01:02:31,660 +يستطيع انكاره أي إنسانممكن تبعا نحسب الـ Delta G + +827 +01:02:31,660 --> 01:02:36,160 +under non-standard conditions بس كان ماعنديش + +828 +01:02:36,160 --> 01:02:40,240 +standard conditions فبيقول ال calculate Delta G at + +829 +01:02:40,240 --> 01:02:45,780 +298 Kelvin for a mixture of مش K لأ أي قيم أي قيم + +830 +01:02:45,780 --> 01:02:49,300 +زي المثال اللي أخدناه أول مثال mixture of واحد + +831 +01:02:49,300 --> 01:02:55,000 +أتمسفير ناتروجين تلاتة أتمسفير H2 نص أتمسفيرأو + +832 +01:02:55,000 --> 01:02:57,440 +غيروا هدول زي ما بدكم هدى اسمها non standard + +833 +01:02:57,440 --> 01:03:01,080 +conditions غيروا هدى ال pressure زي ما بدكم هدى + +834 +01:03:01,080 --> 01:03:05,420 +اسمها non standard conditions being used in the + +835 +01:03:05,420 --> 01:03:08,520 +hyper process provided ده delta G not سالب تلاتة و + +836 +01:03:08,520 --> 01:03:10,680 +تلاتين و تلاتة و عشرة كيلوجول per mole and Q + +837 +01:03:10,680 --> 01:03:13,760 +بتساوي تسعة و تلاتة فعشرة او سالب تلاتة هو حسب ال + +838 +01:03:13,760 --> 01:03:19,800 +Q لهدول أمونيا تربية على ال H أُس تلاتة في ال + +839 +01:03:19,800 --> 01:03:23,280 +نيتروجينالـ Pressures تبعتهم فبيقول الـ Delta U + +840 +01:03:23,280 --> 01:03:27,580 +سوى Delta G Note زائد الـ RT لإن الـ Q minus 37.3 + +841 +01:03:27,580 --> 01:03:35,280 +kilojoule per mole زائد الـ R في الـ T حولنا الـ R + +842 +01:03:35,280 --> 01:03:41,080 +من جول لكيلوجول لإن الـ Q تمام فبيطلع عندى سالب 44 + +843 +01:03:41,080 --> 01:03:51,410 +.9 هو نفس القيمة لأ هذه كانت واحد أتمسفيرخلّينها + +844 +01:03:51,410 --> 01:03:54,570 +نص اللي هي ال ammonia فتغير طبعا تغيرت القيمة لكن + +845 +01:03:54,570 --> 01:03:57,710 +إذا كان شفته كيف اتغيرت؟ اتغيرت الأمور negative + +846 +01:03:57,710 --> 01:04:05,350 +سالم مثلا 1.4 فتغير ال .. خلّيني أقول الظروف بتغير + +847 +01:04:05,350 --> 01:04:07,870 +قيمة ال delta G أيضا + +848 +01:04:15,090 --> 01:04:18,390 +يعني الـ Larger value للـ Delta G بتقول والله ال + +849 +01:04:18,390 --> 01:04:22,190 +driving force لتكوين الأمونيا بتزيد + +850 +01:04:24,460 --> 01:04:27,460 +يبقى هذه هي الـ delta G equations ممكن نقول والله + +851 +01:04:27,460 --> 01:04:31,540 +الـ delta G not minus RT لن ال Q طبعا لأن ال K at + +852 +01:04:31,540 --> 01:04:36,140 +equilibrium لأن ال Q بتساوي ال K او بتساوي delta H + +853 +01:04:36,140 --> 01:04:40,220 +not minus T delta S not او بتساوي ال delta G minus + +854 +01:04:40,220 --> 01:04:43,860 +RT لن ال Q لأن ال delta G بتساوي delta G not زاد + +855 +01:04:43,860 --> 01:04:47,940 +ال RT لن ال Q فأنا بتبني المعادلة او بتساوي + +856 +01:04:47,940 --> 01:04:52,490 +summation M delta G notF لـproducts minus + +857 +01:04:52,490 --> 01:04:57,590 +summation دلتا G او اذا كان في عندى delta G نقطة + +858 +01:04:57,590 --> 01:05:01,090 +لـreactants و لـproducts برضه هذا كلام صحيح يعنى + +859 +01:05:01,090 --> 01:05:06,070 +ففي عندى عدة علاقات بتحكم ال delta G وممكن ان + +860 +01:05:06,070 --> 01:05:09,810 +استخدم اي واحدة فيهم فى حل المسائل ابتجين الان + +861 +01:05:09,810 --> 01:05:13,690 +نقطة صغيرة بقول فى بعض الأحيان في عندى تفاعل ال + +862 +01:05:13,690 --> 01:05:18,560 +delta G الو موجبةهل معنى الكلام انه خلاص فش إيه + +863 +01:05:18,560 --> 01:05:22,160 +الحيلة فهذا التفاعل مش راح يمشي إلى اليمين؟ قال لأ + +864 +01:05:22,160 --> 01:05:29,040 +ممكن انا اذا كان لجيت التفاعل آخر ال delta G له + +865 +01:05:29,040 --> 01:05:34,520 +سالبة وهذا التفاعل بتفاعل مع أحد نواتج التفاعل + +866 +01:05:34,520 --> 01:05:41,470 +الأولفممكن التفاعل الأول يصير spontaneous ففي عندى + +867 +01:05:41,470 --> 01:05:44,730 +تفاعل non spontaneous زي .. زي ال zinc sulfide + +868 +01:05:44,730 --> 01:05:48,030 +يتحول ل zinc solid زائد sulfur ال delta G نور + +869 +01:05:48,030 --> 01:05:51,310 +تبعته مية تمانية تسعين كالوجول purple very + +870 +01:05:51,310 --> 01:05:55,890 +positive يعني ماتحصلش non spontaneous .. non + +871 +01:05:55,890 --> 01:06:01,460 +spontaneousلكن في عندى تفاعل تانى ال S Solid زائد + +872 +01:06:01,460 --> 01:06:06,380 +ال O2 Gas بيعطينى S O2 Gas ال Delta Genot تبعته + +873 +01:06:06,380 --> 01:06:10,700 +very negative سالب تلت مية طب هذا ال S هيه ممكن + +874 +01:06:10,700 --> 01:06:15,520 +يتفاعل مع ال Oxygen اه وبالتالي يعطينى S O2 فلو + +875 +01:06:15,520 --> 01:06:19,800 +جيت جماعة المعادلتين هدول مع بعض لو جيت جماعة + +876 +01:06:19,800 --> 01:06:24,260 +المعادلتين بقول coupling the two reactions gives + +877 +01:06:24,260 --> 01:06:35,230 +Zinc Sulphideزائد اكسجين اه من هذا رحمة هذا اذا + +878 +01:06:35,230 --> 01:06:39,890 +زنك سالفايت زائد اكسجين زنك صليب اللي هو هايه + +879 +01:06:39,890 --> 01:06:44,910 +النتج اللي انا بديه زائد SO2 جاز جداش الدل تجي + +880 +01:06:44,910 --> 01:06:48,550 +لهذا التفاعل قال احنا جمعنا هدول و بنجمعهم لأنه + +881 +01:06:48,550 --> 01:06:53,250 +هذا state functionبنجمعهم delta g note مية تمانية + +882 +01:06:53,250 --> 01:07:03,870 +وتسعين سالب تلت مية فبيطلع عنده سالب مية واتناش + +883 +01:07:07,150 --> 01:07:13,110 +زائد سالب هذه هذه يعني زائد مية وتمانية وتسعين + +884 +01:07:13,110 --> 01:07:16,430 +يعني هي مجموعة ما نهان جماعتهم زائد مية وتمانية + +885 +01:07:16,430 --> 01:07:20,710 +وتسعين بتعطيني سالب مية واطن عاش لأنه حصلت على هذا + +886 +01:07:20,710 --> 01:07:24,930 +التفاعل من مجموع الأتنين فابد أجمع ال delta G زي + +887 +01:07:24,930 --> 01:07:29,910 +ما كنا بنجمع ال delta Hفمجموعهم سالب 112 يعني + +888 +01:07:29,910 --> 01:07:34,230 +التفاعل ايش صار؟ التفاعل صار spontaneous هذا + +889 +01:07:34,230 --> 01:07:42,830 +بنقوله coupling يعني عملية جمع two reactions واحد + +890 +01:07:42,830 --> 01:07:48,210 +بيكون non spontaneous والتاني spontaneous فالنتيجة + +891 +01:07:48,210 --> 01:07:53,670 +طبعا ان التفاعل ال non spontaneous صار ممكن صار + +892 +01:07:53,670 --> 01:08:00,510 +spontaneousالان ببساطة خالص يعني فكرة صغيرة بنقول + +893 +01:08:00,510 --> 01:08:05,670 +انه شغلة ال coupling of reactions يعني هادي كتير + +894 +01:08:05,670 --> 01:08:10,310 +مشهورة في ال living organisms يعني عموماتفاعلات + +895 +01:08:10,310 --> 01:08:13,390 +كتير تُعتبر منها spontaneous ممكن إنه نعملها + +896 +01:08:13,390 --> 01:08:19,950 +coupling لتفاعل spontaneous أحصل على spontaneous + +897 +01:08:19,950 --> 01:08:23,750 +process لمن spontaneous process أصلا فمثلا في + +898 +01:08:23,750 --> 01:08:28,590 +الجسم الجلوكوز بيتأكسد ل CO2 و water و بيعطينا + +899 +01:08:28,590 --> 01:08:32,150 +طاقة يعني ال delta G تبعته negative spontaneous + +900 +01:08:32,150 --> 01:08:37,150 +and the energy released convert ADP هذا low free + +901 +01:08:37,150 --> 01:08:46,710 +energy moleculeانتوا ATP يعني اتفاعل ADP إلى ATP + +902 +01:08:46,710 --> 01:08:48,310 +هذا non spontaneous + +903 +01:08:50,960 --> 01:08:53,440 +فبدوا طاقة عشان يصبحوا spontaneous، بدوا نعملوا + +904 +01:08:53,440 --> 01:08:57,140 +coupling مع حاجة تانية، فهذا لما نعمل ناخد الطاقة + +905 +01:08:57,140 --> 01:09:01,220 +اللي .. لأن هذا low energy و هذا high energy، + +906 +01:09:01,220 --> 01:09:04,700 +فمعنى الكلام الـ Delta G positive لهذا التفاعل، + +907 +01:09:04,700 --> 01:09:09,080 +لكن اه، فإيش اللي بنقوله احنا؟ ناخد الطاقة ال free + +908 +01:09:09,080 --> 01:09:15,320 +energy من ال glucose، و بتحول هذه الطاقة ال ADP ل + +909 +01:09:15,320 --> 01:09:19,860 +ال ATP high free energy content، و ال ATP اللي + +910 +01:09:19,860 --> 01:09:25,150 +هالجهة اتصاريعني ATP، الـ ADP اللي صار ATP، هذا + +911 +01:09:25,150 --> 01:09:30,770 +بيعطي الطاقة تبعته مرتين لها مكونات أبسط في الجسم + +912 +01:09:30,770 --> 01:09:35,310 +و بيعمل منها خلايا، بيعمل منها membranes، كل + +913 +01:09:35,310 --> 01:09:39,800 +المشاطات الحيوية تبعت الجسموبيرجع تاني لل ADP، ال + +914 +01:09:39,800 --> 01:09:43,720 +ADP بده طاقة عشان يتحول تاني لل ATP، بياخدها من ال + +915 +01:09:43,720 --> 01:09:48,460 +glucose، because بيصير ATP، ال ATP بيعطي ..بالتالي + +916 +01:09:48,460 --> 01:09:53,060 +الطاقة تبعته ل .. يعني أو بيستخدم الطاقة تبعته + +917 +01:09:53,060 --> 01:10:00,210 +لعمل عمليات حيوية أخرىهذا ال ATP ادينين تراي + +918 +01:10:00,210 --> 01:10:03,510 +فوسفات يعني في تلاتة فوسفات هذا ادينين تراي فوسفات + +919 +01:10:03,510 --> 01:10:06,350 +واحد فوسفات تلاتة فوسفات تلاتة ادينين تراي فوسفات + +920 +01:10:06,350 --> 01:10:10,970 +ال ATP ادينين داي فوسفات هي فوسفات هي فوسفات داي + +921 +01:10:10,970 --> 01:10:17,770 +يعني بس اتنين فهن بنعطيله energy لل ATP بتحول لل + +922 +01:10:17,770 --> 01:10:25,160 +ATP ال ATP بيعطي ال energy تبعتهللجسم يعني بيعمل + +923 +01:10:25,160 --> 01:10:29,680 +عمليات حيوية مختلفة بتحول جزيئات بسيطة لجزيئات + +924 +01:10:29,680 --> 01:10:33,820 +اكتر تعقيدا الى اخره فبيتحول تاني لل ADP و هكذا + +925 +01:10:33,820 --> 01:10:39,790 +دورة مستمرةفهذا الشكل اللي برضه هتشوفوه في الكتاب + +926 +01:10:39,790 --> 01:10:43,470 +الـ Glucose Oxidation بيعطينا CO2 و H2O و High + +927 +01:10:43,470 --> 01:10:49,170 +Energy ال High Energy بتحول ال ADP لل ATP ال ATP + +928 +01:10:49,170 --> 01:10:54,350 +بتعمل Cellular Development Cell Constituents بتحول + +929 +01:10:54,350 --> 01:10:58,570 +ال Simpler Molecules لأشياء تانية و بترجع تاني لل + +930 +01:10:58,570 --> 01:11:04,680 +ADP و هكذاوهذه الرسمة جميلة مثل المكان اللي + +931 +01:11:04,680 --> 01:11:08,940 +متعودين عليه يعني فهي ال food مع ال oxygen بيعطينا + +932 +01:11:08,940 --> 01:11:14,020 +CO2 H2O يعني glucose food مع oxygen هذا أعطاني + +933 +01:11:14,020 --> 01:11:19,820 +طاقة الآن الطاقة الزايدة هذه شغلت هذا ال terce + +934 +01:11:19,820 --> 01:11:25,760 +يعني ال terce هذا حول ال ATP ل ADP دهر للطاقة + +935 +01:11:25,760 --> 01:11:29,140 +الزيادة حولت ال simpler molecules ل more complex + +936 +01:11:29,140 --> 01:11:36,100 +moleculesو هكذا فا استفدت + +937 +01:11:36,100 --> 01:11:40,920 +من التفاعلات المختلفة + +938 +01:11:40,920 --> 01:11:45,540 +اللي عادة بتعطيني more energy علشان أشغل تفاعلات + +939 +01:11:45,540 --> 01:11:51,820 +أخرى بحاجة إلى energy طبعا جسم الإنسان بيستخدم هذه + +940 +01:11:51,820 --> 01:12:00,510 +العمليات بكفاءة عالية للغايةاحنا يعني هيك بنكون + +941 +01:12:00,510 --> 01:12:09,350 +خلصنا المساق بتمنى ان شاء الله انه نكون استفدنا + +942 +01:12:15,460 --> 01:12:20,640 +التواجد دي هكون موجود كل يوم من الساعة عشرة لصلاة + +943 +01:12:20,640 --> 01:12:26,960 +الظهر فأي حد عنده سؤال ممكن يسأل في عندنا واجب + +944 +01:12:26,960 --> 01:12:33,640 +موعده يعني كمان يومين بتهيألي في عندنا واجب على + +945 +01:12:33,640 --> 01:12:39,880 +الصفحة موجود فبتجيبوه للواجب في أي وقت يعني في + +946 +01:12:39,880 --> 01:12:45,570 +موعده المحدد على الصفحة يعنيو هيك بنقولكم يعني + +947 +01:12:45,570 --> 01:12:49,090 +اعطيكم العافية و ان شاء الله بنتمنالكم التوفيق و + +948 +01:12:49,090 --> 01:12:53,430 +لعلي طبعا ما اشوفكمش مساقات تانية لأنه طبعا انتوا + +949 +01:12:53,430 --> 01:12:57,290 +مهندسات يعني فماقدر .. ماالكمش اللي غير هذا المساق + +950 +01:12:57,290 --> 01:13:00,990 +في الكيميا فبتمنالكم التوفيق و برك الله فيكم + diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ovT6o4D8qvk.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ovT6o4D8qvk.srt new file mode 100644 index 0000000000000000000000000000000000000000..6ba831d6de1d7972fe60d70fe89a4204603cc793 --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ovT6o4D8qvk.srt @@ -0,0 +1,3775 @@ +1 +00:00:20,750 --> 00:00:25,390 +بسم الله الرحمن الرحيم، إذا الله راضي، اليوم بنكمل + +2 +00:00:25,390 --> 00:00:29,710 +في الـ stoichiometry calculations with chemical + +3 +00:00:29,710 --> 00:00:33,410 +formulas and equations. شوفنا في الحصة الماضية بعض + +4 +00:00:33,410 --> 00:00:37,670 +الحسابات الكيميائية المختلفة، والحصة هذه إن شاء + +5 +00:00:37,670 --> 00:00:44,470 +الله بنحاول إنه يعني نؤكد فهمنا للـ Stoichiometry + +6 +00:00:44,470 --> 00:00:50,630 +ونوسع مدى الحسابات اللي ممكن أن نعملها. فمثلا لو + +7 +00:00:50,630 --> 00:00:57,770 +عندي 2H2 زائد O2 بتعطينا 2H2O. قولنا إنه لازم + +8 +00:00:57,770 --> 00:01:01,010 +المعادلة تكون موزونة علشان أقدر أعمل أي حسابات + +9 +00:01:01,520 --> 00:01:05,880 +كيميائية. فالمعادلة بالشكل هذا طبعا موزونة. فبقول + +10 +00:01:05,880 --> 00:01:10,420 +في عندي إما أن أقول two molecules of H2, one + +11 +00:01:10,420 --> 00:01:14,960 +molecule of O2 بتعطينا اثنين molecules of H2O أو + +12 +00:01:14,960 --> 00:01:19,780 +لو كبرنا الكمية فبقول اثنين mole من ال H2 بتتفاعل + +13 +00:01:19,780 --> 00:01:24,100 +مع one mole من ال O2 بتعطينا اثنين mole من ال H2O. + +14 +00:01:24,100 --> 00:01:29,070 +طبعا الاثنين mole هذه ممكن أحولها لجرامات. المول + +15 +00:01:29,070 --> 00:01:32,250 +ممكن أحوله للجرامات. المول ممكن أحوله للجرامات + +16 +00:01:32,250 --> 00:01:36,170 +لكن إذا لم نقدر نقول هنا اثنين جرام بتفاعل مثلا مع + +17 +00:01:36,170 --> 00:01:40,050 +واحد جرام. لأ، هذه دائما المواد تتفاعل بنسبة عدد + +18 +00:01:40,050 --> 00:01:47,070 +مولاتها أو الـ mole ratio في كل تفاعل لازم تكون محددة + +19 +00:01:47,070 --> 00:01:49,270 +بالـ chemical equation اللي هي الـ balance chemical + +20 +00:01:49,270 --> 00:01:52,530 +equation. بدنا ننتبه إنه في الـ text تبعنا، الـ text + +21 +00:01:52,530 --> 00:02:02,780 +book بيجيب لنا هذا الرمز. بيجيب لنا + +22 +00:02:02,780 --> 00:02:09,340 +هذا الرمز. بيجيب لنا هذا الرمز. بيجيب لنا هذا الرمز + +23 +00:02:09,340 --> 00:02:16,920 +بيجيب لنا + +24 +00:02:16,920 --> 00:02:18,820 +هذا الرمز. بيجيب لنا هذا الرمز. بيجيب لنا هذا الرمز + +25 +00:02:18,820 --> 00:02:18,940 +بيجيب لنا هذا الرمز. بيجيب لنا هذا الرمز. بيجيب لنا هذا + +26 +00:02:18,940 --> 00:02:19,680 +الرمز. بيجيب لنا هذا الرمز. بيجيب لنا هذا الرمز + +27 +00:02:19,680 --> 00:02:20,140 +بيجيب لنا هذا الرمز. بيجيب لنا هذا الرمز. بيجيب لنا هذا + +28 +00:02:20,140 --> 00:02:20,320 +الرمز. بيجيب لنا هذا الرمز. بيجيب لنا هذا الرمز + +29 +00:02:20,320 --> 00:02:26,180 +الرمز. بيجيتمام؟ فبدنا ننتبه لهذه الإشارة، هذه بتشير + +30 +00:02:26,180 --> 00:02:31,280 +لأنه في عندي equivalency أو equivalent quantities + +31 +00:02:31,280 --> 00:02:41,780 +مش تساوي في عدد المولات على الإطلاق. طيب الآن نأكد + +32 +00:02:41,780 --> 00:02:47,520 +هذا المفهوم ونحاول أن نتطلع على بعض الـ Mall + +33 +00:02:47,520 --> 00:02:51,520 +Relationships اللي عندي. فأقول مثلا في عندي معادلة + +34 +00:02:51,520 --> 00:02:54,780 +2C4H10 + +35 +00:02:54,780 --> 00:03:00,160 +زائد 13 O2 بتعطي 8 CO2 زائد 10 ماء. هذه معادلة + +36 +00:03:00,160 --> 00:03:03,700 +موزونة. طبعا بإمكاني أني أوزنها لو بدي أوزنها، ببدأ + +37 +00:03:03,700 --> 00:03:08,510 +من هنا، ببدأ بهذا المراكز وأوزن، والله في عندي مثلا + +38 +00:03:08,510 --> 00:03:13,570 +C4، إذا بدي أحط عند الـCO2 4 وهكذا. H10، بدي أحاول + +39 +00:03:13,570 --> 00:03:18,110 +أحط هناك 5، لكن لما أجى أعد الـ Oxygen بلاقي إنه + +40 +00:03:18,110 --> 00:03:23,270 +لازم أحط هان 13 على 2، وبالتالي بدي أضرب في 2 ما + +41 +00:03:23,270 --> 00:03:27,230 +علينا الوزن شفناه سابقا، لكن لازم نعرف نوزن + +42 +00:03:27,230 --> 00:03:31,090 +المعادلة كويسة كثير. اللي بيهمني من هذه الـ slide ده + +43 +00:03:31,090 --> 00:03:34,430 +إن أحاول أبني الـ mole relationships لأن كل + +44 +00:03:34,430 --> 00:03:38,830 +حساباتنا سواء كانت في تفاعل أو في مادة واحدة قائمة + +45 +00:03:38,830 --> 00:03:43,530 +على أساس الـ Stoichiometry بالـ mole relationships. + +46 +00:03:43,530 --> 00:03:47,450 +العلاقة المولية، لأن المول أنا ممكن أحوله لـ grams + +47 +00:03:47,450 --> 00:03:51,650 +المول ممكن أحوله لـ number of atoms، لكن المول هو + +48 +00:03:51,650 --> 00:03:54,950 +أيه؟ يعتبر حجر الزاوية في حساباتي. فبدا أقول عدد + +49 +00:03:54,950 --> 00:03:57,730 +مولات الـ C4H10 قديش؟ + +50 +00:04:00,060 --> 00:04:07,520 +اثنين. عدد مولات الـ O2 يبقى عدد مولات الـ C4H10 + +51 +00:04:07,520 --> 00:04:11,580 +أكبر ولا أقل من عدد مولات الـ O2؟ أقل، يبقى هذا هي + +52 +00:04:11,580 --> 00:04:19,460 +اثنين على ثلاثة عشر. طيب نيجي number of moles of C4H10 + +53 +00:04:19,460 --> 00:04:26,100 +بالنسبة للـ CO2، اثنين على ثمانية. ليه؟ كمان مره عشان + +54 +00:04:26,100 --> 00:04:28,980 +نعرف إيش ثمانية على اثنين عشان بس نتأكد لإنه عدد مولات + +55 +00:04:28,980 --> 00:04:32,660 +الـC4H10 أقل من الـCO2 فلازم النتيجة اللي بين + +56 +00:04:32,660 --> 00:04:38,700 +جثنينها تكون كثير صحيح؟ طيب طب عدد مولات الـC4H10 + +57 +00:04:38,700 --> 00:04:45,600 +بالنسبة للـH2O، هذه 2 هذه 10، يبقى الـC4H10 أقل، يبقى + +58 +00:04:45,600 --> 00:04:55,360 +2 على 10. طيب عدد مولات الـO2 بالنسبة للـ CO2، O2 لـ CO2 + +59 +00:04:55,360 --> 00:05:02,200 +أكبر، هي ثلاثة عشر هي، عشان ثلاثة عشر على ثمانية صحيح. طيب + +60 +00:05:02,200 --> 00:05:06,540 +عدد مولات الـ O2 بالنسبة للـ H2O، هي الـ O2 هي الـ H2O + +61 +00:05:06,540 --> 00:05:14,900 +ثلاثة عشر على عشرة. عدد مولات الـ CO2 بالنسبة للمياه، الـ + +62 +00:05:14,900 --> 00:05:19,220 +CO2 ثمانية، المياه عشرة، ثمانية على عشرة. إذا كان + +63 +00:05:19,220 --> 00:05:26,010 +عملنا هذه الـ relations بس فقط شفنا من المعادلة إيش + +64 +00:05:26,010 --> 00:05:28,830 +الـ mole relationships. المسألة خلصت لإنه بعد هيك + +65 +00:05:28,830 --> 00:05:31,870 +إيش الخطوة الثانية؟ بتدوج الـ diagrams حلو كثير + +66 +00:05:31,870 --> 00:05:35,370 +الـ mol of substance اللي هي هذه أو هذه، المول إيش + +67 +00:05:35,370 --> 00:05:37,930 +بتساوي؟ جرام من الـ substance على الـ formula + +68 +00:05:37,930 --> 00:05:41,810 +weight للـ substance. انتهينا. جرام للـ substance أو + +69 +00:05:41,810 --> 00:05:44,250 +جرام للـ substance على الـ formula weight للـ + +70 +00:05:44,250 --> 00:05:50,460 +substance. ولو بدي أجيب عدد الجزيئات بتضرب عدد + +71 +00:05:50,460 --> 00:05:53,180 +المولات في الـ Avogadro's number. كل مسائل محلولة + +72 +00:05:53,180 --> 00:05:57,850 +لإنه شوفنا المثلث تبعنا، شوفنا المثلث، المثلث كان + +73 +00:05:57,850 --> 00:06:02,370 +بيقول والله gram لـ number بقدرش. gram لـ mole، اه + +74 +00:06:02,370 --> 00:06:08,470 +بقسم على الـ formula ايه؟ مول لـ number + +75 +00:06:08,470 --> 00:06:11,750 +بدي أضرب في عدد avogadro. مول في number في عدد + +76 +00:06:11,750 --> 00:06:15,690 +avogadro. يفجأه هي، لو قولنا هي المثلث تبعنا بس عشان + +77 +00:06:15,690 --> 00:06:24,020 +نتذكر، هي الـ mole، هي الـ gram، هي الـ number of atoms + +78 +00:06:24,020 --> 00:06:31,280 +أو molecules. لجرام كيف بيتحولش مباشرة لجرام للمول؟ + +79 +00:06:31,280 --> 00:06:35,700 +جرام بده نقسم على الـ formula. طب المول للـ number جرام + +80 +00:06:35,700 --> 00:06:42,700 +بده نضرب في 6.02 في 10 قوّة 23. هي كل المسائل تبعتنا + +81 +00:06:42,700 --> 00:06:46,240 +كلها إترسمت في هذا المحور. طب كيف أجيب المول مدام + +82 +00:06:46,240 --> 00:06:52,040 +محور إيه هذا؟ هو بالشكل هذا ماشي يا جماعة؟ طب حد يقول + +83 +00:06:52,040 --> 00:06:56,860 +لي مثلا، خلينا + +84 +00:06:56,860 --> 00:07:03,360 +نطلع على تفصيل لهذا الكلام ونطبقه على أمثلة + +85 +00:07:03,360 --> 00:07:08,480 +حقيقية ونشوف قديش الحسابات بتكون سهلة خالص معانا. + +86 +00:07:14,120 --> 00:07:17,820 +هي نفس الكلام، بقول 2C4H10 بس التفاعل اللي كان + +87 +00:07:17,820 --> 00:07:23,280 +عندنا، لو بدي أنا أقول mol C4H10 بالنسبة للـ O2 فهدا + +88 +00:07:23,280 --> 00:07:27,560 +2 على 13 مظبوط. طب أنا الآن بدي أعوض، بقول هان ها + +89 +00:07:27,560 --> 00:07:32,260 +mol C4H10 يعني جرام C4H10 على الـ formula C4H10. + +90 +00:07:32,260 --> 00:07:35,680 +الـ formula طبعا من الجدول الدوري بجيب الأوزان + +91 +00:07:35,680 --> 00:07:39,610 +الذرية وبجمعها، يبقى هذه محلولة. الآن الـ 2 على 13 + +92 +00:07:39,610 --> 00:07:42,890 +ثابتة. الـ mol O2 أبارع عن ايه؟ الـ gram O2 على + +93 +00:07:42,890 --> 00:07:45,850 +formula O2. الـ formula O2 معروفة، فلو أنا عارف الـ + +94 +00:07:45,850 --> 00:07:48,830 +gram C4H10 بعرف الـ gram O2. لو عارف الـ gram + +95 +00:07:48,830 --> 00:07:54,490 +O2 بعرف الـ C4H10 صح؟ ولو بدي أحول لعدد بدي + +96 +00:07:54,490 --> 00:07:57,930 +أضرب المولات تبعتي في عدد Avogadro. ها مش هنهدي + +97 +00:07:57,930 --> 00:08:01,050 +بعض. الخطوة هذه بس المولات بتروح في عدد Avogadro. طب + +98 +00:08:01,050 --> 00:08:05,050 +ليش نتطلع هذا؟ الـ mol C2 ولا 8 على 2؟ ها الـ C2 أكبر + +99 +00:08:05,590 --> 00:08:09,170 +CO2، إيه؟ mol CO2 ثمانية، هذه اثنين، يبقى ثمانية على + +100 +00:08:09,170 --> 00:08:13,490 +اثنين، mol C14. طب كيف بتحل المسألة؟ حل المسألة بس إن + +101 +00:08:13,490 --> 00:08:18,110 +أحول المول لجرام كويس، أو أعوض عنه يعني. اه، جرام + +102 +00:08:18,110 --> 00:08:21,970 +CO2 على formula CO2، ثمانية على اثنين زي ما هي. + +103 +00:08:21,970 --> 00:08:28,150 +جرام C14 على formula C14. هاي كل المسائل، نشوف + +104 +00:08:28,150 --> 00:08:33,600 +تطبيقات، نشوف تطبيقات على هذا الكلام. بيقول لي + +105 +00:08:33,600 --> 00:08:37,540 +consider the combustion of butane اللي هو الـ C4H10. + +106 +00:08:37,540 --> 00:08:40,560 +شوفنا في الحصة الماضية إنه هو الـ fuel اللي بيستخدم + +107 +00:08:40,560 --> 00:08:43,080 +بالـ disposable general purpose lighters، اللي هي + +108 +00:08:43,080 --> 00:08:46,360 +الولاعات اللي بيبقوا في الأسواق. calculate the mass + +109 +00:08:46,360 --> 00:08:52,820 +of CO2 produced when one gram of C4H10 is burned. لو + +110 +00:08:52,820 --> 00:09:00,860 +حرقنا واحد جرام من هذا. بقول هو طالب إيش؟ طالب الـ + +111 +00:09:00,860 --> 00:09:08,030 +gram CO2، يبقى بدي أجيب أنا في الحقيقة الـ mol CO2. إيش + +112 +00:09:08,030 --> 00:09:12,210 +في عندي الـC4H10، يبقى العلاقة اللي بدي إياها فقط هذا + +113 +00:09:12,210 --> 00:09:17,570 +هي هذا وهذا. هاي اللي بلزمونه من المعادلة. حل لو + +114 +00:09:17,570 --> 00:09:21,090 +حلينا عادي، هأقول لكم كيف بنحل بعد شوية بس نخلص هذا + +115 +00:09:21,090 --> 00:09:24,750 +كيف بنحل بطريقة اللي أنا قلت لكم قبل هيك، بس أقول في + +116 +00:09:24,750 --> 00:09:29,630 +الأول بنجيب الـ mol C4H10، هذه خطوات. mol C4H10 بتساوي + +117 +00:09:29,630 --> 00:09:34,080 +جرام على الـ formula وطلع عندي هالرقم. طيب الـ mol CO2 + +118 +00:09:34,080 --> 00:09:38,560 +طلع أربع أمثال الـ C4H10 اللي بتفاعل معاه + +119 +00:09:38,560 --> 00:09:42,500 +يبقى أربعة لإنه ثمانية على اثنين. CO2 هي ثمانية على + +120 +00:09:42,500 --> 00:09:47,800 +اثنين بيعطيني هذا الرقم. إذا لجرام CO2 بتضرب الـ mol + +121 +00:09:47,800 --> 00:09:53,750 +CO2 في الـ formula. ممكن أحل هيك أو أو أحل بخطوة + +122 +00:09:53,750 --> 00:09:56,950 +واحدة بس اللي هي dimensional analysis، أقول والله + +123 +00:09:56,950 --> 00:10:00,790 +أنا بدي جرام CO2. إيش عندي معطى؟ قال واحد جرام + +124 +00:10:00,790 --> 00:10:06,250 +C4H10، أنا ما بديش جرام C4H10، بدي أحط جرام C4H10 تحت + +125 +00:10:06,250 --> 00:10:10,670 +علاقة الجرام بالمول بس. إذا بقول ثمانية وخمسين جرام + +126 +00:10:10,670 --> 00:10:14,170 +C4H10 هي الـ formula weight معبر عنها بالجرامات، هي + +127 +00:10:14,170 --> 00:10:19,790 +عبارة عن واحد مول C4H10. فراح الجرام مع الجرام. طب + +128 +00:10:19,790 --> 00:10:24,490 +أنا في عندي مول C4H10، ما بديش C4H10 من أصله، فابدأ أحط + +129 +00:10:24,490 --> 00:10:29,030 +المول C4H10 وين؟ تحت، فبيقول من المعادلة اثنين مول + +130 +00:10:29,030 --> 00:10:34,370 +C4H10 بيعطيني ثمانية مول CO2، هذه equivalence مش + +131 +00:10:34,370 --> 00:10:38,690 +تساوي. هذه ايه؟ العلامة اللي قلناها قبل شوية، + +132 +00:10:38,690 --> 00:10:42,390 +equivalence، لأن هذا هي يوجد 2 مول تتفاعل مع 8 مول + +133 +00:10:42,390 --> 00:10:46,970 +CO2. طب أنا ما بديش مول CO2، بأحطه تحت، يالها هذه 44 جرام + +134 +00:10:46,970 --> 00:10:51,290 +CO2. إذا انحلت المسألة، لأن أنا بدي جرام CO2 وأصرت + +135 +00:10:51,290 --> 00:10:55,430 +لجرام CO2. لكن هحل بعض المسائل بالشكل هذا أنا، لكن + +136 +00:10:55,430 --> 00:10:59,310 +ما بديش ياكم تحلوا هيك. فيه أسهل، فيه أسهل. ابني جي + +137 +00:10:59,310 --> 00:11:06,430 +للأسهل، بقول هي المعادلة، حلو كثير. الـ mol CO2 عدد + +138 +00:11:06,430 --> 00:11:12,590 +مولات الـ CO2 ثمانية، عدد مولات الـ C4H10 اثنين + +139 +00:11:12,590 --> 00:11:16,010 +يبقى عدد مولات الـ CO2 ثمانية على اثنين من عدد + +140 +00:11:16,010 --> 00:11:19,950 +مولات الـ C4H10. هذه أول خطوة أعملها صح، خلصت. + +141 +00:11:19,950 --> 00:11:25,210 +المسألة لأنه بدعوت تحت هذه بقيمتها إجرام CO2 على + +142 +00:11:25,210 --> 00:11:28,090 +فورمولاوية CO2 ثمانية على اثنين زي ما هي إجرام + +143 +00:11:28,090 --> 00:11:32,900 +C4H10 على فورمولاوية C4H10 وبال تعويض طبعا مباشر + +144 +00:11:32,900 --> 00:11:35,840 +جرام CO2 على 44 هو الـ formula weight ثمانية على + +145 +00:11:35,840 --> 00:11:40,600 +اثنين واحد اللي هي عدد جرامات الـ C14 على 58 انتهت + +146 +00:11:40,600 --> 00:11:46,060 +المسألة فلو حلينا هيك أنا بأعتقد أنه مش ممكن نغلط + +147 +00:11:46,060 --> 00:11:51,840 +والحل بسيط للغاية ما فيش فيه أي مشاكل طيب نتطلع على + +148 +00:11:51,840 --> 00:12:00,040 +نفس المسألة لكن نحسب حاجة ثانية mass of water بيقول + +149 +00:12:00,040 --> 00:12:05,620 +أنه حرقنا واحد جرام من الـ C4H10 فبدنا + +150 +00:12:05,620 --> 00:12:09,420 +نعرف قداش مية تكونت طبعا ممكن أنا كمان مرة ممكن + +151 +00:12:09,420 --> 00:12:16,140 +أنا نعم صحيح العلاقة المية و الـ C4H10 بس خلينا نحل + +152 +00:12:16,140 --> 00:12:19,980 +بخطوات الخطوة الأولى بجيب المول C4H10 بيدقول + +153 +00:12:19,980 --> 00:12:25,690 +جرامات على الفورمولويت حلوبتجيب المول H2O عشرة على + +154 +00:12:25,690 --> 00:12:29,770 +اثنين من المول plus C أربعة عشرة عشرة لإنه خمس + +155 +00:12:29,770 --> 00:12:33,710 +أمثال شايفين هذا اثنين هذا عشرة اه يبقى بدي أقول + +156 +00:12:33,710 --> 00:12:38,230 +والله خمسة في الرقم هذا طب أنا بدي إجراء ميه إذا + +157 +00:12:38,230 --> 00:12:40,670 +بدي أقول والله المول ميه اللي طلع عندي في + +158 +00:12:40,670 --> 00:12:45,470 +الفورمولوات هي الـ point O 862 في 18 بتطلع عندي + +159 +00:12:45,470 --> 00:12:48,920 +الجواب ممكن أحل بخطة واحدة كالتالي أقول والله أنا + +160 +00:12:48,920 --> 00:12:52,380 +بدي جرام ميه حلو ايش معايا قال والله معايا واحد + +161 +00:12:52,380 --> 00:12:57,020 +جرام C4H10 أنا ما بديش واحد جرام C4H10 بديش جرام + +162 +00:12:57,020 --> 00:12:59,840 +C4H10 فاين اللي بدي أحطها بدي أحطها تحت في المقام + +163 +00:13:00,640 --> 00:13:04,140 +طب ايش متكافئة الـ formula weight عبارة عن واحد مول + +164 +00:13:04,140 --> 00:13:06,100 +الـ formula weight معبر عنها بالجرامات عبارة عن + +165 +00:13:06,100 --> 00:13:09,840 +واحد مول يبقى واحد مول ثمانية وخمسين جرام C4H10 هي + +166 +00:13:09,840 --> 00:13:15,920 +ثمانية وخمسين أو جرام C4H10 مع جرام C4H10 صار عند + +167 +00:13:15,920 --> 00:13:22,510 +واحد مول C4H10 أنا ما بديش مول C4H10 أنا بدي جرام H2O + +168 +00:13:22,510 --> 00:13:27,730 +إذا بدي أحط المول C4H10 تحت فبدي أقول كل اثنين مول + +169 +00:13:27,730 --> 00:13:34,370 +C4H10 بتعطيني عشرة مول هذه equivalency مش تساوي + +170 +00:13:34,370 --> 00:13:38,750 +equivalency فهيها اثنين مول الـ C4H10 بتعطي عشرة + +171 +00:13:38,750 --> 00:13:43,090 +مول H2O هي راحت هذه مع هذه حلو صار عندي مول H2O + +172 +00:13:43,090 --> 00:13:47,570 +سهلة بدي أقول كل مول H2O ثمنتاشر جرام H2O حلت + +173 +00:13:47,570 --> 00:13:52,060 +المسألة لكن ليش أعمل هيك أو هيك ما عندي الحل مباشر + +174 +00:13:52,060 --> 00:13:56,280 +على طول هاي المعادلة بقول والله mol H2O بتساوي + +175 +00:13:56,280 --> 00:14:02,900 +عشرة على اثنين mol C4H10 صح المسألة خلصت ليه؟ لأنه + +176 +00:14:02,900 --> 00:14:06,460 +بس بتعود عن المول ما فيش تعويض عن المول إلا بحاجة + +177 +00:14:06,460 --> 00:14:09,500 +واحدة بس هالجيت إجرام على الـ formula wet هاي المول + +178 +00:14:09,500 --> 00:14:13,480 +يبقى جرام H2O على formula wet H2O عشرة على اثنين + +179 +00:14:13,480 --> 00:14:19,090 +إجرام C4H10 على formula wet C4H10 إجرام H2O هذه + +180 +00:14:19,090 --> 00:14:23,110 +مجهولة بدنا إياها تمنتعش الفورمولوات عشرة على اثنين زي + +181 +00:14:23,110 --> 00:14:27,190 +ما هي واحد إجرام C4H10 على الفورمولوات ثمانية + +182 +00:14:27,190 --> 00:14:32,870 +وخمسين المسألة انحلت بتهيأ لهيك يعني أسهل كثير + +183 +00:14:32,870 --> 00:14:38,190 +أسهل كثير لإيش بدي يعني يعني أخد خطوات أو أعمل + +184 +00:14:38,190 --> 00:14:42,290 +خطوة كبيرة ممكن أرلف أي شيء فيها لإيش أخد خطوات أو + +185 +00:14:42,290 --> 00:14:43,310 +أعمل خطوة كبيرة ممكن أرلف أي شيء فيها لإيش أخد + +186 +00:14:43,310 --> 00:14:45,850 +لإيش أخد خطوات أو أعمل خطوات كبيرة ممكن طيب نشوف + +187 +00:14:45,850 --> 00:14:50,410 +كمان حاجة نحسب حاجة ثانية من نفس المعادلة يبقى + +188 +00:14:50,410 --> 00:14:57,890 +بنحسب كمية الـ O2 consumed يبقى حرجت البيوتين فعايز + +189 +00:14:57,890 --> 00:15:02,950 +كمية من الـ O2 فبتعرف كم جرام O2 الواحد جرام من الـ + +190 +00:15:02,950 --> 00:15:07,990 +CH4 CH4H10 بيقوز يبقى هاي علبة CH4H10 و الـ O2 بس + +191 +00:15:08,820 --> 00:15:11,560 +مدام المعادلة الموزونة فبقول كمان مرة المول C + +192 +00:15:11,560 --> 00:15:13,720 +أربعة أش عشرة واحد على ثمانية خمسية على الـ formula + +193 +00:15:13,720 --> 00:15:16,860 +weight هاي الخطوات المول O2 تلاتاشر اثنين في المول + +194 +00:15:16,860 --> 00:15:21,080 +C أربعة أش عشرة يعني point one one two الـ gram O2 + +195 +00:15:21,080 --> 00:15:24,080 +مول O2 في الـ formula weight حلو بطلع عندنا نتيجة + +196 +00:15:24,080 --> 00:15:28,260 +ما فيش مشكلة خطوات لكن ممكن أن أوقف عند أي خطوة + +197 +00:15:28,260 --> 00:15:31,520 +ممكن ما أعملش خطوة صح بالطريقة اللي أنا علمكم إياها + +198 +00:15:31,520 --> 00:15:35,320 +قبل شوية ما فيش مجال للخطأ نجي نطلع على الحل بخطوة + +199 +00:15:35,320 --> 00:15:38,360 +واحدة بقول أنا بدي جرام O2 لكن عندي بس واحد جرام + +200 +00:15:38,360 --> 00:15:44,060 +C4H10 ما بديش جرام C4H10 فبقول 58 جرام C4H10 اللي هي + +201 +00:15:44,060 --> 00:15:47,940 +الفم ولا ويت وعبّر عالم الجرامات تكافئ واحد مول من + +202 +00:15:47,940 --> 00:15:52,220 +الـ C4H10 يعني كل واحد مول فيه من الـ C4H10 فيه 58 + +203 +00:15:52,220 --> 00:15:57,340 +جرام طب أنا ما بديش مول فاعده تحت جال اثنين مول C4H10 + +204 +00:15:57,340 --> 00:16:02,080 +يتفاعل مع 13 مول من الـ O2 هذه equivalency مش + +205 +00:16:02,080 --> 00:16:06,280 +تساوي إيكوفلانسي طيب ما بديش مول O2 هاي المول O2 + +206 +00:16:06,280 --> 00:16:09,500 +تحت اثنين وتلاتين جرام O2 بيطلع عندي الجواب طب + +207 +00:16:09,500 --> 00:16:14,560 +تعالوا نشوف نتألف مع الطريقة عندي المعادلة هذا و + +208 +00:16:14,560 --> 00:16:16,900 +هذا هاي المطلوبين يعني في الشغل هاي اللي لازم .. + +209 +00:16:16,900 --> 00:16:21,020 +بس اثنين مش أكثر فبقول المول O2 المطلوب دائما بحطه + +210 +00:16:21,020 --> 00:16:24,860 +على اليسار سار الأكسجين على اليسار مول O2 لإني ما بفهمش في + +211 +00:16:24,860 --> 00:16:29,430 +حاجة غير المولات فاجيب المول O2 مول O2 تلتاشر مول + +212 +00:16:29,430 --> 00:16:33,910 +C4H10 اثنين إذا عدد مولات الـ O2 أكبر بالضرورة من + +213 +00:16:33,910 --> 00:16:39,770 +عدد مولات الـ C4H10 فبالتالي 13 على 2 مول C4H10 + +214 +00:16:39,770 --> 00:16:44,070 +الآن بقول المسألة خلصت لأنه بس بالتعويض عن المول + +215 +00:16:44,070 --> 00:16:47,510 +بقيمتها والتعويض عن المول بقيمتها بس حاجة واحدة + +216 +00:16:47,510 --> 00:16:51,610 +للآن إن إجرام ألفون مولاويت من المادة فبقول هنا + +217 +00:16:51,610 --> 00:16:55,820 +جرام O2 على فورمولا ويت اوتو تلات عشر على اثنين زي + +218 +00:16:55,820 --> 00:17:01,420 +ما هي إجرام C4H10 على فورمولا ويت C4H10 معناه كلام + +219 +00:17:01,420 --> 00:17:03,560 +إجرام اوتو على اثنين و تلاتين تلات عشر على اثنين + +220 +00:17:03,560 --> 00:17:08,440 +هذا ثابت واحد على ثمانية وخمسين إجرام اوتو فورا + +221 +00:17:08,440 --> 00:17:16,520 +النتيجة جدامي تعالوا نطلع على مسألة ثانية بيقول + +222 +00:17:16,520 --> 00:17:20,380 +determine how many grams of water are produced in + +223 +00:17:21,420 --> 00:17:25,500 +The Oxidation of One Gram of Glucose وهي رمزها C6 + +224 +00:17:25,500 --> 00:17:30,560 +H12 O6 هي الأكسجين بأكسد لجلوكوز فبيطلع عنده CO2 + +225 +00:17:30,560 --> 00:17:34,280 +ومية فعايزين نحسب how many grams of water are + +226 +00:17:34,280 --> 00:17:39,200 +produced يبقى لو حبيت أشتغل خطوة خطوة بقول والله + +227 +00:17:39,200 --> 00:17:44,100 +المول جلوكوز جرام جلوكوز واحد على مية و ثمانين + +228 +00:17:44,100 --> 00:17:46,420 +formula weight هاي اللي فيناحسب من الجدول الدوري + +229 +00:17:46,420 --> 00:17:51,270 +مجموع الأوزان الذرية معبر عنها بجرامة المول واتر + +230 +00:17:51,270 --> 00:17:55,990 +لحظة المول واتر ستة المول الجلوكوز جد ايش واحد + +231 +00:17:55,990 --> 00:18:00,910 +بنكتبش إذا المول واتر ستة أمثال عدده ستة أمثال المول + +232 +00:18:00,910 --> 00:18:04,350 +الجلوكوز يبقى المول واتر ستة في عدد مولات الجلوكوز + +233 +00:18:04,350 --> 00:18:07,530 +يبقى عدد مولات الجلوكوز هي لو ضربتها في ستة بيطلع + +234 +00:18:07,530 --> 00:18:12,430 +عندي المول واتر إجرام واتر المول واتر في 18 اللي هي + +235 +00:18:12,430 --> 00:18:15,450 +الـ formula المعطى المعطى المعطى المعطى المعطى + +236 +00:18:15,450 --> 00:18:28,150 +المعطى المعطى المعطى المعطى المعطى المعطى المعطى + +237 +00:18:28,230 --> 00:18:32,810 +equivalency term لكن أنا برضه ما بديش مول C6H12O6 أنا + +238 +00:18:32,810 --> 00:18:38,610 +بدي ميه فبقول كل واحد مول C6H12O6 يتفق يعطي أو + +239 +00:18:38,610 --> 00:18:43,990 +ينتج ستة مول من الـ H2O هذه برضه ايه equivalency + +240 +00:18:44,680 --> 00:18:51,420 +هيها مش أنه عدد مولات الجلوكوز ستة أمثال عدد مولات + +241 +00:18:51,420 --> 00:18:55,700 +الميه غلط عدد مولات الميه هي ستة أمثال للجلوكوز لكن + +242 +00:18:55,700 --> 00:18:59,160 +هذه equivalency بتقول كل مول من الجلوكوز produces + +243 +00:18:59,160 --> 00:19:03,820 +6 moles of water هي هيك بنقراها طب أنا ما بديش مول + +244 +00:19:03,820 --> 00:19:07,060 +ميه بحط تحت مول ميه 18 جرام ميه بيعطيلي النتيجة + +245 +00:19:07,060 --> 00:19:12,280 +لكن خذوا الأسهل المعادلة أنا عندي مياه و Glucose + +246 +00:19:12,280 --> 00:19:17,000 +يبقى مول مياه بتساوي ستة في مول Glucose انحلت + +247 +00:19:17,000 --> 00:19:19,740 +المسألة لأن الآن بتدعوت بس جرام مياه على الـ + +248 +00:19:19,740 --> 00:19:22,480 +formula weight مياه عنها دي تحتها على طول تساوي + +249 +00:19:22,480 --> 00:19:25,480 +ستة هي هي مول Glucose يعني جرام Glucose على + +250 +00:19:25,480 --> 00:19:28,400 +formula weight للـ Glucose إجرام مياه على ثمانتاش + +251 +00:19:28,400 --> 00:19:32,800 +ستة إجرام Glucose معايا واحد مية و ثمانين إجرام + +252 +00:19:32,800 --> 00:19:37,460 +بتطلع النتيجة فورا لو أنا عارف جداش الـ oxygen بقدر + +253 +00:19:37,460 --> 00:19:42,460 +أعرف الجلوكوز فيعني interchangeable يعني عندك دائما + +254 +00:19:42,460 --> 00:19:47,460 +لو اشتغلت زيك مادة واحدة المجهولة فلازم تعرف + +255 +00:19:47,460 --> 00:19:51,120 +تجيبيها ما فيش عندنا أكثر من مادة مجهولة نفس الكلام + +256 +00:19:51,120 --> 00:19:55,360 +بيقول لي determine how many grams of oxygen are + +257 +00:19:55,360 --> 00:19:59,740 +consumed in the oxidation of واحد جرام من الجلوكوز + +258 +00:20:01,250 --> 00:20:05,050 +جداش أكسجين راح يتفاعل مع واحد جرام جلوكوز حلو + +259 +00:20:05,050 --> 00:20:09,490 +كثير نفس الكلام بالظبط فبقول مول أكسجين بطلعه مول + +260 +00:20:09,490 --> 00:20:10,730 +أكسجين بطلعه مول أكسجين بطلعه مول أكسجين بطلعه مول + +261 +00:20:10,730 --> 00:20:12,070 +أكسجين بطلعه مول أكسجين بطلعه مول أكسجين بطلعه مول + +262 +00:20:12,070 --> 00:20:13,410 +أكسجين بطلعه مول أكسجين بطلعه مول أكسجين بطلعه مول + +263 +00:20:13,410 --> 00:20:16,050 +أكسجين بطلعه مول أكسجين بطلعه مول أكسجين بطلعه مول + +264 +00:20:16,050 --> 00:20:26,770 +أكسجين بطلعه مول أكسجين + +265 +00:20:26,770 --> 00:20:32,590 +بطلع ما بديش واحد مول ما بديش مولات C6H12O6 بقول كل + +266 +00:20:32,590 --> 00:20:39,010 +مول C6H12O6 يتفاعل مع هيك بنقراها يتفاعل مع 6 mol + +267 +00:20:39,010 --> 00:20:43,290 +O2 هيك الـ dimension الـ analysis بيعتمد الـ + +268 +00:20:43,290 --> 00:20:46,650 +equivalences التكافؤات من المعادلة ايش بتفاعل مع + +269 +00:20:46,650 --> 00:20:51,710 +ايش ايش بيعطي ايش مش أعداد ما بديش مول اوتو هي مول + +270 +00:20:51,710 --> 00:20:55,590 +اوتو اثنين وتلاتين جرام اوتو فبيطلع عند النتيجة + +271 +00:20:55,590 --> 00:21:00,350 +مباشرة لكن أنا بدي أتحل هيك مول اوتو هو المجهول + +272 +00:21:00,350 --> 00:21:04,710 +اه ستة أمثال مول من الجلوكوز والآن مول اوتو جرام + +273 +00:21:04,710 --> 00:21:08,870 +اوتو على الفورمولوات ستة مول C6H12 هو ستة جرام + +274 +00:21:08,870 --> 00:21:12,790 +C6H12 هو ستة على الفورمولوات فعند الجرام اوتو + +275 +00:21:12,790 --> 00:21:15,930 +مجهولة اثنين وتلاتين ستة واحد جرام على مية و + +276 +00:21:15,930 --> 00:21:22,150 +ثمانين تطلع النتيجة مباشرة يمكن هذه آخر مسألة + +277 +00:21:22,150 --> 00:21:25,950 +معناها تقريبا في هذا الموضوع decomposition of + +278 +00:21:25,950 --> 00:21:31,070 +KClO3 لو بدنا نسميها .. لو بدنا نسميها بنسميها + +279 +00:21:31,070 --> 00:21:34,430 +لجسمين هذا الـ metal ion و هذه .. هذه ايش اسمها؟ + +280 +00:21:35,440 --> 00:21:41,820 +Echlorate لأن مجموعة الهالوجينات الـCl الـBr الـO + +281 +00:21:41,820 --> 00:21:48,100 +الـ Reference compound الأكسيانيون في A تلاتة + +282 +00:21:48,100 --> 00:21:51,800 +أكسجين فهذا الـ 8 فهذا 8 بالظبط يعني فهذا + +283 +00:21:51,800 --> 00:21:55,520 +Chlorate وهذا Potassium فهذا Potassium Chlorate + +284 +00:21:55,520 --> 00:22:02,140 +Potassium Chlorate طيب فبيقول أن هذا المركب يتفكك + +285 +00:22:07,460 --> 00:22:11,680 +عشان نحضر كميات قليلة من الأكسجين لأن الباطينة لو + +286 +00:22:11,680 --> 00:22:16,600 +يعني سخّنّاها مهلّنها لأنه أعتقد أنا ممكن يكون يعني + +287 +00:22:16,600 --> 00:22:20,340 +منفجر إلى حد ما يعني فلو سخّنّاها مهّل فممكن يعطيني + +288 +00:22:20,340 --> 00:22:24,900 +شوية إيه؟ Oxygen فانا بدي .. بقولي how many grams + +289 +00:22:24,900 --> 00:22:28,280 +of oxygen can be prepared from أربع و نص جرام KClO3 + +290 +00:22:28,280 --> 00:22:32,120 +؟ عندي أربع و نص جرام من هذا، كم جرام أكسجين + +291 +00:22:32,120 --> 00:22:36,810 +بيعطيني؟ اسمعوا، راح أحل هيك على طول أقول والله مول + +292 +00:22:36,810 --> 00:22:41,550 +O2 اللي اللي بيطلع أبارعا خدوا بالكم هذا تلاتة هذا + +293 +00:22:41,550 --> 00:22:44,490 +اتنين يبقى عدد مولات الأكسجين أكثر ولا أقل من KClO3 + +294 +00:22:44,490 --> 00:22:47,530 +أكثر إذا تلاتة على اتنين واحد ونص ماحدش + +295 +00:22:47,530 --> 00:22:50,870 +يكتبلي اتنين على تلاتة عدد مولات الأكسجين إيش + +296 +00:22:50,870 --> 00:22:54,350 +مالها أكثر تلاتة إذا تلاتة على اتنين وهنا بيقول + +297 +00:22:54,350 --> 00:22:57,690 +تلاتة على اتنين عدد المولات تلاتة على اتنين مول + +298 +00:22:57,690 --> 00:23:03,700 +KClO3 المسألة خلصت لأنه بس بتضاعف عن المول + +299 +00:23:03,700 --> 00:23:06,240 +بالجرام على الفورمولوات جرام O2 على الفورمولوات + +300 +00:23:06,240 --> 00:23:09,720 +O2 تلاتة على اتنين زي ما هي جرام KClO3 تلاتة على + +301 +00:23:09,720 --> 00:23:13,520 +الفورمولوات KClO3 وبالتالي جرام أكسجين على + +302 +00:23:13,520 --> 00:23:17,180 +32 تلاتة على اتنين 4.5 جرام KClO3 + +303 +00:23:17,180 --> 00:23:19,640 +تلاتة على 122.6 من عشرة اللي هي + +304 +00:23:19,640 --> 00:23:26,240 +الفورمولوات بيطلع عندي 1.76 أول + +305 +00:23:26,240 --> 00:23:31,660 +خطوتين؟ لأ لأ زي ما بدك هذا طريق .. هذا يعني ما فيش + +306 +00:23:31,660 --> 00:23:34,280 +.. بس بتحلي هيك على طول مباشرة يعني هاي الحل اللي + +307 +00:23:34,280 --> 00:23:38,220 +قدامك بالزمكيش هذا أبسط أنواع الحل اللي مش ممكن + +308 +00:23:38,220 --> 00:23:44,260 +يعني نغلط فيها لإنه الحسابات الكيميائية التامة + +309 +00:23:44,260 --> 00:23:47,560 +اللي هي زي اللي بناخدها احنا هال gateهذه الحسابات + +310 +00:23:47,560 --> 00:23:52,660 +بتعتمد أساسا على المولات فمدام عندك المعادلة أو + +311 +00:23:52,660 --> 00:23:59,440 +حتى المادة يعني لو جالك والله كم جرام أكسوجين + +312 +00:23:59,440 --> 00:24:06,920 +خلنا نقول how many grams + +313 +00:24:06,920 --> 00:24:13,540 +of oxygen are present + +314 +00:24:16,430 --> 00:24:23,990 +إن أربع و نص جرام KClO3 أنا بتعرف هذه مش + +315 +00:24:23,990 --> 00:24:26,850 +معادلة هذه عبارة عن مادة واحدة بتعرف إيه كم جرام + +316 +00:24:26,850 --> 00:24:34,030 +أكسجين فيها كيف بقى حل خليني بحل كتالة بقول هاي الـ + +317 +00:24:34,030 --> 00:24:40,670 +KClO3 طلع معايا بتعطيني + +318 +00:24:40,670 --> 00:24:43,670 +اتنين بس بالدوزن المعادلة كيف بتدوزنها بالنسبة + +319 +00:24:43,670 --> 00:24:49,360 +للأكسجين بس ماذا أضيف؟ اتنين هنا و تلاتة هنا حلو + +320 +00:24:49,360 --> 00:24:56,300 +جداً فبقول تلاتة مول أكسجين بيساوي تلاتة على اتنين + +321 +00:24:56,300 --> 00:25:01,780 +مول KClO3 هو نفس الحل نفس الحل لحظة لأن هو الوضع + +322 +00:25:01,780 --> 00:25:04,580 +الأكسجيني يعني ما هو جامد هنا هو نفسه يعني لو بس + +323 +00:25:04,580 --> 00:25:08,240 +حتى من مدار المعادلة من مدار معرفة المعادلة مدام + +324 +00:25:08,240 --> 00:25:11,240 +عندي المادة و بتشوف قد إيش فيها أكسجين مثلاً فبيقول + +325 +00:25:11,240 --> 00:25:15,200 +والله بحط المادة بتعطيني بس أكسجين طب خدوا بالكم + +326 +00:25:15,200 --> 00:25:20,020 +من مسألة يعني مثلاً لو جالي قد إيش عندنا how many grams + +327 +00:25:20,020 --> 00:25:21,720 +of carbon + +328 +00:25:25,160 --> 00:25:31,160 +I represent in أربع و نص جرام C6H12O6 + +329 +00:25:31,160 --> 00:25:33,520 +مش بحاجة اللي يعمل لي حاجة على طول بقول هي + +330 +00:25:33,520 --> 00:25:40,420 +الـC6H12O6 كم كربون بتعطيني إيه؟ ستة كربون، إذا + +331 +00:25:40,420 --> 00:25:47,900 +المول كربون بده يساوي ستة مول C6H12O6 المول كربون + +332 +00:25:47,900 --> 00:25:52,490 +جرام كربون على أطلعاش بدها تساوي ستة في المول + +333 +00:25:52,490 --> 00:25:55,590 +اللي 4.5 جرام على 180 انتهت + +334 +00:25:55,590 --> 00:25:59,870 +المسألة كل الشغل اللي اشتغلناه سابقاً بتحل هيك سواء + +335 +00:25:59,870 --> 00:26:03,670 +مادة واحدة أو chemical reaction سواء مادة واحدة أو + +336 +00:26:03,670 --> 00:26:07,250 +chemical reaction كل الحل عندي من المول + +337 +00:26:07,250 --> 00:26:10,170 +relationships لو أعطاك مادة واحدة طلع المادة + +338 +00:26:10,170 --> 00:26:16,090 +المجهولة منها بس use ليها أوزنها زي ما شفنا في ال + +339 +00:26:16,090 --> 00:26:20,090 +.. زي هين برضه، ما نفعش تقول ال C6H12 بتعطيني + +340 +00:26:20,090 --> 00:26:24,550 +كربوناً، لا يا عم مش كربوناً، ستة طيب، حلو كثير + +341 +00:26:24,550 --> 00:26:29,170 +خلينا .. نتطلع + +342 +00:26:29,170 --> 00:26:33,890 +الآن على .. يعني الموضوع تقريباً يعني الآخر من + +343 +00:26:33,890 --> 00:26:37,330 +ناحية عملية قبل الآخر في جزئية صغيرة في آخر + +344 +00:26:37,330 --> 00:26:39,890 +المحاضرة راح نقولها في حاجة اسمها limiting + +345 +00:26:39,890 --> 00:26:44,720 +reactant ما هو limiting reactant؟ طبعاً يأتيك سؤال + +346 +00:26:44,720 --> 00:26:47,520 +في الامتحان ممكن النصف النهائي على limiting + +347 +00:26:47,520 --> 00:26:51,440 +reactant لأنه مهم ما هو limiting reactant؟ والله يا + +348 +00:26:51,440 --> 00:26:55,480 +جماعة limiting reactant هو المادة اللي بتحدد قيمة + +349 +00:26:55,480 --> 00:27:00,060 +النواتج اللي بتحدد قيمة النواتج يعني مثلاً لو أنا + +350 +00:27:00,060 --> 00:27:03,520 +عندي كل اتنين مول من ال H2 مع كم مول هيدرو أكسجين + +351 +00:27:03,520 --> 00:27:09,200 +بتفعله طب افرضه عندي هنا مية مية مول أكسجين وعندي + +352 +00:27:09,200 --> 00:27:13,230 +هنا بس اتنين الاتنين هيتفعلوا مع الاتنين .. الاتنين + +353 +00:27:13,230 --> 00:27:17,390 +هيتفعلوا مع واحد ويظل تسعة و تسعين معايا لإن أنا + +354 +00:27:17,390 --> 00:27:21,490 +عندي كمية كبيرة فمش دائماً المواد اللي بنخلطها + +355 +00:27:21,490 --> 00:27:25,310 +بتكون لها نفس الكمية مدام مش نفس الكمية إذا ما كانش + +356 +00:27:25,310 --> 00:27:30,470 +نفس الكمية كم moles .. كم moles حسب المعادلة فالأصل + +357 +00:27:30,470 --> 00:27:35,630 +أنه في مادة بتكون موجودة بكميات قليلة هي التي + +358 +00:27:35,630 --> 00:27:39,190 +تحدد كمية الناتج يعني ها لما يكون عندي 100 مول + +359 +00:27:39,190 --> 00:27:44,890 +أكسجين مش هأحصل على 200 مول ماء مستحيل لأن الـ 200 + +360 +00:27:44,890 --> 00:27:47,890 +مول ماء بدهم 200 مول هيدروجين وأنا ما فيش عندي إلا + +361 +00:27:47,890 --> 00:27:53,550 +غير اتنين فإلا هأحصل بس على 2 مول ماء طب والأكسجين + +362 +00:27:53,550 --> 00:27:58,300 +للزيادة هيزيد تمام فالـ limiting reactant هو ال + +363 +00:27:58,300 --> 00:28:05,320 +reactant المتفاعل اللي موجود بقلة ينتهي تماماً نعم + +364 +00:28:05,320 --> 00:28:10,940 +وكيف بتعرف قال هو اللي بيعطي الكمية الأقل من ال + +365 +00:28:10,940 --> 00:28:15,020 +products يعني الـ products كميتها تعتمد على ال + +366 +00:28:15,020 --> 00:28:18,720 +limiting reactant ليه؟ لأن المتفاعل الآخر هيكون + +367 +00:28:18,720 --> 00:28:23,440 +موجود بإيه؟ بوفرة excess ال excess هتظلها زيادة + +368 +00:28:24,880 --> 00:28:29,840 +تمام؟ في عندنا 50 طالبة وفي عندنا قلم واحد بس + +369 +00:28:29,840 --> 00:28:34,520 +تاخذوا طالبة واحدة مش هيك طب والتسعة والأربعين + +370 +00:28:34,520 --> 00:28:39,000 +جادين هيك زي هيك بالظبط تفاعل طالبة واحدة بس بتسهل + +371 +00:28:39,000 --> 00:28:42,420 +قلمها ده مثلاً هتاخده أو يعني إيه جلصيبة حظها أنه + +372 +00:28:42,420 --> 00:28:46,580 +تتفاعل معه تاخده أخدته طب والتسعة والأربعين زيادة + +373 +00:28:46,580 --> 00:28:51,800 +مش هيعملوا إشي صحيح؟ يفاجئ أن نتيجة طالبة مع قلم هي + +374 +00:28:51,800 --> 00:28:57,080 +عبارة عن واحد بسمش هيك فالـ limiting reactant هو + +375 +00:28:57,080 --> 00:29:01,500 +عبارة عن الـ reactant اللي بتعتمد عليه كمية النواتج + +376 +00:29:01,500 --> 00:29:07,380 +وهو المادة التي تنتهي في التفاعل تنتهي قيمتها بعد + +377 +00:29:07,380 --> 00:29:13,120 +التفاعل صفر انتهت خلصت وكلها اتحولت إلى نواتج لكن + +378 +00:29:13,120 --> 00:29:16,480 +كمية النواتج تعتبر لو يعني وهل بدنا نحسب كمية + +379 +00:29:16,480 --> 00:29:20,580 +النواتج من الهيدروجين جار والله 2 مول هيدروجين + +380 +00:29:20,580 --> 00:29:24,970 +2 مول ماء 2 مول هيدروجين بيعطوا 2 مول ماء + +381 +00:29:24,970 --> 00:29:28,950 +نفس عددهم طيب الـ 100 مول أكسجين المفروض يعطوا ضعف + +382 +00:29:28,950 --> 00:29:32,850 +عدد ماء 200 مول ماء طب ما بيعطوهوش 200 مول ماء ليه + +383 +00:29:32,850 --> 00:29:35,850 +لأنه الهيدروجين خلص الاتنين خلصوا لما اتكونت 2 + +384 +00:29:35,850 --> 00:29:39,170 +مول ماء خلص ووقف التفاعل لأنه ما فيش عندنا أي + +385 +00:29:39,170 --> 00:29:43,680 +هيدروجين فالهيدروجين في هذه الحالة يعتبر إيه؟ ال + +386 +00:29:43,680 --> 00:29:48,580 +limiting reactant ماشي يبقى في التفاعل أي تفاعل + +387 +00:29:48,580 --> 00:29:52,140 +مهم جداً بالنسبة لي أن أعرف إيش هو الـ limiting + +388 +00:29:52,140 --> 00:29:55,100 +reactant مهم جداً بالنسبة لي أعرف إيش هو الـ + +389 +00:29:55,100 --> 00:29:59,940 +limiting reactant لأنه عليه حتى يتوقف كل حساباتي + +390 +00:30:01,990 --> 00:30:08,890 +وبالتالي يعني ضروري جداً أن نفهم كيف نتعرف على ال + +391 +00:30:08,890 --> 00:30:12,610 +limiting reactant بداية علشان نقدر نعمل حساباتنا + +392 +00:30:12,610 --> 00:30:17,230 +صح هذا كلام ما تجيش يعني أو وين بلزمني لما أستخدم + +393 +00:30:17,230 --> 00:30:21,090 +كمية من A وكمية من B بدهم يتفعلوا بدهم يعطوني الـ C + +394 +00:30:21,090 --> 00:30:26,110 +و D مثلاً كمية من A وكمية من B فبقول ساعتها طيب + +395 +00:30:26,110 --> 00:30:30,230 +يتفاعل حتتوقف على كمية A ولا على كمية B تعالوا + +396 +00:30:30,230 --> 00:30:34,710 +نشوف على الأقل على الأقل حسب المعادلة تعالوا نشوف + +397 +00:30:34,710 --> 00:30:38,510 +في أنا strategies أو يعني بعض الـ استراتيجيات اللي + +398 +00:30:38,510 --> 00:30:41,450 +نعرف فيها الـ limiting reaction في البداية إيش + +399 +00:30:41,450 --> 00:30:46,770 +بنقول كلها قوانين يعني أو rules سهلة جداً جداً بقول + +400 +00:30:46,770 --> 00:30:51,410 +في البداية لازم نوزن المعادلة الكيميائية وأنا + +401 +00:30:51,410 --> 00:30:54,330 +هأفرجيكم طريقتين لحساب الـ Limiting reactant + +402 +00:30:54,330 --> 00:31:00,270 +طريقتين حلوين كثير برضه ما تغلطوش ففي البداية بدنا + +403 +00:31:00,270 --> 00:31:02,290 +المعادلة تكون موزونة من غير ما المعادلة تكون + +404 +00:31:02,290 --> 00:31:05,110 +موزونة وهذا شرط في كل الحسابات الكيميائية زي ما + +405 +00:31:05,110 --> 00:31:09,150 +قلت سابقاً بدون معادلة موزونة كل حساباتنا مش لها + +406 +00:31:09,150 --> 00:31:13,180 +أي قيمة يبقى المعادلة بتكون موزونة في البداية، بدنا + +407 +00:31:13,180 --> 00:31:16,320 +نحوّل إذا كان في جرامات من A وجرامات من B، + +408 +00:31:16,320 --> 00:31:18,200 +بدنا نحولّهم إلى مولات، لأننا ما نفهمش في + +409 +00:31:18,200 --> 00:31:21,480 +الجرامات، والمعادلة موجودة مش في الجرامات، + +410 +00:31:21,480 --> 00:31:23,980 +موجودة في المولات، هذه الـ coefficients اللي فيها + +411 +00:31:23,980 --> 00:31:28,860 +مولات، مش جرامات، وبالتالي لازم الكميات اللي عندي + +412 +00:31:28,860 --> 00:31:34,410 +من A ومن B إيش تكون بإيه؟ بالمولات الحاجة التالتة + +413 +00:31:34,410 --> 00:31:39,630 +قال بدي أقسم عدد المولات المقطعة في المسألة على الـ + +414 +00:31:39,630 --> 00:31:49,550 +coefficients اللي في المعادلة يعني مثلاً أنا + +415 +00:31:49,550 --> 00:31:56,090 +هل استخدمت مثلاً 4 أو 5 moles هل استخدمت + +416 +00:31:56,090 --> 00:32:00,010 +3 moles فابد أشوف أنه الـ Limiting reaction + +417 +00:32:00,010 --> 00:32:03,530 +بقسم 5 على 2 2.5 3 على 1 3 هذا أقل إذا هذا هو الـ Limiting reaction هذا + +418 +00:32:03,530 --> 00:32:08,790 +الخطوة بس عشان أوجد إيش هو الـ Limiting reaction + +419 +00:32:08,790 --> 00:32:10,850 +بستفيدش منها بس بعملها هيك عشان أوجد إيه الـ + +421 +00:32:15,010 --> 00:32:17,670 +Limiting reaction هذا اللي هو الحاجة الّتي بختار + +422 +00:32:17,670 --> 00:32:20,770 +ال smaller value اتنين و نص أو تلاتة لأ اتنين و نص + +423 +00:32:20,770 --> 00:32:26,670 +بعرف أنه إيش اللي هيزيد الأكسجين فهذه ال rules كمان + +424 +00:32:26,670 --> 00:32:30,790 +مرة بقول بكتب المعادلة موزونة بعد ما أكتب المعادلة + +425 +00:32:30,790 --> 00:32:34,130 +موزونة بحول لجرامات اللي عندي لمولات كان عندي + +426 +00:32:34,130 --> 00:32:39,090 +جرامات بعدين بقسم كل mole من مادة على ال + +427 +00:32:39,090 --> 00:32:42,030 +coefficient الـ mole coefficient تبعها بطلع عند + +428 +00:32:42,030 --> 00:32:45,990 +قيمة بختار الأقل بكون هو إيه الـ limiting reactant + +429 +00:32:45,990 --> 00:32:51,950 +تعالوا نطلع مثال في عندنا عشرة مول H2 and سبعة مول of + +430 +00:32:51,950 --> 00:32:55,390 +O2 بقول هيها عشرة مول سبعة مول هاي المعادلة + +431 +00:32:55,390 --> 00:33:00,610 +الموزونة هنا 2 H2 + O2 بتعطينا نواتج طب + +432 +00:33:00,610 --> 00:33:03,510 +العشرة مول ولا السبعة مول بقول عشرة على اتنين خمسة + +433 +00:33:03,510 --> 00:33:07,030 +سبعة على واحد سبعة إذًا إيش الـ limiting reactant الـ + +434 +00:33:07,030 --> 00:33:09,270 +H2 انتهينا طيب + +435 +00:33:14,270 --> 00:33:17,910 +في عندي طريقة تانية يعني لو نسيتي تعملي هيك إيش + +436 +00:33:17,910 --> 00:33:21,950 +تسوي لو نسيتي تعملي هيك بقول أول حاجة بنحول ل + +437 +00:33:21,950 --> 00:33:29,730 +مولات حولنا لمولات إيش الناتج مول O2 صح مول H2O + +438 +00:33:29,730 --> 00:33:34,650 +هي الناتج طيب لما نكون في عندي عشرة مول + +439 +00:33:39,050 --> 00:33:46,190 +العشرة أكمل عدد مولات المية الناتج يعني المول water + +440 +00:33:46,190 --> 00:33:53,410 +إيش بيساوي المول H2 بيساوي عشرة اللي هو الناتج طب + +441 +00:33:53,410 --> 00:34:02,430 +عدد مولات المية بده يساوي ضعف مول + +442 +00:34:03,670 --> 00:34:08,370 +أوكسجين بدي يساوي 14 يبقى أنه اللي أعطى عدد أقل أو + +443 +00:34:08,370 --> 00:34:13,570 +كمية أقل من النواتج يظهر الـ H2 هو الـ limiting + +444 +00:34:13,570 --> 00:34:17,010 +reactant الكمية الأقل بتمتج عن الـ chemical .. عن + +445 +00:34:17,010 --> 00:34:20,910 +الـ limiting reactant كمان مرة قلت أنا بطلع على + +446 +00:34:20,910 --> 00:34:24,770 +النواتج وبشوف أكمل طالع منها من كل واحدة منهم + +447 +00:34:24,770 --> 00:34:28,790 +فبقول والله المول المية بتساوي المول الـ H2 لأنه + +448 +00:34:28,790 --> 00:34:32,010 +اتنين واتنين يعني نفس العدد عدد مولات المية سواء + +449 +00:34:32,010 --> 00:34:36,070 +عدد مولات الـ H2 يبقى عدد مولات المية عشرة هذا لو + +450 +00:34:36,070 --> 00:34:41,790 +كان يعني الـ H2 هو المحدد طيب لو كان الـ O2 بقول الـ + +451 +00:34:41,790 --> 00:34:46,250 +O2 mol H2O بتساوي هات اتنين ضعف عدد مولات الأكسجين + +452 +00:34:46,250 --> 00:34:49,530 +يعني اتنين في سبعة يعني 14 إيش اللي أعطى كمية + +453 +00:34:49,530 --> 00:34:54,210 +نواتج أقل إذًا الـ H2 هو الـ limiting reactant سيان + +454 +00:34:54,210 --> 00:34:58,170 +بدك تشتغل زي هيك حلو بدك تشتغل زي هيك برضه حلو مش + +455 +00:34:58,170 --> 00:35:04,060 +عندي مشكلة يعني أي طريقة ترتاح عليها كويس يعني + +456 +00:35:04,060 --> 00:35:14,280 +الطرقتين سهلين ومباشرات بشكل كبير طيب + +457 +00:35:14,280 --> 00:35:18,000 +نيجي لِمثال وبرضه الحلو بال يعني نوجد الـ limiting + +458 +00:35:18,000 --> 00:35:20,680 +record بالطريقتين بيقول the most important + +459 +00:35:20,680 --> 00:35:24,880 +commercial process for converting into from the + +460 +00:35:24,880 --> 00:35:29,370 +air النيتروجين اللي يحتوي على الكمباونز الانتو + +461 +00:35:29,370 --> 00:35:31,410 +نيتروجين الانتو نيتروجين الانتو نيتروجين الانتو + +462 +00:35:31,410 --> 00:35:32,110 +نيتروجين الانتو نيتروجين الانتو نيتروجين الانتو + +463 +00:35:32,110 --> 00:35:36,930 +نيتروجين الانتو نيتروجين الانتو نيتروجين الانتو + +464 +00:35:36,930 --> 00:35:42,270 +نيتروجين الانتو نيتروجين الانتو نيتروجين الانتو + +465 +00:35:42,270 --> 00:35:46,010 +نيتروجين الانتو نيتروجين الانتو نيتروجين الانتو + +466 +00:35:46,010 --> 00:35:48,930 +نيتروجين الانتو نيتروجين الانتو نيتروجين الانتو + +467 +00:35:48,930 --> 00:35:51,650 +نيتروجين الانتو نيتروجين الانتو نيتروجين الانتو + +468 +00:35:51,650 --> 00:35:57,410 +نيتروجين الانتو نيتروجين بيفعلهم على الهيدروجين + +469 +00:35:57,410 --> 00:36:00,690 +بيحضروا منه الأمونيا ومن الأمونيا بيحضروا مركبات + +470 +00:36:00,690 --> 00:36:04,710 +كتيرة خالص فإيش بيقول سؤاله how many moles of + +471 +00:36:04,710 --> 00:36:11,330 +ammonia can be formed from تلاتة mole نيتروجين and + +472 +00:36:11,330 --> 00:36:18,930 +six mole هيدروجين بقول ها في البداية في البداية + +473 +00:36:18,930 --> 00:36:23,830 +لازم مدام يعطاني المادتين كمياتهم لازم نعرف هل هم + +474 +00:36:23,830 --> 00:36:27,490 +بتفعلوا كلهم ولا في unlimited reactant فغالبا + +475 +00:36:27,490 --> 00:36:30,570 +بيكون unlimited reactant فإيش بقول؟ بدي أشوف الـ + +476 +00:36:30,570 --> 00:36:34,150 +unlimited reactant تلاتة على واحد ستة على تلاتة + +477 +00:36:34,150 --> 00:36:41,290 +اتنين إذًا الـ hydrogen هو المحدد طيب بلاش بقول الـ + +478 +00:36:41,290 --> 00:36:45,770 +nitrogen خليني أقول الـ ammonia أنا بدي الـ ammonia + +479 +00:36:45,770 --> 00:36:52,870 +الـ ammonia مول أمونيا سوى اتنين في المول النيتروجين + +480 +00:36:52,870 --> 00:36:57,630 +لإن هد واحد هد اتنين الأمونيا ضعف إذًا ستة طب + +481 +00:36:57,630 --> 00:37:04,690 +المول الأمونيا بتساوي تلاتة اتنين اتنين على تلاتة + +482 +00:37:04,690 --> 00:37:11,370 +في مولات الـ oxygen مولات الهيدروجين بتساوي اتنين + +483 +00:37:11,370 --> 00:37:18,520 +على تلاتة في ستة بنساوي أربعة، إذًا أنهي مادة اللي + +484 +00:37:18,520 --> 00:37:22,000 +بتعطي الكمية الأقل من النواتج الـ H2 إذًا هي الـ H2 + +485 +00:37:22,000 --> 00:37:26,060 +limiting reactant؟ من وجهة نظركم أنهي أسهل؟ + +486 +00:37:26,060 --> 00:37:29,820 +الأولانية ولا هذه؟ التانية أسهل، التانية أسهل، التانية + +487 +00:37:29,820 --> 00:37:29,880 +أسهل، التانية أسهل، التانية أسهل، التانية أسهل، التانية + +488 +00:37:29,880 --> 00:37:31,180 +أسهل، التانية أسهل، التانية أسهل، التانية أسهل، التانية + +489 +00:37:31,180 --> 00:37:31,560 +أسهل، التانية أسهل، التانية أسهل، التانية أسهل، التانية + +490 +00:37:31,560 --> 00:37:35,240 +أسهل، التانية أسهل، التانية أسهل، التانية أسهل، التانية + +491 +00:37:35,240 --> 00:37:38,460 +أسهل، التانية ما فيش عيني أي ممكنة، بس المهم أنه + +492 +00:37:38,460 --> 00:37:42,980 +يعني أنا شخصيا ما بحبش الحفظ، أنا بستخدم الأولى، بس + +493 +00:37:42,980 --> 00:37:46,500 +أنا شخصيا ما بحبش الحفظ يعني، فأنا بحب أن الشغل يعني + +494 +00:37:46,500 --> 00:37:49,980 +على طول دائما يكون في بالنا كيف نحسبها، فالـ LR + +495 +00:37:49,980 --> 00:37:51,880 +اللي هو اللي بيجري أكتر هو اللي بيعطي كمية أقل من + +496 +00:37:51,880 --> 00:37:56,220 +النواتج، طب بنشوف، مبشرة، بمجرد النظر بتبين، يعني + +497 +00:37:56,220 --> 00:38:03,490 +مش شرط حتى إنه نعمل التفاعل، طيب قَال لنا أن هذا هو الـ + +498 +00:38:03,490 --> 00:38:09,630 +limiting reactant طيب الـ reaction 2H2 + +499 +00:38:09,630 --> 00:38:14,350 ++ O2 بيعطينا 2H2O هو استخدام لتصنيع كهربائية + +500 +00:38:14,350 --> 00:38:16,590 +في مصدر ميزة ميزة ميزة ميزة ميزة ميزة ميزة ميزة + +501 +00:38:16,590 --> 00:38:17,930 +ميزة ميزة ميزة ميزة ميزة ميزة ميزة ميزة ميزة ميزة + +502 +00:38:17,930 --> 00:38:18,110 +ميزة ميزة ميزة ميزة ميزة ميزة ميزة ميزة ميزة ميزة + +503 +00:38:18,110 --> 00:38:18,450 +ميزة ميزة ميزة ميزة ميزة ميزة ميزة ميزة ميزة ميزة + +504 +00:38:18,450 --> 00:38:27,150 +ميزة ميزة ميزة ميزة ميزة + +505 +00:38:27,650 --> 00:38:31,730 +تمام؟ بطارية .. بطارية وقود بيقولولها يعني هبطيها + +506 +00:38:31,730 --> 00:38:35,410 +الوقود مباشرة وهي بتطلع كهربا مش هي store + +507 +00:38:35,410 --> 00:38:39,110 +البطاريات العادية بتعمل storage للكهربا لأ هذه لأ + +508 +00:38:39,110 --> 00:38:42,550 +هذه بتعطيها مواد وبتحولها فورًا لإيه؟ لكهربا اسمها + +509 +00:38:42,550 --> 00:38:48,090 +fuel cell suppose افترض أنه a fuel cell contains + +510 +00:38:48,090 --> 00:38:51,910 +150 grams hydrogen and 1500 grams of oxygen how + +511 +00:38:51,910 --> 00:38:55,810 +many grams of water can form؟ بدنا نجيب المولات + +512 +00:38:55,810 --> 00:38:58,970 +المولات للهيدروجين 150 على 2 75 + +513 +00:38:58,970 --> 00:39:03,530 +هيها 75 المولات للأكسجين 1500 + +514 +00:39:03,530 --> 00:39:08,450 +على 32 46.875 خيص طب أنا بدي أعرف أنه الـ limiting + +515 +00:39:08,450 --> 00:39:13,250 +reactant 75 على 2 37.5 + +516 +00:39:13,250 --> 00:39:17,530 +46 على 1 46.875 + +517 +00:39:17,530 --> 00:39:22,110 +هذه الـ LR برضه يعني لو حبينا مستحيل خالص مجرد + +518 +00:39:29,570 --> 00:39:35,190 +النظر المول مية تساوي المول هيدروجين المول مية + +519 +00:39:35,190 --> 00:39:37,650 +تساوي المول هيدروجين + +520 +00:39:40,710 --> 00:39:47,250 +المول مية تساوي المول هيدروجين لكن المول مية ضعف اه + +521 +00:39:47,250 --> 00:39:50,270 +ضعف يعني اتنين في إيه في 46.875 يطلع 93.75 + +522 +00:39:50,270 --> 00:39:52,430 +لـ 75 لأ الـ 75 هو الـ + +523 +00:39:52,430 --> 00:39:55,430 +limiting reactant ليه؟ لأنه الـ limiting reactant + +524 +00:39:55,430 --> 00:39:59,790 +لازم يعطيني الكمية الأقل من الـ products فسيان زي + +525 +00:39:59,790 --> 00:40:04,430 +ما نحسب equius بيقول how many grams of water can + +526 +00:40:04,430 --> 00:40:10,530 +form دائما الزيادة أو المادة الموجودة بزيادة ب .. + +527 +00:40:10,530 --> 00:40:16,570 +يعني بعتبرهاش في أي .. في أي حسابات إلا إذا كان + +528 +00:40:16,570 --> 00:40:20,330 +طلب مني طب قد إيش موجودة زيادة منها أما إن بسيبها + +529 +00:40:20,330 --> 00:40:23,350 +الحسابات تعتمد بس على الـ limiting reactor ف أنا + +530 +00:40:23,350 --> 00:40:27,250 +عندي الآن هو طالب إيه how many grams water فعلى + +531 +00:40:27,250 --> 00:40:31,930 +طول لو أنت بعد نفسك طلبتنا بقول والله المول بحللها + +532 +00:40:31,930 --> 00:40:38,690 +هيك أنا ولا لأ اه المول Water هي عبارة عن مول + +533 +00:40:38,690 --> 00:40:42,410 +هيدروجين، نفس العدد، إذًا جرام water على الـ form + +534 +00:40:42,410 --> 00:40:44,670 +of weight water، جرام هيدروجين على الـ form of + +535 +00:40:44,670 --> 00:40:48,050 +weight هيدروجين، جرام water على 18، 150 جرام + +536 +00:40:48,050 --> 00:40:51,250 +هيدروجين على الـ form of weight الاتشو عبارة عن 2، + +537 +00:40:51,250 --> 00:40:56,220 +يبقى جرام water 1350 جرام 1350 + +538 +00:40:56,220 --> 00:41:01,120 +جرام ماشي يا جماعة اعتمدنا بس الهيدروجين ليه؟ لأن + +539 +00:41:01,120 --> 00:41:03,680 +الهيدروجين هو الـ limiting reactant هذا موجود + +540 +00:41:03,680 --> 00:41:08,620 +بزيادة، لا يستخدم في الحسابات إلا إذا كان طلب منه + +541 +00:41:08,620 --> 00:41:14,740 +قد إيش ضايل منه بعد التفاعل طيب زي هذا السؤال، زي + +542 +00:41:14,740 --> 00:41:21,330 +هذا السؤال، بيقول 2 H2 + O2 بتعطينا H2O هذا + +543 +00:41:21,330 --> 00:41:23,750 +التفاعل يستخدم لإنتاج كهربائية في سلّة الحيوانات + +544 +00:41:23,750 --> 00:41:28,170 +الهيدروجينية إذا كانت السلّة تحتوي على 150 جرام + +545 +00:41:28,170 --> 00:41:31,370 +حيوانات هيدروجينية و 1500 جرام أكسجين نفس السؤال + +546 +00:41:31,370 --> 00:41:37,040 +كم عدد جرام أكسجين غير تفاعل سيبقى؟ how many grams + +547 +00:41:37,040 --> 00:41:43,040 +كم جرام أكسجين بده إيه؟ بده يظل بعد التفاعل عشان + +548 +00:41:43,040 --> 00:41:46,120 +أجيب how many grams will be left لازم يبقى كم جرام + +549 +00:41:46,120 --> 00:41:49,800 +تفاعل فشوف الـ limiting reactant هو معروف قد إيش + +550 +00:41:49,800 --> 00:41:53,980 +هيتفاعل معاه حسب المعادلة فبقول الله اه يبقى المعل + +551 +00:41:53,980 --> 00:42:00,710 +أكسجين بده يساوي نص المول الهيدروجين وبعدين هان إيش + +552 +00:42:00,710 --> 00:42:05,470 +بقول بقول جرام أكسجين على فورمولة ويت أكسجين بيساوي + +553 +00:42:05,470 --> 00:42:10,450 +نص المول هيدروجين ما هو معايا مش مشكلة المول عبارة + +554 +00:42:10,450 --> 00:42:14,730 +عن جرام هيدروجين على الفورمولة ويت هيدروجين محسب + +555 +00:42:15,310 --> 00:42:17,650 +فبجيب جرام أكسجين على طول هذا اللي إيه؟ اللي + +556 +00:42:17,650 --> 00:42:23,410 +اتفاعل طبعا عندي الكلي اللي بزيادة فبقسم الكلي + +557 +00:42:23,410 --> 00:42:27,510 +ناقص اللي اتفاعل بكون هو اللي إيه؟ اللي left دائما + +558 +00:42:27,510 --> 00:42:30,490 +هذا الـ procedure اللي بستكتبه عشان أجيب الكمية + +559 +00:42:30,490 --> 00:42:34,630 +الزائدة فعلى سبيل المثال بقول مول أكسجين reacted + +561 +00:42:34,630 --> 00:42:38,610 +نصف مول هيدروجين يعني نصف في هذه القيمة سبعة وثلاثين + +562 +00:42:39,280 --> 00:42:43,580 +أو نصف مول من ال oxygen يعني كم جرام؟ جال سبعة و + +563 +00:42:43,580 --> 00:42:46,520 +ثلاث و نصف مول في ال formula 1200 طب أنا عندي 1500 + +564 +00:42:46,520 --> 00:42:52,200 +1500 ناقص التفاعل 1200 طب عن ال 300 هدول زيادة + +565 +00:42:52,200 --> 00:43:01,860 +بعملوش حاجة التفاعل خلص وهم أيه موجودين طيب + +566 +00:43:01,860 --> 00:43:08,960 +في التفاعل اتنين ألومنيوم و ثلاثة كلورين بتفعل و + +567 +00:43:08,960 --> 00:43:12,500 +بتعطينا اثنين ألومنيوم كلوريد هذا combination إذا + +568 +00:43:12,500 --> 00:43:15,660 +كانتين بتكونوا واحد combination combination + +569 +00:43:15,660 --> 00:43:20,120 +reaction if واحد و نصف مول of ألومنيوم and ثلاثة + +570 +00:43:20,120 --> 00:43:23,940 +مول of Cl2 are mixed هاي واحد و نصف مول هتريحني و + +571 +00:43:23,940 --> 00:43:27,740 +هان ثلاثة مول are mixed find the limiting reactant + +572 +00:43:27,740 --> 00:43:31,340 +على طول واحد و نصف على اثنين point seven five ثلاثة + +573 +00:43:31,340 --> 00:43:35,120 +على ثلاثة واحد إذن هذا هو الـ Limiting Reactance + +574 +00:43:35,120 --> 00:43:37,960 +يبقى هنا يبقى هذا مش هنستخدمه في الحسابات انتهى + +575 +00:43:37,960 --> 00:43:41,220 +هنا خلاص مافي استخدامه في الحسابات إلا إذا كان + +576 +00:43:41,220 --> 00:43:47,360 +جالي جداش فيه زيادة من الكلورين طيب يبقى عرفنا + +577 +00:43:47,360 --> 00:43:53,120 +إيش هو Limiting Reactance إيش بيقول how many moles + +578 +00:43:53,120 --> 00:43:57,600 +of aluminum chloride are formed هل في عندي 1.75 + +579 +00:43:57,600 --> 00:44:03,170 +كان جداش جالي 1.5 الاثنين بتعطوا اثنين إذن اللي على + +580 +00:44:03,170 --> 00:44:07,010 +طول المول aluminum chloride واحد و نصف لأن المول + +581 +00:44:07,010 --> 00:44:09,790 +aluminum chloride how many moles of aluminum + +582 +00:44:09,790 --> 00:44:12,370 +chloride are formed هي نفس ال aluminum المول + +583 +00:44:12,370 --> 00:44:15,990 +aluminum chloride تساوي المول aluminum أيه يا بنات هي + +584 +00:44:15,990 --> 00:44:24,690 +مول AlCl ثلاثة اثنين تساوي مول Al لأنه اثنين أو + +585 +00:44:24,690 --> 00:44:28,190 +اثنين على اثنين يعني واحد ماشي إذا هذه واحد و نصف + +586 +00:44:28,190 --> 00:44:32,930 +وبجد تانية واحد و نصف How many moles of excess + +587 +00:44:32,930 --> 00:44:37,790 +reactant will be left at the end of reaction؟ جداش + +588 +00:44:37,790 --> 00:44:44,150 +رايح يزيد عندنا جداش رايح يزيد من الكلوريد فبقول + +589 +00:44:44,150 --> 00:44:48,850 +أنا في البداية أشوف جداش اتفاعل فالمول Cl2 بدها + +590 +00:44:48,850 --> 00:44:54,450 +تساوي ثلاثة على اثنين مول Al المول Cl2 reacted + +591 +00:44:54,450 --> 00:44:59,170 +يعني بتكون جرام أقول لأ هو بده بس المولز لزيادة + +592 +00:44:59,170 --> 00:45:02,090 +how many moles ولا لأ how many moles اه بس المولز + +593 +00:45:02,090 --> 00:45:06,650 +المول Cl2 بتساوي ثلاثة على اثنين في المول + +594 +00:45:06,650 --> 00:45:11,930 +aluminum واحد و نصف بتساوي two point two five ين ولا + +595 +00:45:11,930 --> 00:45:16,370 +two point two five برش جد ماكان اه two point two + +596 +00:45:16,370 --> 00:45:19,930 +five إذن ان المول left الثلاثة ناقص ال two point + +597 +00:45:19,930 --> 00:45:26,060 +two five ثلاثة ناقص المعايا يا بنات؟ ثلاثة minus + +598 +00:45:26,060 --> 00:45:29,420 +two point two five هذا هو اللي اتفاعل هذا الكلي + +599 +00:45:29,420 --> 00:45:33,480 +يبقى هاي اللي زاد point seven five mole هذه مسألة + +600 +00:45:33,480 --> 00:45:36,400 +كتير سهلة ليش حاطيلها في الآخر مش عارف أنا هذه + +601 +00:45:36,400 --> 00:45:39,720 +المفروض تكون أول مسألة لأن مافيش فيها أي حسابات + +602 +00:45:39,720 --> 00:45:48,160 +مباشرة يعني طيب عندي المسألة هذه بتقول when a 2 + +603 +00:45:48,160 --> 00:45:53,080 +gram strip of zinc metal يعني عندي strip من zinc + +604 +00:45:53,080 --> 00:45:56,600 +metal is placed in aqueous solution containing 2.5 + +605 +00:45:56,600 --> 00:46:00,300 +gram silver nitrate حطيناها في محلول مائي من ال + +606 +00:46:00,300 --> 00:46:03,420 +silver nitrate اللي بيحتوي على 2.5 gram silver + +607 +00:46:03,420 --> 00:46:07,400 +nitrate حلو ال reaction هذا هو zinc solid بتفاعل + +608 +00:46:07,400 --> 00:46:10,380 +مع silver nitrate بيعطيني silver solid زي zinc + +609 +00:46:10,380 --> 00:46:14,650 +nitrate تمام هاي التفاعل موزون بقول لي which + +610 +00:46:14,650 --> 00:46:17,970 +reactant is limiting حلو كتير نشتغل واحدة واحدة + +611 +00:46:17,970 --> 00:46:22,590 +بدي أجيب ال moles من الزنك هاي ال moles زنك اثنين + +612 +00:46:22,590 --> 00:46:25,370 +جرام على الفورمولا اتوميك weight يعني point + +613 +00:46:25,370 --> 00:46:29,410 +oh three oh five eight طيب ال moles النيتريت جال + +614 +00:46:29,410 --> 00:46:32,710 +والله ال moles اثنين و نص جرام اللي هي وزنتها على + +615 +00:46:32,710 --> 00:46:35,230 +one six nine point nine point oh one four seven + +616 +00:46:35,230 --> 00:46:41,700 +فبعدين بحقق point oh three 0.0158 فوق الزنك والـ + +617 +00:46:41,700 --> 00:46:49,240 +silver nitrate 0.0147 هذا على واحد 0.03058 هذا على + +618 +00:46:49,240 --> 00:46:53,960 +اثنين 0.074 + +619 +00:46:53,960 --> 00:47:00,240 +تقريبا ثلاثة اش سبعة مثلا اش زي هيك في أو كمان وهي + +620 +00:47:00,240 --> 00:47:04,720 +كمان أو واضح إنه طبعا هذا أجل يبجي هذا هو ال + +621 +00:47:04,720 --> 00:47:09,620 +limiting reactor ولو حبيناها .. لو حبيناها ممكن + +622 +00:47:09,620 --> 00:47:14,880 +جدًا أن نقول ال + +623 +00:47:14,880 --> 00:47:21,100 +.. الزنك هذا بيعطي ضعف عدد مولات ال silver مثلا + +624 +00:47:21,100 --> 00:47:26,040 +ضعف الزنك يعني point oh six من هنا هذا بيعطي + +625 +00:47:26,040 --> 00:47:35,260 +silver مول silver بتساوي اثنين في مول zinc بتساوي + +626 +00:47:35,260 --> 00:47:41,700 +point oh six مول سلفر نيتريت + +627 +00:47:41,700 --> 00:47:47,400 +مول سلفر + +628 +00:47:47,400 --> 00:47:52,320 +نيتريت مول سلفر نيتريت + +629 +00:47:54,330 --> 00:47:59,010 +بسيب من الـ 0.01 أقل كتير من الـ 0.06 يفاجئ الـ + +630 +00:47:59,010 --> 00:48:03,210 +silver nitrate هي العامل المحدد فسواء اشتغلت على + +631 +00:48:03,210 --> 00:48:07,350 +أنه بطلع عندي نواتج أقل أو اشتغلت على تجسيم على ال + +632 +00:48:07,350 --> 00:48:10,570 +coefficients سيئة بطلع عندنا دائما ال silver + +633 +00:48:10,570 --> 00:48:14,970 +nitrate هو العامل المحدد إذا بسيب الزنك في حاله + +634 +00:48:14,970 --> 00:48:17,770 +ليه؟ لأنه مش هيلزمني في الحسابات حاجة موجودة + +635 +00:48:17,770 --> 00:48:21,350 +بزيادة بتلزمنيش سواء زيادة كيلو ولا اثنين كيلو ولا + +636 +00:48:21,350 --> 00:48:25,590 +عشرة كيلو ولا ألف كيلو بهمني هو زيادة فبتخليش في + +637 +00:48:25,590 --> 00:48:29,530 +الحسابات إلا إذا كنا نحسب جداش متبقي منه طب نمرط + +638 +00:48:29,530 --> 00:48:37,030 +بيه .. بها يهال اه هذا بفرجيكم كيف .. ماشي مول + +639 +00:48:37,030 --> 00:48:40,890 +سلفر زي اللي حسبت لكم قبل شوية يعني النواتج أفرجيكم + +640 +00:48:40,890 --> 00:48:46,190 +طيب الآن بتقول how many grams of silver will form + +641 +00:48:46,190 --> 00:48:50,370 +بقول والله المول سلفر بيساوي المول سلفر نيتريت ليش + +642 +00:48:50,370 --> 00:48:53,890 +قلت مول سلفر نيتريت مش مول زنك لأن زنك مش limited + +643 +00:48:53,890 --> 00:48:56,530 +أكثر أنا بدي limited أكثر أكثر فهان اثنين على + +644 +00:48:56,530 --> 00:48:59,640 +اثنين يعني واحد فهنجرام Silver على الـ Atomic + +645 +00:48:59,640 --> 00:49:02,220 +weight للسلفر جرام Silver Nitrate على ال Formula + +646 +00:49:02,220 --> 00:49:05,160 +weight للسلفر نيتريت، لاحظوا هذا هو هذا وهذا هو + +647 +00:49:05,160 --> 00:49:10,080 +هذا، عدد مولات السلفر اثنين، عدد مولات السلفر نيتريت + +648 +00:49:10,080 --> 00:49:13,980 +اثنين، إذا عدد مولات السلفر يساوي عدد مولات السلفر + +649 +00:49:13,980 --> 00:49:19,980 +نيتريت، هاي حساباتنا، بنعد عدد طيب بنعوض جرام سيلفر + +650 +00:49:19,980 --> 00:49:24,920 +على 107.9 أتم كويتلاس سيلفر 2.5 جرام سيلفر نيتريات + +651 +00:49:24,920 --> 00:49:31,260 +على 109.9 بيطلع عندي الجرام سيلفر 1.39 طب كمان + +652 +00:49:31,260 --> 00:49:35,200 +مسألة هي نفسها بنكمل في C منها how many grams of + +653 +00:49:35,200 --> 00:49:38,560 +zinc nitrate will form هاي المعادلة نصف الجرامات ده + +654 +00:49:38,560 --> 00:49:44,870 +أحسنتي أحسنتي mole zinc nitrate وواحد مول سلفر + +655 +00:49:44,870 --> 00:49:49,750 +نيتريت اثنين إذا المول زنك نيتريت نصف المول سلفر + +656 +00:49:49,750 --> 00:49:55,520 +نيتريت تمام والآن خلصت المسألة تعويض جرام على ال + +657 +00:49:55,520 --> 00:49:57,500 +formula weight جرام على ال formula weight وانتهت + +658 +00:49:57,500 --> 00:50:00,640 +المسألة يبقى gram zinc nitrate على formula weight + +659 +00:50:00,640 --> 00:50:03,760 +لل zinc nitrate بتساوي نصف جرام silver nitrate على + +660 +00:50:03,760 --> 00:50:06,860 +ال formula weight لل silver nitrate يعني gram zinc + +661 +00:50:06,860 --> 00:50:12,660 +nitrate على 189 و 4 من 10 نصف ثابتة زي ما هي اثنين + +662 +00:50:12,660 --> 00:50:17,480 +و نصف على 169 و 9 من 10 بيطلع إن الجرام zinc كنا + +663 +00:50:17,480 --> 00:50:21,080 +نطلع نفس النتيجة هنا يبقى هذه فيها غلطة فيهم واحدة + +664 +00:50:21,080 --> 00:50:24,360 +منهم إنّها cut to paste يعني فتأكدوا من الرقمين + +665 +00:50:24,360 --> 00:50:27,960 +هدول هذا هو اللي جابله تأكدوا من الرقمين إنّهوا + +666 +00:50:27,960 --> 00:50:35,020 +الصح فيهم وجيبوا يعني الإجابة الصحيحة آخر جزء من + +667 +00:50:35,020 --> 00:50:41,260 +هذا المثال بيقول how many grams of the excess + +668 +00:50:41,260 --> 00:50:45,100 +reactant are left at the end of reaction عشان أجيب + +669 +00:50:45,100 --> 00:50:47,940 +ال excess reactant لازم أجيب كمية التفاعل + +670 +00:50:47,940 --> 00:50:51,780 +stoichiometrically فبقول والله هاي التفاعل المول + +671 +00:50:51,780 --> 00:50:55,940 +زنك عدده عدد مولات الزنك نصف عدد مولات ال silver + +672 +00:50:55,940 --> 00:51:00,380 +nitrate إذا المول زنك بتبدأ يساوي نصف مول ال silver + +673 +00:51:00,380 --> 00:51:03,940 +nitrate جرام زنك على ال atomic weight للزنك نصف + +674 +00:51:03,940 --> 00:51:06,300 +جرام silver nitrate على ال formula silver nitrate + +675 +00:51:06,300 --> 00:51:10,040 +يبقى جرام زنك على 65.4 ال atomic weight للزنك + +676 +00:51:10,040 --> 00:51:14,680 +نصف اثنين و نصف جرام silver nitrate على ال 169.9 + +677 +00:51:14,680 --> 00:51:18,760 +بيطلع ال جرام زنك reacted 0.480 جرام لكن أنا + +678 +00:51:18,760 --> 00:51:22,960 +موجود عندي ال zink strip كده اثنين يبقى اثنين ناقص + +679 +00:51:22,960 --> 00:51:31,700 +0.480 بيطلع عندي 1.52 ماشي يا جماعة الآن + +680 +00:51:31,700 --> 00:51:39,620 +يعني آخر نقطة في هذا ال chapter نتكلم + +681 +00:51:39,620 --> 00:51:42,200 +عن ال theoretical yield والـ actual yield + +682 +00:51:42,200 --> 00:51:46,600 +theoretical yield والـ actual yield يعني أنا عندي + +683 +00:51:46,600 --> 00:51:51,760 +مثلا مادتين بتفاعلوا ممكن أحسب زي ما حسبت قبل شوية + +684 +00:51:51,760 --> 00:51:57,900 +كمية النواتج مثلًا أحسبها حسابًا وأعرفها بالظبط جداش + +685 +00:51:57,900 --> 00:52:01,480 +هذه الكمية اللي أنا بحسبها حساب اسمها theoretical + +686 +00:52:01,480 --> 00:52:06,900 +yield يعني اه الناتج ال ايه النظري بحسبه حساب لكن + +687 +00:52:06,900 --> 00:52:10,180 +من ناحية عملية هل بالفعل لو حطيت stoichiometric + +688 +00:52:10,180 --> 00:52:14,180 +amounts يعني A بتفعل تمامًا مع B هل بيعطيني نفس + +689 +00:52:14,180 --> 00:52:21,760 +الكمية اللي نظريًا بحسبها بقول مش شرط مش شرط ليش مش + +690 +00:52:21,760 --> 00:52:25,100 +شرط أول حاجة التفاعل ممكن مايكونش تم 100% ممكن يكون + +691 +00:52:25,100 --> 00:52:31,290 +تم 98% 95% فممكن مايكونش تم الحاجة الثانية كمان حتى + +692 +00:52:31,290 --> 00:52:34,810 +لو كان تام مية في المية مش راح أقدر أحسب actual + +693 +00:52:34,810 --> 00:52:39,350 +yield بيساوي ال theoretical yield ليه؟ لأن مثلا في + +694 +00:52:39,350 --> 00:52:43,310 +عندي مادتين اتفعلوا كونوا راسب كونوا راسب أنا بدي + +695 +00:52:43,310 --> 00:52:48,650 +أجي أجمع الراسب هذا وأوزنه لما جمعته هل بقدر أرفع + +696 +00:52:48,650 --> 00:52:50,910 +كله من الزجاج اللي هو موجود إلا يبقى اللي معلق + +697 +00:52:50,910 --> 00:52:54,790 +حاجات فداقما كمية ال actual yield اللي أنا بحصل + +698 +00:52:54,790 --> 00:53:00,330 +عليه بتكون أقل من ال theoretical وبالتالي ممكن + +699 +00:53:00,330 --> 00:53:04,590 +أحسب حاجة بقولها percent yield النسبة المئوية + +700 +00:53:04,590 --> 00:53:08,390 +للناتج percent yield قالت هي ال actual yield على ال + +701 +00:53:08,390 --> 00:53:10,930 +theoretical yield لو كان ال actual yield يساوي ال + +702 +00:53:10,930 --> 00:53:14,980 +theoretical yield وهذا مستحيل يعني سيكون عندي 100 + +703 +00:53:14,980 --> 00:53:19,180 +من 100 لكن هو دائماً أقل من 100% فتعالَ نطلع على + +704 +00:53:19,180 --> 00:53:24,080 +مثال أو مثالين نتعلّم فيهما كيف نحسب ال + +705 +00:53:24,080 --> 00:53:27,300 +theoretical yield و ال actual yield لابدّ أن يكون + +706 +00:53:27,300 --> 00:53:30,500 +معنا طبعاً ال actual yield لا نحسبه حسابياً، + +707 +00:53:30,500 --> 00:53:34,100 +بلّ نُجري التجربة عملياً ونقوم بوزن مثلاً + +708 +00:53:34,100 --> 00:53:37,680 +الناتج أو نعرف الناتج، فيُسمّى على ال theoretical + +709 +00:53:37,680 --> 00:53:41,780 +لِكي نحصل على ال percent yield فنتطلّع على المسألة + +710 +00:53:41,780 --> 00:53:49,680 +التالية، يقول: adipic acidاللي هو H2C6H8O4 + +711 +00:53:49,680 --> 00:53:53,760 +is made commercially by a reaction between + +712 +00:53:53,760 --> 00:53:58,700 +Cyclohexane and O2 يعني عندما يتفاعل ال Cyclohexane + +713 +00:53:58,700 --> 00:54:03,340 +مع ال O2 تجارياً، هو ممكن أن أحضر ال adipic acid ونحصل على + +714 +00:54:03,340 --> 00:54:08,060 +عندنا ماء، نقول: assume that you carry out this + +715 +00:54:08,060 --> 00:54:14,350 +reaction with 25 gram of Cyclohexane والتي + +716 +00:54:14,350 --> 00:54:18,530 +Cyclohexane هو الـ limiting reactant، يعني الـ 25 + +717 +00:54:18,530 --> 00:54:22,010 +جرام هو الـ limiting reactant، ما هو؟ أول سؤال: What + +718 +00:54:22,010 --> 00:54:24,710 +is the theoretical yield of adipic acid؟ + +719 +00:54:24,710 --> 00:54:27,230 +theoretical يعني نحسب حسب المعادلة، زي ما حسبنا + +720 +00:54:27,230 --> 00:54:30,530 +سابقا، كل حساباتنا من المعادلة، هذه أول واحدة، نقول + +721 +00:54:30,530 --> 00:54:34,190 +خلينا نأخذ واحدة واحدة، هاي ال Cyclohexane يتفاعل + +722 +00:54:34,190 --> 00:54:37,850 +مع الأكسجين يعطينا adipic acid، فنقول: مول أنا أريد + +723 +00:54:37,850 --> 00:54:40,810 +أن أحسب جرام adipic acid، ما أفهمش في الجرامات، مول + +724 +00:54:40,810 --> 00:54:46,610 +adipic acid 2، 2 مول Cyclohexane، 2، إذا + +725 +00:54:46,610 --> 00:54:50,230 +ال مول adipic acid يساوي عدد مولات ال adipic + +726 +00:54:50,230 --> 00:54:54,730 +acid تساوي عدد مولات ال Cyclohexane، الآن الترجمة + +727 +00:54:54,730 --> 00:54:59,190 +الترجمة تقول: والله جرام على الفورمولا ويت جرام + +728 +00:54:59,190 --> 00:55:02,910 +على الفورمولا ويت فقط، فجرام adipic acid على ال + +729 +00:55:02,910 --> 00:55:06,550 +atomic على الفورمولا ويت، عفواً، ليس atomic، فورمولا ويت + +730 +00:55:06,550 --> 00:55:12,600 +لل adipic acid تساوي جرام cyclohexane على ال formula + +731 +00:55:12,600 --> 00:55:15,440 +weight للـ Cyclohexane، يبقى لجرام adipic acid على ال + +732 +00:55:15,440 --> 00:55:18,480 +146، اللي هي ال formula weight تساوي لجرام + +733 +00:55:18,480 --> 00:55:23,720 +Cyclohexane اللي 25 gram على ال formula weight 84، إذاً + +734 +00:55:23,720 --> 00:55:28,900 +لجرام adipic acid 43.5، هذه لجرامات النظرية، المفروض + +735 +00:55:28,900 --> 00:55:34,160 +أن أحصل عليها، بدأت أحسب حسب المعادلة، فهي لجرامات + +736 +00:55:34,160 --> 00:55:40,030 +النظرية، اللي الأصل أن أحصل عليها من المعادلة، نحصل + +737 +00:55:40,030 --> 00:55:43,790 +عليها، يعني نحصل عليها من المعادلة، جرامات نظرية + +738 +00:55:43,790 --> 00:55:49,930 +this is the theoretical yield، طيب في بيقول if + +739 +00:55:49,930 --> 00:55:57,870 +you obtain إذا حصلت على 33.5 جرام أديبك أسيد، ما هي + +740 +00:55:57,870 --> 00:56:01,370 +% yield في التجربة؟ + +741 +00:56:09,310 --> 00:56:12,650 +الـ Percent yield، ونقول: والله لا يوجد أسهل منها، الـ + +742 +00:56:12,650 --> 00:56:14,630 +Percent yield يساوي الـ Actual yield على الـ + +743 +00:56:14,630 --> 00:56:17,050 +Theoretical yield، 33.5 اللي هو + +744 +00:56:17,050 --> 00:56:22,310 +الـ actual yield العملية، المختبرة، التجربة التجريبية + +745 +00:56:22,310 --> 00:56:26,950 +على النظرية، اللي يطلع عندي 77% + +746 +00:56:26,950 --> 00:56:31,130 +إذاً ال Percent yield عندي فقط 77% + +747 +00:56:31,130 --> 00:56:33,090 +مثال آخر + +748 +00:56:35,740 --> 00:56:39,940 +يقول: imagine you are working on ways to improve + +749 +00:56:39,940 --> 00:56:45,060 +the process by which iron ore containing iron 2 O3 + +750 +00:56:45,060 --> 00:56:48,660 +is converted into iron، يعني أنا الغرض من هذه + +751 +00:56:48,660 --> 00:56:53,500 +العملية أن أحوّل iron 2 O3 إلى ال iron، فكيف أريد + +752 +00:56:53,500 --> 00:56:56,060 +أن أفعل هذا الكلام؟ أقوم بعمل reduction باستخدام الـ + +753 +00:56:56,060 --> 00:57:01,770 +CO، أقوم بعمل reduction باستخدام الـ carbon monoxide + +754 +00:57:01,770 --> 00:57:07,570 +الـ CO يتسمّى الاثنان هذا nonmetal وهذا nonmetal + +755 +00:57:07,570 --> 00:57:12,310 +يبقى هذا covalent compound أو هذا عبارة عن binary + +756 +00:57:13,190 --> 00:57:17,650 +Inorganic compound، يعني في ال groups المتأخرة على + +757 +00:57:17,650 --> 00:57:21,830 +اليمين، عندما نأتي إلى ال binary inorganic compounds نستخدم + +758 +00:57:21,830 --> 00:57:25,450 +ال mono وال di وال tri وال tetra الأخرى، فهذا + +759 +00:57:25,450 --> 00:57:29,750 +carbon واحدة، لا نقول mono carbon، لأن mono لا تأتي في + +760 +00:57:29,750 --> 00:57:33,770 +الأول، فـ carbon، أكسجين واحدة، mono oxide، لو كان فيه + +761 +00:57:33,770 --> 00:57:37,550 +اثنتان carbon، bi oxide، طيب برضه هذه فيها تسمية هي + +762 +00:57:37,550 --> 00:57:38,930 +carbon dioxide هي أمامنا + +763 +00:57:42,120 --> 00:57:48,260 +طيب يا جماعة فنقول: ماذا نقول؟ نسأل السؤال، نقول: if + +764 +00:57:48,260 --> 00:57:52,560 +you start with 150 grams Fe2O3 as the limiting + +765 +00:57:52,560 --> 00:57:55,980 +reactant what is the theoretical yield of iron؟ لو + +766 +00:57:55,980 --> 00:58:00,490 +كان عندي 150 gram من هذا، فما هو ال iron اللي أحصل + +767 +00:58:00,490 --> 00:58:03,910 +عليه من ناحية نظرية، من ناحية نظرية يعني حساباً، فنقول + +768 +00:58:03,910 --> 00:58:08,070 +ال minimum iron 2، ال minimum iron 2، و + +769 +00:58:08,070 --> 00:58:11,150 +3، 1، إذا ال minimum iron ضعيف، ال minimum + +770 +00:58:11,150 --> 00:58:15,720 +iron 2 أو 3، ما دام عملنا هذه المعادلة، المسألة + +771 +00:58:15,720 --> 00:58:19,820 +انتهت، لأن مجرد أن نقوم بها، نبدأ نقول جرام على ال + +772 +00:58:19,820 --> 00:58:22,220 +formula weight، ال atomic weight، جرام على ال + +773 +00:58:22,220 --> 00:58:24,380 +formula weight، فـ جرام iron على ال atomic weight + +774 +00:58:24,380 --> 00:58:28,460 +لل iron تساوي 2 في جرام iron 2 O3 على ال + +775 +00:58:28,460 --> 00:58:31,460 +formula weight لل iron 2 O3، نبدأ جرام iron على + +776 +00:58:31,460 --> 00:58:37,540 +55.8 تساوي 2 في 150، الأرقام اللي + +777 +00:58:37,540 --> 00:58:40,800 +معطاة، اللي في المسألة على ال formula weight 159 + +778 +00:58:40,800 --> 00:58:46,640 +.7، يطلع عندي 114.8، هذا لو كانت المعادلة تسير ب + +779 +00:58:46,640 --> 00:58:47,160 +100% + +780 +00:58:49,950 --> 00:58:53,430 +الكفاءة ممكن أن تكون 100% لكن ممكن ألا تكون الكفاءة + +781 +00:58:53,430 --> 00:58:56,730 +100%، وممكن أن يكون في أسباب أخرى، بس عارفين أن الكفاءة + +782 +00:58:56,730 --> 00:59:02,150 +ليست 100%، فخلينا نشوف B من المسألة، B تقول if + +783 +00:59:02,150 --> 00:59:09,220 +you're actual Iron yield is 87.9%، يعني لو كان من + +784 +00:59:09,220 --> 00:59:13,840 +ناحية تجريبية، من ناحية يعني من ناحية مقتبر عملية + +785 +00:59:13,840 --> 00:59:18,440 +فقط الوزن اللي حصلت عليه ليس 104 وشوية بل 87.9 + +786 +00:59:18,440 --> 00:59:22,380 +%، what is the percent yield، قال: والله ال percent + +787 +00:59:22,380 --> 00:59:24,400 +yield يساوي ال actual yield على ال theoretical yield في + +788 +00:59:24,400 --> 00:59:29,440 +100%، يعني ال percent yield 87.9% على 104.8% في 100 + +789 +00:59:29,440 --> 00:59:40,840 +% يطلع 83.9%، ماشي يا جماعة، أتمنى يعني أن الشبطة + +790 +00:59:40,840 --> 00:59:43,160 +الـ Stoichiometry تأتي في الحقيقة منها أسئلة كثيرة + +791 +00:59:43,160 --> 00:59:48,060 +لأنها حسابية، والامتحان غالباً يأتيك يعني جزء كبير + +792 +00:59:48,060 --> 00:59:51,100 +منه multiple choice، يعني تختار الإجابة الصحيحة + +793 +00:59:51,100 --> 00:59:52,780 +فعشان لا تكتبوا كثيراً + +794 +00:59:56,450 --> 01:00:00,430 +يعني والإجابة التابعة تكون محددة، فيأتي منه أسئلة + +795 +01:00:00,430 --> 01:00:03,990 +كثيرة في الامتحان، فاهتموا به بالزيادة، أتمنى + +796 +01:00:03,990 --> 01:00:07,190 +أن تراجعوا الكلام اللي أنا يعني قلته من أول ال + +797 +01:00:07,190 --> 01:00:10,030 +chapter وطريقة عرضي للموضوع وتحاولوا أنكم + +798 +01:00:10,030 --> 01:00:14,640 +تستوعبوا هذه الأسئلة اللي ذكرناها، أتمنى كثيراً أن + +799 +01:00:14,640 --> 01:00:19,000 +تعيدوا حلّ كل الأمثلة اللي حليتها في الحصة، و + +800 +01:00:19,000 --> 01:00:22,940 +تتأكدوا أنه يطلع معكم نفس النتائج اللي أنا طلعتها + +801 +01:00:22,940 --> 01:00:26,980 +ولو كان عندكم أيّ مشكلة، المفروض أنكم تشوفوني فيه + +802 +01:00:26,980 --> 01:00:30,660 +معنا، وننتقل للشبكة اللي بعده، تتحدث عن ال + +803 +01:00:30,660 --> 01:00:37,020 +aqueous solutions بشكل عام، يعني فما هي التفاعلات + +804 +01:00:37,020 --> 01:00:41,370 +اللي تتم في ال aqueous Solutions، كل chapter عليه + +805 +01:00:41,370 --> 01:00:45,350 +عليه أسئلة، سنُنزِّلها لكم إن شاء الله، طيب يا جماعة + +806 +01:00:45,350 --> 01:00:52,690 +يبقى الآن ننتقل إلى chapter الرابع في الكتاب، يعني + +807 +01:00:52,690 --> 01:00:57,590 +chapter الثالث في المساق يتحدث عن ال reactions in + +808 +01:00:57,590 --> 01:01:01,230 +aqueous solutions، كلمة aqueous تعني water + +809 +01:01:01,230 --> 01:01:04,790 +solutions، يعني محاليل مائية، في المحاليل المائية + +810 +01:01:04,790 --> 01:01:10,060 +يبقى reactions في المحاليل المائية، ماذا ندرس في هذا + +811 +01:01:10,060 --> 01:01:14,220 +الفصل؟ في هذا الفصل ندرس الخصائص العامة للمحاليل، + +812 +01:01:14,220 --> 01:01:17,620 +بعض الخصائص العامة، ليس كل الخصائص، بعض الخصائص + +813 +01:01:17,620 --> 01:01:23,200 +العامة للمحاليل المائية، وأهمها في الحقيقة، بعدين + +814 +01:01:23,200 --> 01:01:27,420 +نطلع على المحاليل المائية اللي يحصل خلالها ترسيب، + +815 +01:01:27,420 --> 01:01:31,460 +يعني لو خلطت مادتين وتكوّن عندنا رواسب، أيش المواد + +816 +01:01:31,460 --> 01:01:34,220 +اللي تعطيني رواسب؟ وايش المواد اللي لا تعطيني + +817 +01:01:34,220 --> 01:01:38,070 +رواسب؟ كويس؟ يعني لو خلطت أيّ مادتين، هل سيحصل رواسب + +818 +01:01:38,070 --> 01:01:41,530 +ولا لا؟ أريد أن أشوف هذا الكلام، أريد أن أتعرف على المواد + +819 +01:01:41,530 --> 01:01:45,330 +اللي تعطيني رواسب، والمواد اللي لا تعطيش رواسب، في + +820 +01:01:45,330 --> 01:01:50,370 +خصائص مشتركة عادةً يمكن التعرف عليها بحيث أنه تكون + +821 +01:01:50,370 --> 01:01:55,230 +في بالنا نحكم على الكثير جداً أو كثيراً جداً من + +822 +01:01:55,230 --> 01:01:59,830 +المركبات، هل هي مركبات ذائبة أم مركبات لا تذوب في + +823 +01:01:59,830 --> 01:02:03,520 +الماء، يعني عبارة عن رواسب، نريد أن نتكلم عن ال + +824 +01:02:03,520 --> 01:02:07,760 +reactions لل acids و ال bases، ال reactions للأحماض + +825 +01:02:07,760 --> 01:02:11,680 +والقواعد، ونرى ما هو الحمض وما هي القاعدة، و + +826 +01:02:11,680 --> 01:02:14,700 +كيف يحصل عند neutralization reaction عندما يتفاعل + +827 +01:02:14,700 --> 01:02:19,060 +الحمض مع القاعدة، نريد أن نتكلم عن الأكسدة والاختزال، + +828 +01:02:19,060 --> 01:02:22,460 +تفاعلات الأكسدة والاختزال هي التفاعلات اللي يتم + +829 +01:02:22,460 --> 01:02:27,640 +خلالها انتقال إلكترونات، فنطلع على تفاعلات الأكسدة + +830 +01:02:27,640 --> 01:02:30,340 +والاختزال، كيف ممكن + +831 +01:02:33,640 --> 01:02:37,720 +أن نعبر عن تركيز المحاليل، المحاليل، لو ذوّبت فيها كمية + +832 +01:02:37,720 --> 01:02:40,420 +معينة من المادة صار في تركيز معين للمادة في + +833 +01:02:40,420 --> 01:02:44,360 +المحلول، طيب كيف أعبر عن تركيز المواد في المحاليل + +834 +01:02:44,360 --> 01:02:49,100 +برضه هذا سأدرسه، وفي الآخر خالص سأقول: والله سأعمل + +835 +01:02:49,100 --> 01:02:54,280 +calculations للمحاليل المختلفة، سأرى يعني كيف أعمل + +836 +01:02:54,280 --> 01:02:58,680 +الحسابات الكيميائية للمحاليل المائية ككل، يعني ال + +837 +01:02:58,680 --> 01:03:02,470 +solutes اللي فيها، التفاعلات تبعها، نفس الكلام اللي + +838 +01:03:02,470 --> 01:03:06,170 +شفناه هناك بالضبط، لكن ممكن أن أقدّم له مفهوم جديد + +839 +01:03:06,170 --> 01:03:10,850 +بالإضافة إلى جرام على ال formula weight تساوي mole + +840 +01:03:10,850 --> 01:03:15,230 +فممكن أن أقدّم له مفهوم جديد ستشوفونه في حينه يعني، بس برضه + +841 +01:03:15,230 --> 01:03:18,550 +هو عبارة عن الـ mole يعني الـ mole بعبر عنه بطريقة + +842 +01:03:18,550 --> 01:03:24,670 +أخرى غير جرام على الـ formula weight الآن ننتقل + +843 +01:03:24,670 --> 01:03:29,990 +للموضوع بقول لما نتحدث عن الـ general properties للـ + +844 +01:03:29,990 --> 01:03:34,390 +aqua solutions بتحدث بداية عن أن والله المحلول + +845 +01:03:34,390 --> 01:03:40,500 +يتكون من مذيب ومذاب solvent or solute solvent اللي + +846 +01:03:40,500 --> 01:03:44,240 +هو المذيب و solute اللي هو المادة المذابة فلو + +847 +01:03:44,240 --> 01:03:48,260 +دوبنا مثلًا ملح في الميه بقول والله الميه هي المذيب + +848 +01:03:48,260 --> 01:03:51,680 +solvent و الملح اللي أنا بدوبه هو الـ solute + +849 +01:03:51,680 --> 01:03:58,920 +فالمذيب اللي هو الـ solvent هو المادة الموجودة + +850 +01:03:58,920 --> 01:04:04,840 +بوفرة كثيرة و الـ solute هو المادة الموجودة بشكل + +851 +01:04:04,840 --> 01:04:09,440 +أقل جزء يعني لو قلنا المحلول عبارة عن solute أو + +852 +01:04:09,440 --> 01:04:12,980 +solvent فالـ solvent هو المكون الأعظم من المحلول و + +853 +01:04:12,980 --> 01:04:16,800 +الـ solute هو المكون الأقل للمحلول فهذا مفهوم الـ + +854 +01:04:16,800 --> 01:04:20,660 +solute و الـ solvent ذكرت لما قدود سكر في الميه + +855 +01:04:20,660 --> 01:04:27,240 +مثلًا دوبنا مثلًا معلقة سكر في لتر ميه، بقول السكر + +856 +01:04:27,240 --> 01:04:31,780 +عبارة عن solute والـ لتر ميه هذا عبارة عن solvent + +857 +01:04:31,780 --> 01:04:34,600 +فالـ solvent هو الموجود بوفرة والـ solute هو الموجود + +858 +01:04:34,600 --> 01:04:42,550 +بكمية أقل أيّضًا المحاليل يمكن أن نعبر عنها على أساس + +859 +01:04:42,550 --> 01:04:46,790 +هل هي electrically conductive ولا non conductive + +860 +01:04:46,790 --> 01:04:51,010 +المحاليل إذا كانت يعني كيف بتحصل عملية الـ + +861 +01:04:51,010 --> 01:04:53,130 +conduction أو كيف ممكن نقول والله conductive ولا + +862 +01:04:53,130 --> 01:04:56,150 +non conductive بقول إذا كان المحاليل فيها أيونات + +863 +01:04:56,150 --> 01:05:00,960 +الأيونات تحمل charges موجبة وسالبة الـ charges + +864 +01:05:00,960 --> 01:05:05,480 +متكافئة يعني عدد الأيونات السالبة مش عدد تركيز + +865 +01:05:05,480 --> 01:05:09,840 +الأيونات السالبة يساوي تركيز الأيونات الموجبة بحيث + +866 +01:05:09,840 --> 01:05:14,000 +أن الـ net charge لأي محلول صفر الـ net charge لأي + +867 +01:05:14,000 --> 01:05:19,650 +محلول صفريبقى المحلول بيحتوي على أيونات والأيونات + +868 +01:05:19,650 --> 01:05:23,590 +هذه موجبة وسالبة بقول إذا كان المحلول يحتوي على + +869 +01:05:23,590 --> 01:05:27,810 +أيونات فهو يوصل للكهرباء وبالتالي هو electrically + +870 +01:05:27,810 --> 01:05:31,050 +conductive يعني electrolytic solution بنقوله + +871 +01:05:31,050 --> 01:05:36,960 +electrolytic solution بيحتوي على electrolyte أما زي + +872 +01:05:36,960 --> 01:05:42,300 +مثلًا الـ NaCl في الميه ما يكونش NaCl بيكون Na Plus + +873 +01:05:42,300 --> 01:05:53,320 +Cl Minus حلو كالسيوم مثلًا Nitrate Ca2 موجب NO3 + +874 +01:05:53,320 --> 01:05:58,560 +سالب كويس وهتدخل كل المركبات الأيونية بتتفكك في + +875 +01:05:58,560 --> 01:06:03,040 +الميه وبتعطيني أيونات أو بالأحرى بتعطيني + +876 +01:06:03,040 --> 01:06:04,920 +Electrolytic Solutions + +877 +01:06:07,080 --> 01:06:12,580 +أما المركبات التي لا تتفتت في الماء مثلًا السكر، + +878 +01:06:12,580 --> 01:06:15,460 +لو دوبنا السكر في الماء، يبقى لنا سكر، لا تتحول + +879 +01:06:15,460 --> 01:06:22,740 +إلى أيونات، إذا السكر هذا يعطينا محلول، لكن المحلول + +880 +01:06:22,740 --> 01:06:27,510 +لا يوصل إلى الكهربا لأنه لا يحتوي على أيونات وكل + +881 +01:06:27,510 --> 01:06:34,530 +المركبات غير الأيونية يعني لا توصل للكهرباء + +882 +01:06:34,530 --> 01:06:40,510 +وبالتالي هي non electrolytic أو non conductive + +883 +01:06:40,510 --> 01:06:50,110 +solutions مثال بسيط جدا، هذه مياه pure يعني إيش + +884 +01:06:50,110 --> 01:06:53,750 +مجترة تمامًا ما فيش فيها أيونات تفعل حاجة لو فيها + +885 +01:06:53,750 --> 01:06:58,030 +أيونات قليلة جدا عشرة أس سالب سبعة molar H بلس + +886 +01:06:58,030 --> 01:07:01,270 +وعشرة أس سالب سبعة molar hydroxide عشان الـ pH + +887 +01:07:01,270 --> 01:07:05,830 +تبعيتها تكون متعادلة يعني فالـ pure water فيها لازم + +888 +01:07:05,830 --> 01:07:09,210 +لازم يكون فيها بس عدد الأيونات قليل جدا فهي non + +889 +01:07:09,210 --> 01:07:15,620 +conductive تعالوا نحط لمبة بتضويش طب تعالى نحط سكر + +890 +01:07:15,620 --> 01:07:21,080 +على المحلول، المحلول هي فيه قطبين موصولين بالكهربا + +891 +01:07:21,080 --> 01:07:27,320 +وموصل فيه عندنا لمبة، إذا كان فيه تيار راح تضوي، + +892 +01:07:27,320 --> 01:07:30,500 +ما فيش تيار مش راح تضوي، فهذا نفس الكلام، بما أن + +893 +01:07:30,500 --> 01:07:37,200 +السكروز اللي هو السكر للأكل يعني، تبع الشاي وغيره، + +894 +01:07:37,200 --> 01:07:42,050 +سكروز بنقوله السكروز بما أنه non electrolyte + +895 +01:07:42,050 --> 01:07:48,550 +فمحلوله non conductive وبالتالي برضه اللمبة ما + +896 +01:07:48,550 --> 01:07:56,010 +يعني بتضوي لكن لو حطينا NaCl فورا أيونات Na plus Cl + +897 +01:07:56,010 --> 01:07:59,650 +minus بنلاحظ أن اللمبة بتضوي على طول + +898 +01:08:02,880 --> 01:08:07,660 +طيب الـ ionic compounds في الحقيقة وهي solid بتكون + +899 +01:08:07,660 --> 01:08:13,360 +crystalline موجودة في crystal معينة بشكل معين فهذا + +900 +01:08:13,360 --> 01:08:19,420 +شكل مثلًا الـ NaCl هو solid لكن لما ينحط في الميه + +901 +01:08:19,420 --> 01:08:26,930 +بتبدأ الميه تاخد أيونات الكلورايد وأيونات الصوديوم + +902 +01:08:26,930 --> 01:08:31,350 +تبقى إيه يعني زي اللي بتشدهم من المحلول ليه لأنه + +903 +01:08:31,350 --> 01:08:39,970 +زي ما هنشوف الميه الـ oxygen partial negative و الـ + +904 +01:08:39,970 --> 01:08:43,970 +hydrogen partial positive partial positive فالـ + +905 +01:08:43,970 --> 01:08:48,150 +oxygen بيجرب من الصوديوم وبيشده لأنه إيه الصوديوم + +906 +01:08:48,150 --> 01:08:53,800 +موجب NA plus هيها فبيبدأ يشده طب والهيدروجين يبدأ + +907 +01:08:53,800 --> 01:08:57,100 +يشد الكلورايد لأن الكلورايد إيش مالها سالبة وبالتالي + +908 +01:08:57,100 --> 01:09:01,000 +بيبدأ الـ Sodium الكلورايد يتفكك وتتفكك ويتحول للـ N + +909 +01:09:01,000 --> 01:09:05,120 +A plus و الـ C L minus بعد فترة هنلاقي إنه المحلول + +910 +01:09:05,120 --> 01:09:08,540 +ما فيه أي NaCl كان هذا دايب يعني وطبعًا الـ NaCl + +911 +01:09:08,540 --> 01:09:12,560 +دايب فكله راح ينتشر في المحلول بالتساوي ويصير + +912 +01:09:12,560 --> 01:09:17,240 +عندنا محلول من كلوريد الـ Sodium اللي هو عبارة عن + +913 +01:09:17,240 --> 01:09:23,850 +NA plus و Cl- يبقى في الـ solid form والله اه الـ + +914 +01:09:23,850 --> 01:09:26,190 +Na بلس و الـ Cl المنزل موجودين لكن موجودين على حالة + +915 +01:09:26,190 --> 01:09:30,520 +crystal في crystal lattice معين شكل معين لكن في + +916 +01:09:30,520 --> 01:09:36,180 +المحلول كله بيتحول لإيه؟ للأيونات عملية بنقولها + +917 +01:09:36,180 --> 01:09:40,260 +solvation إذا كان solvent لكن الـ solvent لو كان + +918 +01:09:40,260 --> 01:09:44,000 +ماء بنسمي العملية hydration إيش العملية الـ + +919 +01:09:44,000 --> 01:09:47,560 +solvation أو الـ hydration؟ هي إحاطة جزيئات الـ + +920 +01:09:47,560 --> 01:09:53,260 +solvent بالأيون و hydration إحاطة جزيئات الميه + +921 +01:09:53,260 --> 01:09:58,300 +بالأيون وحاطة جزيئات الميه بالأيون بحيث إنه زي ما + +922 +01:09:58,300 --> 01:10:03,980 +حكيت بتحاول هذه الـ solvents مهما كانت أو الميه + +923 +01:10:03,980 --> 01:10:09,900 +أنها تشد الأيونات من الكريستال وبالتالي تخلي + +924 +01:10:09,900 --> 01:10:17,180 +الـ crystal تدوب فمثلًا هاي الـ NaCl مثلًا يعني بنلاحظ + +925 +01:10:17,180 --> 01:10:18,500 +أنه إذا كان لاحظته + +926 +01:10:21,200 --> 01:10:26,900 +لو نطلع عليها، هذه أكيد Na+, ليه؟ لأنه .. إيش اللي + +927 +01:10:26,900 --> 01:10:33,160 +مجرب عليها؟ الـ Oxygen السالب وبالتالي هذا كله + +928 +01:10:33,160 --> 01:10:39,720 +بنسميه Hydrated Ion Hydrated Ion Hydrated Sodium + +929 +01:10:39,720 --> 01:10:45,130 +Ion ماشي لو كان يعني أيّ solvent ثاني بنقوله + +930 +01:10:45,130 --> 01:10:50,290 +solvated sodium ion مثلًا solvation بس عشان ميه + +931 +01:10:50,290 --> 01:10:54,250 +بنقوله إيه hydration طب نيجي نتطلع هنا لاحظوا إيش + +932 +01:10:54,250 --> 01:10:58,730 +إيش اللي مقترب من الـ chloride الهيدروجين لأنه + +933 +01:10:58,730 --> 01:11:02,900 +الهيدروجين إيش ماله partialPositive بيقولوا + +934 +01:11:02,900 --> 01:11:06,040 +partial بتعرفوا رياضيات الـ partial؟ آه Delta + +935 +01:11:06,040 --> 01:11:11,140 +بيقولوا partial positive وهكذا طيب بعد فترة عملوا + +936 +01:11:11,140 --> 01:11:17,360 +برضه هذا hydrated كلوريد أيون طب هذا اللي بيتام معاه يعني أيونات الميه آه ممكن هذا يتغير بهذا ممكن + +937 +01:11:17,360 --> 01:11:20,460 +هذا يتغير بواحد ثاني فيه تبادل لكن بشكل عام بيضلوا + +938 +01:11:20,460 --> 01:11:24,080 +hydrated في المحلول وبما أن الـ .. الـ hydrated + +939 +01:11:24,080 --> 01:11:28,740 +ions هذه وهذه حرّت الحركة في المحلول فبعد فترة + +940 +01:11:28,740 --> 01:11:33,100 +المحلول بيصير متجانس تمامًا متجانس تمامًا تركيز + +941 +01:11:33,100 --> 01:11:38,940 +أيونات الـ chloride و الـ sodium في أيّ مكان فيه واحد + +942 +01:11:38,940 --> 01:11:43,580 +يعني المحلول بيصير محلول حقيقي متجانس تمامًا طيب يا + +943 +01:11:43,580 --> 01:11:50,000 +جماعة بعتقد يعني هذا كفاية اليوم وإذا الله راد + +944 +01:11:50,000 --> 01:11:56,140 +الحصة الجاية بنكمل طبعًا في هذا الـ chapter يعطيكم + +945 +01:11:56,140 --> 01:12:01,040 +العافية + +946 +01:12:01,040 --> 01:12:01,400 +العافية diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ovT6o4D8qvk_raw.json b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ovT6o4D8qvk_raw.json new file mode 100644 index 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355.22, "text": "عدد الجزيئات بتضرب عدد المُلات في الـ Avogadro's number كل مسائل محلولة لأنه شوفنا المثلف تبعنا", "tokens": [3615, 3215, 3215, 25724, 11622, 1829, 19986, 9307, 39894, 11242, 25513, 6225, 3215, 3215, 9673, 10859, 1211, 9307, 8978, 2423, 39184, 11667, 664, 345, 340, 311, 1230, 28242, 47524, 16373, 1211, 3714, 5016, 1211, 12610, 3660, 5296, 33456, 3224, 13412, 38688, 8315, 9673, 12984, 46538, 6055, 3555, 3615, 8315], "avg_logprob": -0.36343749463558195, "compression_ratio": 1.213740458015267, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 347.66, "end": 348.48, "word": "عدد", "probability": 0.8338216145833334}, {"start": 348.48, "end": 349.3, "word": " الجزيئات", "probability": 0.84375}, {"start": 349.3, "end": 350.18, "word": " بتضرب", "probability": 0.6673990885416666}, {"start": 350.18, "end": 350.46, "word": " عدد", "probability": 0.990234375}, {"start": 350.46, "end": 350.8, "word": " المُلات", "probability": 0.677947998046875}, {"start": 350.8, "end": 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مول تتفاعل مع 8 مول CO2 طب انا بديش مول CO2 بحطه تحت يالها ده 44 جرام CO2 اذا انحلت المسألة لأن انا بدي جرام CO2 و اصرت لجرام CO2 لكن هحل بعض المسائل بالشكل هذا انا لكن بديش ياكم تحلوا هيك فيه أسهل فيه أسهل ابني جي للأسهل بقول هي المعادلة حلو كتير", "tokens": [3224, 24192, 1975, 1829, 3224, 22807, 18863, 37440, 3660, 13672, 1829, 12174, 1211, 8315, 11296, 12174, 36150, 13412, 2407, 10632, 9052, 655, 5296, 33456, 23758, 39896, 7251, 29245, 3215, 568, 3714, 12610, 6055, 2655, 5172, 995, 30241, 20449, 1649, 3714, 12610, 3002, 17, 23032, 3555, 1975, 8315, 4724, 16254, 8592, 3714, 12610, 3002, 17, 4724, 5016, 9566, 3224, 6055, 33753, 7251, 6027, 11296, 11778, 3224, 16408, 10874, 2288, 10943, 3002, 17, 1975, 15730, 16472, 5016, 1211, 2655, 9673, 3794, 10721, 37977, 5296, 33456, 1975, 8315, 4724, 16254, 10874, 2288, 10943, 3002, 17, 4032, 1975, 9381, 43500, 5296, 7435, 2288, 10943, 3002, 17, 44381, 8032, 5016, 1211, 45030, 11242, 9673, 3794, 16373, 1211, 20666, 8592, 28820, 23758, 1975, 8315, 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شايفين هذا اتنين هذا عشرة اه يبقى بدي أقول والله خمسة في الرقم هذا طب أنا بدي إجراء ميه إذا بدي أقول والله المول ميه اللي طلع عندي في الفورمولوات هي ال point O 862 في 18 بتطلع عندي الجواب", "tokens": [3555, 2655, 7435, 1829, 3555, 9673, 12610, 389, 17, 46, 6225, 8592, 25720, 15844, 1975, 2655, 1863, 9957, 9154, 9673, 12610, 1804, 383, 5551, 25513, 27884, 6225, 8592, 25720, 6225, 8592, 25720, 5296, 28814, 1863, 3224, 16490, 2304, 3794, 5551, 2304, 12984, 6027, 13412, 995, 33911, 9957, 23758, 1975, 2655, 1863, 9957, 23758, 6225, 8592, 25720, 1975, 3224, 7251, 3555, 4587, 7578, 4724, 16254, 5551, 39648, 16070, 43761, 16490, 2304, 3794, 3660, 8978, 34892, 4587, 2304, 23758, 23032, 3555, 41850, 4724, 16254, 11933, 7435, 2288, 16606, 3714, 1829, 3224, 11933, 15730, 4724, 16254, 5551, 39648, 16070, 43761, 9673, 12610, 3714, 1829, 3224, 13672, 1829, 23032, 1211, 3615, 18871, 16254, 8978, 27188, 13063, 2304, 12610, 2407, 9307, 39896, 2423, 935, 422, 26687, 17, 8978, 2443, 39894, 9566, 1211, 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"probability": 0.9140625}, {"start": 753.39, "end": 753.53, "word": " بدي", "probability": 0.4647216796875}, {"start": 753.53, "end": 753.71, "word": " أقول", "probability": 0.80224609375}, {"start": 753.71, "end": 754.15, "word": " والله", "probability": 0.733642578125}, {"start": 754.15, "end": 755.27, "word": " خمسة", "probability": 0.9725341796875}, {"start": 755.27, "end": 755.39, "word": " في", "probability": 0.88134765625}, {"start": 755.39, "end": 755.73, "word": " الرقم", "probability": 0.9814453125}, {"start": 755.73, "end": 756.07, "word": " هذا", "probability": 0.93310546875}, {"start": 756.07, "end": 756.55, "word": " طب", "probability": 0.865234375}, {"start": 756.55, "end": 756.67, "word": " أنا", "probability": 0.650390625}, {"start": 756.67, "end": 756.95, "word": " بدي", "probability": 0.9697265625}, {"start": 756.95, "end": 757.51, "word": " إجراء", "probability": 0.81646728515625}, {"start": 757.51, "end": 757.91, "word": " ميه", "probability": 0.7130533854166666}, {"start": 757.91, "end": 758.23, "word": " إذا", "probability": 0.680908203125}, {"start": 758.23, "end": 758.45, "word": " بدي", "probability": 0.95556640625}, {"start": 758.45, "end": 758.57, "word": " أقول", "probability": 0.94384765625}, {"start": 758.57, "end": 758.95, "word": " والله", "probability": 0.91064453125}, {"start": 758.95, "end": 759.39, "word": " المول", "probability": 0.93359375}, {"start": 759.39, "end": 759.63, "word": " ميه", "probability": 0.9326171875}, {"start": 759.63, "end": 759.75, "word": " اللي", "probability": 0.941162109375}, {"start": 759.75, "end": 759.97, "word": " طلع", "probability": 0.9586588541666666}, {"start": 759.97, "end": 760.27, "word": " عندي", "probability": 0.820556640625}, {"start": 760.27, "end": 760.67, "word": " في", "probability": 0.92529296875}, {"start": 760.67, "end": 761.37, "word": " الفورمولوات", "probability": 0.6500651041666666}, {"start": 761.37, "end": 761.97, "word": " هي", "probability": 0.5771484375}, {"start": 761.97, "end": 762.25, "word": " ال", "probability": 0.88037109375}, {"start": 762.25, "end": 762.49, "word": " point", "probability": 0.81884765625}, {"start": 762.49, "end": 762.85, "word": " O", "probability": 0.192138671875}, {"start": 762.85, "end": 763.87, "word": " 862", "probability": 0.69677734375}, {"start": 763.87, "end": 764.01, "word": " في", "probability": 0.6591796875}, {"start": 764.01, "end": 764.51, "word": " 18", "probability": 0.48681640625}, {"start": 764.51, "end": 765.19, "word": " بتطلع", "probability": 0.74200439453125}, {"start": 765.19, "end": 765.47, "word": " عندي", "probability": 0.937744140625}, {"start": 765.47, "end": 765.99, "word": " الجواب", "probability": 0.9524739583333334}], "temperature": 1.0}, {"id": 31, "seek": 77984, "start": 766.88, "end": 779.84, "text": "ممكن احل بخطة واحدة كالتالي اقول والله انا بدي جرام ميه حلو ايش معايا قال والله معايا واحد جرام C4H10 انا بديش واحد جرام C4H10 بديش جرام C4H10 فاين اللي بدي احطها بدي احطها تحت في المقام", "tokens": [2304, 43020, 1975, 5016, 1211, 4724, 9778, 9566, 3660, 36764, 24401, 3660, 9122, 6027, 2655, 6027, 1829, 1975, 39648, 16070, 43761, 1975, 8315, 4724, 16254, 10874, 2288, 10943, 3714, 1829, 3224, 11331, 1211, 2407, 1975, 1829, 8592, 20449, 995, 25528, 50239, 36764, 1211, 43761, 20449, 995, 25528, 36764, 24401, 10874, 2288, 10943, 383, 19, 39, 3279, 1975, 8315, 4724, 16254, 8592, 36764, 24401, 10874, 2288, 10943, 383, 19, 39, 3279, 4724, 16254, 8592, 10874, 2288, 10943, 383, 19, 39, 3279, 6156, 995, 9957, 13672, 1829, 4724, 16254, 1975, 5016, 9566, 11296, 4724, 16254, 1975, 5016, 9566, 11296, 6055, 33753, 8978, 9673, 4587, 10943], "avg_logprob": -0.24384014036219853, "compression_ratio": 2.0445859872611467, "no_speech_prob": 8.344650268554688e-07, "words": [{"start": 766.88, "end": 767.0, "word": "ممكن", "probability": 0.52154541015625}, {"start": 767.0, "end": 767.26, "word": " احل", "probability": 0.8185221354166666}, {"start": 767.26, "end": 767.6, "word": " بخطة", 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weight معبر عنها بالجرامات عبارة عن واحد مول يبقى واحد مول تمانية وخمسين جرام C4H10 هي تمانية وخمسين او جرام C4H10 مع جرام C4H10 صار عند واحد مول C4H10", "tokens": [9566, 3555, 1975, 1829, 8592, 44650, 4117, 31845, 19986, 3660, 2423, 8513, 3364, 6225, 3555, 9640, 3660, 18871, 36764, 24401, 3714, 12610, 2423, 8513, 3364, 20449, 26890, 18871, 11296, 20666, 7435, 2288, 10943, 9307, 6225, 3555, 9640, 3660, 18871, 36764, 24401, 3714, 12610, 7251, 3555, 4587, 7578, 36764, 24401, 3714, 12610, 46811, 7649, 10632, 4032, 9778, 2304, 3794, 9957, 10874, 2288, 10943, 383, 19, 39, 3279, 39896, 46811, 7649, 10632, 4032, 9778, 2304, 3794, 9957, 1975, 2407, 10874, 2288, 10943, 383, 19, 39, 3279, 20449, 10874, 2288, 10943, 383, 19, 39, 3279, 20328, 9640, 43242, 36764, 24401, 3714, 12610, 383, 19, 39, 3279], "avg_logprob": -0.18494590973624817, "compression_ratio": 2.035928143712575, "no_speech_prob": 0.0, "words": [{"start": 780.64, "end": 780.94, "word": "طب", "probability": 0.49188232421875}, 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785.04, "word": " معبر", "probability": 0.68212890625}, {"start": 785.04, "end": 785.24, "word": " عنها", "probability": 0.932861328125}, {"start": 785.24, "end": 785.74, "word": " بالجرامات", "probability": 0.80263671875}, {"start": 785.74, "end": 785.98, "word": " عبارة", "probability": 0.9725341796875}, {"start": 785.98, "end": 786.1, "word": " عن", "probability": 0.99560546875}, {"start": 786.1, "end": 786.36, "word": " واحد", "probability": 0.984619140625}, {"start": 786.36, "end": 786.58, "word": " مول", "probability": 0.9833984375}, {"start": 786.58, "end": 787.3, "word": " يبقى", "probability": 0.9456787109375}, {"start": 787.3, "end": 787.74, "word": " واحد", "probability": 0.9599609375}, {"start": 787.74, "end": 788.02, "word": " مول", "probability": 0.979736328125}, {"start": 788.02, "end": 788.4, "word": " تمانية", "probability": 0.8746744791666666}, {"start": 788.4, "end": 788.76, "word": " وخمسين", "probability": 0.830859375}, {"start": 788.76, "end": 789.02, "word": " جرام", "probability": 0.9441731770833334}, {"start": 789.02, "end": 789.72, "word": " C4H10", "probability": 0.78997802734375}, {"start": 789.72, "end": 789.84, "word": " هي", "probability": 0.86328125}, {"start": 789.84, "end": 790.18, "word": " تمانية", "probability": 0.9482421875}, {"start": 790.18, "end": 790.52, "word": " وخمسين", "probability": 0.94814453125}, {"start": 790.52, "end": 790.98, "word": " او", "probability": 0.853271484375}, {"start": 790.98, "end": 791.48, "word": " جرام", "probability": 0.790771484375}, {"start": 791.48, "end": 792.4, "word": " C4H10", "probability": 0.9769287109375}, {"start": 792.4, "end": 792.56, "word": " مع", "probability": 0.935546875}, {"start": 792.56, "end": 793.1, "word": " جرام", "probability": 0.9747721354166666}, {"start": 793.1, "end": 795.08, "word": " C4H10", "probability": 0.9908447265625}, {"start": 795.08, "end": 795.72, "word": " صار", "probability": 0.89453125}, {"start": 795.72, "end": 795.92, "word": " عند", "probability": 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formula", "probability": 0.58740234375}], "temperature": 1.0}, {"id": 44, "seek": 110815, "start": 1093.85, "end": 1108.15, "text": "المعطى المعطى المعطى المعطى المعطى المعطى المعطى المعطى المعطى المعطى المعطى المعطى", "tokens": [45340, 3615, 9566, 7578, 9673, 3615, 9566, 7578, 9673, 3615, 9566, 7578, 9673, 3615, 9566, 7578, 9673, 3615, 9566, 7578, 9673, 3615, 9566, 7578, 9673, 3615, 9566, 7578, 9673, 3615, 9566, 7578, 9673, 3615, 9566, 7578, 9673, 3615, 9566, 7578, 9673, 3615, 9566, 7578, 9673, 3615, 9566, 7578], "avg_logprob": -0.4193239893232073, "compression_ratio": 6.2, "no_speech_prob": 0.0, "words": [{"start": 1093.85, "end": 1094.33, "word": "المعطى", "probability": 0.420257568359375}, {"start": 1094.33, "end": 1094.33, "word": " المعطى", "probability": 0.527679443359375}, {"start": 1094.33, "end": 1094.49, "word": " المعطى", "probability": 0.57147216796875}, {"start": 1094.49, "end": 1094.81, "word": " المعطى", "probability": 0.671478271484375}, {"start": 1094.81, "end": 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"هيها مش انه عدد مولات الجلوكوز 6 امثال عدد مولات الميه غلط عدد مولات الميه هي 6 امثال لجلوكوز لكن هذه equivalency بتقول كل مول من الجلوكوز produces 6 moles of water هي هيك بنقراها طب انا بديش مول ميه بحط تحت مول ميه 18 جرام ميه بيعطيلي النتيجة لكن خدوا الأسهل", "tokens": [3224, 1829, 11296, 37893, 16472, 3224, 6225, 3215, 3215, 3714, 12610, 9307, 25724, 1211, 2407, 4117, 2407, 11622, 1386, 1975, 2304, 12984, 6027, 6225, 3215, 3215, 3714, 12610, 9307, 9673, 1829, 3224, 32771, 1211, 9566, 6225, 3215, 3215, 3714, 12610, 9307, 9673, 1829, 3224, 39896, 1386, 1975, 2304, 12984, 6027, 5296, 7435, 1211, 2407, 4117, 2407, 11622, 44381, 29538, 9052, 3020, 39894, 39648, 28242, 3714, 12610, 9154, 25724, 1211, 2407, 4117, 2407, 11622, 14725, 1386, 34286, 295, 1281, 39896, 39896, 4117, 44945, 4587, 23557, 11296, 23032, 3555, 1975, 8315, 4724, 16254, 8592, 3714, 12610, 3714, 1829, 3224, 4724, 5016, 9566, 6055, 33753, 3714, 12610, 3714, 1829, 3224, 2443, 10874, 2288, 10943, 3714, 1829, 3224, 4724, 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"end": 3114.44, "text": "ماشي يا جماعة الآن يعني أخر نقطة في هذا ال chapter نتكلم عن ال theoretical yield و ال actual yield theoretical yield و ال actual yield يعني أنا عندي مثلا مادتين بتفاعلوا ممكن أحسب زي ما حسبت قبل شوية كمية النواتج مثلا", "tokens": [2304, 33599, 1829, 35186, 10874, 15042, 27884, 6024, 48506, 37495, 22653, 5551, 34740, 8717, 47432, 3660, 8978, 23758, 2423, 7187, 8717, 2655, 4117, 19528, 18871, 2423, 20864, 11257, 4032, 2423, 3539, 11257, 20864, 11257, 4032, 2423, 3539, 11257, 37495, 22653, 41850, 18871, 16254, 50113, 15040, 3714, 18513, 2655, 9957, 39894, 5172, 995, 30241, 14407, 3714, 43020, 5551, 5016, 35457, 30767, 1829, 19446, 11331, 35457, 2655, 12174, 36150, 13412, 2407, 10632, 9122, 2304, 10632, 28239, 2407, 9307, 7435, 50113, 15040], "avg_logprob": -0.1545898485928774, "compression_ratio": 1.711340206185567, "no_speech_prob": 0.0, "words": [{"start": 3087.6, "end": 3088.04, "word": "ماشي", "probability": 0.8499348958333334}, {"start": 3088.04, "end": 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"probability": 0.79541015625}, {"start": 3115.88, "end": 3116.36, "word": " حساب", "probability": 0.9923502604166666}, {"start": 3116.36, "end": 3117.1, "word": " وبعرفها", "probability": 0.78118896484375}, {"start": 3117.1, "end": 3117.4, "word": " بالظبط", "probability": 0.9642333984375}, {"start": 3117.4, "end": 3117.9, "word": " جداش", "probability": 0.5968424479166666}, {"start": 3117.9, "end": 3118.38, "word": " هذه", "probability": 0.5556640625}, {"start": 3118.38, "end": 3118.84, "word": " الكمية", "probability": 0.8101399739583334}, {"start": 3118.84, "end": 3119.0, "word": " اللي", "probability": 0.79150390625}, {"start": 3119.0, "end": 3119.08, "word": " أنا", "probability": 0.42626953125}, {"start": 3119.08, "end": 3119.5, "word": " بحسبها", "probability": 0.9788818359375}, {"start": 3119.5, "end": 3119.96, "word": " حساب", "probability": 0.990234375}, {"start": 3119.96, "end": 3120.76, "word": " اسمها", "probability": 0.9661458333333334}, {"start": 3120.76, "end": 3121.48, 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Cyclohexane and O2 يعني لما يتفعل ال Cyclohexane مع ال O2 تجاريا هو ممكن أحضر ال adipic acid و بطلع عندى ميه بقول assume that you carry out this reaction with 25 gram of Cyclohexane", "tokens": [6027, 20292, 31439, 389, 17, 34, 21, 39, 23, 46, 19, 307, 1027, 41751, 538, 257, 5480, 1296, 10295, 66, 752, 675, 87, 1929, 293, 422, 17, 37495, 22653, 5296, 15042, 7251, 2655, 5172, 30241, 2423, 10295, 66, 752, 675, 87, 1929, 20449, 2423, 422, 17, 6055, 7435, 9640, 25528, 31439, 3714, 43020, 5551, 5016, 11242, 2288, 2423, 614, 647, 299, 8258, 4032, 4724, 9566, 1211, 3615, 43242, 7578, 3714, 1829, 3224, 4724, 39648, 6552, 300, 291, 3985, 484, 341, 5480, 365, 3552, 21353, 295, 10295, 66, 752, 675, 87, 1929], "avg_logprob": -0.15208899148780367, "compression_ratio": 1.3408071748878925, "no_speech_prob": 0.0, "words": [{"start": 3225.62, "end": 3225.92, "word": "اللي", "probability": 0.69384765625}, {"start": 3225.92, "end": 3226.1, "word": " هو", "probability": 0.94677734375}, {"start": 3226.1, 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أحسب جرام adipic acid مافهمش في الجرامات مول adipic acid", "tokens": [2407, 6027, 31371, 10295, 66, 752, 675, 87, 1929, 31439, 2423, 39184, 22083, 4515, 394, 37495, 22653, 2423, 39184, 3552, 10874, 2288, 10943, 31439, 2423, 39184, 22083, 4515, 394, 1975, 1829, 3224, 22807, 5551, 12610, 8608, 33604, 6027, 708, 307, 264, 20864, 11257, 295, 614, 647, 299, 8258, 22807, 20864, 37495, 22653, 4724, 5016, 35457, 11331, 3794, 16758, 8315, 9673, 3615, 18513, 37977, 30767, 1829, 19446, 11331, 35457, 8315, 8608, 16758, 4587, 995, 28242, 11331, 3794, 16758, 9307, 8315, 9154, 9673, 3615, 18513, 37977, 29538, 5551, 12610, 36764, 24401, 3660, 4724, 39648, 16490, 20292, 8315, 8717, 47283, 3215, 36764, 24401, 3660, 36764, 24401, 3660, 8032, 47302, 2423, 10295, 66, 752, 675, 87, 1929, 1975, 2655, 5172, 995, 30241, 20449, 16247, 4117, 3794, 7435, 9957, 4724, 40228, 9566, 1829, 8315, 614, 647, 299, 8258, 6156, 3555, 39648, 3714, 12610, 41850, 4724, 16254, 5551, 5016, 35457, 10874, 2288, 10943, 614, 647, 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"end": 3333.02, "word": " فهي", "probability": 0.9816080729166666}, {"start": 3333.02, "end": 3334.16, "word": " لجرامات", "probability": 0.97099609375}, {"start": 3334.16, "end": 3334.84, "word": " النظرية", "probability": 0.9893798828125}, {"start": 3334.84, "end": 3335.24, "word": " اللي", "probability": 0.905517578125}, {"start": 3335.24, "end": 3335.86, "word": " الاصل", "probability": 0.7642415364583334}, {"start": 3335.86, "end": 3336.24, "word": " ان", "probability": 0.87353515625}, {"start": 3336.24, "end": 3336.9, "word": " احصل", "probability": 0.9874674479166666}, {"start": 3336.9, "end": 3337.4, "word": " عليها", "probability": 0.993408203125}, {"start": 3337.4, "end": 3337.76, "word": " من", "probability": 0.994140625}, {"start": 3337.76, "end": 3338.64, "word": " المعادلة", "probability": 0.99560546875}], "temperature": 1.0}, {"id": 139, "seek": 335085, "start": 3339.27, "end": 3350.85, "text": "بحصل عليها يعني بحصل عليها من المعادلة جرامات نظرية this is the theoretical yield طب في بيمنه بيقول if you obtain", "tokens": [3555, 5016, 36520, 25894, 11296, 37495, 22653, 4724, 5016, 36520, 25894, 11296, 9154, 9673, 3615, 18513, 37977, 10874, 2288, 10943, 9307, 8717, 19913, 2288, 10632, 341, 307, 264, 20864, 11257, 23032, 3555, 8978, 4724, 1829, 27842, 3224, 4724, 1829, 39648, 498, 291, 12701], "avg_logprob": -0.2462713041088798, "compression_ratio": 1.2878787878787878, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 3339.27, "end": 3340.03, "word": "بحصل", "probability": 0.6549479166666666}, {"start": 3340.03, "end": 3340.41, "word": " عليها", "probability": 0.95654296875}, {"start": 3340.41, "end": 3341.01, "word": " يعني", "probability": 0.67919921875}, {"start": 3341.01, "end": 3341.41, "word": " بحصل", "probability": 0.8986002604166666}, {"start": 3341.41, "end": 3341.63, "word": " عليها", "probability": 0.986328125}, {"start": 3341.63, "end": 3341.75, "word": " من", "probability": 0.9521484375}, {"start": 3341.75, "end": 3342.37, "word": 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341630, "start": 3395.74, "end": 3416.3, "text": "بقول imagine you are working on ways to improve the process by which iron ore containing iron 2 O3 is converted into iron يعني أنا الغرض من هذه العملية أن أحول iron 2 O3 إلى ال iron فكيف بدي أعمل هذا الكلام؟ جالب أعمله reduction باستخدام ال CO", "tokens": [3555, 39648, 3811, 291, 366, 1364, 322, 2098, 281, 3470, 264, 1399, 538, 597, 6497, 20865, 19273, 6497, 568, 422, 18, 307, 16424, 666, 6497, 37495, 22653, 41850, 6024, 118, 43042, 9154, 29538, 18863, 42213, 10632, 14739, 5551, 5016, 12610, 6497, 568, 422, 18, 30731, 2423, 6497, 6156, 4117, 33911, 4724, 16254, 5551, 25957, 1211, 23758, 2423, 28820, 10943, 22807, 10874, 6027, 3555, 5551, 25957, 43761, 11004, 4724, 995, 14851, 9778, 3215, 10943, 2423, 3002], "avg_logprob": -0.22944079123829542, "compression_ratio": 1.424778761061947, "no_speech_prob": 0.0, "words": [{"start": 3395.74, "end": 3396.18, "word": "بقول", "probability": 0.4725341796875}, {"start": 3396.18, "end": 3396.66, 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ممكن", "tokens": [4117, 33911, 3714, 43020], "avg_logprob": -0.1109375, "compression_ratio": 0.6818181818181818, "no_speech_prob": 0.0, "words": [{"start": 3749.08, "end": 3749.78, "word": "كيف", "probability": 0.898681640625}, {"start": 3749.78, "end": 3750.34, "word": " ممكن", "probability": 0.975341796875}], "temperature": 1.0}, {"id": 159, "seek": 378142, "start": 3753.64, "end": 3781.42, "text": "أعبر عن تركيز المحاليل المحاليل لو ضوبت فيها كمية معينة من المادة صار في تركيز معين للمادة في المحلول طب كيف أعبر عن تركيز المواد في المحاليل برضه هذا هدرسه و في الآخر خالص هقول والله هعمل calculations للمحاليل المختلفة هشوف يعني كيف أعمل الحسابات الكيميائية للمحاليل المائية ككل يعني ال solutes اللي فيها التفاعلات تبعتها", "tokens": [10721, 3615, 26890, 18871, 6055, 31747, 1829, 11622, 9673, 5016, 6027, 26895, 9673, 5016, 6027, 26895, 45164, 48812, 37746, 2655, 8978, 11296, 9122, 2304, 10632, 20449, 9957, 3660, 9154, 9673, 18513, 3660, 20328, 9640, 8978, 6055, 31747, 1829, 11622, 20449, 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calculations", "probability": 0.319580078125}, {"start": 3770.0, "end": 3771.62, "word": " للمحاليل", "probability": 0.88056640625}, {"start": 3771.62, "end": 3772.54, "word": " المختلفة", "probability": 0.9949951171875}, {"start": 3772.54, "end": 3772.94, "word": " هشوف", "probability": 0.96435546875}, {"start": 3772.94, "end": 3773.7, "word": " يعني", "probability": 0.96240234375}, {"start": 3773.7, "end": 3773.96, "word": " كيف", "probability": 0.966552734375}, {"start": 3773.96, "end": 3774.28, "word": " أعمل", "probability": 0.9000651041666666}, {"start": 3774.28, "end": 3774.82, "word": " الحسابات", "probability": 0.9332275390625}, {"start": 3774.82, "end": 3775.54, "word": " الكيميائية", "probability": 0.9474609375}, {"start": 3775.54, "end": 3776.38, "word": " للمحاليل", "probability": 0.970703125}, {"start": 3776.38, "end": 3777.0, "word": " المائية", "probability": 0.9869791666666666}, {"start": 3777.0, "end": 3778.1, "word": " ككل", "probability": 0.9599609375}, {"start": 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"probability": 0.82958984375}, {"start": 3788.29, "end": 3788.51, "word": " formula", "probability": 0.65966796875}, {"start": 3788.51, "end": 3788.73, "word": " weight", "probability": 0.89990234375}, {"start": 3788.73, "end": 3789.91, "word": " بتساوي", "probability": 0.8868408203125}, {"start": 3789.91, "end": 3790.85, "word": " mole", "probability": 0.270751953125}, {"start": 3790.85, "end": 3791.71, "word": " فممكن", "probability": 0.94677734375}, {"start": 3791.71, "end": 3792.17, "word": " اقدمله", "probability": 0.8944091796875}, {"start": 3792.17, "end": 3792.41, "word": " مفهوم", "probability": 0.9857177734375}, {"start": 3792.41, "end": 3792.67, "word": " جديد", "probability": 0.9889322916666666}, {"start": 3792.67, "end": 3793.17, "word": " حتشوفه", "probability": 0.741552734375}, {"start": 3793.17, "end": 3793.69, "word": " فحينه", "probability": 0.7918701171875}, {"start": 3793.69, "end": 3793.99, "word": " يعني", "probability": 0.7030029296875}, {"start": 3793.99, "end": 3794.91, "word": " بس", "probability": 0.977783203125}, {"start": 3794.91, "end": 3795.23, "word": " برضه", "probability": 0.97802734375}, {"start": 3795.23, "end": 3795.43, "word": " هو", "probability": 0.861328125}, {"start": 3795.43, "end": 3795.81, "word": " عبارة", "probability": 0.9412841796875}, {"start": 3795.81, "end": 3795.97, "word": " عن", "probability": 0.99658203125}, {"start": 3795.97, "end": 3796.09, "word": " ال", "probability": 0.76806640625}, {"start": 3796.09, "end": 3796.27, "word": " mole", "probability": 0.8017578125}, {"start": 3796.27, "end": 3796.51, "word": " يعني", "probability": 0.884521484375}, {"start": 3796.51, "end": 3796.61, "word": " ال", "probability": 0.712890625}, {"start": 3796.61, "end": 3796.77, "word": " mole", "probability": 0.875}, {"start": 3796.77, "end": 3797.15, "word": " بعبر", "probability": 0.676513671875}, {"start": 3797.15, "end": 3797.53, "word": " عنه", "probability": 0.983642578125}, {"start": 3797.53, "end": 3798.55, "word": " بطريقة", "probability": 0.967529296875}, {"start": 3798.55, "end": 3799.15, "word": " أخرى", "probability": 0.9073893229166666}, {"start": 3799.15, "end": 3799.33, "word": " غير", "probability": 0.99072265625}, {"start": 3799.33, "end": 3799.67, "word": " جرام", "probability": 0.90185546875}, {"start": 3799.67, "end": 3799.83, "word": " على", "probability": 0.83056640625}, {"start": 3799.83, "end": 3799.97, "word": " ال", "probability": 0.923828125}, {"start": 3799.97, "end": 3800.39, "word": " formula", "probability": 0.9384765625}, {"start": 3800.39, "end": 3800.87, "word": " weight", "probability": 0.92919921875}], "temperature": 1.0}, {"id": 161, "seek": 381885, "start": 3803.17, "end": 3818.85, "text": "الان ننتقل للموضوع بقول لما نتحدث عن ال general properties لل aqua solutions بتحدث بداية عن ان والله المحلول يتكون من مذيب ومذاب solvent or solute", "tokens": [6027, 7649, 8717, 29399, 4587, 1211, 5296, 19528, 2407, 11242, 45367, 4724, 39648, 5296, 15042, 8717, 2655, 24401, 12984, 18871, 2423, 2674, 7221, 24976, 2373, 64, 6547, 39894, 24401, 12984, 4724, 28259, 10632, 18871, 16472, 16070, 43761, 9673, 5016, 1211, 12610, 7251, 2655, 30544, 9154, 3714, 8848, 1829, 3555, 4032, 2304, 15730, 3555, 33575, 420, 1404, 1169], "avg_logprob": -0.22615840645699664, "compression_ratio": 1.4415584415584415, "no_speech_prob": 0.0, "words": [{"start": 3803.17, "end": 3803.81, "word": "الان", "probability": 0.765380859375}, {"start": 3803.81, "end": 3804.67, "word": " ننتقل", "probability": 0.8695068359375}, {"start": 3804.67, "end": 3805.25, "word": " للموضوع", "probability": 0.928515625}, {"start": 3805.25, "end": 3806.21, "word": " بقول", "probability": 0.58575439453125}, {"start": 3806.21, "end": 3806.93, "word": " لما", "probability": 0.82568359375}, {"start": 3806.93, "end": 3807.49, "word": " نتحدث", "probability": 0.973388671875}, {"start": 3807.49, "end": 3807.81, "word": " عن", "probability": 0.9873046875}, {"start": 3807.81, "end": 3808.71, "word": " ال", "probability": 0.9287109375}, {"start": 3808.71, "end": 3809.03, "word": " general", "probability": 0.475830078125}, {"start": 3809.03, "end": 3809.65, "word": " properties", "probability": 0.87158203125}, {"start": 3809.65, "end": 3809.99, "word": " لل", "probability": 0.39892578125}, {"start": 3809.99, "end": 3810.71, "word": " aqua", "probability": 0.5599365234375}, {"start": 3810.71, "end": 3811.29, "word": " solutions", "probability": 0.8515625}, {"start": 3811.29, "end": 3811.91, "word": " بتحدث", "probability": 0.8564453125}, {"start": 3811.91, "end": 3812.41, "word": " بداية", "probability": 0.9581705729166666}, {"start": 3812.41, "end": 3812.71, "word": " عن", "probability": 0.908203125}, {"start": 3812.71, "end": 3813.23, "word": " ان", "probability": 0.66748046875}, {"start": 3813.23, "end": 3813.69, "word": " والله", "probability": 0.635498046875}, {"start": 3813.69, "end": 3814.39, "word": " المحلول", "probability": 0.9898681640625}, {"start": 3814.39, "end": 3815.75, "word": " يتكون", "probability": 0.9007161458333334}, {"start": 3815.75, "end": 3816.07, "word": " من", "probability": 0.98291015625}, {"start": 3816.07, "end": 3816.55, "word": " مذيب", "probability": 0.8292236328125}, {"start": 3816.55, "end": 3817.17, "word": " ومذاب", "probability": 0.80841064453125}, {"start": 3817.17, "end": 3817.87, "word": " solvent", "probability": 0.70751953125}, {"start": 3817.87, "end": 3818.31, "word": " or", "probability": 0.38134765625}, {"start": 3818.31, "end": 3818.85, "word": " solute", "probability": 0.97021484375}], "temperature": 1.0}, {"id": 162, "seek": 384030, "start": 3819.52, "end": 3840.3, "text": "solvent اللي هو المذيب و solute اللي هو المادة المذابة فلو دوبنا مثلا ملح في الميه بقول والله الميه هي المذيب solvent و الملح اللي انا بدوبه هو ال solute فالمذيب اللي هو ال solvent هو المادة الموجودة بوفرة لكتيرة", "tokens": [30926, 2475, 13672, 1829, 31439, 9673, 8848, 1829, 3555, 4032, 1404, 1169, 13672, 1829, 31439, 9673, 18513, 3660, 9673, 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3821.74, "end": 3822.22, "word": " solute", "probability": 0.838134765625}, {"start": 3822.22, "end": 3822.36, "word": " اللي", "probability": 0.962158203125}, {"start": 3822.36, "end": 3822.48, "word": " هو", "probability": 0.97705078125}, {"start": 3822.48, "end": 3822.82, "word": " المادة", "probability": 0.9661458333333334}, {"start": 3822.82, "end": 3823.4, "word": " المذابة", "probability": 0.8494466145833334}, {"start": 3823.4, "end": 3824.24, "word": " فلو", "probability": 0.9112955729166666}, {"start": 3824.24, "end": 3824.66, "word": " دوبنا", "probability": 0.8235677083333334}, {"start": 3824.66, "end": 3824.98, "word": " مثلا", "probability": 0.912353515625}, {"start": 3824.98, "end": 3825.32, "word": " ملح", "probability": 0.96875}, {"start": 3825.32, "end": 3825.46, "word": " في", "probability": 0.88623046875}, {"start": 3825.46, "end": 3825.98, "word": " الميه", "probability": 0.8483072916666666}, {"start": 3825.98, "end": 3826.58, "word": " بقول", "probability": 0.9052734375}, {"start": 3826.58, "end": 3826.88, "word": " والله", "probability": 0.85791015625}, {"start": 3826.88, "end": 3827.3, "word": " الميه", "probability": 0.9757486979166666}, {"start": 3827.3, "end": 3827.56, "word": " هي", "probability": 0.81396484375}, {"start": 3827.56, "end": 3828.26, "word": " المذيب", "probability": 0.98193359375}, {"start": 3828.26, "end": 3828.94, "word": " solvent", "probability": 0.483154296875}, {"start": 3828.94, "end": 3829.5, "word": " و", "probability": 0.5126953125}, {"start": 3829.5, "end": 3829.88, "word": " الملح", "probability": 0.88916015625}, {"start": 3829.88, "end": 3830.02, "word": " اللي", "probability": 0.9599609375}, {"start": 3830.02, "end": 3830.14, "word": " انا", "probability": 0.716796875}, {"start": 3830.14, "end": 3830.68, "word": " بدوبه", "probability": 0.86669921875}, {"start": 3830.68, "end": 3831.06, "word": " هو", "probability": 0.9873046875}, {"start": 3831.06, "end": 3831.2, "word": " ال", "probability": 0.85546875}, {"start": 3831.2, "end": 3831.68, "word": " solute", "probability": 0.923095703125}, {"start": 3831.68, "end": 3834.04, "word": " فالمذيب", "probability": 0.9732421875}, {"start": 3834.04, "end": 3834.24, "word": " اللي", "probability": 0.9736328125}, {"start": 3834.24, "end": 3834.38, "word": " هو", "probability": 0.99609375}, {"start": 3834.38, "end": 3834.52, "word": " ال", "probability": 0.5693359375}, {"start": 3834.52, "end": 3835.08, "word": " solvent", "probability": 0.9404296875}, {"start": 3835.08, "end": 3837.52, "word": " هو", "probability": 0.6494140625}, {"start": 3837.52, "end": 3838.08, "word": " المادة", "probability": 0.9889322916666666}, {"start": 3838.08, "end": 3838.92, "word": " الموجودة", "probability": 0.9844970703125}, {"start": 3838.92, "end": 3839.62, "word": " بوفرة", "probability": 0.87109375}, {"start": 3839.62, "end": 3840.3, "word": " لكتيرة", "probability": 0.80474853515625}], "temperature": 1.0}, {"id": 163, "seek": 386158, "start": 3841.14, "end": 3861.58, "text": "و ال solute هو المادة الموجودة بشكل أقل جزء يعني لو قلنا المحلول عبارة عن solute او solvent فال solvent هو المكون الأعظم من المحلول و ال solute هو المكون الأقل للمحلول فهذا مفهوم ال solute و ال solvent ذكرت لما قدود سكر في الميه مثلا", "tokens": [2407, 2423, 1404, 1169, 31439, 9673, 18513, 3660, 9673, 29245, 23328, 3660, 4724, 8592, 28820, 5551, 4587, 1211, 10874, 11622, 38207, 37495, 22653, 45164, 12174, 1211, 8315, 9673, 5016, 1211, 12610, 6225, 3555, 9640, 3660, 18871, 1404, 1169, 1975, 2407, 33575, 6156, 6027, 33575, 31439, 9673, 30544, 16247, 3615, 19913, 2304, 9154, 9673, 5016, 1211, 12610, 4032, 2423, 1404, 1169, 31439, 9673, 30544, 16247, 4587, 1211, 5296, 19528, 5016, 1211, 12610, 6156, 3224, 15730, 3714, 5172, 3224, 20498, 2423, 1404, 1169, 4032, 2423, 33575, 29910, 37983, 2655, 5296, 15042, 12174, 3215, 23328, 8608, 37983, 8978, 9673, 1829, 3224, 50113, 15040], "avg_logprob": -0.1441831635956717, "compression_ratio": 2.021505376344086, 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"end": 3857.3, "word": " solute", "probability": 0.973876953125}, {"start": 3857.3, "end": 3857.62, "word": " و", "probability": 0.7431640625}, {"start": 3857.62, "end": 3857.76, "word": " ال", "probability": 0.8154296875}, {"start": 3857.76, "end": 3858.1, "word": " solvent", "probability": 0.92529296875}, {"start": 3858.1, "end": 3858.88, "word": " ذكرت", "probability": 0.8990885416666666}, {"start": 3858.88, "end": 3859.26, "word": " لما", "probability": 0.90966796875}, {"start": 3859.26, "end": 3859.74, "word": " قدود", "probability": 0.73046875}, {"start": 3859.74, "end": 3860.12, "word": " سكر", "probability": 0.922607421875}, {"start": 3860.12, "end": 3860.28, "word": " في", "probability": 0.9443359375}, {"start": 3860.28, "end": 3860.66, "word": " الميه", "probability": 0.8108723958333334}, {"start": 3860.66, "end": 3861.58, "word": " مثلا", "probability": 0.9404296875}], "temperature": 1.0}, {"id": 164, "seek": 387618, "start": 3862.26, "end": 3876.18, "text": "دوبلي مثلا معلجة سكر في لتر ميه، يقول السكر عبارة عن solute وال لتر ميه هذا عبارة عن solvent فال solvent هو الموجود بوفرة وال solute هو الموجود بكمية أقل", "tokens": [3215, 37746, 20292, 50113, 15040, 20449, 1211, 7435, 3660, 8608, 37983, 8978, 5296, 2655, 2288, 3714, 1829, 3224, 12399, 7251, 39648, 21136, 37983, 6225, 3555, 9640, 3660, 18871, 1404, 1169, 16070, 5296, 2655, 2288, 3714, 1829, 3224, 23758, 6225, 3555, 9640, 3660, 18871, 33575, 6156, 6027, 33575, 31439, 9673, 29245, 23328, 4724, 38688, 25720, 16070, 1404, 1169, 31439, 9673, 29245, 23328, 4724, 24793, 10632, 5551, 4587, 1211], "avg_logprob": -0.21668198617065654, "compression_ratio": 1.7310344827586206, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3862.26, "end": 3862.72, "word": "دوبلي", "probability": 0.2720947265625}, {"start": 3862.72, "end": 3862.96, "word": " مثلا", "probability": 0.94189453125}, {"start": 3862.96, "end": 3863.56, "word": " معلجة", "probability": 0.8878173828125}, {"start": 3863.56, "end": 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"end": 3870.48, "word": " هذا", "probability": 0.69482421875}, {"start": 3870.48, "end": 3871.16, "word": " عبارة", "probability": 0.997314453125}, {"start": 3871.16, "end": 3871.34, "word": " عن", "probability": 0.9931640625}, {"start": 3871.34, "end": 3871.78, "word": " solvent", "probability": 0.86083984375}, {"start": 3871.78, "end": 3872.1, "word": " فال", "probability": 0.781005859375}, {"start": 3872.1, "end": 3872.44, "word": " solvent", "probability": 0.91796875}, {"start": 3872.44, "end": 3872.66, "word": " هو", "probability": 0.986328125}, {"start": 3872.66, "end": 3872.98, "word": " الموجود", "probability": 0.9322916666666666}, {"start": 3872.98, "end": 3873.44, "word": " بوفرة", "probability": 0.88037109375}, {"start": 3873.44, "end": 3873.86, "word": " وال", "probability": 0.6728515625}, {"start": 3873.86, "end": 3874.24, "word": " solute", "probability": 0.95703125}, {"start": 3874.24, "end": 3874.32, "word": " هو", "probability": 0.93798828125}, {"start": 3874.32, 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00:00:27,720 +في نفس الموضوع اللي كنا بداني فيه قبل محاضرتين + +3 +00:00:27,720 --> 00:00:32,340 +اللي هو ال precipitation reactions تفاعلات الترسيب + +4 +00:00:32,340 --> 00:00:37,100 +و أيضا تفاعلات ال acids و ال bases acid base + +5 +00:00:37,100 --> 00:00:41,200 +reactions و بداني نتكلم عن ال oxidation reactions + +6 +00:00:41,200 --> 00:00:44,110 +أو ال oxidation reduction reactionsففي الـ + +7 +00:00:44,110 --> 00:00:48,030 +oxidation reduction reactions عشان نشتغل صح عرفنا + +8 +00:00:48,030 --> 00:00:51,490 +إيش يعني أكسدة oxidation فقلنا الأكسدة هي loss of + +9 +00:00:51,490 --> 00:00:56,190 +electrons أو فقد إلكترونات وال reduction هي gain + +10 +00:00:56,190 --> 00:01:01,250 +of electrons يعني اكتساب إلكترونات وبدينا يعني + +11 +00:01:01,250 --> 00:01:05,760 +نشوف بعض الظواهر اللي بتتعلق بالأكسدة والاختزال + +12 +00:01:05,760 --> 00:01:10,000 +وأيضا بعض التفاعلات المشهورة يعني اللي بتشوفها في + +13 +00:01:10,000 --> 00:01:15,260 +الحياة العملية وكيفية تكون الصدق على سبيل المثال + +14 +00:01:15,260 --> 00:01:19,480 +اليوم إذا أراد بنحاول نفصل أكتر في تفاعلات الأكسدة + +15 +00:01:19,480 --> 00:01:23,680 +والاختزال خاصة أنه احنا ذكرنا سابقا أنه هندرس فقط + +16 +00:01:23,680 --> 00:01:28,910 +جزئية واحدة منتفاعلات الأكسدة والاختزال وهي + +17 +00:01:28,910 --> 00:01:33,950 +تفاعلات الأكسدة والاختزال التي تتضمن أحد المعادن + +18 +00:01:38,460 --> 00:01:42,260 +هيكون أحد مكونات تفاعل الأكسد والاختزال، ليه؟ لأن + +19 +00:01:42,260 --> 00:01:45,120 +تفاعل الأكسد والاختزال ممكن تكون واسعة جدا، لكن بس + +20 +00:01:45,120 --> 00:01:50,260 +احنا بنحاول ندرس تفاعل الأكسد والاختزال اللي بيكون + +21 +00:01:50,260 --> 00:01:53,760 +الـmetal أحد أطراف المتفاعلات فيها، لأن تطبيقاته + +22 +00:01:53,760 --> 00:01:57,980 +بالنسبالكم قد تكون يعني مهمة جدا في الحياة العملية + +23 +00:01:58,540 --> 00:02:03,080 +الان بدي اطلع على concept بسميه ال oxidation + +24 +00:02:03,080 --> 00:02:07,100 +number ومنه بدي اعرف ايش يعني اكسدة و ايش يعني + +25 +00:02:07,100 --> 00:02:12,460 +اختزال مرة تانية احنا شوفنا سابقا ان الاكسدة loss + +26 +00:02:12,460 --> 00:02:15,200 +of electrons و الاختزال gain of electrons الان بدي + +27 +00:02:15,200 --> 00:02:18,960 +اعرف الاكسدة علي انها an increase in oxidation + +28 +00:02:18,960 --> 00:02:26,710 +number اي element او اتماو ايون فيه increase في ال + +29 +00:02:26,710 --> 00:02:30,270 +oxidation number بيقول هذا عملية اكسدة تب decrease + +30 +00:02:30,270 --> 00:02:33,170 +in oxidation number يقول هذا عملية اختزال او + +31 +00:02:33,170 --> 00:02:36,330 +reduction اذا هذه تعريف جديد بالنسبالنا لماهية + +32 +00:02:36,330 --> 00:02:40,190 +الاكسدة والاختزال تب ايش هو ال oxidation number؟ + +33 +00:02:40,650 --> 00:02:44,630 +الحقيقة ال oxidation number هو عبارة عن يعني مفهوم + +34 +00:02:44,630 --> 00:02:50,810 +مفهوم ليس له معنى فيزيائي حقيقي يعني مالوش معنى + +35 +00:02:50,810 --> 00:02:55,630 +فيزيائي حقيقي بمعنى أخر أنه ممكن ياخد أي قيم بما + +36 +00:02:55,630 --> 00:03:00,810 +في ذلك كثور يعني مش شرط أن يكون whole number ممكن + +37 +00:03:00,810 --> 00:03:05,890 +ياخد مثلا اتلاقى يعني ال oxidation number عبارة عن + +38 +00:03:05,890 --> 00:03:09,880 +مثلا نص أو تلت ارباع أو مش مشكلةما يهم في ال + +39 +00:03:09,880 --> 00:03:12,060 +oxidation number هو التغير في ال oxidation number + +40 +00:03:12,060 --> 00:03:14,900 +وليس قيمة ال oxidation number بحد ذاته التغير هو + +41 +00:03:14,900 --> 00:03:18,800 +المهم هل بزيد ال oxidation number و لا بقل إذا كان + +42 +00:03:18,800 --> 00:03:22,600 +زاد فهذه عملية اكسدة إذا كان قل فهذه عملية اختزال + +43 +00:03:22,600 --> 00:03:28,250 +فهو يستخدم كمفهوم لتتبععمليات الأكسدة والاختزاة + +44 +00:03:28,250 --> 00:03:31,710 +لكن ليس له مفهوم فيزيائي حقيقي اللي نقدر يعني + +45 +00:03:31,710 --> 00:03:35,870 +نعرفه ونقول والله هو عبارة عن شيء معين يعني ولهذا + +46 +00:03:35,870 --> 00:03:39,890 +السبب زي ما قلت ممكن ياخد أي قيم بما في ذلك كثور + +47 +00:03:39,890 --> 00:03:45,840 +يعني مايكنش whole numberمهم جدا احنا نعرف ال + +48 +00:03:45,840 --> 00:03:47,780 +oxidation number لأن لو عرفنا ال oxidation number + +49 +00:03:47,780 --> 00:03:51,520 +لأي أتم في المتفاعلات وشوفنا هذه الأتم في النواتج + +50 +00:03:51,520 --> 00:03:54,200 +إذا تغير ال oxidation number معناه تفاعل أكسدة + +51 +00:03:54,200 --> 00:03:59,000 +واختزال طب تغير أكثر مجابية إذا هذه أكسدة تغير + +52 +00:03:59,000 --> 00:04:02,920 +يعني لسلبا هذا اختزال فمهم جدا نعرف ال oxidation + +53 +00:04:02,920 --> 00:04:06,160 +number لأنه على أساسه راحين نقدر نعرف هل عندي + +54 +00:04:06,160 --> 00:04:10,460 +أكسدةواختزال تفاعل وإذا كان عندى تفاعل هل هو تفاعل + +55 +00:04:10,460 --> 00:04:13,560 +اكسدة و لا هو تفاعل اختزال ايش الذرات اللى بحصلها + +56 +00:04:13,560 --> 00:04:17,360 +اكسدة ايش الذرات اللى بحصلها اختزال ايش ال rules + +57 +00:04:17,360 --> 00:04:21,900 +اللى بنتبعها فى تحديد ال oxidation number فى rules + +58 +00:04:21,900 --> 00:04:27,820 +داجب ان نتبعها فبقول فى البداية اى element فى + +59 +00:04:27,820 --> 00:04:32,340 +حالته العنصرية العادية بقول والله ال oxidation + +60 +00:04:32,340 --> 00:04:37,160 +number له صفرفمثلا لو اطلعنا على ال Sodium صليت + +61 +00:04:37,160 --> 00:04:40,700 +صفر ال Oxygen number البوتاسيب صليت صفر الألوان + +62 +00:04:40,700 --> 00:04:47,770 +الصليت صفر ال Gold صليت صفرحتى العلاصر الأخرى مثلا + +63 +00:04:47,770 --> 00:04:53,910 +باخد الهيدروجين H2 هذا عنصر H2 gas صفر لأنه مافيش + +64 +00:04:53,910 --> 00:04:56,990 +عليه هذا عنصر العنصر دائما ال oxidation number + +65 +00:04:56,990 --> 00:04:59,370 +تبعه صفر مافيش عليه شحنة زي ما هتشوف بعد شوية + +66 +00:04:59,370 --> 00:05:03,750 +فالعنصر دائما بنقول أن ال oxidation number له جداش + +67 +00:05:03,750 --> 00:05:04,490 +صفر + +68 +00:05:06,900 --> 00:05:11,280 +تانى حاجة يبجى هذا حاجة أخدناها و طلعنا عليها كويس + +69 +00:05:11,280 --> 00:05:13,720 +كتير و فهمنا انه اي عنصر المفروض ان ال oxygen + +70 +00:05:13,720 --> 00:05:20,060 +مرتبعه صفر بتطلع على اي ايون ايون mono atomic ايون + +71 +00:05:20,060 --> 00:05:26,260 +يعني زى sodium plus زى sulfur اتنين سالب مثلا يعني + +72 +00:05:26,260 --> 00:05:33,390 +زىزي ايش بيسموه اذا كان عليه الشحنة aluminum تلاتة + +73 +00:05:33,390 --> 00:05:36,990 +موجب calcium اتنين موجب الشحنة اللي عليه هي ال + +74 +00:05:36,990 --> 00:05:39,650 +oxidation number يعني calcium اتنين موجب ال + +75 +00:05:39,650 --> 00:05:44,130 +oxidation number اتنين موجب aluminum تلاتة موجب اه + +76 +00:05:44,130 --> 00:05:48,190 +تلاتة موجب ال fluorine سالب واحد سالب واحد مثلا + +77 +00:05:48,190 --> 00:05:52,170 +فمدام عليه الشحنة تبعته معروفة الشحنة عليه معروفة + +78 +00:05:52,170 --> 00:05:55,370 +لحاله mono atomic فال oxidation number تبعه عبارة + +79 +00:05:55,370 --> 00:06:00,000 +عن ايه ال charge اللي عليههذا القانون التاني لو + +80 +00:06:00,000 --> 00:06:06,240 +عندي مركب بتكون من أكتر من أتم بالضرورة فبقول هذا + +81 +00:06:06,240 --> 00:06:10,320 +المركب إذا كانه in neutral فمجموع ال oxidation + +82 +00:06:10,320 --> 00:06:15,120 +numbers صفر طب إذا كان عليه شحنة كان مثلا زي أكسي + +83 +00:06:15,120 --> 00:06:19,120 +أميون أو غيره بقول ال oxidation number المجموع + +84 +00:06:19,120 --> 00:06:22,870 +تبعه بدل سوى الشحنة اللي عليهتمام؟ يبقى scan الـ + +85 +00:06:22,870 --> 00:06:26,090 +neutral فال oxidation number له صفر ككل، scan عليه + +86 +00:06:26,090 --> 00:06:29,210 +شحنة فالشحنة هي مجموعة ال oxidation numbers، برضه + +87 +00:06:29,210 --> 00:06:32,350 +هذا حاجة بديهية جدا، الأهم نيجي نطلع على بعض + +88 +00:06:32,350 --> 00:06:37,830 +التفاصيل، بدي أقول إن ال oxygen دائما سالب اتنين، + +89 +00:06:37,830 --> 00:06:40,770 +ال oxygen ال scan موجد فيه مركب فهو دائما بياخد + +90 +00:06:40,770 --> 00:06:45,440 +سالب اتنينتمام؟ في عناصر كتير مش مذكورة هنا لكن + +91 +00:06:45,440 --> 00:06:48,540 +إذا كان فيها أكسجين فهذا بياخد أولوية في التحديد + +92 +00:06:48,540 --> 00:06:53,360 +سالب اتنين إلا في مركب واحد اللي هو البروكسيد ال + +93 +00:06:53,360 --> 00:07:02,970 +O2 سالب فال oxidation number بيكون سالب واحدفهي زي + +94 +00:07:02,970 --> 00:07:08,130 +ال H2O2 ال oxidation number للأكسجين في هذا المركب + +95 +00:07:08,130 --> 00:07:13,250 +pair oxide فسالب واحد بس لكن غير هيك ال oxidation + +96 +00:07:13,250 --> 00:07:16,510 +number للأكسجين دائما سالب اتنين طيب يبقى هذا + +97 +00:07:16,510 --> 00:07:19,250 +قانون برضه خلصنا منه بنجي نتطلع على ال metal + +98 +00:07:19,250 --> 00:07:22,430 +hydrides و اتطلع عليه اش بقول metal hydrides يعني + +99 +00:07:22,430 --> 00:07:27,730 +عندي metal مرتبط بالهيدروجينالهيدروجين اذا كان في + +100 +00:07:27,730 --> 00:07:31,910 +الـ metal hydride فهو سالب واحد غير هيك موجب واحد + +101 +00:07:31,910 --> 00:07:40,960 +يعني مثلا H2O الهيدروجين plus oneلكن مثلا NAH هذا + +102 +00:07:40,960 --> 00:07:44,520 +metal hydride هذا لأ سالب واحد اذا كان موجب واحد + +103 +00:07:44,520 --> 00:07:48,340 +فبس في ال metal hydride يبقى ياخد سالب واحد لكن في + +104 +00:07:48,340 --> 00:07:51,640 +اي مركب اخر موجب واحد يبقى ان انت بيهالي ال + +105 +00:07:51,640 --> 00:07:55,220 +hydrogen موجود في metal hydride ولا لأ كمان مرة + +106 +00:07:55,220 --> 00:07:58,540 +اذا كان موجود في metal hydride فهو سالب واحد لكن + +107 +00:07:58,540 --> 00:08:02,260 +اذا كان موجود في اي مركب اخر موجب واحد يبقى + +108 +00:08:02,260 --> 00:08:05,520 +انتهينا من ال ايه من ال hydrogen نجي لل floor جال + +109 +00:08:05,520 --> 00:08:11,600 +دائما سالب واحددائما الفلوريد F سالب واحد وين + +110 +00:08:11,600 --> 00:08:17,340 +بنلاقيه في مركب مثلا NAF على طول هذا سالب واحد وين + +111 +00:08:17,340 --> 00:08:21,880 +مالاج الفلورين سالب واحد على طول خلصت من الفلورين + +112 +00:08:21,880 --> 00:08:29,700 +ال Oxygen number لأ لكلورين CL CL لكلورين PR و I + +113 +00:08:29,700 --> 00:08:35,200 +سالب واحد إلا إذا كانت مرتبطة مع ال Oxygen فلل + +114 +00:08:35,200 --> 00:08:39,420 +Oxygen الأولويةالـ Cl مرتبطة مع الأكسجين فللأكسجين + +115 +00:08:39,420 --> 00:08:47,940 +الأولوية مثلا لو اتطلعنا على مركب Cl2O3 + +116 +00:08:47,940 --> 00:08:51,600 +بقول هل اعتبر Cl سالب واحد؟ لأ مادة مرتبطة مع + +117 +00:08:51,600 --> 00:08:56,580 +الأكسجين الأولوية لمن؟ للأكسجين اتنين في تلاتة + +118 +00:08:56,580 --> 00:09:02,690 +بالسالب هي سالب ستة إذا الكلورة موجة بتلاتةالتنتين + +119 +00:09:02,690 --> 00:09:06,530 +موجة ب 6 إذا اللي كلورة الواحدة هي ال number تبعها + +120 +00:09:06,530 --> 00:09:11,150 +يبقى دائما اللي كلورين البرومين الايودين سلب واحد + +121 +00:09:11,150 --> 00:09:16,380 +إلا إذا كانت مرتبطة مع مين؟مع ال Oxygen فساعتها ال + +122 +00:09:16,380 --> 00:09:18,480 +Oxygen بياخد الأولوية بنعوض على ال Oxygen و بنسلب + +123 +00:09:18,480 --> 00:09:22,380 +2 و بنطلع قيمة ال Oxidation number لل Clor لل Brom + +124 +00:09:22,380 --> 00:09:26,100 +لل Iodine لفلور لأ لفلور دائما سالب 1 و بتكون + +125 +00:09:26,100 --> 00:09:31,160 +دائما قيمة ال Oxidation number لل Clorine أو لل + +126 +00:09:31,160 --> 00:09:34,520 +Bromine أو لل Iodine قيمة موجبة ليه؟ لأن ال Oxygen + +127 +00:09:34,520 --> 00:09:40,660 +سالب فهي لازم تكون قيمة موجبةفبدنا نتذكر هذه ال + +128 +00:09:40,660 --> 00:09:45,960 +rules ضرورية جدا في الحكم على اي atom جدش ال + +129 +00:09:45,960 --> 00:09:50,220 +oxidation number تبعها فحنشوف بعض الأمثلة انا بدي + +130 +00:09:50,220 --> 00:09:53,900 +اطلع على ال sulfur بس و اطبق القوانين اللي اخدتها + +131 +00:09:53,900 --> 00:09:57,040 +فبيقول لي determine the oxidation number of sulfur + +132 +00:09:57,040 --> 00:10:01,340 +in H2S + +133 +00:10:01,340 --> 00:10:06,150 +هل هذا metal hydride؟ هذا مش metalوبعدين لو كان + +134 +00:10:06,150 --> 00:10:08,110 +متل هيدرايدي ال H بتكون على ناحية التانية على + +135 +00:10:08,110 --> 00:10:12,090 +اليمين فلأ هذه معنى الكلام ال H اتنين موجب لأنها + +136 +00:10:12,090 --> 00:10:16,760 +اتنين يبقى ال S اتنين سالمعلى طول نيجي نطلع لل S8 + +137 +00:10:16,760 --> 00:10:24,160 +هذا عنصر في حالة الانصرية سفر S8 صفر P4 صفر برضه + +138 +00:10:24,160 --> 00:10:31,060 +فسفار P4 صفر طيب SCl2 ال CL سلب واحد فاتنين سلب + +139 +00:10:31,060 --> 00:10:36,360 +اتنين ال S موجب اتنين طيب صادم فيوصلفات الصادم + +140 +00:10:36,360 --> 00:10:40,260 +اتنين يعني اتنين موجب اتنين فواحد اتنين موجب + +141 +00:10:40,440 --> 00:10:45,840 +الأكسجين ستة سالب معنى الكلام ستة و اتنين بده يكون + +142 +00:10:45,840 --> 00:10:49,430 +موجة باربعةزائد أربعة يبقى السلفر زائد أربعة يبقى + +143 +00:10:49,430 --> 00:10:53,510 +نعمله برضه إذا حبيته بنقول والله صفر المجموعة الكل + +144 +00:10:53,510 --> 00:10:55,450 +ال oxidation number زي أنا مافيش عليه أي شحنة + +145 +00:10:55,450 --> 00:10:58,210 +بتساوي اتنين في ال oxidation number للصوديوم زائد + +146 +00:10:58,210 --> 00:11:00,590 +ال oxidation number للسلفر زائد تلاتة في ال + +147 +00:11:00,590 --> 00:11:04,410 +oxidation number للأكسجين بنعود صفر بتساوي اتنين + +148 +00:11:04,410 --> 00:11:06,750 +في واحد ال oxidation number للصوديوم ال oxidation + +149 +00:11:06,750 --> 00:11:10,130 +number للسلفر أنا بديه تلاتة في سالب اتنين اللي هو + +150 +00:11:10,130 --> 00:11:12,330 +الأكسجين بتطلع عند ال oxidation number للسلفر + +151 +00:11:12,330 --> 00:11:17,750 +أربعةطيب السلفات بدنا نشوف في السلفة في السلفات + +152 +00:11:17,750 --> 00:11:23,140 +قداش ال oxygen number بقول والله ال oxygenسالب + +153 +00:11:23,140 --> 00:11:27,480 +تمانية في عند منهم ال oxygen سالب تمانية في عند + +154 +00:11:27,480 --> 00:11:32,760 +منهم سالب اتنين بتام يعني سالب ستة اذا ال sulfur + +155 +00:11:32,760 --> 00:11:37,160 +موجب ستة كيف بدي اعمله موجب ستة كيف بدي اعمله بقول + +156 +00:11:37,160 --> 00:11:41,300 +والله هيها سالب اتنين الشحنة الكلية سالب اتنين + +157 +00:11:41,300 --> 00:11:43,680 +بتها تساوم مجموعة ال oxidation number oxidation + +158 +00:11:43,680 --> 00:11:47,640 +number لل sulfur مجهول اربعة في سالب اتنين سالب + +159 +00:11:47,640 --> 00:11:50,860 +اتنين في اربعة سالب ستة بتروح النحل تاني وصير ايه؟ + +160 +00:11:50,990 --> 00:11:57,790 +موجة ب تمانية و سالب اتنين موجة بستة حلو؟ طيب ال + +161 +00:11:57,790 --> 00:12:02,870 +oxidation number ل ال sulfur في ال sodium تيو + +162 +00:12:02,870 --> 00:12:13,240 +سالفات بيقول مش تترى خلينا نقولهذا يعني ال + +163 +00:12:13,240 --> 00:12:17,900 +Oxidation product من الثيوصالفات بقول ال total + +164 +00:12:17,900 --> 00:12:22,120 +number Oxygen number للصوديام اتنين اتنين موجب هدا + +165 +00:12:22,120 --> 00:12:29,720 +هي طب الستة Oxygen سالم اتناش طب اتناش و اتنين صار + +166 +00:12:29,720 --> 00:12:36,570 +عشرة على اربع اتنين و نصممكن اه ممكن فش مشكلة كيف + +167 +00:12:36,570 --> 00:12:39,550 +بنعرف هذا الكلام برضه؟ بقول بسهولة صفر المجموع + +168 +00:12:39,550 --> 00:12:42,850 +الكلي لأنه مافيش عليه اي شحنة بدي اتنين في ال + +169 +00:12:42,850 --> 00:12:45,210 +oxygen number للصوديوم اربعة في ال oxygen number + +170 +00:12:45,210 --> 00:12:48,210 +للسلفات ستة في ال oxygen number للأكسجين بيطلع + +171 +00:12:48,210 --> 00:12:52,850 +عندى اتنين و نص مش شرط ان يكون عدد صحيح لأنه لا + +172 +00:12:52,850 --> 00:12:56,900 +يهمني قيمةالـ Oxidation number للعنصر أو للـ Ion + +173 +00:12:56,900 --> 00:13:01,660 +اللي بيهمني التغير التغير هو اللي له معنى لكن قيمة + +174 +00:13:01,660 --> 00:13:04,400 +ال Oxidation number ولا أي معنى إلها مافيش معنى + +175 +00:13:04,400 --> 00:13:07,900 +فيزيائي لها لكن التغير هو اللي إيه هو المهم بدي + +176 +00:13:07,900 --> 00:13:12,480 +أطلع على كمان بعض الأمثلة مختلفة مش بس لسه الفضل + +177 +00:13:12,480 --> 00:13:19,700 +أي شيء P2O5 بسميهDiphosphorous Pentoxide لأن هذا + +178 +00:13:19,700 --> 00:13:25,320 +بيناري كمباون موليكولار كمباون باستخدام له المؤن + +179 +00:13:25,320 --> 00:13:28,760 +والداي والتراي وإلى آخره Diphosphorous Pentoxide + +180 +00:13:28,760 --> 00:13:33,580 +بقوله إيه جداش ال ال Oxidation number للفوسفوراس + +181 +00:13:33,580 --> 00:13:36,800 +بقول خمسة في اتنين بعشرة بالسالم إذا هذه عشرة + +182 +00:13:36,800 --> 00:13:40,720 +بالموجة بقى اتنين موجة بخمسة عايزة يا بنات؟ إذا + +183 +00:13:40,720 --> 00:13:44,940 +كان في أي مشكلة احكيليكمان مرة بقول خمسة فى سلب + +184 +00:13:44,940 --> 00:13:47,600 +اتنين هي الاولوية اكسجين الفسوفرس مش موجود فى + +185 +00:13:47,600 --> 00:13:51,500 +القوانين اللى أخدناها فالاولوية بس للإيه للقوانين + +186 +00:13:51,500 --> 00:13:56,000 +اللى أخدناها خمسة فى اتنين اه عشرة بالسالب هي بجهد + +187 +00:13:56,000 --> 00:14:00,100 +عشرة بالموجب على اتنين خمسة موجب صوديوم هيدرايد + +188 +00:14:00,100 --> 00:14:05,680 +بالظبط يعنى فالهيدرايد سالب واحد ال H سالب واحد + +189 +00:14:05,680 --> 00:14:11,130 +اذا الصوديوم موجب واحد منهى بايكرو ميتسبعة اتنين + +190 +00:14:11,130 --> 00:14:14,190 +او سبعة اتنين سالب بقول سبعة في اربعة في اتنين + +191 +00:14:14,190 --> 00:14:17,410 +اربعة عاش بالسالب في منهم اتنين اتناش بالسالب على + +192 +00:14:17,410 --> 00:14:21,910 +اتنين ستة بالموجب او الاسهل ليه اني اجي اقول سالب + +193 +00:14:21,910 --> 00:14:24,410 +اتنين بتساوي اتنين في ال oxidation number للكروم + +194 +00:14:24,410 --> 00:14:28,170 +زائد سبعة في ال oxidation number للأكسجين يبقى + +195 +00:14:28,170 --> 00:14:29,590 +سالب اتنين بتساوي اتنين في ال oxidation number + +196 +00:14:29,590 --> 00:14:32,450 +للكروم زائد سبعة في سالب اتنين معناه كلام ال + +197 +00:14:32,450 --> 00:14:36,410 +oxidation number للكروم بساوي زائد او موجب ستةماشي + +198 +00:14:36,410 --> 00:14:41,990 +يا جماعة طيب ال SNPR 4 على طول ال PR منهيه سالف + +199 +00:14:41,990 --> 00:14:47,530 +واحد زال ال SN موجب اربع موجب اربع ال PPO2 منهيه + +200 +00:14:47,530 --> 00:14:51,470 +ال oxygen ال oxygen سالف اتنين في اتنين سالف اربع + +201 +00:14:51,470 --> 00:14:55,630 +ازال ال PP موجب اربع ال ASH3 هذا metal hydride + +202 +00:14:55,630 --> 00:15:01,000 +سالف واحد ازال ال AS موجب تلاتةكويسك للمعلومات هذا + +203 +00:15:01,000 --> 00:15:04,020 +بيجي كتير منه في الامتحان بس فبدا من انتباه لهذه + +204 +00:15:04,020 --> 00:15:06,840 +القوانين وكافية تطبيقها عشان هيك انا حابب ان + +205 +00:15:06,840 --> 00:15:13,340 +اعطيكم يعني امثلة بالزيادة ونحلها مع بعض الان من + +206 +00:15:13,340 --> 00:15:17,240 +اهم ما يمكن يعني ان نتحدث عنه في ال oxidation + +207 +00:15:17,240 --> 00:15:20,940 +reduction reactions اللي هي ال activity series هل + +208 +00:15:20,940 --> 00:15:30,130 +يعني استطيع توقع حدوث تفاعل ما ولا لأ؟لو قلت اي + +209 +00:15:30,130 --> 00:15:35,290 +عنصر هل يتفاعل مع acid ولا لأ؟ عنصر في حالته + +210 +00:15:35,290 --> 00:15:38,890 +العنصرية كويس مثلا Sodium بتفاعل مع acid ولا لأ؟ + +211 +00:15:38,890 --> 00:15:41,150 +Magnesium بتفاعل مع acid ولا لأ؟ Calcium بتفاعل مع + +212 +00:15:41,150 --> 00:15:44,610 +acid ولا لأ؟ Copper بتفاعل مع acid ولا لأ؟ فبط + +213 +00:15:44,610 --> 00:15:50,750 +بتفاعل مع acid ولا لأ؟ كعنصر أو هل هذا العنصر + +214 +00:15:50,750 --> 00:15:55,910 +بتفاعل مع salt ولا لأ؟ هل يمكن توقعه؟التفاعل أكسدا + +215 +00:15:55,910 --> 00:15:59,430 +واختزال هل بتفاعل مع Salt ولا لأ فهذا شيء مهم جدا + +216 +00:15:59,430 --> 00:16:02,930 +ويعتبر حيوي كتير وطبعا برضه كمان بنسأل عنه كتير في + +217 +00:16:02,930 --> 00:16:06,870 +الامتحان فبقول عشان أعرف هذا الكلام لابد إلا إن + +218 +00:16:06,870 --> 00:16:10,490 +أتحدث عن ال activity series اللي هي خليني أقول + +219 +00:16:10,490 --> 00:16:17,350 +سلسلة نشاط ال electro كيميائي يعني الكهرو كيميائي، + +220 +00:16:17,350 --> 00:16:22,660 +سلسلة نشاط احنا حولنا نرتب العناصركويس ترتيب حسب + +221 +00:16:22,660 --> 00:16:26,540 +النشاط حسب سهولة الأكس ده حسب سهولة أن العنصر + +222 +00:16:26,540 --> 00:16:29,880 +يتأكسد إيش يعني يتأكسد يعني يفقد الإلكترونات إيش + +223 +00:16:29,880 --> 00:16:32,880 +يعني يتأكسد يعني ال oxidation number تبعه يزيد + +224 +00:16:32,880 --> 00:16:36,680 +فإيه يعني يتأكسد يتأكسد يعني يفقد الإلكترونات أو + +225 +00:16:36,680 --> 00:16:40,960 +يعني بنفس الشيء يتأكسد يعني يزيد ال oxidation + +226 +00:16:40,960 --> 00:16:45,940 +number إيه تبعه فاحنا مثلا في عنا ملاحظة في عنا + +227 +00:16:45,940 --> 00:16:50,380 +ملاحظة وجدنا أنه لما نحطالـ Nickel solution زي + +228 +00:16:50,380 --> 00:16:54,960 +Nickel Nitrate في وعة من الحديد هاي وعة حديد Iron + +229 +00:16:54,960 --> 00:17:02,560 +حطينا فيه Nickel Nitrate مثلا محلول و سكرنا عليه + +230 +00:17:02,560 --> 00:17:06,960 +يعني احفظنا ال Nickel Nitrate وين؟ في وعة حديد + +231 +00:17:06,960 --> 00:17:12,580 +خيار عندنا خيار جال لجينا بعد فترة ان الحديد اتاكل + +232 +00:17:12,580 --> 00:17:16,600 +و ال ايه؟ و ال Nickel Nitrate نزلت على الأرض محلول + +233 +00:17:17,990 --> 00:17:23,610 +بتاكل يبجى لا شك انه ال nickel هاد اتفاعل مع ايه؟ + +234 +00:17:23,610 --> 00:17:27,850 +مع ال iron طب هاد كلام مهم جدا عشان نعرف مدى ما + +235 +00:17:27,850 --> 00:17:30,310 +عرفنا خصائص المواد نعرف كيف ممكن نحفظ المواد + +236 +00:17:30,310 --> 00:17:34,930 +المختلفة مثلا يعني فبالتالي هاد ملاحظ عنا طب ليش؟ + +237 +00:17:34,930 --> 00:17:39,570 +ايش اللي حصل؟ جا لابد انه ال iron بما انه ال iron + +238 +00:17:39,570 --> 00:17:47,100 +داب يبجى ال iron بدل ما كان solidأتحول لـ Iron 2 + +239 +00:17:47,100 --> 00:17:52,580 +أو Iron 3 ايش في ال solution aqueous داب يعني ايش + +240 +00:17:52,580 --> 00:17:57,880 +حصل له اكسدة من صفر إلى موجة بتلاتة زاد ال + +241 +00:17:57,880 --> 00:18:00,720 +oxidation number حصل له ايه اكسدة فال activity + +242 +00:18:00,720 --> 00:18:04,720 +series بتقول لي اذا كان في عندى تفاعل ما بيحصل ولا + +243 +00:18:04,720 --> 00:18:07,900 +لأ لو اطلعنا ايضا + +244 +00:18:11,400 --> 00:18:17,720 +الزنك لو حطنا .. لو حطينا محلول كابر 2 plus كويس + +245 +00:18:17,720 --> 00:18:25,640 +كابر 2 plus في وعة زنك solid بنلاحظ برضه انه ال .. + +246 +00:18:25,640 --> 00:18:30,180 +الوعه هذا تاب او الوعه هذا يعني تآكل بينما لو + +247 +00:18:30,180 --> 00:18:37,070 +حطينا ال zinc في ..لو حطينا silver is not .. + +248 +00:18:37,070 --> 00:18:42,070 +هتشوفوا هل جت في ال .. ال .. ال zinc is easier to + +249 +00:18:42,070 --> 00:18:45,670 +.. ال silver برضهاش يتأكسد .. is لو حطيناه في وعة + +250 +00:18:45,670 --> 00:18:48,830 +silver مش هيتأكسد .. لو حطيناه في وعة silver مش + +251 +00:18:48,830 --> 00:18:52,550 +هيتأكسد .. طيب يعني لو حطينا الكبر في وعة silver + +252 +00:18:52,550 --> 00:18:57,550 +هنلاحظ أنه هيدلوا جاعد زي ما هو .. مش هيكرر بالوعة + +253 +00:18:58,220 --> 00:19:01,540 +طب ليش هاد الكلام؟ ايش .. ايش بنقدر نستنتج من يعني + +254 +00:19:01,540 --> 00:19:06,120 +شغلها زي قال تعالوا نرتب العناصر حسب سهولة أجسدتها + +255 +00:19:06,120 --> 00:19:10,140 +حسب سهولة أجسدتها؟ لما نرتبها حسب سهولة أجسدتها + +256 +00:19:10,140 --> 00:19:14,940 +بنقول هاد عندي ال activity series سلسلة النشاط، + +257 +00:19:14,940 --> 00:19:22,770 +كويس؟ فخلينا نطلع هان الجدول التاليالأكتر سهولة في + +258 +00:19:22,770 --> 00:19:27,690 +الـ Oxidation فوق لما نقول هذا الـ Lithium Solid + +259 +00:19:27,690 --> 00:19:31,270 +بتحول ل Lithium Plus زي الإلكترون معنى الكلام إيه؟ + +260 +00:19:31,270 --> 00:19:34,090 +هذا بسهولة بتتحول لإيه؟ لل Lithium Plus لأنه فوق، + +261 +00:19:34,090 --> 00:19:39,290 +في السلسلة فوق نشيط جدا، نشيط جدا بنقول إنه إذا + +262 +00:19:39,290 --> 00:19:43,410 +كان هذا بتتحول بسهولة لأو بتأكسد بسهولة إذا هذا + +263 +00:19:43,410 --> 00:19:50,340 +strong reducing agent عامل مختزل قوي كل مكانيعني + +264 +00:19:50,340 --> 00:19:54,400 +ال Oxidation بتحصل بسهولة معناته .. هذا عامل + +265 +00:19:54,400 --> 00:20:00,480 +مقتزل، بنقول له عامل مقتزل قوي، فهو ايه؟ يعني + +266 +00:20:00,480 --> 00:20:04,880 +استخدم كعامل مقتزل، لحظة ليثيوم، سوديوم، باريوم، + +267 +00:20:04,880 --> 00:20:07,820 +كالسيوم، سوديوم، ماجنيزيوم + +268 +00:20:10,470 --> 00:20:15,250 +الـ Aluminum هذه العناصر لو طلعت عليها هي عناصر + +269 +00:20:15,250 --> 00:20:19,550 +المجموعة الأولى والتانية شايفينها ولا لأ؟ عناصر + +270 +00:20:19,550 --> 00:20:23,330 +المجموعة الأولى والتانية موجودة فوق في على رأس + +271 +00:20:23,330 --> 00:20:27,490 +سلسلة النشاط وانا بدي احاول ان اعطيكم يعني خليني + +272 +00:20:27,490 --> 00:20:32,280 +اقول بلوكاتيعني واضحة علشان ما نقدر ناخد كل شيء، + +273 +00:20:32,280 --> 00:20:35,520 +في exceptions لكل شيء، حتى هان في عندي exceptions، + +274 +00:20:35,520 --> 00:20:38,280 +Lithium، Potassium، ال Sodium جاي هان، المفروض لو + +275 +00:20:38,280 --> 00:20:41,000 +بدنا نقول بينا نحطه هان ال Sodium مثلا، ال Calcium + +276 +00:20:41,000 --> 00:20:45,480 +جاي قبل ال Sodium، ففي عندي .. في عندي شواذ أه، + +277 +00:20:45,480 --> 00:20:48,500 +يعني الشيء مش جاي systematic زي ما أنا بتوقعه من + +278 +00:20:48,500 --> 00:20:51,980 +الجدول الدوري تماما، لكن اللي بشوفه بشكل واضح أنه + +279 +00:20:51,980 --> 00:20:55,220 +والله أه المجموعة الأولى والتانية على رأس سلسلة + +280 +00:20:55,220 --> 00:21:01,460 +النشاط، مافي خلاف في هذا الكلامبعد ذلك تجيه إلى + +281 +00:21:01,460 --> 00:21:06,020 +الـ Transition elements + +282 +00:21:06,020 --> 00:21:09,580 +منجنيز، زنك، كروم، ايرون، كوبلت، نكل .. + +283 +00:21:13,130 --> 00:21:17,430 +تنه led هدول بيكونوا تبهوا انهم بعد ال .. يعني على + +284 +00:21:17,430 --> 00:21:21,450 +اليمين يعني كويس بس تذكروا ال led قبل ال hydrogen + +285 +00:21:21,450 --> 00:21:24,270 +يعني في آخر السلسلة ال led من فوق آخر السلسلة الآن + +286 +00:21:24,270 --> 00:21:27,190 +قبل ال hydrogen اللي هو إيه ال led لأن أنصر مهم + +287 +00:21:27,190 --> 00:21:31,010 +بالنسبة لي ال led أنصر مهم بالنسبة لي ال hydrogen + +288 +00:21:31,010 --> 00:21:35,910 +بفصل حاجتين ال hydrogen بفصل ال hydrogen هذا طبعا + +289 +00:21:35,910 --> 00:21:39,070 +عندي صفر صير اتنين اتش موجب يعني هذا عبارة عن عامل + +290 +00:21:39,070 --> 00:21:44,180 +مختزل لأنه بتأكسدحلو جداش قوي مش كتير قوي لإنه لما + +291 +00:21:44,180 --> 00:21:50,740 +بتزيد القوة فوق لإن ال ease of oxidation فوق ايش + +292 +00:21:50,740 --> 00:21:54,580 +فيه تحت الهيدروجين برضه بدنا نتذكر هذه الشغلة تحت + +293 +00:21:54,580 --> 00:21:58,580 +الهيدروجين ال coin ارفع المالك اللي مش واهم عندي + +294 +00:21:58,580 --> 00:22:03,840 +copper silver platinum gold هدول عناصر ال coins + +295 +00:22:03,840 --> 00:22:08,730 +عناصر الايهالـ coins الـ coinage metals العملات + +296 +00:22:08,730 --> 00:22:12,970 +النقدية ممكن تلاقي والله دهب بجنيه دهب ولا بلاتين + +297 +00:22:12,970 --> 00:22:18,610 +ولا هدول في خلطة منهم كبر سيلفر gold في خلطة منهم + +298 +00:22:18,610 --> 00:22:21,670 +بتلاقي هذه الـ coinage metals الـ coinage metals + +299 +00:22:21,670 --> 00:22:25,450 +بتتأكسدش بسهولة وهذا وضع احنا عارفينه لأنه + +300 +00:22:25,450 --> 00:22:30,410 +بنستخدمها كcoinage أو كزينة وغيره فانا بدي أجسم + +301 +00:22:30,410 --> 00:22:35,770 +العناصر كلها ل3 أقسامقسم المجموعة الأولى والتانية + +302 +00:22:35,770 --> 00:22:39,650 +فوق هذا ناشط جدا لو بده اقارنه في بعض القسم التاني + +303 +00:22:39,650 --> 00:22:43,650 +Transition Metals كويس بعد ما اقلص Transition + +304 +00:22:43,650 --> 00:22:48,250 +Metals بدي اذكر بس ال led ال led جاب لي ايه في اخر + +305 +00:22:48,250 --> 00:22:53,050 +النشاط بعدين بيجينا حاجات مش ناشطة اللي هي ايه ال + +306 +00:22:53,050 --> 00:22:59,970 +coinage metals كبر سلفر جولد بلاتين كويس هي كعرفة + +307 +00:22:59,970 --> 00:23:03,920 +النشاط ايش بدي استفيد منهايش بدي استفيد منه؟ بدي + +308 +00:23:03,920 --> 00:23:10,800 +استفيد منه انه اي metal بيتفاعل مع salt اي metal + +309 +00:23:10,800 --> 00:23:15,700 +اخر تحته يعني اي salt تحته فال calcium بتفاعل مع + +310 +00:23:15,700 --> 00:23:21,060 +ال sodium مثلا ال chloride ايش اللي بيحصل؟ اللي + +311 +00:23:21,060 --> 00:23:25,120 +بيحصل ان ال calcium بدوب و ال sodium بده يصير + +312 +00:23:25,120 --> 00:23:30,980 +solidالـ Magnesium بتفاعل مع .. خلّيني أقول الـ + +313 +00:23:30,980 --> 00:23:36,380 +Aluminium Nitrate ال .. ال Zinc بتفاعل مع ال Iron + +314 +00:23:36,380 --> 00:23:45,280 +لو حبيته ال .. ال Iron اللي طبعا شفناه بتفاعل مع + +315 +00:23:45,280 --> 00:23:50,020 +ال Nickel بتفاعل .. أه عشان هيك إيه؟ كان ال Nickel + +316 +00:23:50,020 --> 00:23:53,220 +لما حطيناه في وعة Iron solid .. وع .. أتأكل ال + +317 +00:23:53,220 --> 00:23:55,920 +Iron ليه؟ لإنه بتفاعل معاه هي التفاعل شفناها قبل + +318 +00:23:55,920 --> 00:24:00,170 +شويةفالتفاعل سهل كثير هذا في بعض الأحيان الناس + +319 +00:24:00,170 --> 00:24:03,210 +بتسميه diagonal rule، diagonal بتعرفوا ال + +320 +00:24:03,210 --> 00:24:07,390 +diagonal؟ القطر، قي القطر، هي من اليسار لليمين، + +321 +00:24:07,390 --> 00:24:11,610 +هذا اه، اي واحد فوق بتفاعل مع ايه؟ مع ال ion اللي + +322 +00:24:11,610 --> 00:24:15,970 +تحته، اي ion، اي metal ion تحته، بتفاعل معاه، لكن + +323 +00:24:15,970 --> 00:24:19,130 +مثلا ال calcium هل بتفاعل مع ال barium 2 plus؟ لأ، + +324 +00:24:19,130 --> 00:24:22,450 +العكس صحيح ال barium هو اللي بتفاعل مع ال calcium + +325 +00:24:22,450 --> 00:24:27,380 +2 plusالبريوم بيختزل ال calcium 2 plus بيصير + +326 +00:24:27,380 --> 00:24:33,220 +calcium والبريوم بيصير بريوم 2 plus يعني كل metal + +327 +00:24:33,220 --> 00:24:37,840 +بتفاعل مع ال salt اللي تحته مع ال metal ion اللي + +328 +00:24:37,840 --> 00:24:42,400 +تحته فقط اي metal ion تحته فممكن هذا يتفاعل + +329 +00:24:42,400 --> 00:24:44,400 +calcium مع ال salt و مع ال manganese و مع ال .. كل + +330 +00:24:44,400 --> 00:24:47,940 +اللي تحته اه بينفع لكن اي واحد تحت مثلا ال + +331 +00:24:47,940 --> 00:24:53,260 +manganese هل بنفع يتفاعل مع ال zinc؟ بنقول لا، + +332 +00:24:53,260 --> 00:25:00,730 +بينفعشمنفعش دائما أسهم من اليسار لليمين لتحت خطوة + +333 +00:25:00,730 --> 00:25:04,890 +خطوة تانية تلاتة مش مشكلة هذه أول نقطة بدنا نذكرها + +334 +00:25:04,890 --> 00:25:10,230 +كويسة كتير و أخرجي أتحرك أخد أمثلة من + +335 +00:25:10,230 --> 00:25:13,930 +نشاط هذه المجموعات اللي هي تعتبر المجموعة الأولى + +336 +00:25:13,930 --> 00:25:18,450 +والتانية تقريبا أنه تتفاعل حتى مع ال cold waterمش + +337 +00:25:18,450 --> 00:25:21,230 +بس مع الـ Acids تتفاعل مع الـ cold water يعني + +338 +00:25:21,230 --> 00:25:25,210 +نشيطة جدا جدا بدي أقول كمان حاجة قبل ما أروح على + +339 +00:25:25,210 --> 00:25:30,150 +الجدول يعني بدي أقول الـ hydrogen قال كل ال metals + +340 +00:25:30,150 --> 00:25:35,830 +اللي فوق ال hydrogen تتفاعل مع ال acids و بتطلع H2 + +341 +00:25:35,830 --> 00:25:41,830 +أي metal مثلا لو طلعناLithium بتفاعل مع الـHCl + +342 +00:25:41,830 --> 00:25:45,610 +ويطلع H2 Potassium بتفاعل مع الـHNO3 ويطلع H2 + +343 +00:25:45,610 --> 00:25:51,090 +Barium بتفاعل مع الـHCl مثلا ويطلع H2 الكالسوم + +344 +00:25:51,090 --> 00:25:55,550 +المجنيزهم الالومنام المنجانيز الذينك الكل بتفاعل + +345 +00:25:55,550 --> 00:26:02,550 +مع ال acid ويطلع H2 هدول ايش قصتهم جال كل اللي فوق + +346 +00:26:02,550 --> 00:26:08,550 +الهيدروجين من هنا React with + +347 +00:26:10,270 --> 00:26:17,870 +acids طب و هان قال do not react with acids لأنها + +348 +00:26:17,870 --> 00:26:22,730 +ثابتة و احنا قلنا قبل شوية انها cornish metals فهي + +349 +00:26:22,730 --> 00:26:26,270 +حلو هيك يبقى هاي الحاجتين اللي استفدناهم من الجدول + +350 +00:26:26,270 --> 00:26:30,490 +جدول بسيط كتير المجموعة الأولى والتانية على رأس + +351 +00:26:30,490 --> 00:26:35,670 +النشاط very strong reducing agent يعني very easily + +352 +00:26:35,670 --> 00:26:40,030 +oxidizedبعدين ال transition elements متوسطة و نذكر + +353 +00:26:40,030 --> 00:26:46,070 +أنه في أخرها ال led بعدين ال coinage metals هذي + +354 +00:26:46,070 --> 00:26:51,430 +والله قال لأ هذي أقل نشاطا مش سهل انها تتأكسد شفنا + +355 +00:26:51,430 --> 00:26:55,210 +تبقى داخل ال rule و بعدين قلنا أي metal أي metal + +356 +00:26:55,210 --> 00:27:01,550 +solid metal فوقالـ Hydrogen جال بتفاعل مع ال .. مع + +357 +00:27:01,550 --> 00:27:06,630 +ال acids و بطلع H2 و أي metal تحت ال hydrogen لا + +358 +00:27:06,630 --> 00:27:12,290 +يتفاعل هذه كل ال .. كل السلسلة يعني خليني اقول انه + +359 +00:27:12,290 --> 00:27:16,250 +بس هذا اللي بدنا نفهمه في exceptions هناك بعض ال + +360 +00:27:16,250 --> 00:27:19,610 +exceptions لكن الصورة الكلية هي الصورة اللي انا + +361 +00:27:19,610 --> 00:27:24,410 +بحكيها الآن خلينا نيجي نطلع على بعض الأمثلة هذا بس + +362 +00:27:24,410 --> 00:27:30,600 +لتذكيرهاأنا جسمت العناصر لجولة الـAlkali هي + +363 +00:27:30,600 --> 00:27:34,580 +الـmost active أو الـmost easily oxidized يعني + +364 +00:27:34,580 --> 00:27:37,900 +الـAlkali و الـAlkaline earth metals هي هما أكتر + +365 +00:27:37,900 --> 00:27:41,900 +حاجة بعدين الـtransition elements و الـlead و كل + +366 +00:27:41,900 --> 00:27:46,280 +هدول جاب للإيه؟ بتفاعلوا مع الـacids طيب و + +367 +00:27:46,280 --> 00:27:50,080 +الـcoinage metals جال هدول least active بتفاعلوش + +368 +00:27:50,080 --> 00:27:55,470 +مع الـacidsنهائيًا خلّيني أطلّع الآن على ال + +369 +00:27:55,470 --> 00:28:00,790 +oxidation of metals by acids هاي عندي أنا المتل + +370 +00:28:00,790 --> 00:28:09,170 +solid المتل solid زائد اتنين HX يعني HCL HBR HL + +371 +00:28:09,170 --> 00:28:14,730 +اخرى كويس فبلاحظ انا انه بيحصل نوع من ال + +372 +00:28:14,730 --> 00:28:20,230 +displacement او ال replacement فالمتلراح ياخد الـ + +373 +00:28:20,230 --> 00:28:25,110 +X اللي هي الانيون والميتل يعني هيحصل له ايه؟ مدام + +374 +00:28:25,110 --> 00:28:28,930 +أخد الانيون يبقى حصل له أكسدة سبميتل موجب، هناخد + +375 +00:28:28,930 --> 00:28:33,010 +أمثلة الـGET تحته على طول والـH اتنين منه صارت H2 + +376 +00:28:33,010 --> 00:28:37,470 +يعني هان الـH كانت موجب واحد صارت جداش صفر يعني + +377 +00:28:37,470 --> 00:28:44,870 +حصل اختزال للـH وحصل أكسدة للميتل هاي مثلا Zinc، + +378 +00:28:44,870 --> 00:28:48,150 +Zinc مع اتنين HPR، كويس + +379 +00:28:50,420 --> 00:28:55,120 +فبقول انا ال zinc هياخد ال PR وهي zinc PR 2 وال 2 + +380 +00:28:55,120 --> 00:29:01,060 +H هتعطينيH2 جاهز الـ H كانت هانموجة بوان صارت صفر + +381 +00:29:01,060 --> 00:29:06,960 +يعني هذه اختزال ال zinc كانت zinc صفر صارت zinc + +382 +00:29:06,960 --> 00:29:15,980 +اتنين يبقى هذه اكسدة طيب خليني اطلع على بعض ال .. + +383 +00:29:15,980 --> 00:29:20,260 +يعني نفس الكلام اللي قلناه بالظبط هاطلع على اي + +384 +00:29:20,260 --> 00:29:24,550 +metal ion فوق الهيدروجين هلاحظ انه بيتفاعل معالاسد + +385 +00:29:24,550 --> 00:29:28,370 +فبقول مثلا ال nickel solid زي اتنين HCl هي ال + +386 +00:29:28,370 --> 00:29:32,550 +nickel هياخد ال اتنين CL هياخد ال nickel CL2 يعني + +387 +00:29:32,550 --> 00:29:35,810 +ال nickel هنا صارت اتنين موجب لان ال CL2 سالب هذا + +388 +00:29:35,810 --> 00:29:43,090 +كان صفر اذا هذه oxidation وال اتنين H طبعا هذه + +389 +00:29:43,090 --> 00:29:47,930 +كانت موجب اتنين او موجب واحد ال H لحالها صارت صفر + +390 +00:29:47,930 --> 00:29:49,330 +يبقى هذه عبارة عن + +391 +00:29:57,460 --> 00:30:03,140 +تفاعل اكسدا او اختزال او تفاعل عادي + +392 +00:30:06,310 --> 00:30:12,730 +هذا HCl وهذا مجنيزيام بلاحظ ان الـ H Plus بتقترب + +393 +00:30:12,730 --> 00:30:17,210 +من المجنيزيام بتاخد منه إلكترونات الـ H Plus هي + +394 +00:30:17,210 --> 00:30:21,470 +الأبيض بتاخد إلكترونات و بتتحول لـ H2 هاتين تان من + +395 +00:30:21,470 --> 00:30:30,330 +هذه H2 وبالتالي النتيجة انه الـ H Plus صارت H2 gas + +396 +00:30:30,330 --> 00:30:34,410 +يعني ال oxidation number لها صفر والمجنيزيام اتحول + +397 +00:30:34,410 --> 00:30:38,990 +من مجنيزيام solidالى magnesium اتنين plus نفس + +398 +00:30:38,990 --> 00:30:42,270 +الكلام اللى كنا بنحكيه فهى ال magnesium صليت زائد + +399 +00:30:42,270 --> 00:30:46,710 +اتنين HCl بيعطينا magnesium Cl2 زائد H2 المجنيزيا + +400 +00:30:46,710 --> 00:30:52,010 +بتاخد الكلور magnesium موجة باتنين سالب اتنين كويس + +401 +00:30:52,010 --> 00:30:56,050 +فهن oxidation هى ها دى الأحمر هدى oxidation من صفر + +402 +00:30:56,050 --> 00:31:00,390 +لموجة باتنين بتطلع الأزراج من plus one ال H الى + +403 +00:31:00,390 --> 00:31:07,810 +صفر بعد كلام هدى عملية reductionكل الـ .. يعني كل + +404 +00:31:07,810 --> 00:31:10,270 +الـ metals اللي فوق الـ hydrogen بتتصرفوا بنفس + +405 +00:31:10,270 --> 00:31:15,730 +الصورة تماماًبيقول لي write the balanced molecular + +406 +00:31:15,730 --> 00:31:18,450 +and net ionic equations for the reaction of + +407 +00:31:18,450 --> 00:31:21,650 +aluminum with hydrobromic acid نفس الكلام بالظبط + +408 +00:31:21,650 --> 00:31:27,450 +aluminum زائد HBr بعرف انا انه بدى يطلع عندى H2 H2 + +409 +00:31:27,450 --> 00:31:32,370 +زائد AlBr3 لأنه هي تفاعل بسمي displacement او + +410 +00:31:32,370 --> 00:31:38,970 +replacement في عندى ال aluminum بيطرد ال H وبياخد + +411 +00:31:38,970 --> 00:31:44,280 +ال Brأو يعني بيحل محل الـH والـH بتحول لـH2 فهذه + +412 +00:31:44,280 --> 00:31:48,800 +موليكولار equation بدي أكتب الشكل على هيئة Ionic + +413 +00:31:48,800 --> 00:31:51,620 +equation Total Ionic equation بيقول Aluminum زي ما + +414 +00:31:51,620 --> 00:31:56,060 +هو solid هذا الـHPR قوي إذا 6H Plus 6PR سالب + +415 +00:31:56,060 --> 00:32:02,040 +الـAluminum PR3 Aluminum تلاتة Aqueous PR6 6PR + +416 +00:32:02,040 --> 00:32:06,880 +الـH2 بتفككش الـH2 بالظبط فبطلها هنبلجي أنه في + +417 +00:32:06,880 --> 00:32:12,710 +عندى 6PRستة PR فببقى اللي عندنا اتنين aluminum + +418 +00:32:12,710 --> 00:32:15,810 +زائد ستة H plus بيعطينا اتنين aluminum تلاتة زائد + +419 +00:32:15,810 --> 00:32:19,430 +تلاتة H2O هذه هي ال net ionic equation + +420 +00:32:22,180 --> 00:32:26,100 +طيب نيجي لأ ال oxidation هيك ال acids وقولنا انه + +421 +00:32:26,100 --> 00:32:29,040 +لو بيعطينا كل الأمثلة .. كل الأمثلة واردة مدان فوق + +422 +00:32:29,040 --> 00:32:32,300 +الهيدروجين بيتفاعل مع ال acid بنفس الطريقة طيب + +423 +00:32:32,300 --> 00:32:34,640 +نيجي نتطلع على ال oxidation of metals by salt + +424 +00:32:34,640 --> 00:32:38,620 +solutions فبقول مثلا مانجانيز هل بتفاعل مع ال lead + +425 +00:32:38,620 --> 00:32:40,360 +nitrate ولا لأ؟ برجع على السلسلة + +426 +00:32:43,890 --> 00:32:47,090 +لأ كان بدي اشترج على السلسلة بقوله سهولة انا عارف + +427 +00:32:47,090 --> 00:32:51,590 +ان ال led تحت كل العناصر ها قلتلكم في الآخر انه + +428 +00:32:51,590 --> 00:32:54,570 +ذكي لانه مهم اذا المنجانيز فوقه بالضرورة + +429 +00:32:54,570 --> 00:32:58,910 +فالمنجانيز بتفعل مع ال led 100% فمع ال led يعني + +430 +00:32:58,910 --> 00:33:04,480 +المنجانيز solid بتفعل مع ال led 2 plusبقول ان + +431 +00:33:04,480 --> 00:33:07,200 +المنجانيز اضافة ليد نيتريت هيتفاعلوا مع بعض + +432 +00:33:07,200 --> 00:33:09,980 +مانجانيز نيتريت اضافة ليد displacement reaction + +433 +00:33:09,980 --> 00:33:14,520 +عادي جدا لاحظوا انه هان المنجانيز كان صفر اتحول + +434 +00:33:14,520 --> 00:33:20,080 +الى منجانيز اتنين موجب وال ليد كان اتنين موجب + +435 +00:33:20,080 --> 00:33:27,240 +اتحول الىمعنى الكلام دائما الإلكترونات اللى طالعة + +436 +00:33:27,240 --> 00:33:34,440 +منها أو اللى بيفقدها ال reducing + +437 +00:33:34,440 --> 00:33:38,280 +agent بده يكتسبها ال oxidizing agent أو يعني + +438 +00:33:38,280 --> 00:33:41,620 +الإلكترونات المفقودة في الأكسد يجب أن يتم + +439 +00:33:41,620 --> 00:33:45,980 +استغلالها في تفاعل الاختزال فواحد منهم أكسد وانت + +440 +00:33:45,980 --> 00:33:50,000 +اختزال لازم الإلكترونات تكون صفرفي الـ net + +441 +00:33:50,000 --> 00:33:53,820 +equation أي إلكترونات على الطرفين لازم مايكونش + +442 +00:33:53,820 --> 00:34:01,480 +عندي أي إلكترون نفس الكلام لو حبنا ال iron و ال + +443 +00:34:01,480 --> 00:34:04,280 +nickel طبعا ماقدرش أعرف إذا كان ال iron هيتفاعل مع + +444 +00:34:04,280 --> 00:34:08,060 +ال nickel 2 plus ولا لأ هذا nickel 2 plus بتكون ال + +445 +00:34:08,060 --> 00:34:12,140 +nitrate إلا إذا كان روحت لل إيه أو إن حافظ ال + +446 +00:34:12,140 --> 00:34:16,480 +series فبقول والله هاي ال nickel هان وين ال iron + +447 +00:34:16,480 --> 00:34:20,760 +مش هان ال iron ال iron هاي و فوقالـ Iron هذا هي هي + +448 +00:34:20,760 --> 00:34:24,980 +الـ Iron Solid وهي ال Nickel اه اذا بيتم التفاعل + +449 +00:34:24,980 --> 00:34:30,320 +بدون ان بيتم التفاعل بجانب انا عارف او جدام ال ال + +450 +00:34:30,320 --> 00:34:33,660 +activity series بعرف ازا كان التفاعل هيتم ولا لأ + +451 +00:34:33,660 --> 00:34:40,220 +فالتفاعل .. و الله لأ انا بدي اكيد احفظ ايه بس انه + +452 +00:34:40,220 --> 00:34:42,660 +على رأس السلسلة ال alkali و ال alkaline earth + +453 +00:34:42,660 --> 00:34:48,500 +metals فبعدهم ال transition metals و اخرهم ال lead + +454 +00:34:50,510 --> 00:34:55,150 +الهيدروجين فاصل الـconige metals فإذا كان جاكي + +455 +00:34:55,150 --> 00:34:58,090 +واحد اذا كان جاكي metal انا بجيب الكيش انا اتنين + +456 +00:34:58,090 --> 00:35:02,140 +metals مش عارفة وين همإلا أجيبلك الـ schedule + +457 +00:35:02,140 --> 00:35:05,700 +للدوري فبتعرف ايه على طول يعني بتاخد الجدول لكن + +458 +00:35:05,700 --> 00:35:08,400 +للأسف حتى الجدول الدوري البريدراتي استخدمه لأن + +459 +00:35:08,400 --> 00:35:11,460 +فيها exceptions فانا بدي البلوكات هادمة السلكون + +460 +00:35:11,460 --> 00:35:14,800 +احنا عارفينها فانت لما اجيبلك اجيبلك مثلا metal من + +461 +00:35:14,800 --> 00:35:18,000 +المجموعة الأولى والتانية مع metal transition او + +462 +00:35:18,000 --> 00:35:21,640 +اجيبلك transition مع مثلا coinage metal معروف + +463 +00:35:21,640 --> 00:35:26,140 +هدوين و هدوينفما بغلب كيش اذا كان على فكرة السؤال + +464 +00:35:26,140 --> 00:35:29,300 +لكن انت في الحياة العملية لو بدك تعرف ايه بدك ترجع + +465 +00:35:29,300 --> 00:35:34,380 +لل activity series نفسها و تشوف هل بينفع او لأ هذا + +466 +00:35:34,380 --> 00:35:36,360 +اللي بدنا نتعلمه لكن بالنسبالي الامتحان مش فارق + +467 +00:35:36,360 --> 00:35:39,140 +انا بجيبلك بس البلوكات هذه اللي تكون عارفاها في + +468 +00:35:39,140 --> 00:35:44,320 +عندي الهيدروجين فوجو الالكالي متل في ال top و + +469 +00:35:44,320 --> 00:35:47,420 +بعدين ال transition elements و بعدين خلنا نقول بس + +470 +00:35:47,420 --> 00:35:50,170 +ال LEDفوق الهيدروجين وبعدين تحته اللي هي الـ + +471 +00:35:50,170 --> 00:35:53,990 +coinage metals على طول Copper Silver Platinum Gold + +472 +00:35:53,990 --> 00:35:57,850 +Copper Silver Platinum Gold فأي واحد فوق بتفعل مع + +473 +00:35:57,850 --> 00:36:02,470 +ال .. مع ال metal ion اللي تحته أي واحد فوق .. فوق + +474 +00:36:02,470 --> 00:36:06,110 +الهيدروجين يعني بتفعل مع ال acids بينما اللي تحت + +475 +00:36:06,110 --> 00:36:08,490 +الهيدروجين مابتفعلش مع ال acids اللي تحت + +476 +00:36:08,490 --> 00:36:11,610 +الهيدروجين بس ال coinage metals يعني زائد ال + +477 +00:36:11,610 --> 00:36:17,410 +mercury مش .. قضية نتذكر حتى ال mercury يعنيطيب + +478 +00:36:17,410 --> 00:36:20,430 +إذا التفاعل بيتنفع هاي ال iron زائد nickel nitrate + +479 +00:36:20,430 --> 00:36:23,730 +بيعطينا iron nitrate زائد nickel solid هاي ال iron + +480 +00:36:23,730 --> 00:36:28,010 +solid صفر اتحول ل iron اتنين هد عملية اكسدة زيادة + +481 +00:36:28,010 --> 00:36:30,190 +في ال oxidation number النكل اتنين اتحول ل nickel + +482 +00:36:30,190 --> 00:36:36,050 +solid هد عملية اختزال لأنه جل ال oxidation number + +483 +00:36:36,050 --> 00:36:38,350 +وهي ال net ionic equation + +484 +00:36:42,470 --> 00:36:46,150 +طيب بيقول لي write the balanced molecular and net + +485 +00:36:46,150 --> 00:36:49,770 +ionic equations for the reaction between magnesium + +486 +00:36:49,770 --> 00:36:54,490 +and cobalt هذي واضحة بدهاش المجنيزيوم وين؟ + +487 +00:36:54,490 --> 00:36:57,750 +المجنيزيوم في المجموعة التانية alkaline earth و ال + +488 +00:36:57,750 --> 00:37:01,650 +.. و النكق و ال cobalt هذ هال transition element + +489 +00:37:01,650 --> 00:37:04,570 +يعني أكيد تحته مش في المجموعة أولى و التانية فطبعا + +490 +00:37:04,570 --> 00:37:06,230 +اللي فوق مدام مش في المجموعة أولى و التانية بتفاعل + +491 +00:37:06,230 --> 00:37:09,070 +معاه المجموعة أولى و التانية بتفاعل معاه أكيد لأنه + +492 +00:37:09,070 --> 00:37:13,910 +تحتها هيكونفلأن هذا هو الـ salt فبقول أنا والله + +493 +00:37:13,910 --> 00:37:17,430 +المجنيزيام ال molecular equation مجنيزيام solid مع + +494 +00:37:17,430 --> 00:37:22,330 +الكوبلت صلفيت المجنيزيام بيحل محل الكوبلت فبياخد + +495 +00:37:22,330 --> 00:37:26,710 +الصلفيت مجنيزيام صلفيت أكيوست زائد كوبلت solid + +496 +00:37:26,710 --> 00:37:29,990 +الكوبلت كان اتنين صار صفر يبجي هذا reduction + +497 +00:37:29,990 --> 00:37:34,570 +المجنيزيام كان صفر صار اتنين يبجي هذا oxidation + +498 +00:37:37,380 --> 00:37:42,600 +فهي الـ Ionic equation لو حبنا بنخلي هذه ايونات + +499 +00:37:42,600 --> 00:37:45,920 +وهذه ايونات فبيطلع معنا في الآخر الصلفية ال + +500 +00:37:45,920 --> 00:37:49,200 +spectator ف ال net ionic equation magnesium solid + +501 +00:37:49,200 --> 00:37:53,400 +زائد كوبل اتنين plus بيعطينا magnesium اتنين plus + +502 +00:37:53,400 --> 00:37:55,640 +زائد كوبل solid + +503 +00:37:59,270 --> 00:38:03,490 +أكتب لكم حاليا أن الـ Magnesium is oxidized إذا هو + +504 +00:38:03,490 --> 00:38:06,410 +الـ reducing agent مدام هو oxidized إذا هو ال + +505 +00:38:06,410 --> 00:38:12,050 +reducing agent و أيضا ال cobalt is reduced إذا هو + +506 +00:38:12,050 --> 00:38:20,430 +ال oxidizing agent طيب هذا + +507 +00:38:20,430 --> 00:38:23,570 +السؤال بيقول will an aqueous solution of iron to + +508 +00:38:23,570 --> 00:38:27,790 +chloride oxidize magnesium metal هاي بقول + +509 +00:38:27,790 --> 00:38:28,770 +magnesium metal + +510 +00:38:32,030 --> 00:38:35,310 +ماجنيزيا باتنين بلس زائد اتنين إلكترون بكتبهم زي + +511 +00:38:35,310 --> 00:38:41,770 +هيك وهي ال iron ايش + +512 +00:38:41,770 --> 00:38:50,410 +يقولنا اكلورايت يعني iron Fe Fe اتنين plus يعني هو + +513 +00:38:50,410 --> 00:38:59,120 +بيقوللي ايشهل ال iron اه ال iron 2 plus موجود تحت + +514 +00:38:59,120 --> 00:39:02,180 +المجنيزيام بالضرورة لأن المجنيزيام الصليد وين + +515 +00:39:02,180 --> 00:39:05,780 +موجود في المجوعة تانية فوق في ال top فأي إشة هيكون + +516 +00:39:05,780 --> 00:39:09,980 +ايه تحته بالضرورة Transition فهذا اه هذا هيتفاعل + +517 +00:39:09,980 --> 00:39:13,540 +مع ال iron chloride بالضرورة فحقول والله مجنيزم + +518 +00:39:13,540 --> 00:39:16,420 +زاد iron chloride تعطيني مجنيزم chloride زاد iron + +519 +00:39:16,560 --> 00:39:22,320 +التفاعل يتم في الـ net ionic equation iron two + +520 +00:39:22,320 --> 00:39:26,420 +اتنين CL سالب ماجنيزيا اتنين plus اتنين CL سالب + +521 +00:39:26,420 --> 00:39:28,400 +فبروح الكلور مع الكلور + +522 +00:39:37,540 --> 00:39:45,700 +الأسئلة واضحة جدا اذا كان عندك احد ال metals من + +523 +00:39:45,700 --> 00:39:50,080 +المجموعة الأولى او التانية او اي اش تحته او احد ال + +524 +00:39:50,080 --> 00:39:55,340 +metals coinage + +525 +00:39:56,320 --> 00:40:00,120 +وفي متل اخر فوجه فبالضرورة تاني هيتفاعل معاه هدول + +526 +00:40:00,120 --> 00:40:03,080 +ماضحين كتير يعني مابدهمش لان اتطلع على activity + +527 +00:40:03,080 --> 00:40:08,000 +series او غيره وصيرنا عارفينه بالضرورة بيقول لي + +528 +00:40:08,000 --> 00:40:11,460 +which of the following metals will be oxidized by + +529 +00:40:11,460 --> 00:40:19,260 +lead nitrate يعني لو عندى zinc solid هل + +530 +00:40:19,260 --> 00:40:24,180 +هيتحول ل zinc 2 plus بإيه + +531 +00:40:24,180 --> 00:40:32,390 +بال leadsolid lead nitrate هل الذنك solid هيتفاعل + +532 +00:40:32,390 --> 00:40:36,970 +مع ال lead 2 plus اللي هو lead nitrate بقول أنا + +533 +00:40:36,970 --> 00:40:40,470 +بالضرورة لأن ال lead اذا كانت .. انت لاحظتي وين + +534 +00:40:40,470 --> 00:40:44,190 +انا قلتلك اتذكريه اخر واحد جابني ال coinage فاه + +535 +00:40:44,190 --> 00:40:50,290 +هيتفاعل معاه طيب اذا هيتفاعل مع ال lead هيتفاعل مع + +536 +00:40:50,290 --> 00:40:53,810 +ال lead nitrate يبقى ال zinc will be oxidized by + +537 +00:40:53,810 --> 00:40:58,170 +leadتو بلس الزنك سيكون اكسيدايت طب نطلع على الزنك + +538 +00:40:58,170 --> 00:41:11,810 +solid مع ال CU هي CU solid CU اتنين بلس CU ات اه + +539 +00:41:11,810 --> 00:41:17,430 +لأ انا بدي اللي ات خطط ماشي هي ال cover solid + +540 +00:41:18,280 --> 00:41:21,880 +بيعطينا cover اتنين plus زي اتنين electron وهي ال + +541 +00:41:21,880 --> 00:41:28,580 +led solid بيعطينا led اتنين plus هل ال cover .. اه + +542 +00:41:28,580 --> 00:41:32,840 +لأ هذا المفروض يكون فوق فهذا مش فوق فال cover + +543 +00:41:32,840 --> 00:41:36,400 +solid لأ لا يتفاعل اللي هيتفاعل هذا لأن هذا هو + +544 +00:41:36,400 --> 00:41:41,540 +اللي ايه بينفعش يعني ال cover solid لا يتفاعل مع + +545 +00:41:41,540 --> 00:41:48,770 +ال ledلأن هذا تحت ال cover لاتفاعل مع ال led 2 + +546 +00:41:48,770 --> 00:41:53,570 +plus طب نتطلع على ال iron كيانه نفس الطريقة نفس + +547 +00:41:53,570 --> 00:41:59,130 +الطريقة هاي عندي انا ال iron solid بيعطينا iron + +548 +00:41:59,130 --> 00:42:03,570 +مثلا two plus زائد اتنين electron وعندي ال led + +549 +00:42:03,570 --> 00:42:11,350 +solid بيعطينا led اتنين plus ال iron solid اه ال + +550 +00:42:11,350 --> 00:42:16,380 +iron هيتفاعل مع ال ledالايرون فوق الليد فهيتفاعل + +551 +00:42:16,380 --> 00:42:19,400 +مع الليد اذا ايرون والبيو اكسيدايز يبقى الاتنين + +552 +00:42:19,400 --> 00:42:22,920 +اللي هيكون هيحصلهم اكسيداشن هو الايرون والزنك + +553 +00:42:22,920 --> 00:42:27,980 +بينما الكبر لا لن يحدث له اي اكسيداشن فبتهيأليه + +554 +00:42:27,980 --> 00:42:34,500 +انه هيكي صارت الأمور عنه واضحة يبقى عندي بس الزنك + +555 +00:42:34,500 --> 00:42:42,660 +والايرون لأنهم الزنك والايرون لأن الليد تحتهمالـ + +556 +00:42:42,660 --> 00:42:50,400 +Cover لأ ما بيحصللوش .. بحصللوش اي Light Exed بالـ + +557 +00:42:50,400 --> 00:42:56,920 +LED Nitrate طيب الآن خلّينا ننتقل لموضوع كتير يعني + +558 +00:42:56,920 --> 00:43:02,180 +مهم برضه و كتير بتيجي منه أجزاء في الامتحان اللي + +559 +00:43:02,180 --> 00:43:05,480 +هو ال concentrations of solutions الآن خلصنا أنواع + +560 +00:43:05,480 --> 00:43:11,030 +التفاعلاتبيهمنيش التفاعل الـ Get-ish نوعه تحديدا، + +561 +00:43:11,030 --> 00:43:15,150 +بيهمني يعني أتعرف على بعض خصائصه، شفنا احنا في + +562 +00:43:15,150 --> 00:43:19,390 +التفاعلات الماضية، تفاعلات الـ precipitationوالـ + +563 +00:43:19,390 --> 00:43:23,550 +Acid Base وهي شفنا الـ Axa دا بالتفصيل وعرفنا مثلا + +564 +00:43:23,550 --> 00:43:27,290 +هل يجوز إلنا إنه من هذه التفاعلات هل يجوز إلنا إنه + +565 +00:43:27,290 --> 00:43:31,110 +مثلا لو عندنا مادة كيميائية نحفظها في وعى مصنوع من + +566 +00:43:31,110 --> 00:43:37,530 +مادة أو يحتوي على أنصر من العناصر يعني الأخرى ولا + +567 +00:43:37,530 --> 00:43:41,270 +لأ يعني نفكر في الموضوع فإذا كان والله فيه تفاعل + +568 +00:43:41,270 --> 00:43:45,270 +لأ مابينفعش لأنه هيدوب زي ما شفنا الـ Nickel + +569 +00:43:45,270 --> 00:43:48,790 +Nitrate أو الـ Nickel 2 Plusبيدوّب الـ Iron على + +570 +00:43:48,790 --> 00:43:52,150 +سبيل المثال فلازم يعني هالجت استوعبنا هذا الكلام + +571 +00:43:52,150 --> 00:43:56,270 +الآن بغض النظر عن نوع التفاعل بدي أطلع على التركيز + +572 +00:43:57,070 --> 00:44:01,050 +تركيزات، تركيزات المحاليل ومنها بدي أطلع على + +573 +00:44:01,050 --> 00:44:04,130 +الحسابات أول حاجة كيف أعرف التركيز، كيف أخفف + +574 +00:44:04,130 --> 00:44:08,390 +المحاليل و أعرف التركيز بعد التخفيف و أيضا لو عندي + +575 +00:44:08,390 --> 00:44:11,590 +تفاعل كيميائي كيف أقدر أعرف جداش من المادة إيه + +576 +00:44:11,590 --> 00:44:17,890 +بتفاعل مع جداش من المادة بيه سواء حجما أو moles أو + +577 +00:44:17,890 --> 00:44:24,220 +كتلةفاحنا بالنسبة لنا مهم جدا في الكيميا انه نعرف + +578 +00:44:24,220 --> 00:44:27,860 +جداش تركيز المحلول، ايش هو تركيز المحلول؟ يعني + +579 +00:44:27,860 --> 00:44:31,780 +جداش من الـsolute ذائب في حجم معين من المحلول، + +580 +00:44:31,780 --> 00:44:35,760 +جداش من الـsolute ذائب في حجم معين من المحلول، + +581 +00:44:35,760 --> 00:44:40,760 +وحدة التعبير عن التركيز بالنسبة لنا هي أهم وحدة هي + +582 +00:44:40,760 --> 00:44:44,800 +الـmolarityيعني من عدد إلى عدد التركيزات المحالية + +583 +00:44:44,800 --> 00:44:48,480 +بالـMolarity كل ما زادت المولارية للمحلول كل ما + +584 +00:44:48,480 --> 00:44:54,540 +كان المحلول مركّز اكتر كل ما كان المحلول مثلا عشرة + +585 +00:44:54,540 --> 00:44:58,680 +مولار مركز اكتر كتير من واحد مولار فكل ما زادت + +586 +00:44:58,680 --> 00:45:01,460 +المولارية كل ما زاد عندي التركيز طب إيش هي + +587 +00:45:01,460 --> 00:45:05,160 +المولارية ده مهمة جدا بالنسبة لنا جال الـMolarity + +588 +00:45:05,160 --> 00:45:10,310 +نرمزلها بالرمز M كبيرة capitalهي عبارة عن عدد + +589 +00:45:10,310 --> 00:45:16,350 +مولات الـ solute المذابة في لتر من المحلول، مش لتر + +590 +00:45:16,350 --> 00:45:20,270 +مية، لأ، لتر من المحلول، يعني الـ total volume بدي + +591 +00:45:20,270 --> 00:45:24,450 +يكون عندي لتر، ممكن المية تكون أقل، لكن الـ total + +592 +00:45:24,450 --> 00:45:28,890 +volume جديش لتر، فانا عندي أكمل من المادة ذائبة في + +593 +00:45:28,890 --> 00:45:33,430 +إيه؟في لتر واحد من المحلول هذه الـMolarity + +594 +00:45:33,430 --> 00:45:39,550 +المولاريتي عدد المولات في كل لتر او ال volume بال + +595 +00:45:39,550 --> 00:45:43,590 +لتر لو حبنا و لو كان عندنا ال volume بال ملي لتر + +596 +00:45:43,590 --> 00:45:46,950 +يعني حاجات قليلة بلاش نقول بتصير ملي مول على الملي + +597 +00:45:46,950 --> 00:45:51,070 +لتر شفنا هذا الكلام سابقا هنحاول بس انه نركز + +598 +00:45:51,070 --> 00:45:53,710 +المعلومات اللي أخدناها سابقا و إذا كان فهمناها + +599 +00:45:53,710 --> 00:45:58,900 +هنلاقي ان هذا كلام سهل للغاية نمشي فيه بسرعةفمثلا + +600 +00:45:58,900 --> 00:46:05,080 +لو بدى احضر ربع لتر من واحد مولار ساليوشن باخد وزن + +601 +00:46:05,080 --> 00:46:10,180 +معين و بحطها في ايه؟ في وعى وبعدين ببدأ احط عليها + +602 +00:46:10,180 --> 00:46:12,880 +ميه شوية شوية بحضر ربع لتر و باخد الوعى هذا عبارة + +603 +00:46:12,880 --> 00:46:18,410 +عن ربع لتر باسعةوبعد ما ادوب المادة في الميه شوية + +604 +00:46:18,410 --> 00:46:24,210 +شوية وبعد ما ادوب المادة بكمل لحجم + +605 +00:46:24,210 --> 00:46:27,650 +المناسب هات بيكون في عندى زى إشارة على انه لهان + +606 +00:46:27,650 --> 00:46:34,990 +الحجم ماشي لكن جديش اخد اه بدي اخد واحد مول في + +607 +00:46:34,990 --> 00:46:39,310 +اللتر يبقى في ربع لتر بدي اخد ربع مول فبشوف ال + +608 +00:46:39,310 --> 00:46:44,010 +formula weight للمادة تبعتيجدّاش باليجرامات بقسمها + +609 +00:46:44,010 --> 00:46:46,790 +على أربعة مثلا في هذه الحالة بعرف جدّاش الوزن اللي + +610 +00:46:46,790 --> 00:46:51,050 +لازم أخدها initially و أدوبها في ربع liter عشان + +611 +00:46:51,050 --> 00:46:56,450 +تعطيني واحد molar الآن تعالوا نتطلع على بعض + +612 +00:46:56,450 --> 00:46:59,390 +الأمثلة بيقول which is more concentrated هذا كلام + +613 +00:46:59,390 --> 00:47:02,990 +عام a solution prepared by dissolving واحد وعشرين + +614 +00:47:02,990 --> 00:47:06,270 +gram sodium fluoride الفورمولة التي تبعته اتنين + +615 +00:47:06,270 --> 00:47:12,160 +واربعيننص مول منه يعني اتنين واربعين لما تكون واحد + +616 +00:47:12,160 --> 00:47:15,880 +اجرام اجرام على الفورمولات هي عدد المولات شفناها + +617 +00:47:15,880 --> 00:47:18,720 +سابقا اجرام على الفورمولات يبقى واحد وعشرين على + +618 +00:47:18,720 --> 00:47:23,960 +اتنين واربعين ايش تعطيني نص مول هذا يعني مركز اكتر + +619 +00:47:23,960 --> 00:47:28,560 +ولا in enough water to make خمسميت مل of solution + +620 +00:47:28,560 --> 00:47:32,680 +او محلول تاني prepared by dissolving عشرة ونص جرام + +621 +00:47:32,680 --> 00:47:36,580 +يعني ربع مول of sodium fluoride in enough waterto + +622 +00:47:36,580 --> 00:47:40,780 +make meat meal of solution نحسب المولارية + +623 +00:47:40,780 --> 00:47:45,040 +المولارية للأول هي عبارة عن عدد المولات اللي هي نص + +624 +00:47:45,040 --> 00:47:49,960 +على الحجم باللتر نص خمسمية ميل يعني نص لتر اللتر + +625 +00:47:49,960 --> 00:47:53,620 +ألف ميل يا جماعة اللتر ألف ميل جال خمسمية ميل نص + +626 +00:47:53,620 --> 00:47:57,520 +لتر بيطلع اندي واحد مولار طب المحلول التاني جال + +627 +00:47:57,520 --> 00:48:01,740 +ربع لتر اللي هو ربع مول هيه على الحجم جداش ميت ميل + +628 +00:48:01,740 --> 00:48:06,460 +يعني عشرliter بيطلع التركيز 2.5 إذا المحلول التاني + +629 +00:48:06,460 --> 00:48:12,080 +أكثر تركيزا من المحلول الأولطيب Inter converting + +630 +00:48:12,080 --> 00:48:14,940 +molarity moles و volume لو بده اجيب ال molarity و + +631 +00:48:14,940 --> 00:48:18,360 +معيا ال volume و عدد المولات بقدر لو بده اجيب ال + +632 +00:48:18,360 --> 00:48:22,940 +volume و عندي ال molarity و المولات بقدر الاخره + +633 +00:48:22,940 --> 00:48:26,140 +فنتطلع على المثال التالي بيقول a solution of + +634 +00:48:26,140 --> 00:48:31,440 +nitric acid is 0.2 molar حلو find the number of + +635 +00:48:31,440 --> 00:48:35,530 +moles in 2 liters ناخد واحدة واحدةأنا عندى الـ + +636 +00:48:35,530 --> 00:48:37,910 +molarity بتساوى المول على ال volume باللتر + +637 +00:48:37,910 --> 00:48:41,490 +المولاريتي جالهينها اتنين من عشرة مولار هي اتنين + +638 +00:48:41,490 --> 00:48:44,930 +من عشرة مولار ال volume جاله اتنين لتر ايه كام مول + +639 +00:48:44,930 --> 00:48:49,690 +فيها بسيطة اه من المعادلة على طول طب نتطلع علبي + +640 +00:48:49,690 --> 00:48:53,750 +بيقول بيده volume of تلاتة من عشرة مولار نيتريك + +641 +00:48:53,750 --> 00:48:57,370 +أسد needed to supply اتنين moles HNO تلاتة بيقول + +642 +00:48:57,370 --> 00:49:02,880 +اذا كان ال moles اتنينو ال .. و ال molar .. و ال + +643 +00:49:02,880 --> 00:49:05,840 +molarity تلاتة من عشرة جداش ال volume جالس ستة و + +644 +00:49:05,840 --> 00:49:08,480 +سبعة من عشرة من المعادلة على طول ماجيكيش حاجة زي + +645 +00:49:08,480 --> 00:49:11,620 +هيك تافه يعني ماظنش ماجيكيش .. بس المهم انه + +646 +00:49:11,620 --> 00:49:17,060 +المعادلة بتحلل كل شيء دائما في الحسابات الكيميائية + +647 +00:49:17,060 --> 00:49:21,400 +بتطلع بس على حاجة واحدةبتطلع على الـ millimoles أو + +648 +00:49:21,400 --> 00:49:25,900 +المولز والمولز بتساوي أحد حاجتين يا إما gram على + +649 +00:49:25,900 --> 00:49:28,140 +ال formula weight يا إما molarity of volume بس + +650 +00:49:28,140 --> 00:49:32,560 +هدول الغرضين الصغار هم اللي بيحلوا أي مسألة حسابية + +651 +00:49:32,560 --> 00:49:37,020 +في الكيميا التحليلية اللي بتاخدوها انتوا ماشي يبقى + +652 +00:49:37,020 --> 00:49:40,420 +المول بده يساوي gram على ال formula weight او + +653 +00:49:40,420 --> 00:49:47,170 +molarity of volume انشوف بعض الأمثلةمثلا عشان أشوف + +654 +00:49:47,170 --> 00:49:50,470 +الأمثلة صح بدي أطلع بس على هذه النقطة مثلا لو أنا + +655 +00:49:50,470 --> 00:49:56,090 +فيه عندي واحد من واحد molar NaCl بقول إذا عندي + +656 +00:49:56,090 --> 00:50:01,370 +واحد molar Na Plus وواحد molar NaCl سالم عندي واحد + +657 +00:50:01,370 --> 00:50:11,510 +molar NaCl واحد molar NaCl يعني واحد molar Na Plus + +658 +00:50:11,510 --> 00:50:20,890 +وهو كمان واحد molarليه؟ لأن عدد ملات ال Sodium في + +659 +00:50:20,890 --> 00:50:23,710 +ال Sodium Chloride بساوي عدد ملات ال Sodium + +660 +00:50:23,710 --> 00:50:27,210 +Chloride عدد ملات ال Sodium في ال Sodium Chloride + +661 +00:50:27,210 --> 00:50:28,610 +بساوي عدد ملات ال Sodium Chloride، إذا تركيزه + +662 +00:50:28,610 --> 00:50:32,410 +بساوي تركيزه، لأن التركيز عادة ملات على الحجم، عدد + +663 +00:50:32,410 --> 00:50:36,890 +ملات الكلور بساوي عدد ملات ال Sodium Chloride، إذا + +664 +00:50:36,890 --> 00:50:39,210 +تركيز الكلور بساوي تركيز ال Sodium Chloride، + +665 +00:50:39,210 --> 00:50:42,490 +ببساطة، حلو كتير، لو جينا نطلع على ال Sodium + +666 +00:50:42,490 --> 00:50:48,470 +Sulphateعندي واحد molar صوديوم صلفيت باشي بقول + +667 +00:50:48,470 --> 00:50:55,510 +واحد molar صوديوم صلفيت بقول هذه بتحتوي على اتنين + +668 +00:50:55,510 --> 00:51:03,850 +molar صوديوم و واحد molar صلفيت ليش؟ ليش؟ تبهوا + +669 +00:51:03,850 --> 00:51:09,590 +شوية هيك تشوفوني بس خليني اقرأها بدي اقولكل مول من + +670 +00:51:09,590 --> 00:51:14,470 +الصوديوم صلفيت بيحتوي على اتنين مول من الصوديوم + +671 +00:51:14,470 --> 00:51:18,290 +يعني عدد مولات الصوديوم ضعف عدد مولات الصوديوم + +672 +00:51:18,290 --> 00:51:22,050 +صلفيت اذا تركيز الصوديوم ضعف تركيز الصوديوم صلفيت + +673 +00:51:22,050 --> 00:51:25,010 +عدد مولات الصوديوم ضعف تركيز عدد مولات الصوديوم + +674 +00:51:25,010 --> 00:51:28,870 +صلفيت اذا تركيز الصوديوم ضعف تركيز الصوديوم صلفيت + +675 +00:51:28,870 --> 00:51:33,490 +وعدد مولات الصلفيت يساوي عدد مولات الصوديوم صلفيت + +676 +00:51:33,490 --> 00:51:36,830 +اذا تركيز الصلفيت يساوي تركيز الصوديوم صلفيت واحد + +677 +00:51:36,830 --> 00:51:42,630 +مولةبدنا بس يعني نعرف هذه الفكرة علشان في كتير من + +678 +00:51:42,630 --> 00:51:48,270 +الأحيان الطلبة بيغلطوا فيها للأسف نطلع على مثال بس + +679 +00:51:48,270 --> 00:51:51,170 +تأكيد على هذا الكلام مش أكتر بيقول what's the + +680 +00:51:51,170 --> 00:51:55,030 +molar concentration of each ion present in؟ بده + +681 +00:51:55,030 --> 00:51:59,770 +تركيز كل أيون في point O25 molar aqua solution + +682 +00:51:59,770 --> 00:52:02,770 +calcium nitrate هاي ال calcium nitrate يا جماعة + +683 +00:52:07,430 --> 00:52:13,490 +قداش مثلا بدي تركيز الكالسيوم نفس .. اه عدد ملات + +684 +00:52:13,490 --> 00:52:16,770 +هيك بقول عدد ملات الكالسيوم يساوي عدد ملات + +685 +00:52:16,770 --> 00:52:19,790 +الكالسيوم نيتريت اذا تركيز الكالسيوم يساوي تركيز + +686 +00:52:19,790 --> 00:52:23,630 +الكالسيوم point oh two five طب عدد ملات النيتريت + +687 +00:52:23,630 --> 00:52:27,370 +ضعف عدد ملات الكالسيوم نيتريت اذا تركيز النيتريت + +688 +00:52:27,370 --> 00:52:30,890 +ضعف تركيز الكالسيوم نيتريت يعني point oh two five + +689 +00:52:30,890 --> 00:52:36,270 +في اتنين طويس point oh fiveماشي نفس الكلام هان + +690 +00:52:36,270 --> 00:52:40,270 +مثلا بيجي بيقول لي the molar concentration of + +691 +00:52:40,270 --> 00:52:44,970 +potassium in 0.015 molar of potassium carbonate + +692 +00:52:44,970 --> 00:52:48,570 +هاي ال potassium carbonate بيقوللي قداش تركيز ال + +693 +00:52:48,570 --> 00:52:52,790 +potassium بقول تركيز ال potassium ضعف تركيز ال + +694 +00:52:52,790 --> 00:52:56,010 +potassium carbonate لأن عدد ملات البوتاسيوم ضعف + +695 +00:52:56,010 --> 00:53:01,030 +عدد ملات البوتاسيوم carbonate وبالتالي 0.015 في 2 + +696 +00:53:04,530 --> 00:53:11,350 +الان خدوا بالكم الحسابات عندي نوعين اما انه انا + +697 +00:53:11,350 --> 00:53:14,990 +بتطلع على مادة واحدة وهذه بتيجي في حالتين بس يا + +698 +00:53:14,990 --> 00:53:20,370 +اما بده احضر مادة من ال solid يا اما بده احضر مادة + +699 +00:53:20,370 --> 00:53:25,210 +عن طريق التخفيف في الحالتين عندي مادة واحدة من ال + +700 +00:53:25,210 --> 00:53:30,010 +solid بده اخد وزن معينة واحطها في حجمبالتخفيف بدي + +701 +00:53:30,010 --> 00:53:35,750 +أخد كمية حجم معين من المركز و أزود الحجم يبقى كمية + +702 +00:53:35,750 --> 00:53:39,390 +المادة من المركز تساوي كمية المادة اللي حصلها + +703 +00:53:39,390 --> 00:53:43,370 +تخفيف فإن حاجة لواحدة واحدة بقول لما بدي أجي أحضر + +704 +00:53:43,370 --> 00:53:50,350 +مادة بقول ال mall of solidالمول من الصليد أو الملي + +705 +00:53:50,350 --> 00:53:51,330 +مول الملي مول الملي مول الملي مول الملي مول الملي + +706 +00:53:51,330 --> 00:53:52,970 +مول الملي مول الملي مول الملي مول الملي مول الملي + +707 +00:53:52,970 --> 00:53:57,270 +مول الملي مول الملي مول الملي مول الملي مول الملي + +708 +00:53:57,270 --> 00:53:57,710 +مول الملي مول الملي مول الملي مول الملي مول الملي + +709 +00:53:57,710 --> 00:53:57,930 +مول الملي مول الملي مول الملي مول الملي مول الملي + +710 +00:53:57,930 --> 00:53:58,370 +مول الملي مول الملي مول الملي مول الملي مول الملي + +711 +00:53:58,370 --> 00:53:58,990 +مول الملي مول الملي مول الملي مول الملي مول الملي + +712 +00:53:58,990 --> 00:54:06,420 +مول الملي مول الملي مول الملي مول المفي الميّه صح؟ + +713 +00:54:06,420 --> 00:54:10,040 +اذا هل تتوقعوا ان عدد المولات يتغير لو أخدت خمسة + +714 +00:54:10,040 --> 00:54:13,840 +ملي مول من مادة وحطيتهم في الميّه؟ بتغير؟ بتغيرش؟ + +715 +00:54:13,840 --> 00:54:16,420 +عشان هيك بقول لازم الملي مول من الـ solid يساوي + +716 +00:54:16,420 --> 00:54:19,140 +الملي مول اللي في المحلول ولا وين هي تروح المادة؟ + +717 +00:54:19,140 --> 00:54:22,900 +المادة لا تفنه ولا تستحدث وين هي تروح؟ مدام وزنت + +718 +00:54:22,900 --> 00:54:26,440 +كمية معينة من المادة اذا هذه الكمية لازم تكون في + +719 +00:54:26,440 --> 00:54:30,620 +المحلول هيك التحضير الان الفكرة ان اعوض عن الملي + +720 +00:54:30,620 --> 00:54:34,650 +مولالملي مول مدام solid بعوض عنه milligram على ال + +721 +00:54:34,650 --> 00:54:40,510 +formula weight طيب تساوي هاي اللي يساوي مدام في + +722 +00:54:40,510 --> 00:54:43,990 +المحلول qualitative volume هذه المثالة بتحيل كل + +723 +00:54:43,990 --> 00:54:48,940 +مسائل التحضير أو هذا الجزءهذا المعادلة بتحل كل + +724 +00:54:48,940 --> 00:54:52,900 +مسائل التحضير كمان مرة الفكرة أن الـ millimoles من + +725 +00:54:52,900 --> 00:54:57,420 +ال solid أنا أخدتهم وحطيتهم وين؟ في الميه إذا عدد + +726 +00:54:57,420 --> 00:55:00,540 +المولات من ال solid يساوي عدد المولات من ال solid + +727 +00:55:00,540 --> 00:55:03,720 +اللي وين؟ اللي في الميه عدد مولات ال solid بعوض + +728 +00:55:03,720 --> 00:55:06,220 +عنه milligram على ال formula weight وعدد مولات ال + +729 +00:55:06,220 --> 00:55:08,580 +solid اللي في الميه بعوض عنها molarity ب volume + +730 +00:55:08,580 --> 00:55:14,010 +هذا المثل بتحل يعني كل مسائل التحضيرنجي للحاجة + +731 +00:55:14,010 --> 00:55:19,130 +التانية عندها لما بدي أجي أخفف أنا مثلا أخدت خمسة + +732 +00:55:19,130 --> 00:55:23,970 +ملي مول من المركز وحطيتهم في liter أكم ملي مول ب + +733 +00:55:23,970 --> 00:55:28,590 +zero خمسة ملي مول طب لو حطيتهم في ميت liter خمسة + +734 +00:55:28,590 --> 00:55:31,630 +ملي مول طب لو حاطهم في الف liter خمسة .. أنا أخدت + +735 +00:55:31,630 --> 00:55:37,290 +خمسة ملي مول ونقلتهم على حجم أوسع والله الخمسة ملي + +736 +00:55:37,290 --> 00:55:39,990 +مول بيضالوا بخمسة ملي مول إذا الـ millimole + +737 +00:55:39,990 --> 00:55:44,780 +substanceاللي أخدتهم من الـ concentrated solution + +738 +00:55:44,780 --> 00:55:48,660 +تساوي دائما الـ minimal substance اللي صارت في ال + +739 +00:55:48,660 --> 00:55:52,300 +dilute solution أخدت خمسة و حطيتهم في خمسة و + +740 +00:55:52,300 --> 00:55:56,640 +نقلتهم على محلول آخر الخمسة ضالهم خمسة سواء كانوا + +741 +00:55:57,820 --> 00:56:00,800 +من ال concentrated solution او في ال dilute + +742 +00:56:00,800 --> 00:56:05,800 +solution مدام اخدت عدد معين من ال millimoles من ال + +743 +00:56:05,800 --> 00:56:08,700 +concentrated اذا ان هذا العدد هو نفسه اللي موجود + +744 +00:56:08,700 --> 00:56:11,720 +في ال dilute علشان هيك بما ان ال trend محليل + +745 +00:56:11,720 --> 00:56:14,920 +مانفعش اكل جرام على ال formula weight فmolarity of + +746 +00:56:14,920 --> 00:56:18,000 +volume تبعت ال concentrated solution وmolarity of + +747 +00:56:18,000 --> 00:56:21,480 +volume تبعت ال dilute solution وهذه بتحيل كل مسائل + +748 +00:56:21,480 --> 00:56:26,300 +التخفيفيبقى هذا أول نوع من أنواع المسائل، لاحظوا + +749 +00:56:26,300 --> 00:56:30,580 +أن هذا النوع يتعلق فقط بمادة واحدة، مافيش عندي + +750 +00:56:30,580 --> 00:56:33,080 +مادة، مافيش عندي تفاعل، مافي تفاعل، مافيش تفاعل، + +751 +00:56:33,080 --> 00:56:36,520 +مادة واحدة بدي أحضر إما محدود مخفف أو بدي أحضر + +752 +00:56:36,520 --> 00:56:40,160 +مادة من الصليد، تمام، يا تخفيف يا مادة من الصليد + +753 +00:56:40,160 --> 00:56:43,640 +على طول، فهذه مادة واحدة، ماحكيش عن التفاعل، + +754 +00:56:43,640 --> 00:56:47,630 +التفاعل هيجي هنا بعد شوية، فتعالوا ناخد أمثلةبيقول + +755 +00:56:47,630 --> 00:56:50,770 +calculate the molarity of a solution made by + +756 +00:56:50,770 --> 00:56:55,270 +dissolving 23.4 gram of sodium sulfate in enough + +757 +00:56:55,270 --> 00:57:00,220 +water to form 125 ml of solutionبقول حلو كتير هذا + +758 +00:57:00,220 --> 00:57:03,760 +عبارة عن تحضير مادة بقول والله ال millimoles من + +759 +00:57:03,760 --> 00:57:06,540 +المادة هذه اللي موجودة في ال solid تساوي ال + +760 +00:57:06,540 --> 00:57:09,700 +millimoles اللي موجودة وين؟ في المحلول فهذا هي + +761 +00:57:09,700 --> 00:57:12,800 +يبقى milligram solid على ال formula weight بتساوي + +762 +00:57:12,800 --> 00:57:15,560 +ال molarity في ال volume millimole من ال solid + +763 +00:57:15,560 --> 00:57:17,900 +اللي هي milligram على ال formula weight millimole + +764 +00:57:17,900 --> 00:57:21,160 +في المحلول اللي هي molarity في ال volume طب ال + +765 +00:57:21,160 --> 00:57:26,310 +solid 23.4 gram يعني في 10 أقصد 3 milligramأنا بدي + +766 +00:57:26,310 --> 00:57:30,850 +أشتغل كله بالملي على الفورمولا ويت لا ال sodium + +767 +00:57:30,850 --> 00:57:33,750 +sulfate اتنين في تلاتة و عشرين واحد في اتنين و + +768 +00:57:33,750 --> 00:57:37,510 +تلاتين اربع في ستاشر عمري اتنين و اربعين ناشي + +769 +00:57:37,510 --> 00:57:41,090 +تساوي ال molarity اللي هو بدوياها في مية و خمسة و + +770 +00:57:41,090 --> 00:57:44,890 +عشرين مل اذا كان انا قولت هنا ملي جرام على + +771 +00:57:44,890 --> 00:57:48,610 +الفورمولا ويت اذا ال volume بإيش بالمل بينما جرام + +772 +00:57:48,610 --> 00:57:54,160 +على الفورمولا ويت ال volume بالليترماشي مول او ملي + +773 +00:57:54,160 --> 00:57:58,100 +مول المول المولارتي في ال volume بال لتر الملي مول + +774 +00:57:58,100 --> 00:58:01,060 +المولارتي في ال volume بالملي لتر اللي بيطلع عندى + +775 +00:58:01,060 --> 00:58:05,140 +واحد و اتنين و تلاتين من مية مولار طب نطلع على + +776 +00:58:05,140 --> 00:58:09,120 +كمان مسألة مش أبسط من هيك بيقول calculate the + +777 +00:58:09,120 --> 00:58:14,400 +molarity of a solution made by dissolving خمسة + +778 +00:58:14,400 --> 00:58:21,720 +إجرامof glucose C6H12O6 in sufficient water to + +779 +00:58:21,720 --> 00:58:24,660 +form exactly 100 ml of solution انا بده احضر + +780 +00:58:24,660 --> 00:58:29,300 +glucose solution عندى وزنه و بدى حجم كويس بده احضر + +781 +00:58:29,300 --> 00:58:33,620 +حجم معين منها فبقول والله الملي مول من ال solid هو + +782 +00:58:33,620 --> 00:58:36,780 +نفس الملي مول اللى فى المحلول اذا ملي جرعة مع ال + +783 +00:58:36,780 --> 00:58:39,500 +formula weight من ال solid molarity فى ال volume + +784 +00:58:39,500 --> 00:58:43,250 +بالمل من المحلولخمس جرام في عشرة أُس تلاتة صارت + +785 +00:58:43,250 --> 00:58:46,250 +ملي جرام على الفورمولاوية مية و تمانين للجلوكوز + +786 +00:58:46,250 --> 00:58:49,810 +ساوى المولاريتى للمحلول اللى طالع عندى في ال + +787 +00:58:49,810 --> 00:58:52,850 +volume بالمل ميت ميل بطلع عندى point two seven + +788 +00:58:52,850 --> 00:59:01,350 +eight ماشي يا جماعة طيب نتطلع على مثلا + +789 +00:59:01,350 --> 00:59:04,630 +بتقولى how many grams of sodium sulfate بتدعرف + +790 +00:59:04,630 --> 00:59:08,950 +الآنأكمجرام من الـ Sodium Sulfate لازمني علشان + +791 +00:59:08,950 --> 00:59:13,250 +احضر 350 مل من 0.5 مولر Sodium Sulfate Solution + +792 +00:59:13,250 --> 00:59:17,430 +بقول نفس الكلام الوزن اللي انا بديها هي عبارة عن + +793 +00:59:17,430 --> 00:59:20,790 +الوزن اللي في المحلول يعني ال millimol اللي انا + +794 +00:59:20,790 --> 00:59:23,470 +بديها هي ال millimol اللي في المحلول نفس الشيء + +795 +00:59:23,470 --> 00:59:26,730 +فبقول millimol solid دائما هاي المادة الواحدة + +796 +00:59:26,730 --> 00:59:30,870 +solid بتساوي millimol in solution المليجرام Sodium + +797 +00:59:30,870 --> 00:59:33,890 +Sulfate انا بديها بتعرف كده وزدتها على ال formula + +798 +00:59:33,890 --> 00:59:37,610 +weightللسوديوم الصلفية نسبة مولاريتي المحلول في ال + +799 +00:59:37,610 --> 00:59:39,910 +volume بالمل المحلول يبقى الملي جرام السوديوم + +800 +00:59:39,910 --> 00:59:43,430 +الصلفية على 142 سبق و نص اللي هي المولاريتي في 350 + +801 +00:59:43,430 --> 00:59:50,270 +مل بيطلع 24850 ملي جرام او 24810 اجرام يبقى عرفة + +802 +00:59:50,270 --> 00:59:53,130 +وزن السوديوم الصلفية مباشرة + +803 +00:59:56,520 --> 00:59:59,920 +How many grams of sodium sulphate are there in 15 + +804 +00:59:59,920 --> 01:00:04,240 +ml of 0.5 molar sodium sulphate؟ أنا عندي 15 مل من + +805 +01:00:04,240 --> 01:00:10,400 +0.5 مولر صليفات صليفة، أكم جرام فيهم؟نفس المنطق + +806 +01:00:10,400 --> 01:00:14,560 +بالظبط نفس المنطق بقول والله ملي جرام صوديوم صلفية + +807 +01:00:14,560 --> 01:00:17,060 +على ال formula weight صوديوم صلفية modality لل + +808 +01:00:17,060 --> 01:00:19,920 +solution في ال volume بالمل أكام ملي جرام صوديوم + +809 +01:00:19,920 --> 01:00:21,860 +صلفية على مية و اتنين و اربعين ال formula weight + +810 +01:00:21,860 --> 01:00:26,880 +ساوين نص في خمستاشر مل بيطلع عندى واحد واحد من عشر + +811 +01:00:26,880 --> 01:00:31,390 +اجرامب بيقول لي how many milliliters of 0.5 molar + +812 +01:00:31,390 --> 01:00:36,130 +sodium sulfate are needed to provide 0.038 mol أنا + +813 +01:00:36,130 --> 01:00:40,630 +بدي 0.038 mol من السودان السلفية طيب أكام مليليتر + +814 +01:00:40,630 --> 01:00:45,260 +بدي أخد منها؟أه بقول والله الـMolarity ملي مول على + +815 +01:00:45,260 --> 01:00:49,140 +الملي ليتر المولاريتي أه بدهاشي مافيش أي إيش solid + +816 +01:00:49,140 --> 01:00:52,240 +ماجبليش سيرة ال solid ولا جرامات ولا غيره أه + +817 +01:00:52,240 --> 01:00:56,960 +المولاريتي ملي مول على الملي ليتر فالمولاريتي نص + +818 +01:00:56,960 --> 01:01:02,200 +الملي مول أه الملي مول هي تمانية و تلاتين من الف + +819 +01:01:02,200 --> 01:01:05,400 +مول تمانية و تلاتين من الف في الف صارت تمانية و + +820 +01:01:05,400 --> 01:01:08,660 +تلاتين ملي مول ملي مول على الملي ليتر اللي بدي + +821 +01:01:08,660 --> 01:01:13,750 +أحسبه بطلع عند الستة و السبعينالان بعض مسائل ال + +822 +01:01:13,750 --> 01:01:18,850 +dilution وزي ما حكيت هذا النوع من المسائل سهل جدا + +823 +01:01:21,440 --> 01:01:24,920 +بدأ أقول ملي مول من المحلول المركز يساوي الملي مول + +824 +01:01:24,920 --> 01:01:28,920 +من المحلول في المحلول المخفف الملي مول اللي باخده + +825 +01:01:28,920 --> 01:01:31,900 +من المحلول المركز يساوي الملي مول اللي موجود في + +826 +01:01:31,900 --> 01:01:36,260 +المحلول المخفف مهما كان التخفيف يعني جداش هو جداش + +827 +01:01:36,260 --> 01:01:45,740 +الحجر مش فارقة معايا فخلينا نطلع على المسألة + +828 +01:01:45,740 --> 01:01:51,110 +التاليةبتقول let's see how we can prepare a dilute + +829 +01:01:51,110 --> 01:01:56,530 +solution from a concentrated one السؤال suppose we + +830 +01:01:56,530 --> 01:02:02,890 +want to prepare 250ml that is يعني بيقولنا ربع لتر + +831 +01:02:02,890 --> 01:02:07,670 +250ml ربع لتر 250 على الف يعني of 0.1 molar + +832 +01:02:07,670 --> 01:02:09,890 +capersulfate solution هاي اللي بده احضره by + +833 +01:02:09,890 --> 01:02:14,010 +diluting واحد molar capersulfate يعني عندي واحد + +834 +01:02:14,010 --> 01:02:21,250 +molar capersulfateبدي احضر منه 250 مل point one + +835 +01:02:21,250 --> 01:02:25,170 +molar تركيز اقل بقول والله ال millimolar روح اخده + +836 +01:02:25,170 --> 01:02:28,270 +من المركز اللي هو ال modularity في ال volume بده + +837 +01:02:28,270 --> 01:02:31,210 +يساوي ال modularity في ال volume من المحلول المخفف + +838 +01:02:31,210 --> 01:02:34,530 +فعلى طول بقول والله ال modularity ال millimolar + +839 +01:02:34,530 --> 01:02:37,210 +substance من ال concentrated solution ساوي ال + +840 +01:02:37,210 --> 01:02:39,570 +millimolar substance اللي موجودة في ال dilute + +841 +01:02:39,570 --> 01:02:42,150 +solution فهن يعني ان ال modularity في ال volume + +842 +01:02:42,150 --> 01:02:44,570 +بالمل من ال concentrated solution ساوي ال + +843 +01:02:44,570 --> 01:02:46,960 +modularity في ال volume من ال dilute solutionالـ + +844 +01:02:46,960 --> 01:02:51,080 +Concentrated solution تركيزه واحد ال volume كم اخد + +845 +01:02:51,080 --> 01:02:56,420 +منه؟ مش عارف بتساوي المولارات اللي انا بدي احضرها + +846 +01:02:56,420 --> 01:03:00,100 +واحد من عشرة كم الحجم اللي بدي احضره 250 مل بيطلع + +847 +01:03:00,100 --> 01:03:05,140 +عندى 25 مل لهذا السبب باخد 25 مل من هذا المحلول و + +848 +01:03:05,140 --> 01:03:09,260 +بانجلهم على وعى بساعة 250 مل و بعدين بكمل بالميه + +849 +01:03:09,260 --> 01:03:16,420 +بيصير عندى محلول واحد من عشرة مولار 250 ملكمان + +850 +01:03:16,420 --> 01:03:19,220 +مثلا نفس المطبخ بيقول how many milliliters of 3 + +851 +01:03:19,220 --> 01:03:23,800 +molar H2SO4 are needed to make 450 ml of 0.1 molar + +852 +01:03:23,800 --> 01:03:29,080 +H2SO4 انا عندي محلول مركز 3 molar لكن بده احضر منه + +853 +01:03:29,080 --> 01:03:35,140 +450 ml واحد من 10 molar فجداش بتاخد من ال 3 molar؟ + +854 +01:03:35,180 --> 01:03:38,540 +عشان أخففهم لـ450 مل فبقول نفس المنطقي الـ + +855 +01:03:38,540 --> 01:03:41,340 +millimole substance من الـ concentrated solution + +856 +01:03:41,340 --> 01:03:44,720 +بتساوي ال millimole substance اللي موجودة في ال + +857 +01:03:44,720 --> 01:03:46,980 +dilute solution اللي بتكون موجودة في ال dilute + +858 +01:03:46,980 --> 01:03:49,520 +solution moderate volume ساوي moderate volume يعني + +859 +01:03:49,520 --> 01:03:53,120 +تلاتة في ال volume بالمل اللي بدي أخده بتساوي 1 من + +860 +01:03:53,120 --> 01:03:58,490 +10 في 450 أو لازم أخد 15 مل منالـ Concentrated + +861 +01:03:58,490 --> 01:04:04,990 +H2SO4 وأحط عليهم 435 مل من المي عشان أحصل على 450 + +862 +01:04:04,990 --> 01:04:11,850 +مل من الـ H2SO4 اللي تركيزه واحد من عشرة مولدأطلع + +863 +01:04:11,850 --> 01:04:15,170 +أيضًا على بعض الأمثلة الخفيفة بيقول لي what volume + +864 +01:04:15,170 --> 01:04:19,130 +of 2.5 molar lead nitrate solution contains 0.05 + +865 +01:04:19,130 --> 01:04:24,130 +molar 0.05 mole of lead مالوش دعوة بحاجة مجرد أنه + +866 +01:04:24,130 --> 01:04:26,950 +عندي أنا المولارات بتساوي milli mole على ال volume + +867 +01:04:26,950 --> 01:04:35,250 +بالمل المولارات 2.5 بده هو 0.05ish mole يعني اذا + +868 +01:04:35,250 --> 01:04:40,270 +كنت بتعود milli mole 0.05 في ألف يعني خمسينخمسين + +869 +01:04:40,270 --> 01:04:42,590 +ميلي مول على ال volume بالميلي volume من العشرين + +870 +01:04:42,590 --> 01:04:49,410 +ميل يبقى في عند عشرين ميل من two point five molar + +871 +01:04:49,410 --> 01:04:54,050 +lead بتحتوي على point oh five مول من ال lead كمان + +872 +01:04:54,050 --> 01:04:58,700 +how many milliliters of five molar K2Dichromate + +873 +01:04:58,700 --> 01:05:01,940 +بوتاسيوم Dichromate solution must be diluted to + +874 +01:05:01,940 --> 01:05:05,440 +prepare 250ml of 0.1 molar solution هذا نفس السؤال + +875 +01:05:05,440 --> 01:05:10,000 +السابق نفس السؤال السابق عندي هذا محلول مركز بدي + +876 +01:05:10,000 --> 01:05:14,520 +أحضر منه محلول مخفف له حجم و تركيز فبقول والله + +877 +01:05:14,520 --> 01:05:18,120 +volume مولارتي في volume بالمل المركز مولارتي في + +878 +01:05:18,120 --> 01:05:20,640 +volume بالمل المخفف معناه كلها قاسة في ال volume + +879 +01:05:20,640 --> 01:05:24,940 +بالمل اللي بدي أخده 0.1 في 200و50 بيطلع ال volume + +880 +01:05:24,940 --> 01:05:30,020 +من المل خمسة إذا بتاخد الخمسة هذه و أخففها ل250 مل + +881 +01:05:30,020 --> 01:05:34,120 +بحصل على المحلول اللي بدي يعني أخيرا if 10 mil of + +882 +01:05:34,120 --> 01:05:37,980 +point of a 10 molar stock solution of sodium + +883 +01:05:37,980 --> 01:05:41,760 +hydroxide is diluted to 250 mil what is the + +884 +01:05:41,760 --> 01:05:45,820 +concentration of the resulting stockساليوشن ايش + +885 +01:05:45,820 --> 01:05:50,940 +تركيز المحلول اللي بقى اللي بقى ال ال ال ناتج يعنى + +886 +01:05:50,940 --> 01:05:57,700 +فانا اخدت عشرة ميل من عشرة مولار Sodium Hydroxide + +887 +01:05:57,700 --> 01:06:02,420 +وخففتهم خلت التركيز النهائي الحجم النهائي متان + +888 +01:06:02,420 --> 01:06:06,580 +وخمسين ميل طب جداش التركيز النهائي؟نفس الكلام + +889 +01:06:06,580 --> 01:06:10,060 +مولاريتي في volume المركز مولاريتي في volume + +890 +01:06:10,060 --> 01:06:14,000 +المخفف بيطلع تركيز المحلول النهائي 4 من 10 بدأ + +891 +01:06:14,000 --> 01:06:17,220 +المكان 10 مولار صار بس 4 من 10 + +892 +01:06:20,320 --> 01:06:23,760 +الان واضحة بالنسبة لنا، لو كان عندي مثالة واحدة + +893 +01:06:23,760 --> 01:06:28,380 +سهلة جدا، يا اما بدي استخدم من الإجراء مع + +894 +01:06:28,380 --> 01:06:30,860 +الـformulates بتساوي mulative volume، يا اما + +895 +01:06:30,860 --> 01:06:33,920 +mulative volume بتساوي mulative volume، طيب الآن + +896 +01:06:33,920 --> 01:06:38,320 +إيش بيحصل لو كان في عندنا chemical reaction؟ لو + +897 +01:06:38,320 --> 01:06:41,600 +كان في عندي مادتين بتتفاعلوا مع بعض، و بدي أحسب + +898 +01:06:41,600 --> 01:06:46,380 +كمية المادة اللي بتتفاعل مع كمية أخرى من المادة + +899 +01:06:46,380 --> 01:06:51,460 +التانيةكيف بدي أعمل؟ بقول في هذه الحالة نتبع + +900 +01:06:51,460 --> 01:06:57,380 +الخطوات التالية أول شغلة بعملها لازم أكتب المعادلة + +901 +01:06:57,380 --> 01:07:01,000 +الموزونة من غير ما نكتب المعادلة الموزونة لأي + +902 +01:07:01,000 --> 01:07:04,420 +تفاعل مافيش حسابات كيميائية من غير ما نكتب + +903 +01:07:04,420 --> 01:07:07,480 +المعادلة الموزونة مافيش عند حسابات كيميائية لازم + +904 +01:07:07,480 --> 01:07:10,780 +المعادلة تكون موزونة لأن أنا بدي أستخدم ال + +905 +01:07:10,780 --> 01:07:13,940 +coefficients أو عدد الملايات في الحسابات فلازم + +906 +01:07:13,940 --> 01:07:20,310 +تكون المعادلة موزونة هذه أول خطوةعشان هيك بدي أجيب + +907 +01:07:20,310 --> 01:07:26,010 +الـ milli mole من المادة A لو كان A N من المادة A + +908 +01:07:26,010 --> 01:07:32,850 +تتفاعل مع M من المادة B تعطيلنا نواتج product فبدي + +909 +01:07:32,850 --> 01:07:40,300 +أجيب عدد مولات Aكويس وعدد مولات بي او ال + +910 +01:07:40,300 --> 01:07:42,900 +millimoles هذي سهلة يا milligram على الفورمولوات + +911 +01:07:42,900 --> 01:07:44,940 +يا molarity of volume يا milligram على الفورمولات + +912 +01:07:44,940 --> 01:07:49,880 +.. لكن عشانه تفاعل في a و b في n و m يعني او x و y + +913 +01:07:49,880 --> 01:07:56,140 +لازم اعرف عدد المولات بشكل صحيح فبتعرف x و y او + +914 +01:07:56,140 --> 01:08:00,240 +خليني اقول هذي x و y عشان كتبها هذي x و y بتعرف + +915 +01:08:00,240 --> 01:08:05,960 +جديش x و yبتعرف جداش X و Y هفرجيكم كيف تعملوا هذا + +916 +01:08:05,960 --> 01:08:10,860 +الكلام يبقى حددت هذه المعادلة هذه عبارة عن حل + +917 +01:08:10,860 --> 01:08:14,760 +المسألة بعد هيك مجرد تعويض بعد هيك مجرد تعويض + +918 +01:08:14,760 --> 01:08:20,800 +فبنجيب قيمة X و Y من المعادلة وبعدين مجرد تعويض يا + +919 +01:08:20,800 --> 01:08:24,390 +بتعويض عن ال millimole بmilligram على الفورولويتيا + +920 +01:08:24,390 --> 01:08:28,930 +مجرد بس هيك خلاص نفس الكلام يبقى ايش افرج هذا عن + +921 +01:08:28,930 --> 01:08:36,030 +الكلام السابق بس شغلة انه والله جديش X وY جديش عدد + +922 +01:08:36,030 --> 01:08:41,790 +المولات للمتفاعلات اللي عندى النسبة المولية بينهم + +923 +01:08:41,790 --> 01:08:46,570 +فتعالوا نطلع كيف بدنا نطبق هذا الكلام على بعض + +924 +01:08:46,570 --> 01:08:53,330 +الأمثلة اللي عندى بقولنظر إلى المثال، كم جرام من + +925 +01:08:53,330 --> 01:08:58,370 +الكالسوم الهيدروكسيد محتاج لإنهاء 25 مل من 0.1 + +926 +01:08:58,370 --> 01:09:02,590 +مولار HNO3؟ هذه المعادلة كالسوم هيدروكسيد زي 2 + +927 +01:09:02,590 --> 01:09:07,270 +HNO3 يعطينا كالسوم 3 زي 2 HO، هذه المعادلة موزونة، + +928 +01:09:07,270 --> 01:09:12,220 +الآن بقول ملي مول من الكالسوم الهيدروكسيدملي مول + +929 +01:09:12,220 --> 01:09:16,880 +من الـ HNO3 الفعل معاه ناحية تانية عدد الملي مول + +930 +01:09:16,880 --> 01:09:19,560 +من الكالسيوم الهيدروكسيد أكمل جداش عدد مولات + +931 +01:09:19,560 --> 01:09:23,580 +الكالسيوم الهيدروكسيد واحد جداش عدد مولات الـ HNO3 + +932 +01:09:23,580 --> 01:09:28,660 +اتنين اذا عدد مولات الكالسيوم الهيدروكسيد نص معاه + +933 +01:09:28,660 --> 01:09:33,730 +يا فنات اذا ال X ع ال Y نصنص طب الآن إيش بده؟ جال + +934 +01:09:33,730 --> 01:09:36,970 +والله بده جداش وزّت ال calcium hydroxide لأن أنا + +935 +01:09:36,970 --> 01:09:40,030 +لازم أعوض عن ال millimole مافيش فايدة أوصلت لهذه + +936 +01:09:40,030 --> 01:09:42,030 +المعادلة بده أعوض عن ال millimole calcium + +937 +01:09:42,030 --> 01:09:45,590 +hydroxide و millimole HNO3 إما milligram على ال + +938 +01:09:45,590 --> 01:09:48,330 +formula أو molarity of volume ال calcium hydroxide + +939 +01:09:48,330 --> 01:09:52,910 +مش معطيني molarity of volume أو طالب milligram إذا + +940 +01:09:52,910 --> 01:09:55,710 +ال milligram على ال formula همعطيني molarity of + +941 +01:09:55,710 --> 01:10:00,280 +volumeباقي نمولاريتيه و volume فمع ده الكلام + +942 +01:10:00,280 --> 01:10:03,440 +milligram calcium hydroxide على ال formula weight + +943 +01:10:03,440 --> 01:10:08,560 +74 و 1 من عشرة بتسوى النص زي ما هي point one في + +944 +01:10:08,560 --> 01:10:11,280 +خمس و عشرين بيطلع ان ال milligram calcium + +945 +01:10:11,280 --> 01:10:18,400 +carbonate اتنين وتسعين نقص ستة من عشرةكمان مثلا + +946 +01:10:18,400 --> 01:10:23,160 +بيقول لي how many grams of sodium hydroxide are + +947 +01:10:23,160 --> 01:10:28,220 +needed to neutralize 20 ml of 0.15 molar H2SO4 + +948 +01:10:28,220 --> 01:10:34,460 +بقول المعادلة اتنين Sodium hydroxide H2SO4 عدد + +949 +01:10:34,460 --> 01:10:38,700 +ملاتظ Sodium hydroxide اتنين عدد ملاتظ H2SO4 واحد + +950 +01:10:38,700 --> 01:10:44,020 +اذا ملي مول Sodium hydroxide اتنين ضعف عدد اتنين + +951 +01:10:44,020 --> 01:10:49,680 +على واحد ملي مول H2SO4ماشي يا جماعة، معنى الكلام + +952 +01:10:49,680 --> 01:10:51,900 +الـ milligram sodium hydroxide على ال formula ويه + +953 +01:10:51,900 --> 01:10:55,760 +ال Sodium hydroxide اتنين هيها في ال moderate ل ال + +954 +01:10:55,760 --> 01:10:59,540 +H2SO4 في ال volume بالملل ل ال H2SO4، بنعوض تعويض + +955 +01:10:59,540 --> 01:11:02,640 +بيطلع على ال milligram 240 milligram Sodium + +956 +01:11:02,640 --> 01:11:09,980 +hydroxide، كمان مسألةبتقول how many liters of 0.5 + +957 +01:11:09,980 --> 01:11:14,080 +molar HCl are needed to react completely with 0.1 + +958 +01:11:14,080 --> 01:11:17,700 +mol of lead nitrate forming a precipitate of lead + +959 +01:11:17,700 --> 01:11:21,180 +chloride تتذكروا الأكلورايد كلها soluble إلا مع + +960 +01:11:21,180 --> 01:11:26,340 +السلفر والمركوراس والليد فهذا ليد مش soluble فبقول + +961 +01:11:26,340 --> 01:11:31,560 +اتنين HCl زائد واحد lead nitrate يعطينا lead + +962 +01:11:31,560 --> 01:11:38,300 +chloride إلى آخرها إذا ال mol HClدعف اتنين مول لد + +963 +01:11:38,300 --> 01:11:41,240 +طب ايش ال مول HCL المولارتي في ال volume بال + +964 +01:11:41,240 --> 01:11:43,180 +letter انا كتبت مول مش ملي مول اذا كانوا ملاحظين + +965 +01:11:43,180 --> 01:11:48,640 +عشان هو ميعطيني قيم كلها جرامات و letter فمولارتي + +966 +01:11:48,640 --> 01:11:52,100 +لل HCL هو مافيش عنده ملي جرامات او جراماتلأن هان + +967 +01:11:52,100 --> 01:11:57,800 +طالب هو volume بال letter وهي المعطيني moles + +968 +01:11:57,800 --> 01:12:03,680 +مباشرة ف 0.5 في ال volume بال letter بتسوا 2 في 1 + +969 +01:12:03,680 --> 01:12:08,980 +من 10 بيطلع عند ال volume بال letter 4 من 10كمان + +970 +01:12:08,980 --> 01:12:12,260 +مثال بيقول what's the molarity of a sodium + +971 +01:12:12,260 --> 01:12:18,060 +hydroxide solution if 48 ml neutralizes 35 ml of 0 + +972 +01:12:18,060 --> 01:12:23,040 +.144 molar H2SO4 لاحظوا برضه مش معطيني او مش طالبي + +973 +01:12:23,040 --> 01:12:27,800 +ملي جرامات بس معطيني volume و molarity و طالب ال + +974 +01:12:27,800 --> 01:12:30,960 +molarity فبقول والله ال sodium hydroxide اتنين ال + +975 +01:12:30,960 --> 01:12:33,840 +H2SO4 واحد اذا عدد ملي ملي مليات ال sodium + +976 +01:12:33,840 --> 01:12:38,280 +hydroxide ضعف عدد ملي مليات ال H2SO4مع هذا الكلام + +977 +01:12:38,280 --> 01:12:41,180 +المولاريتي للصودم هيدروكسيد في ال volume بالملل + +978 +01:12:41,180 --> 01:12:45,360 +للصودم هيدروكسيد اتنين ضعيف المولاريتي لل H2SO4 في + +979 +01:12:45,360 --> 01:12:49,080 +ال volume بالملل للH2SO4 تعويض يظهر ان المولاريتي + +980 +01:12:49,080 --> 01:12:56,370 +0.21 اخر مثال معانابقول how many grams of the + +981 +01:12:56,370 --> 01:13:04,270 +chloride ion in a water sample if عشرين + +982 +01:13:04,270 --> 01:13:07,270 +واتنين مل of point one molar silver is needed to + +983 +01:13:07,270 --> 01:13:11,180 +react with all the chloride in the sampleبقول + +984 +01:13:11,180 --> 01:13:14,620 +والله ال ag plus تتفاعل مع ال chloride تعطينا agCl + +985 +01:13:14,620 --> 01:13:18,800 +كل أملاح ال chloride دائمة مع ده أملاح ال chloride + +986 +01:13:18,800 --> 01:13:24,280 +مع ال ag و ال .. و ال .. و ال .. و ال .. و ال lead + +987 +01:13:24,280 --> 01:13:29,220 +و ال mercurous كويس؟ و ال mercurous فعندي هنا أنا + +988 +01:13:29,220 --> 01:13:33,480 +millimole of Cl سالب متساول millimole silver لأنه + +989 +01:13:33,480 --> 01:13:36,100 +واحد لواحد طب إيش ال millimole الجال milligram + +990 +01:13:36,100 --> 01:13:38,380 +chloride على ال atomic weight لل chloride + +991 +01:13:39,210 --> 01:13:41,730 +الـMolarity للسلفر في الـ Volume للسلفر، على طول + +992 +01:13:41,730 --> 01:13:44,310 +بجيب الـ Milligram للكلورايد، بقول لي طب إذا كان + +993 +01:13:44,310 --> 01:13:50,110 +العينة وزنها 10 جرام، قداش ال percentage كلورايد؟ + +994 +01:13:50,110 --> 01:13:54,210 +آه والله جرامات الكلورايد اللي هي 0.072 gram على + +995 +01:13:54,210 --> 01:13:59,480 +وزن العينة في 100 من 100 بطلع عندي 0.72ضايل علينا + +996 +01:13:59,480 --> 01:14:04,600 +يعني مثلين تلاتة في ال chapter هذا كان بودي ان + +997 +01:14:04,600 --> 01:14:07,640 +اخلصهم لكن للأسف يعني اللي وجه اتخلص وماخلصتهمش + +998 +01:14:07,640 --> 01:14:11,400 +فالحصة اللي جاية بشكل أساسي يعني هتكون + +999 +01:14:11,400 --> 01:14:15,440 +thermochemistry يعني + +1000 +01:14:15,440 --> 01:14:18,020 +اذا كان اللي جت مناسب اكملكم الأمثلة بكملهم مش + +1001 +01:14:18,020 --> 01:14:21,000 +مناسب بعتبر انه انتوا يعني لازم تكونوا عارفينهم + +1002 +01:14:21,000 --> 01:14:23,980 +لأنهم نفس النظام اللي ذكرناه في الشيء هم معلومات + +1003 +01:14:23,980 --> 01:14:26,820 +جديدة فإذا الله راض بنشوفكم الحصة اللي جاية + diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/wLZu0_CAZmI.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/wLZu0_CAZmI.srt new file mode 100644 index 0000000000000000000000000000000000000000..62464b68c6a4091a3a3ad51e7ae0ab1a36210133 --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/wLZu0_CAZmI.srt @@ -0,0 +1,3967 @@ +1 +00:00:21,920 --> 00:00:25,160 +بسم الله الرحمن الرحيم، إذا الله راضي، اليوم نبدأ في + +2 +00:00:25,160 --> 00:00:28,660 +chapter جديد نتكلم فيه عن الـthermochemistry أو + +3 +00:00:28,660 --> 00:00:33,880 +الكيمياء الحرارية، المقصود بالكيمياء الحرارية يعني + +4 +00:00:33,880 --> 00:00:38,440 +هي التفاعلات الكيميائية أو حتى الفيزيائية اللي + +5 +00:00:38,440 --> 00:00:46,070 +بيتم خلالها انتقال حرارة، فبالتالي يعني ممكن احنا في + +6 +00:00:46,070 --> 00:00:50,650 +البداية لو اتكلمنا عن طبيعة الطاقة، إيش هي الـ + +7 +00:00:50,650 --> 00:00:56,250 +energy؟ بنقول يمكن لما نتكلم عن طبيعة المادة، بنقول + +8 +00:00:56,250 --> 00:01:01,130 +سهل جداً أنه نتخيلها، ليه؟ لأن المادة ممكن أنه نشعر + +9 +00:01:01,130 --> 00:01:09,470 +فيها، نلمسها مثلاً، نشوفها، بينما الطاقة كـ يعني concept + +10 +00:01:09,470 --> 00:01:14,500 +كمفهوم، مش مباشر إنه نتحدث عنها لأنه لا نستطيع أنه + +11 +00:01:14,500 --> 00:01:21,300 +يعني نلمسها، يعني بالكثير بس أنه نتحدث عن آثارها + +12 +00:01:21,300 --> 00:01:28,960 +فمش سهل زي الـmatter يعني أو المواد بحد ذاتها، الـ + +13 +00:01:28,960 --> 00:01:34,660 +energy بشكل عام يمكن تعريفها على إنها الـcapacity + +14 +00:01:34,660 --> 00:01:39,070 +to do work or transfer it، الـEnergy يمكن تعريفها + +15 +00:01:39,070 --> 00:01:48,350 +على إنها القدرة على عمل شغل أو نقل حرارة، كويس؟ وهذا + +16 +00:01:48,350 --> 00:01:51,570 +الكلام معناته عشان أنا بدي أفهم energy وبيتكلم عن + +17 +00:01:51,570 --> 00:01:54,590 +الطاقة بشكل عام وبيتكلم عن الـthermochemistry، يبقى + +18 +00:01:54,590 --> 00:01:59,890 +لازم أفهم مفهوم الشغل، الـwork، ومفهوم الحرارة، من + +19 +00:01:59,890 --> 00:02:04,910 +وجهة نظر الكيمياء، من وجهة نظر الكيمياء، لأنه أنا عندي + +20 +00:02:04,910 --> 00:02:08,070 +في الفيزياء ممكن احنا نعرف الشغل زي ما هو معروف، + +21 +00:02:08,600 --> 00:02:11,720 +الشغل اللي هو الـwork بده يساوي الـforce times + +22 +00:02:11,720 --> 00:02:18,520 +distance، هذا التعريف الفيزيائي، عشان هيك بنقول + +23 +00:02:18,520 --> 00:02:21,240 +والله الـwork is the energy used to cause an + +24 +00:02:21,240 --> 00:02:26,910 +object to move against a force، هذا التعريف فيزيائي، + +25 +00:02:26,910 --> 00:02:29,970 +لكن أنا في الكيمياء يعني إيش؟ هل بدي أنقل ذرة من + +26 +00:02:29,970 --> 00:02:33,230 +مكان إلى أزوجها شوية لقدام مثلاً؟ لأ، مش هذا هو + +27 +00:02:33,230 --> 00:02:36,970 +التعريف اللي بيهمني كثير في الكيمياء، فالكيمياء لأ، + +28 +00:02:36,970 --> 00:02:42,550 +هنشوف بالظبط عن إيش بنتحدث لما نتكلم عن الـwork، الـ + +29 +00:02:42,550 --> 00:02:47,110 +heat تعريفها يمكن، مفهوم الـheat is the energy used to + +30 +00:02:47,110 --> 00:02:50,590 +cause the temperature of an object to increase، + +31 +00:02:51,500 --> 00:02:59,520 +مفهوم يعني هي عبارة عن الطاقة اللي بتسبب زيادة في + +32 +00:02:59,520 --> 00:03:04,920 +درجة حرارة أي object، بالطبع الكيمياء زي ما احنا + +33 +00:03:04,920 --> 00:03:08,960 +عارفين بتتحدث عن الـmatter، تتحدث عن المواد بشكل + +34 +00:03:08,960 --> 00:03:17,510 +عام، الكيمياء أيضاً بتتحدث عن الحاجات المصاحبة لهذه + +35 +00:03:17,510 --> 00:03:20,470 +العملية للمادة، تغير المادة، التفاعلات الكيميائية، + +36 +00:03:20,470 --> 00:03:24,210 +طب إيش بيصاحبها؟ نعم، في كثير من الأحيان يصاحب + +37 +00:03:24,210 --> 00:03:28,570 +التغيرات الكيميائية وحتى الفيزيائية تغير في الـ + +38 +00:03:28,570 --> 00:03:32,450 +energy، وبالتالي مبرر إلينا أن ندرس الـenergy لأن + +39 +00:03:32,450 --> 00:03:34,990 +العمليات اللي احنا بدرسها، التفاعلات الكيميائية، + +40 +00:03:34,990 --> 00:03:39,110 +العمليات الفيزيائية اللي بتحصل للمواد الكيميائية، + +41 +00:03:39,110 --> 00:03:44,150 +هذه أيضاً يصاحبها تغير في الطاقة، فمهمتنا في هذا الـ + +42 +00:03:44,150 --> 00:03:49,510 +chapter أن نحاول يعني نسلط الضوء مبدئياً على الطاقة + +43 +00:03:49,510 --> 00:03:52,350 +لأنه هيجيئنا بعد هيك زي ما هنشوف chapter تاني + +44 +00:03:52,350 --> 00:03:55,410 +بيكمل هذا الـchapter نتحدث فيه عن الـ + +45 +00:03:55,410 --> 00:04:00,510 +thermodynamics، الديناميكا الحرارية، شيء بيكمل مفهوم + +46 +00:04:00,510 --> 00:04:04,910 +الطاقة عندنا ومفهوم الـthermochemistry، فالـ + +47 +00:04:04,910 --> 00:04:08,150 +thermochemistry بندرس فيه الـenergy changes + +48 +00:04:08,150 --> 00:04:12,150 +accompanying some physical and chemical changes أو + +49 +00:04:12,150 --> 00:04:19,680 +processes، في مفهوم أوسع منه، ومكمل له اللي هو إيه؟ الـ + +50 +00:04:19,680 --> 00:04:22,700 +thermodynamics، الـthermodynamics هندرسه في chapter + +51 +00:04:22,700 --> 00:04:26,640 +مستقل آخر، chapter معانا كان بود يكون الـchapterين وراء بعض، + +52 +00:04:26,640 --> 00:04:31,460 +لكن احنا بنمشي بترتيب الـchapters في الكتاب، فهنذكره + +53 +00:04:31,460 --> 00:04:36,740 +آخر chapter، لكن هو chapter يعتبر مكمل للـthermochemistry + +54 +00:04:36,740 --> 00:04:41,920 +ومتمم له وموضح له broader concept، مفهوم أوسع للـ + +55 +00:04:41,920 --> 00:04:46,150 +energy، فهنشوف هذا الكلام اللي هندرسه آخر chapter + +56 +00:04:46,150 --> 00:04:51,170 +معانا، صور الـenergy اللي احنا بنعرفها، الـenergy + +57 +00:04:51,170 --> 00:04:54,730 +والله ممكن تكون kinetic energy، وهذه الـkinetic + +58 +00:04:54,730 --> 00:05:01,770 +energy هي الـenergy of motion، طاقة الحركية طبعاً، + +59 +00:05:01,770 --> 00:05:06,750 +الجزيئات والـatoms لها طاقة حركة، لا شك لأن طاقة + +60 +00:05:06,750 --> 00:05:13,910 +الحركة تعرف بإنها نصف Mv²، نصف M اللي هي الـmass، V + +61 +00:05:13,910 --> 00:05:17,830 +التي هي السرعة squared، والذرات لا شك أنه في إلها + +62 +00:05:17,830 --> 00:05:22,550 +mass وفي إلها سرعة تتحرك، فبالتالي إلها kinetic + +63 +00:05:22,550 --> 00:05:26,770 +energy، بنلاحظ إن الـkinetic energy تتناسب طردياً مع + +64 +00:05:26,770 --> 00:05:30,630 +الـmass وتتناسب طردياً مع الـV التي هي السرعة، لكن الـ + +65 +00:05:30,630 --> 00:05:36,430 +V²، فالـkinetic energy تزيد بزيادة الـmass + +66 +00:05:36,430 --> 00:05:42,970 +وتزيد أيضاً بزيادة السرعة، لكن كما قلت يعني احنا + +67 +00:05:42,970 --> 00:05:48,490 +ما نتكلمش عن .. خليني أقول physics، احنا بنتكلم عن + +68 +00:05:48,490 --> 00:05:52,230 +كيمياء وبالتالي حديثي عن الـmass والسرعة بتعلق بالـ + +69 +00:05:52,230 --> 00:05:55,730 +atoms والـmolecules، بتعلق الـmass للـatoms والـ + +70 +00:05:55,730 --> 00:06:00,330 +mass للـmolecules، مش أي حاجة ثانية، مش والله أنا + +71 +00:06:00,330 --> 00:06:05,110 +عندي object مثلاً بدي أرميه، هتلاقي أمثلة زي هي في + +72 +00:06:05,110 --> 00:06:08,720 +الكتاب، لكن مش هي المهمة بالنسبة لنا، بدي أرمي مثلاً + +73 +00:06:08,720 --> 00:06:11,540 +بسرعة معينة، طب وإيه الكتلة معينة؟ طب قد إيش الـ + +74 +00:06:11,540 --> 00:06:13,920 +kinetic energy اللي بده ياخدها؟ مثلاً هذا كلام + +75 +00:06:13,920 --> 00:06:18,560 +موجود، لكن هذا فيزياء مش كيمياء، كويسة؟ الكيمياء بتتعلق + +76 +00:06:18,560 --> 00:06:21,620 +بإيه؟ بالـatoms، بالـmolecules، بالـmolecular + +77 +00:06:21,620 --> 00:06:27,820 +species، ions وغيرها، كل هذا الكلام في الكيمياء عندنا + +78 +00:06:27,820 --> 00:06:31,620 +لكن فيزيائياً نعم ممكن نقول والله أي شيء بيتحرك وإيه + +79 +00:06:31,620 --> 00:06:35,160 +الكتلة فيه وإيه الـkinetic energy؟ وحنشوف كمان + +80 +00:06:35,160 --> 00:06:39,800 +التوسع على هذا المفهوم بعد شوية، بالإضافة لـ + +81 +00:06:39,800 --> 00:06:43,720 +kinetic energy في عندي form من الـenergy مهم جداً + +82 +00:06:43,720 --> 00:06:47,820 +جداً جداً اللي هو الـpotential energy، والـpotential + +83 +00:06:47,820 --> 00:06:52,590 +energy هي عبارة عن طاقة كامنة أو طاقة مختزنة، طاقة + +84 +00:06:52,590 --> 00:06:56,650 +مختزنة أو طاقة كامنة، بتتوقف على إيه؟ إذا كنا نقول + +85 +00:06:56,650 --> 00:07:00,310 +والله الكائن ذي الـenergy هي الـmass والسرعة، طب الـ + +86 +00:07:00,310 --> 00:07:02,670 +potential energy بتتوقف على إيه؟ قال هو والله + +87 +00:07:02,670 --> 00:07:09,160 +بتتوقف على موضع الجسم والـcomposition تبعه وموضعه + +88 +00:07:09,160 --> 00:07:12,420 +بالنسبة للأجسام الثانية فيما يتعلق بالـ + +89 +00:07:12,420 --> 00:07:17,680 +attractions والـrepulsions، يعني مثلاً أنا عندي هذا + +90 +00:07:17,680 --> 00:07:25,510 +الجلم، فيه potential energy هو في الموضوع هذا، بدو + +91 +00:07:25,510 --> 00:07:30,190 +يوجع يعني بدو يفقد جزء من الـpotential energy + +92 +00:07:30,190 --> 00:07:34,130 +تبعته، صحيح هذا الكلام بحسب .. لإيه؟ لأن في عندي + +93 +00:07:34,130 --> 00:07:39,010 +attraction مع القوة الجاذبية، فهذا وضع طبيعي جداً، + +94 +00:07:39,010 --> 00:07:44,330 +لكن كمان مرة بقدر أقول أنا أنه الـ .. أنا مش مهتم + +95 +00:07:44,330 --> 00:07:48,410 +كثير بالجاذبية في الـmolecules والـatoms، أنا مش + +96 +00:07:48,410 --> 00:07:54,150 +مهتم كثير، أنا بقول أنا مهتم أكثر فيما يتعلق بـ .. + +97 +00:07:54,150 --> 00:07:56,850 +هي ليش جاذبية؟ قال attraction، طب أنا عندي الـ + +98 +00:07:56,850 --> 00:07:59,290 +attraction والـrepulsion فيما يتعلق بالـmolecular + +99 +00:07:59,290 --> 00:08:04,950 +species، يتعلق بالشحنات، مش بالإيه، بإن والله يعني + +100 +00:08:04,950 --> 00:08:07,410 +جاذبية وما جاذبية، لأ، الجاذبية تأثيرها very + +101 +00:08:07,410 --> 00:08:11,250 +marginal، هامشي للغاية في الكيمياء، مش كثير بتهمني، + +102 +00:08:11,250 --> 00:08:15,300 +اللي بيهمني إيه؟ اللي هي قوة التجاذب والتنافر بين + +103 +00:08:15,300 --> 00:08:19,140 +الـmolecular species، مثلاً أيونات موجبة، أيونات + +104 +00:08:19,140 --> 00:08:25,040 +سالبة، إلكترونات، بروتونات، بروتونات مع بعض، + +105 +00:08:25,040 --> 00:08:29,480 +إلكترونات مع بعض، أيونات موجبة مع بعض، أيونات + +106 +00:08:29,480 --> 00:08:33,120 +سالبة مع بعض، هذا كله بينشأ عنه potential energy + +107 +00:08:33,120 --> 00:08:35,680 +معينة، فالـpotential energy اللي متحدث عنها، بدي + +108 +00:08:35,680 --> 00:08:38,900 +أفكر بحاجتين، زي ما الـkinetic energy بفكر + +109 +00:08:38,900 --> 00:08:41,780 +بحاجتين، kinetic energy بفكر بالـmass والـvelocity، + +110 +00:08:42,360 --> 00:08:45,460 +الـPotential Energy بدي أدور على الـComposition + +111 +00:08:45,460 --> 00:08:50,580 +والـPosition، الـComposition والـPosition هدول + +112 +00:08:50,580 --> 00:08:53,640 +بيأثروا على إيه؟ على الـStored Energy وبيعطوها + +113 +00:08:53,640 --> 00:08:58,680 +قيمة الطاقة اللي هي الـPotential Energy، يمكن أن + +114 +00:08:58,680 --> 00:09:03,550 +تتحول إلى Kinetic Energy والعكس، ممكن تتحول، يعني + +115 +00:09:03,550 --> 00:09:08,830 +في عندي interconversion للطاقة، فمثلاً هذا الجلم، + +116 +00:09:08,830 --> 00:09:11,430 +قلت أنا هايني أعمله هيك، إيه له potential energy؟ + +117 +00:09:11,430 --> 00:09:16,060 +لكن بما أنه ثابت، قد إيش الـkinetic energy تبعته؟ صفر، + +118 +00:09:16,060 --> 00:09:19,360 +لكن لو سيبته، الـpotential energy عاملة بتنزل والـ + +119 +00:09:19,360 --> 00:09:22,700 +kinetic energy بتزيد، لما نوصل هان صار عندي الـ .. + +120 +00:09:22,700 --> 00:09:26,020 +صار عندي الـkinetic energy له صفر وهو أخذ ممكن + +121 +00:09:26,020 --> 00:09:30,180 +نقول يعني potential energy جديدة، إذا كان والله + +122 +00:09:30,180 --> 00:09:33,140 +يقولنا بالنسبة للأرض، فاه هو يح .. إله لسه + +123 +00:09:33,140 --> 00:09:35,840 +potential energy لأنه برضه كان بإمكانه يعمل + +124 +00:09:35,840 --> 00:09:36,940 +attraction مع الأرض، + +125 +00:09:40,010 --> 00:09:43,170 +وإله potential energy فيما يتعلق بإيه؟ مفهوم آخر، + +126 +00:09:43,170 --> 00:09:46,630 +أنه والله لسه بعيد عن الأرض، لسه فيه كمان يعني، + +127 +00:09:46,630 --> 00:09:50,830 +فهذا .. أما هو لأ، لما يقف على الأرض يعني خلاص، + +128 +00:09:50,830 --> 00:09:53,490 +ما بيقدرش .. ما بيقدرش ينزل أكثر من هيك، فإله + +129 +00:09:53,490 --> 00:09:57,690 +potential energy إله صفر بمفهوم إيه؟ الـposition، + +130 +00:09:57,690 --> 00:10:00,610 +لكن إله ككيمياء بنقول إيه الـpotential energy + +131 +00:10:00,610 --> 00:10:03,270 +بتعلق بالـcomposition، الـcomposition اللي هو الـ + +132 +00:10:03,270 --> 00:10:07,770 +attractions والـrepulsions لإيه؟ للذرات والجزيئات + +133 +00:10:07,770 --> 00:10:15,130 +المكونة له، فمثلاً يعني المثال المشهور دائماً أنه لو + +134 +00:10:15,130 --> 00:10:23,210 +إن حد راكب بسكليت على طلّة وواقف، والطلّة منحدرة + +135 +00:10:23,210 --> 00:10:27,550 +فبنقول بما أنه واقف، فالـpotential energy له عالية، + +136 +00:10:27,550 --> 00:10:31,850 +هي عبارة عن مجموعة لو قلنا الـmasses، الـmass للـ + +137 +00:10:31,850 --> 00:10:37,130 +cyclist والـbicycle، كويس؟ لكن الـkinetic energy صفر، + +138 +00:10:37,130 --> 00:10:41,670 +لأنه واقف، بينما هنا لما بدأ بنلاحظ أنه بيندفع، ليه؟ + +139 +00:10:41,670 --> 00:10:45,850 +لأن الـpotential energy مختزنة موجودة، فبتتحول + +140 +00:10:45,850 --> 00:10:49,690 +لإيه؟ لـkinetic energy، لما يوصل بنقول والله أه الـ + +141 +00:10:49,690 --> 00:10:53,610 +potential energy باستمرار بتقل و ال kinetic energy + +142 +00:10:53,610 --> 00:10:59,650 +باستمرار بتزيد لغاية ما يوصل لـ stop كويس فممكن + +143 +00:10:59,650 --> 00:11:00,670 +تحول + +144 +00:11:03,420 --> 00:11:06,500 +الإنرجي من one form to another form لكن بيطلع على + +145 +00:11:06,500 --> 00:11:08,960 +أن ال energy دائما على إنها كاين تيك و potential + +146 +00:11:08,960 --> 00:11:12,580 +الكاين تيك اللي هيدعو بال mass و ال velocity و ال + +147 +00:11:12,580 --> 00:11:16,140 +potential اللي هيدعو بال position و ال composition + +148 +00:11:16,140 --> 00:11:23,890 +خلاص طب نتطلع الآن على في ما يتعلق بالذرات + +149 +00:11:23,890 --> 00:11:28,330 +والجزئيات تبعاتنا و ال chemistry فبنقول بما أنه + +150 +00:11:28,330 --> 00:11:31,110 +لما أتكلم عن ال potential energy لهذه ال species + +151 +00:11:31,110 --> 00:11:35,670 +أنا بتكلم عن ال attractions و ال repulsion للـ ions + +152 +00:11:35,670 --> 00:11:39,470 +و ال electrons و ال protons كويسة ال nuclear + +153 +00:11:39,470 --> 00:11:43,950 +charge فبالتالي يعني أنا عندي ال potential energy + +154 +00:11:43,950 --> 00:11:46,870 +هي أبعار عن electrostatic potential energy + +155 +00:11:46,870 --> 00:11:50,350 +electrostatic التي نتجة عن الـ Electrical Charges، + +156 +00:11:50,350 --> 00:11:53,870 +فبقولها Electrostatic Potential Energy لأنه لـ + +157 +00:11:53,870 --> 00:11:57,770 +Gravitational Forces، لأ يعني إذا كان لعبة فبتلعب + +158 +00:11:57,770 --> 00:12:01,450 +نجليجياب رول، Very Marginal، زي ما قلنا هامشية جدا + +159 +00:12:01,450 --> 00:12:05,830 +في ما يتعلق بالإيه بال Chemical Systems، لكن اللي + +160 +00:12:07,800 --> 00:12:12,380 +اللي بيأثر على ال potential energy في ال chemical + +161 +00:12:12,380 --> 00:12:16,100 +species جاز ال electrical charges هذي تعتبر طبعا + +162 +00:12:16,100 --> 00:12:23,200 +much more important لو في عندي شحنتين Q1 و Q2 + +163 +00:12:23,200 --> 00:12:26,100 +فبنقدر أقول والله ال electrostatic potential + +164 +00:12:26,100 --> 00:12:29,920 +energy ساوي ثابت الشحنة الأولى في الشحنة التانية + +165 +00:12:29,920 --> 00:12:34,180 +على ال D ممكن الشحنتين يكونوا إيه موجبتين أو + +166 +00:12:34,180 --> 00:12:37,790 +سالبتين يعني بينهم تنافر نفس الشيء وممكن يكونوا + +167 +00:12:37,790 --> 00:12:43,390 +شحنتين مختلفتين وبتالي بينهم تجاذب لكن المهم عندي + +168 +00:12:43,390 --> 00:12:46,490 +أن الـElectrostatic Potential Energy تتناسب ترضيا + +169 +00:12:46,490 --> 00:12:51,770 +مع الشحنات على المسافة بينهم اللي هي D المسافة بين + +170 +00:12:51,770 --> 00:12:57,040 +الشحنتين لو جينا تخيلنا مع بعض في عندي شحنتين like + +171 +00:12:57,040 --> 00:13:00,700 +charges إذا بينهم إيه؟ repulsion يبقى عندي very + +172 +00:13:00,700 --> 00:13:04,580 +high electrostatic potential energy لكن كل ما + +173 +00:13:04,580 --> 00:13:06,760 +حاولنا نبعد هدول التنتين عن بعض ال potential + +174 +00:13:06,760 --> 00:13:09,220 +energy إيش بتجعلها؟ بتقل، بتقل، بتقل، بتقل، بتقل، + +175 +00:13:09,220 --> 00:13:10,840 +بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، + +176 +00:13:10,840 --> 00:13:11,080 +بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، + +177 +00:13:11,080 --> 00:13:13,580 +بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، + +178 +00:13:13,580 --> 00:13:16,460 +بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، + +179 +00:13:16,460 --> 00:13:19,460 +بتقل + +180 +00:13:23,520 --> 00:13:27,100 +فطب لو حاولنا نبعدهم معناه كلمة potential energy + +181 +00:13:27,100 --> 00:13:32,480 +بتزيد بتزيد بتزيد لغاية ما توصل برضه الصفر لهدب + +182 +00:13:32,480 --> 00:13:35,480 +السالب لغاية ما توصل يعني هيك بتزيد لغاية ما توصل + +183 +00:13:35,480 --> 00:13:39,000 +الصفر وكأنه ممكن نعرف احنا ان ال zero + +184 +00:13:39,000 --> 00:13:43,500 +electrostatic potential energy هي لما الشحنات تكون + +185 +00:13:43,500 --> 00:13:47,450 +بعيدة مسافة مقدارها مالانهاية عن بعض البعض سواء + +186 +00:13:47,450 --> 00:13:53,470 +كانت liked charges او different charges فممكن نعرف + +187 +00:13:53,470 --> 00:13:57,710 +الـ zero electrostatic potential energy على انها + +188 +00:13:57,710 --> 00:14:01,990 +هي ال potential energy عندما تكون الشحنات بعيدة عن + +189 +00:14:01,990 --> 00:14:07,770 +بعض البعض مسافة مقدارها infinity وبالتالي بنقدر + +190 +00:14:07,770 --> 00:14:12,080 +نقول إنه الـ Electrostatic Potential Energy بتتوقف + +191 +00:14:12,080 --> 00:14:18,640 +على الشحنات بتزيد لما الشحنات تكون من نفس النوع + +192 +00:14:18,640 --> 00:14:23,760 +موجبة أو سالبة بتقل لما الشحنات تكون مختلفة لكن كل + +193 +00:14:23,760 --> 00:14:28,100 +ما ابعدنا الشحنات عن بعض بنلاحظ إن إذا كان الشحنات + +194 +00:14:28,100 --> 00:14:32,860 +متشابهة هذا وضعي كويس فالـ Potential Energy بتقل + +195 +00:14:32,860 --> 00:14:35,920 +إذا كان الشحنات متشابهة بتقل لما نبعدها عن بعض إذا + +196 +00:14:35,920 --> 00:14:41,230 +كانت مختلفة بتزيد وبالتالي التنتين بيوصلوا إيه؟ + +197 +00:14:41,230 --> 00:14:43,970 +للصفر لأن التعريف الـElectrostatic Potential + +198 +00:14:43,970 --> 00:14:51,850 +Energy يعني بتاخد قيمة عادة سالبة إذا كانت الشحنات + +199 +00:14:51,850 --> 00:14:57,810 +مختلفة وبتاخد قيمة موجبة إذا كانت الشحنات متشابهة + +200 +00:14:57,810 --> 00:15:03,010 +هذا convention بالنسبة لنا إيش وحتاج قياس الطاقة؟ + +201 +00:15:04,210 --> 00:15:07,670 +طبعا الجول احنا بنقول الجول لكن زمان زي ما حناشوف + +202 +00:15:07,670 --> 00:15:11,930 +كانت ال calorie مش هيك كانت ال calorie طيب ال SI + +203 +00:15:11,930 --> 00:15:17,630 +unit لل energy هي الجول طبعا تلفظ جول ايش هو الجول + +204 +00:15:17,630 --> 00:15:20,290 +بالظبط يعني احنا خلينا نتخيل ان في عندنا mass + +205 +00:15:20,290 --> 00:15:24,670 +مقدرها 2 kilogram moving at a speed of one meter + +206 +00:15:24,670 --> 00:15:30,600 +per second بنقول إنه هاديالكتلة اللي بتمشي اللي + +207 +00:15:30,600 --> 00:15:33,660 +وزنها 2 كيلو جرام وبتتحرك بسرعة 1 متر في الثانية + +208 +00:15:33,660 --> 00:15:38,080 +لو طبقنا ال E كايدة بسوا نص MV squared نصف 2 كيلو + +209 +00:15:38,080 --> 00:15:41,200 +جرام 1 متر على ثانية تربيع اللي هي السرعة جاء + +210 +00:15:41,200 --> 00:15:44,040 +بتعطينا 1 كيلو جرام متر تربيع ثانية تربيع على + +211 +00:15:44,040 --> 00:15:49,490 +ثانية تربيع هذا عبارة عن 1 جول إذن بنقول إن هذا + +212 +00:15:49,490 --> 00:15:54,070 +الجسم اللي كتلته 2 كيلو جرام وبتحرك against a + +213 +00:15:54,070 --> 00:15:57,350 +force at a speed of one meter per second إله طاقة + +214 +00:15:57,350 --> 00:16:03,930 +مقدارها واحد جول طبعا احنا ممكن نعرف كمان إن + +215 +00:16:03,930 --> 00:16:08,470 +الواحد الجول هو عبارة عن work فال work عبارة عن + +216 +00:16:08,470 --> 00:16:12,370 +force في ال distance فيمكن تعريفه فيزيائيا تعريف + +217 +00:16:12,370 --> 00:16:15,910 +حلو كتير بنقول a joule is the amount of work done + +218 +00:16:15,910 --> 00:16:20,510 +on a body by a one newton force لنيوتون واحد + +219 +00:16:20,510 --> 00:16:23,870 +كيلوجرام متر على ثانية تربيع فانا عندي force + +220 +00:16:23,870 --> 00:16:28,250 +مقدرها اي واحد نيوتون يعني واحد كيلوجرام متر على + +221 +00:16:28,250 --> 00:16:32,910 +ثانية تربيع that moves the body a distance of واحد + +222 +00:16:32,910 --> 00:16:36,540 +متر in the direction of the force اللي بيحرك ال + +223 +00:16:36,540 --> 00:16:40,680 +إيه؟ الكتلة واحد متر فانا عندي ال distance واحد + +224 +00:16:40,680 --> 00:16:44,920 +متر ال .. واحد نيوتر فلو ضربتهم في بعض بحصل على + +225 +00:16:44,920 --> 00:16:48,400 +الشغل فالشغل بيطلع عندي واحد kilogram متر تربية + +226 +00:16:48,400 --> 00:16:54,400 +على ثالث يعني جول طبعا الجول هو ال SI unit لكن + +227 +00:16:54,400 --> 00:16:58,980 +قديما يعني أو traditionally كنا بنستخدم ال calorie + +228 +00:16:58,980 --> 00:17:03,460 +ال calorie اللي حاليا non SI unit ماهياش SI unit + +229 +00:17:05,170 --> 00:17:09,070 +بنقدر نقول إنه لازال للأسف، ومش فيه يعني للأسف + +230 +00:17:09,070 --> 00:17:13,930 +كتير، هقولكم ليش، لازال للأسف بعض الـママ فيهم + +231 +00:17:13,930 --> 00:17:19,850 +الكيميا والـ Biology والزراعة، ال nutrition + +232 +00:17:19,850 --> 00:17:25,300 +وغيرها، تستخدم ال calorie تستخدم الـ calorie يمكن + +233 +00:17:25,300 --> 00:17:28,900 +يعني احنا ضروري انه نفهم ايش مفهوم ال calorie لانه + +234 +00:17:28,900 --> 00:17:32,060 +كل ال literature السابق قبل الاعتماد الجول على إنه + +235 +00:17:32,060 --> 00:17:35,420 +والله ال SI unit كنا بنستخدم ال calorie فلازم نفهم + +236 +00:17:35,420 --> 00:17:39,940 +ايش ال calorie علشان نستفيد من الدراسات والنتائج + +237 +00:17:39,940 --> 00:17:46,700 +السابقة فلازم نفهم ايش مفهوم ال calorie وكمان ال + +238 +00:17:46,700 --> 00:17:49,740 +gate كمان لازم نعرف ايش مفهوم ال calorie لأن بعض + +239 +00:17:49,740 --> 00:17:54,760 +الأنظمة المهمة لازالة بتستخدمه فالـ calorie بالنسبة + +240 +00:17:54,760 --> 00:17:58,480 +للجول أو نقول ايش تعريف ال calorie قديما جال احنا + +241 +00:17:58,480 --> 00:18:01,560 +بنعرف ال calorie على انها ال amount of energy + +242 +00:18:01,560 --> 00:18:05,100 +required to rate the temperature of one gram of + +243 +00:18:05,100 --> 00:18:10,770 +water من 14.5 إلى 15.5 ليه؟ جال لأنه هيجي معنا في + +244 +00:18:10,770 --> 00:18:16,050 +المستقبل إن الـ specific heat بتتوقف قليلا على + +245 +00:18:16,050 --> 00:18:20,750 +درجة الحرارة عشان هيك لازم نقول عند أي درجة حرارة + +246 +00:18:20,750 --> 00:18:24,950 +فمن 14.5 ل 15.5 مش ضروري يعني نعرف هذا كده مش هيمر + +247 +00:18:24,950 --> 00:18:28,250 +معنا مرات تانية يعني فهو تعريف ال calorie هو + +248 +00:18:28,250 --> 00:18:30,930 +إبارعا كمية الطاقة اللي لازم نعرفها على درجة حرارة + +249 +00:18:31,570 --> 00:18:35,470 +1 جرام من المياه من 14.5 إلى 15.5 ديجريس C أو + +250 +00:18:35,470 --> 00:18:41,450 +كيلفين لأن ديجريس C هي نفسها فيما يتعلق بال value + +251 +00:18:41,450 --> 00:18:47,110 +ديجريس كيلفين لكن هالجيت عشان نعمل relation ما بين + +252 +00:18:47,110 --> 00:18:50,310 +الجول والكالوري لأن الجول هو ال SI unit وبدنا نقدر + +253 +00:18:50,310 --> 00:18:55,750 +نحول بين الإتنين بنقول إنه الكلوري 4.184 جول وH + +254 +00:18:55,750 --> 00:19:00,430 +بين جثين exact يعني بالظبط زي ما نقول المتر ميت + +255 +00:19:00,430 --> 00:19:06,650 +سانتي الفوت اتناشر انش exact value ماشي exact إلها + +256 +00:19:06,650 --> 00:19:13,310 +معنى مهم من ناحية يعني إيش مفهوم القيمة فهذه exact + +257 +00:19:14,920 --> 00:19:19,420 +طبعا في كمان في ما يتعلق بالوحدات الطاقة في عندي + +258 +00:19:19,420 --> 00:19:25,340 +ال nutritional calorie في ال nutrition في ال + +259 +00:19:25,340 --> 00:19:29,080 +nutrition التغذية وما شابه و الأكل عموما بيستخدموا + +260 +00:19:29,080 --> 00:19:31,440 +حاجة بيقولها nutritional calorie ال nutritional + +261 +00:19:31,440 --> 00:19:36,640 +calorie بالنسبة للرمز C كبيرة C كبيرة Cal Cal ال C + +262 +00:19:36,640 --> 00:19:40,460 +إيش مالها؟ Cal Calorie كبير جالة عبارة عن الف + +263 +00:19:40,460 --> 00:19:46,710 +calorie يعني واحد كيلو calorie ماشي فهدف ايش + +264 +00:19:46,710 --> 00:19:49,870 +بيستخدموه في ال nutrition في ال food in general + +265 +00:19:49,870 --> 00:19:54,690 +يعني فلاحظوا إنه لما تلاقيوا C capital معناته إيه + +266 +00:19:54,690 --> 00:19:59,810 +ألف calorie طبعا في كمان وحدة تانية لقياس + +267 +00:19:59,810 --> 00:20:05,930 +الطاقة يعني مش هذكرها هان بالتفصيل لكن يمكن تسمع + +268 +00:20:05,930 --> 00:20:11,440 +عن ال BTU British Thermal Unit لو بدكم تشتريوا مثلا + +269 +00:20:11,440 --> 00:20:16,420 +مكيف أو دفاية أو كذا بتلاقي مكتوب عليها كذا مثلا + +270 +00:20:16,420 --> 00:20:22,160 +عشر تلاف BTU طب هي بتطلع طاقة جال ال BTU كل واحد + +271 +00:20:22,160 --> 00:20:27,000 +BTU ألف و خمسة و خمسين جول ألف و خمسة و خمسين جول + +272 +00:20:27,000 --> 00:20:34,660 +فال BTU برضه من هذه British Thermal Unit هذه تعريف + +273 +00:20:34,660 --> 00:20:39,660 +بريطاني وهي عبارة عن إيه؟ عبارة عن ال BTU هي عبارة + +274 +00:20:39,660 --> 00:20:43,600 +عن كمية الطاقة اللازمة لرفع درج حرارة الميه من + +275 +00:20:43,600 --> 00:20:46,040 +تلاتة و ستين فهرين هايت واحد جرام من الميه من + +276 +00:20:46,040 --> 00:20:48,580 +تلاتة و ستين فهرين هايت لاربعة و ستين فهرين هايت + +277 +00:20:48,580 --> 00:20:51,560 +حتى تعريفهم باستخدام الفهرين هايت لأن هذه الدرجة + +278 +00:20:51,560 --> 00:20:55,240 +المستخدمة درجة الحرارة أو ال scale المستخدم عندهم + +279 +00:20:55,240 --> 00:20:59,820 +لكن مش هيمر معنا يعني ما اعرفش في ال هل هيمر في بعض + +280 +00:20:59,820 --> 00:21:03,480 +الأسئلة و ده لأ لكن لو مري يعني تعرفوا إن ال Btu + +281 +00:21:03,480 --> 00:21:09,010 +عبارة عن ألف وخمسين جول كيف ممكن نحسب ال energy + +282 +00:21:09,010 --> 00:21:14,290 +changes؟ حلو كتير ولا فيه أبسط من هيك نطلع يعني + +283 +00:21:14,290 --> 00:21:17,310 +مثلاً كيناتك energy ونجيب الmass ونجيب ال + +284 +00:21:17,310 --> 00:21:21,170 +velocity نربع ال velocity نص Mv² مافيش فيها يعني + +285 +00:21:21,170 --> 00:21:27,870 +جدال وال potential energy Q1 كيف Q1 Q2 على D برضه + +286 +00:21:27,870 --> 00:21:30,490 +يعني مباشر للغاية فنتطلع على هذا المثال مثل الواحد + +287 +00:21:30,490 --> 00:21:33,850 +بس أنا هأقول لكم هنا بيقول what's the kinetic energy + +288 +00:21:33,850 --> 00:21:38,960 +in joules؟ of a أول حاجة an argon atom moving at a + +289 +00:21:38,960 --> 00:21:44,580 +speed of 650 meter per second في عندي ذرة argon + +290 +00:21:44,580 --> 00:21:50,380 +واحدة بتمشي بسرعة 650 متر على الثانية طب قد إيش ال + +291 +00:21:50,380 --> 00:21:54,980 +kinetic energy لها وهو ب a mole of argon مش ذرة + +292 +00:21:54,980 --> 00:21:59,260 +واحدة لأ mole of argon atoms moving at a speed of + +293 +00:21:59,260 --> 00:22:05,410 +650 meter per second بقول أنا لازم أذكر أوي يعني هو + +294 +00:22:05,410 --> 00:22:08,350 +هيعطينا إن ال AMU one point six six في عشرة أس + +295 +00:22:08,350 --> 00:22:12,390 +سبعة وعشرين كيلوجرام كل واحدة AMU واحدة AMU one + +296 +00:22:12,390 --> 00:22:15,150 +atomic mass unit قد إيش وزنها ال one point six + +297 +00:22:15,150 --> 00:22:19,250 +six في عشرة أس السالب سبعة وعشرين كيلوجرام فلما + +298 +00:22:19,250 --> 00:22:23,580 +يكون عندي one argon atom قال والله الارجون اتوم من + +299 +00:22:23,580 --> 00:22:28,420 +الجدول الدوري 39.9 AMU طب قد إيش وزنه بتحول من AMU + +300 +00:22:28,420 --> 00:22:33,400 +لكيلوجرام؟ بتضرب كل واحدة AMU 1.66×10⁻²⁷ كيلو + +301 +00:22:33,400 --> 00:22:39,780 +جرام يعني معناته 39.9 AMU في 1.66×10⁻²⁷ كيلو جرام + +302 +00:22:39,780 --> 00:22:46,700 +تعطيني 6.6×10⁻²⁶ كيلوجرام هذه وزنه ال إيه الذرة + +303 +00:22:46,700 --> 00:22:51,760 +الواحدة من الارجون الآن عندي الماس والـ Velocity + +304 +00:22:51,760 --> 00:22:57,580 +موجودة إذا نص في ال mass بالكيلوجرام 650 متر على + +305 +00:22:57,580 --> 00:23:00,960 +الثانية اللي هي سرعة تربيع بطلع عندي 1.4 + +306 +00:23:00,960 --> 00:23:03,580 +في عشرة أس سالب عشرين جول طبعاً حاجة قليلة كتير + +307 +00:23:03,580 --> 00:23:06,820 +وبالمناسبة في الفيزياء عندهم واحدة أصغر من الجول + +308 +00:23:06,820 --> 00:23:10,960 +بيقولها ال urge ال urge عشرة أس سالب سبعة من + +309 +00:23:10,960 --> 00:23:14,840 +الجول يعني حسب النظام فعندي كمية قليلة جداً من + +310 +00:23:14,840 --> 00:23:18,200 +الطاقة على أي حال على أي حال طيب + +311 +00:23:20,840 --> 00:23:24,620 +فيه بيه بيقول لي مول المول أنا عارف وزنه وزنه تسعة + +312 +00:23:24,620 --> 00:23:27,920 +وثلاثين وتسعة من عشرة جرام ليه؟ لأن المول هو عبارة + +313 +00:23:27,920 --> 00:23:31,440 +عن جرام atomic weight أو جرام formula weight فال + +314 +00:23:31,440 --> 00:23:33,500 +formula تسعة وثلاثين وتسعة عزا من المول تسعة + +315 +00:23:33,500 --> 00:23:36,360 +وثلاثين وتسعة من عشرة جرام فتسعة وثلاثين وتسعة من + +316 +00:23:36,360 --> 00:23:39,820 +عشرة جرام بتحولها لكيلوجرام بتصير 0.03 + +317 +00:23:39,820 --> 00:23:43,940 +99 كيلوجرام في نص في السرعة تربيع بتطلع + +318 +00:23:43,940 --> 00:23:48,060 +8.4 كيلوجول 8.4 من عشرة كيلو + +319 +00:23:48,060 --> 00:23:53,040 +جول فالحسابات يعني كتير كتير بسيطة بدنا نتذكر إن + +320 +00:23:53,040 --> 00:23:57,940 +الكيناتيك إنرجي بتساوي نص ال mass في ال velocity + +321 +00:23:57,940 --> 00:24:01,560 +تربيع لكن ال mass بالكيلوجرام وال velocity متر + +322 +00:24:01,560 --> 00:24:06,540 +على الثانية كويس ال mass كيلوجرام وال velocity + +323 +00:24:06,540 --> 00:24:12,060 +متر على الثانية اتذكروا هذا من مفهوم الجول لأن + +324 +00:24:12,060 --> 00:24:20,380 +الجول هو ال energy فالجول كيلوجرام في متر تربيع + +325 +00:24:20,380 --> 00:24:23,840 +على ثانية تربيع فتذكروا هذه الوحدات لازم نذكرها + +326 +00:24:23,840 --> 00:24:34,900 +كيلوجرام ومتر السرعة طيب الآن بنجي بنطلع على بعض + +327 +00:24:34,900 --> 00:24:38,620 +المفاهيم الأساسية اللي بدها تدخلنا في دراسة ال + +328 +00:24:38,620 --> 00:24:42,580 +energy changes في ال chemical systems بقول في عندي + +329 +00:24:42,580 --> 00:24:46,870 +تعريف لحاجة بقولها system وحاجة بقولها + +330 +00:24:46,870 --> 00:24:51,590 +surroundings التعريف كتير بسيط قال الكون كله الكون + +331 +00:24:51,590 --> 00:24:56,630 +كله هذا كون متكامل الكون بينقسم لقسمين بينقسم + +332 +00:24:56,630 --> 00:25:00,090 +إلى ال system اللي أنا بأدرسه وال surroundings + +333 +00:25:00,090 --> 00:25:04,930 +اللي حواليه يفجأ الكون بينقسم لقسمين ال universe + +334 +00:25:04,930 --> 00:25:10,950 +بينقسم لقسمين ال system اللي أنا بأدرسه والإيه؟ + +335 +00:25:10,950 --> 00:25:13,050 +وال surroundings اللي هي الشغلات المحيطة + +336 +00:25:13,050 --> 00:25:17,530 +فيه فال system هو الجزء من ال universe تحت الدراسة + +337 +00:25:17,530 --> 00:25:21,010 +اللي أنا بأدرسه يعني لو بدي أدرس بني آدم مثلاً يعني + +338 +00:25:21,010 --> 00:25:24,350 +كل ما يتعلق فيه بقول هذا البني آدم هو إيه؟ ال + +339 +00:25:24,350 --> 00:25:27,970 +system تبعي وكل ما يحيط فيه كل ما يحيط فيه هي + +340 +00:25:27,970 --> 00:25:31,390 +عبارة عن ال surroundings فال system زائد ال + +341 +00:25:31,390 --> 00:25:36,750 +surroundings هو ال universe تمام فال .. طبعاً ال + +342 +00:25:36,750 --> 00:25:42,350 +system limited و well defined part limited و well + +343 +00:25:42,350 --> 00:25:46,410 +defined part limited يعني محدود معروف حدوده well + +344 +00:25:46,410 --> 00:25:49,790 +defined معروف حدوده بالظبط يعني معرف بالظبط إيش هو + +345 +00:25:49,790 --> 00:25:54,450 +فعندي أنا في الكيمياء أي chemical reaction عندي + +346 +00:25:54,450 --> 00:25:59,170 +مثلاً يعني ممكن أقول هو system طب مع ده مثلاً الوعاء + +347 +00:25:59,170 --> 00:26:05,590 +اللي بحيط فيه و وراء الوعاء وكل ما عدا .. أنا عندي + +348 +00:26:05,590 --> 00:26:09,650 +reactants a و b بيعطوني c و d هذا ال system تبعي + +349 +00:26:09,650 --> 00:26:12,630 +كل ما عدا حتى الوعاء اللي موجود فيه هذه يعتبر + +350 +00:26:12,630 --> 00:26:15,610 +surroundings فال system هو ال chemical reaction و + +351 +00:26:15,610 --> 00:26:20,610 +ال surroundings هي كل ما عدا ال chemical reaction + +352 +00:26:20,610 --> 00:26:26,490 +طيب + +353 +00:26:28,120 --> 00:26:33,220 +ال systems أحد ثلاث أنواع ال systems أحد ثلاث أنواع + +354 +00:26:33,220 --> 00:26:39,980 +يا إما بيكون open في البداية يا إما بيكون closed + +355 +00:26:39,980 --> 00:26:45,620 +يا بيكون isolated open system ال system بنقول عنه + +356 +00:26:45,620 --> 00:26:51,980 +open إذا كان بيتبادل ال energy و ال matter هاي + +357 +00:26:51,980 --> 00:26:56,300 +المكونات مكونات الحياة يعني energy و matter إذا كان + +358 +00:26:56,300 --> 00:26:59,960 +بيتبادل ال energy و ال matter مع ال surroundings + +359 +00:26:59,960 --> 00:27:06,720 +هذا open system بيتبادل ال what ال matter و ال + +360 +00:27:06,720 --> 00:27:11,380 +energy لو بدنا نتطلع على البحر ونقول هو open + +361 +00:27:11,380 --> 00:27:15,560 +system ليش open system لأ لأنه والله افترض إنه سخن + +362 +00:27:15,560 --> 00:27:19,380 +فأعطى الحرارة اللي فيه لل surroundings في حد بيمنعه + +363 +00:27:19,380 --> 00:27:25,530 +مباشر في احتكاك مباشر طيب يعني المية اللي فيه + +364 +00:27:25,530 --> 00:27:31,330 +بتتبخر فهو بيعطي لل إيه؟ لل .. لل surroundings + +365 +00:27:31,330 --> 00:27:36,010 +كمان matter منه فهذا يعتبر open system حتى الإنسان + +366 +00:27:36,010 --> 00:27:40,230 +.. اتفضلي المادة .. المادة .. المادة المحسوسة يعني + +367 +00:27:42,090 --> 00:27:46,410 +بقول حتى الإنسان يعتبر open system و الله سخن + +368 +00:27:46,410 --> 00:27:52,590 +بيعطي الحرارة لإيه؟ لو مسك قطعة ثلج يعني مثلاً + +369 +00:27:52,590 --> 00:27:57,610 +بيعطي الحرارة للثلج فهو ال energy بتنتقل وبرضه لو + +370 +00:27:57,610 --> 00:28:02,390 +عرق بيعطي المية لل .. آه فهذا open system بنعتبره + +371 +00:28:02,390 --> 00:28:06,610 +فال open system يعني مثال في عندي مثال عليه لو + +372 +00:28:06,610 --> 00:28:12,030 +أجيت سخنت وعاء فيه مية فالوعاء طبعاً بيسخن بيصير يعطي + +373 +00:28:12,030 --> 00:28:15,750 +الحرارة لل surroundings وأيضاً بخار المية بيروح لل + +374 +00:28:15,750 --> 00:28:18,530 +surroundings فهذا open system هذا يعتبر open + +375 +00:28:18,530 --> 00:28:22,830 +system ممكن + +376 +00:28:22,830 --> 00:28:26,330 +نطلع على نوع ثاني من ال systems نقوله closed + +377 +00:28:26,330 --> 00:28:30,680 +system الـ closed system طلعوا معايا أنتم هنا، يعني + +378 +00:28:30,680 --> 00:28:37,060 +هنا في عندي التفاعل الكيميائي موجود داخل وعاء، + +379 +00:28:37,060 --> 00:28:40,900 +التفاعل الكيميائي، أي تفاعل كيميائي مثلاً هو ال + +380 +00:28:40,900 --> 00:28:43,500 +system تبعي موجود داخل وعاء + +381 +00:28:49,850 --> 00:28:54,810 +خلى هذا الوعاء بيقدر يوصل للحرارة يعني فأنا بقول + +382 +00:28:54,810 --> 00:28:59,210 +بما إنه ال piston مسكر على الوعاء فلن يطلع أي + +383 +00:28:59,210 --> 00:29:03,810 +matter يطلع أي matter ال energy ممكن يتبادل ال + +384 +00:29:03,810 --> 00:29:07,310 +energy لكن ال matter لا فأنا بنقوله closed system + +385 +00:29:07,310 --> 00:29:12,170 +closed system في نوع آخر من ال systems بنقوله + +386 +00:29:12,170 --> 00:29:15,550 +isolated system ال isolated system هذا معزول لا + +387 +00:29:15,550 --> 00:29:21,820 +بيتبادل حرارة ولا بيتبادل مادة يعني محافظ على حاله + +388 +00:29:21,820 --> 00:29:27,000 +حرارته فيه مادته فيه زي ال thermos ال thermos طبعاً + +389 +00:29:27,000 --> 00:29:29,580 +ال thermos كويس هو ال thermos بعد فترة يعني بعد يوم + +390 +00:29:29,580 --> 00:29:33,480 +بنلاحظ إحنا إنه اللي في جله بيبرد لو حطينا فيه + +391 +00:29:33,480 --> 00:29:37,580 +مثلاً قهوة ثاني يوم اللي فيه برد يعني هو بي .. إيه + +392 +00:29:37,580 --> 00:29:45,180 +يعني أقرب شيء للـ isolated system على فرض إنه معزول + +393 +00:29:45,180 --> 00:29:49,400 +تماماً فلن لا راح يتبادل حرارة وبالطبع مش راح + +394 +00:29:49,400 --> 00:29:52,520 +يتبادل matter فمعنى الكلام هذا اللي بنقوله + +395 +00:29:52,520 --> 00:29:55,280 +isolated system + +396 +00:29:57,320 --> 00:30:00,260 +يبقى الـ system ثلاث أنواع إما أنها تكون open وهذا + +397 +00:30:00,260 --> 00:30:04,720 +بيتبادل ال energy و ال matter مع ال surroundings، + +398 +00:30:04,720 --> 00:30:08,640 +يا ما بيكون closed وهذا بيتبادل ال energy بس ال + +399 +00:30:08,640 --> 00:30:12,380 +matter لا، يا بيكون isolated ولا بيتبادل energy + +400 +00:30:12,380 --> 00:30:15,200 +ولا بيتبادل matter + +401 +00:30:19,210 --> 00:30:23,750 +الـ Energy changes عادة في الحياة يعني اللي زي ما + +402 +00:30:23,750 --> 00:30:29,690 +بنشوفها ممكن تكون لها two forms يا إما work يا إما + +403 +00:30:29,690 --> 00:30:34,590 +heat أو الاثنين مع بعض work و heat فال energy it + +404 +00:30:34,590 --> 00:30:35,730 +changes دائماً + +405 +00:30:39,550 --> 00:30:47,590 +بنشوفها إحنا على هيئة work أو heat في الكيمياء + +406 +00:30:47,590 --> 00:30:51,030 +بنقول ال work involved results due to the system + +407 +00:30:51,030 --> 00:30:54,690 +volume pressure exchange آه يبقى مش إنه نحرك + +408 +00:30:57,290 --> 00:31:06,730 +خليني أقول كتلة معينة في رفاص يعني في اتجاه معين، + +409 +00:31:06,730 --> 00:31:11,490 +مسافة معينة، لا بالنسبة لي أنا في الكيمياء ال work + +410 +00:31:11,490 --> 00:31:16,730 +عندي حاجة ثانية ال work يتعلق ب volume pressure + +411 +00:31:16,730 --> 00:31:20,660 +change عادة يتعلق بالـ volume pressure change هذا + +412 +00:31:20,660 --> 00:31:23,020 +ال work اللي أنا بشوفه في الكيمياء وهذا عبارة عن + +413 +00:31:23,020 --> 00:31:27,460 +mechanical work يعني لأنه لما ال volume يزيد بيصير + +414 +00:31:27,460 --> 00:31:31,700 +في عنده حركة فهو يعتبر هذا النوع من أنواع ال work + +415 +00:31:31,700 --> 00:31:38,000 +اسمه mechanical work النوع الثاني من ال energy + +416 +00:31:38,000 --> 00:31:42,220 +transfer ممكن يتم ال transfer يعني من خلال الحرارة + +417 +00:31:42,220 --> 00:31:49,600 +زي إن يكون في جسم طبعاً حار سخن فلو مسكناها بإصبعنا + +418 +00:31:49,600 --> 00:31:53,260 +هيك .. بنلاحظ أن الحرارة بتنتقل من الجسم للإصبع من + +419 +00:31:53,260 --> 00:31:58,120 +ال hotter object لل colder object .. كويس؟ و + +420 +00:31:58,120 --> 00:32:04,700 +العكس صحيح لو يعني واحد مسك أو حاولنا نمسك مثلاً + +421 +00:32:04,700 --> 00:32:09,980 +قطعة ثلج بأصبعنا بس يعني فبنلاحظ أن الأصبع حرارته + +422 +00:32:09,980 --> 00:32:15,000 +بتوقع أعلى فرح تنتقل جزء من حرارته للثلج + +423 +00:32:15,000 --> 00:32:19,600 +فهذا اسمه heat transfer وعادة بتتم من الـ hotter + +424 +00:32:19,600 --> 00:32:27,440 +object إلى الـ colder one فعلى سبيل المثال يعني لو + +425 +00:32:27,440 --> 00:32:31,180 +عندي combustion reaction combustion reaction + +426 +00:32:31,180 --> 00:32:35,020 +شفناها في عندي hydrocarbon بيحترق هذا اللي بنسميها + +427 +00:32:35,020 --> 00:32:38,220 +combustion reaction such as the burning of natural + +428 +00:32:38,220 --> 00:32:42,920 +gas فبقول أن burning of natural gas releases the + +429 +00:32:42,920 --> 00:32:47,200 +potential energy stored إذا كان قلنا في + +430 +00:32:47,200 --> 00:32:49,640 +potential energy وطبيعي أنه في potential energy + +431 +00:32:49,640 --> 00:32:54,760 +فهو خلال عملية الحرق بيحرر الـ potential energy + +432 +00:32:54,760 --> 00:32:58,480 +stored in the molecules of the fuel بيحرر الـ + +433 +00:32:58,480 --> 00:33:03,020 +potential energy الناشئة عن ترابط الذرات الناشئة + +434 +00:33:03,020 --> 00:33:04,580 +عن ترابط الذرات + +435 +00:33:07,690 --> 00:33:10,870 +فبنقول إذا عرفنا أن الـ system تبعه أن هو + +436 +00:33:10,870 --> 00:33:14,130 +عبارة عن الـ combustion reaction هذا وكل ما حوله هو + +437 +00:33:14,130 --> 00:33:17,550 +الـ surroundings بنقول أنه بما أن الـ reaction تبعي + +438 +00:33:17,550 --> 00:33:21,430 +بيطلق حرارة إذن الحرارة راح تنتقل من الـ system إلى + +439 +00:33:21,430 --> 00:33:28,850 +الـ surroundings مهم جدا نعرف اتجاه انتقال الحرارة + +440 +00:33:28,850 --> 00:33:35,770 +أو من الذي يقوم بعملية نقلها مهم جدا هذا الكلام لأنه على + +441 +00:33:35,770 --> 00:33:40,050 +أساسه راح تتوقف حاجة بنسميها الـ internal energy أو + +442 +00:33:40,050 --> 00:33:48,250 +الطاقة الداخلية للـ system اللي عندي فلازم نعرف + +443 +00:33:48,250 --> 00:33:53,250 +الاتجاه هأفرجيكم كيف نتكلم الآن عن الـ first law of + +444 +00:33:53,250 --> 00:33:55,190 +thermodynamics طب قلنا يا أستاذ الـ thermodynamics + +445 +00:33:55,190 --> 00:34:00,790 +سنتحدث عنها يعني في المستقبل نعم لكن يعني خلينا + +446 +00:34:00,790 --> 00:34:02,830 +أقول الـ thermochemistry والـ thermodynamics في + +447 +00:34:02,830 --> 00:34:08,370 +تداخل كبير بينهم فمثلا يعني لو قبل ما نتكلم عن الـ + +448 +00:34:08,370 --> 00:34:12,930 +first law of thermodynamics نتكلم عن حاجة بنسميها + +449 +00:34:12,930 --> 00:34:17,190 +الـ zeroth law of thermodynamics زيرو ثلوج وهذا + +450 +00:34:17,190 --> 00:34:22,690 +بتعلق بالحرارة يعني انتقال الحرارة فبيقول أن إذا + +451 +00:34:22,690 --> 00:34:27,150 +كان في عند جسمين بيختلفوا في درجة الحرارة فبعد فترة + +452 +00:34:27,150 --> 00:34:33,910 +لو صاروا in thermal contact يعني وصلنا في بعض، بعد + +453 +00:34:33,910 --> 00:34:38,610 +فترة ماذا سيحصل؟ الحرارة هتنتقل من واحد للتاني، من + +454 +00:34:38,610 --> 00:34:42,450 +الأعلى للأدنى، وبعدين ماذا؟ لغاية ما يتساووا، صاروا + +455 +00:34:42,450 --> 00:34:45,550 +in thermal equilibrium نسميهم بعد ما كانوا in + +456 +00:34:45,550 --> 00:34:48,450 +thermal contact صاروا in ماذا؟ thermal equilibrium + +457 +00:34:48,450 --> 00:34:56,580 +فلو عندي A وB in thermal equilibrium وB وC in + +458 +00:34:56,580 --> 00:35:02,300 +thermal equilibrium إذاً A وC هيكونوا in thermal + +459 +00:35:02,300 --> 00:35:07,340 +equilibrium if they were in thermal contact لو + +460 +00:35:07,340 --> 00:35:12,400 +جمعناهم مع بعض، هلاحظ أن الحرارة مش راح تنتقل من A + +461 +00:35:12,400 --> 00:35:17,680 +لـ C أو من C لـ A in thermal contact مع B وB in + +462 +00:35:17,680 --> 00:35:21,280 +thermal contact مع C إذاً A وC هيكونوا in thermal + +463 +00:35:21,280 --> 00:35:21,820 +equilibrium + +464 +00:35:34,820 --> 00:35:41,860 +القانون الأول للثرمو داينامكس ببساطة بيقول أن الـ + +465 +00:35:41,860 --> 00:35:45,670 +energy is conserved القانون الأول بيقول ماذا؟ energy + +466 +00:35:45,670 --> 00:35:51,350 +is conserved ماذا يعني هذا الكلام؟ يعني energy can neither + +467 +00:35:51,350 --> 00:35:55,630 +be created nor destroyed هذا زي الـ mass إذا أنتم + +468 +00:35:55,630 --> 00:35:59,250 +مذكرين زي الـ mass energy can neither be created + +469 +00:35:59,250 --> 00:36:07,560 +nor destroyed لكن ممكن تتحول من شكل لآخر فإذن عندي + +470 +00:36:07,560 --> 00:36:10,860 +الـ system وعندي الـ surroundings والله ماذا يعني + +471 +00:36:10,860 --> 00:36:13,900 +القانون الأول للـ thermodynamics إذا كان الـ system فقط + +472 +00:36:13,900 --> 00:36:17,320 +فقد طاقة لابد الا ان الـ surroundings يأخذ نفس الكمية + +473 +00:36:17,320 --> 00:36:21,080 +من الطاقة لأن طاقة الـ system والـ surroundings يجب + +474 +00:36:21,080 --> 00:36:23,540 +أن تكون ثابتة + +475 +00:36:25,280 --> 00:36:27,820 +لا تتغير إذا كان الـ system فقد الطاقة والطاقة + +476 +00:36:27,820 --> 00:36:29,840 +ستذهب إلى الـ surroundings طب إذا كان الـ + +477 +00:36:29,840 --> 00:36:33,260 +surroundings فقد الطاقة ستذهب إلى الـ system الطاقة + +478 +00:36:33,260 --> 00:36:37,760 +عبارة عن work و heat work أو heat أو الإثنين يا + +479 +00:36:37,760 --> 00:36:43,540 +work يا heat يا الإثنين إذا an energy that is lost + +480 +00:36:43,540 --> 00:36:47,500 +by a system must be gained by the surroundings and + +481 +00:36:47,500 --> 00:36:53,650 +vice versa بالعكس صحيح هذا ما معنى ذلك؟ معناه أن الـ + +482 +00:36:53,650 --> 00:36:57,730 +energy is conserved ماذا يعني؟ يعني الـ first law of + +483 +00:36:57,730 --> 00:37:01,850 +thermodynamics قانون سهل جدا وحلو جدا، أليس كذلك؟ + +484 +00:37:01,850 --> 00:37:08,150 +لم نزيد من الشرح فتعالوا نتطلع الآن على الـ internal + +485 +00:37:08,150 --> 00:37:14,910 +energy تكلمنا نحن عن الـ kinetic energy والـ + +486 +00:37:14,910 --> 00:37:18,130 +potential energy نقول يا بنات أن الـ internal + +487 +00:37:18,130 --> 00:37:21,970 +energy هي عبارة عن مجموع جميع أنواع الـ kinetic + +488 +00:37:21,970 --> 00:37:25,270 +energy والـ potential energy في الـ system اللي + +489 +00:37:25,270 --> 00:37:28,850 +عندي لكل مكون من مكونات الـ system هذه الـ internal energy + +490 +00:37:28,850 --> 00:37:33,030 +تحدثنا عن نوعين من أنواع الـ energy تحدثنا عن الـ + +491 +00:37:33,030 --> 00:37:36,750 +kinetic energy والـ potential energy الآن نقول أن + +492 +00:37:38,450 --> 00:37:43,870 +الـ Internal Energy هي عبارة عن مجموع جميع أشكال + +493 +00:37:43,870 --> 00:37:47,710 +الـ Kinetic Energy والـ Potential Energy لجميع الـ + +494 +00:37:47,710 --> 00:37:52,070 +Components المكونة للـ System لماذا؟ لأنه لو أنا + +495 +00:37:52,070 --> 00:37:57,030 +أريد أن أحصل على الـ Energy كل مجموع الـ Kinetic Energy + +496 +00:37:57,030 --> 00:38:00,430 +للـ System أريد أن أرى مجموع الـ Kinetic Energy لكل + +497 +00:38:00,430 --> 00:38:03,430 +component من مكونات الـ System أريد أن أقسم الـ + +498 +00:38:03,430 --> 00:38:06,220 +System إلى مكوناته كل ال .. ال .. ال .. ال .. ال .. + +499 +00:38:06,220 --> 00:38:07,820 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +500 +00:38:07,820 --> 00:38:11,860 +.. ال .. ال .. ال .. ال .. + +501 +00:38:11,860 --> 00:38:12,580 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +502 +00:38:12,580 --> 00:38:14,280 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +503 +00:38:14,280 --> 00:38:15,500 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +504 +00:38:15,500 --> 00:38:15,540 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +505 +00:38:15,540 --> 00:38:17,660 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +506 +00:38:17,660 --> 00:38:18,160 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +507 +00:38:18,160 --> 00:38:18,180 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +508 +00:38:18,180 --> 00:38:19,840 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +509 +00:38:19,840 --> 00:38:21,520 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +510 +00:38:21,520 --> 00:38:25,500 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +511 +00:38:31,870 --> 00:38:36,890 +مثلا لأي تفاعل، reaction system، لأي تفاعل اللي هو + +512 +00:38:36,890 --> 00:38:39,470 +عبارة عن الـ system بتاع، بقول أن الـ energy الداخلية + +513 +00:38:39,470 --> 00:38:43,050 +تحتوي ليس فقط على المواد المتفاعلة والمواد + +514 +00:38:43,050 --> 00:38:48,460 +التي تتفاعل معها، ليس فقط هذه، بل أيضا + +515 +00:38:48,460 --> 00:38:51,400 +the motions and interactions of their nuclei and + +516 +00:38:51,400 --> 00:38:54,960 +electrons التي هي من مكونات الـ system كل شيء كل + +517 +00:38:54,960 --> 00:38:59,660 +شيء طبعا يعني يعني صعب جدا أن نحسب هذا الكلام + +518 +00:38:59,660 --> 00:39:04,910 +تمامًا يعني وهيمر معنا أن نحن يعني لا نستطيع حسابه + +519 +00:39:04,910 --> 00:39:07,770 +في الحقيقة بسهولة، لا نستطيع حسابه لكن ليس مهم + +520 +00:39:07,770 --> 00:39:11,030 +الحساب بعينه زي ما سنرى المهم هو الـ energy + +521 +00:39:11,030 --> 00:39:14,190 +change ليس مهم الـ energy بحد ذاتها ليس مهم الـ + +522 +00:39:14,190 --> 00:39:17,730 +interior الـ energy بحد ذاتها صعبة الحساب جدا لكن + +523 +00:39:17,730 --> 00:39:24,170 +الـ energy change هي المهمة بالنسبة لنا لهذا السبب + +524 +00:39:24,170 --> 00:39:28,560 +بقول أن we generally don't know أو الـ numerical + +525 +00:39:28,560 --> 00:39:31,620 +value of a system's internal energy كم مقدار الـ E + +526 +00:39:31,620 --> 00:39:35,420 +التي هي الـ energy الـ internal لا نعرفها، الـ E التي + +527 +00:39:35,420 --> 00:39:40,180 +حالها لا نعرفها، صعب جدا معرفتها، لكن لحسن الحظ، + +528 +00:39:40,180 --> 00:39:44,180 +لحسن الحظ أن في الـ thermodynamics fortunately or + +529 +00:39:44,180 --> 00:39:49,900 +mainlyأنا مهتم أو مهتمة بالتغييرات في الطاقة + +530 +00:39:49,900 --> 00:39:54,240 +الداخلي دلتا E ليس E دلتا E لحسن الحظ + +531 +00:39:54,240 --> 00:39:59,040 +يمكن حسابها بسهولة هأفرجيكم عدة أمثلة لحساب دلتا + +532 +00:39:59,040 --> 00:40:02,080 +E فإنا أريد دلتا E that accompanies a change in + +533 +00:40:02,080 --> 00:40:03,520 +the system + +534 +00:40:07,300 --> 00:40:13,880 +لو تخيلنا أن الـ system فيه له starting internal + +535 +00:40:13,880 --> 00:40:17,800 +energy نسميها E initial يعني قبل ما يحصل التغيير + +536 +00:40:17,800 --> 00:40:24,380 +مثلًا قبل التفاعل بعد التفاعل صار عندي E final التي + +537 +00:40:24,380 --> 00:40:30,700 +هي الـ final internal energy فبقول عادة دلتا E + +538 +00:40:30,700 --> 00:40:35,160 +هي E final ناقص E initial هذه ومع العلم أن + +539 +00:40:35,160 --> 00:40:40,370 +أنا لا أعرف E final ولا أعرف E initial لكن + +540 +00:40:40,370 --> 00:40:45,350 +دلتا أو الفرق بينهم نعم أستطيع أن أعرفه وهذا هو + +541 +00:40:45,350 --> 00:40:49,910 +المهم بالنسبة لي فيما يتعلق بالـ Thermodynamics + +542 +00:40:49,910 --> 00:40:55,230 +مثلًا + +543 +00:40:55,230 --> 00:41:00,550 +يعني نجي نطلع ونحاول نفسر هذا أكثر هي عندي E + +544 +00:41:00,550 --> 00:41:07,020 +initial حسنا وهي عندي الـ E final لا أستطيع حساب هذه + +545 +00:41:07,020 --> 00:41:11,380 +ولا أستطيع حساب هذه أعرف فقط أن + +546 +00:41:11,380 --> 00:41:17,200 +أن والله الـ system فقد طاقة هأفرجيكم مثلا energy + +547 +00:41:17,200 --> 00:41:21,360 +lost to surroundings لماذا؟ لأن E final أقل من E + +548 +00:41:21,360 --> 00:41:24,790 +final أقل وبالتالي دلتا E سالبة الـ + +549 +00:41:24,790 --> 00:41:28,710 +system ينقص دلتا E سالبة لأن + +550 +00:41:28,710 --> 00:41:32,650 +دلتا E عبارة عن E final ناقص E initial بما + +551 +00:41:32,650 --> 00:41:38,110 +أن الـ final أقل إذن دلتا E سالبة زي ماذا؟ + +552 +00:41:38,110 --> 00:41:45,610 +مثلًا زي مثلا تفاعل يكون طارد للحرارة، + +553 +00:41:45,610 --> 00:41:49,650 +تفاعل يكون طارد للحرارة، يعطي حرارة، زي + +554 +00:41:49,650 --> 00:41:52,230 +combustion reaction، أين ستذهب الحرارة؟ ستذهب + +555 +00:41:52,230 --> 00:41:55,670 +إلى الـ surroundings، يبقى بالضرورة الـ internal + +556 +00:41:55,670 --> 00:42:01,620 +energy للنواتج أقل إذا دلتا E سالبة هذا + +557 +00:42:01,620 --> 00:42:06,180 +ببساطة خالص عكس هذا الكلام لو كان الـ final state + +558 +00:42:06,180 --> 00:42:11,160 +of the system الـ E final الطاقة تبعها أعلى من الـ + +559 +00:42:11,160 --> 00:42:14,280 +initial فمع هذا الكلام الـ energy gained from + +560 +00:42:14,280 --> 00:42:19,420 +surroundings يبقى دلتا E موجبة زي ماذا؟ زي + +561 +00:42:19,420 --> 00:42:22,940 +ما يكون مثلاً الـ system اللي عندي عبارة عن قطعة ثلج + +562 +00:42:22,940 --> 00:42:28,080 +بدها تدوب قطعة ثلج بدها تدوب فإيش؟ بتاخد حرارة من + +563 +00:42:28,080 --> 00:42:31,220 +أين؟ من الـ Ceramics وحرارة الـ system إيش مجردها؟ + +564 +00:42:31,220 --> 00:42:35,660 +بتزيد يعني الـ energy للـ system بتزيد فمعنى الكلام + +565 +00:42:35,660 --> 00:42:47,060 +الـ delta E عندي positive طيب + +566 +00:42:47,060 --> 00:42:51,410 +بقول أنا في الـ thermodynamics عادة الـ + +567 +00:42:51,410 --> 00:42:54,470 +Thermodynamic Quantities والـ Delta E أحد الـ + +568 +00:42:54,470 --> 00:42:57,070 +Thermodynamic Quantities لأن أنا أتكلم عن الـ First + +569 +00:42:57,070 --> 00:42:59,050 +Law of Thermodynamics زي ما سنشهد بعد شوية + +570 +00:43:02,430 --> 00:43:09,230 +والـ unit number قيمة وواحدة كويس، زائد طبعاً هدول + +571 +00:43:09,230 --> 00:43:11,810 +number وواحدة بيعطوني الـ magnitude of the change + +572 +00:43:11,810 --> 00:43:18,810 +زائد إشارة بتدل على الاتجاه هل في زيادة ولا في نقص + +573 +00:43:18,810 --> 00:43:22,410 +فالـ positive delta A بيكون الـ final أكبر من الـ + +574 +00:43:22,410 --> 00:43:27,790 +initial والعكس طبعاً صحيح، لكن في النهاية بدنا + +575 +00:43:27,790 --> 00:43:32,530 +نتذكر أن أي طاقة بيفقدها الـ system بدها تروح للـ + +576 +00:43:32,530 --> 00:43:35,870 +surroundings بالظبط هي هي لأن الـ energy is + +577 +00:43:35,870 --> 00:43:39,850 +conserved وأي طاقة بتفقدها الـ surroundings بدها + +578 +00:43:39,850 --> 00:43:43,770 +تروح للـ system برضه كمان مرة لأن الـ energy is + +579 +00:43:43,770 --> 00:43:48,930 +conserved لو طلعنا على هذا الـ reaction نفس الـ + +580 +00:43:48,930 --> 00:43:54,950 +reaction اللي حكيتلكم عنه أنا H2 زائد O2 بتعطينا + +581 +00:43:54,950 --> 00:44:00,370 +H2O هدول بيحترقوا يبقى التفاعل عندي بعطيني حرارة، + +582 +00:44:00,370 --> 00:44:04,390 +إذاً معنى الكلام الـ final state هتكون لها lower + +583 +00:44:04,390 --> 00:44:08,210 +energy، ليه؟ لأن الحرارة هتروح للـ A للـ + +584 +00:44:08,210 --> 00:44:11,850 +surroundings، فصارت الـ final state لها A، يبقى + +585 +00:44:11,850 --> 00:44:15,010 +الـ delta E عندي أقل من صفر أو negative، الـ delta + +586 +00:44:15,010 --> 00:44:17,830 +E عبارة عن negative value + +587 +00:44:20,360 --> 00:44:26,720 +وعكس هذا الكلام لو كان في عندي مثلاً قطعة + +588 +00:44:26,720 --> 00:44:33,080 +ثلج أو ما شابه إيش علاقة الـ delta E بالـ heat والـ + +589 +00:44:33,080 --> 00:44:42,300 +work relating delta E to heat and work بقول أنا + +590 +00:44:42,300 --> 00:44:47,080 +عندي الـ delta E بتساوي الـ Q زائد W الـ internal + +591 +00:44:47,080 --> 00:44:53,620 +energy الـ Change in internal energy بساوي Q زائد W + +592 +00:44:53,620 --> 00:45:00,340 +بتتوقف على هل الـ Delta E بدنا نشوف والله هل هي + +593 +00:45:00,340 --> 00:45:03,700 +موجبة أو سالبة لأ تتوقف فقط على الحرارة لأ تتوقف + +594 +00:45:03,700 --> 00:45:07,540 +أيضاً على الشغل لأنه مش دائماً الـ system بيعطيني + +595 +00:45:07,540 --> 00:45:11,900 +حرارة فقط يعني مثلاً لو جينا نتطلعنا على الـ system + +596 +00:45:11,900 --> 00:45:20,140 +الماضي هن H2OO2 هدول غازات إيش أعطاني مثلاً هن؟ H2O + +597 +00:45:20,140 --> 00:45:26,820 +إيش؟ Liquid، إذا حجم .. حجم الـ .. الـ system إيش + +598 +00:45:26,820 --> 00:45:31,160 +حصل له؟ كان غازات بتحول لـ Liquid، الغازات حجمها + +599 +00:45:31,160 --> 00:45:34,800 +كبير، الـ Liquid إيش؟ إذا في شغل تم من الـ + +600 +00:45:34,800 --> 00:45:38,450 +surroundings عليه لأنه بده .. بده ينضغطها الـ gate + +601 +00:45:38,450 --> 00:45:43,390 +بده الحجم يقل بده البسطون ينزل ففي شغل تم من الـ + +602 +00:45:43,390 --> 00:45:49,030 +surroundings على الـ system فمش دائماً بس عندي حرارة + +603 +00:45:49,030 --> 00:45:52,450 +لأ في عندي حرارة وفي عندي كمان شغل لازم آخد بالي + +604 +00:45:52,450 --> 00:46:01,300 +من الاتنين فبقول أنا أنه الـ .. ما هي الـ delta E + +605 +00:46:01,300 --> 00:46:06,380 +بتساوي W زائد Q؟ لكن يعني ما هي علاقتها فيهم من + +606 +00:46:06,380 --> 00:46:10,560 +ناحية الـ charges؟ كيف بعرف الـ charge للـ delta E + +607 +00:46:10,560 --> 00:46:16,540 +من قيمة الـ Q والـ W؟ delta E بتساوي Q زائد W؟ هذا + +608 +00:46:16,540 --> 00:46:21,280 +هو نص قانون الـ first law of thermodynamics من + +609 +00:46:21,280 --> 00:46:26,760 +ناحية حسابية الـ Q زائد W طيب، بنقول كيف بتتأثر + +610 +00:46:26,760 --> 00:46:32,410 +الـ delta E بالـ Q والـ W؟ الكاتب كاتب الكتاب بيمثل + +611 +00:46:32,410 --> 00:46:41,210 +الموضوع يعني أو الـ Delta E وكأنها خزنة أو bank + +612 +00:46:41,210 --> 00:46:48,190 +account حساب بنكي إذا كان أوضعنا فيه بيزيد يعني الـ + +613 +00:46:48,190 --> 00:46:53,990 +Delta E موجبة وإذا كان سحبنا منه بيقل الـ delta E + +614 +00:46:53,990 --> 00:46:59,050 +سالبة كويس طيب إيش بنستخدم إنه نودع أو نسحب جال + +615 +00:46:59,050 --> 00:47:06,870 +energy يا Q يا W يعني مثلاً أنا + +616 +00:47:06,870 --> 00:47:09,570 +هان خدوا بالكم بتطلعوا على الـ convention تبعنا + +617 +00:47:09,570 --> 00:47:15,690 +حطيت حرارة حطيت حرارة وين؟ في الـ system هاي الـ + +618 +00:47:15,690 --> 00:47:19,610 +system تبعي حطيت حرارة أنا + +619 +00:47:22,040 --> 00:47:25,960 +الـ Surroundings أعطى الـ System حرارة الـ + +620 +00:47:25,960 --> 00:47:31,220 +Surroundings هي اللي عملت شغل على الـ System لو + +621 +00:47:31,220 --> 00:47:34,480 +الـ System هو اللي عمل شغل معناه فقط طاقة لأنه + +622 +00:47:34,480 --> 00:47:37,500 +يعمل شغل لأ الـ Surroundings هي اللي عملت شغل على + +623 +00:47:37,500 --> 00:47:41,300 +الـ System يبقى هان بقول والله الـ Q أكبر من صفر والـ + +624 +00:47:41,300 --> 00:47:44,400 +W أكبر من صفر يعني أنا بعرف الـ Q والـ W فيما + +625 +00:47:44,400 --> 00:47:49,400 +يتعلق بالـ System هل هو بيكسب ولا بيخسر فهان كسب + +626 +00:47:50,350 --> 00:47:54,890 +الـ Q وكسب W، إذا الـ Q موجباً، الـ Q أكبر من صفر، + +627 +00:47:54,890 --> 00:47:59,890 +الـ W أكبر من صفر، إذا الـ Delta E أكبر من صفر، + +628 +00:47:59,890 --> 00:48:05,090 +ليه؟ لأنه energy deposited into system، الـ energy + +629 +00:48:05,090 --> 00:48:12,250 +deposited، deposit يعني ودعت، ودعت، آه لحظة، إيش + +630 +00:48:12,250 --> 00:48:16,720 +الفلوس أو يعني الـ energy كبرت؟ طيب هان إيش بيحصل لو + +631 +00:48:16,720 --> 00:48:21,340 +الـ system أعطاني طاقة أعطى يعني طاقة إيش يعني أعطى + +632 +00:48:21,340 --> 00:48:25,360 +للـ surroundings حرارة زي ما يكون التفاعل الماضي + +633 +00:48:25,360 --> 00:48:29,620 +أعطى للـ surroundings حرارة والتفاعل الماضي لأ + +634 +00:48:29,620 --> 00:48:35,840 +يعني لأنه برضه الشغل لأ الشغل عكسه الـ work done by + +635 +00:48:35,840 --> 00:48:39,630 +the system الـ system هو اللي عمل شغل مش هو اللي + +636 +00:48:39,630 --> 00:48:43,670 +يعني مش الـ surroundings اللي عملت شغل معنى الكلام + +637 +00:48:43,670 --> 00:48:48,630 +الـ Q أقل من صفر والـ W أقل من صفر إذا الـ delta E + +638 +00:48:48,630 --> 00:48:56,190 +عبارة عن negative value فممكن نعبر عن الـ delta E و + +639 +00:48:56,190 --> 00:49:01,800 +كأنها عبارة عن حساب البنكي إذا كان أوضعنا فيه و + +640 +00:49:01,800 --> 00:49:06,960 +وضعنا إيش يعني؟ يعني أعطيناه حرارة واكتشفنا نعطيه + +641 +00:49:06,960 --> 00:49:10,580 +حرارة لمن يكون هو بحاجة لحرارة يعني حرارة الـ + +642 +00:49:10,580 --> 00:49:15,140 +surroundings أعلى أعطيناه حرارة أو اشتغلنا عليه الـ + +643 +00:49:15,140 --> 00:49:19,360 +surroundings هي اللي عملت عليه شغل بمعنى آخر حجمه + +644 +00:49:19,360 --> 00:49:24,370 +هو بده يقلليه؟ لأنه كان اعتبرنا أن الشغل اللي + +645 +00:49:24,370 --> 00:49:27,530 +عنده هو بس PV work فحجمه هو بيقل اللي بيجي الـ + +646 +00:49:27,530 --> 00:49:30,970 +surroundings هي ليه؟ بدها تعمل شغل عليه، بينما لو + +647 +00:49:30,970 --> 00:49:33,410 +حجمه زاد، معناته هو اللي بيعمل شغل على الـ + +648 +00:49:33,410 --> 00:49:38,090 +surroundings، كويس؟ فلو يعني هان ببساطة لو حجمه + +649 +00:49:38,090 --> 00:49:43,290 +قل، لو حرارته، يعني اكتسب حرارة من الـ + +650 +00:49:43,290 --> 00:49:45,990 +surroundings، يعني هو كان حرارته أقل، آه دي التايم + +651 +00:49:45,990 --> 00:49:50,960 +وجاءت، طيب هان، عكس هذا الكلام، لو هو عامل شغل، يبقى + +652 +00:49:50,960 --> 00:49:56,200 +الـ W أقل من صفر بالنسبة له الـ convention أنا بتكلم + +653 +00:49:56,200 --> 00:49:59,360 +بس عن الـ system يبقى هذه الـ conventions للـ system + +654 +00:49:59,360 --> 00:50:04,060 +ولو هو فقط طاقة إذا الـ Q برضه كمان أقل من صفر هذا + +655 +00:50:04,060 --> 00:50:09,380 +الكلام بتترجم لإنه كتابة when heat is added to a + +656 +00:50:09,380 --> 00:50:16,160 +system or work is done on a system مش byها on فرق + +657 +00:50:16,160 --> 00:50:23,170 +كبير its internal energy increases وطبعاً العكس يعني + +658 +00:50:23,170 --> 00:50:31,110 +صحيح يعني + +659 +00:50:31,110 --> 00:50:35,430 +برضه صياغة أخرى بشكل آخر من كتاب آخر هي عند الـ + +660 +00:50:35,430 --> 00:50:40,610 +system ومعها الـ surroundings لو الـ system اكتسب + +661 +00:50:40,610 --> 00:50:45,630 +heat إذا بالنسبة للـ system الـ Q موجب ليه؟ لأنه + +662 +00:50:45,630 --> 00:50:52,590 +تم إيداع اكتسب طيب لو كان فيه شغل على الـ system الـ + +663 +00:50:52,590 --> 00:50:55,830 +surroundings هي اللي عملت شغل يعني معنى كلام الـ W + +664 +00:50:55,830 --> 00:51:01,530 +أكبر من صفر يبقى الـ delta E موجبة والعكس بيكون + +665 +00:51:01,530 --> 00:51:09,010 +صحيح إذن بنقدر نقول احنا أن الـ delta E زي ما شفنا + +666 +00:51:09,010 --> 00:51:15,600 +بتساوي الـ Q زائد W لكن قيمة الـ Q وقيمة الـ W + +667 +00:51:15,600 --> 00:51:22,720 +بتتوقف على هل الـ system هو اللي بيعطيني حرارة و هل + +668 +00:51:22,720 --> 00:51:26,180 +هو اللي بيعمل شغل أو هل الـ system هو اللي بيكتسب + +669 +00:51:26,180 --> 00:51:31,000 +حرارة وبنعمل عليه شغل طبعاً ممكن واحدة منهم تكون + +670 +00:51:31,000 --> 00:51:34,100 +سالبة والثانية موجبة ممكن يكون والله بيعطي حرارة + +671 +00:51:35,720 --> 00:51:39,660 +وبينعمل عليه شغل فبيكسب من جهة وبيفقد من جهة ممكن + +672 +00:51:39,660 --> 00:51:42,680 +يكون والله العكس ممكن يكون بياخد حرارة لكن هو + +673 +00:51:42,680 --> 00:51:50,460 +بيعمل شغل يعني ممكن أي أي إشارة تكون لـ الـ W والـ Q + +674 +00:51:50,460 --> 00:51:55,080 +مش شرط التان التان يكونوا يا موجبتين يا سالبتين وهنا + +675 +00:51:55,080 --> 00:51:58,220 +بنتطلع على الـ sign conventions وبدي آخد slide ثاني + +676 +00:51:58,220 --> 00:52:04,840 +slide بسيطة يعني سهلة خالص بقول for a Q لما تكون + +677 +00:52:04,840 --> 00:52:08,380 +positive وبتكلم عن إيه فيه ما يتعلق بالـ system هاي + +678 +00:52:08,380 --> 00:52:11,080 +كل شغلي بالـ system مش بس hand كل شغلي بالـ system + +679 +00:52:11,080 --> 00:52:13,700 +أنا مهتم بالـ system لأن أنا بدرس الـ system أنا + +680 +00:52:13,700 --> 00:52:16,720 +مهتم بالـ system فكل ما يتعلق فيه يعني يتعلق بالـ + +681 +00:52:16,720 --> 00:52:22,100 +system فبقول plus means system gains heat طيب الـ + +682 +00:52:22,100 --> 00:52:28,040 +work means work done on system طيب يمكن تلتقى إيش + +683 +00:52:28,040 --> 00:52:33,090 +موجة باه net gain of energy أكس هذا الكلام Q + +684 +00:52:33,090 --> 00:52:38,390 +نيجاتيف means system loses heat system loses heat + +685 +00:52:38,390 --> 00:52:43,870 +و نيجاتيف means work done by مش on by هو اللي + +686 +00:52:43,870 --> 00:52:49,350 +بيعمل شغل يبقى فقط طاقة يبقى سالبة المحصلة Delta A + +687 +00:52:49,350 --> 00:52:50,050 +سالبة + +688 +00:52:54,760 --> 00:52:57,840 +الحجم بيقل مع حجم الـ system بيقل معناته الـ + +689 +00:52:57,840 --> 00:53:03,820 +surroundings هي اللي بتعمل شغل على الـ system أو + +690 +00:53:03,820 --> 00:53:06,000 +لما الـ surroundings هي اللي بتعمل شغل على الـ + +691 +00:53:06,000 --> 00:53:11,020 +system بتكون الـ W موجبة فيما يتعلق بالـ system طيب + +692 +00:53:11,020 --> 00:53:15,600 +ناخد كمان slide لجيتها حلوة يعني وبتلخص شغلات + +693 +00:53:15,600 --> 00:53:19,560 +كتير فيها شوية مفاهيم مش فشش جديد في الحقيقة يعني + +694 +00:53:19,560 --> 00:53:23,260 +لكن بنشوف الـ site convention for a queue الـ queue + +695 +00:53:23,260 --> 00:53:26,080 +أكبر من صفر يعني heat is transferred from the + +696 +00:53:26,080 --> 00:53:31,240 +surroundings to the system مفهومة الـ queue أكبر من + +697 +00:53:31,240 --> 00:53:33,980 +صفر يبقى الـ heat is transferred from the + +698 +00:53:33,980 --> 00:53:37,980 +surroundings to the system طيب الـ Q أقل من صفر + +699 +00:53:37,980 --> 00:53:41,360 +العكس الـ heat is transferred from the system to + +700 +00:53:41,360 --> 00:53:42,200 +the surroundings + +701 +00:53:46,110 --> 00:53:50,550 +في ما يتعلق بالـ W اللي هي إيه ال work بنقول work + +702 +00:53:50,550 --> 00:53:53,790 +أكبر من صفر work is done by the surroundings on + +703 +00:53:53,790 --> 00:53:58,130 +the system طب و أقل من صفر work is done by the + +704 +00:53:58,130 --> 00:54:02,370 +system on the surroundings الآن الـ sign للـ Delta E + +705 +00:54:02,370 --> 00:54:08,230 +Delta E بتساوي Q زائد الـ W لما تكون Q أكبر من صفر و + +706 +00:54:08,230 --> 00:54:13,010 +الـ W أكبر من صفر Delta E أكبر من صفر طبيعيدلتا E + +707 +00:54:13,010 --> 00:54:16,750 +أكبر من صفر لأن دلتا E Q زائد W هذا أكبر من صفر و + +708 +00:54:16,750 --> 00:54:20,710 +هذا أكبر من صفر و هذا أكبر من صفر طب Q أكبر من صفر + +709 +00:54:20,710 --> 00:54:26,390 +و W أقل من صفر آه الـ sign of delta E depends on + +710 +00:54:26,390 --> 00:54:30,670 +the magnitude of the Q and W أنهي أكبر وحدة موجة + +711 +00:54:30,670 --> 00:54:34,350 +بقى الثانية سالمة فبقى الأكبر طب Q هنا عكس هذا + +712 +00:54:34,350 --> 00:54:37,970 +Q أقل من صفر و W أكبر من صفر the sign of Delta E + +713 +00:54:37,970 --> 00:54:41,590 +depends on the magnitude of Q and W طب Q أقل من + +714 +00:54:41,590 --> 00:54:45,390 +صفر و W أقل من صفر إذا الـ Delta E negative نتذكر + +715 +00:54:45,390 --> 00:54:50,130 +هذا الكلام يا بنات حلو كثير و بسيط خالص نتذكره طيب + +716 +00:54:50,130 --> 00:54:53,410 +تعالوا نأخذ اللي كم من مثال نحسب فيه الـ Delta E + +717 +00:54:54,830 --> 00:54:59,010 +فبيقول لي the value of delta E for a system that + +718 +00:54:59,010 --> 00:55:04,210 +performs 13 kilo joule of work on its surroundings + +719 +00:55:04,210 --> 00:55:16,350 +يبقى مين اللي بيعمل الشغل الـ system هو اللي + +720 +00:55:16,350 --> 00:55:22,770 +بيعمل الشغل، إذا الشغل سالب، صحيح هذا الكلام وهو + +721 +00:55:22,770 --> 00:55:28,150 +يفقد 9 كيلو جولز من الحرارة وهو يفقد أيضًا الـ Q + +722 +00:55:28,150 --> 00:55:33,970 +سالب يعني Delta E Q زائد W هذه سالب تسعة وهذه سالب + +723 +00:55:33,970 --> 00:55:39,070 +ثلاثة عشر سالب اثنين وعشرين كيلو جول ماشي؟ طيب بيقول + +724 +00:55:39,070 --> 00:55:43,010 +لي 1000 joules of thermal energy flows into the + +725 +00:55:43,010 --> 00:55:48,040 +system في الخزنة راحوا Q موجب الـ Q بتساوي ألف + +726 +00:55:48,040 --> 00:55:52,340 +جول، at the same time 400 جول of work is done + +727 +00:55:52,340 --> 00:55:56,060 +by the system، مين اللي عامل الشغل؟ إذا فقط بفلو + +728 +00:55:56,060 --> 00:56:00,120 +سالفة، what is the change in the system's internal + +729 +00:56:00,120 --> 00:56:04,700 +energy؟ شايفين قد إيش سهل نحسب الـ Delta E، لكن لو + +730 +00:56:04,700 --> 00:56:10,980 +جاء لي يحسب الـEI والـEF؟ ما أعرفش لكن الـ delta E ساوي + +731 +00:56:10,980 --> 00:56:15,640 +الـ Q زائد الـ W الـ Q هو كسب ألف و خسر أربعمائة إذا + +732 +00:56:15,640 --> 00:56:21,000 +كسب ستمائة جول نطلع + +733 +00:56:21,000 --> 00:56:27,670 +على هذا الـ system تبعنا Gases A and B are confined + +734 +00:56:27,670 --> 00:56:33,030 +in a cylinder and piston + +735 +00:56:47,290 --> 00:56:51,310 +مثل ما يظهر في الفيجور ويتفاعل لتصميم نوع من + +736 +00:56:51,310 --> 00:56:55,310 +الهواء الصلب لحظة A غاز و B غاز وحجمهما كبير + +737 +00:56:55,310 --> 00:56:59,370 +غازات طب لما يكونوا صلب ايش بيصير للحجم؟ الرجال + +738 +00:56:59,370 --> 00:57:01,550 +سعرهم صلب يفجأ + +739 +00:57:03,940 --> 00:57:07,360 +الـ work مين اللي بيعمل الـ work؟ هل هو اللي عمل الـ + +740 +00:57:07,360 --> 00:57:11,500 +work؟ الـ surrounding زي ما عملت الـ work طيب as + +741 +00:57:11,500 --> 00:57:15,140 +the reaction occurs the system loses 1150 جول of + +742 +00:57:15,140 --> 00:57:19,620 +heat يعني تفاعل طارد للحرارة ففقد 1150 of heat + +743 +00:57:19,620 --> 00:57:24,420 +ايش معنى هذا الكلام؟ الـ system فقد Q سالبة لأن الـ + +744 +00:57:24,420 --> 00:57:29,590 +system فقد المصادر تتحرك للأسفل، وكما يتفاعل + +745 +00:57:29,590 --> 00:57:33,790 +الغازين لإصلاح المصادر، وكما يتقل قوة الغاز تحت درجة + +746 +00:57:33,790 --> 00:57:35,310 +درجة درجة درجة درجة درجة درجة درجة درجة درجة درجة + +747 +00:57:35,310 --> 00:57:35,430 +درجة درجة درجة درجة درجة درجة درجة درجة درجة درجة + +748 +00:57:35,430 --> 00:57:35,670 +درجة درجة درجة درجة درجة درجة درجة درجة درجة درجة + +749 +00:57:35,670 --> 00:57:37,730 +درجة درجة درجة درجة درجة درجة درجة درجة درجة درجة + +750 +00:57:37,730 --> 00:57:37,770 +درجة درجة درجة درجة درجة درجة درجة درجة درجة درجة + +751 +00:57:37,770 --> 00:57:39,560 +درجة درجة درجة درجة درجة درجة درجة دالـ + +752 +00:57:39,560 --> 00:57:44,020 +Surroundings بتعمل شغل مقداره 480 جول of work On + +753 +00:57:44,020 --> 00:57:47,140 +the system What is the change in the internal + +754 +00:57:47,140 --> 00:57:50,680 +energy of the system؟ طبيعي جدًا، لو حللناها، بنقول + +755 +00:57:50,680 --> 00:57:55,080 +إن Delta E ساوي Q زائد W، Q بما أنه هو طارد + +756 +00:57:55,080 --> 00:57:59,940 +للحرارة أو بيعطي حرارة، فهو فقد 1150، لكن الـ + +757 +00:57:59,940 --> 00:58:03,540 +Surroundings عملت شغل عليه، فبالتالي اكتسب 480، + +758 +00:58:03,540 --> 00:58:08,840 +فبيطلع عندي سالب 670، المحصلة Delta E سالبة + +759 +00:58:10,740 --> 00:58:14,900 +يعني في المحصلة أن الطاقة انتقلت من الـ system للـ + +760 +00:58:14,900 --> 00:58:19,000 +surroundings طيب كمان مثال بيقول 800 joule of work + +761 +00:58:19,000 --> 00:58:24,440 +is done on a system ايش يعني ايه الـ W موجب ولا + +762 +00:58:24,440 --> 00:58:30,800 +سالب الـ W خليني أطلع خليني أطلع 800 joule of work + +763 +00:58:30,800 --> 00:58:35,300 +is done on the system مش هو اللي عملها واه طبعًا + +764 +00:58:35,300 --> 00:58:38,700 +الـ W موجب بالنسبة للـ .. يعني بحب كثير هنا اللي + +765 +00:58:38,700 --> 00:58:44,130 +عليه work بكسب 500 J of thermal energy is removed + +766 +00:58:44,130 --> 00:58:48,970 +from the system يبقى Q سالبة. طب what is the change + +767 +00:58:48,970 --> 00:58:51,830 +in the system's internal energy؟ طبعًا Delta E Q + +768 +00:58:51,830 --> 00:58:55,710 +زائد W سالب خمسمئة اللي هي كل Q زائد ثمانمائة تم + +769 +00:58:55,710 --> 00:58:59,990 +ثلاثمائة J. The value of Delta E for a system that + +770 +00:58:59,990 --> 00:59:04,290 +performs 111 KJ of work on its surroundings هنمين + +771 +00:59:04,290 --> 00:59:10,170 +المبدل الشغل؟ الـ system is then الـW سالب on its + +772 +00:59:10,170 --> 00:59:15,170 +dynamics and gains بيكتسب 89 kilo joule of heat + +773 +00:59:15,170 --> 00:59:20,930 +يبقى الـ Q زائد 89 الـ W سالب 111 آه الـ net delta + +774 +00:59:20,930 --> 00:59:25,390 +E سالبة طيب + +775 +00:59:25,390 --> 00:59:29,510 +نتطلع على هذه المسألة بيقول when a system فراغ + +776 +00:59:29,510 --> 00:59:32,770 +delta E is always negative وقتش بتكون always + +777 +00:59:32,770 --> 00:59:39,770 +negative صحيح صحيح absorbs heat and does work + +778 +00:59:39,770 --> 00:59:43,650 +absorbs heat لأ هذه الـ Q موجبة هي خلينا نطلع عليها + +779 +00:59:43,650 --> 00:59:54,390 +Q موجبة أو زائد Q يعني does work W سالب gives of + +780 +00:59:54,390 --> 01:00:04,570 +heat سالب does work سالب طب absorbs heat Has work + +781 +01:00:04,570 --> 01:00:19,610 +done on it يعني + +782 +01:00:19,610 --> 01:00:23,050 +عمل عليه الشغل، مش هو اللي عمل، مش هو اللي عمل، + +783 +01:00:23,050 --> 01:00:29,280 +معنى الكلام في عند وقتش بتكون always negative لما + +784 +01:00:29,280 --> 01:00:33,620 +تقول هذه سالبة أو هذه سالبة إذا الخيار عندي بيه + +785 +01:00:33,620 --> 01:00:37,900 +بسيط كثير ممكن يعني الـ chemical و الـ physical + +786 +01:00:37,900 --> 01:00:42,780 +processes نقول عنهم أو نصفهم بأحد وصفين يا إما + +787 +01:00:42,780 --> 01:00:47,560 +أنه ماص للحرارة بمعنى آخر آه أنه بيكتسب حرارة من + +788 +01:00:47,560 --> 01:00:50,560 +الـ surroundings يا إما طارد للحرارة يعني بيعطي + +789 +01:00:50,560 --> 01:00:53,560 +حرارة للـ surroundings فماص الحرارة يعني اللي + +790 +01:00:53,560 --> 01:00:56,480 +بياخذ حرارة من الـ surroundings بيقوله endothermic + +791 +01:00:56,480 --> 01:01:00,280 +process سواء كان chemical أو physical reaction + +792 +01:01:00,280 --> 01:01:02,920 +سواء كان chemical أو physical reaction فالـ + +793 +01:01:02,920 --> 01:01:07,820 +endothermic process هي الـ process اللي خلالها الـ + +794 +01:01:07,820 --> 01:01:12,020 +system بيكتسب حرارة من الـ surroundings يعني بمعنى + +795 +01:01:12,020 --> 01:01:18,980 +آخر لما الـ process تم حرارة الـ system بتقل يعني + +796 +01:01:18,980 --> 01:01:22,800 +مثلًا لو إجينا بدنا ندوب أمونيا كلوريد في الميه + +797 +01:01:22,800 --> 01:01:27,280 +دوبنا الميه كانت حرارة الغرفة لما ندوب بنلاحظ أنه + +798 +01:01:27,280 --> 01:01:33,120 +صار زي الثلج آه هذه process endothermic وبالتالي + +799 +01:01:33,120 --> 01:01:36,800 +هي بتاخد حرارة من ايه؟ من الـ surroundings يعني + +800 +01:01:36,800 --> 01:01:40,100 +الحرارة .. الحرارة added للـ system من الـ + +801 +01:01:40,100 --> 01:01:40,580 +surroundings + +802 +01:01:45,650 --> 01:01:54,090 +الحرارة تدخل للسيستم اندو يعني أنتم برضه + +803 +01:01:54,090 --> 01:01:59,030 +في حاجات كثير بنلاحظها في الحياة العملية مثلًا + +804 +01:02:02,130 --> 01:02:05,110 +لو طلعت على الـ Ammonium Thiocyanate والبريوم + +805 +01:02:05,110 --> 01:02:09,070 +الهيدروكسيد لو خلطناهم مع بعض دوبناهم وخلطناهم مع + +806 +01:02:09,070 --> 01:02:12,790 +بعض بنلاحظ برضه أن الحرارة بتقل في عمليات كثير + +807 +01:02:12,790 --> 01:02:16,190 +الحرارة فيها بتقل يعني بتكون Endothermic وفي من + +808 +01:02:16,190 --> 01:02:21,950 +العمليات بتكون Exothermic Exo يعني out يعني + +809 +01:02:21,950 --> 01:02:27,030 +الحرارة بتخرج هناك الحرارة أنتم بتدخل كويس؟ هي + +810 +01:02:27,030 --> 01:02:30,250 +الحرارة بتخرج a process in which the system + +811 +01:02:30,250 --> 01:02:36,260 +generates heat is called exothermic البروسيس بتكون + +812 +01:02:36,260 --> 01:02:41,360 +exothermic لما طبعًا الـ system يعطينا حرارة مثال + +813 +01:02:41,360 --> 01:02:44,780 +عليه لما يتفاعل الـ aluminum مع الـ iron oxide هذا + +814 +01:02:44,780 --> 01:02:48,960 +اسمه thermite reaction reaction معروف فبيتحول الـ + +815 +01:02:48,960 --> 01:02:52,560 +aluminum oxide والـ iron مع شدة الحرارة بيدوب هو + +816 +01:02:52,560 --> 01:02:56,980 +صلب آه بيتحول لـ solid لكنه ايش ماله بيدوب بينصهر + +817 +01:02:56,980 --> 01:03:02,780 +بحرارة عالية للغاية برضه الـ Exothermic Reactions كل + +818 +01:03:02,780 --> 01:03:06,600 +الـ Combustion Reactions Exothermic Reactions لأنه + +819 +01:03:06,600 --> 01:03:10,680 +لما أنا أجي بدي أحرق الـ Natural Gas بدي أحرق الـ + +820 +01:03:10,680 --> 01:03:15,020 +Diesel أي .. أي Combustion Reaction هينتج عنه + +821 +01:03:15,020 --> 01:03:23,360 +حرارة يعني هو يُعتبر Exothermic Reaction طب + +822 +01:03:23,360 --> 01:03:28,520 +الآن نيجي نتطلع على مفهوم في الـ Thermodynamics في + +823 +01:03:28,520 --> 01:03:35,060 +عندي حاجة بسميها State Function State Function هي + +824 +01:03:35,060 --> 01:03:39,000 +عبارة عن دالة حالة بيقولوها باللغة العربية يعني هي + +825 +01:03:39,000 --> 01:03:46,760 +عبارة عن دالة الظروف + +826 +01:03:46,760 --> 01:03:52,160 +الحالية هي اللي بتحدد قيمتها هي اللي بتحدد قيمتها + +827 +01:03:52,160 --> 01:03:56,640 +مش ظروف الدالة يعني الـ .. الـ conditions المرتبطة + +828 +01:03:56,640 --> 01:04:01,800 +بالدالة هذه هي اللي بتحدد قيمتها مش كيفية الوصول + +829 +01:04:01,800 --> 01:04:05,700 +إلى هذه الحالة مش كيفية الوصول إلى هذه الحالة يعني + +830 +01:04:05,700 --> 01:04:11,770 +مثلًا لو عندك اضرب مثال وأعود ارجع ثاني اضرب مثله + +831 +01:04:11,770 --> 01:04:17,650 +أو ده ارجع ثاني لو قلنا أنه شط بحر غزة يعني لما + +832 +01:04:17,650 --> 01:04:22,870 +توجه فعال كورنيش بيرتفع عن سطح البحر ثلاثين فوت + +833 +01:04:24,960 --> 01:04:29,260 +وبينما لو روحنا على الشجاعية بنلاقي أن ارتفاع الأرض + +834 +01:04:29,260 --> 01:04:34,340 +هناك حوالي 280 فوت عن سطح البحر فبنقول يعني + +835 +01:04:34,340 --> 01:04:41,120 +الارتفاع الـ altitude 280 ناقص 30 هو عبارة عن 250 + +836 +01:04:41,120 --> 01:04:44,880 +فوت من الشط للشجاعية + +837 +01:04:46,330 --> 01:04:50,790 +بغض النظر ها بغض النظر هذه القيمة بتبقى دائمًا + +838 +01:04:50,790 --> 01:04:56,430 +ثابتة ما تتغيرش ما تتغيرش الـ altitude ما بيتغير لأنه عندي + +839 +01:04:56,430 --> 01:05:03,710 +هان الـ الـ كورنيش بعيد ثلاثين والأرض في الشجاعية بعيدة + +840 +01:05:03,710 --> 01:05:07,350 +280 إذا الـ altitude الفرق بينهم 250 + +841 +01:05:07,350 --> 01:05:11,710 +خمسين بقول هذه تعتبر state function لا تتغير مش + +842 +01:05:11,710 --> 01:05:16,140 +مهم كيف بدنا نحسبها المهم أنه دائماً مادام هذه + +843 +01:05:16,140 --> 01:05:18,860 +موجودة هنا عن ثلاثين وهنا عن اثنين وثمانين فالفرق + +844 +01:05:18,860 --> 01:05:23,160 +بينهم اثنين وخمسين لكن المسافة بين شط البحر + +845 +01:05:23,160 --> 01:05:28,440 +والشيجعية قال والله واحد راح مباشرة صاروخ أخذ + +846 +01:05:28,440 --> 01:05:34,840 +مسافة قليلة واحد راح مثلاً من الشيخ ردوان على + +847 +01:05:34,840 --> 01:05:40,500 +الشيجعية واحد راح على جفاليا وبعدين وصل للشط مثلاً + +848 +01:05:40,500 --> 01:05:46,370 +يعني المسافات تتعدد حسب المسار المسافات بتختلف + +849 +01:05:46,370 --> 01:05:51,170 +بالمسار حسب المسار، عشان هي لا تعتبر دالة حالة، + +850 +01:05:51,170 --> 01:05:55,450 +لأنها تتوقف على المسار، دالة الحالة لا تتوقف على + +851 +01:05:55,450 --> 01:05:59,070 +المسار، وين ما روحنا، من وين ما روحنا، مادام طلعنا + +852 +01:05:59,070 --> 01:06:03,950 +من هنا، من ثلاثين، كيف، أي طريق ناخذ أوصلنا الشجعية + +853 +01:06:03,950 --> 01:06:10,350 +الفرق بينهم من 280 لـ 30 250 foot مهما كان الـ altitude + +854 +01:06:10,350 --> 01:06:16,390 +لكن المسافة لا تعتبر دالة حالة الـ altitude دالة + +855 +01:06:16,390 --> 01:06:20,450 +حالة أو مثال على دالة الحالة لكن الـ distance لا + +856 +01:06:20,450 --> 01:06:24,690 +لأن الـ distance تعتمد على المسار فالـ distance لا + +857 +01:06:24,690 --> 01:06:31,820 +تعتبر دالة حالة مثلاً كمان أنا عندي مادة Liquid معينة + +858 +01:06:31,820 --> 01:06:38,140 +إيه الـ density؟ الـ density كذا gram لكل ml مش مهم + +859 +01:06:38,140 --> 01:06:40,300 +كيف أوصل لـ + +860 +01:06:49,470 --> 01:06:55,030 +عن نفس الظروف، درجة الحرارة أو الضغط مثلاً فبلاحظ + +861 +01:06:55,030 --> 01:06:59,270 +أنه دائماً الـ density لها هي نفس الـ density فهذه + +862 +01:06:59,270 --> 01:07:03,830 +دالة حالة بعتبرها دالة حالة فدالة الحالة لا تتوقف + +863 +01:07:03,830 --> 01:07:07,930 +على المسار اللي أنا اتخذته علشان أوصل لهذة الحالة + +864 +01:07:07,930 --> 01:07:16,030 +هذه زي إيش؟ زي إيش؟ زي مثلاً أنا في عندي ماء عند + +865 +01:07:16,030 --> 01:07:21,630 +خمسين degree c عند جداد؟ عند zero degree c، خمسين + +866 +01:07:21,630 --> 01:07:27,130 +gram ماء، روحت سخنتها، صارت ماء خمسين gram لكن عند + +867 +01:07:27,130 --> 01:07:34,580 +خمسة وعشرين degree c، حلو؟ طب في عندي ماء عند 100 + +868 +01:07:34,580 --> 01:07:39,620 +degree C روحت بردتها لما صارت ماء عند 25 degree C + +869 +01:07:39,620 --> 01:07:44,620 +بقول الـ internal energy لهذه الماء اللي عند 50 + +870 +01:07:44,620 --> 01:07:50,000 +gram H2O 25 degree C هذه الـ internal energy لا + +871 +01:07:50,000 --> 01:07:54,340 +تتغير بحسب المسار سواء روحنا والله سخنّا الماء و + +872 +01:07:54,340 --> 01:07:58,620 +حولناها لهذه الحالة أو روحنا بردنا الماء و حولناها + +873 +01:07:58,620 --> 01:08:02,110 +لهذه الحالة الـ Internal Energy واحدة، لا تتوقف على + +874 +01:08:02,110 --> 01:08:06,770 +المسار، مادام عندي ماء، خمسين جرام، عند خمسة و + +875 +01:08:06,770 --> 01:08:10,670 +عشرين ديجري سي، فالـ Internal Energy واحدة، بغض + +876 +01:08:10,670 --> 01:08:16,970 +النظر كيف حصلت على هذه الحالة، كيف حصلت على هذه + +877 +01:08:16,970 --> 01:08:22,530 +الصورة من الماء، الـ present nature للماء أو الـ + +878 +01:08:22,530 --> 01:08:27,670 +present status للماء، لا تتغير الـ Internal energy + +879 +01:08:27,670 --> 01:08:31,630 +دلوقتي ثابتة، بغض النظر عن الطريق اللي وصلت فيه + +880 +01:08:31,630 --> 01:08:39,450 +إليها، تمام؟ فهذه الـ Delta E من هذا الباب، بنقول + +881 +01:08:39,450 --> 01:08:48,970 +إنها تعتبر دالة حالة دالة الحالة عادة هي الدالة + +882 +01:08:48,970 --> 01:08:52,330 +اللي بيكون لها fixed value for a given set of + +883 +01:08:52,330 --> 01:09:00,960 +conditions لها قيمة ثابتة عند ظروف معينة الظروف + +884 +01:09:00,960 --> 01:09:04,500 +المعينة اللي بنحكي عنها إحنا دائماً في الكيمياء + +885 +01:09:04,500 --> 01:09:13,220 +بنتكلم عن الـ pressure والـ temperature والـ volume + +886 +01:09:13,220 --> 01:09:16,560 +والـ amount of substance عادةً والـ amount of + +887 +01:09:16,560 --> 01:09:17,160 +substance + +888 +01:09:21,630 --> 01:09:24,930 +فعادةً يعني هذه الحاجات تعتبر هي الـ conditions + +889 +01:09:24,930 --> 01:09:30,350 +اللي إحنا ممكن نطلع عليها في تقدير أو يعني نقول + +890 +01:09:30,350 --> 01:09:38,570 +والله هل قيمة معينة، هل .. إيش بيسموها؟ قيمة + +891 +01:09:38,570 --> 01:09:42,470 +معينة، هل هي دالة حالة ولا مش دالة حالة؟ + +892 +01:09:46,250 --> 01:09:50,690 +فالـ .. دوال الحالة ليش بنقول هذا كلام جيد لأنه + +893 +01:09:50,690 --> 01:09:54,370 +دالة الحالة فقط تتوقف على الـ current state + +894 +01:09:54,370 --> 01:09:59,230 +وبالتالي التغير فيها عادة يعتمد فقط على الـ initial + +895 +01:09:59,230 --> 01:10:03,730 +state و الـ final state مش مهم هاي initial state + +896 +01:10:03,730 --> 01:10:06,770 +وهاي + +897 +01:10:06,770 --> 01:10:13,680 +final state شوفت أنا ممكن أروح لها مباشرة أتكلم عن + +898 +01:10:13,680 --> 01:10:18,840 +يعني الـ Delta E هي دالة الحالة E دالة حالة و Delta + +899 +01:10:18,840 --> 01:10:23,940 +E دالة حالة هان الفرق واحد طب افرض أنه أنا اتبعت أي + +900 +01:10:23,940 --> 01:10:28,680 +مسار دائماً الـ Delta E ثابتة لا تتغير مش مهم مادام + +901 +01:10:28,680 --> 01:10:31,940 +وصلت مادام بديت من هان وصلت لهان إذا الـ Delta E + +902 +01:10:31,940 --> 01:10:38,320 +دائماً ثابتة لا تتغير أعتقد في عندي مثال جيد يوضح + +903 +01:10:38,320 --> 01:10:39,140 +هذه الصورة + +904 +01:10:46,790 --> 01:10:53,690 +أه فمثلاً مثلاً خلي يطلع أنا عندي الـ charge battery + +905 +01:10:53,690 --> 01:10:58,450 +charge battery يعني البطارية المشحونة هي عبارة عن + +906 +01:10:58,450 --> 01:11:02,570 +الـ initial state عندي يعني عندي بطارية مشحونة هذا + +907 +01:11:02,570 --> 01:11:06,730 +هي و this charge battery هي اللي إيه يعني البطارية + +908 +01:11:06,730 --> 01:11:09,510 +الفاضية هي اللي إيه يعني بدي أفضيها البطارية + +909 +01:11:09,510 --> 01:11:14,000 +الفاضية هي الـ final state تمام بقول أنا ممكن أعمل + +910 +01:11:14,000 --> 01:11:18,960 +هذا الكلام بعدد طرق ممكن مثلاً أن أوصل سلك بين + +911 +01:11:18,960 --> 01:11:25,120 +الموجب والسالب إيش بيحصل؟ قال السلك بيسخن يبقى كل الـ + +912 +01:11:25,120 --> 01:11:31,160 +energy اللي هي الـ delta E اتحولت لـ إيه؟ لهيت يبقى + +913 +01:11:31,160 --> 01:11:38,020 +الـ delta E بتساوي Q زائد W و W صفر ما صار في عندي أي + +914 +01:11:38,020 --> 01:11:42,820 +شغل فيش عندي أي شغل فكل المسافة هذه عبارة عن إيه + +915 +01:11:42,820 --> 01:11:49,520 +اتحولت من charged لـ discharged عن طريق فقد الحرارة + +916 +01:11:49,520 --> 01:11:55,700 +فقط طيب بقول خلينا نطلع على وسيلة ثانية لتفريغ + +917 +01:11:55,700 --> 01:12:00,760 +البطارية جالب الله خلينا نشغل فيها هواية الهواية + +918 +01:12:00,760 --> 01:12:07,340 +أثناء شغلها تعمل تعمل شغل شغل وفي نفس الوقت لو + +919 +01:12:07,340 --> 01:12:10,280 +حطيتي يدك على الموتور من ورا إيش بتلاقيه؟ سخن + +920 +01:12:10,280 --> 01:12:14,460 +شوية فهي تورك بما أن الـ delta E بتساوي + +921 +01:12:17,620 --> 01:12:24,500 +الـ Q زي الـ W جهاز الـ Heat Org من هنا بفهم أن + +922 +01:12:24,500 --> 01:12:28,640 +الـ Delta A الـ Charge Battery لـ الـ Discharge + +923 +01:12:28,640 --> 01:12:34,340 +Battery هذه ثابتة هذه دالة حالة لكن الـ Q و الـ W + +924 +01:12:34,340 --> 01:12:38,620 +ما همّش دوال حالة ليه؟ لأنه والله لو كانت دالة + +925 +01:12:38,620 --> 01:12:42,720 +حالة كان الـ Q بتساوي هذه كلها Q بينما هي انقسمت + +926 +01:12:42,720 --> 01:12:48,800 +الـ Q انقسمت لـ W و انقسمت لـ Heat فالـ Q عندي و الـ W + +927 +01:12:48,800 --> 01:12:53,020 +ما هوش .. ما همّش ده بالحالة .. ليه؟ لأنه بيتوقف + +928 +01:12:53,020 --> 01:12:56,200 +يعني على كيف أنا بدي أفرغ البطارية والله بدي أفرغ + +929 +01:12:56,200 --> 01:13:01,480 +البطارية بإني أعمل شغل .. بعمل شغل و بطلع شوية + +930 +01:13:01,480 --> 01:13:04,680 +heat ممكن .. بدي أفرغ البطارية مثلاً يعتبروا + +931 +01:13:04,680 --> 01:13:07,700 +البطارية حاطيتها في .. إيش بيسموه؟ في flashlight + +932 +01:13:08,880 --> 01:13:12,660 +الـ Flashlight لما أنا أشغله البطارية برضه كمان + +933 +01:13:12,660 --> 01:13:17,280 +بتعطيني حرارة لأنه بيسخن و بتعطيني ضوء فاتحول لإيه + +934 +01:13:17,280 --> 01:13:21,520 + لأنواع مختلفة من الطاقة فبالتالي عند الـ Delta E + +935 +01:13:21,520 --> 01:13:26,680 +تعتبر دالة حالة تتوقف فقط على الـ initial state و + +936 +01:13:26,680 --> 01:13:31,700 +الـ final state لا تتوقف على الطريق هل عملتها عن + +937 +01:13:31,700 --> 01:13:37,580 +طريق كله Heat ولا كله Heat شغل ولا كله شغل عند الـ + +938 +01:13:37,580 --> 01:13:46,760 +Delta A هي عبارة عن دالة حالة بينما الـ + +939 +01:13:46,760 --> 01:13:52,280 +Q والـ W لا تعتبر دوال حالة وإن كان مجموعهما يعتبر + +940 +01:13:52,280 --> 01:13:54,720 +دالة حالة لأنه هو الـ Delta A + +941 +01:14:00,650 --> 01:14:06,290 +بنطلع أيضاً على دالة جديدة تعتبر دالة حالة بنتكلم + +942 +01:14:06,290 --> 01:14:09,350 +من مقدمة صغيرة عنها، في عندي حاجة بيقولها enthalpy + +943 +01:14:09,350 --> 01:14:15,470 +enthalpy جاية من الـ Greek يعني to warm يعني + +944 +01:14:15,470 --> 01:14:20,410 +enthalpy، إحنا في اللغة العربية يعني بنحب نترجم + +945 +01:14:20,410 --> 01:14:24,340 +علينا الـ heat content heat content يعني أو الـ + +946 +01:14:24,340 --> 01:14:28,880 +enthalpy to warm معناته enthalpy أو to warm بقول + +947 +01:14:28,880 --> 01:14:35,780 +إحنا ممكن نعمل combination ما بين أو وجدنا أنه لو + +948 +01:14:35,780 --> 01:14:40,000 +عملنا combination ما بين الـ internal energy و الـ + +949 +01:14:40,000 --> 01:14:44,140 +pressure و الـ volume ممكن نحصل على دالة حالة جديدة + +950 +01:14:44,140 --> 01:14:50,600 +اسمها H أو الـ enthalpy بحيث أن الـ H بتساوي E زائد + +951 +01:14:50,600 --> 01:14:55,200 +PV الـ H اللي هي دالة حالة جديدة بتعبر عن الـ Heat + +952 +01:14:55,200 --> 01:15:01,220 +content في الـ system H بتساوي E زائد PV وحنفُرجيكم + +953 +01:15:01,220 --> 01:15:06,300 +ليش الـ H ليش عملنا هيك؟ ليش حبينا أن نعرف دالة + +954 +01:15:06,300 --> 01:15:12,500 +حالة جديدة اسمها H؟ قال لأنه سهل جداً بعد شوية + +955 +01:15:12,500 --> 01:15:18,080 +حنشوف سهل جداً أنه نحسبها سهل جداً أنه نحسب الـ Heat + +956 +01:15:18,080 --> 01:15:28,600 +content باستخدامها فعلى سبيل المثال خلي تفاعل زي + +957 +01:15:28,600 --> 01:15:36,400 +الـ Zinc بتفاعل مع الـ HCl وإحنا شفنا في سلسلة + +958 +01:15:36,400 --> 01:15:41,400 +النشاط إنه الـ Zinc فوق الـ هيدروجين فبالتالي + +959 +01:15:41,400 --> 01:15:45,760 +بتفاعل مع الـ H Plus أو الـ HCl بعطينا Zinc + +960 +01:15:48,330 --> 01:15:53,990 +2 plus زائد H2 يعني عند الحجم بدّه يزيد يعني لو + +961 +01:15:53,990 --> 01:15:58,370 +جينا طلعناه هان عند الـ zinc وهي هان الـ HCl لو + +962 +01:15:58,370 --> 01:16:03,250 +اجيت لفيت هذا شوية بيحصل أن الـ zinc بيسحل وين داخل + +963 +01:16:03,250 --> 01:16:09,090 +الـ flask فبيتفاعل كويس فإيش بيتكون؟ بيتكون عند حجم + +964 +01:16:09,090 --> 01:16:12,270 +اللي هو الـ H2 فمعنى الكلام الـ system إيش بدّه يعمل؟ + +965 +01:16:13,330 --> 01:16:17,690 +هو اللي بدّه يعمل pushing للـ piston اللي موجود + +966 +01:16:17,690 --> 01:16:20,950 +وبالتالي الحجم بدّه يزيد يعني هو اللي بدّه يعمل work + +967 +01:16:20,950 --> 01:16:27,530 +هو اللي بدّه يعمل work فعندي الـ work هذا بنسميه + +968 +01:16:27,530 --> 01:16:33,090 +expansion work مين اللي عامل الـ work؟ الـ system + +969 +01:16:33,090 --> 01:16:36,150 +إذا الـ work إيه إيش ماله؟ negative و بقدر أقوله الـ + +970 +01:16:36,150 --> 01:16:40,140 +W بتساوي minus P delta V الـ W بتساوي minus P delta + +971 +01:16:40,140 --> 01:16:44,020 +V الـ delta V طبعاً اللي هي الـ V final minus الـ V + +972 +01:16:44,020 --> 01:16:52,180 +initial فلكن عندي الـ الـ الـ W هو P delta V بس a + +973 +01:16:52,180 --> 01:16:57,900 + بالسالب لأنه عندي أنا الـ الـ الـ work هو عبارة عن PV + +974 +01:16:57,900 --> 01:17:02,970 +work الـ work اللي عندي هو عبارة عن PV work بالعكس + +975 +01:17:02,970 --> 01:17:08,170 +لو كان الـ system بدل ما يعطيني gas هو كان gas + +976 +01:17:08,170 --> 01:17:12,890 +و أعطاني solid فال .. آه فبلاحظ أن الـ work بدّه يكون + +977 +01:17:12,890 --> 01:17:15,990 +positive عكسه ليه؟ لأنه بدّه الـ surroundings هي + +978 +01:17:15,990 --> 01:17:22,790 +اللي تعمل work على الـ system فأنا عندي الـ H بتساوي + +979 +01:17:22,790 --> 01:17:30,680 +E زائد PV طب لو أخذنا الـ delta هو الـ ΔH يساوي الـ + +980 +01:17:30,680 --> 01:17:36,840 +D للـ E زائد الـ PV أو Δ E زائد P Δ V زائد V Δ P + +981 +01:17:36,840 --> 01:17:40,960 +لكن إحنا أغلب شغلنا في المختبرات at constant + +982 +01:17:40,960 --> 01:17:46,600 +pressure يعني الـ Delta P إيه؟ الـ Delta P تعتبر + +983 +01:17:46,600 --> 01:17:50,840 +ثابت يعني صفر، Delta P تغير صفر، فبالتالي الـ Delta + +984 +01:17:50,840 --> 01:17:55,100 +H بتساوي Delta + +985 +01:17:55,100 --> 01:18:03,110 +E زائد P Delta V، يبقى هذه هي معادلة الانثالبي إذا + +986 +01:18:03,110 --> 01:18:07,270 +الله راضي، الحصة الجاية بنبدأ منها علشان نعدي + +987 +01:18:07,270 --> 01:18:12,010 +لمفهوم واسع جدا كيف نحسب الـ heat transfer أو الـ + +988 +01:18:12,010 --> 01:18:17,740 +heat change في الـ system، نتطلع على كيفية حساب الـ + +989 +01:18:17,740 --> 01:18:21,680 +Delta H اللي هي بتعبر تعبيرًا صادقًا، في البداية + +990 +01:18:21,680 --> 01:18:25,900 +هنثبت أن هي عبارة عن الـ heat change، وهنشوف إيش + +991 +01:18:25,900 --> 01:18:29,440 +طرق حساب الـ heat change إذا الله راد الحصة + +992 +01:18:29,440 --> 01:18:29,800 +الجاية diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/wLZu0_CAZmI_postprocess.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/wLZu0_CAZmI_postprocess.srt new file mode 100644 index 0000000000000000000000000000000000000000..66ea3241de36bae4c1b3728eec687178625ffb2c --- /dev/null +++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/wLZu0_CAZmI_postprocess.srt @@ -0,0 +1,3968 @@ +1 +00:00:21,920 --> 00:00:25,160 +بسم الله الرحمن الرحيم إذا الله راضي اليوم نبدأ في + +2 +00:00:25,160 --> 00:00:28,660 +chapter جديد نتكلم فيه عن ال thermochemistry أو + +3 +00:00:28,660 --> 00:00:33,880 +الكيمياق الحرارية المقصود بالكيمياق الحرارية يعني + +4 +00:00:33,880 --> 00:00:38,440 +هي التفاعلات الكيميائية أو حتى الفيزيائية اللي + +5 +00:00:38,440 --> 00:00:46,070 +بيتم خلالها انتقال حرارةفبالتالي يعني ممكن احنا في + +6 +00:00:46,070 --> 00:00:50,650 +البداية لو اتكلمنا عن طبيعة الطاقة ايش هي ال + +7 +00:00:50,650 --> 00:00:56,250 +energy بنقول يمكن لما نتكلم عن طبيعة المادة بنقول + +8 +00:00:56,250 --> 00:01:01,130 +سهل جدا انه نتخيلها ليه؟ لأن المادة ممكن انه نشعر + +9 +00:01:01,130 --> 00:01:09,470 +فيها نلمسها مثلا نشوفها بينما الطاقة كيعني concept + +10 +00:01:09,470 --> 00:01:14,500 +كمفهوممش مباشر إنه نتحدث عنها لأنه لا نستطيع أنه + +11 +00:01:14,500 --> 00:01:21,300 +يعني نلمسها يعني بالكتير بس أنه نتحدث عن آثارها + +12 +00:01:21,300 --> 00:01:28,960 +فمش سهل زي ال matter يعني أو المواد بحد ذاتها ال + +13 +00:01:28,960 --> 00:01:34,660 +energy بشكل عام يمكن تعريفها على إنها ال capacity + +14 +00:01:34,660 --> 00:01:39,070 +to do work or transfer itالـ Energy يمكن تعريفها + +15 +00:01:39,070 --> 00:01:48,350 +على إنها القدرة على عمل شغل أو نقل حرارةكويس؟ وهذا + +16 +00:01:48,350 --> 00:01:51,570 +الكلام معناته عشان انا بدي افهم energy وبيتكلم عن + +17 +00:01:51,570 --> 00:01:54,590 +الطاقة بشكل عام وبيتكلم عن ال thermochemistry يبقى + +18 +00:01:54,590 --> 00:01:59,890 +لازم افهم مفهوم الشغل ال work ومفهوم الحرارة من + +19 +00:01:59,890 --> 00:02:04,910 +وجهة نظر الكيميا من وجهة نظر الكيميا لأنه انا عندى + +20 +00:02:04,910 --> 00:02:08,070 +في الفيزيا ممكن احنا نعرف الشغل زي ما هو معروف + +21 +00:02:08,600 --> 00:02:11,720 +الشغل اللي هو ال work بده يساوي ال force times + +22 +00:02:11,720 --> 00:02:18,520 +distance هذا التعريف الفيزيائي عشان هيك بنقول + +23 +00:02:18,520 --> 00:02:21,240 +والله ال work is the energy used to cause an + +24 +00:02:21,240 --> 00:02:26,910 +object to move against a forceهذا التعريف فيزيائي + +25 +00:02:26,910 --> 00:02:29,970 +لكن أنا في الكيميا يعني إيش هل بدي أنقل ذرع من + +26 +00:02:29,970 --> 00:02:33,230 +مكان إلى أزوجها شوية لقدام مثلا؟ لأ مش هذا هو + +27 +00:02:33,230 --> 00:02:36,970 +التعريف اللي بيهمني كتير في الكيميا فالكيميا لأ + +28 +00:02:36,970 --> 00:02:42,550 +هنشوف بالظبط عن إيش بنتحدث لما نتكلم عن ال work ال + +29 +00:02:42,550 --> 00:02:47,110 +heat تعريفها يمكن مفهوم heat is the energy used to + +30 +00:02:47,110 --> 00:02:50,590 +cause the temperature of an object to increase + +31 +00:02:51,500 --> 00:02:59,520 +مفهوم يعني هي عبارة عن الطاقة اللي بتسبب زيادة في + +32 +00:02:59,520 --> 00:03:04,920 +درجة حرارة أي object بالطبع الكيميا زي ما احنا + +33 +00:03:04,920 --> 00:03:08,960 +عارفين بتتحدث عن ال matter تتحدث عن المواد بشكل + +34 +00:03:08,960 --> 00:03:17,510 +عامالكيميا أيضًا بتتحدث عن الحاجات المصاحبة لهذه + +35 +00:03:17,510 --> 00:03:20,470 +العملية للمادة، تغير المادة، التفاعلات الكيميائية، + +36 +00:03:20,470 --> 00:03:24,210 +طب إيش بيصاحبها؟ نعم في كثير من الأحيان يصاحب + +37 +00:03:24,210 --> 00:03:28,570 +التغيرات الكيميائية وحتى الفيزيائيةتغير في ال + +38 +00:03:28,570 --> 00:03:32,450 +energy وبالتالي مبرر إلينا أن ندرس ال energy لأن + +39 +00:03:32,450 --> 00:03:34,990 +العمليات اللي احنا بدرسها التفاعلات الكيميائية + +40 +00:03:34,990 --> 00:03:39,110 +العمليات الفيزيائية اللي بتحصل للمواد الكيميائية + +41 +00:03:39,110 --> 00:03:44,150 +هذه أيضا يصاحبها تغير في الطاقة فمهمتنا في هذا ال + +42 +00:03:44,150 --> 00:03:49,510 +chapter أن نحاول يعني نسلط الضوء مبدئياعلى الطاقة + +43 +00:03:49,510 --> 00:03:52,350 +لأنه هيجييلنا بعد هيك زي ما هنشوف chapter تاني + +44 +00:03:52,350 --> 00:03:55,410 +بيكمل هذا ال chapter نتحدث فيه عن ال + +45 +00:03:55,410 --> 00:04:00,510 +thermodynamics الديناميكا الحرارية شيء بيكمل مفهوم + +46 +00:04:00,510 --> 00:04:04,910 +الطاقة عندنا ومفهوم ال thermochemistry فال + +47 +00:04:04,910 --> 00:04:08,150 +thermochemistry بندرس فيه ال energy changes + +48 +00:04:08,150 --> 00:04:12,150 +accompanying some physical and chemical changes أو + +49 +00:04:12,150 --> 00:04:19,680 +processes في مفهوم أوسع منهومكمل له اللي هو ايه ال + +50 +00:04:19,680 --> 00:04:22,700 +thermodynamics ال thermodynamics هندرسه في شبتر + +51 +00:04:22,700 --> 00:04:26,640 +مستقل آخر شبتر معانا كان بود يكون الشبترين ورا بعض + +52 +00:04:26,640 --> 00:04:31,460 +لكن احنا بنمشي بترتيب الشباتر في الكتاب فهنذكره + +53 +00:04:31,460 --> 00:04:36,740 +آخر شبتر لكن هو شبتر يعتبر مكمل لل thermochemistry + +54 +00:04:36,740 --> 00:04:41,920 +ومتمم له وموضح له broader concept مفهوم أوسع لل + +55 +00:04:41,920 --> 00:04:46,150 +energy فهنشوف هذا الكلام اللي هندرسهأخر chapter + +56 +00:04:46,150 --> 00:04:51,170 +معانا صور ال energy اللي احنا بنعرفها ال energy + +57 +00:04:51,170 --> 00:04:54,730 +والله ممكن تكون kinetic energy وهذه ال kinetic + +58 +00:04:54,730 --> 00:05:01,770 +energy هي ال energy of motion طاقة الحركية طبعا + +59 +00:05:01,770 --> 00:05:06,750 +الجزيئات وال atoms لها طاقة حركة لشك لأن طاقة + +60 +00:05:06,750 --> 00:05:13,910 +الحركة تعرف بإنها نص Mv² نص M اللي هي ال massV + +61 +00:05:13,910 --> 00:05:17,830 +التي هي السرعة squared والذرات لا شك أنه في إلها + +62 +00:05:17,830 --> 00:05:22,550 +mass وفي إلها سرعة تتحرك فبالتالي إلها kinetic + +63 +00:05:22,550 --> 00:05:26,770 +energy بنلاحظ إن ال kinetic energy تمثب ترديا مع + +64 +00:05:26,770 --> 00:05:30,630 +ال mass وتتمثب ترديا مع ال V التي هي السرعة لكن ال + +65 +00:05:30,630 --> 00:05:36,430 +VA squared فال kinetic energy تزيد بزيادة ال mass + +66 +00:05:36,430 --> 00:05:42,970 +وتزيد أيضا بزيادة السرعةلكن كما قلت يعني احنا + +67 +00:05:42,970 --> 00:05:48,490 +ماتتكلمش عن .. خليني اقول physics احنا بنتكلم عن + +68 +00:05:48,490 --> 00:05:52,230 +كيميا وبالتالي حديثي عن ال mass والسرعة بتعلق بال + +69 +00:05:52,230 --> 00:05:55,730 +atoms و ال molecules بتعلق ال mass لل atoms و ال + +70 +00:05:55,730 --> 00:06:00,330 +mass لل molecules مش اي حاجة تانية مش والله انا + +71 +00:06:00,330 --> 00:06:05,110 +عندي object مثلا بدي ارميه هتلاقي أمثلة زي هي في + +72 +00:06:05,110 --> 00:06:08,720 +الكتاب لكن مش هي المهمة بالنسبة لنابدي أرمي مثلا + +73 +00:06:08,720 --> 00:06:11,540 +بسرعة معينة طب و إيه الكتلة معينة؟ طب كداش ال + +74 +00:06:11,540 --> 00:06:13,920 +kinetic energy اللي بده ياخدها؟ مثلا هذا كلام + +75 +00:06:13,920 --> 00:06:18,560 +موجود لكن هذا فيزيا مش كيميا كويسة الكيميا بتتعلق + +76 +00:06:18,560 --> 00:06:21,620 +بإيه؟ بال atoms بال molecules بال molecular + +77 +00:06:21,620 --> 00:06:27,820 +species ions غيرها كل هذا الكلام في الكيميا عندنا + +78 +00:06:27,820 --> 00:06:31,620 +لكن فيزيائيا نعم ممكن نقول والله أي إش بيتحرك و + +79 +00:06:31,620 --> 00:06:35,160 +إيه الكتلة فيه إيه ال kinetic؟Energy وحنشوف كمان + +80 +00:06:35,160 --> 00:06:39,800 +التوسع على هذا المفهوم بعد شوية بالاضافة لـ + +81 +00:06:39,800 --> 00:06:43,720 +Kinetic Energy في عندي form من ال energy مهم جدا + +82 +00:06:43,720 --> 00:06:47,820 +جدا جدا اللي هو ال potential energy وال potential + +83 +00:06:47,820 --> 00:06:52,590 +energy هي عبارة عن طاقة كامنة أو طاقة مختزنةطاقة + +84 +00:06:52,590 --> 00:06:56,650 +مختزنة أو طاقة كاملة بتتوقف على إيه؟ إذا كنا نقول + +85 +00:06:56,650 --> 00:07:00,310 +الله الكائن ذي ال energy هي ال mass والسرعة طب ال + +86 +00:07:00,310 --> 00:07:02,670 +potential energy بتتوقف على إيه؟ قال هو الله + +87 +00:07:02,670 --> 00:07:09,160 +بتتوقف على موضعالجسم و ال composition تبعه و + +88 +00:07:09,160 --> 00:07:12,420 +موضوعه بالنسبة للأجسام التانية فيما يتعلق بال + +89 +00:07:12,420 --> 00:07:17,680 +attractions و ال repulsions يعني مثلا انا عندي هذا + +90 +00:07:17,680 --> 00:07:25,510 +الجلام فيه potential energy هو في الموضوع هذابدو + +91 +00:07:25,510 --> 00:07:30,190 +يوجع يعني بدو يفقد جزء من ال potential energy + +92 +00:07:30,190 --> 00:07:34,130 +تبعته صحيح هذا الكلام بحسب .. لإيه؟ لأن في عندي + +93 +00:07:34,130 --> 00:07:39,010 +attraction مع القوة الجاذبية فهذا وضع طبيعي جدا + +94 +00:07:39,010 --> 00:07:44,330 +لكن كمان مرة بقدر اقول انا انه ال .. انا مش مهتم + +95 +00:07:44,330 --> 00:07:48,410 +كتير بالجاذبية في ال molecules و ال atomsأنا مش + +96 +00:07:48,410 --> 00:07:54,150 +مهتم كتير، أنا بقول أنا مهتم أكتر فيما يتعلق بـ.. + +97 +00:07:54,150 --> 00:07:56,850 +هي ليش جاذبية؟ جال attraction طب أنا عندي ال + +98 +00:07:56,850 --> 00:07:59,290 +attraction و ال repulsion فيما يتعلق بال molecular + +99 +00:07:59,290 --> 00:08:04,950 +species يتعلق بالشحنات، مش بالإيه، بإن الله يعني + +100 +00:08:04,950 --> 00:08:07,410 +جاذبية و ما جاذبية، لأ الجاذبية تأثيرها very + +101 +00:08:07,410 --> 00:08:11,250 +marginal، هامش للغاية في الكيميا، مش كتير بتهمني، + +102 +00:08:11,250 --> 00:08:15,300 +اللي بيهمني إيه؟اللي هي قوة التجاذب والتنافر بين + +103 +00:08:15,300 --> 00:08:19,140 +الـmolecular species مثلا أيونات موجبة، أيونات + +104 +00:08:19,140 --> 00:08:25,040 +سالبة، إلكترونات، بروتونات، بروتونات مع بعض، + +105 +00:08:25,040 --> 00:08:29,480 +إلكترونات مع بعض، أيونات موجبة مع بعض، أيونات + +106 +00:08:29,480 --> 00:08:33,120 +سالبة مع بعض، هذا كله بينشأ عنه potential energy + +107 +00:08:33,120 --> 00:08:35,680 +معينة، فال potential energy اللي متحدث عنها، بدي + +108 +00:08:35,680 --> 00:08:38,900 +أفكر بحاجتين، زي ما ال kinetic energy بفكر + +109 +00:08:38,900 --> 00:08:41,780 +بحاجتين، kinetic energy بفكر بالmass و ال velocity + +110 +00:08:42,360 --> 00:08:45,460 +الـ Potential Energy بدي أدور على الـ Composition + +111 +00:08:45,460 --> 00:08:50,580 +و الـ Position الـ Composition و الـ Position هدول + +112 +00:08:50,580 --> 00:08:53,640 +بيأثروا على إيه؟ على الـ Stored Energy و بيعطوها + +113 +00:08:53,640 --> 00:08:58,680 +قيمة الطاقة اللي هي الـ Potential Energy يمكن أن + +114 +00:08:58,680 --> 00:09:03,550 +تتحول إلى Kinetic Energyوالعكس، ممكن اتحول، يعني + +115 +00:09:03,550 --> 00:09:08,830 +في عندي interconversion للطاقة، فمثلا هذا الجلم، + +116 +00:09:08,830 --> 00:09:11,430 +قلت أنا هايني أعمله هيك، إيه له potential energy؟ + +117 +00:09:11,430 --> 00:09:16,060 +لكن بما أنه ثابت، جداش ال kinetic energy سبعته؟سفر + +118 +00:09:16,060 --> 00:09:19,360 +لكن لو سبته ال potential energy عامال بتجلب و ال + +119 +00:09:19,360 --> 00:09:22,700 +kinetic energy بتزيد لما نوصل هان صار عندي ال .. + +120 +00:09:22,700 --> 00:09:26,020 +صار عندي ال kinetic energy له صفر و هو أخد ممكن + +121 +00:09:26,020 --> 00:09:30,180 +نقول يعني potential energy جديدة إذا كان والله + +122 +00:09:30,180 --> 00:09:33,140 +يقولنا بالنسبة للأرض فاه هو يح .. إله لسه + +123 +00:09:33,140 --> 00:09:35,840 +potential energy لأنه برضه كان بإمكانه يعمل + +124 +00:09:35,840 --> 00:09:36,940 +attraction مع الأرض + +125 +00:09:40,010 --> 00:09:43,170 +وإله potential energy فيما يتعلق بإيه؟ مفهوم آخر، + +126 +00:09:43,170 --> 00:09:46,630 +إنه والله لسه بعيد عن الأرض، لسه فيه كمان يعني، + +127 +00:09:46,630 --> 00:09:50,830 +فهذا .. أما هو لأ، لما يقف على الأرض يعني خلاص، + +128 +00:09:50,830 --> 00:09:53,490 +مابيدوش .. مابقدرش ينزل أكتر من هيك، فإله + +129 +00:09:53,490 --> 00:09:57,690 +potential energy إله صفر بمفهوم إيه؟ ال position، + +130 +00:09:57,690 --> 00:10:00,610 +لكن إلهو ككيميا بنقول إيه ال potential energy + +131 +00:10:00,610 --> 00:10:03,270 +بتعلق بال composition ال composition اللي هو ال + +132 +00:10:03,270 --> 00:10:07,770 +attractions وال repulsions لإيه للذرات والجزيئات + +133 +00:10:07,770 --> 00:10:15,130 +المكونة له فمثلا يعني المثال المشهور دائما انه لو + +134 +00:10:15,130 --> 00:10:23,210 +ان حد راكب بسكليتعلى طلّة وواجف وطلّة منحدرة + +135 +00:10:23,210 --> 00:10:27,550 +فبنقول بما أنه واجف فال potential energy له عالية + +136 +00:10:27,550 --> 00:10:31,850 +هي عبارة عن مجموعة لو قلنا ال masses ال mass لل + +137 +00:10:31,850 --> 00:10:37,130 +cyclist وال bicycleكويس لكن الـ kinetic energy صفر + +138 +00:10:37,130 --> 00:10:41,670 +لأنه واقف بينما هنا لما بدأ بنلاحظ أنه بيندفع ليه؟ + +139 +00:10:41,670 --> 00:10:45,850 +لأن ال potential energy مختزنة موجودة فبتتحول + +140 +00:10:45,850 --> 00:10:49,690 +لإيه؟ ل kinetic energy لما يوصل بنقول والله أه ال + +141 +00:10:49,690 --> 00:10:53,610 +potential energy باستمرار بتقل و ال kinetic energy + +142 +00:10:53,610 --> 00:10:59,650 +باستمرار بتزيد لغاية ما يوصل ل stop كويس فممكن + +143 +00:10:59,650 --> 00:11:00,670 +تحول + +144 +00:11:03,420 --> 00:11:06,500 +الإنرجي من one form to another form لكن بيطلع على + +145 +00:11:06,500 --> 00:11:08,960 +إن ال energy دائما على إنها كاين تيك و potential + +146 +00:11:08,960 --> 00:11:12,580 +الكاين تيك اللي هيدعو بال mass و ال velocity و ال + +147 +00:11:12,580 --> 00:11:16,140 +potential اللي هيدعو بال position و ال composition + +148 +00:11:16,140 --> 00:11:23,890 +خلاصطب نتطلع الآن على في ما يتعلق بالذرات + +149 +00:11:23,890 --> 00:11:28,330 +والجزائيات تبعاتنا و ال chemistry فبنقول بما أنه + +150 +00:11:28,330 --> 00:11:31,110 +لما أتكلم عن ال potential energy لهذه ال species + +151 +00:11:31,110 --> 00:11:35,670 +أنا بتكلم عن ال attractions و ال repulsion لل ions + +152 +00:11:35,670 --> 00:11:39,470 +و ال electrons و ال protons كويسة ال nuclear + +153 +00:11:39,470 --> 00:11:43,950 +charge فبالتالي يعني أنا عندي ال potential energy + +154 +00:11:43,950 --> 00:11:46,870 +هي أبعار عن electrostatic potential energy + +155 +00:11:46,870 --> 00:11:50,350 +electrostaticالتي نتجة عن الـ Electrical Charges، + +156 +00:11:50,350 --> 00:11:53,870 +فبقولها Electrostatic Potential Energy لأنه لـ + +157 +00:11:53,870 --> 00:11:57,770 +Gravitational Forces، لأ يعني إذا كان لعبة فبتلعب + +158 +00:11:57,770 --> 00:12:01,450 +نجليجياب رول، Very Marginal، زي ما قلنا هامشية جدا + +159 +00:12:01,450 --> 00:12:05,830 +في ما يتعلق بالإيه بال Chemical Systems، لكن اللي + +160 +00:12:07,800 --> 00:12:12,380 +اللي بيأثر على ال potential energy في ال chemical + +161 +00:12:12,380 --> 00:12:16,100 +species جاز ال electrical charges هذي تعتبر طبعا + +162 +00:12:16,100 --> 00:12:23,200 +much more important لو في عندي شحنتين Q1 و Q2 + +163 +00:12:23,200 --> 00:12:26,100 +فبنقدر أقول والله ال electrostatic potential + +164 +00:12:26,100 --> 00:12:29,920 +energy ساوي ثابت الشحنة الأولى في الشحنة التانية + +165 +00:12:29,920 --> 00:12:34,180 +على ال D ممكن الشحنتين يكونوا إيه موجبتين أو + +166 +00:12:34,180 --> 00:12:37,790 +سالبتين يعني بينهم تنافر نفس الشيءوممكن يكونوا + +167 +00:12:37,790 --> 00:12:43,390 +شحنتين مختلفتين وبتالي بينهم تجاذب لكن المهم عندي + +168 +00:12:43,390 --> 00:12:46,490 +أن الـElectrostatic Potential Energy تتناسب ترضيا + +169 +00:12:46,490 --> 00:12:51,770 +مع الشحنات على المسافة بينهم اللي هي D المسافة بين + +170 +00:12:51,770 --> 00:12:57,040 +الشحنتينلو جينا تخيلنا مع بعض في عندي شحنتين like + +171 +00:12:57,040 --> 00:13:00,700 +charges إذا بينهم إيه؟ repulsion يبقى عندي very + +172 +00:13:00,700 --> 00:13:04,580 +high electrostatic potential energy لكن كل ما + +173 +00:13:04,580 --> 00:13:06,760 +حاولنا نبعد هدول التنتين عن بعض ال potential + +174 +00:13:06,760 --> 00:13:09,220 +energy إيش بتجعلها؟ بتقل، بتقل، بتقل، بتقل، بتقل، + +175 +00:13:09,220 --> 00:13:10,840 +بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، + +176 +00:13:10,840 --> 00:13:11,080 +بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، + +177 +00:13:11,080 --> 00:13:13,580 +بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، + +178 +00:13:13,580 --> 00:13:16,460 +بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، بتقل، + +179 +00:13:16,460 --> 00:13:19,460 +بتق + +180 +00:13:23,520 --> 00:13:27,100 +فطب لو حلنا نبعدهم معناه كلمة potential energy + +181 +00:13:27,100 --> 00:13:32,480 +بتزيد بتزيد بتزيد لغاية ما توصل برضه الصفر لهدب + +182 +00:13:32,480 --> 00:13:35,480 +السالب لغاية ما توصل يعني هيك بتزيد لغاية ما توصل + +183 +00:13:35,480 --> 00:13:39,000 +الصفر وكأنه ممكن نعرف احنا ان ال zero + +184 +00:13:39,000 --> 00:13:43,500 +electrostatic potential energy هي لما الشحنات تكون + +185 +00:13:43,500 --> 00:13:47,450 +بعيدةمسافة مقدارها مالة نهائية عن بعض البعض سواء + +186 +00:13:47,450 --> 00:13:53,470 +كانت liked charges او different charges فممكن نعرف + +187 +00:13:53,470 --> 00:13:57,710 +الـ zero electrostatic potential energy على انها + +188 +00:13:57,710 --> 00:14:01,990 +هي ال potential energy عندما تكون الشحنات بعيدة عن + +189 +00:14:01,990 --> 00:14:07,770 +بعض البعض مسافة مقدارها infinity وبالتالي بنقدر + +190 +00:14:07,770 --> 00:14:12,080 +نقول انهالـ Electrostatic Potential Energy بتتوقف + +191 +00:14:12,080 --> 00:14:18,640 +على الشحنات بتزيد لما الشحنات تكون من نفس النوع + +192 +00:14:18,640 --> 00:14:23,760 +موجبة أو سالبة بتقل لما الشحنات تكون مختلفة لكن كل + +193 +00:14:23,760 --> 00:14:28,100 +ما ابعدنا الشحنات عن بعض بنلاحظ إن إذا كان الشحنات + +194 +00:14:28,100 --> 00:14:32,860 +متشابهة هذا وضعي كويس فالـ Potential Energy بتقل + +195 +00:14:32,860 --> 00:14:35,920 +إذا كان الشحنات متشابهة بتقل لما نبعدها عن بعض إذا + +196 +00:14:35,920 --> 00:14:41,230 +كانت مختلفة بتزيدوبالتالي التنتين بيوصلوا إيه؟ + +197 +00:14:41,230 --> 00:14:43,970 +للصفر لأن التعريف الـElectrostatic Potential + +198 +00:14:43,970 --> 00:14:51,850 +Energy يعني بتاخد قيمة عادة سالبة إذا كانت الشحنات + +199 +00:14:51,850 --> 00:14:57,810 +مختلفة وبتاخد قيمة موجبة إذا كانت الشحنات متشابهة + +200 +00:14:57,810 --> 00:15:03,010 +هذا convention بالنسبة لنا إيش وحتاج قياس الطاقة؟ + +201 +00:15:04,210 --> 00:15:07,670 +طبعا الجثة احنا بنقول الجول لكن زمان زي ما حناشوف + +202 +00:15:07,670 --> 00:15:11,930 +كانت ال calorie مش هيك كانت ال calorie طيب ال SI + +203 +00:15:11,930 --> 00:15:17,630 +unit لل energy هي الجول طبعا تلفظ جول ايش هو الجول + +204 +00:15:17,630 --> 00:15:20,290 +بالظبط يعني احنا خلينا نتخيل ان في عندنا mass + +205 +00:15:20,290 --> 00:15:24,670 +مقدرها 2 kilogram moving at a speed of one meter + +206 +00:15:24,670 --> 00:15:30,600 +per second بنقول انه هاديالكتلة اللى بتمشي اللى + +207 +00:15:30,600 --> 00:15:33,660 +وزنها 2 كيلو جرام وبتتحرك بسرعة 1 متر في الثانية + +208 +00:15:33,660 --> 00:15:38,080 +لو طبقنا ال E كايدة بسوا نص MV squared نصف 2 كيلو + +209 +00:15:38,080 --> 00:15:41,200 +جرام 1 متر على ثانية تربيع اللى هى السرعة جاء + +210 +00:15:41,200 --> 00:15:44,040 +بتعطينا 1 كيلو جرام متر تربيع ثانية تربيع على + +211 +00:15:44,040 --> 00:15:49,490 +ثانية تربيع هذا عبارة عن 1 جول اذابنقول إن هذا + +212 +00:15:49,490 --> 00:15:54,070 +الجسم اللي كتلته 2 كيلو جرام وبتحرك against a + +213 +00:15:54,070 --> 00:15:57,350 +force at a speed of one meter per second إله طاقة + +214 +00:15:57,350 --> 00:16:03,930 +مقدارها واحد جول طبعا احنا ممكن نعرف كمان إن + +215 +00:16:03,930 --> 00:16:08,470 +الواحد الجول هو عبارة عن work فال work عبارة عن + +216 +00:16:08,470 --> 00:16:12,370 +force في ال distanceفيمكن تعريفه فيزيائيا تعريف + +217 +00:16:12,370 --> 00:16:15,910 +حلو كتير بنقول a joule is the amount of work done + +218 +00:16:15,910 --> 00:16:20,510 +on a body by a one newton force لنيوتون واحد + +219 +00:16:20,510 --> 00:16:23,870 +كيلوجرام متر على ثانية تربيع فانا عندي force + +220 +00:16:23,870 --> 00:16:28,250 +مقدرها اي واحد نيوتون يعني واحد كيلوجرام متر على + +221 +00:16:28,250 --> 00:16:32,910 +ثانية تربيع that moves the body a distance of واحد + +222 +00:16:32,910 --> 00:16:36,540 +متر in the direction of the forceاللي بيحرك ال + +223 +00:16:36,540 --> 00:16:40,680 +إيه؟ الكتلة واحد متر فانا عندي ال distance واحد + +224 +00:16:40,680 --> 00:16:44,920 +متر ال .. واحد نيوتر فلو ضربتهم في بعض بحصل على + +225 +00:16:44,920 --> 00:16:48,400 +الشغل فالشغل بيطلع عندي واحد kilogram متر تربية + +226 +00:16:48,400 --> 00:16:54,400 +على ثالث يعني جول طبعا الجول هو ال SI unit لكن + +227 +00:16:54,400 --> 00:16:58,980 +قديما يعني أو traditionally كنا بنستخدم ال calorie + +228 +00:16:58,980 --> 00:17:03,460 +ال calorie اللي حاليا non SI unit ماهياش SI unit + +229 +00:17:05,170 --> 00:17:09,070 +بنقدر نقول إنه لازال للأسف، ومش فيه يعني للأسف + +230 +00:17:09,070 --> 00:17:13,930 +كتير، هقولكم ليش، لازال للأسف بعض الأرض ماما فيهم + +231 +00:17:13,930 --> 00:17:19,850 +الكيميا والـ Biology والزراعة، ال nutrition + +232 +00:17:19,850 --> 00:17:25,300 +وغيرها، تستخدم ال calorieاستخدم الـ calorie يمكن + +233 +00:17:25,300 --> 00:17:28,900 +يعني احنا ضروري انه نفهم ايش مفهوم ال calorie لانه + +234 +00:17:28,900 --> 00:17:32,060 +كل ال literature السابق قبل الاعتماد الجول على انه + +235 +00:17:32,060 --> 00:17:35,420 +والله ال SI unit كنا بنستخدم ال calorie فلازم نفهم + +236 +00:17:35,420 --> 00:17:39,940 +ايش ال calorie علشان نستفيد من الدراسات والنتائج + +237 +00:17:39,940 --> 00:17:46,700 +السابقة فلازم نفهم ايش مفهوم ال calorie وكمان ال + +238 +00:17:46,700 --> 00:17:49,740 +gate كمان لازم نعرف ايش مفهوم ال calorie لان بعض + +239 +00:17:49,740 --> 00:17:54,760 +الأنظمة المهمة لازالة بتستخدمهفالـ calorie بالنسبة + +240 +00:17:54,760 --> 00:17:58,480 +للجول او نقول ايش تعريف ال calorie قديما جال احنا + +241 +00:17:58,480 --> 00:18:01,560 +بنعرف ال calorie على ان ال amount of energy + +242 +00:18:01,560 --> 00:18:05,100 +required to rate the temperature of one gram of + +243 +00:18:05,100 --> 00:18:10,770 +water من 14.5 إلى 15.5 ليه؟ جال لأنه هيجي معنافي + +244 +00:18:10,770 --> 00:18:16,050 +المستقبل إن الـ specific heat بتتوقف قليلا على + +245 +00:18:16,050 --> 00:18:20,750 +درجة الحرارة عشان هيك لازم نقول عند أي درجة حرارة + +246 +00:18:20,750 --> 00:18:24,950 +فمن 14.5 ل 15.5 مش ضروري يعني نعرف هذا كده مش هيمر + +247 +00:18:24,950 --> 00:18:28,250 +معنا مرات تانية يعني فهو تعريف ال calorie هو + +248 +00:18:28,250 --> 00:18:30,930 +أبارعا كمية الطاقة اللي لازم نعرفها على درجة حرارة + +249 +00:18:31,570 --> 00:18:35,470 +1 جرام من المياه من 14.5 إلى 15.5 ديجريس C أو + +250 +00:18:35,470 --> 00:18:41,450 +كيلفين لأن ديجريس C هي نفسها فيما يتعلق بال value + +251 +00:18:41,450 --> 00:18:47,110 +ديجريس كيلفين لكن هالجيت عشان نعمل relation ما بين + +252 +00:18:47,110 --> 00:18:50,310 +الجول والكالوري لأن الجول هو ال SI unit وبدنا نقدر + +253 +00:18:50,310 --> 00:18:55,750 +نحول بين الإتنين بنقول إنه الكلوري 4.184 جول وH + +254 +00:18:55,750 --> 00:19:00,430 +بين جثين exactيعني بالظبط زي ما نقول المتر ميت + +255 +00:19:00,430 --> 00:19:06,650 +سانتي الفوت اتناشر انش exact value ماشي exact إلها + +256 +00:19:06,650 --> 00:19:13,310 +معنى مهم من ناحية يعني إيش مفهوم القيمة فهذه exact + +257 +00:19:14,920 --> 00:19:19,420 +طبعا في كمان في ما يتعلق بالوحدات الطاقة في عندي + +258 +00:19:19,420 --> 00:19:25,340 +ال nutritional calorie في ال nutrition في ال + +259 +00:19:25,340 --> 00:19:29,080 +nutrition التخضية وما شابه و الأكل عموما بيستخدموا + +260 +00:19:29,080 --> 00:19:31,440 +حاجة بيقولها nutritional calorie ال nutritional + +261 +00:19:31,440 --> 00:19:36,640 +calorie بالنسبة للرمز C كبيرة C كبيرة Cal Cal ال C + +262 +00:19:36,640 --> 00:19:40,460 +إيش مالها؟ Cal Calorie كبير جالة عبارة عن الف + +263 +00:19:40,460 --> 00:19:46,710 +calorie يعني واحد كيلو calorieماشي فهدف ايش + +264 +00:19:46,710 --> 00:19:49,870 +بيستخدموه في ال nutrition في ال food in general + +265 +00:19:49,870 --> 00:19:54,690 +يعني فلاحظوا انه لما تلاقيوا C capital معناته ايه + +266 +00:19:54,690 --> 00:19:59,810 +ألف ألف calorie طبعا في كمان وحدة تانية لقياس + +267 +00:19:59,810 --> 00:20:05,930 +الطاقة يعني مش هذكرها هان بالتفصيل لكن يمكن تسمع + +268 +00:20:05,930 --> 00:20:11,440 +عن ال BTU British Thermal Unitلو بدكم تشتريوا مثلا + +269 +00:20:11,440 --> 00:20:16,420 +مكيف او دفاية او كذا بتلاقي مبتوب عليها كذا مثلا + +270 +00:20:16,420 --> 00:20:22,160 +عشر تلاف BTU طب هي بتطلع طاقة جال ال BTU كل واحد + +271 +00:20:22,160 --> 00:20:27,000 +BTU ألف و خمسة و خمسين جول ألف و خمسة و خمسين جول + +272 +00:20:27,000 --> 00:20:34,660 +فال BTU برضه من هذه British Thermal Unit هذه تعريف + +273 +00:20:34,660 --> 00:20:39,660 +بريطاني وهي عبارة عن ايه؟ عبارة عن ال BTUهي عبارة + +274 +00:20:39,660 --> 00:20:43,600 +عن كمية الطاقة اللازمة لرفع درج حرارة الميه من + +275 +00:20:43,600 --> 00:20:46,040 +تلاتة و ستين فهرين هايت واحد جرام من الميه من + +276 +00:20:46,040 --> 00:20:48,580 +تلاتة و ستين فهرين هايت لاربعة و ستين فهرين هايت + +277 +00:20:48,580 --> 00:20:51,560 +حتى تعريفهم باستخدام الفهرين هايت لأن هذه الدرجة + +278 +00:20:51,560 --> 00:20:55,240 +المستخدمة درجة الحرارة او ال scale المستخدم عندهم + +279 +00:20:55,240 --> 00:20:59,820 +لكن مش هيمر معناه يعني ماعرفش في ال هل هيمر في بعض + +280 +00:20:59,820 --> 00:21:03,480 +الأسئلة و ده لأ لكن لو مري يعني تعرفوا ان ال Btu + +281 +00:21:03,480 --> 00:21:09,010 +عبارة عن الف و خمسين جولكيف ممكن نحسب ال energy + +282 +00:21:09,010 --> 00:21:14,290 +changes؟ حلو كتير و لا فيه أبسط من هيك نطلع يعني + +283 +00:21:14,290 --> 00:21:17,310 +مثلا كيناتك energy و نجيب الmass و نجيب ال + +284 +00:21:17,310 --> 00:21:21,170 +velocity نربع ال velocity نص Mv² مافيش فيها يعني + +285 +00:21:21,170 --> 00:21:27,870 +جدال و ال potential energy Q1 كيف Q1 Q2 على D برضه + +286 +00:21:27,870 --> 00:21:30,490 +يعني مباشر للغاية فنتطلع على هذا المثال مثل الواحد + +287 +00:21:30,490 --> 00:21:33,850 +بس أنا سيقلكم هان بيقول what's the kinetic energy + +288 +00:21:33,850 --> 00:21:38,960 +in joules؟of a أول حاجة an argon atom moving at a + +289 +00:21:38,960 --> 00:21:44,580 +speed of 650 meter per second في عندي ذرة argon + +290 +00:21:44,580 --> 00:21:50,380 +واحدة بتمشي بسرعة 650 متر على الثانية طب جديش ال + +291 +00:21:50,380 --> 00:21:54,980 +kinetic energy لها وهو ب a mole of argon مش ذرة + +292 +00:21:54,980 --> 00:21:59,260 +واحدة لأ mole of argon atoms moving at a speed of + +293 +00:21:59,260 --> 00:22:05,410 +650 meter per secondبقول انا لازم اذكر اوي يعني هو + +294 +00:22:05,410 --> 00:22:08,350 +هيعطيلنا ان ال AMU one point six six في عشرة او + +295 +00:22:08,350 --> 00:22:12,390 +سبعة و عشرين kilogram كل واحدة AMU واحدة AMU one + +296 +00:22:12,390 --> 00:22:15,150 +atomic mass unit قدش وزن التجارة ال one point six + +297 +00:22:15,150 --> 00:22:19,250 +six في عشرة او السالب سبعة و عشرين kilogram فلما + +298 +00:22:19,250 --> 00:22:23,580 +يكون عندي one argon atomقال والله الارجون اتوم من + +299 +00:22:23,580 --> 00:22:28,420 +الجدول الدوري 39.9 AMU طب كداش وزنة بتحول من AMU + +300 +00:22:28,420 --> 00:22:33,400 +لكيلو جرام؟ بتضرب كل واحدة AMU 1.66×10²×27 كيلو + +301 +00:22:33,400 --> 00:22:39,780 +جرام يعني معناته 39.9 AMU في 1.66×10²×27 كيلو جرام + +302 +00:22:39,780 --> 00:22:46,700 +تعطيني 6.6×10²×26 كيلو جرام هذه وزنة ال ايه الذرع + +303 +00:22:46,700 --> 00:22:51,760 +الواحدة من الارجون الان عند الماسوالـ Velocity + +304 +00:22:51,760 --> 00:22:57,580 +موجودة إذا نص في ال mass بالكلوجرام 650 متر على + +305 +00:22:57,580 --> 00:23:00,960 +الثانية اللي هي واحدة السرعة تربيع بطلع عندي 1.4 + +306 +00:23:00,960 --> 00:23:03,580 +فعشرة أقل سالف عشرين جول طبعا حاجة قليلة كتير + +307 +00:23:03,580 --> 00:23:06,820 +وبالمناسبة في الفيزيا عندهم واحدة أصغر من الجول + +308 +00:23:06,820 --> 00:23:10,960 +بيقولها ال urge ال urge عشرة أقل سالف سبعة من + +309 +00:23:10,960 --> 00:23:14,840 +الجول يعني حسب النظام فعندي كمية قليلة جدا من + +310 +00:23:14,840 --> 00:23:18,200 +الطاقة على أي حال على أي حال طيب + +311 +00:23:20,840 --> 00:23:24,620 +في بيه بيقول لي مول المول أنا عارف وزته وزته تسعة + +312 +00:23:24,620 --> 00:23:27,920 +وتلاتين وتسعة من عشرة جرام ليه؟ لأن المول هو عبارة + +313 +00:23:27,920 --> 00:23:31,440 +عن اجرام atomic weight او اجرام formula weight فال + +314 +00:23:31,440 --> 00:23:33,500 +formula تسعة وتلاتين وتسعة عزا من المول تسعة + +315 +00:23:33,500 --> 00:23:36,360 +وتلاتين وتسعة من عشرة جرام فتسعة وتلاتين وتسعة من + +316 +00:23:36,360 --> 00:23:39,820 +عشرة جرام بتحولها لكيلوجرام بتصير point O three + +317 +00:23:39,820 --> 00:23:43,940 +nine nine kilogram في نص في السرعة تربية بتطلع + +318 +00:23:43,940 --> 00:23:48,060 +تمانية واربعة كيلو جولتمنية واربعة من عشرة كيلو + +319 +00:23:48,060 --> 00:23:53,040 +جول فالحسابات يعني كتير كتير بسيطة بدنا نتذكر ان + +320 +00:23:53,040 --> 00:23:57,940 +الكاينة تكي نيرجي بتساوي نص ال mass في ال velocity + +321 +00:23:57,940 --> 00:24:01,560 +تربيع لكن ال mass بال kilogram و ال velocity متر + +322 +00:24:01,560 --> 00:24:06,540 +على الثانية كويس ال mass kilogram و ال velocity + +323 +00:24:06,540 --> 00:24:12,060 +متر على الثانية اتذكروا هذا من مفهوم الجول لأن + +324 +00:24:12,060 --> 00:24:20,380 +الجول هو ال energy فالجولكيلو جرام في متر تربية + +325 +00:24:20,380 --> 00:24:23,840 +على ثانية تربية فتذكروا هذه الوحدات لازم نذكرها + +326 +00:24:23,840 --> 00:24:34,900 +كيلو جرام و متر السرعة طيب الآن بنجي بنطلع على بعض + +327 +00:24:34,900 --> 00:24:38,620 +المفاهيم الأساسية اللي بدها تدخلنا فيه دراسة ال + +328 +00:24:38,620 --> 00:24:42,580 +energy changes في ال chemical systems بقول في عندي + +329 +00:24:42,580 --> 00:24:46,870 +تعريفلا حاجة بقولها system و حاجة بقولها + +330 +00:24:46,870 --> 00:24:51,590 +surroundings التعريف كتير بسيط قال الكون كله الكون + +331 +00:24:51,590 --> 00:24:56,630 +كله هذا كون متكامل الكون بينقسم إلى قسمين بينقسم + +332 +00:24:56,630 --> 00:25:00,090 +إلى ال system اللي أنا بدرسه و ال surroundings + +333 +00:25:00,090 --> 00:25:04,930 +اللي حواليه يفجأ الكون بينقسم لقسمين ال universe + +334 +00:25:04,930 --> 00:25:10,950 +بينقسم لقسمين ال system اللي أنا بدرسهوالإيه؟ + +335 +00:25:10,950 --> 00:25:13,050 +والأقوى ال surroundings اللي هي الشغلات المحيطة + +336 +00:25:13,050 --> 00:25:17,530 +فيه فال system هو الجزء من ال universe تحت الدراسة + +337 +00:25:17,530 --> 00:25:21,010 +اللي أنا بدرسه يعني لو بدي أدرس بني آدم مثلا يعني + +338 +00:25:21,010 --> 00:25:24,350 +كل ما يتعلق فيه بقول هذا البني آدم هو إيه؟ ال + +339 +00:25:24,350 --> 00:25:27,970 +system تبعي وكل ما يحيط فيه كل ما يحيط فيه هي + +340 +00:25:27,970 --> 00:25:31,390 +عبارة عن ال surroundings فال system زاد ال + +341 +00:25:31,390 --> 00:25:36,750 +surroundings هو ال universeتمام فال .. طبعا ال + +342 +00:25:36,750 --> 00:25:42,350 +system limited و well defined part limited و well + +343 +00:25:42,350 --> 00:25:46,410 +defined part limited يعني محدود معروف حدوده well + +344 +00:25:46,410 --> 00:25:49,790 +defined معروف حدوده بالظبط يعني معرف بالظبط ايش هو + +345 +00:25:49,790 --> 00:25:54,450 +فعندي انا في الكيميا اي chemical reaction عندي + +346 +00:25:54,450 --> 00:25:59,170 +مثلا يعني ممكن اقول هو system طب مع دهمثلا الوعى + +347 +00:25:59,170 --> 00:26:05,590 +اللى بحيط فيه و ورا الوعى و كل ما عدا .. انا عندى + +348 +00:26:05,590 --> 00:26:09,650 +reactance a و b بيعطونى c و d هذا ال system تبعى + +349 +00:26:09,650 --> 00:26:12,630 +كل ما عدا حتى الوعى اللى موجود فيه هذه يعتبر + +350 +00:26:12,630 --> 00:26:15,610 +surroundings فال system هو ال chemical reaction و + +351 +00:26:15,610 --> 00:26:20,610 +ال surroundings هي كل ما عدا ال chemical reaction + +352 +00:26:20,610 --> 00:26:26,490 +طيب + +353 +00:26:28,120 --> 00:26:33,220 +ال systems أحد تلت أنواع ال systems أحد تلت أنواع + +354 +00:26:33,220 --> 00:26:39,980 +يا إما بيكون open في البداية يا إما بيكون closed + +355 +00:26:39,980 --> 00:26:45,620 +يا بيكون isolated open system ال system بنقول عنه + +356 +00:26:45,620 --> 00:26:51,980 +open إذا كان بيتبادل ال energy و ال matter هاي + +357 +00:26:51,980 --> 00:26:56,300 +المكونات مكونات الحياة يعني energy و matterإذا كان + +358 +00:26:56,300 --> 00:26:59,960 +بيتبادل ال energy و ال matter مع ال surroundings + +359 +00:26:59,960 --> 00:27:06,720 +هذا open system بيتبادل ال what ال matter و ال + +360 +00:27:06,720 --> 00:27:11,380 +energy لو بدنا نتطلع على البحر و نقول هو open + +361 +00:27:11,380 --> 00:27:15,560 +system ليش open system لأ لأنه والله افترض انه سخن + +362 +00:27:15,560 --> 00:27:19,380 +فاعت الحرارة اللي فيه لل surroundings فى حد بيمنعه + +363 +00:27:19,380 --> 00:27:25,530 +مباشر فى احتكاك مباشرطيب يعني الميه اللى فيه + +364 +00:27:25,530 --> 00:27:31,330 +بتتبخر فهو بيعطي لل إيه؟ لل .. لل surroundings + +365 +00:27:31,330 --> 00:27:36,010 +كمان matter منه فهذا يعتبر open system حتى الإنسان + +366 +00:27:36,010 --> 00:27:40,230 +.. اتفضلي المادة .. المادة .. المادة المحسوسة يعني + +367 +00:27:42,090 --> 00:27:46,410 +بقول حتى الإنسان يعتبر open system و الله سخن + +368 +00:27:46,410 --> 00:27:52,590 +بيعطي الحرارة لإيه؟ لو مسك قطعة ثلج يعني مثلا + +369 +00:27:52,590 --> 00:27:57,610 +بيعطي الحرارة للثلج فهو ال energy بتنتقل و برضه لو + +370 +00:27:57,610 --> 00:28:02,390 +عرج بيعطي الميه لل .. اه فهذا open system بنعتبره + +371 +00:28:02,390 --> 00:28:06,610 +فال open system يعني مثال في عندي مثال عليه لو + +372 +00:28:06,610 --> 00:28:12,030 +إجيت سخنت وعى فيه ميهفالوعى طبعا بيسخن بيصير يعطي + +373 +00:28:12,030 --> 00:28:15,750 +الحرارة لل surroundings وأيضا بخار الميه بروح لل + +374 +00:28:15,750 --> 00:28:18,530 +surroundings فهذا open system هذا يعتبر open + +375 +00:28:18,530 --> 00:28:22,830 +system ممكن + +376 +00:28:22,830 --> 00:28:26,330 +نطلع على نوع تاني من ال systems نقوله closed + +377 +00:28:26,330 --> 00:28:30,680 +systemالـ class system طلعوا معايا انتوا هان، يعني + +378 +00:28:30,680 --> 00:28:37,060 +هان في عندي التفاعل الكيميائي موجود داخل وعاء، + +379 +00:28:37,060 --> 00:28:40,900 +التفاعل الكيميائي، أي تفاعل كيميائي مثلا هو ال + +380 +00:28:40,900 --> 00:28:43,500 +system تبعي موجود داخل وعاء + +381 +00:28:49,850 --> 00:28:54,810 +خلّى هذا الوعى بيقدر يوصل للحرارة يعنى فانا بقول + +382 +00:28:54,810 --> 00:28:59,210 +بما انه ال piston مسكر على الوعى فلأ باطلعش اي + +383 +00:28:59,210 --> 00:29:03,810 +matter طلعش اي matter ال energy ممكن يتبادل ال + +384 +00:29:03,810 --> 00:29:07,310 +energy لكن ال matter لأ فانا بنقوله closed system + +385 +00:29:07,310 --> 00:29:12,170 +closed system في نوع اخر من ال systems بنقوله + +386 +00:29:12,170 --> 00:29:15,550 +isolated system ال isolated system هذا معزول لا + +387 +00:29:15,550 --> 00:29:21,820 +بتبادل حرارة ولا بتبادلمادة يعني محافظ أحاله + +388 +00:29:21,820 --> 00:29:27,000 +حرارته فيه مادته فيه زي ال termos ال termos طبعا + +389 +00:29:27,000 --> 00:29:29,580 +ال termos كويس هو ال termos بعد فترة يعني بعد يوم + +390 +00:29:29,580 --> 00:29:33,480 +بنلاحظ احنا انه اللي في جلبه بيبرد لو حطينا فيه + +391 +00:29:33,480 --> 00:29:37,580 +مثلا جهوة تاني يوم اللي جيه برد يعني هو بت .. ايه + +392 +00:29:37,580 --> 00:29:45,180 +يعنيأقرب شيء للـ isolated system على فرض إنه معزول + +393 +00:29:45,180 --> 00:29:49,400 +تماما فلأ لا راح يتبادل حرارة وبالطبع مش راح + +394 +00:29:49,400 --> 00:29:52,520 +يتبادل matter فمعنى الكلام هذا اللي بنقوله + +395 +00:29:52,520 --> 00:29:55,280 +isolated system + +396 +00:29:57,320 --> 00:30:00,260 +يبقى الـ system ثلاث أنواع إما أنها تكون open وهذا + +397 +00:30:00,260 --> 00:30:04,720 +بتبادل ال energy و ال matter مع ال surroundings، + +398 +00:30:04,720 --> 00:30:08,640 +يا ما بيكون closed وهذا بتبادل ال energy بس ال + +399 +00:30:08,640 --> 00:30:12,380 +matter لأ، يا بيكون isolated و لا بتبادل energy + +400 +00:30:12,380 --> 00:30:15,200 +ولا بتبادل matter + +401 +00:30:19,210 --> 00:30:23,750 +الـ Energy changes عادة في الحياة يعني اللي زي ما + +402 +00:30:23,750 --> 00:30:29,690 +بنشوفها ممكن تكون لها two forms يا إما work يا إما + +403 +00:30:29,690 --> 00:30:34,590 +heat أو الاتنين مع بعض work و heat فال energy it + +404 +00:30:34,590 --> 00:30:35,730 +changes دائما + +405 +00:30:39,550 --> 00:30:47,590 +بنشوفها احنا على هيئة work او heat في الكيميا + +406 +00:30:47,590 --> 00:30:51,030 +بنقول ال work involved results due to the system + +407 +00:30:51,030 --> 00:30:54,690 +volume pressure exchange اه يبقى مش انه نحرك + +408 +00:30:57,290 --> 00:31:06,730 +خلّيني أقول كتلة معينة في رفاص يعني في اتجاه معين، + +409 +00:31:06,730 --> 00:31:11,490 +مسافة معينة، لأ بالنسبة لي أنا في الكيميا ال work + +410 +00:31:11,490 --> 00:31:16,730 +عندي حاجة تانية ال work يتعلق ب volume pressure + +411 +00:31:16,730 --> 00:31:20,660 +changeعادة يتعلق بالـ volume pressure change هذا + +412 +00:31:20,660 --> 00:31:23,020 +ال work اللي انا بشوفه في الكيميا وهذا عبارة عن + +413 +00:31:23,020 --> 00:31:27,460 +mechanical work يعني لأنه لما ال volume يزيد بيصير + +414 +00:31:27,460 --> 00:31:31,700 +في عنده حركة فهو يعتبر هذا النوع من أنواع ال work + +415 +00:31:31,700 --> 00:31:38,000 +اسمه mechanical work النوع التاني من ال energy + +416 +00:31:38,000 --> 00:31:42,220 +transfer ممكن يتم ال transfer يعني من خلال الحرارة + +417 +00:31:42,220 --> 00:31:49,600 +زي ان يكون في جسم طبعا حارسخن فلو مسيكناها بأصبعنا + +418 +00:31:49,600 --> 00:31:53,260 +هيك .. بنلاحظ أن الحرارة بتنتقل من الجسم للأصبع من + +419 +00:31:53,260 --> 00:31:58,120 +ال hotter object ل ال colder object .. كويس؟ و + +420 +00:31:58,120 --> 00:32:04,700 +العكس صحيح لو يعني واحد مسيك أو حاولنا نمسك مثلا + +421 +00:32:04,700 --> 00:32:09,980 +قطعة ثلج بأصبعنا بس يعني فبنلاحظ أن الأصبع الحرارة + +422 +00:32:09,980 --> 00:32:15,000 +بتوقع شمالهاأعلى فرح تنتقل جزء من الحرارة للثلج + +423 +00:32:15,000 --> 00:32:19,600 +فهذا اسمه heat transfer وعادة بتتم من ال hotter + +424 +00:32:19,600 --> 00:32:27,440 +object ل ال colder one فعلى سبيل المثال يعني لو + +425 +00:32:27,440 --> 00:32:31,180 +عندي combustion reaction combustion reaction + +426 +00:32:31,180 --> 00:32:35,020 +شفناها في عندي hydrocarbon بيحترق هذا اللي سمونها + +427 +00:32:35,020 --> 00:32:38,220 +combustion reaction such as the burning of natural + +428 +00:32:38,220 --> 00:32:42,920 +gasفقول هذا البرنج of natural gas releases the + +429 +00:32:42,920 --> 00:32:47,200 +potential energy stored اه اذا كان قلنا في + +430 +00:32:47,200 --> 00:32:49,640 +potential energy وطبيعي انه في potential energy + +431 +00:32:49,640 --> 00:32:54,760 +فهو خلال عملية الحرق بيحرر ال potential energy + +432 +00:32:54,760 --> 00:32:58,480 +stored in the molecules of the fuel بحرر ال + +433 +00:32:58,480 --> 00:33:03,020 +potential energy الناشعة عن ترابط الذرات الناشعة + +434 +00:33:03,020 --> 00:33:04,580 +عن ترابط الذرات + +435 +00:33:07,690 --> 00:33:10,870 +فبنقول إذا كان عرفنا على إنه ال system تبعه إن هو + +436 +00:33:10,870 --> 00:33:14,130 +عبارة عن ال combustion reaction هذا وكل ما ده هو + +437 +00:33:14,130 --> 00:33:17,550 +ال surroundings بنقول إنه بما إنه ال reaction تبعي + +438 +00:33:17,550 --> 00:33:21,430 +بيطلق حرارة إذن الحرارة راح تنتقل من ال system إلى + +439 +00:33:21,430 --> 00:33:28,850 +ال surroundings مهم جدا نعرف اتجاه انتقال الحرارة + +440 +00:33:28,850 --> 00:33:35,770 +أو مين اللي بيعمل الشغلمهم جدا هذا الكلام لأنه على + +441 +00:33:35,770 --> 00:33:40,050 +أساسه راح تتوقف حاجة بتقولها ال internal energy أو + +442 +00:33:40,050 --> 00:33:48,250 +الطاقة الداخلية لل system اللي عندىفلازم نعرف + +443 +00:33:48,250 --> 00:33:53,250 +الاتجاه هفرجيكم كيف نتكلم الآن عن ال first law of + +444 +00:33:53,250 --> 00:33:55,190 +thermodynamics طب قلنا يا أستاذ ال thermodynamics + +445 +00:33:55,190 --> 00:34:00,790 +هيتحدث عنها يعني في المستقبل نعم لكن يعني خلينا + +446 +00:34:00,790 --> 00:34:02,830 +أقول ال thermochemistry و ال thermodynamics في + +447 +00:34:02,830 --> 00:34:08,370 +تداخل كبير بينهم فمثلا يعني لو قبل ما نتكلم عن ال + +448 +00:34:08,370 --> 00:34:12,930 +first law of thermodynamics نتكلم عن حاجة بيقولها + +449 +00:34:12,930 --> 00:34:17,190 +ال zeroth law of thermodynamicsزيرو ثلوج وهذا + +450 +00:34:17,190 --> 00:34:22,690 +بتعلق بالحرارة يعني انتقال الحرارة فبيقول إنه إذا + +451 +00:34:22,690 --> 00:34:27,150 +كان في عند جسمين بيختلفوا في درجة الحرارةفبعد فترة + +452 +00:34:27,150 --> 00:34:33,910 +لو صاروا in thermal contact يعني وصلنا في بعض، بعد + +453 +00:34:33,910 --> 00:34:38,610 +فترة إيش هيحصل؟ الحرارة هتنتقل من واحد للتاني، من + +454 +00:34:38,610 --> 00:34:42,450 +الأعلى للأدنى، وبعدين إيه؟ لغاية ما يتساووا، صاروا + +455 +00:34:42,450 --> 00:34:45,550 +in thermal equilibrium نسميهم بعد ما كانوا in + +456 +00:34:45,550 --> 00:34:48,450 +thermal contact صاروا in إيه؟ thermal equilibrium + +457 +00:34:48,450 --> 00:34:56,580 +فلو عندي A وB in thermal equilibriumوB وC in + +458 +00:34:56,580 --> 00:35:02,300 +thermal equilibrium إذاً A وC هيكونوا in thermal + +459 +00:35:02,300 --> 00:35:07,340 +equilibrium if they were in thermal contact لو + +460 +00:35:07,340 --> 00:35:12,400 +جمعناهم مع بعض، هلاحظ إن الحرارة مش راح تنتقل من A + +461 +00:35:12,400 --> 00:35:17,680 +لC أو من C لأنهم A in thermal contact مع B وB in + +462 +00:35:17,680 --> 00:35:21,280 +thermal contact مع C إذاً A وC هيكونوا in thermal + +463 +00:35:21,280 --> 00:35:21,820 +equilibrium + +464 +00:35:34,820 --> 00:35:41,860 +القانون الأول للثرمو داينامكس ببساطة بيقول ال + +465 +00:35:41,860 --> 00:35:45,670 +energy is conservedالقانون الأول بيقول إيه energy + +466 +00:35:45,670 --> 00:35:51,350 +is conserved إيش يعني قال يعني energy can neither + +467 +00:35:51,350 --> 00:35:55,630 +be created nor destroyed هذا زي ال mass إذا أنتم + +468 +00:35:55,630 --> 00:35:59,250 +مذكرين زي ال mass energy can neither be created + +469 +00:35:59,250 --> 00:36:07,560 +nor destroyed لكن ممكن تتحول من شكل لآخرفانا عندى + +470 +00:36:07,560 --> 00:36:10,860 +ال system وعندى ال surroundings والله ايش معنى + +471 +00:36:10,860 --> 00:36:13,900 +القانون الاول ال thermodynamics اذا ال system فقط + +472 +00:36:13,900 --> 00:36:17,320 +طاقة لابد الا ان ال surroundings ياخد نفس الكمية + +473 +00:36:17,320 --> 00:36:21,080 +من الطاقة لان طاقة ال system و ال surroundings يجب + +474 +00:36:21,080 --> 00:36:23,540 +ان تكون ثابتة + +475 +00:36:25,280 --> 00:36:27,820 +لا تتغير إذا كان ال system فقد الطاقة و الطاقة + +476 +00:36:27,820 --> 00:36:29,840 +بدها تروح لل surroundings طب إذا كان ال + +477 +00:36:29,840 --> 00:36:33,260 +surroundings فقد الطاقة بدها تروح لل system الطاقة + +478 +00:36:33,260 --> 00:36:37,760 +عبارة عن work و heat work او heat او الاتنين يا + +479 +00:36:37,760 --> 00:36:43,540 +work يا heat يا الاتنين إذا an energy that is lost + +480 +00:36:43,540 --> 00:36:47,500 +by a system must be gained by the surroundings and + +481 +00:36:47,500 --> 00:36:53,650 +vice versa بالعكس صحيحهذا ايش مفهومه؟ مفهومه ان ال + +482 +00:36:53,650 --> 00:36:57,730 +energy is conserved ايش يعني؟ يعني ال first law of + +483 +00:36:57,730 --> 00:37:01,850 +thermodynamics قانون سهل كتير وحلو كتير، مش هيك؟ + +484 +00:37:01,850 --> 00:37:08,150 +مدش زيادة شرح فتعالوا نتطلع الآن على ال internal + +485 +00:37:08,150 --> 00:37:14,910 +energy اتكلمنا احناعن الـ kinetic energy و ال + +486 +00:37:14,910 --> 00:37:18,130 +potential energy بنقول يا بنات ان ال internal + +487 +00:37:18,130 --> 00:37:21,970 +energy هي عبارة عن مجموع جميع أنواع ال kinetic + +488 +00:37:21,970 --> 00:37:25,270 +energy و ال potential energy في ال system اللي + +489 +00:37:25,270 --> 00:37:28,850 +عندى لكل مكونة ال system هاي ال internal energy + +490 +00:37:28,850 --> 00:37:33,030 +اتكلمت عن نوعين من أنواع ال energy اتكلمت عن ال + +491 +00:37:33,030 --> 00:37:36,750 +kinetic energy و ال potential energy الآن بقول انه + +492 +00:37:38,450 --> 00:37:43,870 +الـ Internal Energy هي عبارة عن مجموع جميع أشكال + +493 +00:37:43,870 --> 00:37:47,710 +الـ Kinetic Energy والـ Potential Energy لجميع الـ + +494 +00:37:47,710 --> 00:37:52,070 +Components المكونة للـ System لإيه؟ لأنه لو أنا + +495 +00:37:52,070 --> 00:37:57,030 +بدي أجيب الـ Energy كل مجموع الـ Kinetic Energy + +496 +00:37:57,030 --> 00:38:00,430 +للـ System بدي أشوف مجموع الـ Kinetic Energy لكل + +497 +00:38:00,430 --> 00:38:03,430 +component من كمبونات الـ System بدي أجسم الـ + +498 +00:38:03,430 --> 00:38:06,220 +System لكمبوناتوكل ال .. ال .. ال .. ال .. ال .. + +499 +00:38:06,220 --> 00:38:07,820 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +500 +00:38:07,820 --> 00:38:11,860 +.. ال .. ال .. ال .. ال .. + +501 +00:38:11,860 --> 00:38:12,580 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +502 +00:38:12,580 --> 00:38:14,280 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +503 +00:38:14,280 --> 00:38:15,500 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +504 +00:38:15,500 --> 00:38:15,540 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +505 +00:38:15,540 --> 00:38:17,660 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +506 +00:38:17,660 --> 00:38:18,160 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +507 +00:38:18,160 --> 00:38:18,180 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +508 +00:38:18,180 --> 00:38:19,840 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال + +509 +00:38:19,840 --> 00:38:21,520 +.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +510 +00:38:21,520 --> 00:38:25,500 +ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. + +511 +00:38:31,870 --> 00:38:36,890 +مثلا لأي تفاعل، reaction system، لأي تفاعل اللي هو + +512 +00:38:36,890 --> 00:38:39,470 +عبارة عن ال system بتاع، بقول ال energy الداخلية + +513 +00:38:39,470 --> 00:38:43,050 +تحتوي ليس فقط على المحركات والتعامل مع الموارد + +514 +00:38:43,050 --> 00:38:48,460 +التي تتفاعل معهامش بس هدول لأ هايش جال but also + +515 +00:38:48,460 --> 00:38:51,400 +the motions and interactions of their nuclei and + +516 +00:38:51,400 --> 00:38:54,960 +electrons اللي هي من مكونات ال system كل شيء كل + +517 +00:38:54,960 --> 00:38:59,660 +شيء طبعا يعني يعني صعب جدا ان نحسب هذا الكلام + +518 +00:38:59,660 --> 00:39:04,910 +تماما يعني و هيمر معنى انهأحنا يعني مابنقدرش نحسبه + +519 +00:39:04,910 --> 00:39:07,770 +في الحقيقة بسهولة، مابنقدرش نحسبه لكن مش مهم + +520 +00:39:07,770 --> 00:39:11,030 +الحساب تبع عيننا زي ما هنشوف المهم هو ال energy + +521 +00:39:11,030 --> 00:39:14,190 +change مش مهم ال energy بحد ذاتها مش مهم ال + +522 +00:39:14,190 --> 00:39:17,730 +interior ال energy بحد ذاتها صعبة الحساب كتير لكن + +523 +00:39:17,730 --> 00:39:24,170 +ال energy change هي المهمة بالنسبة لنا علشان هيك + +524 +00:39:24,170 --> 00:39:28,560 +بنقول we generally don't knowأو الـ numerical + +525 +00:39:28,560 --> 00:39:31,620 +value of a system's internal energy جدّاش ال E + +526 +00:39:31,620 --> 00:39:35,420 +اللي هي ال energy ال internal نعرفهاش، ال E اللي + +527 +00:39:35,420 --> 00:39:40,180 +حالها مابنعرفها، صعب جدا نعرفها، لكن لحسن الحظ، + +528 +00:39:40,180 --> 00:39:44,180 +لحسن الحظ أنه in thermodynamics fortunately or + +529 +00:39:44,180 --> 00:39:49,900 +mainlyأنا مهتم أو مهتم بالتغييرات في الهواء + +530 +00:39:49,900 --> 00:39:54,240 +الداخلي الدلتا اي مش ال اي الدلتا اي لحسن الحظ + +531 +00:39:54,240 --> 00:39:59,040 +يمكن حسابها بسهولة هفرجيكم عدة أمثلة لحساب الدلتا + +532 +00:39:59,040 --> 00:40:02,080 +اي فانا بدي الدلتا اي that accompanies a change in + +533 +00:40:02,080 --> 00:40:03,520 +the system + +534 +00:40:07,300 --> 00:40:13,880 +لو تخيلنا ان ال system فيه له starting internal + +535 +00:40:13,880 --> 00:40:17,800 +energy بقولها E initial يعني قبل ما يحصل التغيير + +536 +00:40:17,800 --> 00:40:24,380 +مثلا قبل التفاعل بعد التفاعل صار عندي E final اللي + +537 +00:40:24,380 --> 00:40:30,700 +هي ال final internal energy فبقول عادة ال delta E + +538 +00:40:30,700 --> 00:40:35,160 +هي ال E final minus ال E initial هذه و مع العلم ان + +539 +00:40:35,160 --> 00:40:40,370 +انا مش عارف ال E finalولا عارف الـEA initial لكن + +540 +00:40:40,370 --> 00:40:45,350 +الـDelta أو الفرق بينهم أه بستطيع أن أعرفه وهذا هو + +541 +00:40:45,350 --> 00:40:49,910 +المهم بالنسبة لي فيما يتعلق بال Thermodynamics + +542 +00:40:49,910 --> 00:40:55,230 +مثلا + +543 +00:40:55,230 --> 00:41:00,550 +يعني نيجي نطلع ونحاول نفسر هذا أكتر هي عندي E + +544 +00:41:00,550 --> 00:41:07,020 +initial كويس وهي عندي ال E finalلا بقدر احسب هذه + +545 +00:41:07,020 --> 00:41:11,380 +ولا بقدر احسب هذه بعرف omission لكن بقدر اعرف انا + +546 +00:41:11,380 --> 00:41:17,200 +ان والله ال system فقد طاقة هفرجيكم مثلا energy + +547 +00:41:17,200 --> 00:41:21,360 +lost to surroundings ليه؟ لأن ال E final اقل ال E + +548 +00:41:21,360 --> 00:41:24,790 +final اقل وبالتالي ال delta E negativeالـ + +549 +00:41:24,790 --> 00:41:28,710 +Intelligent system decreases delta E negative لأن + +550 +00:41:28,710 --> 00:41:32,650 +الـ delta E عبارة عن E final minus E initial بما + +551 +00:41:32,650 --> 00:41:38,110 +أن ال final أقل إذن ال delta E negative زي إياش + +552 +00:41:38,110 --> 00:41:45,610 +مثلازي مثلا تفاعل يكون اكسوثرميك، + +553 +00:41:45,610 --> 00:41:49,650 +تفاعل يكون طارد الحرارة، بيعطي حرارة، زي + +554 +00:41:49,650 --> 00:41:52,230 +combustion reaction، طب وين الحرارة هتروح؟ هيتروح + +555 +00:41:52,230 --> 00:41:55,670 +على ال surroundings، يبقى بالضرورة ال internal + +556 +00:41:55,670 --> 00:42:01,620 +energy لها النواتج أقلإذا الـ delta E نيجاتيف هذا + +557 +00:42:01,620 --> 00:42:06,180 +ببساطة خالص عكس هذا الكلام لو كان ال final state + +558 +00:42:06,180 --> 00:42:11,160 +of the system ال E final الطاقة تبعتها أعلى فمن ال + +559 +00:42:11,160 --> 00:42:14,280 +initial فمع هذا الكلام ال energy gained from + +560 +00:42:14,280 --> 00:42:19,420 +surroundings يبقى ال delta E positive زي ايه؟ زي + +561 +00:42:19,420 --> 00:42:22,940 +ما يكون مثلا ال system اللي عندي عبارة عن قطعة تلج + +562 +00:42:22,940 --> 00:42:28,080 +بدها تدوب قطعة تلج بدها تدوب فإيه؟ بتاخدحرارة من + +563 +00:42:28,080 --> 00:42:31,220 +أين؟ من الـCeramics وحرارة الـ system إيش مجردها؟ + +564 +00:42:31,220 --> 00:42:35,660 +بتزيد يعني ال energy لل system بتزيد فمعنى الكلام + +565 +00:42:35,660 --> 00:42:47,060 +ال delta E عندي positive طيب + +566 +00:42:47,060 --> 00:42:51,410 +بقول أنا في ال thermodynamics عادةالـ + +567 +00:42:51,410 --> 00:42:54,470 +Thermodynamic Quantities والـ Delta E أحد الـ + +568 +00:42:54,470 --> 00:42:57,070 +Thermodynamic Quantities لأن أنا أتكلم عن الـ Fast + +569 +00:42:57,070 --> 00:42:59,050 +Law of Thermodynamics زي ما سنشهد بعد شوية + +570 +00:43:02,430 --> 00:43:09,230 +و ال unit number قيمة و واحدة كويس زائد طبعا هدول + +571 +00:43:09,230 --> 00:43:11,810 +number و واحدة بيعطوني ال magnitude of the change + +572 +00:43:11,810 --> 00:43:18,810 +زائد إشارة بتدل على الإتجار هل في زيادة ولا في نقص + +573 +00:43:18,810 --> 00:43:22,410 +فال positive delta A بيكون a final أكبر من a + +574 +00:43:22,410 --> 00:43:27,790 +initial و العكس طبعا صحيح لكن في النهاية بدنا + +575 +00:43:27,790 --> 00:43:32,530 +نتذكر أنهأي طاقة بيفقدها ال system بدها تروح لل + +576 +00:43:32,530 --> 00:43:35,870 +surroundings بالظبط هي هي لأن ال energy is + +577 +00:43:35,870 --> 00:43:39,850 +conserved و أي طاقة بتفقدها ال surroundings بدها + +578 +00:43:39,850 --> 00:43:43,770 +تروح لل system برضه كمان مرة لأن ال energy is + +579 +00:43:43,770 --> 00:43:48,930 +conserved لو طلعنا على هذا ال reaction نفس ال + +580 +00:43:48,930 --> 00:43:54,950 +reaction اللي حكيتلكم عنه انا H2 زائد O2 بتعطينا + +581 +00:43:54,950 --> 00:44:00,370 +H2O هدول بيحترقوايبقى التفاعل عندي بعطيني حرارة، + +582 +00:44:00,370 --> 00:44:04,390 +إذاً معنى الكلام الـ final state هتكون لها lower + +583 +00:44:04,390 --> 00:44:08,210 +energy، ليه؟ لأن الحرارة هتروح لـA لل + +584 +00:44:08,210 --> 00:44:11,850 +surroundings، فصلاة الـ final state لها A، يبقى + +585 +00:44:11,850 --> 00:44:15,010 +الـ delta E عندي أقل من صفر أو negative، الـ delta + +586 +00:44:15,010 --> 00:44:17,830 +E عبارة عن negative value + +587 +00:44:20,360 --> 00:44:26,720 +وعكس هذا الكلام لو كان في عندي مثلا قطعة + +588 +00:44:26,720 --> 00:44:33,080 +ثلج او ما شابه ايش علاقة ال delta E بال heat و ال + +589 +00:44:33,080 --> 00:44:42,300 +work relating delta E to heat and work بقول انا + +590 +00:44:42,300 --> 00:44:47,080 +عندي ال delta E بتساوي ال Q زائد W ال internal + +591 +00:44:47,080 --> 00:44:53,620 +energyالـ Change in internal energy بساوي Q زائد W + +592 +00:44:53,620 --> 00:45:00,340 +بتتوقف على هل الـ Delta E بدنا نشوف والله هل هي + +593 +00:45:00,340 --> 00:45:03,700 +موجبة أو سالبة لأ توقف فقط على الحرارة لأ توقف + +594 +00:45:03,700 --> 00:45:07,540 +أيضا على الشغل لأنه مش دائما ال system بيعطيني + +595 +00:45:07,540 --> 00:45:11,900 +حرارة فقط يعني مثلا لو جينا نتطلعنا على ال system + +596 +00:45:11,900 --> 00:45:20,140 +الماضيهن H2OO2 هدول غازات ايش اعطاني مثلا هن؟ H2O + +597 +00:45:20,140 --> 00:45:26,820 +ايش؟ Liquid، اذا حجم .. حجم ال .. ال system ايش + +598 +00:45:26,820 --> 00:45:31,160 +حصل له؟ كان غازات بتحول ل liquid، الغازات حجمها + +599 +00:45:31,160 --> 00:45:34,800 +كبير، ال liquid ايه؟ اذا في شغل تم من ال + +600 +00:45:34,800 --> 00:45:38,450 +surroundings علىلأنه بده .. بده ينضغطها ال gate + +601 +00:45:38,450 --> 00:45:43,390 +بده الحجم جالفة بده البسطون ينزل ففي شغل تم من ال + +602 +00:45:43,390 --> 00:45:49,030 +surroundings على ال system فمش دائما بس عندي حرارة + +603 +00:45:49,030 --> 00:45:52,450 +لأ في عندي حرارة و في عندي كمان شغل لازم أخد بالي + +604 +00:45:52,450 --> 00:46:01,300 +من الاتنين فبقول انا انه ال ..ما هي الـ delta E + +605 +00:46:01,300 --> 00:46:06,380 +بتساوي W زائد Q؟ لكن يعني ما هي علاقتها فيهم من + +606 +00:46:06,380 --> 00:46:10,560 +ناحية الـ charges؟ كيف بعرف الـ charge للـ delta E + +607 +00:46:10,560 --> 00:46:16,540 +من قيمة الـ Q والـ W؟ delta E بتساوي Q زائد W؟ هذا + +608 +00:46:16,540 --> 00:46:21,280 +هو نص قانون الـ first law of thermodynamics من + +609 +00:46:21,280 --> 00:46:26,760 +ناحية حسابية الـ Q زائد W طيب، بنقول كيف بتتأثر + +610 +00:46:26,760 --> 00:46:32,410 +الـ delta E بالـ Q والـ W؟الكاتب كاتب الكتاب بيمثل + +611 +00:46:32,410 --> 00:46:41,210 +الموضوع يعني أو الـ Delta E وكأنها خزنة أو bank + +612 +00:46:41,210 --> 00:46:48,190 +account حساب بنكي إذا كان أوضعنا فيه بزيد يعني ال + +613 +00:46:48,190 --> 00:46:53,990 +Delta E موجبة وإذا كان سحبنا منهبيقل الـ delta E + +614 +00:46:53,990 --> 00:46:59,050 +سالبة كويس طب ايش بنستخدم انه نودع او نسحب جال + +615 +00:46:59,050 --> 00:47:06,870 +energy يا Q يا W يعني مثلا انا + +616 +00:47:06,870 --> 00:47:09,570 +هان خدوا بالكم بتطلعوا على ال convention تبعنا + +617 +00:47:09,570 --> 00:47:15,690 +حطيت حرارة حطيت حرارة وين؟ في ال system هاي ال + +618 +00:47:15,690 --> 00:47:19,610 +system تبعي حطيت حرارة انا + +619 +00:47:22,040 --> 00:47:25,960 +الـ Surroundings أعقط الـ System حرارة الـ + +620 +00:47:25,960 --> 00:47:31,220 +Surroundings هي اللي عملت شغل على الـ System لو + +621 +00:47:31,220 --> 00:47:34,480 +الـ System هو اللي عمل شغل معناه فقط طاقة لأنه + +622 +00:47:34,480 --> 00:47:37,500 +يعمل شغل لأ الـ Surroundings هي اللي عملت شغل على + +623 +00:47:37,500 --> 00:47:41,300 +الـ System يبقى هان بقول والله الـ Q أكبر من صفر و + +624 +00:47:41,300 --> 00:47:44,400 +الـ W أكبر من صفر يعني أنا بعرف الـ Q و الـ W فيما + +625 +00:47:44,400 --> 00:47:49,400 +يتعلق بالـ System هل هو بيكسب ولا بيخسر فهان كسب + +626 +00:47:50,350 --> 00:47:54,890 +الـ Q وكسب W، إذا الـ Q موجبا، الـ Q أكبر من صفر، + +627 +00:47:54,890 --> 00:47:59,890 +الـ W أكبر من صفر، إذا الـ Delta E أكبر من صفر، + +628 +00:47:59,890 --> 00:48:05,090 +ليه؟ لأنه energy deposited into system، ال energy + +629 +00:48:05,090 --> 00:48:12,250 +deposited، deposit يعني داعت، و دعت، أه لحظة، إيش + +630 +00:48:12,250 --> 00:48:16,720 +الفلوس أو يعني ال energy كبرت؟طب هان ايش بيحصل لو + +631 +00:48:16,720 --> 00:48:21,340 +ال system اعطاني طاقة اعطى يعني طاقة ايش يعني اعطى + +632 +00:48:21,340 --> 00:48:25,360 +لل surroundings حرارة زي ما يكون التفاعل الماضي + +633 +00:48:25,360 --> 00:48:29,620 +اعطى لل surroundings حرارة و التفاعل الماضي لأ + +634 +00:48:29,620 --> 00:48:35,840 +يعني لأنه برضه الشغل لأ الشغل عكسه ال work done by + +635 +00:48:35,840 --> 00:48:39,630 +the system ال system هو اللي عمل شغلمش هو اللي + +636 +00:48:39,630 --> 00:48:43,670 +يعني مش ال surroundings اللي عملت شغل معنى الكلام + +637 +00:48:43,670 --> 00:48:48,630 +ال Q أقل من صفر و ال W أقل من صفر اذا ال delta E + +638 +00:48:48,630 --> 00:48:56,190 +عبارة عن negative value فممكن نعبر عن ال delta E و + +639 +00:48:56,190 --> 00:49:01,800 +كأنها عبارة عنحساب البنكي اذا كان اوضعنا فيه و + +640 +00:49:01,800 --> 00:49:06,960 +اوضعنا ايش يعني يعني اعطناه حرارة و اكتشف نعطيه + +641 +00:49:06,960 --> 00:49:10,580 +حرارة لمن يكون هو بحاجة لحرارة يعني حرارة ال + +642 +00:49:10,580 --> 00:49:15,140 +surroundings اعلى اعطناه حرارة او اشتغلنا عليه ال + +643 +00:49:15,140 --> 00:49:19,360 +surroundings هي اللي عملت عليه شغل بمعنى اخر حجمه + +644 +00:49:19,360 --> 00:49:24,370 +هو بده يجلليه؟ لأنه كان اعتبرنا انه الشغل اللي + +645 +00:49:24,370 --> 00:49:27,530 +عنده هو بس PV work فحجبه هو بيقول اللي بيجي ال + +646 +00:49:27,530 --> 00:49:30,970 +surroundings هي ليه؟ بدها تعمل شغل عليه، بينما لو + +647 +00:49:30,970 --> 00:49:33,410 +حجمه زاد، معناته هو اللي بيعمل شغل على ال + +648 +00:49:33,410 --> 00:49:38,090 +surroundings، كويس؟ فلو يعني هان ببساطة لو حجبه + +649 +00:49:38,090 --> 00:49:43,290 +جال، لو حرارته، يعني اكتسب حرارة من ال + +650 +00:49:43,290 --> 00:49:45,990 +surroundings، يعني هو كان حرارته أقل، اه دي التأيم + +651 +00:49:45,990 --> 00:49:50,960 +و جبا، طب هان، عكس هذا كلام، لو هو عامل شغل،يبجي + +652 +00:49:50,960 --> 00:49:56,200 +ال W أقل من صفر بالنسبة له ال convention أنا بتكلم + +653 +00:49:56,200 --> 00:49:59,360 +بس عن ال system يبجي هذه ال conventions لل system + +654 +00:49:59,360 --> 00:50:04,060 +و لو هو فقط طاقة اذا ال Q برضه كمان أقل من صفر هذا + +655 +00:50:04,060 --> 00:50:09,380 +الكلام بتترجم لإنه كتالة when heat is added to a + +656 +00:50:09,380 --> 00:50:16,160 +system or work is done on a system مش byها on فرق + +657 +00:50:16,160 --> 00:50:23,170 +كبيرits internal energy increases وطبعا العكس يعني + +658 +00:50:23,170 --> 00:50:31,110 +صحيح يعني + +659 +00:50:31,110 --> 00:50:35,430 +برضه صياغة أخرة بشكل أخر من كتاب أخر هي عند ال + +660 +00:50:35,430 --> 00:50:40,610 +system ومعها ال surroundings لو ال system اكتسب + +661 +00:50:40,610 --> 00:50:45,630 +heat إذا بالنسبة لل system ال Q موجباليه؟ لأنه + +662 +00:50:45,630 --> 00:50:52,590 +تمإيداع اكتسب طيب لو كان فيه شغل على ال system ال + +663 +00:50:52,590 --> 00:50:55,830 +surroundings هي اللي عملت شغل يعني معنى كلام ال W + +664 +00:50:55,830 --> 00:51:01,530 +أكبر من صفر يبقى ال delta E موجبة والعكس بيكون + +665 +00:51:01,530 --> 00:51:09,010 +صحيح إذن بنقدر نقول احنا ان ال delta E زي ما شفنا + +666 +00:51:09,010 --> 00:51:15,600 +بتبتساوي ال Q زائد W لكن قيمة ال Qوقيمة الـ W + +667 +00:51:15,600 --> 00:51:22,720 +بتتوقف على هل ال system هو اللي بيعطيني حرارة و هل + +668 +00:51:22,720 --> 00:51:26,180 +هو اللي بيعمل شغل أو هل ال system هو اللي بيكتسب + +669 +00:51:26,180 --> 00:51:31,000 +حرارة و بنعمل عليه شغل طبعا ممكن واحدة منهم تكون + +670 +00:51:31,000 --> 00:51:34,100 +سالبة و التانية موجبة ممكن يكون والله بيعطي حرارة + +671 +00:51:35,720 --> 00:51:39,660 +وبينعمل عليه شغل فبيكسب من جهة وبيفقد من جهة ممكن + +672 +00:51:39,660 --> 00:51:42,680 +يكون والله العكس ممكن يكون بياخد حرارة لكن هو + +673 +00:51:42,680 --> 00:51:50,460 +بيعمل شغل يعني ممكن اي اي اشارة تكون ل ال W و ال Q + +674 +00:51:50,460 --> 00:51:55,080 +مش شرط التان تان يكونوا يا موجبتين يا سالبتين وهنا + +675 +00:51:55,080 --> 00:51:58,220 +بنتطلع على ال sign conventions و بدي اخد slide تان + +676 +00:51:58,220 --> 00:52:04,840 +slide بسيطة يعني سهلة خالص بقول for a Qلما اتكون + +677 +00:52:04,840 --> 00:52:08,380 +positive وبتكلم عن ايه فيه ما يتعلق بالsystem هاي + +678 +00:52:08,380 --> 00:52:11,080 +كل شغلي بال system مش بس hand كل شغلي بال system + +679 +00:52:11,080 --> 00:52:13,700 +انا مهتم بال system لان انا بدرس ال system انا + +680 +00:52:13,700 --> 00:52:16,720 +مهتم بال system فكل ما يتعلق فيه يعني يتعلق بال + +681 +00:52:16,720 --> 00:52:22,100 +system فبقول plus means system gains heat طب ال + +682 +00:52:22,100 --> 00:52:28,040 +work means work done on system طيب يمكن تلتقى ايه + +683 +00:52:28,040 --> 00:52:33,090 +موجة باه net gain of energyأكس هذا كلام اكيو + +684 +00:52:33,090 --> 00:52:38,390 +نيجاتيف means system loses heat system loses heat + +685 +00:52:38,390 --> 00:52:43,870 +و نيجاتيف means work done by مش on by هو اللي + +686 +00:52:43,870 --> 00:52:49,350 +بيعمل شغل يبقى فقط فاقة يبقى سالبة المحصلة Delta A + +687 +00:52:49,350 --> 00:52:50,050 +سالبة + +688 +00:52:54,760 --> 00:52:57,840 +الحجم بيقل مع حجم ال system بيقل معناته ال + +689 +00:52:57,840 --> 00:53:03,820 +surroundings هي اللي بتعمل شغل على ال system او + +690 +00:53:03,820 --> 00:53:06,000 +لما ال surroundings هي اللي بتعمل شغل على ال + +691 +00:53:06,000 --> 00:53:11,020 +system بتكون ال W موجة فيما يتعلق بال systemطيب + +692 +00:53:11,020 --> 00:53:15,600 +ناخد كمان slide لجيتها حلوة يعنى و بتلخص شغلات + +693 +00:53:15,600 --> 00:53:19,560 +كتير فيها شوية مفاهيم مش فشش جديد في الحقيقة يعنى + +694 +00:53:19,560 --> 00:53:23,260 +لكن بنشوف ال site convention for a queue ال queue + +695 +00:53:23,260 --> 00:53:26,080 +أكبر من صفر يعني heat is transferred from the + +696 +00:53:26,080 --> 00:53:31,240 +surroundings to the system مفهومة ال queue أكبر من + +697 +00:53:31,240 --> 00:53:33,980 +صفر يبقى ال heat is transferred from the + +698 +00:53:33,980 --> 00:53:37,980 +surroundings to the systemطيب الـ Q أقل من صفر + +699 +00:53:37,980 --> 00:53:41,360 +العكس الـ heat is transferred from the system to + +700 +00:53:41,360 --> 00:53:42,200 +the surroundings + +701 +00:53:46,110 --> 00:53:50,550 +فى ما يتعلق بالـ W اللى هي إيه ال work بنقول work + +702 +00:53:50,550 --> 00:53:53,790 +أكبر من صفر work is done by the surroundings on + +703 +00:53:53,790 --> 00:53:58,130 +the system طب و أقل من صفر جال work is done by the + +704 +00:53:58,130 --> 00:54:02,370 +system on the surroundings الآن ال sign لل Delta E + +705 +00:54:02,370 --> 00:54:08,230 +Delta E بتساوي Q زي ال W لما تكون Q أكبر من صفر و + +706 +00:54:08,230 --> 00:54:13,010 +ال W أكبر من صفر Delta E أكبر من صفر طبيعىدلتا A + +707 +00:54:13,010 --> 00:54:16,750 +أكبر من صفر لأن دلتا A Q زائد W هذا أكبر من صفر و + +708 +00:54:16,750 --> 00:54:20,710 +هذا أكبر من صفر و هذا أكبر من صفر طب Q أكبر من صفر + +709 +00:54:20,710 --> 00:54:26,390 +و W أقل من صفر آه الـ sign of delta A depends on + +710 +00:54:26,390 --> 00:54:30,670 +the magnitude of the Q and W أنهي أكبروحدة موجة + +711 +00:54:30,670 --> 00:54:34,350 +بقى التانية السالمة فبقى الأكبر طب كيوها عكس هذا + +712 +00:54:34,350 --> 00:54:37,970 +كيو أقل من صفر و W أكبر صفر the sign of Delta E + +713 +00:54:37,970 --> 00:54:41,590 +depends on the magnitude of Q and W طب كيو أقل من + +714 +00:54:41,590 --> 00:54:45,390 +صفر و W أقل من صفر إذا ال Delta E negative نتذكر + +715 +00:54:45,390 --> 00:54:50,130 +هذا كلام يا بنات حلو كتير و بسيط خالص نتذكره طيب + +716 +00:54:50,130 --> 00:54:53,410 +تعالوا ناخد اللي أكام من مثال نحسب فيه ال Delta E + +717 +00:54:54,830 --> 00:54:59,010 +فبيقول لي the value of delta E for a system that + +718 +00:54:59,010 --> 00:55:04,210 +performs 13 kilo joule of work on its surroundings + +719 +00:55:04,210 --> 00:55:16,350 +يبقى مين اللي بيعمل الشغل الـ system هو اللي + +720 +00:55:16,350 --> 00:55:22,770 +بيعمل الشغل، اذا الشغل سالم، صحيح هذا الكلاموهو + +721 +00:55:22,770 --> 00:55:28,150 +يفقد 9 كيلو جولز من النار وهو يفقد أيضًا الـ Q + +722 +00:55:28,150 --> 00:55:33,970 +سالب يعني Delta E Q زائد W هذه سالب تسعة وهذه سالب + +723 +00:55:33,970 --> 00:55:39,070 +تلتاش سالب اتنين وعشرين كيلو جولة ماشي؟ طيب بيقول + +724 +00:55:39,070 --> 00:55:43,010 +لي hundred joules of thermal energy flows into the + +725 +00:55:43,010 --> 00:55:48,040 +system في الخزنة راحوا Q positiveالـ Q بتساوي ألف + +726 +00:55:48,040 --> 00:55:52,340 +جول، at the same time أربعمية جول of work is done + +727 +00:55:52,340 --> 00:55:56,060 +by the system، مين اللي عامل الشغل؟ إذا فقط بفليو + +728 +00:55:56,060 --> 00:56:00,120 +سالفة، what is the change in the system's internal + +729 +00:56:00,120 --> 00:56:04,700 +energy؟ شايفين قداش سهل نحسب الـ Delta E، لكن لو + +730 +00:56:04,700 --> 00:56:10,980 +جالي يحسب الـEI والـEF؟ ماعرفشلكن الـ delta A ساوي + +731 +00:56:10,980 --> 00:56:15,640 +الـ Q زي الـ W الـ Q هو كسب ألف و خسر أربعمية إذا + +732 +00:56:15,640 --> 00:56:21,000 +كسب ستمية جول نطلع + +733 +00:56:21,000 --> 00:56:27,670 +على هذا الـ system تبعناGases A and B are confined + +734 +00:56:27,670 --> 00:56:33,030 +in a cylinder and piston + +735 +00:56:47,290 --> 00:56:51,310 +مثل ما يظهر في الفيجور و يتفاعل لتصميم نوع من + +736 +00:56:51,310 --> 00:56:55,310 +الهواء الصليد لحظة A غاز و B غاز و حجمهم كبير + +737 +00:56:55,310 --> 00:56:59,370 +غازات طب لما نيكونوا صليد ايش بنجرح الحجم؟ رجال + +738 +00:56:59,370 --> 00:57:01,550 +سعره صليد يفجأ + +739 +00:57:03,940 --> 00:57:07,360 +الـ work مين اللي بيعمل ال work؟ هل هو اللي عمل ال + +740 +00:57:07,360 --> 00:57:11,500 +work؟ ال surrounding زي اللي عملت ال work طيب as + +741 +00:57:11,500 --> 00:57:15,140 +the reaction occurs the system loses 1150 جول of + +742 +00:57:15,140 --> 00:57:19,620 +heat يعني اتفاعل طارد للحرارة ففقد 1150 of heat + +743 +00:57:19,620 --> 00:57:24,420 +إيش معنى هذا الكلام؟ ال system فقد Q سالبة لأن ال + +744 +00:57:24,420 --> 00:57:29,590 +system فقدالمصادر تتحرك للأسفل، وكما يتفاعل + +745 +00:57:29,590 --> 00:57:33,790 +الجازين لإصلاح مصادر، وكما يتقل قوة الجاز تحت درجة + +746 +00:57:33,790 --> 00:57:35,310 +درجة درجة درجة درجة درجة درجة درجة درجة درجة درجة + +747 +00:57:35,310 --> 00:57:35,430 +درجة درجة درجة درجة درجة درجة درجة درجة درجة درجة + +748 +00:57:35,430 --> 00:57:35,670 +درجة درجة درجة درجة درجة درجة درجة درجة درجة درجة + +749 +00:57:35,670 --> 00:57:37,730 +درجة درجة درجة درجة درجة درجة درجة درجة درجة درجة + +750 +00:57:37,730 --> 00:57:37,770 +درجة درجة درجة درجة درجة درجة درجة درجة درجة درجة + +751 +00:57:37,770 --> 00:57:39,560 +درجة درجة درجة درجة درجة درجة درجة دالـ + +752 +00:57:39,560 --> 00:57:44,020 +Surroundings بتعمل شغل مقداره 480 جولوف وورك On + +753 +00:57:44,020 --> 00:57:47,140 +the system What is the change in the internal + +754 +00:57:47,140 --> 00:57:50,680 +energy of the system؟ طبيعي جدا، لو حللناها، بنقول + +755 +00:57:50,680 --> 00:57:55,080 +إن Delta E ساوية Q زاية W، Q بما إن هو طارد + +756 +00:57:55,080 --> 00:57:59,940 +للحرارة أو بيعطي حرارة، فهو فقد 1150، لكن الـ + +757 +00:57:59,940 --> 00:58:03,540 +Surroundings عملت شغل عليه، فبالتالي اكتسب 480، + +758 +00:58:03,540 --> 00:58:08,840 +فبطلع عندي سالب 670، المحصلة Delta E سالبة + +759 +00:58:10,740 --> 00:58:14,900 +يعني في المحصلة ان الطاقة انتقلت من ال system لل + +760 +00:58:14,900 --> 00:58:19,000 +surroundings طيب كمان مثال بيقول 800 joule of work + +761 +00:58:19,000 --> 00:58:24,440 +is done on a system ايش يعني ايه ال W موجب ولا + +762 +00:58:24,440 --> 00:58:30,800 +سالب ال W خلاني اطلع خلاني اطلع 800 joule of work + +763 +00:58:30,800 --> 00:58:35,300 +is done on the system مش هو اللي عملها و اه طبعا + +764 +00:58:35,300 --> 00:58:38,700 +ال W موجب بالنسبة لل .. يعني بحب كتير هنا اللي + +765 +00:58:38,700 --> 00:58:44,130 +عليه work بكسب500 J of thermal energy is removed + +766 +00:58:44,130 --> 00:58:48,970 +from the system يبقى Q سالبة.طب what is the change + +767 +00:58:48,970 --> 00:58:51,830 +in the system's internal energy؟ طبعا Delta E Q + +768 +00:58:51,830 --> 00:58:55,710 +زائد W سالب خمسمية اللي هي كل Q زائد تمانمية تم + +769 +00:58:55,710 --> 00:58:59,990 +تلاتمية J. The value of Delta E for a system that + +770 +00:58:59,990 --> 00:59:04,290 +performs 111 KJ of work on its surroundings هنمين + +771 +00:59:04,290 --> 00:59:10,170 +المبدل الشغل؟الـ system is then الـW سالب on its + +772 +00:59:10,170 --> 00:59:15,170 +dynamics and gains بيكتسب 89 kilo joule of heat + +773 +00:59:15,170 --> 00:59:20,930 +يبقى الـ Q زائد 89 الـ W سالب 111 اه ال net delta + +774 +00:59:20,930 --> 00:59:25,390 +E سالبة طيب + +775 +00:59:25,390 --> 00:59:29,510 +نتطلع على هذه المسألة بيقول when a system فراغ + +776 +00:59:29,510 --> 00:59:32,770 +delta E is always negative وقتش بتكون always + +777 +00:59:32,770 --> 00:59:39,770 +negativeصحيح صحيح absorbs heat and does work + +778 +00:59:39,770 --> 00:59:43,650 +absorbs heat لأ هذه ال Q موجبة هي خلينا نطلع عليها + +779 +00:59:43,650 --> 00:59:54,390 +Q موجبة أو زائد Q يعني does work W سالب gives of + +780 +00:59:54,390 --> 01:00:04,570 +heat سالب does work سالب طب absorbs heatHas work + +781 +01:00:04,570 --> 01:00:19,610 +done on it يعني + +782 +01:00:19,610 --> 01:00:23,050 +عمل عليه الشغل، مش هو اللي عمل، مش هو اللي عمل، + +783 +01:00:23,050 --> 01:00:29,280 +معنى الكلام في عند وقتش بتكون always negativeلما + +784 +01:00:29,280 --> 01:00:33,620 +تقول هذه سالبة أو هذه سالبة إذا الخيار عندي بيه + +785 +01:00:33,620 --> 01:00:37,900 +بسيط كتير ممكن يعني ال chemical و ال physical + +786 +01:00:37,900 --> 01:00:42,780 +processes نقول عنهم أو نوصفهم بأحد و أصفين يا إما + +787 +01:00:42,780 --> 01:00:47,560 +أنه ماصد الحرارةبمعنى آخر آه إنه بيكتسب حرارة من + +788 +01:00:47,560 --> 01:00:50,560 +ال surroundings يا إما طارد الحرارة يعني بيعطي + +789 +01:00:50,560 --> 01:00:53,560 +حرارة لل surroundings فالمصد الحرارة يعني اللي + +790 +01:00:53,560 --> 01:00:56,480 +بياخد حرارة من ال surroundings بيقوله endothermic + +791 +01:00:56,480 --> 01:01:00,280 +process سواء كان chemical أو physical reaction + +792 +01:01:00,280 --> 01:01:02,920 +سواء كان chemical أو physical reaction فال + +793 +01:01:02,920 --> 01:01:07,820 +endothermic process هي ال process اللي خلالها ال + +794 +01:01:07,820 --> 01:01:12,020 +system بيكتسب حرارة من ال surroundingsيعني بمعنى + +795 +01:01:12,020 --> 01:01:18,980 +أخر لما ال process تم حرارة ال system بتجل يعني + +796 +01:01:18,980 --> 01:01:22,800 +مثلا لو إجينا بدنا ندوب أمونيا ميكلورايد في الميه + +797 +01:01:22,800 --> 01:01:27,280 +دوبنا الميه كانت حرارة الغرفة لما ندوب بنلاحظ أنه + +798 +01:01:27,280 --> 01:01:33,120 +صار زي التلج أه هذه process endothermic وبالتالي + +799 +01:01:33,120 --> 01:01:36,800 +هي بتاخد حرارة من أيه؟ من ال surroundings يعني + +800 +01:01:36,800 --> 01:01:40,100 +الحرارة .. الحرارة added لل system من ال + +801 +01:01:40,100 --> 01:01:40,580 +surroundings + +802 +01:01:45,650 --> 01:01:54,090 +الحرارة تدخل للسيستم اندو يعني انتوا برضه + +803 +01:01:54,090 --> 01:01:59,030 +في حاجات كتير بنلاحظها في الحياة العملية مثلا + +804 +01:02:02,130 --> 01:02:05,110 +لو طلعت على الـ Ammonium Thiocyanate والبريوم + +805 +01:02:05,110 --> 01:02:09,070 +الهيدروكسيد لو خلطناهم مع بعض دوبناهم وخلطناهم مع + +806 +01:02:09,070 --> 01:02:12,790 +بعض بنلاحظ برضه أن الحرارة بتقل في عمليات كتيرة + +807 +01:02:12,790 --> 01:02:16,190 +الحرارة فيها بتقل يعني بتكون Endothermic وفي من + +808 +01:02:16,190 --> 01:02:21,950 +العمليات بتكون Exothermic Exo يعني out يعني + +809 +01:02:21,950 --> 01:02:27,030 +الحرارة بتخرج هناك الحرارة انتوا بتدخل كويس؟ هي + +810 +01:02:27,030 --> 01:02:30,250 +الحرارة بتخرج a process in which the system + +811 +01:02:30,250 --> 01:02:36,260 +generatesheat is called exothermic البروسيس بتكون + +812 +01:02:36,260 --> 01:02:41,360 +exothermic لما طبعا ال system يعطينا حرارة مثال + +813 +01:02:41,360 --> 01:02:44,780 +عليه لما يتفعل ال aluminum مع ال iron oxide هذا + +814 +01:02:44,780 --> 01:02:48,960 +اسمه thermite reaction reaction معروف فبيتحول ال + +815 +01:02:48,960 --> 01:02:52,560 +aluminum oxide وال iron مع شدة الحرارة بيدوب هو + +816 +01:02:52,560 --> 01:02:56,980 +solid اه بيتحول ل solid لكنه ايش ماله بيدوب بينسهر + +817 +01:02:56,980 --> 01:03:02,780 +حرارة عالية للغايةبرضه الـ Exothermic Reactions كل + +818 +01:03:02,780 --> 01:03:06,600 +الـ Combustion Reactions Exothermic Reactions لأنه + +819 +01:03:06,600 --> 01:03:10,680 +لما أنا أجي بدي أحرج الـ Natural Gas بدي أحرج الـ + +820 +01:03:10,680 --> 01:03:15,020 +Diesel أي .. أي Combustion Reaction هينتج عنه + +821 +01:03:15,020 --> 01:03:23,360 +حرارة يعني هو يُعتبر Exothermic Reaction طب + +822 +01:03:23,360 --> 01:03:28,520 +الآن نيجي نتطلع على مفهومفي الـ Thermodynamics في + +823 +01:03:28,520 --> 01:03:35,060 +عندي حاجة بسميها State Function State Function هي + +824 +01:03:35,060 --> 01:03:39,000 +عبارة عن دالة حالة بيقولوها باللغة العربية يعني هي + +825 +01:03:39,000 --> 01:03:46,760 +عبارة عن دالة الظروف + +826 +01:03:46,760 --> 01:03:52,160 +الحالية هي اللي بتحدد قيمتهاهي اللي بتحدد قيمتها + +827 +01:03:52,160 --> 01:03:56,640 +مش ظروف الدالة يعني ال .. ال conditions المرتبطة + +828 +01:03:56,640 --> 01:04:01,800 +بالدالة هذه هي اللي بتحدد قيمتها مش كيفية الوصول + +829 +01:04:01,800 --> 01:04:05,700 +إلى هذه الحالة مش كيفية الوصول إلى هذه الحالة يعني + +830 +01:04:05,700 --> 01:04:11,770 +مثلا لو عندك اضرب مثال و اعود ارجع تانيأضرب مثله + +831 +01:04:11,770 --> 01:04:17,650 +أو ده ارجع تاني لو قلنا انه شط بحر غزة يعني لما + +832 +01:04:17,650 --> 01:04:22,870 +توجه فعال كورنيش بيرتفع عن سطح البحر تلاتين فوت + +833 +01:04:24,960 --> 01:04:29,260 +وبينما لو روحنا على الشجعية بنلاقي ان ارتفاع الأرض + +834 +01:04:29,260 --> 01:04:34,340 +هناك حوالي 280 فوت عن سطح البحر فبنقول يعني + +835 +01:04:34,340 --> 01:04:41,120 +الارتفاع ال altitude 280 ناقص 30 هو عبارة عن 250 + +836 +01:04:41,120 --> 01:04:44,880 +فوت من الشط لشجعية + +837 +01:04:46,330 --> 01:04:50,790 +بغض النظر ها بغض النظر هذه القيمة بتبقى دائما + +838 +01:04:50,790 --> 01:04:56,430 +ثابتة تتغيرش تتغيرش ال altitude مابيتغير لأنه عندي + +839 +01:04:56,430 --> 01:05:03,710 +هان ال ال كورنيش بعيد تلاتين والأرض في شجعية بعيدة + +840 +01:05:03,710 --> 01:05:07,350 +متين و تمانين اذا ال altitude الفرق بينهم متين و + +841 +01:05:07,350 --> 01:05:11,710 +خمسين بقول هذه تعتبر state function لا تتغير مش + +842 +01:05:11,710 --> 01:05:16,140 +مهم كيف بدنا نحسبهاالمهم انه دايما مادام هذه + +843 +01:05:16,140 --> 01:05:18,860 +موجودة هنا عن تلاتين وهنا عن متين و تمانين فالفرق + +844 +01:05:18,860 --> 01:05:23,160 +بينهم متين و خمسين لكن المسافة بين شط البحر + +845 +01:05:23,160 --> 01:05:28,440 +والشيجعية قال والله واحد راح مباشرة صاروخ أخد + +846 +01:05:28,440 --> 01:05:34,840 +مسافة قليلة واحد راح مثلا من الشيخ ردوان على + +847 +01:05:34,840 --> 01:05:40,500 +الشيجعية واحد راح على جفاليا وبعدين وصل للشط مثلا + +848 +01:05:40,500 --> 01:05:46,370 +يعني المسافات تتعدد حسب المسارالمسافات بتختلف + +849 +01:05:46,370 --> 01:05:51,170 +بالمسار حسب المسار، عشان هي لا تعتبر دالة حالة، + +850 +01:05:51,170 --> 01:05:55,450 +لأنها تتوقف على المسار، دالة الحالة لا تتوقف على + +851 +01:05:55,450 --> 01:05:59,070 +المسار، وين ما روحنا، من وين ما روحنا، مادام طلعنا + +852 +01:05:59,070 --> 01:06:03,950 +من هنا، من تلاتين، كيف، أي طريق ناخدووصلنا الشجعية + +853 +01:06:03,950 --> 01:06:10,350 +الفرق بينهم من 280 ل 30 250 foot مهما ك altitude + +854 +01:06:10,350 --> 01:06:16,390 +لكن المسافة لا تعتبر دالة حالة ال altitude دالت + +855 +01:06:16,390 --> 01:06:20,450 +حالة او مثال على دالة الحالة لكن ال distance لأ + +856 +01:06:20,450 --> 01:06:24,690 +لأن ال distance تعتمد على المسار فال distance لا + +857 +01:06:24,690 --> 01:06:31,820 +تعتبر دالة حالة مثلا كمان انا عندي مادةLiquid معين + +858 +01:06:31,820 --> 01:06:38,140 +إيه ال density؟ ال density كذا gram لكل مل مش مهم + +859 +01:06:38,140 --> 01:06:40,300 +كيف أوصل ل + +860 +01:06:49,470 --> 01:06:55,030 +عن نفس الظروف، درجة الحرارة أو الضغط مثلا فبلاحظ + +861 +01:06:55,030 --> 01:06:59,270 +انه دائما ال density لها هي نفس ال density فهذه + +862 +01:06:59,270 --> 01:07:03,830 +دالة حالة بعتبرها دالة حالة فدالة الحالة لا تتوقف + +863 +01:07:03,830 --> 01:07:07,930 +على المسار اللي انا اتخذته علشان اوصل له الحالة + +864 +01:07:07,930 --> 01:07:16,030 +هذه زي ايشزي ايش؟ زي مثلا انا في عندي مية عند + +865 +01:07:16,030 --> 01:07:21,630 +خمسين degree c عند جداش؟ عند zero degree c، خمسين + +866 +01:07:21,630 --> 01:07:27,130 +gram مية، روحت سخنتها، صارت مية خمسين gram لكن عند + +867 +01:07:27,130 --> 01:07:34,580 +خمسة وعشرين degree c، حلو؟طب في عند مية عند 100 + +868 +01:07:34,580 --> 01:07:39,620 +degree C روحت بردتها لما صارت مية عند 25 degree C + +869 +01:07:39,620 --> 01:07:44,620 +بقول ال internal energy لهذه المية اللي عند 50 + +870 +01:07:44,620 --> 01:07:50,000 +gram H2O 25 degree C هذه ال internal energy لا + +871 +01:07:50,000 --> 01:07:54,340 +تتغير بحسب المسار سواء روحنا و الله سخننا المية و + +872 +01:07:54,340 --> 01:07:58,620 +حولناها لهذه الحالة او روحنا بردنا المية و حولناها + +873 +01:07:58,620 --> 01:08:02,110 +لهذه الحالةالـ Internal Energy واحدة، لا تتوقف على + +874 +01:08:02,110 --> 01:08:06,770 +المسار، مادام عندي ميّه، خمسين جرام، عند خمسة و + +875 +01:08:06,770 --> 01:08:10,670 +عشرين ديجري سي، فالـ Internal Energy واحدة، بغض + +876 +01:08:10,670 --> 01:08:16,970 +النظر كيف حصلت على هذه الحالة، كيف حصلت على هذه + +877 +01:08:16,970 --> 01:08:22,530 +الصورة من الميّه، ال present nature للميّه أو ال + +878 +01:08:22,530 --> 01:08:27,670 +present status للميّه، لا تتغيرالـ Internal energy + +879 +01:08:27,670 --> 01:08:31,630 +دلوقتي ثابتة، بغض النظر عن الطريق اللي وصلت في + +880 +01:08:31,630 --> 01:08:39,450 +إلها، تمام؟ فهذه الـ Delta E من هذا الباب، بنقول + +881 +01:08:39,450 --> 01:08:48,970 +إنها تعتبر دالة حالة دالة الحالة عادة هي الدالة + +882 +01:08:48,970 --> 01:08:52,330 +اللي بيكون لها fixed value for a given set of + +883 +01:08:52,330 --> 01:09:00,960 +conditionsالها قيمة ثابتة عند ظروف معينة الظروف + +884 +01:09:00,960 --> 01:09:04,500 +المعينة اللي بنحكي عنها احنا دائما في الكيميا + +885 +01:09:04,500 --> 01:09:13,220 +بنتكلم عن ال pressure وال temperature وال volume + +886 +01:09:13,220 --> 01:09:16,560 +وال amount of substance عادة وال amount of + +887 +01:09:16,560 --> 01:09:17,160 +substance + +888 +01:09:21,630 --> 01:09:24,930 +فعادةً يعني هذه الحاجات تعتبر هي ال conditions + +889 +01:09:24,930 --> 01:09:30,350 +اللي احنا ممكن نطلع عليها في تقدير أو يعني نقول + +890 +01:09:30,350 --> 01:09:38,570 +والله هل قيمة معينة، هل .. إيش بيسموها؟ قيمة + +891 +01:09:38,570 --> 01:09:42,470 +معينة، هل هي دالة حالة ولا مش دالة حالة؟ + +892 +01:09:46,250 --> 01:09:50,690 +فال .. دوال الحالة ليش بنقول هذا كلام جيد لأنه + +893 +01:09:50,690 --> 01:09:54,370 +دالة الحالة فقط تتوقف على ال current state + +894 +01:09:54,370 --> 01:09:59,230 +وبالتالي التغير فيها عادة يعتمد فقط على ال initial + +895 +01:09:59,230 --> 01:10:03,730 +state و ال final state مش مهم هاي initial state + +896 +01:10:03,730 --> 01:10:06,770 +وهاي + +897 +01:10:06,770 --> 01:10:13,680 +final state شوفت أنا ممكن أروحلها مباشرةأتكلم عن + +898 +01:10:13,680 --> 01:10:18,840 +يعني الـ Delta E هي دالة الحالة E دلت حالة و Delta + +899 +01:10:18,840 --> 01:10:23,940 +E دلت حالة هان الفرق واحد طب افرضه ان انا اتبعت اي + +900 +01:10:23,940 --> 01:10:28,680 +مسار دائما ال Delta E ثابتة لا تتغير مش مهم مادام + +901 +01:10:28,680 --> 01:10:31,940 +وصلت مادام بديت من هان وصلت لهان اذا ال Delta E + +902 +01:10:31,940 --> 01:10:38,320 +دائما ثابتة لا تتغير اعتقد في عندي مثال جيد يوضح + +903 +01:10:38,320 --> 01:10:39,140 +هذه الصورة + +904 +01:10:46,790 --> 01:10:53,690 +أه فمثلا مثلا خلّا يطلع أنا عندي ال charge battery + +905 +01:10:53,690 --> 01:10:58,450 +charge battery يعني البطارية المشحونة هي عبارة عن + +906 +01:10:58,450 --> 01:11:02,570 +ال initial state عندي يعني عندي بطارية مشحونة هدا + +907 +01:11:02,570 --> 01:11:06,730 +هي و this charge battery هي اللي ايه يعني البطارية + +908 +01:11:06,730 --> 01:11:09,510 +الفاضية هي اللي ايه يعني بدي افضيها البطارية + +909 +01:11:09,510 --> 01:11:14,000 +الفاضية هي ال final stateتمام بقول انا ممكن اعمل + +910 +01:11:14,000 --> 01:11:18,960 +هذا الكلام بعدد طرق ممكن مثلا ان اوصل سلك بين + +911 +01:11:18,960 --> 01:11:25,120 +الموجب والسالب ايش بحصل جال السلك بيسخن يبقى كل ال + +912 +01:11:25,120 --> 01:11:31,160 +energy اللي هي ال delta E اتحولت ل ايه؟ لهيت يبقى + +913 +01:11:31,160 --> 01:11:38,020 +ال delta E بتساوي Q زائد W وW صفرماصارش في عندى اي + +914 +01:11:38,020 --> 01:11:42,820 +شغل فىش عندى اي شغل فكل المسافة هذه عبارة عن ايه + +915 +01:11:42,820 --> 01:11:49,520 +اتحولت من charged ل discharged عن طريق فقد الحرارة + +916 +01:11:49,520 --> 01:11:55,700 +فقط طيب بقول خلينا نتطلع على وسيلة تانية لتفريغ + +917 +01:11:55,700 --> 01:12:00,760 +البطارية جالب الله خلينا نشغل فيها هواية الهواية + +918 +01:12:00,760 --> 01:12:07,340 +أثناء شغلها تعمل تعمل شغلشغل و في نفس الوقت لو + +919 +01:12:07,340 --> 01:12:10,280 +حطيتي إيدك على الموتور من ورا إيش بتلاقيه؟ سخن + +920 +01:12:10,280 --> 01:12:14,460 +شوية فهي تورك بما أن ال delta E بتساوي + +921 +01:12:17,620 --> 01:12:24,500 +الـ Q زي الـ W جهاز الـ Heat Org من هنا بفهم ان + +922 +01:12:24,500 --> 01:12:28,640 +الـ Delta A الـ Charge Battery ل الـ Discharge + +923 +01:12:28,640 --> 01:12:34,340 +Battery هذه ثابتة هذه دالة حالة لكن الـ Q و الـ W + +924 +01:12:34,340 --> 01:12:38,620 +ما هماش دوا الحالة ليه؟ لأنه والله لو كانت دالة + +925 +01:12:38,620 --> 01:12:42,720 +حالة كان الـ Q بتساوي هذه كلها Q بينما هي انجسمت + +926 +01:12:42,720 --> 01:12:48,800 +الـ Q انجسمت ل W و انجسمت ل Heatفالـ Q عندي و ال W + +927 +01:12:48,800 --> 01:12:53,020 +ما هوش .. ماهماش ده بالحالة .. ليه؟ لأنه بيتوقف + +928 +01:12:53,020 --> 01:12:56,200 +يعني على كيف أنا بده أفرغ البطارية والله بده أفرغ + +929 +01:12:56,200 --> 01:13:01,480 +البطارية بإني أعمل شغل .. بعمل شغل و بطلع شوية + +930 +01:13:01,480 --> 01:13:04,680 +heat ممكن .. بده أفرغ البطارية مثلا يعتبروا + +931 +01:13:04,680 --> 01:13:07,700 +البطارية حاطيتها في .. إيش بيسموه؟ في flashlight + +932 +01:13:08,880 --> 01:13:12,660 +الـ Flashlight لما أنا أشغله البطارية برضه كمان + +933 +01:13:12,660 --> 01:13:17,280 +بتعطيني حرارة لأنه بيسخن وبتعطيني ضوء فاتحول لإيه + +934 +01:13:17,280 --> 01:13:21,520 +لأنواع مختلفة من الطاقة فبالتالي عند الـ Delta E + +935 +01:13:21,520 --> 01:13:26,680 +تعتبر دالة حالة تتوقف فقط على ال initial state و + +936 +01:13:26,680 --> 01:13:31,700 +ال final state لا تتوقف على الطريق هل عملتها عن + +937 +01:13:31,700 --> 01:13:37,580 +طريق كله هيت ولا كله هيته شغل ولا كله شغلعند الـ + +938 +01:13:37,580 --> 01:13:46,760 +Delta A هي عبارة عن دالة حالة بينما الـ + +939 +01:13:46,760 --> 01:13:52,280 +Q والـ W لا تعتبر دوال حالة وإن كان مجموعهم يعتبر + +940 +01:13:52,280 --> 01:13:54,720 +دالة حالة لأن هو الـ Delta A + +941 +01:14:00,650 --> 01:14:06,290 +بنطلع أيضًا على دالة جديدة تعتبر دالة حالة بنتكلم + +942 +01:14:06,290 --> 01:14:09,350 +من مقدمة صغيرة عنها، في عندى حاجة بيقولها enthalpy + +943 +01:14:09,350 --> 01:14:15,470 +enthalpy جاية من الجريك يعني to warm يعني + +944 +01:14:15,470 --> 01:14:20,410 +enthalpy، احنا في اللغة العربية يعني بنحب نترجم + +945 +01:14:20,410 --> 01:14:24,340 +علنا ال heat contentheat content يعني او ال + +946 +01:14:24,340 --> 01:14:28,880 +enthalpy to warm معناته enthalpy أو to warm بقول + +947 +01:14:28,880 --> 01:14:35,780 +احنا ممكن نعمل combination ما بين او وجدنا انه لو + +948 +01:14:35,780 --> 01:14:40,000 +عملنا combination ما بين ال internal energy و ال + +949 +01:14:40,000 --> 01:14:44,140 +pressure و ال volume ممكن نحصل على دالة حالة جديدة + +950 +01:14:44,140 --> 01:14:50,600 +اسمها H او ال enthalpy بحيث انه ال H بتساوي E زائد + +951 +01:14:50,600 --> 01:14:55,200 +PVالـ H اللي هي دالة حالة جديدة بتعبر عن الـ Heat + +952 +01:14:55,200 --> 01:15:01,220 +content في الـ system H بتساوي E زائد PV وحنفرجيكم + +953 +01:15:01,220 --> 01:15:06,300 +ليش الـ H ليش عملنا هيك؟ ليش حبينا أن نعرف دالة + +954 +01:15:06,300 --> 01:15:12,500 +حالة جديدة اسمها H؟ قال لأنه سهل جدا بعد شوية + +955 +01:15:12,500 --> 01:15:18,080 +حنشوف سهل جدا أنه نحسبها سهل جدا أنه نحسب الـ Heat + +956 +01:15:18,080 --> 01:15:28,600 +content باستخدامهافعلى سبيل المثال خلّي تفاعل زي + +957 +01:15:28,600 --> 01:15:36,400 +الـ Zinc بتفاعل مع الـ HCl واحنا شوفنا في سلسلة + +958 +01:15:36,400 --> 01:15:41,400 +النشاط إنه الـ Zinc فوق الـ الهيدروجين فبتالي + +959 +01:15:41,400 --> 01:15:45,760 +بتفاعل مع الـ H Plus أو الـ HCl بعطينا Zinc + +960 +01:15:48,330 --> 01:15:53,990 +2 plus زائد H2 يعني عند الحجم بده يزيد يعني لو + +961 +01:15:53,990 --> 01:15:58,370 +جينا اطلعناه هان عند ال zinc وهي هان ال HCl لو + +962 +01:15:58,370 --> 01:16:03,250 +اجيت لفيت هذا شوية بيحصل ان ال zinc بيسحل وين داخل + +963 +01:16:03,250 --> 01:16:09,090 +ال flask فبيتفاعل كويس فإيش بيتكون؟ بيتكون عند حجم + +964 +01:16:09,090 --> 01:16:12,270 +اللي هو ال H2 فمعنى الكلام ال system إيش بده يعمل؟ + +965 +01:16:13,330 --> 01:16:17,690 +هو اللي بده يعمل pushing للـ piston اللي موجود + +966 +01:16:17,690 --> 01:16:20,950 +وبالتالي الحجم بده يزيد يعني هو اللي بده يعمل work + +967 +01:16:20,950 --> 01:16:27,530 +هو اللي بده يعمل work فعندي ال work هذا بنسميه + +968 +01:16:27,530 --> 01:16:33,090 +expansion work مين اللي عامل ال work؟ ال system + +969 +01:16:33,090 --> 01:16:36,150 +اذا ال work ايه اش ماله؟ negative و بقدر اقوله ال + +970 +01:16:36,150 --> 01:16:40,140 +W بتسوى minus P delta Vالـ W بتساوي minus P delta + +971 +01:16:40,140 --> 01:16:44,020 +V الـ delta V طبعا اللي هي ال V final minus ال V + +972 +01:16:44,020 --> 01:16:52,180 +initial فلكن عندي ال ال ال W هو P delta V بس A + +973 +01:16:52,180 --> 01:16:57,900 +بالسالب لأنه عندي انا ال ال ال work هو عبارة عن PV + +974 +01:16:57,900 --> 01:17:02,970 +work ال work اللي عندي هو عبارة عن PV workفالعكس + +975 +01:17:02,970 --> 01:17:08,170 +لو كان ال system بدل ما يعطيني gas هو كان gas + +976 +01:17:08,170 --> 01:17:12,890 +واعطاني solid فال .. اه فبلاحظ ان ال work بدو يكون + +977 +01:17:12,890 --> 01:17:15,990 +positive عكسه ليه؟ لأنه بدو ال surroundings هي + +978 +01:17:15,990 --> 01:17:22,790 +اللي تعمل work على ال system فانا عندي ال H بتساوي + +979 +01:17:22,790 --> 01:17:30,680 +E زائد PV طب لو أخدنا ال deltaهو الـ ΔH يساوي الـ + +980 +01:17:30,680 --> 01:17:36,840 +D للـ E زائد الـ PV أو Δ E زائد P Δ V زائد V Δ P + +981 +01:17:36,840 --> 01:17:40,960 +لكن احنا أغلب شغلنا في المختبرات at constant + +982 +01:17:40,960 --> 01:17:46,600 +pressure يعني الـ Delta P إيه؟ الـ Delta P تعتبر + +983 +01:17:46,600 --> 01:17:50,840 +ثابت يعني صفر Delta P تغير صفر فبالتالي الـ Delta + +984 +01:17:50,840 --> 01:17:55,100 +H بتساوي Delta + +985 +01:17:55,100 --> 01:18:03,110 +E زائد P Delta Vيبقى هذه هي المعادلة الانثالبي إذا + +986 +01:18:03,110 --> 01:18:07,270 +الله راضي الحصة الجاية بنبدأ منها علشان نعدي + +987 +01:18:07,270 --> 01:18:12,010 +لمفهوم واسع جدا كيف نحسب ال heat transfer أو ال + +988 +01:18:12,010 --> 01:18:17,740 +heat change في ال systemنتطلع على كيفية حساب الـ + +989 +01:18:17,740 --> 01:18:21,680 +Delta H اللي هي بتعبر تعبير صادقة، في البداية + +990 +01:18:21,680 --> 01:18:25,900 +هنثبت أن هي عبارة عن الـ heated change و هنشوف أيش + +991 +01:18:25,900 --> 01:18:29,440 +طرق حساب الـ heated change إذا الله راد الحصة + +992 +01:18:29,440 --> 01:18:29,800 +الجاية +