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+1
+00:00:21,670 --> 00:00:24,050
+Assalamualaikum warahmatullahi wabarakatuh.
+
+2
+00:00:26,990 --> 00:00:30,410
+Today, inshallah, in the lecture before the last,
+
+3
+00:00:30,950 --> 00:00:35,930
+we are going to complete the reading passage, the
+
+4
+00:00:35,930 --> 00:00:37,450
+third passage.
+
+5
+00:00:40,490 --> 00:00:47,810
+Job Dreams. The title of the third text is The
+
+6
+00:00:47,810 --> 00:00:54,480
+Cowboy in the Sky. This job is the cowboy in the
+
+7
+00:00:54,480 --> 00:01:01,960
+sky. The iron worker who works up in the sky. His
+
+8
+00:01:01,960 --> 00:01:09,480
+name is Michel Doyle. Michel Doyle, iron worker.
+
+9
+00:01:11,920 --> 00:01:16,620
+A quotation from his conversation is, many of
+
+10
+00:01:16,620 --> 00:01:21,480
+today's iron workers are descendants of the men
+
+11
+00:01:21,480 --> 00:01:25,980
+who built New York's first skyscrapers.
+
+12
+00:01:30,260 --> 00:01:34,140
+Michel Doyle is an iron worker. He works with the
+
+13
+00:01:34,140 --> 00:01:41,080
+iron, iron of the building. In New York City, He
+
+14
+00:01:41,080 --> 00:01:44,760
+works in New York City. He is an iron worker. Iron
+
+15
+00:01:44,760 --> 00:01:53,120
+worker. He is one of the 150 iron workers
+
+16
+00:01:53,120 --> 00:02:01,000
+currently erecting the steel frame of the new 40
+
+17
+00:02:01,000 --> 00:02:07,430
+-story building in Times Square. These iron
+
+18
+00:02:07,430 --> 00:02:14,150
+workers are known as cowboys in the sky. Now he is
+
+19
+00:02:14,150 --> 00:02:17,830
+working in a big building. A building of 40
+
+20
+00:02:17,830 --> 00:02:23,810
+stories. A building of 40 stories. What is his
+
+21
+00:02:23,810 --> 00:02:27,830
+job? His job is iron worker. The worker of the
+
+22
+00:02:27,830 --> 00:02:28,270
+iron.
+
+23
+00:02:31,630 --> 00:02:39,200
+He is one of the best 150. uh-huh currently
+
+24
+00:02:39,200 --> 00:02:44,240
+building in the times square so we're in new york
+
+25
+00:02:44,240 --> 00:02:49,660
+in times square uh-huh the name of the square
+
+26
+00:02:49,660 --> 00:02:57,220
+times square these the 100 or the 50 these iron
+
+27
+00:02:57,220 --> 00:03:00,620
+workers or these workers the famous iron workers
+
+28
+00:03:00,620 --> 00:03:06,710
+are known as cowboys in the sky Because they are
+
+29
+00:03:06,710 --> 00:03:11,030
+like the cowboys, but not on land. They are on the
+
+30
+00:03:11,030 --> 00:03:15,910
+sky. Why? Because they have dangerous job.
+
+31
+00:03:16,550 --> 00:03:20,350
+Dangerous job. Their job is in the air, in the
+
+32
+00:03:20,350 --> 00:03:23,230
+sky. They work with the iron.
+
+33
+00:03:26,310 --> 00:03:32,340
+The first question, how did you get your job? Iron
+
+34
+00:03:32,340 --> 00:03:38,700
+work is a trade that is still handed down from
+
+35
+00:03:38,700 --> 00:03:48,740
+father to son. Handed down. Passed down. It goes
+
+36
+00:03:48,740 --> 00:03:56,860
+from father to son, from son to son, etc. So, all
+
+37
+00:03:56,860 --> 00:04:01,310
+the family is iron worker. From father to son,
+
+38
+00:04:01,690 --> 00:04:05,710
+many of today's ironworkers are descendants of the
+
+39
+00:04:05,710 --> 00:04:10,570
+men who built New York's first skyscrapers.
+
+40
+00:04:15,550 --> 00:04:20,690
+New York is famous for its skyscrapers. New York
+
+41
+00:04:20,690 --> 00:04:24,890
+is full of skyscrapers, high buildings, towers.
+
+42
+00:04:26,350 --> 00:04:30,970
+The people who worked there at first They have
+
+43
+00:04:30,970 --> 00:04:36,110
+sons and their sons have sons. So we call them,
+
+44
+00:04:36,790 --> 00:04:43,450
+this trade is handed down from father to son. Who
+
+45
+00:04:43,450 --> 00:04:47,850
+are these people? Many of today's hired workers
+
+46
+00:04:47,850 --> 00:04:54,140
+are descendants. come from? They originally are
+
+47
+00:04:54,140 --> 00:04:58,780
+from the men who built in New York first
+
+48
+00:04:58,780 --> 00:05:05,940
+skyscrapers in the past. My great grandfather, not
+
+49
+00:05:05,940 --> 00:05:09,920
+my grandfather, the father of my grandfather, the
+
+50
+00:05:09,920 --> 00:05:15,580
+father of my grandfather, came over from Ireland.
+
+51
+00:05:16,060 --> 00:05:20,890
+He came from Ireland. He is Irish. He's from
+
+52
+00:05:20,890 --> 00:05:24,910
+Ireland, he is Irish. He was from Ireland, so he
+
+53
+00:05:24,910 --> 00:05:31,890
+was Irish. In 1930, why? To work on the
+
+54
+00:05:31,890 --> 00:05:35,810
+construction of the Empire State Building.
+
+55
+00:05:38,410 --> 00:05:42,370
+His great-grandfather came to New York from
+
+56
+00:05:42,370 --> 00:05:47,680
+Ireland. Why? To work with the Empire State
+
+57
+00:05:47,680 --> 00:05:51,100
+Building. My grandfather, my father and
+
+58
+00:05:51,100 --> 00:05:56,600
+grandfather were also ironworkers. So all the
+
+59
+00:05:56,600 --> 00:06:04,560
+family are ironworkers. The son, Michel, father,
+
+60
+00:06:04,980 --> 00:06:10,300
+grandfather, great grandfather, all of them work
+
+61
+00:06:10,300 --> 00:06:15,960
+with the skyscrapers of New York. The New York's
+
+62
+00:06:15,960 --> 00:06:21,120
+first skyscrapers until now. So the question whose
+
+63
+00:06:21,120 --> 00:06:27,280
+job was handed down, handed down, so passed down
+
+64
+00:06:27,280 --> 00:06:35,680
+from father to son. Michelle. Michelle Doyle.
+
+65
+00:06:36,540 --> 00:06:43,490
+Michelle Doyle. This number? Number? Number three,
+
+66
+00:06:44,010 --> 00:06:44,830
+Michelle Doyle.
+
+67
+00:06:47,590 --> 00:06:52,170
+The second paragraph, what do you like most about
+
+68
+00:06:52,170 --> 00:06:59,850
+it? What do you like most about your job? To me, I
+
+69
+00:06:59,850 --> 00:07:05,990
+workers are the kings of construction. The most
+
+70
+00:07:05,990 --> 00:07:12,270
+important job in building is is the iron worker.
+
+71
+00:07:13,270 --> 00:07:18,050
+It means the most important job in building the
+
+72
+00:07:18,050 --> 00:07:22,850
+skyscrapers is the iron workers. So here to me
+
+73
+00:07:22,850 --> 00:07:28,330
+originally iron workers are kings of construction.
+
+74
+00:07:30,310 --> 00:07:36,050
+We make the skeleton. We make the skeleton that
+
+75
+00:07:37,290 --> 00:07:42,370
+other workers build on. So what is their job?
+
+76
+00:07:43,670 --> 00:07:48,550
+Their job is to make the first skeleton that all
+
+77
+00:07:48,550 --> 00:07:51,710
+the other workers build on it. So they are number
+
+78
+00:07:51,710 --> 00:07:58,210
+one. And all the other workers after them. We have
+
+79
+00:07:58,210 --> 00:08:03,170
+real pride in our work. We are proud of our work.
+
+80
+00:08:04,290 --> 00:08:09,710
+You look at the news at the New York skyline and
+
+81
+00:08:09,710 --> 00:08:17,290
+think, I helped build that. He's proud of his job.
+
+82
+00:08:19,030 --> 00:08:24,370
+He's proud of it. Why? When he looks at the
+
+83
+00:08:24,370 --> 00:08:33,250
+skyline, he says, I helped. I helped. build that.
+
+84
+00:08:33,690 --> 00:08:38,070
+I am one of the workers who built that. I am proud
+
+85
+00:08:38,070 --> 00:08:43,490
+of myself because I helped in this building. He
+
+86
+00:08:43,490 --> 00:08:50,410
+helped in this building. Also, we work hard. We
+
+87
+00:08:50,410 --> 00:08:57,910
+work hard. We play hard. Work hard and play hard.
+
+88
+00:08:58,390 --> 00:09:03,070
+We got on well We have good relationship with
+
+89
+00:09:03,070 --> 00:09:10,830
+together with each other. So all the workers get
+
+90
+00:09:10,830 --> 00:09:18,210
+on well with each other. We are workers depend on
+
+91
+00:09:18,210 --> 00:09:24,110
+each other for our lives. We depend on each other
+
+92
+00:09:24,110 --> 00:09:34,010
+for our lives. O and the B The salary is good. The
+
+93
+00:09:34,010 --> 00:09:38,570
+salary is good. So the question here, who gets on
+
+94
+00:09:38,570 --> 00:09:43,490
+well with the people they work with? Michelle
+
+95
+00:09:43,490 --> 00:09:52,730
+Doyle and Linda and Stanley. So number one, two
+
+96
+00:09:52,730 --> 00:09:58,070
+and three. Who is number three? Michelle Doyle.
+
+97
+00:10:06,170 --> 00:10:07,270
+The next question.
+
+98
+00:10:17,770 --> 00:10:24,110
+What's an average day like? You never stop in this
+
+99
+00:10:24,110 --> 00:10:29,730
+job. You are working all the time. You are working
+
+100
+00:10:29,730 --> 00:10:36,260
+all the time. You never stop in this job. eight
+
+101
+00:10:36,260 --> 00:10:41,860
+hours a day from seven in the morning until three
+
+102
+00:10:41,860 --> 00:10:46,300
+in the afternoon eight hours every day it's hard
+
+103
+00:10:46,300 --> 00:10:53,780
+work you are moving all the time moving all the
+
+104
+00:10:53,780 --> 00:11:03,950
+time the crane the crane uh-huh lifts the iron
+
+105
+00:11:03,950 --> 00:11:08,670
+graders it lifts the iron graders like this the
+
+106
+00:11:08,670 --> 00:11:17,930
+iron and like this the iron it lifts it moves the
+
+107
+00:11:17,930 --> 00:11:25,370
+iron upright it moves it and you have to move them
+
+108
+00:11:25,370 --> 00:11:27,970
+into place so
+
+109
+00:11:30,250 --> 00:11:36,410
+The crane lifts the iron and you catch it or put
+
+110
+00:11:36,410 --> 00:11:40,170
+it in the place, the good place, the correct place
+
+111
+00:11:40,170 --> 00:11:47,330
+for building. There is always danger. It is not
+
+112
+00:11:47,330 --> 00:11:53,950
+safe. It is always danger. It's a fact of life for
+
+113
+00:11:53,950 --> 00:11:59,250
+us. It is a fact of life. So any mistake, we can
+
+114
+00:11:59,250 --> 00:12:05,390
+die. It's very dangerous. The iron in the air and
+
+115
+00:12:05,390 --> 00:12:10,550
+we move it in the correct place, in the sky. It's
+
+116
+00:12:10,550 --> 00:12:14,910
+very dangerous. The cowboy in the sky. The second
+
+117
+00:12:14,910 --> 00:12:17,930
+one, have you made any sacrifices to do this job?
+
+118
+00:12:18,930 --> 00:12:24,990
+Yes, one big one, physical health. What is the
+
+119
+00:12:24,990 --> 00:12:31,810
+sacrifice? Health. Physical health, the wear and
+
+120
+00:12:31,810 --> 00:12:38,430
+tear of
+
+121
+00:12:38,430 --> 00:12:41,950
+the body is
+
+122
+00:12:41,950 --> 00:12:48,270
+enormous, big, very big. All our body is injured
+
+123
+00:12:48,270 --> 00:12:51,870
+here and there. All the clothes are torn here and
+
+124
+00:12:51,870 --> 00:12:58,240
+there. I've fallen three times. I have fallen
+
+125
+00:12:58,240 --> 00:13:06,900
+three times. My father fell two stories. I fell
+
+126
+00:13:06,900 --> 00:13:10,660
+three times. What about my father? My father fell
+
+127
+00:13:10,660 --> 00:13:16,240
+two stories. The second floor, the third floor.
+
+128
+00:13:16,480 --> 00:13:21,360
+Two floors. Two stories. Lost a finger. Also, my
+
+129
+00:13:21,360 --> 00:13:29,820
+father lost a finger and broke his ankles and he
+
+130
+00:13:29,820 --> 00:13:35,240
+broke his legs here. He broke his ankles. So it is
+
+131
+00:13:35,240 --> 00:13:40,380
+a dangerous job for him and for his father,
+
+132
+00:13:40,860 --> 00:13:44,000
+grandfather and the great grandfather. It is not
+
+133
+00:13:44,000 --> 00:13:49,000
+easy. It is dangerous job. Here, what would you
+
+134
+00:13:49,000 --> 00:13:54,860
+like to do next? I'd like to work on something
+
+135
+00:13:54,860 --> 00:14:01,400
+really important, like my great grandfather did.
+
+136
+00:14:02,240 --> 00:14:07,460
+So what would he like to do? He wanted to do
+
+137
+00:14:07,460 --> 00:14:12,020
+something bigger. He wanted to work in a famous
+
+138
+00:14:12,020 --> 00:14:15,600
+building, a famous skyscraper, not an ordinary
+
+139
+00:14:15,600 --> 00:14:21,540
+one, like his grandfather and his grandfather. his
+
+140
+00:14:21,540 --> 00:14:27,220
+great grandfather. Oh, like my father did, like
+
+141
+00:14:27,220 --> 00:14:31,980
+his father or his grandfather, who helped build
+
+142
+00:14:31,980 --> 00:14:39,860
+the World Trade Center. So his great grandfather
+
+143
+00:14:39,860 --> 00:14:46,820
+and his grandfather helped in this famous
+
+144
+00:14:46,820 --> 00:14:50,040
+building. This famous skyscraper. What is it?
+
+145
+00:14:50,600 --> 00:14:57,380
+World Trade Center. It's weird. Strange. It's
+
+146
+00:14:57,380 --> 00:15:03,980
+strange. It's weird. He helped build it and I
+
+147
+00:15:03,980 --> 00:15:09,620
+helped take it away. They helped building it and I
+
+148
+00:15:09,620 --> 00:15:12,580
+myself built taking this building away.
+
+149
+00:15:14,940 --> 00:15:16,320
+The last one.
+
+150
+00:15:26,470 --> 00:15:30,350
+What advice would you give to someone who wanted
+
+151
+00:15:30,350 --> 00:15:37,070
+to do your job? What is the advice? You need to be
+
+152
+00:15:37,070 --> 00:15:45,230
+strong. You need to be strong, really strong. You
+
+153
+00:15:45,230 --> 00:15:51,550
+have to be okay with height. You have to be okay
+
+154
+00:15:51,550 --> 00:15:58,760
+with height. It usually takes about a year to get
+
+155
+00:15:58,760 --> 00:16:04,060
+used to it. How long did it take? It took about a
+
+156
+00:16:04,060 --> 00:16:08,940
+year to be accustomed to the height with this
+
+157
+00:16:08,940 --> 00:16:14,540
+building, with this work as iron worker. Many
+
+158
+00:16:14,540 --> 00:16:24,390
+guys, many young people try it once. Many young
+
+159
+00:16:24,390 --> 00:16:29,690
+people come to work with us just one time, then
+
+160
+00:16:29,690 --> 00:16:35,760
+pack off. and say, so most people when they come
+
+161
+00:16:35,760 --> 00:16:38,940
+to work with us, they work for one day. After
+
+162
+00:16:38,940 --> 00:16:45,300
+this, they leave. They then back off and say, this
+
+163
+00:16:45,300 --> 00:16:50,740
+is not for me. I can't bear it. No, no, no. I
+
+164
+00:16:50,740 --> 00:16:55,000
+can't bear it. So they leave the job quickly after
+
+165
+00:16:55,000 --> 00:17:01,320
+the first time. So we have here two words. We have
+
+166
+00:17:01,320 --> 00:17:08,160
+get on well with and was handed down. These are
+
+167
+00:17:08,160 --> 00:17:13,760
+the last two phrasal verbs. What's the meaning of
+
+168
+00:17:13,760 --> 00:17:17,300
+get on well with? We say that you have a good
+
+169
+00:17:17,300 --> 00:17:21,630
+relationship with. We said it before. What about
+
+170
+00:17:21,630 --> 00:17:27,510
+was handed down? It means passed down. Passed
+
+171
+00:17:27,510 --> 00:17:34,450
+down. And by the end of this paragraph, we come to
+
+172
+00:17:34,450 --> 00:17:40,610
+the ten questions in general. So here are the ten
+
+173
+00:17:40,610 --> 00:17:42,710
+questions. All the questions.
+
+174
+00:17:45,210 --> 00:17:50,770
+You understand? So quickly, we want to answer
+
+175
+00:17:50,770 --> 00:17:57,330
+these questions generally. Number one, who gets on
+
+176
+00:17:57,330 --> 00:18:05,070
+well with the people they work with? Number one,
+
+177
+00:18:05,630 --> 00:18:12,670
+two, and three. Number one, two, and three. Who
+
+178
+00:18:12,670 --> 00:18:19,860
+are they? The first one is Stanley Linda And
+
+179
+00:18:19,860 --> 00:18:23,760
+Michelle, uh-huh number two who took up gymnastics
+
+180
+00:18:23,760 --> 00:18:30,760
+Linda number two Linda who hasn't come up with an
+
+181
+00:18:30,760 --> 00:18:38,420
+experiment to do in a space yet Stanley and and
+
+182
+00:18:38,420 --> 00:18:42,200
+Linda Yeah Uh-huh
+
+183
+00:18:47,960 --> 00:18:51,220
+Or Stanley, only Stanley, yes.
+
+184
+00:18:55,720 --> 00:18:59,420
+Number four, whose job was handed down from father
+
+185
+00:18:59,420 --> 00:19:06,240
+to son? Michelle, yeah. Who is cut off from his or
+
+186
+00:19:06,240 --> 00:19:14,250
+her family? Linda and Stanley. Who finds it
+
+187
+00:19:14,250 --> 00:19:17,330
+exciting to end up in different cities and
+
+188
+00:19:17,330 --> 00:19:25,610
+countries? Both of them. Linda and
+
+189
+00:19:25,610 --> 00:19:31,810
+Stanley. Again, who often takes off at the
+
+190
+00:19:31,810 --> 00:19:38,410
+moment's notes? Stanley. Who came across an ad?
+
+191
+00:19:39,230 --> 00:19:44,690
+Stanley. Who wants to carry on working until they
+
+192
+00:19:44,690 --> 00:19:51,250
+are at least 50s? Linda. And who gave up work as a
+
+193
+00:19:51,250 --> 00:19:59,770
+lawyer? Linda. So these are the answers to all of
+
+194
+00:19:59,770 --> 00:20:03,350
+the 10 questions in general, but we answered it
+
+195
+00:20:03,350 --> 00:20:06,570
+after each paragraph, each one under each
+
+196
+00:20:06,570 --> 00:20:10,210
+paragraph. You understand? Yes. Again,
+
+197
+00:20:14,880 --> 00:20:17,380
+This is the answer. Who can read the first
+
+198
+00:20:17,380 --> 00:20:22,860
+question and give me the answer. Who gets on well
+
+199
+00:20:22,860 --> 00:20:26,760
+with the people they work with. All of them. All
+
+200
+00:20:26,760 --> 00:20:31,180
+of them. All the jobs. Number two. Who talks of
+
+201
+00:20:31,180 --> 00:20:37,100
+the Germanist Linda Stewart. Yes. Three.
+
+202
+00:20:41,800 --> 00:20:44,780
+Who hasn't come up with an experiment to do
+
+203
+00:20:44,780 --> 00:20:50,900
+experiments yet? Stanley Carras Whose
+
+204
+00:20:50,900 --> 00:20:56,160
+job was handed down from father to son? Mr. Doyle
+
+205
+00:20:56,160 --> 00:21:05,720
+Who is cut off from his family? Stanley and Linda
+
+206
+00:21:05,720 --> 00:21:07,680
+And number six
+
+207
+00:21:11,720 --> 00:21:15,420
+Who finds it
+
+208
+00:21:15,420 --> 00:21:19,340
+exciting to get to end up in different cities and
+
+209
+00:21:19,340 --> 00:21:24,660
+they can rest in a sunny country. Sunny country,
+
+210
+00:21:24,760 --> 00:21:34,500
+yes. And Linda Spellman. Number seven. Yes? Who
+
+211
+00:21:34,500 --> 00:21:39,700
+often takes the off at the weekends Stanley.
+
+212
+00:21:39,800 --> 00:21:41,980
+Stanley Curtis. Yes. Number eight.
+
+213
+00:21:47,440 --> 00:21:53,440
+Stanley. And number nine. Yeah.
+
+214
+00:21:57,800 --> 00:21:58,580
+Linda.
+
+215
+00:22:01,680 --> 00:22:04,440
+Uh huh. And the last one. Yeah.
+
+216
+00:22:08,230 --> 00:22:18,450
+Yes, so Now we have All the phrasal verbs We want
+
+217
+00:22:18,450 --> 00:22:21,330
+to connect it with the meaning. So this is the
+
+218
+00:22:21,330 --> 00:22:24,950
+meaning of the underlined phrasal verbs This is
+
+219
+00:22:24,950 --> 00:22:31,570
+the meaning of the underlined phrasal verbs Again
+
+220
+00:22:33,630 --> 00:22:37,630
+Who gets on well with the people they work with?
+
+221
+00:22:37,830 --> 00:22:41,690
+Now, I don't want the question, who? No, I want
+
+222
+00:22:41,690 --> 00:22:45,910
+the meaning of the phrasal verbs. So this
+
+223
+00:22:45,910 --> 00:22:51,670
+underlined phrasal verbs means is what? Have a
+
+224
+00:22:51,670 --> 00:22:56,610
+good relationship with. Again, what's the meaning
+
+225
+00:22:56,610 --> 00:23:01,910
+of gets on well with? have a good relationship
+
+226
+00:23:01,910 --> 00:23:06,890
+with number two who took up gymnastics took up
+
+227
+00:23:06,890 --> 00:23:15,250
+means start doing start doing who hasn't come up
+
+228
+00:23:15,250 --> 00:23:19,810
+with an experiment to do in space yet come up with
+
+229
+00:23:19,810 --> 00:23:26,990
+means think of yeah whose job was handed down from
+
+230
+00:23:26,990 --> 00:23:34,110
+father to son It means passed down. Passed down.
+
+231
+00:23:35,230 --> 00:23:41,130
+Who is cut off from his or her family? Cut off
+
+232
+00:23:41,130 --> 00:23:46,970
+from means separated from. Who finds it exciting
+
+233
+00:23:46,970 --> 00:23:52,870
+to end up in different cities and countries? End
+
+234
+00:23:52,870 --> 00:23:59,770
+up means finally find yourself. Who often takes
+
+235
+00:23:59,770 --> 00:24:06,010
+off at the moment's notes, leave the ground and
+
+236
+00:24:06,010 --> 00:24:16,730
+fly. Who came across an ad, find by chance. Again,
+
+237
+00:24:17,250 --> 00:24:22,750
+who wants to carry on working until they are at
+
+238
+00:24:22,750 --> 00:24:28,760
+least 50, continue. The last one, who gave up work
+
+239
+00:24:28,760 --> 00:24:34,720
+as a lawyer? Stopped working. So now again, I want
+
+240
+00:24:34,720 --> 00:24:38,660
+to ask the question, but not with this word, with
+
+241
+00:24:38,660 --> 00:24:45,080
+the meaning. Who had a good relationship with the
+
+242
+00:24:45,080 --> 00:24:49,240
+people they worked with? Number two, who started
+
+243
+00:24:49,240 --> 00:24:55,780
+doing gymnastics? Three, who hasn't think of an
+
+244
+00:24:55,780 --> 00:25:01,600
+experiment to do in space yet, whose job was
+
+245
+00:25:01,600 --> 00:25:05,580
+passed down from father to son, passed down from
+
+246
+00:25:05,580 --> 00:25:11,900
+father to son. Five, who is separated from his or
+
+247
+00:25:11,900 --> 00:25:18,000
+her family. Six, who finds it exciting to finally
+
+248
+00:25:18,000 --> 00:25:20,400
+find himself in different cities and countries.
+
+249
+00:25:22,020 --> 00:25:26,300
+who often leave
+
+250
+00:25:26,300 --> 00:25:31,740
+the ground and fly at the moment's notes, who
+
+251
+00:25:31,740 --> 00:25:39,800
+finally find by chance an ad, find by chance.
+
+252
+00:25:40,700 --> 00:25:44,660
+Number nine, who wants to continue working until
+
+253
+00:25:44,660 --> 00:25:51,950
+they are at least 50s, who stopped doing as a
+
+254
+00:25:51,950 --> 00:25:57,310
+lawyer. So these 10 phrasal verbs are important.
+
+255
+00:25:57,930 --> 00:26:01,510
+These are the phrasal verbs and these are the
+
+256
+00:26:01,510 --> 00:26:06,930
+meanings. We have to translate each one in
+
+257
+00:26:06,930 --> 00:26:17,090
+English. Who can read? Yes, just read the phrasal
+
+258
+00:26:17,090 --> 00:26:22,290
+verb and the meaning. Gets on well with, have a
+
+259
+00:26:22,290 --> 00:26:27,150
+good relationship with. Talk up, start talking
+
+260
+00:26:27,150 --> 00:26:35,950
+down. Talk up when you need talk up. Hand down,
+
+261
+00:26:36,150 --> 00:26:41,470
+pass down. Pass down. Cut off from, separated
+
+262
+00:26:41,470 --> 00:26:49,170
+from. To end up, finally find yourself. Yeah.
+
+263
+00:26:50,130 --> 00:26:50,570
+Next.
+
+264
+00:26:56,210 --> 00:27:02,610
+And the
+
+265
+00:27:02,610 --> 00:27:03,530
+one before the last.
+
+266
+00:27:06,490 --> 00:27:10,350
+Stop doing.
+
+267
+00:27:11,130 --> 00:27:16,670
+Again, get on well with, have a good relationship
+
+268
+00:27:16,670 --> 00:27:17,130
+with
+
+269
+00:27:21,600 --> 00:27:27,240
+End up with, think of. Was handed down, passed
+
+270
+00:27:27,240 --> 00:27:33,840
+down. Cut off from, separated from. End up,
+
+271
+00:27:34,360 --> 00:27:39,440
+finally find yourself. Takes off, leave the ground
+
+272
+00:27:39,440 --> 00:27:46,300
+and fly. Came across, find by chance. Carry on,
+
+273
+00:27:47,340 --> 00:27:51,910
+continue. Give up. Stop doing.
+
+274
+00:27:56,070 --> 00:27:56,630
+Yes.
+
+275
+00:28:11,610 --> 00:28:12,750
+Now,
+
+276
+00:28:14,940 --> 00:28:19,560
+Page 57, we have an exercise about the present
+
+277
+00:28:19,560 --> 00:28:20,140
+perfect.
+
+278
+00:28:33,420 --> 00:28:39,520
+The president has resigned or has been resigned.
+
+279
+00:28:40,690 --> 00:28:44,390
+The president has resigned or has been resigned?
+
+280
+00:28:45,970 --> 00:28:50,650
+Has resigned. He is the door of the action. He
+
+281
+00:28:50,650 --> 00:28:57,890
+resigned. He has resigned. And a new president has
+
+282
+00:28:57,890 --> 00:28:59,170
+been elected.
+
+283
+00:29:03,420 --> 00:29:08,520
+Again, the president has resigned and a new
+
+284
+00:29:08,520 --> 00:29:12,680
+president has been elected. This is in the present
+
+285
+00:29:12,680 --> 00:29:15,700
+perfect and this is in the present perfect
+
+286
+00:29:15,700 --> 00:29:22,320
+passive. Present perfect passive. The other one.
+
+287
+00:29:24,600 --> 00:29:28,540
+His resignation announced or was announced
+
+288
+00:29:28,540 --> 00:29:32,520
+yesterday? Was announced because it is passive.
+
+289
+00:29:34,250 --> 00:29:40,190
+This thing, resignation, leaving the job, was
+
+290
+00:29:40,190 --> 00:29:45,790
+announced yesterday on television. Because this is
+
+291
+00:29:45,790 --> 00:29:48,770
+not a subject, it is an object. So it is in that
+
+292
+00:29:48,770 --> 00:29:50,110
+passive.
+
+293
+00:29:51,810 --> 00:29:55,870
+Number three, where did you go or where have you
+
+294
+00:29:55,870 --> 00:30:05,180
+gone on your last holiday? It was fabulous. So the
+
+295
+00:30:05,180 --> 00:30:09,820
+answer is, where did you go?
+
+296
+00:30:12,760 --> 00:30:18,660
+Where did you go? Where did you go? Why? Because
+
+297
+00:30:18,660 --> 00:30:23,720
+it is in the last holiday in the past. In the
+
+298
+00:30:23,720 --> 00:30:27,820
+past. So it is a question in the past simple.
+
+299
+00:30:28,880 --> 00:30:31,720
+Question in the past simple. Why? Because we have
+
+300
+00:30:31,720 --> 00:30:37,400
+on your last holiday. On your last holiday is a
+
+301
+00:30:37,400 --> 00:30:42,360
+time phrase in the past. And here, why is this in
+
+302
+00:30:42,360 --> 00:30:46,760
+the past? Because we have yesterday and we have
+
+303
+00:30:46,760 --> 00:30:52,820
+but here we don't have a time phrase. So it should
+
+304
+00:30:52,820 --> 00:30:55,640
+be in the present perfect and in the present
+
+305
+00:30:55,640 --> 00:30:57,100
+perfect passive.
+
+306
+00:30:59,540 --> 00:31:03,700
+The president
+
+307
+00:31:03,700 --> 00:31:11,800
+has resigned and a new president has been elected.
+
+308
+00:31:16,060 --> 00:31:20,360
+His resignation
+
+309
+00:31:20,360 --> 00:31:26,480
+was announced yesterday on television. Yesterday
+
+310
+00:31:26,480 --> 00:31:36,260
+on Kelvin in the past we use past simple Fabulous
+
+311
+00:31:36,260 --> 00:31:39,920
+Number
+
+312
+00:31:39,920 --> 00:31:48,060
+four Number
+
+313
+00:31:48,060 --> 00:31:50,220
+four did
+
+314
+00:31:51,820 --> 00:31:58,280
+Did John ever go or has John ever been to Paris?
+
+315
+00:32:00,420 --> 00:32:06,560
+Has John ever been to Paris? Oh, yes. Five times.
+
+316
+00:32:07,360 --> 00:32:12,420
+Without time phrase. So we usually say, has John
+
+317
+00:32:12,420 --> 00:32:17,360
+ever been? Has he ever been? Not did you ever?
+
+318
+00:32:18,040 --> 00:32:21,430
+Because it is in the past until now. Present?
+
+319
+00:32:21,870 --> 00:32:28,750
+Perfect. Has John ever been to Paris? Oh yes, five
+
+320
+00:32:28,750 --> 00:32:35,890
+times. Number five. The plane took off or has
+
+321
+00:32:35,890 --> 00:32:40,290
+taken off a few minutes ago. Took off. Why?
+
+322
+00:32:41,170 --> 00:32:46,590
+Because we have a go in the past. Timing phrase in
+
+323
+00:32:46,590 --> 00:32:51,720
+the past. The plane took off a few minutes ago
+
+324
+00:32:51,720 --> 00:33:01,820
+Number six A huge snow storm It is the double of
+
+325
+00:33:01,820 --> 00:33:12,160
+the action has hit It has hit Toronto over 40 cm
+
+326
+00:33:12,160 --> 00:33:21,350
+of snow Has fallen over the past 12 hours.
+
+327
+00:33:23,110 --> 00:33:32,810
+Residents have been advised to
+
+328
+00:33:32,810 --> 00:33:38,870
+stay at home. Again. Has John ever been to Paris?
+
+329
+00:33:39,750 --> 00:33:44,990
+Number five. The plane took off a few minutes ago.
+
+330
+00:33:45,530 --> 00:33:53,540
+Six. A huge snow storm has hit Toronto. Over 40 cm
+
+331
+00:33:53,540 --> 00:33:57,280
+of snow has fallen over the past 12 hours.
+
+332
+00:33:58,180 --> 00:34:03,760
+Residents have been advised, someone advised the
+
+333
+00:34:03,760 --> 00:34:13,840
+people to stay at home. Who can read? Has John
+
+334
+00:34:13,840 --> 00:34:16,700
+ever been to Paris? Oh yes, five times.
+
+335
+00:34:22,390 --> 00:34:41,030
+Next Last one Yes,
+
+336
+00:34:41,830 --> 00:34:42,570
+so
+
+337
+00:34:54,560 --> 00:34:58,680
+Open your book page 61. We have conversation
+
+338
+00:34:58,680 --> 00:35:07,120
+conversation We
+
+339
+00:35:07,120 --> 00:35:15,200
+have five short conversation Number one This is in
+
+340
+00:35:15,200 --> 00:35:19,680
+everyday language on the phone Everyday language
+
+341
+00:35:19,680 --> 00:35:26,640
+everyday English on the phone Hello, could I, we
+
+342
+00:35:26,640 --> 00:35:31,480
+want to choose from these words. Could I speak to
+
+343
+00:35:31,480 --> 00:35:36,400
+Sam Jackson, please? Speak to.
+
+344
+00:35:41,100 --> 00:35:47,180
+Number B. I'm afraid. I'm afraid.
+
+345
+00:35:50,380 --> 00:35:56,900
+It means I'm sorry. I'm sorry, Mr. Jackson's in a
+
+346
+00:35:56,900 --> 00:35:59,220
+meeting. He is in a meeting.
+
+347
+00:36:01,780 --> 00:36:07,700
+It won't be over until three. So the meeting will
+
+348
+00:36:07,700 --> 00:36:15,540
+be until three. Can I take a message? Can I take a
+
+349
+00:36:15,540 --> 00:36:16,020
+message?
+
+350
+00:36:20,460 --> 00:36:27,130
+Yes please. Could you ask him to phone me? I think
+
+351
+00:36:27,130 --> 00:36:34,490
+he's got my number, but I'll give it
+
+352
+00:36:34,490 --> 00:36:41,750
+to you again just in case it's seven four three
+
+353
+00:36:41,750 --> 00:36:48,870
+two one nine one eight six You understand? Who can
+
+354
+00:36:48,870 --> 00:36:55,570
+read A and B? A and B Hello, could I speak? I
+
+355
+00:36:55,570 --> 00:36:59,710
+speak to Sam Jackson, please. I'm afraid Mr.
+
+356
+00:36:59,830 --> 00:37:04,030
+Jackson in a meeting. It won't be over until
+
+357
+00:37:04,030 --> 00:37:08,830
+three. Can I take a message? Yes, please. Could
+
+358
+00:37:08,830 --> 00:37:13,390
+you ask him to phone me? I think he got my number,
+
+359
+00:37:13,910 --> 00:37:19,230
+but I will give it to him again just in case. Just
+
+360
+00:37:19,230 --> 00:37:19,750
+in case.
+
+361
+00:37:25,690 --> 00:37:33,530
+Yes, this is number one number two a Can I have
+
+362
+00:37:33,530 --> 00:37:42,670
+extension can I have Extension Can
+
+363
+00:37:42,670 --> 00:37:48,570
+I have extension two one seven three, please Could
+
+364
+00:37:48,570 --> 00:37:49,590
+you give me this number?
+
+365
+00:37:53,350 --> 00:37:58,630
+The line is busy. No, the line is busy. The line
+
+366
+00:37:58,630 --> 00:38:03,950
+is busy.
+
+367
+00:38:05,210 --> 00:38:10,370
+The line is busy at the moment. No, it's busy. So
+
+368
+00:38:10,370 --> 00:38:15,430
+this number is busy. Would you like to hold, to
+
+369
+00:38:15,430 --> 00:38:19,130
+wait? Would you like to wait a little? To hold
+
+370
+00:38:19,130 --> 00:38:26,640
+means what? to wait shall I give you again after a
+
+371
+00:38:26,640 --> 00:38:33,320
+while wait a minute yes please five seconds later
+
+372
+00:38:33,320 --> 00:38:42,820
+after this waiting I'm putting putting
+
+373
+00:38:42,820 --> 00:38:47,280
+you through
+
+374
+00:38:50,060 --> 00:38:54,700
+I'm putting you through now. Now you can talk to
+
+375
+00:38:54,700 --> 00:39:00,060
+him. You can talk to him. I'm putting you through.
+
+376
+00:39:00,320 --> 00:39:06,500
+I connected it with you. Thank you. You
+
+377
+00:39:06,500 --> 00:39:14,550
+understand? Again, A and B. I have extension 2173,
+
+378
+00:39:15,530 --> 00:39:19,490
+please. The line is busy at the moment. Would you
+
+379
+00:39:19,490 --> 00:39:24,330
+like to halt? Yes, please. I am putting you
+
+380
+00:39:24,330 --> 00:39:28,610
+through now. Thank you. Again.
+
+381
+00:39:34,450 --> 00:39:39,900
+Number three. Could I speak to Alison short? I'm
+
+382
+00:39:39,900 --> 00:39:48,760
+afraid she isn't at her desk. At her desk at the
+
+383
+00:39:48,760 --> 00:39:52,220
+moment. Do you want to hold? Do you want to wait?
+
+384
+00:39:53,220 --> 00:40:00,720
+No, don't worry. I'll phone back. Phone back
+
+385
+00:40:00,720 --> 00:40:01,980
+later.
+
+386
+00:40:04,440 --> 00:40:06,940
+Yes? A and B?
+
+387
+00:40:10,870 --> 00:40:17,350
+A and B. Could I speak to Alison Shaw? I am afraid
+
+388
+00:40:17,350 --> 00:40:20,410
+she isn't at her desk at the moment. Do you want
+
+389
+00:40:20,410 --> 00:40:28,930
+to hold? No, don't worry. I will phone back later.
+
+390
+00:40:29,850 --> 00:40:35,130
+Number four. Can I speak to Trenice Cameron
+
+391
+00:40:35,130 --> 00:40:37,790
+please? Speaking.
+
+392
+00:40:41,050 --> 00:40:45,890
+Speaking means I'm speaking. I am the person ah
+
+393
+00:40:45,890 --> 00:40:53,430
+Mr. Cameron this is This
+
+394
+00:40:53,430 --> 00:41:02,310
+is holy lakas, I'm phoning About
+
+395
+00:41:02,310 --> 00:41:10,530
+a letter I got this morning Mm-hmm Yes A and B A
+
+396
+00:41:10,530 --> 00:41:11,330
+and B.
+
+397
+00:41:15,210 --> 00:41:24,790
+And the
+
+398
+00:41:24,790 --> 00:41:28,370
+last one. Hello, this is income international.
+
+399
+00:41:29,830 --> 00:41:37,190
+There's no one here to take your
+
+400
+00:41:37,190 --> 00:41:39,270
+call.
+
+401
+00:41:41,180 --> 00:41:47,560
+At the moment, please leave a message.
+
+402
+00:41:52,660 --> 00:42:03,020
+And we'll get back to you. We'll get back to
+
+403
+00:42:03,020 --> 00:42:13,090
+you as soon as we can. Yes, you can read. A and B.
+
+404
+00:42:14,830 --> 00:42:17,910
+Number A? Yes. Hello, this is Income
+
+405
+00:42:17,910 --> 00:42:22,010
+International. There is no one here to take your
+
+406
+00:42:22,010 --> 00:42:25,690
+call. At the moment, please leave a message and we
+
+407
+00:42:25,690 --> 00:42:30,430
+will get back to you as soon as we can. Yes, so
+
+408
+00:42:30,430 --> 00:42:33,810
+this is a recorded message. A recorded message on
+
+409
+00:42:33,810 --> 00:42:37,780
+the phone. After this lecture, inshallah, next
+
+410
+00:42:37,780 --> 00:42:41,020
+time we will have the last lecture about the
+
+411
+00:42:41,020 --> 00:42:45,740
+phrasal verbs. About the phrasal verbs literal,
+
+412
+00:42:46,180 --> 00:42:51,400
+idiomatic, separable and inseparable. و السلام
+
+413
+00:42:51,400 --> 00:42:53,380
+عليكم و رحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/AIWnDA4lhlY_raw.json b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/AIWnDA4lhlY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..d0dcc35a079d2704b265c21ca00668c6f6907751
--- /dev/null
+++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/AIWnDA4lhlY_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4947, "start": 21.11, "end": 49.47, "text": " Assalamualaikum warahmatullahi wabarakatuh. Today, inshallah, we will continue with the modal verbs of obligations and suggestions. Today, inshallah, we are going to take must, should, and revise have to, can in the positive and in the negative.", "tokens": [6281, 23819, 901, 64, 35518, 1516, 545, 15677, 858, 27783, 261, 455, 23346, 267, 3232, 13, 2692, 11, 1028, 71, 13492, 11, 321, 486, 2354, 365, 264, 39745, 30051, 295, 26234, 293, 13396, 13, 2692, 11, 1028, 71, 13492, 11, 321, 366, 516, 281, 747, 1633, 11, 820, 11, 293, 44252, 362, 281, 11, 393, 294, 264, 3353, 293, 294, 264, 3671, 13], "avg_logprob": -0.21691893925890326, "compression_ratio": 1.5471698113207548, "no_speech_prob": 0.0, "words": [{"start": 21.110000000000007, "end": 22.03, "word": " Assalamualaikum", "probability": 0.674658203125}, {"start": 22.03, "end": 22.75, "word": " warahmatullahi", "probability": 0.7927734375}, {"start": 22.75, "end": 23.31, "word": " wabarakatuh.", "probability": 0.85498046875}, {"start": 24.79, "end": 25.09, "word": " Today,", "probability": 0.798828125}, {"start": 25.23, "end": 25.41, "word": " inshallah,", "probability": 0.670166015625}, {"start": 26.07, "end": 26.21, "word": " we", "probability": 0.94921875}, {"start": 26.21, "end": 26.37, "word": " will", "probability": 0.76708984375}, {"start": 26.37, "end": 26.85, "word": " continue", "probability": 0.90625}, {"start": 26.85, "end": 27.61, "word": " with", "probability": 0.89306640625}, {"start": 27.61, "end": 27.75, "word": " the", "probability": 0.88427734375}, {"start": 27.75, "end": 27.95, "word": " modal", "probability": 0.495361328125}, {"start": 27.95, "end": 28.41, "word": " verbs", "probability": 0.92529296875}, {"start": 28.41, "end": 30.33, "word": " of", "probability": 0.8740234375}, {"start": 30.33, "end": 30.97, "word": " obligations", "probability": 0.8017578125}, {"start": 30.97, "end": 32.49, "word": " and", "probability": 0.90771484375}, {"start": 32.49, "end": 33.23, "word": " suggestions.", "probability": 0.93017578125}, {"start": 36.57, "end": 37.49, "word": " Today,", "probability": 0.89892578125}, {"start": 37.59, "end": 37.73, "word": " inshallah,", "probability": 0.9191080729166666}, {"start": 37.85, "end": 37.93, "word": " we", "probability": 0.95361328125}, {"start": 37.93, "end": 38.03, "word": " are", "probability": 0.869140625}, {"start": 38.03, "end": 38.23, "word": " going", "probability": 0.94482421875}, {"start": 38.23, "end": 38.45, "word": " to", "probability": 0.9677734375}, {"start": 38.45, "end": 38.83, "word": " take", "probability": 0.8671875}, {"start": 38.83, "end": 40.69, "word": " must,", "probability": 0.69970703125}, {"start": 41.33, "end": 42.09, "word": " should,", "probability": 0.97265625}, {"start": 43.49, "end": 43.67, "word": " and", "probability": 0.93896484375}, {"start": 43.67, "end": 44.19, "word": " revise", "probability": 0.91845703125}, {"start": 44.19, "end": 44.65, "word": " have", "probability": 0.5302734375}, {"start": 44.65, "end": 44.99, "word": " to,", "probability": 0.9716796875}, {"start": 46.13, "end": 46.57, "word": " can", "probability": 0.9619140625}, {"start": 46.57, "end": 47.91, "word": " in", "probability": 0.398193359375}, {"start": 47.91, "end": 48.01, "word": " the", "probability": 0.91552734375}, {"start": 48.01, "end": 48.31, "word": " positive", "probability": 0.935546875}, {"start": 48.31, "end": 48.83, "word": " and", "probability": 0.875}, {"start": 48.83, "end": 49.03, "word": " in", "probability": 0.9375}, {"start": 49.03, "end": 49.15, "word": " the", "probability": 0.91943359375}, {"start": 49.15, "end": 49.47, "word": " negative.", "probability": 0.93701171875}], "temperature": 1.0}, {"id": 2, "seek": 8028, "start": 52.36, "end": 80.28, "text": " The first exercise will be about signs. What do these signs mean? Use have to or don't have to. It means obligation or no obligation. And can count. Can count. It means permission, no permission.", "tokens": [440, 700, 5380, 486, 312, 466, 7880, 13, 708, 360, 613, 7880, 914, 30, 8278, 362, 281, 420, 500, 380, 362, 281, 13, 467, 1355, 20326, 420, 572, 20326, 13, 400, 393, 1207, 13, 1664, 1207, 13, 467, 1355, 11226, 11, 572, 11226, 13], "avg_logprob": -0.11736110846201579, "compression_ratio": 1.5076923076923077, "no_speech_prob": 0.0, "words": [{"start": 52.36, "end": 52.58, "word": " The", "probability": 0.85791015625}, {"start": 52.58, "end": 52.9, "word": " first", "probability": 0.87890625}, {"start": 52.9, "end": 53.64, "word": " exercise", "probability": 0.95068359375}, {"start": 53.64, "end": 54.66, "word": " will", "probability": 0.83984375}, {"start": 54.66, "end": 54.82, "word": " be", "probability": 0.95703125}, {"start": 54.82, "end": 55.26, "word": " about", "probability": 0.92041015625}, {"start": 55.26, "end": 55.86, "word": " signs.", "probability": 0.8369140625}, {"start": 57.86, "end": 58.34, "word": " What", "probability": 0.87744140625}, {"start": 58.34, "end": 58.74, "word": " do", "probability": 0.9482421875}, {"start": 58.74, "end": 59.14, "word": " these", "probability": 0.8623046875}, {"start": 59.14, "end": 59.56, "word": " signs", "probability": 0.8212890625}, {"start": 59.56, "end": 60.12, "word": " mean?", "probability": 0.96630859375}, {"start": 61.24, "end": 61.78, "word": " Use", "probability": 0.92431640625}, {"start": 61.78, "end": 62.56, "word": " have", "probability": 0.4306640625}, {"start": 62.56, "end": 62.9, "word": " to", "probability": 0.9521484375}, {"start": 62.9, "end": 63.88, "word": " or", "probability": 0.865234375}, {"start": 63.88, "end": 64.62, "word": " don't", "probability": 0.9794921875}, {"start": 64.62, "end": 64.96, "word": " have", "probability": 0.95654296875}, {"start": 64.96, "end": 65.28, "word": " to.", "probability": 0.9677734375}, {"start": 66.04, "end": 66.16, "word": " It", "probability": 0.95458984375}, {"start": 66.16, "end": 66.48, "word": " means", "probability": 0.94140625}, {"start": 66.48, "end": 67.42, "word": " obligation", "probability": 0.90673828125}, {"start": 67.42, "end": 68.94, "word": " or", "probability": 0.93603515625}, {"start": 68.94, "end": 69.94, "word": " no", "probability": 0.95166015625}, {"start": 69.94, "end": 70.52, "word": " obligation.", "probability": 0.94970703125}, {"start": 72.4, "end": 72.74, "word": " And", "probability": 0.9013671875}, {"start": 72.74, "end": 73.4, "word": " can", "probability": 0.92626953125}, {"start": 73.4, "end": 74.52, "word": " count.", "probability": 0.67578125}, {"start": 75.24, "end": 75.64, "word": " Can", "probability": 0.79052734375}, {"start": 75.64, "end": 76.44, "word": " count.", "probability": 0.87255859375}, {"start": 77.04, "end": 77.64, "word": " It", "probability": 0.9638671875}, {"start": 77.64, "end": 77.92, "word": " means", "probability": 0.93994140625}, {"start": 77.92, "end": 78.58, "word": " permission,", "probability": 0.9130859375}, {"start": 79.5, "end": 79.88, "word": " no", "probability": 0.9404296875}, {"start": 79.88, "end": 80.28, "word": " permission.", "probability": 0.92724609375}], "temperature": 1.0}, {"id": 3, "seek": 10981, "start": 81.97, "end": 109.81, "text": " Or not allowed to. Allowed to. Can and allowed to, the same meaning. So we can use can or allowed to. Or can't, isn't, aren't, I'm not allowed to. The first one. The first one. Smoking. No smoking. 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You can't smoke here. You can't smoke here. 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And what about here? You can't park here. What about this? You can't drive faster than 50 miles an hour.", "tokens": [509, 393, 380, 8439, 510, 13, 400, 437, 466, 510, 30, 509, 393, 380, 3884, 510, 13, 708, 466, 341, 30, 509, 393, 380, 3332, 4663, 813, 2625, 6193, 364, 1773, 13], "avg_logprob": -0.1279592803030303, "compression_ratio": 1.3368421052631578, "no_speech_prob": 0.0, "words": [{"start": 139.61, "end": 139.93, "word": " You", "probability": 0.40576171875}, {"start": 139.93, "end": 141.41, "word": " can't", "probability": 0.9619140625}, {"start": 141.41, "end": 141.75, "word": " smoke", "probability": 0.88623046875}, {"start": 141.75, "end": 142.15, "word": " here.", "probability": 0.84326171875}, {"start": 143.11, "end": 143.29, "word": " And", "probability": 0.79833984375}, {"start": 143.29, "end": 143.43, "word": " what", "probability": 0.9228515625}, {"start": 143.43, "end": 143.71, "word": " about", "probability": 0.9091796875}, {"start": 143.71, "end": 144.05, "word": " here?", "probability": 0.8466796875}, {"start": 146.77, "end": 147.59, "word": " You", "probability": 0.94775390625}, {"start": 147.59, "end": 149.65, "word": " can't", "probability": 0.97216796875}, {"start": 149.65, "end": 151.05, "word": " park", "probability": 0.9423828125}, {"start": 151.05, "end": 151.49, "word": " here.", "probability": 0.85009765625}, {"start": 152.83, "end": 153.15, "word": " What", "probability": 0.83447265625}, {"start": 153.15, "end": 153.33, "word": " about", "probability": 0.90576171875}, {"start": 153.33, "end": 153.69, "word": " this?", "probability": 0.93505859375}, {"start": 155.97, "end": 156.49, "word": " You", "probability": 0.9580078125}, {"start": 156.49, "end": 158.83, "word": " can't", "probability": 0.9716796875}, {"start": 158.83, "end": 161.07, "word": " drive", "probability": 0.93359375}, {"start": 161.07, "end": 162.49, "word": " faster", "probability": 0.8583984375}, {"start": 162.49, "end": 163.05, "word": " than", "probability": 0.94921875}, {"start": 163.05, "end": 164.03, "word": " 50", "probability": 0.859375}, {"start": 164.03, "end": 164.63, "word": " miles", "probability": 0.73876953125}, {"start": 164.63, "end": 168.09, "word": " an", "probability": 0.611328125}, {"start": 168.09, "end": 168.33, "word": " hour.", "probability": 0.94140625}], "temperature": 1.0}, {"id": 6, "seek": 19497, "start": 169.37, "end": 194.97, "text": " What about that? Number five. You can't take photographs. What about this? No skateboarding. You can't skateboard.", "tokens": [708, 466, 300, 30, 5118, 1732, 13, 509, 393, 380, 747, 17649, 13, 708, 466, 341, 30, 883, 32204, 278, 13, 509, 393, 380, 32204, 13], "avg_logprob": -0.16464120039233454, "compression_ratio": 1.3068181818181819, "no_speech_prob": 0.0, "words": [{"start": 169.37, "end": 169.59, "word": " What", "probability": 0.76220703125}, {"start": 169.59, "end": 169.77, "word": " about", "probability": 0.90771484375}, {"start": 169.77, "end": 170.07, "word": " that?", "probability": 0.796875}, {"start": 170.19, "end": 170.33, "word": " Number", "probability": 0.84716796875}, {"start": 170.33, "end": 170.75, "word": " five.", "probability": 0.73779296875}, {"start": 172.13, "end": 172.29, "word": " You", "probability": 0.845703125}, {"start": 172.29, "end": 173.59, "word": " can't", "probability": 0.96875}, {"start": 173.59, "end": 174.97, "word": " take", "probability": 0.85595703125}, {"start": 174.97, "end": 176.01, "word": " photographs.", "probability": 0.7919921875}, {"start": 181.59, "end": 182.99, "word": " What", "probability": 0.72998046875}, {"start": 182.99, "end": 183.19, "word": " about", "probability": 0.91162109375}, {"start": 183.19, "end": 183.57, "word": " this?", "probability": 0.94970703125}, {"start": 185.41, "end": 186.15, "word": " No", "probability": 0.9443359375}, {"start": 186.15, "end": 187.69, "word": " skateboarding.", "probability": 0.8359375}, {"start": 188.85, "end": 189.41, "word": " You", "probability": 0.94775390625}, {"start": 189.41, "end": 193.07, "word": " can't", "probability": 0.97314453125}, {"start": 193.07, "end": 194.97, "word": " skateboard.", "probability": 0.7939453125}], "temperature": 1.0}, {"id": 7, "seek": 22548, "start": 196.64, "end": 225.48, "text": " Mm-hmm. You can't skateboard Yes, if you look again, so these are the four Examples of can't Or the fifth example of can't You can't smoke here You can't smoke here You can't", "tokens": [8266, 12, 10250, 13, 509, 393, 380, 32204, 1079, 11, 498, 291, 574, 797, 11, 370, 613, 366, 264, 1451, 48591, 295, 393, 380, 1610, 264, 9266, 1365, 295, 393, 380, 509, 393, 380, 8439, 510, 509, 393, 380, 8439, 510, 509, 393, 380], "avg_logprob": -0.21319443782170613, "compression_ratio": 1.5486725663716814, "no_speech_prob": 0.0, "words": [{"start": 196.64, "end": 197.06, "word": " Mm", "probability": 0.537109375}, {"start": 197.06, "end": 197.18, "word": "-hmm.", "probability": 0.893310546875}, {"start": 197.5, "end": 197.64, "word": " You", "probability": 0.939453125}, {"start": 197.64, "end": 198.62, "word": " can't", "probability": 0.904541015625}, {"start": 198.62, "end": 199.4, "word": " skateboard", "probability": 0.86328125}, {"start": 199.4, "end": 204.36, "word": " Yes,", "probability": 0.865234375}, {"start": 204.52, "end": 204.92, "word": " if", "probability": 0.95947265625}, {"start": 204.92, "end": 205.0, "word": " you", "probability": 0.95654296875}, {"start": 205.0, "end": 205.16, "word": " look", "probability": 0.97216796875}, {"start": 205.16, "end": 205.56, "word": " again,", "probability": 0.95751953125}, {"start": 205.92, "end": 206.9, "word": " so", "probability": 0.92236328125}, {"start": 206.9, "end": 207.16, "word": " these", "probability": 0.8564453125}, {"start": 207.16, "end": 207.54, "word": " are", "probability": 0.94384765625}, {"start": 207.54, "end": 207.92, "word": " the", "probability": 0.91796875}, {"start": 207.92, "end": 208.34, "word": " four", "probability": 0.91455078125}, {"start": 208.34, "end": 210.6, "word": " Examples", "probability": 0.56201171875}, {"start": 210.6, "end": 211.38, "word": " of", "probability": 0.97314453125}, {"start": 211.38, "end": 211.92, "word": " can't", "probability": 0.62103271484375}, {"start": 211.92, "end": 213.22, "word": " Or", "probability": 0.356201171875}, {"start": 213.22, "end": 213.4, "word": " the", "probability": 0.92333984375}, {"start": 213.4, "end": 214.0, "word": " fifth", "probability": 0.90869140625}, {"start": 214.0, "end": 214.54, "word": " example", "probability": 0.9775390625}, {"start": 214.54, "end": 214.76, "word": " of", "probability": 0.97021484375}, {"start": 214.76, "end": 215.18, "word": " can't", "probability": 0.906982421875}, {"start": 215.18, "end": 216.28, "word": " You", "probability": 0.59912109375}, {"start": 216.28, "end": 217.0, "word": " can't", "probability": 0.974853515625}, {"start": 217.0, "end": 217.94, "word": " smoke", "probability": 0.76611328125}, {"start": 217.94, "end": 218.4, "word": " here", "probability": 0.85400390625}, {"start": 218.4, "end": 219.5, "word": " You", "probability": 0.381591796875}, {"start": 219.5, "end": 220.68, "word": " can't", "probability": 0.970703125}, {"start": 220.68, "end": 221.88, "word": " smoke", "probability": 0.6123046875}, {"start": 221.88, "end": 222.34, "word": " here", "probability": 0.8193359375}, {"start": 222.34, "end": 224.78, "word": " You", "probability": 0.9072265625}, {"start": 224.78, "end": 225.48, "word": " can't", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 8, "seek": 25550, "start": 227.1, "end": 255.5, "text": " Park here. You can park here at weekends. You can. Number four, you can't drive faster than 50 miles per hour. There, number five, you can't take photographs.", "tokens": [4964, 510, 13, 509, 393, 3884, 510, 412, 23595, 13, 509, 393, 13, 5118, 1451, 11, 291, 393, 380, 3332, 4663, 813, 2625, 6193, 680, 1773, 13, 821, 11, 1230, 1732, 11, 291, 393, 380, 747, 17649, 13], "avg_logprob": -0.1812900694516989, "compression_ratio": 1.347457627118644, "no_speech_prob": 0.0, "words": [{"start": 227.1, "end": 227.6, "word": " Park", "probability": 0.443115234375}, {"start": 227.6, "end": 228.12, "word": " here.", "probability": 0.81787109375}, {"start": 229.4, "end": 230.3, "word": " You", "probability": 0.94091796875}, {"start": 230.3, "end": 230.52, "word": " can", "probability": 0.94970703125}, {"start": 230.52, "end": 230.82, "word": " park", "probability": 0.93017578125}, {"start": 230.82, "end": 231.2, "word": " here", "probability": 0.86083984375}, {"start": 231.2, "end": 231.6, "word": " at", "probability": 0.72021484375}, {"start": 231.6, "end": 232.14, "word": " weekends.", "probability": 0.93505859375}, {"start": 232.82, "end": 232.92, "word": " You", "probability": 0.87255859375}, {"start": 232.92, "end": 233.3, "word": " can.", "probability": 0.94677734375}, {"start": 237.4, "end": 237.84, "word": " Number", "probability": 0.5126953125}, {"start": 237.84, "end": 238.14, "word": " four,", "probability": 0.828125}, {"start": 238.34, "end": 238.52, "word": " you", "probability": 0.90625}, {"start": 238.52, "end": 240.12, "word": " can't", "probability": 0.970458984375}, {"start": 240.12, "end": 241.9, "word": " drive", "probability": 0.88525390625}, {"start": 241.9, "end": 242.62, "word": " faster", "probability": 0.8876953125}, {"start": 242.62, "end": 242.96, "word": " than", "probability": 0.94384765625}, {"start": 242.96, "end": 243.34, "word": " 50", "probability": 0.8251953125}, {"start": 243.34, "end": 243.84, "word": " miles", "probability": 0.71826171875}, {"start": 243.84, "end": 244.92, "word": " per", "probability": 0.93994140625}, {"start": 244.92, "end": 245.24, "word": " hour.", "probability": 0.9375}, {"start": 247.2, "end": 248.2, "word": " There,", "probability": 0.5947265625}, {"start": 248.46, "end": 248.62, "word": " number", "probability": 0.94091796875}, {"start": 248.62, "end": 249.04, "word": " five,", "probability": 0.9033203125}, {"start": 249.56, "end": 249.7, "word": " you", "probability": 0.94775390625}, {"start": 249.7, "end": 251.04, "word": " can't", "probability": 0.97314453125}, {"start": 251.04, "end": 253.9, "word": " take", "probability": 0.85009765625}, {"start": 253.9, "end": 255.5, "word": " photographs.", "probability": 0.77978515625}], "temperature": 1.0}, {"id": 9, "seek": 28405, "start": 257.73, "end": 284.05, "text": " And number nine, you can't skateboard. So here we can use can't or aren't allowed to. The same meaning. If I want to repeat it again, I can say you aren't allowed to smoke here. You aren't allowed to park here.", "tokens": [400, 1230, 4949, 11, 291, 393, 380, 32204, 13, 407, 510, 321, 393, 764, 393, 380, 420, 3212, 380, 4350, 281, 13, 440, 912, 3620, 13, 759, 286, 528, 281, 7149, 309, 797, 11, 286, 393, 584, 291, 3212, 380, 4350, 281, 8439, 510, 13, 509, 3212, 380, 4350, 281, 3884, 510, 13], "avg_logprob": -0.1497395783662796, "compression_ratio": 1.5514705882352942, "no_speech_prob": 0.0, "words": [{"start": 257.73, "end": 257.97, "word": " And", "probability": 0.475830078125}, {"start": 257.97, "end": 258.15, "word": " number", "probability": 0.87939453125}, {"start": 258.15, "end": 258.61, "word": " nine,", "probability": 0.72607421875}, {"start": 259.25, "end": 259.37, "word": " you", "probability": 0.63623046875}, {"start": 259.37, "end": 261.35, "word": " can't", "probability": 0.972412109375}, {"start": 261.35, "end": 264.25, "word": " skateboard.", "probability": 0.7333984375}, {"start": 266.57, "end": 267.05, "word": " So", "probability": 0.84912109375}, {"start": 267.05, "end": 268.15, "word": " here", "probability": 0.66162109375}, {"start": 268.15, "end": 268.43, "word": " we", "probability": 0.75146484375}, {"start": 268.43, "end": 268.65, "word": " can", "probability": 0.94482421875}, {"start": 268.65, "end": 268.93, "word": " use", "probability": 0.87646484375}, {"start": 268.93, "end": 269.61, "word": " can't", "probability": 0.881103515625}, {"start": 269.61, "end": 270.49, "word": " or", "probability": 0.8984375}, {"start": 270.49, "end": 271.03, "word": " aren't", "probability": 0.959716796875}, {"start": 271.03, "end": 271.57, "word": " allowed", "probability": 0.91357421875}, {"start": 271.57, "end": 271.85, "word": " to.", "probability": 0.95361328125}, {"start": 272.17, "end": 272.41, "word": " The", "probability": 0.7646484375}, {"start": 272.41, "end": 272.61, "word": " same", "probability": 0.91455078125}, {"start": 272.61, "end": 272.95, "word": " meaning.", "probability": 0.84814453125}, {"start": 273.91, "end": 274.39, "word": " If", "probability": 0.91650390625}, {"start": 274.39, "end": 274.51, "word": " I", "probability": 0.95556640625}, {"start": 274.51, "end": 274.71, "word": " want", "probability": 0.876953125}, {"start": 274.71, "end": 274.95, "word": " to", "probability": 0.96875}, {"start": 274.95, "end": 275.41, "word": " repeat", "probability": 0.91455078125}, {"start": 275.41, "end": 275.55, "word": " it", "probability": 0.94775390625}, {"start": 275.55, "end": 275.93, "word": " again,", "probability": 0.95361328125}, {"start": 276.33, "end": 276.65, "word": " I", "probability": 0.9921875}, {"start": 276.65, "end": 276.83, "word": " can", "probability": 0.94580078125}, {"start": 276.83, "end": 277.11, "word": " say", "probability": 0.951171875}, {"start": 277.11, "end": 277.87, "word": " you", "probability": 0.48193359375}, {"start": 277.87, "end": 278.47, "word": " aren't", "probability": 0.94140625}, {"start": 278.47, "end": 278.91, "word": " allowed", "probability": 0.90869140625}, {"start": 278.91, "end": 279.13, "word": " to", "probability": 0.96875}, {"start": 279.13, "end": 279.51, "word": " smoke", "probability": 0.8701171875}, {"start": 279.51, "end": 279.89, "word": " here.", "probability": 0.85498046875}, {"start": 281.23, "end": 281.99, "word": " You", "probability": 0.9365234375}, {"start": 281.99, "end": 282.45, "word": " aren't", "probability": 0.95166015625}, {"start": 282.45, "end": 282.97, "word": " allowed", "probability": 0.90771484375}, {"start": 282.97, "end": 283.29, "word": " to", "probability": 0.970703125}, {"start": 283.29, "end": 283.65, "word": " park", "probability": 0.93994140625}, {"start": 283.65, "end": 284.05, "word": " here.", "probability": 0.85693359375}], "temperature": 1.0}, {"id": 10, "seek": 31445, "start": 286.3, "end": 314.46, "text": " You aren't allowed to drive faster than 50 miles per hour. You aren't allowed to take photographs. You aren't allowed to skateboard. The same meaning. So we can use count and are allowed to. If it's negative, aren't.", "tokens": [509, 3212, 380, 4350, 281, 3332, 4663, 813, 2625, 6193, 680, 1773, 13, 509, 3212, 380, 4350, 281, 747, 17649, 13, 509, 3212, 380, 4350, 281, 32204, 13, 440, 912, 3620, 13, 407, 321, 393, 764, 1207, 293, 366, 4350, 281, 13, 759, 309, 311, 3671, 11, 3212, 380, 13], "avg_logprob": -0.134497544929093, "compression_ratio": 1.5611510791366907, "no_speech_prob": 0.0, "words": [{"start": 286.3, "end": 286.7, "word": " You", "probability": 0.66357421875}, {"start": 286.7, "end": 287.22, "word": " aren't", "probability": 0.894775390625}, {"start": 287.22, "end": 287.72, "word": " allowed", "probability": 0.90771484375}, {"start": 287.72, "end": 287.92, "word": " to", "probability": 0.97021484375}, {"start": 287.92, "end": 288.28, "word": " drive", "probability": 0.92822265625}, {"start": 288.28, "end": 288.68, "word": " faster", "probability": 0.89404296875}, {"start": 288.68, "end": 289.02, "word": " than", "probability": 0.94873046875}, {"start": 289.02, "end": 289.46, "word": " 50", "probability": 0.8857421875}, {"start": 289.46, "end": 289.96, "word": " miles", "probability": 0.54736328125}, {"start": 289.96, "end": 290.6, "word": " per", "probability": 0.943359375}, {"start": 290.6, "end": 290.92, "word": " hour.", "probability": 0.94287109375}, {"start": 292.04, "end": 292.92, "word": " You", "probability": 0.95703125}, {"start": 292.92, "end": 294.08, "word": " aren't", "probability": 0.94384765625}, {"start": 294.08, "end": 294.52, "word": " allowed", "probability": 0.912109375}, {"start": 294.52, "end": 294.76, "word": " to", "probability": 0.96923828125}, {"start": 294.76, "end": 295.02, "word": " take", "probability": 0.8642578125}, {"start": 295.02, "end": 295.6, "word": " photographs.", "probability": 0.7646484375}, {"start": 297.2, "end": 297.58, "word": " You", "probability": 0.955078125}, {"start": 297.58, "end": 298.08, "word": " aren't", "probability": 0.954345703125}, {"start": 298.08, "end": 298.54, "word": " allowed", "probability": 0.9111328125}, {"start": 298.54, "end": 298.78, "word": " to", "probability": 0.97021484375}, {"start": 298.78, "end": 299.16, "word": " skateboard.", "probability": 0.7998046875}, {"start": 299.92, "end": 300.04, "word": " The", "probability": 0.77880859375}, {"start": 300.04, "end": 300.24, "word": " same", "probability": 0.91748046875}, {"start": 300.24, "end": 300.58, "word": " meaning.", "probability": 0.85302734375}, {"start": 301.2, "end": 301.34, "word": " So", "probability": 0.90576171875}, {"start": 301.34, "end": 301.48, "word": " we", "probability": 0.8056640625}, {"start": 301.48, "end": 301.66, "word": " can", "probability": 0.94580078125}, {"start": 301.66, "end": 301.98, "word": " use", "probability": 0.87255859375}, {"start": 301.98, "end": 303.6, "word": " count", "probability": 0.72216796875}, {"start": 303.6, "end": 306.6, "word": " and", "probability": 0.73046875}, {"start": 306.6, "end": 307.64, "word": " are", "probability": 0.9072265625}, {"start": 307.64, "end": 309.2, "word": " allowed", "probability": 0.91650390625}, {"start": 309.2, "end": 311.04, "word": " to.", "probability": 0.93798828125}, {"start": 312.28, "end": 313.06, "word": " If", "probability": 0.93505859375}, {"start": 313.06, "end": 313.22, "word": " it's", "probability": 0.7099609375}, {"start": 313.22, "end": 313.68, "word": " negative,", "probability": 0.93408203125}, {"start": 313.96, "end": 314.46, "word": " aren't.", "probability": 0.955078125}], "temperature": 1.0}, {"id": 11, "seek": 33705, "start": 315.73, "end": 337.05, "text": " aren't allowed to. If it's positive, can and are allowed to. If the subject is singular, we use is. If it's I, we use am. I am allowed to. He is allowed to. They are allowed to. 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They aren't allowed to. You aren't allowed to. So we can use can and can't easier. Yes. Let's go back again. Yes, now complete. 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You have to show your passport. You have to use it before June 16th. You have to fasten your seat belt. Again.", "tokens": [20277, 362, 281, 1689, 1266, 14160, 11, 457, 2227, 500, 380, 362, 281, 1689, 1340, 13, 509, 362, 281, 855, 428, 24694, 13, 509, 362, 281, 764, 309, 949, 6928, 3165, 392, 13, 509, 362, 281, 38716, 428, 6121, 10750, 13, 3764, 13], "avg_logprob": -0.14604048159989444, "compression_ratio": 1.4596774193548387, "no_speech_prob": 0.0, "words": [{"start": 488.24, "end": 488.72, "word": " Others", "probability": 0.66455078125}, {"start": 488.72, "end": 489.02, "word": " have", "probability": 0.90087890625}, {"start": 489.02, "end": 489.2, "word": " to", "probability": 0.9736328125}, {"start": 489.2, "end": 489.62, "word": " pay", "probability": 0.9384765625}, {"start": 489.62, "end": 490.18, "word": " 10", "probability": 0.82177734375}, {"start": 490.18, "end": 490.54, "word": " euros,", "probability": 0.58251953125}, {"start": 490.9, "end": 490.98, "word": " but", "probability": 0.91796875}, {"start": 490.98, "end": 491.36, "word": " children", "probability": 0.82568359375}, {"start": 491.36, "end": 492.18, "word": " don't", "probability": 0.9619140625}, {"start": 492.18, "end": 492.46, "word": " have", "probability": 0.9501953125}, {"start": 492.46, "end": 492.64, "word": " to", "probability": 0.9736328125}, {"start": 492.64, "end": 492.82, "word": " pay", "probability": 0.88427734375}, {"start": 492.82, "end": 493.18, "word": " anything.", "probability": 0.8642578125}, {"start": 494.28, "end": 495.04, "word": " You", "probability": 0.91796875}, {"start": 495.04, "end": 495.24, "word": " have", "probability": 0.9453125}, {"start": 495.24, "end": 495.38, "word": " to", "probability": 0.96826171875}, {"start": 495.38, "end": 495.6, "word": " show", "probability": 0.94921875}, {"start": 495.6, "end": 495.8, "word": " your", "probability": 0.8974609375}, {"start": 495.8, "end": 496.18, "word": " passport.", "probability": 0.9599609375}, {"start": 498.12, "end": 498.32, "word": " You", "probability": 0.9462890625}, {"start": 498.32, "end": 498.56, "word": " have", "probability": 0.94091796875}, {"start": 498.56, "end": 498.68, "word": " to", "probability": 0.9609375}, {"start": 498.68, "end": 498.86, "word": " use", "probability": 0.89892578125}, {"start": 498.86, "end": 499.02, "word": " it", "probability": 0.93896484375}, {"start": 499.02, "end": 499.54, "word": " before", "probability": 0.87890625}, {"start": 499.54, "end": 500.18, "word": " June", "probability": 0.89990234375}, {"start": 500.18, "end": 501.1, "word": " 16th.", "probability": 0.88525390625}, {"start": 501.84, "end": 502.22, "word": " You", "probability": 0.94921875}, {"start": 502.22, "end": 502.52, "word": " have", "probability": 0.94482421875}, {"start": 502.52, "end": 503.08, "word": " to", "probability": 0.96923828125}, {"start": 503.08, "end": 503.6, "word": " fasten", "probability": 0.90966796875}, {"start": 503.6, "end": 505.1, "word": " your", "probability": 0.890625}, {"start": 505.1, "end": 505.48, "word": " seat", "probability": 0.97998046875}, {"start": 505.48, "end": 505.94, "word": " belt.", "probability": 0.54052734375}, {"start": 507.7, "end": 508.46, "word": " Again.", "probability": 0.8037109375}], "temperature": 1.0}, {"id": 18, "seek": 54740, "start": 518.48, "end": 547.4, "text": " Admission adults have to pay 10 euros, but the children don't have to. Here there is obligation and no obligation. Obligation for the adults, no obligation for the children. What about here? You have to fasten your seat belt.", "tokens": [1999, 29797, 8865, 362, 281, 1689, 1266, 14160, 11, 457, 264, 2227, 500, 380, 362, 281, 13, 1692, 456, 307, 20326, 293, 572, 20326, 13, 4075, 5073, 399, 337, 264, 8865, 11, 572, 20326, 337, 264, 2227, 13, 708, 466, 510, 30, 509, 362, 281, 38716, 428, 6121, 10750, 13], "avg_logprob": -0.21476716387505626, "compression_ratio": 1.5804195804195804, "no_speech_prob": 0.0, "words": [{"start": 518.48, "end": 518.98, "word": " Admission", "probability": 0.769775390625}, {"start": 518.98, "end": 519.98, "word": " adults", "probability": 0.74658203125}, {"start": 519.98, "end": 520.58, "word": " have", "probability": 0.94873046875}, {"start": 520.58, "end": 521.62, "word": " to", "probability": 0.97802734375}, {"start": 521.62, "end": 522.98, "word": " pay", "probability": 0.67333984375}, {"start": 522.98, "end": 523.58, "word": " 10", "probability": 0.822265625}, {"start": 523.58, "end": 524.08, "word": " euros,", "probability": 0.75830078125}, {"start": 524.32, "end": 525.56, "word": " but", "probability": 0.92724609375}, {"start": 525.56, "end": 525.74, "word": " the", "probability": 0.84521484375}, {"start": 525.74, "end": 526.26, "word": " children", "probability": 0.841796875}, {"start": 526.26, "end": 528.04, "word": " don't", "probability": 0.88671875}, {"start": 528.04, "end": 528.54, "word": " have", "probability": 0.951171875}, {"start": 528.54, "end": 528.9, "word": " to.", "probability": 0.9453125}, {"start": 530.22, "end": 530.76, "word": " Here", "probability": 0.72802734375}, {"start": 530.76, "end": 530.94, "word": " there", "probability": 0.71142578125}, {"start": 530.94, "end": 531.02, "word": " is", "probability": 0.7412109375}, {"start": 531.02, "end": 531.58, "word": " obligation", "probability": 0.81787109375}, {"start": 531.58, "end": 532.66, "word": " and", "probability": 0.90625}, {"start": 532.66, "end": 533.34, "word": " no", "probability": 0.9384765625}, {"start": 533.34, "end": 533.92, "word": " obligation.", "probability": 0.94482421875}, {"start": 534.46, "end": 535.22, "word": " Obligation", "probability": 0.94775390625}, {"start": 535.22, "end": 535.44, "word": " for", "probability": 0.94140625}, {"start": 535.44, "end": 535.62, "word": " the", "probability": 0.89892578125}, {"start": 535.62, "end": 536.06, "word": " adults,", "probability": 0.904296875}, {"start": 536.6, "end": 536.74, "word": " no", "probability": 0.888671875}, {"start": 536.74, "end": 537.18, "word": " obligation", "probability": 0.9423828125}, {"start": 537.18, "end": 537.62, "word": " for", "probability": 0.951171875}, {"start": 537.62, "end": 537.9, "word": " the", "probability": 0.84375}, {"start": 537.9, "end": 538.94, "word": " children.", "probability": 0.83349609375}, {"start": 540.06, "end": 540.4, "word": " What", "probability": 0.82177734375}, {"start": 540.4, "end": 540.6, "word": " about", "probability": 0.90625}, {"start": 540.6, "end": 540.92, "word": " here?", "probability": 0.85791015625}, {"start": 541.46, "end": 541.9, "word": " You", "probability": 0.93505859375}, {"start": 541.9, "end": 542.2, "word": " have", "probability": 0.95068359375}, {"start": 542.2, "end": 542.42, "word": " to", "probability": 0.96875}, {"start": 542.42, "end": 543.06, "word": " fasten", "probability": 0.81396484375}, {"start": 543.06, "end": 546.7, "word": " your", "probability": 0.434326171875}, {"start": 546.7, "end": 547.06, "word": " seat", "probability": 0.974609375}, {"start": 547.06, "end": 547.4, "word": " belt.", "probability": 0.53466796875}], "temperature": 1.0}, {"id": 19, "seek": 57596, "start": 549.7, "end": 575.96, "text": " It is necessary, obligation. And here, you have to show your passport, obligation. The last one, you have to use it before 16th June or June the 16th. So in this exercise, we revise can and can't. Have to, don't have to.", "tokens": [467, 307, 4818, 11, 20326, 13, 400, 510, 11, 291, 362, 281, 855, 428, 24694, 11, 20326, 13, 440, 1036, 472, 11, 291, 362, 281, 764, 309, 949, 3165, 392, 6928, 420, 6928, 264, 3165, 392, 13, 407, 294, 341, 5380, 11, 321, 44252, 393, 293, 393, 380, 13, 3560, 281, 11, 500, 380, 362, 281, 13], "avg_logprob": -0.12870420952295436, "compression_ratio": 1.5136986301369864, "no_speech_prob": 0.0, "words": [{"start": 549.7, "end": 549.86, "word": " It", "probability": 0.70361328125}, {"start": 549.86, "end": 549.98, "word": " is", "probability": 0.9033203125}, {"start": 549.98, "end": 550.48, "word": " necessary,", "probability": 0.88232421875}, {"start": 550.76, "end": 551.04, "word": " obligation.", "probability": 0.88134765625}, {"start": 552.08, "end": 552.24, "word": " And", "probability": 0.92919921875}, {"start": 552.24, "end": 552.54, "word": " here,", "probability": 0.8583984375}, {"start": 552.94, "end": 553.06, "word": " you", "probability": 0.95166015625}, {"start": 553.06, "end": 553.28, "word": " have", "probability": 0.95263671875}, {"start": 553.28, "end": 553.42, "word": " to", "probability": 0.97021484375}, {"start": 553.42, "end": 553.66, "word": " show", "probability": 0.94775390625}, {"start": 553.66, "end": 553.88, "word": " your", "probability": 0.90087890625}, {"start": 553.88, "end": 554.5, "word": " passport,", "probability": 0.96826171875}, {"start": 555.42, "end": 555.92, "word": " obligation.", "probability": 0.91845703125}, {"start": 559.2, "end": 559.84, "word": " The", "probability": 0.88134765625}, {"start": 559.84, "end": 560.04, "word": " last", "probability": 0.873046875}, {"start": 560.04, "end": 560.28, "word": " one,", "probability": 0.921875}, {"start": 560.44, "end": 560.52, "word": " you", "probability": 0.96142578125}, {"start": 560.52, "end": 560.76, "word": " have", "probability": 0.9501953125}, {"start": 560.76, "end": 560.92, "word": " to", "probability": 0.9716796875}, {"start": 560.92, "end": 561.18, "word": " use", "probability": 0.890625}, {"start": 561.18, "end": 561.36, "word": " it", "probability": 0.9443359375}, {"start": 561.36, "end": 561.86, "word": " before", "probability": 0.87744140625}, {"start": 561.86, "end": 562.68, "word": " 16th", "probability": 0.82861328125}, {"start": 562.68, "end": 563.04, "word": " June", "probability": 0.82470703125}, {"start": 563.04, "end": 563.36, "word": " or", "probability": 0.63525390625}, {"start": 563.36, "end": 563.7, "word": " June", "probability": 0.91259765625}, {"start": 563.7, "end": 563.9, "word": " the", "probability": 0.7431640625}, {"start": 563.9, "end": 564.58, "word": " 16th.", "probability": 0.9775390625}, {"start": 567.24, "end": 567.88, "word": " So", "probability": 0.9462890625}, {"start": 567.88, "end": 568.02, "word": " in", "probability": 0.8515625}, {"start": 568.02, "end": 568.16, "word": " this", "probability": 0.94482421875}, {"start": 568.16, "end": 568.72, "word": " exercise,", "probability": 0.96142578125}, {"start": 569.42, "end": 569.76, "word": " we", "probability": 0.96044921875}, {"start": 569.76, "end": 570.5, "word": " revise", "probability": 0.82421875}, {"start": 570.5, "end": 572.06, "word": " can", "probability": 0.7724609375}, {"start": 572.06, "end": 572.92, "word": " and", "probability": 0.9365234375}, {"start": 572.92, "end": 573.46, "word": " can't.", "probability": 0.970947265625}, {"start": 574.08, "end": 574.54, "word": " Have", "probability": 0.89794921875}, {"start": 574.54, "end": 574.8, "word": " to,", "probability": 0.96826171875}, {"start": 575.2, "end": 575.46, "word": " don't", "probability": 0.978515625}, {"start": 575.46, "end": 575.74, "word": " have", "probability": 0.9521484375}, {"start": 575.74, "end": 575.96, "word": " to.", "probability": 0.9638671875}], "temperature": 1.0}, {"id": 20, "seek": 60514, "start": 577.16, "end": 605.14, "text": " In short, we revise the obligation and no obligation. Obligation and no obligation. Also permission and no permission. Yes, before this, I want you to", "tokens": [682, 2099, 11, 321, 44252, 264, 20326, 293, 572, 20326, 13, 4075, 5073, 399, 293, 572, 20326, 13, 2743, 11226, 293, 572, 11226, 13, 1079, 11, 949, 341, 11, 286, 528, 291, 281], "avg_logprob": -0.1547564272494877, "compression_ratio": 1.5729166666666667, "no_speech_prob": 0.0, "words": [{"start": 577.16, "end": 577.42, "word": " In", "probability": 0.8583984375}, {"start": 577.42, "end": 577.82, "word": " short,", "probability": 0.95263671875}, {"start": 578.24, "end": 578.4, "word": " we", "probability": 0.9521484375}, {"start": 578.4, "end": 578.86, "word": " revise", "probability": 0.75732421875}, {"start": 578.86, "end": 579.44, "word": " the", "probability": 0.79638671875}, {"start": 579.44, "end": 580.2, "word": " obligation", "probability": 0.91748046875}, {"start": 580.2, "end": 581.12, "word": " and", "probability": 0.93017578125}, {"start": 581.12, "end": 581.64, "word": " no", "probability": 0.88232421875}, {"start": 581.64, "end": 582.2, "word": " obligation.", "probability": 0.8916015625}, {"start": 583.18, "end": 584.0, "word": " Obligation", "probability": 0.9016927083333334}, {"start": 584.0, "end": 584.72, "word": " and", "probability": 0.92138671875}, {"start": 584.72, "end": 585.32, "word": " no", "probability": 0.9521484375}, {"start": 585.32, "end": 585.84, "word": " obligation.", "probability": 0.9375}, {"start": 586.76, "end": 587.18, "word": " Also", "probability": 0.93603515625}, {"start": 587.18, "end": 587.96, "word": " permission", "probability": 0.55224609375}, {"start": 587.96, "end": 588.94, "word": " and", "probability": 0.916015625}, {"start": 588.94, "end": 589.66, "word": " no", "probability": 0.93994140625}, {"start": 589.66, "end": 590.18, "word": " permission.", "probability": 0.935546875}, {"start": 599.36, "end": 600.48, "word": " Yes,", "probability": 0.5546875}, {"start": 600.56, "end": 600.94, "word": " before", "probability": 0.865234375}, {"start": 600.94, "end": 601.42, "word": " this,", "probability": 0.9453125}, {"start": 601.98, "end": 604.36, "word": " I", "probability": 0.99658203125}, {"start": 604.36, "end": 604.62, "word": " want", "probability": 0.87646484375}, {"start": 604.62, "end": 604.82, "word": " you", "probability": 0.95947265625}, {"start": 604.82, "end": 605.14, "word": " to", "probability": 0.970703125}], "temperature": 1.0}, {"id": 21, "seek": 63141, "start": 606.27, "end": 631.41, "text": " Work in pairs. Read these to each other. But I want each one to answer aloud. Number one, this sign, what does it mean? Use can or can't, have to or don't have to. This is the answer. Who can read? 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Yes, the same meaning. You can't smoke here or you are not allowed to smoke here. Number three. Yes. You can't part here. You can't part here at weekend. 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Number nine. Yes. Fasting. You can't. Yes. Skateboard. Yes. Is it clear? Yes. Now this is about what? Permission? 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About what? Obligation? No obligation. Yes, who can read? Yes. I don't have to pay 10 euros, but children don't have to pay anything. Good. Number six. You have to show your passport. And number eight. 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Yes. And the last one, number seven. Yeah, yes. So this is revision about obligation and permission of the last lecture. 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So I think we should look here. Number one, I think we should buy some guide books. Why?", "tokens": [492, 820, 13, 407, 286, 519, 321, 820, 574, 510, 13, 5118, 472, 11, 286, 519, 321, 820, 2256, 512, 5934, 3642, 13, 1545, 30], "avg_logprob": -0.2735877266296974, "compression_ratio": 1.1904761904761905, "no_speech_prob": 0.0, "words": [{"start": 868.9699999999999, "end": 869.81, "word": " We", "probability": 0.498291015625}, {"start": 869.81, "end": 870.65, "word": " should.", "probability": 0.9482421875}, {"start": 873.89, "end": 874.31, "word": " So", "probability": 0.56982421875}, {"start": 874.31, "end": 874.85, "word": " I", "probability": 0.71484375}, {"start": 874.85, "end": 875.17, "word": " think", "probability": 0.91796875}, {"start": 875.17, "end": 875.41, "word": " we", "probability": 0.95751953125}, {"start": 875.41, "end": 875.89, "word": " should", "probability": 0.96826171875}, {"start": 875.89, "end": 878.65, "word": " look", "probability": 0.2471923828125}, {"start": 878.65, "end": 879.01, "word": " here.", "probability": 0.83837890625}, {"start": 879.19, "end": 879.35, "word": " Number", "probability": 0.859375}, {"start": 879.35, "end": 879.61, "word": " one,", "probability": 0.912109375}, {"start": 880.07, "end": 880.21, "word": " I", "probability": 0.99462890625}, {"start": 880.21, "end": 880.75, "word": " think", "probability": 0.91259765625}, {"start": 880.75, "end": 881.29, "word": " we", "probability": 0.962890625}, {"start": 881.29, "end": 881.65, "word": " should", "probability": 0.96826171875}, {"start": 881.65, "end": 882.23, "word": " buy", "probability": 0.91943359375}, {"start": 882.23, "end": 882.67, "word": " some", "probability": 0.892578125}, {"start": 882.67, "end": 882.99, "word": " guide", "probability": 0.97607421875}, {"start": 882.99, "end": 883.41, "word": " books.", "probability": 0.59619140625}, {"start": 885.39, "end": 885.75, "word": " Why?", "probability": 0.77685546875}], "temperature": 1.0}, {"id": 31, "seek": 90717, "start": 889.29, "end": 907.17, "text": " They'll give us a lot of information. So this exercise is about grammar and vocabulary. Grammar and vocabulary. The grammar here is giving suggestions with using I think or I don't think.", "tokens": [814, 603, 976, 505, 257, 688, 295, 1589, 13, 407, 341, 5380, 307, 466, 22317, 293, 19864, 13, 22130, 6209, 293, 19864, 13, 440, 22317, 510, 307, 2902, 13396, 365, 1228, 286, 519, 420, 286, 500, 380, 519, 13], "avg_logprob": -0.1424804650247097, "compression_ratio": 1.4461538461538461, "no_speech_prob": 0.0, "words": [{"start": 889.29, "end": 889.85, "word": " They'll", "probability": 0.636962890625}, {"start": 889.85, "end": 890.25, "word": " give", "probability": 0.87744140625}, {"start": 890.25, "end": 890.57, "word": " us", "probability": 0.94482421875}, {"start": 890.57, "end": 890.85, "word": " a", "probability": 0.9794921875}, {"start": 890.85, "end": 890.99, "word": " lot", "probability": 0.9580078125}, {"start": 890.99, "end": 891.15, "word": " of", "probability": 0.9677734375}, {"start": 891.15, "end": 891.87, "word": " information.", "probability": 0.849609375}, {"start": 892.55, "end": 892.63, "word": " So", "probability": 0.81494140625}, {"start": 892.63, "end": 892.87, "word": " this", "probability": 0.84619140625}, {"start": 892.87, "end": 893.61, "word": " exercise", "probability": 0.65966796875}, {"start": 893.61, "end": 894.01, "word": " is", "probability": 0.9482421875}, {"start": 894.01, "end": 894.27, "word": " about", "probability": 0.9130859375}, {"start": 894.27, "end": 894.77, "word": " grammar", "probability": 0.9013671875}, {"start": 894.77, "end": 895.59, "word": " and", "probability": 0.9296875}, {"start": 895.59, "end": 896.23, "word": " vocabulary.", "probability": 0.83740234375}, {"start": 896.91, "end": 897.41, "word": " Grammar", "probability": 0.90869140625}, {"start": 897.41, "end": 898.11, "word": " and", "probability": 0.9296875}, {"start": 898.11, "end": 898.71, "word": " vocabulary.", "probability": 0.73828125}, {"start": 899.41, "end": 899.53, "word": " The", "probability": 0.82861328125}, {"start": 899.53, "end": 899.77, "word": " grammar", "probability": 0.9169921875}, {"start": 899.77, "end": 900.09, "word": " here", "probability": 0.85009765625}, {"start": 900.09, "end": 900.53, "word": " is", "probability": 0.94189453125}, {"start": 900.53, "end": 902.23, "word": " giving", "probability": 0.85595703125}, {"start": 902.23, "end": 903.57, "word": " suggestions", "probability": 0.8720703125}, {"start": 903.57, "end": 905.03, "word": " with", "probability": 0.7236328125}, {"start": 905.03, "end": 905.51, "word": " using", "probability": 0.9296875}, {"start": 905.51, "end": 905.91, "word": " I", "probability": 0.461181640625}, {"start": 905.91, "end": 906.29, "word": " think", "probability": 0.92236328125}, {"start": 906.29, "end": 906.57, "word": " or", "probability": 0.91796875}, {"start": 906.57, "end": 906.77, "word": " I", "probability": 0.9951171875}, {"start": 906.77, "end": 906.91, "word": " don't", "probability": 0.979248046875}, {"start": 906.91, "end": 907.17, "word": " think.", "probability": 0.9140625}], "temperature": 1.0}, {"id": 32, "seek": 93452, "start": 908.38, "end": 934.52, "text": " When I say I think, it's bitter, polite. I think we should buy guidebooks. They'll give us a lot of information. Here, I don't think, I don't think we should take plenty of sun cream.", "tokens": [1133, 286, 584, 286, 519, 11, 309, 311, 13871, 11, 25171, 13, 286, 519, 321, 820, 2256, 5934, 15170, 13, 814, 603, 976, 505, 257, 688, 295, 1589, 13, 1692, 11, 286, 500, 380, 519, 11, 286, 500, 380, 519, 321, 820, 747, 7140, 295, 3295, 4689, 13], "avg_logprob": -0.28555484693877553, "compression_ratio": 1.393939393939394, "no_speech_prob": 0.0, "words": [{"start": 908.38, "end": 908.6, "word": " When", "probability": 0.59423828125}, {"start": 908.6, "end": 908.7, "word": " I", "probability": 0.9794921875}, {"start": 908.7, "end": 908.8, "word": " say", "probability": 0.9091796875}, {"start": 908.8, "end": 908.94, "word": " I", "probability": 0.578125}, {"start": 908.94, "end": 909.18, "word": " think,", "probability": 0.9267578125}, {"start": 909.3, "end": 909.4, "word": " it's", "probability": 0.65771484375}, {"start": 909.4, "end": 909.64, "word": " bitter,", "probability": 0.2724609375}, {"start": 910.32, "end": 910.76, "word": " polite.", "probability": 0.96533203125}, {"start": 911.62, "end": 912.3, "word": " I", "probability": 0.62109375}, {"start": 912.3, "end": 912.96, "word": " think", "probability": 0.89306640625}, {"start": 912.96, "end": 913.56, "word": " we", "probability": 0.93994140625}, {"start": 913.56, "end": 914.1, "word": " should", "probability": 0.96533203125}, {"start": 914.1, "end": 914.5, "word": " buy", "probability": 0.908203125}, {"start": 914.5, "end": 915.92, "word": " guidebooks.", "probability": 0.7076416015625}, {"start": 916.66, "end": 917.04, "word": " They'll", "probability": 0.70361328125}, {"start": 917.04, "end": 917.3, "word": " give", "probability": 0.87548828125}, {"start": 917.3, "end": 917.64, "word": " us", "probability": 0.94384765625}, {"start": 917.64, "end": 918.0, "word": " a", "probability": 0.9931640625}, {"start": 918.0, "end": 918.14, "word": " lot", "probability": 0.95947265625}, {"start": 918.14, "end": 918.3, "word": " of", "probability": 0.96728515625}, {"start": 918.3, "end": 918.94, "word": " information.", "probability": 0.84375}, {"start": 921.24, "end": 921.7, "word": " Here,", "probability": 0.64111328125}, {"start": 924.82, "end": 925.38, "word": " I", "probability": 0.9775390625}, {"start": 925.38, "end": 928.24, "word": " don't", "probability": 0.970947265625}, {"start": 928.24, "end": 928.68, "word": " think,", "probability": 0.9189453125}, {"start": 929.0, "end": 929.44, "word": " I", "probability": 0.6728515625}, {"start": 929.44, "end": 930.12, "word": " don't", "probability": 0.981689453125}, {"start": 930.12, "end": 930.44, "word": " think", "probability": 0.9208984375}, {"start": 930.44, "end": 930.92, "word": " we", "probability": 0.93505859375}, {"start": 930.92, "end": 932.08, "word": " should", "probability": 0.96044921875}, {"start": 932.08, "end": 932.8, "word": " take", "probability": 0.89892578125}, {"start": 932.8, "end": 933.36, "word": " plenty", "probability": 0.9423828125}, {"start": 933.36, "end": 933.76, "word": " of", "probability": 0.97021484375}, {"start": 933.76, "end": 934.02, "word": " sun", "probability": 0.78125}, {"start": 934.02, "end": 934.52, "word": " cream.", "probability": 0.666015625}], "temperature": 1.0}, {"id": 33, "seek": 96338, "start": 939.7, "end": 963.38, "text": " Yes. We should take. We should take. So I think we should take plenty of sun cream. Why? It will be hot. It will be really hot. So here should or shouldn't.", "tokens": [1079, 13, 492, 820, 747, 13, 492, 820, 747, 13, 407, 286, 519, 321, 820, 747, 7140, 295, 3295, 4689, 13, 1545, 30, 467, 486, 312, 2368, 13, 467, 486, 312, 534, 2368, 13, 407, 510, 820, 420, 4659, 380, 13], "avg_logprob": -0.21595982639562517, "compression_ratio": 1.5392156862745099, "no_speech_prob": 0.0, "words": [{"start": 939.7, "end": 940.58, "word": " Yes.", "probability": 0.49462890625}, {"start": 942.18, "end": 943.06, "word": " We", "probability": 0.853515625}, {"start": 943.06, "end": 943.32, "word": " should", "probability": 0.9716796875}, {"start": 943.32, "end": 943.76, "word": " take.", "probability": 0.85205078125}, {"start": 944.76, "end": 945.64, "word": " We", "probability": 0.360595703125}, {"start": 945.64, "end": 945.88, "word": " should", "probability": 0.9697265625}, {"start": 945.88, "end": 946.28, "word": " take.", "probability": 0.888671875}, {"start": 946.62, "end": 947.34, "word": " So", "probability": 0.86279296875}, {"start": 947.34, "end": 947.66, "word": " I", "probability": 0.853515625}, {"start": 947.66, "end": 947.94, "word": " think", "probability": 0.9189453125}, {"start": 947.94, "end": 948.18, "word": " we", "probability": 0.955078125}, {"start": 948.18, "end": 948.44, "word": " should", "probability": 0.9697265625}, {"start": 948.44, "end": 949.12, "word": " take", "probability": 0.8955078125}, {"start": 949.12, "end": 950.32, "word": " plenty", "probability": 0.91015625}, {"start": 950.32, "end": 950.76, "word": " of", "probability": 0.96923828125}, {"start": 950.76, "end": 950.96, "word": " sun", "probability": 0.78515625}, {"start": 950.96, "end": 951.4, "word": " cream.", "probability": 0.7177734375}, {"start": 952.44, "end": 952.72, "word": " Why?", "probability": 0.849609375}, {"start": 953.72, "end": 954.58, "word": " It", "probability": 0.88818359375}, {"start": 954.58, "end": 954.76, "word": " will", "probability": 0.89453125}, {"start": 954.76, "end": 955.16, "word": " be", "probability": 0.9560546875}, {"start": 955.16, "end": 956.6, "word": " hot.", "probability": 0.8544921875}, {"start": 958.18, "end": 959.06, "word": " It", "probability": 0.94091796875}, {"start": 959.06, "end": 959.24, "word": " will", "probability": 0.89404296875}, {"start": 959.24, "end": 959.58, "word": " be", "probability": 0.9521484375}, {"start": 959.58, "end": 960.12, "word": " really", "probability": 0.90380859375}, {"start": 960.12, "end": 960.54, "word": " hot.", "probability": 0.93701171875}, {"start": 961.28, "end": 961.98, "word": " So", "probability": 0.94384765625}, {"start": 961.98, "end": 962.3, "word": " here", "probability": 0.833984375}, {"start": 962.3, "end": 962.78, "word": " should", "probability": 0.6552734375}, {"start": 962.78, "end": 963.0, "word": " or", "probability": 0.8896484375}, {"start": 963.0, "end": 963.38, "word": " shouldn't.", "probability": 0.953125}], "temperature": 1.0}, {"id": 34, "seek": 99263, "start": 965.35, "end": 992.63, "text": " should. So instead of saying we should, we say I think we should. Why? Because it is more polite. It is formal. It is a good way to give suggestion. So here, pack too many clothes. Shouldn't. 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We say, I don't think we should. I don't think we should take too many clothes. Clothes. Why? Our bags will be too heavy to carry. Too heavy that we can't carry it.", "tokens": [492, 4659, 380, 13, 492, 584, 11, 286, 500, 380, 519, 321, 820, 13, 286, 500, 380, 519, 321, 820, 747, 886, 867, 5534, 13, 2033, 4624, 13, 1545, 30, 2621, 10405, 486, 312, 886, 4676, 281, 3985, 13, 11395, 4676, 300, 321, 393, 380, 3985, 309, 13], "avg_logprob": -0.14461097425344038, "compression_ratio": 1.4793388429752066, "no_speech_prob": 0.0, "words": [{"start": 993.53, "end": 993.75, "word": " We", "probability": 0.80517578125}, {"start": 993.75, "end": 994.13, "word": " shouldn't.", "probability": 0.792236328125}, {"start": 994.31, "end": 994.41, "word": " We", "probability": 0.884765625}, {"start": 994.41, "end": 994.63, "word": " say,", "probability": 0.908203125}, {"start": 994.77, "end": 994.89, "word": " I", "probability": 0.74072265625}, {"start": 994.89, "end": 995.17, "word": " don't", "probability": 0.9833984375}, {"start": 995.17, "end": 995.53, "word": " think", "probability": 0.91650390625}, {"start": 995.53, "end": 995.73, "word": " we", "probability": 0.9580078125}, {"start": 995.73, "end": 996.07, "word": " should.", "probability": 0.9609375}, {"start": 996.41, "end": 997.09, "word": " I", "probability": 0.97216796875}, {"start": 997.09, "end": 997.35, "word": " don't", "probability": 0.982666015625}, {"start": 997.35, "end": 997.63, "word": " think", "probability": 0.91455078125}, {"start": 997.63, "end": 997.87, "word": " we", "probability": 0.9609375}, {"start": 997.87, "end": 998.13, "word": " should", "probability": 0.96923828125}, {"start": 998.13, "end": 998.61, "word": " take", "probability": 0.88232421875}, {"start": 998.61, "end": 999.15, "word": " too", "probability": 0.916015625}, {"start": 999.15, "end": 999.65, "word": " many", "probability": 0.890625}, {"start": 999.65, "end": 1001.27, "word": " clothes.", "probability": 0.66259765625}, {"start": 1001.81, "end": 1002.33, "word": " Clothes.", "probability": 0.89501953125}, {"start": 1003.41, "end": 1003.61, "word": " Why?", "probability": 0.72216796875}, {"start": 1006.79, "end": 1007.41, "word": " Our", "probability": 0.87646484375}, {"start": 1007.41, "end": 1011.99, "word": " bags", "probability": 0.88720703125}, {"start": 1011.99, "end": 1012.37, "word": " will", "probability": 0.81201171875}, {"start": 1012.37, "end": 1012.59, "word": " be", "probability": 0.96240234375}, {"start": 1012.59, "end": 1012.83, "word": " too", "probability": 0.93505859375}, {"start": 1012.83, "end": 1013.13, "word": " heavy", "probability": 0.849609375}, {"start": 1013.13, "end": 1013.31, "word": " to", "probability": 0.9462890625}, {"start": 1013.31, "end": 1013.69, "word": " carry.", "probability": 0.93359375}, {"start": 1014.33, "end": 1015.01, "word": " Too", "probability": 0.86279296875}, {"start": 1015.01, "end": 1015.35, "word": " heavy", "probability": 0.82373046875}, {"start": 1015.35, "end": 1016.07, "word": " that", "probability": 0.8642578125}, {"start": 1016.07, "end": 1016.27, "word": " we", "probability": 0.96337890625}, {"start": 1016.27, "end": 1016.73, "word": " can't", "probability": 0.973876953125}, {"start": 1016.73, "end": 1017.03, "word": " carry", "probability": 0.9404296875}, {"start": 1017.03, "end": 1017.47, "word": " it.", "probability": 0.9423828125}], "temperature": 1.0}, {"id": 36, "seek": 104769, "start": 1018.93, "end": 1047.69, "text": " So heavy that we can't carry it or too heavy to carry. Number four, take anything valuable. I don't think we should take anything valuable. Why? We might lose it. So this is number four. We might lose it. 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I think we should go to Japan first. I think we, or I don't think we, I think we, yes, I think we should go to Japan first. I have some friends there.", "tokens": [1037, 281, 3367, 700, 13, 286, 519, 321, 820, 352, 281, 3367, 700, 13, 286, 519, 321, 11, 420, 286, 500, 380, 519, 321, 11, 286, 519, 321, 11, 2086, 11, 286, 519, 321, 820, 352, 281, 3367, 700, 13, 286, 362, 512, 1855, 456, 13], "avg_logprob": -0.17436835233201373, "compression_ratio": 1.8681318681318682, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1049.61, "end": 1049.91, "word": " Go", "probability": 0.5654296875}, {"start": 1049.91, "end": 1050.09, "word": " to", "probability": 0.97314453125}, {"start": 1050.09, "end": 1050.39, "word": " Japan", "probability": 0.79833984375}, {"start": 1050.39, "end": 1050.81, "word": " first.", "probability": 0.8740234375}, {"start": 1052.11, "end": 1052.33, "word": " I", "probability": 0.958984375}, {"start": 1052.33, "end": 1052.99, "word": " think", "probability": 0.92822265625}, {"start": 1052.99, "end": 1053.65, "word": " we", "probability": 0.94775390625}, {"start": 1053.65, "end": 1054.21, "word": " should", "probability": 0.96630859375}, {"start": 1054.21, "end": 1054.57, "word": " go", "probability": 0.96533203125}, {"start": 1054.57, "end": 1055.33, "word": " to", "probability": 0.9658203125}, {"start": 1055.33, "end": 1055.77, "word": " Japan", "probability": 0.82958984375}, {"start": 1055.77, "end": 1056.33, "word": " first.", "probability": 0.88623046875}, {"start": 1057.17, "end": 1057.81, "word": " I", "probability": 0.51123046875}, {"start": 1057.81, "end": 1059.11, "word": " think", "probability": 0.85595703125}, {"start": 1059.11, "end": 1059.41, "word": " we,", "probability": 0.94580078125}, {"start": 1059.59, "end": 1059.73, "word": " or", "probability": 0.90966796875}, {"start": 1059.73, "end": 1059.87, "word": " I", "probability": 0.97314453125}, {"start": 1059.87, "end": 1059.99, "word": " don't", "probability": 0.938232421875}, {"start": 1059.99, "end": 1060.25, "word": " think", "probability": 0.91943359375}, {"start": 1060.25, "end": 1060.45, "word": " we,", "probability": 0.935546875}, {"start": 1060.79, "end": 1060.93, "word": " I", "probability": 0.96728515625}, {"start": 1060.93, "end": 1061.21, "word": " think", "probability": 0.92578125}, {"start": 1061.21, "end": 1061.53, "word": " we,", "probability": 0.921875}, {"start": 1061.69, "end": 1062.13, "word": " yes,", "probability": 0.86181640625}, {"start": 1062.27, "end": 1062.53, "word": " I", "probability": 0.99169921875}, {"start": 1062.53, "end": 1062.75, "word": " think", "probability": 0.91552734375}, {"start": 1062.75, "end": 1063.07, "word": " we", "probability": 0.95751953125}, {"start": 1063.07, "end": 1064.27, "word": " should", "probability": 0.9453125}, {"start": 1064.27, "end": 1064.47, "word": " go", "probability": 0.9697265625}, {"start": 1064.47, "end": 1064.59, "word": " to", "probability": 0.96875}, {"start": 1064.59, "end": 1064.81, "word": " Japan", "probability": 0.82470703125}, {"start": 1064.81, "end": 1065.31, "word": " first.", "probability": 0.87744140625}, {"start": 1068.61, "end": 1069.25, "word": " I", "probability": 0.794921875}, {"start": 1069.25, "end": 1069.67, "word": " have", "probability": 0.94970703125}, {"start": 1069.67, "end": 1069.93, "word": " some", "probability": 0.900390625}, {"start": 1069.93, "end": 1070.47, "word": " friends", "probability": 0.8173828125}, {"start": 1070.47, "end": 1071.75, "word": " there.", "probability": 0.87158203125}], "temperature": 1.0}, {"id": 38, "seek": 110570, "start": 1077.32, "end": 1105.7, "text": " What about this? Go anywhere dangerous. No. I don't think we should go anywhere dangerous. I don't think we should go anywhere dangerous. It would be really stupid. This number? Six. The last one. Yes.", "tokens": [708, 466, 341, 30, 1037, 4992, 5795, 13, 883, 13, 286, 500, 380, 519, 321, 820, 352, 4992, 5795, 13, 286, 500, 380, 519, 321, 820, 352, 4992, 5795, 13, 467, 576, 312, 534, 6631, 13, 639, 1230, 30, 11678, 13, 440, 1036, 472, 13, 1079, 13], "avg_logprob": -0.2037760429084301, "compression_ratio": 1.6694214876033058, "no_speech_prob": 0.0, "words": [{"start": 1077.32, "end": 1077.56, "word": " What", "probability": 0.7646484375}, {"start": 1077.56, "end": 1077.74, "word": " about", "probability": 0.90478515625}, {"start": 1077.74, "end": 1078.0, "word": " this?", "probability": 0.94140625}, {"start": 1078.32, "end": 1078.64, "word": " Go", "probability": 0.64794921875}, {"start": 1078.64, "end": 1079.2, "word": " anywhere", "probability": 0.75830078125}, {"start": 1079.2, "end": 1079.84, "word": " dangerous.", "probability": 0.880859375}, {"start": 1080.44, "end": 1080.64, "word": " No.", "probability": 0.68701171875}, {"start": 1080.88, "end": 1081.06, "word": " I", "probability": 0.8671875}, {"start": 1081.06, "end": 1081.26, "word": " don't", "probability": 0.977783203125}, {"start": 1081.26, "end": 1082.3, "word": " think", "probability": 0.923828125}, {"start": 1082.3, "end": 1082.5, "word": " we", "probability": 0.9453125}, {"start": 1082.5, "end": 1082.86, "word": " should", "probability": 0.9677734375}, {"start": 1082.86, "end": 1083.36, "word": " go", "probability": 0.9560546875}, {"start": 1083.36, "end": 1084.52, "word": " anywhere", "probability": 0.7783203125}, {"start": 1084.52, "end": 1085.94, "word": " dangerous.", "probability": 0.87890625}, {"start": 1087.26, "end": 1087.34, "word": " I", "probability": 0.69189453125}, {"start": 1087.34, "end": 1087.56, "word": " don't", "probability": 0.97900390625}, {"start": 1087.56, "end": 1087.98, "word": " think", "probability": 0.91845703125}, {"start": 1087.98, "end": 1088.86, "word": " we", "probability": 0.927734375}, {"start": 1088.86, "end": 1090.42, "word": " should", "probability": 0.9677734375}, {"start": 1090.42, "end": 1090.62, "word": " go", "probability": 0.437744140625}, {"start": 1090.62, "end": 1091.08, "word": " anywhere", "probability": 0.78857421875}, {"start": 1091.08, "end": 1091.86, "word": " dangerous.", "probability": 0.89208984375}, {"start": 1092.6, "end": 1093.12, "word": " It", "probability": 0.794921875}, {"start": 1093.12, "end": 1094.7, "word": " would", "probability": 0.9248046875}, {"start": 1094.7, "end": 1095.08, "word": " be", "probability": 0.951171875}, {"start": 1095.08, "end": 1095.76, "word": " really", "probability": 0.87353515625}, {"start": 1095.76, "end": 1096.24, "word": " stupid.", "probability": 0.9560546875}, {"start": 1097.0, "end": 1097.14, "word": " This", "probability": 0.70458984375}, {"start": 1097.14, "end": 1097.44, "word": " number?", "probability": 0.875}, {"start": 1098.76, "end": 1099.68, "word": " Six.", "probability": 0.60107421875}, {"start": 1101.46, "end": 1101.88, "word": " The", "probability": 0.8681640625}, {"start": 1101.88, "end": 1102.1, "word": " last", "probability": 0.86767578125}, {"start": 1102.1, "end": 1102.46, "word": " one.", "probability": 0.92822265625}, {"start": 1104.78, "end": 1105.7, "word": " Yes.", "probability": 0.806640625}], "temperature": 1.0}, {"id": 39, "seek": 113564, "start": 1106.64, "end": 1135.64, "text": " I think we should have some vaccination before traveling. Why? We don't want to get ill. This is number seven. So all these examples of suggestions or advice here we use I think or I don't think. I think we should. I don't think we should.", "tokens": [286, 519, 321, 820, 362, 512, 16498, 949, 9712, 13, 1545, 30, 492, 500, 380, 528, 281, 483, 3171, 13, 639, 307, 1230, 3407, 13, 407, 439, 613, 5110, 295, 13396, 420, 5192, 510, 321, 764, 286, 519, 420, 286, 500, 380, 519, 13, 286, 519, 321, 820, 13, 286, 500, 380, 519, 321, 820, 13], "avg_logprob": -0.14692982037862143, "compression_ratio": 1.5483870967741935, "no_speech_prob": 0.0, "words": [{"start": 1106.64, "end": 1106.9, "word": " I", "probability": 0.77734375}, {"start": 1106.9, "end": 1107.2, "word": " think", "probability": 0.91845703125}, {"start": 1107.2, "end": 1107.4, "word": " we", "probability": 0.94970703125}, {"start": 1107.4, "end": 1107.78, "word": " should", "probability": 0.95703125}, {"start": 1107.78, "end": 1109.22, "word": " have", "probability": 0.90966796875}, {"start": 1109.22, "end": 1109.78, "word": " some", "probability": 0.87890625}, {"start": 1109.78, "end": 1110.82, "word": " vaccination", "probability": 0.759765625}, {"start": 1110.82, "end": 1112.74, "word": " before", "probability": 0.435546875}, {"start": 1112.74, "end": 1113.24, "word": " traveling.", "probability": 0.6533203125}, {"start": 1113.96, "end": 1114.2, "word": " Why?", "probability": 0.8330078125}, {"start": 1114.66, "end": 1114.9, "word": " We", "probability": 0.8681640625}, {"start": 1114.9, "end": 1115.28, "word": " don't", "probability": 0.97314453125}, {"start": 1115.28, "end": 1116.86, "word": " want", "probability": 0.88818359375}, {"start": 1116.86, "end": 1117.56, "word": " to", "probability": 0.970703125}, {"start": 1117.56, "end": 1118.66, "word": " get", "probability": 0.935546875}, {"start": 1118.66, "end": 1119.32, "word": " ill.", "probability": 0.81982421875}, {"start": 1120.02, "end": 1120.3, "word": " This", "probability": 0.806640625}, {"start": 1120.3, "end": 1120.42, "word": " is", "probability": 0.9375}, {"start": 1120.42, "end": 1120.74, "word": " number", "probability": 0.9111328125}, {"start": 1120.74, "end": 1121.98, "word": " seven.", "probability": 0.68505859375}, {"start": 1123.28, "end": 1123.62, "word": " So", "probability": 0.8291015625}, {"start": 1123.62, "end": 1124.06, "word": " all", "probability": 0.78125}, {"start": 1124.06, "end": 1124.46, "word": " these", "probability": 0.83154296875}, {"start": 1124.46, "end": 1124.96, "word": " examples", "probability": 0.85888671875}, {"start": 1124.96, "end": 1125.84, "word": " of", "probability": 0.95263671875}, {"start": 1125.84, "end": 1126.74, "word": " suggestions", "probability": 0.87255859375}, {"start": 1126.74, "end": 1127.82, "word": " or", "probability": 0.9375}, {"start": 1127.82, "end": 1128.7, "word": " advice", "probability": 0.91552734375}, {"start": 1128.7, "end": 1130.0, "word": " here", "probability": 0.45703125}, {"start": 1130.0, "end": 1130.24, "word": " we", "probability": 0.69140625}, {"start": 1130.24, "end": 1130.5, "word": " use", "probability": 0.8720703125}, {"start": 1130.5, "end": 1130.72, "word": " I", "probability": 0.5419921875}, {"start": 1130.72, "end": 1131.0, "word": " think", "probability": 0.92578125}, {"start": 1131.0, "end": 1131.26, "word": " or", "probability": 0.908203125}, {"start": 1131.26, "end": 1131.42, "word": " I", "probability": 0.9931640625}, {"start": 1131.42, "end": 1131.56, "word": " don't", "probability": 0.97998046875}, {"start": 1131.56, "end": 1131.84, "word": " think.", "probability": 0.91455078125}, {"start": 1132.38, "end": 1132.62, "word": " I", "probability": 0.97021484375}, {"start": 1132.62, "end": 1133.12, "word": " think", "probability": 0.90966796875}, {"start": 1133.12, "end": 1133.42, "word": " we", "probability": 0.95458984375}, {"start": 1133.42, "end": 1133.9, "word": " should.", "probability": 0.96484375}, {"start": 1134.24, "end": 1134.44, "word": " I", "probability": 0.99365234375}, {"start": 1134.44, "end": 1134.64, "word": " don't", "probability": 0.97998046875}, {"start": 1134.64, "end": 1134.96, "word": " think", "probability": 0.9169921875}, {"start": 1134.96, "end": 1135.18, "word": " we", "probability": 0.95654296875}, {"start": 1135.18, "end": 1135.64, "word": " should.", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 40, "seek": 116541, "start": 1136.29, "end": 1165.41, "text": " The first one for something needed. The other one is for something we don't need. I want you to work in pairs. Make match A with B, but begin with, I think we should. And here, I don't think we should. Yes, work in pairs. Work in pairs.", "tokens": [440, 700, 472, 337, 746, 2978, 13, 440, 661, 472, 307, 337, 746, 321, 500, 380, 643, 13, 286, 528, 291, 281, 589, 294, 15494, 13, 4387, 2995, 316, 365, 363, 11, 457, 1841, 365, 11, 286, 519, 321, 820, 13, 400, 510, 11, 286, 500, 380, 519, 321, 820, 13, 1079, 11, 589, 294, 15494, 13, 6603, 294, 15494, 13], "avg_logprob": -0.1669606862048949, "compression_ratio": 1.6344827586206896, "no_speech_prob": 0.0, "words": [{"start": 1136.29, "end": 1136.51, "word": " The", "probability": 0.640625}, {"start": 1136.51, "end": 1136.87, "word": " first", "probability": 0.88671875}, {"start": 1136.87, "end": 1137.19, "word": " one", "probability": 0.931640625}, {"start": 1137.19, "end": 1137.57, "word": " for", "probability": 0.650390625}, {"start": 1137.57, "end": 1139.51, "word": " something", "probability": 0.84423828125}, {"start": 1139.51, "end": 1141.25, "word": " needed.", "probability": 0.88671875}, {"start": 1142.13, "end": 1142.27, "word": " The", "probability": 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So what's the difference between should and have to? Should is personal. Have to is impersonal.", "tokens": [1079, 11, 300, 311, 1547, 13, 407, 437, 311, 264, 2649, 1296, 820, 293, 362, 281, 30, 6454, 307, 2973, 13, 3560, 281, 307, 38147, 304, 13], "avg_logprob": -0.12869699139680182, "compression_ratio": 1.2340425531914894, "no_speech_prob": 0.0, "words": [{"start": 1229.73, "end": 1230.19, "word": " Yes,", "probability": 0.81494140625}, {"start": 1230.33, "end": 1230.59, "word": " that's", "probability": 0.952392578125}, {"start": 1230.59, "end": 1230.93, "word": " enough.", "probability": 0.875}, {"start": 1232.11, "end": 1232.39, "word": " So", "probability": 0.88623046875}, {"start": 1232.39, "end": 1233.77, "word": " what's", "probability": 0.813720703125}, {"start": 1233.77, "end": 1233.97, "word": " the", "probability": 0.9287109375}, {"start": 1233.97, "end": 1234.63, "word": " difference", "probability": 0.861328125}, {"start": 1234.63, "end": 1235.73, "word": " between", "probability": 0.8837890625}, {"start": 1235.73, "end": 1237.01, "word": " should", "probability": 0.8515625}, {"start": 1237.01, "end": 1238.49, "word": " and", "probability": 0.9248046875}, {"start": 1238.49, "end": 1239.35, "word": " have", "probability": 0.9560546875}, {"start": 1239.35, "end": 1239.59, "word": " to?", "probability": 0.9560546875}, {"start": 1242.29, "end": 1242.83, "word": " Should", "probability": 0.794921875}, {"start": 1242.83, "end": 1243.95, "word": " is", "probability": 0.94921875}, {"start": 1243.95, "end": 1245.15, "word": " personal.", "probability": 0.8740234375}, {"start": 1246.63, "end": 1247.09, "word": " Have", "probability": 0.9091796875}, {"start": 1247.09, "end": 1247.37, "word": " to", "probability": 0.95849609375}, {"start": 1247.37, "end": 1247.89, "word": " is", "probability": 0.93701171875}, {"start": 1247.89, "end": 1249.43, "word": " impersonal.", "probability": 0.96533203125}], "temperature": 1.0}, {"id": 44, "seek": 127967, "start": 1251.79, "end": 1279.67, "text": " Have to is impersonal, not from me, from some other things. But if it's from me, I say should. Again, should is mild obligation. Mild obligation. But have to, general obligation. What about have got to? 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If it is general, I use have to. Yes? If it is personal, I say should. And when there is absence of obligation, absence of obligation, I use shouldn't. 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So which is better to say you should or I think you should. I think we should. You shouldn't or I don't think you should. I don't think you should. I want each of you to read number one. Yes. Number one. Yes. I think we should buy some guide books.", "tokens": [34170, 380, 420, 286, 500, 380, 519, 321, 820, 13, 407, 597, 307, 1101, 281, 584, 291, 820, 420, 286, 519, 291, 820, 13, 286, 519, 321, 820, 13, 509, 4659, 380, 420, 286, 500, 380, 519, 291, 820, 13, 286, 500, 380, 519, 291, 820, 13, 286, 528, 1184, 295, 291, 281, 1401, 1230, 472, 13, 1079, 13, 5118, 472, 13, 1079, 13, 286, 519, 321, 820, 2256, 512, 5934, 3642, 13], "avg_logprob": -0.16026183036533562, "compression_ratio": 2.05, "no_speech_prob": 0.0, "words": [{"start": 1310.94, "end": 1311.52, "word": " Shouldn't", "probability": 0.7412109375}, {"start": 1311.52, "end": 1311.88, "word": " or", "probability": 0.6923828125}, {"start": 1311.88, "end": 1312.42, "word": " I", "probability": 0.919921875}, {"start": 1312.42, "end": 1312.58, "word": " don't", "probability": 0.9775390625}, {"start": 1312.58, "end": 1312.84, "word": " think", "probability": 0.91943359375}, {"start": 1312.84, "end": 1313.0, "word": " we", "probability": 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Very good. Number two. I think you should take plenty of sun cream. They will give us a lot of power. It will be really hot. Really hot. Yes. 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Number four. Yes. We. I don't think we. Yes. Yes. 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Uh-huh. We might lose it. Yes. I think we should go to Japan first. I have some friends there. Number six. I don't think we should. 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We don't want to get ill. So this is the answer. Again, this is the answer. Also, I want someone to read again. Yes.", "tokens": [400, 264, 1036, 472, 13, 492, 500, 380, 528, 281, 483, 3171, 13, 407, 341, 307, 264, 1867, 13, 3764, 11, 341, 307, 264, 1867, 13, 2743, 11, 286, 528, 1580, 281, 1401, 797, 13, 1079, 13], "avg_logprob": -0.1782483533024788, "compression_ratio": 1.3636363636363635, "no_speech_prob": 0.0, "words": [{"start": 1427.83, "end": 1428.19, "word": " And", "probability": 0.431396484375}, {"start": 1428.19, "end": 1429.03, "word": " the", "probability": 0.91015625}, {"start": 1429.03, "end": 1429.25, "word": " last", "probability": 0.8779296875}, {"start": 1429.25, "end": 1429.73, "word": " one.", "probability": 0.92431640625}, {"start": 1431.89, "end": 1432.79, "word": " We", "probability": 0.431640625}, {"start": 1432.79, "end": 1438.13, "word": " don't", "probability": 0.9482421875}, {"start": 1438.13, "end": 1438.41, "word": " want", "probability": 0.8916015625}, {"start": 1438.41, "end": 1440.27, "word": " to", "probability": 0.970703125}, {"start": 1440.27, "end": 1440.49, "word": " get", "probability": 0.93701171875}, {"start": 1440.49, "end": 1440.81, "word": " ill.", "probability": 0.85400390625}, {"start": 1442.01, "end": 1442.91, "word": " So", "probability": 0.8330078125}, {"start": 1442.91, "end": 1443.61, "word": " this", "probability": 0.8447265625}, {"start": 1443.61, "end": 1444.05, "word": " is", "probability": 0.94921875}, {"start": 1444.05, "end": 1447.09, "word": " the", "probability": 0.82080078125}, {"start": 1447.09, "end": 1447.55, "word": " answer.", "probability": 0.95703125}, {"start": 1449.37, "end": 1449.79, "word": " Again,", "probability": 0.83837890625}, {"start": 1450.39, "end": 1450.65, "word": " this", "probability": 0.94140625}, {"start": 1450.65, "end": 1450.75, "word": " is", "probability": 0.9453125}, {"start": 1450.75, "end": 1450.89, "word": " the", "probability": 0.92578125}, {"start": 1450.89, "end": 1451.25, "word": " answer.", "probability": 0.955078125}, {"start": 1452.77, "end": 1453.61, "word": " Also,", "probability": 0.91943359375}, {"start": 1454.15, "end": 1454.35, "word": " I", "probability": 0.986328125}, {"start": 1454.35, "end": 1454.51, "word": " want", "probability": 0.876953125}, {"start": 1454.51, "end": 1454.75, "word": " someone", "probability": 0.9375}, {"start": 1454.75, "end": 1454.99, "word": " to", "probability": 0.96826171875}, {"start": 1454.99, "end": 1455.29, "word": " read", "probability": 0.97021484375}, {"start": 1455.29, "end": 1456.11, "word": " again.", "probability": 0.6328125}, {"start": 1456.89, "end": 1457.21, "word": " Yes.", "probability": 0.95556640625}], "temperature": 1.0}, {"id": 51, "seek": 149001, "start": 1462.91, "end": 1490.01, "text": " Number two. I think we should take plenty of sun cream. It will be really hot. Three. I don't think we should pack too many clothes. Our days will be too hectic to time. Four. 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Yes Six Yes And the last one Yes Very good. So this is an exercise about", "tokens": [8266, 12, 10250, 293, 1230, 1732, 13, 1079, 11678, 1079, 400, 264, 1036, 472, 1079, 4372, 665, 13, 407, 341, 307, 364, 5380, 466], "avg_logprob": -0.2653125, "compression_ratio": 1.0898876404494382, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1491.87, "end": 1492.19, "word": " Mm", "probability": 0.476318359375}, {"start": 1492.19, "end": 1492.51, "word": "-hmm", "probability": 0.845458984375}, {"start": 1492.51, "end": 1492.97, "word": " and", "probability": 0.61767578125}, {"start": 1492.97, "end": 1493.21, "word": " number", "probability": 0.9248046875}, {"start": 1493.21, "end": 1493.79, "word": " five.", "probability": 0.86328125}, {"start": 1493.83, "end": 1494.41, "word": " Yes", "probability": 0.97119140625}, {"start": 1494.41, "end": 1500.57, "word": " Six", "probability": 0.5830078125}, {"start": 1500.57, "end": 1502.77, "word": " Yes", "probability": 0.405517578125}, {"start": 1502.77, "end": 1505.89, "word": " And", "probability": 0.60888671875}, {"start": 1505.89, "end": 1508.19, "word": " the", "probability": 0.9208984375}, {"start": 1508.19, "end": 1508.41, "word": " last", "probability": 0.86962890625}, {"start": 1508.41, "end": 1509.55, "word": " one", "probability": 0.93701171875}, {"start": 1509.55, "end": 1510.73, "word": " Yes", "probability": 0.501953125}, {"start": 1510.73, "end": 1516.01, "word": " Very", "probability": 0.78515625}, {"start": 1516.01, "end": 1516.29, "word": " good.", "probability": 0.9287109375}, {"start": 1516.55, "end": 1516.75, "word": " So", "probability": 0.97216796875}, {"start": 1516.75, "end": 1516.99, "word": " this", "probability": 0.94873046875}, {"start": 1516.99, "end": 1518.17, "word": " is", "probability": 0.95556640625}, {"start": 1518.17, "end": 1518.87, "word": " an", "probability": 0.716796875}, {"start": 1518.87, "end": 1519.23, "word": " exercise", "probability": 0.96044921875}, {"start": 1519.23, "end": 1520.19, "word": " about", "probability": 0.91357421875}], "temperature": 1.0}, {"id": 53, "seek": 154840, "start": 1520.84, "end": 1548.4, "text": " suggestion we use, I think we should or I don't think we should. If there's something good, I think we should. If there's something bad, I don't think we should. Yes. What kind of obligation is it? It is mild. It is mild, not strong. Not strong. We have mild and strong. 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No, I won't. Yes, I will. Yes, grandmother. I will. No, I won't. Yes. Grandmother, you mustn't lose your passport. Anthony, no, I won't. No, I won't. Yes. So this example, A, B. 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Grandmother and Anthony. Yes, I want someone to read. Yes. Yes. Strong obligation. Without smiling. No. You must look after your money. Someone else. Someone else.", "tokens": [6757, 11930, 293, 15853, 13, 6757, 11930, 293, 15853, 13, 1079, 11, 286, 528, 1580, 281, 1401, 13, 1079, 13, 1079, 13, 22792, 20326, 13, 9129, 16005, 13, 883, 13, 509, 1633, 574, 934, 428, 1460, 13, 8734, 1646, 13, 8734, 1646, 13], "avg_logprob": -0.23615057156844574, "compression_ratio": 1.4881889763779528, "no_speech_prob": 0.0, "words": [{"start": 1740.98, "end": 1741.64, "word": " Grandmother", "probability": 0.697265625}, {"start": 1741.64, "end": 1742.76, "word": " and", "probability": 0.8603515625}, {"start": 1742.76, "end": 1743.26, "word": " Anthony.", "probability": 0.87060546875}, {"start": 1745.38, "end": 1746.54, "word": " Grandmother", "probability": 0.6177978515625}, {"start": 1746.54, "end": 1748.3, "word": " and", "probability": 0.89990234375}, {"start": 1748.3, "end": 1748.76, "word": " Anthony.", "probability": 0.89013671875}, {"start": 1750.1, "end": 1750.9, "word": " Yes,", "probability": 0.9326171875}, {"start": 1750.92, "end": 1751.0, "word": " I", "probability": 0.99365234375}, {"start": 1751.0, "end": 1751.16, "word": " want", "probability": 0.873046875}, {"start": 1751.16, "end": 1751.32, "word": " someone", "probability": 0.93994140625}, {"start": 1751.32, "end": 1751.5, "word": " to", "probability": 0.9658203125}, {"start": 1751.5, "end": 1751.74, "word": " read.", "probability": 0.97265625}, {"start": 1753.0, "end": 1753.22, "word": " Yes.", "probability": 0.8876953125}, {"start": 1754.16, "end": 1755.24, "word": " Yes.", "probability": 0.62109375}, {"start": 1756.02, "end": 1756.5, "word": " Strong", "probability": 0.90087890625}, {"start": 1756.5, "end": 1757.06, "word": " obligation.", "probability": 0.916015625}, {"start": 1758.34, "end": 1759.02, "word": " Without", "probability": 0.82373046875}, {"start": 1759.02, "end": 1759.64, "word": " smiling.", "probability": 0.9765625}, {"start": 1760.4, "end": 1760.4, "word": " No.", "probability": 0.63671875}, {"start": 1761.74, "end": 1762.36, "word": " You", "probability": 0.50537109375}, {"start": 1762.36, "end": 1762.72, "word": " must", "probability": 0.88525390625}, {"start": 1762.72, "end": 1763.12, "word": " look", "probability": 0.9580078125}, {"start": 1763.12, "end": 1763.54, "word": " after", "probability": 0.8251953125}, {"start": 1763.54, "end": 1763.9, "word": " your", "probability": 0.89453125}, {"start": 1763.9, "end": 1764.26, "word": " money.", "probability": 0.9306640625}, {"start": 1764.86, "end": 1765.8, "word": " Someone", "probability": 0.42626953125}, {"start": 1765.8, "end": 1766.52, "word": " else.", "probability": 0.91015625}, {"start": 1766.64, "end": 1766.82, "word": " Someone", "probability": 0.943359375}, {"start": 1766.82, "end": 1767.08, "word": " else.", "probability": 0.9248046875}], "temperature": 1.0}, {"id": 62, "seek": 179612, "start": 1769.56, "end": 1796.12, "text": " Yes. No, no. You must look after your money. Yes. I will. Yes, grandmother. Grandma. I will. Yes, two. Another two. Yes, two. Talk to strangers. No, I won't. No, grandma. I won't. The same. 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No I want. Yes. Yeah. You mustn't drink too much beer. No grandma I want. Yes. 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And the last one. Last one. You must study hard. 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You must study hard for the midterm exam. Yes, that's enough. So when I say must, it means strong obligation. When I say should, it is mild obligation, suggestion or advice. So we have must and should.", "tokens": [509, 1633, 808, 2440, 13, 509, 1633, 2979, 1152, 337, 264, 2062, 7039, 1139, 13, 1079, 11, 300, 311, 1547, 13, 407, 562, 286, 584, 1633, 11, 309, 1355, 2068, 20326, 13, 1133, 286, 584, 820, 11, 309, 307, 15154, 20326, 11, 16541, 420, 5192, 13, 407, 321, 362, 1633, 293, 820, 13], "avg_logprob": -0.13635705439028917, "compression_ratio": 1.4966442953020134, "no_speech_prob": 0.0, "words": [{"start": 1864.17, "end": 1864.89, "word": " You", "probability": 0.388916015625}, {"start": 1864.89, "end": 1865.17, "word": " must", "probability": 0.8857421875}, {"start": 1865.17, "end": 1865.41, "word": " come", "probability": 0.74951171875}, {"start": 1865.41, "end": 1865.93, "word": " early.", "probability": 0.97314453125}, {"start": 1869.11, "end": 1869.21, "word": " You", "probability": 0.7197265625}, {"start": 1869.21, "end": 1869.47, "word": " must", "probability": 0.8955078125}, {"start": 1869.47, "end": 1869.81, "word": " study", "probability": 0.931640625}, {"start": 1869.81, "end": 1870.09, "word": " hard", "probability": 0.90869140625}, {"start": 1870.09, "end": 1870.31, "word": " for", "probability": 0.94775390625}, {"start": 1870.31, "end": 1870.47, "word": " the", "probability": 0.89013671875}, {"start": 1870.47, "end": 1871.19, "word": " midterm", "probability": 0.787353515625}, {"start": 1871.19, "end": 1871.77, "word": " exam.", "probability": 0.96337890625}, {"start": 1874.43, "end": 1874.71, "word": " Yes,", "probability": 0.60546875}, {"start": 1875.07, "end": 1876.69, "word": " that's", "probability": 0.921630859375}, {"start": 1876.69, "end": 1876.91, "word": " enough.", "probability": 0.85498046875}, {"start": 1878.09, "end": 1878.55, "word": " So", "probability": 0.94384765625}, {"start": 1878.55, "end": 1878.79, "word": " when", "probability": 0.81005859375}, {"start": 1878.79, "end": 1878.93, "word": " I", "probability": 0.99609375}, {"start": 1878.93, "end": 1879.15, "word": " say", "probability": 0.943359375}, {"start": 1879.15, "end": 1879.51, "word": " must,", "probability": 0.7177734375}, {"start": 1879.95, "end": 1880.29, "word": " it", "probability": 0.94580078125}, {"start": 1880.29, "end": 1880.51, "word": " means", "probability": 0.93505859375}, {"start": 1880.51, "end": 1881.19, "word": " strong", "probability": 0.8291015625}, {"start": 1881.19, "end": 1881.75, "word": " obligation.", "probability": 0.94384765625}, {"start": 1882.43, "end": 1882.53, "word": " When", "probability": 0.8779296875}, {"start": 1882.53, "end": 1882.69, "word": " I", "probability": 0.9755859375}, {"start": 1882.69, "end": 1882.85, "word": " say", "probability": 0.931640625}, {"start": 1882.85, "end": 1883.17, "word": " should,", "probability": 0.96533203125}, {"start": 1884.67, "end": 1885.09, "word": " it", "probability": 0.9365234375}, {"start": 1885.09, "end": 1885.31, "word": " is", "probability": 0.9306640625}, {"start": 1885.31, "end": 1886.05, "word": " mild", "probability": 0.86865234375}, {"start": 1886.05, "end": 1887.03, "word": " obligation,", "probability": 0.93505859375}, {"start": 1887.43, "end": 1887.87, "word": " suggestion", "probability": 0.8037109375}, {"start": 1887.87, "end": 1888.27, "word": " or", "probability": 0.75634765625}, {"start": 1888.27, "end": 1888.89, "word": " advice.", "probability": 0.92041015625}, {"start": 1890.25, "end": 1890.97, "word": " So", "probability": 0.697265625}, {"start": 1890.97, "end": 1891.19, "word": " we", "probability": 0.92822265625}, {"start": 1891.19, "end": 1891.47, "word": " have", "probability": 0.939453125}, {"start": 1891.47, "end": 1892.23, "word": " must", "probability": 0.8662109375}, {"start": 1892.23, "end": 1892.73, "word": " and", "probability": 0.92578125}, {"start": 1892.73, "end": 1893.01, "word": " should.", "probability": 0.974609375}], "temperature": 1.0}, {"id": 66, "seek": 191967, "start": 1894.27, "end": 1919.67, "text": " And if I use have to, it is general but non-personal. Non-personal. Not from me. But from me, I say must. Must or should. But if it is not from me, I say have to. If it is now, just now or soon, have got to.", "tokens": [400, 498, 286, 764, 362, 281, 11, 309, 307, 2674, 457, 2107, 12, 36649, 13, 8774, 12, 36649, 13, 1726, 490, 385, 13, 583, 490, 385, 11, 286, 584, 1633, 13, 13252, 420, 820, 13, 583, 498, 309, 307, 406, 490, 385, 11, 286, 584, 362, 281, 13, 759, 309, 307, 586, 11, 445, 586, 420, 2321, 11, 362, 658, 281, 13], "avg_logprob": -0.19717261431709168, "compression_ratio": 1.6, "no_speech_prob": 0.0, "words": [{"start": 1894.27, "end": 1894.49, "word": " And", "probability": 0.59033203125}, {"start": 1894.49, "end": 1894.61, "word": " if", "probability": 0.953125}, {"start": 1894.61, "end": 1894.77, "word": " I", "probability": 0.96484375}, {"start": 1894.77, "end": 1895.03, "word": " use", "probability": 0.85986328125}, {"start": 1895.03, "end": 1895.45, "word": " have", "probability": 0.62841796875}, {"start": 1895.45, "end": 1895.73, "word": " to,", "probability": 0.9619140625}, {"start": 1896.63, "end": 1897.01, "word": " it", "probability": 0.93115234375}, {"start": 1897.01, "end": 1897.15, "word": " is", "probability": 0.880859375}, {"start": 1897.15, "end": 1897.55, "word": " general", "probability": 0.87646484375}, {"start": 1897.55, "end": 1899.13, "word": " but", "probability": 0.471435546875}, {"start": 1899.13, "end": 1899.57, "word": " non", "probability": 0.89892578125}, {"start": 1899.57, "end": 1900.15, "word": "-personal.", "probability": 0.81640625}, {"start": 1901.29, "end": 1901.81, "word": " Non", "probability": 0.3681640625}, {"start": 1901.81, "end": 1902.23, "word": "-personal.", "probability": 0.88720703125}, {"start": 1902.47, "end": 1902.67, "word": " Not", "probability": 0.9443359375}, {"start": 1902.67, "end": 1902.95, "word": " from", "probability": 0.87353515625}, {"start": 1902.95, "end": 1903.29, "word": " me.", "probability": 0.96533203125}, {"start": 1903.67, "end": 1903.89, "word": " But", "probability": 0.90576171875}, {"start": 1903.89, "end": 1904.15, "word": " from", "probability": 0.736328125}, {"start": 1904.15, "end": 1904.43, "word": " me,", "probability": 0.96533203125}, {"start": 1904.57, "end": 1904.69, "word": " I", "probability": 0.98876953125}, {"start": 1904.69, "end": 1904.99, "word": " say", "probability": 0.92529296875}, {"start": 1904.99, "end": 1905.75, "word": " must.", "probability": 0.77392578125}, {"start": 1906.45, "end": 1907.13, "word": " Must", "probability": 0.6630859375}, {"start": 1907.13, "end": 1907.85, "word": " or", "probability": 0.71728515625}, {"start": 1907.85, "end": 1908.47, "word": " should.", "probability": 0.95166015625}, {"start": 1909.39, "end": 1909.85, "word": " But", "probability": 0.93701171875}, {"start": 1909.85, "end": 1910.03, "word": " if", "probability": 0.9404296875}, {"start": 1910.03, "end": 1910.15, "word": " it", "probability": 0.94775390625}, {"start": 1910.15, "end": 1910.23, "word": " is", "probability": 0.8125}, {"start": 1910.23, "end": 1910.39, "word": " not", "probability": 0.9423828125}, {"start": 1910.39, "end": 1910.63, "word": " from", "probability": 0.880859375}, {"start": 1910.63, "end": 1910.97, "word": " me,", "probability": 0.96337890625}, {"start": 1911.49, "end": 1911.67, "word": " I", "probability": 0.99169921875}, {"start": 1911.67, "end": 1911.95, "word": " say", "probability": 0.93359375}, {"start": 1911.95, "end": 1912.43, "word": " have", "probability": 0.87939453125}, {"start": 1912.43, "end": 1912.69, "word": " to.", "probability": 0.96826171875}, {"start": 1913.99, "end": 1914.41, "word": " If", "probability": 0.93017578125}, {"start": 1914.41, "end": 1914.49, "word": " it", "probability": 0.92333984375}, {"start": 1914.49, "end": 1914.61, "word": " is", "probability": 0.74365234375}, {"start": 1914.61, "end": 1915.05, "word": " now,", "probability": 0.9306640625}, {"start": 1915.41, "end": 1915.57, "word": " just", "probability": 0.8955078125}, {"start": 1915.57, "end": 1916.17, "word": " now", "probability": 0.94873046875}, {"start": 1916.17, "end": 1916.85, "word": " or", "probability": 0.52587890625}, {"start": 1916.85, "end": 1917.31, "word": " soon,", "probability": 0.9638671875}, {"start": 1918.07, "end": 1918.43, "word": " have", "probability": 0.927734375}, {"start": 1918.43, "end": 1919.11, "word": " got", "probability": 0.92822265625}, {"start": 1919.11, "end": 1919.67, "word": " to.", "probability": 0.97265625}], "temperature": 1.0}, {"id": 67, "seek": 194531, "start": 1921.25, "end": 1945.31, "text": " So what's the difference between should and must? Must is strong, strong obligation, but should is mild. Yes, mild obligation. Yes, so again should is personal, have to is impersonal and general.", "tokens": [407, 437, 311, 264, 2649, 1296, 820, 293, 1633, 30, 13252, 307, 2068, 11, 2068, 20326, 11, 457, 820, 307, 15154, 13, 1079, 11, 15154, 20326, 13, 1079, 11, 370, 797, 820, 307, 2973, 11, 362, 281, 307, 38147, 304, 293, 2674, 13], "avg_logprob": -0.20632102645256303, "compression_ratio": 1.4848484848484849, "no_speech_prob": 0.0, "words": [{"start": 1921.25, "end": 1921.47, "word": " So", "probability": 0.75439453125}, {"start": 1921.47, "end": 1921.67, "word": " what's", "probability": 0.740478515625}, {"start": 1921.67, "end": 1921.73, "word": " the", "probability": 0.900390625}, {"start": 1921.73, "end": 1922.03, "word": " difference", "probability": 0.85986328125}, {"start": 1922.03, "end": 1922.51, "word": " between", "probability": 0.8701171875}, {"start": 1922.51, "end": 1922.95, "word": " should", "probability": 0.916015625}, {"start": 1922.95, "end": 1923.39, "word": " and", "probability": 0.9384765625}, {"start": 1923.39, "end": 1923.93, "word": " must?", "probability": 0.8544921875}, {"start": 1925.91, "end": 1926.25, "word": " Must", "probability": 0.6669921875}, {"start": 1926.25, "end": 1926.47, "word": " is", "probability": 0.939453125}, {"start": 1926.47, "end": 1927.15, "word": " strong,", "probability": 0.52783203125}, {"start": 1927.63, "end": 1928.69, "word": " strong", "probability": 0.8759765625}, {"start": 1928.69, "end": 1929.23, "word": " obligation,", "probability": 0.92138671875}, {"start": 1929.81, "end": 1930.15, "word": " but", "probability": 0.92431640625}, {"start": 1930.15, "end": 1931.43, "word": " should", "probability": 0.9482421875}, {"start": 1931.43, "end": 1931.81, "word": " is", "probability": 0.89111328125}, {"start": 1931.81, "end": 1932.57, "word": " mild.", "probability": 0.86572265625}, {"start": 1933.35, "end": 1933.69, "word": " Yes,", "probability": 0.9130859375}, {"start": 1933.99, "end": 1934.25, "word": " mild", "probability": 0.9287109375}, {"start": 1934.25, "end": 1934.89, "word": " obligation.", "probability": 0.92578125}, {"start": 1936.55, "end": 1937.55, "word": " Yes,", "probability": 0.53125}, {"start": 1937.83, "end": 1938.11, "word": " so", "probability": 0.92333984375}, {"start": 1938.11, "end": 1938.73, "word": " again", "probability": 0.927734375}, {"start": 1938.73, "end": 1939.65, "word": " should", "probability": 0.744140625}, {"start": 1939.65, "end": 1939.99, "word": " is", "probability": 0.94677734375}, {"start": 1939.99, "end": 1940.61, "word": " personal,", "probability": 0.89404296875}, {"start": 1941.11, "end": 1942.11, "word": " have", "probability": 0.943359375}, {"start": 1942.11, "end": 1942.35, "word": " to", "probability": 0.96435546875}, {"start": 1942.35, "end": 1943.43, "word": " is", "probability": 0.92919921875}, {"start": 1943.43, "end": 1944.27, "word": " impersonal", "probability": 0.977783203125}, {"start": 1944.27, "end": 1944.79, "word": " and", "probability": 0.8232421875}, {"start": 1944.79, "end": 1945.31, "word": " general.", "probability": 0.919921875}], "temperature": 1.0}, {"id": 68, "seek": 196686, "start": 1948.4, "end": 1966.86, "text": " Again, this exercise about mild obligation or about suggestions. The same like that one, page 33. Make suggestions as before. Use I think, I don't think.", "tokens": [3764, 11, 341, 5380, 466, 15154, 20326, 420, 466, 13396, 13, 440, 912, 411, 300, 472, 11, 3028, 11816, 13, 4387, 13396, 382, 949, 13, 8278, 286, 519, 11, 286, 500, 380, 519, 13], "avg_logprob": -0.24531249148505074, "compression_ratio": 1.2727272727272727, "no_speech_prob": 0.0, "words": [{"start": 1948.4, "end": 1948.98, "word": " Again,", "probability": 0.8056640625}, {"start": 1949.24, "end": 1949.44, "word": " this", "probability": 0.8515625}, {"start": 1949.44, "end": 1949.98, "word": " exercise", "probability": 0.90478515625}, {"start": 1949.98, "end": 1951.52, "word": " about", "probability": 0.3134765625}, {"start": 1951.52, "end": 1952.42, "word": " mild", "probability": 0.7109375}, {"start": 1952.42, "end": 1953.28, "word": " obligation", "probability": 0.7275390625}, {"start": 1953.28, "end": 1953.92, "word": " or", "probability": 0.8310546875}, {"start": 1953.92, "end": 1954.36, "word": " about", "probability": 0.810546875}, 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He's ill. He is ill. So use either I think or I don't think. I think he should go to bed. So I think he should go to bed. Go to bed. 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Go to bed, don't go to work. But I don't want imperative. I want suggestion. If I say go, don't go, it's okay. But it is imperative. No, I want it to be mild. So I want it to make suggestions, not orders. Not orders.", "tokens": [1692, 11, 352, 281, 2901, 11, 500, 380, 352, 281, 589, 13, 1037, 281, 2901, 11, 500, 380, 352, 281, 589, 13, 583, 286, 500, 380, 528, 32490, 13, 286, 528, 16541, 13, 759, 286, 584, 352, 11, 500, 380, 352, 11, 309, 311, 1392, 13, 583, 309, 307, 32490, 13, 883, 11, 286, 528, 309, 281, 312, 15154, 13, 407, 286, 528, 309, 281, 652, 13396, 11, 406, 9470, 13, 1726, 9470, 13], "avg_logprob": -0.14541666269302367, "compression_ratio": 1.8, "no_speech_prob": 0.0, "words": [{"start": 2027.5, "end": 2028.06, "word": " Here,", "probability": 0.3759765625}, {"start": 2028.54, "end": 2028.7, "word": " go", "probability": 0.8125}, {"start": 2028.7, "end": 2028.92, "word": " to", "probability": 0.97802734375}, {"start": 2028.92, "end": 2029.2, "word": " bed,", "probability": 0.96337890625}, {"start": 2029.6, "end": 2029.92, "word": " don't", "probability": 0.96484375}, {"start": 2029.92, "end": 2030.18, "word": " go", "probability": 0.966796875}, {"start": 2030.18, "end": 2030.44, "word": " to", "probability": 0.96533203125}, {"start": 2030.44, "end": 2031.02, "word": " work.", "probability": 0.92333984375}, {"start": 2031.66, "end": 2031.94, "word": " Go", "probability": 0.52099609375}, {"start": 2031.94, "end": 2032.16, "word": " to", "probability": 0.97412109375}, {"start": 2032.16, "end": 2032.5, "word": " bed,", "probability": 0.9521484375}, {"start": 2032.94, "end": 2033.26, "word": " don't", "probability": 0.97509765625}, {"start": 2033.26, "end": 2033.52, "word": " go", "probability": 0.96435546875}, {"start": 2033.52, "end": 2033.78, "word": " to", "probability": 0.9658203125}, {"start": 2033.78, "end": 2034.2, "word": " work.", "probability": 0.921875}, {"start": 2034.44, "end": 2034.84, "word": " But", "probability": 0.92333984375}, {"start": 2034.84, "end": 2035.0, "word": " I", "probability": 0.958984375}, {"start": 2035.0, "end": 2035.24, "word": " don't", "probability": 0.978759765625}, {"start": 2035.24, "end": 2035.52, "word": " want", "probability": 0.8955078125}, {"start": 2035.52, "end": 2036.04, "word": " imperative.", "probability": 0.861328125}, {"start": 2036.78, "end": 2037.04, "word": " I", "probability": 0.9931640625}, {"start": 2037.04, "end": 2037.4, "word": " want", "probability": 0.876953125}, {"start": 2037.4, "end": 2038.14, "word": " suggestion.", "probability": 0.70703125}, {"start": 2039.26, "end": 2039.82, "word": " If", "probability": 0.91259765625}, {"start": 2039.82, "end": 2039.96, "word": " I", "probability": 0.98828125}, {"start": 2039.96, "end": 2040.28, "word": " say", "probability": 0.9501953125}, {"start": 2040.28, "end": 2041.16, "word": " go,", "probability": 0.56884765625}, {"start": 2041.42, "end": 2041.64, "word": " don't", "probability": 0.970703125}, {"start": 2041.64, "end": 2041.86, "word": " go,", "probability": 0.96484375}, {"start": 2041.94, "end": 2042.04, "word": " it's", "probability": 0.943359375}, {"start": 2042.04, "end": 2042.32, "word": " okay.", "probability": 0.8564453125}, {"start": 2042.8, "end": 2043.16, "word": " But", "probability": 0.94580078125}, {"start": 2043.16, "end": 2043.32, "word": " it", "probability": 0.92724609375}, {"start": 2043.32, "end": 2043.5, "word": " is", "probability": 0.8974609375}, {"start": 2043.5, "end": 2044.06, "word": " imperative.", "probability": 0.90087890625}, {"start": 2044.68, "end": 2044.84, "word": " No,", "probability": 0.93212890625}, {"start": 2045.0, "end": 2045.18, "word": " I", "probability": 0.99755859375}, {"start": 2045.18, "end": 2045.4, "word": " want", "probability": 0.87841796875}, {"start": 2045.4, "end": 2045.56, "word": " it", "probability": 0.9482421875}, {"start": 2045.56, "end": 2045.7, "word": " to", "probability": 0.96728515625}, {"start": 2045.7, "end": 2045.88, "word": " be", "probability": 0.95849609375}, {"start": 2045.88, "end": 2046.38, "word": " mild.", "probability": 0.87060546875}, {"start": 2047.36, "end": 2047.92, "word": " So", "probability": 0.86865234375}, {"start": 2047.92, "end": 2048.26, "word": " I", "probability": 0.80078125}, {"start": 2048.26, "end": 2048.46, "word": " want", "probability": 0.8369140625}, {"start": 2048.46, "end": 2048.66, "word": " it", "probability": 0.89599609375}, {"start": 2048.66, "end": 2048.88, "word": " to", "probability": 0.96630859375}, {"start": 2048.88, "end": 2049.84, "word": " make", "probability": 0.7705078125}, {"start": 2049.84, "end": 2050.64, "word": " suggestions,", "probability": 0.85791015625}, {"start": 2050.98, "end": 2051.2, "word": " not", "probability": 0.94091796875}, {"start": 2051.2, "end": 2051.74, "word": " orders.", "probability": 0.8583984375}, {"start": 2053.1, "end": 2053.66, "word": " Not", "probability": 0.82763671875}, {"start": 2053.66, "end": 2054.26, "word": " orders.", "probability": 0.86865234375}], "temperature": 1.0}, {"id": 72, "seek": 208446, "start": 2055.0, "end": 2084.46, "text": " Not imperative. Directly. No. Indirectly. So, I think he should go to bed. Good. Politely. I don't think he should go to work. Number two. I have lost my cheat book and credit cards. Give him advice. Advice or suggestions. Use I think or I don't think. 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I think he should go to the bank. Also, yeah, I think he should stop the cheat books. I think he should stop the cheat books. I think he should go to the bank. You understand? Yes.", "tokens": [286, 519, 415, 820, 352, 281, 264, 3765, 13, 286, 519, 415, 820, 352, 281, 264, 3765, 13, 2743, 11, 1338, 11, 286, 519, 415, 820, 1590, 264, 17470, 3642, 13, 286, 519, 415, 820, 1590, 264, 17470, 3642, 13, 286, 519, 415, 820, 352, 281, 264, 3765, 13, 509, 1223, 30, 1079, 13], "avg_logprob": -0.21051136526194486, "compression_ratio": 2.193877551020408, "no_speech_prob": 0.0, "words": [{"start": 2085.17, "end": 2085.71, "word": " I", "probability": 0.5595703125}, {"start": 2085.71, "end": 2085.91, "word": " think", "probability": 0.9072265625}, {"start": 2085.91, "end": 2086.07, "word": " he", "probability": 0.84228515625}, {"start": 2086.07, "end": 2086.25, "word": " should", "probability": 0.96240234375}, {"start": 2086.25, "end": 2086.45, "word": " go", "probability": 0.85400390625}, {"start": 2086.45, "end": 2086.59, "word": " to", "probability": 0.9345703125}, {"start": 2086.59, "end": 2086.69, "word": " the", "probability": 0.91943359375}, {"start": 2086.69, "end": 2086.89, "word": " bank.", "probability": 0.85107421875}, {"start": 2087.85, "end": 2087.89, "word": " I", "probability": 0.2763671875}, {"start": 2087.89, "end": 2088.21, "word": " think", "probability": 0.9130859375}, {"start": 2088.21, "end": 2088.53, "word": " he", "probability": 0.9638671875}, {"start": 2088.53, "end": 2089.05, "word": " should", "probability": 0.96630859375}, {"start": 2089.05, "end": 2089.31, "word": " go", "probability": 0.5361328125}, {"start": 2089.31, "end": 2089.43, "word": " to", "probability": 0.9365234375}, {"start": 2089.43, "end": 2089.59, "word": " the", "probability": 0.919921875}, {"start": 2089.59, "end": 2090.13, "word": " bank.", "probability": 0.9287109375}, {"start": 2092.23, "end": 2092.77, "word": " Also,", "probability": 0.74365234375}, {"start": 2094.37, "end": 2094.97, "word": " yeah,", "probability": 0.6279296875}, {"start": 2095.21, "end": 2097.47, "word": " I", "probability": 0.994140625}, {"start": 2097.47, "end": 2097.73, "word": " think", "probability": 0.916015625}, {"start": 2097.73, "end": 2097.93, "word": " he", "probability": 0.96533203125}, {"start": 2097.93, "end": 2098.17, "word": " should", "probability": 0.96826171875}, {"start": 2098.17, "end": 2098.85, "word": " stop", "probability": 0.93603515625}, {"start": 2098.85, "end": 2100.55, "word": " the", "probability": 0.76806640625}, {"start": 2100.55, "end": 2100.83, "word": " cheat", "probability": 0.1748046875}, {"start": 2100.83, "end": 2101.29, "word": " books.", "probability": 0.84521484375}, {"start": 2102.29, "end": 2102.43, "word": " I", "probability": 0.73681640625}, {"start": 2102.43, "end": 2103.37, "word": " think", "probability": 0.923828125}, {"start": 2103.37, "end": 2103.55, "word": " he", "probability": 0.96337890625}, {"start": 2103.55, "end": 2103.77, "word": " should", "probability": 0.97021484375}, {"start": 2103.77, "end": 2104.89, "word": " stop", "probability": 0.85498046875}, {"start": 2104.89, "end": 2105.43, "word": " the", "probability": 0.90576171875}, {"start": 2105.43, "end": 2105.67, "word": " cheat", "probability": 0.7236328125}, {"start": 2105.67, "end": 2105.93, "word": " books.", "probability": 0.88330078125}, {"start": 2106.23, "end": 2106.35, "word": " I", "probability": 0.99169921875}, {"start": 2106.35, "end": 2106.61, "word": " think", "probability": 0.91552734375}, {"start": 2106.61, "end": 2106.77, "word": " he", "probability": 0.958984375}, {"start": 2106.77, "end": 2106.97, "word": " should", "probability": 0.9697265625}, {"start": 2106.97, "end": 2107.33, "word": " go", "probability": 0.9677734375}, {"start": 2107.33, "end": 2107.91, "word": " to", "probability": 0.96923828125}, {"start": 2107.91, "end": 2108.05, "word": " the", "probability": 0.92578125}, {"start": 2108.05, "end": 2108.39, "word": " bank.", "probability": 0.9296875}, {"start": 2109.89, "end": 2110.43, "word": " You", "probability": 0.57861328125}, {"start": 2110.43, "end": 2110.67, "word": " understand?", "probability": 0.82373046875}, {"start": 2111.47, "end": 2112.01, "word": " Yes.", "probability": 0.9365234375}], "temperature": 1.0}, {"id": 74, "seek": 213880, "start": 2114.12, "end": 2138.8, "text": " Number two. Number three. Tony got his driving license last week and now he wants to drive from London to Edinburgh. Oh, just now. I think now he should drive. Should drive? No, shouldn't drive.", "tokens": [5118, 732, 13, 5118, 1045, 13, 10902, 658, 702, 4840, 10476, 1036, 1243, 293, 586, 415, 2738, 281, 3332, 490, 7042, 281, 41215, 13, 876, 11, 445, 586, 13, 286, 519, 586, 415, 820, 3332, 13, 6454, 3332, 30, 883, 11, 4659, 380, 3332, 13], "avg_logprob": -0.25084919579651044, "compression_ratio": 1.3928571428571428, "no_speech_prob": 0.0, "words": [{"start": 2114.12, "end": 2114.38, "word": " Number", "probability": 0.78466796875}, {"start": 2114.38, "end": 2114.64, "word": " two.", "probability": 0.6796875}, {"start": 2114.94, "end": 2115.02, "word": " Number", "probability": 0.8857421875}, {"start": 2115.02, "end": 2115.34, "word": " three.", "probability": 0.919921875}, {"start": 2116.2, "end": 2116.44, "word": " Tony", "probability": 0.7021484375}, {"start": 2116.44, "end": 2116.8, "word": " got", "probability": 0.92333984375}, {"start": 2116.8, "end": 2117.02, "word": " his", "probability": 0.96728515625}, {"start": 2117.02, "end": 2117.44, "word": " driving", "probability": 0.9462890625}, {"start": 2117.44, "end": 2117.86, "word": " license", "probability": 0.7998046875}, {"start": 2117.86, "end": 2118.26, "word": " last", "probability": 0.873046875}, {"start": 2118.26, "end": 2118.72, "word": " week", "probability": 0.9453125}, {"start": 2118.72, "end": 2119.4, "word": " and", "probability": 0.5634765625}, {"start": 2119.4, "end": 2119.82, "word": " now", "probability": 0.953125}, {"start": 2119.82, "end": 2120.2, "word": " he", "probability": 0.9404296875}, {"start": 2120.2, "end": 2120.48, "word": " wants", "probability": 0.837890625}, {"start": 2120.48, "end": 2120.68, "word": " to", "probability": 0.97119140625}, {"start": 2120.68, "end": 2121.1, "word": " drive", "probability": 0.91796875}, {"start": 2121.1, "end": 2121.44, "word": " from", "probability": 0.892578125}, {"start": 2121.44, "end": 2121.76, "word": " London", "probability": 0.84619140625}, {"start": 2121.76, "end": 2122.04, "word": " to", "probability": 0.97509765625}, {"start": 2122.04, "end": 2122.4, "word": " Edinburgh.", "probability": 0.84814453125}, {"start": 2123.48, "end": 2123.78, "word": " Oh,", "probability": 0.71875}, {"start": 2124.0, "end": 2124.62, "word": " just", "probability": 0.908203125}, {"start": 2124.62, "end": 2125.1, "word": " now.", "probability": 0.953125}, {"start": 2125.98, "end": 2126.24, "word": " I", "probability": 0.80224609375}, {"start": 2126.24, "end": 2126.58, "word": " think", "probability": 0.91015625}, {"start": 2126.58, "end": 2126.84, "word": " now", "probability": 0.30908203125}, {"start": 2126.84, "end": 2127.24, "word": " he", "probability": 0.755859375}, {"start": 2127.24, "end": 2127.7, "word": " should", "probability": 0.9443359375}, {"start": 2127.7, "end": 2128.4, "word": " drive.", "probability": 0.77685546875}, {"start": 2136.14, "end": 2136.34, "word": " Should", "probability": 0.345458984375}, {"start": 2136.34, "end": 2136.7, "word": " drive?", "probability": 0.62255859375}, {"start": 2137.2, "end": 2137.92, "word": " No,", "probability": 0.92724609375}, {"start": 2138.08, "end": 2138.44, "word": " shouldn't", "probability": 0.8994140625}, {"start": 2138.44, "end": 2138.8, "word": " drive.", "probability": 0.923828125}], "temperature": 1.0}, {"id": 75, "seek": 216176, "start": 2139.88, "end": 2161.76, "text": " I don't think he should drive. So here, no, not good. Again, yes. I don't think he should drive. Yes, he should fly. I think he should fly. It means go by plane. 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She sleeps all day long. Yes? Advise me, give suggestions. I think you should buy her an alarm clock. I think you should buy her an alarm clock. Yeah.", "tokens": [1222, 26866, 4653, 1177, 380, 483, 484, 295, 2901, 1826, 24040, 13, 1240, 37991, 439, 786, 938, 13, 1079, 30, 13634, 908, 385, 11, 976, 13396, 13, 286, 519, 291, 820, 2256, 720, 364, 14183, 7830, 13, 286, 519, 291, 820, 2256, 720, 364, 14183, 7830, 13, 865, 13], "avg_logprob": -0.14703125655651092, "compression_ratio": 1.525925925925926, "no_speech_prob": 0.0, "words": [{"start": 2165.35, "end": 2165.65, "word": " My", "probability": 0.66455078125}, {"start": 2165.65, "end": 2166.01, "word": " teenage", "probability": 0.92236328125}, {"start": 2166.01, "end": 2166.59, "word": " daughter", "probability": 0.91552734375}, {"start": 2166.59, "end": 2167.09, "word": " doesn't", "probability": 0.92138671875}, {"start": 2167.09, "end": 2167.31, "word": " get", "probability": 0.93701171875}, {"start": 2167.31, "end": 2167.67, "word": " out", "probability": 0.88525390625}, {"start": 2167.67, "end": 2167.91, "word": " of", "probability": 0.9677734375}, {"start": 2167.91, "end": 2168.09, "word": " bed", "probability": 0.95947265625}, {"start": 2168.09, "end": 2168.55, "word": " until", "probability": 0.87353515625}, {"start": 2168.55, "end": 2169.13, "word": " noon.", "probability": 0.94677734375}, {"start": 2169.81, "end": 2169.93, "word": " She", "probability": 0.87939453125}, {"start": 2169.93, "end": 2170.29, "word": " sleeps", "probability": 0.85302734375}, {"start": 2170.29, "end": 2170.57, "word": " all", "probability": 0.93505859375}, {"start": 2170.57, "end": 2171.79, "word": " day", "probability": 0.83544921875}, {"start": 2171.79, "end": 2172.37, "word": " long.", "probability": 0.87744140625}, {"start": 2173.75, "end": 2174.07, "word": " Yes?", "probability": 0.7890625}, {"start": 2177.15, "end": 2177.97, "word": " Advise", "probability": 0.77099609375}, {"start": 2177.97, "end": 2178.25, "word": " me,", "probability": 0.9609375}, {"start": 2178.63, "end": 2178.79, "word": " give", "probability": 0.88916015625}, {"start": 2178.79, "end": 2179.41, "word": " suggestions.", "probability": 0.8642578125}, {"start": 2180.29, "end": 2180.51, "word": " I", "probability": 0.98046875}, {"start": 2180.51, "end": 2180.99, "word": " think", "probability": 0.9140625}, {"start": 2180.99, "end": 2181.43, "word": " you", "probability": 0.94677734375}, {"start": 2181.43, "end": 2181.69, "word": " should", "probability": 0.96533203125}, {"start": 2181.69, "end": 2182.09, "word": " buy", "probability": 0.91357421875}, {"start": 2182.09, "end": 2182.61, "word": " her", "probability": 0.904296875}, {"start": 2182.61, "end": 2183.13, "word": " an", "probability": 0.93505859375}, {"start": 2183.13, "end": 2183.43, "word": " alarm", "probability": 0.7802734375}, {"start": 2183.43, "end": 2183.73, "word": " clock.", "probability": 0.85546875}, {"start": 2185.35, "end": 2186.27, "word": " I", "probability": 0.6044921875}, {"start": 2186.27, "end": 2187.43, "word": " think", "probability": 0.92236328125}, {"start": 2187.43, "end": 2189.15, "word": " you", "probability": 0.87548828125}, {"start": 2189.15, "end": 2189.55, "word": " should", "probability": 0.96533203125}, {"start": 2189.55, "end": 2189.95, "word": " buy", "probability": 0.89013671875}, {"start": 2189.95, "end": 2190.53, "word": " her", "probability": 0.96142578125}, {"start": 2190.53, "end": 2191.27, "word": " an", "probability": 0.9462890625}, {"start": 2191.27, "end": 2191.55, "word": " alarm", "probability": 0.87744140625}, {"start": 2191.55, "end": 2192.07, "word": " clock.", "probability": 0.85888671875}, {"start": 2192.97, "end": 2193.89, "word": " Yeah.", "probability": 0.76953125}], "temperature": 1.0}, {"id": 77, "seek": 221990, "start": 2195.72, "end": 2219.9, "text": " I never have any money. I don't have any money. Give advice, give suggestions. I don't think, I don't think, I think you should find a job. 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Yeah. I'm really fed up with my job.", "tokens": [286, 519, 436, 820, 1699, 257, 1326, 924, 11, 732, 420, 1045, 924, 11, 406, 3165, 13, 865, 13, 286, 478, 534, 4636, 493, 365, 452, 1691, 13], "avg_logprob": -0.2428610037113058, "compression_ratio": 1.0842105263157895, "no_speech_prob": 0.0, "words": [{"start": 2249.5199999999995, "end": 2250.3599999999997, "word": " I", "probability": 0.572265625}, {"start": 2250.3599999999997, "end": 2251.2, "word": " think", "probability": 0.6953125}, {"start": 2251.2, "end": 2257.66, "word": " they", "probability": 0.4501953125}, {"start": 2257.66, "end": 2259.36, "word": " should", "probability": 0.68212890625}, {"start": 2259.36, "end": 2266.38, "word": " wait", "probability": 0.5810546875}, {"start": 2266.38, "end": 2268.5, "word": " a", "probability": 0.56787109375}, {"start": 2268.5, "end": 2268.78, "word": " few", "probability": 0.89306640625}, {"start": 2268.78, "end": 2269.2, "word": " years,", "probability": 0.91748046875}, {"start": 2269.46, "end": 2269.64, "word": " two", "probability": 0.8173828125}, {"start": 2269.64, "end": 2269.8, "word": " or", "probability": 0.95849609375}, {"start": 2269.8, "end": 2270.02, "word": " three", "probability": 0.93701171875}, {"start": 2270.02, "end": 2270.46, "word": " years,", "probability": 0.9130859375}, {"start": 2271.02, "end": 2271.58, "word": " not", "probability": 0.890625}, {"start": 2271.58, "end": 2272.04, "word": " 16.", "probability": 0.61328125}, {"start": 2273.04, "end": 2273.3, "word": " Yeah.", "probability": 0.54345703125}, {"start": 2274.92, "end": 2275.76, "word": " I'm", "probability": 0.961669921875}, {"start": 2275.76, "end": 2276.08, "word": " really", "probability": 0.876953125}, {"start": 2276.08, "end": 2276.3, "word": " fed", "probability": 0.95361328125}, {"start": 2276.3, "end": 2276.44, "word": " up", "probability": 0.96484375}, {"start": 2276.44, "end": 2276.58, "word": " with", "probability": 0.9013671875}, {"start": 2276.58, "end": 2276.74, "word": " my", "probability": 0.96923828125}, {"start": 2276.74, "end": 2277.02, "word": " job.", "probability": 0.97314453125}], "temperature": 1.0}, {"id": 80, "seek": 230500, "start": 2277.9, "end": 2305.0, "text": " I'm really fed up with my job. I think you should find a new job. Yes? Yes, because you are fed up with your job, so you should change it. You should find some job else. My grandparents complained they don't go out enough. They don't go out enough. So", "tokens": [286, 478, 534, 4636, 493, 365, 452, 1691, 13, 286, 519, 291, 820, 915, 257, 777, 1691, 13, 1079, 30, 1079, 11, 570, 291, 366, 4636, 493, 365, 428, 1691, 11, 370, 291, 820, 1319, 309, 13, 509, 820, 915, 512, 1691, 1646, 13, 1222, 21876, 33951, 436, 500, 380, 352, 484, 1547, 13, 814, 500, 380, 352, 484, 1547, 13, 407], "avg_logprob": -0.18229166146308656, "compression_ratio": 1.605095541401274, "no_speech_prob": 0.0, "words": [{"start": 2277.9, "end": 2278.2, "word": " I'm", "probability": 0.85302734375}, {"start": 2278.2, "end": 2278.58, "word": " really", "probability": 0.87646484375}, {"start": 2278.58, "end": 2278.88, "word": " fed", "probability": 0.94970703125}, {"start": 2278.88, "end": 2279.02, "word": " up", "probability": 0.96826171875}, {"start": 2279.02, "end": 2279.16, "word": " with", "probability": 0.908203125}, {"start": 2279.16, "end": 2279.32, "word": " my", "probability": 0.970703125}, {"start": 2279.32, "end": 2279.6, "word": " job.", "probability": 0.97119140625}, {"start": 2281.28, "end": 2281.48, "word": " I", "probability": 0.88037109375}, {"start": 2281.48, "end": 2281.86, "word": " think", "probability": 0.892578125}, {"start": 2281.86, "end": 2282.12, "word": " you", "probability": 0.953125}, {"start": 2282.12, "end": 2282.44, "word": " should", "probability": 0.9638671875}, {"start": 2282.44, "end": 2284.08, "word": " find", "probability": 0.85546875}, {"start": 2284.08, "end": 2284.58, "word": " a", "probability": 0.9853515625}, {"start": 2284.58, "end": 2284.76, "word": " new", "probability": 0.9052734375}, {"start": 2284.76, "end": 2285.06, "word": " job.", "probability": 0.97119140625}, {"start": 2287.2, "end": 2287.84, "word": " Yes?", "probability": 0.45703125}, {"start": 2288.34, "end": 2288.98, "word": " Yes,", "probability": 0.509765625}, {"start": 2289.0, "end": 2289.32, "word": " because", "probability": 0.88671875}, {"start": 2289.32, "end": 2289.44, "word": " you", "probability": 0.95947265625}, {"start": 2289.44, "end": 2289.56, "word": " are", "probability": 0.88720703125}, {"start": 2289.56, "end": 2289.76, "word": " fed", "probability": 0.95458984375}, {"start": 2289.76, "end": 2289.88, "word": " up", "probability": 0.9697265625}, {"start": 2289.88, "end": 2290.06, "word": " with", "probability": 0.8994140625}, {"start": 2290.06, "end": 2290.2, "word": " your", "probability": 0.89111328125}, {"start": 2290.2, "end": 2290.54, "word": " job,", "probability": 0.97021484375}, {"start": 2290.94, "end": 2291.12, "word": " so", "probability": 0.67041015625}, {"start": 2291.12, "end": 2291.9, "word": " you", "probability": 0.9306640625}, {"start": 2291.9, "end": 2292.16, "word": " should", "probability": 0.96923828125}, {"start": 2292.16, "end": 2292.86, "word": " change", "probability": 0.89794921875}, {"start": 2292.86, "end": 2293.06, "word": " it.", "probability": 0.943359375}, {"start": 2293.2, "end": 2293.3, "word": " You", "probability": 0.943359375}, {"start": 2293.3, "end": 2293.46, "word": " should", "probability": 0.9658203125}, {"start": 2293.46, "end": 2293.7, "word": " find", "probability": 0.88232421875}, {"start": 2293.7, "end": 2294.02, "word": " some", "probability": 0.8662109375}, {"start": 2294.02, "end": 2294.5, "word": " job", "probability": 0.796875}, {"start": 2294.5, "end": 2294.76, "word": " else.", "probability": 0.8818359375}, {"start": 2295.78, "end": 2296.18, "word": " My", "probability": 0.96435546875}, {"start": 2296.18, "end": 2296.68, "word": " grandparents", "probability": 0.84326171875}, {"start": 2296.68, "end": 2297.72, "word": " complained", "probability": 0.52197265625}, {"start": 2297.72, "end": 2298.2, "word": " they", "probability": 0.48828125}, {"start": 2298.2, "end": 2298.7, "word": " don't", "probability": 0.943115234375}, {"start": 2298.7, "end": 2299.06, "word": " go", "probability": 0.96533203125}, {"start": 2299.06, "end": 2299.6, "word": " out", "probability": 0.89501953125}, {"start": 2299.6, "end": 2300.12, "word": " enough.", "probability": 0.88818359375}, {"start": 2301.4, "end": 2302.0, "word": " They", "probability": 0.77099609375}, {"start": 2302.0, "end": 2302.3, "word": " don't", "probability": 0.981201171875}, {"start": 2302.3, "end": 2302.5, "word": " go", "probability": 0.9638671875}, {"start": 2302.5, "end": 2302.8, "word": " out", "probability": 0.89208984375}, {"start": 2302.8, "end": 2303.16, "word": " enough.", "probability": 0.87646484375}, {"start": 2304.36, "end": 2305.0, "word": " So", "probability": 0.93701171875}], "temperature": 1.0}, {"id": 81, "seek": 233087, "start": 2306.03, "end": 2330.87, "text": " I think they should go out. Yes, but they complain. I think they should join a club. I think they should join a club. Again. So any answer is correct. Look here.", "tokens": [286, 519, 436, 820, 352, 484, 13, 1079, 11, 457, 436, 11024, 13, 286, 519, 436, 820, 3917, 257, 6482, 13, 286, 519, 436, 820, 3917, 257, 6482, 13, 3764, 13, 407, 604, 1867, 307, 3006, 13, 2053, 510, 13], "avg_logprob": -0.22580030487804878, "compression_ratio": 1.5576923076923077, "no_speech_prob": 0.0, "words": [{"start": 2306.03, "end": 2306.33, "word": " I", "probability": 0.64111328125}, {"start": 2306.33, "end": 2307.01, "word": " think", "probability": 0.9248046875}, {"start": 2307.01, "end": 2308.51, "word": " they", "probability": 0.322509765625}, {"start": 2308.51, "end": 2308.85, "word": " should", "probability": 0.9638671875}, {"start": 2308.85, "end": 2309.55, "word": " go", "probability": 0.9609375}, {"start": 2309.55, "end": 2309.87, "word": " out.", "probability": 0.88427734375}, {"start": 2311.53, "end": 2312.45, "word": " Yes,", "probability": 0.65771484375}, {"start": 2312.53, "end": 2312.81, "word": " but", "probability": 0.91650390625}, {"start": 2312.81, "end": 2314.39, "word": " they", "probability": 0.7919921875}, {"start": 2314.39, "end": 2314.89, "word": " complain.", "probability": 0.57080078125}, {"start": 2316.37, "end": 2316.59, "word": " I", "probability": 0.9619140625}, {"start": 2316.59, "end": 2317.11, "word": " think", "probability": 0.92333984375}, {"start": 2317.11, "end": 2317.49, "word": " they", "probability": 0.90185546875}, {"start": 2317.49, "end": 2317.97, "word": " should", "probability": 0.96728515625}, {"start": 2317.97, "end": 2318.83, "word": " join", "probability": 0.880859375}, {"start": 2318.83, "end": 2319.17, "word": " a", "probability": 0.9951171875}, {"start": 2319.17, "end": 2319.43, "word": " club.", "probability": 0.97021484375}, {"start": 2320.77, "end": 2320.87, "word": " I", "probability": 0.5966796875}, {"start": 2320.87, "end": 2321.25, "word": " think", "probability": 0.92431640625}, {"start": 2321.25, "end": 2321.69, "word": " they", "probability": 0.89404296875}, {"start": 2321.69, "end": 2322.27, "word": " should", "probability": 0.96728515625}, {"start": 2322.27, "end": 2323.59, "word": " join", "probability": 0.884765625}, {"start": 2323.59, "end": 2323.99, "word": " a", "probability": 0.9970703125}, {"start": 2323.99, "end": 2324.25, "word": " club.", "probability": 0.96875}, {"start": 2326.15, "end": 2326.69, "word": " Again.", "probability": 0.83837890625}, {"start": 2327.59, "end": 2327.97, "word": " So", "probability": 0.91552734375}, {"start": 2327.97, "end": 2328.19, "word": " any", "probability": 0.5810546875}, {"start": 2328.19, "end": 2328.47, "word": " answer", "probability": 0.96484375}, {"start": 2328.47, "end": 2328.69, "word": " is", "probability": 0.947265625}, {"start": 2328.69, "end": 2329.17, "word": " correct.", "probability": 0.90625}, {"start": 2330.13, "end": 2330.61, "word": " Look", "probability": 0.7861328125}, {"start": 2330.61, "end": 2330.87, "word": " here.", "probability": 0.85302734375}], "temperature": 1.0}, {"id": 82, "seek": 236828, "start": 2340.8, "end": 2368.28, "text": " Who can read the answers of this exercise or any other answer? This is a suggested answer. Yes, number two. I think you should follow the back and stop your chicks. Two, three. I don't think he should drive. I think he should fly. Either this or this or both of them.", "tokens": [2102, 393, 1401, 264, 6338, 295, 341, 5380, 420, 604, 661, 1867, 30, 639, 307, 257, 10945, 1867, 13, 1079, 11, 1230, 732, 13, 286, 519, 291, 820, 1524, 264, 646, 293, 1590, 428, 42214, 13, 4453, 11, 1045, 13, 286, 500, 380, 519, 415, 820, 3332, 13, 286, 519, 415, 820, 3603, 13, 13746, 341, 420, 341, 420, 1293, 295, 552, 13], "avg_logprob": -0.20800781110301614, "compression_ratio": 1.558139534883721, "no_speech_prob": 0.0, "words": [{"start": 2340.8, "end": 2341.06, "word": " Who", "probability": 0.61328125}, {"start": 2341.06, "end": 2341.42, "word": " can", "probability": 0.9443359375}, {"start": 2341.42, "end": 2342.46, "word": " read", "probability": 0.86962890625}, {"start": 2342.46, "end": 2343.14, "word": " the", "probability": 0.904296875}, {"start": 2343.14, "end": 2343.5, "word": " answers", "probability": 0.875}, {"start": 2343.5, "end": 2343.7, "word": " of", "probability": 0.89599609375}, {"start": 2343.7, "end": 2343.86, "word": " this", "probability": 0.94140625}, {"start": 2343.86, "end": 2344.3, "word": " exercise", "probability": 0.95703125}, {"start": 2344.3, "end": 2345.3, "word": " or", "probability": 0.6923828125}, {"start": 2345.3, "end": 2345.68, "word": " any", "probability": 0.90869140625}, {"start": 2345.68, "end": 2346.48, "word": " other", "probability": 0.890625}, {"start": 2346.48, "end": 2346.9, "word": " answer?", "probability": 0.95263671875}, {"start": 2347.7, "end": 2347.96, "word": " This", "probability": 0.8291015625}, {"start": 2347.96, "end": 2348.16, "word": " is", "probability": 0.95166015625}, {"start": 2348.16, "end": 2348.36, "word": " a", "probability": 0.98681640625}, {"start": 2348.36, "end": 2348.74, "word": " suggested", "probability": 0.75634765625}, {"start": 2348.74, "end": 2349.22, "word": " answer.", "probability": 0.96240234375}, {"start": 2349.58, "end": 2349.68, "word": " Yes,", "probability": 0.865234375}, {"start": 2349.76, "end": 2349.88, "word": " number", "probability": 0.8994140625}, {"start": 2349.88, "end": 2351.1, "word": " two.", "probability": 0.65185546875}, {"start": 2351.56, "end": 2351.86, "word": " I", "probability": 0.529296875}, {"start": 2351.86, "end": 2352.08, "word": " think", "probability": 0.82080078125}, {"start": 2352.08, "end": 2352.26, "word": " you", "probability": 0.826171875}, {"start": 2352.26, "end": 2352.5, "word": " should", "probability": 0.962890625}, {"start": 2352.5, "end": 2352.78, "word": " follow", "probability": 0.55419921875}, {"start": 2352.78, "end": 2352.98, "word": " the", "probability": 0.87255859375}, {"start": 2352.98, "end": 2353.26, "word": " back", "probability": 0.349609375}, {"start": 2353.26, "end": 2353.56, "word": " and", "probability": 0.91357421875}, {"start": 2353.56, "end": 2353.88, "word": " stop", "probability": 0.853515625}, {"start": 2353.88, "end": 2354.18, "word": " your", "probability": 0.87890625}, {"start": 2354.18, "end": 2354.74, "word": " chicks.", "probability": 0.6005859375}, {"start": 2356.06, "end": 2356.2, "word": " Two,", "probability": 0.59033203125}, {"start": 2357.44, "end": 2358.56, "word": " three.", "probability": 0.74267578125}, {"start": 2359.84, "end": 2359.84, "word": " I", "probability": 0.68017578125}, {"start": 2359.84, "end": 2360.02, "word": " don't", "probability": 0.963623046875}, {"start": 2360.02, "end": 2360.36, "word": " think", "probability": 0.9189453125}, {"start": 2360.36, "end": 2360.58, "word": " he", "probability": 0.91357421875}, {"start": 2360.58, "end": 2360.84, "word": " should", "probability": 0.93212890625}, {"start": 2360.84, "end": 2361.24, "word": " drive.", "probability": 0.90625}, {"start": 2361.4, "end": 2361.52, "word": " I", "probability": 0.96337890625}, {"start": 2361.52, "end": 2361.76, "word": " think", "probability": 0.9169921875}, {"start": 2361.76, "end": 2362.06, "word": " he", "probability": 0.91650390625}, {"start": 2362.06, "end": 2363.0, "word": " should", "probability": 0.935546875}, {"start": 2363.0, "end": 2363.54, "word": " fly.", "probability": 0.7978515625}, {"start": 2365.94, "end": 2366.18, "word": " Either", "probability": 0.8740234375}, {"start": 2366.18, "end": 2366.68, "word": " this", "probability": 0.9423828125}, {"start": 2366.68, "end": 2367.24, "word": " or", "probability": 0.90283203125}, {"start": 2367.24, "end": 2367.56, "word": " this", "probability": 0.92919921875}, {"start": 2367.56, "end": 2367.8, "word": " or", "probability": 0.7060546875}, {"start": 2367.8, "end": 2367.98, "word": " both", "probability": 0.87744140625}, {"start": 2367.98, "end": 2368.1, "word": " of", "probability": 0.96826171875}, {"start": 2368.1, "end": 2368.28, "word": " them.", "probability": 0.8828125}], "temperature": 1.0}, {"id": 83, "seek": 239673, "start": 2369.59, "end": 2396.73, "text": " These are two suggestions, yes? With I don't think and with I think. One is enough. Yes. Thank you. Number four. Yes, reading. Number four, I think you should buy here an arm clock. Number five, I don't think you should buy so many new clothes. I think you should get a job.", "tokens": [1981, 366, 732, 13396, 11, 2086, 30, 2022, 286, 500, 380, 519, 293, 365, 286, 519, 13, 1485, 307, 1547, 13, 1079, 13, 1044, 291, 13, 5118, 1451, 13, 1079, 11, 3760, 13, 5118, 1451, 11, 286, 519, 291, 820, 2256, 510, 364, 3726, 7830, 13, 5118, 1732, 11, 286, 500, 380, 519, 291, 820, 2256, 370, 867, 777, 5534, 13, 286, 519, 291, 820, 483, 257, 1691, 13], "avg_logprob": -0.21573660160814012, "compression_ratio": 1.6768292682926829, "no_speech_prob": 0.0, "words": [{"start": 2369.59, "end": 2369.89, "word": " These", "probability": 0.73291015625}, {"start": 2369.89, "end": 2370.05, "word": " are", "probability": 0.93896484375}, {"start": 2370.05, "end": 2370.23, "word": " two", "probability": 0.8642578125}, {"start": 2370.23, "end": 2370.73, "word": " suggestions,", "probability": 0.8681640625}, {"start": 2370.93, "end": 2371.17, "word": " yes?", "probability": 0.80712890625}, {"start": 2371.91, "end": 2372.07, "word": " With", "probability": 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Now look at the grammar spot. Look at the sentences below. 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The first question. Which sentence expresses strong obligation? You must. Yes. So here must fall strong obligation. You understand? Now, which sentence expresses a suggestion? Should. 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This exercise is about the modal verbs. Permission, no permission. Obligation, no obligation. Strong obligation, mild obligation, suggestion, advice. General exercise.", "tokens": [12753, 613, 16579, 13, 639, 5380, 307, 466, 264, 39745, 30051, 13, 41006, 3106, 11, 572, 11226, 13, 4075, 5073, 399, 11, 572, 20326, 13, 22792, 20326, 11, 15154, 20326, 11, 16541, 11, 5192, 13, 6996, 5380, 13], "avg_logprob": -0.19551281516368574, "compression_ratio": 1.5196850393700787, "no_speech_prob": 0.0, "words": [{"start": 2545.74, "end": 2546.14, "word": " Correct", "probability": 0.467041015625}, {"start": 2546.14, "end": 2547.02, "word": " these", "probability": 0.84326171875}, {"start": 2547.02, "end": 2547.64, "word": " sentences.", "probability": 0.93701171875}, {"start": 2548.24, "end": 2548.8, "word": " This", "probability": 0.87744140625}, {"start": 2548.8, "end": 2549.28, "word": " exercise", "probability": 0.94921875}, {"start": 2549.28, "end": 2549.56, "word": " is", "probability": 0.95166015625}, {"start": 2549.56, "end": 2550.04, "word": " about", "probability": 0.904296875}, {"start": 2550.04, "end": 2551.58, "word": " the", "probability": 0.77099609375}, {"start": 2551.58, "end": 2551.9, "word": " modal", "probability": 0.8115234375}, {"start": 2551.9, "end": 2552.38, "word": " verbs.", "probability": 0.9208984375}, {"start": 2554.58, "end": 2555.28, "word": " Permission,", "probability": 0.942626953125}, {"start": 2556.56, "end": 2556.72, "word": " no", "probability": 0.8173828125}, {"start": 2556.72, "end": 2557.28, "word": " permission.", "probability": 0.92236328125}, {"start": 2558.44, "end": 2559.58, "word": " Obligation,", "probability": 0.97119140625}, {"start": 2560.46, "end": 2560.66, "word": " no", "probability": 0.9365234375}, {"start": 2560.66, "end": 2561.22, "word": " obligation.", "probability": 0.92919921875}, {"start": 2561.98, "end": 2562.32, "word": " Strong", "probability": 0.876953125}, {"start": 2562.32, "end": 2563.08, "word": " obligation,", "probability": 0.90478515625}, {"start": 2563.74, "end": 2563.98, "word": " mild", "probability": 0.91943359375}, {"start": 2563.98, "end": 2564.56, "word": " obligation,", "probability": 0.919921875}, {"start": 2565.2, "end": 2565.62, "word": " suggestion,", "probability": 0.78466796875}, {"start": 2566.38, "end": 2566.94, "word": " advice.", "probability": 0.91455078125}, {"start": 2567.68, "end": 2568.6, "word": " General", "probability": 0.71044921875}, {"start": 2568.6, "end": 2569.98, "word": " exercise.", "probability": 0.94482421875}], "temperature": 1.0}, {"id": 90, "seek": 259916, "start": 2571.34, "end": 2599.16, "text": " Check it. Correct these sentences. Do you can? This is wrong. Why? Because can is an auxiliary verb. It should, we should begin it in the, in the questions. Yes, no questions. We should use the auxiliary verbs. Am is are was were and?", "tokens": [6881, 309, 13, 12753, 613, 16579, 13, 1144, 291, 393, 30, 639, 307, 2085, 13, 1545, 30, 1436, 393, 307, 364, 43741, 9595, 13, 467, 820, 11, 321, 820, 1841, 309, 294, 264, 11, 294, 264, 1651, 13, 1079, 11, 572, 1651, 13, 492, 820, 764, 264, 43741, 30051, 13, 2012, 307, 366, 390, 645, 293, 30], "avg_logprob": -0.2516163859901757, "compression_ratio": 1.5064102564102564, "no_speech_prob": 0.0, "words": [{"start": 2571.34, "end": 2571.66, "word": " Check", "probability": 0.2396240234375}, {"start": 2571.66, "end": 2571.98, "word": " it.", "probability": 0.9169921875}, {"start": 2572.24, "end": 2572.46, "word": " Correct", "probability": 0.75537109375}, {"start": 2572.46, "end": 2572.78, "word": " these", "probability": 0.82421875}, {"start": 2572.78, "end": 2573.22, "word": " sentences.", "probability": 0.93115234375}, {"start": 2573.64, "end": 2573.84, "word": " Do", "probability": 0.79833984375}, {"start": 2573.84, "end": 2574.6, "word": " you", "probability": 0.96923828125}, {"start": 2574.6, "end": 2575.46, "word": " can?", "probability": 0.689453125}, {"start": 2578.3, "end": 2578.84, "word": " This", "probability": 0.619140625}, {"start": 2578.84, "end": 2579.74, "word": " is", "probability": 0.947265625}, {"start": 2579.74, "end": 2580.1, "word": " wrong.", "probability": 0.93408203125}, {"start": 2580.42, "end": 2580.72, "word": " Why?", "probability": 0.89453125}, {"start": 2581.6, "end": 2582.36, "word": " Because", "probability": 0.8720703125}, {"start": 2582.36, "end": 2582.98, "word": " can", "probability": 0.69189453125}, {"start": 2582.98, "end": 2583.46, "word": " is", "probability": 0.93115234375}, {"start": 2583.46, "end": 2584.1, "word": " an", "probability": 0.90234375}, {"start": 2584.1, "end": 2584.8, "word": " auxiliary", "probability": 0.92333984375}, {"start": 2584.8, "end": 2585.38, "word": " verb.", "probability": 0.8955078125}, {"start": 2586.54, "end": 2586.78, "word": " It", "probability": 0.56005859375}, {"start": 2586.78, "end": 2587.2, "word": " should,", "probability": 0.95654296875}, {"start": 2587.58, "end": 2588.44, "word": " we", "probability": 0.94580078125}, {"start": 2588.44, "end": 2588.66, "word": " should", "probability": 0.96533203125}, {"start": 2588.66, "end": 2589.04, "word": " begin", "probability": 0.89111328125}, {"start": 2589.04, "end": 2589.38, "word": " it", "probability": 0.90234375}, {"start": 2589.38, "end": 2589.68, "word": " in", "probability": 0.90966796875}, {"start": 2589.68, "end": 2589.9, "word": " the,", "probability": 0.9130859375}, {"start": 2589.92, "end": 2590.54, "word": " in", "probability": 0.90771484375}, {"start": 2590.54, "end": 2590.68, "word": " the", "probability": 0.91796875}, {"start": 2590.68, "end": 2591.3, "word": " questions.", "probability": 0.94189453125}, {"start": 2591.86, "end": 2592.36, "word": " Yes,", "probability": 0.9521484375}, {"start": 2592.44, "end": 2592.56, "word": " no", "probability": 0.92431640625}, {"start": 2592.56, "end": 2593.16, "word": " questions.", "probability": 0.93994140625}, {"start": 2593.4, "end": 2593.6, "word": " We", "probability": 0.9599609375}, {"start": 2593.6, "end": 2593.82, "word": " should", "probability": 0.95556640625}, {"start": 2593.82, "end": 2594.26, "word": " use", "probability": 0.8408203125}, {"start": 2594.26, "end": 2595.0, "word": " the", "probability": 0.8828125}, {"start": 2595.0, "end": 2595.34, "word": " auxiliary", "probability": 0.64501953125}, {"start": 2595.34, "end": 2595.8, "word": " verbs.", "probability": 0.916015625}, {"start": 2596.46, "end": 2597.22, "word": " Am", "probability": 0.74169921875}, {"start": 2597.22, "end": 2597.54, "word": " is", "probability": 0.74462890625}, {"start": 2597.54, "end": 2597.86, "word": " are", "probability": 0.76318359375}, {"start": 2597.86, "end": 2598.18, "word": " was", "probability": 0.67236328125}, {"start": 2598.18, "end": 2598.42, "word": " were", "probability": 0.7109375}, {"start": 2598.42, "end": 2599.16, "word": " and?", "probability": 0.8857421875}], "temperature": 1.0}, {"id": 91, "seek": 262835, "start": 2599.71, "end": 2628.35, "text": " Should? Can? Yes, all the models, the same. So here, we can't use do. No, we can use can. So can you help me? Why? Because it is something like is, like was. But we don't use do. Why? Because do is for the full verb. No, this is a granular verb. 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Number two. What time have you two start work? Have to is not an auxiliary. It is a full verb. It is a full verb. 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So we don't say have. Do you have to? So what time do you have to start work? Why? Because this is a full verb. Because it is a full verb, I can use do. 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So, what time do you have to? What time does she have to? What time will you have to? You understand? We can use will, do, or does, or will, or did. What time did you have to? 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So this is a full verb. With a full verb, I use auxiliary, do, does, did. And in the future, we use will. Is it clear? Yes. Number three. We are not allowed to wear jeans at school. No. No negate nouns. 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And with allowed to, we use be. It means am, is, are, was, where. So here am is are. Am is are and not. Not no. So am not isn't.", "tokens": [4281, 929, 13, 400, 365, 4350, 281, 11, 321, 764, 312, 13, 467, 1355, 669, 11, 307, 11, 366, 11, 390, 11, 689, 13, 407, 510, 669, 307, 366, 13, 2012, 307, 366, 293, 406, 13, 1726, 572, 13, 407, 669, 406, 1943, 380, 13], "avg_logprob": -0.264775808090749, "compression_ratio": 1.2952380952380953, "no_speech_prob": 0.0, "words": [{"start": 2772.54, "end": 2773.34, "word": " Verbs.", "probability": 0.752685546875}, {"start": 2775.82, "end": 2775.82, "word": " And", "probability": 0.54541015625}, {"start": 2775.82, "end": 2777.3, "word": " with", "probability": 0.81396484375}, {"start": 2777.3, "end": 2778.48, "word": " allowed", "probability": 0.59814453125}, {"start": 2778.48, "end": 2778.8, "word": " to,", "probability": 0.95263671875}, {"start": 2779.0, "end": 2779.08, "word": " we", "probability": 0.95361328125}, {"start": 2779.08, "end": 2779.34, "word": " use", "probability": 0.8701171875}, {"start": 2779.34, "end": 2779.62, "word": " be.", "probability": 0.7353515625}, {"start": 2780.24, "end": 2780.54, "word": " It", "probability": 0.9501953125}, {"start": 2780.54, "end": 2780.86, "word": " means", "probability": 0.93359375}, {"start": 2780.86, "end": 2781.26, "word": " am,", "probability": 0.6845703125}, {"start": 2781.32, "end": 2781.6, "word": " is,", "probability": 0.9599609375}, {"start": 2781.76, "end": 2782.04, "word": " are,", "probability": 0.9521484375}, {"start": 2782.58, "end": 2782.86, "word": " was,", "probability": 0.966796875}, {"start": 2782.94, "end": 2783.18, "word": " where.", "probability": 0.5234375}, {"start": 2784.02, "end": 2784.28, "word": " So", "probability": 0.9580078125}, {"start": 2784.28, "end": 2784.68, "word": " here", "probability": 0.83935546875}, {"start": 2784.68, "end": 2785.24, "word": " am", "probability": 0.47119140625}, {"start": 2785.24, "end": 2785.56, "word": " is", "probability": 0.64599609375}, {"start": 2785.56, "end": 2786.0, "word": " are.", "probability": 0.94580078125}, {"start": 2787.62, "end": 2788.42, "word": " Am", "probability": 0.96435546875}, {"start": 2788.42, "end": 2789.98, "word": " is", "probability": 0.88818359375}, {"start": 2789.98, "end": 2791.14, "word": " are", "probability": 0.955078125}, {"start": 2791.14, "end": 2792.6, "word": " and", "probability": 0.615234375}, {"start": 2792.6, "end": 2793.06, "word": " not.", "probability": 0.93994140625}, {"start": 2793.64, "end": 2793.98, "word": " Not", "probability": 0.79296875}, {"start": 2793.98, "end": 2794.22, "word": " no.", "probability": 0.395751953125}, {"start": 2794.88, "end": 2795.26, "word": " So", "probability": 0.9521484375}, {"start": 2795.26, "end": 2796.14, "word": " am", "probability": 0.60595703125}, {"start": 2796.14, "end": 2796.62, "word": " not", "probability": 0.9404296875}, {"start": 2796.62, "end": 2798.7, "word": " isn't.", "probability": 0.879638671875}], "temperature": 1.0}, {"id": 98, "seek": 282870, "start": 2799.44, "end": 2828.7, "text": " aren't. So here we are, we aren't, we aren't allowed. We aren't allowed because the negative of are is aren't, is, isn't, am, am not. And we use be allowed to. It, it gives the meaning of can't. Yes. 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Negative. The negative is with aunt, not with no. Look at number five, number four. We know can. Can is an auxiliary. 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So here, can't. Why? Because we are stuck not with it to make negative.", "tokens": [13252, 77, 380, 13, 407, 510, 11, 393, 380, 13, 1545, 30, 1436, 321, 366, 5541, 406, 365, 309, 281, 652, 3671, 13], "avg_logprob": -0.4889322643478711, "compression_ratio": 1.0125, "no_speech_prob": 0.0, "words": [{"start": 2860.57, "end": 2861.31, "word": " Mustn't.", "probability": 0.6000162760416666}, {"start": 2861.59, "end": 2861.85, "word": " So", "probability": 0.81591796875}, {"start": 2861.85, "end": 2862.29, "word": " here,", "probability": 0.7666015625}, {"start": 2862.81, "end": 2864.15, "word": " can't.", "probability": 0.88916015625}, {"start": 2866.07, "end": 2866.45, "word": " Why?", "probability": 0.80322265625}, {"start": 2866.69, "end": 2866.87, "word": " Because", "probability": 0.64794921875}, {"start": 2866.87, "end": 2867.09, "word": " we", "probability": 0.3818359375}, {"start": 2867.09, "end": 2867.37, "word": " are", "probability": 0.50439453125}, {"start": 2867.37, "end": 2867.91, "word": " stuck", "probability": 0.1422119140625}, {"start": 2867.91, "end": 2868.39, "word": " not", "probability": 0.51611328125}, {"start": 2868.39, "end": 2869.51, "word": " with", "probability": 0.83154296875}, {"start": 2869.51, "end": 2869.69, "word": " it", "probability": 0.845703125}, {"start": 2869.69, "end": 2869.85, "word": " to", "probability": 0.87890625}, {"start": 2869.85, "end": 2870.05, "word": " make", "probability": 0.94384765625}, {"start": 2870.05, "end": 2870.41, "word": " negative.", "probability": 0.779296875}], "temperature": 1.0}, {"id": 101, "seek": 290451, "start": 2875.53, "end": 2904.51, "text": " My mother have, have, have to. No, has. Yes. So we say has to. Why? The singular has to. The plural have to. With I have to. But in the past, all the pronouns had to. In the future, all the pronouns will have to. 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Here passengers must to have a ticket, must to know, must", "tokens": [42818, 380, 11, 1943, 380, 11, 3212, 380, 11, 5183, 13, 583, 321, 393, 380, 584, 406, 366, 11, 406, 307, 13, 883, 307, 572, 11, 1943, 380, 13, 509, 1223, 30, 883, 307, 264, 3671, 337, 264, 48184, 13, 583, 406, 307, 264, 3671, 337, 264, 9595, 13, 1692, 18436, 1633, 281, 362, 257, 10550, 11, 1633, 281, 458, 11, 1633], "avg_logprob": -0.261904776096344, "compression_ratio": 1.6028368794326242, "no_speech_prob": 0.0, "words": [{"start": 2953.63, "end": 2954.59, "word": " mustn't,", "probability": 0.6343994140625}, {"start": 2955.05, "end": 2955.81, "word": " isn't,", "probability": 0.973388671875}, {"start": 2956.33, "end": 2956.87, "word": " aren't,", "probability": 0.9521484375}, {"start": 2956.93, "end": 2957.41, "word": " etc.", "probability": 0.78955078125}, {"start": 2958.07, "end": 2958.51, "word": " But", "probability": 0.794921875}, {"start": 2958.51, "end": 2958.95, "word": " we", "probability": 0.8642578125}, {"start": 2958.95, "end": 2959.23, "word": " can't", "probability": 0.6944580078125}, {"start": 2959.23, "end": 2959.33, "word": " say", "probability": 0.95263671875}, {"start": 2959.33, "end": 2959.63, "word": " not", "probability": 0.71142578125}, {"start": 2959.63, "end": 2960.03, "word": " are,", "probability": 0.86181640625}, {"start": 2960.45, "end": 2960.65, "word": " not", "probability": 0.900390625}, {"start": 2960.65, "end": 2961.13, "word": " is.", "probability": 0.94970703125}, {"start": 2962.49, "end": 2962.65, "word": " No", "probability": 0.6435546875}, {"start": 2962.65, "end": 2963.11, "word": " is", "probability": 0.921875}, {"start": 2963.11, "end": 2963.61, "word": " no,", "probability": 0.57568359375}, {"start": 2964.15, "end": 2964.67, "word": " isn't.", "probability": 0.9658203125}, {"start": 2965.19, "end": 2965.29, "word": " You", "probability": 0.591796875}, {"start": 2965.29, "end": 2965.55, "word": " understand?", "probability": 0.8193359375}, {"start": 2966.39, "end": 2966.71, "word": " No", "probability": 0.90576171875}, {"start": 2966.71, "end": 2967.71, "word": " is", "probability": 0.90185546875}, {"start": 2967.71, "end": 2967.91, "word": " the", "probability": 0.85009765625}, {"start": 2967.91, "end": 2968.25, "word": " negative", "probability": 0.92919921875}, {"start": 2968.25, "end": 2968.67, "word": " for", "probability": 0.93505859375}, {"start": 2968.67, "end": 2968.87, "word": " the", "probability": 0.78662109375}, {"start": 2968.87, "end": 2969.29, "word": " nouns.", "probability": 0.94287109375}, {"start": 2969.97, "end": 2970.63, "word": " But", "probability": 0.90478515625}, {"start": 2970.63, "end": 2970.99, "word": " not", "probability": 0.8837890625}, {"start": 2970.99, "end": 2971.61, "word": " is", "probability": 0.89453125}, {"start": 2971.61, "end": 2971.77, "word": " the", "probability": 0.90576171875}, {"start": 2971.77, "end": 2972.07, "word": " negative", "probability": 0.93505859375}, {"start": 2972.07, "end": 2972.41, "word": " for", "probability": 0.9482421875}, {"start": 2972.41, "end": 2972.59, "word": " the", "probability": 0.9208984375}, {"start": 2972.59, "end": 2972.95, "word": " verb.", "probability": 0.8251953125}, {"start": 2974.73, "end": 2974.97, "word": " Here", "probability": 0.55322265625}, {"start": 2974.97, "end": 2975.69, "word": " passengers", "probability": 0.80322265625}, {"start": 2975.69, "end": 2976.35, "word": " must", "probability": 0.8916015625}, {"start": 2976.35, "end": 2977.11, "word": " to", "probability": 0.64990234375}, {"start": 2977.11, "end": 2978.03, "word": " have", "probability": 0.95556640625}, {"start": 2978.03, "end": 2978.71, "word": " a", "probability": 0.9892578125}, {"start": 2978.71, "end": 2979.15, "word": " ticket,", "probability": 0.919921875}, {"start": 2980.05, "end": 2980.49, "word": " must", "probability": 0.85205078125}, {"start": 2980.49, "end": 2981.01, "word": " to", "probability": 0.8291015625}, {"start": 2981.01, "end": 2981.55, "word": " know,", "probability": 0.387451171875}, {"start": 2982.33, "end": 2983.03, "word": " must", "probability": 0.869140625}], "temperature": 1.0}, {"id": 105, "seek": 301347, "start": 2984.85, "end": 3013.47, "text": " And all the modal verbs do not take to. So we say must have without to. We use to just with ought to. Ought to and have to. But have to is not a modal. It is have to and we use ought to. So what's the negative of ought to?", "tokens": [400, 439, 264, 39745, 30051, 360, 406, 747, 281, 13, 407, 321, 584, 1633, 362, 1553, 281, 13, 492, 764, 281, 445, 365, 13416, 281, 13, 422, 1599, 281, 293, 362, 281, 13, 583, 362, 281, 307, 406, 257, 39745, 13, 467, 307, 362, 281, 293, 321, 764, 13416, 281, 13, 407, 437, 311, 264, 3671, 295, 13416, 281, 30], "avg_logprob": -0.20632684719367106, "compression_ratio": 1.60431654676259, "no_speech_prob": 0.0, "words": [{"start": 2984.85, "end": 2985.21, "word": " And", "probability": 0.4326171875}, {"start": 2985.21, "end": 2985.95, "word": " all", "probability": 0.91259765625}, {"start": 2985.95, "end": 2988.93, "word": " the", "probability": 0.52880859375}, {"start": 2988.93, "end": 2989.17, "word": " modal", "probability": 0.60498046875}, {"start": 2989.17, "end": 2989.65, "word": " verbs", "probability": 0.9345703125}, {"start": 2989.65, "end": 2990.29, "word": " do", "probability": 0.83837890625}, {"start": 2990.29, "end": 2990.53, "word": " not", "probability": 0.9501953125}, {"start": 2990.53, "end": 2990.91, "word": " take", "probability": 0.87158203125}, {"start": 2990.91, "end": 2991.17, "word": " to.", "probability": 0.318603515625}, {"start": 2992.01, "end": 2992.61, "word": " So", "probability": 0.89208984375}, {"start": 2992.61, "end": 2993.39, "word": " we", "probability": 0.77001953125}, {"start": 2993.39, "end": 2993.67, "word": " say", "probability": 0.9189453125}, {"start": 2993.67, "end": 2994.35, "word": " must", "probability": 0.65673828125}, {"start": 2994.35, "end": 2995.25, "word": " have", "probability": 0.802734375}, {"start": 2995.25, "end": 2998.35, "word": " without", "probability": 0.419921875}, {"start": 2998.35, "end": 2998.93, "word": " to.", "probability": 0.888671875}, {"start": 2999.57, "end": 2999.87, "word": " We", "probability": 0.93505859375}, {"start": 2999.87, "end": 3000.17, "word": " use", "probability": 0.73828125}, {"start": 3000.17, "end": 3000.43, "word": " to", "probability": 0.95068359375}, {"start": 3000.43, "end": 3000.95, "word": " just", "probability": 0.85302734375}, {"start": 3000.95, "end": 3001.41, "word": " with", "probability": 0.90966796875}, {"start": 3001.41, "end": 3001.73, "word": " ought", "probability": 0.411865234375}, {"start": 3001.73, "end": 3002.29, "word": " to.", "probability": 0.97119140625}, {"start": 3002.79, "end": 3003.39, "word": " Ought", "probability": 0.810546875}, {"start": 3003.39, "end": 3003.93, "word": " to", "probability": 0.9716796875}, {"start": 3003.93, "end": 3004.81, "word": " and", "probability": 0.6669921875}, {"start": 3004.81, "end": 3005.63, "word": " have", "probability": 0.9560546875}, {"start": 3005.63, "end": 3005.91, "word": " to.", "probability": 0.9541015625}, {"start": 3006.45, "end": 3006.57, "word": " But", "probability": 0.93505859375}, {"start": 3006.57, "end": 3006.81, "word": " have", "probability": 0.93896484375}, {"start": 3006.81, "end": 3006.91, "word": " to", "probability": 0.955078125}, {"start": 3006.91, "end": 3007.05, "word": " is", "probability": 0.908203125}, {"start": 3007.05, "end": 3007.15, "word": " not", "probability": 0.94482421875}, {"start": 3007.15, "end": 3007.29, "word": " a", "probability": 0.9677734375}, {"start": 3007.29, "end": 3007.51, "word": " modal.", "probability": 0.958984375}, {"start": 3008.39, "end": 3008.73, "word": " It", "probability": 0.8876953125}, {"start": 3008.73, "end": 3008.93, "word": " is", "probability": 0.93408203125}, {"start": 3008.93, "end": 3009.27, "word": " have", "probability": 0.9404296875}, {"start": 3009.27, "end": 3009.55, "word": " to", "probability": 0.970703125}, {"start": 3009.55, "end": 3010.25, "word": " and", "probability": 0.46630859375}, {"start": 3010.25, "end": 3010.51, "word": " we", "probability": 0.95703125}, {"start": 3010.51, "end": 3010.81, "word": " use", "probability": 0.8759765625}, {"start": 3010.81, "end": 3011.11, "word": " ought", "probability": 0.93994140625}, {"start": 3011.11, "end": 3011.35, "word": " to.", "probability": 0.97216796875}, {"start": 3011.57, "end": 3011.67, "word": " So", "probability": 0.94140625}, {"start": 3011.67, "end": 3011.87, "word": " what's", "probability": 0.88916015625}, {"start": 3011.87, "end": 3011.99, "word": " the", "probability": 0.89697265625}, {"start": 3011.99, "end": 3012.25, "word": " negative", "probability": 0.91064453125}, {"start": 3012.25, "end": 3012.87, "word": " of", "probability": 0.96826171875}, {"start": 3012.87, "end": 3013.17, "word": " ought", "probability": 0.9052734375}, {"start": 3013.17, "end": 3013.47, "word": " to?", "probability": 0.97412109375}], "temperature": 1.0}, {"id": 106, "seek": 304433, "start": 3015.19, "end": 3044.33, "text": " Otent two. Yes. The negative of Ot two is Otent two. Can we use two after the models? No. Can play. We can't say can't play. Can play. Must play. Should play. So don't use two.", "tokens": [12936, 317, 732, 13, 1079, 13, 440, 3671, 295, 12936, 732, 307, 12936, 317, 732, 13, 1664, 321, 764, 732, 934, 264, 5245, 30, 883, 13, 1664, 862, 13, 492, 393, 380, 584, 393, 380, 862, 13, 1664, 862, 13, 13252, 862, 13, 6454, 862, 13, 407, 500, 380, 764, 732, 13], "avg_logprob": -0.2986438814199196, "compression_ratio": 1.4873949579831933, "no_speech_prob": 0.0, "words": [{"start": 3015.19, "end": 3015.91, "word": " Otent", "probability": 0.44610595703125}, {"start": 3015.91, "end": 3016.27, "word": " two.", "probability": 0.3759765625}, {"start": 3016.57, "end": 3016.81, "word": " Yes.", "probability": 0.6953125}, {"start": 3017.11, "end": 3017.29, "word": " The", "probability": 0.84228515625}, {"start": 3017.29, "end": 3017.61, "word": " negative", "probability": 0.92041015625}, {"start": 3017.61, "end": 3018.05, "word": " of", "probability": 0.94921875}, {"start": 3018.05, "end": 3018.35, "word": " Ot", "probability": 0.365234375}, {"start": 3018.35, "end": 3020.19, "word": " two", "probability": 0.293212890625}, {"start": 3020.19, "end": 3023.27, "word": " is", "probability": 0.345458984375}, {"start": 3023.27, "end": 3025.25, "word": " Otent", "probability": 0.81884765625}, {"start": 3025.25, "end": 3026.93, "word": " two.", "probability": 0.8681640625}, {"start": 3029.27, "end": 3029.99, "word": " Can", "probability": 0.94140625}, {"start": 3029.99, "end": 3030.19, "word": " we", "probability": 0.9560546875}, {"start": 3030.19, "end": 3030.47, "word": " use", "probability": 0.86669921875}, {"start": 3030.47, "end": 3030.69, "word": " two", "probability": 0.80029296875}, {"start": 3030.69, "end": 3031.19, "word": " after", "probability": 0.8193359375}, {"start": 3031.19, "end": 3031.39, "word": " the", "probability": 0.91650390625}, {"start": 3031.39, "end": 3031.73, "word": " models?", "probability": 0.7978515625}, {"start": 3032.03, "end": 3032.33, "word": " No.", "probability": 0.88525390625}, {"start": 3033.15, "end": 3033.55, "word": " Can", "probability": 0.87255859375}, {"start": 3033.55, "end": 3033.93, "word": " play.", "probability": 0.7802734375}, {"start": 3034.69, "end": 3034.93, "word": " We", "probability": 0.8984375}, {"start": 3034.93, "end": 3035.21, "word": " can't", "probability": 0.88427734375}, {"start": 3035.21, "end": 3035.35, "word": " say", "probability": 0.955078125}, {"start": 3035.35, "end": 3035.85, "word": " can't", "probability": 0.64892578125}, {"start": 3035.85, "end": 3036.19, "word": " play.", "probability": 0.8857421875}, {"start": 3036.75, "end": 3037.03, "word": " Can", "probability": 0.890625}, {"start": 3037.03, "end": 3037.47, "word": " play.", "probability": 0.90380859375}, {"start": 3038.61, "end": 3038.87, "word": " Must", "probability": 0.7822265625}, {"start": 3038.87, "end": 3039.31, "word": " play.", "probability": 0.95654296875}, {"start": 3040.31, "end": 3040.53, "word": " Should", "probability": 0.9287109375}, {"start": 3040.53, "end": 3040.99, "word": " play.", "probability": 0.95068359375}, {"start": 3042.49, "end": 3043.21, "word": " So", "probability": 0.70751953125}, {"start": 3043.21, "end": 3043.73, "word": " don't", "probability": 0.938232421875}, {"start": 3043.73, "end": 3044.05, "word": " use", "probability": 0.88037109375}, {"start": 3044.05, "end": 3044.33, "word": " two.", "probability": 0.8984375}], "temperature": 1.0}, {"id": 107, "seek": 306622, "start": 3045.18, "end": 3066.22, "text": " Also, can we use S? No. We can use S with the model. We can't say musts, cans. No. No S. No IG. I love canning. I love shooting. No, no, no, no IG form.", "tokens": [2743, 11, 393, 321, 764, 318, 30, 883, 13, 492, 393, 764, 318, 365, 264, 2316, 13, 492, 393, 380, 584, 1633, 82, 11, 21835, 13, 883, 13, 883, 318, 13, 883, 26367, 13, 286, 959, 393, 773, 13, 286, 959, 5942, 13, 883, 11, 572, 11, 572, 11, 572, 26367, 1254, 13], "avg_logprob": -0.22164352045015054, "compression_ratio": 1.3909090909090909, "no_speech_prob": 0.0, "words": [{"start": 3045.18, "end": 3045.7, "word": " Also,", "probability": 0.87939453125}, {"start": 3046.42, "end": 3046.9, "word": " can", "probability": 0.92333984375}, {"start": 3046.9, "end": 3047.08, "word": " we", "probability": 0.9560546875}, {"start": 3047.08, "end": 3047.36, "word": " use", "probability": 0.8740234375}, {"start": 3047.36, "end": 3047.7, "word": " S?", "probability": 0.4443359375}, {"start": 3048.54, "end": 3049.26, "word": " No.", "probability": 0.90771484375}, {"start": 3049.7, "end": 3050.16, "word": " We", "probability": 0.91650390625}, {"start": 3050.16, "end": 3050.48, "word": " can", "probability": 0.94384765625}, {"start": 3050.48, "end": 3050.74, "word": " use", "probability": 0.6806640625}, {"start": 3050.74, "end": 3051.04, "word": " S", "probability": 0.90380859375}, {"start": 3051.04, "end": 3051.28, "word": " with", "probability": 0.88916015625}, {"start": 3051.28, "end": 3051.44, "word": " the", "probability": 0.8544921875}, {"start": 3051.44, "end": 3051.74, "word": " model.", "probability": 0.75634765625}, {"start": 3052.46, "end": 3052.58, "word": " We", "probability": 0.908203125}, {"start": 3052.58, "end": 3052.96, "word": " can't", "probability": 0.910888671875}, {"start": 3052.96, "end": 3053.2, "word": " say", "probability": 0.943359375}, {"start": 3053.2, "end": 3054.6, "word": " musts,", "probability": 0.4898681640625}, {"start": 3054.96, "end": 3055.7, "word": " cans.", "probability": 0.464599609375}, {"start": 3055.98, "end": 3056.26, "word": " No.", "probability": 0.951171875}, {"start": 3056.52, "end": 3056.92, "word": " No", "probability": 0.931640625}, {"start": 3056.92, "end": 3057.3, "word": " S.", "probability": 0.9072265625}, {"start": 3058.22, "end": 3058.56, "word": " No", "probability": 0.92626953125}, {"start": 3058.56, "end": 3058.92, "word": " IG.", "probability": 0.219970703125}, {"start": 3059.76, "end": 3060.48, "word": " I", "probability": 0.9736328125}, {"start": 3060.48, "end": 3060.94, "word": " love", "probability": 0.9560546875}, {"start": 3060.94, "end": 3061.82, "word": " canning.", "probability": 0.935791015625}, {"start": 3062.22, "end": 3062.48, "word": " I", "probability": 0.9970703125}, {"start": 3062.48, "end": 3062.98, "word": " love", "probability": 0.95361328125}, {"start": 3062.98, "end": 3063.34, "word": " shooting.", "probability": 0.9072265625}, {"start": 3063.76, "end": 3064.06, "word": " No,", "probability": 0.96240234375}, {"start": 3064.2, "end": 3064.4, "word": " no,", "probability": 0.9453125}, {"start": 3064.48, "end": 3064.74, "word": " no,", "probability": 0.95068359375}, {"start": 3064.78, "end": 3065.24, "word": " no", "probability": 0.94384765625}, {"start": 3065.24, "end": 3065.7, "word": " IG", "probability": 0.76953125}, {"start": 3065.7, "end": 3066.22, "word": " form.", "probability": 0.89306640625}], "temperature": 1.0}, {"id": 108, "seek": 309479, "start": 3067.79, "end": 3094.79, "text": " It does not take to, it does not take s, it does not take ing. So we should use the model with the verb without to, except for ought to and have to. But with have to in the singular, we say has to. But what about can? Oh, can for all the pronouns.", "tokens": [467, 775, 406, 747, 281, 11, 309, 775, 406, 747, 262, 11, 309, 775, 406, 747, 3957, 13, 407, 321, 820, 764, 264, 2316, 365, 264, 9595, 1553, 281, 11, 3993, 337, 13416, 281, 293, 362, 281, 13, 583, 365, 362, 281, 294, 264, 20010, 11, 321, 584, 575, 281, 13, 583, 437, 466, 393, 30, 876, 11, 393, 337, 439, 264, 35883, 13], "avg_logprob": -0.21286057692307692, "compression_ratio": 1.6423841059602649, "no_speech_prob": 0.0, "words": [{"start": 3067.79, "end": 3068.01, "word": " It", "probability": 0.662109375}, {"start": 3068.01, "end": 3068.19, "word": " does", "probability": 0.935546875}, {"start": 3068.19, "end": 3068.37, "word": " not", "probability": 0.953125}, {"start": 3068.37, "end": 3068.61, "word": " take", "probability": 0.890625}, {"start": 3068.61, "end": 3068.89, "word": " to,", "probability": 0.374267578125}, {"start": 3069.43, "end": 3069.89, "word": " it", "probability": 0.91845703125}, {"start": 3069.89, "end": 3070.09, "word": " 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No difference. The difference is just with the full verb have to. Yes. This is the answer and we finish with this exercise. I want you to read aloud. 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Do you have to? If it is he, does he have to? Does she or he have to? Have, not has.", "tokens": [708, 565, 30, 1144, 291, 362, 281, 30, 759, 309, 307, 415, 11, 775, 415, 362, 281, 30, 4402, 750, 420, 415, 362, 281, 30, 3560, 11, 406, 575, 13], "avg_logprob": -0.29032259218154416, "compression_ratio": 1.2467532467532467, "no_speech_prob": 0.0, "words": [{"start": 3151.66, "end": 3152.58, "word": " What", "probability": 0.2403564453125}, {"start": 3152.58, "end": 3153.1, "word": " time?", "probability": 0.78955078125}, {"start": 3153.56, "end": 3154.0, "word": " Do", "probability": 0.74365234375}, {"start": 3154.0, "end": 3154.7, "word": " you", "probability": 0.9736328125}, {"start": 3154.7, "end": 3155.46, "word": " have", "probability": 0.9658203125}, {"start": 3155.46, "end": 3155.82, "word": " to?", "probability": 0.9482421875}, {"start": 3157.0, "end": 3157.5, "word": " If", "probability": 0.75927734375}, {"start": 3157.5, "end": 3157.64, "word": " it", "probability": 0.87939453125}, {"start": 3157.64, "end": 3157.76, "word": " is", "probability": 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In the past, they had to, they didn't have to, I didn't have to for other persons. So here, question with have to, do you have to? Number three, we aren't allowed to wear. It means what? 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We shouldn't. We mustn't. We don't have to. Yes. And if it is he, he can't. She, she can't. I can't. We use can for all the persons. My mother has to.", "tokens": [1144, 437, 291, 528, 13, 492, 4659, 380, 13, 492, 42818, 380, 13, 492, 500, 380, 362, 281, 13, 1079, 13, 400, 498, 309, 307, 415, 11, 415, 393, 380, 13, 1240, 11, 750, 393, 380, 13, 286, 393, 380, 13, 492, 764, 393, 337, 439, 264, 14453, 13, 1222, 2895, 575, 281, 13], "avg_logprob": -0.1467329507524317, "compression_ratio": 1.352, "no_speech_prob": 0.0, "words": [{"start": 3260.97, "end": 3261.35, "word": " Do", "probability": 0.65869140625}, {"start": 3261.35, "end": 3261.99, "word": " what", "probability": 0.9375}, {"start": 3261.99, "end": 3262.35, "word": " you", "probability": 0.96630859375}, {"start": 3262.35, "end": 3262.73, "word": " want.", "probability": 0.8798828125}, {"start": 3262.87, "end": 3263.03, "word": " We", "probability": 0.90673828125}, {"start": 3263.03, "end": 3263.65, "word": " shouldn't.", "probability": 0.93359375}, {"start": 3264.01, "end": 3264.17, "word": " We", "probability": 0.955078125}, {"start": 3264.17, "end": 3264.69, "word": " mustn't.", "probability": 0.957275390625}, {"start": 3265.03, "end": 3265.19, "word": " We", "probability": 0.94189453125}, {"start": 3265.19, "end": 3265.41, "word": " don't", "probability": 0.9794921875}, {"start": 3265.41, "end": 3265.65, "word": " have", "probability": 0.95751953125}, {"start": 3265.65, "end": 3265.89, "word": " to.", "probability": 0.95361328125}, {"start": 3267.11, "end": 3267.55, "word": " Yes.", "probability": 0.5517578125}, {"start": 3268.83, "end": 3269.07, "word": " And", "probability": 0.91357421875}, {"start": 3269.07, "end": 3269.23, "word": " if", "probability": 0.95166015625}, {"start": 3269.23, "end": 3269.37, "word": " it", "probability": 0.9482421875}, {"start": 3269.37, "end": 3269.53, "word": " is", "probability": 0.79638671875}, {"start": 3269.53, "end": 3269.79, "word": " he,", "probability": 0.8369140625}, {"start": 3270.13, "end": 3270.63, "word": " he", "probability": 0.93896484375}, {"start": 3270.63, "end": 3271.07, "word": " can't.", "probability": 0.97412109375}, {"start": 3271.43, "end": 3271.63, "word": " She,", "probability": 0.89794921875}, {"start": 3271.89, "end": 3272.05, "word": " she", "probability": 0.91357421875}, {"start": 3272.05, "end": 3272.43, "word": " can't.", "probability": 0.9755859375}, {"start": 3272.65, "end": 3272.81, "word": " I", "probability": 0.9853515625}, {"start": 3272.81, "end": 3273.23, "word": " can't.", "probability": 0.9755859375}, {"start": 3273.85, "end": 3273.99, "word": " We", "probability": 0.92919921875}, {"start": 3273.99, "end": 3274.27, "word": " use", "probability": 0.837890625}, {"start": 3274.27, "end": 3274.53, "word": " can", "probability": 0.873046875}, {"start": 3274.53, "end": 3274.77, "word": " for", "probability": 0.935546875}, {"start": 3274.77, "end": 3275.01, "word": " all", "probability": 0.849609375}, {"start": 3275.01, "end": 3275.13, "word": " the", "probability": 0.89453125}, {"start": 3275.13, "end": 3275.59, "word": " persons.", "probability": 0.90283203125}, {"start": 3276.37, "end": 3276.69, "word": " My", "probability": 0.9130859375}, {"start": 3276.69, "end": 3278.13, "word": " mother", "probability": 0.82080078125}, {"start": 3278.13, "end": 3278.85, "word": " has", "probability": 0.69775390625}, {"start": 3278.85, "end": 3279.13, "word": " to.", "probability": 0.91943359375}], "temperature": 1.0}, {"id": 116, "seek": 330634, "start": 3282.86, "end": 3306.34, "text": " Don't say halves. No, has. So have plus is, is has. So my mother has to work very hard six days a week. Has to. In the plural, have to. You, you shouldn't smoke.", "tokens": [1468, 380, 584, 38490, 13, 883, 11, 575, 13, 407, 362, 1804, 307, 11, 307, 575, 13, 407, 452, 2895, 575, 281, 589, 588, 1152, 2309, 1708, 257, 1243, 13, 8646, 281, 13, 682, 264, 25377, 11, 362, 281, 13, 509, 11, 291, 4659, 380, 8439, 13], "avg_logprob": -0.2493489614377419, "compression_ratio": 1.296, "no_speech_prob": 0.0, "words": [{"start": 3282.86, "end": 3283.16, "word": " Don't", "probability": 0.853759765625}, {"start": 3283.16, "end": 3283.4, "word": " say", "probability": 0.94140625}, {"start": 3283.4, "end": 3283.98, "word": " halves.", "probability": 0.421630859375}, {"start": 3284.4, "end": 3284.66, "word": " No,", "probability": 0.91015625}, {"start": 3285.5, "end": 3285.98, "word": " has.", "probability": 0.71728515625}, {"start": 3286.32, "end": 3286.72, "word": " So", "probability": 0.935546875}, {"start": 3286.72, "end": 3287.1, "word": " have", "probability": 0.611328125}, {"start": 3287.1, "end": 3287.46, "word": " plus", "probability": 0.89453125}, {"start": 3287.46, "end": 3287.86, "word": " is,", "probability": 0.39892578125}, {"start": 3288.34, "end": 3288.66, "word": " is", "probability": 0.87744140625}, {"start": 3288.66, "end": 3289.38, "word": " has.", "probability": 0.81982421875}, {"start": 3289.76, "end": 3290.12, "word": " So", "probability": 0.95361328125}, {"start": 3290.12, "end": 3290.34, "word": " my", "probability": 0.93505859375}, {"start": 3290.34, "end": 3290.64, "word": " mother", "probability": 0.86669921875}, {"start": 3290.64, "end": 3291.34, "word": " has", "probability": 0.93505859375}, {"start": 3291.34, "end": 3291.62, "word": " to", "probability": 0.97265625}, {"start": 3291.62, "end": 3292.0, "word": " work", "probability": 0.919921875}, {"start": 3292.0, "end": 3292.44, "word": " very", "probability": 0.859375}, {"start": 3292.44, "end": 3293.04, "word": " hard", "probability": 0.888671875}, {"start": 3293.04, "end": 3294.24, "word": " six", "probability": 0.54736328125}, {"start": 3294.24, "end": 3296.38, "word": " days", "probability": 0.92041015625}, {"start": 3296.38, "end": 3296.84, "word": " a", "probability": 0.986328125}, {"start": 3296.84, "end": 3297.3, "word": " week.", "probability": 0.93701171875}, {"start": 3298.08, "end": 3298.48, "word": " Has", "probability": 0.9443359375}, {"start": 3298.48, "end": 3298.78, "word": " to.", "probability": 0.91943359375}, {"start": 3299.72, "end": 3299.88, "word": " In", "probability": 0.607421875}, {"start": 3299.88, "end": 3300.02, "word": " the", "probability": 0.91015625}, {"start": 3300.02, "end": 3300.2, "word": " plural,", "probability": 0.415283203125}, {"start": 3301.08, "end": 3302.46, "word": " have", "probability": 0.912109375}, {"start": 3302.46, "end": 3302.74, "word": " to.", "probability": 0.96044921875}, {"start": 3304.26, "end": 3304.7, "word": " You,", "probability": 0.91552734375}, {"start": 3305.32, "end": 3305.42, "word": " you", "probability": 0.9560546875}, {"start": 3305.42, "end": 3305.92, "word": " shouldn't", "probability": 0.962646484375}, {"start": 3305.92, "end": 3306.34, "word": " smoke.", "probability": 0.88623046875}], "temperature": 1.0}, {"id": 117, "seek": 333033, "start": 3308.29, "end": 3330.33, "text": " It's bad for your health. Shouldn't. Not no should. No, shouldn't. And the last one, passengers must have, must go, must play. So here we don't use to. And Inshallah this is the end of this lecture. Thank you very much.", "tokens": [467, 311, 1578, 337, 428, 1585, 13, 34170, 380, 13, 1726, 572, 820, 13, 883, 11, 4659, 380, 13, 400, 264, 1036, 472, 11, 18436, 1633, 362, 11, 1633, 352, 11, 1633, 862, 13, 407, 510, 321, 500, 380, 764, 281, 13, 400, 682, 2716, 13492, 341, 307, 264, 917, 295, 341, 7991, 13, 1044, 291, 588, 709, 13], "avg_logprob": -0.20533853868643442, "compression_ratio": 1.4379084967320261, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 3308.29, "end": 3308.67, "word": " It's", "probability": 0.6934814453125}, {"start": 3308.67, "end": 3308.99, "word": " bad", "probability": 0.94921875}, {"start": 3308.99, "end": 3309.19, "word": " for", "probability": 0.94873046875}, {"start": 3309.19, "end": 3309.37, "word": " your", "probability": 0.884765625}, {"start": 3309.37, "end": 3309.79, "word": " health.", "probability": 0.90869140625}, {"start": 3310.27, "end": 3310.83, "word": " Shouldn't.", "probability": 0.86376953125}, {"start": 3310.93, "end": 3311.07, "word": " Not", "probability": 0.73876953125}, {"start": 3311.07, "end": 3311.31, "word": " no", "probability": 0.53564453125}, {"start": 3311.31, "end": 3311.63, "word": " should.", "probability": 0.82568359375}, {"start": 3312.27, "end": 3312.55, "word": " No,", "probability": 0.85546875}, {"start": 3312.83, "end": 3314.09, "word": " shouldn't.", "probability": 0.9365234375}, {"start": 3315.01, "end": 3315.51, "word": " And", "probability": 0.8564453125}, {"start": 3315.51, "end": 3315.65, "word": " the", "probability": 0.9130859375}, {"start": 3315.65, "end": 3315.89, "word": " last", "probability": 0.8740234375}, {"start": 3315.89, "end": 3316.19, "word": " one,", "probability": 0.93798828125}, {"start": 3316.53, "end": 3316.87, "word": " passengers", "probability": 0.9072265625}, {"start": 3316.87, "end": 3317.75, "word": " must", "probability": 0.8779296875}, {"start": 3317.75, "end": 3318.45, "word": " have,", "probability": 0.857421875}, {"start": 3318.91, "end": 3319.33, "word": " must", "probability": 0.888671875}, {"start": 3319.33, "end": 3319.89, "word": " go,", "probability": 0.9609375}, {"start": 3320.23, "end": 3320.51, "word": " must", "probability": 0.876953125}, {"start": 3320.51, "end": 3320.99, "word": " play.", "probability": 0.9453125}, {"start": 3321.37, "end": 3321.57, "word": " So", "probability": 0.951171875}, {"start": 3321.57, "end": 3321.95, "word": " here", "probability": 0.7978515625}, {"start": 3321.95, "end": 3322.61, "word": " we", "probability": 0.58251953125}, {"start": 3322.61, "end": 3322.91, "word": " don't", "probability": 0.979736328125}, {"start": 3322.91, "end": 3323.37, "word": " use", "probability": 0.875}, {"start": 3323.37, "end": 3324.17, "word": " to.", "probability": 0.64306640625}, {"start": 3326.25, "end": 3326.93, "word": " And", "probability": 0.92919921875}, {"start": 3326.93, "end": 3327.35, "word": " Inshallah", "probability": 0.6848958333333334}, {"start": 3327.35, "end": 3327.67, "word": " this", "probability": 0.52197265625}, {"start": 3327.67, "end": 3327.89, "word": " is", "probability": 0.94970703125}, {"start": 3327.89, "end": 3328.03, "word": " the", "probability": 0.9248046875}, {"start": 3328.03, "end": 3328.23, "word": " end", "probability": 0.900390625}, {"start": 3328.23, "end": 3328.41, "word": " of", "probability": 0.96826171875}, {"start": 3328.41, "end": 3328.59, "word": " this", "probability": 0.93994140625}, {"start": 3328.59, "end": 3328.93, "word": " lecture.", "probability": 0.94140625}, {"start": 3329.47, "end": 3329.69, "word": " Thank", "probability": 0.8916015625}, {"start": 3329.69, "end": 3329.83, "word": " you", "probability": 0.9609375}, {"start": 3329.83, "end": 3330.03, "word": " very", "probability": 0.8447265625}, {"start": 3330.03, "end": 3330.33, "word": " much.", "probability": 0.9140625}], "temperature": 1.0}], "language": "en", "language_probability": 1.0, "duration": 3331.599, "duration_after_vad": 3137.117499999988}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/AIWnDA4lhlY_raw.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/AIWnDA4lhlY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b494e61cd29c2025c1740f0d4b56eb17d7356fc3
--- /dev/null
+++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/AIWnDA4lhlY_raw.srt
@@ -0,0 +1,2064 @@
+1
+00:00:21,110 --> 00:00:25,090
+Assalamualaikum warahmatullahi wabarakatuh. Today,
+
+2
+00:00:25,230 --> 00:00:28,410
+inshallah, we will continue with the modal verbs
+
+3
+00:00:28,410 --> 00:00:33,230
+of obligations and suggestions.
+
+4
+00:00:36,570 --> 00:00:40,690
+Today, inshallah, we are going to take must,
+
+5
+00:00:41,330 --> 00:00:48,310
+should, and revise have to, can in the positive
+
+6
+00:00:48,310 --> 00:00:49,470
+and in the negative.
+
+7
+00:00:52,360 --> 00:00:58,740
+The first exercise will be about signs. What do
+
+8
+00:00:58,740 --> 00:01:06,160
+these signs mean? Use have to or don't have to. It
+
+9
+00:01:06,160 --> 00:01:14,520
+means obligation or no obligation. And can count.
+
+10
+00:01:15,240 --> 00:01:22,870
+Can count. It means permission, no permission. Or
+
+11
+00:01:22,870 --> 00:01:28,350
+not allowed to. Allowed to. Can and allowed to,
+
+12
+00:01:28,470 --> 00:01:34,810
+the same meaning. So we can use can or allowed to.
+
+13
+00:01:35,410 --> 00:01:42,310
+Or can't, isn't, aren't, I'm not allowed to. The
+
+14
+00:01:42,310 --> 00:01:49,310
+first one. The first one. Smoking. No smoking. No
+
+15
+00:01:49,310 --> 00:01:51,860
+smoking. So,
+
+16
+00:01:54,460 --> 00:02:02,660
+yes, here we can use can't. You can't smoke here.
+
+17
+00:02:03,640 --> 00:02:06,140
+You can't smoke here.
+
+18
+00:02:12,680 --> 00:02:16,120
+Number two, also we can
+
+19
+00:02:19,610 --> 00:02:24,050
+You can't smoke here. And what about here?
+
+20
+00:02:26,770 --> 00:02:38,830
+You can't park here. What about this? You can't
+
+21
+00:02:38,830 --> 00:02:48,090
+drive faster than 50 miles an
+
+22
+00:02:48,090 --> 00:02:54,970
+hour. What about that? Number five. You can't take
+
+23
+00:02:54,970 --> 00:02:56,010
+photographs.
+
+24
+00:03:01,590 --> 00:03:13,070
+What about this? No skateboarding. You can't
+
+25
+00:03:13,070 --> 00:03:14,970
+skateboard.
+
+26
+00:03:16,640 --> 00:03:24,360
+Mm-hmm. You can't skateboard Yes,
+
+27
+00:03:24,520 --> 00:03:30,600
+if you look again, so these are the four Examples
+
+28
+00:03:30,600 --> 00:03:37,000
+of can't Or the fifth example of can't You can't
+
+29
+00:03:37,000 --> 00:03:47,600
+smoke here You can't smoke here You can't Park
+
+30
+00:03:47,600 --> 00:03:53,300
+here. You can park here at weekends. You can.
+
+31
+00:03:57,400 --> 00:04:03,840
+Number four, you can't drive faster than 50 miles
+
+32
+00:04:03,840 --> 00:04:13,900
+per hour. There, number five, you can't take
+
+33
+00:04:13,900 --> 00:04:15,500
+photographs.
+
+34
+00:04:17,730 --> 00:04:24,250
+And number nine, you can't skateboard.
+
+35
+00:04:26,570 --> 00:04:32,410
+So here we can use can't or aren't allowed to. The
+
+36
+00:04:32,410 --> 00:04:36,830
+same meaning. If I want to repeat it again, I can
+
+37
+00:04:36,830 --> 00:04:42,450
+say you aren't allowed to smoke here. You aren't
+
+38
+00:04:42,450 --> 00:04:48,280
+allowed to park here. You aren't allowed to drive
+
+39
+00:04:48,280 --> 00:04:54,520
+faster than 50 miles per hour. You aren't allowed
+
+40
+00:04:54,520 --> 00:04:58,780
+to take photographs. You aren't allowed to
+
+41
+00:04:58,780 --> 00:05:03,600
+skateboard. The same meaning. So we can use count
+
+42
+00:05:03,600 --> 00:05:11,040
+and are allowed to.
+
+43
+00:05:12,280 --> 00:05:18,110
+If it's negative, aren't. aren't allowed to. If
+
+44
+00:05:18,110 --> 00:05:23,190
+it's positive, can and are allowed to. If the
+
+45
+00:05:23,190 --> 00:05:28,250
+subject is singular, we use is. If it's I, we use
+
+46
+00:05:28,250 --> 00:05:33,430
+am. I am allowed to. He is allowed to. They are
+
+47
+00:05:33,430 --> 00:05:37,050
+allowed to. In the negative, I'm not allowed to.
+
+48
+00:05:38,140 --> 00:05:42,300
+He isn't allowed to. They aren't allowed to. You
+
+49
+00:05:42,300 --> 00:05:46,020
+aren't allowed to. So we can use can and can't
+
+50
+00:05:46,020 --> 00:05:51,560
+easier. Yes. Let's go back again.
+
+51
+00:06:05,180 --> 00:06:07,360
+Yes, now complete. Here.
+
+52
+00:06:11,690 --> 00:06:19,870
+Others have to pay 10 pounds or 10 euros. Others
+
+53
+00:06:19,870 --> 00:06:28,510
+have to pay 10 euros. But the children, children
+
+54
+00:06:28,510 --> 00:06:31,950
+don't
+
+55
+00:06:31,950 --> 00:06:40,080
+have to pay anything. So others have to pay have
+
+56
+00:06:40,080 --> 00:06:50,420
+to be but the children don't have to pay anything
+
+57
+00:06:50,420 --> 00:06:56,600
+obligation and no obligation have to obligation
+
+58
+00:06:56,600 --> 00:07:02,540
+don't have to no obligation what about this
+
+59
+00:07:02,540 --> 00:07:04,880
+passport
+
+60
+00:07:08,610 --> 00:07:15,770
+You have to show your passport. You have to show
+
+61
+00:07:15,770 --> 00:07:19,990
+your
+
+62
+00:07:19,990 --> 00:07:20,510
+passport.
+
+63
+00:07:26,350 --> 00:07:37,550
+And here, use by June 16. You have to use. You
+
+64
+00:07:37,550 --> 00:07:44,060
+have to use it before June 16th.
+
+65
+00:07:47,340 --> 00:07:54,320
+And here you have to fasten. You have to fasten
+
+66
+00:07:54,320 --> 00:07:58,600
+seed
+
+67
+00:07:58,600 --> 00:08:06,340
+pills. You have to fasten it. It's necessary. So
+
+68
+00:08:06,340 --> 00:08:11,360
+here Others have to pay 10 euros, but children
+
+69
+00:08:11,360 --> 00:08:15,800
+don't have to pay anything. You have to show your
+
+70
+00:08:15,800 --> 00:08:22,220
+passport. You have to use it before June 16th. You
+
+71
+00:08:22,220 --> 00:08:28,460
+have to fasten your seat belt. Again.
+
+72
+00:08:38,480 --> 00:08:45,740
+Admission adults have to pay 10 euros, but the
+
+73
+00:08:45,740 --> 00:08:51,580
+children don't have to. Here there is obligation
+
+74
+00:08:51,580 --> 00:08:56,740
+and no obligation. Obligation for the adults, no
+
+75
+00:08:56,740 --> 00:09:01,900
+obligation for the children. What about here? You
+
+76
+00:09:01,900 --> 00:09:06,700
+have to fasten your
+
+77
+00:09:06,700 --> 00:09:12,540
+seat belt. It is necessary, obligation. And here,
+
+78
+00:09:12,940 --> 00:09:15,920
+you have to show your passport, obligation.
+
+79
+00:09:19,200 --> 00:09:23,040
+The last one, you have to use it before 16th June
+
+80
+00:09:23,040 --> 00:09:24,580
+or June the 16th.
+
+81
+00:09:27,240 --> 00:09:34,540
+So in this exercise, we revise can and can't. Have
+
+82
+00:09:34,540 --> 00:09:39,440
+to, don't have to. In short, we revise the
+
+83
+00:09:39,440 --> 00:09:45,320
+obligation and no obligation. Obligation and no
+
+84
+00:09:45,320 --> 00:09:50,180
+obligation. Also permission and no permission.
+
+85
+00:09:59,360 --> 00:10:07,450
+Yes, before this, I want you to Work in pairs.
+
+86
+00:10:09,030 --> 00:10:15,210
+Read these to each other. But I want each one to
+
+87
+00:10:15,210 --> 00:10:21,070
+answer aloud. Number one, this sign, what does it
+
+88
+00:10:21,070 --> 00:10:27,290
+mean? Use can or can't, have to or don't have to.
+
+89
+00:10:27,490 --> 00:10:31,410
+This is the answer. Who can read? Yes?
+
+90
+00:10:34,910 --> 00:10:40,770
+You can't smoke here or you are not allowed to
+
+91
+00:10:40,770 --> 00:10:45,750
+smoke here. Yes, the same meaning. You can't smoke
+
+92
+00:10:45,750 --> 00:10:50,050
+here or you are not allowed to smoke here. Number
+
+93
+00:10:50,050 --> 00:10:56,290
+three. Yes. You can't part here. You can't part
+
+94
+00:10:56,290 --> 00:10:58,190
+here at weekend. Yes.
+
+95
+00:11:02,560 --> 00:11:10,220
+Yeah. So here can, can. No permission, but here
+
+96
+00:11:10,220 --> 00:11:18,300
+permission. Yes. Number four. Yeah. Number four.
+
+97
+00:11:19,820 --> 00:11:25,760
+Yes. You can't drive faster or you aren't allowed
+
+98
+00:11:25,760 --> 00:11:31,020
+to drive faster. Faster than 50 miles per hour.
+
+99
+00:11:31,990 --> 00:11:37,230
+Yes, number five. Yes. You can't or aren't allowed
+
+100
+00:11:37,230 --> 00:11:42,490
+to take photographs. Yes, we say can't and aren't.
+
+101
+00:11:43,450 --> 00:11:48,810
+Can't and aren't. You can't take photographs or
+
+102
+00:11:48,810 --> 00:11:53,590
+you aren't allowed to take photographs. Can't and
+
+103
+00:11:53,590 --> 00:12:02,060
+aren't. Again. You can't or aren't allowed Thank
+
+104
+00:12:02,060 --> 00:12:05,220
+you. Number nine. Yes.
+
+105
+00:12:09,300 --> 00:12:18,860
+Fasting. You can't. Yes. Skateboard. Yes. Is it
+
+106
+00:12:18,860 --> 00:12:27,340
+clear? Yes. Now this is about what? Permission? No
+
+107
+00:12:27,340 --> 00:12:32,810
+permission. This one. About what? Obligation? No
+
+108
+00:12:32,810 --> 00:12:39,310
+obligation. Yes, who can read? Yes. I don't have
+
+109
+00:12:39,310 --> 00:12:43,510
+to pay 10 euros, but children don't have to pay
+
+110
+00:12:43,510 --> 00:12:50,070
+anything. Good. Number six. You have to show your
+
+111
+00:12:50,070 --> 00:12:56,090
+passport. And number eight. You have to pass in
+
+112
+00:12:56,090 --> 00:13:01,700
+your seat first. Built. Yes. And the last one,
+
+113
+00:13:01,960 --> 00:13:02,700
+number seven.
+
+114
+00:13:08,680 --> 00:13:14,000
+Yeah, yes. So this is revision about obligation
+
+115
+00:13:14,000 --> 00:13:20,260
+and permission of the last lecture. Today, another
+
+116
+00:13:20,260 --> 00:13:21,960
+exercise, a new one.
+
+117
+00:13:30,360 --> 00:13:37,860
+Yes, we generally use should and ought to, to give
+
+118
+00:13:37,860 --> 00:13:45,160
+the meaning of suggestion or advice. I can say you
+
+119
+00:13:45,160 --> 00:13:49,340
+should come early, you ought to come early. But
+
+120
+00:13:49,340 --> 00:13:56,580
+generally we use I think or I don't think. Instead
+
+121
+00:13:56,580 --> 00:14:00,280
+of saying shouldn't, We say, I don't think.
+
+122
+00:14:00,760 --> 00:14:04,440
+Instead of saying should, I say, I think you
+
+123
+00:14:04,440 --> 00:14:12,300
+should. So when I say, I think, it is better than
+
+124
+00:14:12,300 --> 00:14:19,080
+to use we should or you should. Say, I think. If
+
+125
+00:14:19,080 --> 00:14:27,060
+it is negative, say, I don't think. I don't think.
+
+126
+00:14:28,970 --> 00:14:30,650
+We should.
+
+127
+00:14:33,890 --> 00:14:40,210
+So I think we should look here. Number one, I
+
+128
+00:14:40,210 --> 00:14:45,750
+think we should buy some guide books. Why?
+
+129
+00:14:49,290 --> 00:14:52,870
+They'll give us a lot of information. So this
+
+130
+00:14:52,870 --> 00:14:57,410
+exercise is about grammar and vocabulary. Grammar
+
+131
+00:14:57,410 --> 00:15:02,230
+and vocabulary. The grammar here is giving
+
+132
+00:15:02,230 --> 00:15:07,170
+suggestions with using I think or I don't think.
+
+133
+00:15:08,380 --> 00:15:12,960
+When I say I think, it's bitter, polite. I think
+
+134
+00:15:12,960 --> 00:15:18,300
+we should buy guidebooks. They'll give us a lot of
+
+135
+00:15:18,300 --> 00:15:21,700
+information. Here,
+
+136
+00:15:24,820 --> 00:15:33,360
+I don't think, I don't think we should take plenty
+
+137
+00:15:33,360 --> 00:15:34,520
+of sun cream.
+
+138
+00:15:39,700 --> 00:15:48,180
+Yes. We should take. We should take. So I think we
+
+139
+00:15:48,180 --> 00:15:55,160
+should take plenty of sun cream. Why? It will be
+
+140
+00:15:55,160 --> 00:15:56,600
+hot.
+
+141
+00:15:58,180 --> 00:16:03,000
+It will be really hot. So here should or
+
+142
+00:16:03,000 --> 00:16:08,130
+shouldn't. should. So instead of saying we should,
+
+143
+00:16:08,410 --> 00:16:13,570
+we say I think we should. Why? Because it is more
+
+144
+00:16:13,570 --> 00:16:20,770
+polite. It is formal. It is a good way to give
+
+145
+00:16:20,770 --> 00:16:27,590
+suggestion. So here, pack too many clothes.
+
+146
+00:16:29,990 --> 00:16:33,750
+Shouldn't. But instead of saying shouldn't, We
+
+147
+00:16:33,750 --> 00:16:37,090
+shouldn't. We say, I don't think we should. I
+
+148
+00:16:37,090 --> 00:16:41,270
+don't think we should take too many clothes.
+
+149
+00:16:41,810 --> 00:16:43,610
+Clothes. Why?
+
+150
+00:16:46,790 --> 00:16:51,990
+Our bags
+
+151
+00:16:51,990 --> 00:16:56,270
+will be too heavy to carry. Too heavy that we
+
+152
+00:16:56,270 --> 00:17:01,850
+can't carry it. So heavy that we can't carry it or
+
+153
+00:17:01,850 --> 00:17:09,270
+too heavy to carry. Number four, take anything
+
+154
+00:17:09,270 --> 00:17:15,470
+valuable. I don't think we should take anything
+
+155
+00:17:15,470 --> 00:17:21,910
+valuable. Why? We might lose it. So this is number
+
+156
+00:17:21,910 --> 00:17:30,810
+four. We might lose it. Again, Go to Japan first.
+
+157
+00:17:32,110 --> 00:17:39,410
+I think we should go to Japan first. I think we,
+
+158
+00:17:39,590 --> 00:17:43,070
+or I don't think we, I think we, yes, I think we
+
+159
+00:17:43,070 --> 00:17:45,310
+should go to Japan first.
+
+160
+00:17:48,610 --> 00:17:51,750
+I have some friends there.
+
+161
+00:17:57,320 --> 00:18:01,060
+What about this? Go anywhere dangerous. No. I
+
+162
+00:18:01,060 --> 00:18:07,340
+don't think we should go anywhere dangerous. I
+
+163
+00:18:07,340 --> 00:18:13,120
+don't think we should go anywhere dangerous. It
+
+164
+00:18:13,120 --> 00:18:22,100
+would be really stupid. This number? Six. The last
+
+165
+00:18:22,100 --> 00:18:30,820
+one. Yes. I think we should have some vaccination
+
+166
+00:18:30,820 --> 00:18:39,320
+before traveling. Why? We don't want to get ill.
+
+167
+00:18:40,020 --> 00:18:45,840
+This is number seven. So all these examples of
+
+168
+00:18:45,840 --> 00:18:51,420
+suggestions or advice here we use I think or I
+
+169
+00:18:51,420 --> 00:18:55,180
+don't think. I think we should. I don't think we
+
+170
+00:18:55,180 --> 00:19:02,270
+should. The first one for something needed. The
+
+171
+00:19:02,270 --> 00:19:08,670
+other one is for something we don't need. I want
+
+172
+00:19:08,670 --> 00:19:14,750
+you to work in pairs. Make match A with B, but
+
+173
+00:19:14,750 --> 00:19:20,610
+begin with, I think we should. And here, I don't
+
+174
+00:19:20,610 --> 00:19:25,250
+think we should. Yes, work in pairs. Work in
+
+175
+00:19:25,250 --> 00:19:25,410
+pairs.
+
+176
+00:19:51,490 --> 00:19:52,890
+Thank you.
+
+177
+00:20:20,450 --> 00:20:21,850
+Thank you very much.
+
+178
+00:20:29,730 --> 00:20:34,630
+Yes, that's enough. So what's the difference
+
+179
+00:20:34,630 --> 00:20:45,150
+between should and have to? Should is personal.
+
+180
+00:20:46,630 --> 00:20:49,430
+Have to is impersonal.
+
+181
+00:20:51,790 --> 00:20:57,150
+Have to is impersonal, not from me, from some
+
+182
+00:20:57,150 --> 00:21:00,370
+other things. But if it's from me, I say should.
+
+183
+00:21:02,110 --> 00:21:08,150
+Again, should is mild obligation. Mild obligation.
+
+184
+00:21:08,950 --> 00:21:13,750
+But have to, general obligation. What about have
+
+185
+00:21:13,750 --> 00:21:21,620
+got to? Obligation for now or soon. If the
+
+186
+00:21:21,620 --> 00:21:27,280
+obligation is now or soon, I use have got to. If
+
+187
+00:21:27,280 --> 00:21:35,560
+it is general, I use have to. Yes? If it is
+
+188
+00:21:35,560 --> 00:21:41,900
+personal, I say should. And when there is absence
+
+189
+00:21:41,900 --> 00:21:46,540
+of obligation, absence of obligation, I use
+
+190
+00:21:46,540 --> 00:21:51,520
+shouldn't. Or I don't think we should. Shouldn't
+
+191
+00:21:51,520 --> 00:21:55,740
+or I don't think we should. So which is better to
+
+192
+00:21:55,740 --> 00:21:59,820
+say you should or I think you should. I think we
+
+193
+00:21:59,820 --> 00:22:02,960
+should. You shouldn't or I don't think you should.
+
+194
+00:22:03,160 --> 00:22:07,680
+I don't think you should. I want each of you to
+
+195
+00:22:07,680 --> 00:22:11,400
+read number one. Yes. Number one.
+
+196
+00:22:14,400 --> 00:22:20,940
+Yes. I think we should buy some guide books. They
+
+197
+00:22:20,940 --> 00:22:23,880
+will give us a lot of information. Very good.
+
+198
+00:22:24,480 --> 00:22:31,260
+Number two. I think you should take plenty of sun
+
+199
+00:22:31,260 --> 00:22:38,500
+cream. They will give us a lot of power. It will
+
+200
+00:22:38,500 --> 00:22:43,920
+be really hot. Really hot. Yes. Number three.
+
+201
+00:22:49,270 --> 00:22:49,930
+Clothes.
+
+202
+00:22:54,230 --> 00:22:56,870
+Number four. Yes.
+
+203
+00:23:02,570 --> 00:23:05,930
+We. I don't think we.
+
+204
+00:23:11,790 --> 00:23:13,030
+Yes.
+
+205
+00:23:15,190 --> 00:23:21,980
+Yes. Number four. We might lose it. Uh-huh. We
+
+206
+00:23:21,980 --> 00:23:25,800
+might lose it. Yes. I think we should go to Japan
+
+207
+00:23:25,800 --> 00:23:34,080
+first. I have some friends there. Number six. I
+
+208
+00:23:34,080 --> 00:23:42,220
+don't think we should. I don't think we should go
+
+209
+00:23:42,220 --> 00:23:43,500
+anywhere dangerous.
+
+210
+00:23:47,830 --> 00:23:58,130
+And the last one. We don't
+
+211
+00:23:58,130 --> 00:24:07,090
+want to get ill. So this is the
+
+212
+00:24:07,090 --> 00:24:14,510
+answer. Again, this is the answer. Also, I want
+
+213
+00:24:14,510 --> 00:24:17,210
+someone to read again. Yes.
+
+214
+00:24:22,910 --> 00:24:27,450
+Number two. I think we should take plenty of sun
+
+215
+00:24:27,450 --> 00:24:34,090
+cream. It will be really hot. Three. I don't think
+
+216
+00:24:34,090 --> 00:24:42,970
+we should pack too many clothes. Our days will be
+
+217
+00:24:42,970 --> 00:24:48,630
+too hectic to time. Four. I don't think we should
+
+218
+00:24:48,630 --> 00:24:53,790
+take anything valuable. Mm-hmm and number five.
+
+219
+00:24:53,830 --> 00:25:00,570
+Yes Six
+
+220
+00:25:00,570 --> 00:25:05,890
+Yes And
+
+221
+00:25:05,890 --> 00:25:16,010
+the last one Yes Very
+
+222
+00:25:16,010 --> 00:25:22,460
+good. So this is an exercise about suggestion we
+
+223
+00:25:22,460 --> 00:25:28,960
+use, I think we should or I don't think we should.
+
+224
+00:25:29,440 --> 00:25:33,240
+If there's something good, I think we should. If
+
+225
+00:25:33,240 --> 00:25:35,640
+there's something bad, I don't think we should.
+
+226
+00:25:36,620 --> 00:25:41,800
+Yes. What kind of obligation is it? It is mild. It
+
+227
+00:25:41,800 --> 00:25:46,980
+is mild, not strong. Not strong. We have mild and
+
+228
+00:25:46,980 --> 00:25:51,460
+strong. Now, we want to take strong obligation
+
+229
+00:25:51,460 --> 00:26:00,240
+strong by using must by using must or mustn't
+
+230
+00:26:00,240 --> 00:26:06,540
+obligation no obligation so here work with a
+
+231
+00:26:06,540 --> 00:26:10,820
+partner make similar conversations between Anthony
+
+232
+00:26:10,820 --> 00:26:16,390
+and his grandmother grandmother restrict Yes. Use
+
+233
+00:26:16,390 --> 00:26:21,090
+the promise and must or mustn't. Why here we use
+
+234
+00:26:21,090 --> 00:26:27,030
+must and mustn't? Because the grandmother is
+
+235
+00:26:27,030 --> 00:26:32,390
+speaking to the boy and she is anxious. She's
+
+236
+00:26:32,390 --> 00:26:36,370
+anxious about him. She loves him a lot and he
+
+237
+00:26:36,370 --> 00:26:41,300
+wanted to travel. So Don't make, make something.
+
+238
+00:26:41,520 --> 00:26:46,060
+Do this, don't do this. But this is rules. This is
+
+239
+00:26:46,060 --> 00:26:49,800
+imperative. Instead of saying, do it, we say, you
+
+240
+00:26:49,800 --> 00:26:55,560
+must do it. Don't do it, you mustn't do it. Yes.
+
+241
+00:26:56,600 --> 00:27:00,700
+So grandmother, you must try to ask every week.
+
+242
+00:27:02,840 --> 00:27:08,280
+Yes, I will. He can't say, but yes, I will. No, I
+
+243
+00:27:08,280 --> 00:27:12,900
+won't. Yes, I will. Yes, grandmother. I will. No,
+
+244
+00:27:12,980 --> 00:27:16,400
+I won't. Yes. Grandmother, you mustn't lose your
+
+245
+00:27:16,400 --> 00:27:22,780
+passport. Anthony, no, I won't. No, I won't. Yes.
+
+246
+00:27:23,140 --> 00:27:26,380
+So this example, A, B.
+
+247
+00:27:29,760 --> 00:27:36,520
+Yes. Another one, two, three, four, five, six,
+
+248
+00:27:36,700 --> 00:27:42,800
+seven, eight. I want the grandmother to say these
+
+249
+00:27:42,800 --> 00:27:48,200
+things. And the answer is yes, I will. No, I
+
+250
+00:27:48,200 --> 00:27:53,640
+won't. Okay. Okay. Yes. So here, look after your
+
+251
+00:27:53,640 --> 00:28:00,180
+money. You must look after your money. Yes, I
+
+252
+00:28:00,180 --> 00:28:05,670
+will. You must. Look after your money. Yes, I
+
+253
+00:28:05,670 --> 00:28:11,490
+will. You mustn't talk to strangers. No, I won't.
+
+254
+00:28:14,010 --> 00:28:20,890
+You mustn't go out when it's dark. You mustn't
+
+255
+00:28:20,890 --> 00:28:22,310
+drink too much beer.
+
+256
+00:28:24,990 --> 00:28:32,820
+You must make sure you eat well. You must have a
+
+257
+00:28:32,820 --> 00:28:39,360
+path regularly. You must phone us if you are in
+
+258
+00:28:39,360 --> 00:28:45,100
+trouble. You mustn't go anywhere that's dangerous.
+
+259
+00:28:45,840 --> 00:28:48,500
+So this is the conversation between the
+
+260
+00:28:48,500 --> 00:28:51,900
+grandmother and Anthony. So here again,
+
+261
+00:28:53,980 --> 00:28:58,940
+grandmother
+
+262
+00:29:00,980 --> 00:29:08,760
+Grandmother and Anthony. Grandmother and Anthony.
+
+263
+00:29:10,100 --> 00:29:16,500
+Yes, I want someone to read. Yes. Yes. Strong
+
+264
+00:29:16,500 --> 00:29:23,120
+obligation. Without smiling. No. You must look
+
+265
+00:29:23,120 --> 00:29:30,120
+after your money. Someone else. Someone else. Yes.
+
+266
+00:29:30,120 --> 00:29:35,120
+No, no. You must look after your money. Yes. I
+
+267
+00:29:35,120 --> 00:29:40,820
+will. Yes, grandmother. Grandma. I will. Yes, two.
+
+268
+00:29:41,180 --> 00:29:48,340
+Another two. Yes, two. Talk to strangers.
+
+269
+00:29:49,240 --> 00:29:56,120
+No, I won't. No, grandma. I won't. The same. Yes.
+
+270
+00:30:05,240 --> 00:30:14,080
+No grandma I want. No I want. Yes. Yeah. You
+
+271
+00:30:14,080 --> 00:30:17,760
+mustn't drink too much beer. No grandma I want.
+
+272
+00:30:19,340 --> 00:30:19,500
+Yes.
+
+273
+00:30:23,620 --> 00:30:26,700
+You must make sure you eat well.
+
+274
+00:30:41,150 --> 00:30:43,230
+And here.
+
+275
+00:30:51,570 --> 00:30:58,110
+And the last one. Last one. You must study hard.
+
+276
+00:31:00,330 --> 00:31:01,970
+Yes teacher.
+
+277
+00:31:04,170 --> 00:31:05,930
+You must come early.
+
+278
+00:31:09,110 --> 00:31:11,770
+You must study hard for the midterm exam.
+
+279
+00:31:14,430 --> 00:31:20,510
+Yes, that's enough. So when I say must, it means
+
+280
+00:31:20,510 --> 00:31:26,050
+strong obligation. When I say should, it is mild
+
+281
+00:31:26,050 --> 00:31:32,230
+obligation, suggestion or advice. So we have must
+
+282
+00:31:32,230 --> 00:31:37,550
+and should. And if I use have to, it is general
+
+283
+00:31:37,550 --> 00:31:43,890
+but non-personal. Non-personal. Not from me. But
+
+284
+00:31:43,890 --> 00:31:50,230
+from me, I say must. Must or should. But if it is
+
+285
+00:31:50,230 --> 00:31:56,170
+not from me, I say have to. If it is now, just now
+
+286
+00:31:56,170 --> 00:32:02,030
+or soon, have got to. So what's the difference
+
+287
+00:32:02,030 --> 00:32:08,690
+between should and must? Must is strong, strong
+
+288
+00:32:08,690 --> 00:32:14,250
+obligation, but should is mild. Yes, mild
+
+289
+00:32:14,250 --> 00:32:22,110
+obligation. Yes, so again should is personal, have
+
+290
+00:32:22,110 --> 00:32:25,310
+to is impersonal and general.
+
+291
+00:32:28,400 --> 00:32:33,920
+Again, this exercise about mild obligation or
+
+292
+00:32:33,920 --> 00:32:35,460
+about suggestions.
+
+293
+00:32:37,960 --> 00:32:42,620
+The same like that one, page 33. Make suggestions
+
+294
+00:32:42,620 --> 00:32:49,320
+as before. Use I think, I don't think. I think or
+
+295
+00:32:49,320 --> 00:32:53,440
+I don't think and should so I don't want you to
+
+296
+00:32:53,440 --> 00:32:58,540
+use shouldn't no say I don't think you should I
+
+297
+00:32:58,540 --> 00:33:02,720
+don't think he should I don't think she should
+
+298
+00:33:02,720 --> 00:33:07,960
+this is if we are speaking about shouldn't but if
+
+299
+00:33:07,960 --> 00:33:11,740
+I'm saying should no say I think you should I
+
+300
+00:33:11,740 --> 00:33:14,540
+think we should I think he should etc
+
+301
+00:33:18,840 --> 00:33:23,540
+The first one, Peter's got the flu. He's ill. He
+
+302
+00:33:23,540 --> 00:33:28,120
+is ill. So use either I think or I don't think. I
+
+303
+00:33:28,120 --> 00:33:37,080
+think he should go to bed. So I think he should go
+
+304
+00:33:37,080 --> 00:33:44,820
+to bed. Go to bed. Or I don't think he should go
+
+305
+00:33:44,820 --> 00:33:52,160
+to work. Here, go to bed, don't go to work. Go to
+
+306
+00:33:52,160 --> 00:33:55,520
+bed, don't go to work. But I don't want
+
+307
+00:33:55,520 --> 00:34:01,640
+imperative. I want suggestion. If I say go, don't
+
+308
+00:34:01,640 --> 00:34:05,560
+go, it's okay. But it is imperative. No, I want it
+
+309
+00:34:05,560 --> 00:34:11,200
+to be mild. So I want it to make suggestions, not
+
+310
+00:34:11,200 --> 00:34:18,040
+orders. Not orders. Not imperative. Directly. No.
+
+311
+00:34:18,640 --> 00:34:23,260
+Indirectly. So, I think he should go to bed. Good.
+
+312
+00:34:23,680 --> 00:34:27,040
+Politely. I don't think he should go to work.
+
+313
+00:34:27,920 --> 00:34:33,200
+Number two. I have lost my cheat book and credit
+
+314
+00:34:33,200 --> 00:34:41,060
+cards. Give him advice. Advice or suggestions. Use
+
+315
+00:34:41,060 --> 00:34:46,250
+I think or I don't think. Yes? I think he should
+
+316
+00:34:46,250 --> 00:34:50,130
+go to the bank. I think he should go to the bank.
+
+317
+00:34:52,230 --> 00:35:00,830
+Also, yeah, I think he should stop the cheat
+
+318
+00:35:00,830 --> 00:35:06,350
+books. I think he should stop the cheat books. I
+
+319
+00:35:06,350 --> 00:35:10,670
+think he should go to the bank. You understand?
+
+320
+00:35:11,470 --> 00:35:17,020
+Yes. Number two. Number three. Tony got his
+
+321
+00:35:17,020 --> 00:35:20,680
+driving license last week and now he wants to
+
+322
+00:35:20,680 --> 00:35:26,240
+drive from London to Edinburgh. Oh, just now. I
+
+323
+00:35:26,240 --> 00:35:28,400
+think now he should drive.
+
+324
+00:35:36,140 --> 00:35:41,060
+Should drive? No, shouldn't drive. I don't think
+
+325
+00:35:41,060 --> 00:35:46,180
+he should drive. So here, no, not good. Again,
+
+326
+00:35:46,340 --> 00:35:49,800
+yes. I don't think he should drive.
+
+327
+00:35:52,720 --> 00:35:56,980
+Yes, he should fly. I think he should fly. It
+
+328
+00:35:56,980 --> 00:36:01,760
+means go by plane. Because he's a new driver.
+
+329
+00:36:05,350 --> 00:36:08,550
+My teenage daughter doesn't get out of bed until
+
+330
+00:36:08,550 --> 00:36:14,070
+noon. She sleeps all day long. Yes?
+
+331
+00:36:17,150 --> 00:36:21,690
+Advise me, give suggestions. I think you should
+
+332
+00:36:21,690 --> 00:36:30,530
+buy her an alarm clock. I think you should buy her
+
+333
+00:36:30,530 --> 00:36:38,600
+an alarm clock. Yeah. I never have any money. I
+
+334
+00:36:38,600 --> 00:36:44,080
+don't have any money. Give advice, give
+
+335
+00:36:44,080 --> 00:36:44,800
+suggestions.
+
+336
+00:36:47,280 --> 00:36:53,300
+I don't think, I don't think, I think you should
+
+337
+00:36:53,300 --> 00:36:59,300
+find a job. I don't think you should buy too many
+
+338
+00:36:59,300 --> 00:37:03,860
+clothes. too many clothes yes I think you should
+
+339
+00:37:03,860 --> 00:37:11,080
+have a job a new job yes so any answer is correct
+
+340
+00:37:11,080 --> 00:37:16,720
+give advice give suggestions by using I think or I
+
+341
+00:37:16,720 --> 00:37:21,560
+don't think here Jane and Paul are only 16 but
+
+342
+00:37:21,560 --> 00:37:27,200
+they want to get married 16 16 and they want to
+
+343
+00:37:27,200 --> 00:37:37,660
+get married I think they
+
+344
+00:37:37,660 --> 00:37:46,380
+should wait
+
+345
+00:37:46,380 --> 00:37:55,760
+a few years, two or three years, not 16. Yeah. I'm
+
+346
+00:37:55,760 --> 00:37:59,160
+really fed up with my job. I'm really fed up with
+
+347
+00:37:59,160 --> 00:38:07,840
+my job. I think you should find a new job. Yes?
+
+348
+00:38:08,340 --> 00:38:11,900
+Yes, because you are fed up with your job, so you
+
+349
+00:38:11,900 --> 00:38:14,760
+should change it. You should find some job else.
+
+350
+00:38:15,780 --> 00:38:19,600
+My grandparents complained they don't go out
+
+351
+00:38:19,600 --> 00:38:28,510
+enough. They don't go out enough. So I think they
+
+352
+00:38:28,510 --> 00:38:37,110
+should go out. Yes, but they complain. I think
+
+353
+00:38:37,110 --> 00:38:43,590
+they should join a club. I think they should join
+
+354
+00:38:43,590 --> 00:38:50,610
+a club. Again. So any answer is correct. Look
+
+355
+00:38:50,610 --> 00:38:50,870
+here.
+
+356
+00:39:00,800 --> 00:39:05,680
+Who can read the answers of this exercise or any
+
+357
+00:39:05,680 --> 00:39:09,680
+other answer? This is a suggested answer. Yes,
+
+358
+00:39:09,760 --> 00:39:13,560
+number two. I think you should follow the back and
+
+359
+00:39:13,560 --> 00:39:20,580
+stop your chicks. Two, three. I don't think he
+
+360
+00:39:20,580 --> 00:39:26,680
+should drive. I think he should fly. Either this
+
+361
+00:39:26,680 --> 00:39:30,230
+or this or both of them. These are two
+
+362
+00:39:30,230 --> 00:39:34,970
+suggestions, yes? With I don't think and with I
+
+363
+00:39:34,970 --> 00:39:41,430
+think. One is enough. Yes. Thank you. Number four.
+
+364
+00:39:44,690 --> 00:39:48,730
+Yes, reading. Number four, I think you should buy
+
+365
+00:39:48,730 --> 00:39:52,630
+here an arm clock. Number five, I don't think you
+
+366
+00:39:52,630 --> 00:39:56,130
+should buy so many new clothes. I think you should
+
+367
+00:39:56,130 --> 00:39:59,710
+get a job. So here too, I don't think they, I
+
+368
+00:39:59,710 --> 00:40:03,110
+think you, et cetera. Number six. Number six, I
+
+369
+00:40:03,110 --> 00:40:06,510
+don't think they should wait a few years. Number
+
+370
+00:40:06,510 --> 00:40:10,610
+seven, I think you should try to find one you
+
+371
+00:40:10,610 --> 00:40:13,270
+like. Number eight, I think they should join a
+
+372
+00:40:13,270 --> 00:40:19,650
+club. Again, working birds, working birds. Look at
+
+373
+00:40:19,650 --> 00:40:25,190
+the question and of the answer. Yes, working
+
+374
+00:40:25,190 --> 00:40:25,490
+birds.
+
+375
+00:40:28,290 --> 00:40:29,630
+The exercise and the answer.
+
+376
+00:40:43,850 --> 00:40:49,750
+Now look at the grammar spot. Look at the
+
+377
+00:40:49,750 --> 00:40:54,390
+sentences below. We should take traveler's cheeks.
+
+378
+00:40:55,950 --> 00:41:00,730
+You must look after your money. The first
+
+379
+00:41:00,730 --> 00:41:04,530
+question. Which sentence expresses strong
+
+380
+00:41:04,530 --> 00:41:10,450
+obligation? You must. Yes. So here must fall
+
+381
+00:41:10,450 --> 00:41:16,110
+strong obligation. You understand? Now, which
+
+382
+00:41:16,110 --> 00:41:22,590
+sentence expresses a suggestion? Should. So here
+
+383
+00:41:22,590 --> 00:41:28,210
+with suggestion. So this is strong and this is
+
+384
+00:41:28,210 --> 00:41:34,210
+mild. What type of verbs are should and must?
+
+385
+00:41:35,210 --> 00:41:40,610
+Should and must are modal verbs. They are modal
+
+386
+00:41:40,610 --> 00:41:41,210
+verbs.
+
+387
+00:41:44,590 --> 00:41:51,830
+Modal verbs. Also take care that should means
+
+388
+00:41:51,830 --> 00:42:02,520
+ought to. should means ought to should means
+
+389
+00:42:02,520 --> 00:42:08,760
+ought to the
+
+390
+00:42:08,760 --> 00:42:15,280
+same use now
+
+391
+00:42:15,280 --> 00:42:16,920
+let's go to the last exercise
+
+392
+00:42:25,740 --> 00:42:30,040
+Correct these sentences. This exercise is about
+
+393
+00:42:30,040 --> 00:42:37,280
+the modal verbs. Permission, no permission.
+
+394
+00:42:38,440 --> 00:42:43,980
+Obligation, no obligation. Strong obligation, mild
+
+395
+00:42:43,980 --> 00:42:49,980
+obligation, suggestion, advice. General exercise.
+
+396
+00:42:51,340 --> 00:42:55,460
+Check it. Correct these sentences. Do you can?
+
+397
+00:42:58,300 --> 00:43:04,800
+This is wrong. Why? Because can is an auxiliary
+
+398
+00:43:04,800 --> 00:43:10,680
+verb. It should, we should begin it in the, in the
+
+399
+00:43:10,680 --> 00:43:15,000
+questions. Yes, no questions. We should use the
+
+400
+00:43:15,000 --> 00:43:20,130
+auxiliary verbs. Am is are was were and? Should?
+
+401
+00:43:20,410 --> 00:43:25,010
+Can? Yes, all the models, the same. So here, we
+
+402
+00:43:25,010 --> 00:43:30,130
+can't use do. No, we can use can. So can you help
+
+403
+00:43:30,130 --> 00:43:33,370
+me? Why? Because it is something like is, like
+
+404
+00:43:33,370 --> 00:43:39,250
+was. But we don't use do. Why? Because do is for
+
+405
+00:43:39,250 --> 00:43:44,310
+the full verb. No, this is a granular verb. So the
+
+406
+00:43:44,310 --> 00:43:48,350
+question is, can you
+
+407
+00:43:49,480 --> 00:43:50,720
+Help me.
+
+408
+00:43:53,500 --> 00:44:00,580
+Number two. What time have you two start work?
+
+409
+00:44:02,160 --> 00:44:09,880
+Have to is not an auxiliary. It is a full verb. It
+
+410
+00:44:09,880 --> 00:44:14,920
+is a full verb. So when it is a full verb, I can
+
+411
+00:44:14,920 --> 00:44:25,020
+use do, does, did. Yes. So we don't say have. Do
+
+412
+00:44:25,020 --> 00:44:28,440
+you
+
+413
+00:44:28,440 --> 00:44:36,680
+have to? So what time do you have to start work?
+
+414
+00:44:37,960 --> 00:44:43,480
+Why? Because this is a full verb. Because it is a
+
+415
+00:44:43,480 --> 00:44:49,490
+full verb, I can use do. If it is has to, I use
+
+416
+00:44:49,490 --> 00:44:57,170
+does if it is had to I use dead if it is will have
+
+417
+00:44:57,170 --> 00:45:05,110
+to will so in the present have to has to do does
+
+418
+00:45:05,110 --> 00:45:12,230
+in the past had to did in the future will have to
+
+419
+00:45:12,230 --> 00:45:17,740
+the question is with Will. So, what time do you
+
+420
+00:45:17,740 --> 00:45:22,720
+have to? What time does she have to? What time
+
+421
+00:45:22,720 --> 00:45:28,000
+will you have to? You understand? We can use will,
+
+422
+00:45:28,400 --> 00:45:37,960
+do, or does, or will, or did. What time did you
+
+423
+00:45:37,960 --> 00:45:42,990
+have to? Present, past, and the future. You
+
+424
+00:45:42,990 --> 00:45:47,470
+understand? So this is a full verb. With a full
+
+425
+00:45:47,470 --> 00:45:50,850
+verb, I use auxiliary, do, does, did. And in the
+
+426
+00:45:50,850 --> 00:45:57,590
+future, we use will. Is it clear? Yes. Number
+
+427
+00:45:57,590 --> 00:46:03,090
+three. We are not allowed to wear jeans at school.
+
+428
+00:46:04,170 --> 00:46:13,340
+No. No negate nouns. But we want to negate Verbs.
+
+429
+00:46:15,820 --> 00:46:21,600
+And with allowed to, we use be. It means am, is,
+
+430
+00:46:21,760 --> 00:46:32,600
+are, was, where. So here am is are. Am is are and
+
+431
+00:46:32,600 --> 00:46:41,540
+not. Not no. So am not isn't. aren't. So here we
+
+432
+00:46:41,540 --> 00:46:46,820
+are, we aren't, we aren't allowed. We aren't
+
+433
+00:46:46,820 --> 00:46:50,920
+allowed because the negative of are is aren't, is,
+
+434
+00:46:51,260 --> 00:47:00,540
+isn't, am, am not. And we use be allowed to. It,
+
+435
+00:47:00,740 --> 00:47:07,420
+it gives the meaning of can't. Yes. So here the
+
+436
+00:47:07,420 --> 00:47:15,200
+answer is we Aunt allowed to wear jeans at school.
+
+437
+00:47:16,360 --> 00:47:20,160
+Negative. The negative is with aunt, not with no.
+
+438
+00:47:21,820 --> 00:47:28,180
+Look at number five, number four. We know can. Can
+
+439
+00:47:28,180 --> 00:47:34,100
+is an auxiliary. Isn't, aren't, am not, wouldn't,
+
+440
+00:47:34,660 --> 00:47:44,150
+won't, can't, shouldn't, Mustn't. So here, can't.
+
+441
+00:47:46,070 --> 00:47:50,050
+Why? Because we are stuck not with it to make
+
+442
+00:47:50,050 --> 00:47:50,410
+negative.
+
+443
+00:47:55,530 --> 00:48:03,750
+My mother have, have, have to. No, has. Yes. So we
+
+444
+00:48:03,750 --> 00:48:10,010
+say has to. Why? The singular has to. The plural
+
+445
+00:48:10,010 --> 00:48:16,910
+have to. With I have to. But in the past, all the
+
+446
+00:48:16,910 --> 00:48:21,130
+pronouns had to. In the future, all the pronouns
+
+447
+00:48:21,130 --> 00:48:28,160
+will have to. In the singular, has to has to
+
+448
+00:48:28,160 --> 00:48:34,240
+plural have to with I have to the singular first
+
+449
+00:48:34,240 --> 00:48:38,180
+person have to the singular third person has to
+
+450
+00:48:38,180 --> 00:48:44,280
+and the negative is doesn't have to doesn't have
+
+451
+00:48:44,280 --> 00:48:50,580
+to so here positive We can't say have to, we say
+
+452
+00:48:50,580 --> 00:48:55,260
+has to. So my mother has to work very hard six
+
+453
+00:48:55,260 --> 00:49:01,420
+days a week. Number six, you not should, you
+
+454
+00:49:01,420 --> 00:49:08,980
+shouldn't.
+
+455
+00:49:09,080 --> 00:49:15,810
+So again, we say can't, shouldn't. mustn't, isn't,
+
+456
+00:49:16,330 --> 00:49:22,650
+aren't, etc. But we can't say not are, not is. No
+
+457
+00:49:22,650 --> 00:49:28,250
+is no, isn't. You understand? No is the negative
+
+458
+00:49:28,250 --> 00:49:32,590
+for the nouns. But not is the negative for the
+
+459
+00:49:32,590 --> 00:49:40,490
+verb. Here passengers must to have a ticket, must
+
+460
+00:49:40,490 --> 00:49:50,910
+to know, must And all the modal verbs do not take
+
+461
+00:49:50,910 --> 00:49:58,350
+to. So we say must have without
+
+462
+00:49:58,350 --> 00:50:04,810
+to. We use to just with ought to. Ought to and
+
+463
+00:50:04,810 --> 00:50:09,550
+have to. But have to is not a modal. It is have to
+
+464
+00:50:09,550 --> 00:50:12,870
+and we use ought to. So what's the negative of
+
+465
+00:50:12,870 --> 00:50:20,190
+ought to? Otent two. Yes. The negative of Ot two
+
+466
+00:50:20,190 --> 00:50:23,270
+is
+
+467
+00:50:23,270 --> 00:50:26,930
+Otent two.
+
+468
+00:50:29,270 --> 00:50:34,930
+Can we use two after the models? No. Can play. We
+
+469
+00:50:34,930 --> 00:50:40,530
+can't say can't play. Can play. Must play. Should
+
+470
+00:50:40,530 --> 00:50:50,160
+play. So don't use two. Also, can we use S? No. We
+
+471
+00:50:50,160 --> 00:50:54,600
+can use S with the model. We can't say musts,
+
+472
+00:50:54,960 --> 00:51:02,980
+cans. No. No S. No IG. I love canning. I love
+
+473
+00:51:02,980 --> 00:51:08,610
+shooting. No, no, no, no IG form. It does not take
+
+474
+00:51:08,610 --> 00:51:14,890
+to, it does not take s, it does not take ing. So
+
+475
+00:51:14,890 --> 00:51:20,010
+we should use the model with the verb without to,
+
+476
+00:51:20,530 --> 00:51:27,430
+except for ought to and have to. But with have to
+
+477
+00:51:27,430 --> 00:51:30,770
+in the singular, we say has to. But what about
+
+478
+00:51:30,770 --> 00:51:36,770
+can? Oh, can for all the pronouns. should for all
+
+479
+00:51:36,770 --> 00:51:39,630
+the pronouns. No difference. The difference is
+
+480
+00:51:39,630 --> 00:51:44,850
+just with the full verb have to. Yes.
+
+481
+00:51:48,830 --> 00:51:51,870
+This is the answer and we finish with this
+
+482
+00:51:51,870 --> 00:51:57,770
+exercise. I want you to read aloud.
+
+483
+00:52:00,150 --> 00:52:05,820
+So these are correct sentences. Number one. Yes.
+
+484
+00:52:07,420 --> 00:52:15,020
+Can you help me? Can you help me? It is a, an
+
+485
+00:52:15,020 --> 00:52:18,780
+auxiliary verb. We begin with an auxiliary verb to
+
+486
+00:52:18,780 --> 00:52:23,460
+make yes, no question. The answer is yes, I can or
+
+487
+00:52:23,460 --> 00:52:26,180
+no, I can't. Yes. Number two.
+
+488
+00:52:31,660 --> 00:52:38,020
+What time? Do you have to? If it is he,
+
+489
+00:52:41,680 --> 00:52:47,740
+does he have to?
+
+490
+00:52:48,920 --> 00:52:54,960
+Does she or
+
+491
+00:52:54,960 --> 00:53:02,510
+he have to? Have, not has. but in the positive has
+
+492
+00:53:02,510 --> 00:53:08,530
+to in the negative has in the negative don't have
+
+493
+00:53:08,530 --> 00:53:15,250
+to in the question does he have to he doesn't have
+
+494
+00:53:15,250 --> 00:53:23,330
+to again do you have to does does he have to in
+
+495
+00:53:23,330 --> 00:53:29,630
+the negative he He doesn't have to, they don't
+
+496
+00:53:29,630 --> 00:53:34,930
+have to. In the past, they had to, they didn't
+
+497
+00:53:34,930 --> 00:53:40,110
+have to, I didn't have to for other persons. So
+
+498
+00:53:40,110 --> 00:53:45,870
+here, question with have to, do you have to?
+
+499
+00:53:46,530 --> 00:53:50,990
+Number three, we aren't allowed to wear. It means
+
+500
+00:53:50,990 --> 00:53:55,740
+what? It means we can't. We can't, but without
+
+501
+00:53:55,740 --> 00:54:02,500
+too. We can't, it means can't. We can't wear jeans
+
+502
+00:54:02,500 --> 00:54:07,140
+at school. So the negative is aren't, not not or
+
+503
+00:54:07,140 --> 00:54:11,560
+no, no aren't. Yes, not with the helping verb.
+
+504
+00:54:13,160 --> 00:54:19,280
+Number four, we can't. Not no can. No, we can't.
+
+505
+00:54:20,970 --> 00:54:25,190
+Do what you want. We shouldn't. We mustn't. We
+
+506
+00:54:25,190 --> 00:54:31,070
+don't have to. Yes. And if it is he, he can't.
+
+507
+00:54:31,430 --> 00:54:35,130
+She, she can't. I can't. We use can for all the
+
+508
+00:54:35,130 --> 00:54:39,130
+persons. My mother has to.
+
+509
+00:54:42,860 --> 00:54:48,660
+Don't say halves. No, has. So have plus is, is
+
+510
+00:54:48,660 --> 00:54:56,840
+has. So my mother has to work very hard six days a
+
+511
+00:54:56,840 --> 00:55:05,420
+week. Has to. In the plural, have to. You, you
+
+512
+00:55:05,420 --> 00:55:09,790
+shouldn't smoke. It's bad for your health.
+
+513
+00:55:10,270 --> 00:55:15,650
+Shouldn't. Not no should. No, shouldn't. And the
+
+514
+00:55:15,650 --> 00:55:20,510
+last one, passengers must have, must go, must
+
+515
+00:55:20,510 --> 00:55:27,670
+play. So here we don't use to. And Inshallah this
+
+516
+00:55:27,670 --> 00:55:30,330
+is the end of this lecture. Thank you very much.
+
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/AoovNUk16ew_raw.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/AoovNUk16ew_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..04503801b8d0873ea6bdd9aca7cc96481d67a26d
--- /dev/null
+++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/AoovNUk16ew_raw.srt
@@ -0,0 +1,1684 @@
+1
+00:00:20,750 --> 00:00:25,730
+Assalamualaikum warahmatullahi wabarakatuh Today
+
+2
+00:00:25,730 --> 00:00:29,670
+inshallah, we are going to study the modal verbs
+
+3
+00:00:29,670 --> 00:00:39,250
+The modal verbs Has about three units in this book
+
+4
+00:00:39,250 --> 00:00:47,710
+today part one it is modal verbs obligation and
+
+5
+00:00:47,710 --> 00:00:55,310
+permission The first part obligation and
+
+6
+00:00:55,310 --> 00:01:08,110
+permission when I say obligation It means must Or
+
+7
+00:01:08,110 --> 00:01:14,130
+should Or
+
+8
+00:01:14,130 --> 00:01:27,490
+have to have to Yes. Also, we can say, have got
+
+9
+00:01:27,490 --> 00:01:28,810
+to.
+
+10
+00:01:31,030 --> 00:01:41,350
+So these four verbs are about obligation. And what
+
+11
+00:01:41,350 --> 00:01:44,330
+about permission? Permission, we have can,
+
+12
+00:01:47,170 --> 00:01:55,830
+and be allowed
+
+13
+00:01:55,830 --> 00:01:59,290
+to.
+
+14
+00:02:01,690 --> 00:02:08,450
+In fact, modal verbs are so many and each one has
+
+15
+00:02:08,450 --> 00:02:16,050
+at least two meanings. So we usually express
+
+16
+00:02:17,750 --> 00:02:22,750
+The modal verbs to give extra meaning, some new
+
+17
+00:02:22,750 --> 00:02:30,070
+meaning. They are auxiliaries. And they can be
+
+18
+00:02:30,070 --> 00:02:37,350
+used in positive, negative, questions, and short
+
+19
+00:02:37,350 --> 00:02:44,190
+answers. Positive, negative, questions, and short
+
+20
+00:02:44,190 --> 00:02:44,610
+answers.
+
+21
+00:02:47,940 --> 00:02:54,540
+Yes, these are the two bases of this lecture I'm
+
+22
+00:02:54,540 --> 00:03:02,340
+sorry, but I have to go now Now page 30 Test your
+
+23
+00:03:02,340 --> 00:03:10,520
+grammar Look at the sentences I can go I should go
+
+24
+00:03:10,520 --> 00:03:18,200
+I must go I have to go These are in the Positive
+
+25
+00:03:18,200 --> 00:03:23,860
+in the affirmative The question number one write
+
+26
+00:03:23,860 --> 00:03:28,680
+the negatives Number two write the questions
+
+27
+00:03:28,680 --> 00:03:32,880
+Number three write the third person singular
+
+28
+00:03:32,880 --> 00:03:38,620
+Number four which verb is different. So this is
+
+29
+00:03:38,620 --> 00:03:44,600
+the first exercise If I want to deal with the
+
+30
+00:03:44,600 --> 00:03:51,810
+first one negative So I say, I can't go. I
+
+31
+00:03:51,810 --> 00:03:59,310
+shouldn't go. I mustn't go. So we can use not,
+
+32
+00:03:59,870 --> 00:04:10,030
+not, not. The first three verbs are modal verbs.
+
+33
+00:04:10,390 --> 00:04:15,170
+But this one, like the modal verbs, but it is a
+
+34
+00:04:15,170 --> 00:04:20,950
+full verb. It has the meaning and the use of the
+
+35
+00:04:20,950 --> 00:04:26,730
+modal verbs, but it is really a full verb. Full
+
+36
+00:04:26,730 --> 00:04:33,790
+verb in form, but as a modal verb in meaning and
+
+37
+00:04:33,790 --> 00:04:39,470
+in use. So when I want to give the The negative, I
+
+38
+00:04:39,470 --> 00:04:43,270
+can't say haven't, no. This is a full verb, like
+
+39
+00:04:43,270 --> 00:04:51,810
+write, speak, go, drive. So the negative is don't
+
+40
+00:04:51,810 --> 00:04:59,760
+have to. This is the negative. Why? Don't have to
+
+41
+00:04:59,760 --> 00:05:03,320
+because it is something like write, play, speak,
+
+42
+00:05:03,560 --> 00:05:07,360
+full verb. Don't write, don't speak, don't play,
+
+43
+00:05:07,620 --> 00:05:13,380
+don't have to. Now, number two. Write the
+
+44
+00:05:13,380 --> 00:05:20,860
+questions. The questions. Can I
+
+45
+00:05:20,860 --> 00:05:23,040
+go
+
+46
+00:05:29,030 --> 00:05:40,730
+I go must I go again can I go should I go must I
+
+47
+00:05:40,730 --> 00:05:45,790
+go what about have to know it's like it's a full
+
+48
+00:05:45,790 --> 00:05:53,830
+verb so the question is do I have to go. Do I have
+
+49
+00:05:53,830 --> 00:06:00,930
+to go? So the question is, do I have to go?
+
+50
+00:06:03,090 --> 00:06:09,490
+We finished number two, the questions. Now write
+
+51
+00:06:09,490 --> 00:06:16,450
+the third person singular. He or she. So here we
+
+52
+00:06:16,450 --> 00:06:27,220
+see he. Yes, now it's clear. That's enough Now he
+
+53
+00:06:27,220 --> 00:06:40,020
+can go yes he or she can go he should go he must
+
+54
+00:06:40,020 --> 00:06:49,760
+go he has because had plus is For the present. So
+
+55
+00:06:49,760 --> 00:06:59,060
+it becomes has. Has to. She has to go. She has to
+
+56
+00:06:59,060 --> 00:07:06,120
+go. So with he or she, we use has to. We don't say
+
+57
+00:07:06,120 --> 00:07:11,940
+have to. But with the modal, the same. But with
+
+58
+00:07:11,940 --> 00:07:15,540
+the full verb have to, it's different. Has to.
+
+59
+00:07:16,220 --> 00:07:22,950
+Now, Which verb is different? This is different.
+
+60
+00:07:23,750 --> 00:07:27,790
+This is different. What is it? Have to is
+
+61
+00:07:27,790 --> 00:07:33,650
+different. Why? Because it has the meaning and use
+
+62
+00:07:33,650 --> 00:07:40,310
+of the modal verb. The form is of the full verb.
+
+63
+00:07:40,950 --> 00:07:44,650
+The use, when I use it in the grammar, it is like
+
+64
+00:07:44,650 --> 00:07:48,310
+the full verb. Because it is a full verb. But
+
+65
+00:07:48,310 --> 00:07:54,250
+these three are all modal verbs. Modal verbs of
+
+66
+00:07:54,250 --> 00:07:58,710
+obligation and permission. This one is for
+
+67
+00:07:58,710 --> 00:08:05,630
+permission and these two are for obligation. Yes,
+
+68
+00:08:05,890 --> 00:08:09,290
+this is for permission and these two are for
+
+69
+00:08:09,290 --> 00:08:17,090
+obligation If I want to write the answer here are
+
+70
+00:08:17,090 --> 00:08:21,510
+the answers The
+
+71
+00:08:21,510 --> 00:08:24,850
+answers
+
+72
+00:08:24,850 --> 00:08:28,030
+with the negative I can't go I shouldn't go I
+
+73
+00:08:28,030 --> 00:08:32,530
+mustn't go I don't have to go Don't have to go
+
+74
+00:08:32,530 --> 00:08:36,550
+different With the question, can I go? Should I
+
+75
+00:08:36,550 --> 00:08:44,130
+go? Must I go? Do I have to go? Different. What
+
+76
+00:08:44,130 --> 00:08:49,570
+about he or she? She can go. She should go. She
+
+77
+00:08:49,570 --> 00:08:59,150
+must go. She has to go. So, have to is different.
+
+78
+00:09:00,490 --> 00:09:04,810
+have to is different it behaves like a modal verb
+
+79
+00:09:04,810 --> 00:09:11,470
+in meaning and use in meaning and use like the
+
+80
+00:09:11,470 --> 00:09:17,150
+modal verb but like a full verb in in form it
+
+81
+00:09:17,150 --> 00:09:21,730
+means in grammar in grammar it is like the full
+
+82
+00:09:21,730 --> 00:09:28,390
+verb this is the first exercise Is it clear? I
+
+83
+00:09:28,390 --> 00:09:32,870
+want someone to read number one again. Yes. I
+
+84
+00:09:32,870 --> 00:09:36,210
+can't go. I shouldn't go. I mustn't go. I don't
+
+85
+00:09:36,210 --> 00:09:39,050
+have to go. Yes. So this is the negative. Now what
+
+86
+00:09:39,050 --> 00:09:42,890
+about the question? Yes. Can I go? Should I go?
+
+87
+00:09:43,030 --> 00:09:47,750
+Must I go? Do I have to go? What about the third
+
+88
+00:09:47,750 --> 00:09:53,590
+singular person? Yes. He, she can go. One of them.
+
+89
+00:09:53,710 --> 00:09:54,130
+He or she.
+
+90
+00:09:59,030 --> 00:10:04,150
+So, what's the difference? Have to. Have to is
+
+91
+00:10:04,150 --> 00:10:08,630
+what? Have to is different because it behaves like
+
+92
+00:10:08,630 --> 00:10:14,610
+a modal verb in meaning and use, but it's like a
+
+93
+00:10:14,610 --> 00:10:21,790
+full verb in form. So, can and can't express
+
+94
+00:10:21,790 --> 00:10:23,030
+permission.
+
+95
+00:10:26,720 --> 00:10:32,380
+and must and have to express obligation. Yes.
+
+96
+00:10:33,480 --> 00:10:34,980
+Thank you.
+
+97
+00:10:43,260 --> 00:10:52,380
+Now, another exercise, discussing grammar. Put
+
+98
+00:10:52,380 --> 00:10:55,380
+these sentences into the negative
+
+99
+00:10:57,600 --> 00:11:03,780
+The question and the past. So this is another
+
+100
+00:11:03,780 --> 00:11:09,420
+exercise about the modal verbs. Modal verbs of
+
+101
+00:11:09,420 --> 00:11:15,400
+what? Of obligation and permission. Look here,
+
+102
+00:11:15,440 --> 00:11:21,080
+this one. Henry can swim. Henry can swim. It is
+
+103
+00:11:21,080 --> 00:11:28,380
+what? It is positive or it is affirmative. I want
+
+104
+00:11:28,380 --> 00:11:33,100
+it after this. I want it to be in the negative. So
+
+105
+00:11:33,100 --> 00:11:41,960
+Henry can't swim. Can't swim. Can't within. What
+
+106
+00:11:41,960 --> 00:11:49,000
+about the question? Can Henry swim? Can Henry
+
+107
+00:11:49,000 --> 00:11:52,300
+swim? This is the question. Now what about the
+
+108
+00:11:52,300 --> 00:11:56,140
+past? Henry could swim.
+
+109
+00:11:58,230 --> 00:12:02,590
+So the question here is to make three more
+
+110
+00:12:02,590 --> 00:12:07,690
+sentences. The first one in the negative, the
+
+111
+00:12:07,690 --> 00:12:11,810
+second one in the question, the third one in the
+
+112
+00:12:11,810 --> 00:12:17,800
+past. So here, I have to. This is obligation. I
+
+113
+00:12:17,800 --> 00:12:22,460
+have to wear a uniform. Take care. Pay more
+
+114
+00:12:22,460 --> 00:12:26,460
+attention to have to. Why? Because it is like the
+
+115
+00:12:26,460 --> 00:12:32,000
+full verb in form. So here, I have to wear a
+
+116
+00:12:32,000 --> 00:12:41,300
+uniform. The negative is I don't have to.
+
+117
+00:12:42,480 --> 00:12:46,840
+I don't have to, to what? To wear the uniform.
+
+118
+00:12:49,700 --> 00:13:01,620
+What about the question? Do I have to wear a
+
+119
+00:13:01,620 --> 00:13:10,480
+uniform? Now about the past. The past of have to
+
+120
+00:13:10,480 --> 00:13:16,050
+is Had to. Who can tell me the third singular of
+
+121
+00:13:16,050 --> 00:13:23,570
+have to? The third singular person. He, she has
+
+122
+00:13:23,570 --> 00:13:29,590
+to. If it is he, we say he has to. In the
+
+123
+00:13:29,590 --> 00:13:36,890
+negative, doesn't have to. Doesn't have to. Yes.
+
+124
+00:13:37,110 --> 00:13:46,420
+Now in the past, I, uh huh. Had to wear a uniform.
+
+125
+00:13:47,300 --> 00:13:51,560
+Is it clear? Yes. I want someone to read the three
+
+126
+00:13:51,560 --> 00:13:59,520
+sentences. Yes. I don't have to wear a uniform. Do
+
+127
+00:13:59,520 --> 00:14:03,980
+I have to wear a uniform? I had to wear a uniform.
+
+128
+00:14:04,280 --> 00:14:09,580
+Yes. So here we say, I don't have, do I have had
+
+129
+00:14:09,580 --> 00:14:14,370
+to. Yes. Now this is number one. No, number two.
+
+130
+00:14:15,070 --> 00:14:18,090
+Number two. Now let's go to number three.
+
+131
+00:14:20,830 --> 00:14:23,990
+She has to.
+
+132
+00:14:25,410 --> 00:14:31,450
+We have have to for the I, we and the plural. Has
+
+133
+00:14:31,450 --> 00:14:36,310
+to for the third singular person. So she
+
+134
+00:14:42,010 --> 00:14:45,070
+Doesn't have to work.
+
+135
+00:14:49,250 --> 00:14:53,190
+So here it is positive. It is positive. And this
+
+136
+00:14:53,190 --> 00:15:02,470
+is the negative. What about the question? Does she
+
+137
+00:15:02,470 --> 00:15:13,260
+have to? Yes. two, two work hard? And the question
+
+138
+00:15:13,260 --> 00:15:21,040
+mark. What about the third past? She had
+
+139
+00:15:21,040 --> 00:15:25,960
+to work hard.
+
+140
+00:15:26,720 --> 00:15:32,360
+Had to. Does she have to? She doesn't have to. I
+
+141
+00:15:32,360 --> 00:15:37,900
+want someone to read again. Yes.She has to work
+
+142
+00:15:37,900 --> 00:15:44,900
+hard. She doesn't have to work
+
+143
+00:15:44,900 --> 00:15:52,260
+hard. Yes, is it clear? So again, have to, don't
+
+144
+00:15:52,260 --> 00:16:00,390
+have to, do I have to But she has to, she doesn't
+
+145
+00:16:00,390 --> 00:16:06,730
+have to, does she have to, she had to in the past.
+
+146
+00:16:10,990 --> 00:16:11,910
+Okay.
+
+147
+00:16:15,690 --> 00:16:22,370
+The fourth one, he can, he can. It is permission.
+
+148
+00:16:23,270 --> 00:16:29,530
+He can, it is positive. It is affirmative. He can
+
+149
+00:16:29,530 --> 00:16:33,610
+do what he likes. The negative,
+
+150
+00:16:36,750 --> 00:16:43,170
+he can't do what
+
+151
+00:16:43,170 --> 00:16:49,410
+he likes. Can't. The question,
+
+152
+00:16:51,370 --> 00:16:59,990
+The question, can he do what he likes? The third
+
+153
+00:16:59,990 --> 00:17:01,850
+one passed.
+
+154
+00:17:04,210 --> 00:17:09,610
+He could do
+
+155
+00:17:09,610 --> 00:17:19,330
+what he likes. Yes. Who can read again? Yes.
+
+156
+00:17:21,620 --> 00:17:27,600
+Can he do what he likes? Can he do what he likes?
+
+157
+00:17:28,080 --> 00:17:30,500
+Can he do what he likes?
+
+158
+00:17:33,140 --> 00:17:41,400
+Can he do what
+
+159
+00:17:41,400 --> 00:17:45,000
+he likes? Can he do what he likes? Can he do what
+
+160
+00:17:45,000 --> 00:17:53,070
+he likes? Can he do what he likes? Now again, we
+
+161
+00:17:53,070 --> 00:17:59,010
+are allowed to wear jeans. It is positive. We are
+
+162
+00:17:59,010 --> 00:18:04,870
+allowed to... It means we aren't. We aren't
+
+163
+00:18:04,870 --> 00:18:12,110
+allowed. And the negative are aren't. So the
+
+164
+00:18:12,110 --> 00:18:18,250
+negative, we aren't allowed
+
+165
+00:18:19,840 --> 00:18:26,700
+to wear jeans jeans then
+
+166
+00:18:26,700 --> 00:18:32,300
+question we question
+
+167
+00:18:32,300 --> 00:18:46,180
+yes are we allowed to wear a uniform jeans jeans
+
+168
+00:18:46,180 --> 00:18:46,920
+sorry
+
+169
+00:18:49,430 --> 00:18:59,390
+To wear jeans. The same. Now past. We were allowed
+
+170
+00:18:59,390 --> 00:19:02,950
+to
+
+171
+00:19:02,950 --> 00:19:09,530
+wear a uniform. Jeans. Also jeans. Yes. Don't
+
+172
+00:19:09,530 --> 00:19:17,230
+forget jeans. The same. Yes. I want someone to
+
+173
+00:19:17,230 --> 00:19:17,630
+read again.
+
+174
+00:19:31,730 --> 00:19:42,850
+Yes, very good.
+
+175
+00:19:43,090 --> 00:19:50,730
+So we have positive, negative, question passed
+
+176
+00:19:50,730 --> 00:20:02,310
+passed or third person pronoun yes again this is
+
+177
+00:20:02,310 --> 00:20:07,010
+the answers and I want all of you to work in pairs
+
+178
+00:20:07,010 --> 00:20:14,450
+to do these things work
+
+179
+00:20:14,450 --> 00:20:20,990
+in pairs and Make three sentences for each one.
+
+180
+00:20:22,050 --> 00:20:22,710
+Work in pairs.
+
+181
+00:20:27,190 --> 00:20:32,670
+Work in pairs. Say the sentences to your friend
+
+182
+00:20:32,670 --> 00:20:35,490
+and your friend says to you, to your colleague, to
+
+183
+00:20:35,490 --> 00:20:35,890
+your partner.
+
+184
+00:20:44,040 --> 00:20:55,680
+I love Korea. I love Korea. I love
+
+185
+00:20:55,680 --> 00:20:58,460
+Korea.
+
+186
+00:21:00,500 --> 00:21:06,560
+I love Korea.
+
+187
+00:21:07,990 --> 00:21:12,950
+Yes, that's enough. Now, three sentences. What are
+
+188
+00:21:12,950 --> 00:21:19,830
+they? Negative, watching and fast. I want someone
+
+189
+00:21:19,830 --> 00:21:26,490
+again to read again. Yes. I don't have to wear any
+
+190
+00:21:26,490 --> 00:21:31,740
+form. Do I have to wear any form? thank you number
+
+191
+00:21:31,740 --> 00:21:36,060
+two she doesn't have to work hard does she have to
+
+192
+00:21:36,060 --> 00:21:40,280
+work hard she she didn't have to work hard yes
+
+193
+00:21:40,280 --> 00:21:47,320
+four yes he can't do what he likes can he do what
+
+194
+00:21:47,320 --> 00:21:50,960
+he likes he couldn't do what he likes yes number
+
+195
+00:21:50,960 --> 00:21:54,400
+five yes we aren't allowed to
+
+196
+00:22:04,130 --> 00:22:11,830
+Very good. Now, aren't allowed to, it means what?
+
+197
+00:22:13,050 --> 00:22:20,890
+Count. It means count. Like this. The same. Either
+
+198
+00:22:20,890 --> 00:22:25,810
+we say can't or aren't allowed to. But when the
+
+199
+00:22:25,810 --> 00:22:33,270
+subject is I, I am allowed to. When the subject is
+
+200
+00:22:33,270 --> 00:22:40,230
+I, I am allowed to. He is allowed to. We are
+
+201
+00:22:40,230 --> 00:22:44,190
+allowed to. The negative, I am not allowed to. She
+
+202
+00:22:44,190 --> 00:22:49,390
+is not allowed to. They are not allowed to or they
+
+203
+00:22:49,390 --> 00:22:55,470
+aren't, isn't, etc. Yes, thank you. Now, look
+
+204
+00:22:55,470 --> 00:22:55,810
+here.
+
+205
+00:22:59,140 --> 00:23:01,900
+Also, we are still in the obligation and
+
+206
+00:23:01,900 --> 00:23:08,000
+permission. Now, we are speaking about obligation,
+
+207
+00:23:08,960 --> 00:23:15,700
+limit, exercise. Look at the chart. Make true
+
+208
+00:23:15,700 --> 00:23:20,960
+sentences about you, about yourself, and your
+
+209
+00:23:20,960 --> 00:23:27,520
+family. You and your family. Example, I don't have
+
+210
+00:23:27,520 --> 00:23:33,520
+to do the cooking. I. We have two in the plural.
+
+211
+00:23:34,900 --> 00:23:40,220
+My parents and my grandparents. And all the other
+
+212
+00:23:40,220 --> 00:23:45,440
+is in the singular. But this one is in the first
+
+213
+00:23:45,440 --> 00:23:51,080
+singular. First singular person without S. But the
+
+214
+00:23:51,080 --> 00:23:58,440
+third, the third with S. So here, I have to or has
+
+215
+00:23:58,440 --> 00:24:07,120
+to have to my parents have to yes so I my parents
+
+216
+00:24:07,120 --> 00:24:15,280
+have to I have to but my mother has to my father
+
+217
+00:24:15,280 --> 00:24:27,080
+has to my sister has to my brother has to my
+
+218
+00:24:27,080 --> 00:24:35,630
+husband has to my husband has to my wife has to so
+
+219
+00:24:35,630 --> 00:24:41,350
+with the third singular person we use has to with
+
+220
+00:24:41,350 --> 00:24:44,690
+the first singular person and first plural person
+
+221
+00:24:44,690 --> 00:24:51,410
+I and we have to with the plural Have to. We have
+
+222
+00:24:51,410 --> 00:24:58,550
+to. They have to. I have to. But he, she, it has
+
+223
+00:24:58,550 --> 00:25:08,850
+to. All the pronouns that take is take has. That
+
+224
+00:25:08,850 --> 00:25:16,470
+take am or are, it takes have. So these, we use
+
+225
+00:25:16,470 --> 00:25:27,170
+have. But this has two. You understand? So here, I
+
+226
+00:25:27,170 --> 00:25:31,550
+have two, my parents have two,
+
+227
+00:25:34,390 --> 00:25:41,530
+she, he, she, he, she, he has two. But this one,
+
+228
+00:25:42,350 --> 00:25:49,060
+they, they have two. Yes. Is it clear? Yes. I want
+
+229
+00:25:49,060 --> 00:25:53,280
+you to work in Paris. Choose any of these. Any of
+
+230
+00:25:53,280 --> 00:25:58,280
+these. Why? Because all of them are logical. I
+
+231
+00:25:58,280 --> 00:26:03,420
+have to go to work. I have to get up early. I have
+
+232
+00:26:03,420 --> 00:26:10,000
+to go shopping. I have to clean my room. I have to
+
+233
+00:26:10,000 --> 00:26:16,700
+do the cooking. I have to take out the rubbish. I
+
+234
+00:26:16,700 --> 00:26:21,280
+have to do the washing. I have to do the washing
+
+235
+00:26:21,280 --> 00:26:25,160
+up. This is with I. But don't choose all of them.
+
+236
+00:26:26,000 --> 00:26:29,400
+Just choose one. One for you, one for your
+
+237
+00:26:29,400 --> 00:26:31,420
+parents, one for your sister, one for your
+
+238
+00:26:31,420 --> 00:26:36,610
+brother. Working parents. Yes. All of them, the
+
+239
+00:26:36,610 --> 00:26:40,370
+same meaning with what? With have to and has to.
+
+240
+00:26:41,530 --> 00:26:47,790
+With have to or has to. In the positive. Yes.
+
+241
+00:27:08,240 --> 00:27:11,640
+All the answers are correct. Yes?
+
+242
+00:27:26,840 --> 00:27:36,180
+Yes, that's enough. Now let's go to, to what? To
+
+243
+00:27:36,180 --> 00:27:40,600
+don't
+
+244
+00:27:40,600 --> 00:27:46,560
+have to and doesn't have to. For the negative,
+
+245
+00:27:47,040 --> 00:27:53,240
+this is for ruler and I, and this is for what? For
+
+246
+00:27:53,240 --> 00:28:01,760
+he and she. Yes? Yes. So, have to, the negative is
+
+247
+00:28:01,760 --> 00:28:06,200
+don't have to. Has to, the negative is doesn't
+
+248
+00:28:06,200 --> 00:28:10,980
+have to. Make more examples, but now in the
+
+249
+00:28:10,980 --> 00:28:11,320
+negative.
+
+250
+00:28:14,210 --> 00:28:20,250
+I don't have to go to work. I don't have to get up
+
+251
+00:28:20,250 --> 00:28:23,970
+early. My mother doesn't have to clean my room,
+
+252
+00:28:24,350 --> 00:28:30,390
+etc. So make more questions, more sentences, but
+
+253
+00:28:30,390 --> 00:28:33,790
+this time negative, not positive. So these are the
+
+254
+00:28:33,790 --> 00:28:38,470
+positive and this now is the negative.
+
+255
+00:28:46,880 --> 00:28:48,120
+All of them now negative.
+
+256
+00:29:05,720 --> 00:29:10,200
+Is it
+
+257
+00:29:10,200 --> 00:29:16,430
+clear? Yes. Now that's enough. Now we want to
+
+258
+00:29:16,430 --> 00:29:21,710
+change from the positive or the negative. No, now
+
+259
+00:29:21,710 --> 00:29:26,570
+we want to the past. What is the past of have to
+
+260
+00:29:26,570 --> 00:29:31,250
+had to for singular and plural for all persons.
+
+261
+00:29:32,230 --> 00:29:38,140
+All persons take had to and The negative of the
+
+262
+00:29:38,140 --> 00:29:46,100
+past didn't have to. For all persons. For all of
+
+263
+00:29:46,100 --> 00:29:52,140
+them. Now make questions or sentences about the
+
+264
+00:29:52,140 --> 00:30:00,160
+past. Positive and negative. Positive and
+
+265
+00:30:00,160 --> 00:30:00,760
+negative.
+
+266
+00:30:03,190 --> 00:30:05,390
+So this is the positive and this is the negative.
+
+267
+00:30:05,550 --> 00:30:09,410
+Here the past, positive and negative. Yes, make
+
+268
+00:30:09,410 --> 00:30:12,190
+sentences in the past.
+
+269
+00:30:22,090 --> 00:30:23,090
+Yes, that's enough.
+
+270
+00:30:32,840 --> 00:30:38,960
+That's enough. I want you to give me examples of
+
+271
+00:30:38,960 --> 00:30:44,700
+all kinds. Positive, negative, present, past. Yes?
+
+272
+00:30:45,920 --> 00:30:52,920
+Everything. Yes. My brother didn't have to do the
+
+273
+00:30:52,920 --> 00:31:02,600
+cooking. Yes. I had to go to work. Yes. My sister
+
+274
+00:31:02,600 --> 00:31:07,500
+has to clean my room. Has to. Has to clean my
+
+275
+00:31:07,500 --> 00:31:12,680
+room. Yes. My mother has to do the cooking. Yes.
+
+276
+00:31:13,200 --> 00:31:18,680
+My brother has
+
+277
+00:31:18,680 --> 00:31:23,820
+to take out the trash. Yes. My sister has to do
+
+278
+00:31:23,820 --> 00:31:26,680
+the washing. Yes. Thank you very much. Now it's
+
+279
+00:31:26,680 --> 00:31:28,880
+very clear. Yes. Now
+
+280
+00:31:33,190 --> 00:31:35,630
+Again, we have another exercise.
+
+281
+00:31:38,330 --> 00:31:42,590
+This C is the same as in the previous exercise.
+
+282
+00:31:42,990 --> 00:31:48,030
+The same ones. But here we have a new exercise.
+
+283
+00:31:48,790 --> 00:31:56,570
+Yes? With C. Now, complete the sentences with with
+
+284
+00:31:56,570 --> 00:32:06,380
+what? With have got to or has got to and a line
+
+285
+00:32:06,380 --> 00:32:13,980
+from c this one from exercise two so at first i
+
+286
+00:32:13,980 --> 00:32:20,580
+want you to choose either has got to or have got
+
+287
+00:32:20,580 --> 00:32:28,060
+to have with what with the plural and the fourth
+
+288
+00:32:28,060 --> 00:32:37,820
+person singular Has with he or she or it. We can
+
+289
+00:32:37,820 --> 00:32:46,620
+contract it into the. So here, where is my
+
+290
+00:32:46,620 --> 00:32:55,220
+briefcase? I choose one. I got
+
+291
+00:32:55,220 --> 00:33:02,310
+to choose. Now here. At first, we want to choose
+
+292
+00:33:02,310 --> 00:33:06,670
+either have got to or has got to. Number two, look
+
+293
+00:33:06,670 --> 00:33:13,530
+at those dirty plates. We've got
+
+294
+00:33:13,530 --> 00:33:21,550
+to. Number three, Balima and Charles don't have
+
+295
+00:33:21,550 --> 00:33:23,410
+any food in their house.
+
+296
+00:33:25,850 --> 00:33:29,390
+They've got to.
+
+297
+00:33:31,520 --> 00:33:35,380
+Yes. John needs to get an alarm clock.
+
+298
+00:33:38,660 --> 00:33:51,360
+He's got to so and so. Here, he's got. Why? He.
+
+299
+00:33:51,880 --> 00:33:59,870
+But here? They. Here? We've here I'm number five.
+
+300
+00:34:00,010 --> 00:34:08,510
+I haven't got any clean socks. I've Yes Got two so
+
+301
+00:34:08,510 --> 00:34:15,910
+-and-so The chips L. So the waiter Has
+
+302
+00:34:15,910 --> 00:34:20,370
+or S has got two
+
+303
+00:34:21,380 --> 00:34:25,640
+So what's the difference between have to and have
+
+304
+00:34:25,640 --> 00:34:36,220
+got to? The same. We can use have to or have got
+
+305
+00:34:36,220 --> 00:34:48,650
+to. Also has to or has got to. But generally, have
+
+306
+00:34:48,650 --> 00:34:54,090
+to obligation and have got to obligation both of
+
+307
+00:34:54,090 --> 00:34:57,890
+them are obligation but when I say have got to it
+
+308
+00:34:57,890 --> 00:35:03,570
+means now obligation for now or soon after a
+
+309
+00:35:03,570 --> 00:35:09,290
+little while now or just now I say have got to but
+
+310
+00:35:09,290 --> 00:35:15,380
+generally have to And if I confused which one I
+
+311
+00:35:15,380 --> 00:35:20,360
+can use, have two is okay. Have two is okay. But
+
+312
+00:35:20,360 --> 00:35:24,020
+if you want to limit it, if it is now or soon,
+
+313
+00:35:24,740 --> 00:35:27,520
+it's better to say have got two. And the Americans
+
+314
+00:35:27,520 --> 00:35:31,780
+say gota. The Americans say gota. I got to speak.
+
+315
+00:35:32,590 --> 00:35:36,410
+English it means I have to Speak English. I've got
+
+316
+00:35:36,410 --> 00:35:39,950
+to speak English. Yes gota in the everyday
+
+317
+00:35:39,950 --> 00:35:45,730
+language So here where's my briefcase? I've got to
+
+318
+00:35:45,730 --> 00:35:55,210
+Uh-huh Go to work I've got to go to work Yes, I
+
+319
+00:35:55,210 --> 00:36:00,290
+want my briefcase because I've got to go to work.
+
+320
+00:36:00,390 --> 00:36:05,430
+I have to go to work. I have to go to work. But
+
+321
+00:36:05,430 --> 00:36:09,090
+because it is now, just now, look at those dirty
+
+322
+00:36:09,090 --> 00:36:09,670
+plates.
+
+323
+00:36:12,850 --> 00:36:20,290
+We've got to, we've got to, dirty plates.
+
+324
+00:36:23,890 --> 00:36:29,260
+Washing or washing up. Washing up. Why? Because
+
+325
+00:36:29,260 --> 00:36:33,000
+washing up means the plates. But the clothes, we
+
+326
+00:36:33,000 --> 00:36:37,660
+use washing. Washing for the clothes. Washing up
+
+327
+00:36:37,660 --> 00:36:43,300
+for the plates, spoons, etc. Look at those dirty
+
+328
+00:36:43,300 --> 00:36:47,940
+plates. We've got to do the washing up. Number
+
+329
+00:36:47,940 --> 00:36:48,700
+three
+
+330
+00:36:52,230 --> 00:36:56,810
+Balima and Charles don't have any food in their
+
+331
+00:36:56,810 --> 00:37:03,850
+house. They've got to go
+
+332
+00:37:03,850 --> 00:37:09,430
+shopping. Go shopping. Why? They don't have
+
+333
+00:37:09,430 --> 00:37:13,310
+anything in their house. They have got to go
+
+334
+00:37:13,310 --> 00:37:17,570
+shopping. Tomorrow? No, now. Just now, soon.
+
+335
+00:37:18,050 --> 00:37:24,010
+Because it is now or soon, we use have got to. But
+
+336
+00:37:24,010 --> 00:37:27,650
+when it is generally, we say, we use have to.
+
+337
+00:37:28,290 --> 00:37:33,630
+Number four. Is it clear? Yes. Number four. John
+
+338
+00:37:33,630 --> 00:37:40,140
+needs to get an alarm clock. He's got to get up
+
+339
+00:37:40,140 --> 00:37:47,300
+early. Yes. Number four. Get up early. Alarm clock
+
+340
+00:37:47,300 --> 00:37:53,480
+for what? For getting up early. Yes. Sean needs to
+
+341
+00:37:53,480 --> 00:37:57,000
+get an alarm clock. He's got to get up early
+
+342
+00:37:57,000 --> 00:38:02,500
+tomorrow. Number five. I haven't got any clean
+
+343
+00:38:02,500 --> 00:38:11,100
+socks. I've got to Do the washing. Do the washing.
+
+344
+00:38:13,540 --> 00:38:18,240
+Huh? Socks? Clothes. So wash it. Use them. Number
+
+345
+00:38:18,240 --> 00:38:24,780
+six. The chief's ill. He is ill. The chief is ill.
+
+346
+00:38:25,300 --> 00:38:32,080
+So the waiter, the waiter, the waiter's got to do
+
+347
+00:38:32,080 --> 00:38:39,230
+the cooking. Number six. Do the cooking.
+
+348
+00:38:42,290 --> 00:38:46,850
+Is it clear? Yes. I want you again to work in
+
+349
+00:38:46,850 --> 00:38:52,370
+pairs to complete these six sentences from A and
+
+350
+00:38:52,370 --> 00:38:54,930
+C. Yes, work in pairs.
+
+351
+00:39:23,180 --> 00:39:24,400
+Yeah, this is
+
+352
+00:39:51,920 --> 00:39:56,480
+Yes, now I want some of you to do number one.
+
+353
+00:39:57,680 --> 00:39:59,360
+Number one, yes.
+
+354
+00:40:02,300 --> 00:40:02,920
+Yes,
+
+355
+00:40:05,540 --> 00:40:08,940
+number two. Number two, yes.
+
+356
+00:40:16,460 --> 00:40:25,940
+Yes, we've got to Yes
+
+357
+00:40:25,940 --> 00:40:37,580
+to do the washing up Yes number three Very
+
+358
+00:40:37,580 --> 00:40:38,880
+good number
+
+359
+00:40:42,720 --> 00:40:50,300
+Four. Yes. John needs to get an alarm clock. He's
+
+360
+00:40:50,300 --> 00:40:55,220
+got to get up early tomorrow. Good. And the last
+
+361
+00:40:55,220 --> 00:41:01,900
+one. The one before the last. Yes. I haven't got
+
+362
+00:41:01,900 --> 00:41:07,280
+any clean socks. I have to do washing. Yes. And
+
+363
+00:41:07,280 --> 00:41:10,980
+number six, the last one. Yes.
+
+364
+00:41:16,100 --> 00:41:21,180
+The waiter has got not the waiter and he just one
+
+365
+00:41:21,180 --> 00:41:27,040
+the waiters The
+
+366
+00:41:27,040 --> 00:41:32,540
+cooking yes, the waiter Is it means the waiter has
+
+367
+00:41:32,540 --> 00:41:41,500
+got to is got to it means He has to the waiter has
+
+368
+00:41:41,500 --> 00:41:52,320
+to Has got to Do the cooking. The last one. This
+
+369
+00:41:52,320 --> 00:41:55,300
+is the answers. These are the answers.
+
+370
+00:42:00,520 --> 00:42:07,440
+Yes. Number one. Yes, my dream. Right here. I've
+
+371
+00:42:07,440 --> 00:42:10,260
+got to go to the war. Two.
+
+372
+00:42:15,470 --> 00:42:21,630
+Three. Pamela and Carlos don't have any food in
+
+373
+00:42:21,630 --> 00:42:27,490
+their house. They've got to go shopping. And
+
+374
+00:42:27,490 --> 00:42:31,510
+number four. Yes. Sean needs to get an alarm
+
+375
+00:42:31,510 --> 00:42:35,410
+clock. He's got to get up early tomorrow. And
+
+376
+00:42:35,410 --> 00:42:40,030
+number five. I haven't got any pizza, but I have
+
+377
+00:42:40,030 --> 00:42:45,930
+got two delicious ones. The last one. Yes,
+
+378
+00:42:48,830 --> 00:42:53,570
+and this is the grammar spot. Which two sentences
+
+379
+00:42:53,570 --> 00:42:58,170
+mean the same? Now we have three sentences. Which
+
+380
+00:42:58,170 --> 00:43:03,650
+two of them means the same. I am allowed to stay
+
+381
+00:43:03,650 --> 00:43:07,430
+at my friend's house tonight. I can stay at my
+
+382
+00:43:07,430 --> 00:43:10,550
+friend's house tonight. I have to stay at my
+
+383
+00:43:10,550 --> 00:43:14,490
+friend's house tonight. So which two sentences
+
+384
+00:43:14,490 --> 00:43:18,330
+mean the same? Yes.
+
+385
+00:43:21,170 --> 00:43:28,950
+Yes. I'm allowed to and can. They mean the same.
+
+386
+00:43:31,660 --> 00:43:36,460
+But have to is different. So have to is for
+
+387
+00:43:36,460 --> 00:43:42,080
+obligation. But can, I'm allowed to for
+
+388
+00:43:42,080 --> 00:43:45,880
+permission. Yes. Now, which sentences express
+
+389
+00:43:45,880 --> 00:43:53,100
+obligation? Which sentence one? This? Yes. Have
+
+390
+00:43:53,100 --> 00:43:58,920
+to. The sentence, the third one. Which sentence is
+
+391
+00:43:58,920 --> 00:44:09,350
+to? Express permission Can and am allowed to Yes,
+
+392
+00:44:09,590 --> 00:44:14,370
+so this is The last word in this subject number
+
+393
+00:44:14,370 --> 00:44:18,350
+two complete the sentences with with what we have
+
+394
+00:44:18,350 --> 00:44:26,470
+to Don't have to positive and negative Number
+
+395
+00:44:26,470 --> 00:44:34,130
+one children have to go to school have to
+
+396
+00:44:34,130 --> 00:44:45,050
+millionaires don't have to wear don't have to wear
+
+397
+00:44:45,050 --> 00:44:47,490
+you
+
+398
+00:44:50,680 --> 00:44:55,120
+Don't have to go to England if you want to learn
+
+399
+00:44:55,120 --> 00:45:03,760
+English. You can study English at home. So you
+
+400
+00:45:03,760 --> 00:45:09,000
+don't
+
+401
+00:45:09,000 --> 00:45:14,260
+have to go to England if you want to study
+
+402
+00:45:14,260 --> 00:45:18,730
+English. Number four. One, two, three, four.
+
+403
+00:45:18,870 --> 00:45:24,170
+Number four. In England, you have to. Yes.
+
+404
+00:45:27,410 --> 00:45:34,010
+You have to drive on the left. Number three. Have
+
+405
+00:45:34,010 --> 00:45:41,050
+good to and have to both
+
+406
+00:45:41,050 --> 00:45:48,280
+express obligation. Yes. have got to and have to
+
+407
+00:45:48,280 --> 00:45:51,640
+both express obligation when I say have to it
+
+408
+00:45:51,640 --> 00:45:57,980
+means what have to has to had to when I say have
+
+409
+00:45:57,980 --> 00:46:09,560
+got to or has got to yes have got to refers to an
+
+410
+00:46:09,560 --> 00:46:12,360
+obligation when now
+
+411
+00:46:14,720 --> 00:46:20,320
+or soon now or soon so they are the same but this
+
+412
+00:46:20,320 --> 00:46:24,240
+is for now and this is general have to general but
+
+413
+00:46:24,240 --> 00:46:29,980
+have got to now or soon yes it's often reduced
+
+414
+00:46:29,980 --> 00:46:40,430
+reduced to gota gota when we speak I've got to I
+
+415
+00:46:40,430 --> 00:46:44,570
+got to speak English. Yes, especially in American
+
+416
+00:46:44,570 --> 00:46:49,170
+English So most Americans say I got a it means I
+
+417
+00:46:49,170 --> 00:46:54,790
+have got to Example I have got to I got to go now
+
+418
+00:46:54,790 --> 00:47:02,330
+I've got to go now. I have got to go now Bye Thank
+
+419
+00:47:02,330 --> 00:47:08,360
+you very much and bye Because I've got to go now.
+
+420
+00:47:09,080 --> 00:47:12,720
+Thank you very much. Inshallah next time prepare
+
+421
+00:47:12,720 --> 00:47:16,200
+yourself for the midterm exam.
+
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/DZ8ssZe6k_w_raw.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/DZ8ssZe6k_w_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5d7a8bdb1b6591ecd08b35067ea19fb511010aa7
--- /dev/null
+++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/DZ8ssZe6k_w_raw.srt
@@ -0,0 +1,2492 @@
+1
+00:00:21,330 --> 00:00:25,330
+Assalamualaikum warahmatullahi wabarakatuh. Good
+
+2
+00:00:25,330 --> 00:00:28,930
+afternoon. Today, inshallah, we are going to take
+
+3
+00:00:28,930 --> 00:00:34,690
+a reading passage about my kind of holiday. A
+
+4
+00:00:34,690 --> 00:00:39,130
+reading passage about my kind of holiday. Karen
+
+5
+00:00:39,130 --> 00:00:39,690
+Saunders.
+
+6
+00:00:44,190 --> 00:00:49,290
+She travels for her job. But when it's her own
+
+7
+00:00:49,290 --> 00:00:54,770
+holiday, Karen Saunders stays at home. Karen
+
+8
+00:00:54,770 --> 00:01:00,530
+Saunders works in a travel agency. All her work is
+
+9
+00:01:00,530 --> 00:01:06,110
+traveling. When she's traveling, it's her work.
+
+10
+00:01:06,630 --> 00:01:11,290
+But when she's at home, it's her holiday. On the
+
+11
+00:01:11,290 --> 00:01:16,370
+contrary, people travel on holidays. Karen
+
+12
+00:01:16,370 --> 00:01:19,750
+Saunders, when she stays at home, it's her own
+
+13
+00:01:19,750 --> 00:01:22,730
+holiday. When she travels, it's her work.
+
+14
+00:01:26,470 --> 00:01:31,710
+The first paragraph, Karen Saunders has her own
+
+15
+00:01:31,710 --> 00:01:36,730
+travel agency in Mayfair, London, that sends
+
+16
+00:01:36,730 --> 00:01:40,490
+people all over the world on their dream holidays.
+
+17
+00:01:42,820 --> 00:01:47,200
+So she was in a travel agency and before sending
+
+18
+00:01:47,200 --> 00:01:53,480
+people to certain countries, she herself goes
+
+19
+00:01:53,480 --> 00:01:59,120
+there. She goes to countries, to places before
+
+20
+00:01:59,120 --> 00:02:01,560
+sending people to these places.
+
+21
+00:02:04,250 --> 00:02:08,970
+She needs to know where she's sending them So why
+
+22
+00:02:08,970 --> 00:02:13,570
+she travels because she needs to know where she's
+
+23
+00:02:13,570 --> 00:02:17,810
+sending people So
+
+24
+00:02:17,810 --> 00:02:26,870
+she goes on working holidays Four or five times a
+
+25
+00:02:26,870 --> 00:02:29,930
+year So
+
+26
+00:02:31,470 --> 00:02:36,990
+Her holiday is working holidays. Working holidays.
+
+27
+00:02:37,830 --> 00:02:45,910
+Business. Business. How many times? Four or five
+
+28
+00:02:45,910 --> 00:02:54,970
+times a year. Every year. Yearly. Annually. So the
+
+29
+00:02:54,970 --> 00:03:01,730
+question here, what is Karen's job? What is her
+
+30
+00:03:01,730 --> 00:03:09,710
+job? Her job, she is not a teacher. No, she has
+
+31
+00:03:09,710 --> 00:03:16,110
+her own travel agency. She has an agency, travel
+
+32
+00:03:16,110 --> 00:03:20,490
+agency. This is her work, travel agents.
+
+33
+00:03:23,370 --> 00:03:27,730
+The second question, why does she take working
+
+34
+00:03:27,730 --> 00:03:34,190
+holidays? Why does she take working holidays? So
+
+35
+00:03:34,190 --> 00:03:40,210
+this working holiday is her work. Why? Because she
+
+36
+00:03:40,210 --> 00:03:46,430
+needs to know where she is sending people. Where
+
+37
+00:03:46,430 --> 00:03:50,590
+she is sending people. So before sending people,
+
+38
+00:03:51,050 --> 00:03:56,590
+she herself traveled. Traveled to these places. So
+
+39
+00:03:56,590 --> 00:04:05,060
+needs to know. should know, have to know where the
+
+40
+00:04:05,060 --> 00:04:10,300
+place, the place where she is sending these people
+
+41
+00:04:10,300 --> 00:04:17,600
+or the people. Two questions. The first answer,
+
+42
+00:04:18,520 --> 00:04:23,800
+what is Karen's job? She has her travel agency.
+
+43
+00:04:25,060 --> 00:04:29,480
+That's enough. Why does she take working holidays?
+
+44
+00:04:30,320 --> 00:04:33,580
+Because she needs to know where she is sending
+
+45
+00:04:33,580 --> 00:04:38,420
+people. Where she is sending people.
+
+46
+00:04:41,040 --> 00:04:46,080
+Is it clear? Yeah. I want someone to read the
+
+47
+00:04:46,080 --> 00:04:50,720
+first question and the answer. Number one. Yes.
+
+48
+00:04:51,530 --> 00:04:55,570
+What is Karen's job? She has her own travel
+
+49
+00:04:55,570 --> 00:05:00,330
+agency. She helps people plan holidays. Yes.
+
+50
+00:05:00,850 --> 00:05:04,570
+Generally, she has her own travel agency. Number
+
+51
+00:05:04,570 --> 00:05:09,330
+two. Yes. Why does she take work on holidays? She
+
+52
+00:05:09,330 --> 00:05:15,330
+needs to know where she is sending people. She
+
+53
+00:05:15,330 --> 00:05:20,600
+needs to know where she is sending people. The
+
+54
+00:05:20,600 --> 00:05:24,260
+people who came to her agency to travel, to take
+
+55
+00:05:24,260 --> 00:05:28,540
+holidays, she knows where to send them. So she
+
+56
+00:05:28,540 --> 00:05:32,620
+needs to know, she wants to know where she is
+
+57
+00:05:32,620 --> 00:05:37,600
+sending these people. Is it clear? So this is the
+
+58
+00:05:37,600 --> 00:05:38,500
+general introduction.
+
+59
+00:05:42,040 --> 00:05:48,640
+The general introduction. Now, the first Paragraph
+
+60
+00:05:48,640 --> 00:05:53,840
+after the, the first paragraph after the
+
+61
+00:05:53,840 --> 00:05:59,200
+introduction. My ideal holiday. My perfect
+
+62
+00:05:59,200 --> 00:06:06,040
+holiday. My holiday. Who's my? Karen Saunders.
+
+63
+00:06:06,800 --> 00:06:12,400
+Karen Saunders holiday. Karen Saunders ideal
+
+64
+00:06:12,400 --> 00:06:21,050
+holiday. My ideal holiday has
+
+65
+00:06:21,050 --> 00:06:25,690
+a little bit of everything. This is a very good
+
+66
+00:06:25,690 --> 00:06:26,170
+idea.
+
+67
+00:06:29,670 --> 00:06:32,530
+The ideal holiday has a little bit of everything.
+
+68
+00:06:33,570 --> 00:06:37,330
+Many people like to have a little bit of
+
+69
+00:06:37,330 --> 00:06:42,130
+everything. It's good. But some people just know
+
+70
+00:06:42,130 --> 00:06:46,550
+very much about two or three things. He's a
+
+71
+00:06:46,550 --> 00:06:49,290
+teacher of English, everything English, English
+
+72
+00:06:49,290 --> 00:06:53,910
+and no more than English. No, it's better to know
+
+73
+00:06:53,910 --> 00:07:02,540
+very big a little bit of everything in reading,
+
+74
+00:07:02,900 --> 00:07:09,000
+writing, holiday, working, any hobbies, any
+
+75
+00:07:09,000 --> 00:07:12,340
+activities, all the activities, a little bit of
+
+76
+00:07:12,340 --> 00:07:17,760
+everything. So he says, my ideal holiday has a
+
+77
+00:07:17,760 --> 00:07:20,380
+little bit, a little bit from here, a little bit
+
+78
+00:07:20,380 --> 00:07:21,560
+from here, a little bit from here, a little bit
+
+79
+00:07:21,560 --> 00:07:27,820
+from everything. A little bit of everything. I
+
+80
+00:07:27,820 --> 00:07:35,760
+like lazing. I like lazing. Generally, she likes
+
+81
+00:07:35,760 --> 00:07:41,340
+lazing. What's the meaning of lazing? Doing
+
+82
+00:07:41,340 --> 00:07:47,940
+nothing. Doing nothing. She likes doing nothing.
+
+83
+00:07:48,760 --> 00:07:54,680
+Yes. On a beach. Where is it? On the beach? On a
+
+84
+00:07:54,680 --> 00:08:00,290
+beach. So she likes going to the sea, playing,
+
+85
+00:08:01,170 --> 00:08:06,650
+running, eating, watching, doing nothing, no work,
+
+86
+00:08:06,730 --> 00:08:12,650
+no job. With a pile of books. What's the meaning
+
+87
+00:08:12,650 --> 00:08:16,830
+of with a pile of books? It means she likes
+
+88
+00:08:16,830 --> 00:08:24,130
+reading. She likes reading. So I like living and
+
+89
+00:08:25,100 --> 00:08:30,100
+Reading, doing nothing on the beach and reading.
+
+90
+00:08:31,360 --> 00:08:37,320
+But then after this, I get bored. Bored or boring.
+
+91
+00:08:38,790 --> 00:08:42,970
+bored because bored for people ed for people i
+
+92
+00:08:42,970 --> 00:08:48,210
+they but then i get bored and i need to do
+
+93
+00:08:48,210 --> 00:08:52,950
+something uh-huh after doing nothing she wanted to
+
+94
+00:08:52,950 --> 00:08:57,930
+do something uh-huh she likes to stay on beach
+
+95
+00:08:57,930 --> 00:09:05,270
+without any job but she likes reading after this i
+
+96
+00:09:05,270 --> 00:09:12,060
+love exploring she likes exploring exploring new
+
+97
+00:09:12,060 --> 00:09:19,320
+places so she likes lazy reading and exploring in
+
+98
+00:09:19,320 --> 00:09:27,020
+new places by car by metro on a train by plane no
+
+99
+00:09:27,020 --> 00:09:36,300
+on foot on foot ah so she likes exploring in new
+
+100
+00:09:36,300 --> 00:09:42,330
+places especially on foot walking in the markets
+
+101
+00:09:42,330 --> 00:09:47,370
+in the for the restaurants for the churches so on
+
+102
+00:09:47,370 --> 00:09:51,910
+walking not driving many people like exploring
+
+103
+00:09:51,910 --> 00:10:00,150
+places with a car or with a metro train taxi you
+
+104
+00:10:00,150 --> 00:10:07,010
+know she likes on foot So exploring she likes
+
+105
+00:10:07,010 --> 00:10:10,970
+exploring new places especially on foot and
+
+106
+00:10:10,970 --> 00:10:18,050
+something else nosing nosing around she likes
+
+107
+00:10:18,050 --> 00:10:22,870
+nosing around so stop and look here stop and look
+
+108
+00:10:22,870 --> 00:10:26,410
+here stop and look here stop and look there stop
+
+109
+00:10:26,410 --> 00:10:31,670
+and look over there stopping and looking When we
+
+110
+00:10:31,670 --> 00:10:35,830
+go to the market, when we go to any place, a new
+
+111
+00:10:35,830 --> 00:10:40,990
+place, we like to stop and look. Stop and look.
+
+112
+00:10:41,190 --> 00:10:46,730
+This is called nosing around. Stopping and
+
+113
+00:10:46,730 --> 00:10:51,850
+watching. Stopping to look around in. Stopping to
+
+114
+00:10:51,850 --> 00:10:54,590
+look here and there and there and there and there.
+
+115
+00:10:54,930 --> 00:11:01,430
+This means stopping to look around. It means
+
+116
+00:11:01,430 --> 00:11:10,350
+nosing. Nosing around in churches. She likes
+
+117
+00:11:10,350 --> 00:11:19,070
+stopping to look at churches, shops, museums, and
+
+118
+00:11:19,070 --> 00:11:22,550
+restaurants. All the places. All the buildings.
+
+119
+00:11:24,910 --> 00:11:32,680
+Also, I'm very into cooking. I'm very into cooking
+
+120
+00:11:32,680 --> 00:11:38,300
+and very means I'm very interested. I'm very much
+
+121
+00:11:38,300 --> 00:11:45,300
+interested. I like most. I like something most. So
+
+122
+00:11:45,300 --> 00:11:49,600
+I'm very it means I like this very much into
+
+123
+00:11:49,600 --> 00:11:55,260
+cooking. I like cooking. I like cooking food,
+
+124
+00:11:56,480 --> 00:12:01,920
+new meals. New dishes. I'm very into cooking. It
+
+125
+00:12:01,920 --> 00:12:07,620
+means she likes cooking. So I love going around
+
+126
+00:12:07,620 --> 00:12:12,380
+markets. Because she likes cooking, she goes to
+
+127
+00:12:12,380 --> 00:12:18,860
+the market. And food stores. The supermarkets.
+
+128
+00:12:19,900 --> 00:12:26,020
+Markets and supermarkets. Or the food stores. Food
+
+129
+00:12:26,020 --> 00:12:26,420
+shops.
+
+130
+00:12:29,180 --> 00:12:34,220
+This is about her perfect holiday, her ideal
+
+131
+00:12:34,220 --> 00:12:39,160
+holiday. Her holiday is not traveling. No. Her
+
+132
+00:12:39,160 --> 00:12:44,700
+holiday is look here and there, cooking, watching,
+
+133
+00:12:45,200 --> 00:12:49,860
+nothing. The question, what is her idea about a
+
+134
+00:12:49,860 --> 00:12:55,790
+perfect holiday? What is Karen's idea about her
+
+135
+00:12:55,790 --> 00:12:58,830
+ideal holiday, her perfect holiday?
+
+136
+00:13:04,070 --> 00:13:12,090
+Her idea about a perfect holiday is having
+
+137
+00:13:12,090 --> 00:13:17,460
+a little bit of everything. having a little bit of
+
+138
+00:13:17,460 --> 00:13:20,180
+everything take something from here and from here
+
+139
+00:13:20,180 --> 00:13:23,520
+and from here and from here it it means has a
+
+140
+00:13:23,520 --> 00:13:28,340
+little bit of everything has a little bit a little
+
+141
+00:13:28,340 --> 00:13:32,080
+from here and here and there and etc so a little
+
+142
+00:13:32,080 --> 00:13:38,220
+bit of everything this is the answer a little bit
+
+143
+00:13:38,220 --> 00:13:42,100
+of everything
+
+144
+00:13:46,320 --> 00:13:47,780
+A little bit of everything.
+
+145
+00:13:50,460 --> 00:13:58,720
+Like what? Like what? This means what? It means
+
+146
+00:13:58,720 --> 00:14:07,500
+lazing, reading, exploring in new places, nosing
+
+147
+00:14:07,500 --> 00:14:12,620
+around in churches, shops, museums and
+
+148
+00:14:12,620 --> 00:14:15,280
+restaurants. All these.
+
+149
+00:14:20,210 --> 00:14:26,290
+Cooking, going around markets, going around food
+
+150
+00:14:26,290 --> 00:14:31,750
+stores. So this is the meaning of have a little
+
+151
+00:14:31,750 --> 00:14:36,830
+bit of everything. Some people like food, just
+
+152
+00:14:36,830 --> 00:14:42,990
+food, only food. Some other people like talking,
+
+153
+00:14:43,650 --> 00:14:47,320
+only talking. Some people like reading or
+
+154
+00:14:47,320 --> 00:14:52,960
+listening or watching, just one, writing. No, she
+
+155
+00:14:52,960 --> 00:14:57,800
+likes to have a little bit of everything in every
+
+156
+00:14:57,800 --> 00:15:07,440
+branch of our life. So the answer here, what
+
+157
+00:15:07,440 --> 00:15:10,960
+is her idea of a perfect holiday? A little bit of
+
+158
+00:15:10,960 --> 00:15:14,950
+everything. A little bit of everything. It means
+
+159
+00:15:14,950 --> 00:15:20,170
+colon Lazing on a beach staying on the beach
+
+160
+00:15:20,170 --> 00:15:26,430
+without any work reading exploring new places
+
+161
+00:15:26,430 --> 00:15:35,530
+Going around markets and food stores Now
+
+162
+00:15:35,530 --> 00:15:43,860
+the next question Find words that has nearly the
+
+163
+00:15:43,860 --> 00:15:48,040
+same meaning as these words. I will give you some
+
+164
+00:15:48,040 --> 00:15:54,920
+words in a simple language, and I want to find the
+
+165
+00:15:54,920 --> 00:15:58,140
+meaning of these words from the passage, from the
+
+166
+00:15:58,140 --> 00:16:02,820
+text. So the first one, doing nothing. It means
+
+167
+00:16:02,820 --> 00:16:08,590
+lazing. The other one stopping to look around in
+
+168
+00:16:08,590 --> 00:16:15,150
+stopping to look it means nosing around in so
+
+169
+00:16:15,150 --> 00:16:21,170
+stopping to look it means nosing stopping stop to
+
+170
+00:16:21,170 --> 00:16:26,570
+look nose stopping to look nosing nose nosing uh
+
+171
+00:16:26,570 --> 00:16:34,270
+-huh I'm very interested in it means I'm very into
+
+172
+00:16:34,270 --> 00:16:40,850
+or I'm into shorted contracted without saying
+
+173
+00:16:40,850 --> 00:16:44,490
+interested I'm very it means I'm very interested
+
+174
+00:16:44,490 --> 00:16:51,190
+is it clear again I want someone to read first
+
+175
+00:16:51,190 --> 00:16:55,930
+question and give me the answer give
+
+176
+00:16:55,930 --> 00:17:00,170
+me the question and the answer yeah
+
+177
+00:17:00,950 --> 00:17:05,590
+What is her idea of a perfect holiday? A little
+
+178
+00:17:05,590 --> 00:17:09,530
+bit of everything. A little bit of everything,
+
+179
+00:17:09,970 --> 00:17:12,990
+coral. It means so on and so on and so on. What
+
+180
+00:17:12,990 --> 00:17:16,250
+does it mean? Placing on a beach, reading,
+
+181
+00:17:16,670 --> 00:17:21,090
+exploring new places, going around markets and
+
+182
+00:17:21,090 --> 00:17:25,410
+food stores. Food stores, yes, very good. All from
+
+183
+00:17:25,410 --> 00:17:30,800
+here, Her ideal holiday has a little bit of
+
+184
+00:17:30,800 --> 00:17:35,440
+everything. She likes lazing. She likes books. She
+
+185
+00:17:35,440 --> 00:17:39,140
+likes exploring new places. She likes nosing
+
+186
+00:17:39,140 --> 00:17:44,240
+around in many places. She likes cooking. She
+
+187
+00:17:44,240 --> 00:17:48,900
+likes going around markets and going around food
+
+188
+00:17:48,900 --> 00:17:54,140
+stores. Do you understand? This is her ideal
+
+189
+00:17:54,140 --> 00:17:59,940
+holiday. What about you? What about you? My ideal
+
+190
+00:17:59,940 --> 00:18:05,160
+holiday is sleeping. Sleeping all day and night.
+
+191
+00:18:06,580 --> 00:18:10,760
+What about you? Reading, reading for the exams.
+
+192
+00:18:10,980 --> 00:18:15,460
+And you? Watching television. And you? Standing on
+
+193
+00:18:15,460 --> 00:18:20,140
+the internet. And you? Writing short stories. What
+
+194
+00:18:20,140 --> 00:18:23,850
+about you? No, taking care of my children. What
+
+195
+00:18:23,850 --> 00:18:29,530
+about you going to the sea? Yes, but she has a
+
+196
+00:18:29,530 --> 00:18:34,370
+little bit of everything. The second one. However,
+
+197
+00:18:36,270 --> 00:18:43,530
+however, when
+
+198
+00:18:43,530 --> 00:18:48,750
+I say however, it is what? It is a sentence
+
+199
+00:18:48,750 --> 00:18:54,290
+adverb. It means what? It means we have something
+
+200
+00:18:54,290 --> 00:18:59,650
+different. Although she likes so and so, but she
+
+201
+00:19:00,560 --> 00:19:04,860
+Like so and so. Something different. How? They
+
+202
+00:19:04,860 --> 00:19:09,540
+know. However, not moreover. If I say moreover, I
+
+203
+00:19:09,540 --> 00:19:13,220
+want to add information. When I say however, I
+
+204
+00:19:13,220 --> 00:19:17,440
+want to add a contrast information or contrast
+
+205
+00:19:17,440 --> 00:19:21,680
+information. Something different. So we call this
+
+206
+00:19:21,680 --> 00:19:27,370
+what? Sentence adverb. The sentence adverb give me
+
+207
+00:19:27,370 --> 00:19:30,830
+an idea about the paragraph or about the sentence,
+
+208
+00:19:31,310 --> 00:19:33,670
+the coming sentence, the coming paragraph.
+
+209
+00:19:34,250 --> 00:19:38,210
+However, yes, what's the difference? I must
+
+210
+00:19:38,210 --> 00:19:45,270
+confess that my favorite holiday resort is home. I
+
+211
+00:19:45,270 --> 00:19:47,510
+like everything, little bit of everything, here
+
+212
+00:19:47,510 --> 00:19:50,830
+and there and there and there. Yes, but I must
+
+213
+00:19:50,830 --> 00:19:55,960
+confess, I must say that my favorite holiday
+
+214
+00:19:55,960 --> 00:20:02,600
+resort, the place of my holiday is home. Home is
+
+215
+00:20:02,600 --> 00:20:06,580
+the best. Yes, my home is the best holiday resort.
+
+216
+00:20:07,540 --> 00:20:13,310
+I travel so much in in my job that just waking up
+
+217
+00:20:13,310 --> 00:20:20,750
+in my own bed is heaven she travels a lot and she
+
+218
+00:20:20,750 --> 00:20:26,270
+usually dreams of waking in the morning where at
+
+219
+00:20:26,270 --> 00:20:32,910
+home waking up at her home ah so waking up at home
+
+220
+00:20:32,910 --> 00:20:38,410
+is The best is heaven. Why? Because she's always
+
+221
+00:20:38,410 --> 00:20:42,050
+outside. She's always here and there and there.
+
+222
+00:20:42,530 --> 00:20:47,550
+Rarely she is at home. So she usually hopes to
+
+223
+00:20:47,550 --> 00:20:54,950
+stay at home. So here I travel so much in my job
+
+224
+00:20:54,950 --> 00:21:02,500
+that just waking up In my own bed, in my own bed
+
+225
+00:21:02,500 --> 00:21:08,920
+at home with my family is heaven. Paradise is the
+
+226
+00:21:08,920 --> 00:21:18,000
+best. I put around, put around the
+
+227
+00:21:18,000 --> 00:21:26,430
+house in my pajamas. Puta means walking. Easily.
+
+228
+00:21:27,430 --> 00:21:33,490
+Slowly. Without purpose. Without purpose. At ease.
+
+229
+00:21:34,150 --> 00:21:40,630
+At my home. With my pyjamas. Easy. With my
+
+230
+00:21:40,630 --> 00:21:45,270
+pyjamas. Read the paper. The local paper. The
+
+231
+00:21:45,270 --> 00:21:51,090
+local newspaper. Do some gardening. Gardening.
+
+232
+00:21:51,650 --> 00:21:56,580
+Working in the garden. shop for some food in my
+
+233
+00:21:56,580 --> 00:22:00,980
+own country, my own place, then make a delicious
+
+234
+00:22:00,980 --> 00:22:04,600
+meal myself.
+
+235
+00:22:05,920 --> 00:22:10,460
+in the evening. So all these at home. But when she
+
+236
+00:22:10,460 --> 00:22:17,440
+works outside abroad, she doesn't do these things.
+
+237
+00:22:17,720 --> 00:22:22,020
+So she always hopes to stay at home. She always
+
+238
+00:22:22,020 --> 00:22:29,620
+dreams of waking up in her own bed at home, in her
+
+239
+00:22:29,620 --> 00:22:34,580
+house with her family. Why? Because waking up in
+
+240
+00:22:34,580 --> 00:22:40,400
+her bed and put her going in her house, reading
+
+241
+00:22:40,400 --> 00:22:44,680
+the paper, doing some gardening, shopping for
+
+242
+00:22:44,680 --> 00:22:50,220
+food, making meals, and eat them in the evening.
+
+243
+00:22:50,780 --> 00:22:54,540
+So this is her hobby.
+
+244
+00:22:55,220 --> 00:22:59,900
+Now, why does she spend her holiday at home? She
+
+245
+00:22:59,900 --> 00:23:07,280
+spends her holiday Where? At home. So she dreams
+
+246
+00:23:07,280 --> 00:23:11,320
+of her home. She dreams of her home. Why? Because
+
+247
+00:23:11,320 --> 00:23:17,700
+it is the holiday. The holiday is home. Why?
+
+248
+00:23:18,320 --> 00:23:24,380
+Because she spends
+
+249
+00:23:24,380 --> 00:23:28,470
+her holiday at home, not abroad. Because she
+
+250
+00:23:28,470 --> 00:23:36,570
+travels so much. She travels so much in her job.
+
+251
+00:23:37,570 --> 00:23:43,130
+So because she travels, she travels so much. So
+
+252
+00:23:43,130 --> 00:23:48,990
+the holiday is at home. On the contrary. Working
+
+253
+00:23:48,990 --> 00:23:54,910
+is outside. Holiday inside at home. Yeah.
+
+254
+00:23:57,290 --> 00:24:04,090
+Move around without any hurry. Move around without
+
+255
+00:24:04,090 --> 00:24:09,830
+hurry. My mother at home walk around the house
+
+256
+00:24:09,830 --> 00:24:12,970
+here and there and there and there without a
+
+257
+00:24:12,970 --> 00:24:18,470
+hurry. What's it? It means putter.
+
+258
+00:24:19,450 --> 00:24:23,590
+Putter around.
+
+259
+00:24:27,600 --> 00:24:32,160
+Put around means walking or moving without hurry.
+
+260
+00:24:34,440 --> 00:24:39,320
+She has her own travel agency. Why she spends her
+
+261
+00:24:39,320 --> 00:24:43,320
+holiday at home? Because she has her own travel
+
+262
+00:24:43,320 --> 00:24:52,640
+agency and she travels so much. She travels so
+
+263
+00:24:52,640 --> 00:25:00,080
+much. She travels So much.
+
+264
+00:25:07,280 --> 00:25:13,940
+Yes. What's the meaning of move around? It means
+
+265
+00:25:13,940 --> 00:25:20,100
+put around, put around. Yes, someone to read the
+
+266
+00:25:20,100 --> 00:25:27,160
+question and the answer. Hmm. Why does she spend
+
+267
+00:25:27,160 --> 00:25:33,580
+holidays at home? She travels so much. And my job
+
+268
+00:25:33,580 --> 00:25:40,040
+that just work here. Yeah. And the meaning, the
+
+269
+00:25:40,040 --> 00:25:41,140
+synonyms?
+
+270
+00:25:44,240 --> 00:25:49,540
+Move around without any hurry. Putter around. Put
+
+271
+00:25:49,540 --> 00:25:55,220
+it around. Put it around. Yes. Usually, I expect
+
+272
+00:25:55,220 --> 00:26:00,400
+that all of you prepare these paragraphs at home.
+
+273
+00:26:01,720 --> 00:26:05,920
+I expect you to prepare these paragraphs, this
+
+274
+00:26:05,920 --> 00:26:12,520
+text, at home. Now, next. My business holiday.
+
+275
+00:26:19,280 --> 00:26:27,140
+now we leave the holiday at home and now the
+
+276
+00:26:27,140 --> 00:26:31,860
+business the business her business is also holiday
+
+277
+00:26:31,860 --> 00:26:36,760
+but business holiday working working holiday work
+
+278
+00:26:36,760 --> 00:26:42,920
+not holiday not for pleasure no for work so now
+
+279
+00:26:42,920 --> 00:26:49,260
+let's come to the Business. Her business. But her
+
+280
+00:26:49,260 --> 00:26:52,820
+business is holidays. So we call it her business
+
+281
+00:26:52,820 --> 00:26:57,400
+holidays. Not holiday for pleasure. For pleasure
+
+282
+00:26:57,400 --> 00:27:02,840
+at home. But now the work is business. I have
+
+283
+00:27:02,840 --> 00:27:08,340
+three trips coming up. Now Karen Saunders speak
+
+284
+00:27:08,340 --> 00:27:14,350
+about her job. She travels abroad four or three
+
+285
+00:27:14,350 --> 00:27:20,350
+times a year. Yes. Now she says, I have three
+
+286
+00:27:20,350 --> 00:27:25,110
+trips coming up. How many times she will travel
+
+287
+00:27:25,110 --> 00:27:33,050
+this year? Three times, three trips coming up in
+
+288
+00:27:33,050 --> 00:27:39,450
+the future. I'm looking forward to going to Canada
+
+289
+00:27:39,450 --> 00:27:44,760
+soon. what is the first place she intended to go
+
+290
+00:27:44,760 --> 00:27:51,860
+to canada yes canada is the first one soon soon
+
+291
+00:27:51,860 --> 00:27:58,200
+shortly now i'm looking forward to this too is a
+
+292
+00:27:58,200 --> 00:28:02,880
+preposition a preposition not the two infinitive
+
+293
+00:28:02,880 --> 00:28:09,570
+if it is two infinitive i want to study I need to
+
+294
+00:28:09,570 --> 00:28:14,670
+go, this is too infinitive. No, this is too as a
+
+295
+00:28:14,670 --> 00:28:19,930
+preposition. because it is a preposition we use a
+
+296
+00:28:19,930 --> 00:28:26,130
+noun after it so we say to going huh to going why
+
+297
+00:28:26,130 --> 00:28:29,930
+because it is a preposition i'm looking forward to
+
+298
+00:28:29,930 --> 00:28:33,810
+going i'm looking forward to hearing i'm looking
+
+299
+00:28:33,810 --> 00:28:37,670
+i'm looking forward to visiting or sometimes we
+
+300
+00:28:37,670 --> 00:28:42,180
+say i look forward to hearing I look forward to
+
+301
+00:28:42,180 --> 00:28:46,940
+visiting listening seeing uh-huh so to is
+
+302
+00:28:46,940 --> 00:28:53,280
+preposition and this is gerund ieg don't use go
+
+303
+00:28:53,280 --> 00:28:59,600
+after this too we use we say going see seeing etc
+
+304
+00:28:59,600 --> 00:29:04,600
+so she says I'm looking forward to going to Canada
+
+305
+00:29:04,600 --> 00:29:08,980
+soon so the first trip the first business holiday
+
+306
+00:29:11,030 --> 00:29:15,270
+that are coming soon is to Canada. This is the
+
+307
+00:29:15,270 --> 00:29:21,810
+first one. To Canada, where I'm staying for four
+
+308
+00:29:21,810 --> 00:29:28,490
+nights at the ice hotel. She will spend four
+
+309
+00:29:28,490 --> 00:29:36,210
+nights at the ice hotel. Ice hotel. Hotel made of
+
+310
+00:29:36,210 --> 00:29:44,350
+ice. Hotel building made of ice not of block. No
+
+311
+00:29:44,350 --> 00:29:54,130
+This is a giant igloo This is a big ice house a
+
+312
+00:29:54,130 --> 00:30:00,670
+big ice house igloo ice house or how ice building
+
+313
+00:30:00,670 --> 00:30:10,270
+So this hotel is made of ice It is built from ice.
+
+314
+00:30:12,250 --> 00:30:19,110
+Situated in Monteminsi Fall Park. This name. This
+
+315
+00:30:19,110 --> 00:30:23,890
+is the place. This is the place. What is it? What
+
+316
+00:30:23,890 --> 00:30:28,990
+is this place? Just 20 minutes from downtown
+
+317
+00:30:28,990 --> 00:30:36,180
+Quebec. From Quebec. So this is the city and it is
+
+318
+00:30:36,180 --> 00:30:42,880
+20 minutes far away from Kubik. When we say how
+
+319
+00:30:42,880 --> 00:30:47,980
+long, we can say either the distance or the time.
+
+320
+00:30:48,940 --> 00:30:53,140
+The time. How long did it take you to go to Rafah?
+
+321
+00:30:53,620 --> 00:30:57,290
+Half an hour. 30 kilometers.
+
+322
+00:30:59,930 --> 00:31:04,310
+So with how long? We answer either in the distance
+
+323
+00:31:04,310 --> 00:31:09,650
+or in the period of time. It takes 20 minutes or
+
+324
+00:31:09,650 --> 00:31:15,970
+it takes 30 miles. So here it is situated in
+
+325
+00:31:15,970 --> 00:31:21,590
+Mottibensi Fall Park. What is it? It is 20 minutes
+
+326
+00:31:21,590 --> 00:31:27,410
+from Kubik. It is 20 minutes from cubic. It's
+
+327
+00:31:27,410 --> 00:31:32,310
+about 20 minutes far away from cubic. Where is
+
+328
+00:31:32,310 --> 00:31:37,230
+cubic? Downtown. Downtown in the middle of a
+
+329
+00:31:37,230 --> 00:31:41,650
+cubic. The middle, in the center. In the center of
+
+330
+00:31:41,650 --> 00:31:49,130
+the city. So the distance between the ice hotel
+
+331
+00:31:49,130 --> 00:31:55,130
+and the center of the city, cubic, is about 20
+
+332
+00:31:55,130 --> 00:31:59,530
+minutes. It's about 20 minutes. How long is it?
+
+333
+00:31:59,970 --> 00:32:07,310
+It's about 20 minutes. It is made from this hotel.
+
+334
+00:32:08,630 --> 00:32:14,210
+The ice hotel is made from 4
+
+335
+00:32:14,210 --> 00:32:25,620
+,500 tons of snow. Tons of snow. This is snow. huh
+
+336
+00:32:25,620 --> 00:32:38,960
+light snow and 250 tons of ice of ice uh-huh so
+
+337
+00:32:38,960 --> 00:32:46,380
+four thousand five hundred tons of snow and 250
+
+338
+00:32:46,380 --> 00:32:54,440
+tons of ice solid yes and it takes How long does
+
+339
+00:32:54,440 --> 00:32:59,980
+it take to build? Five weeks. Five weeks to build.
+
+340
+00:33:00,260 --> 00:33:03,900
+The duration of building, the time of building is
+
+341
+00:33:03,900 --> 00:33:12,180
+five weeks. This is the description about the Ice
+
+342
+00:33:12,180 --> 00:33:16,920
+Hotel. The Ice Hotel. What is it? It is in Canada.
+
+343
+00:33:17,900 --> 00:33:24,410
+Where in Canada? Near downtown Cubic. about 20
+
+344
+00:33:24,410 --> 00:33:29,430
+minutes from that cubic from the downtown cubic
+
+345
+00:33:29,430 --> 00:33:33,890
+this is the first holiday the first business
+
+346
+00:33:33,890 --> 00:33:39,070
+holiday for caring sounders the first one is to
+
+347
+00:33:39,070 --> 00:33:43,390
+canada what to canada in the ice hotel was it near
+
+348
+00:33:43,390 --> 00:33:51,230
+cubic how did they build it they built it using
+
+349
+00:33:52,320 --> 00:33:59,080
+Snow and ice. How long does it take to build? Five
+
+350
+00:33:59,080 --> 00:33:59,600
+weeks.
+
+351
+00:34:02,780 --> 00:34:11,460
+It's clear, yes? I will stay open for three
+
+352
+00:34:11,460 --> 00:34:17,040
+months. It will stay open for three months. Which
+
+353
+00:34:17,040 --> 00:34:21,020
+it? The hotel. The hotel
+
+354
+00:34:30,880 --> 00:34:38,920
+this hotel will be open will stay open for how
+
+355
+00:34:38,920 --> 00:34:44,920
+many months three months just three months why why
+
+356
+00:34:44,920 --> 00:34:51,640
+not all the year no just three months in winter
+
+357
+00:34:51,640 --> 00:34:57,770
+why because when the spring arrives After winter,
+
+358
+00:34:58,110 --> 00:35:03,710
+it comes spring. When spring arrives, it will
+
+359
+00:35:03,710 --> 00:35:10,010
+melt. Which it? The hotel. The hotel will finish.
+
+360
+00:35:10,990 --> 00:35:16,750
+Will melt. Becomes water. It will become water.
+
+361
+00:35:17,190 --> 00:35:22,310
+So, after three months, at most, there is no
+
+362
+00:35:22,310 --> 00:35:27,550
+hotel. It is water. It is melt. You understand? So
+
+363
+00:35:27,550 --> 00:35:32,310
+this hotel, which takes about five weeks to build,
+
+364
+00:35:33,330 --> 00:35:38,050
+stays open just for three months. After this,
+
+365
+00:35:38,430 --> 00:35:43,250
+spring comes and it will be melt. It will change
+
+366
+00:35:43,250 --> 00:35:44,870
+into water. No hotel.
+
+367
+00:35:47,580 --> 00:35:54,420
+then it will be built again for next year. So next
+
+368
+00:35:54,420 --> 00:35:59,820
+year in winter, they will build a hotel again
+
+369
+00:35:59,820 --> 00:36:04,940
+either maybe in a different place. So maybe in the
+
+370
+00:36:04,940 --> 00:36:09,200
+city place or in a different place from the
+
+371
+00:36:09,200 --> 00:36:14,500
+beginning with ice and snow for five weeks to
+
+372
+00:36:14,500 --> 00:36:19,650
+build a new one. Different place, not the same
+
+373
+00:36:19,650 --> 00:36:23,610
+place, maybe at a different place, maybe at the
+
+374
+00:36:23,610 --> 00:36:30,390
+same place, maybe. Each room, this hotel, which
+
+375
+00:36:30,390 --> 00:36:35,250
+lasts for three months, each room in this hotel is
+
+376
+00:36:35,250 --> 00:36:41,890
+supplied with, contains what? A sleeping bag. It
+
+377
+00:36:41,890 --> 00:36:48,930
+contains each room, Each room has a sleeping bag.
+
+378
+00:36:49,370 --> 00:36:59,770
+Bag for sleeping. Not beds. No, it is a bag. Made
+
+379
+00:36:59,770 --> 00:37:06,190
+from deer skins. From the skins of the deer, the
+
+380
+00:37:06,190 --> 00:37:13,120
+animal. So this bag will be warm. will be warm. It
+
+381
+00:37:13,120 --> 00:37:19,140
+is made of deer skins. The hotel has two art
+
+382
+00:37:19,140 --> 00:37:24,960
+galleries. Apart from the rooms with sleeping bags
+
+383
+00:37:24,960 --> 00:37:31,380
+made of the skin of deer, we have two art
+
+384
+00:37:31,380 --> 00:37:36,720
+galleries. Galleries, you know art galleries? Mm
+
+385
+00:37:36,720 --> 00:37:40,240
+-hmm for sculptures. Mm-hmm sometimes for
+
+386
+00:37:40,240 --> 00:37:45,220
+paintings Uh-huh. So in this hotel or this hotel
+
+387
+00:37:45,220 --> 00:37:51,760
+has two art galleries Featuring giving showing
+
+388
+00:37:51,760 --> 00:37:58,900
+showing what showing ice sculptures. Ah Not Not
+
+389
+00:37:58,900 --> 00:38:04,470
+pictures. No ice sculptures So in these two
+
+390
+00:38:04,470 --> 00:38:09,590
+galleries, in this hotel, we can see what? Ice
+
+391
+00:38:09,590 --> 00:38:16,470
+sculptures and an ice cinema. Oh, there is an ice
+
+392
+00:38:16,470 --> 00:38:21,950
+cinema. So we have two ice galleries and a cinema.
+
+393
+00:38:23,270 --> 00:38:29,510
+Two ice galleries and a cinema. Which one? An ice
+
+394
+00:38:29,510 --> 00:38:34,830
+cinema. So all the buildings in this hotel are
+
+395
+00:38:34,830 --> 00:38:39,070
+made of ice. We have two ice galleries and an ice
+
+396
+00:38:39,070 --> 00:38:47,330
+cinema. One cinema. It also has a bar. Two
+
+397
+00:38:47,330 --> 00:38:52,940
+galleries. Cinema and a bar for drinking alcohol.
+
+398
+00:38:53,500 --> 00:38:59,620
+It is bad in our religion. We don't want bars at
+
+399
+00:38:59,620 --> 00:39:04,820
+all. And we don't go there. It is forbidden. But
+
+400
+00:39:04,820 --> 00:39:10,460
+here it has a bar. Not for us. It has a bar where
+
+401
+00:39:10,460 --> 00:39:15,740
+all the drinks come
+
+402
+00:39:15,740 --> 00:39:21,220
+in glasses. All the drinks in this hotel comes in
+
+403
+00:39:21,220 --> 00:39:26,800
+glasses what made of ice ah glasses made of ice
+
+404
+00:39:26,800 --> 00:39:31,480
+cinema ice cinema galleries ice galleries all
+
+405
+00:39:32,520 --> 00:39:36,340
+Everything in the building is made from ice. Of
+
+406
+00:39:36,340 --> 00:39:43,180
+course, I will visit them all. She says, when I go
+
+407
+00:39:43,180 --> 00:39:46,440
+to this hotel, I will visit everything, all of
+
+408
+00:39:46,440 --> 00:39:51,340
+them, the galleries, cinema and the bar. But if
+
+409
+00:39:51,340 --> 00:39:57,680
+you go there, don't go to the bar. Don't approach
+
+410
+00:39:57,680 --> 00:40:06,130
+the place. A question. Animals are mentioned We
+
+411
+00:40:06,130 --> 00:40:11,430
+say some animals in the passage which ones? And
+
+412
+00:40:11,430 --> 00:40:22,610
+why? We said about deer deer deer skins It is deer
+
+413
+00:40:22,610 --> 00:40:30,710
+skins why they say the word deer because because
+
+414
+00:40:31,450 --> 00:40:35,710
+The hotel or each hotel, each room is supplied
+
+415
+00:40:35,710 --> 00:40:42,010
+with a sleeping bag made of or made from deer
+
+416
+00:40:42,010 --> 00:40:42,870
+skins.
+
+417
+00:40:46,390 --> 00:40:51,870
+Deer sleeping bags in the ice hotel are made of
+
+418
+00:40:51,870 --> 00:40:57,170
+deer skins. Deer skins, the skin of the deer.
+
+419
+00:40:58,480 --> 00:41:00,880
+Again the question you can read the question and
+
+420
+00:41:00,880 --> 00:41:12,220
+give me the answer So
+
+421
+00:41:12,220 --> 00:41:17,620
+this is a comprehension question to test you in
+
+422
+00:41:17,620 --> 00:41:21,680
+some places If you understand the passage or not,
+
+423
+00:41:21,680 --> 00:41:26,040
+generally they are quick questions now
+
+424
+00:41:27,690 --> 00:41:30,050
+The other one. Now we finish Canada.
+
+425
+00:41:37,350 --> 00:41:43,750
+So the first trip is where? To Canada. Where in
+
+426
+00:41:43,750 --> 00:41:49,440
+Canada? In Quebec. What's in Quebec? Near. cubic.
+
+427
+00:41:49,780 --> 00:41:55,080
+How far is it? It is the ice hotel. How far is it?
+
+428
+00:41:55,600 --> 00:42:00,580
+It's about 20 miles. No, no, not 20 miles, 20
+
+429
+00:42:00,580 --> 00:42:05,680
+minutes, maybe 20 miles also. So this hotel, what
+
+430
+00:42:05,680 --> 00:42:10,870
+is special about this hotel? It is not natural. It
+
+431
+00:42:10,870 --> 00:42:15,950
+is made of ice. Really? Yeah. And how can we sleep
+
+432
+00:42:15,950 --> 00:42:20,410
+there? We have sleeping bags. Really? Yeah. They
+
+433
+00:42:20,410 --> 00:42:25,890
+are made of deer skins. What can we see in this
+
+434
+00:42:25,890 --> 00:42:33,610
+hotel? We see two ice galleries, a cinema, a bar,
+
+435
+00:42:34,130 --> 00:42:41,110
+and all the drinks are often in glasses. Glasses,
+
+436
+00:42:41,170 --> 00:42:46,030
+not really glasses. No, glasses made of ice. And
+
+437
+00:42:46,030 --> 00:42:51,430
+how long does it take to build? Five weeks. And
+
+438
+00:42:51,430 --> 00:42:56,770
+after this, when spring comes, when spring comes,
+
+439
+00:42:56,850 --> 00:43:02,180
+it will melt. It will vanish. It will be nothing.
+
+440
+00:43:02,960 --> 00:43:08,880
+It melts, changes to water. So all this hotel and
+
+441
+00:43:08,880 --> 00:43:12,500
+everything in it, just for three months. And then
+
+442
+00:43:12,500 --> 00:43:17,300
+the next year, they built it again. Is it in the
+
+443
+00:43:17,300 --> 00:43:20,600
+same place? Maybe in the same place or in a
+
+444
+00:43:20,600 --> 00:43:26,510
+different place. Is it clear? So after this
+
+445
+00:43:26,510 --> 00:43:33,690
+preparation for visiting Canada, after Canada,
+
+446
+00:43:34,750 --> 00:43:40,090
+Karen Saunders are going to some other place where
+
+447
+00:43:40,090 --> 00:43:45,570
+I, in complete contrast to the Ice Hotel,
+
+448
+00:43:46,510 --> 00:43:50,810
+something completely different. I'm going to
+
+449
+00:43:50,810 --> 00:43:57,890
+Dubai. So after Canada, after the ice, the ice
+
+450
+00:43:57,890 --> 00:44:03,670
+hotel, she will go to Dubai, the hot country. On
+
+451
+00:44:03,670 --> 00:44:07,570
+the contrary, complete contrast. Complete
+
+452
+00:44:07,570 --> 00:44:13,230
+contrast. I'm going to Dubai. Going to Dubai,
+
+453
+00:44:13,350 --> 00:44:20,440
+intention or arrangement? I'm going. I'm going is
+
+454
+00:44:20,440 --> 00:44:26,160
+it arrangement or intention it is it is
+
+455
+00:44:26,160 --> 00:44:31,060
+arrangement why because going to dubai not going
+
+456
+00:44:31,060 --> 00:44:37,620
+to play going to visit no going to and the noun so
+
+457
+00:44:37,620 --> 00:44:42,000
+this is the present continuous huh so the present
+
+458
+00:44:42,000 --> 00:44:46,720
+continuous express an idea about arrangement,
+
+459
+00:44:47,260 --> 00:44:52,580
+future arrangement. So Karen Saunders arranged to
+
+460
+00:44:52,580 --> 00:44:57,440
+visit Dubai after Canada.
+
+461
+00:44:59,040 --> 00:45:03,200
+What is the difference between Dubai and Canada?
+
+462
+00:45:03,700 --> 00:45:10,820
+This is cold and this is hot. I'm going to Dubai
+
+463
+00:45:10,820 --> 00:45:16,090
+the following month. The following month not next
+
+464
+00:45:16,090 --> 00:45:19,250
+month. So next month is main. No, no, no the
+
+465
+00:45:19,250 --> 00:45:23,930
+following month from her speaking From her
+
+466
+00:45:23,930 --> 00:45:26,830
+speaking maybe before three or four years. She's
+
+467
+00:45:26,830 --> 00:45:29,610
+speaking about something in the past So the
+
+468
+00:45:29,610 --> 00:45:33,090
+following month, so this is in the indirect speech
+
+469
+00:45:33,090 --> 00:45:37,610
+In the direct speech we say next month in the
+
+470
+00:45:37,610 --> 00:45:42,030
+indirect like here. We say the following month so
+
+471
+00:45:42,030 --> 00:45:45,990
+here I'm going to Dubai for the following month.
+
+472
+00:45:46,530 --> 00:45:53,530
+Why? Why? To stay a few days. Here, she will stay
+
+473
+00:45:53,530 --> 00:45:58,770
+for a few days. Four or five or six days. But in
+
+474
+00:45:58,770 --> 00:46:03,750
+Canada, just four nights. Four nights at the
+
+475
+00:46:03,750 --> 00:46:09,810
+hotel. But here, five days in Dubai. At the
+
+476
+00:46:09,810 --> 00:46:15,070
+spectacular Porj Al Arab. Ah, spectacular Burj Al
+
+477
+00:46:15,070 --> 00:46:19,190
+Arab, the wonderful Burj Al Arab, the wonderful
+
+478
+00:46:19,190 --> 00:46:23,610
+tower, the wonderful Arabian tower. So this
+
+479
+00:46:23,610 --> 00:46:27,610
+wonderful building in Arabic, which means the
+
+480
+00:46:27,610 --> 00:46:33,830
+Arabian tower. So she will go to Dubai, where? To
+
+481
+00:46:33,830 --> 00:46:38,290
+the Arabian tower. It is called in Arabic, Burj Al
+
+482
+00:46:38,290 --> 00:46:47,570
+Arab. It's shaped Like a giant sail. Like a sail,
+
+483
+00:46:47,790 --> 00:46:52,310
+giant sail. Not like the hotel. The hotel was a
+
+484
+00:46:52,310 --> 00:46:57,670
+giant igloo. But here it is a giant sail. You know
+
+485
+00:46:57,670 --> 00:47:05,790
+sail? This sail of the ship, of the boat. So in
+
+486
+00:47:05,790 --> 00:47:09,310
+Dubai, the hotel in Dubai, Burj Al Arab in Dubai
+
+487
+00:47:09,310 --> 00:47:16,270
+is like the Seal. Giant seal. And it rises
+
+488
+00:47:16,270 --> 00:47:23,730
+dramatically out of the Arabian Gulf. So it is
+
+489
+00:47:23,730 --> 00:47:25,890
+built where? Where?
+
+490
+00:47:28,810 --> 00:47:35,650
+You see? Here. In the Gulf. In the water. in the
+
+491
+00:47:35,650 --> 00:47:44,630
+water. So here it rises dramatically out of the
+
+492
+00:47:44,630 --> 00:47:48,130
+Arabian Gulf, in the Arabian Gulf. Dramatically
+
+493
+00:47:48,130 --> 00:47:53,430
+means in an impressive way, in an exciting way,
+
+494
+00:47:54,070 --> 00:48:00,890
+something beautiful, wonderful. Where? In the
+
+495
+00:48:00,890 --> 00:48:06,880
+Arabian Gulf. What shape is it? It's like a giant
+
+496
+00:48:06,880 --> 00:48:07,840
+sail.
+
+497
+00:48:09,920 --> 00:48:13,980
+It rises dramatically out of the Arabian Gulf.
+
+498
+00:48:14,820 --> 00:48:20,100
+Each room in this hotel, the Bajir Arab, each room
+
+499
+00:48:20,100 --> 00:48:27,250
+in this hotel has sea views. You can see The water
+
+500
+00:48:27,250 --> 00:48:32,950
+from every room. So each room in this hotel has a
+
+501
+00:48:32,950 --> 00:48:38,350
+panorama on the sea, on the Gulf, on the Arabian
+
+502
+00:48:38,350 --> 00:48:38,710
+Gulf.
+
+503
+00:48:41,570 --> 00:48:43,810
+A question here, what's the meaning of in an
+
+504
+00:48:43,810 --> 00:48:47,970
+exciting and impressive way? Dramatically.
+
+505
+00:48:55,170 --> 00:48:59,510
+So this is a word from the passage. And this is a
+
+506
+00:48:59,510 --> 00:49:01,670
+word, the meaning of this word.
+
+507
+00:49:08,090 --> 00:49:10,430
+So you can give me the answer again here.
+
+508
+00:49:14,190 --> 00:49:17,010
+Read this.
+
+509
+00:49:23,260 --> 00:49:28,500
+Dramatically. One word. This is an adverb. And
+
+510
+00:49:28,500 --> 00:49:32,240
+this is an adverb. An adverb with what? With way.
+
+511
+00:49:32,920 --> 00:49:39,980
+In a good way. Will. In a careful way. Carefully.
+
+512
+00:49:40,900 --> 00:49:47,360
+In an exciting way. Dramatically. Or method. Or
+
+513
+00:49:47,360 --> 00:49:50,380
+style. Something like this. So, dramatically means
+
+514
+00:49:50,380 --> 00:49:52,880
+in an exciting way.
+
+515
+00:49:57,920 --> 00:50:02,420
+What will you do in Dubai? What will you do in
+
+516
+00:50:02,420 --> 00:50:08,160
+Dubai? In Bogy Arab. I really want to try the
+
+517
+00:50:08,160 --> 00:50:11,640
+restaurant in the tube at the top next to the
+
+518
+00:50:11,640 --> 00:50:20,640
+Hulubad. So Karen Saunders is going to Dubai. Why?
+
+519
+00:50:21,120 --> 00:50:28,470
+She wants to try the restaurant. to eat from the
+
+520
+00:50:28,470 --> 00:50:33,870
+Arabian food, to see if it is good or bad. So I
+
+521
+00:50:33,870 --> 00:50:39,510
+really want to try to have an experience of the
+
+522
+00:50:39,510 --> 00:50:43,610
+restaurant, the food, the Arab food, in the tube,
+
+523
+00:50:43,990 --> 00:50:48,990
+the top, at the top next to the helipad. So
+
+524
+00:50:48,990 --> 00:50:55,320
+helipad, like here, This place, when I look at the
+
+525
+00:50:55,320 --> 00:51:02,020
+sea, it is called helipad. So at the top, we have
+
+526
+00:51:02,020 --> 00:51:07,340
+a restaurant and we have a balcony or a hole to
+
+527
+00:51:07,340 --> 00:51:11,680
+look at the water. So in the restaurant, she will
+
+528
+00:51:11,680 --> 00:51:15,400
+try some food, the restaurant. After this, she
+
+529
+00:51:15,400 --> 00:51:20,520
+goes to see the water or the Arabian Gulf. Other
+
+530
+00:51:20,520 --> 00:51:28,370
+must-do's Must-do's include shopping. After going
+
+531
+00:51:28,370 --> 00:51:32,030
+to the restaurant, after looking at the panorama
+
+532
+00:51:32,030 --> 00:51:39,070
+of the Arabian Gulf, don't forget to
+
+533
+00:51:39,070 --> 00:51:43,750
+go shopping. So the visit to Dubai should include
+
+534
+00:51:43,750 --> 00:51:48,460
+shopping in the markets. Shopping in the markets.
+
+535
+00:51:48,860 --> 00:51:53,020
+This is essential. This is necessary. Must do's.
+
+536
+00:51:53,520 --> 00:51:57,380
+Don't forget. Don't miss it. It is necessary. When
+
+537
+00:51:57,380 --> 00:52:00,780
+we go to Egypt, don't forget to see the Nile.
+
+538
+00:52:02,080 --> 00:52:06,340
+Don't forget to see the pyramids. Don't forget to
+
+539
+00:52:06,340 --> 00:52:12,640
+visit the Liberty Square. At Tahrir Square. Don't
+
+540
+00:52:12,640 --> 00:52:20,070
+forget to See the metro, the underground. So this
+
+541
+00:52:20,070 --> 00:52:24,430
+is special about Cairo, about Egypt. And if you go
+
+542
+00:52:24,430 --> 00:52:29,190
+to Alexandria, don't forget to go to the sea. But
+
+543
+00:52:29,190 --> 00:52:33,110
+here in Dubai, don't forget to go shopping.
+
+544
+00:52:34,370 --> 00:52:37,670
+Shopping in the markets called souk. In Arabic,
+
+545
+00:52:38,270 --> 00:52:45,130
+souk. Souks. Aswaq. You can buy designer clothes
+
+546
+00:52:45,130 --> 00:52:50,410
+You can buy from this souk designer clothes and
+
+547
+00:52:50,410 --> 00:52:56,750
+new clothes with good designer modern modern a new
+
+548
+00:52:56,750 --> 00:53:03,150
+fashion perfumes good perfumes expensive ones
+
+549
+00:53:03,150 --> 00:53:07,330
+perfumes and spices
+
+550
+00:53:09,300 --> 00:53:14,840
+paper yes but what I want is some gold jewelry
+
+551
+00:53:14,840 --> 00:53:22,900
+because she is a girl she wants jewelry yes made
+
+552
+00:53:22,900 --> 00:53:28,900
+of gold I'm going I'm also going to visit the
+
+553
+00:53:28,900 --> 00:53:36,240
+camel races so the must do's don't forget to go
+
+554
+00:53:36,240 --> 00:53:44,190
+shopping and to visit the camel racing. So the
+
+555
+00:53:44,190 --> 00:53:47,530
+shopping and the camel racing is essential if you
+
+556
+00:53:47,530 --> 00:53:53,090
+want to Dubai. Now we finished. We finished Dubai.
+
+557
+00:53:53,790 --> 00:54:00,310
+After Dubai, the next trip after Dubai is
+
+558
+00:54:00,310 --> 00:54:04,010
+different again. Also, it is something different.
+
+559
+00:54:04,970 --> 00:54:07,290
+So the first one is different from the other, from
+
+560
+00:54:07,290 --> 00:54:11,890
+the second. Canada is different from Dubai. Now,
+
+561
+00:54:12,230 --> 00:54:16,230
+the third trip is also different. Different again.
+
+562
+00:54:16,590 --> 00:54:22,210
+It's Abu Bawabs rivers. The rivers of Abu Bawabs.
+
+563
+00:54:22,390 --> 00:54:26,490
+Abu Bawabs rivers. Where is it? In silos. What is
+
+564
+00:54:26,490 --> 00:54:32,090
+silos? In Tanzania. So she will go after Dubai to
+
+565
+00:54:32,090 --> 00:54:40,780
+Tanzania. Tanzania in the in the silos rivers for
+
+566
+00:54:40,780 --> 00:54:47,200
+a seven-day safari for a seven-day holiday for
+
+567
+00:54:47,200 --> 00:54:53,970
+hunting seven day Look here, we have 70, one word,
+
+568
+00:54:54,350 --> 00:55:00,070
+compound adjective, without s, without s, and with
+
+569
+00:55:00,070 --> 00:55:05,970
+a hyphen, without if and with a hyphen. So it is
+
+570
+00:55:05,970 --> 00:55:11,690
+as one compound adjective. So why will she go to
+
+571
+00:55:11,690 --> 00:55:18,230
+Tanzania for a seven-day safari, a visit, and I'm
+
+572
+00:55:18,230 --> 00:55:22,740
+looking forward to so-and-so? So what's the
+
+573
+00:55:22,740 --> 00:55:25,700
+meaning of animals? I mentioned which ones and
+
+574
+00:55:25,700 --> 00:55:28,760
+why. Here also there are animals I mentioned. What
+
+575
+00:55:28,760 --> 00:55:36,180
+are they? Camel. Camel races. Camel races. What
+
+576
+00:55:36,180 --> 00:55:40,780
+about things that should not be missed? The
+
+577
+00:55:40,780 --> 00:55:46,660
+meaning of this? Must do's.
+
+578
+00:55:46,920 --> 00:55:54,210
+Must do's. So the answer here Camels. You can
+
+579
+00:55:54,210 --> 00:55:58,370
+visit camel races in Dubai. Again, what's the
+
+580
+00:55:58,370 --> 00:56:01,910
+meaning of things that should not be missed? Must
+
+581
+00:56:01,910 --> 00:56:03,210
+do's.
+
+582
+00:56:04,970 --> 00:56:10,750
+After this, in the third, journey or the third
+
+583
+00:56:10,750 --> 00:56:15,650
+holiday, we have one brochure. One brochure. What
+
+584
+00:56:15,650 --> 00:56:19,770
+about the brochures here? About two things. A
+
+585
+00:56:19,770 --> 00:56:24,270
+brochure about two things. What are they? What to
+
+586
+00:56:24,270 --> 00:56:31,670
+see in Tanzania. What to see and what to do. What
+
+587
+00:56:31,670 --> 00:56:35,470
+to see and what to do. What to see there? A
+
+588
+00:56:35,470 --> 00:56:39,800
+brochure about visiting Tanzania. Saying each
+
+589
+00:56:39,800 --> 00:56:47,980
+treetop room, treetop, compound adjective as one
+
+590
+00:56:47,980 --> 00:56:56,620
+word. Each room has views over the vast forested
+
+591
+00:56:56,620 --> 00:57:01,260
+banks, banks of the river. So Tanzania is full of
+
+592
+00:57:01,260 --> 00:57:08,940
+rivers and wood forests. So here, each one room in
+
+593
+00:57:08,940 --> 00:57:15,120
+this wood has views over the vast, the big, the
+
+594
+00:57:15,120 --> 00:57:19,540
+big faucet banks of the refugee river. So this is
+
+595
+00:57:19,540 --> 00:57:23,740
+one river from the Tanzania's rivers, refugee
+
+596
+00:57:23,740 --> 00:57:28,420
+rivers. What about it? Which runs through one of
+
+597
+00:57:28,420 --> 00:57:33,680
+the largest game reserves, game reserves for their
+
+598
+00:57:33,680 --> 00:57:38,340
+animals. In Africa. So when you go to Tanzania,
+
+599
+00:57:39,200 --> 00:57:47,080
+you will have rooms in the forest. Rooms in the
+
+600
+00:57:47,080 --> 00:57:51,300
+forest. And it is on the river. Refugee river. It
+
+601
+00:57:51,300 --> 00:57:57,080
+is in a game reserves. What is it? In Africa. What
+
+602
+00:57:57,080 --> 00:58:04,400
+to do? Doing. Two things. Safari by land. By land
+
+603
+00:58:04,400 --> 00:58:10,710
+rover. Safari by click. Safari by Mercedes. Safari
+
+604
+00:58:10,710 --> 00:58:15,650
+by Jeep. No, no, no, no. By Land Rover. Why?
+
+605
+00:58:15,750 --> 00:58:19,570
+Because it's strong. It is strong and protected.
+
+606
+00:58:20,270 --> 00:58:24,610
+This car, this car is strong car, like the Jeep.
+
+607
+00:58:25,450 --> 00:58:30,810
+So Safari, a journey by the Jeep. A journey means
+
+608
+00:58:30,810 --> 00:58:40,270
+Safari by Land Rover. In search of what? Why we go
+
+609
+00:58:40,270 --> 00:58:44,550
+with a Jeep like this? In search of elephants,
+
+610
+00:58:46,310 --> 00:58:52,430
+rhinos, and lions. So this is in the wood. These
+
+611
+00:58:52,430 --> 00:58:56,430
+animals are on land. Or if you don't want the
+
+612
+00:58:56,430 --> 00:59:04,460
+land, or by boat. You can go by boat. Either By
+
+613
+00:59:04,460 --> 00:59:08,080
+land or by boat? By boat along the refugee river
+
+614
+00:59:08,080 --> 00:59:15,260
+again. In search of what? Crocodile, hippos, and
+
+615
+00:59:15,260 --> 00:59:23,280
+rare birds. So either to go for a trip by boat or
+
+616
+00:59:23,280 --> 00:59:27,260
+by land rover. Here, animals are mentioned. Which
+
+617
+00:59:27,260 --> 00:59:33,740
+one and why? All these animals. six animals in the
+
+618
+00:59:33,740 --> 00:59:38,060
+water and on land. Why they are mentioned? Why
+
+619
+00:59:38,060 --> 00:59:42,820
+they are mentioned? Because they are mentioned in
+
+620
+00:59:42,820 --> 00:59:46,780
+Tanzania, you can see elephants, rhinoceros,
+
+621
+00:59:47,200 --> 00:59:53,900
+lions, crocodiles, hippos, and rare bird. Why? To
+
+622
+00:59:53,900 --> 00:59:57,040
+see them. Wassalamualaikum warahmatullahi
+
+623
+00:59:57,040 --> 00:59:58,980
+wabarakatuh. Thank you very much.
+
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/GswgQNNiHgg.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/GswgQNNiHgg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7d81bc742b4b80c7fec01374ca9ac984968563f3
--- /dev/null
+++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/GswgQNNiHgg.srt
@@ -0,0 +1,1444 @@
+
+1
+00:00:20,980 --> 00:00:26,200
+Assalamualaikum Warahmatullahi Wabarakatuh. Today, 
+
+2
+00:00:26,380 --> 00:00:29,540
+Inshallah, we are going to study present perfect 
+
+3
+00:00:29,540 --> 00:00:35,620
+symbol in the active and in the passive. With these 
+
+4
+00:00:35,620 --> 00:00:40,000
+two pages, unit seven. The first exercise, how do 
+
+5
+00:00:40,000 --> 00:00:46,820
+you do? It asks about the job. So answer these 
+
+6
+00:00:46,820 --> 00:00:51,180
+questions about you. Number one, what do you do? 
+
+7
+00:00:51,340 --> 00:00:55,780
+It means, what is your job? Say, I'm a student, 
+
+8
+00:00:56,620 --> 00:01:02,660
+I'm a teacher, I'm an engineer. Number two, how 
+
+9
+00:01:02,660 --> 00:01:05,780
+long have you been or have you had your present 
+
+10
+00:01:05,780 --> 00:01:13,660
+job? For two years, since 2011. Or sometimes I 
+
+11
+00:01:13,660 --> 00:01:19,210
+say, I don't have a job. I'm a student. Yeah. 
+
+12
+00:01:19,910 --> 00:01:25,170
+Number three, what did you do before that? I 
+
+13
+00:01:25,170 --> 00:01:31,630
+worked in a bank. I was at school. Number four, 
+
+14
+00:01:32,210 --> 00:01:36,370
+which foreign countries have you been to? I have 
+
+15
+00:01:36,370 --> 00:01:40,710
+been to China, I have been to Canada, to America, 
+
+16
+00:01:41,510 --> 00:01:45,330
+or I say I have never been to any foreign 
+
+17
+00:01:45,330 --> 00:01:50,650
+countries. Number four, when and why did you go 
+
+18
+00:01:50,650 --> 00:01:57,290
+there? When I went there in 2011. 
+
+19
+00:01:59,110 --> 00:02:04,090
+Again, number five, when and why did you go there? 
+
+20
+00:02:06,140 --> 00:02:12,280
+I went there in 2011. Why? I went there on 
+
+21
+00:02:12,280 --> 00:02:19,940
+business. Now the question is what tenses are used 
+
+22
+00:02:19,940 --> 00:02:27,420
+in the questions? The first one with do it is the 
+
+23
+00:02:27,420 --> 00:02:34,220
+present simple. The second one with have had 
+
+24
+00:02:35,590 --> 00:02:43,570
+present perfect simple. Number three with did and 
+
+25
+00:02:43,570 --> 00:02:54,150
+do, past simple. Number four with have been, present 
+
+26
+00:02:54,150 --> 00:03:02,690
+perfect simple and the last one, did and go, past 
+
+27
+00:03:02,690 --> 00:03:10,620
+simple. Now, after this introduction, we come to the 
+
+28
+00:03:10,620 --> 00:03:12,960
+quick answers again. 
+
+29
+00:03:17,660 --> 00:03:23,140
+So I'm a student. The question for how long is for 
+
+30
+00:03:23,140 --> 00:03:28,420
+two years, since 2001. I don't have a job. I'm a 
+
+31
+00:03:28,420 --> 00:03:34,070
+student. Here, the question of what did you do 
+
+32
+00:03:34,070 --> 00:03:37,770
+before that? I worked in a bank or I was at 
+
+33
+00:03:37,770 --> 00:03:43,910
+school. Number four, which foreign countries have 
+
+34
+00:03:43,910 --> 00:03:49,550
+you been to? I've been to Hungary and Canada. And the 
+
+35
+00:03:49,550 --> 00:03:57,910
+last one, when and why? When I went in 1993 or 10 
+
+36
+00:03:57,910 --> 00:04:04,110
+years ago. Why, I went there on business or I went 
+
+37
+00:04:04,110 --> 00:04:05,830
+there on holiday? 
+
+38
+00:04:07,710 --> 00:04:13,170
+And the next question, the first one is present 
+
+39
+00:04:13,170 --> 00:04:18,810
+simple. Number three and five, past simple. Number 
+
+40
+00:04:18,810 --> 00:04:23,070
+two and four, present perfect simple. 
+
+41
+00:04:27,480 --> 00:04:37,900
+Now, Nancy is being interviewed. She answered some 
+
+42
+00:04:37,900 --> 00:04:44,320
+questions. So here, does Nancy work for the 
+
+43
+00:04:44,320 --> 00:04:50,420
+Intertech? She said, I work for the Intertech. So 
+
+44
+00:04:50,420 --> 00:04:56,980
+she said, I work. So does she still work for 
+
+45
+00:04:56,980 --> 00:05:04,010
+Intertech? Yes. Yes, she does. 
+
+46
+00:05:06,830 --> 00:05:14,590
+She said, I worked for the BBC World Service. I 
+
+47
+00:05:14,590 --> 00:05:24,750
+worked, some finished events. So does she still 
+
+48
+00:05:24,750 --> 00:05:30,130
+work for the BBC? No, because she used the past 
+
+49
+00:05:30,130 --> 00:05:33,770
+simple. It's finished. A finished action. So here 
+
+50
+00:05:33,770 --> 00:05:38,570
+we say, no, she doesn't. 
+
+51
+00:05:41,970 --> 00:05:48,150
+So here, yes, she still worked for the Intertech. 
+
+52
+00:05:48,410 --> 00:05:53,550
+But here, no, because she worked for the BBC World 
+
+53
+00:05:53,550 --> 00:06:00,520
+Service in the past. Now, Nancy says, I work for 
+
+54
+00:06:00,520 --> 00:06:04,060
+Intertech Publishing. I have worked there for 
+
+55
+00:06:04,060 --> 00:06:09,240
+nearly five years. I worked for the BBC World 
+
+56
+00:06:09,240 --> 00:06:12,620
+Service. These three questions, this is in the 
+
+57
+00:06:12,620 --> 00:06:16,160
+past, in the present simple, and this is in the 
+
+58
+00:06:16,160 --> 00:06:24,170
+present perfect, and this is in the past simple. 
+
+59
+00:06:24,830 --> 00:06:28,190
+So the question here, what are the differences? 
+
+60
+00:06:29,670 --> 00:06:32,510
+The first one, present. 
+
+61
+00:06:34,690 --> 00:06:35,690
+Simple. 
+
+62
+00:06:39,310 --> 00:06:47,470
+The second one, present. Simple. Present. Perfect. 
+
+63
+00:06:48,950 --> 00:06:49,950
+Simple. 
+
+64
+00:06:53,180 --> 00:06:59,960
+The third one, I worked, past simple. What are the 
+
+65
+00:06:59,960 --> 00:07:03,960
+different tenses? Present simple, present perfect 
+
+66
+00:07:03,960 --> 00:07:11,800
+simple, past simple. Why are they used? She used, I 
+
+67
+00:07:11,800 --> 00:07:19,640
+work because she still works there. And here, she 
+
+68
+00:07:19,640 --> 00:07:29,350
+works in or for it until now. From the past until 
+
+69
+00:07:29,350 --> 00:07:36,630
+now. And here, a finished action. She is not 
+
+70
+00:07:36,630 --> 00:07:40,370
+working for the BBC now. So it is a finished 
+
+71
+00:07:40,370 --> 00:07:43,810
+action. When it is finished, we use past simple. 
+
+72
+00:07:45,070 --> 00:07:51,260
+When it is still, it is present simple. Uh-huh. 
+
+73
+00:07:51,700 --> 00:07:56,860
+And if you are speaking about today, referring to 
+
+74
+00:07:56,860 --> 00:08:00,160
+the past, we use present perfect. 
+
+75
+00:08:03,640 --> 00:08:15,280
+Look here. The answer for 
+
+76
+00:08:15,280 --> 00:08:20,220
+these questions. Yes, she does. No, she doesn't. 
+
+77
+00:08:20,730 --> 00:08:27,290
+Number two, Nancy says, I work for 
+
+78
+00:08:27,290 --> 00:08:32,290
+Intertech Publishing because she works for them 
+
+79
+00:08:32,290 --> 00:08:36,970
+now. So it is the present simple. She works now, 
+
+80
+00:08:37,410 --> 00:08:41,310
+so it is the present simple. She says, this is 
+
+81
+00:08:41,310 --> 00:08:44,250
+number one, the second one. She says, I have 
+
+82
+00:08:44,250 --> 00:08:50,080
+worked there for nearly five years because she's 
+
+83
+00:08:50,080 --> 00:08:58,100
+talking about pastime and present time. Pastime 
+
+84
+00:08:58,100 --> 00:09:02,420
+and present time. She began working for them, 
+
+85
+00:09:02,900 --> 00:09:08,640
+began working for them five years ago and she 
+
+86
+00:09:08,640 --> 00:09:12,880
+still works for 
+
+87
+00:09:12,880 --> 00:09:18,880
+them now. So we call this present perfect. Why 
+
+88
+00:09:18,880 --> 00:09:24,400
+because it's now and in the past. The third one, she 
+
+89
+00:09:24,400 --> 00:09:30,840
+says, I worked. I worked for the BBC World Service 
+
+90
+00:09:30,840 --> 00:09:38,400
+because she doesn't work there anymore. Uh-huh. She 
+
+91
+00:09:38,400 --> 00:09:45,130
+doesn't work there anymore, it's a finished action, 
+
+92
+00:09:45,130 --> 00:09:50,610
+finished, completely finished in the past. So it is 
+
+93
+00:09:50,610 --> 00:10:05,470
+past simple. Next also grammar 
+
+94
+00:10:05,470 --> 00:10:11,070
+reference page 143. Introduction 
+
+95
+00:10:11,070 --> 00:10:12,170
+to the present perfect 
+
+96
+00:10:17,350 --> 00:10:24,170
+The same form, have plus the past participle exists 
+
+97
+00:10:24,170 --> 00:10:29,690
+in many Arabian languages. But the usage in 
+
+98
+00:10:29,690 --> 00:10:34,630
+English is different. In English, the present 
+
+99
+00:10:34,630 --> 00:10:40,530
+perfect is essentially a present tense. So the 
+
+100
+00:10:40,530 --> 00:10:44,750
+present perfect is a present tense. 
+
+101
+00:10:46,510 --> 00:10:52,910
+But it also expresses the effect. It expresses the 
+
+102
+00:10:52,910 --> 00:10:57,610
+effect of the past actions and activities on the 
+
+103
+00:10:57,610 --> 00:11:01,650
+present. The effects of these actions or 
+
+104
+00:11:01,650 --> 00:11:06,470
+activities were in the present. So when I say 
+
+105
+00:11:06,470 --> 00:11:10,770
+present perfect, it means the present. But with 
+
+106
+00:11:10,770 --> 00:11:15,950
+the effects of the past. So this diagram is clear. 
+
+107
+00:11:17,160 --> 00:11:21,580
+We have past. We have present. But the present 
+
+108
+00:11:21,580 --> 00:11:26,300
+perfect speaks about the present connected with 
+
+109
+00:11:26,300 --> 00:11:29,800
+the past. With the past events or with the past 
+
+110
+00:11:29,800 --> 00:11:30,280
+effects. 
+
+111
+00:11:33,280 --> 00:11:36,920
+Present perfect means before now. 
+
+112
+00:11:39,260 --> 00:11:45,260
+The present perfect does not express when an 
+
+113
+00:11:45,260 --> 00:11:51,060
+action happened. If we say when, we should use the 
+
+114
+00:11:51,060 --> 00:11:55,220
+past simple. Without when, we use the present 
+
+115
+00:11:55,220 --> 00:12:01,020
+perfect. So here, the present perfect does not 
+
+116
+00:12:01,020 --> 00:12:07,320
+express when an action happened. If we say the 
+
+117
+00:12:07,320 --> 00:12:13,880
+exact time, so we have some verbs and we want to 
+
+118
+00:12:13,880 --> 00:12:14,900
+put them 
+
+119
+00:12:18,430 --> 00:12:27,770
+So now, go, the past simple of go is went and the 
+
+120
+00:12:27,770 --> 00:12:32,290
+past participle, gone. 
+
+121
+00:12:32,930 --> 00:12:37,230
+So we use this in the present simple, and we use 
+
+122
+00:12:37,230 --> 00:12:39,950
+this in the past simple, and we use this in the 
+
+123
+00:12:39,950 --> 00:12:45,830
+perfect, and in the passive. Perfect and the 
+
+124
+00:12:45,830 --> 00:12:53,050
+passive, also with negative adjective. Write, wrote 
+
+125
+00:12:53,050 --> 00:13:08,250
+written, drive, drove, driven, lose, lost, lost, have, had, 
+
+126
+00:13:08,250 --> 00:13:17,530
+had, read, read, read. Yes, who can read? Yeah. Go and gun. Right 
+
+127
+00:13:17,530 --> 00:13:23,030
+road written. Drive, drop, driven. Driven. Driven. 
+
+128
+00:13:23,230 --> 00:13:27,790
+Drive, drop, driven. Lose, lost, lost. Have, had, 
+
+129
+00:13:27,910 --> 00:13:32,390
+had. Read, read, read. Right road written. Sleep, 
+
+130
+00:13:32,550 --> 00:13:37,150
+slept, slept. Be, was, were, been. Eat, ate, eaten. 
+
+131
+00:13:37,410 --> 00:13:42,850
+Win, won, won. Meet, meet, meet. Yeah. Yes. Go and 
+
+132
+00:13:42,850 --> 00:13:43,150
+gun. 
+
+133
+00:14:07,110 --> 00:14:18,130
+When I say B, it means, M is R, M is R. Yes. Now, we 
+
+134
+00:14:18,130 --> 00:14:27,470
+want to match between A and B. Nancy says 
+
+135
+00:14:27,470 --> 00:14:31,450
+something about her life. So these are events of 
+
+136
+00:14:31,450 --> 00:14:36,930
+Nancy's life. And these are time expressions. 
+
+137
+00:14:39,350 --> 00:14:45,680
+Now this, is to match between line in A with a 
+
+138
+00:14:45,680 --> 00:14:51,020
+line in B. Number one, she was born. Nancy. Nancy 
+
+139
+00:14:51,020 --> 00:14:59,400
+was born. Nancy was born in 
+
+140
+00:14:59,400 --> 00:15:06,460
+Argentina in 1969. Number two, she went to school 
+
+141
+00:15:06,460 --> 00:15:11,180
+in Buenos Aires. She went to school in Buenos 
+
+142
+00:15:11,180 --> 00:15:15,430
+Aires until she was 11. 
+
+143
+00:15:18,410 --> 00:15:28,390
+She studied modern languages and journalism for 
+
+144
+00:15:28,390 --> 00:15:35,570
+three years at University College London. Number 
+
+145
+00:15:35,570 --> 00:15:38,150
+four, she's worked for Intertech 
+
+146
+00:15:41,100 --> 00:15:43,720
+for the last five years. 
+
+147
+00:15:46,200 --> 00:15:51,920
+She left the BBC five years ago. 
+
+148
+00:15:54,840 --> 00:15:58,360
+Number six, she lived in Berlin. 
+
+149
+00:16:02,320 --> 00:16:05,440
+She lived in Berlin. 
+
+150
+00:16:11,950 --> 00:16:18,690
+Yes, while she was working for the BBC. 
+
+151
+00:16:22,610 --> 00:16:28,070
+Number seven, she's been married twice. 
+
+152
+00:16:29,770 --> 00:16:30,370
+Twice. Twice. 
+
+153
+00:16:35,590 --> 00:16:43,740
+She's visited Japan a few times. Number nine, she 
+
+154
+00:16:43,740 --> 00:16:48,160
+hasn't heard if she got the job at World Watch 
+
+155
+00:16:48,160 --> 00:16:50,340
+Europe yet. 
+
+156
+00:16:53,680 --> 00:16:59,440
+Who can read? Number one, she was born in 
+
+157
+00:16:59,440 --> 00:17:06,040
+Argentina in 1969. Two, she went to school in 
+
+158
+00:17:06,040 --> 00:17:07,420
+Buenos Aires. 
+
+159
+00:17:12,110 --> 00:17:13,310
+Uh-huh. Three. 
+
+160
+00:17:19,410 --> 00:17:20,450
+Journalism. 
+
+161
+00:17:25,790 --> 00:17:26,830
+Four. 
+
+162
+00:17:36,690 --> 00:17:38,390
+Next. Yeah. 
+
+163
+00:17:42,020 --> 00:17:43,420
+Six. 
+
+164
+00:17:48,960 --> 00:17:50,360
+Next. 
+
+165
+00:17:52,960 --> 00:17:55,600
+Twice. Eight. 
+
+166
+00:17:57,860 --> 00:18:06,970
+A few times. Yes. And the last one. Yeah. She 
+
+167
+00:18:06,970 --> 00:18:12,570
+hasn't heard if she got the job at work, work with 
+
+168
+00:18:12,570 --> 00:18:13,650
+Europe. 
+
+169
+00:18:15,950 --> 00:18:32,430
+Yes. So this is about Nancy. And now again, 
+
+170
+00:18:32,850 --> 00:18:37,490
+who can read the answer? Yeah. She was born in 
+
+171
+00:18:37,490 --> 00:18:40,090
+Argentina in 1969. 
+
+172
+00:18:42,550 --> 00:18:48,550
+Two. She went to school in Paris after she went to 
+
+173
+00:18:48,550 --> 00:18:54,910
+Le Mans. Three. She studied in London and 
+
+174
+00:18:54,910 --> 00:18:59,250
+Jerusalem for 10 years at the best college in Le 
+
+175
+00:18:59,250 --> 00:19:05,170
+Mans. Four. She worked for Antarctic for the last 
+
+176
+00:19:13,020 --> 00:19:17,580
+She lived in Berlin while she was working for the 
+
+177
+00:19:17,580 --> 00:19:25,400
+BBC. She's been married twice. She visited Japan a 
+
+178
+00:19:25,400 --> 00:19:32,500
+few times. She hasn't heard if she got the job at 
+
+179
+00:19:32,500 --> 00:19:36,570
+World Watch or anywhere. Yeah. So here, 
+
+180
+00:19:41,110 --> 00:19:44,510
+look 
+
+181
+00:19:44,510 --> 00:19:46,550
+at the exercise next. 
+
+182
+00:19:58,830 --> 00:20:02,630
+Here are today's news headlines. 
+
+183
+00:20:06,220 --> 00:20:11,380
+These headlines are from the TV. But look at the 
+
+184
+00:20:11,380 --> 00:20:16,840
+pictures before. It is in the newspaper. In the 
+
+185
+00:20:16,840 --> 00:20:20,980
+newspaper, they give a title headlines in short. 
+
+186
+00:20:21,580 --> 00:20:24,420
+But when we are speaking on the TV, we are 
+
+187
+00:20:24,420 --> 00:20:31,520
+speaking completely, fully. So the first one, 
+
+188
+00:20:32,440 --> 00:20:39,850
+convicted murderer. Charles Witkins has escaped 
+
+189
+00:20:39,850 --> 00:20:47,710
+from Bill March prison in South London. This is in the 
+
+190
+00:20:47,710 --> 00:20:54,610
+prison, perfect, active or passive? Active. 
+
+191
+00:20:54,830 --> 00:21:01,050
+Why? Because this is the person Charles Witkins 
+
+192
+00:21:
+
+223
+00:24:21,180 --> 00:24:27,260
+fight in Las Vegas. So he was finished.
+
+224
+00:24:28,120 --> 00:24:34,660
+He will not play anymore. He was defeated. So he's
+
+225
+00:24:34,660 --> 00:24:39,200
+knocked out. He was defeated. So this sentence and
+
+226
+00:24:39,200 --> 00:24:44,800
+this sentence are in the passive. And this is in
+
+227
+00:24:44,800 --> 00:24:51,830
+the passive. So can we answer some questions
+
+228
+00:24:51,830 --> 00:24:58,910
+about the first one? When we ask the question, we
+
+229
+00:24:58,910 --> 00:25:04,070
+say, who has escaped from the prison? Yes, we can.
+
+230
+00:25:04,650 --> 00:25:09,350
+So here we have an exercise,
+
+231
+00:25:09,790 --> 00:25:14,210
+say, who escaped from the jail? Can we answer this
+
+232
+00:25:14,210 --> 00:25:21,450
+question? Yes. But who has hit the Caribbean or
+
+233
+00:25:21,450 --> 00:25:25,930
+who has awarded the novelist the Nobel Prize?
+
+234
+00:25:32,230 --> 00:25:36,050
+Here, can we say who awarded them the Nobel Prize?
+
+235
+00:25:36,590 --> 00:25:39,890
+No, because it is in the passive. It is not
+
+236
+00:25:39,890 --> 00:25:44,880
+important. But here, When the sentence is in the
+
+237
+00:25:44,880 --> 00:25:50,460
+active, we can answer who or what. If it's
+
+238
+00:25:50,460 --> 00:25:55,180
+passive, we can't answer who or what. So if we
+
+239
+00:25:55,180 --> 00:25:58,840
+look at the questions here,
+
+240
+00:26:06,520 --> 00:26:11,640
+Which of these questions can you answer? Which
+
+241
+00:26:11,640 --> 00:26:17,160
+can't you answer? Why? Why? The first one, who has
+
+242
+00:26:17,160 --> 00:26:20,120
+escaped from the jail? Can you answer this
+
+243
+00:26:20,120 --> 00:26:27,980
+question? Yeah. Why? Because it is active. Who has
+
+244
+00:26:27,980 --> 00:26:31,300
+awarded the novelists the Nobel Prize? Who gave
+
+245
+00:26:31,300 --> 00:26:35,670
+them the Nobel Prize? We don't know. So can you
+
+246
+00:26:35,670 --> 00:26:40,470
+answer this question? No. Why? Because it is
+
+247
+00:26:40,470 --> 00:26:46,050
+passive. The object is more important than the
+
+248
+00:26:46,050 --> 00:26:50,650
+subject. Number three. What has hit the Caribbean?
+
+249
+00:26:51,610 --> 00:26:55,190
+Yes. Hurricane Jeffrey. We know it. So we can
+
+250
+00:26:55,190 --> 00:26:58,710
+answer this. Why? Because it is in the active.
+
+251
+00:26:59,850 --> 00:27:04,500
+Number four. Who has laid off the workers? We
+
+252
+00:27:04,500 --> 00:27:08,040
+don't know. We are more interested than the 2000
+
+253
+00:27:08,040 --> 00:27:13,380
+workers who are laid off. But we don't know who
+
+254
+00:27:13,380 --> 00:27:19,260
+laid them off. It is in the passive. Who has
+
+255
+00:27:19,260 --> 00:27:24,720
+knocked out Desmond Lewis? We don't know. But he
+
+256
+00:27:24,720 --> 00:27:30,840
+was knocked out. This is in the passive. So,
+
+257
+00:27:31,910 --> 00:27:34,250
+number one and number three can be answered
+
+258
+00:27:34,250 --> 00:27:38,530
+because they are in the active, number two, four, and
+
+259
+00:27:38,530 --> 00:27:41,630
+five can't be answered because they are in the
+
+260
+00:27:41,630 --> 00:27:45,910
+passive. Yes, which sentence in exercise two are
+
+261
+00:27:45,910 --> 00:27:55,610
+active. This is active and this is active and
+
+262
+00:27:55,610 --> 00:27:58,310
+which is passive. This is passive.
+
+263
+00:28:02,390 --> 00:28:08,870
+passive, passive. Yes.
+
+264
+00:28:08,870 --> 00:28:12,830
+So here
+
+265
+00:28:12,830 --> 00:28:22,470
+let's study something new, listen
+
+266
+00:28:22,470 --> 00:28:27,250
+to me, students, can answer question one and three
+
+267
+00:28:27,250 --> 00:28:35,050
+but not two, four, and five. Charles Witkins has
+
+268
+00:28:35,050 --> 00:28:39,890
+escaped from the jail. Hurricane Jeffrey has hit
+
+269
+00:28:39,890 --> 00:28:43,810
+the Caribbean. They are in the active. But we
+
+270
+00:28:43,810 --> 00:28:47,270
+don't know the answers to the other questions
+
+271
+00:28:47,270 --> 00:28:52,870
+because they are in the present passive, because
+
+272
+00:28:52,870 --> 00:28:57,010
+they are in the passive. Who did the action is not
+
+273
+00:28:57,010 --> 00:29:03,360
+mentioned. Because it is not as important as the
+
+274
+00:29:03,360 --> 00:29:08,560
+action itself, when the action is important, active
+
+275
+00:29:08,560 --> 00:29:13,500
+when the action is not important, passive. So the
+
+276
+00:29:13,500 --> 00:29:16,960
+active is question number one and three, the
+
+277
+00:29:16,960 --> 00:29:22,100
+passive is question two, four, and five. Now the
+
+278
+00:29:22,100 --> 00:29:29,060
+explanation again, use the passive means we don't
+
+279
+00:29:29,060 --> 00:29:35,920
+know for sure who did the action. When we use the
+
+280
+00:29:35,920 --> 00:29:41,440
+passive, we are not sure who did the action, even
+
+281
+00:29:41,440 --> 00:29:47,400
+if we can guess. But guessing is not necessary. Who
+
+282
+00:29:47,400 --> 00:29:52,380
+or what did the action is not as important in
+
+283
+00:29:52,380 --> 00:29:55,920
+these sentences as the fact that the action
+
+284
+00:29:55,920 --> 00:30:01,640
+happened. So we are concerned with the action, not
+
+285
+00:30:01,640 --> 00:30:05,480
+with the doer of the action. If we are concerned
+
+286
+00:30:05,480 --> 00:30:08,980
+with the doer of the action, it is active. When
+
+287
+00:30:08,980 --> 00:30:10,760
+the doer of the action, is that important?
+
+288
+00:30:12,480 --> 00:30:19,360
+Passive. Use of the present perfect here
+
+289
+00:30:19,360 --> 00:30:23,380
+emphasizes the present importance of the events
+
+290
+00:30:23,380 --> 00:30:30,240
+mentioned, that the convicted murderer is still at
+
+291
+00:30:30,240 --> 00:30:37,930
+large. He escaped. That the workers are now
+
+292
+00:30:37,930 --> 00:30:42,710
+without jobs. So this is the action. The workers,
+
+293
+00:30:42,970 --> 00:30:49,390
+the 2000 workers are without jobs. And Damon Lewis
+
+294
+00:30:49,390 --> 00:30:54,670
+lost the fight. Lost the fight. This is the
+
+295
+00:30:54,670 --> 00:30:59,930
+action. Note, we use the present perfect tense and
+
+296
+00:30:59,930 --> 00:31:04,990
+not the past simple in sentences one and three
+
+297
+00:31:04,990 --> 00:31:10,630
+because there is no specific time mentioned. So
+
+298
+00:31:10,630 --> 00:31:13,250
+what's the difference between present perfect and
+
+299
+00:31:13,250 --> 00:31:18,970
+past simple? The past simple has a time. Time
+
+300
+00:31:18,970 --> 00:31:22,890
+phrase. But the present perfect, no time phrase.
+
+301
+00:31:23,250 --> 00:31:29,900
+Either in the active or in the passive. For the
+
+302
+00:31:29,900 --> 00:31:35,860
+events, if there was a time phrase, we would say
+
+303
+00:31:35,860 --> 00:31:44,000
+convicted murderer Charles Watkins escaped from
+
+304
+00:31:44,000 --> 00:31:51,140
+Belmarsh Prison in South London when? Last night.
+
+305
+00:31:51,940 --> 00:31:56,980
+So if we mention the time, it should be in the
+
+306
+00:31:56,980 --> 00:32:02,300
+past simple. If we don't mention the time, we must
+
+307
+00:32:02,300 --> 00:32:08,380
+use the present perfect, either in the active or in
+
+308
+00:32:08,380 --> 00:32:09,120
+the passive.
+
+309
+00:32:17,760 --> 00:32:19,100
+Also, here,
+
+310
+00:32:23,100 --> 00:32:29,120
+We have another simple exercise about using the
+
+311
+00:32:29,120 --> 00:32:33,440
+adverbs used in the present perfect. In the present
+
+312
+00:32:33,440 --> 00:32:42,760
+perfect, we use just, yet, already, ever, never
+
+313
+00:32:43,890 --> 00:32:51,290
+and they are mid position adverbs except
+
+314
+00:32:51,290 --> 00:32:58,270
+yet. Yet is in position. So here, I have washed my
+
+315
+00:32:58,270 --> 00:33:02,770
+hair. The question is discuss where the words in
+
+316
+00:33:02,770 --> 00:33:06,550
+the box can go in these sentences. There are
+
+317
+00:33:06,550 --> 00:33:11,030
+several possibilities. So this sentence is okay. I
+
+318
+00:33:11,030 --> 00:33:15,090
+want to add words from the box. Why? Because they
+
+319
+00:33:15,090 --> 00:33:18,970
+are connected with the present perfect. So I say, I
+
+320
+00:33:18,970 --> 00:33:22,930
+have. I have just
+
+321
+00:33:24,580 --> 00:33:33,620
+I have just washed my hair. Also, already. I
+
+322
+00:33:33,620 --> 00:33:43,540
+have already washed my hair. Also, I use never. I
+
+323
+00:33:43,540 --> 00:33:48,460
+have never washed my hair. So how many words can
+
+324
+00:33:48,460 --> 00:33:53,180
+we use in the first one? Three. I have just, I
+
+325
+00:33:53,180 --> 00:33:56,420
+have already, I have never. What's the meaning of
+
+326
+00:33:56,420 --> 00:34:06,280
+just? Recently. It means very recently. What's the
+
+327
+00:34:06,280 --> 00:34:12,500
+meaning of already? Before now. It means before
+
+328
+00:34:12,500 --> 00:34:15,520
+now. What's the meaning of never?
+
+329
+00:34:18,550 --> 00:34:24,070
+Never in my life, at any time in my life, at any
+
+330
+00:34:24,070 --> 00:34:27,730
+time in my life. So this is the first one. The
+
+331
+00:34:27,730 --> 00:34:31,930
+answer is, I have just, I have already, I have never
+
+332
+00:34:31,930 --> 00:34:37,890
+washed my hair, the second one, have you played
+
+333
+00:34:37,890 --> 00:34:38,830
+basketball?
+
+334
+00:34:41,240 --> 00:34:45,100
+Have you played basketball? Put some words from
+
+335
+00:34:45,100 --> 00:34:52,180
+here. Have you just... Have you just... So here we
+
+336
+00:34:52,180 --> 00:34:58,880
+use just. Have you just played basketball? Also, we
+
+337
+00:34:58,880 --> 00:35:04,160
+use already. Have
+
+338
+00:35:04,160 --> 00:35:10,400
+you already played basketball
+
+339
+00:35:10,400 --> 00:35:19,640
+here? Have you just, have you already, or have you
+
+340
+00:35:19,640 --> 00:35:28,380
+ever? Ever means at any time in your life, at any
+
+341
+00:35:28,380 --> 00:35:33,220
+time in your life, so
+
+342
+00:35:33,220 --> 00:35:38,360
+also we can use yet. We use yet in the questions
+
+343
+00:35:38,360 --> 00:35:42,120
+and in the negative, but at the end of the
+
+344
+00:35:42,120 --> 00:35:48,340
+sentence, so here, have you played football yet?
+
+345
+00:35:49,300 --> 00:35:54,020
+Uh-huh. So here we have three words, and here we
+
+346
+00:35:54,020 --> 00:35:59,420
+have four words. Just, already, never, just, already
+
+347
+00:35:59,420 --> 00:36:06,520
+ever, and yet. Also, so this is the answer. Have
+
+348
+00:36:06,520 --> 00:36:15,630
+you just, have you already, have you ever, and have
+
+349
+00:36:15,630 --> 00:36:22,210
+with yet. So, just this exercise just to show you
+
+350
+00:36:22,210 --> 00:36:30,910
+the position of mid adverb, present perfect. Also
+
+351
+00:36:30,910 --> 00:36:31,570
+here again
+
+352
+00:36:42,000 --> 00:36:45,860
+Number three, he hasn't learned to drive.
+
+353
+00:36:48,260 --> 00:36:54,180
+He hasn't learned to drive yet. Why? Because we
+
+354
+00:36:54,180 --> 00:36:59,160
+use yet with the negative and with the question.
+
+355
+00:37:00,580 --> 00:37:07,020
+Also, he has ever. He hasn't ever. Why ever, not
+
+356
+00:37:07,020 --> 00:37:13,940
+never? Ever, not never. Because not ever means
+
+357
+00:37:13,940 --> 00:37:18,760
+never. If we have not, we can't say never. But
+
+358
+00:37:18,760 --> 00:37:23,720
+without not, we can say never. It means he has never
+
+359
+00:37:23,720 --> 00:37:30,260
+learned, or he hasn't ever learned. Number three,
+
+360
+00:37:30,260 --> 00:37:39,660
+number four, they have finished. The exercise, we can
+
+361
+00:37:39,660 --> 00:37:47,700
+use, they have just, they have already finished the
+
+362
+00:37:47,700 --> 00:37:53,730
+exercise, but not with never. Why? Because it is a
+
+363
+00:37:53,730 --> 00:37:59,430
+quick action. Quick action. But not at any time in
+
+364
+00:37:59,430 --> 00:38:03,990
+his life. No. If the verb is long, we can use
+
+365
+00:38:03,990 --> 00:38:08,210
+never or ever. But if it is short, very short, we
+
+366
+00:38:08,210 --> 00:38:16,730
+can't use ever and never. Number five. She has
+
+367
+00:38:16,730 --> 00:38:18,450
+learned foreign languages.
+
+368
+00:38:21,260 --> 00:38:24,500
+Mm-hmm. She has learned a foreign language. She
+
+369
+00:38:24,500 --> 00:38:29,060
+has just learned. She has already learned. She has
+
+370
+00:38:29,060 --> 00:38:32,860
+never learned. Because learning takes a long time,
+
+371
+00:38:32,920 --> 00:38:37,300
+but with finish, short time. So we can't say never
+
+372
+00:38:37,300 --> 00:38:45,780
+again. This one again. We have met your teacher. We
+
+373
+00:38:45,780 --> 00:38:51,920
+have just met, we have already met, we have never met
+
+374
+00:38:51,920 --> 00:38:59,480
+uh-huh, the same, number seven, question, have you
+
+375
+00:38:59,480 --> 00:39:07,280
+just, have you just finished, have you just finished
+
+376
+00:39:07,280 --> 00:39:15,990
+yet, uh-huh. Why? Because it is a short verb, so we
+
+377
+00:39:15,990 --> 00:39:18,870
+can't use never or ever.
+
+378
+00:39:22,310 --> 00:39:28,410
+And here, we have also, already. The last question
+
+379
+00:39:28,410 --> 00:39:33,090
+also questions. So these are the same, and these
+
+380
+00:39:33,090 --> 00:39:40,960
+are the same. Has it just stopped raining? Has it
+
+381
+00:39:40,960 --> 00:39:46,160
+stopped raining yet? Has it already? So we use
+
+382
+00:39:46,160 --> 00:39:50,940
+just, and already, and yet. What's the meaning of
+
+383
+00:39:50,940 --> 00:39:51,320
+yet?
+
+384
+00:39:54,180 --> 00:40:00,540
+Up to now or up till, until now. What's the meaning
+
+385
+00:40:00,540 --> 00:40:05,780
+of ever and ever? At any time in your life or not
+
+386
+00:40:05,780 --> 00:40:12,490
+at any time in your life. Just, recently. Already
+
+387
+00:40:12,490 --> 00:40:20,810
+before that. And inshallah, next time, next time, we
+
+388
+00:40:20,810 --> 00:40:28,970
+will do a short exercise about how to use the
+
+389
+00:40:28,970 --> 00:40:33,150
+present simple and the present perfect in the
+
+390
+00:40:33,150 --> 00:40:36,950
+active and in the passive. Thank you very much.
+
+391
+00:40:37,210 --> 00:40:39,590
+Wassalamualaikum warahmatullahi wabarakatuh.
+
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/GswgQNNiHgg_raw.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/GswgQNNiHgg_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3a63af8c98fdb353cffef25b0801db31a0d29a46
--- /dev/null
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@@ -0,0 +1,1564 @@
+1
+00:00:20,980 --> 00:00:26,200
+Assalamualaikum Warahmatullahi Wabarakatuh Today,
+
+2
+00:00:26,380 --> 00:00:29,540
+Inshallah, we are going to study present perfect
+
+3
+00:00:29,540 --> 00:00:35,620
+symbol in the active and in the passive With these
+
+4
+00:00:35,620 --> 00:00:40,000
+two pages, unit seven The first exercise, how do
+
+5
+00:00:40,000 --> 00:00:46,820
+you do? It asks about the job So answer these
+
+6
+00:00:46,820 --> 00:00:51,180
+questions about you. Number one, what do you do?
+
+7
+00:00:51,340 --> 00:00:55,780
+It means, what is your job? Say, I'm a student,
+
+8
+00:00:56,620 --> 00:01:02,660
+I'm a teacher, I'm an engineer. Number two, how
+
+9
+00:01:02,660 --> 00:01:05,780
+long have you been or have you had your present
+
+10
+00:01:05,780 --> 00:01:13,660
+job? For two years, since 2011. Or sometimes I
+
+11
+00:01:13,660 --> 00:01:19,210
+say, I don't have a job. I'm a student. Yeah.
+
+12
+00:01:19,910 --> 00:01:25,170
+Number three, what did you do before that? I
+
+13
+00:01:25,170 --> 00:01:31,630
+worked in a bank. I was at school. Number four,
+
+14
+00:01:32,210 --> 00:01:36,370
+which foreign countries have you been to? I have
+
+15
+00:01:36,370 --> 00:01:40,710
+been to China, I have been to Canada, to America,
+
+16
+00:01:41,510 --> 00:01:45,330
+or I say I have never been to any foreign
+
+17
+00:01:45,330 --> 00:01:50,650
+countries. Number four, when and why did you go
+
+18
+00:01:50,650 --> 00:01:57,290
+there? When I went there in 2011.
+
+19
+00:01:59,110 --> 00:02:04,090
+Again, number five, when and why did you go there?
+
+20
+00:02:06,140 --> 00:02:12,280
+I went there in 2011. Why? I went there on
+
+21
+00:02:12,280 --> 00:02:19,940
+business Now the question is what tenses are used
+
+22
+00:02:19,940 --> 00:02:27,420
+in the questions The first one with do it is the
+
+23
+00:02:27,420 --> 00:02:34,220
+present simple The second one with have had
+
+24
+00:02:35,590 --> 00:02:43,570
+present perfect simple number three with did and
+
+25
+00:02:43,570 --> 00:02:54,150
+do past simple number four with have been present
+
+26
+00:02:54,150 --> 00:03:02,690
+perfect simple and the last one did and go past
+
+27
+00:03:02,690 --> 00:03:10,620
+simple now After this introduction, we come to the
+
+28
+00:03:10,620 --> 00:03:12,960
+quick answers again.
+
+29
+00:03:17,660 --> 00:03:23,140
+So I'm a student. The question for how long is for
+
+30
+00:03:23,140 --> 00:03:28,420
+two years since 2001. I don't have a job. I'm a
+
+31
+00:03:28,420 --> 00:03:34,070
+student. Here, the question of what did you do
+
+32
+00:03:34,070 --> 00:03:37,770
+before that? I worked in a bank or I was at
+
+33
+00:03:37,770 --> 00:03:43,910
+school. Number four, which foreign countries have
+
+34
+00:03:43,910 --> 00:03:49,550
+you had? I've been to Hungary and Canada. And the
+
+35
+00:03:49,550 --> 00:03:57,910
+last one, when and why? When I went in 1993 or 10
+
+36
+00:03:57,910 --> 00:04:04,110
+years ago. Why I went there on business or I went
+
+37
+00:04:04,110 --> 00:04:05,830
+there on holiday?
+
+38
+00:04:07,710 --> 00:04:13,170
+And the next question, the first one is present
+
+39
+00:04:13,170 --> 00:04:18,810
+simple. Number three and five, past simple. Number
+
+40
+00:04:18,810 --> 00:04:23,070
+two and four, present perfect simple.
+
+41
+00:04:27,480 --> 00:04:37,900
+Now, Nancy is being interviewed. She answered some
+
+42
+00:04:37,900 --> 00:04:44,320
+questions. So here, does Nancy work for the
+
+43
+00:04:44,320 --> 00:04:50,420
+Intertech? She said, I work for the Intertech. So
+
+44
+00:04:50,420 --> 00:04:56,980
+she said, I work. So does she still work for
+
+45
+00:04:56,980 --> 00:05:04,010
+Intertech? Yes. Yes, she does.
+
+46
+00:05:06,830 --> 00:05:14,590
+She said, I worked for the BBC World Service. I
+
+47
+00:05:14,590 --> 00:05:24,750
+worked some finished events. So does she still
+
+48
+00:05:24,750 --> 00:05:30,130
+work for the BBC? No, because she used the past
+
+49
+00:05:30,130 --> 00:05:33,770
+simple. It's finished. A finished action. So here
+
+50
+00:05:33,770 --> 00:05:38,570
+we say, no, she doesn't.
+
+51
+00:05:41,970 --> 00:05:48,150
+So here, yes, she still worked for the Intertech.
+
+52
+00:05:48,410 --> 00:05:53,550
+But here, no, because she worked for the BBC World
+
+53
+00:05:53,550 --> 00:06:00,520
+Service in the past. Now, Nancy says, I work for
+
+54
+00:06:00,520 --> 00:06:04,060
+Intertech Publishing. I have worked there for
+
+55
+00:06:04,060 --> 00:06:09,240
+nearly five years. I worked for the BBC World
+
+56
+00:06:09,240 --> 00:06:12,620
+Service. These three questions, this is in the
+
+57
+00:06:12,620 --> 00:06:16,160
+past, in the present simple, and this is in the
+
+58
+00:06:16,160 --> 00:06:24,170
+present perfect, and this is in the Past simple.
+
+59
+00:06:24,830 --> 00:06:28,190
+So the question here, what are the differences?
+
+60
+00:06:29,670 --> 00:06:32,510
+The first one. Present.
+
+61
+00:06:34,690 --> 00:06:35,690
+Simple.
+
+62
+00:06:39,310 --> 00:06:47,470
+The second one. Present. Simple. Present. Perfect.
+
+63
+00:06:48,950 --> 00:06:49,950
+Simple.
+
+64
+00:06:53,180 --> 00:06:59,960
+The third one, I worked, past simple. What are the
+
+65
+00:06:59,960 --> 00:07:03,960
+different tenses? Present simple, present perfect
+
+66
+00:07:03,960 --> 00:07:11,800
+simple, past simple. Why are they used? She used I
+
+67
+00:07:11,800 --> 00:07:19,640
+work because she still works there. And here, she
+
+68
+00:07:19,640 --> 00:07:29,350
+works in or for it until now. From the past until
+
+69
+00:07:29,350 --> 00:07:36,630
+now. And here, a finished action. She is not
+
+70
+00:07:36,630 --> 00:07:40,370
+working for the BBC now. So it is a finished
+
+71
+00:07:40,370 --> 00:07:43,810
+action. When it is finished, we use past simple.
+
+72
+00:07:45,070 --> 00:07:51,260
+When it is still, it is present simple. Uh-huh.
+
+73
+00:07:51,700 --> 00:07:56,860
+And if you are speaking about today, referring to
+
+74
+00:07:56,860 --> 00:08:00,160
+the past, we use present perfect.
+
+75
+00:08:03,640 --> 00:08:15,280
+Look here. The answer for
+
+76
+00:08:15,280 --> 00:08:20,220
+these questions. Yes, she does. No, she doesn't.
+
+77
+00:08:20,730 --> 00:08:27,290
+Number two, Nancy says, I work for
+
+78
+00:08:27,290 --> 00:08:32,290
+Intertech Publishing because she works for them
+
+79
+00:08:32,290 --> 00:08:36,970
+now. So it is the present simple. She works now,
+
+80
+00:08:37,410 --> 00:08:41,310
+so it is the present simple. She says, this is
+
+81
+00:08:41,310 --> 00:08:44,250
+number one, the second one. She says, I have
+
+82
+00:08:44,250 --> 00:08:50,080
+worked there for nearly five years because she's
+
+83
+00:08:50,080 --> 00:08:58,100
+talking about pastime and present time. Pastime
+
+84
+00:08:58,100 --> 00:09:02,420
+and present time. She began working for them,
+
+85
+00:09:02,900 --> 00:09:08,640
+began working for them five years ago and she
+
+86
+00:09:08,640 --> 00:09:12,880
+still works for
+
+87
+00:09:12,880 --> 00:09:18,880
+them now. So we call this present Perfect why
+
+88
+00:09:18,880 --> 00:09:24,400
+because it's now and in the past The third one she
+
+89
+00:09:24,400 --> 00:09:30,840
+says I worked I worked For the BBC World Service
+
+90
+00:09:30,840 --> 00:09:38,400
+because she doesn't work there anymore Uh-huh. She
+
+91
+00:09:38,400 --> 00:09:45,130
+doesn't work there anymore it's a finished Action
+
+92
+00:09:45,130 --> 00:09:50,610
+finished completely finished in the past. So it is
+
+93
+00:09:50,610 --> 00:10:05,470
+past simple Next also Grammar
+
+94
+00:10:05,470 --> 00:10:11,070
+reference page 143 Introduction
+
+95
+00:10:11,070 --> 00:10:12,170
+to the present perfect
+
+96
+00:10:17,350 --> 00:10:24,170
+The same form have plus the past participle exists
+
+97
+00:10:24,170 --> 00:10:29,690
+in many Arabian languages. But the usage in
+
+98
+00:10:29,690 --> 00:10:34,630
+English is different. In English, the present
+
+99
+00:10:34,630 --> 00:10:40,530
+perfect is essentially a present tense. So the
+
+100
+00:10:40,530 --> 00:10:44,750
+present perfect is a present tense.
+
+101
+00:10:46,510 --> 00:10:52,910
+But it also expresses the effect. It expresses the
+
+102
+00:10:52,910 --> 00:10:57,610
+effect of the past actions and activities on the
+
+103
+00:10:57,610 --> 00:11:01,650
+present. The effects of these actions or
+
+104
+00:11:01,650 --> 00:11:06,470
+activities were in the present. So when I say
+
+105
+00:11:06,470 --> 00:11:10,770
+present perfect, it means the present. But with
+
+106
+00:11:10,770 --> 00:11:15,950
+the effects of the past. So this diagram is clear.
+
+107
+00:11:17,160 --> 00:11:21,580
+We have past. We have present. But the present
+
+108
+00:11:21,580 --> 00:11:26,300
+perfect speaks about the present connected with
+
+109
+00:11:26,300 --> 00:11:29,800
+the past. With the past events or with the past
+
+110
+00:11:29,800 --> 00:11:30,280
+effects.
+
+111
+00:11:33,280 --> 00:11:36,920
+Present perfect means before now.
+
+112
+00:11:39,260 --> 00:11:45,260
+The present perfect does not express when an
+
+113
+00:11:45,260 --> 00:11:51,060
+action happened. If we say when, we should use the
+
+114
+00:11:51,060 --> 00:11:55,220
+past simple. Without when, we use the present
+
+115
+00:11:55,220 --> 00:12:01,020
+perfect. So here, the present perfect does not
+
+116
+00:12:01,020 --> 00:12:07,320
+express when an action happened. If we say the
+
+117
+00:12:07,320 --> 00:12:13,880
+exact time, so we have some verbs and we want to
+
+118
+00:12:13,880 --> 00:12:14,900
+put them
+
+119
+00:12:18,430 --> 00:12:27,770
+So now go, the past simple of go is went and the
+
+120
+00:12:27,770 --> 00:12:32,290
+past participle gone.
+
+121
+00:12:32,930 --> 00:12:37,230
+So we use this in the present simple and we use
+
+122
+00:12:37,230 --> 00:12:39,950
+this in the past simple and we use this in the
+
+123
+00:12:39,950 --> 00:12:45,830
+perfect and in the passive. Perfect and the
+
+124
+00:12:45,830 --> 00:12:53,050
+passive also with negative adjective write wrote
+
+125
+00:12:53,050 --> 00:13:08,250
+written drive drove driven lose lost lost have had
+
+126
+00:13:08,250 --> 00:13:17,530
+had read yes who can read Yeah. Go and gun. Right
+
+127
+00:13:17,530 --> 00:13:23,030
+road written. Drive, drop, driven. Driven. Driven.
+
+128
+00:13:23,230 --> 00:13:27,790
+Drive, drop, driven. Lose, lost, lost. Have, had,
+
+129
+00:13:27,910 --> 00:13:32,390
+had. Read, read, read. Right road written. Sleep,
+
+130
+00:13:32,550 --> 00:13:37,150
+slept, slept. Be was, were, been. Eat, ate, eaten.
+
+131
+00:13:37,410 --> 00:13:42,850
+Win, won, won. Meet, meet, meet. Yeah. Yes. Go and
+
+132
+00:13:42,850 --> 00:13:43,150
+gun.
+
+133
+00:14:07,110 --> 00:14:18,130
+When I say B, it means M is R M is R. Yes. Now, we
+
+134
+00:14:18,130 --> 00:14:27,470
+want to match between A and B. Nancy says
+
+135
+00:14:27,470 --> 00:14:31,450
+something about her life. So these are events of
+
+136
+00:14:31,450 --> 00:14:36,930
+Nancy's life. And these are time expressions.
+
+137
+00:14:39,350 --> 00:14:45,680
+Now this, is to match between line in A with a
+
+138
+00:14:45,680 --> 00:14:51,020
+line in B. Number one. She was born Nancy. Nancy
+
+139
+00:14:51,020 --> 00:14:59,400
+was born. Nancy was born in
+
+140
+00:14:59,400 --> 00:15:06,460
+Argentina in 1969. Number two. She went to school
+
+141
+00:15:06,460 --> 00:15:11,180
+in Buenos Aires. She went to school in Buenos
+
+142
+00:15:11,180 --> 00:15:15,430
+Aires. until she was 11.
+
+143
+00:15:18,410 --> 00:15:28,390
+She studied modern languages and journalism for
+
+144
+00:15:28,390 --> 00:15:35,570
+three years at University College London. Number
+
+145
+00:15:35,570 --> 00:15:38,150
+four, she's worked for Intertech.
+
+146
+00:15:41,100 --> 00:15:43,720
+for the last five years.
+
+147
+00:15:46,200 --> 00:15:51,920
+She left the BBC five years ago.
+
+148
+00:15:54,840 --> 00:15:58,360
+Number six, she lived in Berlin.
+
+149
+00:16:02,320 --> 00:16:05,440
+She lived in Berlin.
+
+150
+00:16:11,950 --> 00:16:18,690
+Yes, while she was working for the BBC.
+
+151
+00:16:22,610 --> 00:16:28,070
+Number seven. She's been married twice.
+
+152
+00:16:29,770 --> 00:16:30,370
+Twice. Twice.
+
+153
+00:16:35,590 --> 00:16:43,740
+She's visited Japan. A few times. Number nine, she
+
+154
+00:16:43,740 --> 00:16:48,160
+hasn't heard if she got the job at World Watch
+
+155
+00:16:48,160 --> 00:16:50,340
+Europe yet.
+
+156
+00:16:53,680 --> 00:16:59,440
+Who can read? Number one, she was born in
+
+157
+00:16:59,440 --> 00:17:06,040
+Argentina in 1969. Two, she went to school in
+
+158
+00:17:06,040 --> 00:17:07,420
+Buenos Aires.
+
+159
+00:17:12,110 --> 00:17:13,310
+Uh-huh. Three.
+
+160
+00:17:19,410 --> 00:17:20,450
+Journalism.
+
+161
+00:17:25,790 --> 00:17:26,830
+Four.
+
+162
+00:17:36,690 --> 00:17:38,390
+Next. Yeah.
+
+163
+00:17:42,020 --> 00:17:43,420
+Six.
+
+164
+00:17:48,960 --> 00:17:50,360
+Next.
+
+165
+00:17:52,960 --> 00:17:55,600
+Twice. Eight.
+
+166
+00:17:57,860 --> 00:18:06,970
+A few times. Yes. And the last one. Yeah. She
+
+167
+00:18:06,970 --> 00:18:12,570
+hasn't heard if she got the job at work, work with
+
+168
+00:18:12,570 --> 00:18:13,650
+Europe.
+
+169
+00:18:15,950 --> 00:18:32,430
+Yes. So this is about Nancy. And now again,
+
+170
+00:18:32,850 --> 00:18:37,490
+who can read the answer? Yeah. She was born in
+
+171
+00:18:37,490 --> 00:18:40,090
+Argentina in 1969.
+
+172
+00:18:42,550 --> 00:18:48,550
+Two. She went to school in Paris after she went to
+
+173
+00:18:48,550 --> 00:18:54,910
+Le Mans. Three. She studied in London and
+
+174
+00:18:54,910 --> 00:18:59,250
+Jerusalem for 10 years at the best college in Le
+
+175
+00:18:59,250 --> 00:19:05,170
+Mans. Four. She worked for Antarctic for the last
+
+176
+00:19:13,020 --> 00:19:17,580
+She lived in Berlin while she was working for the
+
+177
+00:19:17,580 --> 00:19:25,400
+BBC. She's been married twice. She visited Japan a
+
+178
+00:19:25,400 --> 00:19:32,500
+few times. She hasn't heard if she got the job at
+
+179
+00:19:32,500 --> 00:19:36,570
+World Watch or anywhere. Yeah. So here,
+
+180
+00:19:41,110 --> 00:19:44,510
+look
+
+181
+00:19:44,510 --> 00:19:46,550
+at the exercise next.
+
+182
+00:19:58,830 --> 00:20:02,630
+Here are today's news headlines.
+
+183
+00:20:06,220 --> 00:20:11,380
+This headlines is from the TV. But look at the
+
+184
+00:20:11,380 --> 00:20:16,840
+pictures before. It is in the newspaper. In the
+
+185
+00:20:16,840 --> 00:20:20,980
+newspaper, they give a title headlines in short.
+
+186
+00:20:21,580 --> 00:20:24,420
+But when we are speaking on the TV, we are
+
+187
+00:20:24,420 --> 00:20:31,520
+speaking completely, fully. So the first one,
+
+188
+00:20:32,440 --> 00:20:39,850
+convicted murderer. Charles Witkins has escaped
+
+189
+00:20:39,850 --> 00:20:47,710
+from Bill March prison in South London. This is in
+
+190
+00:20:47,710 --> 00:20:54,610
+the prison, perfect, active or passive? Active.
+
+191
+00:20:54,830 --> 00:21:01,050
+Why? Because this is the person Charles Witkins
+
+192
+00:21:01,050 --> 00:21:07,210
+has escaped. Uh-huh. So it is present perfect, but
+
+193
+00:21:07,210 --> 00:21:16,350
+what is it passive? No, no active. Yeah Number
+
+194
+00:21:16,350 --> 00:21:23,210
+two, uh, two Spanish novelists Two Spanish
+
+195
+00:21:23,210 --> 00:21:28,790
+novelists look at the picture the picture Have
+
+196
+00:21:28,790 --> 00:21:31,630
+been awarded have
+
+197
+00:21:32,980 --> 00:21:40,100
+being awarded the
+
+198
+00:21:40,100 --> 00:21:44,040
+Nobel Prize for literature. Is it active or
+
+199
+00:21:44,040 --> 00:21:46,440
+passive? Passive. Yeah.
+
+200
+00:21:50,580 --> 00:21:55,500
+So we have a picture and here we have full
+
+201
+00:21:55,500 --> 00:22:02,160
+sentences. So two Spanish novelists have been
+
+202
+00:22:02,160 --> 00:22:07,620
+awarded the Nobel Prize for literature. Who
+
+203
+00:22:07,620 --> 00:22:11,500
+awarded the Nobel Prize? We don't know. It is not
+
+204
+00:22:11,500 --> 00:22:17,860
+important. So it is passive. Now, Hurricane
+
+205
+00:22:17,860 --> 00:22:21,880
+Jeffrey has
+
+206
+00:22:21,880 --> 00:22:28,080
+hit the
+
+207
+00:22:28,080 --> 00:22:33,290
+Caribbean. has hit, this is the, the door of the
+
+208
+00:22:33,290 --> 00:22:37,150
+action. The hurricane Jeffrey has hit the
+
+209
+00:22:37,150 --> 00:22:42,230
+Caribbean. Is it active or passive? Active.
+
+210
+00:22:46,490 --> 00:22:51,830
+Causing widespread damage in Puerto Rico. Yeah.
+
+211
+00:22:52,510 --> 00:23:00,490
+Number four, two thousand workers from
+
+212
+00:23:00,490 --> 00:23:11,050
+a UK car factory have been
+
+213
+00:23:11,050 --> 00:23:20,750
+laid off. Finished. Stop working. They are not
+
+214
+00:23:20,750 --> 00:23:25,230
+necessary for the factory. So they finished them.
+
+215
+00:23:25,910 --> 00:23:33,570
+So 2000 workers have been laid off. Why? Due to.
+
+216
+00:23:34,150 --> 00:23:42,190
+Because of. Because of. Due to. Owing to. This to
+
+217
+00:23:42,190 --> 00:23:46,850
+is a preposition. It is like because of due to
+
+218
+00:23:46,850 --> 00:23:51,530
+what? A slowdown in the economy because of the
+
+219
+00:23:51,530 --> 00:23:56,770
+slowdown in the economy. And the last sentence,
+
+220
+00:23:56,930 --> 00:24:05,230
+number five, Desmond Lewis has been knocked out.
+
+221
+00:24:06,610 --> 00:24:13,070
+Has been knocked out.
+
+222
+00:24:15,620 --> 00:24:21,180
+in the fifth round of his heavyweight championship
+
+223
+00:24:21,180 --> 00:24:27,260
+fight in Las Vegas. So he was finished.
+
+224
+00:24:28,120 --> 00:24:34,660
+He will not play anymore. He was defeated. So he's
+
+225
+00:24:34,660 --> 00:24:39,200
+knocked out. He was defeated. So this sentence and
+
+226
+00:24:39,200 --> 00:24:44,800
+this sentence are in the passive. And this is in
+
+227
+00:24:44,800 --> 00:24:51,830
+the? Passive. So can we answer some questions
+
+228
+00:24:51,830 --> 00:24:58,910
+about the first one? When we ask the question, we
+
+229
+00:24:58,910 --> 00:25:04,070
+say, who has escaped from the prison? Yes, we can.
+
+230
+00:25:04,650 --> 00:25:09,350
+So here we have an exercise,
+
+231
+00:25:09,790 --> 00:25:14,210
+say, who escaped from the jail? Can we answer this
+
+232
+00:25:14,210 --> 00:25:21,450
+question? Yes. But who has hit the Caribbean or
+
+233
+00:25:21,450 --> 00:25:25,930
+who has awarded the novelist the Nobel Prize?
+
+234
+00:25:32,230 --> 00:25:36,050
+Here, can we say who awarded them the Nobel Prize?
+
+235
+00:25:36,590 --> 00:25:39,890
+No, because it is in the passive. It is not
+
+236
+00:25:39,890 --> 00:25:44,880
+important. But here, When the sentence is in the
+
+237
+00:25:44,880 --> 00:25:50,460
+active, we can answer who or what. If it's
+
+238
+00:25:50,460 --> 00:25:55,180
+passive, we can't answer who or what. So if we
+
+239
+00:25:55,180 --> 00:25:58,840
+look at the questions here,
+
+240
+00:26:06,520 --> 00:26:11,640
+Which of these questions can you answer? Which
+
+241
+00:26:11,640 --> 00:26:17,160
+can't you answer? Why? Why? The first one, who has
+
+242
+00:26:17,160 --> 00:26:20,120
+escaped from the jail? Can you answer this
+
+243
+00:26:20,120 --> 00:26:27,980
+question? Yeah. Why? Because it is active. Who has
+
+244
+00:26:27,980 --> 00:26:31,300
+awarded the novelists the Nobel Prize? Who gave
+
+245
+00:26:31,300 --> 00:26:35,670
+them the Nobel Prize? We don't know. So can you
+
+246
+00:26:35,670 --> 00:26:40,470
+answer this question? No. Why? Because it is
+
+247
+00:26:40,470 --> 00:26:46,050
+passive. The object is more important than the
+
+248
+00:26:46,050 --> 00:26:50,650
+subject. Number three. What has hit the Caribbean?
+
+249
+00:26:51,610 --> 00:26:55,190
+Yes. Hurricane Jeffrey. We know it. So we can
+
+250
+00:26:55,190 --> 00:26:58,710
+answer this. Why? Because it is in the active.
+
+251
+00:26:59,850 --> 00:27:04,500
+Number four. Who has laid off the workers? We
+
+252
+00:27:04,500 --> 00:27:08,040
+don't know. We are more interested than the 2000
+
+253
+00:27:08,040 --> 00:27:13,380
+workers who are laid off. But we don't know who
+
+254
+00:27:13,380 --> 00:27:19,260
+laid them off. It is in the passive. Who has
+
+255
+00:27:19,260 --> 00:27:24,720
+knocked out Desmond Lewis? We don't know. But he
+
+256
+00:27:24,720 --> 00:27:30,840
+was knocked off. This is in the passive. So,
+
+257
+00:27:31,910 --> 00:27:34,250
+number one and number three can be answered
+
+258
+00:27:34,250 --> 00:27:38,530
+because they are in the active number two four and
+
+259
+00:27:38,530 --> 00:27:41,630
+five can't be answered because they are in the
+
+260
+00:27:41,630 --> 00:27:45,910
+passive yes which sentence in exercise two are
+
+261
+00:27:45,910 --> 00:27:55,610
+active this is active and this is active and
+
+262
+00:27:55,610 --> 00:27:58,310
+which is passive this is passive
+
+263
+00:28:02,390 --> 00:28:08,870
+passive passive yes
+
+264
+00:28:08,870 --> 00:28:12,830
+so here
+
+265
+00:28:12,830 --> 00:28:22,470
+let's study something new listen
+
+266
+00:28:22,470 --> 00:28:27,250
+to me students can answer question one and three
+
+267
+00:28:27,250 --> 00:28:35,050
+but not two four and five Charles Witkins has
+
+268
+00:28:35,050 --> 00:28:39,890
+escaped from the jail. Hurricane Jeffrey has hit
+
+269
+00:28:39,890 --> 00:28:43,810
+the Caribbean. They are in the active. But we
+
+270
+00:28:43,810 --> 00:28:47,270
+don't know the answers to the other questions
+
+271
+00:28:47,270 --> 00:28:52,870
+because they are in the present passive because
+
+272
+00:28:52,870 --> 00:28:57,010
+they are in the passive. Who did the action is not
+
+273
+00:28:57,010 --> 00:29:03,360
+mentioned. because it is not as important as the
+
+274
+00:29:03,360 --> 00:29:08,560
+action itself when the action is important active
+
+275
+00:29:08,560 --> 00:29:13,500
+when the action is not important passive so the
+
+276
+00:29:13,500 --> 00:29:16,960
+active is a question number one and three the
+
+277
+00:29:16,960 --> 00:29:22,100
+passive question two four and five now the
+
+278
+00:29:22,100 --> 00:29:29,060
+explanation again use the passive Means we don't
+
+279
+00:29:29,060 --> 00:29:35,920
+know for sure who did the action When we use the
+
+280
+00:29:35,920 --> 00:29:41,440
+passive, we are not sure who did the action even
+
+281
+00:29:41,440 --> 00:29:47,400
+if we can guess But guessing is not necessary. Who
+
+282
+00:29:47,400 --> 00:29:52,380
+or what did the action is not as important in
+
+283
+00:29:52,380 --> 00:29:55,920
+these sentences as the fact that the action
+
+284
+00:29:55,920 --> 00:30:01,640
+happened. So we are concerned with the action, not
+
+285
+00:30:01,640 --> 00:30:05,480
+with the doer of the action. If we are concerned
+
+286
+00:30:05,480 --> 00:30:08,980
+with the doer of the action, it is active. When
+
+287
+00:30:08,980 --> 00:30:10,760
+the doer of the action, is that important?
+
+288
+00:30:12,480 --> 00:30:19,360
+Passive. Use of the present perfect here
+
+289
+00:30:19,360 --> 00:30:23,380
+emphasizes the present importance of the events
+
+290
+00:30:23,380 --> 00:30:30,240
+mentioned, that the convicted murderer is still at
+
+291
+00:30:30,240 --> 00:30:37,930
+large. He escaped. That the workers are now
+
+292
+00:30:37,930 --> 00:30:42,710
+without jobs. So this is the action. The workers,
+
+293
+00:30:42,970 --> 00:30:49,390
+the 2000 workers are without jobs. And Damon Lewis
+
+294
+00:30:49,390 --> 00:30:54,670
+lost the fight. Lost the fight. This is the
+
+295
+00:30:54,670 --> 00:30:59,930
+action. Note, we use the present perfect tense and
+
+296
+00:30:59,930 --> 00:31:04,990
+not the past simple in sentences one and three
+
+297
+00:31:04,990 --> 00:31:10,630
+because there is no specific time mentioned. So
+
+298
+00:31:10,630 --> 00:31:13,250
+what's the difference between present perfect and
+
+299
+00:31:13,250 --> 00:31:18,970
+past simple? The past simple has a time. Time
+
+300
+00:31:18,970 --> 00:31:22,890
+phrase. But the present perfect, no time phrase.
+
+301
+00:31:23,250 --> 00:31:29,900
+Either in the active or in the passive. For the
+
+302
+00:31:29,900 --> 00:31:35,860
+events, if there was a time phrase, we would say
+
+303
+00:31:35,860 --> 00:31:44,000
+convicted murderer Charles Watkins escaped from
+
+304
+00:31:44,000 --> 00:31:51,140
+Belmarsh Prison in South London when? Last night.
+
+305
+00:31:51,940 --> 00:31:56,980
+So if we mention the time, it should be in the
+
+306
+00:31:56,980 --> 00:32:02,300
+past simple. If we don't mention the time, we must
+
+307
+00:32:02,300 --> 00:32:08,380
+use the present perfect either in the active or in
+
+308
+00:32:08,380 --> 00:32:09,120
+the passive.
+
+309
+00:32:17,760 --> 00:32:19,100
+Also here,
+
+310
+00:32:23,100 --> 00:32:29,120
+We have another simple exercise about using the
+
+311
+00:32:29,120 --> 00:32:33,440
+adverbs used in the present perfect In the present
+
+312
+00:32:33,440 --> 00:32:42,760
+perfect, we use just, yet, already, ever, never
+
+313
+00:32:43,890 --> 00:32:51,290
+and they are mid position adverbs except
+
+314
+00:32:51,290 --> 00:32:58,270
+yet yet is in position So here I have washed my
+
+315
+00:32:58,270 --> 00:33:02,770
+hair. The question is discuss where the words in
+
+316
+00:33:02,770 --> 00:33:06,550
+the box can go in these sentences. There are
+
+317
+00:33:06,550 --> 00:33:11,030
+several possibilities. So this sentence is okay. I
+
+318
+00:33:11,030 --> 00:33:15,090
+want to add words from the box. Why? Because they
+
+319
+00:33:15,090 --> 00:33:18,970
+are connected with the present perfect. So I say I
+
+320
+00:33:18,970 --> 00:33:22,930
+have I have just
+
+321
+00:33:24,580 --> 00:33:33,620
+I have just washed my hair. Also already I
+
+322
+00:33:33,620 --> 00:33:43,540
+have already washed my hair. Also I use never I
+
+323
+00:33:43,540 --> 00:33:48,460
+have never washed my hair. So how many words can
+
+324
+00:33:48,460 --> 00:33:53,180
+we use in the first one? Three. I have just, I
+
+325
+00:33:53,180 --> 00:33:56,420
+have already, I have never. What's the meaning of
+
+326
+00:33:56,420 --> 00:34:06,280
+just? Recently. It means very recently. What's the
+
+327
+00:34:06,280 --> 00:34:12,500
+meaning of already? Before now. It means before
+
+328
+00:34:12,500 --> 00:34:15,520
+now. What's the meaning of never?
+
+329
+00:34:18,550 --> 00:34:24,070
+Never in my life at any time in my life at any
+
+330
+00:34:24,070 --> 00:34:27,730
+time in my life. So this is the first one The
+
+331
+00:34:27,730 --> 00:34:31,930
+answer is I have just I have already I have never
+
+332
+00:34:31,930 --> 00:34:37,890
+washed my hair the second one Have you played
+
+333
+00:34:37,890 --> 00:34:38,830
+basketball?
+
+334
+00:34:41,240 --> 00:34:45,100
+Have you played basketball? Put some words from
+
+335
+00:34:45,100 --> 00:34:52,180
+here Have you just... Have you just... So here we
+
+336
+00:34:52,180 --> 00:34:58,880
+use just Have you just played basketball? Also, we
+
+337
+00:34:58,880 --> 00:35:04,160
+use already Have
+
+338
+00:35:04,160 --> 00:35:10,400
+you already played basketball
+
+339
+00:35:10,400 --> 00:35:19,640
+here? have you just have you already or have you
+
+340
+00:35:19,640 --> 00:35:28,380
+ever ever means at any time in your life at any
+
+341
+00:35:28,380 --> 00:35:33,220
+time in your life so
+
+342
+00:35:33,220 --> 00:35:38,360
+also we can use yet we use yet in the questions
+
+343
+00:35:38,360 --> 00:35:42,120
+and in the negative But at the end of the
+
+344
+00:35:42,120 --> 00:35:48,340
+sentence, so here, have you played football yet?
+
+345
+00:35:49,300 --> 00:35:54,020
+Uh-huh. So here we have three words and here we
+
+346
+00:35:54,020 --> 00:35:59,420
+have four words. Just already never, just already
+
+347
+00:35:59,420 --> 00:36:06,520
+ever and yet. Also, so this is the answer. Have
+
+348
+00:36:06,520 --> 00:36:15,630
+you just, have you already have you ever and have
+
+349
+00:36:15,630 --> 00:36:22,210
+with yet so just this exercise just to show you
+
+350
+00:36:22,210 --> 00:36:30,910
+the position of mid adverb present perfect also
+
+351
+00:36:30,910 --> 00:36:31,570
+here again
+
+352
+00:36:42,000 --> 00:36:45,860
+Number three, he hasn't learned to drive.
+
+353
+00:36:48,260 --> 00:36:54,180
+He hasn't learned to drive yet. Why? Because we
+
+354
+00:36:54,180 --> 00:36:59,160
+use yet with the negative and with the question.
+
+355
+00:37:00,580 --> 00:37:07,020
+Also, he has ever. He hasn't ever. Why ever, not
+
+356
+00:37:07,020 --> 00:37:13,940
+never? Ever, not never. Because not ever means
+
+357
+00:37:13,940 --> 00:37:18,760
+never if we have not we can't say never But
+
+358
+00:37:18,760 --> 00:37:23,720
+without not we can say never It means he has never
+
+359
+00:37:23,720 --> 00:37:30,260
+learned or he hasn't ever learned Number three
+
+360
+00:37:30,260 --> 00:37:39,660
+number four they have finished The exercise we can
+
+361
+00:37:39,660 --> 00:37:47,700
+use they have just they have already finished the
+
+362
+00:37:47,700 --> 00:37:53,730
+exercise but not with Never. Why? Because it is a
+
+363
+00:37:53,730 --> 00:37:59,430
+quick action. Quick action. But not at any time in
+
+364
+00:37:59,430 --> 00:38:03,990
+his life. No. If the verb is long, we can use
+
+365
+00:38:03,990 --> 00:38:08,210
+never or ever. But if it is short, very short, we
+
+366
+00:38:08,210 --> 00:38:16,730
+can't use ever and never. Number five. She has
+
+367
+00:38:16,730 --> 00:38:18,450
+learned foreign languages.
+
+368
+00:38:21,260 --> 00:38:24,500
+Mm-hmm. She has learned a foreign language. She
+
+369
+00:38:24,500 --> 00:38:29,060
+has just Learned she has already learned she has
+
+370
+00:38:29,060 --> 00:38:32,860
+never learned Because learning takes a long time,
+
+371
+00:38:32,920 --> 00:38:37,300
+but with finish Short time so we can't say never
+
+372
+00:38:37,300 --> 00:38:45,780
+again This one again. We have met your teacher We
+
+373
+00:38:45,780 --> 00:38:51,920
+have just metwe have already met we have never met
+
+374
+00:38:51,920 --> 00:38:59,480
+uh-huh the same number seven question have you
+
+375
+00:38:59,480 --> 00:39:07,280
+just have you just finished have you just finished
+
+376
+00:39:07,280 --> 00:39:15,990
+yet uh-huh Why? Because it is a short verb. So we
+
+377
+00:39:15,990 --> 00:39:18,870
+can't use never or ever.
+
+378
+00:39:22,310 --> 00:39:28,410
+And here we have also already. The last question
+
+379
+00:39:28,410 --> 00:39:33,090
+also questions. So these are the same. And these
+
+380
+00:39:33,090 --> 00:39:40,960
+are the same. Has it just stopped raining? Has it
+
+381
+00:39:40,960 --> 00:39:46,160
+stopped raining yet? Has it already? So we use
+
+382
+00:39:46,160 --> 00:39:50,940
+just and already and yet. What's the meaning of
+
+383
+00:39:50,940 --> 00:39:51,320
+yet?
+
+384
+00:39:54,180 --> 00:40:00,540
+Up to now or up till until now. What's the meaning
+
+385
+00:40:00,540 --> 00:40:05,780
+of ever and ever? At any time in your life or not
+
+386
+00:40:05,780 --> 00:40:12,490
+at any time in your life. Just recently, already
+
+387
+00:40:12,490 --> 00:40:20,810
+before that. And inshallah next time, next time we
+
+388
+00:40:20,810 --> 00:40:28,970
+will do a short exercise about how to use the
+
+389
+00:40:28,970 --> 00:40:33,150
+present simple and the present perfect in the
+
+390
+00:40:33,150 --> 00:40:36,950
+active and in the passive. Thank you very much.
+
+391
+00:40:37,210 --> 00:40:39,590
+Wassalamualaikum warahmatullahi wabarakatuh.
+
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/MA8JC9RlsNI.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/MA8JC9RlsNI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0782698dd3c12d98be66e8b8e2a45c986c6658a8
--- /dev/null
+++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/MA8JC9RlsNI.srt
@@ -0,0 +1,1619 @@
+
+1
+00:00:20,690 --> 00:00:26,210
+Assalamualaikum Warahmatullahi Wabarakatuh. Today 
+
+2
+00:00:26,210 --> 00:00:30,770
+Inshallah. We're going to study how to express
+
+3
+00:00:30,770 --> 00:00:38,970
+numbers and dates in writing. Before
+
+4
+00:00:38,970 --> 00:00:43,250
+dealing with numbers and dates, we will choose 
+
+5
+00:00:43,250 --> 00:00:49,210
+between three verbs: do, go, and play. 
+
+6
+00:00:53,000 --> 00:01:00,340
+We usually use play when there is a game and there 
+
+7
+00:01:00,340 --> 00:01:10,500
+is a ball, so we say play football, play tennis, play 
+
+8
+00:01:10,500 --> 00:01:18,520
+basketball, play golf, play volleyball. If you look
+
+9
+00:01:18,520 --> 00:01:23,830
+here, I can use play with volleyball. 
+
+10
+00:01:26,450 --> 00:01:28,270
+With golf. 
+
+11
+00:01:32,290 --> 00:01:34,570
+With basketball. 
+
+12
+00:01:37,450 --> 00:01:38,650
+With football.
+
+13
+00:01:42,030 --> 00:01:49,490
+So, when there is a ball and games, we use play. 
+
+14
+00:01:51,150 --> 00:01:56,490
+When there is ING, an activity with ING, we use
+
+15
+00:01:56,490 --> 00:02:02,270
+go. Go. So snowboarding,
+
+16
+00:02:03,030 --> 00:02:08,870
+go fishing, go. 
+
+17
+00:02:13,010 --> 00:02:24,360
+Jogging, go. And mountain biking, go. 
+
+18
+00:02:26,440 --> 00:02:35,020
+If there is no ING and no ball, I use do. So here, 
+
+19
+00:02:35,780 --> 00:02:41,320
+do aerobics and do yoga.
+
+20
+00:02:42,780 --> 00:02:49,480
+So, when we are asked to choose between play,
+
+21
+00:02:52,190 --> 00:03:00,250
+go and do, we
+
+22
+00:03:00,250 --> 00:03:09,150
+use this for balls and go for the ing and
+
+23
+00:03:09,150 --> 00:03:22,210
+this for no ing except for boxing. Do boxing. Yes. 
+
+24
+00:03:23,110 --> 00:03:29,250
+We want someone to read. Yes. Go snowboarding. Go 
+
+25
+00:03:29,250 --> 00:03:31,630
+aerobics. 
+
+26
+00:03:32,470 --> 00:03:35,890
+Play volleyball. Go fishing. Play golf. Go
+
+27
+00:03:35,890 --> 00:03:40,750
+jogging. Play basketball. Play football. Do yoga. 
+
+28
+00:03:41,190 --> 00:03:45,690
+Go mountain biking. Yes. So, when I use go, it
+
+29
+00:03:45,690 --> 00:03:52,990
+means go or went or will go in a sentence. In all
+
+30
+00:03:52,990 --> 00:03:58,790
+tenses. Play, blade, easy blade, heavy blade, 
+
+31
+00:03:59,090 --> 00:04:07,190
+football. When I say do, do, did, is doing, will
+
+32
+00:04:07,190 --> 00:04:12,170
+do, have done. In all tenses. Not just in the 
+
+33
+00:04:12,170 --> 00:04:18,540
+present. In all tenses. Now, after this, we are
+
+34
+00:04:18,540 --> 00:04:18,880
+going. 
+
+35
+00:04:22,380 --> 00:04:23,360
+So the answer. 
+
+36
+00:04:35,180 --> 00:04:39,880
+The answer again. Someone else read the answer. 
+
+37
+00:04:41,900 --> 00:04:47,120
+Yes. Play golf, do yoga, 
+
+38
+00:04:48,760 --> 00:04:52,400
+do aerobics,
+
+39
+00:04:52,560 --> 00:04:59,060
+go jogging, 
+
+40
+00:04:59,060 --> 00:05:02,260
+go
+
+41
+00:05:02,260 --> 00:05:07,900
+mountain biking, play volleyball, play basketball,
+
+42
+00:05:08,640 --> 00:05:15,270
+go fishing. Yes. So again, play football, play 
+
+43
+00:05:15,270 --> 00:05:20,870
+basketball, play golf. Here, play volleyball. Why?
+
+44
+00:05:21,070 --> 00:05:26,170
+Because there is a team, and it's a game and there 
+
+45
+00:05:26,170 --> 00:05:32,210
+is a ball. With go, because there is an IG with 
+
+46
+00:05:32,210 --> 00:05:37,310
+the activity, we use go. Go fishing, go
+
+47
+00:05:37,310 --> 00:05:41,490
+snowboarding, go jogging, and go mountain biking. 
+
+48
+00:05:43,710 --> 00:05:50,470
+Without IG and without a ball, we use do. Do yoga
+
+49
+00:05:50,470 --> 00:05:59,250
+and do aerobics. The rules are as follows. We use 
+
+50
+00:05:59,250 --> 00:06:07,970
+play with a game which uses a ball, a game with a
+
+51
+00:06:07,970 --> 00:06:15,790
+ball. A game with a ball. Often, when there is a 
+
+52
+00:06:15,790 --> 00:06:22,050
+game and there's a ball in teams, more than one 
+
+53
+00:06:22,050 --> 00:06:28,930
+team. So, because of these, we use play for the 
+
+54
+00:06:28,930 --> 00:06:35,900
+ball in a game, in teams, play. Okay, the second 
+
+55
+00:06:35,900 --> 00:06:45,380
+rule, we use go. Go, or when he's going, will go with
+
+56
+00:06:45,380 --> 00:06:53,420
+a sporting activity ending in ing. An activity with 
+
+57
+00:06:53,420 --> 00:06:57,580
+ing, sporting
+
+58
+00:06:57,580 --> 00:07:06,680
+activity with ig. And we do with sporting activity 
+
+59
+00:07:06,680 --> 00:07:12,280
+the same, but often an exercise activity, not
+
+60
+00:07:12,280 --> 00:07:17,540
+ending with ing, without ing. 
+
+61
+00:07:19,000 --> 00:07:25,600
+Is it clear? Yes. Now we
+
+62
+00:07:25,600 --> 00:07:30,620
+will study how to express numbers.
+
+63
+00:07:36,870 --> 00:07:42,990
+This is an important part of this unit. In the 
+
+64
+00:07:42,990 --> 00:07:51,990
+exams, usually he asks you to write the numbers in 
+
+65
+00:07:51,990 --> 00:07:59,890
+letters. Write the numbers in letters. So, if
+
+66
+00:07:59,890 --> 00:08:02,470
+I want to express the numbers, I should express it
+
+67
+00:08:02,470 --> 00:08:09,660
+in letters, in words. So, I say one, two, three, 
+
+68
+00:08:10,060 --> 00:08:18,160
+four, five, six, seven, eight, nine, ten, eleven, 
+
+69
+00:08:18,620 --> 00:08:25,220
+twelve. This is one group, one word. Another
+
+70
+00:08:25,220 --> 00:08:31,140
+group. Thirteen, fourteen, 
+
+71
+00:08:32,160 --> 00:08:41,740
+fifteen, sixteen, eighteen, nineteen. Just. Yes.
+
+72
+00:08:42,000 --> 00:08:48,100
+So, we have from one to twelve. One group. Another
+
+73
+00:08:48,100 --> 00:08:54,520
+group from thirteen to nineteen. Here, we use teen. 
+
+74
+00:08:55,980 --> 00:09:02,760
+Yes. Teen. So, when I use teen, it is stressed. 
+
+75
+00:09:05,170 --> 00:09:11,610
+This is on the teen: thirteen, fourteen, fifteen,
+
+76
+00:09:12,210 --> 00:09:19,310
+sixteen, seventeen, eighteen, nineteen. So, I use 
+
+77
+00:09:19,310 --> 00:09:22,610
+teen and pronounce it more than the other
+
+78
+00:09:22,610 --> 00:09:27,970
+syllables. Also, we should give attention to the 
+
+79
+00:09:27,970 --> 00:09:35,320
+number fifteen. We have five and fifteen. Five 
+
+80
+00:09:35,320 --> 00:09:39,040
+and
+
+81
+00:09:39,040 --> 00:09:41,960
+fifteen.
+
+82
+00:09:43,300 --> 00:09:48,980
+So, this is one, two, the third one. From twenty to
+
+83
+00:09:48,980 --> 00:09:52,380
+ninety.
+
+84
+00:09:53,720 --> 00:09:54,840
+Twenty. 
+
+85
+00:09:59,140 --> 00:10:09,760
+30, 40, 50, 60, 70, 80, 90. The stress is on the 
+
+86
+00:10:09,760 --> 00:10:13,820
+first syllable, not on the second. So, when we say
+
+87
+00:10:13,820 --> 00:10:14,700
+40, 
+
+88
+00:10:17,040 --> 00:10:23,020
+40, the stress is on the fourth syllable. Also, 40 
+
+89
+00:10:23,020 --> 00:10:29,510
+is different from four. We have four, and 40.
+
+90
+00:10:29,890 --> 00:10:36,870
+Four, F-O-U-R. Forty, without U. Five, with V. 
+
+91
+00:10:37,470 --> 00:10:47,710
+Without V, with F. So, we have five, fifteen, 4, 40. 
+
+92
+00:10:47,710 --> 00:10:54,050
+14. When I say 14, the stress is on the teen. When I say 
+
+93
+00:10:54,050 --> 00:11:03,450
+40, on the first syllable, 40, 60, 70, 80, 90. Yes. Now, 
+
+94
+00:11:03,450 --> 00:11:11,030
+what about the number from 21 to 99 without the 
+
+95
+00:11:11,030 --> 00:11:25,880
+tenths? We have 21, 22, 23, 24, 25, 26, 27, 28, 29, 
+
+96
+00:11:26,520 --> 00:11:32,100
+30, 31, 32. What's the difference? We have a 
+
+97
+00:11:32,100 --> 00:11:37,940
+hyphen. When there are two words as one number, we
+
+98
+00:11:37,940 --> 00:11:40,980
+put a hyphen between them. So, we have twenty
+
+99
+00:11:43,310 --> 00:11:53,150
+twenty hyphen one. One word. Twenty twenty 
+
+100
+00:11:53,150 --> 00:12:00,110
+two. Thirty thirty 
+
+101
+00:12:00,110 --> 00:12:04,390
+six. Ninety 
+
+102
+00:12:04,390 --> 00:12:08,410
+nine. 
+
+103
+00:12:09,660 --> 00:12:16,980
+So, here, we should write a hyphen, a small dash
+
+104
+00:12:16,980 --> 00:12:23,560
+between the two words. Now, we finished from 1 to 
+
+105
+00:12:23,560 --> 00:12:31,240
+12, from 13 to 19, from 20 to 90, from 21 to 99.
+
+106
+00:12:31,780 --> 00:12:36,850
+Here, we put a hyphen. Here, the stress is on the
+
+107
+00:12:36,850 --> 00:12:41,830
+first syllable. Here, the stress is on the second 
+
+108
+00:12:41,830 --> 00:12:46,910
+syllable. Here, it is a dictation. Now, after 
+
+109
+00:12:46,910 --> 00:12:55,270
+this, we come to the hundreds. So, we say one
+
+110
+00:12:55,270 --> 00:13:00,430
+hundred. One thousand 
+
+111
+00:13:05,920 --> 00:13:06,720
+One million. 
+
+112
+00:13:13,100 --> 00:13:18,540
+One billion. Two billion. Three billion. Two 
+
+113
+00:13:18,540 --> 00:13:22,820
+million. Two thousand. Five hundred. Six thousand. 
+
+114
+00:13:23,140 --> 00:13:27,920
+Without S. Without S. When we say hundred.
+
+115
+00:13:30,720 --> 00:13:31,260
+Hundred. 
+
+116
+00:13:35,960 --> 00:13:40,760
+Two hundred, without S. Three hundred. Four hundred.
+
+117
+00:13:40,760 --> 00:13:47,860
+Five thousand, without 
+
+118
+00:13:47,860 --> 00:14:02,750
+S. Six million, without S. Yes. Now, if we are speaking 
+
+119
+00:14:02,750 --> 00:14:06,750
+about millions in general, meaning a long number, 
+
+120
+00:14:06,970 --> 00:14:11,690
+a very big number. Millions of people came to 
+
+121
+00:14:11,690 --> 00:14:17,830
+Gaza. Millions of birds died. Hundreds of people 
+
+122
+00:14:19,210 --> 00:14:24,030
+came early. Thousands of people use the internet. 
+
+123
+00:14:24,510 --> 00:14:27,810
+So, when I say generally a big number of something,
+
+124
+00:14:28,230 --> 00:14:33,170
+of some people, we say hundreds, millions of 
+
+125
+00:14:33,170 --> 00:14:38,510
+people. But here, three million, five million,
+
+126
+00:14:38,830 --> 00:14:44,890
+twenty-two thousand, a ten hundred. Hundred,
+
+127
+00:14:45,330 --> 00:14:53,210
+million, thousand, billion, without S. Now, after
+
+128
+00:14:53,210 --> 00:14:58,150
+this introduction, we come to the fourth exercise. 
+
+129
+00:15:00,390 --> 00:15:04,890
+Is it right? Yes. So, here, the first number, 
+
+130
+00:15:06,350 --> 00:15:08,710
+fifteen.
+
+131
+00:15:09,630 --> 00:15:16,730
+This is in the second syllable. So, I say, Fifteen. 
+
+132
+00:15:17,610 --> 00:15:20,630
+Fifteen. Fifteen. 
+
+133
+00:15:24,630 --> 00:15:29,030
+Fifteen. Fifteen. Fifteen. Fifteen. Fifteen. 
+
+134
+00:15:29,090 --> 00:15:34,750
+Fifteen. Fifteen. Fifteen. Fifteen. Fifteen. 
+
+135
+00:15:34,870 --> 00:15:37,590
+Fifteen. Fifteen. Fifteen. Fifteen. Fifteen.
+
+136
+00:15:37,590 --> 00:15:42,010
+Fifteen. Fifteen. Fifteen. Fifteen. Fifteen.
+
+137
+00:15:43,050 --> 00:15:43,750
+Fifteen. Fifteen. Fifteen. Fifteen. Fifteen. 
+
+138
+00:15:43,750 --> 00:15:50,350
+Fifteen. Fifteen. Yes? Now, here, again. Ninety. 
+
+139
+00:15:51,370 --> 00:15:56,250
+Ninety. Ninety. Ninety. But here? Nineteen. 
+
+140
+00:16:00,310 --> 00:16:08,770
+Teen. Right? Now, again. Here, seventy-two.
+
+141
+00:16:09,170 --> 00:16:10,430
+Seventy-two. 
+
+142
+00:16:15,290 --> 00:16:23,530
+Hyphen two. Seventy two. But here, thirty 
+
+143
+00:16:23,530 --> 00:16:29,670
+hyphen six, okay. 
+
+144
+00:16:29,670 --> 00:16:40,690
+Now look there, one hundred or a hundred and twenty
+
+145
+00:16:40,690 --> 00:16:50,750
+hyphen eight. One hundred or a hundred? A hundred 
+
+146
+00:16:50,750 --> 00:17:03,650
+and twenty eight, one
+
+147
+00:17:03,650 --> 00:17:14,010
+hundred. Here, one thousand. One thousand.
+
+148
+00:17:18,570 --> 00:17:24,250
+One thousand, five hundred, without and. We put and 
+
+149
+00:17:24,250 --> 00:17:35,110
+at the last item. One thousand, five hundred and 
+
+150
+00:17:35,110 --> 00:17:41,830
+twenty. Look 
+
+151
+00:17:41,830 --> 00:17:54,320
+here, four hundred and six. Four hundred, four
+
+152
+00:17:54,320 --> 00:18:08,680
+hundred and six. Look here, eight hundred and fifty
+
+153
+00:18:08,680 --> 00:18:16,440
+eight hundred and
+
+154
+00:18:16,440 --> 00:18:18,260
+fifty
+
+155
+00:18:22,190 --> 00:18:32,930
+Now, two hundred and forty hyphen forty-seven. Two 
+
+156
+00:18:32,930 --> 00:18:39,370
+hundred and 
+
+157
+00:18:39,370 --> 00:18:43,570
+forty
+
+158
+00:18:43,570 --> 00:18:48,930
+hyphens without you. Forty-seven. 
+
+159
+00:18:51,960 --> 00:18:58,400
+We don't say hyphen. We write hyphen. Yes. Now, is 
+
+160
+00:18:58,400 --> 00:19:04,460
+it clear? Yes. This one. Five thousand. Five
+
+161
+00:19:04,460 --> 00:19:12,200
+thousand. This one. One hundred thousand. One 
+
+162
+00:19:12,200 --> 00:19:19,580
+hundred thousand. This one. Two million. Two
+
+163
+00:19:19,580 --> 00:19:25,090
+million. We generally put a comma after the first 
+
+164
+00:19:25,090 --> 00:19:29,490
+and the second three figures or three numbers. 
+
+165
+00:19:30,890 --> 00:19:35,450
+One, two, three, comma. One, two, three, comma. If
+
+166
+00:19:35,450 --> 00:19:38,270
+there are another three, comma. Two, without comma. 
+
+167
+00:19:38,710 --> 00:19:43,130
+Yes? So, here, a hundred thousand, or one hundred
+
+168
+00:19:43,130 --> 00:19:51,380
+thousand. Two million. Five thousand. Two hundred. 
+
+169
+00:19:52,180 --> 00:19:59,260
+And. So, we put and with the last item. Two hundred 
+
+170
+00:19:59,260 --> 00:20:08,240
+and forty-seven. This one. Fifty. Fifteen. Ninety.
+
+171
+00:20:08,880 --> 00:20:15,940
+Nineteen. Eight hundred and fifty. And fifty. Four
+
+172
+00:20:15,940 --> 00:20:17,840
+hundred and six. 
+
+173
+00:20:20,540 --> 00:20:29,200
+72 hyphen, 36 hyphen. Is it clear? I want someone
+
+174
+00:20:29,200 --> 00:20:37,480
+to read these after I clean the board. Yes? Now, I 
+
+175
+00:20:37,480 --> 00:20:42,240
+want some of you to read the number as one line, 
+
+176
+00:20:42,620 --> 00:20:50,270
+one line, one line, three lines. Yes. Fifteen.
+
+177
+00:20:56,270 --> 00:20:59,570
+I'm going to hear the word teen. 
+
+178
+00:21:05,310 --> 00:21:06,350
+Yes. 
+
+179
+00:21:12,130 --> 00:21:17,070
+Another one. Yes. Ninety. Ninety. Nineteen. Eight 
+
+180
+00:21:17,070 --> 00:21:22,310
+hundred and fifty, thirty-six, one thousand, five
+
+181
+00:21:22,310 --> 00:21:26,570
+hundred and twenty. Yes. Yes. Two hundred and
+
+182
+00:21:26,570 --> 00:21:30,630
+forty-seven, five thousand, one hundred thousand,
+
+183
+00:21:32,870 --> 00:21:36,270
+two million. Very good. One hundred thousand, two 
+
+184
+00:21:36,270 --> 00:21:41,760
+million. Again, again. Fifteen, fifty, four
+
+185
+00:21:41,760 --> 00:21:45,320
+hundred and six, seventy-two, one hundred and 
+
+186
+00:21:45,320 --> 00:21:46,900
+eight and twenty-eight. 
+
+187
+00:21:50,140 --> 00:21:56,080
+Ninety, nineteen, eight hundred and fifty, thirty
+
+188
+00:21:56,080 --> 00:22:02,060
+-six, one thousand, five hundred and twenty-two. 
+
+189
+00:22:03,040 --> 00:22:07,320
+Two hundred and forty-seven, five thousand,
+
+190
+00:22:09,870 --> 00:22:16,350
+Yes. So, the most important thing is teen. 
+
+191
+00:22:17,890 --> 00:22:19,290
+Fifteen. 
+
+192
+00:22:22,310 --> 00:22:24,990
+Yes, here. Hundred
+
+223
+00:27:06,850 --> 00:27:13,930
+We have also Euros 400
+
+224
+00:27:13,930 --> 00:27:24,610
+euros. We bought what?  We also have Yen
+
+225
+00:27:24,610 --> 00:27:28,110
+60
+
+226
+00:27:28,110 --> 00:27:30,950
+yen Japan
+
+227
+00:27:35,440 --> 00:27:45,400
+So also we have fifty pence, fifty pence, forty
+
+228
+00:27:45,400 --> 00:27:54,720
+pence, one penny, one penny, three pence, four pence
+
+229
+00:27:54,720 --> 00:28:00,200
+ninety nine pence. Yes. Three pence. Forty pence. So
+
+230
+00:28:00,200 --> 00:28:04,460
+this is four pence. And with the dollar we use
+
+231
+00:28:05,660 --> 00:28:09,220
+cents. We
+
+232
+00:28:09,220 --> 00:28:15,500
+use cents. So if it is one cent, we use cent and
+
+233
+00:28:15,500 --> 00:28:21,780
+the plural is cents. 
+
+234
+00:28:21,780 --> 00:28:26,280
+cents 
+
+235
+00:28:26,280 --> 00:28:33,520
+the plural. Penny? Singular. So we have pennies and 
+
+236
+00:28:33,520 --> 00:28:39,390
+cents. Cents with the dollar, pence with the
+
+237
+00:28:39,390 --> 00:28:47,010
+pound. So with these words, we use "S". But with
+
+238
+00:28:47,010 --> 00:28:53,290
+yen, we don't use "S". Three yen. A hundred yen, not
+
+239
+00:28:53,290 --> 00:29:02,270
+yens. Dollars, pounds, euros. Clear? Yes.
+
+240
+00:29:04,290 --> 00:29:10,700
+Something else. I want to use... Is it clear?
+
+241
+00:29:16,580 --> 00:29:28,740
+Now, this is fraction. This is a quarter.
+
+242
+00:29:40,090 --> 00:29:46,310
+A quarter. And this is a third. 
+
+243
+00:29:48,350 --> 00:29:55,750
+And this is a half. Or without "a". We can say half. 
+
+244
+00:29:56,530 --> 00:30:01,830
+We can say half. Half or a half. But here, a
+
+245
+00:30:01,830 --> 00:30:05,110
+third. Also, we have
+
+246
+00:30:10,550 --> 00:30:16,670
+a fifth, a sixth, 
+
+247
+00:30:17,750 --> 00:30:21,610
+a ninth. If it is two,
+
+248
+00:30:27,410 --> 00:30:32,110
+two eighths, 
+
+249
+00:30:33,030 --> 00:30:43,420
+three sevenths, nine or two thirds. Two, instead
+
+250
+00:30:43,420 --> 00:30:51,380
+of a third, if it is two, two thirds. So we put "S"
+
+251
+00:30:51,380 --> 00:30:59,860
+with the bows, dollars, yen, shekels, and with 
+
+252
+00:30:59,860 --> 00:31:02,680
+thirds,
+
+253
+00:31:03,880 --> 00:31:08,000
+quarters, fourths, etc. Yes?
+
+254
+00:31:11,910 --> 00:31:15,830
+Look here, say the numbers. About what? About
+
+255
+00:31:15,830 --> 00:31:23,830
+money? Now, this is money. Four hundred pounds. 
+
+256
+00:31:24,530 --> 00:31:28,210
+Four hundred pounds. 
+
+257
+00:31:28,870 --> 00:31:31,290
+Fifty pence.
+
+258
+00:31:33,570 --> 00:31:34,510
+Nine 
+
+259
+00:31:40,900 --> 00:31:50,140
+nine and forty-nine euros. And forty and forties
+
+260
+00:31:50,140 --> 00:32:03,340
+and forty. Forty. So yes, we use "here". If I want to
+
+261
+00:32:03,340 --> 00:32:09,500
+use them. Yes, look here quickly.
+
+262
+00:32:22,210 --> 00:32:32,690
+and forty cents.
+
+263
+00:32:32,690 --> 00:32:37,390
+And not "point" and forty cents. 
+
+264
+00:32:41,800 --> 00:32:43,280
+47 euros.
+
+265
+00:32:46,780 --> 00:32:50,680
+Sometimes we can use "and", sometimes we can leave 
+
+266
+00:32:50,680 --> 00:32:57,060
+it. So here we leave "and". So we say 47 euros, 99, 
+
+267
+00:32:57,560 --> 00:32:58,240
+99.
+
+268
+00:33:02,460 --> 00:33:09,320
+5,000 yen, without "S". Without "S". Here we have "S".
+
+269
+00:33:09,640 --> 00:33:15,940
+Here, no "S". One hundred dollars.
+
+270
+00:33:17,240 --> 00:33:22,980
+Don't say "one hundred, two hundred dollars". No. Two
+
+271
+00:33:22,980 --> 00:33:31,700
+hundred dollars. So dollars, euros, pounds with "S".
+
+272
+00:33:32,140 --> 00:33:37,710
+Yen without "S". Is it clear? Now, look here.
+
+273
+00:33:38,310 --> 00:33:38,850
+Fraction.
+
+274
+00:33:41,370 --> 00:33:50,090
+A quarter. Three quarters. So with the fraction,
+
+275
+00:33:50,290 --> 00:33:54,070
+we use "this". We use "this" in all the numbers except 
+
+276
+00:33:54,070 --> 00:34:01,710
+for the hundred, thousand, million, trillion, etc.
+
+277
+00:34:02,670 --> 00:34:11,000
+A quarter, three quarters, thirds. Two thirds, seven
+
+278
+00:34:11,000 --> 00:34:20,180
+eighths. Seven eighths. Seven eighths
+
+279
+00:34:20,180 --> 00:34:29,860
+Twelve and a half. Twelve and a half. Twelve and a 
+
+280
+00:34:29,860 --> 00:34:37,220
+half. Twelve and a third and two thirds and three
+
+281
+00:34:37,220 --> 00:34:44,680
+quarters. It's clear? So numbers, money,
+
+282
+00:34:45,820 --> 00:34:46,360
+fractions.
+
+283
+00:34:50,160 --> 00:34:59,920
+I want to test you with something. But after this,
+
+284
+00:35:00,220 --> 00:35:01,800
+we will take percentages.
+
+285
+00:35:22,530 --> 00:35:25,330
+Decimals. Decimals. 
+
+286
+00:35:27,630 --> 00:35:32,090
+6.2.
+
+287
+00:35:32,510 --> 00:35:44,870
+Here we use what? "Point". 17 with hyphen. 17.25.
+
+288
+00:35:47,850 --> 00:35:53,070
+25. Why? I'm asking you to write. Yes, ask, write.
+
+289
+00:35:54,570 --> 00:35:58,710
+17.25.
+
+290
+00:35:59,510 --> 00:36:08,270
+When we type 25, we put "point two"
+
+291
+00:36:08,270 --> 00:36:09,870
+five.
+
+292
+00:36:14,050 --> 00:36:15,610
+50 percent.
+
+293
+00:36:20,230 --> 00:36:21,630
+Percent.
+
+294
+00:36:25,370 --> 00:36:32,930
+What about this? Seventy-five point seven percent.
+
+295
+00:36:33,790 --> 00:36:41,070
+Seventy-five point seven percent. Yes. One hundred
+
+296
+00:36:41,070 --> 00:36:47,590
+percent. So here we have decimals and percentages.
+
+297
+00:36:49,040 --> 00:36:56,360
+This is the percentage. You understand? Now, what 
+
+298
+00:36:56,360 --> 00:36:57,040
+about this? 
+
+299
+00:37:01,120 --> 00:37:03,900
+A tenth. Equals for what?
+
+300
+00:37:07,540 --> 00:37:12,940
+Ten percent. That's good. Now, what about this?
+
+301
+00:37:15,980 --> 00:37:18,580
+A third. Equals for what? 
+
+302
+00:37:21,490 --> 00:37:23,270
+Percentages. Yes.
+
+303
+00:37:28,130 --> 00:37:29,530
+Yes.
+
+304
+00:37:31,830 --> 00:37:32,190
+No.
+
+305
+00:37:36,810 --> 00:37:40,430
+Third. Yes.
+
+306
+00:37:47,910 --> 00:37:57,350
+Thirty-three point three percent. Thirty-three 
+
+307
+00:37:57,350 --> 00:38:06,630
+point three percent. Yes, now. What about this? A 
+
+308
+00:38:06,630 --> 00:38:12,270
+fourth? A fourth? No, a quarter. We say a quarter. A
+
+309
+00:38:12,270 --> 00:38:17,010
+quarter. A quarter. And the percentage is?
+
+310
+00:38:33,950 --> 00:38:45,590
+25%. A quarter equals 25%. What about this? 
+
+311
+00:38:50,100 --> 00:38:58,920
+Yes, 50%. Very good. 50% equals what 
+
+312
+00:38:58,920 --> 00:39:12,880
+about this? 2 thirds. 2 thirds. 70
+
+313
+00:39:12,880 --> 00:39:17,780
+no, 2 
+
+314
+00:39:17,780 --> 00:39:18,980
+thirds equals
+
+315
+00:39:21,860 --> 00:39:29,360
+point six, point six 
+
+316
+00:39:29,360 --> 00:39:42,060
+point 
+
+317
+00:39:42,060 --> 00:39:44,320
+seven percent. 
+
+318
+00:39:50,700 --> 00:39:54,140
+Sixty-six point seven percent equals four two 
+
+319
+00:39:54,140 --> 00:40:00,820
+-thirds. Now three
+
+320
+00:40:00,820 --> 00:40:08,520
+quarters. Seventy-five. Yes, seventy-five percent. 
+
+321
+00:40:09,720 --> 00:40:15,480
+What about nine 
+
+322
+00:40:15,480 --> 00:40:18,200
+tenths? Ninety percent. 
+
+323
+00:40:23,010 --> 00:40:34,610
+Yes? Clear? So, a tenth equals 10%. A third, 33
+
+324
+00:40:34,610 --> 00:40:43,150
+.3%. A quarter, 25%. 
+
+325
+00:40:43,150 --> 00:40:55,550
+A half, 50%. Two thirds, 66.7%. Three quarters,
+
+326
+00:40:56,250 --> 00:41:05,170
+seventy-five percent. Nine tenths, ninety percent.
+
+327
+00:41:06,130 --> 00:41:11,790
+And I have something now in my mind. What if I 
+
+328
+00:41:11,790 --> 00:41:19,590
+say... 
+
+329
+00:41:22,360 --> 00:41:27,300
+Big numbers. Or like this.
+
+330
+00:41:31,960 --> 00:41:35,300
+In English,
+
+331
+00:41:36,020 --> 00:41:48,940
+we say 22 over 47. Over 47. 22 over 47. Here, 15
+
+332
+00:41:48,940 --> 00:41:54,350
+over 45. Yes? Now,
+
+333
+00:41:56,710 --> 00:41:57,250
+it's clear?
+
+334
+00:42:00,010 --> 00:42:04,030
+No, no, over, over. We use the word "over". Yes. 
+
+335
+00:42:05,590 --> 00:42:12,430
+Yes. I want someone again to read these decimals 
+
+336
+00:42:12,430 --> 00:42:15,270
+and percentages. Yes. 
+
+337
+00:42:23,210 --> 00:42:29,870
+Yes. The first one. 6.2. "Point". You should write 
+
+338
+00:42:29,870 --> 00:42:38,410
+"point" and say "point". Yes. 17.25 percent.
+
+339
+00:42:38,890 --> 00:42:44,030
+Yes. 50 percent. Yes.
+
+340
+00:42:49,230 --> 00:42:57,590
+uh-huh 75.7 percent. And the last one 100 percent
+
+341
+00:42:57,590 --> 00:43:03,170
+Yes. Decimals and percentages, now. What about dates? 
+
+342
+00:43:03,170 --> 00:43:08,250
+Something different, something different completely 
+
+343
+00:43:08,250 --> 00:43:15,130
+different. So this is clear, okay, now
+
+344
+00:43:15,130 --> 00:43:19,910
+we want, when we study the dates. The first thing 
+
+345
+00:43:19,910 --> 00:43:25,790
+we use is the
+
+346
+00:43:25,790 --> 00:43:30,490
+months of the year. The months of the year. What
+
+347
+00:43:30,490 --> 00:43:36,510
+are the 12 months of the year? December, January, 
+
+348
+00:43:36,890 --> 00:43:43,580
+the first one, January. February, listen to me,
+
+349
+00:43:44,000 --> 00:43:50,220
+listen to me, January, February, March, April,
+
+350
+00:43:50,560 --> 00:43:58,800
+June, May, June, July, August, September, October, 
+
+351
+00:43:59,340 --> 00:44:05,030
+November, December, and December. Again. January,
+
+352
+00:44:05,470 --> 00:44:09,750
+February, March, April, May, June, July, August,
+
+353
+00:44:09,990 --> 00:44:14,330
+September, October, November, and December, in 
+
+354
+00:44:14,330 --> 00:44:20,110
+writing, in full. Yes. This is one. Another thing. 
+
+355
+00:44:21,350 --> 00:44:26,750
+Look here, the dates now. What is it? It is not
+
+356
+00:44:26,750 --> 00:44:30,830
+one thousand five. No, no, no, no. It is 1995. 
+
+357
+00:44:33,840 --> 00:44:37,140
+Because it's a year. A year. Not a number. Not a
+
+358
+00:44:37,140 --> 00:44:41,640
+big number. No. So it is nineteen ninety-five. 
+
+359
+00:44:43,420 --> 00:44:52,060
+What's this? Two thousand and twenty. 
+
+360
+00:44:53,800 --> 00:44:59,780
+This year, now, two thousand and thirteen. 
+
+361
+00:45:01,570 --> 00:45:07,510
+Two thousand and twenty, two thousand and twenty. 
+
+362
+00:45:07,510 --> 00:45:13,530
+What about this? Seventeen eighty
+
+363
+00:45:13,530 --> 00:45:20,830
+nine, with what? With a hyphen. Seventeen. One word. 
+
+364
+00:45:20,830 --> 00:45:26,010
+Seventeen or seventy. Seventeen. You should
+
+365
+00:45:26,010 --> 00:45:33,870
+pronounce "teen" clearly. Seventeen 89, without "end".
+
+366
+00:45:34,830 --> 00:45:43,850
+Without "end". Two numbers. 1789. These are years.
+
+367
+00:45:44,490 --> 00:45:54,510
+What about this? It's very important. It is the
+
+368
+00:45:54,510 --> 00:46:03,690
+15th of. So the answer here, look here. The 
+
+369
+00:46:03,690 --> 00:46:07,030
+fifteenth 
+
+370
+00:46:07,030 --> 00:46:08,470
+of.
+
+371
+00:46:11,730 --> 00:46:21,010
+We should use "of", and the and the "th". So the 
+
+372
+00:46:21,010 --> 00:46:29,140
+fifteenth of. Number one. The first of. Number
+
+373
+00:46:29,140 --> 00:46:35,920
+two, the second of. So we have the first, second, 
+
+374
+00:46:36,540 --> 00:46:38,400
+third,
+
+375
+00:46:39,680 --> 00:46:50,220
+fourth, the first of, the second of, the third of, 
+
+376
+00:46:51,480 --> 00:46:57,890
+also the fourth, the fourth of, the fifth of. The 
+
+377
+00:46:57,890 --> 00:47:04,130
+sixth of, the seventh of, what? The month of July,
+
+378
+00:47:04,590 --> 00:47:10,670
+of January, of August, of September. What about 
+
+379
+00:47:10,670 --> 00:47:19,930
+19? The 19th of 20, the 20th of 13, the 13th of 
+
+380
+00:47:19,930 --> 00:47:21,410
+21.
+
+381
+00:47:27,990 --> 00:47:36,830
+21. The 21st, the
+
+382
+00:47:36,830 --> 00:47:40,950
+22nd, 
+
+383
+00:47:40,950 --> 00:47:46,790
+the 23rd
+
+384
+00:47:46,790 --> 00:47:52,310
+of. Also, we have the 30 
+
+385
+00:47:55,330 --> 00:47:56,250
+31st.
+
+386
+00:48:00,070 --> 00:48:04,990
+And this is the last day of the month. 
+
+387
+00:48:07,570 --> 00:48:15,490
+Yes, 31st. The 31st of January. The 31st of
+
+388
+00:48:15,490 --> 00:48:22,910
+September. No, September the 8th, December. Yes.
+
+389
+00:48:24,890 --> 00:48:38,070
+The 31st of January, of March, of May, of July, 
+
+390
+00:48:38,470 --> 00:48:48,610
+August, October and December. Yes? Do you 
+
+391
+00:48:48,610 --> 00:48:55,120
+understand this? Yes, thank you. The 15th of what?
+
+392
+00:48:55,740 --> 00:49:06,760
+July. Capital. July. Yes. What is this? Nineteen
+
+393
+00:49:06,760 --> 00:49:14,460
+ninety four. Nineteen ninety-four. Nineteen ninety 
+
+394
+00:49:14,460 --> 00:49:18,800
+four. Nineteen ninety-four. Nineteen ninety-four. 
+
+395
+00:49:18,880 --> 00:49:20,380
+Nineteen ninety-four. Nineteen ninety-four.
+
+396
+00:49:25,680 --> 00:49:34,100
+Is it right like this? Yes. No. What? Hyphen. 94. 
+
+397
+00:49:34,880 --> 00:49:39,200
+Hyphen. Don't forget the hyphen. So here, what's 
+
+398
+00:49:39,200 --> 00:49:47,840
+the date today here? It is the 15th of July, 1994. 
+
+399
+00:49:49,080 --> 00:49:54,710
+The 15th of May, Nineteen ninety-four, ninety-six.
+
+400
+00:49:55,370 --> 00:49:59,110
+Yes? Clear? What about this?
+
+401
+00:50:02,430 --> 00:50:12,530
+The 30th of October, two thousand and two. And two. 
+
+402
+00:50:13,170 --> 00:50:14,610
+So the answer here. 
+
+403
+00:50:23,660 --> 00:50:26,980
+What about the telephone number? Yes, that
+
+404
+00:50:26,980 --> 00:50:31,000
+telephone number. The telephone number is very
+
+405
+00:50:31,000 --> 00:50:41,740
+easy. So we have, we have zero. 
+
+406
+00:50:44,880 --> 00:50:50,630
+But we don't say "zero, zero". We say what? "O". Oh is 
+
+407
+00:50:50,630 --> 00:50:55,490
+positive. Zero is negative. Uh-huh. So don't say 
+
+408
+00:50:55,490 --> 00:51:05,890
+zero. No, so say what? Oh. Oh one eight six five 
+
+409
+00:51:05,890 --> 00:51:14,170
+again. Oh one eight six five. What a minute. Double
+
+410
+00:51:14,170 --> 00:51:21,980
+five. Ah, what is it? Double five. Six, eight, 
+
+411
+00:51:22,280 --> 00:51:31,800
+nine, O. O. Again. Hello. Yes. What's your number?
+
+412
+00:51:32,120 --> 00:51:36,440
+What's your telephone number? It's O1865.
+
+413
+00:51:38,
+
+445
+00:55:23,570 --> 00:55:29,410
+The 13th of October, November, December,
+
+446
+00:55:30,190 --> 00:55:36,030
+September, July, August, January, February, March,
+
+447
+00:55:36,270 --> 00:55:40,550
+April, May, June, July, August, September,
+
+448
+00:55:41,070 --> 00:55:46,290
+October, November, December, 12. Twelve. So when
+
+449
+00:55:46,290 --> 00:55:48,990
+we give you the date, you have to say the 15th of
+
+450
+00:55:48,990 --> 00:55:53,470
+May 1992, the 15th of July 2013.
+
+451
+00:55:55,290 --> 00:56:00,390
+And this is the telephone number. Don't forget to
+
+452
+00:56:00,390 --> 00:56:04,950
+say O and double. I want someone to read these
+
+453
+00:56:04,950 --> 00:56:06,170
+again aloud.
+
+454
+00:56:18,230 --> 00:56:38,410
+Yes 6.2 17.25 50% 75.7% 100% Thank you 1995 2020 7
+
+455
+00:56:38,410 --> 00:56:50,180
+8 9 15 July 1994 13 The 3rd of October 2002. Yes.
+
+456
+00:56:52,980 --> 00:56:54,040
+Telephone numbers
+
+457
+00:56:54,040 --> 00:57:14,020
+0186555689080045165775459196771303
+
+458
+00:57:14,890 --> 00:57:21,390
+Now the last short exercise. What is this? Five.
+
+459
+00:57:23,970 --> 00:57:26,370
+Sixty-five.
+
+460
+00:57:28,750 --> 00:57:37,770
+Two hundred and sixty-five. Two thousand, two
+
+461
+00:57:37,770 --> 00:57:41,110
+hundred and sixty-five.
+
+462
+00:57:44,670 --> 00:57:52,030
+Forty-two thousand two hundred and sixty-five.
+
+463
+00:57:54,010 --> 00:58:01,050
+Eight hundred and forty
+
+464
+00:58:01,050 --> 00:58:06,890
+-two thousand two hundred and sixty-five. We use
+
+465
+00:58:06,890 --> 00:58:11,170
+here and and here and again.
+
+466
+00:58:35,470 --> 00:58:38,410
+Assalamualaikum Warahmatullahi Wabarakatuh 
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/QjisdqFBo_o.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/QjisdqFBo_o.srt
new file mode 100644
index 0000000000000000000000000000000000000000..eaddf85005f0b440bae7ba1243086559ce02e8b6
--- /dev/null
+++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/QjisdqFBo_o.srt
@@ -0,0 +1,1535 @@
+1
+00:00:20,530 --> 00:00:23,110
+Assalamualaikum warahmatullahi wabarakatuh.
+
+2
+00:00:25,750 --> 00:00:32,310
+Inshallah this will be the last lecture and we
+
+3
+00:00:32,310 --> 00:00:38,490
+hope that all of you will get high marks and will
+
+4
+00:00:38,490 --> 00:00:39,010
+succeed.
+
+5
+00:00:46,640 --> 00:00:50,240
+Our lecture for today is phrasal verbs.
+
+6
+00:00:55,020 --> 00:01:02,280
+There are
+
+7
+00:01:02,280 --> 00:01:07,500
+many examples of phrasal verbs in the reading text
+
+8
+00:01:07,500 --> 00:01:16,320
+on page 58 to 59. Examples, I came across an ad.
+
+9
+00:01:17,930 --> 00:01:22,670
+It's exciting to end up in different cities, etc.
+
+10
+00:01:23,150 --> 00:01:27,650
+We have about 10 phrasal verbs in the reading
+
+11
+00:01:27,650 --> 00:01:33,150
+passage. Number two, some phrasal verbs are
+
+12
+00:01:33,150 --> 00:01:36,870
+literal and
+
+13
+00:01:36,870 --> 00:01:46,370
+some are idiomatic. It means some verbs are easy,
+
+14
+00:01:46,970 --> 00:01:52,790
+we can translate them word by word without keeping
+
+15
+00:01:52,790 --> 00:01:58,030
+by heart. We can translate it word by word. So it
+
+16
+00:01:58,030 --> 00:02:08,470
+is literal. But some other verbs are idiomatic. So
+
+17
+00:02:08,470 --> 00:02:13,950
+we have to keep their meaning by heart. We have to
+
+18
+00:02:13,950 --> 00:02:19,670
+keep their meaning by heart, not word by word. So
+
+19
+00:02:19,670 --> 00:02:24,590
+the phrasal verbs generally are idiomatic, but
+
+20
+00:02:24,590 --> 00:02:31,610
+sometimes are literal. Examples. Literal she
+
+21
+00:02:31,610 --> 00:02:37,910
+looked out of the window at the sunset Now she
+
+22
+00:02:37,910 --> 00:02:42,870
+looked out So we translate looked and we translate
+
+23
+00:02:42,870 --> 00:02:48,610
+out So if we translate word by word it is literal
+
+24
+00:02:48,610 --> 00:02:52,070
+So
+
+25
+00:02:52,070 --> 00:02:55,170
+What
+
+26
+00:02:55,170 --> 00:03:02,360
+did she do she looked out of of the window. But
+
+27
+00:03:02,360 --> 00:03:08,160
+here, the idiomatic one, we don't translate it
+
+28
+00:03:08,160 --> 00:03:13,100
+word by word. No. We translate it by heart. We
+
+29
+00:03:13,100 --> 00:03:18,440
+know its meaning before. So, look out. Take care.
+
+30
+00:03:19,360 --> 00:03:26,960
+Not looking by eyes. No. take a look out take care
+
+31
+00:03:26,960 --> 00:03:33,340
+take care that dog is going to bite you that dog
+
+32
+00:03:33,340 --> 00:03:39,500
+is going to bite you so the same word looked out
+
+33
+00:03:39,500 --> 00:03:45,900
+and looked out but this is literal we translate it
+
+34
+00:03:45,900 --> 00:03:48,840
+according to the verb itself the meaning of the
+
+35
+00:03:48,840 --> 00:03:53,330
+verb but here we translate it as a whole we keep
+
+36
+00:03:53,330 --> 00:03:58,330
+it by heart look out means means take care that
+
+37
+00:03:58,330 --> 00:04:02,030
+dog is going to bite you so sometimes when we see
+
+38
+00:04:02,030 --> 00:04:06,470
+the phrasal verbs if it is not literal it is
+
+39
+00:04:06,470 --> 00:04:10,550
+idiomatic if it is not idiomatic it is literal but
+
+40
+00:04:10,550 --> 00:04:15,050
+generally they are idiomatic but sometimes they
+
+41
+00:04:15,050 --> 00:04:17,590
+are literal easy example
+
+42
+00:04:22,860 --> 00:04:27,380
+another example literal
+
+43
+00:04:27,380 --> 00:04:33,260
+or idiomatic we have to say if the phrasal verb is
+
+44
+00:04:33,260 --> 00:04:37,100
+literal or idiomatic in these pairs of sentences
+
+45
+00:04:37,100 --> 00:04:44,100
+one meaning of the phrasal verb is literal and
+
+46
+00:04:44,100 --> 00:04:52,820
+the other is idiomatic say which is which So here
+
+47
+00:04:52,820 --> 00:05:00,720
+the plane has taken off The plane has taken off
+
+48
+00:05:00,720 --> 00:05:05,300
+Taken off take give me and take give and take. No,
+
+49
+00:05:05,340 --> 00:05:09,320
+no, no So it is idiomatic. So take off here is
+
+50
+00:05:09,320 --> 00:05:20,340
+idiomatic It is idiomatic Please
+
+51
+00:05:20,340 --> 00:05:28,310
+take take off take off we translate take and off
+
+52
+00:05:28,310 --> 00:05:34,670
+take off your coat and sit down so we translate
+
+53
+00:05:34,670 --> 00:05:38,210
+this word and this word so it is literal
+
+54
+00:05:41,620 --> 00:05:44,560
+So the meaning here is literal, but the meaning
+
+55
+00:05:44,560 --> 00:05:48,720
+here is idiomatic. The literal means we translate
+
+56
+00:05:48,720 --> 00:05:53,720
+word by word, word by word. But here we can't
+
+57
+00:05:53,720 --> 00:05:57,020
+translate it word by word. Why? Because it is
+
+58
+00:05:57,020 --> 00:06:05,040
+Azahul. Number two. Oh, no, the lights have gone
+
+59
+00:06:05,040 --> 00:06:10,440
+out again. Gone out. It's not a matter of go and
+
+60
+00:06:10,440 --> 00:06:16,280
+come. No, no. Gone out. As one there, it is
+
+61
+00:06:16,280 --> 00:06:23,520
+idiomatic. Stopped. Idiomatic. It means stop.
+
+62
+00:06:25,940 --> 00:06:33,070
+Number B. If you go out, take an umbrella it's
+
+63
+00:06:33,070 --> 00:06:37,750
+going to rain go out a matter of going really
+
+64
+00:06:37,750 --> 00:06:45,630
+going go out so it is literal literal meaning it
+
+65
+00:06:45,630 --> 00:06:48,630
+has a literal meaning we translate it word by word
+
+66
+00:06:48,630 --> 00:06:54,830
+as it is it is not difficult so here it is
+
+67
+00:06:54,830 --> 00:06:59,920
+idiomatic literal idiomatic literal go out go out
+
+68
+00:06:59,920 --> 00:07:09,540
+go out here stop but here no go out come in go out
+
+69
+00:07:09,540 --> 00:07:15,200
+etc the third one a and b on the phone hello hello
+
+70
+00:07:15,200 --> 00:07:21,000
+i can't hear you i think you have been cut off cut
+
+71
+00:07:21,000 --> 00:07:30,890
+off cut no not cut No? Yes, we don't translate it
+
+72
+00:07:30,890 --> 00:07:36,830
+word by word. No, we say cut off as idiomatic. So
+
+73
+00:07:36,830 --> 00:07:42,950
+number A is idiomatic. Cut off. Cut the
+
+74
+00:07:42,950 --> 00:07:46,350
+connection. Without connection. Stop the
+
+75
+00:07:46,350 --> 00:07:46,770
+connection.
+
+76
+00:07:51,250 --> 00:08:01,240
+Next, she cut Cut off. So it is literal. Cut off.
+
+77
+00:08:01,780 --> 00:08:06,320
+It's a cutting. Yes, cutting. So it is literal.
+
+78
+00:08:07,640 --> 00:08:14,420
+She cut off a big piece of meat and gave it to the
+
+79
+00:08:14,420 --> 00:08:25,410
+dog. Number four. She looked up and smiled. Look
+
+80
+00:08:25,410 --> 00:08:33,810
+by eyes. Yes. Look up. So it is literal. Why?
+
+81
+00:08:34,030 --> 00:08:37,470
+Because we translated it look and this is up in
+
+82
+00:08:37,470 --> 00:08:42,890
+the sky. We looked up. Yes, the meaning of look
+
+83
+00:08:42,890 --> 00:08:45,730
+the same, the meaning of go and cut the same
+
+84
+00:08:45,730 --> 00:08:50,190
+meaning. But here I looked up the word in the
+
+85
+00:08:50,190 --> 00:08:57,220
+dictionary. No, this is it means search search it
+
+86
+00:08:57,220 --> 00:09:00,500
+does not it has not a connection with look no no
+
+87
+00:09:00,500 --> 00:09:04,280
+not a matter of look no it is searching search i
+
+88
+00:09:04,280 --> 00:09:07,700
+search the word in the dictionary so this is
+
+89
+00:09:07,700 --> 00:09:14,480
+idiomatic generally
+
+90
+00:09:14,480 --> 00:09:19,640
+the literal words we don't look their meaning up
+
+91
+00:09:19,640 --> 00:09:23,110
+in the dictionary why because they are easy Look,
+
+92
+00:09:23,690 --> 00:09:30,250
+cut, come, put, the same verb. But if it has not a
+
+93
+00:09:30,250 --> 00:09:33,410
+meaning like this, literal, so it is idiomatic. I
+
+94
+00:09:33,410 --> 00:09:38,510
+should look it up in the dictionary. Here, can you
+
+95
+00:09:38,510 --> 00:09:44,690
+pick up my pen for me? It's under the chair. Pick
+
+96
+00:09:44,690 --> 00:09:50,210
+up, give it to me. So literal, yes, it is literal.
+
+97
+00:09:53,960 --> 00:10:03,720
+Put down. Big up. It is a matter of big and up. I
+
+98
+00:10:03,720 --> 00:10:07,240
+picked up some Italians when I was working in
+
+99
+00:10:07,240 --> 00:10:12,280
+Rome. No. So this is idiomatic. It means learn.
+
+100
+00:10:13,100 --> 00:10:20,720
+Learn. So this is Idiomatic. It means learn. So
+
+101
+00:10:20,720 --> 00:10:23,100
+there is no connection between the word and the
+
+102
+00:10:23,100 --> 00:10:25,860
+meaning. When there is no connection, it is
+
+103
+00:10:25,860 --> 00:10:30,120
+idiomatic. When there is connection, it is
+
+104
+00:10:30,120 --> 00:10:34,240
+literal. So here's the question. Are these verbs
+
+105
+00:10:34,240 --> 00:10:39,940
+literal or idiomatic? The first one, take off.
+
+106
+00:10:42,650 --> 00:10:45,990
+Idiomatic. Why? I can't translate the word take
+
+107
+00:10:45,990 --> 00:10:51,490
+then off. No. Here I translated take and off. Take
+
+108
+00:10:51,490 --> 00:11:00,290
+off. Yes or take off. Gun out. Stop working. But
+
+109
+00:11:00,290 --> 00:11:07,770
+here go out. Go out walking. Here cut off. No
+
+110
+00:11:07,770 --> 00:11:11,830
+connection. No connection. But here cut
+
+111
+00:11:14,630 --> 00:11:20,330
+Mm-hmm a matter of cutting Look up looking by eyes
+
+112
+00:11:20,330 --> 00:11:26,510
+So it is literal But here no Look up means search
+
+113
+00:11:26,510 --> 00:11:36,910
+Again pick up pick up Easy translation word by
+
+114
+00:11:36,910 --> 00:11:40,330
+word. So it is literal but pick up here means
+
+115
+00:11:40,330 --> 00:11:46,930
+learn I learned some Italian when I was working in
+
+116
+00:11:46,930 --> 00:11:49,710
+Rome. You understand this? Yes. So here's the
+
+117
+00:11:49,710 --> 00:11:54,350
+answer. The first one idiomatic, the second one
+
+118
+00:11:54,350 --> 00:11:58,590
+literal. Idiomatic, literal. Idiomatic, literal.
+
+119
+00:11:58,690 --> 00:12:01,610
+But here, literal, idiomatic. Literal, idiomatic.
+
+120
+00:12:01,830 --> 00:12:07,910
+Who can read? Yes? The plane has just taken off.
+
+121
+00:12:09,130 --> 00:12:16,470
+Taking off. What's the meaning of take off? No, it
+
+122
+00:12:16,470 --> 00:12:17,870
+has a meaning.
+
+123
+00:12:20,350 --> 00:12:29,990
+Leave the ground and fly. Leave the ground and
+
+124
+00:12:29,990 --> 00:12:36,390
+fly. We studied it before. Leave the ground and
+
+125
+00:12:36,390 --> 00:12:44,410
+fly. But here, it is translated take off so it
+
+126
+00:12:44,410 --> 00:12:53,350
+means remove remove yeah so the plane has just
+
+127
+00:12:53,350 --> 00:12:57,150
+taken off please take off your coat and sit down
+
+128
+00:12:57,150 --> 00:13:04,850
+thank you so here take off remove remove the
+
+129
+00:13:04,850 --> 00:13:06,670
+jacket remove the coat
+
+130
+00:13:09,640 --> 00:13:10,360
+Two.
+
+131
+00:13:13,840 --> 00:13:18,260
+Number eight, oh no, the lens have get out again.
+
+132
+00:13:19,160 --> 00:13:24,880
+Number three, if you go out, it's a number. An
+
+133
+00:13:24,880 --> 00:13:27,840
+umbrella. It's going to rain.
+
+134
+00:13:30,700 --> 00:13:33,740
+So here it means stop.
+
+135
+00:13:35,380 --> 00:13:43,620
+And here it means leave the ground and fly leave
+
+136
+00:13:43,620 --> 00:13:55,640
+the ground and fly here
+
+137
+00:13:55,640 --> 00:14:03,740
+number three yes on the phone hello hello i can't
+
+138
+00:14:03,740 --> 00:14:09,430
+hear you i thinkwe have been cut off it means stop
+
+139
+00:14:09,430 --> 00:14:12,690
+stop
+
+140
+00:14:12,690 --> 00:14:20,070
+connection no connection stop connection no
+
+141
+00:14:20,070 --> 00:14:25,290
+connection she cut off a big piece of meat and
+
+142
+00:14:25,290 --> 00:14:32,540
+give it to the dog cut off it means cut cut So
+
+143
+00:14:32,540 --> 00:14:36,280
+here on the phone. Hello. Yes. Who can read it
+
+144
+00:14:36,280 --> 00:14:40,720
+again? Yeah. On the phone. Hello. Hello. I can't
+
+145
+00:14:40,720 --> 00:14:44,100
+hear you. I think we have been cut off. Cut off.
+
+146
+00:14:44,200 --> 00:14:48,740
+It means stop the connection. No connection. But
+
+147
+00:14:48,740 --> 00:14:52,220
+here she cut off a big pieces of meat and gave it
+
+148
+00:14:52,220 --> 00:14:57,300
+to the dog. So cut off it means cut. We say cut
+
+149
+00:14:57,300 --> 00:15:03,980
+up. It means cut into little pieces. Cut up. It
+
+150
+00:15:03,980 --> 00:15:08,980
+means cut into little pieces. But when I say eat,
+
+151
+00:15:09,320 --> 00:15:15,500
+eat up the food. Ali ate up the food. It means he
+
+152
+00:15:15,500 --> 00:15:23,340
+ate everything. Nothing left. Nothing left. He ate
+
+153
+00:15:23,340 --> 00:15:26,120
+up all the food. It means he ate up the food.
+
+154
+00:15:26,680 --> 00:15:32,640
+Nothing left. Yes. So this is idiomatic and this
+
+155
+00:15:32,640 --> 00:15:35,520
+is literal because we translate word by word.
+
+156
+00:15:36,200 --> 00:15:39,980
+Number four, she looked up and smiled. Literal.
+
+157
+00:15:41,740 --> 00:15:44,020
+Number B, I looked up the word in the dictionary.
+
+158
+00:15:44,700 --> 00:15:47,660
+Look up means search. Yes, who can read number
+
+159
+00:15:47,660 --> 00:15:53,400
+four? She looked up and smiled. Literal.
+
+160
+00:16:01,060 --> 00:16:03,920
+It means search.
+
+161
+00:16:05,720 --> 00:16:09,500
+Good. Now, number five. The last one. Yes.
+
+162
+00:16:14,100 --> 00:16:20,680
+Pick up.
+
+163
+00:16:21,000 --> 00:16:25,000
+The same verb, pick. But here pick up means learn.
+
+164
+00:16:25,580 --> 00:16:32,200
+Here it means learn. So we translate or we give
+
+165
+00:16:32,200 --> 00:16:36,000
+the meaning of the phrasal verbs which are
+
+166
+00:16:36,000 --> 00:16:39,700
+idiomatic. But if it is literal, it is translated
+
+167
+00:16:39,700 --> 00:16:44,360
+by itself. Word by word. Word by word. Yes, easy.
+
+168
+00:16:45,260 --> 00:16:48,180
+You understand this? Yes. Who can read again?
+
+169
+00:16:48,600 --> 00:16:52,620
+Quickly. Number one. The plane has just taken off.
+
+170
+00:16:52,900 --> 00:16:58,500
+Taken off. Taken off. Please take off your coat
+
+171
+00:16:58,500 --> 00:17:03,570
+and Yeah. Number two.
+
+172
+00:17:18,290 --> 00:17:24,110
+Yes. So here, go out. Easy. Easy. Yes. Number
+
+173
+00:17:24,110 --> 00:17:30,900
+three. Hello, hello. I can't hear you. I think we
+
+174
+00:17:30,900 --> 00:17:35,380
+have been cut off. She cut off a big piece of meat
+
+175
+00:17:35,380 --> 00:17:40,760
+and gave it to the dog. So the second one is
+
+176
+00:17:40,760 --> 00:17:45,100
+cutting. But the first one, no. Separated. Yes.
+
+177
+00:17:46,240 --> 00:17:51,120
+She looked up and smiled. I looked up the word in
+
+178
+00:17:51,120 --> 00:17:54,950
+the chat. So looked here look using the eyes but
+
+179
+00:17:54,950 --> 00:18:03,970
+here no search searched The last one Yeah Can you
+
+180
+00:18:03,970 --> 00:18:07,870
+pick up my pen for me? It's under your chair. I
+
+181
+00:18:07,870 --> 00:18:11,450
+picked up some Italian when I was working in Rome.
+
+182
+00:18:11,690 --> 00:18:16,430
+Uh-huh. So here picking something Catching
+
+183
+00:18:16,430 --> 00:18:26,370
+something But here pick up means learn Yes Now
+
+184
+00:18:26,370 --> 00:18:27,950
+another exercise
+
+185
+00:18:39,450 --> 00:18:43,610
+this exercise speaks about separable and
+
+186
+00:18:43,610 --> 00:18:51,530
+inseparable we say direct indirect direct indirect
+
+187
+00:18:51,530 --> 00:18:57,970
+separable inseparable we have two questions here
+
+188
+00:18:57,970 --> 00:19:04,090
+replace the words in italics with a pronoun The
+
+189
+00:19:04,090 --> 00:19:07,670
+first thing is replacing the words with a pronoun.
+
+190
+00:19:08,310 --> 00:19:12,150
+Look at the first one. He turned on the light.
+
+191
+00:19:12,850 --> 00:19:19,790
+This italic word with what? The pronoun is it.
+
+192
+00:19:21,910 --> 00:19:26,930
+Look at number two. I'm looking for my glasses. My
+
+193
+00:19:26,930 --> 00:19:29,830
+glasses. Glasses.
+
+194
+00:19:33,890 --> 00:19:39,990
+Them Them The pronoun is them here it singular
+
+195
+0
+
+223
+00:22:39,670 --> 00:22:46,080
+not before it. But if it is a noun, Before or 
+
+224
+00:22:46,080 --> 00:22:49,720
+after? So the question here is replace the
+
+225
+00:22:49,720 --> 00:22:53,500
+underlined words or the italic words with a
+
+226
+00:22:53,500 --> 00:22:58,540
+pronoun and change it. So I say here, he turned on
+
+227
+00:22:58,540 --> 00:23:05,660
+the light. It means he turned it on. Good. So he 
+
+228
+00:23:05,660 --> 00:23:11,340
+turned it on, not on it. It on. You understand?
+
+229
+00:23:12,460 --> 00:23:17,040
+Number two, I'm looking for my glasses. I'm
+
+230
+00:23:17,040 --> 00:23:23,180
+looking for them. But about four. If the particle
+
+231
+00:23:23,180 --> 00:23:28,380
+is a preposition, if the particle, this is the 
+
+232
+00:23:28,380 --> 00:23:33,400
+particle. If the particle is a preposition, we
+
+233
+00:23:33,400 --> 00:23:38,820
+can't put it alone after the pronoun. We can't.
+
+234
+00:23:39,240 --> 00:23:46,140
+Why? Because it needs an object it needs a word
+
+235
+00:23:46,140 --> 00:23:50,300
+after it it needs an object so this is a 
+
+236
+00:23:50,300 --> 00:23:55,360
+preposition and this is a the object ah so if it 
+
+237
+00:23:55,360 --> 00:24:00,640
+is a preposition don't put it after the pronoun no
+
+238
+00:24:00,640 --> 00:24:04,560
+we put it before it because we have a preposition
+
+239
+00:24:04,560 --> 00:24:09,770
+and a pronoun or a noun So if it is separable,
+
+240
+00:24:10,250 --> 00:24:15,150
+this is separable. Okay, I should use it. But this 
+
+241
+00:24:15,150 --> 00:24:21,870
+one, no. It is inseparable. Inseparable. So this 
+
+242
+00:24:21,870 --> 00:24:27,130
+one is inseparable. You understand? inseparable.
+
+243
+00:24:27,910 --> 00:24:30,390
+What's the meaning of separable? We can separate
+
+244
+00:24:30,390 --> 00:24:34,790
+it. Which one? This one? No, this one can't be
+
+245
+00:24:34,790 --> 00:24:38,890
+separated. So it is inseparable. But this one 
+
+246
+00:24:38,890 --> 00:24:43,530
+should be separated. So it is separable. We 
+
+247
+00:24:43,530 --> 00:24:47,750
+should, we can separate it. We can separate it 
+
+248
+00:24:47,750 --> 00:24:52,450
+with the noun. But with the pronoun, we should. 
+
+249
+00:24:53,130 --> 00:24:57,450
+Separate it with the with the noun if it is the 
+
+250
+00:24:57,450 --> 00:25:01,970
+light we can put the particle after or before But 
+
+251
+00:25:01,970 --> 00:25:07,190
+if it is a pronoun It should be after the pronoun. 
+
+252
+00:25:07,610 --> 00:25:12,930
+So the question is replace the italic words with a 
+
+253
+00:25:12,930 --> 00:25:19,590
+pronoun uh-huh after this it can be separable or 
+
+254
+00:25:19,590 --> 00:25:24,450
+inseparable this one is inseparable this one she's 
+
+255
+00:25:24,450 --> 00:25:31,130
+taken off her boots she's taken her boots off but 
+
+256
+00:25:31,130 --> 00:25:41,270
+with them with them off we should use off after
+
+257
+00:25:41,270 --> 00:25:48,210
+the object so we say she's taken them off can we
+
+258
+00:25:48,210 --> 00:25:53,450
+say we've She's taken off them? No. But with the
+
+259
+00:25:53,450 --> 00:25:56,770
+noun? Okay. With the noun? Okay. But with the 
+
+260
+00:25:56,770 --> 00:26:01,690
+pronoun? No. So here the answer is she's taken 
+
+261
+00:26:01,690 --> 00:26:10,090
+them off. Number four. He took up golf when he 
+
+262
+00:26:10,090 --> 00:26:15,390
+retired. he started doing started doing started
+
+263
+00:26:15,390 --> 00:26:27,230
+doing something so here he took it up yes it up he
+
+264
+00:26:27,230 --> 00:26:32,670
+took it up when he retired he took it up we can't 
+
+265
+00:26:32,670 --> 00:26:38,060
+say we He took up it. No, because it is not a
+
+266
+00:26:38,060 --> 00:26:41,160
+preposition. It is a particle. As we call them, 
+
+267
+00:26:41,280 --> 00:26:44,460
+all of them, we call them a particle. But if it is
+
+268
+00:26:44,460 --> 00:26:49,180
+a preposition, we can't put it alone. Number four,
+
+269
+00:26:49,980 --> 00:26:56,620
+I get on well with my parents. Okay, I get on well 
+
+270
+00:26:56,620 --> 00:27:04,640
+with my parents, with them. Them with? No. So this 
+
+271
+00:27:04,640 --> 00:27:12,180
+is with is a preposition. So it is inseparable. It
+
+272
+00:27:12,180 --> 00:27:19,040
+should be here. Don't change it. Why? Because with 
+
+273
+00:27:19,040 --> 00:27:27,860
+is a preposition. The preposition needs a noun or 
+
+274
+00:27:27,860 --> 00:27:32,320
+needs a pronoun after it. But the particle don't 
+
+275
+00:27:32,320 --> 00:27:41,950
+need it. Here, I came across the ad. I came across
+
+276
+00:27:41,950 --> 00:27:48,790
+it. Across here is a preposition. So we can't move
+
+277
+00:27:48,790 --> 00:27:55,790
+it. We can't move it. It should be here.
+
+278
+00:27:57,450 --> 00:28:03,490
+So number two, five, six are inseparable. Why?
+
+279
+00:28:04,280 --> 00:28:09,760
+Because four with across here is like a 
+
+280
+00:28:09,760 --> 00:28:16,680
+preposition. Number seven. I looked up the words
+
+281
+00:28:16,680 --> 00:28:22,040
+in my dictionary. I looked up them. No, I looked 
+
+282
+00:28:22,040 --> 00:28:29,160
+them up. So here we omit up from here and put it
+
+283
+00:28:29,160 --> 00:28:30,140
+after it. 
+
+284
+00:28:37,270 --> 00:28:42,010
+So the answer is I looked them up in my
+
+285
+00:28:42,010 --> 00:28:46,690
+dictionary. I looked them up. So the question
+
+286
+00:28:46,690 --> 00:28:50,510
+here, what is the question? Replace the word with 
+
+287
+00:28:50,510 --> 00:28:57,590
+a pronoun and you can change if it is separable or
+
+288
+00:28:57,590 --> 00:29:02,310
+inseparable. Separable, move it after the pronoun. 
+
+289
+00:29:02,990 --> 00:29:06,030
+Inseparable, leave it as it is before the pronoun.
+
+290
+00:29:07,690 --> 00:29:11,390
+Number eight and the last one, the waiter took
+
+291
+00:29:11,390 --> 00:29:17,350
+away them. Took away them? No, took them away. 
+
+292
+00:29:18,070 --> 00:29:25,330
+Took them away. So we omit this away and we put it 
+
+293
+00:29:25,330 --> 00:29:36,620
+where? Here. So we are going to read the correct 
+
+294
+00:29:36,620 --> 00:29:40,120
+sentences with the pronoun because the author he 
+
+295
+00:29:40,120 --> 00:29:44,280
+replaced the words in italics with a pronoun read
+
+296
+00:29:44,280 --> 00:29:47,880
+them with the pronoun but if the particle is a 
+
+297
+00:29:47,880 --> 00:29:54,420
+preposition don't move it don't separate it and if 
+
+298
+00:29:54,420 --> 00:30:00,300
+it's a particle we have to separate it number one 
+
+299
+00:30:00,300 --> 00:30:06,290
+uh-huh yeah He turned it on separable or 
+
+300
+00:30:06,290 --> 00:30:10,290
+inseparable? Separable. What is the separable? The 
+
+301
+00:30:10,290 --> 00:30:13,090
+verb here is separable. Turned on is separable. 
+
+302
+00:30:14,530 --> 00:30:17,210
+Number two. Yeah. 
+
+303
+00:30:20,650 --> 00:30:25,070
+I'm looking for them inseparable. Not separable.
+
+304
+00:30:25,630 --> 00:30:30,010
+Why? Because this is like a preposition. It needs
+
+305
+00:30:30,010 --> 00:30:35,870
+an object. Number three. She is taking them off.
+
+306
+00:30:36,890 --> 00:30:38,430
+Separable. Four.
+
+307
+00:30:41,690 --> 00:30:47,470
+He took it up when he returned. Separable. And
+
+308
+00:30:47,470 --> 00:30:54,850
+number five? Five gets on well with them. With
+
+309
+00:30:54,850 --> 00:30:59,630
+them inseparable. We can't separate it. We can't
+
+310
+00:30:59,630 --> 00:31:02,270
+separate it. We shouldn't separate it. It's wrong.
+
+311
+00:31:04,470 --> 00:31:10,690
+I came across inseparable. Inseparable. Away 
+
+312
+00:31:10,690 --> 00:31:18,690
+inseparable. Took them away inseparable. So the
+
+313
+00:31:18,690 --> 00:31:28,680
+answer here, turn it on. Look for them. Take them 
+
+314
+00:31:28,680 --> 00:31:37,220
+off. Look it up with them. Get on well with them. 
+
+315
+00:31:39,560 --> 00:31:48,100
+I came across it. Across it. I looked them up. I
+
+316
+00:31:48,100 --> 00:31:53,540
+looked them up in my dictionary. The waiter took
+
+317
+00:31:53,540 --> 00:31:59,220
+the egg, no, took them up, took them away, took 
+
+318
+00:31:59,220 --> 00:32:04,080
+them away, take away, take away, took it away, 
+
+319
+00:32:04,380 --> 00:32:09,220
+take it away, not take it, take away it, no, take
+
+320
+00:32:09,220 --> 00:32:17,840
+it away, look it up, turn it on, turn it on, take 
+
+321
+00:32:17,840 --> 00:32:19,660
+it off, take them off
+
+322
+00:32:26,920 --> 00:32:31,960
+So here, two words, separable and inseparable, 
+
+323
+00:32:32,220 --> 00:32:38,260
+according to the meaning of the Italic or the 
+
+324
+00:32:38,260 --> 00:32:41,300
+meaning of the phrasal verbs. So we have how many
+
+325
+00:32:41,300 --> 00:32:46,460
+steps? Two. The first one is replace the words 
+
+326
+00:32:46,460 --> 00:32:51,060
+with a pronoun, then make it separable or 
+
+327
+00:32:51,060 --> 00:32:54,320
+inseparable. Yeah. 
+
+328
+00:32:57,660 --> 00:33:02,560
+Now, let's come to the last exercise on our
+
+329
+00:33:02,560 --> 00:33:08,540
+syllabus in the last lecture. This is the last
+
+330
+00:33:08,540 --> 00:33:14,460
+exercise in the last lecture. We have how many 
+
+331
+00:33:14,460 --> 00:33:19,340
+sentences? No, ten sentences.
+
+332
+00:33:20,380 --> 00:33:25,500
+One, two, one, two, one, two. So we have how many 
+
+333
+00:33:25,500 --> 00:33:30,100
+sentences? Ten sentences. But the answer, we use 
+
+334
+00:33:30,100 --> 00:33:36,260
+one for two. One preserved verb for two. So here
+
+335
+00:33:36,260 --> 00:33:43,200
+verbs, the title is verbs with two particles, not 
+
+336
+00:33:43,200 --> 00:33:47,020
+one. Two particles. So how many words are there?
+
+337
+00:33:47,660 --> 00:33:52,560
+Three. The verb and the two particles. The verb
+
+338
+00:33:53,590 --> 00:33:59,630
+and two particles. How many? Three. The verb and
+
+339
+00:33:59,630 --> 00:34:04,750
+two particles. The verb and two particles. The 
+
+340
+00:34:04,750 --> 00:34:09,230
+verb and two particles. The verb and two
+
+341
+00:34:09,230 --> 00:34:16,030
+particles. So in this exercise, we will have verbs
+
+342
+00:34:16,030 --> 00:34:18,710
+with two particles. We call them phrasal verbs. 
+
+343
+00:34:19,430 --> 00:34:25,380
+But with two particles, not one. Number one. How
+
+344
+00:34:25,380 --> 00:34:32,340
+do you manage to put 
+
+345
+00:34:32,340 --> 00:34:34,020
+up with?
+
+346
+00:34:38,880 --> 00:34:48,600
+The second one. Most parents want to put up with.
+
+347
+00:34:49,080 --> 00:34:56,190
+The same. The same. So how do you manage to 
+
+348
+00:34:56,190 --> 00:35:05,790
+succeed in putting up with the noise from your 
+
+349
+00:35:05,790 --> 00:35:11,920
+neighbors? Your neighbors is not good. How do you
+
+350
+00:35:11,920 --> 00:35:17,800
+manage to How were you able to? Put up with 
+
+351
+00:35:17,800 --> 00:35:24,320
+tolerate it means tolerate accept tolerate it
+
+352
+00:35:24,320 --> 00:35:30,320
+means Tolerate
+
+353
+00:35:30,320 --> 00:35:38,080
+or accept Mm-hmm So how do you manage to tolerate 
+
+354
+00:35:38,080 --> 00:35:44,440
+the noise from your neighbors? Most parents won't
+
+355
+00:35:44,440 --> 00:35:48,980
+put up with or tolerate bad behavior from their 
+
+356
+00:35:48,980 --> 00:35:54,240
+children. So tolerate means accept. 
+
+357
+00:35:57,760 --> 00:36:04,900
+Number two. Broke I have no money. I broke all the
+
+358
+00:36:04,900 --> 00:36:12,740
+money have gone I'm look I have to I have to Come
+
+359
+00:36:12,740 --> 00:36:25,240
+up Come up with Come up with means find means find 
+
+360
+00:36:25,240 --> 00:36:29,200
+It means find
+
+361
+00:36:31,280 --> 00:36:37,380
+I have to find an idea. I have to find an idea for 
+
+362
+00:36:37,380 --> 00:36:41,180
+making money. All the money have gone. I have no 
+
+363
+00:36:41,180 --> 00:36:48,560
+money. I'm broke. So I have to find an idea for
+
+364
+00:36:48,560 --> 00:36:53,460
+making money. The second one. We need to come up
+
+365
+00:36:53,460 --> 00:37:03,400
+with. Find. Come up with. a solution to this 
+
+366
+00:37:03,400 --> 00:37:10,740
+problem. We need to, we should find a solution to 
+
+367
+00:37:10,740 --> 00:37:15,560
+this problem. It's easy. So here the meaning is 
+
+368
+00:37:15,560 --> 00:37:19,660
+find. Here the meaning is tolerate. It means
+
+369
+00:37:19,660 --> 00:37:27,200
+accept, tolerate, accept. The third one has the
+
+370
+00:37:27,200 --> 00:37:41,350
+photocopia run out of run out of finish it means
+
+371
+00:37:41,350 --> 00:37:51,670
+finish health
+
+372
+00:37:51,670 --> 00:37:59,080
+photocopia finish paper again Mm-hmm. The children
+
+373
+00:37:59,080 --> 00:38:08,020
+always Always run out
+
+374
+00:38:08,020 --> 00:38:16,860
+of Bill rings you You run out of the lecture as
+
+375
+00:38:16,860 --> 00:38:24,250
+soon as the teacher finish Uh-huh. So run Running
+
+376
+00:38:24,250 --> 00:38:27,930
+out of school. So what's the difference between 
+
+377
+00:38:27,930 --> 00:38:31,950
+run out of and run out of? This is idiomatic and
+
+378
+00:38:31,950 --> 00:38:37,690
+this one is literal. So it is different. We have 
+
+379
+00:38:37,690 --> 00:38:44,770
+two different meanings. Number four. How well do
+
+380
+00:38:44,770 --> 00:38:50,750
+you get on with?
+
+381
+00:38:56,870 --> 00:39:01,070
+With How will do you get on with your colleagues?
+
+382
+00:39:02,070 --> 00:39:05,530
+How is your good relationship? With your friends
+
+383
+00:39:05,530 --> 00:39:09,390
+with your colleagues classmates Good we have good 
+
+384
+00:39:09,390 --> 00:39:17,610
+relationship. So get on with good get on with Yes, 
+
+385
+00:39:18,710 --> 00:39:25,370
+so it means what? have a good relationship with it 
+
+386
+00:39:25,370 --> 00:39:35,790
+means have a good relationship with 
+
+387
+00:39:35,790 --> 00:39:39,530
+how 
+
+388
+00:39:39,530 --> 00:39:42,450
+would you have a good relationship with your 
+
+389
+00:39:42,450 --> 00:39:47,470
+colleagues with your friends second one our
+
+390
+00:39:47,470 --> 00:39:56,940
+teacher told us toto get on get on means continue
+
+391
+00:39:56,940 --> 00:40:03,020
+continue continue continue the work continue with 
+
+392
+00:40:03,020 --> 00:40:06,380
+our
+
+393
+00:40:06,380 --> 00:40:14,260
+work quietly go on continue with your work so this 
+
+394
+00:40:14,260 --> 00:40:21,160
+is the first one is idiomatic and the second one
+
+395
+00:40:21,160 --> 00:40:27,440
+is literal. So our teacher told us to continue get 
+
+396
+00:40:27,440 --> 00:40:41,220
+on get on means continue on with yes continue The
+
+397
+00:40:41,220 --> 00:40:45,120
+last one she's Looking
+
+398
+00:40:49,910 --> 00:40:57,770
+forward to Going on holiday Mm-hmm. She wait with 
+
+399
+00:40:57,770 --> 00:41:04,590
+a pleasure anticipate expect Huh, so so she is
+
+400
+00:41:04,590 --> 00:41:08,030
+expecting with a pleasure going on holiday 
+
+401
+00:41:08,030 --> 00:41:17,170
+anticipating it means anticipate with 
+
+402
+00:41:21,530 --> 00:41:23,670
+Pleasure Anticipate with the pleasure means
+
+403
+00:41:23,670 --> 00:41:25,790
+expecting with the pleasure expect with the 
+
+404
+00:41:25,790 --> 00:41:30,050
+pleasure wait with the pleasure So she's looking 
+
+405
+00:41:30,050 --> 00:41:35,410
+forward to going on holiday And we are looking 
+
+406
+00:41:35,410 --> 00:41:39,830
+forward to meeting you very much it means we are
+
+407
+00:41:39,830 --> 00:41:46,450
+Anticipating with the pleasure two meeting you 
+
+408
+00:41:46,450 --> 00:41:52,870
+very much. You understand this? So this is the two 
+
+409
+00:41:52,870 --> 00:41:55,390
+meanings are the same. Here the two meanings are
+
+410
+00:41:55,390 --> 00:41:58,460
+the same. The first one and the second one are the
+
+411
+00:41:58,460 --> 00:42:00,260
+same. The second one and the third one are the
+
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/SiSQ5LE0UNc_raw.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/SiSQ5LE0UNc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e22306f656f6254c6069766774817dfcf2bfde54
--- /dev/null
+++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/SiSQ5LE0UNc_raw.srt
@@ -0,0 +1,2588 @@
+1
+00:00:21,110 --> 00:00:23,470
+Assalamualaikum warahmatullahi wabarakatuh.
+
+2
+00:00:26,130 --> 00:00:32,390
+Good afternoon. Today, inshallah, we will take
+
+3
+00:00:32,390 --> 00:00:35,410
+some
+
+4
+00:00:35,410 --> 00:00:40,470
+exercises about the present simple tense and the
+
+5
+00:00:40,470 --> 00:00:46,290
+present continuous and also the passives, the
+
+6
+00:00:46,290 --> 00:00:47,030
+passive forms.
+
+7
+00:00:54,980 --> 00:01:00,980
+it is unit 2, get happy sentences,
+
+8
+00:01:01,960 --> 00:01:07,140
+simple or continuous passive, sport, numbers and
+
+9
+00:01:07,140 --> 00:01:12,460
+dates in
+
+10
+00:01:12,460 --> 00:01:18,500
+this exercise inshallah we look at your pair of
+
+11
+00:01:18,500 --> 00:01:25,320
+sentences which one is correct one is correct and
+
+12
+00:01:25,320 --> 00:01:32,040
+one is incorrect correct and incorrect so they
+
+13
+00:01:32,040 --> 00:01:37,560
+have a teenage son they are having a teenage son
+
+14
+00:01:37,560 --> 00:01:46,560
+now this verb is a state verb it
+
+15
+00:01:46,560 --> 00:01:53,100
+means position when i use have as a state verb
+
+16
+00:01:53,620 --> 00:01:57,020
+meaning position we should use it in the present
+
+17
+00:01:57,020 --> 00:02:03,380
+simple all the state verbs can't be used in the
+
+18
+00:02:03,380 --> 00:02:06,900
+continuous they should be used in the present
+
+19
+00:02:06,900 --> 00:02:15,020
+simple so have here is a state verb so this is
+
+20
+00:02:15,020 --> 00:02:24,210
+correct and this is incorrect so use have We don't
+
+21
+00:02:24,210 --> 00:02:36,610
+use are having. Yes. Now she
+
+22
+00:02:36,610 --> 00:02:41,570
+speaks five languages. She's speaking five
+
+23
+00:02:41,570 --> 00:02:45,450
+languages. One is Kurdish and one is in Kurdish.
+
+24
+00:02:45,990 --> 00:02:53,250
+Which one is Kurdish? Speaks, yes. She speaks five
+
+25
+00:02:53,250 --> 00:02:58,630
+languages. We can't say she is speaking five
+
+26
+00:02:58,630 --> 00:03:01,770
+languages. Why? Because it is impossible,
+
+27
+00:03:02,510 --> 00:03:07,910
+impossible to use speaking in this context,
+
+28
+00:03:07,910 --> 00:03:11,530
+because I can't speak five languages at the same
+
+29
+00:03:11,530 --> 00:03:17,530
+time. So this is right and this is wrong. Correct
+
+30
+00:03:17,530 --> 00:03:26,240
+and correct. Now, this is connected and this is
+
+31
+00:03:26,240 --> 00:03:28,340
+unconnected. Next.
+
+32
+00:03:33,420 --> 00:03:42,440
+Don't turn off the TV. I watch it. Don't watch the
+
+33
+00:03:42,440 --> 00:03:48,400
+TV. I'm watching it. Yes. The first one was wrong.
+
+34
+00:03:50,900 --> 00:03:57,620
+Right. Yes. So this is incorrect. And this is
+
+35
+00:03:57,620 --> 00:04:05,340
+correct. So I use watching it because it is now at
+
+36
+00:04:05,340 --> 00:04:10,060
+the moment. Don't turn off the TV now at the
+
+37
+00:04:10,060 --> 00:04:16,420
+moment. Why? Because I am watching it. We can't
+
+38
+00:04:16,420 --> 00:04:23,710
+say I watch it. Now, number four. Number four.
+
+39
+00:04:25,990 --> 00:04:26,510
+Yes?
+
+40
+00:04:29,030 --> 00:04:33,350
+The second is true. Very good. And the first one
+
+41
+00:04:33,350 --> 00:04:42,910
+is? Incorrect. Oh, no. Now I say no, no. Oh, no.
+
+42
+00:04:43,610 --> 00:04:48,090
+It's raining. at the moment it's raining we can't
+
+43
+00:04:48,090 --> 00:04:54,690
+say it rains because it rains is principle but
+
+44
+00:04:54,690 --> 00:04:59,090
+here continuous so here or no something happens
+
+45
+00:04:59,090 --> 00:05:06,690
+now it's raining number
+
+46
+00:05:06,690 --> 00:05:07,170
+five
+
+47
+00:05:10,300 --> 00:05:14,740
+we are thinking opera is boring we think opera is
+
+48
+00:05:14,740 --> 00:05:22,160
+boring this verb has two meanings it is if it is a
+
+49
+00:05:22,160 --> 00:05:29,140
+state there it means opinion uh-huh but if it is
+
+50
+00:05:29,140 --> 00:05:34,240
+thinking something happens now action verb no i
+
+51
+00:05:34,240 --> 00:05:38,540
+want a state verb so
+
+52
+00:05:40,220 --> 00:05:45,360
+The second, the second one is called it. We think,
+
+53
+00:05:45,940 --> 00:05:52,820
+we believe, generally. Opera is boring.
+
+54
+00:05:54,420 --> 00:05:58,760
+So we can't say we are thinking. No, I'm thinking
+
+55
+00:05:58,760 --> 00:06:02,160
+of something. I'm thinking about something just
+
+56
+00:06:02,160 --> 00:06:07,960
+now. I'm thinking of my brother. I'm thinking
+
+57
+00:06:07,960 --> 00:06:14,020
+about a problem but here I think we think it means
+
+58
+00:06:14,020 --> 00:06:18,040
+I believe we believe we believe opera is boring
+
+59
+00:06:18,040 --> 00:06:23,100
+boring or bored boring because we use the ie for
+
+60
+00:06:23,100 --> 00:06:29,820
+the things and situations but if it is ed it is
+
+61
+00:06:29,820 --> 00:06:37,970
+for people amazed amazing fascinated fascinating
+
+62
+00:06:37,970 --> 00:06:46,250
+exhausted exhausting bored boring all the ed forms
+
+63
+00:06:46,250 --> 00:06:52,270
+are for the people and the ing for the situations
+
+64
+00:06:52,270 --> 00:06:57,070
+sometimes we can use the ing but it is impolite
+
+65
+00:06:57,070 --> 00:06:58,430
+impolite
+
+66
+00:07:00,890 --> 00:07:03,990
+the last one number six English speaks all over
+
+67
+00:07:03,990 --> 00:07:07,170
+the world English is spoken all over the world
+
+68
+00:07:07,170 --> 00:07:12,690
+which one is correct the second one yeah it is in
+
+69
+00:07:12,690 --> 00:07:17,790
+the passive English can't speak English people
+
+70
+00:07:17,790 --> 00:07:21,930
+speak English Ali speaks English but English
+
+71
+00:07:21,930 --> 00:07:28,890
+itself yes can't speak so English is spoken uh-huh
+
+72
+00:07:30,160 --> 00:07:34,460
+Yes. Yes. This is in the passive, in the passive.
+
+73
+00:07:34,760 --> 00:07:40,020
+So this is wrong and this is right. Again, we want
+
+74
+00:07:40,020 --> 00:07:43,560
+you to read the correct sentences, just the
+
+75
+00:07:43,560 --> 00:07:46,240
+correct sentences. The first one.
+
+76
+00:07:48,920 --> 00:07:49,700
+Yes.
+
+77
+00:07:52,620 --> 00:07:59,880
+They have a teenage son. Number two. She speaks
+
+78
+00:07:59,880 --> 00:08:05,140
+five languages. She speaks five languages. Number
+
+79
+00:08:05,140 --> 00:08:12,800
+three. Doctor of the TV are watching it. Next. Oh
+
+80
+00:08:12,800 --> 00:08:17,900
+no, it's raining. Oh no, it's raining. Next.
+
+81
+00:08:20,880 --> 00:08:29,770
+We think opera is boring. Yes, again. Yes, or the
+
+82
+00:08:29,770 --> 00:08:30,550
+sentence again.
+
+83
+00:08:33,350 --> 00:08:35,330
+Yes, and the last one.
+
+84
+00:08:38,950 --> 00:08:43,210
+Yes, English is spoken, not speaking. Spoken
+
+85
+00:08:43,210 --> 00:08:48,390
+because it is in the passive. Now, we want to
+
+86
+00:08:48,390 --> 00:08:49,970
+discuss the answers again.
+
+87
+00:08:56,030 --> 00:09:01,630
+So this is the answer. Number one. They have a
+
+88
+00:09:01,630 --> 00:09:05,490
+teenage son is correct. Why?
+
+89
+00:09:08,410 --> 00:09:12,630
+Have means position. I have something.
+
+90
+00:09:15,450 --> 00:09:22,990
+Is a state verb. So this is a state verb. Not
+
+91
+00:09:22,990 --> 00:09:28,610
+action verb. I'm having dinner. I'm having a path.
+
+92
+00:09:29,770 --> 00:09:33,210
+Action. But here, no, it is not action. It is
+
+93
+00:09:33,210 --> 00:09:38,730
+position. And can't be used in the continuous. All
+
+94
+00:09:38,730 --> 00:09:42,050
+the state verbs can't be used in the continuous.
+
+95
+00:09:43,870 --> 00:09:47,830
+But the action verbs can be used in the present
+
+96
+00:09:47,830 --> 00:09:51,370
+simple and in the present continuous. But the
+
+97
+00:09:51,370 --> 00:09:56,380
+state verb They should be used in the present
+
+98
+00:09:56,380 --> 00:10:01,260
+simple all the times. Number two, she speaks five
+
+99
+00:10:01,260 --> 00:10:05,580
+languages correct. She speaks five languages
+
+100
+00:10:05,580 --> 00:10:08,260
+correct. She's speaking five languages is
+
+101
+00:10:08,260 --> 00:10:12,400
+impossible. It is impossible to speak five
+
+102
+00:10:12,400 --> 00:10:16,780
+languages at the same time. We can speak one
+
+103
+00:10:16,780 --> 00:10:21,240
+language, two languages, but not five. you can't
+
+104
+00:10:21,240 --> 00:10:26,180
+speak five languages at the same time okay now
+
+105
+00:10:26,180 --> 00:10:31,040
+number three don't turn off the tv i'm watching it
+
+106
+00:10:31,040 --> 00:10:34,980
+is correct so this sentence is correct why the
+
+107
+00:10:34,980 --> 00:10:40,680
+watching is happening at the moment uh-huh the
+
+108
+00:10:40,680 --> 00:10:46,810
+watching is happening at this moment i watch it
+
+109
+00:10:46,810 --> 00:10:52,530
+means that you do this regularly or habitually not
+
+110
+00:10:52,530 --> 00:10:57,950
+now if it is now watching I'm watching if it is a
+
+111
+00:10:57,950 --> 00:11:03,690
+habit I watch so the situation here is now at the
+
+112
+00:11:03,690 --> 00:11:10,150
+moment so we use watching it is incorrect in this
+
+113
+00:11:10,150 --> 00:11:13,470
+context in this meaning it's incorrect to say
+
+114
+00:11:13,470 --> 00:11:13,850
+watch
+
+115
+00:11:16,640 --> 00:11:23,420
+number four unknown it's raining it's raining now
+
+116
+00:11:23,420 --> 00:11:28,440
+so the raining happens now so we should use the
+
+117
+00:11:28,440 --> 00:11:34,540
+continuous with now at the moment at this moment
+
+118
+00:11:34,540 --> 00:11:39,880
+continuous if it is a habit it is present simple
+
+119
+00:11:39,880 --> 00:11:43,740
+so here the meaning is now it's happening it's
+
+120
+00:11:43,740 --> 00:11:52,180
+raining now at the moment Now, at the moment, it
+
+121
+00:11:52,180 --> 00:11:58,160
+rains is used to describe typical weather for a
+
+122
+00:11:58,160 --> 00:12:04,820
+place or season generally, not now. It never,
+
+123
+00:12:05,080 --> 00:12:10,960
+often, always rains here. It sometimes rains here.
+
+124
+00:12:11,440 --> 00:12:15,660
+It usually rains here. It never rains. in Saudi
+
+125
+00:12:15,660 --> 00:12:22,660
+Arabia and et cetera in winter. Number five, we
+
+126
+00:12:22,660 --> 00:12:27,540
+think opera
+
+127
+00:12:27,540 --> 00:12:36,160
+is boring. This is correct. Think is opinion. It
+
+128
+00:12:36,160 --> 00:12:43,460
+is an opinion. Is a state there. because it is an
+
+129
+00:12:43,460 --> 00:12:47,700
+opinion it is a state verb and all the state verbs
+
+130
+00:12:47,700 --> 00:12:53,160
+should be in the present simple and can't be used
+
+131
+00:12:53,160 --> 00:12:59,980
+in the continuous why why because it is state verb
+
+132
+00:12:59,980 --> 00:13:05,560
+you can use think in the present continuous when
+
+133
+00:13:05,560 --> 00:13:09,980
+it is something that is happening now for example
+
+134
+00:13:09,980 --> 00:13:15,600
+i am thinking about my Gary Flynn. I'm thinking
+
+135
+00:13:15,600 --> 00:13:22,940
+about my brother, my sister. I'm thinking of going
+
+136
+00:13:22,940 --> 00:13:28,040
+to Spain on holiday. So when it is an action verb,
+
+137
+00:13:28,260 --> 00:13:32,020
+I can use it in the present and in the present
+
+138
+00:13:32,020 --> 00:13:34,880
+simple and in the present continuous. But if it is
+
+139
+00:13:34,880 --> 00:13:40,980
+a state verb, meaning opinion, belief, I should
+
+140
+00:13:40,980 --> 00:13:48,700
+use it in the present simple number six English is
+
+141
+00:13:48,700 --> 00:13:53,040
+spoken all over the world is correct why because
+
+142
+00:13:53,040 --> 00:14:00,340
+people speak English is also possible people speak
+
+143
+00:14:00,340 --> 00:14:05,080
+English English is spoken active and passive but
+
+144
+00:14:05,080 --> 00:14:10,280
+English itself can't speak the English language
+
+145
+00:14:10,280 --> 00:14:17,530
+can't speak it is spoken and so must be used
+
+146
+00:14:17,530 --> 00:14:21,950
+passively in the passive so here because I begin
+
+147
+00:14:21,950 --> 00:14:26,750
+with English it should be in the passive if I use
+
+148
+00:14:26,750 --> 00:14:30,190
+it in the active people people speak English
+
+149
+00:14:30,190 --> 00:14:35,650
+English is spoken all over the world this is clear
+
+150
+00:14:35,650 --> 00:14:41,190
+let's
+
+151
+00:14:52,160 --> 00:14:58,800
+Now, after this exercise, we will discuss a short
+
+152
+00:14:58,800 --> 00:15:04,840
+paragraph. It is non-authentic, non-authentic
+
+153
+00:15:04,840 --> 00:15:08,680
+material. It is not natural. It is just because of
+
+154
+00:15:08,680 --> 00:15:14,520
+the grammar. So this paragraph or this text is for
+
+155
+00:15:14,520 --> 00:15:18,180
+the grammar. Sometimes it is for the vocabulary.
+
+156
+00:15:20,300 --> 00:15:23,820
+And when it is for reading, it is authentic
+
+157
+00:15:23,820 --> 00:15:27,700
+material for reading comprehension. But this is
+
+158
+00:15:27,700 --> 00:15:29,840
+not for reading comprehension. This is for what?
+
+159
+00:15:30,460 --> 00:15:35,980
+To elicit some grammar points or some vocabulary
+
+160
+00:15:35,980 --> 00:15:42,920
+now this is for grammar I don't think I don't know
+
+161
+00:15:42,920 --> 00:15:47,540
+if I'm happy the title of this paragraph is I
+
+162
+00:15:47,540 --> 00:15:56,300
+don't know if I'm happy it is by Sydney Fisk age
+
+163
+00:15:56,300 --> 00:16:00,720
+45 work
+
+164
+00:16:01,430 --> 00:16:09,230
+Work. You know work? Work. Like this. Work.
+
+165
+00:16:12,350 --> 00:16:20,290
+Work. Not work. No, work. Sidney Fisk is a lawyer.
+
+166
+00:16:21,490 --> 00:16:27,670
+Is he a lawyer? Yes. Is he an engineer? No, he
+
+167
+00:16:27,670 --> 00:16:36,060
+isn't. He is A lawyer. He is paid very well. He is
+
+168
+00:16:36,060 --> 00:16:42,640
+paid very well. His salary is good. Very good. So
+
+169
+00:16:42,640 --> 00:16:46,340
+this sentence, is it a good thing or a bad thing?
+
+170
+00:16:47,040 --> 00:16:52,400
+This is a good thing about Sidney Fisk. This is
+
+171
+00:16:52,400 --> 00:16:57,640
+something good. But he usually has to work long
+
+172
+00:16:57,640 --> 00:17:04,210
+hours. He works for an international company in
+
+173
+00:17:04,210 --> 00:17:12,350
+Dallas, Texas. So he travels a lot in his job. He
+
+174
+00:17:12,350 --> 00:17:15,670
+travels or he's traveling? Travels.
+
+175
+00:17:19,090 --> 00:17:28,170
+He usually has. Has or have? Has. Yes. Aha. Aha.
+
+176
+00:17:28,810 --> 00:17:34,430
+Sydney Fisk is is or am or are is because it is
+
+177
+00:17:34,430 --> 00:17:38,750
+singular here it is in the passive it is in the
+
+178
+00:17:38,750 --> 00:17:44,310
+passive is and past participle is and the past
+
+179
+00:17:44,310 --> 00:17:52,530
+participle is the passive yes he works works or is
+
+180
+00:17:52,530 --> 00:17:57,970
+working works habit generally state He works for
+
+181
+00:17:57,970 --> 00:18:02,630
+an international company in Dallas, Texas, so he
+
+182
+00:18:02,630 --> 00:18:10,590
+travels a lot in his job. At the moment, now, he
+
+183
+00:18:10,590 --> 00:18:17,150
+is working. At the moment, he is working. He is
+
+184
+00:18:17,150 --> 00:18:22,690
+working or he works? Why? At the moment, now. It
+
+185
+00:18:22,690 --> 00:18:28,850
+is in the present continuous. In Mexico. Now, at
+
+186
+00:18:28,850 --> 00:18:33,410
+the moment, he's working in Mexico. And next week,
+
+187
+00:18:33,650 --> 00:18:39,490
+he is traveling. Next week also, he's traveling.
+
+188
+00:18:41,590 --> 00:18:46,050
+His intention is to travel. So we say next week
+
+189
+00:18:46,050 --> 00:18:48,970
+he's traveling because he prepared everything.
+
+190
+00:18:49,850 --> 00:18:51,970
+When he prepares something, we use the present
+
+191
+00:18:51,970 --> 00:18:58,650
+continuous. So, next week, he's traveling to
+
+192
+00:18:58,650 --> 00:19:06,070
+France. He prepared himself. Now, I want you to
+
+193
+00:19:06,070 --> 00:19:10,890
+give me something good. The good things about
+
+194
+00:19:10,890 --> 00:19:17,850
+Sydney. The good thing, he's paid very well. This
+
+195
+00:19:17,850 --> 00:19:21,730
+is one. Also,
+
+196
+00:19:24,870 --> 00:19:30,170
+Yes. He travels.
+
+197
+00:19:31,570 --> 00:19:37,630
+Travels. So the traveling and the money is
+
+198
+00:19:37,630 --> 00:19:40,530
+something good. Yes.
+
+199
+00:19:44,630 --> 00:19:46,090
+Next one
+
+200
+00:19:55,250 --> 00:20:03,990
+Home life. Home life. Home. Sidney is married. Is
+
+201
+00:20:03,990 --> 00:20:09,710
+married. And he's got two children.
+
+202
+00:20:12,630 --> 00:20:17,950
+He's got or he have? He has. Has got. Yes. Don't
+
+203
+00:20:17,950 --> 00:20:25,970
+forget. Has got. Aged eleven and fourteen. He
+
+204
+00:20:25,970 --> 00:20:29,630
+rarely sees
+
+205
+00:20:29,630 --> 00:20:34,110
+his children. Is it something good or something
+
+206
+00:20:34,110 --> 00:20:40,610
+bad? Yes, so this is something bad. Rarely, rarely
+
+207
+00:20:40,610 --> 00:20:43,610
+sees his children. Something bad.
+
+208
+00:20:45,630 --> 00:20:49,770
+Because so much of his time is spent away from
+
+209
+00:20:49,770 --> 00:20:50,250
+home.
+
+210
+00:20:54,440 --> 00:20:58,040
+Much of his time is spent. This one is in the
+
+211
+00:20:58,040 --> 00:21:05,320
+passive. Is paid and is spent in the passive.
+
+212
+00:21:09,560 --> 00:21:14,700
+So much of his time is spent away from home. Is
+
+213
+00:21:14,700 --> 00:21:18,900
+something good or bad? Something bad. This is
+
+214
+00:21:18,900 --> 00:21:25,160
+something bad. What about marriage? Good, yes,
+
+215
+00:21:25,220 --> 00:21:25,840
+something good.
+
+216
+00:21:30,560 --> 00:21:36,160
+He's got a beautiful house. A beautiful house is
+
+217
+00:21:36,160 --> 00:21:41,320
+something good. So we have something good about
+
+218
+00:21:41,320 --> 00:21:46,640
+Sid's life and something bad about his life, the
+
+219
+00:21:46,640 --> 00:21:51,820
+same. So here, a beautiful house, good, married.
+
+220
+00:21:52,540 --> 00:22:00,580
+Good. Travels. Good. Yes. And bed. Bed. Good.
+
+221
+00:22:00,780 --> 00:22:04,280
+Children. He has children. He has a family. This
+
+222
+00:22:04,280 --> 00:22:10,980
+is something good. In a suppit of Dallas. Suppit.
+
+223
+00:22:11,280 --> 00:22:14,000
+This is something like this. And this is.
+
+224
+00:22:19,280 --> 00:22:26,240
+Suppit of Dallas. it's very big with eight
+
+225
+00:22:26,240 --> 00:22:33,420
+bedrooms it refers to what it refers to what the
+
+226
+00:22:33,420 --> 00:22:39,920
+house the house yes very big with eight bedrooms
+
+227
+00:22:39,920 --> 00:22:44,360
+eight bedroom or bedrooms yes because it is plural
+
+228
+00:22:44,360 --> 00:22:52,210
+yes his wife is an interior designer What does his
+
+229
+00:22:52,210 --> 00:22:59,290
+wife do? She is an internal designer. Is she a
+
+230
+00:22:59,290 --> 00:23:04,530
+teacher? Is she an engineer? No, she is a, an
+
+231
+00:23:04,530 --> 00:23:11,230
+interior designer. A or ah? Ah, because it begins
+
+232
+00:23:11,230 --> 00:23:18,050
+with a vowel. Yes. So what about big? Something
+
+233
+00:23:18,050 --> 00:23:18,910
+good.
+
+234
+00:23:22,450 --> 00:23:28,310
+Now, is it clear? Yes. Is it authentic material?
+
+235
+00:23:28,730 --> 00:23:33,310
+No, it is not authentic, not natural. We just
+
+236
+00:23:33,310 --> 00:23:35,530
+write it because of the grammar.
+
+237
+00:23:51,120 --> 00:23:57,120
+Now, free time. We are speaking about Sydney's
+
+238
+00:23:57,120 --> 00:24:02,860
+life, Sydney's work, and now about Sydney's free
+
+239
+00:24:02,860 --> 00:24:11,600
+time. If he is at home, at the weekend, he and his
+
+240
+00:24:11,600 --> 00:24:19,080
+wife sometimes play golf. Play golf. Can we say go
+
+241
+00:24:19,080 --> 00:24:27,910
+golf? No. Play golf. Do golf? No. We use play when
+
+242
+00:24:27,910 --> 00:24:33,690
+there is a ball. Play football. Play basketball.
+
+243
+00:24:34,630 --> 00:24:40,450
+Play golf. But when I say go, we use go with the
+
+244
+00:24:40,450 --> 00:24:49,750
+ing activities. If there is no ing, I use do. So
+
+245
+00:24:49,750 --> 00:24:53,690
+we have three words connected with activities. If
+
+246
+00:24:53,690 --> 00:24:59,050
+it is about a ball, we use play. So we use play
+
+247
+00:24:59,050 --> 00:25:11,030
+when there is a ball. And we use go when
+
+248
+00:25:11,030 --> 00:25:16,290
+there is I and G.
+
+249
+00:25:19,120 --> 00:25:29,080
+and we use do like here but without ing without
+
+250
+00:25:29,080 --> 00:25:36,200
+ing we will study this in detail next
+
+251
+00:25:36,200 --> 00:25:41,560
+time inshallah now but that doesn't happen very
+
+252
+00:25:41,560 --> 00:25:47,000
+often doesn't or didn't doesn't because i'm
+
+253
+00:25:47,000 --> 00:25:54,060
+speaking about a habit The Zen, they never have,
+
+254
+00:25:54,320 --> 00:26:00,740
+have or has, because they never have much time to
+
+255
+00:26:00,740 --> 00:26:05,820
+relax together. Is it good or bad about his life?
+
+256
+00:26:06,820 --> 00:26:10,220
+This is something bad about his life.
+
+257
+00:26:13,980 --> 00:26:20,190
+Is he happy? He says he doesn't know if he's
+
+258
+00:26:20,190 --> 00:26:27,130
+happy. He's too busy. So busy is something good
+
+259
+00:26:27,130 --> 00:26:36,490
+about his life. But too busy is something bad. I'm
+
+260
+00:26:36,490 --> 00:26:41,670
+busy. That's good. I'm too busy. No, it's bad. But
+
+261
+00:26:41,670 --> 00:26:49,060
+he's too busy to think about it. Now, There is a
+
+262
+00:26:49,060 --> 00:26:53,180
+exercise.
+
+263
+00:27:03,840 --> 00:27:08,020
+You see the exercise? At the top of the page? At
+
+264
+00:27:08,020 --> 00:27:11,440
+the top of the page? What do you think are the
+
+265
+00:27:11,440 --> 00:27:17,160
+good and bad things about Sydney's life? Just now,
+
+266
+00:27:17,380 --> 00:27:21,860
+we discussed something good and something bad. The
+
+267
+00:27:21,860 --> 00:27:26,880
+possible answer is, the good thing is what? Well
+
+268
+00:27:26,880 --> 00:27:33,280
+paid, travels, married with a family, beautiful
+
+269
+00:27:33,280 --> 00:27:38,760
+big house, busy. What about the bad things?
+
+270
+00:27:39,800 --> 00:27:44,720
+Doesn't see his children much, often away from
+
+271
+00:27:44,720 --> 00:27:52,570
+home, Not much time to relax. Too busy. I want
+
+272
+00:27:52,570 --> 00:27:56,510
+someone to read this. Yes. Yes.
+
+273
+00:28:02,870 --> 00:28:03,650
+Yes,
+
+274
+00:28:09,670 --> 00:28:12,850
+someone
+
+275
+00:28:12,850 --> 00:28:17,840
+else. Mm hmm. God, well paid, travels, married,
+
+276
+00:28:18,020 --> 00:28:21,440
+with family, beautiful big house, busy. Bad,
+
+277
+00:28:21,620 --> 00:28:24,580
+doesn't see his children much, often away from
+
+278
+00:28:24,580 --> 00:28:28,180
+home, not much time to relax, too busy. Yes, now
+
+279
+00:28:28,180 --> 00:28:33,920
+in pairs, discuss this answer with your partner.
+
+280
+00:28:34,540 --> 00:28:37,540
+Discuss the good thing and the bad thing. And
+
+281
+00:28:37,540 --> 00:28:39,960
+what's your opinion about this? Yes, discuss with
+
+282
+00:28:39,960 --> 00:28:40,360
+each other.
+
+283
+00:28:59,130 --> 00:29:01,370
+Thank you very much.
+
+284
+00:29:27,520 --> 00:29:33,880
+Yes, that's enough. That's enough. There are two
+
+285
+00:29:33,880 --> 00:29:37,200
+generic questions. Do you think his life is
+
+286
+00:29:37,200 --> 00:29:42,840
+exciting or boring? Good or bad? Is it? It is
+
+287
+00:29:42,840 --> 00:29:50,960
+boring. Someone may say it is exciting. It's your
+
+288
+00:29:50,960 --> 00:29:51,840
+own answer.
+
+289
+00:29:54,520 --> 00:30:01,620
+Would you like to have a life like Sydney's? Some
+
+290
+00:30:01,620 --> 00:30:07,180
+may say yes, some may say no, it's up to you. Do
+
+291
+00:30:07,180 --> 00:30:12,060
+you know any people with similar lives? Yes, my
+
+292
+00:30:12,060 --> 00:30:19,480
+uncle, my father, my brother, my neighbor. Are
+
+293
+00:30:19,480 --> 00:30:25,400
+they happy? Maybe, maybe they are happy or they
+
+294
+00:30:25,400 --> 00:30:31,790
+are not happy. Now this paragraph just to discuss
+
+295
+00:30:31,790 --> 00:30:36,710
+some grammar this one
+
+296
+00:30:36,710 --> 00:30:40,850
+now
+
+297
+00:30:40,850 --> 00:30:49,850
+grammar
+
+298
+00:30:49,850 --> 00:30:56,550
+spot find these words in the text about Sidney
+
+299
+00:30:56,550 --> 00:31:02,270
+Fisk Go back to the paragraph, to the paragraphs,
+
+300
+00:31:02,430 --> 00:31:06,730
+the passage. Find these words, often, rarely,
+
+301
+00:31:07,490 --> 00:31:15,570
+never, usually, usually, often, rarely, never.
+
+302
+00:31:17,110 --> 00:31:21,710
+Have you found them? Have you found them in the
+
+303
+00:31:21,710 --> 00:31:27,950
+passage? Yes. What kind of words are they?
+
+304
+00:31:31,970 --> 00:31:34,650
+What are their names in the grammar?
+
+305
+00:31:37,710 --> 00:31:41,450
+They use in the present simple. But we call them?
+
+306
+00:31:41,890 --> 00:31:46,170
+They are keywords sometimes. Yes. But what do we
+
+307
+00:31:46,170 --> 00:31:51,610
+call them? Adverbs. Yes, they are adverbs.
+
+308
+00:31:54,910 --> 00:32:00,340
+Adverbs of which kind? No, not for the time.
+
+309
+00:32:01,080 --> 00:32:10,220
+Adverb of frequency. It happens every time, every
+
+310
+00:32:10,220 --> 00:32:13,820
+four hours, every five minutes, every five days,
+
+311
+00:32:14,040 --> 00:32:18,420
+every ten years, and so on. So we call them adverb
+
+312
+00:32:18,420 --> 00:32:24,300
+of frequency. Adverb of frequency.
+
+313
+00:32:28,220 --> 00:32:32,620
+But if I say I want adverb of time, I use
+
+314
+00:32:32,620 --> 00:32:38,960
+tomorrow, yesterday, next time, adverb of place,
+
+315
+00:32:40,000 --> 00:32:45,340
+here, there, under the table, inside, outside,
+
+316
+00:32:45,540 --> 00:32:50,780
+etc. But these are usually, sometimes, often,
+
+317
+00:32:51,280 --> 00:32:57,130
+rarely, they are adverbs of frequency. Adverbs of
+
+318
+00:32:57,130 --> 00:33:00,150
+frequency. They are used for the present simple.
+
+319
+00:33:01,830 --> 00:33:07,530
+Yes. Now, this is number one. The second question.
+
+320
+00:33:09,390 --> 00:33:15,310
+What tense are most of the verbs in the text? If
+
+321
+00:33:15,310 --> 00:33:19,750
+we look at the passage, most of the verbs, not
+
+322
+00:33:19,750 --> 00:33:25,050
+all, most of them are in the which tense? Present
+
+323
+00:33:25,050 --> 00:33:29,730
+simple. Yes, most of the verbs are in the present
+
+324
+00:33:29,730 --> 00:33:33,670
+Simple
+
+325
+00:33:33,670 --> 00:33:42,390
+yes, why? Why? Yes, because it is about the
+
+326
+00:33:42,390 --> 00:33:50,050
+general lifestyle of Sydney and habits about
+
+327
+00:33:50,050 --> 00:33:56,390
+Sydney's habit, habit and his lifestyle. So the
+
+328
+00:33:56,390 --> 00:34:01,910
+prison symbol is used most of the time. The third
+
+329
+00:34:01,910 --> 00:34:09,910
+question, find two examples, each in the text of
+
+330
+00:34:09,910 --> 00:34:14,110
+the prison continuous, And the present simple
+
+331
+00:34:14,110 --> 00:34:19,870
+passive. So all the verbs are in the present
+
+332
+00:34:19,870 --> 00:34:26,610
+simple except for two in the present continuous
+
+333
+00:34:26,610 --> 00:34:31,990
+and two in the present simple passive. What are
+
+334
+00:34:31,990 --> 00:34:35,010
+these two in the present continuous?
+
+335
+00:34:36,990 --> 00:34:38,170
+The sentence.
+
+336
+00:34:42,550 --> 00:34:51,370
+He's at the moment going. He's working.
+
+337
+00:34:52,170 --> 00:34:57,630
+He's working in Mexico. This is one. The second
+
+338
+00:34:57,630 --> 00:35:04,930
+one. Yes. Next week he's traveling
+
+339
+00:35:04,930 --> 00:35:11,920
+to France. So the two verbs are about what? Uh
+
+340
+00:35:11,920 --> 00:35:18,080
+-huh. The first one traveling and
+
+341
+00:35:18,080 --> 00:35:19,680
+working.
+
+342
+00:35:21,940 --> 00:35:26,400
+Is working is traveling. So these are two
+
+343
+00:35:26,400 --> 00:35:31,960
+sentences about the present continuous. We use am
+
+344
+00:35:31,960 --> 00:35:38,160
+is are plus the infinitive with ing. Yes. What are
+
+345
+00:35:38,160 --> 00:35:45,310
+the keywords for this now? at the moment look
+
+346
+00:35:45,310 --> 00:35:52,390
+listen sometimes we use next week if we prepare
+
+347
+00:35:52,390 --> 00:35:56,810
+something yes now we want two verbs verbs in the
+
+348
+00:35:56,810 --> 00:36:06,490
+present simple passive just two he uh-huh yes yes
+
+349
+00:36:06,490 --> 00:36:10,650
+it's spent away spent
+
+350
+00:36:10,650 --> 00:36:18,610
+away Time is spent away and the other one? Yes?
+
+351
+00:36:19,450 --> 00:36:19,750
+Yes?
+
+352
+00:36:22,910 --> 00:36:30,330
+He is paid. He is paid very well. He is paid.
+
+353
+00:36:32,390 --> 00:36:34,950
+So, very well.
+
+354
+00:36:37,850 --> 00:36:44,130
+So these two examples about what? Present simple
+
+355
+00:36:44,130 --> 00:36:50,430
+passive. What are the verbs? Is is paid and is
+
+356
+00:36:50,430 --> 00:36:54,130
+spent. What about the present continuous? Is
+
+357
+00:36:54,130 --> 00:36:59,570
+traveling is working. So and all the other verbs
+
+358
+00:36:59,570 --> 00:37:04,430
+are in the present continuous except these four.
+
+359
+00:37:05,390 --> 00:37:09,130
+You understand? So after is we can use the
+
+360
+00:37:09,130 --> 00:37:14,820
+continuous when it is present continuous active if
+
+361
+00:37:14,820 --> 00:37:20,740
+it is passive I use is and the past participle if
+
+362
+00:37:20,740 --> 00:37:24,640
+the subject here the object of the sentence we say
+
+363
+00:37:24,640 --> 00:37:29,160
+is and the past participle if it is active in the
+
+364
+00:37:29,160 --> 00:37:37,760
+continuous we use is and I am very good so here
+
+365
+00:37:40,570 --> 00:37:47,790
+Which auxiliary verb is used to form these four
+
+366
+00:37:47,790 --> 00:37:56,010
+sentences? Which auxiliary verb? Yes, we see B. It
+
+367
+00:37:56,010 --> 00:38:02,580
+means is, are, am. But we call it B, verb to be.
+
+368
+00:38:03,160 --> 00:38:07,380
+So verb to be in the present, M is R. In the past,
+
+369
+00:38:07,600 --> 00:38:11,640
+was where? So here in the present continuous and
+
+370
+00:38:11,640 --> 00:38:16,300
+in the present simple passive, we use verb to be.
+
+371
+00:38:16,940 --> 00:38:20,600
+In all the passives, we use verb to be. In the
+
+372
+00:38:20,600 --> 00:38:24,160
+continuous, in all the continuous, we use verb to
+
+373
+00:38:24,160 --> 00:38:29,400
+be. If it's in the present, we use M is R.in the
+
+374
+00:38:29,400 --> 00:38:35,220
+past was and where in the passive also the same if
+
+375
+00:38:35,220 --> 00:38:38,300
+it is in the present the passive in the present we
+
+376
+00:38:38,300 --> 00:38:43,760
+use am is are in the past was where today our
+
+377
+00:38:43,760 --> 00:38:48,200
+lesson is about the present simple and the present
+
+378
+00:38:48,200 --> 00:38:51,120
+continuous so we use verb to be in the present
+
+379
+00:38:51,120 --> 00:38:55,380
+continuous and we use the passives we use the
+
+380
+00:38:55,380 --> 00:38:59,160
+passives in all the tenses we use be in all the
+
+381
+00:38:59,160 --> 00:39:03,540
+tenses yes now complete the questions and answers
+
+382
+00:39:03,540 --> 00:39:07,560
+with the correct auxiliary verbs so this exercise
+
+383
+00:39:07,560 --> 00:39:14,280
+about what about auxiliary verbs the correct one
+
+384
+00:39:14,280 --> 00:39:23,840
+in the auxiliary verbs we have be do and have B
+
+385
+00:39:23,840 --> 00:39:28,800
+means am, is, are, was, where have means have,
+
+386
+00:39:28,860 --> 00:39:36,260
+has, had do, thus, did so here auxiliary anyone
+
+387
+00:39:36,260 --> 00:39:43,960
+you understand? so here these questions are about
+
+388
+00:39:43,960 --> 00:39:49,900
+what? about Sidney Fisk questions about him so he
+
+389
+00:39:49,900 --> 00:39:53,250
+travels a lot Ah, we are speaking about present.
+
+390
+00:39:53,850 --> 00:39:57,610
+So the question is capital.
+
+391
+00:39:59,950 --> 00:40:05,030
+Does he travel a lot? Yes, he does.
+
+392
+00:40:06,730 --> 00:40:12,950
+Yes, he does. Pretty clear? Yes. Number B. Yes.
+
+393
+00:40:15,230 --> 00:40:19,410
+Does he work in a? Does she work?
+
+394
+00:40:22,980 --> 00:40:27,540
+No, she doesn't. I want you to write the answer.
+
+395
+00:40:35,300 --> 00:40:36,020
+Now.
+
+396
+00:40:50,810 --> 00:40:55,310
+Yes, thank you very much. Because it is no, we use
+
+397
+00:40:55,310 --> 00:41:00,550
+does it. The same auxiliary verb and not. Number
+
+398
+00:41:00,550 --> 00:41:08,150
+C. Yes. Yes, write it.
+
+399
+00:41:11,770 --> 00:41:17,410
+Can we use does? No, because the subject is they.
+
+400
+00:41:20,980 --> 00:41:24,800
+Yes, they do. Can we say don't? No, because it is
+
+401
+00:41:24,800 --> 00:41:30,580
+affirmative. Number or question number D. Yes.
+
+402
+00:41:31,280 --> 00:41:32,080
+Yes.
+
+403
+00:41:36,380 --> 00:41:43,760
+Do you? Do or does? Do. Why? Because you is used
+
+404
+00:41:43,760 --> 00:41:45,680
+as plural.
+
+405
+00:41:51,670 --> 00:41:57,490
+Thank you. So these four sentences about the
+
+406
+00:41:57,490 --> 00:42:03,430
+present simple in the question we use do or does
+
+407
+00:42:03,430 --> 00:42:11,030
+with the short answer we use do or don't does or
+
+408
+00:42:11,030 --> 00:42:16,810
+doesn't in the negative don't and doesn't now what
+
+409
+00:42:16,810 --> 00:42:17,890
+about this yes
+
+410
+00:42:22,050 --> 00:42:26,570
+Is it what? Active or passive? Passive, because we
+
+411
+00:42:26,570 --> 00:42:28,210
+have past participle. Yes.
+
+412
+00:42:38,330 --> 00:42:44,270
+Yes. Is he paid a lot? Yes, he is. This is in
+
+413
+00:42:44,270 --> 00:42:49,370
+capital letter and this is in small. The last one.
+
+414
+00:42:49,910 --> 00:42:53,920
+Yes. Is he working in France at the moment? No, he
+
+415
+00:42:53,920 --> 00:42:59,100
+isn't. What this is it? Present continuous. What
+
+416
+00:42:59,100 --> 00:43:05,240
+about this? Present simple passive and this is
+
+417
+00:43:05,240 --> 00:43:07,340
+present continuous. Yes.
+
+418
+00:43:10,160 --> 00:43:14,900
+So we use is for the present continuous and for
+
+419
+00:43:14,900 --> 00:43:20,560
+the present passive. But In the present passive,
+
+420
+00:43:20,800 --> 00:43:23,980
+it is followed by past participle. In the present
+
+421
+00:43:23,980 --> 00:43:29,920
+continuous, it is followed by I-E-G form. Is he
+
+422
+00:43:29,920 --> 00:43:35,460
+working, is or are? Is, because he. Is he working,
+
+423
+00:43:35,560 --> 00:43:39,120
+present continuous? In France, at the moment, no,
+
+424
+00:43:39,280 --> 00:43:47,040
+he isn't. And I want someone to read this one by
+
+425
+00:43:47,040 --> 00:43:51,730
+one, yes. Number one, does he travel a lot? Yes,
+
+426
+00:43:51,870 --> 00:43:58,270
+yes he does. Two Does she work in a band? Yes, no
+
+427
+00:43:58,270 --> 00:44:07,750
+she doesn't. C Do you play tennis?
+
+428
+00:44:07,930 --> 00:44:08,450
+No, I don't.
+
+429
+00:44:11,450 --> 00:44:15,970
+E Is he bad a lot? Yes, he is. F
+
+430
+00:44:20,940 --> 00:44:28,060
+Thank you very much. What we call usually,
+
+431
+00:44:28,280 --> 00:44:33,020
+sometimes, often, never. Adverbs of frequency.
+
+432
+00:44:34,590 --> 00:44:39,270
+Most of the verbs in this text are in the present
+
+433
+00:44:39,270 --> 00:44:43,170
+simple. Just four are not in the present simple.
+
+434
+00:44:43,310 --> 00:44:46,410
+What are they? Two in the present continuous and
+
+435
+00:44:46,410 --> 00:44:51,580
+two in the present simple passive. It's paid, it's
+
+436
+00:44:51,580 --> 00:44:54,700
+spent, passive. It's working, it's travelling,
+
+437
+00:44:55,440 --> 00:45:00,500
+continuous. These are questions and short answers.
+
+438
+00:45:01,380 --> 00:45:05,860
+Yes, no questions and short answers. The answers
+
+439
+00:45:05,860 --> 00:45:12,280
+may be with yes or with no. With yes, we use not.
+
+440
+00:45:12,900 --> 00:45:17,280
+With no, we don't use not. If it is not, we can
+
+441
+00:45:17,280 --> 00:45:20,260
+use additional information. We can add
+
+442
+00:45:20,260 --> 00:45:24,140
+information. If it is with not, we can add. And
+
+443
+00:45:24,140 --> 00:45:26,240
+we, it's up to us, yes.
+
+444
+00:45:33,660 --> 00:45:36,440
+So the auxiliary verbs that is used in the present
+
+445
+00:45:36,440 --> 00:45:43,170
+continuous and in the present passive is be. B.
+
+446
+00:45:43,670 --> 00:45:48,230
+What does it mean B? M is R. And if it is in the
+
+447
+00:45:48,230 --> 00:45:54,330
+past? Wasn't where. This is the answers.
+
+448
+00:45:57,290 --> 00:46:01,070
+Number one. What is the answer? They are all what?
+
+449
+00:46:02,010 --> 00:46:08,050
+Adverbs of frequency. Number two. The present
+
+450
+00:46:08,050 --> 00:46:14,110
+simple. The present Symbol, and here adjectives
+
+451
+00:46:14,110 --> 00:46:20,490
+of? Frequencies. The birds are mostly in distance
+
+452
+00:46:20,490 --> 00:46:24,970
+because the general lifestyle and daily habits of
+
+453
+00:46:24,970 --> 00:46:29,870
+Sydney are being described. We describe his life.
+
+454
+00:46:31,070 --> 00:46:35,870
+We describe his general lifestyle. We describe his
+
+455
+00:46:35,870 --> 00:46:42,060
+daily habits. Because it is a habit, and general
+
+456
+00:46:42,060 --> 00:46:48,200
+lifestyle we use the present symbol we use the
+
+457
+00:46:48,200 --> 00:46:53,960
+present symbol number three present continuous he
+
+458
+00:46:53,960 --> 00:46:57,600
+is working in mexico he is traveling to france
+
+459
+00:46:57,600 --> 00:47:03,600
+what are they the present continuous next the
+
+460
+00:47:03,600 --> 00:47:07,740
+present symbol passive he is paid very well his
+
+461
+00:47:07,740 --> 00:47:16,220
+time is spent this is Passive, we use is and is.
+
+462
+00:47:17,260 --> 00:47:24,000
+Next to is past participle, past participle. The
+
+463
+00:47:24,000 --> 00:47:31,300
+auxiliary verb be is used to form the passive and
+
+464
+00:47:31,300 --> 00:47:38,490
+the continuous. B is used for the passive and for
+
+465
+00:47:38,490 --> 00:47:41,810
+the continuous with the passive we use the present
+
+466
+00:47:41,810 --> 00:47:46,170
+the past participle and with the continuous we use
+
+467
+00:47:46,170 --> 00:47:53,570
+the ing form now number four questions yes no
+
+468
+00:47:53,570 --> 00:48:00,070
+questions and short answers does he travel a lot
+
+469
+00:48:00,070 --> 00:48:04,230
+yes he does does he work in a bank no she doesn't
+
+470
+00:48:05,180 --> 00:48:10,280
+Do they play golf? Yes, they do. Do you play
+
+471
+00:48:10,280 --> 00:48:16,560
+tennis? No, I don't. You, for you. Is he paid a
+
+472
+00:48:16,560 --> 00:48:20,440
+lot? Yes, he is. Is he working in France at the
+
+473
+00:48:20,440 --> 00:48:27,280
+moment? No, he isn't. Is it clear? Good? Yes. Now,
+
+474
+00:48:27,860 --> 00:48:33,860
+I want you to do this exercise.
+
+475
+00:48:35,290 --> 00:48:36,470
+Also about Sydney.
+
+476
+00:48:39,470 --> 00:48:44,310
+Now, complete the questions about Sydney, then ask
+
+477
+00:48:44,310 --> 00:48:48,690
+and answer them with a partner. At first, we want
+
+478
+00:48:48,690 --> 00:48:53,190
+to what? We want to make the question. Then after
+
+479
+00:48:53,190 --> 00:48:57,390
+this, I want you in pairs to ask and answer them
+
+480
+00:48:57,390 --> 00:49:02,190
+in pairs. So at first, I want to make the
+
+481
+00:49:02,190 --> 00:49:07,450
+question. Yes, number one, the first point,
+
+482
+00:49:08,050 --> 00:49:15,750
+married, he, we are speaking about Sydney, he. And
+
+483
+00:49:15,750 --> 00:49:23,490
+the question is, is he married? Yes, he is. Is he
+
+484
+00:49:23,490 --> 00:49:28,690
+married? Yes, he is. Another question about
+
+485
+00:49:28,690 --> 00:49:33,170
+Sydney. What does
+
+486
+00:49:33,170 --> 00:49:42,080
+he do? uh-huh what does he do what does he do the
+
+487
+00:49:42,080 --> 00:49:46,620
+other question questions now then the answer yes
+
+488
+00:49:46,620 --> 00:49:52,800
+where does he
+
+489
+00:49:52,800 --> 00:49:59,160
+live what does he live next
+
+490
+00:49:59,160 --> 00:50:13,400
+has he got any children has he got next yes
+
+491
+00:50:13,400 --> 00:50:19,580
+over there what
+
+492
+00:50:19,580 --> 00:50:29,480
+does we say there and we say over there huh there
+
+493
+00:50:29,480 --> 00:50:41,470
+and over there yes next over there does
+
+494
+00:50:41,470 --> 00:50:54,450
+he play the one before the last there working
+
+495
+00:50:54,450 --> 00:51:03,630
+is he and the last one Is he? Yeah.
+
+496
+00:51:06,950 --> 00:51:15,670
+So these are some questions about Sydney, WHA
+
+497
+00:51:15,670 --> 00:51:19,790
+questions. Most of them are WHA questions. What
+
+498
+00:51:19,790 --> 00:51:23,270
+about the first exercise? Yes, no questions. Now,
+
+499
+00:51:24,350 --> 00:51:27,690
+WHA questions and some other. Yes. Again, number
+
+500
+00:51:27,690 --> 00:51:33,890
+one. I want you to read the questions. Yes. Number
+
+501
+00:51:33,890 --> 00:51:40,750
+two? What does he do?
+
+502
+00:51:42,630 --> 00:51:46,450
+Where does he live? Has he got any children?
+
+503
+00:51:50,710 --> 00:51:54,150
+Yes, next?
+
+504
+00:51:55,630 --> 00:52:00,770
+Which sport does he play? Where is he working at
+
+505
+00:52:00,770 --> 00:52:08,410
+the moment? The last one. Now I want you to work
+
+506
+00:52:08,410 --> 00:52:14,250
+in pairs. Ask and answer. Ask and answer these
+
+507
+00:52:14,250 --> 00:52:18,170
+questions with your partner. Ask the questions and
+
+508
+00:52:18,170 --> 00:52:26,010
+answer it. Yes. In pairs. In twos. Yes. Yes.
+
+509
+00:52:26,270 --> 00:52:30,570
+That's enough. I want you. I want to hear you now.
+
+510
+00:52:31,540 --> 00:52:38,040
+Yes, these two. For the first question. These are
+
+511
+00:52:38,040 --> 00:52:41,400
+good questions. Raise your voice. These are good
+
+512
+00:52:41,400 --> 00:52:45,340
+questions, but these questions about you. I want
+
+513
+00:52:45,340 --> 00:52:51,320
+about Sydney. I'm speaking about Sydney. Some
+
+514
+00:52:51,320 --> 00:52:54,220
+other two? About Sydney. Raise your voice. Yes,
+
+515
+00:52:54,700 --> 00:53:02,570
+two. What does he do? His job. He's a lawyer. He
+
+516
+00:53:02,570 --> 00:53:09,430
+is a lawyer. Is he married? Yes, he is. What does
+
+517
+00:53:09,430 --> 00:53:18,370
+he do? He's a lawyer. The job. Yes. Where does he
+
+518
+00:53:18,370 --> 00:53:21,030
+live? In?
+
+519
+00:53:25,620 --> 00:53:30,560
+Dallas or in Texas Dallas or in a big house in
+
+520
+00:53:30,560 --> 00:53:35,980
+Dallas. Yeah, so he Works in or we can say in a
+
+521
+00:53:35,980 --> 00:53:47,780
+big house in Dallas Yes He's
+
+522
+00:53:47,780 --> 00:53:57,840
+got two children he's got two children Next one.
+
+523
+00:53:59,000 --> 00:54:00,080
+Two.
+
+524
+00:54:04,040 --> 00:54:08,540
+She is.
+
+525
+00:54:08,720 --> 00:54:15,560
+She is an interior designer. She is an interior
+
+526
+00:54:15,560 --> 00:54:18,420
+designer. Next.
+
+527
+00:54:21,320 --> 00:54:29,230
+Two. Two. Yes. Which sport does he play? Golf.
+
+528
+00:54:29,810 --> 00:54:34,490
+Golf. Golf. Golf. Golf. Golf. Golf. Golf. Golf.
+
+529
+00:54:34,490 --> 00:54:34,950
+Golf. Golf. Golf. Golf. Golf. Golf. Golf. Golf.
+
+530
+00:54:34,950 --> 00:54:37,230
+Golf. Golf. Golf. Golf. Golf. Golf. Golf. Golf.
+
+531
+00:54:37,230 --> 00:54:38,050
+Golf. Golf. Golf. Golf. Golf. Golf. Golf. Golf.
+
+532
+00:54:38,050 --> 00:54:38,470
+Golf. Golf. Golf. Golf. Golf. Golf. Golf. Golf.
+
+533
+00:54:38,470 --> 00:54:38,950
+Golf. Golf. Golf. Golf. Golf. Golf. Golf. Golf.
+
+534
+00:54:38,950 --> 00:54:38,950
+Golf. Golf. Golf. Golf. Golf. Golf. Golf. Golf.
+
+535
+00:54:39,070 --> 00:54:39,150
+Golf. Golf. Golf. Golf. Golf. Golf. Golf. Golf.
+
+536
+00:54:39,150 --> 00:54:39,150
+Golf. Golf. Golf. Golf. Golf. Golf. Golf. Golf.
+
+537
+00:54:39,150 --> 00:54:39,330
+Golf. Golf. Golf. Golf. Golf. Golf. Golf. Golf.
+
+538
+00:54:39,330 --> 00:54:41,950
+Golf. Golf. Golf. Golf. Golf. Golf. Golf. Golf.
+
+539
+00:54:41,950 --> 00:54:42,010
+Golf. Golf. Golf. Golf. Golf. Golf. Golf. Golf.
+
+540
+00:54:42,010 --> 00:54:42,330
+Golf. Golf. Golf. Golf. Golf. Golf. Golf. Golf.
+
+541
+00:54:42,330 --> 00:54:42,890
+Golf. Golf. Golf.
+
+542
+00:54:45,610 --> 00:54:46,250
+Golf.
+
+543
+00:54:54,660 --> 00:55:01,240
+In Mexico. Yes. The last one. The last one. Yes,
+
+544
+00:55:01,300 --> 00:55:03,880
+too. Yes, he is.
+
+545
+00:55:06,500 --> 00:55:11,180
+I want two of you to read all the questions in
+
+546
+00:55:11,180 --> 00:55:16,200
+front of the class. Number one. And number. Yes.
+
+547
+00:55:16,360 --> 00:55:21,840
+Number one here. And some other one. Yes. Yes.
+
+548
+00:55:23,600 --> 00:55:27,240
+Yes, I want you to ask the question and you answer
+
+549
+00:55:27,240 --> 00:55:35,500
+it. Is he married? Yes, he is. What does he do? He
+
+550
+00:55:35,500 --> 00:55:44,860
+is a lawyer. Where does he live? He lives in a big
+
+551
+00:55:44,860 --> 00:55:48,180
+house in Dallas He lives in a big house in Dallas,
+
+552
+00:55:48,180 --> 00:55:51,460
+yes Has he got any children? Yes, he got two
+
+553
+00:55:51,460 --> 00:55:53,960
+children What does his wife do?
+
+554
+00:55:56,840 --> 00:56:01,800
+Interior designer Which
+
+555
+00:56:01,800 --> 00:56:06,300
+sport does he play? He play sometimes, play golf
+
+556
+00:56:06,650 --> 00:56:10,830
+He sometimes play. He sometimes play. We put
+
+557
+00:56:10,830 --> 00:56:14,750
+never, sometimes, usually before the verb. Where
+
+558
+00:56:14,750 --> 00:56:19,390
+is he working at the moment? In Mexico. Is he paid
+
+559
+00:56:19,390 --> 00:56:22,950
+very well? Yes, he is. Thank you very much. Thank
+
+560
+00:56:22,950 --> 00:56:31,310
+you. Another two. Yes. Another two. Yes, number
+
+561
+00:56:31,310 --> 00:56:35,410
+one. Number one. Number two. Yes.
+
+562
+00:56:47,640 --> 00:56:55,350
+What does he do? He is loyal. Where does he live?
+
+563
+00:56:56,030 --> 00:57:02,270
+In Dallas. Has he got any children? Yes, he has
+
+564
+00:57:02,270 --> 00:57:12,600
+got two children. What does his wife do? She is an
+
+565
+00:57:12,600 --> 00:57:16,860
+intelligent interior designer.
+
+566
+00:57:17,860 --> 00:57:23,820
+She sports does he play golf?
+
+567
+00:57:23,940 --> 00:57:32,260
+He sometimes play golf. Where is he working at the
+
+568
+00:57:32,260 --> 00:57:40,040
+moment? In Mexico, yes. The last one. Is he paid?
+
+569
+00:57:42,600 --> 00:57:45,960
+Yes, he is. Yes, he is. Thank you very much. Now,
+
+570
+00:57:46,160 --> 00:57:53,000
+the answer is, is he married? Yes, he is. What
+
+571
+00:57:53,000 --> 00:58:00,180
+does he do? He is a lawyer. Where does he live? In
+
+572
+00:58:00,180 --> 00:58:03,620
+a big house in Dallas, Texas. Has he got any
+
+573
+00:58:03,620 --> 00:58:07,860
+children? Yes, he has got two. What does his wife
+
+574
+00:58:07,860 --> 00:58:12,580
+do? She's an interior designer. Which sport does
+
+575
+00:58:12,580 --> 00:58:19,090
+he play? He sometimes plays golf. Where is he
+
+576
+00:58:19,090 --> 00:58:23,650
+working at the moment? In Mexico. Is he paid very
+
+577
+00:58:23,650 --> 00:58:27,830
+well? Yes, he is. Again, I want one to read all of
+
+578
+00:58:27,830 --> 00:58:32,290
+them. Yes. Is he married? Yes, he is. What does he
+
+579
+00:58:32,290 --> 00:58:37,660
+do? He's a lawyer. Where does he live? In a big
+
+580
+00:58:37,660 --> 00:58:46,180
+house in Dallas, Texas. Texas. Has he got any
+
+581
+00:58:46,180 --> 00:58:50,500
+children? Yes, he's got two. What does his wife
+
+582
+00:58:50,500 --> 00:58:52,240
+do? She's in a trip.
+
+583
+00:58:54,990 --> 00:59:00,590
+Interior designer. Which sport does he play? He
+
+584
+00:59:00,590 --> 00:59:05,930
+sometimes play golf. Where is he working at the
+
+585
+00:59:05,930 --> 00:59:09,070
+moment? In Mexico. Is he paid very well? Yes, he
+
+586
+00:59:09,070 --> 00:59:15,010
+is. Thank you very much. Thank you. Now, we
+
+587
+00:59:15,010 --> 00:59:22,150
+finished the exercises in the student book now
+
+588
+00:59:22,150 --> 00:59:28,110
+this is grammar reference quickly we are going to
+
+589
+00:59:28,110 --> 00:59:33,230
+look quickly at the grammar here present simple
+
+590
+00:59:33,230 --> 00:59:42,230
+the form I we you they work in the negative don't
+
+591
+00:59:42,230 --> 00:59:50,910
+work he she it works doesn't work Positive and
+
+592
+00:59:50,910 --> 00:59:56,190
+negative. What about the question? Where do I, we,
+
+593
+00:59:56,550 --> 01:00:03,130
+you, they live? Where does he, she, it live?
+
+594
+01:00:03,410 --> 01:00:10,230
+Clear? Now, do you live in Bristol? The short
+
+595
+01:00:10,230 --> 01:00:16,270
+answer, yes, we do. Does he have a car? short
+
+596
+01:00:16,270 --> 01:00:21,830
+answer no he doesn't so here we speak about the
+
+597
+01:00:21,830 --> 01:00:27,210
+present simple positive negative question and
+
+598
+01:00:27,210 --> 01:00:34,070
+short answer positive negative question and short
+
+599
+01:00:34,070 --> 01:00:41,470
+answer look here use use of the present simple the
+
+600
+01:00:41,470 --> 01:00:44,710
+present simple is used to express what the present
+
+601
+01:00:44,710 --> 01:00:50,480
+simple An action that happens again and again.
+
+602
+01:00:50,880 --> 01:00:59,340
+Habit. A fact that is always true. A fact that is
+
+603
+01:00:59,340 --> 01:01:05,120
+always true. Here action happens again and again.
+
+604
+01:01:05,340 --> 01:01:10,860
+It is habit. A fact that is true for a long time.
+
+605
+01:01:11,360 --> 01:01:20,720
+State. So examples, I go to work by car. She
+
+606
+01:01:20,720 --> 01:01:25,860
+drinks 10 cups of coffee a day, every day, daily.
+
+607
+01:01:28,040 --> 01:01:34,400
+I wash without this, without this, here with this.
+
+608
+01:01:35,140 --> 01:01:40,380
+Now, look here, a fact. Ronaldo comes from Brazil,
+
+609
+01:01:41,240 --> 01:01:48,460
+comes from. Some birds fly south in winter. My
+
+610
+01:01:48,460 --> 01:01:55,820
+daughter has brown eyes. What about the third
+
+611
+01:01:55,820 --> 01:02:05,000
+kind? It is about a steak. He works in a bank. I
+
+612
+01:02:05,000 --> 01:02:10,800
+live in a flat near the center of town. I prefer
+
+613
+01:02:10,800 --> 01:02:19,860
+coffee to t to t so the present simple tense is
+
+614
+01:02:19,860 --> 01:02:28,780
+used in the habit or the fact or state now quickly
+
+615
+01:02:28,780 --> 01:02:34,420
+grammar reference spelling of the verb plus s
+
+616
+01:02:43,490 --> 01:02:48,910
+Spelling of the verb plus S. Most verbs add S to
+
+617
+01:02:48,910 --> 01:02:54,990
+the base form of the verb. Once, eats, helps,
+
+618
+01:02:55,470 --> 01:03:03,510
+drives. This is easy. Add ES to the verbs that end
+
+619
+01:03:03,510 --> 01:03:05,670
+in hissing sound.
+
+620
+01:03:11,250 --> 01:03:12,850
+So kisses,
+
+621
+01:03:15,070 --> 01:03:23,950
+washes, watches, fixes, goes. So we add S
+
+622
+01:03:23,950 --> 01:03:28,250
+generally, and if it ends with a hissing sound, we
+
+623
+01:03:28,250 --> 01:03:34,830
+use ES. This is number one, two, three. Verbs that
+
+624
+01:03:34,830 --> 01:03:43,990
+end in a consonant plus Y Change the Y to IES.
+
+625
+01:03:45,270 --> 01:03:53,590
+Carry, carry, carries. Fly, flies. Worry, worries.
+
+626
+01:03:54,050 --> 01:04:00,550
+Cry, cries. Instead of Y, we use IES. But verbs
+
+627
+01:04:00,550 --> 01:04:07,470
+that end in a vowel plus Y only add S. If we have
+
+628
+01:04:07,470 --> 01:04:13,750
+Y and E. U, by, not consonant. If this is
+
+629
+01:04:13,750 --> 01:04:18,570
+consonant, we change Y into IES. But if this is a
+
+630
+01:04:18,570 --> 01:04:29,530
+vowel, just S. Say A, says. Play, enjoys. Also,
+
+631
+01:04:31,230 --> 01:04:34,430
+what about the present continuous? The same.
+
+632
+01:04:39,810 --> 01:04:45,750
+positive and negative I am I am not he she it is
+
+633
+01:04:45,750 --> 01:04:53,310
+isn't we you they are aren't eating easy next
+
+634
+01:04:53,310 --> 01:05:00,790
+question what is are I he she it we you they doing
+
+635
+01:05:00,790 --> 01:05:06,440
+what are you doing Here, the short answer, are you
+
+636
+01:05:06,440 --> 01:05:10,300
+going by train? Yes, I am. No, I am not.
+
+637
+01:05:14,540 --> 01:05:21,620
+Spelling of the verb plus ing. Go, going. Most
+
+638
+01:05:21,620 --> 01:05:28,420
+verbs add ing to the past forms. Go, going. Wear,
+
+639
+01:05:29,280 --> 01:05:36,580
+wearing. Busy? eat eating verbs that end in one e
+
+640
+01:05:36,580 --> 01:05:44,140
+lose the e if it ends with e so here smoke like
+
+641
+01:05:44,140 --> 01:05:53,700
+this smoking come we omit e hope hoping right we
+
+642
+01:05:53,700 --> 01:05:57,740
+omit the e and write ing verbs
+
+643
+01:05:59,080 --> 01:06:05,560
+that in E E, double E, don't drop the E. If
+
+644
+01:06:05,560 --> 01:06:09,820
+there's one, drop it. If there are two, leave it.
+
+645
+01:06:10,540 --> 01:06:18,560
+Agree, agreeing. See, seeing. But lie, lying.
+
+646
+01:06:19,600 --> 01:06:21,760
+Wassalamualaikum warahmatullahi wabarakatuh.
+
+647
+01:06:22,940 --> 01:06:24,280
+Inshallah next time.
+
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/Y2jr8Qbqdmk.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/Y2jr8Qbqdmk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d90903784dc3438b5046c847274c9eef7030cd9a
--- /dev/null
+++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/Y2jr8Qbqdmk.srt
@@ -0,0 +1,1199 @@
+
+1
+00:00:22,160 --> 00:00:24,260
+Assalamualaikum warahmatullahi wabarakatuh.
+
+2
+00:00:26,920 --> 00:00:33,760
+Today, inshallah, we are going to take how to 
+
+3
+00:00:33,760 --> 00:00:39,480
+express giving opinions, asking for opinions and 
+
+4
+00:00:39,480 --> 00:00:40,600
+giving opinions.
+
+5
+00:00:44,440 --> 00:00:47,520
+Page 29
+
+6
+00:00:50,070 --> 00:00:52,630
+We have everyday language or everyday English 
+
+7
+00:00:52,630 --> 00:01:01,910
+giving opinions. Before doing this exercise, we 
+
+8
+00:01:01,910 --> 00:01:09,810
+are going to write one word. What do the 
+
+9
+00:01:09,810 --> 00:01:14,810
+underlying words refer to in these sentences?
+
+10
+00:01:16,730 --> 00:01:24,190
+Number A It was really pouring. I fell asleep 
+
+11
+00:01:24,190 --> 00:01:34,070
+during the first act. Because we have act, so it 
+
+12
+00:01:34,070 --> 00:01:43,170
+is a play. Yes. So the answer is a play. So it 
+
+13
+00:01:43,170 --> 00:01:49,110
+refers to a play. Not to a novel. Because novels 
+
+14
+00:01:50,720 --> 00:01:58,340
+Chapters. Books, chapters. Yes. Number B. I didn't 
+
+15
+00:01:58,340 --> 00:02:04,500
+like this first one, but I couldn't put his latest 
+
+16
+00:02:04,500 --> 00:02:14,220
+one down until the last page. So this one and the 
+
+17
+00:02:14,220 --> 00:02:23,930
+last page, yes, speaks about a book or a novel yes 
+
+18
+00:02:23,930 --> 00:02:35,070
+a book or a novel yes
+
+19
+00:02:35,070 --> 00:02:38,890
+number 
+
+20
+00:02:38,890 --> 00:02:47,170
+c it was excellent have you seen it yet It stars 
+
+21
+00:02:47,170 --> 00:02:54,790
+Julia Kerchow and Anthony Bellini Yes,
+
+22
+00:02:54,990 --> 00:03:11,470
+it is a film So, it here refers to a film Yes, 
+
+23
+00:03:11,790 --> 00:03:18,770
+because we have stars The weird star films. 
+
+24
+00:03:21,210 --> 00:03:28,050
+Number D. She's usually good, but I don't think 
+
+25
+00:03:28,050 --> 00:03:38,450
+she was right for this part. This part. Yes. And 
+
+26
+00:03:38,450 --> 00:03:43,050
+because it's she, it is an actress. 
+
+27
+00:03:47,660 --> 00:03:52,760
+Or a film star. 
+
+28
+00:03:58,800 --> 00:04:05,200
+I think they spoil them. They always give them 
+
+29
+00:04:05,200 --> 00:04:13,080
+whatever they want. Whatever they want. They give 
+
+30
+00:04:13,080 --> 00:04:17,290
+them whatever they want. So they are Children 
+
+31
+00:04:17,290 --> 00:04:23,930
+their children. Yes, so them Refers 
+
+32
+00:04:23,930 --> 00:04:32,090
+to their children Their 
+
+33
+00:04:32,090 --> 00:04:39,370
+children Number if It 
+
+34
+00:04:39,370 --> 00:04:47,090
+was It was a nice break But the weather wasn't 
+
+35
+00:04:47,090 --> 00:04:56,330
+very good So it refers to a holiday Yes, it refers 
+
+36
+00:04:56,330 --> 00:05:02,810
+to a holiday Or 
+
+37
+00:05:02,810 --> 00:05:07,870
+vacation, break Vacation, break, holiday 
+
+38
+00:05:07,870 --> 00:05:13,470
+Generally, we say holiday They 
+
+39
+00:05:13,470 --> 00:05:14,430
+were delicious 
+
+40
+00:05:18,280 --> 00:05:25,260
+Joan had tomato and mozzarella. And I had tuna and 
+
+41
+00:05:25,260 --> 00:05:32,300
+sweet corn. Pizzas. Yes, they are pizzas. Pizza. 
+
+42
+00:05:32,700 --> 00:05:39,120
+Pizzas. Why? Mozzarella. Tomato. Delicious.
+
+43
+00:05:39,860 --> 00:05:45,040
+Something weird. Yes, number H and the last one. 
+
+44
+00:05:45,500 --> 00:05:50,450
+It was really exciting. it was really exciting or 
+
+45
+00:05:50,450 --> 00:05:56,230
+excited exciting because it but if i say i am 
+
+46
+00:05:56,230 --> 00:06:03,070
+excited yes it was really exciting especially when 
+
+47
+00:06:03,070 --> 00:06:08,530
+david storrett scored in the closing minutes 
+
+48
+00:06:08,530 --> 00:06:15,070
+scored means Yes, it's called a goal. So it is a 
+
+49
+00:06:15,070 --> 00:06:23,350
+match. Football match. Yes, football match.
+
+50
+00:06:25,890 --> 00:06:31,870
+So it is clear here. Again, we want to read these 
+
+51
+00:06:31,870 --> 00:06:35,630
+sentences without 
+
+52
+00:06:35,630 --> 00:06:39,930
+pronoun, with the word. With the word refers to. 
+
+53
+00:06:40,610 --> 00:06:43,910
+With the word it refers to. So here we say the 
+
+54
+00:06:43,910 --> 00:06:51,390
+play, the play was really boring. Etcetera. Yes, 
+
+55
+00:06:51,490 --> 00:06:55,010
+number one. Yes. The play was really boring. I 
+
+56
+00:06:55,010 --> 00:07:02,360
+feel asleep during the game. Yes. So if I say the 
+
+57
+00:07:02,360 --> 00:07:07,420
+place, okay, if I say it, it means the place. We 
+
+58
+00:07:07,420 --> 00:07:11,600
+generally don't use the pronoun unless the speaker 
+
+59
+00:07:11,600 --> 00:07:18,100
+and the listener know to whom I am speaking, who 
+
+60
+00:07:18,100 --> 00:07:21,600
+I'm speaking about. So we can't use the pronoun 
+
+61
+00:07:21,600 --> 00:07:28,140
+unless we, I and you know who he was. When I say 
+
+62
+00:07:28,140 --> 00:07:34,280
+she, Who is she? You know and I know. If I know 
+
+63
+00:07:34,280 --> 00:07:38,240
+the pronoun and you don't know it, I can't say the 
+
+64
+00:07:38,240 --> 00:07:41,720
+pronoun. Yes, if you know it and I don't know it, 
+
+65
+00:07:42,040 --> 00:07:45,060
+we can't use the pronoun. So when do we use 
+
+66
+00:07:45,060 --> 00:07:50,020
+pronouns? When both persons, the first person and 
+
+67
+00:07:50,020 --> 00:07:53,980
+the second person know the reference to this 
+
+68
+00:07:53,980 --> 00:08:00,000
+pronoun. Yes. So here, when I say it, it refers to 
+
+69
+00:08:00,000 --> 00:08:05,580
+something. So from the meaning of the sentence, it 
+
+70
+00:08:05,580 --> 00:08:09,160
+means something. What is it here? The plane. Yes.
+
+71
+00:08:09,320 --> 00:08:14,020
+Number two. Number B. Yes. I didn't like his first 
+
+72
+00:08:14,020 --> 00:08:20,600
+book, but I couldn't put his letters one down 
+
+73
+00:08:20,600 --> 00:08:22,400
+until the last page. 
+
+74
+00:08:25,540 --> 00:08:30,540
+the book yes or we can say novel the novel the 
+
+75
+00:08:30,540 --> 00:08:36,440
+story uh-huh yes yes
+
+76
+00:08:36,440 --> 00:08:45,760
+now i want to replace it with a noun yes a film 
+
+77
+00:08:45,760 --> 00:08:50,600
+was excellent the film was excellent have you seen 
+
+78
+00:08:50,600 --> 00:08:53,020
+it yet it starts julia
+
+79
+00:08:55,980 --> 00:09:03,560
+Kershaw and Anthony Pirini. Yes. Good. She.
+
+80
+00:09:07,660 --> 00:09:13,420
+The actress is usually good, but I don't think she 
+
+81
+00:09:13,420 --> 00:09:19,740
+was right for the part. For this part. This part 
+
+82
+00:09:19,740 --> 00:09:26,840
+of the acting. Yes. I want to bless them with 
+
+83
+00:09:26,840 --> 00:09:31,100
+their children. Yes. I think they are small 
+
+84
+00:09:31,100 --> 00:09:36,180
+children. Their children. They always give them 
+
+85
+00:09:36,180 --> 00:09:44,300
+whatever they want. Whatever. Whatever. Anything. 
+
+86
+00:09:45,260 --> 00:09:52,100
+Whatever. Whoever. Wherever. Wherever. Any place.
+
+87
+00:09:53,100 --> 00:09:58,500
+Whatever, anything, whoever, any person. Yes.
+
+88
+00:09:59,920 --> 00:10:07,920
+Number F or letter F. Yes. A holiday was a nice 
+
+89
+00:10:07,920 --> 00:10:12,840
+break, but the weather wasn't very good. Yes. So 
+
+90
+00:10:12,840 --> 00:10:15,820
+here we use what? 
+
+91
+00:10:17,080 --> 00:10:18,780
+The holiday. 
+
+92
+00:10:22,430 --> 00:10:23,350
+And they, 
+
+93
+00:10:25,730 --> 00:10:29,390
+yes, the pizzas. 
+
+94
+00:10:31,890 --> 00:10:37,830
+You know mozzarella? 
+
+95
+00:10:39,330 --> 00:10:45,950
+Yes. Cheese. Yes. Good. The last one, the last 
+
+96
+00:10:45,950 --> 00:10:54,950
+one. Yes Especially
+
+97
+00:10:54,950 --> 00:10:59,890
+David
+
+98
+00:10:59,890 --> 00:11:07,610
+start When 
+
+99
+00:11:07,610 --> 00:11:13,690
+David scored scored in the closing minute Huh 
+
+100
+00:11:13,690 --> 00:11:21,580
+scored means He scored a goal. Yes. Is it right?
+
+101
+00:11:22,420 --> 00:11:30,700
+Clear? Yes. So if we again, this is the answers.
+
+102
+00:11:46,590 --> 00:11:54,310
+I want you to work in pairs for each sentence. You 
+
+103
+00:11:54,310 --> 00:11:58,570
+say the sentence and your partner say the word. 
+
+104
+00:11:59,070 --> 00:12:00,250
+Yes, work in pairs.
+
+105
+00:12:38,670 --> 00:12:43,230
+Now change roles. Change. 
+
+106
+00:12:46,090 --> 00:12:51,510
+It's one of 
+
+107
+00:12:51,510 --> 00:12:52,230
+my favorite books.
+
+108
+00:12:54,770 --> 00:12:57,570
+It's one of my favorite books.
+
+109
+00:13:34,490 --> 00:13:42,390
+Thank you. That's enough. I want you To think of 
+
+110
+00:13:42,390 --> 00:13:47,170
+some things.
+
+111
+00:13:50,070 --> 00:13:59,490
+And some things you did. Some things you did last 
+
+112
+00:13:59,490 --> 00:14:00,290
+week.
+
+113
+00:14:11,970 --> 00:14:18,470
+and also some places
+
+114
+00:14:18,470 --> 00:14:22,410
+you 
+
+115
+00:14:22,410 --> 00:14:32,350
+went to last week and 
+
+116
+00:14:32,350 --> 00:14:47,800
+also some people you met Last week Yes, think of 
+
+117
+00:14:47,800 --> 00:14:57,060
+some things like what I went or I Something you 
+
+118
+00:14:57,060 --> 00:15:04,140
+did I watched Watched 
+
+119
+00:15:04,140 --> 00:15:10,020
+a film Yes,
+
+120
+00:15:10,180 --> 00:15:11,420
+I cooked 
+
+121
+00:15:15,250 --> 00:15:26,750
+a meal I visited my uncle 
+
+122
+00:15:26,750 --> 00:15:29,810
+what else?
+
+123
+00:15:32,950 --> 00:15:43,870
+I did my homework something
+
+124
+00:15:43,870 --> 00:15:56,850
+else? I completed my research Yes, I finished my 
+
+125
+00:15:56,850 --> 00:16:03,810
+research I 
+
+126
+00:16:03,810 --> 00:16:10,970
+repaired my
+
+127
+00:16:10,970 --> 00:16:12,690
+mobile
+
+128
+00:16:15,910 --> 00:16:24,770
+Yes, so I Want all of you to think of some things 
+
+129
+00:16:24,770 --> 00:16:31,490
+you did last week like these Uh-huh Now the 
+
+130
+00:16:31,490 --> 00:16:38,950
+question what was it like what was it like? Mm-hmm
+
+131
+00:16:38,950 --> 00:16:49,100
+question What was it like. When I say what was it 
+
+132
+00:16:49,100 --> 00:16:54,480
+like, I am asking about the adjective. It was 
+
+133
+00:16:54,480 --> 00:16:59,620
+good. It was excellent. It was really difficult. 
+
+134
+00:17:00,700 --> 00:17:03,640
+It was highly appreciated. 
+
+135
+00:17:05,540 --> 00:17:11,920
+It was so and so. So now, with a partner, think of 
+
+136
+00:17:11,920 --> 00:17:15,840
+something and ask, what is it like? What was it 
+
+137
+00:17:15,840 --> 00:17:21,020
+like? Because it is in the past. If it is now, I 
+
+138
+00:17:21,020 --> 00:17:24,080
+say, what is it like? But if it is in the past,
+
+139
+00:17:24,300 --> 00:17:28,500
+what was it like? So I watched a film. What was it 
+
+140
+00:17:28,500 --> 00:17:31,160
+like? Well, it was boring. 
+
+141
+00:17:33,720 --> 00:17:37,740
+I cooked a meal. What was delicious. It was really 
+
+142
+00:17:37,740 --> 00:17:45,200
+delicious. I visit my uncle. What was he like? 
+
+143
+00:17:45,380 --> 00:17:51,760
+Yes. So here we say What was he like? He was fine. 
+
+144
+00:17:52,520 --> 00:17:56,720
+He was fine. He was ill. He was extremely ill. 
+
+145
+00:17:57,600 --> 00:18:03,690
+Yes. I did my homework. What was it like? It was 
+
+146
+00:18:03,690 --> 00:18:09,670
+difficult. It was long. It was easy. It was 
+
+147
+00:18:09,670 --> 00:18:15,350
+repeated, etc. etc. I finished my research. What 
+
+148
+00:18:15,350 --> 00:18:19,750
+was it like? It was complicated.
+
+149
+00:18:21,350 --> 00:18:27,130
+It was complicated. It was easy. It was useful.
+
+150
+00:18:27,910 --> 00:18:31,310
+Etc. You understand? Also here, I repaired my 
+
+151
+00:18:31,310 --> 00:18:36,250
+mobile. What was it like? It was good. Expensive.
+
+152
+00:18:36,570 --> 00:18:41,150
+Great. Etc. So I want you now again to work in 
+
+153
+00:18:41,150 --> 00:18:46,190
+pairs. Think of something you did last week and 
+
+154
+00:18:46,190 --> 00:18:50,630
+ask what was it like? Yes. In pairs.
+
+155
+00:18:57,450 --> 00:18:57,890
+Thank you very much.
+
+156
+00:19:43,850 --> 00:19:51,350
+So we call this asking for opinions and here 
+
+157
+00:19:51,350 --> 00:19:58,200
+giving opinions. Asking for opinions and giving 
+
+158
+00:19:58,200 --> 00:20:03,660
+opinions. Our subject for today, our lesson for 
+
+159
+00:20:03,660 --> 00:20:07,400
+today is giving opinions. How can we give opinions 
+
+160
+00:20:07,400 --> 00:20:12,180
+when someone asks for opinions? What was it like?
+
+161
+00:20:12,980 --> 00:20:18,890
+It was really exciting. What was it like? It was 
+
+162
+00:20:18,890 --> 00:20:24,550
+boring. Question and answer. It is asking for 
+
+163
+00:20:24,550 --> 00:20:32,150
+opinions and giving opinions. Yes. Yes, go on. Go 
+
+164
+00:20:32,150 --> 00:20:32,390
+on.
+
+165
+00:20:50,870 --> 00:20:59,790
+Another question. What did 
+
+166
+00:20:59,790 --> 00:21:04,250
+you think 
+
+167
+00:21:07,410 --> 00:21:13,430
+of what did you think of it? What did you think of 
+
+168
+00:21:13,430 --> 00:21:19,030
+it? It means, what was it like? But we can't 
+
+169
+00:21:19,030 --> 00:21:23,570
+change. We say what? What did you think of it?
+
+170
+00:21:23,910 --> 00:21:26,810
+What did you think of your meal? What did you 
+
+171
+00:21:26,810 --> 00:21:31,690
+think of your uncle? So instead of it, we can use 
+
+172
+00:21:31,690 --> 00:21:37,590
+something else. Yes, again, work in pairs and ask 
+
+173
+00:21:37,590 --> 00:21:39,930
+this question and get the same answer. 
+
+174
+00:21:50,230 --> 00:21:50,950
+Yes? 
+
+175
+00:22:04,110 --> 00:22:07,950
+We can also add another question because we ask 
+
+176
+00:22:07,950 --> 00:22:13,430
+for opinions. We can say this or this or we can 
+
+177
+00:22:13,430 --> 00:22:26,470
+say, did you like it? Did you like it? Yes, it was 
+
+178
+00:22:26,470 --> 00:22:30,730
+really exciting. Yes, it was really. 
+
+179
+00:22:34,200 --> 00:22:39,580
+Happy. Or we say, no, it was boring. No, it was 
+
+180
+00:22:39,580 --> 00:22:45,100
+difficult. So these three questions are for asking 
+
+181
+00:22:45,100 --> 00:22:50,240
+for opinions. Yes. Again, working girls, ask any 
+
+182
+00:22:50,240 --> 00:22:52,220
+of these questions and give the answer.
+
+183
+00:23:15,500 --> 00:23:22,540
+Yes, that's enough. Now, we want to 
+
+184
+00:23:25,650 --> 00:23:31,190
+Think of some places you went to. So I will clean 
+
+185
+00:23:31,190 --> 00:23:34,890
+this and think of places. Yes, it's enough?
+
+186
+00:23:40,450 --> 00:23:43,670
+Some places you went to.
+
+187
+00:23:46,510 --> 00:23:50,750
+Rafah, the new supermarket.
+
+188
+00:23:56,690 --> 00:23:58,670
+The park. 
+
+189
+00:24:03,190 --> 00:24:07,270
+Yes. What is? The sea. 
+
+190
+00:24:10,510 --> 00:24:12,530
+The university. 
+
+191
+00:24:17,490 --> 00:24:17,690
+Yes.
+
+192
+00:24:23,650 --> 00:24:30,390
+So these places I went to last week, what was it 
+
+193
+00:24:30,390 --> 00:24:35,530
+like? What was it like? Say yesterday I went to 
+
+194
+00:24:35,530 --> 00:24:39,570
+the university. What was it like? It was 
+
+195
+00:24:39,570 --> 00:24:45,730
+marvelous. Marvelous. It was beautiful. It was 
+
+196
+00:24:45,730 --> 00:24:52,530
+
+223
+00:28:14,130 --> 00:28:14,550
+what?
+
+224
+00:28:18,550 --> 00:28:26,950
+my grandmother my
+
+225
+00:28:26,950 --> 00:28:30,830
+sister
+
+226
+00:28:30,830 --> 00:28:34,590
+Ali's
+
+227
+00:28:34,590 --> 00:28:47,780
+brother Ali's brother My friend. My uncle.
+
+228
+00:28:49,720 --> 00:28:56,260
+What was he like? What did you think of him? Do
+
+229
+00:28:56,260 --> 00:29:01,400
+you like him? Yes. Do you like him? Yes. Of
+
+230
+00:29:01,400 --> 00:29:06,440
+course, he is kind. Etc. Yes. Working period is
+
+231
+00:29:06,440 --> 00:29:08,660
+the same for people
+
+232
+00:29:15,250 --> 00:29:26,030
+Yes, now look at this chart. We have opinions and
+
+233
+00:29:26,030 --> 00:29:33,730
+we have asking for opinions. Opinions and asking
+
+234
+00:29:33,730 --> 00:29:41,250
+for opinions. So did you like the film? Did you
+
+235
+00:29:41,250 --> 00:29:49,150
+like the film? This is asking for opinion. It was
+
+236
+00:29:49,150 --> 00:29:54,270
+excellent. Have you seen it yet? It stars Julia
+
+237
+00:29:54,270 --> 00:29:59,690
+Cashow and Anthony Bellini. So this is C.
+
+238
+00:30:02,190 --> 00:30:08,550
+So we want to answer or to give opinion from the
+
+239
+00:30:08,550 --> 00:30:13,410
+first exercise. Number two, what did you think of
+
+240
+00:30:13,410 --> 00:30:21,030
+the play? What did you think of the play? Yes, it
+
+241
+00:30:21,030 --> 00:30:21,630
+was.
+
+242
+00:30:27,370 --> 00:30:27,890
+Yeah.
+
+243
+00:30:33,230 --> 00:30:37,030
+So what
+
+244
+00:30:37,030 --> 00:30:40,130
+did you think of the play? Did you like the play?
+
+245
+00:30:41,430 --> 00:30:46,510
+What was the play like? The same. Yes? When we ask
+
+246
+00:30:46,510 --> 00:30:53,410
+for opinions, we can use, do you like? Do you
+
+247
+00:30:53,410 --> 00:30:56,730
+like? Or did you like? Or what did you think of?
+
+248
+00:30:58,330 --> 00:31:02,350
+Or what
+
+249
+00:31:02,350 --> 00:31:08,480
+was it like? You understand? Three types of asking
+
+250
+00:31:08,480 --> 00:31:14,300
+for opinions. Either by saying, did you like? Or
+
+251
+00:31:14,300 --> 00:31:19,500
+what did you think of? Or what was it like? What
+
+252
+00:31:19,500 --> 00:31:24,300
+was it like? Yes, the same meaning. And here we
+
+253
+00:31:24,300 --> 00:31:32,260
+give the opinions. Yes. Number three, did you like
+
+254
+00:31:32,260 --> 00:31:32,720
+the pizzas?
+
+255
+00:31:38,130 --> 00:31:39,410
+Yes,
+
+256
+00:31:41,910 --> 00:31:50,390
+so this is G this is one Two and this is three
+
+257
+00:31:50,390 --> 00:31:58,140
+Number four Yes Do you like Malcolm Buckley's
+
+258
+00:31:58,140 --> 00:32:02,120
+novel? I didn't like his first one, but I couldn't
+
+259
+00:32:02,120 --> 00:32:07,000
+put his latest one down until the last page. Yeah.
+
+260
+00:32:07,640 --> 00:32:11,220
+So this is number four.
+
+261
+00:32:13,280 --> 00:32:19,100
+Or here we can say what this, what number? A, G,
+
+262
+00:32:20,020 --> 00:32:28,960
+D, B, and number five. What do you think of their
+
+263
+00:32:28,960 --> 00:32:34,200
+children? Did you like their children? Yes, I did.
+
+264
+00:32:34,540 --> 00:32:40,600
+What were their children like? The same? Yes? The
+
+265
+00:32:40,600 --> 00:32:43,860
+answer? I think they spoiled them. They always
+
+266
+00:32:43,860 --> 00:32:48,560
+give them whatever they want. Yeah. Yes. So this
+
+267
+00:32:48,560 --> 00:32:51,360
+is number E or here number
+
+268
+00:32:56,230 --> 00:33:00,950
+Yes. So what we call this? These things asking for
+
+269
+00:33:00,950 --> 00:33:06,630
+opinions and this giving opinions, asking for
+
+270
+00:33:06,630 --> 00:33:11,530
+opinions, giving opinions. Yes. Number six. Huh?
+
+271
+00:33:11,630 --> 00:33:16,790
+What was your holiday like? Yes. It was a nice
+
+272
+00:33:16,790 --> 00:33:19,950
+break, but the weather wasn't very good. Uh huh.
+
+273
+00:33:20,500 --> 00:33:25,960
+Yeah, so this is number six and here we can use F
+
+274
+00:33:25,960 --> 00:33:29,140
+Again
+
+275
+00:33:29,140 --> 00:33:41,120
+number seven. Mm-hmm. Yes Yeah,
+
+276
+00:33:45,660 --> 00:33:55,930
+so this number D And here number seven. The last
+
+277
+00:33:55,930 --> 00:33:56,750
+one. Yes.
+
+278
+00:34:04,750 --> 00:34:05,690
+Yeah.
+
+279
+00:34:09,150 --> 00:34:16,890
+So this is H and this is number eight. Is the idea
+
+280
+00:34:16,890 --> 00:34:17,330
+clear?
+
+281
+00:34:19,990 --> 00:34:23,770
+So, here we concentrate on two things. Asking for
+
+282
+00:34:23,770 --> 00:34:26,450
+opinions and giving opinions. Questions and
+
+283
+00:34:26,450 --> 00:34:29,630
+answers. But not generally questions. No,
+
+284
+00:34:29,770 --> 00:34:33,710
+opinions. Your point of view. I think so and so.
+
+285
+00:34:33,970 --> 00:34:40,910
+You can think so and so. Yes. Now, did you watch
+
+286
+00:34:40,910 --> 00:34:45,770
+the film last night? Yes, I did. What was it like?
+
+287
+00:34:46,850 --> 00:34:50,770
+It was excellent. Did you meet your uncle last
+
+288
+00:34:50,770 --> 00:34:56,910
+week? Yes, I did. What do you think of him? What
+
+289
+00:34:56,910 --> 00:35:02,470
+did you think of him? He's fine. Yes. Now, did you
+
+290
+00:35:02,470 --> 00:35:07,290
+meet your teacher yesterday? Yes. Yes, I did. What
+
+291
+00:35:07,290 --> 00:35:11,130
+was he like? Huh? What was it? Did you like it?
+
+292
+00:35:11,290 --> 00:35:16,650
+Yes. Yes. I want you again to work in pairs asking
+
+293
+00:35:16,650 --> 00:35:21,130
+like these questions. Questions and answers.
+
+294
+00:35:21,870 --> 00:35:24,730
+Asking for opinions and giving opinions. Remember
+
+295
+00:35:24,730 --> 00:35:27,350
+that we have three kinds of asking for opinions.
+
+296
+00:35:27,730 --> 00:35:32,630
+What are they? Did you like? What did you think
+
+297
+00:35:32,630 --> 00:35:36,230
+of? And what was it like? Yes.
+
+298
+00:35:39,750 --> 00:35:40,950
+Gone.
+
+299
+00:36:06,950 --> 00:36:08,190
+Thank you very much.
+
+300
+00:36:40,600 --> 00:36:47,000
+That's enough? Yes? Now again? These are the
+
+301
+00:36:47,000 --> 00:36:53,160
+answers. Just one. Yes. Number one. A, B, two.
+
+302
+00:36:54,490 --> 00:36:59,930
+Yes, these two. Yes. It was excellent. Have you
+
+303
+00:36:59,930 --> 00:37:03,950
+seen it yet? It started Julia Kershaw and Antonio
+
+304
+00:37:03,950 --> 00:37:10,070
+Milani. Thank you. Number two. Yes. Yes, the two.
+
+305
+00:37:18,990 --> 00:37:26,340
+Yes, again. Number three. Yes, you were the
+
+306
+00:37:26,340 --> 00:37:26,700
+partner.
+
+307
+00:37:36,300 --> 00:37:42,380
+Number four. Yes, you both.
+
+308
+00:37:53,760 --> 00:38:00,640
+Yes, thank you number five Yes,
+
+309
+00:38:00,820 --> 00:38:05,780
+you Yes
+
+310
+00:38:05,780 --> 00:38:13,220
+number
+
+311
+00:38:13,220 --> 00:38:13,820
+six
+
+312
+00:38:21,930 --> 00:38:27,390
+Number seven. Yes.
+
+313
+00:38:32,770 --> 00:38:38,690
+And the
+
+314
+00:38:38,690 --> 00:38:40,990
+last one. Yes.
+
+315
+00:38:50,880 --> 00:38:56,340
+Thank you. So generally, when we speak with each
+
+316
+00:38:56,340 --> 00:39:00,100
+other, we are asking about or we're asking for
+
+317
+00:39:00,100 --> 00:39:03,740
+opinions. Don't forget to ask one type of these
+
+318
+00:39:03,740 --> 00:39:11,060
+three questions. Did you like the film? What was
+
+319
+00:39:11,060 --> 00:39:15,820
+or what did you think of the film? Did you like
+
+320
+00:39:15,820 --> 00:39:20,840
+the film? Or here we say, what was the film like?
+
+321
+00:39:21,740 --> 00:39:27,760
+Again, what was the film like? And did you like
+
+322
+00:39:27,760 --> 00:39:33,020
+the film or what did you think of the film? Yes.
+
+323
+00:39:33,460 --> 00:39:40,420
+So these three questions have nearly the same
+
+324
+00:39:40,420 --> 00:39:45,500
+meaning. In the answer, we can use any of these
+
+325
+00:39:45,500 --> 00:39:48,860
+examples. Wassalamu alaikum wa rahmatullah wa
+
+326
+00:39:48,860 --> 00:39:51,180
+barakatuh. Thank you very much.
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/gP7wLsXLbww.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/gP7wLsXLbww.srt
new file mode 100644
index 0000000000000000000000000000000000000000..31b4a71cceafedc670575d6c466bf548c3e579dc
--- /dev/null
+++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/gP7wLsXLbww.srt
@@ -0,0 +1,1794 @@
+
+1
+00:00:20,700 --> 00:00:26,400
+Assalamualaikum warahmatullahi wabarakatuh Today
+
+2
+00:00:26,400 --> 00:00:29,980
+inshallah, we are going to take some adjectives
+
+3
+00:00:29,980 --> 00:00:36,240
+and some sounds adjectives for food town and
+
+4
+00:00:36,240 --> 00:00:44,140
+people Three kinds of adjectives for towns food
+
+5
+00:00:44,140 --> 00:00:48,640
+and people Yes
+
+6
+00:00:48,640 --> 00:00:59,960
+page 52 and 53 the first exercise we have food we
+
+7
+00:00:59,960 --> 00:01:05,800
+have some adjectives connected with food all these
+
+8
+00:01:05,800 --> 00:01:12,380
+adjectives are connected with food except four at
+
+9
+00:01:12,380 --> 00:01:17,260
+first we will omit four adjectives because they
+
+10
+00:01:17,260 --> 00:01:19,480
+don't go with food
+
+11
+00:01:21,890 --> 00:01:26,390
+So here disgusted. Disgusted connected with
+
+12
+00:01:26,390 --> 00:01:33,090
+people, not with food. I am disgusted because the
+
+13
+00:01:33,090 --> 00:01:37,750
+food is disgusting. So disgusting here is with
+
+14
+00:01:37,750 --> 00:01:43,060
+food. Okay. But disgusted with people so the ed
+
+15
+00:01:43,060 --> 00:01:49,920
+some adjectives have ed for people and the ing for
+
+16
+00:01:49,920 --> 00:01:55,480
+things in general junk
+
+17
+00:01:55,480 --> 00:02:03,340
+food yes junk food okay fast
+
+18
+00:02:03,340 --> 00:02:09,560
+food okay we have fast food Pizza is a fast food.
+
+19
+00:02:09,800 --> 00:02:14,120
+Hamburger is a fast food. Tamiya is a fast food,
+
+20
+00:02:14,420 --> 00:02:25,720
+etc. Delicious Delicious food Delicious food Yes
+
+21
+00:02:25,720 --> 00:02:31,900
+tasteless Has no taste tasteless food. Okay
+
+22
+00:02:31,900 --> 00:02:38,520
+tasteless food Hmm. We have fresh food.
+
+23
+00:02:41,020 --> 00:02:45,660
+Any kind of food, not the word food, any kind of
+
+24
+00:02:45,660 --> 00:02:53,240
+food, huh? Fresh Bamya, fresh, yes, rice, etc.
+
+25
+00:02:54,460 --> 00:03:01,820
+Plain. plain food it means one kind just one kind
+
+26
+00:03:01,820 --> 00:03:08,100
+simple one kind plain food just one kind of food
+
+27
+00:03:08,100 --> 00:03:12,120
+okay tasteful no
+
+28
+00:03:14,230 --> 00:03:19,330
+Tasteful We use tasteful for people Ali is
+
+29
+00:03:19,330 --> 00:03:24,510
+tasteful He speaks politely And he eats politely
+
+30
+00:03:24,510 --> 00:03:30,070
+He behaves politely He is tasteful All of us
+
+31
+00:03:30,070 --> 00:03:34,470
+should be tasteful Especially when we deal with
+
+32
+00:03:34,470 --> 00:03:42,010
+people So this is Can't go with food But tasteless
+
+33
+00:03:43,000 --> 00:03:47,980
+Tasty with food but tasteful. No for people a
+
+34
+00:03:47,980 --> 00:03:54,020
+tasteful man a tasteful Man yes disgusting. Uh
+
+35
+00:03:54,020 --> 00:03:59,000
+-huh. Yes disgusting Uh-huh. When I eat it when I
+
+36
+00:03:59,000 --> 00:04:02,260
+see it when I see the food I am This it is
+
+37
+00:04:02,260 --> 00:04:07,700
+disgusting. So I am disgusted Like this. Uh-huh
+
+38
+00:04:07,700 --> 00:04:19,530
+Frozen food Okay. Yes, we say frozen food and We
+
+39
+00:04:19,530 --> 00:04:26,630
+say rich rich food, yeah rich food it is full of
+
+40
+00:04:26,630 --> 00:04:34,890
+Ingredients it's full of cheese oil meat Something
+
+41
+00:04:34,890 --> 00:04:40,830
+like this, huh? Yeah, so rich food Homegrown
+
+42
+00:04:42,600 --> 00:04:49,060
+Homegrown. It is grown at home. Not ready. So
+
+43
+00:04:49,060 --> 00:04:54,780
+homemade food. Homemade homegrown vegetables.
+
+44
+00:04:55,220 --> 00:05:00,000
+Homegrown vegetables. Homegrown food. It means
+
+45
+00:05:00,000 --> 00:05:05,740
+food that is grown at home. Local. Yes, local.
+
+46
+00:05:06,780 --> 00:05:18,060
+Yes. And we have vegetarian yes vegetarian food
+
+47
+00:05:18,060 --> 00:05:26,200
+not of meat no vegetarian of plants or plants yes
+
+48
+00:05:26,200 --> 00:05:32,680
+so vegetarian food is good wealthy
+
+49
+00:05:32,680 --> 00:05:39,360
+wealthy has a lot of money yes no no we don't say
+
+50
+00:05:39,890 --> 00:05:44,630
+Wealthy food. We say wealthy wealthy man. Uh-huh
+
+51
+00:05:44,630 --> 00:05:50,750
+wealthy millionaire, etc Starving
+
+52
+00:05:50,750 --> 00:05:57,650
+very hungry hungry Extremely hungry. Uh-huh
+
+53
+00:05:57,650 --> 00:06:02,550
+extremely hungry. No, no this for people so
+
+54
+00:06:02,550 --> 00:06:09,120
+tasteful starving, wealthy, for people. Also
+
+55
+00:06:09,120 --> 00:06:16,320
+disgusted for people, not for food. So we have
+
+56
+00:06:16,320 --> 00:06:21,620
+four words not connected with food. What are they?
+
+57
+00:06:22,120 --> 00:06:28,230
+Disgusted, wealthy, Tasteful and starving.
+
+58
+00:06:28,870 --> 00:06:33,390
+Starving. I was starving. My brother was starving
+
+59
+00:06:33,390 --> 00:06:36,710
+when he arrived home. He was very hungry,
+
+60
+00:06:37,330 --> 00:06:42,070
+extremely hungry. He went quickly to the kitchen.
+
+61
+00:06:42,990 --> 00:06:47,030
+Most of us, when we arrive at home, we go straight
+
+62
+00:06:47,030 --> 00:06:53,270
+to the kitchen. When we are starving. But when we
+
+63
+00:06:53,270 --> 00:06:57,330
+are hungry, we can wait. But starving I can't wait
+
+64
+00:06:57,330 --> 00:07:02,570
+So again who can read the adjectives connected
+
+65
+00:07:02,570 --> 00:07:12,010
+with the food Yes junk food Disgusting
+
+66
+00:07:12,010 --> 00:07:15,250
+food
+
+67
+00:07:19,760 --> 00:07:23,740
+Thank you. Yes, someone else. Yeah. French food,
+
+68
+00:07:24,140 --> 00:07:29,280
+homegrown food, vegetarian food, tasteless food,
+
+69
+00:07:29,640 --> 00:07:33,100
+delicious food, fast food, fresh food, junk food,
+
+70
+00:07:33,280 --> 00:07:37,120
+disgusting food. Yes, again and again. Yes. Junk
+
+71
+00:07:37,120 --> 00:07:40,180
+food, fast food, fresh food, delicious food,
+
+72
+00:07:40,400 --> 00:07:45,660
+tasteless food, bland Vegetarian food, homegrown
+
+73
+00:07:45,660 --> 00:07:53,420
+food, rich food, frozen food. Again, again, the
+
+74
+00:07:53,420 --> 00:07:57,320
+last time, again, yes. Vegan food, fresh food,
+
+75
+00:07:57,440 --> 00:08:00,480
+fast food, delicious food, testes food, bland
+
+76
+00:08:00,480 --> 00:08:04,860
+food, vegetarian food, homegrown food, rich food,
+
+77
+00:08:05,040 --> 00:08:08,920
+frozen food, disgusting food. Very good. Thank
+
+78
+00:08:08,920 --> 00:08:13,900
+you. So the first part of the exercise is about
+
+79
+00:08:13,900 --> 00:08:17,080
+food. So here in each group, four of the
+
+80
+00:08:17,080 --> 00:08:21,840
+adjectives can't go with the noun. This is the
+
+81
+00:08:21,840 --> 00:08:26,060
+noun. Which ones these four are not connected with
+
+82
+00:08:26,060 --> 00:08:27,400
+food.
+
+83
+00:08:29,700 --> 00:08:36,680
+Is it clear? Don't confuse with disgusting and
+
+84
+00:08:36,680 --> 00:08:42,100
+disgusted. We say wealthy for people and rich for
+
+85
+00:08:42,100 --> 00:08:48,520
+food. Rich for food and wealthy with people. And
+
+86
+00:08:48,520 --> 00:08:54,060
+when we say tasty or tasteless food, but not
+
+87
+00:08:54,060 --> 00:08:59,700
+tasteful. Tasteful for people. Also, we say fresh
+
+88
+00:08:59,700 --> 00:09:05,840
+food, fast food, frozen food, homegrown One word.
+
+89
+00:09:06,340 --> 00:09:10,240
+Hyphenated word. Two words as one word. Adjective.
+
+90
+00:09:10,760 --> 00:09:15,500
+Compound adjective. Compound adjective. Yeah.
+
+91
+00:09:24,700 --> 00:09:28,200
+So this is the question and this is the answer.
+
+92
+00:09:30,740 --> 00:09:36,840
+Next. We have some adjectives connected with town.
+
+93
+00:09:38,020 --> 00:09:45,520
+We say excited town. No, we don't say excited
+
+94
+00:09:45,520 --> 00:09:52,660
+town. Why? Excited for people. But exciting for
+
+95
+00:09:52,660 --> 00:09:59,190
+things. Exciting town. But not excited. I was
+
+96
+00:09:59,190 --> 00:10:03,530
+excited because the town was exciting.
+
+97
+00:10:05,370 --> 00:10:12,950
+Amazed, amazing. Disgusted, disgusting. People and
+
+98
+00:10:12,950 --> 00:10:16,770
+non-people. People non people or sometimes we say
+
+99
+00:10:16,770 --> 00:10:21,730
+people and situation Situation with ing people
+
+100
+00:10:21,730 --> 00:10:25,650
+with ed but not all the adjective Some adjectives
+
+101
+00:10:25,650 --> 00:10:30,550
+a group a small group of adjectives Home hometown
+
+102
+00:10:30,550 --> 00:10:36,530
+hometown. Yes. What is your hometown? Gaza and you
+
+103
+00:10:36,530 --> 00:10:40,350
+saudi arabia I was born in saudi arabia. So my
+
+104
+00:10:40,350 --> 00:10:46,950
+hometown is Saudi Arabia. Say I was born in such a
+
+105
+00:10:46,950 --> 00:10:53,230
+town. So we say hometown. What is your hometown in
+
+106
+00:10:53,230 --> 00:10:54,970
+Palestine? So and so.
+
+107
+00:11:03,610 --> 00:11:08,470
+Old town. Old town. Yes. Jericho is an old town.
+
+108
+00:11:09,090 --> 00:11:14,230
+Gaza is an old town. But Al Zahra? No. Al Zahra is
+
+109
+00:11:14,230 --> 00:11:21,650
+a new town. Not old. So we have old town and new
+
+110
+00:11:21,650 --> 00:11:25,720
+or modern. If it is modern, modern. If it is not
+
+111
+00:11:25,720 --> 00:11:30,200
+modern, new. Maybe not modern, but new and old.
+
+112
+00:11:30,660 --> 00:11:35,380
+Sometimes it is modern. Modern like this? Modern
+
+113
+00:11:35,380 --> 00:11:39,560
+town. Yes, it has metro, it has underground,
+
+114
+00:11:40,100 --> 00:11:44,180
+restaurants and so on. Buildings. So it is modern.
+
+115
+00:11:45,160 --> 00:11:50,240
+University town. University town. Town for the
+
+116
+00:11:50,240 --> 00:11:54,340
+university. The main building in the town is a
+
+117
+00:11:54,340 --> 00:11:58,500
+university. So all the houses and most of the
+
+118
+00:11:58,500 --> 00:12:02,080
+people there connected with the university. So
+
+119
+00:12:02,080 --> 00:12:07,500
+this town is university town. It means it has a
+
+120
+00:12:07,500 --> 00:12:10,880
+big university and most of the jobs there are
+
+121
+00:12:10,880 --> 00:12:16,580
+connected with university. So it is a university
+
+122
+00:12:16,580 --> 00:12:20,980
+town for all the people the pupils the students
+
+123
+00:12:20,980 --> 00:12:25,860
+and so on students doctors and books workshops etc
+
+124
+00:12:25,860 --> 00:12:30,500
+polluted
+
+125
+00:12:30,500 --> 00:12:37,080
+town polluted yes yes new york is a polluted town
+
+126
+00:12:37,080 --> 00:12:44,020
+polluted polluted uh-huh not polluting No, this
+
+127
+00:12:44,020 --> 00:12:49,960
+gas is polluting. This smoke is polluting. Why?
+
+128
+00:12:50,160 --> 00:12:54,100
+Because it causes pollution. It causes pollution.
+
+129
+00:12:54,500 --> 00:13:01,020
+But when it is polluted, it is bad. It is bad. I
+
+130
+00:13:01,020 --> 00:13:04,860
+can't eat polluted food. Why? Because it's
+
+131
+00:13:04,860 --> 00:13:10,420
+polluted. But what causes pollution? This smoke
+
+132
+00:13:10,420 --> 00:13:14,140
+causing pollution. So the smoke is polluting.
+
+133
+00:13:16,300 --> 00:13:23,200
+Capital. Capital town. Capital city. Capital city.
+
+134
+00:13:23,820 --> 00:13:31,510
+So I can't say capital Town. I say capital city.
+
+135
+00:13:31,990 --> 00:13:35,770
+What is the capital city of Palestine? Jerusalem.
+
+136
+00:13:36,650 --> 00:13:41,590
+What is the capital city of Egypt? Cairo. What is
+
+137
+00:13:41,590 --> 00:13:46,290
+the capital city of the USA? Washington DC. What
+
+138
+00:13:46,290 --> 00:13:51,370
+is the capital city of Japan? Tokyo. What is the
+
+139
+00:13:51,370 --> 00:13:58,390
+capital city of Peru? Lima, etc. Now industrial.
+
+140
+00:13:59,470 --> 00:14:03,950
+Industrial town. Yes, San Francisco is an
+
+141
+00:14:03,950 --> 00:14:08,430
+industrial town. Because it is full of factories.
+
+142
+00:14:09,250 --> 00:14:14,130
+Full of factories and workshops. Industries. They
+
+143
+00:14:14,130 --> 00:14:17,310
+make cars. They make new things. So it is
+
+144
+00:14:17,310 --> 00:14:22,180
+industrial town. Okay. What about agricultural?
+
+145
+00:14:24,520 --> 00:14:31,200
+Yes, because it is full of growing. People grow
+
+146
+00:14:31,200 --> 00:14:35,340
+food. Most of the people grow food. So
+
+147
+00:14:35,340 --> 00:14:44,000
+agricultural town is okay. What about busy? Busy
+
+148
+00:14:44,000 --> 00:14:51,740
+town, crowded. A lot of action, motions. Yes, yes.
+
+149
+00:14:52,000 --> 00:14:59,380
+Busy. Busy town. Young town? No. Young people?
+
+150
+00:15:00,420 --> 00:15:05,980
+Young people? But small town? Okay. Small town?
+
+151
+00:15:06,080 --> 00:15:09,840
+Okay. But not young. So we have small? Okay.
+
+152
+00:15:10,740 --> 00:15:14,220
+Small, but not young. Young for people, small for
+
+153
+00:15:14,220 --> 00:15:14,660
+things.
+
+154
+00:15:20,430 --> 00:15:26,490
+Now, antique, antique now, antique building, but
+
+155
+00:15:26,490 --> 00:15:34,530
+not antique town. So this is old for things, old
+
+156
+00:15:34,530 --> 00:15:39,710
+for things, but not for towns, towns, old towns,
+
+157
+00:15:40,110 --> 00:15:43,390
+historic towns. We have historic town. Very good.
+
+158
+00:15:44,400 --> 00:15:48,880
+Hysteric. Hysteric, not hysterical. Hysteric means
+
+159
+00:15:48,880 --> 00:15:54,600
+important town. Hysteric means important. Hysteric
+
+160
+00:15:54,600 --> 00:15:59,040
+town. It means important town. Gaza is a hysteric
+
+161
+00:15:59,040 --> 00:16:02,240
+town. It means Gaza is an important town.
+
+162
+00:16:04,960 --> 00:16:11,180
+Cosmopolitan Okay cosmopolitan town cosmopolitan
+
+163
+00:16:11,180 --> 00:16:17,060
+town it means a town with Many people from all of
+
+164
+00:16:17,060 --> 00:16:22,140
+from all over the world from many nationalities So
+
+165
+00:16:22,140 --> 00:16:27,100
+New York has many nationalities Japanese
+
+166
+00:16:27,100 --> 00:16:35,800
+Palestinian Egyptian Sudanese, Lebanese, and it
+
+167
+00:16:35,800 --> 00:16:42,000
+has from Greek from all over the world. It has
+
+168
+00:16:42,000 --> 00:16:45,240
+nationality or nationalities from all over the
+
+169
+00:16:45,240 --> 00:16:50,360
+world. Not just one kind. Jeddah in Saudi Arabia
+
+170
+00:16:50,360 --> 00:16:57,040
+is a cosmopolitan City. Why? Because there you can
+
+171
+00:16:57,040 --> 00:17:02,080
+see many nationalities. A lot of nationalities.
+
+172
+00:17:02,260 --> 00:17:07,940
+Not one or two or three. No, many, many. So we
+
+173
+00:17:07,940 --> 00:17:17,340
+have the fourth one. Which one? Capital. And
+
+174
+00:17:17,340 --> 00:17:18,920
+excited.
+
+175
+00:17:20,360 --> 00:17:27,840
+One, two, three, four. Yes. So these four are not
+
+176
+00:17:27,840 --> 00:17:34,960
+for the town. You understand which one? Yeah. All
+
+177
+00:17:34,960 --> 00:17:38,880
+the others are connected with town, but these four
+
+178
+00:17:38,880 --> 00:17:42,380
+are not connected with town. So we can't say young
+
+179
+00:17:42,380 --> 00:17:48,110
+town. No, we can't say antique town. No Also, we
+
+180
+00:17:48,110 --> 00:17:51,310
+can't say excited. No, we say exciting town
+
+181
+00:17:51,310 --> 00:17:56,270
+Exciting town capital. No capital. We say
+
+182
+00:17:56,270 --> 00:18:02,030
+industrial town Industrial town hometown here we
+
+183
+00:18:02,030 --> 00:18:05,930
+can't we can't say antique we say old new small
+
+184
+00:18:05,930 --> 00:18:10,230
+And here we can say small not young You
+
+185
+00:18:10,230 --> 00:18:15,600
+understand? Easy or difficult? Easy. And these
+
+186
+00:18:15,600 --> 00:18:18,700
+adjectives are important also. Yes, who can read?
+
+187
+00:18:38,180 --> 00:18:38,900
+Cosmopolitan
+
+188
+00:18:42,170 --> 00:18:52,090
+Because it's a blatant town Yes Here
+
+189
+00:18:52,090 --> 00:18:57,510
+we say modern Modern not modern No modern in
+
+190
+00:18:57,510 --> 00:19:03,750
+Arabic in English modern in English modern modern
+
+191
+00:19:03,750 --> 00:19:06,450
+Yes again Yes
+
+192
+00:19:33,360 --> 00:19:43,130
+polluted not you pollution Pollution. Polluted.
+
+193
+00:19:43,390 --> 00:19:48,530
+Polluting. Not you. Not you.
+
+194
+00:19:49,730 --> 00:19:59,170
+Polluting. Polluted. Pollution. Enough? Clear?
+
+195
+00:19:59,530 --> 00:20:00,390
+Yes.
+
+196
+00:20:13,070 --> 00:20:20,150
+The third one, adjectives
+
+197
+00:
+
+223
+00:22:51,160 --> 00:22:55,680
+sophisticated. You have a good argument and you can 
+
+224
+00:22:55,680 --> 00:22:57,700
+speak very well and you can understand very well. 
+
+225
+00:22:58,000 --> 00:23:05,780
+So it's good. Bored. I am bored. I am bored 
+
+226
+00:23:05,780 --> 00:23:10,080
+because the weather is awful. I have so many 
+
+227
+00:23:10,080 --> 00:23:15,680
+works. I'm bored. So bored with people.
+
+228
+00:23:17,440 --> 00:23:22,140
+Some people are not good. See, they are not good.
+
+229
+00:23:22,720 --> 00:23:26,180
+Their speech is not good. Their behavior is not
+
+230
+00:23:26,180 --> 00:23:30,980
+good. So when I stay with them, I am bored. Why? 
+
+231
+00:23:31,810 --> 00:23:37,310
+Because they are boring. They are boring. They 
+
+232
+00:23:37,310 --> 00:23:43,050
+make me bored. So sometimes we can say boring 
+
+233
+00:23:43,050 --> 00:23:47,350
+people. But sometimes it's impolite. Impolite to 
+
+234
+00:23:47,350 --> 00:23:51,730
+say this in front of them. Uh-huh. It's not good 
+
+235
+00:23:51,730 --> 00:23:56,690
+to say you are boring. No, Your aunt is boring. No,
+
+236
+00:23:56,910 --> 00:24:00,070
+your sister is boring. No, it's not good, but it 
+
+237
+00:24:00,070 --> 00:24:04,990
+is sometimes found why boring because She is not
+
+238
+00:24:04,990 --> 00:24:08,610
+beautiful. She's not clever. She's all the time.
+
+239
+00:24:08,670 --> 00:24:12,410
+She speaks about one subject, She can't laugh. She 
+
+240
+00:24:12,410 --> 00:24:18,690
+can't make friends. So she is boring. So boring 
+
+241
+00:24:18,690 --> 00:24:22,630
+people are not good. You understand? But take 
+
+242
+00:24:22,630 --> 00:24:26,090
+care. It's not good to say boring for people, but
+
+243
+00:24:26,090 --> 00:24:34,750
+it is found. Yes, wealthy. Wealthy. She has a lot
+
+244
+00:24:34,750 --> 00:24:37,730
+of money. She's wealthy. I have a lot of money.
+
+245
+00:24:37,810 --> 00:24:44,460
+I'm wealthy. So we have young. sophisticated and 
+
+246
+00:24:44,460 --> 00:24:53,400
+shy, shy speaks little, don't speak too much, don't 
+
+247
+00:24:53,400 --> 00:25:03,100
+act too much, shy, you know, shy, yes, starving
+
+248
+00:25:03,100 --> 00:25:08,600
+starving means very, very hungry, extremely hungry
+
+249
+00:25:08,600 --> 00:25:15,100
+when he goes, when he arrives at home, he goes
+
+250
+00:25:15,100 --> 00:25:18,840
+directly to the kitchen. Directly to the kitchen. 
+
+251
+00:25:18,940 --> 00:25:20,380
+Why? Because he is starving. 
+
+252
+00:25:23,900 --> 00:25:30,200
+What about elderly? My elderly sister. My elderly 
+
+253
+00:25:30,200 --> 00:25:30,820
+sister.
+
+254
+00:25:33,650 --> 00:25:41,270
+Old, but she is polite, sophisticated, clever. But 
+
+255
+00:25:41,270 --> 00:25:45,830
+we can't say old sister. Why? When I say my old 
+
+256
+00:25:45,830 --> 00:25:52,450
+sister, it means old. Old, unmarried, not wanted. 
+
+257
+00:25:53,110 --> 00:25:59,250
+Old. Not good to say old. We say Elderly. My 
+
+258
+00:25:59,250 --> 00:26:04,490
+elderly sister. So this is a good adjective for old 
+
+259
+00:26:04,490 --> 00:26:08,350
+people. But don't say old people, old sister, old 
+
+260
+00:26:08,350 --> 00:26:17,770
+brother. No, say elderly. For respect. We have 
+
+261
+00:26:17,770 --> 00:26:20,050
+sociable. 
+
+262
+00:26:22,270 --> 00:26:29,910
+Sociable girl. Sociable girl, she can behave well
+
+263
+00:26:29,910 --> 00:26:35,090
+she can deal with people, she is polite, she can
+
+264
+00:26:35,090 --> 00:26:39,910
+talk very well, lovely, sociable, connected with the
+
+265
+00:26:39,910 --> 00:26:45,110
+society, she can live in a society so she is 
+
+266
+00:26:45,110 --> 00:26:51,030
+sociable, outgoing, outgoing. 
+
+267
+00:26:52,930 --> 00:26:59,250
+This one is shy. His brother is shy, but he is
+
+268
+00:26:59,250 --> 00:27:06,030
+outgoing. Outgoing means he knows everything. He 
+
+269
+00:27:06,030 --> 00:27:10,580
+knows everything. He can. behave well in every 
+
+270
+00:27:10,580 --> 00:27:15,780
+situation. He can wear well, he can communicate
+
+271
+00:27:15,780 --> 00:27:18,540
+with people, and he can go and out and go to the
+
+272
+00:27:18,540 --> 00:27:22,700
+market, speak very well. But shy? No, no, no, no, 
+
+273
+00:27:22,700 --> 00:27:28,000
+no, no. So shy? Not good. Outgoing? Good. But some
+
+274
+00:27:28,000 --> 00:27:32,860
+people prefer their wives to be shy, not to be
+
+275
+00:27:32,860 --> 00:27:36,840
+outgoing. Some other people prefer their wives to 
+
+276
+00:27:36,840 --> 00:27:43,660
+be outgoing. Outgoing. Know everything. But they 
+
+277
+00:27:43,660 --> 00:27:47,660
+don't want her to be shy. You understand? So we
+
+278
+00:27:47,660 --> 00:27:50,780
+have shy and outgoing.
+
+279
+00:27:51,820 --> 00:27:58,960
+What about rude? Rude. Something like boring. We 
+
+280
+00:27:58,960 --> 00:28:02,840
+don't say rude. But some people are rude. They
+
+281
+00:28:02,840 --> 00:28:06,940
+speak in a very bad way. They behave in a very bad
+
+282
+00:28:06,940 --> 00:28:13,630
+way. They speak loudly and not good. So we don't 
+
+283
+00:28:13,630 --> 00:28:18,990
+like rude people. We love polite people. Polite, 
+
+284
+00:28:19,250 --> 00:28:24,110
+not rude. So we have polite and rude. Rude means 
+
+285
+00:28:24,110 --> 00:28:25,690
+impolite.
+
+286
+00:28:32,190 --> 00:28:36,050
+All of it? Yes. Who can read some of these
+
+287
+00:28:36,050 --> 00:28:40,430
+adjectives with people? With my sister? With your 
+
+288
+00:28:40,430 --> 00:28:44,090
+brother? With your uncle? What is this grade?
+
+289
+00:28:57,010 --> 00:29:07,110
+So when I say people, 
+
+290
+00:29:07,330 --> 00:29:14,070
+I mean sister, brother, man, woman, worker
+
+291
+00:29:14,760 --> 00:29:18,660
+engineer, teacher, you understand? All people.
+
+292
+00:29:19,280 --> 00:29:24,140
+Again. Yes. Young people, bored people, wealthy 
+
+293
+00:29:24,140 --> 00:29:27,240
+people, boring people, sociable people, outgoing
+
+294
+00:29:27,240 --> 00:29:31,820
+people, rude people, tall people, starving people,
+
+295
+00:29:32,040 --> 00:29:38,920
+shy people, elderly people, sophisticated people.
+
+296
+00:29:39,140 --> 00:29:44,330
+Sophisticated. Yes. Speaks very well. Yeah. people 
+
+297
+00:29:44,330 --> 00:29:50,090
+sophisticated people, poor people, boring people 
+
+298
+00:29:50,090 --> 00:29:56,930
+with the poor people, sociable, sociable 
+
+299
+00:29:56,930 --> 00:30:02,550
+sociable people, outgoing people, rude people, tall
+
+300
+00:30:02,550 --> 00:30:09,510
+people, shy people, elderly, elderly people, thank you 
+
+301
+00:30:09,510 --> 00:30:13,860
+very much, Is it clear? So we have three kinds of 
+
+302
+00:30:13,860 --> 00:30:17,860
+adjectives, some adjectives connected with food,
+
+303
+00:30:17,860 --> 00:30:22,180
+some other connected with town, some other 
+
+304
+00:30:22,180 --> 00:30:26,440
+connected with people, after this we have exercise
+
+305
+00:30:26,440 --> 00:30:36,120
+about all these now
+
+306
+00:30:36,120 --> 00:30:43,650
+from these adjectives, we will choose some of for
+
+307
+00:30:43,650 --> 00:30:47,650
+this exercise, the adjective may be simple or 
+
+308
+00:30:47,650 --> 00:30:54,630
+comparative or superlative, Old, 
+
+309
+00:30:55,350 --> 00:31:01,450
+older, oldest, Tall, taller, tallest, Expensive,
+
+310
+00:31:01,750 --> 00:31:06,590
+more expensive, the most expensive, etc., so it 
+
+311
+00:31:06,590 --> 00:31:11,920
+might be simple with adjectives, it might be simple 
+
+312
+00:31:11,920 --> 00:31:17,820
+or comparative for two, or superlative with more
+
+313
+00:31:17,820 --> 00:31:27,020
+than two forms, number one, a and b conversation, a
+
+314
+00:31:27,020 --> 00:31:32,700
+and b, number a, nick is really quiet and shy
+
+315
+00:31:37,240 --> 00:31:41,820
+quiet and shy. He never says a word. Uh-huh. He is 
+
+316
+00:31:41,820 --> 00:31:49,620
+shy. So this is for, for what? For people. Yeah. 
+
+317
+00:31:50,240 --> 00:31:54,720
+His brother is much, when I use much, I use much
+
+318
+00:31:54,720 --> 00:32:02,060
+more, much more outgoing, outgoing, outgoing,
+
+319
+00:32:04,160 --> 00:32:05,800
+outgoing.
+
+320
+00:32:12,980 --> 00:32:20,900
+Number two, what's Carrie's boyfriend like? What is 
+
+321
+00:32:20,900 --> 00:32:27,080
+he like? About what? About people. What is he 
+
+322
+00:32:27,080 --> 00:32:30,980
+like? What is her boyfriend like? Her boyfriend? 
+
+323
+00:32:32,360 --> 00:32:38,280
+Well, he is tall
+
+324
+00:32:45,720 --> 00:32:52,320
+dark, and handsome. Okay, he's okay. Tall, dark, 
+
+325
+00:32:52,540 --> 00:32:58,580
+not white, and handsome, chic, good looking. But, 
+
+326
+00:32:59,080 --> 00:33:07,220
+what is but? But he is not very polite. He is
+
+327
+00:33:07,220 --> 00:33:19,060
+handsome, tall, dark, Yes, but he is not very
+
+328
+00:33:19,060 --> 00:33:19,600
+polite.
+
+329
+00:33:22,440 --> 00:33:27,600
+I say when I want to say someone is rude, we don't
+
+330
+00:33:27,600 --> 00:33:31,900
+say rude. We can say impolite, but it is better to 
+
+331
+00:33:31,900 --> 00:33:37,040
+use not very. So he's not very polite. She's not 
+
+332
+00:33:37,040 --> 00:33:41,620
+very beautiful. She's not very tall. Instead of
+
+333
+00:33:41,620 --> 00:33:46,580
+saying ugly, now we say she's not very beautiful.
+
+334
+00:33:47,160 --> 00:33:50,640
+He's short. Not good. Not good style. We say he's 
+
+335
+00:33:50,640 --> 00:33:55,480
+not very tall. He's impolite. No, he's not very
+
+336
+00:33:55,480 --> 00:34:01,310
+polite. Clever. He's not clever. He's stupid. No, 
+
+337
+00:34:01,470 --> 00:34:05,230
+don't say he's stupid. Say he is not very clever.
+
+338
+00:34:06,230 --> 00:34:11,210
+So he, but he is not very polite. In fact, he is 
+
+339
+00:34:11,210 --> 00:34:19,290
+even we have than, so we have root and are.
+
+340
+00:34:21,890 --> 00:34:27,990
+Ruder than Carrie. Oh, Carrie is rude. And he, her 
+
+341
+00:34:27,990 --> 00:34:32,390
+boyfriend is rude, but not rude, Ruder than her.
+
+342
+00:34:33,490 --> 00:34:42,010
+So bad and worse. She is bad, but he is worse. So 
+
+343
+00:34:42,010 --> 00:34:47,850
+you understand here, he is tall for people. Ruder
+
+344
+00:34:47,850 --> 00:34:54,000
+than for people, much more outgoing for people and
+
+345
+00:34:54,000 --> 00:34:59,460
+also shy. You understand? So the first two 
+
+346
+00:34:59,460 --> 00:35:05,780
+examples are about people. They are about people.
+
+347
+00:35:07,000 --> 00:35:11,900
+The third one. Oh, this is the answer.
+
+348
+00:35:22,430 --> 00:35:31,650
+Uh-huh. Shy and more outgoing because we have 
+
+349
+00:35:31,650 --> 00:35:41,590
+much, much more, much more. Tall and rudder 
+
+350
+00:35:41,590 --> 00:35:49,520
+than. We have rudder. Is it clear? So these two 
+
+351
+00:35:49,520 --> 00:35:57,920
+examples are about people. Next 
+
+352
+00:35:57,920 --> 00:36:06,120
+number three, How 
+
+353
+00:36:06,120 --> 00:36:07,580
+was your lunch? 
+
+354
+00:36:10,680 --> 00:36:16,460
+It was 
+
+355
+00:36:16,460 --> 00:36:31,110
+awful, it was awful. The pizza was disgusting.
+
+356
+00:36:37,010 --> 00:36:42,970
+So I
+
+357
+00:36:42,970 --> 00:36:46,890
+was disgusted. Why? Because the pizza was
+
+358
+00:36:48,200 --> 00:36:53,700
+disgusting. We were really starving.
+
+359
+00:36:58,960 --> 00:37:04,460
+Very hungry. Extremely hungry. But we still
+
+360
+00:37:04,460 --> 00:37:10,100
+couldn't eat it. We were very, very hungry, but we
+
+361
+00:37:10,100 --> 00:37:14,020
+couldn't eat their pizza. Why? Because the pizza
+
+362
+00:37:14,020 --> 00:37:23,460
+was disgusting. So this is about what? About food.
+
+363
+00:37:25,660 --> 00:37:33,760
+Next. These tomatoes are really delicious.
+
+364
+00:37:34,200 --> 00:37:35,320
+Delicious.
+
+365
+00:37:40,180 --> 00:37:44,940
+So and
+
+366
+00:37:44,940 --> 00:37:52,060
+here we have Good. Something smiling. So these
+
+367
+00:37:52,060 --> 00:37:57,400
+tomatoes are really delicious. Good tasting. Did 
+
+368
+00:37:57,400 --> 00:38:01,600
+you grow them yourselves? Did you grow them 
+
+369
+00:38:01,600 --> 00:38:06,820
+yourselves at home? Yes, we did. All our 
+
+370
+00:38:06,820 --> 00:38:15,060
+vegetables are home grown. Home grown.
+
+371
+00:38:17,730 --> 00:38:20,970
+Ah, we grow everything at home. All the 
+
+372
+00:38:20,970 --> 00:38:24,450
+vegetables, we grow them at home. We don't buy 
+
+373
+00:38:24,450 --> 00:38:28,750
+from the supermarket. No, we plant them ourselves.
+
+374
+00:38:29,250 --> 00:38:36,250
+So they are homegrown. Yes, but if it is a cake, a
+
+375
+00:38:36,250 --> 00:38:42,890
+cake, pizza, it is homemade. Homemade. This pizza
+
+376
+00:38:42,890 --> 00:38:50,040
+is homemade, not ready made. Ready-made, I buy it. 
+
+377
+00:38:50,320 --> 00:38:56,140
+But homemade, we prepare it at home. We prepare it 
+
+378
+00:38:56,140 --> 00:39:01,280
+at home. Our bread is homemade. But if it is 
+
+379
+00:39:01,280 --> 00:39:06,660
+vegetables, fruits, it is homegrown.
+
+380
+00:39:08,580 --> 00:39:14,760
+So this is about, about what? About food. Number 
+
+381
+00:39:14,760 --> 00:39:20,190
+five. Did you have a good time in London? This is
+
+382
+00:39:20,190 --> 00:39:26,610
+about what? About a town. About a town. Yeah. Did 
+
+383
+00:39:26,610 --> 00:39:31,230
+you have a good time in London? Yeah, we had a 
+
+384
+00:39:31,230 --> 00:39:40,630
+great time. There's so much to do. It's, it's, it's
+
+385
+00:39:40,630 --> 00:39:42,810
+really exciting.
+
+386
+00:39:48,220 --> 00:39:53,520
+Exciting or excited? No, I am excited because
+
+387
+00:39:53,520 --> 00:39:55,780
+London is exciting. 
+
+388
+00:39:59,480 --> 00:40:04,040
+And there are so many people from all over the 
+
+389
+00:40:04,040 --> 00:40:09,680
+world. Many people from all over the world. Many
+
+390
+00:40:09,680 --> 00:40:14,780
+people from all over the world. I think it's 
+
+391
+00:40:14,780 --> 00:40:15,900
+nearly as
+
+392
+00:40:27,100 --> 00:40:37,920
+as New York, and London are both cosmopolitan. They 
+
+393
+00:40:37,920 --> 00:40:42,560
+have many nationalities. They have many 
+
+394
+00:40:42,560 --> 00:40:48,090
+nationalities. Both of them are the same. London 
+
+395
+00:40:48,090 --> 00:40:50,450
+and New York.
+
+396
+00:40:53,330 --> 00:40:56,790
+Now after this, who can read?
+
+397
+00:41:00,510 --> 00:41:09,910
+How was your lunch ago? It was awful. The pizza
+
+398
+00:41:09,910 --> 00:41:11,790
+was disgusting. 
+
+399
+00:41:14,330 --> 00:41:22,510
+But we still pulling it deep, among these tomatoes 
+
+400
+00:41:22,510 --> 00:41:27,950
+are These
+
+401
+00:41:27,950 --> 00:41:37,390
+tomatoes are really delicious. Did you grow them
+
+402
+00:41:37,390 --> 00:41:42,390
+yourselves? Yes, we did. All our vegetables are
+
+403
+00:41:42,390 --> 00:41:47,330
+home grown. Yes, thank you. Number five.
+
+404
+00:42:04,250 --> 00:42:10,470
+Exciting city or exciting town. No, city because it
+
+405
+00:42:10,470 --> 00:42:15,050
+is capital. What is the capital city of England?
+
+406
+00:42:16,490 --> 00:42:21,650
+London. So many people from all over the world. I
+
+407
+00:42:21,650 --> 00:42:28,530
+think it's nearly as cosmopolitan as New York.
+
+408
+00:42:28,850 --> 00:42:36,490
+Both are the same. So the answer again 
+
+409
+00:42:43,160 --> 00:42:53,420
+Who can read? Again Again,
+
+410
+00:42:55,200 --> 00:42:56,020
+someone else? 
+
+411
+00:43:02,480 --> 00:43:11,920
+Amin, Amin Astafadi, yes? Just think
+
+412
+00
+
+445
+00:47:05,060 --> 00:47:09,340
+Then press the number of your card. Something like 
+
+446
+00:47:09,340 --> 00:47:16,860
+this. So it is on the telephone. Yes, we say it is
+
+447
+00:47:16,860 --> 00:47:22,480
+on a telephone. On a telephone.
+
+448
+00:47:25,080 --> 00:47:25,880
+Poking.
+
+449
+00:47:29,870 --> 00:47:36,530
+Line. You say poking line. You reserve. You reserve
+
+450
+00:47:36,530 --> 00:47:40,170
+something we say poking. Poking means reserving 
+
+451
+00:47:40,170 --> 00:47:47,710
+keeping. So telephone poking line, poking for
+
+452
+00:47:47,710 --> 00:47:54,430
+reserving a place, a seat in the cinema or theater.
+
+453
+00:47:56,360 --> 00:48:01,040
+I want to book a ticket. I want to buy a ticket.
+
+454
+00:48:01,880 --> 00:48:07,520
+You understand? So this is on a telephone, but not 
+
+455
+00:48:07,520 --> 00:48:13,020
+generally, no, in a booking line. The line for
+
+456
+00:48:13,020 --> 00:48:17,540
+booking, for buying tickets. I can buy tickets,
+
+457
+00:48:18,300 --> 00:48:22,800
+books, many things by the telephone. So the
+
+458
+00:48:22,800 --> 00:48:28,150
+tickets is here on a telephone booking line.
+
+459
+00:48:31,250 --> 00:48:34,510
+Please place 
+
+460
+00:48:34,510 --> 00:48:42,010
+your tray tables on the passengers. Place, put
+
+461
+00:48:42,010 --> 00:48:49,050
+your tables, tray tables on the train. The tray in 
+
+462
+00:48:49,050 --> 00:48:54,310
+front of you, we call it tray table. Tray table, all
+
+463
+00:48:54,310 --> 00:48:58,690
+the tray tables in front of you, place your tray 
+
+464
+00:48:58,690 --> 00:49:04,950
+tables in their fully upright position. Not like this. No,
+
+465
+00:49:04,950 --> 00:49:11,330
+like this. Some animals walk upright. Upright like
+
+466
+00:49:11,330 --> 00:49:18,020
+this. Some people don't or can't walk upright like
+
+467
+00:49:18,020 --> 00:49:21,560
+us. They call it this. Huh, no, no I don't want like
+
+468
+00:49:21,560 --> 00:49:26,760
+this, down right. No, upright. Yes. Upright. Uh-huh, like 
+
+469
+00:49:26,760 --> 00:49:33,780
+this. So, place in his put your trays where upright. 
+
+470
+00:49:33,780 --> 00:49:39,480
+Fully, completely upright, not like this. No.
+
+471
+00:49:39,480 --> 00:49:48,300
+Completely. Uh-huh. And look. Closed, closed positions.
+
+472
+00:49:48,300 --> 00:49:53,540
+So, if this is the tray in front of you, don't make
+
+473
+00:49:53,540 --> 00:49:57,940
+it like this. No. Make it like this and close it. The 
+
+474
+00:49:57,940 --> 00:50:02,640
+position of what? Of upright and closed. Because we 
+
+475
+00:50:02,640 --> 00:50:10,000
+are descending, yeah. So fix it upright and close it. 
+
+476
+00:50:10,000 --> 00:50:11,920
+So what is it?
+
+477
+00:50:15,220 --> 00:50:24,480
+A plane. On a plane they ask you to place your
+
+478
+00:50:24,480 --> 00:50:30,060
+table upright and close it, close it. So we call it 
+
+479
+00:50:30,060 --> 00:50:36,660
+upright and locked positions, yeah. Upright and
+
+480
+00:50:36,660 --> 00:50:42,020
+locked positions. How would you like your money?
+
+481
+00:50:44,110 --> 00:50:51,990
+Fives. Fifties. Coins. Hundreds. How you write? 
+
+482
+00:50:52,750 --> 00:50:56,830
+How would you like your money? I'm ready to give
+
+483
+00:50:56,830 --> 00:51:01,330
+you any kind. Twenties? Twenties? Okay. Twenties.
+
+484
+00:51:01,630 --> 00:51:10,530
+Coins? Coins. So, it is in a bank. In a bank. 
+
+485
+00:51:13,540 --> 00:51:18,640
+In a bank, sometimes the cashier asks you, how
+
+486
+00:51:18,640 --> 00:51:26,100
+would you like your money? Just looking. Thanks.
+
+487
+00:51:27,260 --> 00:51:37,380
+Just looking. Thanks. Was it in reply to? In reply
+
+488
+00:51:37,380 --> 00:51:39,720
+to? To what?
+
+489
+00:51:42,585 --> 00:51:50,050
+Assistant. We call it sales assistant. Sales 
+
+490
+00:51:50,050 --> 00:51:52,150
+assistant.
+
+491
+00:51:55,850 --> 00:52:01,430
+In reply to sale assistant. Where?
+
+492
+00:52:05,330 --> 00:52:10,210
+In reply to a sale assistant asking
+
+493
+00:52:13,010 --> 00:52:16,970
+While he is asking you, what is he asking? What is
+
+494
+00:52:16,970 --> 00:52:29,050
+the question? Can I help you? The last one. So
+
+495
+00:52:29,050 --> 00:52:32,570
+when you are in a remote street, can I help you?
+
+496
+00:52:33,410 --> 00:52:37,550
+Just looking. Just looking. I'm not going to buy.
+
+497
+00:52:37,810 --> 00:52:41,510
+Just looking. Most people go to the markets, just
+
+498
+00:52:41,510 --> 00:52:45,860
+looking. The last one, we apologize for the delay 
+
+499
+00:52:45,860 --> 00:52:51,440
+on the 18.13 service. This is on a station 
+
+500
+00:52:51,440 --> 00:52:57,560
+announcement. On a station announcement.
+
+501
+00:53:01,940 --> 00:53:07,480
+On the station, train station. And if we want to,
+
+502
+00:53:08,580 --> 00:53:11,800
+the short form is the answer, this answer.
+
+503
+00:53:17,670 --> 00:53:24,970
+Again. So the
+
+504
+00:53:24,970 --> 00:53:32,290
+first one is on the radio. The second one is on a 
+
+505
+00:53:32,290 --> 00:53:36,990
+telephone booking line. The third one is on a 
+
+506
+00:53:36,990 --> 00:53:39,950
+plane. Next.
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/wdl_kanQ7Tc.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/wdl_kanQ7Tc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3bf23862f875b674ba3962cffd6055e0b677ca08
--- /dev/null
+++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/wdl_kanQ7Tc.srt
@@ -0,0 +1,1619 @@
+
+1
+00:00:20,770 --> 00:00:25,070
+Assalamualaikum warahmatullahi wabarakatuh Good
+
+2
+00:00:25,070 --> 00:00:31,790
+afternoon Today inshallah We will discuss some
+
+3
+00:00:31,790 --> 00:00:38,210
+exercises about vocabulary Phonetic symbols and
+
+4
+00:00:38,210 --> 00:00:48,330
+everyday language or everyday English At first We 
+
+5
+00:00:48,330 --> 00:00:48,630
+will
+
+6
+00:00:51,840 --> 00:01:01,680
+We will deal with parts of speech. Parts of
+
+7
+00:01:01,680 --> 00:01:03,340
+speech.
+
+8
+00:01:08,360 --> 00:01:21,160
+We will take a noun. Number two, verb. Three, 
+
+9
+00:01:22,060 --> 00:01:22,640
+adjective.
+
+10
+00:01:25,800 --> 00:01:36,020
+And number four, adverb. So, we will deal with 
+
+11
+00:01:36,020 --> 00:01:41,660
+these four parts of speech. The first one is noun.
+
+12
+00:01:42,640 --> 00:01:49,690
+Noun, it is a name of something or some people or
+
+13
+00:01:49,690 --> 00:01:56,750
+some animals this noun can 
+
+14
+00:01:56,750 --> 00:02:02,710
+be used as a subject or as an object of the
+
+15
+00:02:02,710 --> 00:02:14,530
+sentence number two a verb the verb can 
+
+16
+00:02:14,530 --> 00:02:20,480
+be in the present or in the past it can be regular
+
+17
+00:02:20,480 --> 00:02:26,800
+or irregular can be in all the tenses present 
+
+18
+00:02:26,800 --> 00:02:31,480
+simple past simple present perfect present 
+
+19
+00:02:31,480 --> 00:02:37,340
+continuous past continuous and can be in the
+
+20
+00:02:37,340 --> 00:02:44,960
+active or in the passive now the adjective the
+
+21
+00:02:44,960 --> 00:02:50,660
+adjective may be short adjective Long adjective.
+
+22
+00:02:52,280 --> 00:02:58,420
+These adjectives also can be regular or irregular. 
+
+23
+00:03:00,960 --> 00:03:02,640
+The adverb.
+
+24
+00:03:05,200 --> 00:03:08,300
+So the adjective also describes the noun.
+
+25
+00:03:09,680 --> 00:03:13,440
+Describes the noun. Or maybe the complement of the 
+
+26
+00:03:13,440 --> 00:03:21,850
+sentence. The adverb. is an additional verb that
+
+27
+00:03:21,850 --> 00:03:26,130
+describes everything except the noun. It may 
+
+28
+00:03:26,130 --> 00:03:31,710
+describe the verb or the adjective or another
+
+29
+00:03:31,710 --> 00:03:32,150
+adverb.
+
+30
+00:03:35,330 --> 00:03:46,130
+So the noun may be small or big. The verb may be 
+
+31
+00:03:46,130 --> 00:03:54,420
+one or more than one. The adjective may end with 
+
+32
+00:03:54,420 --> 00:04:06,180
+full, all or OUS or ANT 
+
+33
+00:04:06,180 --> 00:04:18,080
+or ENT or it may end with ED or ING so these are
+
+34
+00:04:18,080 --> 00:04:24,460
+for the adjectives as for the adverb generally it
+
+35
+00:04:24,460 --> 00:04:33,300
+ends with ly or some other mid position adverbs 
+
+36
+00:04:33,300 --> 00:04:45,630
+like still yet just only etc the verb might be in
+
+37
+00:04:45,630 --> 00:04:53,170
+all the tenses we studied before. The noun, maybe
+
+38
+00:04:53,170 --> 00:04:56,070
+any noun according to their meaning.
+
+39
+00:04:59,330 --> 00:05:05,610
+Now, if I write the word agi.
+
+40
+00:05:09,310 --> 00:05:16,710
+Agi. This agi is not an English word. Something
+
+41
+00:05:16,710 --> 00:05:23,130
+like this. Not English. Not Arabic. We want to use
+
+42
+00:05:23,130 --> 00:05:27,910
+it in four sentences just to say it might be a
+
+43
+00:05:27,910 --> 00:05:33,630
+verb or a noun or an adjective or an adverb. How?
+
+44
+00:05:34,070 --> 00:05:37,650
+From its shape. So 
+
+45
+00:05:40,840 --> 00:05:46,540
+Let's deal with these suffixes. Now, let's look at 
+
+46
+00:05:46,540 --> 00:05:51,200
+the passive speech and meaning. We use the word
+
+47
+00:05:51,200 --> 00:05:58,360
+agi. These sentences all contain the nonsense word 
+
+48
+00:05:58,360 --> 00:05:59,180
+agi.
+
+49
+00:06:01,820 --> 00:06:07,240
+Is agi 
+
+50
+00:06:07,240 --> 00:06:15,340
+used as an adverb? Or an adjective, a noun, or an 
+
+51
+00:06:15,340 --> 00:06:21,780
+adverb. How do you know? Now, ugly is not an
+
+52
+00:06:21,780 --> 00:06:27,720
+English word. In this exercise, we want to look at
+
+53
+00:06:27,720 --> 00:06:32,670
+the words in general. Number one, I couldn't hear 
+
+54
+00:06:32,670 --> 00:06:37,750
+the film because the man next to me was eating his 
+
+55
+00:06:37,750 --> 00:06:43,790
+agi so loudly. He was eating his agi. So agi here
+
+56
+00:06:43,790 --> 00:06:51,450
+is a noun. Yes. Number two, there was a lot of
+
+57
+00:06:51,450 --> 00:06:55,450
+snow on the road. Unfortunately, 
+
+58
+00:06:58,480 --> 00:07:04,080
+Uh-huh. On some ice and crashed into a tree. Ugly
+
+59
+00:07:04,080 --> 00:07:11,920
+here is a verb. Yes. So here is a verb. And here
+
+60
+00:07:11,920 --> 00:07:19,140
+is a noun. Noun. Number three. When Pierre and
+
+61
+00:07:19,140 --> 00:07:26,790
+Madeleine met, they feel ugly in love. and got 
+
+62
+00:07:26,790 --> 00:07:36,650
+married one month later ugly is adverb number
+
+63
+00:07:36,650 --> 00:07:45,970
+four after an ugly day at work with meetings and 
+
+64
+00:07:45,970 --> 00:07:49,690
+phone calls all day I was ready for a quiet 
+
+65
+00:07:49,690 --> 00:07:52,750
+evening so ugly here is an adjective 
+
+66
+00:07:57,190 --> 00:08:00,770
+Now, can you guess what agi means in the four 
+
+67
+00:08:00,770 --> 00:08:05,990
+sentences? Yes. The first one is a noun. The
+
+68
+00:08:05,990 --> 00:08:10,830
+second one is a verb. The third one is an adverb. 
+
+69
+00:08:11,290 --> 00:08:15,610
+And the fourth one is an adjective. Now, which
+
+70
+00:08:15,610 --> 00:08:19,190
+real English word, real English noun, which real 
+
+71
+00:08:19,190 --> 00:08:23,090
+English word goes in each sentence? If you look at 
+
+72
+00:08:23,090 --> 00:08:25,090
+the first one, the noun, which noun? 
+
+73
+00:08:28,530 --> 00:08:33,470
+Yes. This one. This one. Number one. Popcorn.
+
+74
+00:08:34,590 --> 00:08:41,830
+Something we eat. Number two. Number two. A verb.
+
+75
+00:08:42,970 --> 00:08:51,330
+Yes. Skidded. Skidded. Number three. 
+
+76
+00:08:55,030 --> 00:09:00,130
+Passionately. Passionately. Passion. Passionately. 
+
+77
+00:09:01,390 --> 00:09:04,130
+The last one number four. 
+
+78
+00:09:06,270 --> 00:09:14,210
+Hectic. It's number four. So I want you to read 
+
+79
+00:09:14,210 --> 00:09:18,850
+these sentences with the real words. with the real 
+
+80
+00:09:18,850 --> 00:09:22,590
+worlds, not the nonsense worlds. So this world is 
+
+81
+00:09:22,590 --> 00:09:27,270
+now, we don't want it. We don't want this. And we 
+
+82
+00:09:27,270 --> 00:09:28,050
+don't want this.
+
+83
+00:09:31,550 --> 00:09:36,810
+Yes, one. Yes. I couldn't hear the film because 
+
+84
+00:09:36,810 --> 00:09:40,630
+the man next to me was eating his popcorn so
+
+85
+00:09:40,630 --> 00:09:46,360
+loudly. Yes. Number two. There was a lot of snow 
+
+86
+00:09:46,360 --> 00:09:53,960
+on the road. Unfortunately, I skidded 
+
+87
+00:09:53,960 --> 00:09:58,640
+on some ice and crashed into a tree. Very good.
+
+88
+00:09:58,940 --> 00:10:06,820
+Number three? Number three? Yes. When Beer and
+
+89
+00:10:06,820 --> 00:10:09,880
+Madeleine met, they felt
+
+90
+00:10:13,320 --> 00:10:19,380
+Passionately in love and got married one month
+
+91
+00:10:19,380 --> 00:10:26,440
+later. Later, yes. Number four. After an hectic
+
+92
+00:10:26,440 --> 00:10:31,840
+day at work with meetings and fun concerts all 
+
+93
+00:10:31,840 --> 00:10:34,980
+day, all day, I was ready for a quiet evening. 
+
+94
+00:10:35,500 --> 00:10:41,700
+Very good. Very good. So today we studied four 
+
+95
+00:10:41,700 --> 00:10:48,640
+parts of speech. The noun, adjective, the verb,
+
+96
+00:10:48,900 --> 00:10:53,940
+and the adverb. The noun for naming something. The 
+
+97
+00:10:53,940 --> 00:10:58,140
+adjective for describing something. The verb for 
+
+98
+00:10:58,140 --> 00:11:02,680
+the action. And the adverb to describe any word in
+
+99
+00:11:02,680 --> 00:11:06,300
+a sentence except for the noun.
+
+100
+00:11:14,540 --> 00:11:17,560
+And these are the answers.
+
+101
+00:11:24,680 --> 00:11:33,020
+Yes, a noun, it means popcorn. A verb in the past, 
+
+102
+00:11:33,120 --> 00:11:37,220
+it means skidded. An adverb, it means 
+
+103
+00:11:37,220 --> 00:11:43,200
+passionately. An adjective, it means hectic. It 
+
+104
+00:11:43,200 --> 00:11:53,630
+means very busy. Yes now, today,
+
+105
+00:11:53,890 --> 00:12:00,610
+Inshallah, we will study a new exercise. It's
+
+106
+00:12:00,610 --> 00:12:05,410
+about phonetic, 
+
+107
+00:12:05,830 --> 00:12:08,910
+phonetic symbols. Phonetic symbols.
+
+108
+00:12:12,730 --> 00:12:17,130
+Spelling and pronunciation. In these groups, three 
+
+109
+00:12:17,130 --> 00:12:23,050
+words rhyme. Three words rhyme. It has the same 
+
+110
+00:12:23,050 --> 00:12:27,790
+rhythm, the same sound. Three of these words are
+
+111
+00:12:27,790 --> 00:12:32,350
+the same sound, have the same sound. They rhyme.
+
+112
+00:12:33,670 --> 00:12:40,590
+But one is different. Three have the same sound, 
+
+113
+00:12:41,030 --> 00:12:47,670
+but one is different. Work with a partner in twos 
+
+114
+00:12:47,670 --> 00:12:54,350
+and read them aloud. Underline, put a line under 
+
+115
+00:12:54,350 --> 00:12:58,470
+the word, the word in each group which has a 
+
+116
+00:12:58,470 --> 00:13:05,150
+different vowel sound. The different one, we 
+
+117
+00:13:05,150 --> 00:13:11,500
+underline it. And the other three, okay. So here I
+
+118
+00:13:11,500 --> 00:13:22,040
+will work with you. Good food would stood. So here 
+
+119
+00:13:22,040 --> 00:13:23,360
+I'm dealing with.
+
+120
+00:13:27,460 --> 00:13:32,740
+So English language is not phonetic. We don't 
+
+121
+00:13:32,740 --> 00:13:36,900
+pronounce every letter and every combination of
+
+122
+00:13:36,900 --> 00:13:41,200
+two or three letters may have different sound. So 
+
+123
+00:13:41,200 --> 00:13:50,400
+this is O O O O O O O O O O O O O O O O O O O O O 
+
+124
+00:13:50,400 --> 00:13:56,740
+O O O
+
+125
+00:13:56,740 --> 00:13:56,800
+O O O O O O O O O O O O O O O O O O O O O O O O O
+
+126
+00:13:56,800 --> 00:13:57,020
+O O O O O O O O O O O O O O O O O O O O O O O O O
+
+127
+00:13:57,020 --> 00:13:57,520
+O O O O O O O O O O O O O O O O O O O O O O O O O
+
+128
+00:13:57,520 --> 00:13:58,340
+O O O O O O O O O O O O O O O O O O O O O O O O O
+
+129
+00:13:58,340 --> 00:13:58,840
+O O O O O O O O O O O O O O O O O O O O O O O O O
+
+130
+00:13:58,840 --> 00:13:58,900
+O O O
+
+131
+00:14:02,170 --> 00:14:10,310
+Yes? So if I look here, the symbol for the sound.
+
+132
+00:14:11,910 --> 00:14:15,370
+The symbol for the sound. We have today two
+
+133
+00:14:15,370 --> 00:14:19,530
+symbols. The first one is U.
+
+134
+00:14:27,730 --> 00:14:32,230
+We write the symbol and two slashes between two 
+
+135
+00:14:32,230 --> 00:14:36,630
+slashes. This symbol is just for pronunciation. 
+
+136
+00:14:37,370 --> 00:14:41,130
+When I open the dictionary and I want to look some
+
+137
+00:14:41,130 --> 00:14:46,490
+words up, I find some of these symbols. Today we
+
+138
+00:14:46,490 --> 00:14:49,290
+will study just these symbols, not all of them.
+
+139
+00:14:49,970 --> 00:14:53,790
+And if you want to study more, we can refer to 
+
+140
+00:14:53,790 --> 00:14:55,810
+page 159. 
+
+141
+00:14:57,310 --> 00:15:02,750
+So the sound, this, the symbol, this is U.
+
+142
+00:15:05,730 --> 00:15:07,250
+And what about this? 
+
+143
+00:15:11,170 --> 00:15:17,930
+It's U. These are international symbols. This is 
+
+144
+00:15:17,930 --> 00:15:24,110
+for U and this is for U. So if I ask you to look 
+
+145
+00:15:24,110 --> 00:15:24,950
+up the word
+
+146
+00:15:30,940 --> 00:15:37,660
+This one. Is it like this or like this? If it is 
+
+147
+00:15:37,660 --> 00:15:43,340
+new, I must look it up in the dictionary. It is
+
+148
+00:15:43,340 --> 00:15:55,080
+like this. So it is tomb. It is tomb. Yes. Now, if 
+
+149
+00:15:55,080 --> 00:15:58,240
+I want to choose one symbol, is it this or this?
+
+150
+00:16:00,420 --> 00:16:08,340
+Uh-huh. This one is like this one. Yes. So this is 
+
+151
+00:16:08,340 --> 00:16:13,840
+the symbol and this is the word. So I can deal 
+
+152
+00:16:13,840 --> 00:16:17,000
+with two things, these for the symbols and these
+
+153
+00:16:17,000 --> 00:16:21,100
+for the words. You understand? So in the 
+
+154
+00:16:21,100 --> 00:16:25,320
+dictionary, when I saw, when I want to look it to
+
+155
+00:16:25,320 --> 00:16:28,500
+look good up in the dictionary, it's written like,
+
+156
+00:16:29,540 --> 00:16:29,860
+uh-huh.
+
+157
+00:16:33,620 --> 00:16:38,220
+What does it mean? Good. What about this?
+
+158
+00:16:40,860 --> 00:16:46,940
+Wood. And what about this? Stone.
+
+159
+00:16:52,040 --> 00:16:56,080
+It's clear? Yes. What about these words?
+
+160
+00:16:59,300 --> 00:17:03,320
+Two. Two. And this?
+
+161
+00:17:08,380 --> 00:17:12,020
+Moon. Very good. And what about this?
+
+162
+00:17:16,880 --> 00:17:22,360
+Tool. Now we studied two symbols. What are they? U 
+
+163
+00:17:22,360 --> 00:17:31,600
+and U. Example? Good wood stood and food. Yes.
+
+164
+00:17:33,760 --> 00:17:35,500
+It's okay? Yes.
+
+165
+00:17:41,520 --> 00:17:45,060
+Now, the other one.
+
+166
+00:17:47,620 --> 00:17:59,520
+Bread, head, read, read. So two sounds. Which one
+
+167
+00:17:59,520 --> 00:18:07,840
+is different? Read. This one. Very good. So what 
+
+168
+00:18:07,840 --> 00:18:15,880
+is the symbol of E? The symbol of E. It's this
+
+169
+00:18:15,880 --> 00:18:22,820
+one. So we studied some symbols. What are they?
+
+170
+00:18:28,770 --> 00:18:37,630
+And now E This
+
+171
+00:18:37,630 --> 00:18:45,890
+is bread Is it like this? So this is a symbol for 
+
+172
+00:18:45,890 --> 00:19:00,730
+E So E read E bread Head bread Okay? If I write 
+
+173
+00:19:00,730 --> 00:19:07,990
+Meat
+
+174
+00:19:07,990 --> 00:19:14,690
+Deal 
+
+175
+00:19:14,690 --> 00:19:20,470
+Meat
+
+176
+00:19:26,500 --> 00:19:28,660
+C. What about this?
+
+177
+00:19:32,480 --> 00:19:35,680
+Sid. And this? 
+
+178
+00:19:38,340 --> 00:19:40,780
+Dead. And this?
+
+179
+00:19:43,800 --> 00:19:46,960
+Head. No.
+
+180
+00:19:49,700 --> 00:19:50,460
+The word.
+
+181
+00:19:56,610 --> 00:20:06,970
+Head. Head. And this? Bread. When we write the 
+
+182
+00:20:06,970 --> 00:20:11,150
+symbols, we should write them between two slashes. 
+
+183
+00:20:11,890 --> 00:20:17,310
+It means that these are not letters. They are
+
+184
+00:20:17,310 --> 00:20:25,540
+symbols. They are symbols. Yes. Okay. Finished? So 
+
+185
+00:20:25,540 --> 00:20:31,760
+this is E and this is A. If I want to odd one out 
+
+186
+00:20:31,760 --> 00:20:36,000
+here, I choose read because read is the different. 
+
+187
+00:20:37,120 --> 00:20:37,980
+Now, okay. 
+
+188
+00:20:41,780 --> 00:20:50,540
+Number three. We have two sounds A, A and A.
+
+189
+00:20:53,120 --> 00:20:56,200
+Made. Blade. Set.
+
+190
+00:20:59,000 --> 00:21:06,420
+Which one out? Set. Yes. So this is different. And 
+
+191
+00:21:06,420 --> 00:21:15,100
+here? E. So this E for set. What about these? A 
+
+192
+00:21:15,100 --> 00:21:20,980
+for A. So if I say
+
+193
+00:21:26,750 --> 00:21:31,710
+Name And this?
+
+194
+00:21:39,150 --> 00:21:49,610
+Same Mew
+
+195
+00:21:
+
+223
+00:25:59,750 --> 00:26:08,190
+ear, deer, here, near, ear, but the other one air,
+
+224
+00:26:08,430 --> 00:26:17,930
+air, pear, where, yes number six a,
+
+225
+00:26:18,490 --> 00:26:28,290
+o, air, o, one sound, one sound, but it is long if
+
+226
+00:26:28,290 --> 00:26:33,430
+the sound, the symbol, one word, one thing, it is
+
+227
+00:26:33,430 --> 00:26:40,270
+short. If there are two, we say them diphthongs.
+
+228
+00:26:41,150 --> 00:26:45,190
+We call them diphthongs. If there's one, short
+
+229
+00:26:45,190 --> 00:26:49,590
+vowel. Short vowel, if there's one. If there are
+
+230
+00:26:49,590 --> 00:27:02,550
+two, diphthong. Diphthong. We say short vowel.
+
+231
+00:27:04,190 --> 00:27:08,130
+This is one. For one. If there are two.
+
+232
+00:27:13,070 --> 00:27:18,890
+Diphthong. How many? Two. If it is one with a
+
+233
+00:27:18,890 --> 00:27:32,150
+colon, it is long. Vowel if it has what colon
+
+234
+00:27:32,150 --> 00:27:38,770
+so the colon one sound but long uh-huh one sound
+
+235
+00:27:38,770 --> 00:27:44,090
+but long what about diphthong two sounds two
+
+236
+00:27:44,090 --> 00:27:54,960
+sounds next to each other so here a o one a Oh,
+
+237
+00:27:55,580 --> 00:28:00,880
+but here Oh,
+
+238
+00:28:02,960 --> 00:28:10,440
+oh, two will change. Oh colon one sound one sound
+
+239
+00:28:10,440 --> 00:28:16,020
+with colon it is long vowel if there are two
+
+240
+00:28:16,020 --> 00:28:24,570
+diphthong it is one short so here work. Where is
+
+241
+00:28:24,570 --> 00:28:31,430
+work? The first one. Yes, this is work. Work.
+
+242
+00:28:31,910 --> 00:28:44,150
+Fawk. Walk. Fawk. Work. Fawk. Walk. Fawk.
+
+243
+00:28:48,010 --> 00:29:01,300
+Now, this is air and this is o one but long one
+
+244
+00:29:01,300 --> 00:29:08,420
+after this exercise we will deal with the answers
+
+245
+00:29:08,420 --> 00:29:20,140
+now
+
+246
+00:29:30,740 --> 00:29:34,660
+I want someone to read the first one, the symbols
+
+247
+00:29:34,660 --> 00:29:37,480
+and the words. Yes.
+
+248
+00:29:41,140 --> 00:29:47,260
+Yes. So we underlined food. And here, if you want
+
+249
+00:29:47,260 --> 00:29:52,100
+to underline, underline what? The second. Number
+
+250
+00:29:52,100 --> 00:30:03,390
+two. Yes. E, E, read, head, read, read. The
+
+251
+00:30:03,390 --> 00:30:07,090
+underlying word is read. Yes. And the symbol?
+
+252
+00:30:09,990 --> 00:30:18,010
+This is the first. Number three. Yes.
+
+253
+00:30:20,630 --> 00:30:32,480
+Very good. Yes. So this is paid, made, played, set
+
+254
+00:30:32,480 --> 00:30:37,600
+number four
+
+255
+00:30:37,600 --> 00:30:43,960
+phone,
+
+256
+00:30:44,180 --> 00:30:47,880
+phone, phone, phone, phone, phone, phone, phone,
+
+257
+00:30:47,880 --> 00:30:50,180
+phone, phone, phone, phone, phone, phone, phone,
+
+258
+00:30:51,020 --> 00:30:51,660
+phone, phone, phone, phone, phone, phone, phone,
+
+259
+00:30:51,660 --> 00:30:52,680
+phone, phone, phone, phone, phone, phone, phone,
+
+260
+00:30:52,680 --> 00:30:56,100
+phone, phone, phone, phone, phone, phone, phone,
+
+261
+00:30:56,100 --> 00:30:56,120
+phone, phone, phone, phone, phone, phone, phone,
+
+262
+00:30:56,120 --> 00:31:03,020
+phone, phone two movements so this one is for what
+
+263
+00:31:03,020 --> 00:31:12,420
+about this pair
+
+264
+00:31:12,420 --> 00:31:18,260
+underline
+
+265
+00:31:18,260 --> 00:31:24,820
+it and here the first one the first one very good
+
+266
+00:31:24,820 --> 00:31:30,420
+the last one the last one. Yes. Yes.
+
+267
+00:31:35,220 --> 00:31:47,580
+Again. Work. The first one. Here is English
+
+268
+00:31:47,580 --> 00:31:53,870
+spelling is not phonetic. What does it mean? It
+
+269
+00:31:53,870 --> 00:31:59,290
+means the same combination, two or three, the same
+
+270
+00:31:59,290 --> 00:32:04,390
+combination of letters can be pronounced in
+
+271
+00:32:04,390 --> 00:32:10,190
+different way. In different way. So how can I say
+
+272
+00:32:10,190 --> 00:32:17,550
+this? Double O. I don't know. In the sentence. In
+
+273
+00:32:17,550 --> 00:32:19,830
+the sentence. How can I pronounce this?
+
+274
+00:32:22,800 --> 00:32:27,620
+I don't know. I want a sentence and this one I
+
+275
+00:32:27,620 --> 00:32:35,840
+don't know why because it might be E or I, A or A,
+
+276
+00:32:36,680 --> 00:32:46,520
+U or U now let's come to another exercise to deal
+
+277
+00:32:46,520 --> 00:32:54,770
+with this so when I ask you, odd one out, odd one
+
+278
+00:32:54,770 --> 00:33:04,090
+out, it means underline or circle the word which
+
+279
+00:33:04,090 --> 00:33:10,830
+has a different sound. The word which has a
+
+280
+00:33:10,830 --> 00:33:14,470
+different sound. If I say odd one out and I
+
+281
+00:33:14,470 --> 00:33:16,910
+underline the letter like this,
+
+282
+00:33:21,630 --> 00:33:26,550
+Odd one out. Read. Aha. Here.
+
+283
+00:33:29,590 --> 00:33:34,890
+Odd one out. Food. Yes. Here.
+
+284
+00:33:38,450 --> 00:33:46,210
+Odd one out. Shed. I read them and find the
+
+285
+00:33:46,210 --> 00:33:54,090
+different one. Again. Foam. Done, sun, one, phone,
+
+286
+00:33:55,310 --> 00:34:04,650
+deer, here, pear, near, pear, work, fork, walk,
+
+287
+00:34:05,370 --> 00:34:11,950
+pork. It is where. You understand? So there is
+
+288
+00:34:11,950 --> 00:34:14,970
+another question. Another question.
+
+289
+00:34:20,860 --> 00:34:22,040
+Another exercise.
+
+290
+00:34:30,400 --> 00:34:35,900
+Here we have some words in symbols, in
+
+291
+00:34:35,900 --> 00:34:39,880
+transcription, and I want you to write the English
+
+292
+00:34:39,880 --> 00:34:40,280
+word.
+
+293
+00:34:43,030 --> 00:34:47,530
+So if the question is transcribe the word, you
+
+294
+00:34:47,530 --> 00:34:54,010
+write it like this. This is transcription. But if
+
+295
+00:34:54,010 --> 00:34:57,790
+I say like this, give the English word, we write
+
+296
+00:34:57,790 --> 00:35:02,340
+the word. So this one. I also want to read, to
+
+297
+00:35:02,340 --> 00:35:06,540
+write. Here are some of the words from exercise
+
+298
+00:35:06,540 --> 00:35:12,120
+two in phonetic symbols. So these words are in
+
+299
+00:35:12,120 --> 00:35:16,200
+phonetic symbols. Read them aloud and write them.
+
+300
+00:35:16,560 --> 00:35:20,140
+Yes. Can you read? Can you write? So this is
+
+301
+00:35:20,140 --> 00:35:21,960
+spelling. Yes.
+
+302
+00:35:26,700 --> 00:35:37,210
+Good. Yes. Thank you. Food. Food. Number two. Yes.
+
+303
+00:35:38,490 --> 00:35:44,670
+Near. Yes, write it because it is spelling.
+
+304
+00:35:49,790 --> 00:35:55,650
+Thank you. Number three.
+
+305
+00:35:56,750 --> 00:35:58,150
+Stood.
+
+306
+00:36:11,690 --> 00:36:19,890
+Thank you. Number four. What is it? Bed. Bed. Yes.
+
+307
+00:36:31,850 --> 00:36:38,570
+Very good. Thank you. Number five. Number five.
+
+308
+00:36:39,190 --> 00:36:43,410
+What is it? Read. Read. Yes.
+
+309
+00:36:53,510 --> 00:37:01,870
+Yes. Yes. Yes. Number six.
+
+310
+00:37:04,010 --> 00:37:05,210
+Yes.
+
+311
+00:37:07,270 --> 00:37:08,850
+Four. Yes.
+
+312
+00:37:15,390 --> 00:37:23,550
+Work very good.
+
+313
+00:37:23,690 --> 00:37:30,990
+Thank you. And number seven phone
+
+314
+00:37:41,370 --> 00:37:45,990
+Yes, thank you. The last one. The last one.
+
+315
+00:38:00,170 --> 00:38:06,210
+Yes, thank you. Now, we want to add some exercises
+
+316
+00:38:06,210 --> 00:38:10,370
+like number eight, number nine,
+
+317
+00:38:22,590 --> 00:38:24,630
+This is one. Ten.
+
+318
+00:38:31,510 --> 00:38:32,590
+Eleven.
+
+319
+00:39:06,600 --> 00:39:13,060
+Yes. I want four of you. Yes. C. C.
+
+320
+00:39:17,920 --> 00:39:24,460
+Very good.
+
+321
+00:39:24,560 --> 00:39:29,840
+Thank you. But ten? One.
+
+322
+00:39:38,480 --> 00:39:38,480
+Yes.
+
+323
+00:39:44,780 --> 00:39:49,940
+And now eleven. Yes. Two.
+
+324
+00:40:02,860 --> 00:40:07,800
+The last one. The last one. Yes. Good.
+
+325
+00:40:24,740 --> 00:40:30,620
+Thank you. Now, maybe some words have the same
+
+326
+00:40:30,620 --> 00:40:39,040
+pronunciation, like sea or sea.
+
+327
+00:40:42,540 --> 00:40:51,600
+This one, one or one, one, two, three. This one is
+
+328
+00:40:51,600 --> 00:40:53,560
+two or
+
+329
+00:40:56,050 --> 00:41:02,390
+two this is good now this is called phonetic
+
+330
+00:41:02,390 --> 00:41:10,030
+symbols these are of three kinds short vowel long
+
+331
+00:41:10,030 --> 00:41:17,330
+vowel with colon and diphthong so now
+
+332
+00:41:25,400 --> 00:41:31,400
+Yes, thank you very much because
+
+333
+00:41:31,400 --> 00:41:39,460
+this subject is important I will teach you some
+
+334
+00:41:39,460 --> 00:41:43,320
+other symbols
+
+335
+00:41:43,320 --> 00:41:50,040
+These symbols are for the consonant so we have
+
+336
+00:41:50,040 --> 00:41:50,600
+this symbol
+
+337
+00:41:53,630 --> 00:42:01,850
+This is ش as in shop
+
+338
+00:42:01,850 --> 00:42:06,670
+She
+
+339
+00:42:06,670 --> 00:42:21,270
+We have this one ش ش choose choose
+
+340
+00:42:33,650 --> 00:42:39,790
+Chair match shop
+
+341
+00:42:39,790 --> 00:42:44,970
+She we
+
+342
+00:42:44,970 --> 00:42:50,930
+have ij
+
+343
+00:42:50,930 --> 00:42:55,590
+ij ij like
+
+344
+00:43:02,180 --> 00:43:14,440
+just just like jump jump yes
+
+345
+00:43:14,440 --> 00:43:27,140
+now what about this? ga ga ja ga like
+
+346
+00:43:41,810 --> 00:43:49,910
+Graped give orange
+
+347
+00:43:49,910 --> 00:43:50,970
+Show
+
+348
+00:44:05,840 --> 00:44:25,960
+Now, also we have think
+
+349
+00:44:25,960 --> 00:44:30,420
+thin
+
+350
+00:44:30,420 --> 00:44:31,080
+month
+
+351
+00:44:39,090 --> 00:44:44,350
+but we have, this one is the,
+
+352
+00:44:45,410 --> 00:44:51,970
+the, like this
+
+353
+00:44:51,970 --> 00:44:56,170
+mother
+
+354
+00:44:56,170 --> 00:44:59,610
+than
+
+355
+00:44:59,610 --> 00:45:03,330
+or
+
+356
+00:45:03,330 --> 00:45:11,540
+though. So these are what? Consonant we call them
+
+357
+00:45:11,540 --> 00:45:18,140
+consonant so
+
+358
+00:45:18,140 --> 00:45:21,080
+we have short vowel long vowel diphthong and
+
+359
+00:45:21,080 --> 00:45:26,720
+consonants if I write these words and write
+
+360
+00:45:26,720 --> 00:45:32,840
+another one like she
+
+361
+00:45:32,840 --> 00:45:35,400
+shop she
+
+362
+00:45:38,540 --> 00:45:43,380
+Show and share.
+
+363
+00:45:43,920 --> 00:45:49,820
+Which one is different? Share. Now here, choose,
+
+364
+00:45:51,200 --> 00:45:53,560
+share, match,
+
+365
+00:45:57,600 --> 00:45:59,140
+machine.
+
+366
+00:46:00,640 --> 00:46:09,090
+Machine. So machine is different just jump orange
+
+367
+00:46:09,090 --> 00:46:14,010
+and glad
+
+368
+00:46:14,010 --> 00:46:19,930
+glad because it is different. Huh? What is it?
+
+369
+00:46:20,930 --> 00:46:30,570
+Chair like this and this sha and this ga different
+
+370
+00:46:30,570 --> 00:46:34,880
+and this good and orange.
+
+371
+00:46:37,940 --> 00:46:41,800
+So it is think,
+
+372
+00:46:42,360 --> 00:46:45,660
+then, month, father.
+
+373
+00:46:48,860 --> 00:46:52,120
+This, mada, then,
+
+374
+00:46:55,660 --> 00:47:02,580
+thought. Thought is different. So this is tha and
+
+375
+00:47:02,580 --> 00:47:10,670
+this is that and this is it this is just an
+
+376
+00:47:10,670 --> 00:47:17,070
+introduction if you want to see all these symbols
+
+377
+00:47:17,070 --> 00:47:29,750
+refer to page one five eight one five eight the
+
+378
+00:47:29,750 --> 00:47:33,350
+last page one five eight
+
+379
+00:47:38,020 --> 00:47:44,100
+Phonetic symbols so
+
+380
+00:47:44,100 --> 00:47:57,540
+this is coincident p as in pen b as in big this is
+
+381
+00:47:57,540 --> 00:48:06,620
+p for papa and this is b for bravo p for papa ba
+
+382
+00:48:06,620 --> 00:48:18,400
+for bravo ta as in tea so it's this one da as in
+
+383
+00:48:18,400 --> 00:48:24,580
+do ka, cat ga,
+
+384
+00:48:26,340 --> 00:48:32,600
+go kha, four va, very
+
+385
+00:48:38,600 --> 00:48:43,220
+Yes. Look at the table of the consonants. We have
+
+386
+00:48:43,220 --> 00:48:52,260
+ba for pen, ba for big, pa for papa, and bra for
+
+387
+00:48:52,260 --> 00:49:06,480
+bravo. Ta, yes, here. And da for do. Ka, cat.
+
+388
+00:49:10,540 --> 00:49:16,920
+go for very
+
+389
+00:49:16,920 --> 00:49:20,140
+some
+
+390
+00:49:20,140 --> 00:49:23,700
+zoo
+
+391
+00:49:23,700 --> 00:49:37,060
+and live and many so some symbols are easy and
+
+392
+00:49:37,060 --> 00:49:41,600
+some symbols are difficult. We should study the
+
+393
+00:49:41,600 --> 00:49:52,360
+difficult ones. Now, n as in near and
+
+394
+00:49:52,360 --> 00:49:56,440
+ha
+
+395
+00:49:56,440 --> 00:50:04,470
+for happy so this is not letters. They are sounds.
+
+396
+00:50:05,090 --> 00:50:11,630
+What is it? Not h. No. Ra for red.
+
+397
+00:50:14,330 --> 00:50:20,810
+Ya for yes. So we have ya.
+
+398
+00:50:22,510 --> 00:50:25,230
+Wa for want.
+
+399
+00:50:32,130 --> 00:50:39,170
+For think, yes? Think the,
+
+400
+00:50:39,850 --> 00:50:44,330
+for the, the, yes?
+
+401
+00:50:47,990 --> 00:51:01,010
+Sh, for she, sh and we have ja, for ja television.
+
+402
+00:51:01,810 --> 00:51:06,590
+Aha. Aha. Jah. This is jah.
+
+403
+00:51:08,930 --> 00:51:19,150
+Ch for child. Ch for child.
+
+404
+00:51:20,990 --> 00:51:26,750
+And ij. Jah for german. German. Aha.
+
+405
+00:51:31,900 --> 00:51:41,720
+And english for english reading. So these are the
+
+406
+00:51:41,720 --> 00:51:45,960
+difficult ones. And the first one easy. Why?
+
+407
+00:51:46,340 --> 00:51:49,460
+Because they are similar to the letters. The same
+
+408
+00:51:49,460 --> 00:51:53,360
+as letters. Sound and letter, the same, easy. But
+
+409
+00:51:53,360 --> 00:51:57,540
+it is different like these. They are difficult.
+
+410
+00:51:58,060 --> 00:52:01,540
+But when we study them, they will be easy.
+
+411
+00:52:12,380 --> 00:52:18,120
+Now what
+
+412
+00:52:18,120 --> 00:52:19,400
+about the other?
+
+413
+00:52:39,270 --> 00:52:56,050
+a cat fat chat a father car par o hut lot got o
+
+414
+00:52:56,050 --> 00:53:12,130
+more morning walk u good stood u u you, food, a,
+
+415
+00:53:13,130 --> 00:53:23,570
+cut, shot, one, a, bear, learn, a, pita, pita,
+
+416
+00:53:24,310 --> 00:53:24,790
+about.
+
+417
+00:53:27,410 --> 00:53:35,670
+What are these? Diphthongs. These are what? Two
+
+418
+00:53:35,670 --> 00:53:53,550
+vowels. a as in name u as in know i my hide find i
+
+419
+00:53:53,550 --> 00:54:05,290
+how how cow oy oy boy
+
+420
+00:54:07,880 --> 00:54:19,220
+Ear. Here. Near. Dear. Air. Where. Learn. Yes.
+
+421
+00:54:19,460 --> 00:54:32,160
+Where. Uwa. Tua. Tua. Aha. And this is the end of
+
+422
+00:54:32,
+
+445
+00:57:08,090 --> 00:57:14,570
+Number A, strong, full-time, film, drive, phone,
+
+446
+00:57:14,930 --> 00:57:24,290
+try on. The first one, strong, coffee, full-time,
+
+447
+00:57:48,400 --> 00:57:53,980
+So this is strong coffee
+
+448
+00:58:00,160 --> 00:58:05,720
+strong coffee, film star, fall in love, full-time
+
+449
+00:58:05,720 --> 00:58:12,560
+job, drive carefully, and try on a jumper. And the
+
+450
+00:58:12,560 --> 00:58:18,600
+last exercise, we studied it before. Sorry, I'm
+
+451
+00:58:18,600 --> 00:58:20,680
+late. I got stuck in traffic.
+
+452
+00:58:23,540 --> 00:58:28,530
+And so on. So we studied this before. السلام عليكم
+
+453
+00:58:28,530 --> 00:58:31,530
+ورحمة الله وبركاته وبرك الله فيكم وإلى اللقاء إن
+
+454
+00:58:31,530 --> 00:58:33,390
+شاء الله المرة القادمة. السلام عليكم 
+
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/xFugr8BRqM4.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/xFugr8BRqM4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2ab41545d0c80a1dc5fa4e57dd151a71363b1cfa
--- /dev/null
+++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/xFugr8BRqM4.srt
@@ -0,0 +1,2083 @@
+
+1
+00:00:21,080 --> 00:00:23,360
+Assalamualaikum warahmatullahi wabarakatuh.
+
+2
+00:00:26,200 --> 00:00:33,520
+Good afternoon. Today, inshallah, we will study a
+
+3
+00:00:33,520 --> 00:00:38,700
+reading passage, a reading passage. The title is
+
+4
+00:00:38,700 --> 00:00:46,360
+Wonders of the modern world. Wonders of the modern
+
+5
+00:00:46,360 --> 00:00:52,290
+world. Modern is the opposite of Ancient. We don't
+
+6
+00:00:52,290 --> 00:00:55,650
+want to speak about the ancient wonders. No, the
+
+7
+00:00:55,650 --> 00:00:56,530
+modern wonders.
+
+8
+00:01:06,270 --> 00:01:10,130
+We have six wonders of the world.
+
+9
+00:01:13,670 --> 00:01:19,310
+International travel, medical science, the
+
+10
+00:01:19,310 --> 00:01:27,250
+internet, agriculture, space travel, the Olympic
+
+11
+00:01:27,250 --> 00:01:35,850
+games. These six titles will
+
+12
+00:01:35,850 --> 00:01:42,730
+deal with six paragraphs and we want to write each
+
+13
+00:01:42,730 --> 00:01:47,950
+one title in each paragraph so
+
+14
+00:01:51,560 --> 00:01:59,140
+I want you to, before reading the passage, we will
+
+15
+00:01:59,140 --> 00:02:06,200
+put the title. And before the titles, there is a,
+
+16
+00:02:13,900 --> 00:02:14,480
+yes.
+
+17
+00:02:17,000 --> 00:02:18,780
+We have an introduction
+
+18
+00:02:21,480 --> 00:02:29,640
+Introduction. The Modern Wonders of the World. I
+
+19
+00:02:29,640 --> 00:02:34,260
+don't believe that today's wonders are similar in
+
+20
+00:02:34,260 --> 00:02:39,520
+kind to the wonders of the ancient world. Today's
+
+21
+00:02:39,520 --> 00:02:43,040
+wonders are different from the ancient wonders.
+
+22
+00:02:44,220 --> 00:02:49,350
+They were all buildings, such as the pyramids in
+
+23
+00:02:49,350 --> 00:02:54,450
+Egypt or other architectural structures. So the
+
+24
+00:02:54,450 --> 00:02:58,510
+ancient were all buildings. Today, they are not
+
+25
+00:02:58,510 --> 00:03:03,990
+buildings. Over the past 10 years, we have seen
+
+26
+00:03:03,990 --> 00:03:08,770
+amazing technological and scientific achievements.
+
+27
+00:03:10,750 --> 00:03:14,530
+The wonders of modern world are all about
+
+28
+00:03:14,530 --> 00:03:17,490
+achievements, scientific achievements,
+
+29
+00:03:18,270 --> 00:03:22,890
+technological and scientific achievements. These
+
+30
+00:03:22,890 --> 00:03:28,930
+are surely our modern wonders. So the wonders in
+
+31
+00:03:28,930 --> 00:03:34,670
+the past, the ancient, were all buildings. Today,
+
+32
+00:03:35,550 --> 00:03:39,790
+the wonders are achievements, technological and
+
+33
+00:03:39,790 --> 00:03:41,390
+scientific achievements.
+
+34
+00:03:44,130 --> 00:03:51,210
+If we look at the first paragraph, it
+
+35
+00:03:51,210 --> 00:03:58,210
+is about one of the six or of the seven wonders.
+
+36
+00:03:59,010 --> 00:04:04,090
+Read it quickly to find the title for this. We
+
+37
+00:04:04,090 --> 00:04:07,130
+want to choose it from the, here,
+
+38
+00:04:09,550 --> 00:04:14,430
+six. We want to choose one for each paragraph. This
+
+39
+00:04:14,430 --> 00:04:20,650
+paragraph, what do you think the title may be, the
+
+40
+00:04:20,650 --> 00:04:27,030
+internet. Very good. So the title is the internet.
+
+41
+00:04:27,030 --> 00:04:32,770
+Also
+
+42
+00:04:32,770 --> 00:04:39,740
+in the first exercise, we have 12 words connected
+
+43
+00:04:39,740 --> 00:04:45,040
+with the six wonders. We want to choose two for
+
+44
+00:04:45,040 --> 00:04:50,400
+each title. So the internet. What are the two
+
+45
+00:04:50,400 --> 00:04:53,920
+words from the exercise here?
+
+46
+00:04:57,920 --> 00:05:02,740
+Here, so this is the internet. The first
+
+47
+00:05:02,740 --> 00:05:06,830
+paragraph. I want to choose two words connected
+
+48
+00:05:06,830 --> 00:05:13,670
+with the internet. Number one, online. Yes. So this is
+
+49
+00:05:13,670 --> 00:05:20,270
+one, and the other one, yes, website. Website very
+
+50
+00:05:20,270 --> 00:05:25,110
+good, website. So the internet, number one, connected
+
+51
+00:05:25,110 --> 00:05:30,450
+with two words. What are they? Airlines and website.
+
+52
+00:05:30,450 --> 00:05:37,670
+So here, number one. Now let's do number two.
+
+53
+00:05:41,270 --> 00:05:42,750
+This is number two.
+
+54
+00:05:49,350 --> 00:05:53,530
+Yes. What is the title? What is the title of
+
+55
+00:05:53,530 --> 00:05:54,150
+number two?
+
+56
+00:05:57,310 --> 00:05:58,070
+Yes.
+
+57
+00:06:00,450 --> 00:06:07,220
+Space travel. Yes. So the title is Space travel.
+
+58
+00:06:10,400 --> 00:06:16,580
+What are the two words connected with space
+
+59
+00:06:16,580 --> 00:06:17,100
+travel?
+
+60
+00:06:20,300 --> 00:06:21,260
+Yes,
+
+61
+00:06:24,620 --> 00:06:28,560
+so this is space travel, number two. What are the
+
+62
+00:06:28,560 --> 00:06:29,140
+two words?
+
+63
+00:06:32,480 --> 00:06:36,260
+Solar system, very good, number two. And another
+
+64
+00:06:36,260 --> 00:06:45,740
+word? Yes? Galaxies, yes, galaxies. So this is
+
+65
+00:06:45,740 --> 00:06:50,320
+number two. So if we look at the second paragraph
+
+66
+00:06:50,320 --> 00:06:57,940
+in general, the title is space travel. And if we
+
+67
+00:06:57,940 --> 00:07:01,970
+look at the first exercise, we can connect the two
+
+68
+00:07:01,970 --> 00:07:11,670
+words, solar system and galaxies. Yes. Now the
+
+69
+00:07:11,670 --> 00:07:27,470
+third paragraph again, the third paragraph, number
+
+70
+00:07:27,470 --> 00:07:35,960
+three. Number three. Yes. What is the title of
+
+71
+00:07:35,960 --> 00:07:42,740
+number three generally? Yes.
+
+72
+00:07:42,740 --> 00:07:50,100
+Medical science, medical science.
+
+73
+00:07:50,100 --> 00:07:56,140
+And there are two words connected with medical
+
+74
+00:07:56,140 --> 00:08:05,160
+science. They are. They are health
+
+75
+00:08:05,160 --> 00:08:12,440
+care
+
+76
+00:08:12,440 --> 00:08:21,500
+and penicillin.
+
+77
+00:08:24,740 --> 00:08:29,930
+So these words, two words are in the exercise. Now
+
+78
+00:08:29,930 --> 00:08:37,350
+let's go to number four. So this is number three.
+
+79
+00:08:40,430 --> 00:08:42,310
+Now, number four.
+
+80
+00:08:46,050 --> 00:08:50,110
+So what is the title for number four?
+
+81
+00:08:53,450 --> 00:08:57,450
+Yes. International Travel. Very good.
+
+82
+00:09:07,520 --> 00:09:10,880
+And we want to connect two words in the
+
+83
+00:09:10,880 --> 00:09:18,180
+international travel. They are airlines. Yes. In
+
+84
+00:09:18,180 --> 00:09:25,240
+lines, in lines, and within lines, abroad, and
+
+85
+00:09:25,240 --> 00:09:34,340
+airlines. Yes. Abroad and airlines, so these are the
+
+86
+00:09:34,340 --> 00:09:38,760
+two words connected with international travel.
+
+87
+00:09:38,760 --> 00:09:46,520
+Let's go to number five, number
+
+88
+00:09:46,520 --> 00:09:53,660
+five. What's the title? Yes.
+
+89
+00:09:53,660 --> 00:10:00,340
+The Olympic games, yes. The title is The Olympic
+
+90
+00:10:00,340 --> 00:10:00,820
+games.
+
+91
+00:10:09,960 --> 00:10:18,580
+And what are the two words? Yes. Competition and
+
+92
+00:10:18,580 --> 00:10:23,200
+race.
+
+93
+00:10:28,420 --> 00:10:33,380
+Drug abuse. Very good. Drug abuse. What is it?
+
+94
+00:10:34,160 --> 00:10:39,920
+Drug abuse, yes. Drug abuse, meaning using the
+
+95
+00:10:39,920 --> 00:10:45,820
+drugs in a wrong way. So the fifth paragraph will
+
+96
+00:10:45,820 --> 00:10:48,920
+be on the Olympic games, and here are the two
+
+97
+00:10:48,920 --> 00:10:54,320
+words connected with them. Next, number six.
+
+98
+00:10:55,810 --> 00:11:01,090
+Number six. What's the title of number six? Uh
+
+99
+00:11:01,090 --> 00:11:07,030
+-huh. Yes. Agriculture. Very good.
+
+100
+00:11:11,210 --> 00:11:14,690
+Agriculture. And what are the two words connected
+
+101
+00:11:14,690 --> 00:11:23,050
+with it? Corn. Yes. With corn. Corn. And?
+
+102
+00:11:25,610 --> 00:11:36,530
+Famine, very good, and famine. Yes. So now let's go
+
+103
+00:11:36,530 --> 00:11:48,010
+back to the title again. Uh
+
+104
+00:11:48,010 --> 00:11:54,250
+-huh. So in the first exercise
+
+105
+00:11:56,650 --> 00:12:03,950
+I want to answer it. So this is number one, and
+
+106
+00:12:03,950 --> 00:12:13,370
+here I say one and one. Two, number two, which one?
+
+107
+00:12:16,490 --> 00:12:22,270
+Medical science? Space travel? Yes. So this is the
+
+108
+00:12:22,270 --> 00:12:29,700
+second paragraph. Which two? Solar system and
+
+109
+00:12:29,700 --> 00:12:38,740
+galaxies. Number three? Medical science. It
+
+110
+00:12:38,740 --> 00:12:45,620
+is healthcare and penicillin.
+
+111
+00:12:51,960 --> 00:12:54,460
+International travel. International travel. Number
+
+112
+00:12:54,460 --> 00:13:03,300
+four. Airlines. Airlines. Abroad. And abroad.
+
+113
+00:13:06,720 --> 00:13:11,720
+The Olympic games. The Olympic games. Number five.
+
+114
+00:13:12,000 --> 00:13:17,800
+Competition. Competition. Drug abuse. And drug
+
+115
+00:13:17,800 --> 00:13:19,480
+abuse. Drug abuse.
+
+116
+00:13:22,390 --> 00:13:23,870
+The last paragraph,
+
+117
+00:13:26,190 --> 00:13:30,570
+corn and
+
+118
+00:13:30,570 --> 00:13:37,350
+famine. So this is the answer for the first
+
+119
+00:13:37,350 --> 00:13:38,230
+exercise.
+
+120
+00:13:40,550 --> 00:13:46,810
+Is it clear? So this is about vocabulary. Six
+
+121
+00:13:46,810 --> 00:13:52,950
+words and twelve words. Eighteen. So now we will
+
+122
+00:13:52,950 --> 00:13:59,210
+study 18 words, these ones. Now the second
+
+123
+00:13:59,210 --> 00:14:03,650
+exercise is finished? Yes.
+
+124
+00:14:06,750 --> 00:14:12,590
+So this
+
+125
+00:14:12,590 --> 00:14:17,370
+is the answer. International travel, airlines
+
+126
+00:14:19,210 --> 00:14:22,350
+and abroad. I also want to read the first one. Yes.
+
+127
+00:14:22,350 --> 00:14:30,570
+Number two, number
+
+128
+00:14:30,570 --> 00:14:34,530
+three, yes.
+
+129
+00:14:34,530 --> 00:14:40,430
+We say the internet. The internet. We usually say
+
+130
+00:14:40,430 --> 00:14:45,480
+that if the word begins with a consonant, if the
+
+131
+00:14:45,480 --> 00:14:49,940
+word begins with a consonant, we say that. If it
+
+132
+00:14:49,940 --> 00:14:56,480
+begins with a vowel, we say the. So here, the
+
+133
+00:14:56,480 --> 00:15:00,760
+internet, the apple, the envelope. But that book,
+
+134
+00:15:01,080 --> 00:15:07,540
+that boy. So here, yes again. The internet, online,
+
+135
+00:15:07,540 --> 00:15:11,600
+website. Very good, yes. Next, agriculture.
+
+136
+00:15:14,510 --> 00:15:19,830
+Yes, yes, corn,
+
+137
+00:15:21,250 --> 00:15:23,670
+famine, yes, next,
+
+138
+00:15:25,690 --> 00:15:28,790
+yes,
+
+139
+00:15:29,110 --> 00:15:34,350
+solar system, galaxies, the last one, the Olympic
+
+140
+00:15:34,350 --> 00:15:41,770
+games, drug abuse.
+
+141
+00:15:42,890 --> 00:15:48,810
+Yes, so here we use up. This is it. Makes negative
+
+142
+00:15:48,810 --> 00:15:58,430
+normal, abnormal. Normal, abnormal, use, abuse. Yes.
+
+143
+00:15:58,430 --> 00:16:07,770
+Something like un in impossible, impossible, happy,
+
+144
+00:16:07,770 --> 00:16:15,350
+unhappy. Correct, incorrect. Correct? Incorrect.
+
+145
+00:16:15,710 --> 00:16:21,650
+Normal? Abnormal. Youth? Abnormal. Yes. So this is
+
+146
+00:16:21,650 --> 00:16:23,270
+the second,
+
+147
+00:16:25,130 --> 00:16:30,810
+or this is the first exercise. Finished? Yes. The
+
+148
+00:16:30,810 --> 00:16:31,410
+second one.
+
+149
+00:16:34,770 --> 00:16:41,070
+Now we want to arrange these words, these titles,
+
+150
+00:16:42,510 --> 00:16:47,050
+into the paragraphs. We will put each title in
+
+151
+00:16:47,050 --> 00:16:49,590
+each paragraph. So this is the answer. Number one
+
+152
+00:16:49,590 --> 00:16:54,450
+is the internet. Paragraph number one is about the
+
+153
+00:16:54,450 --> 00:17:03,190
+internet. Number two, three, four, five, and the
+
+154
+00:17:03,190 --> 00:17:08,490
+last one, agriculture. Now let's come to the
+
+155
+00:17:08,490 --> 00:17:11,670
+passage itself. Uh-huh. This is the first
+
+156
+00:17:11,670 --> 00:17:19,050
+paragraph. It's everywhere. So we have a question.
+
+157
+00:17:20,310 --> 00:17:22,770
+This question, we want to answer this question
+
+158
+00:17:22,770 --> 00:17:28,330
+from the paragraph. Yes, this is number one. What
+
+159
+00:17:28,330 --> 00:17:33,770
+is the question? What has changed because of the
+
+160
+00:17:33,770 --> 00:17:39,030
+internet? The internet changed something. What is
+
+161
+00:17:39,030 --> 00:17:43,690
+this thing? Another question, what will happen
+
+162
+00:17:43,690 --> 00:17:48,290
+with the internet in the future? What the internet
+
+163
+00:17:48,290 --> 00:17:52,730
+will be like in the future? Now what has the
+
+164
+00:17:52,730 --> 00:17:56,930
+internet changed, and what will happen in the
+
+165
+00:17:56,930 --> 00:18:00,410
+future? So the question is, what has changed
+
+166
+00:18:00,410 --> 00:18:04,210
+because of the internet? The first part. The
+
+167
+00:18:04,210 --> 00:18:09,510
+second part, what will happen with the internet in
+
+168
+00:18:09,510 --> 00:18:18,580
+the future? So here, it's everywhere. More than
+
+169
+00:18:18,580 --> 00:18:22,780
+half a billion people use it. What does it mean?
+
+170
+00:18:23,000 --> 00:18:28,200
+The internet, yes. It refers to the internet. What
+
+171
+00:18:28,200 --> 00:18:34,620
+does this word, or this pronoun refer to? It refers
+
+172
+00:18:34,620 --> 00:18:42,690
+to the internet, yes. And the number of people who
+
+173
+00:18:42,690 --> 00:18:48,770
+are online increases. Increases, the opposite of
+
+174
+00:18:48,770 --> 00:18:55,730
+decrease. Yes. Here the opposite of decrease by a
+
+175
+00:18:55,730 --> 00:19:00,270
+hundred million every year. What's the meaning
+
+176
+00:19:00,270 --> 00:19:07,910
+every year? Every year means yearly, a year. Uh-huh.
+
+177
+00:19:08,440 --> 00:19:17,260
+Per year. What's month? Every month, monthly. A
+
+178
+00:19:17,260 --> 00:19:24,800
+month. Per month. Weekly. Every week, a week.
+
+179
+00:19:25,420 --> 00:19:29,680
+Per week. All the same meaning. Yes. So here
+
+180
+00:19:29,680 --> 00:19:36,520
+increases by the by 100 million every year. In
+
+181
+00:19:36,520 --> 00:19:44,480
+1994, there were only a few hundred web pages. A
+
+182
+00:19:44,480 --> 00:19:50,940
+few hundred web pages. A few for the countable. A
+
+183
+00:19:50,940 --> 00:19:57,000
+little for the uncountable. So because pages we use
+
+184
+00:19:57,000 --> 00:20:05,990
+a few, not a little. Yes. And today there are
+
+185
+00:20:05,990 --> 00:20:10,890
+billions. In the past, a hundred million. Now,
+
+186
+00:20:11,650 --> 00:20:17,830
+billions. Yes. It has revolutionized the way we
+
+187
+00:20:17,830 --> 00:20:23,770
+live and work. It has changed, completely changed.
+
+188
+00:20:24,610 --> 00:20:30,630
+What? Changed the way we live and the way we work.
+
+189
+00:20:31,210 --> 00:20:37,540
+So the internet changed our life, our work, the
+
+190
+00:20:37,540 --> 00:20:44,800
+way we live, and the way we work. But we are still
+
+191
+00:20:44,800 --> 00:20:49,960
+in the early days. Now the internet is in the
+
+192
+00:20:49,960 --> 00:20:56,700
+early days, at the beginning. Soon, there will be
+
+193
+00:20:56,700 --> 00:21:00,440
+in the future, there will be more and more
+
+194
+00:21:00,440 --> 00:21:03,580
+interactivity between
+
+195
+00:21:05,350 --> 00:21:11,470
+the user and the website. So these are two things
+
+196
+00:21:11,470 --> 00:21:17,730
+with two things we use between. With more than two
+
+197
+00:21:17,730 --> 00:21:22,330
+things, we use among.
+
+198
+00:21:22,330 --> 00:21:32,930
+We use among. So among for more than two, but with
+
+199
+00:21:32,930 --> 00:21:42,000
+two, we use between. Yes. Here two, here more than
+
+200
+00
+
+223
+00:23:50,490 --> 00:23:51,830
+give instructions.
+
+224
+00:23:54,270 --> 00:24:00,970
+Instructions. Using the, using speech, by
+
+225
+00:24:00,970 --> 00:24:08,070
+speaking. So, if I look at the, this paragraph, to
+
+226
+00:24:08,070 --> 00:24:14,240
+finish it, yes? So this is the title and these are
+
+227
+00:24:14,240 --> 00:24:17,880
+the two words connected with it. And this is the
+
+228
+00:24:17,880 --> 00:24:20,860
+question and this is the answer. Who can read the
+
+229
+00:24:20,860 --> 00:24:24,800
+answer? The question and the answer. Yes, the
+
+230
+00:24:24,800 --> 00:24:27,740
+question. What has changed because of the
+
+231
+00:24:27,740 --> 00:24:32,200
+internet? What will happen with the internet? The
+
+232
+00:24:32,200 --> 00:24:37,380
+answer? The way we live and work, there will be
+
+233
+00:24:37,380 --> 00:24:42,910
+more interactivity. Interactivity between the
+
+234
+00:24:42,910 --> 00:24:47,410
+user and the website. And the website. Yes. And.
+
+235
+00:24:47,470 --> 00:24:51,730
+And we will be able to give interaction using
+
+236
+00:24:51,730 --> 00:24:55,810
+speech. Using speech. Very good. Yes. Who can read
+
+237
+00:24:55,810 --> 00:25:00,680
+the answer again? The answer again? Yes. The way
+
+238
+00:25:00,680 --> 00:25:05,280
+we live and work, there will be more interactivity
+
+239
+00:25:05,280 --> 00:25:09,240
+between the user and the website and we will be
+
+240
+00:25:09,240 --> 00:25:16,080
+able to give instructions using speech. Very good.
+
+241
+00:25:16,300 --> 00:25:20,600
+So now we finish the first paragraph. Let's go to
+
+242
+00:25:20,600 --> 00:25:22,860
+the second paragraph. Yes?
+
+243
+00:25:28,470 --> 00:25:32,810
+You understand? We will deal with each paragraph
+
+244
+00:25:32,810 --> 00:25:38,730
+in isolation. So the second paragraph. In 1969,
+
+245
+00:25:40,290 --> 00:25:45,890
+Neil Armstrong stepped, walked. Stepped, it means
+
+246
+00:25:45,890 --> 00:25:53,490
+walked. Landed, landed. Out of his space capsule,
+
+247
+00:25:55,250 --> 00:26:00,880
+yes? onto the surface of the moon. So he stepped
+
+248
+00:26:00,880 --> 00:26:05,540
+on the moon. He landed on the moon and made his
+
+249
+00:26:05,540 --> 00:26:10,800
+famous statement. He made his famous statement. He
+
+250
+00:26:10,800 --> 00:26:15,200
+said something. Neil Armstrong landed on the moon
+
+251
+00:26:15,200 --> 00:26:20,520
+and he said one sentence. What is it? That's one
+
+252
+00:26:20,520 --> 00:26:27,450
+small step for a man. One giant leap for mankind.
+
+253
+00:26:28,110 --> 00:26:33,310
+It's very small step, but it is a big change for
+
+254
+00:26:33,310 --> 00:26:39,290
+the mankind. Giant, huge, huge step for the
+
+255
+00:26:39,290 --> 00:26:42,010
+mankind, for the people, all the people of the
+
+256
+00:26:42,010 --> 00:26:49,390
+world. Since then, since then, what does since
+
+257
+00:26:49,390 --> 00:26:55,680
+then refer to? It refers to what? Then, here,
+
+258
+00:26:55,860 --> 00:27:03,380
+then. Then refer to what? Refer to 1969.
+
+259
+00:27:05,620 --> 00:27:11,700
+It is about the time. It refers about previous
+
+260
+00:27:11,700 --> 00:27:19,420
+time. Since 1969, or since then, there have been
+
+261
+00:27:19,420 --> 00:27:25,690
+space props to Mars. Jupiter, Saturn, and even to
+
+262
+00:27:25,690 --> 00:27:31,770
+the Sun. So after the Moon, now there are props to
+
+263
+00:27:31,770 --> 00:27:38,290
+where? To Mars, Jupiter, Saturn, and even to the
+
+264
+00:27:38,290 --> 00:27:47,010
+Sun. One day, a space observatory will study how
+
+265
+00:27:47,010 --> 00:27:51,290
+the first stars and galaxies began. In the future,
+
+266
+00:27:52,250 --> 00:27:58,550
+they will study and discover how the galaxies and
+
+267
+00:27:58,550 --> 00:28:06,110
+the stars began, the beginning of them. So far, it
+
+268
+00:28:06,110 --> 00:28:10,230
+seems that we are alone in the universe. In the
+
+269
+00:28:10,230 --> 00:28:13,350
+past, we thought that we are alone.
+
+270
+00:28:15,970 --> 00:28:20,630
+there are no signs yet that there is intelligent
+
+271
+00:28:20,630 --> 00:28:25,490
+life outside our own solar system. In the past,
+
+272
+00:28:25,810 --> 00:28:29,090
+they thought that we are alone here on the earth,
+
+273
+00:28:29,890 --> 00:28:36,550
+but and say that there are no signs yet until now
+
+274
+00:28:36,550 --> 00:28:41,790
+that there is intelligent life, life, people.
+
+275
+00:28:43,480 --> 00:28:47,060
+outside our own solar system. The solar system are
+
+276
+00:28:47,060 --> 00:28:53,840
+the nine planets of the solar system. Yes, Earth,
+
+277
+00:28:54,200 --> 00:29:01,200
+Jupiter, Saturn, et cetera. Now, but who knows
+
+278
+00:29:01,200 --> 00:29:07,800
+what the future holds? Allahu a'lam in the future
+
+279
+00:29:07,800 --> 00:29:13,370
+will find intelligent life on other planet, maybe.
+
+280
+00:29:14,010 --> 00:29:18,230
+But until now, no, there are no signs that there
+
+281
+00:29:18,230 --> 00:29:23,950
+is life on other planets. The question is, what
+
+282
+00:29:23,950 --> 00:29:30,710
+has happened in space exploration since 1969?
+
+283
+00:29:32,850 --> 00:29:37,990
+What has happened? So, yes,
+
+284
+00:29:41,390 --> 00:29:45,530
+Mm-hmm. What has happened? What has happened?
+
+285
+00:29:47,970 --> 00:29:55,630
+There have been space props to where? To Mars,
+
+286
+00:29:55,770 --> 00:30:00,990
+Jupiter, Saturn and the Sun. What has happened in
+
+287
+00:30:00,990 --> 00:30:06,210
+space? There have been space props to these
+
+288
+00:30:06,210 --> 00:30:08,410
+planets and even to the Sun.
+
+289
+00:30:13,820 --> 00:30:18,200
+Now, who can read the title again?
+
+290
+00:30:22,500 --> 00:30:25,200
+What are the two words connected with it?
+
+291
+00:30:28,120 --> 00:30:33,520
+Yes. Now, who can read the question? The second
+
+292
+00:30:33,520 --> 00:30:40,880
+question? Yes. The answer?
+
+293
+00:30:42,210 --> 00:30:47,350
+The answer? Space props have been to Mars,
+
+294
+00:30:47,670 --> 00:30:51,630
+Jupiter, Saturn and the Sun. Yes, so these have
+
+295
+00:30:51,630 --> 00:30:57,150
+been to these places or there have been space
+
+296
+00:30:57,150 --> 00:31:02,770
+props or space props have been to Mars, Jupiter,
+
+297
+00:31:03,530 --> 00:31:10,010
+Saturn and the Sun. So this is the end of the
+
+298
+00:31:10,010 --> 00:31:14,350
+second paragraph. Let's come to the third one.
+
+299
+00:31:21,490 --> 00:31:26,330
+The question, the question is, what is the most
+
+300
+00:31:26,330 --> 00:31:31,330
+noticeable result of better health care? Now we
+
+301
+00:31:31,330 --> 00:31:36,560
+have health care. How can we see it? What is the
+
+302
+00:31:36,560 --> 00:31:41,320
+result of this better health care? Let's read the
+
+303
+00:31:41,320 --> 00:31:47,560
+paragraph number three. Surely nothing has done
+
+304
+00:31:47,560 --> 00:31:52,340
+more for the comfort and happiness of the human
+
+305
+00:31:52,340 --> 00:31:58,620
+race than the advances in health care. So we have
+
+306
+00:31:58,620 --> 00:32:07,710
+advances in health care. This advances is above
+
+307
+00:32:07,710 --> 00:32:13,270
+all, the first one. Nothing before it. So this is
+
+308
+00:32:13,270 --> 00:32:18,770
+the most important thing happened recently. What
+
+309
+00:32:18,770 --> 00:32:26,110
+is it? Advances. Development in health care.
+
+310
+00:32:27,130 --> 00:32:32,190
+Nothing before it. This is the first one. We have
+
+311
+00:32:32,190 --> 00:32:39,190
+the word Surely, sure, surely, surely is adjective
+
+312
+00:32:39,190 --> 00:32:47,310
+or adverb? Adverb, because it has a guy. Surely is
+
+313
+00:32:47,310 --> 00:32:55,970
+the only word with sugar that has S, U, and S, U.
+
+314
+00:32:56,490 --> 00:33:03,290
+So sure, sugar, This is the only two words that
+
+315
+00:33:03,290 --> 00:33:12,270
+has su pronounced as sha. Or this sha will be like
+
+316
+00:33:12,270 --> 00:33:18,750
+this. Inshallah we will study it. So, surely
+
+317
+00:33:18,750 --> 00:33:25,810
+nothing has done more for the comfort. Comfort is
+
+318
+00:33:25,810 --> 00:33:30,850
+a noun. Comfort is a noun. What is the adjective?
+
+319
+00:33:33,590 --> 00:33:37,330
+Comfortable. The adjective is comfortable.
+
+320
+00:33:38,190 --> 00:33:43,490
+Comfortable. Altogether. Comfortable. Comfortable.
+
+321
+00:33:43,950 --> 00:33:50,390
+The adverb is comfortably. Comfortably. Yes. So
+
+322
+00:33:50,390 --> 00:33:54,510
+this is a noun and the adjective is comfortable.
+
+323
+00:33:56,090 --> 00:33:58,610
+The adverb is comfortably.
+
+324
+00:34:02,550 --> 00:34:10,870
+More is the opposite of less. Very good. Yes. So
+
+325
+00:34:10,870 --> 00:34:16,790
+happiness is the noun. The adjective is happy.
+
+326
+00:34:17,150 --> 00:34:23,550
+Yes, happy. Very good. Now, How many millions of
+
+327
+00:34:23,550 --> 00:34:28,090
+people have benefited from the humble aspirin, the
+
+328
+00:34:28,090 --> 00:34:32,990
+simple aspirin? This aspirin is very simple, but
+
+329
+00:34:32,990 --> 00:34:40,290
+it has benefited many worlds, many people. All the
+
+330
+00:34:40,290 --> 00:34:45,850
+people have benefited from the aspirin. So it's
+
+331
+00:34:45,850 --> 00:34:51,770
+very good discovery. Yes. How many lives How many
+
+332
+00:34:51,770 --> 00:34:58,290
+lives has penicillin saved? The penicillin is a
+
+333
+00:34:58,290 --> 00:35:03,630
+very important discovery in medicine. So it saved
+
+334
+00:35:03,630 --> 00:35:09,950
+a lot of people. A huge number of people. So the
+
+335
+00:35:09,950 --> 00:35:15,870
+penicillin saved many people greatly. Average life
+
+336
+00:35:15,870 --> 00:35:21,220
+expectancy, average. What's the meaning of
+
+337
+00:35:21,220 --> 00:35:27,140
+average? What's the average of four, five, six?
+
+338
+00:35:28,160 --> 00:35:33,380
+Five. Yes. The average is four, five, and six is
+
+339
+00:35:33,380 --> 00:35:39,220
+five. Yes. So average life expectancy, we expect
+
+340
+00:35:39,220 --> 00:35:43,540
+something. Worldwide. What's the meaning of
+
+341
+00:35:43,540 --> 00:35:46,600
+worldwide? Worldwide.
+
+342
+00:35:49,790 --> 00:35:54,370
+all over the world all over the world uh-huh so
+
+343
+00:35:54,370 --> 00:35:57,290
+the average life expectancy in all over the world
+
+344
+00:35:57,290 --> 00:36:05,590
+has risen dramatically greatly has risen uh-huh so
+
+345
+00:36:05,590 --> 00:36:16,850
+how over the past 100 years from about 27 in 1900
+
+346
+00:36:16,850 --> 00:36:27,110
+to 77 today so this life average or average life
+
+347
+00:36:27,110 --> 00:36:36,030
+expectancy raised from 47 to 77 nowadays but this
+
+348
+00:36:36,030 --> 00:36:41,890
+is in 1900 so the question is what is the most
+
+349
+00:36:41,890 --> 00:36:44,930
+noticeable result of better health care
+
+350
+00:36:47,910 --> 00:36:54,170
+Yes? Yes, this one. Average life expectancy has
+
+351
+00:36:54,170 --> 00:36:58,590
+risen dramatically. So this is the answer. This is
+
+352
+00:36:58,590 --> 00:37:05,470
+the answer. Average life expectancy worldwide has
+
+353
+00:37:05,470 --> 00:37:07,330
+risen dramatically, greatly.
+
+354
+00:37:12,250 --> 00:37:20,050
+So again, the title of this paragraph is Medical
+
+355
+00:37:20,050 --> 00:37:22,330
+Science. The two words connected with it,
+
+356
+00:37:25,010 --> 00:37:29,210
+healthcare and penicillin. The question is, what's
+
+357
+00:37:29,210 --> 00:37:30,910
+the most noticeable result of better
+
+358
+00:37:30,910 --> 00:37:35,270
+healthcare? The answer is, average life expectancy
+
+359
+00:37:35,270 --> 00:37:41,990
+has risen dramatically. Now, let's go to paragraph
+
+360
+00:37:41,990 --> 00:37:43,770
+number four.
+
+361
+00:37:48,520 --> 00:37:50,100
+Is it clear? Yes.
+
+362
+00:37:54,480 --> 00:37:59,700
+So I want you to prepare these paragraphs at home
+
+363
+00:37:59,700 --> 00:38:04,460
+before the lecture and after the lecture. Yes,
+
+364
+00:38:04,640 --> 00:38:11,720
+this is number four. Number four. It's, we are,
+
+365
+00:38:12,720 --> 00:38:16,480
+look, look here at the question. Before reading,
+
+366
+00:38:18,050 --> 00:38:25,610
+we read the questions. X equals, X means a number,
+
+367
+00:38:26,290 --> 00:38:32,310
+equals the number of people who traveled abroad in
+
+368
+00:38:32,310 --> 00:38:35,910
+the 19th century. So the number of people who
+
+369
+00:38:35,910 --> 00:38:38,610
+traveled abroad in the 19th century, maybe 4
+
+370
+00:38:38,610 --> 00:38:42,210
+million, 5 million, 6 million, we don't know
+
+371
+00:38:42,210 --> 00:38:46,990
+exactly. So it is X. So this number of people who
+
+372
+00:38:46,990 --> 00:38:52,800
+traveled in the 19th century it's okay now what
+
+373
+00:38:52,800 --> 00:38:59,960
+does x also means so this is x in the past and we
+
+374
+00:38:59,960 --> 00:39:04,280
+want this x nowadays so x in the past it means
+
+375
+00:39:04,280 --> 00:39:07,960
+what the number of people who traveled abroad in
+
+376
+00:39:07,960 --> 00:39:12,560
+the 19th century what about x also means now we
+
+377
+00:39:12,560 --> 00:39:16,600
+will answer this question from the paragraph we
+
+378
+00:39:16,600 --> 00:39:23,220
+are a world on the move. A moving world. Airlines
+
+379
+00:39:23,220 --> 00:39:27,520
+carry more than 1.5 billion people to their
+
+380
+00:39:27,520 --> 00:39:32,280
+destinations, to their places every year.
+
+381
+00:39:35,100 --> 00:39:42,080
+More than 1.5. So we call this what? Point. We
+
+382
+00:39:42,080 --> 00:39:48,820
+study the numbers. Next lecture, Inshallah. To
+
+383
+00:39:48,820 --> 00:39:56,860
+their destination. So, their refers to what? To
+
+384
+00:39:56,860 --> 00:40:04,100
+people. Yes, it refers to people. It is estimated
+
+385
+00:40:04,100 --> 00:40:09,240
+that at any one time, at any one moment, at a
+
+386
+00:40:09,240 --> 00:40:15,590
+moment these days, Nowadays, at one time, at one
+
+387
+00:40:15,590 --> 00:40:20,910
+moment, there are as many people traveling in
+
+388
+00:40:20,910 --> 00:40:24,790
+airplanes as the total number of people who
+
+389
+00:40:24,790 --> 00:40:28,390
+traveled abroad in the whole of the 19th century.
+
+390
+00:40:29,470 --> 00:40:34,090
+So the people who traveled now in one moment,
+
+391
+00:40:34,850 --> 00:40:41,270
+similar equals to what? the number of people who
+
+392
+00:40:41,270 --> 00:40:45,030
+traveled abroad in the 19th century in all the
+
+393
+00:40:45,030 --> 00:40:51,510
+century so what does x also means x means the
+
+394
+00:40:51,510 --> 00:41:02,790
+number of people who who not traveled now who who
+
+395
+00:41:02,790 --> 00:41:07,160
+is traveling who are traveling in airplanes or who
+
+396
+00:41:07,160 --> 00:41:12,840
+are in aeroplanes just now yes
+
+397
+00:41:12,840 --> 00:41:21,280
+in aeroplanes where nowadays yes just now at one
+
+398
+00:41:21,280 --> 00:41:25,000
+time at the moment so now the people who are
+
+399
+00:41:25,000 --> 00:41:29,940
+online now now now at this time the people who are
+
+400
+00:41:29,940 --> 00:41:35,090
+online similar to or equals to The number of
+
+401
+00:41:35,090 --> 00:41:37,530
+people who traveled in the 19th century, in all
+
+402
+00:41:37,530 --> 00:41:47,050
+the century. But I have no idea how they work it
+
+403
+00:41:47,050 --> 00:41:53,990
+out. Work out. Work out, count onto the
+
+404
+00:41:53,990 --> 00:41:57,570
+calculator. I don't know how they count this. It's
+
+405
+00:41:57,570 --> 00:42:02,760
+difficult. The writer say, I don't know. or I have
+
+406
+00:42:02,760 --> 00:42:07,100
+no idea how they, the scientists, worked this out
+
+407
+00:42:07,100 --> 00:42:13,760
+and they sent this. So here again, the answer is X
+
+408
+00:42:13,760 --> 00:42:18,600
+means what? The number of people in airplanes, in
+
+409
+00:42:18,600 --> 00:42:23,900
+airlines now, in airplanes at any one moment, at
+
+410
+00:42:23,900 --> 00:42:27,580
+any time. At any one time, the number of people
+
+411
+00:42:27,580 --> 00:42:34,290
+who are in aeroplanes flying similar to the whole
+
+412
+00:42:34,290 --> 00:42:42,870
+19th century. Is it clear? Yes. Now, I want
+
+413
+00:42:42,870 --> 00:42:4
+
+445
+00:45:49,150 --> 00:45:53,110
+for the future of mankind. So there is a hope.
+
+446
+00:45:54,390 --> 00:45:57,510
+What is the hope? What is the hope from? From the
+
+447
+00:45:57,510 --> 00:46:02,370
+Olympic Games. How? Because every four years, they
+
+448
+00:46:02,370 --> 00:46:05,830
+come, all the world come together, come together
+
+449
+00:46:05,830 --> 00:46:10,050
+in peace and friendship. So this means that we
+
+450
+00:46:10,050 --> 00:46:15,370
+will hope in the future that there will be hope
+
+451
+00:46:15,370 --> 00:46:20,010
+again for the future of mankind, better future of
+
+452
+00:46:20,010 --> 00:46:23,670
+mankind. The question is, what are the good and
+
+453
+00:46:23,670 --> 00:46:29,230
+bad things about the Olympics? So we have the good
+
+454
+00:46:29,230 --> 00:46:35,810
+and we have the bad. So the Olympic Games are
+
+455
+00:46:35,810 --> 00:46:40,860
+good, but also They are bad. What are the good
+
+456
+00:46:40,860 --> 00:46:43,900
+things and what are the bad things about the
+
+457
+00:46:43,900 --> 00:46:51,840
+Olympics? Let's see the answer. So, the good
+
+458
+00:46:51,840 --> 00:46:57,300
+things, what is it? A competition in which every
+
+459
+00:46:57,300 --> 00:47:03,960
+country takes part. This is good. All the world or
+
+460
+00:47:03,960 --> 00:47:05,120
+all the countries of the world
+
+461
+00:47:07,810 --> 00:47:10,970
+Yes, takes part with each other. Now, coming
+
+462
+00:47:10,970 --> 00:47:16,250
+together in peace and friendship. So all the world
+
+463
+00:47:16,250 --> 00:47:20,970
+come together in peace and friendship. Also, we
+
+464
+00:47:20,970 --> 00:47:24,850
+feel hope for the future. This is good. What is
+
+465
+00:47:24,850 --> 00:47:29,370
+the bad thing? The bad thing is commercialization,
+
+466
+00:47:30,270 --> 00:47:36,830
+greed and drug abuse. They love money. Yes, and
+
+467
+00:47:36,830 --> 00:47:39,790
+they want everything and they use the drugs
+
+468
+00:47:39,790 --> 00:47:41,550
+wrongly.
+
+469
+00:47:43,210 --> 00:47:49,110
+So this is number five. Is it clear? Yes. I want
+
+470
+00:47:49,110 --> 00:47:50,670
+someone to read the title.
+
+471
+00:47:53,770 --> 00:47:57,150
+Yes. The Olympic Games. The Olympic Games. What
+
+472
+00:47:57,150 --> 00:47:57,790
+are the two words?
+
+473
+00:48:01,290 --> 00:48:05,250
+Drug abuse. Yes. The question. Someone to give me
+
+474
+00:48:05,250 --> 00:48:13,250
+the question. Yes. The good and the bad things.
+
+475
+00:48:13,370 --> 00:48:15,790
+Yes. The good. Yes.
+
+476
+00:48:18,490 --> 00:48:19,930
+What is the bad thing?
+
+477
+00:48:33,050 --> 00:48:40,990
+Commercialization, greed, drug abuse. Yes. Now,
+
+478
+00:48:42,050 --> 00:48:42,770
+number six.
+
+479
+00:48:49,970 --> 00:48:57,770
+Number six, what's it about? Agriculture. Yes. So
+
+480
+00:48:57,770 --> 00:49:05,110
+the question here, what point was Jonathan Swift,
+
+481
+00:49:05,970 --> 00:49:09,690
+the writer. Jonathan Swift, what point was
+
+482
+00:49:09,690 --> 00:49:15,070
+Jonathan Swift making about farmers and
+
+483
+00:49:15,070 --> 00:49:23,470
+politicians? So here, the writer Swift speak about
+
+484
+00:49:23,470 --> 00:49:28,980
+the farmers and the politicians, the farmers and
+
+485
+00:49:28,980 --> 00:49:35,200
+politicians. What is the point about them? Read
+
+486
+00:49:35,200 --> 00:49:39,820
+the passage silently and I will read it aloud to
+
+487
+00:49:39,820 --> 00:49:43,840
+find out the answer. In 1724,
+
+488
+00:49:46,200 --> 00:49:51,260
+Jonathan Swift wrote, he wrote something, whoever
+
+489
+00:49:51,260 --> 00:49:58,600
+makes two blades of a grass or two ears of corn
+
+490
+00:49:58,600 --> 00:50:06,700
+grow where only one grew before oh this is the
+
+491
+00:50:06,700 --> 00:50:13,320
+subject of the of the sentence the person who make
+
+492
+00:50:13,320 --> 00:50:19,660
+two instead of one the person or the people who
+
+493
+00:50:19,660 --> 00:50:25,450
+make two things instead of one two Two blades of
+
+494
+00:50:25,450 --> 00:50:32,950
+grasses, two, or two ears of corn, two things.
+
+495
+00:50:34,950 --> 00:50:41,090
+Instead of one, it's bitter. Who gives me two
+
+496
+00:50:41,090 --> 00:50:44,290
+instead of one, bitter. Two hundred instead of one
+
+497
+00:50:44,290 --> 00:50:48,510
+hundred, bitter. One thousand instead of one
+
+498
+00:50:48,510 --> 00:50:52,030
+hundred, better, more, I want more. So here she
+
+499
+00:50:52,030 --> 00:50:56,730
+says, whoever, anyone, whoever makes two blades of
+
+500
+00:50:56,730 --> 00:51:00,910
+grass or two areas of corn grow where only one
+
+501
+00:51:00,910 --> 00:51:09,030
+grew before, serves. So here, serves. Serves
+
+502
+00:51:09,030 --> 00:51:14,530
+mankind. Serves people. Good for people. Will be
+
+503
+00:51:14,530 --> 00:51:20,700
+good for people. The one with two instead of one.
+
+504
+00:51:21,700 --> 00:51:28,480
+Better than the whole race of politicians. So the
+
+505
+00:51:28,480 --> 00:51:35,280
+politicians here are not very good. Why? Because
+
+506
+00:51:35,280 --> 00:51:41,500
+they can't do this. So here in Europe, our farmers
+
+507
+00:51:41,500 --> 00:51:48,120
+have done this. In Europe, The farmers make two
+
+508
+00:51:48,120 --> 00:51:58,420
+instead of one. Make bigger crops. Now, in 1907,
+
+509
+00:52:00,580 --> 00:52:09,620
+whole villages in France died of hunger. Whole
+
+510
+00:52:09,620 --> 00:52:17,610
+villages died of hunger. Now in Europe, We can't
+
+511
+00:52:17,610 --> 00:52:23,290
+eat all the food we produce. Good. So in the past,
+
+512
+00:52:23,630 --> 00:52:30,090
+people died of hunger. Now we have more food. So
+
+513
+00:52:30,090 --> 00:52:34,350
+it is good or bad? Good. So the farmers are good.
+
+514
+00:52:34,730 --> 00:52:39,150
+Why? Because in the past, people died because of
+
+515
+00:52:39,150 --> 00:52:44,070
+hunger. Now we eat everything and we have more
+
+516
+00:52:44,070 --> 00:52:49,640
+food. So the farmers are excellent. Two instead of
+
+517
+00:52:49,640 --> 00:52:59,740
+one. Now, if only we hope, we hope, we hope, all
+
+518
+00:52:59,740 --> 00:53:05,820
+of us, we hope, if only politicians could find a
+
+519
+00:53:05,820 --> 00:53:09,640
+way to share it with those parts of the world
+
+520
+00:53:09,640 --> 00:53:11,840
+where there is famine.
+
+521
+00:53:14,100 --> 00:53:18,280
+So the politicians can't do this thing. The
+
+522
+00:53:18,280 --> 00:53:23,800
+farmers can, but the politicians can't. So here,
+
+523
+00:53:24,340 --> 00:53:29,820
+we hope if only politicians could find, they did
+
+524
+00:53:29,820 --> 00:53:33,000
+not find, they did not find. We hope they will
+
+525
+00:53:33,000 --> 00:53:37,000
+find or they could find, you understand? We hope
+
+526
+00:53:37,000 --> 00:53:42,190
+they could find a way, a method to share it, what
+
+527
+00:53:42,190 --> 00:53:46,170
+is it? The food. The food, the additional food.
+
+528
+00:53:46,450 --> 00:53:50,050
+With what? With those parts of the world where
+
+529
+00:53:50,050 --> 00:53:54,250
+there is famine. So we have some countries with
+
+530
+00:53:54,250 --> 00:53:57,470
+more food, some countries with no food. We hope
+
+531
+00:53:57,470 --> 00:54:00,670
+that the politicians will give these countries
+
+532
+00:54:00,670 --> 00:54:08,630
+some food. So the question is, what point was
+
+533
+00:54:09,570 --> 00:54:12,070
+Jonathan Swift making about farmers and
+
+534
+00:54:12,070 --> 00:54:16,610
+politicians, the answer is farmers grow food that
+
+535
+00:54:16,610 --> 00:54:24,030
+feeds the world. Good, very good. But politicians
+
+536
+00:54:24,030 --> 00:54:29,770
+don't seem capable of making decisions. They
+
+537
+00:54:29,770 --> 00:54:35,650
+can't. They can't. They can't decide which will
+
+538
+00:54:37,070 --> 00:54:42,470
+Prevent famine. So why there is famine? Because
+
+539
+00:54:42,470 --> 00:54:48,510
+Britishers don't give these countries food. So we
+
+540
+00:54:48,510 --> 00:54:52,210
+hope that Britishers will give the additional food
+
+541
+00:54:52,210 --> 00:54:56,270
+to these countries who suffer from famine, from
+
+542
+00:54:56,270 --> 00:55:03,770
+lack of food. So the title is agriculture and the
+
+543
+00:55:03,770 --> 00:55:09,840
+two words are corn and Famine, lack of food. Yes.
+
+544
+00:55:10,080 --> 00:55:15,580
+What about the last? The last paragraph. The last
+
+545
+00:55:15,580 --> 00:55:23,200
+paragraph. Yes. We are still here. We are still
+
+546
+00:55:23,200 --> 00:55:29,620
+here. The last wonder of the wooden world. The
+
+547
+00:55:29,620 --> 00:55:34,690
+last wonder. Number one. Number? Seven. Number?
+
+548
+00:55:35,090 --> 00:55:39,930
+Seven. What is wonder number seven? We are still
+
+549
+00:55:39,930 --> 00:55:45,010
+here. Alhamdulillah, we are alive. This is the
+
+550
+00:55:45,010 --> 00:55:48,370
+wonder of the world. The last wonder of the modern
+
+551
+00:55:48,370 --> 00:55:54,230
+world is simply that we are still here. We are
+
+552
+00:55:54,230 --> 00:55:57,940
+still here. So this is the wonder of the world. We
+
+553
+00:55:57,940 --> 00:56:04,640
+have had nuclear weapons. We have weapons, nuclear
+
+554
+00:56:04,640 --> 00:56:11,240
+weapons that destroy all the world. For over 50
+
+555
+00:56:11,240 --> 00:56:15,220
+years. So we have weapon, nuclear weapon for about
+
+556
+00:56:15,220 --> 00:56:20,300
+what? For about 50 years. That could destroy, that
+
+557
+00:56:20,300 --> 00:56:22,300
+will kill the world.
+
+558
+00:56:27,620 --> 00:56:30,700
+Since 1950s, we have nuclear power, nuclear
+
+559
+00:56:30,700 --> 00:56:36,180
+weapon. But until now, they did not use it. So
+
+560
+00:56:36,180 --> 00:56:41,280
+this is wonder of the world. The seventh wonder of
+
+561
+00:56:41,280 --> 00:56:47,260
+the world. So over 50 years, that could, what's
+
+562
+00:56:47,260 --> 00:56:53,000
+that? Weapons could destroy the world. What's
+
+563
+00:56:53,000 --> 00:56:57,720
+that? Refer to what? To nuclear. weapons could
+
+564
+00:56:57,720 --> 00:57:03,220
+mean destroy the world but we haven't used them
+
+565
+00:57:03,220 --> 00:57:07,900
+did we use the nuclear power nuclear weapons no
+
+566
+00:57:07,900 --> 00:57:12,400
+it's the wonder of the world but we haven't used
+
+567
+00:57:12,400 --> 00:57:17,460
+them to do it alhamdulillah they did not use the
+
+568
+00:57:17,460 --> 00:57:24,560
+nuclear weapons this is surely of course the
+
+569
+00:57:24,560 --> 00:57:30,860
+greatest wonder of all of all the seven so the
+
+570
+00:57:30,860 --> 00:57:37,000
+question is we are still here why is this a wonder
+
+571
+00:57:37,000 --> 00:57:44,580
+we haven't used nuclear weapons to destroy the
+
+572
+00:57:44,580 --> 00:57:51,000
+world yet yes so this is the end of
+
+573
+00:57:54,240 --> 00:57:59,100
+This reading passage, which is about wonders of
+
+574
+00:57:59,100 --> 00:57:59,900
+the modern world.
+
diff --git a/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/xJQ-QwBzbcQ_raw.srt b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/xJQ-QwBzbcQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..19bb02b4f2dad770f45ca83ba22570f1ef49ea9a
--- /dev/null
+++ b/PL9fwy3NUQKwZQm1WzCEzA1TRC9joCRwzb/xJQ-QwBzbcQ_raw.srt
@@ -0,0 +1,1420 @@
+1
+00:00:20,940 --> 00:00:25,740
+Assalamualaikum warahmatullahi wabarakatuh. Good
+
+2
+00:00:25,740 --> 00:00:30,560
+afternoon. Today, inshallah, we are going to study
+
+3
+00:00:30,560 --> 00:00:37,380
+or to complete the previous lessons. We are going
+
+4
+00:00:37,380 --> 00:00:43,160
+to study about the prediction and certainty with
+
+5
+00:00:43,160 --> 00:00:49,540
+will, want. And I think I don't think.
+
+6
+00:00:53,150 --> 00:00:58,490
+If you look at the first exercise, discussing
+
+7
+00:00:58,490 --> 00:01:04,950
+grammar. Work with a partner and
+
+8
+00:01:04,950 --> 00:01:07,550
+align the correct verb form.
+
+9
+00:01:10,510 --> 00:01:15,630
+Number one. So we are going to choose between two
+
+10
+00:01:15,630 --> 00:01:21,670
+alternatives. Will or going to. Or will and the
+
+11
+00:01:21,670 --> 00:01:26,320
+present continuous. The first one, why are you
+
+12
+00:01:26,320 --> 00:01:31,160
+putting on your coat? Why are you putting on your
+
+13
+00:01:31,160 --> 00:01:38,760
+coat? Because I'll take, I'm going to take the dog
+
+14
+00:01:38,760 --> 00:01:45,540
+for a walk. He's going to take the dog for a walk.
+
+15
+00:01:45,740 --> 00:01:48,360
+So we say I'll or I'm going to.
+
+16
+00:01:52,350 --> 00:01:57,290
+Going to. So here we use going to.
+
+17
+00:02:00,610 --> 00:02:11,390
+Why? Why? Because it is decision before speaking.
+
+18
+00:02:12,810 --> 00:02:19,010
+Decision before speaking. He's ready to go out.
+
+19
+00:02:19,450 --> 00:02:24,590
+Why? To take the dog with him. So this is a quick
+
+20
+00:02:24,590 --> 00:02:28,590
+decision. No, I'm going to, it means past decision
+
+21
+00:02:28,590 --> 00:02:32,710
+or decision before the time of speaking.
+
+22
+00:02:35,710 --> 00:02:43,670
+So if I want to write why I say Decision before
+
+23
+00:02:43,670 --> 00:02:47,730
+speaking. Number two.
+
+24
+00:02:49,950 --> 00:02:55,950
+Would you like to go out for a drink tonight? How
+
+25
+00:02:55,950 --> 00:03:01,990
+about tomorrow night? I'm calling you. I'll call
+
+26
+00:03:01,990 --> 00:03:09,030
+you or I'm calling you. I'm calling.
+
+27
+00:03:10,330 --> 00:03:14,290
+Calling is calling is easy without preparation
+
+28
+00:03:14,290 --> 00:03:20,870
+without arrangement So this is I will It is
+
+29
+00:03:20,870 --> 00:03:27,270
+promise promise or decision at the time of
+
+30
+00:03:27,270 --> 00:03:31,410
+speaking decision at the moment of speaking a
+
+31
+00:03:31,410 --> 00:03:38,410
+spontaneous decision quick decision Number three
+
+32
+00:03:40,820 --> 00:03:49,400
+Number three. What is the score? Six to zero.
+
+33
+00:03:51,520 --> 00:03:57,620
+They are going to lose. They lose. They are going
+
+34
+00:03:57,620 --> 00:04:04,460
+to lose. Yeah. They are going to lose. What is it?
+
+35
+00:04:08,040 --> 00:04:08,840
+Prediction.
+
+36
+00:04:11,260 --> 00:04:15,580
+Evidence. Yes, it is a prediction with evidence.
+
+37
+00:04:16,020 --> 00:04:24,220
+The evidence is six to zero. So this evidence make
+
+38
+00:04:24,220 --> 00:04:28,840
+they are going to lose, not they will lose. Yes.
+
+39
+00:04:31,100 --> 00:04:32,380
+Number four.
+
+40
+00:04:35,480 --> 00:04:38,320
+It's Tony's birthday next week.
+
+41
+00:04:41,300 --> 00:04:48,840
+Is it? I didn't know. I will send. I'm sending.
+
+42
+00:04:49,020 --> 00:04:55,000
+I'm going to send them a card. I will. Why?
+
+43
+00:04:55,580 --> 00:05:01,560
+Because it is a quick decision. Decision at the
+
+44
+00:05:01,560 --> 00:05:07,420
+moment of speaking. Just now. Quickly. But going
+
+45
+00:05:07,420 --> 00:05:14,270
+to Past intention. No. Because the birthday, he
+
+46
+00:05:14,270 --> 00:05:17,190
+knew about his birthday just now. So quickly he
+
+47
+00:05:17,190 --> 00:05:29,610
+said, I'll send him a card. Yeah. Number five. Are
+
+48
+00:05:29,610 --> 00:05:35,690
+you and Alan still going out together? Oh, yes.
+
+49
+00:05:36,690 --> 00:05:43,850
+We're getting married in June.
+
+50
+00:05:44,990 --> 00:05:50,110
+We're getting arrangement. Yes. Now they arranged
+
+51
+00:05:50,110 --> 00:05:54,690
+to get married. They're going to be husband and
+
+52
+00:05:54,690 --> 00:06:01,250
+wife. So this is arrangement, not quick decision.
+
+53
+00:06:02,110 --> 00:06:09,220
+Again, Aryu and Alan. you and her still going out
+
+54
+00:06:09,220 --> 00:06:14,860
+together oh yes we're going to get married in June
+
+55
+00:06:14,860 --> 00:06:23,980
+finished we arranged everything number five where
+
+56
+00:06:23,980 --> 00:06:28,380
+are you going on holiday this year we haven't
+
+57
+00:06:28,380 --> 00:06:35,020
+decided we have been decided we might go or we are
+
+58
+00:06:35,020 --> 00:06:41,280
+going to Italy. We haven't decided. There is no
+
+59
+00:06:41,280 --> 00:06:48,340
+decision. So we might go. We might go to Italy.
+
+60
+00:06:49,760 --> 00:06:56,180
+Maybe yes, maybe no. You understand? So here we
+
+61
+00:06:56,180 --> 00:07:01,260
+choose all of them means future. But this is
+
+62
+00:07:02,800 --> 00:07:07,300
+Correct. This is incorrect. Why? Because this is
+
+63
+00:07:07,300 --> 00:07:12,400
+intention before speaking, but this is at the time
+
+64
+00:07:12,400 --> 00:07:16,960
+of speaking. No, according to the sequence or to
+
+65
+00:07:16,960 --> 00:07:20,500
+the context, I'm going to take the dog for a walk.
+
+66
+00:07:21,760 --> 00:07:30,410
+Here, I'll call you offer or a quick decision. or
+
+67
+00:07:30,410 --> 00:07:36,150
+promise yes promise here so here what's the score
+
+68
+00:07:36,150 --> 00:07:43,570
+six to zero so prediction with evidence this is
+
+69
+00:07:43,570 --> 00:07:46,270
+the evidence and this is the prediction they are
+
+70
+00:07:46,270 --> 00:07:50,530
+going to lose number
+
+71
+00:07:50,530 --> 00:07:58,360
+four is it's Tony's birthday I didn't know. I
+
+72
+00:07:58,360 --> 00:08:03,060
+yelled him a card. Quick decision. Quick decision.
+
+73
+00:08:04,340 --> 00:08:11,500
+Five. Are you and her still going out together? We
+
+74
+00:08:11,500 --> 00:08:16,100
+finished. We arranged everything. We are getting
+
+75
+00:08:16,100 --> 00:08:21,420
+married in June. We arranged everything. Number
+
+76
+00:08:21,420 --> 00:08:26,540
+six. Were you going on holiday this year? We
+
+77
+00:08:26,540 --> 00:08:33,540
+haven't decided. We might go. Work in pairs. Say
+
+78
+00:08:33,540 --> 00:08:38,560
+the two sentences and say why. Why did we choose
+
+79
+00:08:38,560 --> 00:08:40,520
+this? Work in pairs.
+
+80
+00:08:51,000 --> 00:09:03,340
+That's enough. Yes. So These are the answers The
+
+81
+00:09:03,340 --> 00:09:12,060
+answers number one I'm going to take Decision made
+
+82
+00:09:12,060 --> 00:09:19,400
+before speaking Okay I'll call spontaneous
+
+83
+00:09:19,400 --> 00:09:26,040
+decision or promise spontaneous means quick Quick
+
+84
+00:09:26,040 --> 00:09:31,720
+decision. Yes, it means decision at the moment of
+
+85
+00:09:31,720 --> 00:09:36,360
+speaking. Number three, they are going to lose.
+
+86
+00:09:38,180 --> 00:09:44,160
+Prediction based on present evidence. Prediction
+
+87
+00:09:44,160 --> 00:09:50,640
+with evidence. Prediction with evidence. Four,
+
+88
+00:09:51,660 --> 00:09:57,180
+I'll send spontaneous decision. Quick decision.
+
+89
+00:09:57,640 --> 00:10:02,140
+Decision at the time of speaking. We are getting
+
+90
+00:10:02,140 --> 00:10:08,060
+married. Arrangement. Future arrangement. We
+
+91
+00:10:08,060 --> 00:10:10,220
+arranged everything before.
+
+92
+00:10:12,720 --> 00:10:20,320
+We might go. Not certain. Uncertain. Possibility.
+
+93
+00:10:21,380 --> 00:10:27,490
+Not sure. Not certain. It's the future, but it is
+
+94
+00:10:27,490 --> 00:10:28,390
+uncertain.
+
+95
+00:10:32,250 --> 00:10:38,150
+Okay. Someone read the first one. Yes. I'm going
+
+96
+00:10:38,150 --> 00:10:46,210
+to take this assignment before speaking. To I'll
+
+97
+00:10:46,210 --> 00:10:49,490
+call spontaneous decision and promise. Spontaneous
+
+98
+00:10:49,490 --> 00:10:55,980
+decision and promise. Decision or promise. Three.
+
+99
+00:10:57,980 --> 00:11:05,900
+Prediction with
+
+100
+00:11:05,900 --> 00:11:06,980
+evidence.
+
+101
+00:11:08,960 --> 00:11:15,840
+Four. Spontaneous decision.
+
+102
+00:11:16,380 --> 00:11:20,700
+I yell. Generally speaking, we say I yell. The
+
+103
+00:11:20,700 --> 00:11:26,130
+negative I want. But the full form will. Yes.
+
+104
+00:11:27,050 --> 00:11:32,110
+Future arrangement.
+
+105
+00:11:32,930 --> 00:11:39,270
+Future arrangement. Arrangement. Not certain.
+
+106
+00:11:41,810 --> 00:11:49,830
+Uncertain. Possibility. Not sure. Okay. Is it
+
+107
+00:11:49,830 --> 00:11:52,830
+clear? So when I ask you to choose between going
+
+108
+00:11:52,830 --> 00:11:57,330
+to and will and the present continuous, there
+
+109
+00:11:57,330 --> 00:12:00,930
+should be a reason. Reason why I choose this
+
+110
+00:12:00,930 --> 00:12:06,110
+instead of this. There should be a reason. Now
+
+111
+00:12:06,110 --> 00:12:09,150
+make
+
+112
+00:12:09,150 --> 00:12:15,590
+sentences using I think with will and the promotes
+
+113
+00:12:15,590 --> 00:12:25,230
+in a. match them with a sentence in B so here this
+
+114
+00:12:25,230 --> 00:12:33,470
+is grammar and vocabulary at first I want to use I
+
+115
+00:12:33,470 --> 00:12:43,010
+think why? to be more polite don't say I will I
+
+116
+00:12:43,010 --> 00:12:43,470
+shall
+
+117
+00:12:47,250 --> 00:12:52,170
+Say, I think. Every time say, I think. For
+
+118
+00:12:52,170 --> 00:13:01,450
+everything say, I think. So here I think Jerry
+
+119
+00:13:01,450 --> 00:13:04,490
+will
+
+120
+00:13:04,490 --> 00:13:07,550
+win
+
+121
+00:13:07,550 --> 00:13:14,030
+the tennis match. Number two, I think it will
+
+122
+00:13:16,620 --> 00:13:27,040
+Be a nice day tomorrow. I think I will pass
+
+123
+00:13:27,040 --> 00:13:37,760
+my exam on Friday. I think you will like the film.
+
+124
+00:13:40,180 --> 00:13:43,180
+I think we will
+
+125
+00:13:45,960 --> 00:13:51,460
+to the airport in time I
+
+126
+00:13:51,460 --> 00:14:01,900
+think you will get the job again say this part of
+
+127
+00:14:01,900 --> 00:14:07,920
+the sentences number one usually say I think I
+
+128
+00:14:07,920 --> 00:14:12,560
+think I think if it's negative I don't think yes
+
+129
+00:14:16,950 --> 00:14:24,030
+I think it will be a nice day tomorrow. Yes. I
+
+130
+00:14:24,030 --> 00:14:30,090
+think I will pass my exam on Friday. Yes. I think
+
+131
+00:14:30,090 --> 00:14:36,310
+you won't like the phone. The phone, yes. Five
+
+132
+00:14:36,310 --> 00:14:39,210
+over there.
+
+133
+00:14:44,370 --> 00:14:48,130
+In time. Yes. Number six and the last one. I think
+
+134
+00:14:48,130 --> 00:14:54,130
+you will get better. So these are I think so and
+
+135
+00:14:54,130 --> 00:14:59,830
+so. So when I say I think it's good. It is okay.
+
+136
+00:14:59,890 --> 00:15:03,330
+Okay. It is not okay. Never mind. So I think it's
+
+137
+00:15:03,330 --> 00:15:09,790
+polite way of saying your opinion. When you want
+
+138
+00:15:09,790 --> 00:15:12,830
+to say your opinion about something, say I think.
+
+139
+00:15:13,630 --> 00:15:18,850
+I think if it is positive if it is negative say I
+
+140
+00:15:18,850 --> 00:15:23,370
+don't think you understand so this is the grammar
+
+141
+00:15:23,370 --> 00:15:29,290
+part of the exercise now we want according to this
+
+142
+00:15:29,290 --> 00:15:32,510
+meaning or to the meaning here we want to choose
+
+143
+00:15:32,510 --> 00:15:39,750
+one sentence from B so I think Jerry will win the
+
+144
+00:15:39,750 --> 00:15:42,510
+tennis match choose
+
+145
+00:15:45,890 --> 00:15:54,270
+Yes. Number? Yes. Two. So here, this is number
+
+146
+00:15:54,270 --> 00:16:01,430
+one. He's been playing really well lately. Again,
+
+147
+00:16:01,670 --> 00:16:06,190
+say the sentence or the sentence. Yes. I think he
+
+148
+00:16:06,190 --> 00:16:10,150
+will win the tennis match. He has been playing
+
+149
+00:16:10,150 --> 00:16:13,540
+really well lately. Uh-huh. So this is the reason.
+
+150
+00:16:13,740 --> 00:16:17,040
+This is the evidence. Uh-huh. The evidence of
+
+151
+00:16:17,040 --> 00:16:23,080
+this. Yes. The justification. Justification. The
+
+152
+00:16:23,080 --> 00:16:27,200
+reason. The complement of the sentence in order to
+
+153
+00:16:27,200 --> 00:16:33,380
+be logic. Number two. Hmm. Yeah. I think it will
+
+154
+00:16:33,380 --> 00:16:39,660
+be a nice day tomorrow. The forecast is for warm
+
+155
+00:16:39,660 --> 00:16:42,700
+and dry weather. So this is number two.
+
+156
+00:16:45,940 --> 00:16:50,640
+I think it will be a nice day tomorrow. Why? The
+
+157
+00:16:50,640 --> 00:16:58,780
+forecast is for warm and dry weather. The
+
+158
+00:16:58,780 --> 00:17:03,200
+direction generally is for what? Warm and dry
+
+159
+00:17:03,200 --> 00:17:06,840
+weather. All the speaking are about warm and dry
+
+160
+00:17:06,840 --> 00:17:14,110
+weather. Yes. Number three. Yes. I think I will
+
+161
+00:17:14,110 --> 00:17:18,890
+pass my exam on Friday. I have been studying for
+
+162
+00:17:18,890 --> 00:17:27,530
+weeks. I've been studying for weeks. So when you
+
+163
+00:17:27,530 --> 00:17:31,830
+say I'll pass my exam on Friday, this is a
+
+164
+00:17:31,830 --> 00:17:36,160
+prediction. general prediction and this is the
+
+165
+00:17:36,160 --> 00:17:41,040
+reason the justification i've been studying for
+
+166
+00:17:41,040 --> 00:17:50,960
+weeks uh-huh yeah number four you will like the
+
+167
+00:17:50,960 --> 00:17:53,500
+film it's a wonderful story and
+
+168
+00:18:00,520 --> 00:18:05,580
+It's a wonderful story. The story of the film is
+
+169
+00:18:05,580 --> 00:18:14,600
+wonderful. And the acting is excellent. So I think
+
+170
+00:18:14,600 --> 00:18:18,800
+you will like the film because it is a wonderful
+
+171
+00:18:18,800 --> 00:18:24,260
+story and the acting is excellent. So I choose
+
+172
+00:18:24,260 --> 00:18:28,200
+this according to the meaning, to the context.
+
+173
+00:18:30,780 --> 00:18:38,780
+Number five. I think we'll get to the airport in
+
+174
+00:18:38,780 --> 00:18:41,340
+time, but we'd better get going.
+
+175
+00:18:44,700 --> 00:18:50,740
+Number five. I think we'll get to the airport in
+
+176
+00:18:50,740 --> 00:18:54,080
+time, but we'd better
+
+177
+00:18:58,720 --> 00:19:04,580
+going to go now just now. Peter. Uh-huh. Uh-huh.
+
+178
+00:19:04,660 --> 00:19:11,920
+And number six. Yes. I think you will get the job.
+
+179
+00:19:12,060 --> 00:19:15,140
+You have the right qualifications and plenty of
+
+180
+00:19:15,140 --> 00:19:21,180
+experience. So this is number six. I think you
+
+181
+00:19:21,180 --> 00:19:24,960
+will get the job. Why? You have the right
+
+182
+00:19:24,960 --> 00:19:30,740
+qualifications. the certificates and plenty of
+
+183
+00:19:30,740 --> 00:19:34,660
+experience not two or three months no many years
+
+184
+00:19:34,660 --> 00:19:39,280
+so you have got two things the qualifications and
+
+185
+00:19:39,280 --> 00:19:41,780
+the experience so you are the suitable for this
+
+186
+00:19:41,780 --> 00:19:45,220
+job I think you will get the job because you are
+
+187
+00:19:45,220 --> 00:19:48,820
+excellent you have the qualifications and the
+
+188
+00:19:48,820 --> 00:19:53,720
+experience also again I want you to work in pairs
+
+189
+00:19:53,720 --> 00:20:00,560
+match A with B And don't forget to use I think in
+
+190
+00:20:00,560 --> 00:20:00,860
+pairs.
+
+191
+00:20:15,880 --> 00:20:23,400
+Yes, I want you to read these six sentences aloud.
+
+192
+00:20:25,780 --> 00:20:42,040
+Yes, individually. Yes, number one. Number two.
+
+193
+00:20:43,460 --> 00:20:47,760
+Yes. I think it will be a nice day tomorrow. The
+
+194
+00:20:47,760 --> 00:20:51,840
+forecast is for warm and dry weather. Number
+
+195
+00:20:51,840 --> 00:20:57,670
+three. Yes. I think I will pass my exam on Friday.
+
+196
+00:20:58,070 --> 00:21:04,630
+I have been studying four years. Four? I think you
+
+197
+00:21:04,630 --> 00:21:07,570
+will like it. It's a wonderful story and the
+
+198
+00:21:07,570 --> 00:21:14,950
+acting is excellent. Next? Yeah? Yeah? I think we
+
+199
+00:21:14,950 --> 00:21:15,990
+will come.
+
+200
+00:21:21,600 --> 00:21:23,000
+Yes,
+
+201
+00:21:27,400 --> 00:21:39,380
+the last one Over there Thank
+
+202
+00:21:39,380 --> 00:21:43,220
+you now These are the answers
+
+203
+00:21:52,740 --> 00:21:56,240
+Again also. Again. Number one again.
+
+204
+00:22:02,480 --> 00:22:08,680
+Two. Yeah. I think it will be a nice day tomorrow.
+
+205
+00:22:08,840 --> 00:22:12,580
+The forecast is for warm and dry weather. Yes.
+
+206
+00:22:12,660 --> 00:22:15,380
+Here. Yes. Uh huh.
+
+207
+00:22:22,760 --> 00:22:30,620
+I think I went best my exam Exam Exam on Friday I
+
+208
+00:22:30,620 --> 00:22:37,680
+have been studying for weeks Yeah, next Yes I
+
+209
+00:22:37,680 --> 00:22:41,260
+think you like the film, it's wonderful story and
+
+210
+00:22:41,260 --> 00:22:47,740
+exciting and acting is excellent Five Harzine I
+
+211
+00:22:47,740 --> 00:22:50,960
+think we'll get to the airport in time but with
+
+212
+00:22:56,880 --> 00:23:01,960
+I think you will get the job you have the right
+
+213
+00:23:01,960 --> 00:23:06,740
+qualification and plenty of experience thank you
+
+214
+00:23:06,740 --> 00:23:13,580
+now let's go to the second exercise make
+
+215
+00:23:13,580 --> 00:23:21,070
+sentences using I don't think with will and the
+
+216
+00:23:21,070 --> 00:23:25,050
+prompts in A in exercise 3 match them with the
+
+217
+00:23:25,050 --> 00:23:31,310
+sentence in C. So this is the first one with A and
+
+218
+00:23:31,310 --> 00:23:38,290
+this is the new one C. But I will say I don't
+
+219
+00:23:38,290 --> 00:23:45,610
+think because the justification is negative. Now
+
+220
+00:23:45,610 --> 00:23:54,460
+the second exercise We wanted to match A with C. A
+
+221
+00:23:54,460 --> 00:24:01,840
+with C. But we use here, I don't think.
+
+222
+00:24:03,800 --> 00:24:12,920
+I don't think. So, I don't think Jerry will, the
+
+223
+00:24:12,920 --> 00:24:19,100
+same, will win the tennis match. Gone. Yes. Number
+
+224
+00:24:19,100 --> 00:24:21,440
+two. The first part.
+
+225
+00:24:24,860 --> 00:24:29,900
+Yeah? I don't think it will be a nice day
+
+226
+00:24:29,900 --> 00:24:37,640
+tomorrow. Uh-huh. Wow. Number three. Yes? I don't
+
+227
+00:24:37,640 --> 00:24:45,260
+think I will pass my exam on Friday. Four. Yeah? I
+
+228
+00:24:45,260 --> 00:24:49,960
+don't think you will like that. Uh-huh.
+
+229
+00:24:53,080 --> 00:24:57,640
+Again. I don't think we will get to the airport in
+
+230
+00:24:57,640 --> 00:25:03,940
+time. Number six. I don't think you will get the
+
+231
+00:25:03,940 --> 00:25:09,780
+job. So this is the grammar point of the exercise.
+
+232
+00:25:10,140 --> 00:25:14,780
+Again, number one. Quickly. Quickly. I don't think
+
+233
+00:25:14,780 --> 00:25:19,920
+Jerry will win the tennis match. Two. I don't
+
+234
+00:25:19,920 --> 00:25:24,070
+think it will be around this time. Three. I don't
+
+235
+00:25:24,070 --> 00:25:25,990
+think I will lose my job.
+
+236
+00:25:30,290 --> 00:25:35,130
+Four. I don't
+
+237
+00:25:35,130 --> 00:25:42,130
+think we will get a job. Next. I don't think we
+
+238
+00:25:42,130 --> 00:25:48,530
+will get a job. The last one. I don't think we
+
+239
+00:25:48,530 --> 00:25:54,500
+will get a job. Aha. So now the justification or
+
+240
+00:25:54,500 --> 00:25:58,640
+the reason is different. The reason here is
+
+241
+00:25:58,640 --> 00:26:04,780
+different. Why? Because I don't think negative. So
+
+242
+00:26:04,780 --> 00:26:08,400
+I don't think so and so because number one,
+
+243
+00:26:09,020 --> 00:26:10,420
+because yes.
+
+244
+00:26:13,480 --> 00:26:14,380
+Yeah.
+
+245
+00:26:17,740 --> 00:26:18,640
+Yes.
+
+246
+00:26:22,500 --> 00:26:29,160
+He hasn't practiced for weeks. He is lazy. He is
+
+247
+00:26:29,160 --> 00:26:33,620
+lazy without practicing. So I don't think Jerry
+
+248
+00:26:33,620 --> 00:26:38,580
+will win the tennis match. He hasn't practiced for
+
+249
+00:26:38,580 --> 00:26:48,980
+weeks. Logic. Yes. Now number two. Yes. I don't
+
+250
+00:26:48,980 --> 00:26:54,980
+think it will be a nice day tomorrow. The forecast
+
+251
+00:26:54,980 --> 00:26:58,780
+said rainy and windy. Yeah, the forecast said
+
+252
+00:26:58,780 --> 00:27:03,780
+rainy and windy. The opposite of that one. Rainy
+
+253
+00:27:03,780 --> 00:27:08,120
+and windy. So it's not a good, a nice day
+
+254
+00:27:08,120 --> 00:27:11,240
+tomorrow. Why? Because the forecast all about
+
+255
+00:27:11,240 --> 00:27:15,580
+what? About rain and wind. Rainy and windy. Number
+
+256
+00:27:15,580 --> 00:27:24,720
+three. Yeah. I haven't
+
+257
+00:27:24,720 --> 00:27:29,800
+studied at all. So I don't think I'll pass my exam
+
+258
+00:27:29,800 --> 00:27:36,760
+on Friday. Why? I haven't studied at all Next
+
+259
+00:27:36,760 --> 00:27:41,460
+number four Yes
+
+260
+00:27:42,350 --> 00:27:47,130
+I think I don't think you will like مثلًا it's a
+
+261
+00:27:47,130 --> 00:27:53,410
+big boring boring boring boring
+
+262
+00:27:53,410 --> 00:28:00,740
+or bored I am bored but the film is boring so I
+
+263
+00:28:00,740 --> 00:28:04,320
+don't think you will like the film it means you
+
+264
+00:28:04,320 --> 00:28:08,500
+won't like the film you won't like the film but
+
+265
+00:28:08,500 --> 00:28:12,920
+generally we say I think and I don't think instead
+
+266
+00:28:12,920 --> 00:28:16,700
+of saying will and want so we say the negative
+
+267
+00:28:16,700 --> 00:28:22,040
+with think uh-huh so here I don't think with will
+
+268
+00:28:22,040 --> 00:28:30,930
+I don't think we uh-huh yes I don't think we will
+
+269
+00:28:30,930 --> 00:28:35,730
+get the airport in time. There's too much traffic.
+
+270
+00:28:36,470 --> 00:28:43,730
+Too much traffic. There's too much traffic. Busy.
+
+271
+00:28:45,330 --> 00:28:46,830
+The last one.
+
+272
+00:28:54,290 --> 00:28:58,610
+They are looking for someone with more experience.
+
+273
+00:28:59,350 --> 00:29:07,090
+So this is number six. Again, working pairs. But
+
+274
+00:29:07,090 --> 00:29:12,970
+don't forget to use I don't think. I don't think
+
+275
+00:29:12,970 --> 00:29:18,690
+so and so. Yes, working pairs. Now that's enough.
+
+276
+00:29:19,510 --> 00:29:20,910
+Again, reading aloud.
+
+277
+00:29:26,740 --> 00:29:31,180
+Reading aloud again. Number one. I don't think
+
+278
+00:29:31,180 --> 00:29:34,740
+Jerry will win the tennis match. He hasn't
+
+279
+00:29:34,740 --> 00:29:40,420
+practiced for weeks. Again. I don't think Jerry
+
+280
+00:29:40,420 --> 00:29:44,500
+will win the tennis match. He hasn't practiced for
+
+281
+00:29:44,500 --> 00:29:49,640
+weeks. Two. I don't think it will be a nice day
+
+282
+00:29:49,640 --> 00:29:52,900
+tomorrow. The forecast said rainy and windy.
+
+283
+00:29:53,160 --> 00:29:58,980
+Three. I don't think I passed my exam on Friday. I
+
+284
+00:29:58,980 --> 00:30:04,120
+haven't studied at all. Four. I don't think we
+
+285
+00:30:04,120 --> 00:30:07,100
+have, we have liked the film. It is a bit boring.
+
+286
+00:30:08,340 --> 00:30:13,640
+Five. I don't think we'll get to, get to the
+
+287
+00:30:13,640 --> 00:30:16,460
+airport in time. There's too much at the traffic.
+
+288
+00:30:17,380 --> 00:30:21,200
+Six. And the last one. Yes. I don't think you will
+
+289
+00:30:21,200 --> 00:30:24,340
+get a job. They're looking for someone with more
+
+290
+00:30:25,010 --> 00:30:27,750
+Aha, they are looking for some for someone with
+
+291
+00:30:27,750 --> 00:30:30,470
+more experience. You don't have any experience.
+
+292
+00:30:30,830 --> 00:30:39,510
+Yes next also again Again
+
+293
+00:30:39,510 --> 00:30:42,510
+number one Two
+
+294
+00:30:51,540 --> 00:30:54,520
+I don't think it will be a nice day tomorrow than
+
+295
+00:30:54,520 --> 00:31:01,040
+on your birthday except rain and sun 3 I don't
+
+296
+00:31:01,040 --> 00:31:05,280
+think I will pass my exam on Friday, I haven't
+
+297
+00:31:05,280 --> 00:31:11,640
+studied at all 4 I don't think you will like the
+
+298
+00:31:11,640 --> 00:31:15,340
+film, it's a bit boring 5
+
+299
+00:31:21,550 --> 00:31:33,790
+The last one So
+
+300
+00:31:33,790 --> 00:31:38,590
+now we started I think and I don't think and this
+
+301
+00:31:38,590 --> 00:31:45,120
+last exercise about you about you yourself So here
+
+302
+00:31:45,120 --> 00:31:51,480
+make true sentences about you. Starting with I
+
+303
+00:31:51,480 --> 00:31:55,360
+think or I don't think. Both of them are correct.
+
+304
+00:31:55,860 --> 00:32:01,300
+I think or I don't think. If you believe in this,
+
+305
+00:32:01,640 --> 00:32:04,720
+say I think. If you don't believe in this, say I
+
+306
+00:32:04,720 --> 00:32:09,460
+don't think. Without compliment. And if you want
+
+307
+00:32:09,460 --> 00:32:13,040
+to add something, you can add something. If you
+
+308
+00:32:13,040 --> 00:32:18,980
+want to add, It's up to you. Now, I think I'll
+
+309
+00:32:18,980 --> 00:32:24,040
+have a
+
+310
+00:32:24,040 --> 00:32:30,720
+bath tonight. I think I'll have a bath tonight.
+
+311
+00:32:31,440 --> 00:32:35,320
+No, no. I don't think I'll have a bath tonight.
+
+312
+00:32:36,940 --> 00:32:43,620
+It's cold. I think I'll have a bath tonight. uh
+
+313
+00:32:43,620 --> 00:32:48,180
+-huh it's hot something like this yes so we can
+
+314
+00:32:48,180 --> 00:32:53,680
+add something and we can stop number two say I
+
+315
+00:32:53,680 --> 00:32:56,860
+think or I don't think yes I don't think the
+
+316
+00:32:56,860 --> 00:33:00,820
+teacher will give us a lot of homework I don't
+
+317
+00:33:00,820 --> 00:33:02,660
+think the teacher will give us a lot of homework
+
+318
+00:33:02,660 --> 00:33:09,470
+but another prediction I think the teacher will
+
+319
+00:33:09,470 --> 00:33:12,330
+give us a lot of homework. So this is the
+
+320
+00:33:12,330 --> 00:33:19,410
+prediction. Say are you? He will? Are you? If you
+
+321
+00:33:19,410 --> 00:33:22,950
+think so, say I think. If you don't think so, say
+
+322
+00:33:22,950 --> 00:33:28,210
+I don't think. Number three. Yes.
+
+323
+00:33:32,470 --> 00:33:36,570
+I don't think I will eat out tonight. I don't have
+
+324
+00:33:36,570 --> 00:33:42,590
+any money. I don't have any money. Yes. Number
+
+325
+00:33:42,590 --> 00:33:43,790
+four.
+
+326
+00:33:46,470 --> 00:33:51,830
+Yes. I don't think it will rain tomorrow. Yeah.
+
+327
+00:33:52,410 --> 00:33:56,610
+Yeah, because we are in April. We are in April.
+
+328
+00:33:58,370 --> 00:34:07,030
+Five. Five. I think I will go shopping this
+
+329
+00:34:07,030 --> 00:34:14,410
+afternoon. Hmm. Because my mother told me to buy a
+
+330
+00:34:14,410 --> 00:34:21,210
+lot of things and I have money. Yeah. Six.
+
+331
+00:34:25,830 --> 00:34:33,330
+Yeah. My partner. My partner will be a millionaire
+
+332
+00:34:33,330 --> 00:34:42,250
+one day. Hmm. Why? Why? Because he will sell his
+
+333
+00:34:42,250 --> 00:34:47,930
+land. He will sell his five cars. Uh-huh. Or he
+
+334
+00:34:47,930 --> 00:34:53,550
+were, he was a millionaire and he now he's going
+
+335
+00:34:53,550 --> 00:34:58,250
+to be a millionaire. Yes. Number seven. And the
+
+336
+00:34:58,250 --> 00:35:01,850
+last one, Harazin. I don't think we'll have an
+
+337
+00:35:01,850 --> 00:35:08,190
+exam this week. Really? Yes, again, again, number
+
+338
+00:35:08,190 --> 00:35:11,510
+one again, number one again, but this time in
+
+339
+00:35:11,510 --> 00:35:16,890
+pairs. Say this, I think, I don't think, and you
+
+340
+00:35:16,890 --> 00:35:18,130
+can say something.
+
+341
+00:35:22,290 --> 00:35:28,090
+Yes, that's enough. Again, these are examples with
+
+342
+00:35:28,090 --> 00:35:32,450
+I think or I don't think. Number one, choose one
+
+343
+00:35:32,450 --> 00:35:37,610
+again, or I think or I don't think. Yes.
+
+344
+00:35:40,770 --> 00:35:42,930
+One, just one.
+
+345
+00:35:46,710 --> 00:35:47,790
+Two.
+
+346
+00:35:52,370 --> 00:35:53,770
+Three.
+
+347
+00:35:58,330 --> 00:35:59,730
+Four.
+
+348
+00:36:03,350 --> 00:36:04,750
+Again.
+
+349
+00:36:08,230 --> 00:36:18,070
+Yeah, next Number
+
+350
+00:36:18,070 --> 00:36:26,890
+six Yeah Millionaire
+
+351
+00:36:26,890 --> 00:36:32,350
+one day one day the future number seven Yeah
+
+352
+00:36:36,040 --> 00:36:40,240
+Hmm, I think we'll have an exam this week No,
+
+353
+00:36:40,440 --> 00:36:44,900
+we'll have exam after three weeks Thank you very
+
+354
+00:36:44,900 --> 00:36:49,820
+much See you next time Wassalamualaikum
+
+355
+00:36:49,820 --> 00:36:51,000
+Warahmatullahi Wabarakatuh
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/-FGdKV34BaI_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/-FGdKV34BaI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e788c314a4a15252152fe6b9e9765d1765768423
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/-FGdKV34BaI_postprocess.srt
@@ -0,0 +1,2284 @@
+1
+00:00:21,650 --> 00:00:25,530
+بسم الله الرحمن الرحيم اليوم ان شاء الله هنواصل مع
+
+2
+00:00:25,530 --> 00:00:28,970
+اللي هو الاستقرار الرياضي او mathematical
+
+3
+00:00:28,970 --> 00:00:33,350
+induction بدأنا بداية يمكن مقدمة قصيرة في المحاضرة
+
+4
+00:00:33,350 --> 00:00:36,270
+الماضية اليوم ان شاء الله هنشوف بالتفصيل مع بعض
+
+5
+00:00:36,270 --> 00:00:41,250
+الأمثلة و هذه المهارةو .. او هذه الطريقة من طرق
+
+6
+00:00:41,250 --> 00:00:46,290
+البرهان الرياضي طريقة مهمة جدا اه طبعا هي خاصة
+
+7
+00:00:46,290 --> 00:00:49,750
+بنوع معين من ال statements بنوع معين من ال
+
+8
+00:00:49,750 --> 00:00:56,240
+statements فاحنا متعامل مع statements for all andB
+
+9
+00:00:56,240 --> 00:01:02,860
+of N فإذا أول ملاحظة ان هي بتبرهن اللي هو تقارير
+
+10
+00:01:02,860 --> 00:01:06,520
+تحتوي على مكمم الشمول for all هذا هو الشرط الوحيد
+
+11
+00:01:06,520 --> 00:01:11,920
+لأ في كمان شرط بدنا ال universeيبدأ من عدد صحيح
+
+12
+00:01:11,920 --> 00:01:18,020
+معين N0 ويمشي على التتابع N0 plus 1 N0 plus 2 و
+
+13
+00:01:18,020 --> 00:01:22,280
+هكذا طبعا مبدئيا هناخده U تساوي ال natural number
+
+14
+00:01:22,280 --> 00:01:26,640
+كبداية كبداية يعني هنبدأ N0 تساوي واحد و بعدين
+
+15
+00:01:26,640 --> 00:01:31,260
+هنعمم لكن هذه الصورة العامة لكن احنا كتسهيل هنبدأ
+
+16
+00:01:31,260 --> 00:01:36,360
+ان N0 تساوي واحد و بعدين هنعمم نسترجع مع بعض ماذا
+
+17
+00:01:37,960 --> 00:01:42,020
+بنص ال principle of mathematical induction مبدأ
+
+18
+00:01:42,020 --> 00:01:45,540
+الاستقراء الرياضي بقول لي عشان أثبت أن هذه الجملة
+
+19
+00:01:45,540 --> 00:01:50,280
+صحيحة بدي خطوطين رئيسيتين الخطوة الأولى أثبت أنه
+
+20
+00:01:50,280 --> 00:01:53,260
+نقطة البداية اللي هي إذا كانت ال U بتساوي ال
+
+21
+00:01:53,260 --> 00:01:56,840
+natural number فبدي أثبت P of 1 is true طب لو كانت
+
+22
+00:01:56,840 --> 00:02:00,660
+ال U بتبدأ من N0 بدي أثبت أن P of N0 is true فهي
+
+23
+00:02:00,660 --> 00:02:03,370
+عندي نقطة بدايةفالخطوة الأولى بتقول في عندي نقطة
+
+24
+00:02:03,370 --> 00:02:07,270
+بداية بيسموها ال base step الخطوة الأساسية الخطوة
+
+25
+00:02:07,270 --> 00:02:11,750
+الأساسية بعدين في عندي شرط تاني وهو جملة شرطية إذا
+
+26
+00:02:11,750 --> 00:02:15,290
+كانت ال statement صحيحة عند ال K لازم تكون صحيحة
+
+27
+00:02:15,290 --> 00:02:20,110
+عند ال K plus one جملة شرطية فدول هم الشرطين P of
+
+28
+00:02:20,110 --> 00:02:23,890
+one is trueاللي ممكن نستبدلها بـ P of N zero is
+
+29
+00:02:23,890 --> 00:02:27,690
+true بشكل عام بشكل عام والشرط التاني جملة شرطية
+
+30
+00:02:27,690 --> 00:02:31,450
+إذا كانت صحية عند ال K فهي صحية عند ال K plus one
+
+31
+00:02:31,450 --> 00:02:36,970
+ويمكن زي ما احنا شبهناها لو في عنا إيش إنارةعدت
+
+32
+00:02:36,970 --> 00:02:40,930
+لمبات ادت هو مصادر للإضاءة فانا بهمني اول واحدة
+
+33
+00:02:40,930 --> 00:02:44,790
+اشبكها بيه المصدر الكهربا ب .. ب .. ب .. ب .. بفيش
+
+34
+00:02:44,790 --> 00:02:47,690
+الكهربا اللي هي B of one او B of one zero ف B في
+
+35
+00:02:47,690 --> 00:02:50,970
+بداية بعدين اذا ضوط الأولى التانية بتاخد كهربا
+
+36
+00:02:50,970 --> 00:02:54,570
+منها بتاخد كهربا منها و العاشرة بتاخد من التاسعة و
+
+37
+00:02:54,570 --> 00:02:57,350
+ال .. و ال K plus one بتاخد من K بشكل عام المية
+
+38
+00:02:57,350 --> 00:03:00,790
+واحد ليش بتضوي لإن بتاخد كهربا من المية ضوى و هكذا
+
+39
+00:03:00,950 --> 00:03:03,970
+وواضح الشرط التاني بيدا المعنى بها دا المعنى
+
+40
+00:03:03,970 --> 00:03:08,150
+فهدولة هما الشرطين هنشوف كيف بنطبقهم بالأمثلة وكيف
+
+41
+00:03:08,150 --> 00:03:14,230
+نستخدمه في البراهيمأه فهنا أن المثال الأول طبعا
+
+42
+00:03:14,230 --> 00:03:19,070
+قلنا احنا أي statement على صورة for all n P of n و
+
+43
+00:03:19,070 --> 00:03:21,970
+ال universe مبدئيا هناخده natural number و ممكن
+
+44
+00:03:21,970 --> 00:03:25,670
+بعدين نعمم البداية مش ضروري تكون واحد ممكن تكون اي
+
+45
+00:03:25,670 --> 00:03:28,530
+عدد صحيح اخر ممكن تكون صفر ممكن تكون سالب خمسة
+
+46
+00:03:28,530 --> 00:03:31,590
+ممكن تكون عشرة مافيش شرط لكن نبدأ بالتبسيط ان
+
+47
+00:03:31,590 --> 00:03:35,580
+البداية تكون الواحدفطبعا هناك أنواع متعددة من هذه
+
+48
+00:03:35,580 --> 00:03:38,400
+ال statements اللي بتحتوي على المكمن for all و
+
+49
+00:03:38,400 --> 00:03:44,240
+بتحتوي على اللي هو عدد صحيح n عسبين المثال بعض
+
+50
+00:03:44,240 --> 00:03:48,940
+المتطابقات اللي بتحتوي صيغة قانون للجمع لو بدي
+
+51
+00:03:48,940 --> 00:03:54,700
+أجمع الأعداد لعصور تلاتة J ناقص اتنين تلاتة J ناقص
+
+52
+00:03:54,700 --> 00:03:58,660
+اتنين بدي أجمعهم من J بتسوي واحد إلى ال N بدي
+
+53
+00:03:58,660 --> 00:04:02,480
+أجمعهم بقول للقانون أن الجواب على طول مغير ما تحسب
+
+54
+00:04:02,610 --> 00:04:08,170
+هو نص ال N في تلاتة N ناقص واحد هذا قانون طب كيف
+
+55
+00:04:08,170 --> 00:04:11,050
+بدنا نثبته؟ طبعا بنتطلع أن هذا عبارة عن statement
+
+56
+00:04:11,050 --> 00:04:13,990
+على صورة for all N و ال universe هو ال natural
+
+57
+00:04:13,990 --> 00:04:19,410
+number P of N فخلينا نبدأ الحل مع بعض solution
+
+58
+00:04:19,410 --> 00:04:26,830
+فأول شيء we have to prove خلينا نكبر الخط شوية
+
+59
+00:04:35,160 --> 00:04:45,220
+We have to prove the statement
+
+60
+00:04:45,220 --> 00:04:56,440
+B of N وهي عبارة عن summation J من 1 ل N ثلاثة J
+
+61
+00:04:56,440 --> 00:05:06,030
+ناقص 2 تساوي نص في N في ثلاثة N ناقص واحدلمين ده
+
+62
+00:05:06,030 --> 00:05:11,450
+تكون صحيحة؟ for all and تنتمي للuniverse اللي هو
+
+63
+00:05:11,450 --> 00:05:14,330
+مين مجموعة الأعداد الطبيعية فهذه هي ال statement
+
+64
+00:05:14,330 --> 00:05:17,610
+بقيت صيغة السؤال مرة تانية عشان أؤكد فاحنا فيها
+
+65
+00:05:17,610 --> 00:05:20,850
+إنا صورة for all and P of N بس كتبناها بالشكل
+
+66
+00:05:20,850 --> 00:05:23,790
+العام حطينا for all بعد ال statement بعد ال
+
+67
+00:05:23,790 --> 00:05:26,290
+statement مش قبلها كله صح فهذه على الصيغة اللي
+
+68
+00:05:26,290 --> 00:05:31,060
+حكيناهاfor all n, b of n من الكون السؤال الـ
+
+69
+00:05:31,060 --> 00:05:34,500
+natural number من الـ open sentence b of n اللي هي
+
+70
+00:05:34,500 --> 00:05:38,800
+ال summation j من واحد ل n تلاتة j ناقص اتنين
+
+71
+00:05:38,800 --> 00:05:43,720
+بتسوي نص n في تلاتة n ناقص واحد واضح السؤال؟ واضح
+
+72
+00:05:43,720 --> 00:05:47,400
+السؤال تمام بدنا نثبته هذا فهذا مثال ممكن نثبته
+
+73
+00:05:47,400 --> 00:05:51,100
+بال induction لأنه على صيغة for all n, b of n و
+
+74
+00:05:51,100 --> 00:05:54,080
+الـ n natural number في عندنا خطوتين رئيسيتين
+
+75
+00:05:54,080 --> 00:06:05,230
+فهنبدأ بالخطوة الأولى واحدبدنا نثبت ان بي
+
+76
+00:06:05,230 --> 00:06:11,580
+of one is true فهذه الخطوة الأولىفهذه الخطوة
+
+77
+00:06:11,580 --> 00:06:16,740
+الأولى هذه الخطوة خطوة أساسية لا غنى عنها لكنها
+
+78
+00:06:16,740 --> 00:06:20,680
+سهلة ويمكن المثال تبعنا بيساعدنا هلجيت احنا؟ مين
+
+79
+00:06:20,680 --> 00:06:24,320
+أصعب خطوة؟ بدنا كهرباء يمدلنا اللمبات ويشبكهم لكن
+
+80
+00:06:24,320 --> 00:06:27,160
+عشان نشغل بدنا أي ولاد صغير ممكن يشبك الفيش وانتهى
+
+81
+00:06:27,160 --> 00:06:30,820
+فهذه الخطوة هي إيش؟ نشبك الفيش يعني ندى مصدر لأول
+
+82
+00:06:30,820 --> 00:06:33,840
+لمبة وبعدين كل لمبة تاخد من التانية فإذا هذه عملية
+
+83
+00:06:33,840 --> 00:06:37,420
+سهلة لكنها أساسية وإلا كل شغل الكهرباء هيروح إيش؟
+
+84
+00:06:37,420 --> 00:06:40,920
+سدا لأنه إذا ما شبكناشأه لكن هو شغل الرئيسي
+
+85
+00:06:40,920 --> 00:06:44,700
+والأساسي والصعب لكنه مالواش فايدة إذا مافيش مصدر
+
+86
+00:06:44,700 --> 00:06:48,860
+كهربا يوصل لأول لمبة تمام؟ فلنثبت أن P of 1 is
+
+87
+00:06:48,860 --> 00:06:53,360
+true طيب خليني نشوف إيش هي P of 1 ما هي P of 1
+
+88
+00:06:53,360 --> 00:06:58,060
+نفسرها نقطين فوق بعض ونتبهوا للرموز بحطش يساوي
+
+89
+00:06:58,060 --> 00:07:01,700
+لأنها دي مش مقدار رياضي يساوي ولا تكافؤ لأنها مش
+
+90
+00:07:01,700 --> 00:07:05,040
+statement P of 1 statement؟ لأ اه بينا نفسرها ما
+
+91
+00:07:05,040 --> 00:07:12,360
+هي P of 1 هذه قلنا P of Nبنعود عن N بواحد إذا ال P
+
+92
+00:07:12,360 --> 00:07:18,440
+of 1 بدي أثبت أن summation J من واحد لواحد تلاتة J
+
+93
+00:07:18,440 --> 00:07:22,580
+ناقص اتنين و لا تلاتة في واحد تلاتة J لأن ببدل عن
+
+94
+00:07:22,580 --> 00:07:28,170
+N هي P of N N إيه تتساوي نصفي واحد في تلاتة في
+
+95
+00:07:28,170 --> 00:07:32,130
+واحد ناقص واحد هذا أشماله بدأ أثبت أنه true IP of
+
+96
+00:07:32,130 --> 00:07:35,290
+one بدنا نثبت أن هذا يكون true هذه عبارة عن
+
+97
+00:07:35,290 --> 00:07:37,670
+المتطابقة لو أكتشف الكون true إذا اليمين ساوى
+
+98
+00:07:37,670 --> 00:07:42,170
+اليسار إذا اليمين ساوى اليسار إيش نعمل فك اليسار و
+
+99
+00:07:42,170 --> 00:07:46,490
+فك اليمين بسطيهم هذه عبارة عن sigma ماذا يعني رمز
+
+100
+00:07:46,490 --> 00:07:50,050
+ال sigma في الرياضيات في عندي دليل J بيبدأ من
+
+101
+00:07:50,050 --> 00:07:53,570
+البداية و بتم زيد واحد واحد زي ال universe وهم جدا
+
+102
+00:07:53,570 --> 00:07:56,590
+تمامأه فإذا أنا بدا بدا جيه بتبدأ من واحد وحتى ما
+
+103
+00:07:56,590 --> 00:07:59,370
+تزيد واحد لحد ما توصل للنهاية اللي هي الواحد إذا
+
+104
+00:07:59,370 --> 00:08:01,530
+بتبدأ من واحد وينتهي بواحد فاش فيه اللي حد واحدة
+
+105
+00:08:01,530 --> 00:08:04,690
+فاش فيه اللي حد واحد إذا هذا الطرف اللي هو عبارة
+
+106
+00:08:04,690 --> 00:08:09,230
+عن إيش تلاتة في واحد ناقص اتنين بديها تساوي جداش
+
+107
+00:08:09,230 --> 00:08:14,870
+نصف جداش في اتنين فهل واحد تساوي واحد صحيح إذا بي
+
+108
+00:08:14,870 --> 00:08:22,210
+of one is true thus بي of one is true فسهلة دايما
+
+109
+00:08:22,210 --> 00:08:27,400
+سهلةفي المعظم هي أسهل خطوة في ال induction لكنها
+
+110
+00:08:27,400 --> 00:08:31,020
+مهمة زي ما يبدو شبك الفيش أي واحد فينا بيعرف يشبك
+
+111
+00:08:31,020 --> 00:08:37,420
+لكن قولله أعمل شبكة كهربائي مختلف واضح؟ أي سؤال؟
+
+112
+00:08:37,420 --> 00:08:43,360
+تفضليلأ، هو إيش؟ هي بي .. وين؟ أنا هنا عوضت جيه
+
+113
+00:08:43,360 --> 00:08:45,880
+بواحد، آه، لأنه بدأ فك الـ Sigma بس دايما،
+
+114
+00:08:45,880 --> 00:08:49,900
+مانتصرعش عشان ما نخلطش، هالجيه تقولنا بي of one ال
+
+115
+00:08:49,900 --> 00:08:52,960
+.. ال بي هي بي of ان، حطينا بعد الان واحد، الآن
+
+116
+00:08:52,960 --> 00:08:56,240
+يجيشت الخطوة التانية، بدأ فك ال Sigma، ماذا يعني
+
+117
+00:08:56,240 --> 00:08:59,500
+ال Sigma؟ هي دليل جيه، إيش جيه بتاخد؟ تبدأ من
+
+118
+00:08:59,500 --> 00:09:02,900
+واحد، بعدين بتزيد، لحد ما توصل لإيش، لنهاية، بدأت
+
+119
+00:09:02,900 --> 00:09:05,400
+بواحد، هتنتهي بواحد، إذا خلاص، تاخد واحد و توقف،
+
+120
+00:09:05,400 --> 00:09:10,330
+ولا لأ؟ فعوضنا جيه بصحوا واحدمش في ال V of N واضح؟
+
+121
+00:09:10,330 --> 00:09:13,870
+فنفرج بين الحاجتين نزل الخطوة رقم اتنين خلينا
+
+122
+00:09:13,870 --> 00:09:20,040
+نكتبها لإن احنا في أول مثالwill show او want to
+
+123
+00:09:20,040 --> 00:09:23,700
+show that ايش الشرط التاني في ال induction؟ اذا
+
+124
+00:09:23,700 --> 00:09:27,760
+كانت B of K is true لازم تكون implies B of K plus
+
+125
+00:09:27,760 --> 00:09:35,240
+one is true B of K is true implies B of K plus one
+
+126
+00:09:35,240 --> 00:09:42,700
+is true بدنا نثبت هذه الخطوة وين؟
+
+127
+00:09:42,700 --> 00:09:44,300
+مين بتسأليش السؤال؟
+
+128
+00:09:48,450 --> 00:09:54,430
+فإذا هذه خطوة رقم اتنين نحللها
+
+129
+00:09:54,430 --> 00:10:01,090
+و نتعامل فيها فكتبنا نص طبعي مبدأ استقرار رياضيأه
+
+130
+00:10:01,090 --> 00:10:04,670
+بدنا نثبت هذه الجملة أو هذه التقرير هذه ال
+
+131
+00:10:04,670 --> 00:10:08,690
+statement .. statement شرطية conditional و اتعلمنا
+
+132
+00:10:08,690 --> 00:10:12,710
+في المحاضرة الأخيرة إذا بدنا نثبت B implies Q ال
+
+133
+00:10:12,710 --> 00:10:16,490
+directly proofش بيقول assume B is true ليش؟ لأن لو
+
+134
+00:10:16,490 --> 00:10:19,910
+ال B false nothing to prove لأن إذا مافيش وعد
+
+135
+00:10:19,910 --> 00:10:23,250
+مافيش مشكلة احنا حرينلكن وين اللي بدنا نشتغل إذا
+
+136
+00:10:23,250 --> 00:10:26,950
+وعدنا بدنا نشتهد أو بدنا يجب علينا أن نوفي بالوعد
+
+137
+00:10:26,950 --> 00:10:30,590
+فوين الشغل دايما مطلوب لما ال B تكون true اللي هو
+
+138
+00:10:30,590 --> 00:10:34,370
+أيه الشرط لازم أثبت أن جواب الشرط يكون صحيح كيف
+
+139
+00:10:34,370 --> 00:10:36,930
+ببدأ البرهان ستتذكروا اللي عملنا بنقوله assume
+
+140
+00:10:36,930 --> 00:10:41,030
+that الشرط is true بيه is true فاحنا هنبدأ البرهان
+
+141
+00:10:41,030 --> 00:10:42,570
+نقوله assume
+
+142
+00:10:45,160 --> 00:10:50,260
+B of K خليني بس أفسرها لإن هو دي بشكل أهم في هذا
+
+143
+00:10:50,260 --> 00:10:55,220
+المثال B of K ماذا تعني؟ اه B of N قلناها دهياك B
+
+144
+00:10:55,220 --> 00:11:00,480
+of N يعني summation J من واحد لوين؟ ل K بعد ال N
+
+145
+00:11:00,480 --> 00:11:07,330
+ده حط Kتلاتة جيه ناقص اتنين ايش تساوي نص في كيه في
+
+146
+00:11:07,330 --> 00:11:11,630
+تلاتة كيه ناقص واحد هذا مهم جدا هذا اسمه induction
+
+147
+00:11:11,630 --> 00:11:15,390
+hypothesis هنشوف كيف دوره بيبلعب assume that P of
+
+148
+00:11:15,390 --> 00:11:21,990
+K is true ايش مطلوب اثبت ان P of K plus one is
+
+149
+00:11:21,990 --> 00:11:32,190
+true we have to show that P of K plus oneاللي هي
+
+150
+00:11:32,190 --> 00:11:37,820
+إيش عبارة عن إيش برضه نقاش نفسرهاSummation من واحد
+
+151
+00:11:37,820 --> 00:11:42,380
+لوين ل K plus one تلاتة جيه ناقص اتنين بتتغير
+
+152
+00:11:42,380 --> 00:11:48,860
+مابتتغيرش ايش بتسوي نص في جداش في K plus one افتح
+
+153
+00:11:48,860 --> 00:11:55,100
+جوس تلاتة في K plus one ناقص one فكل وين في N
+
+154
+00:11:55,100 --> 00:11:59,820
+بنعوض عنها K plus one لما نحط عن P of K بدل N
+
+155
+00:11:59,820 --> 00:12:05,580
+بنعوض K وها كده واضح اه تمام اذا هذا هوالشرط
+
+156
+00:12:05,580 --> 00:12:11,130
+التاني وهذا تفسيرهتمام إذا نبدأ نثبت هذا الكلام
+
+157
+00:12:11,130 --> 00:12:16,710
+الآن كحالة خاصة كيف نتعامل مع ال sigma مع ال
+
+158
+00:12:16,710 --> 00:12:20,790
+summation وكيف نثبت خطوة ال induction هذه خطوة ال
+
+159
+00:12:20,790 --> 00:12:23,570
+induction طبعا هذه متطابقة ممكن أبدأ من أي طرف
+
+160
+00:12:23,570 --> 00:12:28,450
+أوصل للتاني كقاعدة عشان نوصل نبدأ من الطرف اليسار
+
+161
+00:12:28,450 --> 00:12:30,810
+نبدأ من ال sigma اللي هي فيها إمكانية أنه نشتغل و
+
+162
+00:12:30,810 --> 00:12:33,990
+نبسط و نطلع بنتاج في حاجة ممكن نعمل فهنبدأ من
+
+163
+00:12:33,990 --> 00:12:39,920
+الطرف اليسار nowالطرف اليسار J من واحد لـ K plus
+
+164
+00:12:39,920 --> 00:12:48,270
+one تلاتة J ناقص اتنينوين لأ ال K معطى يعني ال K
+
+165
+00:12:48,270 --> 00:12:51,870
+معطى صارت induction hypothesis معطى اه لأن اش بقول
+
+166
+00:12:51,870 --> 00:12:56,390
+اذا كانت B of K is true لازم تؤدي انه K plus one
+
+167
+00:12:56,390 --> 00:13:00,890
+is true هذه جملة شرطية قلنا لو كان ال B of K false
+
+168
+00:13:00,890 --> 00:13:03,250
+اذا دايما الجملة الشرطية ترفض اذا مادي مش مطلوب من
+
+169
+00:13:03,250 --> 00:13:06,450
+ايش طب ان هيش .. ايش .. وين .. وين شغل مطلوب اذا
+
+170
+00:13:06,450 --> 00:13:10,330
+كانت ال B of K true I assume it is true ايش لازم
+
+171
+00:13:10,330 --> 00:13:14,040
+اثبت لازم اثبت انه صحيح ان K plus oneفهذه جملة
+
+172
+00:13:14,040 --> 00:13:17,360
+شرطية، فهذا دائما يجب أن نتعلم، هذه مبدأ أساسي من
+
+173
+00:13:17,360 --> 00:13:20,140
+مبادئ الرياضيات اللي احنا اشتغلنا عليه كل الأسابيع
+
+174
+00:13:20,140 --> 00:13:22,540
+الماضية، تلت أسابيع، هذا أسبوع الرابع احنا في
+
+175
+00:13:22,540 --> 00:13:26,580
+المصاد، فهذا بنتعلم أي جملة شرطية عشان أبرهنها
+
+176
+00:13:26,580 --> 00:13:30,480
+أنها صحيحة، بفترض أن الشرط صحيح، و بأثبت أن جواب
+
+177
+00:13:30,480 --> 00:13:35,520
+الصح أنه صحيح، واضح؟ تمامنيجي نشوف هذه الـ Sigma
+
+178
+00:13:35,520 --> 00:13:39,720
+طبعا خطوة عامة في ال induction لازم و احنا بنشتغل
+
+179
+00:13:39,720 --> 00:13:44,720
+عشان نثبت ان بي of k plus one is true لازم نكتبها
+
+180
+00:13:44,720 --> 00:13:49,040
+بدلالة الخطوة السابقة بي of k لازم نستفيد من هذه
+
+181
+00:13:49,040 --> 00:13:51,520
+الخطوة اللي هي بيسموها induction hypothesis اه دي
+
+182
+00:13:51,520 --> 00:13:55,560
+قاعدة عامة اذا انت برهنتي و ما استخدمتهاش 99% حل
+
+183
+00:13:55,560 --> 00:13:58,760
+الغلط مديش هقول 100% لأنه ممكن يكون فلازم تكون
+
+184
+00:13:58,760 --> 00:14:01,820
+المواطن استفيد منه لأن زي ما حكينا في الرياضيات
+
+185
+00:14:01,820 --> 00:14:06,450
+مافيش حاجة بتاعة بتاعةولا ازواج ولا تجميل لأ كله
+
+186
+00:14:06,450 --> 00:14:10,290
+لضروري كله ضروري لازم نستخدمه فهنا بنحاول نكتب هذه
+
+187
+00:14:10,290 --> 00:14:17,570
+بدلالة ايه ممتاز طيب هذا مطلوب المعطى هو sigma بس
+
+188
+00:14:17,570 --> 00:14:21,790
+واقف عند ال K فالسؤال المطروح هل بقدر اكتب ال
+
+189
+00:14:21,790 --> 00:14:25,470
+sigma اللي واقف عند K plus one بدلالة ال sigma
+
+190
+00:14:25,470 --> 00:14:29,860
+اللي واقف عند ال K نعم لأن هذالو بدنا نفكه ال
+
+191
+00:14:29,860 --> 00:14:34,200
+sigma هذا رمز في الرياضيات مين حقيقته المفكوك لو
+
+192
+00:14:34,200 --> 00:14:38,160
+فكناها هذه خليني اول مثال بتعمله بالتفصيل و
+
+193
+00:14:38,160 --> 00:14:41,240
+بالتفصيل ال momentum هذا ايش معناته هذه ال sigma
+
+194
+00:14:41,240 --> 00:14:45,860
+يعني عوض ج بتسوى واحد بتصير تلاتة ناقص اتنين بعدين
+
+195
+00:14:45,860 --> 00:14:49,840
+عوض ج بتسوى اتنين بتصير ستة ناقص اتنين اللي هي ايش
+
+196
+00:14:50,050 --> 00:14:53,570
+تلاتة في اتنين طبعا ماعيش معناته ال sigma اه تعالى
+
+197
+00:14:53,570 --> 00:14:57,570
+زائد ايش بعده بنعود جيهم الساعة وتلاتة تسعة ناقص
+
+198
+00:14:57,570 --> 00:15:02,610
+اتنين وها كذا مين الحد الأخير عشان بتكتب اللي
+
+199
+00:15:02,610 --> 00:15:07,930
+جابله بهمني بتعود عن جيه ب K plus one اذا تلاتة ب
+
+200
+00:15:07,930 --> 00:15:14,110
+K plus one ناقص اتنين ومين اللي جابله Kناقص اتنين
+
+201
+00:15:14,110 --> 00:15:18,670
+وهم بمشي بيقياش بالترتيب واضحة هذه الـ Sigma؟ هيك
+
+202
+00:15:18,670 --> 00:15:22,250
+معناه الـ Sigma، هذا تعريف الـ Sigma إذا فهمناه،
+
+203
+00:15:22,250 --> 00:15:25,450
+بحنفهم من اللي بعده فمعناه الـ Sigma بيت من واحد،
+
+204
+00:15:25,450 --> 00:15:28,850
+وبعدين بتاخد اياش اتنين، تلاتة، وين بتوقف؟ لنهاية
+
+205
+00:15:28,850 --> 00:15:31,710
+ال summation، مثلا بيسموه اياش Upper Bound of
+
+206
+00:15:31,710 --> 00:15:33,990
+Summation، بتتذكر المتفاضل الألف؟ بيسميه الحد
+
+207
+00:15:33,990 --> 00:15:39,190
+الأعلى للمجموع، و البداية بيسموه Lower Bound، الحد
+
+208
+00:15:39,190 --> 00:15:42,620
+الأدنى لل-Summation، هي نقطة البدايةطبعا انا بدي
+
+209
+00:15:42,620 --> 00:15:47,520
+اكتب الـSigma لـK ماشي معناته؟ معناته خد كل الحدود
+
+210
+00:15:47,520 --> 00:15:51,760
+لعند الحد قبل الأخير مع بعض وخل الحد الأخير لحاله،
+
+211
+00:15:51,760 --> 00:15:55,640
+هيك معناته يعني هديش معناها لو بدي افسرها؟ يعني
+
+212
+00:15:55,640 --> 00:15:59,420
+معناها إيش؟ حُد جيب تسوى واحدو 2 و 3 و اين اتوقف
+
+213
+00:15:59,420 --> 00:16:03,560
+عند ال K يعني بتوقف عند هنا بنفع اعيد كتابة هذا
+
+214
+00:16:03,560 --> 00:16:06,340
+الكلام يعني اشغل هدول كله محطهم في Sigma و هذا
+
+215
+00:16:06,340 --> 00:16:09,400
+خلال الحال بنفع لإنه من خواص ال Sigma او من ..
+
+216
+00:16:09,400 --> 00:16:14,790
+اللي هو فوائد ال Sigma واستخداماتها تمامإذا نعيد
+
+217
+00:16:14,790 --> 00:16:20,370
+الكتابة إذا هذا ممكن أكتبه على صورة sigma من واحد
+
+218
+00:16:20,370 --> 00:16:26,250
+ل K تلاتة J ناقص اتنين هذا مين معبر؟ عبر عن كل
+
+219
+00:16:26,250 --> 00:16:31,610
+الحدود طب و هذا إيش؟ لحاله زائد تلاتة K إيش؟
+
+220
+00:16:31,610 --> 00:16:38,030
+انبسطها يا دي تلاتة K زائد واحد لأن تلاتة K زائد
+
+221
+00:16:38,030 --> 00:16:43,780
+تلاتة ناقص اتنين إذا هذا كتبناه لحاله و بسطناهمش
+
+222
+00:16:43,780 --> 00:16:46,240
+همشي لما تكون كله واضح لإن هو هذي اللي .. يعني
+
+223
+00:16:46,240 --> 00:16:49,900
+اللي بنشرحه بالتفصيل الآن مكررهوش بعدين لإن هو ده
+
+224
+00:16:49,900 --> 00:16:56,440
+أول مثال متبين؟ فضل واحدة واحدة لإن واحد احنا ليش
+
+225
+00:16:56,440 --> 00:17:00,180
+مستخدم ال sigma؟ بنستخدم ال sigma للتعبير عن مجميع
+
+226
+00:17:00,180 --> 00:17:03,540
+حدود كثيرة للاختصاء فلما يكون حد لحاله بيحطله
+
+227
+00:17:03,540 --> 00:17:06,500
+sigma ليش؟ ممكن أحطله sigma بس مافيش منه فايد بدي
+
+228
+00:17:06,500 --> 00:17:09,480
+أحطله ساعته sigma أيش؟ J من K plus one ل K plus
+
+229
+00:17:09,480 --> 00:17:15,650
+one فمالهش فايد غيره فضلأه خيرش عملته هي ال sigma
+
+230
+00:17:15,650 --> 00:17:19,710
+فكيتها هي مفكوكها واضح؟ بتعرفي تتعامل مع ال sigma
+
+231
+00:17:19,710 --> 00:17:23,470
+تمام قولت أنا بيدستفيد من هذا المقطة اللي هو ايش
+
+232
+00:17:23,470 --> 00:17:27,310
+بيسموه induction hypothesis اللي هو مقطة الاستقرار
+
+233
+00:17:27,310 --> 00:17:31,510
+طب هد شماله بتحدث عن sigma من 1 ل K ال sigma اللي
+
+234
+00:17:31,510 --> 00:17:35,570
+عندك من 1 ل K plus 1 فسألت نفسي السؤال التالي هل
+
+235
+00:17:35,570 --> 00:17:39,590
+بقيت صياغة هذه و أعملها sigma ل عند K ممكن إذا
+
+236
+00:17:39,590 --> 00:17:44,840
+أخدت الحدود من 1 ل K و سبت الأخر لحقفهذا لو فكّيت
+
+237
+00:17:44,840 --> 00:17:48,900
+هذا بمعنى آخر بتوصل لهدولة كلهم ولا لأ؟ لو فكّتيه
+
+238
+00:17:48,900 --> 00:17:52,680
+ال sigma، طبعا هذا بيسوي هذا، صح؟ وهذا لحاله
+
+239
+00:17:52,680 --> 00:17:58,460
+التالت، انتبع معاه؟ مرتان، عيد، يمكن أنت من هلأ أن
+
+240
+00:17:58,460 --> 00:18:02,990
+مش شايفهصعب عليكي؟ ماشي طب فكي من هال لهال لو بدكي
+
+241
+00:18:02,990 --> 00:18:06,370
+تفكي ال sigma ايش بتعمليه جهته سوى واحد صح؟ جهته
+
+242
+00:18:06,370 --> 00:18:10,230
+سوى اتنين مين اخر واحد؟ جهته سوى كده، اذا هدول
+
+243
+00:18:10,230 --> 00:18:14,050
+الحدود كلهم مش بيسووا ال sigma هذي واضحيت؟ اه و
+
+244
+00:18:14,050 --> 00:18:18,280
+هذا هو الحد الأخيرأي سؤال فإذا دائما و أبدا أنا ال
+
+245
+00:18:18,280 --> 00:18:21,700
+sigma ممكن أعيد كتابتها و أفصل منها بعض الحدود بس
+
+246
+00:18:21,700 --> 00:18:25,720
+و إيش و أكتبها صح الشاهد مين بيقول إنه حل صح لو
+
+247
+00:18:25,720 --> 00:18:30,340
+فكيت ال sigma بتديني نفس المقدار ممتاز الآن إحنا
+
+248
+00:18:30,340 --> 00:18:33,860
+جاهزين نستخدم ال induction hypothesis هذه ال sigma
+
+249
+00:18:33,860 --> 00:18:36,780
+إشمالها هي بتساوي هذا المقدار لإنه معطج اللي أسيوم
+
+250
+00:18:36,780 --> 00:18:40,200
+يعني إنه هذا true اتفقنا في البرهان إن المعطيات
+
+251
+00:18:40,200 --> 00:18:43,540
+إشمالها trueكلها true فإذا هذا أصبح ماله true
+
+252
+00:18:43,540 --> 00:18:47,600
+فبعدين قلتله assume يعني هذا صار متفق على صحته
+
+253
+00:18:47,600 --> 00:18:53,280
+متفق على صحته إذا الأن هذا يساوي إيش بيساوي نص في
+
+254
+00:18:53,280 --> 00:18:58,860
+K في تلاتة K ناقص واحد زائد هذا ينزل زي ما هو من
+
+255
+00:18:58,860 --> 00:19:03,200
+وين جبت الخطوة هذه by induction hypothesis اه
+
+256
+00:19:03,200 --> 00:19:07,100
+فنقوله هنا من وين جبناها من induction hypothesis
+
+257
+00:19:11,770 --> 00:19:17,130
+هذه دليللا بديش اكتب كل الأدلة لإن في بعض أمور
+
+258
+00:19:17,130 --> 00:19:21,770
+متعودين عليها من حواصة sigma وهذه الأمور قديمة أه
+
+259
+00:19:21,770 --> 00:19:26,470
+الآن مرة تانية بعد ما فكنا ال sigma وحطناها في
+
+260
+00:19:26,470 --> 00:19:30,270
+صيغة تخليني أقدر السفيد من ال induction hypothesis
+
+261
+00:19:30,270 --> 00:19:32,750
+استخدمنا ال induction hypothesis هاي ال induction
+
+262
+00:19:32,750 --> 00:19:37,150
+hypothesis بقول المجموع من واحد ل K بيساوي نص في K
+
+263
+00:19:37,150 --> 00:19:40,710
+في تلاتة K نقص واحد وهذا الterminal زي ما هو واضحش
+
+264
+00:19:40,710 --> 00:19:45,150
+اللي عملته هداك صحيح إذا استخدمتهتمام؟ الان جاهزين
+
+265
+00:19:45,150 --> 00:19:48,490
+احنا جاهزين .. ايش؟ بدنا نثبت ان هذا الكلام صحيح
+
+266
+00:19:48,490 --> 00:19:51,670
+بدنا نوصل هذه الصيغة .. اه الان بدنا من الطرف
+
+267
+00:19:51,670 --> 00:19:55,570
+اليسار بنوصل لطرف اليمين عشان نختارد منه واضح ان
+
+268
+00:19:55,570 --> 00:19:57,770
+الصيغة دي ايش فيها فيها K plus و انا عامل مشترك
+
+269
+00:19:57,770 --> 00:20:01,410
+فنحاول ناخد K plus و انا عامل مشترك من هذه انبسط
+
+270
+00:20:01,410 --> 00:20:05,610
+عملية حسابية ماتبقى تلاتة .. هذه عبارة عن نص ناخد
+
+271
+00:20:05,610 --> 00:20:09,960
+النص عامل مشترك لانه بدي نص برضهبصير ايش؟ تلاتة K
+
+272
+00:20:09,960 --> 00:20:13,900
+تربيع ناقص K زائد .. اذا النص عامل مشترك ايش بدي
+
+273
+00:20:13,900 --> 00:20:19,360
+اضرب هنا؟ في اتنين زائد ستة K زائد اتنين و احط
+
+274
+00:20:19,360 --> 00:20:22,960
+المقامات اضرب في اتنين وجسمي على اتنين تمام؟ انبسط
+
+275
+00:20:22,960 --> 00:20:28,380
+كمان شوية تلاتة K تربيع زائد خمسة K زائد اتنين
+
+276
+00:20:28,380 --> 00:20:32,780
+مظبوط؟ طب انا ايش بدي؟ بدي K plus one عامل مشترك
+
+277
+00:20:32,780 --> 00:20:36,560
+احللوانا عارف ان k plus one لازم تكون عالم
+
+278
+00:20:36,560 --> 00:20:39,900
+المشترك، بنفع ايش بده يتم؟ تلاتة k زي اتنين،
+
+279
+00:20:39,900 --> 00:20:42,960
+مصبوب؟ لأن هذه تلاتة k تربيع، اذا هذه k ايش بده
+
+280
+00:20:42,960 --> 00:20:47,380
+يتم؟ تلاتة k، هذه اتنين، واحدة ايش بده يتم؟ اتنين،
+
+281
+00:20:47,380 --> 00:20:51,240
+هل جتفت؟ اتأكد ان التحليل صح، اضربيهم، بطلع صح ولا
+
+282
+00:20:51,240 --> 00:20:56,440
+صح، طب هل هذا بيسوي هذا؟ طبعا، لأن هذه تلاتة k زي
+
+283
+00:20:56,440 --> 00:21:00,300
+التلاتة ناقص واحد، وهو المطلوب يثبته، اه، فإذن
+
+284
+00:21:02,870 --> 00:21:07,790
+P of K plus one is true وانتهى
+
+285
+00:21:07,790 --> 00:21:12,790
+البرهن .. وانتهى البرهن في أي سؤال .. في أي
+
+286
+00:21:12,790 --> 00:21:15,490
+السفسار .. هذا أول مثال ان شاء الله هناخد كمان
+
+287
+00:21:15,490 --> 00:21:18,310
+مثال برضه على ال sigma ان شاء الله الأمور .. بنعيد
+
+288
+00:21:18,310 --> 00:21:21,370
+الخطوات و القمر اللي فيه أي مشكلة ان شاء الله مع
+
+289
+00:21:21,370 --> 00:21:25,640
+التكرار يكون أوضحفهذه هي الخطوات في عندنا خطوات
+
+290
+00:21:25,640 --> 00:21:30,060
+عامة لل induction وفي عندنا بعض الخطوات الخاصة
+
+291
+00:21:30,060 --> 00:21:33,200
+بالمثال اللي هو كيف اتعامل مع ال sigma كيف اتعامل
+
+292
+00:21:33,200 --> 00:21:44,340
+مع ال sigma في
+
+293
+00:21:44,340 --> 00:21:48,770
+عندنا كمان مثالبس عشان أستفيد من مساحة اللوح
+
+294
+00:21:48,770 --> 00:21:53,910
+مضايقاني شوية المساحة مش مكافية فخليني أفسر بعض
+
+295
+00:21:53,910 --> 00:22:00,350
+الأمور تحت المثال نفسه تحت المثال نفسه اه برضه هنا
+
+296
+00:22:00,350 --> 00:22:07,170
+صيغة جامعة صيغة جامعة ممكن نحولها لصيغة سيجما نعم
+
+297
+00:22:07,170 --> 00:22:10,970
+لصيغة سيجما فخلينا نبدأ الحل من هنا solution
+
+298
+00:22:12,950 --> 00:22:18,650
+الـ P of N عندنا الـ open sentence تلاتة زائد
+
+299
+00:22:18,650 --> 00:22:23,910
+يحداج زائد تسعة عشر زائد زائد تمانية N ناقص خمسة
+
+300
+00:22:23,910 --> 00:22:30,100
+بتساوي أربعة N تربيع ناقص Mمصبوط وبدش نثبتها انها
+
+301
+00:22:30,100 --> 00:22:35,900
+for all n لكل n قبضة صحيحة هذا المقدار عبارة عن
+
+302
+00:22:35,900 --> 00:22:40,540
+مجموع غير منتهي من العناصر او عدد كبير من العناصر
+
+303
+00:22:40,540 --> 00:22:46,460
+ممكن نستخدم ال sigma فهذا ممكن اعيد كتابته sigma j
+
+304
+00:22:46,460 --> 00:22:57,760
+من 1 ل n 8j ناقص 5 تساوي 4n تربية ناقص nممكن اناقش
+
+305
+00:22:57,760 --> 00:23:03,480
+كتابته صح ولا مش صح فكى وشوفى حط جيب تسوى واحد
+
+306
+00:23:03,480 --> 00:23:07,660
+بتصيب تلاتة حط جيب تسوى اتنين ستاش ناقص خمسة احداش
+
+307
+00:23:07,660 --> 00:23:11,180
+حط جيب تسوى تلاتة اربع عشرين ناقص خمسة تسعة عشر
+
+308
+00:23:11,180 --> 00:23:15,800
+وها كده وين وقف عن جيب تسوى انافهذا تماماً
+
+309
+00:23:15,800 --> 00:23:20,580
+فالمفكوك هو حقيقة المجموع و ال sigma رمز sigma رمز
+
+310
+00:23:20,580 --> 00:23:24,880
+للاختصار اه فبدنا نعرف نتعامل مع ال sigma هذه لأنه
+
+311
+00:23:24,880 --> 00:23:27,880
+أداة أساسية في الرياضيات لو في عندنا مجموعة كيف
+
+312
+00:23:27,880 --> 00:23:31,240
+نفك ال sigma أو نكتب بدلالة ال sigma بدلالة ال
+
+313
+00:23:31,240 --> 00:23:33,780
+sigma فإذا هذا اللي بدنا نثبت وبدنا نثبت for all n
+
+314
+00:23:33,780 --> 00:23:36,940
+P of n is true والان وين بتتمهي لل natural number
+
+315
+00:23:36,940 --> 00:23:43,500
+مثال زي المثال الأول تماما مع اختلاف بتفاصيل من
+
+316
+00:23:43,500 --> 00:23:44,140
+نفس النوع
+
+317
+00:23:46,900 --> 00:23:53,160
+تمام ففي أن الهيكل العام لل induction في خطوطين
+
+318
+00:23:53,160 --> 00:24:02,600
+الخطوة الأولى we have to show that
+
+319
+00:24:02,600 --> 00:24:09,060
+if P of 1 is true نبدأ
+
+320
+00:24:09,060 --> 00:24:15,200
+نشتغل سهلة P of 1ماذا تعني P of 1؟ بتلي N of 1
+
+321
+00:24:15,200 --> 00:24:20,580
+يعني بدي أثبت أنه summation من واحد لواحد تمانية J
+
+322
+00:24:20,580 --> 00:24:26,020
+ناقص خمسة بتساوي قداش أربع في واحد ناقص واحد،
+
+323
+00:24:26,020 --> 00:24:30,200
+نظبط؟ أربع تربيع أربع في N تربيع اللي واحد تربيع
+
+324
+00:24:30,200 --> 00:24:33,810
+ناقص واحديعني بدي أثبت أن مفكوك الـ Sigma بيساوي
+
+325
+00:24:33,810 --> 00:24:37,610
+تلاتة طيب، من فوق، من واحد لواحد، يعني مافيش لحد
+
+326
+00:24:37,610 --> 00:24:41,290
+وحيد، عوض عن دي بتساوي واحد، تمانية ناقص خمسة
+
+327
+00:24:41,290 --> 00:24:51,170
+بتساوي تلاتة، true، إذا الـP of one is true فإذا
+
+328
+00:24:51,170 --> 00:24:58,200
+الـP of one is true أي سؤالفهذه قطوة أساسية لكن
+
+329
+00:24:58,200 --> 00:25:03,660
+بسيطة دايما سهلة هذه قاعدة أنه دايما بالبداية اللي
+
+330
+00:25:03,660 --> 00:25:07,200
+هي N0 و احنا بدأنا أن ناخد N0 بس واحد للتبسيط
+
+331
+00:25:07,200 --> 00:25:11,020
+بتكون بهذه السهولة لإنه تعويض مباشر تعويض مباشر
+
+332
+00:25:11,020 --> 00:25:15,480
+ليش أنا لأ نشتغل الآن الخطوة التانية الخطوة
+
+333
+00:25:15,480 --> 00:25:18,580
+التانية اللي هي خلينا نكتبها و نشوف كيف نتعامل
+
+334
+00:25:18,580 --> 00:25:26,470
+معها نعيد الخطوة أه بدنا نثبت we have to provethat
+
+335
+00:25:26,470 --> 00:25:35,690
+b of k is true implies b of k plus one is true
+
+336
+00:25:35,690 --> 00:25:39,130
+تمام؟
+
+337
+00:25:39,130 --> 00:25:43,670
+واضح؟ بعيد عن induction قلنا خطوطين واحد واثنين
+
+338
+00:25:43,670 --> 00:25:47,590
+هذا ما يعني induction بشكل عام الآن في هذا المثال
+
+339
+00:25:47,590 --> 00:25:53,280
+طبعا أول شيء هذه جملة شرطيةعشان أبرهنها عن طريق
+
+340
+00:25:53,280 --> 00:25:57,280
+البرهان الرياضي المباشر بفترض أن الشرط صحيح وبأثبت
+
+341
+00:25:57,280 --> 00:26:01,140
+أن جواب الشرط صحيح فهنقول له assume that P of K is
+
+342
+00:26:01,140 --> 00:26:07,240
+trueعملية أساسية و بتكررها جدا فهذا بنتعلمه و
+
+343
+00:26:07,240 --> 00:26:11,760
+بناقش يكون بالنسبة لنا متمكنين منه و زي ما هتقولنا
+
+344
+00:26:11,760 --> 00:26:14,940
+هي .. بنتعلم أساسي مبادئ الرياضيات كيف بنبدأ
+
+345
+00:26:14,940 --> 00:26:19,140
+البرهان و كيف إيش بننطلف البرهان فهذه أول نوع يمكن
+
+346
+00:26:19,140 --> 00:26:22,300
+أسهل مثال هيمر علينا و هيمر علينا كتير كيف نتعامل
+
+347
+00:26:22,300 --> 00:26:25,460
+مع الجملة الشرطية فأول شي هقوله assume that اللي
+
+348
+00:26:25,460 --> 00:26:30,020
+هو P of K is true assume that
+
+349
+00:26:30,960 --> 00:26:34,880
+B of K طبعا عشان انا بدي استفيد منها خليني افسرها
+
+350
+00:26:34,880 --> 00:26:38,840
+ماذا يعني B of K is true B of K بالكلام هذا إيش
+
+351
+00:26:38,840 --> 00:26:43,960
+معناه هاي B of N يعني summation من واحد لوين ل K
+
+352
+00:26:43,960 --> 00:26:48,480
+إيش الصيغة العامة تمانية G ناقص خمسة إيش بده تساوي
+
+353
+00:26:48,480 --> 00:26:53,740
+أربعة K تربيع ناقص K is true
+
+354
+00:26:56,490 --> 00:27:01,290
+إذاً هذا أصبح إيش؟ معي معطى هذا أصبح براصيدي ممكن
+
+355
+00:27:01,290 --> 00:27:05,650
+أستخدمه وجد محتاجه اه طب إيش المطلوب مني أثبته؟ ان
+
+356
+00:27:05,650 --> 00:27:12,670
+بي of k plus one is true we must show that
+
+357
+00:27:14,790 --> 00:27:20,870
+بـ k plus one اللي هي نفسرها من واحد ل k plus one
+
+358
+00:27:20,870 --> 00:27:27,810
+تمانية j ناقص خمسة تساوي أربعة في k plus one لكل
+
+359
+00:27:27,810 --> 00:27:30,610
+تربيع ناقص k plus one is it true
+
+360
+00:27:34,540 --> 00:27:39,640
+واضح فاحنا بنعيد في قواعي في هيكلية عامة وفي بعض
+
+361
+00:27:39,640 --> 00:27:42,640
+الخصوصيات إيش الاختلاف إيش معناه P of K في هذا
+
+362
+00:27:42,640 --> 00:27:46,040
+المثال إيش معناه P of K plus one في هذا المثال لكن
+
+363
+00:27:46,040 --> 00:27:51,120
+الخطوات الرئيسية نفس الخطوات متابعين نبدأ نشتغل
+
+364
+00:27:51,120 --> 00:27:55,180
+بدنا نثبت هذا زي المثال الماضي في عندنا Sigma نبدأ
+
+365
+00:27:55,180 --> 00:27:59,460
+من الطرف اليسار Now إيش بدأت أعمل بدأت أعمل
+
+366
+00:27:59,460 --> 00:28:02,480
+المطلوب مني بدأ أثبته فنبدأ من الطرف اليسار
+
+367
+00:28:02,480 --> 00:28:11,360
+summationj من واحد إلى k plus one تمانية j ناقص
+
+368
+00:28:11,360 --> 00:28:17,540
+خمسةتساوى واحدة واحدة بس في تعليق بس خفيف ماشي
+
+369
+00:28:17,540 --> 00:28:22,260
+فدائما و أبدا هذه قاعدة عامة لل induction عشان
+
+370
+00:28:22,260 --> 00:28:26,620
+أثبت أن B of K plus one is true لازم أكتبها بدلالة
+
+371
+00:28:26,620 --> 00:28:29,580
+B of K عشان أستفيد من ال induction hypothesis فهذه
+
+372
+00:28:29,580 --> 00:28:33,680
+خطوة رئيسية فأصبح المطلوب مني كيف أكتب الخطوة K
+
+373
+00:28:33,680 --> 00:28:37,740
+plus one بدلالة الخطوة K بدي أستفيد من هذا المعطى
+
+374
+00:28:37,960 --> 00:28:41,280
+بدي أستفيد من هذا المعطى فطبعا بديش أعيد توي كيف
+
+375
+00:28:41,280 --> 00:28:45,260
+بنحاول نكتب الـ Sigma آخر حد بنفقه لحال فخلّي الـ
+
+376
+00:28:45,260 --> 00:28:49,240
+Sigma لعند الـ K زي ما هي مغلق لعند الـ K من 1 ل K
+
+377
+00:28:49,240 --> 00:28:55,480
+8 J ناقص 5 طيب وين الحد الأخير؟ أعود عن J K plus 1
+
+378
+00:28:55,480 --> 00:29:04,130
+plus 8 في K plus 1 minus 5خطوة بسيطة لازم الكل
+
+379
+00:29:04,130 --> 00:29:08,090
+يعرفها نعيد كمان مرة ايش اللي عملناها هي ال sigma
+
+380
+00:29:08,090 --> 00:29:11,690
+انا باديه من واحد ل k plus one ممكن افك ال sigma
+
+381
+00:29:11,690 --> 00:29:15,430
+بالطريقة اللي بديها ممكن اخلي اول حد لحال اخر حد
+
+382
+00:29:15,430 --> 00:29:18,890
+لحال ايش بده اعمل ال sigma بدل ما هي من واحد ل k
+
+383
+00:29:18,890 --> 00:29:22,810
+plus one هوقفها عند ال k ايش معناته؟ بده اعود k
+
+384
+00:29:22,810 --> 00:29:25,430
+جيه بتسوي k plus one اخليها لحالي و ال sigma
+
+385
+00:29:25,430 --> 00:29:28,950
+الباقى خليها مغلقة فبده افتحها بس من اخر حدبدي
+
+386
+00:29:28,950 --> 00:29:32,250
+أفتحها من الآخر، لكن جوا خليها مغلقة زي ما هي طبعا
+
+387
+00:29:32,250 --> 00:29:34,990
+إيش ال .. إيش الميار إن الشغل صح؟ لو فكيت هذه
+
+388
+00:29:34,990 --> 00:29:38,010
+وفكيت هذه بديني نفس الشيء، لو بفكيتهم بشكل صريح
+
+389
+00:29:38,010 --> 00:29:41,810
+وفصلت تفصيل، بديني نفس الشيء، واضحة هذه الخطوة؟ طب
+
+390
+00:29:41,810 --> 00:29:45,450
+وعملناها بتفصيل أكتر، بس الآن اختصرنا شوية، ممتاز،
+
+391
+00:29:45,450 --> 00:29:47,810
+الآن جاهزين نستخدم ال induction hypothesis
+
+392
+00:29:52,220 --> 00:29:55,880
+أيش بيقول ليه؟ وانا حد تحطته في مستطيل هنا ان الـ
+
+393
+00:29:55,880 --> 00:29:59,480
+Sigma هذه ممكن نستبدلها بمين؟ أربع K تربيع ناقص K
+
+394
+00:29:59,480 --> 00:30:05,860
+إذاً هذا يساوي أربع K تربيع ناقص K وهذه زي ما هي
+
+395
+00:30:05,860 --> 00:30:14,050
+بس نبسطها زائد تمانية K زائد تلاتة اتبعين؟الكل
+
+396
+00:30:14,050 --> 00:30:16,850
+متابع معاه؟ بالناس احنا بعد ما نخلص نرجع لها
+
+397
+00:30:16,850 --> 00:30:20,510
+خلّيني نرجع في النقطة نفسها بيكون أسهلنا اتبعين؟
+
+398
+00:30:20,510 --> 00:30:23,710
+بنكمل الآن، ممتاز، الآن ماتم عليا خلصت عملية
+
+399
+00:30:23,710 --> 00:30:27,830
+حسابية، وين أنا مطلوب أوصل؟ مطلوب أوصل لهنا، طيب
+
+400
+00:30:27,830 --> 00:30:32,090
+هذه لو أنا طلعت عليها بالتفصيل، خلّيني أبسطها
+
+401
+00:30:32,090 --> 00:30:35,290
+شوية، ممكن اخد من هنا K Plus وانا عامل مشاركة،
+
+402
+00:30:35,290 --> 00:30:39,330
+خلّيني اكتب هناك بلس وان عامل مشترك، مظبوط؟ ايش
+
+403
+00:30:39,330 --> 00:30:44,690
+بيتام؟ بيتام اربعة في ك بلس وان ناقص واحد، صح؟
+
+404
+00:30:44,690 --> 00:30:47,830
+يعني هذه ايش .. ايش .. وين .. وين رايح انا؟ لك بلس
+
+405
+00:30:47,830 --> 00:30:53,560
+وان اربعة ك زائد تلاتةفليش إيش اللي عملته؟ المبدأ
+
+406
+00:30:53,560 --> 00:30:56,800
+اللي حاولت تعلمكوا إياه و بدنا نتعلمهم مع بعض و
+
+407
+00:30:56,800 --> 00:31:00,340
+احنا بنشتغل دايما عيننا على المطلوب وين رايح أنا
+
+408
+00:31:00,340 --> 00:31:04,760
+وصلت لخطوة قطعت سوء كبير طيب هل انتهى البرهان؟ بدأ
+
+409
+00:31:04,760 --> 00:31:07,680
+أتأكد إنه انتهى ولا لأ إنه صح بدأ أشوف أين .. إيش
+
+410
+00:31:07,680 --> 00:31:11,540
+كان مطلوب؟ بدأ أوصل لهنا إيش أعمل؟ أبسط و أخد K
+
+411
+00:31:11,540 --> 00:31:17,040
+plus و أنا أعمل مشترك انبسط فدي تساوي 4K تربيع زي
+
+412
+00:31:17,040 --> 00:31:24,090
+7Kزائد تلاتة فالسؤال هل هذه بتساوي هذهك بممكن
+
+413
+00:31:24,090 --> 00:31:28,590
+احللها k plus one في جداش في اربع k زائد تلاتة
+
+414
+00:31:28,590 --> 00:31:39,810
+طبعا صح فكهم بطلع صح مصبوط اه اذا انتهى البرهان is
+
+415
+00:31:39,810 --> 00:31:45,110
+true وبالتالي البرهان انتهىفهذه خطوات الـ Sigma هي
+
+416
+00:31:45,110 --> 00:31:49,790
+مثلين فارجو أن الكل يكون عنده المقدرة للتعامل مع
+
+417
+00:31:49,790 --> 00:31:52,130
+الأسلحة ال induction اللي بتتعامل مع الـ Sigma فده
+
+418
+00:31:52,130 --> 00:31:55,370
+أولا نشتغل على ال induction ونوع معين من الأمثلة
+
+419
+00:31:55,370 --> 00:31:58,370
+اللي فيها Sigma وفيها قانون للجامعة بنتعامل معاه
+
+420
+00:31:58,370 --> 00:32:05,910
+بهذه الصور أي سؤال؟
+
+421
+00:32:05,910 --> 00:32:11,840
+K plus one عامل مشترك، حللناطب ليش k plus one؟ لأن
+
+422
+00:32:11,840 --> 00:32:15,160
+ايه؟ انا عارف اين بدي اروح اتأكدت بيطلع صح، بيطلع
+
+423
+00:32:15,160 --> 00:32:20,380
+صح، اذا كلامي حل كله صحيح فدائما عينك على المطلوب
+
+424
+00:32:20,380 --> 00:32:24,240
+عشان تعرف حالك وصلتي ولا ماوصلتيليش لإن مش البرهان
+
+425
+00:32:24,240 --> 00:32:28,260
+بيبدأ بالمعطيات بيمشي خطوة بعد خطوة بشكل طريق منطق
+
+426
+00:32:28,260 --> 00:32:34,840
+لحد ما ينتهي بالمطلوب ينتهي بالمطلوب نشوف كمان
+
+427
+00:32:34,840 --> 00:32:40,360
+مثالبرضه مثال على ال induction لكن من نوع آخر ليس
+
+428
+00:32:40,360 --> 00:32:44,460
+sigma وانما بدنا نثبت متباين الآن بدنا نثبت
+
+429
+00:32:44,460 --> 00:32:48,920
+متطابقة فيها sigma بدنا نثبت متباين ففي هذا المثال
+
+430
+00:32:51,230 --> 00:32:55,330
+في عيننا بدنا نثبت ان for all natural number for
+
+431
+00:32:55,330 --> 00:33:01,050
+all N تنتمي لل N بدنا نثبت P of N is true واش ال P
+
+432
+00:33:01,050 --> 00:33:05,990
+of N تبعت هذا المثال تلاتة أس N أكبر أو تساوي
+
+433
+00:33:05,990 --> 00:33:08,430
+اتنين أس N زائد واحد
+
+434
+00:33:14,180 --> 00:33:18,020
+فالان بدنا نتعامل مع open sentence من نوع جديد مش
+
+435
+00:33:18,020 --> 00:33:24,340
+متطابقة وانما متباينة علاقة اكبر من او يساوي نبدأ
+
+436
+00:33:24,340 --> 00:33:27,520
+بالخطوات العامة و بعدين نشوف ايش الخصوصيات الجديدة
+
+437
+00:33:27,520 --> 00:33:32,520
+في يد المثال فطبعا ال solution نبدأ من ايش بي of
+
+438
+00:33:32,520 --> 00:33:36,360
+one is true بي of one is true
+
+439
+00:33:40,360 --> 00:33:43,780
+فمرة تانية في طريقتين للكتابة يا بدأ اكتب we want
+
+440
+00:33:43,780 --> 00:33:46,880
+to prove P of K is true او اكتب P of 1 is true وحط
+
+441
+00:33:46,880 --> 00:33:50,180
+علامة استفهام ايش بنفهم منه ان هذا مطلوب مش جزء من
+
+442
+00:33:50,180 --> 00:33:53,100
+الحل لأن لو قلت P of 1 is true خلص الحل طب وينه
+
+443
+00:33:53,100 --> 00:33:57,820
+ماثبتيهوش فبنثبته فانا اختصارا يا بكتب I want to
+
+444
+00:33:57,820 --> 00:34:00,500
+prove that P of 1 is true او بقول P of 1 is true
+
+445
+00:34:00,500 --> 00:34:03,500
+وحط علامة استفهام يعني هذا مطلوب هذا مطلوب نبدأ
+
+446
+00:34:03,500 --> 00:34:08,590
+نفسر ما هي P of 1 في هذا السؤالتلاتة اقصوا واحد
+
+447
+00:34:08,590 --> 00:34:11,550
+اكبر او يساوي اتنين اقصوا واحد زايد واحد true ولا
+
+448
+00:34:11,550 --> 00:34:18,610
+مش true؟ true لان تلاتة اكبر او يساوي تلاتة ولا
+
+449
+00:34:18,610 --> 00:34:22,050
+لسه في حد بيشكوا ان تلاتة اكبر او يساوي تلاتة؟ حد
+
+450
+00:34:22,050 --> 00:34:26,450
+يقولي لا هذه اتساوي مش اكبر او يساوي فحلنا المشكلة
+
+451
+00:34:26,450 --> 00:34:29,690
+دي صح؟ لان هذه R جزء منها true اذا ان هي كلها true
+
+452
+00:34:29,690 --> 00:34:33,770
+فخلاص مدناش حد يتردد بعدين فهذه true تمام ال R
+
+453
+00:34:33,770 --> 00:34:40,180
+الخطوة رقم اتنينبرضه بدك تكتب بشكل مختصر إيش هي P
+
+454
+00:34:40,180 --> 00:34:47,340
+of K is true implies P of K plus one is true إيش
+
+455
+00:34:47,340 --> 00:34:51,760
+هذا ماله؟ هذا مطلوب، حط على انت استفهامعلامة
+
+456
+00:34:51,760 --> 00:34:54,460
+استفامة عشان القارئ يعرف ان انت لسه مابديتيش الحل
+
+457
+00:34:54,460 --> 00:34:57,220
+بس قاعدة بتفكر انت إيش اللي بدك تعمليه أو بتحط
+
+458
+00:34:57,220 --> 00:35:00,580
+عنوان للخطوة اللي بدك تشتغليها فارجو هذه الأمور
+
+459
+00:35:00,580 --> 00:35:05,140
+مهمة جدا و أساسية في قراءة البرهان و كتابة البرهان
+
+460
+00:35:05,140 --> 00:35:09,260
+تقرا انت بتعرف تقرا برهانك لو انسيت بعد مدة و غيرك
+
+461
+00:35:09,260 --> 00:35:13,660
+يعرف يقرأ مصحح كان في المحاضرات المباشرة او بعد
+
+462
+00:35:13,660 --> 00:35:18,260
+هيك لو بدك تكتبي في أي موضوعيكون طريقة الكتابة حسب
+
+463
+00:35:18,260 --> 00:35:21,100
+العراف المتعرف عليها وبالتالي بتسهل القراءة لإن ما
+
+464
+00:35:21,100 --> 00:35:25,820
+بنفعش أبدأ البرهان بالمطلوب وإنما بقول أنا مطلوب
+
+465
+00:35:25,820 --> 00:35:29,000
+إن أثبت هذا الكلام I want to prove أو أنا تستفهم
+
+466
+00:35:29,000 --> 00:35:32,540
+نفس المعنى نختصر ممتاز جملة شرطية أشوف نبدأها
+
+467
+00:35:32,540 --> 00:35:36,420
+Assume إن الشرط صحيح Assume إن ال condition صحيح
+
+468
+00:35:36,420 --> 00:35:45,720
+Assume B of K اللي هي عبارة تلاتة أس Kأكبر او
+
+469
+00:35:45,720 --> 00:35:47,780
+يساوي اتنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+470
+00:35:47,780 --> 00:35:48,640
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+471
+00:35:48,640 --> 00:35:49,360
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+472
+00:35:49,360 --> 00:35:52,260
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+473
+00:35:52,260 --> 00:35:55,140
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+474
+00:35:55,140 --> 00:35:57,300
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+475
+00:35:57,300 --> 00:35:59,580
+اثنين اثنين اثنين اثنين اثنين اثنين اثنprove أو
+
+476
+00:35:59,580 --> 00:36:05,100
+show كله نفس المعنى to prove that B of K plus one
+
+477
+00:36:05,100 --> 00:36:09,300
+is true اللي هي إيش معناها تلاتة أس K plus one
+
+478
+00:36:09,300 --> 00:36:14,140
+أكبر أو تساوي اتنين أس K plus one زائد واحد is
+
+479
+00:36:14,140 --> 00:36:21,340
+true واحدة واحدة واحدة واحدة اه
+
+480
+00:36:26,400 --> 00:36:30,800
+فلجيت في أي طالبة عندها مشكلة في تفسير P of 1 P of
+
+481
+00:36:30,800 --> 00:36:35,840
+K P of K plus one وضحت هذه أول شيء تمها في بعض
+
+482
+00:36:35,840 --> 00:36:38,980
+الأمور المتقدمة بس هذا أساسي يعني ماتظنيش أنه تمت
+
+483
+00:36:38,980 --> 00:36:41,500
+إيش الأمور هذه بدنا نتعلمها و طبعا الصحيحة بسيطة
+
+484
+00:36:41,500 --> 00:36:44,240
+لكن اللي لم يتعلمها مش هيعرف يشتغل لو أنه عوض بدل
+
+485
+00:36:44,240 --> 00:36:48,880
+K N أو عوض بسيط الخطأ أو عوض في ال K plus one في
+
+486
+00:36:48,880 --> 00:36:52,540
+مكان خاطق مش هيعرف يوصل لأنه ياشتغل يدوي على هدف
+
+487
+00:36:52,540 --> 00:36:57,740
+مش هو الهدف الصحيح يدوي على هدف آخر خطأتمام إذا
+
+488
+00:36:57,740 --> 00:37:01,040
+بدنا نثبت هذا الكلام فهذه متباينة بنتعلم اليوم
+
+489
+00:37:01,040 --> 00:37:03,300
+مهارة جديدة في هذا المثال في هذا المثال في مهارة
+
+490
+00:37:03,300 --> 00:37:06,140
+جديدة هذه مش sigma بدنا نحاول نشوف كيف نتعامل مع
+
+491
+00:37:06,140 --> 00:37:09,740
+المتباينات طب على المتباينة ممكن نبدأ من أي طرف بس
+
+492
+00:37:09,740 --> 00:37:14,460
+ننتبه بدنا نبدأ نكبر ولا نزغر بدأنا من اليسار
+
+493
+00:37:14,460 --> 00:37:17,840
+بنبدأ نزغر العدد عشان نوصل للمطلوب بدأنا من اليمين
+
+494
+00:37:17,840 --> 00:37:20,420
+بنبدأ نكبر لحد ما نوصل للمطلوب خلينا نبدأ من
+
+495
+00:37:20,420 --> 00:37:24,860
+اليسار خلينا نبدأ من اليسار تمام
+
+496
+00:37:26,790 --> 00:37:33,390
+فالان هذا هو المطلوب أبدأ أبرهنه Now تلاتة أس K
+
+497
+00:37:33,390 --> 00:37:39,250
+plus one ايش قلنا قاعدة عامة عشان أستفيد لازم أدته
+
+498
+00:37:39,250 --> 00:37:42,810
+بالحالة K plus one بدلات الحالة رقم K ايش الحالة
+
+499
+00:37:42,810 --> 00:37:46,130
+رقم K فيها اللي هو دايما .. دعنا نحطه دايما
+
+500
+00:37:46,130 --> 00:37:51,010
+بمستطيل عشان ما ننساهش لأنه هنستخدمهتلاتة أُس K
+
+501
+00:37:51,010 --> 00:37:54,930
+كيف ممكن أكتب تلاتة أُس K plus one تلاتة أُس K
+
+502
+00:37:54,930 --> 00:38:00,310
+عملية من جمع الأسس فهذه لأ ليس إلا تلاتة في تلاتة
+
+503
+00:38:00,310 --> 00:38:04,590
+أُس K ممتاز فشوفنا ال sigma كيف بنحولها بنفك ال
+
+504
+00:38:04,590 --> 00:38:09,090
+term الأخير فالضرب من قوانين الأسس جمع للأسس ممتاز
+
+505
+00:38:09,610 --> 00:38:12,410
+طيب هلجيت أعملنا؟ بنا نستخدم ال induction ال
+
+506
+00:38:12,410 --> 00:38:16,130
+induction إيش بيقوللي؟ تلاتة أس كأكبر أو تساوي
+
+507
+00:38:16,130 --> 00:38:19,770
+اتنين أس ك زائد واحد إيش اللي ممكن أعمله؟ خلّينا
+
+508
+00:38:19,770 --> 00:38:23,550
+إذا بينكي للبعض واضحة للبعض مش واضحة نعمل همش إحنا
+
+509
+00:38:23,550 --> 00:38:27,570
+هلجيت هذه الخطوة خلينا نعملها همش أنا عندي تلاتة
+
+510
+00:38:27,570 --> 00:38:31,830
+أس ك أكبر أو تساوي اتنين أس ك plus one هذا معتصر
+
+511
+00:38:31,830 --> 00:38:35,410
+صحيحعشان اوصل ليها دي ايش بتعمل اضرب الطرفين
+
+512
+00:38:35,410 --> 00:38:38,870
+بتلاتة لو ضربنا متباينة بتلاتة بتحافظ على الترتيب
+
+513
+00:38:38,870 --> 00:38:41,590
+ولا بتعكس الترتيب ولا مالاش قاعدة بتحافظ على
+
+514
+00:38:41,590 --> 00:38:44,950
+الترتيب لأن تلاتة موجة فهذا بيقوللي ان تلاتة في
+
+515
+00:38:44,950 --> 00:38:49,090
+تلاتة أس كي أكبر أو يساوي تلاتة في اتنين أس كي
+
+516
+00:38:49,090 --> 00:38:54,590
+زائد واحد تمام؟ واضح؟ اه إذا واضح ألتقل هنا إذا من
+
+517
+00:38:54,590 --> 00:38:59,230
+هذه الخطوة بقدر أكتب هذا أن هو أكبر أو يساوي تلاتة
+
+518
+00:38:59,230 --> 00:39:04,520
+في اتنين أس كي زائد واحدمظبوط؟ من وين جيبت هذه؟ من
+
+519
+00:39:04,520 --> 00:39:07,880
+induction hypothesis فهنا أحط هنا إيش دالي ليه؟
+
+520
+00:39:07,880 --> 00:39:11,680
+induction باختصار hypothesis مافيش واسعة كتير
+
+521
+00:39:12,190 --> 00:39:16,630
+Induction Hypothesis واضح؟ اه طبعا اعملنا انجاز
+
+522
+00:39:16,630 --> 00:39:21,410
+كبير جدا طب وصلنا نشوف احنا وين بدنا نوصل؟ بدنا
+
+523
+00:39:21,410 --> 00:39:25,290
+نوصل اتنين از ك plus one زائد واحد على اليسار فبدى
+
+524
+00:39:25,290 --> 00:39:30,330
+افكر ايش علاقة هذا بهذا؟ خليني انبسط علاقة الخطوة
+
+525
+00:39:30,330 --> 00:39:32,370
+اللى وصلتلها المرحلة اللى وصلتلها بالمرحلة
+
+526
+00:39:32,370 --> 00:39:39,550
+المطلوبة خليني ابسطها هذه تساوي تلاتة2 أس K زائد 3
+
+527
+00:39:39,550 --> 00:39:45,450
+فوق الجزء طبعا ممكن حد يقول طب هذه تساوي هذه صحيح
+
+528
+00:39:45,450 --> 00:39:49,350
+علاقة هذه مع هذه تساوي لكن علاقة هذه مع الأولى
+
+529
+00:39:49,350 --> 00:39:52,430
+أكبر منها فأنا بحافظ أنه أنا كأن بقرأ أن هذه
+
+530
+00:39:52,430 --> 00:39:56,010
+بوجودة هنا تنصح لو كتبتها بس تنتبهوا أن هذه
+
+531
+00:39:56,010 --> 00:39:59,690
+علاقتها مع هذه تساويها لكن مع الأولى أصغر منها
+
+532
+00:39:59,690 --> 00:40:06,970
+فتبتدي هؤلاء العمليات واضح الملاحظة عيدأنتوا بين
+
+533
+00:40:06,970 --> 00:40:11,170
+اتلات الكلز واحدة واحدة واحدة؟ وين؟ هان؟ لأ جابت
+
+534
+00:40:11,170 --> 00:40:15,630
+هان، انت الأكبر اه ممكن، ممكن للتأكيد، بس لو
+
+535
+00:40:15,630 --> 00:40:21,030
+اختصرت مش صح لما انتقرت من هان لهان علاقة هذا
+
+536
+00:40:21,030 --> 00:40:25,090
+المقدار بيد المقدار يساوي ولا أكبر منه؟ يساوي،
+
+537
+00:40:25,090 --> 00:40:28,230
+يساوي، طب ليش هنا حطيت أكبر منه يساوي؟ لأن هادي
+
+538
+00:40:28,230 --> 00:40:33,370
+مفروض يكون هنااللي هو الطرف اليساري شغال معاه، بس
+
+539
+00:40:33,370 --> 00:40:36,630
+عشان أؤكد أنه علاقته الأصلي فهذه تساوي هذه، لكن
+
+540
+00:40:36,630 --> 00:40:39,990
+أكبر من هذه، أصغر من هذه، بس، طبعا، بس بدنا ننتبه،
+
+541
+00:40:39,990 --> 00:40:42,770
+إذا حاطينا يساوي مش غلط، بس ننتبه، بس يساويش مع
+
+542
+00:40:42,770 --> 00:40:46,630
+هذه، يساوي مع الخطوة البينية، ممتاز، إذا إحنا هينا
+
+543
+00:40:46,630 --> 00:40:52,240
+هنا، هنا في المرحلة هذه، ونايحين على هناكيف ممكن
+
+544
+00:40:52,240 --> 00:40:55,800
+اوصل من تلاتة في اتنين اوس كي لاتنين اوس كي plus
+
+545
+00:40:55,800 --> 00:41:00,920
+one؟ بدي ابدّر التلاتة باتنين، بنفع؟ بنفع، ليش؟
+
+546
+00:41:00,920 --> 00:41:05,160
+انكمل الهامش أنا عندي التلاتة اكبر او تساوي اتنين،
+
+547
+00:41:05,160 --> 00:41:08,860
+مصبوط؟ ولا حد عنده اعتراض؟ اه، طب اضرب في اتنين
+
+548
+00:41:08,860 --> 00:41:09,440
+اوس كي؟
+
+549
+00:41:15,100 --> 00:41:19,660
+مظبوط؟ لأنه برضه موجه ب 2K هذه هي مين؟ 2K plus 1
+
+550
+00:41:19,660 --> 00:41:25,800
+إذا ممكن أبدل هذا المقدار ب 2K plus 1 ولا لأ؟
+
+551
+00:41:28,690 --> 00:41:32,410
+متابعين؟ أعيد؟ ان أعيد؟ لأ، هو يعني لازم نشرحها،
+
+552
+00:41:32,410 --> 00:41:35,910
+الآن التلاتة أكبر تساوي اتنين، متفقين؟ أضرب
+
+553
+00:41:35,910 --> 00:41:39,130
+الطرفين في اتنين أوس كي، بتصير تلاتة في اتنين أوس
+
+554
+00:41:39,130 --> 00:41:43,110
+كي أكبر أو يساوي اتنين ضرب اتنين أوس كي، اللي هي
+
+555
+00:41:43,110 --> 00:41:45,470
+اتنين أوس كي plus one، gemalosis، إذا الممكن أشتغل
+
+556
+00:41:45,470 --> 00:41:48,090
+هذه الخطوة، بدلت هذا المقدار بمقدار أصغر منه
+
+557
+00:41:48,670 --> 00:41:52,950
+التلاتة طبعا ماكملتش انا بس وقفت عشان اتأكد اوصلنا
+
+558
+00:41:52,950 --> 00:41:57,150
+اقتربنا جدا تم بدر التلاتة بواحد بنفع؟ بنفع لان
+
+559
+00:41:57,150 --> 00:42:03,130
+التلاتة اكبر من واحد وهو
+
+560
+00:42:03,130 --> 00:42:07,620
+المطلوب اثباتهاه فهنا طبعا في شغل أكتر من ال sigma
+
+561
+00:42:07,620 --> 00:42:11,880
+لكن على نفس المبادئ الخطوات الرئيسية نفسها لكن
+
+562
+00:42:11,880 --> 00:42:15,160
+التفاصيل احتاجة بعض المجهود و دايما انا عندي ال
+
+563
+00:42:15,160 --> 00:42:18,100
+induction hypothesis هو الأساس و بعدين ببدأ أشوف
+
+564
+00:42:18,100 --> 00:42:21,120
+أنا أيش اللي بدي إياه و هل ممكن أبدل أو ماببدلش
+
+565
+00:42:21,120 --> 00:42:24,100
+بسأل نفسي و ممكن أعمل بها مش أتأكد إن الخطوة صحيحة
+
+566
+00:42:24,100 --> 00:42:28,530
+أو لالأ كيف الواحد بدلت التلاتة بعدد أصغر منه عشان
+
+567
+00:42:28,530 --> 00:42:31,830
+أنا جاعت بصغر .. أه كل مالي بصغر .. أه تلاتة أبقى
+
+568
+00:42:31,830 --> 00:42:35,390
+أصغر منه .. بدلت هذا بيبقى أصغر منه .. بنفع لأن
+
+569
+00:42:35,390 --> 00:42:39,750
+أنا رايح أيش بصغر المقدار .. بصغر المقدار .. أي
+
+570
+00:42:39,750 --> 00:42:43,290
+سؤال .. أه فهنا بدنا نوقف المحاضرة و نستكمل ان شاء
+
+571
+00:42:43,290 --> 00:42:44,010
+الله ساعتين تان
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/5VeDSAHw2ZU_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/5VeDSAHw2ZU_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..17be96bea1b9b31c0a3b6e4359579576e1168212
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/5VeDSAHw2ZU_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3076, "start": 20.18, "end": 30.76, "text": "بسم الله الرحمن الرحيم نواصل مع المجموعات وتكافؤ المجموعات والمجموعة القابلة للعدد numberable أو countable", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 2407, 33546, 1211, 20449, 9673, 7435, 2304, 45367, 9307, 34683, 4117, 31845, 33604, 9673, 7435, 2304, 45367, 9307, 16070, 2304, 7435, 2304, 2407, 27884, 25062, 16758, 37977, 24976, 22488, 3215, 1230, 712, 34051, 1207, 712], "avg_logprob": -0.21773098441569702, "compression_ratio": 1.4552845528455285, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 20.18, "end": 20.52, "word": "بسم", "probability": 0.877197265625}, {"start": 20.52, "end": 20.7, "word": " الله", "probability": 0.95361328125}, {"start": 20.7, "end": 21.08, "word": " الرحمن", "probability": 0.974609375}, {"start": 21.08, "end": 21.5, "word": " الرحيم", "probability": 0.9959309895833334}, {"start": 21.5, "end": 22.8, "word": " نواصل", "probability": 0.85650634765625}, {"start": 22.8, "end": 23.18, "word": " مع", "probability": 0.82421875}, {"start": 23.18, "end": 24.42, "word": " المجموعات", "probability": 0.9556640625}, {"start": 24.42, "end": 25.34, "word": " وتكافؤ", "probability": 0.72528076171875}, {"start": 25.34, "end": 26.28, "word": " المجموعات", "probability": 0.9138671875}, {"start": 26.28, "end": 27.5, "word": " والمجموعة", "probability": 0.8187662760416666}, {"start": 27.5, "end": 28.02, "word": " القابلة", "probability": 0.9811197916666666}, {"start": 28.02, "end": 28.8, "word": " للعدد", "probability": 0.8343098958333334}, {"start": 28.8, "end": 29.4, "word": " numberable", "probability": 0.5201568603515625}, {"start": 29.4, "end": 29.74, "word": " أو", "probability": 0.7080078125}, {"start": 29.74, "end": 30.76, "word": " countable", "probability": 0.965087890625}], "temperature": 1.0}, {"id": 2, "seek": 6653, "start": 36.79, "end": 66.53, "text": "فاحنا كنا أعرفنا أن مجموعتين متكافئتين يمكن أهم النقاط إذا جدنا الـ lag bijection بين المجموعتين X و Y بيقول عنهم أنه الـ quipotence اللي هو بنكتبهم بيد الشكل X تكافئ ال Y عدديًا أو ال quipotence إذا في بينهم bijection يعني ده اللي one to one and one to one شيء منطقي أنا لما أقول يا دي مجموعة فيها خمس صفحات و واحد فيها خمس مزات متكافئتين عدديًا بيهمنيش نتساوي فيه مختلف مش نفس العناصر لكن بيهمني العدد فلازم يكون فيه إشتناقظ واحد لواحد", "tokens": [5172, 39319, 8315, 9122, 8315, 5551, 3615, 28480, 8315, 14739, 3714, 7435, 2304, 45367, 2655, 9957, 44650, 4117, 31845, 19986, 2655, 9957, 7251, 43020, 5551, 16095, 28239, 4587, 41193, 11933, 15730, 10874, 3215, 8315, 2423, 39184, 8953, 3228, 1020, 313, 49374, 9673, 7435, 2304, 45367, 2655, 9957, 1783, 4032, 398, 4724, 1829, 39648, 18871, 16095, 14739, 3224, 2423, 39184, 421, 647, 310, 655, 13672, 1829, 31439, 44945, 4117, 2655, 3555, 16095, 4724, 25708, 25124, 28820, 1783, 6055, 4117, 31845, 19986, 2423, 398, 6225, 3215, 16254, 14111, 995, 34051, 2423, 421, 647, 310, 655, 11933, 15730, 8978, 49374, 16095, 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"probability": 0.916015625}, {"start": 63.73, "end": 64.07, "word": " بيهمني", "probability": 0.9739990234375}, {"start": 64.07, "end": 64.63, "word": " العدد", "probability": 0.98193359375}, {"start": 64.63, "end": 65.01, "word": " فلازم", "probability": 0.76904296875}, {"start": 65.01, "end": 65.21, "word": " يكون", "probability": 0.905029296875}, {"start": 65.21, "end": 65.45, "word": " فيه", "probability": 0.860595703125}, {"start": 65.45, "end": 65.85, "word": " إشتناقظ", "probability": 0.5829264322916666}, {"start": 65.85, "end": 66.17, "word": " واحد", "probability": 0.91455078125}, {"start": 66.17, "end": 66.53, "word": " لواحد", "probability": 0.9156901041666666}], "temperature": 1.0}, {"id": 3, "seek": 8995, "start": 66.87, "end": 89.95, "text": "أيضًا عرفنا إن المجموعة بتكون Denominable إذا كانت تكافئ الـnatural number وهذا الشيء الطبيعي إنه قلنا مجموعة الـnatural number هي مجموعة العد بنادر واحد اتنين قابلة العد طبعًا في أن مصطلح لو تسموه Denominable إذا بتكافئ الان فالـdenominable دائمًا infinite لأنه بتكافئ الـnatural number و الـnatural number كواش infinite في مصطلح ال countable ال countable فيه حالتين طبعًا لا يكون finite أو denominable", "tokens": [10721, 1829, 11242, 14111, 995, 6225, 28480, 8315, 36145, 9673, 7435, 2304, 2407, 27884, 39894, 30544, 6458, 6981, 712, 11933, 15730, 25961, 2655, 6055, 4117, 31845, 19986, 2423, 39184, 16296, 1230, 37037, 15730, 25124, 1829, 38207, 41950, 21292, 3615, 1829, 36145, 3224, 12174, 1211, 8315, 3714, 7435, 2304, 2407, 27884, 2423, 39184, 16296, 1230, 39896, 3714, 7435, 2304, 2407, 27884, 18863, 3215, 4724, 8315, 3215, 2288, 36764, 24401, 1975, 2655, 1863, 9957, 12174, 16758, 37977, 18863, 3215, 23032, 3555, 3615, 14111, 995, 8978, 14739, 3714, 9381, 9566, 1211, 5016, 45164, 6055, 38251, 2407, 3224, 6458, 6981, 712, 11933, 15730, 39894, 4117, 31845, 19986, 2423, 7649, 6156, 6027, 39184, 1556, 6981, 712, 11778, 16373, 2304, 14111, 995, 13785, 5296, 33456, 3224, 39894, 4117, 31845, 19986, 2423, 39184, 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X 1 زاد X 2 ليش؟ ليش؟", "tokens": [1863, 8592, 38688, 32239, 8592, 8978, 3224, 34937, 1975, 2655, 9566, 1211, 3615, 14407, 15844, 23758, 45164, 8717, 7435, 1211, 8315, 568, 1783, 502, 15844, 41950, 28480, 16712, 7649, 1829, 1975, 1829, 8592, 39894, 9381, 13546, 22807, 502, 6055, 3794, 995, 45865, 568, 8978, 1783, 502, 30767, 18513, 1783, 568, 32239, 8592, 22807, 32239, 8592, 22807], "avg_logprob": -0.3437499916344358, "compression_ratio": 1.3450704225352113, "no_speech_prob": 0.0, "words": [{"start": 359.96, "end": 360.44, "word": "نشوف", "probability": 0.6962076822916666}, {"start": 360.44, "end": 360.68, "word": " ليش", "probability": 0.800537109375}, {"start": 360.68, "end": 361.02, "word": " فيه", "probability": 0.5654296875}, {"start": 361.02, "end": 361.44, "word": " contradiction", "probability": 0.69189453125}, {"start": 361.44, "end": 369.58, "word": " اتطلعوا", "probability": 0.6805013020833334}, {"start": 369.58, "end": 369.74, "word": " على", "probability": 0.646484375}, 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"word": " تساوي", "probability": 0.64739990234375}, {"start": 374.62, "end": 375.04, "word": " 2", "probability": 0.9736328125}, {"start": 375.04, "end": 375.22, "word": " في", "probability": 0.350830078125}, {"start": 375.22, "end": 375.4, "word": " X", "probability": 0.95849609375}, {"start": 375.4, "end": 375.66, "word": " 1", "probability": 0.6376953125}, {"start": 375.66, "end": 375.92, "word": " زاد", "probability": 0.69189453125}, {"start": 375.92, "end": 376.08, "word": " X", "probability": 0.990234375}, {"start": 376.08, "end": 376.42, "word": " 2", "probability": 0.80322265625}, {"start": 376.42, "end": 378.72, "word": " ليش؟", "probability": 0.8045247395833334}, {"start": 378.72, "end": 379.3, "word": " ليش؟", "probability": 0.9498697916666666}], "temperature": 1.0}, {"id": 16, "seek": 41029, "start": 385.13, "end": 410.29, "text": "مضاعفات الاتنين مضاعفات الاتنين مضاعفات الاتنين مضاعفات الاتنين مضاعفات الاتنين مضاعفات الاتنين مضاعفات الاتنين", "tokens": [2304, 11242, 45761, 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{"start": 402.03, "end": 403.75, "word": " مضاعفات", "probability": 0.80302734375}, {"start": 403.75, "end": 404.21, "word": " الاتنين", "probability": 0.9228515625}, {"start": 404.21, "end": 406.89, "word": " مضاعفات", "probability": 0.84482421875}, {"start": 406.89, "end": 407.79, "word": " الاتنين", "probability": 0.9483642578125}, {"start": 407.79, "end": 409.51, "word": " مضاعفات", "probability": 0.877294921875}, {"start": 409.51, "end": 409.75, "word": " الاتنين", "probability": 0.9635009765625}, {"start": 409.75, "end": 410.25, "word": " مضاعفات", "probability": 0.89755859375}, {"start": 410.25, "end": 410.29, "word": " الاتنين", "probability": 0.9693603515625}], "temperature": 1.0}, {"id": 17, "seek": 43284, "start": 414.12, "end": 432.84, "text": "ليش؟ هو ماشي بس انا يعني احنا نشوف ده ماحنا نتصرعش لأ وين الغلط لأ بعدين هيو طلع ال contradiction يعني و احنا طول ما احنا ماشيين صح هيتضح معنا اللي هو اما احنا جولنا بده هنا بدي أثبت دالة معرفة one to one أخدت عنصرين في ال domain 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فده", "probability": 0.91552734375}, {"start": 1131.85, "end": 1132.19, "word": " بتراحم", "probability": 0.547607421875}, {"start": 1132.19, "end": 1132.47, "word": " مبادش", "probability": 0.5948486328125}, {"start": 1132.47, "end": 1132.73, "word": " شكل", "probability": 0.966064453125}], "temperature": 1.0}, {"id": 46, "seek": 114993, "start": 1133.51, "end": 1149.93, "text": "اللي هو هذا في هذا المثال اللي هو إيش N واحدة تساوي خمسة تمام الآن إيش بدي أعمل هذا العنصر أنا عرفته أول واحد إيش ماله بدي أحطه على شجة بدي أحطه على جهة عشان ماعيدش أكرر و أختار أخر مرة خلصت X خمسة عرفناها هنروح نشطبها إنه هذا إيش رتبناها", "tokens": [6027, 20292, 31439, 23758, 8978, 23758, 9673, 12984, 6027, 13672, 1829, 31439, 11933, 1829, 8592, 426, 36764, 24401, 3660, 6055, 3794, 995, 45865, 16490, 2304, 3794, 3660, 46811, 10943, 6024, 48506, 11933, 1829, 8592, 4724, 16254, 5551, 25957, 1211, 23758, 18863, 1863, 9381, 2288, 41850, 6225, 28480, 47395, 5551, 12610, 36764, 24401, 11933, 1829, 8592, 3714, 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"probability": 0.65234375}, {"start": 1142.43, "end": 1142.77, "word": " شجة", "probability": 0.8199869791666666}, {"start": 1142.77, "end": 1143.27, "word": " بدي", "probability": 0.91748046875}, {"start": 1143.27, "end": 1143.45, "word": " أحطه", "probability": 0.9910888671875}, {"start": 1143.45, "end": 1143.55, "word": " على", "probability": 0.7861328125}, {"start": 1143.55, "end": 1143.71, "word": " جهة", "probability": 0.87255859375}, {"start": 1143.71, "end": 1143.91, "word": " عشان", "probability": 0.9578450520833334}, {"start": 1143.91, "end": 1144.33, "word": " ماعيدش", "probability": 0.6947021484375}, {"start": 1144.33, "end": 1144.67, "word": " أكرر", "probability": 0.9225260416666666}, {"start": 1144.67, "end": 1144.77, "word": " و", "probability": 0.470947265625}, {"start": 1144.77, "end": 1145.09, "word": " أختار", "probability": 0.9430338541666666}, {"start": 1145.09, "end": 1145.23, "word": " أخر", "probability": 0.787109375}, {"start": 1145.23, "end": 1145.59, "word": 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واحد بعد هيك؟ التمانية، فإيش بتقولله الـ gate؟ أه الآن let n2، هذا أصغر تاني واحد يعني، أول شيء أصغر دليل مطلقاً في كل العناصر الواحد، بعدين أصغر تاني دليل، بدا رتبه بترتيب تصعده، فإيش بكيف ده اكتبها؟ let n2 be the smallest subscript", "tokens": [3224, 1863, 32887, 5016, 8717, 3215, 13063, 3714, 9957, 5551, 9381, 17082, 2288, 36764, 24401, 39182, 39896, 4117, 22807, 16712, 2304, 7649, 10632, 12399, 6156, 28814, 1829, 8592, 39894, 39648, 43761, 2423, 39184, 8539, 22807, 5551, 3224, 6024, 48506, 718, 297, 17, 12399, 23758, 5551, 9381, 17082, 2288, 6055, 7649, 1829, 36764, 24401, 37495, 22653, 12399, 5551, 12610, 44049, 38207, 5551, 9381, 17082, 2288, 11778, 20292, 1211, 3714, 9566, 1211, 4587, 995, 14111, 8978, 28242, 18863, 1863, 33546, 2288, 2423, 14407, 24401, 12399, 39182, 9957, 5551, 9381, 17082, 2288, 6055, 7649, 1829, 11778, 20292, 1211, 12399, 4724, 28259, 12602, 2655, 3555, 3224, 39894, 43500, 1829, 3555, 6055, 9381, 3615, 3215, 3224, 12399, 6156, 28814, 1829, 8592, 4724, 4117, 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"end": 1161.76, "word": " أول", "probability": 0.832275390625}, {"start": 1161.76, "end": 1162.02, "word": " شيء", "probability": 0.468017578125}, {"start": 1162.02, "end": 1162.34, "word": " أصغر", "probability": 0.98193359375}, {"start": 1162.34, "end": 1162.64, "word": " دليل", "probability": 0.9851888020833334}, {"start": 1162.64, "end": 1163.44, "word": " مطلقاً", "probability": 0.8302001953125}, {"start": 1163.44, "end": 1163.58, "word": " في", "probability": 0.8330078125}, {"start": 1163.58, "end": 1163.78, "word": " كل", "probability": 0.994140625}, {"start": 1163.78, "end": 1164.28, "word": " العناصر", "probability": 0.837646484375}, {"start": 1164.28, "end": 1164.94, "word": " الواحد،", "probability": 0.8236083984375}, {"start": 1164.94, "end": 1165.26, "word": " بعدين", "probability": 0.933349609375}, {"start": 1165.26, "end": 1165.66, "word": " أصغر", "probability": 0.9783935546875}, {"start": 1165.66, "end": 1166.0, "word": " تاني", "probability": 0.9855143229166666}, {"start": 1166.0, "end": 1166.4, "word": " دليل،", "probability": 0.9598388671875}, {"start": 1166.4, "end": 1166.52, "word": " بدا", "probability": 0.3746337890625}, {"start": 1166.52, "end": 1166.78, "word": " رتبه", "probability": 0.8385009765625}, {"start": 1166.78, "end": 1167.08, "word": " بترتيب", "probability": 0.65887451171875}, {"start": 1167.08, "end": 1167.8, "word": " تصعده،", "probability": 0.8319498697916666}, {"start": 1167.8, "end": 1168.04, "word": " فإيش", "probability": 0.9827880859375}, {"start": 1168.04, "end": 1168.32, "word": " بكيف", "probability": 0.669189453125}, {"start": 1168.32, "end": 1168.4, "word": " ده", "probability": 0.80029296875}, {"start": 1168.4, "end": 1169.1, "word": " اكتبها؟", "probability": 0.9242350260416666}, {"start": 1169.1, "end": 1169.28, "word": " let", "probability": 0.86474609375}, {"start": 1169.28, "end": 1169.74, "word": " n2", "probability": 0.9521484375}, {"start": 1169.74, "end": 1170.18, "word": " be", "probability": 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مع النظرية and if Y is infinite then", "tokens": [56, 307, 1207, 712, 23758, 3714, 3555, 33599, 25720, 5296, 33456, 3224, 9154, 16712, 3615, 16572, 5172, 498, 398, 307, 13785, 550, 7866, 712, 9154, 8717, 19913, 2288, 10632, 9673, 46958, 10632, 6225, 8592, 7649, 39896, 1975, 4117, 8592, 1863, 14407, 11296, 8717, 31371, 7435, 3660, 12602, 3555, 9566, 2407, 11296, 20449, 28239, 19913, 2288, 10632, 293, 498, 398, 307, 13785, 550], "avg_logprob": -0.245039683485788, "compression_ratio": 1.4458598726114649, "no_speech_prob": 0.0, "words": [{"start": 1518.16, "end": 1518.86, "word": "Y", "probability": 0.5224609375}, {"start": 1518.86, "end": 1519.94, "word": " is", "probability": 0.70458984375}, {"start": 1519.94, "end": 1520.92, "word": " countable", "probability": 0.959228515625}, {"start": 1520.92, "end": 1524.38, "word": " هذا", "probability": 0.399169921875}, {"start": 1524.38, "end": 1525.08, "word": " مباشرة", "probability": 0.847900390625}, {"start": 1525.08, "end": 1525.58, "word": 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" تكون", "probability": 0.987548828125}, {"start": 1582.3, "end": 1582.66, "word": " ناشم،", "probability": 0.7099609375}, {"start": 1582.66, "end": 1582.78, "word": " ممكن", "probability": 0.92626953125}, {"start": 1582.78, "end": 1582.96, "word": " تكون", "probability": 0.992431640625}, {"start": 1582.96, "end": 1583.4, "word": " denominable", "probability": 0.8824869791666666}, {"start": 1583.4, "end": 1583.6, "word": " أو", "probability": 0.90478515625}, {"start": 1583.6, "end": 1584.24, "word": " finite،", "probability": 0.9306640625}, {"start": 1584.24, "end": 1585.3, "word": " مختلف،", "probability": 0.83038330078125}, {"start": 1585.3, "end": 1585.86, "word": " فهذه", "probability": 0.9295247395833334}, {"start": 1585.86, "end": 1587.24, "word": " نتيجة", "probability": 0.8902587890625}], "temperature": 1.0}, {"id": 65, "seek": 161772, "start": 1609.08, "end": 1617.72, "text": "proposition جداش هذا خمسة جداش مكتوبة خمسة تلاتة proposition خمسة تلاتة", "tokens": [79, 1513, 5830, 10874, 3215, 33599, 23758, 16490, 2304, 3794, 3660, 10874, 3215, 33599, 3714, 4117, 2655, 37746, 3660, 16490, 2304, 3794, 3660, 6055, 1211, 9307, 3660, 24830, 16490, 2304, 3794, 3660, 6055, 1211, 9307, 3660], "avg_logprob": -0.28293918274544383, "compression_ratio": 1.4666666666666666, "no_speech_prob": 0.0, "words": [{"start": 1609.08, "end": 1609.96, "word": "proposition", "probability": 0.6673990885416666}, {"start": 1609.96, "end": 1610.84, "word": " جداش", "probability": 0.5835774739583334}, {"start": 1610.84, "end": 1610.96, "word": " هذا", "probability": 0.268798828125}, {"start": 1610.96, "end": 1611.34, "word": " خمسة", "probability": 0.895751953125}, {"start": 1611.34, "end": 1611.68, "word": " جداش", "probability": 0.8201497395833334}, {"start": 1611.68, "end": 1612.1, "word": " مكتوبة", "probability": 0.8189453125}, {"start": 1612.1, "end": 1612.48, "word": " خمسة", "probability": 0.904296875}, {"start": 1612.48, "end": 1613.62, "word": " تلاتة", "probability": 0.905517578125}, {"start": 1613.62, "end": 1616.7, "word": " proposition", "probability": 0.373046875}, {"start": 1616.7, "end": 1617.28, "word": " خمسة", "probability": 0.9827880859375}, {"start": 1617.28, "end": 1617.72, "word": " تلاتة", "probability": 0.9913330078125}], "temperature": 1.0}, {"id": 66, "seek": 164621, "start": 1620.25, "end": 1646.21, "text": "اتحاد denominable set مع مجموعة من عنصر واحد بتامه denominable طبعا شيء منطقي لأن قبل العدو زيت عليه عنصر بتامها قبل اللي عده هنشوف طبعا ال trick بسيط في البرهان و خلينا نتعلمه فطبعا هنا فينا جملة شرطية فناخد الجملة الشرطية إذا الشرط صحيح prove assume X is denominable", "tokens": [9307, 5016, 18513, 1441, 6981, 712, 992, 20449, 3714, 7435, 2304, 2407, 27884, 9154, 18871, 9381, 2288, 36764, 24401, 39894, 10943, 3224, 1441, 6981, 712, 23032, 3555, 3615, 995, 44049, 38207, 9154, 9566, 38436, 5296, 33456, 12174, 36150, 18863, 3215, 2407, 30767, 36081, 47356, 18871, 9381, 2288, 39894, 10943, 11296, 12174, 36150, 13672, 1829, 6225, 3215, 3224, 8032, 1863, 8592, 38688, 23032, 3555, 3615, 995, 2423, 4282, 4724, 3794, 1829, 9566, 8978, 2423, 26890, 3224, 7649, 4032, 16490, 20292, 8315, 8717, 2655, 3615, 19528, 3224, 6156, 9566, 3555, 3615, 995, 34105, 8978, 8315, 10874, 2304, 37977, 13412, 2288, 9566, 10632, 6156, 1863, 47283, 3215, 25724, 2304, 37977, 25124, 2288, 9566, 10632, 11933, 15730, 25124, 2288, 9566, 20328, 5016, 1829, 5016, 7081, 6552, 1783, 307, 1441, 6981, 712], "avg_logprob": -0.19897460320498794, "compression_ratio": 1.7389558232931728, "no_speech_prob": 0.0, "words": [{"start": 1620.25, "end": 1621.09, "word": "اتحاد", "probability": 0.7110188802083334}, {"start": 1621.09, "end": 1621.63, "word": " denominable", "probability": 0.5603841145833334}, {"start": 1621.63, "end": 1621.91, "word": " set", "probability": 0.6298828125}, {"start": 1621.91, "end": 1622.25, "word": " مع", "probability": 0.93896484375}, {"start": 1622.25, "end": 1623.19, "word": " مجموعة", "probability": 0.9107421875}, {"start": 1623.19, "end": 1623.35, "word": " من", "probability": 0.990234375}, {"start": 1623.35, "end": 1623.67, "word": " عنصر", "probability": 0.9881184895833334}, {"start": 1623.67, "end": 1623.93, "word": " واحد", "probability": 0.99267578125}, {"start": 1623.93, "end": 1624.35, "word": " بتامه", "probability": 0.6878255208333334}, {"start": 1624.35, "end": 1624.81, "word": " denominable", "probability": 0.8264973958333334}, {"start": 1624.81, "end": 1625.23, "word": " طبعا", "probability": 0.8892822265625}, {"start": 1625.23, "end": 1625.43, "word": " شيء", "probability": 0.908447265625}, {"start": 1625.43, "end": 1625.85, "word": " منطقي", "probability": 0.8479817708333334}, {"start": 1625.85, "end": 1626.85, "word": " لأن", "probability": 0.760498046875}, {"start": 1626.85, "end": 1627.37, "word": " قبل", "probability": 0.97216796875}, {"start": 1627.37, "end": 1627.53, "word": " العدو", "probability": 0.6670328776041666}, {"start": 1627.53, "end": 1627.67, "word": " زيت", "probability": 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"probability": 0.8720703125}, {"start": 1632.27, "end": 1632.83, "word": " البرهان", "probability": 0.92822265625}, {"start": 1632.83, "end": 1633.37, "word": " و", "probability": 0.97314453125}, {"start": 1633.37, "end": 1633.63, "word": " خلينا", "probability": 0.83203125}, {"start": 1633.63, "end": 1634.41, "word": " نتعلمه", "probability": 0.97060546875}, {"start": 1634.41, "end": 1634.79, "word": " فطبعا", "probability": 0.84931640625}, {"start": 1634.79, "end": 1635.21, "word": " هنا", "probability": 0.619140625}, {"start": 1635.21, "end": 1635.47, "word": " فينا", "probability": 0.605224609375}, {"start": 1635.47, "end": 1635.71, "word": " جملة", "probability": 0.9627278645833334}, {"start": 1635.71, "end": 1636.15, "word": " شرطية", "probability": 0.989013671875}, {"start": 1636.15, "end": 1636.57, "word": " فناخد", "probability": 0.9482421875}, {"start": 1636.57, "end": 1636.87, "word": " الجملة", "probability": 0.9547526041666666}, {"start": 1636.87, "end": 1637.25, "word": " الشرطية", "probability": 0.9825439453125}, {"start": 1637.25, "end": 1637.37, "word": " إذا", "probability": 0.6396484375}, {"start": 1637.37, "end": 1637.61, "word": " الشرط", "probability": 0.9474283854166666}, {"start": 1637.61, "end": 1638.11, "word": " صحيح", "probability": 0.82635498046875}, {"start": 1638.11, "end": 1638.45, "word": " prove", "probability": 0.501953125}, {"start": 1638.45, "end": 1642.19, "word": " assume", "probability": 0.751953125}, {"start": 1642.19, "end": 1645.03, "word": " X", "probability": 0.64404296875}, {"start": 1645.03, "end": 1645.65, "word": " is", "probability": 0.94873046875}, {"start": 1645.65, "end": 1646.21, "word": " denominable", "probability": 0.8512369791666666}], "temperature": 1.0}, {"id": 67, "seek": 167227, "start": 1648.31, "end": 1672.27, "text": "X is innumerable يعني تكافئ إلى N اكتب اختصاراً ماشي الحال X is innumerable يعني تكافئ إلى N هيك التعريف اه طبعاً و بدنا ناخد ايش ال singleton set and let X0 be any element لأنه جالب ال every يعني for all فبتاخدش تشتغل بشكل عام ب any element", "tokens": [55, 307, 7714, 15583, 712, 37495, 22653, 6055, 4117, 31845, 19986, 30731, 426, 1975, 4117, 2655, 3555, 1975, 46456, 9381, 9640, 995, 14111, 3714, 33599, 1829, 21542, 6027, 1783, 307, 7714, 15583, 712, 37495, 22653, 6055, 4117, 31845, 19986, 30731, 426, 39896, 4117, 16712, 3615, 16572, 5172, 1975, 3224, 23032, 3555, 3615, 995, 14111, 4032, 47525, 8315, 8717, 47283, 3215, 1975, 1829, 8592, 2423, 1522, 14806, 992, 293, 718, 1783, 15, 312, 604, 4478, 5296, 33456, 3224, 10874, 6027, 3555, 2423, 633, 37495, 22653, 337, 439, 6156, 3555, 2655, 47283, 3215, 8592, 6055, 8592, 2655, 17082, 1211, 4724, 8592, 28820, 6225, 10943, 4724, 604, 4478], "avg_logprob": -0.3354952962331052, "compression_ratio": 1.6401869158878504, "no_speech_prob": 0.0, "words": [{"start": 1648.31, "end": 1648.65, "word": "X", "probability": 0.08740234375}, {"start": 1648.65, "end": 1648.81, "word": " is", "probability": 0.85888671875}, {"start": 1648.81, "end": 1649.37, "word": " innumerable", "probability": 0.6170654296875}, {"start": 1649.37, "end": 1650.07, "word": " يعني", "probability": 0.7626953125}, {"start": 1650.07, "end": 1650.51, "word": " تكافئ", "probability": 0.61016845703125}, {"start": 1650.51, "end": 1650.65, "word": " إلى", "probability": 0.31298828125}, {"start": 1650.65, "end": 1650.77, "word": " N", "probability": 0.63671875}, {"start": 1650.77, "end": 1651.07, "word": " اكتب", "probability": 0.80523681640625}, {"start": 1651.07, "end": 1652.41, "word": " اختصاراً", "probability": 0.7425537109375}, {"start": 1652.41, "end": 1652.67, "word": " ماشي", "probability": 0.7248128255208334}, {"start": 1652.67, "end": 1653.05, "word": " الحال", "probability": 0.85205078125}, {"start": 1653.05, "end": 1653.83, "word": " X", "probability": 0.7197265625}, {"start": 1653.83, "end": 1653.99, "word": " is", "probability": 0.79443359375}, {"start": 1653.99, "end": 1654.35, "word": " innumerable", "probability": 0.9757486979166666}, {"start": 1654.35, "end": 1654.51, "word": " يعني", "probability": 0.96337890625}, {"start": 1654.51, "end": 1654.85, "word": " تكافئ", "probability": 0.991943359375}, {"start": 1654.85, "end": 1655.03, "word": " إلى", "probability": 0.806640625}, {"start": 1655.03, "end": 1655.17, "word": " N", "probability": 0.97021484375}, {"start": 1655.17, "end": 1655.43, "word": " هيك", "probability": 0.732666015625}, {"start": 1655.43, "end": 1656.01, "word": " التعريف", "probability": 0.987548828125}, {"start": 1656.01, "end": 1656.51, "word": " اه", "probability": 0.6341552734375}, {"start": 1656.51, "end": 1656.91, "word": " طبعاً", "probability": 0.916015625}, {"start": 1656.91, "end": 1657.01, "word": " و", "probability": 0.8857421875}, {"start": 1657.01, "end": 1657.21, "word": " بدنا", "probability": 0.793701171875}, {"start": 1657.21, "end": 1657.57, "word": " ناخد", "probability": 0.9890950520833334}, {"start": 1657.57, "end": 1657.75, "word": " ايش", "probability": 0.5671793619791666}, {"start": 1657.75, "end": 1657.89, "word": " ال", "probability": 0.51806640625}, {"start": 1657.89, "end": 1658.29, "word": " singleton", "probability": 0.6300048828125}, {"start": 1658.29, "end": 1658.69, "word": " set", "probability": 0.69140625}, {"start": 1658.69, "end": 1659.47, "word": " and", "probability": 0.7548828125}, {"start": 1659.47, "end": 1661.67, "word": " let", "probability": 0.919921875}, {"start": 1661.67, "end": 1663.47, "word": " X0", "probability": 0.7607421875}, {"start": 1663.47, "end": 1664.47, "word": " be", "probability": 0.826171875}, {"start": 1664.47, "end": 1665.23, "word": " any", "probability": 0.9091796875}, {"start": 1665.23, "end": 1665.69, "word": " element", "probability": 0.95751953125}, {"start": 1665.69, "end": 1667.41, "word": " لأنه", "probability": 0.8068033854166666}, {"start": 1667.41, "end": 1667.59, "word": " جالب", "probability": 0.3376871744791667}, {"start": 1667.59, "end": 1667.65, "word": " ال", "probability": 0.765625}, {"start": 1667.65, "end": 1667.93, "word": " every", "probability": 0.677734375}, {"start": 1667.93, "end": 1668.11, "word": " يعني", "probability": 0.955078125}, {"start": 1668.11, "end": 1668.33, "word": " for", "probability": 0.9462890625}, {"start": 1668.33, "end": 1668.57, "word": " all", "probability": 0.9580078125}, {"start": 1668.57, "end": 1669.09, "word": " فبتاخدش", "probability": 0.6866455078125}, {"start": 1669.09, "end": 1669.29, "word": " تشتغل", "probability": 0.7708984375}, {"start": 1669.29, "end": 1669.53, "word": " بشكل", "probability": 0.96826171875}, {"start": 1669.53, "end": 1670.73, "word": " عام", "probability": 0.98193359375}, {"start": 1670.73, "end": 1671.65, "word": " ب", "probability": 0.88623046875}, {"start": 1671.65, "end": 1671.91, "word": " any", "probability": 0.56640625}, {"start": 1671.91, "end": 1672.27, "word": " element", "probability": 0.9599609375}], "temperature": 1.0}, {"id": 68, "seek": 169451, "start": 1676.43, "end": 1694.51, "text": "في عندي أكم احتمال للـ X0 واش هم .. يا طبعا في احتمالات متعددة بس ايش احتمالات .. في الاحتمالات المهمة ايش لازم ااخد؟ انا بدي ااخد الاتحاد X اتحاد الـ X0 هل هذا دايما لما .. لما باخد اتحاد بضيف عنصر ولا ممكن مايضفش؟", "tokens": [41185, 18871, 16254, 5551, 24793, 1975, 33753, 2304, 6027, 24976, 39184, 1783, 15, 4032, 33599, 8032, 2304, 4386, 35186, 23032, 3555, 3615, 995, 8978, 1975, 33753, 2304, 6027, 9307, 44650, 22488, 41891, 4724, 3794, 1975, 1829, 8592, 1975, 33753, 2304, 6027, 9307, 4386, 8978, 42963, 33753, 2304, 6027, 9307, 9673, 16095, 3660, 1975, 1829, 8592, 5296, 31377, 2304, 1975, 47283, 3215, 22807, 1975, 8315, 4724, 16254, 1975, 47283, 3215, 2423, 9307, 5016, 18513, 1783, 1975, 2655, 5016, 18513, 2423, 39184, 1783, 15, 8032, 1211, 23758, 11778, 47302, 15042, 5296, 15042, 4386, 5296, 15042, 4724, 47283, 3215, 1975, 2655, 5016, 18513, 4724, 11242, 33911, 18871, 9381, 2288, 49429, 3714, 43020, 19446, 1829, 11242, 5172, 8592, 22807], "avg_logprob": 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لاني اعتبار أول شي الأولى السهلة if X0 تنتمي لل X then ال X اتحاد ال X0 تساوي X وهذه تكافئ الآن خلصنا مافيش اختلاف اذا هنشتغل نياش ليست عنصر في ال X الاحتمال التاني الآن assume", "tokens": [10721, 3224, 5551, 5016, 3794, 1863, 23032, 3555, 3615, 995, 5296, 31377, 2304, 8717, 47283, 3215, 27188, 30241, 5296, 7649, 1829, 1975, 34268, 3555, 9640, 5551, 12610, 44049, 16247, 12610, 7578, 21136, 3224, 37977, 498, 1783, 15, 6055, 29399, 2304, 1829, 24976, 1783, 550, 2423, 1783, 1975, 2655, 5016, 18513, 2423, 1783, 15, 6055, 3794, 995, 45865, 1783, 37037, 24192, 6055, 4117, 31845, 19986, 6024, 48506, 16490, 1211, 9381, 8315, 19446, 41185, 8592, 1975, 46456, 15040, 5172, 1975, 15730, 8032, 1863, 8592, 2655, 17082, 1211, 8717, 1829, 33599, 32239, 14851, 18871, 9381, 2288, 8978, 2423, 1783, 42963, 33753, 2304, 6027, 16712, 7649, 1829, 6024, 48506, 6552], "avg_logprob": -0.2922021167300572, "compression_ratio": 1.5963302752293578, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 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X", "probability": 0.81591796875}, {"start": 1724.01, "end": 1724.85, "word": " ففعلًا", "probability": 0.791943359375}, {"start": 1724.85, "end": 1725.03, "word": " في", "probability": 0.53759765625}, {"start": 1725.03, "end": 1725.55, "word": " إضافة", "probability": 0.95751953125}, {"start": 1725.55, "end": 1725.79, "word": " هنا", "probability": 0.943359375}, {"start": 1725.79, "end": 1726.23, "word": " في", "probability": 0.56494140625}, {"start": 1726.23, "end": 1726.61, "word": " إضافة", "probability": 0.982177734375}, {"start": 1726.61, "end": 1727.17, "word": " فعليًا", "probability": 0.86259765625}, {"start": 1727.17, "end": 1727.79, "word": " مش", "probability": 0.79345703125}, {"start": 1727.79, "end": 1728.17, "word": " كل", "probability": 0.98291015625}, {"start": 1728.17, "end": 1728.87, "word": " اتحاد", "probability": 0.8919677734375}, {"start": 1728.87, "end": 1729.47, "word": " إضافة", "probability": 0.979736328125}, {"start": 1729.47, "end": 1730.15, "word": " 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"text": "طبعا هنا لازم اذكر هذا الكلام اللي شرحته مش ذاك هو اللي لازم اكتبه اه where x تساوي x one إلى مانا نهاية اه then f is a bijection وهذا بدي اتركه ك exercise", "tokens": [9566, 3555, 3615, 995, 34105, 5296, 31377, 2304, 1975, 8848, 37983, 23758, 2423, 28820, 10943, 13672, 1829, 13412, 2288, 33753, 3224, 37893, 29910, 995, 4117, 31439, 13672, 1829, 5296, 31377, 2304, 1975, 4117, 2655, 3555, 3224, 1975, 3224, 689, 2031, 6055, 3794, 995, 45865, 2031, 472, 30731, 3714, 7649, 995, 8717, 11296, 10632, 1975, 3224, 550, 283, 307, 257, 3228, 1020, 313, 37037, 15730, 4724, 16254, 1975, 2655, 31747, 3224, 9122, 5380], "avg_logprob": -0.23672944552277866, "compression_ratio": 1.4404761904761905, "no_speech_prob": 0.0, "words": [{"start": 1911.87, "end": 1912.79, "word": "طبعا", "probability": 0.810791015625}, {"start": 1912.79, "end": 1913.19, "word": " هنا", "probability": 0.9501953125}, {"start": 1913.19, "end": 1914.91, "word": " لازم", "probability": 0.97119140625}, {"start": 1914.91, 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"end": 1919.23, "word": " where", "probability": 0.83984375}, {"start": 1919.23, "end": 1921.37, "word": " x", "probability": 0.496826171875}, {"start": 1921.37, "end": 1922.21, "word": " تساوي", "probability": 0.807861328125}, {"start": 1922.21, "end": 1923.27, "word": " x", "probability": 0.962890625}, {"start": 1923.27, "end": 1923.69, "word": " one", "probability": 0.451171875}, {"start": 1923.69, "end": 1924.29, "word": " إلى", "probability": 0.60546875}, {"start": 1924.29, "end": 1924.57, "word": " مانا", "probability": 0.74609375}, {"start": 1924.57, "end": 1924.97, "word": " نهاية", "probability": 0.91748046875}, {"start": 1924.97, "end": 1927.29, "word": " اه", "probability": 0.757568359375}, {"start": 1927.29, "end": 1927.69, "word": " then", "probability": 0.85986328125}, {"start": 1927.69, "end": 1929.59, "word": " f", "probability": 0.53369140625}, {"start": 1929.59, "end": 1930.51, "word": " is", "probability": 0.96435546875}, {"start": 1930.51, "end": 1930.67, "word": " a", "probability": 0.865234375}, {"start": 1930.67, "end": 1932.63, "word": " bijection", "probability": 0.8264973958333334}, {"start": 1932.63, "end": 1934.45, "word": " وهذا", "probability": 0.6734619140625}, {"start": 1934.45, "end": 1934.67, "word": " بدي", "probability": 0.618896484375}, {"start": 1934.67, "end": 1935.19, "word": " اتركه", "probability": 0.9041748046875}, {"start": 1935.19, "end": 1936.17, "word": " ك", "probability": 0.9892578125}, {"start": 1936.17, "end": 1936.89, "word": " exercise", "probability": 0.56201171875}], "temperature": 1.0}, {"id": 78, "seek": 197183, "start": 1945.13, "end": 1971.83, "text": "خلّيني بس عشان الفكرة تكتمل في مثال مرتبط فيها ممكن نعتبره نتيجة يعني لل proposition ممكن نعتبره نتيجة لل proposition تعميم", "tokens": [9778, 1211, 11703, 9957, 1829, 4724, 3794, 6225, 8592, 7649, 27188, 4117, 25720, 6055, 4117, 39237, 1211, 8978, 50113, 6027, 3714, 43500, 3555, 9566, 8978, 11296, 3714, 43020, 8717, 34268, 26890, 3224, 8717, 31371, 7435, 3660, 37495, 22653, 24976, 24830, 3714, 43020, 8717, 34268, 26890, 3224, 8717, 31371, 7435, 3660, 24976, 24830, 37279, 2304, 32640], "avg_logprob": -0.13525391263621195, "compression_ratio": 1.632, "no_speech_prob": 0.0, "words": [{"start": 1945.13, "end": 1945.77, "word": "خلّيني", "probability": 0.84521484375}, {"start": 1945.77, "end": 1945.95, "word": " بس", "probability": 0.59429931640625}, {"start": 1945.95, "end": 1946.23, "word": " عشان", "probability": 0.9332682291666666}, {"start": 1946.23, "end": 1946.67, "word": " الفكرة", "probability": 0.9925130208333334}, {"start": 1946.67, "end": 1947.07, "word": " تكتمل", "probability": 0.900634765625}, {"start": 1947.07, "end": 1947.17, "word": " في", "probability": 0.8662109375}, {"start": 1947.17, "end": 1947.47, "word": " مثال", "probability": 0.992431640625}, {"start": 1947.47, "end": 1947.89, "word": " مرتبط", "probability": 0.9925537109375}, {"start": 1947.89, "end": 1948.39, "word": " فيها", "probability": 0.96728515625}, {"start": 1948.39, "end": 1949.37, "word": " ممكن", "probability": 0.927490234375}, {"start": 1949.37, "end": 1949.81, "word": " نعتبره", "probability": 0.791015625}, {"start": 1949.81, "end": 1950.25, "word": " نتيجة", "probability": 0.9947509765625}, {"start": 1950.25, "end": 1950.43, "word": " يعني", "probability": 0.754150390625}, {"start": 1950.43, "end": 1950.81, "word": " لل", "probability": 0.52099609375}, {"start": 1950.81, "end": 1951.21, "word": " proposition", "probability": 0.59814453125}, {"start": 1951.21, "end": 1952.93, "word": " ممكن", "probability": 0.7861328125}, {"start": 1952.93, "end": 1953.71, "word": " نعتبره", "probability": 0.9949951171875}, {"start": 1953.71, "end": 1954.47, "word": " نتيجة", "probability": 0.9951171875}, {"start": 1954.47, "end": 1954.69, "word": " لل", "probability": 0.931640625}, {"start": 1954.69, "end": 1955.75, "word": " proposition", "probability": 0.9013671875}, {"start": 1955.75, "end": 1971.83, "word": " تعميم", "probability": 0.9226888020833334}], "temperature": 1.0}, {"id": 79, "seek": 200224, "start": 1973.46, "end": 2002.24, "text": "denominable اضفنا عليها عدد بتامة denominable بقولي طب اضفنا عليها عدد محدود من العناصر برضه بتامة denominable فهي تعميل اضفنا واحد denominable كمان واحد صاروا اتنين برضه denominable وها كذا فبقولي prove if X is a denominable and Y is a finite set مش بس عنصر واحد X0 finite set then X union Y is denominable solution فطبعا .. اه بس خليني اكتب ال X is denominable", "tokens": [1556, 6981, 712, 1975, 11242, 5172, 8315, 25894, 11296, 6225, 3215, 3215, 39894, 10943, 3660, 1441, 6981, 712, 4724, 39648, 1829, 23032, 3555, 1975, 11242, 5172, 8315, 25894, 11296, 6225, 3215, 3215, 3714, 24401, 23328, 9154, 18863, 1863, 33546, 2288, 4724, 43042, 3224, 39894, 10943, 3660, 1441, 6981, 712, 6156, 3224, 1829, 37279, 2304, 26895, 1975, 11242, 5172, 8315, 36764, 24401, 1441, 6981, 712, 9122, 2304, 7649, 36764, 24401, 20328, 9640, 14407, 1975, 2655, 1863, 9957, 4724, 43042, 3224, 1441, 6981, 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{"start": 1986.04, "end": 1986.28, "word": " كذا", "probability": 0.94921875}, {"start": 1986.28, "end": 1986.98, "word": " فبقولي", "probability": 0.78070068359375}, {"start": 1986.98, "end": 1987.2, "word": " prove", "probability": 0.8427734375}, {"start": 1987.2, "end": 1987.4, "word": " if", "probability": 0.94091796875}, {"start": 1987.4, "end": 1987.6, "word": " X", "probability": 0.6123046875}, {"start": 1987.6, "end": 1987.74, "word": " is", "probability": 0.92529296875}, {"start": 1987.74, "end": 1987.8, "word": " a", "probability": 0.84521484375}, {"start": 1987.8, "end": 1988.22, "word": " denominable", "probability": 0.8408203125}, {"start": 1988.22, "end": 1988.5, "word": " and", "probability": 0.92822265625}, {"start": 1988.5, "end": 1988.74, "word": " Y", "probability": 0.9453125}, {"start": 1988.74, "end": 1988.92, "word": " is", "probability": 0.966796875}, {"start": 1988.92, "end": 1989.04, "word": " a", "probability": 0.9677734375}, {"start": 1989.04, "end": 1989.5, "word": " finite", "probability": 0.98583984375}, {"start": 1989.5, "end": 1989.76, "word": " set", "probability": 0.97021484375}, {"start": 1989.76, "end": 1989.98, "word": " مش", "probability": 0.814453125}, {"start": 1989.98, "end": 1990.16, "word": " بس", "probability": 0.95849609375}, {"start": 1990.16, "end": 1990.48, "word": " عنصر", "probability": 0.9685872395833334}, {"start": 1990.48, "end": 1990.72, "word": " واحد", "probability": 0.982666015625}, {"start": 1990.72, "end": 1991.14, "word": " X0", "probability": 0.46136474609375}, {"start": 1991.14, "end": 1991.66, "word": " finite", "probability": 0.459716796875}, {"start": 1991.66, "end": 1992.1, "word": " set", "probability": 0.97314453125}, {"start": 1992.1, "end": 1992.54, "word": " then", "probability": 0.7958984375}, {"start": 1992.54, "end": 1992.9, "word": " X", "probability": 0.9658203125}, {"start": 1992.9, "end": 1993.22, "word": " union", "probability": 0.7509765625}, {"start": 1993.22, "end": 1993.58, "word": " Y", "probability": 0.99072265625}, {"start": 1993.58, "end": 1993.96, "word": " is", "probability": 0.9677734375}, {"start": 1993.96, "end": 1994.62, "word": " denominable", "probability": 0.8756510416666666}, {"start": 1994.62, "end": 1996.46, "word": " solution", "probability": 0.931640625}, {"start": 1996.46, "end": 1998.66, "word": " فطبعا", "probability": 0.97890625}, {"start": 1998.66, "end": 1999.88, "word": " ..", "probability": 0.34423828125}, {"start": 1999.88, "end": 2000.26, "word": " اه", "probability": 0.6785888671875}, {"start": 2000.26, "end": 2000.44, "word": " بس", "probability": 0.86328125}, {"start": 2000.44, "end": 2001.06, "word": " خليني", "probability": 0.67236328125}, {"start": 2001.06, "end": 2001.42, "word": " اكتب", "probability": 0.8701171875}, {"start": 2001.42, "end": 2001.54, "word": " ال", "probability": 0.576171875}, {"start": 2001.54, "end": 2001.68, "word": " X", "probability": 0.87158203125}, {"start": 2001.68, "end": 2001.84, "word": " is", "probability": 0.96240234375}, {"start": 2001.84, "end": 2002.24, "word": " denominable", "probability": 0.8951822916666666}], "temperature": 1.0}, {"id": 80, "seek": 202556, "start": 2002.86, "end": 2025.56, "text": "let x ما زال denomable ممكن اكتب بـ x واحد إلى ما لا نهاية be a denomable set and let y برضه بقدر ارقمها لانه finite بس ايه ايش؟ بيجي في الترقيم هنا، ايه الفرق؟ be a finite set", "tokens": [2631, 2031, 19446, 30767, 6027, 1441, 298, 712, 3714, 43020, 1975, 4117, 2655, 3555, 4724, 39184, 2031, 36764, 24401, 30731, 19446, 20193, 8717, 11296, 10632, 312, 257, 1441, 298, 712, 992, 293, 718, 288, 4724, 43042, 3224, 4724, 28543, 2288, 1975, 2288, 4587, 2304, 11296, 5296, 7649, 3224, 19362, 4724, 3794, 1975, 1829, 3224, 1975, 1829, 8592, 22807, 4724, 1829, 7435, 1829, 8978, 16712, 2288, 4587, 32640, 34105, 12399, 1975, 1829, 3224, 27188, 2288, 4587, 22807, 312, 257, 19362, 992], "avg_logprob": -0.3288966049382716, "compression_ratio": 1.4772727272727273, "no_speech_prob": 0.0, "words": [{"start": 2002.86, "end": 2003.28, "word": "let", "probability": 0.27099609375}, {"start": 2003.28, "end": 2003.82, "word": " x", "probability": 0.483154296875}, {"start": 2003.82, "end": 2005.06, "word": " ما", "probability": 0.5166015625}, {"start": 2005.06, "end": 2005.28, "word": " زال", "probability": 0.985107421875}, {"start": 2005.28, "end": 2005.72, "word": " denomable", "probability": 0.4847412109375}, {"start": 2005.72, "end": 2006.02, "word": " ممكن", "probability": 0.7047119140625}, {"start": 2006.02, "end": 2006.28, "word": " اكتب", "probability": 0.85906982421875}, {"start": 2006.28, "end": 2006.4, "word": " بـ", "probability": 0.652587890625}, {"start": 2006.4, "end": 2006.54, "word": " x", "probability": 0.5185546875}, {"start": 2006.54, "end": 2006.92, "word": " واحد", "probability": 0.6275634765625}, {"start": 2006.92, "end": 2007.1, "word": " إلى", "probability": 0.80029296875}, {"start": 2007.1, "end": 2007.28, "word": " ما", "probability": 0.63818359375}, {"start": 2007.28, "end": 2007.38, "word": " لا", "probability": 0.578125}, {"start": 2007.38, "end": 2007.68, "word": " نهاية", "probability": 0.93603515625}, {"start": 2007.68, "end": 2007.82, "word": " be", "probability": 0.2171630859375}, {"start": 2007.82, "end": 2009.9, "word": " a", "probability": 0.438232421875}, {"start": 2009.9, "end": 2011.4, "word": " denomable", "probability": 0.8419596354166666}, {"start": 2011.4, "end": 2011.82, "word": " set", "probability": 0.9248046875}, {"start": 2011.82, "end": 2016.04, "word": " and", "probability": 0.71826171875}, {"start": 2016.04, "end": 2018.06, "word": " let", "probability": 0.9111328125}, {"start": 2018.06, "end": 2018.62, "word": " y", "probability": 0.9228515625}, {"start": 2018.62, "end": 2019.18, "word": " برضه", "probability": 0.9689127604166666}, {"start": 2019.18, "end": 2019.52, "word": " بقدر", "probability": 0.8499348958333334}, {"start": 2019.52, "end": 2019.94, "word": " ارقمها", "probability": 0.92294921875}, {"start": 2019.94, "end": 2020.18, "word": " لانه", "probability": 0.6219075520833334}, {"start": 2020.18, "end": 2020.56, "word": " finite", "probability": 0.5947265625}, {"start": 2020.56, "end": 2021.9, "word": " بس", "probability": 0.956787109375}, {"start": 2021.9, "end": 2022.08, "word": " ايه", "probability": 0.7835286458333334}, {"start": 2022.08, "end": 2022.64, "word": " ايش؟", "probability": 0.4918212890625}, {"start": 2022.64, "end": 2022.86, "word": " بيجي", "probability": 0.837158203125}, {"start": 2022.86, "end": 2022.94, "word": " في", "probability": 0.5712890625}, {"start": 2022.94, "end": 2023.44, "word": " الترقيم", "probability": 0.9630126953125}, {"start": 2023.44, "end": 2023.7, "word": " هنا،", "probability": 0.6846923828125}, {"start": 2023.7, "end": 2023.82, "word": " ايه", "probability": 0.8885091145833334}, {"start": 2023.82, "end": 2024.54, "word": " الفرق؟", "probability": 0.9351806640625}, {"start": 2024.54, "end": 2024.68, "word": " be", "probability": 0.1451416015625}, {"start": 2024.68, "end": 2024.86, "word": " a", "probability": 0.97314453125}, {"start": 2024.86, "end": 2025.22, "word": " finite", "probability": 0.982421875}, {"start": 2025.22, "end": 2025.56, "word": " set", "probability": 0.96484375}], "temperature": 1.0}, {"id": 81, "seek": 205311, "start": 2033.67, "end": 2053.11, "text": "طبعاً برضه هنا فايدة الـ proposition كيف نرتاح بدل ما ناخد احتمالات ان هدول ممكن عناصر يكون تقاطة وما يضفوش هنعتمد على المثال السابق درسنا الاحتمالات الان بدي اعملهم على صورة ايش كل مرة بنزيد واحد واحد هي العملية فبدي اعرف مجموعات بالشكل التالي let", "tokens": [9566, 3555, 3615, 995, 14111, 4724, 43042, 3224, 34105, 6156, 995, 25708, 3660, 2423, 39184, 24830, 9122, 33911, 8717, 43500, 39319, 47525, 1211, 19446, 8717, 47283, 3215, 1975, 33753, 2304, 6027, 9307, 16472, 8032, 3215, 12610, 3714, 43020, 18871, 33546, 2288, 7251, 30544, 6055, 4587, 41193, 3660, 4032, 15042, 7251, 11242, 5172, 2407, 8592, 8032, 1863, 34268, 2304, 3215, 15844, 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"probability": 0.55029296875}, {"start": 2036.53, "end": 2036.95, "word": " كيف", "probability": 0.800537109375}, {"start": 2036.95, "end": 2037.45, "word": " نرتاح", "probability": 0.9334309895833334}, {"start": 2037.45, "end": 2037.65, "word": " بدل", "probability": 0.89208984375}, {"start": 2037.65, "end": 2037.73, "word": " ما", "probability": 0.319580078125}, {"start": 2037.73, "end": 2037.93, "word": " ناخد", "probability": 0.95703125}, {"start": 2037.93, "end": 2038.59, "word": " احتمالات", "probability": 0.9796875}, {"start": 2038.59, "end": 2038.99, "word": " ان", "probability": 0.57421875}, {"start": 2038.99, "end": 2039.23, "word": " هدول", "probability": 0.8487955729166666}, {"start": 2039.23, "end": 2039.47, "word": " ممكن", "probability": 0.90673828125}, {"start": 2039.47, "end": 2039.85, "word": " عناصر", "probability": 0.86572265625}, {"start": 2039.85, "end": 2040.03, "word": " يكون", "probability": 0.912841796875}, {"start": 2040.03, "end": 2040.41, "word": " تقاطة", 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"word": " على", "probability": 0.56494140625}, {"start": 2046.49, "end": 2046.75, "word": " صورة", "probability": 0.9939778645833334}, {"start": 2046.75, "end": 2046.91, "word": " ايش", "probability": 0.6803385416666666}, {"start": 2046.91, "end": 2047.09, "word": " كل", "probability": 0.7431640625}, {"start": 2047.09, "end": 2047.23, "word": " مرة", "probability": 0.98046875}, {"start": 2047.23, "end": 2047.59, "word": " بنزيد", "probability": 0.7960611979166666}, {"start": 2047.59, "end": 2047.87, "word": " واحد", "probability": 0.726806640625}, {"start": 2047.87, "end": 2048.15, "word": " واحد", "probability": 0.96630859375}, {"start": 2048.15, "end": 2048.29, "word": " هي", "probability": 0.6279296875}, {"start": 2048.29, "end": 2048.79, "word": " العملية", "probability": 0.9461263020833334}, {"start": 2048.79, "end": 2049.71, "word": " فبدي", "probability": 0.8253580729166666}, {"start": 2049.71, "end": 2050.15, "word": " اعرف", "probability": 0.7711588541666666}, {"start": 2050.15, "end": 2050.99, "word": " مجموعات", "probability": 0.97861328125}, {"start": 2050.99, "end": 2051.45, "word": " بالشكل", "probability": 0.96142578125}, {"start": 2051.45, "end": 2051.99, "word": " التالي", "probability": 0.89794921875}, {"start": 2051.99, "end": 2053.11, "word": " let", "probability": 0.5302734375}], "temperature": 1.0}, {"id": 82, "seek": 208092, "start": 2055.75, "end": 2080.93, "text": "فطبعا أول مرة بدي أضيف Y1 بعدين بدي أضيف Y2 وكذا بدي نمشي بالترتيب فبنسميهم let X1 capital X1 عبارة عن X إتحاد Y1 بدي نضيف نقوا واحدة واحدة مانعش نضيفهم مرة واحدة مانعش يطفوا المكيال عندنا أو يطفوا الوعاء فبتدريجي فنضيف Y1 Y2 X2 بتساوي X1", "tokens": [5172, 9566, 3555, 3615, 995, 5551, 12610, 3714, 25720, 4724, 16254, 5551, 11242, 33911, 398, 16, 39182, 9957, 4724, 16254, 5551, 11242, 33911, 398, 17, 4032, 4117, 15730, 4724, 16254, 8717, 2304, 8592, 1829, 20666, 2655, 2288, 31371, 3555, 6156, 3555, 1863, 38251, 1829, 16095, 718, 1783, 16, 4238, 1783, 16, 6225, 3555, 9640, 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"end": 2069.79, "word": " واحدة", "probability": 0.98193359375}, {"start": 2069.79, "end": 2070.03, "word": " مانعش", "probability": 0.51513671875}, {"start": 2070.03, "end": 2070.27, "word": " نضيفهم", "probability": 0.8734130859375}, {"start": 2070.27, "end": 2070.45, "word": " مرة", "probability": 0.850341796875}, {"start": 2070.45, "end": 2070.91, "word": " واحدة", "probability": 0.98974609375}, {"start": 2070.91, "end": 2071.43, "word": " مانعش", "probability": 0.776031494140625}, {"start": 2071.43, "end": 2072.53, "word": " يطفوا", "probability": 0.8072509765625}, {"start": 2072.53, "end": 2072.87, "word": " المكيال", "probability": 0.66680908203125}, {"start": 2072.87, "end": 2073.11, "word": " عندنا", "probability": 0.627685546875}, {"start": 2073.11, "end": 2073.17, "word": " أو", "probability": 0.5380859375}, {"start": 2073.17, "end": 2073.45, "word": " يطفوا", "probability": 0.979248046875}, {"start": 2073.45, "end": 2074.01, "word": " الوعاء", "probability": 0.7376302083333334}, {"start": 2074.01, "end": 2075.03, "word": " فبتدريجي", "probability": 0.8038504464285714}, {"start": 2075.03, "end": 2075.53, "word": " فنضيف", "probability": 0.70947265625}, {"start": 2075.53, "end": 2076.11, "word": " Y1", "probability": 0.97607421875}, {"start": 2076.11, "end": 2077.73, "word": " Y2", "probability": 0.615966796875}, {"start": 2077.73, "end": 2078.45, "word": " X2", "probability": 0.880859375}, {"start": 2078.45, "end": 2080.03, "word": " بتساوي", "probability": 0.645050048828125}, {"start": 2080.03, "end": 2080.93, "word": " X1", "probability": 0.986572265625}], "temperature": 1.0}, {"id": 83, "seek": 210906, "start": 2082.46, "end": 2109.06, "text": "اتحاد Y2 بعد ما ضفتله لعنصر الأول كبرتها شويه أكبرها كمان مرة و هكذا لأن أخر إشي XK تساوي XK ناقص one اتحاد YK وهدي ليست الا مين X اتحاد ال Y ولا لأ", "tokens": [9307, 5016, 18513, 398, 17, 39182, 19446, 48812, 5172, 2655, 43761, 5296, 3615, 1863, 9381, 2288, 16247, 12610, 9122, 26890, 2655, 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"end": 2086.06, "word": " الأول", "probability": 0.705810546875}, {"start": 2086.06, "end": 2086.66, "word": " كبرتها", "probability": 0.66015625}, {"start": 2086.66, "end": 2086.96, "word": " شويه", "probability": 0.7352701822916666}, {"start": 2086.96, "end": 2087.38, "word": " أكبرها", "probability": 0.790283203125}, {"start": 2087.38, "end": 2087.58, "word": " كمان", "probability": 0.9729817708333334}, {"start": 2087.58, "end": 2087.84, "word": " مرة", "probability": 0.984130859375}, {"start": 2087.84, "end": 2088.24, "word": " و", "probability": 0.5302734375}, {"start": 2088.24, "end": 2088.8, "word": " هكذا", "probability": 0.8623046875}, {"start": 2088.8, "end": 2090.16, "word": " لأن", "probability": 0.895263671875}, {"start": 2090.16, "end": 2091.98, "word": " أخر", "probability": 0.6710205078125}, {"start": 2091.98, "end": 2092.58, "word": " إشي", "probability": 0.8533528645833334}, {"start": 2092.58, "end": 2095.0, "word": " XK", "probability": 0.820556640625}, {"start": 2095.0, "end": 2097.58, "word": " تساوي", "probability": 0.9058837890625}, {"start": 2097.58, "end": 2099.46, "word": " XK", "probability": 0.88916015625}, {"start": 2099.46, "end": 2099.94, "word": " ناقص", "probability": 0.8360595703125}, {"start": 2099.94, "end": 2100.28, "word": " one", "probability": 0.54248046875}, {"start": 2100.28, "end": 2103.58, "word": " اتحاد", "probability": 0.9302978515625}, {"start": 2103.58, "end": 2104.86, "word": " YK", "probability": 0.963134765625}, {"start": 2104.86, "end": 2105.82, "word": " وهدي", "probability": 0.5008544921875}, {"start": 2105.82, "end": 2106.14, "word": " ليست", "probability": 0.965576171875}, {"start": 2106.14, "end": 2106.32, "word": " الا", "probability": 0.46875}, {"start": 2106.32, "end": 2106.62, "word": " مين", "probability": 0.74853515625}, {"start": 2106.62, "end": 2107.68, "word": " X", "probability": 0.83935546875}, {"start": 2107.68, "end": 2108.14, "word": " اتحاد", "probability": 0.9505615234375}, {"start": 2108.14, "end": 2108.32, "word": " ال", "probability": 0.623046875}, {"start": 2108.32, "end": 2108.48, "word": " Y", "probability": 0.85546875}, {"start": 2108.48, "end": 2108.8, "word": " ولا", "probability": 0.52294921875}, {"start": 2108.8, "end": 2109.06, "word": " لأ", "probability": 0.965087890625}], "temperature": 1.0}, {"id": 84, "seek": 213890, "start": 2110.34, "end": 2138.9, "text": "X إتحاد الـ Y فانا بدي أمشيهم واحدة واحدة فخلص الآن من ال proposition بما أن X is denomable إذا X1 هو denomable بما أن X1 هو denomable إذا X2 هو denomable و هكذا فعفضية ال proposition فإذا XK هو denomable by a proposition خمسة تلاتة XK is denomable", "tokens": [55, 11933, 2655, 5016, 18513, 2423, 39184, 398, 6156, 7649, 995, 4724, 16254, 5551, 2304, 8592, 1829, 16095, 36764, 24401, 3660, 36764, 24401, 3660, 6156, 9778, 1211, 9381, 6024, 48506, 9154, 2423, 24830, 4724, 15042, 14739, 1783, 307, 1441, 298, 712, 11933, 15730, 1783, 16, 31439, 1441, 298, 712, 4724, 15042, 14739, 1783, 16, 31439, 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2112.94, "word": " واحدة", "probability": 0.95947265625}, {"start": 2112.94, "end": 2113.22, "word": " واحدة", "probability": 0.9684244791666666}, {"start": 2113.22, "end": 2113.86, "word": " فخلص", "probability": 0.9097900390625}, {"start": 2113.86, "end": 2115.72, "word": " الآن", "probability": 0.7705078125}, {"start": 2115.72, "end": 2117.84, "word": " من", "probability": 0.974609375}, {"start": 2117.84, "end": 2118.0, "word": " ال", "probability": 0.9580078125}, {"start": 2118.0, "end": 2118.44, "word": " proposition", "probability": 0.70849609375}, {"start": 2118.44, "end": 2120.98, "word": " بما", "probability": 0.968017578125}, {"start": 2120.98, "end": 2121.16, "word": " أن", "probability": 0.460693359375}, {"start": 2121.16, "end": 2121.42, "word": " X", "probability": 0.95166015625}, {"start": 2121.42, "end": 2121.52, "word": " is", "probability": 0.2275390625}, {"start": 2121.52, "end": 2121.92, "word": " denomable", "probability": 0.4801432291666667}, {"start": 2121.92, "end": 2122.1, "word": " إذا", "probability": 0.576904296875}, {"start": 2122.1, "end": 2122.44, "word": " X1", "probability": 0.846435546875}, {"start": 2122.44, "end": 2122.5, "word": " هو", "probability": 0.23095703125}, {"start": 2122.5, "end": 2122.92, "word": " denomable", "probability": 0.7518717447916666}, {"start": 2122.92, "end": 2123.82, "word": " بما", "probability": 0.92529296875}, {"start": 2123.82, "end": 2123.98, "word": " أن", "probability": 0.80126953125}, {"start": 2123.98, "end": 2124.38, "word": " X1", "probability": 0.97705078125}, {"start": 2124.38, "end": 2124.48, "word": " هو", "probability": 0.66796875}, {"start": 2124.48, "end": 2124.88, "word": " denomable", "probability": 0.9645182291666666}, {"start": 2124.88, "end": 2125.18, "word": " إذا", "probability": 0.9765625}, {"start": 2125.18, "end": 2125.48, "word": " X2", "probability": 0.9970703125}, {"start": 2125.48, "end": 2125.6, "word": " هو", "probability": 0.97998046875}, {"start": 2125.6, "end": 2125.88, "word": " denomable", "probability": 0.9554036458333334}, {"start": 2125.88, "end": 2126.0, "word": " و", "probability": 0.75830078125}, {"start": 2126.0, "end": 2126.36, "word": " هكذا", "probability": 0.8517252604166666}, {"start": 2126.36, "end": 2126.92, "word": " فعفضية", "probability": 0.610693359375}, {"start": 2126.92, "end": 2127.0, "word": " ال", "probability": 0.453369140625}, {"start": 2127.0, "end": 2127.3, "word": " proposition", "probability": 0.89404296875}, {"start": 2127.3, "end": 2127.84, "word": " فإذا", "probability": 0.8792317708333334}, {"start": 2127.84, "end": 2128.34, "word": " XK", "probability": 0.88427734375}, {"start": 2128.34, "end": 2128.66, "word": " هو", "probability": 0.3701171875}, {"start": 2128.66, "end": 2129.1, "word": " denomable", "probability": 0.9469401041666666}, {"start": 2129.1, "end": 2129.98, "word": " by", "probability": 0.69970703125}, {"start": 2129.98, "end": 2131.1, "word": " a", "probability": 0.50146484375}, {"start": 2131.1, "end": 2131.76, "word": " proposition", "probability": 0.876953125}, {"start": 2131.76, "end": 2135.52, "word": " خمسة", "probability": 0.83612060546875}, {"start": 2135.52, "end": 2136.14, "word": " تلاتة", "probability": 0.948486328125}, {"start": 2136.14, "end": 2137.46, "word": " XK", "probability": 0.877197265625}, {"start": 2137.46, "end": 2138.32, "word": " is", "probability": 0.861328125}, {"start": 2138.32, "end": 2138.9, "word": " denomable", "probability": 0.9256184895833334}], "temperature": 1.0}, {"id": 85, "seek": 214987, "start": 2144.33, "end": 2149.87, "text": "وهو المطلوب فإن وقف هنا إن شاء الله", "tokens": [2407, 3224, 2407, 9673, 9566, 1211, 37746, 6156, 28814, 1863, 4032, 4587, 5172, 34105, 36145, 13412, 16606, 21984], "avg_logprob": -0.2440378226731953, "compression_ratio": 1.0161290322580645, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2144.33, "end": 2144.75, "word": "وهو", "probability": 0.9309895833333334}, {"start": 2144.75, "end": 2145.17, "word": " المطلوب", "probability": 0.9825439453125}, {"start": 2145.17, "end": 2149.03, "word": " فإن", "probability": 0.6299641927083334}, {"start": 2149.03, "end": 2149.31, "word": " وقف", "probability": 0.84423828125}, {"start": 2149.31, "end": 2149.45, "word": " هنا", "probability": 0.369384765625}, {"start": 2149.45, "end": 2149.59, "word": " إن", "probability": 0.423095703125}, {"start": 2149.59, "end": 2149.73, "word": " شاء", "probability": 0.986328125}, {"start": 2149.73, "end": 2149.87, "word": " الله", "probability": 0.9599609375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2149.9588125, "duration_after_vad": 1999.6956249999932}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/5kawOfcrw3A.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/5kawOfcrw3A.srt
new file mode 100644
index 0000000000000000000000000000000000000000..120901f808330fb1cdcb6e4c65fc4e9335312d21
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/5kawOfcrw3A.srt
@@ -0,0 +1,2301 @@
+1
+00:00:21,080 --> 00:00:25,500
+بسم الله الرحمن الرحيم اليوم المحاضرة الثالثة في
+
+2
+00:00:25,500 --> 00:00:32,180
+اللي هو التقارير وروابطها هنستكمل تعريفنا للروابط 
+
+3
+00:00:32,180 --> 00:00:36,240
+اللي تستخدم في تكوين التقارير المركبة من التقارير
+
+4
+00:00:36,240 --> 00:00:41,380
+البسيطة كما ذكرنا في المحاضرات السابقة هناك خمس 
+
+5
+00:00:41,380 --> 00:00:46,160
+روابط وهي الـNegation  الـ negation اللي هي not أداتها
+
+6
+00:00:46,160 --> 00:00:49,420
+وفي عندنا ال conjunction الإختيار وأداتها أو هي ال
+
+7
+00:00:49,420 --> 00:00:53,660
+andأيضًا في عندنا disjunction الفصل وأداتها or وفي 
+
+8
+00:00:53,660 --> 00:00:57,720
+عندنا الجمل الشرطية وهي if then  اه اليوم هنستكمل
+
+9
+00:00:57,720 --> 00:01:01,680
+بالرابط الخامس والأخير وهو the biconditional
+
+10
+00:01:01,680 --> 00:01:06,700
+ثنائية الشرطية طبعًا كمعلومة جانبية المقطع bi هذا 
+
+11
+00:01:06,700 --> 00:01:09,620
+بتكرر كتير وهو يعني ثنائي زي ما ممكن مر علينا في 
+
+12
+00:01:09,620 --> 00:01:13,560
+تفاضل با نظرية ثلث حدين binomial theorem nominal
+
+13
+00:01:13,560 --> 00:01:16,880
+حد binomial وهنا conditional و biconditional بس
+
+14
+00:01:16,880 --> 00:01:20,420
+هذه بس تعليق بالنسبة للمصطلح طبعا على نفس السياسة 
+
+15
+00:01:20,420 --> 00:01:24,900
+هنبدأ إيش التعريف وإيش الرمز وكيف يقرأ ومع مين
+
+16
+00:01:24,900 --> 00:01:28,040
+بتعامل من ال statement مع واحدة أو اثنتين وبعدين
+
+17
+00:01:28,040 --> 00:01:32,340
+كيف نحصل قيمة الصدق لتقرير مركب يحتوي على الرابط
+
+18
+00:01:32,340 --> 00:01:35,120
+if and only if إذا عرفنا قيمة الصدق لمين؟
+
+19
+00:01:35,120 --> 00:01:38,560
+للمركبات، لل statement الأساسية البسيطة اللي بتكون
+
+20
+00:01:38,560 --> 00:01:42,210
+هذه ال statement فنبدأ طبعًا أول شيء طبعًا الروابط
+
+21
+00:01:42,210 --> 00:01:46,390
+الخامسة زي ما لاحظنا وهذا الخامس أنه جميعها أربع
+
+22
+00:01:46,390 --> 00:01:48,370
+منها تدخل على two statements تتعامل مع two 
+
+23
+00:01:48,370 --> 00:01:49,810
+statements إلا الأولى اللي هي النافية بتتعامل مع 
+
+24
+00:01:49,810 --> 00:01:52,150
+statement واحدة فأول شيء بيقوللي أنه أنا لو في 
+
+25
+00:01:52,150 --> 00:01:56,820
+عندي two statements B وQبعمل عليهم رابط if and
+
+26
+00:01:56,820 --> 00:02:00,820
+only في رمزه السهم في الاتجاهين فبقول هذا هو ال
+
+27
+00:02:00,820 --> 00:02:03,720
+connective هذا هو الرابق زي ما نقول نحن ال plus 
+
+28
+00:02:03,720 --> 00:02:06,940
+أداة الجامع فهذا هو ال connective لو برمزنا مين لل
+
+29
+00:02:06,940 --> 00:02:09,800
+biconditional إيش اسمه؟ biconditional فانا فيه
+
+30
+00:02:09,800 --> 00:02:13,340
+عندي رمز زي ما هدا .. هدا رمزوايش اسمه؟ رمز الجمع
+
+31
+00:02:13,340 --> 00:02:17,160
+.. اه .. تمام؟ فهي نهيأيش اسمه .. الرمز هذا الـ
+
+32
+00:02:17,160 --> 00:02:20,380
+biconditional طيب، مع مين بتعامل؟ مع two
+
+33
+00:02:20,380 --> 00:02:22,780
+statements .. مع two statements .. بنحط بينهم زي 
+
+34
+00:02:22,780 --> 00:02:26,100
+ما هيك كيف بنقرا هذه ال statement؟ ب .. if and 
+
+35
+00:02:26,100 --> 00:02:29,180
+only .. if P and Q .. قراءة واحدة، هي القراءة المعروفة
+
+36
+00:02:29,180 --> 00:02:34,180
+الوحيدة، هي أول شي المقدمة الآن أنا عندي statement
+
+37
+00:02:34,180 --> 00:02:38,740
+بيدا الشكل بعرف معلومات عن قيمة الصدق لل بي والكيو
+
+38
+00:02:38,740 --> 00:02:42,840
+طب كيف اجيب قيمة الصدق للكل؟ بدي أعرفها ياها اه كما
+
+39
+00:02:42,840 --> 00:02:46,100
+لاحظنا زي ال conditional مش هيدينا الجدول بشكل
+
+40
+00:02:46,100 --> 00:02:49,040
+مباشر لأنه احنا وصلنا لمرحلة متقدمة نوعا ما
+
+41
+00:02:49,040 --> 00:02:54,600
+فهيديناياها بتكافؤ في جملة قديمة أو جملة معروفة
+
+42
+00:02:54,600 --> 00:02:58,840
+وهذا التعريف بيفسر أو ببرر الاسم biconditional 
+
+43
+00:02:59,060 --> 00:03:02,300
+فبقول لي قيمة الصدق عشان تحصل قيمة الصدق لل if and 
+
+44
+00:03:02,300 --> 00:03:07,060
+only if statement اشمالها تكافئ من if P then Q
+
+45
+00:03:07,060 --> 00:03:11,480
+and if Q then P يعني اشمالهم عشان تكون هذه ال if
+
+46
+00:03:11,480 --> 00:03:14,220
+and only if true لازم ال statement الثانية تكون 
+
+47
+00:03:14,220 --> 00:03:16,700
+true عشان هذه تكون false لازم الثانية تكون false
+
+48
+00:03:16,700 --> 00:03:23,530
+فأنا بقدر أحصل قيمة الصدق للجملة if P then Q and if 
+
+49
+00:03:23,530 --> 00:03:26,870
+Q then P بقدر أحسبه ولا بقدرش؟ بقدر أعرفها 
+
+50
+00:03:26,870 --> 00:03:29,570
+هذه وأعرفها هذه وأعرفها الآن فأنا ما زال عندي
+
+51
+00:03:29,570 --> 00:03:33,890
+قدرة على معرفة قيمة الصدق لهذه ال statement بعرف
+
+52
+00:03:33,890 --> 00:03:36,650
+قيمة الصدق لمين؟ لل if P and only if Q فاحنا بنعرفها بهذه
+
+53
+00:03:36,650 --> 00:03:39,660
+الشكل طبعًا زي ما حكوا إن الشاهدين مهم جداً إن
+
+54
+00:03:39,660 --> 00:03:43,580
+نلاحظ أنه ملاحظين أيوش جانت تكافئ two conditional
+
+55
+00:03:43,580 --> 00:03:46,540
+statement عشان هيك بقى biconditional if P then Q
+
+56
+00:03:46,540 --> 00:03:50,400
+هي جملة شرطية ال P فيها الشرط وال Q جواب الشرط و
+
+57
+00:03:50,400 --> 00:03:54,700
+الثانية العكس ال Q هي الشرط و ال P هي جواب الشرط
+
+58
+00:03:54,700 --> 00:04:00,260
+فهي تكافئ two conditional statement واضح؟ أي سؤال، 
+
+59
+00:04:00,260 --> 00:04:02,900
+فهذا هو التعريف التكافؤ وهذا مهم جدًا، هتعتمد عليه
+
+60
+00:04:02,900 --> 00:04:07,040
+في كثير من الأحيان في التعامل مع ال if and only 
+
+61
+00:04:07,040 --> 00:04:10,160
+if statement طبعًا احنا اختصارًا بدل ما كل مرة 
+
+62
+00:04:10,160 --> 00:04:13,340
+بنحسب اللي هو الجدول، هنديكوا جدول جاهز برضه اللي
+
+63
+00:04:13,340 --> 00:04:17,370
+ممكن نساعده مباشرة زي ال if ده فالجدول بيكون 
+
+64
+00:04:17,370 --> 00:04:23,370
+بالصورة التالية بيكون ال true إذا كان ال Q وال P
+
+65
+00:04:23,370 --> 00:04:27,250
+اللي هو نفس قيمة السطر true مع بعض أو false مع بعض 
+
+66
+00:04:27,250 --> 00:04:30,150
+اللي هو أول سطر في الجدول وآخر سطر غيرك بتكون
+
+67
+00:04:30,150 --> 00:04:33,810
+false طبعًا ليش؟ لأنه أنا بدي يكون هذه true وهذه
+
+68
+00:04:33,810 --> 00:04:39,860
+true هذه true طبعًا هذه P صح اه فإحنا لما نيجي نعلّل
+
+69
+00:04:39,860 --> 00:04:44,280
+بالنص true then false .. false .. false and
+
+70
+00:04:44,280 --> 00:04:46,560
+anything .. false هاي اللي .. إيش الثاني .. هذه
+
+71
+00:04:46,560 --> 00:04:50,680
+واضحة؟ ليش هذه false؟ لإن true then false .. false
+
+72
+00:04:50,680 --> 00:04:54,860
+.. false and anything .. false طيب هذه false then 
+
+73
+00:04:54,860 --> 00:04:58,020
+true .. true لكن إيه العكس true then false الثانية
+
+74
+00:04:58,020 --> 00:05:03,020
+.. false true and false false لكن دولة لأ هذه 
+
+75
+00:05:03,020 --> 00:05:05,600
+ماتفرجش لإن أنا بقول لك true than true true و true
+
+76
+00:05:05,600 --> 00:05:08,860
+than true الترتيب مش مهم هنا false than anything
+
+77
+00:05:08,860 --> 00:05:13,040
+true false than anything true true and true true 
+
+78
+00:05:13,040 --> 00:05:17,820
+واضح؟ أي سؤال فهذا الجدول وهذا تفسيره عشان لو 
+
+79
+00:05:17,820 --> 00:05:21,340
+نسيناه كيف نتذكره فهم طبعًا اللي هي علاقة بالتكافؤ
+
+80
+00:05:21,340 --> 00:05:24,200
+هنشوف بعد قليل فهم يا true هي إذا تكون اثنتين true
+
+81
+00:05:24,200 --> 00:05:29,080
+أو اثنتين false عشان يكون الكل true فهنا بنلخص هذه 
+
+82
+00:05:29,080 --> 00:05:32,360
+الملاحظة فبنقول إن ال if and only if بتكون true
+
+83
+00:05:32,360 --> 00:05:36,260
+إذا كانت اثنتين يا true مع بعض يا false مع بعض اللي 
+
+84
+00:05:36,260 --> 00:05:39,420
+لهم نفس قيمة الصدق نشوف أمثلة دائمًا احنا بنشوف
+
+85
+00:05:39,420 --> 00:05:43,540
+نحاول أمثلة عشان نحاول نستوعب هذا بشكل أفضل ونعرف 
+
+86
+00:05:43,540 --> 00:05:46,880
+كيف بنطبق هذا التعريف وهذه الملاحظات بشكل جيد 
+
+87
+00:05:46,880 --> 00:05:50,980
+فنبدأ في المثال الأول التقليدي اللي هو true or 
+
+88
+00:05:50,980 --> 00:05:54,840
+false equation فهنا المثال الأول ممكن أنا أحله هنا
+
+89
+00:05:54,840 --> 00:06:00,430
+بهمش وبعدين هنحط الجواب مباشرة solution ف
+
+90
+00:06:00,430 --> 00:06:03,130
+determine whether the following statements are
+
+91
+00:06:03,130 --> 00:06:08,830
+true or false المثال الأول A فبنحلل المركبات
+
+92
+00:06:08,830 --> 00:06:15,910
+بنستنتج لجملة ال compound statement فبقولي one is
+
+93
+00:06:15,910 --> 00:06:21,550
+odd  الواحد عدد فردي true ولا false true if and only
+
+94
+00:06:21,550 --> 00:06:25,510
+if الجملة التالية three is even فالس if and only
+
+95
+00:06:25,510 --> 00:06:31,550
+if فالس فإيش الجملة true if and only if فالس فالس 
+
+96
+00:06:31,550 --> 00:06:35,570
+فإذا في طرف مختلف قيمة الصدق معاه فبنفعش فهذه
+
+97
+00:06:35,570 --> 00:06:42,450
+false بي نشوف كمان مثال absolute value of five
+
+98
+00:06:42,450 --> 00:06:49,460
+equals minus five false if and only if five greater
+
+99
+00:06:49,460 --> 00:06:55,620
+than zero true false if and only if true false هاي 
+
+100
+00:06:55,620 --> 00:06:59,140
+بنتعود أنه إذا الواحدة فيهم مختلفة عن الثانية
+
+101
+00:06:59,140 --> 00:07:07,260
+بتكون الكل false square root of four equal two true 
+
+102
+00:07:07,260 --> 00:07:11,360
+لاحدش يقولي false لازم يكون plus minus لأ الجزر
+
+103
+00:07:11,360 --> 00:07:14,320
+التربيعي ده لأ تدينا قيمة واحدة وهي القيمة الموجبة
+
+104
+00:07:14,320 --> 00:07:20,000
+تمام if and only if two squared equals four true 
+
+105
+00:07:20,000 --> 00:07:21,800
+if and only if true
+
+106
+00:07:26,390 --> 00:07:32,110
+نشوف كمان مثال five is greater than six false if
+
+107
+00:07:32,110 --> 00:07:35,810
+and only if five is even false إيش الجملة كلها
+
+108
+00:07:35,810 --> 00:07:42,610
+true false if and only if false true أي yes و no 
+
+109
+00:07:42,610 --> 00:07:46,830
+فبيقد البساطة بنطبق مباشرة بعد هيك بنتعود بنصير
+
+110
+00:07:46,830 --> 00:07:52,150
+أمور بالنسبالي إن شاء الله بسيطة نشوف كمان مثال بس
+
+111
+00:07:52,150 --> 00:07:54,250
+نمسح هذا الجواب 
+
+112
+00:08:02,000 --> 00:08:04,020
+مثال الثاني
+
+113
+00:08:06,560 --> 00:08:10,100
+construct the truth table for the compound 
+
+114
+00:08:10,100 --> 00:08:15,200
+statement P and Q if and only if P برضه اللي هو 
+
+115
+00:08:15,200 --> 00:08:18,080
+عايش بالنسبة إحنا أداء من الأدوات اللي بنستخدمها
+
+116
+00:08:18,080 --> 00:08:22,140
+في الحكم على بعض الأمور اللي هي الجدول الصدق ففي 
+
+117
+00:08:22,140 --> 00:08:26,080
+مثال برضه بنأكد على كيف نستخدم الجدول الصدق في
+
+118
+00:08:26,080 --> 00:08:30,920
+العملية فبنعمل كيف نكون أو ننشئ جدول صدق طبعًا
+
+119
+00:08:30,920 --> 00:08:34,580
+قلنا في هذا الحل أول خطوة بدي أعرفها كم simple
+
+120
+00:08:34,580 --> 00:08:37,630
+statement فيه يعني باختصار كم رمز هي هيك يعني
+
+121
+00:08:37,630 --> 00:08:42,070
+فعندنا اثنين فعندنا ال P وال Q ما فيش غيرهم ما حدش 
+
+122
+00:08:42,070 --> 00:08:44,610
+يقول فيه ثلاثة فده مهم فإذا تكون أول شيء في عندي
+
+123
+00:08:44,610 --> 00:08:48,690
+أول شي عمودين رئيسيين اللي هم ال P وال Q وما زال
+
+124
+00:08:48,690 --> 00:08:51,530
+فيه اثنين إذا ما فيه عندناش اثنين أقصى اثنين أربع
+
+125
+00:08:51,530 --> 00:08:57,270
+احتمالات أربع صفوف أخرى غير أسماء ال statement ففي
+
+126
+00:08:57,270 --> 00:09:01,070
+عندنا أربع احتمالات فبعدين نحطهم نبدأ بالترتيب 
+
+127
+00:09:01,740 --> 00:09:06,140
+فأسهل طريقة أنه نجسم الأول إلى نصفين فعنا أربع 
+
+128
+00:09:06,140 --> 00:09:08,640
+احتمالات بيصيروا يا إما احتمالين واحتمالين true true 
+
+129
+00:09:08,640 --> 00:09:13,360
+false false الثاني نجسم من النص إلى نصفين يعني من 
+
+130
+00:09:13,360 --> 00:09:17,560
+النص فاضي تقول true false اللي هو كل اثنتين بنجسمهم
+
+131
+00:09:17,560 --> 00:09:22,150
+true false انتهت العملية طيب نيجي نحلل العملية فيها 
+
+132
+00:09:22,150 --> 00:09:24,990
+إن دي أنا P and Q والاقواس دايمًا مقدمة على 
+
+133
+00:09:24,990 --> 00:09:29,390
+أي شيء آخر فلازم نحسب قيمة الصدق لمين ل P and Q
+
+134
+00:09:29,390 --> 00:09:33,070
+أولًا فبدنا هذا الجدول طبعًا بنرجع لين قاعدة ال and 
+
+135
+00:09:33,070 --> 00:09:37,130
+شوف تراكمية مش كل واحد لحال فبنتعلم true and true 
+
+136
+00:09:37,130 --> 00:09:41,610
+true true and false false false and true false 
+
+137
+00:09:41,610 --> 00:09:45,350
+false and false false طبعًا بكرا هتحفظوه على طول
+
+138
+00:09:45,350 --> 00:09:48,970
+مازال and مرة بتكون true من أربع في هذه الحالة على 
+
+139
+00:09:48,970 --> 00:09:53,370
+طول بعدين إيش فيه عندنا ال if and only if P and 
+
+140
+00:09:53,370 --> 00:09:58,730
+Q if and only if P بدنا نحسبها بدنا هذه مع هذه 
+
+141
+00:09:58,730 --> 00:10:03,730
+if and only if true if and only if true true true
+
+142
+00:10:03,730 --> 00:10:07,490
+if and only if false false false if and only if
+
+143
+00:10:07,490 --> 00:10:12,460
+false true false if and only if false true فهذا هو
+
+144
+00:10:12,460 --> 00:10:17,080
+جدول الصرخ بهذه البساطة وبهذا الوضوح أتوقع أنه أمر
+
+145
+00:10:17,080 --> 00:10:23,080
+سهل شوية تدريب خفيف وتركيز ما نستعجلش ما نخربش
+
+146
+00:10:23,080 --> 00:10:28,300
+الترتيبات ننسى احتمال فالأمر بهذه السهولة أي سؤال؟
+
+147
+00:10:28,300 --> 00:10:37,740
+نشوف مثال آخر أه
+
+148
+00:10:37,740 --> 00:10:41,070
+يمكن نحتاج نحل فإيش بيقولنا السؤال؟ It's the
+
+149
+00:10:41,070 --> 00:10:48,240
+statement B then Q equivalent to the statement if 
+
+150
+00:10:48,240 --> 00:10:53,780
+not Q then not B هل هدول ال two statements
+
+151
+00:10:53,780 --> 00:10:58,680
+متكافئين منطقيا إكسب لين؟ طبعا ليش بقول لها إكسب
+
+152
+00:10:58,680 --> 00:11:01,660
+لين؟ عم مقولش yes or no هم متكافئين ولا لأ؟ بدي
+
+153
+00:11:01,660 --> 00:11:04,360
+أنا أتوضح ليش إذا متكافئين ليش وإذا مش متكافئين
+
+154
+00:11:04,360 --> 00:11:08,520
+ليش عم بدنا الجواب يكون ماعيش مدعوم مبرر منطقيا
+
+155
+00:11:08,520 --> 00:11:12,190
+ليش أنت اخترت أن هدول متكافئين ولا لأ؟ فإذاً هذا
+
+156
+00:11:12,190 --> 00:11:15,730
+السؤال طبعاً احنا ممكن مر علينا تكافأ في المحاضرة
+
+157
+00:11:15,730 --> 00:11:18,730
+الماضية وعرفنا إن بنقول على Twisted من متكافئتين
+
+158
+00:11:18,730 --> 00:11:22,150
+إذا إلهم قيم نفس قيمة الصدق في جميع الاحتمالات
+
+159
+00:11:22,150 --> 00:11:27,750
+المنطقية الممكنة، فده هو التكافأ، فأنا عشان لو جالي
+
+160
+00:11:27,750 --> 00:11:30,910
+اثبت على طول بدي اعمل جدول صدق و اثبت ان هما هذا
+
+161
+00:11:30,910 --> 00:11:34,130
+الكلام بتحقق الشرط طب لو جالي اختبر بدي ايضا
+
+162
+00:11:34,130 --> 00:11:37,670
+استخدم جدول الصدق و اقارن و اشوف مش عارف انه هيطلع
+
+163
+00:11:37,670 --> 00:11:40,230
+نفس الاشي ولا لأ اذا طلع نفس الاشي هقول متكافئين
+
+164
+00:11:40,230 --> 00:11:43,890
+اذا ماطلعش نفس الشيء هقول متكافئين مين أداتنا في
+
+165
+00:11:43,890 --> 00:11:49,110
+الحل جدول الصدق فإذا نخلين احنا ممكن ننصح حدى لأنه
+
+166
+00:11:49,110 --> 00:11:52,470
+فيش وثاء هنا فمفيدنا نستخدم جداول الصدق
+
+167
+00:11:58,010 --> 00:12:07,490
+فهنا مثال التالت solution by truth table استخدام
+
+168
+00:12:07,490 --> 00:12:11,770
+جدول صدق ولا صفر؟ اه فطبعا بدنا نعيش نشوف هدول التنتين
+
+169
+00:12:11,770 --> 00:12:16,410
+هنعمل two statements يعني فسؤالنا هنا انه هنفحص هل
+
+170
+00:12:16,410 --> 00:12:23,160
+ب FB then Q تكافئ if it's not a Q then it's not a P
+
+171
+00:12:23,160 --> 00:12:27,440
+نفحص هذا الكلام، هذا ليس مطلوب ممكن أحط علامة
+
+172
+00:12:27,440 --> 00:12:30,000
+استفهام وأنا بجاوب عشان أعرف إن هذا هو المطلوب أو
+
+173
+00:12:30,000 --> 00:12:34,460
+أقول I want to show عشان اللي يقرأ يعرف إن هذا ليس
+
+174
+00:12:34,460 --> 00:12:39,790
+الحل بحاول أفهم السؤال بحاول أحط إيش المطلوب أفسره
+
+175
+00:12:39,790 --> 00:12:43,810
+بطريقة مختلفة قرأت السؤال افهمته بحاول أحوله لرموز
+
+176
+00:12:43,810 --> 00:12:47,730
+أعيد صياغته بشكل أقرب لمين للحل فاحنا هنستخدم
+
+177
+00:12:47,730 --> 00:12:51,690
+جدول الصدق فلازم كيف نعمل هذا الكلام؟ اليمين
+
+178
+00:12:51,690 --> 00:12:56,610
+بنعمله عمود و اليسار عمود و بنقارن فيه إيش قيمة
+
+179
+00:12:56,610 --> 00:13:01,300
+الصدق فهنعمل جدول صدق طبعاً في عندنا كام statement
+
+180
+00:13:01,300 --> 00:13:06,280
+بسيطة أساسية بينتين B و Q فإذا في عندنا أربع
+
+181
+00:13:06,280 --> 00:13:15,780
+احتمالات فنجسم الجدول إلى أربع صفوف هي أربع يكفي
+
+182
+00:13:15,780 --> 00:13:21,100
+تمام، الآن نبدأ نشوف إيش نحسب، بدنا نحسب بـ FB
+
+183
+00:13:21,100 --> 00:13:25,710
+then Q على طول ممكن نحسبها جاهزة إذا حابين مباشرة،
+
+184
+00:13:25,710 --> 00:13:29,910
+طبعا أول شي هي هذه true true false false true
+
+185
+00:13:29,910 --> 00:13:35,330
+false true false اه فالجهة هذه true then true true
+
+186
+00:13:35,330 --> 00:13:42,550
+بعدين false false true if if then آسف أنا معلق مع
+
+187
+00:13:42,550 --> 00:13:46,750
+الجدول الصحيح اه true then false false false then
+
+188
+00:13:46,750 --> 00:13:52,040
+true true true تمام هذه if then تمام بالنسبة هذه
+
+189
+00:13:52,040 --> 00:13:55,960
+بدنا نحسب أولا الشيء اللي إيه الشيء النفي not Q و
+
+190
+00:13:55,960 --> 00:14:01,620
+بدنا not B و بعدين بدنا if not Q then not B طبعا
+
+191
+00:14:01,620 --> 00:14:05,620
+هذه هتكون عكسها فهتكون false true false true هذه
+
+192
+00:14:05,620 --> 00:14:10,500
+هتكون false false true true احنا حافظين بمباشرة
+
+193
+00:14:11,810 --> 00:14:15,590
+امتبعين؟ نستكمل يعني؟ تمام، هاي الترتيب هنا مهم في
+
+194
+00:14:15,590 --> 00:14:21,130
+ال if then false then false true true then false
+
+195
+00:14:21,130 --> 00:14:27,920
+false false then true true true then true true فهي
+
+196
+00:14:27,920 --> 00:14:32,220
+احنا عملنا جدول صدق بنفس الحالة لما تكون نفس السطر
+
+197
+00:14:32,220 --> 00:14:35,560
+هنا مهم جدا ان استخدمه عشان اقارن مطلوب مني اقارن
+
+198
+00:14:35,560 --> 00:14:39,380
+بين هذه ال statement يعني هذا العمود وبين هذه ال
+
+199
+00:14:39,380 --> 00:14:45,260
+statement اللي يعني هذا العمود فنقارن true مع بعض
+
+200
+00:14:45,260 --> 00:14:51,860
+true false false true true true true اذا ما هو
+
+201
+00:14:51,860 --> 00:14:55,260
+الاستنتاج فعلا متكافئتين اذا احنا ايش هنعلق نقول
+
+202
+00:14:55,260 --> 00:15:04,900
+هنا we seefrom the table that
+
+203
+00:15:04,900 --> 00:15:15,040
+المطلوب هي b then q تكافئ not q then not فاحنا
+
+204
+00:15:15,040 --> 00:15:19,460
+عرفنا إنهم متكافئين وأثبتنا له إنهم متكافئين
+
+205
+00:15:19,460 --> 00:15:26,630
+وأثبتنا إنهم متكافئين أي سؤال بينفع يحلوا على قانون
+
+206
+00:15:26,630 --> 00:15:27,710
+الـ BDNQ
+
+207
+00:15:30,860 --> 00:15:34,460
+لسه ما وصلناش احنا لسه بنستخدم نبني واحدة واحدة
+
+208
+00:15:34,460 --> 00:15:37,800
+هل جيت؟ بنستخدم المعلومات اللي اتعلمناها تمام؟
+
+209
+00:15:37,800 --> 00:15:40,340
+فاحنا بنمشي واحدة واحدة ونبني كل معلومة أيش اللي
+
+210
+00:15:40,340 --> 00:15:44,180
+شرحناها أيش اللي عرفناها ونستخدمه فلما نوصل هنقول
+
+211
+00:15:44,180 --> 00:15:46,740
+إنه إيش خيارات الحل حتى الآن أداة الوحيدة truth
+
+212
+00:15:46,740 --> 00:15:49,560
+table وعندي تعريف إيش معنى التكافأت حتى الآن
+
+213
+00:15:49,560 --> 00:15:52,680
+هندركز على عادي النقطة فبناشي نستبقى الأحداث وإن
+
+214
+00:15:52,680 --> 00:15:56,720
+شاء الله احنا في حينه طبعا بيكون السؤال بنتذكر
+
+215
+00:15:56,720 --> 00:16:03,480
+بنشوف إنه في طُرُخ متعددة ولا لأ تمام زي ما احنا
+
+216
+00:16:03,480 --> 00:16:09,810
+شوفنا في عدة روابط أن أحيانا في أكتر من كلمة باللغة
+
+217
+00:16:09,810 --> 00:16:13,410
+الانجليزية بتعمل نفس الشيء زي ال and و ال but و
+
+218
+00:16:13,410 --> 00:16:17,250
+while و although وفي ال if then في عندنا ستة اللي
+
+219
+00:16:17,250 --> 00:16:18,830
+هو اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+220
+00:16:18,830 --> 00:16:19,130
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+221
+00:16:19,130 --> 00:16:19,310
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+222
+00:16:19,310 --> 00:16:19,530
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+223
+00:16:19,530 --> 00:16:20,330
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+224
+00:16:20,330 --> 00:16:21,390
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+225
+00:16:21,390 --> 00:16:22,310
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+226
+00:16:22,310 --> 00:16:25,470
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+227
+00:16:34,810 --> 00:16:39,610
+أو طبعاً أول شيء الوضع الأسهل والمباشر اللي هو if
+
+228
+00:16:39,610 --> 00:16:43,290
+and only بنقول بي if and only if q مين فيه بدائل
+
+229
+00:16:43,290 --> 00:16:47,550
+بي is equivalent to q زي ما حكينا ولاحظنا ان هي في
+
+230
+00:16:47,550 --> 00:16:50,850
+تكافأ true true او false false مع بعض فممكن نقول
+
+231
+00:16:50,850 --> 00:16:56,550
+انواش ال بي is equivalent to q الحالة التالتة بي is
+
+232
+00:16:56,550 --> 00:16:59,750
+necessarily and sufficient لأنه احنا قلنا في نقية
+
+233
+00:16:59,750 --> 00:17:04,470
+الشرطية فال بي هي شرط في الجملة الأولى و جواب شرط
+
+234
+00:17:04,470 --> 00:17:07,070
+للتانية فهي is necessarily and sufficient
+
+235
+00:17:07,070 --> 00:17:09,230
+sufficient and insufficient و ده الكلام كتير
+
+236
+00:17:09,230 --> 00:17:11,170
+نستخدمه في الرياضيات sufficient and insufficient
+
+237
+00:17:11,170 --> 00:17:13,950
+نستخدمه كتير في النظريات فده ضروري نفهم لما يقول
+
+238
+00:17:13,950 --> 00:17:17,170
+بي is sufficiently and insufficient في ال Q يعني
+
+239
+00:17:17,170 --> 00:17:19,650
+هذا يشملها by conditional statement هذا معناه ان
+
+240
+00:17:19,650 --> 00:17:26,100
+بي if and only if a Q واضح؟ بس هدولة التلت حالات
+
+241
+00:17:26,100 --> 00:17:30,200
+بتستخدمها فى أننا الآن مثال نطبق على هذا الكلام
+
+242
+00:17:30,200 --> 00:17:34,980
+Translate the given compound statements ترجم
+
+243
+00:17:34,980 --> 00:17:39,300
+الجمال المركبة أو التقارير المركبة إلى into a
+
+244
+00:17:39,300 --> 00:17:42,960
+symbolic form نحاول نستخدم الرموز using the
+
+245
+00:17:42,960 --> 00:17:47,630
+suggested symbols هيدينا statements و هيختار علينا
+
+246
+00:17:47,630 --> 00:17:50,410
+الرمز اللي بدنا ايه ايش نستخدم نحن نحويله لرموز
+
+247
+00:17:50,410 --> 00:17:54,850
+انا عندي statement ده رموز بيه ايه و هكذا و نستخدم
+
+248
+00:17:54,850 --> 00:17:59,650
+اذا و ما هو الموقع نشوف الآن السؤال فالفرع الأول
+
+249
+00:17:59,650 --> 00:18:05,150
+بيقول لي a natural number is even if and only if
+
+250
+00:18:05,150 --> 00:18:08,450
+it is divisible by two يعني هذه جمد رياضية معروفة
+
+251
+00:18:08,450 --> 00:18:10,830
+كيف بقاش معنات even يعني يقبل قسمها اتنين زوجي
+
+252
+00:18:10,830 --> 00:18:14,850
+يقبل قسمها اتنين فهي .. دي حقيقة رياضية معبر عنها
+
+253
+00:18:14,850 --> 00:18:20,220
+ب statement if and only if طبعا يدّيني بين جثين E
+
+254
+00:18:20,220 --> 00:18:23,040
+و D يعني أرمز لل statement الأولى اللي هي even
+
+255
+00:18:23,040 --> 00:18:27,960
+بالحرف capital E ولأ divisible من كلمة divisible
+
+256
+00:18:27,960 --> 00:18:36,040
+بالرمز D فنبدأ اللي هو الحل ممكن .. ممكن الحل هنا
+
+257
+00:18:36,040 --> 00:18:44,500
+فهذا المثال وهي solution وهي A فطبعا احنا هنقول له
+
+258
+00:18:45,210 --> 00:18:54,210
+let e denotes the statement ليه اياش a natural
+
+259
+00:18:54,210 --> 00:19:04,610
+number is even is
+
+260
+00:19:04,610 --> 00:19:10,770
+even بعد ال statement الأول and let d denotes
+
+261
+00:19:14,200 --> 00:19:22,100
+A natural number is divisible
+
+262
+00:19:22,100 --> 00:19:32,420
+يقبل القسمة by two فإذا ال statement is
+
+263
+00:19:32,420 --> 00:19:36,840
+B
+
+264
+00:19:36,840 --> 00:19:44,530
+A E if and only if D فده هو الرمز فهذه جملة ثنائية
+
+265
+00:19:44,530 --> 00:19:48,090
+الشرطية فهذه جملة ثنائية الشرطية ممكن تحويلها
+
+266
+00:19:48,090 --> 00:19:52,950
+لرموز E if and only if D إيش معناته E يعني عدد
+
+267
+00:19:52,950 --> 00:19:58,250
+اللي بيكون زوجي فقط وإذا فقط يقبل قسمة على اتنين
+
+268
+00:19:58,250 --> 00:20:10,670
+نشوف كمان مثل أتوقع بقدر أمسح هنا بي
+
+269
+00:20:12,700 --> 00:20:16,380
+A matrix has an inverse المصفوفة إليها معكوس
+
+270
+00:20:16,380 --> 00:20:21,280
+whenever its determinant is not zero
+
+271
+00:20:28,680 --> 00:20:33,080
+فهنا على الملاحظة في المحاضرة الماضية كما لو كنتش
+
+272
+00:20:33,080 --> 00:20:36,880
+تستخدم if then منها whenever قلنا ايش اكيو و
+
+273
+00:20:36,880 --> 00:20:40,420
+whenever بي اكيو و whenever بي فإذا هنا بالنسبة
+
+274
+00:20:40,420 --> 00:20:45,800
+لنا اللي بيكون الأولى هي جواب الشرط و اللي بعد
+
+275
+00:20:45,800 --> 00:20:49,740
+whenever هي الشرط هنعملهم نعملهم مع بعض أول شيء
+
+276
+00:20:49,740 --> 00:20:53,580
+برضه زي بطوي طبعا احنا ممكن نكتب بشكل مطول زي هيك
+
+277
+00:20:53,580 --> 00:20:58,000
+او نحط اختصارة هي I من كلمة inverse هتشملها a
+
+278
+00:20:58,000 --> 00:21:13,890
+matrix Has an inverse و
+
+279
+00:21:13,890 --> 00:21:20,970
+Z من كلمة zero I من كلمة inverse The determinant
+
+280
+00:21:20,970 --> 00:21:24,710
+is not zero
+
+281
+00:21:33,970 --> 00:21:40,990
+of a matrix ممكن نكمل يعني بشكل is ممكن نقول is 
+
+282
+00:21:40,990 --> 00:21:44,150
+not zero نحط انه فيه مع الرمز أو ان فيه بعدين كله
+
+283
+00:21:44,150 --> 00:21:53,270
+صح ايش حابين زي ما هي is not zero فإذا 
+
+284
+00:21:53,270 --> 00:21:53,990
+ال statement
+
+285
+00:22:00,100 --> 00:22:04,520
+is .. اه فهي مهم جدا نبتدأ انها طبعا قليلة
+
+286
+00:22:04,520 --> 00:22:07,680
+للاستخدام if then مباشرة أكثر لكن أنا ايش قلنا ان
+
+287
+00:22:07,680 --> 00:22:14,390
+الأولى هي بتكون فدي if z then ك I هيك بتكون 
+
+288
+00:22:14,390 --> 00:22:18,330
+whenever .. فاحنا قلنا q whenever ب .. اه هذه كيف
+
+289
+00:22:18,330 --> 00:22:24,310
+بنترجمها if b then q فهذه كأحد الاحتمالات تفضل نعم
+
+290
+00:22:24,310 --> 00:22:27,330
+ال not دخلناها مع ال z كل ال z بتنتظر مظلة كل
+
+291
+00:22:27,330 --> 00:22:30,910
+الجملة فاحنا جسمناها جزئين الفرع الأول ال
+
+292
+00:22:30,910 --> 00:22:33,970
+statement قوله عملناها I و التاني z لو عملنا ال z
+
+293
+00:22:33,970 --> 00:22:36,770
+من غير not كان قولنا not z فانا شرحت لكم و أنتم
+
+294
+00:22:36,770 --> 00:22:42,750
+اخترتم أن خليها زي ما هي كله صح أي سؤال تفضلي
+
+295
+00:22:45,370 --> 00:22:49,950
+احنا في الملاحظة هنا في المحاضرة الماضية قلنا أن
+
+296
+00:22:49,950 --> 00:22:57,270
+if B then Q بتترجم ستة حلول منها Q is whenever B 
+
+297
+00:22:57,270 --> 00:23:00,330
+فهنا لما أقول اللي هو ايش صارت ال statement عندي
+
+298
+00:23:00,330 --> 00:23:03,510
+صارت ال statement عندي الجزء الأول سميناه I 
+
+299
+00:23:03,510 --> 00:23:08,770
+whenever Z فديهي ترجمتها if Z then Q if Z then I
+
+300
+00:23:08,770 --> 00:23:14,810
+آسف واضح في نفس القاعدة فانا لو أنا ايش قلنا هنا B
+
+301
+00:23:14,810 --> 00:23:22,430
+then Q ايش بالترجمة Q whenever بي تمام فال
+
+302
+00:23:22,430 --> 00:23:24,730
+statement اللي عندي لو جيت أترجم الجملة اللي عندي 
+
+303
+00:23:24,730 --> 00:23:32,390
+ايش قلنا الجزء الأول I مظبوط whenever Z ايش Z فأجي
+
+304
+00:23:32,390 --> 00:23:42,550
+أترجمها ايش صارت Z واضح أي سؤال نشوف
+
+305
+00:23:42,550 --> 00:23:43,530
+كمان مثال
+
+306
+00:23:51,740 --> 00:23:57,700
+C a function is differentiable at a point only if
+
+307
+00:23:57,700 --> 00:24:03,060
+it is continuous at that point فهذه only if فقلنا
+
+308
+00:24:03,060 --> 00:24:07,860
+هنا برضه بي only if Q فهذه زي ما بتعني هيك أيضا
+
+309
+00:24:07,860 --> 00:24:14,860
+بتعني بي only if Q فنستخدم القاعدة هذه إن شاء الله
+
+310
+00:24:14,860 --> 00:24:20,520
+في الحل نبدأ أولا بالرموز فdifferentiable  نترجمه
+
+311
+00:24:20,520 --> 00:24:25,120
+لمين؟ a function is 
+
+312
+00:24:25,120 --> 00:24:28,260
+differentiable
+
+313
+00:24:28,260 --> 00:24:33,860
+at a point ده
+
+314
+00:24:33,860 --> 00:24:38,960
+لقابل الاشتقاق عن نقطة a function اللي هو الـ c من
+
+315
+00:24:38,960 --> 00:24:43,980
+continuous a function is continuous
+
+316
+00:24:48,880 --> 00:24:53,940
+at a point طبعا هنا عشان فصلناهم point point فبصير 
+
+317
+00:24:53,940 --> 00:25:01,360
+ايش إشارة لها فال statement فايش 
+
+318
+00:25:01,360 --> 00:25:04,320
+ال statement قلنا ايش only if بتكون الأول هو
+
+319
+00:25:04,320 --> 00:25:08,520
+الشرط والتاني هو جواب الشرط إذا نفسه يكون if D
+
+320
+00:25:08,520 --> 00:25:13,420
+then C if D then C وهذه جهودنا مشهورة يعني نظرية
+
+321
+00:25:13,420 --> 00:25:18,430
+في رياضيات كل ده لقبل الاشتقاق فهي متصلة معروفة أي
+
+322
+00:25:18,430 --> 00:25:27,030
+سؤال هذه 
+
+323
+00:25:27,030 --> 00:25:31,710
+نهاية ال section إن شاء الله هنتقل لل section 
+
+324
+00:25:31,710 --> 00:25:33,350
+التالي 1-3
+
+325
+00:25:49,710 --> 00:25:53,570
+فاحنا في ال section الأول والتاني درسنا ايش معناه
+
+326
+00:25:53,570 --> 00:25:57,670
+statement والروابط وتعريفاتها وكيف نتعامل معها كيف 
+
+327
+00:25:57,670 --> 00:26:01,470
+نوجد قيمة الصدق ل statement تحتوي على هذه الروابط
+
+328
+00:26:01,470 --> 00:26:05,410
+أيضا شفنا ايش الاستخدام ايش المفردات المتكافئة أو 
+
+329
+00:26:05,410 --> 00:26:09,110
+المترادفة لتستخدم نفس الرابط في كل واحدة منهم الآن
+
+330
+00:26:09,110 --> 00:26:15,000
+ننتقل لمصطلحات جديدة طبعا بنستمر مع المنطق والتعامل 
+
+331
+00:26:15,000 --> 00:26:18,520
+مع ال statement بس من ناحية أخرى فهنتحدث عن
+
+332
+00:26:18,520 --> 00:26:25,000
+ثلاثة مصطلحات tautology وهي تقرير مطلق الصواب بنعرفها
+
+333
+00:26:25,000 --> 00:26:28,340
+هتيجي التعريف بعد شوية موجود تقرير مطلق الصواب
+
+334
+00:26:28,340 --> 00:26:32,560
+implication تضمين و equivalence مرت علينا بس كمان 
+
+335
+00:26:32,560 --> 00:26:37,390
+مرة هنزورها من زاوية أخرى تكافؤ التقارير مطلقة
+
+336
+00:26:37,390 --> 00:26:44,220
+الصواب والتضمين والتكافؤ إذا نعرف الأنواع فنبدأ
+
+337
+00:26:44,220 --> 00:26:48,780
+بالـ tautology أو تقرير مطلق الصواب تقرير مطلق 
+
+338
+00:26:48,780 --> 00:26:53,040
+الصواب عشان نمهد لهذا التقرير أو لهذا المصطلح
+
+339
+00:26:53,040 --> 00:26:56,520
+خليني نشوف مثال أفلان إنه يمكن في الأول لو حطينا
+
+340
+00:26:56,520 --> 00:26:59,500
+التعريف مباشرة يصير في عنا مفاجأة ايش معنات هل في
+
+341
+00:26:59,500 --> 00:27:01,880
+statement دائما بتكون صحيحة؟ قلنا لل statement 
+
+342
+00:27:01,880 --> 00:27:04,440
+تكون either true or false فهي لما تكون بسيطة هذه 
+
+343
+00:27:04,440 --> 00:27:08,280
+الاحتمالين لكن لو كانت دائما الـ true هي بسميها
+
+344
+00:27:08,280 --> 00:27:10,860
+tautology مطلق الصواب يعني دائما صحيحة فنشوف مثال 
+
+345
+00:27:11,100 --> 00:27:15,220
+نشوف مثال عشان ندل إنه قد ايش ممكن يحدث عشان ما
+
+346
+00:27:15,220 --> 00:27:20,700
+نستغربش ففي عندنا مثال بيقول construct a truth
+
+347
+00:27:20,700 --> 00:27:27,280
+table for the statement be or not be فده مثال و أي 
+
+348
+00:27:27,280 --> 00:27:31,820
+solution سؤال بسيط من أبسط الأسئلة اللي هتمر علينا
+
+349
+00:27:31,820 --> 00:27:35,380
+في هذا المصطلح بدنا نكون جدول صدق مش طالب مننا ولا 
+
+350
+00:27:35,380 --> 00:27:39,240
+شيء جدول صدق ل statement كم simple statement فيه
+
+351
+00:27:39,240 --> 00:27:43,760
+واحدة إذا نعمل جدول فيها كم صف .. صفوف أحسن نعم
+
+352
+00:27:43,760 --> 00:27:48,280
+فعنا بيه بس هي لحالها والباقي كله بده حساب وفيها 
+
+353
+00:27:48,280 --> 00:27:53,100
+احتمالين يا true يا false فجدول صغير بعد الشكل
+
+354
+00:27:53,100 --> 00:27:57,150
+بعدين ايش بدنا بنحسب not بيهاللي هي على طول false
+
+355
+00:27:57,150 --> 00:28:02,250
+and true وبعدين بنحسب بي or not بي هاي كل العملية
+
+356
+00:28:02,250 --> 00:28:09,450
+true or false true false or true true فعنا 
+
+357
+00:28:09,450 --> 00:28:14,570
+compound statement دائما true دائما true فهذا كان
+
+358
+00:28:14,570 --> 00:28:18,230
+مثال على ال totologies اه فهنا في ممكن نصير عندنا
+
+359
+00:28:18,230 --> 00:28:22,010
+statements تكون دائما true دائما true نسميها 
+
+360
+00:28:22,010 --> 00:28:26,220
+tautology متقايش تقرير مطلق صح دائما صحيح يعني هي
+
+361
+00:28:26,220 --> 00:28:28,940
+الـ definition ايش تعريف الـ tautology؟ a 
+
+362
+00:28:28,940 --> 00:28:32,880
+statement تقرير is said to be a tautology بنقول 
+
+363
+00:28:32,880 --> 00:28:36,080
+على statement ما أو تقرير ما إنه tautology إنه 
+
+364
+00:28:36,080 --> 00:28:40,440
+مطلق صواب وقت ايش if it is true إذا كان صواب أو 
+
+365
+00:28:40,440 --> 00:28:44,420
+صحيح for every assignment of a truth value .. 
+
+366
+00:28:44,420 --> 00:28:48,200
+truth values to its component في جميع الاحتمالات 
+
+367
+00:28:48,200 --> 00:28:52,530
+المنطقية الممكنة ايش ما ندى احتمال للمركبات ايش 
+
+368
+00:28:52,530 --> 00:28:56,190
+بيطلع الجواب true اديناها true true اديناها false
+
+369
+00:28:56,190 --> 00:28:59,590
+true فهذا بيسميه tautology دائما صحيح في جميع
+
+370
+00:28:59,590 --> 00:29:04,110
+الاحتمالات المنطقية الممكنة فهذا هو ما يعرف بتقرير 
+
+371
+00:29:04,110 --> 00:29:10,030
+مطلق الصواب أو tautology خلينا نشوف مثال
+
+372
+00:29:25,830 --> 00:29:31,610
+Solution ايش المثال بيقول show that the statement 
+
+373
+00:29:31,610 --> 00:29:39,410
+طبعا q if q then if تحجسين if and only if b and q
+
+374
+00:29:39,410 --> 00:29:43,050
+is a tautology في عندنا statement طويلة مش مهتمش 
+
+375
+00:29:43,050 --> 00:29:47,490
+كثير بالقرايتها بيقول لي اثبت انها tautology كيف 
+
+376
+00:29:47,490 --> 00:29:49,870
+نثبت هنا تطولوجيا؟ هي التعريف نيجي لأن نرجع 
+
+377
+00:29:49,870 --> 00:29:54,210
+للتعريف هذه قاعدتنا دائما هيك في الرياضيات نعمل في 
+
+378
+00:29:54,210 --> 00:29:56,970
+عنا أي مصطلح يقول لي أثبت أنه دالة differentiable
+
+379
+00:29:56,970 --> 00:29:58,770
+ايش بده أعمل؟ ايش معنى ال differentiable؟
+
+380
+00:29:58,770 --> 00:30:01,090
+continuous ايش معنى ال continuous؟ ففي عندنا التعريف
+
+381
+00:30:01,090 --> 00:30:04,410
+هو الأساس لا طبعا في ممكن ان غير التعريف ممكن يكون
+
+382
+00:30:04,410 --> 00:30:07,970
+ان نظريات قواعد أدوات أخرى تساعدنا في الاثبات لكن
+
+383
+00:30:07,970 --> 00:30:11,130
+اهم حاجة ايش من نقطة البداية التعريف التطولوجيا
+
+384
+00:30:11,130 --> 00:30:14,390
+طلعت الصمر علينا بنعرف عنه حاجة غير التعريف؟ لا إذا 
+
+385
+00:30:14,390 --> 00:30:17,480
+بنا نركز على التعريف بنعرف كيف نطبق التعريف بقول 
+
+386
+00:30:17,480 --> 00:30:20,980
+ليه اثبت ان هذا تتولجي ايش يعني تتولجي يعني ليش
+
+387
+00:30:20,980 --> 00:30:24,020
+دائما true طب كيف بتثبت ان ال statement دائما true
+
+388
+00:30:24,020 --> 00:30:28,360
+ايش قاعدتي عن طريق truth table اه فإذا هنا هنقول 
+
+389
+00:30:28,360 --> 00:30:35,760
+له solution we will use truth table
+
+390
+00:30:46,280 --> 00:30:53,060
+to show that the statement أو the given statement
+
+391
+00:30:57,940 --> 00:31:02,540
+is always true اختصارا في جميع اللياش احتمال انها
+
+392
+00:31:02,540 --> 00:31:06,900
+دائما صحيح تمام فهذه هي طريقتنا في كل تعامل مع 
+
+393
+00:31:06,900 --> 00:31:09,900
+رياضة إن شاء الله هذه هنكرر الفيلم نشوف السؤال
+
+394
+00:31:09,900 --> 00:31:14,340
+بأحاول أفسرّه و يمكن أُصيغه بصيغة أخرى دي مهمة جدا و ايش
+
+395
+00:31:14,340 --> 00:31:17,900
+و بعدين نحاول نتعامل معه من وين بدنا ايش المطلوب و
+
+396
+00:31:17,900 --> 00:31:21,160
+كيف بدنا نوصل اه فطبعا هنعمل جدول الصدق عرفنا 
+
+397
+00:31:21,160 --> 00:31:24,600
+الأداء اللي بده ايش المطلوب واوش طريقنا للوصول
+
+398
+00:31:24,600 --> 00:31:28,500
+للمطلوب فهذه طريقة مهمة في حل المسائل بشكل في 
+
+399
+00:31:28,500 --> 00:31:32,180
+الرياضيات أو بشكل عام فطبعا نيجي لل statement كم
+
+400
+00:31:32,180 --> 00:31:36,020
+symbol واحد فيها تنتهي في P و Q وفيش غيرها فإذا
+
+401
+00:31:36,020 --> 00:31:41,260
+بدنا أربع احتمالات مع عمودين رئيسيين P and Q مع
+
+402
+00:31:41,260 --> 00:31:45,420
+أربع احتمالات هاي اثنين وهاي كمان اثنين
+
+403
+00:31:49,290 --> 00:31:54,370
+تمام فطبعا كالعادة true true false false العمودي 
+
+404
+00:31:54,370 --> 00:31:59,330
+الأول true false true false العمودي الثاني ايش
+
+405
+00:31:59,330 --> 00:32:03,510
+مطلوب نحسب أول بي and كيو الأقواس الداخلية فانت
+
+406
+00:32:03,510 --> 00:32:07,210
+فينا جوس وبعدين فينا جوس أكبر بنحسب بي and كيو
+
+407
+00:32:07,210 --> 00:32:12,940
+الكل يعرف يحسبها true مرة بس غير هيك false مباشرة
+
+408
+00:32:12,940 --> 00:32:17,940
+أحب أن أضيع وقت ايش بعدين نحسب بي if and only if بي 
+
+409
+00:32:17,940 --> 00:32:21,420
+if and only if بي if and only if بي if and only if
+
+410
+00:32:21,420 --> 00:32:21,600
+بي if and only if بي if and only if بي if and 
+
+411
+00:32:21,600 --> 00:32:21,640
+only if بي if and only if بي if and only if بي if
+
+412
+00:32:21,640 --> 00:32:22,420
+and only if بي if and only if بي if and only if بي
+
+413
+00:32:22,420 --> 00:32:23,080
+if and only if بي if and only if بي if and only if
+
+414
+00:32:23,080 --> 00:32:23,100
+only if بي if and only if بي if and only if بي
+
+415
+00:32:23,100 --> 00:32:23,200
+if and only if بي if and only if بي if and only if
+
+416
+00:32:23,200 --> 00:32:25,340
+only if بي if and only if بي if and only if بي
+
+417
+00:32:25,340 --> 00:32:30,420
+if and only if بي if and only if بي if and only if
+
+418
+00:32:30,420 --> 00:32:34,800
+بي if
+
+419
+00:32:34,800 --> 00:32:41,520
+and only if بي if 
+
+420
+00:32:41,520 --> 00:32:48,810
+only if أي سؤال، في أي طالب عنده مشكلة في الجداول، 
+
+421
+00:32:48,810 --> 00:32:53,850
+الأمر بسيط، إذا أي حد نفسر له لأنه يعني أمر بسيط،
+
+422
+00:32:53,850 --> 00:32:57,210
+المفروض إن ما حدش يكون عنده مشكلة، فلو في أي
+
+423
+00:32:57,210 --> 00:33:00,530
+استفسار، أي صعوبة، بنفسرها إن شاء الله عشان الأمر 
+424
+00:33:00,530 --> 00:33:03,240
+يكون واضح تماماً 
+
+425
+00:33:03,240 --> 00:33:05,340
+ 
+426
+00:33:05,340 --> 00:33:07,200
+ 
+
+427
+00:33:21,420 --> 00:33:25,900
+العمد تمام نبدأ نشتغل قاعدة if then true then true
+
+428
+00:33:25,900 --> 00:33:32,480
+true false then false true true then true true
+
+429
+00:33:32,480 --> 00:33:36,660
+false then anything true إيش قال أثبت أنه
+
+430
+00:33:36,660 --> 00:33:39,420
+tautology تطلع tautology لو ما طلعش طلع دائماً
+
+431
+00:33:39,420 --> 00:33:42,060
+true tautology يعني دائماً true إذا أنا هنقول إيه
+
+432
+00:33:42,060 --> 00:33:45,180
+عشان أعلق from the table we see that the given
+
+433
+00:33:45,180 --> 00:33:51,980
+statement is a tautology from or by the table we
+
+434
+00:33:51,980 --> 00:33:56,140
+see that the
+
+435
+00:33:56,140 --> 00:34:02,320
+given statement is
+
+436
+00:34:02,320 --> 00:34:09,180
+a tautology أي
+
+437
+00:34:09,180 --> 00:34:13,940
+سؤال فهذا هو التعريف وهكذا نستطيع أن نطبق عليه
+
+438
+00:34:19,310 --> 00:34:24,710
+طبعاً التوتولوجيز مهمين جداً بالنسبة لنا لأنهم
+
+439
+00:34:24,710 --> 00:34:29,630
+هيكونوا لنا القواعد المنطقية اللي بنتعامل معها في
+
+440
+00:34:29,630 --> 00:34:34,870
+أن نتأكد أن استنتاجنا أو تفكيرنا منطقياً صحيح أو 
+
+441
+00:34:34,870 --> 00:34:38,740
+لا فالـ Totality مهمة جداً ممكن نستخدمها في
+
+442
+00:34:38,740 --> 00:34:41,420
+البراهين في أي خطوة من خطوات البراهين وطبعاً هي
+
+443
+00:34:41,420 --> 00:34:47,720
+بتولدنا أو تنشئنا القواعد تبع المنطقية اللي
+
+444
+00:34:47,720 --> 00:34:50,060
+بنستخدمها في اللي هو البراهين
+
+445
+00:34:52,620 --> 00:34:56,820
+أي سؤال فهذا ال journal is تالت الأول من العنوان
+
+446
+00:34:56,820 --> 00:34:59,040
+Totology في عندنا implications و في عندنا
+
+447
+00:34:59,040 --> 00:35:03,560
+equivalent ننتقل للمصطلح الثاني أو الفهم الثاني
+
+448
+00:35:03,560 --> 00:35:06,600
+التضمين implication من implies implication
+
+449
+00:35:06,600 --> 00:35:12,840
+implications وهي التضمين التضمين بشكل مختصر هو
+
+450
+00:35:12,840 --> 00:35:18,150
+عبارة عن جملة شرطية دائماً صحيحة هي عبارة عن جملة
+
+451
+00:35:18,150 --> 00:35:25,410
+شرطية مطلقة الصواب فكل تضمين هو totology لكن
+
+452
+00:35:25,410 --> 00:35:28,190
+العكس غير صحيح فلو أنا في قدرة إحنا إيش قلنا
+
+453
+00:35:28,190 --> 00:35:32,030
+totology هو statement دائماً صحيحة طب إذا كانت هذه
+
+454
+00:35:32,030 --> 00:35:34,330
+ال statement هي جملة شرطية و دائماً صحيحة إيه بتكون
+
+455
+00:35:34,330 --> 00:35:37,030
+totology وإيش بتكون بنفس الوقت implication بسميها
+
+456
+00:35:37,030 --> 00:35:41,200
+تضمين فان التعريف let capital B and capital Q be
+
+457
+00:35:41,200 --> 00:35:43,780
+two statements أي two statements، simple، compact،
+
+458
+00:35:43,780 --> 00:35:46,360
+مفرّغش، شفت المثال هذا كيف؟ مفرّغش، أن هو two
+
+459
+00:35:46,360 --> 00:35:50,680
+statements بتعامل if the conditional statement if
+
+460
+00:35:50,680 --> 00:35:53,580
+the conditional .. جملة الشرطية if B then Q is
+
+461
+00:35:53,580 --> 00:35:57,300
+autotology، دائماً true، then it is called an
+
+462
+00:35:57,300 --> 00:36:01,400
+implication، بسميها تضمين، هذا طبعاً زي ما تشوف في
+
+463
+00:36:01,400 --> 00:36:04,640
+كل سياستنا دائماً رموز، دائماً رموز، ليه شفنا رموز؟
+
+464
+00:36:04,640 --> 00:36:08,950
+سهم بس في خطين متوازيين مقطع left then أشمله تساهم
+
+465
+00:36:08,950 --> 00:36:12,970
+خط واحد هنا في خطين برضه يتجه لليمين لإنه علاقة
+
+466
+00:36:12,970 --> 00:36:17,550
+فيه إيش بنقراها؟ بنقراها if then بنقراها بي
+
+467
+00:36:17,550 --> 00:36:22,130
+implies Q بي implies Q فتضمين من تضمين قلنا
+
+468
+00:36:22,130 --> 00:36:27,210
+implies فإيش ما هو التضمين؟ هو عبارة عن جملة شرطية
+
+469
+00:36:27,210 --> 00:36:31,930
+مطلقة الصواب جملة شرطية مطلقة الصواب إيه السؤال؟
+
+470
+00:36:34,590 --> 00:36:37,970
+كيف؟ زي example .. آه هذا ممكن نعمل تضمين صحيح
+
+471
+00:36:37,970 --> 00:36:42,870
+فهذا ممكن هذا نقول إيش بي Q implies صحيح لأنه
+
+472
+00:36:42,870 --> 00:36:47,970
+هي جملة شرطية وهي totology نشوف مثال الأول
+
+473
+00:37:05,610 --> 00:37:11,170
+المثال الأول show that if B then B is an
+
+474
+00:37:11,170 --> 00:37:15,850
+implication إتدانى جملة شرطية وجالي أثبت أنها 
+
+475
+00:37:15,850 --> 00:37:20,810
+تضمين إيش يعني؟ بدي أثبت إنها totology أي بمعنى
+
+476
+00:37:20,810 --> 00:37:23,490
+آخر بدي أثبت أن هذه جملة اسمها دائماً ال true دائماً
+
+477
+00:37:23,490 --> 00:37:27,090
+ال true خليني أكتب هذا الكلام solution لأن هذا مهم 
+
+478
+00:37:27,090 --> 00:37:32,490
+جداً أن نفسر السؤال هذه السياسة أرجو أن يكون هناك
+
+479
+00:37:32,490 --> 00:37:35,670
+شاهدين من المثال المثال المطلوب المباشر له
+
+480
+00:37:35,670 --> 00:37:39,410
+والسياسة التي نتبعها والحقيقة هذه سنستخدمها دائماً
+
+481
+00:37:39,410 --> 00:37:42,290
+وهذه ستساعدكم كثيراً في المثال وإن شاء الله في
+
+482
+00:37:42,290 --> 00:37:45,150
+المثالات الأخرى كيف نتعامل مع الأمثلة كيف نتعامل
+
+483
+00:37:45,150 --> 00:37:47,790
+مع البراهين إيش المعطيات إيش المطلوب وكيف نتعامل
+
+484
+00:37:47,790 --> 00:37:53,430
+فإذا إحنا أول الشيء we have to show المطلوب مننا
+
+485
+00:37:53,430 --> 00:37:56,030
+that
+
+486
+00:37:56,790 --> 00:38:00,870
+اللي هو implication بي .. if b then b is a
+
+487
+00:38:00,870 --> 00:38:10,490
+tautology فهي
+
+488
+00:38:10,490 --> 00:38:18,490
+البنية أو that is بمعنى آخر ممكن نفسر that is if b
+
+489
+00:38:18,490 --> 00:38:25,200
+then b is always true فهذه السياسة قعدت صياغة 
+
+490
+00:38:25,200 --> 00:38:29,400
+المطلوب سياسة مهمة جداً في حل مسائل الرياضيات أو في
+
+491
+00:38:29,400 --> 00:38:32,600
+البراهين فهذه بدنا نتعلمها إن شاء الله شوية شوية و
+
+492
+00:38:32,600 --> 00:38:35,540
+نتعود عليها لأنها حد ساعدنا كثير في دراسة الرياضية
+
+493
+00:38:35,540 --> 00:38:41,740
+تمام خلاص كيف بنثبت جدول الصدق إذا we will use
+
+494
+00:38:41,740 --> 00:38:48,680
+truth table تمام
+
+495
+00:38:49,610 --> 00:38:52,530
+كم simple statement فيه واحدة إذا في عندنا بس
+
+496
+00:38:52,530 --> 00:38:56,430
+إيه هي احتمالات فعندنا بي وإيه هي في عندنا بس
+
+497
+00:38:56,430 --> 00:39:01,850
+احتمالين true or false طيب
+
+498
+00:39:01,850 --> 00:39:06,290
+كيف بدي أحسب بي if then بي true ده true طب كيف 
+
+499
+00:39:06,290 --> 00:39:09,500
+بدي أعملها على الجدول؟ انسج هو أحسن انسج العمود كمان
+
+500
+00:39:09,500 --> 00:39:12,840
+مرة عشان إحنا متعودين أنه بنقول في العمود فانا بدي 
+
+501
+00:39:12,840 --> 00:39:15,680
+إيش انسج هو إيش الضروري واحد طب الثاني لو عملت
+
+502
+00:39:15,680 --> 00:39:20,140
+كمان مرة لأ ضروري لإيش لأنه ممكن يفيدني فانا هعمل
+
+503
+00:39:20,140 --> 00:39:24,280
+بي كمان مرة طب ممكن أغيّر الترتيب هنا لأ بنفعش لأن
+
+504
+00:39:24,280 --> 00:39:29,160
+هو نفسها بنفعش فانتبهوا لهذه الأمور فالأهم بدنا بي
+
+505
+00:39:29,160 --> 00:39:34,360
+then بي ال true then true true false then false
+
+506
+00:39:34,360 --> 00:39:37,060
+إيش ال true ففعلاً totality
+
+507
+00:39:40,810 --> 00:39:48,850
+نقوله هنا by the table we
+
+508
+00:39:48,850 --> 00:39:53,450
+see or we have from the table أو by the table إيش
+
+509
+00:39:53,450 --> 00:39:58,030
+هي أن إيش بي then بي is a implication ممكن أكتب
+
+510
+00:39:58,030 --> 00:40:03,230
+أو إيش أكتب باختصار بي implies بي P implies P وده
+
+511
+00:40:03,230 --> 00:40:07,910
+منطق يعني إذا حاجة صحيحة فبتأمل صحيحة يعني إذا ..
+
+512
+00:40:07,910 --> 00:40:11,010
+إذا ال .. ده قبل الاشتقاق فقبل الاشتقاق يعني بعيد
+
+513
+00:40:11,010 --> 00:40:13,890
+نفس الجملة فده قاعدة منطقية إذا هذه صحيحة فهي ده
+
+514
+00:40:13,890 --> 00:40:18,630
+من الصحيحة أي سؤال؟ أي سؤال؟ بسيطة جداً بحسب 
+
+515
+00:40:18,630 --> 00:40:21,630
+الصحيحة يعني المثال بسيط بس عشان نوضح الأهداف اللي
+
+516
+00:40:21,630 --> 00:40:25,010
+هي كيف طريقة أهم من طريقة الحل هل حين الأمر
+
+517
+00:40:25,010 --> 00:40:26,830
+مشهدان؟ آه طبعاً
+
+518
+00:40:31,850 --> 00:40:34,850
+لأ الـ tautology أي statement لو ال statement
+
+519
+00:40:34,850 --> 00:40:37,850
+مافيش فيها إيه؟ يعني لو أنا فيه عندي زي المثال 
+
+520
+00:40:37,850 --> 00:40:42,410
+اللي عملناه be or not be فهذه الـ tautology، تظبط؟
+
+521
+00:40:42,410 --> 00:40:48,650
+هل هذه implication؟ لأنها من جملة شرطية في مصطلحين،
+
+522
+00:40:48,650 --> 00:40:51,450
+انتبه، غرزي، معلش، يعني يمكن تكون السؤال عند فيه
+
+523
+00:40:51,450 --> 00:40:54,630
+غبش وعند آخرين، فنركز مع بعض هكذا، الـ tautology
+
+524
+00:40:54,630 --> 00:40:59,330
+هي statement بغض النظر عن إيش، إيش مركباتها، إيش
+
+525
+00:40:59,330 --> 00:41:02,630
+الروابط اللي فيها، تكون دائماً true زي هذه، هذه
+
+526
+00:41:02,630 --> 00:41:06,950
+tautology لأنها دائماً true لكن ال implication هي
+
+527
+00:41:06,950 --> 00:41:11,780
+statement شرطية conditional statement هنا يحط إن
+
+528
+00:41:11,780 --> 00:41:17,340
+الرابط الرئيسي تبعها إيش هو الشرطية فينحدد في حالة
+
+529
+00:41:17,340 --> 00:41:20,260
+يعني من حالات الـ tautology يعني هذه الـ tautology
+
+530
+00:41:20,260 --> 00:41:24,040
+لكن ليست implication هذه implication وهي بنفس
+
+531
+00:41:24,040 --> 00:41:26,220
+الوقت هذه ال statement طبعاً ما بقولش أن هذه الـ 
+
+532
+00:41:26,220 --> 00:41:30,340
+tautology هذه الـ tautology واضحة واضحة ولا لأ
+
+533
+00:41:30,340 --> 00:41:34,780
+فأرجو التفريق فكل tautology وكل implication هو الـ
+
+534
+00:41:34,780 --> 00:41:36,700
+tautology لكن ليش العكس غير صحيح
+
+535
+00:41:42,800 --> 00:41:49,000
+ممكن نستغل المتبقي في كمان مثال هنا نفس الصيغة
+
+536
+00:41:49,000 --> 00:41:57,880
+show that B and Q implies Q and B أبدأ
+
+537
+00:41:57,880 --> 00:42:03,940
+الكتابة من فوق example 2 solution مع بعض بدنا
+
+538
+00:42:03,940 --> 00:42:08,320
+نصيغه إيش المطلوب؟ بدنا نثبت إن الجملة الشرطية 
+
+539
+00:42:08,320 --> 00:42:14,710
+إنها tautology فإذا خلينا نفسر want أو we have to
+
+540
+00:42:14,710 --> 00:42:23,470
+show that is B and Q then Q and B فأرجو التركيز،
+
+541
+00:42:23,470 --> 00:42:25,630
+يعني أنا أشوف رياضيات دقيقة، ما ينفعش أكتب له نفسي
+
+542
+00:42:25,630 --> 00:42:29,450
+أبدأ أفسر له أنّه تولوجي، لأ، آه، فالرموز مهمة، واحد
+
+543
+00:42:29,450 --> 00:42:31,350
+يقول لما هاد ساهم وهاد ساهم، لأ، هاد الساهم له
+
+544
+00:42:31,350 --> 00:42:34,050
+معنى زي ما تشوفين وهاد الساهم له معنى، فلازم
+
+545
+00:42:34,050 --> 00:42:37,050
+نستخدمه في المكان وفي الوقت الصحيح وفي مكانه 
+
+546
+00:42:37,050 --> 00:42:41,070
+الصحيح ف we want to show that is a tautology
+
+547
+00:42:44,310 --> 00:42:49,170
+أو إن هيّ دائماً true نفس البعض بس إحنا عشان هيّ 
+
+548
+00:42:49,170 --> 00:42:52,470
+بنبني relation جديدة عليها القضية طبعاً بنستخدم
+
+549
+00:42:52,470 --> 00:42:58,390
+هيّ جدول الصدق فنكوّن
+
+550
+00:42:58,390 --> 00:43:02,270
+جدول الصدق أكمل statement بسيطة تان تان ففي عندنا
+
+551
+00:43:02,270 --> 00:43:08,210
+أربع احتمالات مع عمودين رئيسيا لل P و لل Q ففي
+
+552
+00:43:08,210 --> 00:43:16,260
+عندنا أربع احتمالات ف ..الصحيح والصحيح والخاطئ
+
+553
+00:43:16,260 --> 00:43:26,000
+والخاطئ الصحيح والخاطئ والخاطئ أي سؤال نبدأ
+
+554
+00:43:26,000 --> 00:43:31,000
+إيش فيه عندنا P and Q بدنا نحسب P أو قيمة الصدق لل P
+
+555
+00:43:31,000 --> 00:43:35,660
+and Q الصحيح والخاطئ والخاطئ والخاطئ حسبناها أكثر
+
+556
+00:43:35,660 --> 00:43:39,360
+من مرة ما في مشكلة الآن بقول أعكس الترتيب P and Q
+
+557
+00:43:40,580 --> 00:43:43,860
+فبنلاقي نفس الحاجة طبعاً وهذا هو اللي بدنا نثبته
+
+558
+00:43:43,860 --> 00:43:48,040
+الحقيقة أن هنا عملية الـ AND إبدالية فرابط الـ AND
+
+559
+00:43:48,040 --> 00:43:52,320
+منطقياً إبدالي الترتيب فيه غير مهم الآخرش اللي بدنا
+
+560
+00:43:52,320 --> 00:43:56,220
+نثبته هو الـ Indication فالـ Indication لا يدخل في 
+
+561
+00:43:56,220 --> 00:43:58,740
+جدول الصدق لأن جدول الصدق متعامل مع الـ statement
+
+562
+00:43:58,740 --> 00:44:01,520
+نفسها اللي فيها رابط من الروابط البسيطة الأصلية
+
+563
+00:44:01,520 --> 00:44:04,500
+لكن هذه الـ implies ليست رابط هذه عبارة عن 
+
+564
+00:44:04,500 --> 00:44:07,940
+statement  و تاتولوجي و إنها تاتولوجي فاحنا الآن
+
+565
+00:44:07,940 --> 00:44:15,260
+بدنا نعمل  P and Q then Q and P فبنحسب نسبة أنها
+
+566
+00:44:15,260 --> 00:44:19,020
+دائما true تمام
+
+567
+00:44:19,020 --> 00:44:23,500
+فهي بدنا نشتغل على دولتين مع بعض هي السهم true
+
+568
+00:44:23,500 --> 00:44:28,260
+then true true false then false true false then
+
+569
+00:44:28,260 --> 00:44:32,680
+false true false then false true فإذا فعلا
+
+570
+00:44:32,680 --> 00:44:43,910
+tautology from the table we see that .. ممكن أقول إن
+
+571
+00:44:43,910 --> 00:44:46,730
+هذه  is a tautology أو أقوله زي ما هو مطلوب
+
+572
+00:44:46,730 --> 00:44:55,850
+اختصاراً P and Q implies Q and .. أي سؤال
+
+573
+00:45:01,310 --> 00:45:05,450
+تمام، هذا جيد لكي ننهي في تمرين إضافية موجودة
+
+574
+00:45:05,450 --> 00:45:09,430
+عندكم مكتوبة الـ P implies P and P P and Q implies
+
+575
+00:45:09,430 --> 00:45:13,810
+Q زي ما هي الأول ممكن تعمل implies للتاني نوقف هنا
+
+576
+00:45:13,810 --> 00:45:15,330
+إن شاء الله المرة القادمة سنبدأ في theorem 
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/5kawOfcrw3A_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/5kawOfcrw3A_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..08001254fec23f055e25914ab46956a36220475b
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/5kawOfcrw3A_postprocess.srt
@@ -0,0 +1,2304 @@
+1
+00:00:21,080 --> 00:00:25,500
+بسم الله الرحمن الرحيم اليوم المحاضرة التالتة في
+
+2
+00:00:25,500 --> 00:00:32,180
+اللي هو التقارير وروابطها هنستكمل تعريفنا للروابط
+
+3
+00:00:32,180 --> 00:00:36,240
+اللي تستخدم في تكوين التقارير المركبة من التقارير
+
+4
+00:00:36,240 --> 00:00:41,380
+البسيطة كما ذكرنا في المحاضرات السابقة هناك خمس
+
+5
+00:00:41,380 --> 00:00:46,160
+روابط وهي الـNeffy الـ Negation اللي هي not أداتها
+
+6
+00:00:46,160 --> 00:00:49,420
+وفي عندنا ال conjunction الإخترار وأداتها أو هي ال
+
+7
+00:00:49,420 --> 00:00:53,660
+andأيضًا في عندنا disjunction الفصل وعداتها or وفي
+
+8
+00:00:53,660 --> 00:00:57,720
+عندنا الجمل الشرطية وهي if then اه اليوم هنستكمل
+
+9
+00:00:57,720 --> 00:01:01,680
+بالرابط الخامس والأخير وهو the biconditional
+
+10
+00:01:01,680 --> 00:01:06,700
+ثنائية الشرطية طبعًا كمعلومة جانبية المقطع by هذا
+
+11
+00:01:06,700 --> 00:01:09,620
+بتكرر كتير وهو يعني ثنائي زي ما ممكن مر علينا في
+
+12
+00:01:09,620 --> 00:01:13,560
+تفاضل با نظرية ثلث حدين binomial theorem nominal
+
+13
+00:01:13,560 --> 00:01:16,880
+حد binomial و هنا conditional و biconditional بس
+
+14
+00:01:16,880 --> 00:01:20,420
+هذه بس تعليق بالنسبة للمصطلحطبعا على نفس السياسة
+
+15
+00:01:20,420 --> 00:01:24,900
+هنبدأ إيش التعريف وإيش الرمز وكيف يقرأ ومع مين
+
+16
+00:01:24,900 --> 00:01:28,040
+بتعامل من ال statement مع واحدة أو تنتين وبعدين
+
+17
+00:01:28,040 --> 00:01:32,340
+كيف نحصل قيمة الصدق لتقرير مركب يحتوي على الرابط
+
+18
+00:01:32,340 --> 00:01:35,120
+if and only if إذا عرفنا قيمة الصدق لمين؟
+
+19
+00:01:35,120 --> 00:01:38,560
+للمركبات، لل statement الأساسية البسيطة اللي بتكون
+
+20
+00:01:38,560 --> 00:01:42,210
+هذه ال statementفنبدأ طبعاً أول شيء طبعاً الروابط
+
+21
+00:01:42,210 --> 00:01:46,390
+الخامسة زي ما لاحظنا و هذا الخامس أنه جميعها أربع
+
+22
+00:01:46,390 --> 00:01:48,370
+منها تدخل على two statements تتعامل مع two
+
+23
+00:01:48,370 --> 00:01:49,810
+statements إلا الأولى اللي هي النافية بتتعامل مع
+
+24
+00:01:49,810 --> 00:01:52,150
+statement واحدة فأول شيء بيقوللي أنه انا لو في
+
+25
+00:01:52,150 --> 00:01:56,820
+عندي two statements B وQبعمل عليهم رابط if and
+
+26
+00:01:56,820 --> 00:02:00,820
+only في رمزه السهم في الاتجاهين فبقول هذا هو ال
+
+27
+00:02:00,820 --> 00:02:03,720
+connective هذا هو الرابق زي ما نقول نحن ال plus
+
+28
+00:02:03,720 --> 00:02:06,940
+أداة الجامع فهذا هو ال connective لو برمزنا مين لل
+
+29
+00:02:06,940 --> 00:02:09,800
+by conditional ايش اسمه؟ by conditional فانا فيه
+
+30
+00:02:09,800 --> 00:02:13,340
+عندي رمز زي ما هدا .. هدا رمزواش اسمه؟ رمز الجمع
+
+31
+00:02:13,340 --> 00:02:17,160
+.. اه .. تمام؟ فهي نهيأش اسمه .. الرمز هذا الـ
+
+32
+00:02:17,160 --> 00:02:20,380
+biconditional طيب، مع مين بتعامل؟ مع two
+
+33
+00:02:20,380 --> 00:02:22,780
+statements .. مع two statements .. بنحط بينهم زي
+
+34
+00:02:22,780 --> 00:02:26,100
+ما هيك كيف بنقرا هذه ال statement؟ ب .. if and
+
+35
+00:02:26,100 --> 00:02:29,180
+only .. FQ .. قراءة واحدة، هي القراءة المعروفة
+
+36
+00:02:29,180 --> 00:02:34,180
+الوحيدة، هي أول شي المقدمةالان انا عندي statement
+
+37
+00:02:34,180 --> 00:02:38,740
+بيدا الشكل بعرف معلومات عن قيمة الصدق لل بي والكيو
+
+38
+00:02:38,740 --> 00:02:42,840
+طب كيف اجيب قيمة الصدق للكل؟ بدي اعرفناياها اه كما
+
+39
+00:02:42,840 --> 00:02:46,100
+لاحظنا زي ال conditional مش هيدينا الجدول بشكل
+
+40
+00:02:46,100 --> 00:02:49,040
+مباشر لأنه احنا وصلنا لمرحلة متقدمة نوعا ما
+
+41
+00:02:49,040 --> 00:02:54,600
+فهيديناياها بتكافؤ في جملة قديمة او جملة معروفة
+
+42
+00:02:54,600 --> 00:02:58,840
+وهذا التعريف بيفسر او ببرر الاسم by conditional
+
+43
+00:02:59,060 --> 00:03:02,300
+فبقول لي قيمة الصدق عشان تحصل قيمة الصدق لل if and
+
+44
+00:03:02,300 --> 00:03:07,060
+only if statement اشمالها تكافئ من b if b then q
+
+45
+00:03:07,060 --> 00:03:11,480
+and if q then b يعني اشمالهم عشان تكون هذه ال if
+
+46
+00:03:11,480 --> 00:03:14,220
+and only if true لازم ال statement التاني تكون
+
+47
+00:03:14,220 --> 00:03:16,700
+true عشان هذه تكون false لازم التاني تكون false
+
+48
+00:03:16,700 --> 00:03:23,530
+فانا بقدر احصل قيمة الصدق للجملةb then q and if b
+
+49
+00:03:23,530 --> 00:03:26,870
+then q then b بقدر أحسبه ولا بقدرش؟ بقدر أعرفنا
+
+50
+00:03:26,870 --> 00:03:29,570
+هذه و أعرفنا هذه و أعرفنا الأن فأنا ما زال عندي
+
+51
+00:03:29,570 --> 00:03:33,890
+قدرة على معرفة قيمة الصدق لهذه ال statement بعرف
+
+52
+00:03:33,890 --> 00:03:36,650
+قيمة الصدق لمن؟ لل F and only F فاحنا بنعرفها بهذه
+
+53
+00:03:36,650 --> 00:03:39,660
+الشكلةطبعا زي ما حكوا ان الشاهدين المهم جدا ان
+
+54
+00:03:39,660 --> 00:03:43,580
+نلاحظ انه ملاحظين ايوش جانت تكافئ two conditional
+
+55
+00:03:43,580 --> 00:03:46,540
+statement عشان هيك بقى biconditional if b then q
+
+56
+00:03:46,540 --> 00:03:50,400
+هي جملة شرطية ال b فيها الشرط و ال q جواب الشرط و
+
+57
+00:03:50,400 --> 00:03:54,700
+التانية العكس ال q هي الشرط و ال b هي جواب الشرط
+
+58
+00:03:54,700 --> 00:04:00,260
+فهي تكافئ two conditional statementواضح؟ أي سؤال،
+
+59
+00:04:00,260 --> 00:04:02,900
+فهذا هو التعريف التكافو وهذا مهم جدًا، هتعتمد عليه
+
+60
+00:04:02,900 --> 00:04:07,040
+في كثير من الأحيان في التعامل مع الـ if and only
+
+61
+00:04:07,040 --> 00:04:10,160
+if statement طبعًا احنا اختصارًا بدل ما كل مرة
+
+62
+00:04:10,160 --> 00:04:13,340
+بنحسب اللي هو الجدول، هنديكوا جدول جاهز برضه اللي
+
+63
+00:04:13,340 --> 00:04:17,370
+ممكن نساعده مباشرة زي ال if دهفالجدول بيكون
+
+64
+00:04:17,370 --> 00:04:23,370
+بالصورة التالية بيكون ال true إذا كان ال q و ال b
+
+65
+00:04:23,370 --> 00:04:27,250
+اللي هو نفس قيمة السطر true مع بعض أو false مع بعض
+
+66
+00:04:27,250 --> 00:04:30,150
+اللي هو أول سطر في الجدول و آخر سطر غيرك بتكون
+
+67
+00:04:30,150 --> 00:04:33,810
+false طبعا ليش؟ لأنه أنا بدي يكون هذه true و هذه
+
+68
+00:04:33,810 --> 00:04:39,860
+true هذه true طبعا هذه b صحأه فإحنا لما نيجي نعلّل
+
+69
+00:04:39,860 --> 00:04:44,280
+بالنص true then false .. false .. false and
+
+70
+00:04:44,280 --> 00:04:46,560
+anything .. false هاي اللي .. إيش التاني .. هذه
+
+71
+00:04:46,560 --> 00:04:50,680
+واضحة؟ ليش هذه false؟ لإن true then false .. false
+
+72
+00:04:50,680 --> 00:04:54,860
+.. false and anything .. false طيب هذه false then
+
+73
+00:04:54,860 --> 00:04:58,020
+true .. true لكن إيه العكس true then false التانية
+
+74
+00:04:58,020 --> 00:05:03,020
+.. falsetrue and false false لكن دولة لأ هذه
+
+75
+00:05:03,020 --> 00:05:05,600
+ماتفرجش لإن انا بقول لك true than true true و true
+
+76
+00:05:05,600 --> 00:05:08,860
+than true الترتيب مش مهم هنا false than anything
+
+77
+00:05:08,860 --> 00:05:13,040
+true false than anything true true and true true
+
+78
+00:05:13,040 --> 00:05:17,820
+واضح؟ أي سؤال فهذا الجدول وهذا تفسيره عشان لو
+
+79
+00:05:17,820 --> 00:05:21,340
+انسناه كيف نتذكره فهم طبعا اللي هى علاقة بالتكافح
+
+80
+00:05:21,340 --> 00:05:24,200
+هنشوف بعد قليل فهم يا true هي إذا تكون تنتين true
+
+81
+00:05:24,200 --> 00:05:29,080
+أو تنتين false عشان يكون الكل trueفهنا بنلخص هذه
+
+82
+00:05:29,080 --> 00:05:32,360
+الملاحظة فبنقول ان ال if and only if بتكون true
+
+83
+00:05:32,360 --> 00:05:36,260
+إذا كانت انتين يا true مع بعض يا false مع بعض اللي
+
+84
+00:05:36,260 --> 00:05:39,420
+لهم نفس قيمة الصدقة نشوف أمثلة دايما احنا بنشوف
+
+85
+00:05:39,420 --> 00:05:43,540
+نحاول أمثلة عشان نحاول نستوعب هذا بشكل أفضل و نعرف
+
+86
+00:05:43,540 --> 00:05:46,880
+كيف بنطبق هذا التعريف و هذه الملاحظات بشكل جيد
+
+87
+00:05:46,880 --> 00:05:50,980
+فنبدأ في المثال الأول التقليدي اللي هو true or
+
+88
+00:05:50,980 --> 00:05:54,840
+false equation فهنا المثال الأول ممكن أنا أحله هنا
+
+89
+00:05:54,840 --> 00:06:00,430
+بهمش و بعدين هنحط الجوابمباشرة solution ف
+
+90
+00:06:00,430 --> 00:06:03,130
+determine whether the following statements are
+
+91
+00:06:03,130 --> 00:06:08,830
+true or false المثال الأول A فبنحلل المركبات
+
+92
+00:06:08,830 --> 00:06:15,910
+بنستنتج لجملة ال compound statement فبقولي one is
+
+93
+00:06:15,910 --> 00:06:21,550
+all الواحد عدد فردي true ولا false trueif and only
+
+94
+00:06:21,550 --> 00:06:25,510
+if الجملة التالية three is even فالس if and only
+
+95
+00:06:25,510 --> 00:06:31,550
+if فالس فإيش الجملة true if and only if فالس فالس
+
+96
+00:06:31,550 --> 00:06:35,570
+فإذا في طرف مختلف قيمة الصدق معاه فبنفعش فهذه
+
+97
+00:06:35,570 --> 00:06:42,450
+false بي نشوف كمان مثال absolute value of five
+
+98
+00:06:42,450 --> 00:06:49,460
+equals minus five falseif and only if five greater
+
+99
+00:06:49,460 --> 00:06:55,620
+than zero true false if and only if true false هاي
+
+100
+00:06:55,620 --> 00:06:59,140
+بنتعود انه اذا الواحدة فيهم مختلفة عن التانية
+
+101
+00:06:59,140 --> 00:07:07,260
+بتكون الكل false square root of four equal twotrue
+
+102
+00:07:07,260 --> 00:07:11,360
+لاحدش يقولي false لازم يكون plus minus لأ الجزر
+
+103
+00:07:11,360 --> 00:07:14,320
+التربيعي ده لأ تدينا قيمة واحدة و هي القيمة الموجب
+
+104
+00:07:14,320 --> 00:07:20,000
+تمام if and only if two squared equals four true
+
+105
+00:07:20,000 --> 00:07:21,800
+if and only if true
+
+106
+00:07:26,390 --> 00:07:32,110
+نشوف كمان مثال five is greater than six false if
+
+107
+00:07:32,110 --> 00:07:35,810
+and only if five is even false إيش الجملة كلها
+
+108
+00:07:35,810 --> 00:07:42,610
+true false if and only if false true أي yes و no
+
+109
+00:07:42,610 --> 00:07:46,830
+فبيقد البساطة بنطبق مباشرة بعد هيك بنتعود بنصير
+
+110
+00:07:46,830 --> 00:07:52,150
+أمور بالنسبالي ان شاء الله بسيطة نشوف كمان مثال بس
+
+111
+00:07:52,150 --> 00:07:54,250
+نمسح هذا الجواب
+
+112
+00:08:02,000 --> 00:08:04,020
+مثال التاني
+
+113
+00:08:06,560 --> 00:08:10,100
+construct the truth table for the compound
+
+114
+00:08:10,100 --> 00:08:15,200
+statement P and Q if and only if P برضه اللي هو
+
+115
+00:08:15,200 --> 00:08:18,080
+عايش بالنسبة احنا اداء من الأدوات اللي بنستخدمها
+
+116
+00:08:18,080 --> 00:08:22,140
+في الحكم على بعض الأمور اللي هي الجدول الصدق ففي
+
+117
+00:08:22,140 --> 00:08:26,080
+مثال برضه بنأكد على كيف نستخدم الجدول الصدق في
+
+118
+00:08:26,080 --> 00:08:30,920
+العملية فبنعمل كيف نكون أو ننشئ جدول صدق طبعا
+
+119
+00:08:30,920 --> 00:08:34,580
+قولنا في هذا الحل أول خطوة بدى أعرفها أكم simple
+
+120
+00:08:34,580 --> 00:08:37,630
+statement فيهيعني باختصار أكم رمز هي هيك يعني
+
+121
+00:08:37,630 --> 00:08:42,070
+فعندنا اتنين فعندنا ال B و ال Q مافيش غيرهم ماحدش
+
+122
+00:08:42,070 --> 00:08:44,610
+يقول فيه تلاتة فده مهم فإذا تكون أول شيء في عندي
+
+123
+00:08:44,610 --> 00:08:48,690
+أول شي عمودين رئيسيين اللي هم ال B و ال Q و ما زال
+
+124
+00:08:48,690 --> 00:08:51,530
+فيه اتنين إذا مافيه عناياش اتنين أقصى اتنين أربع
+
+125
+00:08:51,530 --> 00:08:57,270
+احتمالات أربع صفوف أخرى غير أسماء ال statement ففي
+
+126
+00:08:57,270 --> 00:09:01,070
+عندنا أربع احتمالات فبعدين نحطهم نبدأ بالترتيب
+
+127
+00:09:01,740 --> 00:09:06,140
+فأسهل طريقة أنه نجسم الأول إلى نصفين فعنا أربع
+
+128
+00:09:06,140 --> 00:09:08,640
+احتمالات بيصيروا ياش احتمالين واحتمالين true true
+
+129
+00:09:08,640 --> 00:09:13,360
+false false التاني نجسم من النص إلى نصفين يعني من
+
+130
+00:09:13,360 --> 00:09:17,560
+النص فازي تقول true false اللي هو كل تنتين بنجسمهم
+
+131
+00:09:17,560 --> 00:09:22,150
+true false انتهت العمليةطيب نيجى نحلل العملية فيها
+
+132
+00:09:22,150 --> 00:09:24,990
+ان دي انا B and Q و الاش دايما الاقواص مقدمة على
+
+133
+00:09:24,990 --> 00:09:29,390
+اي شيء اخر فلازم نحسب قيمة الصدق لمين ل B and Q
+
+134
+00:09:29,390 --> 00:09:33,070
+اولا فبدنا هذا الجدول طبعا بنرجع لين قاعدة ال and
+
+135
+00:09:33,070 --> 00:09:37,130
+شوف تراكمية مش كل واحد لحال فبنتعلم true and true
+
+136
+00:09:37,130 --> 00:09:41,610
+true true and false false false and true false
+
+137
+00:09:41,610 --> 00:09:45,350
+false and false falseطبعا بكرا هتحفظوه على طول
+
+138
+00:09:45,350 --> 00:09:48,970
+مازال and مرة بتكون true من أربع في هذه الحالة على
+
+139
+00:09:48,970 --> 00:09:53,370
+طول بعدين إيش فيه عندنا ال if and only if بي and
+
+140
+00:09:53,370 --> 00:09:58,730
+كيو if and only if بي بدنا نحسبها بدنا هذه مع هذه
+
+141
+00:09:58,730 --> 00:10:03,730
+if and only if true if and only if true true true
+
+142
+00:10:03,730 --> 00:10:07,490
+if and only if false false false if and only if
+
+143
+00:10:07,490 --> 00:10:12,460
+false true false if and only if false trueفهذا هو
+
+144
+00:10:12,460 --> 00:10:17,080
+جدول الصرخ بهذه البساطة وبهذا الوضوح أتوقع أنه أمر
+
+145
+00:10:17,080 --> 00:10:23,080
+سهل شوية تدريب خفيف وتركيز ما نستعجلش ما نخربش
+
+146
+00:10:23,080 --> 00:10:28,300
+الترتيبات ننسى احتمال فالأمر بهذه السهولة أي سؤال؟
+
+147
+00:10:28,300 --> 00:10:37,740
+نشوف مثال آخر أه
+
+148
+00:10:37,740 --> 00:10:41,070
+يمكن نحتاج نحل فإيش بيقولنا السؤال؟It's the
+
+149
+00:10:41,070 --> 00:10:48,240
+statementB then Q equivalent to the statement if
+
+150
+00:10:48,240 --> 00:10:53,780
+not Q then not B هل هدول ال two statements
+
+151
+00:10:53,780 --> 00:10:58,680
+متكافئين منطقيا إكسب لين؟ طبعا ليش بقول لها إكسب
+
+152
+00:10:58,680 --> 00:11:01,660
+لين؟ عم مقولش yes or no هم متكافئين ولا لأ؟ بدي
+
+153
+00:11:01,660 --> 00:11:04,360
+أنا أتوضح ليش إذا متكافئين ليش وإذا مش متكافئين
+
+154
+00:11:04,360 --> 00:11:08,520
+ليش عم بدنا الجواب يكون ماعيش مدعوم مبرر منطقيا
+
+155
+00:11:08,520 --> 00:11:12,190
+ليش أنت اخترت أن هدول متكافئين ولا لأ؟فإذاً هذا
+
+156
+00:11:12,190 --> 00:11:15,730
+السؤال طبعاً احنا ممكن مر علينا تكافأ في المحاضرة
+
+157
+00:11:15,730 --> 00:11:18,730
+الماضية وعرفنا إن بنقول على Twisted من متكافئتين
+
+158
+00:11:18,730 --> 00:11:22,150
+إذا إلهم قيم نفس قيمة الصدق في جميع الاحتمالات
+
+159
+00:11:22,150 --> 00:11:27,750
+المنطقية الممكنة، فده هو التكافأ، فأنا عشانلو جالي
+
+160
+00:11:27,750 --> 00:11:30,910
+اثبت على طول بدي اعمل جدول صدق و اثبت ان هما هذا
+
+161
+00:11:30,910 --> 00:11:34,130
+الكلام بتحقق الشرط طب لو جالي اختبر بدي ايضا
+
+162
+00:11:34,130 --> 00:11:37,670
+استخدم جدول الصدق و اقارن و اشوف مش عارف انه هيطلع
+
+163
+00:11:37,670 --> 00:11:40,230
+نفس الاشي ولا لأ اذا طلع نفس الاشي هقول متكافئين
+
+164
+00:11:40,230 --> 00:11:43,890
+اذا ماطلعش نفسي اشي هقول متكافئين مين أداتنا في
+
+165
+00:11:43,890 --> 00:11:49,110
+الحل جدول الصدق فإذا نخلين احنا ممكن ننصح حدى لانه
+
+166
+00:11:49,110 --> 00:11:52,470
+فيش وثاء هنا فمفيدنا نستخدم جداول الصدق
+
+167
+00:11:58,010 --> 00:12:07,490
+فهنا مثال التالت solution by truth table استخدام
+
+168
+00:12:07,490 --> 00:12:11,770
+يد ولا صفر؟ اه فطبعا بدنا نعيش نشوف هدول التنتين
+
+169
+00:12:11,770 --> 00:12:16,410
+هنعمل two statements يعني فسؤالنا هنا انه هنفحص هل
+
+170
+00:12:16,410 --> 00:12:23,160
+ب FB then Q تكافئif it's not a Q then it's not a P
+
+171
+00:12:23,160 --> 00:12:27,440
+نفحص هذا الكلام، هذا ليس مطلوب ممكن أحط علامة
+
+172
+00:12:27,440 --> 00:12:30,000
+استفهام وأنا بجاوب عشان أعرف إن هذا هو المطلوب أو
+
+173
+00:12:30,000 --> 00:12:34,460
+أقول I want to show عشان اللي يقرأ يعرف إن هذا ليس
+
+174
+00:12:34,460 --> 00:12:39,790
+الحلبحاول أفهم السؤال بحاول أحط إيش المطلوب أفسره
+
+175
+00:12:39,790 --> 00:12:43,810
+بطريقة مختلفة قرأت السؤال افهمته بحاول أحوله لرموز
+
+176
+00:12:43,810 --> 00:12:47,730
+أعيد صياغته بشكل أقرب لمين للحال فاحنا هنستخدم
+
+177
+00:12:47,730 --> 00:12:51,690
+جدول الصدق فلازم كيف نعمل هذا الكلام؟ اليمين
+
+178
+00:12:51,690 --> 00:12:56,610
+بنعمله عمود و اليسار عمود و بنقارن فيه إيش قيمة
+
+179
+00:12:56,610 --> 00:13:01,300
+الصدق فهنعمل جدول صدقطبعاً في عندنا كام statement
+
+180
+00:13:01,300 --> 00:13:06,280
+بسيطة أساسية بينتين B و Q فإذا في عندنا أربع
+
+181
+00:13:06,280 --> 00:13:15,780
+احتمالات فنجسم الجدول إلى أربع صفوف هي أربع يكفي
+
+182
+00:13:15,780 --> 00:13:21,100
+تمام، الآن نبدأ نشوف إيش نحسب، بدنا نحسب بـ FB
+
+183
+00:13:21,100 --> 00:13:25,710
+then Q على طول ممكن نحسبها جاهزة إذا حابينمباشرة،
+
+184
+00:13:25,710 --> 00:13:29,910
+طبعا أول شي هي هذه true true false false true
+
+185
+00:13:29,910 --> 00:13:35,330
+false true false اه فالجهة هذه true then true true
+
+186
+00:13:35,330 --> 00:13:42,550
+بعدين false false true if if then آسف أنا معلق مع
+
+187
+00:13:42,550 --> 00:13:46,750
+الجدول الصحيح اه true then false false false then
+
+188
+00:13:46,750 --> 00:13:52,040
+true true true تمام هذه if then تمامبالنسبة هذه
+
+189
+00:13:52,040 --> 00:13:55,960
+بدنا نحسب أولا الشيء اللي إيه الشيء النفي not Q و
+
+190
+00:13:55,960 --> 00:14:01,620
+بدنا not B و بعدين بدنا if not Q then not B طبعا
+
+191
+00:14:01,620 --> 00:14:05,620
+هذه هتكون عكسها فهتكون false true false true هذه
+
+192
+00:14:05,620 --> 00:14:10,500
+هتكون false false true true احنا حافظين بمباشرة
+
+193
+00:14:11,810 --> 00:14:15,590
+امتبعين؟ نستكمل يعني؟ تمام، هاي الترتيب هنا مهم في
+
+194
+00:14:15,590 --> 00:14:21,130
+ال if then false then false true true then false
+
+195
+00:14:21,130 --> 00:14:27,920
+false false then true true true then true trueفهي
+
+196
+00:14:27,920 --> 00:14:32,220
+احنا عملنا جدول صدق بنفس الحالة لما تكون نفس السطر
+
+197
+00:14:32,220 --> 00:14:35,560
+هنا مهم جدا ان استخدمه عشان اقارن مطلوب مني اقارن
+
+198
+00:14:35,560 --> 00:14:39,380
+بين هذه ال statement يعني هذا العمود وبين هذه ال
+
+199
+00:14:39,380 --> 00:14:45,260
+statement اللي يعني هذا العمود فنقارن true مع بعض
+
+200
+00:14:45,260 --> 00:14:51,860
+true false false true true true true اذا ما هو
+
+201
+00:14:51,860 --> 00:14:55,260
+الاستنتاج فعلا متكافئتين اذا احنا ايش هنعلق نقول
+
+202
+00:14:55,260 --> 00:15:04,900
+هنا we seefrom the table that
+
+203
+00:15:04,900 --> 00:15:15,040
+المطلوب هي b then q تكافئ not q then not فاحنا
+
+204
+00:15:15,040 --> 00:15:19,460
+عرفنا إنهم متكافئين وأثبتنا له إنهم متكافئين
+
+205
+00:15:19,460 --> 00:15:26,630
+وأثبتنا إنهم متكافئين أي سؤالبينفع يحلوا على قانون
+
+206
+00:15:26,630 --> 00:15:27,710
+الـ BDNQ
+
+207
+00:15:30,860 --> 00:15:34,460
+لسه ماديوصلناش احنا لسه بنستخدم نبني واحدة واحدة
+
+208
+00:15:34,460 --> 00:15:37,800
+هلجيت؟ بنستخدم المعلومات اللي اتعلمناها تمام؟
+
+209
+00:15:37,800 --> 00:15:40,340
+فاحنا بنمشي واحدة واحدة ونبني كل معلومة أيش اللي
+
+210
+00:15:40,340 --> 00:15:44,180
+شرحناها أيش اللي عرفناها ونستخدمه فلما نوصل هنقول
+
+211
+00:15:44,180 --> 00:15:46,740
+إنه إيش خيارات الحل حتى الآن أداة الوحيدة truth
+
+212
+00:15:46,740 --> 00:15:49,560
+table وعندي تعريف إيش معنى التكافأت حتى الآن
+
+213
+00:15:49,560 --> 00:15:52,680
+هندركز على عادى النقطة فبناشي نستبقى الأحداث وإن
+
+214
+00:15:52,680 --> 00:15:56,720
+شاء الله احنا في حينه طبعا بيكون السؤال بنتذكر
+
+215
+00:15:56,720 --> 00:16:03,480
+بنشوف إنه في طرُخ متعددة ولا لأتمام زي ما احنا
+
+216
+00:16:03,480 --> 00:16:09,810
+شوفنا في عدةروابط أن أحيانا في أكتر من كلمة باللغة
+
+217
+00:16:09,810 --> 00:16:13,410
+الليجوزية بتعمل نفس الشيء زي ال and و ال but و
+
+218
+00:16:13,410 --> 00:16:17,250
+while و although وفي ال if then في عندنا ستة اللي
+
+219
+00:16:17,250 --> 00:16:18,830
+هو اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+220
+00:16:18,830 --> 00:16:19,130
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+221
+00:16:19,130 --> 00:16:19,310
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+222
+00:16:19,310 --> 00:16:19,530
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+223
+00:16:19,530 --> 00:16:20,330
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+224
+00:16:20,330 --> 00:16:21,390
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+225
+00:16:21,390 --> 00:16:22,310
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+226
+00:16:22,310 --> 00:16:25,470
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+227
+00:16:34,810 --> 00:16:39,610
+أو طبعاً أول شيء الوضع الأسهل والمباشر اللي هو if
+
+228
+00:16:39,610 --> 00:16:43,290
+and only بنقول بي if and only if q مين فيه بدائل
+
+229
+00:16:43,290 --> 00:16:47,550
+بي is equivalent to q زي ما حكينا ولاحظنا ان هي في
+
+230
+00:16:47,550 --> 00:16:50,850
+تكافأ true true او false false مع بعض فممكن نقول
+
+231
+00:16:50,850 --> 00:16:56,550
+انواش ال بي is equivalent to qالحالة التالتة بي is
+
+232
+00:16:56,550 --> 00:16:59,750
+necessarily and sufficient لأنه احنا قلنا في نقية
+
+233
+00:16:59,750 --> 00:17:04,470
+الشرطية فال بي هي شرط في الجملة الأولى و جواب شرط
+
+234
+00:17:04,470 --> 00:17:07,070
+للتانية فهي is necessarily and sufficient
+
+235
+00:17:07,070 --> 00:17:09,230
+sufficient and insufficient و ده الكلام كتير
+
+236
+00:17:09,230 --> 00:17:11,170
+نستخدمه في الرياضيات sufficient and insufficient
+
+237
+00:17:11,170 --> 00:17:13,950
+نستخدمه كتير في النظريات فده ضروري نفهم لما يقول
+
+238
+00:17:13,950 --> 00:17:17,170
+بي is sufficiently and insufficient في ال Q يعني
+
+239
+00:17:17,170 --> 00:17:19,650
+هذا يشملها by conditional statement هذا معناه ان
+
+240
+00:17:19,650 --> 00:17:26,100
+بي if and only if a Q واضح؟بس هدولة التلت حالات
+
+241
+00:17:26,100 --> 00:17:30,200
+بتستخدمها فى أننا الآن مثال نطبق على هذا الكلام
+
+242
+00:17:30,200 --> 00:17:34,980
+Translate the given compound statements ترجم
+
+243
+00:17:34,980 --> 00:17:39,300
+الجمال المركبة أو التقارير المركبة إلى into a
+
+244
+00:17:39,300 --> 00:17:42,960
+symbolic form نحاول نستخدم الرموز using the
+
+245
+00:17:42,960 --> 00:17:47,630
+suggested symbolsهيدينا statements و هيختار علينا
+
+246
+00:17:47,630 --> 00:17:50,410
+الرمز اللي بدنا ايه ايش نستخدم نحن نحويله لرموز
+
+247
+00:17:50,410 --> 00:17:54,850
+انا عندي statement ده رموز بيه ايه و هكذا و نستخدم
+
+248
+00:17:54,850 --> 00:17:59,650
+اذا و ما هو الموقع نشوف الآن السؤالفالفرع الأول
+
+249
+00:17:59,650 --> 00:18:05,150
+بيقول لي a natural number is even if and only if
+
+250
+00:18:05,150 --> 00:18:08,450
+it is divisible by two يعني هذه جمد رياضية معروفة
+
+251
+00:18:08,450 --> 00:18:10,830
+كيف بقاش معنات even يعني يقبل قسمها اتنين زوجي
+
+252
+00:18:10,830 --> 00:18:14,850
+يقبل قسمها اتنين فهي .. دي حقيقة رياضية معبر عنها
+
+253
+00:18:14,850 --> 00:18:20,220
+ب statement if and only ifطبعا يدّيني بين جثين E
+
+254
+00:18:20,220 --> 00:18:23,040
+وD يعني أرمز لل statement الأولى اللي هي even
+
+255
+00:18:23,040 --> 00:18:27,960
+بالحرف capital E ولأ divisible من كلمة divisible
+
+256
+00:18:27,960 --> 00:18:36,040
+بالرمز D فنبدأ اللي هو الحل ممكن .. ممكن الحل هنا
+
+257
+00:18:36,040 --> 00:18:44,500
+فهذا المثال وهي solution وهي A فطبعا احنا هنقول له
+
+258
+00:18:45,210 --> 00:18:54,210
+let e denotes the statement ليه اياش a natural
+
+259
+00:18:54,210 --> 00:19:04,610
+number is even is
+
+260
+00:19:04,610 --> 00:19:10,770
+even بعد ال statement الأول and let d denotes
+
+261
+00:19:14,200 --> 00:19:22,100
+A natural number is divisible
+
+262
+00:19:22,100 --> 00:19:32,420
+يقبل القسمة by two فإذا ال statement is
+
+263
+00:19:32,420 --> 00:19:36,840
+B
+
+264
+00:19:36,840 --> 00:19:44,530
+A E if and only if D فده هو الرمزفهذه جملة ثنائية
+
+265
+00:19:44,530 --> 00:19:48,090
+الشرطية فهذه جملة ثنائية الشرطية ممكن تحويلها
+
+266
+00:19:48,090 --> 00:19:52,950
+لرموز E if and only if D إيش معناته E يعني عدد
+
+267
+00:19:52,950 --> 00:19:58,250
+اللي بيكون زوجي فقط وإذا فقط يقبل قسمة على اتنين
+
+268
+00:19:58,250 --> 00:20:10,670
+نشوف كمان مثل أتوقع بقدر أمسح هنا بي
+
+269
+00:20:12,700 --> 00:20:16,380
+A matrix has an inverse المصفوفة إليها معكوس
+
+270
+00:20:16,380 --> 00:20:21,280
+whenever its determinant is not zero
+
+271
+00:20:28,680 --> 00:20:33,080
+فهنا على الملاحظة في المحاضرة الماضية كما لو كنتش
+
+272
+00:20:33,080 --> 00:20:36,880
+تستخدم if then منها whenever قلنا ايش اكيو و
+
+273
+00:20:36,880 --> 00:20:40,420
+whenever بي اكيو و whenever بي فإذا هنا بالنسبة
+
+274
+00:20:40,420 --> 00:20:45,800
+لنا اللي بيكون الأولى هي جواب الشرط و اللي بعد
+
+275
+00:20:45,800 --> 00:20:49,740
+whenever هي الشرط هنعملهم نعملهم مع بعض أول شيء
+
+276
+00:20:49,740 --> 00:20:53,580
+برضه زي بطوي طبعا احنا ممكن نكتب بشكل مطول زي هيك
+
+277
+00:20:53,580 --> 00:20:58,000
+او نحط اختصارة هي I من كلمة inverse هتشملها a
+
+278
+00:20:58,000 --> 00:21:13,890
+matrixHas an inverse و
+
+279
+00:21:13,890 --> 00:21:20,970
+Z من كلمة zero I من كلمة inverse The determinant
+
+280
+00:21:20,970 --> 00:21:24,710
+is not zero
+
+281
+00:21:33,970 --> 00:21:40,990
+of a matrix ممكن نكمل يعني بشكل is ممكن نقول is
+
+282
+00:21:40,990 --> 00:21:44,150
+not zero نحط انه فيه مع الرمز او ان فيه بعدين كله
+
+283
+00:21:44,150 --> 00:21:53,270
+صح ايش حابين زي ما هي is not zero فإذا
+
+284
+00:21:53,270 --> 00:21:53,990
+ال statement
+
+285
+00:22:00,100 --> 00:22:04,520
+is .. اه فهي مهم جدا نبتدأ انها طبعا قليلة
+
+286
+00:22:04,520 --> 00:22:07,680
+للاستخدام if then مباشرة اكتر لكن انا ايش قولنا ان
+
+287
+00:22:07,680 --> 00:22:14,390
+الأولى هي بتكون فدي if z then ك I هيك بتكونف
+
+288
+00:22:14,390 --> 00:22:18,330
+whenever .. فاحنا قلنا q whenever ب .. اه هذه كيف
+
+289
+00:22:18,330 --> 00:22:24,310
+بنترجمها if b then q فهذه كأحد الاحتمالات تفضل نعم
+
+290
+00:22:24,310 --> 00:22:27,330
+ال not دخلناها مع ال z كل ال z بتنطر مظلة كل
+
+291
+00:22:27,330 --> 00:22:30,910
+الجملة فاحنا جسمناها جزئين الفرع الأول ال
+
+292
+00:22:30,910 --> 00:22:33,970
+statement قوله عملناها I و التاني z لو عملنا ال z
+
+293
+00:22:33,970 --> 00:22:36,770
+من غير not كان قولنا not z فانا شورتكوا و انتوا
+
+294
+00:22:36,770 --> 00:22:42,750
+اختارتهوا انه خليها زي ما هي كله صح أي سؤال تفضلي
+
+295
+00:22:45,370 --> 00:22:49,950
+أحنا في الملاحظة هنا في المحاضرة الماضية قلنا ان
+
+296
+00:22:49,950 --> 00:22:57,270
+if B then Q بتترجم ست حلال منها Q is whenever B
+
+297
+00:22:57,270 --> 00:23:00,330
+فهنا لما أقول اللي هو ايش صارت ال statement عندي
+
+298
+00:23:00,330 --> 00:23:03,510
+صارت ال statement عندي الجزء الأول صمناه I
+
+299
+00:23:03,510 --> 00:23:08,770
+whenever Z فديهش ترجمتها if Z then Q if Z then I
+
+300
+00:23:08,770 --> 00:23:14,810
+أسف واضح في نفس القاعدة فانا لو انا ايش قلنا هناB
+
+301
+00:23:14,810 --> 00:23:22,430
+then Q إيش بالترجم Q whenever بي تمام فال
+
+302
+00:23:22,430 --> 00:23:24,730
+statement اللي عندي لو جيت أترجم الجملة اللي عندي
+
+303
+00:23:24,730 --> 00:23:32,390
+إيش قلنا الجزء الأول I مظبوط whenever Z إيش Z فأجي
+
+304
+00:23:32,390 --> 00:23:42,550
+أترجمها إيش صارت Z واضح أي سؤال نشوف
+
+305
+00:23:42,550 --> 00:23:43,530
+كمان مثال
+
+306
+00:23:51,740 --> 00:23:57,700
+C a function is differentiable at a point only if
+
+307
+00:23:57,700 --> 00:24:03,060
+it is continuous at that point فهذه only if فقلنا
+
+308
+00:24:03,060 --> 00:24:07,860
+هنا برضه بي only if Q فهذه زي ما بتعني هيك أيضا
+
+309
+00:24:07,860 --> 00:24:14,860
+بتعني بي only if Q فنستخدم القاعدة هذه ان شاء الله
+
+310
+00:24:14,860 --> 00:24:20,520
+في الحل نبدأ أولا بالرموز فdifferentiable ديترمز
+
+311
+00:24:20,520 --> 00:24:25,120
+لمين؟ a function is
+
+312
+00:24:25,120 --> 00:24:28,260
+differentiable
+
+313
+00:24:28,260 --> 00:24:33,860
+at a point ده
+
+314
+00:24:33,860 --> 00:24:38,960
+لقابل اشتقاق عن نقطة a function اللي هو الـ c من
+
+315
+00:24:38,960 --> 00:24:43,980
+continuous a function is continuous
+
+316
+00:24:48,880 --> 00:24:53,940
+at a point طبعا هنا عشان فصلناهم point point فبصير
+
+317
+00:24:53,940 --> 00:25:01,360
+إيش إشارة لها فال statement فإيش
+
+318
+00:25:01,360 --> 00:25:04,320
+ال statement قولنا إيش only if بتكون الأول هو
+
+319
+00:25:04,320 --> 00:25:08,520
+الشرط والتاني هو جواب الشرط إذا نفسه يكون if D
+
+320
+00:25:08,520 --> 00:25:13,420
+then C if D then D وهذه جهودنا مشهورة يعني نظرية
+
+321
+00:25:13,420 --> 00:25:18,430
+في رياضات كل ده لقبل اشتقاق فهي متصلة معروفةأي
+
+322
+00:25:18,430 --> 00:25:27,030
+سؤال هذه
+
+323
+00:25:27,030 --> 00:25:31,710
+نهاية ال section ان شاء الله هنتقل لل section
+
+324
+00:25:31,710 --> 00:25:33,350
+التالي 1-3
+
+325
+00:25:49,710 --> 00:25:53,570
+فإحنا في ال section الأول والتاني درسنا إيش معناته
+
+326
+00:25:53,570 --> 00:25:57,670
+statement والروابط وتعريفاتها وكيف نتعامل معها كيف
+
+327
+00:25:57,670 --> 00:26:01,470
+نوجد قيمة الصدق ل statement تحتوي على هذه الروابط
+
+328
+00:26:01,470 --> 00:26:05,410
+أيضا شوفنا إيش الاستخدام إيش المفردات المتكافئة أو
+
+329
+00:26:05,410 --> 00:26:09,110
+المتردفة لتستخدم نفس الرابط في كل واحدة منهم الآن
+
+330
+00:26:09,110 --> 00:26:15,000
+ننتقل لمصطلحات جديدةطبعا بنستمر مع المنطق والتعامل
+
+331
+00:26:15,000 --> 00:26:18,520
+مع ال statement بس منهياش من زوايا أخرى فهنتحدث عن
+
+332
+00:26:18,520 --> 00:26:25,000
+تلت مصطلحات totology وهي تقرير مطلق الصواب بنعرفها
+
+333
+00:26:25,000 --> 00:26:28,340
+هتيجي التعريف بعد شوية موجود تقرير مطلق الصواب
+
+334
+00:26:28,340 --> 00:26:32,560
+implication تضمين و equivalence مرت علينا بس كمان
+
+335
+00:26:32,560 --> 00:26:37,390
+مرة هنزورها من زاوية أخرى تكافأالتقارير مطلقة
+
+336
+00:26:37,390 --> 00:26:44,220
+الصواب والتضمين والتكافؤ إذا نعرب الأنواعفنبدأ
+
+337
+00:26:44,220 --> 00:26:48,780
+بالـ tautology أو تقرير مطلق الصواب تقرير مطلق
+
+338
+00:26:48,780 --> 00:26:53,040
+الصواب عشان نمهد لهذا التقرير أو لهذا المصطلح
+
+339
+00:26:53,040 --> 00:26:56,520
+خلّيني نشوف مثال أفلان إنه يمكن في الأول لو حطينا
+
+340
+00:26:56,520 --> 00:26:59,500
+التعريف مباشرة يصير في عنا مفاجأة أيش معنات، هل في
+
+341
+00:26:59,500 --> 00:27:01,880
+statement دايما بتكون صحيحة؟ قولنا لل statement
+
+342
+00:27:01,880 --> 00:27:04,440
+تكون either true or false فهي لما تكون بسيطة، هذه
+
+343
+00:27:04,440 --> 00:27:08,280
+الاحتمالين لكن لو كانت دايما الـ true هي بسميها
+
+344
+00:27:08,280 --> 00:27:10,860
+tautology، مطلق الصواب يعني دايما صحيحة فنشوف مثال
+
+345
+00:27:11,100 --> 00:27:15,220
+نشوف مثال عشان ندل إنه قديش ممكن يحدث عشان ما
+
+346
+00:27:15,220 --> 00:27:20,700
+نستغربش ففي عندنا مثال بيقول construct a truth
+
+347
+00:27:20,700 --> 00:27:27,280
+table for the statement be or not be فده مثال واي
+
+348
+00:27:27,280 --> 00:27:31,820
+solutionسؤال بسيط من أبسط الأسئلة اللى هتمور علينا
+
+349
+00:27:31,820 --> 00:27:35,380
+في هذا المصحق بدنا نكوّن جدول صدق مش طالب مننا ولا
+
+350
+00:27:35,380 --> 00:27:39,240
+إشي جدول صدق ل statement أكم simple statement فيه
+
+351
+00:27:39,240 --> 00:27:43,760
+واحدة إذا نعمل جدول فيها أكم صف .. صفات أحسن نعم
+
+352
+00:27:43,760 --> 00:27:48,280
+فعنا بيه بس هي لحالها والباقى كله بده حساب وفيها
+
+353
+00:27:48,280 --> 00:27:53,100
+إحتمالين يا true يا false فجدول صغير بعد الشكل
+
+354
+00:27:53,100 --> 00:27:57,150
+بعدين إيش بدنا بنحسب not بيهاللي هي على طول false
+
+355
+00:27:57,150 --> 00:28:02,250
+and true وبعدين بنحسب بي or not بي هاي كل العملية
+
+356
+00:28:02,250 --> 00:28:09,450
+true or false true false or true true فعنا
+
+357
+00:28:09,450 --> 00:28:14,570
+compound statement دايما true دايما true فهذا كان
+
+358
+00:28:14,570 --> 00:28:18,230
+مثال على ال totologies اه فهنا في ممكن نصير عندنا
+
+359
+00:28:18,230 --> 00:28:22,010
+statements تكون دايما true دايما true نسميها
+
+360
+00:28:22,010 --> 00:28:26,220
+totology متقايش تقرير مطلق صح دايما صحيح يعنيفهي
+
+361
+00:28:26,220 --> 00:28:28,940
+الـ definition، إيش تعريف الـ tautology؟ a
+
+362
+00:28:28,940 --> 00:28:32,880
+statement، تقرير is said to be a tautology، بنقول
+
+363
+00:28:32,880 --> 00:28:36,080
+على statement ما أو تقرير ما إنه tautology، إنه
+
+364
+00:28:36,080 --> 00:28:40,440
+مطلق صواب وقت إيش، if it is true، إذا كان صواب أو
+
+365
+00:28:40,440 --> 00:28:44,420
+صحيح for every assignment of a truth value ..
+
+366
+00:28:44,420 --> 00:28:48,200
+truth values to its component في جميع الاحتمالات
+
+367
+00:28:48,200 --> 00:28:52,530
+المنطقية الممكنة، إيش ما ندى؟احتمال للمركبات ايش
+
+368
+00:28:52,530 --> 00:28:56,190
+بيطلع الجواب true اتدناها true true اتدناها false
+
+369
+00:28:56,190 --> 00:28:59,590
+true فهذا بيسميه totology دايما صحيح في جميع
+
+370
+00:28:59,590 --> 00:29:04,110
+الاحتمالات المنطقية الممكنة فهذا هو ما يعرف بتقرير
+
+371
+00:29:04,110 --> 00:29:10,030
+مطلق الصواب او totology خلينا نشوف مثال
+
+372
+00:29:25,830 --> 00:29:31,610
+Solution ايش المثال بيقول show that the statement
+
+373
+00:29:31,610 --> 00:29:39,410
+طبعا q if q then if تحجسين if and only if b and q
+
+374
+00:29:39,410 --> 00:29:43,050
+is a tautology فى عندنا statement طويلة مش مانهتمش
+
+375
+00:29:43,050 --> 00:29:47,490
+كتير بالقرايتها بيقوللي اثبت انها tautologyكيف
+
+376
+00:29:47,490 --> 00:29:49,870
+نثبت هنا تطولوجيا؟ هي التعريف نيجي لأن نرجع
+
+377
+00:29:49,870 --> 00:29:54,210
+للتعريف هذه قاعدتنا دايما هيك في الرياضيات نعمل في
+
+378
+00:29:54,210 --> 00:29:56,970
+عنا أي مصطلح يقول لي أثبت أنه دالة differentiable
+
+379
+00:29:56,970 --> 00:29:58,770
+إيش بده أعمل؟ إيش معنى ال differentiable؟
+
+380
+00:29:58,770 --> 00:30:01,090
+continuous إيش معنى ال continuous؟ ففي عنا التعريف
+
+381
+00:30:01,090 --> 00:30:04,410
+هو الأساس لأ طبعا في ممكن أن غير التعريف ممكن يكون
+
+382
+00:30:04,410 --> 00:30:07,970
+أن نظريات قواعد أدوات أخرى تساعدنا في الإثبات لكن
+
+383
+00:30:07,970 --> 00:30:11,130
+أهم حاجة إيش من نقطة البداية التعريف التطولوجيا
+
+384
+00:30:11,130 --> 00:30:14,390
+تول الصمر علينا بنعرف عنه حاجة غير التعريف؟ لأ إذا
+
+385
+00:30:14,390 --> 00:30:17,480
+بنا نركز على التعريفبنعرف كيف نطبق التعريف بقول
+
+386
+00:30:17,480 --> 00:30:20,980
+ليه اثبت ان هذا تتولجي ايش يعني تتولجي يعني ليش
+
+387
+00:30:20,980 --> 00:30:24,020
+دايما true طب كيف بتثبت ان ال statement دايما true
+
+388
+00:30:24,020 --> 00:30:28,360
+ايش قاداتي عن طريق truth table اه فإذا هنا هنقول
+
+389
+00:30:28,360 --> 00:30:35,760
+له solution we will use truth table
+
+390
+00:30:46,280 --> 00:30:53,060
+to show that the statement او the given statement
+
+391
+00:30:57,940 --> 00:31:02,540
+is always true اختصارا في جميع اللياش احتمالا انها
+
+392
+00:31:02,540 --> 00:31:06,900
+دايما صحيح تمام فهذه هي طريقتنا في كل تعامل مع
+
+393
+00:31:06,900 --> 00:31:09,900
+رياضة ان شاء الله هذه هنكرر الفيلم بشوف السؤال
+
+394
+00:31:09,900 --> 00:31:14,340
+بحاول افسره و يمكن اصيغه بصيغة اخرى دي مهم جدا ويش
+
+395
+00:31:14,340 --> 00:31:17,900
+و بعدين نحاول نتعامل معه من وين بدنا ايش المطلوب و
+
+396
+00:31:17,900 --> 00:31:21,160
+كيف بدنا نوصلأه فطبعا هنعمل يدوى الصدق عرفنا
+
+397
+00:31:21,160 --> 00:31:24,600
+الأداء اللي بده إيش المطلوب وإيش طريقنا للوصول
+
+398
+00:31:24,600 --> 00:31:28,500
+للمطلوب فهذه طريقة مهمة في حل المسائل بشكل في
+
+399
+00:31:28,500 --> 00:31:32,180
+الرياضيات أو بشكل عام فطبعا نيجي لل statement أكم
+
+400
+00:31:32,180 --> 00:31:36,020
+symbol واحد فيها تنتهي في P و Q وفيش غيرها فإذا
+
+401
+00:31:36,020 --> 00:31:41,260
+بدنا أربع احتمالات مع عمودين رئيسيين P and Q مع
+
+402
+00:31:41,260 --> 00:31:45,420
+أربع احتمالات هاي اتنين وهاي كمان اتنين
+
+403
+00:31:49,290 --> 00:31:54,370
+تمام فطبعا كالعادة true true false false العمودي
+
+404
+00:31:54,370 --> 00:31:59,330
+الأول true false true false العمودي الثاني ايش
+
+405
+00:31:59,330 --> 00:32:03,510
+مطلوب نحسب أول بي and كيو الأقواس الداخلية فانت
+
+406
+00:32:03,510 --> 00:32:07,210
+فينا جوس و بعدين فينا جوس أكبر فبنحسب بي and كيو
+
+407
+00:32:07,210 --> 00:32:12,940
+الكل يعرف يحسب ا true مرة بس غير هيك falseمباشرة
+
+408
+00:32:12,940 --> 00:32:17,940
+بحب نضيع وقت ايش بعدين نحسب بي if and only if بي
+
+409
+00:32:17,940 --> 00:32:21,420
+if and only if بي if and only if بي if and only if
+
+410
+00:32:21,420 --> 00:32:21,600
+بي if and only if بي if and only if بي if and only
+
+411
+00:32:21,600 --> 00:32:21,640
+if بي if and only if بي if and only if بي if and
+
+412
+00:32:21,640 --> 00:32:22,420
+only if بي if and only if بي if and only if بي if
+
+413
+00:32:22,420 --> 00:32:23,080
+and only if بي if and only if بي if and only if بي
+
+414
+00:32:23,080 --> 00:32:23,100
+if and only if بي if and only if بي if and only if
+
+415
+00:32:23,100 --> 00:32:23,200
+only if بي if and only if بي if and only if بي if
+
+416
+00:32:23,200 --> 00:32:25,340
+and only if بي if and only if بي if and only if بي
+
+417
+00:32:25,340 --> 00:32:30,420
+if and only if بي if and only if بي if and only if
+
+418
+00:32:30,420 --> 00:32:34,800
+بي if
+
+419
+00:32:34,800 --> 00:32:41,520
+and only if بي if and
+
+420
+00:32:41,520 --> 00:32:48,810
+only ifأي سؤال، في أي طالب عنده مشكلة في الجداول،
+
+421
+00:32:48,810 --> 00:32:53,850
+الأمر بسيط، إذا أي حد نفسر لأنه يعني أمر بسيط،
+
+422
+00:32:53,850 --> 00:32:57,210
+المفروض إن ماحدش يكون عنده مشكلة، فلو في أي
+
+423
+00:32:57,210 --> 00:33:00,530
+استفسار، أي صعوبة، بنفسرها إن شاء الله عشان الأمر
+
+424
+00:33:00,530 --> 00:33:03,240
+يكون واضحتمام الخطوة اللي ايه ايه ايه ايه ايه ايه
+
+425
+00:33:03,240 --> 00:33:05,340
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+426
+00:33:05,340 --> 00:33:07,200
+ايه ايه
+
+427
+00:33:21,420 --> 00:33:25,900
+العمد تمام نبدأ نشتغل غاعدة if then true then true
+
+428
+00:33:25,900 --> 00:33:32,480
+true false then false true true then true true
+
+429
+00:33:32,480 --> 00:33:36,660
+false then anything true ايش قال اثبت انه
+
+430
+00:33:36,660 --> 00:33:39,420
+tautology تطلع tautology لو ما طلعاش طلع دايما
+
+431
+00:33:39,420 --> 00:33:42,060
+true tautology يعني دايما true اذا انا هنقول ايه
+
+432
+00:33:42,060 --> 00:33:45,180
+عشان اعلق from the table we see that the given
+
+433
+00:33:45,180 --> 00:33:51,980
+statement is a tautology from or by the tablewe
+
+434
+00:33:51,980 --> 00:33:56,140
+see that the
+
+435
+00:33:56,140 --> 00:34:02,320
+given statement is
+
+436
+00:34:02,320 --> 00:34:09,180
+a tautology أي
+
+437
+00:34:09,180 --> 00:34:13,940
+سؤال فهذا هو التعريف وهكذا نستطيع أن نطبق عليه
+
+438
+00:34:19,310 --> 00:34:24,710
+طبعا التوتولوجيز مهمين جدا بالنسبة لنا لأنهم
+
+439
+00:34:24,710 --> 00:34:29,630
+هيكونولنا القواعد المنطقية اللي بنتعامل معها في
+
+440
+00:34:29,630 --> 00:34:34,870
+انه نتأكد ان استنتاجنا او تفكيرنا منطقيا صحيح او
+
+441
+00:34:34,870 --> 00:34:38,740
+لافالـ Totality مهمة جداً ممكن نستخدمها في
+
+442
+00:34:38,740 --> 00:34:41,420
+البراهين في أي خطوة من خطوات البراهين وطبعاً هي
+
+443
+00:34:41,420 --> 00:34:47,720
+بتولدنا أو تنشئنا القواعد تبع المنطقية اللي
+
+444
+00:34:47,720 --> 00:34:50,060
+بنستخدمها في اللي هو البراهين
+
+445
+00:34:52,620 --> 00:34:56,820
+أي سؤال فهذا ال journal is تلت الأول من العنوان
+
+446
+00:34:56,820 --> 00:34:59,040
+Totology في عندنا implications و في عندنا
+
+447
+00:34:59,040 --> 00:35:03,560
+equivalent ننتقل للمصطلح التاني أو البفهم التاني
+
+448
+00:35:03,560 --> 00:35:06,600
+التضمين implication من implies implication
+
+449
+00:35:06,600 --> 00:35:12,840
+implications وهي التضمين التضمين بشكل مختصر هو
+
+450
+00:35:12,840 --> 00:35:18,150
+عبارة عن جملة شرطية دايما صحيحةهي عبارة عن جملة
+
+451
+00:35:18,150 --> 00:35:25,410
+شرطية مطلقة الصوابر فكل تضمين هو totology لكن
+
+452
+00:35:25,410 --> 00:35:28,190
+العكس غير صحيح فلو انا في قدرة احنا ايش قولنا
+
+453
+00:35:28,190 --> 00:35:32,030
+totology هو statement دايما صحيحة طب اذا كانت هذه
+
+454
+00:35:32,030 --> 00:35:34,330
+ال statement هي جملة شرطية و دايما صحيحة ايه بتكون
+
+455
+00:35:34,330 --> 00:35:37,030
+totology واش بتكون بنفس الوقت implication بسميها
+
+456
+00:35:37,030 --> 00:35:41,200
+تضمين فان التعريفlet capital B and capital Q be
+
+457
+00:35:41,200 --> 00:35:43,780
+two statements اي two statements، simple، compact،
+
+458
+00:35:43,780 --> 00:35:46,360
+مفرجش، شفت المثال هذا كيف؟ مفرجش، ان هو two
+
+459
+00:35:46,360 --> 00:35:50,680
+statements بتعامل if the conditional statement if
+
+460
+00:35:50,680 --> 00:35:53,580
+the conditional .. جملة الشرطية if B then Q is
+
+461
+00:35:53,580 --> 00:35:57,300
+autotology، دايما true، then it is called an
+
+462
+00:35:57,300 --> 00:36:01,400
+implication، بسميها تضمين، هذا طبعا زي ما تشوف في
+
+463
+00:36:01,400 --> 00:36:04,640
+كل سياستنا دايما رموز، دايما رموز، ليه شوفنا رموز؟
+
+464
+00:36:04,640 --> 00:36:08,950
+سهمبس في خطين متوازين مقطع left then اشمله تساهم
+
+465
+00:36:08,950 --> 00:36:12,970
+خط واحد هنا في خطين برضه يتجه لليمين لإنه علاقة
+
+466
+00:36:12,970 --> 00:36:17,550
+فيه إيش بنقراها؟ بنقراها if then بنقراها بي
+
+467
+00:36:17,550 --> 00:36:22,130
+implies اكيو بي implies اكيو فتضمين من تضمين قولنا
+
+468
+00:36:22,130 --> 00:36:27,210
+implies فإيش ما هو التضمين؟ هو عبارة عن جملة شرطية
+
+469
+00:36:27,210 --> 00:36:31,930
+مطلقة الصواب جملة شرطية مطلقة الصواب أيه السؤال؟
+
+470
+00:36:34,590 --> 00:36:37,970
+كيف؟ زي example .. اه هذا ممكن نعمل تضمين صحيح
+
+471
+00:36:37,970 --> 00:36:42,870
+فهذا ممكن هذا نقول إيش بي ا كيو implies صحيح لأنه
+
+472
+00:36:42,870 --> 00:36:47,970
+هي جملة شرطية وهي totology نشوف مثال الأول
+
+473
+00:37:05,610 --> 00:37:11,170
+المثال الأول show that if B then B is an
+
+474
+00:37:11,170 --> 00:37:15,850
+implication اتدانى جملة شرطية وجالى اثبت انها
+
+475
+00:37:15,850 --> 00:37:20,810
+تضمين ايه يعني؟ بدي اثبت انها totology اي بمعنى
+
+476
+00:37:20,810 --> 00:37:23,490
+اخر بدي اثبت ان هذه جملة اسمها دايما ال true دايما
+
+477
+00:37:23,490 --> 00:37:27,090
+ال true خليني اكتب هذا الكلام solution لان هذا مهم
+
+478
+00:37:27,090 --> 00:37:32,490
+جدا ان نفسر السؤال هذه السياسةأرجو أن يكون هناك
+
+479
+00:37:32,490 --> 00:37:35,670
+شاهدين من المثال المثال المطلوب المباشر له
+
+480
+00:37:35,670 --> 00:37:39,410
+والسياسة التي نتبعها والحقيقة هذه سنستخدمها دائما
+
+481
+00:37:39,410 --> 00:37:42,290
+وهذه ستساعدكم كثيرا في المثاق وإن شاء الله في
+
+482
+00:37:42,290 --> 00:37:45,150
+المثاقات الأخرى كيف نتعامل مع الأمثلة كيف نتعامل
+
+483
+00:37:45,150 --> 00:37:47,790
+مع البراهين أيش المعطيات أيش المطلوب وكيف نتعامل
+
+484
+00:37:47,790 --> 00:37:53,430
+فإذا احنا أول الشيء we have to show المطلوب مننا
+
+485
+00:37:53,430 --> 00:37:56,030
+that
+
+486
+00:37:56,790 --> 00:38:00,870
+اللي هو implication بي .. if b then b is a
+
+487
+00:38:00,870 --> 00:38:10,490
+tautology فهي
+
+488
+00:38:10,490 --> 00:38:18,490
+البنية او that is بمعنى آخر ممكن نفسر that is if b
+
+489
+00:38:18,490 --> 00:38:25,200
+then b is always trueفهذه السياسة قعدت سياغة
+
+490
+00:38:25,200 --> 00:38:29,400
+المطلوب سياسة مهمة جدا في حل مسائل الرياضيات أو في
+
+491
+00:38:29,400 --> 00:38:32,600
+البراهين فهذه بدنا نتعلمها ان شاء الله شوية شوية و
+
+492
+00:38:32,600 --> 00:38:35,540
+نتعود عليها لأنها حد ساعدنا كتير في دراسة الرياضية
+
+493
+00:38:35,540 --> 00:38:41,740
+تمام خلاص كيف بنثبت جدول الصدق اذا we will use
+
+494
+00:38:41,740 --> 00:38:48,680
+truth table تمام
+
+495
+00:38:49,610 --> 00:38:52,530
+أكم simple statement فيه واحدة إذا في عندنا بس
+
+496
+00:38:52,530 --> 00:38:56,430
+إيهاش احتمالين فعندنا بي و إيهاش في عندنا بس
+
+497
+00:38:56,430 --> 00:39:01,850
+احتمالين true or false طيب
+
+498
+00:39:01,850 --> 00:39:06,290
+كيف بدي أحسب بيه if then بيه true ده true طب كيف
+
+499
+00:39:06,290 --> 00:39:09,500
+بدي أعملها ع الجدول؟انسح هو احسن انسح العمول كمان
+
+500
+00:39:09,500 --> 00:39:12,840
+مرة عشان احنا متعودين انه بنقول في العمول فانا بدي
+
+501
+00:39:12,840 --> 00:39:15,680
+إيش أنسح هو إيش الدروري واحد طب التاني لو عملت
+
+502
+00:39:15,680 --> 00:39:20,140
+كمان مرة لأ دره لإيش لأنه ممكن افيدني فانا هعمل
+
+503
+00:39:20,140 --> 00:39:24,280
+بيه كمان مرة طب ممكن أغير الترتيب هنا لأ بنفعش لإن
+
+504
+00:39:24,280 --> 00:39:29,160
+هو نفسها بنفعش فانتبهوا لهذه الأمور فالأهم بدنا بي
+
+505
+00:39:29,160 --> 00:39:34,360
+then بي ال true then true true false then false
+
+506
+00:39:34,360 --> 00:39:37,060
+إيش ال true ففعلا totality
+
+507
+00:39:40,810 --> 00:39:48,850
+نقوله هنا by the table we
+
+508
+00:39:48,850 --> 00:39:53,450
+see or we have from the table او by the table ايش
+
+509
+00:39:53,450 --> 00:39:58,030
+هي انه ايش بي then بي is a implication ممكن اكتب
+
+510
+00:39:58,030 --> 00:40:03,230
+او ايش اكتب باختصارة بي implies بيP implies P وده
+
+511
+00:40:03,230 --> 00:40:07,910
+منطق يعني إذا حاجة صحيحة فبتأمل صحيحة يعني إذا ..
+
+512
+00:40:07,910 --> 00:40:11,010
+إذا ال .. ده قبل الاشتقاء فقبل الاشتقاء يعني بعيد
+
+513
+00:40:11,010 --> 00:40:13,890
+نفس الجملة فده قاعدة منطقية إذا هذه صحيحة فهي ده
+
+514
+00:40:13,890 --> 00:40:18,630
+من الصحيحة أي سؤال؟ أي سؤال؟ بسيطة جدا بحسب
+
+515
+00:40:18,630 --> 00:40:21,630
+الصحيحة يعني المثال بسيط بس عشان نوضح الأهداف اللي
+
+516
+00:40:21,630 --> 00:40:25,010
+هي كيف طريقة أهم من طريقة الحل هل حين الأمر
+
+517
+00:40:25,010 --> 00:40:26,830
+مشهدان؟ أه طبعا
+
+518
+00:40:31,850 --> 00:40:34,850
+لأ الـ tautology أي statement لو ال statement
+
+519
+00:40:34,850 --> 00:40:37,850
+مافيش فيها ايه؟ يعني لو أنا فيه عندي زي المثال
+
+520
+00:40:37,850 --> 00:40:42,410
+اللي عملناه be or not be فهذه الـ tautology، تظبط؟
+
+521
+00:40:42,410 --> 00:40:48,650
+هل هذه implication؟ لأنها من جملة شرطيةفي مصطلحين،
+
+522
+00:40:48,650 --> 00:40:51,450
+انتبه، غرزي، معلش، يعني يمكن تكون السؤال عند فيه
+
+523
+00:40:51,450 --> 00:40:54,630
+غبش و عند أخرين، فنركز مع بعض هكذا، الـ tautology
+
+524
+00:40:54,630 --> 00:40:59,330
+هي statement بغض النظر عن إيش، إيش مركباتها، إيش
+
+525
+00:40:59,330 --> 00:41:02,630
+الروابط اللي فيها، تكون دايما true زي هذه، هذه
+
+526
+00:41:02,630 --> 00:41:06,950
+tautology لأنه دايما true لكن ال implication هي
+
+527
+00:41:06,950 --> 00:41:11,780
+statement شرطياconditional statement هنا يحط إن
+
+528
+00:41:11,780 --> 00:41:17,340
+الرابط الرئيسي تبعها إيش هو الشرطية فانحدد في حالة
+
+529
+00:41:17,340 --> 00:41:20,260
+يعني من حالات الـ tautology يعني هذه الـ tautology
+
+530
+00:41:20,260 --> 00:41:24,040
+لكن ليست implication هذه implication وهي بنفس
+
+531
+00:41:24,040 --> 00:41:26,220
+الوقت هذه ال statement طبعا ما بقولش أن هذه الـ
+
+532
+00:41:26,220 --> 00:41:30,340
+tautology هذه الـ tautology واضح واضحة ولا لأ
+
+533
+00:41:30,340 --> 00:41:34,780
+فأرجو التفريق فكل tautology وكل implication هو الـ
+
+534
+00:41:34,780 --> 00:41:36,700
+tautology لكن ليش العكس غير صحيح
+
+535
+00:41:42,800 --> 00:41:49,000
+ممكن نستغل المتبقى في كمان مثال هنا نفس الصيغة
+
+536
+00:41:49,000 --> 00:41:57,880
+show that B and Q implies Q and B أبدأ
+
+537
+00:41:57,880 --> 00:42:03,940
+الكتابة من فوق example 2 solution مع بعض بدنا
+
+538
+00:42:03,940 --> 00:42:08,320
+نصيغه إيش المطلوب؟ بدنا نثبت إن الجملة الشرطية
+
+539
+00:42:08,320 --> 00:42:14,710
+إنها tautology فإذا خلينا نفسرwant أو we have to
+
+540
+00:42:14,710 --> 00:42:23,470
+show that is B and Q then Q and B فأرجو التركيز،
+
+541
+00:42:23,470 --> 00:42:25,630
+يعني أنا أشوف درياضيات دقيقة، ماينفعش أكتبله نفسي
+
+542
+00:42:25,630 --> 00:42:29,450
+أبدأ أفسبره أنه تولوجي، لأ، أه، فالرموز مهمة، واحد
+
+543
+00:42:29,450 --> 00:42:31,350
+يقول لما هاد ساهم و هاد ساهم، لأ، هاد الساهم له
+
+544
+00:42:31,350 --> 00:42:34,050
+معنى زي ما تشايفين و هاد الساهم له معنى، فلازم
+
+545
+00:42:34,050 --> 00:42:37,050
+نستخدمه في المكان و في الوقت الصحيح و في مكانه
+
+546
+00:42:37,050 --> 00:42:41,070
+الصحيح ف we want to show that is a tautology
+
+547
+00:42:44,310 --> 00:42:49,170
+أو إن هاياش دايما true نفس البعض بس احنا عشان هياش
+
+548
+00:42:49,170 --> 00:42:52,470
+بنبني relation جديدة عليها القضية طبعا بنستخدم
+
+549
+00:42:52,470 --> 00:42:58,390
+هياش جدول الصدق فنكوّن
+
+550
+00:42:58,390 --> 00:43:02,270
+جدول الصدق أكمل statement بسيطة تان تان ففي عندنا
+
+551
+00:43:02,270 --> 00:43:08,210
+أربع احتمالات مع عمودين رئيسيا لل P و لل Q ففي
+
+552
+00:43:08,210 --> 00:43:16,260
+عندنا أربع احتمالات ف ..الصحيح والصحيح والخاطئ
+
+553
+00:43:16,260 --> 00:43:26,000
+والخاطئ الصحيح والخاطئ والخاطئ اي سؤال نبدأ
+
+554
+00:43:26,000 --> 00:43:31,000
+اشفيه عندنا P and Q بدنا نحسب P او قيمة الصدق لل P
+
+555
+00:43:31,000 --> 00:43:35,660
+and Q الصحيح والخاطئ والخاطئ والخاطئ حسفناها اكتر
+
+556
+00:43:35,660 --> 00:43:39,360
+من مرة مافي مشكلة الان بقول اعكس الترتيب P and Q
+
+557
+00:43:40,580 --> 00:43:43,860
+فبنلاقي نفس الحاجة طبعا وهذا هو اللي بدنا نثبته
+
+558
+00:43:43,860 --> 00:43:48,040
+الحقيقة أن هنا عملية الـ AND إبدالية فرابط الـ AND
+
+559
+00:43:48,040 --> 00:43:52,320
+منطقيا إبدالي الترتيب فيه غير مهم الأخرش اللي بدنا
+
+560
+00:43:52,320 --> 00:43:56,220
+نثبته هو الـ Indication فالـ Indication لا يدخل في
+
+561
+00:43:56,220 --> 00:43:58,740
+جدول الصدق لأن جدول الصدق متعامل مع ال statement
+
+562
+00:43:58,740 --> 00:44:01,520
+نفسها اللي فيها رابط من الروابط البسيطة الأصلية
+
+563
+00:44:01,520 --> 00:44:04,500
+لكن هذه الـ implies ليست رابط هذه عبارة عن
+
+564
+00:44:04,500 --> 00:44:07,940
+statement و تاتولوجي و إنها تاتولوجي فاحنا الان
+
+565
+00:44:07,940 --> 00:44:15,260
+بدنا نعملB and Q then Q and B فبنحسب نسبة أنها
+
+566
+00:44:15,260 --> 00:44:19,020
+دائما true تمام
+
+567
+00:44:19,020 --> 00:44:23,500
+فهي بدنا نشتغل على دولة تنتين مع بعض هي السهم true
+
+568
+00:44:23,500 --> 00:44:28,260
+then true true false then false true false then
+
+569
+00:44:28,260 --> 00:44:32,680
+false true false then false true فإذا فعلا
+
+570
+00:44:32,680 --> 00:44:43,910
+totology from the tablewe see that .. ممكن أقول إن
+
+571
+00:44:43,910 --> 00:44:46,730
+هذه is a tautology أو أقوله زي ما هو مطلوب
+
+572
+00:44:46,730 --> 00:44:55,850
+اختصاراً V and Q implies Q and .. أي سؤال
+
+573
+00:45:01,310 --> 00:45:05,450
+تمام، هذا جيد لكي ننهي في تمرين إضافية موجودة
+
+574
+00:45:05,450 --> 00:45:09,430
+عندكم مكتوبة الـ B implies B and B B and Q implies
+
+575
+00:45:09,430 --> 00:45:13,810
+Q زي ما هي الأول ممكن تعمل implies للتاني نوقف هنا
+
+576
+00:45:13,810 --> 00:45:15,330
+ان شاء الله المرة القادمة سنبدأ في theorem
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/8meu521dv0U.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/8meu521dv0U.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9d2c573d1505f76c91dcaf370ad43c35bd867c05
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/8meu521dv0U.srt
@@ -0,0 +1,2227 @@
+1
+00:00:19,760 --> 00:00:24,200
+بسم الله الرحمن الرحيم ففي آخر محاضرة احنا بدأنا 
+
+2
+00:00:24,200 --> 00:00:28,060
+كمقدمة سريعة على ال cardinal number خلينا نعيد على 
+
+3
+00:00:28,060 --> 00:00:32,460
+السريع ف cardinal numbers and cardinal arithmetic
+
+4
+00:00:32,460 --> 00:00:37,060
+الأعداد الأصلية ممكن نعرفها وطبعًا و العمليات 
+
+5
+00:00:37,060 --> 00:00:42,210
+الحسابية على هذه الأعداد فطبعًا الأعداد اللي هو
+
+6
+00:00:42,210 --> 00:00:47,530
+الأصلية هي أعداد هنستخدمها للتعبير عن عدد عناصر
+
+7
+00:00:47,530 --> 00:00:51,670
+المجموعات طبعًا ما فيش نظام من الأنظمة اللي بنعرفها 
+
+8
+00:00:51,670 --> 00:00:54,170
+للأعداد الطبيعية ولا الأعداد الصحيحة ولا الأعداد
+
+9
+00:00:54,170 --> 00:00:58,930
+الحقيقية بتقدر تقوم بهذا المقام وتعبر عن اللي هو 
+
+10
+00:00:58,930 --> 00:01:02,430
+أعداد المجموعات بشكل عام لأن زي ما احنا شفنا فيه 
+
+11
+00:01:02,430 --> 00:01:06,510
+مجموعات infinite لكن مختلفين ففي عندنا the
+
+12
+00:01:06,510 --> 00:01:09,990
+numerable sets اللي هي عدد عناصرها بـ كافة عدد عناصر
+
+13
+00:01:09,990 --> 00:01:15,080
+الـ N و  numerable sets زي الـ R أو الفترة من
+
+14
+00:01:15,080 --> 00:01:18,440
+صفر لواحد وهذه Infinite وهذه Infinite لكن مختلفة
+
+15
+00:01:18,440 --> 00:01:22,620
+ما أقدرش أقول إنها Infinity مثلاً وهذه Infinity نفس
+
+16
+00:01:22,620 --> 00:01:26,840
+الرمز ما نفعش لذلك بدنا نظام جديد من الأعداد يقدر
+
+17
+00:01:26,840 --> 00:01:31,120
+يعبر عن هذه المجموعات ويفرق بينها ونقدر نشتغل عليه
+
+18
+00:01:31,120 --> 00:01:34,260
+في عملية طبعًا ما زال عملنا نظام جديد من الأعداد
+
+19
+00:01:34,260 --> 00:01:37,840
+بدنا نشوف خواصه كيف نجمع الأعداد هذه كيف نضربها
+
+20
+00:01:37,840 --> 00:01:41,980
+وبعض الأمور فطبعًا احنا عرفنا اللي هو ال cardinal
+
+21
+00:01:41,980 --> 00:01:46,420
+numbers طبعًا بطريقة بسيطة ومباشرة فيه أربع قواعد
+
+22
+00:01:46,420 --> 00:01:53,260
+القاعدة الأولى اللي سميناها C1 الـ cardinal numbers
+
+23
+00:01:53,260 --> 00:01:58,880
+دالة أعداد خاصة بالمجموعات بتعبر عن المجموعات فكل 
+
+24
+00:01:58,880 --> 00:02:05,660
+مجموعة set A يقابلها cardinal number عبرنا عنه بـ 
+ 
+25
+00:02:05,660 --> 00:02:11,670
+cardinal number of A أول أربع حروف والعكس صحيح فكل 
+
+26
+00:02:11,670 --> 00:02:15,070
+مجموعة بيقابلها cardinal number وكل cardinal number
+
+27
+00:02:15,070 --> 00:02:18,630
+لازم يعبر عن مجموعة يعني ما نفعش أقول مثلاً ان في
+
+28
+00:02:18,630 --> 00:02:21,650
+أنا عندي cardinal number بيساوي خمسة اه الخمسة دي
+
+29
+00:02:21,650 --> 00:02:26,710
+مش بتعبر عن وزن كمية معينة لأ بتعبر عن عدد عناصر
+
+30
+00:02:26,710 --> 00:02:29,970
+المجموعة لازم فما نفعش فدايمًا ال cardinal numbers
+
+31
+00:02:29,970 --> 00:02:35,130
+مرتبط ارتباط وثيق بعدد عناصر المجموعات فكل مجموعة
+
+32
+00:02:35,130 --> 00:02:39,210
+بقدر أشوف cardinal number بيعبر عنها وكل cardinal
+
+33
+00:02:39,210 --> 00:02:42,570
+number لازم يكون فيه مجموعة بيعبر عنها بقى بقى بقى
+
+34
+00:02:42,570 --> 00:02:44,470
+كذا بدأت من المجموعة بقدر ألاقي ال cardinal number 
+
+35
+00:02:44,470 --> 00:02:47,910
+المناسب بدأت من cardinal number بقدر ألاقي مجموعة 
+
+36
+00:02:47,910 --> 00:02:54,830
+مناسبة أتعبر عنه القاعدة رقم اتنين ان المجموعة 
+
+37
+00:02:54,830 --> 00:02:57,790
+الوحيدة اللي cardinality بتساوي صفر هي الـ Phi اه
+
+38
+00:02:57,790 --> 00:03:03,860
+فاحنا عندنا ال cardinality للمجموعة ما بتساوي صفر
+
+39
+00:03:03,860 --> 00:03:08,200
+if and only if هذه المجموعة هي الـ Phi فإذا أول
+
+40
+00:03:08,200 --> 00:03:10,800
+cardinal number نريد أن نعرف أن هو الصفر فالصفر
+
+41
+00:03:10,800 --> 00:03:13,740
+cardinal number لأنه بيعبر عن مجموعة مين الـ Phi
+
+42
+00:03:13,740 --> 00:03:20,700
+المجموعة الفارغة القاعدة رقم تلاتة انه طبعًا احنا
+
+43
+00:03:20,700 --> 00:03:26,630
+نعرف احنا بنحاول نعمل مفهوم، نقول احنا ليش جبنا
+
+44
+00:03:26,630 --> 00:03:29,030
+أعداد جديدة لأن الأعداد الطبيعية مش كافية، طب
+
+45
+00:03:29,030 --> 00:03:31,450
+الأعداد الطبيعية ممكن تتعبر عن المجموعات نعم إذا
+
+46
+00:03:31,450 --> 00:03:33,950
+كانت finite لكن ما بتكفيش لحالها، المشكلة في الـ
+
+47
+00:03:33,950 --> 00:03:37,370
+infinite لذلك لو كان عندنا مجموعة فيها مائة عنصر
+
+48
+00:03:37,370 --> 00:03:40,570
+جدًا cardinality تبعتها؟ مية، على طول، فكيف عبرنا
+
+49
+00:03:40,570 --> 00:03:46,310
+عنه؟ قلنا إذا ال A تكافئ أن K فهذا يؤدي إن ال
+
+50
+00:03:46,310 --> 00:03:51,210
+cardinality للـ A تساوي K finite على طول مباشرة
+
+51
+00:03:51,210 --> 00:03:55,850
+القاعدة الرابعة والأخيرة انه إذا كانت ال A تكافئ
+
+52
+00:03:55,850 --> 00:04:00,110
+ال B if and only if ال cardinality لل A تساوي ال
+
+53
+00:04:00,110 --> 00:04:05,390
+cardinality لل B فـ دولة أربع قواعد بيخلونا نقدر
+
+54
+00:04:05,390 --> 00:04:08,970
+نعرف ال cardinal numbers ونتعامل معاهم فـ الآن إن 
+
+55
+00:04:08,970 --> 00:04:13,990
+شاء الله هنتقل لنقطة جديدة طبعًا هذا ملخص للمرة
+
+56
+00:04:13,990 --> 00:04:19,670
+الماضية الآن هنتحدث عن ترتيب هذه الأرقام مين أصغر
+
+57
+00:04:19,670 --> 00:04:21,950
+من مين؟ طبعًا الصفر أصغر من واحد الواحد أصغر من
+
+58
+00:04:21,950 --> 00:04:26,010
+اتنين طب ليش ال cardinality مثلاً لل natural number
+
+59
+00:04:26,010 --> 00:04:30,440
+و cardinality لل real number مين أصغر من مين؟ أصغر 
+
+60
+00:04:30,440 --> 00:04:33,500
+من الريال وهكذا نعبر عن هذا الموضوع بشكل طبعًا نحط
+
+61
+00:04:33,500 --> 00:04:36,720
+التعريف ونشهد الكلام اللي حكيناه صح ولا مش صح أنت
+
+62
+00:04:36,720 --> 00:04:40,040
+احنا قلنا إنه إيش يعني زي ما حكيت لزميلاتكوا إن 
+
+63
+00:04:40,040 --> 00:04:47,690
+ال cardinality لل N أصغر من ال cardinality لل R طب
+
+64
+00:04:47,690 --> 00:04:50,110
+.. طب مين بيقول صح ومين بيقول خطأ؟ نشوف مين
+
+65
+00:04:50,110 --> 00:04:53,110
+المعيار؟ مين الحكم بينا؟ نشوف هذا الموضوع فهنا
+
+66
+00:04:53,110 --> 00:04:56,930
+الموضوع طبعًا ال section التاني ordering of the
+
+67
+00:04:56,930 --> 00:05:00,190
+cardinal numbers ordering يعني ترتيب اه كيف ترتيب؟
+
+68
+00:05:00,190 --> 00:05:03,350
+مين صغير؟ مين كبير؟ مين أكبر؟ وهكذا اه وفي عندنا
+
+69
+00:05:03,350 --> 00:05:07,630
+طبعًا اللي هنتحدث فيه عندنا the Schroeder-Bernstein
+
+70
+00:05:07,630 --> 00:05:11,470
+theorem في نظرية للعالمين Schroeder و Bernstein
+
+71
+00:05:13,860 --> 00:05:20,080
+فطبعًا أول شيء هنعمل مصطلح جديد فيه إن احنا
+
+72
+00:05:20,080 --> 00:05:25,380
+المجموعات قسمناها لـ finite و infinite set واحنا
+
+73
+00:05:25,380 --> 00:05:28,760
+قلنا ال cardinal number مرتبطة في المجموعات تبقى
+
+74
+00:05:28,760 --> 00:05:34,050
+لهذا التقسيم هنقسم ال cardinal number لقسمين برضه
+
+75
+00:05:34,050 --> 00:05:38,070
+إذا ال cardinal number بيقابل finite set هنسميه 
+
+76
+00:05:38,070 --> 00:05:41,530
+finite cardinal number وإذا بيقابل infinite set
+
+77
+00:05:41,530 --> 00:05:44,530
+هنسميه transfinite مش infinite cardinal number
+
+78
+00:05:44,530 --> 00:05:47,890
+trans معناه ما بعد الـ finite ما بعد الـ finite
+
+79
+00:05:47,890 --> 00:05:52,210
+فهنستخدم المصطلح هذا فعنا العنوان finite and
+
+80
+00:05:52,210 --> 00:05:56,070
+transfinite cardinal number فأول حاجة a cardinal
+
+81
+00:05:56,070 --> 00:06:00,110
+number of a finite set is called a finite cardinal
+
+82
+00:06:00,110 --> 00:06:02,960
+number اه فإذا ال cardinal number بيقابل مجموع
+
+83
+00:06:02,960 --> 00:06:06,400
+finite بيسميه finite number finite cardinal number
+
+84
+00:06:06,400 --> 00:06:10,800
+طبعًا a cardinal number of an infinite set is
+
+85
+00:06:10,800 --> 00:06:14,600
+called a transfinite ما بعد الـ finite ما بعد الـ
+
+86
+00:06:14,600 --> 00:06:18,980
+finite إيش cardinal number في هذا المصطلح هنستخدم 
+
+87
+00:06:18,980 --> 00:06:23,440
+طبعًا كمثال ال zero cardinal number ولا لأ لأنه 
+
+88
+00:06:23,440 --> 00:06:28,270
+بيقابل الـ Phi finite ولا transfinite finite الواحد
+
+89
+00:06:28,270 --> 00:06:31,370
+cardinal number صح لأنه بيقابل مين الـ singleton
+
+90
+00:06:31,370 --> 00:06:35,330
+set وهو finite ولا transfinite finite طيب الـ
+
+91
+00:06:35,330 --> 00:06:40,190
+cardinality لأن transfinite واضحة فهذه مثال بسيطة
+
+92
+00:06:40,190 --> 00:06:43,810
+على طول لأن ليش ال N infinite وال R برضه 
+
+93
+00:06:43,810 --> 00:06:46,390
+transfinite ال cardinality تبع التواجد كذا الـ
+
+94
+00:06:46,390 --> 00:06:51,370
+cardinal number بنزعج فهذه التعريف بكل بساطة وبكل
+
+95
+00:06:51,370 --> 00:06:55,550
+بشكل مباشر الآن نجي للموضوع الرئيسي وهو الاش
+
+96
+00:06:55,550 --> 00:07:03,970
+الترتيب فـ أنا في عندي أنا cardinal numbers أنا أنا 
+
+97
+00:07:03,970 --> 00:07:08,390
+أنا أنا أنا أنا
+
+98
+00:07:08,390 --> 00:07:10,410
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا 
+
+99
+00:07:10,410 --> 00:07:10,450
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا 
+
+100
+00:07:10,450 --> 00:07:10,670
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا 
+
+101
+00:07:10,670 --> 00:07:10,870
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+102
+00:07:10,870 --> 00:07:10,910
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+103
+00:07:10,910 --> 00:07:12,230
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+104
+00:07:12,230 --> 00:07:12,850
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+105
+00:07:12,850 --> 00:07:16,270
+أنا أنا أنا أنا عندي الـ Cardinal numbers بجيب
+
+106
+00:07:16,270 --> 00:07:18,910
+المجموعات اللي بتقبلهم وهأقارن بين المجموعات بصورة
+
+107
+00:07:18,910 --> 00:07:21,850
+معينة فهذا الطريقة اللي احنا هنعتمدها فعنا 
+
+108
+00:07:21,850 --> 00:07:25,250
+التعريف الثالث let A و B be sets اه فعشان هيك
+
+109
+00:07:25,250 --> 00:07:28,110
+الكلام مش منفك احنا متحدث عن Cardinal numbers
+
+110
+00:07:28,110 --> 00:07:31,710
+لكن دايمًا إيش فيه؟ مجموعات الموضوع لا ينفصل عن
+
+111
+00:07:31,710 --> 00:07:37,380
+المجموعات بنقول إن cardinality of A is less than or
+
+112
+00:07:37,380 --> 00:07:41,400
+equal أقل أو يساوي أيش الرمز؟ رمز أصغر من أو
+
+113
+00:07:41,400 --> 00:07:43,580
+يساوي في العداد العادية في العداد الحقيقية يعني
+
+114
+00:07:43,580 --> 00:07:46,620
+نفس الشيء اه بنقول ليش we write cardinality of A
+
+115
+00:07:46,620 --> 00:07:50,040
+أقل أو يساوي cardinal number of B إذا كالعادة في
+
+116
+00:07:50,040 --> 00:07:54,420
+إن مفهوم في إن الرمز تبعه بتم إن التعريف صح؟
+
+117
+00:07:54,420 --> 00:07:57,380
+كنا دايمًا نعرف نحكي بعد الصوت اه اه وقت إيش
+
+118
+00:07:57,380 --> 00:08:01,720
+بنقول هذا الكلام if A is equibotent to a subset
+
+119
+00:08:01,720 --> 00:08:06,810
+of B معنى تكافئ مجموعة جزئية من الـ B فأنا بتحدث عن 
+
+120
+00:08:06,810 --> 00:08:13,090
+مجموعة A وهي مجموعة B بتحدث عن ال cardinal number
+
+121
+00:08:13,090 --> 00:08:17,910
+بدي أعبر عن حجم المجموعة فبدي أقول إن هذه حجم 
+
+122
+00:08:17,910 --> 00:08:21,870
+المجموعة أصغر أو يساوي حجم المجموعة هذه وقت إيش
+
+123
+00:08:21,870 --> 00:08:25,590
+إذا كانت ال A تكافئ من مين؟ subset من الـ B وليه
+
+124
+00:08:25,590 --> 00:08:30,630
+كنا نسميها B0 هدولة تكافئ الـ A فإيه؟ تكافئ subset
+
+125
+00:08:30,630 --> 00:08:33,790
+طبعًا subset ممكن تساويها لأن subset ما جاليش proper
+
+126
+00:08:33,790 --> 00:08:37,450
+subset subset تكافئ ده subset عشان إيه أصغر من أو 
+
+127
+00:08:37,450 --> 00:08:41,750
+يساوي أصغر من أو يساوي فإذا هذه أول شيء علاقة أصغر 
+
+128
+00:08:41,750 --> 00:08:45,750
+من أو يساوي فإذا أنا بحولها من لغة المقارنة بين
+
+129
+00:08:45,750 --> 00:08:48,910
+cardinal numbers من أعداد أصلية للمقارنة بين
+
+130
+00:08:48,910 --> 00:08:51,830
+مجموعات طبعًا تكافئ إيش صار بال bijection وهكذا
+
+131
+00:08:51,830 --> 00:08:58,090
+فبنرجع للموضوع السابق تمام فهذه علاقة أصغر من أو 
+
+132
+00:08:58,090 --> 00:09:02,570
+يساوي طالب يقول أصغر من مش يساوي فبقول we say that
+
+133
+00:09:02,570 --> 00:09:06,810
+cardinal of A is less than cardinality of B and
+
+134
+00:09:06,810 --> 00:09:09,790
+right نفس الإشارة بنشيل ال if تساوي نفس الرمز 
+
+135
+00:09:09,790 --> 00:09:12,570
+بستخدم نفس الرمز مع الأرقام الحقيقية مع العدات
+
+136
+00:09:12,570 --> 00:09:17,330
+الحقيقية if وقتاش إذا هي أصغر منها أو يساويها لكن لا
+
+137
+00:09:17,330 --> 00:09:22,130
+تساوي ما فيش تساوي ما فيش تساوي and cardinality of A 
+
+138
+00:09:22,130 --> 00:09:26,980
+لا تساوي cardinality of B هل احنا عرفنا تساوي الـ
+
+139
+00:09:26,980 --> 00:09:29,920
+Cardinality عشان هذه نفيها؟ عرفناها 
+
+140
+00:09:33,610 --> 00:09:38,050
+فإذا إيش ماله؟ إذا هي تكافئ صبصة منها ولا تكافئها 
+
+141
+00:09:38,050 --> 00:09:42,290
+صارت، هي تكافئ  Subset منها ولا تكافئها نفسها، هيك
+
+142
+00:09:42,290 --> 00:09:44,930
+بده يصير، لأنه إيش معناته؟ إنه ما زال احنا عرفنا
+
+143
+00:09:44,930 --> 00:09:47,930
+التساوي، لأ بيقولوا لا تساوي شمالها  the negation،
+
+144
+00:09:47,930 --> 00:09:50,510
+the negation على طول، ففيش مشكلة أطلع، فإذا هذا
+
+145
+00:09:50,510 --> 00:09:53,710
+التعريف يعتبر هيك كام، فإذا هو أوش عرف أصغر من أو
+
+146
+00:09:53,710 --> 00:09:59,460
+يساوي، وبدلالته عرف من أصغر منه فقط أو بدلالته زاد
+
+147
+00:09:59,460 --> 00:10:04,340
+من عدم التساوي اللي هو the negation تبع التساوي
+
+148
+00:10:04,340 --> 00:10:12,060
+تفضلي نحاول 
+
+149
+00:10:12,060 --> 00:10:18,840
+نقرب الصورة ال gate نقول الأربع أصغر من الخمسة كيف
+
+150
+00:10:18,840 --> 00:10:25,170
+بدي أعرفها؟ to Cathy أن الأربع أصغر من الخمسة and
+
+151
+00:10:25,170 --> 00:10:28,490
+الأربع لا تساوي الخمسة هيك تقريبا بنعمل حاجة بهذا
+
+152
+00:10:28,490 --> 00:10:37,670
+الشكل هيك بدي أعمل لأن هو عرف أصغر من أو يساوي في
+
+153
+00:10:37,670 --> 00:10:42,120
+واحد، مظبوط؟ أعرف أصغر من أو يساوي هو بدأ بتعرف مين
+
+154
+00:10:42,120 --> 00:10:46,000
+أصغر من أو يساوي في رقم واحد، وبعدين أعرف أصغر من 
+
+155
+00:10:46,000 --> 00:10:50,320
+فقط لحالها بكيف أعرفها بدلالة أصغر من أو يساوي و
+
+156
+00:10:50,320 --> 00:10:55,400
+بدلالة عدم التساوي، عدم التساوي خليني أكتبها بطريقة
+
+157
+00:10:55,400 --> 00:10:59,760
+جديدة، قد يكون الصورة أوضحة، مش غلط خليني أشوف إيش
+
+158
+00:10:59,760 --> 00:11:05,180
+بقول هو الآن خليني أعبر عن هذا بشكل مختلف، أول شي
+
+159
+00:11:05,180 --> 00:11:11,960
+واحد بنقول عليه Cardinality للـ A أصغر أو يساوي
+
+160
+00:11:11,960 --> 00:11:16,020
+Cardinality للـ B هذا المصطلح الجديد، مظبوط؟ بدنا 
+
+161
+00:11:16,020 --> 00:11:21,180
+نعرفه كيف عرفه؟ يكافئ إذا جهش كانت الـ A شمالها
+
+162
+00:11:21,180 --> 00:11:30,000
+تكافئ Subset من الـ B هذا اختصارا، واضح؟ واضح؟
+
+163
+00:11:30,000 --> 00:11:36,630
+تمام، الآن بدي أعرف مصطلح جديد Cardinality للـ A
+
+164
+00:11:36,630 --> 00:11:43,110
+أقل من الـ Cardinality للـ B بده يعرف مصطلح جديد 
+
+165
+00:11:43,110 --> 00:11:47,570
+حاولنا نتحرر من العلاقات اللي احنا عارفينها أصغر
+
+166
+00:11:47,570 --> 00:11:51,070
+من تبعة العدد الحقيقية نتحرر منها، أنا عندي مفهوم
+
+167
+00:11:51,070 --> 00:11:57,530
+جديد بيستخدم بس نفس الرمز هيك نفكر كيف بده يعرفها
+
+168
+00:11:57,530 --> 00:12:01,990
+بده يعرفها بدلالات مصطلح اللي فوق زاد مصطلح آخر، فهذه 
+
+169
+00:12:01,990 --> 00:12:08,410
+تكافئ أن Cardinality للـ A أصغر من أو تساوي
+
+170
+00:12:08,410 --> 00:12:18,370
+Cardinality للـ B and Cardinality لل A لا تساوي
+
+171
+00:12:18,370 --> 00:12:25,640
+Cardinality لل B زي احسنتي، احنا بيقولوا الوقتش
+
+172
+00:12:25,640 --> 00:12:29,140
+بتكون Proper Subset إذا هي Subset ولا تساوي على
+
+173
+00:12:29,140 --> 00:12:34,580
+نفس النموذج فأنت ماتخلكيش أنت ملزقة أو معلقة
+
+174
+00:12:34,580 --> 00:12:36,960
+بالتعريف القديم أصغر من أو يساوي تبع الأعداد بهذا
+
+175
+00:12:36,960 --> 00:12:40,690
+الشكل، لأ، فهو إيش عرفه؟ قال جيت أنا بدي أثبت أنه
+
+176
+00:12:40,690 --> 00:12:43,970
+أقعد حينما نشوف الأمثلة أنه Cardinal Number واحد
+
+177
+00:12:43,970 --> 00:12:46,550
+أصغر من Cardinal Number اتنين، إيش مطلوب أثبت؟
+
+178
+00:12:46,550 --> 00:12:49,210
+أثبت أنه أصغر منه أو يسوي، كيف بدي أثبت هو يتعريض؟
+
+179
+00:12:49,210 --> 00:12:51,770
+وكيف بدي أثبت أنه لا يسوي؟ كيف بدي أثبته؟ قاعدة
+
+180
+00:12:51,770 --> 00:12:54,950
+رقم C4، واضحيت؟ أه فاحنا هيبقى نفكر شوية بطريقة
+
+181
+00:12:54,950 --> 00:12:55,430
+مجرد
+
+182
+00:12:59,610 --> 00:13:03,790
+المثال الأول هذه في مثال مباشر، اثبت أن ال
+
+183
+00:13:03,790 --> 00:13:06,150
+Cardinality للـ N أصغر من Cardinality للـ R اللي
+
+184
+00:13:06,150 --> 00:13:14,610
+حكيناه بنثبت أن إيش فعلا هذا الكلام صحيح، مثالنا
+
+185
+00:13:14,610 --> 00:13:19,230
+الأول خليكم
+
+186
+00:13:19,230 --> 00:13:25,250
+معايا، المثال الأول أثبت أن الـ Cardinal للـ N أقل 
+
+187
+00:13:25,250 --> 00:13:28,430
+من الـ Cardinal للـ R، مطلوب مننا نعمل حاجتين أثبت
+
+188
+00:13:28,430 --> 00:13:37,990
+أنها أصغر منها و يسويها ولا تسوى، Solution بدي
+
+189
+00:13:37,990 --> 00:13:41,370
+أثبت أن الـ N أو الـ Cardinality للـ N أصغر من الـ ..
+
+190
+00:13:41,370 --> 00:13:45,710
+أو تساوي الـ Cardinal Number للـ R، خلينا نحط هذا إيش
+
+191
+00:13:45,710 --> 00:13:48,770
+الجزء الأول، واحد Cardinality
+
+192
+00:13:50,350 --> 00:13:55,410
+للـ N أصغر أو يساوي Cardinality للـ R، هذا مطلوب
+
+193
+00:13:55,410 --> 00:14:01,030
+الأول، طيب خلّي هذا الكلام صريح أه مطلوبين في ال A 
+
+194
+00:14:01,030 --> 00:14:05,850
+لأنه And بدي أدتره أدتره طيب بداجي أفسر إيش معناته
+
+195
+00:14:05,850 --> 00:14:08,150
+أن الـ Cardinality أصغر من أو تساوي أن الـ And تكافئ 
+
+196
+00:14:08,150 --> 00:14:11,610
+Subset من الـ A، مين بعرف Subset من الـ R تكافئ الـ
+
+197
+00:14:11,610 --> 00:14:18,640
+N And أنا نفسي أحسنت أه فهنا الـ And تكافئ الـ N وهي
+
+198
+00:14:18,640 --> 00:14:24,600
+Subset من الـ R على طول Implies الـ Cardinality للـ N
+
+199
+00:14:24,600 --> 00:14:30,540
+أصغر أو يساوي Cardinality للـ R، فهذه أول شيء
+
+200
+00:14:30,540 --> 00:14:35,730
+بسهولة جدا، احنا متوقعين أن الـ N Subset من الـ R، إذا
+
+201
+00:14:35,730 --> 00:14:38,290
+ما هيش أعداد عناصر الـ N أصغر أو يساوي أعداد عناصر الـ R
+
+202
+00:14:38,290 --> 00:14:42,850
+فعلا بنسجم مع توقعاتنا السابق ممتاز، الخطوة التانية 
+
+203
+00:14:42,850 --> 00:14:47,810
+بدي أثبت أن Cardinality للـ N لا تساوي الـ
+
+204
+00:14:47,810 --> 00:14:54,350
+Cardinality للـ R، هذا مطلوبنا رقم اتنين، مين عنده
+
+205
+00:14:54,350 --> 00:15:00,390
+حل؟ صحيح ليش؟
+
+206
+00:15:01,460 --> 00:15:03,740
+أثبتناها أنها إيش لو لو لو لو لو لو لو لو لو لو لو
+
+207
+00:15:03,740 --> 00:15:03,900
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+208
+00:15:03,900 --> 00:15:04,880
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+209
+00:15:04,880 --> 00:15:06,000
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+210
+00:15:06,000 --> 00:15:06,260
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+211
+00:15:06,260 --> 00:15:07,700
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+212
+00:15:07,700 --> 00:15:11,460
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+213
+00:15:11,460 --> 00:15:11,560
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+214
+00:15:11,560 --> 00:15:11,640
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+215
+00:15:11,640 --> 00:15:15,060
+لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+216
+00:15:15,060 --> 00:15:23,380
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+217
+00:15:23,380 --> 00:15:27,390
+لو لو لولات كافر واضحة هذه ولا أكتبها أه أه فهذا
+
+218
+00:15:27,390 --> 00:15:33,170
+يؤدي أن إيش الـ Cardinality للـ R لا تساوي الـ
+
+219
+00:15:33,170 --> 00:15:39,250
+Cardinality للـ N طبعا الـ N واحد و اتنين يؤدي أن
+
+220
+00:15:39,250 --> 00:15:45,470
+الـ Cardinality للـ N أصغر من الـ Cardinality للـ R
+
+221
+00:15:49,800 --> 00:15:53,240
+فيمكن هنا من زاوية أخرى لأننا وجدت عدم التساوي
+
+222
+00:15:53,240 --> 00:15:57,020
+لحاله بقول واحدة أكبر من التانية طب لما أثبت أنه
+
+223
+00:15:57,020 --> 00:15:59,860
+هي من الصغيرة اللي متوقع أن تكون الصغيرة بقول خلصت
+
+224
+00:15:59,860 --> 00:16:03,300
+طب فهي زاوية أخرى فانا بقول بيسووش بعض إذا في
+
+225
+00:16:03,300 --> 00:16:05,600
+واحدة أكبر من التانية، طب لما أعرف أن الـ Card نادر
+
+226
+00:16:05,600 --> 00:16:08,420
+الـ N هي الأصغر إذا إن هي ليش على طول هي الصغيرة
+
+227
+00:16:08,420 --> 00:16:16,510
+فهنا بدنا حاجتين بدنا حاجتين نشوف كمان مثال اثبته 
+
+228
+00:16:16,510 --> 00:16:21,630
+أن الـ Cardinality للـ N أكبر من 2017، الـ Cardinality
+
+229
+00:16:21,630 --> 00:16:24,830
+الـ Natural Number عددها أكبر من 2017، طبعا منطقي
+
+230
+00:16:24,830 --> 00:16:31,490
+ولا لأ هل هي فيها 2017 عنصر لعداد الطبيعية لأكتر
+
+231
+00:16:31,490 --> 00:16:38,090
+طبعا 2017 للـ N احنا في 2017 في نهايته بس هي خصوص في
+
+232
+00:16:38,090 --> 00:16:41,310
+2017 يعني هي عدد يعني مش مش قضية
+
+233
+00:16:44,730 --> 00:16:50,990
+تمام، كيف بدنا نشتغل؟ في عندنا مجموعة هي الـ N وفي
+
+234
+00:16:50,990 --> 00:16:53,930
+عندنا Cardinal Number 2017، هذا Cardinal Number 
+
+235
+00:16:53,930 --> 00:16:57,870
+فعشان أشتغل بدي أجيب مجموعات فإذا أول شي بدي أجيب 
+
+236
+00:16:57,870 --> 00:17:02,990
+مجموعة وكافة اللي قاهش اللي هو اللي قاهش 2017 إن 
+
+237
+00:17:02,990 --> 00:17:09,450
+2017 كيف تسوى 2017 هذا المثال الرقم 2، Fa solution
+
+238
+00:17:09,450 --> 00:17:13,730
+أقوله Let A تساوي بس اختصار عشان ماتامش أكتبله
+
+239
+00:17:13,730 --> 00:17:19,950
+2017 وانسى الـ 17 خلاص ساميها A فعلى طول Then 
+
+240
+00:17:19,950 --> 00:17:28,990
+Cardinality للـ A تساوي 2017 أه بدنا نشتغل نفس 
+
+241
+00:17:28,990 --> 00:17:32,870
+العملية خطوطين واحد
+
+242
+00:17:34,400 --> 00:17:40,300
+بدي أثبت أن Cardinality للـ A أقل أو تساوي الـ 
+
+243
+00:17:40,300 --> 00:17:47,400
+Cardinality للـ N هذا المطلوب الأول فبشبت
+
+244
+00:17:47,400 --> 00:17:52,650
+أسأل نفسي هل الـ A تكافئ Subset من الـ N ومين هي؟ هي
+
+245
+00:17:52,650 --> 00:17:56,090
+نفسها تكافئ نفسها صحيح فإذا هنا برضه على نفس 
+
+246
+00:17:56,090 --> 00:18:01,430
+المنوال A تكافئ الـ A وهي Subset من الـ N Implies 
+
+247
+00:18:01,430 --> 00:18:07,390
+Cardinality للـ A أقل أو يساوي Cardinality للـ N 
+
+248
+00:18:07,390 --> 00:18:15,910
+أيوة الخطوة التانية Cardinality للـ A لا تساوي
+
+249
+00:18:15,910 --> 00:18:25,850
+Cardinality للـ N كيف نثبتها؟ أحسنتِ، ممتاز، زي
+
+250
+00:18:25,850 --> 00:18:29,030
+عديك ما زالت Denumerable و Undenumerable، هذه على طول فبنقول 
+
+251
+00:18:29,030 --> 00:18:40,110
+له الـ A is finite and N is infinite implies الـ A
+
+252
+00:18:40,110 --> 00:18:48,630
+لا تكافئ الـ N وهذا يؤدي إن Cardinality للـ A لا
+
+253
+00:18:48,630 --> 00:18:52,290
+تساوي Cardinality للـ N
+
+254
+00:19:02,090 --> 00:19:08,630
+تمام الآن واحد و اتنين Implies الـ 2017 اللي
+
+255
+00:19:08,630 --> 00:19:14,890
+هي Cardinality للـ A أقل من Cardinality للـ N
+
+256
+00:19:14,890 --> 00:19:20,570
+بالتأكيد فإذا هنا مع دول المثاليين ومضحكتنا الصورة
+
+257
+00:19:20,570 --> 00:19:24,690
+كيف نثبت علاقة أصغر من فيها مطلوبين نثبت أنه في 
+
+258
+00:19:24,690 --> 00:19:29,050
+علاقة أصغر من أو يساوي تبقى للتعريف وفي عدم تساوي 
+
+259
+00:19:29,050 --> 00:19:37,850
+عدم تساوي شرطين عشان نوصل لهذه الصورة أي سؤال نشوف
+
+260
+00:19:37,850 --> 00:19:44,370
+مثال على نفس الموضوع لكن من زوايا أخرى Let A and B 
+
+261
+00:19:44,370 --> 00:19:49,330
+be two sets prove that يكتب لنا Cardinality
+
+262
+00:19:49,330 --> 00:19:52,950
+لمجموعة أصغر أو يساوي بمفهوم جديد بقول Cardinality
+
+263
+00:19:52,950 --> 00:19:56,910
+ل A أقل أو تساوي بـ F and only if ممكن يستخدم كتعريف
+
+264
+00:19:56,910 --> 00:20:00,190
+لأن فـ And only if there exists an injection إذا
+
+265
+00:20:00,190 --> 00:20:04,610
+كدرت تلاقي One to One Function من A لـ B من A لـ B
+
+266
+00:20:05,260 --> 00:20:10,180
+فهنا نكتب السؤال و نبدأ نحله اللي هو طبعا جملة By
+
+267
+00:20:10,180 --> 00:20:13,600
+Conditional باتجاهين واحدة واحدة فبقول طبعا الـ A و
+
+268
+00:20:13,600 --> 00:20:19,810
+الـ B دولة مجموعات بدنا نثبت أن Cardinality للـ A
+
+269
+00:20:19,810 --> 00:20:25,990
+أقل أو تساوي Cardinality للـ B هي Statement If and 
+
+270
+00:20:25,990 --> 00:20:29,830
+only if يعني تكافئ، وقولنا مافيش فرق أكتبك أو اكتبت
+
+271
+00:20:29,830 --> 00:20:34,450
+تلات شحطات كل واحد There exists an injection A
+
+272
+00:20:34,450 --> 00:20:39,110
+Function from A to B و تكون Injection There exists 
+
+273
+00:20:39,110 --> 00:20:45,910
+a function from A to B with F is one to one فهذه
+
+274
+00:20:45,910 --> 00:20:52,490
+الجملة التانية فهذا المطلوب Solution نبدأ بالاتجاه 
+
+275
+00:20:52,490 --> 00:20:56,410
+الأول أن
+
+276
+00:20:56,410 --> 00:21:03,130
+اليسار Implies اليمين Cardinality of A أقل أو
+
+277
+00:21:03,130 --> 00:21:09,970
+يساوي Cardinality of B Implies There exists F من A
+
+278
+00:21:09,970 --> 00:21:19,150
+لـ B One to One F is one to one هذا المطلوب أه طبعا
+
+279
+00:21:19,150 --> 00:21:27,310
+على طول Assume Cardinality of A أقل أو يساوي 
+
+280
+00:21:27,310 --> 00:21:33,890
+Cardinality of B بدنا
+
+281
+00:21:33,890 --> 00:21:38,750
+نبحث عن دالة F من A ل B تكون one to one و one to one خلينا
+
+282
+00:21:38,750 --> 00:21:45,110
+نكتب we want to find a function
+
+283
+00:21:47,410 --> 00:21:53,630
+المهارات بناء من نفس الاتجاه F من A ل B such that
+
+284
+00:21:53,630 --> 00:21:55,090
+F is one to one
+
+285
+00:21:58,580 --> 00:22:03,180
+فبندور على دالة تكون one to one مهارات كررت معنا
+
+286
+00:22:03,180 --> 00:22:07,320
+عدة مرات في عدة مواضيع كيف نعمل بناء نعمل
+
+287
+00:22:07,320 --> 00:22:11,360
+construction لدالة بين مجموعتين لما كنا نثبت
+
+288
+00:22:11,360 --> 00:22:13,500
+infinite كنا من المجموع على نفسها تكون one to one
+
+289
+00:22:13,500 --> 00:22:17,040
+وليس أنتو لما نعمل اللي وكنا اللي هو التكافؤ تكون
+
+290
+00:22:17,040 --> 00:22:19,980
+one to one و أنتو بين a و b و لما نكون denumerable
+
+291
+00:22:19,980 --> 00:22:24,700
+بين المجموع و بين الان كله بدور على دالةفطبعا سؤال
+
+292
+00:22:24,700 --> 00:22:28,800
+التقليدي هل بتدور في تفادر ال calculus؟ لأ، وين
+
+293
+00:22:28,800 --> 00:22:34,540
+تدور؟ في المعطيات، في في المعطيات دوال؟ اه بما أن
+
+294
+00:22:34,540 --> 00:22:37,700
+هذه أصغر هي تستوي هذه، إذا هذه تكافئ 6 من ال B،
+
+295
+00:22:37,700 --> 00:22:41,340
+أحسنتي، اه فإذا نشتغل، شايفين فاحنا كيف الأفكار،
+
+296
+00:22:41,340 --> 00:22:43,980
+المبادرة اللي بتعلمها؟ اه هي من أول ما بدينا
+
+297
+00:22:43,980 --> 00:22:47,280
+البرهانة جملة شرطية كيف نبدأها، اشترد إن الشرط
+
+298
+00:22:47,280 --> 00:22:53,220
+صحيح و بنشتغل، اه فديعمليات أساسية لازم نتعلمها
+
+299
+00:22:53,220 --> 00:22:59,340
+مهارات لا غنى عنها في التعامل مع البراهين فإذا هنا
+
+300
+00:22:59,340 --> 00:23:04,480
+since نكتبله أو نكتبله now كل الطرق التعبير صحيحة
+
+301
+00:23:04,480 --> 00:23:10,300
+since cardinality لل
+
+302
+00:23:10,300 --> 00:23:21,810
+a أقل أو يساوي cardinality لل b we have الـ A تكافئ
+
+303
+00:23:21,810 --> 00:23:26,230
+subset أسميها B0 عشان ندربطها في الـ B أو أي أسم
+
+304
+00:23:26,230 --> 00:23:30,250
+كله صح زي ما اتفقنا مافيش اسم غلط لكن الواحد
+
+305
+00:23:30,250 --> 00:23:34,070
+بيختار اسم يكون مناسب تمام طبعا مابديش يابسن تكافئ
+
+306
+00:23:34,070 --> 00:23:43,770
+بدي دال لاسمها بمعنى there exist G من A إلى B0
+
+307
+00:23:43,770 --> 00:23:48,810
+والـ G أبيجيكشن طبعا ممكن أعبر عنها بالشكل هذا أو
+
+308
+00:23:48,810 --> 00:23:53,890
+الـ B صبصة من الـ P تمام فممكن نحاول وإن احنا ممكن
+
+309
+00:23:53,890 --> 00:23:56,790
+نعرف ال F بدالة ال GF غيرها المقاطيات مافيش
+
+310
+00:23:56,790 --> 00:24:02,210
+فبنحاول نشوف هل هي بتكفي و لا بتكفيش نعمل صورة هي
+
+311
+00:24:02,210 --> 00:24:09,130
+عندنا ال A و هي عندنا ال B و هي B0 جواها و هي اللي
+
+312
+00:24:09,130 --> 00:24:14,650
+بتكفي فانا عندي دالة من هان لهان من هان لهان أنا
+
+313
+00:24:14,650 --> 00:24:23,740
+بدي دالة الآن من A لـ B بدي أف بدي أعرف أف لت أف من
+
+314
+00:24:23,740 --> 00:24:34,860
+A ل B بي given by مرة تانية دلالتها طيب كيف؟ أف of
+
+315
+00:24:34,860 --> 00:24:43,820
+X تساوي نعملتان تان ضروري ليش؟ أحسنتي؟
+
+316
+00:24:44,420 --> 00:24:48,760
+المجال كله ايه؟ مااختلفش المجال؟ ايش اللي اختلف
+
+317
+00:24:48,760 --> 00:24:52,020
+المجال المقابل؟ اه تتذكروا في نظرية قولنا ايه
+
+318
+00:24:52,020 --> 00:24:56,300
+المجال المقابل؟ وعاء كان الوعاء صغير بدنا نكبره
+
+319
+00:24:56,300 --> 00:24:59,740
+بتتغيرش ايه؟ بتتغيرش بتبطل on to ممكن وانا بديها
+
+320
+00:24:59,740 --> 00:25:01,980
+تكون on to لأ بديها تمه one to one بحافظ عليها
+
+321
+00:25:01,980 --> 00:25:05,020
+فعطوا ال G of Aفعشان هيك انا حاول تعمل الرسمة عشان
+
+322
+00:25:05,020 --> 00:25:08,020
+اشوف احنا .. وين التغيير؟ ال domain مغطى كله ف G
+
+323
+00:25:08,020 --> 00:25:14,060
+هي G و ال F تفرجش اه لان ال G مغطية اه يعني هي في
+
+324
+00:25:14,060 --> 00:25:17,620
+.. في .. في .. امثلة سابقة كانت الدالة بإننا نكبر
+
+325
+00:25:17,620 --> 00:25:20,540
+ال domain فاضطرينا نغطي ال G ثم نقول مش مغطى لكن
+
+326
+00:25:20,540 --> 00:25:23,660
+الآن ال domain مغطى اه و بدنا يبقى one to one حتى
+
+327
+00:25:23,660 --> 00:25:30,200
+ما هي one to one اه طبعا one to one then F is one
+
+328
+00:25:30,200 --> 00:25:35,430
+to one ليش؟ لأن ال G is one to oneخلصت فهي نجينا
+
+329
+00:25:35,430 --> 00:25:45,110
+one to one function بكل سهولة أي سؤال فالأفكار
+
+330
+00:25:45,110 --> 00:25:50,970
+تتكرر معنا مرة و مرتين و تلاتة فارجو نتعلم و ان كل
+
+331
+00:25:50,970 --> 00:25:54,850
+هذه الأمثلة تصير عندنا حصيلة من الأفكار و كيف
+
+332
+00:25:54,850 --> 00:25:59,050
+نعملها و كيف نتعامل معها و ينقدر نقلد هذه الأفكار
+
+333
+00:25:59,050 --> 00:26:08,060
+للتجاه التاني الآن اتنينThere exists f من a ل b
+
+334
+00:26:08,060 --> 00:26:19,220
+with f is one to one implies cardinality لل a أقل
+
+335
+00:26:19,220 --> 00:26:24,120
+أو تساوي cardinality لل b طبعا كالعادة assume
+
+336
+00:26:24,120 --> 00:26:34,120
+there exists a function f from a to b such that F
+
+337
+00:26:34,120 --> 00:26:42,620
+is one to one بدي أثبت إنه ال A كاردينالت لل A أقل
+
+338
+00:26:42,620 --> 00:26:46,240
+أو يسوى كاردينالت لل B يعني ال A تكافئ subset من
+
+339
+00:26:46,240 --> 00:26:49,240
+ال B نعم
+
+340
+00:26:50,420 --> 00:26:53,860
+أحسنتي فهذه فكرة سابقة عملناها في المحاضرات
+
+341
+00:26:53,860 --> 00:26:57,300
+الماضية مرتين ماقدرناش نلاقي one to one and onto
+
+342
+00:26:57,300 --> 00:27:00,300
+لما أثبتنا أن الان نكوس أند نمرابون فقلنا هي تكافئ
+
+343
+00:27:00,300 --> 00:27:04,020
+من المجال المقابل ومنه اشتغلنا فانا على طول مباشرة
+
+344
+00:27:04,020 --> 00:27:11,320
+بما أن هذه one to one فهذا يقول إن ال A تكافئ F في
+
+345
+00:27:11,320 --> 00:27:15,390
+ال A الصورة على طول كانت واقعية one to one كيف
+
+346
+00:27:15,390 --> 00:27:18,390
+أخلّيها onto أصغر المجال المقابل المجال المقابل
+
+347
+00:27:18,390 --> 00:27:22,250
+يبقى من المجال المقابل المجال المقابل يبقى من
+
+348
+00:27:22,250 --> 00:27:26,090
+المجال المقابل المجال المقابل المجال المقابل
+
+349
+00:27:26,090 --> 00:27:26,370
+المجال المقابل المجال المقابل المجال المقابل
+
+350
+00:27:26,370 --> 00:27:26,670
+المجال المقابل المجال المقابل المجال المقابل
+
+351
+00:27:26,670 --> 00:27:27,690
+المجال المقابل المجال المقابل المجال المقابل
+
+352
+00:27:27,690 --> 00:27:27,970
+المجال المقابل المجال المقابل المجال المقابل
+
+353
+00:27:27,970 --> 00:27:29,210
+المجال المقابل المجال المقابل المجال المقابل
+
+354
+00:27:29,210 --> 00:27:36,530
+المجال المقابل المجفهذه من الطرق المهمة ممكن تعتمد
+
+355
+00:27:36,530 --> 00:27:41,930
+عليها عشان تثبت أن الـ A أقل أو يسوى B يكفي أننا
+
+356
+00:27:41,930 --> 00:27:46,150
+نجد دالة one to one على طول فبتصير H تكافئ المدى و
+
+357
+00:27:46,150 --> 00:27:49,770
+المدى دائما سبسط من مين؟ من المجال المقارن فهذه
+
+358
+00:27:49,770 --> 00:27:53,830
+فكرة تتكرر معنا و trick مستخدم في الرياضيات في هذا
+
+359
+00:27:53,830 --> 00:27:55,930
+الموضوع ممكن نستخدمه
+
+360
+00:28:07,230 --> 00:28:11,530
+فأرجو طريقة التفكير في الرياضيات، طريقة براهين
+
+361
+00:28:11,530 --> 00:28:15,250
+النظريات، حل الأمثلة، ففي أفكار بتتكرر، فهذه
+
+362
+00:28:15,250 --> 00:28:18,230
+المهارات لازم نتعلمها، يعني مع التكرار، نشوف كيف
+
+363
+00:28:18,230 --> 00:28:21,150
+الناس بتفكر، و بنجرب ما زال هذه الفكرة متكررة في
+
+364
+00:28:21,150 --> 00:28:25,800
+أكتر من مكان، ممكن تنجح في حل كثير من المثالفين
+
+365
+00:28:25,800 --> 00:28:29,460
+الآن هنوصل لنظرية الرئيسية Schroeder-Bernstein
+
+366
+00:28:29,460 --> 00:28:33,160
+theorem لكن قبل ذلك في عندنا نظرية تمهيدية اللي
+
+367
+00:28:33,160 --> 00:28:36,780
+هنسميها اللمّة هناخدها من غير برهان طبعا اللي بيحب
+
+368
+00:28:36,780 --> 00:28:40,620
+يتطلع على البرهان الموجود في الكتاب بقول if B is a
+
+369
+00:28:40,620 --> 00:28:46,360
+subset of A and if there exists an injection من A
+
+370
+00:28:46,360 --> 00:28:51,990
+لB then there exists a bijection من A لB هو بيقول
+
+371
+00:28:51,990 --> 00:28:55,890
+لي إذا قدرت ألاقي دالة injection من A ل subset من
+
+372
+00:28:55,890 --> 00:28:59,610
+نفسها بس عشان نشوف الصورة عشان نتصور هى في عندنا
+
+373
+00:28:59,610 --> 00:29:06,150
+ال A و ال B مالها subset منها ال B subset و أنا
+
+374
+00:29:06,150 --> 00:29:10,330
+اقدرت الاقي دالة one to one بين ال A و بين ال B
+
+375
+00:29:10,330 --> 00:29:14,050
+هذه الدالة بقدر اخليها bijection بقدر اخليها
+
+376
+00:29:14,050 --> 00:29:17,910
+bijection أو يعني اعرف منها bijection اه فانا عندى
+
+377
+00:29:17,910 --> 00:29:21,150
+اقدرت الاقي F من A ل B تكون one to one فبقدر منها
+
+378
+00:29:21,150 --> 00:29:25,410
+اولد H تكون اللى هو ايش bijection من A ل B فهذه
+
+379
+00:29:25,410 --> 00:29:29,550
+اللى ما اللى هنعتمد عليها في برهان النظرية القادمة
+
+380
+00:29:29,550 --> 00:29:32,630
+النظرية
+
+381
+00:29:32,630 --> 00:29:38,090
+الرئيسية نظرية فكرتها كالتالي خلّينا نشوف و احنا
+
+382
+00:29:38,090 --> 00:29:46,670
+هنوصله و بعدين أقرأها بشكل تفصيل هذه
+
+383
+00:29:46,670 --> 00:29:51,850
+النظرية ال trick مشهور في الرياضيات يستخدم كثيرا
+
+384
+00:29:51,850 --> 00:29:54,690
+طبعا في موضوع متعدد احنا هنستخدمه هنا في موضوع
+
+385
+00:29:54,690 --> 00:30:00,170
+محدد لو احنا في التحليل الحقيقي او في ال calculus
+
+386
+00:30:00,170 --> 00:30:06,440
+بدنا نثبت ان X تساوي Y مثلًا في بعض الأحيان ماقدرش
+
+387
+00:30:06,440 --> 00:30:11,400
+أوصل بشكل مباشر فهذه أحيانًا بنعملها بالصورة
+
+388
+00:30:11,400 --> 00:30:17,780
+التالية إن ال X أقل أو تساوي ال Y أن Y أقل أو
+
+389
+00:30:17,780 --> 00:30:24,300
+تساوي X هذا الـ trick المشهور بقدرش انا اعمل تساوي
+
+390
+00:30:24,300 --> 00:30:29,140
+لكن بعمل متباينتين فالأول أصغر أو يساوي التاني و
+
+391
+00:30:29,140 --> 00:30:32,020
+التاني أصغر أو يساوي الأول بتكون انتهت بتكون انتهت
+
+392
+00:30:32,020 --> 00:30:35,420
+العملية بيصير في عندي ايش تساوي بيصير عندنا تساوي
+
+393
+00:30:35,420 --> 00:30:38,450
+فاحنا نفس القضية الآن عشان اثبت ان ال cardinal
+
+394
+00:30:38,450 --> 00:30:41,550
+number لل A بي ساوي ال cardinal number لل B هثبت
+
+395
+00:30:41,550 --> 00:30:46,010
+ان هذا اقل من او يساوي التاني و التاني اقل او
+
+396
+00:30:46,010 --> 00:30:51,650
+يساوي الاول فحنروح بهذه الصورة لكن جال ما نشتغل
+
+397
+00:30:51,650 --> 00:30:54,450
+على ال cardinal number هنشتغل على مجموعات لان ال
+
+398
+00:30:54,450 --> 00:30:55,370
+cardinal number مجموعة
+
+399
+00:30:58,210 --> 00:31:01,090
+عشان أثبت التساويش بأننا نتكافئ لـ number متساويين
+
+400
+00:31:01,090 --> 00:31:05,090
+يعني A تكافئ الـ B فبتثبت هذه خلّيني أكتبها بنفس
+
+401
+00:31:05,090 --> 00:31:07,670
+الشغل عشان أعطيكوا الفكرة الرئيسية وبعدين نقرأها
+
+402
+00:31:07,670 --> 00:31:16,230
+مع بعض كيف بتثبت هذه؟ هثبت أن الـ A تكافئ B0
+
+403
+00:31:16,230 --> 00:31:22,480
+subset من الـ B ما عيش معناته؟ ان هذه قصتي أصغر أوي
+
+404
+00:31:22,480 --> 00:31:27,000
+السوية و ايش هأعمل؟ و أثبت أن الـ B تكافئ sub H A0
+
+405
+00:31:27,000 --> 00:31:31,940
+sub 6 مليون من الـ A فهذه ملخص النظرية واضحة؟
+
+406
+00:31:31,940 --> 00:31:38,060
+واضحة التناظر؟ واضحة ولا مش واضح؟ واضحة؟ خلاص نقرأ
+
+407
+00:31:38,060 --> 00:31:45,180
+النظرية الـ A
+
+408
+00:31:45,180 --> 00:31:49,580
+تكافئ
+
+409
+00:31:49,580 --> 00:31:57,140
+subset من ال B و ال B تكافئ
+
+410
+00:31:57,140 --> 00:31:58,260
+subset من ال A
+
+411
+00:32:03,400 --> 00:32:06,120
+النظرية جاية بهذا التجاه وليس بالتكافئة لكن هي نفس
+
+412
+00:32:06,120 --> 00:32:09,160
+العملية جاية بهذا التجاه النظرية هيك معناه النظرية
+
+413
+00:32:09,160 --> 00:32:16,200
+بسبب هيك بدت يعمل نظرية ال proof خلينا
+
+414
+00:32:16,200 --> 00:32:20,260
+نكتب النص نظرية
+
+415
+00:32:20,260 --> 00:32:26,680
+6 1 أول نظرية في هذا ال chapter طبعا النظرية بهذا
+
+416
+00:32:26,680 --> 00:32:28,680
+الصورة ال proof
+
+417
+00:32:33,650 --> 00:32:38,330
+طبعا هناخد ان كل الشرط صحيح ال a و ال b sets
+
+418
+00:32:38,330 --> 00:32:48,910
+فهنقوله هنا assume او let assume a and b are sets
+
+419
+00:32:48,910 --> 00:32:57,150
+such that ايش بتقولي ال a تكافئ نسميها a b not
+
+420
+00:33:01,560 --> 00:33:09,200
+و هي subset من ال B and ال B تكافئ A not subset من 
+
+421
+00:33:09,200 --> 00:33:19,400
+الـ A خلصنا اه اه بدنا نثبت الآن we will prove that
+
+422
+00:33:19,400 --> 00:33:25,260
+الـ A تكافئ الـ B الـ A تكافئ الـ B
+
+423
+00:33:32,140 --> 00:33:34,880
+أه فبنثبت أن الـ A تكافئ الـ B عم بدنا Byjection
+
+424
+00:33:34,880 --> 00:33:39,800
+أه طبعًا عشان أسفيد من اللمّة اللمّة بتقول إذا قدرت
+
+425
+00:33:39,800 --> 00:33:44,500
+تلاقي one to one بين مجموعة و subset منها بتكون
+
+426
+00:33:44,500 --> 00:33:48,140
+خلاص الـ Byjection انتهت لأن هنا طبعًا ليش اللمّة
+
+427
+00:33:48,140 --> 00:33:51,880
+مهمة لأنه بوفر بدل ما أنا أقعد أدور ع الدالة تكون
+
+428
+00:33:51,880 --> 00:33:54,440
+بدي أنا إياها one to one و أنتوا بلس الوقت بكوني
+
+429
+00:33:54,440 --> 00:33:56,500
+مركز بسعى لإن تكونوا one to one و الباقي بيجيني
+
+430
+00:33:56,500 --> 00:34:00,790
+أوتوماتيك بيجيني بشكل مباشر من النظرية فالآن أنا
+
+431
+00:34:00,790 --> 00:34:04,830
+عشان أخفف عن نفسي واخفف المتطلبات اللي مطلوبة من
+
+432
+00:34:04,830 --> 00:34:08,790
+الدالة اللي بحاول أعملها تصميم بحاول أكوّنها
+
+433
+00:34:08,790 --> 00:34:12,610
+وأسفيد أنه بس أركز على one to one بدنا نحاول نشوف
+
+434
+00:34:12,610 --> 00:34:15,790
+إيش المواطيات اللي عندي احنا بنثبت أن الـ A تكافئ
+
+435
+00:34:15,790 --> 00:34:20,490
+الـ B فبدنا one to one and onto الدالة من A لـ B طب
+
+436
+00:34:20,490 --> 00:34:25,300
+هل الـ B صفصت من الـ A أو الـ A صفصت من الـ B؟ لأ لأ،
+
+437
+00:34:25,300 --> 00:34:29,720
+مين فيه subset من بعض؟ الـ A0 لو قدرت أثبت أن الـ
+
+438
+00:34:29,720 --> 00:34:33,840
+A تكافئ الـ A0 خلصنا لأنه transitive العملية فاحنا
+
+439
+00:34:33,840 --> 00:34:41,640
+هنثبت أن الـ A تكافئ الـ A0 الحقيقة we will prove
+
+440
+00:34:41,640 --> 00:34:47,610
+that A تكافئ الـ A0 على طول و بالـ Transit بتكون
+
+441
+00:34:47,610 --> 00:34:50,670
+خلصت العملية واضحكت؟ ليش بدلت بالـ A0؟ ليش بعد الـ
+
+442
+00:34:50,670 --> 00:34:53,610
+A0 تعامله أسهل؟ عشان بيستخدم اللي .. لأن الـ A0
+
+443
+00:34:53,610 --> 00:34:57,630
+subset من مين؟ من الـ A ممتاز، بدنا دالة، هنعرف
+
+444
+00:34:57,630 --> 00:35:01,330
+دالة من A لـ A0 تكون one to one و bijection أه،
+
+445
+00:35:01,330 --> 00:35:05,050
+بدنا نعتمد على مين؟ المعطيات، لأن دول المجموعات مش
+
+446
+00:35:05,050 --> 00:35:09,450
+عارفين إيش عناصرها في في المعطيات دوال؟ نعم أه،
+
+447
+00:35:09,450 --> 00:35:13,890
+جلل الـ A تكافئ الـ B0 ففي دالة من A لـ B أه، now
+
+448
+00:35:15,900 --> 00:35:21,180
+الـ A تكافئ الـ B 0 implies there exists a
+
+449
+00:35:21,180 --> 00:35:28,880
+function نسميها مثلًا main F1 من A لـ B0 by diction
+
+450
+00:35:28,880 --> 00:35:35,720
+بنفس السلوك الـ B تكافئ الـ A0 بقدر ألاقي command
+
+451
+00:35:35,720 --> 00:35:44,950
+function F2 من وين ل وين من B لـ A0 تمام نشوف كيف
+
+452
+00:35:44,950 --> 00:35:53,790
+بنعرف الآن جاهزين نعرف الدالة هعرف الدالة let f من
+
+453
+00:35:53,790 --> 00:36:04,870
+a لـ a 0 be given by بدي أعرف الـ f اه بنشوف كيف
+
+454
+00:36:04,870 --> 00:36:12,650
+بنعرفها احنا إيش فيه عندنا في عندنا هاي اللي هو الـ
+
+455
+00:36:12,650 --> 00:36:22,830
+A و جواها A0 و في عندنا هنا الـ B و جواها B0 عندنا
+
+456
+00:36:22,830 --> 00:36:32,930
+دالة F1 من A لـ B0 هذه F1 و في عندنا دالة F2 من B لـ
+
+457
+00:36:32,930 --> 00:36:42,320
+A0 و في عندنا دالة من B لـ A0 هذه F2 فانا بتبدأ من
+
+458
+00:36:42,320 --> 00:36:48,420
+A وارجع للـ A0 إيش ممكن أعمل؟ composition احسنتم
+
+459
+00:36:48,420 --> 00:36:58,010
+فاحنا هنعرف F of X تساوي من .. هنبدأ أول شي تكون F1 و
+
+460
+00:36:58,010 --> 00:37:04,030
+بعدين F2 F1 تاخدها من A لـ B حتى لو B0 الـ B0 جوجل
+
+461
+00:37:04,030 --> 00:37:10,470
+هو الـ B و بعدين نرجحها تاني F of X F2 بها ده
+
+462
+00:37:10,470 --> 00:37:15,730
+الشكل اه طبعًا إذا هذا الصورة مش واضحة كثير هي
+
+463
+00:37:15,730 --> 00:37:23,530
+الصورة هيعني إيه؟ هنوديها F1
+
+464
+00:37:23,530 --> 00:37:29,050
+بتوديها لمين؟ لـ B0 اللي هي جزء من الـ B و الـ B
+
+465
+00:37:29,050 --> 00:37:35,930
+أكبر و بعدين الـ F2 بترجح لمين؟ لـ A0 تمام 100% اه
+
+466
+00:37:35,930 --> 00:37:39,430
+فطبعًا الـ gate حثبت ان هذه one to one و يكفي لأن
+
+467
+00:37:39,430 --> 00:37:43,110
+صارت عندي one to one من A لـ subset منها و الـ B
+
+468
+00:37:43,110 --> 00:37:46,910
+فعطول بقدر ألاقي الـ bijection اه F is one to one
+
+469
+00:37:50,380 --> 00:37:55,600
+فناخد عنصرين X1 و X2 تنتمي لـ A
+
+470
+00:38:06,660 --> 00:38:11,540
+أه طبعًا كان الصعوبة كيف .. يعني لو أنه .. أخليها
+
+471
+00:38:11,540 --> 00:38:14,640
+تكون one to one لإن أنتوا في صعوبة ليش لأن هنا
+
+472
+00:38:14,640 --> 00:38:18,600
+الدالة بتاخدش .. بتغطيش كل الـ B بس عند الـ B زي
+
+473
+00:38:18,600 --> 00:38:21,280
+الوضع الجزر فلكن هنا اللي ما هي اللي بيدي تساعدني
+
+474
+00:38:21,280 --> 00:38:26,900
+بيدي أتكمل العمل such that F of X1 تساوي F of X2
+
+475
+00:38:26,900 --> 00:38:33,120
+بداية إثبات الـ one to one بعدها كيش بنعمل؟ بنستخدم
+
+476
+00:38:33,120 --> 00:38:43,510
+القاعدة التعريف فهذا يؤدي F2 of F1 of X1 تساوي F2 
+
+477
+00:38:43,510 --> 00:38:46,190
+of F1 of X1
+
+478
+00:38:52,460 --> 00:38:58,620
+فطبعًا هنا X1 و X2 عندهم عدة ظلمات مخبيين تحتهم
+
+479
+00:38:58,620 --> 00:39:03,480
+نتخلص منهم بالترتيب الصحيح فطبعًا أول شيء أن الـ F2
+
+480
+00:39:03,480 --> 00:39:06,720
+is one to one فلازم الـ جو يساوي الجو فبنطلع عليها
+
+481
+00:39:06,720 --> 00:39:12,380
+كأن هذي Y1 و هذي Y2 فالآن هذا يؤدي أن F1 of X1
+
+482
+00:39:12,380 --> 00:39:19,470
+تساوي F1 of X2 ليش؟ لأن F2 is one to one عم تبقين؟
+
+483
+00:39:19,470 --> 00:39:22,070
+ليش الـ F2 1 to 1؟ لأنه بيبقى rejection مش بس 1 to
+
+484
+00:39:22,070 --> 00:39:26,210
+1 اه و الآن الـ F1 برضه 1 to 1 بيدين انه X1 تسوى X2
+
+485
+00:39:26,210 --> 00:39:36,090
+لأنه الـ F1 is 1 to 1 اه thus F is 1 to 1 اه لجيت
+
+486
+00:39:36,090 --> 00:39:40,190
+one to one function من مجموعة لصفة ست منها الآن by
+
+487
+00:39:40,190 --> 00:39:45,070
+لمّة لمّة
+
+488
+00:39:45,070 --> 00:39:48,050
+أظن 6 1 رقمها اه
+
+489
+00:39:50,090 --> 00:39:55,890
+there exists H من A لـ A0 تكون bijection وهو
+
+490
+00:39:55,890 --> 00:40:07,310
+المطلوب تمام
+
+491
+00:40:07,310 --> 00:40:11,950
+نتيجة الكلام اللي حكيناه هذا التعبير بلغة
+
+492
+00:40:11,950 --> 00:40:15,570
+المجموعات التعبير بلغة الـ cardinal numbers و هنا
+
+493
+00:40:15,570 --> 00:40:18,710
+يعني زي ما حكينا هذا الشبطر نفس الكلام اللي كنا
+
+494
+00:40:18,710 --> 00:40:21,730
+بنشرحه و بنتحدث عنه كثير من الصلاحات في شبطر خمسة
+
+495
+00:40:21,730 --> 00:40:24,590
+بس بنحكيها بلغة الـ cardinal number فهنا بقول if a
+
+496
+00:40:24,590 --> 00:40:28,630
+and b are such that cardinal number of a أقل أو
+
+497
+00:40:28,630 --> 00:40:31,070
+يساوي cardinal number of b كتبته في البداية و
+
+498
+00:40:31,070 --> 00:40:33,530
+cardinal number of b أقل أو يساوي cardinal number
+
+499
+00:40:33,530 --> 00:40:38,400
+of a فالتانية متساوي إذا X أقل تسوى Y و Y أقل تسوى
+
+500
+00:40:38,400 --> 00:40:42,440
+X فـ X تسوى Y نفس الكلام تمامًا فهذه نتيجة مباشرة
+
+501
+00:40:42,440 --> 00:40:46,060
+واضحة
+
+502
+00:40:46,060 --> 00:40:50,500
+أه؟ بدأت أوضح؟ واضحة جدًا على طول من نظري فعلًا
+
+503
+00:40:50,500 --> 00:40:55,760
+نتيجة الآن هنحاول نجاوب في هذا الـ section على
+
+504
+00:40:55,760 --> 00:41:00,760
+السؤال التالي هلجتنا فيه أن الـ cardinal number
+
+505
+00:41:00,760 --> 00:41:06,130
+تحدثنا عن ترتيبهم تقريبًا خلصنا هنا خلينا نعمل
+
+506
+00:41:06,130 --> 00:41:09,570
+الصورة التالية أرجو التركيز معي عشان نفهم مش اللي
+
+507
+00:41:09,570 --> 00:41:16,590
+بنعمله هلجت لو قلنا لكم مين أصغر cardinal number؟
+
+508
+00:41:16,590 --> 00:41:20,430
+الصفر، أه لسه مش أنتوا مش تعبديوا، الصفر، أه فإنها
+
+509
+00:41:20,430 --> 00:41:25,510
+جت الصفر أصغر من الواحد أصغر من التاني أصغر أصغر
+
+510
+00:41:25,510 --> 00:41:32,470
+أصغر من الـ cardinality للـ N أصغر من cardinality للـ
+
+511
+00:41:32,470 --> 00:41:37,890
+R فالسؤال في مجموعة الـ cardinality إيها أكبر من
+
+512
+00:41:37,890 --> 00:41:45,270
+cardinality للـ R؟ في .. أكبر شيء بتعرفوه .. أقول
+
+513
+00:41:45,270 --> 00:41:48,970
+أكبر شيء بعرفه أنا .. لأ في .. حنث بتانه في .. و في
+
+514
+00:41:48,970 --> 00:41:52,110
+هدول ليش بيمتدوا .. ما بيجفوش .. فيش سقف .. كل
+
+515
+00:41:52,110 --> 00:41:55,790
+cardinal number في cardinal number أكبر منه .. كل
+
+516
+00:41:55,790 --> 00:42:00,970
+cardinal number في عدد أصلي أكبر منه فهذه يمكن اللي
+
+517
+00:42:00,970 --> 00:42:04,430
+هو اللي بدي احنا نعمله فطبعًا cardinal number of a
+
+518
+00:42:04,430 --> 00:42:06,610
+power set إيش اللي بيكبر المجموعة ناخد الـ power
+
+519
+00:42:06,610 --> 00:42:09,410
+set تبعتها إذا مجموعة إذا عندكوا الـ R كبيرة كثير
+
+520
+00:42:09,410 --> 00:42:13,150
+خد الـ power of R شوفوا إيش بيصير تمام و في عندنا
+
+521
+00:42:13,150 --> 00:42:15,130
+اللي هو نظرية contours theorem
+
+522
+00:42:20,880 --> 00:42:25,280
+النظرية بتقول if X is a set then cardinality للـ X
+
+523
+00:42:25,280 --> 00:42:31,340
+بشكل عام أقل من cardinality
+
+524
+00:42:31,340 --> 00:42:40,540
+للـ power of X يمكن أنا نشر
+
+525
+00:42:40,540 --> 00:42:44,780
+على البرهان بشكل كامل لأن نخليها للمرة الجاية لكن
+
+526
+00:42:44,780 --> 00:42:49,220
+بس بدنا نبدأ نفكر بأشياء معينة نتعود عليها لأنها
+
+527
+00:42:49,220 --> 00:42:55,000
+هتكون غريبة هتكون غريبة طبعًا احنا إيش مطلوب مننا
+
+528
+00:42:55,000 --> 00:42:57,180
+نثبت خلينا بس هيك نعمل كهامش
+
+529
+00:42:59,820 --> 00:43:03,260
+ونفكر بالطريقة الثانية عشان اللي هو المهد للمحاضرة
+
+530
+00:43:03,260 --> 00:43:09,460
+القادمة ع سبيل المثال لو أخذنا الـ X بتساوي مجموعة
+
+531
+00:43:09,460 --> 00:43:21,380
+واحد واتنين نرجع للـ power of X X
+
+532
+00:43:21,380 --> 00:43:27,640
+نفسي نعم طبعًا احنا لما كانت finite المجموعة X كان
+
+533
+00:43:27,640 --> 00:43:31,120
+الـ power of X إيش فيها 2 أُس عدد المجموعة فهذا إن
+
+534
+00:43:31,120 --> 00:43:34,080
+شاء الله هنعمّمه هنعمّمه بشكل عام حتى لو infinite
+
+535
+00:43:34,080 --> 00:43:38,380
+هنوصل بدا الشكل فالهدف طبعًا نبدأ لو أن نتصور بعض
+
+536
+00:43:38,380 --> 00:43:43,540
+الأمور فلو قلنا بهذا الشكل كيف نعرف دالة من X لـ
+
+537
+00:43:43,540 --> 00:43:49,880
+power of X كيف نعرف دالة من X لـ power of X نبدأ
+
+538
+00:43:49,880 --> 00:43:56,390
+نفكر فيهم للوقت لو أنا عرفنا دالة F من X the power
+
+539
+00:43:56,390 --> 00:44:04,630
+of x by f of x تساوي مجموعة الـ X غريبة ده اللي قد
+
+540
+00:44:04,630 --> 00:44:11,770
+شوية خلينا تتخمر منها اليوم السبت طبعًا احسن لأ وين
+
+541
+00:44:11,770 --> 00:44:15,770
+هذي وين هذي بالـ power صح يعني كيف عندي هنا f
+
+542
+00:44:15,770 --> 00:44:19,210
+الواحد إيش بتساوي مجموعة الـ واحد تنتمي هنا ولا
+
+543
+00:44:19,210 --> 00:44:24,660
+ما تنتميش اه f التنين مجموعة التنين إيش رأيكوا
+
+544
+00:44:24,660 --> 00:44:28,940
+الدالة دي one to one؟ وليس أنتوا صحيح، ليست أنتوا
+
+545
+00:44:28,940 --> 00:44:31,860
+واضحة، ليست أنتوا صحيح، واضحة لأن الـ five مش صورة
+
+546
+00:44:31,860 --> 00:44:35,460
+حدى ولا الـ X صورة حدى، لكنها one to one طبعًا، هي
+
+547
+00:44:35,460 --> 00:44:41,400
+one to one، آه، الآن بقدر أتحدث عن حاجة زي إن X
+
+548
+00:44:41,400 --> 00:44:47,900
+تنتمي للـ F of one؟ رموز غريبة، لكن منطقية صارت،
+
+549
+00:44:47,900 --> 00:44:53,590
+صح؟ مش الـ F of one مجموعة؟ عشان نفهم البرهان تنتمي
+
+550
+00:44:53,590 --> 00:44:59,370
+أو لا تنتمي طبعًا الواحد تنتمي نعم اي اي لو answer
+
+551
+00:44:59,370 --> 00:45:04,990
+ما يعني أنا جيت لك و قولت لك واحد true صح اتنين
+
+552
+00:45:04,990 --> 00:45:13,450
+false تمام اه فان شاء الله طيب إذا مش واضح الك هيها
+
+553
+00:45:13,450 --> 00:45:18,050
+صح
+
+554
+00:45:18,050 --> 00:45:19,450
+واضحت
+
+555
+00:45:23,010 --> 00:45:28,450
+تمام مثال لأ لأ كابتن الـ X هذا كان مثال فشوية شوية
+
+556
+00:45:28,450 --> 00:45:30,990
+ان شاء الله عند اكتوب البرهان هحتاج عادل رموز ان
+
+557
+00:45:30,990 --> 00:45:33,390
+شاء الله يوم السبت بنرجع للموضوع واحدة مرة ثانية
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/8meu521dv0U_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/8meu521dv0U_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8826d1c8e8d2accb187f8bb6636e47a74eb1b37c
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/8meu521dv0U_postprocess.srt
@@ -0,0 +1,2228 @@
+1
+00:00:19,760 --> 00:00:24,200
+بسم الله الرحمن الرحيم ففي آخر محاضرة احنا بدأنا
+
+2
+00:00:24,200 --> 00:00:28,060
+كمقدمة سريعة على ال cardinal number خلينا نعيد على
+
+3
+00:00:28,060 --> 00:00:32,460
+السريع ف cardinal numbers and cardinal arithmetic
+
+4
+00:00:32,460 --> 00:00:37,060
+الاعداد الأصلية ممكن نعرفها وطبعا و العملات
+
+5
+00:00:37,060 --> 00:00:42,210
+الحسابية على هذه الاعدادفطبعا الأعداد اللي هو
+
+6
+00:00:42,210 --> 00:00:47,530
+الأصلية هي أعداد هنستخدمها للتعبير عن عدد عناصر
+
+7
+00:00:47,530 --> 00:00:51,670
+المجموعات طبعا مافيش نظام من الأنظمة اللي بنعرفها
+
+8
+00:00:51,670 --> 00:00:54,170
+للاعداد الطبيعية ولا الأعداد الصحيحة ولا الأعداد
+
+9
+00:00:54,170 --> 00:00:58,930
+الحقيقية بتقدر تقوم بهذا المقام وتعبر عن اللي هو
+
+10
+00:00:58,930 --> 00:01:02,430
+أعداد المجموعات بشكل عام لأن زي ما احنا شوفنا فيه
+
+11
+00:01:02,430 --> 00:01:06,510
+مجموعات infinite لكن مختلفين ففي عندنا the
+
+12
+00:01:06,510 --> 00:01:09,990
+numerable sets اللي هي عدد عناصرها بكافة عدد عناصر
+
+13
+00:01:09,990 --> 00:01:15,080
+الأنوفي نمض Numerable sets زي الـ R أو الفترة من
+
+14
+00:01:15,080 --> 00:01:18,440
+صفر لواحد وهذه Infinite وهذه Infinite لكن مختلفة
+
+15
+00:01:18,440 --> 00:01:22,620
+ماقدرش أقول إنها Infinity مثلا وهذه Infinity نفس
+
+16
+00:01:22,620 --> 00:01:26,840
+الرمز مانفعش لذلك بدنا نظام جديد من الاعداد يقدر
+
+17
+00:01:26,840 --> 00:01:31,120
+يعبر عن هذه المجموعات ويفرخ بينها ونقدر نشتر عليه
+
+18
+00:01:31,120 --> 00:01:34,260
+في عملية طبعا ما زال عملنا نظام جديد من الاعداد
+
+19
+00:01:34,260 --> 00:01:37,840
+بدنا نشوف خواصه كيف نجمع الاعداد هذه كيف نضربها
+
+20
+00:01:37,840 --> 00:01:41,980
+وبعض الأمورفطبعا احنا عرفنا اللي هو ال cardinal
+
+21
+00:01:41,980 --> 00:01:46,420
+numbers طبعا بطريقة بسيطة و مباشرة فيه أربع قواعد
+
+22
+00:01:46,420 --> 00:01:53,260
+القاعدة الأولى اللي سمناها C1الـ cardinal numbers
+
+23
+00:01:53,260 --> 00:01:58,880
+دولة أعداد خاصة بالمجموعات بتعبر عن المجموعات فكل
+
+24
+00:01:58,880 --> 00:02:05,660
+مجموعة set A يقابلها cardinal number عبرنا عنه باش
+
+25
+00:02:05,660 --> 00:02:11,670
+cardinal number of A أول أربع حروف والعكس صحيحفكل
+
+26
+00:02:11,670 --> 00:02:15,070
+مجموعة بيقبلها cardinal number وكل cardinal number
+
+27
+00:02:15,070 --> 00:02:18,630
+لازم يعبر عن مجموعة يعني مانفعش اقول مثلا ان في
+
+28
+00:02:18,630 --> 00:02:21,650
+انا عندي cardinal number بيساوي خمسة اه الخمسة دي
+
+29
+00:02:21,650 --> 00:02:26,710
+مش بتعبر عن وزن كمية معينة لأ بتعبر عن عدد عناصر
+
+30
+00:02:26,710 --> 00:02:29,970
+المجموعة لازم فمانفعش فدائما ال cardinal numbers
+
+31
+00:02:29,970 --> 00:02:35,130
+مرتبط ارتباط وثيق بعدد عناصر المجموعات فكل مجموعة
+
+32
+00:02:35,130 --> 00:02:39,210
+بقدر اشوف cardinal number بيعبر عنهاوكل cardinal
+
+33
+00:02:39,210 --> 00:02:42,570
+number لازم يكون فيه مجموعة بيعبر عنها بقى بقى بقى
+
+34
+00:02:42,570 --> 00:02:44,470
+كذا بدأت من المجموعة بقدر ألاقي ال cardinal number
+
+35
+00:02:44,470 --> 00:02:47,910
+المناسب بدأت من cardinal number بقدر ألاقي مجموعة
+
+36
+00:02:47,910 --> 00:02:54,830
+مناسبة اتعبر عنه القاعدة رقم اتنين ان المجموعة
+
+37
+00:02:54,830 --> 00:02:57,790
+الوحيدة اللي cardinality بتساوي صفر هي ال five اه
+
+38
+00:02:57,790 --> 00:03:03,860
+فاحنا عندنا ال cardinalityللمجموعة ما بتساوي صفر
+
+39
+00:03:03,860 --> 00:03:08,200
+if and only if هذه المجموعة هي الـ Phi فإذا أول
+
+40
+00:03:08,200 --> 00:03:10,800
+cardinal number نريد أن نعرف أن هو الصفر فالصفر
+
+41
+00:03:10,800 --> 00:03:13,740
+cardinal number لأنه بعبر عن مجموعة مين الـ Phi
+
+42
+00:03:13,740 --> 00:03:20,700
+المجموعة الفارقة القاعدة رقم تلاتة انه طبعا احنا
+
+43
+00:03:20,700 --> 00:03:26,630
+نعماحنا بنحاول نعمل مفهوم، نقول احنا ليش جيبنا
+
+44
+00:03:26,630 --> 00:03:29,030
+أعداد جديدة لإن الأعداد الطبيعية مش كافية، طب
+
+45
+00:03:29,030 --> 00:03:31,450
+الأعداد الطبيعية ممكن تتعبر عن المجموعات نعم إذا
+
+46
+00:03:31,450 --> 00:03:33,950
+كانت finite، لكن مابتكفيش لحالك، المشكلة في ال
+
+47
+00:03:33,950 --> 00:03:37,370
+infinite، لذلك لو كان عندنا مجموعة فيها مائة عنصر،
+
+48
+00:03:37,370 --> 00:03:40,570
+جداش cardinality تبعتها؟ مية، على طول، فكيف عبرنا
+
+49
+00:03:40,570 --> 00:03:46,310
+عنه؟ قولنا إذا ال A تكافئ أن K، فهذا يؤدي إن ال
+
+50
+00:03:46,310 --> 00:03:51,210
+cardinalityللـ A تساوي K finite على طول مباشرة
+
+51
+00:03:51,210 --> 00:03:55,850
+القاعدة الرابعة و الأخيرة أنه إذا كانت ال A تكافئ
+
+52
+00:03:55,850 --> 00:04:00,110
+ال B if and only if ال cardinality لل A تساوي ال
+
+53
+00:04:00,110 --> 00:04:05,390
+cardinality لل B فدولة أربع قواعد بيخلونا نقدر
+
+54
+00:04:05,390 --> 00:04:08,970
+نعرف ال cardinal numbers و نتعامل معاهمفالان ان
+
+55
+00:04:08,970 --> 00:04:13,990
+شاء الله هنتقل لنقطة جديدة طبعا هذا ملخص للمرة
+
+56
+00:04:13,990 --> 00:04:19,670
+الماضية الان هنتحدث عن ترتيب هذه الأرقام مين أصغر
+
+57
+00:04:19,670 --> 00:04:21,950
+من مين طبعا الصفر أصغر من واحد الواحد أصغر من
+
+58
+00:04:21,950 --> 00:04:26,010
+اتنين طب ليش ال cardinality مثلا لل natural number
+
+59
+00:04:26,010 --> 00:04:30,440
+و cardinality لل real number مين أصغر من مين؟أصغر
+
+60
+00:04:30,440 --> 00:04:33,500
+من الريال و هكذا نعبر عن هذا الموضوع بشكل طبعا نحط
+
+61
+00:04:33,500 --> 00:04:36,720
+التعريف و نشهد الكلام اللي حكيناه صح ولا مش صح انت
+
+62
+00:04:36,720 --> 00:04:40,040
+احنا قولنا انه ايش يعني زي ما حاكرت زميلاتكوا ان
+
+63
+00:04:40,040 --> 00:04:47,690
+ال cardinality لل N أصغر من ال cardinality لل Rطب
+
+64
+00:04:47,690 --> 00:04:50,110
+.. طب مين بيقول صح و مين بيقول خطأ؟ نشوف مين
+
+65
+00:04:50,110 --> 00:04:53,110
+المعيار؟ مين الحكم بينا؟ نشوف هذا الموضوع فهنا
+
+66
+00:04:53,110 --> 00:04:56,930
+الموضوع طبعا ال section التاني ordering of the
+
+67
+00:04:56,930 --> 00:05:00,190
+cardinal numbers ordering يعني ترتيب اه كيف ترتيب؟
+
+68
+00:05:00,190 --> 00:05:03,350
+مين صغير؟ مين كبير؟ مين أكبر؟ و هكذا اه و في عندنا
+
+69
+00:05:03,350 --> 00:05:07,630
+طبعا اللي هتحدث في عندنا the Schroeder-Bernstein
+
+70
+00:05:07,630 --> 00:05:11,470
+theorem في نظرية للعالمين Schroeder و Bernstein
+
+71
+00:05:13,860 --> 00:05:20,080
+فطبعا اول شي هنعمل مصطلح جديد فيه ان احنا
+
+72
+00:05:20,080 --> 00:05:25,380
+المجموعات قسمناها ل finite و infinite set و احنا
+
+73
+00:05:25,380 --> 00:05:28,760
+قلنا ال cardinal number مرتبطة في المجموعات تبقى
+
+74
+00:05:28,760 --> 00:05:34,050
+لهذا التقسيم هنقسم ال cardinal number لقسمينبرضه
+
+75
+00:05:34,050 --> 00:05:38,070
+إذا ال cardinal number بيقابل finite set هنسميه
+
+76
+00:05:38,070 --> 00:05:41,530
+finite cardinal number وإذا بيقابل infinite set
+
+77
+00:05:41,530 --> 00:05:44,530
+هنسميه transfinite مش infinite cardinal number
+
+78
+00:05:44,530 --> 00:05:47,890
+trans معناه ما بعد ال finite ما بعد ال finite
+
+79
+00:05:47,890 --> 00:05:52,210
+فهنستخدم المصطلح هذا فعنا العنوان finite and
+
+80
+00:05:52,210 --> 00:05:56,070
+transfinite cardinal number فأول حاجة a cardinal
+
+81
+00:05:56,070 --> 00:06:00,110
+number of a finite set is called a finite cardinal
+
+82
+00:06:00,110 --> 00:06:02,960
+numberأه فإذا ال cardinal number بيقابل مجموع
+
+83
+00:06:02,960 --> 00:06:06,400
+finite بيسميه finite number finite cardinal number
+
+84
+00:06:06,400 --> 00:06:10,800
+طبعا a cardinal number of an infinite set is
+
+85
+00:06:10,800 --> 00:06:14,600
+called a transfinite ما بعد ال finite ما بعد ال
+
+86
+00:06:14,600 --> 00:06:18,980
+finite إيش cardinal number في هذا المصطلح هنستخدم
+
+87
+00:06:18,980 --> 00:06:23,440
+طبعا كمثال ال zero cardinal number ولا لأ لأنه
+
+88
+00:06:23,440 --> 00:06:28,270
+بيقابل ال five finite ولا transfinitefinite الواحد
+
+89
+00:06:28,270 --> 00:06:31,370
+cardinal number صح لأنه بيقابل مين ال singleton
+
+90
+00:06:31,370 --> 00:06:35,330
+set و هو finite و لا transfinite finite طيب ال
+
+91
+00:06:35,330 --> 00:06:40,190
+cardinality لان transfinite واضحة فهذه مثال بسيطة
+
+92
+00:06:40,190 --> 00:06:43,810
+على طول لأن ليش ال N infinite و ال R برضه
+
+93
+00:06:43,810 --> 00:06:46,390
+transfinite ال cardinality تبع التواحد كذا ال
+
+94
+00:06:46,390 --> 00:06:51,370
+cardinal number بنزعج فهذه التعريف بكل بساطة و بكل
+
+95
+00:06:51,370 --> 00:06:55,550
+بشكل مباشر الآن نجي للموضوع الرئيسي و هو الاش
+
+96
+00:06:55,550 --> 00:07:03,970
+الترتيبفانا في عندى انا cardinal numbers انا انا
+
+97
+00:07:03,970 --> 00:07:08,390
+انا انا انا انا
+
+98
+00:07:08,390 --> 00:07:10,410
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+99
+00:07:10,410 --> 00:07:10,450
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+100
+00:07:10,450 --> 00:07:10,670
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+101
+00:07:10,670 --> 00:07:10,870
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+102
+00:07:10,870 --> 00:07:10,910
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+103
+00:07:10,910 --> 00:07:12,230
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+104
+00:07:12,230 --> 00:07:12,850
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+105
+00:07:12,850 --> 00:07:16,270
+انا انا انا انا اعندي الـ Cardinal numbers بجيب
+
+106
+00:07:16,270 --> 00:07:18,910
+المجموعات اللي بتقبلهم و هقارن بين المجموعات بصورة
+
+107
+00:07:18,910 --> 00:07:21,850
+معينة، فهذا الطريقة اللي احنا هنعتمدها، فعنا
+
+108
+00:07:21,850 --> 00:07:25,250
+التعريف التالت let A و B be sets، اه فعشان هيك
+
+109
+00:07:25,250 --> 00:07:28,110
+الكلام مش منفك، احنا متحدث عن Cardinal numbers،
+
+110
+00:07:28,110 --> 00:07:31,710
+لكن دايما إيش فيه؟ مجموعات، الموضوع لا ينفصل عن
+
+111
+00:07:31,710 --> 00:07:37,380
+المجموعاتبنقول إن cardinality of A is less than or
+
+112
+00:07:37,380 --> 00:07:41,400
+equal أقل أو يساوي، أيش الرمز؟ رمز أصغر من أو
+
+113
+00:07:41,400 --> 00:07:43,580
+يساوي في العداد العادية، في العداد الحقيقية، يعني
+
+114
+00:07:43,580 --> 00:07:46,620
+نفس الشيء، أه بنقول ليش we write cardinality of A
+
+115
+00:07:46,620 --> 00:07:50,040
+أقل أو يساوي cardinal number of B، إذا كالعادة، في
+
+116
+00:07:50,040 --> 00:07:54,420
+أن مفهوم، في أن الرمز تبعه، بتم أن التعريف، صح؟
+
+117
+00:07:54,420 --> 00:07:57,380
+كنا دايما نعرف نحكي بعد الصوت، أه، أه، وقت إيش
+
+118
+00:07:57,380 --> 00:08:01,720
+بنقول هذا الكلام؟ if A is equibotent to a subset
+
+119
+00:08:01,720 --> 00:08:06,810
+of Bمعنى تكافئ مجموعة جزئية من الـ B فانا بتحدث عن
+
+120
+00:08:06,810 --> 00:08:13,090
+مجموعة A وهي مجموعة B بتحدث عن ال cardinal number
+
+121
+00:08:13,090 --> 00:08:17,910
+بدي أعبر عن حجم المجموعة فبدي أقول إن هذه حجم
+
+122
+00:08:17,910 --> 00:08:21,870
+المجموعة أصغر أو يساوي حجم المجموعة هذه وقت إيش
+
+123
+00:08:21,870 --> 00:08:25,590
+إذا كانت ال A تكافئ من مين؟ subset من ال B وليه
+
+124
+00:08:25,590 --> 00:08:30,630
+كنا نسميها B0 هدولة تكافئ ال Aفإيه؟ تكافئ subset
+
+125
+00:08:30,630 --> 00:08:33,790
+طبعا subset ممكن تسويها لأن subset ما جاليش proper
+
+126
+00:08:33,790 --> 00:08:37,450
+subset subset تكافئ ده subset عشان أيه أصغر من أو
+
+127
+00:08:37,450 --> 00:08:41,750
+يساوي أصغر من أو يساوي فإذا هذه أول شي علاقة أصغر
+
+128
+00:08:41,750 --> 00:08:45,750
+من أو يساوي فإذا أنا بحولها من لغة المقارنة بين
+
+129
+00:08:45,750 --> 00:08:48,910
+cardinal numbers من أعداد أصلية للمقارنة بين
+
+130
+00:08:48,910 --> 00:08:51,830
+مجموعات طبعا تكافئ ايش صار بال debijection و هكذا
+
+131
+00:08:51,830 --> 00:08:58,090
+فبنرجع للموضوع السابقتمام فهذه علاقة أصغر من أو
+
+132
+00:08:58,090 --> 00:09:02,570
+يساوي طالب يقول أصغر من مش يساوي فبقول we say that
+
+133
+00:09:02,570 --> 00:09:06,810
+cardinal of A is less than cardinality of B and
+
+134
+00:09:06,810 --> 00:09:09,790
+right نفس الإشارة بنشيل ال if تساوي نفس الرمز
+
+135
+00:09:09,790 --> 00:09:12,570
+بستخدم نفس الرمز مع الأرقام الحقيقية مع العدات
+
+136
+00:09:12,570 --> 00:09:17,330
+الحقية if وقتاش إذا هي أصغر منها أو يساويها لكن لا
+
+137
+00:09:17,330 --> 00:09:22,130
+تساوي مافيش تساوي مافيش تساوي and cardinality of A
+
+138
+00:09:22,130 --> 00:09:26,980
+لا تساوي cardinality of Bهل احنا عرفنا تساوية الـ
+
+139
+00:09:26,980 --> 00:09:29,920
+Cardinality عشان هذه نفيها؟ عرفناها
+
+140
+00:09:33,610 --> 00:09:38,050
+فإذا إيش ماله؟ إذا هي تكافئ صبصة منها ولا تكافئها
+
+141
+00:09:38,050 --> 00:09:42,290
+صارت، هي تكافئ صبصة منها ولا تكافئها نفسها، هيك
+
+142
+00:09:42,290 --> 00:09:44,930
+بده يصير، لأنه إيش معناته؟ إنه ما زال أحنا عرفنا
+
+143
+00:09:44,930 --> 00:09:47,930
+التساوي، لأ بيقولوا لا تساوي شمالها ال negation،
+
+144
+00:09:47,930 --> 00:09:50,510
+ال negation على طول، ففيش مشكلة أطلع، فإذا هذا
+
+145
+00:09:50,510 --> 00:09:53,710
+التعريف يعتبر هيك كام، فإذا هو أوش عرف أصغر من أو
+
+146
+00:09:53,710 --> 00:09:59,460
+يساويوبدلالته عرف من أصغر منه فقط أو بدلالته زاد
+
+147
+00:09:59,460 --> 00:10:04,340
+من عدم التساوي اللي هو ال negation تبع التساوي
+
+148
+00:10:04,340 --> 00:10:12,060
+تفضلي نحاول
+
+149
+00:10:12,060 --> 00:10:18,840
+نقرب الصورة ال gate نقول الأربع أصغر من الخمسة كيف
+
+150
+00:10:18,840 --> 00:10:25,170
+بدي أعرفها؟to cathy أن الأربع أصغر من الخمسة and
+
+151
+00:10:25,170 --> 00:10:28,490
+الأربع لا تساوي الخمسة هيك تقريبا بنعمل حاجة بهذا
+
+152
+00:10:28,490 --> 00:10:37,670
+الشكل هيك بدي أعمل لأن هو عرف أصغر من أو يساوي في
+
+153
+00:10:37,670 --> 00:10:42,120
+واحد، مظبوط؟أعرف أصغر من أو يساوي هو بدأ بتعرف مين
+
+154
+00:10:42,120 --> 00:10:46,000
+أصغر من أو يساوي في رقم واحد و بعدين أعرف أصغر من
+
+155
+00:10:46,000 --> 00:10:50,320
+فقط لحالها بكيف أعرفها بدلالة أصغر من أو يساوي و
+
+156
+00:10:50,320 --> 00:10:55,400
+بدلالة عدم التساوي عدم التساوي خليني أكتبها بطريقة
+
+157
+00:10:55,400 --> 00:10:59,760
+جديدة قد يكون الصورة أوضحة مش غلط خليني أشوف إيش
+
+158
+00:10:59,760 --> 00:11:05,180
+بقول هو الآن خليني أعبر عن هذا بشكل مختلف أول شي
+
+159
+00:11:05,180 --> 00:11:11,960
+واحدبنقول على أنه Cardinality للـ A أصغر أو يساوي
+
+160
+00:11:11,960 --> 00:11:16,020
+Cardinality للـ B هذا المصطلح الجديد، مظبوط؟ بدنا
+
+161
+00:11:16,020 --> 00:11:21,180
+نعرفه كيف عرفه يكافئ إذا جهش كانت الـ A إشمالها
+
+162
+00:11:21,180 --> 00:11:30,000
+تكافئ subset من الـ B هذا اختصارا، واضح؟ واضح؟
+
+163
+00:11:30,000 --> 00:11:36,630
+تمام، الآن بدي أعرف مصطلح جديد Cardinalityللـ A
+
+164
+00:11:36,630 --> 00:11:43,110
+أقل من الـ cardinality للـ B بده يعرف مصطلح جديد
+
+165
+00:11:43,110 --> 00:11:47,570
+حاولنا نتحرر من العلاقات اللي احنا عارفينها أصغر
+
+166
+00:11:47,570 --> 00:11:51,070
+من تبعة العدد الحقية نتحرر منها انا عندي مفهوم
+
+167
+00:11:51,070 --> 00:11:57,530
+جديد بيستخدم بس نفس الرمز هيك نفكر كيف بده يعرفها
+
+168
+00:11:57,530 --> 00:12:01,990
+بده يعرفها بدلات مصطلح اللي فوق زاد مصطلح آخر فهذه
+
+169
+00:12:01,990 --> 00:12:08,410
+تكافئ أن ال cardinalityللـ A أصغر من أو تساوي
+
+170
+00:12:08,410 --> 00:12:18,370
+Cardinality للـ B and Cardinality لل A لا تساوي
+
+171
+00:12:18,370 --> 00:12:25,640
+Cardinality لل Bزي احسنتى احنا بيقولوا الوقتش
+
+172
+00:12:25,640 --> 00:12:29,140
+بتكون proper subset اذا هي subset ولا تساوي على
+
+173
+00:12:29,140 --> 00:12:34,580
+نفس النموذج فانت ماتخلكيش انت ملزجة او معلقة
+
+174
+00:12:34,580 --> 00:12:36,960
+بالتعريف القديم اصغر من او يساوي تبع الاعداد بهذا
+
+175
+00:12:36,960 --> 00:12:40,690
+الشكل لأفهو أيش عرفه؟ قال جيت أنا بدي أثبت أنه
+
+176
+00:12:40,690 --> 00:12:43,970
+أقعد حينما نشوف الأمثلة أنه cardinal number واحد
+
+177
+00:12:43,970 --> 00:12:46,550
+أصغر من cardinal number اتنين، إيش مطلوب أثبت؟
+
+178
+00:12:46,550 --> 00:12:49,210
+أثبت أنه أصغر منه أو يسوي، كيف بدي أثبت هو يتعريض؟
+
+179
+00:12:49,210 --> 00:12:51,770
+وكيف بدي أثبت أنه لا يسوي؟ كيف بدي أثبته؟ قاعدة
+
+180
+00:12:51,770 --> 00:12:54,950
+رقم C4، واضحيت؟ أه فاحنا هيبقى نفكر شوية بطريقة
+
+181
+00:12:54,950 --> 00:12:55,430
+مجرد
+
+182
+00:12:59,610 --> 00:13:03,790
+المثال الأول هذه في مثال مباشر اثبت ان ال
+
+183
+00:13:03,790 --> 00:13:06,150
+cardinality لان اصغر من ال cardinality لل R اللي
+
+184
+00:13:06,150 --> 00:13:14,610
+حكيناه بنثبت ان ايش فعلا هذا الكلام صحيح مثالنا
+
+185
+00:13:14,610 --> 00:13:19,230
+الأول خليكم
+
+186
+00:13:19,230 --> 00:13:25,250
+معاياالمثال الأول اثبت أن الـ cardinal للـ N أقل
+
+187
+00:13:25,250 --> 00:13:28,430
+من ال cardinal لل R مطلوب مننا نعمل حاجتين أثبت
+
+188
+00:13:28,430 --> 00:13:37,990
+أنها أصغر منها و يسويها ولا تسوى فسلويشن بدي
+
+189
+00:13:37,990 --> 00:13:41,370
+أثبت أن ال N أو ال cardinality لل N أصغر من ال ..
+
+190
+00:13:41,370 --> 00:13:45,710
+أو تساوي ال cardinal number لل R خلينا نحط هذا إيش
+
+191
+00:13:45,710 --> 00:13:48,770
+الجزء الأول واحد cardinality
+
+192
+00:13:50,350 --> 00:13:55,410
+للأن أصغر أو يساوي cardinality لل R هذا مطلوب
+
+193
+00:13:55,410 --> 00:14:01,030
+الأول طيب خلّي هذا الكلام صريح اه مطلوبين في ال A
+
+194
+00:14:01,030 --> 00:14:05,850
+لأنه and بدي ادتره ادتره طيب بداجي افسر ايش معناته
+
+195
+00:14:05,850 --> 00:14:08,150
+ان ال cardinality اصغر من او تساوي ان ال and تكافئ
+
+196
+00:14:08,150 --> 00:14:11,610
+subset من ال A مين بعرف subset من ال R تكافئ ال
+
+197
+00:14:11,610 --> 00:14:18,640
+and انا نفسي احسنت اه فهنا ال andتكافئ ال N وهي
+
+198
+00:14:18,640 --> 00:14:24,600
+subset من ال R على طول implies ال cardinality لل N
+
+199
+00:14:24,600 --> 00:14:30,540
+أصغر أو يساوي ال cardinality لل R فهذه أول شيء
+
+200
+00:14:30,540 --> 00:14:35,730
+بسهولة جداأحنا متوقعين أن الـN subset من الـR إذا
+
+201
+00:14:35,730 --> 00:14:38,290
+ما هيش أدد عناصر الـN أصغر أو يساوي أدد عناصر الـR
+
+202
+00:14:38,290 --> 00:14:42,850
+فعلا بنسجم مع توقعاتنا السابق ممتاز الخطوة التانية
+
+203
+00:14:42,850 --> 00:14:47,810
+بدي أثبت أن ال cardinality للـN لا تساوي ال
+
+204
+00:14:47,810 --> 00:14:54,350
+cardinality للـR هذا مطلوبنا رقم اتنين مين عنده
+
+205
+00:14:54,350 --> 00:15:00,390
+حل؟ صحيح ليش؟
+
+206
+00:15:01,460 --> 00:15:03,740
+أثبتناها أنها إيش لو لو لو لو لو لو لو لو لو لو لو
+
+207
+00:15:03,740 --> 00:15:03,900
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+208
+00:15:03,900 --> 00:15:04,880
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+209
+00:15:04,880 --> 00:15:06,000
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+210
+00:15:06,000 --> 00:15:06,260
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+211
+00:15:06,260 --> 00:15:07,700
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+212
+00:15:07,700 --> 00:15:11,460
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+213
+00:15:11,460 --> 00:15:11,560
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+214
+00:15:11,560 --> 00:15:11,640
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+215
+00:15:11,640 --> 00:15:15,060
+لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+216
+00:15:15,060 --> 00:15:23,380
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+217
+00:15:23,380 --> 00:15:27,390
+لو لو لولات كافر واضحة هذه ولا اكتبها اه اه فهذا
+
+218
+00:15:27,390 --> 00:15:33,170
+يؤدي انه ايش ال cardinality لل R لا تساوي ال
+
+219
+00:15:33,170 --> 00:15:39,250
+cardinality لل N طبعا ال N واحد و اتنين يؤدي انه
+
+220
+00:15:39,250 --> 00:15:45,470
+ال cardinality لل N اصغر من ال cardinality لل R
+
+221
+00:15:49,800 --> 00:15:53,240
+فيمكن هنا من زاوية أخرى لأننا وجدت عدم التساوي
+
+222
+00:15:53,240 --> 00:15:57,020
+لحاله بقول واحدة أكبر من التانية طب لما أثبت أنه
+
+223
+00:15:57,020 --> 00:15:59,860
+هي من الصغيرة اللي متوقع أن تكون الصغيرة بقول خلصت
+
+224
+00:15:59,860 --> 00:16:03,300
+طب فهي زاوية أخرى فانا بقول بيسووش بعض إذا في
+
+225
+00:16:03,300 --> 00:16:05,600
+واحدة أكبر من التانية طب لما أعرف أن ال card نادر
+
+226
+00:16:05,600 --> 00:16:08,420
+الأن هي الأصغر إذا ان هي ليش على طول هي الصغيرة
+
+227
+00:16:08,420 --> 00:16:16,510
+فهنا بدنا حاشتين بدنا حاشتيننشوف كمان مثال اثبته
+
+228
+00:16:16,510 --> 00:16:21,630
+ان الـ cardinality لان اكبر من 2017 ال cardinality
+
+229
+00:16:21,630 --> 00:16:24,830
+ال natural number عددها اكبر من 2017 طبعا منطقي
+
+230
+00:16:24,830 --> 00:16:31,490
+ولا لأ هل هي فيها 2017 عنصر لعداد الطبيعية لأكتر
+
+231
+00:16:31,490 --> 00:16:38,090
+طبعا 2017 لان احنا في 2017 في نهايته بس هي خصوص في
+
+232
+00:16:38,090 --> 00:16:41,310
+2017 يعني هي عدد يعني مش مش قضية
+
+233
+00:16:44,730 --> 00:16:50,990
+تمام كيف بدنا نشتغل؟ في عندنا مجموعة هي الان وفي
+
+234
+00:16:50,990 --> 00:16:53,930
+عندنا cardinal number 2017 هذا cardinal number
+
+235
+00:16:53,930 --> 00:16:57,870
+فعشان أشتغل بدي أجيب مجموعات فإذا أول شي بدي أجيب
+
+236
+00:16:57,870 --> 00:17:02,990
+مجموعة وكافة اللي قاهش اللي هو اللي قاهش 2017 ان
+
+237
+00:17:02,990 --> 00:17:09,450
+2017 كيف تسوى 2017 هذا المثال الرقم 2فا solution
+
+238
+00:17:09,450 --> 00:17:13,730
+اقوله let A تساوي بس اختصار عشان ماتامش اكتبله
+
+239
+00:17:13,730 --> 00:17:19,950
+2017 وانسى ال 17 خلاص ساميها A فعلى طول then
+
+240
+00:17:19,950 --> 00:17:28,990
+cardinality لل A تساوي 2017 اه بدنا نشتغل نفس
+
+241
+00:17:28,990 --> 00:17:32,870
+العملية خطوطين واحد
+
+242
+00:17:34,400 --> 00:17:40,300
+بدي أثبت أن ال cardinality لل A أقل أو تساوي ال
+
+243
+00:17:40,300 --> 00:17:47,400
+cardinality لل N هذا المطلوب الأول فبشبت
+
+244
+00:17:47,400 --> 00:17:52,650
+أسأل نفسي هل ال A تكافئ صبصة من ال N و مين هي؟هي
+
+245
+00:17:52,650 --> 00:17:56,090
+نفسها تكافئ نفسها صحيح فإذا هنا برضه على نفس
+
+246
+00:17:56,090 --> 00:18:01,430
+المنوال A تكافئ ال A وهي subset من ال N implies
+
+247
+00:18:01,430 --> 00:18:07,390
+cardinality لل A أقل أو يساوي ال cardinality لل N
+
+248
+00:18:07,390 --> 00:18:15,910
+أيوة الخطوة التانية ال cardinality لل A لا تساوي
+
+249
+00:18:15,910 --> 00:18:25,850
+ال cardinality لل N كيف نثبتها؟أحسنتِ، ممتاز، زي
+
+250
+00:18:25,850 --> 00:18:29,030
+عديك ما زالت دينمربل لاندنمربل، هذه على طول فبنقول
+
+251
+00:18:29,030 --> 00:18:40,110
+له الـ A is finite and N is infinite implies ال A
+
+252
+00:18:40,110 --> 00:18:48,630
+لا تكافئ ال N وهذا يؤدي إن ال cardinality لل A لا
+
+253
+00:18:48,630 --> 00:18:52,290
+تساوي ال cardinality لل N
+
+254
+00:19:02,090 --> 00:19:08,630
+تمام الان واحد و اتنين implies الفين و سبعتاش اللي
+
+255
+00:19:08,630 --> 00:19:14,890
+هي ال cardinality لل a أقل من ال cardinality للأ
+
+256
+00:19:14,890 --> 00:19:20,570
+بالتأكيدفإذا هنا مع دول المثاليين ومضحكتنا الصورة
+
+257
+00:19:20,570 --> 00:19:24,690
+كيف نثبت علاقة أصغر من فيها مطلوبين نثبت أنه في
+
+258
+00:19:24,690 --> 00:19:29,050
+علاقة أصغر من أو يساوي تبقى للتعريف وفي عدم تساوي
+
+259
+00:19:29,050 --> 00:19:37,850
+عدم تساوي شرطين عشان نوصل لهذه الصورة أي سؤالنشوف
+
+260
+00:19:37,850 --> 00:19:44,370
+مثال على نفس الموضوع لكن من زوايا أخرى let a and b
+
+261
+00:19:44,370 --> 00:19:49,330
+be two sets prove that يكتب لنا cardinality
+
+262
+00:19:49,330 --> 00:19:52,950
+لمجموعة أصغر أو يساوي بمفهوم جديد بقول cardinality
+
+263
+00:19:52,950 --> 00:19:56,910
+ل a أقل أو تساوي بف and only if ممكن يستخدم كتعريف
+
+264
+00:19:56,910 --> 00:20:00,190
+لأن ف and only if there exists an injection إذا
+
+265
+00:20:00,190 --> 00:20:04,610
+كدرت تلاقي one to one function من a ل b من a ل b
+
+266
+00:20:05,260 --> 00:20:10,180
+فهنا نكتب السؤال و نبدأ نحله اللي هو طبعا جملة by
+
+267
+00:20:10,180 --> 00:20:13,600
+conditional باتجاهين واحدة واحدة فبقول طبعا ال a و
+
+268
+00:20:13,600 --> 00:20:19,810
+ال b دولة مجموعات بدنا نثبت انه cardinalityللـ A
+
+269
+00:20:19,810 --> 00:20:25,990
+أقل أو تساوي cardinality للـ B هي statement if and
+
+270
+00:20:25,990 --> 00:20:29,830
+only if يعني تكافئ وقولنا مافيش فرق اكتبك او اكتبت
+
+271
+00:20:29,830 --> 00:20:34,450
+تلات شحطات كل واحد there exists an injection a
+
+272
+00:20:34,450 --> 00:20:39,110
+function from A to B و تكون injection there exists
+
+273
+00:20:39,110 --> 00:20:45,910
+a function from A to B with F is one to one فهذه
+
+274
+00:20:45,910 --> 00:20:52,490
+الجملة التانيةفهذا المطلوب solution نبدأ بالاتجاه
+
+275
+00:20:52,490 --> 00:20:56,410
+الأول أن
+
+276
+00:20:56,410 --> 00:21:03,130
+اليسار implies اليمين cardinality of A أقل أو
+
+277
+00:21:03,130 --> 00:21:09,970
+يساوي cardinality of B implies there exists F من A
+
+278
+00:21:09,970 --> 00:21:19,150
+لB one to one F is one to one هذا المطلوبأه طبعا
+
+279
+00:21:19,150 --> 00:21:27,310
+على طول assume cardinality of A أقل او يساوي
+
+280
+00:21:27,310 --> 00:21:33,890
+cardinality of B بدنا
+
+281
+00:21:33,890 --> 00:21:38,750
+نبحث عن دالة F من A ل B تكون to one و to one خلينا
+
+282
+00:21:38,750 --> 00:21:45,110
+نكتب we want to find a function
+
+283
+00:21:47,410 --> 00:21:53,630
+المهارات بناء من نفس الاتجاه F من A ل B such that
+
+284
+00:21:53,630 --> 00:21:55,090
+F is one to one
+
+285
+00:21:58,580 --> 00:22:03,180
+فبندور على دالة تكون one to one مهارات كررت معنا
+
+286
+00:22:03,180 --> 00:22:07,320
+عدة مرات في عدة مواضيع كيف نعمل بناء نعمل
+
+287
+00:22:07,320 --> 00:22:11,360
+construction لدالة بين مجموعتين لما كنا نثبت
+
+288
+00:22:11,360 --> 00:22:13,500
+infinite كنا من المجموع على نفسها تكون one to one
+
+289
+00:22:13,500 --> 00:22:17,040
+وليس انتوا لما نعمل اللي وكنا اللي هو التكافؤ تكون
+
+290
+00:22:17,040 --> 00:22:19,980
+one to one و أنتوا بين a و b و لما نكون denomable
+
+291
+00:22:19,980 --> 00:22:24,700
+بين المجموع و بين الان كله بدور على دالةفطبعا سؤال
+
+292
+00:22:24,700 --> 00:22:28,800
+التقليدي هل بتدور في تفادر ال calculus؟ لأ، وين
+
+293
+00:22:28,800 --> 00:22:34,540
+تدور؟ في المعطيات، في في المعطيات دوال؟ اه بما أن
+
+294
+00:22:34,540 --> 00:22:37,700
+هذه أصغر هي تستوي هذه، إذا هذه تكافئ 6 من ال B،
+
+295
+00:22:37,700 --> 00:22:41,340
+أحسنتي، اه فإذا نشتغل، شايفين فاحنا كيف الأفكار،
+
+296
+00:22:41,340 --> 00:22:43,980
+المبادرة اللي بتعلمها؟ اه هي من أول ما بدينا
+
+297
+00:22:43,980 --> 00:22:47,280
+البرهانة جملة شرطية كيف نبدأها، اشترد إن الشرط
+
+298
+00:22:47,280 --> 00:22:53,220
+صحيح و بنشتغل، اه فديعمليات أساسية لازم نتعلمها
+
+299
+00:22:53,220 --> 00:22:59,340
+مهارات لاغنى عنها في التعامل مع البراهين فإذا هنا
+
+300
+00:22:59,340 --> 00:23:04,480
+since نكتبله أو نكتبله now كل الطرق التعبير صحيحة
+
+301
+00:23:04,480 --> 00:23:10,300
+since cardinality لل
+
+302
+00:23:10,300 --> 00:23:21,810
+a أقل أو يساوي cardinality لل b we haveالـ A تكافئ
+
+303
+00:23:21,810 --> 00:23:26,230
+subset أسميها B0 عشان ندربطها في الـ B أو أي أسم
+
+304
+00:23:26,230 --> 00:23:30,250
+كله صح زي ما اتفقنا مافيش اسم غلط لكن الواحد
+
+305
+00:23:30,250 --> 00:23:34,070
+بيختار اسم يكون مناسب تمام طبعا مابديش يابسن تكافئ
+
+306
+00:23:34,070 --> 00:23:43,770
+بدي دال لاسمها بمعنى there exist G من A إلى B0
+
+307
+00:23:43,770 --> 00:23:48,810
+والـ G أبيجيكشن طبعا ممكن أعبر عنها بالشكل هذاأو
+
+308
+00:23:48,810 --> 00:23:53,890
+الـ B صبصة من الـ P تمام فممكن نحاول وإن احنا ممكن
+
+309
+00:23:53,890 --> 00:23:56,790
+نعرف ال F بدالة ال GF غيرها المقاطيات مافيش
+
+310
+00:23:56,790 --> 00:24:02,210
+فبنحاول نشوف هل هي بتكفي و لا بتكفيش نعمل صورة هي
+
+311
+00:24:02,210 --> 00:24:09,130
+عندنا ال A و هي عندنا ال B و هي B0 جواها و هي اللي
+
+312
+00:24:09,130 --> 00:24:14,650
+بتكفي فانا عندي دالة من هان لهان من هان لهان أنا
+
+313
+00:24:14,650 --> 00:24:23,740
+بدي دالة الآن من Aلـ B بدي أف بدي أعرف أف لت أف من
+
+314
+00:24:23,740 --> 00:24:34,860
+A ل B بي given by مرة تانية دلالتها طيب كيف؟ أف of
+
+315
+00:24:34,860 --> 00:24:43,820
+X تساوي نعملتان تان ضروري ليش؟ أحسنتي؟
+
+316
+00:24:44,420 --> 00:24:48,760
+المجال كله ايه؟ مااختلفش المجال؟ ايش اللي اختلف
+
+317
+00:24:48,760 --> 00:24:52,020
+المجال المقابل؟ اه تتذكروا في نظرية قولنا ايه
+
+318
+00:24:52,020 --> 00:24:56,300
+المجال المقابل؟ وعاء كان الوعاء صغير بدنا نكبره
+
+319
+00:24:56,300 --> 00:24:59,740
+بتتغيرش ايه؟ بتتغيرش بتبطل on to ممكن وانا بديها
+
+320
+00:24:59,740 --> 00:25:01,980
+تكون on to لأ بديها تمه one to one بحافظ عليها
+
+321
+00:25:01,980 --> 00:25:05,020
+فعطوا ال G of Aفعشان هيك انا حاول تعمل الرسمة عشان
+
+322
+00:25:05,020 --> 00:25:08,020
+اشوف احنا .. وين التغيير؟ ال domain مغطى كله ف G
+
+323
+00:25:08,020 --> 00:25:14,060
+هي G و ال F تفرجش اه لان ال G مغطية اه يعني هي في
+
+324
+00:25:14,060 --> 00:25:17,620
+.. في .. في .. امثلة سابقة كانت الدالة بإننا نكبر
+
+325
+00:25:17,620 --> 00:25:20,540
+ال domain فاضطرينا نغطي ال G ثم نقول مش مغطى لكن
+
+326
+00:25:20,540 --> 00:25:23,660
+الآن ال domain مغطى اه و بدنا يبقى one to one حتى
+
+327
+00:25:23,660 --> 00:25:30,200
+ما هي one to one اه طبعا one to one then F is one
+
+328
+00:25:30,200 --> 00:25:35,430
+to one ليش؟ لأن ال G is one to oneخلصت فهي نجينا
+
+329
+00:25:35,430 --> 00:25:45,110
+one to one function بكل سهولة أي سؤال فالأفكار
+
+330
+00:25:45,110 --> 00:25:50,970
+تتكرر معنا مرة و مرتين و تلاتة فارجو نتعلم و ان كل
+
+331
+00:25:50,970 --> 00:25:54,850
+هذه الأمثلة تصير عندنا حصيلة من الأفكار و كيف
+
+332
+00:25:54,850 --> 00:25:59,050
+نعملها و كيف نتعامل معها و ينقدر نقلد هذه الأفكار
+
+333
+00:25:59,050 --> 00:26:08,060
+للتجاه التاني الآن اتنينThere exists f من a ل b
+
+334
+00:26:08,060 --> 00:26:19,220
+with f is one to one implies cardinality لل a أقل
+
+335
+00:26:19,220 --> 00:26:24,120
+أو تساوي cardinality لل b طبعا كالعادة assume
+
+336
+00:26:24,120 --> 00:26:34,120
+there exists a function f from a to b such thatF
+
+337
+00:26:34,120 --> 00:26:42,620
+is one to one بدي أثبت إنه ال A كاردينالت لل A أقل
+
+338
+00:26:42,620 --> 00:26:46,240
+أو يسوى كاردينالت لل B يعني ال A تكافئ subset من
+
+339
+00:26:46,240 --> 00:26:49,240
+ال B نعم
+
+340
+00:26:50,420 --> 00:26:53,860
+أحسنتي فهذه فكرة سابقة عملناها في المحاضرات
+
+341
+00:26:53,860 --> 00:26:57,300
+الماضية مرتين ماقدرناش نلاقي one to one and unto
+
+342
+00:26:57,300 --> 00:27:00,300
+لما أثبتنا أن الان نكوس أند نمرابون فقلنا هي تكافئ
+
+343
+00:27:00,300 --> 00:27:04,020
+من المجال المقابل ومنه اشتغلنا فانا على طول مباشرة
+
+344
+00:27:04,020 --> 00:27:11,320
+بما أن هذه one to one فهذا يقول إن ال A تكافئ F في
+
+345
+00:27:11,320 --> 00:27:15,390
+ال Aالصورة على طول كانت واقعية one to one كيف
+
+346
+00:27:15,390 --> 00:27:18,390
+أخلّيها on two أصغر المجال المقابل المجال المقابل
+
+347
+00:27:18,390 --> 00:27:22,250
+يبقى من المجال المقابل المجال المقابل يبقى من
+
+348
+00:27:22,250 --> 00:27:26,090
+المجال المقابل المجال المقابل المجال المقابل
+
+349
+00:27:26,090 --> 00:27:26,370
+المجال المقابل المجال المقابل المجال المقابل
+
+350
+00:27:26,370 --> 00:27:26,670
+المجال المقابل المجال المقابل المجال المقابل
+
+351
+00:27:26,670 --> 00:27:27,690
+المجال المقابل المجال المقابل المجال المقابل
+
+352
+00:27:27,690 --> 00:27:27,970
+المجال المقابل المجال المقابل المجال المقابل
+
+353
+00:27:27,970 --> 00:27:29,210
+المجال المقابل المجال المقابل المجال المقابل
+
+354
+00:27:29,210 --> 00:27:36,530
+المجال المقابل المجفهذه من الطرق المهمة ممكن تعتمد
+
+355
+00:27:36,530 --> 00:27:41,930
+عليها عشان تثبت أن الـ A أقل أو يسوى B يكفي أننا
+
+356
+00:27:41,930 --> 00:27:46,150
+نجد دالة one to one على طول فبتصير H تكافئ المدى و
+
+357
+00:27:46,150 --> 00:27:49,770
+المدى دائما سبسط من مين؟ من المجال المقارن فهذه
+
+358
+00:27:49,770 --> 00:27:53,830
+فكرة تتكرر معنا و trick مستخدم في الرياضيات في هذا
+
+359
+00:27:53,830 --> 00:27:55,930
+الموضوع ممكن نستخدمه
+
+360
+00:28:07,230 --> 00:28:11,530
+فأرجو طريقة التفكير في الرياضيات، طريقة براهين
+
+361
+00:28:11,530 --> 00:28:15,250
+النظريات، حل الأمثلة، ففي أفكار بتتكرر، فهذه
+
+362
+00:28:15,250 --> 00:28:18,230
+المهارات لازم نتعلمها، يعني مع التكرار، نشوف كيف
+
+363
+00:28:18,230 --> 00:28:21,150
+الناس بتفكر، و بنجرب ما زال هذه الفكرة متكررة في
+
+364
+00:28:21,150 --> 00:28:25,800
+أكتر من مكان، ممكن تنجح في حل كثير من المثالفين
+
+365
+00:28:25,800 --> 00:28:29,460
+الآن هنوصل لنظرية الرئيسية Schroeder-Bernstein
+
+366
+00:28:29,460 --> 00:28:33,160
+theorem لكن قبل ذلك في عندنا نظرية تمهيدية اللي
+
+367
+00:28:33,160 --> 00:28:36,780
+هنسميها اللمّة هناخدها من غير برهان طبعا اللي بيحب
+
+368
+00:28:36,780 --> 00:28:40,620
+يتطلع على البرهان الموجود في الكتاب بقول if B is a
+
+369
+00:28:40,620 --> 00:28:46,360
+subset of A and if there exists an injection من A
+
+370
+00:28:46,360 --> 00:28:51,990
+لB then there exists a bijection من A لBهو بيقول
+
+371
+00:28:51,990 --> 00:28:55,890
+لي إذا قدرت ألاقي دالة injection من A ل subset من
+
+372
+00:28:55,890 --> 00:28:59,610
+نفسها بس عشان نشوف الصورة عشان نتصور هى في عندنا
+
+373
+00:28:59,610 --> 00:29:06,150
+ال A و ال B مالها subset منها ال B subsetو انا
+
+374
+00:29:06,150 --> 00:29:10,330
+اقدرت الاقي دالة one to one بين ال A و بين ال B
+
+375
+00:29:10,330 --> 00:29:14,050
+هذه الدالة بقدر اخليها bijection بقدر اخليها
+
+376
+00:29:14,050 --> 00:29:17,910
+bijection او يعني اعرف منها bijection اه فانا عندى
+
+377
+00:29:17,910 --> 00:29:21,150
+اقدرت الاقي F من A ل B تكون one to one فبقدر منها
+
+378
+00:29:21,150 --> 00:29:25,410
+اولد H تكون اللى هو ايش bijection من A ل B فهذه
+
+379
+00:29:25,410 --> 00:29:29,550
+اللى ما اللى هنعتمد عليها في برهان النظرية القادمة
+
+380
+00:29:29,550 --> 00:29:32,630
+النظرية
+
+381
+00:29:32,630 --> 00:29:38,090
+الرئيسيةنظرية فكرتها كالتالي خلّينا نشوف و احنا
+
+382
+00:29:38,090 --> 00:29:46,670
+هنوصله و بعدين أقرأها بشكل تفصيل هذه
+
+383
+00:29:46,670 --> 00:29:51,850
+النظرية ال trick مشهور في الرياضيات يستخدم كثيرا
+
+384
+00:29:51,850 --> 00:29:54,690
+طبعا في موضوع متعدد احنا هنستخدمه هنا في موضوع
+
+385
+00:29:54,690 --> 00:30:00,170
+محدد لو احنا في التحليل الحقيقي او في ال calculus
+
+386
+00:30:00,170 --> 00:30:06,440
+بدنا نثبت ان X تساوي Yمثلًا في بعض الأحيان ماقدرش
+
+387
+00:30:06,440 --> 00:30:11,400
+أوصل بشكل مباشر فهذه أحيانًا بنعملها بالصورة
+
+388
+00:30:11,400 --> 00:30:17,780
+التالية إن ال X أقل أو تساوي ال Y أن Y أقل أو
+
+389
+00:30:17,780 --> 00:30:24,300
+تساوي Xهذا الـ trick المشهور بقدرش انا اعمل تساوي
+
+390
+00:30:24,300 --> 00:30:29,140
+لكن بعمل متباينتين فالأول أصغر أو يساوي التاني و
+
+391
+00:30:29,140 --> 00:30:32,020
+التاني أصغر أو يساوي الأول بتكون انتهت بتكون انتهت
+
+392
+00:30:32,020 --> 00:30:35,420
+العملية بيصير في عندي ايش تساوي بيصير عندنا تساوي
+
+393
+00:30:35,420 --> 00:30:38,450
+فاحنا نفس القضية الآنعشان اثبت ان ال cardinal
+
+394
+00:30:38,450 --> 00:30:41,550
+number لل A بي ساوي ال cardinal number لل B هثبت
+
+395
+00:30:41,550 --> 00:30:46,010
+ان هذا اقل من او يساوي التاني و التاني اقل او
+
+396
+00:30:46,010 --> 00:30:51,650
+يساوي الاول فحنروح بهذه الصورة لكن جال ما نشتغل
+
+397
+00:30:51,650 --> 00:30:54,450
+على ال cardinal number هنشتغل على مجموعات لان ال
+
+398
+00:30:54,450 --> 00:30:55,370
+cardinal number مجموعة
+
+399
+00:30:58,210 --> 00:31:01,090
+عشان أثبت التساويش بأننا نتكافئ لـ number متساويين
+
+400
+00:31:01,090 --> 00:31:05,090
+يعني A تكافئ الـ B فبتثبت هذه خلّيني أكتبها بنفس
+
+401
+00:31:05,090 --> 00:31:07,670
+الشغل عشان أعطيكوا الفكرة الرئيسية وبعدين نقرأها
+
+402
+00:31:07,670 --> 00:31:16,230
+مع بعض كيف بتثبت هذه؟ هثبت أن الـ A تكافئ B0
+
+403
+00:31:16,230 --> 00:31:22,480
+subset من الـ Bماعيش معناته؟ ان هذه قصتي أصغر أوي
+
+404
+00:31:22,480 --> 00:31:27,000
+السوية و ايش هأعمل؟ و أثبت أن الـ B تكافئ sub H A0
+
+405
+00:31:27,000 --> 00:31:31,940
+sub 6 مليون من الـ A فهذه ملخص النظرية واضحة؟
+
+406
+00:31:31,940 --> 00:31:38,060
+واضحة التناظر؟ واضحة ولا مش واضح؟ واضحة؟ خلاص نقرأ
+
+407
+00:31:38,060 --> 00:31:45,180
+النظريةالـ A
+
+408
+00:31:45,180 --> 00:31:49,580
+تكافئ
+
+409
+00:31:49,580 --> 00:31:57,140
+subset من ال B و ال B تكافئ
+
+410
+00:31:57,140 --> 00:31:58,260
+subset من ال A
+
+411
+00:32:03,400 --> 00:32:06,120
+النظرية جاية بهذا التجاه وليس بالتكافئة لكن هي نفس
+
+412
+00:32:06,120 --> 00:32:09,160
+العملية جاية بهذا التجاه النظرية هيك معناه النظرية
+
+413
+00:32:09,160 --> 00:32:16,200
+بسبب هيك بدت يعمل نظرية ال proof خلينا
+
+414
+00:32:16,200 --> 00:32:20,260
+نكتب النص نظرية
+
+415
+00:32:20,260 --> 00:32:26,680
+6 1 أول نظرية في هذا ال chapter طبعا النظرية بهذا
+
+416
+00:32:26,680 --> 00:32:28,680
+الصورة ال proof
+
+417
+00:32:33,650 --> 00:32:38,330
+طبعا هناخد ان كل الشرط صحيح ال a و ال b sits
+
+418
+00:32:38,330 --> 00:32:48,910
+فهنقوله هنا assume او let assume a and b are sits
+
+419
+00:32:48,910 --> 00:32:57,150
+such that ايش بتقولي ال a تكافئ نسميها a b not
+
+420
+00:33:01,560 --> 00:33:09,200
+و هي subset من ال B and ال B تكافئ A not subset من
+
+421
+00:33:09,200 --> 00:33:19,400
+ال A خلصنا اه اه بدنا نثبت الان we will prove that
+
+422
+00:33:19,400 --> 00:33:25,260
+ال A تكافئ ال B ال A تكافئ ال B
+
+423
+00:33:32,140 --> 00:33:34,880
+أه فبنثبت أن الـ A تكافئ الـ B عم بدنا Byjection
+
+424
+00:33:34,880 --> 00:33:39,800
+أه طبعا عشان أسفيد من اللمّة اللمّة بتقول إذا قدرت
+
+425
+00:33:39,800 --> 00:33:44,500
+تلاقي one to one بين مجموعة و subset منها بتكون
+
+426
+00:33:44,500 --> 00:33:48,140
+خلاص ال Byjection انتهت لأن هنا طبعا ليش اللمّة
+
+427
+00:33:48,140 --> 00:33:51,880
+مهمة لأنه بوفر بدل ما أنا أقعد أدور ع الدالة تكون
+
+428
+00:33:51,880 --> 00:33:54,440
+بدي أنا إياها one to one و أنتوا بلس الوقت بكوني
+
+429
+00:33:54,440 --> 00:33:56,500
+مركز بسعى لإن تكونوا one to one و الباقي بيجيني
+
+430
+00:33:56,500 --> 00:34:00,790
+اتوماتيك بيجيني بشكل مباشر من النظريةفالان انا
+
+431
+00:34:00,790 --> 00:34:04,830
+عشان اخفف عن نفسي واخفف المتطلبات اللى مطلوبة من
+
+432
+00:34:04,830 --> 00:34:08,790
+الدالة اللى بحاول اعملها تصميم بحاول اكوّنها
+
+433
+00:34:08,790 --> 00:34:12,610
+واسفيد انه بس اركز على one to one بدنا نحاول نشوف
+
+434
+00:34:12,610 --> 00:34:15,790
+ايش المواطيات اللى عندي احنا بنثبت ان ال A تكافئ
+
+435
+00:34:15,790 --> 00:34:20,490
+ال B فبدنا one to one and onto الدالة من A ل B طب
+
+436
+00:34:20,490 --> 00:34:25,300
+هل ال B صفصت من ال A او ال A صفصت من ال B؟ لألأ،
+
+437
+00:34:25,300 --> 00:34:29,720
+مين فيه subset من بعض؟ الـ A0 لو قدرت أثبت أن الـ
+
+438
+00:34:29,720 --> 00:34:33,840
+A تكافئ الـ A0 خلصنا لأنه transitive العملية فاحنا
+
+439
+00:34:33,840 --> 00:34:41,640
+هنثبت أن الـ A تكافئ الـ A0 الحقيقة we will prove
+
+440
+00:34:41,640 --> 00:34:47,610
+that A تكافئ الـ A0على طول و بالـ Transit بتكون
+
+441
+00:34:47,610 --> 00:34:50,670
+خلصت العملية واضحكت؟ ليش بدلت بالـ A0؟ ليش بعد الـ
+
+442
+00:34:50,670 --> 00:34:53,610
+A0 تعامله أسهل؟ عشان بيستخدم اللي .. لأن الـ A0
+
+443
+00:34:53,610 --> 00:34:57,630
+subset من مين؟ من الـ A ممتاز، بدنا دالة، هنعرف
+
+444
+00:34:57,630 --> 00:35:01,330
+دالة من A ل A0 تكون one to one و bijection أه،
+
+445
+00:35:01,330 --> 00:35:05,050
+بدنا نعتمد على مين؟ المعطيات، لأن دول المجموعات مش
+
+446
+00:35:05,050 --> 00:35:09,450
+عارفين إيش عناصرها في في المعطيات دوال؟ نعم أه،
+
+447
+00:35:09,450 --> 00:35:13,890
+جلل الـ A تكافئ الـ B0 ففي دالة من A ل B أه، now
+
+448
+00:35:15,900 --> 00:35:21,180
+الـ A تكافئ الـ B 0 implies there exists a
+
+449
+00:35:21,180 --> 00:35:28,880
+function نسميها مثلا main F1 من A ل B0 by diction
+
+450
+00:35:28,880 --> 00:35:35,720
+بنفس السلوك الـ B تكافئ ال A0 بقدر ألاقي command
+
+451
+00:35:35,720 --> 00:35:44,950
+function F2 من وين ل وين من B ل A0تمام نشوف كيف
+
+452
+00:35:44,950 --> 00:35:53,790
+بنعرف الان جاهزين نعرف الدالة هعرف الدالة let f من
+
+453
+00:35:53,790 --> 00:36:04,870
+a ل a 0 be given by بدي اعرف ال f اه بنشوف كيف
+
+454
+00:36:04,870 --> 00:36:12,650
+بنعرفها احنا ايش فيه عندنافي عندنا هاي اللي هو ال
+
+455
+00:36:12,650 --> 00:36:22,830
+A و جواها A0 و في عندنا هنا ال B و جواها B0 عندنا
+
+456
+00:36:22,830 --> 00:36:32,930
+دالة F1 من A ل B0 هذه F1 و في عندنا دالة F2 من B ل
+
+457
+00:36:32,930 --> 00:36:42,320
+A0 و في عندنا دالة من Bلـ A0 هذه F2 فانا بتبدأ من
+
+458
+00:36:42,320 --> 00:36:48,420
+A وارجع للـ A0 ايش ممكن اعمل؟ composition احسنتم
+
+459
+00:36:48,420 --> 00:36:58,010
+فاحنا هنعرف F of X تساوي من .. هنبدأ أولش تكون F1و
+
+460
+00:36:58,010 --> 00:37:04,030
+بعدين F2 F1 تاخدها من A ل B حتى لو B0 الـ B0 جوجل
+
+461
+00:37:04,030 --> 00:37:10,470
+هو الـ B و بعدين نرجحها تاني F of X F2 بها ده
+
+462
+00:37:10,470 --> 00:37:15,730
+الشكل اه طبعا اذا هذا الصورة مش واضحة كتير هي
+
+463
+00:37:15,730 --> 00:37:23,530
+الصورة هيعنى ايه؟ هنوديها F1
+
+464
+00:37:23,530 --> 00:37:29,050
+بتوديها لمين؟لـ B0 اللي هي جزء من الـ B و الـ B
+
+465
+00:37:29,050 --> 00:37:35,930
+أكبر و بعدين ال F2 بترجح لمين؟ لـ A0 تمام 100% اه
+
+466
+00:37:35,930 --> 00:37:39,430
+فطبعا الـ gate حثبت ان هذه one to one و يكفي لان
+
+467
+00:37:39,430 --> 00:37:43,110
+صارت عندي one to one من A ل subset منها و ال B
+
+468
+00:37:43,110 --> 00:37:46,910
+فعطول بقدر ألاقي ال bijection اه F is one to one
+
+469
+00:37:50,380 --> 00:37:55,600
+فناخد عنصرين X1 و X2 تنتمي لـ A
+
+470
+00:38:06,660 --> 00:38:11,540
+أه طبعا كان الصعوبة كيف .. يعني لو أنه .. أخليها
+
+471
+00:38:11,540 --> 00:38:14,640
+تكون one to one لإن أنتوا في صعوبة ليش لأن هنا
+
+472
+00:38:14,640 --> 00:38:18,600
+الدالة بتاخدش .. بتغطيش كل ال B بس عند ال B زي
+
+473
+00:38:18,600 --> 00:38:21,280
+الوضع الجزر فلكن هنا اللي ما هي اللي بيدي تساعدني
+
+474
+00:38:21,280 --> 00:38:26,900
+بيدي أتكمل العمل such that F of X1 تساوي F of X2
+
+475
+00:38:26,900 --> 00:38:33,120
+بداية إثبات ال one to one بعدها كيش بنعمل؟ بنستخدم
+
+476
+00:38:33,120 --> 00:38:43,510
+القاعدة التعريف فهذا يؤديF2 of F1 of X1 تساوي F2
+
+477
+00:38:43,510 --> 00:38:46,190
+of F1 of X1
+
+478
+00:38:52,460 --> 00:38:58,620
+فطبعا هنا X1 و X2 عندهم عدة ظلمات مخبيين تحتهم
+
+479
+00:38:58,620 --> 00:39:03,480
+نتخلص منهم بالترتيب الصحيح فطبعا أول شيء أن ال F2
+
+480
+00:39:03,480 --> 00:39:06,720
+is one to one فلازم ال جو يساوي الجو فبنطلع عليها
+
+481
+00:39:06,720 --> 00:39:12,380
+كأن هذي Y1 و هذي Y2 فالأن هذا يؤدي أن F1 of X1
+
+482
+00:39:12,380 --> 00:39:19,470
+تساوي F1 of X2 ليش؟ لأن F2 is one to oneعم تبقين؟
+
+483
+00:39:19,470 --> 00:39:22,070
+ليش ال F2 1 to 1؟ لأنه بيبقى rejection مش بس 1 to
+
+484
+00:39:22,070 --> 00:39:26,210
+1 اه و الآن ال F1 برضه 1 to 1 بيدين انه X1 تسوى X2
+
+485
+00:39:26,210 --> 00:39:36,090
+لأنه ال F1 is 1 to 1 اه thus F is 1 to 1 اه لجيت
+
+486
+00:39:36,090 --> 00:39:40,190
+one to one function من مجموعة لصفة ست منها الآن by
+
+487
+00:39:40,190 --> 00:39:45,070
+لمّة لمّة
+
+488
+00:39:45,070 --> 00:39:48,050
+أظن 6 1 رقمها اه
+
+489
+00:39:50,090 --> 00:39:55,890
+there exists H من A ل A0 تكون bijection وهو
+
+490
+00:39:55,890 --> 00:40:07,310
+المطلوب تمام
+
+491
+00:40:07,310 --> 00:40:11,950
+نتيجة الكلام اللي حكيناهفهذا التعبير بلغة
+
+492
+00:40:11,950 --> 00:40:15,570
+المجموعات التعبير بلغة ال cardinal numbers و هنا
+
+493
+00:40:15,570 --> 00:40:18,710
+يعني زي ما حكينا هذا الشبطر نفس الكلام اللي كنا
+
+494
+00:40:18,710 --> 00:40:21,730
+بنشرحه و بنتحدث عنه كتير من الصلاحات في شبطر خمسة
+
+495
+00:40:21,730 --> 00:40:24,590
+بس بنحكيها بلغة ال cardinal number فهنا بقول if a
+
+496
+00:40:24,590 --> 00:40:28,630
+and b are such that cardinal number of a أقل أو
+
+497
+00:40:28,630 --> 00:40:31,070
+يساوي cardinal number of b كتبته في البداية و
+
+498
+00:40:31,070 --> 00:40:33,530
+cardinal number of b أقل أو يساوي cardinal number
+
+499
+00:40:33,530 --> 00:40:38,400
+of a فالتانية متساويإذا X أقل تسوى Y و Y أقل تسوى
+
+500
+00:40:38,400 --> 00:40:42,440
+X فـ X تسوى Y نفس الكلام تمامًا فهذه نتيجة مباشرة
+
+501
+00:40:42,440 --> 00:40:46,060
+واضحة
+
+502
+00:40:46,060 --> 00:40:50,500
+أه؟ بدأت أوضح؟ واضحة جدًا على طول من نظري فعلا
+
+503
+00:40:50,500 --> 00:40:55,760
+نتيجة الآن هنحاول نجاوب في هذا ال section على
+
+504
+00:40:55,760 --> 00:41:00,760
+السؤال التالي هلجتنا فيه أن ال cardinal number
+
+505
+00:41:00,760 --> 00:41:06,130
+تحدثنا عن ترتيبهم تقريبًا خلصنا هناخلّينا نعمل
+
+506
+00:41:06,130 --> 00:41:09,570
+الصورة التالية أرجو التركيز معي عشان نفهم مش اللي
+
+507
+00:41:09,570 --> 00:41:16,590
+بنعمله هلجت لو قلنا لكم مين أصغر cardinal number؟
+
+508
+00:41:16,590 --> 00:41:20,430
+الصفر، أه لسه مش انتوا مش تعبديوا، الصفر، أه فإنها
+
+509
+00:41:20,430 --> 00:41:25,510
+جت الصفر أصغر من الواحد أصغر من التاني أصغر أصغر
+
+510
+00:41:25,510 --> 00:41:32,470
+أصغر من ال cardinality لل N أصغر من cardinality لل
+
+511
+00:41:32,470 --> 00:41:37,890
+Rفالسؤال في مجموعة ال cardinality إيها أكبر من
+
+512
+00:41:37,890 --> 00:41:45,270
+cardinality لل R؟ في .. أكبر شي بتعرفوه .. أقول
+
+513
+00:41:45,270 --> 00:41:48,970
+أكبر شي بعرفه أنا .. لأ في .. حنث بتانه في .. و في
+
+514
+00:41:48,970 --> 00:41:52,110
+هدول ليش بيمتدوا .. مابيجفوش .. فيش سقف .. كل
+
+515
+00:41:52,110 --> 00:41:55,790
+cardinal number في cardinal number أكبر منه .. كل
+
+516
+00:41:55,790 --> 00:42:00,970
+cardinal number فيعدد أصلي أكبر منه فهذه يمكن اللي
+
+517
+00:42:00,970 --> 00:42:04,430
+هو اللي بدي احنا نعمله فطبعا cardinal number of a
+
+518
+00:42:04,430 --> 00:42:06,610
+power set إيش اللي بيكبر المجموعة ناخد ال power
+
+519
+00:42:06,610 --> 00:42:09,410
+set تبعتها إذا مجموعة إذا عندكوا ال R كبيرة كتير
+
+520
+00:42:09,410 --> 00:42:13,150
+خد ال power of R شوفوا إيش بيصير تمام و في عندنا
+
+521
+00:42:13,150 --> 00:42:15,130
+اللي هو نظرية contours theorem
+
+522
+00:42:20,880 --> 00:42:25,280
+النظرية بتقول if X is a set then cardinality لل X
+
+523
+00:42:25,280 --> 00:42:31,340
+بشكل عام أقل من cardinality
+
+524
+00:42:31,340 --> 00:42:40,540
+لل power of Xيمكن انا نشر
+
+525
+00:42:40,540 --> 00:42:44,780
+على البرهان بشكل كامل لان نخليها للمرة الجاية لكن
+
+526
+00:42:44,780 --> 00:42:49,220
+بس بدنا نبدأ نفكر باشياء معينة نتعود عليها لانها
+
+527
+00:42:49,220 --> 00:42:55,000
+هتكون غريبة هتكون غريبة طبعا احنا ايش مطلوب مننا
+
+528
+00:42:55,000 --> 00:42:57,180
+نثبت خلينا بس هيك نعمل كهامش
+
+529
+00:42:59,820 --> 00:43:03,260
+ونفكر بالطريقة التانية عشان اللي هو المهد للمحاضرة
+
+530
+00:43:03,260 --> 00:43:09,460
+القادمة ع سبيل المثال لو أخدنا ال X بتساوي مجموعة
+
+531
+00:43:09,460 --> 00:43:21,380
+واحد واتنين نرجع لل power of X X
+
+532
+00:43:21,380 --> 00:43:27,640
+نفسي نعم طبعا احنا لما كانت finite المجموعة Xكان
+
+533
+00:43:27,640 --> 00:43:31,120
+الـ power of X إيش فيها 2 أُس عدد المجموعة فهذا إن
+
+534
+00:43:31,120 --> 00:43:34,080
+شاء الله هنعمّمه هنعمّمه بشكل عام حتى لو infinite
+
+535
+00:43:34,080 --> 00:43:38,380
+هنوصل بدا الشكل فالهدف طبعاً نبدأ لو أن نتصور بعض
+
+536
+00:43:38,380 --> 00:43:43,540
+الأمور فلو قلنا بهذا الشكل كيف نعرف دالة من X ل
+
+537
+00:43:43,540 --> 00:43:49,880
+power of X كيف نعرف دالة من X ل power of X نبدأ
+
+538
+00:43:49,880 --> 00:43:56,390
+نفكر فيهم للوقت لو أنا أعرفنا دالة F من Xthe power
+
+539
+00:43:56,390 --> 00:44:04,630
+of x by f of x تساوي مجموعة ال X غريبة ده اللي قد
+
+540
+00:44:04,630 --> 00:44:11,770
+شوية خلينا تتخمر منها اليوم السبت طبعا احسن لأ وين
+
+541
+00:44:11,770 --> 00:44:15,770
+هذي وين هذي بال power صح يعني كيف عندي هنا f
+
+542
+00:44:15,770 --> 00:44:19,210
+الواحد ايش بتساوي مجموعة ال واحد تنتمي هنا ولا
+
+543
+00:44:19,210 --> 00:44:24,660
+ماتنتميش اه f التنين مجموعة التنينإيش رأيكوا
+
+544
+00:44:24,660 --> 00:44:28,940
+الدالة دي one to one؟ وليس أنتوا صحيح، ليست أنتوا
+
+545
+00:44:28,940 --> 00:44:31,860
+واضحة، ليست أنتوا صحيح، واضحة لأن ال five مش صورة
+
+546
+00:44:31,860 --> 00:44:35,460
+حدى ولا ال X صورة حدى، لكنها one to one طبعا، هي
+
+547
+00:44:35,460 --> 00:44:41,400
+one to one، آه، الآن بقدر أتحدث عن حاجة زي إن X
+
+548
+00:44:41,400 --> 00:44:47,900
+تنتمي لل F of one؟ رموز غريبة، لكن منطقية صارت،
+
+549
+00:44:47,900 --> 00:44:53,590
+صح؟ مش ال F of one مجموعة؟عشان نفهم البرهان تنتمي
+
+550
+00:44:53,590 --> 00:44:59,370
+او لا تنتمي طبعا الواحد تنتمي نعم اي اي لو answer
+
+551
+00:44:59,370 --> 00:45:04,990
+ما يعني انا جيتلك و قولتلك واحد true صح اتنين
+
+552
+00:45:04,990 --> 00:45:13,450
+false تمام اه فان شاء الله طيب اذا مش واضحالك هيها
+
+553
+00:45:13,450 --> 00:45:18,050
+صح
+
+554
+00:45:18,050 --> 00:45:19,450
+واضحت
+
+555
+00:45:23,010 --> 00:45:28,450
+تمام مثال لأ لأ كابتن ال X هذا كان مثال فشوية شوية
+
+556
+00:45:28,450 --> 00:45:30,990
+ان شاء الله عند اكتوب البرهان هحتاج عادل رموز ان
+
+557
+00:45:30,990 --> 00:45:33,390
+شاء الله يوم السبت بنرجع للموضوع واحدة مرة ثانية
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/8meu521dv0U_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/8meu521dv0U_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..a9be0657d283153139760522796cf416d7dffe8f
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/8meu521dv0U_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3876, "start": 19.76, "end": 38.76, "text": "بسم الله الرحمن الرحيم ففي آخر محاضرة احنا بدأنا كمقدمة سريعة على ال cardinal number خلينا نعيد على السريع ف cardinal numbers and cardinal arithmetic الاعداد الأصلية ممكن نعرفها وطبعا و العملات الحسابية على هذه الاعداد", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 6156, 41185, 19753, 34740, 3714, 5016, 46958, 25720, 1975, 5016, 8315, 47525, 10721, 8315, 9122, 2304, 28543, 46007, 8608, 16572, 27884, 15844, 2423, 2920, 2071, 1230, 16490, 1211, 9957, 995, 8717, 3615, 25708, 15844, 21136, 16572, 3615, 6156, 2920, 2071, 3547, 293, 2920, 2071, 42973, 42963, 22488, 18513, 16247, 9381, 1211, 10632, 3714, 43020, 8717, 3615, 28480, 11296, 4032, 9566, 3555, 3615, 995, 4032, 18863, 42213, 9307, 21542, 3794, 16758, 10632, 15844, 29538, 42963, 22488, 18513], "avg_logprob": -0.20512355361566986, "compression_ratio": 1.7376237623762376, "no_speech_prob": 0.0, "words": [{"start": 19.76, "end": 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"فطبعا الأعداد اللي هو الأصلية هي أعداد هنستخدمها للتعبير عن عدد عناصر المجموعات طبعا مافيش نظام من الأنظمة اللي بنعرفها للاعداد الطبيعية ولا الأعداد الصحيحة ولا الأعداد الحقيقية بتقدر تقوم بهذا المقام وتعبر عن اللي هو أعداد المجموعات بشكل عام لأن زي ما احنا شوفنا فيه مجموعات infinite لكن مختلفين ففي عندنا the numerable sets اللي هي عدد عناصرها بكافة عدد عناصر الأن", "tokens": [5172, 9566, 3555, 3615, 995, 16247, 22488, 18513, 13672, 1829, 31439, 16247, 9381, 1211, 10632, 39896, 5551, 22488, 18513, 8032, 1863, 14851, 9778, 40448, 11296, 24976, 2655, 3615, 3555, 13546, 18871, 6225, 3215, 3215, 18871, 33546, 2288, 9673, 7435, 2304, 45367, 9307, 23032, 3555, 3615, 995, 19446, 41185, 8592, 8717, 19913, 10943, 9154, 16247, 1863, 19913, 46007, 13672, 1829, 44945, 3615, 28480, 11296, 5296, 15040, 22488, 18513, 41950, 21292, 3615, 10632, 49429, 16247, 22488, 18513, 31767, 5016, 1829, 5016, 3660, 49429, 16247, 22488, 18513, 21542, 38436, 4587, 10632, 39894, 28543, 2288, 6055, 4587, 20498, 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95.96, "end": 96.36, "word": " نجمع", "probability": 0.899658203125}, {"start": 96.36, "end": 96.76, "word": " الاعداد", "probability": 0.9739583333333334}, {"start": 96.76, "end": 97.0, "word": " هذه", "probability": 0.5224609375}, {"start": 97.0, "end": 97.26, "word": " كيف", "probability": 0.896728515625}, {"start": 97.26, "end": 97.84, "word": " نضربها", "probability": 0.9935302734375}, {"start": 97.84, "end": 98.78, "word": " وبعض", "probability": 0.795654296875}, {"start": 98.78, "end": 99.22, "word": " الأمور", "probability": 0.9697265625}], "temperature": 1.0}, {"id": 4, "seek": 11032, "start": 99.64, "end": 110.32, "text": "فطبعا احنا عرفنا اللي هو ال cardinal numbers طبعا بطريقة بسيطة و مباشرة فيه أربع قواعد القاعدة الأولى اللي سمناها C1", "tokens": [5172, 9566, 3555, 3615, 995, 1975, 5016, 8315, 6225, 28480, 8315, 13672, 1829, 31439, 2423, 2920, 2071, 3547, 23032, 3555, 3615, 995, 4724, 9566, 16572, 28671, 4724, 3794, 1829, 9566, 3660, 4032, 3714, 3555, 33599, 25720, 8978, 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ال infinite، لذلك لو كان عندنا مجموعة فيها مائة عنصر، جداش cardinality تبعتها؟ مية، على طول، فكيف عبرنا عنه؟ قولنا إذا ال A تكافئ أن K، فهذا يؤدي إن ال cardinality", "tokens": [39319, 8315, 44945, 5016, 995, 12610, 8717, 25957, 1211, 3714, 5172, 3224, 20498, 12399, 8717, 39648, 1975, 5016, 8315, 32239, 8592, 10874, 1829, 3555, 8315, 5551, 22488, 18513, 10874, 16254, 41891, 5296, 28814, 1863, 16247, 22488, 18513, 41950, 21292, 3615, 10632, 37893, 9122, 31845, 10632, 12399, 23032, 3555, 16247, 22488, 18513, 41950, 21292, 3615, 10632, 3714, 43020, 6055, 2655, 3615, 3555, 2288, 18871, 9673, 7435, 2304, 45367, 9307, 8717, 25957, 11933, 15730, 25961, 2655, 19362, 12399, 44381, 3714, 16758, 2655, 4117, 41185, 8592, 5296, 5016, 6027, 4117, 12399, 9673, 8592, 28820, 3660, 8978, 2423, 13785, 12399, 5296, 8848, 23275, 45164, 25961, 43242, 8315, 3714, 7435, 2304, 2407, 27884, 8978, 11296, 3714, 16373, 3660, 18871, 9381, 2288, 12399, 10874, 3215, 33599, 2920, 259, 1860, 6055, 3555, 34268, 11296, 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تبعتها؟", "probability": 0.88466796875}, {"start": 218.57, "end": 218.87, "word": " مية،", "probability": 0.7313639322916666}, {"start": 218.87, "end": 218.99, "word": " على", "probability": 0.962890625}, {"start": 218.99, "end": 219.49, "word": " طول،", "probability": 0.9431966145833334}, {"start": 219.49, "end": 220.17, "word": " فكيف", "probability": 0.7190755208333334}, {"start": 220.17, "end": 220.57, "word": " عبرنا", "probability": 0.8465169270833334}, {"start": 220.57, "end": 221.15, "word": " عنه؟", "probability": 0.9363606770833334}, {"start": 221.15, "end": 221.51, "word": " قولنا", "probability": 0.8063151041666666}, {"start": 221.51, "end": 221.73, "word": " إذا", "probability": 0.914306640625}, {"start": 221.73, "end": 221.93, "word": " ال", "probability": 0.927734375}, {"start": 221.93, "end": 222.19, "word": " A", "probability": 0.281982421875}, {"start": 222.19, "end": 223.25, "word": " تكافئ", "probability": 0.8924560546875}, {"start": 223.25, "end": 223.67, "word": " أن", "probability": 0.223388671875}, {"start": 223.67, "end": 225.25, "word": " K،", "probability": 0.840576171875}, {"start": 225.25, "end": 225.63, "word": " فهذا", "probability": 0.7328287760416666}, {"start": 225.63, "end": 225.97, "word": " يؤدي", "probability": 0.880859375}, {"start": 225.97, "end": 226.17, "word": " إن", "probability": 0.3994140625}, {"start": 226.17, "end": 226.31, "word": " ال", "probability": 0.5498046875}, {"start": 226.31, "end": 226.95, "word": " cardinality", "probability": 0.8359375}], "temperature": 1.0}, {"id": 10, "seek": 24767, "start": 227.67, "end": 247.67, "text": "للـ A تساوي K finite على طول مباشرة القاعدة الرابعة و الأخيرة أنه إذا كانت ال A تكافئ ال B if and only if ال cardinality لل A تساوي ال cardinality لل B فدولة أربع قواعد بيخلونا نقدر نعرف ال cardinal numbers و نتعامل معاهم", "tokens": [1211, 1211, 39184, 316, 6055, 3794, 995, 45865, 591, 19362, 15844, 23032, 12610, 3714, 3555, 33599, 25720, 25062, 995, 22488, 3660, 34892, 16758, 27884, 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{"start": 562.95, "end": 563.43, "word": " cardinality", "probability": 0.9111328125}, {"start": 563.43, "end": 563.67, "word": " of", "probability": 0.986328125}, {"start": 563.67, "end": 563.85, "word": " B", "probability": 0.99267578125}], "temperature": 1.0}, {"id": 24, "seek": 56991, "start": 564.3, "end": 569.92, "text": "هل احنا عرفنا تساوية الـ Cardinality عشان هذه نفيها؟ عرفناها", "tokens": [3224, 1211, 1975, 5016, 8315, 6225, 28480, 8315, 6055, 3794, 995, 2407, 10632, 2423, 39184, 11877, 259, 1860, 6225, 8592, 7649, 29538, 8717, 41185, 11296, 22807, 6225, 28480, 8315, 11296], "avg_logprob": -0.30922380185896353, "compression_ratio": 1.1111111111111112, "no_speech_prob": 0.0, "words": [{"start": 564.3, "end": 565.0, "word": "هل", "probability": 0.7666015625}, {"start": 565.0, "end": 565.18, "word": " احنا", "probability": 0.8465169270833334}, {"start": 565.18, "end": 565.58, "word": " عرفنا", "probability": 0.7939453125}, {"start": 565.58, "end": 566.86, "word": " تساوية", "probability": 0.7908203125}, {"start": 566.86, "end": 566.98, "word": " الـ", "probability": 0.5030517578125}, {"start": 566.98, "end": 567.46, "word": " Cardinality", "probability": 0.8033854166666666}, {"start": 567.46, "end": 568.06, "word": " عشان", "probability": 0.7455240885416666}, {"start": 568.06, "end": 568.18, "word": " هذه", "probability": 0.371826171875}, {"start": 568.18, "end": 569.34, "word": " نفيها؟", "probability": 0.9139404296875}, {"start": 569.34, "end": 569.92, "word": " عرفناها", "probability": 0.883544921875}], "temperature": 1.0}, {"id": 25, "seek": 59421, "start": 573.61, "end": 594.21, "text": "فإذا إيش ماله؟ إذا هي تكافئ صبصة منها ولا تكافئها صارت، هي تكافئ صبصة منها ولا تكافئها نفسها، هيك بده يصير، لأنه إيش معناته؟ إنه ما زال أحنا عرفنا التساوي، لأ بيقولوا لا تساوي شمالها ال negation، ال negation على طول، ففيش مشكلة أطلع، فإذا هذا التعريف يعتبر هيك كام، فإذا هو أوش عرف أصغر من أو يساوي", "tokens": [5172, 28814, 15730, 11933, 1829, 8592, 3714, 6027, 3224, 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{"start": 578.95, "end": 579.09, "word": " هي", "probability": 0.900390625}, {"start": 579.09, "end": 579.59, "word": " تكافئ", "probability": 0.9957275390625}, {"start": 579.59, "end": 580.03, "word": " صبصة", "probability": 0.9921875}, {"start": 580.03, "end": 580.39, "word": " منها", "probability": 0.99365234375}, {"start": 580.39, "end": 580.67, "word": " ولا", "probability": 0.87158203125}, {"start": 580.67, "end": 581.33, "word": " تكافئها", "probability": 0.99638671875}, {"start": 581.33, "end": 582.13, "word": " نفسها،", "probability": 0.958740234375}, {"start": 582.13, "end": 582.29, "word": " هيك", "probability": 0.802978515625}, {"start": 582.29, "end": 582.47, "word": " بده", "probability": 0.5653076171875}, {"start": 582.47, "end": 582.97, "word": " يصير،", "probability": 0.875}, {"start": 582.97, "end": 583.25, "word": " لأنه", "probability": 0.6739908854166666}, {"start": 583.25, "end": 583.33, "word": " إيش", "probability": 0.9505208333333334}, {"start": 583.33, "end": 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ال", "probability": 0.77783203125}, {"start": 587.25, "end": 587.93, "word": " negation،", "probability": 0.7869466145833334}, {"start": 587.93, "end": 588.11, "word": " ال", "probability": 0.91845703125}, {"start": 588.11, "end": 588.49, "word": " negation", "probability": 0.903564453125}, {"start": 588.49, "end": 588.63, "word": " على", "probability": 0.85791015625}, {"start": 588.63, "end": 588.95, "word": " طول،", "probability": 0.95751953125}, {"start": 588.95, "end": 589.17, "word": " ففيش", "probability": 0.7093912760416666}, {"start": 589.17, "end": 589.55, "word": " مشكلة", "probability": 0.9931640625}, {"start": 589.55, "end": 590.07, "word": " أطلع،", "probability": 0.84755859375}, {"start": 590.07, "end": 590.31, "word": " فإذا", "probability": 0.9607747395833334}, {"start": 590.31, "end": 590.51, "word": " هذا", "probability": 0.8447265625}, {"start": 590.51, "end": 590.93, "word": " التعريف", "probability": 0.99462890625}, {"start": 590.93, "end": 591.27, "word": " 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التساوي اللي هو ال negation تبع التساوي تفضلي نحاول نقرب الصورة ال gate نقول الأربع أصغر من الخمسة كيف بدي أعرفها؟", "tokens": [37746, 3215, 1211, 6027, 47395, 6225, 28480, 9154, 5551, 9381, 17082, 2288, 9154, 3224, 6156, 47432, 34051, 47525, 1211, 6027, 47395, 30767, 18513, 9154, 6225, 40448, 16712, 3794, 995, 45865, 13672, 1829, 31439, 2423, 2485, 399, 6055, 3555, 3615, 16712, 3794, 995, 45865, 6055, 5172, 11242, 20292, 8717, 5016, 995, 12610, 8717, 4587, 25513, 31767, 13063, 3660, 2423, 8539, 8717, 39648, 16247, 25513, 3615, 5551, 9381, 17082, 2288, 9154, 33962, 2304, 3794, 3660, 9122, 33911, 4724, 16254, 5551, 3615, 28480, 11296, 22807], "avg_logprob": -0.21140812965760747, "compression_ratio": 1.7083333333333333, "no_speech_prob": 0.0, "words": [{"start": 594.82, "end": 595.6, "word": "وبدلالته", "probability": 0.92158203125}, {"start": 595.6, "end": 596.18, "word": " عرف", "probability": 0.646240234375}, {"start": 596.18, "end": 596.44, "word": " من", "probability": 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"end": 603.34, "word": " negation", "probability": 0.6351318359375}, {"start": 603.34, "end": 603.82, "word": " تبع", "probability": 0.8653971354166666}, {"start": 603.82, "end": 604.34, "word": " التساوي", "probability": 0.9866943359375}, {"start": 604.34, "end": 606.14, "word": " تفضلي", "probability": 0.8162841796875}, {"start": 606.14, "end": 612.06, "word": " نحاول", "probability": 0.82415771484375}, {"start": 612.06, "end": 612.48, "word": " نقرب", "probability": 0.8111979166666666}, {"start": 612.48, "end": 614.48, "word": " الصورة", "probability": 0.97705078125}, {"start": 614.48, "end": 614.72, "word": " ال", "probability": 0.461669921875}, {"start": 614.72, "end": 615.12, "word": " gate", "probability": 0.537109375}, {"start": 615.12, "end": 616.02, "word": " نقول", "probability": 0.683349609375}, {"start": 616.02, "end": 616.5, "word": " الأربع", "probability": 0.8391927083333334}, {"start": 616.5, "end": 616.86, "word": " أصغر", "probability": 0.9935302734375}, {"start": 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{"start": 626.19, "end": 626.31, "word": " لا", "probability": 0.73779296875}, {"start": 626.31, "end": 626.71, "word": " تساوي", "probability": 0.8912353515625}, {"start": 626.71, "end": 627.11, "word": " الخمسة", "probability": 0.98876953125}, {"start": 627.11, "end": 627.29, "word": " هيك", "probability": 0.66455078125}, {"start": 627.29, "end": 627.67, "word": " تقريبا", "probability": 0.980859375}, {"start": 627.67, "end": 628.03, "word": " بنعمل", "probability": 0.7023518880208334}, {"start": 628.03, "end": 628.29, "word": " حاجة", "probability": 0.96142578125}, {"start": 628.29, "end": 628.49, "word": " بهذا", "probability": 0.56005859375}, {"start": 628.49, "end": 628.83, "word": " الشكل", "probability": 0.99462890625}, {"start": 628.83, "end": 629.83, "word": " هيك", "probability": 0.78515625}, {"start": 629.83, "end": 629.97, "word": " بدي", "probability": 0.7286376953125}, {"start": 629.97, "end": 630.41, "word": " أعمل", "probability": 0.9090169270833334}, {"start": 630.41, 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بدلالة أصغر من أو يساوي و بدلالة عدم التساوي عدم التساوي خليني أكتبها بطريقة جديدة قد يكون الصورة أوضحة مش غلط خليني أشوف إيش بقول هو الآن خليني أعبر عن هذا بشكل مختلف أول شي واحد", "tokens": [10721, 3615, 28480, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 31439, 47525, 10721, 39894, 3615, 28480, 3714, 9957, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 8978, 12602, 4587, 2304, 36764, 24401, 4032, 39182, 9957, 5551, 3615, 28480, 5551, 9381, 17082, 2288, 9154, 6156, 47432, 5296, 5016, 6027, 11296, 4724, 4117, 33911, 5551, 3615, 28480, 11296, 47525, 1211, 6027, 3660, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 4032, 47525, 1211, 6027, 3660, 6225, 40448, 16712, 3794, 995, 45865, 6225, 40448, 16712, 3794, 995, 45865, 16490, 1211, 9957, 1829, 5551, 4117, 2655, 3555, 11296, 4724, 9566, 16572, 28671, 10874, 16254, 41891, 12174, 3215, 7251, 30544, 31767, 13063, 3660, 34051, 11242, 5016, 3660, 37893, 32771, 1211, 9566, 16490, 1211, 9957, 1829, 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0.8232421875}, {"start": 819.77, "end": 819.91, "word": " ال", "probability": 0.76708984375}, {"start": 819.91, "end": 820.41, "word": " cardinality", "probability": 0.7737630208333334}, {"start": 820.41, "end": 820.55, "word": " لل", "probability": 0.73779296875}, {"start": 820.55, "end": 820.69, "word": " N", "probability": 0.81201171875}, {"start": 820.69, "end": 821.05, "word": " أصغر", "probability": 0.9744873046875}, {"start": 821.05, "end": 821.15, "word": " من", "probability": 0.837890625}, {"start": 821.15, "end": 821.27, "word": " ال", "probability": 0.5546875}, {"start": 821.27, "end": 821.37, "word": " ..", "probability": 0.25830078125}, {"start": 821.37, "end": 821.73, "word": " أو", "probability": 0.6552734375}, {"start": 821.73, "end": 822.13, "word": " تساوي", "probability": 0.8226318359375}, {"start": 822.13, "end": 822.25, "word": " ال", "probability": 0.5986328125}, {"start": 822.25, "end": 822.51, "word": " cardinal", "probability": 0.91162109375}, {"start": 822.51, "end": 822.79, "word": " number", "probability": 0.966796875}, {"start": 822.79, "end": 822.97, "word": " لل", "probability": 0.85693359375}, {"start": 822.97, "end": 823.25, "word": " R", "probability": 0.87353515625}, {"start": 823.25, "end": 824.69, "word": " خلينا", "probability": 0.7396647135416666}, {"start": 824.69, "end": 825.25, "word": " نحط", "probability": 0.85009765625}, {"start": 825.25, "end": 825.45, "word": " هذا", "probability": 0.7626953125}, {"start": 825.45, "end": 825.71, "word": " إيش", "probability": 0.6861572265625}, {"start": 825.71, "end": 825.99, "word": " الجزء", "probability": 0.96923828125}, {"start": 825.99, "end": 826.35, "word": " الأول", "probability": 0.990966796875}, {"start": 826.35, "end": 827.21, "word": " واحد", "probability": 0.866455078125}, {"start": 827.21, "end": 828.77, "word": " cardinality", "probability": 0.8684895833333334}], "temperature": 1.0}, {"id": 36, "seek": 85575, "start": 830.35, "end": 855.75, "text": "للأن أصغر أو يساوي cardinality لل R هذا مطلوب الأول طيب خلّي هذا الكلام صريح اه مطلوبين في ال A لأنه and بدي ادتره ادتره طيب بداجي افسر ايش معناته ان ال cardinality اصغر من او تساوي ان ال and تكافئ subset من ال A مين بعرف subset من ال R تكافئ ال and انا نفسي احسنت اه فهنا ال and", "tokens": [1211, 1211, 10721, 1863, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 2920, 259, 1860, 24976, 497, 23758, 3714, 9566, 1211, 37746, 16247, 12610, 23032, 1829, 3555, 16490, 1211, 11703, 1829, 23758, 2423, 28820, 10943, 20328, 16572, 5016, 1975, 3224, 3714, 9566, 1211, 37746, 9957, 8978, 2423, 316, 5296, 33456, 3224, 293, 4724, 16254, 1975, 3215, 2655, 2288, 3224, 1975, 3215, 2655, 2288, 3224, 23032, 1829, 3555, 47525, 26108, 1829, 1975, 36178, 2288, 1975, 1829, 8592, 20449, 8315, 47395, 16472, 2423, 2920, 259, 1860, 1975, 9381, 17082, 2288, 9154, 1975, 2407, 6055, 3794, 995, 45865, 16472, 2423, 293, 6055, 4117, 31845, 19986, 25993, 9154, 2423, 316, 3714, 9957, 45030, 28480, 25993, 9154, 2423, 497, 6055, 4117, 31845, 19986, 2423, 293, 1975, 8315, 8717, 36178, 1829, 1975, 5016, 3794, 29399, 1975, 3224, 6156, 3224, 8315, 2423, 293], "avg_logprob": -0.2373188344248827, "compression_ratio": 1.8589211618257262, "no_speech_prob": 0.0, "words": [{"start": 830.3499999999999, "end": 831.0699999999999, "word": "للأن", "probability": 0.73590087890625}, {"start": 831.0699999999999, "end": 831.79, "word": " أصغر", "probability": 0.9425048828125}, {"start": 831.79, "end": 831.99, "word": " أو", "probability": 0.8046875}, {"start": 831.99, "end": 832.63, "word": " يساوي", "probability": 0.9578857421875}, {"start": 832.63, "end": 833.95, "word": " cardinality", "probability": 0.8795572916666666}, {"start": 833.95, "end": 834.19, "word": " لل", "probability": 0.8876953125}, {"start": 834.19, "end": 834.47, "word": " R", "probability": 0.1390380859375}, {"start": 834.47, "end": 835.03, "word": " هذا", "probability": 0.71728515625}, {"start": 835.03, "end": 835.41, "word": " مطلوب", "probability": 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{"start": 841.41, "end": 841.57, "word": " and", "probability": 0.2437744140625}, {"start": 841.57, "end": 841.79, "word": " بدي", "probability": 0.594482421875}, {"start": 841.79, "end": 842.07, "word": " ادتره", "probability": 0.536328125}, {"start": 842.07, "end": 842.77, "word": " ادتره", "probability": 0.94794921875}, {"start": 842.77, "end": 843.49, "word": " طيب", "probability": 0.9723307291666666}, {"start": 843.49, "end": 844.13, "word": " بداجي", "probability": 0.54833984375}, {"start": 844.13, "end": 844.69, "word": " افسر", "probability": 0.8844401041666666}, {"start": 844.69, "end": 845.43, "word": " ايش", "probability": 0.83203125}, {"start": 845.43, "end": 845.85, "word": " معناته", "probability": 0.9708658854166666}, {"start": 845.85, "end": 845.97, "word": " ان", "probability": 0.6103515625}, {"start": 845.97, "end": 846.09, "word": " ال", "probability": 0.84521484375}, {"start": 846.09, "end": 846.51, "word": " cardinality", "probability": 0.8297526041666666}, {"start": 846.51, "end": 846.81, "word": " اصغر", "probability": 0.82867431640625}, {"start": 846.81, "end": 846.91, "word": " من", "probability": 0.93408203125}, {"start": 846.91, "end": 847.03, "word": " او", "probability": 0.807373046875}, {"start": 847.03, "end": 847.31, "word": " تساوي", "probability": 0.971923828125}, {"start": 847.31, "end": 847.43, "word": " ان", "probability": 0.79541015625}, {"start": 847.43, "end": 847.51, "word": " ال", "probability": 0.95068359375}, {"start": 847.51, "end": 847.67, "word": " and", "probability": 0.89013671875}, {"start": 847.67, "end": 848.15, "word": " تكافئ", "probability": 0.977294921875}, {"start": 848.15, "end": 848.41, "word": " subset", "probability": 0.330078125}, {"start": 848.41, "end": 848.65, "word": " من", "probability": 0.99609375}, {"start": 848.65, "end": 848.79, "word": " ال", "probability": 0.97412109375}, {"start": 848.79, "end": 848.93, "word": " A", "probability": 0.77001953125}, {"start": 848.93, "end": 849.85, "word": " مين", "probability": 0.8271484375}, {"start": 849.85, "end": 850.31, "word": " بعرف", "probability": 0.8291015625}, {"start": 850.31, "end": 850.65, "word": " subset", "probability": 0.87451171875}, {"start": 850.65, "end": 850.89, "word": " من", "probability": 0.9951171875}, {"start": 850.89, "end": 850.99, "word": " ال", "probability": 0.95654296875}, {"start": 850.99, "end": 851.13, "word": " R", "probability": 0.94873046875}, {"start": 851.13, "end": 851.49, "word": " تكافئ", "probability": 0.9931640625}, {"start": 851.49, "end": 851.61, "word": " ال", "probability": 0.96728515625}, {"start": 851.61, "end": 851.75, "word": " and", "probability": 0.5244140625}, {"start": 851.75, "end": 852.41, "word": " انا", "probability": 0.6962890625}, {"start": 852.41, "end": 852.85, "word": " نفسي", "probability": 0.931640625}, {"start": 852.85, "end": 853.47, "word": " احسنت", "probability": 0.913818359375}, {"start": 853.47, "end": 853.97, "word": " اه", "probability": 0.685546875}, {"start": 853.97, "end": 854.61, "word": " فهنا", "probability": 0.90234375}, {"start": 854.61, "end": 855.37, "word": " ال", "probability": 0.9140625}, {"start": 855.37, "end": 855.75, "word": " and", "probability": 0.9306640625}], "temperature": 1.0}, {"id": 37, "seek": 87134, "start": 856.64, "end": 871.34, "text": "تكافئ ال N وهي subset من ال R على طول implies ال cardinality لل N أصغر أو يساوي ال cardinality لل R فهذه أول شيء بسهولة جدا", "tokens": [2655, 4117, 31845, 19986, 2423, 426, 37037, 1829, 25993, 9154, 2423, 497, 15844, 23032, 12610, 18779, 2423, 2920, 259, 1860, 24976, 426, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 2423, 2920, 259, 1860, 24976, 497, 6156, 3224, 24192, 5551, 12610, 44049, 38207, 4724, 3794, 3224, 12610, 3660, 10874, 28259], "avg_logprob": -0.19335937671936476, "compression_ratio": 1.2836879432624113, "no_speech_prob": 0.0, "words": [{"start": 856.64, "end": 857.38, "word": "تكافئ", "probability": 0.92333984375}, {"start": 857.38, "end": 857.58, "word": " ال", "probability": 0.74609375}, {"start": 857.58, "end": 857.88, "word": " N", "probability": 0.368896484375}, {"start": 857.88, "end": 858.64, "word": " وهي", "probability": 0.790283203125}, {"start": 858.64, "end": 859.06, "word": " subset", "probability": 0.7421875}, {"start": 859.06, "end": 859.42, "word": " من", "probability": 0.98974609375}, {"start": 859.42, "end": 859.6, "word": " ال", "probability": 0.7275390625}, {"start": 859.6, "end": 859.98, "word": " R", "probability": 0.95068359375}, {"start": 859.98, "end": 860.42, "word": " على", "probability": 0.8935546875}, {"start": 860.42, "end": 860.82, "word": " طول", "probability": 0.98876953125}, {"start": 860.82, "end": 861.68, "word": " implies", "probability": 0.63623046875}, {"start": 861.68, "end": 862.22, "word": " ال", "probability": 0.2998046875}, {"start": 862.22, "end": 863.14, "word": " cardinality", "probability": 0.8844401041666666}, {"start": 863.14, "end": 864.12, "word": " لل", "probability": 0.54296875}, {"start": 864.12, "end": 864.6, "word": " N", "probability": 0.9208984375}, {"start": 864.6, "end": 865.56, "word": " أصغر", "probability": 0.93701171875}, {"start": 865.56, "end": 865.72, "word": " أو", "probability": 0.8291015625}, {"start": 865.72, "end": 866.32, "word": " يساوي", "probability": 0.9599609375}, {"start": 866.32, "end": 867.0, "word": " ال", "probability": 0.7177734375}, {"start": 867.0, "end": 867.84, "word": " cardinality", "probability": 0.8976236979166666}, {"start": 867.84, "end": 868.62, "word": " لل", "probability": 0.91748046875}, {"start": 868.62, "end": 868.92, "word": " R", "probability": 0.8740234375}, {"start": 868.92, "end": 869.96, "word": " فهذه", "probability": 0.5845540364583334}, {"start": 869.96, "end": 870.22, "word": " أول", "probability": 0.95458984375}, {"start": 870.22, "end": 870.54, "word": " شيء", "probability": 0.705078125}, {"start": 870.54, "end": 871.06, "word": " بسهولة", "probability": 0.9857421875}, {"start": 871.06, "end": 871.34, "word": " جدا", "probability": 0.99169921875}], "temperature": 1.0}, {"id": 38, "seek": 90039, "start": 872.25, "end": 900.39, "text": "أحنا متوقعين أن الـN subset من الـR إذا ما هيش أدد عناصر الـN أصغر أو يساوي أدد عناصر الـR فعلا بنسجم مع توقعاتنا السابق ممتاز الخطوة التانية بدي أثبت أن ال cardinality للـN لا تساوي ال cardinality للـR هذا مطلوبنا رقم اتنين مين عنده حل؟ صحيح ليش؟", "tokens": [10721, 5016, 8315, 44650, 30543, 3615, 9957, 14739, 2423, 39184, 45, 1422, 3854, 9154, 2423, 39184, 49, 11933, 15730, 19446, 39896, 8592, 5551, 3215, 3215, 18871, 33546, 2288, 2423, 39184, 45, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 5551, 3215, 3215, 18871, 33546, 2288, 2423, 39184, 49, 6156, 3615, 15040, 44945, 3794, 7435, 2304, 20449, 6055, 30543, 3615, 9307, 8315, 21136, 16758, 4587, 3714, 2304, 2655, 31377, 33962, 9566, 2407, 3660, 16712, 7649, 10632, 4724, 16254, 5551, 12984, 3555, 2655, 14739, 2423, 2920, 259, 1860, 24976, 39184, 45, 20193, 6055, 3794, 995, 45865, 2423, 2920, 259, 1860, 24976, 39184, 49, 23758, 3714, 9566, 1211, 37746, 8315, 12602, 4587, 2304, 1975, 2655, 1863, 9957, 3714, 9957, 43242, 3224, 11331, 1211, 22807, 20328, 5016, 1829, 5016, 32239, 8592, 22807], "avg_logprob": -0.2281250052727186, "compression_ratio": 1.7542372881355932, "no_speech_prob": 0.0, "words": [{"start": 872.25, "end": 872.85, "word": "أحنا", "probability": 0.6061197916666666}, {"start": 872.85, "end": 873.65, "word": " متوقعين", "probability": 0.8565673828125}, {"start": 873.65, "end": 874.39, "word": " أن", "probability": 0.42724609375}, {"start": 874.39, "end": 874.67, "word": " الـN", "probability": 0.3997395833333333}, {"start": 874.67, "end": 875.07, "word": " subset", "probability": 0.34320068359375}, {"start": 875.07, "end": 875.21, "word": " من", "probability": 0.98291015625}, {"start": 875.21, "end": 875.55, "word": " الـR", "probability": 0.9104817708333334}, {"start": 875.55, "end": 875.73, "word": " إذا", "probability": 0.66064453125}, 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لان احنا في 2017 في نهايته بس هي خصوص في 2017 يعني هي عدد يعني مش مش قضية", "tokens": [1863, 8592, 38688, 9122, 2304, 7649, 50113, 6027, 1975, 12984, 3555, 47395, 16472, 2423, 39184, 2920, 259, 1860, 5296, 7649, 1975, 4117, 26890, 9154, 6591, 2423, 2920, 259, 1860, 2423, 3303, 1230, 6225, 3215, 3215, 11296, 1975, 4117, 26890, 9154, 6591, 23032, 3555, 3615, 995, 9154, 9566, 38436, 49429, 5296, 10721, 8032, 1211, 39896, 8978, 11296, 6591, 18871, 9381, 2288, 5296, 22488, 18513, 41950, 21292, 3615, 10632, 5296, 10721, 4117, 2655, 2288, 23032, 3555, 3615, 995, 6591, 5296, 7649, 1975, 5016, 8315, 8978, 6591, 8978, 8717, 11296, 36081, 3224, 4724, 3794, 39896, 16490, 9381, 2407, 9381, 8978, 6591, 37495, 22653, 39896, 6225, 3215, 3215, 37495, 22653, 37893, 37893, 12174, 11242, 10632], "avg_logprob": -0.21861048814441478, "compression_ratio": 1.7668161434977578, "no_speech_prob": 0.0, "words": [{"start": 972.81, "end": 973.39, "word": "نشوف", "probability": 0.8922526041666666}, {"start": 973.39, "end": 974.03, "word": " كمان", "probability": 0.8238118489583334}, {"start": 974.03, "end": 975.17, "word": " مثال", "probability": 0.989013671875}, {"start": 975.17, "end": 976.51, "word": " اثبته", "probability": 0.8245849609375}, {"start": 976.51, "end": 976.97, "word": " ان", "probability": 0.77734375}, {"start": 976.97, "end": 977.39, "word": " الـ", "probability": 0.59521484375}, {"start": 977.39, "end": 978.15, "word": " cardinality", "probability": 0.6460164388020834}, {"start": 978.15, "end": 978.49, "word": " لان", "probability": 0.5557861328125}, {"start": 978.49, "end": 978.85, "word": " اكبر", "probability": 0.87353515625}, {"start": 978.85, "end": 978.99, "word": " من", "probability": 0.97998046875}, {"start": 978.99, "end": 979.67, "word": " 2017", "probability": 0.796875}, {"start": 979.67, "end": 981.03, "word": " ال", "probability": 0.76025390625}, {"start": 981.03, "end": 981.63, "word": " cardinality", "probability": 0.8681640625}, {"start": 981.63, "end": 981.81, "word": " ال", "probability": 0.376953125}, {"start": 981.81, "end": 982.07, "word": " natural", "probability": 0.68017578125}, {"start": 982.07, "end": 982.55, "word": " number", "probability": 0.9755859375}, {"start": 982.55, "end": 983.05, "word": " عددها", "probability": 0.9793701171875}, {"start": 983.05, "end": 983.37, "word": " اكبر", "probability": 0.9562174479166666}, {"start": 983.37, "end": 983.45, "word": " من", "probability": 0.98779296875}, {"start": 983.45, "end": 984.05, "word": " 2017", "probability": 0.88623046875}, {"start": 984.05, "end": 984.43, "word": " طبعا", "probability": 0.9434814453125}, {"start": 984.43, "end": 984.83, "word": " منطقي", "probability": 0.80419921875}, {"start": 984.83, "end": 985.01, "word": " ولا", "probability": 0.767578125}, {"start": 985.01, "end": 985.35, "word": " لأ", "probability": 0.8740234375}, {"start": 985.35, "end": 986.39, "word": " هل", "probability": 0.71240234375}, {"start": 986.39, "end": 986.53, "word": " هي", "probability": 0.7880859375}, {"start": 986.53, "end": 986.95, "word": " فيها", "probability": 0.880126953125}, {"start": 986.95, "end": 987.67, "word": " 2017", "probability": 0.86328125}, {"start": 987.67, "end": 988.41, "word": " عنصر", "probability": 0.9646809895833334}, {"start": 988.41, "end": 988.75, "word": " لعداد", "probability": 0.7660319010416666}, {"start": 988.75, "end": 989.29, "word": " الطبيعية", "probability": 0.875732421875}, {"start": 989.29, "end": 991.49, "word": " لأكتر", "probability": 0.85458984375}, {"start": 991.49, "end": 994.03, "word": " طبعا", "probability": 0.93310546875}, {"start": 994.03, "end": 994.57, "word": " 2017", "probability": 0.8232421875}, {"start": 994.57, "end": 995.15, "word": " لان", "probability": 0.5517578125}, {"start": 995.15, "end": 995.31, "word": " احنا", "probability": 0.9249674479166666}, {"start": 995.31, "end": 995.41, "word": " في", "probability": 0.86328125}, {"start": 995.41, "end": 995.95, "word": " 2017", "probability": 0.87451171875}, {"start": 995.95, "end": 996.23, "word": " في", "probability": 0.6689453125}, {"start": 996.23, "end": 996.65, "word": " نهايته", "probability": 0.907470703125}, {"start": 996.65, "end": 996.87, "word": " بس", "probability": 0.96728515625}, {"start": 996.87, "end": 997.39, "word": " هي", "probability": 0.222412109375}, {"start": 997.39, "end": 997.93, "word": " خصوص", "probability": 0.966064453125}, {"start": 997.93, "end": 998.09, "word": " في", "probability": 0.416259765625}, {"start": 998.09, "end": 998.61, "word": " 2017", "probability": 0.71728515625}, {"start": 998.61, "end": 999.19, "word": " يعني", "probability": 0.842041015625}, {"start": 999.19, "end": 1000.03, "word": " هي", "probability": 0.6171875}, {"start": 1000.03, "end": 1000.37, "word": " عدد", "probability": 0.9697265625}, {"start": 1000.37, "end": 1000.59, "word": " يعني", "probability": 0.936767578125}, {"start": 1000.59, "end": 1000.83, "word": " مش", "probability": 0.9677734375}, {"start": 1000.83, "end": 1001.03, "word": " مش", "probability": 0.337646484375}, {"start": 1001.03, "end": 1001.31, "word": " قضية", "probability": 0.9514973958333334}], "temperature": 1.0}, {"id": 43, "seek": 102731, "start": 1004.73, "end": 1027.31, "text": "تمام كيف بدنا نشتغل؟ في عندنا مجموعة هي الان وفي عندنا cardinal number 2017 هذا cardinal number فعشان أشتغل بدي أجيب مجموعات فإذا أول شي بدي أجيب مجموعة وكافة اللي قاهش اللي هو اللي قاهش 2017 ان 2017 كيف تسوى 2017 هذا المثال الرقم 2", "tokens": [39237, 10943, 9122, 33911, 47525, 8315, 8717, 8592, 2655, 17082, 1211, 22807, 8978, 43242, 8315, 3714, 7435, 2304, 45367, 3660, 39896, 2423, 7649, 4032, 41185, 43242, 8315, 2920, 2071, 1230, 6591, 23758, 2920, 2071, 1230, 6156, 3615, 8592, 7649, 5551, 8592, 2655, 17082, 1211, 4724, 16254, 5551, 7435, 1829, 3555, 3714, 7435, 2304, 45367, 9307, 6156, 28814, 15730, 5551, 12610, 44049, 4724, 16254, 5551, 7435, 1829, 3555, 3714, 7435, 2304, 2407, 27884, 4032, 4117, 31845, 3660, 13672, 1829, 12174, 40294, 8592, 13672, 1829, 31439, 13672, 1829, 12174, 40294, 8592, 6591, 16472, 6591, 9122, 33911, 6055, 3794, 2407, 7578, 6591, 23758, 9673, 12984, 6027, 34892, 4587, 2304, 568], "avg_logprob": -0.279803237705319, "compression_ratio": 1.875, "no_speech_prob": 0.0, "words": [{"start": 1004.7299999999999, "end": 1005.4499999999999, "word": "تمام", "probability": 0.8291015625}, {"start": 1005.4499999999999, "end": 1006.17, "word": " كيف", "probability": 0.828369140625}, {"start": 1006.17, "end": 1006.41, "word": " بدنا", "probability": 0.797607421875}, {"start": 1006.41, "end": 1008.17, "word": " نشتغل؟", "probability": 0.9195149739583334}, {"start": 1008.17, "end": 1008.49, "word": " في", "probability": 0.44140625}, {"start": 1008.49, "end": 1008.85, "word": " عندنا", "probability": 0.833740234375}, {"start": 1008.85, "end": 1009.51, "word": " مجموعة", "probability": 0.8517578125}, {"start": 1009.51, "end": 1009.65, "word": " هي", "probability": 0.453369140625}, {"start": 1009.65, "end": 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1015.75, "end": 1015.95, "word": " أجيب", "probability": 0.9501953125}, {"start": 1015.95, "end": 1016.57, "word": " مجموعات", "probability": 0.979296875}, {"start": 1016.57, "end": 1017.01, "word": " فإذا", "probability": 0.6520182291666666}, {"start": 1017.01, "end": 1017.27, "word": " أول", "probability": 0.918701171875}, {"start": 1017.27, "end": 1017.37, "word": " شي", "probability": 0.67724609375}, {"start": 1017.37, "end": 1017.61, "word": " بدي", "probability": 0.780029296875}, {"start": 1017.61, "end": 1017.87, "word": " أجيب", "probability": 0.9832763671875}, {"start": 1017.87, "end": 1018.29, "word": " مجموعة", "probability": 0.882763671875}, {"start": 1018.29, "end": 1018.65, "word": " وكافة", "probability": 0.7801513671875}, {"start": 1018.65, "end": 1018.77, "word": " اللي", "probability": 0.57818603515625}, {"start": 1018.77, "end": 1019.19, "word": " قاهش", "probability": 0.4921875}, {"start": 1019.19, "end": 1019.57, "word": " اللي", "probability": 0.93994140625}, {"start": 1019.57, "end": 1019.69, "word": " هو", "probability": 0.8515625}, {"start": 1019.69, "end": 1019.81, "word": " اللي", "probability": 0.6837158203125}, {"start": 1019.81, "end": 1019.97, "word": " قاهش", "probability": 0.7473958333333334}, {"start": 1019.97, "end": 1020.73, "word": " 2017", "probability": 0.46923828125}, {"start": 1020.73, "end": 1022.99, "word": " ان", "probability": 0.296630859375}, {"start": 1022.99, "end": 1024.35, "word": " 2017", "probability": 0.767578125}, {"start": 1024.35, "end": 1025.11, "word": " كيف", "probability": 0.8759765625}, {"start": 1025.11, "end": 1025.37, "word": " تسوى", "probability": 0.67864990234375}, {"start": 1025.37, "end": 1026.09, "word": " 2017", "probability": 0.8740234375}, {"start": 1026.09, "end": 1026.49, "word": " هذا", "probability": 0.454833984375}, {"start": 1026.49, "end": 1026.83, "word": " المثال", "probability": 0.8502604166666666}, {"start": 1026.83, "end": 1027.11, "word": " الرقم", "probability": 0.978515625}, {"start": 1027.11, "end": 1027.31, "word": " 2", "probability": 0.71240234375}], "temperature": 1.0}, {"id": 44, "seek": 105286, "start": 1028.65, "end": 1052.87, "text": "فا solution اقوله let A تساوي بس اختصار عشان ماتامش اكتبله 2017 وانسى ال 17 خلاص ساميها A فعلى طول then cardinality لل A تساوي 2017 اه بدنا نشتغل نفس العملية خطوطين واحد", "tokens": [5172, 995, 3827, 1975, 39648, 3224, 718, 316, 6055, 3794, 995, 45865, 4724, 3794, 1975, 46456, 9381, 9640, 6225, 8592, 7649, 3714, 9307, 10943, 8592, 1975, 4117, 2655, 3555, 43761, 6591, 4032, 7649, 3794, 7578, 2423, 3282, 16490, 1211, 33546, 8608, 10943, 1829, 11296, 316, 6156, 3615, 23942, 23032, 12610, 550, 2920, 259, 1860, 24976, 316, 6055, 3794, 995, 45865, 6591, 1975, 3224, 47525, 8315, 8717, 8592, 2655, 17082, 1211, 8717, 36178, 18863, 42213, 10632, 16490, 9566, 2407, 9566, 9957, 36764, 24401], "avg_logprob": -0.27522589140627757, "compression_ratio": 1.4126984126984128, "no_speech_prob": 0.0, "words": [{"start": 1028.65, "end": 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1034.21, "end": 1034.75, "word": " وانسى", "probability": 0.44415283203125}, {"start": 1034.75, "end": 1034.87, "word": " ال", "probability": 0.6103515625}, {"start": 1034.87, "end": 1035.21, "word": " 17", "probability": 0.5283203125}, {"start": 1035.21, "end": 1035.57, "word": " خلاص", "probability": 0.96142578125}, {"start": 1035.57, "end": 1036.15, "word": " ساميها", "probability": 0.8211669921875}, {"start": 1036.15, "end": 1036.37, "word": " A", "probability": 0.748046875}, {"start": 1036.37, "end": 1037.95, "word": " فعلى", "probability": 0.8577473958333334}, {"start": 1037.95, "end": 1038.33, "word": " طول", "probability": 0.996337890625}, {"start": 1038.33, "end": 1039.95, "word": " then", "probability": 0.736328125}, {"start": 1039.95, "end": 1042.09, "word": " cardinality", "probability": 0.91943359375}, {"start": 1042.09, "end": 1044.65, "word": " لل", "probability": 0.6787109375}, {"start": 1044.65, "end": 1045.03, "word": " A", "probability": 0.8046875}, {"start": 1045.03, "end": 1045.81, "word": " تساوي", "probability": 0.960693359375}, {"start": 1045.81, "end": 1046.47, "word": " 2017", "probability": 0.87255859375}, {"start": 1046.47, "end": 1048.07, "word": " اه", "probability": 0.7113037109375}, {"start": 1048.07, "end": 1048.55, "word": " بدنا", "probability": 0.63134765625}, {"start": 1048.55, "end": 1048.81, "word": " نشتغل", "probability": 0.9732421875}, {"start": 1048.81, "end": 1048.99, "word": " نفس", "probability": 0.996337890625}, {"start": 1048.99, "end": 1049.93, "word": " العملية", "probability": 0.9708658854166666}, {"start": 1049.93, "end": 1050.57, "word": " خطوطين", "probability": 0.92041015625}, {"start": 1050.57, "end": 1052.87, "word": " واحد", "probability": 0.93603515625}], "temperature": 1.0}, {"id": 45, "seek": 107180, "start": 1054.4, "end": 1071.8, "text": "بدي أثبت أن ال cardinality لل A أقل أو تساوي ال cardinality لل N هذا المطلوب الأول فبشبت أسأل نفسي هل ال A تكافئ صبصة من ال N و مين هي؟", "tokens": [3555, 16254, 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"probability": 0.52490234375}, {"start": 1109.17, "end": 1109.35, "word": " الـ", "probability": 0.71826171875}, {"start": 1109.35, "end": 1109.63, "word": " A", "probability": 0.492431640625}, {"start": 1109.63, "end": 1110.75, "word": " is", "probability": 0.91455078125}, {"start": 1110.75, "end": 1111.55, "word": " finite", "probability": 0.990234375}, {"start": 1111.55, "end": 1113.27, "word": " and", "probability": 0.89208984375}, {"start": 1113.27, "end": 1114.45, "word": " N", "probability": 0.81103515625}, {"start": 1114.45, "end": 1115.47, "word": " is", "probability": 0.962890625}, {"start": 1115.47, "end": 1116.27, "word": " infinite", "probability": 0.9189453125}, {"start": 1116.27, "end": 1118.45, "word": " implies", "probability": 0.859375}, {"start": 1118.45, "end": 1119.69, "word": " ال", "probability": 0.84716796875}, {"start": 1119.69, "end": 1120.11, "word": " A", "probability": 0.42529296875}, {"start": 1120.11, "end": 1120.89, "word": " لا", "probability": 0.77783203125}, {"start": 1120.89, "end": 1121.59, "word": " تكافئ", "probability": 0.9681396484375}, {"start": 1121.59, "end": 1121.75, "word": " ال", "probability": 0.88525390625}, {"start": 1121.75, "end": 1122.01, "word": " N", "probability": 0.98193359375}, {"start": 1122.01, "end": 1123.53, "word": " وهذا", "probability": 0.802978515625}, {"start": 1123.53, "end": 1124.11, "word": " يؤدي", "probability": 0.92333984375}, {"start": 1124.11, "end": 1124.97, "word": " إن", "probability": 0.408203125}, {"start": 1124.97, "end": 1125.15, "word": " ال", "probability": 0.677734375}, {"start": 1125.15, "end": 1126.01, "word": " cardinality", "probability": 0.84521484375}, {"start": 1126.01, "end": 1127.33, "word": " لل", "probability": 0.74169921875}, {"start": 1127.33, "end": 1127.85, "word": " A", "probability": 0.89990234375}, {"start": 1127.85, "end": 1128.63, "word": " لا", "probability": 0.68115234375}, {"start": 1128.63, "end": 1129.39, "word": " تساوي", "probability": 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cardinality", "probability": 0.8522135416666666}, {"start": 1149.57, "end": 1150.53, "word": " لل", "probability": 0.6982421875}, {"start": 1150.53, "end": 1150.91, "word": " a", "probability": 0.379638671875}, {"start": 1150.91, "end": 1151.69, "word": " أقل", "probability": 0.8580729166666666}, {"start": 1151.69, "end": 1152.27, "word": " من", "probability": 0.98681640625}, {"start": 1152.27, "end": 1152.41, "word": " ال", "probability": 0.7119140625}, {"start": 1152.41, "end": 1153.21, "word": " cardinality", "probability": 0.8855794270833334}, {"start": 1153.21, "end": 1154.89, "word": " للأ", "probability": 0.5450439453125}, {"start": 1154.89, "end": 1155.95, "word": " بالتأكيد", "probability": 0.94150390625}], "temperature": 1.0}, {"id": 49, "seek": 117619, "start": 1157.05, "end": 1176.19, "text": "فإذا هنا مع دول المثاليين ومضحكتنا الصورة كيف نثبت علاقة أصغر من فيها مطلوبين نثبت أنه في علاقة أصغر من أو يساوي تبقى للتعريف وفي عدم تساوي عدم تساوي شرطين عشان نوصل لهذه الصورة أي 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1164.23, "word": " نثبت", "probability": 0.9757080078125}, {"start": 1164.23, "end": 1164.49, "word": " أنه", "probability": 0.730712890625}, {"start": 1164.49, "end": 1164.69, "word": " في", "probability": 0.95458984375}, {"start": 1164.69, "end": 1165.31, "word": " علاقة", "probability": 0.8880208333333334}, {"start": 1165.31, "end": 1165.69, "word": " أصغر", "probability": 0.989013671875}, {"start": 1165.69, "end": 1165.81, "word": " من", "probability": 0.98974609375}, {"start": 1165.81, "end": 1165.97, "word": " أو", "probability": 0.96337890625}, {"start": 1165.97, "end": 1166.47, "word": " يساوي", "probability": 0.984375}, {"start": 1166.47, "end": 1167.19, "word": " تبقى", "probability": 0.898681640625}, {"start": 1167.19, "end": 1167.81, "word": " للتعريف", "probability": 0.9888671875}, {"start": 1167.81, "end": 1168.13, "word": " وفي", "probability": 0.87841796875}, {"start": 1168.13, "end": 1168.55, "word": " عدم", "probability": 0.8203125}, {"start": 1168.55, "end": 1169.05, "word": " تساوي", "probability": 0.976806640625}, {"start": 1169.05, "end": 1169.65, "word": " عدم", "probability": 0.672607421875}, {"start": 1169.65, "end": 1170.11, "word": " تساوي", "probability": 0.9822998046875}, {"start": 1170.11, "end": 1170.69, "word": " شرطين", "probability": 0.9061279296875}, {"start": 1170.69, "end": 1171.27, "word": " عشان", "probability": 0.9420572916666666}, {"start": 1171.27, "end": 1171.63, "word": " نوصل", "probability": 0.9767252604166666}, {"start": 1171.63, "end": 1172.11, "word": " لهذه", "probability": 0.95458984375}, {"start": 1172.11, "end": 1173.67, "word": " الصورة", "probability": 0.9938151041666666}, {"start": 1173.67, "end": 1175.69, "word": " أي", "probability": 0.72509765625}, {"start": 1175.69, "end": 1176.19, "word": " سؤال", "probability": 0.9845377604166666}], "temperature": 1.0}, {"id": 50, "seek": 120460, "start": 1177.49, "end": 1204.61, "text": "نشوف مثال على نفس الموضوع لكن من زوايا أخرى let a and b be two sets prove that يكتب لنا cardinality لمجموعة أصغر أو يساوي بمفهوم جديد بقول cardinality ل a أقل أو تساوي بف and only if ممكن يستخدم كتعريف لأن ف and only if there exists an injection إذا كدرت تلاقي one to one function من a ل b من a ل b", "tokens": [1863, 8592, 38688, 50113, 6027, 15844, 8717, 36178, 9673, 2407, 11242, 45367, 44381, 9154, 30767, 14407, 25528, 5551, 34740, 7578, 718, 257, 293, 272, 312, 732, 6352, 7081, 300, 7251, 4117, 2655, 3555, 5296, 8315, 2920, 259, 1860, 5296, 2304, 7435, 2304, 2407, 27884, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 4724, 2304, 5172, 3224, 20498, 10874, 16254, 3215, 4724, 39648, 2920, 259, 1860, 5296, 257, 5551, 4587, 1211, 34051, 6055, 3794, 995, 45865, 4724, 5172, 293, 787, 498, 3714, 43020, 7251, 14851, 9778, 40448, 9122, 2655, 3615, 16572, 5172, 5296, 33456, 6156, 293, 787, 498, 456, 8198, 364, 22873, 11933, 15730, 9122, 3215, 43500, 6055, 15040, 38436, 472, 281, 472, 2445, 9154, 257, 5296, 272, 9154, 257, 5296, 272], "avg_logprob": -0.2632113787216869, "compression_ratio": 1.578358208955224, "no_speech_prob": 0.0, "words": [{"start": 1177.49, "end": 1177.85, "word": "نشوف", "probability": 0.869140625}, {"start": 1177.85, "end": 1178.41, "word": " مثال", "probability": 0.9140625}, {"start": 1178.41, "end": 1179.11, "word": " على", "probability": 0.384033203125}, {"start": 1179.11, "end": 1179.29, "word": " نفس", "probability": 0.995361328125}, {"start": 1179.29, "end": 1179.79, "word": " الموضوع", "probability": 0.9989013671875}, {"start": 1179.79, "end": 1180.23, "word": " لكن", "probability": 0.87109375}, {"start": 1180.23, "end": 1181.15, "word": " من", "probability": 0.98046875}, {"start": 1181.15, "end": 1181.69, "word": " زوايا", "probability": 0.92333984375}, {"start": 1181.69, "end": 1182.63, "word": " أخرى", "probability": 0.9606119791666666}, {"start": 1182.63, "end": 1183.13, "word": " let", "probability": 0.304443359375}, {"start": 1183.13, "end": 1183.59, "word": " a", "probability": 0.3876953125}, {"start": 1183.59, "end": 1184.09, "word": " and", "probability": 0.90673828125}, {"start": 1184.09, "end": 1184.37, "word": " b", "probability": 0.9677734375}, {"start": 1184.37, "end": 1184.61, "word": " be", "probability": 0.52978515625}, {"start": 1184.61, "end": 1184.99, "word": " two", "probability": 0.89404296875}, {"start": 1184.99, "end": 1185.43, "word": " sets", "probability": 0.95166015625}, {"start": 1185.43, "end": 1186.11, "word": " prove", "probability": 0.239013671875}, {"start": 1186.11, "end": 1186.73, "word": " that", "probability": 0.93505859375}, {"start": 1186.73, "end": 1188.49, "word": " يكتب", "probability": 0.603790283203125}, {"start": 1188.49, "end": 1188.69, "word": " لنا", "probability": 0.617919921875}, {"start": 1188.69, "end": 1189.33, "word": " cardinality", "probability": 0.78857421875}, {"start": 1189.33, "end": 1190.29, "word": " لمجموعة", "probability": 0.82421875}, {"start": 1190.29, "end": 1190.63, "word": " أصغر", "probability": 0.94140625}, {"start": 1190.63, "end": 1190.73, "word": " أو", "probability": 0.91064453125}, {"start": 1190.73, "end": 1191.07, "word": " يساوي", "probability": 0.888671875}, {"start": 1191.07, "end": 1191.43, "word": " بمفهوم", "probability": 0.945703125}, {"start": 1191.43, "end": 1191.85, "word": " جديد", "probability": 0.9781901041666666}, {"start": 1191.85, "end": 1192.37, "word": " بقول", "probability": 0.55322265625}, {"start": 1192.37, "end": 1192.95, "word": " cardinality", "probability": 0.8251953125}, {"start": 1192.95, "end": 1193.07, "word": " ل", "probability": 0.4609375}, {"start": 1193.07, "end": 1193.23, "word": " a", "probability": 0.447021484375}, {"start": 1193.23, "end": 1193.73, "word": " أقل", "probability": 0.9837239583333334}, {"start": 1193.73, "end": 1193.83, "word": " أو", "probability": 0.82470703125}, {"start": 1193.83, "end": 1194.11, "word": " تساوي", "probability": 0.9375}, {"start": 1194.11, "end": 1194.47, "word": " بف", "probability": 0.54547119140625}, {"start": 1194.47, "end": 1194.67, "word": " and", "probability": 0.90380859375}, {"start": 1194.67, "end": 1194.91, "word": " only", "probability": 0.87451171875}, {"start": 1194.91, "end": 1195.33, "word": " if", "probability": 0.90087890625}, {"start": 1195.33, "end": 1195.73, "word": " ممكن", "probability": 0.5892333984375}, {"start": 1195.73, "end": 1196.37, "word": " يستخدم", "probability": 0.66644287109375}, {"start": 1196.37, "end": 1196.91, "word": " كتعريف", "probability": 0.9615234375}, {"start": 1196.91, "end": 1197.09, "word": " لأن", "probability": 0.85107421875}, {"start": 1197.09, "end": 1197.23, "word": " ف", "probability": 0.311279296875}, {"start": 1197.23, "end": 1197.41, "word": " and", "probability": 0.78955078125}, {"start": 1197.41, "end": 1197.55, "word": " only", "probability": 0.88037109375}, {"start": 1197.55, "end": 1197.83, "word": " if", "probability": 0.91259765625}, {"start": 1197.83, "end": 1198.39, "word": " there", "probability": 0.66162109375}, {"start": 1198.39, "end": 1198.75, "word": " exists", "probability": 0.609375}, {"start": 1198.75, "end": 1199.01, "word": " an", "probability": 0.84765625}, {"start": 1199.01, "end": 1199.53, "word": " injection", "probability": 0.9296875}, {"start": 1199.53, "end": 1200.19, "word": " إذا", "probability": 0.788818359375}, {"start": 1200.19, "end": 1200.45, "word": " كدرت", "probability": 0.6468098958333334}, {"start": 1200.45, "end": 1200.81, "word": " تلاقي", "probability": 0.7222493489583334}, {"start": 1200.81, "end": 1201.11, "word": " one", "probability": 0.89306640625}, {"start": 1201.11, "end": 1201.29, "word": " to", "probability": 0.759765625}, {"start": 1201.29, "end": 1201.45, "word": " one", "probability": 0.95263671875}, {"start": 1201.45, "end": 1202.01, "word": " function", "probability": 0.94921875}, {"start": 1202.01, "end": 1202.47, "word": " من", "probability": 0.98974609375}, {"start": 1202.47, "end": 1202.67, "word": " a", "probability": 0.91650390625}, {"start": 1202.67, "end": 1202.79, "word": " ل", "probability": 0.88720703125}, {"start": 1202.79, "end": 1202.95, "word": " b", "probability": 0.5888671875}, {"start": 1202.95, "end": 1203.57, "word": " من", "probability": 0.90625}, {"start": 1203.57, "end": 1203.95, "word": " a", "probability": 0.9609375}, {"start": 1203.95, "end": 1204.39, "word": " ل", "probability": 0.97802734375}, {"start": 1204.39, "end": 1204.61, "word": " b", "probability": 0.90625}], "temperature": 1.0}, {"id": 51, "seek": 121790, "start": 1205.26, "end": 1217.9, "text": "فهنا نكتب السؤال و نبدأ نحله اللي هو طبعا جملة by conditional باتجاهين واحدة واحدة فبقول طبعا ال a و ال b دولة مجموعات بدنا نثبت انه cardinality", "tokens": [5172, 3224, 8315, 8717, 4117, 2655, 3555, 21136, 33604, 6027, 4032, 8717, 44510, 10721, 8717, 5016, 43761, 13672, 1829, 31439, 23032, 3555, 3615, 995, 10874, 2304, 37977, 538, 27708, 4724, 9307, 7435, 40294, 9957, 36764, 24401, 3660, 36764, 24401, 3660, 6156, 3555, 39648, 23032, 3555, 3615, 995, 2423, 257, 4032, 2423, 272, 11778, 12610, 3660, 3714, 7435, 2304, 45367, 9307, 47525, 8315, 8717, 12984, 3555, 2655, 16472, 3224, 2920, 259, 1860], "avg_logprob": -0.16265191406839424, "compression_ratio": 1.4596273291925466, "no_speech_prob": 0.0, "words": [{"start": 1205.26, "end": 1205.72, "word": "فهنا", "probability": 0.7255859375}, {"start": 1205.72, "end": 1206.84, "word": " نكتب", "probability": 0.98583984375}, {"start": 1206.84, "end": 1207.44, "word": " السؤال", "probability": 0.9923502604166666}, {"start": 1207.44, "end": 1207.56, "word": " و", "probability": 0.95361328125}, {"start": 1207.56, "end": 1207.82, "word": " نبدأ", "probability": 0.8001302083333334}, {"start": 1207.82, "end": 1208.34, "word": " نحله", "probability": 0.8946940104166666}, {"start": 1208.34, "end": 1208.72, "word": " اللي", "probability": 0.7978515625}, {"start": 1208.72, "end": 1208.96, "word": " هو", "probability": 0.97998046875}, {"start": 1208.96, "end": 1209.38, "word": " طبعا", "probability": 0.838134765625}, {"start": 1209.38, "end": 1209.98, "word": " جملة", "probability": 0.95458984375}, {"start": 1209.98, "end": 1210.18, "word": " by", "probability": 0.365478515625}, {"start": 1210.18, "end": 1210.76, "word": " conditional", "probability": 0.8857421875}, {"start": 1210.76, "end": 1211.62, "word": " باتجاهين", "probability": 0.92392578125}, {"start": 1211.62, "end": 1211.96, "word": " واحدة", "probability": 0.9296875}, {"start": 1211.96, "end": 1212.26, "word": " واحدة", "probability": 0.9772135416666666}, {"start": 1212.26, "end": 1213.02, "word": " فبقول", "probability": 0.7683919270833334}, {"start": 1213.02, "end": 1213.3, "word": " طبعا", "probability": 0.9378662109375}, {"start": 1213.3, "end": 1213.42, "word": " ال", "probability": 0.8720703125}, {"start": 1213.42, "end": 1213.48, "word": " a", "probability": 0.3564453125}, {"start": 1213.48, "end": 1213.6, "word": " و", "probability": 0.8974609375}, {"start": 1213.6, "end": 1213.64, "word": " ال", "probability": 0.86474609375}, {"start": 1213.64, "end": 1213.78, "word": " b", "probability": 0.953125}, {"start": 1213.78, "end": 1214.22, "word": " دولة", "probability": 0.8356119791666666}, {"start": 1214.22, "end": 1215.42, "word": " مجموعات", "probability": 0.96484375}, {"start": 1215.42, "end": 1215.88, "word": " بدنا", "probability": 0.648193359375}, {"start": 1215.88, "end": 1216.26, "word": " نثبت", "probability": 0.99169921875}, {"start": 1216.26, "end": 1216.72, "word": " انه", "probability": 0.789306640625}, {"start": 1216.72, "end": 1217.9, "word": " cardinality", "probability": 0.90478515625}], "temperature": 1.0}, {"id": 52, "seek": 124675, "start": 1218.91, "end": 1246.75, "text": "للـ A أقل أو تساوي cardinality للـ B هي statement if and only if يعني تكافئ وقولنا مافيش فرق اكتبك او اكتبت تلات شحطات كل واحد there exists an injection a function from A to B و تكون injection there exists a function from A to B with F is one to one فهذه الجملة التانية", "tokens": [1211, 1211, 39184, 316, 5551, 4587, 1211, 34051, 6055, 3794, 995, 45865, 2920, 259, 1860, 24976, 39184, 363, 39896, 5629, 498, 293, 787, 498, 37495, 22653, 6055, 4117, 31845, 19986, 4032, 39648, 8315, 19446, 41185, 8592, 6156, 2288, 4587, 1975, 4117, 2655, 3555, 4117, 1975, 2407, 1975, 4117, 2655, 3555, 2655, 6055, 1211, 9307, 13412, 5016, 9566, 9307, 28242, 36764, 24401, 456, 8198, 364, 22873, 257, 2445, 490, 316, 281, 363, 4032, 6055, 30544, 22873, 456, 8198, 257, 2445, 490, 316, 281, 363, 365, 479, 307, 472, 281, 472, 6156, 3224, 24192, 25724, 2304, 37977, 16712, 7649, 10632], "avg_logprob": -0.2110164204631189, "compression_ratio": 1.5341880341880343, "no_speech_prob": 0.0, "words": [{"start": 1218.91, "end": 1219.47, "word": "للـ", "probability": 0.6731770833333334}, {"start": 1219.47, "end": 1219.81, "word": " A", "probability": 0.50146484375}, {"start": 1219.81, "end": 1220.89, "word": " أقل", "probability": 0.9186197916666666}, {"start": 1220.89, "end": 1221.09, "word": " أو", "probability": 0.88916015625}, {"start": 1221.09, "end": 1221.69, "word": " تساوي", "probability": 0.960693359375}, {"start": 1221.69, "end": 1223.17, "word": " cardinality", "probability": 0.7788899739583334}, {"start": 1223.17, "end": 1223.57, "word": " للـ", "probability": 0.625732421875}, {"start": 1223.57, "end": 1223.81, "word": " B", "probability": 0.70947265625}, {"start": 1223.81, "end": 1224.09, "word": " هي", "probability": 0.580078125}, {"start": 1224.09, "end": 1224.79, "word": " statement", "probability": 0.8232421875}, {"start": 1224.79, "end": 1225.69, "word": " if", "probability": 0.8466796875}, {"start": 1225.69, "end": 1225.99, "word": " and", "probability": 0.95166015625}, {"start": 1225.99, "end": 1226.33, "word": " only", "probability": 0.9189453125}, {"start": 1226.33, "end": 1226.73, "word": " if", "probability": 0.97900390625}, {"start": 1226.73, "end": 1227.01, "word": " يعني", "probability": 0.83056640625}, {"start": 1227.01, "end": 1227.69, "word": " تكافئ", "probability": 0.9056396484375}, {"start": 1227.69, "end": 1228.31, "word": " وقولنا", "probability": 0.4832763671875}, {"start": 1228.31, "end": 1228.61, "word": " مافيش", "probability": 0.8740234375}, {"start": 1228.61, "end": 1228.85, "word": " فرق", "probability": 0.9485677083333334}, {"start": 1228.85, "end": 1229.29, "word": " اكتبك", "probability": 0.8185546875}, {"start": 1229.29, "end": 1229.41, "word": " او", "probability": 0.86474609375}, {"start": 1229.41, "end": 1229.83, "word": " اكتبت", "probability": 0.8232421875}, {"start": 1229.83, "end": 1230.19, "word": " تلات", "probability": 0.7713216145833334}, {"start": 1230.19, "end": 1230.63, "word": " شحطات", "probability": 0.843994140625}, {"start": 1230.63, "end": 1230.97, "word": " كل", "probability": 0.91015625}, {"start": 1230.97, "end": 1231.45, "word": " واحد", "probability": 0.996337890625}, {"start": 1231.45, "end": 1232.03, "word": " there", "probability": 0.67822265625}, {"start": 1232.03, "end": 1232.59, "word": " exists", "probability": 0.5966796875}, {"start": 1232.59, "end": 1233.25, "word": " an", "probability": 0.876953125}, {"start": 1233.25, "end": 1233.77, "word": " injection", "probability": 0.92626953125}, {"start": 1233.77, "end": 1234.45, "word": " a", "probability": 0.7197265625}, {"start": 1234.45, "end": 1234.89, "word": " function", "probability": 0.970703125}, {"start": 1234.89, "end": 1235.31, "word": " from", "probability": 0.92822265625}, {"start": 1235.31, "end": 1235.65, "word": " A", "probability": 0.87158203125}, {"start": 1235.65, "end": 1235.81, "word": " to", "probability": 0.9765625}, {"start": 1235.81, "end": 1236.21, "word": " B", "probability": 0.9931640625}, {"start": 1236.21, "end": 1238.11, "word": " و", "probability": 0.270751953125}, {"start": 1238.11, "end": 1238.33, "word": " تكون", "probability": 0.798583984375}, {"start": 1238.33, "end": 1238.73, "word": " injection", "probability": 0.95556640625}, {"start": 1238.73, "end": 1238.91, "word": " there", "probability": 0.458251953125}, {"start": 1238.91, "end": 1239.11, "word": " exists", "probability": 0.6064453125}, {"start": 1239.11, "end": 1239.27, "word": " a", "probability": 0.97900390625}, {"start": 1239.27, "end": 1239.63, "word": " function", "probability": 0.96728515625}, {"start": 1239.63, "end": 1240.17, "word": " from", "probability": 0.89501953125}, {"start": 1240.17, "end": 1240.37, "word": " A", "probability": 0.98486328125}, {"start": 1240.37, "end": 1240.51, "word": " to", "probability": 0.98486328125}, {"start": 1240.51, "end": 1240.83, "word": " B", "probability": 0.99658203125}, {"start": 1240.83, "end": 1241.57, "word": " with", "probability": 0.90283203125}, {"start": 1241.57, "end": 1243.39, "word": " F", "probability": 0.7939453125}, {"start": 1243.39, "end": 1243.85, "word": " is", "probability": 0.8984375}, {"start": 1243.85, "end": 1244.11, "word": " one", "probability": 0.82470703125}, {"start": 1244.11, "end": 1244.23, "word": " to", "probability": 0.89306640625}, {"start": 1244.23, "end": 1244.57, "word": " one", "probability": 0.93994140625}, {"start": 1244.57, "end": 1245.91, "word": " فهذه", "probability": 0.82763671875}, {"start": 1245.91, "end": 1246.27, "word": " الجملة", "probability": 0.94189453125}, {"start": 1246.27, "end": 1246.75, "word": " التانية", "probability": 0.8208821614583334}], "temperature": 1.0}, {"id": 53, "seek": 127793, "start": 1248.41, "end": 1277.93, "text": "فهذا المطلوب solution نبدأ بالاتجاه الأول أن اليسار implies اليمين cardinality of A أقل أو يساوي cardinality of B implies there exists F من A لB one to one F is one to one هذا المطلوب", "tokens": [5172, 3224, 15730, 9673, 9566, 1211, 37746, 3827, 8717, 44510, 10721, 20666, 9307, 7435, 40294, 16247, 12610, 14739, 45595, 3794, 9640, 18779, 45595, 2304, 9957, 2920, 259, 1860, 295, 316, 5551, 4587, 1211, 34051, 7251, 3794, 995, 45865, 2920, 259, 1860, 295, 363, 18779, 456, 8198, 479, 9154, 316, 5296, 33, 472, 281, 472, 479, 307, 472, 281, 472, 23758, 9673, 9566, 1211, 37746], "avg_logprob": -0.17415865384615384, "compression_ratio": 1.521472392638037, "no_speech_prob": 0.0, "words": [{"start": 1248.41, "end": 1248.93, "word": "فهذا", "probability": 0.83203125}, {"start": 1248.93, "end": 1249.41, "word": " المطلوب", "probability": 0.9478759765625}, {"start": 1249.41, "end": 1249.95, "word": " solution", "probability": 0.61865234375}, {"start": 1249.95, "end": 1251.83, "word": " نبدأ", "probability": 0.93896484375}, {"start": 1251.83, "end": 1252.49, "word": " بالاتجاه", "probability": 0.968017578125}, {"start": 1252.49, "end": 1253.17, "word": " الأول", "probability": 0.945068359375}, {"start": 1253.17, "end": 1256.41, "word": " أن", "probability": 0.279296875}, {"start": 1256.41, "end": 1257.37, "word": " اليسار", "probability": 0.8963216145833334}, {"start": 1257.37, "end": 1258.09, "word": " implies", "probability": 0.2841796875}, {"start": 1258.09, "end": 1258.97, "word": " اليمين", "probability": 0.7978515625}, {"start": 1258.97, "end": 1260.91, "word": " cardinality", "probability": 0.88525390625}, {"start": 1260.91, "end": 1261.21, "word": " of", "probability": 0.95849609375}, {"start": 1261.21, "end": 1261.69, "word": " A", "probability": 0.5849609375}, {"start": 1261.69, "end": 1262.93, "word": " أقل", "probability": 0.91455078125}, {"start": 1262.93, "end": 1263.13, "word": " أو", "probability": 0.8896484375}, {"start": 1263.13, "end": 1263.71, "word": " يساوي", "probability": 0.957763671875}, {"start": 1263.71, "end": 1264.53, "word": " cardinality", "probability": 0.9202473958333334}, {"start": 1264.53, "end": 1264.77, "word": " of", "probability": 0.98046875}, {"start": 1264.77, "end": 1265.21, "word": " B", "probability": 0.9853515625}, {"start": 1265.21, "end": 1266.53, "word": " implies", "probability": 0.876953125}, {"start": 1266.53, "end": 1267.27, "word": " there", "probability": 0.7744140625}, {"start": 1267.27, "end": 1267.93, "word": " exists", "probability": 0.40576171875}, {"start": 1267.93, "end": 1268.95, "word": " F", "probability": 0.701171875}, {"start": 1268.95, "end": 1269.73, "word": " من", "probability": 0.96484375}, {"start": 1269.73, "end": 1269.97, "word": " A", "probability": 0.9111328125}, {"start": 1269.97, "end": 1270.45, "word": " لB", "probability": 0.69873046875}, {"start": 1270.45, "end": 1271.23, "word": " one", "probability": 0.72216796875}, {"start": 1271.23, "end": 1271.41, "word": " to", "probability": 0.92138671875}, {"start": 1271.41, "end": 1271.69, "word": " one", "probability": 0.9423828125}, {"start": 1271.69, "end": 1273.51, "word": " F", "probability": 0.43505859375}, {"start": 1273.51, "end": 1273.73, "word": " is", "probability": 0.84716796875}, {"start": 1273.73, "end": 1273.97, "word": " one", "probability": 0.9482421875}, {"start": 1273.97, "end": 1274.13, "word": " to", "probability": 0.96533203125}, {"start": 1274.13, "end": 1274.81, "word": " one", "probability": 0.9453125}, {"start": 1274.81, "end": 1277.47, "word": " هذا", "probability": 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{"start": 1297.57, "end": 1297.79, "word": " و", "probability": 0.70166015625}, {"start": 1297.79, "end": 1297.95, "word": " to", "probability": 0.62060546875}, {"start": 1297.95, "end": 1298.21, "word": " one", "probability": 0.9052734375}, {"start": 1298.21, "end": 1298.75, "word": " خلينا", "probability": 0.6781005859375}, {"start": 1298.75, "end": 1299.13, "word": " نكتب", "probability": 0.9964599609375}, {"start": 1299.13, "end": 1300.11, "word": " we", "probability": 0.45751953125}, {"start": 1300.11, "end": 1300.73, "word": " want", "probability": 0.9326171875}, {"start": 1300.73, "end": 1302.01, "word": " to", "probability": 0.9765625}, {"start": 1302.01, "end": 1302.71, "word": " find", "probability": 0.9306640625}, {"start": 1302.71, "end": 1304.39, "word": " a", "probability": 0.97998046875}, {"start": 1304.39, "end": 1305.11, "word": " function", "probability": 0.97802734375}], "temperature": 1.0}, {"id": 55, "seek": 131509, "start": 1307.41, "end": 1315.09, "text": "المهارات بناء من نفس الاتجاه F من A ل B such that F is one to one", "tokens": [6027, 2304, 3224, 9640, 9307, 44945, 16606, 9154, 8717, 36178, 2423, 9307, 7435, 40294, 479, 9154, 316, 5296, 363, 1270, 300, 479, 307, 472, 281, 472], "avg_logprob": -0.3148148103996559, "compression_ratio": 1.0574712643678161, "no_speech_prob": 0.0, "words": [{"start": 1307.41, "end": 1308.21, "word": "المهارات", "probability": 0.753564453125}, {"start": 1308.21, "end": 1308.89, "word": " بناء", "probability": 0.51312255859375}, {"start": 1308.89, "end": 1308.93, "word": " من", "probability": 0.321044921875}, {"start": 1308.93, "end": 1309.05, "word": " نفس", "probability": 0.9794921875}, {"start": 1309.05, "end": 1309.61, "word": " الاتجاه", "probability": 0.8734130859375}, {"start": 1309.61, "end": 1310.39, "word": " F", "probability": 0.478759765625}, {"start": 1310.39, "end": 1311.25, "word": " من", "probability": 0.88427734375}, {"start": 1311.25, "end": 1311.61, "word": " A", "probability": 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تكون one to one وليس انتوا لما نعمل اللي وكنا اللي هو التكافؤ تكون one to one و أنتوا بين a و b و لما نكون denomable بين المجموع و بين الان كله بدور على دالة", "tokens": [5172, 3555, 1863, 3215, 13063, 15844, 11778, 6027, 3660, 6055, 30544, 472, 281, 472, 3714, 3224, 9640, 9307, 9122, 2288, 43500, 20449, 8315, 6225, 41891, 3714, 2288, 9307, 8978, 6225, 41891, 3714, 2407, 46958, 40228, 9122, 33911, 8717, 25957, 1211, 44945, 16606, 8717, 25957, 1211, 6435, 5296, 3215, 6027, 3660, 49374, 3714, 7435, 2304, 45367, 2655, 9957, 5296, 15042, 9122, 8315, 8717, 12984, 3555, 2655, 13785, 9122, 8315, 9154, 9673, 7435, 2304, 45367, 15844, 8717, 36178, 11296, 6055, 30544, 472, 281, 472, 4032, 20292, 3794, 16472, 2655, 14407, 5296, 15042, 8717, 25957, 1211, 13672, 1829, 4032, 4117, 8315, 13672, 1829, 31439, 16712, 4117, 31845, 33604, 6055, 30544, 472, 281, 472, 4032, 14739, 2655, 14407, 49374, 257, 4032, 272, 4032, 5296, 15042, 8717, 30544, 1441, 298, 712, 49374, 9673, 7435, 2304, 45367, 4032, 49374, 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وين تدور؟ في المعطيات، في في المعطيات دوال؟ اه بما أن هذه أصغر هي تستوي هذه، إذا هذه تكافئ 6 من ال B، أحسنتي، اه فإذا نشتغل، شايفين فاحنا كيف الأفكار، المبادرة اللي بتعلمها؟ اه هي من أول ما بدينا البرهانة جملة شرطية كيف نبدأها، اشترد إن الشرط صحيح و بنشتغل، اه فدي", "tokens": [5172, 9566, 3555, 3615, 995, 8608, 33604, 6027, 16712, 4587, 20292, 16254, 8032, 1211, 39894, 3215, 13063, 8978, 6055, 5172, 18513, 2288, 2423, 33400, 22807, 5296, 10721, 12399, 4032, 9957, 6055, 3215, 13063, 22807, 8978, 9673, 3615, 9566, 1829, 9307, 12399, 8978, 8978, 9673, 3615, 9566, 1829, 9307, 11778, 2407, 6027, 22807, 1975, 3224, 4724, 15042, 14739, 29538, 5551, 9381, 17082, 2288, 39896, 6055, 14851, 45865, 29538, 12399, 11933, 15730, 29538, 6055, 4117, 31845, 19986, 1386, 9154, 2423, 363, 12399, 5551, 5016, 3794, 29399, 1829, 12399, 1975, 3224, 6156, 28814, 15730, 8717, 8592, 2655, 17082, 1211, 12399, 13412, 995, 33911, 9957, 6156, 39319, 8315, 9122, 33911, 16247, 5172, 4117, 9640, 12399, 9673, 3555, 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التعبير صحيحة since cardinality لل a أقل أو يساوي cardinality لل b we have", "tokens": [25957, 20292, 9307, 5551, 3794, 32277, 10632, 5296, 31377, 2304, 8717, 2655, 3615, 19528, 11296, 3714, 3224, 9640, 9307, 5296, 5718, 118, 1863, 7578, 18871, 11296, 8978, 16712, 3615, 10943, 1211, 20449, 29739, 23557, 3224, 9957, 6156, 28814, 15730, 34105, 1670, 8717, 4117, 2655, 36150, 3224, 34051, 8717, 4117, 2655, 36150, 3224, 586, 28242, 41950, 2288, 4587, 16712, 3615, 3555, 13546, 20328, 5016, 1829, 5016, 3660, 1670, 2920, 259, 1860, 24976, 257, 5551, 4587, 1211, 34051, 7251, 3794, 995, 45865, 2920, 259, 1860, 24976, 272, 321, 362], "avg_logprob": -0.19318181377920238, "compression_ratio": 1.5935828877005347, "no_speech_prob": 0.0, "words": [{"start": 1370.72, "end": 1371.6, "word": "عمليات", "probability": 0.9248046875}, {"start": 1371.6, "end": 1372.26, "word": " أساسية", "probability": 0.9527587890625}, {"start": 1372.26, "end": 1372.64, "word": " لازم", "probability": 0.9456380208333334}, 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0.919189453125}], "temperature": 1.0}, {"id": 99, "seek": 240917, "start": 2390.09, "end": 2409.17, "text": "there exists H من A ل A0 تكون bijection وهو المطلوب تمام نتيجة الكلام اللي حكيناه", "tokens": [15456, 8198, 389, 9154, 316, 5296, 316, 15, 6055, 30544, 3228, 1020, 313, 37037, 2407, 9673, 9566, 1211, 37746, 46811, 10943, 8717, 31371, 7435, 3660, 2423, 28820, 10943, 13672, 1829, 11331, 4117, 1829, 8315, 3224], "avg_logprob": -0.2565104059047169, "compression_ratio": 1.1495327102803738, "no_speech_prob": 0.0, "words": [{"start": 2390.09, "end": 2390.49, "word": "there", "probability": 0.254150390625}, {"start": 2390.49, "end": 2390.91, "word": " exists", "probability": 0.6865234375}, {"start": 2390.91, "end": 2391.43, "word": " H", "probability": 0.443115234375}, {"start": 2391.43, "end": 2392.31, "word": " من", "probability": 0.90771484375}, {"start": 2392.31, "end": 2392.53, "word": " A", "probability": 0.7783203125}, {"start": 2392.53, "end": 2392.67, "word": " ل", 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المجموعات التعبير بلغة ال cardinal numbers و هنا يعني زي ما حكينا هذا الشبطر نفس الكلام اللي كنا بنشرحه و بنتحدث عنه كتير من الصلاحات في شبطر خمسة بس بنحكيها بلغة ال cardinal number فهنا بقول if a and b are such that cardinal number of a أقل أو يساوي cardinal number of b كتبته في البداية و cardinal number of b أقل أو يساوي cardinal number of a فالتانية متساوي", "tokens": [5172, 3224, 15730, 16712, 3615, 3555, 13546, 4724, 1211, 17082, 3660, 9673, 7435, 2304, 45367, 9307, 16712, 3615, 3555, 13546, 4724, 1211, 17082, 3660, 2423, 2920, 2071, 3547, 4032, 34105, 37495, 22653, 30767, 1829, 19446, 11331, 4117, 1829, 8315, 23758, 25124, 3555, 9566, 2288, 8717, 36178, 2423, 28820, 10943, 13672, 1829, 9122, 8315, 44945, 46309, 5016, 3224, 4032, 44945, 2655, 24401, 12984, 18871, 3224, 9122, 2655, 13546, 9154, 31767, 15040, 5016, 9307, 8978, 13412, 3555, 9566, 2288, 16490, 2304, 3794, 3660, 4724, 3794, 44945, 5016, 4117, 1829, 11296, 4724, 1211, 17082, 3660, 2423, 2920, 2071, 1230, 6156, 3224, 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0.8719482421875}, {"start": 2691.81, "end": 2693.59, "word": " تنتمي", "probability": 0.8468017578125}, {"start": 2693.59, "end": 2693.69, "word": " او", "probability": 0.813232421875}, {"start": 2693.69, "end": 2693.79, "word": " لا", "probability": 0.86865234375}, {"start": 2693.79, "end": 2694.17, "word": " تنتمي", "probability": 0.9862060546875}, {"start": 2694.17, "end": 2694.39, "word": " طبعا", "probability": 0.8013916015625}, {"start": 2694.39, "end": 2694.67, "word": " الواحد", "probability": 0.9601236979166666}, {"start": 2694.67, "end": 2695.59, "word": " تنتمي", "probability": 0.9822998046875}, {"start": 2695.59, "end": 2697.03, "word": " نعم", "probability": 0.64794921875}, {"start": 2697.03, "end": 2698.59, "word": " اي", "probability": 0.5985107421875}, {"start": 2698.59, "end": 2698.77, "word": " اي", "probability": 0.82275390625}, {"start": 2698.77, "end": 2699.05, "word": " لو", "probability": 0.7587890625}, {"start": 2699.05, "end": 2699.37, "word": " answer", "probability": 0.6611328125}, {"start": 2699.37, "end": 2699.61, "word": " ما", "probability": 0.87353515625}, {"start": 2699.61, "end": 2700.13, "word": " يعني", "probability": 0.742431640625}, {"start": 2700.13, "end": 2700.27, "word": " انا", "probability": 0.67041015625}, {"start": 2700.27, "end": 2700.53, "word": " جيتلك", "probability": 0.7716471354166666}, {"start": 2700.53, "end": 2700.61, "word": " و", "probability": 0.80712890625}, {"start": 2700.61, "end": 2700.91, "word": " قولتلك", "probability": 0.8446044921875}, {"start": 2700.91, "end": 2701.41, "word": " واحد", "probability": 0.987060546875}, {"start": 2701.41, "end": 2703.21, "word": " true", "probability": 0.8984375}, {"start": 2703.21, "end": 2703.67, "word": " صح", "probability": 0.947265625}, {"start": 2703.67, "end": 2704.99, "word": " اتنين", "probability": 0.90771484375}, {"start": 2704.99, "end": 2707.13, "word": " false", "probability": 0.8193359375}, {"start": 2707.13, "end": 2708.29, "word": " تمام", "probability": 0.839599609375}, {"start": 2708.29, "end": 2708.71, "word": " اه", "probability": 0.631103515625}, {"start": 2708.71, "end": 2709.09, "word": " فان", "probability": 0.8369140625}, {"start": 2709.09, "end": 2709.27, "word": " شاء", "probability": 0.925048828125}, {"start": 2709.27, "end": 2709.47, "word": " الله", "probability": 0.95654296875}, {"start": 2709.47, "end": 2711.97, "word": " طيب", "probability": 0.9423828125}, {"start": 2711.97, "end": 2712.43, "word": " اذا", "probability": 0.856689453125}, {"start": 2712.43, "end": 2712.59, "word": " مش", "probability": 0.984375}, {"start": 2712.59, "end": 2713.03, "word": " واضحالك", "probability": 0.758935546875}, {"start": 2713.03, "end": 2713.45, "word": " هيها", "probability": 0.822021484375}, {"start": 2713.45, "end": 2718.05, "word": " صح", "probability": 0.985595703125}, {"start": 2718.05, "end": 2719.45, "word": " واضحت", "probability": 0.8203125}], "temperature": 1.0}, {"id": 112, "seek": 273339, "start": 2723.01, "end": 2733.39, "text": "تمام مثال لأ لأ كابتن ال X هذا كان مثال فشوية شوية ان شاء الله عند اكتوب البرهان هحتاج عادل رموز ان شاء الله يوم السبت بنرجع للموضوع واحدة مرة ثانية", "tokens": [39237, 10943, 50113, 6027, 5296, 10721, 5296, 10721, 9122, 16758, 2655, 1863, 2423, 1783, 23758, 25961, 50113, 6027, 6156, 8592, 2407, 10632, 13412, 2407, 10632, 16472, 13412, 16606, 21984, 43242, 1975, 4117, 2655, 2407, 3555, 2423, 26890, 3224, 7649, 8032, 33753, 26108, 6225, 18513, 1211, 12602, 2304, 2407, 11622, 16472, 13412, 16606, 21984, 7251, 20498, 21136, 3555, 2655, 44945, 47341, 3615, 5296, 19528, 2407, 11242, 45367, 36764, 24401, 3660, 3714, 25720, 38637, 7649, 10632], "avg_logprob": -0.32416666825612384, "compression_ratio": 1.7320261437908497, "no_speech_prob": 0.0, "words": [{"start": 2723.01, "end": 2723.57, "word": "تمام", "probability": 0.683349609375}, {"start": 2723.57, "end": 2724.13, "word": " مثال", "probability": 0.7646484375}, {"start": 2724.13, "end": 2724.71, "word": " لأ", "probability": 0.57159423828125}, {"start": 2724.71, "end": 2724.99, "word": " لأ", "probability": 0.865234375}, {"start": 2724.99, "end": 2725.43, "word": " كابتن", "probability": 0.60357666015625}, {"start": 2725.43, "end": 2725.51, "word": " ال", "probability": 0.5927734375}, {"start": 2725.51, "end": 2725.63, "word": " X", "probability": 0.787109375}, {"start": 2725.63, "end": 2725.83, "word": " هذا", "probability": 0.3095703125}, {"start": 2725.83, "end": 2725.97, "word": " كان", "probability": 0.9296875}, {"start": 2725.97, "end": 2726.83, "word": " مثال", "probability": 0.9951171875}, {"start": 2726.83, "end": 2728.21, "word": " فشوية", "probability": 0.69757080078125}, {"start": 2728.21, "end": 2728.45, "word": " شوية", "probability": 0.9703776041666666}, {"start": 2728.45, "end": 2728.55, "word": " ان", "probability": 0.72509765625}, {"start": 2728.55, "end": 2728.65, "word": " شاء", "probability": 0.97900390625}, {"start": 2728.65, "end": 2728.69, "word": " الله", "probability": 0.94287109375}, {"start": 2728.69, "end": 2728.91, "word": " عند", "probability": 0.3466796875}, {"start": 2728.91, "end": 2729.23, "word": " اكتوب", "probability": 0.54912109375}, {"start": 2729.23, "end": 2729.51, "word": " البرهان", "probability": 0.78961181640625}, {"start": 2729.51, "end": 2729.89, "word": " هحتاج", "probability": 0.87646484375}, {"start": 2729.89, "end": 2730.19, "word": " عادل", "probability": 0.582275390625}, {"start": 2730.19, "end": 2730.61, "word": " رموز", "probability": 0.978515625}, {"start": 2730.61, "end": 2730.99, "word": " ان", "probability": 0.64599609375}, {"start": 2730.99, "end": 2731.07, "word": " شاء", "probability": 0.9853515625}, {"start": 2731.07, "end": 2731.13, "word": " الله", "probability": 0.9658203125}, {"start": 2731.13, "end": 2731.29, "word": " يوم", "probability": 0.976318359375}, {"start": 2731.29, "end": 2731.65, "word": " السبت", "probability": 0.7843424479166666}, {"start": 2731.65, "end": 2732.29, "word": " بنرجع", "probability": 0.92529296875}, {"start": 2732.29, "end": 2732.67, "word": " للموضوع", "probability": 0.7830078125}, {"start": 2732.67, "end": 2732.93, "word": " واحدة", "probability": 0.67529296875}, {"start": 2732.93, "end": 2733.13, "word": " مرة", "probability": 0.735107421875}, {"start": 2733.13, "end": 2733.39, "word": " ثانية", "probability": 0.8202311197916666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2733.5691875, "duration_after_vad": 2605.63562499999}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/8meu521dv0U_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/8meu521dv0U_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a83c5a74fcff0c3ce1f2bdfebd6b683947786962
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/8meu521dv0U_raw.srt
@@ -0,0 +1,2244 @@
+1
+00:00:19,760 --> 00:00:24,200
+بسم الله الرحمن الرحيم ففي آخر محاضرة احنا بدأنا
+
+2
+00:00:24,200 --> 00:00:28,060
+كمقدمة سريعة على ال cardinal number خلينا نعيد على
+
+3
+00:00:28,060 --> 00:00:32,460
+السريع ف cardinal numbers and cardinal arithmetic
+
+4
+00:00:32,460 --> 00:00:37,060
+الاعداد الأصلية ممكن نعرفها وطبعا و العملات
+
+5
+00:00:37,060 --> 00:00:42,210
+الحسابية على هذه الاعدادفطبعا الأعداد اللي هو
+
+6
+00:00:42,210 --> 00:00:47,530
+الأصلية هي أعداد هنستخدمها للتعبير عن عدد عناصر
+
+7
+00:00:47,530 --> 00:00:51,670
+المجموعات طبعا مافيش نظام من الأنظمة اللي بنعرفها
+
+8
+00:00:51,670 --> 00:00:54,170
+للاعداد الطبيعية ولا الأعداد الصحيحة ولا الأعداد
+
+9
+00:00:54,170 --> 00:00:58,930
+الحقيقية بتقدر تقوم بهذا المقام وتعبر عن اللي هو
+
+10
+00:00:58,930 --> 00:01:02,430
+أعداد المجموعات بشكل عام لأن زي ما احنا شوفنا فيه
+
+11
+00:01:02,430 --> 00:01:06,510
+مجموعات infinite لكن مختلفين ففي عندنا the
+
+12
+00:01:06,510 --> 00:01:09,990
+numerable sets اللي هي عدد عناصرها بكافة عدد عناصر
+
+13
+00:01:09,990 --> 00:01:15,080
+الأنوفي نمض Numerable sets زي الـ R أو الفترة من
+
+14
+00:01:15,080 --> 00:01:18,440
+صفر لواحد وهذه Infinite وهذه Infinite لكن مختلفة
+
+15
+00:01:18,440 --> 00:01:22,620
+ماقدرش أقول إنها Infinity مثلا وهذه Infinity نفس
+
+16
+00:01:22,620 --> 00:01:26,840
+الرمز مانفعش لذلك بدنا نظام جديد من الاعداد يقدر
+
+17
+00:01:26,840 --> 00:01:31,120
+يعبر عن هذه المجموعات ويفرخ بينها ونقدر نشتر عليه
+
+18
+00:01:31,120 --> 00:01:34,260
+في عملية طبعا ما زال عملنا نظام جديد من الاعداد
+
+19
+00:01:34,260 --> 00:01:37,840
+بدنا نشوف خواصه كيف نجمع الاعداد هذه كيف نضربها
+
+20
+00:01:37,840 --> 00:01:41,980
+وبعض الأمورفطبعا احنا عرفنا اللي هو ال cardinal
+
+21
+00:01:41,980 --> 00:01:46,420
+numbers طبعا بطريقة بسيطة و مباشرة فيه أربع قواعد
+
+22
+00:01:46,420 --> 00:01:53,260
+القاعدة الأولى اللي سمناها C1الـ cardinal numbers
+
+23
+00:01:53,260 --> 00:01:58,880
+دولة أعداد خاصة بالمجموعات بتعبر عن المجموعات فكل
+
+24
+00:01:58,880 --> 00:02:05,660
+مجموعة set A يقابلها cardinal number عبرنا عنه باش
+
+25
+00:02:05,660 --> 00:02:11,670
+cardinal number of A أول أربع حروف والعكس صحيحفكل
+
+26
+00:02:11,670 --> 00:02:15,070
+مجموعة بيقبلها cardinal number وكل cardinal number
+
+27
+00:02:15,070 --> 00:02:18,630
+لازم يعبر عن مجموعة يعني مانفعش اقول مثلا ان في
+
+28
+00:02:18,630 --> 00:02:21,650
+انا عندي cardinal number بيساوي خمسة اه الخمسة دي
+
+29
+00:02:21,650 --> 00:02:26,710
+مش بتعبر عن وزن كمية معينة لأ بتعبر عن عدد عناصر
+
+30
+00:02:26,710 --> 00:02:29,970
+المجموعة لازم فمانفعش فدائما ال cardinal numbers
+
+31
+00:02:29,970 --> 00:02:35,130
+مرتبط ارتباط وثيق بعدد عناصر المجموعات فكل مجموعة
+
+32
+00:02:35,130 --> 00:02:39,210
+بقدر اشوف cardinal number بيعبر عنهاوكل cardinal
+
+33
+00:02:39,210 --> 00:02:42,570
+number لازم يكون فيه مجموعة بيعبر عنها بقى بقى بقى
+
+34
+00:02:42,570 --> 00:02:44,470
+كذا بدأت من المجموعة بقدر ألاقي ال cardinal number
+
+35
+00:02:44,470 --> 00:02:47,910
+المناسب بدأت من cardinal number بقدر ألاقي مجموعة
+
+36
+00:02:47,910 --> 00:02:54,830
+مناسبة اتعبر عنه القاعدة رقم اتنين ان المجموعة
+
+37
+00:02:54,830 --> 00:02:57,790
+الوحيدة اللي cardinality بتساوي صفر هي ال five اه
+
+38
+00:02:57,790 --> 00:03:03,860
+فاحنا عندنا ال cardinalityللمجموعة ما بتساوي صفر
+
+39
+00:03:03,860 --> 00:03:08,200
+if and only if هذه المجموعة هي الـ Phi فإذا أول
+
+40
+00:03:08,200 --> 00:03:10,800
+cardinal number نريد أن نعرف أن هو الصفر فالصفر
+
+41
+00:03:10,800 --> 00:03:13,740
+cardinal number لأنه بعبر عن مجموعة مين الـ Phi
+
+42
+00:03:13,740 --> 00:03:20,700
+المجموعة الفارقة القاعدة رقم تلاتة انه طبعا احنا
+
+43
+00:03:20,700 --> 00:03:26,630
+نعماحنا بنحاول نعمل مفهوم، نقول احنا ليش جيبنا
+
+44
+00:03:26,630 --> 00:03:29,030
+أعداد جديدة لإن الأعداد الطبيعية مش كافية، طب
+
+45
+00:03:29,030 --> 00:03:31,450
+الأعداد الطبيعية ممكن تتعبر عن المجموعات نعم إذا
+
+46
+00:03:31,450 --> 00:03:33,950
+كانت finite، لكن مابتكفيش لحالك، المشكلة في ال
+
+47
+00:03:33,950 --> 00:03:37,370
+infinite، لذلك لو كان عندنا مجموعة فيها مائة عنصر،
+
+48
+00:03:37,370 --> 00:03:40,570
+جداش cardinality تبعتها؟ مية، على طول، فكيف عبرنا
+
+49
+00:03:40,570 --> 00:03:46,310
+عنه؟ قولنا إذا ال A تكافئ أن K، فهذا يؤدي إن ال
+
+50
+00:03:46,310 --> 00:03:51,210
+cardinalityللـ A تساوي K finite على طول مباشرة
+
+51
+00:03:51,210 --> 00:03:55,850
+القاعدة الرابعة و الأخيرة أنه إذا كانت ال A تكافئ
+
+52
+00:03:55,850 --> 00:04:00,110
+ال B if and only if ال cardinality لل A تساوي ال
+
+53
+00:04:00,110 --> 00:04:05,390
+cardinality لل B فدولة أربع قواعد بيخلونا نقدر
+
+54
+00:04:05,390 --> 00:04:08,970
+نعرف ال cardinal numbers و نتعامل معاهمفالان ان
+
+55
+00:04:08,970 --> 00:04:13,990
+شاء الله هنتقل لنقطة جديدة طبعا هذا ملخص للمرة
+
+56
+00:04:13,990 --> 00:04:19,670
+الماضية الان هنتحدث عن ترتيب هذه الأرقام مين أصغر
+
+57
+00:04:19,670 --> 00:04:21,950
+من مين طبعا الصفر أصغر من واحد الواحد أصغر من
+
+58
+00:04:21,950 --> 00:04:26,010
+اتنين طب ليش ال cardinality مثلا لل natural number
+
+59
+00:04:26,010 --> 00:04:30,440
+و cardinality لل real number مين أصغر من مين؟أصغر
+
+60
+00:04:30,440 --> 00:04:33,500
+من الريال و هكذا نعبر عن هذا الموضوع بشكل طبعا نحط
+
+61
+00:04:33,500 --> 00:04:36,720
+التعريف و نشهد الكلام اللي حكيناه صح ولا مش صح انت
+
+62
+00:04:36,720 --> 00:04:40,040
+احنا قولنا انه ايش يعني زي ما حاكرت زميلاتكوا ان
+
+63
+00:04:40,040 --> 00:04:47,690
+ال cardinality لل N أصغر من ال cardinality لل Rطب
+
+64
+00:04:47,690 --> 00:04:50,110
+.. طب مين بيقول صح و مين بيقول خطأ؟ نشوف مين
+
+65
+00:04:50,110 --> 00:04:53,110
+المعيار؟ مين الحكم بينا؟ نشوف هذا الموضوع فهنا
+
+66
+00:04:53,110 --> 00:04:56,930
+الموضوع طبعا ال section التاني ordering of the
+
+67
+00:04:56,930 --> 00:05:00,190
+cardinal numbers ordering يعني ترتيب اه كيف ترتيب؟
+
+68
+00:05:00,190 --> 00:05:03,350
+مين صغير؟ مين كبير؟ مين أكبر؟ و هكذا اه و في عندنا
+
+69
+00:05:03,350 --> 00:05:07,630
+طبعا اللي هتحدث في عندنا the Schroeder-Bernstein
+
+70
+00:05:07,630 --> 00:05:11,470
+theorem في نظرية للعالمين Schroeder و Bernstein
+
+71
+00:05:13,860 --> 00:05:20,080
+فطبعا اول شي هنعمل مصطلح جديد فيه ان احنا
+
+72
+00:05:20,080 --> 00:05:25,380
+المجموعات قسمناها ل finite و infinite set و احنا
+
+73
+00:05:25,380 --> 00:05:28,760
+قلنا ال cardinal number مرتبطة في المجموعات تبقى
+
+74
+00:05:28,760 --> 00:05:34,050
+لهذا التقسيم هنقسم ال cardinal number لقسمينبرضه
+
+75
+00:05:34,050 --> 00:05:38,070
+إذا ال cardinal number بيقابل finite set هنسميه
+
+76
+00:05:38,070 --> 00:05:41,530
+finite cardinal number وإذا بيقابل infinite set
+
+77
+00:05:41,530 --> 00:05:44,530
+هنسميه transfinite مش infinite cardinal number
+
+78
+00:05:44,530 --> 00:05:47,890
+trans معناه ما بعد ال finite ما بعد ال finite
+
+79
+00:05:47,890 --> 00:05:52,210
+فهنستخدم المصطلح هذا فعنا العنوان finite and
+
+80
+00:05:52,210 --> 00:05:56,070
+transfinite cardinal number فأول حاجة a cardinal
+
+81
+00:05:56,070 --> 00:06:00,110
+number of a finite set is called a finite cardinal
+
+82
+00:06:00,110 --> 00:06:02,960
+numberأه فإذا ال cardinal number بيقابل مجموع
+
+83
+00:06:02,960 --> 00:06:06,400
+finite بيسميه finite number finite cardinal number
+
+84
+00:06:06,400 --> 00:06:10,800
+طبعا a cardinal number of an infinite set is
+
+85
+00:06:10,800 --> 00:06:14,600
+called a transfinite ما بعد ال finite ما بعد ال
+
+86
+00:06:14,600 --> 00:06:18,980
+finite إيش cardinal number في هذا المصطلح هنستخدم
+
+87
+00:06:18,980 --> 00:06:23,440
+طبعا كمثال ال zero cardinal number ولا لأ لأنه
+
+88
+00:06:23,440 --> 00:06:28,270
+بيقابل ال five finite ولا transfinitefinite الواحد
+
+89
+00:06:28,270 --> 00:06:31,370
+cardinal number صح لأنه بيقابل مين ال singleton
+
+90
+00:06:31,370 --> 00:06:35,330
+set و هو finite و لا transfinite finite طيب ال
+
+91
+00:06:35,330 --> 00:06:40,190
+cardinality لان transfinite واضحة فهذه مثال بسيطة
+
+92
+00:06:40,190 --> 00:06:43,810
+على طول لأن ليش ال N infinite و ال R برضه
+
+93
+00:06:43,810 --> 00:06:46,390
+transfinite ال cardinality تبع التواحد كذا ال
+
+94
+00:06:46,390 --> 00:06:51,370
+cardinal number بنزعج فهذه التعريف بكل بساطة و بكل
+
+95
+00:06:51,370 --> 00:06:55,550
+بشكل مباشر الآن نجي للموضوع الرئيسي و هو الاش
+
+96
+00:06:55,550 --> 00:07:03,970
+الترتيبفانا في عندى انا cardinal numbers انا انا
+
+97
+00:07:03,970 --> 00:07:08,390
+انا انا انا انا
+
+98
+00:07:08,390 --> 00:07:10,410
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+99
+00:07:10,410 --> 00:07:10,450
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+100
+00:07:10,450 --> 00:07:10,670
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+101
+00:07:10,670 --> 00:07:10,870
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+102
+00:07:10,870 --> 00:07:10,910
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+103
+00:07:10,910 --> 00:07:12,230
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+104
+00:07:12,230 --> 00:07:12,850
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+105
+00:07:12,850 --> 00:07:12,850
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+106
+00:07:12,850 --> 00:07:16,270
+انا انا انا انا اعندي الـ Cardinal numbers بجيب
+
+107
+00:07:16,270 --> 00:07:18,910
+المجموعات اللي بتقبلهم و هقارن بين المجموعات بصورة
+
+108
+00:07:18,910 --> 00:07:21,850
+معينة، فهذا الطريقة اللي احنا هنعتمدها، فعنا
+
+109
+00:07:21,850 --> 00:07:25,250
+التعريف التالت let A و B be sets، اه فعشان هيك
+
+110
+00:07:25,250 --> 00:07:28,110
+الكلام مش منفك، احنا متحدث عن Cardinal numbers،
+
+111
+00:07:28,110 --> 00:07:31,710
+لكن دايما إيش فيه؟ مجموعات، الموضوع لا ينفصل عن
+
+112
+00:07:31,710 --> 00:07:37,380
+المجموعاتبنقول إن cardinality of A is less than or
+
+113
+00:07:37,380 --> 00:07:41,400
+equal أقل أو يساوي، أيش الرمز؟ رمز أصغر من أو
+
+114
+00:07:41,400 --> 00:07:43,580
+يساوي في العداد العادية، في العداد الحقيقية، يعني
+
+115
+00:07:43,580 --> 00:07:46,620
+نفس الشيء، أه بنقول ليش we write cardinality of A
+
+116
+00:07:46,620 --> 00:07:50,040
+أقل أو يساوي cardinal number of B، إذا كالعادة، في
+
+117
+00:07:50,040 --> 00:07:54,420
+أن مفهوم، في أن الرمز تبعه، بتم أن التعريف، صح؟
+
+118
+00:07:54,420 --> 00:07:57,380
+كنا دايما نعرف نحكي بعد الصوت، أه، أه، وقت إيش
+
+119
+00:07:57,380 --> 00:08:01,720
+بنقول هذا الكلام؟ if A is equibotent to a subset
+
+120
+00:08:01,720 --> 00:08:06,810
+of Bمعنى تكافئ مجموعة جزئية من الـ B فانا بتحدث عن
+
+121
+00:08:06,810 --> 00:08:13,090
+مجموعة A وهي مجموعة B بتحدث عن ال cardinal number
+
+122
+00:08:13,090 --> 00:08:17,910
+بدي أعبر عن حجم المجموعة فبدي أقول إن هذه حجم
+
+123
+00:08:17,910 --> 00:08:21,870
+المجموعة أصغر أو يساوي حجم المجموعة هذه وقت إيش
+
+124
+00:08:21,870 --> 00:08:25,590
+إذا كانت ال A تكافئ من مين؟ subset من ال B وليه
+
+125
+00:08:25,590 --> 00:08:30,630
+كنا نسميها B0 هدولة تكافئ ال Aفإيه؟ تكافئ subset
+
+126
+00:08:30,630 --> 00:08:33,790
+طبعا subset ممكن تسويها لأن subset ما جاليش proper
+
+127
+00:08:33,790 --> 00:08:37,450
+subset subset تكافئ ده subset عشان أيه أصغر من أو
+
+128
+00:08:37,450 --> 00:08:41,750
+يساوي أصغر من أو يساوي فإذا هذه أول شي علاقة أصغر
+
+129
+00:08:41,750 --> 00:08:45,750
+من أو يساوي فإذا أنا بحولها من لغة المقارنة بين
+
+130
+00:08:45,750 --> 00:08:48,910
+cardinal numbers من أعداد أصلية للمقارنة بين
+
+131
+00:08:48,910 --> 00:08:51,830
+مجموعات طبعا تكافئ ايش صار بال debijection و هكذا
+
+132
+00:08:51,830 --> 00:08:58,090
+فبنرجع للموضوع السابقتمام فهذه علاقة أصغر من أو
+
+133
+00:08:58,090 --> 00:09:02,570
+يساوي طالب يقول أصغر من مش يساوي فبقول we say that
+
+134
+00:09:02,570 --> 00:09:06,810
+cardinal of A is less than cardinality of B and
+
+135
+00:09:06,810 --> 00:09:09,790
+right نفس الإشارة بنشيل ال if تساوي نفس الرمز
+
+136
+00:09:09,790 --> 00:09:12,570
+بستخدم نفس الرمز مع الأرقام الحقيقية مع العدات
+
+137
+00:09:12,570 --> 00:09:17,330
+الحقية if وقتاش إذا هي أصغر منها أو يساويها لكن لا
+
+138
+00:09:17,330 --> 00:09:22,130
+تساوي مافيش تساوي مافيش تساوي and cardinality of A
+
+139
+00:09:22,130 --> 00:09:26,980
+لا تساوي cardinality of Bهل احنا عرفنا تساوية الـ
+
+140
+00:09:26,980 --> 00:09:29,920
+Cardinality عشان هذه نفيها؟ عرفناها
+
+141
+00:09:33,610 --> 00:09:38,050
+فإذا إيش ماله؟ إذا هي تكافئ صبصة منها ولا تكافئها
+
+142
+00:09:38,050 --> 00:09:42,290
+صارت، هي تكافئ صبصة منها ولا تكافئها نفسها، هيك
+
+143
+00:09:42,290 --> 00:09:44,930
+بده يصير، لأنه إيش معناته؟ إنه ما زال أحنا عرفنا
+
+144
+00:09:44,930 --> 00:09:47,930
+التساوي، لأ بيقولوا لا تساوي شمالها ال negation،
+
+145
+00:09:47,930 --> 00:09:50,510
+ال negation على طول، ففيش مشكلة أطلع، فإذا هذا
+
+146
+00:09:50,510 --> 00:09:53,710
+التعريف يعتبر هيك كام، فإذا هو أوش عرف أصغر من أو
+
+147
+00:09:53,710 --> 00:09:59,460
+يساويوبدلالته عرف من أصغر منه فقط أو بدلالته زاد
+
+148
+00:09:59,460 --> 00:10:04,340
+من عدم التساوي اللي هو ال negation تبع التساوي
+
+149
+00:10:04,340 --> 00:10:12,060
+تفضلي نحاول
+
+150
+00:10:12,060 --> 00:10:18,840
+نقرب الصورة ال gate نقول الأربع أصغر من الخمسة كيف
+
+151
+00:10:18,840 --> 00:10:25,170
+بدي أعرفها؟to cathy أن الأربع أصغر من الخمسة and
+
+152
+00:10:25,170 --> 00:10:28,490
+الأربع لا تساوي الخمسة هيك تقريبا بنعمل حاجة بهذا
+
+153
+00:10:28,490 --> 00:10:37,670
+الشكل هيك بدي أعمل لأن هو عرف أصغر من أو يساوي في
+
+154
+00:10:37,670 --> 00:10:42,120
+واحد، مظبوط؟أعرف أصغر من أو يساوي هو بدأ بتعرف مين
+
+155
+00:10:42,120 --> 00:10:46,000
+أصغر من أو يساوي في رقم واحد و بعدين أعرف أصغر من
+
+156
+00:10:46,000 --> 00:10:50,320
+فقط لحالها بكيف أعرفها بدلالة أصغر من أو يساوي و
+
+157
+00:10:50,320 --> 00:10:55,400
+بدلالة عدم التساوي عدم التساوي خليني أكتبها بطريقة
+
+158
+00:10:55,400 --> 00:10:59,760
+جديدة قد يكون الصورة أوضحة مش غلط خليني أشوف إيش
+
+159
+00:10:59,760 --> 00:11:05,180
+بقول هو الآن خليني أعبر عن هذا بشكل مختلف أول شي
+
+160
+00:11:05,180 --> 00:11:11,960
+واحدبنقول على أنه Cardinality للـ A أصغر أو يساوي
+
+161
+00:11:11,960 --> 00:11:16,020
+Cardinality للـ B هذا المصطلح الجديد، مظبوط؟ بدنا
+
+162
+00:11:16,020 --> 00:11:21,180
+نعرفه كيف عرفه يكافئ إذا جهش كانت الـ A إشمالها
+
+163
+00:11:21,180 --> 00:11:30,000
+تكافئ subset من الـ B هذا اختصارا، واضح؟ واضح؟
+
+164
+00:11:30,000 --> 00:11:36,630
+تمام، الآن بدي أعرف مصطلح جديد Cardinalityللـ A
+
+165
+00:11:36,630 --> 00:11:43,110
+أقل من الـ cardinality للـ B بده يعرف مصطلح جديد
+
+166
+00:11:43,110 --> 00:11:47,570
+حاولنا نتحرر من العلاقات اللي احنا عارفينها أصغر
+
+167
+00:11:47,570 --> 00:11:51,070
+من تبعة العدد الحقية نتحرر منها انا عندي مفهوم
+
+168
+00:11:51,070 --> 00:11:57,530
+جديد بيستخدم بس نفس الرمز هيك نفكر كيف بده يعرفها
+
+169
+00:11:57,530 --> 00:12:01,990
+بده يعرفها بدلات مصطلح اللي فوق زاد مصطلح آخر فهذه
+
+170
+00:12:01,990 --> 00:12:08,410
+تكافئ أن ال cardinalityللـ A أصغر من أو تساوي
+
+171
+00:12:08,410 --> 00:12:18,370
+Cardinality للـ B and Cardinality لل A لا تساوي
+
+172
+00:12:18,370 --> 00:12:25,640
+Cardinality لل Bزي احسنتى احنا بيقولوا الوقتش
+
+173
+00:12:25,640 --> 00:12:29,140
+بتكون proper subset اذا هي subset ولا تساوي على
+
+174
+00:12:29,140 --> 00:12:34,580
+نفس النموذج فانت ماتخلكيش انت ملزجة او معلقة
+
+175
+00:12:34,580 --> 00:12:36,960
+بالتعريف القديم اصغر من او يساوي تبع الاعداد بهذا
+
+176
+00:12:36,960 --> 00:12:40,690
+الشكل لأفهو أيش عرفه؟ قال جيت أنا بدي أثبت أنه
+
+177
+00:12:40,690 --> 00:12:43,970
+أقعد حينما نشوف الأمثلة أنه cardinal number واحد
+
+178
+00:12:43,970 --> 00:12:46,550
+أصغر من cardinal number اتنين، إيش مطلوب أثبت؟
+
+179
+00:12:46,550 --> 00:12:49,210
+أثبت أنه أصغر منه أو يسوي، كيف بدي أثبت هو يتعريض؟
+
+180
+00:12:49,210 --> 00:12:51,770
+وكيف بدي أثبت أنه لا يسوي؟ كيف بدي أثبته؟ قاعدة
+
+181
+00:12:51,770 --> 00:12:54,950
+رقم C4، واضحيت؟ أه فاحنا هيبقى نفكر شوية بطريقة
+
+182
+00:12:54,950 --> 00:12:55,430
+مجرد
+
+183
+00:12:59,610 --> 00:13:03,790
+المثال الأول هذه في مثال مباشر اثبت ان ال
+
+184
+00:13:03,790 --> 00:13:06,150
+cardinality لان اصغر من ال cardinality لل R اللي
+
+185
+00:13:06,150 --> 00:13:14,610
+حكيناه بنثبت ان ايش فعلا هذا الكلام صحيح مثالنا
+
+186
+00:13:14,610 --> 00:13:19,230
+الأول خليكم
+
+187
+00:13:19,230 --> 00:13:25,250
+معاياالمثال الأول اثبت أن الـ cardinal للـ N أقل
+
+188
+00:13:25,250 --> 00:13:28,430
+من ال cardinal لل R مطلوب مننا نعمل حاجتين أثبت
+
+189
+00:13:28,430 --> 00:13:37,990
+أنها أصغر منها و يسويها ولا تسوى فسلويشن بدي
+
+190
+00:13:37,990 --> 00:13:41,370
+أثبت أن ال N أو ال cardinality لل N أصغر من ال ..
+
+191
+00:13:41,370 --> 00:13:45,710
+أو تساوي ال cardinal number لل R خلينا نحط هذا إيش
+
+192
+00:13:45,710 --> 00:13:48,770
+الجزء الأول واحد cardinality
+
+193
+00:13:50,350 --> 00:13:55,410
+للأن أصغر أو يساوي cardinality لل R هذا مطلوب
+
+194
+00:13:55,410 --> 00:14:01,030
+الأول طيب خلّي هذا الكلام صريح اه مطلوبين في ال A
+
+195
+00:14:01,030 --> 00:14:05,850
+لأنه and بدي ادتره ادتره طيب بداجي افسر ايش معناته
+
+196
+00:14:05,850 --> 00:14:08,150
+ان ال cardinality اصغر من او تساوي ان ال and تكافئ
+
+197
+00:14:08,150 --> 00:14:11,610
+subset من ال A مين بعرف subset من ال R تكافئ ال
+
+198
+00:14:11,610 --> 00:14:18,640
+and انا نفسي احسنت اه فهنا ال andتكافئ ال N وهي
+
+199
+00:14:18,640 --> 00:14:24,600
+subset من ال R على طول implies ال cardinality لل N
+
+200
+00:14:24,600 --> 00:14:30,540
+أصغر أو يساوي ال cardinality لل R فهذه أول شيء
+
+201
+00:14:30,540 --> 00:14:35,730
+بسهولة جداأحنا متوقعين أن الـN subset من الـR إذا
+
+202
+00:14:35,730 --> 00:14:38,290
+ما هيش أدد عناصر الـN أصغر أو يساوي أدد عناصر الـR
+
+203
+00:14:38,290 --> 00:14:42,850
+فعلا بنسجم مع توقعاتنا السابق ممتاز الخطوة التانية
+
+204
+00:14:42,850 --> 00:14:47,810
+بدي أثبت أن ال cardinality للـN لا تساوي ال
+
+205
+00:14:47,810 --> 00:14:54,350
+cardinality للـR هذا مطلوبنا رقم اتنين مين عنده
+
+206
+00:14:54,350 --> 00:15:00,390
+حل؟ صحيح ليش؟
+
+207
+00:15:01,460 --> 00:15:03,740
+أثبتناها أنها إيش لو لو لو لو لو لو لو لو لو لو لو
+
+208
+00:15:03,740 --> 00:15:03,740
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+209
+00:15:03,740 --> 00:15:03,900
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+210
+00:15:03,900 --> 00:15:04,880
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+211
+00:15:04,880 --> 00:15:06,000
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+212
+00:15:06,000 --> 00:15:06,260
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+213
+00:15:06,260 --> 00:15:07,700
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+214
+00:15:07,700 --> 00:15:11,460
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+215
+00:15:11,460 --> 00:15:11,560
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+216
+00:15:11,560 --> 00:15:11,640
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+217
+00:15:11,640 --> 00:15:15,060
+لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+218
+00:15:15,060 --> 00:15:15,060
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+219
+00:15:15,060 --> 00:15:23,380
+لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو لو
+
+220
+00:15:23,380 --> 00:15:27,390
+لو لو لولات كافر واضحة هذه ولا اكتبها اه اه فهذا
+
+221
+00:15:27,390 --> 00:15:33,170
+يؤدي انه ايش ال cardinality لل R لا تساوي ال
+
+222
+00:15:33,170 --> 00:15:39,250
+cardinality لل N طبعا ال N واحد و اتنين يؤدي انه
+
+223
+00:15:39,250 --> 00:15:45,470
+ال cardinality لل N اصغر من ال cardinality لل R
+
+224
+00:15:49,800 --> 00:15:53,240
+فيمكن هنا من زاوية أخرى لأننا وجدت عدم التساوي
+
+225
+00:15:53,240 --> 00:15:57,020
+لحاله بقول واحدة أكبر من التانية طب لما أثبت أنه
+
+226
+00:15:57,020 --> 00:15:59,860
+هي من الصغيرة اللي متوقع أن تكون الصغيرة بقول خلصت
+
+227
+00:15:59,860 --> 00:16:03,300
+طب فهي زاوية أخرى فانا بقول بيسووش بعض إذا في
+
+228
+00:16:03,300 --> 00:16:05,600
+واحدة أكبر من التانية طب لما أعرف أن ال card نادر
+
+229
+00:16:05,600 --> 00:16:08,420
+الأن هي الأصغر إذا ان هي ليش على طول هي الصغيرة
+
+230
+00:16:08,420 --> 00:16:16,510
+فهنا بدنا حاشتين بدنا حاشتيننشوف كمان مثال اثبته
+
+231
+00:16:16,510 --> 00:16:21,630
+ان الـ cardinality لان اكبر من 2017 ال cardinality
+
+232
+00:16:21,630 --> 00:16:24,830
+ال natural number عددها اكبر من 2017 طبعا منطقي
+
+233
+00:16:24,830 --> 00:16:31,490
+ولا لأ هل هي فيها 2017 عنصر لعداد الطبيعية لأكتر
+
+234
+00:16:31,490 --> 00:16:38,090
+طبعا 2017 لان احنا في 2017 في نهايته بس هي خصوص في
+
+235
+00:16:38,090 --> 00:16:41,310
+2017 يعني هي عدد يعني مش مش قضية
+
+236
+00:16:44,730 --> 00:16:50,990
+تمام كيف بدنا نشتغل؟ في عندنا مجموعة هي الان وفي
+
+237
+00:16:50,990 --> 00:16:53,930
+عندنا cardinal number 2017 هذا cardinal number
+
+238
+00:16:53,930 --> 00:16:57,870
+فعشان أشتغل بدي أجيب مجموعات فإذا أول شي بدي أجيب
+
+239
+00:16:57,870 --> 00:17:02,990
+مجموعة وكافة اللي قاهش اللي هو اللي قاهش 2017 ان
+
+240
+00:17:02,990 --> 00:17:09,450
+2017 كيف تسوى 2017 هذا المثال الرقم 2فا solution
+
+241
+00:17:09,450 --> 00:17:13,730
+اقوله let A تساوي بس اختصار عشان ماتامش اكتبله
+
+242
+00:17:13,730 --> 00:17:19,950
+2017 وانسى ال 17 خلاص ساميها A فعلى طول then
+
+243
+00:17:19,950 --> 00:17:28,990
+cardinality لل A تساوي 2017 اه بدنا نشتغل نفس
+
+244
+00:17:28,990 --> 00:17:32,870
+العملية خطوطين واحد
+
+245
+00:17:34,400 --> 00:17:40,300
+بدي أثبت أن ال cardinality لل A أقل أو تساوي ال
+
+246
+00:17:40,300 --> 00:17:47,400
+cardinality لل N هذا المطلوب الأول فبشبت
+
+247
+00:17:47,400 --> 00:17:52,650
+أسأل نفسي هل ال A تكافئ صبصة من ال N و مين هي؟هي
+
+248
+00:17:52,650 --> 00:17:56,090
+نفسها تكافئ نفسها صحيح فإذا هنا برضه على نفس
+
+249
+00:17:56,090 --> 00:18:01,430
+المنوال A تكافئ ال A وهي subset من ال N implies
+
+250
+00:18:01,430 --> 00:18:07,390
+cardinality لل A أقل أو يساوي ال cardinality لل N
+
+251
+00:18:07,390 --> 00:18:15,910
+أيوة الخطوة التانية ال cardinality لل A لا تساوي
+
+252
+00:18:15,910 --> 00:18:25,850
+ال cardinality لل N كيف نثبتها؟أحسنتِ، ممتاز، زي
+
+253
+00:18:25,850 --> 00:18:29,030
+عديك ما زالت دينمربل لاندنمربل، هذه على طول فبنقول
+
+254
+00:18:29,030 --> 00:18:40,110
+له الـ A is finite and N is infinite implies ال A
+
+255
+00:18:40,110 --> 00:18:48,630
+لا تكافئ ال N وهذا يؤدي إن ال cardinality لل A لا
+
+256
+00:18:48,630 --> 00:18:52,290
+تساوي ال cardinality لل N
+
+257
+00:19:02,090 --> 00:19:08,630
+تمام الان واحد و اتنين implies الفين و سبعتاش اللي
+
+258
+00:19:08,630 --> 00:19:14,890
+هي ال cardinality لل a أقل من ال cardinality للأ
+
+259
+00:19:14,890 --> 00:19:20,570
+بالتأكيدفإذا هنا مع دول المثاليين ومضحكتنا الصورة
+
+260
+00:19:20,570 --> 00:19:24,690
+كيف نثبت علاقة أصغر من فيها مطلوبين نثبت أنه في
+
+261
+00:19:24,690 --> 00:19:29,050
+علاقة أصغر من أو يساوي تبقى للتعريف وفي عدم تساوي
+
+262
+00:19:29,050 --> 00:19:37,850
+عدم تساوي شرطين عشان نوصل لهذه الصورة أي سؤالنشوف
+
+263
+00:19:37,850 --> 00:19:44,370
+مثال على نفس الموضوع لكن من زوايا أخرى let a and b
+
+264
+00:19:44,370 --> 00:19:49,330
+be two sets prove that يكتب لنا cardinality
+
+265
+00:19:49,330 --> 00:19:52,950
+لمجموعة أصغر أو يساوي بمفهوم جديد بقول cardinality
+
+266
+00:19:52,950 --> 00:19:56,910
+ل a أقل أو تساوي بف and only if ممكن يستخدم كتعريف
+
+267
+00:19:56,910 --> 00:20:00,190
+لأن ف and only if there exists an injection إذا
+
+268
+00:20:00,190 --> 00:20:04,610
+كدرت تلاقي one to one function من a ل b من a ل b
+
+269
+00:20:05,260 --> 00:20:10,180
+فهنا نكتب السؤال و نبدأ نحله اللي هو طبعا جملة by
+
+270
+00:20:10,180 --> 00:20:13,600
+conditional باتجاهين واحدة واحدة فبقول طبعا ال a و
+
+271
+00:20:13,600 --> 00:20:19,810
+ال b دولة مجموعات بدنا نثبت انه cardinalityللـ A
+
+272
+00:20:19,810 --> 00:20:25,990
+أقل أو تساوي cardinality للـ B هي statement if and
+
+273
+00:20:25,990 --> 00:20:29,830
+only if يعني تكافئ وقولنا مافيش فرق اكتبك او اكتبت
+
+274
+00:20:29,830 --> 00:20:34,450
+تلات شحطات كل واحد there exists an injection a
+
+275
+00:20:34,450 --> 00:20:39,110
+function from A to B و تكون injection there exists
+
+276
+00:20:39,110 --> 00:20:45,910
+a function from A to B with F is one to one فهذه
+
+277
+00:20:45,910 --> 00:20:52,490
+الجملة التانيةفهذا المطلوب solution نبدأ بالاتجاه
+
+278
+00:20:52,490 --> 00:20:56,410
+الأول أن
+
+279
+00:20:56,410 --> 00:21:03,130
+اليسار implies اليمين cardinality of A أقل أو
+
+280
+00:21:03,130 --> 00:21:09,970
+يساوي cardinality of B implies there exists F من A
+
+281
+00:21:09,970 --> 00:21:19,150
+لB one to one F is one to one هذا المطلوبأه طبعا
+
+282
+00:21:19,150 --> 00:21:27,310
+على طول assume cardinality of A أقل او يساوي
+
+283
+00:21:27,310 --> 00:21:33,890
+cardinality of B بدنا
+
+284
+00:21:33,890 --> 00:21:38,750
+نبحث عن دالة F من A ل B تكون to one و to one خلينا
+
+285
+00:21:38,750 --> 00:21:45,110
+نكتب we want to find a function
+
+286
+00:21:47,410 --> 00:21:53,630
+المهارات بناء من نفس الاتجاه F من A ل B such that
+
+287
+00:21:53,630 --> 00:21:55,090
+F is one to one
+
+288
+00:21:58,580 --> 00:22:03,180
+فبندور على دالة تكون one to one مهارات كررت معنا
+
+289
+00:22:03,180 --> 00:22:07,320
+عدة مرات في عدة مواضيع كيف نعمل بناء نعمل
+
+290
+00:22:07,320 --> 00:22:11,360
+construction لدالة بين مجموعتين لما كنا نثبت
+
+291
+00:22:11,360 --> 00:22:13,500
+infinite كنا من المجموع على نفسها تكون one to one
+
+292
+00:22:13,500 --> 00:22:17,040
+وليس انتوا لما نعمل اللي وكنا اللي هو التكافؤ تكون
+
+293
+00:22:17,040 --> 00:22:19,980
+one to one و أنتوا بين a و b و لما نكون denomable
+
+294
+00:22:19,980 --> 00:22:24,700
+بين المجموع و بين الان كله بدور على دالةفطبعا سؤال
+
+295
+00:22:24,700 --> 00:22:28,800
+التقليدي هل بتدور في تفادر ال calculus؟ لأ، وين
+
+296
+00:22:28,800 --> 00:22:34,540
+تدور؟ في المعطيات، في في المعطيات دوال؟ اه بما أن
+
+297
+00:22:34,540 --> 00:22:37,700
+هذه أصغر هي تستوي هذه، إذا هذه تكافئ 6 من ال B،
+
+298
+00:22:37,700 --> 00:22:41,340
+أحسنتي، اه فإذا نشتغل، شايفين فاحنا كيف الأفكار،
+
+299
+00:22:41,340 --> 00:22:43,980
+المبادرة اللي بتعلمها؟ اه هي من أول ما بدينا
+
+300
+00:22:43,980 --> 00:22:47,280
+البرهانة جملة شرطية كيف نبدأها، اشترد إن الشرط
+
+301
+00:22:47,280 --> 00:22:53,220
+صحيح و بنشتغل، اه فديعمليات أساسية لازم نتعلمها
+
+302
+00:22:53,220 --> 00:22:59,340
+مهارات لاغنى عنها في التعامل مع البراهين فإذا هنا
+
+303
+00:22:59,340 --> 00:23:04,480
+since نكتبله أو نكتبله now كل الطرق التعبير صحيحة
+
+304
+00:23:04,480 --> 00:23:10,300
+since cardinality لل
+
+305
+00:23:10,300 --> 00:23:21,810
+a أقل أو يساوي cardinality لل b we haveالـ A تكافئ
+
+306
+00:23:21,810 --> 00:23:26,230
+subset أسميها B0 عشان ندربطها في الـ B أو أي أسم
+
+307
+00:23:26,230 --> 00:23:30,250
+كله صح زي ما اتفقنا مافيش اسم غلط لكن الواحد
+
+308
+00:23:30,250 --> 00:23:34,070
+بيختار اسم يكون مناسب تمام طبعا مابديش يابسن تكافئ
+
+309
+00:23:34,070 --> 00:23:43,770
+بدي دال لاسمها بمعنى there exist G من A إلى B0
+
+310
+00:23:43,770 --> 00:23:48,810
+والـ G أبيجيكشن طبعا ممكن أعبر عنها بالشكل هذاأو
+
+311
+00:23:48,810 --> 00:23:53,890
+الـ B صبصة من الـ P تمام فممكن نحاول وإن احنا ممكن
+
+312
+00:23:53,890 --> 00:23:56,790
+نعرف ال F بدالة ال GF غيرها المقاطيات مافيش
+
+313
+00:23:56,790 --> 00:24:02,210
+فبنحاول نشوف هل هي بتكفي و لا بتكفيش نعمل صورة هي
+
+314
+00:24:02,210 --> 00:24:09,130
+عندنا ال A و هي عندنا ال B و هي B0 جواها و هي اللي
+
+315
+00:24:09,130 --> 00:24:14,650
+بتكفي فانا عندي دالة من هان لهان من هان لهان أنا
+
+316
+00:24:14,650 --> 00:24:23,740
+بدي دالة الآن من Aلـ B بدي أف بدي أعرف أف لت أف من
+
+317
+00:24:23,740 --> 00:24:34,860
+A ل B بي given by مرة تانية دلالتها طيب كيف؟ أف of
+
+318
+00:24:34,860 --> 00:24:43,820
+X تساوي نعملتان تان ضروري ليش؟ أحسنتي؟
+
+319
+00:24:44,420 --> 00:24:48,760
+المجال كله ايه؟ مااختلفش المجال؟ ايش اللي اختلف
+
+320
+00:24:48,760 --> 00:24:52,020
+المجال المقابل؟ اه تتذكروا في نظرية قولنا ايه
+
+321
+00:24:52,020 --> 00:24:56,300
+المجال المقابل؟ وعاء كان الوعاء صغير بدنا نكبره
+
+322
+00:24:56,300 --> 00:24:59,740
+بتتغيرش ايه؟ بتتغيرش بتبطل on to ممكن وانا بديها
+
+323
+00:24:59,740 --> 00:25:01,980
+تكون on to لأ بديها تمه one to one بحافظ عليها
+
+324
+00:25:01,980 --> 00:25:05,020
+فعطوا ال G of Aفعشان هيك انا حاول تعمل الرسمة عشان
+
+325
+00:25:05,020 --> 00:25:08,020
+اشوف احنا .. وين التغيير؟ ال domain مغطى كله ف G
+
+326
+00:25:08,020 --> 00:25:14,060
+هي G و ال F تفرجش اه لان ال G مغطية اه يعني هي في
+
+327
+00:25:14,060 --> 00:25:17,620
+.. في .. في .. امثلة سابقة كانت الدالة بإننا نكبر
+
+328
+00:25:17,620 --> 00:25:20,540
+ال domain فاضطرينا نغطي ال G ثم نقول مش مغطى لكن
+
+329
+00:25:20,540 --> 00:25:23,660
+الآن ال domain مغطى اه و بدنا يبقى one to one حتى
+
+330
+00:25:23,660 --> 00:25:30,200
+ما هي one to one اه طبعا one to one then F is one
+
+331
+00:25:30,200 --> 00:25:35,430
+to one ليش؟ لأن ال G is one to oneخلصت فهي نجينا
+
+332
+00:25:35,430 --> 00:25:45,110
+one to one function بكل سهولة أي سؤال فالأفكار
+
+333
+00:25:45,110 --> 00:25:50,970
+تتكرر معنا مرة و مرتين و تلاتة فارجو نتعلم و ان كل
+
+334
+00:25:50,970 --> 00:25:54,850
+هذه الأمثلة تصير عندنا حصيلة من الأفكار و كيف
+
+335
+00:25:54,850 --> 00:25:59,050
+نعملها و كيف نتعامل معها و ينقدر نقلد هذه الأفكار
+
+336
+00:25:59,050 --> 00:26:08,060
+للتجاه التاني الآن اتنينThere exists f من a ل b
+
+337
+00:26:08,060 --> 00:26:19,220
+with f is one to one implies cardinality لل a أقل
+
+338
+00:26:19,220 --> 00:26:24,120
+أو تساوي cardinality لل b طبعا كالعادة assume
+
+339
+00:26:24,120 --> 00:26:34,120
+there exists a function f from a to b such thatF
+
+340
+00:26:34,120 --> 00:26:42,620
+is one to one بدي أثبت إنه ال A كاردينالت لل A أقل
+
+341
+00:26:42,620 --> 00:26:46,240
+أو يسوى كاردينالت لل B يعني ال A تكافئ subset من
+
+342
+00:26:46,240 --> 00:26:49,240
+ال B نعم
+
+343
+00:26:50,420 --> 00:26:53,860
+أحسنتي فهذه فكرة سابقة عملناها في المحاضرات
+
+344
+00:26:53,860 --> 00:26:57,300
+الماضية مرتين ماقدرناش نلاقي one to one and unto
+
+345
+00:26:57,300 --> 00:27:00,300
+لما أثبتنا أن الان نكوس أند نمرابون فقلنا هي تكافئ
+
+346
+00:27:00,300 --> 00:27:04,020
+من المجال المقابل ومنه اشتغلنا فانا على طول مباشرة
+
+347
+00:27:04,020 --> 00:27:11,320
+بما أن هذه one to one فهذا يقول إن ال A تكافئ F في
+
+348
+00:27:11,320 --> 00:27:15,390
+ال Aالصورة على طول كانت واقعية one to one كيف
+
+349
+00:27:15,390 --> 00:27:18,390
+أخلّيها on two أصغر المجال المقابل المجال المقابل
+
+350
+00:27:18,390 --> 00:27:22,250
+يبقى من المجال المقابل المجال المقابل يبقى من
+
+351
+00:27:22,250 --> 00:27:26,090
+المجال المقابل المجال المقابل المجال المقابل
+
+352
+00:27:26,090 --> 00:27:26,370
+المجال المقابل المجال المقابل المجال المقابل
+
+353
+00:27:26,370 --> 00:27:26,670
+المجال المقابل المجال المقابل المجال المقابل
+
+354
+00:27:26,670 --> 00:27:27,690
+المجال المقابل المجال المقابل المجال المقابل
+
+355
+00:27:27,690 --> 00:27:27,970
+المجال المقابل المجال المقابل المجال المقابل
+
+356
+00:27:27,970 --> 00:27:27,970
+المجال المقابل المجال المقابل المجال المقابل
+
+357
+00:27:27,970 --> 00:27:29,210
+المجال المقابل المجال المقابل المجال المقابل
+
+358
+00:27:29,210 --> 00:27:36,530
+المجال المقابل المجفهذه من الطرق المهمة ممكن تعتمد
+
+359
+00:27:36,530 --> 00:27:41,930
+عليها عشان تثبت أن الـ A أقل أو يسوى B يكفي أننا
+
+360
+00:27:41,930 --> 00:27:46,150
+نجد دالة one to one على طول فبتصير H تكافئ المدى و
+
+361
+00:27:46,150 --> 00:27:49,770
+المدى دائما سبسط من مين؟ من المجال المقارن فهذه
+
+362
+00:27:49,770 --> 00:27:53,830
+فكرة تتكرر معنا و trick مستخدم في الرياضيات في هذا
+
+363
+00:27:53,830 --> 00:27:55,930
+الموضوع ممكن نستخدمه
+
+364
+00:28:07,230 --> 00:28:11,530
+فأرجو طريقة التفكير في الرياضيات، طريقة براهين
+
+365
+00:28:11,530 --> 00:28:15,250
+النظريات، حل الأمثلة، ففي أفكار بتتكرر، فهذه
+
+366
+00:28:15,250 --> 00:28:18,230
+المهارات لازم نتعلمها، يعني مع التكرار، نشوف كيف
+
+367
+00:28:18,230 --> 00:28:21,150
+الناس بتفكر، و بنجرب ما زال هذه الفكرة متكررة في
+
+368
+00:28:21,150 --> 00:28:25,800
+أكتر من مكان، ممكن تنجح في حل كثير من المثالفين
+
+369
+00:28:25,800 --> 00:28:29,460
+الآن هنوصل لنظرية الرئيسية Schroeder-Bernstein
+
+370
+00:28:29,460 --> 00:28:33,160
+theorem لكن قبل ذلك في عندنا نظرية تمهيدية اللي
+
+371
+00:28:33,160 --> 00:28:36,780
+هنسميها اللمّة هناخدها من غير برهان طبعا اللي بيحب
+
+372
+00:28:36,780 --> 00:28:40,620
+يتطلع على البرهان الموجود في الكتاب بقول if B is a
+
+373
+00:28:40,620 --> 00:28:46,360
+subset of A and if there exists an injection من A
+
+374
+00:28:46,360 --> 00:28:51,990
+لB then there exists a bijection من A لBهو بيقول
+
+375
+00:28:51,990 --> 00:28:55,890
+لي إذا قدرت ألاقي دالة injection من A ل subset من
+
+376
+00:28:55,890 --> 00:28:59,610
+نفسها بس عشان نشوف الصورة عشان نتصور هى في عندنا
+
+377
+00:28:59,610 --> 00:29:06,150
+ال A و ال B مالها subset منها ال B subsetو انا
+
+378
+00:29:06,150 --> 00:29:10,330
+اقدرت الاقي دالة one to one بين ال A و بين ال B
+
+379
+00:29:10,330 --> 00:29:14,050
+هذه الدالة بقدر اخليها bijection بقدر اخليها
+
+380
+00:29:14,050 --> 00:29:17,910
+bijection او يعني اعرف منها bijection اه فانا عندى
+
+381
+00:29:17,910 --> 00:29:21,150
+اقدرت الاقي F من A ل B تكون one to one فبقدر منها
+
+382
+00:29:21,150 --> 00:29:25,410
+اولد H تكون اللى هو ايش bijection من A ل B فهذه
+
+383
+00:29:25,410 --> 00:29:29,550
+اللى ما اللى هنعتمد عليها في برهان النظرية القادمة
+
+384
+00:29:29,550 --> 00:29:32,630
+النظرية
+
+385
+00:29:32,630 --> 00:29:38,090
+الرئيسيةنظرية فكرتها كالتالي خلّينا نشوف و احنا
+
+386
+00:29:38,090 --> 00:29:46,670
+هنوصله و بعدين أقرأها بشكل تفصيل هذه
+
+387
+00:29:46,670 --> 00:29:51,850
+النظرية ال trick مشهور في الرياضيات يستخدم كثيرا
+
+388
+00:29:51,850 --> 00:29:54,690
+طبعا في موضوع متعدد احنا هنستخدمه هنا في موضوع
+
+389
+00:29:54,690 --> 00:30:00,170
+محدد لو احنا في التحليل الحقيقي او في ال calculus
+
+390
+00:30:00,170 --> 00:30:06,440
+بدنا نثبت ان X تساوي Yمثلًا في بعض الأحيان ماقدرش
+
+391
+00:30:06,440 --> 00:30:11,400
+أوصل بشكل مباشر فهذه أحيانًا بنعملها بالصورة
+
+392
+00:30:11,400 --> 00:30:17,780
+التالية إن ال X أقل أو تساوي ال Y أن Y أقل أو
+
+393
+00:30:17,780 --> 00:30:24,300
+تساوي Xهذا الـ trick المشهور بقدرش انا اعمل تساوي
+
+394
+00:30:24,300 --> 00:30:29,140
+لكن بعمل متباينتين فالأول أصغر أو يساوي التاني و
+
+395
+00:30:29,140 --> 00:30:32,020
+التاني أصغر أو يساوي الأول بتكون انتهت بتكون انتهت
+
+396
+00:30:32,020 --> 00:30:35,420
+العملية بيصير في عندي ايش تساوي بيصير عندنا تساوي
+
+397
+00:30:35,420 --> 00:30:38,450
+فاحنا نفس القضية الآنعشان اثبت ان ال cardinal
+
+398
+00:30:38,450 --> 00:30:41,550
+number لل A بي ساوي ال cardinal number لل B هثبت
+
+399
+00:30:41,550 --> 00:30:46,010
+ان هذا اقل من او يساوي التاني و التاني اقل او
+
+400
+00:30:46,010 --> 00:30:51,650
+يساوي الاول فحنروح بهذه الصورة لكن جال ما نشتغل
+
+401
+00:30:51,650 --> 00:30:54,450
+على ال cardinal number هنشتغل على مجموعات لان ال
+
+402
+00:30:54,450 --> 00:30:55,370
+cardinal number مجموعة
+
+403
+00:30:58,210 --> 00:31:01,090
+عشان أثبت التساويش بأننا نتكافئ لـ number متساويين
+
+404
+00:31:01,090 --> 00:31:05,090
+يعني A تكافئ الـ B فبتثبت هذه خلّيني أكتبها بنفس
+
+405
+00:31:05,090 --> 00:31:07,670
+الشغل عشان أعطيكوا الفكرة الرئيسية وبعدين نقرأها
+
+406
+00:31:07,670 --> 00:31:16,230
+مع بعض كيف بتثبت هذه؟ هثبت أن الـ A تكافئ B0
+
+407
+00:31:16,230 --> 00:31:22,480
+subset من الـ Bماعيش معناته؟ ان هذه قصتي أصغر أوي
+
+408
+00:31:22,480 --> 00:31:27,000
+السوية و ايش هأعمل؟ و أثبت أن الـ B تكافئ sub H A0
+
+409
+00:31:27,000 --> 00:31:31,940
+sub 6 مليون من الـ A فهذه ملخص النظرية واضحة؟
+
+410
+00:31:31,940 --> 00:31:38,060
+واضحة التناظر؟ واضحة ولا مش واضح؟ واضحة؟ خلاص نقرأ
+
+411
+00:31:38,060 --> 00:31:45,180
+النظريةالـ A
+
+412
+00:31:45,180 --> 00:31:49,580
+تكافئ
+
+413
+00:31:49,580 --> 00:31:57,140
+subset من ال B و ال B تكافئ
+
+414
+00:31:57,140 --> 00:31:58,260
+subset من ال A
+
+415
+00:32:03,400 --> 00:32:06,120
+النظرية جاية بهذا التجاه وليس بالتكافئة لكن هي نفس
+
+416
+00:32:06,120 --> 00:32:09,160
+العملية جاية بهذا التجاه النظرية هيك معناه النظرية
+
+417
+00:32:09,160 --> 00:32:16,200
+بسبب هيك بدت يعمل نظرية ال proof خلينا
+
+418
+00:32:16,200 --> 00:32:20,260
+نكتب النص نظرية
+
+419
+00:32:20,260 --> 00:32:26,680
+6 1 أول نظرية في هذا ال chapter طبعا النظرية بهذا
+
+420
+00:32:26,680 --> 00:32:28,680
+الصورة ال proof
+
+421
+00:32:33,650 --> 00:32:38,330
+طبعا هناخد ان كل الشرط صحيح ال a و ال b sits
+
+422
+00:32:38,330 --> 00:32:48,910
+فهنقوله هنا assume او let assume a and b are sits
+
+423
+00:32:48,910 --> 00:32:57,150
+such that ايش بتقولي ال a تكافئ نسميها a b not
+
+424
+00:33:01,560 --> 00:33:09,200
+و هي subset من ال B and ال B تكافئ A not subset من
+
+425
+00:33:09,200 --> 00:33:19,400
+ال A خلصنا اه اه بدنا نثبت الان we will prove that
+
+426
+00:33:19,400 --> 00:33:25,260
+ال A تكافئ ال B ال A تكافئ ال B
+
+427
+00:33:32,140 --> 00:33:34,880
+أه فبنثبت أن الـ A تكافئ الـ B عم بدنا Byjection
+
+428
+00:33:34,880 --> 00:33:39,800
+أه طبعا عشان أسفيد من اللمّة اللمّة بتقول إذا قدرت
+
+429
+00:33:39,800 --> 00:33:44,500
+تلاقي one to one بين مجموعة و subset منها بتكون
+
+430
+00:33:44,500 --> 00:33:48,140
+خلاص ال Byjection انتهت لأن هنا طبعا ليش اللمّة
+
+431
+00:33:48,140 --> 00:33:51,880
+مهمة لأنه بوفر بدل ما أنا أقعد أدور ع الدالة تكون
+
+432
+00:33:51,880 --> 00:33:54,440
+بدي أنا إياها one to one و أنتوا بلس الوقت بكوني
+
+433
+00:33:54,440 --> 00:33:56,500
+مركز بسعى لإن تكونوا one to one و الباقي بيجيني
+
+434
+00:33:56,500 --> 00:34:00,790
+اتوماتيك بيجيني بشكل مباشر من النظريةفالان انا
+
+435
+00:34:00,790 --> 00:34:04,830
+عشان اخفف عن نفسي واخفف المتطلبات اللى مطلوبة من
+
+436
+00:34:04,830 --> 00:34:08,790
+الدالة اللى بحاول اعملها تصميم بحاول اكوّنها
+
+437
+00:34:08,790 --> 00:34:12,610
+واسفيد انه بس اركز على one to one بدنا نحاول نشوف
+
+438
+00:34:12,610 --> 00:34:15,790
+ايش المواطيات اللى عندي احنا بنثبت ان ال A تكافئ
+
+439
+00:34:15,790 --> 00:34:20,490
+ال B فبدنا one to one and onto الدالة من A ل B طب
+
+440
+00:34:20,490 --> 00:34:25,300
+هل ال B صفصت من ال A او ال A صفصت من ال B؟ لألأ،
+
+441
+00:34:25,300 --> 00:34:29,720
+مين فيه subset من بعض؟ الـ A0 لو قدرت أثبت أن الـ
+
+442
+00:34:29,720 --> 00:34:33,840
+A تكافئ الـ A0 خلصنا لأنه transitive العملية فاحنا
+
+443
+00:34:33,840 --> 00:34:41,640
+هنثبت أن الـ A تكافئ الـ A0 الحقيقة we will prove
+
+444
+00:34:41,640 --> 00:34:47,610
+that A تكافئ الـ A0على طول و بالـ Transit بتكون
+
+445
+00:34:47,610 --> 00:34:50,670
+خلصت العملية واضحكت؟ ليش بدلت بالـ A0؟ ليش بعد الـ
+
+446
+00:34:50,670 --> 00:34:53,610
+A0 تعامله أسهل؟ عشان بيستخدم اللي .. لأن الـ A0
+
+447
+00:34:53,610 --> 00:34:57,630
+subset من مين؟ من الـ A ممتاز، بدنا دالة، هنعرف
+
+448
+00:34:57,630 --> 00:35:01,330
+دالة من A ل A0 تكون one to one و bijection أه،
+
+449
+00:35:01,330 --> 00:35:05,050
+بدنا نعتمد على مين؟ المعطيات، لأن دول المجموعات مش
+
+450
+00:35:05,050 --> 00:35:09,450
+عارفين إيش عناصرها في في المعطيات دوال؟ نعم أه،
+
+451
+00:35:09,450 --> 00:35:13,890
+جلل الـ A تكافئ الـ B0 ففي دالة من A ل B أه، now
+
+452
+00:35:15,900 --> 00:35:21,180
+الـ A تكافئ الـ B 0 implies there exists a
+
+453
+00:35:21,180 --> 00:35:28,880
+function نسميها مثلا main F1 من A ل B0 by diction
+
+454
+00:35:28,880 --> 00:35:35,720
+بنفس السلوك الـ B تكافئ ال A0 بقدر ألاقي command
+
+455
+00:35:35,720 --> 00:35:44,950
+function F2 من وين ل وين من B ل A0تمام نشوف كيف
+
+456
+00:35:44,950 --> 00:35:53,790
+بنعرف الان جاهزين نعرف الدالة هعرف الدالة let f من
+
+457
+00:35:53,790 --> 00:36:04,870
+a ل a 0 be given by بدي اعرف ال f اه بنشوف كيف
+
+458
+00:36:04,870 --> 00:36:12,650
+بنعرفها احنا ايش فيه عندنافي عندنا هاي اللي هو ال
+
+459
+00:36:12,650 --> 00:36:22,830
+A و جواها A0 و في عندنا هنا ال B و جواها B0 عندنا
+
+460
+00:36:22,830 --> 00:36:32,930
+دالة F1 من A ل B0 هذه F1 و في عندنا دالة F2 من B ل
+
+461
+00:36:32,930 --> 00:36:42,320
+A0 و في عندنا دالة من Bلـ A0 هذه F2 فانا بتبدأ من
+
+462
+00:36:42,320 --> 00:36:48,420
+A وارجع للـ A0 ايش ممكن اعمل؟ composition احسنتم
+
+463
+00:36:48,420 --> 00:36:58,010
+فاحنا هنعرف F of X تساوي من .. هنبدأ أولش تكون F1و
+
+464
+00:36:58,010 --> 00:37:04,030
+بعدين F2 F1 تاخدها من A ل B حتى لو B0 الـ B0 جوجل
+
+465
+00:37:04,030 --> 00:37:10,470
+هو الـ B و بعدين نرجحها تاني F of X F2 بها ده
+
+466
+00:37:10,470 --> 00:37:15,730
+الشكل اه طبعا اذا هذا الصورة مش واضحة كتير هي
+
+467
+00:37:15,730 --> 00:37:23,530
+الصورة هيعنى ايه؟ هنوديها F1
+
+468
+00:37:23,530 --> 00:37:29,050
+بتوديها لمين؟لـ B0 اللي هي جزء من الـ B و الـ B
+
+469
+00:37:29,050 --> 00:37:35,930
+أكبر و بعدين ال F2 بترجح لمين؟ لـ A0 تمام 100% اه
+
+470
+00:37:35,930 --> 00:37:39,430
+فطبعا الـ gate حثبت ان هذه one to one و يكفي لان
+
+471
+00:37:39,430 --> 00:37:43,110
+صارت عندي one to one من A ل subset منها و ال B
+
+472
+00:37:43,110 --> 00:37:46,910
+فعطول بقدر ألاقي ال bijection اه F is one to one
+
+473
+00:37:50,380 --> 00:37:55,600
+فناخد عنصرين X1 و X2 تنتمي لـ A
+
+474
+00:38:06,660 --> 00:38:11,540
+أه طبعا كان الصعوبة كيف .. يعني لو أنه .. أخليها
+
+475
+00:38:11,540 --> 00:38:14,640
+تكون one to one لإن أنتوا في صعوبة ليش لأن هنا
+
+476
+00:38:14,640 --> 00:38:18,600
+الدالة بتاخدش .. بتغطيش كل ال B بس عند ال B زي
+
+477
+00:38:18,600 --> 00:38:21,280
+الوضع الجزر فلكن هنا اللي ما هي اللي بيدي تساعدني
+
+478
+00:38:21,280 --> 00:38:26,900
+بيدي أتكمل العمل such that F of X1 تساوي F of X2
+
+479
+00:38:26,900 --> 00:38:33,120
+بداية إثبات ال one to one بعدها كيش بنعمل؟ بنستخدم
+
+480
+00:38:33,120 --> 00:38:43,510
+القاعدة التعريف فهذا يؤديF2 of F1 of X1 تساوي F2
+
+481
+00:38:43,510 --> 00:38:46,190
+of F1 of X1
+
+482
+00:38:52,460 --> 00:38:58,620
+فطبعا هنا X1 و X2 عندهم عدة ظلمات مخبيين تحتهم
+
+483
+00:38:58,620 --> 00:39:03,480
+نتخلص منهم بالترتيب الصحيح فطبعا أول شيء أن ال F2
+
+484
+00:39:03,480 --> 00:39:06,720
+is one to one فلازم ال جو يساوي الجو فبنطلع عليها
+
+485
+00:39:06,720 --> 00:39:12,380
+كأن هذي Y1 و هذي Y2 فالأن هذا يؤدي أن F1 of X1
+
+486
+00:39:12,380 --> 00:39:19,470
+تساوي F1 of X2 ليش؟ لأن F2 is one to oneعم تبقين؟
+
+487
+00:39:19,470 --> 00:39:22,070
+ليش ال F2 1 to 1؟ لأنه بيبقى rejection مش بس 1 to
+
+488
+00:39:22,070 --> 00:39:26,210
+1 اه و الآن ال F1 برضه 1 to 1 بيدين انه X1 تسوى X2
+
+489
+00:39:26,210 --> 00:39:36,090
+لأنه ال F1 is 1 to 1 اه thus F is 1 to 1 اه لجيت
+
+490
+00:39:36,090 --> 00:39:40,190
+one to one function من مجموعة لصفة ست منها الآن by
+
+491
+00:39:40,190 --> 00:39:45,070
+لمّة لمّة
+
+492
+00:39:45,070 --> 00:39:48,050
+أظن 6 1 رقمها اه
+
+493
+00:39:50,090 --> 00:39:55,890
+there exists H من A ل A0 تكون bijection وهو
+
+494
+00:39:55,890 --> 00:40:07,310
+المطلوب تمام
+
+495
+00:40:07,310 --> 00:40:11,950
+نتيجة الكلام اللي حكيناهفهذا التعبير بلغة
+
+496
+00:40:11,950 --> 00:40:15,570
+المجموعات التعبير بلغة ال cardinal numbers و هنا
+
+497
+00:40:15,570 --> 00:40:18,710
+يعني زي ما حكينا هذا الشبطر نفس الكلام اللي كنا
+
+498
+00:40:18,710 --> 00:40:21,730
+بنشرحه و بنتحدث عنه كتير من الصلاحات في شبطر خمسة
+
+499
+00:40:21,730 --> 00:40:24,590
+بس بنحكيها بلغة ال cardinal number فهنا بقول if a
+
+500
+00:40:24,590 --> 00:40:28,630
+and b are such that cardinal number of a أقل أو
+
+501
+00:40:28,630 --> 00:40:31,070
+يساوي cardinal number of b كتبته في البداية و
+
+502
+00:40:31,070 --> 00:40:33,530
+cardinal number of b أقل أو يساوي cardinal number
+
+503
+00:40:33,530 --> 00:40:38,400
+of a فالتانية متساويإذا X أقل تسوى Y و Y أقل تسوى
+
+504
+00:40:38,400 --> 00:40:42,440
+X فـ X تسوى Y نفس الكلام تمامًا فهذه نتيجة مباشرة
+
+505
+00:40:42,440 --> 00:40:46,060
+واضحة
+
+506
+00:40:46,060 --> 00:40:50,500
+أه؟ بدأت أوضح؟ واضحة جدًا على طول من نظري فعلا
+
+507
+00:40:50,500 --> 00:40:55,760
+نتيجة الآن هنحاول نجاوب في هذا ال section على
+
+508
+00:40:55,760 --> 00:41:00,760
+السؤال التالي هلجتنا فيه أن ال cardinal number
+
+509
+00:41:00,760 --> 00:41:06,130
+تحدثنا عن ترتيبهم تقريبًا خلصنا هناخلّينا نعمل
+
+510
+00:41:06,130 --> 00:41:09,570
+الصورة التالية أرجو التركيز معي عشان نفهم مش اللي
+
+511
+00:41:09,570 --> 00:41:16,590
+بنعمله هلجت لو قلنا لكم مين أصغر cardinal number؟
+
+512
+00:41:16,590 --> 00:41:20,430
+الصفر، أه لسه مش انتوا مش تعبديوا، الصفر، أه فإنها
+
+513
+00:41:20,430 --> 00:41:25,510
+جت الصفر أصغر من الواحد أصغر من التاني أصغر أصغر
+
+514
+00:41:25,510 --> 00:41:32,470
+أصغر من ال cardinality لل N أصغر من cardinality لل
+
+515
+00:41:32,470 --> 00:41:37,890
+Rفالسؤال في مجموعة ال cardinality إيها أكبر من
+
+516
+00:41:37,890 --> 00:41:45,270
+cardinality لل R؟ في .. أكبر شي بتعرفوه .. أقول
+
+517
+00:41:45,270 --> 00:41:48,970
+أكبر شي بعرفه أنا .. لأ في .. حنث بتانه في .. و في
+
+518
+00:41:48,970 --> 00:41:52,110
+هدول ليش بيمتدوا .. مابيجفوش .. فيش سقف .. كل
+
+519
+00:41:52,110 --> 00:41:55,790
+cardinal number في cardinal number أكبر منه .. كل
+
+520
+00:41:55,790 --> 00:42:00,970
+cardinal number فيعدد أصلي أكبر منه فهذه يمكن اللي
+
+521
+00:42:00,970 --> 00:42:04,430
+هو اللي بدي احنا نعمله فطبعا cardinal number of a
+
+522
+00:42:04,430 --> 00:42:06,610
+power set إيش اللي بيكبر المجموعة ناخد ال power
+
+523
+00:42:06,610 --> 00:42:09,410
+set تبعتها إذا مجموعة إذا عندكوا ال R كبيرة كتير
+
+524
+00:42:09,410 --> 00:42:13,150
+خد ال power of R شوفوا إيش بيصير تمام و في عندنا
+
+525
+00:42:13,150 --> 00:42:15,130
+اللي هو نظرية contours theorem
+
+526
+00:42:20,880 --> 00:42:25,280
+النظرية بتقول if X is a set then cardinality لل X
+
+527
+00:42:25,280 --> 00:42:31,340
+بشكل عام أقل من cardinality
+
+528
+00:42:31,340 --> 00:42:40,540
+لل power of Xيمكن انا نشر
+
+529
+00:42:40,540 --> 00:42:44,780
+على البرهان بشكل كامل لان نخليها للمرة الجاية لكن
+
+530
+00:42:44,780 --> 00:42:49,220
+بس بدنا نبدأ نفكر باشياء معينة نتعود عليها لانها
+
+531
+00:42:49,220 --> 00:42:55,000
+هتكون غريبة هتكون غريبة طبعا احنا ايش مطلوب مننا
+
+532
+00:42:55,000 --> 00:42:57,180
+نثبت خلينا بس هيك نعمل كهامش
+
+533
+00:42:59,820 --> 00:43:03,260
+ونفكر بالطريقة التانية عشان اللي هو المهد للمحاضرة
+
+534
+00:43:03,260 --> 00:43:09,460
+القادمة ع سبيل المثال لو أخدنا ال X بتساوي مجموعة
+
+535
+00:43:09,460 --> 00:43:21,380
+واحد واتنين نرجع لل power of X X
+
+536
+00:43:21,380 --> 00:43:27,640
+نفسي نعم طبعا احنا لما كانت finite المجموعة Xكان
+
+537
+00:43:27,640 --> 00:43:31,120
+الـ power of X إيش فيها 2 أُس عدد المجموعة فهذا إن
+
+538
+00:43:31,120 --> 00:43:34,080
+شاء الله هنعمّمه هنعمّمه بشكل عام حتى لو infinite
+
+539
+00:43:34,080 --> 00:43:38,380
+هنوصل بدا الشكل فالهدف طبعاً نبدأ لو أن نتصور بعض
+
+540
+00:43:38,380 --> 00:43:43,540
+الأمور فلو قلنا بهذا الشكل كيف نعرف دالة من X ل
+
+541
+00:43:43,540 --> 00:43:49,880
+power of X كيف نعرف دالة من X ل power of X نبدأ
+
+542
+00:43:49,880 --> 00:43:56,390
+نفكر فيهم للوقت لو أنا أعرفنا دالة F من Xthe power
+
+543
+00:43:56,390 --> 00:44:04,630
+of x by f of x تساوي مجموعة ال X غريبة ده اللي قد
+
+544
+00:44:04,630 --> 00:44:11,770
+شوية خلينا تتخمر منها اليوم السبت طبعا احسن لأ وين
+
+545
+00:44:11,770 --> 00:44:15,770
+هذي وين هذي بال power صح يعني كيف عندي هنا f
+
+546
+00:44:15,770 --> 00:44:19,210
+الواحد ايش بتساوي مجموعة ال واحد تنتمي هنا ولا
+
+547
+00:44:19,210 --> 00:44:24,660
+ماتنتميش اه f التنين مجموعة التنينإيش رأيكوا
+
+548
+00:44:24,660 --> 00:44:28,940
+الدالة دي one to one؟ وليس أنتوا صحيح، ليست أنتوا
+
+549
+00:44:28,940 --> 00:44:31,860
+واضحة، ليست أنتوا صحيح، واضحة لأن ال five مش صورة
+
+550
+00:44:31,860 --> 00:44:35,460
+حدى ولا ال X صورة حدى، لكنها one to one طبعا، هي
+
+551
+00:44:35,460 --> 00:44:41,400
+one to one، آه، الآن بقدر أتحدث عن حاجة زي إن X
+
+552
+00:44:41,400 --> 00:44:47,900
+تنتمي لل F of one؟ رموز غريبة، لكن منطقية صارت،
+
+553
+00:44:47,900 --> 00:44:53,590
+صح؟ مش ال F of one مجموعة؟عشان نفهم البرهان تنتمي
+
+554
+00:44:53,590 --> 00:44:59,370
+او لا تنتمي طبعا الواحد تنتمي نعم اي اي لو answer
+
+555
+00:44:59,370 --> 00:45:04,990
+ما يعني انا جيتلك و قولتلك واحد true صح اتنين
+
+556
+00:45:04,990 --> 00:45:13,450
+false تمام اه فان شاء الله طيب اذا مش واضحالك هيها
+
+557
+00:45:13,450 --> 00:45:18,050
+صح
+
+558
+00:45:18,050 --> 00:45:19,450
+واضحت
+
+559
+00:45:23,010 --> 00:45:28,450
+تمام مثال لأ لأ كابتن ال X هذا كان مثال فشوية شوية
+
+560
+00:45:28,450 --> 00:45:30,990
+ان شاء الله عند اكتوب البرهان هحتاج عادل رموز ان
+
+561
+00:45:30,990 --> 00:45:33,390
+شاء الله يوم السبت بنرجع للموضوع واحدة مرة ثانية
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/FF3N6KnUv3M_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/FF3N6KnUv3M_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4ce5a44271ab7fe5b8b2934fd8764ea3e9aa3eac
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/FF3N6KnUv3M_postprocess.srt
@@ -0,0 +1,2428 @@
+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 اتنين اللي بتحدث عن اللي هو
+
+6
+00:00:37,180 --> 00:00:41,540
+التكافؤ العددي للمجموع فطبعا احنا كنا فيهن نظرية
+
+7
+00:00:41,540 --> 00:00:45,760
+أثبتنا انه فيهن معيار للمجموعة ان تكون finite و
+
+8
+00:00:45,760 --> 00:00:49,910
+يمكن هذا يكون بديل للتعريففبتكون ال 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 نصب K يعني فيها K من العناصر ال K طبعا ما
+
+12
+00:00:59,050 --> 00:01:02,210
+زال K تنتبل ال N يعني K أكبر شهوة يا فيها Zero من
+
+13
+00:01:02,210 --> 00:01:05,070
+العناصر يا فيها واحد أو اتنين أو عشرة من العناصر و
+
+14
+00:01:05,070 --> 00:01:09,470
+هكذا أه 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
+أخرش ملاحظة حكيمها أه الحالة دلوقتي هنطبق على هذا
+
+17
+00:01:15,670 --> 00:01:18,980
+المفهوم إنش بالنسبة ال proposition برضه مهملو 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 تبع حمجدش بيكون فيه تلاتين دايما،
+
+20
+00:01:27,580 --> 00:01:30,960
+أقل أو يسوء تلاتين، آه، فلكن هواش بشكل تمتم و
+
+21
+00:01:30,960 --> 00:01:33,740
+finite، آه فهي العنوان تبع ال proposition the
+
+22
+00:01:33,740 --> 00:01:39,750
+unionof two finite sets is finite اتحاد مجموعتين
+
+23
+00:01:39,750 --> 00:01:43,410
+منتهيتين بتمه منتهى فطبعا نص ال proposition بشكل
+
+24
+00:01:43,410 --> 00:01:49,510
+دقيق او شكل صريح if A and B are finite sets then A
+
+25
+00:01:49,510 --> 00:01:54,750
+union B is finite خليني نشوف القرهان معضع فهذا ال
+
+26
+00:01:54,750 --> 00:01:59,410
+proposition خمسة
+
+27
+00:01:59,410 --> 00:02:01,130
+تلاتة will prove
+
+28
+00:02:03,840 --> 00:02:06,780
+طبعا زي ما شايفين اليوم شرطية فنبدأ نقش نفترض ان
+
+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 فدولة
+
+31
+00:02:22,140 --> 00:02:26,080
+مجموعتين finite بدنا نثبت ان 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 تستخدم التعريف هنا ليست infinite أو بده تستخدم
+
+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؟ أه طبعا زي الملاحظة اللي
+
+37
+00:03:01,140 --> 00:03:04,460
+حكيناها أنه لما ناخد الاتحاد مش دايما إذا فيه خمس
+
+38
+00:03:04,460 --> 00:03:07,800
+أو عشر بطلع 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 صحطيب، الـ M من المعطيات
+
+41
+00:03:14,930 --> 00:03:18,930
+الـ A finite في النظرية السابقة، يا في ياته كافي
+
+42
+00:03:18,930 --> 00:03:22,490
+أنصب K فيها bijection بينها بنصب K والـ B برضه
+
+43
+00:03:22,490 --> 00:03:26,630
+finite، إذا يا في يا إما ياته كافي أنصب 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
+عشر التانية، متروه كل عشر، ربما يكون 15، لكنها
+
+46
+00:03:31,170 --> 00:03:34,210
+finite، فبناخد ده 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، منتصلتين،
+
+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 فهكذا، 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 والـB
+
+53
+00:03:55,470 --> 00:04:00,690
+لا تساوي Phi، then أو إيش ما كانت الـB، بيكون الـA
+
+54
+00:04:00,690 --> 00:04:04,090
+مش ضرورة، مش قضية، إيه اتحاد الـB في هذه الحداشر
+
+55
+00:04:04,090 --> 00:04:07,810
+في ساوي؟ الـB، لأنه يشكل الـA finite، وهذا شماله
+
+56
+00:04:07,810 --> 00:04:08,470
+finite
+
+57
+00:04:13,650 --> 00:04:18,190
+نستبعله على جهة خلصناه العكس هو يمكن أن نقضهم مع
+
+58
+00:04:18,190 --> 00:04:22,810
+بعض لو كانت ال a ليست في و ال b هي اللي في برضه
+
+59
+00:04:22,810 --> 00:04:28,430
+الاتحادش بده يساوي a و ال a إشمالها finite كتبناها
+
+60
+00:04:28,430 --> 00:04:33,820
+في أول البرهان ممتازفيه ايضا احتمال انهم يكونوا
+
+61
+00:04:33,820 --> 00:04:36,540
+متساويين وليس تنتين فاي او متساويين او حتى لو
+
+62
+00:04:36,540 --> 00:04:39,260
+كانوا متساويين وليس تنتين فاي ايش بيكون اتحادهم
+
+63
+00:04:39,260 --> 00:04:42,060
+واحدة منهم لو كانوا كلهم متطابق فهذه هناخدها مع
+
+64
+00:04:42,060 --> 00:04:47,960
+بعض if A تساوي B كانوا فاي او مش فاي 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 finalفدول أول احتمالات سهلة وورهانهم
+
+67
+00:04:59,330 --> 00:05:02,590
+سهل أخدناهم على جهها لأنه بدأ أخد الحالة الأخيرة
+
+68
+00:05:02,590 --> 00:05:05,390
+هي اللي بدأ شغل الحالة الرابعة أو الأخيرة الآن
+
+69
+00:05:05,390 --> 00:05:09,790
+هناخد الحالة الأخيرة اللي هي إيش أن ال A لا تسوى
+
+70
+00:05:09,790 --> 00:05:13,110
+بي ولا واحدة فيهم فا ولا واحدة فيهم فا الآن بدأش
+
+71
+00:05:13,110 --> 00:05:20,390
+أخد الحالة الأخيرة assume A لا تسوى فا بي لا تسوى
+
+72
+00:05:20,390 --> 00:05:26,480
+فا وA لا تسوى بيلا تساوي 100 ناخد الحالة لهذا 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 فارقة فده واحدة فيها
+
+75
+00:05:34,260 --> 00:05:37,980
+عشرة والتاني إيش فيها خمس عشر فالاتحاد يكون أصغر
+
+76
+00:05:37,980 --> 00:05:41,700
+أو يسوي خمسة وعشرين نشوف كيف نعرف العدد بالظبط إنه
+
+77
+00:05:41,700 --> 00:05:46,120
+إيش بيسوي خمس عشر22 و لا 25 و لا 24 هنعمل ال trick
+
+78
+00:05:46,120 --> 00:05:49,740
+بسيط قبل هيك ممكن يكون ذكرته لكن هنشوف طبعا و
+
+79
+00:05:49,740 --> 00:05:53,920
+اكتشف يكون لو فيه خمسة و عشر الاتحاد خمساش لو كانت
+
+80
+00:05:53,920 --> 00:05:57,320
+قاطة of five فهذا معناته فانا سؤالي الآن كيف اكتب
+
+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 و مشهور
+
+83
+00:06:06,260 --> 00:06:10,940
+انا ذكرته لكن بذكركوا فيه مرتين هي عندي مجموعة ايه
+
+84
+00:06:11,500 --> 00:06:17,100
+وهي مجموعة D وهي A وهي D من الاتحاد التنتين مع بعض
+
+85
+00:06:17,100 --> 00:06:24,520
+لو أخدت هي ال 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 unionP ناقص إيه؟ لأن هذا المنطقة
+
+89
+00:06:42,220 --> 00:06:46,060
+هي مين؟ P ناقص إيه اللي تمت صح؟ واضحة ولا مش
+
+90
+00:06:46,060 --> 00:06:51,600
+واضحة؟ تمت 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 منفسرتين فدائما هذا ال trick اللي بيناعمل
+
+93
+00:06:58,260 --> 00:07:01,000
+فهذا ال trick اللي بيناعمل ممتاز الآن بدنا نبدأ
+
+94
+00:07:01,000 --> 00:07:03,920
+يشقن علم يعني كل هدفنا العناص 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
+البرهاننبدأ الآن ال B ناقص A هي subset من مين؟ من
+
+97
+00:07:17,980 --> 00:07:22,860
+ال B و لا لأ؟ هي subset من ال B و ال B finite إذن
+
+98
+00:07:22,860 --> 00:07:25,720
+هذه برضه finite نظرية خمسة واحد اللي أصغر من ال
+
+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 F ليش؟ لأن ال A لا تساوي ممتاز
+
+102
+00:07:46,890 --> 00:07:51,250
+فإذا نصلنا عشان هيك احنا خدنا الحل هذه مجموعة اللي
+
+103
+00:07:51,250 --> 00:07:54,390
+بشتر عليها يمين بيناقص A الآن بنركز عليها، بدنا
+
+104
+00:07:54,390 --> 00:07:57,620
+نشتر شوية لأنه احنا عندنا معلومات عن ال Aتبعين
+
+105
+00:07:57,620 --> 00:08:00,220
+معايا يا أخوات؟ احنا ال A عندنا معلومات لكن ال B
+
+106
+00:08:00,220 --> 00:08:03,400
+نقصي ماعندنا اش ماعندنا معلومات لكن هنشتق
+
+107
+00:08:03,400 --> 00:08:06,620
+المعلومات هنستنتج المعلومات بكل سهولة أولا ال B
+
+108
+00:08:06,620 --> 00:08:09,420
+نقصي هذا جزء من ال P إذا هي S أصغر من ال finite
+
+109
+00:08:09,420 --> 00:08:12,660
+فاينايت طب ال finite إيه الاحتمالية؟ يا في يا
+
+110
+00:08:12,660 --> 00:08:16,760
+بكافي and K طب هي ممكن تكون في مستحيل مزال مش مش
+
+111
+00:08:16,760 --> 00:08:22,500
+في تكون مكافي and sub K for some K فإذا بس
+
+112
+00:08:23,850 --> 00:08:29,490
+ب ماذا يعني تكافئ sub k؟ بقدر الرقم على صورة بي
+
+113
+00:08:29,490 --> 00:08:33,730
+واحد بي كي بي
+
+114
+00:08:33,730 --> 00:08:44,960
+واحد بي اتنين بي كي بي ناقص ايه؟ بي ناقص ممتازفإذا
+
+115
+00:08:44,960 --> 00:08:48,380
+أنا دول العناصر اللي هنا إيش هرقمهم بي واحد بي
+
+116
+00:08:48,380 --> 00:08:52,540
+اتنين بيجي جدش ومعاشرة فبي واحد لبي عشرة الآن بنفس
+
+117
+00:08:52,540 --> 00:08:56,400
+الاسلوب برضه ال a مش في 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 في is finite implies a تساوي a واحد a
+
+120
+00:09:12,320 --> 00:09:19,970
+اتنين a جدشلأ عشرة و عشرة ليه؟ ام for some عدد
+
+121
+00:09:19,970 --> 00:09:23,490
+حقيقة عدد صحيح ام صح واحدة فيها عشرة واحدة فيها
+
+122
+00:09:23,490 --> 00:09:27,300
+عشرين واحدة فيها خمسة واحدة فيها خمساش مش عادةبس
+
+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
+هيتكول من هدول مع هدول، فيه عصر مشترك بينهم؟ لأ،
+
+127
+00:09:42,920 --> 00:09:46,580
+جدتش هيكون المجموعة العناصر؟ K زائد N، أحسنته،
+
+128
+00:09:46,580 --> 00:09:54,600
+فبنثبت إنه هادي finite فبتكافئ M sub K خلينا نكتب،
+
+129
+00:09:54,600 --> 00:10:03,520
+We willProof 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 بس بعد الصورة طبعا تتكتب
+
+132
+00:10:18,800 --> 00:10:23,920
+اختصارا متابعين معاه؟ اه هي نفسها لمين؟ لمين ضايق
+
+133
+00:10:23,920 --> 00:10:29,660
+انك متابعينه؟مثل M sub N K زي R N 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 ال bijection سهل جدا ال bijection وفكرته من
+
+136
+00:10:39,960 --> 00:10:45,350
+وين كيف بتعلم الولد الصغير عملية العدهو بتتذكروا
+
+137
+00:10:45,350 --> 00:10:48,950
+اللي له أخه أو له أخت أو جريب أو من أخه الصغير
+
+138
+00:10:48,950 --> 00:10:52,230
+بتعلم العدل؟ إيش بيقولوله؟ بيقولوا هاي مجموعة فيها
+
+139
+00:10:52,230 --> 00:10:56,190
+أربع طفحات وهي مجموعة فيها تلت طفحات فإذا أربع زي
+
+140
+00:10:56,190 --> 00:10:58,690
+التلت إيش بيساوي؟ بيقول هاي أد واحد، اتنين، تلت،
+
+141
+00:10:58,690 --> 00:11:02,710
+أربع، خلاص بتعد المجموعة التانية 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 نعدلنين؟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 B given by F of
+
+147
+00:12:00,140 --> 00:12:06,040
+X تساوينرجع للمثال، ليش عملنا؟ لما كنا ناخد من P
+
+148
+00:12:06,040 --> 00:12:10,860
+نقول P1 كداش رقمها؟ واحد P2 كبنا عدت اتنين فهنقول
+
+149
+00:12:10,860 --> 00:12:15,480
+له هذه 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؟ اتنين
+
+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 أعد؟ ايه
+
+154
+00:12:36,490 --> 00:12:39,910
+واحد، ايش رقمها؟ k plus one ايه خمسة، ايش رقمها؟ k
+
+155
+00:12:39,910 --> 00:12:44,430
+plus خمسة لأن ك خلصت في الأول، خلصت أعد، هي عشرة،
+
+156
+00:12:44,430 --> 00:12:46,550
+بعدين بدي أعد إحداث، لما تحط إيديك أول مرة
+
+157
+00:12:46,550 --> 00:12:49,390
+تستخدمهم، مظبوط، فدهي، طبعا هذي one to one and one
+
+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 بتعلمها في ابتدائي
+
+161
+00:13:06,610 --> 00:13:11,690
+و بيحطوها بس بلغة أبسط لا يساعد فهذه اذا اي فتوفة
+
+162
+00:13:11,690 --> 00:13:14,630
+يناجست اتحادهم تكون final فاحنا حلقين .. غطينا كل
+
+163
+00:13:14,630 --> 00:13:20,730
+احتمالات .. بيكون هيك خلصنا ودا نهاية ال .. اي
+
+164
+00:13:20,730 --> 00:13:26,170
+استفسار؟ اي سؤال؟ففكرة بسيطة ونشوف احنا كيف طبعا
+
+165
+00:13:26,170 --> 00:13:29,230
+زي ان كنت بدأنا في عندي عدة أمثلة الآن انك صار
+
+166
+00:13:29,230 --> 00:13:32,810
+الأمور متقدمة شوية كده بنكون الدوال اتعلمنا انه
+
+167
+00:13:32,810 --> 00:13:35,750
+كان في صعوبة في البداية لأنه لسه كان اول مرة
+
+168
+00:13:35,750 --> 00:13:39,710
+بنتعامل لكن شوفنا بعض ال tricks بعض الملاحظات بعض
+
+169
+00:13:39,710 --> 00:13:43,450
+الإرشادات بدأت خزينتنا او ايه اللي خلفية تبعتنا
+
+170
+00:13:43,450 --> 00:13:46,410
+تزداد عنها صار أمثلة و متعددة و ممكن نسفيد منها و
+
+171
+00:13:46,410 --> 00:13:50,930
+نقلدهاونقلتها نشوف مين المثال بناسب شغلنا نعمله
+
+172
+00:13:50,930 --> 00:13:54,290
+كمان مرة أحيانا ممكن ماينطبقش تماما 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
+وطبعا 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 لل
+
+176
+00:14:03,990 --> 00:14:08,890
+section 5-2هيتحدث عن موضوع بيتطبق في الموضوع
+
+177
+00:14:08,890 --> 00:14:12,650
+الماضي و برضه هذا هيقوي معرفتنا و يمكن يدّينا
+
+178
+00:14:12,650 --> 00:14:16,870
+زاوية أخرى للنظر تساعدنا .. تساعدنا في العمل طبعا
+
+179
+00:14:16,870 --> 00:14:22,080
+مع زاوية أخرى العنوان equipotence of sixطبعا
+
+180
+00:14:22,080 --> 00:14:28,280
+equibotenance 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 .. تساويوقاعة فيها أربعين مقاعد فهدولة
+
+187
+00:14:43,260 --> 00:14:46,040
+بنفعوا يقعدوا على هدولة بنفعوا القاعة بتسعة فهذا
+
+188
+00:14:46,040 --> 00:14:49,740
+تكافئه 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
+التكافئ 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 المجملأ، 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
+بيهمناه، فأقول المجموعتين، فيها أربعين، أربعين
+
+198
+00:15:19,790 --> 00:15:23,330
+كرسي، فيها أربعين طالبة، فيها أربعين طفاحة، البهم
+
+199
+00:15:23,330 --> 00:15:28,460
+بالمين عدد العناصر، فحننظر من هذا الزمنتمام فانا
+
+200
+00:15:28,460 --> 00:15:32,420
+طبعا 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 ان 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 مقعدفهي فيه تناظر هي عملية العدل
+
+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 اتنين يعني
+
+208
+00:15:56,840 --> 00:15:59,740
+بقابل لعدد رقم اتنين فهذه عملية بقدر ألاقي تناظر
+
+209
+00:15:59,740 --> 00:16:02,380
+هذا اللي بقدر أكافر ليش هدول أربعين و هدول 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
+العدل فلما أقول إنهم متكافئين عدديًا لكل عنصر
+
+213
+00:16:13,280 --> 00:16:16,710
+يقابل عنصر والعكس صحيح تناظر واحدلواحد فهذه
+
+214
+00:16:16,710 --> 00:16:18,970
+الطريقة اللي انت عاملها مع العدو طب ليش مايقولوا
+
+215
+00:16:18,970 --> 00:16:21,970
+ليش هذه فيها عشر و هذه فيها عشرة لأن عشرة تنطبق مع
+
+216
+00:16:21,970 --> 00:16:25,070
+ال finite لو كانت infinite طب هذي فيها infinite و
+
+217
+00:16:25,070 --> 00:16:27,310
+هذي فيها infinite كيف بدأ اقارن ال infinite مع ال
+
+218
+00:16:27,310 --> 00:16:32,230
+infinite مينفعش فهذا هو الطريقة الصحيحة اللي بتنفع
+
+219
+00:16:32,230 --> 00:16:36,900
+تنطبق على ال finite و على ال infinitesفطبعا .. 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
+ماتتبقاش مع ال infinity و بعدين هنشوف أن مجموعها
+
+222
+00:16:43,120 --> 00:16:46,380
+infinite و مجموعها infinite لكن مختلفين، بيكفقوش
+
+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، اه فبقول لي does not apply when x
+
+225
+00:16:54,920 --> 00:16:58,520
+and y are infinite setsit seems natural يبدو يعني
+
+226
+00:16:58,520 --> 00:17:01,140
+العلماء هم بيفكروا لقوا أنه 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 التالفففي عندنا التعريف
+
+233
+00:17:24,790 --> 00:17:28,030
+التالف، إذا عشان أقارن بين مجموعتين من حيث العدد،
+
+234
+00:17:28,030 --> 00:17:30,630
+واكتش بيكونوا متكافئتين عدديًا، إذا كدت 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 مواضحة من الصياغ لما .. مش ال
+
+241
+00:17:56,840 --> 00:18:00,460
+statement عشان أقول أن دي يساوي و أن دي تكافئ زي
+
+242
+00:18:00,460 --> 00:18:03,420
+ما أحط ال bride لما أحط ال 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
+تكافئ 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 abjectionفإذا أنا
+
+248
+00:18:20,490 --> 00:18:29,810
+بقول الـ x تكافئ ال y there exists a bijection f
+
+249
+00:18:29,810 --> 00:18:36,670
+من x ل 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 و بعدين نطور حالنا لأنه الأن برضه
+
+252
+00:18:44,860 --> 00:18:48,760
+تقريبا بنفس الدائرة لو جالي أثبت أنه مجموعتين
+
+253
+00:18:48,760 --> 00:18:51,640
+متكافئتين عدديا، إيش مطلب منيه؟ ألاجي by diction
+
+254
+00:18:51,640 --> 00:18:55,400
+بينهم ال infinite دالة من مجموع على نفسها، هنا
+
+255
+00:18:55,400 --> 00:18:58,240
+مجموعتين مختلفتين و تكون one to one و ليست unto،
+
+256
+00:18:58,240 --> 00:19:01,000
+بس كان one to one و ليست unto، الآن بدي دالة بين
+
+257
+00:19:01,000 --> 00:19:04,740
+مجموعتين مختلفتين one to one و unto فتقريبا بنظر
+
+258
+00:19:04,740 --> 00:19:10,140
+بنفس الدائرة بس مع اختلاف نبدأ بمثال بسيط جداعشان
+
+259
+00:19:10,140 --> 00:19:13,920
+بس نقلش 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 هدا التعليق باختصار، ونشوف المثال الأول، هو
+
+262
+00:19:24,120 --> 00:19:28,930
+يبقى مثال بسيططبعا فيها دي مجموعتين ال X تساوي
+
+263
+00:19:28,930 --> 00:19:33,610
+واحد اتنين تلاتة و ال Y تساوي عدد ال Bi و عدد جزر
+
+264
+00:19:33,610 --> 00:19:37,850
+الخمسة و العدد E هدول كلهم عدد حقيقية ايش بيميزهم؟
+
+265
+00:19:37,850 --> 00:19:41,930
+كلهم غير نسبية اه كلهم عدد غير نسبية لا ال Bi نسبي
+
+266
+00:19:41,930 --> 00:19:45,470
+ولا جزر الخمسة نسبي ولا ال E نسبي اللي هي 2.7 و ال
+
+267
+00:19:45,470 --> 00:19:48,090
+Bi تلاتة point واحد كذا كذا و جزر الخمسة بيساوي
+
+268
+00:19:48,090 --> 00:19:51,150
+اتنين كثر كلهم ولا عدد فيهم مقدر احطه على صورة بس
+
+269
+00:19:51,150 --> 00:19:54,310
+و مقاه كلها عدد غير نسبية هذه المجموعة كافية؟ هذه
+
+270
+00:19:54,310 --> 00:19:57,830
+المجموعة عدديا ولا لأ؟واضح تلاتة و تلاتة 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 one to two فعنا هنا ال X فاكروا مع بعض
+
+273
+00:20:04,110 --> 00:20:07,810
+عملاها اكتبوا السؤال بشكل مختلف هو Y تساوي مين؟ ال
+
+274
+00:20:07,810 --> 00:20:12,290
+by و الجزر الخمسة و ال E اه فانا بدأ بالده الحل
+
+275
+00:20:12,290 --> 00:20:14,810
+كيف بدأ اتبين ان هذول متكافئة في اتهان؟ بدأ اعرف
+
+276
+00:20:14,810 --> 00:20:17,450
+دالة من X ل Y تكون one to one and one to two كيف
+
+277
+00:20:17,450 --> 00:20:22,720
+بدأ اعرف .. كيف بدأ بدأ السؤال؟ let F من X ل Ybe
+
+278
+00:20:22,720 --> 00:20:27,100
+given by أحسنتوا جيدا by طبعا 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 اختراح اعرفولي
+
+281
+00:20:39,120 --> 00:20:42,280
+الدالة بدي الدالة سهلة جدا إيش بدنا نعرفها عفوا 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 ال domain و كل عنصر له صورة ده ل one to one
+
+285
+00:20:58,900 --> 00:21:01,700
+ولا مش one to one لإنه مافيش شيش عنصر راح له صورة
+
+286
+00:21:01,700 --> 00:21:04,180
+انتوا ولا مش انتوا انتوا هطلنا كل ال domain بدي
+
+287
+00:21:04,180 --> 00:21:13,190
+اثبات ولا خلص خلص then f is a binaryطبعاً 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 تكافئها 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 تكافر، يعني هذه العلاقة
+
+298
+00:21:59,320 --> 00:22:03,580
+هي علاقة اللي هو reflexive، symmetric وtransitive
+
+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؟ مجموعاتفإذا 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 ال S هل هي
+
+305
+00:22:25,320 --> 00:22:30,580
+متكافية عدديا ولا لا؟ متكافية عدديا ولا لا؟ بقول
+
+306
+00:22:30,580 --> 00:22:35,900
+define a relation R on S مجموعة المجموعاتXY 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 ال S مجموعة مجموعة if
+
+309
+00:22:43,640 --> 00:22:47,820
+and only if X تكافئ Y عدديا، هذه العلاقة بقول هذول
+
+310
+00:22:47,820 --> 00:22:51,600
+ألهم علاقة مع بعض إذا كانوا متكافئين عدديا 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
+ليه؟ هذه العلاقة reflexiveSymmetric 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 منات
+
+317
+00:23:21,060 --> 00:23:24,780
+Reflexive أرجعلكوا عشان ال 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 عدديًا واضحة ولا مش واضحة طب لو قلتلك
+
+320
+00:23:31,220 --> 00:23:34,820
+اتديني بيجيبشين بين X و بين نفسهامين عنده
+
+321
+00:23:34,820 --> 00:23:38,320
+bijection بين مجموعه نفسها؟ اخلطوا مش مشكلة
+
+322
+00:23:38,320 --> 00:23:41,700
+اتعلموا احكوا احكوا ايش هي؟ بدي دالة بدي bijection
+
+323
+00:23:41,700 --> 00:23:45,760
+من X ل X ال identity ال identity صحيح فهي خلصنا
+
+324
+00:23:45,760 --> 00:23:49,440
+أثبتنا أننا نفلكسها فانتها؟ طب هي symmetric لو
+
+325
+00:23:49,440 --> 00:23:52,980
+قلنا إن ال X تكافئ ال Y أيش معناه؟ في bijection من
+
+326
+00:23:52,980 --> 00:23:57,720
+X ل Y طب كيف ده تصير من Y ل X؟ G inverse فهي صارت
+
+327
+00:23:57,720 --> 00:24:02,420
+أيش؟ أثبتها إيش تم نثبت؟ إنها transitX تكافئ ال Y
+
+328
+00:24:02,420 --> 00:24:06,040
+يعني فيه bijection من X ل Y و Y تكافئ ال Z يعني
+
+329
+00:24:06,040 --> 00:24:09,840
+فيه bijection من Y ل Z مين بدي bijection من X ل Z؟
+
+330
+00:24:09,840 --> 00:24:14,740
+إيش أعمل؟ composition .. composition .. أه فعلا
+
+331
+00:24:14,740 --> 00:24:17,200
+شرحتوا ليها ال exercise تكتبوها في البيت ال proof
+
+332
+00:24:17,200 --> 00:24:26,140
+exercise حدثوا ليها شفوا عليكوا تكتب notation
+
+333
+00:24:26,140 --> 00:24:33,100
+أه طبعا كالعادةمنحبش نكتب كتير في رياضيات فالآن
+
+334
+00:24:33,100 --> 00:24:36,680
+احنا هيتعامل 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 ايش بده اكتب هنا؟ there
+
+337
+00:24:43,600 --> 00:24:48,600
+exists F من X بده تساهمش لحطوة كلمة bijection بده
+
+338
+00:24:48,600 --> 00:24:52,840
+اختصرهافبكتب ان كل دالة بيحط سهم كل احنا اتفقنا
+
+339
+00:24:52,840 --> 00:24:58,100
+الدالة بنحط اسم الدالة نقطين فوق بعض ال domain سهم
+
+340
+00:24:58,100 --> 00:25:01,980
+الـ codomain طيب لو كانت y-jection بنحط بدل السهم
+
+341
+00:25:01,980 --> 00:25:04,520
+بنحطها ده معناه انك تشوف هنا يوجد دالة من X ل Y
+
+342
+00:25:04,520 --> 00:25:08,180
+وهي one to one and unto 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 انه الفترة من واحد لاتنين
+
+345
+00:25:29,060 --> 00:25:35,040
+تكافئ الفترة من zero لاتنين ايش الفترات هدول هم
+
+346
+00:25:35,040 --> 00:25:38,280
+مجموعات من الاعداد الحقيقية يعني ايش الفترة من
+
+347
+00:25:38,280 --> 00:25:41,320
+واحد لاتنين كل الاعداد الحقيقية اللي اكبر من واحد
+
+348
+00:25:41,320 --> 00:25:43,960
+واصغر من اتنين واللي من صفر لاتنين نفس الشيء اللي
+
+349
+00:25:43,960 --> 00:25:46,860
+اكبر من صفر واصغر من اتنين فانا بدنا نثبت ان هدول
+
+350
+00:25:46,860 --> 00:25:53,060
+المجموعاتين متكافئتين فهذا المثالالأول طبعا أنا فى
+
+351
+00:25:53,060 --> 00:25:57,480
+عندي هى حط الإعداد هى الصفر وهى الواحد وهى الاتنين
+
+352
+00:25:57,480 --> 00:26:01,980
+المجموعة الأولى اللى هنا من صفر من واحد لاتنين
+
+353
+00:26:01,980 --> 00:26:10,200
+والتانية من وين من صفر لاتنين طبعا
+
+354
+00:26:10,200 --> 00:26:12,300
+أنا ممكن البعض الناس يقول إيه غريبة طبعا دى جدا
+
+355
+00:26:12,300 --> 00:26:17,970
+مرتين لأ عدد عناصرهم متساوىعدد عناصرهم متساوى بدنا
+
+356
+00:26:17,970 --> 00:26:22,510
+نثبت إنهم فعلا كعدد عناصر متكافئتين مجموعتين
+
+357
+00:26:22,510 --> 00:26:28,610
+مختلفتين ظاهريا واحدة ضعف التانية لكنهم في الحقيقة
+
+358
+00:26:28,610 --> 00:26:32,550
+عدد عناصرهم واحد طبعا 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 ل 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 haveto 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 او اكتبوا كيابة لكي اقولوا مثال
+
+364
+00:27:00,150 --> 00:27:06,970
+لكم بالتصيب ا find f such that f
+
+365
+00:27:06,970 --> 00:27:13,950
+is one to one and hundred by diction فبدنا نعرف
+
+366
+00:27:13,950 --> 00:27:25,630
+دالةللـ 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 أحنا بندور في نفس الدائرة وإن
+
+369
+00:27:34,640 --> 00:27:37,760
+كان بشكل مختلف دايما مطلوب مني أجيب دالة من عندي
+
+370
+00:27:37,760 --> 00:27:41,320
+دالة مناسبة طبعا 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 أنتم one to one and أنتم أه بنفع أدور
+
+374
+00:27:51,500 --> 00:27:56,920
+في دفضر ال calculus؟ ليش بنفعش أعداد حقيقية أعداد
+
+375
+00:27:56,920 --> 00:28:01,210
+حقية فيه في المعطيات دوال؟ مافيشهدول أعداد حقية
+
+376
+00:28:01,210 --> 00:28:04,470
+بنفع أدور في دفتر ال calculus فبدنا دالة من دفتر
+
+377
+00:28:04,470 --> 00:28:07,990
+ال calculus من ال calculus دالة فيها جمع فيها طرح
+
+378
+00:28:07,990 --> 00:28:12,650
+فيها sin فيها cos تكون one to one and unto 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 أن
+
+381
+00:28:22,410 --> 00:28:27,170
+شو بشح نوع ما نحنا؟اش احنا بنعمل؟ خلّينا طبعا
+
+382
+00:28:27,170 --> 00:28:31,770
+كنقطة بداية ممكن واحد يحاول و دايما في try and
+
+383
+00:28:31,770 --> 00:28:34,170
+error الواحد بيحاول و ممكن يخطط لكن بتعلم من
+
+384
+00:28:34,170 --> 00:28:37,210
+أخطائه و بيشوف إذا هالي فشلة بدور على جهة تانية
+
+385
+00:28:37,210 --> 00:28:40,770
+لحد ما ينجح ممكن أنا طريقة بتفكير بتفكر بالطريقة
+
+386
+00:28:40,770 --> 00:28:45,730
+التالية بدي دالة تنقل الواحد لل zero تنقل الواحد
+
+387
+00:28:45,730 --> 00:28:51,930
+لل zero وتنقل التنين للتنين تنقل التنين للتنينفي
+
+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 التنين .. بتنقل
+
+390
+00:28:59,970 --> 00:29:05,890
+الواحد للصفر و بتنقل التنين للواحد ايش نعمل؟
+
+391
+00:29:05,890 --> 00:29:12,830
+عادي مبدأيا نجلت الواحد للصفر و نجلت التنين للتنين
+
+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 انت و لا انت و لا انا اجرب اه a given by أول
+
+394
+00:29:19,990 --> 00:29:25,940
+شي واحدis one to one كيف نفترض أنها one to one؟
+
+395
+00:29:25,940 --> 00:29:30,880
+let x1 و x2 وين؟ في ال domain مين تنتمي لمين؟ واحد
+
+396
+00:29:30,880 --> 00:29:34,260
+و اتنينها شايف؟ بدنا نكون دقيقين، هه نتعلم فاحنا
+
+397
+00:29:34,260 --> 00:29:37,740
+بناخد عن صورين في 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 و لا في حد عنده اعتراض؟ اه x مع 2 و y مع 1
+
+401
+00:30:01,070 --> 00:30:04,790
+فإذا الدالة فعلا 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
+ان شاء الله الصحيح نثبت أنها on to f is on to كيف
+
+404
+00:30:17,370 --> 00:30:20,410
+نثبت أنها on to 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، و احنا مهارة بنحاول
+
+409
+00:30:40,980 --> 00:30:44,740
+نتعلمها طيب، إيش معناه أقل في X؟ إتنين في X نقص
+
+410
+00:30:44,740 --> 00:30:49,180
+واحدة تساوي Y إيش بنعمل في الهامش؟ بنحل ل X بدلة
+
+411
+00:30:49,180 --> 00:30:53,480
+ال 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 فعلا بين
+
+413
+00:30:58,820 --> 00:31:01,880
+الواحد و بين التنين و إن صورتها بتساوي Y و إن
+
+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 زي 1 ثم أول شيء بدي أثبت إن X بين
+
+416
+00:31:20,140 --> 00:31:24,840
+1 و 2 كيف؟ أنا عندي ال Y وين أخدتها ال Y؟ ال Y من
+
+417
+00:31:24,840 --> 00:31:29,000
+0 إلى 2 مظبوط؟ بدي أنا أشوف ال X بين ال 0 و بين ال
+
+418
+00:31:29,000 --> 00:31:32,680
+1 و بين ال 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 1
+
+420
+00:31:39,320 --> 00:31:45,390
+زي 2أقل من اتنين صح ولا مش صح؟ اه فإذا إيش then
+
+421
+00:31:45,390 --> 00:31:51,810
+خلينا نكتبها white بتكتب الهامر implies x تنتمي
+
+422
+00:31:51,810 --> 00:31:55,590
+للزيرو لواحد اتنين وهو الايه المكتوبة الأول اتنين
+
+423
+00:31:55,590 --> 00:32:08,640
+تمام آخر حاجة and وهي الهامر f of xتساوي 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 و بتطرف 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 و ناخد فترتين
+
+428
+00:32:30,510 --> 00:32:33,450
+مختلفتين دايما ممكن نشتغل بهذه الشكلة فالحقيقة أنه
+
+429
+00:32:33,450 --> 00:32:38,770
+هذا و هنعممه 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 بعدهسالب
+
+433
+00:32:56,040 --> 00:33:03,640
+باية اتنين باية اتنين الفترة هالي تكافئ كل ا ا هذا
+
+434
+00:33:03,640 --> 00:33:05,740
+ال infinity ما هي نص ال infinity انفنتي مش نص ال
+
+435
+00:33:05,740 --> 00:33:09,400
+infinity انفنتي انفنتي هذي المظبوط هذي فبعدين نثبت
+
+436
+00:33:09,400 --> 00:33:15,500
+او ايه كيف نثبت ايه ايش التانية اه مش هنحلوها لسه
+
+437
+00:33:15,500 --> 00:33:20,920
+هنحلوها مع بعض هنحلوها مع بعض فمعين من المدور
+
+438
+00:33:20,920 --> 00:33:24,940
+function معين مع بعض أكيد هنخشهم مع بعضهنقشها مع
+
+439
+00:33:24,940 --> 00:33:33,920
+بعض فهنا
+
+440
+00:33:33,920 --> 00:33:40,340
+F تخلصناه مثال
+
+441
+00:33:40,340 --> 00:33:49,840
+رحم اتنين اه let F من سالب بايع اتنين لبايع اتنين
+
+442
+00:33:49,840 --> 00:33:50,660
+لل R
+
+443
+00:33:54,780 --> 00:34:03,200
+be given by f of x تساوي وين بتدوروا جاعدين؟ في
+
+444
+00:34:03,200 --> 00:34:10,940
+تفاقد الأحرار في دالة مشهورة جدا ارجعوا
+
+445
+00:34:10,940 --> 00:34:14,160
+على تفاضل باه والدالة هادي one to one and unto
+
+446
+00:34:14,160 --> 00:34:17,220
+عشان انها inverse tan inverse فهي بيبدأ تركها يقول
+
+447
+00:34:17,220 --> 00:34:18,040
+باجي عليك وخلاص
+
+448
+00:34:28,040 --> 00:34:31,100
+أبايجي تتذكروا احنا كيف عرفنا التان inverse؟ طبعا
+
+449
+00:34:31,100 --> 00:34:35,860
+التان في الأصل معرفة على كل ال R معدى عدد فردي في
+
+450
+00:34:35,860 --> 00:34:39,680
+بايع 2 فهي معرفة من سالب بايع 2 لبايع 2 و من بايع
+
+451
+00:34:39,680 --> 00:34:43,120
+2 لتلاتة بايع 2 و هكذا عشان نخليها one to one
+
+452
+00:34:43,120 --> 00:34:46,080
+أخدنا جزء فهي حصلت one to one لما أخدنا فترة من
+
+453
+00:34:46,080 --> 00:34:49,720
+الفترات طبعا هي انتوا على طول لأن كلها رسمتها
+
+454
+00:34:49,720 --> 00:34:53,180
+بتتذكروا الرسم كيف؟هيّا، بس درسوها من الفترة اللي
+
+455
+00:34:53,180 --> 00:34:56,700
+بديها، ده .. من سلة باعتنا ماباعتنا واش مهل، أغطّط
+
+456
+00:34:56,700 --> 00:34:59,460
+كل ال R من سلة infinite إلى infinite، أه فهو one
+
+457
+00:34:59,460 --> 00:35:02,060
+to one and unto طبعا عشان تفتحوها one to one يمكن
+
+458
+00:35:02,060 --> 00:35:05,340
+صعب نفبتها بالتعريف لكن ممكن تجي ل ال calculus إن
+
+459
+00:35:05,340 --> 00:35:08,740
+التفاضل و إنها تزايدية و هكذا، تزايدية تاني،
+
+460
+00:35:08,740 --> 00:35:10,900
+فبتطلع one to one، فعشان هيك نرجع ل ال calculus
+
+461
+00:35:10,900 --> 00:35:13,860
+فهو one to one و unto فعلا، لإن ال .. ال .. ال ..
+
+462
+00:35:13,860 --> 00:35:16,680
+ال .. هو إيش من هنا أعرفها؟ المادة تبعها كل R،
+
+463
+00:35:16,680 --> 00:35:19,480
+ارجع لتفاضل بها، فهو one to one and unto فليه ف
+
+464
+00:35:21,070 --> 00:35:24,130
+فاحنا إيش عملنا .. يعني نحكي أنتوا أنه بتغفل كل
+
+465
+00:35:24,130 --> 00:35:26,330
+المجال و خلاص؟ لأ إن المجال تبعها، ال calculus
+
+466
+00:35:26,330 --> 00:35:30,330
+بيساوي اه، فأطول هذي إيش المجال تبعها بيساوي اه،
+
+467
+00:35:30,330 --> 00:35:33,530
+بيساوي اه طيب إيش .. إيش .. إيش نثبتناه المثاليين
+
+468
+00:35:33,530 --> 00:35:37,370
+مع بعض؟ أثبتنا إنه كل فترة تقريبا تكافئ فترة،
+
+469
+00:35:37,370 --> 00:35:40,410
+نعملنا كام مثال، الحقيقة كل فترة مفتوحة تكافئ فترة
+
+470
+00:35:40,410 --> 00:35:44,350
+مفتوحةوالفترة باية اتنين باية اتنين تكافئ ال ا ..
+
+471
+00:35:44,350 --> 00:35:46,830
+طب الباية اتنين باية اتنين سال باية اتنين بتكافئ
+
+472
+00:35:46,830 --> 00:35:50,910
+واحد zero مثلا بتكافئ ا .. فإيه صار .. كل أي فترة
+
+473
+00:35:50,910 --> 00:35:54,450
+تكافئ أي فترة مفتوحة .. أي فترة مفتوحة .. ان شاء
+
+474
+00:35:54,450 --> 00:35:58,170
+الله تاخد الفترة من صفر لواحد من عشر .. تكافئ كل ا
+
+475
+00:35:58,170 --> 00:36:01,770
+.. أي فترة مفتوحة تكافئ ال ا .. تكافئ ال ا .. و
+
+476
+00:36:01,770 --> 00:36:01,990
+ادي
+
+477
+00:36:06,210 --> 00:36:09,530
+أه فده لسه هنجيله .. هنديعله مرة تانية أي فترة
+
+478
+00:36:09,530 --> 00:36:11,730
+مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة .. أي
+
+479
+00:36:11,730 --> 00:36:11,950
+فترة مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة ..
+
+480
+00:36:11,950 --> 00:36:12,690
+أي فترة مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة
+
+481
+00:36:12,690 --> 00:36:17,970
+.. أي فترة مفتوحة .. أي فترة مفتوحة .. أي فترة
+
+482
+00:36:17,970 --> 00:36:22,630
+مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة .. أي
+
+483
+00:36:22,630 --> 00:36:25,770
+فترة مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة ..
+
+484
+00:36:25,770 --> 00:36:28,710
+أي فترة مفتوحة .. أي فلأن هو إيش العلاقة؟ هي علاقة
+
+485
+00:36:28,710 --> 00:36:31,230
+إيش؟ equivalence relation، يعني transitive فأنا
+
+486
+00:36:31,230 --> 00:36:34,270
+عندي أي فترة تكافئ سالب بايع اتنين على بايع اتنين
+
+487
+00:36:34,270 --> 00:36:36,430
+وسالب بايع اتنين على بايع اتنين بتكافئ لأ لإن
+
+488
+00:36:36,430 --> 00:36:40,650
+سهولة عشان التهن إذا كل فترة مفتوحة تكافئ أ فترة
+
+489
+00:36:40,650 --> 00:36:44,710
+transitive نشوف مثال المخلخة بدها شوية شغل عشان
+
+490
+00:36:44,710 --> 00:36:47,530
+اللي هو النقطة اللي جوا بدها شوية شغل موجودة في
+
+491
+00:36:47,530 --> 00:36:54,650
+الكتاب نشوف مثال مختلف نوعا ما بقولي إذا في عندي
+
+492
+00:36:54,650 --> 00:37:01,580
+مجموعةو إيه بجبعتين؟ الأولى ناقص التانية يكافئ
+
+493
+00:37:01,580 --> 00:37:05,840
+التانية ناقص الأولى فدوله مجبعتين متكافئتين خلينا
+
+494
+00:37:05,840 --> 00:37:10,480
+نشوف البرهان أو الحل و نشوف رسمه ممكن تساعدنا نشوف
+
+495
+00:37:10,480 --> 00:37:18,600
+رسمه ممكن تساعدنا هذا
+
+496
+00:37:18,600 --> 00:37:21,860
+يمكن تكون أسهل من الأمثلة الماضية التصور تبعها
+
+497
+00:37:21,860 --> 00:37:28,340
+يكون أسهلهي عندنا مجموعتين طبعا هذه X وهذه Y طبعا
+
+498
+00:37:28,340 --> 00:37:34,940
+هذه المنطقة .. هذه X ناقص Y وهذه المنطقة Y ناقص S
+
+499
+00:37:34,940 --> 00:37:41,120
+لأن الاتحاد مشترك فهذه هي الفكرة .. فهذه هي الفكرة
+
+500
+00:37:41,120 --> 00:37:45,140
+واضحة إذا منطق الكلام .. الكلام منطقي فبدنا نبرهنه
+
+501
+00:37:45,140 --> 00:37:49,100
+.. بدنا نكتبه بلغة رياضية مايواضحة من الصورة ..
+
+502
+00:37:49,100 --> 00:37:53,830
+الصورة مش مرهقة فالآن دعنا هذا المثال التالدطب
+
+503
+00:37:53,830 --> 00:38:01,590
+عشان ده عنده موضوع prove that if ف assume x
+
+504
+00:38:01,590 --> 00:38:09,690
+ناقص y تكافئ y ناقص x بدنا نثبت ان x تكافئ y كيف
+
+505
+00:38:09,690 --> 00:38:13,950
+بدنا نثبتها؟ بدي bijection من x ل y بدنا دالة من x
+
+506
+00:38:13,950 --> 00:38:18,820
+ل yنرجع على دفتر ال calculus؟ ولا خلاص نسكره الآن؟
+
+507
+00:38:18,820 --> 00:38:23,140
+مانفعش الآن، مانفعش، مانفعش، بدنا إذا بنعرف دالة F
+
+508
+00:38:23,140 --> 00:38:26,440
+من X ل Y تكون one to one عند أنتم، من وين بدنا
+
+509
+00:38:26,440 --> 00:38:29,960
+ندور عليها؟ بالمعطيات، في في المعطيات، نعم، هاي و
+
+510
+00:38:29,960 --> 00:38:32,820
+مش هدية السوم، إذا بقدر ألاقي دالة one to one عند
+
+511
+00:38:32,820 --> 00:38:37,360
+أنتم، من X ناقص Y ل Y ناقص X، هذا يؤدي، there
+
+512
+00:38:37,360 --> 00:38:44,290
+exist G اختصارا، هاي bijection معناها، صح؟بعدين
+
+513
+00:38:44,290 --> 00:38:47,050
+مكتوبة bijection، الإكتوبة بدا الشكل، اتعودتوا على
+
+514
+00:38:47,050 --> 00:38:50,210
+الرمز الجديد؟ يعني فيه bijection من X نقص Y ل Y
+
+515
+00:38:50,210 --> 00:38:53,310
+نقصي، الآن أنا جاهز أعرف الدالة، شوفت الفكرة اللي
+
+516
+00:38:53,310 --> 00:38:55,850
+أحنا قولنا فيها، بالله في حول الدائرة، نفس
+
+517
+00:38:55,850 --> 00:38:59,590
+الدائرة، و نفس الأفكار تتكرر بشكل بس إيش، متقارن،
+
+518
+00:38:59,590 --> 00:39:05,650
+هعرفه دالة، let F من X ل Y be given
+
+519
+00:39:09,620 --> 00:39:13,140
+G of X to Z طبعا هعتمد في تعريف عالميين على الـG
+
+520
+00:39:13,140 --> 00:39:17,320
+الفكرة مرت علينا تقريبا مشابهة لكن إيش ميزة الـG
+
+521
+00:39:17,320 --> 00:39:21,700
+معرفة على جزء من الـX مش على كل الـX معرفة من وين؟
+
+522
+00:39:21,700 --> 00:39:26,400
+من X ناقص Y فبتكمل الدمان طب إذن أول شي هعرفها G
+
+523
+00:39:26,400 --> 00:39:32,940
+of X إذا الـX وين؟ في الـX ناقص Y بتام هنا الفرق
+
+524
+00:39:32,940 --> 00:39:35,060
+هنا الباقي إيش عرفها؟
+
+525
+00:39:38,550 --> 00:39:43,410
+أولش هنا انا هي ال domain ال domain كل X المنطقة
+
+526
+00:39:43,410 --> 00:39:49,490
+هذه انا معرف عليها G هذه المنطقة مش معرف عليها G
+
+527
+00:39:49,490 --> 00:39:54,190
+صح؟ بدي اكمل انا عشان يكون اقص من X لكي اتعرف على
+
+528
+00:39:54,190 --> 00:39:58,070
+كل ال G هذا بيشبه اول مثال يمكن حليناه في ال
+
+529
+00:39:58,070 --> 00:40:02,330
+infinite cell ايش اعرفها هنا؟ال identity بنفع نفس
+
+530
+00:40:02,330 --> 00:40:05,190
+الشيء لأن هدول إيش فيه؟ هدول عناصر بيكافؤوا هدول
+
+531
+00:40:05,190 --> 00:40:07,670
+فيه تناظر بين هدول و بين هدول طب هذا كيف بناظر
+
+532
+00:40:07,670 --> 00:40:10,730
+نفسه؟ لأنه نفسه مشترك فكل عنصر هو بناظر نفسه هنا
+
+533
+00:40:10,730 --> 00:40:17,470
+لأنه مشترك فدي هسميها X زي X وين تنتمي للتقاطةلأن
+
+534
+00:40:17,470 --> 00:40:21,890
+هذه المنطقة هي التقاطة فهي تكمل من كل ال X فال X
+
+535
+00:40:21,890 --> 00:40:30,110
+مما تتكون تتكون من X ناقص Y إتحاد التقاطة ففي X
+
+536
+00:40:30,110 --> 00:40:35,290
+ناقص Y جي معرفة أدت الغلط وخدمتني بس أي مقدرة الجي
+
+537
+00:40:35,290 --> 00:40:39,170
+طيب في الباقي ال identity إيه بتصرف؟ بالنسبة لهذه
+
+538
+00:40:39,170 --> 00:40:42,590
+one to one أد one to one تعرف تفكروها ولا لا؟
+
+539
+00:40:42,590 --> 00:40:43,490
+المفروض تعرف
+
+540
+00:40:57,520 --> 00:41:00,500
+is one to one شفتوا الأفكار كام تتكرر ده؟ ده يمكن
+
+541
+00:41:00,500 --> 00:41:05,300
+الأول مرة تكون غريبة افهمتوا منها 5% تتكرر كمان
+
+542
+00:41:05,300 --> 00:41:09,860
+مرة بترتفع نسبة الفهم 10% 20% مع التكرار أرجو أنه
+
+543
+00:41:09,860 --> 00:41:14,020
+نسبة تعلى عن ال 50% و هكذا بيصير في الأمر كويس
+
+544
+00:41:14,020 --> 00:41:22,920
+slit x1 و x2 في domain ال Fلأ ركزوا مش غير تحطوا
+
+545
+00:41:22,920 --> 00:41:26,280
+مستطيل و أنتوا شاطرين بالتزويج و بالأمور زي هيك
+
+546
+00:41:26,280 --> 00:41:28,740
+عشان تتبعوا اتركزوا هنا و هنا و أنتوا تشتغلوا اه
+
+547
+00:41:28,740 --> 00:41:32,500
+فانا مش هروح لل G انا بشغل على ال F بداشي أدي ال F
+
+548
+00:41:32,500 --> 00:41:35,880
+one to one ايش أعمل؟ عنصرين في ال domain تبع ال F
+
+549
+00:41:35,880 --> 00:41:41,180
+اه so what are we going to solve؟
+
+550
+00:41:41,180 --> 00:41:45,980
+بدي
+
+551
+00:41:45,980 --> 00:41:49,700
+أستخدم التعريف التعريف ده لمعرفة متعددة القاعدة
+
+552
+00:41:49,700 --> 00:41:50,480
+أربع حالة
+
+553
+00:41:54,410 --> 00:42:00,610
+طبعا لو كانوا التنين في X-Y إيش التعريف؟ G of X1
+
+554
+00:42:00,610 --> 00:42:07,310
+تساوي G of X2 إذا كان X1 و X2 في X-Y وناخد برضه
+
+555
+00:42:07,310 --> 00:42:11,310
+التانية السهلة لو كانوا التنين في التقاطة X1 تساوي
+
+556
+00:42:11,310 --> 00:42:16,990
+X2 إذا X1 و X2 في X مقاطع الواحد لما يكونوا التنين
+
+557
+00:42:16,990 --> 00:42:20,870
+مع بعض يا في المنطقة الأولى يا في المنطقة التانية
+
+558
+00:42:20,870 --> 00:42:26,990
+بيتعمل حالتين كل واحد في منطقة مختلفةف G of X1
+
+559
+00:42:26,990 --> 00:42:33,990
+تساوي X2 لو كانت X1 في المنطقة الـ minus و X2 في
+
+560
+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 ماقصر طبعا كالعادةفيه تنتين
+
+562
+00:42:50,650 --> 00:42:54,650
+هيدوني X1 تساوي X2 واحدة فيهم واضحة وتنتين 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 ا 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 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 ل 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 التاني
+
+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 Yمرة تانية 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 لاتنتمي، خلاصP 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 Fis onto .. اه هحسب ال image مش هستخدم
+
+584
+00:44:44,120 --> 00:44:48,680
+الصورة التانية هاخد ال Y و أجيبها صورة مين هحسب ال
+
+585
+00:44:48,680 --> 00:44:54,250
+image مباشرة فهو هحسب F of Xفيه 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 Fx-y اتحاد f of 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 one to two اشملها
+
+598
+00:45:47,300 --> 00:45:49,820
+one to one and one to two 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 ل 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 مصطلق 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/FF3N6KnUv3M_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/FF3N6KnUv3M_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2beba070a5d73cf7771dbfa5ac0f61cf77427b16
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/FF3N6KnUv3M_raw.srt
@@ -0,0 +1,2436 @@
+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 اتنين اللي بتحدث عن اللي هو
+
+6
+00:00:37,180 --> 00:00:41,540
+التكافؤ العددي للمجموع فطبعا احنا كنا فيهن نظرية
+
+7
+00:00:41,540 --> 00:00:45,760
+أثبتنا انه فيهن معيار للمجموعة ان تكون finite و
+
+8
+00:00:45,760 --> 00:00:49,910
+يمكن هذا يكون بديل للتعريففبتكون ال 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 نصب K يعني فيها K من العناصر ال K طبعا ما
+
+12
+00:00:59,050 --> 00:01:02,210
+زال K تنتبل ال N يعني K أكبر شهوة يا فيها Zero من
+
+13
+00:01:02,210 --> 00:01:05,070
+العناصر يا فيها واحد أو اتنين أو عشرة من العناصر و
+
+14
+00:01:05,070 --> 00:01:09,470
+هكذا أه 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
+أخرش ملاحظة حكيمها أه الحالة دلوقتي هنطبق على هذا
+
+17
+00:01:15,670 --> 00:01:18,980
+المفهوم إنش بالنسبة ال proposition برضه مهملو 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 تبع حمجدش بيكون فيه تلاتين دايما،
+
+20
+00:01:27,580 --> 00:01:30,960
+أقل أو يسوء تلاتين، آه، فلكن هواش بشكل تمتم و
+
+21
+00:01:30,960 --> 00:01:33,740
+finite، آه فهي العنوان تبع ال proposition the
+
+22
+00:01:33,740 --> 00:01:39,750
+unionof two finite sets is finite اتحاد مجموعتين
+
+23
+00:01:39,750 --> 00:01:43,410
+منتهيتين بتمه منتهى فطبعا نص ال proposition بشكل
+
+24
+00:01:43,410 --> 00:01:49,510
+دقيق او شكل صريح if A and B are finite sets then A
+
+25
+00:01:49,510 --> 00:01:54,750
+union B is finite خليني نشوف القرهان معضع فهذا ال
+
+26
+00:01:54,750 --> 00:01:59,410
+proposition خمسة
+
+27
+00:01:59,410 --> 00:02:01,130
+تلاتة will prove
+
+28
+00:02:03,840 --> 00:02:06,780
+طبعا زي ما شايفين اليوم شرطية فنبدأ نقش نفترض ان
+
+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 فدولة
+
+31
+00:02:22,140 --> 00:02:26,080
+مجموعتين finite بدنا نثبت ان 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 تستخدم التعريف هنا ليست infinite أو بده تستخدم
+
+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؟ أه طبعا زي الملاحظة اللي
+
+37
+00:03:01,140 --> 00:03:04,460
+حكيناها أنه لما ناخد الاتحاد مش دايما إذا فيه خمس
+
+38
+00:03:04,460 --> 00:03:07,800
+أو عشر بطلع 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 صحطيب، الـ M من المعطيات
+
+41
+00:03:14,930 --> 00:03:18,930
+الـ A finite في النظرية السابقة، يا في ياته كافي
+
+42
+00:03:18,930 --> 00:03:22,490
+أنصب K فيها bijection بينها بنصب K والـ B برضه
+
+43
+00:03:22,490 --> 00:03:26,630
+finite، إذا يا في يا إما ياته كافي أنصب 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
+عشر التانية، متروه كل عشر، ربما يكون 15، لكنها
+
+46
+00:03:31,170 --> 00:03:34,210
+finite، فبناخد ده 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، منتصلتين،
+
+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 فهكذا، 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 والـB
+
+53
+00:03:55,470 --> 00:04:00,690
+لا تساوي Phi، then أو إيش ما كانت الـB، بيكون الـA
+
+54
+00:04:00,690 --> 00:04:04,090
+مش ضرورة، مش قضية، إيه اتحاد الـB في هذه الحداشر
+
+55
+00:04:04,090 --> 00:04:07,810
+في ساوي؟ الـB، لأنه يشكل الـA finite، وهذا شماله
+
+56
+00:04:07,810 --> 00:04:08,470
+finite
+
+57
+00:04:13,650 --> 00:04:18,190
+نستبعله على جهة خلصناه العكس هو يمكن أن نقضهم مع
+
+58
+00:04:18,190 --> 00:04:22,810
+بعض لو كانت ال a ليست في و ال b هي اللي في برضه
+
+59
+00:04:22,810 --> 00:04:28,430
+الاتحادش بده يساوي a و ال a إشمالها finite كتبناها
+
+60
+00:04:28,430 --> 00:04:33,820
+في أول البرهان ممتازفيه ايضا احتمال انهم يكونوا
+
+61
+00:04:33,820 --> 00:04:36,540
+متساويين وليس تنتين فاي او متساويين او حتى لو
+
+62
+00:04:36,540 --> 00:04:39,260
+كانوا متساويين وليس تنتين فاي ايش بيكون اتحادهم
+
+63
+00:04:39,260 --> 00:04:42,060
+واحدة منهم لو كانوا كلهم متطابق فهذه هناخدها مع
+
+64
+00:04:42,060 --> 00:04:47,960
+بعض if A تساوي B كانوا فاي او مش فاي 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 finalفدول أول احتمالات سهلة وورهانهم
+
+67
+00:04:59,330 --> 00:05:02,590
+سهل أخدناهم على جهها لأنه بدأ أخد الحالة الأخيرة
+
+68
+00:05:02,590 --> 00:05:05,390
+هي اللي بدأ شغل الحالة الرابعة أو الأخيرة الآن
+
+69
+00:05:05,390 --> 00:05:09,790
+هناخد الحالة الأخيرة اللي هي إيش أن ال A لا تسوى
+
+70
+00:05:09,790 --> 00:05:13,110
+بي ولا واحدة فيهم فا ولا واحدة فيهم فا الآن بدأش
+
+71
+00:05:13,110 --> 00:05:20,390
+أخد الحالة الأخيرة assume A لا تسوى فا بي لا تسوى
+
+72
+00:05:20,390 --> 00:05:26,480
+فا وA لا تسوى بيلا تساوي 100 ناخد الحالة لهذا 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 فارقة فده واحدة فيها
+
+75
+00:05:34,260 --> 00:05:37,980
+عشرة والتاني إيش فيها خمس عشر فالاتحاد يكون أصغر
+
+76
+00:05:37,980 --> 00:05:41,700
+أو يسوي خمسة وعشرين نشوف كيف نعرف العدد بالظبط إنه
+
+77
+00:05:41,700 --> 00:05:46,120
+إيش بيسوي خمس عشر22 و لا 25 و لا 24 هنعمل ال trick
+
+78
+00:05:46,120 --> 00:05:49,740
+بسيط قبل هيك ممكن يكون ذكرته لكن هنشوف طبعا و
+
+79
+00:05:49,740 --> 00:05:53,920
+اكتشف يكون لو فيه خمسة و عشر الاتحاد خمساش لو كانت
+
+80
+00:05:53,920 --> 00:05:57,320
+قاطة of five فهذا معناته فانا سؤالي الآن كيف اكتب
+
+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 و مشهور
+
+83
+00:06:06,260 --> 00:06:10,940
+انا ذكرته لكن بذكركوا فيه مرتين هي عندي مجموعة ايه
+
+84
+00:06:11,500 --> 00:06:17,100
+وهي مجموعة D وهي A وهي D من الاتحاد التنتين مع بعض
+
+85
+00:06:17,100 --> 00:06:24,520
+لو أخدت هي ال 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 unionP ناقص إيه؟ لأن هذا المنطقة
+
+89
+00:06:42,220 --> 00:06:46,060
+هي مين؟ P ناقص إيه اللي تمت صح؟ واضحة ولا مش
+
+90
+00:06:46,060 --> 00:06:51,600
+واضحة؟ تمت 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 منفسرتين فدائما هذا ال trick اللي بيناعمل
+
+93
+00:06:58,260 --> 00:07:01,000
+فهذا ال trick اللي بيناعمل ممتاز الآن بدنا نبدأ
+
+94
+00:07:01,000 --> 00:07:03,920
+يشقن علم يعني كل هدفنا العناص 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
+البرهاننبدأ الآن ال B ناقص A هي subset من مين؟ من
+
+97
+00:07:17,980 --> 00:07:22,860
+ال B و لا لأ؟ هي subset من ال B و ال B finite إذن
+
+98
+00:07:22,860 --> 00:07:25,720
+هذه برضه finite نظرية خمسة واحد اللي أصغر من ال
+
+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 F ليش؟ لأن ال A لا تساوي ممتاز
+
+102
+00:07:46,890 --> 00:07:51,250
+فإذا نصلنا عشان هيك احنا خدنا الحل هذه مجموعة اللي
+
+103
+00:07:51,250 --> 00:07:54,390
+بشتر عليها يمين بيناقص A الآن بنركز عليها، بدنا
+
+104
+00:07:54,390 --> 00:07:57,620
+نشتر شوية لأنه احنا عندنا معلومات عن ال Aتبعين
+
+105
+00:07:57,620 --> 00:08:00,220
+معايا يا أخوات؟ احنا ال A عندنا معلومات لكن ال B
+
+106
+00:08:00,220 --> 00:08:03,400
+نقصي ماعندنا اش ماعندنا معلومات لكن هنشتق
+
+107
+00:08:03,400 --> 00:08:06,620
+المعلومات هنستنتج المعلومات بكل سهولة أولا ال B
+
+108
+00:08:06,620 --> 00:08:09,420
+نقصي هذا جزء من ال P إذا هي S أصغر من ال finite
+
+109
+00:08:09,420 --> 00:08:12,660
+فاينايت طب ال finite إيه الاحتمالية؟ يا في يا
+
+110
+00:08:12,660 --> 00:08:16,760
+بكافي and K طب هي ممكن تكون في مستحيل مزال مش مش
+
+111
+00:08:16,760 --> 00:08:22,500
+في تكون مكافي and sub K for some K فإذا بس
+
+112
+00:08:23,850 --> 00:08:29,490
+ب ماذا يعني تكافئ sub k؟ بقدر الرقم على صورة بي
+
+113
+00:08:29,490 --> 00:08:33,730
+واحد بي كي بي
+
+114
+00:08:33,730 --> 00:08:44,960
+واحد بي اتنين بي كي بي ناقص ايه؟ بي ناقص ممتازفإذا
+
+115
+00:08:44,960 --> 00:08:48,380
+أنا دول العناصر اللي هنا إيش هرقمهم بي واحد بي
+
+116
+00:08:48,380 --> 00:08:52,540
+اتنين بيجي جدش ومعاشرة فبي واحد لبي عشرة الآن بنفس
+
+117
+00:08:52,540 --> 00:08:56,400
+الاسلوب برضه ال a مش في 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 في is finite implies a تساوي a واحد a
+
+120
+00:09:12,320 --> 00:09:19,970
+اتنين a جدشلأ عشرة و عشرة ليه؟ ام for some عدد
+
+121
+00:09:19,970 --> 00:09:23,490
+حقيقة عدد صحيح ام صح واحدة فيها عشرة واحدة فيها
+
+122
+00:09:23,490 --> 00:09:27,300
+عشرين واحدة فيها خمسة واحدة فيها خمساش مش عادةبس
+
+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
+هيتكول من هدول مع هدول، فيه عصر مشترك بينهم؟ لأ،
+
+127
+00:09:42,920 --> 00:09:46,580
+جدتش هيكون المجموعة العناصر؟ K زائد N، أحسنته،
+
+128
+00:09:46,580 --> 00:09:54,600
+فبنثبت إنه هادي finite فبتكافئ M sub K خلينا نكتب،
+
+129
+00:09:54,600 --> 00:10:03,520
+We willProof 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 بس بعد الصورة طبعا تتكتب
+
+132
+00:10:18,800 --> 00:10:23,920
+اختصارا متابعين معاه؟ اه هي نفسها لمين؟ لمين ضايق
+
+133
+00:10:23,920 --> 00:10:29,660
+انك متابعينه؟مثل M sub N K زي R N 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 ال bijection سهل جدا ال bijection وفكرته من
+
+136
+00:10:39,960 --> 00:10:45,350
+وين كيف بتعلم الولد الصغير عملية العدهو بتتذكروا
+
+137
+00:10:45,350 --> 00:10:48,950
+اللي له أخه أو له أخت أو جريب أو من أخه الصغير
+
+138
+00:10:48,950 --> 00:10:52,230
+بتعلم العدل؟ إيش بيقولوله؟ بيقولوا هاي مجموعة فيها
+
+139
+00:10:52,230 --> 00:10:56,190
+أربع طفحات وهي مجموعة فيها تلت طفحات فإذا أربع زي
+
+140
+00:10:56,190 --> 00:10:58,690
+التلت إيش بيساوي؟ بيقول هاي أد واحد، اتنين، تلت،
+
+141
+00:10:58,690 --> 00:11:02,710
+أربع، خلاص بتعد المجموعة التانية 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 نعدلنين؟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 B given by F of
+
+147
+00:12:00,140 --> 00:12:06,040
+X تساوينرجع للمثال، ليش عملنا؟ لما كنا ناخد من P
+
+148
+00:12:06,040 --> 00:12:10,860
+نقول P1 كداش رقمها؟ واحد P2 كبنا عدت اتنين فهنقول
+
+149
+00:12:10,860 --> 00:12:15,480
+له هذه 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؟ اتنين
+
+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 أعد؟ ايه
+
+154
+00:12:36,490 --> 00:12:39,910
+واحد، ايش رقمها؟ k plus one ايه خمسة، ايش رقمها؟ k
+
+155
+00:12:39,910 --> 00:12:44,430
+plus خمسة لأن ك خلصت في الأول، خلصت أعد، هي عشرة،
+
+156
+00:12:44,430 --> 00:12:46,550
+بعدين بدي أعد إحداث، لما تحط إيديك أول مرة
+
+157
+00:12:46,550 --> 00:12:49,390
+تستخدمهم، مظبوط، فدهي، طبعا هذي one to one and one
+
+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 بتعلمها في ابتدائي
+
+161
+00:13:06,610 --> 00:13:11,690
+و بيحطوها بس بلغة أبسط لا يساعد فهذه اذا اي فتوفة
+
+162
+00:13:11,690 --> 00:13:14,630
+يناجست اتحادهم تكون final فاحنا حلقين .. غطينا كل
+
+163
+00:13:14,630 --> 00:13:20,730
+احتمالات .. بيكون هيك خلصنا ودا نهاية ال .. اي
+
+164
+00:13:20,730 --> 00:13:26,170
+استفسار؟ اي سؤال؟ففكرة بسيطة ونشوف احنا كيف طبعا
+
+165
+00:13:26,170 --> 00:13:29,230
+زي ان كنت بدأنا في عندي عدة أمثلة الآن انك صار
+
+166
+00:13:29,230 --> 00:13:32,810
+الأمور متقدمة شوية كده بنكون الدوال اتعلمنا انه
+
+167
+00:13:32,810 --> 00:13:35,750
+كان في صعوبة في البداية لأنه لسه كان اول مرة
+
+168
+00:13:35,750 --> 00:13:39,710
+بنتعامل لكن شوفنا بعض ال tricks بعض الملاحظات بعض
+
+169
+00:13:39,710 --> 00:13:43,450
+الإرشادات بدأت خزينتنا او ايه اللي خلفية تبعتنا
+
+170
+00:13:43,450 --> 00:13:46,410
+تزداد عنها صار أمثلة و متعددة و ممكن نسفيد منها و
+
+171
+00:13:46,410 --> 00:13:50,930
+نقلدهاونقلتها نشوف مين المثال بناسب شغلنا نعمله
+
+172
+00:13:50,930 --> 00:13:54,290
+كمان مرة أحيانا ممكن ماينطبقش تماما 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
+وطبعا 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 لل
+
+176
+00:14:03,990 --> 00:14:08,890
+section 5-2هيتحدث عن موضوع بيتطبق في الموضوع
+
+177
+00:14:08,890 --> 00:14:12,650
+الماضي و برضه هذا هيقوي معرفتنا و يمكن يدّينا
+
+178
+00:14:12,650 --> 00:14:16,870
+زاوية أخرى للنظر تساعدنا .. تساعدنا في العمل طبعا
+
+179
+00:14:16,870 --> 00:14:22,080
+مع زاوية أخرى العنوان equipotence of sixطبعا
+
+180
+00:14:22,080 --> 00:14:28,280
+equibotenance 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 --> 00:14:39,280
+تساوي .. تساوي .. تساوي .. تساوي .. تساوي .. تساوي
+
+187
+00:14:39,280 --> 00:14:39,280
+.. تساوي .. تساوي .. تساوي .. تساوي .. تساوي ..
+
+188
+00:14:39,280 --> 00:14:43,260
+تساوي .. تساويوقاعة فيها أربعين مقاعد فهدولة
+
+189
+00:14:43,260 --> 00:14:46,040
+بنفعوا يقعدوا على هدولة بنفعوا القاعة بتسعة فهذا
+
+190
+00:14:46,040 --> 00:14:49,740
+تكافئه بقول إن عدد مقاعد القاعة يكافئ على الطالبات
+
+191
+00:14:49,740 --> 00:14:52,240
+المجموعة إذا هدول مجموعتين متكافئتين لما ييجوا
+
+192
+00:14:52,240 --> 00:14:54,540
+الطالبات يدخلوا في القاع القاع بتكافئهم فهذا
+
+193
+00:14:54,540 --> 00:14:56,840
+التكافئ العددي فعشان هيك في ناس بيحطوا مصطلح
+
+194
+00:14:56,840 --> 00:15:01,460
+numerically equivalent sets المجموعات المتكافئة
+
+195
+00:15:01,460 --> 00:15:05,260
+عدديًا equivalent sets المجموعات المتكافئة عدديًا
+
+196
+00:15:05,260 --> 00:15:08,800
+مش متساوية لأنه هد مجموع الطالبات وهد قاعة فيها
+
+197
+00:15:08,800 --> 00:15:13,850
+كراسي هدول نفس المجملأ، فواضح؟ فبننظر علشان بيهمنا
+
+198
+00:15:13,850 --> 00:15:16,950
+إيش بيهمنا بالمجموعة، العدد تبعها، إيش نوع العناصر
+
+199
+00:15:16,950 --> 00:15:19,790
+بيهمناه، فأقول المجموعتين، فيها أربعين، أربعين
+
+200
+00:15:19,790 --> 00:15:23,330
+كرسي، فيها أربعين طالبة، فيها أربعين طفاحة، البهم
+
+201
+00:15:23,330 --> 00:15:28,460
+بالمين عدد العناصر، فحننظر من هذا الزمنتمام فانا
+
+202
+00:15:28,460 --> 00:15:32,420
+طبعا كمقدمة بقول لي two finite sets X and Y have
+
+203
+00:15:32,420 --> 00:15:35,600
+the same number of elements if and only if there
+
+204
+00:15:35,600 --> 00:15:38,240
+is a bijection F احنا اللي بتاوي حاكيناها ده اللي
+
+205
+00:15:38,240 --> 00:15:43,960
+تلعب ليش بقول ان المجموعة اللي فيها أربعين طالبة و
+
+206
+00:15:43,960 --> 00:15:47,540
+القاعة اللي فيها أربعين مقعد متكافئين لأن كل مقعد
+
+207
+00:15:47,540 --> 00:15:50,680
+.. كل طالبة لها مقعدفهي فيه تناظر هي عملية العدل
+
+208
+00:15:50,680 --> 00:15:53,560
+ليش أنا بقول هذا العنصر الأول إذا هذا بقابل لعدد
+
+209
+00:15:53,560 --> 00:15:56,840
+واحد في الأعداد الطبيعية هذا العنصر رقم اتنين يعني
+
+210
+00:15:56,840 --> 00:15:59,740
+بقابل لعدد رقم اتنين فهذه عملية بقدر ألاقي تناظر
+
+211
+00:15:59,740 --> 00:16:02,380
+هذا اللي بقدر أكافر ليش هدول أربعين و هدول أربعين
+
+212
+00:16:02,380 --> 00:16:06,320
+يعني فيه تناظر في هذا المقعد للطالبة فاطمة هذا
+
+213
+00:16:06,320 --> 00:16:09,540
+المقعد لعائشة هذا لخديجة هي التناظر فإذا هذه عملية
+
+214
+00:16:09,540 --> 00:16:13,280
+العدل فلما أقول إنهم متكافئين عدديًا لكل عنصر
+
+215
+00:16:13,280 --> 00:16:16,710
+يقابل عنصر والعكس صحيح تناظر واحدلواحد فهذه
+
+216
+00:16:16,710 --> 00:16:18,970
+الطريقة اللي انت عاملها مع العدو طب ليش مايقولوا
+
+217
+00:16:18,970 --> 00:16:21,970
+ليش هذه فيها عشر و هذه فيها عشرة لأن عشرة تنطبق مع
+
+218
+00:16:21,970 --> 00:16:25,070
+ال finite لو كانت infinite طب هذي فيها infinite و
+
+219
+00:16:25,070 --> 00:16:27,310
+هذي فيها infinite كيف بدأ اقارن ال infinite مع ال
+
+220
+00:16:27,310 --> 00:16:32,230
+infinite مينفعش فهذا هو الطريقة الصحيحة اللي بتنفع
+
+221
+00:16:32,230 --> 00:16:36,900
+تنطبق على ال finite و على ال infinitesفطبعا .. لأن
+
+222
+00:16:36,900 --> 00:16:40,620
+هنا بقول لأ رغم أن كلمة اللي هو the same number
+
+223
+00:16:40,620 --> 00:16:43,120
+ماتتبقاش مع ال infinity و بعدين هنشوف أن مجموعها
+
+224
+00:16:43,120 --> 00:16:46,380
+infinite و مجموعها infinite لكن مختلفين، بيكفقوش
+
+225
+00:16:46,380 --> 00:16:49,620
+بعض، فإذا ناقش عملية اللي هو العدد مش .. مش .. مش
+
+226
+00:16:49,620 --> 00:16:54,920
+مناسبة كتعريف، اه فبقول لي does not apply when x
+
+227
+00:16:54,920 --> 00:16:58,520
+and y are infinite setsit seems natural يبدو يعني
+
+228
+00:16:58,520 --> 00:17:01,140
+العلماء هم بيفكروا لقوا أنه من الطبيعي كلمة
+
+229
+00:17:01,140 --> 00:17:04,500
+التناظر one to one هي التعريف المناسب عشان أخارن
+
+230
+00:17:04,500 --> 00:17:08,240
+بين مجموعتين وفعلا نجحوا وحطوا التعريف اللي هنشوفه
+
+231
+00:17:08,240 --> 00:17:11,800
+بعد قليل two infinite sets that are in one to one
+
+232
+00:17:11,800 --> 00:17:16,040
+correspondence have or are of the same size ممكن
+
+233
+00:17:16,040 --> 00:17:20,460
+أقول إن عددهم متساوي أو لهم نفس الحجم الحقيقي عدد
+
+234
+00:17:20,460 --> 00:17:24,790
+العدد ففي عندنا التعريف التالفففي عندنا التعريف
+
+235
+00:17:24,790 --> 00:17:28,030
+التالف، إذا عشان أقارن بين مجموعتين من حيث العدد،
+
+236
+00:17:28,030 --> 00:17:30,630
+واكتش بيكونوا متكافئتين عدديًا، إذا كدت ألاجد
+
+237
+00:17:30,630 --> 00:17:34,670
+بينهم تناظر واحد لواحد، اللي هو إيش؟ Bijection Two
+
+238
+00:17:34,670 --> 00:17:39,350
+sets X and Y are said to be equipotent يعني
+
+239
+00:17:39,350 --> 00:17:43,350
+متكافئتين عدديًا، denoted by إيش الرمز؟ كالعادة،
+
+240
+00:17:43,350 --> 00:17:47,030
+شوفوا احنا، مبادئ مبادئ، في مفهوم تكافؤ المجموعات
+
+241
+00:17:47,030 --> 00:17:53,540
+عدديًا، إيش الرمز سببه؟X تكافئ Y عدديًا زي إشارة
+
+242
+00:17:53,540 --> 00:17:56,840
+النفي بس طبعًا مواضحة من الصياغ لما .. مش ال
+
+243
+00:17:56,840 --> 00:18:00,460
+statement عشان أقول أن دي يساوي و أن دي تكافئ زي
+
+244
+00:18:00,460 --> 00:18:03,420
+ما أحط ال bride لما أحط ال bride مع الدالة تفاضل
+
+245
+00:18:03,420 --> 00:18:06,940
+لما أحطها على مجموعة مكملة فالصياغ بيوضع فده هو
+
+246
+00:18:06,940 --> 00:18:10,100
+الرمز فده ليش المفهوم؟ إيش المصطلح؟ Equipotence
+
+247
+00:18:10,100 --> 00:18:13,640
+تكافئ المجموعة العددية إيش رمزه؟ هاي الرمز تبعه
+
+248
+00:18:13,640 --> 00:18:17,660
+إيش تعريفه؟ بقول إيه؟ if there is إيش؟ if there
+
+249
+00:18:17,660 --> 00:18:20,490
+exists أو there is نفس المعنى abjectionفإذا أنا
+
+250
+00:18:20,490 --> 00:18:29,810
+بقول الـ x تكافئ ال y there exists a bijection f
+
+251
+00:18:29,810 --> 00:18:36,670
+من x ل y فده هو التعريف هي الرمز وهي التعريف واضح؟
+
+252
+00:18:36,670 --> 00:18:41,580
+أي استفسار؟تمام، هنبدأ نشوف بعض الأمثلة البسيطة و
+
+253
+00:18:41,580 --> 00:18:44,860
+نؤكد على التعريف و بعدين نطور حالنا لأنه الأن برضه
+
+254
+00:18:44,860 --> 00:18:48,760
+تقريبا بنفس الدائرة لو جالي أثبت أنه مجموعتين
+
+255
+00:18:48,760 --> 00:18:51,640
+متكافئتين عدديا، إيش مطلب منيه؟ ألاجي by diction
+
+256
+00:18:51,640 --> 00:18:55,400
+بينهم ال infinite دالة من مجموع على نفسها، هنا
+
+257
+00:18:55,400 --> 00:18:58,240
+مجموعتين مختلفتين و تكون one to one و ليست unto،
+
+258
+00:18:58,240 --> 00:19:01,000
+بس كان one to one و ليست unto، الآن بدي دالة بين
+
+259
+00:19:01,000 --> 00:19:04,740
+مجموعتين مختلفتين one to one و unto فتقريبا بنظر
+
+260
+00:19:04,740 --> 00:19:10,140
+بنفس الدائرة بس مع اختلاف نبدأ بمثال بسيط جداعشان
+
+261
+00:19:10,140 --> 00:19:13,920
+بس نقلش نثبت المفهوم، نثبت المفهوم، وين احنا
+
+262
+00:19:13,920 --> 00:19:19,440
+وصلنا؟ وصلنا هنا، تمام؟
+
+263
+00:19:19,440 --> 00:19:24,120
+فإذا هدا التعليق باختصار، ونشوف المثال الأول، هو
+
+264
+00:19:24,120 --> 00:19:28,930
+يبقى مثال بسيططبعا فيها دي مجموعتين ال X تساوي
+
+265
+00:19:28,930 --> 00:19:33,610
+واحد اتنين تلاتة و ال Y تساوي عدد ال Bi و عدد جزر
+
+266
+00:19:33,610 --> 00:19:37,850
+الخمسة و العدد E هدول كلهم عدد حقيقية ايش بيميزهم؟
+
+267
+00:19:37,850 --> 00:19:41,930
+كلهم غير نسبية اه كلهم عدد غير نسبية لا ال Bi نسبي
+
+268
+00:19:41,930 --> 00:19:45,470
+ولا جزر الخمسة نسبي ولا ال E نسبي اللي هي 2.7 و ال
+
+269
+00:19:45,470 --> 00:19:48,090
+Bi تلاتة point واحد كذا كذا و جزر الخمسة بيساوي
+
+270
+00:19:48,090 --> 00:19:51,150
+اتنين كثر كلهم ولا عدد فيهم مقدر احطه على صورة بس
+
+271
+00:19:51,150 --> 00:19:54,310
+و مقاه كلها عدد غير نسبية هذه المجموعة كافية؟ هذه
+
+272
+00:19:54,310 --> 00:19:57,830
+المجموعة عدديا ولا لأ؟واضح تلاتة و تلاتة طيب لو
+
+273
+00:19:57,830 --> 00:20:00,770
+قلت بدنا نجيب .. بدنا دالة من هالهال تكون one to
+
+274
+00:20:00,770 --> 00:20:04,110
+one and one to two فعنا هنا ال X فاكروا مع بعض
+
+275
+00:20:04,110 --> 00:20:07,810
+عملاها اكتبوا السؤال بشكل مختلف هو Y تساوي مين؟ ال
+
+276
+00:20:07,810 --> 00:20:12,290
+by و الجزر الخمسة و ال E اه فانا بدأ بالده الحل
+
+277
+00:20:12,290 --> 00:20:14,810
+كيف بدأ اتبين ان هذول متكافئة في اتهان؟ بدأ اعرف
+
+278
+00:20:14,810 --> 00:20:17,450
+دالة من X ل Y تكون one to one and one to two كيف
+
+279
+00:20:17,450 --> 00:20:22,720
+بدأ اعرف .. كيف بدأ بدأ السؤال؟ let F من X ل Ybe
+
+280
+00:20:22,720 --> 00:20:27,100
+given by أحسنتوا جيدا by طبعا هذه دالة عدد عناصر
+
+281
+00:20:27,100 --> 00:20:30,060
+محدود دلوقت ده قاعد ولا ممكن ندّي كل عنصر وش صوته
+
+282
+00:20:30,060 --> 00:20:39,120
+ممكن مين عندها مثال أو عندها حل اختراح اعرفولي
+
+283
+00:20:39,120 --> 00:20:42,280
+الدالة بدي الدالة سهلة جدا إيش بدنا نعرفها عفوا في
+
+284
+00:20:42,280 --> 00:20:43,060
+واحد إيش بدنا نعرفها
+
+285
+00:20:52,100 --> 00:20:55,380
+خلصنا فعدي ده اللي اتعرفت ولا ما اتعرفتش فعرفت كل
+
+286
+00:20:55,380 --> 00:20:58,900
+عناصر ال domain و كل عنصر له صورة ده ل one to one
+
+287
+00:20:58,900 --> 00:21:01,700
+ولا مش one to one لإنه مافيش شيش عنصر راح له صورة
+
+288
+00:21:01,700 --> 00:21:04,180
+انتوا ولا مش انتوا انتوا هطلنا كل ال domain بدي
+
+289
+00:21:04,180 --> 00:21:13,190
+اثبات ولا خلص خلص then f is a binaryطبعاً واضح، بس
+
+290
+00:21:13,190 --> 00:21:15,330
+هنا بس أنا عايش فهذه مقدمة كانت مثالها البسيط، بس
+
+291
+00:21:15,330 --> 00:21:18,070
+إيش الفكرة؟ فواضح ليش هذه التناظر؟ هذه مجموعة
+
+292
+00:21:18,070 --> 00:21:20,770
+متساوي المجموعة؟ لأ، ولا subset منها، لكنهم
+
+293
+00:21:20,770 --> 00:21:23,610
+متكافئتين، فيها تلت عناصر وفيها تلت عناصر، فنبدأ
+
+294
+00:21:23,610 --> 00:21:29,550
+بالمثال البسيط هذا، تمام، نظرية
+
+295
+00:21:38,830 --> 00:21:43,350
+عملية التكافؤ العددي، هذه علاقة، أنا عندي
+
+296
+00:21:43,350 --> 00:21:46,590
+مجموعتين، ممكن أقول مجموعة تساوي مجموعة، علاقة
+
+297
+00:21:46,590 --> 00:21:50,430
+التساوي أو ممكن أقول تساوي تكافئها عددي، هذه
+
+298
+00:21:50,430 --> 00:21:56,220
+علاقة، كعلاقة، هل هي علاقة تكافؤ ولا لا؟بدنا نشوف
+
+299
+00:21:56,220 --> 00:21:59,320
+النظرية بتقول نعم هي علاقة تكافر، يعني هذه العلاقة
+
+300
+00:21:59,320 --> 00:22:03,580
+هي علاقة اللي هو reflexive، symmetric وtransitive
+
+301
+00:22:03,580 --> 00:22:07,400
+فبقول لو أخدت مجموعة تشوف النظرية let S be a non
+
+302
+00:22:07,400 --> 00:22:11,200
+-empty collection of non-empty sets هي علاقة مع من
+
+303
+00:22:11,200 --> 00:22:15,040
+معرفها، إيش عدسرها؟ مجموعاتفإذا إيش بدي أخد؟ بدي
+
+304
+00:22:15,040 --> 00:22:18,320
+أعرف علاقة على مجموعة من المجموعات فالمجموعة
+
+305
+00:22:18,320 --> 00:22:22,240
+الكبيرة هي S إيش عناصرها؟ مجموعات إيش بدي أدرس؟
+
+306
+00:22:22,240 --> 00:22:25,320
+بدي أدرس علاقة المجموعات هذه لجوه ال S هل هي
+
+307
+00:22:25,320 --> 00:22:30,580
+متكافية عدديا ولا لا؟ متكافية عدديا ولا لا؟ بقول
+
+308
+00:22:30,580 --> 00:22:35,900
+define a relation R on S مجموعة المجموعاتXY في الـ
+
+309
+00:22:35,900 --> 00:22:39,340
+R و أنا عديتهم رمز كبير X و Y ليش؟ عشان هم مجموعات
+
+310
+00:22:39,340 --> 00:22:43,640
+عشان العناصر هنا مجموعات لأن ال S مجموعة مجموعة if
+
+311
+00:22:43,640 --> 00:22:47,820
+and only if X تكافئ Y عدديا، هذه العلاقة بقول هذول
+
+312
+00:22:47,820 --> 00:22:51,600
+ألهم علاقة مع بعض إذا كانوا متكافئين عدديا يعني
+
+313
+00:22:51,600 --> 00:22:55,020
+هذه المجموعة هذول أشمالهم تمتكافئين بصبوط إذا
+
+314
+00:22:55,020 --> 00:22:59,320
+بنتموا لمين للأرض بعد و هكذا بقول لي then إيش
+
+315
+00:22:59,320 --> 00:23:01,520
+النتيجة؟ إيش النظر اللي بتقول؟ R is an equivalence
+
+316
+00:23:01,520 --> 00:23:06,500
+ليه؟ هذه العلاقة reflexiveSymmetric و Transitive و
+
+317
+00:23:06,500 --> 00:23:13,820
+Transitive فهذه نظرية خمسة خمسة طب ليش بتنهار
+
+318
+00:23:13,820 --> 00:23:21,060
+Reflexive, Symmetric و Transitive أول شيء إيش منات
+
+319
+00:23:21,060 --> 00:23:24,780
+Reflexive أرجعلكوا عشان ال quiz يعني كل مجموعة
+
+320
+00:23:24,780 --> 00:23:27,680
+اللي علاقة مع نفسها كل عنصر اللي هو مجموعة كل X
+
+321
+00:23:27,680 --> 00:23:31,220
+تكافئ نفسها عدديًا واضحة ولا مش واضحة طب لو قلتلك
+
+322
+00:23:31,220 --> 00:23:34,820
+اتديني بيجيبشين بين X و بين نفسهامين عنده
+
+323
+00:23:34,820 --> 00:23:38,320
+bijection بين مجموعه نفسها؟ اخلطوا مش مشكلة
+
+324
+00:23:38,320 --> 00:23:41,700
+اتعلموا احكوا احكوا ايش هي؟ بدي دالة بدي bijection
+
+325
+00:23:41,700 --> 00:23:45,760
+من X ل X ال identity ال identity صحيح فهي خلصنا
+
+326
+00:23:45,760 --> 00:23:49,440
+أثبتنا أننا نفلكسها فانتها؟ طب هي symmetric لو
+
+327
+00:23:49,440 --> 00:23:52,980
+قلنا إن ال X تكافئ ال Y أيش معناه؟ في bijection من
+
+328
+00:23:52,980 --> 00:23:57,720
+X ل Y طب كيف ده تصير من Y ل X؟ G inverse فهي صارت
+
+329
+00:23:57,720 --> 00:24:02,420
+أيش؟ أثبتها إيش تم نثبت؟ إنها transitX تكافئ ال Y
+
+330
+00:24:02,420 --> 00:24:06,040
+يعني فيه bijection من X ل Y و Y تكافئ ال Z يعني
+
+331
+00:24:06,040 --> 00:24:09,840
+فيه bijection من Y ل Z مين بدي bijection من X ل Z؟
+
+332
+00:24:09,840 --> 00:24:14,740
+إيش أعمل؟ composition .. composition .. أه فعلا
+
+333
+00:24:14,740 --> 00:24:17,200
+شرحتوا ليها ال exercise تكتبوها في البيت ال proof
+
+334
+00:24:17,200 --> 00:24:26,140
+exercise حدثوا ليها شفوا عليكوا تكتب notation
+
+335
+00:24:26,140 --> 00:24:33,100
+أه طبعا كالعادةمنحبش نكتب كتير في رياضيات فالآن
+
+336
+00:24:33,100 --> 00:24:36,680
+احنا هيتعامل مع bijection بشكل كثير لأن التعريف
+
+337
+00:24:36,680 --> 00:24:39,360
+اعتمد على bijection فبعد ما اكتب there exists a
+
+338
+00:24:39,360 --> 00:24:43,600
+bijection F from X to Y ايش بده اكتب هنا؟ there
+
+339
+00:24:43,600 --> 00:24:48,600
+exists F من X بده تساهمش لحطوة كلمة bijection بده
+
+340
+00:24:48,600 --> 00:24:52,840
+اختصرهافبكتب ان كل دالة بيحط سهم كل احنا اتفقنا
+
+341
+00:24:52,840 --> 00:24:58,100
+الدالة بنحط اسم الدالة نقطين فوق بعض ال domain سهم
+
+342
+00:24:58,100 --> 00:25:01,980
+الـ codomain طيب لو كانت y-jection بنحط بدل السهم
+
+343
+00:25:01,980 --> 00:25:04,520
+بنحطها ده معناه انك تشوف هنا يوجد دالة من X ل Y
+
+344
+00:25:04,520 --> 00:25:08,180
+وهي one to one and unto اختصار فده رمز هنستخدمه
+
+345
+00:25:08,180 --> 00:25:12,920
+رمز هنستخدمه نشوف أمثلة
+
+346
+00:25:21,160 --> 00:25:29,060
+المثال الأول بدنا نثبت انه الفترة من واحد لاتنين
+
+347
+00:25:29,060 --> 00:25:35,040
+تكافئ الفترة من zero لاتنين ايش الفترات هدول هم
+
+348
+00:25:35,040 --> 00:25:38,280
+مجموعات من الاعداد الحقيقية يعني ايش الفترة من
+
+349
+00:25:38,280 --> 00:25:41,320
+واحد لاتنين كل الاعداد الحقيقية اللي اكبر من واحد
+
+350
+00:25:41,320 --> 00:25:43,960
+واصغر من اتنين واللي من صفر لاتنين نفس الشيء اللي
+
+351
+00:25:43,960 --> 00:25:46,860
+اكبر من صفر واصغر من اتنين فانا بدنا نثبت ان هدول
+
+352
+00:25:46,860 --> 00:25:53,060
+المجموعاتين متكافئتين فهذا المثالالأول طبعا أنا فى
+
+353
+00:25:53,060 --> 00:25:57,480
+عندي هى حط الإعداد هى الصفر وهى الواحد وهى الاتنين
+
+354
+00:25:57,480 --> 00:26:01,980
+المجموعة الأولى اللى هنا من صفر من واحد لاتنين
+
+355
+00:26:01,980 --> 00:26:10,200
+والتانية من وين من صفر لاتنين طبعا
+
+356
+00:26:10,200 --> 00:26:12,300
+أنا ممكن البعض الناس يقول إيه غريبة طبعا دى جدا
+
+357
+00:26:12,300 --> 00:26:17,970
+مرتين لأ عدد عناصرهم متساوىعدد عناصرهم متساوى بدنا
+
+358
+00:26:17,970 --> 00:26:22,510
+نثبت إنهم فعلا كعدد عناصر متكافئتين مجموعتين
+
+359
+00:26:22,510 --> 00:26:28,610
+مختلفتين ظاهريا واحدة ضعف التانية لكنهم في الحقيقة
+
+360
+00:26:28,610 --> 00:26:32,550
+عدد عناصرهم واحد طبعا هذا عشان هم الفنانين فلنثبت
+
+361
+00:26:32,550 --> 00:26:37,290
+إنهم متكافئتين فالآن إيش بدنا بدنا bijection من 1
+
+362
+00:26:37,290 --> 00:26:39,950
+,2 ل 0,2 هي حتى الآن هي النظرية الوحيدة اللي
+
+363
+00:26:39,950 --> 00:26:42,890
+معناها أو هو التعريف أسئلة معناها نظرية فإذا هنا
+
+364
+00:26:42,890 --> 00:26:56,170
+we haveto find f من 1 إلى 2 لمن؟ لـ 0 إلى 2 بدنا
+
+365
+00:26:56,170 --> 00:27:00,150
+دالة من 0 إلى 1 او اكتبوا كيابة لكي اقولوا مثال
+
+366
+00:27:00,150 --> 00:27:06,970
+لكم بالتصيب ا find f such that f
+
+367
+00:27:06,970 --> 00:27:13,950
+is one to one and hundred by diction فبدنا نعرف
+
+368
+00:27:13,950 --> 00:27:25,630
+دالةللـ F من 1,2 إلى 0,2 بـ given bar بدنا
+
+369
+00:27:25,630 --> 00:27:26,530
+نعرف الـ F
+
+370
+00:27:31,280 --> 00:27:34,640
+نفكر مع بعض فأقول أحنا بندور في نفس الدائرة وإن
+
+371
+00:27:34,640 --> 00:27:37,760
+كان بشكل مختلف دايما مطلوب مني أجيب دالة من عندي
+
+372
+00:27:37,760 --> 00:27:41,320
+دالة مناسبة طبعا لما كل نسبة infinite بدنا هي تكون
+
+373
+00:27:41,320 --> 00:27:43,920
+one to one وليس أنتم من المجموع على نفسها لكن في
+
+374
+00:27:43,920 --> 00:27:47,460
+التكافئة والعدد دي دالة بين مجموعتين وبدنا هي تكون
+
+375
+00:27:47,460 --> 00:27:51,500
+one to one و أنتم one to one and أنتم أه بنفع أدور
+
+376
+00:27:51,500 --> 00:27:56,920
+في دفضر ال calculus؟ ليش بنفعش أعداد حقيقية أعداد
+
+377
+00:27:56,920 --> 00:28:01,210
+حقية فيه في المعطيات دوال؟ مافيشهدول أعداد حقية
+
+378
+00:28:01,210 --> 00:28:04,470
+بنفع أدور في دفتر ال calculus فبدنا دالة من دفتر
+
+379
+00:28:04,470 --> 00:28:07,990
+ال calculus من ال calculus دالة فيها جمع فيها طرح
+
+380
+00:28:07,990 --> 00:28:12,650
+فيها sin فيها cos تكون one to one and unto خلينا
+
+381
+00:28:12,650 --> 00:28:17,390
+نفكر مع بعض .. خلينا نفكر مع بعض كيف بنوجد الدالة
+
+382
+00:28:17,390 --> 00:28:22,410
+المناسبة أن
+
+383
+00:28:22,410 --> 00:28:27,170
+شو بشح نوع ما نحنا؟اش احنا بنعمل؟ خلّينا طبعا
+
+384
+00:28:27,170 --> 00:28:31,770
+كنقطة بداية ممكن واحد يحاول و دايما في try and
+
+385
+00:28:31,770 --> 00:28:34,170
+error الواحد بيحاول و ممكن يخطط لكن بتعلم من
+
+386
+00:28:34,170 --> 00:28:37,210
+أخطائه و بيشوف إذا هالي فشلة بدور على جهة تانية
+
+387
+00:28:37,210 --> 00:28:40,770
+لحد ما ينجح ممكن أنا طريقة بتفكير بتفكر بالطريقة
+
+388
+00:28:40,770 --> 00:28:45,730
+التالية بدي دالة تنقل الواحد لل zero تنقل الواحد
+
+389
+00:28:45,730 --> 00:28:51,930
+لل zero وتنقل التنين للتنين تنقل التنين للتنينفي
+
+390
+00:28:51,930 --> 00:28:57,050
+هنا سمعت كلام X ناقص واحد جيد بس واحدة واحدة جربي
+
+391
+00:28:57,050 --> 00:28:59,970
+اكتبي في رياضة اكتبي اه بتنقل التنين .. بتنقل
+
+392
+00:28:59,970 --> 00:29:05,890
+الواحد للصفر و بتنقل التنين للواحد ايش نعمل؟
+
+393
+00:29:05,890 --> 00:29:12,830
+عادي مبدأيا نجلت الواحد للصفر و نجلت التنين للتنين
+
+394
+00:29:12,830 --> 00:29:16,950
+صح؟ ممتفقين؟ طيب إذا بقيتش تبدأش اجرب هل هي one to
+
+395
+00:29:16,950 --> 00:29:19,990
+one انت و لا انت و لا انا اجرب اه a given by أول
+
+396
+00:29:19,990 --> 00:29:25,940
+شي واحدis one to one كيف نفترض أنها one to one؟
+
+397
+00:29:25,940 --> 00:29:30,880
+let x1 و x2 وين؟ في ال domain مين تنتمي لمين؟ واحد
+
+398
+00:29:30,880 --> 00:29:34,260
+و اتنينها شايف؟ بدنا نكون دقيقين، هه نتعلم فاحنا
+
+399
+00:29:34,260 --> 00:29:37,740
+بناخد عن صورين في domain الدالة صورهم متساوي such
+
+400
+00:29:37,740 --> 00:29:48,180
+that f of x1 تساوي f of x2 then إيش أعمل؟
+
+401
+00:29:51,130 --> 00:29:56,930
+2 في x1 ناقص 1 سواء 2 و في x2 ناقص 1 وهذا يودّي x1
+
+402
+00:29:56,930 --> 00:30:01,070
+سواء x2 و لا في حد عنده اعتراض؟ اه x مع 2 و y مع 1
+
+403
+00:30:01,070 --> 00:30:04,790
+فإذا الدالة فعلا one to one انجحنا نجاح فاحنا نص
+
+404
+00:30:04,790 --> 00:30:10,010
+الطريق انجحنا is one to one فممتاز ماشيين بالطريق
+
+405
+00:30:10,010 --> 00:30:17,370
+ان شاء الله الصحيح نثبت أنها on to f is on to كيف
+
+406
+00:30:17,370 --> 00:30:20,410
+نثبت أنها on to ناخد عنصر في المجال المقابل let y
+
+407
+00:30:21,770 --> 00:30:25,290
+أو نحسب اللي ماشي، كله صح تخلينا نشتغل عليها، من
+
+408
+00:30:25,290 --> 00:30:31,370
+وين؟ من 0 و 2 بدنا ندور على X، بدنا X .. خلينا
+
+409
+00:30:31,370 --> 00:30:37,230
+نعمل الهمش بدنا X وين؟ من 1 و 2، بحيث F of X تساوي
+
+410
+00:30:37,230 --> 00:30:40,980
+Y، صح؟عارجي على كل قنده، و احنا مهارة بنحاول
+
+411
+00:30:40,980 --> 00:30:44,740
+نتعلمها طيب، إيش معناه أقل في X؟ إتنين في X نقص
+
+412
+00:30:44,740 --> 00:30:49,180
+واحدة تساوي Y إيش بنعمل في الهامش؟ بنحل ل X بدلة
+
+413
+00:30:49,180 --> 00:30:53,480
+ال Y آه، فهذا بيقدي إن X مش بنساوي Y على اتنين
+
+414
+00:30:53,480 --> 00:30:58,820
+زائد واحد إيش بتثبت؟ بتديها حاجتين، إن X فعلا بين
+
+415
+00:30:58,820 --> 00:31:01,880
+الواحد و بين التنين و إن صورتها بتساوي Y و إن
+
+416
+00:31:01,880 --> 00:31:03,800
+صورتها بتساوي Y طيب، نشوف
+
+417
+00:31:14,340 --> 00:31:20,140
+X تساوي Y على 2 زي 1 ثم أول شيء بدي أثبت إن X بين
+
+418
+00:31:20,140 --> 00:31:24,840
+1 و 2 كيف؟ أنا عندي ال Y وين أخدتها ال Y؟ ال Y من
+
+419
+00:31:24,840 --> 00:31:29,000
+0 إلى 2 مظبوط؟ بدي أنا أشوف ال X بين ال 0 و بين ال
+
+420
+00:31:29,000 --> 00:31:32,680
+1 و بين ال 2 إيش أعمل؟ أكسب على 2 فده بيقول إن 0
+
+421
+00:31:32,680 --> 00:31:39,320
+على Y على 2 على 1 أجمع 1 للطرفين بيصير 1 أقل من 1
+
+422
+00:31:39,320 --> 00:31:45,390
+زي 2أقل من اتنين صح ولا مش صح؟ اه فإذا إيش then
+
+423
+00:31:45,390 --> 00:31:51,810
+خلينا نكتبها white بتكتب الهامر implies x تنتمي
+
+424
+00:31:51,810 --> 00:31:55,590
+للزيرو لواحد اتنين وهو الايه المكتوبة الأول اتنين
+
+425
+00:31:55,590 --> 00:32:08,640
+تمام آخر حاجة and وهي الهامر f of xتساوي F of Y ع
+
+426
+00:32:08,640 --> 00:32:13,440
+2 زائد 1 وتساوي Y لإيش؟ إيش الدالة بتعمل؟ الدالة
+
+427
+00:32:13,440 --> 00:32:16,500
+بتطرح واحد و بتطرف اتنين فمية لمية، اه فإذا فعلا
+
+428
+00:32:16,500 --> 00:32:26,900
+الدالة plus F ازمها وهو المطلوب، وهو المطلوب تمام؟
+
+429
+00:32:26,900 --> 00:32:30,510
+أي سؤال؟فياريت هذه نتدرب عليها و ناخد فترتين
+
+430
+00:32:30,510 --> 00:32:33,450
+مختلفتين دايما ممكن نشتغل بهذه الشكلة فالحقيقة أنه
+
+431
+00:32:33,450 --> 00:32:38,770
+هذا و هنعممه بعد شوية كل فترة تكافئ فترة فإيه زمان
+
+432
+00:32:38,770 --> 00:32:42,990
+مش أكبر منها طلع عدديا متكافئتين .. متكافئتين
+
+433
+00:32:42,990 --> 00:32:50,510
+بقوله الصدمة بصحي منها صدمة فاللي مصدوم أن واحد
+
+434
+00:32:50,510 --> 00:32:56,040
+اتنين تكافئ Zero اتنين يشوف المثال اللي بعدهسالب
+
+435
+00:32:56,040 --> 00:33:03,640
+باية اتنين باية اتنين الفترة هالي تكافئ كل ا ا هذا
+
+436
+00:33:03,640 --> 00:33:05,740
+ال infinity ما هي نص ال infinity انفنتي مش نص ال
+
+437
+00:33:05,740 --> 00:33:09,400
+infinity انفنتي انفنتي هذي المظبوط هذي فبعدين نثبت
+
+438
+00:33:09,400 --> 00:33:15,500
+او ايه كيف نثبت ايه ايش التانية اه مش هنحلوها لسه
+
+439
+00:33:15,500 --> 00:33:20,920
+هنحلوها مع بعض هنحلوها مع بعض فمعين من المدور
+
+440
+00:33:20,920 --> 00:33:24,940
+function معين مع بعض أكيد هنخشهم مع بعضهنقشها مع
+
+441
+00:33:24,940 --> 00:33:33,920
+بعض فهنا
+
+442
+00:33:33,920 --> 00:33:40,340
+F تخلصناه مثال
+
+443
+00:33:40,340 --> 00:33:49,840
+رحم اتنين اه let F من سالب بايع اتنين لبايع اتنين
+
+444
+00:33:49,840 --> 00:33:50,660
+لل R
+
+445
+00:33:54,780 --> 00:34:03,200
+be given by f of x تساوي وين بتدوروا جاعدين؟ في
+
+446
+00:34:03,200 --> 00:34:10,940
+تفاقد الأحرار في دالة مشهورة جدا ارجعوا
+
+447
+00:34:10,940 --> 00:34:14,160
+على تفاضل باه والدالة هادي one to one and unto
+
+448
+00:34:14,160 --> 00:34:17,220
+عشان انها inverse tan inverse فهي بيبدأ تركها يقول
+
+449
+00:34:17,220 --> 00:34:18,040
+باجي عليك وخلاص
+
+450
+00:34:28,040 --> 00:34:31,100
+أبايجي تتذكروا احنا كيف عرفنا التان inverse؟ طبعا
+
+451
+00:34:31,100 --> 00:34:35,860
+التان في الأصل معرفة على كل ال R معدى عدد فردي في
+
+452
+00:34:35,860 --> 00:34:39,680
+بايع 2 فهي معرفة من سالب بايع 2 لبايع 2 و من بايع
+
+453
+00:34:39,680 --> 00:34:43,120
+2 لتلاتة بايع 2 و هكذا عشان نخليها one to one
+
+454
+00:34:43,120 --> 00:34:46,080
+أخدنا جزء فهي حصلت one to one لما أخدنا فترة من
+
+455
+00:34:46,080 --> 00:34:49,720
+الفترات طبعا هي انتوا على طول لأن كلها رسمتها
+
+456
+00:34:49,720 --> 00:34:53,180
+بتتذكروا الرسم كيف؟هيّا، بس درسوها من الفترة اللي
+
+457
+00:34:53,180 --> 00:34:56,700
+بديها، ده .. من سلة باعتنا ماباعتنا واش مهل، أغطّط
+
+458
+00:34:56,700 --> 00:34:59,460
+كل ال R من سلة infinite إلى infinite، أه فهو one
+
+459
+00:34:59,460 --> 00:35:02,060
+to one and unto طبعا عشان تفتحوها one to one يمكن
+
+460
+00:35:02,060 --> 00:35:05,340
+صعب نفبتها بالتعريف لكن ممكن تجي ل ال calculus إن
+
+461
+00:35:05,340 --> 00:35:08,740
+التفاضل و إنها تزايدية و هكذا، تزايدية تاني،
+
+462
+00:35:08,740 --> 00:35:10,900
+فبتطلع one to one، فعشان هيك نرجع ل ال calculus
+
+463
+00:35:10,900 --> 00:35:13,860
+فهو one to one و unto فعلا، لإن ال .. ال .. ال ..
+
+464
+00:35:13,860 --> 00:35:16,680
+ال .. هو إيش من هنا أعرفها؟ المادة تبعها كل R،
+
+465
+00:35:16,680 --> 00:35:19,480
+ارجع لتفاضل بها، فهو one to one and unto فليه ف
+
+466
+00:35:21,070 --> 00:35:24,130
+فاحنا إيش عملنا .. يعني نحكي أنتوا أنه بتغفل كل
+
+467
+00:35:24,130 --> 00:35:26,330
+المجال و خلاص؟ لأ إن المجال تبعها، ال calculus
+
+468
+00:35:26,330 --> 00:35:30,330
+بيساوي اه، فأطول هذي إيش المجال تبعها بيساوي اه،
+
+469
+00:35:30,330 --> 00:35:33,530
+بيساوي اه طيب إيش .. إيش .. إيش نثبتناه المثاليين
+
+470
+00:35:33,530 --> 00:35:37,370
+مع بعض؟ أثبتنا إنه كل فترة تقريبا تكافئ فترة،
+
+471
+00:35:37,370 --> 00:35:40,410
+نعملنا كام مثال، الحقيقة كل فترة مفتوحة تكافئ فترة
+
+472
+00:35:40,410 --> 00:35:44,350
+مفتوحةوالفترة باية اتنين باية اتنين تكافئ ال ا ..
+
+473
+00:35:44,350 --> 00:35:46,830
+طب الباية اتنين باية اتنين سال باية اتنين بتكافئ
+
+474
+00:35:46,830 --> 00:35:50,910
+واحد zero مثلا بتكافئ ا .. فإيه صار .. كل أي فترة
+
+475
+00:35:50,910 --> 00:35:54,450
+تكافئ أي فترة مفتوحة .. أي فترة مفتوحة .. ان شاء
+
+476
+00:35:54,450 --> 00:35:58,170
+الله تاخد الفترة من صفر لواحد من عشر .. تكافئ كل ا
+
+477
+00:35:58,170 --> 00:36:01,770
+.. أي فترة مفتوحة تكافئ ال ا .. تكافئ ال ا .. و
+
+478
+00:36:01,770 --> 00:36:01,990
+ادي
+
+479
+00:36:06,210 --> 00:36:09,530
+أه فده لسه هنجيله .. هنديعله مرة تانية أي فترة
+
+480
+00:36:09,530 --> 00:36:11,730
+مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة .. أي
+
+481
+00:36:11,730 --> 00:36:11,950
+فترة مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة ..
+
+482
+00:36:11,950 --> 00:36:12,690
+أي فترة مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة
+
+483
+00:36:12,690 --> 00:36:17,970
+.. أي فترة مفتوحة .. أي فترة مفتوحة .. أي فترة
+
+484
+00:36:17,970 --> 00:36:22,630
+مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة .. أي
+
+485
+00:36:22,630 --> 00:36:25,770
+فترة مفتوحة .. أي فترة مفتوحة .. أي فترة مفتوحة ..
+
+486
+00:36:25,770 --> 00:36:28,710
+أي فترة مفتوحة .. أي فلأن هو إيش العلاقة؟ هي علاقة
+
+487
+00:36:28,710 --> 00:36:31,230
+إيش؟ equivalence relation، يعني transitive فأنا
+
+488
+00:36:31,230 --> 00:36:34,270
+عندي أي فترة تكافئ سالب بايع اتنين على بايع اتنين
+
+489
+00:36:34,270 --> 00:36:36,430
+وسالب بايع اتنين على بايع اتنين بتكافئ لأ لإن
+
+490
+00:36:36,430 --> 00:36:40,650
+سهولة عشان التهن إذا كل فترة مفتوحة تكافئ أ فترة
+
+491
+00:36:40,650 --> 00:36:44,710
+transitive نشوف مثال المخلخة بدها شوية شغل عشان
+
+492
+00:36:44,710 --> 00:36:47,530
+اللي هو النقطة اللي جوا بدها شوية شغل موجودة في
+
+493
+00:36:47,530 --> 00:36:54,650
+الكتاب نشوف مثال مختلف نوعا ما بقولي إذا في عندي
+
+494
+00:36:54,650 --> 00:37:01,580
+مجموعةو إيه بجبعتين؟ الأولى ناقص التانية يكافئ
+
+495
+00:37:01,580 --> 00:37:05,840
+التانية ناقص الأولى فدوله مجبعتين متكافئتين خلينا
+
+496
+00:37:05,840 --> 00:37:10,480
+نشوف البرهان أو الحل و نشوف رسمه ممكن تساعدنا نشوف
+
+497
+00:37:10,480 --> 00:37:18,600
+رسمه ممكن تساعدنا هذا
+
+498
+00:37:18,600 --> 00:37:21,860
+يمكن تكون أسهل من الأمثلة الماضية التصور تبعها
+
+499
+00:37:21,860 --> 00:37:28,340
+يكون أسهلهي عندنا مجموعتين طبعا هذه X وهذه Y طبعا
+
+500
+00:37:28,340 --> 00:37:34,940
+هذه المنطقة .. هذه X ناقص Y وهذه المنطقة Y ناقص S
+
+501
+00:37:34,940 --> 00:37:41,120
+لأن الاتحاد مشترك فهذه هي الفكرة .. فهذه هي الفكرة
+
+502
+00:37:41,120 --> 00:37:45,140
+واضحة إذا منطق الكلام .. الكلام منطقي فبدنا نبرهنه
+
+503
+00:37:45,140 --> 00:37:49,100
+.. بدنا نكتبه بلغة رياضية مايواضحة من الصورة ..
+
+504
+00:37:49,100 --> 00:37:53,830
+الصورة مش مرهقة فالآن دعنا هذا المثال التالدطب
+
+505
+00:37:53,830 --> 00:38:01,590
+عشان ده عنده موضوع prove that if ف assume x
+
+506
+00:38:01,590 --> 00:38:09,690
+ناقص y تكافئ y ناقص x بدنا نثبت ان x تكافئ y كيف
+
+507
+00:38:09,690 --> 00:38:13,950
+بدنا نثبتها؟ بدي bijection من x ل y بدنا دالة من x
+
+508
+00:38:13,950 --> 00:38:18,820
+ل yنرجع على دفتر ال calculus؟ ولا خلاص نسكره الآن؟
+
+509
+00:38:18,820 --> 00:38:23,140
+مانفعش الآن، مانفعش، مانفعش، بدنا إذا بنعرف دالة F
+
+510
+00:38:23,140 --> 00:38:26,440
+من X ل Y تكون one to one عند أنتم، من وين بدنا
+
+511
+00:38:26,440 --> 00:38:29,960
+ندور عليها؟ بالمعطيات، في في المعطيات، نعم، هاي و
+
+512
+00:38:29,960 --> 00:38:32,820
+مش هدية السوم، إذا بقدر ألاقي دالة one to one عند
+
+513
+00:38:32,820 --> 00:38:37,360
+أنتم، من X ناقص Y ل Y ناقص X، هذا يؤدي، there
+
+514
+00:38:37,360 --> 00:38:44,290
+exist G اختصارا، هاي bijection معناها، صح؟بعدين
+
+515
+00:38:44,290 --> 00:38:47,050
+مكتوبة bijection، الإكتوبة بدا الشكل، اتعودتوا على
+
+516
+00:38:47,050 --> 00:38:50,210
+الرمز الجديد؟ يعني فيه bijection من X نقص Y ل Y
+
+517
+00:38:50,210 --> 00:38:53,310
+نقصي، الآن أنا جاهز أعرف الدالة، شوفت الفكرة اللي
+
+518
+00:38:53,310 --> 00:38:55,850
+أحنا قولنا فيها، بالله في حول الدائرة، نفس
+
+519
+00:38:55,850 --> 00:38:59,590
+الدائرة، و نفس الأفكار تتكرر بشكل بس إيش، متقارن،
+
+520
+00:38:59,590 --> 00:39:05,650
+هعرفه دالة، let F من X ل Y be given
+
+521
+00:39:09,620 --> 00:39:13,140
+G of X to Z طبعا هعتمد في تعريف عالميين على الـG
+
+522
+00:39:13,140 --> 00:39:17,320
+الفكرة مرت علينا تقريبا مشابهة لكن إيش ميزة الـG
+
+523
+00:39:17,320 --> 00:39:21,700
+معرفة على جزء من الـX مش على كل الـX معرفة من وين؟
+
+524
+00:39:21,700 --> 00:39:26,400
+من X ناقص Y فبتكمل الدمان طب إذن أول شي هعرفها G
+
+525
+00:39:26,400 --> 00:39:32,940
+of X إذا الـX وين؟ في الـX ناقص Y بتام هنا الفرق
+
+526
+00:39:32,940 --> 00:39:35,060
+هنا الباقي إيش عرفها؟
+
+527
+00:39:38,550 --> 00:39:43,410
+أولش هنا انا هي ال domain ال domain كل X المنطقة
+
+528
+00:39:43,410 --> 00:39:49,490
+هذه انا معرف عليها G هذه المنطقة مش معرف عليها G
+
+529
+00:39:49,490 --> 00:39:54,190
+صح؟ بدي اكمل انا عشان يكون اقص من X لكي اتعرف على
+
+530
+00:39:54,190 --> 00:39:58,070
+كل ال G هذا بيشبه اول مثال يمكن حليناه في ال
+
+531
+00:39:58,070 --> 00:40:02,330
+infinite cell ايش اعرفها هنا؟ال identity بنفع نفس
+
+532
+00:40:02,330 --> 00:40:05,190
+الشيء لأن هدول إيش فيه؟ هدول عناصر بيكافؤوا هدول
+
+533
+00:40:05,190 --> 00:40:07,670
+فيه تناظر بين هدول و بين هدول طب هذا كيف بناظر
+
+534
+00:40:07,670 --> 00:40:10,730
+نفسه؟ لأنه نفسه مشترك فكل عنصر هو بناظر نفسه هنا
+
+535
+00:40:10,730 --> 00:40:17,470
+لأنه مشترك فدي هسميها X زي X وين تنتمي للتقاطةلأن
+
+536
+00:40:17,470 --> 00:40:21,890
+هذه المنطقة هي التقاطة فهي تكمل من كل ال X فال X
+
+537
+00:40:21,890 --> 00:40:30,110
+مما تتكون تتكون من X ناقص Y إتحاد التقاطة ففي X
+
+538
+00:40:30,110 --> 00:40:35,290
+ناقص Y جي معرفة أدت الغلط وخدمتني بس أي مقدرة الجي
+
+539
+00:40:35,290 --> 00:40:39,170
+طيب في الباقي ال identity إيه بتصرف؟ بالنسبة لهذه
+
+540
+00:40:39,170 --> 00:40:42,590
+one to one أد one to one تعرف تفكروها ولا لا؟
+
+541
+00:40:42,590 --> 00:40:43,490
+المفروض تعرف
+
+542
+00:40:57,520 --> 00:41:00,500
+is one to one شفتوا الأفكار كام تتكرر ده؟ ده يمكن
+
+543
+00:41:00,500 --> 00:41:05,300
+الأول مرة تكون غريبة افهمتوا منها 5% تتكرر كمان
+
+544
+00:41:05,300 --> 00:41:09,860
+مرة بترتفع نسبة الفهم 10% 20% مع التكرار أرجو أنه
+
+545
+00:41:09,860 --> 00:41:14,020
+نسبة تعلى عن ال 50% و هكذا بيصير في الأمر كويس
+
+546
+00:41:14,020 --> 00:41:22,920
+slit x1 و x2 في domain ال Fلأ ركزوا مش غير تحطوا
+
+547
+00:41:22,920 --> 00:41:26,280
+مستطيل و أنتوا شاطرين بالتزويج و بالأمور زي هيك
+
+548
+00:41:26,280 --> 00:41:28,740
+عشان تتبعوا اتركزوا هنا و هنا و أنتوا تشتغلوا اه
+
+549
+00:41:28,740 --> 00:41:32,500
+فانا مش هروح لل G انا بشغل على ال F بداشي أدي ال F
+
+550
+00:41:32,500 --> 00:41:35,880
+one to one ايش أعمل؟ عنصرين في ال domain تبع ال F
+
+551
+00:41:35,880 --> 00:41:41,180
+اه so what are we going to solve؟
+
+552
+00:41:41,180 --> 00:41:45,980
+بدي
+
+553
+00:41:45,980 --> 00:41:49,700
+أستخدم التعريف التعريف ده لمعرفة متعددة القاعدة
+
+554
+00:41:49,700 --> 00:41:50,480
+أربع حالة
+
+555
+00:41:54,410 --> 00:42:00,610
+طبعا لو كانوا التنين في X-Y إيش التعريف؟ G of X1
+
+556
+00:42:00,610 --> 00:42:07,310
+تساوي G of X2 إذا كان X1 و X2 في X-Y وناخد برضه
+
+557
+00:42:07,310 --> 00:42:11,310
+التانية السهلة لو كانوا التنين في التقاطة X1 تساوي
+
+558
+00:42:11,310 --> 00:42:16,990
+X2 إذا X1 و X2 في X مقاطع الواحد لما يكونوا التنين
+
+559
+00:42:16,990 --> 00:42:20,870
+مع بعض يا في المنطقة الأولى يا في المنطقة التانية
+
+560
+00:42:20,870 --> 00:42:26,990
+بيتعمل حالتين كل واحد في منطقة مختلفةف G of X1
+
+561
+00:42:26,990 --> 00:42:33,990
+تساوي X2 لو كانت X1 في المنطقة الـ minus و X2 في
+
+562
+00:42:33,990 --> 00:42:41,730
+التقاطع و هنا العكس X1 تساوي G of X2 إذا X1 في
+
+563
+00:42:41,730 --> 00:42:50,650
+التقاطع و X2 في X ماقصر طبعا كالعادةفيه تنتين
+
+564
+00:42:50,650 --> 00:42:54,650
+هيدوني X1 تساوي X2 واحدة فيهم واضحة وتنتين هيدوني
+
+565
+00:42:54,650 --> 00:42:58,050
+contradiction طبعا هالي ليش بتديني X1 لأنه G is
+
+566
+00:42:58,050 --> 00:43:04,010
+one to one اه فهذا يؤدي طبعا كله بينهم ا X1 تساوي
+
+567
+00:43:04,010 --> 00:43:09,230
+X1 ليش لأنه G is one to one وطبعا X1 تساوي X2 لأنه
+
+568
+00:43:09,230 --> 00:43:17,030
+مفت الباقي contradiction ليش هالي بقولي ان G of X1
+
+569
+00:43:17,030 --> 00:43:23,100
+تساوي X2 X2 وين؟في التقاطع، وهل ممكن تكون الـG من
+
+570
+00:43:23,100 --> 00:43:27,820
+وين لوين الـG؟ من X ناقص Y ل Y ناقص X، عمره ما
+
+571
+00:43:27,820 --> 00:43:30,240
+بتكون الصورة هنا، الصورة هنا لازم تكون، فده
+
+572
+00:43:30,240 --> 00:43:35,580
+مستحيل، فهذا Contradiction هأضحك مرة في التاني
+
+573
+00:43:35,580 --> 00:43:42,820
+نفسي Contradiction، ليش؟ لأن X2 لا تنتمي للـG of X
+
+574
+00:43:42,820 --> 00:43:48,880
+ناقص Yمرة تانية الـG من أين تأخذ عناصر؟ من هنا إلى
+
+575
+00:43:48,880 --> 00:43:52,340
+هنا، لا تودّههم إلى التقاطع فلما تكون X2 في
+
+576
+00:43:52,340 --> 00:43:55,380
+التقاطع، فممكن أن يكون صورة مستحيلة نفس القضية،
+
+577
+00:43:55,380 --> 00:43:58,780
+لما تكون X1 في التقاطع، مستحيل أن تكون صورة مستحيل
+
+578
+00:43:58,780 --> 00:44:02,060
+أن تكون صورة، فنفس الأفكار تتكرر، فأرجعوا أن الفهم
+
+579
+00:44:02,060 --> 00:44:09,200
+.. نسبة الفهم تزداد Contradiction لأن
+
+580
+00:44:09,200 --> 00:44:16,070
+X1 الآن لاتنتمي، خلاصP or P P P or contradiction P
+
+581
+00:44:16,070 --> 00:44:19,550
+وبالتالي
+
+582
+00:44:19,550 --> 00:44:26,850
+F is one to one هنثبت
+
+583
+00:44:26,850 --> 00:44:32,670
+on to برضه برضه سريعة سهلة و برضه هنستخدم ال trick
+
+584
+00:44:32,670 --> 00:44:36,950
+برضه صعب خلنا نستخدمها في الإعادة إفادة كما يُقال
+
+585
+00:44:36,950 --> 00:44:44,120
+اثنين Fis onto .. اه هحسب ال image مش هستخدم
+
+586
+00:44:44,120 --> 00:44:48,680
+الصورة التانية هاخد ال Y و أجيبها صورة مين هحسب ال
+
+587
+00:44:48,680 --> 00:44:54,250
+image مباشرة فهو هحسب F of Xفيه trick مشهور
+
+588
+00:44:54,250 --> 00:44:56,850
+بنعملهش نعمل ده لمعرفة بالتيزيق بنجذّق ال domain
+
+589
+00:44:56,850 --> 00:45:04,550
+فحكته بال X على صورة مين X ناقص Y اتحاد X تقاطع ال
+
+590
+00:45:04,550 --> 00:45:07,650
+Y مش هيك عملناها مش هيك عرفناها عملناها جزئين
+
+591
+00:45:07,650 --> 00:45:12,350
+الرسم مثلا محيطة الطريق واضح تمام معروف أن ال F
+
+592
+00:45:12,350 --> 00:45:20,000
+تتوزع عن اتحاد فده بيساوي Fx-y اتحاد f of x تقاطع
+
+593
+00:45:20,000 --> 00:45:24,920
+ال y ليش عملت هيك؟ لأن ال f تعريفة هنا هي g
+
+594
+00:45:24,920 --> 00:45:28,040
+وتعريفة
+
+595
+00:45:28,040 --> 00:45:30,700
+هنا identity يعني المجموعة العنصر بتعمل زي ما هو و
+
+596
+00:45:30,700 --> 00:45:34,020
+المجموعة بتعمل زي ما هي فدي ليست إلا x تقاطع ال y
+
+597
+00:45:34,020 --> 00:45:41,060
+في حد عنده أي مشكلة هنا؟سهل حتى الآن، ولا لأ؟ فهو
+
+598
+00:45:41,060 --> 00:45:44,080
+فيه trick بسيط الآن، ده طبعا هو مش صعب لكنه بنتبه،
+
+599
+00:45:44,080 --> 00:45:47,300
+الان ال G اشملها one to one and one to two اشملها
+
+600
+00:45:47,300 --> 00:45:49,820
+one to one and one to two ان ال domain صورة مين؟
+
+601
+00:45:49,820 --> 00:45:52,340
+المجال المقابل، إذا بقى ال G دالة من وين لو وين،
+
+602
+00:45:52,340 --> 00:45:55,340
+عنكم مكتوب، من X ناقص Y ل Y ناقص X، فده إيش
+
+603
+00:45:55,340 --> 00:46:01,980
+بيساوي؟ Y ناقص X، إتحاد التقاطع، يعني مين؟ يعني Y،
+
+604
+00:46:01,980 --> 00:46:07,560
+بس عكس للصورة، يعني إحنا قاعد الصورة هيكفكنا هادي
+
+605
+00:46:07,560 --> 00:46:10,620
+مع هادي .. هادي صارت هادي مع هادي .. إيش صارت؟
+
+606
+00:46:10,620 --> 00:46:14,060
+واحد .. فنجلنا من هناك لهناك .. كل هذا مصطلق واحد
+
+607
+00:46:14,060 --> 00:46:19,140
+.. وي زي إيش وي on ..
+
+608
+00:46:19,140 --> 00:46:24,700
+is on .. وهو المضمون .. فإن شاء الله المحاضرة
+
+609
+00:46:24,700 --> 00:46:25,260
+تجيبنا كذلك
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/I64ZBj8Mh0U_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/I64ZBj8Mh0U_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a1ef6b12f8deb3f801fb68c72120ec798c7a08bf
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/I64ZBj8Mh0U_postprocess.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/L2Gx8IFuLy4.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/L2Gx8IFuLy4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3d4061fa60426cecb45329b14b6894e5e7a232bb
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/L2Gx8IFuLy4.srt
@@ -0,0 +1,2748 @@
+1
+00:00:20,690 --> 00:00:24,030
+بسم الله الرحمن الرحيم في المحاضرة الأخيرة بدأنا
+
+2
+00:00:24,030 --> 00:00:26,950
+الحديث عن البرهان اللي هو طبعًا كان عنوان ال
+
+3
+00:00:26,950 --> 00:00:30,170
+section proof of validity هنواصل مع هذا الموضوع إن 
+
+4
+00:00:30,170 --> 00:00:34,810
+شاء الله هذا ال section  الحقيقة بننهي فيه اللي هو 
+
+5
+00:00:34,810 --> 00:00:39,070
+المقدمة المنطقية اللي محتاجينها في الرياضيات
+
+6
+00:00:39,450 --> 00:00:43,890
+فبنتحدث في البداية عن البرهان المنطقي لل argument
+
+7
+00:00:43,890 --> 00:00:48,730
+أو اللي هي الحجة ومن ثم هنتقل للبرهان الرياضي
+
+8
+00:00:48,730 --> 00:00:51,910
+فاحنا أول شيء بناخد فكرة عن البرهان المنطقي اللي هي
+
+9
+00:00:51,910 --> 00:00:56,780
+مقدمة لموضوعنا الرئيسي وهو البرهان الرياضي يذكرنا
+
+10
+00:00:56,780 --> 00:00:59,960
+في المحاضرة الماضية عشان نراجع سريعًا عشان الموضوع
+
+11
+00:00:59,960 --> 00:01:04,860
+لسه موضّحش بشكل كافي على ما أعتقد أن ال argument
+
+12
+00:01:04,860 --> 00:01:11,940
+عبارة عن statements سلسلة من تقارير البعض منها
+
+13
+00:01:11,940 --> 00:01:16,660
+بنسميه مقدمات أو معطيات each one عدد معين each one 
+
+14
+00:01:16,660 --> 00:01:20,220
+وفي عندنا حاجة بنسميها إيش ال conclusion therefore
+
+15
+00:01:20,220 --> 00:01:25,430
+conclusion معين statement فهذه بسموها argument بقول
+
+16
+00:01:25,430 --> 00:01:28,150
+على هذه الـ argument إنها صحيحة البرهان المنطقي
+
+17
+00:01:28,150 --> 00:01:32,830
+إنها صحيحة إذا كان ال conjunction يعني إيش H1 and
+
+18
+00:01:32,830 --> 00:01:40,070
+H2 and and HN implies B يعني إذا كانت هذا كله
+
+19
+00:01:40,070 --> 00:01:43,510
+صحيح فهذه صحيحة بتكون true مش implies يعني بتكون
+
+20
+00:01:43,510 --> 00:01:46,770
+تولّجي يعني true فلازم إذا كانت المقدمات صحيحة عشان
+
+21
+00:01:46,770 --> 00:01:49,710
+ذلك بقول المنطق لابد أن الاستنتاج يكون صحيح قبل ما
+
+22
+00:01:49,710 --> 00:01:53,150
+المنطق بيقوله إذا المقدمات المعطيات صحيحة
+
+23
+00:01:53,150 --> 00:01:58,340
+فالإستنتاج صحيح فهذه النقطة الأولى الآن هذه جملة
+
+24
+00:01:58,340 --> 00:02:03,280
+اعتدنا عليها عبارة عن تضمين لإثبات التضمين هناك
+
+25
+00:02:03,280 --> 00:02:07,200
+طريقتان الأولى باستخدام الجداول لكنها صحيح أنها 
+
+26
+00:02:07,200 --> 00:02:10,280
+عملية سهلة لكن أحيانًا بتكون غير عملية لنا كبيرة
+
+27
+00:02:10,280 --> 00:02:14,900
+جدا لأن إذا شفنا مثال في عندنا خمسة من التقارير
+
+28
+00:02:14,900 --> 00:02:19,240
+الأساسية فبدي جدول 32 احتمال فهذا بيخلي العمر شوية
+
+29
+00:02:19,240 --> 00:02:25,380
+فيه صعوبة أو فيه طول ومش قابل لمين للتطبيق لذلك كان
+
+30
+00:02:25,380 --> 00:02:28,340
+في طريقة بديلة وهي الـ Deductive Reasoning الـ
+
+31
+00:02:28,340 --> 00:02:30,960
+Deductive Reasoning كلنا بنستخدمها في إثبات اللي
+
+32
+00:02:30,960 --> 00:02:34,160
+هو ال implications والتكافؤة هذه عبارة عن
+
+33
+00:02:34,160 --> 00:02:38,420
+implication ممكن استخدام الـ Deductive Reasoning
+
+34
+00:02:38,420 --> 00:02:44,250
+فهذه الطريقة هي المعتمدة الآن احنا تعلمنا جديد
+
+35
+00:02:44,250 --> 00:02:47,070
+طريقة الكتابة في طريقة productive reasoning كنت
+
+36
+00:02:47,070 --> 00:02:51,210
+أنا أبدأ من اليسار وأمشي بخطوات منطقية أطبّق قواعد
+
+37
+00:02:51,210 --> 00:02:55,550
+المنطق لحد ما أوصل لليمين هذه الطريقة اللي هي متبعة و
+
+38
+00:02:55,550 --> 00:03:00,110
+بتكون مناسبة إذا كان طرف اليسار صغير نسبيًا لما
+
+39
+00:03:00,110 --> 00:03:03,250
+يكون كبير بيصير متبط المناسبة وعشان هيك احنا لما
+
+40
+00:03:03,250 --> 00:03:05,850
+نشوف احنا لو مر علينا برنامج رياضي سابقًا عمره ما
+
+41
+00:03:05,850 --> 00:03:08,440
+انكتب بهذه الطريقة وإنما يُكتب على صورة إيش
+
+42
+00:03:08,440 --> 00:03:11,180
+statement منفصلة على statement منفصلة فإذا احنا
+
+43
+00:03:11,180 --> 00:03:14,160
+بنتعلم في هذه المحاضرة أو لقول إيه أدينا مثال
+
+44
+00:03:14,160 --> 00:03:17,320
+تمهيد المرة الماضية إنه إعادة كتابة الـ deductive
+
+45
+00:03:17,320 --> 00:03:21,120
+reasoning بطريقة جديدة بطريقة جديدة ما هي الطريقة
+
+46
+00:03:21,120 --> 00:03:25,320
+الجديدة طبعًا قلنا ال proof of validity هو عبارة عن
+
+47
+00:03:25,320 --> 00:03:29,640
+إيش sequence يعني إيش متتابعة أو متسلسلة من
+
+48
+00:03:29,640 --> 00:03:33,340
+التقارير إيش ده تكون هذه التقارير يا إما معطيات
+
+49
+00:03:33,720 --> 00:03:39,360
+ومنسلم بصحتها صحيحة أو إنه التقرير استنتجناه مما
+
+50
+00:03:39,360 --> 00:03:44,520
+سبق بطريقة منطقية صحيحة بطريقة منطقية صحيحة فهذه
+
+51
+00:03:44,520 --> 00:03:48,980
+هو طريقة الكتابة فأنا عشان أشتغل بيد الصورة إيش
+
+52
+00:03:48,980 --> 00:03:55,490
+بعمل بروح برقمهذا ال proof of validity فبروح برقم
+
+53
+00:03:55,490 --> 00:03:59,390
+المعطيات لإنه ممكن أستخدمها لكن ال conclusion بحطه
+
+54
+00:03:59,390 --> 00:04:04,690
+على سطر منفصل وبرقموش ليش لأن البرهان لا يستخدم
+
+55
+00:04:04,690 --> 00:04:08,370
+الاستنتاج في الوصول للنتيجة وإنما ينتهي
+
+56
+00:04:08,370 --> 00:04:12,010
+بالاستنتاج هذه نقطة مهمة جدا هذه قاعدة فعمر ما
+
+57
+00:04:12,010 --> 00:04:16,250
+يكون الاستنتاج جزء من البرهان وإنما يكون نهاية
+
+58
+00:04:16,250 --> 00:04:20,260
+البرهان و صدقتنتهي البرهان فعشان هيك بقولك ف a
+
+59
+00:04:20,260 --> 00:04:22,700
+proof .. a formal proof of validity البرهان
+
+60
+00:04:22,700 --> 00:04:26,500
+المنطقي وزيّه البرهان الرياضي إيش ماله؟ of a given
+
+61
+00:04:26,500 --> 00:04:30,540
+argument is a sequence متتابعة من اللي هو إيش زي
+
+62
+00:04:30,540 --> 00:04:33,020
+ما شفنا المثال اللي حليناه مع بعض قدت اللي هو
+
+63
+00:04:33,020 --> 00:04:36,680
+خطوات of a statement تقارير عبارة عن إيش التقارير
+
+64
+00:04:36,680 --> 00:04:39,820
+اللي ممكن تكون؟ أولًا في معطيات بتكون معطيات ال
+
+65
+00:04:39,820 --> 00:04:41,860
+conclusion لأ عشان هيكميزنا هذا يقولنا إيش
+
+66
+00:04:41,860 --> 00:04:44,420
+hypothesis ممكن تستخدمها في البرهان ال conclusion
+
+67
+00:04:44,420 --> 00:04:49,320
+لا يمكن تستخدمه في البرهان is either a hypothesis
+
+68
+00:04:49,320 --> 00:04:53,140
+or of the argument or follows from the preceding
+
+69
+00:04:53,140 --> 00:04:56,990
+أنا وصلت لخطوة معينة ممكن أستخدم كل ما سبق في
+
+70
+00:04:56,990 --> 00:04:59,570
+الوصول لوحدة جديدة.. لوحدة جديدة وهكذا اه
+
+71
+00:04:59,570 --> 00:05:03,810
+follows from preceding statements كيف؟ by a non
+
+72
+00:05:03,810 --> 00:05:07,070
+valid argument بقاعدة معروفة أو بالحقيقة معروفة
+
+73
+00:05:07,070 --> 00:05:09,770
+أنها صحيحة بقدر أستخدم أي حاجة أنا عرفت أنها صحيحة
+
+74
+00:05:09,770 --> 00:05:13,150
+ممكن أستخدمها واستنتاج حاجة جديدة وهكذا وهكذا
+
+75
+00:05:13,150 --> 00:05:16,950
+طيب كيف بنتهي البرهان؟ إيش بقول له؟ ending with the
+
+76
+00:05:16,950 --> 00:05:21,600
+conclusion بينتهي بالمطلوب، لكن المطلوب عمره ما 
+
+77
+00:05:21,600 --> 00:05:24,280
+يكون بالنصف، لازم يكون في النهاية، لازم يكون في
+
+78
+00:05:24,280 --> 00:05:26,880
+النهاية فإحنا هذه الطريقة، بنعيد الكتابة بتاعة
+
+79
+00:05:26,880 --> 00:05:31,720
+الكلام، بنرقم هؤلاء، بنقول أول سطر H1، أول سطر H1،
+
+80
+00:05:31,720 --> 00:05:32,140
+أول سطر H1، أول سطر H1، أول سطر H1، أول سطر H1،
+
+81
+00:05:32,140 --> 00:05:35,160
+أول سطر H1، أول سطر H1، أول سطر H1، أول سطر H1،
+
+82
+00:05:35,160 --> 00:05:45,260
+أول سطر H1، أول سطر H1، أول سطر H1، أول سطر H1، أ
+
+83
+00:05:45,770 --> 00:05:49,850
+خلّينا نطبّق على مثال جديد في هذا المثال الأول على
+
+84
+00:05:49,850 --> 00:05:53,780
+ال proof of validity بشكل رسمي بصيغة السؤال
+
+85
+00:05:53,780 --> 00:05:57,140
+Construct a formal proof of validity for the
+
+86
+00:05:57,140 --> 00:06:00,660
+following argument فقدامنا argument تتكوّل من two
+
+87
+00:06:00,660 --> 00:06:05,280
+hypothesis من two مقدمات واستنتاج Therefore هذه
+
+88
+00:06:05,280 --> 00:06:08,620
+النقطة تتنقط مع بعض ليه إيش.. إذا.. إذا مش 
+
+89
+00:06:08,620 --> 00:06:11,440
+تخدمها في العربي اه Therefore يعني في الإنجليزي
+
+90
+00:06:11,440 --> 00:06:15,400
+Therefore فهنبدأ الحل مع بعض ونعيد إيش.. نؤكد على
+
+91
+00:06:15,400 --> 00:06:20,140
+هذا الكلام فهذا المثال الأول وهي solution أو proof
+
+92
+00:06:20,140 --> 00:06:25,030
+كله صحيح تعطينا solution أو proof كله صح فأول خطوة
+
+93
+00:06:25,030 --> 00:06:28,310
+بأرقم ال hypothesis فهي الخطوة اللي عندي إيش 
+
+94
+00:06:28,310 --> 00:06:36,350
+ماعندي معطيات عندي W or H and L فدي واحد اه بدل ما
+
+95
+00:06:36,350 --> 00:06:39,730
+أحقق مبدأ من ال implies بدأ بدأ بدأ الشكل اثنين ال
+
+96
+00:06:39,730 --> 00:06:46,590
+hypothesis التانية W or H و بكتب عذن D هذه كلها
+
+97
+00:06:46,590 --> 00:06:50,530
+statement واحدة مظبوط اه thereforeبحط اللي هو 
+
+98
+00:06:50,530 --> 00:06:56,350
+backslash يك therefore اللي هو WRD برقمهاش ولا 
+
+99
+00:06:56,350 --> 00:06:59,850
+بحطها ضمنه لأنه الاش هذا الحل بيكون مرقم أي 
+
+100
+00:06:59,850 --> 00:07:04,010
+statement الآن كلها ضمن الحل لكن هذه لأ هذه منفصلة
+
+101
+00:07:04,010 --> 00:07:08,350
+هذه نهاية الحل هذه نهاية الحل هذه مهمة جدا إذا أول
+
+102
+00:07:08,350 --> 00:07:12,450
+شيء بنعيد كتابة ال argument بنرقم المعطيات وبنخلي
+
+103
+00:07:12,450 --> 00:07:14,930
+ال conclusion على جهة لأنه احنا مش هنستخدمه في
+
+104
+00:07:14,930 --> 00:07:19,130
+الحل لكنه مهم هو هيقولنا الحل انتهى ولا لأ الحل
+
+105
+00:07:19,130 --> 00:07:26,220
+انتهى ولا لأ أي سؤال هذا بديل لمين ان أقول H1 and
+
+106
+00:07:26,220 --> 00:07:29,360
+H2 implies ليه هيش ال conclusion فهي الطريقة 
+
+107
+00:07:29,360 --> 00:07:33,220
+الجديدة للكتابة الآن هنبدأ نشتغل بطرق القواعد
+
+108
+00:07:33,220 --> 00:07:35,920
+والاستدلال وال deductive reasoning لحد ما نوصل
+
+109
+00:07:35,920 --> 00:07:39,900
+لمين للمطلوب إيش ممكن نعمل فهي عندنا هذه وعندنا
+
+110
+00:07:39,900 --> 00:07:43,860
+هذه إيش مطلوب؟ مطلوب أوصل ل W و D خلينا نفكر بصوت
+
+111
+00:07:43,860 --> 00:07:47,140
+عالي طيب عشان أوصل إنّه تكون هذه true بدي على الأقل
+
+112
+00:07:47,140 --> 00:07:50,520
+واحدة منهم true لو قدرت أثبت إنّ W true أو D true
+
+113
+00:07:50,520 --> 00:07:52,560
+بكون انتهى العملية صح؟ ما هي كل ما تعلمنا في
+
+114
+00:07:52,560 --> 00:07:55,680
+المنطقية هي اللي إيش علمنا ال R وال N وهكذا طيب
+
+115
+00:07:55,680 --> 00:07:58,500
+من وين ممكن أوصل ال D؟ ال statement الوحيد اللي
+
+116
+00:07:58,500 --> 00:08:01,860
+فيه D هي هذه طب وقت إيش بتكون هذه الـD true إذا
+
+117
+00:08:01,860 --> 00:08:03,980
+كانت هذه الـD true؟ اللي هو الـmodel's fullness لو
+
+118
+00:08:03,980 --> 00:08:07,200
+قدرت أثبت إنه هذا true ممكن أثبت إنه الـD true طيب
+
+119
+00:08:07,200 --> 00:08:09,960
+من وين أثبت إنه W and H true من الأولى؟ بس إيش
+
+120
+00:08:09,960 --> 00:08:13,020
+مالعيش بدي أعمل.. بدي أعمل توزيع فإذا الأول خطوة
+
+121
+00:08:13,020 --> 00:08:18,340
+مطلوبة مني تلاتة من واحد أعمل توزيع W RH
+
+122
+00:08:21,410 --> 00:08:27,830
+NWRL من وين جبت الخطوة هذه جبتها من واحد وبقانون 
+
+123
+00:08:27,830 --> 00:08:30,290
+main التوزيع Distributive law
+
+124
+00:08:35,850 --> 00:08:39,450
+أي سؤال فهذه الطريقة لو أنا كنت كاتبهم كلهم مع بعض
+
+125
+00:08:39,450 --> 00:08:42,170
+طبما هذا الجزء أنا مش مستخدمه ليش هتمنع أنسخه فهذه
+
+126
+00:08:42,170 --> 00:08:46,030
+الطريقة الأنسب في الكتاب طبعًا الآن احنا ليش قلنا
+
+127
+00:08:46,030 --> 00:08:49,510
+بدنا مين بدنا هذه عندي two statements وبينهم
+
+128
+00:08:49,510 --> 00:08:53,130
+conjunction true إذا الطرفين ال true أنا بدي هذه بس
+
+129
+00:08:53,130 --> 00:08:58,630
+بقدر أستنتجها فاربعة و or اتش مزال الآن دي true
+
+130
+00:08:58,630 --> 00:09:01,910
+إذا هذه true وهذه true طب مين محتاج أنا محتاج
+
+131
+00:09:01,910 --> 00:09:05,530
+الأولى اه اثنتين صح لكن مين المفيد إله مين المحتاج
+
+132
+00:09:05,530 --> 00:09:09,570
+وأنا الأولى فبقدر أستنتجها من وين جبناها من تلاتة
+
+133
+00:09:09,570 --> 00:09:13,920
+والتبسيط simplification Simplification law
+
+134
+00:09:13,920 --> 00:09:20,160
+متابعين؟ واضح؟ تمام؟ اه اقتربنا جدًا الآن أربعة و
+
+135
+00:09:20,160 --> 00:09:23,280
+اثنين هي اللي كنا بنفكر فيها ومودة سبوني نص بيقول
+
+136
+00:09:23,280 --> 00:09:28,160
+لي دي is true فالجهة الخامسة HD من وين جيبناها؟ من
+
+137
+00:09:28,160 --> 00:09:30,900
+أربعة واثنين ومودة سبوني نص
+
+138
+00:09:34,730 --> 00:09:40,530
+موداس بونمس تمام؟ اه تمام هاي دي واش قلنا توي إذا
+
+139
+00:09:40,530 --> 00:09:44,410
+الـD true فإيه دي or anything is true طب كيف
+
+140
+00:09:44,410 --> 00:09:48,850
+أكتبها بالقانون المنطق؟ بال addition أحسنتي ف6 إذا 
+
+141
+00:09:48,850 --> 00:09:53,190
+نهدي  من وين؟ من 5 وقانون الـaddition
+
+142
+00:09:53,190 --> 00:10:00,470
+addition lawخلصنا تقريبا ايش بدي أعمل؟ ممكن أعمل
+
+143
+00:10:00,470 --> 00:10:04,270
+إبدال في 7WRD
+
+144
+00:10:04,270 --> 00:10:13,590
+جيبناها من 6 والـCommutative law فهذا
+
+145
+00:10:13,590 --> 00:10:18,610
+البرهان بهذه الطريقة طبعا الـargument إلى حد ما مش
+
+146
+00:10:18,610 --> 00:10:23,350
+كبيرة لكن ابني اتعلم الطريقة الجديدة فهذا اسمه Pro
+
+147
+00:10:24,680 --> 00:10:29,740
+نقطة خامسة من أربعة أو اثنين عشان هيك الترقيم مهم
+
+148
+00:10:29,740 --> 00:10:34,600
+من هذا الدليل أربعة أو اثنين كيف هي بي ثم كيو و بي
+
+149
+00:10:34,600 --> 00:10:42,660
+مقدمة بونص بيقول لي كيو مقدمة بونص بي ثم كيو و بي
+
+150
+00:10:42,660 --> 00:10:50,220
+مقدمة بونص واضحة فهي بي و هدي و هدي و هدي و هدي و 
+
+151
+00:10:50,220 --> 00:10:56,820
+هدي هدي و هدي بيقول لي دي trueأي سؤال هو بمعنى آخر
+
+152
+00:10:56,820 --> 00:11:00,660
+أنا عندي هذه true إذا وعدت هو بالوعد فدي لازم تكون
+
+153
+00:11:00,660 --> 00:11:11,040
+true أي سؤال نشوف
+
+154
+00:11:11,040 --> 00:11:18,900
+كمان مثال مثال آخر في عندنا three hypothesis ثلاث
+
+155
+00:11:18,900 --> 00:11:22,280
+مقدمات ثلاث مقدمات وفي عندنا conclusion فالمثال
+
+156
+00:11:22,280 --> 00:11:29,330
+التاني كيف نبدأ الحل أو البرهان كله صح بعادة كتابة 
+
+157
+00:11:29,330 --> 00:11:34,190
+الـargument وبنرقم المعطيات لأنها جزء من البرهان
+
+158
+00:11:34,190 --> 00:11:37,290
+لكن الـconclusion بنكتبه بشكل منفصل بالطريقة اللي
+
+159
+00:11:37,290 --> 00:11:41,390
+مكتوبة في السؤال فعنا if L then M هذي ايه ايه ايه
+
+160
+00:11:41,390 --> 00:11:42,650
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+161
+00:11:42,650 --> 00:11:45,930
+ايه ايه ايه ايه ايه ايه ايه
+
+162
+00:11:47,150 --> 00:11:51,430
+الـthen K الأقواس مهمة جداً لأن الأقواس بتقول إن
+
+163
+00:11:51,430 --> 00:11:55,590
+هذه ايش مقدمة على ايش الـif then الثانية ثلاث not
+
+164
+00:11:55,590 --> 00:12:00,970
+B and L بعدين therefore K هذه مش جزء من الحل هذه
+
+165
+00:12:00,970 --> 00:12:04,950
+نهاية الحل اللي هي الـK كـconclusion فهي بداية
+
+166
+00:12:04,950 --> 00:12:09,860
+الحل هنبدأ الآن بدنا نوصل لـK بدنا نوصل لـK طبعا
+
+167
+00:12:09,860 --> 00:12:14,160
+الـK موجودة هنا فعشان أوصل لـK اللي هنا ايش ممكن
+
+168
+00:12:14,160 --> 00:12:17,200
+أعمل  نصف لو عرفت أن هذه P then Q لو
+
+169
+00:12:17,200 --> 00:12:21,160
+قدرت أفترض أن هذه true بوصل بقترب من الـK بقترب من
+
+170
+00:12:21,160 --> 00:12:25,760
+الـK كيف نوصل أن M or N طب ما فيش هنا إلا M هنا
+
+171
+00:12:25,760 --> 00:12:29,700
+عشان أوصل لـM بدي L بدي L الـL موجودة ولا مش 
+
+172
+00:12:29,700 --> 00:12:33,980
+موجودة؟ من وين؟ واش أعمل؟ تبسيط Simplification
+
+173
+00:12:33,980 --> 00:12:39,220
+فالآن أربعة أل من وين جبناها؟ جبناها من ثلاث
+
+174
+00:12:39,220 --> 00:12:44,190
+والـSimplification law Simplification law فالآن احنا
+
+175
+00:12:44,190 --> 00:12:47,950
+بنحاول نحلل اه طبعا ممكن واحد يجرب لكن إذا برضه
+
+176
+00:12:47,950 --> 00:12:51,090
+فكرنا بهذه الطريقة بيكون أفضل فإذا نقل فده مرة 
+
+177
+00:12:51,090 --> 00:12:55,190
+ثانية أكد إذا في عندنا and true فالتنتين true مين
+
+178
+00:12:55,190 --> 00:12:58,130
+اللي أخذها اللي بتفيدني التنتين لو قلت top بيه صح
+
+179
+00:12:58,130 --> 00:13:02,050
+قلت الـصح ليش أخذت الـلإن وحدة اللي بديها فكان سؤال
+
+180
+00:13:02,050 --> 00:13:08,290
+يعني بعد الطلبة أن B and Q implies B وimplies Q
+
+181
+00:13:08,290 --> 00:13:11,830
+لأن احنا حللناها قلنا ما زال الـand true إذا الـ
+
+182
+00:13:11,830 --> 00:13:14,410
+and ثاني true وأنا ايش بأخذ اللي بديه اللي
+
+183
+00:13:14,410 --> 00:13:20,030
+بيفيدني تمام الآن الـواحد ايش بديني ام مودس بوننس
+
+184
+00:13:20,030 --> 00:13:25,190
+مودس بوننس فهنا خمسة اكتب هنا اللي هو ياش ام من وين
+
+185
+00:13:25,190 --> 00:13:33,190
+جبناها ياش من واحد وأربعة ومودس بوننسأي سؤال تفضلي
+
+186
+00:13:33,190 --> 00:13:36,610
+هنا
+
+187
+00:13:36,610 --> 00:13:40,750
+a not
+
+188
+00:13:40,750 --> 00:13:45,790
+b هذي طبعا هذي اللي هي الـb والـqأه طبعا .. طبعا
+
+189
+00:13:45,790 --> 00:13:47,670
+.. هي هي اللي جيت أنا .. أنا جيت بقى .. معلش أنا 
+
+190
+00:13:47,670 --> 00:13:49,370
+ماناجي واحد ميقول لي مين اتقدم .. أنا .. ب .. ب ..
+
+191
+00:13:49,370 --> 00:13:52,950
+في عندي N الـN دي اللي هي طرفين .. اه بغض النظر هي
+
+192
+00:13:52,950 --> 00:13:56,710
+بسيطة الطرف ولا قوة ولا مُركّب فأنا الطرفين L و
+
+193
+00:13:56,710 --> 00:13:59,270
+not P وممكن يكون مُركّب أكتر من هيك أنا بحكي P
+
+194
+00:13:59,270 --> 00:14:02,670
+and Q بشكل عام طرف وطرف التنتين صحيحتين فبأخده
+
+195
+00:14:02,670 --> 00:14:08,730
+كله كامل صح تمام الآن وصلنا للـM اقتربنا من هذه
+
+196
+00:14:08,730 --> 00:14:15,350
+ممكن ايش نعمل addition 6 M or N جبناها من
+
+197
+00:14:15,350 --> 00:14:21,510
+الخمسة والـaddition addition تمام الآن ستة واثنين
+
+198
+00:14:21,510 --> 00:14:25,030
+ايش بتديني الـthen كهذه كلها كتلة واحدة شايفين كيف
+
+199
+00:14:25,030 --> 00:14:27,730
+الأمر بتتعامل مش دائماً بتدخل بالتفاصيل أنا أحيانا 
+
+200
+00:14:27,730 --> 00:14:31,090
+بتطلع نظرتها ايش خارجية فها دي بي وها دي كيو كلها
+
+201
+00:14:31,090 --> 00:14:35,510
+دي كيو فالآن قولنا السابعة اللي هي ايش الـthen ك
+
+202
+00:14:35,510 --> 00:14:39,490
+من وين جبناها من ستة أو من اثنين وستة
+
+203
+00:14:42,650 --> 00:14:46,010
+فمهم جداً قانون الـModus Vernum مهم جداً تمام
+
+204
+00:14:46,010 --> 00:14:50,610
+اقتربنا احنا بدنا K بدنا K الآن الـو K سبعة و
+
+205
+00:14:50,610 --> 00:14:55,350
+ثمانية خلينا اكتب هنا آسف سبعة وأربعة سبعة و
+
+206
+00:14:55,350 --> 00:14:59,510
+أربعة  بدنا K وهو المطلوب اللي هو أربعة وسبعة و
+
+207
+00:14:59,510 --> 00:15:03,930
+Modus Vernum مرة ثانية وهو المطلوب أثبته ووصلنا
+
+208
+00:15:03,930 --> 00:15:09,500
+للنتيجة السادسة من وين جبناها ها دي true true or
+
+209
+00:15:09,500 --> 00:15:13,100
+anything true addition قانون الـA موجود القانون
+
+210
+00:15:13,100 --> 00:15:17,240
+بشكل المجرد بحاول أنا أذكركم فيه true or anything
+
+211
+00:15:17,240 --> 00:15:21,220
+true فهذه ما زالت true أضف لها أي شيء بالـor بتظلها
+
+212
+00:15:21,220 --> 00:15:24,140
+true لأن أنا عارف إن جزء الـtrue ضامنه والآن بغض
+
+213
+00:15:24,140 --> 00:15:29,540
+النظر عن الآن طبعا طبعا طبعا كل خطوة عشان هيك الـ
+
+214
+00:15:29,540 --> 00:15:32,300
+conclusion بنحطهاش لأن احنا بدنا نثبت إنه true مش
+
+215
+00:15:32,300 --> 00:15:35,780
+عارفين لكن المعطى true وأي خطوة وصلت لها بتكون
+
+216
+00:15:35,780 --> 00:15:39,140
+true لأن كيف استنتجتها بطريقة منطقية صحيحة هي
+
+217
+00:15:39,140 --> 00:15:42,280
+دليلة، إذا كله true وأنا متأكد منه، فلازم ابني 
+
+218
+00:15:42,280 --> 00:15:46,080
+كله يكون true وأمشي عليه واحدة واحدة واستخدم كل
+
+219
+00:15:46,080 --> 00:15:46,940
+اللي وصلت له
+
+220
+00:15:50,480 --> 00:15:53,340
+إذا كان موجود نستخدمه هو اللي كتب القانون لأ هو
+
+221
+00:15:53,340 --> 00:15:57,080
+اللي قال القانون لأ ما توي عمل نقل هو ايش التوزيع
+
+222
+00:15:57,080 --> 00:16:01,660
+تكافؤه لأ ما فيش حاجة بتقول هيك ما فيش حاجة لأ كل
+
+223
+00:16:01,660 --> 00:16:04,900
+القوانين وحسبناها قوانين الاستدلال كلهم مسموح
+
+224
+00:16:04,900 --> 00:16:07,580
+استخدامهم كلهم مسموح استخدامهم
+
+225
+00:16:12,390 --> 00:16:15,530
+خلينا نربط طبعاً، المنطق اللي متعامل معاه في
+
+226
+00:16:15,530 --> 00:16:18,690
+الرياضيات وفي المنطق موجود وين ما كان، حتى موجود
+
+227
+00:16:18,690 --> 00:16:21,190
+في تدبرنا للقرآن، موجود زي ما شوفنا في الشعر، في
+
+228
+00:16:21,190 --> 00:16:24,630
+الحكمة، أين ما كان، موجود البرهان، فهذا الكلام
+
+229
+00:16:24,630 --> 00:16:28,870
+المنطقي اللي بتفق عليه كل الناس الأسوياء، كل الناس
+
+230
+00:16:28,870 --> 00:16:31,690
+اللي بتفكر بطريقة علمية، ما حدش ممكن يرفض هذا
+
+231
+00:16:31,690 --> 00:16:36,710
+الكلام المنطقي اللي نعتمد عليه فمثلاً هذه كلمة الـ
+
+232
+00:16:36,710 --> 00:16:40,610
+argument قامت الحجة كيف سيدنا إبراهيم عليه السلام
+
+233
+00:16:40,610 --> 00:16:46,110
+أقام الحجة على الملك نمرود ونمرود بهت، ما قدرش 
+
+234
+00:16:46,110 --> 00:16:51,890
+يواجه أو ينفّي الكلام، فأعوذ بالله من الشيطان الرجيم،
+
+235
+00:16:51,890 --> 00:16:55,130
+أنا أمطر إلى الذي حج إبراهيم في ربه أن أطاه الله
+
+236
+00:16:55,130 --> 00:16:59,490
+الملك، إذ قال إبراهيم ربي الذي يحيي ويميت، قال أنا
+
+237
+00:16:59,490 --> 00:17:05,420
+أحيي ويميت طبعاً هذه رد عليها حاول أنه يجادل ويقول
+
+238
+00:17:05,420 --> 00:17:08,100
+أنا المسؤول عن الحياة والموت طب جاب له دليل آخر
+
+239
+00:17:08,100 --> 00:17:11,960
+ما قدرش يواجه فيه ليش؟ قال إبراهيم وإن الله يأتي
+
+240
+00:17:11,960 --> 00:17:16,160
+بالشمس من المشرق فأتي بها من المغرب فبهت الذي كفر
+
+241
+00:17:16,160 --> 00:17:20,260
+والله لا يهدي القوم الظالمين وين الشاهد هنا؟ طبعاً
+
+242
+00:17:20,260 --> 00:17:24,600
+هنا حط له القاعدة بيقول له أن ربنا هو اللي بيجيب
+
+243
+00:17:24,600 --> 00:17:27,460
+الشمس من المشرق فهو لو قال أنا اللي بجيبها من
+
+244
+00:17:27,460 --> 00:17:30,790
+المشرق ايش بدي أقول له؟ طب دي بقى من المغرب، حريكة،
+
+245
+00:17:30,790 --> 00:17:33,370
+مش أنت المسؤول عنها؟ أه، فبتناقض، لو أنت كنت
+
+246
+00:17:33,370 --> 00:17:35,750
+بتقدر أنك تجيبها من المشرق وأنت بتجيبها، إذا أنت
+
+247
+00:17:35,750 --> 00:17:37,890
+مقدر تجيبها من الشمال ومن الجنوب، أه، فهنا هي
+
+248
+00:17:37,890 --> 00:17:41,750
+القاعدة وهنا في التناقض، فهنا برهان وفعلاً أقدر
+
+249
+00:17:41,750 --> 00:17:44,610
+أنه يقيم الحجة على الملك، فاحنا البرهان مش بس في
+
+250
+00:17:44,610 --> 00:17:49,620
+الرياضيات، وين ما كان، بنستخدم المنطق أيضاً هنا
+
+251
+00:17:49,620 --> 00:17:52,700
+برضه اللي هو برهان بطريقة اللي هو التناقض بنسميها
+
+252
+00:17:52,700 --> 00:17:54,800
+اللي احنا .. بما هدرع .. هنشوفها طريقة ثانية
+
+253
+00:17:54,800 --> 00:17:59,580
+للبرهان ما اتخذ الله من ولده وما كان معه من إله
+
+254
+00:17:59,580 --> 00:18:03,920
+إذا لذهب كل إله بما خلق ولا على بعضهم على بعض
+
+255
+00:18:03,920 --> 00:18:07,680
+سبحان الله عما يصفون فهذه تبقى قيمة دليل على
+
+256
+00:18:07,680 --> 00:18:12,500
+وحدانية الله بقول نفترض جدلاً إنه في أكثر من إله
+
+257
+00:18:12,500 --> 00:18:16,240
+طبعاً إلهين عظيمين، بدهم يتنازعوا الأمر، ولا لأ؟
+
+258
+00:18:16,240 --> 00:18:18,760
+آه، كان ايش صار؟ كان صار فساد في الأرض، كان صار
+
+259
+00:18:18,760 --> 00:18:21,300
+فساد في الأرض، فهنا برهن على وحدانية الله
+
+260
+00:18:21,300 --> 00:18:25,040
+بتناقض، لو افترضنا جدلاً إنه في أكثر من إله، كان
+
+261
+00:18:25,040 --> 00:18:27,500
+صار فيه فساد في الأرض، ولكن ايش؟ احنا شايفين إنه
+
+262
+00:18:27,500 --> 00:18:31,520
+ما فيش فساد، نظام دقيق جداً، فهذا بدل على وحدانية
+
+263
+00:18:31,520 --> 00:18:34,700
+الخالق سبحانه وتعالى، فهذا بيسموه برهان بالتناقض،
+
+264
+00:18:34,700 --> 00:18:38,780
+بفترض إنه شيء خطأ، بوصل لتناقض، إذا ما فرضته خطأ
+
+265
+00:18:38,780 --> 00:18:44,750
+هو صح، لأن من وين جاء التناقض؟ من إني فممكن أن يكون
+
+266
+00:18:44,750 --> 00:18:47,790
+هذا صحيح لأننا اتفقنا أن الـstatement يا true يا
+
+267
+00:18:47,790 --> 00:18:51,950
+false إذا كانت حالتنا force إذا كانت true فهذا
+
+268
+00:18:51,950 --> 00:18:55,810
+المنطق اللي يعتمد في كل الحياة وحتى في تدبرنا
+
+269
+00:18:55,810 --> 00:19:01,160
+للقرآن وفي الشريعة وفي وين ما كان في حياتنا برضه
+
+270
+00:19:01,160 --> 00:19:04,720
+سيدنا إبراهيم هنا برضه كيف أقام الحجة على قومه في
+
+271
+00:19:04,720 --> 00:19:09,180
+عبادة الأصنام وطلاه لأكيد أن أصنامكم بعد أن تولوا
+
+272
+00:19:09,180 --> 00:19:12,520
+مدبرين فجعلهم جذاذاً إلا كبيرا لهم لعلهم إليه
+
+273
+00:19:12,520 --> 00:19:15,620
+يرجعون فهنا ايش؟ أقام عليهم الحجة ويقول لهم أنتوا
+
+274
+00:19:15,620 --> 00:19:18,620
+هذه أصنام تنفعكم ومتفيدكم طب بدناش نجيب لصغار
+
+275
+00:19:18,620 --> 00:19:22,030
+سيبهم لصغار خدوا الكبير فيهم هينفع ولا لأ؟ أقام
+
+276
+00:19:22,030 --> 00:19:25,470
+عليهم الحجة قالوا من فعل هذا بألهتنا إنه لمن
+
+277
+00:19:25,470 --> 00:19:29,590
+الظالمين قالوا سمعنا فتنة يذكرهم يقال له إبراهيم
+
+278
+00:19:29,590 --> 00:19:33,710
+قالوا فأتوا به على أعين الناس لعلهم يشهدون قالوا
+
+279
+00:19:33,710 --> 00:19:37,950
+أنت فعلت هذا بألهتنا يا إبراهيم هنا الآن قال بل
+
+280
+00:19:37,950 --> 00:19:40,930
+فعله كبيرهم هذا فاسألهم إن كانوا ينطقون، برضه 
+
+281
+00:19:40,930 --> 00:19:45,670
+برعان بالتناقض، فبقولهم هي أكبر الآلهة، طب إيش؟ طب
+
+282
+00:19:45,670 --> 00:19:49,610
+هو مفعلهاش هو، طب يقولكوا من اللي فعل على الأقل،
+
+283
+00:19:49,610 --> 00:19:54,330
+مش هو يحارس عليهم وشايفهم، فرجعوا إلى أنفسهم، هنا
+
+284
+00:19:54,330 --> 00:19:58,170
+قام عليهم الحجة، فرجعوا إلى أنفسهم فقالوا إنكم 
+
+285
+00:19:58,170 --> 00:20:00,970
+أنتم الظالمون، فإيش؟ بل الإنسان هو على نفسية
+
+286
+00:20:00,970 --> 00:20:04,150
+بصيرة، ولو ألقى معذيرة، في أنفسهم عرفوا إنهم على
+
+287
+00:20:04,150 --> 00:20:09,860
+غلط، لكن الكبر فثم نكسوا على رؤوسهم لقد علمت ما
+
+288
+00:20:09,860 --> 00:20:13,700
+هؤلاء ينطقون طبعا هؤلاء اعترفوا وبنفس الوقت برضه
+
+289
+00:20:13,700 --> 00:20:17,440
+بيجادلوا بيجادلوا رغم أنهم أُقيم عليهم الحجة قال
+
+290
+00:20:17,440 --> 00:20:20,640
+أفتعبدون من دون الله ما لا ينفعكم شيئا ولا يدركم 
+
+291
+00:20:20,640 --> 00:20:24,520
+أقام عليهم الحجة الآن أوفل لكم من ما تعبدون من دون
+
+292
+00:20:24,520 --> 00:20:29,200
+الله أفلا تعقلون فهي المنطق تماما بنفس الأسلوب
+
+293
+00:20:29,200 --> 00:20:35,060
+وهذا جيد أنه ..نستعلم الرياضيات بتفيدنا في حياتنا 
+
+294
+00:20:35,060 --> 00:20:38,260
+وتحصيصنا برضه بتفيدنا في كل مناحي الحياة وهذه أمثلة
+
+295
+00:20:38,260 --> 00:20:43,630
+كيف نتدبر في القرآن فهذه بعض الأمثلة على ما يُعرف
+
+296
+00:20:43,630 --> 00:20:48,290
+بالبرهان غير المباشر البرهان غير المباشر indirect
+
+297
+00:20:48,290 --> 00:20:52,790
+proof فهذه طبعا طريقة ما سبق بيسموه البرهان
+
+298
+00:20:52,790 --> 00:20:57,670
+المباشر ببدأ فيه من المعطيات وبوصل فيه للنتيجة أو 
+
+299
+00:20:57,670 --> 00:21:02,230
+للإستنتاج هذا بيسموه البرهان المباشر في البرهان 
+
+300
+00:21:02,230 --> 00:21:07,730
+غير المباشر بننفي المطلوب آه طيب واحد يقول أنت
+
+301
+00:21:07,730 --> 00:21:11,130
+قلت إن عمره المطلوب بيكون جزء من البرهان آه نفسه
+
+302
+00:21:11,130 --> 00:21:15,610
+بيكونش لكن نفيه ممكن يكون نفيه نفيه المطلوب ممكن
+
+303
+00:21:15,610 --> 00:21:19,690
+يكون جزء من البرهان أو من الحل فهنا بقول طبعا
+
+304
+00:21:19,690 --> 00:21:23,280
+approve اللي هو indirect approve وهو يعتمد على
+
+305
+00:21:23,280 --> 00:21:26,660
+reduction of absurdity اللي هو نقد النقي نقد
+
+306
+00:21:26,660 --> 00:21:29,520
+النقي اللي إحنا بنقول نفترض جدلا إن هذا صحيح 
+
+307
+00:21:29,520 --> 00:21:32,480
+وبعدين بننقضه إذا ما زياش إذا ما هذا مش صحيح إذا
+
+308
+00:21:32,480 --> 00:21:36,360
+هو خطأ أنا قضيت عليه إذا عكسه هو الصحيح عكسه هو الصحيح
+
+309
+00:21:37,750 --> 00:21:41,590
+فالـ indirect proof of validity is done by إيش
+
+310
+00:21:41,590 --> 00:21:47,450
+نعمل؟ أول حاجة بنعمل بنضيف مؤتة جديدة أو مقدمة
+
+311
+00:21:47,450 --> 00:21:50,030
+جديدة هي عبارة عن مين؟ the negation of the
+
+312
+00:21:50,030 --> 00:21:55,310
+conclusion بننفي المطلوب و بنحطه يصير كمؤتة مرة
+
+313
+00:21:55,310 --> 00:21:58,730
+ثانية مافيش تناقض الـ conclusion نفسه أمره ما بيكون
+
+314
+00:21:58,730 --> 00:22:02,430
+جزء من الحل لكن نفيه ممكن يكون جزء من البرهان أو 
+
+315
+00:22:02,430 --> 00:22:05,850
+الحل بس باش بال indirect proof أو البرهان غير
+
+316
+00:22:05,850 --> 00:22:10,160
+المباشر and then بعد ما نعمل هيك .. كيف بنتهي الحل؟
+
+317
+00:22:10,160 --> 00:22:13,360
+بنتهيش بالـ conclusion المرة هذه وإنما بنتهي بإننا
+
+318
+00:22:13,360 --> 00:22:16,640
+نوصل لتناقض بس لو وصلنا لتناقض .. آه ليش فيه
+
+319
+00:22:16,640 --> 00:22:20,140
+تناقض؟ طب إيش عرفنا إنه التناقض أدى إنه الـ
+
+320
+00:22:20,140 --> 00:22:24,440
+conclusion صحيح؟ لأن ما أعطيه إليه كله صح إحنا إيش
+
+321
+00:22:24,440 --> 00:22:28,900
+عملنا؟ نفيت المطلوب والباقي كل شغلي أنا كله صح طب 
+
+322
+00:22:28,900 --> 00:22:31,800
+من وين يجي الخلل؟ فيش من نف المطلوب من نف 
+
+323
+00:22:31,800 --> 00:22:34,160
+المطلوب إذا ما زال نف المطلوب هو الخلل هو الخطأ
+
+324
+00:22:34,160 --> 00:22:36,980
+إذا عكسه هو الصحيح لأن المطلوب صحيح فأدي بيكون
+
+325
+00:22:36,980 --> 00:22:41,500
+وصلنا للعمل طبعا فبالتالي أنا موصلتش للمطلوب بشكل
+
+326
+00:22:41,500 --> 00:22:46,280
+مباشر وإنما أثبتت خطأ خطأه إنه لا يمكن يكون خطأ
+
+327
+00:22:46,280 --> 00:22:50,060
+فسنتجت إنه صواب فبطريقة غير مباشرة بطريقة غير 
+
+328
+00:22:50,060 --> 00:22:54,420
+مباشرة فكيف بنعرف إن البرهان انتهى؟ أول ما نوصل لـ
+
+329
+00:22:54,420 --> 00:22:57,900
+contradiction بكون البرهان انتهى as soon as a
+
+330
+00:22:57,900 --> 00:23:05,180
+contradiction is obtained the proof is complete أي
+
+331
+00:23:05,180 --> 00:23:12,810
+سؤالأه فهنا المثال الأول give an indirect proof of
+
+332
+00:23:12,810 --> 00:23:16,250
+validity for the following argument فعنا argument
+
+333
+00:23:16,250 --> 00:23:19,370
+بدنا نبرهنها بطريقة البرهان غير المباشرة طبعا ممكن 
+
+334
+00:23:19,370 --> 00:23:22,110
+نبرهنها بطريقة مباشرة بس لأن هنحل بطريقة جديدة
+
+335
+00:23:22,110 --> 00:23:26,790
+نتعلم الطريقة الجديدة و نعيد الكلام اللي حكيناه
+
+336
+00:23:26,790 --> 00:23:33,040
+ونطبقه بشكل عملي ونشوف كيف بده يصير فهذا المثال
+
+337
+00:23:33,040 --> 00:23:36,300
+الأول على الـ indirect proof ونبدأ بالبرهان أو الـ
+
+338
+00:23:36,300 --> 00:23:41,700
+solution البداية نفس البداية، بنرقم المعطيات B, R,
+
+339
+00:23:41,880 --> 00:23:54,190
+Q, then R معطى ثاني S, then B and U المعطى الثالث Q
+
+340
+00:23:54,190 --> 00:24:00,390
+or S إيش المطلوب؟ لسه، لسه، تستعيدلوش، إحنا من
+
+341
+00:24:00,390 --> 00:24:04,930
+الأهل يومين تبعيد كتابتنا طبعا لو direct proof 
+
+342
+00:24:04,930 --> 00:24:08,130
+ممكن أستخدم من واحد لتلاتة حد ما أوصل للـ R الآن
+
+343
+00:24:08,130 --> 00:24:11,230
+بنعمل indirect proof أول خطوة إيش بنعمل؟ بننفي
+
+344
+00:24:11,230 --> 00:24:15,950
+المطلوب أربعة not R طب إيش اللي عملنا دليلنا؟ واحد 
+
+345
+00:24:15,950 --> 00:24:21,460
+يبدو يقرأ، بنقول له هذه خطوة indirect proof direct
+
+346
+00:24:21,460 --> 00:24:28,020
+approved فمهم جدا التنظيم والكتابة والتوضيح لنفس
+
+347
+00:24:28,020 --> 00:24:30,540
+الإنسان لأن المكتب ممكن يسهى بعدين من أين اتجه 
+
+348
+00:24:30,540 --> 00:24:34,420
+بسهولة ممكن يتراجع ويحلق وأيضا لأي قارئ آخر فأنا
+
+349
+00:24:34,420 --> 00:24:37,360
+أول ما أطلع نطق آه طب أقول من أين جاء بهذه بعرف
+
+350
+00:24:37,360 --> 00:24:40,880
+أنه يعمل برهان بالتناقض فأبدأ أركز وابدأ أعرف أن
+
+351
+00:24:40,880 --> 00:24:43,220
+وقت إيش البرهان هينتهي إذا وصلنا إلى contradiction
+
+352
+00:24:43,220 --> 00:24:46,620
+ممتاز فحنبدأ نشتغل بعدين كل الشغل لوحدنا نفس
+
+353
+00:24:46,620 --> 00:24:50,000
+القواعد لحد ما نوصل لـ contradiction طيب إن not R
+
+354
+00:24:50,000 --> 00:24:55,120
+إيش ممكن نعمل واحد وأربعة modus tollens إذا مش
+
+355
+00:24:55,120 --> 00:25:02,220
+هتقدر توفي بالوعد ما توعدش فهنا خمسة not ب أو ر كيو 
+
+356
+00:25:02,220 --> 00:25:07,320
+فهذه جيبناها من واحد وأربعة modus tollens ممكن
+
+357
+00:25:07,320 --> 00:25:12,570
+نكتب باختصار أي سؤال؟ انتبهين؟ تمام اقتربنا ولا لا؟
+
+358
+00:25:12,570 --> 00:25:16,370
+إيش ممكن نعمل؟ إحنا بدنا تناقض طب مين التناقض؟
+
+359
+00:25:16,370 --> 00:25:20,790
+واحد ونفيه الشيء وناقضه طب مين هم؟ ما بنعرفش اهو
+
+360
+00:25:20,790 --> 00:25:24,510
+التسهيل إيش يطلع معنى؟ المهم يطلع statement والنفي
+
+361
+00:25:24,510 --> 00:25:28,130
+تبعها موجودين بحصل على contradiction طب ممكن نعمل
+
+362
+00:25:28,130 --> 00:25:35,530
+De Morganism not B and not Q فهنا جيبناها من خمسة
+
+363
+00:25:35,530 --> 00:25:36,350
+De Morganism
+
+364
+00:25:39,340 --> 00:25:44,400
+de Morgan's law ممتاز فهنا ممكن أنقش أبسط وحصلت
+
+365
+00:25:44,400 --> 00:25:48,380
+على نط بي ونط Q هدول صح إذا لو وصلت لـ بي صح أو Q 
+
+366
+00:25:48,380 --> 00:25:51,260
+صح بكون انتهت صار عندي تناقض فأنا صار عندي نفي لـ
+
+367
+00:25:51,260 --> 00:25:54,500
+two statements لو وصلت لإثبات لواحدة فيهم بكون
+
+368
+00:25:54,500 --> 00:26:00,100
+البرهان انتهت خلينا نشوف المص نكمل فهنا بدأنا إحنا
+
+369
+00:26:00,100 --> 00:26:05,500
+نتعمق في الحل ونتقدم فأنا ممكن آخد بنعمل
+
+370
+00:26:05,500 --> 00:26:09,090
+simplification مين اللي بدنا إحنا ناطقين U؟ أنت حافظين
+
+371
+00:26:09,090 --> 00:26:15,610
+الحل؟ آه هذه من ستة طب ليش مش ناطقين B؟ آه طيب خلينا 
+
+372
+00:26:15,610 --> 00:26:18,250
+نشوف فهذه إيش؟ هذه من ستة simplification
+
+373
+00:26:18,250 --> 00:26:24,050
+simplification تمام بدنا نحاول نوصل لحاجة ثانية
+
+374
+00:26:24,050 --> 00:26:30,470
+تبسيط جملة وجملة وبينهم conjunction المزاري والـ 
+
+375
+00:26:30,470 --> 00:26:35,070
+conjunction الـ true إذا الطرفين الـ true هو نطبق
+
+376
+00:26:35,070 --> 00:26:39,450
+اللي بدنا إياه يعملنا شوف تمانية أنا مش واضح على ليش و
+
+377
+00:26:39,450 --> 00:26:42,830
+ثمانية قاعدة برضه من ستة و simplification أنا بدور
+
+378
+00:26:42,830 --> 00:26:47,310
+على contradiction هدفي أوصل لجملة ونقيدها أو 
+
+379
+00:26:47,310 --> 00:26:53,020
+تقرير ونقيده تمام؟ فإذن هنا واضح اللي بقدر أقوله
+
+380
+00:26:53,020 --> 00:26:56,820
+الآن إحنا بندور على B أو Q إذا واحدة فيهم ونقطة 
+
+381
+00:26:56,820 --> 00:26:59,240
+حصلنا عليهم وعندنا Not B و Not Q بنوصل لـ
+
+382
+00:26:59,240 --> 00:27:01,760
+Contradiction أي واحدة فيهم تؤدي الغرض أي واحدة
+
+383
+00:27:01,760 --> 00:27:05,140
+فيهم تؤدي الغرض طيب من وين نوجد الـQ أو Not B؟ في
+
+384
+00:27:05,140 --> 00:27:10,980
+عندنا تلاتة إيش ممكن نعمل؟ اللي هو إيش؟ سبعة وتلاتة
+
+385
+00:27:10,980 --> 00:27:15,480
+مازال true or as true إذا على الأقل واحدة true طب 
+
+386
+00:27:15,480 --> 00:27:18,620
+إذا في .. إذا q false لازم as تكون true آه فهذه
+
+387
+00:27:18,620 --> 00:27:22,860
+تسعة فبنقول إيش؟ اللي هو as من وين جيبناها دي؟
+
+388
+00:27:22,860 --> 00:27:27,400
+جيبناها من سبعة ومن تلاتة واللي هو القانون إيش؟
+
+389
+00:27:27,400 --> 00:27:33,030
+ابزردم نسيت اسم القانون اللي هي عبارة عن إيش
+
+390
+00:27:33,030 --> 00:27:39,510
+القانون بي or كيو and نقطة كيو implies بي هي 
+
+391
+00:27:39,510 --> 00:27:44,860
+القانون injunction in syllogism آه disjunction .. 
+
+392
+00:27:44,860 --> 00:27:49,220
+disjunction in syllogism آه تمام آه اللي هو يعني
+
+393
+00:27:49,220 --> 00:27:52,740
+الفصل المنطقي قانون الفصل المنطقي تمام قانون الفصل
+
+394
+00:27:52,740 --> 00:27:56,700
+المنطقي واضح فهنا في عندي or طبعا إحنا فسرناها ما
+
+395
+00:27:56,700 --> 00:27:59,960
+زال هذه true على الأقل واحدة true طب q false لأن
+
+396
+00:27:59,960 --> 00:28:03,440
+نقطة q هي الـ true مظبوط إذا لازم أسد كل true آه
+
+397
+00:28:03,440 --> 00:28:09,450
+اقتربنا الآن S true لازم هذه تكون true فـ modus ponens
+
+398
+00:28:09,450 --> 00:28:13,410
+هل جيت إحنا في الخطوة العاشرة اللي و Q بي 
+
+399
+00:28:13,410 --> 00:28:19,390
+and يو بي and يو من وين جبناها جبناها من اتنين
+
+400
+00:28:19,390 --> 00:28:25,270
+وتسعة ومودس بوننس مظبوط هو دا spontaneous اختراق 
+
+401
+00:28:25,270 --> 00:28:30,730
+خلصنا بي simplification احداشر بي جيبناها من عشرة
+
+402
+00:28:30,730 --> 00:28:36,090
+وقانون أكثر بساطة الآن هذه true وهذه false نعمل 
+
+403
+00:28:36,090 --> 00:28:40,230
+conjunction نوصل لـ contradiction اتناش اللي هي بي 
+
+404
+00:28:40,230 --> 00:28:44,710
+and not بي جيبناها من احداشر وثمانية وعملنا 
+
+405
+00:28:44,710 --> 00:28:49,090
+conjunction conjunction بقدر أعمل كل مكان ليش أي
+
+406
+00:28:49,090 --> 00:28:52,110
+خطوطين true ممكن ذهش الآن تبعتهم تكون true فطبعا
+
+407
+00:28:52,110 --> 00:28:54,490
+contradiction انتهى هنا contradiction
+
+408
+00:29:04,720 --> 00:29:08,320
+contradiction وانتهى البرهان أول لما أوصل
+
+409
+00:29:08,320 --> 00:29:11,580
+لـ contradiction انتهى البرهان فإحنا كنا متوقعين not
+
+410
+00:29:11,580 --> 00:29:15,000
+Q أو Q أو P و not P طلعت P و not P اللي أدتنا
+
+411
+00:29:15,000 --> 00:29:20,400
+الهدف اللي بدناه وهو الـ contradiction أي سؤال فهذا 
+
+412
+00:29:20,400 --> 00:29:24,380
+بيسموه indirect proof طبعا على أصبح الـ relic الـ R
+
+413
+00:29:24,380 --> 00:29:30,280
+صحيح تمام
+
+414
+00:29:30,280 --> 00:29:30,740
+فضل
+
+415
+00:29:33,490 --> 00:29:36,110
+آه هي الـ indirect proof إحنا ما بنقول في الـ 
+
+416
+00:29:36,110 --> 00:29:40,670
+indirect proof بدايته نفي المطلوب ونهايته الوصول
+
+417
+00:29:40,670 --> 00:29:44,610
+إلى contradiction هيك القاعدة هيك شرحنا طيب، ماشي؟
+
+418
+00:29:44,610 --> 00:29:48,030
+لأن إيش معنى contradiction؟ أشرح مرة ثانية الكلام
+
+419
+00:29:48,030 --> 00:29:50,530
+اللي حكيته بشكل عام هنا ما زال فيه contradiction
+
+420
+00:29:50,530 --> 00:29:55,090
+إذا في واحدة من واحد لـ اتناش .. من واحد لـ 
+
+421
+00:29:55,090 --> 00:29:59,830
+أحدها غلط تمام؟ طبعًا أنا واضح من واحد لتلاتة مقطع
+
+422
+00:29:59,830 --> 00:30:04,360
+إذا مش صحيح يكون غلط من خمسة إلى كله هينجح دليل
+
+423
+00:30:04,360 --> 00:30:07,520
+إذا كان هذا صح تمام المشكلة أربع اللي هيبدأ تقول
+
+424
+00:30:07,520 --> 00:30:10,260
+تبعي أنا قلت نطقها إذا هذه اللي عملت ال
+
+425
+00:30:10,260 --> 00:30:13,220
+contradiction إذا هذه لازم تكون false إذا عكسها هو
+
+426
+00:30:13,220 --> 00:30:16,660
+الـ true واضحة؟ هي هيك الـ .. هيك .. اللي هو فلسفة
+
+427
+00:30:16,660 --> 00:30:20,120
+الموضوع هيك الشرح لكن بشكل عام الش القاعدة بشكلها
+
+428
+00:30:20,120 --> 00:30:23,200
+المجرد ابنن في المطلوب أول ما نوصل لـ contradiction
+
+429
+00:30:23,200 --> 00:30:28,220
+انتهى البرهان اللي هو غير المباشر واضح؟ أي سؤال؟
+
+430
+00:30:28,220 --> 00:30:29,520
+نشوف كمان مثال
+
+431
+00:30:33,760 --> 00:30:37,880
+الأخر خطوة قولنا احنا إيش اتفقنا كل اللي قدام هذا
+
+432
+00:30:37,880 --> 00:30:42,500
+true مظبوط الـ B true اللي هو الـ 11 true و 8 true
+
+433
+00:30:42,500 --> 00:30:45,800
+إذا الآن تبعدهم الـ true فالـ conjunction ده لما ما
+
+434
+00:30:45,800 --> 00:30:48,100
+زال أنا عارف two statements is true فالـ
+
+435
+00:30:48,100 --> 00:30:52,420
+conjunction تباعهم بيكون true فدايمًا إيه بقرأ فما
+
+436
+00:30:52,420 --> 00:30:55,600
+زال هذي true و هذي true إذا الآن تبعدهم أيضًا true
+
+437
+00:30:55,600 --> 00:31:01,800
+طبعًا هذا هي contradiction أي سؤال؟ خلينا نشوف كمان
+
+438
+00:31:01,800 --> 00:31:05,720
+مثال give an indirect proof of validity for the
+
+439
+00:31:05,720 --> 00:31:10,840
+following argument في عندنا كمان مثال خلينا نبدأ 
+
+440
+00:31:10,840 --> 00:31:14,980
+الحل هنا أيضًا
+
+441
+00:31:14,980 --> 00:31:24,880
+prove
+
+442
+00:31:24,880 --> 00:31:29,980
+أو solution طبعًا كالعادة هنبدأ بترقيم المواطيات A
+
+443
+00:31:29,980 --> 00:31:44,860
+or BA or B اتنين Not B or D Therefore A or D نبدأ
+
+444
+00:31:44,860 --> 00:31:50,440
+البرهان واحدة واحدة فبجلّي indirect بدي أبدأ بنفل
+
+445
+00:31:50,440 --> 00:31:54,440
+المطلوب فالخطوة الأولى في البرهان الغير مباشر بدنا 
+
+446
+00:31:54,440 --> 00:31:59,340
+ننفي A or D من وين هذا بدنا .. اللي هو .. قولنا
+
+447
+00:31:59,340 --> 00:32:06,520
+إيش؟ خطوة هذه indirect proof indirect proof برهان
+
+448
+00:32:06,520 --> 00:32:13,120
+غير مباشر تمام إيش ممكن نعمل الآن؟ D Morgan's and
+
+449
+00:32:13,120 --> 00:32:15,920
+not D D Morgan's law
+
+450
+00:32:20,620 --> 00:32:25,440
+الآن ممكن نعمل تبسيط بسّطت إثنتين ولا واحدة واضحة؟
+
+451
+00:32:25,440 --> 00:32:30,740
+من بدناها؟ من أربع طبعًا هاد من وين جبناها؟ دي
+
+452
+00:32:30,740 --> 00:32:35,960
+مورجانز من تلاتة تلاتة دي مورجانز اللي جيت من أربع
+
+453
+00:32:35,960 --> 00:32:43,790
+simplification تمام double negation وين؟ واحدة
+
+454
+00:32:43,790 --> 00:32:47,270
+واحدة بنناقش احنا ما فيش مشكلة أي مقترح مستعدين
+
+455
+00:32:47,270 --> 00:32:54,730
+نجربه ونشوف الآن خمسة واحد خمسة و واحد بدينا بي ..
+
+456
+00:32:54,730 --> 00:32:58,430
+بدينا بي .. بدينا بي .. هندور احنا على مين؟ على ا
+
+457
+00:32:58,430 --> 00:33:02,150
+أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو
+
+458
+00:33:02,150 --> 00:33:02,230
+أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو
+
+459
+00:33:02,230 --> 00:33:02,410
+أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو
+
+460
+00:33:02,410 --> 00:33:02,470
+أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو أو
+
+461
+00:33:02,470 --> 00:33:09,990
+أو أو أو أو أو أو أو
+
+462
+00:33:09,990 --> 00:33:15,090
+أو ا
+
+463
+00:33:19,880 --> 00:33:23,160
+إذا احتجناها بناخدها زي تو .. التنتين صح .. بس أنا
+
+464
+00:33:23,160 --> 00:33:25,860
+.. وسألت .. جالوا simplification .. قلتوا من مين
+
+465
+00:33:25,860 --> 00:33:29,260
+آخد؟ جالوا خد نط إيه؟ مشيت معهم .. ولو عدت ..
+
+466
+00:33:29,260 --> 00:33:32,340
+رجعتلها برجعلها .. كله صح .. دائمًا .. كل اللي
+
+467
+00:33:32,340 --> 00:33:35,960
+قدامي صح .. وبرجعله .. برجع .. جت بعد خمس خطوات
+
+468
+00:33:35,960 --> 00:33:38,780
+.. روحت قلت من .. من أربع simplification نط دي صح
+
+469
+00:33:38,780 --> 00:33:42,260
+.. فمش ضروري يعني في نفس الوقت .. واضح؟ تمام .. هل
+
+470
+00:33:42,260 --> 00:33:47,520
+جت بيه واتنين؟ برضه اللي هو فصل منطقي لأنه بيقول
+
+471
+00:33:47,520 --> 00:33:50,820
+بيه is true إذا not بيه is false إذا لازم دي تكون 
+
+472
+00:33:50,820 --> 00:33:55,680
+true فالآن اللي هو سبعة دي من وين جبتها؟ جبتها من
+
+473
+00:33:55,680 --> 00:34:00,260
+ستة واتنين و disjunctive syllogism فصل المنطق
+
+474
+00:34:00,260 --> 00:34:04,180
+تمام؟
+
+475
+00:34:04,180 --> 00:34:10,040
+في حد لجأ contradiction ولا لسه؟ وين؟ لسه لسه ما فيش
+
+476
+00:34:10,040 --> 00:34:14,400
+شيء اه .. اه في أننا الجهة تحتاجنا ممتاز فالآن
+
+477
+00:34:14,400 --> 00:34:18,880
+نعمل simplification من أربع فالآن تمانية اللي هو
+
+478
+00:34:18,880 --> 00:34:23,260
+إيش not D من وين جبناها؟ من أربع و simplification
+
+479
+00:34:23,260 --> 00:34:28,180
+فأنا ممكن أرجع اه الآن D و not D contradiction
+
+480
+00:34:28,180 --> 00:34:35,020
+تسعة D and not D اللي هو من تمانية وسبعة و
+
+481
+00:34:35,020 --> 00:34:35,400
+conjunction
+
+482
+00:34:43,810 --> 00:34:52,230
+أه فطبعًا contradiction وانتهى البرهن فأدي
+
+483
+00:34:52,230 --> 00:34:58,150
+اللي هو البرهان بالتناقض بيبدأ بنفي المطلوب وبينتهي
+
+484
+00:34:58,150 --> 00:35:02,350
+عندما نصل إلى contradiction لشيء ونقيل لشيء ونقيل
+
+485
+00:35:08,360 --> 00:35:11,540
+يعني هنا فيه قدام حل واصل لـ contradiction مختلفة مش
+
+486
+00:35:11,540 --> 00:35:16,440
+شرط كله صح المهم لـ contradiction المهم نصل
+
+487
+00:35:16,440 --> 00:35:21,300
+لـ contradiction إن شاء الله هنعلق عليه مرة ثانية في
+
+488
+00:35:21,300 --> 00:35:27,590
+البرهان الرياضية فالآن هنمر على أو نبدأ بالبرهان
+
+489
+00:35:27,590 --> 00:35:31,370
+الرياضي فاحنا الـ gate أخذنا القاعدة الأساسية أو
+
+490
+00:35:31,370 --> 00:35:36,170
+الكمية الضرورية من المنطق اللي بتمهد لنا وبعد هيك
+
+491
+00:35:36,170 --> 00:35:40,430
+نعتمد عليها ونبني عليها كل اللي هو البرهان
+
+492
+00:35:40,430 --> 00:35:43,850
+الرياضية البرهان الرياضية فالآن بننتقل لـ
+
+493
+00:35:43,850 --> 00:35:53,350
+mathematical proofs البرهان الرياضية تفضلي هدى
+
+494
+00:35:53,350 --> 00:35:59,450
+وهدى صحيح كيف R؟ لأ، ما ينفعش، ما ينفعش، أنت بتعمل إيش
+
+495
+00:35:59,450 --> 00:36:01,430
+أنت الـ Y .. إيش في عندك؟ هذي الـ true .. هذي الـ
+
+496
+00:36:01,430 --> 00:36:04,930
+true فالـ R تبعته بتكون الـ true بس بتفيدك .. إيش
+
+497
+00:36:04,930 --> 00:36:10,190
+بتفيدك؟
+
+498
+00:36:10,190 --> 00:36:15,130
+يعني بين واحدة وبين واحدة تعملي R؟ ما مر عليا هنا
+
+499
+00:36:15,130 --> 00:36:19,050
+بتفيد اه لأن دائمًا احنا نعتبر هدول true فالـ
+
+500
+00:36:19,050 --> 00:36:21,650
+conjunction تبعهم true هيك القاعدة يعني دائمًا أنا
+
+501
+00:36:21,650 --> 00:36:23,730
+إيش بحطه .. لكن هدى true وهدى true مش أو فاش دي
+
+502
+00:36:23,730 --> 00:36:26,470
+على الـ أو .. الآن لأن هدى true وهدى true فالآن
+
+503
+00:36:26,470 --> 00:36:29,390
+تبقى هدهم true فليش ألجأ للـ أو؟ لأ ما فيش داعي إن
+
+504
+00:36:29,390 --> 00:36:31,670
+أنا ألجأ للـ أو لأن أنا عارف إثنتين true فإذا إيش
+
+505
+00:36:31,670 --> 00:36:38,810
+الـ conjunction تبعهم true مش الـ disjunction مش
+
+506
+00:36:38,810 --> 00:36:43,930
+شرط الترتيب بالأرقام المهم إنه أجيبتهم باستخدام
+
+507
+00:36:43,930 --> 00:36:47,710
+هدول بالقانون المناسب لأ لأ هو في الأصل بينهم and
+
+508
+00:36:47,710 --> 00:36:56,610
+صح في الأصل بينهم and فهذه مرور سريع على البرهان
+
+509
+00:36:56,610 --> 00:37:01,320
+المنطقي ننتقل للبب الموضوع تبعنا وهو البرهان
+
+510
+00:37:01,320 --> 00:37:05,760
+الرياضي فطبعًا البرهان مهم لعلماء المنطق ولعلماء
+
+511
+00:37:05,760 --> 00:37:09,480
+الرياضيات وهذا الجزء اللي بيخصنا فالـ proofs are
+
+512
+00:37:09,480 --> 00:37:12,640
+essential in mathematical reasoning because they
+
+513
+00:37:12,640 --> 00:37:15,180
+demonstrate that the conclusions are true طبعًا
+
+514
+00:37:15,180 --> 00:37:19,260
+البرهان مهم جدًا لأنه بيثبت أن الاستنتاج هو صحيح
+
+515
+00:37:19,260 --> 00:37:24,570
+فهذا مهم جدًا أنا بدي قاعدة بدي مقدمات وبصل لنتيجة
+
+516
+00:37:24,570 --> 00:37:27,630
+تب ليش النتيجة صحيحة؟ بدي برهان على إن النتيجة
+
+517
+00:37:27,630 --> 00:37:35,670
+صحيحة بشكل عام، أي تفسير رياضي for a conclusion has
+
+518
+00:37:35,670 --> 00:37:38,970
+no value، ما لهوش أي قيمة إلا إذا كان مدعوم ببرهان
+
+519
+00:37:38,970 --> 00:37:44,450
+رياضي، أي تعليق رياضي، أي قاعدة، حقيقة، إذا ما فيش
+
+520
+00:37:44,450 --> 00:37:48,110
+برهان، بيكون ما لهوش قيمة، فلابد إن الناس يكون
+
+521
+00:37:48,110 --> 00:37:51,830
+معتمد على برهان مقبول، مقبول من يحكم إنه مقبول أو
+
+522
+00:37:51,830 --> 00:37:55,450
+مش مقبول؟ قواعد المنطق، المنطق اللي هو اللي يعتمد
+
+523
+00:37:55,450 --> 00:38:02,210
+عليها بهذا الشكل ما هو البرهان؟ هو عبارة عن تبرير
+
+524
+00:38:02,210 --> 00:38:07,250
+كامل على صحة تقرير معين اللي بيسموه نظرية أو
+
+525
+00:38:07,250 --> 00:38:15,690
+النتيجة فالبرهان هو تبرير أو إثبات لصحة تقرير معين
+
+526
+00:38:15,690 --> 00:38:17,290
+فده هو البرهان
+
+527
+00:38:20,370 --> 00:38:24,930
+بشكل عام، إيش بتبدأ النظرية؟ في أنها مُعطى أو
+
+528
+00:38:24,930 --> 00:38:29,950
+البرهان، مُعطى، بتكون مُعطى في النظرية أو في
+
+529
+00:38:29,950 --> 00:38:33,370
+أشياء عارفينها سابقًا من استخدامها، لأن في حقائق،
+
+530
+00:38:33,370 --> 00:38:36,510
+لو عشان هيك الرياضيات، تعلم تراكم، يعني أحيانًا،
+
+531
+00:38:36,510 --> 00:38:39,620
+يعني وأنا ببرهن، ممكن أستخدم فيفا غورف من الضروري
+
+532
+00:38:39,620 --> 00:38:42,420
+يكون في كل نظرية كتبت في ثغر هذه صارت نظرية معروفة
+
+533
+00:38:42,420 --> 00:38:47,680
+ممكن استخدامها في أي مكان and proceeds by correct
+
+534
+00:38:47,680 --> 00:38:51,480
+reasoning باستخدام قواعد التفكير الاستدلالي
+
+535
+00:38:51,480 --> 00:38:56,420
+الصحيحة لوين لـ conclusion أو اللي هي التقرير
+
+536
+00:38:56,420 --> 00:38:59,920
+اللي احنا بندعي صحته اللي هو claimed statement
+
+537
+00:38:59,920 --> 00:39:03,040
+بندعي صحته طبعًا ليش بيكون احنا بنقول ادعاء لحد ما
+
+538
+00:39:03,040 --> 00:39:06,800
+نبرهن بنصير احنا اتفقنا إنه صحيح لأنه لسه كان
+
+539
+00:39:06,800 --> 00:39:12,470
+ادعاء طبعًا يعتبر اللي هو البرهان أو عبارة عن
+
+540
+00:39:12,470 --> 00:39:17,290
+argument بلغة المنطق طبعًا وفي كل خطوة في عندنا
+
+541
+00:39:17,290 --> 00:39:21,810
+تبرير منطقي ليش كل خطوة من الخطوات ليش كل تقرير
+
+542
+00:39:21,810 --> 00:39:24,950
+بيجي من اللي جابه وباستخدام القواعد المعروفة
+
+543
+00:39:24,950 --> 00:39:28,830
+والمتفق عليها إن كل statement صحيحة وكل خطوة
+
+544
+00:39:28,830 --> 00:39:33,550
+صحيحة طبقًا لمن؟ لقواعد الرياضيات ونظريات
+
+545
+00:39:33,550 --> 00:39:37,310
+الرياضيات اللي هي متفق على صحتها أو مبرهنة بشكل
+
+546
+00:39:37,310 --> 00:39:43,140
+مسبق طبعًا أنا الكلام اللي بدي أحكيه الآن هو كلام
+
+547
+00:39:43,140 --> 00:39:49,140
+يعني معظمه إنشائي لكنه يعتبر دليل دليل هيفيدنا
+
+548
+00:39:49,140 --> 00:39:52,420
+أكيد في هذا المصحح لأنه احنا لسه مبتدئين وممكن
+
+549
+00:39:52,420 --> 00:39:57,560
+يفيدنا في دراستنا المسبقة فاحنا هندي كلام عام طبعًا
+
+550
+00:39:57,560 --> 00:40:01,420
+عرفنا إيش هو البرهان هنشوف قواعد البرهان كيف نبدأ
+
+551
+00:40:01,420 --> 00:40:06,040
+البرهان كيف ننهي البرهان ما هي أنواع البرهان
+
+552
+00:40:06,040 --> 00:40:10,390
+المستخدمة وهكذا فهذا الكلام ضروري يكون معناه دليل
+
+553
+00:40:10,390 --> 00:40:13,930
+نرجع له في هذا المصاق وأتوقع إنه ممكن يكون مفيد في
+
+554
+00:40:13,930 --> 00:40:17,730
+مصاقات رياضية أخرى فطبعًا أول شيء قواعد البرهان
+
+555
+00:40:17,730 --> 00:40:21,090
+الأساسية basic approved rules ما هي قواعد البرهان
+
+556
+00:40:21,090 --> 00:40:24,210
+بشكل عام إيش ممكن أعمل بالبرهان وأنا مطمئن إن هذا
+
+557
+00:40:24,210 --> 00:40:27,830
+الخطوة صحيحة اه فبقول ليه في عندنا أربع قواعد
+
+558
+00:40:27,830 --> 00:40:32,330
+بتدينا اللي هو إرشاد حوالين إيش اللي ممكن أنا
+
+559
+00:40:32,330 --> 00:40:36,930
+أعمله كتقارير ممكن أستخدمها في البرهان وأنا مطمئن
+
+560
+00:40:36,930 --> 00:40:43,450
+إنه هذه الخطوة أو هذه العملية عملية صحيحة أول قاعدة 
+
+561
+00:40:43,450 --> 00:40:47,750
+بيقول لي at any time state an assumption ممكن في 
+
+562
+00:40:47,750 --> 00:40:51,930
+أي خطوة ايش آخذ الفرضية المعطيات ممكن استخدمها an
+
+563
+00:40:51,930 --> 00:40:56,690
+axiom مسلمة .. مسلمة يعني أو نظرية or a wisely 
+**approved** result
+
+564
+00:40:56,690 --> 00:41:01,350
+approved result فاحنا ممكن نستخدم المعطيات
+
+565
+00:41:01,350 --> 00:41:06,910
+المسلمات والنظريات المبرهنة سابقاً فدي قاعدة عامة
+
+566
+00:41:06,910 --> 00:41:12,660
+شيء أنا متفق عليه أنه مسلمة زي نظرية في عندي فرضية
+
+567
+00:41:12,660 --> 00:41:15,560
+معطية برضه ايش ب .. ب .. ب .. بعتبرها صحيحة
+
+568
+00:41:15,560 --> 00:41:18,160
+المعطلة ده بيعتبرها صحيحة طيب في نظرية سابقة
+
+569
+00:41:18,160 --> 00:41:21,980
+مبرهنة بقدر استخدمها وجهة ما بده بدون أي مشاكل
+
+570
+00:41:21,980 --> 00:41:26,450
+فهذه القاعدة الأولى القاعدة الثانية بيسموها قاعدة
+
+571
+00:41:26,450 --> 00:41:30,370
+اللي هو الإحلال replacement ممكن أستبدل شيء بشيء
+
+572
+00:41:30,370 --> 00:41:34,110
+بيقول لي في أي زمان ممكن ا state a statement
+
+573
+00:41:34,110 --> 00:41:37,310
+equivalent to any statement earlier in the proof
+
+574
+00:41:37,310 --> 00:41:40,330
+أنا عندي statement معينة خطوة طبعا زي ما اتفقنا كل 
+
+575
+00:41:40,330 --> 00:41:43,720
+واحدة أنا بعتقدها true طب هاد ال statement بصورتها
+
+576
+00:41:43,720 --> 00:41:47,900
+الحالية مش فيداني ممكن أعيد كتابتها بصورة مكافئة
+
+577
+00:41:47,900 --> 00:41:50,960
+منطقيا equivalent وبدون أي مشاكل هاد دايما بقدر
+
+578
+00:41:50,960 --> 00:41:54,840
+أعمله عملية استبدال ل statement ب statement مكافئة
+
+579
+00:41:54,840 --> 00:41:58,800
+منطقيا مسموح فيه في أي وقت وفي أي زمان وفي أي 
+
+580
+00:41:58,800 --> 00:42:02,120
+مكان من البرهان فهي القاعدة الثانية إذا القاعدة 
+
+581
+00:42:02,120 --> 00:42:06,400
+الأولى استخدام المعطيات أو النظريات اللي سبق
+
+582
+00:42:06,400 --> 00:42:10,730
+برهانها والمسلمات صحيحة استبدال statement ب
+
+583
+00:42:10,730 --> 00:42:14,070
+statement تكافئها منطقيا ما يهاش برضه مسموح في كل
+
+584
+00:42:14,070 --> 00:42:17,690
+مكان وفي كل زمان، ده قاعدة، فدول احنا إيهاش أمور
+
+585
+00:42:17,690 --> 00:42:19,890
+ممكن نعملها، هم بيقولوا احنا مطمئنين انك شوفنا صح
+
+586
+00:42:21,310 --> 00:42:27,050
+The tautology rule قاعدة التقرير المطلق الصواب
+
+587
+00:42:27,050 --> 00:42:30,310
+بيقول برضه في أي زمان state a sentence whose
+
+588
+00:42:30,310 --> 00:42:33,490
+simple translation is a tautology ما زال في عندنا
+
+589
+00:42:33,490 --> 00:42:38,990
+أي statement إذا حولناها لرموز المنطق وطلعت هي
+
+590
+00:42:38,990 --> 00:42:42,190
+دايما مطلقة الصواب برضه ممكن نستخدمها تعتبر كقاعدة
+
+591
+00:42:42,190 --> 00:42:45,750
+قاعدة منطقية يعني هنا قاعدة منطقية يعني الفرق بين
+
+592
+00:42:45,750 --> 00:42:48,610
+تلاتة وواحد تلاقوا واحد بيحكيلي عن نظرية رياضيات
+
+593
+00:42:48,610 --> 00:42:52,250
+قصد ايش سبق استخدامها ببرهان تلاتة بتحدث عن مين
+
+594
+00:42:52,250 --> 00:42:55,890
+عن قواعد المنطق عن قواعد المنطق ممكن نستخدمها
+
+595
+00:42:55,890 --> 00:43:01,740
+القاعدة الرابعة The Modus Ponens Rule قاعدة الـ
+
+596
+00:43:01,740 --> 00:43:05,560
+Modus Ponens اللي هي بتتعمل في جملة شرطية وعرفت
+
+597
+00:43:05,560 --> 00:43:08,980
+أن الشرط صحيح بقدر أستنتج أن جواب الشرط صحيح دائما
+
+598
+00:43:08,980 --> 00:43:12,760
+فبقول لي at any time after B لأن في عندي جملة
+
+599
+00:43:12,760 --> 00:43:19,460
+شرطية P then q وبي and بي then q أبير ما زال زهر
+
+600
+00:43:19,460 --> 00:43:23,100
+ايش معناه التنتين صح بي and بي then q على طول اشوف
+
+601
+00:43:23,100 --> 00:43:27,500
+النتيجة say that q is true فانا في عندي في سطر ما
+
+602
+00:43:27,500 --> 00:43:31,760
+في عندي بي وفي سطر ما في عندي بي then q فإيش ماله
+
+603
+00:43:31,760 --> 00:43:34,800
+على طول بقدر أستنتج therefore q على طول طبعا و
+
+604
+00:43:34,800 --> 00:43:38,220
+خطوة فهذه هيش modus ponens قاعدة منطقية مهمة جدا
+
+605
+00:43:38,440 --> 00:43:41,940
+فهذه بعض القواعد اللي بنستخدمها كثيراً في البرهان
+
+606
+00:43:41,940 --> 00:43:45,440
+ودائماً بنستخدمها ويستخدموها وانتوا مطمئنين ان هذه
+
+607
+00:43:45,440 --> 00:43:50,960
+القواعد ما فيش أي إشكالية في استخدامها طبعا ال
+
+608
+00:43:50,960 --> 00:43:53,720
+modus ponens طبعا بيعتمد على القاعدة المعروفة هذا
+
+609
+00:43:53,720 --> 00:44:05,500
+هي بس هنا للتذكير فيها للتذكير في القاعدة طرق
+
+610
+00:44:05,500 --> 00:44:12,870
+البرهان الرياضي في خمس طرق رئيسية هنتحدث عنها في
+
+611
+00:44:12,870 --> 00:44:17,140
+البرهان الرياضي الطريقة الأولى زي ما احنا طبعا كنا
+
+612
+00:44:17,140 --> 00:44:19,020
+متحدثين عن البرهان المنطقي، الآن متحدثين عن البرهان
+
+613
+00:44:19,020 --> 00:44:23,320
+الرياضي البرهان المباشر the Direct Proof ما هو ال
+
+614
+00:44:23,320 --> 00:44:27,580
+Direct Proof؟ هو بيقول عبارة ال logical step by
+
+615
+00:44:27,580 --> 00:44:31,520
+step خطوة خطوة بشكل منطقي عبارة عن argument زي ما 
+
+616
+00:44:31,520 --> 00:44:35,560
+كنا بنكتب from the given conditions من الشروط أو
+
+617
+00:44:35,560 --> 00:44:39,400
+المعطيات لحد ما نوصل لمن؟ للمطلوب فكيف ال direct
+
+618
+00:44:39,400 --> 00:44:44,440
+proof بيبدأ بالمعطيات وينتهي بالمطلوب مهم جدا
+
+619
+00:44:44,440 --> 00:44:47,480
+هذه الملاحظة هذا بيسموه برهان مباشر
+
+620
+00:44:51,710 --> 00:44:57,470
+النوع الثاني Proof by Exhaustion أو Proof by
+
+621
+00:44:57,470 --> 00:45:00,850
+Case Analysis هذا يمكن ما يمرش على بالمنطق لكن أنا
+
+622
+00:45:00,850 --> 00:45:04,270
+ممر بالرياضي يعني في ايش كيف هذا الكلام أنا عندي 
+
+623
+00:45:04,270 --> 00:45:09,310
+مطلوب معين مش قادر أبرهنه بشكل عام بجزئه إلى أجزاء
+
+624
+00:45:09,310 --> 00:45:13,410
+طبعا عدد محدود finite cases وبقدر ايش كل جزء 
+
+625
+00:45:13,410 --> 00:45:17,070
+أبرهنه على جهة أبرهنه بشكل منفصل فبقول لي في هذه
+
+626
+00:45:17,070 --> 00:45:17,610
+الطريقة 
+
+627
+00:45:25,690 --> 00:45:33,380
+بنبرهن كل واحدة بشكل منفصل النوع الثالث أو الطريقة
+
+628
+00:45:33,380 --> 00:45:37,500
+الثالثة Proof by Contraposition اللي هو المعكوس
+
+629
+00:45:37,500 --> 00:45:41,040
+المكافئ Contraposition اللي احنا شرحناه في
+
+630
+00:45:41,040 --> 00:45:44,320
+Proof of Contrapositive or Contrapositive Proof 
+
+631
+00:45:44,320 --> 00:45:48,220
+طبعا هذا يستخدم مع مين؟ مع الجملة الشرطية مع
+
+632
+00:45:48,220 --> 00:45:51,280
+الجملة الشرطية كيف بنعمل؟ بدل ما نبرهن الجملة
+
+633
+00:45:51,280 --> 00:45:56,270
+الشرطية بنبرهن المكافئ .. المعكوس المكافئ تبعها هذا
+
+634
+00:45:56,270 --> 00:45:59,910
+يعتبر برهان غير مباشر برضه بيسموه برهان غير مباشر
+
+635
+00:45:59,910 --> 00:46:03,750
+لأنه أنا ما برهنتش المطلوب مباشرة وانما برهنت حاجة 
+
+636
+00:46:03,750 --> 00:46:07,490
+مكافئة طبعا بيعتمد على مين؟ أن P then q تكافئ
+
+637
+00:46:07,490 --> 00:46:11,510
+not q then not P فانا بدل ما اقدر اشتغل على P
+
+638
+00:46:11,510 --> 00:46:14,410
+then q بس على المكافئة تبعها فهذه بيسموها Contra
+
+639
+00:46:14,410 --> 00:46:19,520
+positive proof فطبعا it is an indirect proof 
+
+640
+00:46:19,520 --> 00:46:23,660
+بيسموه برهان غير مباشر طبعا أولا نثبت أن not Q
+
+641
+00:46:23,660 --> 00:46:28,710
+then not P is true وبتالي مكافئها أيضا ال true يعني
+
+642
+00:46:28,710 --> 00:46:30,450
+ما فيش فيها contradiction؟ لأ ما فيش فيها 
+
+643
+00:46:30,450 --> 00:46:32,930
+contradiction، هذه الحدود، احنا طبعا شوية هنقولنا
+
+644
+00:46:32,930 --> 00:46:36,890
+هذا بس مرور سريع وإن شاء الله هنطبق عليهم كلهم ال
+
+645
+00:46:36,890 --> 00:46:39,670
+proof by contradiction هذا هو ال indirect proof 
+
+646
+00:46:39,670 --> 00:46:41,970
+تبع المنطقة بيسموه proof by contradiction اللي هو
+
+647
+00:46:41,970 --> 00:46:44,790
+اسم مختلف، اه برضه هذا indirect proof، إذا في 
+
+648
+00:46:44,790 --> 00:46:47,350
+عندنا نوعين من ال indirect proof ال proof اللي هو 
+
+649
+00:46:47,350 --> 00:46:49,770
+by contradiction وby contraposition أو by 
+
+650
+00:46:49,770 --> 00:46:53,520
+contrapositive طبعا هذا هو اللي توي مرينا عليه بال
+
+651
+00:46:53,520 --> 00:46:56,060
+logic ف a proof by contradiction is an indirect
+
+652
+00:46:56,060 --> 00:46:59,720
+proof method طريقة برهان غير مباشرة طبعا عشان 
+
+653
+00:46:59,720 --> 00:47:04,620
+تعتمد تعتمد على ال tautology بي تكافئ not P then 
+
+654
+00:47:04,620 --> 00:47:07,560
+not Q and Q اللي هي نقض النقيد القاعدة اللي بتعتمد
+
+655
+00:47:07,560 --> 00:47:11,800
+عليها بتعتمد على نقض النقيد كيف عملنا احنا مطلوب
+
+656
+00:47:11,800 --> 00:47:15,700
+بيه إذا نفينا ال P بنوصل لتناقض بنوصل لتناقض
+
+657
+00:47:15,700 --> 00:47:18,960
+فهذا بيسموها نقض النقيد طبعا ايش بتبدأ it is to 
+
+658
+00:47:18,960 --> 00:47:22,420
+prove a statement P is true we prove that not 
+
+659
+00:47:22,420 --> 00:47:25,900
+P اللي هو بنبدأ إنه هذا صح وبنوصل لمين؟ لتناقض 
+
+660
+00:47:25,900 --> 00:47:30,910
+وبنوصل لتناقض زي ما توي عملنا في ال logic طبعا زي
+
+661
+00:47:30,910 --> 00:47:34,030
+ما ذكرنا، ايش القاعدة المنطقية اللي يعتمد عليها 
+
+662
+00:47:34,030 --> 00:47:36,830
+هذا الكلام؟ ال logic behind such a proof is that
+
+663
+00:47:36,830 --> 00:47:40,610
+if a statement cannot be false، نحن وصلنا لتناقض 
+
+664
+00:47:40,610 --> 00:47:43,590
+يعني، إنه مستحيل تكون خطأ، إذا ناشي يتكون، هي 
+
+665
+00:47:43,590 --> 00:47:50,200
+صواب، then it must be true، الكلام اللي شرحنا فطبعا 
+
+666
+00:47:50,200 --> 00:47:53,300
+thus to prove by contradiction that a statement P 
+
+667
+00:47:53,300 --> 00:47:58,160
+is true we temporarily assume نفترض جدلا مؤقتا بأن
+
+668
+00:47:58,160 --> 00:48:03,420
+P is false ونصل إلى أن هذا مستحيل إذا نجا الـ P 
+
+669
+00:48:03,420 --> 00:48:03,820
+true
+
+670
+00:48:07,240 --> 00:48:10,980
+النوع الطريقة الخامسة عشان أنهي prove by 
+
+671
+00:48:10,980 --> 00:48:14,040
+mathematical induction البرهان باستخدام الاستقراء 
+
+672
+00:48:14,040 --> 00:48:16,700
+الرياضي وهذا طبعا إن شاء الله هنشرحه بالتفصيل في 
+
+673
+00:48:16,700 --> 00:48:21,060
+ال section القادم طبعا هذا يستخدم لنوع معين من ال
+
+674
+00:48:21,060 --> 00:48:23,600
+statements وهو ال statement تحتوي على ال
+
+675
+00:48:23,600 --> 00:48:28,900
+quantifier for all n P of n for all n P of n طب
+
+676
+00:48:28,900 --> 00:48:33,160
+بتنفع مع أي quantifier؟ لأ هنا ال n بيكون عدد صحيح
+
+677
+00:48:33,470 --> 00:48:36,670
+الـ N بيتكون عدد صحيح بتبدأ من عدد صحيح معين
+
+678
+00:48:36,670 --> 00:48:40,350
+وبتروح للمالا نهاية فبقول لي طبعا هذا بيستخدم
+
+679
+00:48:40,350 --> 00:48:45,110
+على statement على صورة for all N P of N involving
+
+680
+00:48:45,110 --> 00:48:48,610
+integers N greater than or equal to some initial
+
+681
+00:48:48,610 --> 00:48:51,970
+integer N زيهم بتعتمد على ايش؟ أن ال universe ايش 
+
+682
+00:48:51,970 --> 00:48:54,350
+بيكون ال universe؟ مجموعة من العدد الصحيحة بتبدأ
+
+683
+00:48:54,350 --> 00:48:57,670
+من عدد صحيح معين إلى مالا نهاية إلى مالا نهاية
+
+684
+00:48:59,130 --> 00:49:02,410
+تمام فهذه الطرق الخامسة طبعا احنا هنا ما جينااش
+
+685
+00:49:02,410 --> 00:49:05,830
+نحفظهم وانما بس بنمر عليهم ولما نستخدمهم بنقول 
+
+686
+00:49:05,830 --> 00:49:08,630
+احنا استخدمنا هذه الطريقة وهكذا نوقف هنا إن شاء
+
+687
+00:49:08,630 --> 00:49:08,690
+الله 
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/NMvqONpuXs4_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/NMvqONpuXs4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6326416ffb606b8d9500af923b5a4d48beb0d322
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/NMvqONpuXs4_raw.srt
@@ -0,0 +1,2564 @@
+1
+00:00:21,830 --> 00:00:26,270
+بسم الله الرحمن الرحيم نواصل مع ال cardinal number
+
+2
+00:00:26,270 --> 00:00:31,330
+وكنا في المحاضرة الأخيرة بنتحدث عن ضرب ال cardinal
+
+3
+00:00:31,330 --> 00:00:35,490
+number فاحنا عرفنا عملتين حتى الآن عرفنا الجمع و
+
+4
+00:00:35,490 --> 00:00:40,290
+الضرب نعيد على السريع عشان لو في عندي two cardinal
+
+5
+00:00:40,290 --> 00:00:44,130
+number a و b بدي أجيب a زائد b مطلوب مني أجيب
+
+6
+00:00:44,130 --> 00:00:47,750
+مجموعة ال cardinal تلها a و مجموعة ال cardinal
+
+7
+00:00:47,750 --> 00:00:53,600
+تلها bو تقطحهم يساوي فاي فبكون a زائد b بيساوي ال
+
+8
+00:00:53,600 --> 00:01:01,380
+cardinality لمن؟ للاتحاد هذه واحدة عشان اجيب الدرب
+
+9
+00:01:01,380 --> 00:01:08,990
+a في b بدي مجموعتينبغض النظر تقطحهم في أو مش في
+
+10
+00:01:08,990 --> 00:01:13,070
+بيفرقش كتير فبصير عندنا a في b ليس الا ال
+
+11
+00:01:13,070 --> 00:01:17,750
+cardinality لل a Cartesian ال b فدول احنا
+
+12
+00:01:17,750 --> 00:01:21,930
+الموضوعين اللي درسناهم وشوفنا انه هذا التعريفات
+
+13
+00:01:21,930 --> 00:01:25,430
+تعريفات علمية صحيحة دايما بقدر اجيب المجموعات
+
+14
+00:01:25,430 --> 00:01:30,560
+المطلوبةودايماً هذا لا يعتمد لو شخصين مختلفين
+
+15
+00:01:30,560 --> 00:01:33,840
+جابوا مجموعات مختلفة بس نفس الشروط الجواب ما
+
+16
+00:01:33,840 --> 00:01:37,820
+بتغيرش فإذا هذا تعريف علمي موضوعي لا يعتمد على
+
+17
+00:01:37,820 --> 00:01:43,020
+الإنسان مش شخصي مش و يتنظر لأ بيعتمد بشكل عام على
+
+18
+00:01:43,020 --> 00:01:47,040
+الأمور العلمية فقط بشكل مجرد فيمكن حلينا بعض
+
+19
+00:01:47,040 --> 00:01:51,730
+الأمثلة الآن وصلنا لمثال رقم تلاتةخاصية مهمة من
+
+20
+00:01:51,730 --> 00:01:57,830
+خواص الأعداد الحقيقية تتوفر أيضًا لـ Cardinal
+
+21
+00:01:57,830 --> 00:02:01,870
+Number طبعًا هذه خاصية مهمة من خواص الأعداد
+
+22
+00:02:01,870 --> 00:02:05,270
+الحقيقية إنه إذا حصل ضرب عددين بيساوي صفر على
+
+23
+00:02:05,270 --> 00:02:09,650
+الأقل واحد بيهم بيساوي صفر وهذه الخاصية هي مفتاح
+
+24
+00:02:09,650 --> 00:02:13,730
+لحل كثير من المعادلات نحولها لمعادلة صفرية ليش؟
+
+25
+00:02:13,730 --> 00:02:17,090
+عشان نحل اللي نقدر نعمل بعد الشكل طبعًا هذا الكلام
+
+26
+00:02:17,090 --> 00:02:21,810
+مش متوفر في المصفوفاتبقدر ألاقي مصفوفتين ولا واحدة
+
+27
+00:02:21,810 --> 00:02:24,870
+فيهم مصفوفة صفرية وحاصل ضرب بيساوي صفر، فالأمر مش
+
+28
+00:02:24,870 --> 00:02:28,730
+automatic أنه إذا حاصل ضرب مقدارين بيساوي صفر فعلى
+
+29
+00:02:28,730 --> 00:02:31,250
+الأقل واحد فيهم بيساوي صفر، لأ، في العدادة
+
+30
+00:02:31,250 --> 00:02:35,430
+الحقيقية صحيح، في المصفوفات غير صحيح، في ال
+
+31
+00:02:35,430 --> 00:02:37,850
+cardinal number أيضا صحيح، في ال cardinal number
+
+32
+00:02:37,850 --> 00:02:40,620
+صحيحفهنشوف كيف نثبتها بالنسبة للـ Cardinal Number
+
+33
+00:02:40,620 --> 00:02:44,780
+فهنا بدنا نتعلم إنه مش كل شيء إحنا نعممه بسهولة،
+
+34
+00:02:44,780 --> 00:02:48,640
+إحنا متعودين إنه الجامع إبدالي، فكل عملية وانما
+
+35
+00:02:48,640 --> 00:02:51,800
+بفكر إنه إبدال، أنا ببدله زي ما بدي، لأ، في عمليات
+
+36
+00:02:51,800 --> 00:02:54,730
+إبدالية، عمليات غير إبدالية في الرياضياتو أثناء
+
+37
+00:02:54,730 --> 00:02:57,110
+دراستنا ان شاء الله هنشوف هذه الأمور طبعا احنا فيه
+
+38
+00:02:57,110 --> 00:03:00,490
+مثال برضه مشهور ضرب المصفات غير إبدالي ال
+
+39
+00:03:00,490 --> 00:03:03,670
+composition للدوال غير إبدالي فالقضية دايما احنا
+
+40
+00:03:03,670 --> 00:03:06,250
+عشان هيك الرياضات تدرس هذه الأمور تعملها نظريات و
+
+41
+00:03:06,250 --> 00:03:09,430
+تثبتها عشان نشوف مسموح استخدامها أو غير مسموح
+
+42
+00:03:09,430 --> 00:03:15,980
+خليني أشوف حل هذا المثالفهذا المثال رقم 3 طبعا إذا
+
+43
+00:03:15,980 --> 00:03:20,560
+بدنا نلخصه بقول ليه إذا كان كله cardinal number XY
+
+44
+00:03:20,560 --> 00:03:27,260
+تساوي 0 implies X تساوي 0 أو Y تساوي 0 طبعا كله
+
+45
+00:03:27,260 --> 00:03:29,780
+cardinal number فهذا هو المطلوب ونحط على انت
+
+46
+00:03:29,780 --> 00:03:32,980
+استفهام عشان القاري يعرف إنه احنا بنعيد صياغة
+
+47
+00:03:32,980 --> 00:03:37,180
+السؤال فطبعا كالعادة نفترض إن هذا الكلام صحيح
+
+48
+00:03:37,180 --> 00:03:44,370
+assume XY تساوي 0عشان أقدر أشتغل سياستنا اطلاعها
+
+49
+00:03:44,370 --> 00:03:47,610
+بنجيه بنحول من اللي هو لغة ال cardinal numbers
+
+50
+00:03:47,610 --> 00:03:56,390
+لللغة المجموعة اه فالان نقوله ايش let XY be sets
+
+51
+00:03:56,390 --> 00:04:07,130
+such that ال cardinality لل X تساوي small x and ال
+
+52
+00:04:07,130 --> 00:04:11,700
+cardinalityY تساوي small y
+
+53
+00:04:19,400 --> 00:04:23,360
+بتساوي small y تمام اه خلينا احنا ايش بدنا نثبت
+
+54
+00:04:23,360 --> 00:04:26,380
+بدنا نثبت انه يا اما x small x بتساوي 0 او y
+
+55
+00:04:26,380 --> 00:04:30,340
+بتساوي 0 يعني بنثبت يا اما capital X بتساوي فاي او
+
+56
+00:04:30,340 --> 00:04:33,900
+capital Y تساوي فاي فلو بدنا نعيد سياقة السؤال ان
+
+57
+00:04:33,900 --> 00:04:37,060
+هذا الكلام صحيح فهذا معناته ما زال x y بتساوي 0
+
+58
+00:04:37,060 --> 00:04:41,400
+اذا ان ال cardinality ل X cross Y بتساوي صفر فالان
+
+59
+00:04:41,400 --> 00:04:49,590
+nowXY ليست إلا الـ cardinality للـ X across الـ Y
+
+60
+00:04:49,590 --> 00:04:58,650
+فبالتالي thus XY تساوي 0 implies ال cardinality لل
+
+61
+00:04:58,650 --> 00:05:03,650
+X cross ال Y تساوي 0 طبعا هذا if and only if X
+
+62
+00:05:03,650 --> 00:05:10,000
+cross ال Y تساوي 5فانا الآن المطلوب أثبت أنه يا
+
+63
+00:05:10,000 --> 00:05:13,380
+إما X بتساوي فاي يا capital Y بتساوي فاي هيك اتحول
+
+64
+00:05:13,380 --> 00:05:19,440
+السؤال بال indirect على طول فالآن أقول له assume
+
+65
+00:05:19,440 --> 00:05:24,980
+طبعا هنا فإذا إحنا إيش صار بدنا نكتب we have to
+
+66
+00:05:24,980 --> 00:05:33,040
+prove that X تساوي فاي or capital Y تساوي فاي
+
+67
+00:05:33,040 --> 00:05:40,880
+فهنعملها بإيش indirect proof assumeX لا تساوي في و
+
+68
+00:05:40,880 --> 00:05:46,900
+Y لا تساوي في indirect proof شوفت الارثة كيف صارت
+
+69
+00:05:46,900 --> 00:05:54,520
+او proof by contradiction proof by contradiction
+
+70
+00:05:54,520 --> 00:06:02,220
+اي سؤالتبعين هذه كلها أمور مبادئ أساسية إذا في أي
+
+71
+00:06:02,220 --> 00:06:06,760
+استفسار في أي نقطة مستغربينها مش واضحة بنائي
+
+72
+00:06:06,760 --> 00:06:10,700
+فطبعاً هي كانت اللي هي P or Q بدنا نثبت في إيش
+
+73
+00:06:10,700 --> 00:06:15,580
+قلنا له ا assume not P or Q اللي بتكافي not P and
+
+74
+00:06:15,580 --> 00:06:23,100
+not Q فهنا بدل ما كانت X تساوي في أو Y تساوي في
+
+75
+00:06:24,010 --> 00:06:28,770
+عملنا لها negation إيش صارت؟ X لا تساوي فيه و Y لا
+
+76
+00:06:28,770 --> 00:06:32,070
+تساوي فيه تمام إيش معناة X لا تساوي فيه؟ فيها أقل
+
+77
+00:06:32,070 --> 00:06:43,350
+أنصر هناك X مستخدمة A تنتمي لل X و B تنتمي لل Yلأ
+
+78
+00:06:43,350 --> 00:06:46,470
+لجأت عنصر في مجموعتين بيقول بيكون الزوج المرتب في
+
+79
+00:06:46,470 --> 00:06:52,370
+الكارة C فده implies A B تنتمي لل X across Y طب
+
+80
+00:06:52,370 --> 00:06:56,810
+هداش معناته لا يساوي في فده مناد X cross Y لا
+
+81
+00:06:56,810 --> 00:07:01,870
+تساوي في Contradiction خليها
+
+82
+00:07:01,870 --> 00:07:06,310
+ده Contradiction
+
+83
+00:07:10,720 --> 00:07:19,260
+فإذا انتهت العملية وخلصنا thus x تساوي 5 او y
+
+84
+00:07:19,260 --> 00:07:24,540
+تساوي 5 وهذا يؤدي إلى small x اللي هي ال
+
+85
+00:07:24,540 --> 00:07:29,700
+cardinality للcapital X تساوي 0 او small y اللي هي
+
+86
+00:07:29,700 --> 00:07:36,130
+ال cardinality للcapital Y تساوي 0 وهو المطلوبفمرة
+
+87
+00:07:36,130 --> 00:07:40,790
+تانية استفدنا من معلوماتنا عن المجموعات ونجيب
+
+88
+00:07:40,790 --> 00:07:44,910
+معلومة عن الـ cardinal numbers فإذا هذا اتحول
+
+89
+00:07:44,910 --> 00:07:49,390
+السؤال من إنه الـ cardinal X Y تسوى زره ك cardinal
+
+90
+00:07:49,390 --> 00:07:52,310
+number implies X تسوى زره أو Y تسوى زره إلى السؤال
+
+91
+00:07:52,310 --> 00:07:55,630
+إذا كانت X الـ Cartesian product مع الـ Y بتسوى
+
+92
+00:07:55,630 --> 00:07:59,690
+فاي فimplies X تسوى فاي أو Y تسوى فاي وهذا يخلن
+
+93
+00:07:59,690 --> 00:08:02,490
+السؤال من هنا حتى ما موجود في التمرين فبنثبته بكل
+
+94
+00:08:02,490 --> 00:08:11,850
+سهولةأي سؤالنشوف مثال آخر مثال الرابع قالت XY and
+
+95
+00:08:11,850 --> 00:08:16,770
+Z be cardinal numbers prove that إذا كانت الـ X
+
+96
+00:08:16,770 --> 00:08:21,730
+سوى Y ضربنا الطرفين بـ Z تتغيرش، طبعا هذا معروف
+
+97
+00:08:21,730 --> 00:08:25,170
+بالـ real numbers برضه هنا نحاول نتحرر مش احنا على
+
+98
+00:08:25,170 --> 00:08:27,570
+طول ما دي إيش إيش إيش اللي جيبناها جديد، هذا
+
+99
+00:08:27,570 --> 00:08:30,590
+cardinal numbers لسه بنحاول نثبت هذه الخواص اللي
+
+100
+00:08:30,590 --> 00:08:34,010
+احنا متعودين عليها للأعداد الحقيقية هل تستمر مع ال
+
+101
+00:08:34,010 --> 00:08:37,770
+cardinal number أو لا تستمرفبقولي ان انا بتستمر لو
+
+102
+00:08:37,770 --> 00:08:42,430
+انا عندي طرفين متساويين ضربت الطرفين بنفس المقدار
+
+103
+00:08:42,430 --> 00:08:47,190
+Z بحافظ على التساوي بحافظ على التساوي نشوف الحل
+
+104
+00:08:47,190 --> 00:08:54,310
+فهذا المثال الرابع طبعا نعيد سياقته ان X تساوي Y
+
+105
+00:08:54,310 --> 00:08:59,930
+implies X في Z تساوي Y في Z هذا المطلوب solution
+
+106
+00:09:00,540 --> 00:09:05,500
+طبعا كالعادة بدي أجيب مجموعات لت كابيتال X كابيتال
+
+107
+00:09:05,500 --> 00:09:15,280
+Y and كابيتال Z بيه six such that cardinality
+
+108
+00:09:15,280 --> 00:09:21,700
+لكابيتال X تساوي small x كارديناليتي لكابيتال Y
+
+109
+00:09:21,700 --> 00:09:27,200
+تساوي small y and كارديناليتي لكابيتال Z تساوي
+
+110
+00:09:27,200 --> 00:09:27,880
+small z
+
+111
+00:09:32,670 --> 00:09:35,490
+نعيد صياغة السؤال ونشوف احنا ايش اللي بدنا ياه
+
+112
+00:09:35,490 --> 00:09:40,270
+نحاوله من لغة ال cardinal number للغة المجموعة انا
+
+113
+00:09:40,270 --> 00:09:46,610
+ايش عندي معلومات معلومات ان x تساوي y فالان now x
+
+114
+00:09:46,610 --> 00:09:53,270
+تساوي y ايش معناته ان ال cardinality لل x تساوي ال
+
+115
+00:09:53,270 --> 00:09:59,590
+cardinality لل yيعني X تكافئ الـ Y صح صح مايهاش ..
+
+116
+00:09:59,590 --> 00:10:02,250
+اللي هي symmetric relation فإذا أنا ده تكافئ و أنا
+
+117
+00:10:02,250 --> 00:10:05,990
+ده واحد فعلينا معلومة مهمة جدا بدنا نحاول نستفيد
+
+118
+00:10:05,990 --> 00:10:14,090
+منها طب احنا إيش بدنا نثبت؟ we want to prove XZ
+
+119
+00:10:14,090 --> 00:10:17,470
+تساوي YZ بمعنى
+
+120
+00:10:19,340 --> 00:10:24,220
+إن الـ Cardinality للـ X cross Z تساوي الـ
+
+121
+00:10:24,220 --> 00:10:29,680
+Cardinality للـ Y cross Z وده إيش معناته؟ بدي أثبت
+
+122
+00:10:29,680 --> 00:10:41,340
+إن الـ Y تكافئ Thus, we have to prove X cross Z
+
+123
+00:10:41,340 --> 00:10:44,540
+تكافئ Y cross Z
+
+124
+00:10:49,310 --> 00:10:54,490
+فهنا هذا التحويل المفروض يكون بسيط وانتعود عليه
+
+125
+00:10:54,490 --> 00:10:58,390
+كلنا لأنه زي ما تشايفين بهذه البساطة في الجامعة في
+
+126
+00:10:58,390 --> 00:11:01,490
+الدرب وحنشوف ان شاء الله في ال section الأخير في
+
+127
+00:11:01,490 --> 00:11:04,390
+الاصوات كمان نفس القضية انا بديني cardinal number
+
+128
+00:11:04,390 --> 00:11:07,830
+بجيب المجموعات وبحول السؤال من لغة ال cardinal
+
+129
+00:11:07,830 --> 00:11:10,950
+number إلى لغة المجموعات طبعا هذا بديني اللي هو
+
+130
+00:11:10,950 --> 00:11:13,310
+إمكانيات أوسع لأنه انا عندي كتير معلومات عن
+
+131
+00:11:13,310 --> 00:11:16,030
+المجموعات وعن التكافة وهذه الأمور chapter 5
+
+132
+00:11:16,030 --> 00:11:20,260
+وchapter 3 بقدر إيش استعين بيهم ممتازبدنا ندور على
+
+133
+00:11:20,260 --> 00:11:26,620
+bijection من X across الـ Z لـ Y across الـ Z طبعا
+
+134
+00:11:26,620 --> 00:11:29,960
+مش هنجيب من ال calculus زي ما اتفقنا لإن المجموعات
+
+135
+00:11:29,960 --> 00:11:33,160
+مش عارفين إيش عناصرهم فهندور في المعطيات ممكن
+
+136
+00:11:33,160 --> 00:11:40,300
+يساعدنا فيه في المعطيات نعم فالأن ناو او خلّيني
+
+137
+00:11:40,300 --> 00:11:48,690
+أكتر نكرر since X تكافئ ال YThere exists a
+
+138
+00:11:48,690 --> 00:11:52,850
+bijection نسميها مثلا G من X ل Y لأن أنا بدور على
+
+139
+00:11:52,850 --> 00:12:00,150
+F أه في غيرهم؟ لأ إذا دلوقتي نحاول نعرف هنعرف let
+
+140
+00:12:00,150 --> 00:12:12,540
+F من X across الـ Z إلى Y across الـ Z be givenby
+
+141
+00:12:12,540 --> 00:12:18,140
+given by نحاول نرسم صورة ممكن تساعدنا شوفوا إحنا
+
+142
+00:12:18,140 --> 00:12:25,280
+إيش عندنا في عندنا X تكافئ ال Y وفي عندنا مجموعة
+
+143
+00:12:25,280 --> 00:12:29,740
+نفسها Z دفناها على الطرفين بس بالضرب ال Cartesian
+
+144
+00:12:29,740 --> 00:12:36,400
+productفاضفناها على الطرفين فطبعا مين علاقة X مع Y
+
+145
+00:12:36,400 --> 00:12:41,640
+مين بي .. بي .. اللي هو بيوفرليها الـG الـG بتديني
+
+146
+00:12:41,640 --> 00:12:45,520
+التكافئة طب مين Z مع Z؟ الـIdentity ولا لأ لأنه
+
+147
+00:12:45,520 --> 00:12:49,240
+نفسها واضحة؟ اه فطبعا هذه بتشبه لما أثبتنا ان X
+
+148
+00:12:49,240 --> 00:12:54,300
+ناقص Yتكافئ Y ناقص X implies X تكافئ Y لأنه قلنا
+
+149
+00:12:54,300 --> 00:12:57,360
+أياش المشترك و أياش التقاطع و هنا نفس الشيء بس
+
+150
+00:12:57,360 --> 00:13:01,420
+بنحاول الأمور مش اتحاد فيه كارتيسيا فيه كارتيسيا
+
+151
+00:13:01,420 --> 00:13:11,700
+لذلك هأعرفها بشكل التالي F of A C إيش تساوي G of A
+
+152
+00:13:11,700 --> 00:13:19,540
+و C فمين اللي بنقول أي ال A شوفوا نعمل الصورةهي
+
+153
+00:13:19,540 --> 00:13:25,680
+عندي A في الـ X وعندي C في الـ Z بدا نقولهم لها
+
+154
+00:13:25,680 --> 00:13:31,020
+مين منجل من A ل Y؟ الـ G صح و الـ C خليها زي ما هي
+
+155
+00:13:31,020 --> 00:13:36,800
+واضحة؟ واضحة ولا مش واضحة؟ تمام طيب هذا انا ممكن
+
+156
+00:13:36,800 --> 00:13:39,600
+يكون تخميني او تفكيري بدا أتأكد منه ايش بدي اعمل
+
+157
+00:13:39,600 --> 00:13:43,500
+بدي أثبت ان هي one to one and on تشوففهذا دايما
+
+158
+00:13:43,500 --> 00:13:46,740
+عشان هيك لازم نشتغل بشكل كامل عشان نعرف أنه
+
+159
+00:13:46,740 --> 00:13:51,520
+تخميننا تصميمنا للدالة صحيح لأنه مش دايما و مش
+
+160
+00:13:51,520 --> 00:13:54,680
+هتيجي من أول مرة واحدة زي ما حكينا في أشياء كتير
+
+161
+00:13:54,680 --> 00:13:58,360
+بتيجي مع المحاولات و أحيانا كتير المحاولات القاطعة
+
+162
+00:13:58,770 --> 00:14:00,830
+بتقولنا إيه السبعية ده، الكلام ده ممكن يتقربنا،
+
+163
+00:14:00,830 --> 00:14:03,590
+نشوف وين الخلل وين اللي ما خليهاش one to one وين
+
+164
+00:14:03,590 --> 00:14:06,590
+اللي خليها خارج الدمية، بدنا ننتبه زي هذا، إن
+
+165
+00:14:06,590 --> 00:14:10,290
+هالـG هذي وفعلا هل هدولة في الـY زد؟ نعم، الـC في
+
+166
+00:14:10,290 --> 00:14:13,070
+الـZ في الـZ طيب، و الـA في الـX، وين الـG of A
+
+167
+00:14:13,070 --> 00:14:16,830
+بتكون؟ في الـY، صح، فعلا، فاحنا في المكان الصحيح،
+
+168
+00:14:16,830 --> 00:14:23,860
+فنبدأ نشوف، واحد F is one to one، إيش نعمل؟ناخد
+
+169
+00:14:23,860 --> 00:14:28,020
+عنصرين من ال domain إيش عناصر ال domain؟ أزواج
+
+170
+00:14:28,020 --> 00:14:37,120
+مرتبة فنسميها A1 C1 and A2 احنا نسميها C؟ لأ C
+
+171
+00:14:37,120 --> 00:14:43,920
+ماشي C2 تنتمي لل X X Z أه خلصنا بداية ال one to
+
+172
+00:14:43,920 --> 00:14:49,600
+one؟ لأ such thatكم مرة السنة كتبينها؟ عدة مرات
+
+173
+00:14:49,600 --> 00:14:53,060
+عشان كله يعرف يبدأ كيف يبدأ ال one-to-one قلنا
+
+174
+00:14:53,060 --> 00:14:58,380
+البداية مهمة جدا F of A2C2 إذا بدأنا صح هذه الخطوة
+
+175
+00:14:58,380 --> 00:15:01,320
+الأولى على الطريق الصحيح نبدأ صح نعرف نبدأ و هذه
+
+176
+00:15:01,320 --> 00:15:04,340
+البدايات صارت standard مابدأتش تفكير أنا كيف بدي
+
+177
+00:15:04,340 --> 00:15:07,760
+أبدأ أن A subset من B معروف كيف بدي أبدأ one-to
+
+178
+00:15:07,760 --> 00:15:10,760
+-one معروف كيف بدي أبدأ on two معروف مهم جدا هذه
+
+179
+00:15:10,760 --> 00:15:14,570
+البدايات و طبعافي أمور بتكون أنها واضحة بنستخدمها
+
+180
+00:15:14,570 --> 00:15:18,090
+طبعا في تفاصيل أحيانا بتكون أصعب لكن بنبدأ بنعرف
+
+181
+00:15:18,090 --> 00:15:21,710
+إيش نعمل إيش ممكن أعمل أستخدم تعريف الدالة برضه و
+
+182
+00:15:21,710 --> 00:15:24,370
+هذا فكرة كريه إذا الدالة معرفة أستخدم أحاول أبصر
+
+183
+00:15:24,370 --> 00:15:28,450
+أنا عندي هذه المعطيات فهذا على طول إيش F of A1 C1
+
+184
+00:15:28,450 --> 00:15:37,490
+ليس إلا G of A1 C1 بدأ تساوي G of A2 C2 ممتاز
+
+185
+00:15:39,090 --> 00:15:43,030
+في طالب عنده صعوبة في أن تعمل هذا الكلام؟ مفروض لا
+
+186
+00:15:43,030 --> 00:15:46,410
+و لا لا؟ أمر سهل، شايفين؟ أحنا خطوات تتكرر، بس
+
+187
+00:15:46,410 --> 00:15:49,050
+للأمور، أه لأن أنا وين عيني على المطلوب، إيش
+
+188
+00:15:49,050 --> 00:15:55,770
+مطلوب؟ إنه A1 C1 تساوي A2 C2 يعني A1 تساوي A2 و C1
+
+189
+00:15:55,770 --> 00:16:01,090
+تساوي C2، انشوف أزواج مرتبش بيقولّي G of A1 تساوي
+
+190
+00:16:01,090 --> 00:16:07,030
+G of A2 and C1 تساوي C2، هذا مطلوب خلصت منه، طيب
+
+191
+00:16:07,030 --> 00:16:07,890
+هذه ممكن أنا
+
+192
+00:16:10,720 --> 00:16:14,560
+أجشر الـ A1 و أجيل الـ G و أتخلص منها نعم ليش؟
+
+193
+00:16:14,560 --> 00:16:19,640
+لأنها one to one فهذا يؤدي A1 تساوي A2 ليش؟ لأن
+
+194
+00:16:19,640 --> 00:16:23,460
+الـ G is one to one فعلا الـ G one to one نعم هي
+
+195
+00:16:23,460 --> 00:16:27,540
+بيجيكشن برجع الشؤوف مش على كافة يعني مش حفظ لأ
+
+196
+00:16:27,540 --> 00:16:30,180
+بنتأكد المعلومات لأنه يمكن يكون كل عمر غلط طيب
+
+197
+00:16:30,180 --> 00:16:34,900
+فصارت A1 تساوي A2 و C1 تساوي C2 مع بعضش بدوني
+
+198
+00:16:34,900 --> 00:16:47,650
+الزوج المرتب يساوي الزوج المرتبC1 تساوي A2 C2 نقيم
+
+199
+00:16:47,650 --> 00:16:50,770
+شغلنا، ايش اللي عملناه؟ نشوف خلصناه ولا ماخلصناه
+
+200
+00:16:50,770 --> 00:16:55,650
+بدأنا بعنصرين هم أزواج مرتبة لكن هم عنصرين في ال
+
+201
+00:16:55,650 --> 00:17:00,230
+domain صورهم متساوية أثبتنا إن العنصرين متساويين
+
+202
+00:17:00,230 --> 00:17:05,270
+إذا ندالة one to one نكمل and وبالتالي
+
+203
+00:17:07,600 --> 00:17:12,900
+is one to one فهذه بداية ال one to one وهذه
+
+204
+00:17:12,900 --> 00:17:18,220
+النهاية التفاصيل بتصعب أو بتكون سهلة بتختلف من
+
+205
+00:17:18,220 --> 00:17:22,280
+مثال لمثال لكن هذه هي الهيكلية ومفروض نبدأ نشتغل
+
+206
+00:17:22,280 --> 00:17:26,140
+ونشوف الخطوات طبعا في بعض الأمور بتكون مباشرة وفي
+
+207
+00:17:26,140 --> 00:17:29,560
+بعض الأمور بتكون شوية شغل لكن أرجو أنه نبدأ صح
+
+208
+00:17:29,560 --> 00:17:32,880
+نبدأ صح هذه الخطوة الأولى وطبعا وجد ما نقدر نقدر
+
+209
+00:17:32,880 --> 00:17:36,220
+نشتغل نشتغل وإن شاء الله يعني اتوقع إذا بدأنا صح
+
+210
+00:17:36,220 --> 00:17:39,430
+واشتغلناالنسبة الكبيرة من الأسئلة بتنحل وانت تشوف
+
+211
+00:17:39,430 --> 00:17:42,370
+أسئلة الامتحانات السابقة أو أسئلة للكتاب بتنحل بعد
+
+212
+00:17:42,370 --> 00:17:46,430
+الطريقة ولا ما بتنحلش تمام نشوف الخطوة رقم اتنين
+
+213
+00:17:46,430 --> 00:17:53,690
+ال F is unto برضه
+
+214
+00:17:53,690 --> 00:17:59,510
+فيه بداية تقليديةطبعا الانتو الحقيقة فيها طريقتين
+
+215
+00:17:59,510 --> 00:18:02,990
+لكن الطريقة الاكثر استخداما باخد عنصر من المجال
+
+216
+00:18:02,990 --> 00:18:08,590
+المقابل let من عناصر المجال المقابل زوج مرتب في ال
+
+217
+00:18:08,590 --> 00:18:12,510
+Y و في ال Z ايش نسميها مثلا Y مستخدمة خلينا نقول
+
+218
+00:18:12,510 --> 00:18:20,090
+مثلا بي .. ولا نسميها اس اسم مختلفوليكن U و V
+
+219
+00:18:20,090 --> 00:18:27,750
+تنتمي لـ Y across Z وعمل الهامش المشهور ايش بدنا؟
+
+220
+00:18:27,750 --> 00:18:34,470
+بدنا U V تساوي F of A C for some A C في ال X طب هد
+
+221
+00:18:34,470 --> 00:18:40,200
+ايش بتساوي؟ هد بتساوي G of A و Cبتعرف تحلي
+
+222
+00:18:40,200 --> 00:18:45,160
+المعادلة هذه؟ انحلت فبدنا U تساوي G of A و بدنا V
+
+223
+00:18:45,160 --> 00:18:49,160
+تساوي C احنا بندور ع مين؟ بندور ع C و A الـ C
+
+224
+00:18:49,160 --> 00:18:53,420
+انعرفر انا U V يعني أنا بقولك let يعني هدول اللي
+
+225
+00:18:53,420 --> 00:18:57,380
+صاروا معطيها معاك اعطيتك U و V بدك تجيبلي الـ C و
+
+226
+00:18:57,380 --> 00:19:01,080
+A اه الـ C قلت بيساوي V ما الـ V معطية فانت قلتيلي
+
+227
+00:19:01,080 --> 00:19:04,160
+الـ C بيساوي V خلصنا الـ C بدنا نجيب الـ A من وين
+
+228
+00:19:04,160 --> 00:19:10,510
+نجيبها؟من الـ «G inverse» بس بمعنى هو بقية «G
+
+229
+00:19:10,510 --> 00:19:14,350
+inverse» الحل لكن هنكتبها بطريقة مختلفة كيف؟ احنا
+
+230
+00:19:14,350 --> 00:19:19,430
+عندنا ال «U» في ال «Y» والـ «G» أنته إذا كل عنصر
+
+231
+00:19:19,430 --> 00:19:22,350
+في ال «Y» هو صورة بقدر ألاقي ال «L» مقابلة هنكتبها
+
+232
+00:19:22,350 --> 00:19:24,770
+بس بشكل مغير نفس ال «G inverse» لكن هنكتبها
+
+233
+00:19:24,770 --> 00:19:31,510
+بالكلام التالي أه أه Now «U»
+
+234
+00:19:31,510 --> 00:19:39,370
+تنتمي لل «Y»and G is onto لأن التفكير و الهامش هو
+
+235
+00:19:39,370 --> 00:19:43,930
+اللي يجعلني أكتب أنا عندي عنصر U في الـ Y يمكن
+
+236
+00:19:43,930 --> 00:19:47,450
+أسميها Y بس الـ Y مستخدمة إيش بيكون صورة؟ فده
+
+237
+00:19:47,450 --> 00:19:56,550
+بيقول لي U تساوي F of A for أسف G صحيح صحيح for
+
+238
+00:19:56,550 --> 00:20:05,020
+some A تنتمي لل Xللـ X لأن هي الـ G عينكوا عليها
+
+239
+00:20:05,020 --> 00:20:09,400
+وحطوها مستطيلة مثلا مش واضح عادية وممكن تكتبوا هنا
+
+240
+00:20:09,400 --> 00:20:13,820
+G دلّة من X ل Y أخدت عنصر في المجال المقابل ودلّة
+
+241
+00:20:13,820 --> 00:20:16,480
+on تبدي كون صورة من إيش لعنصر في ال domain الآن
+
+242
+00:20:16,480 --> 00:20:19,240
+بدي أعرفله ال A و ال C إيش هقوله هل جيت ال A هيني
+
+243
+00:20:19,240 --> 00:20:22,580
+لجيت A لأن هو يقولنا there exists وقولنا C تساوي U
+
+244
+00:20:22,580 --> 00:20:27,300
+فإيش هقوله الآن let A اللي هو إيش اللي احنا ندور
+
+245
+00:20:27,300 --> 00:20:27,700
+عليها
+
+246
+00:20:31,540 --> 00:20:33,680
+لأ لأ الـ U و الـ V مغطيين لإني بدي أدور على الـ A
+
+247
+00:20:33,680 --> 00:20:40,460
+و الـ C أه فالأن ممكن نقوله take لإن مافيش معادلة
+
+248
+00:20:40,460 --> 00:20:49,400
+أكتبها takeA C تساوي A و V خلينا نقول ناخدها ال A
+
+249
+00:20:49,400 --> 00:20:54,040
+هي ال A اللي استخدمتها اه طبعا then ايش مطلوب مني
+
+250
+00:20:54,040 --> 00:20:58,300
+حاجتين اثبت ان ال A C في ال domain اللي هو X cross
+
+251
+00:20:58,300 --> 00:21:03,510
+Z و اثبت ان صورتها بتساوي main UV اول شيءالـ A
+
+252
+00:21:03,510 --> 00:21:08,730
+والـ C ليش تنتمي للـ X cross الـ Z ليش؟ لأن الـ V
+
+253
+00:21:08,730 --> 00:21:12,830
+من الـ Z إذا الـ C في الـ Z والـ A من وين جيبناها؟
+
+254
+00:21:12,830 --> 00:21:22,010
+من الـ A وين من الـ X إذا فعلا صح and نكتب هنا and
+
+255
+00:21:22,010 --> 00:21:25,530
+FAC
+
+256
+00:21:25,530 --> 00:21:34,030
+إيش بتساوي؟ G of A وCG of A ايش بتساوي U وC ايش
+
+257
+00:21:34,030 --> 00:21:39,290
+بتساوي V فخلصنا اه فاختارناهم بعد الشكل اه فطبعا
+
+258
+00:21:39,290 --> 00:21:45,590
+فبالتاليF is on اتأكدنا يعني وين الصعوبة هنا
+
+259
+00:21:45,590 --> 00:21:48,710
+الصعوبة في الهامش والكتابة بتعكس الهامش كله عملية
+
+260
+00:21:48,710 --> 00:21:53,570
+تأكيد لأسئلة فدائما هو الهامش مهم لكنه بتنكتبش هيك
+
+261
+00:21:53,570 --> 00:21:55,750
+البرهان بدي نكتب الصورة هذي هي الصورة اللي قعدت
+
+262
+00:21:55,750 --> 00:21:58,870
+فانا بحل و بعدين بكتب في كتير أشياء زي هيك إذا
+
+263
+00:21:58,870 --> 00:22:02,570
+بتتذكروا لما كنا بنثبت اللي هو ال delta epsilon
+
+264
+00:22:02,570 --> 00:22:05,830
+definition كنا بروح بنحل و بنوجد دلتة و الدلتة
+
+265
+00:22:05,830 --> 00:22:08,210
+المفروض إحنا نجيبها من أولاحنا بيقولوا let epsilon
+
+266
+00:22:08,210 --> 00:22:11,750
+choose delta اطول، لكن احنا من وين الـDelta؟ من
+
+267
+00:22:11,750 --> 00:22:14,870
+الآخر، لكن الكتابة بتبدأ وها كذا، ففي أشياء اكتئك
+
+268
+00:22:14,870 --> 00:22:19,630
+في الرياضيات، في هامش، في حسابات بتكون أولوية، لكن
+
+269
+00:22:19,630 --> 00:22:22,790
+في الكتابة بتنعكس العملية، الترتيب الكتابة مختلف،
+
+270
+00:22:22,790 --> 00:22:27,450
+وها دي نفس الشيءواضحة أي سؤال فطبعا هنا عشان انا
+
+271
+00:22:27,450 --> 00:22:30,970
+ماقلتلهش let كذا يسوى كذا لأنه سميت الـA مباشرة لو
+
+272
+00:22:30,970 --> 00:22:34,910
+سميتها مثلا هنا Alpha و Beta كان قولت لت الف Beta
+
+273
+00:22:34,910 --> 00:22:38,970
+تسوى إيش؟ AC نفس المعنى المهم أنا مش مابديه أقدر
+
+274
+00:22:38,970 --> 00:22:41,970
+ألاقي عنصر AC في ال domain صورته تسوى UV لاجيته
+
+275
+00:22:41,970 --> 00:22:45,710
+ولا مالاجيتش؟ نعم الـC مباشرة أخدتها تسوى V و الـA
+
+276
+00:22:45,710 --> 00:22:48,150
+من وين جبتها؟ من إنه الـG on two I gather there
+
+277
+00:22:48,150 --> 00:22:52,250
+exists A فانا وجدت الـA والـC أخدتها تسوى V وانتهت
+
+278
+00:22:52,250 --> 00:22:59,450
+العملطبعاً واحد واثنين بيحلوا السؤال implies X
+
+279
+00:22:59,450 --> 00:23:06,470
+times Z تكافئ X times Y وهذا يؤدي إلى X في Z تساوي
+
+280
+00:23:06,470 --> 00:23:12,950
+Y في Z
+
+281
+00:23:12,950 --> 00:23:16,610
+وهو المطلوب فهنا
+
+282
+00:23:17,590 --> 00:23:22,250
+صار مر علينا عدة أمثلة كيف بنعمل تصميم للدوال و
+
+283
+00:23:22,250 --> 00:23:24,750
+الـ construction كيف نستفيد من المعطيات طبعا
+
+284
+00:23:24,750 --> 00:23:27,790
+صورتنا على الهيئة اللي موجودة عندنا و كيف نستفيد
+
+285
+00:23:27,790 --> 00:23:33,650
+منها أرجو هذه الأمثلة كلها تكون عندنا حصيلة جيدة
+
+286
+00:23:33,650 --> 00:23:37,030
+نقدر نشتغل عليها أتوقع هذه نهاية ال section الآن
+
+287
+00:23:37,030 --> 00:23:44,690
+ننتقل لل section الأخير 6-6 أي سؤال؟تمام فال
+
+288
+00:23:44,690 --> 00:23:49,390
+section السادس والاخير العملية التالتةفاحنا عرفنا
+
+289
+00:23:49,390 --> 00:23:52,830
+الجامعة والضرب الآن هنعرف الأسس exponentiation of
+
+290
+00:23:52,830 --> 00:23:56,350
+cardinal number لما يعون اندي two cardinal number
+
+291
+00:23:56,350 --> 00:24:03,270
+X و Y بدي اعرف X أس Y X أس Y اه طبعا التعريف الأسس
+
+292
+00:24:03,270 --> 00:24:08,730
+بشكل عام لل real numbers بيبدأ اي طالب علم طالب
+
+293
+00:24:08,730 --> 00:24:11,490
+رياضيات يتعامل اول شي بتعامل مع الأسس الصحيحة
+
+294
+00:24:11,490 --> 00:24:15,570
+الموجبة فبيعرفوله X تربيه عبارة عن X في XX تكعيب
+
+295
+00:24:15,570 --> 00:24:19,170
+عبارة عن X تربية في X وهكذا فـ X أُس N إذا الـ N
+
+296
+00:24:19,170 --> 00:24:22,190
+عدد صحيح موجب ليس إن الـ X مضروبة في نفس الـ N من
+
+297
+00:24:22,190 --> 00:24:25,750
+المرات طبعا دي بنطور بنعرف الأسس اللي هي إيش
+
+298
+00:24:25,750 --> 00:24:30,910
+الكثرية على عدد نسبي ما هي X أُس 2 ع 3 ما هي X أُس
+
+299
+00:24:30,910 --> 00:24:34,050
+اللي هو نص وهكذا طبعا بعرفوها عن طريق اللي هو
+
+300
+00:24:34,050 --> 00:24:38,000
+الجذورأه هو مثلا الجزر التربيه لهذا X أُس نص هو
+
+301
+00:24:38,000 --> 00:24:40,780
+عبارة عن العدد اللي مربع بيساوي X هيك بعرفوها بهذا
+
+302
+00:24:40,780 --> 00:24:43,960
+الشكل عن طريق اليسار طبعا و بعدين بنتمنا نعمم لما
+
+303
+00:24:43,960 --> 00:24:47,420
+شوفنا يمكن في calculus باه الأسس غير النسبية لما
+
+304
+00:24:47,420 --> 00:24:51,560
+بيقول مثلا X أُس جزر التنين X أُس باي X أُس E هذا
+
+305
+00:24:51,560 --> 00:24:54,440
+بنعرفه عن طريق مين؟ اللغارتم، عن طريق اللغارتم
+
+306
+00:24:54,440 --> 00:24:57,620
+فهذه طريقة التعامل مع الأسس بالنسبة للأعداد
+
+307
+00:24:57,620 --> 00:25:01,740
+الحقيقيةفما هي الطريقة اللى هنعرّف فيها القصص للـ
+
+308
+00:25:01,740 --> 00:25:05,540
+Cardinal numbers للأعداد الأصلية طبعا هنا نتعامل
+
+309
+00:25:05,540 --> 00:25:09,660
+مع أعداد صحيحة موجبة ونتعامل معاش مع ال infinite
+
+310
+00:25:09,660 --> 00:25:14,160
+زي الالف نل والسي نت بتعريف يكون عام لل finite
+
+311
+00:25:14,160 --> 00:25:18,240
+cardinal number و لل transfinite cardinal number
+
+312
+00:25:18,240 --> 00:25:25,520
+طبعا هنشوف طبعا بدلات المجموعاتعشان نعرف الجامع
+
+313
+00:25:25,520 --> 00:25:31,480
+أخدنا اتحاد المجموعتين عشان نعرف الضرب أخدنا الـ
+
+314
+00:25:31,480 --> 00:25:36,040
+Cartesian product للمجموعتين عشان نعرف الأسس الآن
+
+315
+00:25:36,040 --> 00:25:42,720
+هنكون مجموعة جديدة مجموعة جديدة خالص بشكل مختلف
+
+316
+00:25:42,720 --> 00:25:47,840
+خلينا بس نعمل اللي هو graph أو diagram يوضح لنا
+
+317
+00:25:47,840 --> 00:25:53,640
+الأمور فانا في عندي two cardinal number X وYمن الـ
+
+318
+00:25:53,640 --> 00:25:56,820
+X بجيب مجموعة capital X كارديناليت اللي لها small
+
+319
+00:25:56,820 --> 00:26:02,020
+x و من ال Y بجيب مجموعة capital Y فادول المجموعتين
+
+320
+00:26:02,020 --> 00:26:07,540
+هشتغل عليهم فالان أول شيء إذا X تقاطع ال Y يساوي
+
+321
+00:26:07,540 --> 00:26:12,320
+فاي فعرفنا X زائد Y بيساوي الكارديناليت للاتحاد
+
+322
+00:26:12,320 --> 00:26:19,340
+هاي واحد صح؟إتنين من غير شرط على طول عرفنا x في y
+
+323
+00:26:19,340 --> 00:26:24,520
+تساوي ال cardinality لمن؟ لل x times ال y بدون أي
+
+324
+00:26:24,520 --> 00:26:30,660
+شروط الآن العملية التالتة بدنا نعرف y أُس x ولا x
+
+325
+00:26:30,660 --> 00:26:38,970
+أُس y بدنا نعرف y أُس x بدنا نعرف y أُس xأه فطبعا
+
+326
+00:26:38,970 --> 00:26:43,050
+هنا احنا أجرينا العمليات اللي هو على المجموعات
+
+327
+00:26:43,050 --> 00:26:46,270
+أخدنا الاتحاد أخدنا الـ Cartesian product طبعا
+
+328
+00:26:46,270 --> 00:26:51,550
+ماخدناش الفرق الـ minus ماخدناش اللي هو التقاطع
+
+329
+00:26:51,550 --> 00:26:57,310
+إيش ممكن ناخد؟ إيش المجموعة المناسبة؟ طبعا الحقيقة
+
+330
+00:26:57,310 --> 00:27:04,570
+من الخبرات السابقة وجد أن لو فينا مجموعتين عدد
+
+331
+00:27:04,570 --> 00:27:10,780
+عناصرهم finiteفاللي بعبّر عن الأسس هي عدد الدوال
+
+332
+00:27:10,780 --> 00:27:14,280
+من مجموعة لمجموعة عدد الدوال هو اللي بعبّر عنها
+
+333
+00:27:14,280 --> 00:27:17,740
+الكلام طبعا هنا جلنا الجامع ايش عبّر عنه عدد عناصر
+
+334
+00:27:17,740 --> 00:27:21,080
+الاتحاد الدرب ايش عبّر عنه عدد عناصر الـ Cartesian
+
+335
+00:27:21,080 --> 00:27:23,320
+product زي ما عملنا بتذكروا اللي هيش المربعات
+
+336
+00:27:23,320 --> 00:27:28,660
+بالنسبة للأسس المجموعة المناسبة هي مجموعة كل
+
+337
+00:27:28,660 --> 00:27:34,660
+الدوال من X إلى Y فهذه هي الcardinalة التي هنستخدم
+
+338
+00:27:34,660 --> 00:27:42,570
+رمز جديدY أُس X مجموعة جديدة Y أُس X إيش الـ Y أُس
+
+339
+00:27:42,570 --> 00:27:46,110
+X؟ في مجموعة أُس مجموعة؟ لأ، هذا رمز، أه واضح؟
+
+340
+00:27:46,110 --> 00:27:49,150
+ماحدش يقوللي إيش مجموعة أُس مجموعة إيش معناها؟ مش
+
+341
+00:27:49,150 --> 00:27:52,530
+معروف، هذا مجرد رمز، طب مين هذا الرمز؟ طبعا، ليش
+
+342
+00:27:52,530 --> 00:27:56,110
+عملوه هيك؟ عشان نسجن مع هذا الرمز، اختاروا الرمز
+
+343
+00:27:56,110 --> 00:27:58,410
+عشان نسجن مع هذا الرمز، بدنا نعرف هذه المجموعة
+
+344
+00:27:58,410 --> 00:28:02,510
+فالطبعية تشوف الهيكلية، ننتبه، هي عندي مجموعة تشري
+
+345
+00:28:02,510 --> 00:28:06,740
+بيت اتحادجيبت كارتيسيا جيبت مجموعة جديدة فهذه
+
+346
+00:28:06,740 --> 00:28:09,900
+اسمها مجموعة وهذه مجموعة وهذه مجموعة طبعا هذوله
+
+347
+00:28:09,900 --> 00:28:13,200
+مألوفين من chapter 3 هذه مجموعة جديدة أول مرة تمر
+
+348
+00:28:13,200 --> 00:28:16,320
+علينا مجموعة جديدة ورمز جديد أول مرة يمر علينا
+
+349
+00:28:16,320 --> 00:28:23,760
+فبنحاول نعرف من هذا الرمز Y أُس X إيش قلناها ده
+
+350
+00:28:23,760 --> 00:28:30,620
+مجموعة إذا مجموعة إيش عناصرها دوال مجموعة عناصرها
+
+351
+00:28:30,620 --> 00:28:36,800
+دوال Fبحيث انه بدي اكتب حيث انه هيك عشان انا بدأ
+
+352
+00:28:36,800 --> 00:28:40,580
+استخدم نجوطين في مكان اخر اويس فال F هي دالة من
+
+353
+00:28:40,580 --> 00:28:48,820
+وين لوين من X ل Y function فهذه كل عناصرها دوال
+
+354
+00:28:48,820 --> 00:28:55,700
+عناصرها دوال بهذا الشكل اه مثلا ايش لو أخدنا بعض
+
+355
+00:28:55,700 --> 00:29:04,630
+اللي هو الأمثلة يعني مثلا لو قلنا Rأُس R مين
+
+356
+00:29:04,630 --> 00:29:11,650
+بنتمئلها بدنا دالة من R لـ R مثلا ال X تربيع مثلا
+
+357
+00:29:11,650 --> 00:29:16,130
+F لو كون F في X تساوي X تربيع اللي كون معرفة sign
+
+358
+00:29:16,130 --> 00:29:22,760
+ال Xو هكذا دوال واضحة تكون دوال من الى اه من R ل R
+
+359
+00:29:22,760 --> 00:29:27,860
+ايش الدالة لازم تكون continuous لأ اي دالة بس دالة
+
+360
+00:29:27,860 --> 00:29:30,560
+لازم تكون one to one مش بالضروري لازم تكون one to
+
+361
+00:29:30,560 --> 00:29:34,340
+لأ اي دالة ايش يعني دالة يعني علاقة و تكون ايش
+
+362
+00:29:34,340 --> 00:29:37,460
+مالها ال domain بيغطي كل ال domain و ايش لكل عنصر
+
+363
+00:29:37,460 --> 00:29:42,460
+الصورة بس دالة اه فبديكون دوال بسإيش الهبس دالة؟
+
+364
+00:29:42,460 --> 00:29:45,960
+أي خاصية تانية لأ يعني ال constant function موجودة
+
+365
+00:29:45,960 --> 00:29:49,040
+ولا مش موجودة؟ يعني f of x سوا واحد دالة الواحد
+
+366
+00:29:49,040 --> 00:29:53,340
+دالة التنين كلهم دوال كدالة طبعا مش عارف كيف اكتب
+
+367
+00:29:53,340 --> 00:29:56,860
+بشكل مقتصر يعني الأمر ممكن نكتبها واضحة فعنصرهم
+
+368
+00:29:56,860 --> 00:30:01,800
+دوال عنصرهم دوالأه فهو بيقول ليه بهذا الشكل we
+
+369
+00:30:01,800 --> 00:30:06,100
+define Y أُس X هي ال cardinality لل Y أُس X وطبعا
+
+370
+00:30:06,100 --> 00:30:10,220
+ليش اختاروا الرمز هذا عشان ينسجم مع اللي هو الأسس
+
+371
+00:30:10,220 --> 00:30:13,380
+بقى ليس عليه فده رمز فأرجو أول نقطة نعرف أن هذا
+
+372
+00:30:13,380 --> 00:30:17,560
+مجرد رمز و هي عبارة عن مجموعة عناصرها دوال دوال من
+
+373
+00:30:17,560 --> 00:30:21,480
+وين لوين من اللي فوق للي تحت من X ل Y نشوف للترتيب
+
+374
+00:30:21,480 --> 00:30:21,980
+مهم جدا
+
+375
+00:30:26,960 --> 00:30:30,500
+طبعاً كالمنهج اللي احنا ماشيين فيه أي تعريف بدنا
+
+376
+00:30:30,500 --> 00:30:35,300
+نحطه واضح انه انا لازم اجيب X و Y بقدر اجيب X و Y
+
+377
+00:30:35,300 --> 00:30:39,740
+بقدر اتفقنا عليها ده من C1 بتم السؤال لو غيرت ال X
+
+378
+00:30:39,740 --> 00:30:42,720
+و Y جيبت مدلهم مجموعتين A و B بتغير انها تشجر ولا
+
+379
+00:30:42,720 --> 00:30:46,460
+بتغيرش شفنا انه هنا بتغيرش و هنا بتغيرش لكن هنا
+
+380
+00:30:46,460 --> 00:30:49,020
+لسه جديد اول مرة يمر علينا نثبت ان هنا برضه بتغيرش
+
+381
+00:30:49,020 --> 00:30:52,800
+اه فإيش بدنا نثبت بدنا نثبت لو كانت X تكافئ A
+
+382
+00:30:52,800 --> 00:30:57,470
+أسدلنا X بمجموعة تانية كبت ال Aو إذا بدلنا ال Y
+
+383
+00:30:57,470 --> 00:31:02,710
+بمجموعة تانية P ف Y أُس X تكافئ P أُس A لهم هذه
+
+384
+00:31:02,710 --> 00:31:05,270
+المجموعات فهذا الكلام We need to show that the
+
+385
+00:31:05,270 --> 00:31:08,010
+above definition is independent of the choice لا
+
+386
+00:31:08,010 --> 00:31:10,550
+يعتمد على الاختيار، مايعتمدش على الشخص اللي بيجري
+
+387
+00:31:10,550 --> 00:31:14,210
+العملية بس أي واحد بيتزن بالتعليمات، بيتزن
+
+388
+00:31:14,210 --> 00:31:19,530
+بالشروط، لازم يوصل لمن؟ لنفس الجواب فمش مهم إن ال
+
+389
+00:31:19,530 --> 00:31:23,470
+X و ال Y أي مجموعتين تحت نفس الشروط تؤدي نفس الغرض
+
+390
+00:31:23,470 --> 00:31:27,050
+فعنا نظرية التاليةأه طبعا هذه النظرية بتكمل انه
+
+391
+00:31:27,050 --> 00:31:30,970
+قلنا لما ال A تكافئ اللي هو مثلا X و ال B تكافئ ال
+
+392
+00:31:30,970 --> 00:31:33,290
+Y و التقاط of I و التقاط of I فالاتحاد يكافئ
+
+393
+00:31:33,290 --> 00:31:36,450
+الاتحاد، ده نظرية، بعدين قلنا A شمله برضه إذا ال A
+
+394
+00:31:36,450 --> 00:31:38,950
+تكافئ ال X و ال B تكافئ ال Y فال Cartesian يكافئ
+
+395
+00:31:38,950 --> 00:31:42,210
+ال Cartesian، الآن عشان نكمل الصورة بدنا نثبت أنه
+
+396
+00:31:42,210 --> 00:31:46,790
+مين؟ Y أُس X تكافئ مين؟ B أُس A، نفس الصورة، فهي
+
+397
+00:31:46,790 --> 00:31:54,530
+النظريةlet a, b و x and y, b sits such that ال a
+
+398
+00:31:54,530 --> 00:31:59,410
+تكافئ ال x و ال b تكافئ ال y then b أس a اللي هي
+
+399
+00:31:59,410 --> 00:32:02,970
+مجموعة كل الدوال من a ل b تكافئ مجموعة كل الدوال
+
+400
+00:32:02,970 --> 00:32:15,510
+من x ل y ده خلينا نشوف البرهان مع بعض فهذه
+
+401
+00:32:17,030 --> 00:32:31,690
+نظرية 6 6 بدي أثبت أن P أس A تكافئ Y أس X prove
+
+402
+00:32:35,470 --> 00:32:39,850
+الحقيقة ان الموضوع شويه بده تركيز شويه ننفتح لان
+
+403
+00:32:39,850 --> 00:32:43,530
+الموضوع شويه يعني زي ما قلنا مش مألوف اه وين
+
+404
+00:32:43,530 --> 00:32:47,170
+المشكلة ان عناصر المجموعات هي دوال الان عشان اثبت
+
+405
+00:32:47,170 --> 00:32:54,170
+التكافؤ بدي دالة من B أُس Aلـ Y أُس A فبدنا دالة
+
+406
+00:32:54,170 --> 00:32:58,270
+بهذا الشكل خلّيني أحاول نتعرف على المجموعات اللي
+
+407
+00:32:58,270 --> 00:33:00,450
+بتتعامل معاهم عشان نعرف كيف بنعمل construction
+
+408
+00:33:00,450 --> 00:33:04,850
+للدالة هذه أه طبعا فده يعني أنا بدأ أدخل على حاجة
+
+409
+00:33:04,850 --> 00:33:07,610
+مجهولة كيف بنتعامل مع عناصرها لأ حاول أتعرف على
+
+410
+00:33:07,610 --> 00:33:11,830
+عناصر فممكن تصير في شوية ألفة أدخل في العمق أعرف
+
+411
+00:33:11,830 --> 00:33:16,090
+كيف بدي أعمل الدالة أه بالنسبة إلينا احنا بدنا من
+
+412
+00:33:16,090 --> 00:33:21,860
+اللي هو B أس A هي المجموعة الأولىB أُس A هذه
+
+413
+00:33:21,860 --> 00:33:30,560
+مجموعة إيش عناصرها عبارة عن دوال F من A لB بدنا
+
+414
+00:33:30,560 --> 00:33:36,420
+نوديها لمجموعة تانية اللي هي Y أو Y أُس X إيش
+
+415
+00:33:36,420 --> 00:33:43,160
+عناصرها دوال وليكن G من X لY بندور على دالة من هان
+
+416
+00:33:43,160 --> 00:33:50,000
+لهان إيش أسمي الدالة هذهH ممكن بس أنا بدي أجيبلكم
+
+417
+00:33:50,000 --> 00:33:54,120
+اسم زي ما قولنا فيه اسم غلط لأ لكن فيه اسم أحسن من
+
+418
+00:33:54,120 --> 00:34:00,280
+اسم بدي أسميها أنا ابصاي ابصاي عرف لاتيني ابصاي
+
+419
+00:34:00,280 --> 00:34:06,760
+بيقول الفاظ ابصاي حرف لاتيني ابصايipsi لما انا جيب
+
+420
+00:34:06,760 --> 00:34:13,860
+رمز غريب؟ لما رمز غريب؟ عشان هذه الدالة ايش العناص
+
+421
+00:34:13,860 --> 00:34:17,300
+اللي بتشتري عليها؟ دوال فبدي هيك تكون كبيرة شوية
+
+422
+00:34:17,300 --> 00:34:21,440
+عشان تحتضن الدوال الصغيرة لان هداش ايش بتعمل
+
+423
+00:34:21,440 --> 00:34:26,700
+بipsi؟ هتاخد الدالة F من هنا وتوديها ل G فال G هنا
+
+424
+00:34:26,700 --> 00:34:32,420
+بدي الجين اللي هنا ايش تكون؟ ipsi of Fفعشان هيك
+
+425
+00:34:32,420 --> 00:34:36,040
+ماسميتاتش H عشان ما يختلطوش مع بعض طبعا زي ما قلنا
+
+426
+00:34:36,040 --> 00:34:39,380
+مافيش رمز غلط و رمزي يعني ممكن نسميها capital F بس
+
+427
+00:34:39,380 --> 00:34:43,560
+أنا حاببت أعمله رمز غريب شوية عشان دال الدوال هذه
+
+428
+00:34:43,560 --> 00:34:47,460
+عناصرها دوال طبعا أي رمز بيبقى واضح فاحنا بس حبينا
+
+429
+00:34:47,460 --> 00:34:51,160
+نسميه بـ Psi بياد الشكل طبعا أي اسم لكن حاولنا
+
+430
+00:34:51,160 --> 00:34:55,460
+نبعده عن ال small عشان نميز بين عناصر الدوالاللي
+
+431
+00:34:55,460 --> 00:34:59,400
+في B A وفي X Y و بين الدالة اللي بتشترع عليهم هذه
+
+432
+00:34:59,400 --> 00:35:03,380
+الدالة الكبيرة واضحة هذه القضية تمام فإذا هذه أول
+
+433
+00:35:03,380 --> 00:35:09,680
+نقطة فبدنا هذا الدالة تاخد دالة F توديها لدالة G
+
+434
+00:35:09,680 --> 00:35:14,960
+توديها لدالة G بتكون هي عندي عنصر دالة من A ل B
+
+435
+00:35:14,960 --> 00:35:19,280
+بتخليها دالة من وين ل وين من X ل Y بتخليها دالة من
+
+436
+00:35:19,280 --> 00:35:26,060
+X ل Y فإيش بدنا نعملخلّينا نرسم لكم برضه diagram
+
+437
+00:35:26,060 --> 00:35:30,680
+ممكن يساعدنا احنا في عندنا هي ال F نرسمها هي عندنا
+
+438
+00:35:30,680 --> 00:35:37,700
+من A ل B وفي عندنا دالة F بدنا ننقلها في Psi تصير
+
+439
+00:35:37,700 --> 00:35:44,500
+دالة من X ل Y اللي هي G تساوي Psi ل F هيك و بدنا
+
+440
+00:35:44,500 --> 00:35:51,840
+نديهاأه تمام فإذا بدي أسأل نفسي مين العلاقة بين
+
+441
+00:35:51,840 --> 00:35:55,820
+السطر الأول والسطر التاني؟ في علاقات؟ نعم في
+
+442
+00:35:55,820 --> 00:36:01,700
+علاقات جال لإنه ال X تكافئ ال Y و .. و .. أسف ال A
+
+443
+00:36:01,700 --> 00:36:05,780
+تكافئ ال X و ال B تكافئ ال Y إذا أنا في عندي
+
+444
+00:36:05,780 --> 00:36:11,080
+bijection من هان لهان و ليكن H و في عندي bijection
+
+445
+00:36:11,080 --> 00:36:19,010
+من هان لهان و ليكن K تمامأه فانا بدي الآن دالة ال
+
+446
+00:36:19,010 --> 00:36:25,170
+F دالة بتاخد عناصر من A بتسويهم ل B ال G دالة
+
+447
+00:36:25,170 --> 00:36:29,850
+بتاخد عناصر من X بتوديهم ل Y فكيف أخلي دالة بدل ما
+
+448
+00:36:29,850 --> 00:36:34,450
+هي ال domain تبعها A والمجال المقابل B يصير ال
+
+449
+00:36:34,450 --> 00:36:40,300
+domain تبعها X والمجال المقابل Yفالان نعم
+
+450
+00:36:40,300 --> 00:36:44,480
+composition أحسنتى قبل ما تفكروا خليني انا يش اكتب
+
+451
+00:36:44,480 --> 00:36:47,540
+بعض الأمور التمهيدية اللى احنا رسمناها فالان اول
+
+452
+00:36:47,540 --> 00:36:54,880
+شيء احنا كله كله مجموعات ممتاز الان A تكافئ ال X
+
+453
+00:36:54,880 --> 00:37:02,140
+and B تكافئ ال Y implies there exist a bijection H
+
+454
+00:37:02,140 --> 00:37:09,130
+من A ل X مختصر انا bijection صح؟ andThere exists a
+
+455
+00:37:09,130 --> 00:37:13,830
+bijection سميته K من و إلى و من B إلى Y بدي أعمله
+
+456
+00:37:13,830 --> 00:37:23,010
+لأنه بدي أستخدمه أه الآن Now لت إبصي من B أُس A
+
+457
+00:37:23,010 --> 00:37:33,240
+إلى X أو Y أُس X Y أُس X بدي أعرف الدالةأه لما
+
+458
+00:37:33,240 --> 00:37:36,680
+أقولكوا ادوني دالة، إيش لازم نعرف الدالة؟ في تلات
+
+459
+00:37:36,680 --> 00:37:39,620
+حاجات لتعريف الدالة، بتتذكروا؟ لو رجعتوا في الأول،
+
+460
+00:37:39,620 --> 00:37:42,380
+قولنا إيش ال function؟ هي triple، تلات حاجات، في
+
+461
+00:37:42,380 --> 00:37:45,740
+relation وفي مجال ومجال مقابل، فانا هنا إيش؟
+
+462
+00:37:45,740 --> 00:37:49,200
+اديتله المجال والمجال المقابل، تم اديله العلاقةهذه
+
+463
+00:37:49,200 --> 00:37:52,180
+العلاقة بديها يا إما قاعدة، يا بكتبها على أزواج
+
+464
+00:37:52,180 --> 00:37:54,660
+مرتبة، طبعا أزواج مرتبة إذا كان ال domain محدود،
+
+465
+00:37:54,660 --> 00:37:57,540
+إذا مش محدود، مينفعش أديها أزواج مرتبة، فلازم
+
+466
+00:37:57,540 --> 00:38:01,760
+أديله القاعدة، ف let psi، فلما يقولي عرف ده لأ،
+
+467
+00:38:01,760 --> 00:38:06,150
+كيب ده كله دول، كل دول إيه، letالـ F لت بصي لت
+
+468
+00:38:06,150 --> 00:38:10,770
+capital F لت فاي لت الف لت بيتا اي اسم .. اه اسمته
+
+469
+00:38:10,770 --> 00:38:14,210
+بي a function من الى هذه واحدة و بعدين اش اقوله
+
+470
+00:38:14,210 --> 00:38:18,230
+given by اه بده اديه القاعدة لت بصي a function من
+
+471
+00:38:18,230 --> 00:38:25,370
+ايه من ايه لإيه بي given by بي given byبـ Psi إيش
+
+472
+00:38:25,370 --> 00:38:29,570
+بتاخد عناصر من هنا مش حلو أسميهم X مش مناسب إيش
+
+473
+00:38:29,570 --> 00:38:32,130
+نسميهم F لأن زي ما عملنا الصورة عشان أتذكر أنهم
+
+474
+00:38:32,130 --> 00:38:39,110
+دوال عشان أتذكر أنهم دوال of F تساوي بديها دالة من
+
+475
+00:38:39,110 --> 00:38:43,470
+وين تبدأ تصير من X في هذا الرسمة مين الدالة بتبدأ
+
+476
+00:38:43,470 --> 00:38:47,650
+من X؟ H inverse أحسنتها فهذه أول شيء بدي H inverse
+
+477
+00:38:49,170 --> 00:38:53,890
+Composition بدأت من هنا نشوف الصورة بدأنا من هنا
+
+478
+00:38:53,890 --> 00:38:57,630
+وين بدنا نروح لل Y في الطريق اللي عندها بدأت تتعمد
+
+479
+00:38:57,630 --> 00:39:01,650
+على ال F هنروح لل A مع ال H inverse مين بيودينا ال
+
+480
+00:39:01,650 --> 00:39:05,130
+F يتودينا لل B مين بيوصلنا لل Y ال K اذا ال A
+
+481
+00:39:05,130 --> 00:39:12,660
+شماله هذا Circle F Circle Kفعملت الدالة هذه هل جيت
+
+482
+00:39:12,660 --> 00:39:15,860
+هذه الدالة من X ل Y ولا مش من X ل Y؟ واضحة من
+
+483
+00:39:15,860 --> 00:39:19,700
+الرسم، صح؟ لأن H inverse من أين تبدأ؟ من X ل A
+
+484
+00:39:19,700 --> 00:39:23,200
+والـ F من أين بتوديها؟ بتوصلها لـ B والـ K بتوصلها
+
+485
+00:39:23,200 --> 00:39:27,180
+لمين؟ لـ Y، composition أه فطبعا هنا شيء طبيعي أنه
+
+486
+00:39:27,180 --> 00:39:30,240
+أنا عندي دالة في العمليات اللي على الدوال لما بقول
+
+487
+00:39:30,240 --> 00:39:32,800
+إيه و أعرف دالة على الـ real ممكن أضرب الـ X
+
+488
+00:39:32,800 --> 00:39:36,040
+باتنين ممكن أربحها، ممكن أخدها للـ sine طب دالة
+
+489
+00:39:36,040 --> 00:39:37,960
+إيش العمليات اللي موجودة على الدوال؟ فيه الـ
+
+490
+00:39:37,960 --> 00:39:41,200
+compositionوفيه الجماعة وفيه الدرب وفيه وها كذا
+
+491
+00:39:41,200 --> 00:39:43,860
+وفيه التفاضل مثلا ممكن صح ولا لأ بس المهم ان انا
+
+492
+00:39:43,860 --> 00:39:46,980
+كيف بدي اعملها ايش المطلوب مني فانا حولتها من دالة
+
+493
+00:39:46,980 --> 00:39:53,740
+من A ل B إلى دالة G من X ل Y أي سؤال طبعا الأمر مش
+
+494
+00:39:53,740 --> 00:39:57,260
+بسيط لكن احنا فكرنا مع بعض وحاولنا نشوف هذه الأمور
+
+495
+00:39:58,340 --> 00:40:00,800
+ممتاز نشوف أن هذه هل هي الغرض اللي بدنا ياه
+
+496
+00:40:00,800 --> 00:40:04,620
+بيجيكشن ولا مش بيجيكشن طبعا انتبهوا كيف تحتاج
+
+497
+00:40:04,620 --> 00:40:07,780
+تعملوا على ال F طب ال K و ال H ده لمن؟ ثوابت لأنه
+
+498
+00:40:07,780 --> 00:40:10,740
+لكل بيشتغلوا لما بغير الدالة مين بتغير بس ال F
+
+499
+00:40:10,740 --> 00:40:13,880
+فانا عندي ب ساي و في F مختلفة لو أخد دالة جديدة
+
+500
+00:40:13,880 --> 00:40:17,220
+مثلا Alpha هتصير إيش K Circle Alpha Circle Alpha
+
+501
+00:40:17,220 --> 00:40:23,720
+هدو كأنهم ثوابت واضحة؟ بالنسبة له نشوف واحد ب ساي
+
+502
+00:40:23,720 --> 00:40:31,130
+is one to oneأه طيب الدالة قولتولي صعبة بصدق طب
+
+503
+00:40:31,130 --> 00:40:34,470
+كيف نثبت one to one كيف نبدأ صعب البداية لأ نفس
+
+504
+00:40:34,470 --> 00:40:38,230
+المبدأ عنصرين في ال domain في إيش هقوله let إيش
+
+505
+00:40:38,230 --> 00:40:43,130
+يسميهم اه ممتاز وين بنتموا لل domain وين ال domain
+
+506
+00:40:43,130 --> 00:40:53,710
+هيو بيقص ايه such that شوف يا نتعلم بsi F1 تساوي
+
+507
+00:40:53,710 --> 00:41:00,490
+بsi F2ممتاز؟ في صعوبة؟ اه فاحنا ارجو انه نتعلم
+
+508
+00:41:00,490 --> 00:41:06,330
+مانخافش في أمور صعبة بتفق لكن في أمور ثابتة و كيبت
+
+509
+00:41:06,330 --> 00:41:09,290
+ده مانخافش هيا one to one ايش معت one to one
+
+510
+00:41:09,290 --> 00:41:13,530
+عنصرين في المجال صورهم متساوي طب ممكن اعمل كمان
+
+511
+00:41:13,530 --> 00:41:17,850
+خطوة نعم الدالة معرفة و لا مش معرفة نعود في الدالة
+
+512
+00:41:17,850 --> 00:41:26,940
+فهذا يؤدييؤدى انه K Circle H F1 Circle H Inverse
+
+513
+00:41:26,940 --> 00:41:34,280
+تساوي K Circle F2 Circle H Inverse في
+
+514
+00:41:34,280 --> 00:41:38,660
+صعوبة؟غير الـ Construction تبع الدالة، صعبة صعبة،
+
+515
+00:41:38,660 --> 00:41:41,140
+اللي بالصحيح كيف وجدناها، فيها صعوبة، فيها صعوبة،
+
+516
+00:41:41,140 --> 00:41:45,340
+لكن اللي بعده هيك فيه صعوبة، لأ، إيش مطلوب منها،
+
+517
+00:41:45,340 --> 00:41:48,360
+إيش عايزش ندورها، إحنا إيش هدفنا، أف واحد تساوي أف
+
+518
+00:41:48,360 --> 00:41:52,080
+اتنين، و أنا وصلت لهذه العلاقة، إيش أعمل، أجسم و
+
+519
+00:41:52,080 --> 00:41:57,340
+أطرح و أضرب؟ الـ one to one إيش
+
+520
+00:41:57,340 --> 00:42:01,820
+بيقول، إذا تساوت قيم الدالتين عند عناصر عناصر في
+
+521
+00:42:01,820 --> 00:42:08,920
+عناصر متساويةنفكر ال composition كيفمن غير عنصر
+
+522
+00:42:08,920 --> 00:42:14,140
+بنفع؟ احنا بنعرف ان F circle G of X تساوي F of G
+
+523
+00:42:14,140 --> 00:42:20,560
+of X خلينا نبدأ واحدة واحدة خلينا نفكر مع بعض ايش
+
+524
+00:42:20,560 --> 00:42:26,340
+مطلوب عينكوا على المطلوب انا بدي F1 تساوي F2 صح؟
+
+525
+00:42:26,340 --> 00:42:30,940
+على ان تستفهى ايش هدولة اشمال هم هدولة F1 و F2؟
+
+526
+00:42:30,940 --> 00:42:35,520
+دوال وقت ايش بقول عدلتين متساويتين؟ نظرية تلاتة
+
+527
+00:42:35,520 --> 00:42:40,340
+سبعة؟لازم يكون نفس المجال و المجال المقابل كمان و
+
+528
+00:42:40,340 --> 00:42:45,200
+الصور لكل ال domain متساوية فانا بدي شرطين هذا if
+
+529
+00:42:45,200 --> 00:42:50,100
+and only if واحد ال F1 و ال F2 من نفس ال domain
+
+530
+00:42:50,100 --> 00:42:55,020
+اللي هم من A ل B و هم هيك و لا مش هيك؟ هم هيك من
+
+531
+00:42:55,020 --> 00:42:59,620
+أين أخدتهم؟ هيه صح و لا مش صح؟ إيش معناه أنهم في B
+
+532
+00:42:59,620 --> 00:43:04,230
+أس A؟إيش معناتها إنها دوال منقلة بمشاكل مجموعة
+
+533
+00:43:04,230 --> 00:43:07,630
+تفاقنا واحدة واحدة هذا الشرط إيش الشرط التاني and
+
+534
+00:43:07,630 --> 00:43:12,870
+عشان انه F1 أو خلّيني أكتبها for all X في ال
+
+535
+00:43:12,870 --> 00:43:18,970
+domain F1 of X تساوي F2 of X فده اللي هو المطلوب
+
+536
+00:43:20,790 --> 00:43:23,650
+إذا هذا المطلوب، نمشي واحدة واحدة، ما نتصرعش، أه؟
+
+537
+00:43:23,650 --> 00:43:27,010
+فاحنا جيت عندنا دوال، هيصق الأمور، احنا بدأنا
+
+538
+00:43:27,010 --> 00:43:30,290
+بداية نفسها، بدي أثبت أن أنصرين متساوين، بس
+
+539
+00:43:30,290 --> 00:43:32,990
+الأعناص اللي عندنا دول مش أعداد ولا قيم عادية، هما
+
+540
+00:43:32,990 --> 00:43:36,330
+دوال، كيف ده لابد تسوي ده، لهاي الشرطين، يكونوا من
+
+541
+00:43:36,330 --> 00:43:39,330
+نفس المجال، وإليهم لايهش إلى نفس المجال المقابل
+
+542
+00:43:40,130 --> 00:43:43,650
+وعلى كل عناصر المجال قيمهم متساوي فنبدأ واحدة
+
+543
+00:43:43,650 --> 00:43:46,590
+واحدة خليني اكتب هذا الكلام ونبدأ نشوف كيف بدنا
+
+544
+00:43:46,590 --> 00:43:51,370
+نحل اه فالان اول اشي طبعا هذه سهلة وواضحة نقوله
+
+545
+00:43:51,370 --> 00:43:57,010
+اول شيء since اف اه طبعا احنا وي و اه خليني اكتب
+
+546
+00:43:57,010 --> 00:44:07,010
+هنا we haveto show that F1 to F2 اه هذه لجينا في
+
+547
+00:44:07,010 --> 00:44:10,190
+صعوبة في حالها مظبوط نخليها على جهها و هنرجعها و
+
+548
+00:44:10,190 --> 00:44:13,510
+هنشوف كيف نستخدمها لإن هي المفتاح لكن المشلجيين مش
+
+549
+00:44:13,510 --> 00:44:16,830
+قادرين نحلها مباشرة لإنه مش عمليات حسابية مش ضربوا
+
+550
+00:44:16,830 --> 00:44:20,170
+الجسم كأن لو انه عدد كأنجسمنا و طرحنا من الطرفين و
+
+551
+00:44:20,170 --> 00:44:22,730
+خلصنا لكن عشان هذه فخليها هذه المعادلة اللي
+
+552
+00:44:22,730 --> 00:44:25,710
+هنستخدمها على جهها وشوف التحليل اللي بدنا إياها
+
+553
+00:44:25,960 --> 00:44:29,940
+فأول شيء we want to prove X و F1 تسوي F2 مظبوط طيب
+
+554
+00:44:29,940 --> 00:44:36,060
+بما أن F1 و F2 تنتمي لل B قُس A إيش في عندنا؟ we
+
+555
+00:44:36,060 --> 00:44:45,100
+have F1 دالة من A ل B and F2 دالة من A ل B هذا إيش
+
+556
+00:44:45,100 --> 00:44:54,340
+معناته؟ we can apply theorem تلاتة سبعة thus
+
+557
+00:44:56,890 --> 00:45:00,850
+to show that
+
+558
+00:45:00,850 --> 00:45:12,210
+F1 تساوي F2 we have to show that for all X تنتمي
+
+559
+00:45:12,210 --> 00:45:20,930
+لل A F1 of X تساوي F2 of X بالتفصيل كاملا كتبت هذا
+
+560
+00:45:20,930 --> 00:45:24,210
+بدي يا هذا يمكن خلصنا منه يمكن نرجعله بالانتو مش
+
+561
+00:45:24,210 --> 00:45:30,600
+مشكلةأي سؤال تمام؟ اه فإذا احنا وصلنا كان مطلوب
+
+562
+00:45:30,600 --> 00:45:34,740
+نثبت F1 تسوى F2 حللنا لجينا بدنا نستخدم نظرية
+
+563
+00:45:34,740 --> 00:45:38,400
+تلاتة سبعة فأصبح السؤال اللي صار بدي أثبت for all
+
+564
+00:45:38,400 --> 00:45:42,260
+X تنتمي لل X F1 of X تسوى F2 of X كيف بثبت هذه
+
+565
+00:45:42,260 --> 00:45:46,360
+الجملة؟ let X تنتمي لل A مظبوط من for all اتفقنا
+
+566
+00:45:46,360 --> 00:45:53,120
+عليها أكتر من مرة فحقوله let X تنتمي لل A بدنا
+
+567
+00:45:53,120 --> 00:45:58,750
+نثبت هذه تسوى هذه مابديش اكتبهاتمام ايش يعني كنت
+
+568
+00:45:58,750 --> 00:46:03,750
+هذه مهمة جدا بدي استخدمها واستفيد منها هل هدول
+
+569
+00:46:03,750 --> 00:46:07,370
+دوال مظبوط اه ممكن اطبق الدلتين على ال X ما زالوا
+
+570
+00:46:07,370 --> 00:46:09,990
+متساويين لازم يكونوا ياش ممكن اطبقهم على ال X بس
+
+571
+00:46:09,990 --> 00:46:12,990
+بشرط يزال ال X يكون في دومانهم هدول دوال من وين
+
+572
+00:46:12,990 --> 00:46:17,270
+لوين هدول ال ψ دي هدول دوال من X ل Y اه دي ال ψ
+
+573
+00:46:17,270 --> 00:46:19,950
+بيه من ال point دي دوال من X ل Y و ال small x هده
+
+574
+00:46:19,950 --> 00:46:25,600
+من وين في Aفمش هيصبت مباشرة فابدى انا حاجة تكون
+
+575
+00:46:25,600 --> 00:46:29,040
+وين عشان اقدر اطبق هذه اللي واستفيد منها بدي عنصر
+
+576
+00:46:29,040 --> 00:46:34,100
+يكون في ال Xلأن هدول دوال من X ل Y عشان أقدر أطبق
+
+577
+00:46:34,100 --> 00:46:39,000
+هدول أستفيد من تسويهم دالتين متساويتين بنطبقوا على
+
+578
+00:46:39,000 --> 00:46:42,160
+أي عنصر هيكونوا يديني نفس القيمة هيك معناتهم صح؟
+
+579
+00:46:42,160 --> 00:46:45,500
+هدول دالتين لو سمناهم Alpha و Beta فإيش معنات أن
+
+580
+00:46:45,500 --> 00:46:48,860
+Alpha تساوي Beta؟ يعني for all X وين؟ in capital X
+
+581
+00:46:48,860 --> 00:46:52,140
+لأنه دوال من X ل Y بتكون Alpha of X تساوي Beta of
+
+582
+00:46:52,140 --> 00:46:56,380
+X تمام؟ فبدنا هذا ال X من إيه؟ نجيبله عنصر وين
+
+583
+00:46:56,380 --> 00:47:02,790
+موجود في ال capital X بقدر ألاجيإيش علاقة A و X؟
+
+584
+00:47:02,790 --> 00:47:12,070
+من ده الـH من A ل X؟ الـH inverse فالآن لت X تنتمي
+
+585
+00:47:12,070 --> 00:47:20,170
+لكابيتل X since H inverse من X لوين الـH inverse؟
+
+586
+00:47:20,170 --> 00:47:27,140
+لل A إيش معلها؟ bijection يعني أنتواأنتم عنصر في
+
+587
+00:47:27,140 --> 00:47:31,000
+المجال المقابل تكون صورة لعنصر من الـ Xأنا أخدت
+
+588
+00:47:31,000 --> 00:47:33,920
+عنصر في المجال المقابل A مرة تانية اللي قُمّال
+
+589
+00:47:33,920 --> 00:47:37,360
+عشان أنا جديد مش مألوف أنا بدي أرد و بدي أجيب أخدت
+
+590
+00:47:37,360 --> 00:47:42,180
+عنصر X بس أنا بدي عنصر من وين؟ عنصر X في الـA بدي
+
+591
+00:47:42,180 --> 00:47:45,740
+عنصر في الـX من البربط A مع X الـH inverse أو الـH
+
+592
+00:47:45,740 --> 00:47:49,460
+المناسب فأنا بدي أستخدم خاصية الندالة Onto أخدت
+
+593
+00:47:49,460 --> 00:47:52,140
+عنصر في المجال المقابل لازم يكون صورة عنصر من وين؟
+
+594
+00:47:52,140 --> 00:47:54,720
+من ال domain وهذا العنصر اللي بدور عليه فهذه H
+
+595
+00:47:54,720 --> 00:47:59,960
+inverseis a bijection يعني on to خلّيني أقول is on
+
+596
+00:47:59,960 --> 00:48:04,240
+to بشكل أساسي implies او since بتنفعش فيها implies
+
+597
+00:48:04,240 --> 00:48:09,640
+is on to a there exist مثلا عنصراش يسميه وليه يكون
+
+598
+00:48:09,640 --> 00:48:14,340
+بيه تنتمي لل X خلّيني أكتبه هنرجع مرة تانية نقرعها
+
+599
+00:48:14,340 --> 00:48:21,860
+مع بعض such that X تساومين H inverse ال Bفانا بدور
+
+600
+00:48:21,860 --> 00:48:26,760
+على عنصر وين في الـ X هو B إيش علاقته مع الـ X؟ هو
+
+601
+00:48:26,760 --> 00:48:31,460
+لازم يكون بالـ bijection هو صورة الـ X بدي يكون أو
+
+602
+00:48:31,460 --> 00:48:35,620
+هو ال inverse موجود فهذه لجهة العنصر طيب إيش اللي
+
+603
+00:48:35,620 --> 00:48:38,660
+وصلته؟ اللي إيش استفدت منه؟ الآن الـ B عنصر في الـ
+
+604
+00:48:38,660 --> 00:48:42,040
+X ممكن أطبق عليه الطرفين هدول نشوف بيؤدي الغرض ولا
+
+605
+00:48:42,040 --> 00:48:48,420
+لأ نشوف آه آه الآن فنستخدم هذه وليكن الـ star
+
+606
+00:48:48,420 --> 00:48:49,100
+أسميها
+
+607
+00:48:52,000 --> 00:48:58,940
+Now star implies فالـ
+
+608
+00:48:58,940 --> 00:49:04,980
+A بتستفيد منها عنصر في الدمين المشترك لدالتين هدول
+
+609
+00:49:04,980 --> 00:49:10,140
+لازم الدالتين يكونوا متساويين فبديلي K circle F1
+
+610
+00:49:10,140 --> 00:49:16,540
+circle H inverse of B يسوى K circle F2 circle H
+
+611
+00:49:16,540 --> 00:49:23,860
+inverse للـ Bفنشوف الدقة كيف هدول دلتين متساويتين
+
+612
+00:49:23,860 --> 00:49:27,700
+إذا قيمهم متساوية بس وين مش على أي عناصر عناصر ال
+
+613
+00:49:27,700 --> 00:49:31,320
+domain تبعهم ال X مش مناسبة طب أنا بدي عنصر في ال
+
+614
+00:49:31,320 --> 00:49:34,540
+capital X فيه بقدر أربط X اللي في ال A مع ال
+
+615
+00:49:34,540 --> 00:49:38,280
+capital X نعم عن طريق ال what ال bijection الآن
+
+616
+00:49:38,280 --> 00:49:41,640
+وصلنا ولا ماوصلناش هاي هدفنا هاي هدفنا تشوف هذا
+
+617
+00:49:41,640 --> 00:49:48,500
+إيش معناته هذه ليست إلا K of F1 of H inverse of P
+
+618
+00:49:49,510 --> 00:49:58,970
+بدا تساوي K of F2 of H inverse of Pالآن ممكن
+
+619
+00:49:58,970 --> 00:50:02,550
+استخدم one to one k is one to one which inverse
+
+620
+00:50:02,550 --> 00:50:09,310
+بتساوي x implies f one of x تساوي f two of x عملت
+
+621
+00:50:09,310 --> 00:50:13,910
+اتنين مع بعض ليش لإن ال k is one to one إذا بقدر
+
+622
+00:50:13,910 --> 00:50:19,610
+أنتزع هذا الغلاف واضحة و بعدين صارت مين نزعنا ال k
+
+623
+00:50:19,610 --> 00:50:26,250
+أصبح f of و هذه إيشهي ليس إلا X سمّيناها X ولأن H
+
+624
+00:50:26,250 --> 00:50:34,870
+inverse of B تساوي X وهو المطلوب فإيش صار thus F1
+
+625
+00:50:34,870 --> 00:50:43,430
+تساوي F2 وبالتالي and hence من ال one to one؟ من
+
+626
+00:50:43,430 --> 00:50:49,290
+المركز لسه من ال one؟ F1 تساوي F2 إحنا مش فنثبت ال
+
+627
+00:50:49,290 --> 00:50:50,450
+size one to one
+
+628
+00:50:54,900 --> 00:51:03,980
+أه فالرياضيات دقة و ايش في بدها يكون صحيحة فالانأه
+
+629
+00:51:03,980 --> 00:51:07,320
+في مثلا بقول بقولهم اثبتوا ان X is infinite set
+
+630
+00:51:07,320 --> 00:51:10,220
+بقولوا ان انا اثبت X one to one في مجموعة one to
+
+631
+00:51:10,220 --> 00:51:13,240
+one لا فيش حاجة اسمها مجموعة one to one اه طبعا
+
+632
+00:51:13,240 --> 00:51:17,280
+فيها ده خطأ كبير فاحش طب هنا إيش نعمل أنا في عندي
+
+633
+00:51:17,280 --> 00:51:20,280
+بدأ أثبت بـPsi one to one و هي دالة طب واحد كتب لي
+
+634
+00:51:20,280 --> 00:51:22,880
+F one to one مين ال F؟ لأ أنا بدي بـPsi one to one
+
+635
+00:51:22,880 --> 00:51:25,720
+طبعا F one to one ممكن أقبلها دالة بس مش هي اللي
+
+636
+00:51:25,720 --> 00:51:28,520
+بدور عليها شوفت الدقة كيف مش مجموعة بدأ ميز بين
+
+637
+00:51:28,520 --> 00:51:31,980
+مجموعة و دالة بدأ أثبت بدأ ميز بين دالة و دالة مين
+
+638
+00:51:31,980 --> 00:51:37,180
+اللي بشتر عليه؟في عناصر هما دوال Small F ودي دالة
+
+639
+00:51:37,180 --> 00:51:41,960
+كبيرة بـ Psi بتشتغل عليها هذه العناصر فلازم نركز و
+
+640
+00:51:41,960 --> 00:51:46,320
+ننتبه ان شاء الله المحاضرة دي بنكمل و هنثبت ان Psi
+
+641
+00:51:46,320 --> 00:51:46,500
+is
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/NTo9q63N_fY.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/NTo9q63N_fY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0da3bf3d4cd3c9144f529cf088edd0d82abb027b
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/NTo9q63N_fY.srt
@@ -0,0 +1,2543 @@
+1
+00:00:20,860 --> 00:00:23,920
+بسم الله الرحمن الرحيم إن شاء الله اليوم هنكمل مع
+
+2
+00:00:23,920 --> 00:00:28,400
+اللي هو الـ compliments مكملات المجموعات فبس نتذكر
+
+3
+00:00:28,400 --> 00:00:32,200
+احنا عرفنا حاجتين فيما يعرف به اللي هو المكملة 
+
+4
+00:00:32,200 --> 00:00:35,060
+النسبية أو الـ relative compliment لو في عندنا
+
+5
+00:00:35,060 --> 00:00:41,180
+مجموعتين a و b فعرفنا اللي هو a minus الـ b وهي
+
+6
+00:00:41,180 --> 00:00:46,060
+مكملة الـ b في الـ a وتساوي عناصر اللي موجودة في الـ
+
+7
+00:00:46,060 --> 00:00:50,890
+a و غير موجودة في الـ b x such that x تنتمي للـ a and
+
+8
+00:00:50,890 --> 00:00:55,830
+X لا تنتمي للـ B فهذه تسموها relative complement of
+
+9
+00:00:55,830 --> 00:01:01,310
+B in A أو تجاوزا الـ 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 الـ universal set أي عبارة عن U اللي هي الـ
+
+13
+00:01:13,630 --> 00:01:17,880
+universal ناقص Aفهي العناصر اللي موجودة في الـ U
+
+14
+00:01:17,880 --> 00:01:21,180
+خارج الـ A وغير موجودة في الـ A أو باختصار العناصر
+
+15
+00:01:21,180 --> 00:01:25,180
+عايش خارج الـ A أيضا تحدثنا عن بعض الخواص فقلنا
+
+16
+00:01:25,180 --> 00:01:28,600
+مكملة المكملة بتدينا المجموعة نفسها مكملة الـ Phi U
+
+17
+00:01:28,600 --> 00:01:33,300
+مكملة الـ U prime أو الـ U هي الـ Phi تقاطع أي مجموعة
+
+18
+00:01:33,300 --> 00:01:37,410
+مع مكملتها الـ Phi الاتحاد المجموعة مع مكملتها بيدينا كل
+
+19
+00:01:37,410 --> 00:01:40,870
+الـ universal set و طبعا إذا كانت الـ A subset من الـ
+
+20
+00:01:40,870 --> 00:01:44,070
+B فالـ contrapositive بتصير مكملة الـ B subset من
+
+21
+00:01:44,070 --> 00:01:47,710
+مكملة الـ A و طبعا النقطة الأخيرة مهمة هشوف عليها
+
+22
+00:01:47,710 --> 00:01:51,630
+تتبقى قرابة متعددة بقدر أكتب الـ A minus B بديهش
+
+23
+00:01:51,630 --> 00:01:54,700
+عبارة عن إيه تقاطع مكملة الـ B لأنه إيش بدنا العناصر
+
+24
+00:01:54,700 --> 00:01:58,800
+اللي خارج الـ B؟ العناصر لإنه من هنا هذا هي A تنتمي
+
+25
+00:01:58,800 --> 00:02:03,200
+لـ A و B و X لا تنتمي لـ B طبعا إيش X لا تنتمي لـ B؟
+
+26
+00:02:03,200 --> 00:02:06,920
+يعني X في المكملة و في N بصير تقاطع فدي النقطة إن
+
+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 الـ
+
+30
+00:02:19,140 --> 00:02:23,540
+logic وعمليات الـ 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 المكملة فإذا 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 الـ
+
+36
+00:02:41,950 --> 00:02:44,370
+Demorgan's أشمالها كانت بتدخل النفي على الـ and و
+
+37
+00:02:44,370 --> 00:02:48,430
+الـ or طبعا بلغة المجموعات النفي هو المكملة و الـ
+
+38
+00:02:48,430 --> 00:02:51,730
+and و الـ or إيش هيصيروا؟ تقاطعوا اتحاد فالفرع
+
+39
+00:02:51,730 --> 00:02:56,080
+الأول بيقوللي مكملة الاتحاد هي تقاطع المكملات مكملة
+
+40
+00:02:56,080 --> 00:03:00,480
+الاتحاد هي تقاطع المكملات هي دخلت على إيش صارت نفي
+
+41
+00:03:00,480 --> 00:03:04,100
+الطرفين والآخر 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 الأسلوب 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 الـ logic
+
+46
+00:03:18,780 --> 00:03:23,980
+demorgan's law حسيبه exercise خليني 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 الأمثلة المثال الأول بيقول let A, B and
+
+49
+00:03:36,950 --> 00:03:42,710
+C be any sets مقدمة زي ما اتعودنا فطبعا المفروض
+
+50
+00:03:42,710 --> 00:03:47,030
+أنه 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 شيء
+
+52
+00:03:51,150 --> 00:03:54,650
+كيف نتعامل معه طيب إيش المطلوب بيقول decide قرر
+
+53
+00:03:54,650 --> 00:04:00,650
+أو حدد whether the set A 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 تساوي A تقاطع الـ B minus A
+
+57
+00:04:19,730 --> 00:04:24,350
+تقاطع الـ C يعني بمعنى آخر هل التقاطع بتوزع على الـ
+
+58
+00:04:24,350 --> 00:04:28,550
+minus فده السؤال فبقول الـ 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 لـ approve or disapprove بدنا نقرر هل هذه
+
+62
+00:04:40,690 --> 00:04:44,850
+صحيحة و طبعا و نثبت أو هي خاطئة و ندى مثال عكسي
+
+63
+00:04:44,850 --> 00:04:49,070
+طبعا ممكن احنا بهذا النوع من الأسئلة اللي يعتبر
+
+64
+00:04:49,070 --> 00:04:51,750
+فيه أصعب من السؤال لما أقول prove مباشرة أو
+
+65
+00:04:51,750 --> 00:04:54,390
+disapprove بيكون داني جزء من الجواب لأن أنا بدي
+
+66
+00:04:54,390 --> 00:04:57,890
+أقرر أولا هل هي true وديها برهان أو هل هي false
+
+67
+00:04:57,890 --> 00:05:02,200
+وديها مثال عكسي في 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 وبعدين بكون إيش بكمل الحل
+
+70
+00:05:09,320 --> 00:05:12,260
+طيب ما قدرت 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 وأنا متأكد إن البرهان صحيح بكون
+
+73
+00:05:19,540 --> 00:05:23,230
+أنا إيش أثبتت إنها صحيحة بنفس الوقت لاجيت فيه صعوبة
+
+74
+00:05:23,230 --> 00:05:25,950
+في البرهانة في مشاكل ممكن أكتشف إنها مش .. بشكل
+
+75
+00:05:25,950 --> 00:05:29,450
+عام صحيحة لأنه حلاجي أنه إيش مش قادر أنا أثبتها و
+
+76
+00:05:29,450 --> 00:05:32,310
+.. وأثناء الاثبات بلاقي وين المشكلة و وين الخلل
+
+77
+00:05:32,310 --> 00:05:35,630
+هذا ممكن كمان يديني إيش وكيف أجيب المثال عكسي ..
+
+78
+00:05:35,630 --> 00:05:38,730
+كيف أجيب المثال عكسي فذا احنا بـ بأحد الطرح في
+
+79
+00:05:38,730 --> 00:05:41,850
+الـ prove or disprove إن نحاول إيش نعمل prove نعمل
+
+80
+00:05:41,850 --> 00:05:44,610
+prove وأنا هذا اللي بدنا نحاول طيب لو حاولنا بدنا
+
+81
+00:05:44,610 --> 00:05:48,460
+نعمل عملية prove لهذه طبعاً 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 أستخدم إيش؟ 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 الـ solution خلينا
+
+88
+00:06:07,180 --> 00:06:13,740
+نبدأ من الطرف اليمين A تقاطع الـ B ناقص A تقاطع الـ
+
+89
+00:06:13,740 --> 00:06:19,270
+C بدي أشتغل عليها الشاهد من المثال يوحي نشوف أنه في
+
+90
+00:06:19,270 --> 00:06:22,750
+آخر فرع فرع إيه في نظرية اثنين خمسة بيقول لي بقدر
+
+91
+00:06:22,750 --> 00:06:27,130
+أكتب الـ minus بدل الـ 8 تقاطع مع المكملة فهذا يساوي
+
+92
+00:06:27,130 --> 00:06:34,130
+الأولى تقاطع مكملة الثانية هذا ماشي اللي هو إيه
+
+93
+00:06:34,130 --> 00:06:37,370
+تقاطع الـ c لكل prime من وين جبته هذا من نظرية
+
+94
+00:06:37,370 --> 00:06:40,550
+اثنين خمسة اثنين خمسة الفرع إيه إذا حابين
+
+95
+00:06:40,550 --> 00:06:44,950
+بالتخصيص فإذن بدلنا هذه عبارة عن إيش؟ هي هذه X
+
+96
+00:06:44,950 --> 00:06:50,410
+وهذه Y فـ X ناقص Y تساوي X تقاطع مكملة الـ 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 إيه، هد هي فهذا يساوي،
+
+99
+00:06:58,850 --> 00:07:07,300
+بدك تبرهان، بيساوي A تقاطع الـ B تقاطع A' Union C'
+
+100
+00:07:07,880 --> 00:07:11,900
+نظرية اثنين ستة أو دي مورجان كله صح نظرية اثنين
+
+101
+00:07:11,900 --> 00:07:20,240
+ستة تمام انتبه ممتاز إيش ممكن نعمل الآن؟ ممكن 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 أعمل هذه كتلة واحدة اه ما فتح حاش
+
+104
+00:07:28,220 --> 00:07:32,980
+الآن واخد هذه الأولى مع الثانية وبعدين مع الثالثة
+
+105
+00:07:32,980 --> 00:07:39,680
+فهذا بدي أعمله توزيع A تقاطع الـ B تقاطع الـ A prime
+
+106
+00:07:39,680 --> 00:07:47,160
+اتحاد برضه نفسها الأولى A تقاطع الـ B تقاطع الـ 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 أنا بشتغل بشوف إيش ممكن أعمل وأين عيني على
+
+110
+00:08:00,010 --> 00:08:03,290
+المطلوب عيني على المطلوب عشان ما أتوّهش لإن في ممكن
+
+111
+00:08:03,290 --> 00:08:06,650
+أعمل عمليات صحيحة لكن غير مفيدة احنا برياضة تبنينا
+
+112
+00:08:06,650 --> 00:08:10,150
+حاجة صحيحة ومفيدة اه إذا عملنا حاجة غلط مشكلة وإذا
+
+113
+00:08:10,150 --> 00:08:12,890
+عملنا حاجات غير مفيدة بتتوهنا بتودينا ياش بعيد
+
+114
+00:08:12,890 --> 00:08:16,370
+عن الهدف اللي بدنا إياه وين احنا رايحين احنا رايحين
+
+115
+00:08:16,370 --> 00:08:21,320
+على الطرف هذا اللي هي عبارة عن A تقاطع B ناقص C
+
+116
+00:08:21,320 --> 00:08:26,180
+اللي هي إيش؟ B تقاطع C' ممكن نكتبها كهمش فهذه ممكن
+
+117
+00:08:26,180 --> 00:08:30,600
+أحطها بهمش أحطها بوين طرف معين فأنا رايح هنا اللي
+
+118
+00:08:30,600 --> 00:08:35,970
+هي عبارة عن A تقاطع B تقاطع C' طيب ممتاز هذا أنا
+
+119
+00:08:35,970 --> 00:08:40,090
+وين رايح؟ وين أنا وصلت؟ هي هنا إيه التقاطع بيه
+
+120
+00:08:40,090 --> 00:08:43,790
+تقاطع C prime؟ بديها هيها موجودة، إذا أنت اما تخلص
+
+121
+00:08:43,790 --> 00:08:47,290
+من هذا، اه إيش هتخلص منه؟ امحيه وخلاص؟ مع إيه 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، ممتاز في 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 وأعيش وتجميع إبدال
+
+126
+00:09:03,720 --> 00:09:09,160
+وتجميع فإذا هذا يساوي يساوي A تقاطع A' خليهم مع
+
+127
+00:09:09,160 --> 00:09:13,400
+بعض تقاطع الـ B أرجو أن يكون الكلام هذا بدأ يوضح
+
+128
+00:09:13,400 --> 00:09:16,560
+معناه كيف أنه يتعامل وليست تجميع وليست توزيع
+
+129
+00:09:16,560 --> 00:09:24,020
+وقال إبدال بعدين اتحاد هذا عبارة عن إيه؟ تقاطع الـ
+
+130
+00:09:24,020 --> 00:09:27,400
+B تقاطع الـ C' خليني 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 وإبقاش وإبدال إبدال في الفقرة الأولى
+
+134
+00:09:41,480 --> 00:09:45,660
+وبعدين إيه وتجميع وفي الثانية بس تجميع واضح تمام
+
+135
+00:09:45,660 --> 00:09:49,140
+الآن في عندنا نظرية اثنين خمسة بتقول A تقاطع A
+
+136
+00:09:49,140 --> 00:09:55,680
+برايم بيساوي في تقاطع الـ B واحدة واحدة Union A
+
+137
+00:09:55,680 --> 00:09:59,900
+تقاطع B تقاطع C برايم ليس إلا B ناقص C فأنا
+
+138
+00:09:59,900 --> 00:10:04,640
+استخدمت نظرية اثنين خمسة اثنين خمسة في الحالتين
+
+139
+00:10:04,640 --> 00:10:14,620
+استخدمت نظرية اثنين خمسة أي سؤال متابعين تمام بي و
+
+140
+00:10:14,620 --> 00:10:18,580
+في مين بين عناصر مشتركة ما فيش اه ما فيش اطلاق فدي
+
+141
+00:10:18,580 --> 00:10:25,460
+بتسوّي في فاي في اتحاد a تقاطع b minus c اه هذا
+
+142
+00:10:25,460 --> 00:10:30,420
+من وين جبناه اللي هو a في تقاطع الـ b تساوي فاي
+
+143
+00:10:30,420 --> 00:10:36,060
+واضحة تمام اه طيب a في اتحاد أي حاجة أي حاجة جبناها 
+
+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
+2.4 theoremاتنين أربعة 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 إذا اشتغلت true لو أنا في مرحلة
+
+148
+00:10:57,260 --> 00:11:00,800
+ما لجأت أنه في صعوبة وبشوف الصعوبة وينها إيش اللي 
+
+149
+00:11:00,800 --> 00:11:04,300
+مشعليني أمشي واصل للمطلوب بقدر أجيب المثال العكسي
+
+150
+00:11:04,300 --> 00:11:11,080
+إذا قدرنا فإذا ممكن هنا نعلق thus عليه إيش تقاطع 
+
+151
+00:11:11,080 --> 00:11:18,840
+الـ b minus c فعلاً يساوي a تقاطع الـ b minus a تقاطع 
+
+152
+00:11:18,840 --> 00:11:21,760
+الـ c فصار عندنا إيش التقاطع بتوزّع على الـ minus 
+
+153
+00:11:21,760 --> 00:11:30,900
+صحيح أي سؤال؟ متبيّن؟ صح، إذا ننتقل لنقطة ثانية
+
+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 الآن proveما جالّيش prove or disprove أو
+
+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 يساوي 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
+تساوي b ناقص a انعكست العملية انعكست العملية طبعاً
+
+160
+00:12:08,980 --> 00:12:11,520
+ما زال جالي prove إذا أنا على طول بدي أقوله prove
+
+161
+00:12:11,520 --> 00:12:15,240
+مش بدي أقول له خطأ ولا صح خلاص prove أو solution
+
+162
+00:12:15,240 --> 00:12:19,430
+كلّه صح proof طبعاً خلّيني أعيد الصياغة ما فيش تساوي 
+
+163
+00:12:19,430 --> 00:12:22,950
+مجموعات بس الـ a والـ 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؟ الـ trick اللي استخدمنا نظرية 2.5 نحول من
+
+167
+00:12:36,870 --> 00:12:44,190
+minus لتقاطع فهذا مفيد جداً فأي a' تقاطع من؟ b' لكلّ
+
+168
+00:12:44,190 --> 00:12:50,950
+برايم نظرية 2.5 طبعاً ننتبه في ناس مكملة مين إيش ما
+
+169
+00:12:50,950 --> 00:12:54,230
+تكون مكملة بـ prime في هذا السؤال أو إيش كانت
+
+170
+00:12:54,230 --> 00:12:58,390
+مكملة a تقاطع أو b تقاطع c ما إيش ما تكون احنا 
+
+171
+00:12:58,390 --> 00:13:03,530
+بنقول في عندي مجموعة ما x ناقص مجموعة ما y إيش
+
+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 نفكّر بيد الشمول بيد العمومية عشان نقدر 
+
+174
+00:13:11,610 --> 00:13:15,970
+نشتغل صح تمام احنا وإيش رايحين؟ رايحين على b ناقص a
+
+175
+00:13:15,970 --> 00:13:19,930
+ليه b تقاطع a' طيب إيش ممكن أعمل؟ double
+
+176
+00:13:19,930 --> 00:13:23,890
+negation أو a' مكملة المكمل هي المجموعة نفسها فده
+
+177
+00:13:23,890 --> 00:13:28,950
+بيساوي a' تقاطع الـ b نظرية برضه 2.5 بس الفرع 
+
+178
+00:13:28,950 --> 00:13:34,400
+الأول تمام إيش نعمل تبديل لأن إيش رايح دايماً عيني 
+
+179
+00:13:34,400 --> 00:13:38,160
+على إيش رايح احنا رايحين على b ناقص a يعني b تقاطع 
+
+180
+00:13:38,160 --> 00:13:41,260
+الـ a هي دي رايحين حابين يكتبوها هنا على طول هذا 
+
+181
+00:13:41,260 --> 00:13:44,400
+عبارة عن إيه؟ b تقاطع الـ a' وأنا وصلت هنا إيش أعمل 
+
+182
+00:13:44,400 --> 00:13:49,000
+تبديل؟ وتساوي b تقاطع الـ a'  commutative law
+
+183
+00:13:49,000 --> 00:13:54,260
+commutative law خلصنا وهو b ناقص a نظرية 2.5
+
+184
+00:14:01,810 --> 00:14:06,990
+وهو المطلوب فهذه الحقيقة الفرع هذا كثير بساعدنا أن
+
+185
+00:14:06,990 --> 00:14:10,690
+نحوّل الـ minus لتقاطع وبعدين نقدر نشتغل بخواص
+
+186
+00:14:10,690 --> 00:14:17,970
+التقاطع وخواص الاتحاد وهكذا أي سؤال نشوف مثال جديد
+
+187
+00:14:17,970 --> 00:14:24,440
+المثال رقم تلاتة let a and b be sets prove that b
+
+188
+00:14:24,440 --> 00:14:28,620
+subset من a prime if and only if a تقاطع الـ b
+
+189
+00:14:28,620 --> 00:14:34,040
+يساوي فاي في عندنا جملة إيش ثنائية الشرطية خليني 
+
+190
+00:14:34,040 --> 00:14:39,480
+أعيد صياغة السؤال المثال الثالث طبعاً المقدمة واضحة 
+
+191
+00:14:39,480 --> 00:14:44,700
+مافيش ده عن صيغة بس مجموعة فبقول b subset من a
+
+192
+00:14:44,700 --> 00:14:48,760
+prime if and only if طبعاً بتافّة هنا true فممكن 
+
+193
+00:14:48,760 --> 00:14:54,720
+أعملها تكافؤ اللي هو إيش a تقاطع الـ b يساوي فاي هذا
+
+194
+00:14:54,720 --> 00:14:56,780
+هو المطلوب solution
+
+195
+00:14:58,930 --> 00:15:03,110
+فمرة ثانية عشان أبرهن اللي هو if and only if
+
+196
+00:15:03,110 --> 00:15:06,450
+statement فيه أنا طريقتين two parts theorem وهذا 
+
+197
+00:15:06,450 --> 00:15:10,390
+بننصح فيه خصوصاً احنا في مبادئ الرياضيات لأنه الشغل
+
+198
+00:15:10,390 --> 00:15:14,390
+في التكافؤ بده دقة شديدة لأنه إذا أي خطوة ما كانتش
+
+199
+00:15:14,390 --> 00:15:17,230
+تكافؤ بكون اللي بالبرهان نصف راح اه بيكونوا يقولوا
+
+200
+00:15:17,230 --> 00:15:19,990
+احنا أثبتنا النص والنص الثاني ما عملنا ه فاحنا
+
+201
+00:15:19,990 --> 00:15:23,190
+هنستخدم طريقة إيش two parts proof بننصح فيها 
+
+202
+00:15:23,190 --> 00:15:27,090
+نجسمها لمين؟ لـ two implications أو لـ 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
+إيش معناه two parts؟ يعني حاجات اسمها two 
+
+206
+00:15:41,490 --> 00:15:45,410
+conditional الأول implies الثاني والثاني 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
+أقول لما أقول two parts جزئين نبدأ بالـ part first
+
+209
+00:15:52,990 --> 00:16:00,770
+part الجزء الأول فالجزء 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 فاي we want
+
+214
+00:16:27,960 --> 00:16:38,880
+to prove a تقاطع الـ b تساوي فاي أي سؤالهنا في 
+
+215
+00:16:38,880 --> 00:16:43,940
+ملاحظة مهمة وبرضه ممكن نعتبرها كنصيحة عامة كيف
+
+216
+00:16:43,940 --> 00:16:48,420
+نثبت أنّ مجموعة ما فيها 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
+الثانية طبعاً x and تملي فيها 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 طبعاً
+
+221
+00:17:00,840 --> 00:17:05,160
+مش قاعدة عشان نثبت أن مجموعة ما فيها هنستخدم a
+
+222
+00:17:05,160 --> 00:17:09,280
+proof by contradiction indirect proof اه فلتسهيل
+
+223
+00:17:09,280 --> 00:17:13,340
+العملية عشان تثبتي إذا جالك تثبتي مجموعة ما فيها من
+
+224
+00:17:13,340 --> 00:17:17,420
+الطرق الفعّالة بتنجح في الغالب إذا مش دايماً 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 ونوصل لمين؟ لـ contradiction فانا إيش
+
+227
+00:17:22,620 --> 00:17:27,360
+هقوله الآن هقوله assume إيش؟ المطلوب false مظبوط؟
+
+228
+00:17:27,360 --> 00:17:30,420
+مش هيك تعلمناه فهقوله assume إن هذه لا تساوي
+
+229
+00:17:30,420 --> 00:17:34,720
+فيه فهقوله إيه؟ a تقاطع الـ b لا تساوي فيه إيش 
+
+230
+00:17:34,720 --> 00:17:37,060
+معمّلة أنا جاهد؟ معمّلة اللي جايش approved by
+
+231
+00:17:37,060 --> 00:17:37,780
+contradiction
+
+232
+00:17:44,470 --> 00:17:47,930
+طبعاً لو قلت indirect proof بقبلها لكن الـ indirect
+
+233
+00:17:47,930 --> 00:17:50,190
+proof فيه كمان اللي هو contrapositive لكن إيه أو 
+
+234
+00:17:50,190 --> 00:17:51,910
+by contradiction فاحنا بدنا بالضبط 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 اه بقول من الأفضل مش دايماً
+
+238
+00:18:03,630 --> 00:18:07,290
+الشرط لكنّه هذه طريقة فعّالة والحقيقة 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؟ أحسنتِ، يعني أنتِ
+
+241
+00:18:15,540 --> 00:18:17,840
+فاكرة مع نفسك حتى إيش بيقولي إنّ 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 التقاطع فده 
+
+244
+00:18:24,260 --> 00:18:30,440
+بيقول لي implies there exists x، x تنتمي لمن؟ للـ a
+
+245
+00:18:30,440 --> 00:18:33,280
+تقاطع الـ b مش للفاي للّي مش فارغ للّي مش 
+
+246
+00:18:33,280 --> 00:18:36,780
+فارغ تقاطع الـ b، من وين جبنا هذا؟ مين نقول له
+
+247
+00:18:36,780 --> 00:18:41,360
+دليلنا؟ تعريف الـ فاي ما شوفوا إيش معناه فاضي؟ ما فيش
+
+248
+00:18:41,360 --> 00:18:43,500
+فيه ولا عنصر طيب إيش اللي مش فاضي؟ فيه على الأقل 
+
+249
+00:18:43,500 --> 00:18:47,520
+عنصر واضح؟ تمام ممتاز لأ الآن بندور على 
+
+250
+00:18:47,520 --> 00:18:52,680
+contradiction نحاول نفسر إيش معناه أنّ يوجد عنصر
+
+251
+00:18:52,680 --> 00:19:00,040
+now x تنتمي للـ a تقاطع الـ b ماذا تعني؟ and x
+
+252
+00:19:00,040 --> 00:19:04,680
+تنتمي للـ b تعريف ما هيش؟ التقاطع of intersection
+
+253
+00:19:04,680 --> 00:19:09,380
+ممتاز أنا وإيش بدور على contradiction يا بدي أطلع 
+
+254
+00:19:09,380 --> 00:19:13,060
+إيه اللي هو يا x لا تنتمي للـ b يا x لا تنتمي للـ a
+
+255
+00:19:13,060 --> 00:19:16,400
+هي اللي عندي بدي حالة كون هي الجملة اللي عندي بدي 
+
+256
+00:19:16,400 --> 00:19:20,820
+أوّصل إنّ b and not b إيش وين ندور؟ ندور.. إيش
+
+257
+00:19:20,820 --> 00:19:24,580
+المعطيات؟ قول لي إنّ الـ b subset من الـ a' فاللي في
+
+258
+00:19:24,580 --> 00:19:27,480
+الـ b وين؟ موجود في الـ a' اه هو eo هتوصل
+
+259
+00:19:27,480 --> 00:19:30,900
+للـ contradiction صحيح فهذا على طول implies مش تكافؤ
+
+260
+00:19:30,900 --> 00:19:36,500
+x تنتمي للـ a and x تنتمي للـ a' ليش؟ لأنّ الـ b 
+
+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
+طبعاً دي إيش معناتها؟ x لا تنتمي فهذا x تنتمي للـ a
+
+263
+00:19:44,520 --> 00:19:49,720
+and x لا تنتمي للـ a طبعاً تعريف الـ prime طبعاً
+
+264
+00:19:49,720 --> 00:19:55,760
+contradiction وانتهى 
+
+265
+00:19:55,760 --> 00:19:59,180
+البرهان طبعاً ممكن أعلق وأقوله إيش فبالتالي إنها
+
+266
+00:19:59,180 --> 00:20:03,040
+بتساوي فاي لكن لو ما كتبتش إيش صحيح thus أو
+
+267
+00:20:03,040 --> 00:20:09,660
+therefore a تقاطع الـ b فعلاً هو فارغ 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 فارغ أي سؤال
+
+270
+00:20:19,770 --> 00:20:26,470
+بنروح لاتجاه الثاني أو الجزء الثاني 2
+
+271
+00:20:26,470 --> 00:20:35,150
+فهنقول له إيش a تقاطع الـ b يساوي فاي implies b 
+
+272
+00:20:35,150 --> 00:20:40,370
+subset من a prime هذا مطلوب كالعادة هقوله إيش
+
+273
+00:20:40,370 --> 00:20:46,510
+assume إنّ الـ b true أو الشرط صحيح تساوي فاي we
+
+274
+00:20:46,510 --> 00:20:54,050
+want to prove جواب الشرط to prove that
+
+275
+00:20:54,050 --> 00:21:04,210
+b is a subset of a' فمشيّين 
+
+276
+00:21:04,210 --> 00:21:09,800
+على نفس المنهج أحياناً بنختصر أحياناً بنكتب بشكل
+
+277
+00:21:09,800 --> 00:21:13,240
+مفصّل لكن ما غيرناش 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 متعدّدة كيف نثبت subset تعلمتِ 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 any element such that أو اندتز 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  إبراهيم 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 B فانا
+
+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 أنتم شايفين احنا بنشوف المسألة، بنفهمها،
+
+305
+00:23:36,550 --> 00:23:39,410
+بنكتبها، بنشوف إيش 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 إثبات مجموعة تساوي
+
+310
+00:23:53,870 --> 00:24:03,200
+مجموعة بعد المثال الرابع اللي هو a-b-c تساوي a-b
+
+311
+00:24:03,200 --> 00:24:10,690
+union c solution كم طريقة للحل على 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 if and only if ل X التانية هذه الطريقة
+
+314
+00:24:17,350 --> 00:24:20,830
+تعريفه دائما 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
+ك 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 رأيكم نبدأ من اليمين
+
+319
+00:24:34,030 --> 00:24:37,420
+ولا اليسار نبدأ 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 تقاطع
+
+322
+00:24:48,220 --> 00:24:57,180
+مكملة الثاني C لكل براي، نظرية 2 5 الآن
+
+323
+00:24:57,180 --> 00:25:03,200
+إيش نعمل؟ De Morgan's، اه فده يساوي A تقاطع B'
+
+324
+00:25:03,780 --> 00:25:09,760
+تقاطع C' نظرية 2.6 أو De Morgan 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؟ وصلنا احنا بس طبعا بدنا نكتبها .. بدنا
+
+331
+00:25:38,450 --> 00:25:41,930
+نكتبها فطبعا هذا بيقول لي إيش؟ غير الأقواس يعني إيش
+
+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 الآن بس حطيهاش
+
+334
+00:25:52,110 --> 00:26:00,570
+النظرية ناقص b تقاطع ناقص c نظرية اتنين خمسة وهو
+
+335
+00:26:00,570 --> 00:26:08,090
+المطلوب واضح فدائما بكتب و بوصل و بعمل و بطلع على
+
+336
+00:26:08,090 --> 00:26:10,770
+المطلوب عشان اعرف إيش اللي بده اعمله فبيساعدني كثير
+
+337
+00:26:10,770 --> 00:26:14,390
+لأن في أشياء كثيرة صحيحة لكن مين المفيد وين هو
+
+338
+00:26:14,390 --> 00:26:18,470
+الهدف تبعي اللي بيحدد وين بده أوصل للهدف اللي أنا
+
+339
+00:26:18,470 --> 00:26:24,210
+رايح له أي سؤال فارجو
+
+340
+00:26:24,210 --> 00:26:28,190
+أن هذه الأمثلة تكون عطتنا فكرة كافية نحل أمثلة
+
+341
+00:26:28,190 --> 00:26:31,810
+الكتاب نحل القال ونكون جاهزين 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 اثنين 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 أداة 
+
+345
+00:26:53,740 --> 00:26:59,260
+مساعدة بتساعدنا في فهم المواضيع في أحيانًا 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 تحللنا جزء من السؤال
+
+348
+00:27:05,220 --> 00:27:10,810
+وبعدين نعرف إيش اللي بدنا إياه فالحقيقة 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 والتقاطع والمكمل
+
+351
+00:27:20,690 --> 00:27:26,570
+أول فرق طبعا John Venn هو عالم إنجليزي عالم رياضيات و
+
+352
+00:27:26,570 --> 00:27:31,850
+logic اسمه John Venn طبعا ولد في 1834 وتوفي في
+
+353
+00:27:31,850 --> 00:27:38,070
+1923 فده عالم عاش مدة طويلة صحيح فطبعا نسبة
+
+354
+00:27:38,070 --> 00:27:44,120
+لهذا العالم طبعا كيف القواعد الرسم طبعا في عرف
+
+355
+00:27:44,120 --> 00:27:47,160
+متعارف عليه طبعا أنا ممكن أرسم أي حد تساعدني ممكن
+
+356
+00:27:47,160 --> 00:27:51,740
+لكن عرفًا كيف المتعارف عليه بقولي بنرسم ال universal
+
+357
+00:27:51,740 --> 00:27:54,960
+set اللي هي إيش عبارة عن مجموعة تخيلية مش حقيقية
+
+358
+00:27:54,960 --> 00:27:57,880
+لأن بيقولوا له 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 معين وبحطه في القاع
+
+362
+00:28:11,540 --> 00:28:14,800
+في إحدى الزوايا في اليمين أو اليسار فهذا yes ال
+
+363
+00:28:14,800 --> 00:28:18,060
+universe إذاً هذا هو إطار 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 وهي متفق عليها رياضيًا بالرغم أن ال
+
+370
+00:28:40,950 --> 00:28:46,170
+Venn diagram يعني هي أسهل كثير 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 جاك أقول وهأرسمي بده رسمة هذا سؤال لكن
+
+374
+00:28:57,650 --> 00:29:01,350
+هو لا يعتبر برهان فهو ليس .. اه فبيقول له 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 الحقيقي إنما هي أداة مساعدة أداة مساعدة أيضا
+
+377
+00:29:10,300 --> 00:29:14,560
+طبعا في استخدامها محدود إذا كثر المجموعات بيصير
+
+378
+00:29:14,560 --> 00:29:18,860
+عملية غير عملية الرسم بيصير إيش صعب أن أقدر أوضح
+
+379
+00:29:18,860 --> 00:29:21,500
+فبقول إذا أكثر من ثلاث 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
+محدود طبعا في صور نمطية طبعا ما بتجيش كل الحالات
+
+382
+00:29:29,420 --> 00:29:33,820
+فهذه أشهر الصور في الصورة الأولى في عندنا اللي هو
+
+383
+00:29:33,820 --> 00:29:36,760
+الاتحاد فهو هي ال A و ال B والمظلة اللي هو
+
+384
+00:29:36,760 --> 00:29:39,580
+الاتحاد لأنه يا في ال A يا في ال B طبعا زي ما
+
+385
+00:29:39,580 --> 00:29:43,560
+تشوفين الدائرتين تقطعهم file يسمونهم
+
+386
+00:29:43,560 --> 00:29:47,280
+disjoint منفصلين نرسمهم بعيد عن بعض نرسمهم بعيد عن
+
+387
+00:29:47,280 --> 00:29:50,160
+بعض زي ما الرسم الثاني في الرسم الثالثة 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 universe طبعا التقاطع واضح عندنا 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 ال A خارج ال B فانا بدي كل ال A مع ده التقاطع
+
+393
+00:30:10,340 --> 00:30:14,040
+اللي مع ال B بس بدي جزء من ال A وخارج ال B فهذه
+
+394
+00:30:14,040 --> 00:30:17,220
+رسومات نمطية طبعا بتغطي جميع الحالات وإنما هذه الصور
+
+395
+00:30:17,220 --> 00:30:20,160
+النمطية المتعرف 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؟ لا، الأخيرة مش
+
+398
+00:30:28,590 --> 00:30:32,510
+مكملة، مكملة نسبية، مش مكملة مطلقة، مكملة ال A
+
+399
+00:30:32,510 --> 00:30:37,090
+بالنسبة لل B، فهي عناصر ال A خارج ال B، بس،
+
+400
+00:30:37,090 --> 00:30:41,350
+ما تعطيكش المكملة العامة، هي U ناقص ال A، فمختلفة،
+
+401
+00:30:41,350 --> 00:30:44,790
+هنا لا، 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 المسائل السؤال الأول رسم مباشر ما بدوش 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 ونقارن خلينا
+
+406
+00:31:01,890 --> 00:31:13,010
+نحلهم مع بعض نشوف فعلا بطلع نفس الشيء ولا لا فده
+
+407
+00:31:13,010 --> 00:31:17,640
+المثال الأول Solution 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 هي دائرة بنعملها
+
+411
+00:31:33,070 --> 00:31:37,150
+طبعا مش .. مدناش نجيب فرجار وكذا تقريبي كله اه
+
+412
+00:31:37,150 --> 00:31:41,390
+إيش 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 أو
+
+414
+00:31:45,210 --> 00:31:50,890
+نحط خطوط بدنا إيش؟ فهذه هي B prime طيب بدنا
+
+415
+00:31:50,890 --> 00:31:54,250
+تقاطعها مع ال A بدنا نجيب A ونجيب التقاطع هي ال A
+
+416
+00:31:55,400 --> 00:32:00,060
+هي ال A تقاطعها مع B' وين تقاطعها مع B'؟ اللي
+
+417
+00:32:00,060 --> 00:32:04,980
+مشترك، مش مع ال B، مع ال B' اللي هو A مظبوط؟
+
+418
+00:32:04,980 --> 00:32:08,300
+اللي هي فعلا A ناقص B، لو ظهرت الرسمة فعلا 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 أيه 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 أه فالصورة النمطية أه عشان أقارن هي
+
+425
+00:32:34,770 --> 00:32:38,610
+فعلا أيه ناقص فيه بتطلع نفس الرسم أي سؤال
+
+426
+00:32:41,620 --> 00:32:45,440
+نشوف مثال والحقيقة ده مثال الحقيقة هو أكثر 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 احنا 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 الثاني 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 الثانية، طبعا يمكن
+
+443
+00:34:01,810 --> 00:34:05,500
+صعب أرسم مع نفس الرسمة، خذنا نرسم مع الرسمة ونقارن
+
+444
+00:34:05,500 --> 00:34:08,820
+بين الرسمتين بس بدي أحاول إيش أثبت 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 إيش بده الآن بده A' تقاطع B' نبدأ نحسبهم
+
+448
+00:34:22,840 --> 00:34:27,960
+واحدة واحدة هي ال A وين A' خارج ال A خارج ال A
+
+449
+00:34:27,960 --> 00:34:34,000
+خليه بيعمله بالأحمر هي 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 ما فيش 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
+أو 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 شرط هنا 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 احنا
+
+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
+بيقول لي؟ بيقول لي إذا في عنصر في الـA، عنصر في الـA
+
+473
+00:36:23,720 --> 00:36:28,820
+وين يكون؟ ياها، ياها هل بالضروري يكون خارج الـ B؟
+
+474
+00:36:28,820 --> 00:36:33,900
+واضح أنه لا، ها هي مرة ثانية، 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، أو 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 الثالث والأخير بقول لي
+
+481
+00:37:09,300 --> 00:37:16,520
+ال A و ال B subset من مجموعة كبيرة X فبقول لي 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
+التقاطعات و هل بتوزع الاتحاد هيك معناها هنشوف 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 أنهم 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 B هي 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
+ما بنفعش 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 B طيب، 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 الاتحاد فنقرن
+
+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 أعيد إيش آخر
+
+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 الحمرة و 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 لأ الآن 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 المجموعات indexed 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 المعينة طبعا
+
+532
+00:41:35,950 --> 00:41:39,810
+أول شيء 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 بقول له collection of objects طب ال family
+
+535
+00:41:48,830 --> 00:41:52,010
+برضه collection of objects طب إيش 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 التنتيجة هنا
+
+540
+00:42:11,090 --> 00:42:14,390
+طبعا بيقول لي 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
+تكرار كلهم مختلفين على بعض بيقول لي 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
+العرف، 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 بسيطة اللي 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 لأ احنا 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 وإيش معناه set وإيش الفرق بينهم؟
+
+562
+00:43:41,020 --> 00:43:44,430
+إيش الهدف الرئيسي من هذا الـ section؟ الهدف الرئيسي
+
+563
+00:43:44,430 --> 00:43:48,350
+في هذا الـ 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 sets 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 sets هذه النقطة الأولى طيب لما
+
+569
+00:44:07,590 --> 00:44:08,830
+يكون أنا عندي فضل
+
+570
+00:44:13,860 --> 00:44:17,200
+هي عضو في الـ family بتبدأ تكون المجموعة member
+
+571
+00:44:17,200 --> 00:44:24,280
+هتحاول مع family of sets family of sets ممكن ممكن
+
+572
+00:44:24,280 --> 00:44:26,720
+هدقق بشكل عام بس احنا هدفنا الرئيسي طبعا الـ family
+
+573
+00:44:26,720 --> 00:44:30,020
+بشكل عام collection of objects هدول الـ 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
+الـ section إيش هدفنا هنتعامل مع family of sets موضوعنا
+
+576
+00:44:36,960 --> 00:44:39,320
+الرئيسي لكن هل كل family هي family of sets 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 وهي family اه وفي تكرار بس بالنسبة ك ..
+
+579
+00:44:52,970 --> 00:44:57,530
+ك ستة كم عنصر فيها نين ك family تلاتة بس إيه الفرق
+
+580
+00:44:57,530 --> 00:45:00,990
+مش مشكلة تمام إذا نقول إن احنا هدفنا الرئيسي إن
+
+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
+أنا جالي في عندي three sets إيش ممكن أرمزلهم ABC
+
+583
+00:45:07,710 --> 00:45:11,910
+بكل سهولة طب لو في عندي خمسة إيش بده أبدأ أقول A,B
+
+584
+00:45:11,910 --> 00:45:15,190
+,C,D وأعدل كل الحروف؟ لأ، من الأفضل أقوله A1,A2
+
+585
+00:45:15,190 --> 00:45:18,770
+,A3 وهكذا فهذه عملية الترقيم، عملية التسمية هي
+
+586
+00:45:18,770 --> 00:45:22,790
+عملية indexing، عملية أرشفة، لو بده يرشف كتب، إيش
+
+587
+00:45:22,790 --> 00:45:26,350
+بده يعمل؟ ممكن إيش، بده يحط لهم إيش، طابعة معينة
+
+588
+00:45:26,540 --> 00:45:30,660
+يرقمهم ترقيم معين يسميهم تسمية معينة يقسمهم تقسيم
+
+589
+00:45:30,660 --> 00:45:33,780
+معين ويرتبهم 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 أو بيتطلب إن إيش أرقمهم
+
+593
+00:45:46,460 --> 00:45:50,620
+بشكل معين أسميهم بشكل معين هذه العملية التسمية أو
+
+594
+00:45:50,620 --> 00:45:53,920
+الترقيم بيسموها عملية إيش أرشفة أو indexing أو
+
+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 أنا في عندي عشرة أو خمسة بدي أسميهم a1,
+
+597
+00:46:01,020 --> 00:46:06,260
+a2, a10 طبعا هل بالضروري أنا أرقم ترقيم؟ لأ مش
+
+598
+00:46:06,260 --> 00:46:11,020
+بالضروري ممكن أسميهم إيش a a a sub a أو 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 إيش مجموعة الأرشفة indexing set indexing set
+
+602
+00:46:23,360 --> 00:46:27,690
+فهي الصيغة العامة بها 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
+بيستخدمونها للترقيم أو للتسمية 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 إن 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 الرمز دي small gamma والأولى capital
+
+609
+00:46:51,670 --> 00:46:57,520
+gamma والتانية small gamma فهدي small gamma وهذه
+
+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 للـ element و capital للمجموعة بقول لكل
+
+612
+00:47:06,000 --> 00:47:11,160
+عنصر small gamma بتنتمي لـ capital gamma احنا هنصحب
+
+613
+00:47:11,160 --> 00:47:15,180
+أو 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 الصورة افترض أنه في مكتبة كبيرة من الكتب
+
+616
+00:47:25,210 --> 00:47:31,070
+بدنا نأرشفها بطريقة معينة بحيث يسهل الوصول إلى
+
+617
+00:47:31,070 --> 00:47:35,450
+الكتب إيش ما عملنا؟ جبنا بطاقات أو طوابع وحطينا
+
+618
+00:47:35,450 --> 00:47:37,950
+على هدول الطوابع اسمها أنا عارف الكتب، بدي أ
+
+619
+00:47:37,950 --> 00:47:41,730
+أرشفهم، فعملت تقسيمة ف أنا المجموعة اللي فيها
+
+620
+00:47:41,730 --> 00:47:45,110
+الطوابع هي الـ 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 ولزقت عليه الكتاب 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
+جبت الكتاب اللي هو a و روحت لزقتها عليه فصارت a
+
+626
+00:48:02,550 --> 00:48:06,030
+sub gamma فماشي عملت أرشف الـ 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 gamma واضحة 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 لملائمة 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 sets كيف الرمز إلها كيف صارت بعد
+
+633
+00:48:30,760 --> 00:48:33,810
+مرتبة خلاص كل كتاب والطبيعة تبعته والطوابع 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_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/O98m-m2qojg_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..027279e09457d8f9bb8e2c191b0457a651940d77
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/O98m-m2qojg_raw.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/PBRa0MHjhZs.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/PBRa0MHjhZs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1932906d59bc406e4a8a1fc411d83559aa3b5812
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/PBRa0MHjhZs.srt
@@ -0,0 +1,2455 @@
+1
+00:00:19,670 --> 00:00:23,550
+بسم الله الرحمن الرحيم إن شاء الله نواصل احنا
+
+2
+00:00:23,550 --> 00:00:28,110
+بدأنا بداية مختصرة اللي هو الـdenumerable and non
+
+3
+00:00:28,110 --> 00:00:31,130
+-denumerable sets وبشكل خاص بدأنا من ال infinite
+
+4
+00:00:31,130 --> 00:00:36,050
+set المجموعة غير المنتهية أو اللانهائية فانتهيت بس
+
+5
+00:00:36,050 --> 00:00:40,680
+اللي هو التعريف لأنه مهم جدا فنقول 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 مكافئ إن 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 proper subset من X proper subset
+
+12
+00:01:04,460 --> 00:01:07,500
+من X فهدول صورتين متكافئتين و احنا بنشتغل مع
+
+13
+00:01:07,500 --> 00:01:10,380
+الصورة الثانية 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 finite فطبعا
+
+17
+00:01:22,100 --> 00:01:26,640
+احنا شفنا أول مثال وانه مجموعة الأعداد الطبيعية أي
+
+18
+00:01:26,640 --> 00:01:30,240
+الأعداد الصحيحة الموجبة هي infinite set وأوجدنا
+
+19
+00:01:30,240 --> 00:01:33,020
+اللازمة دالة طبعا ممكن يكون فيه أكثر من دالة احنا
+
+20
+00:01:33,020 --> 00:01:37,400
+أخذنا f of x بتساوي 2x زي 2x وظبطت معنا طبعا ممكن
+
+21
+00:01:37,400 --> 00:01:40,900
+أن نشوف خيارات أخرى لكن هذا قد الغرض لأنه بده لاجي
+
+22
+00:01:40,900 --> 00:01:46,630
+الدالة خلينا نشوف كمان نظرية نبدأ نشوف مين الأمثل
+
+23
+00:01:46,630 --> 00:01:49,850
+اللي هتكون متعارف علينا ومعروفة طبعا من هنا نطالع
+
+24
+00:01:49,850 --> 00:01:52,450
+احنا عارفين أن ال N infinite فهذه تعتبر نظرية ممكن
+
+25
+00:01:52,450 --> 00:01:55,870
+تستخدمها في أي مكان ال proposition النظرية الثانية
+
+26
+00:01:55,870 --> 00:01:59,630
+أو 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
+هدول إيش finite set are finite فنشوف 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 شفنا 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
+أنه Phi is finite طبعا زي ما احنا شايفين التعريف
+
+38
+00:02:51,580 --> 00:02:55,680
+عرف ال infinite ما عرفش ال finite جاء في ال finite
+
+39
+00:02:55,680 --> 00:02:59,280
+هي ال negation لذلك من الأنسب أن 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 إيش بنعمل approved by
+
+43
+00:03:13,660 --> 00:03:16,860
+contradiction خليني بس اكتب تحت عشان أحافظ 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 إيش
+
+46
+00:03:28,200 --> 00:03:33,400
+معناه الـ finite التعريف فده معناه 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 and F of Phi proper 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
+بدأنا 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 إيش دليل هنا؟ Definition of infinite
+
+54
+00:04:10,540 --> 00:04:15,150
+set Infinite set هذا اللي استخدمته اه فاستخدمت
+
+55
+00:04:15,150 --> 00:04:18,770
+التعريف لأن حتى الآن طب الآن هذا إيش بيؤدي طب F of
+
+56
+00:04:18,770 --> 00:04:22,590
+Phi إيش بتساوي Phi proper من ال Phi ليش لأن فيه
+
+57
+00:04:22,590 --> 00:04:26,070
+نظرية بتقولي F of Phi تساوي Phi هاي دليلي صحيح
+
+58
+00:04:26,070 --> 00:04:33,860
+تمام إيش رأيكم إيش نعمل بعد هيك خلص البرهان ولا
+
+59
+00:04:33,860 --> 00:04:37,320
+ما خلصش؟ اه Contradiction .. اه ليش؟ لأن الـ Phi
+
+60
+00:04:37,320 --> 00:04:39,620
+بيجبى إيش معنى تبروبرت؟ لا تساوي Phi؟
+
+61
+00:04:39,620 --> 00:04:42,040
+Contradiction .. اه فده معناه أن Phi لا تساوي Phi
+
+62
+00:04:42,040 --> 00:04:44,220
+فده إيش؟ Contradiction .. خلص البرهان
+
+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 أن أعلمكم
+
+65
+00:04:51,300 --> 00:04:54,680
+ياه وكيف نعرف أن البرهان انتهى Contradiction لأنه
+
+66
+00:04:54,680 --> 00:04:57,260
+دي إيش معناها أن 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 ما نفعش
+
+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 خذنا نأخذ مجموعة من
+
+72
+00:05:15,420 --> 00:05:21,810
+عنصر واحد فنقول هنا let A أو X إذا 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 أثبت أن ال X finite بنثبت أن ال X finite
+
+76
+00:05:37,710 --> 00:05:47,480
+by contradiction assume X is infinite عشان بنعمل
+
+77
+00:05:47,480 --> 00:05:53,080
+prove by contradiction بس عشان الواحد يتابع 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 الاستدلالي 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 معكم، يمكن أول مثال كان
+
+82
+00:06:07,360 --> 00:06:10,000
+صعوبة، إيش معناه not infinite؟ بقدر ألاقي دالة
+
+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
+لنفسها such 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 خليكوا 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 واحد مرت 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 وعندنا
+
+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 فهدول 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 أمثلتنا 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 بالعامية و ال infinite كبيرة
+
+104
+00:07:58,640 --> 00:08:01,320
+اللي أكبر منها بتاعتها infinite اللي هي ال super
+
+105
+00:08:01,320 --> 00:08:05,340
+set شوفوا 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 converge وإذا
+
+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
+الثاني 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 infinite و 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 علينا 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 بدأت
+
+126
+00:09:29,890 --> 00:09:32,570
+تكون infinite هي المطلوب فهي نعبر أولش نأخذ
+
+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 set في 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 المطلوب فنعبّرنا عنه إيش معناه
+
+134
+00:10:12,910 --> 00:10:18,090
+every super set for all Y أي مجموعة كبيرة Y تحتوي
+
+135
+00:10:18,090 --> 00:10:21,750
+الـ X والـ X finite بدأت تكون برضه الـ Y infinite
+
+136
+00:10:21,750 --> 00:10:27,060
+تكون الـ Y infinite أه 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 البرهان فهذه مهارات ممتازة أن يتعلم let y
+
+139
+00:10:36,480 --> 00:10:44,130
+be a set such that أه هي بكتب هيك يا بكتب X subset
+
+140
+00:10:44,130 --> 00:10:47,090
+إيه اللي بدلنا إياها كله اللي بيريحكوا X subset من 
+
+141
+00:10:47,090 --> 00:10:50,150
+الـ Y يمكن هذي إحنا متعودين عليها فالـ Y هي الكبيرة
+
+142
+00:10:50,150 --> 00:10:53,430
+هي الـ super set هي الـ Y مطلوب أثبت إن الـ 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 لـ Y أنا مدشن على الـ Y تكون one
+
+145
+00:11:00,110 --> 00:11:03,430
+to one و تكون اللي هو الـ 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 الـ Y المطلوب أثبت أن الـ Y is
+
+149
+00:11:17,700 --> 00:11:29,200
+infinite من Y لـ Y such that G F F is one to one
+
+150
+00:11:29,200 --> 00:11:37,820
+and صورة الـ Y برابر من الـ Y برابر من الـ 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 الـ natural number مين عنده اقتراح
+
+155
+00:11:54,290 --> 00:11:59,090
+على أن يتعرف للـ F اعملوا 
+
+156
+00:11:59,090 --> 00:12:04,450
+عصف ذهني زي ما بيقولوا اقترحواعرفوني الـ 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 الـ 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
+
+163
+00:12:26,350 --> 00:12:26,430
+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
+
+165
+00:12:26,770 --> 00:12:31,230
+انا انا انا
+
+166
+00:12:31,230 --> 00:12:38,810
+أنا ولا طفاح ولا موز ولا بوردجان؟ مش عارفين، ممتاز،
+
+167
+00:12:38,810 --> 00:12:41,590
+احنا اللي بده أوصله إليه، لما أنا لسه قالت مش
+
+168
+00:12:41,590 --> 00:12:44,430
+عارفين إيش عناصر الواد، الواد بقى بجموعة عامة،
+
+169
+00:12:44,430 --> 00:12:50,830
+عناصرها مش معروفة، بنك دوال الـ calculus سكروه 
+
+170
+00:12:50,830 --> 00:12:55,130
+مانفعناش لأن وداك معرف على دوال هيش ريال لريال اه
+
+171
+00:12:55,130 --> 00:12:59,250
+بدنا نشوف مكان آخر نعرف منه بدنا نشوف مكان آخر
+
+172
+00:12:59,250 --> 00:13:02,730
+بدنا بنك آخر بنك الـ calculus مفلس بالنسبالنا غير 
+
+173
+00:13:02,730 --> 00:13:09,320
+مناسب بدنا ندور على مكان مناسب طيب، من وين نعرف؟ من
+
+174
+00:13:09,320 --> 00:13:13,800
+وين نعرف؟ إيش في عينكوا؟ في هذا النوع، في الغالب،
+
+175
+00:13:13,800 --> 00:13:17,480
+بدي أعتمد على دوال معطية في السؤال، في الغالب، هذه
+
+176
+00:13:17,480 --> 00:13:21,520
+كنصيحة، كإرشاد، بدنا نتعرف على دوال معطية في 
+
+177
+00:13:21,520 --> 00:13:25,080
+السؤال، في عيننا دوال معطية في السؤال؟ إيش مالها
+
+178
+00:13:25,080 --> 00:13:28,740
+الـ X؟ Infinite، إيش معنات Infinite؟ بقدر ألاقي
+
+179
+00:13:28,740 --> 00:13:32,710
+دالة، في أيه المفتاح؟ آه، هاي هنا، بدي دوالفو بس 
+
+180
+00:13:32,710 --> 00:13:35,230
+واحدة واحدة بس أنا بدي أعرف ده لوحدة ماني بس إذا
+
+181
+00:13:35,230 --> 00:13:39,050
+الـ F معرفة فإذا الـ F معرفة هذي هي إيش بيصير عندي
+
+182
+00:13:39,050 --> 00:13:42,210
+أنا إي حاجة أشتغل عليها خليني أشوف كيف .. طبعا
+
+183
+00:13:42,210 --> 00:13:45,210
+الأمثلة في البداية فشيء طبيعي أن أنتوا تكونوا بعاد
+
+184
+00:13:45,210 --> 00:13:48,710
+عنها شوية شوية الأمور تتحسن تمام فانا بدي أدور على
+
+185
+00:13:48,710 --> 00:13:52,010
+الـ F الآن بدي أشوف وين مظادر إذا إحنا بنتعلم هنا 
+
+186
+00:13:53,050 --> 00:13:55,890
+تفكير المجرد تتذكر لما تقول إن احنا عرفنا الـ
+
+187
+00:13:55,890 --> 00:13:58,450
+composition ماعرفناش الجمع أو الطرح للدوال بشكل
+
+188
+00:13:58,450 --> 00:14:01,670
+عام لإنه مش ضروري كل عناصر بيكون فيها جمع زي هنا 
+
+189
+00:14:01,670 --> 00:14:05,430
+إيش عرفنا إنه 2X معرفة لإن هو مش أرقام إيش معرفنا
+
+190
+00:14:05,430 --> 00:14:08,810
+إن الجمع معرف الـ sign معرفة مش معرفة على الـ Y لإن
+
+191
+00:14:08,810 --> 00:14:11,610
+الـ Y مش عارفين إيش عناصرها بشكل عام نشتغل فالآن
+
+192
+00:14:11,610 --> 00:14:14,930
+هنشوف كيف بنجيب الدالة من المعطيات لإن هو دي معرفة
+
+193
+00:14:14,930 --> 00:14:18,750
+و هتتكرر معنا فالآن نبدأ نقول له الـ gate X أشمالها
+
+194
+00:14:18,750 --> 00:14:25,400
+is infinite X is infiniteو هذه المهارة حكيناها قبل
+
+195
+00:14:25,400 --> 00:14:28,300
+ايه عندك معلومات اكتبوها حتى لو بالهمش تشوف انت
+
+196
+00:14:28,300 --> 00:14:31,880
+إيش عندك إمكانيات و انت دايما عينك وين على المطلوب
+
+197
+00:14:31,880 --> 00:14:34,860
+هينحطينا المطلوب و نقولنا بندور على جيه دورنا في 
+
+198
+00:14:34,860 --> 00:14:38,000
+دفاضر الـ calculus قولنا بتبفع ناس بندور في مكان
+
+199
+00:14:38,000 --> 00:14:42,380
+آخر فندورش أن مواطيات تفتحنا الباب للحل ولا بتفتحش
+
+200
+00:14:42,380 --> 00:14:46,160
+اه فالـ excess finite implies there exist إيش 
+
+201
+00:14:46,160 --> 00:14:51,910
+يسميها الـ F مشغول هنسميها اسم جديد جيهمن X لـ X
+
+202
+00:14:51,910 --> 00:15:05,850
+such that G is one to one and G of X برابر من X هذا
+
+203
+00:15:05,850 --> 00:15:10,910
+معناه infinite هتطيها في السؤال، هتطيها في الهامش،
+
+204
+00:15:10,910 --> 00:15:13,110
+هتطيها على الأقل جانبية، لكن هذا مُعطَب، نحاول
+
+205
+00:15:13,110 --> 00:15:17,630
+نستفيد منه فالآن بنتعلمها دي المهارة، هنعرف الـF
+
+206
+00:15:17,630 --> 00:15:21,570
+بدلالة الـG كيف؟ نفكر مع بعض، نفكر مع بعض، إحنا
+
+207
+00:15:21,570 --> 00:15:31,470
+إيش عندنا الصورة؟ عندنا Y كبيرة وفيها X جواها و جوا
+
+208
+00:15:31,470 --> 00:15:36,750
+عناصر كل الـ Y اللي في الـ X معرف عليهم الـ G شايفها
+
+209
+00:15:36,750 --> 00:15:41,390
+معرف عليهم مش معروفة بشكل صريح لكن معرفة معرفة و
+
+210
+00:15:41,390 --> 00:15:45,610
+بتام عندنا الباقي بتام عندنا الباقي بدنا ياها من Y
+
+211
+00:15:45,610 --> 00:15:50,730
+لـ Y نعمل كمان نسخة من الـ Y كمان نسخة من الـ Y فبدنا 
+
+212
+00:15:50,730 --> 00:15:55,470
+دالة من hand لـ hand فانا هعرف .. وانتبه okay بنفكر
+
+213
+00:15:55,470 --> 00:15:58,570
+عشان نتعرف .. هبدأ أقوله let F مش هيك قلناه .. مش
+
+214
+00:15:58,570 --> 00:16:01,650
+هيك حلينا natural number .. بدنا نكرر .. هقوله let
+
+215
+00:16:01,650 --> 00:16:10,010
+F من Y إلى Y be given by .. بدأ أعرف الـ F .. by F
+
+216
+00:16:10,010 --> 00:16:16,830
+of X تساويلو كانت الـ X في الـ capital X فالـ G معرف
+
+217
+00:16:16,830 --> 00:16:24,930
+عليها فهقوله تساوي G of X إذا X وين في الـ capital
+
+218
+00:16:24,930 --> 00:16:29,830
+X ممتازة بتنفعه ولا بتنفعش؟ تنفع لأن الـ G هذه 
+
+219
+00:16:29,830 --> 00:16:32,970
+الدالة بتقدر الغرض أشمالها one to one و أشمالها
+
+220
+00:16:32,970 --> 00:16:38,010
+بتزغر كذا not onto بتزغر الصورة كأنها طيب في عندي
+
+221
+00:16:38,010 --> 00:16:45,100
+هنا مكان إضافي اللي هو إيش بيمثل هنا Y ناقص X ما
+
+222
+00:16:45,100 --> 00:16:49,460
+تبقى لأنه مفهوش .. مفهو .. ده اللي اوقفها من Y لـ Y
+
+223
+00:16:49,460 --> 00:16:53,980
+لازم الناس اللي هيجي تغطي كل الـ domain كيف اعرفها؟
+
+224
+00:16:53,980 --> 00:16:58,360
+كيف نعرفها؟ X اه .. ايه؟ X من ان اعرفها identity
+
+225
+00:16:58,360 --> 00:17:02,570
+function بدنا نعرفه Identity Function ايه اسمه لك
+
+226
+00:17:02,570 --> 00:17:05,450
+يا حبي؟ نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+227
+00:17:05,450 --> 00:17:07,130
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+228
+00:17:07,130 --> 00:17:07,450
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+229
+00:17:07,450 --> 00:17:10,410
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+230
+00:17:10,410 --> 00:17:14,930
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+231
+00:17:14,930 --> 00:17:16,730
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+232
+00:17:16,730 --> 00:17:24,410
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+233
+00:17:24,410 --> 00:17:30,070
+نفسي نفسي نمش أنتوا لكن أنا إيش عملت مش على كل
+
+234
+00:17:30,070 --> 00:17:33,790
+اللي عرفتها identity بس على جزء عندي جزء فانا إيش
+
+235
+00:17:33,790 --> 00:17:37,450
+اللي بده أعمله عشان بس نفكر مع بعض هذا الجزء بديش 
+
+236
+00:17:37,450 --> 00:17:41,510
+أصغره صورته مش هتصغر لإن احنا إيش بنعمل بناخد
+
+237
+00:17:41,510 --> 00:17:45,170
+المجموعة و بنخلي صورتها أصغر proper subset مظبوط
+
+238
+00:17:45,170 --> 00:17:47,990
+فكأنه الدالة اللي بتأول عليها هي دالة بتعمل عمل
+
+239
+00:17:47,990 --> 00:17:52,370
+تصغير للصورة فبالنسبة للـ identity هذا الجزء بتنجله
+
+240
+00:17:52,370 --> 00:17:56,220
+زي ما هو بيصغرهاش لكن مين اللي بيصغر اللي جوه الـ X
+
+241
+00:17:56,220 --> 00:17:59,420
+ليه الـ G بتقوم بعملية تصغير يكفيني، بتديش كل
+
+242
+00:17:59,420 --> 00:18:01,940
+الدالة جزء منها، لو جزء منها صغر يكفي، بتقدي
+
+243
+00:18:01,940 --> 00:18:05,740
+الغرض، فهذه هنثبت أنه بتحقق الشرطين، هنثبت أن هذه 
+
+244
+00:18:05,740 --> 00:18:09,060
+الدالة هي التعريف الصحيح، فبدنا ننتبه، لما نعرف
+
+245
+00:18:09,060 --> 00:18:11,840
+الدالة، نشوف الدالة ممكن تتعرف ولا لأ، في عنا 
+
+246
+00:18:11,840 --> 00:18:15,320
+مجموعة مجرد عامة لا يمكنني أن أعرف عليها عمليات
+
+247
+00:18:15,320 --> 00:18:18,560
+حسابية أو أعرف دوال الـ Calculus طيب، من الدوال
+
+248
+00:18:18,560 --> 00:18:20,360
+التي تنفع أن تتعرف دائما؟ لو Identity تنفع أن 
+
+249
+00:18:20,360 --> 00:18:23,380
+تتعرف دائما، لأنه لا يوجد أي عملية حسابية لأي
+
+250
+00:18:23,380 --> 00:18:26,160
+مجموعة؟ أو نحن استفدنا من هذا الـL مُعرّف، أيش ما
+
+251
+00:18:26,160 --> 00:18:29,120
+تكون تكون الـG مُعرّف أصلا استفدنا منها، لنرى هل
+
+252
+00:18:29,120 --> 00:18:32,360
+هذه تنفع ولا لا تنفع؟ هل هناك أحد عنده الصفصار
+
+253
+00:18:32,360 --> 00:18:35,380
+متبعين؟ فإذن هذا المفتاح، هذه الصعوبة التي أتكلم
+
+254
+00:18:35,380 --> 00:18:39,340
+عنها كيف نكون الـF؟ طبعا لسه الأمثلة تتعدد معنا
+
+255
+00:18:39,340 --> 00:18:39,820
+وشوية ش
+
+256
+00:18:43,680 --> 00:18:47,020
+أي استفسار؟ متابعين؟ تمام، نثبت إن الـ App هي one
+
+257
+00:18:47,020 --> 00:18:54,640
+-to-one وإن ليش ليست on فنبدأ .. نعم .. أه بس 
+
+258
+00:18:54,640 --> 00:18:57,220
+بتاخدوا .. تشوفوا مع بعض كيف بيكون، على أنه بتاخد
+
+259
+00:18:57,220 --> 00:18:59,920
+عنصرين من الـ domain طب لو عنصرين ممكن يكونوا في X
+
+260
+00:18:59,920 --> 00:19:03,000
+و الـ G بتحللنا المشكلة، طب لو واحد هنا و واحد هنا،
+
+261
+00:19:03,000 --> 00:19:05,680
+إيش بيصير؟ هنشتغلها كلها، خليني أنا أخدها واحدة
+
+262
+00:19:05,680 --> 00:19:10,020
+واحدة خليني أخدها واحدة واحدة ده نبدأ خطوة خطوة و
+
+263
+00:19:10,020 --> 00:19:15,380
+نشوف إيش الاحتمالات و النظرة الأولية بالسهولة صح
+
+264
+00:19:15,380 --> 00:19:20,300
+ولا مش صح فهيبدأ أثبت أن F is one to one F is one
+
+265
+00:19:20,300 --> 00:19:24,680
+to one بدنا نثبت طبعا كالعادة هاخد عنصرين من الـ
+
+266
+00:19:24,680 --> 00:19:31,640
+domain let X1 X2 من domain الـ F؟ Y فننتبه و نركز
+
+267
+00:19:31,640 --> 00:19:34,420
+في الحل تنتبه من الـ Y such that
+
+268
+00:19:37,280 --> 00:19:44,720
+F of X1 تساوي F of X2 إيش مطلوب مني؟ مطلوب مني
+
+269
+00:19:44,720 --> 00:19:48,980
+أثبت إن X1 تساوي X2 هذا هو الهدف تبعي أوصلنا الـ F
+
+270
+00:19:48,980 --> 00:19:53,260
+هنا معرفة بالتجزيق اللي عبارة عن اتحاد يعني اتحاد
+
+271
+00:19:53,260 --> 00:19:57,520
+إيش؟ يعني or ففي عندي الحقيقة أربع احتمالات يا
+
+272
+00:19:57,520 --> 00:20:01,800
+العنصرين مع بعض في الـ X، يا العنصرين مع بعض خارج
+
+273
+00:20:01,800 --> 00:20:05,400
+الـ X في Y ناقص X، أو واحد دي هو واحد برا، الأول
+
+274
+00:20:05,400 --> 00:20:08,180
+أو التاني، فعندي أربع احتمالات، أربع احتمالات،
+
+275
+00:20:08,180 --> 00:20:10,600
+لحقيقة الاحتمالات التانية ممكن أضمهم مع بعض، بس
+
+276
+00:20:10,600 --> 00:20:12,860
+حتى لو خلينا نكتبهم بالتفصيل، متفرجش كتير، و هم
+
+277
+00:20:12,860 --> 00:20:15,260
+متشابهين، لأنه احنا قولنا X واحد و X اتنين من
+
+278
+00:20:15,260 --> 00:20:17,120
+الأول و الأتنين التاني، متفرجش معنا كتير، لكن
+
+279
+00:20:17,120 --> 00:20:20,720
+خلينا نشتغلهم بالتفصيل، فهذا يؤدي، في عندي أربع
+
+280
+00:20:20,720 --> 00:20:27,080
+احتمالات لو كانوا X1 و X2 في الـ Capital X إيش 
+
+281
+00:20:27,080 --> 00:20:30,060
+تعريفهم؟ بدي أستخدم التعريف الآن بس التعريف هيدينا 
+
+282
+00:20:30,060 --> 00:20:32,960
+أربع احتمالات وهذه المهارة هتيجي معنا أكثر من مرة
+
+283
+00:20:32,960 --> 00:20:35,880
+هذا ال trick اللي هنا بنستخدمه ففي عندنا أربع
+
+284
+00:20:35,880 --> 00:20:39,620
+احتمالات خلينا نعملهم بيد الشكل عشان ما فيش واسعة
+
+285
+00:20:39,620 --> 00:20:47,280
+فإما تكون G of X1 تساوي G of X2 وقتاش؟ إذا X1 و X2
+
+286
+00:20:47,280 --> 00:20:52,170
+وين موجودين؟ في الـ Capital X هي التعريف إذا الاثنين 
+
+287
+00:20:52,170 --> 00:20:55,990
+مع بعض يومًا الـ X فإيه إن تعريف الـ F الـ F بتكون G 
+
+288
+00:20:55,990 --> 00:21:00,190
+لو سمحت هنا فإذا كانت X1 في الـ capital X إيش تعريف
+
+289
+00:21:00,190 --> 00:21:04,590
+الـ F؟ G و X2 نفس القضية طيب، الآن لو كانوا الاثنين
+
+290
+00:21:04,590 --> 00:21:08,370
+برا طبعا بينهم هدولة كلهم Or لأنها دي هاش اتحاد
+
+291
+00:21:08,370 --> 00:21:11,150
+فأو لو كانوا الاثنين برا دي وكنت عارفهم الـ identity
+
+292
+00:21:11,150 --> 00:21:16,390
+X1 تساوي X2 وقتاش؟ إذا X1 و X2 موجودين في الـ Y
+
+293
+00:21:16,390 --> 00:21:23,220
+ناقص X أه طبعا كله بينهم R أو طبعا لو كانت X1 في الـ
+
+294
+00:21:23,220 --> 00:21:30,280
+X و X2 في الـ Y ناقص X إيش بيكون؟ الـ X1 في الـ X إيش
+
+295
+00:21:30,280 --> 00:21:34,340
+تعريف الـ F؟ F of X .. G of X1 و الـ X2 من برة إيش
+
+296
+00:21:34,340 --> 00:21:40,500
+بيكون تعريفها؟ X2 نفس القضية لو كانت X2 في الـ X و
+
+297
+00:21:40,500 --> 00:21:45,500
+X1 في الـ Y ناقص X بتشبهها إيش بيكون؟ تعريف الـ A of
+
+298
+00:21:45,500 --> 00:21:53,980
+X1 X1و X2 جي و X2 طبعا كله R R R هدولة أربع
+
+299
+00:21:53,980 --> 00:21:57,620
+احتمالات واحدة منهم بتكون على الأقل صحيحة واحدة
+
+300
+00:21:57,620 --> 00:22:04,150
+منهم بتكون صحيحة واضحة فهذه دالة يعني هذه إيش نتعلم
+
+301
+00:22:04,150 --> 00:22:08,810
+منها كيف أثبت أنه دالة معرفة بالتزيق اختراع متعدد
+
+302
+00:22:08,810 --> 00:22:13,270
+القاعدة كيف أثبت أنه one to one كيف أثبت أنه one
+
+303
+00:22:13,270 --> 00:22:18,690
+to one فكل احتمال بديني باش تغلق و بداشه طبعا آخر
+
+304
+00:22:18,690 --> 00:22:22,710
+احتمال جاهز هدف أن أوصل أن X1 تساوي X2 مظبوط هذا
+
+305
+00:22:22,710 --> 00:22:25,380
+جاهز أه طبعا عشان بينهم or بينفع أعمل 
+
+306
+00:22:25,380 --> 00:22:28,180
+simplification وأقول ما هي x1 سو x2 وخلصت وجهها
+
+307
+00:22:28,180 --> 00:22:30,940
+للباقي لأ عشان or ما فيش simplification فإيش لازم
+
+308
+00:22:30,940 --> 00:22:33,800
+نقول عن دي؟ يا contradiction or anything تؤدي 
+
+309
+00:22:33,800 --> 00:22:37,820
+anything أو أيضا بتنسيقون تكافئوا قولوا يطلع x1 سو
+
+310
+00:22:37,820 --> 00:22:43,810
+x2 أه فهذا يؤدي الآن بدي أكتبهم بالشكل التالي طيب،
+
+311
+00:22:43,810 --> 00:22:47,730
+هذا الأخير معروف، طيب الأول بتديني برضه X1 تساوي
+
+312
+00:22:47,730 --> 00:22:53,190
+X2، ليش؟ لأن الـ G is one to one لأن الـ G is one
+
+313
+00:22:53,190 --> 00:22:56,910
+to one، يمكن أكتبهم بشكل، بنفس الأسلوب أفضل، هذا
+
+314
+00:22:56,910 --> 00:23:02,250
+يؤدي X1 تساوي X2، ليش؟ لأن الـ G is one to one،
+
+315
+00:23:02,250 --> 00:23:06,150
+بنفس المنهج، والأخيرة ما أحنا جاهزة، X1 تساوي X2
+
+316
+00:23:06,150 --> 00:23:10,630
+لأنه طبعا R، بدنا نشوف كله R، هذه طبعا من الأول،
+
+317
+00:23:10,630 --> 00:23:15,530
+من التعريف ما فيش مشكلة، فهذا الاحتمال الرابع، بدنا
+
+318
+00:23:15,530 --> 00:23:19,510
+نشوف الاحتمالين التانين إيش بتتوقعوا من الاحتمال
+
+319
+00:23:19,510 --> 00:23:23,950
+اللي في النص يدونا X1 تساوي X2 ولا Contradiction؟
+
+320
+00:23:23,950 --> 00:23:28,790
+هي اللي بنفعلها، إيش بتدونا؟ Contradiction،
+
+321
+00:23:28,790 --> 00:23:34,390
+Contradiction، ليش؟ أه ليش ما ينفعش هال gate لما يقول
+
+322
+00:23:34,390 --> 00:23:40,430
+لي x2 بتساوي صورة x1 أه ليش؟ لأن ال g من y متودة من
+
+323
+00:23:40,430 --> 00:23:44,890
+x ل x فلما يقول x1 في x صورتها هو أنك تكون في x هو
+
+324
+00:23:44,890 --> 00:23:48,230
+x1 ومش بتقول في y نقص x يعني ليست في ال x فده
+
+325
+00:23:48,230 --> 00:23:50,710
+contradiction فهنا contradiction
+
+326
+00:23:53,360 --> 00:23:59,240
+Contradiction، ليش؟ أكتبلكوا السبب لأن X2 اللي هي
+
+327
+00:23:59,240 --> 00:24:08,780
+إيش في الأول تنتمي للـG of X subset من الـX and X2
+
+328
+00:24:08,780 --> 00:24:12,320
+لا تنتمي للـX، هاي الـContradiction X2 في الـY
+
+329
+00:24:12,320 --> 00:24:15,620
+ناقص X، إيش معناه؟ في الـY وليست في الـX، أه
+
+330
+00:24:15,620 --> 00:24:19,000
+التانية زيها، تشبهها بس العكس، اتضحوا، برضه
+
+331
+00:24:19,000 --> 00:24:26,640
+Contradiction، لو سمحتوا أه ليش؟ لأن X1 تنتمي لصورة
+
+332
+00:24:26,640 --> 00:24:32,200
+G of X وهي بربع صفر من X و X1 نشمالها لا تنتمي لل
+
+333
+00:24:32,200 --> 00:24:37,200
+X لأنه إيش بيقول هنا؟ X1 خارج ال X طب X1 صورة ..
+
+334
+00:24:37,200 --> 00:24:40,600
+صورة G والـ G من وين لوين؟ من X لX، ما ينفعش تكون
+
+335
+00:24:40,600 --> 00:24:45,540
+خارج، فcontradiction تمام؟ الآن B or contradiction
+
+336
+00:24:45,540 --> 00:24:49,180
+or contradiction or B؟ بيدينا B، idempotency
+
+337
+00:24:49,180 --> 00:24:51,940
+ونظرية واحد سبعة، وهو المطلوب
+
+338
+00:24:59,060 --> 00:25:07,200
+أه فهنا هذا يؤدي إن X1 تساوي X2 نظرية 1 7 و P or B
+
+339
+00:25:07,200 --> 00:25:12,760
+تكافئ بي I don't want to answer تمام وهو المطلوب
+
+340
+00:25:12,760 --> 00:25:18,760
+فإذا أثبتنا نبدأ له one to one thus FG احنا بنشر
+
+341
+00:25:18,760 --> 00:25:23,440
+على F is one to one أي سؤال
+
+342
+00:25:26,020 --> 00:25:29,200
+واضح؟ فإذن هذه .. يمكن أول مثال هيمر علينا عدة
+
+343
+00:25:29,200 --> 00:25:33,020
+أمثلة كيف نثبت إن ده لمتعددة القاعدة إنها one to
+
+344
+00:25:33,020 --> 00:25:37,400
+one نفس الطريقة نشوف الخطوة الثانية بإن نثبت إنها
+
+345
+00:25:37,400 --> 00:25:42,400
+جاية F of Y برابر من ال Y هذا المطلوب الثاني إذا 
+
+346
+00:25:42,400 --> 00:25:49,910
+حبينا نرقم بنرقم مطلوب إيه؟ شوفنا في المثال السابق
+
+347
+00:25:49,910 --> 00:25:53,590
+وفي الملاحظة عشان أثبت إيش مطلوب؟ أثبت أن هناك عنصر
+
+348
+00:25:53,590 --> 00:25:57,970
+في ال Y غير موجود في ال F of Y خليني أكتبها We
+
+349
+00:25:57,970 --> 00:26:08,410
+have to find Y تنتمي لل Y and Y لا تنتمي لل F of Y
+
+350
+00:26:08,410 --> 00:26:13,370
+بدنا عنصر الزيادة بدنا عنصر الزيادة بدنا ندور على 
+
+351
+00:26:13,370 --> 00:26:19,200
+هذا العنصر بدنا ندور على عنصر الزيادة وين الـ G؟
+
+352
+00:26:19,200 --> 00:26:22,640
+طبعا في المثال الماضي كنا عارفين أن الصور كلها 
+
+353
+00:26:22,640 --> 00:26:25,380
+زوجية فاخدنا له واحد فردي الواحد تذكروا المثال تبع
+
+354
+00:26:25,380 --> 00:26:27,860
+المعادلة السابعة طب الآن احنا عارفين الصور إيش 
+
+355
+00:26:27,860 --> 00:26:30,980
+بتكون بالظبط مش عارفين برضه نفس الخضية لما يكون
+
+356
+00:26:30,980 --> 00:26:35,060
+الشغل عام يطلع المعطيات إيش عندنا معطيات؟ عندنا من
+
+357
+00:26:35,060 --> 00:26:39,660
+المعطيات أن الـ G of X برابر subset برابر subset
+
+358
+00:26:39,660 --> 00:26:42,900
+ما عنش تقريبا نفس المجموعة هي عندنا .. إيش الصورة؟ 
+
+359
+00:26:42,900 --> 00:26:48,460
+خلينا نشوف ما هيي الـ X و F of X وينها؟ جواها الـ F
+
+360
+00:26:48,460 --> 00:26:52,480
+of X بس هيي الـ X و هيي الـ F of X الـ brother subset
+
+361
+00:26:52,480 --> 00:26:59,300
+وهان الـ X ففي عنصرها الزيادة صح؟ من الأول هل هذا
+
+362
+00:26:59,300 --> 00:27:02,800
+هو بتام عنصر الزيادة؟ الحقيقة نعم هو المرشح
+
+363
+00:27:02,800 --> 00:27:05,180
+والحقيقة هو اللي بنجح لأنه زي ما قلنا مين اللي
+
+364
+00:27:05,180 --> 00:27:12,290
+بيظغر الـ .. آسف الـ G هذي هذي G مش F هي أيّاش 
+
+365
+00:27:12,290 --> 00:27:15,990
+بتنجولها نفسها لإن الـ F أيش بتعمل جوا الـ X زي ما هي
+
+366
+00:27:15,990 --> 00:27:20,990
+.. أه زي ما هي فهذه مش صورة أي حد تحت الـ G و طب و
+
+367
+00:27:20,990 --> 00:27:24,030
+الـ F أيش بتعمل جوا العنصر X لإن هي بتحرفها G مش
+
+368
+00:27:24,030 --> 00:27:27,790
+تعرفها G إذا هو هيتمه برضه مش صورة حد أه فحناخد الـ
+
+369
+00:27:27,790 --> 00:27:35,730
+answer ده الـ A البرهان since G of capital X برابر
+
+370
+00:27:35,730 --> 00:27:47,080
+من الـ X إيش فيه؟ We have X تنتمي للكابتل X and أو 
+
+371
+00:27:47,080 --> 00:27:55,260
+there exist و X شمالها لا تنتمي لل G of X فهذا هو
+
+372
+00:27:55,260 --> 00:28:01,140
+العنصر اللي بندور عليه خلينا نسميه Y عشان 
+
+373
+00:28:01,140 --> 00:28:05,420
+نطبق مع الكلام اللي تحته هل هذا الـ Y اللي بدور عليه؟
+
+374
+00:28:05,420 --> 00:28:12,000
+بدنا نثبت إن هو نفسه إنه هو العنصر اللي بدور عليه
+
+375
+00:28:12,000 --> 00:28:15,360
+هو نفس العنصر اللي بدور عليه فاحنا بدنا نثبت إن
+
+376
+00:28:15,360 --> 00:28:19,460
+هذا الـ Y فعلا ينتمي ل F of Y
+
+377
+00:28:22,700 --> 00:28:26,320
+هو ينتمي لل Y ولا ينتمي لل F of Y فهنا خلينا
+
+378
+00:28:26,320 --> 00:28:31,760
+نحطها claim ادعاء Y هي اللي بدور عليها تنتمي لل Y
+
+379
+00:28:31,760 --> 00:28:36,480
+and Y لا تنتمي لل F of Y هو العنصر اللي بدور عليه
+
+380
+00:28:36,480 --> 00:28:39,700
+بدنا نثبت هذا الكلام فنثبت هذا الكلام prove
+
+381
+00:28:42,620 --> 00:28:46,560
+فهذا الجزئية بس عشان أحط البرهان بنطبق ونقدر نخرج 
+
+382
+00:28:46,560 --> 00:28:51,880
+تمام أول شيء Y تنتمي ل Y بسهولة لأن ال Y في ال X و
+
+383
+00:28:51,880 --> 00:28:56,180
+ال X برابر subset من ال X فإذا هنا Y تنتمي ل X
+
+384
+00:28:56,180 --> 00:29:00,760
+implies Y تنتمي ل Y لإيش؟ لأن X subset من Y من
+
+385
+00:29:00,760 --> 00:29:03,800
+البداية أخدناها ولا لأ؟ مش هيقولنا هي super set
+
+386
+00:29:03,800 --> 00:29:09,600
+فدي أخدناها تمام بتام الجزء الثاني الجزء الثاني
+
+387
+00:29:09,600 --> 00:29:15,300
+هعمله by contradiction هعمله by contradiction نفترض 
+
+388
+00:29:15,300 --> 00:29:22,280
+أن ال Y في ال F of Y assume Y تنتمي لل F of Y
+
+389
+00:29:22,280 --> 00:29:27,660
+خلينا بس نتابع الكلام نكون أتوقع هي نفس الخيار
+
+390
+00:29:27,660 --> 00:29:30,180
+صحيح بس هتأكد عشان ما نروحش بعيد
+
+391
+00:30:07,060 --> 00:30:16,310
+لأ تابع غالبا الكلام صحيح فال Y تساوي تنتمي لل F of
+
+392
+00:30:16,310 --> 00:30:20,350
+Y نوصل إلى Contradiction نعمل By Contradiction
+
+393
+00:30:20,350 --> 00:30:24,570
+prove للجزء هذا By Contradiction و تعلمنا أنه
+
+394
+00:30:24,570 --> 00:30:27,930
+احنا ممكن ضمن البرهان نعمل أجزاء زي ما بدنا
+
+395
+00:30:27,930 --> 00:30:32,490
+Contradiction إيش معناه أن ال Y في صورة ال capital
+
+396
+00:30:32,490 --> 00:30:37,470
+Y أن هي صورة عنصر من ال capital Y Y تساوي F of X
+
+397
+00:30:38,210 --> 00:30:44,850
+for some x تنتمي للـ y طيب إيش تعريف الـ F محيتها 
+
+398
+00:30:44,850 --> 00:30:51,960
+أنا احتمالية فالـ Y يا بتساوي G of X إذا الـ X
+
+399
+00:30:51,960 --> 00:30:57,440
+تنتمي للـ X أو بتساوي X إذا الـ X تنتمي لمن؟ للـ Y
+
+400
+00:30:57,440 --> 00:31:01,460
+ناقص X بدنا نثبت أن الاثنتين احتمالاتين or أن 
+
+401
+00:31:01,460 --> 00:31:04,500
+الاثنتين Contradiction، بنوصل لـ Contradiction طيب،
+
+402
+00:31:04,500 --> 00:31:10,420
+هل ينفع أن الـ Y تساوي G of X؟ احنا من وين اخترنا
+
+403
+00:31:10,420 --> 00:31:16,530
+الـ Y؟ الـ Y شمالها هي لا تنتمي لل G of X فهذا
+
+404
+00:31:16,530 --> 00:31:20,150
+مستحيل Contradiction أه Contradiction فهذا
+
+405
+00:31:20,150 --> 00:31:24,670
+Contradiction Or
+
+406
+00:31:24,670 --> 00:31:30,450
+فده الأول طيب بنفعل Y تساوي X طب ال X .. إيش ال X؟
+
+407
+00:31:30,450 --> 00:31:35,850
+وين موجودة ال X؟ ال X موجودة في ال Y و ال X لا
+
+408
+00:31:35,850 --> 00:31:40,810
+تنتمي لل X ال X لا تنتمي لل X
+
+409
+00:31:46,070 --> 00:31:52,810
+ما ينفعش ليش تكون X لأنه لو X تنتمي لل Y ولا تنتمي لل
+
+410
+00:31:52,810 --> 00:31:57,390
+X بيدينا برضه contradiction لأن ال Y موجودة في ال
+
+411
+00:31:57,390 --> 00:31:59,650
+X صحيح فهذا برضه contradiction فهذا إيش برضه
+
+412
+00:31:59,650 --> 00:32:05,700
+contradiction وهو الموضوع فإذن ليش هذا الكلام غير 
+
+413
+00:32:05,700 --> 00:32:09,600
+صحيح؟ لأن ال Y في ال X أصلا، ما ينفعش تكون خارج، ف
+
+414
+00:32:09,600 --> 00:32:13,620
+Y تسوى X لأنه .. طبعا هنا ليش؟ لأن ال Y تنتمي لل
+
+415
+00:32:13,620 --> 00:32:19,340
+X، طبعا هنا ليش؟ لأن ال Y لا تنتمي لمين؟ لل G of
+
+416
+00:32:19,340 --> 00:32:24,280
+X، فهنا طبعا هي كل واحدة وسبب تتحدث، وانتهت العمل
+
+417
+00:32:27,540 --> 00:32:31,420
+طبعا الأمور شوية زي ما حكينا مش .. مش سلسة أو مش 
+
+418
+00:32:31,420 --> 00:32:35,060
+مباشرة فلكن احنا بنحاول نشوف اللي هو البنية 
+
+419
+00:32:35,060 --> 00:32:38,880
+الأساسية للشغل آه كيبنا نثبت إنها infinite بندور
+
+420
+00:32:38,880 --> 00:32:42,840
+على دالة وتعلمنا إنه ما زال مجموعة مجردة ما ينفعش 
+
+421
+00:32:42,840 --> 00:32:45,660
+أجيب دوال من دوال الـ calculus لإنه مش معرفين ممكن
+
+422
+00:32:45,660 --> 00:32:49,600
+يكونوا أه فشوفنا من المعطيات استفدنا جيبنا الدالة F
+
+423
+00:32:49,600 --> 00:32:54,280
+عرفناها بـ G طبعا مش بشكل متطابق تماما كملنا من عندنا
+
+424
+00:32:54,280 --> 00:32:57,580
+وانجحنا أه طبعا فاثبتنا أنها one to one وانجحنا 
+
+425
+00:32:57,580 --> 00:33:00,720
+نثبت أنها one to one تم ندوي على عنصر زيادة موجود
+
+426
+00:33:00,720 --> 00:33:03,860
+في المجموعة أو مش موجود في الصورة ولاجناها من ..
+
+427
+00:33:03,860 --> 00:33:06,820
+برضه من المعطيات ولاجناها برضه من المعطيات طبعا
+
+428
+00:33:06,820 --> 00:33:12,010
+اختارناها بشكل مناسب واثبتنا فعلا أنه بيحقق الشروط
+
+429
+00:33:12,010 --> 00:33:15,710
+فطبعا احنا قلنا افترض أن هو صورة بنتظر تقول ده
+
+430
+00:33:15,710 --> 00:33:19,530
+contradiction مستحيل فطبعا إيش معنى الصورة؟ أه وهي
+
+431
+00:33:19,530 --> 00:33:23,650
+الاحتمالين طب لو كان G of X بتكون الـ Y وين؟ لو
+
+432
+00:33:23,650 --> 00:33:27,510
+كانت تنتمي للـ G of X فده مستحيل ولو كانت X بتكون
+
+433
+00:33:27,510 --> 00:33:31,330
+وين؟ في الـ capital X أه لإيه؟ لأن الـ Y بالـ capital 
+
+434
+00:33:31,330 --> 00:33:35,110
+X وإيش ويش ويش الـ Y؟ بقول إيش؟ Y ناقص X مينفعش
+
+435
+00:33:35,110 --> 00:33:44,150
+فصارت contradiction نشوف فرع بيه السهل فرع بيه هذا
+
+436
+00:33:44,150 --> 00:33:50,210
+كله إيه؟ طبع نظرية الأولى
+
+437
+00:33:50,210 --> 00:33:52,650
+بعدين بنعلق على امتحان آخر خلينا نكمل نرجع
+
+438
+00:33:52,650 --> 00:33:56,970
+الامتحان كل مجزّي من الـ finite set هو finite
+
+439
+00:33:56,970 --> 00:34:00,610
+خلّيني أولا أحط الجملة لأن البرهان هي تعمل على
+
+440
+00:34:00,610 --> 00:34:05,170
+السابق بسهولة لأنه عملية negation وهنعملها بشكل 
+
+441
+00:34:05,170 --> 00:34:10,730
+مباشر فخلّيني أشوف هنا البرهان بشكل مشابه let X be
+
+442
+00:34:10,730 --> 00:34:18,150
+a finite set إيش المطلوب؟
+
+443
+00:34:18,150 --> 00:34:26,240
+we have to prove that نفس العملية الماضية بس اختلاف
+
+444
+00:34:26,240 --> 00:34:33,440
+أنه بدل super set subset for all y such that y
+
+445
+00:34:33,440 --> 00:34:48,240
+subset من الـ X الـ Y is finite ال
+
+446
+00:34:48,240 --> 00:34:56,380
+Y is finite فطبعا كالعادة بدنا نبداش let Y be a set
+
+447
+00:34:56,380 --> 00:35:01,800
+such that طبعا عشان for all الـ Y subset من الـ X
+
+448
+00:35:01,800 --> 00:35:06,340
+بدنا يثبت أن الـ Y finite طبعا زي حتى اللي مر علينا
+
+449
+00:35:06,340 --> 00:35:09,560
+كل الـ finite اللي عملناها by contradiction assume
+
+450
+00:35:09,560 --> 00:35:13,060
+Y 
+
+451
+00:35:13,060 --> 00:35:18,660
+is infinite افترض 
+
+452
+00:35:18,660 --> 00:35:22,790
+أن الـ Y infinite بدنا يفرض أن هذا المستحيل العملية
+
+453
+00:35:22,790 --> 00:35:27,930
+بس انتباه انتبهوا الـ Y infinite والـ X أكبر منها
+
+454
+00:35:27,930 --> 00:35:30,970
+لازم تكون infinite بالباش بالنظرية توي أثمتناها
+
+455
+00:35:30,970 --> 00:35:36,710
+الفرع اللي اتصابها أثمتها X is infinite مين دليلي
+
+456
+00:35:36,710 --> 00:35:44,170
+نظرية خمسة واحد A فرع A طبعا contradiction لأن X
+
+457
+00:35:44,170 --> 00:35:45,550
+شمالها finite
+
+458
+00:35:52,200 --> 00:35:56,240
+فهذه برهانة قصيرة جدا بيد السهولة اعتمد على فرع A
+
+459
+00:35:56,240 --> 00:36:01,160
+فهو المهم ففرع A هو الأساسي
+
+460
+00:36:01,160 --> 00:36:15,420
+ففرع A هو الأساسي نظرية
+
+461
+00:36:15,420 --> 00:36:16,060
+5-2
+
+462
+00:36:20,810 --> 00:36:24,970
+طبعاً ممكن تستخدميها ممكن تستخدميها مهمة جدا إذا 
+
+463
+00:36:24,970 --> 00:36:28,070
+قدرت تثبت فالجيت أنا مثلا لو قالك اثبت أن الـ Z
+
+464
+00:36:28,070 --> 00:36:28,450
+infinite
+
+465
+00:36:33,450 --> 00:36:36,670
+على طول مباشرة فإن واضح ما زال أثبتنا أن نحن
+
+466
+00:36:36,670 --> 00:36:40,110
+ماشيين بيد الشكل للحقيقة ليش أثبتنا أن N هي الـ
+
+467
+00:36:40,110 --> 00:36:42,830
+infinite هي أصغر infinite 6 للحقيقة فلجيت الـ Z
+
+468
+00:36:42,830 --> 00:36:45,130
+infinite على طول و الـ Q infinite و الـ R infinite
+
+469
+00:36:45,130 --> 00:36:48,310
+كل المجموعات الأكبر منها infinite كلها infinite
+
+470
+00:36:48,310 --> 00:36:53,210
+على طول هذا كام مثال فهذه نظرية مهمة جدا النظرية
+
+471
+00:36:53,210 --> 00:36:56,790
+التانية برضه نظرية مهمة طبعاً العنوان العريض الـ
+
+472
+00:36:56,790 --> 00:37:00,750
+how ولا النتيجة اللي بعده بيقول لي no bijections
+
+473
+00:37:00,750 --> 00:37:03,810
+أو no bijection between infinite and finite set
+
+474
+00:37:03,810 --> 00:37:08,450
+مستحيل أقدر ألاجي تناظر بين مجموعتين واحدة finite
+
+475
+00:37:08,450 --> 00:37:12,010
+واحدة infinite هذا مستحيل نتخيله مع بعض ما هوش
+
+476
+00:37:12,010 --> 00:37:15,730
+معاه التناظر كل عنصر له نظير في المجموعة التانية
+
+477
+00:37:15,730 --> 00:37:19,090
+فهذا بيقول أن واش عناصرهم بتكون متساوي لعدد ولا لأ
+
+478
+00:37:19,090 --> 00:37:21,090
+أه فهو بيقول لي إذا كانت واحدة infinite واحدة
+
+479
+00:37:21,090 --> 00:37:24,500
+finite مستحيل إذا الكلام يكون صحيح بنشوف كيف بنثبت
+
+480
+00:37:24,500 --> 00:37:30,400
+هذه الحقيقة النظرية اللي هو بشكل مباشر let G from
+
+481
+00:37:30,400 --> 00:37:34,870
+X to Y be a one to one correspondence هذه اسمها
+
+482
+00:37:34,870 --> 00:37:36,710
+يعني اسم by ejection one to one correspondence هو
+
+483
+00:37:36,710 --> 00:37:41,470
+المصطلح الآخر بقول إذا X infinite فالـ Y infinite
+
+484
+00:37:41,470 --> 00:37:45,170
+فهذه أول جزء من النظرية أنا لجيت one to one
+
+485
+00:37:45,170 --> 00:37:47,730
+correspondence بين مجموعتين إذا واحدة infinite
+
+486
+00:37:47,730 --> 00:37:50,450
+التانية لازم تكون infinite طب واحد يقول التانية
+
+487
+00:37:50,450 --> 00:37:52,830
+جالة إذا كانت الـ X infinite فالـ Y infinite طب
+
+488
+00:37:52,830 --> 00:37:57,190
+والعكس لو الـ F infinite برضه صح، ليش؟ لأن الـ F in
+
+489
+00:37:57,190 --> 00:38:00,090
+a bijection is an F in a G inverse as if G is in a
+
+490
+00:38:00,090 --> 00:38:02,750
+bijection، G inverse برضه bijection، من Y لأكس،
+
+491
+00:38:02,750 --> 00:38:06,290
+فالعملية ماشية باتجاهين، بس ودانا اسم العنوان وانت
+
+492
+00:38:06,290 --> 00:38:10,210
+تطبقي واتعممي، فده هو العنوان الرئيسي، إذا عندي
+
+493
+00:38:10,210 --> 00:38:13,430
+مجموعتين بينهم bijection، فواحدة Infinite، التانية
+
+494
+00:38:13,430 --> 00:38:16,410
+لازم تكون Infinite، طبعا بالنسبة يادر اتجاه من X ل
+
+495
+00:38:16,410 --> 00:38:19,110
+Y، بستخدم الـG كbijection، طب من Y ل X، إيش
+
+496
+00:38:19,110 --> 00:38:21,450
+هستخدم؟ G inverse، وهي بتكون bijection على طول
+
+497
+00:38:21,450 --> 00:38:25,200
+النظرية السابقة، فده بس ملاحظة سريعة خلّينا نشوف
+
+498
+00:38:25,200 --> 00:38:32,880
+البرهة فاحنا بدنا نشوف البرهة وإن
+
+499
+00:38:32,880 --> 00:38:35,400
+شاء الله بنبني على بعض ما تعلمناه في البرهان
+
+500
+00:38:35,400 --> 00:38:44,440
+السابق مع بعض الإختلافات القليلة theorem 5-2
+
+501
+00:38:44,440 --> 00:38:50,540
+approved طبعا فيه مواطيات let g from a be a
+
+502
+00:38:50,540 --> 00:38:55,410
+bijection خلّينا نكتبها لإن محتاجينها let g من x ل
+
+503
+00:38:55,410 --> 00:39:00,190
+y be a bijection one to one يعني bijection اتعود
+
+504
+00:39:00,190 --> 00:39:04,570
+على المصطلح هي أه بقول لي if x is infinite اذا هدا
+
+505
+00:39:04,570 --> 00:39:11,110
+يشمله الشرط بنفترض أن هو ياش معطق assume x
+
+506
+00:39:11,110 --> 00:39:20,350
+is infinite إيش مطلوب أثبت أن الـ y infinite we
+
+507
+00:39:20,350 --> 00:39:29,560
+have to prove Y is infinite تمام
+
+508
+00:39:29,560 --> 00:39:33,560
+فهذا كل ما بقى دي رياضيات ماعملتش كل هذا معلومات
+
+509
+00:39:33,560 --> 00:39:37,240
+جديدة معلومات قديمة أسف طيب بدي أثبت أن الـ Y
+
+510
+00:39:37,240 --> 00:39:41,200
+infinite يعني إيش بدي؟ بدي دالة F من Y ل Y one to
+
+511
+00:39:41,200 --> 00:39:48,120
+one و proper subset we must find او have to find a
+
+512
+00:39:48,120 --> 00:39:58,820
+function F من Y ل Y such that F is one to one and
+
+513
+00:39:58,820 --> 00:40:05,620
+F الـ Y اقرب من الـ Y فبد أن هدول الشرطين يتحقق فبد
+
+514
+00:40:05,620 --> 00:40:06,400
+أعرف الـ F
+
+515
+00:40:09,410 --> 00:40:16,590
+من Y ل Y بي given by هذا ليه؟ إيش مفتاح الحل هذا ال
+
+516
+00:40:16,590 --> 00:40:21,050
+use الأول فكيف 
+
+517
+00:40:21,050 --> 00:40:26,700
+بدنا نعرف الـ F بنفع نجيب من دفاتر الـ calculus؟ لأ،
+
+518
+00:40:26,700 --> 00:40:29,820
+أه هنا نفعي، شوف ده العملية بتدل، لأن الـ Y جالي
+
+519
+00:40:29,820 --> 00:40:34,420
+مجموعة، إيش عناصرها مش عارف، أعداد، مش أعداد،
+
+520
+00:40:34,420 --> 00:40:38,060
+فواكه، كراسي، مش عارف، مجموعة، أي مجموعة، العمليات
+
+521
+00:40:38,060 --> 00:40:40,880
+الحسابية معرفة مش معرفة، مش عارف، دهش مشاكل عامة،
+
+522
+00:40:40,880 --> 00:40:45,010
+إذا أين بده أدور؟ في المعطيات عن دوال اتساعدني بدي
+
+523
+00:40:45,010 --> 00:40:48,650
+ادور عن دوال اتساعدني في دوال في المعطيات نعم قال
+
+524
+00:40:48,650 --> 00:40:52,510
+لي فيه G قال لي فيه G بس هنا الصورة مختلفة عن
+
+525
+00:40:52,510 --> 00:40:57,650
+الصورة الماضية كنا هناك نشتغل في X و Y مجموعة أكبر
+
+526
+00:40:57,650 --> 00:41:00,370
+منها الآن الـ X و Y دولة مش ضرورة تكون سبسط من بعض
+
+527
+00:41:00,370 --> 00:41:06,130
+بشكل عام فاحنا عندنا الصورة التالية هي في عندنا X
+
+528
+00:41:06,530 --> 00:41:11,970
+الرسم بيساعد وفي عندنا Y وفي عندنا G واحنا
+
+529
+00:41:11,970 --> 00:41:16,030
+بندور على دالة F من Y ل Y نعمل كمان نسخة من Y
+
+530
+00:41:16,030 --> 00:41:26,050
+بندور على F من Y ل Y بندور على function F من Y ل Y
+
+531
+00:41:26,050 --> 00:41:31,150
+بدنا نعرفها بشكل مناسب تكون one to one وليست
+
+532
+00:41:31,150 --> 00:41:38,810
+انتوا الـ G one to one إيش نعمل؟ بدنا نعرف الـ F
+
+533
+00:41:38,810 --> 00:41:43,990
+الأمور أصعب من السابق أصعب من السابق لكن هنا بنشوف
+
+534
+00:41:43,990 --> 00:41:48,410
+الأمثلة وبن count هنعمل .. مين أداتنا؟ الـ G
+
+535
+00:41:48,410 --> 00:41:52,190
+اتفقنا؟ إذا إحنا ندور على المعطيات وهي الـ G بدنا
+
+536
+00:41:52,190 --> 00:41:56,570
+نعمل الـ trick بدنا نبدأ من الـ Y وبدنا نستخدم الـ G
+
+537
+00:41:56,570 --> 00:42:02,050
+بنفع أبدأ من الـ Y مع الـ G؟ لأ الـ Y .. الـ G من وين؟
+
+538
+00:42:02,050 --> 00:42:06,250
+من X ل Y لكن ممكن أبدأ بمين؟ بالـ G inverse بالـ G
+
+539
+00:42:06,250 --> 00:42:08,890
+inverse لأن هو دي إيش one to bijection فالـ
+
+540
+00:42:08,890 --> 00:42:14,280
+inverse معروف فانا هبدأ من Y في الـ G inverse الـ G
+
+541
+00:42:14,280 --> 00:42:18,900
+inverse وين بيوديني؟ بيوديني على الـ X فانا هبدأ من
+
+542
+00:42:18,900 --> 00:42:24,200
+Y بالـ G inverse ووداني على الـ X بدي ارجع للـ Y مين
+
+543
+00:42:24,200 --> 00:42:29,260
+ممكن يرجعني للـ Y؟ ممكن يرجعني الـ G ممكن يرجعني ..
+
+544
+00:42:29,260 --> 00:42:34,100
+أنا الـ G inverse من وين لوين؟ الـ G inverse من Y ل
+
+545
+00:42:34,100 --> 00:42:38,800
+X أه ممكن الـ G ترجعني للـ Y بس بكون أنا ليش ماعملتش
+
+546
+00:42:38,800 --> 00:42:41,980
+إشي أنا بده أروح من Y ل X بكون ليش؟ لأن الـ G
+
+547
+00:42:41,980 --> 00:42:45,120
+inverse مع الـ G هذي one to one and unto مابتنفعش
+
+548
+00:42:45,120 --> 00:42:48,140
+مين اللي بيقوم بعملية التصغير اللي قلنا عنه اللي
+
+549
+00:42:48,140 --> 00:42:51,880
+بيدينا صورة مش unto الـ F فلازم ندخل الـ F على الخط
+
+550
+00:42:52,320 --> 00:42:55,280
+بدنا ندخل الـ F في العملية لأنه قلنا مين اللي
+
+551
+00:42:55,280 --> 00:42:58,860
+بيصغر فيه دالة بتصغر في العملية بتصغر الصورة الـ F
+
+552
+00:42:58,860 --> 00:43:04,920
+هندخل الـ F بشكل مناسب مانفعش أبدأ من الـ G مباشرة
+
+553
+00:43:04,920 --> 00:43:07,660
+بدنا نبدأ بالـ G inverse فهنعرف الـ F بشكل التالي
+
+554
+00:43:07,660 --> 00:43:13,660
+given by F بدنا ن .. لأ الـ F بدنا .. هي اللي بدنا
+
+555
+00:43:13,660 --> 00:43:18,560
+نعرفها بدنا نعرفها فإيش كيف الـ G في عندنا دالة
+
+556
+00:43:18,560 --> 00:43:19,320
+أخرة احنا لأ
+
+557
+00:43:33,720 --> 00:43:39,620
+لسه مش كافي الأمور فلسه الجيل حد مش نافع بدنا ندور
+
+558
+00:43:39,620 --> 00:43:43,600
+ع كمان دالة بدنا command دلّة فالـ G لحالة مش 
+
+559
+00:43:43,600 --> 00:43:47,800
+مكافية للتركيز في عندنا command دلّة أه فعندنا
+
+560
+00:43:47,800 --> 00:43:50,280
+command .. في عندنا command دلّة X is infinite في 
+
+561
+00:43:50,280 --> 00:43:55,060
+command دلّة فالعملية هنا ما ضبطتش فالان X is
+
+562
+00:43:55,060 --> 00:44:00,500
+infinite implies there exist function الجي والاف 
+
+563
+00:44:00,500 --> 00:44:08,800
+موجودين خلينا نسمي اسم جديد H من X ل X such that H
+
+564
+00:44:08,800 --> 00:44:15,620
+is one to one and H of X برابر من X فالعملية الآن
+
+565
+00:44:15,620 --> 00:44:20,920
+مختلفة شوية فحستخدم الـH الـH فالآن G inverse
+
+566
+00:44:20,920 --> 00:44:25,820
+بتودينا من Y لX اللي بيظغر مين الـH أسف مش الـF
+
+567
+00:44:25,820 --> 00:44:28,280
+اللي أفضل دي المطلوبة صح هي بتظغر بس هذا مطلوب مش
+
+568
+00:44:28,280 --> 00:44:32,420
+معطى لكن H هي اللي بتظغر بتاخدنا من وين لوين من X
+
+569
+00:44:32,420 --> 00:44:37,820
+لنفسها من X لنفسها بتدينا H أو بعدين الـG بترجعنا
+
+570
+00:44:37,820 --> 00:44:42,400
+للـY فبكون بدينا من Y ورجعنا للـY فحنعرف الآن اه
+
+571
+00:44:42,400 --> 00:44:45,900
+فهنا يمكن هذه الخطوة هتكون قبل فهذه الخطوة هتيجي
+
+572
+00:44:45,900 --> 00:44:57,480
+بعد فهقوله هنا let F من Y ل Y be given by F of X
+
+573
+00:44:57,480 --> 00:45:03,040
+تساوي كيف عرفناها؟ بدأنا بإيش؟ G inverse أول شيء
+
+574
+00:45:03,040 --> 00:45:08,780
+G inverse بعدين إيش ركبنا؟ H بعدين ركبنا ال G of X
+
+575
+00:45:10,070 --> 00:45:13,550
+خلّينا .. طبعا ممكن احنا وإحنا بنحاول .. بن .. بن
+
+576
+00:45:13,550 --> 00:45:16,710
+.. بن .. بنخربش، بنعمل مسودة، بنعمل هامش، بنحاول،
+
+577
+00:45:16,710 --> 00:45:21,410
+نشوف شغلنا صح ولا مش صح الـG inverse ده لأنّ 
+
+578
+00:45:21,410 --> 00:45:28,410
+الرسمة دي مرة ثانية، بطريقة مختلفة بدنا دالة من
+
+579
+00:45:28,410 --> 00:45:32,450
+واي لوين؟ من واي لواي، نشوف الصورة، بنتعلم هذه
+
+580
+00:45:32,450 --> 00:45:38,330
+المهارة، فانا بدأت من واي G inverse وين بتوديها؟ ال
+
+581
+00:45:38,330 --> 00:45:41,630
+X ال G دالة من X ل Y خدت ال inverse تبعها طب ال
+
+582
+00:45:41,630 --> 00:45:46,470
+inverse exist نعم لأنه الدالة one to one هلجيت من
+
+583
+00:45:46,470 --> 00:45:51,630
+X طبقت ال H وين وددتها؟ على ال X و طب ليش دخلت ال
+
+584
+00:45:51,630 --> 00:45:55,830
+H؟ ما وددتكاش مكان جديد خلتك في نفس المحل بس H
+
+585
+00:45:55,830 --> 00:45:59,410
+بتلعب دور ال H تصغير بتصغر الصورة هي مهمة جدا لإن
+
+586
+00:45:59,410 --> 00:46:03,470
+هيها هي اللي بتزغر الصورة بعد هي إيش عملت طبقت الجي
+
+587
+00:46:03,470 --> 00:46:08,510
+كمان مرة وين رجعتني الجي لل one فالصورة صحيحة
+
+588
+00:46:08,510 --> 00:46:12,970
+فالصورة صحيحة تمّ أثبت أنّ هذه ال F فعلا one to one
+
+589
+00:46:12,970 --> 00:46:16,450
+و أنّها إيش و بتدينا الصورة not onto يعني الصورة
+
+590
+00:46:16,450 --> 00:46:22,750
+أصغر فبنثبت أنّ ال F one to one و أنّها بإيش بتزغر
+
+591
+00:46:22,750 --> 00:46:30,150
+الصورة فال Fis one to one هذا واحد هنثبته ويمكن
+
+592
+00:46:30,150 --> 00:46:36,910
+هذا سهل أعمله بسرعة خلّي الجزء الثاني هو الأصعب
+
+593
+00:46:36,910 --> 00:46:41,550
+فغالبنا نعمل هذا الجزء السهل فناخد عنصرين let X1 و
+
+594
+00:46:41,550 --> 00:46:52,190
+X2 في ال Y such that F of X1 تساوي F of X2 بداية
+
+595
+00:46:52,190 --> 00:46:56,370
+ال one to one كالعادة ما يمكننا فعله باستخدام تعريف
+
+596
+00:46:56,370 --> 00:47:04,770
+الدالة كالعادة فهذا بيقول لي G of H of G of X1
+
+597
+00:47:04,770 --> 00:47:13,250
+تساوي G of H of G inverse of X2 مشاكل اللي هو
+
+598
+00:47:13,250 --> 00:47:19,230
+تعريف الدالة Circle تلاتة مع بعض الآن بدي أوصل أنّ
+
+599
+00:47:19,230 --> 00:47:24,110
+X1 تساوي X2 هذه ال X1 في عليها أغلفة متعددة تلت
+
+600
+00:47:24,110 --> 00:47:27,810
+أغلفة بدي أحاول أنزعهم واحدة واحدة لحد ما أوصل أنّ
+
+601
+00:47:27,810 --> 00:47:32,430
+X1 تساوي X2 بس بنتزعهم بطريقة رياضية صحيحة كيف
+
+602
+00:47:32,430 --> 00:47:35,190
+ننتزع ال G؟
+
+603
+00:47:36,700 --> 00:47:43,240
+فيه أسهل .. فيه أسهل أنّ قيمتين الـG and قيمة معينة
+
+604
+00:47:43,240 --> 00:47:48,140
+Y1 تساوي الـG and Y2 والـG مالها one to one and on
+
+605
+00:47:48,140 --> 00:47:50,880
+two فبتدينا اللي جوا لازم يساوي اللي جوا .. اه
+
+606
+00:47:50,880 --> 00:47:57,500
+فهنا على طول يؤدي H of G inverse of X تساوي H of G
+
+607
+00:47:57,500 --> 00:48:02,240
+inverse of X2 ليش؟ لأنّ الـ F أو S في الـ G is one
+
+608
+00:48:02,240 --> 00:48:06,680
+to one هي one to one and unto نفس الفكرة ما الـ H
+
+609
+00:48:06,680 --> 00:48:12,720
+برضه one to one فهذا يؤدي إنّ G inverse of X تساوي
+
+610
+00:48:12,720 --> 00:48:16,950
+G inverse of X2 لأنّ الـ H is one to one طب وال G
+
+611
+00:48:16,950 --> 00:48:20,590
+inverse برضه one to one نعم لأنّه بيجيكشن و هذا
+
+612
+00:48:20,590 --> 00:48:25,590
+يؤدي أنّ X1 تساوي X2 لأنّه G inverse is one to one
+
+613
+00:48:25,590 --> 00:48:32,350
+وهو المطلوب تمت جزئية خليها للمرة الجاية لأنّ فيها
+
+614
+00:48:32,350 --> 00:48:34,990
+صعوبة خلينا نأخر 
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/PBRa0MHjhZs_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/PBRa0MHjhZs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2b585897ed7c4f8df43ad7b4ba5b068a2f78a91f
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/PBRa0MHjhZs_postprocess.srt
@@ -0,0 +1,2456 @@
+1
+00:00:19,670 --> 00:00:23,550
+بسم الله الرحمن الرحيم ان 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 --> 00:12:31,230
+انا انا انا
+
+166
+00:12:31,230 --> 00:12:38,810
+اناولا طفاح ولا موز ولا بوردجان؟ مش عارفين، ممتاز،
+
+167
+00:12:38,810 --> 00:12:41,590
+احنا اللي بده اوصله اليه، لما أنا لسه قالت مش
+
+168
+00:12:41,590 --> 00:12:44,430
+عارفين ايش عناصر الواد، الواد بقى بجموعة عامة،
+
+169
+00:12:44,430 --> 00:12:50,830
+عناصرها مش معروفة،بنك دوال ال calculus سكروه
+
+170
+00:12:50,830 --> 00:12:55,130
+مانفعناش لأن وداك معرف على دوال هيش ريال لريال اه
+
+171
+00:12:55,130 --> 00:12:59,250
+بدنا نشوف مكان اخر نعرف منه بدنا نشوف مكان اخر
+
+172
+00:12:59,250 --> 00:13:02,730
+بدنا بنك اخر بنك ال calculus مفلس بالنسبالنا غير
+
+173
+00:13:02,730 --> 00:13:09,320
+مناسب بدنا ندور على مكان مناسبطيب، من وين نعرف؟ من
+
+174
+00:13:09,320 --> 00:13:13,800
+وين نعرف؟ إيش في عينكوا؟ في هذا النوع، في الغالب،
+
+175
+00:13:13,800 --> 00:13:17,480
+بدي أعتمد على دوال معطية في السؤال، في الغالب، هذه
+
+176
+00:13:17,480 --> 00:13:21,520
+كنصيحة، كإرشاد، بدنا نتعرف على دوال معطية في
+
+177
+00:13:21,520 --> 00:13:25,080
+السؤال، في عيننا دوال معطية في السؤال؟ إيش مالها
+
+178
+00:13:25,080 --> 00:13:28,740
+ال X؟ Infinite، إيش معنات Infinite؟ بقدر ألاقي
+
+179
+00:13:28,740 --> 00:13:32,710
+دالة، في أيه المفتاح؟ آه، هاي هنا، بدي دوالفو بس
+
+180
+00:13:32,710 --> 00:13:35,230
+واحدة واحدة بس أنا بدي أعرف ده لوحدة ماني بس إذا
+
+181
+00:13:35,230 --> 00:13:39,050
+ال F معرفة فإذا ال F معرفة هذي هي إيش بيصير عندي
+
+182
+00:13:39,050 --> 00:13:42,210
+أنا إي حاجة أشتغل عليها خليني أشوف كيف .. طبعا
+
+183
+00:13:42,210 --> 00:13:45,210
+الأمثلة في البداية فشيء طبيعي أن أنتوا تكونوا بعاد
+
+184
+00:13:45,210 --> 00:13:48,710
+عنها شوية شوية الأمور تتحسن تمام فانا بدي أدور على
+
+185
+00:13:48,710 --> 00:13:52,010
+ال F الآن بدي أشوف وين مظادر إذا إحنا بنتعلم هنا
+
+186
+00:13:53,050 --> 00:13:55,890
+تفكير المجرد تتذكر لما تقول إن احنا عرفنا ال
+
+187
+00:13:55,890 --> 00:13:58,450
+composition ماعرفناش الجمع أو الطرح للدوال بشكل
+
+188
+00:13:58,450 --> 00:14:01,670
+عام لإنه مش ضروري كل عناصر بيكون فيها جمع زي هنا
+
+189
+00:14:01,670 --> 00:14:05,430
+إيش عرفنا إنه 2X معرفة لإن هو مش أرقام إيش معرفنا
+
+190
+00:14:05,430 --> 00:14:08,810
+إن الجمع معرف ال sign معرفة مش معرفة على ال Y لإن
+
+191
+00:14:08,810 --> 00:14:11,610
+ال Y مش عارفين إيش عناصرها بشكل عام نشتغل فالآن
+
+192
+00:14:11,610 --> 00:14:14,930
+هنشوف كيف بنجيب الدالة من المعطيات لإن هو دي معرفة
+
+193
+00:14:14,930 --> 00:14:18,750
+و هتتكرر معنا فالآن نبدأ نقول له ال gate X أشمالها
+
+194
+00:14:18,750 --> 00:14:25,400
+is infinite X is infiniteو هذه المهارة حكيناها قبل
+
+195
+00:14:25,400 --> 00:14:28,300
+ايه عندك معلومات اكتبوها حتى لو بالهمش تشوف انت
+
+196
+00:14:28,300 --> 00:14:31,880
+إيش عندك إمكانيات و انت دايما عينك وين على المطلوب
+
+197
+00:14:31,880 --> 00:14:34,860
+هينحطينا المطلوب و نقولنا بندور على جيه دورنا في
+
+198
+00:14:34,860 --> 00:14:38,000
+دفاضر ال calculus قولنا بتبفع ناس بندور في مكان
+
+199
+00:14:38,000 --> 00:14:42,380
+آخر فندورش أن مواطيات تفتحنا الباب للحل ولا بتفتحش
+
+200
+00:14:42,380 --> 00:14:46,160
+اه فال excess finite implies there exist ايش
+
+201
+00:14:46,160 --> 00:14:51,910
+يسميها ال F مشغول هنسميها اسم جديد جيهمن X ل X
+
+202
+00:14:51,910 --> 00:15:05,850
+such that G is one to one and G of X برابر من Xهذا
+
+203
+00:15:05,850 --> 00:15:10,910
+معناه infinite هتطيها في السؤال، هتطيها في الهامش،
+
+204
+00:15:10,910 --> 00:15:13,110
+هتطيها على الأقل جانبية، لكن هذا مُعطَب، نحاول
+
+205
+00:15:13,110 --> 00:15:17,630
+نستفيد منه فالآن بنتعلمها دي المهارة، هنعرف الـF
+
+206
+00:15:17,630 --> 00:15:21,570
+بدلالة الـG كيف؟ نفكر مع بعض، نفكر مع بعض، إحنا
+
+207
+00:15:21,570 --> 00:15:31,470
+إيش عندنا الصورة؟ عندنا Y كبيرة وفيها X جواهاو جوا
+
+208
+00:15:31,470 --> 00:15:36,750
+عناصر كل ال Y اللي في ال X معرف عليهم ال G شايفها
+
+209
+00:15:36,750 --> 00:15:41,390
+معرف عليهم مش معروفة بشكل صريح لكن معرفة معرفة و
+
+210
+00:15:41,390 --> 00:15:45,610
+بتام عندنا الباقي بتام عندنا الباقي بدنا ياها من Y
+
+211
+00:15:45,610 --> 00:15:50,730
+ل Y نعمل كمان نسخة من ال Y كمان نسخة من ال Y فبدنا
+
+212
+00:15:50,730 --> 00:15:55,470
+دالة من hand ل handفانا هعرف .. وانتبه okay بنفكر
+
+213
+00:15:55,470 --> 00:15:58,570
+عشان نتعرف .. هبدأ أقوله let F مش هيك قلناه .. مش
+
+214
+00:15:58,570 --> 00:16:01,650
+هيك حلينا natural number .. بدنا نكرر .. هقوله let
+
+215
+00:16:01,650 --> 00:16:10,010
+F من Y إلى Y be given by .. بدأ أعرف ال F .. by F
+
+216
+00:16:10,010 --> 00:16:16,830
+of X تساويلو كانت ال X في ال capital X فال G معرف
+
+217
+00:16:16,830 --> 00:16:24,930
+عليها فهقوله تساوي G of X إذا X وين في ال capital
+
+218
+00:16:24,930 --> 00:16:29,830
+X ممتازة بتنفعه ولا بتنفعش؟ تنفع لأن ال G هذه
+
+219
+00:16:29,830 --> 00:16:32,970
+الدالة بتقدر الغرض اشمالها one to one و اشمالها
+
+220
+00:16:32,970 --> 00:16:38,010
+بتزغر كذا not onto بتزغر الصورة كأنها طيب في عندي
+
+221
+00:16:38,010 --> 00:16:45,100
+هنا مكان إضافي اللي هو إيش بيمثل هناY ناقص X ما
+
+222
+00:16:45,100 --> 00:16:49,460
+تبقى لأنه مفهوش .. مفهو .. ده اللي اوقفها من Y ل Y
+
+223
+00:16:49,460 --> 00:16:53,980
+لازم الناس اللي هيجي تغطي كل ال domain كيف اعرفها؟
+
+224
+00:16:53,980 --> 00:16:58,360
+كيف نعرفها؟ X اه .. ايه؟ X من ان اعرفها identity
+
+225
+00:16:58,360 --> 00:17:02,570
+functionبدنا نعرفه Identity Function ايه اسمه لك
+
+226
+00:17:02,570 --> 00:17:05,450
+يا حبي؟ نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+227
+00:17:05,450 --> 00:17:07,130
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+228
+00:17:07,130 --> 00:17:07,450
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+229
+00:17:07,450 --> 00:17:10,410
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+230
+00:17:10,410 --> 00:17:14,930
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+231
+00:17:14,930 --> 00:17:16,730
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+232
+00:17:16,730 --> 00:17:24,410
+نفسي نفسي نفسي نفسي نفسي نفسي نفسي
+
+233
+00:17:24,410 --> 00:17:30,070
+نفسي نفسي نمش أنتوا لكن أنا إيش عملت مش على كل
+
+234
+00:17:30,070 --> 00:17:33,790
+اللي عرفتها identity بس على جزء عندي جزء فانا إيش
+
+235
+00:17:33,790 --> 00:17:37,450
+اللي بده أعمله عشان بس نفكر مع بعض هذا الجزء بديش
+
+236
+00:17:37,450 --> 00:17:41,510
+أصغره صورته مش هتصغر لإن احنا إيش بنعمل بناخد
+
+237
+00:17:41,510 --> 00:17:45,170
+المجموعة و بنخلي صورتها أصغر proper subset مظبوط
+
+238
+00:17:45,170 --> 00:17:47,990
+فكأنه الدالة اللي بتأول عليها هي دالة بتعمل عمل
+
+239
+00:17:47,990 --> 00:17:52,370
+تصغير للصورة فبالنسبة لل identity هذا الجزء بتنجله
+
+240
+00:17:52,370 --> 00:17:56,220
+زي ما هو بيصغرهاش لكن مين اللي بيصغراللي جوه ال X
+
+241
+00:17:56,220 --> 00:17:59,420
+ليه ال G بتقوم بعملية تصغير يكفيني، بتديش كل
+
+242
+00:17:59,420 --> 00:18:01,940
+الدالة جزء منها، لو جزء منها صغر يكفي، بتقدي
+
+243
+00:18:01,940 --> 00:18:05,740
+الغرض، فهذه هنثبت أنه بتحقق الشرطين، هنثبت أن هذه
+
+244
+00:18:05,740 --> 00:18:09,060
+الدالة هي التعريف الصحيح، فبدنا ننتبه، لما نعرف
+
+245
+00:18:09,060 --> 00:18:11,840
+الدالة، نشوف الدالة ممكن تتعرف ولا لأ، في عنا
+
+246
+00:18:11,840 --> 00:18:15,320
+مجموعة مجرد عامةلا يمكنني أن أعرف عليها عمليات
+
+247
+00:18:15,320 --> 00:18:18,560
+حسابية أو أعرف دوال الـ Calculus طيب، من الدوال
+
+248
+00:18:18,560 --> 00:18:20,360
+التي تنفع أن تتعرف دائما؟ لو Identity تنفع أن
+
+249
+00:18:20,360 --> 00:18:23,380
+تتعرف دائما، لأنه لا يوجد أي عملية حسابية لأي
+
+250
+00:18:23,380 --> 00:18:26,160
+مجموعة؟ أو نحن استفدنا من هذا الـL مُعرّف، أيش ما
+
+251
+00:18:26,160 --> 00:18:29,120
+تكون تكون الـG مُعرّف أصلا استفدنا منها، لنرى هل
+
+252
+00:18:29,120 --> 00:18:32,360
+هذه تنفع ولا لا تنفع؟ هل هناك أحد عنده الصفصار
+
+253
+00:18:32,360 --> 00:18:35,380
+متبعين؟ فإذن هذا المفتاح، هذه الصعوبة التي أتكلم
+
+254
+00:18:35,380 --> 00:18:39,340
+عنها كيف نكون الـF؟ طبعا لسه الأمثلة تتعدد معنا
+
+255
+00:18:39,340 --> 00:18:39,820
+وشوية ش
+
+256
+00:18:43,680 --> 00:18:47,020
+أي استفسار؟ متابعين؟ تمام، نثبت إن الـ App هي one
+
+257
+00:18:47,020 --> 00:18:54,640
+-to-one وإن ليش ليست on فنبدأ .. نعم .. أه بس
+
+258
+00:18:54,640 --> 00:18:57,220
+بتاخدوا .. تشوفوا مع بعض كيف بيكون، على أنه بتاخد
+
+259
+00:18:57,220 --> 00:18:59,920
+عنصرين من ال domain طب لو عنصرين ممكن يكونوا في X
+
+260
+00:18:59,920 --> 00:19:03,000
+و ال G بتحللنا المشكلة، طب لو واحد هنا و واحد هنا،
+
+261
+00:19:03,000 --> 00:19:05,680
+إيش بيصير؟ هنشتغلها كلها، خليني أنا أخدها واحدة
+
+262
+00:19:05,680 --> 00:19:10,020
+واحدةخلّيني أخدها واحدة واحدة ده نبدأ خطوة خطوة و
+
+263
+00:19:10,020 --> 00:19:15,380
+نشوف إيش الاحتمالات والنظرة الأولية بالسهولة صح
+
+264
+00:19:15,380 --> 00:19:20,300
+ولا مش صح فهيبدأ أثبت أن F is one to one F is one
+
+265
+00:19:20,300 --> 00:19:24,680
+to one بدنا نثبت طبعا كالعادة هاخد عنصرين من ال
+
+266
+00:19:24,680 --> 00:19:31,640
+domain let X1 X2 من domain ال F؟ Y فننتبه و نركز
+
+267
+00:19:31,640 --> 00:19:34,420
+في الحل تنتبه من ال Y such that
+
+268
+00:19:37,280 --> 00:19:44,720
+F of X1 تساوي F of X2 إيش مطلوب مني؟ مطلوب مني
+
+269
+00:19:44,720 --> 00:19:48,980
+أثبت إن X1 تساوي X2 هذا هو الهدف تبعي أوصلنا ال F
+
+270
+00:19:48,980 --> 00:19:53,260
+هنا معرفة بالتجزيق اللي عبارة عن اتحاد يعني اتحاد
+
+271
+00:19:53,260 --> 00:19:57,520
+إيش؟ يعني or ففي عندي الحقيقة أربع احتمالاتيا
+
+272
+00:19:57,520 --> 00:20:01,800
+العنصرين مع بعض في الـ X، يا العنصرين مع بعض خارج
+
+273
+00:20:01,800 --> 00:20:05,400
+الـ X في Y ناقص X، أو واحد دي هو واحد برا، الأول
+
+274
+00:20:05,400 --> 00:20:08,180
+أو التاني، فعندي أربع احتمالات، أربع احتمالات،
+
+275
+00:20:08,180 --> 00:20:10,600
+لحقيقة الاحتمالات التانية ممكن أضمهم مع بعض، بس
+
+276
+00:20:10,600 --> 00:20:12,860
+حتى لو خلينا نكتبهم بالتفصيل، متفرجش كتير، و هم
+
+277
+00:20:12,860 --> 00:20:15,260
+متشابهين، لأنه احنا قولنا X واحد و X اتنين من
+
+278
+00:20:15,260 --> 00:20:17,120
+الأول و الأتنين التاني، متفرجش معنا كتير، لكن
+
+279
+00:20:17,120 --> 00:20:20,720
+خلينا نشتغلهم بالتفصيل، فهذا يؤدي، في عندي أربع
+
+280
+00:20:20,720 --> 00:20:27,080
+احتمالاتلو كانوا X1 و X2 في الـ Capital X إيش
+
+281
+00:20:27,080 --> 00:20:30,060
+تعريفهم؟ بدي أستخدم التعريف الآن بس التعريف هيدينا
+
+282
+00:20:30,060 --> 00:20:32,960
+أربع احتمالات وهذه المهارة هتيجي معنا أكتر من مرة
+
+283
+00:20:32,960 --> 00:20:35,880
+هذا ال trick اللي هنا بنستخدمه ففي عندنا أربع
+
+284
+00:20:35,880 --> 00:20:39,620
+احتمالات خلينا نعملهم بيد الشكل عشان مافيش واسعة
+
+285
+00:20:39,620 --> 00:20:47,280
+فإما تكون G of X1 تساوي G of X2 وقتاش إذا X1 و X2
+
+286
+00:20:47,280 --> 00:20:52,170
+وين موجودين؟ في ال Capital Xهي التعريف إذا التنين
+
+287
+00:20:52,170 --> 00:20:55,990
+مع بعض يوما ال X فإيه ان تعريف ال F ال F بتكون G
+
+288
+00:20:55,990 --> 00:21:00,190
+لو سمحت هنا فإذا كانت X1 في ال capital X إيش تعريف
+
+289
+00:21:00,190 --> 00:21:04,590
+ال F؟ G و X2 نفس القضية طيب، الآن لو كانوا التنين
+
+290
+00:21:04,590 --> 00:21:08,370
+برا طبعا بينهم هدولة كلهم Or لأنها دي هاش اتحاد
+
+291
+00:21:08,370 --> 00:21:11,150
+فأو لو كانوا التنين برا دي وكنت عارفهم ال identity
+
+292
+00:21:11,150 --> 00:21:16,390
+X1 تساوي X2 وقتهاش إذا X1 و X2 موجودين في ال Y
+
+293
+00:21:16,390 --> 00:21:23,220
+ناقص Xأه طبعا كله بينهم R أو طبعا لو كانت X1 في ال
+
+294
+00:21:23,220 --> 00:21:30,280
+X و X2 في ال Y ناقص X إيش بيكون؟ ال X1 في ال X إيش
+
+295
+00:21:30,280 --> 00:21:34,340
+تعريف ال F؟ F of X .. G of X1 و ال X2 من برة إيش
+
+296
+00:21:34,340 --> 00:21:40,500
+بيكون تعريفها؟ X2 نفس القضية لو كانت X2 في ال X و
+
+297
+00:21:40,500 --> 00:21:45,500
+X1 في ال Y ناقص X بتشبهها إيش بيكون؟ تعريف ال A of
+
+298
+00:21:45,500 --> 00:21:53,980
+X1 X1و X2 جي و X2 طبعا كله R R R هدولة أربع
+
+299
+00:21:53,980 --> 00:21:57,620
+احتمالات واحدة منهم بتكون على الأقل صحية واحدة
+
+300
+00:21:57,620 --> 00:22:04,150
+منهم بتكون صحيةواضحة فهذه دالة يعني هذه ايش نتعلم
+
+301
+00:22:04,150 --> 00:22:08,810
+منها كيف اثبت انه دالة معرفة بالتيزيق اختراع متعدد
+
+302
+00:22:08,810 --> 00:22:13,270
+القاعدة كيف اثبت انه one to one كيف اثبت انه one
+
+303
+00:22:13,270 --> 00:22:18,690
+to one فكل احتمال بديني باش تغلق و بداشه طبعا اخر
+
+304
+00:22:18,690 --> 00:22:22,710
+احتمال جاهز هدف ان اوصل ان X1 تساوي X2 مظبوط هذا
+
+305
+00:22:22,710 --> 00:22:25,380
+جاهزأه طبعا عشان بينهم or بينفع أعمل
+
+306
+00:22:25,380 --> 00:22:28,180
+simplification وأقول ما هي x1 سو x2 وخلصت وجهها
+
+307
+00:22:28,180 --> 00:22:30,940
+للباقي لأ عشان or مافيش simplification فإيش لازم
+
+308
+00:22:30,940 --> 00:22:33,800
+نقول عن دي؟ يا contradiction or anything تؤدي
+
+309
+00:22:33,800 --> 00:22:37,820
+anything أو أيضا بتنسيقون تكافئوا قولوا يطلع x1 سو
+
+310
+00:22:37,820 --> 00:22:43,810
+x2 أه فهذا يؤدي الآن بدي أكتبهم بالشكل التاليطيب،
+
+311
+00:22:43,810 --> 00:22:47,730
+هذا الأخير معروف، طيب الأول بتديني برضه X1 تساوي
+
+312
+00:22:47,730 --> 00:22:53,190
+X2، ليش؟ لأن الـ G is one to one لأن الـ G is one
+
+313
+00:22:53,190 --> 00:22:56,910
+to one، يمكن أكتبهم بشكل، بنفس الأسلوب أفضل، هذا
+
+314
+00:22:56,910 --> 00:23:02,250
+يؤدي X1 تساوي X2، ليش؟ لأن الـ G is one to one،
+
+315
+00:23:02,250 --> 00:23:06,150
+بنفس المنهج، والأخيرة ما أحنا جاهزة، X1 تساوي X2
+
+316
+00:23:06,150 --> 00:23:10,630
+لأنه طبعاً R، بدنا نشوف كله R، هذه طبعاً من الأول،
+
+317
+00:23:10,630 --> 00:23:15,530
+من التعريففيش مشكلة، فهذا الاحتمال الرابع، بدنا
+
+318
+00:23:15,530 --> 00:23:19,510
+نشوف الاحتمالين التانين إيش بتتوقعوا من الاحتمال
+
+319
+00:23:19,510 --> 00:23:23,950
+اللي في النص يدونا X1 تساوي X2 ولا Contradiction؟
+
+320
+00:23:23,950 --> 00:23:28,790
+هي اللي بنفعلها، إيش بتدونا؟ Contradiction،
+
+321
+00:23:28,790 --> 00:23:34,390
+Contradiction، ليش؟أه ليش مينفعش هال gate لما يقول
+
+322
+00:23:34,390 --> 00:23:40,430
+لي x2 بتساوي صورة x1 أه ليش لأن ال g من y متودة من
+
+323
+00:23:40,430 --> 00:23:44,890
+x ل x فلما يقول x1 في x صورة هو أنك تكون في x هو
+
+324
+00:23:44,890 --> 00:23:48,230
+x1 ومش بتقول في y نقص x يعني ليست في ال x فده
+
+325
+00:23:48,230 --> 00:23:50,710
+contradiction فهنا contradiction
+
+326
+00:23:53,360 --> 00:23:59,240
+Contradiction، ليش؟ أكتبلكوا السبب لأن X2 اللي هي
+
+327
+00:23:59,240 --> 00:24:08,780
+إيش في الأول تنتمي للـG of X subset من الـX and X2
+
+328
+00:24:08,780 --> 00:24:12,320
+لا تنتمي للـX، هاي الـContradiction X2 في الـY
+
+329
+00:24:12,320 --> 00:24:15,620
+ناقص X، إيش معناته؟ في الـY وليست في الـX، أه
+
+330
+00:24:15,620 --> 00:24:19,000
+التانية زيها، تشبهها بس العكس، اتضحوا، برضه
+
+331
+00:24:19,000 --> 00:24:26,640
+Contradiction، لو سمحتواأه ليش؟ لأن X1 تنتمي لصورة
+
+332
+00:24:26,640 --> 00:24:32,200
+G of X وهي بربع صفر من X و X1 نشمالها لا تنتمي لل
+
+333
+00:24:32,200 --> 00:24:37,200
+X لأنه إيش بيقول هنا؟ X1 خارج ال X طب X1 صورة ..
+
+334
+00:24:37,200 --> 00:24:40,600
+صورة G والـ G من وين لوين؟ من X لX، بينفعش تكون
+
+335
+00:24:40,600 --> 00:24:45,540
+خارج، فcontradiction تمام؟ الآن B or contradiction
+
+336
+00:24:45,540 --> 00:24:49,180
+or contradiction or B؟ بيدينا B، idempotency
+
+337
+00:24:49,180 --> 00:24:51,940
+ونظرية واحد سبعة، وهو المطلوب
+
+338
+00:24:59,060 --> 00:25:07,200
+أه فهنا هذا يؤدي إن X1 تساوي X2 نظرية 1 7 و P or B
+
+339
+00:25:07,200 --> 00:25:12,760
+تكافئ بي I don't want to answer تمام و هو المطلوب
+
+340
+00:25:12,760 --> 00:25:18,760
+فإذا أثبتنا نبدأ له one to one thus FG احنا بنشر
+
+341
+00:25:18,760 --> 00:25:23,440
+على F is one to one أي سؤال
+
+342
+00:25:26,020 --> 00:25:29,200
+واضح؟ فإذن هذه .. يمكن أول مثال هيمر علينا عدة
+
+343
+00:25:29,200 --> 00:25:33,020
+أمثلة كيف نثبت إن ده لمتعددة القاعدة إنها one to
+
+344
+00:25:33,020 --> 00:25:37,400
+one نفس الطريقة نشوف الخطوة التانية بإن نثبت إنها
+
+345
+00:25:37,400 --> 00:25:42,400
+جاية F of Y برابر من ال Y هذا المطلوب التاني إذا
+
+346
+00:25:42,400 --> 00:25:49,910
+حبينا نرقم بنرقم مطلوب إيه؟شوفنا في المثال السابق
+
+347
+00:25:49,910 --> 00:25:53,590
+وفي الملاحظة عشان اثبت ايش مطلوب اثبت ان هناك عنصر
+
+348
+00:25:53,590 --> 00:25:57,970
+في ال Y غير موجود في ال F of Y خليني اكتبها We
+
+349
+00:25:57,970 --> 00:26:08,410
+have to find Y تنتمي لل Y and Y لا تنتمي لل F of Y
+
+350
+00:26:08,410 --> 00:26:13,370
+بدنا عنصر الزيادة بدنا عنصر الزيادة بدنا ندور على
+
+351
+00:26:13,370 --> 00:26:19,200
+هذا العنصر بدنا ندور على عنصر الزيادةوين الـ G؟
+
+352
+00:26:19,200 --> 00:26:22,640
+طبعا في المثال الماضي كنا عارفين أن الصور كلها
+
+353
+00:26:22,640 --> 00:26:25,380
+زوجية فاخدنا له واحد فرد الواحد تذكروا المثال تبع
+
+354
+00:26:25,380 --> 00:26:27,860
+المعادرة السابعة طب الآن احنا عارفين الصور ايش
+
+355
+00:26:27,860 --> 00:26:30,980
+بتكون بالظبط مش عارفين برضه نفس الخضية لما يكون
+
+356
+00:26:30,980 --> 00:26:35,060
+الشغل عام يطلع المعطيات إيش عندنا معطيات؟ عندنا من
+
+357
+00:26:35,060 --> 00:26:39,660
+المعطيات أن الـ G of X برابر subset برابر subset
+
+358
+00:26:39,660 --> 00:26:42,900
+ماعنش تقريبا نفس المجموعة هي عندنا .. إيش الصورة؟
+
+359
+00:26:42,900 --> 00:26:48,460
+خلينا نشوفما هيي ال X و F of X وينها؟ جواها ال F
+
+360
+00:26:48,460 --> 00:26:52,480
+of X بس هيي ال X و هيي ال F of X ال brother subset
+
+361
+00:26:52,480 --> 00:26:59,300
+وهان ال X ففي عنصرها الزيادة صح؟ من الأول هل هذا
+
+362
+00:26:59,300 --> 00:27:02,800
+هو بتام عنصر الزيادة؟ الحقيقة نعم هو المرشح
+
+363
+00:27:02,800 --> 00:27:05,180
+والحقيقة هو اللي بنجح لأنه زي ما قلنا مين اللي
+
+364
+00:27:05,180 --> 00:27:12,290
+بيظغر ال .. آسف ال G هذي هذي G مش Fمهي أياش
+
+365
+00:27:12,290 --> 00:27:15,990
+بتنجولها نفسها لإن ال Fاش بتعمل جوا ال X زي ما هي
+
+366
+00:27:15,990 --> 00:27:20,990
+.. اه زي ما هي فهذه مش صورة أي حد تحت ال G و طب و
+
+367
+00:27:20,990 --> 00:27:24,030
+ال Fاش بتعمل جوا العنصر X لإن هي بتحرفها G مش
+
+368
+00:27:24,030 --> 00:27:27,790
+تعرفها G إذا هو هيتمه برضه مش صورة حد اه فحناخد ال
+
+369
+00:27:27,790 --> 00:27:35,730
+answer ده ال A البرهان since G of capital X برابر
+
+370
+00:27:35,730 --> 00:27:47,080
+من ال X ايش فيه؟We have X تنتمي للكابتل X and أو
+
+371
+00:27:47,080 --> 00:27:55,260
+there exist و X شمالها لا تنتمي لل G of X فهذا هو
+
+372
+00:27:55,260 --> 00:28:01,140
+العنصر اللي بندور عليه خلينا نسميه Y عشان
+
+373
+00:28:01,140 --> 00:28:05,420
+نطبق مع الكلام اللي تحتهل هذا ال Y اللي بدور عليه؟
+
+374
+00:28:05,420 --> 00:28:12,000
+بدنا نثبت إن هو نفسه إنه هو العنصر اللي بدور عليه
+
+375
+00:28:12,000 --> 00:28:15,360
+هو نفس العنصر اللي بدور عليه فاحنا بدنا نثبت إن
+
+376
+00:28:15,360 --> 00:28:19,460
+هذا ال Y فعلا ينتمي ل F of Y
+
+377
+00:28:22,700 --> 00:28:26,320
+هو ينتمي لل Y ولا ينتمي لل F of Y فهنا خلّينا
+
+378
+00:28:26,320 --> 00:28:31,760
+نحطها claim ادعاء Y هي اللي بدور عليها تنتمي لل Y
+
+379
+00:28:31,760 --> 00:28:36,480
+and Y لا تنتمي لل F of Y هو العنصر اللي بدور عليه
+
+380
+00:28:36,480 --> 00:28:39,700
+بدنا نثبت هذا الكلام فنثبت هذا الكلام prove
+
+381
+00:28:42,620 --> 00:28:46,560
+فهذا الجزئية بس عشان احط البرهان بنطب و نقدر نخرج
+
+382
+00:28:46,560 --> 00:28:51,880
+تمام اول شئ Y تنتمي ل Y بسهولة لأن ال Y في ال X و
+
+383
+00:28:51,880 --> 00:28:56,180
+ال X برابر subset من ال X فإذا هنا Y تنتمي ل X
+
+384
+00:28:56,180 --> 00:29:00,760
+implies Y تنتمي ل Y لإيش؟ لأن X subset من Y من
+
+385
+00:29:00,760 --> 00:29:03,800
+البداية أخدناها ولا لأ؟ مش هيقولنا هي super set
+
+386
+00:29:03,800 --> 00:29:09,600
+فدي أخدناها تمام بتام الجزء التاني الجزء التاني
+
+387
+00:29:09,600 --> 00:29:15,300
+هعمله by contradictionهعمله by contradiction نفترض
+
+388
+00:29:15,300 --> 00:29:22,280
+ان ال Y في ال F of Y assume Y تنتمي لل F of Y
+
+389
+00:29:22,280 --> 00:29:27,660
+خلينا بس نتابع الكلام نكون أتوقع هي نفس الخيار
+
+390
+00:29:27,660 --> 00:29:30,180
+صحيح بس هتأكد عشان ما نروحش بعيد
+
+391
+00:30:07,060 --> 00:30:16,310
+لأ تابعغالبا الكلام صحيح فال Y تساوي تنتمي لل F of
+
+392
+00:30:16,310 --> 00:30:20,350
+Y نوصل إلى Contradiction نعمل By Contradiction
+
+393
+00:30:20,350 --> 00:30:24,570
+prove للجزء هذا By Contradiction و اتعلمنا انه
+
+394
+00:30:24,570 --> 00:30:27,930
+احنا ممكن ضمن البرهان نعمل اجزاء زي ما بدنا
+
+395
+00:30:27,930 --> 00:30:32,490
+Contradiction ايش معناه ان ال Y في صورة ال capital
+
+396
+00:30:32,490 --> 00:30:37,470
+Y ان هي صورة عنصر من ال capital Y Y تساوي F of X
+
+397
+00:30:38,210 --> 00:30:44,850
+for some x تنتمي للـ y طيب إيش تعريف ال F محيتها
+
+398
+00:30:44,850 --> 00:30:51,960
+أنا احتماليةفالـ Y يا بتساوي G of X إذا الـ X
+
+399
+00:30:51,960 --> 00:30:57,440
+تنتمي للـ X أو بتساوي X إذا الـ X تنتمي لمن؟ للـ Y
+
+400
+00:30:57,440 --> 00:31:01,460
+ناقص X بدنا نثبت أن التنتين احكمالين أور أن
+
+401
+00:31:01,460 --> 00:31:04,500
+التنتين Contradiction، بنوصل لـ Contradiction طيب،
+
+402
+00:31:04,500 --> 00:31:10,420
+هل بنفع أن الـ Y تساوي G of X؟ احنا من وين اخترنا
+
+403
+00:31:10,420 --> 00:31:16,530
+الـ Y؟ الـ Y شمالهاهي لا تنتمي لل G of X فهذا
+
+404
+00:31:16,530 --> 00:31:20,150
+مستحيل Contradiction اه Contradiction فهذا
+
+405
+00:31:20,150 --> 00:31:24,670
+Contradiction Or
+
+406
+00:31:24,670 --> 00:31:30,450
+فده الأول طيب بنفعل Y تساوي X طب ال X .. ايش ال X؟
+
+407
+00:31:30,450 --> 00:31:35,850
+وين موجودة ال X؟ ال X موجودة في ال Y و ال X لا
+
+408
+00:31:35,850 --> 00:31:40,810
+تنتمي لل X ال X لا تنتمي لل X
+
+409
+00:31:46,070 --> 00:31:52,810
+بنفعش ليش تكون X لأنه لو X تنتمي لل Y ولا تنتمي لل
+
+410
+00:31:52,810 --> 00:31:57,390
+X بيدينا برضه contradiction لأن ال Y موجودة في ال
+
+411
+00:31:57,390 --> 00:31:59,650
+X صحيح فهذا برضه contradiction فهذا أيش برضه
+
+412
+00:31:59,650 --> 00:32:05,700
+contradiction وهو الموضوعفإذن ليش هذا الكلام غير
+
+413
+00:32:05,700 --> 00:32:09,600
+صحيح؟ لأن ال Y في ال X أصلا، ماينفعش تكون خارج، ف
+
+414
+00:32:09,600 --> 00:32:13,620
+Y تسوى X لأنه .. طبعا هنا ليش؟ لأن ال Y تنتمي لل
+
+415
+00:32:13,620 --> 00:32:19,340
+X، طبعا هنا ليش؟ لأن ال Y لا تنتمي لمين؟ لل G of
+
+416
+00:32:19,340 --> 00:32:24,280
+X، فهنا طبعا هي كل واحدة وسبب تتحدث، وانتهت العمل
+
+417
+00:32:27,540 --> 00:32:31,420
+طبعاً الأمور شوية زي ما حكينا مش .. مش سالسة أو مش
+
+418
+00:32:31,420 --> 00:32:35,060
+مباشرة فلكن احنا بنحاول نشوف اللي هو البنية
+
+419
+00:32:35,060 --> 00:32:38,880
+الأساسية للشغل آه كيبنا نثبت إنها infinite بندور
+
+420
+00:32:38,880 --> 00:32:42,840
+على دالة وتعلمنا إنه ما زال مجموعة مجردة ماينفعش
+
+421
+00:32:42,840 --> 00:32:45,660
+أجيب دوال من دوال ال calculus لإنه مش معرفين ممكن
+
+422
+00:32:45,660 --> 00:32:49,600
+يكونواأه فشوفنا من المعطيات استفدنا جيبنا الدالة F
+
+423
+00:32:49,600 --> 00:32:54,280
+عرفناها ب G طبعا مش بشكل متطابق تماما كملنا من عنا
+
+424
+00:32:54,280 --> 00:32:57,580
+وانجحنا اه طبعا فاثبتنا انها one to one وانجحنا
+
+425
+00:32:57,580 --> 00:33:00,720
+نثبت انها one to one تم ندوي على عنصر زيادة موجود
+
+426
+00:33:00,720 --> 00:33:03,860
+في المجموع او مش موجود في الصورة ولاجناها من ..
+
+427
+00:33:03,860 --> 00:33:06,820
+برضه من المعطيات ولاجناها برضه من المعطيات طبعا
+
+428
+00:33:06,820 --> 00:33:12,010
+اختارناها بشكل مناسب واثبتنا فعلا انهبيحقق الشروط
+
+429
+00:33:12,010 --> 00:33:15,710
+فطبعا احنا قلنا افترض ان هو صورة بنتظر تقول ده
+
+430
+00:33:15,710 --> 00:33:19,530
+contradiction مستحيل فطبعا ايش معنى الصورة؟ اه وهي
+
+431
+00:33:19,530 --> 00:33:23,650
+الاحتمالين طب لو كان G of X بتكون ال Y وين؟ لو
+
+432
+00:33:23,650 --> 00:33:27,510
+كانت تنتمي لل G of X فده مستحيل و لو كانت X بتكون
+
+433
+00:33:27,510 --> 00:33:31,330
+وين؟ في ال capital X اه لإيه؟ لأن ال Y بال capital
+
+434
+00:33:31,330 --> 00:33:35,110
+X و ايش ويش ويش ال Y؟ بقول ايش؟ Y ناقص X مينفعش
+
+435
+00:33:35,110 --> 00:33:44,150
+فصارت contradictionنشوف فرع بيه السهل فرع بيه هذا
+
+436
+00:33:44,150 --> 00:33:50,210
+كله ايه طبع نظرية الأولى
+
+437
+00:33:50,210 --> 00:33:52,650
+بعدين بنعلق على امتحان اخر خلينا نكمل نرجع
+
+438
+00:33:52,650 --> 00:33:56,970
+الامتحانكل مجزّي من الـ finite set هو finite
+
+439
+00:33:56,970 --> 00:34:00,610
+خلّيني أولا أحط الجملة لأن البرهان هي تعمل على
+
+440
+00:34:00,610 --> 00:34:05,170
+السابق بسهولة لأنه عملية negation و هنعملها بشكل
+
+441
+00:34:05,170 --> 00:34:10,730
+مباشر فخلّيني أشوف هنا البرهان بشكل مشابه let X be
+
+442
+00:34:10,730 --> 00:34:18,150
+a finite set إيش المطلوب؟
+
+443
+00:34:18,150 --> 00:34:26,240
+we have to prove thatنفس العملية الماضية بس اختلاف
+
+444
+00:34:26,240 --> 00:34:33,440
+انه بدل super set subset for all y such that y
+
+445
+00:34:33,440 --> 00:34:48,240
+subset من ال X ال Y is finite ال
+
+446
+00:34:48,240 --> 00:34:56,380
+Y is finite فطبعا كالعادة بدنا نبداش let Ybe a set
+
+447
+00:34:56,380 --> 00:35:01,800
+such that طبعا عشان for all ال Y subset من ال X
+
+448
+00:35:01,800 --> 00:35:06,340
+بدنا يثبت ان ال Y finite طبعا زي حتى اللي مر علينا
+
+449
+00:35:06,340 --> 00:35:09,560
+كل ال finite اللي عملناها by contradiction assume
+
+450
+00:35:09,560 --> 00:35:13,060
+Y
+
+451
+00:35:13,060 --> 00:35:18,660
+is infinite افترض
+
+452
+00:35:18,660 --> 00:35:22,790
+ان ال Y infinite بدنا يفرض ان هذا المستحيلالعملية
+
+453
+00:35:22,790 --> 00:35:27,930
+بس انتباه انتبهوا ال Y infinite وال X أكبر منها
+
+454
+00:35:27,930 --> 00:35:30,970
+لازم تكون infinite بالباش بالنظرية توي أثمتناها
+
+455
+00:35:30,970 --> 00:35:36,710
+الفرع اللي اتصابها أثمتها X is infinite مين دليلي
+
+456
+00:35:36,710 --> 00:35:44,170
+نظرية خمسة واحد A فرع A طبعا contradiction لأن X
+
+457
+00:35:44,170 --> 00:35:45,550
+شمالها finite
+
+458
+00:35:52,200 --> 00:35:56,240
+فهذه برهانة قصيرة جدا بيد السهولة اعتمد على فرع A
+
+459
+00:35:56,240 --> 00:36:01,160
+فهو المهم ففرع A هو الأساسي
+
+460
+00:36:01,160 --> 00:36:15,420
+ففرع A هو الأساسي نظرية
+
+461
+00:36:15,420 --> 00:36:16,060
+5-2
+
+462
+00:36:20,810 --> 00:36:24,970
+طبعاً ممكن تستخدميها ممكن تستخدميها مهمة جدا إذا
+
+463
+00:36:24,970 --> 00:36:28,070
+قدرت تثبت فالجيت انا مثلا لو قالك اثبت ان ال Z
+
+464
+00:36:28,070 --> 00:36:28,450
+infinite
+
+465
+00:36:33,450 --> 00:36:36,670
+على طول مباشرة فإن واضح ما زال أثبتنا أن نحن
+
+466
+00:36:36,670 --> 00:36:40,110
+ماشيين بيد الشكل للحقيقة ليش أثبتنا أن N هي ال
+
+467
+00:36:40,110 --> 00:36:42,830
+infinite هي أصغر infinite 6 للحقيقة فلجيت ال Z
+
+468
+00:36:42,830 --> 00:36:45,130
+infinite على طول و ال Q infinite و ال R infinite
+
+469
+00:36:45,130 --> 00:36:48,310
+كل المجموعات الأكبر منها infinite كلها infinite
+
+470
+00:36:48,310 --> 00:36:53,210
+على طول هذا كام مثال فهذه نظرية مهمة جداالنظرية
+
+471
+00:36:53,210 --> 00:36:56,790
+التانية برضه نظرية مهمة طبعاً العنوان العريض الـ
+
+472
+00:36:56,790 --> 00:37:00,750
+how و لا النتيجة اللي بعده بيقول لي no bijections
+
+473
+00:37:00,750 --> 00:37:03,810
+أو no bijection between infinite and finite set
+
+474
+00:37:03,810 --> 00:37:08,450
+مستحيل أقدر ألاجي تناظر بين مجموعتين واحدة finite
+
+475
+00:37:08,450 --> 00:37:12,010
+واحدة infinite هذا مستحيل نتخيله مع بعض ما هوش
+
+476
+00:37:12,010 --> 00:37:15,730
+معاه التناظر كل عنصر له نظير في المجموعة التانية
+
+477
+00:37:15,730 --> 00:37:19,090
+فهذا بيقول ان واش عناصرهم بتكون متساوي لعدد ولا لأ
+
+478
+00:37:19,090 --> 00:37:21,090
+اه فهو بيقول لي إذا كانت واحدة infinite واحدة
+
+479
+00:37:21,090 --> 00:37:24,500
+finite مستحيل إذا الكلام يكون صحيحبنشوف كيف بنثبت
+
+480
+00:37:24,500 --> 00:37:30,400
+هذه الحقيقة النظرية اللي هو بشكل مباشر let G from
+
+481
+00:37:30,400 --> 00:37:34,870
+X to Y be a one to one correspondenceهذه اسمها
+
+482
+00:37:34,870 --> 00:37:36,710
+يعني اسم by ejection one to one correspondence هو
+
+483
+00:37:36,710 --> 00:37:41,470
+المصطلح الآخر بقول إذا X infinite فال Y infinite
+
+484
+00:37:41,470 --> 00:37:45,170
+فهذه أول جزء من النظرية أنا لجيت one to one
+
+485
+00:37:45,170 --> 00:37:47,730
+correspondence بين مجموعتين إذا واحدة infinite
+
+486
+00:37:47,730 --> 00:37:50,450
+التانية لازم تكون infinite طب واحد يقول التانية
+
+487
+00:37:50,450 --> 00:37:52,830
+جالة إذا كانت ال X infinite فال Y infinite طب
+
+488
+00:37:52,830 --> 00:37:57,190
+والعكس لو ال F infiniteبرضه صح، ليش؟ لأن الـ F in
+
+489
+00:37:57,190 --> 00:38:00,090
+a bijection is an F in a G inverse as if G is in a
+
+490
+00:38:00,090 --> 00:38:02,750
+bijection، G inverse برضه bijection، من Y لأكس،
+
+491
+00:38:02,750 --> 00:38:06,290
+فالعملية ماشية باتجاهين، بس ودانا اسم العنوان وانت
+
+492
+00:38:06,290 --> 00:38:10,210
+تطبقي واتعممي، فده هو العنوان الرئيسي، إذا عندي
+
+493
+00:38:10,210 --> 00:38:13,430
+مجموعتين بينهم bijection، فواحدة Infinite، التانية
+
+494
+00:38:13,430 --> 00:38:16,410
+لازم تكون Infinite، طبعا بالنسبة يادر اتجاه من X ل
+
+495
+00:38:16,410 --> 00:38:19,110
+Y، بستخدم الـG كbijection، طب من Y ل X، إيش
+
+496
+00:38:19,110 --> 00:38:21,450
+هستخدم؟ G inverse، وهي بتكون bijection على طول
+
+497
+00:38:21,450 --> 00:38:25,200
+النظرية السابقة، فده بس ملاحظة سريعةخلّينا نشوف
+
+498
+00:38:25,200 --> 00:38:32,880
+البرهة فاحنا بدنا نشوف البرهة وإن
+
+499
+00:38:32,880 --> 00:38:35,400
+شاء الله بنبني على بعض ما تعلمناه في البرهان
+
+500
+00:38:35,400 --> 00:38:44,440
+السابق مع بعض الإختلافات القليلة theorem 5-2
+
+501
+00:38:44,440 --> 00:38:50,540
+approved طبعا فيه مواطيات let g from a be a
+
+502
+00:38:50,540 --> 00:38:55,410
+bijection خلّينا نكتبها لإن محتاجينهاlet g من x ل
+
+503
+00:38:55,410 --> 00:39:00,190
+y be a bijection one to one يعني bijection اتعود
+
+504
+00:39:00,190 --> 00:39:04,570
+على المصطلح هى اه بقوللي if x is infinite اذا هدا
+
+505
+00:39:04,570 --> 00:39:11,110
+يشمله الشرط بنفترض ان هو ياش معطق assume x
+
+506
+00:39:11,110 --> 00:39:20,350
+is infinite ايش مطلوب اثبت ان ال y infinite we
+
+507
+00:39:20,350 --> 00:39:29,560
+haveto prove Y is infinite تمام
+
+508
+00:39:29,560 --> 00:39:33,560
+فهذا كل ما بقى دي رياضيات ماعملتش كل هذا معلومات
+
+509
+00:39:33,560 --> 00:39:37,240
+جديدة معلومات قديمة أسف طيب بدي أثبت أن ال Y
+
+510
+00:39:37,240 --> 00:39:41,200
+infinite يعني إيش بدي بدي دالة F من Y ل Y one to
+
+511
+00:39:41,200 --> 00:39:48,120
+one و proper subset we mustFind او have to find a
+
+512
+00:39:48,120 --> 00:39:58,820
+function F من Y ل Y such that F is one to one and
+
+513
+00:39:58,820 --> 00:40:05,620
+F ال Y اقرب من ال Y فبد ان هدول الشرطين يتحقق فبد
+
+514
+00:40:05,620 --> 00:40:06,400
+اعرف ال F
+
+515
+00:40:09,410 --> 00:40:16,590
+من Y ل Y بي given by هذا ليهيش مفتاح الحل هذا ال
+
+516
+00:40:16,590 --> 00:40:21,050
+use الأول فكيف
+
+517
+00:40:21,050 --> 00:40:26,700
+بدنا نعرف ال Fبنفع نجيب من دفاتر ال calculus؟ لأ،
+
+518
+00:40:26,700 --> 00:40:29,820
+اه هنا نفعي، شوف ده العملية بتدل، لإن ال Y جالي
+
+519
+00:40:29,820 --> 00:40:34,420
+مجموعة، إيش عناصرها مش عارف، أعداد، مش أعداد،
+
+520
+00:40:34,420 --> 00:40:38,060
+فواكه، كراسي، مش عارف، مجموعة، أي مجموعة، العمليات
+
+521
+00:40:38,060 --> 00:40:40,880
+الحسابية معرفة مش معرفة، مش عارف، دهش مشاكل عامة،
+
+522
+00:40:40,880 --> 00:40:45,010
+إذا أين بده أدور؟في المعطيات عن دوال اتساعدني بدي
+
+523
+00:40:45,010 --> 00:40:48,650
+ادور عن دوال اتساعدني في دوال في المعطيات نعم قال
+
+524
+00:40:48,650 --> 00:40:52,510
+لي فيه G قال ليه فيه G بس هنا الصورة مختلفة عن
+
+525
+00:40:52,510 --> 00:40:57,650
+الصورة الماضية كنا هناك نشتغل في X و Y مجموعة أكبر
+
+526
+00:40:57,650 --> 00:41:00,370
+منها الآن ال X و Y دولة مش ضرورة تكون سبسط من بعض
+
+527
+00:41:00,370 --> 00:41:06,130
+بشكل عام فاحنا عندنا الصورة التالية هي في عندنا X
+
+528
+00:41:06,530 --> 00:41:11,970
+الرسم بيساعد و في عندنا Y و في عندنا G و احنا
+
+529
+00:41:11,970 --> 00:41:16,030
+بندور على دالة F من Y ل Y نعمل كمان نسخة من Y
+
+530
+00:41:16,030 --> 00:41:26,050
+بندور على F من Y ل Y بندور على function F من Y ل Y
+
+531
+00:41:26,050 --> 00:41:31,150
+بدنا انعرفها بشكل مناسب تكون one to one و ليست
+
+532
+00:41:31,150 --> 00:41:38,810
+انتوا ال G one to one ايش نعمل؟بدنا نعرف الـ F
+
+533
+00:41:38,810 --> 00:41:43,990
+الأمور أصعب من السابق أصعب من السابق لكن هنا بنشوف
+
+534
+00:41:43,990 --> 00:41:48,410
+الأمثلة و بن count هنعمل .. مين أداتنا؟ الـ G
+
+535
+00:41:48,410 --> 00:41:52,190
+اتفقنا؟ إذا إحنا ندور على المعطيات وهي الـ G بدنا
+
+536
+00:41:52,190 --> 00:41:56,570
+نعمل ال trickبدنا نبدأ من ال Y و بدنا نستخدم ال G
+
+537
+00:41:56,570 --> 00:42:02,050
+بنفع أبدأ من ال Y مع ال G؟ لأ ال Y .. ال G من وين؟
+
+538
+00:42:02,050 --> 00:42:06,250
+من X ل Y لكن ممكن أبدأ بمين؟ بال G inverse بال G
+
+539
+00:42:06,250 --> 00:42:08,890
+inverse لإن هو دي إيش one two bijection فال
+
+540
+00:42:08,890 --> 00:42:14,280
+inverse معروف فانا هبدأ من Y في ال G inverseالـ G
+
+541
+00:42:14,280 --> 00:42:18,900
+inverse وين بيوديني؟ بيوديني على ال X فانا هبدأ من
+
+542
+00:42:18,900 --> 00:42:24,200
+Y بالـ G inverse ووداني على ال X بدي ارجع لل Y مين
+
+543
+00:42:24,200 --> 00:42:29,260
+ممكن يرجعني لل Y؟ ممكن يرجعني ال G ممكن يرجعني ..
+
+544
+00:42:29,260 --> 00:42:34,100
+انا ال G inverse من وين لوين؟ ال G inverse من Y ل
+
+545
+00:42:34,100 --> 00:42:38,800
+Xأه ممكن ال G ترجعني لل Y بس بكون أنا ليش ماعملتش
+
+546
+00:42:38,800 --> 00:42:41,980
+إشي أنا بده أروح من Y ل X بكون ليش لأن ال G
+
+547
+00:42:41,980 --> 00:42:45,120
+inverse مع ال G هذي one to one and unto مابتنفعش
+
+548
+00:42:45,120 --> 00:42:48,140
+مين اللي بيقوم بعملية التصغير اللي قلنا عنه اللي
+
+549
+00:42:48,140 --> 00:42:51,880
+بيدينا صورة مش unto ال F فلازم ندخل ال F على الخط
+
+550
+00:42:52,320 --> 00:42:55,280
+بدنا ندخل الـ F في العملية لأنه قلنا مين اللي
+
+551
+00:42:55,280 --> 00:42:58,860
+بيصغر فيه دالة بتصغر في العملية بتصغر الصورة الـ F
+
+552
+00:42:58,860 --> 00:43:04,920
+هندخل الـ F بشكل مناسب مانفعش أبدأ من الـ G مباشرة
+
+553
+00:43:04,920 --> 00:43:07,660
+بدنا نبدأ بالـ G inverse فهنعرف الـ F بشكل التالي
+
+554
+00:43:07,660 --> 00:43:13,660
+given by F بدنا ن .. لأ ال F بدنا .. هي اللي بدنا
+
+555
+00:43:13,660 --> 00:43:18,560
+نعرفها بدنا نعرفها فإيش كيف الـ G في عندنا دالة
+
+556
+00:43:18,560 --> 00:43:19,320
+أخرة احنا لأ
+
+557
+00:43:33,720 --> 00:43:39,620
+لسه مش كافي الأمور فلسه الجيل حد مش نافع بدنا ندور
+
+558
+00:43:39,620 --> 00:43:43,600
+ع كمان دالةبيدنا command دلّة فالـ G لحالة مش
+
+559
+00:43:43,600 --> 00:43:47,800
+مكافية للتركيز في عندنا command دلّة اه فعندنا
+
+560
+00:43:47,800 --> 00:43:50,280
+command .. في عندنا command دلّة X is infinite في
+
+561
+00:43:50,280 --> 00:43:55,060
+command دلّة فالعملية هنا ماضبطتش فالان X is
+
+562
+00:43:55,060 --> 00:44:00,500
+infinite implies there exist function الجي والاف
+
+563
+00:44:00,500 --> 00:44:08,800
+موجودين خلينا نسمي اسم جديد H من X ل X such that H
+
+564
+00:44:08,800 --> 00:44:15,620
+is one to one andH of X برابر من X فالعملية الآن
+
+565
+00:44:15,620 --> 00:44:20,920
+مختلفة شوية فحستخدم الـH الـH فالآن G inverse
+
+566
+00:44:20,920 --> 00:44:25,820
+بتودينا من Y لX اللي بيظغر مين الـH أسف مش الـF
+
+567
+00:44:25,820 --> 00:44:28,280
+اللي أفضل دي المطلوبة صح هي بتظغر بس هذا مطلوب مش
+
+568
+00:44:28,280 --> 00:44:32,420
+معطف لكن H هي اللي بتظغر بتاخدنا من وين لوين من X
+
+569
+00:44:32,420 --> 00:44:37,820
+لنفسها من X لنفسها بتدينا H او بعدين الـG بترجعنا
+
+570
+00:44:37,820 --> 00:44:42,400
+للـY فبكون بدينا من Y ورجعنا للـY فحنعرفالان اه
+
+571
+00:44:42,400 --> 00:44:45,900
+فهنا يمكن هذه الخطوة هتكون قبل فهذه الخطوة هتيجي
+
+572
+00:44:45,900 --> 00:44:57,480
+بعد فهقوله هنا let F من Y ل Y be given by F of X
+
+573
+00:44:57,480 --> 00:45:03,040
+تساوي كيف عرفناها؟ ابدينا بإيش؟ G inverse أول شيء
+
+574
+00:45:03,040 --> 00:45:08,780
+G inverse بعدين إيش ركبنا؟ H بعدين ركبنا ال G of X
+
+575
+00:45:10,070 --> 00:45:13,550
+خلّينا .. طبعا ممكن احنا و احنا بنحاول .. بن .. بن
+
+576
+00:45:13,550 --> 00:45:16,710
+.. بن .. بنخربش، بنعمل مسودة، بنعمل هامش، بنحاول،
+
+577
+00:45:16,710 --> 00:45:21,410
+نشوف شغلنا صح ولا مش صح الـG inverse ده لأن أيد
+
+578
+00:45:21,410 --> 00:45:28,410
+الرسمها دي مرة تانية، بطريقة مختلفة بدنا دالة من
+
+579
+00:45:28,410 --> 00:45:32,450
+واي لوين؟ من واي لواي، نشوف الصورة، بنتعلم هذه
+
+580
+00:45:32,450 --> 00:45:38,330
+المهارة، فانا بدأت من وايG inverse وين بتوديها؟ ال
+
+581
+00:45:38,330 --> 00:45:41,630
+X ال G دالة من X ل Y خدت ال inverse تبعها طب ال
+
+582
+00:45:41,630 --> 00:45:46,470
+inverse exist نعم لأنه الدالة one to one هلجيت من
+
+583
+00:45:46,470 --> 00:45:51,630
+X طبقت ال H وين وددتها؟ على ال X و طب ليش دخلت ال
+
+584
+00:45:51,630 --> 00:45:55,830
+H؟ ماوددتكاش مكان جديد خلتك في نفس المحل بس H
+
+585
+00:45:55,830 --> 00:45:59,410
+بتلعب دور ال H تصغير بتصغر الصورة هي مهمة جدا لإن
+
+586
+00:45:59,410 --> 00:46:03,470
+هيهاهي اللي بتزغر الصورة بعد هي ايش عملت طبقت الجي
+
+587
+00:46:03,470 --> 00:46:08,510
+كمان مرة وين رجعتني الجي لل one فالصورة صحيحة
+
+588
+00:46:08,510 --> 00:46:12,970
+فالصورة صحيحة تم أثبت ان هذه ال F فعلا one to one
+
+589
+00:46:12,970 --> 00:46:16,450
+و انها ايش و بتدينا الصورة not onto يعني الصورة
+
+590
+00:46:16,450 --> 00:46:22,750
+أصغر فبنثبت ان ال F one to one و انها بيش بتزغر
+
+591
+00:46:22,750 --> 00:46:30,150
+الصورة فال Fis one to one هدا واحد هنثبته ويمكن
+
+592
+00:46:30,150 --> 00:46:36,910
+هدا سهل أعمله بسرعة خل الجزء التاني هو الأصعب
+
+593
+00:46:36,910 --> 00:46:41,550
+فغالبنا نعمل هذا الجزء السهل فناخد عنصرين let X1 و
+
+594
+00:46:41,550 --> 00:46:52,190
+X2 في ال Y such that F of X1 تساوي F of X2 بداية
+
+595
+00:46:52,190 --> 00:46:56,370
+ال one to one كالعادةما يمكننا فعله باستخدام تعريف
+
+596
+00:46:56,370 --> 00:47:04,770
+الدالة كالعادة فهذا بيقول لي G of H of G of X1
+
+597
+00:47:04,770 --> 00:47:13,250
+تساوي G of H of G inverse of X2 مشاكل اللي هو
+
+598
+00:47:13,250 --> 00:47:19,230
+تعريف الدالة Circle تلاتة مع بعضالان بدي اوصل ان
+
+599
+00:47:19,230 --> 00:47:24,110
+X1 تساوي X2 هذي ال X1 في عليها اغلفة متعددة تلت
+
+600
+00:47:24,110 --> 00:47:27,810
+اغلفة بدي احاول انتزعهم واحدة واحدة لحد ما اوصل ان
+
+601
+00:47:27,810 --> 00:47:32,430
+X1 تساوي X2 بس بنتزعهم بطريقة رياضية صحية كيف
+
+602
+00:47:32,430 --> 00:47:35,190
+ننتزع ال G؟
+
+603
+00:47:36,700 --> 00:47:43,240
+فيه أسهل .. فيه أسهل أن قيمتين الـG and قيمة معينة
+
+604
+00:47:43,240 --> 00:47:48,140
+Y1 تساوي الـG and Y2 والـG مالها one to one and on
+
+605
+00:47:48,140 --> 00:47:50,880
+two فبتدينا اللي جوا لازم يساوي اللي جوا .. اه
+
+606
+00:47:50,880 --> 00:47:57,500
+فهنا على طول يؤدي Hof G inverse of X تساوي H of G
+
+607
+00:47:57,500 --> 00:48:02,240
+inverse of X2 ليش؟ لأن الـ F أو S في الـ G is one
+
+608
+00:48:02,240 --> 00:48:06,680
+to one هي one to one and unto نفس الفكرة ما الـ H
+
+609
+00:48:06,680 --> 00:48:12,720
+برضه one to one فهذا يؤدي إن G inverse of X تساوي
+
+610
+00:48:12,720 --> 00:48:16,950
+G inverse of X2 لأن الـ H is one to oneطب وال G
+
+611
+00:48:16,950 --> 00:48:20,590
+inverse برضه one to one نعم لأنه بيجيكشن و هذا
+
+612
+00:48:20,590 --> 00:48:25,590
+يؤدي ان X1 تساوي X2 لأنه G inverse is one to one
+
+613
+00:48:25,590 --> 00:48:32,350
+وهو المطلوب تمت جزئية خليها للمرة الجاية لان فيها
+
+614
+00:48:32,350 --> 00:48:34,990
+صعوبة خلينا نأخر
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/QuyDnx6y5Ko_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/QuyDnx6y5Ko_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..29de15e1b17c7eb6c2244217bdda755afeb0de84
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/QuyDnx6y5Ko_postprocess.srt
@@ -0,0 +1,2740 @@
+1
+00:00:20,270 --> 00:00:24,950
+بسم الله الرحمن الرحيم هنواصل مع دراسة العلاقات ال
+
+2
+00:00:24,950 --> 00:00:28,750
+relations وإن شاء الله في هذا section هندخل من
+
+3
+00:00:28,750 --> 00:00:33,150
+زاوية جديدة ونستكمل طبعا استكمال طبعا عنوان
+
+4
+00:00:33,150 --> 00:00:37,300
+partitions التجزيئاتمن اللي هو كلمة part
+
+5
+00:00:37,300 --> 00:00:41,520
+partitions اللي هي تجزيء part جزء partition تجزيء
+
+6
+00:00:41,520 --> 00:00:44,140
+عملية التجزيء and equivalence relations طبعا
+
+7
+00:00:44,140 --> 00:00:45,940
+المصطلح اللي هو equivalence relation مر علينا
+
+8
+00:00:45,940 --> 00:00:49,040
+العلاقات التكافؤ فبهذا ال section ان شاء الله
+
+9
+00:00:49,040 --> 00:00:52,780
+هنستكمل دراسة ال equivalence relations مع المفهوم
+
+10
+00:00:52,780 --> 00:00:58,060
+الجديد وهو التجزيء فطبعا احنا هنبدأ بالتعريف ما هو
+
+11
+00:00:58,060 --> 00:01:01,260
+ال partition المصطلح الجديد بعدين ايش علاقة هذا
+
+12
+00:01:01,260 --> 00:01:04,300
+المصطلح الجديد مع ال equivalence relations كما هي
+
+13
+00:01:04,300 --> 00:01:09,960
+نص العنوانفنبدأ بمصطلح ال partitions ما هو عملية
+
+14
+00:01:09,960 --> 00:01:15,180
+طبعا مصطلح اللغوي تجزيق اه طبعا اي اية تجزيق بنشوف
+
+15
+00:01:15,180 --> 00:01:18,220
+المعنى الاصلاحي ما هو المقصود بكلمة partition
+
+16
+00:01:18,220 --> 00:01:21,320
+بكلمة او مصطلح partition مفهوم بيقول انا في عندي
+
+17
+00:01:21,320 --> 00:01:27,850
+مجموعة ما Xليست فارغة اول شي بقولي let x be a non
+
+18
+00:01:27,850 --> 00:01:30,690
+-empty cell زي ما اتعودنا بنشوف المقدمة و بنحاول
+
+19
+00:01:30,690 --> 00:01:34,430
+نفهم الان بقولي a partition هاي مفهوم اللي بندور
+
+20
+00:01:34,430 --> 00:01:39,170
+عليه بدنا نفهمه ايش الرمز تبعه حرف ال B بيد الشكل
+
+21
+00:01:39,170 --> 00:01:44,830
+ايش هوبقول عبارة عن مجموعة من المجموعات الجزئية
+
+22
+00:01:44,830 --> 00:01:48,990
+غير الفارغة من ال X أه فإيش اللي بده أعمله بالظبط
+
+23
+00:01:48,990 --> 00:01:53,190
+هي عند ال X بده أجزئها نجي نجي للمصطلح بالعامية هي
+
+24
+00:01:53,190 --> 00:01:58,310
+في عند X بده أجزئها بطريقة ما بطريقة ما هي تجزئ
+
+25
+00:01:58,310 --> 00:02:04,250
+تجزئ أي تجزئ بده أجزئها بصورة ما فبقول لل Bتتكون
+
+26
+00:02:04,250 --> 00:02:10,110
+من مجموعات فهي مجموعة مجموعات اي مجموعات لأ بدهم
+
+27
+00:02:10,110 --> 00:02:15,850
+يكونوا subsets من ال X هذا شرط الأول و إيش كمان؟
+
+28
+00:02:15,850 --> 00:02:20,650
+non-empty non-empty subsets فبدي هذه كل A تنتمي لل
+
+29
+00:02:20,650 --> 00:02:27,530
+B تكون إيش؟ غير فارغة A غير فارغة فدي أول نقطة
+
+30
+00:02:27,530 --> 00:02:31,670
+كمان؟ خلص التعريف؟ لأ such that لسه فيه كمان شروط
+
+31
+00:02:33,950 --> 00:02:37,370
+الشرط الوالتاني رغم انه رقم one لان الشرط الاول
+
+32
+00:02:37,370 --> 00:02:40,810
+جاي في الصياغ من غير ترقيد وهذه بتعلمنا ايش؟ دقة
+
+33
+00:02:40,810 --> 00:02:44,310
+القراءة لما نقرع نظرية نقرع تعريف اي شيء لازم نكون
+
+34
+00:02:44,310 --> 00:02:48,110
+دقيقين في القراءة بقول إذا كانت ال a و ال b قلنا
+
+35
+00:02:48,110 --> 00:02:53,000
+هي عناصر ال bمجموعات، يعني لو أخدت مجموعتين غير
+
+36
+00:02:53,000 --> 00:02:56,700
+متساويتين، يعني مجموعتين مختلفتين، إيش لازم
+
+37
+00:02:56,700 --> 00:03:01,120
+يكونوا؟ لازم يكونوا منفصلتين تماماً، إذا كانوا غير
+
+38
+00:03:01,120 --> 00:03:05,300
+متساويتين، مافيهم عنصر مشترك، التقاط يسوي فيه،
+
+39
+00:03:05,300 --> 00:03:10,600
+بمعنى آخر، كل جزئين أو كل مجموعتين في التجزيه، يا
+
+40
+00:03:10,600 --> 00:03:14,540
+متطابقتين، يعني كل عناصرهم مشتركة، يا ولا عنصر
+
+41
+00:03:14,540 --> 00:03:18,220
+مشترك، يا لكل مشترك بصوره متساويتين، يا ولا عنصر
+
+42
+00:03:18,220 --> 00:03:20,790
+مشترك، هيك بقولإذا كانوا غير متساويتين مايوجد
+
+43
+00:03:20,790 --> 00:03:23,810
+حناثة مشتركة متساويتين كلها حناثة مشتركة مايوجد
+
+44
+00:03:23,810 --> 00:03:27,430
+أشياء بدناية هذا إيش فبدي أنا كل جزئين يكونوا
+
+45
+00:03:27,430 --> 00:03:30,610
+مختلفين عن بعض الشرط التالت اللي هو رقم اتنين
+
+46
+00:03:30,610 --> 00:03:35,690
+اتهات كل الأجزاء يساوي ال X يعني هدول الأجزاء
+
+47
+00:03:35,690 --> 00:03:39,870
+عملية التجزئة إشمالها بتغطي كل ال X بديش يتموا في
+
+48
+00:03:39,870 --> 00:03:44,990
+ال X جزء مش مجزة مش مقطع مش مغطى بالتجزية فدولة
+
+49
+00:03:44,990 --> 00:03:49,660
+تلت شروط فدولة تلت شروطخلّينا نجيب مثال من الواقع
+
+50
+00:03:49,660 --> 00:03:54,520
+يكون قريب للعملية اه يمكن طالبات العلوم بيعرفوا ان
+
+51
+00:03:54,520 --> 00:03:56,860
+احنا عندنا في الجامعة طلاب علوم سنة أولى بيدخلوا
+
+52
+00:03:56,860 --> 00:04:00,720
+علوم عام صحيح و بعد نهاية سنة أولى يشف بيخصصوها
+
+53
+00:04:00,720 --> 00:04:04,780
+طيب احنا فندرد مثل ان عندنا ال X من ال X هي كل
+
+54
+00:04:04,780 --> 00:04:08,300
+طلاب العلوم سنة أولىطلاب العلوم سنقول اذا بدنا
+
+55
+00:04:08,300 --> 00:04:11,260
+نجزّقهم يعني بدنا نخصصهم، بدنا نجزّقهم، إيش
+
+56
+00:04:11,260 --> 00:04:15,600
+نجزّقهم؟ قسم كيميا، قسم أحياء، قسم رياضيات و هكذا،
+
+57
+00:04:15,600 --> 00:04:19,100
+فده عملية تقسيم، تجزيق، عملية تقسيم، إيش الشرائح
+
+58
+00:04:19,100 --> 00:04:23,720
+الشروط تبعتنا؟ أول شيء بدي أخلي ولا قسم فاضيبدي
+
+59
+00:04:23,720 --> 00:04:27,100
+انا اوزّق الطلاب بحيث انه لا الكيما يكون فاضي ولا
+
+60
+00:04:27,100 --> 00:04:29,320
+الأحياء فاضية ولا الرياضية فاضية يعني بدي كل قسم
+
+61
+00:04:29,320 --> 00:04:33,320
+يحتوي على طالب على الأقل هذا الشرط الأول non-empty
+
+62
+00:04:33,320 --> 00:04:39,160
+is a subsets فبدنا كل قسم كل جزء غير فاضينقطة
+
+63
+00:04:39,160 --> 00:04:42,920
+تانية، بدنا يا القسمين متطابقين، يا الرياضيات هو
+
+64
+00:04:42,920 --> 00:04:46,100
+نفسه، وإذا كانوا مش متطابقتين، مافيش فيهم أنصر
+
+65
+00:04:46,100 --> 00:04:50,100
+مشترك، بمعنى آخر ممنوع طالب يتحصص ياش تحصصين مع
+
+66
+00:04:50,100 --> 00:04:52,660
+بعض، ماينفعش أدرس رياضيات وفيزيا مع بعض، يا
+
+67
+00:04:52,660 --> 00:04:55,580
+رياضيات يا فيزيا، هيك معناته، ففي انفصال، مافيش
+
+68
+00:04:55,580 --> 00:04:59,730
+أنصر مشترك بين الأقسام المختلفةأه فقسم رياضيات
+
+69
+00:04:59,730 --> 00:05:02,190
+مختلفة عن الفيزيا إذا مافيش طالب مشترك بينهم مافيش
+
+70
+00:05:02,190 --> 00:05:05,070
+طالب يدوسوا التاني مع بعض الشرط التاني الشرط
+
+71
+00:05:05,070 --> 00:05:10,490
+التالت بدي بنهاية سنة أولى كل الطلاب يتخصصوا ممنوع
+
+72
+00:05:10,490 --> 00:05:14,530
+يتموا طالب عام يعني التقسيم هذا الأقسام بدي أغطي
+
+73
+00:05:14,530 --> 00:05:17,270
+كل طلاب سنة أولى اللي هم مايش المجموعة تبعتي اللي
+
+74
+00:05:17,270 --> 00:05:20,440
+باشتغل عليهافواضحة التلت شروط؟ بدناش ولا قسم يكون
+
+75
+00:05:20,440 --> 00:05:23,580
+فاضي، بدناش طالب يكون في قسمين مع بعض في نفس
+
+76
+00:05:23,580 --> 00:05:27,160
+الوقت، بدنا كل الطلاب يتقسموا، يتوزعوا، بدنا كل
+
+77
+00:05:27,160 --> 00:05:30,620
+الطلاب يتخصصوا بمعنى آخر، فهي التلت شروط، ففي تلت
+
+78
+00:05:30,620 --> 00:05:35,200
+شروط، فهذا المثال أرجو أن يوضح الفكرةفطبعاً
+
+79
+00:05:35,200 --> 00:05:38,260
+بيقوللي عملية التقسيم زي ما احنا شرحنا هي عملية
+
+80
+00:05:38,260 --> 00:05:44,240
+تقطيع او تيزيء كله للمجموعة بإيش اشمالهم non-empty
+
+81
+00:05:44,240 --> 00:05:48,760
+disjoint pieces إلى قطع إلى أقسام اشمالها غير
+
+82
+00:05:48,760 --> 00:05:52,980
+فارغة ومنفصلة عن بعض مافيش بينها أناصر مشتركة
+
+83
+00:05:52,980 --> 00:05:59,440
+باختصار شديد نشوف بعض الأمثلةونشوف كيف ممكن نثبت
+
+84
+00:05:59,440 --> 00:06:04,140
+إنه مجموعة من المجموعات الجزئية هي partition ولا
+
+85
+00:06:04,140 --> 00:06:09,020
+لأ ونشوف كيف بنتعامل كعادتنا هنبدأ بمثال بسيط
+
+86
+00:06:09,020 --> 00:06:14,130
+مجموعة صغيرة تتكون من خمس عناصرجسمناها إلى تلت
+
+87
+00:06:14,130 --> 00:06:18,570
+أقسام بقول هل هذا التقصيم ينطبق عليها مصطلح ال
+
+88
+00:06:18,570 --> 00:06:21,490
+partition اللي عرفناه؟ أه لأنه مش أي تجزيق بدنا
+
+89
+00:06:21,490 --> 00:06:25,190
+تجزيق بطريقة ما طريقة معينة فيها شروط زي عملية
+
+90
+00:06:25,190 --> 00:06:27,930
+التقصيص ممكن نظام الجامعة يقول هنا هاي الشروط
+
+91
+00:06:27,930 --> 00:06:31,550
+تبعتي في التقصيم ففي شروط عشان يكون تجزيق بالمعنى
+
+92
+00:06:31,550 --> 00:06:35,310
+الاصطلاحي فجسمهم إلى تلت أيزاق خليني أعمل صورة
+
+93
+00:06:35,310 --> 00:06:41,760
+قريبة ونشوف هيعنى ال Xجسمها لتلت أيزاق واحد تنين
+
+94
+00:06:41,760 --> 00:06:46,060
+تلاتة في الجزء الأول حط الواحد والخمسة في الجزء
+
+95
+00:06:46,060 --> 00:06:50,080
+التاني حط التنين والتلاتة وفي الجزء الأخير حط
+
+96
+00:06:50,080 --> 00:06:52,720
+الأربع على حالة فإيش رايك وحده partition ولا مش
+
+97
+00:06:52,720 --> 00:06:56,660
+partition partition لأنه تلت أيزاق ولا واحد فيهم
+
+98
+00:06:56,660 --> 00:07:01,480
+فاضي مافيش تقاطع بين أي جزئين مختلفين وقواش وقته
+
+99
+00:07:01,480 --> 00:07:04,500
+كل العناصر كل الخمسة كل واحد موجود الجزء اللي
+
+100
+00:07:04,500 --> 00:07:08,850
+بنتبعه فالواحدفي الجزء الأول اتنين في الجزء التاني
+
+101
+00:07:08,850 --> 00:07:12,370
+التلاتة في الجزء التاني الأربع في الجزء التالت
+
+102
+00:07:12,370 --> 00:07:16,070
+وخمسة في الجزء الأول فكله توزع فكله توزع خلينا
+
+103
+00:07:16,070 --> 00:07:19,810
+نشوف طبعا هذا شف هويه كيف بدنا نكتب و نجاوب السؤال
+
+104
+00:07:19,810 --> 00:07:25,610
+فهذا مثلنا الأول فنبدأ
+
+105
+00:07:25,610 --> 00:07:30,660
+ال solutionطبعا طبقا للتعريف بقولنا فيه تلت شروط
+
+106
+00:07:30,660 --> 00:07:34,460
+الشرط الأول مش مرقم وانا يمكن حاطيته طواش بالخط
+
+107
+00:07:34,460 --> 00:07:38,980
+الأحمر حاولت اوضحه non-empty subsets طيب كيف بدنا
+
+108
+00:07:38,980 --> 00:07:42,240
+نبدأ فيه هذا الشرط رغم مش مرقم بدنا نبدأ فيه طبعا
+
+109
+00:07:42,240 --> 00:07:45,180
+ما زال هو مرقم واحد واتنين خلينا نبدأ بشرط هذا
+
+110
+00:07:45,180 --> 00:07:49,320
+مسبق ان رقمه صفر فأول شرط بدي أثبته ايه كيف بدنا
+
+111
+00:07:49,320 --> 00:07:55,730
+نصيغه بقولي الأيزاء non-empty فانا بديfor all a أي
+
+112
+00:07:55,730 --> 00:08:00,530
+جزء في ال partition ايش يكون غير فارق ممكن اصيغة
+
+113
+00:08:00,530 --> 00:08:05,120
+بهذا الشكلفده الشرق صفر مش موجود في التعريف مش
+
+114
+00:08:05,120 --> 00:08:07,980
+موجود في التعريف المرقم لكنه موجود في الصياغ في
+
+115
+00:08:07,980 --> 00:08:11,720
+الجملة الموجودة بيقوللي a partition is a set of
+
+116
+00:08:11,720 --> 00:08:15,380
+non-empty subsets اه فدي بعلمنا القراعة دقيقة لكل
+
+117
+00:08:15,380 --> 00:08:19,040
+كلمة اللي همعنى فأول شي بدي جميع الأجزاء هي
+
+118
+00:08:19,040 --> 00:08:22,040
+الأجزاء مين الأجزاء؟ قولنا هيهم ايه؟ كل جزء اي
+
+119
+00:08:22,040 --> 00:08:26,500
+common غير فارق تقوى كتبنا تقوى كتبنا اه تمام نشوف
+
+120
+00:08:26,500 --> 00:08:30,060
+مين الأجزاء؟ تلاتة في واحد فيهم فارق؟ لأ فنكتبله
+
+121
+00:08:30,450 --> 00:08:35,210
+الجزء الأول واحد خمسة لا يساوي five الجزء التاني
+
+122
+00:08:35,210 --> 00:08:40,190
+اتنين تلاتة لا يساوي five الجزء التالت أربعة لا
+
+123
+00:08:40,190 --> 00:08:47,490
+يساوي five ففعلا الشرط الأول تحقق الشرط
+
+124
+00:08:47,490 --> 00:08:54,470
+التاني هو جملة شرطية بقول A وB في ال partition and
+
+125
+00:08:55,630 --> 00:09:02,870
+A لا تساوي B implies A تقاطع الـ B يساوي FI بدنا
+
+126
+00:09:02,870 --> 00:09:06,010
+نفحص هذا الشرط، طبعا لو كان فيه برهان عام، بدي
+
+127
+00:09:06,010 --> 00:09:10,260
+أفترض إن الشرط صحيح ويقبل الشرطلما يكون المثال عدد
+
+128
+00:09:10,260 --> 00:09:15,540
+قليل بنفحص كل تنتين مع بعض بيقول لي خد كل جزئين اه
+
+129
+00:09:15,540 --> 00:09:18,920
+شوف انا أول شي كنت بعمل بشغل على ايش؟ على
+
+130
+00:09:18,920 --> 00:09:22,920
+المجموعات الجزئية الي يمين عناصر ال partition اللي
+
+131
+00:09:22,920 --> 00:09:27,020
+هي مجموعات فده ايه ايه؟ فبناخد كل جزئين مختلفين
+
+132
+00:09:27,020 --> 00:09:30,160
+تقاطعهم يساوي five فالجزء الأول والتاني تقاطعهم
+
+133
+00:09:30,160 --> 00:09:35,860
+five ولا مش five؟ five فاكتب له واحد خمسة تقاطع
+
+134
+00:09:36,450 --> 00:09:42,430
+إتنين تلاتة يساوي five صح طيب مين كمان أفحص واحد
+
+135
+00:09:42,430 --> 00:09:46,490
+خمسة لازم أفحصها مع الأربعة لأن بقول كل جزئين
+
+136
+00:09:46,490 --> 00:09:50,230
+مختلفين تقطوحهم يساوي five طيب خلصنا الواحد و
+
+137
+00:09:50,230 --> 00:09:53,810
+الخمسة و افحصناها مع التنين تلاتة و مع الأربعة
+
+138
+00:09:53,810 --> 00:09:59,150
+الآن اتنين تلاتة نفحصها مع مين مع الأربعة أفحصها
+
+139
+00:09:59,150 --> 00:10:02,170
+مع الأول لأ ليش لأن التقاطه عبدالي لأن التقاطه
+
+140
+00:10:02,170 --> 00:10:07,910
+عبدالي فنفحص الآنإتنين تلاتة تقاطع الأربعة بيساوي
+
+141
+00:10:07,910 --> 00:10:11,430
+فيا ولا بيساويش بيساوي إذا فعلا وزي ما هي الصورة
+
+142
+00:10:11,430 --> 00:10:15,410
+واضحة بس أنا بكتب كل جزئين منفصلين مافيش فينهم
+
+143
+00:10:15,410 --> 00:10:18,590
+عناصر مشتركة this joins زي ما سمناه فده الشرط
+
+144
+00:10:18,590 --> 00:10:21,970
+التاني الشرط التالت والأخير اللي هو رقم اتنين
+
+145
+00:10:21,970 --> 00:10:25,990
+الاتحاد بالدين المجموعة الأصلية اتحاد الأجزاء
+
+146
+00:10:25,990 --> 00:10:31,350
+بالدين المجموعة الأصليةاتنين اتحاد ال a على ال
+
+147
+00:10:31,350 --> 00:10:35,050
+partition هذا الرمز اللي تعلمناه في section 2-6
+
+148
+00:10:35,050 --> 00:10:39,590
+اللي هو على الفهم اللي سمناه بيساو اكس نفحص اه كان
+
+149
+00:10:39,590 --> 00:10:44,830
+جزء عندي تلاتة واحد خمسة يعني اتحاد مين اتنين
+
+150
+00:10:44,830 --> 00:10:51,950
+تلاتة اتحاد الأربع بيساو اكس ولا بيساويشأربعة خمسة
+
+151
+00:10:51,950 --> 00:10:56,270
+و يساوي X ففعلا صحيح فإذا التلات شروط اتحققت إذا
+
+152
+00:10:56,270 --> 00:11:01,850
+فعلا هذا يعتبر partition Thus B is a partition
+
+153
+00:11:01,850 --> 00:11:09,400
+طبعا of X لل X المعطيةفهذا الشاهد الأساسي من
+
+154
+00:11:09,400 --> 00:11:13,560
+المثال بنشوف ما هي شروط ال partition طبعا اللي هو
+
+155
+00:11:13,560 --> 00:11:16,900
+التحقق من الشروط كان سهل لكن هام نقطة، هذا مثال
+
+156
+00:11:16,900 --> 00:11:20,820
+بسيط بدنا نمر على الشروط و نكتبهم بشكل صريح و كيف
+
+157
+00:11:20,820 --> 00:11:28,040
+نتعامل معهم أي سؤال؟ فضل بمفهش
+
+158
+00:11:28,040 --> 00:11:34,660
+فألا في ولا عنصر في؟ يعني بدك ال في ولا مجموعة ال
+
+159
+00:11:34,660 --> 00:11:42,050
+في؟و مختلف زي ما قلنا صينية فاضية صينية فيها كباية
+
+160
+00:11:42,050 --> 00:11:45,270
+فاضية تعتبر صينية فاضية ولا مليانة مليانة واضحة اه
+
+161
+00:11:45,270 --> 00:11:49,490
+فهذه فاي صينية فاضية طب صينية لو حطنا فيها حاجة
+
+162
+00:11:49,490 --> 00:11:53,550
+فاضية فتصير ايش فيها حاجة فانتبهوا اه هذه مختلفة
+
+163
+00:11:53,550 --> 00:11:56,330
+طبعا هو ال five مش هنصر في ال X فليش هحطه اجزه
+
+164
+00:11:56,330 --> 00:12:01,250
+فانا مهتم ان ايش اوزع عناصر ال X زي ما قلنا مهمين
+
+165
+00:12:01,250 --> 00:12:06,780
+ان نخصص طلاب رياضياتواضحة؟ اه فاحنا مهتمين بال X
+
+166
+00:12:06,780 --> 00:12:13,180
+تمام فإذا هذه فعلا بارتش خلينا نشوف مثال رقم 2 في
+
+167
+00:12:13,180 --> 00:12:17,620
+المثال هو عبارة عن مثال توضيحي مافيش فيه مطلوب بس
+
+168
+00:12:17,620 --> 00:12:22,380
+بدنا نشرحه و نفهمه مع بعضفي هذا المثال بده ياخد
+
+169
+00:12:22,380 --> 00:12:26,380
+الأعداد الصحيحة اللي هي عند مجموعتنا اللي بدنا
+
+170
+00:12:26,380 --> 00:12:31,980
+نقاش انجزقها نقسمها هي ال Z و بده يقسمها قسمين و
+
+171
+00:12:31,980 --> 00:12:35,780
+بده يقسمها قسمين ينطبق عليه شروط مين ال partition
+
+172
+00:12:35,780 --> 00:12:40,520
+شروط التاسعة مين هم القسمين قال ال partition عندك
+
+173
+00:12:40,520 --> 00:12:45,900
+هو مجموعتين E و D مين هم ال E و ال D عرفلي إياهم
+
+174
+00:12:45,900 --> 00:12:53,000
+قال ال E كل عدد صحيح زوجيو ال D كل عدد صحيح فردي،
+
+175
+00:12:53,000 --> 00:12:56,520
+بقول هذه التقسيمة ينطبق عليها شروط ال partition
+
+176
+00:12:56,520 --> 00:13:00,760
+اللي عرفناه، ليش؟ نشوف هل الواحدة فيهم فاضية؟
+
+177
+00:13:00,760 --> 00:13:04,860
+طبعاً لأ، لأن ال E تحتوي على التنين، إذا مش فاضية،
+
+178
+00:13:04,860 --> 00:13:07,660
+ال D تحتوي على الواحد على الأقل، إذا مش فاضية، هي
+
+179
+00:13:07,660 --> 00:13:12,870
+الشرط الأولالشرط التاني، هل الاتنين المختلفين في
+
+180
+00:13:12,870 --> 00:13:16,810
+بينهم عناصر مشتركة؟ بمعنى آخر، بنفعل عدد صحيح
+
+181
+00:13:16,810 --> 00:13:20,070
+ونزوج وفردي بنفس الوقت؟ لأ، إذا الشرط التاني صحيح،
+
+182
+00:13:20,070 --> 00:13:24,890
+هدول مجموعتين مختلفتين ومافيهم ولا عنصر مشتركالشرط
+
+183
+00:13:24,890 --> 00:13:30,150
+التالت هل اتحادهم بيغطي كل الاعداد بمعنى اخر هل كل
+
+184
+00:13:30,150 --> 00:13:33,870
+عدد صحيح بقدر اصنفه زوجي او فردي صحيح طب ال zero
+
+185
+00:13:33,870 --> 00:13:37,330
+ايش؟ زوجي اه متفقين لإن ال zero زوجي يقبل قسم على
+
+186
+00:13:37,330 --> 00:13:40,430
+اتنين و ال zero زوجي ففعلا هذا شروط ال partition
+
+187
+00:13:40,430 --> 00:13:43,850
+فانا عندى اي عدد صحيح بصنفه يا زوجي يا فردي فكل
+
+188
+00:13:43,850 --> 00:13:47,070
+الشروط اتحققتفهذا يعتبر partition تبقى للمصطلح
+
+189
+00:13:47,070 --> 00:13:50,390
+اللي عملناه لأن فيه عندي جزئين ولا واحد فيهم فاضي
+
+190
+00:13:50,390 --> 00:13:53,930
+مش فيه بينهم ولا عنصر مشترك وبيغطوا كل المجموعة
+
+191
+00:13:53,930 --> 00:14:04,370
+الأصلية الـ Z نشوف كمان مثال نشوف كمان مثال الآن
+
+192
+00:14:04,370 --> 00:14:10,350
+هشتغل برضه على الـ Z بس بدي أجسمها تجسيم جديد
+
+193
+00:14:11,500 --> 00:14:16,260
+بتجسمها تقسيم جديد بدل ما ناخد سنة أولى في العلوم
+
+194
+00:14:16,260 --> 00:14:19,420
+ناخد سنة أولى في الهندسة و هنجسم هندسة كهربا هندسة
+
+195
+00:14:19,420 --> 00:14:23,240
+حصوب هندسة مدنية هندسة معمارة بنجسم تقسيم جديد على
+
+196
+00:14:23,240 --> 00:14:27,200
+نفس المجموع تقسيم جديد تلت أقصام بتجسم الـ Z أه
+
+197
+00:14:27,200 --> 00:14:30,300
+بتجسمها تلت أقصام برضه بيقول partition نشوف مين هي
+
+198
+00:14:30,300 --> 00:14:38,520
+الأقصام الأقصام كانت تالي Z0 وتساويكل عدد صحيح
+
+199
+00:14:38,520 --> 00:14:42,560
+اشمله بحيث X ناقص J بدا ياخد J بيساوي 0 في الأول
+
+200
+00:14:42,560 --> 00:14:48,380
+بداك تبقى ناش Z0 Z1 Z2 هاي الأيزاء متفقين؟ طب إيش
+
+201
+00:14:48,380 --> 00:14:52,660
+عرّف لل Z0؟ جاللي عرّف لل Z sub J بشكل عام إذا ال
+
+202
+00:14:52,660 --> 00:14:56,840
+J بتساوي 0 حطي بدل ال J 0 إذا ال J بتساوي 1 حطي
+
+203
+00:14:56,840 --> 00:15:00,260
+بدل ال J 1 و إذا Z2 و إذا Z2 اتنين و هكذا Zero
+
+204
+00:15:00,260 --> 00:15:04,200
+واحد اتنين تمام، نبدأ بنحسب إذا X ناقص Zero إيش
+
+205
+00:15:04,200 --> 00:15:12,380
+بتساوي؟ تلاتة Kfor some K تنتمي للـ Z هذا المجموع
+
+206
+00:15:12,380 --> 00:15:15,300
+الأول هذا القسم الأول من العدد الصحيح بده يقسم
+
+207
+00:15:15,300 --> 00:15:20,740
+نحاول نفهم إيش بتكون هذا القسم بيقول لكل عدد صحيح
+
+208
+00:15:20,740 --> 00:15:25,640
+X ماقص Zero يعني X إيش ماله؟ تلاتة K إيش يعني؟
+
+209
+00:15:25,640 --> 00:15:29,160
+يعني يقبل قسمها تلاتة مين بيقبل قسمها تلاتة؟
+
+210
+00:15:30,670 --> 00:15:36,250
+والتلاتة والناقص تلاتة والستة والناقص ستة والتسعة
+
+211
+00:15:36,250 --> 00:15:41,630
+والناقص تسعة فإذا القسم الأول بتكون من هذه الإعداد
+
+212
+00:15:41,630 --> 00:15:45,890
+الصفر ومضاعفات التلاتة ومضاعفات التلاتة هي عرفنا
+
+213
+00:15:45,890 --> 00:15:50,750
+القسم الأول نشوف القسم التانيزد واحد تساوي تبقى
+
+214
+00:15:50,750 --> 00:15:56,250
+للتعريف كل عدد صحيح بحيث there exist k تنتمي للزد
+
+215
+00:15:56,250 --> 00:15:58,410
+for some بدأ كتابة بدا الشكل مش جولة ممكن كتابة
+
+216
+00:15:58,410 --> 00:16:03,050
+جابل او بعد بحيث ان x ناقص واحد لان جيها بتساوي
+
+217
+00:16:03,050 --> 00:16:08,460
+واحد تساوي تلاتة kتماما بدي اعيد كتابتي عشان
+
+218
+00:16:08,460 --> 00:16:13,700
+اوضحلكوا الصورة X تنتمي لل Z بحيث there exist K
+
+219
+00:16:13,700 --> 00:16:19,100
+تنتمي لل Z اختصارا X تساوي مين تلاتة K زائد واحد
+
+220
+00:16:19,100 --> 00:16:25,140
+اه what you sawإيش علاقتها في الأولى؟ نفسها تلاتة
+
+221
+00:16:25,140 --> 00:16:28,360
+كيبات زائد واحد يعني عبارة عن واحد ..شوف الواحد
+
+222
+00:16:28,360 --> 00:16:31,400
+كيب بتستفيد من المعلومات السابقة زائد أو ناقص
+
+223
+00:16:31,400 --> 00:16:35,840
+تلاتة زائد واحد زائد أو ناقص ستة زائد واحد وها كذا
+
+224
+00:16:37,270 --> 00:16:39,910
+وحدة واحدة بحياتي الصوت بس بشرحها لكوا لأ بدي
+
+225
+00:16:39,910 --> 00:16:44,310
+اكتبها بس انا بدي اشوف من وين جيبناها بالمقارنة مع
+
+226
+00:16:44,310 --> 00:16:49,850
+الأولى بديت بالسهلة و قولنا هيها الأولى X تساوي
+
+227
+00:16:49,850 --> 00:16:54,390
+تلاتة K كتبناها التانية تلاتة K زائد واحد اللي كتب
+
+228
+00:16:54,390 --> 00:16:57,610
+تلاتة K يجمع واحد على كل أنصر طب هذا لو كتبناه
+
+229
+00:16:57,610 --> 00:17:01,970
+بشكل صريح اللي هو Z واحد خديني اكتبه في عندنا أنصر
+
+230
+00:17:01,970 --> 00:17:05,010
+واحد اللي هو الواحد لحاله هذا بدي اكتبه بالنص و
+
+231
+00:17:05,010 --> 00:17:11,270
+اعطيه بوضع ليشهي الواحد تلاتة زائد واحد أربعة ناقص
+
+232
+00:17:11,270 --> 00:17:17,990
+تلاتة زائد واحد سالب اتنين ستة زائد واحد سبعة سالب
+
+233
+00:17:17,990 --> 00:17:22,450
+خمسة و هكذا كيف ماشيين؟ بنزيد تلاتة جاعدين كل ما
+
+234
+00:17:22,450 --> 00:17:25,110
+روحنا على اليمين زيدي تلاتة كل ما روحت على اليسار
+
+235
+00:17:25,110 --> 00:17:30,270
+اطرحي تلاتةفوضحة ليش حطيت الواحد في النصف فامشي
+
+236
+00:17:30,270 --> 00:17:33,590
+الييمين زيدي تلاتة امشي اليسار اترحي تلاتة أو بشكل
+
+237
+00:17:33,590 --> 00:17:36,070
+عام كل ما انت ماشي الييمين بتزيد تلاتة الأعداد،
+
+238
+00:17:36,070 --> 00:17:39,690
+مظبوط؟ هيك ماشي، هيك ماشي، فهي الجزء التاني، القسم
+
+239
+00:17:39,690 --> 00:17:44,690
+التاني خيا نخطب القسم التالت والاخير بيساوي كل عدد
+
+240
+00:17:44,690 --> 00:17:49,070
+صحيح بحيث there exist K and Z، بتبدا ماشي عنا من
+
+241
+00:17:49,070 --> 00:17:53,930
+الأخر خطوة، X إيش بتساوي؟زادي ايش؟ زادي اتنين
+
+242
+00:17:53,930 --> 00:17:58,090
+عملتم خطوطين مع بعض هي نقص اتنين و هنقلت على الطرف
+
+243
+00:17:58,090 --> 00:18:02,010
+التاني واضح؟ امتبعين؟ اه بنفس السياسة هذه عبارة عن
+
+244
+00:18:02,010 --> 00:18:07,750
+مين؟ اتنين زائد او نقص ثلاثة زائد اتنين و هكذا صح؟
+
+245
+00:18:07,750 --> 00:18:10,710
+اختصر الآن بقدر اختصر لان وضحت لك الأولى ايش
+
+246
+00:18:10,710 --> 00:18:15,690
+بتساوي؟ بنفس الاسلوب خلينا نحط اتنين في النصماذا
+
+247
+00:18:15,690 --> 00:18:20,150
+يحصل؟ خمسة و بعدين سالب واحد نفس السياسة ماشي بزيد
+
+248
+00:18:20,150 --> 00:18:26,510
+تلاتة تمانية إحداش and so on سالب أربع and so on
+
+249
+00:18:27,990 --> 00:18:32,510
+فهيزد اتنين، ممتاز؟ فإذا نقسم الاعداد الصحيحة إلى
+
+250
+00:18:32,510 --> 00:18:35,950
+تلت أقسام كما تراهم، بيقول اللي هدول التلت أقسام
+
+251
+00:18:35,950 --> 00:18:39,490
+بيعتبروا partition، تجزيل، انشوف الشروط، هل واحد
+
+252
+00:18:39,490 --> 00:18:42,990
+من التلاتة فاضي؟ وعبارة واضح، لكل إنسان أنه مش
+
+253
+00:18:42,990 --> 00:18:46,710
+فاضي، مش بس أنه في عناصر متعددة، طيب، لو أخدنا أي
+
+254
+00:18:46,710 --> 00:18:51,590
+قسمين، في عناصر مشتركة بين أي قسمين؟ متأكدين؟
+
+255
+00:18:51,590 --> 00:18:57,070
+متأكدين؟ انتوا مش كاتبين كل عناصر، متأكدين؟ وليش؟
+
+256
+00:18:58,920 --> 00:19:02,920
+الحقيقة عشان نفهم .. والاتحاد بيساوي كل Z واضح
+
+257
+00:19:02,920 --> 00:19:05,560
+طبعا .. خلّيني أوضحلكم إياه، إيش الفلسفة اللي
+
+258
+00:19:05,560 --> 00:19:09,660
+موجودة هنا؟ الحقيقة .. هذا التقسيم ينبني على
+
+259
+00:19:09,660 --> 00:19:13,940
+الحقيقة التالية، هو قاعد بيقسم الإعداد الصحيحة
+
+260
+00:19:13,940 --> 00:19:18,000
+طبقا لعلاقتهم في القسمة ع تلاتة، في تلت احتمالات،
+
+261
+00:19:18,000 --> 00:19:21,200
+لا تقل ع رابع لهما، أول شيء يقبل القسمة يعني
+
+262
+00:19:21,200 --> 00:19:27,600
+الباقي صفر، يعني Z0أو الباقي واحد يعني Z واحد كله
+
+263
+00:19:27,600 --> 00:19:30,940
+أي عنصر يقبل قسمه على Z بالباقي واحد لا يقبل قسمه
+
+264
+00:19:30,940 --> 00:19:34,040
+لكن الباقي واحد والتاني الباقي اتنين في احتمال
+
+265
+00:19:34,040 --> 00:19:39,230
+رابع؟ لأحد عنده احتمال رابع يقول لي فش لأن لو ال
+
+266
+00:19:39,230 --> 00:19:42,290
+.. لو الباقي غير الواحد والتانين بيصير يقبل بيصير
+
+267
+00:19:42,290 --> 00:19:45,430
+تلاتة التلاتة مايصير تقبل الباقي أربعة يعني واحد
+
+268
+00:19:45,430 --> 00:19:48,930
+برجع وها كذا فهذه اللي الا احتمالات اذا هل في عدد
+
+269
+00:19:48,930 --> 00:19:51,830
+بيكون الباقي معاه صفر وواحد او اتنين مع بعض لأ
+
+270
+00:19:51,830 --> 00:19:56,160
+واحدة من التلاتة لأ فاش غيره بقدرطب كل عدد صحيح
+
+271
+00:19:56,160 --> 00:19:58,920
+بقدر اصنفع واحد من تلاتة نعم هذه الاحتمالات
+
+272
+00:19:58,920 --> 00:20:02,760
+الموجودة ففعلا هو partition ففعلا partition اي عدد
+
+273
+00:20:02,760 --> 00:20:07,240
+احتمالات واحد من تلاتة في القسمة تلاتة يقبل قسمة
+
+274
+00:20:07,240 --> 00:20:10,700
+ليهو ياش الباقي صفر لا يقبل قسمة الاحتمالين الباقي
+
+275
+00:20:10,700 --> 00:20:13,200
+او واحد او اتنين فش غير هيك ففعلا هذا يعتبر
+
+276
+00:20:13,200 --> 00:20:18,640
+partition او تقسيم بالمعنى الموجود واضح؟ هيكمان
+
+277
+00:20:18,640 --> 00:20:24,670
+مثالتمام أه الآن فهذا هو ال partition وهذا يمكن
+
+278
+00:20:24,670 --> 00:20:27,630
+الأمثلة في البداية طبعا هنرجعله للموضوع مرة تانية
+
+279
+00:20:27,630 --> 00:20:31,430
+فبدنا نشوف علاقته مع ال equivalence relations زي
+
+280
+00:20:31,430 --> 00:20:34,450
+ما العنوان بيقول بيقول there is a close connection
+
+281
+00:20:34,450 --> 00:20:38,930
+في علاقة قوية قريبة between the partition of a non
+
+282
+00:20:38,930 --> 00:20:41,850
+-intesite اللي تاوي اتحدثنا عنه كيف بجزء المجموعة
+
+283
+00:20:41,850 --> 00:20:46,810
+غير الخالية إلى أقسام أو أيساء وبين مصطلح ال
+
+284
+00:20:46,810 --> 00:20:52,080
+equivalence relation أو علاقة التكاففما هي هذه
+
+285
+00:20:52,080 --> 00:20:55,620
+العلاقة؟ يعني الحقيقة إحنا هنوصل في نهاية ال
+
+286
+00:20:55,620 --> 00:21:00,740
+chapter هنثبت إن كل علاقة تكافؤ بتقسم المجموعة
+
+287
+00:21:00,740 --> 00:21:04,740
+تقسيم معين بيكون partition والعكس صحيح كل
+
+288
+00:21:04,740 --> 00:21:08,580
+partition بيعرف علاقة تكافؤ على المجموعة ففي علاقة
+
+289
+00:21:08,580 --> 00:21:11,720
+قوية إذا أنا بعرف equivalence relation بولد منها
+
+290
+00:21:11,720 --> 00:21:14,560
+partition وإذا أنا بعرف partition بولد منها
+
+291
+00:21:14,560 --> 00:21:17,340
+equivalence relation فهذه النظرية اللي هنوصلها في
+
+292
+00:21:17,340 --> 00:21:21,220
+الآخرفنبدأ نشوف كيف بدنا نقسم كيف ال equivalence
+
+293
+00:21:21,220 --> 00:21:25,720
+relation هنبدأ بتعمل عملية partition تقسيم بالشروط
+
+294
+00:21:25,720 --> 00:21:29,320
+اللي حكيناها فبدأ في عندنا التعريف الأول هيعرف ما
+
+295
+00:21:29,320 --> 00:21:33,720
+يُعرف صفوف التكافؤ equivalence classes صفوف
+
+296
+00:21:33,720 --> 00:21:39,100
+التكافؤ بقول لليتE be an equivalence relation الآن
+
+297
+00:21:39,100 --> 00:21:42,320
+كنا زمان نقول relation R لإن كنا بيشتغل على ال
+
+298
+00:21:42,320 --> 00:21:45,900
+relation بشكل عام الآن هنبتنخصص هنشتغل بس على ال
+
+299
+00:21:45,900 --> 00:21:48,500
+equivalence relation فإيش عايز أجابلها الرمز حرف
+
+300
+00:21:48,500 --> 00:21:50,760
+ال E من equivalence طبعا بكتب بهذا الشكل زي
+
+301
+00:21:50,760 --> 00:21:54,000
+الأبسلون أه بده يميزها let E be an equivalence
+
+302
+00:21:54,000 --> 00:21:58,220
+relation on a non empty set X في مجموعة غير خالية
+
+303
+00:21:58,220 --> 00:22:05,700
+Xبقول لي لكل عنصر في ال X بعرف صف ال X We define
+
+304
+00:22:05,700 --> 00:22:10,140
+the equivalence class صف التكافؤ determined by X
+
+305
+00:22:10,140 --> 00:22:15,320
+لأن هو صف ال X كل عنصر في ال X بعرف لي صف تكافؤ كل
+
+306
+00:22:15,320 --> 00:22:19,920
+عنصر بيحدد او بعرف صف تكافؤ ما هو صف التكافؤ اه
+
+307
+00:22:19,920 --> 00:22:23,380
+طبعا ايش رمزه زي ما اتعودنا X على ال epsilon هذا
+
+308
+00:22:23,380 --> 00:22:28,880
+هو الرمز فعنا مصطلحEquivalency class ايش رمزه X
+
+309
+00:22:28,880 --> 00:22:33,680
+slash ال relation هو صف ال X بالنسبة لل relation
+
+310
+00:22:33,680 --> 00:22:39,880
+ال E ما يتمنى يتكون يتكون من كل عناصر ال X للعلاقة
+
+311
+00:22:39,880 --> 00:22:44,000
+مع ال X كل عناصر ال capital X Y للعلاقة مع ال X
+
+312
+00:22:44,000 --> 00:22:50,330
+بمعنى بسيطمثال سهل جدا صف .. ايش معناته؟ في عندنا
+
+313
+00:22:50,330 --> 00:22:55,570
+فاطمة، مين صف فاطمة؟ كل الطالبات اللي بنات صف
+
+314
+00:22:55,570 --> 00:22:59,610
+فاطمة، واضحيت؟ اللي لهم علاقة مع فاطمة، بنفس الصف،
+
+315
+00:22:59,610 --> 00:23:03,570
+فهو أيش بيقول هنا؟ هي أنا عندي X، فاطمة، تمام؟ مين
+
+316
+00:23:03,570 --> 00:23:06,730
+صف فاطمة؟ كل الطالبات بنات صف فاطمة، اللي لهم
+
+317
+00:23:06,730 --> 00:23:10,330
+علاقة مع فاطمة، نفس الصف، واضح؟ فهو أيش ماله؟ مما
+
+318
+00:23:10,330 --> 00:23:14,930
+يتكون صف ال X من كل عناصر Y اللي لهم علاقة مع ال X
+
+319
+00:23:15,090 --> 00:23:17,570
+اللي اللي هم علاقة مع ال X باختصار عنا هتشوف
+
+320
+00:23:17,570 --> 00:23:23,780
+الأمثل هذه أول شيءطمام فانا في عندي صف التكافؤ وفي
+
+321
+00:23:23,780 --> 00:23:28,380
+عندي مجموعة صفوف التكافؤ ايش رمزها؟ رمزها capital
+
+322
+00:23:28,380 --> 00:23:34,060
+X على أبسلون ففي عندي رمزين متقاربين الدقة مهمة في
+
+323
+00:23:34,060 --> 00:23:39,700
+الرياضية زي ما بنقول عنصر بيعملي صف طب مجموعة كل
+
+324
+00:23:39,700 --> 00:23:43,580
+الصفوف مجموعة الصفوف ما هي capital X على أبسلون؟
+
+325
+00:23:43,580 --> 00:23:48,500
+هي كل صف تكافؤ ل X تنتمي لل capital X لل capital X
+
+326
+00:23:48,750 --> 00:23:51,770
+واضح؟ هنشوف طبعا الانفراد، بس هدا إيش؟ قراة
+
+327
+00:23:51,770 --> 00:23:55,450
+للتعريف Remark if Epsilon is an equivalent
+
+328
+00:23:55,450 --> 00:23:57,890
+solution of an unempty set X, then every
+
+329
+00:23:57,890 --> 00:24:02,370
+equivalence class is a subset of X طبعا واضح من
+
+330
+00:24:02,370 --> 00:24:06,270
+التعريف، إيش تعريف الصف؟ بيقول إنه عنصر في ال X
+
+331
+00:24:07,100 --> 00:24:10,640
+وعليه كمان شرط إيه علاقة مع ال X هو عنصر Y في ال
+
+332
+00:24:10,640 --> 00:24:14,280
+capital X إيه علاقة مع ال X إذا من وين بتاخد عناصر
+
+333
+00:24:14,280 --> 00:24:18,580
+الصف من ال X من capital X إذا كل صف تكافأ هو
+
+334
+00:24:18,580 --> 00:24:22,440
+مجموعة جزئية من capital X بنفع يكون عنصر موجود في
+
+335
+00:24:22,440 --> 00:24:26,020
+الصف مش موجود في ال X لأ إذا كل عنصر في الصف هو
+
+336
+00:24:26,020 --> 00:24:29,340
+أصلا من وين؟ في ال X هو جزء من ال X فإذا كل صف
+
+337
+00:24:29,340 --> 00:24:33,100
+تكافأ هو صبصة من مجموعة اللي بشتغل عليها capital X
+
+338
+00:24:33,100 --> 00:24:38,270
+دي ملاحظة مهمةنشوف الأمثلة ونبدأ دايما بالأمثلة
+
+339
+00:24:38,270 --> 00:24:46,890
+البسيطة المثال
+
+340
+00:24:46,890 --> 00:24:52,880
+الأولمدّينا مجموعة من عنصرين مثلها البسيط عشان
+
+341
+00:24:52,880 --> 00:24:57,960
+نستوعب ومدّينا علاقة تكافأ عبارة عن مين الحقيقة
+
+342
+00:24:57,960 --> 00:25:02,440
+هذه ال relation هي X cross ال X جللت أبسلون بيك
+
+343
+00:25:02,440 --> 00:25:05,520
+الأزواج المرتبة كلهم طبعا هذه equivalence relation
+
+344
+00:25:05,960 --> 00:25:08,680
+لأن هو إيش؟ طبعا مابدناش احنا نفحص لإن هو عبارة عن
+
+345
+00:25:08,680 --> 00:25:12,120
+X cross الـX و هاد يقولنا ملاحظة بشكل عام إيش بده؟
+
+346
+00:25:12,120 --> 00:25:16,700
+find X على الأبسلون إيش يعني؟ أوجد مجموعة كل صفوف
+
+347
+00:25:16,700 --> 00:25:21,320
+التكافة يعني أوجد كل صفوف التكافة آه فبدنا نجيب
+
+348
+00:25:21,320 --> 00:25:26,660
+هذا الكلام خليني أكتبها X على الأبسلون تساوي اللي
+
+349
+00:25:26,660 --> 00:25:30,300
+هو إيش؟ كيف التعريف بالظبط؟ عبارة عن إيش؟ X تنتقل
+
+350
+00:25:30,300 --> 00:25:34,770
+على small x such thatx على small x such that x is
+
+351
+00:25:34,770 --> 00:25:39,790
+sentimental to X مش هيك التعليف مكتوب بصيغة نفسها
+
+352
+00:25:39,790 --> 00:25:43,170
+بديش اكتب بصيغة اعتبارها صحيحة لكن بديش اكتب بصيغة
+
+353
+00:25:43,170 --> 00:25:49,610
+جديدة تمام انشوف ايش المحتمل من عناصر X بدنا صف
+
+354
+00:25:49,610 --> 00:25:54,730
+الواحد يعني وبدنا صف التاني هيك معناتهفمجموعة الـ
+
+355
+00:25:54,730 --> 00:25:58,550
+Capital X على ال relation هي مجموعة صفوف التكافأة
+
+356
+00:25:58,550 --> 00:26:02,490
+مجموعة صفوف التكافأة اللي شرحناها واضح؟ تمام عشان
+
+357
+00:26:02,490 --> 00:26:05,890
+أحسبها إيش بدى أحسب؟ صف الواحد وصف التنين نبدأ
+
+358
+00:26:05,890 --> 00:26:10,690
+نحسب صف الواحد مين؟ بنات صف الواحد أو أولاد صف
+
+359
+00:26:10,690 --> 00:26:13,730
+الواحد العناصر اللي هي المعلاقة مع الواحد مين فيه؟
+
+360
+00:26:13,730 --> 00:26:20,570
+الواحد وين كمان؟ والتنينهو لأن واحد واحد تنتمي و
+
+361
+00:26:20,570 --> 00:26:23,810
+واحد اتنين تنتمي، إذا بدنا مين؟ العناصر اللي اللي
+
+362
+00:26:23,810 --> 00:26:27,550
+معلاقة مع الواحد، هدول هم ولاد صف الواحد، واضح؟
+
+363
+00:26:27,550 --> 00:26:31,870
+أيه هو أياش الصف؟ طيب، نيجي نحسب مين؟ ولاد صف
+
+364
+00:26:31,870 --> 00:26:35,610
+التنين، مين اللي معلاقة مع التنين؟ التنين، ومين
+
+365
+00:26:35,610 --> 00:26:42,200
+كمان؟ والواحدتمام؟ إيش صفين هدول؟ طلعوا الواحد
+
+366
+00:26:42,200 --> 00:26:45,400
+والتانين ولات صف واحد، فنفس الصف فانا عندي فاطمة
+
+367
+00:26:45,400 --> 00:26:48,260
+وجيبت بنات صفها وجيبت عايشة بنات صفها طلعوا نفس
+
+368
+00:26:48,260 --> 00:26:51,820
+الصف بنات صف واحد طلعوا متساويين فلمّا يقوللي اكتب
+
+369
+00:26:51,820 --> 00:26:55,060
+x على epsilon إيش بده اكتبله؟ أكم صف؟
+
+370
+00:26:57,530 --> 00:27:01,350
+بس طبعاً مجموعة مجموعات اه؟ مجموعة مجموعات صف واحد
+
+371
+00:27:01,350 --> 00:27:06,490
+فيها طلعت صف واحد فعايزاً أولا نفهم إيش معناه صف
+
+372
+00:27:06,490 --> 00:27:09,430
+التكافؤ العناصر اللي لهم علاقة مع العنصر اللي
+
+373
+00:27:09,430 --> 00:27:12,250
+بحسبله صف التكافؤ طب ما هي capital X على الأبسلون
+
+374
+00:27:12,250 --> 00:27:16,390
+مجموعة صفوف التكافؤ فارجوا أن هذا النقطة تكون واضح
+
+375
+00:27:16,390 --> 00:27:22,770
+نعم لأن نقمة مجموعة تساوي هذه المجموعة كمجموعات لو
+
+376
+00:27:22,770 --> 00:27:26,010
+كتبتها مافيش فايدة لو كتبتها مش غلط لكن مضفليش
+
+377
+00:27:26,010 --> 00:27:29,900
+معلومةلأن هو إيش قال ليه؟ set of a equivalence
+
+378
+00:27:29,900 --> 00:27:33,240
+class فالتكرار مالهوش قيمة لأنه متساويين هدول هدول
+
+379
+00:27:33,240 --> 00:27:37,980
+متساويين و لا لأ كان مجموعة كان مجموعتين متساويتين
+
+380
+00:27:37,980 --> 00:27:41,920
+و لا مش متساويتين متساويتين لأن ترتيب المجموع غير
+
+381
+00:27:41,920 --> 00:27:46,900
+.. غير مهم أحسن بس فبكتبش مرة تانية مهمة جدا هذه
+
+382
+00:27:46,900 --> 00:27:53,740
+هذه هيها بدي مجموع صف الواحد هيه صف التنين نفسه
+
+383
+00:27:53,740 --> 00:28:00,150
+يعني هذا هو إيشصح؟ اكتبه مرتين؟ مالاش قيمة واضحيت؟
+
+384
+00:28:00,150 --> 00:28:03,390
+اه فهي مجموعات المجموعات بدل واحد على قدس نحطتها
+
+385
+00:28:03,390 --> 00:28:09,070
+دي صف الواحد نشوف كمان مثال جديد نشوف مثال تاني
+
+386
+00:28:09,070 --> 00:28:12,770
+عشان أمورته تتضح مثال مع مثال الأمور بتكون أوضح ان
+
+387
+00:28:12,770 --> 00:28:13,130
+شاء الله
+
+388
+00:28:17,440 --> 00:28:22,180
+الان كبرنا العلاقة شوية .. آسف المجموعة شوية بدل
+
+389
+00:28:22,180 --> 00:28:27,860
+عنصرين تلاتة والداني مجموعة ليست x cross ال X مش
+
+390
+00:28:27,860 --> 00:28:31,360
+تسع عناصر اختار طبعا هي equivalence relation من
+
+391
+00:28:31,360 --> 00:28:35,040
+المعطى ماجاليش يثبت هي أغزالياش متبطأة و خاصة بدوا
+
+392
+00:28:35,040 --> 00:28:39,000
+مين؟ مجموعة صفوف التكافئة بدوا مجموعة صفوف
+
+393
+00:28:39,000 --> 00:28:43,080
+التكافئة بدوا capital X على أبسلون اللي هي ايش؟
+
+394
+00:28:43,080 --> 00:28:48,740
+small x على أبسلون بحيث x تنتمي لcapital Xأكم صف
+
+395
+00:28:48,740 --> 00:28:53,260
+ممكن يكونوا؟ تلاتة أدعى بحد الأقصى اتعلمنا من
+
+396
+00:28:53,260 --> 00:28:56,440
+المثال الماضي أنهم بالكتير تلاتة لأنه لو اتكرر
+
+397
+00:28:56,440 --> 00:29:00,840
+بكتبوش مرتين واضحيت؟ اه إذا احنا في عنا عدد الصفوف
+
+398
+00:29:00,840 --> 00:29:04,580
+الحد الأقصى هو عدد عناصر ال X لكن الصف اللي بيكون
+
+399
+00:29:04,580 --> 00:29:07,560
+متساوي بكتبوش إلا مرة واحد مافيش داعي أكتبه مرتين
+
+400
+00:29:07,560 --> 00:29:12,180
+ممتاز نبدأ بالحساب صف الواحد مين اللي له علاقة مع
+
+401
+00:29:12,180 --> 00:29:19,360
+الواحد؟ الواحد والتلاتة في غيرهم؟ لاطبعا صف التنين
+
+402
+00:29:19,360 --> 00:29:26,500
+في الشلة التنين و صف التلاتة الواحد والتلاتة أو
+
+403
+00:29:26,500 --> 00:29:29,600
+التلاتة و واحد اللي هو أشمال و بصار و صف مين
+
+404
+00:29:29,600 --> 00:29:34,980
+فالواحد و التلاتة ولات صف نفس الصف إذا هذه
+
+405
+00:29:34,980 --> 00:29:40,340
+المجموعة كام صف فيها صفين فقط فيها اللي هو إيش
+
+406
+00:29:40,340 --> 00:29:46,000
+واحد و تلاتة و التنين الترتيب مش مهم ففيها صفين
+
+407
+00:29:47,400 --> 00:29:51,760
+فإذا المجموعة الأولى من عنصرين إيش؟ فيها صف واحد
+
+408
+00:29:51,760 --> 00:29:55,520
+العنصر مصر واحد تاني التلات عناصر فيها صفين فيها
+
+409
+00:29:55,520 --> 00:30:05,900
+صفين كمان مثال بدي أضطر أمسح حد و أكتبها تحت أو
+
+410
+00:30:05,900 --> 00:30:06,180
+هنا
+
+411
+00:30:17,280 --> 00:30:23,640
+امعرف علاقة رمزها المربع .. امعرف علاقة رمزها
+
+412
+00:30:23,640 --> 00:30:28,000
+المربع معرفة على أي مجموعة على الأعداد الصحيحة
+
+413
+00:30:28,000 --> 00:30:32,040
+لأنها أيش أزواج مرتبة من Z cross الـZ يعني معرفة
+
+414
+00:30:32,040 --> 00:30:35,640
+على الـZ ما هو التعريف بقول اللي بقول على عددين
+
+415
+00:30:35,640 --> 00:30:39,420
+صحيحين أنهم لهم علاقة .. علاقة مربعة مع بعض إذا
+
+416
+00:30:39,420 --> 00:30:43,990
+مربعاتهم تساوتXY بتكون إيه لهم علاقة في العلاقة
+
+417
+00:30:43,990 --> 00:30:48,230
+إذا X تربية تسوى و Y تربية إيش بده إثبت إن هذا
+
+418
+00:30:48,230 --> 00:30:52,830
+علاقة التكافؤ و إيش كمان و أوجد مجموعة صفوف
+
+419
+00:30:52,830 --> 00:30:56,890
+التكافؤ هنا مطلوبين فبنثبت أولا إنها مجموعة تكافؤ
+
+420
+00:30:56,890 --> 00:31:05,690
+أو علاقة تكافؤ و بدنا نوجد صفوف التكافؤ فهذا
+
+421
+00:31:05,690 --> 00:31:12,170
+المثالالتالت طبعا ففي عندنا مطلوبين رئيسيين أول
+
+422
+00:31:12,170 --> 00:31:16,830
+شيء هذه العلاقة المربعة is an equivalence relation
+
+423
+00:31:16,830 --> 00:31:21,350
+نرتب
+
+424
+00:31:21,350 --> 00:31:27,650
+الحل نجسمه نثبت إنها equivalence relation تلت شروط
+
+425
+00:31:27,650 --> 00:31:34,310
+نثبت أولا إنها reflexive فالمربع is reflexive
+
+426
+00:31:36,920 --> 00:31:39,940
+إنها reflex طبعاً
+
+427
+00:31:41,590 --> 00:31:45,430
+الممكن قد يكون البعض مستغرب، ليش هذا الرمز؟ طب هو
+
+428
+00:31:45,430 --> 00:31:48,070
+مين اللي قال إن الرمز اللي يساوي دوش حتتان ببعض هو
+
+429
+00:31:48,070 --> 00:31:51,230
+يساوي؟ ومين قال إن رمز الجامع هو across؟ اختيار
+
+430
+00:31:51,230 --> 00:31:54,790
+رمز، اه فبنتعلم احنا كتعون رياضيات نفكر بطريقة
+
+431
+00:31:54,790 --> 00:31:59,390
+مجردة، هذا رمز اخترناه، اختار رمز غيري، بنفع،
+
+432
+00:31:59,390 --> 00:32:02,690
+فانهدت رمز، هي علاقة، ليش علاقة التساوي حتتان فوق
+
+433
+00:32:02,690 --> 00:32:06,690
+بعض؟ طب ممكن احط علاقة تساوي مربعة؟ ممكن، طبعا، هل
+
+434
+00:32:06,690 --> 00:32:10,140
+الرمز إيه علاقة بالتعريف؟بالتربية، بالتربية،
+
+435
+00:32:10,140 --> 00:32:12,480
+شايفين؟ X تربية و Y تربية، فإيه علاقة بالمربع؟
+
+436
+00:32:12,480 --> 00:32:15,660
+واضحة؟ نعم، بس، هي القضية، فالقضية إيش؟ مانيش ده،
+
+437
+00:32:15,660 --> 00:32:22,320
+وانا علاقة، هاي رمزة مربع مثلف X و R is S، علاقة،
+
+438
+00:32:22,320 --> 00:32:25,500
+وهي رمزة، بدي أثبت إن علاقة تكافر، فهل هي
+
+439
+00:32:25,500 --> 00:32:28,660
+reflexive؟ إيش معنات reflexive؟ بدي كل عنصره
+
+440
+00:32:28,660 --> 00:32:33,380
+لعلاقة مع نفسه، فطبعاً for all، بدي أقوله letX
+
+441
+00:32:33,380 --> 00:32:37,920
+تنتمي لـ Z any element لأنه for all هل X تربية
+
+442
+00:32:37,920 --> 00:32:43,760
+تساوي X تربية؟ طبعا صح then X تربية تساوي X تربية
+
+443
+00:32:43,760 --> 00:32:49,900
+وبالتالي XX تنتمي لمين؟ للمربع، ماتنسوش، مش R، هي
+
+444
+00:32:49,900 --> 00:32:54,220
+فإذا فعلا X لعلاقة مع نفسها، إذا فعلا reflexive
+
+445
+00:32:54,220 --> 00:33:00,860
+واضحة؟ في أي صعوبة؟ فإذا هذه العلاقة reflexive is
+
+446
+00:33:00,860 --> 00:33:01,720
+reflexive
+
+447
+00:33:06,930 --> 00:33:15,130
+الشرط التاني علاقة التماثل اتنين علاقة المربع is
+
+448
+00:33:15,130 --> 00:33:16,170
+symmetric
+
+449
+00:33:19,690 --> 00:33:24,210
+بمعنى إذا كان في زوج XY في العلاقة معكوسه بيكون
+
+450
+00:33:24,210 --> 00:33:29,070
+فبنفترض أنه في زوج ما في العلاقة assume أو let XY
+
+451
+00:33:29,070 --> 00:33:34,190
+تنتمي للعلاقة بدي أثبت أنه معكوسه في العلاقة طبعا
+
+452
+00:33:34,190 --> 00:33:40,230
+هذا ماذا يعني X تربية تساوي Y تربية طب منفع أبدل؟
+
+453
+00:33:40,230 --> 00:33:44,190
+طب ليش منفع أبدل؟ لأن علاقة تتساوي أشمالها في لغة
+
+454
+00:33:44,190 --> 00:33:49,510
+الرياضياتالعلاقة مش إبدالية علاقة تماثل symmetric
+
+455
+00:33:49,510 --> 00:33:52,030
+هذه علاقة ما هي تساوي علاقة عشان انتوا متعودين
+
+456
+00:33:52,030 --> 00:33:55,850
+عليها لكن التساوي اسمها symmetric تفرجش بقول انا
+
+457
+00:33:55,850 --> 00:33:59,690
+واحد تساوي واحد او واحد زي واحد تساوي اتنين و
+
+458
+00:33:59,690 --> 00:34:02,510
+اتنين تساوي واحد زي واحد تماثل بيسموه بالمصطلح انا
+
+459
+00:34:02,510 --> 00:34:04,610
+انا عارف انتوا عارفين بس مانشوف ايش المصطلح ده
+
+460
+00:34:04,610 --> 00:34:09,090
+صحيح فهذا يؤدي ان y تربيه تساوي x تربيه ليش لأن
+
+461
+00:34:09,090 --> 00:34:16,900
+علاقة التساوي is symmetricخلاص هداش معناته yx في
+
+462
+00:34:16,900 --> 00:34:30,240
+الار thus في المربع صحيح فالمربع is symmetric ففيش
+
+463
+00:34:30,240 --> 00:34:34,780
+أي صعوبة واضح و هي .. انا فاهمين انتوا بس مش
+
+464
+00:34:34,780 --> 00:34:37,780
+المصالح الصحيح مش إبدالينا بسموها ياش تماثل لإنه
+
+465
+00:34:37,780 --> 00:34:41,240
+علاقة مش عملية هادى يكون ايه عملية إبدالية الشرط
+
+466
+00:34:41,240 --> 00:34:46,270
+التالتإن هذه علاقة من المربع إلى خاصية التعدي
+
+467
+00:34:46,270 --> 00:34:53,290
+Transitive فطبعا بدي أخد زوجين بخواص معينة في
+
+468
+00:34:53,290 --> 00:34:59,730
+العلاقة XY في العلاقة and YZ في العلاقة فالسؤال هل
+
+469
+00:34:59,730 --> 00:35:03,570
+XZ في العلاقة صحيح طبعا لنجلبه ايش هنعمل؟ بدنا
+
+470
+00:35:03,570 --> 00:35:07,510
+نستخدم ايش معناته؟ انهم في العلاقة يعني المربع
+
+471
+00:35:07,510 --> 00:35:12,270
+الأول يسووا المربع التاني فهذا يؤديX تربية تساوي Y
+
+472
+00:35:12,270 --> 00:35:20,870
+تربية and Y تربية تساوي Z تربية فهذا يؤدي ان X
+
+473
+00:35:20,870 --> 00:35:25,910
+تربية تساوي Z تربية ليش؟ لأن التساوي اشمالها علاقة
+
+474
+00:35:25,910 --> 00:35:29,090
+Transitive فاهم فيه لأن انا بقول ان مقدار يساوي
+
+475
+00:35:29,090 --> 00:35:32,230
+مقدار والتاني بيساوي التالت بقدر اخد ان الاول
+
+476
+00:35:32,230 --> 00:35:34,990
+يساوي التالت نعرف نستخدم هذه بس احنا ايش ماكناش
+
+477
+00:35:34,990 --> 00:35:39,710
+حاطينا في الصياق او بالمصطلح الصحيح لأن التساوي is
+
+478
+00:35:39,710 --> 00:35:40,470
+a transitive
+
+479
+00:35:42,940 --> 00:35:47,740
+إذا X و Z تنتمي هذا معناته أن X و Z تنتمي لل R وهو
+
+480
+00:35:47,740 --> 00:35:53,700
+المطلوب للمربع صحيح Thus علاقة المربع is
+
+481
+00:35:53,700 --> 00:35:59,380
+transitive طبعا
+
+482
+00:35:59,380 --> 00:36:03,600
+واحد و اتنين و تلاتة بيقولوا إن هذا علاقة تكافئة و
+
+483
+00:36:03,600 --> 00:36:07,320
+تلاتة implies علاقة المربع is an equivalence
+
+484
+00:36:07,320 --> 00:36:07,700
+relation
+
+485
+00:36:15,540 --> 00:36:20,100
+relation تمام فهذه الشروط واتعودنا و بنكتبهم كل
+
+486
+00:36:20,100 --> 00:36:24,540
+مرة التفاصيل بتختلف من مثال لمثال لكن الشروط واحدة
+
+487
+00:36:24,540 --> 00:36:27,740
+فخلصنا من ال use الاول من المطلوب الان نيجي لا ياش
+
+488
+00:36:27,740 --> 00:36:33,640
+بدنا نحسب زد على العلاقة نحط عنوان فرق ايه فبدنا
+
+489
+00:36:33,640 --> 00:36:38,540
+نحسب هذا ايش بيساوي طبعا هذا طبقا للتعريف ايش
+
+490
+00:36:38,540 --> 00:36:43,820
+بيساويبيساوي كل X على العلاقة بحيث small x أيه
+
+491
+00:36:43,820 --> 00:36:51,210
+أشمالها عدد صحيح فبدنا نحسب كل الصفوففي المثالين
+
+492
+00:36:51,210 --> 00:36:55,970
+السابقين كانت المجموعة فيها عنصرين أو تلاتة حسبنا
+
+493
+00:36:55,970 --> 00:37:00,790
+كل الصفوف الآن نقدر نحسب كل الصفوف لل Z لا لكن طب
+
+494
+00:37:00,790 --> 00:37:05,950
+إيش أعمل؟ نبدأ نشتغل ندور عصيغة عامة نبدأ نحاول
+
+495
+00:37:05,950 --> 00:37:09,890
+نشوف بعض الأمثلة فنبدأ إيش نحسب؟ نبدأ بإيش؟ بالصفة
+
+496
+00:37:10,520 --> 00:37:13,920
+دائما إذا مجموعة كبيرة إذا إلها بداية أو نهاية
+
+497
+00:37:13,920 --> 00:37:16,820
+يبدو من بدايتها أو نهايتها، طب مالهاش بداية و
+
+498
+00:37:16,820 --> 00:37:21,560
+نهاية، يبدو من النص، من بداية مناسبة، من أولاد صف
+
+499
+00:37:21,560 --> 00:37:26,880
+الصفر؟ مافيش إلا الصفر، لأن مافيش إلا صفر تربية
+
+500
+00:37:26,880 --> 00:37:31,780
+تساوي صفر تربية، في غيرهم؟ لأ، طب من أولاد صف
+
+501
+00:37:31,780 --> 00:37:36,550
+الواحد؟الواحد والسالب واحد من اللي له معلاقة مع
+
+502
+00:37:36,550 --> 00:37:40,750
+الواحد الواحد والسالب واحد لأن مربعاتهم متساوية و
+
+503
+00:37:40,750 --> 00:37:44,930
+هكذا طيب ممكن .. واضحة الصورة؟ اه اذا اي صف ل X
+
+504
+00:37:44,930 --> 00:37:50,410
+على Z ايش بيساوي؟ بس
+
+505
+00:37:50,410 --> 00:37:57,450
+فخلاص بدي اكتبهم الان فضل لأن
+
+506
+00:37:57,450 --> 00:38:01,590
+ال X ماساوي صفر فالصالب صفري صاوي صفر ال gate
+
+507
+00:38:01,590 --> 00:38:01,850
+master
+
+508
+00:38:11,550 --> 00:38:18,170
+صح؟ مقتنعة ولا مش مقتنعة؟ مش مقتنعة تمع هي ال X هي
+
+509
+00:38:18,170 --> 00:38:23,870
+صفر و سالب صفر كيف يعرف تسلب صفر؟
+
+510
+00:38:26,150 --> 00:38:30,230
+طيب ماشي لما تقول انت ايه و واحد ماقص صفر ايش
+
+511
+00:38:30,230 --> 00:38:33,530
+بيصير واحد طب واحد زاد صفر نفس الشيء مش ماشي لأ
+
+512
+00:38:33,530 --> 00:38:36,510
+فالصفر عادى مالهوش اشارة علشان هيك لأنه اشارته
+
+513
+00:38:36,510 --> 00:38:39,470
+الموجب والسالب هو بديك نفس المخدر ف سالب صفر يساوي
+
+514
+00:38:39,470 --> 00:38:42,670
+صفر يعني او بمعنى اخر سالب واش السالب ماهي سالب
+
+515
+00:38:42,670 --> 00:38:45,910
+واحد سالب واحد في الصفرصفر هي الإشارة من هنا جاية
+
+516
+00:38:45,910 --> 00:38:49,830
+سالب واحد تمام فهي نفسها اه فإذا نكتبله اياها اللي
+
+517
+00:38:49,830 --> 00:38:56,730
+جاهزين نحطله Z على المربع ايش بتساوي؟ بتساوي
+
+518
+00:38:56,730 --> 00:39:05,210
+مجموعات على صورة X و سالب X بحي X تنتمي لمين؟ممكن
+
+519
+00:39:05,210 --> 00:39:08,530
+نقول صفر و واحد في داعي اكتب كمان السلب واحد لأ هو
+
+520
+00:39:08,530 --> 00:39:12,330
+نفس صف الواحد فانا ممكن احطها يعبر عن اي عدد صحيح
+
+521
+00:39:12,330 --> 00:39:18,210
+موجب او صفر زد
+
+522
+00:39:18,210 --> 00:39:22,090
+ممكن تحط زد بس مش دقيق هيك اسهل فهو يا عدد صحيح
+
+523
+00:39:22,090 --> 00:39:25,970
+موجب يا صفر فهو صف الواحد هو صف الصلب واحد صف
+
+524
+00:39:25,970 --> 00:39:29,770
+التنين هو صف الصلب اتنين و هكذا مش للصفر منفصل
+
+525
+00:39:29,770 --> 00:39:32,970
+فهنا وجدنا كل الصفوف
+
+526
+00:39:37,250 --> 00:39:41,750
+فبعض هذه الأمثلة الآن نشوف بعض الأمور اللي مرت
+
+527
+00:39:41,750 --> 00:39:47,990
+علينا الحقيقة هل هذه خواص عامة ولا لأ للصفوف ففي
+
+528
+00:39:47,990 --> 00:39:51,170
+عندنا نظرية رقم تلاتة تلاتة يعني النظرية التالتة
+
+529
+00:39:51,170 --> 00:39:54,030
+في هذا ال chapter the probabilities of equivalence
+
+530
+00:39:54,030 --> 00:39:57,830
+classes خواص صفوف التكافئة يمكن هذا برضه يساعدنا
+
+531
+00:39:57,830 --> 00:40:02,850
+في الحسابات ونشوف أنه الكلام اللي شفناههل كان حالة
+
+532
+00:40:02,850 --> 00:40:07,870
+خاصة كمثال ولا ممكن تعميمه؟ انشوف مقدمة النظرية
+
+533
+00:40:07,870 --> 00:40:13,190
+let E be an equivalence relation on a non-empty
+
+534
+00:40:13,190 --> 00:40:16,550
+set X فانا فيها عندي علاقة تكافأة على مجموعة غير
+
+535
+00:40:16,550 --> 00:40:24,380
+فارقةالخاصية الأولى بيقول لي كل صف إيش ماله عبارة
+
+536
+00:40:24,380 --> 00:40:27,940
+عن non-empty subset of X احنا قلنا هي subset بيقول
+
+537
+00:40:27,940 --> 00:40:31,180
+لي عمره ما بيكون في صف فارغ وشوفنا في الأمثلة طلع
+
+538
+00:40:31,180 --> 00:40:34,140
+معاكوا صف فارغ ما طلعاش طب هل ممكن يطلع في أمثلة
+
+539
+00:40:34,140 --> 00:40:36,700
+أنا مش عارفها يطلع صف فارغ؟ بيقول لي لأ فإذا أول
+
+540
+00:40:36,700 --> 00:40:39,560
+شيء يعني فلو طالب كتبتلي قلتلي أجيبلي الصف و
+
+541
+00:40:39,560 --> 00:40:44,360
+كتبتلي file إيش ممكن؟ غلط بس؟غلط كبير لأنه مافيش
+
+542
+00:40:44,360 --> 00:40:47,860
+فارق اتجيبله عنصر تنسى عنصر بقبل لكن تحط اللي فيه
+
+543
+00:40:47,860 --> 00:40:51,380
+مستحيل إذا بتعرف إنه فيها عندها خطأ واضح؟ مافيش صف
+
+544
+00:40:51,380 --> 00:40:55,420
+بيكون فارق هذه الخاصية الأولى الخاصية التانية
+
+545
+00:40:55,420 --> 00:41:01,200
+بقوللي تقاطع صفين بيساوي في if and only if ال X و
+
+546
+00:41:01,200 --> 00:41:06,020
+ال Y اللي هم علاقة مع بعض بمعنى آخر أي عنصرين اللي
+
+547
+00:41:06,020 --> 00:41:10,280
+هم علاقة مع بعض تقاطع صفهم ليه يساوي فيه و هذا
+
+548
+00:41:10,280 --> 00:41:14,270
+يمكن واضح هم يقولوشاللي هو الطالبتين بنات صف واحد
+
+549
+00:41:14,270 --> 00:41:16,790
+اللي هم علاقة مع بعض فهو صفهم نفس الصف الحقيقية
+
+550
+00:41:16,790 --> 00:41:21,150
+فإن تقاطع صفينهم بيسويش فاق فيه عيش عيب طالبات
+
+551
+00:41:21,150 --> 00:41:27,490
+مشتركات بينهم تمام التلاتة C بقول ل X و Y اللي هم
+
+552
+00:41:27,490 --> 00:41:31,970
+علاقة مع بعض if and only if صفينهم متساويين بتكمل
+
+553
+00:41:31,970 --> 00:41:35,770
+السابقة إذا فاطمة و عيشة اللي هم علاقة مع بعض بنات
+
+554
+00:41:35,770 --> 00:41:40,850
+صف إذا صف فاطمة و صف عيشة واضحة؟ أه دي الصورة بدنا
+
+555
+00:41:40,850 --> 00:41:46,130
+نشوف البرهاننبدأ البرهان خير نبدأ من هنا من
+
+556
+00:41:46,130 --> 00:41:50,530
+البداية خالص و
+
+557
+00:41:50,530 --> 00:41:55,090
+نثبت التلت علاقات
+
+558
+00:41:55,090 --> 00:42:00,630
+البروف
+
+559
+00:42:00,630 --> 00:42:10,650
+و نبدأ بإيه؟بقول لكل صف تكافؤ إيش غير فارغ بمعنى
+
+560
+00:42:10,650 --> 00:42:16,230
+for all x تنتمي لكبتل x كل صف فارغ x على الأبسلون
+
+561
+00:42:16,230 --> 00:42:21,450
+لا تساوي fiveالـ statement الأولى وعادت صياغتها
+
+562
+00:42:21,450 --> 00:42:24,910
+بقول لـ each equivalence يعني every يعني for all
+
+563
+00:42:24,910 --> 00:42:28,110
+كل الصفوف لما مش قولنا هيك اتفقنا انه بتترجم
+
+564
+00:42:28,110 --> 00:42:30,550
+تتذكروا الكلام اللي كنا نحكيه هي اننا بنستخدمه
+
+565
+00:42:30,550 --> 00:42:33,270
+each equivalence class X على أسلون is not an anti
+
+566
+00:42:33,270 --> 00:42:37,490
+subset of X كل صف تكافئ غير فارغ بدي أثبت أن هذا
+
+567
+00:42:37,490 --> 00:42:41,980
+الصف غير فارغمر علينا أمثلة كنا كيف بنثبت إن
+
+568
+00:42:41,980 --> 00:42:45,820
+المجموعة فارغة عن طريق prove by contradiction الآن
+
+569
+00:42:45,820 --> 00:42:48,820
+بدنا نثبت إن المجموعة غير فارغة إيش يعني؟ بدنا
+
+570
+00:42:48,820 --> 00:42:52,660
+نثبت إنه في علاقة لأنصه إيش يجب نقوله؟ بنقوله إيش؟
+
+571
+00:42:52,660 --> 00:42:56,920
+اللي هو قسم الرياضيات غير فارغ، في طالبات، ليش؟
+
+572
+00:42:56,920 --> 00:43:00,020
+بعرف طالب اسمه فاطمو، بديله مثال، خلاص، بدنا نثبت
+
+573
+00:43:00,020 --> 00:43:03,300
+إنه غير فارغ، واضح؟ فلجيت بدنا أنص موجود في الصف،
+
+574
+00:43:03,300 --> 00:43:07,760
+فطبعا عشان الـfor all، إيش بدنا نقوله؟ letX تنتمي
+
+575
+00:43:07,760 --> 00:43:13,500
+للـ Capital X بأي element لما كتبت هذه الجملة؟
+
+576
+00:43:13,500 --> 00:43:17,160
+لأنها كلمة for all فبتثبت أن X على الـ Epsilon
+
+577
+00:43:17,160 --> 00:43:20,820
+يعني هذه الـ equivalence class تبقى X غير فارغ غير
+
+578
+00:43:20,820 --> 00:43:24,720
+فارغ، بتثبت أن X على الـ Epsilon غير فارغ من يعرف
+
+579
+00:43:24,720 --> 00:43:29,540
+لأنصر في صف الـ X؟ أحسنتي، أحسنتي، هذا هي، بس، بكل
+
+580
+00:43:29,540 --> 00:43:32,540
+بساطة هذه النقطة مفتاح للشغل كتير، سنشوفه في
+
+581
+00:43:32,540 --> 00:43:38,830
+البرهان، فأنا على طول thenX تنتمي لمن؟ لـ X أبسلون
+
+582
+00:43:38,830 --> 00:43:43,250
+طب ليش؟ بالتعريف لأن العلاقة equivalence relation
+
+583
+00:43:43,250 --> 00:43:46,590
+يعني reflexive يعني X إلا علاقة مع نفسها إذا X
+
+584
+00:43:46,590 --> 00:43:52,890
+بنصف نفسها، بنصف نفسها، فليش؟ هنا لأن X X تنتمي
+
+585
+00:43:52,890 --> 00:43:55,390
+للأبسلون لأن الأبسلون equivalence relation فخلاص
+
+586
+00:43:55,390 --> 00:44:02,190
+هذا بيقدر أن X على أبسلون لا تساويفبكل بساطة فهذا
+
+587
+00:44:02,190 --> 00:44:05,650
+العنصر على الأقل و لو طلعت على الأمثلة السابقة كنا
+
+588
+00:44:05,650 --> 00:44:09,150
+نبدأ صف الواحد في واحد صف ال zero في zero انتبهوا
+
+589
+00:44:09,150 --> 00:44:12,630
+على كل الأمثلة و الحقيقة دي خاصية أهمة كل صف
+
+590
+00:44:12,630 --> 00:44:15,650
+بتحتوي على أقل عنصر اللي هو مين؟ العنصر المولد
+
+591
+00:44:15,650 --> 00:44:19,330
+للصف أو اللي بيسميه المحدد لصف determined by X
+
+592
+00:44:19,330 --> 00:44:25,670
+فهذا هو صف ال X هذا واحد Bنبدأ بعادة الصياغة
+
+593
+00:44:25,670 --> 00:44:30,470
+الصياغة جملة غائش by conditional بقول X على أبسلون
+
+594
+00:44:30,470 --> 00:44:36,070
+تقاطع Y على أبسلون أو إيه لاتساوي في if and only
+
+595
+00:44:36,070 --> 00:44:45,200
+if XY تنتمي للأبسلونجملة ثنائية الشرطية هنبرهنها
+
+596
+00:44:45,200 --> 00:44:49,100
+two parts approved هنبرهنها two parts approved
+
+597
+00:44:49,100 --> 00:44:53,180
+عشان الأرقام كتيرة ممكن مارقمش هبدأ بالاتجاه الأول
+
+598
+00:44:53,180 --> 00:45:00,380
+الاتجاه الأول اللي هو x على e تقاطع y على e لأ
+
+599
+00:45:00,380 --> 00:45:04,080
+يساوي five implies ممكن أرقم هذه ايه خليني أقول
+
+600
+00:45:04,080 --> 00:45:10,670
+واحد implies ايش x yفي ال E أو ال Epsilon كأبة ال
+
+601
+00:45:10,670 --> 00:45:13,850
+Epsilon بدنا نبدأ بالاشتراك طبعا كالعادة شوف ان
+
+602
+00:45:13,850 --> 00:45:17,790
+احنا في مبادئ اتعلمناها وينما كان جملة شرطية ببدأ
+
+603
+00:45:17,790 --> 00:45:21,010
+ان افترض ان الشرط صحيح assume أو let نفس المعنى
+
+604
+00:45:21,010 --> 00:45:25,510
+ممكن نستخدم هدول المصطلحية assume X على Epsilon
+
+605
+00:45:25,510 --> 00:45:30,160
+تقاطع Y على Epsilon لا تساوي فاإيش مطلوب؟ بدنا
+
+606
+00:45:30,160 --> 00:45:32,200
+نثبت إن الـX وY في العلاقة، يعني إنهم علاقة مع
+
+607
+00:45:32,200 --> 00:45:34,800
+بعض، اكتبيها أو ما تكتبييش، بس خليها في عقلك، هذا
+
+608
+00:45:34,800 --> 00:45:39,860
+لحد الأدنى تمام، إيش معنات إن التقاط علي SoFi في
+
+609
+00:45:39,860 --> 00:45:47,030
+علاقة عنصر مشترك؟ إيش نسميه؟Z أحسنته لجلد Z صح ليش
+
+610
+00:45:47,030 --> 00:45:50,990
+مانجموش X ال X مشهولة وال Y مشهولة فدي بت حرف جديد
+
+611
+00:45:50,990 --> 00:45:57,530
+Z فده بقول ليه there exist Z such that Z تنتمي X
+
+612
+00:45:57,530 --> 00:46:02,150
+على E تقاطع Y على E ليش هذا تعريف الفعل إذا ما
+
+613
+00:46:02,150 --> 00:46:06,550
+كتبتوش بقبلها إيش مش فارغ على الأقل في عنصر إيش
+
+614
+00:46:06,550 --> 00:46:10,970
+عملليش؟ لأن ال X مستخدمة فأنا قاعد بشتر على صف ال
+
+615
+00:46:10,970 --> 00:46:16,090
+one وفيه صف التنين تقطحهم مش فيه فيه أنصر هل
+
+616
+00:46:16,090 --> 00:46:19,850
+الواحد المشترك مش عارف؟ فيه أنصر ما ماعرف لما حط X
+
+617
+00:46:19,850 --> 00:46:22,770
+بكون أنا فرضت أن هو اللي مشترك وإيش عارفني؟ هو في
+
+618
+00:46:22,770 --> 00:46:26,670
+أنصر ما مشترك مش عارفه لازم أغير التسمية فدائما
+
+619
+00:46:26,670 --> 00:46:30,650
+إذا بنستخدم رموز إذا عدنا استخدام الرمز بنكون
+
+620
+00:46:30,650 --> 00:46:33,490
+فرضنا أنه نفس الأنصر اللي بشتر عليه لأنه استخدمته
+
+621
+00:46:33,490 --> 00:46:36,240
+نفسهوزي ما كان سؤالي معلومة ان هو نفسه بيكون
+
+622
+00:46:36,240 --> 00:46:39,120
+استخدام خاطئ وانا بيقيدني و بيخلي يصي صعوبة
+
+623
+00:46:39,120 --> 00:46:43,320
+بالبرهان و ممكن يودني في الطريق الخاطئ تمام ايش
+
+624
+00:46:43,320 --> 00:46:47,860
+ممكن اعمله؟يعني نفك إيش تقاطع نفك التقاطع نفك
+
+625
+00:46:47,860 --> 00:46:50,440
+التقاطع و احنا وان رايحين نطلع على إيش و اين
+
+626
+00:46:50,440 --> 00:46:53,220
+رايحين هذا إيش معناته إن X في صفر ال .. في صفر ال
+
+627
+00:46:53,220 --> 00:46:56,960
+.. Z في صفر ال X يعني X Z في ال .. في ال E و
+
+628
+00:46:56,960 --> 00:47:00,880
+التقاطع شو بيصير and أنا استخدمت حاجتين هستخدم
+
+629
+00:47:00,880 --> 00:47:06,140
+التقاطع و هستخدم التعريف ممكن؟ أه المرحلة بتسمح؟
+
+630
+00:47:06,140 --> 00:47:09,280
+أه بدي أستخدم التقاطع و التعريف و هذا إيش معناته
+
+631
+00:47:09,280 --> 00:47:16,080
+أن Y Z في ال E إيش دليلك؟ تعريف التقاطعوتعريف إيش؟
+
+632
+00:47:16,080 --> 00:47:21,200
+ال equivalence class مظبوط؟ أه في أول الشيء ال Z
+
+633
+00:47:21,200 --> 00:47:24,800
+مشترك في التنتين لأنه في التقاطع طب إيش معناه في
+
+634
+00:47:24,800 --> 00:47:28,440
+الصف؟ ال Z اللي علاقة مع X و ال Z في صف ال Y اللي
+
+635
+00:47:28,440 --> 00:47:33,400
+علاقة مع Y أه أنا وين رايح؟ رايح بدي إيش؟ XY في
+
+636
+00:47:33,400 --> 00:47:39,090
+الأبسلونأنا عندي xz في الأبسلون و yz في الأبسلون،
+
+637
+00:47:39,090 --> 00:47:43,730
+بدي xy في الأبسلون إيش ممكن نعمل؟ ممكن نعمل إيش؟
+
+638
+00:47:43,730 --> 00:47:48,930
+تعدي، أه، طب هدي جاهز للتعدي؟ لأ، لازم يكون نهاية
+
+639
+00:47:48,930 --> 00:47:53,310
+الأول بداية التاني، أه، فهي نهاية الأول z، بقدر
+
+640
+00:47:53,310 --> 00:47:58,710
+أخلي بداية التاني z؟ وليش؟ بقدر؟ بقدر، لأنه إيش؟
+
+641
+00:47:58,710 --> 00:48:01,690
+هدي علاقة تكافؤ، يعني فيها تماثل، واضحة؟ زي ما
+
+642
+00:48:01,690 --> 00:48:07,650
+تقول عملنا reflex فالآن هذا يؤديThere exists z, xz
+
+643
+00:48:07,650 --> 00:48:13,730
+في الأبسلون and yz في الأبسلون، ليش؟ لأن الـE هذه
+
+644
+00:48:13,730 --> 00:48:17,410
+هي symmetric لأن الـ equivalence relation، شايفين
+
+645
+00:48:17,410 --> 00:48:20,990
+المعطيات؟ أه، بدي أستخدمها، ممتاز، الآن تعدي، أه،
+
+646
+00:48:20,990 --> 00:48:27,470
+فهذا zy، صحيح، صحيح، أنا ماغيرتش أي شيء، لأZ Y
+
+647
+00:48:27,470 --> 00:48:31,310
+طبعا قال لي واحد طب ليش ما نعكس التانية كله صح لكن
+
+648
+00:48:31,310 --> 00:48:34,070
+انا ايش بقول لا في المهم انه مش نستخدم ايش الصح
+
+649
+00:48:34,070 --> 00:48:38,330
+ايش الصحيح هو المفيد اه انا وين بده اروح بده XY
+
+650
+00:48:38,330 --> 00:48:41,590
+فبده Z تكون في المصر هي اللي تروح فهذا الترتيب هو
+
+651
+00:48:41,590 --> 00:48:45,090
+المفيد ليه في ترتيبات كتير صحيحة لكن هذا الترتيب
+
+652
+00:48:45,090 --> 00:48:50,230
+المفيد فهذا يؤدي ان XY تنتمي للأبسلون وهو المطلوب
+
+653
+00:48:50,230 --> 00:48:52,650
+لأن ال E is a transit
+
+654
+00:49:01,140 --> 00:49:07,640
+واضح؟ بدنا نشوف الاتجاه التاني لأن if and only if
+
+655
+00:49:07,640 --> 00:49:14,160
+عملنا اتجاه الاتجاه
+
+656
+00:49:14,160 --> 00:49:19,360
+التاني اتنين x y في ال epsilon يؤدي ان الصفين
+
+657
+00:49:19,360 --> 00:49:22,440
+تقاطعهم لا يساوي ف
+
+658
+00:49:25,970 --> 00:49:33,590
+لا يساوي في هذا ال proof أسهل الحقيقة assume x y
+
+659
+00:49:33,590 --> 00:49:39,090
+في ال relation بدي أثبت أنه ليش التقاطع لا يساوي
+
+660
+00:49:39,090 --> 00:49:44,590
+في يعني إيش بديه بدي عنصر مشترك بدنا عنصر مشتركبدي
+
+661
+00:49:44,590 --> 00:49:49,830
+عنصر موجود في الاتنين نفكر مع بعض XY في الأبسلون
+
+662
+00:49:49,830 --> 00:49:53,910
+إيش معناته؟ إن ال X في صف ال Y و ال Y في صف ال X
+
+663
+00:49:53,910 --> 00:49:57,950
+أو ال Y في صف ال X أسهل واضحة مظبوط فده معناته إن
+
+664
+00:49:57,950 --> 00:50:05,210
+Y تنتمي لمين؟ لصف ال X طيب لو اثبتت إن ال Y في صف
+
+665
+00:50:05,210 --> 00:50:08,850
+ال Y انتهت العملية مش بدي عنصر مشترك طيب ال Y ليش
+
+666
+00:50:08,850 --> 00:50:11,990
+في صف ال Y؟ دايما قلنا صح دي لو قلتلك واحد مفتاح
+
+667
+00:50:11,990 --> 00:50:13,290
+أه أه but
+
+668
+00:50:16,830 --> 00:50:20,350
+Y موجودة في صف الـ Y ليش؟ لأن ال relation
+
+669
+00:50:20,350 --> 00:50:23,470
+reflexive لأن كل عنصر له علاقة مع نفسه فدائما كل
+
+670
+00:50:23,470 --> 00:50:27,490
+صف على الأقل بتحتوي عنصر من هو نفسه المولد تنتبهوش
+
+671
+00:50:27,490 --> 00:50:33,890
+للعلاقة is reflexive إذا الـ Y هو الموجودة في
+
+672
+00:50:33,890 --> 00:50:38,970
+التقاطع و
+
+673
+00:50:38,970 --> 00:50:44,190
+هذا معناته أنه لا يساوي فرق لا
+
+674
+00:50:44,190 --> 00:50:44,830
+يساوي
+
+675
+00:50:47,730 --> 00:50:52,030
+تمام؟ واضح؟ اه فهنا طبعا فيه انا هيكلية عامة
+
+676
+00:50:52,030 --> 00:50:56,310
+للبرهان كيف نتعامل مع ال statements وكيف نتعامل مع
+
+677
+00:50:56,310 --> 00:50:58,930
+بعض الأمور طبعا هنا مافيش علاقة سبسيط ولا في علاقة
+
+678
+00:50:58,930 --> 00:51:02,170
+تساوي مجموعات لكن في انا أشياء جديدة طبعا في
+
+679
+00:51:02,170 --> 00:51:05,730
+مجموعة لا تساوي five أو تساوي five كيف نتعامل معها
+
+680
+00:51:05,730 --> 00:51:09,150
+لكن اتعلمنا الآن بعض ال tricks في التعامل مع
+
+681
+00:51:09,150 --> 00:51:13,730
+الصفوف واهم الحوظة اللي لاحظناها ان كل صف غير فارغ
+
+682
+00:51:13,730 --> 00:51:17,610
+لأنه بحتوي على العنصر المولد للصفالعنصر المولد
+
+683
+00:51:17,610 --> 00:51:21,290
+للصف فدايما صف فاطمة مين بيحتوي علاقات فاطمة
+
+684
+00:51:21,290 --> 00:51:23,970
+بيحتوي فاطمة نوقف هنا ان شاء الله المرة دي يابان
+
+685
+00:51:23,970 --> 00:51:24,190
+كامة
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/QuyDnx6y5Ko_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/QuyDnx6y5Ko_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..d3f8e1ebfb3c81273666db52564f20435b7dcfdb
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/QuyDnx6y5Ko_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3527, "start": 20.27, "end": 35.27, "text": "بسم الله الرحمن الرحيم هنواصل مع دراسة العلاقات ال relations وإن شاء الله في هذا section هندخل من زاوية جديدة ونستكمل طبعا استكمال طبعا عنوان partitions التجزيئات", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8032, 1863, 2407, 33546, 1211, 20449, 11778, 23557, 3794, 3660, 18863, 15040, 4587, 9307, 2423, 2299, 4032, 28814, 1863, 13412, 16606, 21984, 8978, 23758, 3541, 8032, 41260, 9778, 1211, 9154, 30767, 995, 2407, 10632, 10874, 16254, 41891, 4032, 1863, 14851, 24793, 1211, 23032, 3555, 3615, 995, 44713, 24793, 6027, 23032, 3555, 3615, 995, 18871, 2407, 7649, 644, 2451, 16712, 7435, 11622, 1829, 19986, 9307], "avg_logprob": -0.11507601552718394, "compression_ratio": 1.5632183908045978, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 20.27, "end": 20.57, "word": "بسم", "probability": 0.86669921875}, {"start": 20.57, "end": 20.71, "word": " الله", "probability": 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"probability": 0.8802897135416666}], "temperature": 1.0}, {"id": 2, "seek": 6520, "start": 35.72, "end": 65.2, "text": "من اللي هو كلمة part partitions اللي هي تجزيء part جزء partition تجزيء عملية التجزيء and equivalence relations طبعا المصطلح اللي هو equivalence relation مر علينا العلاقات التكافؤ فبهذا ال section ان شاء الله هنستكمل دراسة ال equivalence relations مع المفهوم الجديد وهو التجزيء فطبعا احنا هنبدأ بالتعريف ما هو ال partition المصطلح الجديد بعدين ايش علاقة هذا المصطلح الجديد مع ال equivalence relations كما هي نص العنوان", "tokens": [27842, 13672, 1829, 31439, 9122, 19528, 3660, 644, 644, 2451, 13672, 1829, 39896, 6055, 7435, 11622, 1829, 38207, 644, 10874, 11622, 38207, 24808, 6055, 7435, 11622, 1829, 38207, 6225, 42213, 10632, 16712, 7435, 11622, 1829, 38207, 293, 9052, 655, 2299, 23032, 3555, 3615, 995, 9673, 9381, 9566, 1211, 5016, 13672, 1829, 31439, 9052, 655, 9721, 3714, 2288, 25894, 8315, 18863, 15040, 4587, 9307, 16712, 4117, 31845, 33604, 6156, 3555, 3224, 15730, 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{"start": 450.66, "end": 451.4, "word": " الشرط", "probability": 0.93017578125}, {"start": 451.4, "end": 451.86, "word": " الأول", "probability": 0.86376953125}, {"start": 451.86, "end": 452.06, "word": " مش", "probability": 0.939453125}, {"start": 452.06, "end": 452.6, "word": " مرقم", "probability": 0.958984375}, {"start": 452.6, "end": 452.86, "word": " وانا", "probability": 0.7025553385416666}, {"start": 452.86, "end": 453.02, "word": " يمكن", "probability": 0.685791015625}, {"start": 453.02, "end": 453.48, "word": " حاطيته", "probability": 0.8480224609375}, {"start": 453.48, "end": 453.98, "word": " طواش", "probability": 0.3291829427083333}, {"start": 453.98, "end": 454.46, "word": " بالخط", "probability": 0.8912760416666666}, {"start": 454.46, "end": 454.94, "word": " الأحمر", "probability": 0.9586588541666666}, {"start": 454.94, "end": 455.58, "word": " حاولت", "probability": 0.9530029296875}, {"start": 455.58, "end": 456.3, "word": " اوضحه", "probability": 0.8685546875}, {"start": 456.3, "end": 456.86, "word": " non", "probability": 0.480712890625}, {"start": 456.86, "end": 457.44, "word": "-empty", "probability": 0.7991536458333334}, {"start": 457.44, "end": 457.98, "word": " subsets", "probability": 0.92919921875}, {"start": 457.98, "end": 458.54, "word": " طيب", "probability": 0.8693033854166666}, {"start": 458.54, "end": 458.78, "word": " كيف", "probability": 0.87548828125}, {"start": 458.78, "end": 458.98, "word": " بدنا", "probability": 0.773193359375}, {"start": 458.98, "end": 459.52, "word": " نبدأ", "probability": 0.96044921875}, {"start": 459.52, "end": 459.76, "word": " فيه", "probability": 0.971923828125}, {"start": 459.76, "end": 459.96, "word": " هذا", "probability": 0.432861328125}, {"start": 459.96, "end": 460.24, "word": " الشرط", "probability": 0.9637044270833334}, {"start": 460.24, "end": 460.46, "word": " رغم", "probability": 0.9480794270833334}, {"start": 460.46, "end": 460.64, "word": " مش", "probability": 0.58984375}, {"start": 460.64, "end": 461.06, "word": " مرقم", "probability": 0.9859619140625}, {"start": 461.06, "end": 461.28, "word": " بدنا", "probability": 0.908447265625}, {"start": 461.28, "end": 461.52, "word": " نبدأ", "probability": 0.99169921875}, {"start": 461.52, "end": 461.86, "word": " فيه", "probability": 0.9755859375}, {"start": 461.86, "end": 462.24, "word": " طبعا", "probability": 0.9412841796875}, {"start": 462.24, "end": 462.4, "word": " ما", "probability": 0.609375}, {"start": 462.4, "end": 462.58, "word": " زال", "probability": 0.986083984375}, {"start": 462.58, "end": 462.72, "word": " هو", "probability": 0.9482421875}, {"start": 462.72, "end": 463.12, "word": " مرقم", "probability": 0.9912109375}, {"start": 463.12, "end": 463.4, "word": " واحد", "probability": 0.837890625}, {"start": 463.4, "end": 463.86, "word": " واتنين", "probability": 0.84136962890625}, {"start": 463.86, "end": 464.44, "word": " خلينا", "probability": 0.7716064453125}, {"start": 464.44, "end": 464.68, "word": " نبدأ", "probability": 0.9762369791666666}, {"start": 464.68, "end": 465.0, "word": " بشرط", "probability": 0.84716796875}, {"start": 465.0, "end": 465.18, "word": " هذا", "probability": 0.85009765625}, {"start": 465.18, "end": 465.68, "word": " مسبق", "probability": 0.9129231770833334}, {"start": 465.68, "end": 465.84, "word": " ان", "probability": 0.4541015625}, {"start": 465.84, "end": 466.18, "word": " رقمه", "probability": 0.9705810546875}, {"start": 466.18, "end": 466.44, "word": " صفر", "probability": 0.9812825520833334}, {"start": 466.44, "end": 467.12, "word": " فأول", "probability": 0.958984375}, {"start": 467.12, "end": 467.42, "word": " شرط", "probability": 0.9832356770833334}, {"start": 467.42, "end": 467.66, "word": " بدي", "probability": 0.67919921875}, {"start": 467.66, "end": 468.24, "word": " أثبته", "probability": 0.9476318359375}, {"start": 468.24, "end": 468.96, "word": " ايه", "probability": 0.82958984375}, {"start": 468.96, "end": 469.12, "word": " كيف", "probability": 0.906494140625}, {"start": 469.12, "end": 469.32, "word": " بدنا", "probability": 0.93994140625}, {"start": 469.32, "end": 469.88, "word": " نصيغه", "probability": 0.96943359375}, {"start": 469.88, "end": 470.8, "word": " بقولي", "probability": 0.701171875}, {"start": 470.8, "end": 471.88, "word": " الأيزاء", "probability": 0.7403564453125}, {"start": 471.88, "end": 472.2, "word": " non", "probability": 0.91064453125}, {"start": 472.2, "end": 472.78, "word": "-empty", "probability": 0.9186197916666666}, {"start": 472.78, "end": 473.14, "word": " فانا", "probability": 0.9513346354166666}, {"start": 473.14, "end": 473.54, "word": " بدي", "probability": 0.778076171875}], "temperature": 1.0}, {"id": 22, "seek": 48105, "start": 473.93, "end": 481.05, "text": "for all a أي جزء في ال partition ايش يكون غير فارق ممكن اصيغة بهذا الشكل", "tokens": [2994, 439, 257, 36632, 10874, 11622, 38207, 8978, 2423, 24808, 1975, 1829, 8592, 7251, 30544, 32771, 13546, 6156, 9640, 4587, 3714, 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479.03, "word": " غير", "probability": 0.90869140625}, {"start": 479.03, "end": 479.49, "word": " فارق", "probability": 0.731201171875}, {"start": 479.49, "end": 480.07, "word": " ممكن", "probability": 0.90283203125}, {"start": 480.07, "end": 480.53, "word": " اصيغة", "probability": 0.778857421875}, {"start": 480.53, "end": 480.75, "word": " بهذا", "probability": 0.655029296875}, {"start": 480.75, "end": 481.05, "word": " الشكل", "probability": 0.99462890625}], "temperature": 1.0}, {"id": 23, "seek": 51006, "start": 481.7, "end": 510.06, "text": "فده الشرق صفر مش موجود في التعريف مش موجود في التعريف المرقم لكنه موجود في الصياغ في الجملة الموجودة بيقوللي a partition is a set of non-empty subsets اه فدي بعلمنا القراعة دقيقة لكل كلمة اللي همعنى فأول شي بدي جميع الأجزاء هي الأجزاء مين الأجزاء؟ قولنا هيهم ايه؟ كل جزء اي common غير فارق تقوى كتبنا تقوى كتبنا اه تمام نشوف مين الأجزاء؟ تلاتة في واحد فيهم فارق؟ لأ فنكتبله", "tokens": [5172, 3215, 3224, 25124, 2288, 4587, 20328, 5172, 2288, 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"end": 489.68, "word": " partition", "probability": 0.7607421875}, {"start": 489.68, "end": 490.54, "word": " is", "probability": 0.9013671875}, {"start": 490.54, "end": 491.02, "word": " a", "probability": 0.9130859375}, {"start": 491.02, "end": 491.36, "word": " set", "probability": 0.94140625}, {"start": 491.36, "end": 491.72, "word": " of", "probability": 0.970703125}, {"start": 491.72, "end": 492.12, "word": " non", "probability": 0.755859375}, {"start": 492.12, "end": 492.72, "word": "-empty", "probability": 0.7985026041666666}, {"start": 492.72, "end": 493.24, "word": " subsets", "probability": 0.97119140625}, {"start": 493.24, "end": 493.66, "word": " اه", "probability": 0.630126953125}, {"start": 493.66, "end": 493.84, "word": " فدي", "probability": 0.6185302734375}, {"start": 493.84, "end": 494.22, "word": " بعلمنا", "probability": 0.9236653645833334}, {"start": 494.22, "end": 494.6, "word": " القراعة", "probability": 0.8797200520833334}, {"start": 494.6, "end": 495.08, "word": " دقيقة", "probability": 0.8722330729166666}, {"start": 495.08, "end": 495.38, "word": " لكل", "probability": 0.97705078125}, {"start": 495.38, "end": 495.9, "word": " كلمة", "probability": 0.9768880208333334}, {"start": 495.9, "end": 496.18, "word": " اللي", "probability": 0.8701171875}, {"start": 496.18, "end": 496.72, "word": " همعنى", "probability": 0.732373046875}, {"start": 496.72, "end": 497.24, "word": " فأول", "probability": 0.90576171875}, {"start": 497.24, "end": 497.4, "word": " شي", "probability": 0.626953125}, {"start": 497.4, "end": 497.68, "word": " بدي", "probability": 0.7158203125}, {"start": 497.68, "end": 498.04, "word": " جميع", "probability": 0.9890950520833334}, {"start": 498.04, "end": 498.7, "word": " الأجزاء", "probability": 0.9197998046875}, {"start": 498.7, "end": 499.04, "word": " هي", "probability": 0.2445068359375}, {"start": 499.04, "end": 499.46, "word": " الأجزاء", "probability": 0.9627685546875}, {"start": 499.46, "end": 499.6, "word": " مين", "probability": 0.797119140625}, {"start": 499.6, "end": 500.32, "word": " الأجزاء؟", "probability": 0.87841796875}, {"start": 500.32, "end": 500.54, "word": " قولنا", "probability": 0.6453450520833334}, {"start": 500.54, "end": 500.8, "word": " هيهم", "probability": 0.789794921875}, {"start": 500.8, "end": 501.4, "word": " ايه؟", "probability": 0.793212890625}, {"start": 501.4, "end": 501.6, "word": " كل", "probability": 0.87548828125}, {"start": 501.6, "end": 501.9, "word": " جزء", "probability": 0.94873046875}, {"start": 501.9, "end": 502.04, "word": " اي", "probability": 0.6650390625}, {"start": 502.04, "end": 502.42, "word": " common", "probability": 0.390625}, {"start": 502.42, "end": 503.06, "word": " غير", "probability": 0.97705078125}, {"start": 503.06, "end": 503.42, "word": " فارق", "probability": 0.8728841145833334}, {"start": 503.42, "end": 503.66, "word": " تقوى", "probability": 0.70556640625}, {"start": 503.66, "end": 504.12, "word": " كتبنا", "probability": 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"end": 593.41, "word": " مع", "probability": 0.646484375}, {"start": 593.41, "end": 593.81, "word": " الأربعة", "probability": 0.9666341145833334}, {"start": 593.81, "end": 594.37, "word": " الآن", "probability": 0.6593017578125}, {"start": 594.37, "end": 594.73, "word": " اتنين", "probability": 0.90234375}, {"start": 594.73, "end": 595.09, "word": " تلاتة", "probability": 0.990234375}, {"start": 595.09, "end": 595.49, "word": " نفحصها", "probability": 0.97080078125}, {"start": 595.49, "end": 595.61, "word": " مع", "probability": 0.99169921875}, {"start": 595.61, "end": 595.89, "word": " مين", "probability": 0.78564453125}, {"start": 595.89, "end": 596.47, "word": " مع", "probability": 0.57080078125}, {"start": 596.47, "end": 596.99, "word": " الأربعة", "probability": 0.9807942708333334}, {"start": 596.99, "end": 599.15, "word": " أفحصها", "probability": 0.834326171875}, {"start": 599.15, "end": 599.27, "word": " مع", "probability": 0.98095703125}, {"start": 599.27, "end": 599.57, "word": " الأول", "probability": 0.985595703125}, {"start": 599.57, "end": 599.89, "word": " لأ", "probability": 0.8564453125}, {"start": 599.89, "end": 600.31, "word": " ليش", "probability": 0.764404296875}, {"start": 600.31, "end": 600.45, "word": " لأن", "probability": 0.710693359375}, {"start": 600.45, "end": 600.87, "word": " التقاطه", "probability": 0.73388671875}, {"start": 600.87, "end": 601.39, "word": " عبدالي", "probability": 0.7938232421875}, {"start": 601.39, "end": 601.71, "word": " لأن", "probability": 0.875732421875}, {"start": 601.71, "end": 602.17, "word": " التقاطه", "probability": 0.9893798828125}, {"start": 602.17, "end": 602.69, "word": " عبدالي", "probability": 0.991943359375}, {"start": 602.69, "end": 603.41, "word": " فنفحص", "probability": 0.97802734375}, {"start": 603.41, "end": 604.25, "word": " الآن", "probability": 0.83544921875}], "temperature": 1.0}, {"id": 28, "seek": 62761, "start": 604.41, "end": 627.61, "text": "إتنين تلاتة تقاطع الأربعة بيساوي فيا ولا بيساويش بيساوي إذا فعلا وزي ما هي الصورة واضحة بس أنا بكتب كل جزئين منفصلين مافيش فينهم عناصر مشتركة this joins زي ما سمناه فده الشرط التاني الشرط التالت والأخير اللي هو رقم اتنين الاتحاد بالدين المجموعة الأصلية اتحاد الأجزاء بالدين المجموعة الأصلية", "tokens": [28814, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 6055, 4587, 41193, 3615, 16247, 25513, 27884, 4724, 1829, 3794, 995, 45865, 8978, 995, 49429, 4724, 1829, 3794, 995, 45865, 8592, 4724, 1829, 3794, 995, 45865, 11933, 15730, 6156, 3615, 15040, 4032, 11622, 1829, 19446, 39896, 31767, 13063, 3660, 4032, 46958, 5016, 3660, 4724, 3794, 41850, 4724, 4117, 2655, 3555, 28242, 10874, 11622, 19986, 9957, 9154, 5172, 36520, 9957, 19446, 41185, 8592, 8978, 1863, 16095, 18871, 33546, 2288, 37893, 2655, 31747, 3660, 341, 24397, 30767, 1829, 19446, 8608, 2304, 8315, 3224, 6156, 3215, 3224, 25124, 2288, 9566, 16712, 7649, 1829, 25124, 2288, 9566, 16712, 6027, 2655, 16070, 10721, 9778, 13546, 13672, 1829, 31439, 12602, 4587, 2304, 1975, 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{"start": 618.23, "end": 618.59, "word": " الشرط", "probability": 0.9479166666666666}, {"start": 618.59, "end": 619.07, "word": " التاني", "probability": 0.94384765625}, {"start": 619.07, "end": 619.95, "word": " الشرط", "probability": 0.9669596354166666}, {"start": 619.95, "end": 620.47, "word": " التالت", "probability": 0.9510091145833334}, {"start": 620.47, "end": 620.91, "word": " والأخير", "probability": 0.76385498046875}, {"start": 620.91, "end": 621.03, "word": " اللي", "probability": 0.9208984375}, {"start": 621.03, "end": 621.19, "word": " هو", "probability": 0.9912109375}, {"start": 621.19, "end": 621.49, "word": " رقم", "probability": 0.9666341145833334}, {"start": 621.49, "end": 621.97, "word": " اتنين", "probability": 0.9014892578125}, {"start": 621.97, "end": 622.81, "word": " الاتحاد", "probability": 0.83587646484375}, {"start": 622.81, "end": 623.19, "word": " بالدين", "probability": 0.9322916666666666}, {"start": 623.19, "end": 623.65, "word": " المجموعة", "probability": 0.94501953125}, {"start": 623.65, "end": 624.31, "word": " الأصلية", "probability": 0.7955729166666666}, {"start": 624.31, "end": 625.21, "word": " اتحاد", "probability": 0.9688720703125}, {"start": 625.21, "end": 625.99, "word": " الأجزاء", "probability": 0.9844970703125}, {"start": 625.99, "end": 626.51, "word": " بالدين", "probability": 0.9775390625}, {"start": 626.51, "end": 626.95, "word": " المجموعة", "probability": 0.97333984375}, {"start": 626.95, "end": 627.61, "word": " الأصلية", "probability": 0.90576171875}], "temperature": 1.0}, {"id": 29, "seek": 64921, "start": 628.07, "end": 649.21, "text": "اتنين اتحاد ال a على ال partition هذا الرمز اللي تعلمناه في section 2-6 اللي هو على الفهم اللي سمناه بيساو اكس نفحص اه كان جزء عندي تلاتة واحد خمسة يعني اتحاد مين اتنين تلاتة اتحاد الأربع بيساو اكس ولا بيساويش", "tokens": [9307, 1863, 9957, 1975, 2655, 5016, 18513, 2423, 257, 15844, 2423, 24808, 23758, 34892, 2304, 11622, 13672, 1829, 37279, 19528, 8315, 3224, 8978, 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0.930908203125}, {"start": 640.77, "end": 641.71, "word": " واحد", "probability": 0.861328125}, {"start": 641.71, "end": 642.21, "word": " خمسة", "probability": 0.96337890625}, {"start": 642.21, "end": 642.55, "word": " يعني", "probability": 0.879150390625}, {"start": 642.55, "end": 643.49, "word": " اتحاد", "probability": 0.9847412109375}, {"start": 643.49, "end": 643.83, "word": " مين", "probability": 0.77099609375}, {"start": 643.83, "end": 644.83, "word": " اتنين", "probability": 0.8570556640625}, {"start": 644.83, "end": 645.75, "word": " تلاتة", "probability": 0.9718017578125}, {"start": 645.75, "end": 646.53, "word": " اتحاد", "probability": 0.99072265625}, {"start": 646.53, "end": 647.63, "word": " الأربع", "probability": 0.8435872395833334}, {"start": 647.63, "end": 648.31, "word": " بيساو", "probability": 0.94013671875}, {"start": 648.31, "end": 648.49, "word": " اكس", "probability": 0.9563802083333334}, {"start": 648.49, "end": 648.61, "word": " ولا", "probability": 0.8193359375}, {"start": 648.61, "end": 649.21, "word": " بيساويش", "probability": 0.9064127604166666}], "temperature": 1.0}, {"id": 30, "seek": 66551, "start": 650.85, "end": 665.51, "text": "أربعة خمسة و يساوي X ففعلا صحيح فإذا التلات شروط اتحققت إذا فعلا هذا يعتبر partition Thus B is a partition طبعا of X لل X المعطية", "tokens": [10721, 25513, 27884, 16490, 2304, 3794, 3660, 4032, 7251, 3794, 995, 45865, 1783, 6156, 5172, 3615, 15040, 20328, 5016, 1829, 5016, 6156, 28814, 15730, 16712, 1211, 9307, 13412, 32887, 9566, 1975, 2655, 5016, 4587, 38149, 11933, 15730, 6156, 3615, 15040, 23758, 7251, 34268, 26890, 24808, 13827, 363, 307, 257, 24808, 23032, 3555, 3615, 995, 295, 1783, 24976, 1783, 9673, 3615, 9566, 10632], "avg_logprob": -0.24342758551476493, "compression_ratio": 1.348993288590604, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 650.85, "end": 651.39, "word": "أربعة", "probability": 0.7011311848958334}, {"start": 651.39, "end": 651.95, "word": " خمسة", "probability": 0.9434814453125}, {"start": 651.95, "end": 652.23, "word": " و", "probability": 0.634765625}, {"start": 652.23, "end": 652.65, "word": " يساوي", "probability": 0.7841796875}, {"start": 652.65, "end": 652.81, "word": " X", "probability": 0.65673828125}, {"start": 652.81, "end": 653.23, "word": " ففعلا", "probability": 0.7850341796875}, {"start": 653.23, "end": 653.91, "word": " صحيح", "probability": 0.801025390625}, {"start": 653.91, "end": 654.37, "word": " فإذا", "probability": 0.89306640625}, {"start": 654.37, "end": 654.77, "word": " التلات", "probability": 0.8582356770833334}, {"start": 654.77, "end": 655.07, "word": " شروط", "probability": 0.8986002604166666}, {"start": 655.07, "end": 655.83, "word": " اتحققت", "probability": 0.88076171875}, {"start": 655.83, "end": 656.27, "word": " إذا", "probability": 0.7177734375}, {"start": 656.27, "end": 656.67, "word": " فعلا", "probability": 0.9267578125}, {"start": 656.67, "end": 656.85, "word": " هذا", "probability": 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فخلصنا من ال use الاول من المطلوب الان نيجي لا ياش بدنا نحسب زد على العلاقة نحط عنوان فرق ايه فبدنا نحسب هذا ايش بيساوي طبعا هذا طبقا للتعريف ايش بيساوي", "tokens": [4419, 399, 46811, 10943, 6156, 3224, 24192, 25124, 32887, 9566, 4032, 9307, 3615, 23328, 8315, 4032, 44945, 4117, 2655, 3555, 16095, 28242, 3714, 25720, 16712, 5172, 33546, 26895, 39894, 46456, 46538, 9154, 50113, 6027, 32767, 12984, 6027, 44381, 25124, 32887, 9566, 36764, 24401, 3660, 6156, 9778, 1211, 9381, 8315, 9154, 2423, 764, 42963, 12610, 9154, 9673, 9566, 1211, 37746, 2423, 7649, 8717, 1829, 7435, 1829, 20193, 7251, 33599, 47525, 8315, 8717, 5016, 35457, 30767, 3215, 15844, 18863, 15040, 28671, 8717, 5016, 9566, 18871, 2407, 7649, 6156, 2288, 4587, 1975, 1829, 3224, 6156, 44510, 8315, 8717, 5016, 35457, 23758, 1975, 1829, 8592, 4724, 1829, 3794, 995, 45865, 23032, 3555, 3615, 995, 23758, 23032, 3555, 4587, 995, 24976, 2655, 3615, 16572, 5172, 1975, 1829, 8592, 4724, 1829, 3794, 995, 45865], "avg_logprob": 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"no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 3047.7299999999996, "end": 3048.49, "word": "تمام؟", "probability": 0.7854817708333334}, {"start": 3048.49, "end": 3049.25, "word": " واضح؟", "probability": 0.9261474609375}, {"start": 3049.25, "end": 3049.41, "word": " اه", "probability": 0.742919921875}, {"start": 3049.41, "end": 3049.71, "word": " فهنا", "probability": 0.8321940104166666}, {"start": 3049.71, "end": 3050.51, "word": " طبعا", "probability": 0.9603271484375}, {"start": 3050.51, "end": 3050.99, "word": " فيه", "probability": 0.5560302734375}, {"start": 3050.99, "end": 3051.15, "word": " انا", "probability": 0.6278076171875}, {"start": 3051.15, "end": 3051.71, "word": " هيكلية", "probability": 0.8785807291666666}, {"start": 3051.71, "end": 3052.03, "word": " عامة", "probability": 0.99267578125}, {"start": 3052.03, "end": 3052.67, "word": " للبرهان", "probability": 0.9381103515625}, {"start": 3052.67, "end": 3053.21, "word": " كيف", "probability": 0.938232421875}, {"start": 3053.21, "end": 3053.59, "word": " نتعامل", "probability": 0.9875}, {"start": 3053.59, "end": 3053.79, "word": " مع", "probability": 0.75439453125}, {"start": 3053.79, "end": 3053.91, "word": " ال", "probability": 0.8994140625}, {"start": 3053.91, "end": 3054.55, "word": " statements", "probability": 0.91455078125}, {"start": 3054.55, "end": 3055.23, "word": " وكيف", "probability": 0.9099934895833334}, {"start": 3055.23, "end": 3055.87, "word": " نتعامل", "probability": 0.99775390625}, {"start": 3055.87, "end": 3056.31, "word": " مع", "probability": 0.994140625}, {"start": 3056.31, "end": 3056.59, "word": " بعض", "probability": 0.992919921875}, {"start": 3056.59, "end": 3056.99, "word": " الأمور", "probability": 0.9264322916666666}, {"start": 3056.99, "end": 3057.23, "word": " طبعا", "probability": 0.9771728515625}, {"start": 3057.23, "end": 3057.35, "word": " هنا", "probability": 0.9052734375}, {"start": 3057.35, "end": 3057.55, "word": " مافيش", "probability": 0.79443359375}, {"start": 3057.55, "end": 3057.81, "word": " علاقة", "probability": 0.98681640625}, {"start": 3057.81, "end": 3058.31, "word": " سبسيط", "probability": 0.7892578125}, {"start": 3058.31, "end": 3058.49, "word": " ولا", "probability": 0.90087890625}, {"start": 3058.49, "end": 3058.63, "word": " في", "probability": 0.86328125}, {"start": 3058.63, "end": 3058.93, "word": " علاقة", "probability": 0.94580078125}, {"start": 3058.93, "end": 3059.35, "word": " تساوي", "probability": 0.9599609375}, {"start": 3059.35, "end": 3060.03, "word": " مجموعات", "probability": 0.98388671875}, {"start": 3060.03, "end": 3060.51, "word": " لكن", "probability": 0.8955078125}, {"start": 3060.51, "end": 3060.73, "word": " في", "probability": 0.953125}, {"start": 3060.73, "end": 3060.97, "word": " انا", "probability": 0.6375732421875}, {"start": 3060.97, "end": 3061.33, "word": " أشياء", "probability": 0.943115234375}, {"start": 3061.33, "end": 3061.69, "word": " جديدة", "probability": 0.8826497395833334}, {"start": 3061.69, "end": 3061.99, "word": " طبعا", "probability": 0.966064453125}, {"start": 3061.99, "end": 3062.17, "word": " في", "probability": 0.9453125}, {"start": 3062.17, "end": 3063.07, "word": " مجموعة", "probability": 0.9423828125}, {"start": 3063.07, "end": 3063.19, "word": " لا", "probability": 0.4697265625}, {"start": 3063.19, "end": 3063.57, "word": " تساوي", "probability": 0.9521484375}, {"start": 3063.57, "end": 3063.87, "word": " five", "probability": 0.42041015625}, {"start": 3063.87, "end": 3064.03, "word": " أو", "probability": 0.59765625}, {"start": 3064.03, "end": 3064.41, "word": " تساوي", "probability": 0.980712890625}, {"start": 3064.41, "end": 3064.69, "word": " five", "probability": 0.94091796875}, {"start": 3064.69, "end": 3064.87, "word": " كيف", "probability": 0.89599609375}, {"start": 3064.87, "end": 3065.29, "word": " نتعامل", "probability": 0.996875}, {"start": 3065.29, "end": 3065.73, "word": " معها", "probability": 0.96875}, {"start": 3065.73, "end": 3066.25, "word": " لكن", "probability": 0.89208984375}, {"start": 3066.25, "end": 3066.81, "word": " اتعلمنا", "probability": 0.90859375}, {"start": 3066.81, "end": 3067.17, "word": " الآن", "probability": 0.76953125}, {"start": 3067.17, "end": 3067.79, "word": " بعض", "probability": 0.95703125}, {"start": 3067.79, "end": 3067.91, "word": " ال", "probability": 0.86279296875}, {"start": 3067.91, "end": 3068.21, "word": " tricks", "probability": 0.34619140625}, {"start": 3068.21, "end": 3068.51, "word": " في", "probability": 0.828125}, {"start": 3068.51, "end": 3068.99, "word": " التعامل", "probability": 0.9964599609375}, {"start": 3068.99, "end": 3069.15, "word": " مع", "probability": 0.99560546875}, {"start": 3069.15, "end": 3069.73, "word": " الصفوف", "probability": 0.9798177083333334}, {"start": 3069.73, "end": 3070.49, "word": " واهم", "probability": 0.650146484375}, {"start": 3070.49, "end": 3070.95, "word": " الحوظة", "probability": 0.834716796875}, {"start": 3070.95, "end": 3071.01, "word": " اللي", "probability": 0.7025146484375}, {"start": 3071.01, "end": 3071.73, "word": " لاحظناها", "probability": 0.822509765625}, {"start": 3071.73, "end": 3072.13, "word": " ان", "probability": 0.65478515625}, {"start": 3072.13, "end": 3072.47, "word": " كل", "probability": 0.92431640625}, {"start": 3072.47, "end": 3072.85, "word": " صف", "probability": 0.98828125}, {"start": 3072.85, "end": 3073.27, "word": " غير", "probability": 0.937744140625}, {"start": 3073.27, "end": 3073.73, "word": " فارغ", "probability": 0.98828125}, {"start": 3073.73, "end": 3074.17, "word": " لأنه", "probability": 0.8779296875}, {"start": 3074.17, "end": 3074.47, "word": " بحتوي", "probability": 0.7916666666666666}, {"start": 3074.47, "end": 3074.65, "word": " على", "probability": 0.9208984375}, {"start": 3074.65, "end": 3075.19, "word": " العنصر", "probability": 0.81243896484375}, {"start": 3075.19, "end": 3075.85, "word": " المولد", "probability": 0.9786783854166666}, {"start": 3075.85, "end": 3076.29, "word": " للصف", "probability": 0.9778645833333334}], "temperature": 1.0}, {"id": 133, "seek": 308419, "start": 3076.43, "end": 3084.19, "text": "العنصر المولد للصف فدايما صف فاطمة مين بيحتوي علاقات فاطمة بيحتوي فاطمة نوقف هنا ان شاء الله المرة دي يابان كامة", "tokens": [6027, 3615, 1863, 9381, 2288, 9673, 12610, 3215, 24976, 9381, 5172, 6156, 28259, 1829, 15042, 20328, 5172, 6156, 41193, 46007, 3714, 9957, 4724, 1829, 33753, 45865, 11203, 995, 4587, 9307, 6156, 41193, 46007, 4724, 1829, 33753, 45865, 6156, 41193, 46007, 8717, 30543, 5172, 34105, 16472, 13412, 16606, 21984, 9673, 25720, 11778, 1829, 7251, 16758, 7649, 9122, 10943, 3660], "avg_logprob": -0.3233580407449755, "compression_ratio": 1.6451612903225807, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 3076.43, "end": 3076.99, "word": "العنصر", "probability": 0.799853515625}, {"start": 3076.99, "end": 3077.61, "word": " المولد", "probability": 0.9505208333333334}, {"start": 3077.61, "end": 3078.25, "word": " للصف", "probability": 0.9646809895833334}, {"start": 3078.25, "end": 3078.93, "word": " فدايما", "probability": 0.575347900390625}, {"start": 3078.93, "end": 3079.53, "word": " صف", "probability": 0.952392578125}, {"start": 3079.53, "end": 3079.87, "word": " فاطمة", "probability": 0.93994140625}, {"start": 3079.87, "end": 3080.07, "word": " مين", "probability": 0.888916015625}, {"start": 3080.07, "end": 3080.37, "word": " بيحتوي", "probability": 0.843017578125}, {"start": 3080.37, "end": 3080.81, "word": " علاقات", "probability": 0.73931884765625}, {"start": 3080.81, "end": 3081.29, "word": " فاطمة", "probability": 0.9191080729166666}, {"start": 3081.29, "end": 3081.97, "word": " بيحتوي", "probability": 0.7177734375}, {"start": 3081.97, "end": 3082.45, "word": " فاطمة", "probability": 0.9342447916666666}, {"start": 3082.45, "end": 3083.07, "word": " نوقف", "probability": 0.7342122395833334}, {"start": 3083.07, "end": 3083.21, "word": " هنا", "probability": 0.467041015625}, {"start": 3083.21, "end": 3083.33, "word": " ان", "probability": 0.478759765625}, {"start": 3083.33, "end": 3083.45, "word": " شاء", "probability": 0.970458984375}, {"start": 3083.45, "end": 3083.49, "word": " الله", "probability": 0.9658203125}, {"start": 3083.49, "end": 3083.69, "word": " المرة", "probability": 0.6102294921875}, {"start": 3083.69, "end": 3083.81, "word": " دي", "probability": 0.58856201171875}, {"start": 3083.81, "end": 3083.97, "word": " يابان", "probability": 0.5720621744791666}, {"start": 3083.97, "end": 3084.19, "word": " كامة", "probability": 0.76220703125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3084.1440625, "duration_after_vad": 2947.3387499999913}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/R-1opTyixLc.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/R-1opTyixLc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5dccf420c2f56c92e6bedbfe864fac4545b84267
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/R-1opTyixLc.srt
@@ -0,0 +1,2154 @@
+1
+00:00:20,430 --> 00:00:23,890
+بسم الله الرحمن الرحيم في المحاضرة الأخيرة كنا
+
+2
+00:00:23,890 --> 00:00:28,230
+بنتحدث عن طبعا شرحنا ال partition كيف بنجزّئ
+
+3
+00:00:28,230 --> 00:00:32,770
+المجموعة في تلت شروط لازم كل جزء ما يكونش فارغ وكل
+
+4
+00:00:32,770 --> 00:00:36,670
+جزئين يا إما بيكونوا كل عناصرهم مشتركة أي متطابقين
+
+5
+00:00:36,670 --> 00:00:42,240
+أو اللي هو ما disjoint ولا عنصر مشترك، ال Partition 
+
+6
+00:00:42,240 --> 00:00:46,860
+فيه تلت شروط، ولا جزء يكون فارغ، كل جزءين يا إما
+
+7
+00:00:46,860 --> 00:00:50,980
+متطابقين أو disjoint، مافيش ولا عنصر مشترك بينهم،
+
+8
+00:00:50,980 --> 00:00:54,280
+أيضًا اتحاد كل الأجزاء بيدّينا كل ال X، هذا
+
+9
+00:00:54,280 --> 00:00:59,280
+النقطة وضحناها، أيضًا عرفنا صف التكافؤ، هو عبارة
+
+10
+00:00:59,280 --> 00:01:02,380
+عن مجموعة العناصر اللي لهم علاقة، يعني صف التكافؤ
+
+11
+00:01:02,380 --> 00:01:05,140
+لل X هي عبارة عن جميع العناصر اللي لهم علاقة مع ال
+
+12
+00:01:05,140 --> 00:01:08,540
+X، اه طبعًا شوفنا بعض الأمثلة الآن بدنا نستمر مع اللي
+
+13
+00:01:08,540 --> 00:01:12,160
+هو صف التكافؤ و نشوف خواص عامة لصف التكافؤ و يمكن
+
+14
+00:01:12,160 --> 00:01:15,620
+نلاحظنا بعض الأمور المشتركة في الأمثلة لكن هل هذا
+
+15
+00:01:15,620 --> 00:01:21,180
+الملاحظات عامة ولا كانت خاصة بالأمثلة نشوف مع
+
+16
+00:01:21,180 --> 00:01:24,920
+النظرية، فنظرية رقم تلاتة تلاتة أي النظرية الثالثة
+
+17
+00:01:24,920 --> 00:01:28,580
+في chapter تلاتة Properties of Equivalent Classes
+
+18
+00:01:29,510 --> 00:01:33,910
+برهنها .. جيد .. جيد .. اه، فطبعا هنا طبعا الخواص 
+
+19
+00:01:33,910 --> 00:01:37,710
+إن أكدت عليها أن جميع الصفوف غير فارغة ولا صف بيكون 
+
+20
+00:01:37,710 --> 00:01:43,710
+فارغ، الصفين صف ال X وصف ال Y بيكون تقاطعهم لا
+
+21
+00:01:43,710 --> 00:01:46,410
+يساوي Phi if and only if ال X و ال Y لهما علاقة مع
+
+22
+00:01:46,410 --> 00:01:50,910
+بعض، وطبعا C X و Y لهما علاقة مع بعض فقط وإذا فقط
+
+23
+00:01:50,910 --> 00:01:55,030
+صفينهم متساوي، فإذا احنا برهنا A و B طبعا علينا
+
+24
+00:01:55,030 --> 00:02:01,550
+أن نبرهن C .. ممتازة، فاحنا بنستمر مع البرهان والجزء 
+
+25
+00:02:01,550 --> 00:02:06,310
+المتبقي الـ C طبعا الـ C علاقة ايه برضه F and و ال
+
+26
+00:02:06,310 --> 00:02:11,250
+فحنعملها two parts a proof فنبدأ بالاتجاه الأول
+
+27
+00:02:11,250 --> 00:02:19,870
+اللي هو XY لها علاقة مع بعض يؤدي إن صف ال X يساوي 
+
+28
+00:02:19,870 --> 00:02:25,810
+صف ال Y، فهذا هو المطلوب طبعا كالعادة هبدأ أن أفترض
+
+29
+00:02:25,810 --> 00:02:33,350
+أن الشرط صحيح، assume X Y تنتمي لل relation epsilon
+
+30
+00:02:33,350 --> 00:02:40,710
+أو E، مطلوب اثبت أن صف ال X يساوي صف ال Y، فهذا
+
+31
+00:02:40,710 --> 00:02:45,240
+تساوي ايش؟ المطلوب صف ال X يساوي صف ال Y، صف ال X وصف
+
+32
+00:02:45,240 --> 00:02:48,940
+ال Y عبارة عن ايه؟ مجموعات، عبارة عن مجموعات، فبنثبت 
+
+33
+00:02:48,940 --> 00:02:52,400
+أن مجموعة تساوي مجموعة، وهذه مهارة أساسية في 
+
+34
+00:02:52,400 --> 00:02:56,120
+chapter 2 مستمرة معناها، هنبدأ بعنصر من طرف من
+
+35
+00:02:56,120 --> 00:02:59,900
+الأطراف إذا ماشينا تكافئ التساوي انتهى، إذا ماوجدناش
+
+36
+00:02:59,900 --> 00:03:04,080
+نمشي تكافئ بثبت أن الأولى subset من الثانية والثانية
+
+37
+00:03:04,080 --> 00:03:08,620
+subset من الأولى، فهنبدأ بعنصر الآن، فهذه ليش أصلاً مشي
+
+38
+00:03:08,620 --> 00:03:11,640
+الأول؟ لأن نجومنا شرطية، فده إن الشرط صحيح الآن
+
+39
+00:03:11,640 --> 00:03:15,480
+بندثبت تساوي مجموعات ببدأ أنه آخذ عنصر عشوائي من
+
+40
+00:03:15,480 --> 00:03:20,320
+طرف من الأطراف، ايش نسميه العنصر؟ X ولا Y ولا عنصر
+
+41
+00:03:20,320 --> 00:03:24,660
+جديد؟ Z اسمه جديد أو K لأن X و Y مشغولين، فالآن بدي
+
+42
+00:03:24,660 --> 00:03:34,020
+أقوله ايش let Z تنتمي لصف ال X be any element، طبعًا
+
+43
+00:03:34,020 --> 00:03:36,060
+يمكن هذه الطريقة يمكن أول مرة بكتبها، مش عارف إذا
+
+44
+00:03:36,060 --> 00:03:39,060
+ذكرتها، هي نفس الطريقة let Z be any element
+
+45
+00:03:39,060 --> 00:03:44,210
+such that Z تنتمي للطرف اليسار، نفس المعنى، أخذنا
+
+46
+00:03:44,210 --> 00:03:47,910
+عنصر عشوائي عشان هو التعريف كله فيه for all وبدنا
+
+47
+00:03:47,910 --> 00:03:51,190
+نطلع عنصر وين يكون؟ في اليسار، في اليسار بصيغة 
+
+48
+00:03:51,190 --> 00:03:54,430
+الكتابة بشكل مختلف لكن نفس المعنى، ممتاز، بدي 
+
+49
+00:03:54,430 --> 00:03:59,020
+أحاول أوصل ال Z هنا، إيش ممكن أعمله؟ استخدمش تعريف
+
+50
+00:03:59,020 --> 00:04:01,360
+ال equivalence class، وقت إيش ال Z في صف ال X إذا
+
+51
+00:04:01,360 --> 00:04:05,820
+كانت ال Z إلى علاقة مع مين؟ مع ال X، فهذا يؤدي إن X
+
+52
+00:04:05,820 --> 00:04:09,820
+و Z تنتمي لل relation، طبعًا هذه علاقة تكافؤ لأنه
+
+53
+00:04:09,820 --> 00:04:14,240
+تعريف ال equivalence class لكن أتوقع أنه مش هستمر
+
+54
+00:04:14,240 --> 00:04:21,230
+التكافؤ of X على ال relation تمام؟ فال X و Z إلهم
+
+55
+00:04:21,230 --> 00:04:24,870
+علاقة مع ال Epsilon، أنا وين رايح؟ كالعادة أنا عيني 
+
+56
+00:04:24,870 --> 00:04:29,250
+على المطلوب أنا بدي أوصل ال Z لمين؟ لصف ال Y، يعني
+
+57
+00:04:29,250 --> 00:04:34,190
+بدي أثبت إن ال Y إلى علاقة مع ال Z أكتب همش؟ وين
+
+58
+00:04:34,190 --> 00:04:39,830
+رايحين؟ بدنا ال Z تنتمي لصف ال Y، مطلوب يعني بدنا
+
+59
+00:04:39,830 --> 00:04:45,950
+Y Z في ال relation، مطلوب، فالسؤال، عندي X Z في ال
+
+60
+00:04:45,950 --> 00:04:50,240
+relation وعندي X Y في ال relation، إيش ممكن أستخدم؟
+
+61
+00:04:50,240 --> 00:04:53,440
+التعدي، طب إيش عرفك إن أنا أستخدم التعدي؟ لأنه ليه ايش ال
+
+62
+00:04:53,440 --> 00:04:55,960
+epsilon equivalence relation، مقدمة اه أحنا 
+
+63
+00:04:55,960 --> 00:04:58,300
+ماكتبناش لك أنا مقدمة، جالك ليه ال epsilon بيه ال
+
+64
+00:04:58,300 --> 00:05:00,200
+equivalence relation، فالأنا اللي بشتغل معاها دي
+
+65
+00:05:00,200 --> 00:05:02,900
+ليه ايش ال equivalence relation؟ طيب ماشي، أنا عندي 
+
+66
+00:05:02,900 --> 00:05:08,220
+X Y، بدّه أتخلص من ال X بنفع؟ بدّه أبدل، أتخلص من ال X
+
+67
+00:05:08,220 --> 00:05:11,700
+دخلي ال X في النص، X Y بدّه أخليها .. بدّه أخليها إيش 
+
+68
+00:05:11,700 --> 00:05:20,620
+هذي؟ X Y، بدّه أخليها Y X اه Y X اه اه but X Y في ال
+
+69
+00:05:20,620 --> 00:05:25,940
+relation implies Y X في ال relation، ليش؟ لأن 
+
+70
+00:05:25,940 --> 00:05:29,220
+ال relation هي symmetric، الدليل is
+
+71
+00:05:29,220 --> 00:05:37,340
+symmetric، ممتاز هل يتصار X Z أو Y X و X Z بال
+
+72
+00:05:37,340 --> 00:05:42,300
+Transitive؟ اه .. Thus ايش صارت؟ ممكن أكتبها كخط بس
+
+73
+00:05:42,300 --> 00:05:45,520
+مش ضروري إنه conjunction لأن احنا متفقين كل خطوة 
+
+74
+00:05:45,520 --> 00:05:49,040
+في البرهان هي true فهذه true وهذه true، ممكن أضايق 
+
+75
+00:05:49,040 --> 00:05:52,920
+ايه اللي هو ال X ومش بتصير؟ Y Z تنتمي للأبسلون، ليش؟
+
+76
+00:05:52,920 --> 00:05:58,240
+لأن الأبسلون is Transitive، واضحة؟
+
+77
+00:05:58,730 --> 00:06:02,290
+هم تبقين؟ اه فاحنا تمام وهو المطلوب، فهذا معناته
+
+78
+00:06:02,290 --> 00:06:09,070
+إنّه مين؟ إن Y أو Z في صف ال Y فإذن Y برضه Z تنتمي 
+
+79
+00:06:09,070 --> 00:06:15,710
+لصف ال Y، خليني أكتب فورا Thus Y is Z تنتمي لصف ال
+
+80
+00:06:15,710 --> 00:06:20,990
+Y اه
+
+81
+00:06:20,990 --> 00:06:25,070
+فبالتالي أثبتنا، بدأنا من عنصر في صف ال X ووصلنا
+
+82
+00:06:25,070 --> 00:06:27,910
+لصف ال Y مش ماشيين تكافؤ زي ما تشوفين، إذا أثبتنا
+
+83
+00:06:27,910 --> 00:06:28,350
+صف Z
+
+84
+00:06:34,770 --> 00:06:40,330
+فعنا صف ال X هو subset من صف ال Y، فهذا واحد، هذا
+
+85
+00:06:40,330 --> 00:06:44,470
+اللي بدنا إياه، مستقيل مش هذا؟ هذا المهم للإستنتاج
+
+86
+00:06:44,470 --> 00:06:48,570
+فهذه مالهاش داعي لو عملناها مش غلط لكن مش هي
+
+87
+00:06:48,570 --> 00:06:56,130
+المهمة، هذه المهمة، الآن العكس، let Z تنتمي لصف ال Y
+
+88
+00:06:56,130 --> 00:07:00,030
+be any element any element
+
+89
+00:07:02,210 --> 00:07:05,310
+طبعًا لو ما كتبناش any element مفهومة ضمنية لأنه
+
+90
+00:07:05,310 --> 00:07:08,050
+أنا ما أعرفش عليها أي قيد، إذا بدي أخذها للعموم هي
+
+91
+00:07:08,050 --> 00:07:11,910
+بشكل عشوائي، بدي أوصلها وين للآن؟ لل X، فهذا ايش
+
+92
+00:07:11,910 --> 00:07:16,550
+معناته؟ معناته أن Y Z في ال relation، تعريف 
+
+93
+00:07:16,550 --> 00:07:21,700
+الصف ولا لأ، تمام، في أنا عندي هذا ايش ماله؟ هذا
+
+94
+00:07:21,700 --> 00:07:25,060
+ايش فرضية عامة، مظلة لكل البرهان لأنه ايش الجملة
+
+95
+00:07:25,060 --> 00:07:29,720
+الشرطية وأنا جعت بحاول أبرهن مين؟ هذا الجزء فبدأت
+
+96
+00:07:29,720 --> 00:07:33,540
+في الجزء الأول أخذ عنصر من الطرف اليسار ووصلته
+
+97
+00:07:33,540 --> 00:07:37,140
+لليمين، في صار subset، الآن أخذ طرف من اليمين أو
+
+98
+00:07:37,140 --> 00:07:40,320
+عنصر من اليمين بوصله لليسار، إذا كله تحت مين؟ تحت 
+
+99
+00:07:40,320 --> 00:07:44,140
+الشرط إن هذا صحيح، طب الآن Y Z في ال relation واحنا 
+
+100
+00:07:44,140 --> 00:07:48,020
+عندنا مين؟ عندنا X Z في ال relation من مين؟ X أخر
+
+101
+00:07:48,020 --> 00:07:51,920
+X Y في ال relation، من مين بتتخلص؟ من ال Y بتبقى 
+
+102
+00:07:51,920 --> 00:07:58,280
+عاكس زي الأولى؟ لا واضحة أفعالي ايش؟ نقول هنا but
+
+103
+00:07:58,280 --> 00:08:03,940
+ايش؟ X Y تنتمي للأبسلون فبالتالي ايش صار؟ X Y و Y Z
+
+104
+00:08:03,940 --> 00:08:07,880
+بتقول إنّه ايش؟ X Z في الأبسلون لأن الأبسلون is
+
+105
+00:08:07,880 --> 00:08:08,400
+transitive
+
+106
+00:08:12,340 --> 00:08:18,340
+ممتاز، فده ايش معناته؟ Thus ال Z في صف ال X 
+
+107
+00:08:18,340 --> 00:08:22,820
+وبالتالي
+
+108
+00:08:22,820 --> 00:08:28,120
+ايش صار؟ بدأنا من عنصر في صف ال Y ووصلنا لصف ال X 
+
+109
+00:08:28,120 --> 00:08:36,620
+إذا صف ال Y شماله subset من صف ال X، خلاص
+
+110
+00:08:36,620 --> 00:08:42,350
+واحد واثنين بيؤدي إلى التساوي، واحد واثنين يؤدي إن
+
+111
+00:08:42,350 --> 00:08:50,530
+صف ال X يساوي صف ال Y، واضح، فهنا زي ما حكينا كل 
+
+112
+00:08:50,530 --> 00:08:53,870
+خطوة بنمشي طب احنا بدنا نجزّئ، نجزّئ ما فيش مشكلة احنا 
+
+113
+00:08:53,870 --> 00:08:56,370
+ايش اللي بدنا إياه؟ كيف نوصل، المهم نعرف احنا ايش
+
+114
+00:08:56,370 --> 00:09:01,450
+النقطة وايه المطلوب، كل هذا تحت ايش؟ الاتجاه الأول
+
+115
+00:09:01,450 --> 00:09:04,810
+لل if and only if، الآن هنبدأ نشتغل مع الاتجاه
+
+116
+00:09:04,810 --> 00:09:15,070
+الثاني، خليني أشتغل هنا فاحنا العكس الأول، اثنين صف
+
+117
+00:09:15,070 --> 00:09:20,390
+ال X يساوي صف ال Y يؤدي أن X له علاقة مع ال Y
+
+118
+00:09:20,390 --> 00:09:26,190
+للجهة الثانية لل F and only F، وكالعادة ايش بالدب ده؟
+
+119
+00:09:26,190 --> 00:09:35,150
+أن الشرط صحيح، assume صف ال X يساوي صف ال Y المطلوب
+
+120
+00:09:35,150 --> 00:09:37,030
+أن X له علاقة مع ال Y
+
+121
+00:09:41,190 --> 00:09:47,830
+بدي أثبت إن ال X لعلاقة مع ال Y لو فكرنا قليلا
+
+122
+00:09:47,830 --> 00:09:51,650
+أنا بدي ال X لعلاقة مع ال Y من وين ممكن أجيبها؟
+
+123
+00:09:51,650 --> 00:09:54,910
+من تعريف الصف؟ ايش علاقة العلاقة مع الصف؟ لو قدرت
+
+124
+00:09:54,910 --> 00:09:58,950
+أثبت إن ال Y في صف ال X، بكون أصلت، ولا لأ؟ أنا 
+
+125
+00:09:58,950 --> 00:10:03,370
+بدي هذه، وقت شهدت صحيحة، يا ال X في صف ال Y يا
+
+126
+00:10:03,370 --> 00:10:05,790
+ال Y في صف ال X وهي واحد لأنهم في Symmetric، 
+
+127
+00:10:05,790 --> 00:10:10,380
+مظبوط؟ فأنا بدي أثبت إن ال Y في صف ال X طيب احنا 
+
+128
+00:10:10,380 --> 00:10:14,540
+ايش في عندنا؟ في عندنا مفتاح مهم تعلمناه أن كل
+
+129
+00:10:14,540 --> 00:10:18,700
+عنصر وين موجود في صفه، فال Y وين موجودة في صف ال Y
+
+130
+00:10:18,700 --> 00:10:26,110
+فالآن اه، but Y تنتمي لصف ال Y وصف ال Y بيثوي صف
+
+131
+00:10:26,110 --> 00:10:29,590
+ال X، إذا ال Y وين موجودة؟ في صف ال X، implies Y
+
+132
+00:10:29,590 --> 00:10:34,350
+تنتمي لصف ال X وهذا يؤدي إن X Y تنتمي لأبسلون وهو
+
+133
+00:10:34,350 --> 00:10:38,790
+المطلوب، فهذه الجزء سهل جدا، فهذه الجزئية سهلة جدا
+
+134
+00:10:38,790 --> 00:10:43,350
+فإنّا بنؤكد على في نقطة مهمة ولعبت دور في كثير من 
+
+135
+00:10:43,350 --> 00:10:47,410
+البراهين أن العنصر دائما موجود في صف نفسه، فال X
+
+136
+00:10:47,410 --> 00:10:50,430
+دائما في صف ال X، استخدمناها أكثر من مرة، ففعلا هنا
+
+137
+00:10:50,430 --> 00:10:55,680
+برضه حلت لنا الإشكال، فهيك بنكون خلصنا برهان النظرية
+
+138
+00:10:55,680 --> 00:11:04,970
+نظرية أربعة، هنتوجه لهذا الموضوع، اه طبعا الخواص 
+
+139
+00:11:04,970 --> 00:11:11,290
+الموجودة ممكن البعض يكون يعتقد إنّه ولا صف فاضي
+
+140
+00:11:11,290 --> 00:11:16,490
+وإنّه الصفين يا إما تقاطعهما .. تقاطعهما لا يساوي في if 
+
+141
+00:11:16,490 --> 00:11:18,510
+and only if العنصرين اللذين لهما علاقة مع بعض
+
+142
+00:11:18,510 --> 00:11:21,310
+والعنصرين اللذين لهما علاقة مع بعض if and only if 
+
+143
+00:11:21,310 --> 00:11:24,450
+صفوفهم متساوية لو جمعنا B وC بنشوف إن هو دي من
+
+144
+00:11:24,450 --> 00:11:29,690
+خواص ال partition فالآن هيوصل للنقطة هذه أنه كل
+
+145
+00:11:29,690 --> 00:11:34,930
+علاقة التكافؤ بتولد partition أي بقرا عن صفوف
+
+146
+00:11:34,930 --> 00:11:39,510
+التكافؤ فانا عند المجموعة لو حسبت صفوف التكافؤ
+
+147
+00:11:39,510 --> 00:11:43,370
+فبكون جزأتي المجموعة إلى partition ينطبق عليها
+
+148
+00:11:43,370 --> 00:11:47,610
+شروط ال partition فهي لعنوان capital X على أبسلون
+
+149
+00:11:47,610 --> 00:11:52,670
+ياش مجموعة صفوف التكافؤ is a partition of X نقرأ
+
+150
+00:11:52,670 --> 00:11:58,130
+النص بشكل أوضح أو بشكل كامل let epsilon be an
+
+151
+00:11:58,130 --> 00:12:04,260
+equivalence relation on a non-empty set X مجموعة
+
+152
+00:12:04,260 --> 00:12:07,260
+الصفوف التكافؤ اللي هي X على Y is a partition of X
+
+153
+00:12:07,260 --> 00:12:13,180
+بدنا نشوف إنه دائماً صفوف التكافؤ بتكون تجزيه تقسيم
+
+154
+00:12:13,180 --> 00:12:16,700
+لمن؟ للمجموعة إيش معنى التقسيم؟ إنه partition يعني
+
+155
+00:12:16,700 --> 00:12:20,960
+متحقق عليه تلت شروط إنه ولا جزء فارغ أي جزءين يا
+
+156
+00:12:20,960 --> 00:12:26,460
+يتقاطعوا فيه يا بتطابقين في احتمال تالت وإن الاتحاد
+
+157
+00:12:26,460 --> 00:12:30,980
+على كل الصفوف بده يغطي كل ال X خلينا نشوف البرهان
+
+158
+00:12:30,980 --> 00:12:42,690
+مع بعض فهذه نظرية تلاتة أربع approved فطبعاً 
+
+159
+00:12:42,690 --> 00:12:50,050
+بس نذكركوا إحنا بنتحدث عن P تساوي capital X على
+
+160
+00:12:50,050 --> 00:12:55,490
+أبسلون وهذه مما تتكون من small x على أبسلون بحيث
+
+161
+00:12:55,490 --> 00:13:00,420
+small x in capital X فهذه الموجودة في النظرية
+
+162
+00:13:00,420 --> 00:13:04,100
+capital X على Y هي مجموعة صفوف التكافؤ اللي هي ده
+
+163
+00:13:04,100 --> 00:13:07,100
+هما بدي أثبت إنها partition فخلّيني أرمزها برمز B
+
+164
+00:13:07,100 --> 00:13:12,270
+فبنثبت إنها partition تلت شروط فالشرط الأول بدا
+
+165
+00:13:12,270 --> 00:13:16,990
+نثبت أن كل جزء غير فارغ ولا جزء بيكون فارغ فطبعاً
+
+166
+00:13:16,990 --> 00:13:20,450
+نثبت أن for all a in the partition تذكروا المعادلة
+
+167
+00:13:20,450 --> 00:13:24,330
+الماضية a is non-empty a is non-empty خليني
+
+168
+00:13:24,330 --> 00:13:30,310
+أكتبلكوا إياها for all a تنتمي للpartition a لا
+
+169
+00:13:30,310 --> 00:13:34,870
+تساوى five متذكرين؟ هيك اذكرته تمام فانا بدي آخذ
+
+170
+00:13:34,870 --> 00:13:40,280
+ايش عنصر في الـ partition اللي هو مجموعة يعني طيب،
+
+171
+00:13:40,280 --> 00:13:43,640
+كيف صور المجموعات في الـ partition الأن؟ صفر، إذا 
+
+172
+00:13:43,640 --> 00:13:45,860
+بدأ أقول له let a be in the partition يعني إيش ده
+
+173
+00:13:45,860 --> 00:13:50,220
+يساوي؟ X على أبسلون، ممكن أعود بصيغة أخرى، أقول له
+
+174
+00:13:50,220 --> 00:13:56,040
+let small x تنتمي لcapital X لأنه إيش بتكون
+
+175
+00:13:56,040 --> 00:13:59,080
+الصفوف؟ X تنتمي لcapital X كل عنصر بيولد صفر
+
+176
+00:13:59,080 --> 00:14:06,630
+تكافؤ، ولا لأ؟ كل عنصر إيه صفه، فإيش and؟ let small
+
+177
+00:14:06,630 --> 00:14:11,410
+x على أبسلون تنتمي للpartition اللي هو إيش بيساوي
+
+178
+00:14:11,410 --> 00:14:16,510
+x على أبسلون إيه المطلوب منه؟ أثبت إن هذا الصف غير 
+
+179
+00:14:16,510 --> 00:14:22,300
+فارغ بدنا نثبت إن هذا الصف غير فارغ إيش معناه غير
+
+180
+00:14:22,300 --> 00:14:26,800
+فارغ؟ الأقل فيه عنصر واحد كيف ممكن أثبته؟ إذا قدرت
+
+181
+00:14:26,800 --> 00:14:29,580
+أعرف عنصر there exist اه كيف بدأ أثبت أن there
+
+182
+00:14:29,580 --> 00:14:32,500
+exist؟ ماخدناش طريقة عامة ل there exist بس قلنا في
+
+183
+00:14:32,500 --> 00:14:36,160
+بعض الطرح لو قدرت أسميه عنصر موجود انتهى العملية
+
+184
+00:14:36,160 --> 00:14:39,520
+عشان أنا أثبت إن هذه القاعة غير فارغة لو أنا قلت
+
+185
+00:14:39,520 --> 00:14:41,900
+إن في طالب اسمه فاطمة بعرف أنا موجود في القاعة
+
+186
+00:14:41,900 --> 00:14:45,890
+انتهت العملية انتهت العملية، بدأ أسمي فمين يعرف لي
+
+187
+00:14:45,890 --> 00:14:49,290
+عنصر دائماً مضمون أن يكون في صف الـ X؟ الـ X نفسها،
+
+188
+00:14:49,290 --> 00:14:54,490
+اه فانا على طول فالآن then X تنتمي لصف الـ X
+
+189
+00:14:54,490 --> 00:15:00,080
+implies صف الـ X ليه زفافوهو المطلوب، ولا صف ممكن
+
+190
+00:15:00,080 --> 00:15:03,260
+يكون فاضي، على الأقل فيه عنصر واحد، مين؟ العنصر
+
+191
+00:15:03,260 --> 00:15:06,740
+اللي سمي الصف أو اللي ولد الصف لأنه سميها ده الصف
+
+192
+00:15:06,740 --> 00:15:10,580
+اللي ماله اتولد أو اتحدد من ال X، إذا بتتذكروا
+
+193
+00:15:10,580 --> 00:15:13,860
+التعريف، فإذا فعلاً ولا صف ممكن يكون فاضي، فإذا أي
+
+194
+00:15:13,860 --> 00:15:17,400
+صف تكافؤ، لما نحسبه على الأقل هيكون فيه عنصر واحد،
+
+195
+00:15:17,400 --> 00:15:20,120
+وعلى طول وانت مغمض اش تحطيه، جالك جيبي صف الواحد،
+
+196
+00:15:20,120 --> 00:15:23,320
+حط الواحد، جالك جيبي صف فاطمة، حط فاطمة، على طول،
+
+197
+00:15:24,300 --> 00:15:28,780
+دون أي تردد وهذا هو العنصر الأول فإذا هذا الشرط
+
+198
+00:15:28,780 --> 00:15:35,460
+الأول الشرط رقم واحد بدنا أي صفين يا متطابقين يا 
+
+199
+00:15:35,460 --> 00:15:41,720
+لا عنصر مشترك لو إيش بيقول يجلي انه x y في آسف x
+
+200
+00:15:41,720 --> 00:15:48,080
+على ال epsilon في ال partition and اللي هو أي صفين
+
+201
+00:15:48,080 --> 00:15:51,160
+a و b بدك تبقى بنفس الطريقة عشان ما تتخموش اللي
+
+202
+00:15:51,160 --> 00:15:58,730
+هم a و b X على أبسلون وY على أبسلون في الـ B and X
+
+203
+00:15:58,730 --> 00:16:03,830
+على أبسلون لا تساوي Y على أبسلون implies X على
+
+204
+00:16:03,830 --> 00:16:08,450
+أبسلون تقاطع Y على أبسلون بتساوي 5 هيك الشرط بس بدل
+
+205
+00:16:08,450 --> 00:16:12,570
+a و b حطيت مين صفوف لأن الأجزاء هنا يشملها صفوف
+
+206
+00:16:12,570 --> 00:16:17,570
+الأجزاء المعطية ليه صفوف اه فطبعاً كجملة شرطية
+
+207
+00:16:17,570 --> 00:16:25,390
+هفترض أن الشرط صحيح فابدأ بدأله أول شيء let X و
+
+208
+00:16:25,390 --> 00:16:30,910
+Epsilon و Y و Epsilon ينتموا للـ B اللي هي عبارة
+
+209
+00:16:30,910 --> 00:16:35,110
+عن مين طبعاً ليش بحطه ميك لأنه X على Epsilon فانا
+
+210
+00:16:35,110 --> 00:16:37,830
+مش ماخذ أي partition ماخذ partition من نوع معين
+
+211
+00:16:37,830 --> 00:16:41,730
+عناصره عبارة عن صفوف تكافؤ فبكتبهم بيد الشكل بدي
+
+212
+00:16:41,730 --> 00:16:45,390
+أثبت أنه إذا كان او بدي افترض أنه ميكش غير
+
+213
+00:16:45,390 --> 00:16:48,430
+متساويين and assume
+
+214
+00:16:50,150 --> 00:16:57,390
+X على أبسلون لا تساوي Y على أبسلون بدي أثبت أن
+
+215
+00:16:57,390 --> 00:17:02,850
+التقاطع يساوي في بدي أثبت أن التقاطع يساوي في
+
+216
+00:17:02,850 --> 00:17:10,590
+اتطلع عن نظرية الماضية افتح عليها موجودة وسهلة إيش
+
+217
+00:17:10,590 --> 00:17:15,800
+قال لي اه بدي أربط بين B وC جال ليه؟ بس اقرا من
+
+218
+00:17:15,800 --> 00:17:21,600
+هناك اكس انا بتدبط انه مين انه إيش X تقاطع صف ال
+
+219
+00:17:21,600 --> 00:17:25,720
+y لا يقبض يسوى five بتدبطها بدا الشكل نيجي نشوف
+
+220
+00:17:25,720 --> 00:17:32,250
+احنا عايش عنا عدم تساوي عدم تساويمع contrapositive
+
+221
+00:17:32,250 --> 00:17:36,630
+إيش بتصير؟ لو عنصرين ليس لهما علاقة مع بعض و عنصرين
+
+222
+00:17:36,630 --> 00:17:39,510
+مالهم مش علاقة مع بعض إيش هتديني؟ تقاطع بيساوي
+
+223
+00:17:39,510 --> 00:17:43,750
+five فهنعمل .. هنستخدم C و B مع contrapositive
+
+224
+00:17:43,750 --> 00:17:48,150
+طبعاً إحنا بنعرف في ال if and only if statement B
+
+225
+00:17:48,150 --> 00:17:51,050
+implies Q إيش ال contrapositive إلها؟ not Q
+
+226
+00:17:51,050 --> 00:17:56,950
+implies not B طب لما تكون عندنا B if and only if Q
+
+227
+00:17:56,950 --> 00:17:58,410
+إيش ال contrapositive بتبعدها؟
+
+228
+00:18:06,390 --> 00:18:12,370
+ممتازة هنمشي خلينا نطبق انا عندي صف ال X لا يساوي
+
+229
+00:18:12,370 --> 00:18:17,250
+صف ال Y إذا نقش XY لا تنتمي للأبسلون هذا يؤدي ان
+
+230
+00:18:17,250 --> 00:18:24,670
+XY لا تنتمي للأبسلون من وين جبتها؟ جداش؟ تلاتة
+
+231
+00:18:24,670 --> 00:18:28,310
+تلاتة، فرع C إذا حابين، صح؟ Contrapositive بس
+
+232
+00:18:28,310 --> 00:18:32,470
+دكتور implies ولا تكافأت؟ هي تكافؤ، بس أنا مش معنى
+
+233
+00:18:32,470 --> 00:18:36,470
+كثير، لأنه أنا مش بدي implies، فبديش أغلب حالي،
+
+234
+00:18:36,470 --> 00:18:39,650
+تمام؟ لأن التكافؤ بيقول لي إيش؟ كن دقيق، فبدك
+
+235
+00:18:39,650 --> 00:18:43,230
+انتباه شديد، أنا مش معنى بالتكافؤ، فطنشط الانتباه،
+
+236
+00:18:43,230 --> 00:18:48,300
+بدي أخفف عن حالي الانتباه، واضحة؟ متبين؟ اه تمام
+
+237
+00:18:48,300 --> 00:18:52,820
+الآن باستخدام بي إذا كانت لا تنتمي إيش ماله؟ إذا
+
+238
+00:18:52,820 --> 00:18:57,420
+إن تقاطعه بيساوي فاي implies x على أبسلون تقاطع y على
+
+239
+00:18:57,420 --> 00:19:04,340
+أبسلون يساوي فاي برضه إيش نظرية تلاتة تلاتة فرع بي
+
+240
+00:19:04,340 --> 00:19:09,410
+واضحة مع contrapositive مع الـ Contrapositive أي
+
+241
+00:19:09,410 --> 00:19:13,550
+سؤال متبين؟ خلصنا وهو المطلوب اللي هو يش فرع
+
+242
+00:19:13,550 --> 00:19:16,810
+الأول صحيح اللي هو رقم واحد اللي هو يش الشرط
+
+243
+00:19:16,810 --> 00:19:19,570
+الثاني من شروط ال partition تم الشرط الثالث
+
+244
+00:19:19,570 --> 00:19:26,170
+والأخير الشرط الثالث والأخير بدنا الاتحاد يساوي X،
+
+245
+00:19:26,170 --> 00:19:30,590
+مظبوط؟ شرط رقم اتنين اتحاد على كل ال partition
+
+246
+00:19:30,590 --> 00:19:36,070
+ممكن اكتبه بشكل التالي اتحاد جميع الصفوف يعني مظبوط
+
+247
+00:19:36,070 --> 00:19:42,330
+يساوي X هذا الشرط لأنه مرة ثانية أناقنعت صياغته إيش
+
+248
+00:19:42,330 --> 00:19:46,050
+بيقول الشرط اتحاد جميع الأجزاء بيساوي X إيش
+
+249
+00:19:46,050 --> 00:19:49,210
+الأجزاء عندي في هذا النظرية صفوف تكافؤ يعني اتحاد
+
+250
+00:19:49,210 --> 00:19:52,890
+جميع الصفوف بده يديني لمين لل capital X طبعاً كل صف
+
+251
+00:19:52,890 --> 00:19:56,230
+من اللي بيحدده ال X تبعته اللي هي العرف تبع الصف
+
+252
+00:19:56,230 --> 00:20:00,350
+العرف تبع الصف هو X أزاي العرف نسميه فواحد بيسمي
+
+253
+00:20:00,350 --> 00:20:05,470
+الصف فده صف محمد فده صف فاطمة واضح؟ تمام؟ اه بيبقى
+
+254
+00:20:05,470 --> 00:20:10,030
+نثبت هذه العلاقة علاقة إيش؟ تساوي مجموعات، نفس
+
+255
+00:20:10,030 --> 00:20:13,310
+السيطرة، خذ الآنصار من الطرف، امشيتي تكافؤ، خلصنا،
+
+256
+00:20:13,310 --> 00:20:15,930
+امشيتيش تكافؤ، امشي، إن الأولى صبصت من التانية، و
+
+257
+00:20:15,930 --> 00:20:19,490
+العكس، التانية صبصت من الأولى، فنبدأ، طب عم بديش
+
+258
+00:20:19,490 --> 00:20:23,210
+أسمي X أنه X مشغولة، let Y، الـY مش مشغولة الآن،
+
+259
+00:20:23,210 --> 00:20:28,890
+be any element and
+
+260
+00:20:28,890 --> 00:20:34,010
+let أو such that كله صح، and let Y تنتمي للطرف
+
+261
+00:20:34,010 --> 00:20:43,180
+اليسار اتحاد على كل صفوف التكافؤ في
+
+262
+00:20:43,180 --> 00:20:46,400
+أي طالب عنده مشكلة في البداية؟ كيف بنبدأ و ليش
+
+263
+00:20:46,400 --> 00:20:51,460
+بنبدأ؟ تمام؟ إيش ممكن أعمل الآن؟ أفق الاتحاد ..
+
+264
+00:20:51,460 --> 00:20:55,910
+ماذا يعني why أدى اتحاد على كم مجموعة؟ كلهم يعني
+
+265
+00:20:55,910 --> 00:20:58,290
+إيش .. إيش يسمي اتحاد على family يعني لإن العدد مش
+
+266
+00:20:58,290 --> 00:21:01,610
+معروف كم صف فيه مش عارفين لإن شوفنا مثال كم صف
+
+267
+00:21:01,610 --> 00:21:05,250
+مرة طلع معنى تذاكر المربع مال نهاية من الصفوف ممكن
+
+268
+00:21:05,250 --> 00:21:08,270
+يكون عدد محدود ممكن يكون غير محدود فإذا احنا هذا
+
+269
+00:21:08,270 --> 00:21:12,130
+كأن اتحاد على مجموع كل الصفوف اللي عددهم غير محدد
+
+270
+00:21:12,130 --> 00:21:15,430
+.. غير محدد إذا هذا كأن اتحاد على family إيش معناه
+
+271
+00:21:15,430 --> 00:21:18,150
+تعنصر في الاتحاد؟ بتكون على الأقل في واحدة من إيش؟
+
+272
+00:21:18,150 --> 00:21:23,890
+من الأجزاء فإذا هذا يؤدي إن الـ Y تنتمي للـ X على
+
+273
+00:21:23,890 --> 00:21:28,890
+أبسلون for some X تنتمي للـ X
+
+274
+00:21:31,440 --> 00:21:33,800
+اه بيكون واحد من الأجزاء فواحد يقول أنت ليش ما
+
+275
+00:21:33,800 --> 00:21:38,500
+قلتش X على الأبسلون نفس المعنى لأنه إياه كل صف
+
+276
+00:21:38,500 --> 00:21:41,640
+مين اللي بيدل عليه العرف تبعه اللي هو ال X زي
+
+277
+00:21:41,640 --> 00:21:45,240
+عملية إياه كان عملنا عملية indexing عملية أرشفة
+
+278
+00:21:45,240 --> 00:21:50,300
+مظبوط لإن كل X بتعرف صف فأنا ممكن أقول صف ال X أو
+
+279
+00:21:50,300 --> 00:21:52,700
+أقول X ماينافسه إياه بيدل على نفسه أو بيدل على
+
+280
+00:21:52,700 --> 00:21:54,960
+الصفة ولا لأ اه فعادة زي ما كنا نقول إياه كنا 
+
+281
+00:21:54,960 --> 00:21:57,720
+نقول إيش ما كنا نقول there exists a small Gamma
+
+282
+00:21:57,720 --> 00:22:01,660
+in capital Gamma وين الـ X في الـ A Gamma نفس العملية
+
+283
+00:22:01,660 --> 00:22:05,840
+فهنا الصف من اللي بعرفه مش Gamma X فصف الـ X ممتاز
+
+284
+00:22:05,840 --> 00:22:10,540
+الـ Y في صف الـ X أنا بني وين ده وديها ده وديها على
+
+285
+00:22:10,540 --> 00:22:15,720
+Capital X بدي أودّيها على capital X ممكن الصفوف
+
+286
+00:22:15,720 --> 00:22:19,440
+تاخد عناصر من خارج الـ capital X تتذكروا كتبنا
+
+287
+00:22:19,440 --> 00:22:22,320
+ملاحظة أن كل صف هو صف ستم أويان من الـ capital X
+
+288
+00:22:22,320 --> 00:22:26,600
+إيش تعريف الصف؟ جالي Y تنتمي لـ capital X such that
+
+289
+00:22:26,600 --> 00:22:31,700
+Y إلى علاقة مع الـ X فهذه بديهية أن الـ Y تنتمي
+
+290
+00:22:31,700 --> 00:22:35,460
+لـ capital X ليش؟ لأن أي صف هو صف ستم المجموعة
+
+291
+00:22:35,460 --> 00:22:39,410
+الأصلية لأن أنا بعمل relation على مين؟ على الـ X
+
+292
+00:22:39,410 --> 00:22:43,310
+ومين الصفر؟ هو عناصر الـ X اللي اللي علاقة مع الـ
+
+293
+00:22:43,310 --> 00:22:48,970
+X فإذن وضحنا إنه الطرف الأول سهل، thus صار الاتحاد
+
+294
+00:22:48,970 --> 00:22:58,290
+إشماله subset من الـ X، مظبوط، فالاتجاه الأول خلص،
+
+295
+00:22:58,290 --> 00:23:03,040
+فهذا الاتجاه الأول طبعاً مامشيناش تكافؤ وهي هذه
+
+296
+00:23:03,040 --> 00:23:06,040
+الطريقة الأشهر في الرياضيات أو الأعامة عملية
+
+297
+00:23:06,040 --> 00:23:10,480
+التكافؤ قليلة جدا ونادرة فهنا بدينا حرية ومرونة في
+
+298
+00:23:10,480 --> 00:23:16,660
+العمل نعمل اتجاه التاني let Y تنتمي للـ capital X
+
+299
+00:23:16,660 --> 00:23:23,500
+بدي أثبت أن هذا الـ Y موجودة في الاتحاد بدي أثبت أن
+
+300
+00:23:23,500 --> 00:23:29,860
+الـ Y موجودة في الاتحاد اتحاد مين؟ اتحاد الصفوف وقت
+
+301
+00:23:29,860 --> 00:23:33,220
+إيش Y بتكون في اتحاد الصفوف إذا كانت في صف على
+
+302
+00:23:33,220 --> 00:23:37,180
+الأقل؟ طب Y في صف مين بتعرفوها؟ صف نفسها، شايفين
+
+303
+00:23:37,180 --> 00:23:43,880
+كيف كانت النقطة المفتاحية؟ فعلى طول، then Y تنتمي
+
+304
+00:23:43,880 --> 00:23:49,220
+لصف الـ Y إذا نقش مالها في اتحاد الصفوف وهذا يؤدي
+
+305
+00:23:49,220 --> 00:23:56,710
+إن Y تنتمي لاتحاد على الـ capital X للصفوف طبعا و حد
+
+306
+00:23:56,710 --> 00:24:01,070
+يلتخم وين الـ Y؟ ماذا صفوف X؟ لأ ده رمز احنا بنقرع
+
+307
+00:24:01,070 --> 00:24:05,710
+صح ماذا يعني هذا اتحاد جميع الصفوف X تنتمي
+
+308
+00:24:05,710 --> 00:24:09,330
+لـ capital X يعني لما X بتساوي X واحد صف X واحد و صف
+
+309
+00:24:09,330 --> 00:24:13,460
+X اتنين و صف X تلاتة حد الصفوف هيكون صف الـ Y واضحى
+
+310
+00:24:13,460 --> 00:24:17,080
+كيف نقرأ صح؟ يعني في ناس هتستغرب كيف الـ Y في صفوف
+
+311
+00:24:17,080 --> 00:24:20,360
+اتحاد الـ X؟ لأ، ده رمز، أنا إيش قلتش كيف تقرأها
+
+312
+00:24:20,360 --> 00:24:23,640
+صح؟ هذا اتحاد جميع الصفوف الـ Y موجودة في احد
+
+313
+00:24:23,640 --> 00:24:25,540
+الصفوف ولا مش موجودة؟ موجودة في صفف نفسها، إذا
+
+314
+00:24:25,540 --> 00:24:27,520
+موجودة في الاتحاد ولا مش موجودة؟ موجودة في
+
+315
+00:24:27,520 --> 00:24:30,580
+الاتحاد، بس هذا رمز بإننا نقعد نقرأه صح، ممكن يكون
+
+316
+00:24:30,580 --> 00:24:33,620
+خادع للناس اللي ماعنداش خبرة شوية، ممكن يخدعوا
+
+317
+00:24:33,620 --> 00:24:36,440
+فيها أو يلاجوا صعوبة، فإذا خلاص انتهى، بدأنا في
+
+318
+00:24:36,440 --> 00:24:39,120
+عنصر من الطرف اليمين وصلنا
+
+319
+00:24:42,500 --> 00:24:49,260
+subset من اليسار طبعا
+
+320
+00:24:49,260 --> 00:24:57,080
+واحد و اتنين يجعل البرهان انتهى اتحاد
+
+321
+00:24:57,080 --> 00:25:03,780
+الصفوف يساوي المجموعة كلها الان zero واحد و اتنين
+
+322
+00:25:03,780 --> 00:25:11,830
+يدلوا ان هذا ياش partition فهنا zero واحد and اتنين
+
+323
+00:25:11,830 --> 00:25:20,410
+implies X على الابسلون is a partition ففعلا
+
+324
+00:25:20,410 --> 00:25:28,630
+عملية تقسيم المجموعة إلى صفوف تكافؤ هذا التقسيم هو
+
+325
+00:25:28,630 --> 00:25:32,470
+تقسيم نموذجي ينطبق عليه شروط ال partition يعتبر
+
+326
+00:25:32,470 --> 00:25:36,090
+partition بالمعنى الرياضيين يعتبر partition بمعنى
+
+327
+00:25:36,090 --> 00:25:38,910
+الرياضي واضح؟
+
+328
+00:25:40,120 --> 00:25:43,360
+تمام فده طبعا احنا كنا راجعين لنظرية عشان نستلق
+
+329
+00:25:43,360 --> 00:25:48,340
+بها خلينا نشوف بعض الأمثلة الحقيقة فيها ان دي انا
+
+330
+00:25:48,340 --> 00:25:53,300
+اكتر من المثال المثال مايعتبرش جديد تماما لإن احنا
+
+331
+00:25:53,300 --> 00:25:57,140
+قبل هيك كنا بيدينا relation و أثبتنا و جبنا و
+
+332
+00:25:57,140 --> 00:26:01,140
+حسبنا صفوف التكافر لكن ايش الشاهد؟ هنشوف في ضوء
+
+333
+00:26:01,140 --> 00:26:05,310
+النظريتين السابقتين كيف أستخدم خواص ال equivalence
+
+334
+00:26:05,310 --> 00:26:08,810
+classes و تساعدني في الحساب و ايضا بدي اتأكد ان
+
+335
+00:26:08,810 --> 00:26:12,050
+فعلا صفوف التكافئة الشمالية بتعمل partition هنشوف
+
+336
+00:26:12,050 --> 00:26:15,250
+و نلاحظ على الملاحظة ان النظرية بتتطبق على الأمثلة
+
+337
+00:26:15,250 --> 00:26:17,630
+و لا لأ طبعا ما زال ال proof هي صح لكن بدي اشوف ان
+
+338
+00:26:17,630 --> 00:26:21,990
+الكلام صحيح و لا لأ و ممكن استخدم نظرية نقاشأعمل
+
+339
+00:26:21,990 --> 00:26:25,150
+test على حل إنه صح و لا لأ فإحنا في عندنا طريقتين
+
+340
+00:26:25,150 --> 00:26:29,350
+ممكن نستخدم الخواص تساعدنا في الحل و ممكن نستخدم
+
+341
+00:26:29,350 --> 00:26:32,870
+الخواص أن نختبر حالنا صحيح و لا لأ فأي تناقض مع
+
+342
+00:26:32,870 --> 00:26:37,050
+الخواص بيدل على إن حالنا في خطأ ما في خطأ ما تمام
+
+343
+00:26:37,050 --> 00:26:43,390
+فهنا نبدأ كالسياسة العامة مثال بسيط هنبدأ مجموعة
+
+344
+00:26:43,390 --> 00:26:46,150
+صغيرة تتكون من أربع عناصر
+
+345
+00:26:50,300 --> 00:26:54,440
+أه فاحنا إيش بندرس بشكل عام؟ في عندنا مجموعة وفي
+
+346
+00:26:54,440 --> 00:26:59,680
+عندنا علاقة تكافؤ هدولة مع بعض بيولدوا أو بيعرفوا
+
+347
+00:26:59,680 --> 00:27:04,600
+تجزيق partition فالدان المجموعة والدان ال relation
+
+348
+00:27:04,600 --> 00:27:07,860
+طبعا equivalence relation إيش بيقول ليه؟ أوجد صفوف
+
+349
+00:27:07,860 --> 00:27:11,940
+التكافؤ .. أوجد صفوف التكافؤ فسؤال قديم لكن هنحله
+
+350
+00:27:11,940 --> 00:27:16,340
+بنظرة جديدة في ضوء النظريتين السابقتين فهذا المثال
+
+351
+00:27:16,340 --> 00:27:21,010
+الأول Solution، إيش بده؟ بده X على أبسلون، اللي هي
+
+352
+00:27:21,010 --> 00:27:24,350
+مجموعة كل الصفوف، اللي هي تعريفها هي X على أبسلون
+
+353
+00:27:24,350 --> 00:27:29,950
+بحيث X تنتمي لـ capital X في هذا المثال، بما أن
+
+354
+00:27:29,950 --> 00:27:33,390
+الـ capital X أربع عناصر، إذا أنا متوقع يكون عندي
+
+355
+00:27:33,390 --> 00:27:38,430
+إيش؟ أربع صفوف، بدرور يكونوا أربع صفوف مختلفين؟
+
+356
+00:27:38,430 --> 00:27:44,430
+لأ، ممكن يكونوا متطابقين كحد أقصى أربعة صفوف نبدأ
+
+357
+00:27:44,430 --> 00:27:49,430
+نحسبهم واحد واحد بدنا نحسب صف الواحد اه انا طول
+
+358
+00:27:49,430 --> 00:27:53,150
+وانا مغمض بدك تكتب واحد شوف نه ده مفتاح جهنم تطلع
+
+359
+00:27:53,150 --> 00:27:55,770
+على ال relation حط الواحد وانت مغمضة صف الواحد
+
+360
+00:27:55,770 --> 00:27:59,910
+لازم يحتوي على أقل الواحد طب في حاجة غير الواحد لأ
+
+361
+00:27:59,910 --> 00:28:02,230
+مافيش حد اللي علاقة مع الواحد اللي مع نفسه اذا
+
+362
+00:28:02,230 --> 00:28:07,350
+خلاص سكر الصف صف التنين و احنا مغمطين منه نحط
+
+363
+00:28:07,350 --> 00:28:10,750
+التنين و ندور في غيرها ولا لأ؟ في حد اللي علاق مع
+
+364
+00:28:10,750 --> 00:28:16,080
+التنين؟ نعم التلاتة وبما أن الدنيا ليها علاقة مع
+
+365
+00:28:16,080 --> 00:28:20,100
+التلاتة فهي دا يحسب صف التلاتة لأ جال ال X و Y
+
+366
+00:28:20,100 --> 00:28:23,240
+اللي هم علاقة مع بعض if and only if صفوفهم متساوية
+
+367
+00:28:23,240 --> 00:28:27,180
+الخاصية رقم C فإذا على طول و أقول إن هذا هو صف
+
+368
+00:28:27,180 --> 00:28:30,640
+التلاتة شوفت هذي كده إيش نستفيد من الخواص خاصية
+
+369
+00:28:30,640 --> 00:28:34,200
+رقم C ففيش دا هتحسب صف التلاتة لكن ممكن إذا أنت
+
+370
+00:28:34,200 --> 00:28:37,360
+شاكة احسب صف التلاتة تطلع بساوي ولا بسويش لازم
+
+371
+00:28:37,360 --> 00:28:37,940
+تطلع الساوي
+
+372
+00:28:41,080 --> 00:28:44,080
+وهنا مافيش .. بتبطل ال equivalance relation بتبطل
+
+373
+00:28:44,080 --> 00:28:47,520
+ال equivalance relation اه هنا يقولك اي عنصرين
+
+374
+00:28:47,520 --> 00:28:51,780
+اللي هم علاقة مع بعض if and only if صف ال X ليساوي
+
+375
+00:28:51,780 --> 00:28:55,220
+صف ال Y فانت و انت مغمضة إذا كل الشغل صح لازم يصير
+
+376
+00:28:55,220 --> 00:28:59,200
+فيش تناقض كله يتسجل تم علينا نحسب صف الأربعة و
+
+377
+00:28:59,200 --> 00:29:03,060
+بنخلص مش هيهم هذا نحسب و هذا نحسب و بيساوي هذا
+
+378
+00:29:03,060 --> 00:29:06,160
+تملي نحسب هذا صف الأربعة عامة يتكوى من الأربعة في
+
+379
+00:29:06,160 --> 00:29:11,070
+غيرها؟ لأ إذن هدول عايش تلت صفوف مختلفة تلت صفوف
+
+380
+00:29:11,070 --> 00:29:18,330
+مختلفة فانلخص فعنا مجموعة الصفوف هي صف الواحد
+
+381
+00:29:18,330 --> 00:29:23,990
+ويتكون من الواحد صف التنين ويتكون من تنين لتلاتة
+
+382
+00:29:23,990 --> 00:29:28,390
+وصف الأربع يتكون من الأربعه هل هذا partition
+
+383
+00:29:28,390 --> 00:29:32,810
+للمجموعة؟ نعم، مجموعة من أربع عناصر قسمة، تلت
+
+384
+00:29:32,810 --> 00:29:38,270
+أقسام، ولا قسم فاضي، وأي قسمين منفصلين عن بعض، مش
+
+385
+00:29:38,270 --> 00:29:41,310
+عناصر مشتركة، اتحاد ومدانة نفس المجموعة لمدناش،
+
+386
+00:29:41,310 --> 00:29:45,640
+اتدانة، طبعا النظرية تلاتة أربع هنا طبقنا و نستفيد
+
+387
+00:29:45,640 --> 00:29:49,900
+من النظريات نتأكد أن حلنا صح أو يساعدنا في الحل
+
+388
+00:29:49,900 --> 00:29:55,200
+يساعدنا في نختصر بعض خطوات الحل فهنا ساعدنا مكانش
+
+389
+00:29:55,200 --> 00:29:57,680
+في ده نحصل صف التلاتة لأن احنا عارفين أنه هيطلع
+
+390
+00:29:57,680 --> 00:30:02,680
+متساوي طبعا إذا شكنا بنحصل خليني أشوف مثال آخر
+
+391
+00:30:02,680 --> 00:30:09,750
+ممكن يكون أهم المثال رقم 2 ناخد مجموعة كبيرة الآن X
+
+392
+00:30:09,750 --> 00:30:15,650
+تساوي كل الـ Z وعطانا علاقة تكافؤ هي علاقة ذكرناها
+
+393
+00:30:15,650 --> 00:30:20,750
+في المحاضرات الماضية أثبتنا إن و X ناقص Y تساوي 3
+
+394
+00:30:20,750 --> 00:30:25,070
+في K إنها equivalence relation وقلنا إن التلاتة ما
+
+395
+00:30:25,070 --> 00:30:27,730
+لاش أي خاصية ممكن أي عدد صحيح موجبة بيقدر الغرض
+
+396
+00:30:27,730 --> 00:30:31,200
+قلنا لأي M وداكرناها فإنها بده يدينا M2 ساوي 4
+
+397
+00:30:31,200 --> 00:30:34,640
+كمثال آخر فهي equivalence relation إيش بدنا نثبت؟
+
+398
+00:30:34,640 --> 00:30:38,880
+بدنا نحسب صفوف التكافة بدنا نحسب صفوف التكافة
+
+399
+00:30:38,880 --> 00:30:43,240
+solution فبده X أو Z خلّينا نسميها لأن هو Z الآن X
+
+400
+00:30:43,240 --> 00:30:45,960
+سوا و Z نحكي إن أنا بده تكافة؟ أه يو بديكي يا هو
+
+401
+00:30:45,960 --> 00:30:49,020
+ما جالكيش يثبتي جالكي بس بده يحسب صفوف التكافة هو
+
+402
+00:30:49,020 --> 00:30:52,850
+هي معروفة احنا أخدناها مثال فهذه على أبسلون، ماذا
+
+403
+00:30:52,850 --> 00:31:06,850
+يتساوي كل X على أبسلون بحيث X أنتمي لـ Z؟ X
+
+404
+00:31:06,850 --> 00:31:12,550
+بيساوي Z؟ مدينيها بشكل صريح طبعا هذا المثال مفروض
+
+405
+00:31:12,550 --> 00:31:16,560
+يتشابش بالمثال الماضي لكن فيه اختلاف المجموع الان
+
+406
+00:31:16,560 --> 00:31:20,260
+مش finite أبدأ أحسب صف الواحد صف الـ zero لأ فدي
+
+407
+00:31:20,260 --> 00:31:24,040
+infinite فهل ممكن نحسبهم بالدور زي ما عملنا توي لأ
+
+408
+00:31:24,040 --> 00:31:27,900
+بدا ناخد نشوف نحاول كيف نحسب نحسب بعض العناصر و
+
+409
+00:31:27,900 --> 00:31:31,740
+نوجد انه حسبناهم كلهم بتبدو مين النظريتين السابقة
+
+410
+00:31:31,740 --> 00:31:35,240
+يعني من وين ممكن أبدأ من الصفر لإن مافيش لأ بداية
+
+411
+00:31:35,240 --> 00:31:38,380
+المجموع ممكن أبدأ من الصفر نصف خلينا نبدأ من صف
+
+412
+00:31:38,380 --> 00:31:42,920
+الصفر إيش بيساوي صف الصفر؟ بيساوي العناصر اللي
+
+413
+00:31:42,920 --> 00:31:47,780
+علاقة مع الصفر بيساوي Y في الـ Z such that اللي هو
+
+414
+00:31:47,780 --> 00:31:51,440
+صفر أو equal صفر Y تنتمي لل relation خليني أكتبها
+
+415
+00:31:51,440 --> 00:31:57,320
+بالتفصيل تمام، ماذا يعني صفر Y في ال relation؟ إيش
+
+416
+00:31:57,320 --> 00:32:00,420
+معناته أن الـ Y اللي علاقة مع الصفر؟ يعني صفر ناقص
+
+417
+00:32:00,420 --> 00:32:09,040
+Y تساوي 4K for some K في الـ Z تمام واضحة ولا مش
+
+418
+00:32:09,040 --> 00:32:14,380
+واضحة أنا بدي Y إيش الـ Y مالها سالب اربعة K فانا
+
+419
+00:32:14,380 --> 00:32:20,500
+بدي أساوي كل Y في الـ Z على صورة سالب اربعة K for
+
+420
+00:32:20,500 --> 00:32:23,320
+some K في الـ Z 
+
+421
+00:32:26,730 --> 00:32:30,510
+أنا يمكن ماشي بسرعة شوية، واضحة ولا أعيد؟ اه، ها هي
+
+422
+00:32:30,510 --> 00:32:34,450
+تعريف الصف، وهاي الـrelation، إيش معناه إن الـY في 
+
+423
+00:32:34,450 --> 00:32:37,570
+صف الـX اللي هو بيساوي صفر في هذا المثال، إن الـY لا 
+
+424
+00:32:37,570 --> 00:32:40,470
+علاقة مع الصفر، إيش معناه؟ لا علاقة مع الصفر يعني
+
+425
+00:32:40,470 --> 00:32:45,170
+صفر ناقص Y تساوي 4K، أنا مين مهتم؟ مهتم بالـY، فالـY 
+
+426
+00:32:45,170 --> 00:32:50,720
+هتكون على صورة مين؟ سالب 4K، كام ممكن نفسرها هذه؟
+
+427
+00:32:50,720 --> 00:32:54,120
+يعني الـY من مضاعفات الأربعة ولا لأ؟ إيش معناه 
+
+428
+00:32:54,120 --> 00:32:58,660
+أربعة في K؟ فيعني هذا الصف إيش بيساوي؟ طيب وإن 
+
+429
+00:32:58,660 --> 00:33:01,460
+إحنا مغمضين، إحنا بنعرف مين أول واحدة في صف الصفر؟
+
+430
+00:33:01,460 --> 00:33:05,680
+الصفر، صح ولا مش صح؟ لإن الصفر تقبل قسمها على أربعة
+
+431
+00:33:05,680 --> 00:33:09,860
+من مضاعفات الأربعة، مين كمان؟ زاد أو ناقص أربعة، زاد
+
+432
+00:33:09,860 --> 00:33:13,840
+أو ناقص ثمانية، زاد أو ناقص اثنا عشر، and so on فهي 
+
+433
+00:33:13,840 --> 00:33:22,340
+الصف الأول انعرف، فده هو الصف الأول، خلينا نحسب صف
+
+434
+00:33:22,340 --> 00:33:28,780
+الواحد مثلا، خلينا نحسب صف الواحد نشوف لحد ما 
+
+435
+00:33:28,780 --> 00:33:34,780
+الصورة توضحها لأ، نشوف بدنا نجيبهم كلهم ولا لأ، مين 
+
+436
+00:33:34,780 --> 00:33:41,990
+صف الواحد؟ هو واحد ومن غيره هو كل Y في الـZ بحيث الـ
+
+437
+00:33:41,990 --> 00:33:47,170
+Y لعلاقة مع الـواحد، أكتبها 1، Y تنتمي للـ
+
+438
+00:33:47,170 --> 00:33:55,090
+relation وهذا يساوي كل Y، 1-Y تساوي 4K for 
+
+439
+00:33:55,090 --> 00:34:03,840
+some K تنتمي للـZ، هل الصورة واضحة؟ أنا معنى بـY إيش
+
+440
+00:34:03,840 --> 00:34:07,500
+بدنا الـY؟ تحقق 1-Y، إذا مين أنا؟ كيف 
+
+441
+00:34:07,500 --> 00:34:12,400
+نعملها؟ كتابة Y إيش بتساوي؟ فلو حلّينا لـY، صحيح، Y
+
+442
+00:34:12,400 --> 00:34:19,900
+تنتمي للـZ بحيث Y تساوي 1-4K for some
+
+443
+00:34:19,900 --> 00:34:26,610
+K تنتمي للـZ، نبدأ نحسب بعض العناصر، من أول عنصر في
+
+444
+00:34:26,610 --> 00:34:29,730
+الـY، الواحد هيكون في الصف، طب بيه موجود ولا مش 
+
+445
+00:34:29,730 --> 00:34:33,990
+موجود؟ نعم، لو أخدت K بتساوي zero for some K تنتمي 
+
+446
+00:34:33,990 --> 00:34:36,910
+للـZ، طب أخدنا الـzero، ناخد K بتساوي واحد، إيش في
+
+447
+00:34:36,910 --> 00:34:41,370
+الدنيا؟ ايه؟ سالب ثلاثة، الـY، طب خدي K بتساوي سالب 
+
+448
+00:34:41,370 --> 00:34:46,210
+واحد، إيش في الدنيا؟ خمسة، واضحت الصورة ولا مااضحتش؟ وأنت 
+
+449
+00:34:46,210 --> 00:34:49,290
+ماشي اليمين زيدي أربعة، وأنت ماشي اليسار انطرحي 
+
+450
+00:34:49,290 --> 00:34:54,870
+أربعة، فتسعة، ثلاثة عشر، and so on، طبعا، أو خذ K، أخدنا K
+
+451
+00:34:54,870 --> 00:34:58,110
+Zero، واحد، وسالب واحد، خذ K بتساوي سالب اثنين
+
+452
+00:34:58,110 --> 00:35:02,710
+بتدينا تسعة، خذ K بتساوي سالب ثلاثة بتدينا ثلاثة عشر، خذ
+
+453
+00:35:02,710 --> 00:35:07,770
+K بتساوي اثنين بتدينا سالب سبعة، and so on، فهذا صف 
+
+454
+00:35:07,770 --> 00:35:16,910
+الواحد، خلص 
+
+455
+00:35:16,910 --> 00:35:23,460
+الصفوف ولا لسه؟ لأ، لسه، لأنه زي ما أنتم شايفين، وين
+
+456
+00:35:23,460 --> 00:35:27,480
+صف الاثنين؟ مش موجود، اه، لأنه حتى الاثنين مش موجودة في 
+
+457
+00:35:27,480 --> 00:35:31,340
+صف الصفر، طبعا صف الصفر منهانش بسانتش، صف الصفر 
+
+458
+00:35:31,340 --> 00:35:35,550
+بيساوي صف الأربعة، حاضر، بس، وصف الثمانية وصف السالب 
+
+459
+00:35:35,550 --> 00:35:39,010
+أربعة، ففيش داعي أن أعيد أحسب صف الأربعة ولا صف
+
+460
+00:35:39,010 --> 00:35:41,770
+السالب أربعة زي من المحاضرة الماضية، ففيش داعي أحسب
+
+461
+00:35:41,770 --> 00:35:44,770
+صف الخمسة وصف السالب ثلاثة لأنهم متساويين مع هذا
+
+462
+00:35:44,770 --> 00:35:50,570
+الصف، أعيد هنا لعند هنا، واضحة؟ حلّينا المعادلة دي للـ
+
+463
+00:35:50,570 --> 00:35:54,720
+واي، طبعا نبدأ ناخد K، بلّ تتنتبه للـZ، ممكن K تساوي 
+
+464
+00:35:54,720 --> 00:35:57,460
+Zero، فإذا أول عنصر هو الواحد زي ما احنا متوقعين، و
+
+465
+00:35:57,460 --> 00:36:01,640
+لا لأ، طيب لو خدنا K تساوي واحد، 1-4، سالب ثلاثة
+
+466
+00:36:01,640 --> 00:36:05,020
+سالب ثلاثة، طب لو خدنا الـK تساوي سالب واحد، صحيح 
+
+467
+00:36:05,020 --> 00:36:07,940
+خمسة، فواضح إن الصيغة إيش؟ امشي زيدي أربعة وأنت رايح
+
+468
+00:36:07,940 --> 00:36:10,620
+على اليمين، واترحي أربعة وأنت رايح على اليسار
+
+469
+00:36:10,620 --> 00:36:15,300
+نعم؟ اه طبعا، هي ماشي كل ما أنت ... وأنت رايح على 
+
+470
+00:36:15,300 --> 00:36:20,800
+اليمين بزيدي أربعة، وبتمشي، وهذا كام؟ تمام، خلينا نحسب
+
+471
+00:36:20,800 --> 00:36:24,880
+صفة 2 عبارة
+
+472
+00:36:24,880 --> 00:36:32,900
+عن Y بحيث Y إيش بتساوي؟ 2-4K، بس لو عمّمنا، بدي 
+
+473
+00:36:32,900 --> 00:36:36,840
+أختصر الآن لإنه واضحة السياسة ولا لأ؟ اه، فبتنا E
+
+474
+00:36:36,840 --> 00:36:38,180
+على أد شكل، طبعا الـforce sum K 
+
+475
+00:36:43,270 --> 00:36:48,030
+طبعا بنفس الأسلوب، مين أول عنصر؟ الاثنين، لو أخدنا 
+
+476
+00:36:48,030 --> 00:36:52,030
+بتساوي واحد، الـK سالب اثنين، فنفس السياسة، بنزيد 
+
+477
+00:36:52,030 --> 00:36:56,750
+أربعة، فإذا نجي تكون ستة، عشرة، and so on، بنطرح 
+
+478
+00:36:56,750 --> 00:37:03,750
+أربعة، فده صف الاثنين، خلصت كل العناصر ولا ماغطّوش 
+
+479
+00:37:03,750 --> 00:37:09,920
+لسه؟ صف الثلاث لأنه واضح لازم يكون عندنا عايش 
+
+480
+00:37:09,920 --> 00:37:13,180
+equivalence relation بتأدي لـ partition، فلازم
+
+481
+00:37:13,180 --> 00:37:17,240
+الصفوف يغطوا كل العناصر، ف أنا واضح في الصف الأول
+
+482
+00:37:17,240 --> 00:37:23,200
+غطيت مضاعفات الأربعة، في الصف الثاني غطيت الأعداد
+
+483
+00:37:23,200 --> 00:37:27,250
+اللي بتقبل القسم على أربعة والباقي واحد، في الصف
+
+484
+00:37:27,250 --> 00:37:30,770
+الثالث، غطيت الأعداد اللي بتقبل قسمة الأربعة والباقي
+
+485
+00:37:30,770 --> 00:37:34,090
+اثنين، إيش تم احتمال اللي بتقبل أربعة وصافي ثلاثة، و
+
+486
+00:37:34,090 --> 00:37:37,570
+الباقي ثلاثة، وهينتهي، وهينتهي، اه، فطبعا هذه بتساوي
+
+487
+00:37:37,570 --> 00:37:43,410
+طبعا ثلاثة، نفس السياسة، سبعة، أحد عشر، أنسؤ لو حسبته 
+
+488
+00:37:43,410 --> 00:37:49,200
+سالب واحد، سالب خمسة، أنسؤ بس مش غيرهم الآن، لو 
+
+489
+00:37:49,200 --> 00:37:53,020
+طلعت اي عدد، مين بده يحسب هين؟ حسبنا الصفر والواحد
+
+490
+00:37:53,020 --> 00:37:56,480
+والاثنين والثلاثة، صف الأربعة هو صف الصفر، خلص، صف
+
+491
+00:37:56,480 --> 00:37:59,900
+الخمسة هو وين موجود؟ الخمسة موجود هيا وهاكذا، فأي 
+
+492
+00:37:59,900 --> 00:38:04,220
+عدد هتلاقوه موجود، طبعا العدد بعيد إيش بده أعمل؟ هل 
+
+493
+00:38:04,220 --> 00:38:08,080
+اي عدد مثلا بده يحسب صف المائة؟ صف المائة اللي علاقة
+
+494
+00:38:08,080 --> 00:38:11,860
+مع مين؟ مع علاقة مع الصفر؟ اه، بتقبل قسمه على 
+
+495
+00:38:11,860 --> 00:38:15,660
+أربعة لأنه ... ليش؟ لأنه 100-0 بتساوي أربعة 
+
+496
+00:38:15,660 --> 00:38:19,160
+في خمسة وعشرين، صح، وهكذا، فأي عدد هيكون واحدة من
+
+497
+00:38:19,160 --> 00:38:24,360
+الأربعة، فإذا الصفوف كلها، thus، Z على هذه الـ
+
+498
+00:38:24,360 --> 00:38:30,340
+relation بتكون من أربع صفوف، صف الصفر وصف الواحد و
+
+499
+00:38:30,340 --> 00:38:37,460
+صف الاثنين وصف الثلاثة، ف أنا بمساعدة النظرية تأكدت 
+
+500
+00:38:37,460 --> 00:38:40,940
+إن الحساب انتهى، الحساب انتهى، لأنه صار عندي معلومات 
+
+501
+00:38:40,940 --> 00:38:44,700
+تأكد لي إن العملية انتهت، أربع صفوف فقط، وطبعا إيش
+
+502
+00:38:44,700 --> 00:38:49,160
+ولا صف فاضي زي ما أنتم شايفين، ولا صفين فيهم عنصر
+
+503
+00:38:49,160 --> 00:38:54,060
+مشترك، لأنه زي ما هنا بيدينا الحالات الأربع لعملية 
+
+504
+00:38:54,060 --> 00:38:57,700
+القسم على أربعة، يا الباقي صفر، يا الباقي واحد، يا
+
+505
+00:38:57,700 --> 00:39:01,780
+اثنين يا ثلاثة، مافيش احتمال خامس، فهذا بيساعدنا في 
+506
+00:39:01,780 --> 00:39:02,480
+الحساب
+
+507
+00:39:12,780 --> 00:39:21,310
+فتعليق على ما سبق، فإحنا في النظرية الماضية شفنا أو 
+
+508
+00:39:21,310 --> 00:39:26,570
+تعلمنا أن أي equivalence relation بتأدي إلى 
+
+509
+00:39:26,570 --> 00:39:30,390
+partition أو بتولد partition، كيف؟ هذا التجزيق عبارة
+
+510
+00:39:30,390 --> 00:39:34,550
+عن صفوف التكافؤ، فالسؤال اللي هنطرحه، طب هل العكس
+
+511
+00:39:34,550 --> 00:39:38,590
+صحيح؟ هل كل partition بيقدر يعرف equivalence 
+
+512
+00:39:38,590 --> 00:39:43,050
+relation؟ هذا اللي هنشوفه في الدراسة القادمة
+
+513
+00:39:55,520 --> 00:39:59,480
+فإحنا الحقيقة في نهاية الـ search هنوصل للصورة
+
+514
+00:39:59,480 --> 00:40:04,560
+التالية، إذا بدأنا من علاقة تكافؤ بنقدر نولد
+
+515
+00:40:04,560 --> 00:40:08,680
+partition، والـpartition بيولد علاقة تكافؤ هي
+
+516
+00:40:08,680 --> 00:40:11,760
+العلاقة اللي بدأنا منها، ففي دائرة، أنا مكتملة، أنا 
+
+517
+00:40:11,760 --> 00:40:16,150
+دائرة مكتملة، طبعا نص الدائرة خلص، إذا إن كل علاقة 
+
+518
+00:40:16,150 --> 00:40:20,510
+تكافؤ تولد partition، فالسؤال العكسي، هل كل
+
+519
+00:40:20,510 --> 00:40:23,930
+partition بولد علاقة تكافؤ؟ فده اللي هندرسه مع بعض
+
+520
+00:40:23,930 --> 00:40:28,070
+طبعا أول شيء أنا بدي أولد علاقة تكافؤ، فبنشوف كيف
+
+521
+00:40:28,070 --> 00:40:31,330
+نولد علاقة من partition، كيف نولد علاقة من
+
+522
+00:40:31,330 --> 00:40:36,550
+partition، فالعنوان الفرعي relations induced by
+
+523
+00:40:36,550 --> 00:40:42,910
+partition، العلاقات المتولدة من الـpartition، فلو كان
+
+524
+00:40:42,910 --> 00:40:48,250
+عندي partition، كيف منه بدي أعرف علاقة؟ الصورة شكل 
+
+525
+00:40:48,250 --> 00:40:54,950
+الثالث، عندنا مجموعة X مقسمة تقسيم معين
+
+526
+00:41:00,110 --> 00:41:04,410
+مقسمة في partition معين، طبعا خواص الـpartition، ولا
+
+527
+00:41:04,410 --> 00:41:08,190
+جزء فاضي، واي جزءين يا متطابقين يا disjoined يا 
+
+528
+00:41:08,190 --> 00:41:11,710
+مفصلين، وكل الأجزاء اتحادها بيدينا جنب المجموعه، اكسر
+
+529
+00:41:11,710 --> 00:41:20,570
+فإحنا هنعرف الـrelation بالشكل التالي، فالعنصرين
+
+530
+00:41:21,530 --> 00:41:26,830
+هيكون إلهم علاقة مع بعض إذا وقعوا في نفس الجزء، إذا 
+
+531
+00:41:26,830 --> 00:41:30,770
+وقعوا في نفس الجزء، فإحنا في عندنا partitions، أي 
+
+532
+00:41:30,770 --> 00:41:35,830
+أجزاء متعددة، إذا وقع العنصرين في جزء مع بعض، لإن 
+
+533
+00:41:35,830 --> 00:41:38,210
+إحنا عارفين إن الأجزاء دي منفصلة عن بعض، فبينا 
+
+534
+00:41:38,210 --> 00:41:42,430
+نختبرهم إيش إلهم علاقة مع بعض، وإلا مافيش علاقة،
+
+535
+00:41:42,430 --> 00:41:46,250
+فهذه هي الصورة، طبعا إحنا هنمشي بيها تدريج، هنشوف
+
+536
+00:41:46,250 --> 00:41:49,070
+هذا الـrelation ونفهمها، ومن ثم هنثبت إن هذه
+
+537
+00:41:49,070 --> 00:41:52,490
+العلاقة المتولدة بهذه الطريقة دايما هي علاقة
+
+538
+00:41:52,490 --> 00:41:56,570
+تكافؤ، دايما هي علاقة تكافؤ، وهذا إحنا هنثبته في 
+
+539
+00:41:56,570 --> 00:41:59,230
+نظرية فيما بعد
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/R-1opTyixLc_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/R-1opTyixLc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..964b576bbba861870fd8420a572c0b5cba5fa624
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/R-1opTyixLc_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4049, "start": 20.43, "end": 40.49, "text": "بسم الله الرحمن الرحيم في المحاضرة الأخيرة كنا بنتحدث عن طبعا شرحنا ال partition كيف بنجزق المجموعة في تلت شروط لازم كل جزء مايكونش فارغ وكل جزئين يا إما بيكونوا كل عناصرهم مشتركة أي متطابقين أو اللي هو ما disjoint ولا عنصر مشترك", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8978, 9673, 5016, 46958, 25720, 16247, 9778, 48923, 9122, 8315, 4724, 29399, 24401, 12984, 18871, 23032, 3555, 3615, 995, 13412, 2288, 5016, 8315, 2423, 24808, 9122, 33911, 44945, 7435, 11622, 4587, 9673, 7435, 2304, 2407, 27884, 8978, 6055, 1211, 2655, 13412, 32887, 9566, 5296, 31377, 2304, 28242, 10874, 11622, 38207, 19446, 1829, 30544, 8592, 6156, 9640, 17082, 4032, 28820, 10874, 11622, 19986, 9957, 35186, 11933, 15042, 4724, 1829, 30544, 14407, 28242, 18871, 33546, 2288, 16095, 37893, 2655, 31747, 3660, 36632, 44650, 9566, 16758, 4587, 9957, 34051, 13672, 1829, 31439, 19446, 717, 48613, 49429, 18871, 9381, 2288, 37893, 2655, 31747], "avg_logprob": -0.1571100977582669, "compression_ratio": 1.7124463519313304, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 20.43, "end": 20.75, "word": "بسم", "probability": 0.898193359375}, {"start": 20.75, "end": 20.89, "word": " الله", "probability": 0.9716796875}, {"start": 20.89, "end": 21.23, "word": " الرحمن", "probability": 0.9669596354166666}, {"start": 21.23, "end": 21.61, "word": " الرحيم", "probability": 0.9951171875}, {"start": 21.61, "end": 22.39, "word": " في", "probability": 0.464599609375}, {"start": 22.39, "end": 22.83, "word": " المحاضرة", "probability": 0.9443359375}, {"start": 22.83, "end": 23.35, "word": " الأخيرة", "probability": 0.9664713541666666}, {"start": 23.35, "end": 23.89, "word": " كنا", "probability": 0.94287109375}, {"start": 23.89, "end": 24.65, "word": " بنتحدث", "probability": 0.81719970703125}, {"start": 24.65, "end": 24.91, "word": " عن", "probability": 0.9619140625}, {"start": 24.91, "end": 25.35, "word": " طبعا", "probability": 0.8616943359375}, {"start": 25.35, "end": 25.97, "word": " شرحنا", "probability": 0.8853759765625}, {"start": 25.97, "end": 26.09, "word": " ال", "probability": 0.900390625}, {"start": 26.09, "end": 26.51, "word": " partition", "probability": 0.7216796875}, {"start": 26.51, "end": 27.59, "word": " كيف", "probability": 0.937744140625}, {"start": 27.59, "end": 28.23, "word": " بنجزق", "probability": 0.8411865234375}, {"start": 28.23, "end": 28.89, "word": " المجموعة", "probability": 0.9208984375}, {"start": 28.89, "end": 29.11, "word": " في", "probability": 0.9345703125}, {"start": 29.11, "end": 29.39, "word": " تلت", "probability": 0.8570963541666666}, {"start": 29.39, "end": 29.85, "word": " شروط", "probability": 0.8873697916666666}, {"start": 29.85, "end": 30.33, "word": " لازم", "probability": 0.92626953125}, {"start": 30.33, "end": 30.57, "word": " كل", "probability": 0.97265625}, {"start": 30.57, "end": 30.95, "word": " جزء", "probability": 0.99462890625}, 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تمام", "probability": 0.97314453125}, {"start": 813.59, "end": 814.37, "word": " فانا", "probability": 0.84912109375}, {"start": 814.37, "end": 814.55, "word": " بدي", "probability": 0.5079345703125}, {"start": 814.55, "end": 814.87, "word": " اخد", "probability": 0.7145182291666666}, {"start": 814.87, "end": 815.23, "word": " ايش", "probability": 0.794921875}], "temperature": 1.0}, {"id": 35, "seek": 84348, "start": 816.34, "end": 843.48, "text": "عنصر في الـ partition اللي هو مجموعة يعني طيب، كيف صور المجموعات في الـ partition الأن؟ صفر، إذا بدأ أقول له let a be in the partition يعني إيش ده تساوي؟ X على أبسلون، ممكن أعود بصيغة أخرى، أقول له let small x تنتمي لcapital X لأنه إيش بتكون الصفوف؟ X تنتمي لcapital X كل عنصر بيولد صفر تكافه، ولا لأ؟ كل عنصر إيه صفه، فإيش and؟", "tokens": [3615, 1863, 9381, 2288, 8978, 2423, 39184, 24808, 13672, 1829, 31439, 3714, 7435, 2304, 2407, 27884, 37495, 22653, 23032, 1829, 3555, 12399, 9122, 33911, 20328, 13063, 9673, 7435, 2304, 45367, 9307, 8978, 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"word": " بيدينا", "probability": 0.7689208984375}, {"start": 2331.4, "end": 2332.38, "word": " الحالات", "probability": 0.9601236979166666}, {"start": 2332.38, "end": 2333.38, "word": " الأربعة", "probability": 0.8937174479166666}, {"start": 2333.38, "end": 2334.06, "word": " لعملية", "probability": 0.8621826171875}, {"start": 2334.06, "end": 2334.42, "word": " القسم", "probability": 0.958251953125}, {"start": 2334.42, "end": 2334.6, "word": " على", "probability": 0.83154296875}, {"start": 2334.6, "end": 2335.16, "word": " أربعة", "probability": 0.8748372395833334}, {"start": 2335.16, "end": 2335.48, "word": " يا", "probability": 0.57470703125}, {"start": 2335.48, "end": 2335.9, "word": " الباقي", "probability": 0.9593098958333334}, {"start": 2335.9, "end": 2336.32, "word": " صفر", "probability": 0.9357096354166666}, {"start": 2336.32, "end": 2336.68, "word": " يا", "probability": 0.82373046875}, {"start": 2336.68, "end": 2337.08, "word": " الباقي", "probability": 0.98974609375}, {"start": 2337.08, "end": 2337.52, "word": " واحد", "probability": 0.980712890625}, {"start": 2337.52, "end": 2337.7, "word": " يا", "probability": 0.7861328125}, {"start": 2337.7, "end": 2337.98, "word": " اتنين", "probability": 0.93896484375}, {"start": 2337.98, "end": 2338.12, "word": " يا", "probability": 0.84228515625}, {"start": 2338.12, "end": 2338.34, "word": " تلاتة", "probability": 0.9061279296875}, {"start": 2338.34, "end": 2338.54, "word": " مافيش", "probability": 0.884765625}, {"start": 2338.54, "end": 2338.92, "word": " احتمال", "probability": 0.9810791015625}, {"start": 2338.92, "end": 2339.52, "word": " خامس", "probability": 0.9625651041666666}, {"start": 2339.52, "end": 2340.54, "word": " فهذا", "probability": 0.76220703125}, {"start": 2340.54, "end": 2341.56, "word": " بيساعدنا", "probability": 0.97900390625}, {"start": 2341.56, "end": 2341.78, "word": " في", "probability": 0.9794921875}, {"start": 2341.78, "end": 2342.48, "word": " الحساب", "probability": 0.9921875}], "temperature": 1.0}, {"id": 102, "seek": 235848, "start": 2352.78, "end": 2358.48, "text": "فتعليق على ما سبق فاحنا في النظرية الماضية", "tokens": [5172, 2655, 3615, 20292, 4587, 15844, 19446, 8608, 3555, 4587, 6156, 39319, 8315, 8978, 28239, 19913, 2288, 10632, 9673, 46958, 10632], "avg_logprob": -0.1271306804635308, "compression_ratio": 1.1323529411764706, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2352.7799999999997, "end": 2354.04, "word": "فتعليق", "probability": 0.80390625}, {"start": 2354.04, "end": 2354.7, "word": " على", "probability": 0.8388671875}, {"start": 2354.7, "end": 2354.96, "word": " ما", "probability": 0.93310546875}, {"start": 2354.96, "end": 2355.56, "word": " سبق", "probability": 0.9908854166666666}, {"start": 2355.56, "end": 2357.0, "word": " فاحنا", "probability": 0.7503255208333334}, {"start": 2357.0, "end": 2357.12, "word": " في", "probability": 0.94189453125}, {"start": 2357.12, "end": 2357.68, "word": " النظرية", "probability": 0.960693359375}, {"start": 2357.68, "end": 2358.48, "word": " الماضية", "probability": 0.9716796875}], "temperature": 1.0}, {"id": 103, "seek": 238305, "start": 2359.53, "end": 2383.05, "text": "شفنا أو تعلمنا أن أي equivalence relation بتأدي إلى partition أو بتولد partition كيف هذا التجزيق عبارة عن صفوف التكافئة فالسؤال اللي هنطرحه طب هل العكس صحيح؟ هل كل partition بيقدر يعرف equivalence relation؟ هذا اللي هنشوفه في الدراسة القادمة", "tokens": [8592, 5172, 8315, 34051, 37279, 19528, 8315, 14739, 36632, 9052, 655, 9721, 39894, 10721, 16254, 30731, 24808, 34051, 39894, 12610, 3215, 24808, 9122, 33911, 23758, 16712, 7435, 11622, 1829, 4587, 6225, 3555, 9640, 3660, 18871, 20328, 5172, 38688, 16712, 4117, 31845, 19986, 3660, 6156, 6027, 3794, 33604, 6027, 13672, 1829, 8032, 1863, 9566, 2288, 5016, 3224, 23032, 3555, 8032, 1211, 18863, 4117, 3794, 20328, 5016, 1829, 5016, 22807, 8032, 1211, 28242, 24808, 4724, 1829, 28543, 2288, 37495, 28480, 9052, 655, 9721, 22807, 23758, 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{"start": 2372.75, "end": 2372.89, "word": " اللي", "probability": 0.935546875}, {"start": 2372.89, "end": 2373.57, "word": " هنطرحه", "probability": 0.838134765625}, {"start": 2373.57, "end": 2373.91, "word": " طب", "probability": 0.5205078125}, {"start": 2373.91, "end": 2374.15, "word": " هل", "probability": 0.95654296875}, {"start": 2374.15, "end": 2374.55, "word": " العكس", "probability": 0.9938151041666666}, {"start": 2374.55, "end": 2375.39, "word": " صحيح؟", "probability": 0.95791015625}, {"start": 2375.39, "end": 2375.85, "word": " هل", "probability": 0.951171875}, {"start": 2375.85, "end": 2376.25, "word": " كل", "probability": 0.98095703125}, {"start": 2376.25, "end": 2376.85, "word": " partition", "probability": 0.92578125}, {"start": 2376.85, "end": 2377.55, "word": " بيقدر", "probability": 0.981201171875}, {"start": 2377.55, "end": 2377.99, "word": " يعرف", "probability": 0.979736328125}, {"start": 2377.99, "end": 2378.59, "word": " equivalence", "probability": 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2502.43, "word": " علاقة،", "probability": 0.82110595703125}, {"start": 2502.43, "end": 2502.71, "word": " فهذه", "probability": 0.9368489583333334}, {"start": 2502.71, "end": 2502.91, "word": " هي", "probability": 0.6416015625}, {"start": 2502.91, "end": 2503.81, "word": " الصورة،", "probability": 0.8551025390625}, {"start": 2503.81, "end": 2504.63, "word": " طبعا", "probability": 0.8970947265625}, {"start": 2504.63, "end": 2504.75, "word": " احنا", "probability": 0.8177083333333334}, {"start": 2504.75, "end": 2505.19, "word": " هنمشي", "probability": 0.95595703125}, {"start": 2505.19, "end": 2505.33, "word": " بيها", "probability": 0.72314453125}, {"start": 2505.33, "end": 2505.95, "word": " تدريج،", "probability": 0.8634765625}, {"start": 2505.95, "end": 2506.25, "word": " هنشوف", "probability": 0.9521484375}, {"start": 2506.25, "end": 2506.41, "word": " هذا", "probability": 0.285400390625}, {"start": 2506.41, "end": 2506.51, "word": " ال", "probability": 0.7939453125}, {"start": 2506.51, "end": 2506.83, "word": " relation", "probability": 0.90234375}, {"start": 2506.83, "end": 2507.55, "word": " ونفهمها", "probability": 0.87841796875}, {"start": 2507.55, "end": 2508.09, "word": " ومن", "probability": 0.659912109375}, {"start": 2508.09, "end": 2508.35, "word": " ثم", "probability": 0.997314453125}, {"start": 2508.35, "end": 2508.77, "word": " هنثبت", "probability": 0.9658203125}, {"start": 2508.77, "end": 2508.85, "word": " ان", "probability": 0.320556640625}, {"start": 2508.85, "end": 2509.07, "word": " هذه", "probability": 0.78564453125}, {"start": 2509.07, "end": 2509.47, "word": " العلاقة", "probability": 0.8313802083333334}, {"start": 2509.47, "end": 2510.15, "word": " المتولدة", "probability": 0.9739990234375}, {"start": 2510.15, "end": 2510.59, "word": " بهذه", "probability": 0.967041015625}, {"start": 2510.59, "end": 2511.19, "word": " الطريقة", "probability": 0.9920247395833334}, {"start": 2511.19, "end": 2511.97, "word": " دايما", "probability": 0.7874348958333334}, {"start": 2511.97, "end": 2512.13, "word": " هي", "probability": 0.95556640625}, {"start": 2512.13, "end": 2512.49, "word": " علاقة", "probability": 0.9830729166666666}, {"start": 2512.49, "end": 2513.25, "word": " تكافؤ،", "probability": 0.84833984375}, {"start": 2513.25, "end": 2513.63, "word": " دايما", "probability": 0.92919921875}, {"start": 2513.63, "end": 2513.81, "word": " هي", "probability": 0.97412109375}, {"start": 2513.81, "end": 2514.33, "word": " علاقة", "probability": 0.9713541666666666}, {"start": 2514.33, "end": 2515.43, "word": " تكافؤ،", "probability": 0.94892578125}, {"start": 2515.43, "end": 2515.65, "word": " وهذا", "probability": 0.6544596354166666}, {"start": 2515.65, "end": 2515.79, "word": " احنا", "probability": 0.8570963541666666}, {"start": 2515.79, "end": 2516.33, "word": " هنثبته", "probability": 0.94755859375}, {"start": 2516.33, "end": 2516.57, "word": " في", "probability": 0.88134765625}, {"start": 2516.57, "end": 2517.91, "word": " نظرية", "probability": 0.76251220703125}, {"start": 2517.91, "end": 2518.95, "word": " فيما", "probability": 0.668212890625}, {"start": 2518.95, "end": 2519.23, "word": " بعد", "probability": 0.9384765625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2519.5740625, "duration_after_vad": 2405.1987499999937}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/R-1opTyixLc_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/R-1opTyixLc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..29ef2f7a36dfc90c83e91d06c7cf7fa8eb91f056
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/R-1opTyixLc_raw.srt
@@ -0,0 +1,2156 @@
+1
+00:00:20,430 --> 00:00:23,890
+بسم الله الرحمن الرحيم في المحاضرة الأخيرة كنا
+
+2
+00:00:23,890 --> 00:00:28,230
+بنتحدث عن طبعا شرحنا ال partition كيف بنجزق
+
+3
+00:00:28,230 --> 00:00:32,770
+المجموعة في تلت شروط لازم كل جزء مايكونش فارغ وكل
+
+4
+00:00:32,770 --> 00:00:36,670
+جزئين يا إما بيكونوا كل عناصرهم مشتركة أي متطابقين
+
+5
+00:00:36,670 --> 00:00:42,240
+أو اللي هو ما disjoint ولا عنصر مشتركالـ Partition
+
+6
+00:00:42,240 --> 00:00:46,860
+فيه تلت شروط، ولا جزء يكون فارغ، كل جزءين يا إما
+
+7
+00:00:46,860 --> 00:00:50,980
+متطابقين أو disjoint، مافيش ولا عنصر مشترك بينهم،
+
+8
+00:00:50,980 --> 00:00:54,280
+أيضًا الواتحاد كل الأجزاء بدغطي كل ال X، هذا
+
+9
+00:00:54,280 --> 00:00:59,280
+النقطة وضحناها، أيضًا عرفنا صف التكافؤ، هو عبارة
+
+10
+00:00:59,280 --> 00:01:02,380
+عن مجموعة العناصر اللي لهم علاقة، يعني صف التكافؤ
+
+11
+00:01:02,380 --> 00:01:05,140
+لل X هي عبارة عن جميع العناصر اللي لهم علاقة مع ال
+
+12
+00:01:05,140 --> 00:01:08,540
+Xأه طبعا شوفنا بعض الأمثلة الآن بدنا نستمر مع اللي
+
+13
+00:01:08,540 --> 00:01:12,160
+هو صف التكافؤ و نشوف خواص عامة لصف التكافؤ و يمكن
+
+14
+00:01:12,160 --> 00:01:15,620
+نلاحظنا بعض الأمور المشتركة في الأمثلة لكن هل هذا
+
+15
+00:01:15,620 --> 00:01:21,180
+الملاحظات عامة ولا كانت خاصة بالأمثلة نشوف مع
+
+16
+00:01:21,180 --> 00:01:24,920
+النظرية فنظرية رقم تلاتة تلاتة أي النظرية التالتة
+
+17
+00:01:24,920 --> 00:01:28,580
+في chapter تلاتة Properties of Equivalent Classes
+
+18
+00:01:29,510 --> 00:01:33,910
+برهنها .. جيد .. جيد .. اه فطبعا هنا طبعا الخواص
+
+19
+00:01:33,910 --> 00:01:37,710
+ان اكد عليها ان جميع الصفوف غير فارغة ولا صف بيكون
+
+20
+00:01:37,710 --> 00:01:43,710
+فارغ الصفين صف ال X و صف ال Y بيكون تقطعهم لا
+
+21
+00:01:43,710 --> 00:01:46,410
+يساوي Phi if and only if ال X و ال Y له ملاقة مع
+
+22
+00:01:46,410 --> 00:01:50,910
+بعض و طبعا C X و Y له ملاقة مع بعض فقط و إذا فقط
+
+23
+00:01:50,910 --> 00:01:55,030
+صفينهم متساوي فإذا احنا برهننا A و B طبعا علينا
+
+24
+00:01:55,030 --> 00:02:01,550
+انبرهن C .. ممتازةفاحنا بنستمر مع البرهان والجزء
+
+25
+00:02:01,550 --> 00:02:06,310
+المتبقى الـC طبعا الـC علاقة ايه برضه F and والف
+
+26
+00:02:06,310 --> 00:02:11,250
+فحنعملها two parts a proof فنبدأ بالاتجاه الاول
+
+27
+00:02:11,250 --> 00:02:19,870
+اللي هو XYالها علاقة مع بعض يؤدى ان صف ال X يساوي
+
+28
+00:02:19,870 --> 00:02:25,810
+صف ال Y فهذا هو المطلوب طبعا كالعادة هبدأ ان افترض
+
+29
+00:02:25,810 --> 00:02:33,350
+ان الشرط صحيح assume X Y تنتمي لل relation epsilon
+
+30
+00:02:33,350 --> 00:02:40,710
+او E مطلوب اثبت ان صف ال X يساوي صف ال Y فهذا
+
+31
+00:02:40,710 --> 00:02:45,240
+تساوي ايش؟المطلوب صف ال X يسوي صف ال Y صف ال X وصف
+
+32
+00:02:45,240 --> 00:02:48,940
+ال Y عبارة عن إيه؟مجموعات عبارة عن مجموعات فبنثبت
+
+33
+00:02:48,940 --> 00:02:52,400
+أن مجموعة تساوي مجموعة وهذه مهارة أساسية في
+
+34
+00:02:52,400 --> 00:02:56,120
+chapter 2 مستمرة معناها هنبدأ بعنصر من طرف من
+
+35
+00:02:56,120 --> 00:02:59,900
+الأطراف إذا ماشينا تكافئ التساوي انتهى إذا ماجدناش
+
+36
+00:02:59,900 --> 00:03:04,080
+نمشي تكافئ بثبت أن الأولة صفست من التانية والتانية
+
+37
+00:03:04,080 --> 00:03:08,620
+صفست من الأولة فهنبدأ بعنصر الآن فهذه ليش أصلا مشي
+
+38
+00:03:08,620 --> 00:03:11,640
+الأول لأن نجومنا شرطية فده إن الشرط صحيح الآن
+
+39
+00:03:11,640 --> 00:03:15,480
+بندثبت تساوي مجموعات ببدأ أنه أخد عنصر عشوائي من
+
+40
+00:03:15,480 --> 00:03:20,320
+طرف من الأطرافإيش نسميه العنصر؟ X ولا Y ولا عنصر
+
+41
+00:03:20,320 --> 00:03:24,660
+جديد؟ Z اسمه جديد أو K لأن X وY مشغولين فالآن بدي
+
+42
+00:03:24,660 --> 00:03:34,020
+أقوله إيش let Z تنتمي لصف ال X be any element طبعا
+
+43
+00:03:34,020 --> 00:03:36,060
+يمكن هذه الطريقة يمكن أول مرة بكتفها مش عارف إذا
+
+44
+00:03:36,060 --> 00:03:39,060
+ذكرت ولاية هي نفس الطريقة let Z be any element
+
+45
+00:03:39,060 --> 00:03:44,210
+such that Z تنتمي للطرف اليسارنفس المعنى، أخدنا
+
+46
+00:03:44,210 --> 00:03:47,910
+عنصر عشوائي عشان هو التعريف كله فيه for all و بدنا
+
+47
+00:03:47,910 --> 00:03:51,190
+نطلع عنصر وين يكون؟ في اليسار، في اليسار بصيغة
+
+48
+00:03:51,190 --> 00:03:54,430
+الكتابة بشكل مختلف لكن نفس المعنى، ممتاز، بدي
+
+49
+00:03:54,430 --> 00:03:59,020
+أحاول أوصل الزد هنا، إيش ممكن أعمله؟استخدمش تعريف
+
+50
+00:03:59,020 --> 00:04:01,360
+ال equivalence class وقت إيش ال Z في صف ال X إذا
+
+51
+00:04:01,360 --> 00:04:05,820
+كانت ال Z إلى علاقة مع مين مع ال X فهذا يؤدي إن X
+
+52
+00:04:05,820 --> 00:04:09,820
+و Z تنتمي لل relation طبعا هذه علاقة تكافؤ لأنه
+
+53
+00:04:09,820 --> 00:04:14,240
+تعريف ال equivalence class لكن أتوقع أنه مش هستمر
+
+54
+00:04:14,240 --> 00:04:21,230
+التكافؤ of X على ال relation تمام؟فال X و Z إلهم
+
+55
+00:04:21,230 --> 00:04:24,870
+علاقة مع ال Epsilon أنا وين رايح؟ كالعادة أنا عيني
+
+56
+00:04:24,870 --> 00:04:29,250
+على المطلوب أنا بدي أوصل ال Z لمين؟ لصف ال Y يعني
+
+57
+00:04:29,250 --> 00:04:34,190
+بدي أثبت إن ال Y إلى علاقة مع ال Z أكتب همش؟ وين
+
+58
+00:04:34,190 --> 00:04:39,830
+رايحين؟ بدنا ال Z تنتمي لصف ال Y، مطلوب يعني بدنا
+
+59
+00:04:39,830 --> 00:04:45,950
+Y Z في ال relation، مطلوب فالسؤال، عندي X Z في ال
+
+60
+00:04:45,950 --> 00:04:50,240
+relationوعندي x y في ال relation إيش ممكن أستخدم؟
+
+61
+00:04:50,240 --> 00:04:53,440
+التعدي طب إيش عرفك إن أنا تعدي؟ لأنه ليه إيش ال
+
+62
+00:04:53,440 --> 00:04:55,960
+epsilon equivalence relation مقدمة أه أحنا
+
+63
+00:04:55,960 --> 00:04:58,300
+ماكتبناش لك أنا مقدمة جالك ليه ال epsilon بيه ال
+
+64
+00:04:58,300 --> 00:05:00,200
+equivalence relation فالأنا اللي بشتغل معاها دي
+
+65
+00:05:00,200 --> 00:05:02,900
+ليه إيش ال equivalence relation طيب ماشي أنا عندي
+
+66
+00:05:02,900 --> 00:05:08,220
+x y بده أتخلص من ال x بنفع؟ بده أبدل أتخلص من ال x
+
+67
+00:05:08,220 --> 00:05:11,700
+دخلي ال x في النص x y بده أخليها .. بده أخليها إيش
+
+68
+00:05:11,700 --> 00:05:20,620
+هذي؟ x y بده أخليها y x أه y x أه أه butXY في ال
+
+69
+00:05:20,620 --> 00:05:25,940
+relation implies YX في ال relation، ليش؟ لأن
+
+70
+00:05:25,940 --> 00:05:29,220
+الكوين الاسرائيليش فهي symmetric، الدليل is
+
+71
+00:05:29,220 --> 00:05:37,340
+symmetricممتاز هل يتصار XZ او YX و XZ بال
+
+72
+00:05:37,340 --> 00:05:42,300
+Transitive اه .. Thus ايش صارت؟ ممكن اكتبها كخط بس
+
+73
+00:05:42,300 --> 00:05:45,520
+مش ضروري انه conjunction لان احنا متفقين كل خطوة
+
+74
+00:05:45,520 --> 00:05:49,040
+في البرهان هي true فهذه true وهذه true ممكن اضايق
+
+75
+00:05:49,040 --> 00:05:52,920
+ايه اللي هو ال X ومش بتصير؟ YZ تنتمي للأبسلون ليش؟
+
+76
+00:05:52,920 --> 00:05:58,240
+لأن الأبسلون is Transitive واضحة؟
+
+77
+00:05:58,730 --> 00:06:02,290
+هم تبقين؟ اه فاحنا تمام وهو المطلوب فهذا معناته
+
+78
+00:06:02,290 --> 00:06:09,070
+انه مين؟ ان Y أو Z في صف ال Y فإذن Y برضه Z تنتمي
+
+79
+00:06:09,070 --> 00:06:15,710
+لصف ال Y خليني أكتب فورا Thus Y is Z تنتمي لصف ال
+
+80
+00:06:15,710 --> 00:06:20,990
+Y اه
+
+81
+00:06:20,990 --> 00:06:25,070
+فبالتالي أثبتنا بدأنا من عنصر في صف ال X ووصلنا
+
+82
+00:06:25,070 --> 00:06:27,910
+لصف ال Y مش ماشيين تكافؤ زي ما تشوفين إذا أثبتنا
+
+83
+00:06:27,910 --> 00:06:28,350
+صف Z
+
+84
+00:06:34,770 --> 00:06:40,330
+فعنا صف ال X هو subset من صف ال Y فهذا واحد هذا
+
+85
+00:06:40,330 --> 00:06:44,470
+اللي بدنا إياه مستقيل مش هذا هذا المهم للإستنتاج
+
+86
+00:06:44,470 --> 00:06:48,570
+فهذه مالهاش داعي لو عملناها مش غلط لكن مش هي
+
+87
+00:06:48,570 --> 00:06:56,130
+المهمة هذه المهمة الآن العكس let Z تنتمي لصف ال Y
+
+88
+00:06:56,130 --> 00:07:00,030
+ب any element any element
+
+89
+00:07:02,210 --> 00:07:05,310
+طبعا لو ما كتبناش any element مفهومة ضمنية لأنه
+
+90
+00:07:05,310 --> 00:07:08,050
+أنا ماعرفش عليها أي قيط إذا بدي أخدها العموم، هي
+
+91
+00:07:08,050 --> 00:07:11,910
+بشكل عشوائي، بدي أوصلها وين للآن؟ لل X، فهذا إيش
+
+92
+00:07:11,910 --> 00:07:16,550
+معناته؟ معناته أن why is it في ال relation تعريف
+
+93
+00:07:16,550 --> 00:07:21,700
+الصف و لا لأ، تمام في أنا عنديهذا إيش ماله؟ هذا
+
+94
+00:07:21,700 --> 00:07:25,060
+إيش فرضية عامة مظلة لكل البرهان لإنه إيش الجملة
+
+95
+00:07:25,060 --> 00:07:29,720
+الشرطية وأنا جاعت بحاول أبرهن مين هذا الجزء فبدأت
+
+96
+00:07:29,720 --> 00:07:33,540
+في الجزء الأول خد عنصر من الطرف اليسار ووصلته
+
+97
+00:07:33,540 --> 00:07:37,140
+لليمين في صارة subset الآن خد طرف من اليمين أو
+
+98
+00:07:37,140 --> 00:07:40,320
+عنصر من اليمين بوصله لليسار إذا كله تحت مين؟ تحت
+
+99
+00:07:40,320 --> 00:07:44,140
+الشرط إنه هذا صحيح طب الآنYZ في ال relation وإحنا
+
+100
+00:07:44,140 --> 00:07:48,020
+عندنا مين؟ عندنا XZ في ال relation من مين؟ X أخر
+
+101
+00:07:48,020 --> 00:07:51,920
+XY في ال relation من مين بتتخلص؟ من ال Y بتبقى
+
+102
+00:07:51,920 --> 00:07:58,280
+عاكس زي الأولى؟ لأ واضحة أفعالي إيش؟ نقوله هنا but
+
+103
+00:07:58,280 --> 00:08:03,940
+إيش؟ XY تنتمي للأبسلون فبالتالي إيش صار؟ XY وYZ
+
+104
+00:08:03,940 --> 00:08:07,880
+بتقول إنه إيش؟ XZ في الأبسلون لأن الأبسلون is
+
+105
+00:08:07,880 --> 00:08:08,400
+transitive
+
+106
+00:08:12,340 --> 00:08:18,340
+ممتاز فده إيش معناته؟ Thus ال Z في صف ال X
+
+107
+00:08:18,340 --> 00:08:22,820
+وبالتالي
+
+108
+00:08:22,820 --> 00:08:28,120
+إيش صار؟ بدأنا من عنصر في صف ال Y ووصلنا لصف ال X
+
+109
+00:08:28,120 --> 00:08:36,620
+إذا صف ال Y شماله subset من صف ال X خلاص
+
+110
+00:08:36,620 --> 00:08:42,350
+واحد و اتنين بيقدي إلى التساويواحد واتنين يؤدى ان
+
+111
+00:08:42,350 --> 00:08:50,530
+صف ال X يساوي صف ال Y واضح فهنا زى ما حكينا كل
+
+112
+00:08:50,530 --> 00:08:53,870
+خطوة بنمشي طب احنا بدنا نجزق نجزق مافيش مشكلة احنا
+
+113
+00:08:53,870 --> 00:08:56,370
+ايش اللى بدنا يهو كيف نوصل المهم نعرف احنا ايش
+
+114
+00:08:56,370 --> 00:09:01,450
+المقطة و ايش المطلوب كل هذا تحت ايش الاتجاه الاول
+
+115
+00:09:01,450 --> 00:09:04,810
+لل if and only if الان هنبدأ نشتغل مع الاتجاه
+
+116
+00:09:04,810 --> 00:09:15,070
+التانى خلينى اشتغل هنا فاحناالعكس الأول اتنين X صف
+
+117
+00:09:15,070 --> 00:09:20,390
+ال X يساوي صف ال Y يؤدي أن X له علاقة مع ال Y
+
+118
+00:09:20,390 --> 00:09:26,190
+للتجاه التاني لل F and only F وكعادة أيش بالدب ده
+
+119
+00:09:26,190 --> 00:09:35,150
+أن الشرط صحيح assume صف ال X يساوي صف ال Y المطلوب
+
+120
+00:09:35,150 --> 00:09:37,030
+أن X له علاقة مع ال Y
+
+121
+00:09:41,190 --> 00:09:47,830
+بدي أثبت إن الـ X لعلاقة مع الـ Y لو فكرنا قليلا
+
+122
+00:09:47,830 --> 00:09:51,650
+أنا بدي الـ X لعلاقة مع الـ Y من وين ممكن أجيبها
+
+123
+00:09:51,650 --> 00:09:54,910
+من تعريف الصف؟ إيش علاقة العلاقة مع الصف؟ لو أقدرت
+
+124
+00:09:54,910 --> 00:09:58,950
+أثبت إن الـ Y في صف الـ X، بكون أصلت، ولا لأ؟ أنا
+
+125
+00:09:58,950 --> 00:10:03,370
+بدي هذه، وقت شهدت صحيحة، يا الـ X في صف الـ Y، يا
+
+126
+00:10:03,370 --> 00:10:05,790
+الـ Y في صف الـ X، و هي واحد، لأنهم فيه Symmetric،
+
+127
+00:10:05,790 --> 00:10:10,380
+مظبوط؟ فأنا بدي أثبت إن الـ Y في صف الـ Xطيب احنا
+
+128
+00:10:10,380 --> 00:10:14,540
+ايش في عندنا؟ في عندنا مفتاح مهم اتعلمناه ان كل
+
+129
+00:10:14,540 --> 00:10:18,700
+عنصر وين موجود في صفه فال Y وين موجودة في صف ال Y
+
+130
+00:10:18,700 --> 00:10:26,110
+فالان اه butY تنتمي لصف الـY وصف الـY بيثوي صف
+
+131
+00:10:26,110 --> 00:10:29,590
+الـX إذا الـY وين موجودة؟ في صف الـX implies Y
+
+132
+00:10:29,590 --> 00:10:34,350
+تنتمي لصف الـX وهذا يؤدي إن X Y تنتمي لأبسل وهو
+
+133
+00:10:34,350 --> 00:10:38,790
+المطلوب فهذه الجزء سهل جدا فهذه الجزئية سهلة جدا
+
+134
+00:10:38,790 --> 00:10:43,350
+فإنا بنأكد على في نقطة مهمة و لعبة دور في كتير من
+
+135
+00:10:43,350 --> 00:10:47,410
+البراهين إن العنصر دايما موجود في صف نفسه فالـX
+
+136
+00:10:47,410 --> 00:10:50,430
+دايما في صف الـX استخدناها أكتر من مرة ففعلا هنا
+
+137
+00:10:50,430 --> 00:10:55,680
+برضه حلتنا الإشكالفهيك بنكون خلصنا برهان النظرية
+
+138
+00:10:55,680 --> 00:11:04,970
+نظرية أربعة هنتوج هذا الموضوعأه طبعا الخواص
+
+139
+00:11:04,970 --> 00:11:11,290
+الموجودة ممكن البعض يكون Robert أنه ولا صف فاضي
+
+140
+00:11:11,290 --> 00:11:16,490
+وإنه الصفين يا إما تقاطح .. تقاطحهم لا يساوي في if
+
+141
+00:11:16,490 --> 00:11:18,510
+and only if العنصرين اللي لهم علاقة مع بعض
+
+142
+00:11:18,510 --> 00:11:21,310
+والعنصرين اللي لهم علاقة مع بعض if and only if
+
+143
+00:11:21,310 --> 00:11:24,450
+صفوفهم متساوية لو جمعنا B وC بنشوف إن هو دي من
+
+144
+00:11:24,450 --> 00:11:29,690
+خواص ال partition فالآن هيوصل للنقطة هذهانه كل
+
+145
+00:11:29,690 --> 00:11:34,930
+علاقة التكافؤ بتولد partition أي بقرا عن صفوف
+
+146
+00:11:34,930 --> 00:11:39,510
+التكافؤ فانا عند المجموعة لو حسبت صفوف التكافؤ
+
+147
+00:11:39,510 --> 00:11:43,370
+فبكون جزأتي المجموعة إلى partition ينطبق عليها
+
+148
+00:11:43,370 --> 00:11:47,610
+شروط ال partition فهي لعنوان capital X على أبسلون
+
+149
+00:11:47,610 --> 00:11:52,670
+ياش مجموعة صفوف التكافؤ is a partition of X نقرأ
+
+150
+00:11:52,670 --> 00:11:58,130
+النص بشكلأو ضح أو بشكل كامل let epsilon be an
+
+151
+00:11:58,130 --> 00:12:04,260
+equivalence relation on a non-empty set Xمجموعة
+
+152
+00:12:04,260 --> 00:12:07,260
+الصفوف التكافؤ اللي هي X على Y is a partition of X
+
+153
+00:12:07,260 --> 00:12:13,180
+بدنا نشوف إنه دايما صفوف التكافؤ بتكون تجزيه تقسيم
+
+154
+00:12:13,180 --> 00:12:16,700
+لمن؟ للمجموعة إيش معنى التقسيم؟ إنه partition يعني
+
+155
+00:12:16,700 --> 00:12:20,960
+متحبق عليه تلت شروط إنه ولا جزء فارق أي جزءين يا
+
+156
+00:12:20,960 --> 00:12:26,460
+تقطعوا فيه يا بتطابقين في احتمال تالت وإن الاتحاد
+
+157
+00:12:26,460 --> 00:12:30,980
+على كل الصفوف بده يغطي كل ال X خدنا نشوف البرهان
+
+158
+00:12:30,980 --> 00:12:42,690
+مع بعضفهذه نظرية تلاتة أربع approved فطبعا
+
+159
+00:12:42,690 --> 00:12:50,050
+بس نذكركوا إحنا بنتحدث عن P تساوي capital X على
+
+160
+00:12:50,050 --> 00:12:55,490
+أبسلون وهذه مما تتكون من small x على أبسلون بحيث
+
+161
+00:12:55,490 --> 00:13:00,420
+small x in capital Xفهذه الموجودة في النظرية
+
+162
+00:13:00,420 --> 00:13:04,100
+capital X على Y هي مجموعة صفوف التكافأة اللي هي ده
+
+163
+00:13:04,100 --> 00:13:07,100
+هما بدي أثبت إنها partition فخلّيني أرمزها برمز B
+
+164
+00:13:07,100 --> 00:13:12,270
+فبنثبت إنها partition تلت شروط فالشرط الأولبدا
+
+165
+00:13:12,270 --> 00:13:16,990
+نثبت ان كل جزء غير فارق ولا جزء بيكون فارق فطبعا
+
+166
+00:13:16,990 --> 00:13:20,450
+نثبت ان for all a in the partition تذكروا المعادلة
+
+167
+00:13:20,450 --> 00:13:24,330
+الماضية a is non-empty a is non-empty خليني
+
+168
+00:13:24,330 --> 00:13:30,310
+أكتبلكوا إياها for all a تنتمي للpartition a لا
+
+169
+00:13:30,310 --> 00:13:34,870
+تسوى five متذكرين؟ هيك اذكرته تمام فانا بدي اخد
+
+170
+00:13:34,870 --> 00:13:40,280
+ايشعنصر في الـ partition اللي هو مجموعة يعني طيب،
+
+171
+00:13:40,280 --> 00:13:43,640
+كيف صور المجموعات في الـ partition الأن؟ صفر، إذا
+
+172
+00:13:43,640 --> 00:13:45,860
+بدأ أقول له let a be in the partition يعني إيش ده
+
+173
+00:13:45,860 --> 00:13:50,220
+تساوي؟ X على أبسلون، ممكن أعود بصيغة أخرى، أقول له
+
+174
+00:13:50,220 --> 00:13:56,040
+let small x تنتمي لcapital X لأنه إيش بتكون
+
+175
+00:13:56,040 --> 00:13:59,080
+الصفوف؟ X تنتمي لcapital X كل عنصر بيولد صفر
+
+176
+00:13:59,080 --> 00:14:06,630
+تكافه، ولا لأ؟ كل عنصر إيه صفه، فإيش and؟let small
+
+177
+00:14:06,630 --> 00:14:11,410
+x على أبسلون تنتمي للpartition اللي هو إيش بيساوي
+
+178
+00:14:11,410 --> 00:14:16,510
+x على أبسلون إيه المطلوب منه؟ أثبت إن هذا الصف غير
+
+179
+00:14:16,510 --> 00:14:22,300
+فارقبدنا نثبت إن هذا الصف غير فارغ إيش معناه غير
+
+180
+00:14:22,300 --> 00:14:26,800
+فارغ؟ الأقل في عنصر واحد كيف ممكن أثبته؟ إذا قدرت
+
+181
+00:14:26,800 --> 00:14:29,580
+أعرف عنصر there exist أه كيف بدأ أثبت ان there
+
+182
+00:14:29,580 --> 00:14:32,500
+exist؟ ماخدناش طريقة عامة ل there exist بس قلنا في
+
+183
+00:14:32,500 --> 00:14:36,160
+بعض الطرح لو قدرت أسمله عنصر موجود انتهى العملية
+
+184
+00:14:36,160 --> 00:14:39,520
+عشان أنا أثبت إن هذه القاعة غير فارغة لو أنا قلت
+
+185
+00:14:39,520 --> 00:14:41,900
+إن في طالب اسمه فاطمة بعرف أنا موجود في القاعة
+
+186
+00:14:41,900 --> 00:14:45,890
+انتهت العملية انتهت العملية، بدأ أسميفمين يعرف لي
+
+187
+00:14:45,890 --> 00:14:49,290
+عنصر دايما مضمون ان يكون في صف الـ X؟ الـ X نفسها،
+
+188
+00:14:49,290 --> 00:14:54,490
+اه فانا على طول فالان then X تنتمي لصف الـ X
+
+189
+00:14:54,490 --> 00:15:00,080
+implies صف الـ X ليه زفافوهو المطلوب، ولا صف ممكن
+
+190
+00:15:00,080 --> 00:15:03,260
+يكون فاضي، على الأقل فيه عنصر واحد، مين؟ العنصر
+
+191
+00:15:03,260 --> 00:15:06,740
+اللي سمى الصف أو اللي ولد الصف لأنه سميها ده الصف
+
+192
+00:15:06,740 --> 00:15:10,580
+اللي ماله اتولد أو اتحدد من ال X، إذا بتتذكروا
+
+193
+00:15:10,580 --> 00:15:13,860
+التعريف، فإذا فعلا ولا صف ممكن يكون فاضي، فإذا أي
+
+194
+00:15:13,860 --> 00:15:17,400
+صف تكافؤ، لما نحسبه على الأقل هيكون فيه عنصر واحد،
+
+195
+00:15:17,400 --> 00:15:20,120
+وعلى طول وانت مغمضاش تحطيه، جالك جيبي صف الواحد،
+
+196
+00:15:20,120 --> 00:15:23,320
+حط الواحد، جالك جيبي صف فاطمة، حط فاطمة، على طول،
+
+197
+00:15:24,300 --> 00:15:28,780
+دون أي تردد وهذا هو الانصار الأول فإذا هذا الشرط
+
+198
+00:15:28,780 --> 00:15:35,460
+الأول الشرط رقم واحد بدنا أي صفين يا متطابقين يا و
+
+199
+00:15:35,460 --> 00:15:41,720
+لا عنصر مشترك لو ايش بيقول يجلي انه x y في اسف x
+
+200
+00:15:41,720 --> 00:15:48,080
+على ال epsilon في ال partition and اللي هو أي صفين
+
+201
+00:15:48,080 --> 00:15:51,160
+a و b بداك تبقى بنفس الطريقة عشان ما تتخموش اللي
+
+202
+00:15:51,160 --> 00:15:58,730
+هم a و bX على أبسلون وY على أبسلون في الـ B and X
+
+203
+00:15:58,730 --> 00:16:03,830
+على أبسلون لا تساوي Y على أبسلون implies X على
+
+204
+00:16:03,830 --> 00:16:08,450
+أبسلون تقاطع Y على أبسلون بتساوي 5هك الشرط بس بدل
+
+205
+00:16:08,450 --> 00:16:12,570
+a و b حطيت مين صفوف لأن الأجزاء هنا يشملها صفوف
+
+206
+00:16:12,570 --> 00:16:17,570
+الأجزاء المعطية ليه صفوف اه فطبعا كجملة سرطية
+
+207
+00:16:17,570 --> 00:16:25,390
+هفترض ان الشرط صحيح فابدأ بدأله أول شي letX و
+
+208
+00:16:25,390 --> 00:16:30,910
+Epsilon و Y و Epsilon ينتموا للـ B اللي هي عبارة
+
+209
+00:16:30,910 --> 00:16:35,110
+عن مين طبعا ليش بحطه ميك لأنه X على Epsilon فانا
+
+210
+00:16:35,110 --> 00:16:37,830
+مش ماخد اي partition ماخد partition من نوع معين
+
+211
+00:16:37,830 --> 00:16:41,730
+عناصره عبارة عن صفوف تكافه فبكتبهم بيد الشكل بدي
+
+212
+00:16:41,730 --> 00:16:45,390
+أثبت انه إذا كان او بدي افترض انه ميكش غير
+
+213
+00:16:45,390 --> 00:16:48,430
+متساويين and assume
+
+214
+00:16:50,150 --> 00:16:57,390
+X على أبسلون لا تساوي Y على أبسلون بدي أثبت أن
+
+215
+00:16:57,390 --> 00:17:02,850
+التقاطع يساوي في بدي أثبت أن التقاطع يساوي في
+
+216
+00:17:02,850 --> 00:17:10,590
+اتطلع عن نظرية الماضية افتح عليها موجودة وسهلة ايش
+
+217
+00:17:10,590 --> 00:17:15,800
+قال لي اه بدي اربط بين B وCجال ليه؟ بس اقرا من
+
+218
+00:17:15,800 --> 00:17:21,600
+هناك اكس انا بتدبط انه مين انه ايش اكس تقاطع صف ال
+
+219
+00:17:21,600 --> 00:17:25,720
+y لا يقبض يسوى five بتدبطها بدا الشكل نيجي نشوف
+
+220
+00:17:25,720 --> 00:17:32,250
+احنا عايش عنا عدم تساوي عدم تساويمع contrapositive
+
+221
+00:17:32,250 --> 00:17:36,630
+إيش بتصير؟ لو عنصرين ليس لهم علاقة مع بعض و عنصرين
+
+222
+00:17:36,630 --> 00:17:39,510
+مالهم مش علاقة مع بعض إيش هتديني؟ تقاطع بيساوي
+
+223
+00:17:39,510 --> 00:17:43,750
+five فهنعمل .. هنستخدم C و B مع contrapositive
+
+224
+00:17:43,750 --> 00:17:48,150
+طبعا إحنا بنعرف في ال if and only if statement B
+
+225
+00:17:48,150 --> 00:17:51,050
+implies Q إيش ال contrapositive إلها؟ not Q
+
+226
+00:17:51,050 --> 00:17:56,950
+implies not B طب لما تكون عندنا B if and only if Q
+
+227
+00:17:56,950 --> 00:17:58,410
+إيش ال contrapositive بتبعدها؟
+
+228
+00:18:06,390 --> 00:18:12,370
+ممتازة هنمشي خلينا نطبق انا عندي صف ال X لا يسوي
+
+229
+00:18:12,370 --> 00:18:17,250
+صف ال Y اذا نقش XY لا تنتمي للأبسلون هذا يؤدي ان
+
+230
+00:18:17,250 --> 00:18:24,670
+XY لا تنتمي للأبسلون من وين جبتها؟جداش؟ تلاتة
+
+231
+00:18:24,670 --> 00:18:28,310
+تلاتة، فرع C إذا حابين، صح؟ Contrapositive بس
+
+232
+00:18:28,310 --> 00:18:32,470
+دكتور implies ولا تكافأت؟ هي تكافأ، بس أنا مش معنى
+
+233
+00:18:32,470 --> 00:18:36,470
+كتير، لأنه أنا مش بدي implies، فبديش أغلب حالي،
+
+234
+00:18:36,470 --> 00:18:39,650
+تمام؟ لأن التكافأ بيقوللي إيش؟ كن دقيق، فبدك
+
+235
+00:18:39,650 --> 00:18:43,230
+انتباه شديد، أنا مش معنى بالتكافأ، فطنشط الانتباه،
+
+236
+00:18:43,230 --> 00:18:48,300
+بدي أخفف عن حالي الانتباه، واضحة؟متبين؟ اه تمام
+
+237
+00:18:48,300 --> 00:18:52,820
+الان باستخدام بي إذا كانت لاتنتمي إيش ماله؟ إذا
+
+238
+00:18:52,820 --> 00:18:57,420
+انتقاطه بيسوي فاي implies x على أبسلون تقاطه y على
+
+239
+00:18:57,420 --> 00:19:04,340
+أبسلون يسوي فاي برضه إيش نظرية تلاتة تلاتة فرع بي
+
+240
+00:19:04,340 --> 00:19:09,410
+واضحة مع contrapositiveمع الـ Contrapositive أي
+
+241
+00:19:09,410 --> 00:19:13,550
+سؤال متبين؟ خلصنا و هو المطلوب اللي هو يش فرع
+
+242
+00:19:13,550 --> 00:19:16,810
+الأول صحيح اللي هو رقم واحد اللي هو يش الشرط
+
+243
+00:19:16,810 --> 00:19:19,570
+التاني من شروط ال partition تم الشرط التالت
+
+244
+00:19:19,570 --> 00:19:26,170
+والاخير الشرط التالت والاخير بدنا الاتحاد يساوي X،
+
+245
+00:19:26,170 --> 00:19:30,590
+مظبوط؟ شرط رقم اتنين اتحاد على كل ال partition
+
+246
+00:19:30,590 --> 00:19:36,070
+ممكن اكتبه بشكل التالياتحاد جميع الصفوف يعني مظبوط
+
+247
+00:19:36,070 --> 00:19:42,330
+يسوى X هذا الشرقلأنه مرة تانية أناقنعت صياغته إيش
+
+248
+00:19:42,330 --> 00:19:46,050
+بيقول الشرط اتحاد جميع الأيزاق بيساوي X إيش
+
+249
+00:19:46,050 --> 00:19:49,210
+الأيزاق عندي في هذا النظرية صفوف تكافة يعني اتحاد
+
+250
+00:19:49,210 --> 00:19:52,890
+جميع الصفوف بده يديني لمين لل capital X طبعا كل صف
+
+251
+00:19:52,890 --> 00:19:56,230
+من اللي بيحدده ال X تبعته اللي هي العريف تبع الصف
+
+252
+00:19:56,230 --> 00:20:00,350
+العريف تبع الصف هو X أزاي العريف نسميه فواحد بيسمي
+
+253
+00:20:00,350 --> 00:20:05,470
+الصف فده صف محمد فده صف فاطمة واضح؟ تمام؟ أه بيبقى
+
+254
+00:20:05,470 --> 00:20:10,030
+نثبت هذه العلاقةعلاقة إيش؟ تساوي مجموعات، نفس
+
+255
+00:20:10,030 --> 00:20:13,310
+السيطرة، خذ الأنصار من الطرف، امشيتي تكافؤ، خلصنا،
+
+256
+00:20:13,310 --> 00:20:15,930
+امشيتيش تكافؤ، امشي، إن الأولى صبصت من التانية، و
+
+257
+00:20:15,930 --> 00:20:19,490
+العكس، التانية صبصت من الأولى، فنبدأ، طب عم بديش
+
+258
+00:20:19,490 --> 00:20:23,210
+أسمي X أنه X مشغولة، let Y، الـY مش مشغولة الآن،
+
+259
+00:20:23,210 --> 00:20:28,890
+be any element and
+
+260
+00:20:28,890 --> 00:20:34,010
+let أو such that كله صح، and let Y تنتمي للطرف
+
+261
+00:20:34,010 --> 00:20:43,180
+اليساراتحاد على كل صفوف التكافئة في
+
+262
+00:20:43,180 --> 00:20:46,400
+أي طالب عنده مشكلة في البداية؟ كيف بنبدأ و ليش
+
+263
+00:20:46,400 --> 00:20:51,460
+بنبدأ؟ تمام؟ إيش ممكن أعمل الآن؟ أفق الاتحاد ..
+
+264
+00:20:51,460 --> 00:20:55,910
+ماذا يعني why أدى اتحاد على أكم مجموعة؟كلهم يعني
+
+265
+00:20:55,910 --> 00:20:58,290
+ايش .. ايش يسمي اتحاد على family يعني لإن العدد مش
+
+266
+00:20:58,290 --> 00:21:01,610
+معروف أكم صف فيه مش عارفين لإن شوفنا مثال أكم صف
+
+267
+00:21:01,610 --> 00:21:05,250
+مرة طلع معنى تذاكر المربع مال نهاية من الصفوف ممكن
+
+268
+00:21:05,250 --> 00:21:08,270
+يكون عدد محدود ممكن يكون غير محدود فإذا احنا هذا
+
+269
+00:21:08,270 --> 00:21:12,130
+كأن اتحاد على مجموح كل الصفوف اللي عددهم غير محدد
+
+270
+00:21:12,130 --> 00:21:15,430
+.. غير محدد إذا هذا كأن اتحاد على family إيش معناه
+
+271
+00:21:15,430 --> 00:21:18,150
+تعنصر في الاتحاد؟ بتكون على الأقل في واحدة من إيش؟
+
+272
+00:21:18,150 --> 00:21:23,890
+من الأيزاء فإذا هذا يؤديإن الـ Y تنتمل الـ X على
+
+273
+00:21:23,890 --> 00:21:28,890
+أبسلون for some X تنتمل الـ X
+
+274
+00:21:31,440 --> 00:21:33,800
+أه بيكون واحد من الأيزاء فواحد يقول انت ليش ما
+
+275
+00:21:33,800 --> 00:21:38,500
+قلتش X على الأبسلون نفس المعنى لأنه إيهاش كل صف
+
+276
+00:21:38,500 --> 00:21:41,640
+مين اللي بيدل عليه العريف تبعه اللي هو ال X زي
+
+277
+00:21:41,640 --> 00:21:45,240
+عملية إيهاش كان عملنا عملية indexing عملية أرشفة
+
+278
+00:21:45,240 --> 00:21:50,300
+مظبوط لإن كل X بتعرف صف فأنا ممكن أقول صف ال X أو
+
+279
+00:21:50,300 --> 00:21:52,700
+أقول X ماينافسه إيهاش بيدل على نفسه أو بيدل على
+
+280
+00:21:52,700 --> 00:21:54,960
+الصفة ولا لأ أه فعادة زي ما كنا نقول إيهاش كنا
+
+281
+00:21:54,960 --> 00:21:57,720
+نقول إيهاش ما كنا نقول there exists a small Gamma
+
+282
+00:21:57,720 --> 00:22:01,660
+in capital Gamma وين ال X في ال A Gammaنفس العملية
+
+283
+00:22:01,660 --> 00:22:05,840
+فهنا الصف من اللي بعرفه مش Gamma X فصف ال X ممتاز
+
+284
+00:22:05,840 --> 00:22:10,540
+ال Y في صف ال X أنا بني وين ده وديها ده وديها على
+
+285
+00:22:10,540 --> 00:22:15,720
+Capital Xبدي أودّيها على capital X ممكن الصفوف
+
+286
+00:22:15,720 --> 00:22:19,440
+تاخد عناصر من خارج ال capital X تتذكروا كتبنا
+
+287
+00:22:19,440 --> 00:22:22,320
+ملاحظة أن كل صف هو صف ستم أويان من ال capital X
+
+288
+00:22:22,320 --> 00:22:26,600
+إيش تعريف الصف؟ جالي Y تنتمي لcapital X such that
+
+289
+00:22:26,600 --> 00:22:31,700
+Y إلى علاقة مع ال X فهذه بديهية أن ال Y تنتمي
+
+290
+00:22:31,700 --> 00:22:35,460
+لcapital X ليش؟ لأن أي صف هو صف ستم المجموعة
+
+291
+00:22:35,460 --> 00:22:39,410
+الأصليةلأن أنا بعمل relation على مين؟ على الـ X
+
+292
+00:22:39,410 --> 00:22:43,310
+ومين الصفر؟ هو عناصر الـ X اللي اللي علاقة مع الـ
+
+293
+00:22:43,310 --> 00:22:48,970
+X فإذن وضحنا إنه الطرف الأول سهل، thus صار الاتحاد
+
+294
+00:22:48,970 --> 00:22:58,290
+إشماله subset من الـ X، مظبوط، فالاتجاه الأول خلص،
+
+295
+00:22:58,290 --> 00:23:03,040
+فهذا الاتجاه الأولطبعاً مامشيناش تكافؤ وهي هذه
+
+296
+00:23:03,040 --> 00:23:06,040
+الطريقة الأشهر في الرياضيات أو الأعامة عملية
+
+297
+00:23:06,040 --> 00:23:10,480
+التكافؤ قليلة جدا ونادرة فهنا بدينا حرية ومرونة في
+
+298
+00:23:10,480 --> 00:23:16,660
+العمل نعمل اتجاه التاني let Y تنتمي لل capital X
+
+299
+00:23:16,660 --> 00:23:23,500
+بدي أثبت أن هذا ال Y موجودة في الاتحاد بدي أثبت أن
+
+300
+00:23:23,500 --> 00:23:29,860
+ال Y موجودة في الاتحاد اتحاد مين؟ اتحاد الصفوفوقت
+
+301
+00:23:29,860 --> 00:23:33,220
+إيش Y بتكون في اتحاد الصفوف إذا كانت في صف على
+
+302
+00:23:33,220 --> 00:23:37,180
+الأقل؟ طب Y في صف مين بتعرفوها؟ صف نفسها، شايفين
+
+303
+00:23:37,180 --> 00:23:43,880
+كيف كانت النقطة المفتاحية؟ فعلى طول، then Y تنتمي
+
+304
+00:23:43,880 --> 00:23:49,220
+لصف ال Y إذا نقش مالها في اتحاد الصفوف وهذا يؤدي
+
+305
+00:23:49,220 --> 00:23:56,710
+إن Y تنتمي لاتحاد على ال capital X للصفوفطبعا و حد
+
+306
+00:23:56,710 --> 00:24:01,070
+يلتخم وين ال Y؟ ماذا صفوف X؟ لأ ده رمز احنا بنقرع
+
+307
+00:24:01,070 --> 00:24:05,710
+صح ماذا يعني هذا اتحاد جميع الصفوف X تنتمي
+
+308
+00:24:05,710 --> 00:24:09,330
+لcapital X يعني لما X بتساوي X واحد صف X واحد و صف
+
+309
+00:24:09,330 --> 00:24:13,460
+X اتنين و صف X تلاتة حد الصفوف هيكون صف ال Yواضحى
+
+310
+00:24:13,460 --> 00:24:17,080
+كيف نقرأ صح؟ يعني في ناس هتستغرب كيف ال Y في صفوف
+
+311
+00:24:17,080 --> 00:24:20,360
+اتحاد ال X؟ لأ، ده رمز، أنا إيش قلتش كيف تقرأها
+
+312
+00:24:20,360 --> 00:24:23,640
+صح؟ هذا اتحاد جميع الصفوف ال Y موجودة في احد
+
+313
+00:24:23,640 --> 00:24:25,540
+الصفوف ولا مش موجودة؟ موجودة في صفف نفسها، إذا
+
+314
+00:24:25,540 --> 00:24:27,520
+موجودة في الاتحاد ولا مش موجودة؟ موجودة في
+
+315
+00:24:27,520 --> 00:24:30,580
+الاتحاد، بس هذا رمز بإننا نقعد نقرأه صح، ممكن يكون
+
+316
+00:24:30,580 --> 00:24:33,620
+خادع للناس اللي ماعنداش خبرة شوية، ممكن يخدعوا
+
+317
+00:24:33,620 --> 00:24:36,440
+فيها أو يلاجوا صعوبة، فإذا خلاص انتهى، بدأنا في
+
+318
+00:24:36,440 --> 00:24:39,120
+عنصر من الطرف اليمين وصلنا
+
+319
+00:24:42,500 --> 00:24:49,260
+subset من اليسار طبعا
+
+320
+00:24:49,260 --> 00:24:57,080
+واحد و اتنين يجعل البرهان انتهى اتحاد
+
+321
+00:24:57,080 --> 00:25:03,780
+الصفوف يساوي المجموعة كلها الان zero واحد و اتنين
+
+322
+00:25:03,780 --> 00:25:11,830
+يدلوا ان هذا ياش partition فهنا zeroواحد and اتنين
+
+323
+00:25:11,830 --> 00:25:20,410
+implies X على الابسلون is a partition ففعلا
+
+324
+00:25:20,410 --> 00:25:28,630
+عملية تقسيم المجموعة إلى صفوف تكافؤ هذا التقسيم هو
+
+325
+00:25:28,630 --> 00:25:32,470
+تقسيم نموذجي ينطبق عليه شروط ال partition يعتبر
+
+326
+00:25:32,470 --> 00:25:36,090
+partition بالمعنى الرياضيين يعتبر partition بمعنى
+
+327
+00:25:36,090 --> 00:25:38,910
+الرياضي واضح؟
+
+328
+00:25:40,120 --> 00:25:43,360
+تمام فده طبعا احنا كنا راجعين لنظرية عشان نستلق
+
+329
+00:25:43,360 --> 00:25:48,340
+بها خلينا نشوف بعض الأمثلة الحقيقة فيها ان دي انا
+
+330
+00:25:48,340 --> 00:25:53,300
+اكتر من المثال المثال مايعتبرش جديد تماما لإن احنا
+
+331
+00:25:53,300 --> 00:25:57,140
+قبل هيك كنا بيدينا relation و أثبتنا و جبنا و
+
+332
+00:25:57,140 --> 00:26:01,140
+حسبنا صفوف التكافر لكن ايش الشاهد؟ هنشوف في ضوء
+
+333
+00:26:01,140 --> 00:26:05,310
+النظريتين السابقتينكيف أستخدم خواص ال equivalence
+
+334
+00:26:05,310 --> 00:26:08,810
+classes و تساعدني في الحساب و ايضا بدي اتأكد ان
+
+335
+00:26:08,810 --> 00:26:12,050
+فعلا صفوف التكافئة الشمالية بتعمل partition هنشوف
+
+336
+00:26:12,050 --> 00:26:15,250
+و نلاحظ على الملاحظة ان النظرية بتتطبق على الأمثلة
+
+337
+00:26:15,250 --> 00:26:17,630
+و لا لأ طبعا ما زال ال proof هي صح لكن بدي اشوف ان
+
+338
+00:26:17,630 --> 00:26:21,990
+الكلام صحيح و لا لأ و ممكن استخدم نظرية نقاشأعمل
+
+339
+00:26:21,990 --> 00:26:25,150
+test على حل إنه صح و لا لأ فإحنا في عندنا طريقتين
+
+340
+00:26:25,150 --> 00:26:29,350
+ممكن نستخدم الخواص تساعدنا في الحل و ممكن نستخدم
+
+341
+00:26:29,350 --> 00:26:32,870
+الخواص أن نختبر حالنا صحيح و لا لأ فأي تناقض مع
+
+342
+00:26:32,870 --> 00:26:37,050
+الخواص بيدل على إن حالنا في خطأ ما في خطأ ما تمام
+
+343
+00:26:37,050 --> 00:26:43,390
+فهنا نبدأ كالسياسة العامة مثال بسيط هنبدأ مجموعة
+
+344
+00:26:43,390 --> 00:26:46,150
+صغيرة تتكون من أربع عناصر
+
+345
+00:26:50,300 --> 00:26:54,440
+أه فاحنا إيش بندرس بشكل عام؟ في عندنا مجموعة وفي
+
+346
+00:26:54,440 --> 00:26:59,680
+عندنا علاقة تكافؤ هدولة مع بعض بيولدوا أو بيعرفوا
+
+347
+00:26:59,680 --> 00:27:04,600
+تجزيق partition فالدان المجموعة والدان ال relation
+
+348
+00:27:04,600 --> 00:27:07,860
+طبعا equivalence relation إيش بيقول ليه؟ أوجد صفوف
+
+349
+00:27:07,860 --> 00:27:11,940
+التكافؤ .. أوجد صفوف التكافؤ فسؤال قديم لكن هنحله
+
+350
+00:27:11,940 --> 00:27:16,340
+بنظرة جديدة في ضوء النظريتين السابقتين فهذا المثال
+
+351
+00:27:16,340 --> 00:27:21,010
+الأولSolution، إيش بده؟ بده X على أبسلون، اللي هي
+
+352
+00:27:21,010 --> 00:27:24,350
+مجموعة كل الصفوف، اللي هي تعريفها هي X على أبسلون
+
+353
+00:27:24,350 --> 00:27:29,950
+بحيث X تنتمي لcapital X في هذا المثال، بما أن
+
+354
+00:27:29,950 --> 00:27:33,390
+الcapital X أربع عناصر، إذا أنا متوقع يكون عندي
+
+355
+00:27:33,390 --> 00:27:38,430
+إيش؟ أربع صفوف، بدرور يكونوا أربع صفوف مختلفين؟
+
+356
+00:27:38,430 --> 00:27:44,430
+لأ، ممكن يكونوا متطابقينكحد أقصى أربعة صفوف نبدأ
+
+357
+00:27:44,430 --> 00:27:49,430
+نحسبهم واحد واحد بدنا نحسب صف الواحد اه انا طول
+
+358
+00:27:49,430 --> 00:27:53,150
+وانا مغمض بدك تكتب واحد شوف نه ده مفتاح جهنم تطلع
+
+359
+00:27:53,150 --> 00:27:55,770
+على ال relation حط الواحد وانت مغمضة صف الواحد
+
+360
+00:27:55,770 --> 00:27:59,910
+لازم يحتوي على أقل الواحد طب في حاجة غير الواحد لأ
+
+361
+00:27:59,910 --> 00:28:02,230
+مافيش حد اللي علاقة مع الواحد اللي مع نفسه اذا
+
+362
+00:28:02,230 --> 00:28:07,350
+خلاص سكر الصفصف التنين و احنا مغمطين منه نحط
+
+363
+00:28:07,350 --> 00:28:10,750
+التنين و ندور في غيرها ولا لأ؟ في حد اللي علاق مع
+
+364
+00:28:10,750 --> 00:28:16,080
+التنين؟ نعمالتلاتة وبما أن الدنيا ليها علاقة مع
+
+365
+00:28:16,080 --> 00:28:20,100
+التلاتة فهي دا يحسب صف التلاتة لأ جال ال X و Y
+
+366
+00:28:20,100 --> 00:28:23,240
+اللي هم علاقة مع بعض if and only if صفوفهم متساوية
+
+367
+00:28:23,240 --> 00:28:27,180
+الخاصية رقم C فإذا على طول و أقول إن هذا هو صف
+
+368
+00:28:27,180 --> 00:28:30,640
+التلاتة شوفت هذي كده إيش نستفيد من الخواص خاصية
+
+369
+00:28:30,640 --> 00:28:34,200
+رقم C ففيش دا هتحسب صف التلاتة لكن ممكن إذا أنت
+
+370
+00:28:34,200 --> 00:28:37,360
+شاكة احسب صف التلاتة تطلع بساوي ولا بسويش لازم
+
+371
+00:28:37,360 --> 00:28:37,940
+تطلع الساوي
+
+372
+00:28:41,080 --> 00:28:44,080
+وهنا مافيش .. بتبطل ال equivalance relation بتبطل
+
+373
+00:28:44,080 --> 00:28:47,520
+ال equivalance relation اه هنا يقولك اي عنصرين
+
+374
+00:28:47,520 --> 00:28:51,780
+اللي هم علاقة مع بعض if and only if صف ال X ليساوي
+
+375
+00:28:51,780 --> 00:28:55,220
+صف ال Y فانت و انت مغمضة إذا كل الشغل صح لازم يصير
+
+376
+00:28:55,220 --> 00:28:59,200
+فيش تناقض كله يتسجل تم علينا نحسب صف الأربعة و
+
+377
+00:28:59,200 --> 00:29:03,060
+بنخلص مش هيهم هذا نحسب و هذا نحسب و بيساوي هذا
+
+378
+00:29:03,060 --> 00:29:06,160
+تملي نحسب هذا صف الأربعة عامة يتكوى من الأربعة في
+
+379
+00:29:06,160 --> 00:29:11,070
+غيرها؟ لأإذن هدول عايش تلت صفوف مختلفة تلت صفوف
+
+380
+00:29:11,070 --> 00:29:18,330
+مختلفة فانلخص فعنا مجموعة الصفوف هي صف الواحد
+
+381
+00:29:18,330 --> 00:29:23,990
+ويتكون من الواحد صف التنين ويتكون من تنين لتلاتة
+
+382
+00:29:23,990 --> 00:29:28,390
+وصف الأربع يتكون من الأربعهل هذا partition
+
+383
+00:29:28,390 --> 00:29:32,810
+للمجموعة؟ نعم، مجموعة من أربع عناصر قسمة، تلت
+
+384
+00:29:32,810 --> 00:29:38,270
+أقسام، ولا قسم فاضي، وأي قسمين منفصلين عن بعض، مش
+
+385
+00:29:38,270 --> 00:29:41,310
+عناصر مشتركة، اتحاد ومدانة نفس المجموعة لمدناش،
+
+386
+00:29:41,310 --> 00:29:45,640
+اتدانة، طبعا النظرية تلاتة أربعفهنا طبقنا و نستفيد
+
+387
+00:29:45,640 --> 00:29:49,900
+من النظريات نتأكد أن حلنا صح أو يساعدنا في الحل
+
+388
+00:29:49,900 --> 00:29:55,200
+يساعدنا في نختصر بعض خطوات الحل فهنا ساعدنا مكانش
+
+389
+00:29:55,200 --> 00:29:57,680
+في ده نحصل صف التلاتة لأن احنا عارفين أنه هيطلع
+
+390
+00:29:57,680 --> 00:30:02,680
+متساوي طبعا إذا شكنا بنحصل خليني أشوف مثال آخر
+
+391
+00:30:02,680 --> 00:30:09,750
+ممكن يكون أهمالمثال رقم 2 ناخد مجموعة كبيرة الآن X
+
+392
+00:30:09,750 --> 00:30:15,650
+تساوي كل الـ Z وعطانا علاقة تكافؤ هي علاقة ذكرناها
+
+393
+00:30:15,650 --> 00:30:20,750
+في المحاضرات الماضية أثبتنا إن و X ناقص Y تساوي 3
+
+394
+00:30:20,750 --> 00:30:25,070
+في K إنها equivalence relation وقلنا إن التلاتة ما
+
+395
+00:30:25,070 --> 00:30:27,730
+لاش أي خاصية ممكن أي عدد صحيح موجة بيقدر الغرض
+
+396
+00:30:27,730 --> 00:30:31,200
+قلنا لأي Mوداكرناها فإنها بده يدينا M2 ساوي 4
+
+397
+00:30:31,200 --> 00:30:34,640
+كمثال آخر فهي equivalence relation إيش بدنا نثبت؟
+
+398
+00:30:34,640 --> 00:30:38,880
+بدنا نحسب صفوف التكافة بدنا نحسب صفوف التكافة
+
+399
+00:30:38,880 --> 00:30:43,240
+solution فبده X أو Z خلّينا نسميها لأن هو Z الآن X
+
+400
+00:30:43,240 --> 00:30:45,960
+سوا و Z نحكي إن أنا بده تكافة؟ أه يو بديكي يا هو
+
+401
+00:30:45,960 --> 00:30:49,020
+ما جالكيش يثبتي جالكي بس بده يحسب صفوف التكافة هو
+
+402
+00:30:49,020 --> 00:30:52,850
+هي معروفة احنا أخدناها مثالفهذه على أبسلون، ماذا
+
+403
+00:30:52,850 --> 00:31:06,850
+يتساوي كل X على أبسلون بحيث X أنتمي لز؟ X
+
+404
+00:31:06,850 --> 00:31:12,550
+بيساوي ز؟ مدينيها بشكل صريح طبعا هذا المثال مفروض
+
+405
+00:31:12,550 --> 00:31:16,560
+يتشابش بالمثال الماضي لكن فيه اختلافالمجموع الان
+
+406
+00:31:16,560 --> 00:31:20,260
+مش finite أبدأ أحسب صف الواحد صف ال zero لأ فدي
+
+407
+00:31:20,260 --> 00:31:24,040
+infinite فهل ممكن نحسبهم بالدور زي ما عملنا توي لأ
+
+408
+00:31:24,040 --> 00:31:27,900
+بدا ناخد نشوف نحاول كيف نحسب نحسب بعض العناصر و
+
+409
+00:31:27,900 --> 00:31:31,740
+نوجد انه حسبناهم كلهم بتبدو مين النظريتين السابقة
+
+410
+00:31:31,740 --> 00:31:35,240
+يعني من وين ممكن أبدأ من الصفر لإن مافيش لأ بداية
+
+411
+00:31:35,240 --> 00:31:38,380
+المجموع ممكن أبدأ من الصفر نصف خلينا نبدأ من صف
+
+412
+00:31:38,380 --> 00:31:42,920
+الصفرإيش بيساوي صف الصفر؟ بيساوي العناصر اللي
+
+413
+00:31:42,920 --> 00:31:47,780
+علاقة مع الصفر بيساوي Y في الـZ such that اللي هو
+
+414
+00:31:47,780 --> 00:31:51,440
+صفر أو equal صفر Y تنتمي لل relation خليني أكتبها
+
+415
+00:31:51,440 --> 00:31:57,320
+بالتفصيل تمام، ماذا يعني صفر Y في ال relation؟ إيش
+
+416
+00:31:57,320 --> 00:32:00,420
+معناته أن الـY اللي علاقة مع الصفر؟ يعني صفر ناقص
+
+417
+00:32:00,420 --> 00:32:09,040
+Y تساوي 4K for some K في الـZتمام واضحة ولا مش
+
+418
+00:32:09,040 --> 00:32:14,380
+واضحة انا بدي Y ايش ال Y مالها سالب اربعة K فانا
+
+419
+00:32:14,380 --> 00:32:20,500
+بدي ساوي كل Y في ال Z على صورة سالب اربعة K for
+
+420
+00:32:20,500 --> 00:32:23,320
+some K في ال Z
+
+421
+00:32:26,730 --> 00:32:30,510
+أنا يمكن ماشي بسرعة شوية واضحة ولا اعيد اه هاي
+
+422
+00:32:30,510 --> 00:32:34,450
+تعريف الصف وهاي ال relation ايش معناته ان ال Y في
+
+423
+00:32:34,450 --> 00:32:37,570
+صف ال X اللي هو بيسوي صفر في هذا المثال ان ال Y لا
+
+424
+00:32:37,570 --> 00:32:40,470
+علاقة مع الصفر ايش معناته لا علاقة مع الصفر يعني
+
+425
+00:32:40,470 --> 00:32:45,170
+صفر ناقص Y تساوي 4K انا مين مهتم؟ مهتم بال Y فال Y
+
+426
+00:32:45,170 --> 00:32:50,720
+هتكون على صورة مين؟ سالب 4Kكام ممكن نفسرها هذه؟
+
+427
+00:32:50,720 --> 00:32:54,120
+يعني ال Y من المضاعفات الأربعة ولا لأ؟ إيش معناه
+
+428
+00:32:54,120 --> 00:32:58,660
+أربعة في K؟ فيعني هذا الصف إيش بيساوي؟ طيب وإن
+
+429
+00:32:58,660 --> 00:33:01,460
+إحنا مغمضين إحنا بنعرف مين أول واحدة في صف الصفر؟
+
+430
+00:33:01,460 --> 00:33:05,680
+الصفر صح ولا مش صح؟ لإن الصفر تقبل قسمها على أربعة
+
+431
+00:33:05,680 --> 00:33:09,860
+من مضاعفات الأربعة مين كمان؟ زاد أو ناقص أربعة زاد
+
+432
+00:33:09,860 --> 00:33:13,840
+أو ناقص تمانية زاد أو ناقص اتناش and so on فهي
+
+433
+00:33:13,840 --> 00:33:22,340
+الصف الأول انعرففده هو الصف الأول خلينا نحسب صف
+
+434
+00:33:22,340 --> 00:33:28,780
+الواحد مثلا خلينا نحسب صف الواحد نشوف لحد ما
+
+435
+00:33:28,780 --> 00:33:34,780
+الصورة توضحها لأ نشوف بدنا نجيبهم كلهم ولا لأ مين
+
+436
+00:33:34,780 --> 00:33:41,990
+صف الواحد؟هو واحد ومن غيره هو كل Y في ال Z بحيث ال
+
+437
+00:33:41,990 --> 00:33:47,170
+Y لعلاقة مع ال واحد اكتبها واحد Y تنتمي لل
+
+438
+00:33:47,170 --> 00:33:55,090
+relation وهذا يساوي كل Y واحد ناقص Y تساوي 4K for
+
+439
+00:33:55,090 --> 00:34:03,840
+some K تنتمي لل Zهل الصورة واضحة؟ أنا معنى بـY إيش
+
+440
+00:34:03,840 --> 00:34:07,500
+بدنا الـY؟ تحقق واحد ناقص Y إذا مين أنا؟ كيف
+
+441
+00:34:07,500 --> 00:34:12,400
+نعملها؟ كتوبة Y إيش بتساوي؟ فلو حلقنا لـY صحيح Y
+
+442
+00:34:12,400 --> 00:34:19,900
+تنتمي للـZ بحيث Y تساوي واحد ناقص أربعة K for some
+
+443
+00:34:19,900 --> 00:34:26,610
+K تنتمي للـZ نبدأ نحسب بعض العناصرمن أول عنصر في
+
+444
+00:34:26,610 --> 00:34:29,730
+ال Y الواحد هيكون في الصف طب بيه موجود ولا مش
+
+445
+00:34:29,730 --> 00:34:33,990
+موجود نعم لو أخدت كيه بتساوي zero for some K تنتمي
+
+446
+00:34:33,990 --> 00:34:36,910
+لل Z طب أخدنا ال zero ناخد كيه بتساوي واحداش في
+
+447
+00:34:36,910 --> 00:34:41,370
+الدين أيه سالب تلاتة ال Y طب خدي كيه بتساوي سالب
+
+448
+00:34:41,370 --> 00:34:46,210
+واحداش في الدين خمسة واضحت الصورة ولا مااضحتش وانت
+
+449
+00:34:46,210 --> 00:34:49,290
+ماشي الييمين زيدي أربعة وانت ماشي اليسار اتراحي
+
+450
+00:34:49,290 --> 00:34:54,870
+أربعةفتسعة تلتاش and so on طبعا او خد K أخدنا K
+
+451
+00:34:54,870 --> 00:34:58,110
+Zero واحد و سالب واحد خد K بتساوي سالب اتنين
+
+452
+00:34:58,110 --> 00:35:02,710
+بتدينا تسعة خد K بتساوي سالب تلاتة بتدينا تلتاش خد
+
+453
+00:35:02,710 --> 00:35:07,770
+K بتساوي اتنين بتدينا سالب سبعة and so on فهذا صف
+
+454
+00:35:07,770 --> 00:35:16,910
+الواحد خلص
+
+455
+00:35:16,910 --> 00:35:23,460
+الصفوف ولا لسهلأ لسه لأنه زي ما انتوا شايفين وين
+
+456
+00:35:23,460 --> 00:35:27,480
+صف التنين مش موجود اه لأنه حتى التنين مش موجودة في
+
+457
+00:35:27,480 --> 00:35:31,340
+صف الصفر طبعا صف الصفر منهانش بسانتش صف الصفر
+
+458
+00:35:31,340 --> 00:35:35,550
+بيساوي صف الأربعةحاضر بس و صف الثمانية و صف الصالب
+
+459
+00:35:35,550 --> 00:35:39,010
+أربعة ففيش داعي أن أعيد أحسب صف الأربعة ولا صف
+
+460
+00:35:39,010 --> 00:35:41,770
+الصالب أربعة زي من المحاضرة الماضية ففيش داعي أحسب
+
+461
+00:35:41,770 --> 00:35:44,770
+صف الخمسة و صف الصالب تلاتة لأنهم متساويين مع هذا
+
+462
+00:35:44,770 --> 00:35:50,570
+الصف أعيد هنا لعند هنا واضحة حلنا المعادلة دي لل
+
+463
+00:35:50,570 --> 00:35:54,720
+وايطبعا نبدأ ناخد كيبل تتنتبه لل Z ممكن كتسك سوى
+
+464
+00:35:54,720 --> 00:35:57,460
+Zero فإذا أول عنصر هو الواحد زي ما احنا متوقعين و
+
+465
+00:35:57,460 --> 00:36:01,640
+لا لأ طيب لو خدنا كيبل سوى واحد واحد ماقص أربع
+
+466
+00:36:01,640 --> 00:36:05,020
+سالب تلاتة طب لو خدنا الكيبل سوى سالب واحد صيخ
+
+467
+00:36:05,020 --> 00:36:07,940
+خمسة فواضح أن الصيغياش امشي زيدي أربع و انت رايح
+
+468
+00:36:07,940 --> 00:36:10,620
+على اليمين و اتروح هي أربع و انت رايح على اليسار
+
+469
+00:36:10,620 --> 00:36:15,300
+نعم؟ اه طبعا هي ماشي كل ما انت .. و انت رايح على
+
+470
+00:36:15,300 --> 00:36:20,800
+اليمين بزيدي أربع و بتمشي و هذا كام تمامخيّن نحسب
+
+471
+00:36:20,800 --> 00:36:24,880
+صفة 2 عبارة
+
+472
+00:36:24,880 --> 00:36:32,900
+عن Y بحيث Y إيش بتساوي؟ 2-4K بس لو عمّمنا، بدي
+
+473
+00:36:32,900 --> 00:36:36,840
+أختصر الآن لإنه واضحة السياسة ولا لأ؟ أه فبتنا E
+
+474
+00:36:36,840 --> 00:36:38,180
+على أد شكل، طبعا ال force sum K
+
+475
+00:36:43,270 --> 00:36:48,030
+طبعا بنفس الأسلوب، مين أول عنصر؟ التنين، لو أخدنا
+
+476
+00:36:48,030 --> 00:36:52,030
+بتساوي واحد ال K سالب اتنين، فنفس السياسة، بنزيد
+
+477
+00:36:52,030 --> 00:36:56,750
+أربعة، فإذا نجي تكون ستة، عشرة and so on، بنطرح
+
+478
+00:36:56,750 --> 00:37:03,750
+أربعة، فده صف التنين، خلصت كل العناصر ولا مانغطوش
+
+479
+00:37:03,750 --> 00:37:09,920
+لسه؟صف التلاتة لأنه واضح لازم يكون عندنا عايش
+
+480
+00:37:09,920 --> 00:37:13,180
+equivalence relation بتتأدي ل partition فلازم
+
+481
+00:37:13,180 --> 00:37:17,240
+الصفوف يغطوا كل العناصر فانا واضح في الصف الأول
+
+482
+00:37:17,240 --> 00:37:23,200
+غطيت مضاعفات الأربعة في الصف التاني غطيت الأعداد
+
+483
+00:37:23,200 --> 00:37:27,250
+اللي بتقبل القسم على أربعة والباقي واحدفي الصف
+
+484
+00:37:27,250 --> 00:37:30,770
+التالت غطيت الأعداد اللي بتقبل قسم الأربعة والباقي
+
+485
+00:37:30,770 --> 00:37:34,090
+اتنين ايش تم احتمال اللي بتقبل أربعة وصافي تلاتة و
+
+486
+00:37:34,090 --> 00:37:37,570
+الباقي تلاتة و هينتهي و هينتهي اه فطبعا هذه بتساوي
+
+487
+00:37:37,570 --> 00:37:43,410
+طبعا تلاتة نفس السياسة سبعة إحداشت أنسؤ لو حسبته
+
+488
+00:37:43,410 --> 00:37:49,200
+سالب واحد سالب خمسة أنسؤو بس مش غيرهم الان لو
+
+489
+00:37:49,200 --> 00:37:53,020
+طلعته اي عدد مين بده يحسب هين حسبنا الصفر والواحد
+
+490
+00:37:53,020 --> 00:37:56,480
+والاتنين والتلاتة صف الأربعة هو صف الصفر خلص صف
+
+491
+00:37:56,480 --> 00:37:59,900
+الخمسة هو وين موجود الخمسة موجود هيا وها كذا فأي
+
+492
+00:37:59,900 --> 00:38:04,220
+عدد هتلاقوه موجود طبعا العدد بعيد ايش بده اعمل هل
+
+493
+00:38:04,220 --> 00:38:08,080
+اي عدد مثلا بده يحسب صف المية صف المية اللي علاقة
+
+494
+00:38:08,080 --> 00:38:11,860
+مع مينماعلي علاقة مع الصفر؟ أه بتقبل قسمه على
+
+495
+00:38:11,860 --> 00:38:15,660
+أربعة لأنه .. لليش؟ لأنه مية ناقص صفر بتساوي أربعة
+
+496
+00:38:15,660 --> 00:38:19,160
+في خمسة وعشرين صح و هكذا فأي عدد هيكون واحدة من
+
+497
+00:38:19,160 --> 00:38:24,360
+الأربعة فإذا الصفوف كلها thus Z على هذه ال
+
+498
+00:38:24,360 --> 00:38:30,340
+relation بتكون من أربع صفوف صف الصفر و صف الواحد و
+
+499
+00:38:30,340 --> 00:38:37,460
+صف التنين و صف التلاتةفأنا بمساعدة النظرية اتأكدت
+
+500
+00:38:37,460 --> 00:38:40,940
+ان الحساب انتهى الحساب انتهى لأنه صار عندي معلومات
+
+501
+00:38:40,940 --> 00:38:44,700
+اتأكدليه ان العملية انتهت اربع صفوف فقط وطبعا ايش
+
+502
+00:38:44,700 --> 00:38:49,160
+ولا صف فاضي زي ما انتوا شايفين ولا صفين فيهم عنصر
+
+503
+00:38:49,160 --> 00:38:54,060
+مشترك لأنه زي ما هنا بيدينا الحالات الأربعة لعملية
+
+504
+00:38:54,060 --> 00:38:57,700
+القسم على أربعة يا الباقي صفر يا الباقي واحد يا
+
+505
+00:38:57,700 --> 00:39:01,780
+اتنين يا تلاتة مافيش احتمال خامس فهذا بيساعدنا في
+
+506
+00:39:01,780 --> 00:39:02,480
+الحساب
+
+507
+00:39:12,780 --> 00:39:21,310
+فتعليق على ما سبق فاحنا في النظرية الماضيةشفنا أو
+
+508
+00:39:21,310 --> 00:39:26,570
+تعلمنا أن أي equivalence relation بتأدي إلى
+
+509
+00:39:26,570 --> 00:39:30,390
+partition أو بتولد partition كيف هذا التجزيق عبارة
+
+510
+00:39:30,390 --> 00:39:34,550
+عن صفوف التكافئة فالسؤال اللي هنطرحه طب هل العكس
+
+511
+00:39:34,550 --> 00:39:38,590
+صحيح؟ هل كل partition بيقدر يعرف equivalence
+
+512
+00:39:38,590 --> 00:39:43,050
+relation؟ هذا اللي هنشوفه في الدراسة القادمة
+
+513
+00:39:55,520 --> 00:39:59,480
+فاحنا الحقيقة في نهاية ال search هنوصل للصورة
+
+514
+00:39:59,480 --> 00:40:04,560
+التالية إذا بدأنا من علاقة تكافؤ بنقدر نولد
+
+515
+00:40:04,560 --> 00:40:08,680
+partition و ال partition بيولد علاقة تكافؤ هي
+
+516
+00:40:08,680 --> 00:40:11,760
+العلاقة اللي بدأنا منها ففي دائرة أنا مكتملة أنا
+
+517
+00:40:11,760 --> 00:40:16,150
+دائرة مكتملةطبعا نص الدائرة خلص إذا إن كل علاقة
+
+518
+00:40:16,150 --> 00:40:20,510
+تكافؤ تولد partition فالسؤال العكسي هل كل
+
+519
+00:40:20,510 --> 00:40:23,930
+partition بولد علاقة تكافؤ فده اللي هندرسه مع بعض
+
+520
+00:40:23,930 --> 00:40:28,070
+طبعا أول شي أنا بدي أولد علاقة تكافؤ فبنشوف كيف
+
+521
+00:40:28,070 --> 00:40:31,330
+نولد علاقة من partition كيف نولد علاقة من
+
+522
+00:40:31,330 --> 00:40:36,550
+partition فالعنوان الفرعي relations induced by
+
+523
+00:40:36,550 --> 00:40:42,910
+partition العلاقات المتولدة من ال partitionفلو كان
+
+524
+00:40:42,910 --> 00:40:48,250
+عندي partition كيف منه بدي اعرف علاقة الصورة شكل
+
+525
+00:40:48,250 --> 00:40:54,950
+التالت عندنا مجموعة X مقسمة تقسيم معين
+
+526
+00:41:00,110 --> 00:41:04,410
+مقسمة في partition معين طبعا خواص ال partition ولا
+
+527
+00:41:04,410 --> 00:41:08,190
+جزء فاضي و اي جزءين يا متطابقين يا disjoined يا
+
+528
+00:41:08,190 --> 00:41:11,710
+مفصلين و كل الأجزاء اتحادة بالدين جنب الميول اكسر
+
+529
+00:41:11,710 --> 00:41:20,570
+فاحنا هنعرف ال relation بالشكل التالي فالعنصرين
+
+530
+00:41:21,530 --> 00:41:26,830
+هيكون إلهم علاقة مع بعض إذا وقعها في نفس الجزء إذا
+
+531
+00:41:26,830 --> 00:41:30,770
+وقعها في نفس الجزء فاحنا في عندنا partitions أي
+
+532
+00:41:30,770 --> 00:41:35,830
+جزاء متعددة إذا وقع العنصرين في جزء مع بعض لإن
+
+533
+00:41:35,830 --> 00:41:38,210
+أحنا عارفين أن الجزاء دي منفصل عن بعض فبينا
+
+534
+00:41:38,210 --> 00:41:42,430
+نختبرهم إيش إلهم علاقة مع بعضوإلا مافيش علاقة،
+
+535
+00:41:42,430 --> 00:41:46,250
+فهذه هي الصورة، طبعا احنا هنمشي بيها تدريج، هنشوف
+
+536
+00:41:46,250 --> 00:41:49,070
+هذا ال relation ونفهمها ومن ثم هنثبت ان هذه
+
+537
+00:41:49,070 --> 00:41:52,490
+العلاقة المتولدة بهذه الطريقة دايما هي علاقة
+
+538
+00:41:52,490 --> 00:41:56,570
+تكافؤ، دايما هي علاقة تكافؤ، وهذا احنا هنثبته في
+
+539
+00:41:56,570 --> 00:41:59,230
+نظرية فيما بعد
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/RblLD1z_wGY.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/RblLD1z_wGY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1fa79ddcc2be31bf3f0aaaeea6def82f2e426700
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/RblLD1z_wGY.srt
@@ -0,0 +1,1699 @@
+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
+الcardinal numbers وبشكل خاص مع جمع الcardinal 
+
+3
+00:00:28,710 --> 00:00:33,190
+numbers فكنا عرفنا الaddition 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 numbers A and B بدي أجيب
+
+6
+00:00:42,370 --> 00:00:46,850
+مجموعة تقابل الcardinal number A و أجيب مجموعة
+
+7
+00:00:46,850 --> 00:00:50,330
+تقابل الcardinal number B بحيث أنه تقطعهم يسووا
+
+8
+00:00:50,330 --> 00:00:56,650
+∅ اه و بعدين بروح باخد ايش A زائد 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
+الطريقة فكان 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 أنت تجيب الجامعة بدك تجيب مجموعتين A و
+
+13
+00:01:17,330 --> 00:01:21,470
+B تعطوهم ∅ 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 ما حددش 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
+لأ فبهذه الحالة إن هذا فعلا تعريف علمي لأ دائما
+
+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 صحيح فهذه
+
+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 ما أعرفش أقول
+
+28
+00:02:08,080 --> 00:02:14,630
+تلاتة زائد خمسة لو عملناها معداد صحيحة أو حقيقية طب
+
+29
+00:02:14,630 --> 00:02:16,890
+لو عملناهم كcardinal 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 الcardinal number الصفر و كل الأعداد
+
+32
+00:02:21,590 --> 00:02:24,850
+الطبيعية وطبعا في اللي هو الtransfinite cardinal
+
+33
+00:02:24,850 --> 00:02:27,490
+number اللي بقابل المجموعات الinfinite set
+
+34
+00:02:27,490 --> 00:02:30,770
+فبقول لي كcardinal number نجيب التلاتة و الخمسة
+
+35
+00:02:30,770 --> 00:02:35,710
+أنا هنا مثال بسيط جدا بس بدنا نوضع اللي هو إيش نعمل
+
+36
+00:02:35,710 --> 00:02:39,910
+... نكرّس الفكرة فاحنا عندنا هنا الـA بتساوي تلاتة
+
+37
+00:02:39,910 --> 00:02:43,470
+والـB 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 ∅، 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
+ثمانية، تسعة خمسة،
+
+44
+00:03:18,080 --> 00:03:22,480
+ستة، سبعة، ثمانية، تسعة خمسة،
+
+45
+00:03:22,480 --> 00:03:27,760
+ستة، سبعة، ثمانية، تسعة خمسة،
+
+46
+00:03:27,760 --> 00:03:32,540
+ستة، سبعة، ثمانية، تسعة بقى لأ بس عشان تكون سهولة
+
+47
+00:03:32,540 --> 00:03:40,340
+صح صح فطبعا then الcardinality لل a تساوي تلاتة
+
+48
+00:03:40,340 --> 00:03:45,820
+الcardinality لل b تساوي خمسة و ايش كمان و a
+
+49
+00:03:45,820 --> 00:03:51,140
+تقاطع ال b بيساوي ∅ فبالتالي اللي هو تلاتة زائد
+
+50
+00:03:51,140 --> 00:03:56,140
+خمسة بديه يساوي الcardinality 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 ثمانية فهذه هي
+
+54
+00:04:11,600 --> 00:04:14,900
+الفكرة تماما اللي هو كيف بنعلّم أي طفل صغير كيف
+
+55
+00:04:14,900 --> 00:04:20,230
+بنعلمه يجمع بشكل 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
+جلّما نبدأ بالأمثلة الحقيقية اللي بدأ شغل نشوف
+
+58
+00:04:30,270 --> 00:04:35,040
+فيها نظرية ببعض الخواص طبعا 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 لها خاصية التجميع؟ هل لها 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 كذا طبعا
+
+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
+associativity لخاصية التجميع بدي أجمع تلت أعداد
+
+72
+00:05:27,540 --> 00:05:31,560
+X Y و Z أجمع الأول و الثاني و الناتج مع الثالث أو
+
+73
+00:05:31,560 --> 00:05:34,720
+الثاني مع الثالث 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 الأول طبعا هنا اللي بدنا نؤكد
+
+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
+بدخلها من لغة الcardinal number إلى لغة
+
+78
+00:05:53,220 --> 00:05:56,560
+المجموعات وأستفيد من معلوماتي في chapter 5 وفيما
+
+79
+00:05:56,560 --> 00:06:01,900
+سبق وعشان 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 ∅ وإيش كمان؟ وإن الـX بتساوي
+
+82
+00:06:17,960 --> 00:06:21,740
+الـcardinality للـCapital X مثلاً و الsmall y
+
+83
+00:06:21,740 --> 00:06:26,800
+بتساوي الcardinality للCapital 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 للX
+
+86
+00:06:35,340 --> 00:06:41,280
+اتحاد الY مظبوط؟ هاي البداية إيش بدنا نعمل؟ بدنا
+
+87
+00:06:41,280 --> 00:06:44,720
+نبدّل مين من كنا نبدّل؟ الاتحاد لأن الاتحاد في
+
+88
+00:06:44,720 --> 00:06:50,060
+المعلومات السابقة فهذه تساوي الcardinality للY
+
+89
+00:06:50,060 --> 00:06:54,300
+اتحاد الX مين دليلنا؟ إن الاتحاد commutative لأن
+
+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
+بساطة فبكل بساطة الموضوع حولته من موضوع جديد لموضوع
+
+94
+00:07:14,830 --> 00:07:20,030
+قديم استخدمت معلومات قديمة وأثبتت المعلومة الجديدة
+
+95
+00:07:20,030 --> 00:07:27,430
+نشوف عملية اللي هو associativity ليهخاصية 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 آسف 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 أنا أجمع 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 ∅ كل تنتين في مع بعض لأن
+
+103
+00:08:10,710 --> 00:08:14,540
+بالآخر أنا بدي أجيب تلاتة في عندي تلت تلت مجموعة
+
+104
+00:08:14,540 --> 00:08:18,620
+فيها تلت عناصر والثانية أربعة والثالثة خمسة بدي
+
+105
+00:08:18,620 --> 00:08:21,240
+أجمعهم كلهم عن بعض ليش ولا عنصر يتكرر ولا ما تن تان
+
+106
+00:08:21,240 --> 00:08:24,960
+مش شرط يكون مش شرك للتلاتة 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 لكابيتل X بتساوي small x cardinality
+
+109
+00:08:36,820 --> 00:08:42,240
+لكابيتل Y بتساوي small y cardinality لZ تساوي small
+
+110
+00:08:42,240 --> 00:08:53,230
+z تمام 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 الY
+
+112
+00:08:57,350 --> 00:09:04,830
+زائد Z أولا فده عبارة عن cardinality للX اتحاد من
+
+113
+00:09:04,830 --> 00:09:06,810
+Y اتحاد الZ
+
+114
+00:09:10,060 --> 00:09:15,100
+طبعا هنا بس كملاحظة بما أنه تقطع الX مع الY يعني
+
+115
+00:09:15,100 --> 00:09:18,780
+هاد ممكن يعملها كأنها مجموعة A بما أنه هاد تقطعها
+
+116
+00:09:18,780 --> 00:09:21,820
+مع الY ∅ ومع الZ ∅ برضه تقطعها مع الاتحاد
+
+117
+00:09:21,820 --> 00:09:25,260
+∅ بقدر أشتغل عليها بدل شكل فكل الشروط متحقق خلاص
+
+118
+00:09:25,260 --> 00:09:29,180
+الآن نستخدم الassociative لمن؟ للunion فده
+
+119
+00:09:29,180 --> 00:09:34,380
+بتساوي cardinality للX union Y مع بعض بعدين مع ال
+
+120
+00:09:34,380 --> 00:09:38,720
+Z لأنه الunion 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 الcardinal 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 سؤال جلّما 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
+الcardinality 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 ما فيش عدد حقيقي لأنه infinite فبنديله رمز
+
+130
+00:10:24,290 --> 00:10:28,810
+فهذا الرمز هنعمله هذا الرمز اللي قدامكم يقرأ ألف
+
+131
+00:10:28,810 --> 00:10:33,860
+null هذا الحرف طبعا بنكتبه بهذا الشكل حرف مائل هيك
+
+132
+00:10:33,860 --> 00:10:37,320
+زي هي طبعا تشبه الX لكن بتنكتبش بدا الشكل لأن
+
+133
+00:10:37,320 --> 00:10:41,340
+بتنكتبها دولة منفصلين زي الX 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 الرمز عشان
+
+138
+00:10:55,530 --> 00:10:58,130
+نتعامل معاه، هنتعامل معاه كثير لإنه من المجموعات
+
+139
+00:10:58,130 --> 00:11:02,030
+الأساسية يعني هو من أشهر الاتمين لـTransfinite
+
+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 هنديتها 
+
+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 غريبًا 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 بيرمز له 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 ما فيش فيه ولا فراغ أي نقطة على
+
+152
+00:11:45,550 --> 00:11:50,370
+خط الأعداد تمثل عدد حقيقي من خواص الأعداد الحقيقية
+
+153
+00:11:50,370 --> 00:11:55,710
+و هذا يجعله مكتظ جدًا كل نقطة على خط 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 ميزات 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
+ما ينفعش نشغل على الـQ ما ينفعش نشغل على الـZ الـR
+
+159
+00:12:13,610 --> 00:12:17,290
+لأن كل وين ما تمشي فيه أعداد حقيقية أه فدي مهمة جدًا
+
+160
+00:12:17,290 --> 00:12:22,350
+فمن كلمة continuum هناخد حرف الـC فإذا هدول على
+
+161
+00:12:22,350 --> 00:12:25,490
+أترآك اثنين cardinal number مشهورين، اثنين
+
+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 هدول من صراع أعداد، نتعود عليهم
+
+165
+00:12:38,690 --> 00:12:44,320
+ألف null زائد ألف null بدنا نجيب مجموع هدول
+
+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 ونشوف كيف بدنا نحل إيش تتوقع الجواب ال if
+
+168
+00:12:57,920 --> 00:13:04,520
+not أحسنتِ تمام فهذا المثال الأول solution إيش
+
+169
+00:13:04,520 --> 00:13:10,170
+بدنا بدنا مجموعتين، كل مجموعة الـ Cardinal تلها ألف
+
+170
+00:13:10,170 --> 00:13:14,570
+null لكن تقاطعهم بيساوي 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 اثنتين من هدول تقاطعهم
+
+174
+00:13:25,350 --> 00:13:29,460
+بيساوي five الـ even و الـ odd ما بنفعش أخد n و z
+
+175
+00:13:29,460 --> 00:13:32,580
+تقاطعهم بيساويش 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 { n such that n
+
+178
+00:13:44,840 --> 00:13:52,510
+تنتمي للـ n الأعداد الطبيعية الزوجية } and B 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 ما فيش أه طبعا
+
+183
+00:14:08,690 --> 00:14:17,650
+and ال cardinality للـ A تساوي ال cardinality للـ 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
+ما فيش أصغر من Denimrable أو إيش كمان و ال
+
+188
+00:14:30,030 --> 00:14:35,210
+cardinality للـ B بتساوي ال cardinality للـ N أيضًا
+
+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 Phi وكل عدد مجموعة تقابل فأصبح
+
+191
+00:14:48,670 --> 00:14:53,350
+ألف null زائد ألف null بيساوي ال cardinality لمن؟
+
+192
+00:14:53,350 --> 00:14:59,090
+للـ A union B للاتحاد أو هذا إيش بيساوي؟ بيساوي ال
+
+193
+00:14:59,090 --> 00:15:04,650
+cardinality للـ un even اتحاد الـ N O اللي هي ليس
+
+194
+00:15:04,650 --> 00:15:10,970
+إلا N أحسنتِ بتساوي ال cardinality للـ N وتساوي من؟
+
+195
+00:15:10,970 --> 00:15:14,930
+ألف null إذن ألف null زي ألف null بتساوي ألف null
+
+196
+00:15:14,930 --> 00:15:18,610
+و هذا شيء ما هو غريب المفروض يكون عندنا ليش infinite
+
+197
+00:15:18,610 --> 00:15:22,030
+زي infinite تساوي infinity غير لكن لو جالنا مثلًا
+
+198
+00:15:22,030 --> 00:15:26,250
+واحد زي واحد + اثنين بيساوي واحد لكن عشان إنه
+
+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 ألف null زي C ألف null زائد
+
+201
+00:15:41,940 --> 00:15:45,240
+C هدول two cardinal number اثنين اتعرفنا عليهم فهدول
+
+202
+00:15:45,240 --> 00:15:49,400
+أعداد أدنا لها رمز عشان هنبدأ نشتغل عليهم بدنا
+
+203
+00:15:49,400 --> 00:15:54,180
+نجيب الالف null مع نفسها الآن ألف null مع الـ C بدنا
+
+204
+00:15:54,180 --> 00:16:00,240
+مجموعتين solution مجموعة تكون ألف null ال cardinal
+
+205
+00:16:00,240 --> 00:16:03,700
+تتبعتها والثانية ال cardinal تتبعتها الهايه ال C
+
+206
+00:16:03,700 --> 00:16:09,300
+تقاطعهم بيساوي five هذا المثال رقم اثنين أه طبعا مين
+
+207
+00:16:09,300 --> 00:16:11,800
+بنعرف إن ال cardinality لها ألف null أكتر طوي
+
+208
+00:16:11,800 --> 00:16:16,820
+وقولناهم N even, N odd, N zq وهكذا طب مين
+
+209
+00:16:16,820 --> 00:16:20,940
+ال cardinality لها C؟ الـ R وإيش 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 على 01 على 01 أثبتناها بعدين
+
+212
+00:16:27,520 --> 00:16:31,080
+قلنا إن الـ 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 ما فيش
+
+214
+00:16:37,570 --> 00:16:39,850
+ولا عدد بين الصفر وبين ال one فهنا دول هناخد
+
+215
+00:16:39,850 --> 00:16:45,150
+الاثنتين هدول فهنقول له let .. خلّيني نكتب مع بعض
+
+216
+00:16:45,150 --> 00:16:50,130
+and B
+
+217
+00:16:50,130 --> 00:16:55,810
+مع الكتابة بتوضح للي مش واضحًا then أول شيء إيه
+
+218
+00:16:55,810 --> 00:16:59,800
+تقاطع الـ B بساوي فاي ولا لأ؟ ما فيش ولا عدد طبيعي
+
+219
+00:16:59,800 --> 00:17:02,960
+بين الصفر والواحد هذا مفتوح أه ما فيش ولا عدد
+
+220
+00:17:02,960 --> 00:17:06,200
+طبيعي لإنه إيش العداد واحد اثنين وهكذا أه فده أول
+
+221
+00:17:06,200 --> 00:17:12,380
+حاجة طبعا and طبعا ال cardinality للـ a ألف null
+
+222
+00:17:12,380 --> 00:17:18,480
+مظبوط أه وال cardinality للـ b بتساوي c ليش لأن
+
+223
+00:17:18,480 --> 00:17:24,080
+هذه تكافئ الـ R تساوي 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 معه نموذج جيد نتعامل معه 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 لإنه بيريحنا أي
+
+228
+00:17:36,020 --> 00:17:41,080
+تقاطع ما الآن بيساويها إذن thus بالنسبة عندنا إيش
+
+229
+00:17:41,080 --> 00:17:45,180
+بده هو ألف null زائد C ألف null زائد C بتساوي 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 فبننتش
+
+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 ما يجي زي هداك هداك مثال كان سهل ع طول
+
+235
+00:18:11,000 --> 00:18:14,400
+طلعت مباشرة أثبتنا إنه بيساوي ألف null ألف null زي
+
+236
+00:18:14,400 --> 00:18:18,120
+ألف null بيساوي ألف null بشكل مباشر في هذه المواضيع
+
+237
+00:18:18,120 --> 00:18:20,920
+خصوصا لما نكون نتعامل مع الـ C هنستخدم طريقة ثانية
+
+238
+00:18:20,920 --> 00:18:25,540
+عشان أثبت أن X يساوي Y هثبت أن X أصغر أو تساوي Y و Y
+
+239
+00:18:25,540 --> 00:18:28,660
+أصغر أو تساوي X هذا الأسلوب اللي هنستخدمه خصوصا لما
+
+240
+00:18:28,660 --> 00:18:31,760
+نتعامل مع الـ real numbers مع الـ C لإنه العملية
+
+241
+00:18:31,760 --> 00:18:35,660
+شوية كبيرة وما فيش طريقة مباشرة فهنستخدم الطريقة
+
+242
+00:18:35,660 --> 00:18:41,380
+غير المباشرة فأول شيء هثبت إنه طبعا احنا هنثبت إن
+
+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
+شيء هثبت إنه هذه أصغر منها أو تساوي هذه طبعا أسهل
+
+246
+00:18:56,820 --> 00:18:59,800
+المفروض لأن واضح إنها أكبر بشكل أكبر بشكل زائد
+
+247
+00:18:59,800 --> 00:19:05,500
+طبعا أول شي واحد عشان أثبت إنه C أصغر أو تساوي ألف
+
+248
+00:19:05,500 --> 00:19:10,080
+null زائد C بدأنا أثبت هذا الكلام هذا المطلوب ما بتش
+
+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
+المجموعة اللي بتقابله تكافئ subset من المجموعة
+
+251
+00:19:15,540 --> 00:19:19,120
+الثانية، مظبوط؟ فقلنا احنا بالنسبة للسمين بيقابله
+
+252
+00:19:19,120 --> 00:19:23,600
+01 أو R، خلي دايمًا 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 subset فالآن هنا عشان نشتغل
+
+257
+00:19:40,530 --> 00:19:47,950
+هنا إن اللي هو الـ C اللي هو 01 شمالها 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؟ أه تمام
+
+260
+00:19:57,530 --> 00:20:02,470
+هذا معناه على طول إن ال cardinality لهذه المجموعة
+
+261
+00:20:02,470 --> 00:20:10,480
+01 أقل أو يساوي الـ cardinality للـ N union 01 فهذه
+
+262
+00:20:10,480 --> 00:20:13,740
+فكرة مباشرة، واضحة عادي لإنه احنا مش مانعين 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، ما فيش داعي إن أحط تكافئ، فهذا على طول إيش بقى
+
+265
+00:20:18,940 --> 00:20:24,200
+تديني 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 الثاني بدنا نثبت إن الـ Alpha Null زائد
+
+268
+00:20:34,810 --> 00:20:41,650
+C أقل أو تساوي C فبدي
+
+269
+00:20:41,650 --> 00:20:48,190
+الـ Union 01 تكافئ subset من مين؟ بنفع أخد 01؟
+
+270
+00:20:48,190 --> 00:20:55,070
+لأ، رأيت أنا بدي أدور، هاي عني N مع 01 بديها تكافئ
+
+271
+00:20:55,070 --> 00:20:59,470
+subset معينة وليكن X بنفع أخد من الـ 01؟ ما بنفعش
+
+272
+00:20:59,470 --> 00:21:06,870
+لإنيها كبيرة لإنيها مش cross لكن إيش ممكن نعمل ناخد
+
+273
+00:21:06,870 --> 00:21:12,580
+الـ R فدي subset من الـ R فهذه 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 الـ C وصغيرة 01 مجموعة القاردنات
+
+276
+00:21:20,840 --> 00:21:25,600
+اللي لها الـ C وكبيرة R فبنشتغل بهذا الشكل ونتحرك
+
+277
+00:21:25,600 --> 00:21:29,480
+أه فطبعا كيف بدي أشوف إن هذا تكافئ الـ X أصلا كل
+
+278
+00:21:29,480 --> 00:21:35,480
+هذه برضه صبصة من الـ A كل الـ union الـ 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 الـ R و لا لأ واضح
+
+283
+00:21:42,280 --> 00:21:45,760
+هادي و لا مش واضح ليش لأن الـ 01 subset من الـ R و
+
+284
+00:21:45,760 --> 00:21:48,500
+الـ N subset من الـ R فاتحادهم subset من الـ R على
+
+285
+00:21:48,500 --> 00:21:51,240
+طول هذا بيقوللي ان الـ cardinality أصغر من الـ
+
+286
+00:21:51,240 --> 00:21:58,300
+cardinality N union 01 أقل أو تساوي cardinality للـ
+
+287
+00:21:58,300 --> 00:22:04,240
+R فهذا trick مشهور إنه تكون في عيننا مرونة زي ما
+
+288
+00:22:04,240 --> 00:22:09,420
+أنا 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 الـ Infinity مختلفين ونشوف مين الـ 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 الـ 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 الـ R ومين أكبر من الـ 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 الـ 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 الـ 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 الـ A و الـ B بشكل
+
+339
+00:25:47,490 --> 00:25:52,930
+مناسب الان ممكن نبدأ نشتغل فطبعا صار عندنا الـ A
+
+340
+00:25:52,930 --> 00:25:57,090
+زائد واحد ليست الا Cardinality للـ 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 الـ 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 الـ 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 الـ 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 الـ domain، أضافله عنصر، بده أضافله
+
+384
+00:29:49,120 --> 00:29:54,720
+عنصر، فبدنا نعرف الـ F، بدنا نعرف الـ F، بنفع الـ F
+
+385
+00:29:54,720 --> 00:29:59,660
+تعتمد على الـ G؟ بنفع، بس domain الجي صغير، بدنا
+
+386
+00:29:59,660 --> 00:30:05,670
+نعرف إيش؟ صورة الـ 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 الـ X تروح لصورة ماتكونش صورة، لأنه
+
+396
+00:30:39,440 --> 00:30:46,240
+مافيش في عندي هنا، في عندي جوة الـ 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 للـ A ناقص الـ 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 الـ domain من بكافئ الـ 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 الـ trick مشهور عملناه أكتر من مرة
+
+416
+00:32:30,520 --> 00:32:34,200
+صار الـ domain يكافئ الـ image و الـ image subset
+
+417
+00:32:34,200 --> 00:32:40,680
+فهذا بيقول لإنه الـ cardinality للـ A union B أقل أو
+
+418
+00:32:40,680 --> 00:32:44,840
+تساوي الـ cardinality لمن؟ للـ A إيش الـ 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 أنتم 
+
+422
+00:33:05,310 --> 00:33:10,390
+شايفين في أفكار بتتكرر معنا أرجو أنها ساعدتنا في
+
+423
+00:33:10,390 --> 00:33:15,810
+الفهم بشكل أفضل فهذه نهاية هذا ال section إن 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/RblLD1z_wGY_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/RblLD1z_wGY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..04e47ccab7454b99cdd28f812717501f382b29f4
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/RblLD1z_wGY_raw.json
@@ -0,0 +1 @@
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" find", "probability": 0.35498046875}, {"start": 124.9, "end": 125.16, "word": " the", "probability": 0.78125}, {"start": 125.16, "end": 125.7, "word": " cardinal", "probability": 0.959716796875}, {"start": 125.7, "end": 126.04, "word": " sum", "probability": 0.95654296875}, {"start": 126.04, "end": 126.4, "word": " طبعا", "probability": 0.9039306640625}, {"start": 126.4, "end": 126.72, "word": " تلاتة", "probability": 0.81048583984375}, {"start": 126.72, "end": 126.92, "word": " زائد", "probability": 0.8040364583333334}, {"start": 126.92, "end": 127.42, "word": " خمسة", "probability": 0.9588623046875}, {"start": 127.42, "end": 127.88, "word": " ماعرفش", "probability": 0.3828277587890625}, {"start": 127.88, "end": 128.08, "word": " أقول", "probability": 0.8076171875}, {"start": 128.08, "end": 128.36, "word": " تلاتة", "probability": 0.802978515625}, {"start": 128.36, "end": 128.5, "word": " زائد", "probability": 0.89990234375}, {"start": 128.5, "end": 128.76, "word": " خمسة", 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associative", "probability": 0.960693359375}, {"start": 293.44, "end": 294.16, "word": " وخاصية", "probability": 0.79937744140625}, {"start": 294.16, "end": 295.24, "word": " التجميع", "probability": 0.9239501953125}, {"start": 295.24, "end": 295.76, "word": " طبعا", "probability": 0.9208984375}, {"start": 295.76, "end": 296.18, "word": " التجميع", "probability": 0.9835205078125}, {"start": 296.18, "end": 296.46, "word": " مهم", "probability": 0.98681640625}, {"start": 296.46, "end": 296.78, "word": " جدا", "probability": 0.9189453125}, {"start": 296.78, "end": 297.02, "word": " لأنه", "probability": 0.8736979166666666}, {"start": 297.02, "end": 297.32, "word": " بتفتح", "probability": 0.973876953125}, {"start": 297.32, "end": 297.72, "word": " الباب", "probability": 0.986083984375}, {"start": 297.72, "end": 298.16, "word": " أنه", "probability": 0.6571044921875}, {"start": 298.16, "end": 298.28, "word": " أنا", "probability": 0.7470703125}, {"start": 298.28, "end": 298.44, "word": " هنا", "probability": 0.77099609375}, {"start": 298.44, "end": 299.0, "word": " بجمع", "probability": 0.9521484375}, {"start": 299.0, "end": 299.4, "word": " عددين", "probability": 0.897216796875}, {"start": 299.4, "end": 299.6, "word": " وممكن", "probability": 0.728759765625}, {"start": 299.6, "end": 299.84, "word": " أجمع", "probability": 0.9134521484375}, {"start": 299.84, "end": 300.32, "word": " تلاتة", "probability": 0.9532470703125}, {"start": 300.32, "end": 300.6, "word": " عن", "probability": 0.91064453125}, {"start": 300.6, "end": 300.82, "word": " طريق", "probability": 0.9786783854166666}, {"start": 300.82, "end": 301.22, "word": " التجميع", "probability": 0.958740234375}, {"start": 301.22, "end": 301.46, "word": " وها", "probability": 0.7666015625}, {"start": 301.46, "end": 301.68, "word": " كذا", "probability": 0.839599609375}], "temperature": 1.0}, {"id": 13, "seek": 32001, "start": 301.89, "end": 320.01, "text": "طبعا نص النظرية let x, y and z be arbitrary cardinal numbers أي أعداد أصلية أولا عملية الإبدال commutativity x زائد y تصيب y زائد x بدون أي مشاكل تبدأ من التلاتة تبدأ من الخمسة تطلع الجهة التامنية", "tokens": [9566, 3555, 3615, 995, 8717, 9381, 28239, 19913, 2288, 10632, 718, 2031, 11, 288, 293, 710, 312, 23211, 2920, 2071, 3547, 36632, 5551, 22488, 18513, 5551, 9381, 1211, 10632, 5551, 12610, 995, 6225, 42213, 10632, 33688, 44510, 6027, 800, 325, 30142, 2031, 30767, 16373, 3215, 288, 6055, 9381, 1829, 3555, 288, 30767, 16373, 3215, 2031, 47525, 11536, 36632, 37893, 995, 28820, 6055, 44510, 10721, 9154, 16712, 1211, 9307, 3660, 6055, 44510, 10721, 9154, 33962, 2304, 3794, 3660, 6055, 9566, 1211, 3615, 25724, 3224, 3660, 16712, 10943, 1863, 10632], "avg_logprob": -0.3030196575636274, "compression_ratio": 1.532994923857868, "no_speech_prob": 0.0, "words": [{"start": 301.89, "end": 302.49, "word": "طبعا", "probability": 0.76861572265625}, {"start": 302.49, "end": 302.79, "word": " نص", "probability": 0.824462890625}, {"start": 302.79, 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"word": " أصلية", "probability": 0.7689208984375}, {"start": 310.15, "end": 311.21, "word": " أولا", "probability": 0.77294921875}, {"start": 311.21, "end": 311.97, "word": " عملية", "probability": 0.9378255208333334}, {"start": 311.97, "end": 312.57, "word": " الإبدال", "probability": 0.8966471354166666}, {"start": 312.57, "end": 313.39, "word": " commutativity", "probability": 0.6015625}, {"start": 313.39, "end": 314.07, "word": " x", "probability": 0.51513671875}, {"start": 314.07, "end": 314.41, "word": " زائد", "probability": 0.53363037109375}, {"start": 314.41, "end": 314.59, "word": " y", "probability": 0.97412109375}, {"start": 314.59, "end": 314.91, "word": " تصيب", "probability": 0.8131103515625}, {"start": 314.91, "end": 315.15, "word": " y", "probability": 0.43896484375}, {"start": 315.15, "end": 315.49, "word": " زائد", "probability": 0.88525390625}, {"start": 315.49, "end": 315.75, "word": " x", "probability": 0.962890625}, {"start": 315.75, "end": 316.57, "word": " بدون", "probability": 0.948974609375}, {"start": 316.57, "end": 316.75, "word": " أي", "probability": 0.89697265625}, {"start": 316.75, "end": 317.39, "word": " مشاكل", "probability": 0.9816080729166666}, {"start": 317.39, "end": 317.95, "word": " تبدأ", "probability": 0.8912760416666666}, {"start": 317.95, "end": 318.07, "word": " من", "probability": 0.97265625}, {"start": 318.07, "end": 318.49, "word": " التلاتة", "probability": 0.8524169921875}, {"start": 318.49, "end": 318.71, "word": " تبدأ", "probability": 0.8077799479166666}, {"start": 318.71, "end": 318.83, "word": " من", "probability": 0.99267578125}, {"start": 318.83, "end": 319.19, "word": " الخمسة", "probability": 0.97900390625}, {"start": 319.19, "end": 319.39, "word": " تطلع", "probability": 0.69342041015625}, {"start": 319.39, "end": 319.61, "word": " الجهة", "probability": 0.6566569010416666}, {"start": 319.61, "end": 320.01, "word": " التامنية", "probability": 0.67333984375}], "temperature": 1.0}, {"id": 14, "seek": 34534, "start": 320.94, "end": 345.34, "text": "B associativity لخاصية التجميع بدي أجمع تلت أعداد X Y و Z أجمع الأول و التاني و الناتج مع التالت أو التاني مع التالت و الناتج مع الأول كله نفس الشيء خلينا نشوف البرهان مع بعض نظرية 6-4 prove نبدأ بالفرع الأول", "tokens": [33, 4180, 30142, 5296, 9778, 33546, 10632, 16712, 7435, 2304, 40228, 4724, 16254, 5551, 7435, 2304, 3615, 6055, 1211, 2655, 5551, 22488, 18513, 1783, 398, 4032, 1176, 5551, 7435, 2304, 3615, 16247, 12610, 4032, 16712, 7649, 1829, 4032, 28239, 9307, 7435, 20449, 16712, 6027, 2655, 34051, 16712, 7649, 1829, 20449, 16712, 6027, 2655, 4032, 28239, 9307, 7435, 20449, 16247, 12610, 28242, 3224, 8717, 36178, 25124, 1829, 38207, 16490, 20292, 8315, 8717, 8592, 38688, 2423, 26890, 3224, 7649, 20449, 45030, 11242, 8717, 19913, 2288, 10632, 1386, 12, 19, 7081, 8717, 44510, 10721, 20666, 5172, 2288, 3615, 16247, 12610], "avg_logprob": -0.20695152635477027, "compression_ratio": 1.8134715025906736, "no_speech_prob": 0.0, "words": 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"probability": 0.9755859375}, {"start": 340.72, "end": 341.12, "word": " 6", "probability": 0.732421875}, {"start": 341.12, "end": 341.7, "word": "-4", "probability": 0.57977294921875}, {"start": 341.7, "end": 342.38, "word": " prove", "probability": 0.17138671875}, {"start": 342.38, "end": 344.54, "word": " نبدأ", "probability": 0.9197591145833334}, {"start": 344.54, "end": 344.94, "word": " بالفرع", "probability": 0.9267578125}, {"start": 344.94, "end": 345.34, "word": " الأول", "probability": 0.9814453125}], "temperature": 1.0}, {"id": 15, "seek": 37372, "start": 346.26, "end": 373.72, "text": "طبعا هنا اللي بدنا نأكد عليه نفس الطريقة اللي نشتغل عليها عشان أبدأ أجمع بدحولها من لغة ال cardinal number إلى لغة المجموعات واستفيد من معلوماتي في chapter 5 و فيما سبق و عشان إيش أخد المعلومات فطبعا هنا بالنسبة للأول عندنا x و y فنقول له let x و y be sets such that تقطعهم يساوي في", "tokens": [9566, 3555, 3615, 995, 34105, 13672, 1829, 47525, 8315, 8717, 10721, 4117, 3215, 47356, 8717, 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350.82, "word": " بدحولها", "probability": 0.65008544921875}, {"start": 350.82, "end": 350.9, "word": " من", "probability": 0.99462890625}, {"start": 350.9, "end": 351.36, "word": " لغة", "probability": 0.9791666666666666}, {"start": 351.36, "end": 351.88, "word": " ال", "probability": 0.70751953125}, {"start": 351.88, "end": 352.36, "word": " cardinal", "probability": 0.607421875}, {"start": 352.36, "end": 352.74, "word": " number", "probability": 0.97607421875}, {"start": 352.74, "end": 352.96, "word": " إلى", "probability": 0.87158203125}, {"start": 352.96, "end": 353.22, "word": " لغة", "probability": 0.9944661458333334}, {"start": 353.22, "end": 353.84, "word": " المجموعات", "probability": 0.9814453125}, {"start": 353.84, "end": 354.64, "word": " واستفيد", "probability": 0.83575439453125}, {"start": 354.64, "end": 354.76, "word": " من", "probability": 0.99462890625}, {"start": 354.76, "end": 355.42, "word": " معلوماتي", "probability": 0.920703125}, {"start": 355.42, "end": 355.58, "word": " في", "probability": 0.96630859375}, {"start": 355.58, "end": 355.82, "word": " chapter", "probability": 0.66748046875}, {"start": 355.82, "end": 356.2, "word": " 5", "probability": 0.68994140625}, {"start": 356.2, "end": 356.38, "word": " و", "probability": 0.9619140625}, {"start": 356.38, "end": 356.56, "word": " فيما", "probability": 0.6165771484375}, {"start": 356.56, "end": 357.0, "word": " سبق", "probability": 0.8678385416666666}, {"start": 357.0, "end": 357.36, "word": " و", "probability": 0.958984375}, {"start": 357.36, "end": 357.62, "word": " عشان", "probability": 0.8312174479166666}, {"start": 357.62, "end": 357.92, "word": " إيش", "probability": 0.6173502604166666}, {"start": 357.92, "end": 358.48, "word": " أخد", "probability": 0.7389322916666666}, {"start": 358.48, "end": 359.08, "word": " المعلومات", "probability": 0.943359375}, {"start": 359.08, "end": 360.72, "word": " فطبعا", "probability": 0.9556640625}, {"start": 360.72, "end": 360.98, "word": " هنا", 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"probability": 0.7659505208333334}, {"start": 1356.64, "end": 1357.0, "word": " للـ", "probability": 0.61865234375}, {"start": 1357.0, "end": 1357.2, "word": " Real", "probability": 0.452880859375}, {"start": 1357.2, "end": 1357.8, "word": " Numbers", "probability": 0.7364501953125}, {"start": 1357.8, "end": 1358.4, "word": " أو", "probability": 0.90478515625}, {"start": 1358.4, "end": 1358.66, "word": " للـ", "probability": 0.6497802734375}, {"start": 1358.66, "end": 1358.92, "word": " 01", "probability": 0.77099609375}], "temperature": 1.0}, {"id": 55, "seek": 139087, "start": 1363.01, "end": 1390.87, "text": "فطبعا زي ما حكي هنا الأمر مش غريب مع الـ Infinity Infinity زائد Infinity بتساوي Infinity كله تحت هذا العنوان العريض بس مع التفاصيل هنا فالف null زائد الف null الف null الف null زائد C، C مش الف null طبعا ال Infinity مختلفين ونشوف مين ال Infinity المناسبة وهذا اللي خلانا نشتغل قولنا هنا في ال cardinality مش كل ال Infinity زي بعض ومش كل ال infinite set مع بعض في عندنا الآن هي أصغر infinite set لكن في أكبر منها ال R ومين أكبر من ال R؟", "tokens": [5172, 9566, 3555, 3615, 995, 30767, 1829, 19446, 11331, 4117, 1829, 34105, 16247, 29973, 37893, 32771, 16572, 3555, 20449, 2423, 39184, 34762, 34762, 30767, 16373, 3215, 34762, 39894, 3794, 995, 45865, 34762, 28242, 3224, 6055, 33753, 23758, 18863, 1863, 2407, 7649, 18863, 16572, 11242, 4724, 3794, 20449, 16712, 5172, 33546, 26895, 34105, 6156, 6027, 5172, 18184, 30767, 16373, 3215, 27188, 18184, 27188, 18184, 27188, 18184, 30767, 16373, 3215, 383, 12399, 383, 37893, 27188, 18184, 23032, 3555, 3615, 995, 2423, 34762, 3714, 46456, 46538, 9957, 4032, 1863, 8592, 38688, 3714, 9957, 2423, 34762, 9673, 8315, 35457, 3660, 4032, 3224, 15730, 13672, 1829, 16490, 1211, 7649, 995, 8717, 8592, 2655, 17082, 1211, 12174, 12610, 8315, 34105, 8978, 2423, 2920, 259, 1860, 37893, 28242, 2423, 34762, 30767, 1829, 45030, 11242, 4032, 2304, 8592, 28242, 2423, 13785, 992, 20449, 45030, 11242, 8978, 43242, 8315, 6024, 48506, 39896, 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0.8631591796875}, {"start": 1378.91, "end": 1379.11, "word": " مين", "probability": 0.860595703125}, {"start": 1379.11, "end": 1379.19, "word": " ال", "probability": 0.955078125}, {"start": 1379.19, "end": 1379.45, "word": " Infinity", "probability": 0.716796875}, {"start": 1379.45, "end": 1380.01, "word": " المناسبة", "probability": 0.85601806640625}, {"start": 1380.01, "end": 1380.21, "word": " وهذا", "probability": 0.57373046875}, {"start": 1380.21, "end": 1380.31, "word": " اللي", "probability": 0.9775390625}, {"start": 1380.31, "end": 1380.57, "word": " خلانا", "probability": 0.837890625}, {"start": 1380.57, "end": 1381.05, "word": " نشتغل", "probability": 0.99560546875}, {"start": 1381.05, "end": 1381.49, "word": " قولنا", "probability": 0.7682291666666666}, {"start": 1381.49, "end": 1381.69, "word": " هنا", "probability": 0.990234375}, {"start": 1381.69, "end": 1382.03, "word": " في", "probability": 0.96923828125}, {"start": 1382.03, "end": 1382.23, "word": " ال", "probability": 0.90966796875}, {"start": 1382.23, "end": 1382.75, "word": " cardinality", "probability": 0.7710774739583334}, {"start": 1382.75, "end": 1382.89, "word": " مش", "probability": 0.95458984375}, {"start": 1382.89, "end": 1383.09, "word": " كل", "probability": 0.98583984375}, {"start": 1383.09, "end": 1383.17, "word": " ال", "probability": 0.97802734375}, {"start": 1383.17, "end": 1383.47, "word": " Infinity", "probability": 0.6728515625}, {"start": 1383.47, "end": 1383.73, "word": " زي", "probability": 0.98193359375}, {"start": 1383.73, "end": 1383.99, "word": " بعض", "probability": 0.99560546875}, {"start": 1383.99, "end": 1384.33, "word": " ومش", "probability": 0.94580078125}, {"start": 1384.33, "end": 1384.51, "word": " كل", "probability": 0.98583984375}, {"start": 1384.51, "end": 1384.59, "word": " ال", "probability": 0.87060546875}, {"start": 1384.59, "end": 1384.87, "word": " infinite", "probability": 0.27587890625}, {"start": 1384.87, "end": 1385.09, "word": " set", "probability": 0.91259765625}, {"start": 1385.09, "end": 1385.45, "word": " مع", "probability": 0.9443359375}, {"start": 1385.45, "end": 1386.05, "word": " بعض", "probability": 0.989501953125}, {"start": 1386.05, "end": 1386.35, "word": " في", "probability": 0.7646484375}, {"start": 1386.35, "end": 1386.65, "word": " عندنا", "probability": 0.70556640625}, {"start": 1386.65, "end": 1386.89, "word": " الآن", "probability": 0.6741943359375}, {"start": 1386.89, "end": 1387.07, "word": " هي", "probability": 0.7646484375}, {"start": 1387.07, "end": 1387.41, "word": " أصغر", "probability": 0.983154296875}, {"start": 1387.41, "end": 1387.73, "word": " infinite", "probability": 0.87109375}, {"start": 1387.73, "end": 1388.05, "word": " set", "probability": 0.95556640625}, {"start": 1388.05, "end": 1388.41, "word": " لكن", "probability": 0.89990234375}, {"start": 1388.41, "end": 1388.57, "word": " في", "probability": 0.958984375}, {"start": 1388.57, "end": 1388.83, "word": " أكبر", "probability": 0.9720052083333334}, {"start": 1388.83, "end": 1389.05, "word": " منها", "probability": 0.995361328125}, {"start": 1389.05, "end": 1389.17, "word": " ال", "probability": 0.93994140625}, {"start": 1389.17, "end": 1389.37, "word": " R", "probability": 0.5322265625}, {"start": 1389.37, "end": 1389.85, "word": " ومين", "probability": 0.88818359375}, {"start": 1389.85, "end": 1390.23, "word": " أكبر", "probability": 0.8234049479166666}, {"start": 1390.23, "end": 1390.37, "word": " من", "probability": 0.990234375}, {"start": 1390.37, "end": 1390.47, "word": " ال", "probability": 0.9775390625}, {"start": 1390.47, "end": 1390.87, "word": " R؟", "probability": 0.929443359375}], "temperature": 1.0}, {"id": 56, "seek": 141682, "start": 1391.34, "end": 1416.82, "text": "الـ Power of R وها كذا فأرجو أن هذه الصورة تكون واضحة ويعني حاضرة للجميع نشوف مثال برضه يعتبر مثال طبيعي جدا بيقول لي prove that if A is any transfinite cardinal number يعني إيش Infinite يعني بيقابل المجموعة فA زاد واحد تسوى A طبعا مش غريب لأن Infinite زاد واحد تسوى Infinite بنفس السياق اللي بنشتغل في نفس الدائرة تقريبا", "tokens": [6027, 39184, 7086, 295, 497, 4032, 11296, 9122, 15730, 6156, 10721, 47341, 2407, 14739, 29538, 31767, 13063, 3660, 6055, 30544, 4032, 46958, 5016, 3660, 4032, 40228, 22653, 11331, 46958, 25720, 24976, 7435, 2304, 40228, 8717, 8592, 38688, 50113, 6027, 4724, 43042, 3224, 7251, 34268, 26890, 50113, 6027, 23032, 21292, 3615, 1829, 10874, 28259, 4724, 1829, 39648, 32239, 7081, 300, 498, 316, 307, 604, 1145, 5194, 642, 2920, 2071, 1230, 37495, 22653, 11933, 1829, 8592, 43368, 37495, 22653, 4724, 1829, 4587, 16758, 1211, 9673, 7435, 2304, 2407, 27884, 6156, 32, 30767, 18513, 36764, 24401, 6055, 3794, 2407, 7578, 316, 23032, 3555, 3615, 995, 37893, 32771, 16572, 3555, 5296, 33456, 43368, 30767, 18513, 36764, 24401, 6055, 3794, 2407, 7578, 43368, 44945, 36178, 21136, 25528, 4587, 13672, 1829, 44945, 8592, 2655, 17082, 1211, 8978, 8717, 36178, 32748, 16373, 25720, 6055, 4587, 16572, 3555, 995], "avg_logprob": -0.19212147446585373, "compression_ratio": 1.7037037037037037, "no_speech_prob": 0.0, "words": [{"start": 1391.34, "end": 1391.6, "word": "الـ", "probability": 0.685302734375}, {"start": 1391.6, "end": 1391.8, "word": " Power", "probability": 0.5859375}, {"start": 1391.8, "end": 1392.04, "word": " of", "probability": 0.92138671875}, {"start": 1392.04, "end": 1392.26, "word": " R", "probability": 0.919921875}, {"start": 1392.26, "end": 1392.62, "word": " وها", "probability": 0.3856201171875}, {"start": 1392.62, "end": 1392.9, "word": " كذا", "probability": 0.9775390625}, {"start": 1392.9, "end": 1393.7, "word": " فأرجو", "probability": 0.4830322265625}, {"start": 1393.7, "end": 1393.76, "word": " أن", "probability": 0.61474609375}, {"start": 1393.76, "end": 1393.92, "word": " هذه", "probability": 0.779296875}, {"start": 1393.92, "end": 1394.24, "word": " الصورة", "probability": 0.9944661458333334}, {"start": 1394.24, "end": 1394.58, "word": " تكون", "probability": 0.981689453125}, {"start": 1394.58, "end": 1395.42, "word": " واضحة", "probability": 0.970947265625}, {"start": 1395.42, "end": 1396.42, "word": " ويعني", "probability": 0.7526041666666666}, {"start": 1396.42, "end": 1396.8, "word": " حاضرة", "probability": 0.91259765625}, {"start": 1396.8, "end": 1397.26, "word": " للجميع", "probability": 0.950439453125}, {"start": 1397.26, "end": 1398.06, "word": " نشوف", "probability": 0.9269205729166666}, {"start": 1398.06, "end": 1398.54, "word": " مثال", "probability": 0.97802734375}, {"start": 1398.54, "end": 1398.92, "word": " برضه", "probability": 0.9236653645833334}, {"start": 1398.92, "end": 1399.5, "word": " يعتبر", "probability": 0.9503580729166666}, {"start": 1399.5, "end": 1399.94, "word": " مثال", "probability": 0.982421875}, {"start": 1399.94, "end": 1400.44, "word": " طبيعي", "probability": 0.9888916015625}, {"start": 1400.44, "end": 1400.86, "word": " جدا", "probability": 0.990234375}, {"start": 1400.86, "end": 1402.16, "word": " بيقول", "probability": 0.7525227864583334}, {"start": 1402.16, "end": 1402.38, "word": " لي", "probability": 0.348876953125}, {"start": 1402.38, "end": 1402.94, "word": " prove", "probability": 0.459228515625}, {"start": 1402.94, "end": 1403.28, "word": " that", "probability": 0.88134765625}, {"start": 1403.28, "end": 1403.68, "word": " if", "probability": 0.8681640625}, {"start": 1403.68, "end": 1404.02, "word": " A", "probability": 0.638671875}, {"start": 1404.02, "end": 1404.52, "word": " is", "probability": 0.93115234375}, {"start": 1404.52, "end": 1404.92, "word": " any", "probability": 0.892578125}, {"start": 1404.92, "end": 1406.26, "word": " transfinite", "probability": 0.7618815104166666}, {"start": 1406.26, "end": 1406.64, "word": " cardinal", "probability": 0.918212890625}, {"start": 1406.64, "end": 1406.92, "word": " number", "probability": 0.97119140625}, {"start": 1406.92, "end": 1407.12, "word": " يعني", "probability": 0.92138671875}, {"start": 1407.12, "end": 1407.32, "word": " إيش", "probability": 0.6811116536458334}, {"start": 1407.32, "end": 1407.78, "word": " Infinite", "probability": 0.418212890625}, {"start": 1407.78, "end": 1408.32, "word": " يعني", "probability": 0.891357421875}, {"start": 1408.32, "end": 1408.66, "word": " بيقابل", "probability": 0.88701171875}, {"start": 1408.66, "end": 1409.0, "word": " المجموعة", "probability": 0.82958984375}, {"start": 1409.0, "end": 1409.54, "word": " فA", "probability": 0.6466064453125}, {"start": 1409.54, "end": 1409.8, "word": " زاد", "probability": 0.4627685546875}, {"start": 1409.8, "end": 1409.96, "word": " واحد", "probability": 0.931396484375}, {"start": 1409.96, "end": 1410.32, "word": " تسوى", "probability": 0.79638671875}, {"start": 1410.32, "end": 1410.44, "word": " A", "probability": 0.591796875}, {"start": 1410.44, "end": 1410.86, "word": " طبعا", "probability": 0.9398193359375}, {"start": 1410.86, "end": 1411.0, "word": " مش", "probability": 0.939453125}, {"start": 1411.0, "end": 1411.6, 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union B أقل أو تساوي ال cardinality لمن؟ لل A إيش ال cardinality هذه؟ A زائد واحد أقل أو تساوي A وهذا رقم اتنين فواحد و اتنين بيخلصولنا السؤال", "tokens": [41185, 43242, 8315, 11778, 6027, 3660, 9154, 316, 11671, 363, 24976, 39184, 316, 472, 281, 472, 2423, 4282, 37893, 3224, 13063, 6225, 42213, 8315, 3224, 5551, 4117, 2655, 2288, 9154, 3714, 25720, 20328, 9640, 2423, 9274, 7251, 4117, 31845, 19986, 2423, 3256, 4032, 2423, 3256, 25993, 6156, 3224, 15730, 4724, 1829, 39648, 5296, 28814, 1863, 3224, 2423, 2920, 259, 1860, 24976, 316, 11671, 363, 5551, 4587, 1211, 34051, 6055, 3794, 995, 45865, 2423, 2920, 259, 1860, 5296, 27842, 22807, 24976, 316, 11933, 1829, 8592, 2423, 2920, 259, 1860, 29538, 22807, 316, 30767, 16373, 3215, 36764, 24401, 5551, 4587, 1211, 34051, 6055, 3794, 995, 45865, 316, 37037, 15730, 12602, 4587, 2304, 1975, 2655, 1863, 9957, 6156, 14407, 24401, 4032, 1975, 2655, 1863, 9957, 4724, 1829, 9778, 1211, 9381, 12610, 8315, 21136, 33604, 6027], "avg_logprob": -0.1863251951404084, "compression_ratio": 1.7606177606177607, "no_speech_prob": 0.0, "words": [{"start": 1945.5, "end": 1945.72, "word": "في", "probability": 0.189453125}, {"start": 1945.72, "end": 1946.06, "word": " عندنا", "probability": 0.855712890625}, {"start": 1946.06, "end": 1946.46, "word": " دالة", "probability": 0.97705078125}, {"start": 1946.46, "end": 1946.62, "word": " من", "probability": 0.96337890625}, {"start": 1946.62, "end": 1946.86, "word": " A", "probability": 0.468505859375}, {"start": 1946.86, "end": 1947.16, "word": " union", "probability": 0.474853515625}, {"start": 1947.16, "end": 1947.42, "word": " B", "probability": 0.84228515625}, {"start": 1947.42, "end": 1947.78, "word": " للـ", "probability": 0.648193359375}, {"start": 1947.78, "end": 1947.92, "word": " A", "probability": 0.6611328125}, {"start": 1947.92, "end": 1948.38, "word": " one", "probability": 0.399658203125}, {"start": 1948.38, "end": 1948.58, "word": " to", "probability": 0.85205078125}, {"start": 1948.58, "end": 1948.8, "word": " one", "probability": 0.94873046875}, {"start": 1948.8, "end": 1949.02, "word": " ال", "probability": 0.381103515625}, {"start": 1949.02, "end": 1949.12, "word": " trick", "probability": 0.3125}, {"start": 1949.12, "end": 1949.56, "word": " مشهور", "probability": 0.9895833333333334}, {"start": 1949.56, "end": 1949.94, "word": " عملناه", "probability": 0.7030029296875}, {"start": 1949.94, "end": 1950.08, "word": " أكتر", "probability": 0.81866455078125}, {"start": 1950.08, "end": 1950.22, "word": " من", "probability": 0.98876953125}, {"start": 1950.22, "end": 1950.52, "word": " مرة", "probability": 0.98046875}, {"start": 1950.52, "end": 1951.22, "word": " صار", "probability": 0.933837890625}, {"start": 1951.22, "end": 1951.34, "word": " ال", "probability": 0.80859375}, {"start": 1951.34, "end": 1951.62, "word": " domain", "probability": 0.97705078125}, {"start": 1951.62, "end": 1952.2, "word": " يكافئ", "probability": 0.923583984375}, {"start": 1952.2, "end": 1952.34, "word": " ال", "probability": 0.90380859375}, {"start": 1952.34, "end": 1952.7, "word": " image", "probability": 0.89404296875}, {"start": 1952.7, "end": 1953.48, "word": " و", "probability": 0.51318359375}, {"start": 1953.48, "end": 1953.56, "word": " ال", "probability": 0.9423828125}, {"start": 1953.56, "end": 1953.74, "word": " image", "probability": 0.90771484375}, {"start": 1953.74, "end": 1954.2, "word": " subset", "probability": 0.8330078125}, {"start": 1954.2, "end": 1954.52, "word": " فهذا", "probability": 0.8658854166666666}, {"start": 1954.52, "end": 1954.86, "word": " بيقول", "probability": 0.8938802083333334}, {"start": 1954.86, "end": 1955.94, "word": " لإنه", "probability": 0.7244873046875}, {"start": 1955.94, "end": 1956.82, "word": " ال", "probability": 0.6513671875}, {"start": 1956.82, "end": 1957.7, "word": " cardinality", "probability": 0.8943684895833334}, {"start": 1957.7, "end": 1958.78, "word": " لل", "probability": 0.7607421875}, {"start": 1958.78, "end": 1959.12, "word": " A", "probability": 0.857421875}, {"start": 1959.12, "end": 1959.52, "word": " union", "probability": 0.9482421875}, {"start": 1959.52, "end": 1959.92, "word": " B", "probability": 0.9853515625}, {"start": 1959.92, "end": 1960.5, "word": " أقل", "probability": 0.9806315104166666}, {"start": 1960.5, "end": 1960.68, "word": " أو", "probability": 0.94482421875}, {"start": 1960.68, "end": 1961.06, "word": " تساوي", "probability": 0.977294921875}, {"start": 1961.06, "end": 1961.2, "word": " ال", "probability": 0.7763671875}, {"start": 1961.2, "end": 1961.74, "word": " cardinality", "probability": 0.9368489583333334}, {"start": 1961.74, "end": 1963.02, "word": " لمن؟", "probability": 0.6106770833333334}, {"start": 1963.02, "end": 1963.3, "word": " لل", "probability": 0.90625}, {"start": 1963.3, "end": 1963.62, "word": " A", "probability": 0.93505859375}, {"start": 1963.62, "end": 1964.22, "word": " إيش", "probability": 0.7435709635416666}, {"start": 1964.22, "end": 1964.36, "word": " ال", "probability": 0.8896484375}, {"start": 1964.36, "end": 1964.84, "word": " cardinality", "probability": 0.9521484375}, {"start": 1964.84, "end": 1965.8, "word": " هذه؟", "probability": 0.80224609375}, {"start": 1965.8, "end": 1965.96, "word": " A", "probability": 0.81787109375}, {"start": 1965.96, "end": 1966.34, "word": " زائد", "probability": 0.7994791666666666}, {"start": 1966.34, "end": 1966.76, "word": " واحد", "probability": 0.787841796875}, {"start": 1966.76, "end": 1967.34, "word": " أقل", "probability": 0.9519856770833334}, {"start": 1967.34, "end": 1967.44, "word": " أو", "probability": 0.96728515625}, {"start": 1967.44, "end": 1967.88, "word": " تساوي", "probability": 0.9891357421875}, {"start": 1967.88, "end": 1968.1, "word": " A", "probability": 0.78955078125}, {"start": 1968.1, "end": 1970.16, "word": " وهذا", "probability": 0.85791015625}, {"start": 1970.16, "end": 1970.48, "word": " رقم", "probability": 0.9905598958333334}, {"start": 1970.48, "end": 1970.8, "word": " اتنين", "probability": 0.864501953125}, {"start": 1970.8, "end": 1972.52, "word": " فواحد", "probability": 0.88427734375}, {"start": 1972.52, "end": 1972.64, "word": " و", "probability": 0.9462890625}, {"start": 1972.64, "end": 1973.06, "word": " اتنين", "probability": 0.919677734375}, {"start": 1973.06, "end": 1974.2, "word": " بيخلصولنا", "probability": 0.9198521205357143}, {"start": 1974.2, "end": 1975.16, "word": " السؤال", "probability": 0.9952799479166666}], "temperature": 1.0}, {"id": 80, "seek": 200067, "start": 1977.33, "end": 2000.67, "text": "1 و 2 implies a زائد 1 يساوي فهنا زي ما انتوا شايفين في أفكار بتتكرر معنا أرجو أنها اتساعدنا في الفهم بشكل أفضل فهذه نهاية هذا ال section ان شاء الله المرة الجاية بنكمل مع اللي هو ضرب الأعداد الأصلية", "tokens": [16, 4032, 568, 18779, 257, 30767, 16373, 3215, 502, 7251, 3794, 995, 45865, 6156, 3224, 8315, 30767, 1829, 19446, 16472, 2655, 14407, 13412, 995, 33911, 9957, 8978, 5551, 5172, 4117, 9640, 39894, 2655, 37983, 2288, 20449, 8315, 5551, 47341, 2407, 14739, 11296, 1975, 2655, 3794, 995, 22488, 8315, 8978, 27188, 16095, 4724, 8592, 28820, 5551, 5172, 11242, 1211, 6156, 3224, 24192, 8717, 11296, 10632, 23758, 2423, 3541, 16472, 13412, 16606, 21984, 9673, 25720, 25724, 995, 10632, 44945, 24793, 1211, 20449, 13672, 1829, 31439, 48812, 25513, 16247, 22488, 18513, 16247, 36520, 10632], "avg_logprob": -0.2229959281242412, "compression_ratio": 1.642512077294686, "no_speech_prob": 0.0, "words": [{"start": 1977.33, "end": 1977.81, "word": "1", "probability": 0.3173828125}, {"start": 1977.81, "end": 1978.07, "word": " و", "probability": 0.1514892578125}, {"start": 1978.07, "end": 1978.51, "word": " 2", "probability": 0.634765625}, {"start": 1978.51, "end": 1979.43, "word": " implies", "probability": 0.2496337890625}, {"start": 1979.43, "end": 1980.49, "word": " a", "probability": 0.328125}, {"start": 1980.49, "end": 1980.91, "word": " زائد", "probability": 0.4792277018229167}, {"start": 1980.91, "end": 1981.43, "word": " 1", "probability": 0.7021484375}, {"start": 1981.43, "end": 1982.37, "word": " يساوي", "probability": 0.8955078125}, {"start": 1982.37, "end": 1984.83, "word": " فهنا", "probability": 0.6633504231770834}, {"start": 1984.83, "end": 1985.03, "word": " زي", "probability": 0.903564453125}, {"start": 1985.03, "end": 1985.13, "word": " ما", "probability": 0.94921875}, {"start": 1985.13, "end": 1985.31, "word": " انتوا", "probability": 0.7727864583333334}, {"start": 1985.31, "end": 1985.67, "word": " شايفين", "probability": 0.9669189453125}, {"start": 1985.67, "end": 1986.11, "word": " في", "probability": 0.8046875}, {"start": 1986.11, "end": 1986.67, "word": " أفكار", "probability": 0.8961181640625}, {"start": 1986.67, "end": 1987.25, "word": " بتتكرر", "probability": 0.9342041015625}, {"start": 1987.25, "end": 1987.67, "word": " معنا", "probability": 0.982421875}, {"start": 1987.67, "end": 1988.53, "word": " أرجو", "probability": 0.7493489583333334}, {"start": 1988.53, "end": 1988.87, "word": " أنها", "probability": 0.739013671875}, {"start": 1988.87, "end": 1989.71, "word": " اتساعدنا", "probability": 0.8716227213541666}, {"start": 1989.71, "end": 1990.39, "word": " في", "probability": 0.92626953125}, {"start": 1990.39, "end": 1991.93, "word": " الفهم", "probability": 0.943359375}, {"start": 1991.93, "end": 1992.43, "word": " بشكل", "probability": 0.9890950520833334}, {"start": 1992.43, "end": 1993.29, "word": " أفضل", "probability": 0.972900390625}, {"start": 1993.29, "end": 1994.37, "word": " فهذه", "probability": 0.8048502604166666}, {"start": 1994.37, "end": 1994.71, "word": " نهاية", "probability": 0.9138997395833334}, {"start": 1994.71, "end": 1994.95, "word": " هذا", "probability": 0.47900390625}, {"start": 1994.95, "end": 1995.01, "word": " ال", "probability": 0.53125}, {"start": 1995.01, "end": 1995.35, "word": " section", "probability": 0.8466796875}, {"start": 1995.35, "end": 1995.65, "word": " ان", "probability": 0.75830078125}, {"start": 1995.65, "end": 1995.81, "word": " شاء", "probability": 0.966552734375}, {"start": 1995.81, "end": 1995.85, "word": " الله", "probability": 0.95068359375}, {"start": 1995.85, "end": 1996.13, "word": " المرة", "probability": 0.96826171875}, {"start": 1996.13, "end": 1996.55, "word": " الجاية", "probability": 0.8268229166666666}, {"start": 1996.55, "end": 1997.81, "word": " بنكمل", "probability": 0.9485677083333334}, {"start": 1997.81, "end": 1998.27, "word": " مع", "probability": 0.50634765625}, {"start": 1998.27, "end": 1998.89, "word": " اللي", "probability": 0.737060546875}, {"start": 1998.89, "end": 1998.99, "word": " هو", "probability": 0.982421875}, {"start": 1998.99, "end": 1999.27, "word": " ضرب", "probability": 0.96923828125}, {"start": 1999.27, "end": 1999.85, "word": " الأعداد", "probability": 0.9189453125}, {"start": 1999.85, "end": 2000.67, "word": " الأصلية", "probability": 0.8020833333333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2000.88675, "duration_after_vad": 1914.1462499999955}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/SuCRM6Nv8Fg.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/SuCRM6Nv8Fg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d9fde8972fad04623aa2961ffca1ffdcaa261167
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/SuCRM6Nv8Fg.srt
@@ -0,0 +1,3023 @@
+1
+00:00:20,810 --> 00:00:24,780
+بسم الله الرحمن الرحيم،اليوم إن شاء الله هنواصل مع
+
+2
+00:00:24,780 --> 00:00:28,200
+المجموعات في المحاضرة الماضية، يمكن إحنا أخدنا 
+
+3
+00:00:28,200 --> 00:00:31,840
+مقدمة سريعة، سأرجعنا فيها لبعض المفاهيم، طبعًا مفهوم
+
+4
+00:00:31,840 --> 00:00:34,860
+المجموعات من المفاهيم الأساسية اللي جرى علينا في
+
+5
+00:00:34,860 --> 00:00:39,100
+مرحلة مبكرة من الدراسة، لكن إحنا 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 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 إن شاء الله، فإن شاء الله أول مفهوم يتعلق
+
+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، فطبعًا
+
+12
+00:01:04,230 --> 00:01:07,770
+إحنا فيه عندنا المفهوم، عندنا الرمز تبعه، وفيه عندنا
+
+13
+00:01:07,770 --> 00:01:11,510
+التعريف تبعه، فيه يمكن ثلاث نقاط بنتحدث عنها، فأول شيء
+
+14
+00:01:11,510 --> 00:01:14,910
+أنا بيبين عندي مجموعتين، هذه المجموعتين دول 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
+باء، وقت إيش بقول set A capital A تساوي set 
+
+17
+00:01:21,470 --> 00:01:24,810
+capital B، أول شيء 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
+آه طبعًا في الآخر يمكن كتبها A تساوي الـ B، هذا هو
+
+20
+00:01:30,990 --> 00:01:34,800
+الرمز، إذا 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، آه، فبقول له 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
+احتوتا على نفس العناصر، إذا كانت عناصرهم هي نفس
+
+28
+00:01:59,890 --> 00:02:04,570
+العناصر، عناصر الـ A هي نفس عناصر الـ B، وهكذا، آه،
+
+29
+00:02:04,570 --> 00:02:07,590
+فطبعًا الرمز بقول إذا كانت الـ A والـ B 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
+وما أكنتش بقول A تساوي B إذا كانوا بينهم بيحتوي على
+
+32
+00:02:13,810 --> 00:02:19,980
+نفس العناصر، بيحتوي على نفس العناصر، خلينا نشوف إيه 
+
+33
+00:02:19,980 --> 00:02:23,840
+كيف نتعامل منطقيًا 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 قولته ويقوله 
+
+37
+00:02:37,800 --> 00:02:41,380
+بيحتوي جميع العناصر بمعنى العنصر اللي موجود في الـ A
+
+38
+00:02:41,380 --> 00:02:45,500
+لازم يكون موجود في الـ B، واللي في الـ B لازم يكون
+
+39
+00:02:45,500 --> 00:02:50,100
+موجود في الـ A، فهو بيقول للتعريف تبعها for all X، X 
+
+40
+00:02:50,100 --> 00:02:55,620
+ينتمي للـ A if and only if X تنتمي للـ B، بيعني فكل 
+
+41
+00:02:55,620 --> 00:02:58,560
+عنصر إذا كان موجود في الـ A لازم يكون في الـ B، وعكس
+
+42
+00:02:58,560 --> 00:03:00,540
+ذلك، إذا كان موجود في الـ B لازم يكون في الـ A، هذا معناه
+
+43
+00:03:00,540 --> 00:03:04,250
+أنهم بيحتووا على نفس العناصر بلغة الرموز، for all x
+
+44
+00:03:04,250 --> 00:03:08,630
+أي عنصر، أي ما كان، إذا وجد في الأولى لازم يوجد في
+
+45
+00:03:08,630 --> 00:03:11,950
+الثانية والعكس صحيح، إذا وجد في الثانية لازم
+
+46
+00:03:11,950 --> 00:03:15,490
+يوجد في الأولى، واضح؟ آه، فهذه لغة الرموز اللي إحنا 
+
+47
+00:03:15,490 --> 00:03:18,010
+بيقولنا نتعامل معها، ونكتب بطريقة الرموز عشان 
+
+48
+00:03:18,010 --> 00:03:21,410
+نتعامل مع المفهوم، كيف بتثبت إن هم متساويين؟ 
+
+49
+00:03:21,410 --> 00:03:25,170
+بتثبت من for all x، x تنتمي للـ a، if and only if، 
+
+50
+00:03:25,250 --> 00:03:30,460
+x تنتمي للـ b، آه، واضح؟ متابعين؟ خليني أشوف بعض 
+
+51
+00:03:30,460 --> 00:03:32,820
+الأمثلة البسيطة، وبعدين طبعًا هنرجع للتعريف كيف 
+
+52
+00:03:32,820 --> 00:03:37,820
+نتعامل معاه منطقيًا أو بالبرهان، هنشوف مثال بسيط
+
+53
+00:03:37,820 --> 00:03:41,680
+بيقول لي show that capital A وتساوي على حروف
+
+54
+00:03:41,680 --> 00:03:47,500
+الأبجدية ABC is equal to the set capital B وتساوي
+
+55
+00:03:47,500 --> 00:03:51,700
+على الحروف BCA، هدول المجموعتين متساويتين، لو قلت لي
+
+56
+00:03:51,700 --> 00:03:56,260
+show، آه، طبعًا ليش؟ نفس العناصر، الـ A موجودة في الـ
+
+57
+00:03:56,260 --> 00:03:58,900
+capital A وموجودة في الـ capital B، الـ small b
+
+58
+00:03:58,900 --> 00:04:01,500
+موجودة في الـ capital A وموجودة في الـ capital B، و
+
+59
+00:04:01,500 --> 00:04:04,160
+الـ small c موجودة في التنتين، فكل العناصر هم
+
+60
+00:04:04,160 --> 00:04:05,840
+بيحتووا على نفس العناصر، الـ A والـ B بيحتووا على
+
+61
+00:04:05,840 --> 00:04:09,820
+من؟ على الثلاث حروف A, B, C، فإذا هم متساويين، طبعًا إيش
+
+62
+00:04:09,820 --> 00:04:12,640
+مستنتج الشيء من المثال؟ ترتيب العناصر ما لهوش 
+
+63
+00:04:12,640 --> 00:04:15,360
+أهمية في المجموعات، لأنه جالي يحتوي 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 جالس أول، في المحاضرة الثانية،
+
+69
+00:04:31,300 --> 00:04:34,040
+مين جالس آخر، ما يهمّنيش، هذه هي المجموعة، فالترتيب 
+
+70
+00:04:34,040 --> 00:04:37,570
+ما لهوش قيمة في المجموعات، فطبعًا عشان أجيبه بعد
+
+71
+00:04:37,570 --> 00:04:40,410
+السؤال ببساطة ما هي التعريف؟ ليش هدول equal؟ لإنهم
+
+72
+00:04:40,410 --> 00:04:43,270
+بيحتووا على نفس العناصر، لإنهم بيحتووا على نفس
+
+73
+00:04:43,270 --> 00:04:52,010
+العناصر، فده المثال الأول، solution، the 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 or contain the same 
+
+76
+00:05:07,190 --> 00:05:11,230
+elements، من 
+
+77
+00:05:11,230 --> 00:05:17,030
+التعريف، أخذت الجواب من التعريف، لأنهم بيحتوي على 
+
+78
+00:05:17,030 --> 00:05:24,350
+نفس العناصر بكل بساطة، أي سؤال؟ 
+
+79
+00:05:24,350 --> 00:05:28,570
+نشوف 
+
+80
+00:05:28,570 --> 00:05:32,010
+كذا مثال برضه بسيط عشان نؤكد على المفهوم وبعض 
+
+81
+00:05:32,010 --> 00:05:36,190
+الملاحظات، بتقول لي في عندي مجموعة capital A بتساوي
+
+82
+00:05:36,190 --> 00:05:41,530
+عناصر 1، 4، 1، فكم عنصر فيه في الـ A؟ عنصرين،
+
+83
+00:05:41,530 --> 00:05:44,430
+التكرار ما لهوش قيمة في المجموعات، فهدي فيها عنصرين
+
+84
+00:05:44,430 --> 00:05:47,290
+الواحد والأربعة ولا فيها عنصر ثاني؟ أي عناصر، طيب 
+
+85
+00:05:47,290 --> 00:05:50,730
+والـ B بتساوي الواحد والأربعة، هدول هم متساويين، 
+
+86
+00:05:50,730 --> 00:05:54,360
+ليش؟ لأنه بيحتوي على نفس العناصر، فالشاهد الأهم من 
+
+87
+00:05:54,360 --> 00:05:57,820
+المثال أن التكرار برضه ما لهوش أهمية زي الترتيب، 
+
+88
+00:05:57,820 --> 00:06:01,400
+ما لهوش أهمية، والتكرار كأنه لم يكن، ما بنعدش، فأنا
+
+89
+00:06:01,400 --> 00:06:05,040
+بقول من عناصر الـ A واحد وأربعة، بتقول الواحد ظهرت 
+
+90
+00:06:05,040 --> 00:06:08,020
+مرتين، ما ليش داعي، أنا بقول من العناصر واحد وأربعة.
+
+91
+00:06:08,020 --> 00:06:14,060
+واضح؟ فهنا برضه نقول هنا مثال رقم اثنين، مثال رقم 
+
+92
+00:06:14,060 --> 00:06:21,440
+اثنين، ف solution فيها أن الـ A will be have the
+
+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 الـ B، فهدول مثالين بسيطين، واتعلّمنا
+
+96
+00:06:36,930 --> 00:06:41,790
+منهم أن الترتيب مش مهم والتكرار ما لهوش قيمة، العنصر
+
+97
+00:06:41,790 --> 00:06:45,630
+مكتوب أكثر من مرة كأنه يعتبر خطأ مطبعي، أنا 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، أنا بتحصّل له علامة ولا علامتين؟ علامة في
+
+100
+00:06:52,870 --> 00:06:55,650
+الآخر، أنا ما يش ممكن أصحّي هذا الخطأ، فأنا بهمني كم 
+
+101
+00:06:55,650 --> 00:06:59,430
+طالبة عندي؟ عندي تسعين طالبة، اللي كتب الاسم أكثر من
+
+102
+00:06:59,430 --> 00:07:03,190
+مرة ما لهوش قيمة، ما لهوش قيمة، نفس الشيء، نفس القضية.
+
+103
+00:07:07,120 --> 00:07:09,200
+لسه ما وصلناش، واحدة واحدة، لسه ما عرفناش إيش معناه
+
+104
+00:07:09,200 --> 00:07:12,920
+subset، إيش جزئي؟ واحدة واحدة، إحنا لسه عرفنا إيش
+
+105
+00:07:12,920 --> 00:07:16,800
+مجموعة، تعرّفنا عليه إيش بنقصد فيه، وبعدين عرفنا
+
+106
+00:07:16,800 --> 00:07:19,460
+التساوي، لسه ما عرفناش الفرق، 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، بيقول لي بشكل عام، الـ A لا تساوي A بين هدول
+
+109
+00:07:31,920 --> 00:07:36,360
+الأقواس، ليش؟ لأن الـ A هذه لحالة عنصر، وهديك
+
+110
+00:07:36,360 --> 00:07:39,640
+مجموعة بتحتوي على عنصر الـ A، فهدول فيهم فرق، طب
+
+111
+00:07:39,640 --> 00:07:42,900
+إيش الـ 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 إيش؟ 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 بتحتوي على عنصر إيه، فبقول
+
+115
+00:07:54,070 --> 00:07:56,750
+هنا الـ A is an element، عنصر، بغض النظر إيش 
+
+116
+00:07:56,750 --> 00:08:00,390
+محتوياته أو إيش نوعيته، لكن الـ A عبارة عن مجموعة 
+
+117
+00:08:00,390 --> 00:08:03,750
+بتحتوي على عنصر إيه، فبنفرق في رمزي هدول اللي اللي 
+
+118
+00:08:03,750 --> 00:08:06,910
+الأقواس مهمين جدا، وإذا انكتبوه، دائمًا نبيّن إنه فيه
+
+119
+00:08:06,910 --> 00:08:11,040
+مجموعة، طبعًا يسهل نعتبر المجموعة موضوع آخر، موضوع آخر
+
+120
+00:08:11,040 --> 00:08:15,040
+فبنفرق بين هدول الرمزين، فهنا ما فيش تساوي، إيش ممكن
+
+121
+00:08:15,040 --> 00:08:19,100
+أحط بدلًا من علامة التساوي؟ ينتمي، ينتمي، بس مش مجموعة 
+
+122
+00:08:19,100 --> 00:08:23,100
+جزئية، بس ينتمي، العلاقة الوحيدة بين a ومجموعة الـ a
+
+123
+00:08:23,100 --> 00:08:26,960
+ينتمي بس، هذه العلاقة الصحيحة، غير هيك أي علاقة غير 
+
+124
+00:08:26,960 --> 00:08:29,680
+صحيحة، ولا subset صحيحة، لسه ما عرفناهاش، ولا التساوي
+
+125
+00:08:29,680 --> 00:08:34,740
+صحيح، انتبهوا لهذا النقطة، طب نجي لمفهوم ال subset
+
+126
+00:08:34,740 --> 00:08:39,420
+المجموعة الجزئية، subset، بنعرف إيش معناه subset.
+
+127
+00:08:39,420 --> 00:08:45,580
+طبعًا بي ساعدنا يمكن رسم مساعد Venn diagram تقريبًا 
+
+128
+00:08:45,580 --> 00:08:50,340
+فطبعًا 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، فأنا
+
+130
+00:08:53,900 --> 00:08:56,840
+بقول على الـ A subset من الـ B، خلينا نشوف التعريف
+
+131
+00:08:56,840 --> 00:09:00,360
+طبعًا زي المنهج اللي اتبعناه في الشطر الأول أيضًا 
+
+132
+00:09:00,360 --> 00:09:05,530
+اللي اتبعناه، في عندنا مقدمة للتعريف، مقدمة للنظرية، بتقول
+
+133
+00:09:05,530 --> 00:09:08,630
+يا دول الرموز، كيف بده يستخدمهم؟ 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
+الـ A والـ B، بينطبق على أي مجموعات A و B، مش 
+
+136
+00:09:14,570 --> 00:09:19,690
+statements، مش أرقام، وإنما مجموعات، تمام، التعريف أو
+
+137
+00:09:19,690 --> 00:09:26,060
+الجزء الأول من التعريف، إذا 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، فده هو، فكل عناصر الـ A بنفس الوقت موجودة في
+
+140
+00:09:34,560 --> 00:09:38,760
+الـ B، يعني مثلًا 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 الإسلامية واضح؟ فالكل ينتمي
+
+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 يكون يساوي حد على 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 أكتبها 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 جاية تقريباً، واضح؟ فهو ممكن
+
+155
+00:10:29,150 --> 00:10:31,710
+يكتبها بالطريقتين، طبعًا الأولى هي الأكثر شيوعًا،
+
+156
+00:10:31,710 --> 00:10:35,110
+هذه نادرة جدًا، نادرة جدًا، وقت إيش نكتبها؟ في الغالب
+
+157
+00:10:35,110 --> 00:10:38,190
+لما أنا إيش كتبت الـ B وما تمشى وصح على يسارها،
+
+158
+00:10:38,190 --> 00:10:40,910
+بكتبها على اليمين الـ A بس بغير الاتجاه، في الغالب
+
+159
+00:10:40,910 --> 00:10:45,150
+هيك، بقول إذا الـ A subset من الـ B، الـ B إيش بيسميها؟
+
+160
+00:10:45,250 --> 00:10:49,250
+Super set Super set هي الكبيرة هي الكبيرة sub يعني
+
+161
+00:10:49,250 --> 00:10:53,790
+صغيرة جزء هذه هي الكل الأكبر وهكذا فطبعًا هي
+
+162
+00:10:53,790 --> 00:10:58,410
+الصورة هذه جزء من هذه وهذه تحتوي الـ A، الـ B تحتوي
+
+163
+00:10:58,410 --> 00:11:02,530
+الـ A بمعنى Super set من الـ A أي سؤال طبعًا 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 كيف بدأ
+
+166
+00:11:08,930 --> 00:11:14,410
+أثبت إن الـ A subset من الـ B هنشوف الرمز remark، الـ 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 زميلتكم قبل قليل التساوي ممكن
+
+176
+00:11:48,820 --> 00:11:52,480
+ينكتب بلغة ال subset بس إيش الأولى subset من
+
+177
+00:11:52,480 --> 00:11:56,180
+الثانية والثانية subset من الأولى لأنه نفس العناصر
+
+178
+00:11:56,180 --> 00:11:59,940
+فكل عنصر في الـ A موجود في الـ B وكل عنصر في الـ B
+
+179
+00:11:59,940 --> 00:12:04,960
+موجود في الـ A فبقدر أكتبها أن هذه if and only if A
+
+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 لها ممكن أعرفه مباشرة ممكن أعرفه بدلالة
+
+182
+00:12:13,000 --> 00:12:18,000
+من ال subset بدلالة ال subset طبعًا ما أحد يسأل بقدر
+
+183
+00:12:18,000 --> 00:12:21,440
+أجيب هذا التعريف من التعريف الأصلي طبعًا for all
+
+184
+00:12:21,440 --> 00:12:28,040
+مين بقدر أجيب 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 للـ A if
+
+186
+00:12:35,030 --> 00:12:39,950
+and only if X تنتمي للـ B بعد هيك إيش نعمل؟ نحول
+
+187
+00:12:39,950 --> 00:12:44,250
+الـ if لـ and on الـ if إلى and by conditional فهذه
+
+188
+00:12:44,250 --> 00:12:52,050
+تكافئ for all X X تنتمي للـ A then X تنتمي للـ B and
+
+189
+00:12:52,050 --> 00:12:58,770
+X تنتمي للـ B then X تنتمي للـ A، مصبوط؟ طيب، ها، بده
+
+190
+00:12:58,770 --> 00:13:01,430
+أووصل 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 subset و
+
+192
+00:13:03,870 --> 00:13:07,310
+subset، بنفع أوزع الـ for all على الـ and نعم من
+
+193
+00:13:07,310 --> 00:13:10,770
+قواعد ال quantifiers اللي أخذناها، جولة في علاقات
+
+194
+00:13:10,770 --> 00:13:13,390
+مسموحة وفي علاقات فين هم تكافؤوا وفين هم been
+
+195
+00:13:13,390 --> 00:13:15,650
+obliged وفين 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 x X تنتمي للـ B ثم X تنتمي للـ A الآن، مين هذه؟
+
+199
+00:13:33,630 --> 00:13:37,590
+هذه ليست إلا A subset من الـ B تعريف إيه مصبوط، مصبوط
+
+200
+00:13:37,590 --> 00:13:44,070
+طيب والتانية ليست إلا B subset من الـ A وهو اللي بدنا
+
+201
+00:13:44,070 --> 00:13:47,010
+يعني ف أنا 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 تعلمناها قواعد ال quantifiers اللي تعلمناها
+
+204
+00:13:54,230 --> 00:13:58,310
+وال and وكل هذه الأمور ففعلاً التساوي ممكن ينكتب
+
+205
+00:13:58,310 --> 00:14:02,070
+على صورة أن الأولى subset من الثانية والثانية subset
+
+206
+00:14:02,070 --> 00:14:08,670
+من الأولى and واضح؟ أي سؤال نشوف بعض الأمثلة و
+
+207
+00:14:08,670 --> 00:14:12,110
+دايماً 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 واثنين و small a كمش متغير هنا كحرف كحرف
+
+210
+00:14:22,730 --> 00:14:27,310
+اللي هو حرف أبيض وال b هي الحروف a و b والعداد
+
+211
+00:14:27,310 --> 00:14:29,610
+واحد واثنين وثلاثة طبعًا فال a subset من ال b هذا
+
+212
+00:14:29,610 --> 00:14:32,750
+سؤال مباشر مش مطلوب فيه، بس مثال توضيحي، فطبعًا
+
+213
+00:14:32,750 --> 00:14:36,250
+واضح، ليش؟ لأن كل عناصر الـ A موجودة في الـ B الواحد
+
+214
+00:14:36,250 --> 00:14:38,970
+موجودة في الـ B ولا مش موجودة؟ صح، الاثنين موجودة
+
+215
+00:14:38,970 --> 00:14:41,150
+ولا مش موجودة؟ موجودة، الـ A موجودة ولا مش موجودة؟
+
+216
+00:14:41,150 --> 00:14:43,650
+موجودة، انتهت العملية، فكل عناصر الـ A موجودة في
+
+217
+00:14:43,650 --> 00:14:47,410
+الـ B، إذا هي فعلاً الـ A subset من الـ B، واضح؟ هذا
+
+218
+00:14:47,410 --> 00:14:50,670
+المثال البسيط جدًا، مش المعنى، بدي أختبر، كل عناصر
+
+219
+00:14:50,670 --> 00:14:55,270
+الـ A موجودة في الـ B، 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 الـ 1 موجودة في الـ B نعم الـ 2 موجودة في الـ B
+
+222
+00:15:07,050 --> 00:15:11,250
+نعم الثلاثه موجودة في الـ B نعم فدي subset اه في
+
+223
+00:15:11,250 --> 00:15:15,450
+طالبة بتقول إيه 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 تقريباً فيه تساوي محتمل هو
+
+226
+00:15:24,100 --> 00:15:27,480
+جالي كل عناصر الـ A موجودة في الـ B جالي لازم الـ B
+
+227
+00:15:27,480 --> 00:15:30,620
+تكون أكبر؟ لأ جالي لازم يكون في عناصر الـ B عناصر
+
+228
+00:15:30,620 --> 00:15:34,600
+زيادة؟ لأ ف أنا إيش ماختبر؟ هي الواحد موجودة نعم
+
+229
+00:15:34,600 --> 00:15:37,520
+الاثنين موجودة نعم الثلاثه موجودة نعم انتهت العملية
+
+230
+00:15:37,520 --> 00:15:40,580
+أبطل على الـ B أنا أن فيها زيادة ولا ما فيهاش زيادة؟
+
+231
+00:15:40,580 --> 00:15:43,880
+لأ بس أنا بتأكد عناصر الـ A موجودة في الـ B انتهت
+
+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 ما يكونش فيه فراغ يكونوا
+
+237
+00:16:02,060 --> 00:16:07,400
+متطابقين فال subset تحتمل التساوي لكن مش دائم مش
+
+238
+00:16:07,400 --> 00:16:14,790
+دائم ف remark هنا remark منفصل بقول 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
+دائماً هذا صحيح فلأن التساوي موجود زي ما بقول
+
+245
+00:16:36,150 --> 00:16:40,150
+الثلاثه أصغر أو يساوي ثلاثة كل عدد أصغر من A أو
+
+246
+00:16:40,150 --> 00:16:45,780
+يساوي نفسه فنفس القضية كل 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 ال subset هذه تحتمل التساوي، طب لو أنا بدي
+
+251
+00:17:07,260 --> 00:17:10,660
+أكون دقيق وبديش آخذ التساوي بالاعتبار، زي ما احنا
+
+252
+00:17:10,660 --> 00:17:17,600
+فيه عندنا، بالنسبة هنا، اللي بنقارن، المقارن دائمًا
+
+253
+00:17:17,600 --> 00:17:20,690
+مع من أصغر من أو يساوي فأصغر منه يساوي، بتحتمل
+
+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، لوصفية فعلاً إن فيه الجزء من،
+
+258
+00:17:35,470 --> 00:17:40,770
+التساوي منفي، ففي عندنا التعريف We say that a set
+
+259
+00:17:40,770 --> 00:17:49,330
+capital A is a proper subset of a set
+
+260
+00:17:49,330 --> 00:17:51,150
+capital B if and only if
+
+261
+00:17:56,230 --> 00:18:00,690
+الـ A subset من الـ B ولا 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
+إياه ففي هذه الحالة بنميز تمام أه طبعًا قلنا احنا
+
+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
+.. أنت عندك علاقة هذه بقرأها باتجاهين الـ A subset
+
+269
+00:18:34,830 --> 00:18:38,410
+من الـ B طب الـ B هي super set من الـ A زي ما بقوليش
+
+270
+00:18:38,410 --> 00:18:42,830
+الخمسة أصغر من الستة والستة أكبر من الخمسة بقرأها
+
+271
+00:18:42,830 --> 00:18:47,000
+من الجهة الثانية يعني بقرأها من الجهة الثانية نشوف
+
+272
+00:18:47,000 --> 00:18:50,520
+بعض الأمثلة طبعًا مجموعة الأعداد الصحيحة Z هي
+
+273
+00:18:50,520 --> 00:18:53,680
+proper subset من الـ 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 الـ Z موجودة في الـ Q لكن في في
+
+276
+00:19:01,920 --> 00:19:05,660
+الـ Q عناصر زيادة ما فيش تساوي بتطبقوش مع بعض الـ Z
+
+277
+00:19:05,660 --> 00:19:09,800
+جزء من الـ Q والتساوي غير موجود لأن الـ Q أكبر فعلاً
+
+278
+00:19:09,800 --> 00:19:15,140
+في عناصر زيادة واضحة؟ هذا مثال مشهور نشوف كمان
+
+279
+00:19:15,140 --> 00:19:21,300
+مثال لو أخذنا مجموعة الـ A تساوي سالب واحد Zero واحد
+
+280
+00:19:21,300 --> 00:19:24,540
+والـ B واحد وسالب واحد و Zero فالـ A subset من الـ 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 ما ينفعش، إيش أقول proper؟ اه فهنا إيش الـ A
+
+283
+00:19:31,700 --> 00:19:35,560
+subset من الـ B لكن الـ A is not a proper subset of 
+
+284
+00:19:35,560 --> 00:19:39,560
+B واضح؟ اه فهي إيش معنى proper؟ بنفي التساوي، إذا 
+
+285
+00:19:39,560 --> 00:19:43,760
+أنا متأكد أن احتمال التساوي أصبح غير وارد، اه
+
+286
+00:19:43,760 --> 00:19:46,740
+فبقول proper subset، بكون دقيق، اه فأنا 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، وأنا مطمئن،
+
+289
+00:19:52,180 --> 00:19:58,280
+في عندي معلومة زيادة، أي سؤال؟ خلينا نتفق على بعض
+
+290
+00:19:58,280 --> 00:20:03,460
+الرموز if A is not a subset of B بنفي العلاقة،
+
+291
+00:20:03,460 --> 00:20:05,640
+بنقول A subset من الـ B وبنم فيها، بنحط الـ slash
+
+292
+00:20:05,640 --> 00:20:08,540
+المعروف، متعرف عليها الـ slash النفسي زي يساوي لا
+
+293
+00:20:08,540 --> 00:20:13,140
+يساوي، ينتمي لا ينتمي، وهكذا فده الرمز متعارف
+
+294
+00:20:13,140 --> 00:20:20,200
+عليه ممكن استخدامه، مهم؟ خلينا لو بدنا نثبت أنه
+
+295
+00:20:20,200 --> 00:20:24,480
+مجموعة ليست subset خلينا 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، خلينا نعمله، قلنا إنه اسمها
+
+298
+00:20:32,540 --> 00:20:37,420
+subset for 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؟ ولا لأ؟ طب إيش؟ كيف
+
+300
+00:20:41,740 --> 00:20:44,760
+بننفي؟ نفي الـ for all there exist وبننفي اللي
+
+301
+00:20:44,760 --> 00:20:47,380
+جوا بس واحدة واحدة، ما تحطولوش نفي مرتين زي ما أنتو 
+
+302
+00:20:47,380 --> 00:20:50,620
+عاملين في الـ quiz البعض، لأ أنا لما أنفي الـ for all
+
+303
+00:20:50,620 --> 00:20:52,800
+بيصير there exist وبعدين بننفي اللي جوا اه 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
+ما تتكررش، فـ 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 هنا B then Q وتكافئ not B and not Q بيصير 
+
+308
+00:21:12,510 --> 00:21:17,210
+B and not Q مين الـ B؟ X تنتمي لـ A ومين الـ not Q؟ X
+
+309
+00:21:17,210 --> 00:21:21,750
+لا تنتمي لـ B، نفعامتابعين؟ واضحة ولا مش واضحة؟ 
+
+310
+00:21:21,750 --> 00:21:25,350
+واضحة؟ اه فهي هذا الشرط، فإذا أصبحت هيك، فما بديش 
+
+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 صراحة،
+
+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 subset أي سؤال؟ شوفوا كيف جبناها من المنطق
+
+317
+00:21:45,500 --> 00:21:48,460
+شوفوا كيف فسرناها وكيف 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
+وغير موجود في الـ B، المثال بقول اثبت أن الـ A ليست
+
+322
+00:22:05,800 --> 00:22:10,600
+subset من الـ 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 هيكفي، 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 الـ 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، ما دخلناش في
+
+330
+00:22:42,420 --> 00:22:45,820
+البراهين لكن اللي مش فاهم هذه الأمور صعب إن يمشي
+
+331
+00:22:45,820 --> 00:22:50,600
+على الأصعب، فلازم نفهم السهل و نمشي بالتدريج ونوصل
+
+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، بنقول ليه؟ The empty set phi is a subset
+
+336
+00:23:11,970 --> 00:23:16,670
+of every set خلينا أول شي نفهمها بالشفا وهيك زي 
+
+337
+00:23:16,670 --> 00:23:19,430
+ما اتعلمنا في بعض الحالات وبعدين 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 آخر كيف ممكن تكون ليس subset الـ file إذا قدرت
+
+343
+00:23:37,440 --> 00:23:39,660
+تلاقي answer موجود في الـ file وهذا مستحيل وليس
+
+344
+00:23:39,660 --> 00:23:41,840
+موجود في الـ 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 1 طبعاً 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؟ لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ
+
+349
+00:24:03,390 --> 00:24:03,610
+.. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ
+
+350
+00:24:03,610 --> 00:24:04,030
+.. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ
+
+351
+00:24:04,030 --> 00:24:05,610
+.. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ
+
+352
+00:24:05,610 --> 00:24:06,310
+.. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ
+
+353
+00:24:06,310 --> 00:24:07,490
+.. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ
+
+354
+00:24:07,490 --> 00:24:08,110
+.. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ
+
+355
+00:24:08,110 --> 00:24:10,910
+.. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ .. لكلّ 
+
+356
+00:24:13,590 --> 00:24:17,390
+of proof من الـ universe هنا كل المجموعات مجموعات
+
+357
+00:24:17,390 --> 00:24:20,850
+كل المجموعات لأن بيقول every set every set إيه، إيش
+
+358
+00:24:20,850 --> 00:24:25,210
+بتحتوي على الـ file اه هي إيش super set للـ file هي
+
+359
+00:24:25,210 --> 00:24:29,690
+super set للـ file تمام بدنا نثبت هذه للـ statement
+
+360
+00:24:29,690 --> 00:24:34,250
+statement تحتوي على الـ quantifier اه إيش 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 الـ
+
+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 الـ universe مش أعداد صحيحة، هنا إيش
+
+365
+00:24:50,490 --> 00:24:53,650
+العناصر؟ مجموعات، فاحنا إيش قلنا أول ما نشوف for
+
+366
+00:24:53,650 --> 00:24:56,230
+all أقول induction لأ، قلنا بدنا for all بدنا الـ
+
+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
+ما ينفعش فالـ 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 ما ينفعش، طيب في عندنا كان إرشاد
+
+372
+00:25:13,420 --> 00:25:16,600
+قال لي عشان تتعامل مع for all ابدأ الـ statement
+
+373
+00:25:16,600 --> 00:25:20,260
+بايش؟ بالـ 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 الـ 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 الـ B ينطبق على
+
+377
+00:25:29,420 --> 00:25:31,700
+جميع الـ statement بنفس 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 set let capital A be any set إيش بدي
+
+381
+00:25:46,700 --> 00:25:49,500
+أثبت؟ بدي أثبت إن الـ Phi subset من الـ A بيكون
+
+382
+00:25:49,500 --> 00:25:52,320
+البرهان انتهى ولا لأ؟ نعم لأنه إيش بدي؟ بيقول لي 
+
+383
+00:25:52,320 --> 00:25:55,660
+Phi is a subset of every set يعني أي set، لكلّ
+
+384
+00:25:55,660 --> 00:26:04,460
+المجموعات، لأي مجموعة 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
+هي statement أمامك فسرناها for all قاعدين نتعلم
+
+388
+00:26:23,390 --> 00:26:27,110
+كيف نتعامل مع for all بنقول له let العنصر يا مكان
+
+389
+00:26:27,110 --> 00:26:29,710
+بايش؟ بياني، باليان الـ universe ما هو الـ universe؟
+
+390
+00:26:29,710 --> 00:26:32,630
+كل المجموعات يعني بتكون الـ a,k,z لو جالي for all
+
+391
+00:26:32,630 --> 00:26:36,930
+اكسبت من الـ R بقوله X real number وهكذا 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 الـ a ماذا تعني؟ فسرناها الملاحظات نكتبش
+
+394
+00:26:48,360 --> 00:26:52,780
+كلام، أنمل الصفحات، كل شيء 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؟ ما بجيبش حاجة من عندي أنا بجيب
+
+397
+00:27:02,840 --> 00:27:06,770
+من اللي تعلمناها من السابق، نعتمد 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 الـ statement مش هذا هو المطلوب
+
+400
+00:27:12,610 --> 00:27:16,330
+we want to prove إيش بتبدأ الـ statement for all x
+
+401
+00:27:16,330 --> 00:27:22,150
+ممكن أعمل عليها نفس القاعدة أقول له let x بس الـ 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 ما قتش بتقول الـ for all P of X true إذا لكلّ X 
+
+406
+00:27:47,870 --> 00:27:50,670
+الـ P of X كانت true ما هي الـ P of X في هذا الـ
+
+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 نثبت شفتوا بقى هذا
+
+409
+00:28:01,990 --> 00:28:05,690
+التحليل أنا بعمله بالتفصيل طبعاً فيما بعد هذا ممكن
+
+410
+00:28:05,690 --> 00:28:10,850
+نعمله ضمن الحل، مرحلة 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 معه؟ 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 والثاني إيش ما يكون يكون، يا الأول
+
+416
+00:28:28,090 --> 00:28:30,990
+true والثاني true طيب نتطلع على الأول X and Tamil
+
+417
+00:28:30,990 --> 00:28:34,490
+Phi ما هي تنتم؟ ما رأيكم فيها؟ هل هذه ممكن تكون
+
+418
+00:28:34,490 --> 00:28:38,410
+حقيقية؟ حطيتها ملاحظة إنه دائماً 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 البرهان ولا ماخلصش؟ خلص مش هذه البداية وصلت له
+
+422
+00:28:56,310 --> 00:29:00,090
+ولا ماوصلت له والبرهان انتهى ممكن بدي أقلق thus
+
+423
+00:29:00,090 --> 00:29:04,970
+في subset من هنا إذا حابين نعمل خاتمة جيدة
+
+424
+00:29:04,970 --> 00:29:11,790
+ماكتبتوها آخر جملة مش مشكلة واضح؟ فهي وما تعلمناه
+
+425
+00:29:11,790 --> 00:29:16,810
+بنحلل المطلوب بنشوف الـ statement بدي أبرهنها بتعلم
+
+426
+00:29:16,810 --> 00:29:19,650
+كيف أتعامل معها وهتعلم معها كل واحدة لحال يمكن
+
+427
+00:29:19,650 --> 00:29:22,770
+احنا أشهر مثال كان في section 188 هو إيش if then
+
+428
+00:29:22,770 --> 00:29:25,710
+كيف نتعامل معها 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 واضح؟ طب واحد
+
+431
+00:29:35,140 --> 00:29:38,440
+طالب تقول له؟ 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 صحيحة؟ 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 الـ statement الشرطية دائما 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 التعدي
+
+440
+00:30:13,240 --> 00:30:21,720
+بمعنى خلّينا نقرأ ونعمل رسمة مساعدة بقول let A, B
+
+441
+00:30:21,720 --> 00:30:27,200
+and C be sets شايفين المنهج؟ بتكرر معنى إذا الآن
+
+442
+00:30:27,200 --> 00:30:32,250
+اللي بدي أذكره Capital 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 بقول لي if A subset من الـB والـB 
+
+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 وبعدين نشوف البرهان ونحلل فهي
+
+447
+00:30:51,570 --> 00:30:54,660
+بقول لي هي في عندي مجموعة A هي 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 فأنتوا طالبات في قسم الرياضيات فإذا
+
+451
+00:31:06,500 --> 00:31:09,280
+أنتوا طالبات قسم الرياضيات وأنتوا قسم الرياضيات في
+
+452
+00:31:09,280 --> 00:31:11,920
+كلية العلوم فأنتوا طالبات كلية العلوم والكلية 
+
+453
+00:31:11,920 --> 00:31:13,640
+العلوم في الجامعة الإسلامية أنه طالبات في الجامعة
+
+454
+00:31:13,640 --> 00:31:18,460
+الإسلامية صح ولا لأ نفس القاعدة واضح؟ أه فالـ C هي
+
+455
+00:31:18,460 --> 00:31:20,960
+الأكبر لأنها بتحتوي الـ B والـ B بتحتوي ال A فإذا 
+
+456
+00:31:20,960 --> 00:31:23,080
+تقلش ال C بتحتوي ال A ولا بتحتوي أشهر، بتحتوي
+
+457
+00:31:23,080 --> 00:31:27,260
+أشهر واضحة؟ أه تمام، نشوف البرهان خلينا 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 theorem إثنين إثنين 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 وأفسر كيف بدي أبرهن؟ أنا
+
+464
+00:31:56,390 --> 00:32:00,530
+عندي معطيات قال لي 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 ال a وال b
+
+466
+00:32:03,450 --> 00:32:06,450
+وال 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؟ بيقول لي 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 إيش 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 أعمل هيك a
+
+473
+00:32:43,870 --> 00:32:48,930
+subset من ال c is it true أو كيف أكتب أو implies
+
+474
+00:32:48,930 --> 00:32:52,630
+يعني بحطها if then is true كـ 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
+إنها true دائما، نظرية، بدي أثبت إنها true يعني
+
+478
+00:33:02,670 --> 00:33:04,050
+بدي أثبت الـ communication علشان هيك دائما في
+
+479
+00:33:04,050 --> 00:33:07,450
+رياضيّات بيستخدموش تضمين لأنه أنا مطلوب إن أثبت إنها
+
+480
+00:33:07,450 --> 00:33:13,060
+true واضح؟ هذا هو المطلوب واضح؟ تمام هذا المطلوب 
+
+481
+00:33:13,060 --> 00:33:16,880
+أصنعه جملة شرطية كيف نبدأ برهان الجملة الشرطية
+
+482
+00:33:16,880 --> 00:33:21,340
+المباشر افترض أن الشرط صحيح فإيش حداله الآن فيعني 
+
+483
+00:33:21,340 --> 00:33:27,240
+عندي هذا معطى المعطى الثاني 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
+أن المعطى صحيح إيش المطلوب أثبت أنه جواب 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 وكل خطوة بنفسرها أه بحتاج تفسير أكثر 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؟ أنت باين؟ أنا بجيبش حاجة فجأة تسقط من 
+
+492
+00:34:17,850 --> 00:34:21,670
+السماء، بفسر، واحدة واحدة، أنا 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
+أكثر، 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
+معناها هيك 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 واحد غشيم بقول لك 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 عجلة أنا 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 ما عايش بيقول اه قلت اه ورياضة 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
+وإيش نعمل فالعمل منطقي مش عشوائي ممتاز إيش بده
+
+514
+00:36:01,430 --> 00:36:04,490
+يثبت؟ X تنتمي للـC هي آخر مطلوبة بقدر أفسر أكثر من
+
+515
+00:36:04,490 --> 00:36:13,440
+هيك؟ مش حاجة ده we have to show that X تنتمي للـC
+
+516
+00:36:13,440 --> 00:36:17,100
+بقدر أفسر أكثر من هيك؟ لأ، شوفتوا احنا 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
+معها؟ بتحتاج تفسير، بتفسر، بتفسر، صار بدي أثبت 
+
+519
+00:36:23,320 --> 00:36:27,220
+إن X تنتمي للـC تتفسر أكثر من هيك؟ لأ، إيش معنى X 
+
+520
+00:36:27,220 --> 00:36:30,120
+تنتمي للـC؟ ما عندناش 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 للـC أطلع على المعطيات X موجودة 
+
+523
+00:36:38,430 --> 00:36:41,370
+في الـ A ومش في عنده معطيات؟ الـ A subset 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
+subset من الـ B، هاي دليل ممكن أكتبها بهذا الشكل
+
+527
+00:36:53,550 --> 00:36:57,430
+لوقت أكتب since A subset 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 البرهان ما عندناش 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 وإيش وصلنا للمطلوب انتهى البرهان واضح؟
+
+535
+00:37:34,020 --> 00:37:37,580
+أه طبعا هيك 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 خذي 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 أخذ أي عنصر موجود في الـA يكون موجود
+
+540
+00:37:55,210 --> 00:37:58,690
+في الـC هذه ملخصة بس هذه أول مرة فكفكناها
+
+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 false المثال
+
+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 الواحد غلط هدول عمرين
+
+549
+00:38:41,310 --> 00:38:46,110
+مختلفين هدول اه اه لأنها 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 false أه فهنا زي ما دي أقول إيش مثلا
+
+553
+00:38:58,240 --> 00:39:02,220
+اللي هو إيش 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 إيش التقسيم اللي بيجمعهم أه
+
+558
+00:39:14,520 --> 00:39:18,300
+فهذه إيش مختلفين وإنما إيش ممكن نحط علاقة تنتمي
+
+559
+00:39:18,300 --> 00:39:22,770
+أحسنتم تبسط من فعل لأ لأ ما ينفعش، إيش معنى subset؟
+
+560
+00:39:22,770 --> 00:39:25,590
+كل عناصر الأولى عناصر من الثانية، هل الواحد عناصر 
+
+561
+00:39:25,590 --> 00:39:28,410
+من الثانية؟ لأ، الواحد مش عناصر الثانية، مجموعة
+
+562
+00:39:28,410 --> 00:39:31,090
+الواحد هي اللي عناصر الثانية، زي ما هي الرياضيات 
+
+563
+00:39:31,090 --> 00:39:34,490
+مش من كليات الجامعة الإسلامية، الرياضيات ضمن قسم
+
+564
+00:39:34,490 --> 00:39:37,910
+في كلية العلوم، المفهوم مختلف، المفهوم مختلف
+
+565
+00:39:37,910 --> 00:39:42,590
+والتقسيم مختلف لكن هيها .. شوفت مجموعة الواحد
+
+566
+00:39:42,590 --> 00:39:46,630
+والثانية تنتمي لمجموعة .. مجموعة الواحد والثانية
+
+567
+00:39:46,630 --> 00:39:50,470
+كعنصر والثلاثة كعنصر إيش معناها تنتمي؟ لأن عنصر من
+
+568
+00:39:50,470 --> 00:39:56,370
+ضمن العناصر فهذه true في C true فأرجو أن نفرق في هذه الرموز
+
+569
+00:39:56,370 --> 00:40:03,010
+نفرق فيها ونستخدمها بهذه الدقة الفاي تساوي مجموعة
+
+570
+00:40:03,010 --> 00:40:08,650
+الفاي false 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 أشبهلكم إياها هلجيت صينية فاضية فهي صينية
+
+573
+00:40:17,290 --> 00:40:20,110
+فاضية صينية فاضية فيها كوباية فاضية الصينية صارت 
+
+574
+00:40:20,110 --> 00:40:23,350
+فاضية ولا مليانة ورغم أن فيها كوباية فاضية واضح
+
+575
+00:40:23,350 --> 00:40:27,970
+فالفرق في فرق هذه مجموعة فيها عنصر فارغ ما نش ده
+
+576
+00:40:27,970 --> 00:40:28,890
+ولكن فيها حاجة
+
+577
+00:40:32,860 --> 00:40:36,160
+لأن إيش معنى 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 الثانية؟ لأ، مجموعة الواحد هي اللي من
+
+580
+00:40:42,320 --> 00:40:44,560
+عناصر الثانية، زي ما قلنا إن الرياضيات مش من
+
+581
+00:40:44,560 --> 00:40:49,780
+الكليات، هي جوا كلية، بطلعش أنا على التفاصيل، بطلع 
+
+582
+00:40:49,780 --> 00:40:53,060
+من الخارج كعناصر، بيهمني، بيهمني شخصية تنتمي ..
+
+583
+00:40:53,060 --> 00:41:00,960
+تنتمي .. صح، زي الوقع، 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
+إضافة بقول if it is true prove it لما إحنا بقول 
+
+587
+00:41:13,310 --> 00:41:18,930
+نثبت الصحة with a false disapprove it إذا أنا أنا
+
+588
+00:41:18,930 --> 00:41:19,790
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+589
+00:41:19,790 --> 00:41:19,950
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+590
+00:41:19,950 --> 00:41:22,750
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+591
+00:41:22,750 --> 00:41:23,270
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+592
+00:41:23,270 --> 00:41:28,830
+أنا أنا أنا أنا أنا أنا أنا أنا أنا 
+
+593
+00:41:33,850 --> 00:41:39,370
+خلينا نحلهم مع بعض نشوف إيش الأسئلة ونحلها
+
+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
+اثنين وال solution وهي A إذا ال X في ال A وال 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 العبارة للقضية فهذه false فدى 
+
+598
+00:42:03,330 --> 00:42:10,690
+false بدنا ماشي مثال عكسي counter example بدنا
+
+599
+00:42:10,690 --> 00:42:17,710
+مثال عكسي نعم لو ال A subset من 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 ضروري عناصر ال A تكون زي ما توي شفنا 
+
+602
+00:42:24,430 --> 00:42:30,030
+الواحد زي المثال قبل قليل بدنا مثال بدنا مثال عكسي 
+
+603
+00:42:30,030 --> 00:42:35,820
+تمام بدنا 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
+ماتعجبيش حالك وماتتهيش عشان ما تغلطيش عشان يكون
+
+608
+00:42:49,240 --> 00:42:52,060
+المثال واضح فأنا 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 لأن هي شملة شرطية فبدنا ال جتحنا بدنا
+
+611
+00:42:59,540 --> 00:43:04,790
+مجموعة A فيها 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
+بتساوي واحدة خلصنا عشان ما يكون 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 الواحد ولا تكون مثلا اثنين في أي 
+
+617
+00:43:26,870 --> 00:43:32,560
+اختيار أريد 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 ما ليش دعوة أنا بتطلع على عناصر ال B
+
+624
+00:43:57,980 --> 00:44:00,880
+بتطلع بتطلع على النظر الخارجية ما ليش دعوة 
+
+625
+00:44:00,880 --> 00:44:04,120
+بالتفاصيل ما ليش دعوة بالتفاصيل 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 إن شاء الله مع التكرار الأمور تكون أفضل من
+
+629
+00:44:18,480 --> 00:44:26,580
+هك وأوضح مثال B إذا 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 وممكن 
+
+631
+00:44:31,340 --> 00:44:36,840
+مع الرسم تساعدنا ب في الس خلينا نعمل رسم مساعد هي
+
+632
+00:44:36,840 --> 00:44:41,750
+عندي A وهي عندي B بقول لي في عنصر موجود في ال B 
+
+633
+00:44:41,750 --> 00:44:45,330
+وين عناصر ال B؟ يا هنا يا هنا ضروري يكون خارج ال 
+
+634
+00:44:45,330 --> 00:44:48,650
+ايه؟ لأ واضح إنه مش ضروري إنه مش ضروري فهذه طبعا 
+
+635
+00:44:48,650 --> 00:44:51,150
+لما يقول لي طب ممكن تكون صح لأ أنا إيش بده أقول قاعد 
+
+636
+00:44:51,150 --> 00:44:54,090
+تكون دائما صح هيك معاك لأ مش احتمال فلما بده أقول 
+
+637
+00:44:54,090 --> 00:44:56,690
+إن القاعد ده بده تكون دائما صحيحة مش إن احتمال
+
+638
+00:44:56,690 --> 00:45:01,130
+تكون صحيحة أه في بعض الأحيان لأ بنفعل فبندليه مثال 
+
+639
+00:45:01,130 --> 00:45:09,730
+عكسي counter example مثال عكسي أو تمام فناخد إيش ال
+
+640
+00:45:09,730 --> 00:45:14,850
+A مثلا تساوي واحد اثنين ببساطة أه بده يعني إيش ال
+
+641
+00:45:14,850 --> 00:45:20,460
+A subset من ال B بي تساوي عشان تكون subset واحد
+
+642
+00:45:20,460 --> 00:45:25,080
+اثنين على الأقل ثلاثة تمام فبقول لي ال X بدها تكون في 
+
+643
+00:45:25,080 --> 00:45:28,960
+ال B وما تكونش في ال A برضه جملة شرطية بدياش فأنا 
+
+644
+00:45:28,960 --> 00:45:33,400
+عندي مثلا إنه بدها تكون في ال B وال A subset مظبوط
+
+645
+00:45:33,400 --> 00:45:37,780
+وما تكونش بتكون أه بعد المية ليست في ال A بدها 
+
+646
+00:45:37,780 --> 00:45:42,100
+مفيهاش ده تصير جوا ال A فاشفي عندي الأول شيء الواحد 
+
+647
+00:45:42,100 --> 00:45:47,770
+تنتمي لل B الـ A subset 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 ثالث ونهاية ال section هنا إن شاء الله prove
+
+653
+00:46:14,940 --> 00:46:21,160
+that for any sets a,b,c ثلاث مجموعات إذا ال a proper
+
+654
+00:46:21,160 --> 00:46:25,040
+من ال b و ال b proper subset من ال c فال a proper
+
+655
+00:46:25,040 --> 00:46:27,980
+subset من ال c فبرضه علاقة proper 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
+الثالث و solution طبعا هذا المثال اللي هو أهم 
+
+658
+00:46:45,020 --> 00:46:49,480
+بالنسبة لنا كيف نبرهن لأنه براهين النظريات بدنا 
+
+659
+00:46:49,480 --> 00:46:53,480
+نفهمها ونعرف نشتغل زيها مش نعرف نحفظها أه فهنا
+
+660
+00:46:53,480 --> 00:46:56,800
+بدينا كيف نتعامل زي ما تعلمنا 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
+معطى أن الـA والـB 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 إيش ومفهومة ضمنيا حتى لما ذكرتها إيش بقول إيه
+
+665
+00:47:17,010 --> 00:47:24,630
+أثبت if جملة شرطية we want to prove نكتب هنا إيش 
+
+666
+00:47:24,630 --> 00:47:29,770
+المطلوب فالله يقول لي إيش prove that we want أو 
+
+667
+00:47:29,770 --> 00:47:36,850
+have to كله صح to prove that جملة 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 أو 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؟ متابعين؟ واضح؟ يعني إحنا 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
+حاسب 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 شرطية 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
+proper subset من الـ C ممتاز إيش المطلوب؟ we have to 
+
+678
+00:48:36,760 --> 00:48:44,740
+show that ال A proper من ال C وتكافئ إيش معناها
+
+679
+00:48:44,740 --> 00:48:50,300
+proper؟ subset ولا تساوي إن 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 إيش 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 إن هذه true وهذه true فخلينا نقسم على
+
+684
+00:49:12,250 --> 00:49:15,850
+مرحلتين فنبدأ من الجزء الأول بدنا نثبت إن ال A
+
+685
+00:49:15,850 --> 00:49:20,190
+subset من ال C بدنا نثبت إن ال A subset من ال C
+
+686
+00:49:20,190 --> 00:49:26,850
+فده أول جزء بدنا نثبت إن ال A subset من ال C تمام؟
+
+687
+00:49:26,850 --> 00:49:32,350
+أه فيه إن إحنا مقطيات سهل هذا الجزء لأن إيش قلنا 
+
+688
+00:49:32,350 --> 00:49:35,570
+بدنا نثبت إن البروبر transitive طب ما إحنا في 
+
+689
+00:49:35,570 --> 00:49:39,190
+subset transitive طب والبروبر تتضمن ضمنيا إنه
+
+690
+00:49:39,190 --> 00:49:43,050
+يكون subset فأنا 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 إننا هنا نقوله إيش 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 B والـ B proper subset من الـ C 
+
+695
+00:49:59,730 --> 00:50:04,670
+implies الـ B subset من الـ C هذه وهذه ونظرية 
+
+696
+00:50:04,670 --> 00:50:08,190
+اثنين اثنين إيش يؤدوا إن الـ A subset من الـ C أه 
+
+697
+00:50:08,190 --> 00:50:15,230
+إذا thus ممكن أكتب الـ A subset من الـ C من وين؟
+
+698
+00:50:15,230 --> 00:50:21,460
+theorem اثنين اثنين فأنا الجزء السهل وده شيء متوقع
+
+699
+00:50:21,460 --> 00:50:25,460
+ممكن أحط إشي يساوي وأقول for all x لكن أنا بدل ما 
+
+700
+00:50:25,460 --> 00:50:28,480
+أعمل بشكل مطول بأعيد برهان نظرية اثنين اثنين 
+
+701
+00:50:28,480 --> 00:50:32,660
+استخدمت النظرية واضح الفرق؟ اه فالآن أنا ما فصلتش
+
+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 الأول سهل متفقين؟ اه ممكن أعمل بشكل مطول اه
+
+704
+00:50:39,880 --> 00:50:44,360
+بس بكون أطول هذا أقصر البرهان الجزء الثاني بدنا 
+
+705
+00:50:44,360 --> 00:50:51,560
+نثبت أن الـ A لا تساوي الـ C لا تساوي الـ C على أن
+
+706
+00:50:51,560 --> 00:50:57,200
+تستفيد ايش 
+
+707
+00:50:57,200 --> 00:51:03,560
+معناه لا تساوي يساوي يعني هذه سبسط من الأولى
+
+708
+00:51:03,560 --> 00:51:07,640
+والثانية 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
+لا تساوي، لا تساوي، ايش معناه؟ ايش 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 ايش؟
+
+713
+00:51:26,830 --> 00:51:33,290
+A ليست subset من الـC or C ليست subset من الـA صح
+
+714
+00:51:33,290 --> 00:51:37,590
+ولا لأ؟ De Morgan's شايفين؟ اه اللي تعلمناه ممتاز
+
+715
+00:51:37,590 --> 00:51:41,310
+أنا ايش بدي أثبت؟ بدي أثبت انه يا هاذي true يا
+
+716
+00:51:41,310 --> 00:51:44,670
+هاذي true عشان .. بدي أثبت ان الـ or true وقت ايش
+
+717
+00:51:44,670 --> 00:51:47,330
+بيكون الـ 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 الـ 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 الـ or true ايش لازم تكون؟ لازم تكون الـ can يه
+
+721
+00:52:00,440 --> 00:52:03,100
+true فإذا لازم أثبت إن وديك true فهنا دي ده أقول له
+
+722
+00:52:03,100 --> 00:52:13,200
+since الـ A subset من الـ C we have to show that الـ
+
+723
+00:52:13,200 --> 00:52:20,540
+ايش الـ C ليست subset من مين؟ من الـ A هي اللي تبقى
+
+724
+00:52:20,540 --> 00:52:26,600
+وهذا issue كافة كتبناها قبل قليل there exists X X
+
+725
+00:52:26,600 --> 00:52:35,940
+تنتمي للـ A .. آسف للـ C and X لا تنتمي للـ 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 ولا في الشنط ولا وين؟ في المعطيات ..
+
+730
+00:52:57,650 --> 00:53:02,070
+في المعطيات طيب هل ممكن أذكر الـ X بشكل صريح؟ أقول
+
+731
+00:53:02,070 --> 00:53:05,550
+X بتساوي واحد ولا بتساوي صفر؟ ليش؟ لأن الـ A و الـ
+
+732
+00:53:05,550 --> 00:53:08,430
+B و الـ C دول عايشين مجموعات عامة، ايش 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
+لا ما استخدمناش انهم proper ايش معناه ان الـB
+
+737
+00:53:23,230 --> 00:53:27,250
+proper subset من الـC ان الـB تساويش الـC يعني هناك
+
+738
+00:53:27,250 --> 00:53:31,090
+عنصر موجود في الـC غير موجود في الـB اه فالآن بدي
+
+739
+00:53:31,090 --> 00:53:36,970
+أكتب له هنا B proper 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 بتحتوي 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 ايش 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 عناصر في
+
+746
+00:54:03,060 --> 00:54:06,300
+الـ A موجود في الـ B الـ Contrapositive كل عناصر
+
+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 أكتب لكم على السريع ايش 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؟ ايش 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 الـ
+
+756
+00:54:56,870 --> 00:54:57,850
+section إن شاء الله المرة الجديدة
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/e5jENMYP4AM_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/e5jENMYP4AM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..aa4c4ae075bd8261e2289ca9d2c005bc8d24a21e
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/e5jENMYP4AM_raw.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/fKIoi36SRTo_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/fKIoi36SRTo_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..c7e6de122f8b6513e924a95690c0b4ec98f5d8a1
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/fKIoi36SRTo_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3892, "start": 20.92, "end": 38.92, "text": "بسم الله الرحمن الرحيم ان شاء الله اليوم احنا هنكمل مع ال relations طبعا احنا بس بدأنا بداية بسيطة مدخل و طبعا ال chapter كله بتحدث عن العلاقات و الدوال و مفتاح دراسة العلاقات و الدوال هو الأزواج المرتبة", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 16472, 13412, 16606, 21984, 45595, 20498, 1975, 5016, 8315, 8032, 1863, 24793, 1211, 20449, 2423, 2299, 23032, 3555, 3615, 995, 1975, 5016, 8315, 4724, 3794, 47525, 10721, 8315, 4724, 28259, 10632, 4724, 3794, 1829, 9566, 3660, 3714, 3215, 9778, 1211, 4032, 23032, 3555, 3615, 995, 2423, 7187, 28242, 3224, 39894, 24401, 12984, 18871, 18863, 15040, 4587, 9307, 4032, 32748, 2407, 6027, 4032, 3714, 5172, 2655, 39319, 11778, 23557, 3794, 3660, 18863, 15040, 4587, 9307, 4032, 32748, 2407, 6027, 31439, 16247, 11622, 2407, 26108, 9673, 43500, 49401], "avg_logprob": -0.08231608080677688, "compression_ratio": 1.8333333333333333, "no_speech_prob": 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بتوزع على ال difference بتوزع على ال difference خلينا نشوف البرهان فدي نظرية اتنين في شبطة تلاتة theorem تلاتة اتنين way proof", "tokens": [1863, 19913, 2288, 10632, 6055, 7649, 10632, 8717, 19913, 2288, 10632, 5551, 34740, 7578, 28239, 19913, 2288, 10632, 16247, 34740, 7578, 39894, 39648, 16472, 2423, 39184, 22478, 42434, 1674, 39894, 2407, 11622, 3615, 15844, 9154, 22807, 15844, 27188, 2288, 4587, 15844, 2423, 3175, 6156, 3555, 2655, 2407, 11622, 3615, 15844, 2423, 9307, 5016, 18513, 39894, 2407, 11622, 3615, 15844, 16712, 4587, 41193, 3615, 4032, 39894, 2407, 11622, 3615, 15844, 2423, 2649, 39894, 2407, 11622, 3615, 15844, 2423, 2649, 16490, 1211, 9957, 995, 8717, 8592, 38688, 2423, 26890, 3224, 7649, 6156, 16254, 8717, 19913, 2288, 10632, 1975, 2655, 1863, 9957, 8978, 13412, 3555, 9566, 3660, 6055, 1211, 9307, 3660, 20904, 6055, 1211, 9307, 3660, 1975, 2655, 1863, 9957, 636, 8177], "avg_logprob": -0.22734374937911828, "compression_ratio": 2.0514018691588785, "no_speech_prob": 0.0, "words": [{"start": 1009.31, "end": 1009.97, "word": "نظرية", "probability": 0.9207763671875}, {"start": 1009.97, "end": 1010.63, "word": " تانية", "probability": 0.815185546875}, {"start": 1010.63, "end": 1011.55, "word": " نظرية", "probability": 0.8809814453125}, {"start": 1011.55, "end": 1012.47, "word": " أخرى", "probability": 0.9484049479166666}, {"start": 1012.47, "end": 1013.69, "word": " النظرية", "probability": 0.779632568359375}, {"start": 1013.69, "end": 1014.13, "word": " الأخرى", "probability": 0.9794921875}, {"start": 1014.13, "end": 1014.59, "word": " بتقول", "probability": 0.936279296875}, {"start": 1014.59, "end": 1015.11, "word": " ان", "probability": 0.37890625}, {"start": 1015.11, "end": 1015.37, "word": " الـ", "probability": 0.26983642578125}, {"start": 1015.37, "end": 1016.45, "word": " Cartesian", "probability": 0.74658203125}, {"start": 1016.45, "end": 1016.79, "word": " product", "probability": 0.64306640625}, {"start": 1016.79, "end": 1017.29, "word": " بتوزع", "probability": 0.935302734375}, {"start": 1017.29, "end": 1017.47, "word": " على", "probability": 0.78759765625}, {"start": 1017.47, "end": 1017.71, "word": " من؟", "probability": 0.5472412109375}, {"start": 1017.71, "end": 1017.85, "word": " على", "probability": 0.84423828125}, {"start": 1017.85, "end": 1018.31, "word": " الفرق", "probability": 0.9654947916666666}, {"start": 1018.31, "end": 1018.49, "word": " على", "probability": 0.66357421875}, {"start": 1018.49, "end": 1018.97, "word": " ال", "probability": 0.9345703125}, {"start": 1018.97, "end": 1019.39, "word": " minus", "probability": 0.47021484375}, {"start": 1019.39, "end": 1020.79, "word": " فبتوزع", "probability": 0.8016764322916666}, {"start": 1020.79, "end": 1020.91, "word": " على", "probability": 0.9150390625}, {"start": 1020.91, "end": 1021.55, "word": " الاتحاد", "probability": 0.9228515625}, {"start": 1021.55, "end": 1022.49, "word": " بتوزع", "probability": 0.809478759765625}, {"start": 1022.49, "end": 1022.61, "word": " على", "probability": 0.95458984375}, {"start": 1022.61, "end": 1023.33, "word": " التقاطع", "probability": 0.966064453125}, {"start": 1023.33, "end": 1023.69, "word": " و", "probability": 0.56298828125}, {"start": 1023.69, "end": 1024.19, "word": " بتوزع", "probability": 0.92626953125}, {"start": 1024.19, "end": 1024.33, "word": " على", "probability": 0.95458984375}, {"start": 1024.33, "end": 1024.45, "word": " ال", "probability": 0.90625}, {"start": 1024.45, "end": 1024.81, "word": " difference", "probability": 0.8369140625}, {"start": 1024.81, "end": 1025.63, "word": " بتوزع", "probability": 0.9229736328125}, {"start": 1025.63, "end": 1025.93, "word": " على", "probability": 0.95458984375}, {"start": 1025.93, "end": 1026.49, "word": " ال", "probability": 0.97412109375}, {"start": 1026.49, "end": 1026.91, "word": " difference", "probability": 0.84521484375}, {"start": 1026.91, "end": 1027.31, "word": " خلينا", "probability": 0.76123046875}, {"start": 1027.31, "end": 1027.77, "word": " نشوف", "probability": 0.9964192708333334}, {"start": 1027.77, "end": 1028.77, "word": " البرهان", "probability": 0.861328125}, {"start": 1028.77, "end": 1029.97, "word": " فدي", "probability": 0.6243896484375}, {"start": 1029.97, "end": 1030.53, "word": " نظرية", "probability": 0.990234375}, {"start": 1030.53, "end": 1031.37, "word": " اتنين", "probability": 0.821044921875}, {"start": 1031.37, "end": 1031.51, "word": " في", "probability": 0.98095703125}, {"start": 1031.51, "end": 1031.83, "word": " شبطة", "probability": 0.740234375}, {"start": 1031.83, "end": 1032.63, "word": " تلاتة", "probability": 0.9376220703125}, {"start": 1032.63, "end": 1034.19, "word": " theorem", "probability": 0.66845703125}, {"start": 1034.19, "end": 1035.47, "word": " تلاتة", "probability": 0.77459716796875}, {"start": 1035.47, "end": 1035.99, "word": " اتنين", "probability": 0.96630859375}, {"start": 1035.99, "end": 1036.91, "word": " way", "probability": 0.52880859375}, {"start": 1036.91, "end": 1037.79, "word": " proof", "probability": 0.33203125}], "temperature": 1.0}, {"id": 45, "seek": 106161, "start": 1040.54, "end": 1061.62, "text": "أه طبعا مافيش الا فرع واحد في هذه النظرية مش فرعين اه برضه المطلوب statement بسيطة عبارة عن تساوي مجموعات فنفس السياسة خلينا ايش نبدأ من اليمين نتعلم ولا من اليسار اللي بدكوا هي فطبعا هنقوله let الان", "tokens": [10721, 3224, 23032, 3555, 3615, 995, 19446, 41185, 8592, 42963, 6156, 2288, 3615, 36764, 24401, 8978, 29538, 28239, 19913, 2288, 10632, 37893, 6156, 2288, 3615, 9957, 1975, 3224, 4724, 43042, 3224, 9673, 9566, 1211, 37746, 5629, 4724, 3794, 1829, 9566, 3660, 6225, 3555, 9640, 3660, 18871, 6055, 3794, 995, 45865, 3714, 7435, 2304, 45367, 9307, 6156, 1863, 36178, 21136, 25528, 3794, 3660, 16490, 20292, 8315, 1975, 1829, 8592, 8717, 44510, 10721, 9154, 2423, 32640, 9957, 8717, 2655, 3615, 19528, 49429, 9154, 45595, 3794, 9640, 13672, 1829, 47525, 4117, 14407, 39896, 6156, 9566, 3555, 3615, 995, 8032, 1863, 39648, 3224, 718, 2423, 7649], "avg_logprob": -0.14661711743734415, "compression_ratio": 1.6941747572815533, "no_speech_prob": 0.0, "words": [{"start": 1040.54, "end": 1040.8, "word": "أه", "probability": 0.635009765625}, {"start": 1040.8, "end": 1041.04, "word": " طبعا", "probability": 0.9827880859375}, {"start": 1041.04, "end": 1041.24, "word": " مافيش", "probability": 0.9353841145833334}, {"start": 1041.24, "end": 1041.36, "word": " الا", "probability": 0.260498046875}, {"start": 1041.36, "end": 1041.56, "word": " فرع", "probability": 0.9596354166666666}, {"start": 1041.56, "end": 1041.88, "word": " واحد", "probability": 0.988525390625}, {"start": 1041.88, "end": 1041.98, "word": " في", "probability": 0.85986328125}, {"start": 1041.98, "end": 1042.08, "word": " هذه", "probability": 0.86279296875}, {"start": 1042.08, "end": 1042.58, "word": " النظرية", "probability": 0.94775390625}, {"start": 1042.58, "end": 1042.82, "word": " مش", "probability": 0.8662109375}, {"start": 1042.82, "end": 1043.26, "word": " فرعين", "probability": 0.9859619140625}, {"start": 1043.26, "end": 1044.06, "word": " اه", "probability": 0.647216796875}, {"start": 1044.06, "end": 1044.54, "word": " برضه", "probability": 0.9708658854166666}, {"start": 1044.54, "end": 1045.38, "word": " المطلوب", "probability": 0.98388671875}, {"start": 1045.38, "end": 1046.38, "word": " statement", "probability": 0.80615234375}, {"start": 1046.38, "end": 1047.68, "word": " بسيطة", "probability": 0.974609375}, {"start": 1047.68, "end": 1048.52, "word": " عبارة", "probability": 0.990966796875}, {"start": 1048.52, "end": 1048.74, "word": " عن", "probability": 0.994140625}, {"start": 1048.74, "end": 1049.24, "word": " تساوي", "probability": 0.984130859375}, {"start": 1049.24, "end": 1049.88, "word": " مجموعات", "probability": 0.9216796875}, {"start": 1049.88, "end": 1050.36, "word": " فنفس", "probability": 0.94287109375}, {"start": 1050.36, "end": 1051.22, "word": " السياسة", "probability": 0.9808349609375}, {"start": 1051.22, "end": 1052.06, "word": " خلينا", "probability": 0.7809244791666666}, {"start": 1052.06, "end": 1052.8, "word": " ايش", "probability": 0.7377115885416666}, {"start": 1052.8, "end": 1053.24, "word": " نبدأ", "probability": 0.9298502604166666}, {"start": 1053.24, "end": 1053.46, "word": " من", "probability": 0.98974609375}, {"start": 1053.46, "end": 1054.64, "word": " اليمين", "probability": 0.7513020833333334}, {"start": 1054.64, "end": 1056.08, "word": " نتعلم", "probability": 0.9532470703125}, {"start": 1056.08, "end": 1056.22, "word": " ولا", "probability": 0.70947265625}, {"start": 1056.22, "end": 1056.34, "word": " من", "probability": 0.98095703125}, {"start": 1056.34, "end": 1056.74, "word": " اليسار", "probability": 0.9949544270833334}, {"start": 1056.74, "end": 1056.88, "word": " اللي", "probability": 0.872802734375}, {"start": 1056.88, "end": 1057.16, "word": " بدكوا", "probability": 0.78857421875}, {"start": 1057.16, "end": 1057.28, "word": " هي", "probability": 0.615234375}, {"start": 1057.28, "end": 1058.28, "word": " فطبعا", "probability": 0.871630859375}, {"start": 1058.28, "end": 1058.9, "word": " هنقوله", "probability": 0.82763671875}, {"start": 1058.9, "end": 1059.3, "word": " let", "probability": 0.57958984375}, {"start": 1059.3, "end": 1061.62, "word": " الان", "probability": 0.609375}], "temperature": 1.0}, {"id": 46, "seek": 107257, "start": 1062.45, "end": 1072.57, "text": "في ضوء خبرتي من البرهان الماضي ممكن على طول باستعامل مع كارتينيا product ممكن على طول اقوله let x,y be an element", "tokens": [41185, 48812, 2407, 38207, 16490, 26890, 31371, 9154, 2423, 26890, 3224, 7649, 9673, 46958, 1829, 3714, 43020, 15844, 23032, 12610, 4724, 995, 14851, 3615, 10943, 1211, 20449, 9122, 9640, 2655, 9957, 25528, 1674, 3714, 43020, 15844, 23032, 12610, 1975, 39648, 3224, 718, 2031, 11, 88, 312, 364, 4478], "avg_logprob": -0.2989477040816326, "compression_ratio": 1.371212121212121, "no_speech_prob": 0.0, "words": [{"start": 1062.45, "end": 1062.73, "word": "في", "probability": 0.7578125}, {"start": 1062.73, "end": 1063.15, "word": " ضوء", "probability": 0.7779947916666666}, {"start": 1063.15, "end": 1063.73, "word": " خبرتي", "probability": 0.8527018229166666}, {"start": 1063.73, "end": 1063.85, "word": " من", "probability": 0.97412109375}, {"start": 1063.85, "end": 1065.07, "word": " البرهان", "probability": 0.9212646484375}, {"start": 1065.07, "end": 1065.73, "word": " الماضي", "probability": 0.9422200520833334}, {"start": 1065.73, "end": 1066.45, "word": " ممكن", "probability": 0.81884765625}, {"start": 1066.45, "end": 1066.63, "word": " على", "probability": 0.912109375}, {"start": 1066.63, "end": 1066.83, "word": " طول", "probability": 0.991943359375}, {"start": 1066.83, "end": 1067.43, "word": " باستعامل", "probability": 0.8407389322916666}, {"start": 1067.43, "end": 1067.55, "word": " مع", "probability": 0.97412109375}, {"start": 1067.55, "end": 1067.89, "word": " كارتينيا", "probability": 0.469921875}, {"start": 1067.89, "end": 1068.15, "word": " product", "probability": 0.1204833984375}, {"start": 1068.15, "end": 1068.95, "word": " ممكن", "probability": 0.800537109375}, {"start": 1068.95, "end": 1069.11, "word": " على", "probability": 0.90087890625}, {"start": 1069.11, "end": 1069.31, "word": " طول", "probability": 0.99560546875}, {"start": 1069.31, "end": 1069.71, "word": " اقوله", "probability": 0.6936848958333334}, {"start": 1069.71, "end": 1069.99, "word": " let", "probability": 0.81640625}, {"start": 1069.99, "end": 1070.47, "word": " x", "probability": 0.65380859375}, {"start": 1070.47, "end": 1071.23, "word": ",y", "probability": 0.669189453125}, {"start": 1071.23, "end": 1071.95, "word": " be", "probability": 0.495361328125}, {"start": 1071.95, "end": 1072.19, "word": " an", "probability": 0.611328125}, {"start": 1072.19, "end": 1072.57, "word": " element", "probability": 0.9609375}], "temperature": 1.0}, {"id": 47, "seek": 110247, "start": 1074.55, "end": 1102.47, "text": "طبعا هذه عبارة عن فرضيتين مع بعض هو عبارة عن أنصر عشوائي ينتمي لـ Cartesian product إذا لازم يكون زوج مرتب فانا جمعت أكتر من جملة مع بعض ببدأ بممكن أبدأ هيك بالعرفة الممتعرف عليه واضحة اه فأقول ايش be any element let x,y be any element and let let x,y تنتمي من وين نبدأ؟", "tokens": [9566, 3555, 3615, 995, 29538, 6225, 3555, 9640, 3660, 18871, 6156, 43042, 36081, 9957, 20449, 45030, 11242, 31439, 6225, 3555, 9640, 3660, 18871, 14739, 9381, 2288, 6225, 8592, 2407, 16373, 1829, 7251, 29399, 2304, 1829, 5296, 39184, 22478, 42434, 1674, 11933, 15730, 5296, 31377, 2304, 7251, 30544, 30767, 29245, 3714, 43500, 3555, 6156, 7649, 995, 10874, 2304, 34268, 5551, 4117, 2655, 2288, 9154, 10874, 2304, 37977, 20449, 45030, 11242, 4724, 44510, 10721, 4724, 2304, 43020, 5551, 44510, 10721, 39896, 4117, 20666, 3615, 28480, 3660, 9673, 2304, 2655, 3615, 28480, 47356, 4032, 46958, 5016, 3660, 1975, 3224, 6156, 10721, 39648, 1975, 1829, 8592, 312, 604, 4478, 718, 2031, 11, 88, 312, 604, 4478, 293, 718, 718, 2031, 11, 88, 6055, 29399, 2304, 1829, 9154, 4032, 9957, 8717, 44510, 10721, 22807], "avg_logprob": -0.2269230816226739, "compression_ratio": 1.6653696498054475, "no_speech_prob": 0.0, "words": [{"start": 1074.55, "end": 1074.87, "word": "طبعا", "probability": 0.8948974609375}, {"start": 1074.87, "end": 1075.05, "word": " هذه", "probability": 0.375732421875}, {"start": 1075.05, "end": 1075.47, "word": " عبارة", "probability": 0.85015869140625}, {"start": 1075.47, "end": 1075.59, "word": " عن", "probability": 0.98681640625}, {"start": 1075.59, "end": 1076.39, "word": " فرضيتين", "probability": 0.8236083984375}, {"start": 1076.39, "end": 1076.55, "word": " مع", "probability": 0.98193359375}, {"start": 1076.55, "end": 1076.93, "word": " بعض", "probability": 0.98974609375}, {"start": 1076.93, "end": 1077.33, "word": " هو", "probability": 0.51611328125}, {"start": 1077.33, "end": 1077.65, "word": " عبارة", "probability": 0.9600830078125}, {"start": 1077.65, "end": 1077.79, "word": " عن", "probability": 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diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/gWNV6nTT2VQ_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/gWNV6nTT2VQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..92ddeeb2f4927ad805ffa8afef88507eeabdadb3
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/gWNV6nTT2VQ_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4112, "start": 21.38, "end": 41.12, "text": "بسم الله الرحمن الرحيم نواصل في مصداق مبادئ الرياضيات ونظرية المجموعات اليوم إن شاء الله هنواصل في الموضوع اللي هو التفكير الاستدلالي أو التفكير اللي هو القياسي المنطقي أو الاستنباطي ببعض الأحيان بيعربه طبعا هو deductive reasoning", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 2407, 33546, 1211, 8978, 3714, 9381, 28259, 4587, 3714, 3555, 18513, 19986, 2423, 16572, 46958, 1829, 9307, 4032, 1863, 19913, 2288, 10632, 9673, 7435, 2304, 45367, 9307, 45595, 20498, 36145, 13412, 16606, 21984, 8032, 1863, 2407, 33546, 1211, 8978, 9673, 2407, 11242, 45367, 13672, 1829, 31439, 16712, 5172, 4117, 13546, 42963, 14851, 3215, 1211, 6027, 1829, 34051, 16712, 5172, 4117, 13546, 13672, 1829, 31439, 25062, 25528, 3794, 1829, 9673, 1863, 9566, 38436, 34051, 42963, 14851, 1863, 3555, 41193, 1829, 4724, 3555, 3615, 11242, 16247, 5016, 1829, 7649, 4724, 40228, 25513, 3224, 23032, 3555, 3615, 995, 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قلنا هذا هو بشكل عام الـ deductive reasoning طب بهذا ال section هنستخدمه لإثبات التضمين والتكافأة و بعدين هنستخدمه استخدامات متعددة في الرياضيات لكن في هذا ال section بشكل خاص هنستخدمه كطريقة بديلة لجداول الصدق لإثبات", "tokens": [9566, 3555, 3615, 995, 1975, 5016, 8315, 12174, 1211, 8315, 23758, 31439, 4724, 8592, 28820, 6225, 10943, 2423, 39184, 31513, 488, 21577, 23032, 3555, 39627, 15730, 2423, 3541, 8032, 1863, 14851, 9778, 40448, 3224, 5296, 28814, 12984, 3555, 9307, 16712, 11242, 2304, 9957, 16070, 2655, 4117, 31845, 10721, 3660, 4032, 39182, 9957, 8032, 1863, 14851, 9778, 40448, 3224, 44713, 9778, 3215, 10943, 9307, 44650, 22488, 41891, 8978, 2423, 16572, 46958, 1829, 9307, 44381, 8978, 23758, 2423, 3541, 4724, 8592, 28820, 16490, 33546, 8032, 1863, 14851, 9778, 40448, 3224, 9122, 9566, 16572, 28671, 4724, 16254, 37977, 5296, 7435, 28259, 12610, 31767, 3215, 4587, 5296, 28814, 12984, 3555, 9307], "avg_logprob": -0.14901620411762484, "compression_ratio": 1.8421052631578947, 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"end": 178.78, "word": " تنطبق", "probability": 0.9345703125}, {"start": 178.78, "end": 178.94, "word": " عليها", "probability": 0.82080078125}, {"start": 178.94, "end": 179.5, "word": " النظرية،", "probability": 0.91865234375}, {"start": 179.5, "end": 179.62, "word": " إذا", "probability": 0.964599609375}, {"start": 179.62, "end": 180.02, "word": " خطوتي", "probability": 0.8837890625}, {"start": 180.02, "end": 180.46, "word": " صح،", "probability": 0.9235026041666666}, {"start": 180.46, "end": 180.62, "word": " لا", "probability": 0.5498046875}, {"start": 180.62, "end": 181.04, "word": " تنطبق", "probability": 0.9845703125}, {"start": 181.04, "end": 181.44, "word": " النظرية", "probability": 0.8525390625}, {"start": 181.44, "end": 181.56, "word": " إذا", "probability": 0.956298828125}, {"start": 181.56, "end": 181.82, "word": " الخطوة", "probability": 0.9534912109375}, {"start": 181.82, "end": 182.06, "word": " بتكون", "probability": 0.6944580078125}, {"start": 182.06, "end": 182.38, 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"word": " كمان", "probability": 0.9073893229166666}, {"start": 204.37, "end": 204.81, "word": " مثال", "probability": 0.98583984375}, {"start": 204.81, "end": 205.35, "word": " ونأكد", "probability": 0.94580078125}, {"start": 205.35, "end": 205.59, "word": " على", "probability": 0.9541015625}, {"start": 205.59, "end": 206.33, "word": " هذه", "probability": 0.98291015625}, {"start": 206.33, "end": 207.53, "word": " الأفكار", "probability": 0.9830322265625}, {"start": 207.53, "end": 209.63, "word": " فالمثال", "probability": 0.966552734375}, {"start": 209.63, "end": 210.29, "word": " التاني", "probability": 0.9627278645833334}, {"start": 210.29, "end": 210.87, "word": " على", "probability": 0.94970703125}, {"start": 210.87, "end": 211.15, "word": " هذا", "probability": 0.9482421875}, {"start": 211.15, "end": 211.77, "word": " الموضوع", "probability": 0.998779296875}], "temperature": 1.0}, {"id": 9, "seek": 23174, "start": 212.54, "end": 231.74, "text": "أه بطبعا صيغ مدعدي ده الممكن المثال لكن الشاهد اللي هو prove the disjunction syllogism قانون أخدناها من القوانين بتاعة الاستدلال اللي هو P or Q and not P implies Q تضمين احنا قولنا يا equivalence يا implications", "tokens": [10721, 3224, 4724, 9566, 3555, 3615, 995, 20328, 1829, 17082, 3714, 3215, 3615, 16254, 11778, 3224, 9673, 43020, 9673, 12984, 6027, 44381, 25124, 40294, 3215, 13672, 1829, 31439, 7081, 264, 717, 10010, 882, 20223, 664, 1434, 12174, 7649, 11536, 5551, 9778, 3215, 8315, 11296, 9154, 25062, 2407, 7649, 9957, 39894, 995, 27884, 42963, 14851, 3215, 1211, 6027, 13672, 1829, 31439, 430, 420, 1249, 293, 406, 430, 18779, 1249, 6055, 11242, 2304, 9957, 1975, 5016, 8315, 12174, 12610, 8315, 35186, 9052, 655, 35186, 16602], "avg_logprob": -0.22116815422972044, "compression_ratio": 1.507177033492823, "no_speech_prob": 0.0, "words": [{"start": 212.54, "end": 213.24, "word": "أه", "probability": 0.60223388671875}, {"start": 213.24, "end": 213.9, "word": " بطبعا", "probability": 0.7401123046875}, {"start": 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التجاهين اللي حكينا عنها لأ مش تضمين تكافؤ بس بالرمز الآخر by deductive method باستخدام طريقة ال deductive reasoning أو طريقة ال deductive فنبدأ نحل هنا", "tokens": [46955, 264, 256, 1375, 1793, 1975, 12984, 3555, 2655, 25062, 7649, 11536, 37495, 22653, 13672, 1829, 31439, 25062, 7649, 11536, 11778, 47302, 15042, 20328, 5016, 1829, 5016, 4724, 17082, 11242, 28239, 19913, 2288, 18871, 9673, 38251, 7578, 31439, 47525, 3224, 7251, 2655, 5172, 995, 4587, 8592, 36764, 24401, 39896, 14851, 9778, 40448, 33688, 8592, 9640, 3660, 16712, 7649, 10632, 24976, 2655, 4117, 31845, 33604, 8608, 995, 16095, 8978, 16712, 7435, 40294, 9957, 13672, 1829, 11331, 4117, 1829, 8315, 18871, 11296, 5296, 10721, 37893, 6055, 11242, 2304, 9957, 6055, 4117, 31845, 33604, 4724, 3794, 20666, 2288, 2304, 11622, 6024, 95, 34740, 538, 31513, 488, 3170, 4724, 995, 14851, 9778, 3215, 10943, 23032, 16572, 28671, 2423, 31513, 488, 21577, 34051, 23032, 16572, 28671, 2423, 31513, 488, 6156, 1863, 44510, 10721, 8717, 5016, 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new file mode 100644
index 0000000000000000000000000000000000000000..3bf8f87451c43c4ce72ea4947760da2efc98d16b
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/jcagcQfZxPU_raw.json
@@ -0,0 +1 @@
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"probability": 0.98046875}, {"start": 1170.38, "end": 1170.62, "word": " بدنا", "probability": 0.8359375}, {"start": 1170.62, "end": 1170.94, "word": " ننفي", "probability": 0.9724934895833334}, {"start": 1170.94, "end": 1171.18, "word": " هذه", "probability": 0.61083984375}, {"start": 1171.18, "end": 1171.86, "word": " الجملة", "probability": 0.9386393229166666}, {"start": 1171.86, "end": 1172.52, "word": " B", "probability": 0.443359375}, {"start": 1172.52, "end": 1173.28, "word": " or", "probability": 0.939453125}, {"start": 1173.28, "end": 1174.46, "word": " not", "probability": 0.94140625}, {"start": 1174.46, "end": 1175.14, "word": " equal", "probability": 0.83203125}, {"start": 1175.14, "end": 1175.5, "word": " فبدنا", "probability": 0.78076171875}, {"start": 1175.5, "end": 1175.7, "word": " ننفي", "probability": 0.9690755208333334}, {"start": 1175.7, "end": 1175.88, "word": " هذا", "probability": 0.4130859375}, {"start": 1175.88, "end": 1176.26, "word": " العمود", "probability": 0.8816731770833334}, {"start": 1176.26, "end": 1176.88, "word": " أكسه", "probability": 0.713623046875}, {"start": 1176.88, "end": 1177.6, "word": " false", "probability": 0.74853515625}, {"start": 1177.6, "end": 1178.5, "word": " false", "probability": 0.7822265625}, {"start": 1178.5, "end": 1179.1, "word": " true", "probability": 0.98095703125}, {"start": 1179.1, "end": 1179.9, "word": " false", "probability": 0.91162109375}], "temperature": 1.0}, {"id": 48, "seek": 119679, "start": 1180.95, "end": 1196.79, "text": "فزي ما تشوفين عملية سهلة وهي فعلا سهلة فالأمر بسيط بس نستخدم هذه القواعد نقدر نعمل ال truth table لأي statement لأي statement زي ما حكينا في المرة الماضية أي سؤال؟", "tokens": [5172, 11622, 1829, 19446, 6055, 8592, 38688, 9957, 6225, 42213, 10632, 8608, 3224, 37977, 37037, 1829, 6156, 3615, 15040, 8608, 3224, 37977, 6156, 6027, 10721, 29973, 4724, 3794, 1829, 9566, 4724, 3794, 8717, 14851, 9778, 40448, 29538, 25062, 14407, 22488, 8717, 28543, 2288, 8717, 25957, 1211, 2423, 3494, 3199, 5296, 10721, 1829, 5629, 5296, 10721, 1829, 5629, 30767, 1829, 19446, 11331, 4117, 1829, 8315, 8978, 9673, 25720, 9673, 46958, 10632, 36632, 8608, 33604, 6027, 22807], "avg_logprob": -0.1355879891075586, "compression_ratio": 1.576470588235294, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1180.95, "end": 1181.75, "word": "فزي", "probability": 0.7490234375}, {"start": 1181.75, "end": 1181.81, "word": " ما", "probability": 0.958984375}, {"start": 1181.81, "end": 1182.17, "word": " تشوفين", "probability": 0.791015625}, {"start": 1182.17, "end": 1182.47, "word": " عملية", "probability": 0.93896484375}, {"start": 1182.47, "end": 1182.83, "word": " سهلة", "probability": 0.9754231770833334}, {"start": 1182.83, "end": 1183.07, "word": " وهي", "probability": 0.673095703125}, {"start": 1183.07, "end": 1183.37, "word": " فعلا", "probability": 0.93212890625}, {"start": 1183.37, "end": 1183.93, "word": " سهلة", "probability": 0.947265625}, {"start": 1183.93, "end": 1185.47, "word": " فالأمر", "probability": 0.741455078125}, {"start": 1185.47, "end": 1185.87, "word": " بسيط", "probability": 0.995849609375}, {"start": 1185.87, "end": 1186.07, "word": " بس", "probability": 0.932373046875}, {"start": 1186.07, "end": 1186.45, "word": " نستخدم", "probability": 0.970703125}, {"start": 1186.45, "end": 1186.59, "word": " هذه", "probability": 0.83935546875}, {"start": 1186.59, "end": 1187.09, "word": " القواعد", "probability": 0.9635416666666666}, {"start": 1187.09, "end": 1187.99, "word": " نقدر", "probability": 0.8435872395833334}, {"start": 1187.99, "end": 1188.31, "word": " نعمل", "probability": 0.9879557291666666}, {"start": 1188.31, "end": 1188.51, "word": " ال", "probability": 0.56689453125}, {"start": 1188.51, "end": 1189.23, "word": " truth", "probability": 0.779296875}, {"start": 1189.23, "end": 1189.65, "word": " table", "probability": 0.71435546875}, {"start": 1189.65, "end": 1189.93, "word": " لأي", "probability": 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1197.72, "end": 1223.14, "text": "خلّيني أنتقل لنقطة جديدة مهمة اللي هي equivalent statements فهي التقارير المتكافئة التقارير المتكافئة لو أنا عندي تقريرين بقيتش بقول عنهم متكافئين يعني أنا ممكن أستبدل هذه الجملة و أستبدلها بجملة تانية و دول متكافئة تانية و تنصح فالحقيقة في عندنا تعريف لأن دايما احنا بنعطيه اللي بده معنى للصلاحة بالدقيق", "tokens": [9778, 1211, 11703, 9957, 1829, 14739, 2655, 4587, 1211, 5296, 1863, 47432, 3660, 10874, 16254, 41891, 3714, 16095, 3660, 13672, 1829, 39896, 10344, 12363, 6156, 3224, 1829, 16712, 4587, 9640, 13546, 9673, 2655, 4117, 31845, 19986, 3660, 16712, 4587, 9640, 13546, 9673, 2655, 4117, 31845, 19986, 3660, 45164, 41850, 18871, 16254, 6055, 4587, 2288, 13546, 9957, 4724, 4587, 36081, 8592, 4724, 39648, 18871, 16095, 44650, 4117, 31845, 19986, 9957, 37495, 22653, 41850, 3714, 43020, 5551, 14851, 44510, 1211, 29538, 25724, 2304, 37977, 4032, 5551, 14851, 44510, 1211, 11296, 4724, 7435, 2304, 37977, 6055, 7649, 10632, 4032, 11778, 12610, 44650, 4117, 31845, 19986, 3660, 6055, 7649, 10632, 4032, 6055, 1863, 9381, 5016, 6156, 6027, 5016, 38436, 28671, 8978, 43242, 8315, 37279, 16572, 5172, 5296, 33456, 11778, 47302, 15042, 1975, 5016, 8315, 44945, 3615, 9566, 1829, 3224, 13672, 1829, 47525, 3224, 20449, 1863, 7578, 24976, 9381, 15040, 5016, 3660, 20666, 3215, 38436, 4587], "avg_logprob": -0.21134868852402033, "compression_ratio": 1.9706959706959708, "no_speech_prob": 0.0, "words": [{"start": 1197.72, "end": 1198.22, "word": "خلّيني", "probability": 0.86064453125}, {"start": 1198.22, "end": 1198.78, "word": " أنتقل", "probability": 0.822265625}, {"start": 1198.78, "end": 1199.52, "word": " لنقطة", "probability": 0.94482421875}, {"start": 1199.52, "end": 1199.98, "word": " جديدة", "probability": 0.9768880208333334}, {"start": 1199.98, "end": 1201.24, "word": " مهمة", "probability": 0.8771158854166666}, {"start": 1201.24, "end": 1201.82, "word": " اللي", "probability": 0.5516357421875}, {"start": 1201.82, "end": 1202.2, "word": " هي", 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"end": 1212.62, "word": " بقيتش", "probability": 0.502838134765625}, {"start": 1212.62, "end": 1212.8, "word": " بقول", "probability": 0.952880859375}, {"start": 1212.8, "end": 1213.0, "word": " عنهم", "probability": 0.83251953125}, {"start": 1213.0, "end": 1213.58, "word": " متكافئين", "probability": 0.991015625}, {"start": 1213.58, "end": 1213.68, "word": " يعني", "probability": 0.8984375}, {"start": 1213.68, "end": 1213.82, "word": " أنا", "probability": 0.6201171875}, {"start": 1213.82, "end": 1213.96, "word": " ممكن", "probability": 0.982421875}, {"start": 1213.96, "end": 1214.42, "word": " أستبدل", "probability": 0.908447265625}, {"start": 1214.42, "end": 1214.58, "word": " هذه", "probability": 0.93505859375}, {"start": 1214.58, "end": 1215.06, "word": " الجملة", "probability": 0.9542643229166666}, {"start": 1215.06, "end": 1215.64, "word": " و", "probability": 0.79345703125}, {"start": 1215.64, "end": 1216.26, "word": " أستبدلها", "probability": 0.95947265625}, {"start": 1216.26, "end": 1216.64, "word": " بجملة", "probability": 0.96923828125}, {"start": 1216.64, "end": 1216.82, "word": " تانية", "probability": 0.8736979166666666}, {"start": 1216.82, "end": 1216.96, "word": " و", "probability": 0.71728515625}, {"start": 1216.96, "end": 1217.04, "word": " دول", "probability": 0.785888671875}, {"start": 1217.04, "end": 1217.56, "word": " متكافئة", "probability": 0.970703125}, {"start": 1217.56, "end": 1217.72, "word": " تانية", "probability": 0.9225260416666666}, {"start": 1217.72, "end": 1217.8, "word": " و", "probability": 0.5126953125}, {"start": 1217.8, "end": 1218.46, "word": " تنصح", "probability": 0.9134521484375}, {"start": 1218.46, "end": 1219.78, "word": " فالحقيقة", "probability": 0.93154296875}, {"start": 1219.78, "end": 1219.88, "word": " في", "probability": 0.78857421875}, {"start": 1219.88, "end": 1220.08, "word": " عندنا", "probability": 0.553436279296875}, {"start": 1220.08, "end": 1220.5, "word": " تعريف", "probability": 0.99365234375}, {"start": 1220.5, "end": 1220.74, "word": " لأن", "probability": 0.6553955078125}, {"start": 1220.74, "end": 1220.98, "word": " دايما", "probability": 0.6658528645833334}, {"start": 1220.98, "end": 1221.14, "word": " احنا", "probability": 0.7920735677083334}, {"start": 1221.14, "end": 1221.48, "word": " بنعطيه", "probability": 0.607763671875}, {"start": 1221.48, "end": 1221.6, "word": " اللي", "probability": 0.605712890625}, {"start": 1221.6, "end": 1221.76, "word": " بده", "probability": 0.4931640625}, {"start": 1221.76, "end": 1221.98, "word": " معنى", "probability": 0.91943359375}, {"start": 1221.98, "end": 1222.52, "word": " للصلاحة", "probability": 0.676953125}, {"start": 1222.52, "end": 1223.14, "word": " بالدقيق", "probability": 0.9315185546875}], "temperature": 1.0}, {"id": 50, "seek": 123960, "start": 1223.65, "end": 1239.61, "text": "فعنا تعريف two statements capital B and capital Q طبعا زي اللي بتذكروا الفعادة الأولى اليوم اللي قولنا ما زال capital B و capital Q متوقع انهم يكونوا compound لا هنا بقى أكيد بيقولي هي simple او compound اي two statement بغض النظر ايش بيكونوا بقول عنهم انهم", "tokens": [5172, 3615, 8315, 37279, 16572, 5172, 732, 12363, 4238, 363, 293, 4238, 1249, 23032, 3555, 3615, 995, 30767, 1829, 13672, 1829, 39894, 8848, 37983, 14407, 27188, 3615, 18513, 3660, 16247, 12610, 7578, 45595, 20498, 13672, 1829, 12174, 12610, 8315, 19446, 30767, 6027, 4238, 363, 4032, 4238, 1249, 44650, 30543, 3615, 16472, 16095, 7251, 30544, 14407, 14154, 20193, 34105, 4724, 4587, 7578, 5551, 4117, 25708, 4724, 1829, 39648, 1829, 39896, 2199, 1975, 2407, 14154, 1975, 1829, 732, 5629, 4724, 17082, 11242, 28239, 19913, 2288, 1975, 1829, 8592, 4724, 1829, 30544, 14407, 4724, 39648, 18871, 16095, 16472, 16095], "avg_logprob": -0.28318298969072164, "compression_ratio": 1.7342342342342343, "no_speech_prob": 0.0, "words": [{"start": 1223.65, "end": 1224.01, "word": "فعنا", "probability": 0.8074544270833334}, {"start": 1224.01, "end": 1224.53, "word": " تعريف", 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"probability": 0.9811197916666666}], "temperature": 1.0}, {"id": 60, "seek": 146950, "start": 1444.26, "end": 1469.5, "text": "بدي أقارنه مع مين؟ مع هذا العمود فواضح أن هاي force مع بعض و false مع بعض true مع بعض و false مع بعض فواضح من الجدول أنهم فعلا ياش equivalent فنحن نحط بعض و نعمل جدول و نقوله هنا إيش بجيت الحل from the table we see that اللي هو ما ياش نط", "tokens": [3555, 16254, 5551, 4587, 9640, 1863, 3224, 20449, 3714, 9957, 22807, 20449, 23758, 18863, 2304, 23328, 6156, 2407, 46958, 5016, 14739, 8032, 47302, 3464, 20449, 45030, 11242, 4032, 7908, 20449, 45030, 11242, 2074, 20449, 45030, 11242, 4032, 7908, 20449, 45030, 11242, 6156, 2407, 46958, 5016, 9154, 25724, 3215, 12610, 14739, 16095, 6156, 3615, 15040, 7251, 33599, 10344, 6156, 1863, 5016, 1863, 8717, 5016, 9566, 45030, 11242, 4032, 8717, 25957, 1211, 10874, 3215, 12610, 4032, 8717, 39648, 3224, 34105, 11933, 1829, 8592, 4724, 7435, 36081, 21542, 1211, 490, 264, 3199, 321, 536, 300, 13672, 1829, 31439, 19446, 7251, 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و", "probability": 0.28564453125}, {"start": 1456.96, "end": 1457.12, "word": " نعمل", "probability": 0.9212239583333334}, {"start": 1457.12, "end": 1457.44, "word": " جدول", "probability": 0.8790690104166666}, {"start": 1457.44, "end": 1457.56, "word": " و", "probability": 0.5732421875}, {"start": 1457.56, "end": 1457.84, "word": " نقوله", "probability": 0.7478841145833334}, {"start": 1457.84, "end": 1458.06, "word": " هنا", "probability": 0.397705078125}, {"start": 1458.06, "end": 1458.46, "word": " إيش", "probability": 0.8844401041666666}, {"start": 1458.46, "end": 1458.74, "word": " بجيت", "probability": 0.79443359375}, {"start": 1458.74, "end": 1459.14, "word": " الحل", "probability": 0.95947265625}, {"start": 1459.14, "end": 1460.32, "word": " from", "probability": 0.5869140625}, {"start": 1460.32, "end": 1460.6, "word": " the", "probability": 0.8857421875}, {"start": 1460.6, "end": 1461.0, "word": " table", "probability": 0.92041015625}, {"start": 1461.0, "end": 1465.2, "word": " we", "probability": 0.7705078125}, {"start": 1465.2, "end": 1465.6, "word": " see", "probability": 0.94189453125}, {"start": 1465.6, "end": 1466.58, "word": " that", "probability": 0.9560546875}, {"start": 1466.58, "end": 1468.18, "word": " اللي", "probability": 0.782958984375}, {"start": 1468.18, "end": 1468.26, "word": " هو", "probability": 0.96337890625}, {"start": 1468.26, "end": 1468.46, "word": " ما", "probability": 0.576171875}, {"start": 1468.46, "end": 1468.74, "word": " ياش", "probability": 0.736083984375}, {"start": 1468.74, "end": 1469.5, "word": " نط", "probability": 0.598388671875}], "temperature": 1.0}, {"id": 61, "seek": 149105, "start": 1471.17, "end": 1491.05, "text": "بر.q تكافئ not b and q فمن الجدول هذه الجواب الجدول لحاله بكفيه عشان يكون جوابنا جواب نموذج وكامل واضح من الجدول احنا استخدمنا الجدول اللي هو الجدول بيدل على ان الحال صحيح من العمودين اللي هو الرابع العمود الخامس والاخير", "tokens": [26890, 13, 80, 6055, 4117, 31845, 19986, 406, 272, 293, 9505, 6156, 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1480.65, "word": " يكون", "probability": 0.841796875}, {"start": 1480.65, "end": 1481.17, "word": " جوابنا", "probability": 0.90869140625}, {"start": 1481.17, "end": 1481.91, "word": " جواب", "probability": 0.8616536458333334}, {"start": 1481.91, "end": 1482.35, "word": " نموذج", "probability": 0.980859375}, {"start": 1482.35, "end": 1482.93, "word": " وكامل", "probability": 0.89599609375}, {"start": 1482.93, "end": 1483.61, "word": " واضح", "probability": 0.98291015625}, {"start": 1483.61, "end": 1483.73, "word": " من", "probability": 0.97998046875}, {"start": 1483.73, "end": 1484.01, "word": " الجدول", "probability": 0.98583984375}, {"start": 1484.01, "end": 1484.15, "word": " احنا", "probability": 0.7765299479166666}, {"start": 1484.15, "end": 1484.45, "word": " استخدمنا", "probability": 0.76129150390625}, {"start": 1484.45, "end": 1484.79, "word": " الجدول", "probability": 0.9710286458333334}, {"start": 1484.79, "end": 1484.91, "word": " اللي", "probability": 0.641357421875}, 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التالية باستخدام أداة الربط and بنفع؟ نعم لإن انا اتقول اللي عرفناها هنا هي not bhb and not q فبدنا نستخدم هذا الكلام نشوف كيف نعكسها وكيف لما نترجمها حاليا بتجينا نفس المعنى ولا لأ", "tokens": [40294, 34105, 47525, 8315, 8717, 10721, 4117, 3215, 15844, 16712, 3615, 16572, 5172, 13672, 1829, 6225, 42213, 8315, 3224, 5296, 33456, 3224, 3714, 16095, 6156, 44510, 8315, 8717, 2655, 3615, 23328, 47356, 4032, 44510, 8315, 13672, 1829, 31439, 8717, 39237, 19452, 9154, 3224, 6156, 3555, 2655, 3215, 9957, 1829, 50113, 6027, 4724, 1829, 39648, 1829, 2464, 264, 3480, 27708, 5629, 382, 257, 27482, 1975, 4117, 2655, 3555, 25724, 2304, 37977, 25124, 2288, 9566, 10632, 16712, 6027, 10632, 4724, 995, 14851, 9778, 3215, 10943, 5551, 28259, 3660, 2423, 25513, 9566, 293, 44945, 5172, 3615, 22807, 8717, 25957, 5296, 28814, 1863, 1975, 8315, 1975, 2655, 39648, 13672, 1829, 6225, 28480, 8315, 11296, 34105, 39896, 406, 41221, 65, 293, 406, 9505, 6156, 44510, 8315, 8717, 14851, 9778, 40448, 23758, 2423, 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"probability": 0.893310546875}, {"start": 2506.06, "end": 2506.28, "word": " بعد", "probability": 0.875}, {"start": 2506.28, "end": 2506.62, "word": " الوعد", "probability": 0.9319661458333334}, {"start": 2506.62, "end": 2507.14, "word": " لكن", "probability": 0.75048828125}, {"start": 2507.14, "end": 2507.74, "word": " ماحدش", "probability": 0.8375651041666666}, {"start": 2507.74, "end": 2507.94, "word": " طالب", "probability": 0.9622395833333334}, {"start": 2507.94, "end": 2508.18, "word": " منك", "probability": 0.968017578125}, {"start": 2508.18, "end": 2508.48, "word": " الوعد", "probability": 0.9527994791666666}, {"start": 2508.48, "end": 2508.8, "word": " هيك", "probability": 0.6783447265625}, {"start": 2508.8, "end": 2509.02, "word": " يعني", "probability": 0.7265625}, {"start": 2509.02, "end": 2509.18, "word": " هو", "probability": 0.51220703125}, {"start": 2509.18, "end": 2509.74, "word": " هذا", "probability": 0.32177734375}, {"start": 2509.74, "end": 2510.02, "word": " شيء", "probability": 0.82861328125}, {"start": 2510.02, "end": 2510.54, "word": " اختياري", "probability": 0.92294921875}, {"start": 2510.54, "end": 2511.32, "word": " كافي", "probability": 0.8776041666666666}, {"start": 2511.32, "end": 2511.84, "word": " اتحقق", "probability": 0.90732421875}, {"start": 2511.84, "end": 2511.94, "word": " او", "probability": 0.733154296875}, {"start": 2511.94, "end": 2512.58, "word": " مااتحققش", "probability": 0.84326171875}, {"start": 2512.58, "end": 2512.98, "word": " انت", "probability": 0.942138671875}, {"start": 2512.98, "end": 2513.24, "word": " حر", "probability": 0.8955078125}, {"start": 2513.24, "end": 2513.76, "word": " تواعد", "probability": 0.7381184895833334}, {"start": 2513.76, "end": 2513.9, "word": " او", "probability": 0.948486328125}, {"start": 2513.9, "end": 2514.32, "word": " ماتواعدش", "probability": 0.82392578125}, {"start": 2514.32, "end": 2514.5, "word": " انت", "probability": 0.952880859375}, {"start": 2514.5, "end": 2514.74, "word": " حر", "probability": 0.984130859375}, {"start": 2514.74, "end": 2515.18, "word": " لكن", "probability": 0.9296875}, {"start": 2515.18, "end": 2515.46, "word": " اذا", "probability": 0.8408203125}, {"start": 2515.46, "end": 2515.92, "word": " وعدت", "probability": 0.9816080729166666}, {"start": 2515.92, "end": 2516.52, "word": " انت", "probability": 0.902099609375}, {"start": 2516.52, "end": 2516.84, "word": " لازم", "probability": 0.986328125}, {"start": 2516.84, "end": 2517.2, "word": " تحقق", "probability": 0.924072265625}, {"start": 2517.2, "end": 2517.4, "word": " الوعد", "probability": 0.9383138020833334}, {"start": 2517.4, "end": 2517.6, "word": " فـ", "probability": 0.686767578125}, {"start": 2517.6, "end": 2517.68, "word": " Q", "probability": 0.53955078125}, {"start": 2517.68, "end": 2518.12, "word": " نسلي", "probability": 0.6053059895833334}, {"start": 2518.12, "end": 2518.3, "word": " اذا", "probability": 0.7900390625}, {"start": 2518.3, "end": 2518.66, "word": " وعدت", "probability": 0.9938151041666666}, {"start": 2518.66, "end": 2519.14, "word": " ضروري", "probability": 0.97265625}, {"start": 2519.14, "end": 2519.56, "word": " تحقق", "probability": 0.847412109375}, {"start": 2519.56, "end": 2519.86, "word": " الوعد", "probability": 0.9601236979166666}, {"start": 2519.86, "end": 2520.5, "word": " فهذه", "probability": 0.9256184895833334}, {"start": 2520.5, "end": 2520.78, "word": " بتيجي", "probability": 0.8046875}, {"start": 2520.78, "end": 2521.02, "word": " بعض", "probability": 0.972900390625}, {"start": 2521.02, "end": 2521.52, "word": " المعاني", "probability": 0.9571533203125}, {"start": 2521.52, "end": 2522.16, "word": " اللي", "probability": 0.92822265625}, {"start": 2522.16, "end": 2522.62, "word": " ابن", "probability": 0.6263427734375}, {"start": 2522.62, "end": 2523.24, "word": " استخدمها", "probability": 0.953125}, {"start": 2523.24, "end": 2524.68, "word": " مثال", "probability": 0.958740234375}, {"start": 2524.68, "end": 2525.18, "word": " اخر", "probability": 0.779541015625}, {"start": 2525.18, "end": 2526.06, "word": " Q", "probability": 0.4111328125}, {"start": 2526.06, "end": 2526.96, "word": " whenever", "probability": 0.837890625}, {"start": 2526.96, "end": 2528.08, "word": " B", "probability": 0.36181640625}], "temperature": 1.0}, {"id": 107, "seek": 254201, "start": 2532.31, "end": 2542.01, "text": "تمام فهنا إما كان مناسب حتى نتوقف فان شاء الله المرة الجاية بنكمل معه اللي هو الرابط الأخير وهو ال by condition دي كل عافية", "tokens": [39237, 10943, 6156, 3224, 8315, 11933, 15042, 25961, 3714, 8315, 35457, 11331, 49975, 8717, 2655, 30543, 5172, 6156, 7649, 13412, 16606, 21984, 9673, 25720, 25724, 995, 10632, 44945, 24793, 1211, 20449, 3224, 13672, 1829, 31439, 34892, 16758, 9566, 16247, 9778, 13546, 37037, 2407, 2423, 538, 4188, 11778, 1829, 28242, 6225, 31845, 10632], "avg_logprob": -0.2522110894041241, "compression_ratio": 1.4452054794520548, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 2532.31, "end": 2532.75, "word": "تمام", "probability": 0.720947265625}, {"start": 2532.75, "end": 2533.07, "word": " فهنا", "probability": 0.6717122395833334}, {"start": 2533.07, "end": 2533.25, "word": " إما", "probability": 0.365478515625}, {"start": 2533.25, "end": 2533.59, "word": " كان", "probability": 0.9873046875}, {"start": 2533.59, "end": 2534.43, "word": " مناسب", "probability": 0.92431640625}, {"start": 2534.43, "end": 2534.69, "word": " حتى", "probability": 0.911865234375}, {"start": 2534.69, "end": 2535.35, "word": " نتوقف", "probability": 0.991943359375}, {"start": 2535.35, "end": 2536.11, "word": " فان", "probability": 0.5447998046875}, {"start": 2536.11, "end": 2536.33, "word": " شاء", "probability": 0.93017578125}, {"start": 2536.33, "end": 2536.53, "word": " الله", "probability": 0.93408203125}, {"start": 2536.53, "end": 2536.87, "word": " المرة", "probability": 0.96337890625}, {"start": 2536.87, "end": 2537.15, "word": " الجاية", "probability": 0.9244791666666666}, {"start": 2537.15, "end": 2537.63, "word": " بنكمل", "probability": 0.90625}, {"start": 2537.63, "end": 2538.11, "word": " معه", "probability": 0.6767578125}, {"start": 2538.11, "end": 2538.47, "word": " اللي", "probability": 0.832275390625}, {"start": 2538.47, "end": 2538.59, "word": " هو", "probability": 0.98095703125}, {"start": 2538.59, "end": 2538.91, "word": " الرابط", "probability": 0.9635416666666666}, {"start": 2538.91, "end": 2539.37, "word": " الأخير", "probability": 0.89794921875}, {"start": 2539.37, "end": 2539.85, "word": " وهو", "probability": 0.87109375}, {"start": 2539.85, "end": 2540.01, "word": " ال", "probability": 0.8603515625}, {"start": 2540.01, "end": 2540.33, "word": " by", "probability": 0.39453125}, {"start": 2540.33, "end": 2540.85, "word": " condition", "probability": 0.892578125}, {"start": 2540.85, "end": 2541.57, "word": " دي", "probability": 0.6751708984375}, {"start": 2541.57, "end": 2541.69, "word": " كل", "probability": 0.75048828125}, {"start": 2541.69, "end": 2542.01, "word": " عافية", "probability": 0.5904947916666666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2542.23675, "duration_after_vad": 2437.524374999994}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/kzlMpUaJYbM_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/kzlMpUaJYbM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7260f604ace065ca3ada69f3cf31756966705215
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/kzlMpUaJYbM_postprocess.srt
@@ -0,0 +1,2796 @@
+1
+00:00:21,040 --> 00:00:24,640
+بسم الله الرحمن الرحيم اليوم ان شاء الله هنواصل
+
+2
+00:00:24,640 --> 00:00:29,720
+معه اللي هو عائلات مؤرشفة من المجموعات او indexed
+
+3
+00:00:29,720 --> 00:00:34,420
+families of sets كما ذكرت في المحاضرة الماضية كان
+
+4
+00:00:34,420 --> 00:00:39,160
+في مخدمة عن الموضوع الهدف الرئيسي بدناش نطوح و
+
+5
+00:00:39,160 --> 00:00:42,560
+نبعد كتير انه انا بدأ اتعامل مع عدد كبير من
+
+6
+00:00:42,560 --> 00:00:46,810
+المجموعاتالمجموعة أو ال collection لهذه المجموعات
+
+7
+00:00:46,810 --> 00:00:49,370
+هسميه family بدل ما أسميه set of sets هسميها
+
+8
+00:00:49,370 --> 00:00:54,230
+family of sets فده هو الأصل طبعا عشان نسهل العملية
+
+9
+00:00:54,230 --> 00:00:58,310
+للتعامل مع هذا العدد الكبير بنحاول إيش؟ نرتبهم
+
+10
+00:00:58,310 --> 00:01:03,330
+بشكل مناسب أو نرقمهم أو نسميهم أو ن archefهم زي ما
+
+11
+00:01:03,330 --> 00:01:06,490
+حكي أن اللي عنده كتب كتيرة بقى بيرتبهم بالمكتب
+
+12
+00:01:06,490 --> 00:01:08,470
+اللي عنده كتابين بيحطهم كذا في مكان ما و بيلاجيهم
+
+13
+00:01:08,470 --> 00:01:11,450
+لكن اللي عنده مية كتابجيد انه ي archive هم بطريقة
+
+14
+00:01:11,450 --> 00:01:14,310
+معينة عشان يسهل الوصول نفس القضية لو احنا نتعامل
+
+15
+00:01:14,310 --> 00:01:17,590
+مع عدد كبير من المجموعات نحتاج انه ن archive هم
+
+16
+00:01:17,590 --> 00:01:23,290
+نعملهم ترتيب معين نرقمهم نسميهم حتى نسهل العملية
+
+17
+00:01:23,290 --> 00:01:27,950
+فطبعا التعريف يعني بكل بساطة انه انا في عندي
+
+18
+00:01:27,950 --> 00:01:33,420
+family مجموعاتمش مرتبة عشوائية بس عدد كبير فانا
+
+19
+00:01:33,420 --> 00:01:38,240
+بتروح عياش بختار طريقة أرشفة معينة طريقة ترتيب
+
+20
+00:01:38,240 --> 00:01:42,600
+معين ترقيب معين من مقاد المجموعة أو الطريقة
+
+21
+00:01:42,600 --> 00:01:45,540
+بتسميها capital gamma اللي بتاخد منها عياش الأسماء
+
+22
+00:01:45,540 --> 00:01:49,890
+الأرقام اه و بنروح لكلرقم بنقول هذه المجموعة رقم
+
+23
+00:01:49,890 --> 00:01:53,690
+واحد هذه المجموعة رقم اتنين هذه المجموعة فاطمة هذه
+
+24
+00:01:53,690 --> 00:01:56,930
+المجموعة خديجة تسمي المهم ان انا بدأ أسمي ارتب و
+
+25
+00:01:56,930 --> 00:02:00,390
+هكذا فهي كل التعريف باختصار التعريف مش كتير بنطبق
+
+26
+00:02:00,390 --> 00:02:03,130
+عليه اللي هو بنبنيش عليه عمل كتير بس انا بدأ افهم
+
+27
+00:02:03,130 --> 00:02:06,870
+ايش معناه index يعني مرقمة مرتبة طبعا احنا مش
+
+28
+00:02:06,870 --> 00:02:09,910
+بنقولش ترقيم لأن مش ضروري التسمي تكون ارقام ممكن
+
+29
+00:02:09,910 --> 00:02:13,850
+اسميهم بطريقة مش ارقام فهي ممكن اعملهم اي code اي
+
+30
+00:02:13,850 --> 00:02:18,620
+ترقيم اي تكشيفخلّيني أشوف بعض الأمثلة و نبدأ بمثال
+
+31
+00:02:18,620 --> 00:02:21,740
+بسيط جداً طبعا مش هو هذا الهدف الرئيسي أنا فيه
+
+32
+00:02:21,740 --> 00:02:24,880
+عندي family of three sets طبعا مش هذا الهدف احنا
+
+33
+00:02:24,880 --> 00:02:27,540
+بدنا نعمل جمعية كبيرة لكن اللي بيفهم الصغير ممكن
+
+34
+00:02:27,540 --> 00:02:30,460
+يفهم الكبير و هكذا ببدأ واحد بالأمثلة البسيطة و
+
+35
+00:02:30,460 --> 00:02:34,620
+بتدرج في الفهم اه فاول بيقوللي هاي عندك family of
+
+36
+00:02:34,620 --> 00:02:38,260
+three sets اه بيقول ايه و بده ايش بيقوللي هاي
+
+37
+00:02:38,260 --> 00:02:41,620
+طريقة ايش التسمية طريقة الترتيب ايش هي ترقيم
+
+38
+00:02:41,620 --> 00:02:44,500
+متتالي واحد اتنين تلاتة فهي ال capital gamma فانا
+
+39
+00:02:44,500 --> 00:02:48,210
+بدأ اختارلأ ال power set مختلفة ال power set تختصب
+
+40
+00:02:48,210 --> 00:02:51,670
+set من المجموعة نفسها طبعا هي صحيح إنها مجموعة
+
+41
+00:02:51,670 --> 00:02:56,550
+عنصرها مجموعات بس مش كل family هي power set ال
+
+42
+00:02:56,550 --> 00:02:58,970
+power set ممكن تكون family بس احنا بنتعامل معاها ك
+
+43
+00:02:58,970 --> 00:03:03,210
+set فالوضع أيش مختلف يعني حالة خاصة ال power set
+
+44
+00:03:03,210 --> 00:03:06,290
+مش احنا بنتعامل بشكل عام يعني ممكن هدول المجموعات
+
+45
+00:03:06,290 --> 00:03:08,730
+اللي في ال family يكونوا مالو مش علاقة مع بعض لكن
+
+46
+00:03:08,730 --> 00:03:11,230
+اللي في ال power set كلهم sub set من مجموعة معينة
+
+47
+00:03:11,230 --> 00:03:14,980
+ا ايه واضحة دي حالة خاصة ال power setالتماع فبقولي
+
+48
+00:03:14,980 --> 00:03:18,500
+write the family ad as an index family of six
+
+49
+00:03:18,500 --> 00:03:23,100
+indexed by gamma بقولي اكتب هذه العائلة بك مجموعة
+
+50
+00:03:23,100 --> 00:03:28,840
+مرقمة مرتبة مؤرشفة باستخدام ال archive gamma ده هي
+
+51
+00:03:28,840 --> 00:03:32,460
+طريقة الارشفة طريقة التسمي يعني إيش ترقيم طريقة
+
+52
+00:03:32,460 --> 00:03:36,140
+الترقيم فطبعا كيف بنحل؟ خلينا نحل مع بعض العملية
+
+53
+00:03:36,140 --> 00:03:41,150
+سهلةexample one ف solution اه فطبعا بدي اروح انا
+
+54
+00:03:41,150 --> 00:03:46,070
+ايش ايه عندي تلت مجموعات فاقوله let اللي هي ايش a
+
+55
+00:03:46,070 --> 00:03:50,570
+one تساوي المجموعة اللي هي سالب واحد و سالب اتنين
+
+56
+00:03:50,570 --> 00:03:55,670
+اذا انا ايش عملت اول عنصر اول عضو في ال family
+
+57
+00:03:55,670 --> 00:03:58,970
+سميته a one وهي الجالية فرقمته واضح اه فدي
+
+58
+00:03:58,970 --> 00:04:05,200
+المجموعة طبعا بعدين ايش بنعمل a twoA2 تساوي تسمية
+
+59
+00:04:05,200 --> 00:04:13,980
+جاد بسميها المجموعة ABC ABC واضح ليس إلا تسمية
+
+60
+00:04:13,980 --> 00:04:18,300
+أرقيم عملية سهلة لا بدأ حساب ولا شيء مجرد استخدام
+
+61
+00:04:18,300 --> 00:04:24,880
+رموز وتسميات صفر و A و واحد فهي ايه ايه ايه ايه
+
+62
+00:04:24,880 --> 00:04:30,190
+ايه ايه ايهمش .. مش شرط .. مش شرط لأن ال .. يعني
+
+63
+00:04:30,190 --> 00:04:32,390
+الترتيب مش ضروري في ال family احنا قلنا بس
+
+64
+00:04:32,390 --> 00:04:35,450
+التكاريب ضروري الترتيب مش مهم .. مش مهم الترتيب
+
+65
+00:04:35,450 --> 00:04:43,710
+فإن صارت ال family إيش؟ then the family can
+
+66
+00:04:43,710 --> 00:04:48,970
+be written as فبقدرتوا
+
+67
+00:04:48,970 --> 00:04:55,830
+بالfamily المعطية على صورة إيش؟ A1 A2 A3
+
+68
+00:04:58,170 --> 00:05:01,950
+فأحد الفوائد أنه بدل ما اكتبها بطريقة الصريحة هذه
+
+69
+00:05:01,950 --> 00:05:05,650
+لو بدي اكتبها بشكل مختصر بقى ده مختصر بدي أنصر و
+
+70
+00:05:05,650 --> 00:05:07,810
+بقوله اي واحد و اعرف انا اي واحد ايش في ال Turbos
+
+71
+00:05:07,810 --> 00:05:11,830
+فده بسهل التعامل بدل ما اقوله ايش المجموعة الأولى
+
+72
+00:05:11,830 --> 00:05:14,190
+طب انت ايش تقصد بالأولى؟ طب هو الترتيب مش مهم لكن
+
+73
+00:05:14,190 --> 00:05:17,770
+لما قلتله اي واحد صارت معرفة مين هي اي واحد صح؟
+
+74
+00:05:17,770 --> 00:05:22,390
+فده بسهل التعامل فهذه بس أمثلة بسيطة ايش المقصود
+
+75
+00:05:24,000 --> 00:05:28,220
+نشوف كمان مثال مثال أهم شوية و هذا هو الهدف
+
+76
+00:05:28,220 --> 00:05:32,720
+الرئيسي من عملية العائلات والعائلات المؤرشفة في
+
+77
+00:05:32,720 --> 00:05:36,840
+عندي family إيش فيها مالة نهاية من المجموعات
+
+78
+00:05:36,840 --> 00:05:41,200
+infinite number of sets فبقوللي عندي family إيش
+
+79
+00:05:41,200 --> 00:05:44,360
+الأنصار الأول فيها؟ واحد اتنين اتنين أربع تلاتة
+
+80
+00:05:44,360 --> 00:05:49,130
+ستة إلى مالة نهايةأه فهي بيقول ياش بدنا نعمل عملية
+
+81
+00:05:49,130 --> 00:05:52,610
+indexing بدنا نرقمها برضه لنجلمين من وين تاخد
+
+82
+00:05:52,610 --> 00:05:56,930
+الدليل من الان عملية ياش برضه ترقيم عملية ترقيم
+
+83
+00:05:56,930 --> 00:06:03,110
+فهنا هذا المثال رقم اتنين solution طيب ايش رأيكوا
+
+84
+00:06:03,110 --> 00:06:06,290
+مين المجموعة الأولى واحد اتنين طب اتنين خلينا نعمل
+
+85
+00:06:06,290 --> 00:06:10,890
+المثال مع بعض فالجيت احنا في عندنا ا واحد نسمي اش
+
+86
+00:06:10,890 --> 00:06:17,330
+بتساوي واحد و اتنينو إيه اتنين؟ إيش بتساوي؟ اتنين
+
+87
+00:06:17,330 --> 00:06:21,470
+و أربعة و إيه تلاتة؟ طب إيه بشكل عام بدك تكتب؟ إيه
+
+88
+00:06:21,470 --> 00:06:25,230
+أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه
+
+89
+00:06:25,230 --> 00:06:25,350
+أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه
+
+90
+00:06:25,350 --> 00:06:25,430
+أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه
+
+91
+00:06:25,430 --> 00:06:25,830
+أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه
+
+92
+00:06:25,830 --> 00:06:26,470
+أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه
+
+93
+00:06:26,470 --> 00:06:28,950
+أن؟ إيه أن؟ إيه أن؟ إيه أن؟ إيه
+
+94
+00:06:30,860 --> 00:06:35,200
+فكل عدد طبيعي بجيب المجموعة الأولى واحد اتنين
+
+95
+00:06:35,200 --> 00:06:39,820
+العشرة عشر وعشرين الألف ألف ألفين وها كذا في
+
+96
+00:06:39,820 --> 00:06:42,900
+مجموعة .. كل مجموعة مكوّنة من عنصرين واضح النموذج
+
+97
+00:06:42,900 --> 00:06:47,480
+تبعنا واضح التركيب تبع المجموعات الداني أول أمثلة
+
+98
+00:06:47,480 --> 00:06:50,180
+وجالي بتمشي بنفس السياب على نفس النمط على نفس
+
+99
+00:06:50,180 --> 00:06:52,980
+الأسلوب خلاص انتهت فإذا ال family
+
+100
+00:06:56,670 --> 00:07:02,890
+is كيف ممكن نكتبها a sub n بحيث n تنتمي لل n
+
+101
+00:07:02,890 --> 00:07:07,830
+الكلام اللي كتبناه طبعا هذه ممكن انا اكتبها بشكل
+
+102
+00:07:07,830 --> 00:07:10,430
+مختصر ان هي عبارة عن a sub j جيه تنتمي من واحد
+
+103
+00:07:10,430 --> 00:07:12,690
+لاتنين تلاتة فانا ممكن اكتبها بهذا الشكل ايه
+
+104
+00:07:12,690 --> 00:07:17,310
+عملتلها إيش أرشفها عملتلها ترقيم عملتلها indexing
+
+105
+00:07:17,310 --> 00:07:20,930
+عملتلها indexing فخلاص واضح زي ما قلنا a عشرة
+
+106
+00:07:20,930 --> 00:07:24,600
+معروفة15 معروفة خلاص فهي الفهم اللي كتبته بشكل
+
+107
+00:07:24,600 --> 00:07:30,220
+واضح ومغلق وبشكل الأمور أتوقع أهضح من أن هي تخمن
+
+108
+00:07:30,220 --> 00:07:33,140
+الصورة لأ احنا جيبناه الصورة الشيية والصورة العامة
+
+109
+00:07:33,140 --> 00:07:36,460
+فهي ده الهدف كيف اتعامل مع عدد كبير من المجموعات
+
+110
+00:07:36,460 --> 00:07:44,430
+وارتبهم بشكل مناسب بعض الملاحظةطبعاً بقولّي إنه لو
+
+111
+00:07:44,430 --> 00:07:48,830
+أنا أخدت أي family من المجموعات، هل بقدر أعملها
+
+112
+00:07:48,830 --> 00:07:51,510
+عملية indexing؟ بقولّي في الغالب نعم، حتى لو كان
+
+113
+00:07:51,510 --> 00:07:55,770
+بالظاهر إنه مافيش صورة واضحة، يمكن لو كان المثال
+
+114
+00:07:55,770 --> 00:07:59,370
+واضح نوعا ما، حتى لو ماكانش واضح، الحقيقة في معظم
+
+115
+00:07:59,370 --> 00:08:04,860
+الأحيانأنا بقدر ألاقي اللي هو تسميات مناسبة ترقيم
+
+116
+00:08:04,860 --> 00:08:08,140
+مناسب نقول indexing مناسب و أقدر أحول ال family
+
+117
+00:08:08,140 --> 00:08:11,360
+ليش ل index family of this طبعا بشكل عام مش دايما
+
+118
+00:08:11,360 --> 00:08:14,580
+لكن في معظم الأحوال في معظم الأحوال فهذه الملاحظة
+
+119
+00:08:14,580 --> 00:08:21,020
+الأولىالملاحظة التانية بيقول بما أن ال family تشبه
+
+120
+00:08:21,020 --> 00:08:24,500
+المجموعة لأنها collection of objects لذلك هنستخدم
+
+121
+00:08:24,500 --> 00:08:28,760
+نفس الرموز هنستخدم ينتمي نفس الرمز لو بنستخدم ..
+
+122
+00:08:28,760 --> 00:08:32,340
+مش هناخد احنا تقاطع families و اتحاد families لكن
+
+123
+00:08:32,340 --> 00:08:35,320
+احنا هنستخدم رمز ينتمي لو بدنا .. اللي هو member
+
+124
+00:08:35,320 --> 00:08:37,940
+of family اللي ايش هنحطه؟ علاقة ينتمي زي المجموعة
+
+125
+00:08:38,080 --> 00:08:41,520
+زي المجموع يعني هنا إيش بدك تقول مثلا هلجيت ا واحد
+
+126
+00:08:41,520 --> 00:08:44,680
+موجودة في ال family فهيقول إنهاش تنتمي اتنين تنتمي
+
+127
+00:08:44,680 --> 00:08:47,700
+هستخدم نفس الرموز فبقول كل الرموز ممكن استخدامها
+
+128
+00:08:47,700 --> 00:08:50,560
+كل رموز المجموعات ممكن استخدامها مع مين؟ مع
+
+129
+00:08:50,560 --> 00:08:58,410
+العائلات مع ال families أي سؤال؟تمام؟ فهذه المقدمة
+
+130
+00:08:58,410 --> 00:09:02,730
+اللي هو الأساسية عشان نفهم الأنوان اللي هو إيش؟
+
+131
+00:09:02,730 --> 00:09:06,090
+Indexed Families of Cells الهدف الرئيسي و بعيده
+
+132
+00:09:06,090 --> 00:09:11,450
+بكرر ما اتهوش كتير ما تخافوش من الموضوع كل الهدف
+
+133
+00:09:11,450 --> 00:09:15,430
+كيف نتعامل مع عدد كبير من المجموعات و حده حي و ضعف
+
+134
+00:09:15,430 --> 00:09:18,630
+النظريات و في الأمثلة كيف أتعامل مع عدد كبير من
+
+135
+00:09:18,630 --> 00:09:20,950
+المجموعات طبعا تتعامل مع مجموعتين الكل بعرف يتعامل
+
+136
+00:09:20,950 --> 00:09:24,760
+مع مجموعتين مع تلاتة المعظم بلاش نقول للكللما
+
+137
+00:09:24,760 --> 00:09:27,340
+يكتروا بيصير فيه شوية غلبة بنتعلم كيف نتعامل مع
+
+138
+00:09:27,340 --> 00:09:30,320
+عدد كبير جدا من المجموعات حتى لو كانوا مالة نهاية
+
+139
+00:09:30,320 --> 00:09:34,400
+من المجموعات فنبدأ بأول شيء كيف نعرف الاتحاد
+
+140
+00:09:34,400 --> 00:09:38,340
+والتقاطع لعلى ال family أنا في عندي عدد كبير من
+
+141
+00:09:38,340 --> 00:09:41,480
+المجموعات كيف بدي أجيب الاتحاد طبعا احنا عرفنا ان
+
+142
+00:09:41,480 --> 00:09:45,220
+الاتحاد هو بدنا العناص الموجودة على الأقل في واحدة
+
+143
+00:09:45,220 --> 00:09:48,340
+فلو كانوا تنتين بقول يا في الأولى يا في التانية او
+
+144
+00:09:48,340 --> 00:09:51,540
+في التانية طب كانوا تلاتة ممكن اقول في الأولى او
+
+145
+00:09:51,540 --> 00:09:55,300
+في التانية او في التالتة طب لما يكترواإيش البديل
+
+146
+00:09:55,300 --> 00:10:00,340
+لل R؟ there exist تذكره؟ اه فهي مصطلحة there exist
+
+147
+00:10:00,340 --> 00:10:05,020
+فإحنا هنعرف الاتحاد بعلاقة إيش يوجد there exist
+
+148
+00:10:05,020 --> 00:10:10,040
+فهو يقول لي المقدمة let capital F be a family of
+
+149
+00:10:10,040 --> 00:10:14,560
+sets طبعا من المصطلح family أخد حرف ال F وكتبه
+
+150
+00:10:14,560 --> 00:10:19,390
+بشكل شويه غريبلأنه هيك بده يميزه و طبعا بيحاول ياش
+
+151
+00:10:19,390 --> 00:10:23,370
+يعمله هيك شوية مخيف كبير لإنه family of six حاجة
+
+152
+00:10:23,370 --> 00:10:27,710
+كبيرة تمام ف F و بيكتبوها شوية مائلة الخطوط هذه
+
+153
+00:10:27,710 --> 00:10:30,770
+طبعا زي ما تعرفي يعني الرياضيات تستخدم رموز كتيرة
+
+154
+00:10:30,770 --> 00:10:34,390
+و بيحاولوا دايما يميزوا و يغيروا الرمز عن رمز لإن
+
+155
+00:10:34,390 --> 00:10:37,490
+الرموز مش مكافئانة لحقيقة بيستخدم الحروف اللي هو
+
+156
+00:10:37,490 --> 00:10:41,990
+الإنجليزية و اللاتينية و أحيانا ما بيكفوش بنحاول
+
+157
+00:10:41,990 --> 00:10:46,620
+نشوف الرموز المناسب تمام فهذه المقدمةفأول شيء بدي
+
+158
+00:10:46,620 --> 00:10:49,860
+أعرف مصطلح يمكن يكون طبعا هو المصطلح الأصلي هو
+
+159
+00:10:49,860 --> 00:10:53,480
+اتحاد بس ايش بدي أجيب الاتحاد على جميع اللي هو
+
+160
+00:10:53,480 --> 00:10:56,840
+أعضاء ال family فبسميه union على ال family اه انا
+
+161
+00:10:56,840 --> 00:10:59,900
+عندي مجموعات زي هيك مثلا اشجاليه بده اتحاد على هذه
+
+162
+00:10:59,900 --> 00:11:03,260
+ال family يعني اتحاد التلات مجموعات طب بده اتحاد
+
+163
+00:11:03,260 --> 00:11:06,480
+على هذه ال family اتحاد كل المجموعات اللي هي من
+
+164
+00:11:06,480 --> 00:11:09,820
+واش من واحد لما لا نهاية اه فهي المقصود فبقول let
+
+165
+00:11:09,820 --> 00:11:13,520
+F be an arbitrary family of six the union of six
+
+166
+00:11:13,520 --> 00:11:18,030
+in Fاتحاد المجموعات اللي في ال family واضحة؟ ايش
+
+167
+00:11:18,030 --> 00:11:21,730
+ماله؟ denoted by طبعا زي ما قلنا فيه أنه مفهوم فيه
+
+168
+00:11:21,730 --> 00:11:24,790
+أنه الرمز تبعه والتعريف تبعه صحيح؟ فيه أنه مصطلح
+
+169
+00:11:24,790 --> 00:11:28,970
+معين مفهوم معين ايش الرمز تبعه؟ فبقوله انا الاتحاد
+
+170
+00:11:28,970 --> 00:11:32,350
+على ال family اه فانا فيه عندي اكتر من رمز فانا
+
+171
+00:11:32,350 --> 00:11:37,890
+فقوله ايش؟ اتحاد على ال family اه هذا ليس الا رمز
+
+172
+00:11:37,890 --> 00:11:41,730
+ليس الا رمز كيف نقول ال sigma رمز؟ نفس القضية لما
+
+173
+00:11:41,730 --> 00:11:45,410
+يقولك اتحاد مين؟ اتحاد ال F؟ لاالاتحاد على ال
+
+174
+00:11:45,410 --> 00:11:49,330
+family بنقرعها يعني إيش؟ اتحاد جميع المجموعات اللي
+
+175
+00:11:49,330 --> 00:11:52,370
+في ال family واضح؟ هذا مجرد رمز مالوش إيش معنى كده
+
+176
+00:11:52,370 --> 00:11:55,190
+بتاع أحسب، بس أنا إيش بتاع أعرف، إيش بيصيب أو
+
+177
+00:11:55,190 --> 00:11:59,560
+بقوله إيش، ممكن السب دلوقت بقول إيشاتحاد كل
+
+178
+00:11:59,560 --> 00:12:04,240
+المجموعات اللي موجودة في ال family الـ A تنتمي لل
+
+179
+00:12:04,240 --> 00:12:08,560
+family قلنا نفسنا ناخد نفس الرموز اتحاد جميع
+
+180
+00:12:08,560 --> 00:12:12,640
+المجموعات اللي في العائلة اتحاد جميع المجموعات
+
+181
+00:12:12,640 --> 00:12:15,700
+اللي في العائلة اتحاد أي مجموعة بشرط ان المجموعة
+
+182
+00:12:15,700 --> 00:12:17,940
+وين في ال family هذا الشمال و هذا الرمز هذا الرمز
+
+183
+00:12:17,940 --> 00:12:22,320
+هذا او هذا طيب اتحاد المجموعات عبارة عن ايش؟
+
+184
+00:12:22,320 --> 00:12:26,300
+مجموعة فبقول الـ A is the setof all elements جميع
+
+185
+00:12:26,300 --> 00:12:29,960
+العناصر اللي يشملها موجودة على الأقل في واحدة من
+
+186
+00:12:29,960 --> 00:12:32,760
+المجموعات أنا بدي أحفظ اتحاد مجموعات لو بقول اتحاد
+
+187
+00:12:32,760 --> 00:12:35,180
+عشر مجموعات بدي العناصر الموجودة على الأقل في
+
+188
+00:12:35,180 --> 00:12:37,720
+واحدة من العشرة مظبوط لأن فيها all طب لو كانوا
+
+189
+00:12:37,720 --> 00:12:41,620
+أكتر نفس الشيء فبقولي the set of all elements that
+
+190
+00:12:41,620 --> 00:12:46,140
+are in A for some A in the family فما زال اتحاد
+
+191
+00:12:46,140 --> 00:12:48,980
+على ال A لو موجودة في واحدة من هدول طبعا ال A ترمز
+
+192
+00:12:48,980 --> 00:12:52,470
+دو أي واحدة من العائلةفانت تكون على الأقل في واحدة
+
+193
+00:12:52,470 --> 00:12:54,970
+for some there exists ماني for some تكافئ there
+
+194
+00:12:54,970 --> 00:12:59,570
+exists نفس المعنى طيب هاي التعريف بلغة الكلمات في
+
+195
+00:12:59,570 --> 00:13:02,910
+الرموز قال الاتحاد على ال family إيش ماله؟ هو كل X
+
+196
+00:13:02,910 --> 00:13:07,130
+بحيث X تنتمي لمين؟ لعضه من أعضاء العائل على الأقل
+
+197
+00:13:07,130 --> 00:13:11,610
+for some A in the family بمعنى آخر there exists A
+
+198
+00:13:11,610 --> 00:13:16,000
+في ال family تحتوي هذا الأنصار نفس المعنىغيرنا for
+
+199
+00:13:16,000 --> 00:13:18,660
+some هي there exists وممكن نكتبها الـ quantifier
+
+200
+00:13:18,660 --> 00:13:22,160
+يقول يمكن نكتبها جاب ال open sentence وممكن في بعد
+
+201
+00:13:22,160 --> 00:13:26,440
+نفس الشيء فكل هذه من الصلاحات متعارف عليها واضح
+
+202
+00:13:26,440 --> 00:13:31,860
+فهي طبعا باختصار هي العناصر اللي على الأقل في أحد
+
+203
+00:13:31,860 --> 00:13:36,600
+تحتويها أحد عيش مجموعات ال family أحد أعضاء ال
+
+204
+00:13:36,600 --> 00:13:40,760
+family التقاطع بنفس الأسلوب بس بدل ما هي U U
+
+205
+00:13:40,760 --> 00:13:45,510
+مجلوبة نفس الشيءطبعا إيش التقاطع؟ عناصر مشتركة،
+
+206
+00:13:45,510 --> 00:13:48,310
+بدي العناصر الموجودة في كل المجموعات، مش في
+
+207
+00:13:48,310 --> 00:13:51,730
+مجموعتين فقط، لما يقول تقاطع تلت مجموعات، بدي
+
+208
+00:13:51,730 --> 00:13:53,590
+العنصر الموجود في التلاتة مع بعض، مش مشترك بين
+
+209
+00:13:53,590 --> 00:13:55,670
+اتنين، مش مشترك بين التلاتة، مش مشترك بين اتنين،
+
+210
+00:13:55,670 --> 00:13:58,790
+مش مشترك بين التلاتة، مش مشترك عشر مجموعات، مش
+
+211
+00:13:58,790 --> 00:14:03,690
+مشترك بين العشرة، بقى فنفسكفأصبحت زي ما قلنا إيش
+
+212
+00:14:03,690 --> 00:14:07,230
+تعميم ال and ممكن نعتبره for all وإيش تعميم ال or
+
+213
+00:14:07,230 --> 00:14:10,270
+they exist فإحنا ربطنا بينهم جاب ال X صحيح فنفس
+
+214
+00:14:10,270 --> 00:14:14,390
+المعنى فبقول ليه التقاطع نفس الرمز نفس الأسلوب هو
+
+215
+00:14:14,390 --> 00:14:18,530
+كل X تنتمي لإيش لعضه من أعضاء ال family لكل أعضاء
+
+216
+00:14:18,530 --> 00:14:22,830
+ال family تنتمي لل A for all A تنتمي لل F for all
+
+217
+00:14:22,830 --> 00:14:25,490
+كتبناها بالطريقة التانية فإذا لازم تكون هي العناص
+
+218
+00:14:25,490 --> 00:14:29,730
+المشتركة بين جميع المجموعات اللي في العائلة فهي
+
+219
+00:14:29,730 --> 00:14:33,700
+العناص المشتركةخلّيني أشوف بعض الأمثلة عشان نأكد
+
+220
+00:14:33,700 --> 00:14:39,380
+على هذه المعاني و كالعادة نبدأ بمثال بسيط، عندنا
+
+221
+00:14:39,380 --> 00:14:43,200
+family تحتوي على أربع مجموعات، بدّوا الاتحاد على
+
+222
+00:14:43,200 --> 00:14:45,660
+ال family، شوف الرمز هذا الجديد، أه و الواش و
+
+223
+00:14:45,660 --> 00:14:51,300
+التقاطع على ال family، خلّيني أنفسره بشكل الواش
+
+224
+00:14:51,300 --> 00:14:57,420
+تفصيلي، خلّيني أكتب هنا solution
+
+225
+00:14:58,340 --> 00:15:02,400
+أه فطبعا أول شيء خلّيني أؤكد على المصطلح والمفهوم
+
+226
+00:15:02,400 --> 00:15:06,480
+لما يقول لي union على ال family وهي ال family اللي
+
+227
+00:15:06,480 --> 00:15:10,420
+عندك ايش معناته الأولى اتحاد التاني اتحاد التلتة
+
+228
+00:15:10,420 --> 00:15:12,860
+اتحاد الرابعة عشان الأول مثال بدك تقوم بالتفصيل
+
+229
+00:15:12,860 --> 00:15:19,160
+يعني واحد اتنين هذه مجموعة اتحاد واحد تلاتة اتحاد
+
+230
+00:15:19,160 --> 00:15:27,750
+واحد تلاتة اربعة اتحادواحد اتنين خمسة تمام هاي
+
+231
+00:15:27,750 --> 00:15:31,750
+المعنى فهذا رمز وهي معناه الحقيقي زي ال sigma
+
+232
+00:15:31,750 --> 00:15:35,470
+ولمّا نفكها هو معناها الحقيقي فهذا رمز ايش اتحاد
+
+233
+00:15:35,470 --> 00:15:38,590
+على ال family اتحاد جميع المجموعات اللي في ال
+
+234
+00:15:38,590 --> 00:15:41,930
+family واضح فهذا النقطة واضح هذا المثال نادر ما
+
+235
+00:15:41,930 --> 00:15:45,370
+يتكرر هذا مثال بسيط عشان نفهم الأصل ايش فانحنا
+
+236
+00:15:45,370 --> 00:15:48,050
+بنجف على أرض صلبة الآن فاهمين ايش المقصود في اتحاد
+
+237
+00:15:48,050 --> 00:15:53,020
+على ال family تمبدنا الاتحاد، إيش الاتحاد؟ العناصر
+
+238
+00:15:53,020 --> 00:15:54,680
+اللي موجودة على الأقل في واحدة، فإحنا على طول
+
+239
+00:15:54,680 --> 00:15:57,960
+بناخد المجموعة الأولى و بناخدها كلها، التانية، أه
+
+240
+00:15:57,960 --> 00:16:01,240
+بنضيف تلاتة، التالتة بتضيف الأربعة، و الرابعة
+
+241
+00:16:01,240 --> 00:16:04,200
+بتضيف الخمسةفطبعا زي ما انتوا متعودين مافيش شي
+
+242
+00:16:04,200 --> 00:16:07,560
+جديد بس عشان المعدد كبير فالاتحاد بشوف باخد
+
+243
+00:16:07,560 --> 00:16:09,760
+المجموعة الأولى ومجموعة تانية كلها بس إيش بعمل
+
+244
+00:16:09,760 --> 00:16:12,700
+المتكرر بكتب الشكل المحلي بس هي كل الفكرة اللي
+
+245
+00:16:12,700 --> 00:16:15,360
+بعمله ع تنتين بعمله على عشر أو على خمسين مافيش أي
+
+246
+00:16:15,360 --> 00:16:19,560
+إشكال بالنسبة للتقاطع نفس الاسلوب بس مانتش أكرر بس
+
+247
+00:16:19,560 --> 00:16:23,200
+بدنا عناصر مشتركة بين الأربعة كلهم فشيلة الواحد
+
+248
+00:16:24,080 --> 00:16:26,600
+مايقوليش حد إيش، التلاتة هي مشتركة بين اتنين،
+
+249
+00:16:26,600 --> 00:16:29,960
+ماينفعش، المفروض أن اكتب كمان مرة بس تقاطع وبعدين
+
+250
+00:16:29,960 --> 00:16:33,340
+تلتحات، بس مانديش أكتب، واضحة، الفكرة نفس الشيء،
+
+251
+00:16:33,340 --> 00:16:36,360
+فالتقاطع الأربع مجموعات، العناصر مشتركة بين
+
+252
+00:16:36,360 --> 00:16:39,900
+الأربع، بدي يكون موجود في كل الأربع، مافيش للواحد،
+
+253
+00:16:39,900 --> 00:16:42,320
+في غيره موجود بالاربعة؟ لأ، موجود في اتنتين
+
+254
+00:16:42,320 --> 00:16:46,680
+بيكفنيش، موجود مشترك للجميع، مش مشترك بين اتنين،
+
+255
+00:16:46,680 --> 00:16:51,720
+مشترك للجميع، for all، أحسنتي ملاحظات
+
+256
+00:16:52,820 --> 00:16:58,520
+هنمشي احنا ماشيين خطوة خطوة تمام في التعريف قبل
+
+257
+00:16:58,520 --> 00:17:02,520
+قليل عرفنا الاتحاد و التقاطه على ال family بشكل
+
+258
+00:17:02,520 --> 00:17:07,900
+عام مجليش family ايش index family الان هنحاول نخصص
+
+259
+00:17:07,900 --> 00:17:12,300
+اه طبعا الأسهل لما تكون ايش كل الهدف ايش انسهل
+
+260
+00:17:12,300 --> 00:17:15,410
+التعامللما نعملها عملية Archer فبصي العملية أسهل
+
+261
+00:17:15,410 --> 00:17:18,790
+شوية عملية أسهل شوية و تايمة نتذكروا العلاقة
+
+262
+00:17:18,790 --> 00:17:21,670
+حاولوا إيش تسترجعوا ال sigma و إيش دورها ليش
+
+263
+00:17:21,670 --> 00:17:24,310
+بستخدم ال sigma عشان نتعامل مع مجموعة عدد كبير من
+
+264
+00:17:24,310 --> 00:17:27,370
+العناصر صحيح فنفس القضية .. نفس القضية بس هنا مش
+
+265
+00:17:27,370 --> 00:17:30,570
+.. مش مجموعة ال sigma من وين جاي ال sigma ال sigma
+
+266
+00:17:30,570 --> 00:17:33,570
+تقابل حرف ال S بس في اللاتيني و من كلمة some ليس
+
+267
+00:17:33,570 --> 00:17:36,730
+إلا أه فهناك some طبعا هنا ياش you union أه فنفس
+
+268
+00:17:36,730 --> 00:17:40,090
+العملية أه فبقوللي لو أنا حالة خاصة ال family
+
+269
+00:17:40,390 --> 00:17:44,390
+إشمالها index family مؤرشفة كيف بكتب الاتحاد بدل
+
+270
+00:17:44,390 --> 00:17:47,150
+مابكتب اتحاد على ال F بستخدم الدليل بقول a sub
+
+271
+00:17:47,150 --> 00:17:49,490
+gamma زي ما نقول ايش a sub j ماعشغلنا نقول في
+
+272
+00:17:49,490 --> 00:17:53,030
+summation نفس الشيء ف a sub gamma بحيث انه gamma
+
+273
+00:17:53,030 --> 00:17:56,150
+تنتمي لل gamma بدل ما اقوله a تنتمي لل F طب ما هي
+
+274
+00:17:56,150 --> 00:17:59,410
+بدل ما احكي عن a نفسي لان ممكن احكيش على اسمها
+
+275
+00:17:59,410 --> 00:18:02,450
+اللي هو ال gamma الدليل تبعها الدليل تبعهافهيش
+
+276
+00:18:02,450 --> 00:18:05,930
+طريقة جديدة للكتابة طبعا نفس الشغل إيش اتحاد؟ for
+
+277
+00:18:05,930 --> 00:18:10,810
+some بدل ما أقول for some إيه في ال family بدل ما
+
+278
+00:18:10,810 --> 00:18:13,550
+أذكر العنصر باسمه بي .. بي .. بي .. بي .. بي .. بي
+
+279
+00:18:13,550 --> 00:18:13,910
+.. بي .. بي .. بي .. بي .. بي .. بي .. بي .. بي ..
+
+280
+00:18:13,910 --> 00:18:14,010
+بي .. بي .. بي .. بي .. بي .. بي .. بي .. بي .. بي
+
+281
+00:18:14,010 --> 00:18:14,670
+.. بي .. بي .. بي .. بي .. بي .. بي .. بي .. بي ..
+
+282
+00:18:14,670 --> 00:18:15,050
+.. بي .. بي .. بي .. بي .. بي .. بي .. بي .. بي ..
+
+283
+00:18:15,050 --> 00:18:23,470
+بي .. بي .. بي .. بي .. بي .. بي
+
+284
+00:18:23,470 --> 00:18:27,350
+.. ب
+
+285
+00:18:31,570 --> 00:18:37,330
+تمام فإذا احنا في عندنا اعيد في عندنا التعريف اللي
+
+286
+00:18:37,330 --> 00:18:41,490
+هو اتحاد على أي family مؤرشفة مش مؤرشفة مرقمة مش
+
+287
+00:18:41,490 --> 00:18:45,330
+مرقمة تمام الملاحظة بدأت تخصص التعريف لو كانت
+
+288
+00:18:45,330 --> 00:18:50,340
+index بشكل عام فهي الكلام طب لو كانت مرقمةأسهل
+
+289
+00:18:50,340 --> 00:18:53,400
+واسهل حالة خاصة فإذا احنا الحالة العامة التعريف
+
+290
+00:18:53,400 --> 00:18:58,180
+حالة خاصة index حالة أخص منها لما تكونش مرقمة
+
+291
+00:18:58,180 --> 00:19:00,580
+ترقيم بسيط اللي هو أسهل شي زي ال sigma اللي هو
+
+292
+00:19:00,580 --> 00:19:03,300
+يسترقيم عدد صحيح عمو تتالية واحد اتنين تلاتة
+
+293
+00:19:03,300 --> 00:19:07,320
+فبقولي أنا بقدر اكتب الاتحاد ايش زي ال sigma تماما
+
+294
+00:19:07,320 --> 00:19:10,860
+جامعة تساوي واحد لان كيف بدأ اقراها ببدأ من واحد
+
+295
+00:19:10,860 --> 00:19:14,180
+بعد الواحد اتنين تلاتة لكن هنا بعد الجامعة مين
+
+296
+00:19:14,180 --> 00:19:17,520
+بيجي مش عارف احاول الدليل تبعي واضحه ايش الفرق هنا
+
+297
+00:19:17,520 --> 00:19:21,720
+و هنا اه و هيه و هي معناهازي الـ Sigma تماماً بس
+
+298
+00:19:21,720 --> 00:19:25,180
+الـ Sigma كانت plus هنا إيش اتحاد والتقاطع بنفس
+
+299
+00:19:25,180 --> 00:19:28,780
+الأسلوب والتقاطع بنفس الأسلوب فدي كلها رموز
+
+300
+00:19:28,780 --> 00:19:32,580
+هنتعامل معها في هذا section و فيما بعد برضه فبدنا
+
+301
+00:19:32,580 --> 00:19:36,260
+إيش نتعرف نتعلم كيف نتعامل كل الهدف عشان نتعامل
+
+302
+00:19:36,260 --> 00:19:40,540
+عدد كبير من المجموعات فدي مكتوب له A1 اتحاد A2
+
+303
+00:19:40,540 --> 00:19:44,070
+اتحاد A نيش عملتها؟بسهولة زي الـ Sigma Union من 1
+
+304
+00:19:44,070 --> 00:19:47,230
+ل N A J أو A Gamma طبعا عشان احنا مش فين مع
+
+305
+00:19:47,230 --> 00:19:51,270
+الجامعة، بتفرجش، مدى مجرد هاش رمز، دليل، واضح،
+
+306
+00:19:51,270 --> 00:19:57,590
+فهذه مجرد رموز خلينا نشوف مثال عملي يقرب الصورة ان
+
+307
+00:19:57,590 --> 00:20:01,110
+شاء الله أفضل let capital F بيقى family على الصورة
+
+308
+00:20:01,110 --> 00:20:05,970
+اللي عنكم أكم مجموعة في في ال F أو finite ولا
+
+309
+00:20:05,970 --> 00:20:11,710
+infinite؟infinite ليش؟ شوفتوا ال infinite تبع التو
+
+310
+00:20:11,710 --> 00:20:15,250
+كيف كانت نقطة نقطة نقطة نقطة انتهت مانتهتش لكنها
+
+311
+00:20:15,250 --> 00:20:18,690
+دي مانتهي هي اخر واحدة هي اخر واحدة فيا وماشي في n
+
+312
+00:20:18,690 --> 00:20:21,730
+من المجموعات بدت بواحد المجموع الأولى بواحد
+
+313
+00:20:21,730 --> 00:20:24,230
+المجموع التاني بتبدأ باتنين والتالتة بتبدأ بتلاتة
+
+314
+00:20:24,230 --> 00:20:27,530
+والاخيرة بتبدأ ب n اذا مجموع اذا n من المجموعات في
+
+315
+00:20:27,530 --> 00:20:30,630
+اندي n من المجموعات finite finite فبدوا الاتحاد
+
+316
+00:20:30,630 --> 00:20:35,770
+تبعهم خلينا نعملهم أرشفة ونشوف الاتحاد ونشوف مثال
+
+317
+00:20:35,770 --> 00:20:37,850
+على الكلام اللي توي شرحناه على الملاحظة
+
+318
+00:20:40,330 --> 00:20:46,790
+فهنا المثال الأول solution طبعا خلّيني أرشفهم
+
+319
+00:20:46,790 --> 00:20:51,570
+فخلّيني أوضح أن الـ A1 المجموعة الأولى هي واحد
+
+320
+00:20:51,570 --> 00:20:58,970
+المجموعة التانية هي اتنين تلاتة بشكل عام A sub J
+
+321
+00:20:58,970 --> 00:21:03,640
+مين بقدر يشوف الصورة العامةبتبدأ من J واضح انه هي
+
+322
+00:21:03,640 --> 00:21:06,500
+بيقول اي واحد بدأت بواحد اتنين بدأت بتنين اتلاتة
+
+323
+00:21:06,500 --> 00:21:10,520
+بدأت بتلاتة والاخيرة بدأت بان فهذه بتبدأ من J وكيف
+
+324
+00:21:10,520 --> 00:21:19,620
+بتمشي؟ وين بتوقف؟ اتنين J ناقص واحد طبعا جيد طبعا
+
+325
+00:21:19,620 --> 00:21:25,600
+وها كذا J من واحد لانلعن ال A N جي واحد اتنين لعن
+
+326
+00:21:25,600 --> 00:21:30,780
+مين ال N طيب دايما في اي مثال انت خمنتي حاجة
+
+327
+00:21:30,780 --> 00:21:35,440
+بتتأكدي منها افحصي عوض ال واحد عن جي عند ال واحد
+
+328
+00:21:35,440 --> 00:21:38,640
+من وين تبدأ؟ من واحد بتقول انت عند اتنين في واحد
+
+329
+00:21:38,640 --> 00:21:41,720
+ناقص واحد بتنتي عند ال واحد صح طيب خدي جي بتسوي
+
+330
+00:21:41,720 --> 00:21:46,240
+اتنينأه فتكون اتنين تلاتة طب خدي جي بتسوي تلاتة
+
+331
+00:21:46,240 --> 00:21:49,940
+هتكون ايش تلاتة اربع وانت وقف عند اتنين في تلاتة
+
+332
+00:21:49,940 --> 00:21:53,420
+ناقص واحد عند الخمسة صح فاذا ايهاش الترقيم صحيح
+
+333
+00:21:53,420 --> 00:21:59,460
+ممتاز فالفهم اللي عندنا فأول شيء thus ال F ممكن
+
+334
+00:21:59,460 --> 00:22:05,620
+اكتبه بالشكل التالي a sub j بحيث ال j تنتمي من وين
+
+335
+00:22:05,620 --> 00:22:10,250
+لوين من واحد لان هيعملنا لها ترقيمهيكتبناها بشكل
+
+336
+00:22:10,250 --> 00:22:13,990
+إيش مختصر، مظبوط؟ هي a1 و إيش بتساوي a2 و هذا
+
+337
+00:22:13,990 --> 00:22:22,710
+الشكل، أه فلمّا يقول لي إذا Therefore فالاتحاد
+
+338
+00:22:22,710 --> 00:22:30,030
+على ال F ممكن أكتبه بشكل أوضح J من 1 ل N اتحاد
+
+339
+00:22:30,030 --> 00:22:35,210
+لمين؟ a1 اتحاد a2 اتحاد a3 اللي ممكن أكتصر أكتب
+
+340
+00:22:35,210 --> 00:22:39,310
+بهذا الشكل A sub Jفهذا المعنى فشوفتوا احنا بدل من
+
+341
+00:22:39,310 --> 00:22:46,850
+نكتب A1 اتحاد اتنين اختصارا نكتب هذا الشكل تفضل اه
+
+342
+00:22:46,850 --> 00:22:50,470
+هى انا اخر واحدة ج بتساوي انا حدكا حكيت فدلت قعدت
+
+343
+00:22:50,470 --> 00:22:56,710
+حدقاش ايش ماله هذا لما انا بقولك سيجما لأ بس تنتبه
+
+344
+00:22:56,710 --> 00:23:01,470
+بحط انا هنا ايش مثلا اتنين قص ج ايش بنسميها ده
+
+345
+00:23:01,470 --> 00:23:04,930
+العنصر العام فمين العنصر العام في ال family هدا AJ
+
+346
+00:23:04,930 --> 00:23:06,410
+واضحيت اه
+
+347
+00:23:08,860 --> 00:23:13,240
+بالبعد هى اه بنايه لعند الان بدي اقصد لعند الان
+
+348
+00:23:13,240 --> 00:23:20,260
+مانا واضح هنا ان هى النهاية صحيح ماهى هى الفهم
+
+349
+00:23:20,260 --> 00:23:22,820
+اللى مديكى واقف هو وين واقف فى الان فى المعطى وين
+
+350
+00:23:22,820 --> 00:23:27,080
+واقف واضحه اه هو انا من المعطى بديفش حاجة من اني
+
+351
+00:23:27,080 --> 00:23:31,500
+تمام فإذا هذا الشهاد الرئيسى هى فإحنا كتبناها بهذه
+
+352
+00:23:31,500 --> 00:23:36,540
+الصورة واضحهش القضية طبعا إيش بيساوي هذا نحلها
+
+353
+00:23:38,000 --> 00:23:42,820
+إيش نعمل؟ نبدأ إيش؟ أول مجموعة اكتبوها واحد بعدين
+
+354
+00:23:42,820 --> 00:23:45,600
+اكتبوا التانية اكتبوا التالتة و التكرار ما
+
+355
+00:23:45,600 --> 00:23:54,300
+تكتبوهاش وين رايحة؟ فانت
+
+356
+00:23:54,300 --> 00:24:00,420
+كل مرة بتضيف عناصر صح؟ ولمكرر بتضفوش طيب بعض
+
+357
+00:24:00,420 --> 00:24:03,960
+الطالب تقول مش فاضحان ليش الجواب هيك بسيطة كالعادة
+
+358
+00:24:03,960 --> 00:24:09,420
+خدوا اتحاد أول تلت مجموعاتما هو 1 2 3 ايش الاتحاد؟
+
+359
+00:24:09,420 --> 00:24:13,560
+من 1 ل 5 صح؟ وين وقفت؟ عند 2 في 3 تناقص 1 طيب
+
+360
+00:24:13,560 --> 00:24:18,200
+المجموعة الرابعة إيش ده تكون؟ هتكون 4 5 6 7 مظبوط
+
+361
+00:24:18,200 --> 00:24:22,940
+طبقا للقاعدة صح؟ لما دي بتسوي 4 إيش ده تكون؟ 4 5
+
+362
+00:24:22,940 --> 00:24:26,400
+لعين وين توقف؟ عند 2 في 4 تناقص 1 عند 7 طيب ضفوعة
+
+363
+00:24:26,400 --> 00:24:30,660
+الاتحادأه فإذا واضحة كيف ماشية كل مرة بضيف بعض
+
+364
+00:24:30,660 --> 00:24:34,720
+العناصر فإذا مش واضحة من الأول بنحاول إيش نضيف
+
+365
+00:24:34,720 --> 00:24:41,520
+اللي هو اللي بعد وهكذا فده المثال الأول خلينا نشوف
+
+366
+00:24:41,520 --> 00:24:47,540
+كمان مثالنشوف كمان مثال نتعامل مع مجموعات عبارة عن
+
+367
+00:24:47,540 --> 00:24:52,220
+فترات اه طبعا اللي هو ايش اشهر subsets في ال real
+
+368
+00:24:52,220 --> 00:24:55,360
+numbers هي اللي هيش الفترات اللي هيش موضوع مهم في
+
+369
+00:24:55,360 --> 00:25:00,010
+ال calculus فخلينا نشوف كيف بدنا يتعاملمع تقاطة
+
+370
+00:25:00,010 --> 00:25:04,150
+عدد كبير من الفترات أو اتحاد عدد كبير من الفترات
+
+371
+00:25:04,150 --> 00:25:07,790
+طبعا زفس السياسة اللي بتقدريش تاخديها مرة واحدة
+
+372
+00:25:07,790 --> 00:25:10,970
+اخديها بالتقصيد فاحنا طبعا انا في المثال اللي بعده
+
+373
+00:25:10,970 --> 00:25:14,850
+هوصل للمال نهاية لكن كتمهيد هوجف عند الخمسة عشان
+
+374
+00:25:14,850 --> 00:25:20,250
+نفهم ونقدر نعمم وعشان نقدر نعمم المثال رقم اتنين
+
+375
+00:25:21,880 --> 00:25:25,600
+طبعا انا هنا خليني اكتبها أولا بشكل صريح عشان
+
+376
+00:25:25,600 --> 00:25:31,100
+نفهمها فانا مجلد اتحاد N من واحد إلى خمس الفترات
+
+377
+00:25:31,100 --> 00:25:35,800
+من Zero لواحد على N يعني ده ايش معناته؟ بده اتحاد
+
+378
+00:25:35,800 --> 00:25:39,420
+Zero واحد مظبوط زي ال Sigma واحد N بتساوي واحد زي
+
+379
+00:25:39,420 --> 00:25:42,340
+ما بتفكش Sigma اللي بعده بس ايش ده حط plus؟ لأ
+
+380
+00:25:42,340 --> 00:25:50,150
+اتحاد ايش اللي بعده؟ صفر نص اتحاد صفر تلتاتحاد صفر
+
+381
+00:25:50,150 --> 00:25:58,270
+ربع اتحاد صفر خمس اتحاد
+
+382
+00:25:58,270 --> 00:26:00,330
+صفر ربع اتحاد صفر خمس اتحاد صفر ربع اتحاد صفر خمس
+
+383
+00:26:00,330 --> 00:26:02,050
+صفر ربع اتحاد صفر خمس اتحاد صفر ربع اتحاد صفر خمس
+
+384
+00:26:02,050 --> 00:26:03,710
+اتحاد صفر ربع اتحاد صفر خمس اتحاد صفر ربع اتحاد
+
+385
+00:26:03,710 --> 00:26:04,950
+صفر خمس اتحاد صفر خمس اتحاد صفر خمس اتحاد صفر خمس
+
+386
+00:26:04,950 --> 00:26:09,790
+اتحاد صفر خمس اتحاد صفر خمس اتحاد صفلازم نكون احنا
+
+387
+00:26:09,790 --> 00:26:13,410
+عايش بتشبهها بس بدل جامعة هنا عايش اتحاد ممتاز
+
+388
+00:26:13,410 --> 00:26:16,770
+بدنا نجيب الاتحادات هدولة تمام؟ ممكن زي ما
+
+389
+00:26:16,770 --> 00:26:20,010
+اتعلمتوا في الثانوية اتعلمتوا وين ما كان شوية ارسم
+
+390
+00:26:20,010 --> 00:26:24,830
+خط اعداد في اي خط الاعداد واو
+
+391
+00:26:24,830 --> 00:26:29,010
+هاي الصفر المجموعة الأولى من صفر لواحد ومفتوحة
+
+392
+00:26:29,010 --> 00:26:35,290
+فممكن نرسمها بهذا الشكل المجموعة اللي بعدها من صفر
+
+393
+00:26:35,290 --> 00:26:44,540
+لنصمفتوحة هذه نص اللي بعدها من صفر لتلت من صفر
+
+394
+00:26:44,540 --> 00:26:50,940
+لربع من صفر لخمس ايش رايكوا الاتحاد؟ من صفر لواحد
+
+395
+00:26:50,940 --> 00:26:54,120
+لأنه انا ايش ده الاتحاد أخدت أول مجموعة اللي بعده
+
+396
+00:26:54,120 --> 00:26:58,420
+ضعفش جديد؟ لأ جزء منها فإذا الجواب هنا يساوي
+
+397
+00:26:58,420 --> 00:27:02,750
+الفترة من صفر لواحدفكل المجموعات اللي بعدها بياش
+
+398
+00:27:02,750 --> 00:27:07,290
+متضفش جديد كله متكرر فالاتحاد من صفر ل واحد طب
+
+399
+00:27:07,290 --> 00:27:15,190
+التقاطع من صفر ل خمس صحيح طبعا ممكن اكتب بنفس
+
+400
+00:27:15,190 --> 00:27:20,070
+الاسلوب بس بنختصر ايش التقاطع بين المشترك هيه هي
+
+401
+00:27:20,070 --> 00:27:28,630
+من صفر ل خمس من صفر ل واحد على خمس واضح تمام
+
+402
+00:27:34,890 --> 00:27:42,270
+طيب نشوف المثال الأهم تعميم لمثال رقم اتنين لو
+
+403
+00:27:42,270 --> 00:27:46,850
+ماقفناش عند الخمسة روحنا للمالة نهاية اه طبعا زي
+
+404
+00:27:46,850 --> 00:27:49,610
+ما حكيت دايما اللي مش فاهم الخمسة مع بعض تاخد
+
+405
+00:27:49,610 --> 00:27:52,210
+اتنين توقف عند اتنين مش عند الخمسة بعدين توقف عند
+
+406
+00:27:52,210 --> 00:27:56,430
+التلاتة هتلاقي بالتدرج بنفهم الآن هنعمم لو روحنا
+
+407
+00:27:56,430 --> 00:28:03,660
+للمالة نهاية فنبدأ بيش بالاتحادN من واحد إلى ملا
+
+408
+00:28:03,660 --> 00:28:07,780
+نهاية Zero واحد على N بنفع نروح للملا نهاية؟ بنفع
+
+409
+00:28:07,780 --> 00:28:12,140
+تماما احنا قولنا ايش family of six اي عدد ايش
+
+410
+00:28:12,140 --> 00:28:15,220
+الاتحاد؟ صفر واحد نفس الفكرة لأنه زي ما تشايفين
+
+411
+00:28:15,220 --> 00:28:18,700
+بضافش شي جديد اول واحد هو الكبير و كله subset منه
+
+412
+00:28:18,700 --> 00:28:19,880
+فمن صفر لواحد
+
+413
+00:28:27,600 --> 00:28:31,020
+ما هو التقاطة؟ صفر صفر، مجموعة تبدأ من صفر و تنتهي
+
+414
+00:28:31,020 --> 00:28:37,660
+من صفر و مفتوحة، أيش بتكون؟
+
+415
+00:28:37,660 --> 00:28:43,100
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر
+
+416
+00:28:43,100 --> 00:28:43,260
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر
+
+417
+00:28:43,260 --> 00:28:43,340
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر
+
+418
+00:28:43,340 --> 00:28:43,700
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر
+
+419
+00:28:43,700 --> 00:28:49,130
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفماشي، بس
+
+420
+00:28:49,130 --> 00:28:53,590
+هي موجودة؟ هل الصفر موجودة في المجموع الأولى؟ لأ،
+
+421
+00:28:53,590 --> 00:28:56,250
+إذا مش موجودة في التقاطه على طول، أصلا مش موجودة
+
+422
+00:28:56,250 --> 00:29:01,070
+ولا واحدة فيهم، مش موجودة في الكل، الصفر، واضح؟
+
+423
+00:29:01,070 --> 00:29:04,490
+أعيد، أعيد، أعيد، أعيد، أعيد، أعيد، أعيد، أعيد،
+
+424
+00:29:04,490 --> 00:29:04,770
+أعيد، أعيد، أعيد، أعيد، أعيد، أعيد، أعيد، أعيد،
+
+425
+00:29:04,770 --> 00:29:07,150
+أعيد، أعيد، أعيد، أعيد، أعيد، أعيد، أعيد، أعيد،
+
+426
+00:29:07,150 --> 00:29:07,630
+أعيد، أعيد، أعيد، أعيد، أعيد، أعيد، أعيد، أعيد،
+
+427
+00:29:07,630 --> 00:29:10,520
+أعيد، أعيد، أعيد، أعيدبصغر، طب أنا وقفت عند
+
+428
+00:29:10,520 --> 00:29:13,420
+الخمسة، طب وقف عند العشرة، ومين هو حيصير؟ Zero
+
+429
+00:29:13,420 --> 00:29:16,960
+واحد على عشرة، صح؟ طب عند الألف، واحد من ألف، طب
+
+430
+00:29:16,960 --> 00:29:20,780
+لما أنت تروح الملة نهاية؟ Zero، لـ Zero، طب هل الـ
+
+431
+00:29:20,780 --> 00:29:23,100
+Zero موجود في التقاطع كان أصلا؟ مش موجودوله في
+
+432
+00:29:23,100 --> 00:29:25,640
+فترة من الفترات أصلا، كلهم مفتوحة، فكيف يكون في
+
+433
+00:29:25,640 --> 00:29:30,380
+التقاطع؟ كيف هو مشترك ومش موجود فيه؟ واضح؟
+
+434
+00:29:32,340 --> 00:29:35,140
+طب وين الاعتراضة؟ عشان بس ناخد زاوية تانية، مابداش
+
+435
+00:29:35,140 --> 00:29:37,640
+نقول نفس الكلام، اللي مش أوش واضح، حاجات أنتوا،
+
+436
+00:29:37,640 --> 00:29:40,780
+بالنسبة للاتحاد، واضح الاتحاد؟ أه تعميب، طيب،
+
+437
+00:29:40,780 --> 00:29:43,920
+الانطلاع التقاطع، زي ما قلنا المثال، إيش ماله؟ كل
+
+438
+00:29:43,920 --> 00:29:47,140
+مالنا، كل ما كبرت، القني اللي هذي، اللي صارت مالة
+
+439
+00:29:47,140 --> 00:29:49,880
+نهاية، بيصغر الفترة، طب لما القني تروح للمالة
+
+440
+00:29:49,880 --> 00:29:54,220
+نهاية، إيش تكون؟ أه، صفر، طب الفترة صفر صفر، أكم
+
+441
+00:29:54,220 --> 00:29:57,280
+عنصر فيها؟ ولا عنصر، أه، لأننا الصفر مش بنتميش،
+
+442
+00:29:57,280 --> 00:30:02,690
+لأنيعني برضه يمكن إذا حد لسه عنده شك إن الصفر في
+
+443
+00:30:02,690 --> 00:30:05,430
+التقاطع كيف الصفر يكون في التقاطع و هو مش موجود
+
+444
+00:30:05,430 --> 00:30:08,510
+ولا واحدة فيهم؟ هل موجود في هذه الصفر؟ طب خلاص
+
+445
+00:30:08,510 --> 00:30:10,630
+إنتهى إذا مش موجود في التقاطع إذا مش موجود في
+
+446
+00:30:10,630 --> 00:30:13,630
+التقاطع لأن واجهة التقاطع بيكون موجود في الكل إذا
+
+447
+00:30:13,630 --> 00:30:17,890
+مش موجود في الأولى مش موجود في التقاطع لو مخلقة
+
+448
+00:30:17,890 --> 00:30:24,410
+مختلفة لو مخلقة موجود في الكل، مختلفة إحنا الآن
+
+449
+00:30:24,410 --> 00:30:28,090
+هنا بدناش احنا نشتت في ال hygiene يمكن مثالعلى
+
+450
+00:30:28,090 --> 00:30:36,350
+المغلق تمام الآن ننتقل لبعض النظريات بعض الخواص
+
+451
+00:30:36,350 --> 00:30:39,470
+على اتحاد على ال family و تقاطع على ال family
+
+452
+00:30:39,470 --> 00:30:44,730
+النظرية رقم سبعة في هذا ال chapter طبعا في المقدمة
+
+453
+00:30:44,730 --> 00:30:48,010
+كالعادة اللي هي طبعا تمهيد ومهمة وبدنا نقرأها و
+
+454
+00:30:48,010 --> 00:30:52,440
+نفهم أيش اللي بتقولهبقول لي let capital U be a
+
+455
+00:30:52,440 --> 00:30:56,840
+universal set يعني مجموعة كونية المعنى اللي هي
+
+456
+00:30:56,840 --> 00:31:01,440
+مجموعة مرجعية يعني إيش مرجعية كل شغلنا جواها كل
+
+457
+00:31:01,440 --> 00:31:05,420
+عناصرنا جواهاوكل المجموعات اللي متعاملة معاه هيش
+
+458
+00:31:05,420 --> 00:31:08,500
+sub set منها sub set منها فهذا ال universal set
+
+459
+00:31:08,500 --> 00:31:13,580
+and let A sub Gamma بحيث small Gamma and capital
+
+460
+00:31:13,580 --> 00:31:19,180
+Gamma بيه an empty family of sets عائلة فارقة من
+
+461
+00:31:19,180 --> 00:31:22,180
+المجموعات مش فيها ولا عضو يعني مش فيها ولا عضو
+
+462
+00:31:22,180 --> 00:31:26,640
+بيقول بمعنى أخر أنه الدليل مجموعة الأدلة ال
+
+463
+00:31:26,640 --> 00:31:30,240
+indexing set ال Gamma مش ولا fileمازال مافيش ولا
+
+464
+00:31:30,240 --> 00:31:33,480
+اسم اذا مافيش ولا طالبة لما تطلع على قائمة مافيش
+
+465
+00:31:33,480 --> 00:31:36,100
+ولا اسم مسجل في الشعب هذا يعني ولا طالبة مسجلة في
+
+466
+00:31:36,100 --> 00:31:38,600
+الشعب مافيش هيك فهك معناته مافيش ولا اسم .. مافيش
+
+467
+00:31:38,600 --> 00:31:41,520
+ولا اسم اذا أنا ساعد العائلة ايش مالها فارغة عائلة
+
+468
+00:31:41,520 --> 00:31:45,820
+فارغة then أول
+
+469
+00:31:45,820 --> 00:31:50,620
+statement بيقول في اتحاد على هذه ال family الفارغة
+
+470
+00:31:50,620 --> 00:31:54,140
+five من العناصر الموجودة في كل ال family مافيش ولا
+
+471
+00:31:54,140 --> 00:31:58,420
+عنصر .. مافيش ولا عنصر واضحة هذي .. اه واضحة تمام
+
+472
+00:31:59,630 --> 00:32:04,730
+التانية، لكن التقاطع على ال family بيساوي كل ال
+
+473
+00:32:04,730 --> 00:32:10,450
+universal set، هذي صعبة، هذي ايش؟ ماشي ماشي صعبة،
+
+474
+00:32:10,450 --> 00:32:18,150
+بس خلينا نفهمها مع بعض، اه طبعا احنا .. اهبس ولا
+
+475
+00:32:18,150 --> 00:32:21,410
+واحدة واحدة، هذه نقطة فلسفية ومتعتمدة على المنطق،
+
+476
+00:32:21,410 --> 00:32:24,170
+احنا اذا ال issue ماكانش true مش يكون false، هاي
+
+477
+00:32:24,170 --> 00:32:27,550
+المبدأ انا، اذا ماكانش true، بده يكون false، طبعا
+
+478
+00:32:27,550 --> 00:32:31,410
+تقولي هي ال family فاضية، مافيش فيها ولا مجموعة،
+
+479
+00:32:31,410 --> 00:32:34,470
+فلما تقولي مين العناصر المشتركة في العناصر ال
+
+480
+00:32:34,470 --> 00:32:36,470
+family، في المجموعات في ال family، مش واضح، انا
+
+481
+00:32:36,470 --> 00:32:38,930
+لإن مافيش .. اندي مجموعات أشوف مين مشترك بينهم،
+
+482
+00:32:38,930 --> 00:32:43,980
+خلينا ننظرها من زاوية أخرى، اه إيش نقول؟ لأمين
+
+483
+00:32:43,980 --> 00:32:50,560
+العناصر غير المشتركة؟ ليس هناك نفي، أنا لديها مش
+
+484
+00:32:50,560 --> 00:32:54,200
+مجموعة، طب مين العناصر المش مشتركة؟ كلها مش
+
+485
+00:32:54,200 --> 00:32:57,640
+مشتركة، فإيه؟ فانزلنا من ذوت يعني، لأنها مش true
+
+486
+00:32:57,640 --> 00:33:02,790
+of false، ما زال كل العناصر مش مشتركةالعناصر قولنا
+
+487
+00:33:02,790 --> 00:33:06,830
+ايش مالها؟ احنا ايش بنقول؟ مين مش مشترك ولا واحد
+
+488
+00:33:06,830 --> 00:33:10,830
+مش مشترك ولا واحد مش مش كلهم العكس اه اه حال جيت
+
+489
+00:33:10,830 --> 00:33:15,190
+انا ماعنديش مجموعات طب مين مش مشترك بينهم؟ مافيش
+
+490
+00:33:16,730 --> 00:33:20,990
+انت ماعنكيش مجموعات، ماعنكيش مجموعات، مين غير
+
+491
+00:33:20,990 --> 00:33:24,510
+مشترك؟ عندك اللي هو في الشيء .. في الشيء مجموعات
+
+492
+00:33:24,510 --> 00:33:27,870
+أصلا، ال family فاضية، ال family فاضية، فمين
+
+493
+00:33:27,870 --> 00:33:34,630
+العناصر غير المشتركة؟ واحدش، محدد، لأ الكل، يعني
+
+494
+00:33:34,630 --> 00:33:39,070
+اللي .. يعني صح .. صحيحمرة تانية معلش مهي لأ لأ ..
+
+495
+00:33:39,070 --> 00:33:43,550
+مين غير مشترك في الشيء .. فاي .. فإذا ناش .. الكل
+
+496
+00:33:43,550 --> 00:33:47,510
+مشترك .. اللي هي ناش .. التقابل .. الزاوية بالنفي
+
+497
+00:33:47,510 --> 00:33:52,050
+.. بدا تيجي بالنفي .. نعيد كمان مرة .. نعيد كمان
+
+498
+00:33:52,050 --> 00:33:56,670
+مرة .. عشان بس نلخصبدنا نجيها هذه إيش؟ زي الـ
+
+499
+00:33:56,670 --> 00:33:59,750
+prove by contradiction و احنا ممكن نعملها بادئ شكل
+
+500
+00:33:59,750 --> 00:34:01,990
+فاحنا بدنا نسأل نفسنا .. بدناش نسأل نفسنا مين
+
+501
+00:34:01,990 --> 00:34:06,130
+عناصر المشتركة؟ نقول مين غير مشتركة؟ في بتعرف عنصر
+
+502
+00:34:06,130 --> 00:34:08,950
+موجود في واحدة منهم و مش موجود في التانية؟ لأن
+
+503
+00:34:08,950 --> 00:34:11,290
+مافيش واحدة تانية أول و تانية، فإذا أنا بعرفش و لا
+
+504
+00:34:11,290 --> 00:34:14,570
+عنصر، اه، فإذا أنا بعرفش و لا عنصر غير مشتركة، إذا
+
+505
+00:34:14,570 --> 00:34:16,030
+كل عناصر مشتركة
+
+506
+00:34:18,710 --> 00:34:21,470
+ما هي .. إذا .. إذا .. إذا .. إذا الـ .. الـ ..
+
+507
+00:34:21,470 --> 00:34:28,230
+الـ statement false عكسها true طبعا هنثبتهم احنا
+
+508
+00:34:28,230 --> 00:34:31,650
+هنثبتهم إذا احنا مش جادرين طبعا احنا يمكن نفهمهم و
+
+509
+00:34:31,650 --> 00:34:36,330
+نفسرهم بشكل ملموس البرهان هو إيش؟ هيكون الحكم
+
+510
+00:34:36,330 --> 00:34:41,810
+بيننا و بين الموضوع إنها صح ولا لأ خلينا نبرهن
+
+511
+00:34:41,810 --> 00:34:48,350
+ماشي النقطة أنا بتتفق إنها صعبة شويةبس هي لأنه
+
+512
+00:34:48,350 --> 00:34:53,970
+مافيش family فاضية مافيش مجموعات فطبعا ما تقوليش
+
+513
+00:34:53,970 --> 00:34:57,730
+مين المشترك قولي مين اللي مش مشترك مافيش .. بتلاقي
+
+514
+00:34:57,730 --> 00:35:00,310
+اللي مش .. كله مش .. ال .. ال .. مين مش مشترك ولا
+
+515
+00:35:00,310 --> 00:35:06,250
+حد اذا كله مشترك فهي النافي تبعها ال proof طبعا في
+
+516
+00:35:06,250 --> 00:35:11,990
+رم خلينا نشوف البرهان شوية النظرية غريبة صحيح غير
+
+517
+00:35:11,990 --> 00:35:18,430
+متوقعة اللي هو B على الأقل نبدأ بفرع Aبنبدأ نبره
+
+518
+00:35:18,430 --> 00:35:24,970
+الفرع ايه؟الآن هنركز على الأشي الأهم والأساسي بدنا
+
+519
+00:35:24,970 --> 00:35:29,350
+نثبت مجموعة ما أنها Phi ذكرنا في محاضرات سابقة من
+
+520
+00:35:29,350 --> 00:35:32,750
+أفضل الطريقة نعملها Pro by contradiction لأنه زي
+
+521
+00:35:32,750 --> 00:35:36,850
+العملية السابقة كيف أقول إن X تنتمي لل Phi؟ بنفعش
+
+522
+00:35:36,850 --> 00:35:40,490
+أقول فهي أفضل طريقة ان انا .. لأن Phi فاضية كيف
+
+523
+00:35:40,490 --> 00:35:44,050
+بدي أدور على عنصر في Phi؟ بلاجيش لكن أثرش أن
+
+524
+00:35:44,050 --> 00:35:47,110
+أتعامل مع النفي زي توي ما عملنا النفي هو اللي بيحل
+
+525
+00:35:47,110 --> 00:35:49,510
+المشكلة فاحنا هنقول له Assume
+
+526
+00:35:51,460 --> 00:35:57,900
+إن الإتحاد A sub Gamma لا يساوي Phi من وين جيبت
+
+527
+00:35:57,900 --> 00:36:00,680
+هذا؟ من عندك؟ لأ هذا بتعمل prove by contradiction
+
+528
+00:36:00,680 --> 00:36:09,900
+prove by contradiction تمام؟
+
+529
+00:36:11,830 --> 00:36:15,270
+متفقين؟ خلّيني أنسى بيه شوية و نركز مع البرهان
+
+530
+00:36:15,270 --> 00:36:19,110
+فإذا إيش؟ ناخد الصيغة العامة أنا عندي مجموعة ما
+
+531
+00:36:19,110 --> 00:36:23,170
+بدي أثبت إنها مجموعة فارقة أفضل طريقة هي أكثر
+
+532
+00:36:23,170 --> 00:36:27,010
+طريقة فعالية إنه نعملها by contradiction افترض إنه
+
+533
+00:36:27,010 --> 00:36:29,870
+غير فارقة إيش معات غير فارقة؟ على الأقل فيها أنصف
+
+534
+00:36:29,870 --> 00:36:33,950
+فهذا إيش؟ implies there exists X و ال X هو
+
+535
+00:36:33,950 --> 00:36:38,450
+الموجودة في المجموعة غير الفارقة على الفاي بهذا
+
+536
+00:36:38,450 --> 00:36:42,110
+الشكل طبعا إيش هذا ما له تعريف الفاي؟لأنه مش
+
+537
+00:36:42,110 --> 00:36:49,150
+معناته غير فارغة ممتاز تمام ايش ممكن نعمل نفسر
+
+538
+00:36:49,150 --> 00:36:52,010
+وهذا اللي اتعلمناه قبل قليل اتحاد على ال family
+
+539
+00:36:52,010 --> 00:36:57,860
+خلينا نفسرthere exists x ايش معناة x في الاتحاد ان
+
+540
+00:36:57,860 --> 00:37:01,040
+على اقل في واحدة من ال family فده ايش معناته فده
+
+541
+00:37:01,040 --> 00:37:04,880
+ايش جامعة تنتمي لفاي اه ارجع للتعريف قال لي ايش
+
+542
+00:37:04,880 --> 00:37:08,580
+there exists جامعة في في معناته there exists جامعة
+
+543
+00:37:08,580 --> 00:37:12,120
+في ال capital جامعة اللي هي في في في في في في في
+
+544
+00:37:12,120 --> 00:37:13,280
+في في في في في في في في في في في في في في في في في
+
+545
+00:37:13,280 --> 00:37:14,360
+في في في في في في في في في في في في في في في في في
+
+546
+00:37:14,360 --> 00:37:14,420
+في في في في في في في في في في في في في في في في في
+
+547
+00:37:14,420 --> 00:37:15,080
+في في في في في في في في في في في في في في في في في
+
+548
+00:37:15,080 --> 00:37:15,180
+في في في في في في في
+
+549
+00:37:19,970 --> 00:37:26,250
+هذا التعريف نفسه نجلناه هنا تمام صلحنا فاكستان
+
+550
+00:37:26,250 --> 00:37:30,090
+تاميل ال a sub gamma هذا ايش معلومة جيبناها تعريف
+
+551
+00:37:30,090 --> 00:37:34,950
+الاتحاد على ال family definition of union على
+
+552
+00:37:34,950 --> 00:37:39,460
+family memberمش هيك؟ لما كانت جامة ارجع على
+
+553
+00:37:39,460 --> 00:37:44,320
+التعريف قال لي اللي هو الاتحاد جامة تنتمي لجامة في
+
+554
+00:37:44,320 --> 00:37:46,880
+الملاحظة يا أخوات إذا بتتذكروا احنا قولنا أولشي
+
+555
+00:37:46,880 --> 00:37:49,280
+عملنا تعريف على الفهم اللي بشكل عام قولنا إذا كانت
+
+556
+00:37:49,280 --> 00:37:52,900
+index آه كتبناها بعد الشكل جامة تنتمي لجامة الجامة
+
+557
+00:37:52,900 --> 00:37:55,440
+و بدل ما نقول إيه في الفهم اللي قولناه إيش جامة في
+
+558
+00:37:55,440 --> 00:37:57,800
+كبتة الجامة و كبتة الجامة في هذا السؤال الشمالي هي
+
+559
+00:37:57,800 --> 00:38:01,000
+Phi المضحك اللي ناياه فبعد الشكل طبعا أصلنا ل
+
+560
+00:38:01,000 --> 00:38:05,340
+contradiction وين هو؟ there exists gamma and phi
+
+561
+00:38:05,340 --> 00:38:06,140
+بعد contradiction
+
+562
+00:38:11,180 --> 00:38:23,280
+فبالتالي فرضيتنا غلط وعكس هو الصحيح يساوي
+
+563
+00:38:23,280 --> 00:38:27,420
+فعلا طبعا فال contradiction هنا اللي مش واضح حالها
+
+564
+00:38:27,420 --> 00:38:33,420
+هذه contradiction متابعين؟
+
+565
+00:38:33,420 --> 00:38:40,140
+نشوف الفرع رقم B اللي مغلبنا نفهم مش مستوعبين ومش
+
+566
+00:38:40,140 --> 00:38:48,040
+متخيلينفنشوف البرهان .. نشوف البرهان طبعا ال
+
+567
+00:38:48,040 --> 00:38:53,130
+statement اللي عندي simple ولا compoundSimple، أنا
+
+568
+00:38:53,130 --> 00:38:55,370
+أرجعكوا شويه إلى الشبطة الأولة، مافيش إلا
+
+569
+00:38:55,370 --> 00:38:58,310
+statement واحدة، statement هذه، يا true يا false،
+
+570
+00:38:58,310 --> 00:39:00,910
+إحنا نثبت إنها true، نثبت إنها true، لأن statement
+
+571
+00:39:00,910 --> 00:39:04,090
+بيقولي مجموعة تساوي مجموعة، statement فيها and،
+
+572
+00:39:04,090 --> 00:39:07,350
+فيها if then، فيها or، لأ، بيقولي A تساوي B،
+
+573
+00:39:07,350 --> 00:39:09,950
+مجموعة إيه، هو أنا عندي بعرف إيش الـA و بعرف إيش
+
+574
+00:39:09,950 --> 00:39:12,550
+الـB، فبقدر أحكم إنهم true ولا false، فهذه
+
+575
+00:39:12,550 --> 00:39:16,570
+statement بسيطة جدا، بدنا نثبت، أه، إيش اللي بدنا
+
+576
+00:39:16,570 --> 00:39:19,890
+نثبت، تساوي مجموعة، في أننا عدي الطرق،يا هنرجع
+
+577
+00:39:19,890 --> 00:39:23,290
+للتعريف for all x، x في الأولى، if and only if x
+
+578
+00:39:23,290 --> 00:39:26,590
+بالتانية، اللي هي تكافئ إن الأولى صبصت من التانية
+
+579
+00:39:26,590 --> 00:39:28,870
+و التانية صبصت من الأولى، مش هيك بتصير، كتبناها
+
+580
+00:39:28,870 --> 00:39:32,550
+يمكن و لا مرة استخدمناها، لكن شوية هنصير نستخدمها،
+
+581
+00:39:32,550 --> 00:39:37,070
+لأنه زي ما حكيت التكافئ في المرحلة البسيطة، ممكن
+
+582
+00:39:37,070 --> 00:39:40,350
+نمشي تكافئ، لكن في المرحلة المتقدمة، صعوب أن نمشي
+
+583
+00:39:40,350 --> 00:39:43,630
+تكافئ، فاحنا هنكون نعتمد دايما اللي هو two parts
+
+584
+00:39:43,630 --> 00:39:46,230
+proof، دايما ال if and only if في الغالب، هنعملها
+
+585
+00:39:46,230 --> 00:39:49,920
+اتجاهين، هنعملها اتجاهين، صعب نمشي اتطريقها دي
+
+586
+00:39:49,920 --> 00:39:52,520
+الأولى الطريقة التانية ممكن أنا أعملها تساوي
+
+587
+00:39:52,520 --> 00:39:56,780
+مجموعات بس بدي معلومات تكون كبيرة نظريات سابقة حتى
+
+588
+00:39:56,780 --> 00:39:59,880
+أمشي من طرف لطرف طب احنا لسه الاتحاد أدى أول نظرية
+
+589
+00:39:59,880 --> 00:40:02,560
+على اتحاد على ال family مظبوط إذا مش لازم مافيش
+
+590
+00:40:02,560 --> 00:40:06,040
+أمامنا اللي التعريف أمامنا التعريف طب فاحنا هنثبت
+
+591
+00:40:06,040 --> 00:40:09,740
+التساويطبعا الحقيقة أن هذا السؤال مش هنقدر نمشي
+
+592
+00:40:09,740 --> 00:40:13,120
+فيه تكافئه، هنضطر نعمله على اتجاهين، أن الأولى
+
+593
+00:40:13,120 --> 00:40:16,240
+subset من الثانية و التانية subset من الأولى، فبدي
+
+594
+00:40:16,240 --> 00:40:21,140
+أجسمه جزئين، فبدي أنا أثبت بيه الـP الفرع الأول
+
+595
+00:40:21,140 --> 00:40:25,020
+بدل ما أثبت هذا هو المطلوب طبعا المطلوب Gamma
+
+596
+00:40:25,020 --> 00:40:30,140
+تنتمي للـPhi A sub Gamma تساوي U، هذا مطلوبيا
+
+597
+00:40:30,140 --> 00:40:33,260
+بتقولي I want to prove يا بتحطي علامة استفهام ارجو
+
+598
+00:40:33,260 --> 00:40:36,540
+التعود على الأشياء البسيطة دي مهم جدا اه فانا انا
+
+599
+00:40:36,540 --> 00:40:40,040
+اول شي اش بده اعمل بده اجازه لجزئين هثبت انه
+
+600
+00:40:40,040 --> 00:40:46,720
+التقاطع subset من ال U برضه هذا مطلوب فجسمته بدل
+
+601
+00:40:46,720 --> 00:40:51,240
+ما اعمل تساوي هعمل subset على مرحلة ممتازة طبعا
+
+602
+00:40:51,240 --> 00:40:58,260
+الكل بيعرف كيف بنبدأ let X be any element
+
+603
+00:41:00,270 --> 00:41:09,230
+and let X تنتمي تقاطع Gamma تنتمي لفاي A sub Gamma
+
+604
+00:41:09,230 --> 00:41:14,950
+في حد عنده أي صعوبة ماجيبناش أي شي جديد حتى الآن و
+
+605
+00:41:14,950 --> 00:41:17,590
+لا لأ كل و ده أشياء قديمة الآن بدنا ندخل في
+
+606
+00:41:17,590 --> 00:41:22,550
+التفاصيل طيب زي كالعادة انا عند البدايات و عند
+
+607
+00:41:22,550 --> 00:41:28,340
+المعطيات و عيني وين المطلوب اه وين بده اوصل ال Xلل
+
+608
+00:41:28,340 --> 00:41:33,180
+U بدنا نوصل ال X لل U فى حد عندها قصيرة مواصلات
+
+609
+00:41:33,180 --> 00:41:39,040
+آمنة توصل ال X لل U ممكن بس هذا صحيح لكنه غير مفيد
+
+610
+00:41:39,040 --> 00:41:43,330
+طيب نسترجع ما هي ال Uمن هي ال U؟ هي ال universal
+
+611
+00:41:43,330 --> 00:41:46,910
+set إيش معناته؟ أنا جوا، كل شغل جوا، فأنا أخدت
+
+612
+00:41:46,910 --> 00:41:50,570
+عنصر، العنصر هذا بداخله من برا؟ لأ، فهذه بدهية، كل
+
+613
+00:41:50,570 --> 00:41:53,550
+عناصر في ال U فانا كل شغل جوا ال U فعلى طول هذه
+
+614
+00:41:53,550 --> 00:41:58,790
+بدهية then X تنتمي لل U، ليش؟ لأن ال U universal
+
+615
+00:41:58,790 --> 00:42:02,450
+set لأن ال U is a universal set
+
+616
+00:42:06,810 --> 00:42:10,330
+فإذن متحدث احنا على ال universal set كل المجموعات
+
+617
+00:42:10,330 --> 00:42:13,730
+صبصت منها بديهية هذه بكل سهولة اه فإذا أثبتنا أنه
+
+618
+00:42:13,730 --> 00:42:16,710
+فعلا فهذه يعني الحقيقة بداش تثبات فهذه دايما صحيحة
+
+619
+00:42:16,710 --> 00:42:19,350
+أي مجموعة هي صبصت من اليوليان ليش مع ال universal
+
+620
+00:42:19,350 --> 00:42:26,230
+set فإذا هذا أول فرع أو أول جزء خلصناه thus
+
+621
+00:42:26,230 --> 00:42:34,050
+تقاطع a sub gamma صبصت من اليوليان فهذا الجزء
+
+622
+00:42:34,050 --> 00:42:40,520
+الأول خلصناهفدي واحد واضح؟ اه فالأمر يمكن يكون
+
+623
+00:42:40,520 --> 00:42:44,600
+شوية غريب او نكون نسيينه بس ننساش مانات ال U فانا
+
+624
+00:42:44,600 --> 00:42:49,200
+كل شغلي جوا ال U انا هي عند اليوم الإطار تبعه و
+
+625
+00:42:49,200 --> 00:42:53,560
+بشغل جوا فانا أخد ال TX من وين بدي أخدها؟ جوا ال U
+
+626
+00:42:53,560 --> 00:42:58,200
+بطلعش برا مديش أطلع برا تمام نيجي للطرف أو للاتجاه
+
+627
+00:42:58,200 --> 00:43:02,250
+التانيالآن بدنا الـ U subset هذا الأصعب مهو الـ U
+
+628
+00:43:02,250 --> 00:43:06,130
+كبيرة تحتوي الكل فالترابية تحتوي التقاطع الآن
+
+629
+00:43:06,130 --> 00:43:13,010
+للتجاه التاني U subset من مين؟ من التقاطع جامعة
+
+630
+00:43:13,010 --> 00:43:18,910
+تنتمي لـ Phi إيه Sub Gamma على انت استفهام مطلوب
+
+631
+00:43:18,910 --> 00:43:32,840
+كالعادة let X be any element andlet X تنتمي لمن؟
+
+632
+00:43:32,840 --> 00:43:43,400
+لـ U ممتاز X تنتمي لـ U مادي بدهية مادة ناششة ايش
+
+633
+00:43:43,400 --> 00:43:47,040
+ممكن .. بدنا نوصلها لمين؟ للتقاطع بدنا نوصلها
+
+634
+00:43:47,040 --> 00:43:51,440
+للتقاطع ايش ملاحظين؟ ادينا مكتفة مش عارفين نعملش
+
+635
+00:43:51,440 --> 00:43:54,180
+ايش X في الـ U؟ مادي كله X في الـ U طيب ايش ممكن
+
+636
+00:43:54,180 --> 00:43:58,660
+نعمل ال trick؟نعمل indirect proof طب واحد يقول لي
+
+637
+00:43:58,660 --> 00:44:01,940
+indirect proof جوه ال proof فاش مشكلة خليني اكتبها
+
+638
+00:44:01,940 --> 00:44:04,740
+معاكم عشان نشوف كيف لما احنا بنفكر بصوت عالي و
+
+639
+00:44:04,740 --> 00:44:08,180
+بنكتبها مش بيساعدنا الان انا ايش بده اخد عنصر في
+
+640
+00:44:08,180 --> 00:44:11,680
+اليسار ايش مطلوب مني اوصل الي يمين ايش بده اكتب we
+
+641
+00:44:11,680 --> 00:44:14,680
+want عشان تفهموا اللي بقي الخطوة اللي بعدها to
+
+642
+00:44:14,680 --> 00:44:20,410
+prove صح؟ماش بدنا نثبت ان ال X ت prove that X
+
+643
+00:44:20,410 --> 00:44:26,810
+سنتمي للتقاطة Gamma in Phi A Gamma هذا ايش مطلوب
+
+644
+00:44:26,810 --> 00:44:32,340
+أصبحهذا مطلوب أبرهنه ممكن أبرهنه ب direct proof
+
+645
+00:44:32,340 --> 00:44:36,680
+ممكن ممكن أبرهنه ب indirect proof من المانع من
+
+646
+00:44:36,680 --> 00:44:40,420
+المانع فاحنا لما كنا بنحلل في أي فاحنا بدنا نفهم
+
+647
+00:44:40,420 --> 00:44:44,800
+أنه ضروري جدا يا خوات أنا و أنا بحلل البرهان مش
+
+648
+00:44:44,800 --> 00:44:47,960
+ضروري كل البرهان يكون indirect proof ممكن أي جزء
+
+649
+00:44:47,960 --> 00:44:50,880
+منه يكون direct أو indirect أنا ممكن و أنا بجزق في
+
+650
+00:44:50,880 --> 00:44:55,120
+مرحلة ما مطلوب اني أثبت الجزئية هذه كيف أثبتها بأي
+
+651
+00:44:55,120 --> 00:44:58,010
+طريقة رياضية صحيحةأه مش ضروري يكون كل البرهان
+
+652
+00:44:58,010 --> 00:45:01,050
+indirect ولا كله direct لأ انا كل جزئية بدي
+
+653
+00:45:01,050 --> 00:45:03,510
+أبرهنها انا بدي أبرهن حاجة معينة كيف أبرهنها
+
+654
+00:45:03,510 --> 00:45:06,930
+بالطريقة المناسبة أي طريقة صحية فالان انا هعملها
+
+655
+00:45:06,930 --> 00:45:10,710
+دي إيش indirect proof فانا هروح أقوله هنا فلنكتب
+
+656
+00:45:10,710 --> 00:45:15,630
+هنا لأن احنا هننهيه فهقوله الآن إيش دي عمل assume
+
+657
+00:45:15,630 --> 00:45:20,090
+X
+
+658
+00:45:20,090 --> 00:45:28,370
+لا تنتميX لا تنتمي للتقاطع Gamma in Phi A sub
+
+659
+00:45:28,370 --> 00:45:31,370
+Gamma ايش بتعمل؟ بعمله انا prove by contradiction
+
+660
+00:45:31,370 --> 00:45:37,610
+prove by contradiction prove لمين؟ للمقلوب الأخير،
+
+661
+00:45:37,610 --> 00:45:42,060
+للجزئية هذه، لللي مطلبها هذه، واضح؟فأرجو هذه
+
+662
+00:45:42,060 --> 00:45:44,220
+الصورة تكون واضحة، مانكونش احنا إيش بنفكر بالاتجاه
+
+663
+00:45:44,220 --> 00:45:47,200
+واحد، بدأ يكون عندي هذه المرونة و هذه السعة، أنا
+
+664
+00:45:47,200 --> 00:45:50,680
+عندي حاجة بدي أثبتها، كيف أثبتها؟ بأي طريقة رياضية
+
+665
+00:45:50,680 --> 00:45:53,700
+صحيحة، فمش ضروري كل البرهان يكون indirect أو كله
+
+666
+00:45:53,700 --> 00:45:58,220
+يكون direct، تمام، الأن أفسر إيش معناه X لا تنتمي،
+
+667
+00:45:58,220 --> 00:46:00,280
+خليها دي أقبر عن نفي اللي ينتمي، أنا بعرف أفسر
+
+668
+00:46:00,280 --> 00:46:03,120
+اللي ينتمي، هيك التعريف، فهنا على طول هذا إيش
+
+669
+00:46:03,120 --> 00:46:09,560
+يكافئ not X تنتمي Gamma in Phi A sub Gamma، مجرد
+
+670
+00:46:09,560 --> 00:46:13,080
+إيش التفسير؟هذا رمز notation ليس إلا notation هذه
+
+671
+00:46:13,080 --> 00:46:16,220
+ولا لأ؟ هذا رمز إيش معناه أنه فيه؟ هذا معناته
+
+672
+00:46:16,220 --> 00:46:20,080
+ممتاز إيش ممكن أفسر؟ ممكن أفسر التقاطع الآن تقاطع
+
+673
+00:46:20,080 --> 00:46:23,840
+على ال family فهذا يكافئ not إيش معناه X في
+
+674
+00:46:23,840 --> 00:46:27,920
+التقاطع؟ يعني X موجودة في كل المجموعات for all
+
+675
+00:46:27,920 --> 00:46:34,800
+Gamma in Phi ال X تنتمي لمن؟ لل A Gamma من وين
+
+676
+00:46:34,800 --> 00:46:42,280
+جيبته هذا؟ definition تقاطع على ال familyأي سؤال؟
+
+677
+00:46:42,280 --> 00:46:47,580
+متابعين؟ اه ممتاز ايش ممكن اعمل الآن ننفل ليش ال
+
+678
+00:46:47,580 --> 00:46:53,020
+quantifier اه فهذه لأ تكافئ there exist gammaفي
+
+679
+00:46:53,020 --> 00:46:55,980
+الـ Phi ولا not في الـ Phi؟ في الـ Phi، مالاش
+
+680
+00:46:55,980 --> 00:47:01,120
+دعوة، مابديش نقطة فGamma تنتمي للـ Phi such that X
+
+681
+00:47:01,120 --> 00:47:05,880
+لا تنتمي للـ A Gamma النفرة مين؟ للـ P of X، للـ
+
+682
+00:47:05,880 --> 00:47:09,600
+statement من وين جبتها ده؟ Quantifier ايش؟
+
+683
+00:47:09,600 --> 00:47:13,680
+Negation Quantifier
+
+684
+00:47:13,680 --> 00:47:20,040
+Negationقواعد نفي المكمّمات وصلنا لcontradiction
+
+685
+00:47:20,040 --> 00:47:23,900
+ولا ماوصلناش؟ وصلنا there exists جيش Gamma and Phi
+
+686
+00:47:23,900 --> 00:47:30,560
+Contradiction Contradiction
+
+687
+00:47:30,560 --> 00:47:34,200
+إذن
+
+688
+00:47:34,200 --> 00:47:40,240
+فرضية اللي ضيفتها أنا عندي خطأ وعكسها هو الصوار
+
+689
+00:47:40,240 --> 00:47:44,300
+Thus X تنتمي للتقاطع
+
+690
+00:47:46,600 --> 00:47:50,700
+وبالتالي بدأنا من X في ال U أثبتناها إنها في الطرف
+
+691
+00:47:50,700 --> 00:47:58,960
+التاني إذا الأول subset من التاني and hence اللي
+
+692
+00:47:58,960 --> 00:48:08,700
+هو ال U subset من هذا التقاطع فهي
+
+693
+00:48:08,700 --> 00:48:15,280
+واحد و اتنين بديلي التسابقواحد واتنين implies you
+
+694
+00:48:15,280 --> 00:48:25,830
+تساوى التقابل صبكى اي سؤال؟فطبعا يمكن تكون احنا
+
+695
+00:48:25,830 --> 00:48:30,610
+صعب ان نستوعبها مش متخيلينها لكن هي البرهان اذا
+
+696
+00:48:30,610 --> 00:48:34,250
+البرهان احنا متفقين على قواعد المنطق وكل شغل
+
+697
+00:48:34,250 --> 00:48:37,370
+الخطوات متأكدين منها اذا هذه statement صحيحة حتى
+
+698
+00:48:37,370 --> 00:48:40,370
+لو احنا مش قادرين نتخيلها لكن برهانها واضحة قدامنا
+
+699
+00:48:40,370 --> 00:48:43,050
+وقدرنا نفتقر نوقف هنا ان شاء الله
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/mUJTBUAt-Mc_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/mUJTBUAt-Mc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..62b8c12017ce5e2562a3ba5d0c655593c0592f1e
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/mUJTBUAt-Mc_raw.srt
@@ -0,0 +1,1788 @@
+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 --> 00:21:10,960
+طبع الاتحاد طبع الاتحاد طبع الاتحاد طبع الاتحاد
+
+284
+00:21:10,960 --> 00:21:10,960
+طبع الاتحاد طبع الاتحاد طبع الاتحاد طبع الاتحاد
+
+285
+00:21:10,960 --> 00:21:20,040
+طبع الاتحاد طبع الاتحاد طبع الاتحاد طبع الاتحاد
+
+286
+00:21:20,040 --> 00:21:26,140
+طبع الاتحاد طبع الTwo cardinal numbers A and B
+
+287
+00:21:26,140 --> 00:21:31,560
+مطلوب منها جيب A زي B إيش يعمل؟ جال نجيب مجموعتين
+
+288
+00:21:31,560 --> 00:21:37,260
+capital A و capital B جيب
+
+289
+00:21:37,260 --> 00:21:40,400
+مجموعتين زي ما قلنا بنجيب اتنين زي تلاتة جيب
+
+290
+00:21:40,400 --> 00:21:44,280
+مجموعة فيها تلات تفاحات و مجموعة فيها تفاحتين و
+
+291
+00:21:44,280 --> 00:21:49,110
+جيب الاتحادبينفع ياخد أي مجموعة تانية بالشرط ان
+
+292
+00:21:49,110 --> 00:21:54,090
+الـ A تقاطع الـ B يساوي 5 فبعد ما اجيب الاتحاد ايش
+
+293
+00:21:54,090 --> 00:21:58,770
+هروح اجيب ال cardinality اعدهم ايش هذا بيساوي A
+
+294
+00:21:58,770 --> 00:22:04,180
+زاد Bيساوي a زاد b فهذه العملية تمام فبقول ليه ال
+
+295
+00:22:04,180 --> 00:22:08,180
+where a and b are disjoint sits such that بدنا
+
+296
+00:22:08,180 --> 00:22:11,440
+اللي هو مقابل ال a مجموعة ال cardinality بتساوي
+
+297
+00:22:11,440 --> 00:22:14,480
+small a ومقابل ال b مجموعة ال cardinality بتساوي
+
+298
+00:22:14,480 --> 00:22:18,200
+small b طبعا بس يكونوا disjoint بقدر أجيب بهذه
+
+299
+00:22:18,200 --> 00:22:21,900
+الصورة واضحة فالعملية بسيطة وسهلة في الطريقة
+
+300
+00:22:21,900 --> 00:22:26,860
+العملية قبل ما نبدأ نشوف الأمثلة و نشوف بعض الخواص
+
+301
+00:22:26,860 --> 00:22:31,860
+في عندنا نظريةعنوان النظرية addition of cardinal
+
+302
+00:22:31,860 --> 00:22:36,540
+numbers is well defined ماذا يعني هذا؟ هذا سؤال
+
+303
+00:22:36,540 --> 00:22:40,780
+أحياناً بنقابله في الرياضيات أنا فيه عندي تعريف لو
+
+304
+00:22:40,780 --> 00:22:44,560
+رجعنا للتعريف بقول عشان تجيبي المجموع A زائد B
+
+305
+00:22:44,560 --> 00:22:50,260
+جيبلي مجموعتين A و B تقطعهم يساوي Phi و بعدين جيب
+
+306
+00:22:50,260 --> 00:22:55,520
+الاتحاد و أعدهل هذا تعريف يُعتبر تعريف علمي؟ نعم،
+
+307
+00:22:55,520 --> 00:22:58,160
+هناك نقطة دائماً في هذا السؤال الذي نطرحه، لماذا؟
+
+308
+00:22:58,160 --> 00:23:01,320
+لأنه يقول إنك تريد أن تجلب الـA و الـB، طب أنا جبت
+
+309
+00:23:01,320 --> 00:23:04,740
+الـA و الـB، و إجت طالب أخر جابت مجموعتين X و Y،
+
+310
+00:23:04,740 --> 00:23:07,920
+هل الناتج باعتمد على الاختيار للمجموعتين هؤلاء، أو
+
+311
+00:23:07,920 --> 00:23:10,880
+ليس باعتمد؟ لو كان باعتمد، فهو ليس تعريف علمي
+
+312
+00:23:11,290 --> 00:23:14,590
+فبنثبت إن هذا لا يعتمد لأنه بكل جيب وبعدين هل
+
+313
+00:23:14,590 --> 00:23:17,430
+دايما بقدر أجيب المجموعات دول ولا ممكن أعجز
+
+314
+00:23:17,430 --> 00:23:20,170
+وبالتالي مش هقدر أجيب المجموع فهنا السؤال المطروح
+
+315
+00:23:20,170 --> 00:23:23,070
+بهذا الشكل عشان هيك بده أقول إن هذا التعريف تعريف
+
+316
+00:23:23,070 --> 00:23:26,510
+علمي كامل دايما أنا بقدر أجيب المجموعاتين A و B
+
+317
+00:23:26,510 --> 00:23:30,570
+تقطعهم يساوي Phi ولو أحد آخر جاب مجموعتين مختلفتين
+
+318
+00:23:30,570 --> 00:23:33,270
+بنفس الشروط لازم يطلع نفس الجوابعشان يكون تعريف
+
+319
+00:23:33,270 --> 00:23:36,170
+علمى صحيح لا يعتمد على الإنسان اللى بيجري العملية
+
+320
+00:23:36,170 --> 00:23:40,710
+وإنما بيعتمد على التعريف العلمى تبعته وبالتالي هو
+
+321
+00:23:40,710 --> 00:23:43,750
+تعريف علمى لا يعتمد على الشخص اللى بيجري العملية
+
+322
+00:23:43,750 --> 00:23:47,530
+وإنما يعتمد على الخواص والأمور العامة اللى بتجري
+
+323
+00:23:47,530 --> 00:23:53,160
+فعنا هنا النظرية بتقول التاليlet A and B be
+
+324
+00:23:53,160 --> 00:23:56,900
+cardinal numbers أنا مطلوب مني أجيب A زائد B أول
+
+325
+00:23:56,900 --> 00:24:00,520
+شيء بيقوللي دايما و أبدا بتقدر تلاقي مجموعتين
+
+326
+00:24:00,520 --> 00:24:03,580
+واحدة ال cardinality تبعتها small a و واحدة ال
+
+327
+00:24:03,580 --> 00:24:08,780
+cardinality small b و هم disjoint فدايما ممكن فحدش
+
+328
+00:24:08,780 --> 00:24:11,680
+يقوللي رجيب ليه اللي هو أربعة زائد خمسة يقوللي مش
+
+329
+00:24:11,680 --> 00:24:14,120
+هملاقي مجموعتين مستحيل لازم يلاقي مجموعتين
+
+330
+00:24:14,120 --> 00:24:18,360
+فالنظرية بتقوللي إيش بتقدر تلاقي مجموعتينإتنين طيب
+
+331
+00:24:18,360 --> 00:24:22,140
+لو انا اديت اللي هو بقول جيبه المجموع اللي هو A
+
+332
+00:24:22,140 --> 00:24:26,900
+زائد B للمئة طالب اللي هنا أو أقل وكل واحدة لجت
+
+333
+00:24:26,900 --> 00:24:29,360
+مجموعتين مختلفتين لازم يطلع الجواب نفس الجواب مش
+
+334
+00:24:29,360 --> 00:24:31,660
+هتقول انا لجت مجموعتين مختلفتين فطلع مع الجواب
+
+335
+00:24:31,660 --> 00:24:34,980
+مختلف لأ لازم يطلع نفس الجواب النهاية .. اه فكيف
+
+336
+00:24:34,980 --> 00:24:38,340
+بده اعبر عنها بقول لو كان في عندنا مجموعة اربع
+
+337
+00:24:38,340 --> 00:24:44,220
+مجموعاتA1 B1 و A2 و B2 هما عبارة عن مجموعات بحيث
+
+338
+00:24:44,220 --> 00:24:51,420
+طبعا انا مقابل ال A ايش جبت جبت A1 و A2 فال
+
+339
+00:24:51,420 --> 00:24:56,240
+cardinata بعتهم متساوين و مقابل ال B في طالب جابت
+
+340
+00:24:56,240 --> 00:25:01,150
+B1 و في طالب جابت B2أه طبعا الطالب الأولى لما جابت
+
+341
+00:25:01,150 --> 00:25:05,230
+A1 وB1 بدوا تقطوحهم يساوي الفائد والتانية جابت A2
+
+342
+00:25:05,230 --> 00:25:08,850
+وB2 تقطوحهم يساوي الفائد طب الأولى جابت الاتحاد
+
+343
+00:25:08,850 --> 00:25:12,630
+وجابت المجموع بطلع محارة قبل والتانية جابت الاتحاد
+
+344
+00:25:12,630 --> 00:25:15,010
+وجابت المجموع طالما حارة خمس لازم يكون متساوين
+
+345
+00:25:15,010 --> 00:25:17,870
+دايما بطلع متساوين فهذه النظرية بتقول بها الشكل
+
+346
+00:25:17,870 --> 00:25:22,390
+خلينا نشوف البرهان مع بعضخلّينا نشوف البرهان مع
+
+347
+00:25:22,390 --> 00:25:27,130
+بعض فبالتالي لو أنا بدأ أجمع تلاتة زائد أربعة
+
+348
+00:25:27,130 --> 00:25:29,890
+أجيبت تلاتة تفاحات وأربعة تفاحات ولا تلاتة
+
+349
+00:25:29,890 --> 00:25:32,390
+بوردجانات وأربعة بوردجانات ما بيختلفش الجواب
+
+350
+00:25:32,390 --> 00:25:36,290
+المجموعة لو تغيرت المجموعات بس يحققوا الشرطين أن
+
+351
+00:25:36,290 --> 00:25:40,350
+يكونوا كل مجموعة بتعبر عن عدد ولو يكونوا disjoint
+
+352
+00:25:40,350 --> 00:25:45,990
+فالنتج ما بيختلفش فالنتج لن يختلف نشوف البرهان مع
+
+353
+00:25:45,990 --> 00:25:50,190
+بعض تفضل اه
+
+354
+00:25:55,760 --> 00:26:00,000
+كأرقام، بديك تجيب مجموعتين مختلفتين، يعني انت مثلا
+
+355
+00:26:00,000 --> 00:26:04,400
+تعلم طفل الجامع، بديك تعلمه اتنين زي التلاتة
+
+356
+00:26:04,400 --> 00:26:09,280
+بيساوي خمسة، بدي تكون عندك خمس كورات أو خمس طفحات،
+
+357
+00:26:09,280 --> 00:26:12,240
+بينفعش تعملينه مجموعتين من أربع طفحات، تقولها هذه
+
+358
+00:26:12,240 --> 00:26:14,720
+المجموعة الأولى، خلصنا منها، و تروح بعدين تاخد
+
+359
+00:26:14,720 --> 00:26:17,920
+منها عنصر وده، فمافيش تكون عنصر مشترك، صح؟ فهذا هو
+
+360
+00:26:17,920 --> 00:26:18,320
+المعنى
+
+361
+00:26:22,000 --> 00:26:25,640
+أربعة زي التقطع بيسووا تمانية، طب كيف بدك تثبتيها؟
+
+362
+00:26:25,640 --> 00:26:28,700
+بدك تجيبي مجموعتين، مجموعة فيها أربعة طفاحات و
+
+363
+00:26:28,700 --> 00:26:31,640
+مجموعة فيها أربعة طفاحات، بدكون عندك كام طفاحة
+
+364
+00:26:31,640 --> 00:26:34,300
+عشان لازم تكون تمانية، بينفع تعملي مجموعتين في
+
+365
+00:26:34,300 --> 00:26:37,500
+سبعة أو بستة تقولي أنا بدي أعملهم مرتين، أخلصت
+
+366
+00:26:37,500 --> 00:26:40,000
+المجموع الأولى خلاص امحيها و أعمل كمان مجموع
+
+367
+00:26:40,000 --> 00:26:44,390
+تانية، بينفعشواضحة؟ فلا يجب أن يكون تكرار، فلازم
+
+368
+00:26:44,390 --> 00:26:48,330
+يكون هذه المنفصلات هيانة مجموعة و هيانة مجموعة، لا
+
+369
+00:26:48,330 --> 00:26:53,230
+يمكن أن يكون فيهم عنصر مشترك مرة هنا و مرة هنا، لم
+
+370
+00:26:53,230 --> 00:26:56,550
+تُوضح الفكرة؟ كأنك تستطيع تعمل هذه عملية الجامعة
+
+371
+00:26:56,550 --> 00:27:00,310
+بالظبط بعد الصورة، طبعا هو ليش؟ لأنه عندما يعمل
+
+372
+00:27:00,310 --> 00:27:04,490
+الاتحاد عنصر المتكرر، ليس مرتين، صح ولا لأ؟ فلا
+
+373
+00:27:04,490 --> 00:27:09,250
+يجب أن يكون عنصر متكرر، نشوف البرهان، فهذه نظرية 6
+
+374
+00:27:09,250 --> 00:27:09,570
+-3
+
+375
+00:27:14,050 --> 00:27:19,390
+approved طبعا بالنسبة لكل المقدمات معطيات ايش
+
+376
+00:27:19,390 --> 00:27:22,430
+المعطيات ان ال a و ال b cardinal numbers فنبدأ
+
+377
+00:27:22,430 --> 00:27:27,430
+بواحد بدي الاقي مجموعة a و مجموعة b الأولى
+
+378
+00:27:27,430 --> 00:27:29,690
+cardinal تبعتها small a و التانى ال cardinal
+
+379
+00:27:29,690 --> 00:27:34,750
+تبعتها small b و الأهم يكون دوسيون يكونوا دوسيون
+
+380
+00:27:34,750 --> 00:27:40,530
+مين عنده نقطة بدايةأول ما بدّينا ال cardinal
+
+381
+00:27:40,530 --> 00:27:43,230
+numbers قلنا كل cardinal number بيبقى بالمجموع
+
+382
+00:27:43,230 --> 00:27:48,930
+فالـ A هن على طول اللي هو القاعدة C1 implies there
+
+383
+00:27:48,930 --> 00:27:55,190
+exist six X و Y بدي أسميهم مش هم ال A و ال B بدور
+
+384
+00:27:55,190 --> 00:27:58,010
+عليهم لأنهم لسه ممكن يكونوا مت disjoint القاعدة
+
+385
+00:27:58,010 --> 00:27:59,810
+بتقول يوجد such that
+
+386
+00:28:03,260 --> 00:28:08,040
+الـ Cardinality للـ X تساوي Small a والـ
+
+387
+00:28:08,040 --> 00:28:15,020
+Cardinality andالـ cardinality للـ Y تساوي small p
+
+388
+00:28:15,020 --> 00:28:19,100
+فهذه أول قاعدة يقولنا كل cardinal number يقابله
+
+389
+00:28:19,100 --> 00:28:22,860
+مجموعة لأن هذا ياش لا ينفك عنها، لا ينفك عنها تمت
+
+390
+00:28:22,860 --> 00:28:25,820
+عندنا مشكلة التي التقاطع يساوي في فأنا عندي
+
+391
+00:28:25,820 --> 00:28:29,380
+مجموعتين تقطعهم يساوي في أو لو يساوي في مش عارف
+
+392
+00:28:29,380 --> 00:28:33,280
+بدنا نعمل trick بسيط و نكون ال A و ال B نحافظ على
+
+393
+00:28:33,280 --> 00:28:36,880
+ال cardinality لكن نضمن أنه التقاطع يساوي في
+
+394
+00:28:36,880 --> 00:28:42,900
+الفكرة قبل ذلك مرت عليناكيف أكوّن مجموعة كافة الـ
+
+395
+00:28:42,900 --> 00:28:47,660
+X لكن تقاطع .. أو مجموعة كافة الـ Y لكن التقاطع مع
+
+396
+00:28:47,660 --> 00:28:53,180
+الـ X .. التقاطع بينتان ما بعد يكون فاية اتنين X و
+
+397
+00:28:53,180 --> 00:28:57,560
+Y اضربها في اتنين يعني اه Cartesian product ..
+
+398
+00:28:57,560 --> 00:29:06,080
+Cartesian product الآن هنعرف let A تساوي X across
+
+399
+00:29:06,080 --> 00:29:12,800
+اتنينفهذه تكافئ ال X لأنها مش رابطة في واحد لأن هي
+
+400
+00:29:12,800 --> 00:29:16,400
+مش نفس الأزواج كيف هذه تكافئ ال X؟ من ال bijection
+
+401
+00:29:16,400 --> 00:29:25,840
+X تروح ل X اتنين فهذه bijection and let B تساوي Y
+
+402
+00:29:25,840 --> 00:29:31,180
+cross من الواحد مثلا اي عدد غير اتنين cross الواحد
+
+403
+00:29:31,180 --> 00:29:37,950
+then على طول ال cardinalityللـ A تساوي ال
+
+404
+00:29:37,950 --> 00:29:43,550
+cardinality لل X تساوي A لأن هم متكافئين بسهولة فى
+
+405
+00:29:43,550 --> 00:29:48,550
+حد عنده مشكلة أنه يثبت أن X تكافئ هذه فى حد عنده
+
+406
+00:29:48,550 --> 00:29:54,130
+مشكلة ماحدش عنده مشكلة ايش ال bijection F من X ل X
+
+407
+00:29:54,130 --> 00:29:58,090
+cross الواحد ايش بتساوي F من X تساوي الزوج X1 X1
+
+408
+00:29:58,090 --> 00:30:04,960
+على طول and نفس القضية cardinalityللـ B تساوي ال
+
+409
+00:30:04,960 --> 00:30:10,220
+cardinality لل Y تساوي B ايش كمان ال A تقطع ال B
+
+410
+00:30:10,220 --> 00:30:14,400
+فاي ليش؟ لأن مافيش عنصر مشارك بينهم هدولة لأن
+
+411
+00:30:14,400 --> 00:30:17,060
+مافيش واحد احداثي تبقى اتنين و هنا احداثي تبقى
+
+412
+00:30:17,060 --> 00:30:19,960
+اتنين بالصحيح هذا كله دايما الاحداث التاني اتنين و
+
+413
+00:30:19,960 --> 00:30:23,500
+دايما الاحداث التاني واحد فهذا trick بسيط تذكروا
+
+414
+00:30:23,500 --> 00:30:28,800
+لما اثبتنا ان ال infinite union of ال Y دربنا
+
+415
+00:30:28,800 --> 00:30:31,500
+الأنب واحد و اتنين و تلتة ضمننا انهم هم disjoint
+
+416
+00:30:31,500 --> 00:30:37,370
+على طول نفس الفكرةنفس الفكرة فإذا دائما و أبدا
+
+417
+00:30:37,370 --> 00:30:41,830
+بقدر أجيب المجموعات أه إذا ماحدش يقول لي أنا مش
+
+418
+00:30:41,830 --> 00:30:45,910
+قادر أجيب مجموعتين disjoint لأ انت بس جيب أولا من
+
+419
+00:30:45,910 --> 00:30:49,630
+قاعدة C1 جيب مجموعتين ومنهم على طول بتعمل disjoint
+
+420
+00:30:49,630 --> 00:30:52,910
+انك تضرب في 11 و 1 و 2 بيصيروا مختلفين عن بعض
+
+421
+00:30:52,910 --> 00:30:59,230
+اتنينطبعاً فيها جملة شرطية نفترض إن هدولة مجموعات
+
+422
+00:30:59,230 --> 00:31:12,010
+assume كل الشرط صحيح a1, b1, a2 and b2 are sets
+
+423
+00:31:12,010 --> 00:31:22,010
+such that ال cardinality لل a1 تساوي ال
+
+424
+00:31:22,010 --> 00:31:30,600
+cardinality لل a2الـ cardinality للـ B1 تساوي ال
+
+425
+00:31:30,600 --> 00:31:37,800
+cardinality للـ B2 ايش كمان؟ و A1 تقاطع B1 يساوي
+
+426
+00:31:37,800 --> 00:31:45,780
+Phi andA2 تقاطع B2 يساوي 5 إيش بده يثبت إن
+
+427
+00:31:45,780 --> 00:31:48,600
+الcardinality للاتحاد يساوي الcardinality للاتحاد
+
+428
+00:31:48,600 --> 00:31:51,880
+نظرية سابقة أه الآن إيش معناته إن الcardinality
+
+429
+00:31:51,880 --> 00:31:57,780
+يساوي الcardinality فده معناته إن A1 تكافئ A2 وB1
+
+430
+00:31:57,780 --> 00:32:03,380
+تكافئ B2 وتقاطع مع تقاطع 5 وتقاطع مع تقاطع 5
+
+431
+00:32:03,380 --> 00:32:08,220
+فالاتحاد يكافئ الاتحاد نظرية أه فده يؤدي إن A1
+
+432
+00:32:08,220 --> 00:32:14,680
+اتحاد B1تكافئ اتنين اتحاد بيتنين مش عارف نظرية
+
+433
+00:32:14,680 --> 00:32:17,540
+جداش في chapter .. في chapter ايش؟ في chapter خمسة
+
+434
+00:32:17,540 --> 00:32:21,480
+في chapter خمسة خمسة جداش اللي هو ايش قال ال union
+
+435
+00:32:21,480 --> 00:32:26,520
+of bijections is a bijection اه بتذكروها النظرية و
+
+436
+00:32:26,520 --> 00:32:29,600
+هدى معناها اه بتشوف رحام النظرية طبعا هداش معناته
+
+437
+00:32:29,600 --> 00:32:39,200
+ال cardinality تساوي ال cardinality وهو
+
+438
+00:32:39,200 --> 00:32:44,950
+المطلوبفما زال حافظنا على أنه تقاطع في و تقاطع في
+
+439
+00:32:44,950 --> 00:32:47,370
+يتشير إلى يتشير إلى يتشير الكلام إلى يتشير الكلام
+
+440
+00:32:47,370 --> 00:32:49,890
+إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام
+
+441
+00:32:49,890 --> 00:32:51,070
+إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام
+
+442
+00:32:51,070 --> 00:32:52,090
+إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام
+
+443
+00:32:52,090 --> 00:32:52,310
+إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام
+
+444
+00:32:52,310 --> 00:32:52,650
+إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام
+
+445
+00:32:52,650 --> 00:32:54,390
+إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام
+
+446
+00:32:54,390 --> 00:32:56,790
+إلى يتشير الكلام إلى يتشير الكلام إلى يتشير الكلام
+
+447
+00:32:56,790 --> 00:33:00,450
+إلى يتشير الكلام إلى
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/n56Jirv5D38_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/n56Jirv5D38_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6b19064f9ab3f63ceb8ed16e49e7755fbcdeaa7c
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/n56Jirv5D38_postprocess.srt
@@ -0,0 +1,2296 @@
+1
+00:00:19,740 --> 00:00:23,460
+بسم الله الرحمن الرحيم، هنواصل مع الـdenominable
+
+2
+00:00:23,460 --> 00:00:27,440
+sets وطبعا ال section خمسة تلاتة هو مكمل لsection
+
+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 denominable 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
+الـdenominable 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 denominable تمت
+
+11
+00:01:00,540 --> 00:01:04,480
+denominableوعنا 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 ال subset من ال countable بتم ال
+
+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 denomable دفناها عنصر تم ال denomableطب ضفنا
+
+16
+00:01:18,520 --> 00:01:21,640
+لها finite number of elements طبما الـdenimrables
+
+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 denimrable وقت إيش بدها تصير non
+
+19
+00:01:28,960 --> 00:01:33,080
+-denimrable فهنتمنا نكبر فيها لحد ما إيش الـK لطف
+
+20
+00:01:33,080 --> 00:01:36,680
+زي ما بقول واتبطلناش denimrable 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 denimrable للـdenimrable إيش بتصير؟
+
+23
+00:01:44,540 --> 00:01:48,870
+خلينا نشوففالعنوان the union of two denomable sets
+
+24
+00:01:48,870 --> 00:01:52,570
+is denomable حتى لو تفنعها كمان denomable بتامها
+
+25
+00:01:52,570 --> 00:01:57,690
+denomable فعنا نظرية if A and B are denomable sets
+
+26
+00:01:57,690 --> 00:02:04,160
+then A union B is denomable نشوف البراحةفاحنا
+
+27
+00:02:04,160 --> 00:02:08,060
+ماشيين بيدا الاتجاه حد ما نوصل وين ال non
+
+28
+00:02:08,060 --> 00:02:14,500
+-denominable بتكون فهذه نظرية خمسة تسعة او هي
+
+29
+00:02:14,500 --> 00:02:21,300
+البرهة above طبعا جملة شرطية فنبدأ ان الشرط صحيح
+
+30
+00:02:21,300 --> 00:02:27,060
+assume ال A is denominable بتكتب اختصارا to
+
+31
+00:02:27,060 --> 00:02:32,010
+capital N يعني مظبوط و ال B is denominable andالـ
+
+32
+00:02:32,010 --> 00:02:38,430
+B is denomable مطلوب نثبت أن الاتحاد is denomable
+
+33
+00:02:38,430 --> 00:02:46,390
+بدنا نثبت أن الـ A union B is denomable we want to
+
+34
+00:02:46,390 --> 00:02:55,170
+prove A union B is denomable تمام
+
+35
+00:02:55,170 --> 00:03:03,890
+مرة علينا نظرياتبتقول لو مجموعتين متكافئتين او
+
+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 لل union of a
+
+39
+00:03:18,920 --> 00:03:23,340
+bijection او the union of two bijections is a
+
+40
+00:03:23,340 --> 00:03:27,060
+bijection او قلنا انه من معنانها انه اذا كان في
+
+41
+00:03:27,060 --> 00:03:32,760
+عندي X تكافئ ال Y و W تكافئ ال V 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 ال A و
+
+45
+00:03:43,460 --> 00:03:48,340
+ال B اي مجموعتينتقاطعهم 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
+فانا أخد هذه الحالة case one a تقاطع ال b يساوي في
+
+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
+اقول ما زال ال A تكافئ ال N و ال B تكافئ ال N إذا
+
+50
+00:04:13,900 --> 00:04:19,860
+A Union B يكافئ N اتحاد ال Nمنفعش لأن احنا بدنا
+
+51
+00:04:19,860 --> 00:04:22,540
+برضه ادى و التقطع عن فاى و بدنا التنتيان اللى
+
+52
+00:04:22,540 --> 00:04:26,440
+بنوزن معاهم يكون اتحاد و ايه تقطع عن فاى 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 الان 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
+الان وهذه تكافئ الان even and ال b تكافئ الان وهذه
+
+59
+00:05:03,620 --> 00:05:05,400
+تكافئ الان ا
+
+60
+00:05:17,720 --> 00:05:26,200
+Since A تقاطع الـ B يساوي فاي and N E تقاطع ال N O
+
+61
+00:05:26,200 --> 00:05:27,520
+يساوي فاي
+
+62
+00:05:32,840 --> 00:05:40,220
+A union الـ B 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
+اتوقع 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 الـ B لا يساوي فيفي عناصر مشتركة
+
+67
+00:06:04,160 --> 00:06:06,340
+بينهم اه تفضلي
+
+68
+00:06:09,790 --> 00:06:14,170
+لأ إحنا 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 مختلفةواضحت؟ 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 ماقدرتش أعمل الحالة العامة مرة واحدة، فبجسمها،
+
+79
+00:06:52,990 --> 00:06:57,440
+وده شيء مبدع عام في أي مثلةما بيقولك الحمل اللي
+
+80
+00:06:57,440 --> 00:07:01,480
+تجيه لما يتجسم، بنحمل، وعادي مثلة، كلها كبيرة، لأ،
+
+81
+00:07:01,480 --> 00:07:05,420
+أبدأ، ودائما احنا هيك نفكر، يعني عندنا مثلة، 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 شرطماشي إذا
+
+84
+00:07:11,850 --> 00:07:15,830
+أنا الحلقة خلصت منها طب أشوف لو الشرط ماكنش متحقق
+
+85
+00:07:15,830 --> 00:07:20,710
+فيه شرط تاني بعودة على جهة و هكذا نبدأ الآن هنعمل
+
+86
+00:07:20,710 --> 00:07:24,210
+برضه trick مشهور هنا ال trick 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 ال A و عندنا ال B فكرة مرت علينا جبل هيك
+
+89
+00:07:32,290 --> 00:07:37,720
+هي A و هي Bهذه المنطقة إيش اسمها بيناقص A بيناقص B
+
+90
+00:07:37,720 --> 00:07:42,280
+بيناقص A هسميها C فهنعمل ال trick البسيط فهقوله
+
+91
+00:07:42,280 --> 00:07:51,220
+let C تساوي B ناقص A then أول شيء C تقاطع ال A
+
+92
+00:07:51,220 --> 00:07:58,380
+بيساوي Phi صح؟ بسميتها C ليها ال B 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 ماشتغلتش من أول زي هيك و حتى لو كانت
+
+96
+00:08:14,240 --> 00:08:17,820
+Phi لأن الـC ماعنديش كل المعلومات عنها ماعنديش 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 و أستقرق بعض المعلومات عن
+
+100
+00:08:27,500 --> 00:08:31,540
+الـ C من المعطيات إيش كل اللي بعرفه عن الـ C؟ إنها
+
+101
+00:08:31,540 --> 00:08:37,500
+subset من الـ B أحسنتي Now الـ C subset من الـ B
+
+102
+00:08:37,500 --> 00:08:41,860
+الـ B .. أنا بدي معلومات عن الـ C في أي اتجاه؟
+
+103
+00:08:41,860 --> 00:08:44,760
+إنها denominable، إنها finite و هكذا أه الـ C
+
+104
+00:08:44,760 --> 00:08:48,100
+subset من الـ B و الـ B denominable إيش الـ C؟ لأ
+
+105
+00:08:48,100 --> 00:08:54,570
+لأ انتبهوا النظريش بتقوليعني إيه إيش countable؟
+
+106
+00:08:54,570 --> 00:08:57,550
+subset من denomable 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 denomable إذا denomable
+
+110
+00:09:09,870 --> 00:09:14,790
+صارت الحالة الأولى لإن C is denomable وتقطوحها مع
+
+111
+00:09:14,790 --> 00:09:18,650
+ال إيه؟ في صارت الحالة الأولى وإذا finite آخر مثال
+
+112
+00:09:18,650 --> 00:09:22,680
+إن هنا في النظر المحاضرة الماضيةفإيه الصارة؟ هي أي
+
+113
+00:09:22,680 --> 00:09:26,600
+صارة عندها الـ gate الـ C countable وأنا إيش بدور؟
+
+114
+00:09:26,600 --> 00:09:30,780
+بقول A union B اللي بدرسها وختابت A union C فالـ C
+
+115
+00:09:30,780 --> 00:09:33,660
+يا finite والـ A denumerable الـ denumerable اتحاد
+
+116
+00:09:33,660 --> 00:09:37,760
+finite هنا في المعادلة الماضية أو الـ C countable
+
+117
+00:09:37,760 --> 00:09:39,600
+يعني الـ denumerable ممكن تكون و الـ denumerable
+
+118
+00:09:39,600 --> 00:09:42,020
+اتحاد denumerable الـ denumerable 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 خلC is finite or C is
+
+123
+00:09:56,160 --> 00:10:01,660
+denumerable اكتب اختصارا تكافئ الان هو هذا يؤدي
+
+124
+00:10:01,660 --> 00:10:08,680
+على طول ال A union C is denumerable او تكافئ الان
+
+125
+00:10:08,680 --> 00:10:13,380
+خلينا نكتب اختصار ماعنديش مكان كتير وهذا مثال
+
+126
+00:10:13,380 --> 00:10:19,150
+نهينا في المحاضرة الماضية مظبوط ارجعوله orالـ A
+
+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 ماقدرش أعالجه مرة واحدة، هذه الحالة لازم
+
+131
+00:10:34,210 --> 00:10:47,170
+أثبتها عشان أستخدمها فيما بعد امتبعين؟
+
+132
+00:10:47,170 --> 00:10:53,150
+اهنمشي كمان طيب الاتحاد ديناميرابول ديناميرابول طب
+
+133
+00:10:53,150 --> 00:10:56,810
+تلاتة ديناميرابول اتحادهم ديناميرابول وعشرة
+
+134
+00:10:56,810 --> 00:11:00,730
+ديناميرابول اتحادهم ديناميرابول نتيجةبقول 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 تعميمالبرهان بال induction هتركه exercise أن
+
+141
+00:11:34,130 --> 00:11:40,190
+ال statement for all n أكبر ات ساوى 2، ليش؟ لأن
+
+142
+00:11:40,190 --> 00:11:42,590
+اتحاده، لأن اتحاده يشتغل على أكتر من عنصره، أجل من
+
+143
+00:11:42,590 --> 00:11:45,610
+عنصره يعني، صحيح طبعا الجملة إذا كانت a واحد ل a
+
+144
+00:11:45,610 --> 00:11:49,230
+undenumerable فالاتحاد denumerable طبعا 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 exerciseهذه 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 نظريا ان انت 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
+-denimrable أدّينا إيه بإيجيكشن مباشر بينها وبين
+
+152
+00:12:22,290 --> 00:12:25,330
+الان الان ممكن أثبتها بسهولة عن طريق أن أكتبها على
+
+153
+00:12:25,330 --> 00:12:29,450
+صورة اتحاد مجموعتين denimrable 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 مثالSolution طبعا ايش الـ Z؟ الـ Z عبارة عن
+
+156
+00:12:40,420 --> 00:12:44,080
+الـ Natural number مع الاعداد السالبة والصفر فالـ
+
+157
+00:12:44,080 --> 00:12:47,200
+Natural طبعا 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 اتنين وها كذا، مظبوط؟ لما نعوض x بتساوي
+
+162
+00:13:07,980 --> 00:13:11,560
+واحد، بدينا صفر، x بتساوي اتنين، اه فهذه المجموعة،
+
+163
+00:13:11,560 --> 00:13:17,060
+اه then بس عشان اؤكد على الفكرة إيش معناته، ف z
+
+164
+00:13:17,060 --> 00:13:25,400
+عبارة عن مين؟ ان اتحاد الـAالـ N طبعاً نمربل
+
+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 ذاتبت أن الـ A نمربل
+
+167
+00:13:30,660 --> 00:13:38,300
+خلص السؤال نعم نعم الـ A هو نمربل لا أريد أن أكتب
+
+168
+00:13:38,300 --> 00:13:44,380
+بالتفصيل لأن من الـ bijection بينها و بين الـ N؟
+
+169
+00:13:44,380 --> 00:13:53,170
+الـ F بدي ده لمن الـ N لـ Agiven 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 طبعا
+
+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
+طبعا النظرية خمسة تسعة بكل
+
+176
+00:14:29,250 --> 00:14:33,770
+سهولة أه فإن النظريات هذه بتساعدنا مش دائما 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 جزئيا 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
+الـdenimrable نرجع لفكرتنا الرئيسية اللي حكينا
+
+184
+00:15:06,570 --> 00:15:09,790
+فيها من أول المحاضرة احنا بدأنا من الـdenimrable
+
+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 الـdenimrable تم الـdenimrable طب لو
+
+187
+00:15:16,790 --> 00:15:20,070
+ضربنا عملنا Cartesian product طبعا 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 انا اكد عشان اذا
+
+190
+00:15:27,350 --> 00:15:30,290
+عندنا مجموعة فيها خمسة ومجموعة فيها عشر الاتحاد
+
+191
+00:15:30,290 --> 00:15:35,590
+اقل او يساوي خمساش حد لحظة خمساش 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 دينامرابو مزال دينامرابو نشوف
+
+195
+00:15:48,470 --> 00:15:49,430
+البرهان
+
+196
+00:15:52,440 --> 00:15:56,140
+يعني لو أخدنا كل الأزواج المرتبة من الـnatural
+
+197
+00:15:56,140 --> 00:16:00,360
+numbers بتامها المجموعة denominable 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
+طبعا بدي أثبت إنها denominable يا بدى أستخدم
+
+201
+00:16:17,680 --> 00:16:21,320
+النظريات إذا قدرت يا بدى أجيب bijection بينها وبين
+
+202
+00:16:21,320 --> 00:16:26,990
+الانالحقيقة في صعوبة مش هنجيبها بـ bijection هنعمل
+
+203
+00:16:26,990 --> 00:16:31,130
+ال 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 حثبت 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 Nهو 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
+طبعا
+
+210
+00:17:01,760 --> 00:17:04,620
+أنا في الاصل بتدور على ده لتكون one to one and
+
+211
+00:17:04,620 --> 00:17:09,230
+untoوين 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 مثلا خلينا ناخدهم N و M عشان العداد صحيح بدي زوج
+
+214
+00:17:17,970 --> 00:17:22,530
+مرتب يصير عياش عدد واحد عدد طبيعي كمان هنعرفها في
+
+215
+00:17:22,530 --> 00:17:31,790
+trick طبعا 2 أس N في 2 M ناقص 1 2
+
+216
+00:17:31,790 --> 00:17:38,110
+أس N نعمخلّينا نشوف .. خلّينا نشوف اتنين أقصى N
+
+217
+00:17:38,110 --> 00:17:41,190
+يعني مثلا إيش نجيب؟ إيش عن نزاوج مرتب؟ واحد واحد
+
+218
+00:17:41,190 --> 00:17:47,910
+إيش صورة الواحد واحد؟ خلّينا نشوف F of واحد واحد
+
+219
+00:17:47,910 --> 00:17:54,490
+بيساوي إيش؟ اتنين أقصى واحد اتنين 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 إيش ناخد مثلا؟ F of واحد اتنين مثلا إيش بتساوي
+
+222
+00:18:00,550 --> 00:18:07,260
+اتنين في تلاتة ستة صح؟2 أس واحد في تلاتة ستة طيب F
+
+223
+00:18:07,260 --> 00:18:11,820
+of اتنين واحد مثلا ده تصير اربعة في واحد اربعة
+
+224
+00:18:13,130 --> 00:18:16,490
+فالأمور شوية صعبة إنه مش عملية ترتيب ومين .. أصلا
+
+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 فاعرفين، أه تمام؟ فالعملية بدها شوية
+
+229
+00:18:29,370 --> 00:18:32,850
+دقة طبعا أكيد اللي .. اللي محطوها 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 unto أه لأنه زي ما
+
+232
+00:18:40,570 --> 00:18:43,800
+شوفين مثلا هي ليش العداد الفردية مش جادة تطلعطب
+
+233
+00:18:43,800 --> 00:18:48,220
+ممكن نأخذها من هناك؟ ايش كنت تعملي مثلا؟ 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 هده هده بيساعدنا هنشوف أنه بده يساعد نعمل ال
+
+236
+00:18:58,120 --> 00:19:01,220
+trick فطبعا هذه كل الأفكار بتساعدنا أنه مش دايما
+
+237
+00:19:01,220 --> 00:19:04,420
+نلاقي contradiction وإذا ما لاجيناها 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 طبعا
+
+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
+إيش عمل؟ نعود نستخدم تعريف الدالة فهذا يؤدي اتنين
+
+244
+00:19:49,250 --> 00:19:55,510
+أسان واحد في اتنين ام واحد ناقص واحد بتساوي اتنين
+
+245
+00:19:55,510 --> 00:19:58,950
+أسان اتنين في اتنين ام اتنين 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
+الإحداث الأول يساوي الإحداث الأول و الإحداث التاني
+
+249
+00:20:14,760 --> 00:20:20,960
+يساوي الإحداث التاني اه هنا طبعا ليش اختاره بهذا
+
+250
+00:20:20,960 --> 00:20:24,840
+الشكل و اتنين ام ناقص واحد اه كل هذا أثناء البرهان
+
+251
+00:20:24,840 --> 00:20:28,860
+ال one to one هيبين ليش هذا الاختيارالحقيقة ال
+
+252
+00:20:28,860 --> 00:20:32,480
+trick اللي بدي اعمله هو بروح اجسم على اتنين واحدة
+
+253
+00:20:32,480 --> 00:20:39,500
+منهم هروح اجسم فلازم اعرف طبعا هصير ايش عندي اتنين
+
+254
+00:20:39,500 --> 00:20:44,380
+أسن اتنين ناقص انوان بيصير هنا في عندي عدد فردي و
+
+255
+00:20:44,380 --> 00:20:48,400
+الطرف التاني عدد زوجي بس بشرط اذا كان الأسطب على
+
+256
+00:20:48,400 --> 00:20:52,760
+اتنينموجب، بدي ايه يكون اتنين، فعشان يكون العدد
+
+257
+00:20:52,760 --> 00:20:55,220
+اللي لها ده يكون موجب، ايش لازم يكون؟ لازم يكون ان
+
+258
+00:20:55,220 --> 00:20:58,180
+اتنين اكبر من ان واحد، فهذا احتمال، الاحتمال
+
+259
+00:20:58,180 --> 00:21:00,440
+التاني، لو كان العكس، بنقول التاني على الطرف
+
+260
+00:21:00,440 --> 00:21:04,160
+التاني، فباخد بيش الاحتمالين، فحناخد اللي هو
+
+261
+00:21:04,160 --> 00:21:14,050
+الاحتمالين if n1 أكبر من n2then n1 هي الكبيرة ننقل
+
+262
+00:21:14,050 --> 00:21:20,770
+التنين 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 طبعا هذا contradiction هذا
+
+264
+00:21:26,950 --> 00:21:30,070
+زوجي و هذا فردي صح؟ لأن هي الأس تبعت و إيش؟ موجة
+
+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 و لا عيد؟ اه هل جيت احنا الجسم دي واضح و لا
+
+267
+00:21:43,680 --> 00:21:47,120
+مش واضح؟ الجسمين اه لما تكون n واحد اكبر من n
+
+268
+00:21:47,120 --> 00:21:50,000
+اتنين يعني هذا الاشم قص موجب يعني ايش فيها دي
+
+269
+00:21:50,000 --> 00:21:53,060
+اتنين اقص واحد اتنين تربية لأن كل معدات اشملها
+
+270
+00:21:53,060 --> 00:21:55,960
+طبيعية فالفرق فيها رمية واحد اتنين هل جيتها دي
+
+271
+00:21:55,960 --> 00:21:59,960
+فيها اتنين ضرب أي شيء زوجي اتنين ام ناقص واحد
+
+272
+00:21:59,960 --> 00:22:03,780
+اتنين ام ناقص واحد فردي فردي يساوي زوجي ومستحيل
+
+273
+00:22:03,780 --> 00:22:12,280
+contradiction طب العكسإذا N1 أصغر من N2 ثم 2N1-1
+
+274
+00:22:12,280 --> 00:22:19,340
+ستكون 2-N2-N1 ف2N2-1 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 يعرفأن واحد
+
+277
+00:22:30,490 --> 00:22:33,390
+تساوي أن اتنين بدي انا كمان ام واحد تساوي ام اتنين
+
+278
+00:22:33,390 --> 00:22:37,310
+طب مازال أن واحد تساوي أن اتنين بقدر اجسم 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 أنه بالتتابع
+
+281
+00:22:47,370 --> 00:22:50,290
+العملية مش سهلة جد it follows
+
+282
+00:22:53,890 --> 00:22:59,930
+that اتنين ام واحد ناقص واحد تساوي اتنين ام اتنين
+
+283
+00:22:59,930 --> 00:23:04,750
+ناقص واحد ودا يؤدي ام واحد تساوي ام اتنين اه فطبعا
+
+284
+00:23:04,750 --> 00:23:11,150
+hence نعم الزوج المرتب يساوي الزوج المرتب ام واحد
+
+285
+00:23:11,150 --> 00:23:19,830
+تساوي ان اتنين ام اتنين وبالتالي and F is one to
+
+286
+00:23:19,830 --> 00:23:24,150
+oneفأثبتنا إنها one to one رغم أن البرهان لم يكن
+
+287
+00:23:24,150 --> 00:23:27,430
+سهل، بدّو بعض التفكير لأن هذه المشكلة إن أنا في
+
+288
+00:23:27,430 --> 00:23:31,810
+عندي أربع عناصر أو في عندي زوج مرتب وطرف التاني
+
+289
+00:23:31,810 --> 00:23:36,210
+ماعنصر يعني غير عن مرة فكرة من الكارتيسة إلى
+
+290
+00:23:36,210 --> 00:23:38,650
+الكارتيسة كانت سهلة لأنه بقارن فعندي معادلات
+
+291
+00:23:38,650 --> 00:23:41,570
+متعددة في عندي .. كان عندي معادلتين أخدت منها
+
+292
+00:23:41,570 --> 00:23:44,250
+شرطين أو نتيجتين لكن أنا ماعندلي معادلة واحدة و
+
+293
+00:23:44,250 --> 00:23:47,410
+بدأت أنتيج منها مرتين فكان العملية بدها دلي تركة
+
+294
+00:23:47,410 --> 00:23:52,640
+تمامهل دي on two 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 setقلنا 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 الـ
+
+299
+00:24:11,390 --> 00:24:14,850
+bijection أخدنا اللي هو الـ F تكون one to one
+
+300
+00:24:14,850 --> 00:24:18,210
+واخدنا الـ proper هي الصورة اه .. ب .. ب .. ب ..
+
+301
+00:24:18,210 --> 00:24:21,470
+لأ اعتمادًا على أيش فكرة إذا لجد 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 فالأن اه nowبما أن الـ
+
+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 جتهاش اشمالها تكافئ F N cross ال N
+
+306
+00:24:47,540 --> 00:24:53,080
+المدى مظبوط طبعا جيته 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 أخدنا
+
+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؟ أه، فإيش روحنا عملناه؟
+
+311
+00:25:10,340 --> 00:25:13,380
+زغرناه، أخدنا 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 كدرت أثبت أن هذه denominable انتهت
+
+315
+00:25:27,360 --> 00:25:31,780
+العملية لأن هي هذي تكافح denominable وعملية التعدد
+
+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
+الانطيب ليش .. مش جروري 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 أه لأن مستحيل تكون finite أه
+
+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 نكتفه؟ 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 أن F of N cross ال N is innumerable
+
+328
+00:26:38,430 --> 00:26:44,030
+هذه نظرية نظرية جداش infinite subset of
+
+329
+00:26:44,030 --> 00:26:51,850
+denumerable set is denumerable نظرية خمسة تمانية
+
+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
+التالتة وهو المطلوب فهنا ماقدرناش 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 التركيات التي نجعلها أحياناً عندما
+
+340
+00:27:44,610 --> 00:27:49,550
+الأمور لا تصبح مجموعة كبيرة ولا نستطيع إجابة بشكل
+
+341
+00:27:49,550 --> 00:27:50,050
+مباشر
+
+342
+00:27:59,530 --> 00:28:04,450
+مزيد من التوسع دائما حاضر فزي ما احنا شايفين احنا
+
+343
+00:28:04,450 --> 00:28:06,770
+كل ما لقوا بدينا يعني الممكن الفكرة اللي ماشيين
+
+344
+00:28:06,770 --> 00:28:11,070
+فيها جاعدين بنكبر كل ما قاش وانا نوصل هل هتوجه
+
+345
+00:28:11,070 --> 00:28:15,850
+مرحلة ونبطل denim rubble بنشوف بنكبر denim rubble
+
+346
+00:28:15,850 --> 00:28:19,590
+بنكبر denim rubble بدنا نشوف وقت إيش الكلب بده يطف
+
+347
+00:28:19,590 --> 00:28:23,370
+ويتبطل المجموعة denim rubble لمّا جداش نكبرها جداش
+
+348
+00:28:23,370 --> 00:28:30,420
+نضفلها فعنا نتيجة خمسة خمسةInfinite 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 unionبس 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 و بعدها 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 inimitable
+
+355
+00:28:59,400 --> 00:29:02,840
+فالآن إحنا حلا خدنا أي اتحاد مالا نهاية من
+
+356
+00:29:02,840 --> 00:29:06,880
+المجموعات بس يكونوا disjoint بدمر اتحاد inimitable
+
+357
+00:29:07,640 --> 00:29:12,300
+نشوف البرهان و الفكرة تبعها البرهان و إيش بدنا
+
+358
+00:29:12,300 --> 00:29:19,240
+نشتغل معاها for each k تنتمي لأن لأي عدد طبيعي let
+
+359
+00:29:19,240 --> 00:29:25,860
+a sub k be a denominable 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
+الكلامهو يعبّر أن جميع المجموعات مقاومة في الـ
+
+362
+00:29:36,940 --> 00:29:41,320
+Disjoint ما هو معنى الـ Disjoint؟ كل تنتين
+
+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 تنتينفعبّر عنه أن اي جي تقاطع أي ك لأي جي
+
+365
+00:29:51,520 --> 00:29:55,600
+لتساوي ك طبعا التبليش مجال لاتساوي لأن لو بيساووا
+
+366
+00:29:55,600 --> 00:29:58,580
+بعض ما بيكون تقاطعهم بيساوي نفسهم ماعندش 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 denomable الاتحاد is
+
+369
+00:30:06,240 --> 00:30:12,840
+denomable 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، كله يكون صحيح، وإذا أردنا
+
+372
+00:30:23,740 --> 00:30:28,160
+أن نثبت بأنه نمربول فكله مُعطَع، ما هي فكرة
+
+373
+00:30:28,160 --> 00:30:32,100
+البرهان لكي نتابع مع بعض؟طبعا احنا في عندنا نظرية
+
+374
+00:30:32,100 --> 00:30:35,720
+بتقول ان اتحاد الـ bijections بتموا bijection بس
+
+375
+00:30:35,720 --> 00:30:40,540
+في شرط بدنا تقاطع كل المجالات Phi و بدنا 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 ايش الصورة تقريبا تعميم ل case one من النظرية
+
+378
+00:30:48,700 --> 00:30:52,280
+السابقة او من النتيجة السابقة فانا عندي هاي A1
+
+379
+00:30:52,280 --> 00:31:00,520
+تكافئ أنا في عندي A2 تكافئ أنا و هكذافي 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 تقطع حنفاي جاهز بس أنا بدي أجيب
+
+382
+00:31:10,120 --> 00:31:16,800
+أستبدل الان بمجموعات تقطع حنفاي لمّا كانت الانتين
+
+383
+00:31:16,800 --> 00:31:20,300
+العملية سهلة جيبنا N O N E فالآن كيف بدنا نجيب
+
+384
+00:31:20,300 --> 00:31:24,600
+مهلة نهاية من المجموعات هنا كلهم تقطع حنفايفهي
+
+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 جدا، يعني الفكرة يعني فعلا فكرة .. فكرة واضحة
+
+388
+00:31:36,960 --> 00:31:40,440
+وسهلة، بس طبعا كيف تجين الأول مرة، هي القضية، احنا
+
+389
+00:31:40,440 --> 00:31:41,920
+ايش اللي هنعمله؟
+
+390
+00:31:43,800 --> 00:31:48,440
+العملية هنشوف أننا نتحدث عن عدد العناصر مظبوط
+
+391
+00:31:48,440 --> 00:31:52,560
+فبدنا مجموعة عدد العناصر زي الان بالظبط 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
+عملتله كارتيسار و دكت مع عنصر واحد لو عملتله
+
+395
+00:32:02,340 --> 00:32:06,960
+كارتيسار و دكت مع عنصر واحد فالآن هذه المجموعة بدي
+
+396
+00:32:06,960 --> 00:32:11,460
+أستبدلها بان أحسنتي
+
+397
+00:32:12,370 --> 00:32:17,950
+أه حالجين و هذه حالجين
+
+398
+00:32:17,950 --> 00:32:20,510
+هذه تقطوحهم فيه ولا مش فيه لأن ولا واحد هذه
+
+399
+00:32:20,510 --> 00:32:23,150
+الاحداث التانية دايما واحد هذه الاحداث التانية
+
+400
+00:32:23,150 --> 00:32:26,210
+دايما اتنين عمره ما بيصير هذا و هكذا فهي الفكرة
+
+401
+00:32:26,210 --> 00:32:30,390
+فهي الفكرة اللي بدنا نعملها اه فطبعا اللي هو ال
+
+402
+00:32:30,390 --> 00:32:34,070
+bijection واضح ضروري اكتبه ولا لأ مظننيش لأن في
+
+403
+00:32:34,070 --> 00:32:39,230
+ضرورة ان نكتبه مافيش داعي ان نكتب اللي هو ال
+
+404
+00:32:39,230 --> 00:32:49,790
+bijectionخلّيني اكتبه مش مشكلة فالان for each K
+
+405
+00:32:49,790 --> 00:32:58,270
+تنتم إلى ال N let FK من .. بدي اثبت هذا الكلام انه
+
+406
+00:32:58,270 --> 00:33:07,650
+دايما صح على السريع من N إلى N across ال K be
+
+407
+00:33:07,650 --> 00:33:19,950
+given byفك 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 كله من إيش
+
+410
+00:33:30,350 --> 00:33:33,810
+أزواج ان واحد أو ان اتنين أو ان تلان فطبعا 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 thenFK is a bijection exercise
+
+413
+00:33:46,800 --> 00:33:52,500
+اه
+
+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
+التنين لأ بصير تضربت المجموعة باتنين ضعفها مش مش
+
+417
+00:34:05,440 --> 00:34:11,890
+نفسهاهل جيتها دي عدد عناصرها مية؟ وهذا عدد عناصرها
+
+418
+00:34:11,890 --> 00:34:15,110
+واحد؟ جدتش المجموع الكارتيسيان بتام مية؟ لكن لما
+
+419
+00:34:15,110 --> 00:34:18,530
+تقول هنا مية و هنا اتنين تصبحين متين أنا بديها
+
+420
+00:34:18,530 --> 00:34:22,490
+تكافئ واضحة طول لأ؟ اه فمابيديش انا اضعف العدد،
+
+421
+00:34:22,490 --> 00:34:25,470
+انا بدي نفس العدد لما انا بثبت الإحداث التاني
+
+422
+00:34:25,470 --> 00:34:28,910
+مابتغيرش العدد العناصر بس بدل مكتوبهم اللي هو and
+
+423
+00:34:28,910 --> 00:34:36,670
+بدل مكتوبه هنا ال and مين بناظر؟ان واحد مابدش
+
+424
+00:34:36,670 --> 00:34:39,450
+يدياه احتماليا فكل أعدد ماهي مقابله التناظر الصحيح
+
+425
+00:34:39,450 --> 00:34:42,270
+له واضح لكن لما تصير ان مع الواحد ولا ان مع
+
+426
+00:34:42,270 --> 00:34:45,490
+التانين فصار ايه لو تشعب ممكن يزيدوا عضل الأناصر
+
+427
+00:34:45,490 --> 00:34:52,370
+واضحات تمام ف this is a bijection طبعا فالان now
+
+428
+00:34:52,370 --> 00:34:55,530
+كل
+
+429
+00:34:55,530 --> 00:35:05,370
+a k تكافئ ليمين and across ال kمظبوط وليه ايش
+
+430
+00:35:05,370 --> 00:35:13,150
+بيجيكشن ويش كمان and a j تقاطع ال a k تساوي five
+
+431
+00:35:13,150 --> 00:35:16,590
+وهادي
+
+432
+00:35:16,590 --> 00:35:22,030
+تساوي ايش كمان اللي
+
+433
+00:35:22,030 --> 00:35:29,510
+يمين اللي هو n اه بتجيب ال باقي كله اللي هو عبارة
+
+434
+00:35:29,510 --> 00:35:37,420
+عن اللي هو n cross jتقاطع N across الـ K برضه
+
+435
+00:35:37,420 --> 00:35:40,060
+بيسوا Phi هذا اللي عملناها، 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
+و بهذا ال trick صار تقاطع كله Phi، صح؟ أه، فالأن
+
+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 لإنفينيتي AJ يكافئ اتحاد J من واحد
+
+443
+00:36:11,950 --> 00:36:20,170
+لإنفينيتي N across الـJ بس
+
+444
+00:36:20,170 --> 00:36:24,990
+اللي جيت احنا حلنا المشكلة طب اتحاد هدولة هل
+
+445
+00:36:24,990 --> 00:36:27,730
+بيتموا denomable من اتحاد هذا
+
+446
+00:36:35,840 --> 00:36:39,860
+هذا تمرين في الكتاب هذا السؤال في الكتاب اثبت ان
+
+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 نمره 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 ماانتماش فيها اتحاد لماذا روحت على الكارتيسة
+
+451
+00:36:53,500 --> 00:36:57,420
+و بعدها رجعت للاتحاد عشان مديها فخلاص وهي دي نمره
+
+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 فإحنا يعني يمكن إن إحنا ماشيين في
+
+454
+00:37:18,130 --> 00:37:22,010
+اتجاه بنكبر و بنمرع بعض المجموعات اللي بنعرفها
+
+455
+00:37:22,010 --> 00:37:25,390
+طبعا وحدة القياس الـ Merge يعتبر أنها الـ natural
+
+456
+00:37:25,390 --> 00:37:29,970
+number شوفنا الـ Z لجنها denumerable نمشي إلى
+
+457
+00:37:29,970 --> 00:37:33,050
+جدام، 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
+denumerableوهذه نتيجة نتيجة بجموعة 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 خلّينا
+
+463
+00:38:03,520 --> 00:38:08,080
+نشوف البرهان مع بعض ونشوف أيش الأفكار الموجودة فيه
+
+464
+00:38:10,340 --> 00:38:13,840
+طبعا مش هاجتراعب مع الـ Q مش هاجدر أدي بيجيكشن بين
+
+465
+00:38:13,840 --> 00:38:17,860
+الـ Q بين ال N أول شي هجزقها إلى طبعا زي ما
+
+466
+00:38:17,860 --> 00:38:21,240
+اتعلمنا في المثال تبع ال Z لو أنا قدرت أجزقها
+
+467
+00:38:21,240 --> 00:38:24,160
+عبارة عن نصفين، العداد الصحين اللي هو ليش الموجة
+
+468
+00:38:24,160 --> 00:38:27,060
+بالحال والسالب بالحال وطبعا السالب والموجة
+
+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
+ال Q بقدر أكتبها على صورةEq minus الاعداد النسبية
+
+472
+00:38:42,600 --> 00:38:48,880
+السالبة اتحاد الصفر اتحاد الاعداد النسبية الموجب
+
+473
+00:38:48,880 --> 00:38:52,940
+مظبوط
+
+474
+00:38:52,940 --> 00:39:00,140
+اه فطبعا هادي تكافئ هادي صح ايش الدالة بينهم F of
+
+475
+00:39:00,140 --> 00:39:05,730
+X صار سالب Xالسالب والموجب صح؟ والصفر الزيادة لو
+
+476
+00:39:05,730 --> 00:39:07,990
+أقدرت أثبت أنها دي Denimrable فاللي تكفيها
+
+477
+00:39:07,990 --> 00:39:11,090
+Denimrable Automatic وضفنا عليها عنصر Denimrable
+
+478
+00:39:11,090 --> 00:39:14,330
+Proposition صالحة فإحنا هنجزق المثلة مش هنشتر
+
+479
+00:39:14,330 --> 00:39:20,010
+عليها مرة واحدة هنجزقها هنجزقها اه فإذا بينا نثبت
+
+480
+00:39:20,010 --> 00:39:29,530
+أن ال Q plus is Denimrable 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 denominable هنثبت
+
+483
+00:39:44,090 --> 00:39:49,670
+أن العداد النسبي يدنمربل طيب نبدأ نفكر عشان الأمر
+
+484
+00:39:49,670 --> 00:39:53,370
+يعني يرسخ و الفكرة تيجي بالنسبة للعدد النسبي لما
+
+485
+00:39:53,370 --> 00:39:55,530
+أقول عدد النسبي إيش بيجي على بالك؟ نعم
+
+486
+00:39:58,640 --> 00:40:01,520
+ممتاز إذا هو فيه بصته مقام والألف والباه دول إيش
+
+487
+00:40:01,520 --> 00:40:05,320
+بيكونوا أعداد صحيح نترال نترال 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 ناخدنا then X تساوي B على Qfor some طبعا
+
+491
+00:40:27,510 --> 00:40:32,870
+احنا عندنا مثلا النص نكتبها واحدة ع اتنين او اتنين
+
+492
+00:40:32,870 --> 00:40:36,370
+على اربع او خمسة على عشرة لكن لما بدى اعمل انا
+
+493
+00:40:36,370 --> 00:40:39,150
+تمثيل حقيقي لازم اعملها بشكل انه ايش يكون كل
+
+494
+00:40:39,150 --> 00:40:42,230
+المعاملات المشتركة تكون محذوفة فده بنعبر عنه انه
+
+495
+00:40:42,230 --> 00:40:45,930
+يكون ايش المعامل المشترك الأعظم يكون بسواحى فدائما
+
+496
+00:40:45,930 --> 00:40:49,770
+هذا الكلام متوفر لأي عدد نسبة x ممكن نكتبها بهذا
+
+497
+00:40:49,770 --> 00:40:54,880
+الشكل for someP و Q وين موجودين في الـ natural
+
+498
+00:40:54,880 --> 00:40:58,400
+number الآن عشان هي أنا أخدت الـ plus لإنهم موجبين
+
+499
+00:40:58,400 --> 00:41:04,620
+السؤال اللي بيخلّيني أعشها 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 او العامل
+
+504
+00:41:25,160 --> 00:41:32,680
+المشترك الاكبر greatest common divisor of B and Q
+
+505
+00:41:32,680 --> 00:41:37,020
+is one يسوّح، لا أريد أن يتم ولا عامل مشترك، كله
+
+506
+00:41:37,020 --> 00:41:41,720
+بدا اختصر، تمام فهذا سيساعدنا، الآن سنعرف دالة،
+
+507
+00:41:41,720 --> 00:41:45,720
+مين العرف دالة؟ سنستطيع أن نثبت أن الـQ تكافئ الـN
+
+508
+00:41:45,720 --> 00:41:53,520
+ولا الـN cross الـNواضح ان كل عدد نسبة بيصبع عددين
+
+509
+00:41:53,520 --> 00:41:57,000
+طبيعيين فإذا أسهل أشتغل على مين على N نقرص ال N
+
+510
+00:41:57,000 --> 00:42:02,780
+أسهل أشتغل على ال N اقرص ال N فالان هنعرف الدالة
+
+511
+00:42:02,780 --> 00:42:07,820
+بالشكل التالي هنعرفها هل هي one to one and unto
+
+512
+00:42:07,820 --> 00:42:13,900
+اتوقع مش شرط هي one to one and unto لأ مش هتطلع
+
+513
+00:42:13,900 --> 00:42:18,760
+one to one and unto 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 ان كل عدد هنا مكتوب بيد الشكل و
+
+516
+00:42:41,120 --> 00:42:44,340
+طبعا طب ليش انا بدي المعاملة مشتركة سوا واحد عشان
+
+517
+00:42:44,340 --> 00:42:48,520
+لما .. ده اللي هتكون معرفة مانفعش اقوله مثلا الجد
+
+518
+00:42:48,520 --> 00:42:54,720
+اقوله F of نصو 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؟ و كيف ممكن أعرفه؟ واحد اتنين و أنا كيف بدي
+
+522
+00:43:05,980 --> 00:43:09,160
+أعرفه اتنين أربعة؟ هدولة 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 صحفطبعا زي ما بنحكي
+
+525
+00:43:17,830 --> 00:43:21,430
+دايما الرياضيات مش فيها أي شيء ازيادة مش ديقوع 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
+طبعا مش unto الحقيقة ممكن نشوف أنها مش unto then F
+
+529
+00:43:40,490 --> 00:43:46,890
+is one to oneطبعا بضمن ان هذه الأمور بقدر اثبتنها
+
+530
+00:43:46,890 --> 00:43:50,150
+one to one لان كل عنصر قوله representation صحيح
+
+531
+00:43:50,150 --> 00:43:53,810
+one to one مش هنثبتنها انتوا هنعمل trick تبع توي
+
+532
+00:43:53,810 --> 00:43:58,110
+نفس ال trick فما زال one to one بتصير عندنا مين ال
+
+533
+00:43:58,110 --> 00:44:03,730
+Q plus H تكافئ شوف متابعين ولا لأ انا كنت اتقف من
+
+534
+00:44:03,730 --> 00:44:07,650
+وين لوين من ال Q plus لإن نقرص الآن one to one فقط
+
+535
+00:44:07,650 --> 00:44:12,110
+بتكافئ ليش ال image مظبوط نفس ال 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 هلجت 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 فالأن ال subset and F of Q Plus is
+
+541
+00:44:38,890 --> 00:44:45,840
+Infiniteimplies 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 طبعا Q minus تكافئ Q plus Q minusتكافئ
+
+546
+00:45:11,530 --> 00:45:21,850
+EQ plus implies EQ minus is denumerable طبعا
+
+547
+00:45:21,850 --> 00:45:30,510
+فبتم ان 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
+فطبعا يمكن بدت اللي هو الصورة تكتمل شيئا فشيئا،
+
+551
+00:45:56,430 --> 00:46:00,630
+الآن مرتانة في عندنا عنوان الـdenominable sets are
+
+552
+00:46:00,630 --> 00:46:05,450
+the smallest infinite setsفطبعا 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 طبعا أصغر مجموعة هي
+
+556
+00:46:17,170 --> 00:46:19,670
+ال five مافيش 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 ال finite تجينا ال infiniteأصغر infinite set
+
+559
+00:46:26,570 --> 00:46:28,770
+هي الـnatural number، هي الـdenominable، طب في
+
+560
+00:46:28,770 --> 00:46:32,630
+أكبر منها في كل ال infinite زي بعض، لأ، حنوصل لها
+
+561
+00:46:32,630 --> 00:46:35,210
+دي الحقيقة، أه، لكن فأصغر infinite هي
+
+562
+00:46:35,210 --> 00:46:37,570
+الـdenominable set، بعدين فيه الـnon-denominable،
+
+563
+00:46:37,570 --> 00:46:40,230
+حنسميهم، أو الـuncountable، مش جادرين، 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 الاتجاهأه فالمرة الماضية كان العنوان
+
+566
+00:46:46,350 --> 00:46:50,530
+هذا في نظرية جالتلنا أنه any اللي هو ال .. ال ..
+
+567
+00:46:50,530 --> 00:46:53,050
+ال .. كده و استخدمناها 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 أه خلّي البرهان إن
+
+574
+00:47:11,210 --> 00:47:12,190
+شاء الله في المرة القادمة
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/nDXHUPZy834_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/nDXHUPZy834_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..436ca42be34e8da8bc160bef86af919d90a2b6eb
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/nDXHUPZy834_raw.srt
@@ -0,0 +1,2440 @@
+1
+00:00:19,660 --> 00:00:24,820
+بسم الله الرحمن الرحيم هنواصل مع الدوال وبشكل
+
+2
+00:00:24,820 --> 00:00:29,440
+أساسي مع صور المجموعات والصور العكسية للمجموعات
+
+3
+00:00:29,440 --> 00:00:34,940
+فكنا شفنا هدولة تعرفين اه فلو عندنا مجموعة subset
+
+4
+00:00:34,940 --> 00:00:39,060
+من ال domain نقدر نتحدث عن صورة هذه المجموعةفالـ F
+
+5
+00:00:39,060 --> 00:00:42,480
+of A زي ما حكينا هي صور العناص الموجودة في الـ A
+
+6
+00:00:42,480 --> 00:00:45,680
+وده هو التعريف طبعا التعريف للصورة التانية
+
+7
+00:00:45,680 --> 00:00:49,080
+المكافئة هي الصورة المقتصرة هي F of X for X and
+
+8
+00:00:49,080 --> 00:00:51,640
+terminal A يعني صورة العناص اللي في الـ A مقتصرة
+
+9
+00:00:51,640 --> 00:00:54,180
+أحيانا ممكن نستخدم هذا التعريف و أحيانا نستخدم
+
+10
+00:00:54,180 --> 00:00:59,780
+التعريف بشكل كاملهي كل عناصر Y على صورة F of X
+
+11
+00:00:59,780 --> 00:01:03,740
+اللي هي على صورة صور وصور لمين لعناصر من إيه فده
+
+12
+00:01:03,740 --> 00:01:06,960
+التعريف بشكل التفصيل على الجانب الآخر لو أخدنا
+
+13
+00:01:06,960 --> 00:01:10,140
+مجموعة جزئية من المجال المقابل B subset من ال Y
+
+14
+00:01:10,140 --> 00:01:13,320
+نتحدث عن الصورة العكسية لهذه المجموعة inverse
+
+15
+00:01:13,320 --> 00:01:17,960
+image of B هو عبارة عن العناصراللي صورهم في الـ B
+
+16
+00:01:17,960 --> 00:01:22,320
+العناصر X من ال domain اللي صورهم في الـ B فدولة
+
+17
+00:01:22,320 --> 00:01:27,140
+تعريفين وفيها ملاحظة مهمة تستخدم كثيرا وستكون
+
+18
+00:01:27,140 --> 00:01:32,520
+عملية فارقةإذا كانت الـ X في الـ A فصورتها في الـ
+
+19
+00:01:32,520 --> 00:01:36,520
+F في A لكن العكس غير صحيح وشوفنا مثال لكن بالنسبة
+
+20
+00:01:36,520 --> 00:01:40,220
+للتعامل مع الصورة العكسية هذي ال statement if and
+
+21
+00:01:40,220 --> 00:01:43,660
+only if فده هيخلي التعامل مع الصورة العكسية أسهل
+
+22
+00:01:43,660 --> 00:01:47,380
+وحلاجي أن هذه الأمور تتعكس على بعض النظريات و بعض
+
+23
+00:01:47,380 --> 00:01:50,800
+القوانينفيمكن احنا شوفنا المثال عندنا ووقفنا
+
+24
+00:01:50,800 --> 00:01:55,020
+وشوفنا دي الملاحظة، الآن نظرية الأولى في هذا
+
+25
+00:01:55,020 --> 00:01:58,940
+الموضوع، نظرية رقم 9 في الباب كله، في ال chapters
+
+26
+00:01:58,940 --> 00:02:04,640
+طبعا ليه تدينا الخواص الأساسية اللي هو ال image و
+
+27
+00:02:04,640 --> 00:02:07,740
+ال inverse image، the basic properties of images
+
+28
+00:02:07,740 --> 00:02:12,300
+and inverse imagesتمام دايما احنا بنشتغل مع الدوال
+
+29
+00:02:12,300 --> 00:02:16,020
+فطبعا اولش ان يكون في انا DEL F من مجموعة ما
+
+30
+00:02:16,020 --> 00:02:19,640
+capital X الى مجموعة اخرى capital Y then ففي انا
+
+31
+00:02:19,640 --> 00:02:25,000
+الخواص التالي صورة المجموعة الفارغة فهي فارغة فF
+
+32
+00:02:25,000 --> 00:02:28,920
+of Phi is Phi طبعا هل دايما بقدر احصل صورة
+
+33
+00:02:28,920 --> 00:02:32,770
+المجموعة الفارغة؟نعم لأن الـ Fi صبصت من أي مجموعة
+
+34
+00:02:32,770 --> 00:02:35,590
+فهي صبصت من أي domain فلذلك اتهيتنا أن الصورة
+
+35
+00:02:35,590 --> 00:02:38,790
+مُعرّفة عليها لكن الجواب فيه الصورة اللي قد تطلع
+
+36
+00:02:38,790 --> 00:02:43,150
+الجواب فيه النقطة التانية صورة المجموعة اللي فيها
+
+37
+00:02:43,150 --> 00:02:47,310
+عنصر وحيد بسموها singleton setمجموعة من عنصر واحد،
+
+38
+00:02:47,310 --> 00:02:50,550
+إيش هي؟ عبارة عن تتكوّن من عنصر واحد، هي صورة هذا
+
+39
+00:02:50,550 --> 00:02:54,870
+العنصر، فصورة مجموعة الـA هي المجموعة تتكوّن من
+
+40
+00:02:54,870 --> 00:02:58,850
+مين؟ من F of A، من F of A، بكل بساطة، هذا الكلام
+
+41
+00:02:58,850 --> 00:03:01,540
+ممكن يطبق على أي عنصر في الـX، في ال domainلأن هو
+
+42
+00:03:01,540 --> 00:03:04,380
+كل عنصر في الدمان الدالة معرفة عنده، فبقدر أتحدث
+
+43
+00:03:04,380 --> 00:03:07,900
+عن صورة المجموعة بهذا الشكل، طبعا يمكن هذا طبقناه
+
+44
+00:03:07,900 --> 00:03:12,100
+في الأمثلة، هيك بنحسب، لما نقول مجموعة الصورة، لو
+
+45
+00:03:12,100 --> 00:03:14,540
+كانت عدد العناصر المحدودة، ايش بنقول؟ صورة العنصر
+
+46
+00:03:14,540 --> 00:03:17,120
+الأول وصورة العنصر التاني وها كذا، طبعا عنصر واحد
+
+47
+00:03:17,120 --> 00:03:22,430
+بكونش إلا هوالخاصية التالتة، لو أنا عندي مجموعتين
+
+48
+00:03:22,430 --> 00:03:26,270
+واحدة subset من التانية، طبعا الكل في subset من ال
+
+49
+00:03:26,270 --> 00:03:30,030
+domain، ليش؟ عشان انا بتعرف الصورة، فعلاقة صورة
+
+50
+00:03:30,030 --> 00:03:32,350
+المجموعة بتحافظ على علاقة ال subset، فإذا
+
+51
+00:03:32,350 --> 00:03:36,130
+المجموعتين A وB، ال A subset من ال B، فصورة ال A
+
+52
+00:03:36,130 --> 00:03:40,050
+subset من صورة ال B بالتمام، بتحافظوالصورة العكسية
+
+53
+00:03:40,050 --> 00:03:44,070
+بنفس الطريقة لو C subset من الـD فالصورة العكسية
+
+54
+00:03:44,070 --> 00:03:47,670
+للـC بتكون subset من الصورة العكسية للـD بنحافظ
+
+55
+00:03:47,670 --> 00:03:51,370
+على الترتيب طبعا بالنسبة ليش في الفرع C لازم
+
+56
+00:03:51,370 --> 00:03:54,390
+يكونوا كله subset من الـX عشان يكونوا مجموعات من
+
+57
+00:03:54,390 --> 00:03:58,210
+ال domain بتحدث عن صورهم في D ليش بيكونوا subset
+
+58
+00:03:58,210 --> 00:04:02,210
+من Y مجموعات جزئية من المجال المقابل بتحدث عن مين
+
+59
+00:04:02,210 --> 00:04:07,090
+صورهم العكسية صورهم العكسية خلينا نشوف البرهان مع
+
+60
+00:04:07,090 --> 00:04:22,640
+بعضA proof فهذه نظرية تلاتة تسعة ونشوف البرهة
+
+61
+00:04:22,640 --> 00:04:27,160
+نبتدى من ايه؟
+
+62
+00:04:27,160 --> 00:04:33,350
+ايش بدى اثبت فيه؟Statement بسيطة تساوي مجموعتين
+
+63
+00:04:33,350 --> 00:04:37,570
+مجموعة الـ Phi مجموعة والـ F of Phi برضه مجموعة
+
+64
+00:04:37,570 --> 00:04:39,970
+قلنا اتفقنا بدا الشكل بدي أثبت أن مجموعتين
+
+65
+00:04:39,970 --> 00:04:44,550
+متساويتين وبشكل أدق بدي أثبت أن مجموعة ما خالية
+
+66
+00:04:44,550 --> 00:04:48,270
+وهذه مهارة مرت علينا كثيرا إيش الطريقة المفلاة؟ By
+
+67
+00:04:48,270 --> 00:04:50,810
+contradiction فين دا يقول إيش؟ افترض أنها ليست
+
+68
+00:04:50,810 --> 00:04:54,450
+خاليةفشايفين احنا من المبادئ اللي بتعلمها ارجو ان
+
+69
+00:04:54,450 --> 00:04:58,830
+الأمور تكون استقرت و تثبت و تحاولوا تعتمدوا عليها
+
+70
+00:04:58,830 --> 00:05:02,010
+دي هتريحكوا كتير الناس اللي عندهم يعني في صعوبة لو
+
+71
+00:05:02,010 --> 00:05:05,470
+يمشوا علي نصاحي اتوقع هيصير فيه تقدم فهقوله assume
+
+72
+00:05:05,470 --> 00:05:12,550
+ايش هقوله assume ايش F of Phi لا تساوي Phi فماشي
+
+73
+00:05:12,550 --> 00:05:17,170
+بتعمل انت prove by contradiction prove by
+
+74
+00:05:17,170 --> 00:05:21,940
+contradictionاختصار، تمام؟ إيش معناه مجموعة غير
+
+75
+00:05:21,940 --> 00:05:25,100
+خالية؟ على الأقل فيها عنصر، طب هذا العنصر إيش
+
+76
+00:05:25,100 --> 00:05:31,120
+يسميه؟ X ولا Y؟ Y أنسب، لأن F of Y صور، فالصور إيش
+
+77
+00:05:31,120 --> 00:05:34,180
+اللي أنسب يسميهم Y؟ فحقوله طبعا أنا إيش بسمي .. زي
+
+78
+00:05:34,180 --> 00:05:37,800
+ما حكينا، فيش اسم غلط اسم صح، لكن في اسم أريح من
+
+79
+00:05:37,800 --> 00:05:42,060
+اسم، أنسب من اسم، فحقوله إيش؟ There exists Y such
+
+80
+00:05:42,060 --> 00:05:47,360
+that Y تنتمي F of Yيعني طبعا تعريف الـ Phi هذه
+
+81
+00:05:47,360 --> 00:05:52,040
+Definition of Phi إيش معناته غير فارغة، فيها على
+
+82
+00:05:52,040 --> 00:05:56,060
+الأقل أنصر، تمام؟ ماشي، إيش بدنا نعمل؟ نشوف إيش
+
+83
+00:05:56,060 --> 00:05:58,320
+معناته، أنصر في الـF of Phi، تاوي في بداية
+
+84
+00:05:58,320 --> 00:06:01,100
+المحاضرة قولت إيش بتكون الـY في الـF of A؟ يعني
+
+85
+00:06:01,100 --> 00:06:03,960
+هذه صورة، أنصر من وين؟ من الـA، اللي هي Phi في هذا
+
+86
+00:06:03,960 --> 00:06:09,680
+الكلام فده معناته، there exists Y، Y تساوي F of X
+
+87
+00:06:09,980 --> 00:06:16,900
+for some x تنتمي للفاء طب هذا من وين جيبته؟ تعريف
+
+88
+00:06:16,900 --> 00:06:23,860
+ال F في إيه؟ تعريف ال image F في إيه؟ اه
+
+89
+00:06:23,860 --> 00:06:26,240
+contradiction لأن for some يعني there exists x and
+
+90
+00:06:26,240 --> 00:06:33,380
+فأي contradiction والبرهان
+
+91
+00:06:33,380 --> 00:06:37,740
+انتهى برهان by contradiction بينتهي لما نوصل ل
+
+92
+00:06:37,740 --> 00:06:42,070
+contradictionتمام؟ واضح؟ فهذا الفرع الأول بهذه
+
+93
+00:06:42,070 --> 00:06:46,370
+السهولة و بهذه .. ارجونا تكون بيش الكل واضح له و
+
+94
+00:06:46,370 --> 00:06:49,350
+الامور واضحة للجميع لأن فعلا الموضوع بهذه السهولة
+
+95
+00:06:49,350 --> 00:06:51,750
+ما علينا اللي استخدمنا إيش؟ معناته إن الـ Phi غير
+
+96
+00:06:51,750 --> 00:06:54,930
+فارغة بس استخدمنا اسم مناسب لأ .. طب ليش اسم
+
+97
+00:06:54,930 --> 00:06:57,810
+مناسب؟ لو أنا سميتها X كانت غلبة تقول X تسوى 100
+
+98
+00:06:57,810 --> 00:07:01,350
+مش متعود هتلاقي فيها شوية صعوبة أه مش مقلوفة لكن
+
+99
+00:07:01,350 --> 00:07:04,610
+لما تقول Y تسوى F of X مقلوفة أكتر مريح مريحة أكتر
+
+100
+00:07:04,960 --> 00:07:09,480
+تمام نشوف فرع بي فرع بي سهل جدا زي الأمثلة على طول
+
+101
+00:07:09,480 --> 00:07:17,780
+مافيدوش برهان F للمجموعة A ليس إلا مجموعة ال F
+
+102
+00:07:17,780 --> 00:07:22,240
+فيها على طول من التعريف by definition by
+
+103
+00:07:22,240 --> 00:07:27,180
+definition لا تحتاج أي شيء و هذا عملناه في الأمثلة
+
+104
+00:07:28,300 --> 00:07:31,600
+اعملناه في الأمثل طبعا هذا الكلام لأي عنصر يعني
+
+105
+00:07:31,600 --> 00:07:36,580
+مايدوش شغل كتير تمام نيجي لفرقة C اللي ممكن يكون
+
+106
+00:07:36,580 --> 00:07:39,860
+بده شوية شغل فانا لأي عنصر هذا الكلام صحيح لأنه
+
+107
+00:07:39,860 --> 00:07:46,440
+بالتعريففزي ما شايفين a و b كانوا statements بسيطة
+
+108
+00:07:46,440 --> 00:07:51,400
+لكن c statements مركبة فيها جملة شرطية و كما
+
+109
+00:07:51,400 --> 00:07:55,540
+اتعودنا هذه قاعدة لا تتغير جملة شرطية بتفترض ان
+
+110
+00:07:55,540 --> 00:08:03,500
+الشرط صحيح فحنبدأ نقوله assume ال a subset من ال b
+
+111
+00:08:03,500 --> 00:08:09,010
+subset من ال xإيش مطلوب؟ بدنا نثبت إن ال F of A
+
+112
+00:08:09,010 --> 00:08:13,050
+subset من ال F of B أكتر مثال مر علينا .. أكتر
+
+113
+00:08:13,050 --> 00:08:17,110
+مثال مر علينا مطلوب ناخد عنصر من اليسار نوصله
+
+114
+00:08:17,110 --> 00:08:20,070
+بسلامة الله إلى اليمين يعني إيش بسلامة الله؟
+
+115
+00:08:20,070 --> 00:08:24,310
+بطريقة رياضية صحيحة يعني بطريقة رياضية صحيحة بمعنى
+
+116
+00:08:24,310 --> 00:08:27,810
+في الرياضيات .. هذه طريقتنا إنك توصل بإيش؟
+
+117
+00:08:27,810 --> 00:08:30,430
+بالسلامة .. بدنا نوصله بالسلامة بطريقة رياضية صحية
+
+118
+00:08:30,430 --> 00:08:33,910
+طبعا هاخد عنصر .. إيش أسميه؟ X ولا Y؟ Y لأنه صور
+
+119
+00:08:33,910 --> 00:08:39,980
+.. أفضل أن أسميه Ywhy be any element ممكن اكتب ايش
+
+120
+00:08:39,980 --> 00:08:46,300
+تنتمي لمين لل F of A لو ماكتبناش be any element صح
+
+121
+00:08:46,300 --> 00:08:49,220
+اما مفهومه ضمنيا be any element
+
+122
+00:08:53,060 --> 00:08:57,420
+فأنا كل خطوة و في .. في مكانها فصلت ليش كل جملة
+
+123
+00:08:57,420 --> 00:09:01,220
+بكتبها إلها سبب بكتبش بشكل عشوائي و لا لأ أنا
+
+124
+00:09:01,220 --> 00:09:04,320
+فبعرف إيش القضية فأول واحدة إيش ليش قلت أنه assume
+
+125
+00:09:04,320 --> 00:09:07,080
+لإن الجملة شرطية الجملة الشرطية لازم تكون الشرط
+
+126
+00:09:07,080 --> 00:09:10,320
+صحيح و بنثبت أنه جواب الشرط صحيح طيب جواب الشرط
+
+127
+00:09:10,320 --> 00:09:13,460
+عبارة عن ألاخة إيش subset كيف بنثبت ال subset؟
+
+128
+00:09:13,460 --> 00:09:16,360
+بناخد answer من اليسار و بنوصله لليمين ممتاز إيش
+
+129
+00:09:16,360 --> 00:09:19,720
+ممكن أعمل؟ أستخدم التعريف تبع عفو في إيه؟ فهذا
+
+130
+00:09:19,720 --> 00:09:27,610
+بيقول لي أن whyتساوي F of X for some X تنتمي للـA
+
+131
+00:09:27,610 --> 00:09:32,650
+X تنتمي للـA وين بتوصلها أنا للـB؟ إيش علاقة الـA
+
+132
+00:09:32,650 --> 00:09:36,190
+و الـB؟ الـA سبسط من الـB فعيد الكتابة فعيد
+
+133
+00:09:36,190 --> 00:09:39,610
+الكتابة مافيش أسهل من هيك أرجو أنه نحاول ندقق و
+
+134
+00:09:39,610 --> 00:09:46,400
+نتعلم فهذا بيقوللي هذه ماتتغيرشfor some X تنتمي
+
+135
+00:09:46,400 --> 00:09:51,140
+للـB لأن الـA سبسط من الـB فكل عنصر في الـA لازم
+
+136
+00:09:51,140 --> 00:09:54,660
+يكون في الـB طيب أنا عندي صورة عنصر من الـB وين
+
+137
+00:09:54,660 --> 00:10:00,660
+بتكون؟ في صورة الـB وخلصنا Y تنتمي للـF of B تعريف
+
+138
+00:10:00,660 --> 00:10:07,450
+الـF of B definition of F of Bوهو المطلوب فممكن
+
+139
+00:10:07,450 --> 00:10:13,390
+هنا أقلق أو أختم البرهان thus F of A فعلا subset
+
+140
+00:10:13,390 --> 00:10:21,090
+من F of B أي سؤال واضح فالأمور بهذه البساطة بس
+
+141
+00:10:21,090 --> 00:10:24,130
+طبعا الجديد هو التعريف لل F of A استخدمناها مرتين
+
+142
+00:10:24,130 --> 00:10:29,370
+والباقي كله متكرر ليس أيه نشوف فرع D
+
+143
+00:10:33,030 --> 00:10:38,590
+فأرجو من الجميع يحاول يكرر و مش عايب نقلد في
+
+144
+00:10:38,590 --> 00:10:41,950
+البداية لحد ما نياشي يصير عندنا قدرة على الكتابة
+
+145
+00:10:41,950 --> 00:10:46,790
+بشكل منفصل فاحنا بنقلد المثال و بنحل زيه ماعرف
+
+146
+00:10:46,790 --> 00:10:49,590
+طبعا إذا في مثال مختلف كيو و إختلاف أو انفرق لكن
+
+147
+00:10:49,590 --> 00:10:52,700
+نشوف الناس كيف بتحلنشوف الناس كيف بتحققله و نتعلم
+
+148
+00:10:52,700 --> 00:10:56,840
+منهم هذا تلاقى الناس ماعادش بتتعلم لحاله بتعلم جيد
+
+149
+00:10:56,840 --> 00:10:59,780
+و نستفيد من خبرات الآخرين نتعلم لحالنا جيد ممكن
+
+150
+00:10:59,780 --> 00:11:02,480
+يكون بس فأتعب لكن إذا في حاجة معروفة و في ناس
+
+151
+00:11:02,480 --> 00:11:05,280
+عندها طرح معينة طبعا إذا طريقتى أنا مش مرايحاكوا
+
+152
+00:11:05,280 --> 00:11:09,600
+جيبولي طريقة من الكتاب بس ماجيبليش طريقة غير صحيحة
+
+153
+00:11:09,600 --> 00:11:12,040
+بدي طريقة صحيحة أنا مش ضروري طريقتى يعنى أنا
+
+154
+00:11:12,040 --> 00:11:16,060
+مابلزمش بطريقتى لكن بدي طريقة صحيحة تمام نشوف دى
+
+155
+00:11:18,860 --> 00:11:21,700
+نفس القضية بتشبه اللي فوق تماما من حيث اللي هو
+
+156
+00:11:21,700 --> 00:11:24,560
+الشكل العام دي ومنا شرطية هنبدأ نقوله أسيوم إن
+
+157
+00:11:24,560 --> 00:11:29,960
+الشرط صحيح افترض إن الشرط صحيح إيش الشرط؟ C subset
+
+158
+00:11:29,960 --> 00:11:35,560
+من ال D subset من ال Y بدي أثبت علاقة subset إيه؟
+
+159
+00:11:35,560 --> 00:11:39,320
+بدي أخد عنصر من اليسار إيش يسمي X ولا Y؟ X X
+
+160
+00:11:39,320 --> 00:11:43,620
+الصورة العكسية في الدماغ بتكون X أه لإن صورة عكسية
+
+161
+00:11:43,620 --> 00:11:50,150
+وقوله هنا إيش؟ let X تنتميللـ F inverse of C طبعاً
+
+162
+00:11:50,150 --> 00:11:52,450
+بي ال element أو ال arbitrator ال element كله صح
+
+163
+00:11:52,450 --> 00:11:57,310
+لو ما كتبتش ممشي الحقمعروف، مازال أنا أشتغل بشكل
+
+164
+00:11:57,310 --> 00:12:00,470
+عام، إذا الـ X هذه arbitrary لأن مافيش عليها
+
+165
+00:12:00,470 --> 00:12:03,970
+تخصيص، فالأصل اللي نشتغل عليه هو X بالعموم، فهي
+
+166
+00:12:03,970 --> 00:12:08,630
+ليس صيغة عامة تابع، إيش ممكن نعمل؟ نستخدمش تعريف،
+
+167
+00:12:08,630 --> 00:12:11,250
+إذا كانت الـ X في الصورة العكسية، بتكون صورة أوين؟
+
+168
+00:12:11,250 --> 00:12:14,710
+في الـ C، إحنا نشتغل في الـ C، فإيش ما هي الصورة
+
+169
+00:12:14,710 --> 00:12:18,950
+العكسية للـ X؟ لأ، الصورة العكسية للـ C هي العناصر
+
+170
+00:12:18,950 --> 00:12:21,750
+اللي صورهم في الـ C، لو طلعنا على التعريف، فهذا
+
+171
+00:12:21,750 --> 00:12:25,590
+على طول، هذه F and one left في الحقيقةF of X تنتمي
+
+172
+00:12:25,590 --> 00:12:33,870
+للـ C تعريف of F M versus Cفهذا مفتاح، لو روحتي
+
+173
+00:12:33,870 --> 00:12:37,090
+هيك صح، لو روحتي هيك صح فالعنصر بيكون في الصورة
+
+174
+00:12:37,090 --> 00:12:41,250
+العكسية فقط وإذا فقط صورة كانت في المجموعة فهذا
+
+175
+00:12:41,250 --> 00:12:43,910
+مفتاح في الشغل كله وكده .. وشوفتوها الملاحظة كده
+
+176
+00:12:43,910 --> 00:12:47,170
+بناها صحيح؟ اه ما كتبناش، طلعنا عليها في الشريحة
+
+177
+00:12:47,170 --> 00:12:50,330
+اه تمام؟ ممتاز، انا وين رايح؟ بدأ أروح على ال D
+
+178
+00:12:50,330 --> 00:12:53,590
+إيش علاقة ال C مع ال D؟ ما ال C صابست من ال D فهنا
+
+179
+00:12:53,590 --> 00:12:56,350
+.. طبعا بس هنا إيش ده يقول؟ ماينفعش أقول إيه فان
+
+180
+00:12:56,350 --> 00:12:59,790
+دول ليه؟بنفعش أقول if and only if لأنه subset فهنا
+
+181
+00:12:59,790 --> 00:13:03,650
+ال F of X تنتمي لل D ليش؟ لأن ال C subset من ال D
+
+182
+00:13:03,650 --> 00:13:06,810
+طبعا ليش بنفعش if and only if؟ لأن اللي موجود في
+
+183
+00:13:06,810 --> 00:13:10,290
+ال C موجود في ال D لكن العكس غير صحيح بنفع أمشي من
+
+184
+00:13:10,290 --> 00:13:13,790
+ها لها لكن بنفعش أرجع أرجوع الطريق هنا ممنوع،
+
+185
+00:13:13,790 --> 00:13:16,790
+الطريق هنا ممنوع لأنه مش كل عناصر D في ال C لأن ال
+
+186
+00:13:16,790 --> 00:13:20,430
+D أكبر أو تساوي C لكن كل عناصر ال C في ال Dطبعا
+
+187
+00:13:20,430 --> 00:13:23,490
+واضحة؟ تمام، خلصناها لأننا بدنا نعمل عكس إذا
+
+188
+00:13:23,490 --> 00:13:26,130
+الصورة في الـD وين بتكون الـX؟ في الصورة العكسية
+
+189
+00:13:26,130 --> 00:13:28,370
+للـD، لأن هذا F and والـF، بقى وجهة ده ده ماشي من
+
+190
+00:13:28,370 --> 00:13:32,030
+هنا إلى هنا، و العكس صحيح، فهذا implies X تنتمي
+
+191
+00:13:32,030 --> 00:13:34,990
+للـF inverse of D، طبعا لو حاطيت F and والـF هنا
+
+192
+00:13:34,990 --> 00:13:40,250
+صح، كهذه مع هذه علاقة F and والـF، برضه تعريف F
+
+193
+00:13:40,250 --> 00:13:45,700
+inverse الـD، وهو المطلوب، خلصنافبدأت من عنصر من
+
+194
+00:13:45,700 --> 00:13:49,500
+الطرف اليسار وصلته بطريقة صحيحة إذا وصل بالسلامة
+
+195
+00:13:49,500 --> 00:13:52,560
+إلى الطرف اليمين إذا فعلا الأولى subset من التانية
+
+196
+00:13:52,560 --> 00:13:59,850
+ف F inverse C subset من F inverse B وهو اللهزي ما
+
+197
+00:13:59,850 --> 00:14:03,250
+تشايفين فيه أمور قديمة كيف نتعامل مع الجملة شرطية
+
+198
+00:14:03,250 --> 00:14:05,850
+كيف نتعامل مع علاقة subset وفيه أمور جديدة اللي هي
+
+199
+00:14:05,850 --> 00:14:09,090
+استخدام التعريف الصورة المجموعة وصورة العكسية
+
+200
+00:14:09,090 --> 00:14:12,370
+المجموعة واضح فهذا لجديد في الموضوع والباقي كله
+
+201
+00:14:12,370 --> 00:14:16,990
+تكرار لأنه نفس الألاقات مابتتغيرش من موضوع لموضوع
+
+202
+00:14:20,070 --> 00:14:24,850
+خلّيني أشوف أمثلة، كيف ممكن نستفيد من براهين
+
+203
+00:14:24,850 --> 00:14:30,830
+النظريات و نتعلم و نطبق هذه المعارف في حل التمرين
+
+204
+00:14:30,830 --> 00:14:35,150
+أو في براهين لأسئلة أخرى، المعنى ده اللي بنتعلمه،
+
+205
+00:14:35,150 --> 00:14:37,890
+بدنا نقدر إيش، المهارات اللي بتعلمها نطبقها في
+
+206
+00:14:37,890 --> 00:14:44,980
+مكان آخر، نطبقها في مكان آخر تمام، مثالlet f be a
+
+207
+00:14:44,980 --> 00:14:49,560
+function from X to Y بحيث أن صورة الـ X كلها صورة
+
+208
+00:14:49,560 --> 00:14:53,360
+ال domain تساوي Y إيش معناته ده الكلام؟ بمعنى آخر
+
+209
+00:14:53,360 --> 00:14:57,920
+إن ال image اللي هو المدى بيساوي كل Y يعني ده اللي
+
+210
+00:14:57,920 --> 00:15:02,780
+شاملة غطت كل المجال المقابل فالمجال المقابل بيساوي
+
+211
+00:15:02,780 --> 00:15:06,600
+المدى يعني المجال المقابل بيساوي المدى تمامand let
+
+212
+00:15:06,600 --> 00:15:11,480
+B and C be subsets of Y كل واحدة مُعطَيَد تمام
+
+213
+00:15:11,480 --> 00:15:15,420
+prove that إيش المطلوب جملة شرطية إذا كانت الصورة
+
+214
+00:15:15,420 --> 00:15:19,540
+العكسية للـB تساوي الصورة العكسية للـC فإن B تساوي
+
+215
+00:15:19,540 --> 00:15:23,900
+C فإن B تساوي C خلّيني أعيد سياقة السؤال جزء منه
+
+216
+00:15:23,900 --> 00:15:28,380
+مش كله فهنا المطلوب أنه جملة شرطية F inverse الـB
+
+217
+00:15:28,380 --> 00:15:33,700
+subset من F inverse الـC implies B تساوي C
+
+218
+00:15:36,710 --> 00:15:41,390
+أي اه صحيح فهذه ال statement وهذه ال statement
+
+219
+00:15:41,390 --> 00:15:45,330
+بدنا نثبتهم بهذا الشكل ال proof او solution نفس
+
+220
+00:15:45,330 --> 00:15:48,650
+الشيء
+
+221
+00:15:48,650 --> 00:15:53,110
+اه طبعا اه في الشيء .. بس انا اول شي هفترض ان
+
+222
+00:15:53,110 --> 00:16:01,910
+الشرط صحيح فاجله assume f inverse ال b تساوي f
+
+223
+00:16:01,910 --> 00:16:06,590
+inverse ال cمطلوب نثبت هذه العلاقة بدنا ناخد عنصر
+
+224
+00:16:06,590 --> 00:16:09,630
+من الطرف ونمشي فيه إذا مشينا تكافؤ التساويتها
+
+225
+00:16:09,630 --> 00:16:13,330
+وماقدرناش نمشي تكافؤ ونكون عندما نعملنا نص البرهان
+
+226
+00:16:13,330 --> 00:16:16,030
+أنه subset ونضطر ناخد عنصر من اليمين من الـC
+
+227
+00:16:16,030 --> 00:16:19,530
+ونوصله إلى الـB أحنا في الغالب هنستخدم الطريقة
+
+228
+00:16:19,530 --> 00:16:22,210
+التانية أن الأولى subset من التانية والتانية
+
+229
+00:16:22,210 --> 00:16:26,110
+subset من الأولى فنبدأ لاتجاه الأول ممكن أرتب
+
+230
+00:16:26,110 --> 00:16:32,550
+البرهان الـB subset من الـCبرهاني الأول برهاني
+
+231
+00:16:32,550 --> 00:16:36,750
+الجزء الأول من البرهان ثم هاخد عنصر من ال B ال B
+
+232
+00:16:36,750 --> 00:16:43,000
+أسمي العنصر X ولا Y؟انتبهوا اقرأوا ايش ال B و ال C
+
+233
+00:16:43,000 --> 00:16:47,340
+صبصت من وين من Y شوفوا اه بعيد و بكرر ليش انت بتجف
+
+234
+00:16:47,340 --> 00:16:50,640
+هنا لو أخدناه ايش مكان مافيش اسم غلط بس في اسم
+
+235
+00:16:50,640 --> 00:16:53,040
+مريح و انتوا جربوا في البيت اذا لجيتوا حالكوا لما
+
+236
+00:16:53,040 --> 00:16:56,960
+تغيروا الاسم مابتتضيقواش الأمور معكوا سلاسة ماشي
+
+237
+00:16:56,960 --> 00:17:00,780
+اللي جيتوا هذه الملاحظات مفيدة و مريحة اعتمدوها اه
+
+238
+00:17:00,780 --> 00:17:06,480
+فانا هاخد Y let small y تنتمي ل ال B بدأ أوصلها لل
+
+239
+00:17:06,480 --> 00:17:12,850
+Cبدنا نوصلها لل C طيب إيش الطريق .. إيش الطرق
+
+240
+00:17:12,850 --> 00:17:17,270
+المسموحة بين ال B و بين ال C؟ و .. و .. و .. و ..
+
+241
+00:17:17,270 --> 00:17:17,650
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+242
+00:17:17,650 --> 00:17:17,790
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+243
+00:17:17,790 --> 00:17:17,890
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+244
+00:17:17,890 --> 00:17:18,250
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+245
+00:17:18,250 --> 00:17:18,710
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+246
+00:17:18,710 --> 00:17:18,890
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+247
+00:17:18,890 --> 00:17:18,890
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+248
+00:17:18,890 --> 00:17:18,930
+و .. و .. و .. و .. و .. و .. و .. و .. و .. و ..
+
+249
+00:17:18,930 --> 00:17:20,910
+و .. و .. و .. و .. و .. و .. و .. و .. و .. وهيها
+
+250
+00:17:20,910 --> 00:17:25,090
+فهنا بدأ انا اوصل كيف ده تكون ال Y في ال B إذا
+
+251
+00:17:25,090 --> 00:17:28,610
+كانت ال Y في ال B إيش علاقة ال Y مع ال F inverse؟
+
+252
+00:17:28,610 --> 00:17:31,550
+احنا في عنا علاقة وحيدة بالنسبة لل F inverse عندي
+
+253
+00:17:31,550 --> 00:17:37,810
+علاقة هذه مفتاح X تنتمي لل F inverse of B if and
+
+254
+00:17:37,810 --> 00:17:44,680
+only if F of X تنتمي لل Bأه مرة تانية كيف بنفكر يا
+
+255
+00:17:44,680 --> 00:17:49,440
+أخوات انتبهوا كيف بنفكر احنا بدأنا بدنا نوصلها لل
+
+256
+00:17:49,440 --> 00:17:54,140
+C بدنا نشوف مين الوسائل مين الطرق اللي بتوصل من ال
+
+257
+00:17:54,140 --> 00:17:57,960
+B ل C بتطلع على المواطيات هي المواطيات الوحيدة
+
+258
+00:17:57,960 --> 00:18:01,360
+فإذا انا بدي أنقل ال Y لل F inverse of B بينفعش
+
+259
+00:18:01,360 --> 00:18:05,120
+عنصر شكله عام ينتقل من ال B لل F inverse لازم يكون
+
+260
+00:18:05,120 --> 00:18:08,200
+عصورة عصورة عشان أقول إن هو يا ده مصدر و جاي من ال
+
+261
+00:18:08,200 --> 00:18:12,720
+B فهل ال Y أي Y في ال B بقدر أكتبها إنها صورة
+
+262
+00:18:17,510 --> 00:18:21,470
+بشكل عام انتبهوا هنا نقطة مهمة جدا لان المعطيات
+
+263
+00:18:21,470 --> 00:18:24,330
+هنا مهمة جدا و احنا في الغالب لازم نستخدم كل
+
+264
+00:18:24,330 --> 00:18:27,150
+المعطيات اذا ما استخدماش معطيات معينة بيكون فيها
+
+265
+00:18:27,150 --> 00:18:30,170
+خطأ في السؤال و احتمال ضعيف او خطأ في الحل
+
+266
+00:18:30,170 --> 00:18:35,890
+فانتبهوا هنا بشكل عام انا عندي هي ال Y و هي عندي
+
+267
+00:18:35,890 --> 00:18:41,430
+ال B هناهل كل عناصر المجال المقابل هم صور؟ مش
+
+268
+00:18:41,430 --> 00:18:44,330
+بالضروري، وبالتالي ليس من الضروري أن عناصر كل الـB
+
+269
+00:18:44,330 --> 00:18:48,130
+تكون صور، لكن لو لأنه أعطاني أن جل الـY في أول
+
+270
+00:18:48,130 --> 00:18:50,970
+الشيء إشمالة تساوي المدى، إذاً كل عنصر في الـY هو
+
+271
+00:18:50,970 --> 00:18:54,910
+صورة، زوزاه صورة، إذاً هناخد الـY في الـB فهي
+
+272
+00:18:54,910 --> 00:18:59,450
+بالتالي وين؟ في الـY، على طول، الـY تنتمي لـY،
+
+273
+00:18:59,450 --> 00:19:05,270
+ليش؟ لأن الـY، الـB صبست من الـY،
+
+274
+00:19:05,270 --> 00:19:10,640
+طب الـY إيش بتساوي؟F of X فهذا جوا في المعطيات
+
+275
+00:19:10,640 --> 00:19:14,300
+انتبه كل كلمة زي ما حقولنا في الرياضيات كلام دقيق
+
+276
+00:19:14,300 --> 00:19:18,540
+نادر جدا إذا ماكانش مش موجود أصلا يكون كلام بس
+
+277
+00:19:18,540 --> 00:19:22,160
+إنشائي لازم يكون له فايد طيب إيش معناته إن ال Y في
+
+278
+00:19:22,160 --> 00:19:25,120
+ال F of X هي صورة عنصر من ال capital X هاي اللي
+
+279
+00:19:25,120 --> 00:19:29,940
+بدي أنهي ال Y صورة فهذا يؤدي إن Y تساوي F of small
+
+280
+00:19:29,940 --> 00:19:37,770
+x for some X تنتمي لل capital Xفإذا فعلاً هذه الـY
+
+281
+00:19:37,770 --> 00:19:43,390
+صورة هذا مهم بشكل عام مش موجود لكن عشان نجلي إنه
+
+282
+00:19:43,390 --> 00:19:49,130
+المدى يساوي كل الـY إذا كل عناصر الـY صور و الـP
+
+283
+00:19:49,130 --> 00:19:52,830
+subset من الـY إذا كل عناصرها صور الآن صارت
+
+284
+00:19:52,830 --> 00:19:57,210
+العملية سهلة الـY تساوي F of X في الـP if and only
+
+285
+00:19:57,210 --> 00:20:02,760
+if X were موجودة في الـF inverse و الـP فإذا thusY
+
+286
+00:20:02,760 --> 00:20:09,060
+تساوي F of X تنتمي للـB وهذا يؤدي أن F and only F
+
+287
+00:20:09,060 --> 00:20:17,070
+تنتمي للـF inverseفإذن احنا طرق التفكير كيف نفكر
+
+288
+00:20:17,070 --> 00:20:20,890
+في الحل فاحنا قلنا هي احنا البداية بنعرف نبدأ صح و
+
+289
+00:20:20,890 --> 00:20:23,790
+هذا مهم جدا و بعدين دايما عيني على المطلوب و هو
+
+290
+00:20:23,790 --> 00:20:26,950
+الهدف ايش علاقة ال B و ال C؟ العلاقة الوحيدة هي ال
+
+291
+00:20:26,950 --> 00:20:30,570
+F inverse و ال F inverse تحتاج للصور فاحنا قلنا هل
+
+292
+00:20:30,570 --> 00:20:33,110
+بقدر أكتب الأنصر العشوائي على إن صورة؟ في هذا
+
+293
+00:20:33,110 --> 00:20:36,270
+المثال ممكن بشكل عام لأ لكن في هذا المثال ممكن لأن
+
+294
+00:20:36,270 --> 00:20:40,270
+هي المفتاح أن ال Y تساوي F of X و ال B جزء من ال Y
+
+295
+00:20:40,270 --> 00:20:44,160
+واضحة؟الأن خلاص، مشينا، فهذا إيش معناته؟ if and
+
+296
+00:20:44,160 --> 00:20:47,920
+only if X تنتمي للـF inverse of C لأنهم متساويين،
+
+297
+00:20:47,920 --> 00:20:51,680
+أه، ليش؟ طبعا هذا تعريف الـF inverse، definition
+
+298
+00:20:51,680 --> 00:20:57,020
+of F inverse الـB، وهذا لأنه F inverse الـB تساوي
+
+299
+00:20:57,020 --> 00:21:02,420
+F inverse الـC، تمام؟ الآن بتدرجع، أه، هذا إيش
+
+300
+00:21:02,420 --> 00:21:08,720
+معناته؟ F of X تنتمي للـC، اللي هي مين؟ اللي هي Y،
+
+301
+00:21:08,720 --> 00:21:10,560
+أه، فإذاً Y في الـC يروح من المطلوب
+
+302
+00:21:17,420 --> 00:21:22,660
+فقالي ألخص بدأت Y في الـB وصلتها بطريقة رياضية
+
+303
+00:21:22,660 --> 00:21:28,960
+صحيحة للـC إذا الأول subset من التاني
+
+304
+00:21:28,960 --> 00:21:35,490
+B subset من الـCفهذا الجزء الأول إحنا رقمناه
+
+305
+00:21:35,490 --> 00:21:38,730
+بالرقم Command Mark فأرجوا إن الأمور تكون واضحة
+
+306
+00:21:38,730 --> 00:21:42,690
+طبعا فاقمين هيكلية البرهان الأساسي بدأت أثبت علاقة
+
+307
+00:21:42,690 --> 00:21:45,350
+subset نفس الهيكلية البداية و النهاية واحدة لكن
+
+308
+00:21:45,350 --> 00:21:49,150
+ومين اختلاف؟ التفاصيل دخلنا فيها موضوع مين؟ الصورة
+
+309
+00:21:49,150 --> 00:21:52,050
+العكسية هذا هو التفاصيل صرنا كيف انتقلنا عن طريق
+
+310
+00:21:52,050 --> 00:21:55,770
+الصورة العكسية فطبعا هنا تم الجزء التاني احنا بدنا
+
+311
+00:21:55,770 --> 00:21:59,650
+نثبت التساوي فلاقينا رقم اتنين إيش بده أثبت؟ إن C
+
+312
+00:21:59,650 --> 00:22:04,250
+subset من الـB هذا الجزء التانيوهذا نفس الخطوات
+
+313
+00:22:04,250 --> 00:22:10,290
+بدي اتعدوها عشان يتأكدوا عن الفهم فهذا exercise ع
+
+314
+00:22:10,290 --> 00:22:13,970
+تقيدوا نفس الشيء بس دور ال B و ال C يختلف فارجو ان
+
+315
+00:22:13,970 --> 00:22:17,410
+عيدوا اكتبوه بالحرف بس بدلوا ال C و ال B دورهم
+
+316
+00:22:17,410 --> 00:22:25,670
+يتبدل نفس العملية بس الدور يتبدل تمام؟ انت باين؟
+
+317
+00:22:25,670 --> 00:22:34,370
+تمام ننتقل لنقطة جديدة نظرية عشرةأه فاحنا طبعا
+
+318
+00:22:34,370 --> 00:22:39,410
+بنتحدث عن صورة مجموعة و الصورة العكسية لمجموعة طب
+
+319
+00:22:39,410 --> 00:22:42,190
+لو كانت هذه المجموعة مش مجموعة بسيطة مجموعة مكونة
+
+320
+00:22:42,190 --> 00:22:45,650
+من أدت مجموعات كانت اتحاد مجموعات أو تقاطع مجموعات
+
+321
+00:22:45,650 --> 00:22:49,110
+إيش بيصير؟ هل الصورة بتتوزع للاتحاد و التقاطع ولا
+
+322
+00:22:49,110 --> 00:22:52,070
+لأ؟ و الصورة العكسية بتتوزع للاتحاد و التقاطع ولا
+
+323
+00:22:52,070 --> 00:22:55,850
+لأ؟ فده اللي احنا هندرسه في النظريات القادمة هنبدأ
+
+324
+00:22:55,850 --> 00:22:58,430
+بالصورة و بعدين هنشوف الصورة العكسية فبقول لي
+
+325
+00:22:58,430 --> 00:23:01,930
+images of unions and intersectionsبدنا نشوف كيف
+
+326
+00:23:01,930 --> 00:23:05,470
+بتعامل الصور مع التقاطع و مع الاتحاد فطبعا بقول
+
+327
+00:23:05,470 --> 00:23:08,090
+لبداينا .. طبعا مازالت نتحدث عن صور زي اللي بيكون
+
+328
+00:23:08,090 --> 00:23:12,130
+فيها دالة دالة من X ل Y الآن مش هياخد مجموعة من ال
+
+329
+00:23:12,130 --> 00:23:15,470
+X هياخد عدة مجموعات family of sets عشان ياخد
+
+330
+00:23:15,470 --> 00:23:19,110
+اتحادهم تقاطعا بشكل عام .. بشكل عام فبقول لت F
+
+331
+00:23:19,110 --> 00:23:22,470
+بيبقى function from X to Y زي ما اتعلمنا كيف نخلق
+
+332
+00:23:22,470 --> 00:23:27,150
+النظريات و كيف نكون دقيقين و let A sub Gamma بحيث
+
+333
+00:23:27,150 --> 00:23:29,350
+small Gamma and capital Gamma بيبقى family of
+
+334
+00:23:29,350 --> 00:23:32,480
+subsets of Xمهم جداً، المجموعات جزئية من الـ
+
+335
+00:23:32,480 --> 00:23:35,100
+explanation يتحدث عن صورة مجموعة، لازم المجموعات
+
+336
+00:23:35,100 --> 00:23:39,300
+تكون جزء من ال domain، جزء من ال domain ثم القانون
+
+337
+00:23:39,300 --> 00:23:45,260
+الأول بيقول صورة الاتحاد تساوي اتحاد الصور، مظبوط
+
+338
+00:23:45,260 --> 00:23:49,060
+صورة اتحاد المجموعات تساوي اتحاد الصور، فماشي
+
+339
+00:23:49,060 --> 00:23:54,400
+بتدخل على الاتحاد و بتوزع بدون مشاكلطيب صورة
+
+340
+00:23:54,400 --> 00:23:58,740
+التقاطع لا تساوي تقاطع الصور وإنما subset من تقاطع
+
+341
+00:23:58,740 --> 00:24:02,500
+الصور وإنما subset من تقاطع الصور فقط مافيش تساوي
+
+342
+00:24:02,500 --> 00:24:06,620
+مافيش تساوي هنشوف البرهان لتنتين ونشوف ليش مرة كان
+
+343
+00:24:06,620 --> 00:24:09,800
+في تساوي وفي المرة التانية ماكنش فيه تساوي
+
+344
+00:24:09,800 --> 00:24:12,940
+فالعملية
+
+345
+00:24:12,940 --> 00:24:16,080
+مش عشوائية أن أحنا وين ما نشوف نقول نوزع وخلاص لأ
+
+346
+00:24:16,080 --> 00:24:20,120
+هيوق نجحت في الاتحاد لكن في التقاطع مانجحتش بس هيش
+
+347
+00:24:20,120 --> 00:24:20,440
+subset
+
+348
+00:24:27,410 --> 00:24:30,930
+طبعاً يمكن فرع بيه برضه بيعلمنا اللي هو المثال
+
+349
+00:24:30,930 --> 00:24:34,430
+المشهور ما لا يترك كله لا يترك جله و لا يترك جله
+
+350
+00:24:34,430 --> 00:24:37,810
+لا يترك كله فعنا يمكن ما نجحناش أنه يكون فيه تساوي
+
+351
+00:24:37,810 --> 00:24:40,870
+لكن على الأقل فيه أنه معلومة مضمونة اللي هي أنه صد
+
+352
+00:24:40,870 --> 00:24:43,990
+صد مافيش تساوي مايقولوا إنهم مايساويوش بعض خلاص
+
+353
+00:24:43,990 --> 00:24:46,810
+مافيش قانون بينهم لأ في قانون جزء مش القانون
+
+354
+00:24:46,810 --> 00:24:51,150
+الأفضل المثالي لكن في حاجة معروفة في علاقة مضمونة
+
+355
+00:24:51,150 --> 00:24:54,830
+لكن التانية العكسية مش صحيةفالأولى صبصة من التانية
+
+356
+00:24:54,830 --> 00:24:57,450
+لكن العكس غير صحي ماجدرتش أحصل على القانون النموذج
+
+357
+00:24:57,450 --> 00:25:01,390
+هو التساوي لكن احصلت على جزء من القانون وهذا يعتبر
+
+358
+00:25:01,390 --> 00:25:05,290
+مهم وكافي فخلينا نشوف البرهان ونشوف ليش العلاقتين
+
+359
+00:25:05,290 --> 00:25:10,690
+هدولة بهذا الشكل نظرية تلاتة
+
+360
+00:25:10,690 --> 00:25:19,230
+عشر البرهان ونبدأ بالفرع الأول تما علاقة تساوي
+
+361
+00:25:19,230 --> 00:25:24,400
+مجموعاتولا إيش؟ تساوي إيش؟ مجموعات اه في أنا عندي
+
+362
+00:25:24,400 --> 00:25:28,180
+تقاطع مجموعات مجموعة وصورة مجموعة مجموعة فهو تساوي
+
+363
+00:25:28,180 --> 00:25:31,800
+مجموعات الجملة بسيطة لا فيها شرط ولا فيها ولا إشي
+
+364
+00:25:31,800 --> 00:25:35,200
+فبنبدأ من عنصر في طرف إذا مشينا تكافؤ خلصنا
+
+365
+00:25:35,200 --> 00:25:38,960
+مامشيناش تكافؤ وبنمشي من اتجاه التالي فحناخد عنصر
+
+366
+00:25:38,960 --> 00:25:43,500
+إيش يسمي X ولا Y؟ Y لأنه صورة لأنه صورة فهنقوله
+
+367
+00:25:43,500 --> 00:25:50,910
+هنا let Y تنتمي ل .. نبدأ من الطرف اليساراتحاد على
+
+368
+00:25:50,910 --> 00:25:55,950
+الجامعة اي جامعة تمام طبعا be an element واحد يقول
+
+369
+00:25:55,950 --> 00:25:58,950
+ليش بطل تكتب خلاص اتقدمنا شوية لكن هو هل اختلف
+
+370
+00:25:58,950 --> 00:26:02,890
+الحل لأ اكتبوا be an element يعني معروفة دبنية فلو
+
+371
+00:26:02,890 --> 00:26:05,610
+شوية احنا هنبدأ نقتصر في الكتابات لأن المستوى
+
+372
+00:26:05,610 --> 00:26:09,370
+بيتقدم تمام ايش ممكن اعمل مين افك الصورة ولا
+
+373
+00:26:09,370 --> 00:26:12,770
+الاتحاد اول الصورة الصورة تبدأ من الخارج دايما
+
+374
+00:26:12,770 --> 00:26:18,320
+بالفكرة اه فإيش معناه انهالـ Y في صورة مجموعة ان
+
+375
+00:26:18,320 --> 00:26:23,240
+الـ Y هي صورة عنصر من المجموعة الـ Y يشمل يكافئ
+
+376
+00:26:23,240 --> 00:26:32,280
+تعريف لأنه يكافئ Y تساوي F of X for some X تنتمي
+
+377
+00:26:32,280 --> 00:26:36,000
+للاتحاد بدل ما عندي A صار عندي أيه اللي هو ممكن
+
+378
+00:26:36,000 --> 00:26:41,380
+يسميها A في التعريف اتحاد على الـ AG طبعا ده ليس
+
+379
+00:26:41,380 --> 00:26:44,100
+الا mean تعريف of F الـA
+
+380
+00:26:47,130 --> 00:26:49,570
+واضح؟ فهذا هو التعريف اللي احنا نشتغل عليه هذا
+
+381
+00:26:49,570 --> 00:26:53,330
+موضوعنا لجديد اه طيب قبل ما ابدأ اكمل بدي اروح انا
+
+382
+00:26:53,330 --> 00:26:56,170
+اقيد صياغتها دي بس احنا كلنا اتفقنا في section
+
+383
+00:26:56,170 --> 00:27:00,050
+واحد ستة المكمم ممكن اكتبه بالاخر وممكن اكتبه في
+
+384
+00:27:00,050 --> 00:27:04,750
+الأول فحالينا نكتب وين؟ في الأول there exists X
+
+385
+00:27:04,750 --> 00:27:10,290
+تنتمي للاتحاد للـA Gamma Gamma تنتمي للـGamma
+
+386
+00:27:10,290 --> 00:27:15,510
+والـY تساوي F of X تمام
+
+387
+00:27:16,540 --> 00:27:21,400
+إيش بدي أعمل الآن؟ بدي أفك الاتحاد فهدي وكافر
+
+388
+00:27:21,400 --> 00:27:24,960
+there exist x إيش معناه x في الاتحاد؟ طبعا هذه
+
+389
+00:27:24,960 --> 00:27:27,320
+ممكن أكتبها على صورتين there exist x و x في
+
+390
+00:27:27,320 --> 00:27:31,100
+الاتحاد تتعاد على مرحلتين ممكن تنكتب طيب إيش معناه
+
+391
+00:27:31,100 --> 00:27:34,300
+إن ال x في الاتحاد؟ في واحدة من المجموعات على
+
+392
+00:27:34,300 --> 00:27:38,680
+الأقل يعني إيش معناته؟ there exist gamma in gamma
+
+393
+00:27:38,680 --> 00:27:43,020
+و ال x في ال A جامعة و طبعا هذه زي ما هي هذه
+
+394
+00:27:43,020 --> 00:27:47,020
+ماغيرناش ليش؟ لأنه قاعديني نفسر هذا المعنىفهذه
+
+395
+00:27:47,020 --> 00:27:51,740
+معناها هذه ال statement متفقين؟ في حد عنده أي
+
+396
+00:27:51,740 --> 00:27:54,440
+صعوبة في هذا التفسير أو في عنده أي اعتراض؟ إيش
+
+397
+00:27:54,440 --> 00:27:57,420
+معناته إن ال X هنا فهي هنا؟ مجرد بس إيش؟ هذا تعريف
+
+398
+00:27:57,420 --> 00:28:01,440
+مين؟ اتحاد على family دليلك إيش دليلك؟ definition
+
+399
+00:28:01,440 --> 00:28:12,120
+of اتحاد على family باختصار نكمل فاحنا
+
+400
+00:28:12,120 --> 00:28:18,070
+فسرناالطرف وهذا أكتر ما يمكن نفسره ممكن نفسره أكتر
+
+401
+00:28:18,070 --> 00:28:24,050
+من هيك؟ لأ إحنا إيش بدنا؟ بدنا نبدل هنا بدأنا من F
+
+402
+00:28:24,050 --> 00:28:28,710
+بعدين الاتحاد و أين رايحين؟ الاتحاد بعدين ال F طيب
+
+403
+00:28:28,710 --> 00:28:32,230
+التعريف ال function إيش كان؟ there exist x
+
+404
+00:28:32,230 --> 00:28:36,270
+والاتحاد كان هذا فأنا إيش مطلوب من أني أبدل؟ أبدل
+
+405
+00:28:36,270 --> 00:28:39,250
+there exist مع there existطب لو بدلنا there exist
+
+406
+00:28:39,250 --> 00:28:42,970
+مع there exist تكافه ولا implies؟ تكافه لإن قلنا
+
+407
+00:28:42,970 --> 00:28:47,070
+exist مع exist مع بعض تكافه و all مع all تكافه لكن
+
+408
+00:28:47,070 --> 00:28:51,110
+لما يختلطوا في اتجاه صح و اتجاه غير صحيح فإذا هذا
+
+409
+00:28:51,110 --> 00:28:57,690
+بدنا نبدل there exist gamma in gamma there exist x
+
+410
+00:28:58,460 --> 00:29:02,080
+بس بدّلنا هدول اه والباقي نكتبه زي ما هو اكس
+
+411
+00:29:02,080 --> 00:29:07,520
+انتميل ال a جامع و Y تساوي F of X ايش اللي بتعملوا
+
+412
+00:29:07,520 --> 00:29:12,160
+انت ال quantifiers rule قواعد التكميل يعني section
+
+413
+00:29:12,160 --> 00:29:17,510
+6-1 quantifierrules قواعد التكميل لأن هذا هو
+
+414
+00:29:17,510 --> 00:29:20,850
+المفتاح الحقيقة أننا هنشوف البرهان التاني لما نبدر
+
+415
+00:29:20,850 --> 00:29:24,110
+فيش تكافر لكن هنا فيه تكافر خلاص الآن ارجعوا لخطوة
+
+416
+00:29:24,110 --> 00:29:27,710
+التانية لأنه زي ما قلنا هي الاختلاف واحد فيهم
+
+417
+00:29:27,710 --> 00:29:31,810
+تعريف ال F واحد تعريف من الاتحاد الآن نبدأ نرجع
+
+418
+00:29:31,810 --> 00:29:36,110
+للطريق العكسي نبدأ من هنا خلي هذا من الخارج في
+
+419
+00:29:36,110 --> 00:29:36,450
+الآخر
+
+420
+00:29:39,180 --> 00:29:43,560
+توجد X في A Gamma والـ Y صورة هذا الـ X وين وين
+
+421
+00:29:43,560 --> 00:29:47,680
+وين Y بتكون؟ في صورة المجموعة الـ Y صورة عنصر X
+
+422
+00:29:47,680 --> 00:29:49,960
+والعنصر في المجموعة وين بتكون الـ Y؟ في صورة
+
+423
+00:29:49,960 --> 00:29:53,880
+المجموعة فده معناته أن Y تنتمي لمين؟ لل F في A
+
+424
+00:29:53,880 --> 00:30:00,100
+Gammaليس إلا تعريف الـ F of A Gamma أو في F of A،
+
+425
+00:30:00,100 --> 00:30:05,780
+مظبوط؟ واضحة هذه؟ خيّر ال Y F of X ال X وين في ال
+
+426
+00:30:05,780 --> 00:30:09,060
+A Gamma صورتها F of X وين بتكون؟ اللي هي Y في F of
+
+427
+00:30:09,060 --> 00:30:13,600
+A Gamma، واضحة؟واضحة أه ولا لأ؟ واحدة منهم من
+
+428
+00:30:13,600 --> 00:30:16,080
+المقصودة إذا مش واضحة بنقيت وإذا واضحة خلينا نمشي
+
+429
+00:30:16,080 --> 00:30:19,820
+واضحة ولا مش واضحة؟ هاي ال Y صورة عنصر من ال A
+
+430
+00:30:19,820 --> 00:30:22,480
+جامعة وين بتكون ال Y؟ في صوت ال A جامعة، ممتاز،
+
+431
+00:30:22,480 --> 00:30:26,020
+الآن أنا عند ال Y في واحدة من ال F of A جامعة،
+
+432
+00:30:26,020 --> 00:30:28,820
+لجامعة واحدة، وين بتكون؟ في الاتحاد، بتكون في
+
+433
+00:30:28,820 --> 00:30:32,400
+الاتحاد، واحدة يكافئ، اللي هو Y تنتمي للاتحاد على
+
+434
+00:30:32,400 --> 00:30:38,360
+الجامعة F of A جامعة، وهو المطلوب، تعريف الاتحاد،
+
+435
+00:30:38,360 --> 00:30:42,540
+union عن الفعلكل خطوات متكافئة، إذا انتهت الـ S
+
+436
+00:30:42,540 --> 00:30:49,640
+بقى، Thus التساوي انتهى، صورة الاتحاد باختصار
+
+437
+00:30:49,640 --> 00:30:51,700
+تساوي اتحاد الصورة
+
+438
+00:30:55,740 --> 00:31:00,600
+فالحقيقة كل الخطوات تعريف ما قعدت quantifier rules
+
+439
+00:31:00,600 --> 00:31:04,320
+فالتعريفات كلها تكافؤ واحنا بنعرف من section 1-6
+
+440
+00:31:04,320 --> 00:31:08,580
+أن هذه القاعدة برضه تكافؤ فانتهى البرهان واضح؟ أه
+
+441
+00:31:08,580 --> 00:31:11,700
+عشان نقارن الأل مع الخطوة التانية على الجدحة نشوف
+
+442
+00:31:11,700 --> 00:31:17,020
+بيه ليش مدتناش تساوي عشان نشوف و نتبقى العملية مش
+
+443
+00:31:17,020 --> 00:31:21,880
+عشوائيةالعملية لما نقول إننا ندقق إن فيها انتكافة
+
+444
+00:31:21,880 --> 00:31:26,560
+ولا implies مهم لأنه بقاش بترتب عليه معلومات بترتب
+
+445
+00:31:26,560 --> 00:31:31,640
+عليه قرارات تمام نفس القضية هناخد عنصر في الطرف
+
+446
+00:31:31,640 --> 00:31:36,280
+اليسار اللي جيت مجمرين و برضه هنسميه Y تنتمي لل F
+
+447
+00:31:36,280 --> 00:31:45,270
+تقاطع جامع ان جامع اي جامع any elementأيش نعمل من
+
+448
+00:31:45,270 --> 00:31:48,670
+الفُك أول التقاطع على الصورة الصورة زي توي فده
+
+449
+00:31:48,670 --> 00:31:51,850
+معناته أن ال Y بتساوي F of X for some و بتكتبها
+
+450
+00:31:51,850 --> 00:31:56,530
+مباشرة بالطريقة اللي هي مختصرة انه بدل ما يقول for
+
+451
+00:31:56,530 --> 00:32:00,310
+some بتعملها there exists فده على طول تكافئ there
+
+452
+00:32:00,310 --> 00:32:05,810
+exists X تنتمي للمجموعة A اللي هي التقاطع A Gamma
+
+453
+00:32:05,810 --> 00:32:12,520
+و ال Y تساوي F of X هذا ليس إلا نفس الخطوة الأولىF
+
+454
+00:32:12,520 --> 00:32:18,580
+of A تعريف الصورة نفس الخطوة السابقة هنشوف ليش هنا
+
+455
+00:32:18,580 --> 00:32:21,620
+كانت تبسط مش تساوي هاي نفس الخطوة الأولى الآن إيش
+
+456
+00:32:21,620 --> 00:32:26,140
+هنعمل هنفك التقاطع فهدي معناته there exists X زي
+
+457
+00:32:26,140 --> 00:32:31,020
+توه هاي جبل احنا ماحناها there exists X إيش معناة
+
+458
+00:32:31,020 --> 00:32:36,520
+التقاطع for all for all Gamma in Gamma اللي هو إيش
+
+459
+00:32:36,520 --> 00:32:42,030
+X تنتمي لـA Gamma والـY تساوي F of Xزي ما هي تنزل
+
+460
+00:32:42,030 --> 00:32:45,810
+هذا تعريف ايش تقاطع على ال family تقاطع على ال
+
+461
+00:32:45,810 --> 00:32:51,250
+family تمام فنفس الخطوات و ارجو في البيت تراجعوا
+
+462
+00:32:51,250 --> 00:32:55,490
+تحطوا البرهانين جنب بعض نفس الشيء تمام وين المفتاح
+
+463
+00:32:55,490 --> 00:33:00,370
+الآن هل كانت بتبدلبس هنا يعني implies مش تكافه،
+
+464
+00:33:00,370 --> 00:33:03,210
+هاي الفرق there exists مع there exists تكافه لكن
+
+465
+00:33:03,210 --> 00:33:06,370
+there exists مع for all لما أبدل، أه هذه إيش
+
+466
+00:33:06,370 --> 00:33:10,810
+implies for all Gamma in Gamma طبعا بدّي بالاتجاه
+
+467
+00:33:10,810 --> 00:33:15,390
+هذا التاني غلط أصلا لإنه مش تكافه there exists X X
+
+468
+00:33:15,390 --> 00:33:19,250
+تنتمي لأيه؟ Gamma وال Y تساوي F of X برضه هذه
+
+469
+00:33:19,250 --> 00:33:20,250
+quantifier rule
+
+470
+00:33:26,450 --> 00:33:30,190
+ارجعوا ل section 1-6 فالكلام اللي احنا كنا ..
+
+471
+00:33:30,190 --> 00:33:34,530
+تعبنا عليه في البداية عشان هذا فهنا الفرق فإن لو
+
+472
+00:33:34,530 --> 00:33:37,890
+كانت تكافأة هذه الخطوة كانت سارة تساوي فلحن بتكمل
+
+473
+00:33:37,890 --> 00:33:43,390
+نفس الشيء فطبعا هذا implies for all gammaتنتمل
+
+474
+00:33:43,390 --> 00:33:46,890
+الجامعة there exists X ال Y صورة أنصر من ال A هي
+
+475
+00:33:46,890 --> 00:33:49,610
+نفس الشيء إذا إذا ال Y وين في صورة ال F of A جامعة
+
+476
+00:33:49,610 --> 00:33:53,290
+Y تنتمل ال F of A جامعة مافيش اختلاف إطلاقا الآن
+
+477
+00:33:53,290 --> 00:33:59,710
+بس الاختلاف بس الخطوة هذه تعريف F of A جامعة وهذا
+
+478
+00:33:59,710 --> 00:34:04,930
+يؤدي مزال موجودة في كل الصور إذا موجودة في التقاطع
+
+479
+00:34:04,930 --> 00:34:08,210
+Y تنتمل تقاطع F of A جامعة
+
+480
+00:34:13,150 --> 00:34:27,950
+thus صورة التقاطع subset من تقاطع الصورة فهنا
+
+481
+00:34:27,950 --> 00:34:33,590
+الفرق ال quantification أو quantifier rule مهم جدا
+
+482
+00:34:33,590 --> 00:34:39,490
+اذا كانت تساوي او تقف أو تضمى او احيانا بيكون فيش
+
+483
+00:34:39,490 --> 00:34:49,630
+قاعدة اصلا فبناني انتبهأي سؤال واضح طبعا لزيادة
+
+484
+00:34:49,630 --> 00:34:54,770
+الطمأنينة نديكم مثال عكسي أنه مافيش تساوي الأولى
+
+485
+00:34:54,770 --> 00:34:57,450
+تبسط من التانية لكن التانية مش تبسط من الأول
+
+486
+00:34:57,450 --> 00:35:04,190
+هنديكم مثال عكسي بيثبت أن التساوي مش صحيح كقاعدة
+
+487
+00:35:04,190 --> 00:35:08,490
+عامةطبعا ممكن تكون في صدا في بعض الأمثلة التساوي
+
+488
+00:35:08,490 --> 00:35:11,310
+يطلع صح ممكن بس حنا مانحط قاعداش ماتقاعد يعني
+
+489
+00:35:11,310 --> 00:35:15,410
+دايما صحيحة اه ملاش ولا استثناء اه فهنا نشوف فهنا
+
+490
+00:35:15,410 --> 00:35:20,370
+ماخداش دلّة بسيطة دلّة من X ل Y من الواحد الاتنين
+
+491
+00:35:20,370 --> 00:35:23,630
+للتلاتة دلّة
+
+492
+00:35:25,520 --> 00:35:30,380
+إن هذا المثال طبعا ال X تتكون من عنصرين الواحد
+
+493
+00:35:30,380 --> 00:35:33,920
+والاتنين المجال المقابل ال Y فيه عنصر واحد تلاتة
+
+494
+00:35:33,920 --> 00:35:39,260
+والواحد رايح للتلاتة والاتنين رايح للتلاتة أخد
+
+495
+00:35:39,260 --> 00:35:44,080
+الآن مجموعتين جزييتين من ال X فهذه عملها B وهذه
+
+496
+00:35:44,080 --> 00:35:49,280
+عملها Aفطبعا بيقوللي صورة التقاطع سبسط من تقاطع
+
+497
+00:35:49,280 --> 00:35:54,420
+الصور لكن العكس غير صحيح فالان لو أخدنا a تقاطع ال
+
+498
+00:35:54,420 --> 00:35:58,660
+b ايش بيساوي فاي ال a واحد و ال b اتنين مافيش
+
+499
+00:35:58,660 --> 00:36:01,860
+بينهم علاقة مشتركة اذا صورة التقاطع اللي هو بيكون
+
+500
+00:36:01,860 --> 00:36:06,660
+صغيرأيه تقاطع الـ B؟ بتساوي صورة الـ Phi واللي هي
+
+501
+00:36:06,660 --> 00:36:10,540
+Phi نظرية أثبتناها قبل قليل لكن لو حسبنا الصور
+
+502
+00:36:10,540 --> 00:36:14,720
+أولا وبعدين جيبنا التقاطع صورة الأفف إيش بتساوي؟
+
+503
+00:36:14,720 --> 00:36:19,000
+صورة الواحد اللي هي تلاتة أفف واحد وتساوي مجموعة
+
+504
+00:36:19,000 --> 00:36:24,580
+التلاتة وصورة الـ B هي صورة التنين وبرضه بتساوي
+
+505
+00:36:24,580 --> 00:36:32,630
+تلاتة والتقاطع بيساوي تلاتة طبعا لا يساويفهنا f of
+
+506
+00:36:32,630 --> 00:36:39,130
+a تقاطع ال f of b يساوي مجموعة التلاتة لتساوية
+
+507
+00:36:39,130 --> 00:36:44,630
+فعلا فهذه صورة التقاطع أصغر من تقاطع الصور لكن
+
+508
+00:36:44,630 --> 00:36:48,110
+العكس غير صحي مش ده مافيش تساوي فهذه ليست صفصف
+
+509
+00:36:48,110 --> 00:36:51,870
+فهذا مثال بيأكد على النظرية هذا مثال عكسي لو جالك
+
+510
+00:36:51,870 --> 00:36:54,830
+prove or disprove أنه مافيه تساوي هذه مثال بثبت أن
+
+511
+00:36:54,830 --> 00:36:56,850
+هذا ال statement غير صحي
+
+512
+00:37:00,580 --> 00:37:05,140
+أي سؤال؟ متابعين؟ تمام هذا بالنسبة للصور نشوف
+
+513
+00:37:05,140 --> 00:37:09,740
+الصور العكسية الصور العكسية الحقيقة الموضوع أسهل
+
+514
+00:37:09,740 --> 00:37:14,600
+على الحالتين في تساوي فالصورة العكسية للاتحاد
+
+515
+00:37:14,600 --> 00:37:19,420
+تساوي اتحاد الصور العكسية زي الصور أيضا الصورة
+
+516
+00:37:19,420 --> 00:37:24,380
+العكسية التقاطع تساوي تقاطع الصور العكسيةففي حالة
+
+517
+00:37:24,380 --> 00:37:29,100
+الصور فيا إنا إشكالية في التقاطع إنه subset لكن في
+
+518
+00:37:29,100 --> 00:37:33,140
+الصور العكسية التنتين تساوي التنتين تساوي خلينا
+
+519
+00:37:33,140 --> 00:37:38,640
+نبرهن واحدة والتانية نتركها exercise وإن شاء الله
+
+520
+00:37:38,640 --> 00:37:41,900
+نشوف إيش الفرق ليش هنا تصار فيه تساوي ماكانش فيا
+
+521
+00:37:41,900 --> 00:37:50,580
+إنا مشكلة هنا خليني أبرهن B واترك إيش A exercise
+
+522
+00:37:50,580 --> 00:37:58,830
+هلاجي إن هي سهلة جدافطبعا هذه نظرية تلاتة
+
+523
+00:37:58,830 --> 00:38:06,110
+احداشر ابرو في اي استفتار في اي مشكلة تمام خلينا
+
+524
+00:38:06,110 --> 00:38:11,230
+نفرق ايه نتركه exercise و نبرهن بيه ايه exercise
+
+525
+00:38:14,580 --> 00:38:18,900
+وبرضه هذا من الحالات اللي فيها هننسخ خطوة خطوة
+
+526
+00:38:18,900 --> 00:38:22,180
+باختلافات بسيطة فلو عدتوا البرهان اللي بتعمله فيه
+
+527
+00:38:22,180 --> 00:38:25,400
+في رق إيه هتلاجوه بيظبط تماما بدون أي مشاكل نشوف
+
+528
+00:38:25,400 --> 00:38:30,540
+إيش الفرق بين الحالتين تمام بدي أثبت مرضه مجموعة
+
+529
+00:38:30,540 --> 00:38:34,740
+تساوي مجموعة هاخد أنصر أسمي X ولا Y؟ X لأنه هذا في
+
+530
+00:38:34,740 --> 00:38:40,000
+الصورة العكسية فهنقوله let X تنتمي لل F inverse
+
+531
+00:38:40,000 --> 00:38:40,800
+للتقاطع
+
+532
+00:38:43,700 --> 00:38:49,400
+B جامعة اه طبعا هنا في عندنا الملاحظة اللى كتبتها
+
+533
+00:38:49,400 --> 00:38:53,700
+8 مره داشت معناته هذا if and only if صورة العنصر
+
+534
+00:38:53,700 --> 00:39:00,600
+الموجودة في المجموعة بي جامعة F of X السؤال اللى
+
+535
+00:39:00,600 --> 00:39:04,920
+ماقلناش هذا تعريف الصورة العكسية تعريفها أسهل أو
+
+536
+00:39:04,920 --> 00:39:11,580
+التعامل معاه أسهل of F inverse ال Bفهذه هي القضية
+
+537
+00:39:11,580 --> 00:39:17,620
+الآن ماذا نفعل نفك التقاطة if and only if for all
+
+538
+00:39:17,620 --> 00:39:24,660
+Gamma in Gamma f of x تنتمي للـb Gamma اللي هي
+
+539
+00:39:24,660 --> 00:39:32,840
+تعريف التقاطة definition of تقاط على الفملةفهنا
+
+540
+00:39:32,840 --> 00:39:39,480
+كما تلاحظون ماعناش إلا مكمّم واحد مش مكمّمين في
+
+541
+00:39:39,480 --> 00:39:42,320
+الحالتين مافيش إلا مكمّم واحد مش محتاج أبدل على
+
+542
+00:39:42,320 --> 00:39:45,900
+طول الآن بما أن الصورة في ال B وين بيكون ال X؟ في
+
+543
+00:39:45,900 --> 00:39:50,040
+الصورة العكسية مباشرة و هذا تعريف for all gamma in
+
+544
+00:39:50,040 --> 00:39:56,620
+gamma ال X موجودة في الصورة العكسية لل B Gamma نفس
+
+545
+00:39:56,620 --> 00:40:01,840
+الشيء تعريف ال F inversedefinition of F inverse ل
+
+546
+00:40:01,840 --> 00:40:06,960
+B Gamma فهذا الفرق بين هذا النظرية و النظرية
+
+547
+00:40:06,960 --> 00:40:11,620
+السابقة مافي مكممات أبدلها فكانت مع التقاطة أو ما
+
+548
+00:40:11,620 --> 00:40:15,800
+هناك بس إيش هيكون الاختلاف بس مكمم واحد فيه كل مرة
+
+549
+00:40:15,800 --> 00:40:19,640
+خلاص انتهينا هل كده أنا عندي ال X في جميع العناصر
+
+550
+00:40:19,640 --> 00:40:22,020
+في جميع المجموعة زي ما موجود في التقاطة
+
+551
+00:40:28,060 --> 00:40:37,400
+if and only if ال X موجودة في تقاطع ال images طبعا
+
+552
+00:40:37,400 --> 00:40:41,390
+تعريف التقاطعفهذا الفرق ليش هنا فيه تساوي ماكانش
+
+553
+00:40:41,390 --> 00:40:44,390
+فيه تساوي لأنه مافيش مكمّمين هنا التعريف تبع ال
+
+554
+00:40:44,390 --> 00:40:48,250
+inverse أسهل تبع الصورة العكسية أسهل فبكون البرهان
+
+555
+00:40:48,250 --> 00:40:51,610
+هيك انتهى بكون البرهان انتهى طبعا التاني نفس
+
+556
+00:40:51,610 --> 00:40:55,370
+البرهان بس بدل ما تقوله بالتقاطع for all في
+
+557
+00:40:55,370 --> 00:40:58,810
+الاتحاد فيه there exists ليس إليه فأرجو أنه نعيد
+
+558
+00:40:58,810 --> 00:41:07,010
+البرهان و نحاول نتعلم منه نظرية
+
+559
+00:41:07,010 --> 00:41:14,730
+أخرىفاحنا شفناصور الاتحاد وصور التقاطق وصور
+
+560
+00:41:14,730 --> 00:41:18,090
+العكسية للاتحاد والتقاطق وشوفنا الفرق بينهم الآن
+
+561
+00:41:18,090 --> 00:41:21,990
+هنتحدث عن الصورة العكسية للفرق الصورة العكسية
+
+562
+00:41:21,990 --> 00:41:27,610
+للفرق طب هل في صورة الفرق؟ لأ لأن التعامل مع الفرق
+
+563
+00:41:27,610 --> 00:41:32,030
+في الصورة الصورة الصورة الصورة الصورة الصورة
+
+564
+00:41:32,030 --> 00:41:32,030
+الصورة الصورة الصورة الصورة الصورة الصورة الصورة
+
+565
+00:41:32,030 --> 00:41:32,650
+الصورة الصورة الصورة الصورة الصورة الصورة الصورة
+
+566
+00:41:32,650 --> 00:41:32,710
+الصورة الصورة الصورة الصورة الصورة الصورة الصورة
+
+567
+00:41:32,710 --> 00:41:34,710
+الصورة الصورة الصورة الصورة الصورة الصورة الصورة
+
+568
+00:41:34,710 --> 00:41:36,470
+الصورة الصورة الصورة الصورة الصورة الصورة الصورة
+
+569
+00:41:36,470 --> 00:41:44,760
+الصورة الصورة الصورةفي نظرية جديدة احنا شفنا نظرية
+
+570
+00:41:44,760 --> 00:41:49,940
+السابقة عن اتحاد والتقاطع الآن في نظرية عن الفرق
+
+571
+00:41:49,940 --> 00:41:58,020
+بين مجموعتين فبرضه خلينا نبرهنها ويخلينا
+
+572
+00:41:58,020 --> 00:42:04,620
+نكرر التعامل مع التعريف عشان نتعود عليه prove هذا
+
+573
+00:42:04,620 --> 00:42:10,960
+بس فرع واحدالـ F دالة من X إلى Y وفي عندي مجموعتين
+
+574
+00:42:10,960 --> 00:42:14,940
+subset من الـ Y عشان يتحدث عن صورهم العكسية فبقول
+
+575
+00:42:14,940 --> 00:42:19,500
+الصورة العكسية للفرق بين B ناقص C يساوي الفرق بين
+
+576
+00:42:19,500 --> 00:42:24,000
+الصورتين العكسيتين هنشوف البرهان بنفس الطريقة طبعا
+
+577
+00:42:24,000 --> 00:42:28,880
+هنا في تساوي نحاول نمشي تكافئ هناخد عنصر وليكن X
+
+578
+00:42:28,880 --> 00:42:36,600
+اسم مناسب B ناقص Cفهنا بنعيد و بنكرر التعامل
+
+579
+00:42:36,600 --> 00:42:40,820
+السهولة التعامل مع الصورة العكسية فهذه على طول if
+
+580
+00:42:40,820 --> 00:42:47,990
+and only if f في ال X موجودة في ال B ناقصيفدائما
+
+581
+00:42:47,990 --> 00:42:52,730
+فهذا هو المفتاح ال X في الصورة العكسية لل B تكافئ
+
+582
+00:42:52,730 --> 00:42:55,930
+او if and only if F of X في ال B فهذا هو المفتاح
+
+583
+00:42:55,930 --> 00:42:58,870
+الآن نفسر ال inverse طبعا هذا تعريف ال ايش ال F
+
+584
+00:42:58,870 --> 00:43:03,330
+inverse definition للصورة العكسية لمجموعة الماء B
+
+585
+00:43:03,330 --> 00:43:06,670
+ناقص C خلاص اه فطبعا هذا if and only if ايش تعريف
+
+586
+00:43:06,670 --> 00:43:14,070
+الفرق تنتمي للأولى ولا تنتمي للتانى تميء لل C
+
+587
+00:43:16,650 --> 00:43:20,870
+definition تبع الـ minus ممتاز بدنا نبدأ نرجع الآن
+
+588
+00:43:20,870 --> 00:43:23,550
+إذا الصورة في ال B بتكون ال X وين في الصورة
+
+589
+00:43:23,550 --> 00:43:30,390
+العكسية X تنتمي للصورة العكسية لل B and طيب إذا
+
+590
+00:43:30,390 --> 00:43:35,310
+الصورة مش في ال C مستحيل ال X تكون في ال C اه طيب
+
+591
+00:43:35,310 --> 00:43:38,350
+هذا مش واضح حالكوا كتير إيش تعمله طلعوا ال نفي برا
+
+592
+00:43:38,350 --> 00:43:41,110
+طلعوا لأ مش مش روح الكملة طلعوا ال نفي برا دايما
+
+593
+00:43:41,110 --> 00:43:45,440
+إذا في and كنا فيه طلعوه برا فهو عبارة عن نطnot F
+
+594
+00:43:45,440 --> 00:43:48,120
+of X تنتمي للـC زي F of X تنتمي للـC بتكون X وين
+
+595
+00:43:48,120 --> 00:43:54,080
+في الـF inverse للـC زي not X تنتمي للـF inverse
+
+596
+00:43:54,080 --> 00:44:02,170
+of C تنتمي صحيح نفيت مرتين أنافطلعوا النافي برا
+
+597
+00:44:02,170 --> 00:44:09,070
+وفسروا لما قالت F of X not F of X في الـC is not X
+
+598
+00:44:09,070 --> 00:44:11,390
+في الـF inverse فانتوا كافية هذه ال statement if
+
+599
+00:44:11,390 --> 00:44:13,950
+and only if طب مادايش من وين جبته تعريف الـF
+
+600
+00:44:13,950 --> 00:44:19,530
+inverse نفس القانون اللي هنا definition of F
+
+601
+00:44:19,530 --> 00:44:24,170
+inverse of C خلاص مادايش معناته يعني ال X في واحدة
+
+602
+00:44:24,170 --> 00:44:27,390
+و X لاتن تمي مادايش معناته إذا إيش معناته X في مين
+
+603
+00:44:27,390 --> 00:44:34,600
+في الفرق- F inverse C وهو المطلوب كله كذا اكتكع
+
+604
+00:44:34,600 --> 00:44:44,680
+فوق إذا ناش أثبتنا التساوي Therefore
+
+605
+00:44:44,680 --> 00:44:50,780
+صورة ال inverse أو الصورة العكسية لل inverse يساوي
+
+606
+00:44:50,780 --> 00:44:56,100
+الفرق بين الصورة العكسية للفرق يساوي الفرق بين
+
+607
+00:44:56,100 --> 00:45:01,360
+الصورة العكسيةوعلى نفس الترتيب كانت P ناقص C تمت
+
+608
+00:45:01,360 --> 00:45:08,240
+الصورة العكسية لل P ناقص الصورة العكسية لل C تمام
+
+609
+00:45:08,240 --> 00:45:10,180
+هذه نهاية ال section ان شاء الله المرجع ندخل في ال
+
+610
+00:45:10,180 --> 00:45:11,560
+section الجديد نجفن
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/sMoY9RxUmKg_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/sMoY9RxUmKg_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..68e45ab6813833560296dc4fde49f69e006e050c
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/sMoY9RxUmKg_raw.srt
@@ -0,0 +1,2244 @@
+1
+00:00:19,660 --> 00:00:23,040
+بسم الله الرحمن الرحيم هنواصل مع ال cardinal
+
+2
+00:00:23,040 --> 00:00:26,860
+number الاعداد الأصلية زي ما بيقال او ال cardinal
+
+3
+00:00:26,860 --> 00:00:30,680
+number و طبعا في المحاضرة او المحاضرات السابقة
+
+4
+00:00:30,680 --> 00:00:33,640
+عرفنا الجامع اليوم ان شاء الله هنشوف ضرب ال
+
+5
+00:00:33,640 --> 00:00:36,960
+cardinal number فعنوان الموضوع تبعنا او ال section
+
+6
+00:00:36,960 --> 00:00:42,300
+multiplication of cardinal number هنشوف التعريفأه
+
+7
+00:00:42,300 --> 00:00:47,940
+طبعا احنا عشان نعمل الجامع أخدنا two cardinal
+
+8
+00:00:47,940 --> 00:00:52,820
+number بس تذكيرة على السريع جيبنا لكل واحد مجموعة
+
+9
+00:00:52,820 --> 00:00:56,880
+قابله حولناها للغة المجموعات بس في كان عندنا شرط
+
+10
+00:00:58,010 --> 00:01:02,150
+التقاطع يساوي في و اقول لو احنا ايش عملنا جيبنا
+
+11
+00:01:02,150 --> 00:01:07,650
+الاتحاد فعرفنا الجامعة بدلالة الاتحاد الآن هنعرف
+
+12
+00:01:07,650 --> 00:01:11,630
+الضرب بدلالة الـ Cartesian product برضه هنجيب
+
+13
+00:01:11,630 --> 00:01:15,110
+مجموعة اه فالان هذا بالنسبة لمين هذا بالنسبة ل a
+
+14
+00:01:15,110 --> 00:01:20,410
+زائد b الآن الصورة المقابلة لو بدنا نشتغل على ال a
+
+15
+00:01:21,060 --> 00:01:26,620
+ضرب بي فيش رمز لضرب بيحطوش لا X ولا Dot ولا إيش
+
+16
+00:01:26,620 --> 00:01:31,500
+على طول A في B ضرب معروفة هى وقالنا let A and B be
+
+17
+00:01:31,500 --> 00:01:34,700
+cardinal numbers the cardinal product of A and B
+
+18
+00:01:34,700 --> 00:01:38,880
+شوف نفس السياسة هى المفهوم إيش رمزه donated by A
+
+19
+00:01:38,880 --> 00:01:43,770
+في Bلا نقطة ولا X ولا cross ولا حاجة بس A في B على
+
+20
+00:01:43,770 --> 00:01:47,130
+طول هذا الدرب هذا الرمز تبعه is the cardinal
+
+21
+00:01:47,130 --> 00:01:50,490
+number ايش للكارتيس يعني cardinality of A cross ال
+
+22
+00:01:50,490 --> 00:01:54,190
+B A cross ال B طيب ايش علاقة الكارتيس اللي بدأت في
+
+23
+00:01:54,190 --> 00:01:58,500
+عملية الدرب؟ممكن نقربها كيف بنتعلم الضرب في
+
+24
+00:01:58,500 --> 00:02:03,320
+المراحل الأولى من التعليم؟ ممكن ايه؟ كيف بنعمل؟
+
+25
+00:02:03,320 --> 00:02:05,860
+نفترض ان احنا بدنا نضرب عددين في بعض مثلا بدنا
+
+26
+00:02:05,860 --> 00:02:08,720
+نضرب اتنين في تلاتة او تلاتة في أربعة فليجي نكتبهم
+
+27
+00:02:08,720 --> 00:02:13,400
+الاعداد بد الشكل طبعا جداش بدي ممكن امشي و اكتب
+
+28
+00:02:13,400 --> 00:02:17,080
+هنا كمان الاعداد مثلا بدي اجيب اتنين في تلاتة على
+
+29
+00:02:17,080 --> 00:02:21,830
+سبيل المثال لو عدد أكبر هكبرفإيش العملية ممكن نعمل
+
+30
+00:02:21,830 --> 00:02:24,190
+إنه نقول هدولة مثلا اتنين في تلاتة عبارة عن إيش
+
+31
+00:02:24,190 --> 00:02:27,690
+التلاتة مجموعة مرتين بدنا نعدلهم مربعات مجموع أسس
+
+32
+00:02:27,690 --> 00:02:31,450
+مربعات طب كيف نعملهم مع ال Cartesian هذا المربع
+
+33
+00:02:31,450 --> 00:02:34,550
+ليس إلا واحد واحد في الصف الأول في العمود الأول
+
+34
+00:02:34,550 --> 00:02:38,170
+وفي الصف الأول في العمود التاني وفي الصف الأول في
+
+35
+00:02:38,170 --> 00:02:44,250
+العمود التالت وهنا اتنين واحدإتنين إتنين و إتنين
+
+36
+00:02:44,250 --> 00:02:48,330
+تلاتة فإذا عشان أجيب تلاتة في اتنين بدي عدد
+
+37
+00:02:48,330 --> 00:02:52,350
+العناصر هدول المربعات هدول هيوم ستة و هكذا فدي نفس
+
+38
+00:02:52,350 --> 00:02:55,410
+الفكرة فاحنا هنحاوله لـ Cartesian product فعشان
+
+39
+00:02:55,410 --> 00:03:03,600
+أجيبضرب B بدي أجيب مجموعة تقابل الـ A تقابل ال
+
+40
+00:03:03,600 --> 00:03:06,500
+cardinal number A ومجموعة تقابل ال cardinal number
+
+41
+00:03:06,500 --> 00:03:12,820
+B الآن ضروري يكون التقاطع فيه؟ لأ لأن مافيش تشابه
+
+42
+00:03:12,820 --> 00:03:17,180
+مافيش اتحاد ومتكررة في عناصرها اي مجموعتين فبصير
+
+43
+00:03:17,180 --> 00:03:24,770
+عندي A في B تساوي cardinality للـ A crossوهذا
+
+44
+00:03:24,770 --> 00:03:27,730
+الشيء يمكن ذكرناه احنا مش بالتفصيل، لكن قلنا إذا
+
+45
+00:03:27,730 --> 00:03:30,230
+في أنا مجموع تان، واحدة فيها خمسة، واحدة فيها
+
+46
+00:03:30,230 --> 00:03:32,910
+عشرة، فالقارتيس فيه خمسين على طول، فاحنا بنقلها
+
+47
+00:03:32,910 --> 00:03:36,990
+ونحطه بشكل رسمي ونعممه، وحتى نتعامل مع مين، مش مع
+
+48
+00:03:36,990 --> 00:03:39,230
+الـfinite، حتى مع الـinfinite، مع الـinfinite
+
+49
+00:03:39,230 --> 00:03:42,830
+بنعرفه بنفس الطريقة، بنعرفه بنفس الطريقة، فهذا هو
+
+50
+00:03:42,830 --> 00:03:45,390
+القارتيس الـcardinal الـcardinal الكائن اللي هو
+
+51
+00:03:45,390 --> 00:03:49,990
+الدرب الـcardinal numberطبعًا هنا في عندنا نفس
+
+52
+00:03:49,990 --> 00:03:54,150
+السؤال وهذه طبعًا نقطة مهمة في الرياضيات أول شيء
+
+53
+00:03:54,150 --> 00:03:57,270
+أنا عشان أجيب الدرب بدي أجيب A أو B بقدر أجيبهم
+
+54
+00:03:57,270 --> 00:04:00,950
+اتفقنا نعم أو هنا كمان أسهل من الجامعة لأن أي
+
+55
+00:04:00,950 --> 00:04:03,970
+مجموعتين تقاطع بسوا five مش ضروري فهذا دائمًا من
+
+56
+00:04:03,970 --> 00:04:08,830
+المضمن ليه C1 أول أول حاجة في التعريف أو قواعد
+
+57
+00:04:08,830 --> 00:04:12,570
+الcardinal number يقول في أربع قواعد C1 C2 C3 C4
+
+58
+00:04:12,570 --> 00:04:15,410
+فC1 يقول لكل cardinal number بيقابل مجموعة وكل
+
+59
+00:04:15,410 --> 00:04:18,920
+مجموعة تقابل cardinal number انتهىطيب، الآن، طيب،
+
+60
+00:04:18,920 --> 00:04:22,800
+لو أنا جيبت A و B، واحد تاني جاب X و Y بنفس
+
+61
+00:04:22,800 --> 00:04:26,020
+الصفات، الـ .. الـ .. إيش؟ بتغير الجواب؟ بتغيرش،
+
+62
+00:04:26,020 --> 00:04:28,800
+فإذاً هذا مش معتمد على اختيار الشخص أو على الشخص
+
+63
+00:04:28,800 --> 00:04:30,880
+اللي بيجري العملية، إذاً هذا يعطاه فرق إيه إيش؟
+
+64
+00:04:30,880 --> 00:04:34,700
+تعريف علمي، well defined بيسموه، تعريف علمي صحيح،
+
+65
+00:04:34,700 --> 00:04:37,400
+لا يعتمد على الإنسان وإنما شكل الموضوع، وهذه كل
+
+66
+00:04:37,400 --> 00:04:41,240
+العلم المجردة هيكفانا لما بقول مثلا في ثغورث في
+
+67
+00:04:41,240 --> 00:04:43,500
+فلسطين في أمريكا و أين ما كان نفس النظرية
+
+68
+00:04:43,500 --> 00:04:47,900
+مابتختلفش لإن هيش عملية قاعدة عامة أتعريف علمي عام
+
+69
+00:04:47,900 --> 00:04:52,380
+فهو طبعا بقول لإنه لو جيبنا مجموعتين مختلفتين مزال
+
+70
+00:04:52,380 --> 00:04:57,840
+الجيت انا عنديواحد جاب A وواحد جاب X للكرنس
+
+71
+00:04:57,840 --> 00:05:00,700
+الكاردر أيش أيش بيكون هدول متكافئين وواحد جاب Y
+
+72
+00:05:00,700 --> 00:05:04,360
+بيكون هدول أياش متكافئين اه فانا بعرف ان كارتيس
+
+73
+00:05:04,360 --> 00:05:07,420
+كان يكافئ الكارتيس النظرية مباشرة على طول أخدناها
+
+74
+00:05:07,420 --> 00:05:11,580
+قبلين تمام فهذا تعريف تعريف علمي صحيح مش فيه أي
+
+75
+00:05:11,580 --> 00:05:17,240
+مشاكل نبدأ نشوف الأمثلة نبدأ نشوف الأمثلة يمكن
+
+76
+00:05:17,240 --> 00:05:22,320
+حلنا نكتب هنا نبدأ من هناالمثال الأول بيقوللي اثبت
+
+77
+00:05:22,320 --> 00:05:26,900
+انه الواحد هو محاية ضربي بهذا المعنى خد أي
+
+78
+00:05:26,900 --> 00:05:31,260
+cardinal number X اضربه في واحد بيساوي X واحد ده
+
+79
+00:05:31,260 --> 00:05:34,560
+طبعا شيء جيد طبعا في الجامعة هل الـ Zero محاية
+
+80
+00:05:34,560 --> 00:05:37,600
+جامعة في ال cardinal number نعم هيمروا عليكوا في
+
+81
+00:05:37,600 --> 00:05:40,960
+ال exercise ماثبتناهوش لكن نعم ليش؟ لأنك تجيب ال A
+
+82
+00:05:40,960 --> 00:05:45,480
+و ال Phi اتحادهم بيساوي A فبتغيرش فهنا نفس الفكرة
+
+83
+00:05:45,480 --> 00:05:47,340
+فنبدأ هنا solution
+
+84
+00:05:51,810 --> 00:05:54,570
+فطبعا كيف بدنا نشتغل زي ما شوفنا في الجامعة أو في
+
+85
+00:05:54,570 --> 00:05:58,130
+الضربة؟ بنجيب مجموعة تقابل كل cardinal number
+
+86
+00:05:58,130 --> 00:06:02,490
+فبنختار مجموعة يعني فحقول له let مثلا small x ممكن
+
+87
+00:06:02,490 --> 00:06:08,800
+من الجيد نقول capital X بي assetwith او such that
+
+88
+00:06:08,800 --> 00:06:14,000
+نفس الشيء ال cardinality لل capital X تساوي small
+
+89
+00:06:14,000 --> 00:06:16,580
+x و بدنا الآن مجموعة ال cardinality اللي لها
+
+90
+00:06:16,580 --> 00:06:21,660
+بيساوي مين بيساوي واحد ايش ناخدها ال بدكية ال واحد
+
+91
+00:06:21,660 --> 00:06:25,880
+او ال zero مجموعة singleton set singleton set اه
+
+92
+00:06:25,880 --> 00:06:32,060
+على طول then أصبح X ضرب واحد ليست الا ال
+
+93
+00:06:32,060 --> 00:06:37,980
+cardinality ل ال X cross ال Yفهذه الخطوة الأولى في
+
+94
+00:06:37,980 --> 00:06:40,520
+كنا في الجامعة بنقول اتحاد بس كنا فيها انا كمان
+
+95
+00:06:40,520 --> 00:06:44,380
+شرط ان التقاطع يسوى five اه في اخر مثال حالينا
+
+96
+00:06:44,380 --> 00:06:47,360
+المرة الفاترة ماقدرناش ناخد ال P بتسوى واحد قلنا
+
+97
+00:06:47,360 --> 00:06:49,820
+عنصر خارج عشان نضمن التقاطع يسوى five لكن هنا
+
+98
+00:06:49,820 --> 00:06:53,660
+العملية أسهل الدرب هنا في حرية اكتر في الاختيار
+
+99
+00:06:53,660 --> 00:06:57,040
+لإن التقاطع يسوى five مايسويش five يعنينيش واضح
+
+100
+00:06:57,040 --> 00:07:00,440
+ممتاز اه الآن انا ايش بده اثبت ان X بده يسوى واحد
+
+101
+00:07:00,440 --> 00:07:04,780
+يعني ايش بده اثبتبتثبت X تسواح ده ده مطلوب يعني
+
+102
+00:07:04,780 --> 00:07:10,870
+بتثبت ان X كارتيسيان ال Yتكافي X صح؟ هذه لغة ال
+
+103
+00:07:10,870 --> 00:07:13,010
+cardinal number و هذه لغة المجموعات و هذا احنا
+
+104
+00:07:13,010 --> 00:07:14,950
+قلنا ايش اول شيء قلنا ان هذا ال chapter بده يدعم
+
+105
+00:07:14,950 --> 00:07:17,690
+ال chapter الماضي فانا كل الأمور بحولها من لغة ال
+
+106
+00:07:17,690 --> 00:07:19,950
+cardinal number إلى لغة المجموعات و بستخدم
+
+107
+00:07:19,950 --> 00:07:22,430
+معلوماتي من chapter 5 و من ال chapter الماضية كلها
+
+108
+00:07:22,430 --> 00:07:25,990
+في ان ايش اجيب المعلومات لل cardinal number فبدنا
+
+109
+00:07:25,990 --> 00:07:29,590
+نثبت هذا الكلام كيف بدنا نثبت هذا التعريف؟ بدنا
+
+110
+00:07:29,590 --> 00:07:36,130
+bijection بدنا bijection من X cross ال Y ل X فبدنا
+
+111
+00:07:36,130 --> 00:07:40,680
+bijectionطبعا ال y ايش بتساوي هذه عبارة ليست الا
+
+112
+00:07:40,680 --> 00:07:50,320
+واحد بدنا هي تكافي ال x مرت عليكوا هذه انه x في
+
+113
+00:07:50,320 --> 00:07:54,420
+عنصر تكافي عادى عملناها أكتر من مرة أزواج مرتبة
+
+114
+00:07:54,420 --> 00:07:57,700
+تروح لمين لعنصر بقاش كيف الأزواج المرتبة بيكون x
+
+115
+00:07:57,700 --> 00:08:00,460
+واحد بس x مشغولة بلاش نستخدم x اسمه x لأن ال
+
+116
+00:08:00,460 --> 00:08:03,880
+number نستخدم رمز مختلف اه فطبعا هنا ايش هنقوله
+
+117
+00:08:03,880 --> 00:08:14,970
+هنثبتها للكلام نقوله wewill prove that x cross y
+
+118
+00:08:14,970 --> 00:08:21,470
+التي هي الواحد تكافي x تمام سنعرف هذا لـ let f من
+
+119
+00:08:21,470 --> 00:08:31,450
+x cross y إلى x be given by العناصر اللي هنا a
+
+120
+00:08:31,450 --> 00:08:36,350
+واحد كلهم صح؟ اه طبعا هذه ايش عناصرها؟
+
+121
+00:08:38,790 --> 00:08:44,070
+A1 such that A تنتمي لل X لأن الإحداث التاني مثبت،
+
+122
+00:08:44,070 --> 00:08:52,390
+مختلف فبدنا F of A1 ايه تساوي؟ A فانا ال answer هو
+
+123
+00:08:52,390 --> 00:08:58,370
+X موجود في ال capital X سميته A ومع مين؟ مع ال X
+
+124
+00:08:58,370 --> 00:09:03,010
+فالواحد ثابت لمشترك من الكل فبأثرش هي نفسي ندعه ل
+
+125
+00:09:03,010 --> 00:09:06,870
+one to one and untoواضحة الدالة دي وحكيتها قبل
+
+126
+00:09:06,870 --> 00:09:09,450
+اكتر من مرة اشوفها خلّيني هذه المرة نعملها
+
+127
+00:09:09,450 --> 00:09:12,490
+بالتفصيل خلّيني نعملها بالتفصيل نشوف ان ال F is
+
+128
+00:09:12,490 --> 00:09:19,830
+one to one هاي رقم واحد اه فهناخد عنصرين في ال
+
+129
+00:09:19,830 --> 00:09:24,650
+domain ايش العنصرين بيكونوا ايه واحد و واحد and
+
+130
+00:09:24,650 --> 00:09:31,150
+ايه اتنين و واحد تنتمي لل X across ال Y such that
+
+131
+00:09:34,980 --> 00:09:39,940
+F of A 11 تساوي F of A 21
+
+132
+00:09:42,990 --> 00:09:46,410
+أرجو أنه النصائح والطريقة اللي بستخدمها نتعود
+
+133
+00:09:46,410 --> 00:09:50,170
+عليها في البيت و نكتب هو أتوقع أنه لو أنتوا يعني
+
+134
+00:09:50,170 --> 00:09:53,290
+في كتير من المثال الحقيقة ليس إلا أنك تكتب
+
+135
+00:09:53,290 --> 00:09:56,410
+بالطريقة هتلاقي أنها انحلت لحالة بس ابدا و ابدا و
+
+136
+00:09:56,410 --> 00:09:59,770
+صح ابدا و صح و دايما هي المعطيات و هي البداية
+
+137
+00:09:59,770 --> 00:10:02,750
+وعناها المطلوب هتلاقي الأمور سهلة كتير في أشياء
+
+138
+00:10:02,750 --> 00:10:07,170
+كتيرة تمام ايش نعمل بعد هيك نستخدم تعريف الدالة
+
+139
+00:10:07,170 --> 00:10:10,130
+نستخدم تعريف الدالة فده بيقول لي لا دي ليست الا اي
+
+140
+00:10:10,130 --> 00:10:15,840
+واحد تساوي اتنينخلص البرهان؟ لأ ماخلصش لأنه مش بدأ
+
+141
+00:10:15,840 --> 00:10:19,160
+أثبت أن هذا الزوج يساوي .. لسه لأ ال one to one
+
+142
+00:10:19,160 --> 00:10:22,940
+لسه أنا هنجي لل one to one خلص برهان ال one to one
+
+143
+00:10:22,940 --> 00:10:26,360
+لأ لأنه أنا مش مطلوب مني أثبت اي واحد تساوي اتنين
+
+144
+00:10:26,360 --> 00:10:30,620
+ايش مطلوب مني أثبت أن اي واحد واحد تساوي اتنين
+
+145
+00:10:30,620 --> 00:10:35,960
+واحد طبعاً هذا بيدي إلها على طول فهذا يؤدي أن اي
+
+146
+00:10:35,960 --> 00:10:40,940
+واحد واحد يساوي اتنين واحد وهذا يؤدي أن ال F is
+
+147
+00:10:40,940 --> 00:10:46,000
+one to oneلأن إيه في الـ one-to-one؟ بناخد عنصريا
+
+148
+00:10:46,000 --> 00:10:50,380
+من المجال صورهم متساوية و نثبت إن هم المتساويين
+
+149
+00:10:50,380 --> 00:10:54,400
+هاي العنصرية فاحنا نبدأ نفهم صح و نكتب بشكل كامل
+
+150
+00:10:54,400 --> 00:10:58,500
+بشكل كامل و طبعا زي ما دايما بنصح ابدي في البيت
+
+151
+00:10:58,500 --> 00:11:00,760
+اشتغل بشكل كامل عشان في الامتحان تكون عملية
+
+152
+00:11:00,760 --> 00:11:03,480
+ديروتينية انت بتعود عليها بصيبتي عملية تلقائية و
+
+153
+00:11:03,480 --> 00:11:06,320
+هذا كتير بيساعد هذا كتير بيساعد و طبعا يعني يقول
+
+154
+00:11:06,320 --> 00:11:09,900
+ما هو الحل انتهى تقريبا لكن ليش احناان نقصر في
+
+155
+00:11:09,900 --> 00:11:14,460
+أمور و نقصر علامات بدون داعي فالأمر سهل جدا اتنين
+
+156
+00:11:14,460 --> 00:11:22,290
+ال F is on topفدائما نتقن العمل ان الله يحب يدعم
+
+157
+00:11:22,290 --> 00:11:25,450
+لحدكم عمل نتقنه فكملوا العمل واشتغلوا بشكل صحيح
+
+158
+00:11:25,450 --> 00:11:29,970
+تمام انتوا ايش معناته انتوا؟ بدنا ناخد عنصر في
+
+159
+00:11:29,970 --> 00:11:34,090
+المجال المقابل فهنقوله let مين عناصر المجال
+
+160
+00:11:34,090 --> 00:11:39,350
+المقابل؟ عناصر Y ممكن يسميهم او اي شيء small y لأن
+
+161
+00:11:39,350 --> 00:11:43,430
+ايش عناصر X ليست اي اجوال مرتبة let Y تنتمي لل X
+
+162
+00:11:43,430 --> 00:11:49,490
+نعمل هميشنا المشهور ايش بدنا ال Y؟تساوي F لعنصر ما
+
+163
+00:11:49,490 --> 00:11:54,250
+في مين في ال domain إيش عنصر ال domain؟ A و 1 إيش
+
+164
+00:11:54,250 --> 00:11:59,090
+بتساوي؟ A فأنا إيش قاعد بدور؟ إحنا قاعدين بنقول
+
+165
+00:11:59,090 --> 00:12:04,710
+إيش بدنا؟ there exists A1 تنتمي لل X cross Y such
+
+166
+00:12:04,710 --> 00:12:09,450
+that اللي هو Y تساوي F of A1فبعد ما عملنا
+
+167
+00:12:09,450 --> 00:12:12,610
+الهامشيكت ايش بنعمل بنختارها الجيت نختار الاش
+
+168
+00:12:12,610 --> 00:12:16,350
+العنصر اللي في ال domain اللي هو a1 كيف نختاره؟ y1
+
+169
+00:12:16,350 --> 00:12:19,630
+لانه مش جالد هيه ال a بيساوي y و الواحد و الواحد
+
+170
+00:12:19,630 --> 00:12:27,230
+ثابت للكل فحقوله ايه ايه كيف نكتب and let a1 تساوي
+
+171
+00:12:27,230 --> 00:12:33,410
+y1 then ايش مطلوب مني؟ حاجتين انه هذا العنصر فعلا
+
+172
+00:12:33,410 --> 00:12:37,640
+في ال domainينتمي للـ domain اللي هو main X cross
+
+173
+00:12:37,640 --> 00:12:42,000
+الـ Y واضحة طبعا و لا بدي أثبات؟ واضحة لأن الـ A
+
+174
+00:12:42,000 --> 00:12:45,540
+هو اللي جيبناها الـ A هي بتساوي Y و الـ Y في الـ X
+
+175
+00:12:45,540 --> 00:12:47,780
+ما زال الـ A في الـ X و الـ Y في الـ Y ماني الـ Y
+
+176
+00:12:47,780 --> 00:12:53,380
+شي هي مجوة الواحد أه إيش كم يعني بدي أثبت؟ أن F of
+
+177
+00:12:53,380 --> 00:12:57,540
+A1 يعني تساوي مين تساوي إيه؟ و الـ A تساوي واحد و
+
+178
+00:12:57,540 --> 00:13:01,340
+هو المطلوب فإذا فعلا الـ F on two
+
+179
+00:13:05,450 --> 00:13:10,270
+is onto يعني عملية الكتابة ليس إلا حلة المسألة
+
+180
+00:13:10,270 --> 00:13:14,290
+الهامش طبعا موجود لكن بدأ نكتب بشكل صحيح و نبدأ صح
+
+181
+00:13:14,290 --> 00:13:17,530
+و نعرف العنصر اللي في المجال المقابل و العنصر اللي
+
+182
+00:13:17,530 --> 00:13:22,690
+في ال domain طبعا واحد و اتنين يؤدي ان ال F is a
+
+183
+00:13:22,690 --> 00:13:30,630
+bijection وبالتالي صارت ان ال X across ال Y تكافئ
+
+184
+00:13:30,630 --> 00:13:33,450
+ال X وهذا بيؤدي ان ال cardinality تساوي ال
+
+185
+00:13:33,450 --> 00:13:41,990
+cardinalityتساوى cardinality لل X اه طبعا هذه ليست
+
+186
+00:13:41,990 --> 00:13:48,370
+الا X في واحد وهذه X وهو المطلوب فهذه هي ايش كل
+
+187
+00:13:48,370 --> 00:13:52,110
+العملية فهذه من الأفكار البسيطة و اللي احنا
+
+188
+00:13:52,110 --> 00:13:56,690
+ذكرناها قبل هيك لان كان في وقت نعملها بشكل مفصل
+
+189
+00:13:56,690 --> 00:14:03,980
+واضحفي أي صعوبة فدايما نصيحتي انه حاولوا تكتبوا
+
+190
+00:14:03,980 --> 00:14:07,080
+بطريقة و اتعودوا تكتبوا بشكل كامل الطريقة اللي
+
+191
+00:14:07,080 --> 00:14:09,520
+احنا اتعلمناها طبعا مش هي الوحيدة تشوف الكتب كيف
+
+192
+00:14:09,520 --> 00:14:13,420
+تكتب اي طريقة اخرى بس المهم تكتبوا بشكل كامل و
+
+193
+00:14:13,420 --> 00:14:17,160
+تبدو صح البداية الصح بتكون هي الخطوة الأولى في
+
+194
+00:14:17,160 --> 00:14:22,420
+طريق الحل الصحيأيضًا خاصية مهمة مثل الأعداد
+
+195
+00:14:22,420 --> 00:14:26,120
+الحقيقية تدرب في صفر دائمًا صفر هنشوف أن هذا
+
+196
+00:14:26,120 --> 00:14:28,960
+الكلام برضه في ال cardinal number الخاصية الصحيحة
+
+197
+00:14:28,960 --> 00:14:32,080
+اه فبقول prove that صفر في X تساوي صفر for any
+
+198
+00:14:32,080 --> 00:14:36,660
+cardinal number X لأي عدد نضربه في صفر بتامه صفر
+
+199
+00:14:42,220 --> 00:14:45,380
+فطبعاً السؤال بدنا نبدأ المنهج تبعنا دايما زي ما
+
+200
+00:14:45,380 --> 00:14:50,020
+حكينا نبدأ ما نجافش مكتفين إيدينا نبدأ نفكر إيش
+
+201
+00:14:50,020 --> 00:14:53,300
+معطيات و إيش مطلوب فطبعاً أول حاجة بدي أجيب
+
+202
+00:14:53,300 --> 00:14:57,020
+مجموعات مجموعة كاردناطي إليها صفر مفيش غير الـ Phi
+
+203
+00:14:57,020 --> 00:14:59,980
+و بدنا مجموعة كاردناطي تلقاها X بغض النظر إيش هو
+
+204
+00:14:59,980 --> 00:15:03,460
+الـ X بشكل عام فحنقوله الآن هذا المثال رقم 2
+
+205
+00:15:03,460 --> 00:15:07,060
+solution
+
+206
+00:15:14,830 --> 00:15:26,730
+let X be a set such that cardinality لل X تساوي X
+
+207
+00:15:26,730 --> 00:15:31,390
+طبعا تانية بيسميها Y بيسميها B فهي Phi واضح ممكن
+
+208
+00:15:31,390 --> 00:15:38,490
+غير ما نسميها then على طول صفر في X ليس إلا ال
+
+209
+00:15:38,490 --> 00:15:43,630
+cardinality لل Phi ضرب ال Cartesian product مع ال
+
+210
+00:15:43,630 --> 00:15:47,620
+Xبظبط؟ نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+211
+00:15:47,620 --> 00:15:48,440
+نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+212
+00:15:48,440 --> 00:15:49,200
+نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+213
+00:15:49,200 --> 00:15:49,600
+نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+214
+00:15:49,600 --> 00:15:49,620
+نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+215
+00:15:49,620 --> 00:15:51,360
+نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+216
+00:15:51,360 --> 00:15:52,320
+نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+217
+00:15:52,320 --> 00:15:54,160
+نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+218
+00:15:54,160 --> 00:15:54,220
+نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم نعم
+
+219
+00:15:54,220 --> 00:16:00,900
+نعم نعم
+
+220
+00:16:00,900 --> 00:16:13,340
+ن
+
+221
+00:16:14,020 --> 00:16:18,200
+خلّينا نرجع لكم شبطر أول شبطر تلاتة we will prove
+
+222
+00:16:18,200 --> 00:16:25,760
+that فا يمكن أثبتناها قبل هيك أثبتناها خلاص إذا
+
+223
+00:16:25,760 --> 00:16:31,480
+أثبتناها انتهى إذا أثبتناها انتهى إذا خلاص فهذه
+
+224
+00:16:31,480 --> 00:16:38,010
+تساوي ال cardinality للفا وتساوي انتهت العملأه
+
+225
+00:16:38,010 --> 00:16:39,890
+طبعا by contradiction ان افترض انها دي لا تساوي
+
+226
+00:16:39,890 --> 00:16:43,330
+فاي فبدا اقدر ألاجأ عنصر XY في الـ Phi و في ال X
+
+227
+00:16:43,330 --> 00:16:46,170
+فال X في ال Phi ال contradiction انتهت العمل تمام
+
+228
+00:16:47,930 --> 00:16:51,530
+فإذا هذه بكل سهولة فإذا هذا هو المنهج في الجامع
+
+229
+00:16:51,530 --> 00:16:54,230
+وفي الضرب بياخدوا ال cardinal number اللي بده اشتر
+
+230
+00:16:54,230 --> 00:16:57,910
+عليهم بجيب مجموعات تقابلهم في ال Cartesian أي
+
+231
+00:16:57,910 --> 00:17:01,590
+مجموعات تؤدي الغرض في الجامع .. أسف في الضرب بدنا
+
+232
+00:17:01,590 --> 00:17:04,570
+مجموعات أي اشي بتؤدي الغرض في الجامع بده انتبه ان
+
+233
+00:17:04,570 --> 00:17:07,870
+التقاط عساوفة وهذا كل منهج ده مصير لنشتر على مقاش
+
+234
+00:17:07,870 --> 00:17:17,170
+المجموعات تمام، انشوف هنا نظرية قواص الضربأه طبعاً
+
+235
+00:17:17,170 --> 00:17:21,130
+بنشوف هل فيه خاصية الإبدال موجودة ولا لا خاصية
+
+236
+00:17:21,130 --> 00:17:24,590
+التجميع والأن صار عندي عمليتين ضرب و جمع في توزيع
+
+237
+00:17:24,590 --> 00:17:27,990
+ولا مافيش توزيع اه فبتقول ال product .. اه طبعاً
+
+238
+00:17:27,990 --> 00:17:32,270
+هو خاص اللي هو cardinal product أول شيء عملية
+
+239
+00:17:32,270 --> 00:17:36,090
+الضرب في cardinal numbers إبدالية ف X في Y تساوي Y
+
+240
+00:17:36,090 --> 00:17:40,310
+في Xرقم اتنين associativity في خاصية التجميع
+
+241
+00:17:40,310 --> 00:17:43,870
+ودائما بنعيد و بنكرر التجميع هو البوابة اللى
+
+242
+00:17:43,870 --> 00:17:47,710
+بتتخلى العملية الثنائية تتطبق على تلاتة أو أربعة
+
+243
+00:17:47,710 --> 00:17:51,450
+أو خمسة و هكذا فده مهم جدا اه الخاصية التالتة و
+
+244
+00:17:51,450 --> 00:18:01,030
+الأخيرة التوزيع بنقدر نوزع الدرب على الجمع فخلينا
+
+245
+00:18:01,030 --> 00:18:03,550
+نبرهنهم واحدة واحدة
+
+246
+00:18:10,910 --> 00:18:15,830
+ونشوف إيش اللي بتطبق مع الأفكار السابقة أو إيش
+
+247
+00:18:15,830 --> 00:18:24,670
+اللي بده تعديل فدايما بنحاول نشتغل و نبدأ 6
+
+248
+00:18:24,670 --> 00:18:32,690
+5 بروف أو نبدأ برقم واحد بدنا نثبت إن xy تساوي yx
+
+249
+00:18:32,690 --> 00:18:42,530
+فهناخد مجموعتين let X andY besets such that
+
+250
+00:18:42,530 --> 00:18:46,170
+cardinality
+
+251
+00:18:46,170 --> 00:18:56,670
+لX تساوي small x وcardinality لY تساوي small y
+
+252
+00:19:05,510 --> 00:19:08,830
+تمام فالان طبعا ان انا ممكن احط نوان دهامش ايش في
+
+253
+00:19:08,830 --> 00:19:14,710
+عندي في عندي x في y تساوي ال cardinality لل x ضرب
+
+254
+00:19:14,710 --> 00:19:19,810
+ال y كارتيسيا و ال y في x هي ال cardinality لل y
+
+255
+00:19:19,810 --> 00:19:25,050
+cross ال x فدهامش بدي اثبت ان هدول متساويين بدي
+
+256
+00:19:25,050 --> 00:19:29,840
+اثبت ان هدول مجموعتين متكافئتينهذا المطلوب في
+
+257
+00:19:29,840 --> 00:19:32,740
+الاتحاد كانوا متساويين مباشرة لأنه اتحاد ابدالي
+
+258
+00:19:32,740 --> 00:19:36,000
+لكن هل ال kartesian ابدالي؟ لا إذا ماقدرش نثبت
+
+259
+00:19:36,000 --> 00:19:39,720
+انهم متساويين يجب ان نثبت انهم متكافئتين فشايفين
+
+260
+00:19:39,720 --> 00:19:46,640
+الهامش او كيف يفكر فخلينا نكتب we will prove او
+
+261
+00:19:46,640 --> 00:19:55,160
+show that X across Y تكافئ Y across X
+
+262
+00:19:57,670 --> 00:20:03,850
+تمام بدنا by diction من X cross ال Y ل Y cross ال
+
+263
+00:20:03,850 --> 00:20:10,210
+X اه من وين نجيب الدالة اه فين فيعمل ال calculus
+
+264
+00:20:10,210 --> 00:20:17,990
+لا متفقين ندور في المعطيات في في المعطيات اه
+
+265
+00:20:17,990 --> 00:20:26,870
+اه في في اللي هو في المعطيات في دوال بدنا
+
+266
+00:20:29,390 --> 00:20:36,190
+ده لأ بتدينا by diction تمام مافيش دولة إذا بدنا
+
+267
+00:20:36,190 --> 00:20:44,870
+نفكر بشكل مباشر خلينا نعرف let F من X cross ال Y
+
+268
+00:20:44,870 --> 00:20:54,830
+إلى Y across ال X be givenby مافيش دوال بينا نشوف
+
+269
+00:20:54,830 --> 00:20:58,110
+ممكن نعمل دالة مباشرة من غير ما نعتمد على دوال
+
+270
+00:20:58,110 --> 00:21:06,310
+أخرى ممكن f of x y تساوي y x أحسنتي بس إيش نعمل
+
+271
+00:21:06,310 --> 00:21:11,190
+أحنا بس أعمل عكس تغيير الترتيب فأنا بدي أخد الزوج
+
+272
+00:21:11,190 --> 00:21:14,910
+يعني ممكن نعمل صورة إيش العناصر من هنا لو رسمنا
+
+273
+00:21:17,710 --> 00:21:22,910
+نعمل صورة هي X cross ال Y عبارة عن مين؟ ايش
+
+274
+00:21:22,910 --> 00:21:29,050
+عناصرها؟ بلاش نكتب تساوي XY طب Y ال XY مستخدمين؟
+
+275
+00:21:29,050 --> 00:21:35,350
+أه بلاش أستخدم XY للأسف دي خينا نعمل AB عشان ال XY
+
+276
+00:21:35,350 --> 00:21:42,270
+مستخدمين ك cardinal number AB تساوي BA طب يمكن
+
+277
+00:21:42,270 --> 00:21:48,000
+الأحسن أه فهنا طبعا عناصرها مين؟A و B طب ال Y في X
+
+278
+00:21:48,000 --> 00:21:52,660
+إيش عناصرها؟ B و A واضحة، مظبوط؟ أه فواضح إن أنا
+
+279
+00:21:52,660 --> 00:21:56,480
+بدي كل عنصر يروح لعنصر المقابل طب .. طب هذا
+
+280
+00:21:56,480 --> 00:21:58,460
+تخميننا الأولين نثبت أنها one to one و أنتوا
+
+281
+00:21:58,460 --> 00:22:02,620
+بتكونوا تخميننا صح أو تختيرنا صح خليني نثبت فإيش؟
+
+282
+00:22:02,620 --> 00:22:06,080
+بتساوي بدا الشكل فهي عملية هذا الدلش تعمل بس زوجه
+
+283
+00:22:06,080 --> 00:22:09,840
+المرتب إيش تعمله؟ بتعكس ترتيبه، ليس إلا أه، هلجيت
+
+284
+00:22:09,840 --> 00:22:15,960
+أول شيء؟ F is one to one، نشوففناخد عن صورين let
+
+285
+00:22:15,960 --> 00:22:24,400
+a1, b1 and a2, b2 و الموجودين في ال domain صورهم
+
+286
+00:22:24,400 --> 00:22:33,260
+متساوية such that f of a1, b1 تساوي f of a2, b2
+
+287
+00:22:33,260 --> 00:22:38,820
+ممتازة بداية ال one to one اتوقع انه عملية مفروض
+
+288
+00:22:38,820 --> 00:22:45,170
+تكون سهلة ومألوفة ايش نستخدم التعريف؟إيش الصورة
+
+289
+00:22:45,170 --> 00:22:51,430
+بيصير b1 a1 بدي تسوى b2 a2 ليس إلا طيب زوجين
+
+290
+00:22:51,430 --> 00:22:57,790
+مرتبين الأول بيسوى الأول و التاني بيسوى التاني and
+
+291
+00:22:57,790 --> 00:23:03,270
+a1 بيسوى اتنين اه وصلنا ولا لأ لإن احنا بدنا الزوج
+
+292
+00:23:03,270 --> 00:23:09,000
+المرتب يسوى الزوج المرتبأه بدنا a1 b1 تساوي a2 b2
+
+293
+00:23:09,000 --> 00:23:11,380
+ما زال الأول يساوي الأول و التاني يساوي التاني من
+
+294
+00:23:11,380 --> 00:23:18,040
+غض النظر لأنه الأن إبدالية فهذا يؤدي أن a1 b1
+
+295
+00:23:18,040 --> 00:23:23,680
+تساوي a2 b2لأنه بقدر من هنا أروح من هنا ولا لأ و
+
+296
+00:23:23,680 --> 00:23:26,300
+العكس صحيح if and only if لأن أي الأول بيساوي
+
+297
+00:23:26,300 --> 00:23:29,680
+الأول صح والتاني بيساوي التاني صح يعني حتى يعني
+
+298
+00:23:29,680 --> 00:23:32,760
+أحيانا إحنا بدنا ندول عادي نكتبها وإذا مش متأكدين
+
+299
+00:23:32,760 --> 00:23:35,780
+منها نحاول نخرحها نتأكد أنا صح ولا لأ و هذا اللي
+
+300
+00:23:35,780 --> 00:23:38,400
+احنا كنا بيجيب الدليل نفس الشيء أنه نتأكد أن شغلنا
+
+301
+00:23:38,400 --> 00:23:44,050
+صح فهذا بتدل أنه ندلها one to oneF is one to one
+
+302
+00:23:44,050 --> 00:23:47,250
+طبعا انتهى البروحان ليش أيضا بدأنا عنصرين في
+
+303
+00:23:47,250 --> 00:23:50,850
+الدمين صورهم متساوية أثبتنا ان هدول عنصرين متساوية
+
+304
+00:23:50,850 --> 00:23:55,010
+طبعا عناصر الدمين أزواج مرتبة فهم أزواج مركبة نشوف
+
+305
+00:23:55,010 --> 00:24:02,350
+انها on two اتنين F is on twoناخد عنصر وين في
+
+306
+00:24:02,350 --> 00:24:06,510
+المجال المقابل لت بي ايه خلنا نسميه عشان مشينا ان
+
+307
+00:24:06,510 --> 00:24:10,370
+ال B مرتبطة بال Y و ال A مرتبطة بال X تنتمي ل ال Y
+
+308
+00:24:10,370 --> 00:24:16,610
+across ال X ايش بدنا؟ بدنا بي ايه تساوي F of مثلا
+
+309
+00:24:16,610 --> 00:24:21,030
+Alpha Beta عنصر طب هذا ايش بيساوي؟ Beta و Alpha
+
+310
+00:24:21,030 --> 00:24:25,290
+فإيش بده؟ اختار العنصر بي ايه على طول واضح يعني
+
+311
+00:24:25,290 --> 00:24:31,270
+العملية بس عليه أكسر تيو صح؟ فإيش هتقوله and؟خلاص
+
+312
+00:24:31,270 --> 00:24:37,550
+مباشرة مافيش داعي نكتب حتة then a و b وين موجودة
+
+313
+00:24:37,550 --> 00:24:41,730
+إذا b a في ال y إكس زي الفريلاجي بتكون في x cross
+
+314
+00:24:41,730 --> 00:24:44,570
+ال y هيها في الدمان ولا مش في الدمان في الدمان
+
+315
+00:24:44,570 --> 00:24:48,840
+وإيش صورتهابتساوي العنصر اللي أخدته ولا ما
+
+316
+00:24:48,840 --> 00:24:52,380
+بتساويهاش؟ بتساوي طيب طبعا مش ضروري دايما الكلاب
+
+317
+00:24:52,380 --> 00:24:56,420
+متطابق لكن روح الموضوع العمود الفقري للشغل نفسه
+
+318
+00:24:56,420 --> 00:24:59,980
+أخدنا عنصر في المجال المقابل لجناله عنصر في ال
+
+319
+00:24:59,980 --> 00:25:04,040
+domain مناسب صورة العنصر فعلا بتساويه نعم انتهت
+
+320
+00:25:04,040 --> 00:25:07,920
+العملية لأ أنا بحاول أحل أي أسماء
+
+321
+00:25:10,920 --> 00:25:15,560
+أنا بدأ أقول F of مين الـ BA F of مين على طول
+
+322
+00:25:15,560 --> 00:25:17,960
+اتلاقيت أنها سهلة حتى لما انا .. بس حاولت أشتغل
+
+323
+00:25:17,960 --> 00:25:21,880
+عليها فقلت أيه صورة مين ألف و بيتا سميته عشان X و
+
+324
+00:25:21,880 --> 00:25:25,000
+Y مش مشغولين فدي حروف أخرى قد بدنا ممكن .. زي ما
+
+325
+00:25:25,000 --> 00:25:28,600
+بدك يعني أي رموز .. اه فاللي اتلاقيت انه مافيش
+
+326
+00:25:28,600 --> 00:25:31,880
+دعنة قلت بيه إيش يساوي على طول فقلت الـ BA .. ال
+
+327
+00:25:31,880 --> 00:25:36,060
+BA صورة مين AB على طول واضح فبقول إن ال F is on
+
+328
+00:25:36,060 --> 00:25:44,880
+two thus F is on twoطبعاً 1 و 2 بيقول إنه فيه
+
+329
+00:25:44,880 --> 00:25:52,680
+bijection يعني إيش التكافؤ اللي بدنا إياه موجود او
+
+330
+00:25:52,680 --> 00:26:01,760
+بالتالي خلصت العمل therefore
+
+331
+00:26:01,760 --> 00:26:07,230
+xy تساوي yxفما زال مجموعتين متكافئتين فال
+
+332
+00:26:07,230 --> 00:26:09,270
+cardinality تساوي ال cardinality و هدول ال
+
+333
+00:26:09,270 --> 00:26:11,230
+cardinality لهم نفس القضية
+
+334
+00:26:20,280 --> 00:26:23,980
+فبنلاحظ أنه يعني حتى لو مش كل الأسللة انحلت لكن
+
+335
+00:26:23,980 --> 00:26:28,660
+معظم الأسللة بتمشي بنفس الهيكلية وفي نفس الطريقة
+
+336
+00:26:28,660 --> 00:26:32,020
+العادية طبعا في بعض الأسللة بتكون شوية أصعب لكن
+
+337
+00:26:32,020 --> 00:26:38,480
+احنا بنكون قطع نشاط كبير نشوف عملية التجميع يمكن
+
+338
+00:26:38,480 --> 00:26:41,600
+التجميع خلينا نكتب الفكرة و يمكن التفاصيل نتركها
+
+339
+00:26:41,600 --> 00:26:46,500
+لكملأن أتوقع أنه مافيش فيها جديد يمكن التوزيع أهم
+
+340
+00:26:46,500 --> 00:26:50,620
+التوزيع فيها شغل أكتر شوية اتنين بدنا نثبت اللي هو
+
+341
+00:26:50,620 --> 00:27:01,380
+associativity تمام بدنا الآن تلت مجموعات let X,Y,Z
+
+342
+00:27:01,380 --> 00:27:08,620
+be sets such that طبعا
+
+343
+00:27:08,620 --> 00:27:14,520
+cardinalityللكبتل X تساوي small x Cardinality
+
+344
+00:27:14,520 --> 00:27:21,580
+للكبتل Y تساوي small y and Cardinality للكبتل Z
+
+345
+00:27:21,580 --> 00:27:29,440
+تساوي small z طبعا then بدنا نشوف اه طبعا احنا ايش
+
+346
+00:27:29,440 --> 00:27:35,960
+مطلوب مننا ايش احنا فيه عندنا خلينا نكتب X في Y Z
+
+347
+00:27:35,960 --> 00:27:44,590
+هي ليست الا الcardinalityلل X ضرب Y ضرب Z هيك
+
+348
+00:27:44,590 --> 00:27:52,290
+معناها صح؟ هيك معناها والتانية اه اللي هي X في Y
+
+349
+00:27:52,290 --> 00:27:59,110
+في Z تساوي ال cardinality لل X ضرب ال Y أولا
+
+350
+00:27:59,110 --> 00:28:03,810
+والنتج مع Z والنتج
+
+351
+00:28:03,810 --> 00:28:11,130
+مع Zالمطلوب أن أثبت أن هذا يساوي هذا يعني نريد أن
+
+352
+00:28:11,130 --> 00:28:14,530
+نثبت أن هذه المجموعة تكافئها هذه المجموعة هل هي
+
+353
+00:28:14,530 --> 00:28:20,460
+تكافئها ولا بتساويها؟بتسويها الحقيقة يمكن احنا ما
+
+354
+00:28:20,460 --> 00:28:24,200
+هتحدثناش كيف نعمل Cartesian product فطبعا العناصر
+
+355
+00:28:24,200 --> 00:28:28,180
+اللي هنا متساويين بالمعنى اللي هو إيه الصريح ممكن
+
+356
+00:28:28,180 --> 00:28:30,660
+نعمل تكافؤ إذا بنا نمشي بشكل حرفي لكن هم يعتبروا
+
+357
+00:28:30,660 --> 00:28:34,760
+متساويين مين العناصر اللي هان وعناصر اللي هان
+
+358
+00:28:34,760 --> 00:28:45,480
+خلينا نكتب بس شوية عن الموضوع هذا نوضحه إذا
+
+359
+00:28:45,480 --> 00:28:53,770
+حابين ال get بالنسبة إلينانشوف X across Y across Z
+
+360
+00:28:53,770 --> 00:29:00,510
+كمجموعة إيش بتساوي؟ بقى، بتساوي زوج مرتب، إحنا إيه
+
+361
+00:29:00,510 --> 00:29:04,990
+حملنا؟ بحيث العنصر الأول هنا والتاني هنا، فبتساوي
+
+362
+00:29:04,990 --> 00:29:11,410
+X طب التاني إيش يكون؟ برضه زوج مرتب، Y و Z بحيث
+
+363
+00:29:11,410 --> 00:29:16,910
+إنه ال X في ال X و ال Y في ال Y و small z في
+
+364
+00:29:16,910 --> 00:29:22,230
+capital Zفهذه الصورة لكن الحقيقة يمكن هذه الطريقة
+
+365
+00:29:22,230 --> 00:29:27,590
+تكتبش بعد الصورة كم يكتبوها ثلاثي مش .. مش .. مش
+
+366
+00:29:27,590 --> 00:29:31,190
+زوج مرتب ثلاثي مرتب بيسموها فهم تكتب بعد الشكل
+
+367
+00:29:31,190 --> 00:29:35,790
+طبعا إذا ماعملاش نعمل اللي هو إيش التناظر بسهولة
+
+368
+00:29:35,790 --> 00:29:39,890
+التناظر تبحث طبعا بالنسبة إلينا X cross ال Y إذا
+
+369
+00:29:39,890 --> 00:29:47,600
+بدنا نمشي حرفي بدأ تكون إيش XYو Z بهذا الشكل X في
+
+370
+00:29:47,600 --> 00:29:55,100
+X طبعا و Y في Y و Z في Z ليس L تفضلي
+
+371
+00:30:00,110 --> 00:30:03,390
+أه بس إيش بده يكون؟ مازال هو .. إذا يعني .. هلجيت؟
+
+372
+00:30:03,390 --> 00:30:07,130
+بدل .. جزك بدل x و y أه سمي مثلا هذا إيش؟ إذا سمي
+
+373
+00:30:07,130 --> 00:30:10,930
+هذا alpha بس إيش بده يكون؟ بده يكون في هنا إذا ليش
+
+374
+00:30:10,930 --> 00:30:13,490
+بده يكون؟ زوج مرتب برضه أنا ال x و ال y بستخدمهم
+
+375
+00:30:13,490 --> 00:30:17,850
+أكتر من مرة يمكن a,b,c أحسن عشان مش ساخدمين للأسف
+
+376
+00:30:17,850 --> 00:30:23,590
+التعود فإختيار الرموز المناسبة دايما a,b,c
+
+377
+00:30:29,190 --> 00:30:39,170
+فكان من الأفضل إنه نستخدم الحروف بشكل مختلف طبعا
+
+378
+00:30:39,170 --> 00:30:41,870
+زي ما قلنا مافيش رموز غلط و صح لكن في رموز أريح من
+
+379
+00:30:41,870 --> 00:30:46,410
+رموز فطبعا إيش بتثبت إنه هذه تكافئة هذه الحقيقة هم
+
+380
+00:30:46,410 --> 00:30:49,130
+إذا بدنا نمشي بالشكل اللي هو المتعرف عليه بالعرف
+
+381
+00:30:49,130 --> 00:30:51,870
+اللي هو متساوين الحقيقة إذا بدنا نمشي بشكل حرفي
+
+382
+00:30:51,870 --> 00:30:55,670
+دقيق بيكون تكافئة إيش بدي أعمل هدا أو أدي لهدا بس
+
+383
+00:30:55,670 --> 00:30:57,750
+و بعدين بثبت إنه ده ال one to one و one to two
+
+384
+00:30:58,320 --> 00:31:03,220
+واضحة ولا نعملها؟
+
+385
+00:31:03,220 --> 00:31:16,500
+let f من x cross y cross z إلى x cross y cross z
+
+386
+00:31:16,500 --> 00:31:17,400
+be given by
+
+387
+00:31:21,540 --> 00:31:28,840
+F of ايش العناصر هنا A وزوج مرتب ايش تساوي ABC
+
+388
+00:31:28,840 --> 00:31:35,010
+تمام واضحة Aهل جيت الدالة one to one وانتوا
+
+389
+00:31:35,010 --> 00:31:38,850
+بتقدروا تثبتوها؟ أه سهولة زي هذه تقريبا على طول
+
+390
+00:31:38,850 --> 00:31:42,050
+بكون سهولة لإن طبعا الناس بده يقول إن زوج بيسوي
+
+391
+00:31:42,050 --> 00:31:45,030
+زوج إذا كل إحداث يسوي إحداث و بعدين هذا أفصله
+
+392
+00:31:45,030 --> 00:31:48,170
+بعدين يعتبر إحداثي مؤقتا و بعدين هو بيصيريه و هكذا
+
+393
+00:31:48,170 --> 00:31:52,330
+فالأمور سهلة ان شاء الله ف F is one to one او is a
+
+394
+00:31:52,330 --> 00:31:59,590
+bijection a bijection وانتهت العملفهذه أتوقع يكفي
+
+395
+00:31:59,590 --> 00:32:05,250
+لكي ندخل فيها تفاصيلها و تشبه لحد ما الفرع الأول
+
+396
+00:32:05,250 --> 00:32:11,910
+نشوف الفرع التاني التالت آسف الآن بدنا ضرب و بدنا
+
+397
+00:32:11,910 --> 00:32:18,950
+جمع فبدنا تلت مجموعاتبدنا نجمع Y مع Z إذا بدنا
+
+398
+00:32:18,950 --> 00:32:22,490
+المجموعة اللي تقابل الـ Y تكون إيش مع تقاطعها مع
+
+399
+00:32:22,490 --> 00:32:27,230
+مجموعة الـ Z يكون فاي فخلينا نقوله الآن بدي أغير
+
+400
+00:32:27,230 --> 00:32:39,750
+أسماء المجموعات let A, B, C, B, 6 such that B
+
+401
+00:32:39,750 --> 00:32:44,590
+تقاطع الـ C بدنا يسووا فاي صح؟عشان بدي أجيبه Y
+
+402
+00:32:44,590 --> 00:32:49,590
+زائد Z طيب إيش بده كمان؟ بدي ال Cartesian عشان
+
+403
+00:32:49,590 --> 00:32:54,970
+الطرف التاني بدي أجمعه اه ف X في Y اه متابعين؟
+
+404
+00:32:54,970 --> 00:33:00,730
+الآن أنا بدي أجمع فلازم هنا هذه B و هذه C تقاطعهم
+
+405
+00:33:00,730 --> 00:33:07,130
+بيسوا 5 هدولة C و إيش بدنا كمان؟ بدنا A مع B تقاطع
+
+406
+00:33:07,130 --> 00:33:12,600
+ال Aمع الـ C == 5 طيب هل هذا لازم أحطه شرط و لا
+
+407
+00:33:12,600 --> 00:33:16,300
+بقدر أسنتجه من هنا مباشرة بقدر أسنتجه مباشرة إذا
+
+408
+00:33:16,300 --> 00:33:19,780
+هذا إذا هذا في فهذا في موجودة في أحد التمرين على
+
+409
+00:33:19,780 --> 00:33:24,140
+طول فهذا الشرط يكفي يتمنى للتنتين في هذا الشرط
+
+410
+00:33:24,140 --> 00:33:31,620
+يكفي يتمنى للتنتين في then طبعا with with
+
+411
+00:33:31,620 --> 00:33:40,490
+cardinality لل A تساوي Xcardinality لل B تساوي Y
+
+412
+00:33:40,490 --> 00:33:47,150
+والcardinality لل C تساوي Z اه
+
+413
+00:33:47,150 --> 00:33:57,350
+فطبعا then الطرف اليسار X في Y زائد Z ليس الا
+
+414
+00:33:57,350 --> 00:34:06,330
+الcardinality لل X ضرب mean A مش X A سمنها AB
+
+415
+00:34:06,330 --> 00:34:13,370
+Union الـ C هذا الطرف الطرف التاني خلّينا نكتبه
+
+416
+00:34:13,370 --> 00:34:18,750
+and ونشوف إيش بيساويوا بعض أو بيكافؤوا بعض XY زائد
+
+417
+00:34:18,750 --> 00:34:25,330
+XZ ليست إلا لل card نمت لمن؟ X أي قاسف A برضه لو
+
+418
+00:34:25,330 --> 00:34:34,450
+توقع كتبنا A times B على Y اتحاد A times Cفالسؤال
+
+419
+00:34:34,450 --> 00:34:37,530
+بدي أثبت إن هذه المجموعة تكافي هذه المجموعة
+
+420
+00:34:37,530 --> 00:34:44,230
+الحقيقة إنهم متساويتين أثبتناهم قبل ذلك أخدناهم
+
+421
+00:34:44,230 --> 00:34:55,650
+نعرف أن A Cartesian B Union C يساوي A Cartesian B
+
+422
+00:34:55,650 --> 00:35:03,780
+Union A Cartesian Cخلصت فالعملية الآن سهلة جدا
+
+423
+00:35:03,780 --> 00:35:08,880
+خليني
+
+424
+00:35:08,880 --> 00:35:12,280
+برضه أكتب الملاحظة دي عشان ماحدش ينساها we know
+
+425
+00:35:12,280 --> 00:35:15,100
+and moreover
+
+426
+00:35:18,150 --> 00:35:25,590
+طبعا هذه المعلومة يمكن نضيفها هنا moreover a تقاطع
+
+427
+00:35:25,590 --> 00:35:32,730
+c يساوي 5 implies a cross b تقاطع a cross c يساوي
+
+428
+00:35:32,730 --> 00:35:39,150
+5 فإذن therefore خلصنا
+
+429
+00:35:39,150 --> 00:35:47,060
+x في y زائد z تساوي x في y زاد x في zالبرهان بيكون
+
+430
+00:35:47,060 --> 00:35:50,600
+هي كنتة طبعا عملية ان هدولة متساومين توقع نظرية
+
+431
+00:35:50,600 --> 00:35:55,060
+مثبتة نرجع لها وهذه ممكن تثبتها بسهولة ان مازال
+
+432
+00:35:55,060 --> 00:36:02,760
+هدولة تقطحن في بي بي بيؤدي
+
+433
+00:36:02,760 --> 00:36:06,800
+ان ده برضه فعلا لانه لما بدأ ياخد عنصر هنا مشترك
+
+434
+00:36:06,800 --> 00:36:11,500
+يكون زوج مرتب فبتكون الاحداث التاني موجود في وين
+
+435
+00:36:11,500 --> 00:36:13,200
+في ال بي و ال سي contradiction على طول
+
+436
+00:36:18,420 --> 00:36:27,980
+خلّينا نشوف مثال أرجو
+
+437
+00:36:27,980 --> 00:36:32,810
+أن الفكرة الأساسية تكون واضحةفاحنا دايما بناخد ال
+
+438
+00:36:32,810 --> 00:36:36,950
+cardinal numbers بنجيب مجموعات و بنحول الشغل للغة
+
+439
+00:36:36,950 --> 00:36:40,510
+المجموعة او بنشوف بيطلع تساوي تكافؤ ايش المناسب
+
+440
+00:36:40,510 --> 00:36:43,630
+بنقدر نتعامل معاه لأنه عندنا معلومات كتيرة عن
+
+441
+00:36:43,630 --> 00:36:47,870
+نظرية المجموعات من شبط الخمسة في التكافؤ و هكذا و
+
+442
+00:36:47,870 --> 00:36:50,310
+طبعا في شبط التلاتة كيف نتعامل مع اللي هو التساوي
+
+443
+00:36:50,310 --> 00:36:54,130
+المجموعات و هذه الأمور كلها تمام بنثبت ألف ايه انه
+
+444
+00:36:54,130 --> 00:36:57,230
+بنجيب ألف نول في ألف نول المثال الأول
+
+445
+00:37:08,920 --> 00:37:12,380
+أيش تتوقعوا؟ ايش الjawاب؟ الف null infinity في
+
+446
+00:37:12,380 --> 00:37:15,380
+infinity بيساوي infinity من نفس النوع من نفس النوع
+
+447
+00:37:15,380 --> 00:37:19,860
+تمام اه ما زال احنا عارفين خلينا نعمل هامش نفكر مع
+
+448
+00:37:19,860 --> 00:37:23,460
+بعض الف null في الف null تساوي الف null هذا كله
+
+449
+00:37:23,460 --> 00:37:29,080
+هامش طبعا هذا ايش ماله؟ ايش بيقابل؟
+
+450
+00:37:29,080 --> 00:37:32,700
+و هذا ايش بيقابل؟ and طب هدول متكافئين؟
+
+451
+00:37:38,560 --> 00:37:42,200
+الان على طول الحل سهل جدا solution
+
+452
+00:37:44,250 --> 00:37:50,590
+الف null في الف null ليست إلا ال cardinality لل N
+
+453
+00:37:50,590 --> 00:37:55,150
+cross ال N ال N هنا أسهل من الجمع لماذا؟ لأنه إذا
+
+454
+00:37:55,150 --> 00:37:56,950
+أخدت N مع ال N فهي فاعل أو مش فاعل بيهمنيش أخدت N
+
+455
+00:37:56,950 --> 00:38:00,450
+مع ال N طبعا بالنسبة لل الف null هي تقابل بشكل
+
+456
+00:38:00,450 --> 00:38:04,250
+أساسي ال N و ال Z و ال Q و ال N odd و ال N even
+
+457
+00:38:04,250 --> 00:38:07,070
+كله لكن أنا بدأ أختار هنا أسهل شيء فش عندي مشكلة
+
+458
+00:38:07,070 --> 00:38:12,170
+أتعامل مع ال N and we know
+
+459
+00:38:14,900 --> 00:38:19,880
+that n cross n تكافئ ال n نظرية مش عارف جديش نظرية
+
+460
+00:38:19,880 --> 00:38:23,780
+خمسة جديش خمسة عشر على ما أعتقد و لا مش عارف بس
+
+461
+00:38:23,780 --> 00:38:29,980
+خمسة دوروا عليها ان n cross n is denomable نظرية
+
+462
+00:38:29,980 --> 00:38:33,840
+ولا كانت core ولا ريح نظرية مهمة n cross n is
+
+463
+00:38:33,840 --> 00:38:36,600
+denomable is denomable تكافئ ال n فعله طول فده
+
+464
+00:38:36,600 --> 00:38:41,820
+بقول ليه ان الف null في الف null يساوي الف
+
+465
+00:38:53,730 --> 00:38:58,950
+نشوفC في C برضه بتساوي C طبعا اللي هو ال
+
+466
+00:38:58,950 --> 00:39:02,730
+cardinality لل R طبعا هنا ال C بيعرفها لأن ال C مش
+
+467
+00:39:02,730 --> 00:39:08,130
+رمز وحيد يستخدم بس ل cardinality لل R بيستخدم فيه
+
+468
+00:39:08,130 --> 00:39:12,070
+أكتر من مكان لكن الالف null هذا رمز فريد لا يستخدم
+
+469
+00:39:12,070 --> 00:39:14,610
+إلا مع ال cardinality تقريبا فلما بيحط الف null
+
+470
+00:39:14,610 --> 00:39:17,190
+على طول بيعرف لكن ال C استخدمناها قبلك لل
+
+471
+00:39:17,190 --> 00:39:20,550
+contradiction وممكن تستخدمها كرمز عادي متغير لكن
+
+472
+00:39:20,550 --> 00:39:24,450
+الالف null هذا ياش رمز خاص رمز خاص تمام
+
+473
+00:39:27,700 --> 00:39:34,920
+المثال رقم اتنين نفس القضية بدنا نشوف عملية الضرب
+
+474
+00:39:34,920 --> 00:39:41,520
+الآن العملية أصعب لأننا لا نعرف ان ال R cross R
+
+475
+00:39:41,520 --> 00:39:49,220
+تكافئ R لأ ماعناش معلومة زي ذلكهي non-denominable
+
+476
+00:39:49,220 --> 00:39:53,240
+او non-denominable هل بتكافئ R ولا لأ فالان ممكن
+
+477
+00:39:53,240 --> 00:39:57,640
+بدنا نعمل طريقة مختلفة دايما مع ال C بنمشي مع
+
+478
+00:39:57,640 --> 00:40:00,760
+التساوي مباشرة بنمشي اصغر من او يساوي اصغر من او
+
+479
+00:40:00,760 --> 00:40:05,160
+يساوي فاحنا الحقيقة خلينا نقول هنا solution we
+
+480
+00:40:05,160 --> 00:40:16,940
+will لو سمحت show that C في C اقل او تساوي C andC
+
+481
+00:40:16,940 --> 00:40:21,620
+أقل أو تساوي C في C نستخدم هذه اللي هو نظرية مهمة
+
+482
+00:40:21,620 --> 00:40:25,220
+عشان أثبت أن two cardinal number متساويين في طريقة
+
+483
+00:40:25,220 --> 00:40:28,240
+بديلة أثبت أن الأول أصغر أو يساوي التاني و التاني
+
+484
+00:40:28,240 --> 00:40:32,480
+أصغر أو يساوي الأول طبعا نبدأ دايما هذا الجزء أسهل
+
+485
+00:40:32,480 --> 00:40:38,340
+لأنه واضح أنه صغير فنبدأ في هذا الصيغة C أقل أو
+
+486
+00:40:38,340 --> 00:40:45,020
+تساوي C في Cالـ C بتقابل R بشكل أساسي أو بتقابل
+
+487
+00:40:45,020 --> 00:40:49,920
+برضه 01 الفترة فممكن نشتغل على أيه الفترة؟ بدنا
+
+488
+00:40:49,920 --> 00:40:55,500
+الآن .. بدنا المجموعة هنا فخلينا برضه نمشي في
+
+489
+00:40:55,500 --> 00:41:03,920
+الهنش فالـ C ايش تقابل؟ 01 او الـ CC او R طبعاً او
+
+490
+00:41:03,920 --> 00:41:08,440
+الـ C في C بتقابل 01 cross 01 أو cross R و هكذا
+
+491
+00:41:09,960 --> 00:41:13,500
+فإذا عشان أثبت أن هذا أصغر منه أو يسوي بدي أثبت
+
+492
+00:41:13,500 --> 00:41:19,180
+أنه 01 أو R تكافئ subset منها واحدة فيهم يا R يا
+
+493
+00:41:19,180 --> 00:41:24,580
+.. كيف .. كيف ممكن تعملوا؟ كيف أخلي الـR تكافئ
+
+494
+00:41:24,580 --> 00:41:30,860
+subset معينة X من R cross الـR؟ الفكرة مرت عليها
+
+495
+00:41:33,010 --> 00:41:38,290
+الـ R عنصر فردي والـ R cross R أزواج مرتبة كيف
+
+496
+00:41:38,290 --> 00:41:41,690
+بضربها في عنصر أحسنتي فهذه نفس الفكرة فالآن طبعا
+
+497
+00:41:41,690 --> 00:41:47,730
+على طول فالآن احنا نشوف ان الـ R تكافئ R بتكافئش
+
+498
+00:41:47,730 --> 00:41:53,190
+نفسها مش subset هي عشان نعمل subset ناخد R ضرب أي
+
+499
+00:41:53,190 --> 00:41:59,430
+عدد وليكن الواحد وهذا subset من مين؟ من R cross R
+
+500
+00:41:59,430 --> 00:42:03,160
+صح؟لأن هذا يشهد كل أزواج الإحداث التابعة للتاني
+
+501
+00:42:03,160 --> 00:42:05,820
+واحد هذا بداخل كل الإحداث التاني واضحة هذه ولا مش
+
+502
+00:42:05,820 --> 00:42:11,080
+واضحة؟ واضحة؟ واضحة ولا لأ؟ واضحة؟ تمام فهذا على
+
+503
+00:42:11,080 --> 00:42:15,660
+طول يقول إن الـC أصغر أو تساوي C في C فهذه السهلة
+
+504
+00:42:15,660 --> 00:42:24,440
+نشوف الاتجاه التاني اللي هو أصعب شوية رقم
+
+505
+00:42:24,440 --> 00:42:33,050
+2 بدنا C في C أصغر أو تساوي Cفالآن بدأنا نتدور على
+
+506
+00:42:33,050 --> 00:42:44,890
+أن R cross R تكافئ X subset من R أو
+
+507
+00:42:44,890 --> 00:42:51,530
+طبعاً 0101 اللي أسهلنا ايش ممكن نعمل؟ أفكار سابقة
+
+508
+00:42:51,530 --> 00:42:56,730
+أه ممكن ألاجي X مش بسهولة العملية أنا تكافئها، أنا
+
+509
+00:42:56,730 --> 00:43:00,470
+مانفعش ان انا أداري cross R، هذه كانت سهلةطبعا
+
+510
+00:43:00,470 --> 00:43:06,490
+subset .. آسف ممكن نعمل trick مشهور بدل ما ادور
+
+511
+00:43:06,490 --> 00:43:09,490
+على المجموعة و ال byjection ايش اعمل اجيب دلّة one
+
+512
+00:43:09,490 --> 00:43:13,370
+to one فبدل ما ادور على X و byjection اجيب دلّة من
+
+513
+00:43:13,370 --> 00:43:17,210
+R cross ال R لمجموعة تكون و هي subset من R فانا
+
+514
+00:43:17,210 --> 00:43:21,430
+بدأ أدور انها تكون من R cross R ل R او أسهل اللي
+
+515
+00:43:21,430 --> 00:43:30,550
+هاخد 01 01 أسهل فالان هنعرف دلّة let Fمن 01 نقرص
+
+516
+00:43:30,550 --> 00:43:36,390
+01 إلى 01 يعني الأن أنا بدي أبدلهم بدي أعمل 01
+
+517
+00:43:36,390 --> 00:43:43,390
+نقرص 01 to كافق مجموعة subset من 01 فهأاخد دالة
+
+518
+00:43:43,390 --> 00:43:48,510
+one to one هنعمل trick بسيط إيش العناصر اللي هان؟
+
+519
+00:43:48,510 --> 00:43:51,430
+ليش أنا أخد 01؟ عشان العناصر المعروفة 0 boy و 0
+
+520
+00:43:51,430 --> 00:43:55,910
+boy فهناخد given by let F be given
+
+521
+00:43:58,700 --> 00:44:04,200
+by f of كيف الإحداث طبعا هدا يكون زوج مرتب واحد
+
+522
+00:44:04,200 --> 00:44:07,900
+هنا و واحد هنا هدا x و واحد و y كيف بكتبه؟ zero
+
+523
+00:44:07,900 --> 00:44:14,100
+point a واحد او x واحد كله a واحد a اتنين و هكذا
+
+524
+00:44:14,100 --> 00:44:23,260
+فاصلة zero point b واحد b اتنين و هكذا بديها يصير
+
+525
+00:44:23,260 --> 00:44:28,690
+أنصر بزي ما هو زوج مرتب بديها يصير أنصر واحدوبدي
+
+526
+00:44:28,690 --> 00:44:34,190
+يعني يكون بس الدالة one to one فإذا
+
+527
+00:44:34,190 --> 00:44:38,090
+إيش ديكون؟ Zero point صح؟ لأنه بيكون ب zero one
+
+528
+00:44:38,090 --> 00:44:43,470
+برضهلأ لإن بديها تكون subset تكافئ بس subset لل
+
+529
+00:44:43,470 --> 00:44:47,470
+image و خلاص لإن بديش هي تكافئها تكافئ subset منها
+
+530
+00:44:47,470 --> 00:44:52,290
+فيكفي بديها تكون one to one هنعمل trick بسيط عشان
+
+531
+00:44:52,290 --> 00:44:54,850
+أضمن انه one to one ايش اعمل؟ طبعا هدول بنفعل عشان
+
+532
+00:44:54,850 --> 00:44:57,950
+احط واحد و احط التاني وراها لإنه بنتهيش لكن ممكن
+
+533
+00:44:57,950 --> 00:45:06,060
+اعمل بالشكل التالي A1 B1 A2 B2 و هكذاخُد الخانة
+
+534
+00:45:06,060 --> 00:45:07,880
+الأولى وبعدين الخانة الأولى من التانى الخانة
+
+535
+00:45:07,880 --> 00:45:10,500
+التانية من الأول الخانة التانية من التانى وهكذا
+
+536
+00:45:10,500 --> 00:45:13,280
+فصار عدد بدل ما هو كان عدد يعني كيف على سبيل
+
+537
+00:45:13,280 --> 00:45:22,480
+المثال لو قلنا لكم ما هي صورة F 0.1 2 0.351 مثلا
+
+538
+00:45:22,480 --> 00:45:27,180
+ايش بتساوي هذه 0.13251
+
+539
+00:45:27,180 --> 00:45:32,600
+على طول وضحت وضحت الفكرة بديت اخد الخانة الأولى من
+
+540
+00:45:32,600 --> 00:45:36,650
+هنابعدين الخانة الأولى من هنا الخانة التانية
+
+541
+00:45:36,650 --> 00:45:39,030
+الخانة التانية مافيش خانة تانية انا المفروض أحط
+
+542
+00:45:39,030 --> 00:45:42,110
+صفر هنا حقيقة صفر لأنه فيه صفر و خمسة و بعدين
+
+543
+00:45:42,110 --> 00:45:47,010
+البرجين أصفر اه فاك بس في أي الصورة ال zero جاب لل
+
+544
+00:45:47,010 --> 00:45:52,550
+واحد اه صحيح صح صح مظموم يعني احنا أخدنا واحد
+
+545
+00:45:52,550 --> 00:45:59,210
+تلاتة اتنين خمسة zero واحد صحوهكذا فواضحة الفكرة
+
+546
+00:45:59,210 --> 00:46:02,770
+فهذه الفكرة طبعا ممكن أفكر لو أعملت عملية مثلا
+
+547
+00:46:02,770 --> 00:46:06,170
+أضربهم في بعض يعني أضرب الأحداث الأول مع التاني
+
+548
+00:46:06,170 --> 00:46:09,810
+بطلع عدد نفس لكن هل بتتمها one to one يمكن ما تمش
+
+549
+00:46:09,810 --> 00:46:13,010
+one to one بس هذي one to one فهذه الدالة one to
+
+550
+00:46:13,010 --> 00:46:19,870
+one then F is one to one وهذا يؤدي مثلا ال one to
+
+551
+00:46:19,870 --> 00:46:25,350
+one إيش صار؟ Zero one المجال إيش ما له يكافئ من؟
+
+552
+00:46:25,350 --> 00:46:33,280
+ال image0 1 ضرب 0 1 و ال image subset من المجال
+
+553
+00:46:33,280 --> 00:46:38,080
+المقابل ال trick نفسه فال cardinality لهذه ليه c
+
+554
+00:46:38,080 --> 00:46:42,360
+times c أقل من cardinality لهذه ليه yes طبعا واحد
+
+555
+00:46:42,360 --> 00:46:48,820
+و اتنين اه انا مرقمهم اه واحد و اتنين implies c في
+
+556
+00:46:48,820 --> 00:46:53,900
+c تساوي cفطبعا هذه احنا بنعتمد انها تكون one to
+
+557
+00:46:53,900 --> 00:46:58,440
+one لانه هيطلع الصورة تساوي الصورة فوش بيكونوا
+
+558
+00:46:58,440 --> 00:47:01,220
+لازم كل خانة تساوي خانة اللي حاكناه في ايش في
+
+559
+00:47:01,220 --> 00:47:05,160
+نهاية chapter 5 في 5 أربع لما نقول لو أخدنا كمان
+
+560
+00:47:05,160 --> 00:47:11,240
+عنصرين مثلا X1 X2 و Y1 Y2 هنقارن هيصير كل خانة
+
+561
+00:47:11,240 --> 00:47:14,880
+تساوي خانة فبطلع كلهم متساوي فنوقف هنا ان شاء الله
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/vDx9po02VSA_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/vDx9po02VSA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c910d7664aa17d2a468dbf9ae1576dbaa67e0bfc
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/vDx9po02VSA_postprocess.srt
@@ -0,0 +1,2788 @@
+1
+00:00:19,670 --> 00:00:23,330
+إن شاء الله اليوم هنكمل جزء بسيط بتعلق بالدوال
+
+2
+00:00:23,330 --> 00:00:27,770
+وبشكل خاص اللي هو تركيب الدوال composition وإن شاء
+
+3
+00:00:27,770 --> 00:00:30,690
+الله هنبدأ في chapter خمسة اللي هو هتحدث فيه عن
+
+4
+00:00:30,690 --> 00:00:32,810
+اللي هو denominable and non-denominable sets
+
+5
+00:00:32,810 --> 00:00:35,870
+المجموعات القابلة للعد والمجموعات غير القابلة للعد
+
+6
+00:00:35,870 --> 00:00:39,050
+طبعا حسب الوقت ما يسمع طبعا في المحاضرة الأخيرة
+
+7
+00:00:39,050 --> 00:00:43,250
+كنا شفنا هذا التعريفكيف بنعمل اللي هو تركيب من
+
+8
+00:00:43,250 --> 00:00:48,070
+دالتين طبعا الشرط أن يكون المجال المقابل للأولى هو
+
+9
+00:00:48,070 --> 00:00:51,590
+مجال التانية و بنعمل عملية ال composition فبتصيب
+
+10
+00:00:51,590 --> 00:00:54,950
+دالة من المجال الأولى إلى المجال المقابل للتانية
+
+11
+00:00:54,950 --> 00:00:59,930
+أو الأخيرة والتعريف بتبقى بتبقى نطبق من الأقرب لل
+
+12
+00:00:59,930 --> 00:01:05,970
+X ف G circle F of X تساوي G of F of Xبنبدأ نطبق من
+
+13
+00:01:05,970 --> 00:01:08,970
+الأقرب لل X فعشان ذلك نكتب ال F بالأول رغم أنه هي
+
+14
+00:01:08,970 --> 00:01:12,570
+ايش .. طبعا نكتبها بالأول من اليمين عشان هي أقرب
+
+15
+00:01:12,570 --> 00:01:17,290
+لل X هي أقرب لل X طبعا شفنا كملاحظة بالمثال أن
+
+16
+00:01:17,290 --> 00:01:21,270
+عملية ال composition ليس إبدالية ليست إبدالية
+
+17
+00:01:21,270 --> 00:01:24,670
+فالترتيب مهم جدا لكن في لها خاصية مهمة بتتحمل
+
+18
+00:01:24,670 --> 00:01:27,510
+تعفية وهي خاصية التجميع فهي associative
+
+19
+00:01:27,510 --> 00:01:30,350
+associative فحن نثبت هذا الخاصية ف ال composition
+
+20
+00:01:30,350 --> 00:01:34,090
+is associativeأه فطبعا بيقول لي function
+
+21
+00:01:34,090 --> 00:01:38,110
+composition is associative that is إذا كانت ال F
+
+22
+00:01:38,110 --> 00:01:41,210
+دالة من X ل Y بدنا ناخد دلت دوال الآن عشان العملية
+
+23
+00:01:41,210 --> 00:01:44,810
+هي عرفناها على دالتين طب لو نتعامل مع تلت دوال
+
+24
+00:01:44,810 --> 00:01:48,090
+بنفع، بنفع، طب كيف بده أحسب؟ ممكن أحسب الأولى مع
+
+25
+00:01:48,090 --> 00:01:51,150
+التانية و بقى الناتج مع التالتة أو العكس، التانية
+
+26
+00:01:51,150 --> 00:01:53,670
+مع التالتة و الناتج مع الأولى، كله صح، فبيقول لي
+
+27
+00:01:53,670 --> 00:01:58,000
+أندي ال Fمن X ل Y الـ G بتكمل من Y ل Z و الـ H
+
+28
+00:01:58,000 --> 00:02:02,500
+بتكمل من Z ل W فبصير عندي composition جالي تحسبهم
+
+29
+00:02:02,500 --> 00:02:06,360
+بالترتيب التالي اللي هو الأخيرة مع التانية بعدين
+
+30
+00:02:06,360 --> 00:02:09,280
+النتيجة مع الأولى أو الأولى مع التانية بعدين
+
+31
+00:02:09,280 --> 00:02:12,360
+النتيجة مع الأخيرة كله صح بتديني نفس القيمة فحنشوف
+
+32
+00:02:12,360 --> 00:02:18,580
+البرهان مع بعض فطبعا
+
+33
+00:02:18,580 --> 00:02:21,420
+بعض التعليقات و بعدين نشوف كيف البرهان بالتفصيل
+
+34
+00:02:21,420 --> 00:02:31,290
+فهذه نظريةتلاتة خمس عشر طبعا لو طلعنا احنا ايش مع
+
+35
+00:02:31,290 --> 00:02:36,770
+معطق؟ انه كل هذا معطيات وجواب الشرط في الجملة if
+
+36
+00:02:36,770 --> 00:02:40,110
+then مطلوب نثبت انه دالتين متساويتين فاحنا فيها
+
+37
+00:02:40,110 --> 00:02:43,650
+علاقة التساوي على الطرف اليسار في دوال وعلى الطرف
+
+38
+00:02:43,650 --> 00:02:47,630
+اليمين في دوال بدنا نثبت دالتين متساويتين فلو
+
+39
+00:02:47,630 --> 00:02:50,150
+سألنا نفسنا كيف ممكن نثبت انه دالتين متساويتين
+
+40
+00:02:53,320 --> 00:02:57,320
+ممكن كمجموعات نعملهم كعلاقات وكمجموعات، هذه هو
+
+41
+00:02:57,320 --> 00:03:00,560
+التعريف الأصلي، نرجحها لأصلها، كل function هي
+
+42
+00:03:00,560 --> 00:03:03,620
+relation وكل relation هي مجموعة من الأزواج
+
+43
+00:03:03,620 --> 00:03:08,030
+المرتبة، هذه طريقةأو في عندنا نظرية في طريقة أخرى
+
+44
+00:03:08,030 --> 00:03:12,510
+في نظرية تلاتة سبعة بتقول لي عشان تساوي الدوال فيه
+
+45
+00:03:12,510 --> 00:03:16,870
+شرطين الشرط الأول يكونوا بين نفس المجموعتين وشرط
+
+46
+00:03:16,870 --> 00:03:19,870
+التاني أن صورهم يتساوي على جميع نصر الدمين فاحنا
+
+47
+00:03:19,870 --> 00:03:22,570
+في عندنا التعريف الأصلي أنه أعملهم ك relations
+
+48
+00:03:22,570 --> 00:03:25,710
+يعني مجموعات من الأزواج المرتبة أو أستخدم نظرية
+
+49
+00:03:25,710 --> 00:03:28,390
+تلاتة سبعة احنا هنستخدم النظرية لأن نظرية تعبنا
+
+50
+00:03:28,390 --> 00:03:30,970
+عليها وبرهنها هنستفيد منها ليش أن أهيد البرهان
+
+51
+00:03:30,970 --> 00:03:33,450
+تبعها مرة تانية لأنه بدرجة على الأصل فاحنا نستخدم
+
+52
+00:03:33,450 --> 00:03:42,660
+النظريةتلاتة سبعة فهنا prove we will use theorem
+
+53
+00:03:44,270 --> 00:03:47,510
+تلاتة سبعة طبعا تلاتة سبعاش بتقول اللي بتقول لو في
+
+54
+00:03:47,510 --> 00:03:51,150
+دلتين من X ل Y الدلتين الأولى من X ل Y والتانية من
+
+55
+00:03:51,150 --> 00:03:55,850
+X ل Y فبكونوا الدلتين متساويتين if and only if كل
+
+56
+00:03:55,850 --> 00:03:58,490
+عناصر ال domain صور متساوية فاحنا نثبت هذا الكلام
+
+57
+00:03:58,490 --> 00:04:02,350
+فطبعا أول شي بتثبت أن هم دول الدلتين اللي مدينياهم
+
+58
+00:04:02,350 --> 00:04:05,590
+هم من نفس المجموعة لنفس المجموعة اللي هم نفس
+
+59
+00:04:05,590 --> 00:04:09,150
+المجال و اللي هم نفس المجال المقابل خلينا نشوف كيف
+
+60
+00:04:09,150 --> 00:04:14,560
+الصورةطبعا إيش معنات الـ circles هذه؟ في الأولى
+
+61
+00:04:14,560 --> 00:04:18,600
+هنا بيقولّي احسب H Circle G أولا، مظبوط؟ احنا إيش
+
+62
+00:04:18,600 --> 00:04:24,660
+الصورة الكلية عندنا؟ عندنا هي عندنا اللي هو X و هي
+
+63
+00:04:24,660 --> 00:04:29,540
+عندنا Y و هي عندنا Z و هي عندنا W ال F بتشتغل من
+
+64
+00:04:29,540 --> 00:04:34,160
+hand ل hand بعدين G بتكمل العمل و بعدين H بتكمل
+
+65
+00:04:34,160 --> 00:04:39,160
+العملفلو بدأت من الطرف الأول انا عندي اللي هو h
+
+66
+00:04:39,160 --> 00:04:44,480
+circle g ان ننسى هذه h circle g من وين لوين بتكون
+
+67
+00:04:44,480 --> 00:04:51,300
+من y ل w من التعريف فهذه function من y ل w وال F
+
+68
+00:04:52,340 --> 00:04:58,000
+دالة من X ل Y طبعاً فهذا مع بعض implies لو عملت
+
+69
+00:04:58,000 --> 00:05:01,800
+composition هذه عملتها مع بعض كعلاقة الأولى إيش
+
+70
+00:05:01,800 --> 00:05:05,440
+بدأ أبدأ أنا من F أول شيء من X ل Y بعدين من Y ل W
+
+71
+00:05:05,440 --> 00:05:06,940
+إيش بيصيح ال composition اللي التاني تاني دول مع
+
+72
+00:05:06,940 --> 00:05:14,100
+بعض من X ل W فهذا بيقول لي H circle G كعلاقة واحدة
+
+73
+00:05:14,100 --> 00:05:18,020
+كقطعة واحدة بدي أخدهم مع ال F هم function من وين ل
+
+74
+00:05:18,020 --> 00:05:23,640
+وين من X ل Wبس مجرد قراعة احنا ممكن نحكي الكلام
+
+75
+00:05:23,640 --> 00:05:28,260
+بشكل مختصر بس خليني انا اوضح بعدين هذه الأولى اه
+
+76
+00:05:28,260 --> 00:05:32,940
+بعدين في الطرف اليمين احنا نبدأ G Circle F أولا G
+
+77
+00:05:32,940 --> 00:05:39,180
+Circle F ده اللي من وين لوين من X ل Z صح؟والـ H هي
+
+78
+00:05:39,180 --> 00:05:43,660
+ده اللي من و لا وين من Z ل W لما أعمل composition
+
+79
+00:05:43,660 --> 00:05:48,760
+معهم اللي وجهي circle F أولا بعدين H بيصير من و لا
+
+80
+00:05:48,760 --> 00:05:51,640
+وين الأولى من وين من X ل Z و من Z ل W إيش بيصير
+
+81
+00:05:51,640 --> 00:05:54,920
+برضه من X ل W برضه من X ل W
+
+82
+00:05:57,900 --> 00:06:02,000
+طبعاً هذا الكلام الصورة اللي فوق واضح أنا بدأت من
+
+83
+00:06:02,000 --> 00:06:06,820
+X أول خطوة نقلت على ال Y في الخطوة التانية نقلت
+
+84
+00:06:06,820 --> 00:06:09,540
+على ال Z و بعدين نقلت على ال W فكانت العملية
+
+85
+00:06:09,540 --> 00:06:14,500
+الكلية هي من X ل W واضح هذا الكلاملكن انا ايش
+
+86
+00:06:14,500 --> 00:06:18,320
+الكتبته هنا كتبته بدي اشوف كيف بنفسر الطرفين في
+
+87
+00:06:18,320 --> 00:06:22,760
+الطرف الأول هنا بنبدأ نحسب H circle G بعدين
+
+88
+00:06:22,760 --> 00:06:26,100
+بنحسبلها ال F صح؟ هيك معناه الأقواص معناه الأقواص
+
+89
+00:06:26,100 --> 00:06:29,560
+فإذا انا هوش بدي أدرس هذه بعدين أجيب أضيفلها F هنا
+
+90
+00:06:29,560 --> 00:06:34,800
+العكسبدأ أبدأ من حساب F Circle G، بعدين إنها تجمعه
+
+91
+00:06:34,800 --> 00:06:37,860
+H، فيك ما تصير العملية، فإذا أول شرط في نظرية أنه
+
+92
+00:06:37,860 --> 00:06:41,840
+يكون هما كمجموعتين اللي هم نفس ال domain و اللي هم
+
+93
+00:06:41,840 --> 00:06:44,860
+نفس المجال المقابل، و اللي هم نفس مين اللي هو ال
+
+94
+00:06:44,860 --> 00:06:47,700
+range بمصطلحنا، اه فاللي هم نفس المجال و نفس
+
+95
+00:06:47,700 --> 00:06:50,520
+المجال المقابل، فده الشرط الأول، الشرط التاني
+
+96
+00:06:50,520 --> 00:06:53,820
+لجميع عناصر ال domain المشترك اللي هو X، صورهم
+
+97
+00:06:53,820 --> 00:06:56,460
+متساوية بدنا نثبت، فاحنا ناخد عنصر في ال domain،
+
+98
+00:06:56,460 --> 00:07:02,530
+فده الشرط الأولالان let X be any element in X
+
+99
+00:07:02,530 --> 00:07:13,370
+بتثبت ان صورهم متساوية ممكن نكتب مع بعض we want to
+
+100
+00:07:13,370 --> 00:07:18,370
+show that
+
+101
+00:07:19,930 --> 00:07:29,010
+G Circle F Circle H الطرف اليسار of X يساوي صورهم
+
+102
+00:07:29,010 --> 00:07:35,030
+H Circle G Circle F of X هذا هو المطلوب، هيك
+
+103
+00:07:35,030 --> 00:07:38,550
+معناته، في شرطين، عشان الدالتين يتساووا، النظرية
+
+104
+00:07:38,550 --> 00:07:43,700
+بتقوللازم كلهم نفس المجال اللي هو X في هذه النظرية
+
+105
+00:07:43,700 --> 00:07:46,980
+ونفس المجال المقابل اللي هو W في هذه النظرية هذا
+
+106
+00:07:46,980 --> 00:07:50,500
+الشرط الأول الشرط التاني لجميع عناصر ال domain
+
+107
+00:07:50,500 --> 00:07:54,860
+المشترك صورهم متساوي بينا نثبت الشرط التاني تمام
+
+108
+00:07:54,860 --> 00:07:58,600
+طبعا تساوي قيم هدولة هدولة عبارة عن قيم لأن صور
+
+109
+00:07:58,600 --> 00:08:02,520
+صور عند ال X عشان أثبتهم في طريقتين يبدأ ببدأ من
+
+110
+00:08:02,520 --> 00:08:06,100
+طرف بوصل للطرف التاني أو بوصل التنين لإيش نقطة
+
+111
+00:08:06,100 --> 00:08:09,380
+مشتركة لمقدار مشتركة احنا هنعمل الحالة التانية
+
+112
+00:08:09,570 --> 00:08:16,230
+فنبدأ من الطرف الأول now it's circle G مع بعض
+
+113
+00:08:16,230 --> 00:08:22,900
+circle F of Xإيش بتساوي؟ كيف تقرأ هذه؟ تقرأ إنه
+
+114
+00:08:22,900 --> 00:08:25,480
+هذه كتلة و هذه كتلة كال لو في عندنا دالتين لإنه
+
+115
+00:08:25,480 --> 00:08:30,580
+العصر العملية معرفة على دالتين عملية ثنائية ممكن
+
+116
+00:08:30,580 --> 00:08:34,580
+نسميها فهنا هتكون هذه لو سميناها مثلا هذه اللي هي
+
+117
+00:08:34,580 --> 00:08:39,000
+Alpha وهذه Beta إيش بيصير؟ Alpha of و Beta of X
+
+118
+00:08:39,000 --> 00:08:43,760
+فهذه عبارة عن هذه كتلة واحدة H circle G كتلة of F
+
+119
+00:08:43,760 --> 00:08:47,170
+of Xهيك التعريف لأن هذه كتلة واحدة مع بعض بيقول ال
+
+120
+00:08:47,170 --> 00:08:50,410
+ghost هدول بيمشوا مع بعض هيك التعريف الأول هي طبقت
+
+121
+00:08:50,410 --> 00:08:54,650
+مين ال circle الأولى طيب الآننفتح الـ Circle
+
+122
+00:08:54,650 --> 00:08:57,890
+التاني، نفسر هذه، إيش معناته؟ نستنسى، كانوا عنصر A
+
+123
+00:08:57,890 --> 00:09:01,770
+نسميه، فإيش عادي عبارة عن مين؟ عبارة عن H of G و
+
+124
+00:09:01,770 --> 00:09:07,970
+الـ A هذه، وتساوي H of G F of X، فهذا إيش الجزء
+
+125
+00:09:07,970 --> 00:09:10,570
+الأول، فهذا الطرف الأول، طبعا بدل ما أرجع عادي
+
+126
+00:09:10,570 --> 00:09:12,810
+فيها أرجوع، بدي أجيب التاني، أسهل، لأنه بعرف أن
+
+127
+00:09:12,810 --> 00:09:17,470
+أنا أفك F Circle G من التعريف، أجيب الطرف التاني،
+
+128
+00:09:17,470 --> 00:09:25,230
+H Circle G Circle F of Xماذا تعني بعامل هذه كتلة
+
+129
+00:09:25,230 --> 00:09:30,790
+واحدة وهادي H عبارة عن H of G circle F of X هيك
+
+130
+00:09:30,790 --> 00:09:35,150
+تفسيرها هيك معناه الأقواص واضح في الأمر يعني حيانا
+
+131
+00:09:35,150 --> 00:09:37,270
+في بعض الناس بيقول إيش بنعمل وإيش وإيش وإيش وإيش
+
+132
+00:09:37,270 --> 00:09:38,270
+وإيش وإيش وإيش وإيش وإيش وإيش وإيش وإيش وإيش وإيش
+
+133
+00:09:38,270 --> 00:09:38,430
+وإيش وإيش وإيش وإيش وإيش وإيش وإيش وإيش وإيش وإيش
+
+134
+00:09:38,430 --> 00:09:42,070
+وإيش وإيش وإيش وإيش وإيش وإيش وإيش وإيش وإيش وإيش
+
+135
+00:09:42,070 --> 00:09:50,330
+وإيش وإيش وإيش وإ
+
+136
+00:09:52,340 --> 00:09:56,920
+G F of X من التعريف طب هل هدولة التنين متساويين
+
+137
+00:09:56,920 --> 00:10:02,320
+نعم فالتنتين نفس المقدار فإذا واحد واتنين implies
+
+138
+00:10:02,320 --> 00:10:10,220
+H circle G circle F لل X تساوي H circle G circle F
+
+139
+00:10:10,220 --> 00:10:15,980
+لل X فالان هذه الخطوة و هذه الخطوة مع بعض باستخدام
+
+140
+00:10:15,980 --> 00:10:19,340
+نظرية بقول ان دالتين متساويين therefore
+
+141
+00:10:22,230 --> 00:10:26,610
+by theorem ممكن ترجعولها تلاتة سابعة أيش بتقول
+
+142
+00:10:26,610 --> 00:10:31,810
+عندنا الدالة تانية متساوية تانية H circle G circle
+
+143
+00:10:31,810 --> 00:10:35,130
+F كدالة مش قيمة احنا اثبتنا تساوي القيم تساوي
+
+144
+00:10:35,130 --> 00:10:40,300
+الدالة التانية التي هي H circle G circle Fفإذا
+
+145
+00:10:40,300 --> 00:10:43,080
+إحنا لما يكونوا تلت دوال وبدي أعمل بينهم circle
+
+146
+00:10:43,080 --> 00:10:46,320
+اللي بدي يا باخد كل تنتين مع بعض بدأت من الأولى و
+
+147
+00:10:46,320 --> 00:10:48,820
+التانية و بعدين التالتة أو من التانية و التالتة و
+
+148
+00:10:48,820 --> 00:10:52,140
+بعدين الأولى كله صح خاصية التجميع فدائما زي ما
+
+149
+00:10:52,140 --> 00:10:57,320
+حكيتك قبل هيك دائما خاصية التجميع هي الباب إن أعمم
+
+150
+00:10:57,320 --> 00:11:00,700
+عملية من عملية ثنائية تنطبق على أكتر من اتنين هي
+
+151
+00:11:00,700 --> 00:11:03,420
+أعرفنا احنا ال circle على دلتين الآن بقدر أتعرف
+
+152
+00:11:03,420 --> 00:11:06,380
+على تلت دوال و أربعة و خمسة و هكذا لأنه من خاصية
+
+153
+00:11:06,380 --> 00:11:12,510
+التجميعفي أي استفسار واضح فأرجو البروحان صحيح جدا
+
+154
+00:11:12,510 --> 00:11:15,590
+بس ننتبه لن نطفئ النقطة التقنية اللي عملتها انا
+
+155
+00:11:15,590 --> 00:11:17,850
+هذه لأن لو كان في operation وانت مش عارفين انها
+
+156
+00:11:17,850 --> 00:11:20,590
+كيف تستغلوا معها بتكون انت عامله بهذا الشكل نعمل
+
+157
+00:11:20,590 --> 00:11:25,790
+بهذا الصورةتمام نظرية أخيرة في هذا الـ chapter
+
+158
+00:11:25,790 --> 00:11:30,130
+criterion for injection and surjection معيار احنا
+
+159
+00:11:30,130 --> 00:11:32,730
+عندنا تعريف دايما احنا في الرياضيات اللي بنعمل في
+
+160
+00:11:32,730 --> 00:11:35,990
+عندنا مصطلح معين مفهوم معين في عندنا تعريف و أحيان
+
+161
+00:11:35,990 --> 00:11:38,290
+بيكون في عندنا طريقة أخرى زي ما تاول شفنا تساوي
+
+162
+00:11:38,290 --> 00:11:42,450
+الدوال بنرجعله cash كمجموعات من الأزواج المرتبةطب
+
+163
+00:11:42,450 --> 00:11:45,810
+وفي عين النظرية ادتنا طريقة أخرى بديلة فالآن بده
+
+164
+00:11:45,810 --> 00:11:48,390
+يديني طريقة بديلة كيف أثبت أن الدالة one to one أو
+
+165
+00:11:48,390 --> 00:11:51,150
+أنت غير التعريف بده يديني فهذا معيار كيف وقت إيش
+
+166
+00:11:51,150 --> 00:11:54,010
+الدالة بتكون one to one ووقت إيش بتكون أنت ما هو
+
+167
+00:11:54,010 --> 00:11:57,390
+المعيار لو انت تحقق ما هو الشرط إذا تحقق أصبحت
+
+168
+00:11:57,390 --> 00:11:59,970
+الدالة one to one غير التعريف بده يديني طريقة أخرى
+
+169
+00:11:59,970 --> 00:12:03,190
+غير التعريف طبعا بدأ بدالة طبعا لما بتحدث عن one
+
+170
+00:12:03,190 --> 00:12:06,030
+to one أن أنت بتحدث عن مين عن دوال ماينفعش يقول
+
+171
+00:12:06,030 --> 00:12:09,040
+علاقة one to oneلازم يكون دال، فماحنا نتحدث عن
+
+172
+00:12:09,040 --> 00:12:12,620
+دالة تكون injection أو تكون surjective، لكن إيه
+
+173
+00:12:12,620 --> 00:12:16,360
+غير الدوال، ما بنتحدث عن هذا المصطلح، فإذا بدأ بـ
+
+174
+00:12:16,360 --> 00:12:23,920
+function، هذه كمقدمة أساسية، أول شيء إيه؟بقول هناك
+
+175
+00:12:23,920 --> 00:12:28,900
+if there exists a function g من y إلى x دالة
+
+176
+00:12:28,900 --> 00:12:34,200
+بالاتجاه العكسي من y إلى x such that g circle f
+
+177
+00:12:34,200 --> 00:12:40,780
+تساوي I sub x مين الرمز الجديد هذا بقول where I
+
+178
+00:12:40,780 --> 00:12:44,430
+sub xهي عبارة عن function من X ل X ما لهذه الـ
+
+179
+00:12:44,430 --> 00:12:47,230
+function؟ هي الدالة المحايدة الـ identity function
+
+180
+00:12:47,230 --> 00:12:50,590
+on X الدالة المحايدة على الـ X إيش يعني؟ هي دالة
+
+181
+00:12:50,590 --> 00:12:53,590
+من X ل X بتاخدوا عنصر ويبقوا يتوديوا لنفسهم دالة
+
+182
+00:12:53,590 --> 00:12:56,070
+محايدة لإن انت عملش في إيش، محايدة، انت عملش إيش،
+
+183
+00:12:56,070 --> 00:13:02,330
+إذا نبادل الشكل، اه then F is injectiveعشان تثبت
+
+184
+00:13:02,330 --> 00:13:05,830
+ان الدالة injective بدل ما تستخدم التعريف هاي بديل
+
+185
+00:13:05,830 --> 00:13:08,610
+بس مش عارف مين أصل هو التعريف بنشوفه بعدها بقولي
+
+186
+00:13:08,610 --> 00:13:15,450
+بدك تراجع دالة G من Y ل X عكس من المجال المقابللأ
+
+187
+00:13:15,450 --> 00:13:18,730
+المجال إيش شرط الدالة؟ أي دالة بنفعلها؟ إيش
+
+188
+00:13:18,730 --> 00:13:22,890
+معناها؟ بحيث إن الـ G circle F بتساوي الدالة
+
+189
+00:13:22,890 --> 00:13:26,170
+المحايدة على ال domain الأصلي على ال X و أضيح هذا
+
+190
+00:13:26,170 --> 00:13:29,570
+المعيار إذا أنا بدل ما أثبت إنه لكل عنصرين في ال
+
+191
+00:13:29,570 --> 00:13:32,310
+domain صورهم متساوية لازم يتساووا هذا التعريف
+
+192
+00:13:32,310 --> 00:13:35,690
+مصبوط أه في عندي ميارة إيش البديل؟ أدور على دالة G
+
+193
+00:13:35,690 --> 00:13:40,650
+من Y ل X وتخلي G circle F تساوي I ل X فهذا هو إيش
+
+194
+00:13:40,650 --> 00:13:44,550
+البديل مين أسهل؟ خلّيني أجهل هذا السؤال شوية طيب B
+
+195
+00:13:45,840 --> 00:13:49,220
+فهذا معيار، هذا بديل كيف F بتدلل 1 to 1 بطريقة غير
+
+196
+00:13:49,220 --> 00:13:53,040
+التعريف طب on to إيش on to؟ حاجة مشابهة، بقول لي
+
+197
+00:13:53,040 --> 00:13:57,100
+if there exists a function H برضه من Y ل X طب إيش
+
+198
+00:13:57,100 --> 00:14:01,340
+شرطها؟ شرطها إن F circle الـH، لأن الترتيب اختلف،
+
+199
+00:14:01,340 --> 00:14:05,140
+اه الترتيب اختلف، اه لإن هناك إيش بدأ؟ بدأ من F، F
+
+200
+00:14:05,140 --> 00:14:09,880
+من X ل Y، بعدين G كملت من Y ل X، فرجع بصارت H
+
+201
+00:14:09,880 --> 00:14:15,870
+الأولى، من X ل X، احنا كيف الصورة؟ هي Xوهي Y وهي X
+
+202
+00:14:15,870 --> 00:14:21,470
+بدأنا هنا من وين؟ F بعدين هنا إيش؟ G أه كله صار من
+
+203
+00:14:21,470 --> 00:14:26,990
+X لX اللي يمين I X اللي هي I X واضحة؟ Identical من
+
+204
+00:14:26,990 --> 00:14:31,510
+X لX هنا نفس الدوال بس هيختلف الأمر هنا برضه بدأ
+
+205
+00:14:31,510 --> 00:14:35,610
+من X وفي عندنا لأ مش هيبدأ من X هيبدأ من Y الآن
+
+206
+00:14:37,060 --> 00:14:41,460
+عشان الترتيب اختلف لأنه حط ال H أولا فهي عندنا Y و
+
+207
+00:14:41,460 --> 00:14:45,880
+بعدين عندنا X و عندنا Y كمان مرة فهنا جالي H أولا
+
+208
+00:14:45,880 --> 00:14:49,120
+بعدين الدالة اللي بدرسها ال F صار عند ال
+
+209
+00:14:49,120 --> 00:14:52,860
+composition من وين لوين؟ من Y ل Y، Y sub Y
+
+210
+00:14:52,860 --> 00:14:58,280
+المحايدة على ال Y فإذا كانت H circle F أو F circle
+
+211
+00:14:58,280 --> 00:15:03,450
+H بتساوي المحايدة على ال Y بتكون ال F surjectiveأه
+
+212
+00:15:03,450 --> 00:15:07,070
+فهي ده معيار فطريقة معينة غير اللي هو التعريف إن
+
+213
+00:15:07,070 --> 00:15:10,870
+لو كدرت تلاقي Dal H بهذا الشروط بتكون Dal H on
+
+214
+00:15:10,870 --> 00:15:14,310
+خلينا نشوف البرهان بعدين بنرجع نعلق من أسهل هذا
+
+215
+00:15:14,310 --> 00:15:26,170
+ولا التعريف فهذه
+
+216
+00:15:26,170 --> 00:15:34,060
+نظرية تلاتة ست عش ولا خمس عش ست عش ا proveنبدأ من
+
+217
+00:15:34,060 --> 00:15:39,600
+فرق ايه؟ نبدأ من الفرق الأول اه طبعا جملة شرطية
+
+218
+00:15:39,600 --> 00:15:44,200
+انا طبعا ال F ده فوق معطلة لكل ل A و B فده دايما
+
+219
+00:15:44,200 --> 00:15:47,240
+صح اللي هو ال F ده ل من X ل Y بس function مافيش
+
+220
+00:15:47,240 --> 00:15:50,180
+ولا إيش معطل انها function اه بقول if they exist
+
+221
+00:15:50,180 --> 00:15:52,900
+إذا إحنا إيش بدنا نثبت إنه هنا فيها معطلة معطلة
+
+222
+00:15:52,900 --> 00:15:57,050
+فهنقول له إيش assumeالشرط صحيح، شايفين؟ المبادئ ما
+
+223
+00:15:57,050 --> 00:16:02,150
+بتتغيرش Assume there exists a function G من وين
+
+224
+00:16:02,150 --> 00:16:07,650
+لوين، من Y لX إيش مالها؟ Such that كل واحدة معطلة،
+
+225
+00:16:07,650 --> 00:16:11,310
+لأن هذا الشرط صار، لأن هذا شرط الجملة الشرطية Such
+
+226
+00:16:11,310 --> 00:16:18,390
+that G circle F تساوي I لXطبعا ما بديش افسر اي
+
+227
+00:16:18,390 --> 00:16:25,070
+مفصرة قدامك لأن هذا كله شرط الجملة الشرطية a is a
+
+228
+00:16:25,070 --> 00:16:28,690
+then وين جواب الشرط بعد then f is injective بنا
+
+229
+00:16:28,690 --> 00:16:35,070
+نثبت ان f is injective خليني اكتب we want to prove
+
+230
+00:16:35,070 --> 00:16:42,900
+f is one to one اختصرفهي فرع ا كتبناها فرع اش
+
+231
+00:16:42,900 --> 00:16:50,360
+بيقول اذا كان يوجد دالة g من y ل x بحيث g circle F
+
+232
+00:16:50,360 --> 00:16:54,060
+تساوي I ال X ال identity بتاع ال X فبتكون ال F one
+
+233
+00:16:54,060 --> 00:16:57,160
+to one اه اذا هذا موقع طبعا هذا مطلوب اش مطلوب
+
+234
+00:16:57,160 --> 00:17:00,630
+اثبت ال F one to oneكي بنثبت one to one؟ ماعناش
+
+235
+00:17:00,630 --> 00:17:02,730
+اللي بتعريف لسه هذه النظرية مش ميدنا لسه بنثبتها
+
+236
+00:17:02,730 --> 00:17:05,530
+بعدين تصير أداة إضافية لنا طيب إيش التعريف بيقول
+
+237
+00:17:05,530 --> 00:17:09,350
+ناخد عنصرين مختلفين من domain مين ال F أنا بدي
+
+238
+00:17:09,350 --> 00:17:11,910
+أسمة مين اللي هو one to one؟ F فبدي عنصرين من
+
+239
+00:17:11,910 --> 00:17:17,870
+domain ال F إيش هقوله؟ let X1 X2 تنتمي لcapital X
+
+240
+00:17:17,870 --> 00:17:24,710
+domain ال F بأسوارهم متساوي such that F of X1
+
+241
+00:17:24,710 --> 00:17:29,310
+تساوي F of X2هذه بداية إثبات الـ one to one و لا
+
+242
+00:17:29,310 --> 00:17:33,390
+لأ بالتعريف، صح؟ متفقين؟ في حد عنده مشكلة في
+
+243
+00:17:33,390 --> 00:17:36,070
+البداية، كيف يثبت one to one؟ بالتعريف؟ أه لأن
+
+244
+00:17:36,070 --> 00:17:38,970
+أصلا عندي بديل، اللي هو النظرية، و بعدين بنتحدث،
+
+245
+00:17:38,970 --> 00:17:43,900
+بنعلق عليهاطيب إيش المطلوب؟ أثبت إن X1 تساوي X2
+
+246
+00:17:43,900 --> 00:17:49,080
+إيش ممكن نعمل؟ هل الدالة معرفة أستخدم التعريف؟ لأ،
+
+247
+00:17:49,080 --> 00:17:52,640
+جالي function، في أمثلة لو كانت معرفة، كان حاطينا
+
+248
+00:17:52,640 --> 00:17:55,700
+التعريف و حاولنا نعمل حسابات و نوصل إن X1 تساوي
+
+249
+00:17:55,700 --> 00:17:59,320
+X2، مش معرفة طيب إذا أين أدور؟ في المعطيار، إيش
+
+250
+00:17:59,320 --> 00:18:04,040
+عندي في المعطيار؟ عندي G دالة موجودة، إذا المعطية،
+
+251
+00:18:04,040 --> 00:18:10,650
+وإيش متحقق؟ G circle F تساوي I Xإيش ممكن أعمل؟ آه،
+
+252
+00:18:10,650 --> 00:18:14,670
+آخد G للطرفين، مش بدي أسفيد؟ آه، إيش معناه الـG
+
+253
+00:18:14,670 --> 00:18:19,210
+circle F؟ ممكن G تتطبق على الـF، آخد G للطرفين،
+
+254
+00:18:19,210 --> 00:18:23,570
+يؤدي، مقدرين متساويين، لازم تكون صورهم متساوية ولا
+
+255
+00:18:23,570 --> 00:18:26,550
+لأ؟ لأنه ده لابتد .. منفعش تحط عناصر متساوية إلى
+
+256
+00:18:26,550 --> 00:18:31,490
+صور مختلفة، فهذا يؤدي إنه G circle .. آسف، مديش
+
+257
+00:18:31,490 --> 00:18:36,830
+أحط الـcircle أولا، مدي أطبق على الطرفينF X1 تساوي
+
+258
+00:18:36,830 --> 00:18:44,180
+G F X2أطبّق الـ G على الطرفين مين خلّاني أطبّق؟ مش
+
+259
+00:18:44,180 --> 00:18:47,900
+سحر، أه ولا فهل لو أشوف بتاني أشتري من المواطع،
+
+260
+00:18:47,900 --> 00:18:52,460
+بتستفيد من المواطع طيب، هذا كيف بيفسره؟ هذا هو الـ
+
+261
+00:18:52,460 --> 00:18:55,220
+I، بس ليش؟ لأنه من أنا أعطه من التعريف فهذا ليس
+
+262
+00:18:55,220 --> 00:19:02,160
+إلا G circle F of X1 تساوي G circle F of X2 من وين
+
+263
+00:19:02,160 --> 00:19:06,240
+جبته هذا؟ تعريف الـ composition، الـ circle تعريف
+
+264
+00:19:06,240 --> 00:19:11,570
+الـ composition طيب، وما هذا ليس إلا Iهذا I ال X
+
+265
+00:19:11,570 --> 00:19:17,210
+of X1 تساوي I ال X لل X2، ليش؟ لأنه جالي G circle
+
+266
+00:19:17,210 --> 00:19:24,030
+F تساوي I ال X طيب،
+
+267
+00:19:24,030 --> 00:19:29,630
+هذا يوصلني للهدف ولا بوصلنيش؟ ليش؟ لأنه ده لمحيط،
+
+268
+00:19:29,630 --> 00:19:37,340
+لأنه ده لمحيطX1 تساوي X2 لأن I X of X تساوي X for
+
+269
+00:19:37,340 --> 00:19:40,680
+all X هي الدالة المحيطة وهو المطلوب فانا بدأت من
+
+270
+00:19:40,680 --> 00:19:44,760
+عنصرين في ال domain صورهم متساوية أثبتت أن عنصرين
+
+271
+00:19:44,760 --> 00:19:49,540
+متساويين فهذا بديل على أن الدالة one to one thus F
+
+272
+00:19:49,540 --> 00:19:55,780
+is one to one وهو المطلوب وهو المطلوب اتبعين؟
+
+273
+00:19:57,140 --> 00:20:03,080
+في أي سؤال؟ أي استفسار؟ آخر خطوة؟ أه هالجهة هذا هو
+
+274
+00:20:03,080 --> 00:20:07,260
+تعريف هذا واضحة هذه؟ طيب احنا إيش قلنا؟ assume هذا
+
+275
+00:20:07,260 --> 00:20:10,560
+معطى there exists G و G circle F إيش بتساوي؟
+
+276
+00:20:10,560 --> 00:20:13,460
+الدالة المحايدة على ال X بدلتها، مقدار بمقدار
+
+277
+00:20:13,460 --> 00:20:17,280
+يسوى، أه تمام؟ طيب إيش معنى الدالة المحايدة؟ إن
+
+278
+00:20:17,280 --> 00:20:20,620
+العنصر بتعمل زي ما هو ف I capital X لل X واحد هي X
+
+279
+00:20:20,620 --> 00:20:24,480
+واحد و لل X اتنين هي X اتنين، واضح؟ أي استفسار؟
+
+280
+00:20:24,920 --> 00:20:31,680
+متبين؟ خلصنا A بي نفس القضية في جملة شرطية هنبدأ
+
+281
+00:20:31,680 --> 00:20:38,120
+نقول له assume there exist a function H من Y ل X
+
+282
+00:20:38,120 --> 00:20:47,200
+such that اه خليكم معايا تابعوا اه ايش بتساوي I
+
+283
+00:20:47,200 --> 00:20:52,750
+sub Yطبعا ال I sub Y تعريف هي الدالة المحايدة على
+
+284
+00:20:52,750 --> 00:20:58,530
+ال Y إيش بدنا نثبت؟ بدنا نثبت إن F is onto We want
+
+285
+00:20:58,530 --> 00:21:08,250
+to show that F is surjective يعني onto إنها on
+
+286
+00:21:08,250 --> 00:21:13,830
+تمامكيف نثبت انها on two؟ هناخد عنصر من المجال
+
+287
+00:21:13,830 --> 00:21:18,410
+المقابل ونثبت انه صورة فمش هيك نثبت فهنقول له let
+
+288
+00:21:18,410 --> 00:21:21,730
+هي دالة من اين نثبت انها on two؟ ال F ال F دالة من
+
+289
+00:21:21,730 --> 00:21:25,670
+و لا وين؟ من X ل Y فناخد عنصر small y في ال
+
+290
+00:21:25,670 --> 00:21:31,190
+capital Yمطلوب أثبت أن Y تساوي F of X نعمل الهامش
+
+291
+00:21:31,190 --> 00:21:37,150
+زي ما اتعودنا بدنا Y تساوي F of X فالسؤال .. إيش
+
+292
+00:21:37,150 --> 00:21:41,730
+السؤال؟ ما هي X بدلالة Y؟ بدنا نحل لل X بدلالة Y
+
+293
+00:21:41,730 --> 00:21:50,850
+بدنا نحل لل X بدلالة Y إيش نعمل في الهامش؟ Inverse
+
+294
+00:21:50,850 --> 00:21:54,650
+ومش عرفت إنها Inverse قالت بيجيكشن قالت ده لأ في
+
+295
+00:21:54,650 --> 00:22:00,200
+ال .. ده لأ في .. بلا إي سؤالمين عنده فكرة نعمل
+
+296
+00:22:00,200 --> 00:22:03,820
+نفس الفكرة نعمل composition انطبق ال I Y على
+
+297
+00:22:03,820 --> 00:22:07,780
+الطرفين مش ال Y في ال Y إذا I Y تطبق عليها فهذا
+
+298
+00:22:07,780 --> 00:22:14,200
+يؤدي I capital Y of Y تسوي I .. إيه آسف H مش I لأ
+
+299
+00:22:14,200 --> 00:22:23,140
+H بدنا H of Y تسوي H of F of X نفس الفكرة شايفين
+
+300
+00:22:23,140 --> 00:22:27,930
+كيف الأفكار بتتكرر؟ اه طيب هذا إيش بيساوي؟ليس L X
+
+301
+00:22:27,930 --> 00:22:32,530
+ليس L X مش H Circle F تساوي اللي هو ال Y شفتين
+
+302
+00:22:32,530 --> 00:22:39,250
+الترتيب لإنه جالي H F إيش فيه لأ لأ العكس هي F
+
+303
+00:22:39,250 --> 00:22:51,670
+Circle نعكس لأ أنا بدي حل ل X بدي حل ل X بدنا
+
+304
+00:22:51,670 --> 00:22:56,120
+نعمل هيك فهي ال H في الأولفلازم H تكون في الأول،
+
+305
+00:22:56,120 --> 00:22:59,260
+ما يمكنني أن أعكس الترتيب، هو such of circle H
+
+306
+00:22:59,260 --> 00:23:04,040
+لازم
+
+307
+00:23:04,040 --> 00:23:07,740
+H تكون في الأول، ما يمكنني أن أعكس الترتيب، هو
+
+308
+00:23:07,740 --> 00:23:08,480
+أن أعكس الترتيب، هو such of circle H لازم H تكون
+
+309
+00:23:08,480 --> 00:23:09,780
+في الأول، ما يمكنني أن أعكس الترتيب، هو such of
+
+310
+00:23:09,780 --> 00:23:12,380
+circle H لازم H تكون في الأول، ما يمكنني أن أعكس
+
+311
+00:23:12,380 --> 00:23:14,520
+الترتيب، هو such of circle H لازم H تكون في الأول،
+
+312
+00:23:14,520 --> 00:23:15,380
+ما يمكنني أن أعكس الترتيب، هو such of circle H
+
+313
+00:23:15,380 --> 00:23:16,800
+لازم H تكون في الأول، ما يمكنني أن أعكس الترتيب،
+
+314
+00:23:16,800 --> 00:23:18,960
+هو such of circle H لازم H تكون في الأول، ما
+
+315
+00:23:18,960 --> 00:23:21,660
+يمكنني أن أعكس التأنا أخدت الـ Y بس طبعا يمكن الحل
+
+316
+00:23:21,660 --> 00:23:26,600
+مش كتير واضح بس هو قداني مثلا نقول إرشاد كيف أختار
+
+317
+00:23:26,600 --> 00:23:30,440
+ال X الآن بدأ أتأكد بدأ إيش بدأ نثبت أن هذه ال X
+
+318
+00:23:30,440 --> 00:23:34,860
+تنتمي لمين؟ لل domain X وصورتها بتساوي مين؟ بتساوي
+
+319
+00:23:34,860 --> 00:23:39,000
+Y، هذا هو المطلوب، هذا هو المطلوب، أه فأنا أخدت ال
+
+320
+00:23:39,000 --> 00:23:46,720
+Y، إيش هقوله؟ let X تساوي H of Yهل جت أخدت عنصر من
+
+321
+00:23:46,720 --> 00:23:52,040
+ال Y و ال H ده لمن Y لوين ال H ده لمن Y ل X اه من
+
+322
+00:23:52,040 --> 00:23:55,800
+Y ل X اذا ال H معرفة على اسمه ال Y ولا مش معرفة؟
+
+323
+00:23:55,800 --> 00:24:02,020
+معرفة صورتها وين؟ في ال X اه فإذا على طول then ال
+
+324
+00:24:02,020 --> 00:24:07,040
+X تنتمي لل capital X and إيش تعمل؟ بدنا صورتها
+
+325
+00:24:07,040 --> 00:24:11,060
+تساوي Y بدنا صورتها تساوي Y مين صورة ال .. صورة ال
+
+326
+00:24:11,060 --> 00:24:17,550
+F of X إيش بتساوي؟F of X ايش بتساوي؟ نعود عن X هي
+
+327
+00:24:17,550 --> 00:24:26,350
+F of H of Y وتساوي F circle H للـY وتساوي I الـY
+
+328
+00:24:26,350 --> 00:24:30,370
+للـY وتساوي Y وهو المطلوب صح الـhigh machine
+
+329
+00:24:30,370 --> 00:24:35,820
+ماتساعدنيش كتير لكن داني ارشادأه فإيش مطلوب طب
+
+330
+00:24:35,820 --> 00:24:39,880
+خلينا نلخص الأمر إيش معناته أنتوا لأي عنصر في
+
+331
+00:24:39,880 --> 00:24:43,200
+المجال المقابل Y بدي أثبت أنه صورة عنصر من ال
+
+332
+00:24:43,200 --> 00:24:46,200
+domain X فالسؤال بيكون دايما بنحط المعادلة دي و
+
+333
+00:24:46,200 --> 00:24:50,740
+بنحاول نحلها طبعا هنا ماساعدناش كتير الأمر H of Y
+
+334
+00:24:50,740 --> 00:24:53,520
+تساوي X ماقدرناش نحله مباشرة أو ماقدرناش نعملش
+
+335
+00:24:53,520 --> 00:24:57,660
+كتير فانا بدي هذا الكلامفبنفع بنفع لو عوضت هنا نفع
+
+336
+00:24:57,660 --> 00:25:02,360
+معاه فإذا ال X بتساوي H of Y فال X بتساوي اثبتت هي
+
+337
+00:25:02,360 --> 00:25:06,540
+إيش أو اخترت H of Y و قدت الغلط ليش؟ شرطين على X
+
+338
+00:25:06,540 --> 00:25:09,960
+إنه هذا اختيار صحيح ال X في ال domain نعم لأن ال H
+
+339
+00:25:09,960 --> 00:25:13,120
+بتواخد من Y و تودي ال capital X فإذا نسمو ال X في
+
+340
+00:25:13,120 --> 00:25:17,040
+ال capital X طيب صورتها بتساوي Y؟ نعم هاي أثبتناها
+
+341
+00:25:17,040 --> 00:25:23,970
+واضحة؟ فده بتدل على إنه إيش إنها أنتواthus F is
+
+342
+00:25:23,970 --> 00:25:28,610
+surjective أو أنتوا او أنتوا فاحنا استفدنا هنا
+
+343
+00:25:28,610 --> 00:25:33,110
+ماعندناش الحل لأن الدالة مش معروفة لكن اقدرنا نمشي
+
+344
+00:25:33,110 --> 00:25:39,150
+خطوة تعليق بس أخير نصيحة يمكن يكون مين أسهل لو
+
+345
+00:25:39,150 --> 00:25:41,610
+جالك اثبت انه دالة one to one نستخدم التعريف ولا
+
+346
+00:25:41,610 --> 00:25:43,590
+النظرية التعريف
+
+347
+00:25:45,630 --> 00:25:50,030
+التعريف وين صعوبته النظرية كيف تدوري على الـG أو
+
+348
+00:25:50,030 --> 00:25:54,290
+الـH مش بسهولة انت بدك تجيبيها مش أي دالة و تتحقق
+
+349
+00:25:54,290 --> 00:25:57,230
+مش صعب التعريف أسهل عشان هي هتلاقونا دايما نستخدم
+
+350
+00:25:57,230 --> 00:26:02,330
+التعريف إلا في مانع ده خلينا ننهي بمثال خلينا ننهي
+
+351
+00:26:02,330 --> 00:26:06,830
+الشبطة بمثال خليه شوية
+
+352
+00:26:10,350 --> 00:26:16,430
+يعني هو أنا بقول لو كنت مخيّرة التعريف أسهل، هذه
+
+353
+00:26:16,430 --> 00:26:20,950
+نصيحة طبعا
+
+354
+00:26:20,950 --> 00:26:25,560
+ممكن يخيّروا ممكن يشبهفهو النظرية مش كتير عملية
+
+355
+00:26:25,560 --> 00:26:28,520
+فيها صعوبة في تطبيق ليش؟ لأنه مطلوب منك تدور على
+
+356
+00:26:28,520 --> 00:26:32,100
+الـG مش بديك إياه أنت بتجيب الـG وتنجح الـG تكون
+
+357
+00:26:32,100 --> 00:26:36,020
+بتحقق الشروط وعشان أنتوا بديك تدور على H وتنجح
+
+358
+00:26:36,020 --> 00:26:38,440
+الـH مش بسهولة هنشوف نحضر الموضوع من الموضوعات
+
+359
+00:26:38,440 --> 00:26:43,360
+الصعبة في الرياضية قلينا أعيد كتابة اللي هو المثال
+
+360
+00:26:43,360 --> 00:26:50,120
+عشانه مش واضح كتير بقول في دل F من X ل Y إيش
+
+361
+00:26:50,120 --> 00:26:56,060
+مالها؟ Bus functionبدنا نثبت حاجتين بدنا نثبت أن F
+
+362
+00:26:56,060 --> 00:27:02,700
+Circle I X التي مرت علينا بتساوي F وتساوي I Y
+
+363
+00:27:02,700 --> 00:27:07,560
+Circle Fوانتبهوا لدقة الترتيب في الـ composition
+
+364
+00:27:07,560 --> 00:27:11,420
+طبعا عشان ينتبه أنه أول الشيء إيش ال I X من وين ل
+
+365
+00:27:11,420 --> 00:27:14,020
+وين بتودي من X ل X و ال F بتودي من وين من X ل Y،
+
+366
+00:27:14,020 --> 00:27:17,780
+بتكمل، بعدين هنا ال F بتودي من X ل Y و ال I Y من Y
+
+367
+00:27:17,780 --> 00:27:22,320
+ل Y، من Y ل Y، أنا هثبت واحدة فيهم و هترك التاني X
+
+368
+00:27:22,320 --> 00:27:24,560
+الصغير لإنه أريد أن أثبت أن هذه تساوي F و هذه
+
+369
+00:27:24,560 --> 00:27:28,220
+تساوي F، بيكون خلصنا، فأنا هثبت واحدة، solution،
+
+370
+00:27:28,220 --> 00:27:36,130
+بدي أثبت أن F circle I ل X تساوي Fتساوي ايش هذا؟
+
+371
+00:27:36,130 --> 00:27:40,670
+دوال تساوي دوال في عندي خيارين اعملهم علينهم
+
+372
+00:27:40,670 --> 00:27:43,350
+علاقات يعني مجموعات من الأزواج المرتبة و استخدم
+
+373
+00:27:43,350 --> 00:27:46,650
+نظرية تلاتة سبعة هنستخدم نظرية تلاتة سبعة هنستخدم
+
+374
+00:27:46,650 --> 00:27:53,890
+نظرية تلاتة سبعة by theoremتلاتة سبعة تلاتة سبعة
+
+375
+00:27:53,890 --> 00:27:56,510
+عشان ندهش نأكد على البرهان السابق تبع ال
+
+376
+00:27:56,510 --> 00:28:01,050
+composition و نقدر نطبق عليه كمان تطبيق فبدي
+
+377
+00:28:01,050 --> 00:28:04,770
+حاجتين بديهم يكونوا من نفس المجموعتين من نفس
+
+378
+00:28:04,770 --> 00:28:07,890
+المجال إلى نفس المجال المقابل و بعدين صورهم
+
+379
+00:28:07,890 --> 00:28:13,950
+متساوية صورهم متساوية فإذا أول حاجة F circle I ل X
+
+380
+00:28:14,770 --> 00:28:18,570
+ده لا من وين لا وين، من X ل Y لأن هذه من X ل X و
+
+381
+00:28:18,570 --> 00:28:21,870
+هذه بتكمل و برضه ال F و ال F ده لا من وين لا وين
+
+382
+00:28:21,870 --> 00:28:25,170
+ما هو من الدنيا من X ل Y فهذه الشرط الأول للنظرية
+
+383
+00:28:25,170 --> 00:28:31,370
+الشرط التاني ناخد أي عنصر في ال X في ال domain
+
+384
+00:28:31,370 --> 00:28:36,550
+المشترك then صورته
+
+385
+00:28:36,550 --> 00:28:43,520
+تحت ال compositionإيش بيساوي؟ بيساوي F of I ال X
+
+386
+00:28:43,520 --> 00:28:52,900
+لل X طيب و I ال X لل X إيش هو؟ X و هو المطلوبهي بس
+
+387
+00:28:52,900 --> 00:28:56,440
+خلصوا خلصوا ولا ماخلصش اشبطوا بيه نظرية صح أسئلة
+
+388
+00:28:56,440 --> 00:28:59,720
+من الكتاب فأرجوا أن تكونوا قادرين على حل الفرع
+
+389
+00:28:59,720 --> 00:29:03,300
+التاني هي شرطين عشان تساوي الدوال بدنا أولا يكونوا
+
+390
+00:29:03,300 --> 00:29:06,620
+من نفس ال domain لنفس ال code domain يعني نفس
+
+391
+00:29:06,620 --> 00:29:09,380
+المجال و نفس المجال المقابل و الصور كلها متساوي
+
+392
+00:29:09,380 --> 00:29:12,840
+لكل أنصر في ال domain الصور متساوي بيكون الدالتين
+
+393
+00:29:12,840 --> 00:29:17,740
+متساويتين فدي نهاية الشبطة
+
+394
+00:29:36,920 --> 00:29:40,280
+طبعاً Chapter 4 زي ما احنا حكينا يمكن جبل هيك مش
+
+395
+00:29:40,280 --> 00:29:47,080
+مطلوب هنتقل ل Chapter 5والعنوان تبعه Denumerable
+
+396
+00:29:47,080 --> 00:29:51,320
+and Non-denumerable sets طبعا يمكن التعريب أو
+
+397
+00:29:51,320 --> 00:29:54,020
+المصطلح العربي مش كتير يكون دقيق بس احنا ممكن نقول
+
+398
+00:29:54,020 --> 00:29:58,340
+Denumerable قابل للعد من number او Denumerable
+
+399
+00:29:58,340 --> 00:30:01,620
+قابل للعد وNon-denumerable النافع تبعها غير قابل
+
+400
+00:30:01,620 --> 00:30:07,140
+للعد مؤقتا هيك ممكن نعرّب طبعا فده شبطر مهم وشبطر
+
+401
+00:30:07,140 --> 00:30:14,700
+يعني بده تركيزوأنا بحكي إنه يمكن جاية بالصدفة إن
+
+402
+00:30:14,700 --> 00:30:19,000
+إحنا قفزنا عن Chapter 4 والحقيقة دي يمكن القفزة
+
+403
+00:30:19,000 --> 00:30:22,200
+إلى برضه قفزة في المستوى فالـ Chapter اللي جاي
+
+404
+00:30:22,200 --> 00:30:26,960
+هلاجي إنه هنبدأ ندخل في مستويات عليا لذلك أنا أرجو
+
+405
+00:30:26,960 --> 00:30:32,160
+إنه شوية ننتبه ونركز بشكل أكبر شوية المفاهيم هتكون
+
+406
+00:30:32,160 --> 00:30:35,480
+متقدمة بعض الشيء فإحنا في الشباتر التلاتة الأولى
+
+407
+00:30:35,480 --> 00:30:40,050
+كنا متعلم حاجة إسمها فعلا أسس رياضيةتستخدم في كل
+
+408
+00:30:40,050 --> 00:30:43,510
+المواضيع لكن الآن اللي هنستخدمه حلاجي مش دايما مش
+
+409
+00:30:43,510 --> 00:30:47,450
+بنفس الشيوع مش بنفس الشهرة في الاستخدام ويعتبر
+
+410
+00:30:47,450 --> 00:30:50,530
+مفاهيم متقدمة بعض الشيائم زي المفاهيم الأساسية
+
+411
+00:30:50,530 --> 00:30:53,750
+اللي هي المجموعات والإلاقات والـ function فطبعا ان
+
+412
+00:30:53,750 --> 00:30:57,450
+شاء الله احنا هنحاول نبسط جد ما نقدر ومع التبسيط
+
+413
+00:30:57,450 --> 00:31:00,670
+لاجي نحلاجي انه فعلا الأمور بدت تتقدم في المستوى
+
+414
+00:31:00,670 --> 00:31:06,370
+وهذه فرصة انه نربط ونكون مستعدين للمساقات في اللي
+
+415
+00:31:06,370 --> 00:31:12,380
+هو ايشالفصول القادمة إن شاء الله فطبعا إحنا هنا
+
+416
+00:31:12,380 --> 00:31:15,880
+هيتحدث عن بعض الأشياء فـDudkin's definition of an
+
+417
+00:31:15,880 --> 00:31:18,320
+infinite set is used to discuss properties of
+
+418
+00:31:18,320 --> 00:31:21,960
+infinite sets and finite sets فأول شيء مر علينا
+
+419
+00:31:21,960 --> 00:31:25,300
+مفهوم إيش هو الـfinite و ال infinite set لكن كان
+
+420
+00:31:25,300 --> 00:31:30,280
+التعريف تعريف يمكن عام ليس علمي دقيق هنشوف تعريف
+
+421
+00:31:30,280 --> 00:31:37,230
+ينسب للعالموهذا التعريف دقيق وعلمي وحنشوف كيف
+
+422
+00:31:37,230 --> 00:31:41,690
+بنستخدمه في إثبات إنه مجموعة ما infinite أو finite
+
+423
+00:31:41,690 --> 00:31:45,130
+وبعدين برضه نشوف الخواص العام لل infinite sets و
+
+424
+00:31:45,130 --> 00:31:49,650
+ال finite setsبرضه هنثبت حاجة اسمها الـ
+
+425
+00:31:49,650 --> 00:31:53,310
+Denominable Sets في هذا الموضوع، هنقارن بين
+
+426
+00:31:53,310 --> 00:31:56,170
+المجموعات الـ Infinite Sets هل كل الـ Infinite
+
+427
+00:31:56,170 --> 00:31:59,710
+Sets متساوية من حيث الحجم؟ يعني هنثبت مثلا اللي هو
+
+428
+00:31:59,710 --> 00:32:02,570
+مجموعة الأعداد الطبيعية Infinite Set مجموعة
+
+429
+00:32:02,570 --> 00:32:05,570
+الأعداد الصحيحة Infinite Set مجموعة الأعداد اللي
+
+430
+00:32:05,570 --> 00:32:08,410
+هو النسبية Infinite Set و الـ Real Numbers
+
+431
+00:32:08,410 --> 00:32:13,310
+Infinite Set طب هل هدول جت بعض؟ و لا لأ؟ مين أكبر
+
+432
+00:32:13,310 --> 00:32:19,970
+من مين؟مش جات بعض مش كلهم جات بعض هنثبت ان ال
+
+433
+00:32:19,970 --> 00:32:24,910
+natural number جد ال integers جد ال rationales لكن
+
+434
+00:32:24,910 --> 00:32:29,390
+ال real لأ ال real بعيدة كتير عنه فهذه اللي هنشوف
+
+435
+00:32:29,390 --> 00:32:34,210
+انقارن بين denumerable و non-denumerable فهنثبت ان
+
+436
+00:32:34,210 --> 00:32:38,930
+ال denumerables هي أصغر مجموعة غير منتهية أصغر
+
+437
+00:32:38,930 --> 00:32:42,150
+infinite setsبتكافئ ال natural number هي ال N هذه
+
+438
+00:32:42,150 --> 00:32:45,130
+أصغر مجموعة in infinite غير هيك بيكون كبار كتير و
+
+439
+00:32:45,130 --> 00:32:48,670
+بعاد زي ال R و غيره هنشوف فهذه من الموضوع من حيث
+
+440
+00:32:48,670 --> 00:32:51,850
+الحجم ال denumerable sets هم أصغر infinite sets و
+
+441
+00:32:51,850 --> 00:32:54,710
+ال non-denumerable هم infinite sets لكنه كبار كتير
+
+442
+00:32:54,710 --> 00:32:59,010
+عدد عنصرهم كبير جدا طبعا هنشوف أمثلة مين ال
+
+443
+00:32:59,010 --> 00:33:01,330
+denumerable زي ما ذكرته مين ال non-denumerable
+
+444
+00:33:01,330 --> 00:33:05,490
+sets بدنا نشوف بعض الأمثلةأه طبعاً هنبدأ ال
+
+445
+00:33:05,490 --> 00:33:09,310
+section الأول خمسة واحد finite and infinite set زي
+
+446
+00:33:09,310 --> 00:33:14,230
+ما قدمنا هنبدأ بهذا التعريف وكما ذكرت قبل قليل مر
+
+447
+00:33:14,230 --> 00:33:17,310
+علينا في section اتنين واحد بالتحديد تعريف ال
+
+448
+00:33:17,310 --> 00:33:20,850
+finite set عرفناها إن هي المجموعة اللي تحتوي عدد
+
+449
+00:33:20,850 --> 00:33:24,530
+محدود من العناصر إيش معنى عدد محدود؟ إيش يعني؟
+
+450
+00:33:24,530 --> 00:33:28,530
+الكلام مش دقيقة أو كيف نتعامل معاه؟ إيش معنى عدد
+
+451
+00:33:28,530 --> 00:33:31,650
+محدود؟يعني finite number يعني ايش؟ يعني خمسة،
+
+452
+00:33:31,650 --> 00:33:36,470
+عشرة، مية، بدنا نشوف تعريف مختلف يكون قابل للتعامل
+
+453
+00:33:36,470 --> 00:33:40,730
+معه رياضية، فاحنا الآن هنشوف تعريف رياضي دقيق أو
+
+454
+00:33:40,730 --> 00:33:45,250
+أدق من هذا التعريف اللي مر علينا في section 2-1،
+
+455
+00:33:45,250 --> 00:33:49,170
+خلينا نشوف التعريف ويه، بس خليني أقدمله، كيف
+
+456
+00:33:49,170 --> 00:33:55,470
+نعرفه؟لو انتبهنا أو استعادنا التفكير في الـ
+
+457
+00:33:55,470 --> 00:33:58,450
+infinity لما يتعامل معها في الـ real numbers و في
+
+458
+00:33:58,450 --> 00:34:02,450
+النهايات طبعا ال infinity ليس عدد حقيقي و لا لأ
+
+459
+00:34:02,450 --> 00:34:05,490
+عشان هيك بكتب ال R a h o in interval من سالب
+
+460
+00:34:05,490 --> 00:34:09,180
+infinity ل infinity مظبوط هيك بنكتب Rالـ Real
+
+461
+00:34:09,180 --> 00:34:12,360
+Numbers كفترة من سالب Infinity لإنفنتى بنفتحها مش
+
+462
+00:34:12,360 --> 00:34:14,480
+بغلق بغلقها فال Infinity و السالب Infinity دول
+
+463
+00:34:14,480 --> 00:34:18,620
+مجرد رموز بيعبروا عن أعداد بتكبر بدون حدود بنقول
+
+464
+00:34:18,620 --> 00:34:21,420
+هدا بروح هدا بروح لها Infinity أو يبصغر بدون حدود
+
+465
+00:34:21,420 --> 00:34:25,400
+بنقول بروح لسالب Infinity فدول مجرد رموز لكن و
+
+466
+00:34:25,400 --> 00:34:28,340
+أحنا بنتعامل مع النهايات اتعاملنا مع بعض العمليات
+
+467
+00:34:28,340 --> 00:34:31,280
+على ال Infinity فلو قلنا Infinity ناقص واحد
+
+468
+00:34:32,400 --> 00:34:37,520
+infinity طب infinity ضرب نص infinity صحيح فالمميز
+
+469
+00:34:37,520 --> 00:34:40,900
+ال infinity ان لو احنا طرحنا منها بعض الشيء
+
+470
+00:34:40,900 --> 00:34:43,820
+ماتتغيرش اشي صغير او او خدنا نصها او اخدنا تلت
+
+471
+00:34:43,820 --> 00:34:47,200
+ترباعة ما تتغيرش هذا البيئة اللي بيميزها فاحنا
+
+472
+00:34:47,200 --> 00:34:50,620
+هنستخدم هذا المصطلح بدنا نشوف هنعرف المجموعة بتكون
+
+473
+00:34:50,620 --> 00:34:54,160
+infinite اذا أخدنا منها جزء تمه infinite أخدنا
+
+474
+00:34:54,160 --> 00:34:57,020
+منها جزء تمه infinite بهذا الشكل تقريبا التعريف
+
+475
+00:34:57,020 --> 00:35:02,090
+نشوف التعريف ايش بيقولasset capital X الـ set to
+
+476
+00:35:02,090 --> 00:35:05,370
+be infinite احنا هنعرف ال infinite والنفي تبعها
+
+477
+00:35:05,370 --> 00:35:07,870
+هيكون finite ال negation هو اللي هيكون finite
+
+478
+00:35:07,870 --> 00:35:10,070
+هنبدأ بتعريف ال infinite عكس التعريف في section 2
+
+479
+00:35:10,070 --> 00:35:12,850
+.1 عرفنا ال finite وقلنا ياش ال negation تبعه
+
+480
+00:35:12,850 --> 00:35:15,810
+infinite هنا العكس هنبدأ بال infinite set وتقريبا
+
+481
+00:35:15,810 --> 00:35:19,940
+بالكلام اللي أنا حكيتهA set X is said to be
+
+482
+00:35:19,940 --> 00:35:25,040
+infinite if it has a proper subset Y such that
+
+483
+00:35:25,040 --> 00:35:29,440
+there exists a one-to-one correspondence between X
+
+484
+00:35:29,440 --> 00:35:34,180
+and Y هى
+
+485
+00:35:34,180 --> 00:35:37,020
+عندي مجموعة X
+
+486
+00:35:39,080 --> 00:35:43,800
+نحاول التعريف نقرأه واحدة واحدة ونحاول نفهم بقول
+
+487
+00:35:43,800 --> 00:35:47,460
+ليه يوجد proper subset ايش معنى proper subset
+
+488
+00:35:47,460 --> 00:35:51,560
+مجموعة جزئية حقيقية لاتساويها ففي عندي مجموعة
+
+489
+00:35:51,560 --> 00:35:54,720
+صغيرة اصغر منها Y الكلام اللي حكيته هل جت infinite
+
+490
+00:35:54,720 --> 00:35:59,300
+اخدنا منها جزء هاي اللي هو ال Yأخدنا منها Y proper
+
+491
+00:35:59,300 --> 00:36:01,960
+subset يعني جزء زي ما أقول Infinity، Infinity ناقص
+
+492
+00:36:01,960 --> 00:36:04,400
+واحد أو نص ال Infinity أو تلت أرباع ال Infinity،
+
+493
+00:36:04,400 --> 00:36:07,400
+ناخد منها جزء إيش مالها دي؟ بدي أقول إن ال Y
+
+494
+00:36:07,400 --> 00:36:10,440
+Infinite بدي أحكي تقريبا إن ال Y بتامة Infinite،
+
+495
+00:36:10,440 --> 00:36:13,960
+رغم أن هي أصغر من ال X، رغم أن هي أصغر من ال X لأن
+
+496
+00:36:13,960 --> 00:36:16,700
+هي proper subset، مظبوط؟ يعني في عناصر في ال X مش
+
+497
+00:36:16,700 --> 00:36:19,680
+موجودة في ال Y، في عناصر في ال X الزيادة، واضح؟
+
+498
+00:36:19,720 --> 00:36:22,940
+امتبعين؟ بدي أقول إن ال Y تمت Infinite كي بعبّر
+
+499
+00:36:22,940 --> 00:36:26,360
+عنها؟ قال لي هناك one-to-one correspondence بين X
+
+500
+00:36:26,360 --> 00:36:30,080
+و Y هذا معناه أن المتن ده تمت Infinite ليش؟ لأنه
+
+501
+00:36:30,080 --> 00:36:33,260
+كل عنصر في ال X يقابل عنصر في ال Y لأنها one-to
+
+502
+00:36:33,260 --> 00:36:36,440
+-one وكل عنصر في ال Y هو صورة من X لأنها Onto،
+
+503
+00:36:36,440 --> 00:36:39,480
+مظبوط؟ إذا ما زال فيهم عناصر متنازرة إذا دول
+
+504
+00:36:39,480 --> 00:36:43,300
+المجموعتين تقريبا في الحجم متساويتين فأنا عندي
+
+505
+00:36:43,300 --> 00:36:47,800
+مجموعة Infinite أخدت مجموعة أصغر منها شوية تمت
+
+506
+00:36:47,940 --> 00:36:50,200
+infinity هيك معناه ان انت تتكلم عن اسمها لتكافئل
+
+507
+00:36:50,200 --> 00:36:53,280
+ال X بمعنى ال جيزة نقولها infinity أخدنا نصها تمت
+
+508
+00:36:53,280 --> 00:36:56,060
+تكافئل infinity هنا نفس القضية عندنا مجموعة كبيرة
+
+509
+00:36:56,060 --> 00:37:00,460
+X أخدنا مجموعة بروبا صبصة منها تمت تكافئل X من حيث
+
+510
+00:37:00,460 --> 00:37:03,200
+الحجم من حيث الحجم هذا التعريف تقريبا لكن احنا
+
+511
+00:37:03,200 --> 00:37:05,860
+هناخده بشكل مجرد في البداية بس هذا هو المفهوم تبعه
+
+512
+00:37:07,030 --> 00:37:11,930
+in other words بمعنى آخر a set X is infinite تعريف
+
+513
+00:37:11,930 --> 00:37:16,250
+مختلف if and only if there exists an injection هنا
+
+514
+00:37:16,250 --> 00:37:20,370
+الحقيقة بده يشرح هل جيت لو جلي نسيبنا من التقريب
+
+515
+00:37:20,370 --> 00:37:24,390
+نقرأ التعريف بشكل مجرد مباشر كيف بدي أثبت أن X is
+
+516
+00:37:24,390 --> 00:37:29,270
+infinite خليني أكتبها كجملة أو ك statement عشان
+
+517
+00:37:29,270 --> 00:37:30,170
+نفهم
+
+518
+00:37:34,360 --> 00:37:39,000
+إحنا عايش بنعرف .. أرجو التركيز معايا X is
+
+519
+00:37:39,000 --> 00:37:46,420
+infinite إيش بنعمل جادين؟ بنعرف إيش هحط؟ تكافئ، ما
+
+520
+00:37:46,420 --> 00:37:52,100
+زال تعريف، إذا هذه تكافئ، خليني أحط هنا إيش تكافئ؟
+
+521
+00:37:52,100 --> 00:37:55,920
+it has a proper subset، it has كيف ممكن نفسرها؟
+
+522
+00:37:56,370 --> 00:38:01,130
+there exist احسنتي there exist y ايش مالها ال y
+
+523
+00:38:01,130 --> 00:38:07,570
+برابر subset من ال x مظبوط و ايش كمان اه such that
+
+524
+00:38:07,570 --> 00:38:10,210
+there exist a one to one correspondence there
+
+525
+00:38:10,210 --> 00:38:15,350
+exist a function f مثلا نقول ايش from x to y from
+
+526
+00:38:15,350 --> 00:38:20,010
+x to y ايش مالها ال f هذه one to one and unto f is
+
+527
+00:38:20,010 --> 00:38:25,770
+bijection bijection هيك التعريف ممكن يكوننقرأه مرة
+
+528
+00:38:25,770 --> 00:38:30,610
+تانية ال X بتكون infinite إذا قدرنا نلاقي proper
+
+529
+00:38:30,610 --> 00:38:33,690
+subset Y من ال X و بين ال X و بين ال Y إيش فيه
+
+530
+00:38:33,690 --> 00:38:38,650
+بيجيكشن يوجد بيجيكشن بقول لي in other words فهنا
+
+531
+00:38:38,650 --> 00:38:41,090
+عشان أثبت إنه infinite .. infinite إيش المفروض
+
+532
+00:38:41,090 --> 00:38:48,100
+أثبت ألاقي Yوألاقي دالة ألاقي Y بربر من ال X وال F
+
+533
+00:38:48,100 --> 00:38:52,020
+ايش تكون command دالة بين X وY تكون bijection في
+
+534
+00:38:52,020 --> 00:38:55,500
+التعريف التاني هيسهل عليا هقولي كيف اختار ال Y كيف
+
+535
+00:38:55,500 --> 00:39:00,300
+اختار ال Y بدي سهل العملية بقولي هذا يكافر if and
+
+536
+00:39:00,300 --> 00:39:02,560
+only if there exists an injection جالي يبدأ بال
+
+537
+00:39:02,560 --> 00:39:05,940
+function تبدأش من ال Y لأن ال Y هيختارها بشكل
+
+538
+00:39:05,940 --> 00:39:14,330
+مباشر there exists F من X لXبقى يمكن أسميها مختلفة
+
+539
+00:39:14,330 --> 00:39:20,670
+عشان أميز بينها وبين هذه اشمالها one to one بس G
+
+540
+00:39:20,670 --> 00:39:29,770
+is one to one such thatالـ F of X هي proper من الـ
+
+541
+00:39:29,770 --> 00:39:34,630
+X يعني ليست onto هي proper subset من الـ X طيب إيش
+
+542
+00:39:34,630 --> 00:39:38,150
+العلاقة بين هذا التعريف و بين هذا التعريف قال لبدل
+
+543
+00:39:38,150 --> 00:39:42,610
+ما تدور على مجموعة تكون proper subset و تدور على
+
+544
+00:39:42,610 --> 00:39:48,490
+bijection خد ابدأ بالدالة تكون one to one و إيش
+
+545
+00:39:48,490 --> 00:39:52,140
+أعمل؟ و اختار Y إيش تساوي؟الـ image تبقى هذه
+
+546
+00:39:52,140 --> 00:39:56,280
+الدالة المدى تبقى هذه الدالة لأن هنا إيش هذه هي ال
+
+547
+00:39:56,280 --> 00:40:01,460
+Y هذه هي ال Y بدنا نختار Y تساوي هذه ليش؟ كيف أمكن
+
+548
+00:40:01,460 --> 00:40:06,760
+أنا طبقت التعريف اللي فوق لما أخد ال Y هنا إيش بده
+
+549
+00:40:06,760 --> 00:40:14,300
+يعمل؟ لو روحت أنا بدلتX هي نفس الدالة، وروح اتبدلت
+
+550
+00:40:14,300 --> 00:40:18,780
+الـ X بمين؟ بالـ F of X، اللي هو الـ Image، الـ
+
+551
+00:40:18,780 --> 00:40:22,060
+Image بظبط، إيه صارت الدالة؟ بينفع بدل ولا مينفعش؟
+
+552
+00:40:22,060 --> 00:40:24,480
+تتذكروا النظرية إيش؟ قولوا لا، ما هو المجال
+
+553
+00:40:24,480 --> 00:40:30,320
+المقابل؟وعاء يحتوي الصور أنا ممكن أختاره يجيب على
+
+554
+00:40:30,320 --> 00:40:34,800
+جد الصور بالظبط زي هيك ممكن أكبره فهجيت لما أجيه
+
+555
+00:40:34,800 --> 00:40:38,820
+لما أجيه أبدل المجال المقابل على جد الصور بالظبط
+
+556
+00:40:38,820 --> 00:40:41,940
+بتامها دالة ولا بتامش؟ بتامها طب لما أشق الصورة
+
+557
+00:40:41,940 --> 00:40:45,460
+تتدال، هجيت هي one to oneوصغرنا المجال المقابل،
+
+558
+00:40:45,460 --> 00:40:48,140
+إيه صارت؟ one to one and unto لأنه صغرنا المجال
+
+559
+00:40:48,140 --> 00:40:51,280
+المقابل اسمه بيساوي ال image فقط، ال image فقط،
+
+560
+00:40:51,280 --> 00:40:54,840
+فبكون إحنا إيش؟ طبقنا اللي فوق، فانا إيش مبدأ؟ هذا
+
+561
+00:40:54,840 --> 00:40:57,880
+بيديني طريقة أسهل، بدل مبدأ من أن أدور على ال why
+
+562
+00:40:57,880 --> 00:41:00,860
+و أدور على ده اللي تكون one to one and unto، عملية
+
+563
+00:41:00,860 --> 00:41:03,760
+صعبة كتير، قال لإيه ابدا بدالة بس one to one؟
+
+564
+00:41:03,760 --> 00:41:07,050
+وعشان تخليها untoش تعمل، صغر المجال المقابلصغر
+
+565
+00:41:07,050 --> 00:41:10,390
+المجال المقابل وخلّيه يصير one to one و هو المطلوب
+
+566
+00:41:10,390 --> 00:41:17,310
+فالتعريف التاني هو الصورة الأسهل و القابلة للتطبيق
+
+567
+00:41:19,660 --> 00:41:22,600
+التعريف اتنين طبعا هذه ال infinite طبال finite
+
+568
+00:41:22,600 --> 00:41:25,740
+قلنا ال negation إذا مش infinite مش بسميها finite
+
+569
+00:41:25,740 --> 00:41:29,920
+بسميها finite لأنه لأي عدد لو انه finite مقمية
+
+570
+00:41:29,920 --> 00:41:33,740
+ناقص واحد تبطل تتكافئ المية مظبوط في عمية عنصر مية
+
+571
+00:41:33,740 --> 00:41:36,900
+عتنين خمسين لكن infinity على اتنين infinity شفت
+
+572
+00:41:36,900 --> 00:41:41,280
+الفرق أه فهنا الفرق ملاحظة
+
+573
+00:41:45,950 --> 00:41:50,850
+ملاحظة إذا أصبح التعريف هنستخدم الصورة التانية من
+
+574
+00:41:50,850 --> 00:41:54,610
+التعريف في التطبيق لأنها أسهل اسم طلب مني عشان
+
+575
+00:41:54,610 --> 00:41:57,650
+أثبت أن الدالة infinite .. أسف المجموعة infinite
+
+576
+00:41:57,650 --> 00:42:01,510
+بدي أجيب دالة منها إلى نفسها هذا كتير عملية أسهل
+
+577
+00:42:01,510 --> 00:42:04,330
+من المجموعة على نفسها إيش تكون one to one و إيش
+
+578
+00:42:04,330 --> 00:42:07,950
+تكون و تكون ليست onto هي نفسها ليست onto عشان
+
+579
+00:42:07,950 --> 00:42:12,190
+proper subset ال image proper subset بس هي من X
+
+580
+00:42:12,190 --> 00:42:18,110
+لأفف X هي اللي ontoانتبهوا، هلجت؟ هي هذا ال image
+
+581
+00:42:18,110 --> 00:42:21,390
+تبعها، مش هذا هو المدى، إيش ماله؟ proper من ال X،
+
+582
+00:42:21,390 --> 00:42:25,770
+فهي من X ل X، هي onto؟ لأ، لكن من X ل F of X،
+
+583
+00:42:25,770 --> 00:42:29,070
+onto، فانا بزغرها، بزغرها، يعني المجال المقابل
+
+584
+00:42:29,070 --> 00:42:32,290
+capital X، إيش دي يكون؟ أكبر من المدى، بدنا هي
+
+585
+00:42:32,290 --> 00:42:34,900
+يكون أكبر من المدى، هي الشرط التاليفانا مطلوب إنه
+
+586
+00:42:34,900 --> 00:42:37,920
+أدور على دالة تكون one to one، فده مهم جدا، عشان
+
+587
+00:42:37,920 --> 00:42:40,920
+يقولنا فيه صعوبة أوي، يقولنا في النظريات إنك تثبت
+
+588
+00:42:40,920 --> 00:42:44,580
+one to one، بدك دالة جيه تحقق، فإنك تلاجل الدالة،
+
+589
+00:42:44,580 --> 00:42:47,680
+ومش أي دالة بتنفع، هذا مهم جدا، دايما من الأمور
+
+590
+00:42:47,680 --> 00:42:51,530
+الصعبة في الرياضياتليش في تفاضل باه كان الـ
+
+591
+00:42:51,530 --> 00:42:55,170
+Comparison Test والخلطه دي كانت صعبة لأنه كان بدك
+
+592
+00:42:55,170 --> 00:42:57,770
+تثبت إن ده مثلا الـ Improper Integral إنه Diverse
+
+593
+00:42:57,770 --> 00:43:01,550
+أو Converge، بدك تقارنه مع تكامل تاني، فكان مطلوب
+
+594
+00:43:01,550 --> 00:43:04,710
+منك تدوري على تكامل يكون يا Converge يا Diverse،
+
+595
+00:43:04,710 --> 00:43:08,070
+فهنا صعوبة أن أنت بتتدوري حاجة مناسبة، ونفس القضية
+
+596
+00:43:08,070 --> 00:43:10,530
+في الـSeries، هنا نفس القضية، مطلوب مني أنا أدور
+
+597
+00:43:10,530 --> 00:43:13,950
+على دالة واتحقق الشروط، فالعملية مش سهلة بشكل عام،
+
+598
+00:43:13,950 --> 00:43:16,350
+بشكل عام، عشان هيك احنا جولناهم متقدمين، فاحنا
+
+599
+00:43:16,350 --> 00:43:20,430
+مطلوب مننا ندور دالة تكون one toبتكون ال image
+
+600
+00:43:20,430 --> 00:43:23,190
+تباحة proper subset اللي هو أنا مش ليست أنتوا طيب
+
+601
+00:43:23,190 --> 00:43:26,830
+كيف أسمج أن أنا proper subset فالملحظة بتقول بدا
+
+602
+00:43:26,830 --> 00:43:31,950
+الشكل طبعا احنا عارفين أنه دايما ال image هذا ليس
+
+603
+00:43:31,950 --> 00:43:40,030
+إلا image مرت علينا ولا لأ؟صورة الـ X هي المدى الـ
+
+604
+00:43:40,030 --> 00:43:43,910
+Image إحنا إيش قولنا دايما الـ Image إيش ماله؟
+
+605
+00:43:43,910 --> 00:43:46,890
+subset من المجال المقابل فده دايما subset من الـ X
+
+606
+00:43:46,890 --> 00:43:51,190
+عشان إيش معناته proper subset؟ subset ولا تساوي طب
+
+607
+00:43:51,190 --> 00:43:54,490
+هي subset دايما صح إيش بتام عليه أثبت؟ إنها لا
+
+608
+00:43:54,490 --> 00:43:57,790
+تساوي إيش معناته لا تساوي؟ في عنصر زيادة في الـ X
+
+609
+00:43:57,790 --> 00:44:02,300
+في عنصر زيادة في الـ X هي الملاحظة فبقولليأيه؟ a
+
+610
+00:44:02,300 --> 00:44:05,480
+function f from X لنفسها is a function then we
+
+611
+00:44:05,480 --> 00:44:10,580
+know that ال image subset دايما صح نقول مرة نكرره
+
+612
+00:44:10,580 --> 00:44:14,420
+عشان ناخده و نشتغل عليه thus to prove that اللي هو
+
+613
+00:44:14,420 --> 00:44:17,420
+المطلب التاني عشان نثبت إن المجموعة infinite مطلوب
+
+614
+00:44:17,420 --> 00:44:20,060
+إن دي يبدأ إلى one to one و إن ال image تبعها
+
+615
+00:44:20,060 --> 00:44:23,380
+proper subset to prove that f of X is a proper
+
+616
+00:44:23,380 --> 00:44:27,540
+subset of X we only have to prove بس مطلوب مننا إن
+
+617
+00:44:27,540 --> 00:44:30,000
+ال f of X لا تسوى X بس هي المطلوبة لأن ال subset
+
+618
+00:44:30,000 --> 00:44:34,130
+مثبتة دايما صحthat is إيش معناته؟ we have to prove
+
+619
+00:44:34,130 --> 00:44:37,510
+that there is Y in capital X في عنصر في ال Y مش
+
+620
+00:44:37,510 --> 00:44:40,730
+موجود في ال image في عنصر مش الصورة لإنه إيش
+
+621
+00:44:40,730 --> 00:44:44,250
+الصورة بتغطيش كل ال X ال Fx بتغطيش، المادة بيغطيش
+
+622
+00:44:44,250 --> 00:44:51,810
+كل ال X فهذا اللي إيش هنتبقى بيناعود اللي راح يعني
+
+623
+00:44:51,810 --> 00:44:55,050
+انتوا ما بتستعيدلوش، لسه ال 50 دقيقة ما خلصوش
+
+624
+00:44:55,050 --> 00:45:01,290
+خليني بس نشوف مثال عشان يمكن اللي هو الحاولانطبق
+
+625
+00:45:01,290 --> 00:45:03,850
+العملية Proposition
+
+626
+00:45:13,890 --> 00:45:19,890
+أول نظرية أول مثال هنتبقه بقول ليه مجموعة اللي هو
+
+627
+00:45:19,890 --> 00:45:23,010
+الاعداد الطبيعية اللي هي الاعداد الصحيحة الموجبة
+
+628
+00:45:23,010 --> 00:45:25,870
+is an infinite set طبعا كلكم مؤمنين انها infinite
+
+629
+00:45:25,870 --> 00:45:29,910
+set كيه بنتبق عليها التعريف بقول ليه the set N of
+
+630
+00:45:29,910 --> 00:45:35,830
+all natural numbers is an infinite set proposition
+
+631
+00:45:35,830 --> 00:45:40,710
+خمسة
+
+632
+00:45:40,710 --> 00:45:41,870
+واحد approved
+
+633
+00:45:44,210 --> 00:45:48,950
+أه فاحنا إيش عندنا هنا X هي ال end بدنا نثبت أنها
+
+634
+00:45:48,950 --> 00:45:52,270
+infinite فاحنا مصبرود بإننا ندور على الدالة من ال
+
+635
+00:45:52,270 --> 00:45:55,290
+end لأن تكون one to one و ال image تبقى حقيش ماله
+
+636
+00:45:55,290 --> 00:45:59,790
+proper subset ما بيغطيش يعني تكون مش unto فاحنا
+
+637
+00:45:59,790 --> 00:46:06,970
+خلينا نكتب عشان هو المثال we want to find a
+
+638
+00:46:06,970 --> 00:46:13,490
+function نسميها F ولا نسميها G اللي بدكوا يعني Fمن
+
+639
+00:46:13,490 --> 00:46:17,650
+وين لوين من المجموعة على نفسها عشان نثبت انه
+
+640
+00:46:17,650 --> 00:46:24,510
+مجموعة ما انها infinite such that عليها شرطين
+
+641
+00:46:24,510 --> 00:46:32,850
+الدالة F is one to one and F of N is proper من N
+
+642
+00:46:33,620 --> 00:46:37,200
+فأرجو هذا التعريف بدنا نحفظه طبعا تعريف شوية أكبر
+
+643
+00:46:37,200 --> 00:46:40,600
+من التعريفات السابقة لكن هنكرره هنشوف أمثلة متعددة
+
+644
+00:46:40,600 --> 00:46:44,620
+فهذا المطلوب فالسؤال بدنا نبدأ نش أن نعرف ال F
+
+645
+00:46:44,620 --> 00:46:49,240
+دايما البداية هنقوله بقول ليش there exist فإذا
+
+646
+00:46:49,240 --> 00:46:51,920
+لازم أعطيه إياها that there exist فبتعرفله ال F
+
+647
+00:46:51,920 --> 00:47:02,520
+هقوله let F from N to N be given by F of X تساوي
+
+648
+00:47:03,580 --> 00:47:08,200
+أبدأ أرتب ورق اللي بدأ اكتب فيها وفيه هنا مقدمات
+
+649
+00:47:08,200 --> 00:47:12,580
+للبراهين اتعودنا عليهم زي كيف نثبت one to one كيف
+
+650
+00:47:12,580 --> 00:47:15,780
+نثبت مجموعة سبسط من مجموعة فمقدمة بنكتبها بدا
+
+651
+00:47:15,780 --> 00:47:20,260
+الشكل طبعا الجانب الصعب لسه ماعملناهوش فهذه مقدمة
+
+652
+00:47:20,260 --> 00:47:26,620
+ليس الا فبدنا دالة من and ل and بدناياها تكون one
+
+653
+00:47:26,620 --> 00:47:33,360
+to one وليست unto من عنده اقتراحالمربعة بتكونش one
+
+654
+00:47:33,360 --> 00:47:39,180
+to one دالة
+
+655
+00:47:39,180 --> 00:47:43,300
+المحايدة اقتراح جيد هو one to one لكنه onto
+
+656
+00:47:43,300 --> 00:47:50,060
+التربيه بينفع مع ال N يعني بس ايش تجاوزا لأن هنا
+
+657
+00:47:50,060 --> 00:47:55,560
+مافيش عدد اللي يسالب انا هاخد مثال أبسط هاخد 2X
+
+658
+00:47:58,400 --> 00:48:02,520
+طبعا لسه ده أول مثال ماتخافوش هنشدكوا أمثلة متعددة
+
+659
+00:48:02,520 --> 00:48:06,600
+حيصير لنا خبرات و نشوف كيف بنختار الدالة هناخد 2X
+
+660
+00:48:06,600 --> 00:48:10,270
+هدي one to one ولا مش one to one؟one to one طب
+
+661
+00:48:10,270 --> 00:48:14,010
+انتوا لأ لأنه مش كل عدد مش كلهم صور ايش صورها
+
+662
+00:48:14,010 --> 00:48:18,210
+صورها اتنين اربع ستة مغطت كل لان مغطتش كل لان
+
+663
+00:48:18,210 --> 00:48:22,230
+مغطتش كل لان طبعا مع الخبرات هو هذا النقطة الصعبة
+
+664
+00:48:22,230 --> 00:48:25,150
+هذه أصعب نقطة كيف نختار ال F و هنشوف بعض اللي هو
+
+665
+00:48:25,150 --> 00:48:29,090
+الارشادات و مع الخبرات بيصير انها القضية فإذا هذه
+
+666
+00:48:29,090 --> 00:48:32,270
+أول بداية و هنا هي الصعوبة ايش بتثبت انه ال one to
+
+667
+00:48:32,270 --> 00:48:36,660
+one وna probe or subset فهلجيت حثبت انه Fis one to
+
+668
+00:48:36,660 --> 00:48:40,180
+one علامة استفهام بدي أثبته كي بدي أثبت اتعلمنا
+
+669
+00:48:40,180 --> 00:48:43,080
+لسه يمكن أه فعشان هي ممكن ماخدناش أنثى لكتير لإنه
+
+670
+00:48:43,080 --> 00:48:46,000
+هتتكرر المعنى كتير في ال chapter هذا هناخد عنصرين
+
+671
+00:48:46,000 --> 00:48:51,440
+في ال domain صورهم متساوي let X1 و X2 تنتمي لان
+
+672
+00:48:51,440 --> 00:49:00,040
+such that F of X1 تساوي F of X2فهذه بداية برهان
+
+673
+00:49:00,040 --> 00:49:01,960
+الـ one to one باستخدام التعريف مش حاجة على
+
+674
+00:49:01,960 --> 00:49:04,720
+النظرية زي ما اتفقنا طبعا إيش بده يعمل إذا ده
+
+675
+00:49:04,720 --> 00:49:10,440
+لعنده تعريف استخدم التعريف 2 X 1 تساوي 2 X 2 تعريف
+
+676
+00:49:10,440 --> 00:49:16,860
+ال F طبعا X يبقى على 2 وهو المطلوب F is one to one
+
+677
+00:49:16,860 --> 00:49:21,940
+سهل جدا حلو جدا بنثبت إنها not on أو بالتعريف إنها
+
+678
+00:49:21,940 --> 00:49:27,250
+proper subsetفهنا الجزء التاني من البرهان بدنا ال
+
+679
+00:49:27,250 --> 00:49:32,830
+image اللي هو صورة ال N برابر من ال N و الملاحظة
+
+680
+00:49:32,830 --> 00:49:38,610
+ايش جالت انه بدي اثبت ان هذا يكافئ there exist Y
+
+681
+00:49:38,610 --> 00:49:46,050
+in Nوالـ Y لا تنتمي للـ F of N ليسة صورة بدنا عنصر
+
+682
+00:49:46,050 --> 00:49:50,570
+ليس صورة مشاكل ملاحظة حكت؟ احنا قلنا نتمنث بتنايش
+
+683
+00:49:50,570 --> 00:49:58,130
+proper subset بهذا الشكل فعندي هنا Y تساوي 1 تنتمي
+
+684
+00:49:58,130 --> 00:50:05,800
+للـ N but اللي هو 1 لا تساوي F of X اللي هي 2Xfor
+
+685
+00:50:05,800 --> 00:50:10,540
+all x تنتمي للان ليس صورة حد فيش عنصر صورته واحد
+
+686
+00:50:10,540 --> 00:50:14,760
+الصور مين اتنين اربع ستة فخلاص هذا بدل على انه
+
+687
+00:50:14,760 --> 00:50:22,220
+thus f of n برابر من الان اه فطبعا اذا بدي ارقم
+
+688
+00:50:22,220 --> 00:50:28,360
+خليني ارقم واحد واتنين بيقول ان ال x او ال n اللي
+
+689
+00:50:28,360 --> 00:50:30,980
+هي بتسوي n صحيح is infinite
+
+690
+00:50:34,070 --> 00:50:37,270
+أه فطبعا على الأقل هال gate بس احنا نفهم اللي هو
+
+691
+00:50:37,270 --> 00:50:41,330
+الشكل العام عشان أثبت أن مجموعة infinite مطلوبة
+
+692
+00:50:41,330 --> 00:50:44,170
+تدور على دالة تكون one to one و تكون صورتها ال
+
+693
+00:50:44,170 --> 00:50:46,950
+image a proper subset يعني ليس تقنته بدا المعنى
+
+694
+00:50:46,950 --> 00:50:49,730
+أنه إيش ما تقنته لازم نكون غطي، بدا الشكل فده يمكن
+
+695
+00:50:49,730 --> 00:50:52,910
+مؤقتا طبعا من النقطة الأصعب كيف أختار ال F شوية
+
+696
+00:50:52,910 --> 00:50:55,970
+شوية هناخد خبرات و نتعلم، نكتفي بعد القدر ساعتين
+
+697
+00:50:55,970 --> 00:50:57,310
+تان، ان شاء الله هنكمل
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/vRr_TceeePg_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/vRr_TceeePg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0ee9e84e970793f3251116323b4e33e22ff337a1
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/vRr_TceeePg_raw.json
@@ -0,0 +1 @@
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925.24, "word": " V", "probability": 0.5830078125}, {"start": 925.24, "end": 927.12, "word": " إيش", "probability": 0.7671712239583334}, {"start": 927.12, "end": 928.28, "word": " المطلوب؟", "probability": 0.97080078125}, {"start": 928.28, "end": 928.44, "word": " We", "probability": 0.42578125}, {"start": 928.44, "end": 930.0, "word": " want", "probability": 0.90576171875}, {"start": 930.0, "end": 931.28, "word": " طبعاً", "probability": 0.8205078125}, {"start": 931.28, "end": 931.5, "word": " بدنا", "probability": 0.724365234375}, {"start": 931.5, "end": 931.74, "word": " نثبت", "probability": 0.9884033203125}, {"start": 931.74, "end": 931.86, "word": " إنه", "probability": 0.820556640625}, {"start": 931.86, "end": 932.36, "word": " متكافئة،", "probability": 0.8525797526041666}, {"start": 932.36, "end": 932.44, "word": " بدنا", "probability": 0.78173828125}, {"start": 932.44, "end": 932.66, "word": " ندور", "probability": 0.9599609375}, {"start": 932.66, "end": 932.84, "word": " 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Calculus، ماينفعناش، بدنا نشوف على المعايش، المعطيات، في في المعطيات ده ولا أه، كتبتهم أنا أصلا صريح، أه، فهنعتمد عليهم، هنعتمد عليهم، أه، فانا بدي أعرف الـ F، خليني برسومكم، يمكن صورة تساعدكم، let H from X cross W", "tokens": [10721, 12610, 44049, 38207, 5551, 11622, 2407, 26108, 3714, 43500, 3555, 6156, 3224, 8315, 11778, 47302, 15042, 5551, 12610, 44049, 38207, 30767, 1829, 19446, 1975, 2655, 3615, 19528, 8315, 3714, 11622, 6027, 9673, 7435, 2304, 45367, 9307, 2423, 39184, 1783, 4032, 2423, 39184, 398, 11778, 3224, 37893, 20449, 32887, 5172, 18871, 5551, 9381, 2288, 16095, 11933, 15730, 16472, 11242, 5172, 2655, 2288, 2423, 39184, 3511, 36002, 11331, 10859, 1211, 11703, 1829, 6225, 8592, 7649, 6055, 7435, 2655, 3555, 2423, 39184, 3511, 36002, 12399, 19446, 9957, 5172, 3615, 1863, 33599, 12399, 47525, 8315, 8717, 8592, 38688, 15844, 9673, 3615, 47302, 8592, 12399, 9673, 3615, 9566, 1829, 9307, 12399, 8978, 8978, 9673, 3615, 9566, 1829, 9307, 11778, 3224, 49429, 5551, 3224, 12399, 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"end": 1283.88, "text": "تعريف أول ما شغلنا في chapter 3 الأزواج يومرتب ممتاز الآن متدال ل F 1 to 1 ف X1 تساوي X2 والـ G 1 to 1 يزن W1 تساوي W2 ليش؟ لأن الـ F والـ G are one to one أمس أوصلنا نعمل منهم أزواج مرتبة فده بيقول X1 W1 تساوي X2 W2 وهو المطلوب تعريف الأزواج المرتبة thus", "tokens": [2655, 3615, 16572, 5172, 5551, 12610, 19446, 13412, 17082, 1211, 8315, 8978, 7187, 805, 16247, 11622, 2407, 26108, 7251, 20498, 43500, 3555, 3714, 2304, 2655, 31377, 6024, 48506, 44650, 3215, 6027, 5296, 479, 502, 281, 502, 6156, 1783, 16, 6055, 3794, 995, 45865, 1783, 17, 16070, 39184, 460, 502, 281, 502, 7251, 11622, 1863, 343, 16, 6055, 3794, 995, 45865, 343, 17, 32239, 8592, 22807, 5296, 33456, 2423, 39184, 479, 16070, 39184, 460, 366, 472, 281, 472, 5551, 2304, 3794, 34051, 36520, 8315, 8717, 25957, 1211, 9154, 16095, 5551, 11622, 2407, 26108, 3714, 43500, 49401, 6156, 3215, 3224, 4724, 1829, 39648, 1783, 16, 343, 16, 6055, 3794, 995, 45865, 1783, 17, 343, 17, 37037, 2407, 9673, 9566, 1211, 37746, 37279, 16572, 5172, 16247, 11622, 2407, 26108, 9673, 43500, 49401, 8807], "avg_logprob": -0.2263835937012243, "compression_ratio": 1.7063829787234042, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1257.42, "end": 1257.86, "word": "تعريف", "probability": 0.9208984375}, {"start": 1257.86, "end": 1258.16, "word": " أول", "probability": 0.92919921875}, {"start": 1258.16, "end": 1258.3, "word": " ما", "probability": 0.82275390625}, {"start": 1258.3, "end": 1258.74, "word": " شغلنا", "probability": 0.9505615234375}, {"start": 1258.74, "end": 1258.84, "word": " في", "probability": 0.93017578125}, {"start": 1258.84, "end": 1259.06, "word": " chapter", "probability": 0.338134765625}, {"start": 1259.06, "end": 1259.46, "word": " 3", "probability": 0.79248046875}, {"start": 1259.46, "end": 1260.08, "word": " الأزواج", "probability": 0.820556640625}, {"start": 1260.08, "end": 1260.56, "word": " يومرتب", "probability": 0.677001953125}, {"start": 1260.56, "end": 1261.54, "word": " ممتاز", "probability": 0.9459228515625}, {"start": 1261.54, "end": 1261.9, "word": " الآن", "probability": 0.61181640625}, {"start": 1261.9, "end": 1262.3, "word": " متدال", "probability": 0.655029296875}, {"start": 1262.3, "end": 1262.4, "word": " ل", "probability": 0.6015625}, {"start": 1262.4, "end": 1262.56, "word": " F", "probability": 0.55322265625}, {"start": 1262.56, "end": 1262.76, "word": " 1", "probability": 0.454345703125}, {"start": 1262.76, "end": 1262.9, "word": " to", "probability": 0.8603515625}, {"start": 1262.9, "end": 1263.16, "word": " 1", "probability": 0.90234375}, {"start": 1263.16, "end": 1263.72, "word": " ف", "probability": 0.7490234375}, {"start": 1263.72, "end": 1264.18, "word": " X1", "probability": 0.6102294921875}, {"start": 1264.18, "end": 1264.62, "word": " تساوي", "probability": 0.7852783203125}, {"start": 1264.62, "end": 1265.16, "word": " X2", "probability": 0.95556640625}, {"start": 1265.16, "end": 1265.72, "word": " والـ", "probability": 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1269.84, "end": 1270.16, "word": " والـ", "probability": 0.773681640625}, {"start": 1270.16, "end": 1270.4, "word": " G", "probability": 0.82080078125}, {"start": 1270.4, "end": 1271.04, "word": " are", "probability": 0.1793212890625}, {"start": 1271.04, "end": 1271.4, "word": " one", "probability": 0.5634765625}, {"start": 1271.4, "end": 1271.6, "word": " to", "probability": 0.9111328125}, {"start": 1271.6, "end": 1271.9, "word": " one", "probability": 0.951171875}, {"start": 1271.9, "end": 1272.9, "word": " أمس", "probability": 0.76220703125}, {"start": 1272.9, "end": 1273.48, "word": " أوصلنا", "probability": 0.7955729166666666}, {"start": 1273.48, "end": 1274.22, "word": " نعمل", "probability": 0.9384765625}, {"start": 1274.22, "end": 1274.4, "word": " منهم", "probability": 0.970947265625}, {"start": 1274.4, "end": 1274.68, "word": " أزواج", "probability": 0.977783203125}, {"start": 1274.68, "end": 1275.2, "word": " مرتبة", "probability": 0.9825846354166666}, {"start": 1275.2, "end": 1275.8, "word": " فده", "probability": 0.865234375}, {"start": 1275.8, "end": 1276.06, "word": " بيقول", "probability": 0.86572265625}, {"start": 1276.06, "end": 1276.64, "word": " X1", "probability": 0.651123046875}, {"start": 1276.64, "end": 1277.56, "word": " W1", "probability": 0.845458984375}, {"start": 1277.56, "end": 1278.56, "word": " تساوي", "probability": 0.9462890625}, {"start": 1278.56, "end": 1279.3, "word": " X2", "probability": 0.996337890625}, {"start": 1279.3, "end": 1280.48, "word": " W2", "probability": 0.9814453125}, {"start": 1280.48, "end": 1280.94, "word": " وهو", "probability": 0.8427734375}, {"start": 1280.94, "end": 1281.54, "word": " المطلوب", "probability": 0.9857177734375}, {"start": 1281.54, "end": 1281.98, "word": " تعريف", "probability": 0.9345703125}, {"start": 1281.98, "end": 1282.32, "word": " الأزواج", "probability": 0.9578857421875}, {"start": 1282.32, "end": 1282.98, "word": " المرتبة", "probability": 0.9837239583333334}, {"start": 1282.98, "end": 1283.88, "word": " thus", "probability": 0.316162109375}], "temperature": 1.0}, {"id": 55, "seek": 130746, "start": 1285.18, "end": 1307.46, "text": "H is one to one وهو المطلوب لأ فإحنا البداية واحدة عنصرين من ال domain صورهم متساوية لعنصرين متساويين أيا ما كانوا أيا ما كانوا فهذا الجزء الأول الجزء التاني الآن بدنا نثبت أن ال H is one to one", "tokens": [39, 307, 472, 281, 472, 37037, 2407, 9673, 9566, 1211, 37746, 5296, 10721, 6156, 28814, 5016, 8315, 29739, 28259, 10632, 36764, 24401, 3660, 18871, 9381, 2288, 9957, 9154, 2423, 9274, 20328, 13063, 16095, 44650, 3794, 995, 2407, 10632, 5296, 3615, 1863, 9381, 2288, 9957, 44650, 3794, 995, 45865, 9957, 5551, 25528, 19446, 25961, 14407, 5551, 25528, 19446, 25961, 14407, 6156, 3224, 15730, 25724, 11622, 38207, 16247, 12610, 25724, 11622, 38207, 16712, 7649, 1829, 6024, 48506, 47525, 8315, 8717, 12984, 3555, 2655, 14739, 2423, 389, 307, 472, 281, 472], "avg_logprob": -0.16959270064750415, "compression_ratio": 1.7932960893854748, "no_speech_prob": 0.0, "words": [{"start": 1285.18, "end": 1285.66, "word": "H", "probability": 0.78564453125}, {"start": 1285.66, "end": 1286.18, "word": " is", "probability": 0.58203125}, {"start": 1286.18, "end": 1286.78, "word": " one", "probability": 0.80712890625}, {"start": 1286.78, "end": 1286.96, "word": " to", "probability": 0.818359375}, {"start": 1286.96, "end": 1287.18, "word": " one", "probability": 0.94287109375}, {"start": 1287.18, "end": 1288.3, "word": " وهو", "probability": 0.8115234375}, {"start": 1288.3, "end": 1288.86, "word": " المطلوب", "probability": 0.9686279296875}, {"start": 1288.86, "end": 1289.5, "word": " لأ", "probability": 0.56109619140625}, {"start": 1289.5, "end": 1290.1, "word": " فإحنا", "probability": 0.8072509765625}, {"start": 1290.1, "end": 1291.04, "word": " البداية", "probability": 0.97021484375}, {"start": 1291.04, "end": 1292.02, "word": " واحدة", "probability": 0.9654947916666666}, {"start": 1292.02, "end": 1293.3, "word": " عنصرين", "probability": 0.9755859375}, {"start": 1293.3, "end": 1293.44, "word": " من", "probability": 0.99462890625}, {"start": 1293.44, "end": 1293.96, "word": " ال", "probability": 0.93115234375}, {"start": 1293.96, "end": 1294.38, "word": " domain", "probability": 0.7861328125}, {"start": 1294.38, "end": 1295.32, "word": " صورهم", "probability": 0.9884440104166666}, {"start": 1295.32, "end": 1296.0, "word": " متساوية", "probability": 0.97294921875}, {"start": 1296.0, "end": 1296.6, "word": " لعنصرين", "probability": 0.8446858723958334}, {"start": 1296.6, "end": 1297.18, "word": " متساويين", "probability": 0.916796875}, {"start": 1297.18, "end": 1297.4, "word": " أيا", "probability": 0.5445556640625}, {"start": 1297.4, "end": 1297.58, "word": " ما", "probability": 0.9208984375}, {"start": 1297.58, "end": 1298.1, "word": " كانوا", "probability": 0.965576171875}, {"start": 1298.1, "end": 1298.46, "word": " أيا", "probability": 0.6795654296875}, {"start": 1298.46, "end": 1298.7, "word": " ما", "probability": 0.95263671875}, {"start": 1298.7, "end": 1299.22, "word": " كانوا", "probability": 0.92138671875}, {"start": 1299.22, "end": 1299.7, "word": " فهذا", "probability": 0.9635416666666666}, {"start": 1299.7, "end": 1300.34, "word": " الجزء", "probability": 0.9656575520833334}, {"start": 1300.34, "end": 1300.92, "word": " الأول", "probability": 0.9833984375}, {"start": 1300.92, "end": 1302.86, "word": " الجزء", "probability": 0.9768880208333334}, {"start": 1302.86, "end": 1303.3, "word": " التاني", "probability": 0.9401041666666666}, {"start": 1303.3, "end": 1303.62, "word": " الآن", "probability": 0.73388671875}, {"start": 1303.62, "end": 1303.94, "word": " بدنا", "probability": 0.81787109375}, {"start": 1303.94, "end": 1304.22, "word": " نثبت", "probability": 0.9923095703125}, {"start": 1304.22, "end": 1304.34, "word": " أن", "probability": 0.369873046875}, {"start": 1304.34, "end": 1304.48, "word": " ال", "probability": 0.77783203125}, {"start": 1304.48, "end": 1304.78, "word": " H", "probability": 0.50390625}, {"start": 1304.78, "end": 1306.0, "word": " is", "probability": 0.91015625}, {"start": 1306.0, "end": 1307.18, "word": " one", "probability": 0.243408203125}, {"start": 1307.18, "end": 1307.3, "word": " to", "probability": 0.95166015625}, {"start": 1307.3, "end": 1307.46, "word": " one", "probability": 0.943359375}], "temperature": 1.0}, {"id": 56, "seek": 132452, "start": 1313.5, "end": 1324.52, "text": "يعني إيش بدنا نثبت بدنا نثبت إنه H of X across الـ W تساوي اللي هو Y across ال V هذا مطلوب", "tokens": [40228, 22653, 11933, 1829, 8592, 47525, 8315, 8717, 12984, 3555, 2655, 47525, 8315, 8717, 12984, 3555, 2655, 36145, 3224, 389, 295, 1783, 2108, 2423, 39184, 343, 6055, 3794, 995, 45865, 13672, 1829, 31439, 398, 2108, 2423, 691, 23758, 3714, 9566, 1211, 37746], "avg_logprob": -0.23128634275392043, "compression_ratio": 1.320754716981132, "no_speech_prob": 0.0, "words": [{"start": 1313.5, "end": 1314.08, "word": "يعني", "probability": 0.830078125}, {"start": 1314.08, "end": 1314.24, "word": " إيش", "probability": 0.775390625}, {"start": 1314.24, "end": 1314.46, "word": " بدنا", "probability": 0.966552734375}, {"start": 1314.46, "end": 1314.9, "word": " نثبت", "probability": 0.9951171875}, {"start": 1314.9, "end": 1315.32, "word": " بدنا", "probability": 0.675048828125}, {"start": 1315.32, "end": 1315.7, "word": " نثبت", "probability": 0.996826171875}, {"start": 1315.7, "end": 1316.2, "word": " إنه", "probability": 0.60302734375}, {"start": 1316.2, "end": 1317.02, "word": " H", "probability": 0.391357421875}, {"start": 1317.02, "end": 1318.08, "word": " of", "probability": 0.404296875}, {"start": 1318.08, "end": 1318.78, "word": " X", "probability": 0.9765625}, {"start": 1318.78, "end": 1319.64, "word": " across", "probability": 0.5732421875}, {"start": 1319.64, "end": 1319.96, "word": " الـ", "probability": 0.695556640625}, {"start": 1319.96, "end": 1320.38, "word": " W", "probability": 0.55322265625}, {"start": 1320.38, "end": 1321.54, "word": " تساوي", "probability": 0.9100341796875}, {"start": 1321.54, "end": 1322.0, "word": " اللي", "probability": 0.748046875}, {"start": 1322.0, "end": 1322.22, "word": " هو", "probability": 0.97802734375}, {"start": 1322.22, "end": 1322.68, "word": " Y", "probability": 0.97705078125}, {"start": 1322.68, "end": 1323.44, "word": " across", "probability": 0.6953125}, {"start": 1323.44, "end": 1323.66, "word": " ال", "probability": 0.9482421875}, {"start": 1323.66, "end": 1323.84, "word": " V", "probability": 0.43310546875}, {"start": 1323.84, "end": 1324.1, "word": " هذا", "probability": 0.5205078125}, {"start": 1324.1, "end": 1324.52, "word": " مطلوب", "probability": 0.9283447265625}], "temperature": 1.0}, {"id": 57, "seek": 135225, "start": 1328.01, "end": 1352.25, "text": "هل إحنا في عنا نظرية بتقول إن صورة المجموعات تتوزع على الـ Cartesian؟ في عنا نظرية هيك، إحنا كانت لما تتوزع على الاتحاد بتقاطع بس، وفي عنا الصورة العكسية بتتوزع على الـDifference، إذا مافيش عنا، مانقدراش نستخدم زي توي ما عملنا في الاتحاد، إيش نلجأ؟ للتعريف التاني، هناخد عنصر، بس هنستفيد منها، هنحاول نستفيد منها، فإذا أنا أبدأ بعنصر في المجال المقابل، إيش أسميه؟", "tokens": [3224, 1211, 11933, 5016, 8315, 8978, 6225, 8315, 8717, 19913, 2288, 10632, 39894, 39648, 36145, 20328, 13063, 3660, 9673, 7435, 2304, 45367, 9307, 6055, 2655, 2407, 11622, 3615, 15844, 2423, 39184, 22478, 42434, 22807, 8978, 6225, 8315, 8717, 19913, 2288, 10632, 39896, 4117, 12399, 11933, 5016, 8315, 25961, 2655, 5296, 15042, 6055, 2655, 2407, 11622, 3615, 15844, 2423, 9307, 5016, 18513, 39894, 4587, 41193, 3615, 4724, 3794, 12399, 4032, 41185, 6225, 8315, 31767, 13063, 3660, 18863, 4117, 3794, 10632, 39894, 2655, 2407, 11622, 3615, 15844, 2423, 39184, 35, 351, 5158, 12399, 11933, 15730, 19446, 41185, 8592, 6225, 8315, 12399, 19446, 1863, 28543, 2288, 33599, 8717, 14851, 9778, 40448, 30767, 1829, 6055, 45865, 19446, 6225, 42213, 8315, 8978, 2423, 9307, 5016, 18513, 12399, 11933, 1829, 8592, 8717, 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"end": 1632.26, "word": " قابلة", "probability": 0.9674479166666666}, {"start": 1632.26, "end": 1632.9, "word": " للترقيم", "probability": 0.97080078125}, {"start": 1632.9, "end": 1633.52, "word": " لأن", "probability": 0.644775390625}, {"start": 1633.52, "end": 1634.48, "word": " العداد", "probability": 0.6827799479166666}, {"start": 1634.48, "end": 1634.88, "word": " الطبيعي", "probability": 0.9251708984375}, {"start": 1634.88, "end": 1635.16, "word": " هي", "probability": 0.833984375}, {"start": 1635.16, "end": 1636.28, "word": " عناصر", "probability": 0.9147135416666666}, {"start": 1636.28, "end": 1637.12, "word": " العدد", "probability": 0.738525390625}, {"start": 1637.12, "end": 1637.38, "word": " ماعيش", "probability": 0.58013916015625}, {"start": 1637.38, "end": 1637.7, "word": " نقول", "probability": 0.6463623046875}, {"start": 1637.7, "end": 1638.36, "word": " عدد", "probability": 0.652099609375}, {"start": 1638.36, "end": 1638.82, "word": " واحد", "probability": 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{"start": 2312.86, "end": 2313.44, "word": " بتتساوي", "probability": 0.755712890625}, {"start": 2313.44, "end": 2313.76, "word": " n", "probability": 0.282470703125}, {"start": 2313.76, "end": 2314.14, "word": " عيا", "probability": 0.3975830078125}, {"start": 2314.14, "end": 2314.46, "word": " k", "probability": 0.76611328125}, {"start": 2314.46, "end": 2314.96, "word": " او", "probability": 0.6959228515625}, {"start": 2314.96, "end": 2315.08, "word": " two", "probability": 0.18115234375}, {"start": 2315.08, "end": 2315.22, "word": " K", "probability": 0.173828125}, {"start": 2315.22, "end": 2315.34, "word": " في", "probability": 0.49658203125}, {"start": 2315.34, "end": 2315.66, "word": " nK", "probability": 0.591796875}, {"start": 2315.66, "end": 2315.86, "word": " كل", "probability": 0.7841796875}, {"start": 2315.86, "end": 2316.1, "word": " واحد", "probability": 0.996337890625}, {"start": 2316.1, "end": 2316.32, "word": " او", "probability": 0.90673828125}, {"start": 2316.32, "end": 2316.54, "word": " five", "probability": 0.6298828125}, {"start": 2316.54, "end": 2317.14, "word": " فإيه", "probability": 0.7232666015625}, {"start": 2317.14, "end": 2317.46, "word": " واضح", "probability": 0.9339192708333334}, {"start": 2317.46, "end": 2318.34, "word": " فالمثال", "probability": 0.9227294921875}, {"start": 2318.34, "end": 2318.62, "word": " سهل", "probability": 0.9957682291666666}, {"start": 2318.62, "end": 2318.88, "word": " طبعا", "probability": 0.8896484375}, {"start": 2318.88, "end": 2319.18, "word": " التعامل", "probability": 0.8270263671875}, {"start": 2319.18, "end": 2319.28, "word": " مع", "probability": 0.98828125}, {"start": 2319.28, "end": 2319.36, "word": " ال", "probability": 0.92578125}, {"start": 2319.36, "end": 2319.54, "word": " finite", "probability": 0.88916015625}, {"start": 2319.54, "end": 2319.82, "word": " دايما", "probability": 0.9498697916666666}, {"start": 2319.82, "end": 2321.5, "word": " أسهل", "probability": 0.89892578125}, {"start": 2321.5, "end": 2322.78, "word": " نشوف", "probability": 0.8974609375}, {"start": 2322.78, "end": 2323.06, "word": " كمان", "probability": 0.9860026041666666}, {"start": 2323.06, "end": 2323.52, "word": " مثال", "probability": 0.975830078125}], "temperature": 1.0}, {"id": 99, "seek": 235315, "start": 2328.91, "end": 2353.15, "text": "denominable او يبدأ نثبت ان انا countable فهذه اللي هي كل ال odd كل الفرد 2x-1 يعني ايش بتساوي واحد تلاتة هي عوضه عوضه انا بتساوي واحد بتدينا واحد انا بتساوي اتنين بتدينا تلاتة فالعداد الفردية countable يعني ايش بتثبت ان هي ال finite لأ infinite فمزال ال infinite بتكون countable اذا كانت عيش denominable احنا نثبت انها denominable فهذا المثال التالد", "tokens": [1556, 6981, 712, 1975, 2407, 7251, 44510, 10721, 8717, 12984, 3555, 2655, 16472, 1975, 8315, 1207, 712, 6156, 3224, 24192, 13672, 1829, 39896, 28242, 2423, 7401, 28242, 27188, 2288, 3215, 568, 87, 12, 16, 37495, 22653, 1975, 1829, 8592, 39894, 3794, 995, 45865, 36764, 24401, 6055, 1211, 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2347.89, "end": 2348.45, "word": " بتكون", "probability": 0.624267578125}, {"start": 2348.45, "end": 2348.91, "word": " countable", "probability": 0.984619140625}, {"start": 2348.91, "end": 2349.05, "word": " اذا", "probability": 0.90576171875}, {"start": 2349.05, "end": 2349.33, "word": " كانت", "probability": 0.830322265625}, {"start": 2349.33, "end": 2349.53, "word": " عيش", "probability": 0.753173828125}, {"start": 2349.53, "end": 2350.09, "word": " denominable", "probability": 0.6645914713541666}, {"start": 2350.09, "end": 2350.61, "word": " احنا", "probability": 0.5944010416666666}, {"start": 2350.61, "end": 2350.89, "word": " نثبت", "probability": 0.86114501953125}, {"start": 2350.89, "end": 2351.17, "word": " انها", "probability": 0.843505859375}, {"start": 2351.17, "end": 2351.75, "word": " denominable", "probability": 0.8680013020833334}, {"start": 2351.75, "end": 2352.27, "word": " فهذا", "probability": 0.78271484375}, {"start": 2352.27, "end": 2352.65, "word": " المثال", "probability": 0.9788411458333334}, {"start": 2352.65, "end": 2353.15, "word": " التالد", "probability": 0.9274088541666666}], "temperature": 1.0}, {"id": 100, "seek": 238154, "start": 2353.54, "end": 2381.54, "text": "Solution طبعا أول شي اوضحلكوا ن او و هذا من كلمة odd بتسوء واحد تلاتة خمسة و هكذا لو بدأت تعودوا X متسوء واحد اتنين بتدينها هذه العناصر اه فطبعا is infinite فهنثبت انها ايش بتكافئ اللي هو ال natural number كلها we will prove that n o is denumerable", "tokens": [50, 3386, 23032, 3555, 3615, 995, 5551, 12610, 44049, 1975, 2407, 11242, 5016, 23275, 14407, 8717, 1975, 2407, 4032, 23758, 9154, 9122, 19528, 3660, 7401, 39894, 3794, 2407, 38207, 36764, 24401, 6055, 1211, 9307, 3660, 16490, 2304, 3794, 3660, 4032, 8032, 4117, 15730, 45164, 47525, 10721, 2655, 37279, 23328, 14407, 1783, 44650, 3794, 2407, 38207, 36764, 24401, 1975, 2655, 1863, 9957, 39894, 3215, 9957, 11296, 29538, 18863, 1863, 33546, 2288, 1975, 3224, 6156, 9566, 3555, 3615, 995, 307, 13785, 6156, 3224, 1863, 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هذا", "probability": 0.35888671875}, {"start": 2356.82, "end": 2356.96, "word": " من", "probability": 0.91748046875}, {"start": 2356.96, "end": 2357.22, "word": " كلمة", "probability": 0.9762369791666666}, {"start": 2357.22, "end": 2357.54, "word": " odd", "probability": 0.4609375}, {"start": 2357.54, "end": 2358.18, "word": " بتسوء", "probability": 0.536224365234375}, {"start": 2358.18, "end": 2358.6, "word": " واحد", "probability": 0.7318115234375}, {"start": 2358.6, "end": 2359.28, "word": " تلاتة", "probability": 0.8543701171875}, {"start": 2359.28, "end": 2359.76, "word": " خمسة", "probability": 0.957763671875}, {"start": 2359.76, "end": 2359.82, "word": " و", "probability": 0.68310546875}, {"start": 2359.82, "end": 2360.18, "word": " هكذا", "probability": 0.8704427083333334}, {"start": 2360.18, "end": 2360.88, "word": " لو", "probability": 0.8154296875}, {"start": 2360.88, "end": 2361.12, "word": " بدأت", "probability": 0.76416015625}, {"start": 2361.12, "end": 2361.52, "word": " تعودوا", "probability": 0.54931640625}, {"start": 2361.52, "end": 2361.66, "word": " X", "probability": 0.5087890625}, {"start": 2361.66, "end": 2362.16, "word": " متسوء", "probability": 0.7689208984375}, {"start": 2362.16, "end": 2362.48, "word": " واحد", "probability": 0.8916015625}, {"start": 2362.48, "end": 2362.84, "word": " اتنين", "probability": 0.975341796875}, {"start": 2362.84, "end": 2363.34, "word": " بتدينها", "probability": 0.739013671875}, {"start": 2363.34, "end": 2363.48, "word": " هذه", "probability": 0.79052734375}, {"start": 2363.48, "end": 2363.86, "word": " العناصر", "probability": 0.735565185546875}, {"start": 2363.86, "end": 2364.4, "word": " اه", "probability": 0.714599609375}, {"start": 2364.4, "end": 2364.78, "word": " فطبعا", "probability": 0.969140625}, {"start": 2364.78, "end": 2364.96, "word": " is", "probability": 0.80517578125}, {"start": 2364.96, "end": 2365.44, "word": " infinite", "probability": 0.9033203125}, {"start": 2365.44, "end": 2366.56, "word": " فهنثبت", "probability": 0.8234456380208334}, {"start": 2366.56, "end": 2366.94, "word": " انها", "probability": 0.791015625}, {"start": 2366.94, "end": 2367.6, "word": " ايش", "probability": 0.7842610677083334}, {"start": 2367.6, "end": 2368.72, "word": " بتكافئ", "probability": 0.947265625}, {"start": 2368.72, "end": 2368.98, "word": " اللي", "probability": 0.93798828125}, {"start": 2368.98, "end": 2369.08, "word": " هو", "probability": 0.986328125}, {"start": 2369.08, "end": 2369.2, "word": " ال", "probability": 0.96484375}, {"start": 2369.2, "end": 2369.54, "word": " natural", "probability": 0.85205078125}, {"start": 2369.54, "end": 2369.98, "word": " number", "probability": 0.98291015625}, {"start": 2369.98, "end": 2371.16, "word": " كلها", "probability": 0.982421875}, {"start": 2371.16, "end": 2371.74, "word": " we", "probability": 0.4990234375}, {"start": 2371.74, "end": 2373.38, "word": " will", "probability": 0.89892578125}, {"start": 2373.38, "end": 2374.76, "word": 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"seek": 258873, "start": 2561.64, "end": 2588.74, "text": "شوفنا إنه العداد الطبيعي دينامي رابول طبعا هي الميزان هي واحدة القياس احنا كيف بنقيس إن المجموعة دينامي رابول لأ تكافئ أنا ولا ماتكافئش أنا زي ما احنا كيف مثلا بيجيسوا المتر في عندنا في المتحف الفرنسي مظبوط في قطعة من حديد أو ملاي هي بتكون هذه الواحدة هي الميزان لما بنيجي على زمان ماكانوش فيه موازين إلكترونية كانوا في قطعة حديد بيقولوا هذه kilogram واحنا من ميزاننا ال natural number اللي جدها", "tokens": [8592, 38688, 8315, 36145, 3224, 18863, 3215, 18513, 41950, 21292, 3615, 1829, 11778, 9957, 10943, 1829, 12602, 16758, 12610, 23032, 3555, 3615, 995, 39896, 9673, 1829, 11622, 7649, 39896, 36764, 24401, 3660, 25062, 25528, 3794, 1975, 5016, 8315, 9122, 33911, 44945, 38436, 3794, 36145, 9673, 7435, 2304, 2407, 27884, 11778, 9957, 10943, 1829, 12602, 16758, 12610, 5296, 10721, 6055, 4117, 31845, 19986, 41850, 49429, 3714, 9307, 4117, 31845, 19986, 8592, 41850, 30767, 1829, 19446, 1975, 5016, 8315, 9122, 33911, 50113, 15040, 4724, 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"seek": 261661, "start": 2589.35, "end": 2616.61, "text": "denimrable واللي مش جدها مش denimrable هيك بنعمل هي واحدة الميزان تبعها اه فالان بدنا نشوف فاحنا مجموعة مشهورة عندنا العداد الطبيعي الـdenimrable هي الميزان هي القياس تبعنا طب ناخد مجموعة اكبر شوية الـZ الـZ طبعا اكبر من الـN جدها مرة وشوية وزيادة واحد الصفر لان في كل الموجب وفي اقبال السالب والـ0 الزيادة طب هل هد كبيرة كتير عن الـN ولا من ناحية العدد تكافئها؟ تكافئها", "tokens": [1556, 332, 424, 638, 16070, 20292, 37893, 10874, 3215, 11296, 37893, 1441, 332, 424, 638, 39896, 4117, 44945, 25957, 1211, 39896, 36764, 24401, 3660, 9673, 1829, 11622, 7649, 6055, 3555, 3615, 11296, 1975, 3224, 6156, 6027, 7649, 47525, 8315, 8717, 8592, 38688, 6156, 39319, 8315, 3714, 7435, 2304, 2407, 27884, 37893, 3224, 13063, 3660, 43242, 8315, 18863, 3215, 18513, 41950, 21292, 3615, 1829, 2423, 39184, 1556, 332, 424, 638, 39896, 9673, 1829, 11622, 7649, 39896, 25062, 25528, 3794, 6055, 3555, 3615, 8315, 23032, 3555, 8717, 47283, 3215, 3714, 7435, 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مساعدة", "probability": 0.980224609375}, {"start": 2892.25, "end": 2892.67, "word": " طبعا", "probability": 0.955810546875}, {"start": 2892.67, "end": 2892.97, "word": " بديش", "probability": 0.7919921875}, {"start": 2892.97, "end": 2893.09, "word": " انا", "probability": 0.614501953125}, {"start": 2893.09, "end": 2893.47, "word": " اطول", "probability": 0.8435872395833334}, {"start": 2893.47, "end": 2893.75, "word": " اكتر", "probability": 0.955322265625}, {"start": 2893.75, "end": 2893.89, "word": " من", "probability": 0.990234375}, {"start": 2893.89, "end": 2894.17, "word": " هيك", "probability": 0.95068359375}, {"start": 2894.17, "end": 2894.73, "word": " هنثبت", "probability": 0.87724609375}, {"start": 2894.73, "end": 2894.89, "word": " هذه", "probability": 0.54931640625}, {"start": 2894.89, "end": 2894.99, "word": " ال", "probability": 0.488525390625}, {"start": 2894.99, "end": 2895.11, "word": " one", "probability": 0.5009765625}, {"start": 2895.11, "end": 2895.23, "word": " to", "probability": 0.74951171875}, {"start": 2895.23, "end": 2895.41, "word": " one", "probability": 0.95556640625}, {"start": 2895.41, "end": 2895.69, "word": " and", "probability": 0.87158203125}, {"start": 2895.69, "end": 2896.01, "word": " unto", "probability": 0.2900390625}, {"start": 2896.01, "end": 2896.19, "word": " ان", "probability": 0.90087890625}, {"start": 2896.19, "end": 2896.37, "word": " شاء", "probability": 0.95556640625}, {"start": 2896.37, "end": 2896.43, "word": " الله", "probability": 0.95068359375}, {"start": 2896.43, "end": 2896.71, "word": " المرة", "probability": 0.958984375}, {"start": 2896.71, "end": 2897.07, "word": " الجاية", "probability": 0.9207356770833334}, {"start": 2897.07, "end": 2897.19, "word": " و", "probability": 0.8623046875}, {"start": 2897.19, "end": 2897.31, "word": " يمكن", "probability": 0.6702880859375}, {"start": 2897.31, "end": 2897.75, "word": " تحاولوا", "probability": 0.85869140625}, {"start": 2897.75, "end": 2898.01, "word": " فيها", "probability": 0.61962890625}, {"start": 2898.01, "end": 2898.13, "word": " في", "probability": 0.9384765625}, {"start": 2898.13, "end": 2898.35, "word": " البيت", "probability": 0.962890625}, {"start": 2898.35, "end": 2898.69, "word": " نوقف", "probability": 0.8074544270833334}, {"start": 2898.69, "end": 2898.91, "word": " هنا", "probability": 0.34521484375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2899.26675, "duration_after_vad": 2756.0087499999877}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wQn46KUbcbM.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wQn46KUbcbM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5e8814f40936bcf884510cf421f05d3486cf3d5e
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wQn46KUbcbM.srt
@@ -0,0 +1,2227 @@
+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 طبعًا في الموضوع، طبعًا 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 إن 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 الـ 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 المنطقية، طبعًا 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، فطبعًا لابد أنه نفسر ليش احنا بنبدأ
+
+11
+00:01:01,230 --> 00:01:07,640
+بدراسة المنطق كمدخل لدراسة الرياضيات، في 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 نظرية، هذه الطريقة بيسموها طريقة
+
+17
+00:01:31,530 --> 00:01:36,090
+التفكير الاستقرائي أو inductive reasoning، طبعًا هذه
+
+18
+00:01:36,090 --> 00:01:40,050
+مهمة وتستخدم كثير في العلوم، لكنها ليست الطريقة 
+
+19
+00:01:40,050 --> 00:01:45,770
+المفضلة لدى علماء الرياضيات أو في الرياضيات، وإنما
+
+20
+00:01:45,770 --> 00:01:50,790
+طريقة التفكير الأوسع انتشارًا 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 بـ deductive reasoning، في
+
+23
+00:01:59,790 --> 00:02:04,570
+هذه العملية احنا بنهتم طبعًا كما قلنا في الاستقراء
+
+24
+00:02:04,570 --> 00:02:08,930
+بناخد من الأمثلة وبنروح للقاعدة، كأنه بناخد من
+
+25
+00:02:08,930 --> 00:02:15,000
+القاعدة إلى القمة، في 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
+إن احنا مهتمين إن كيف إذا 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
+نبرهن 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 للرياضيات، طب كيف بنحكم إن
+
+35
+00:02:52,140 --> 00:02:55,520
+هذا الاستنتاج صحيح 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
+فطبعًا موضوعنا الرئيسي المرتبط هو موضوع البرهان في 
+
+38
+00:03:07,060 --> 00:03:12,760
+الرياضيات، فالبرهان عبارة عن جزء أساسي من التفكير
+
+39
+00:03:12,760 --> 00:03:16,860
+الرياضي، لأنه طبعًا 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 إن كيف نحكم على 
+
+42
+00:03:23,320 --> 00:03:30,640
+برهاننا إنها صحيحة أو غير صحيحة، فطبعًا 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 الاستنتاج 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
+لا غنى عنها 
+
+49
+00:04:00,180 --> 00:04:05,720
+فدراسة المنطق اللي هو عنوان الـ 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 المنطق، طبعًا الهدف من هذا الـ chapter و
+
+54
+00:04:25,100 --> 00:04:30,880
+الأنواع تبعه أنه طبعًا 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، وخصوصًا المنطق الرياضي اللي بتساعدنا في
+
+57
+00:04:38,180 --> 00:04:42,080
+دراستنا في الرياضيات وإنّه نقدر نكون البرهان أو 
+
+58
+00:04:42,080 --> 00:04:46,440
+نحكم على برهان إنه صح أو غير صحيح أو براهين الناس
+
+59
+00:04:46,440 --> 00:04:52,090
+الآخرين، فطبعًا section الأول في هذا الـ chapter بعد
+
+60
+00:04:52,090 --> 00:04:54,410
+المقدمة اللي حكيناه عن الـ chapter بشكل عام 
+
+61
+00:04:54,410 --> 00:04:59,030
+statements and their connectives، الـ statement طبعًا 
+
+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 الـ section الأول تبعنا 
+
+65
+00:05:11,260 --> 00:05:16,320
+فنقطة البداية في دراسة المنطق هي ما يعرف بالـ 
+
+66
+00:05:16,320 --> 00:05:19,900
+statement أو الـ 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 أو بنعربها تقرير أو قضية أو
+
+71
+00:05:31,400 --> 00:05:34,820
+تقريرة، طبعًا احنا هناخدها بالمعنى الاصطلاحي وليس
+
+72
+00:05:34,820 --> 00:05:37,580
+المعنى اللغوي، طبعًا المعنى الاصطلاحي هنتفق عليه أو 
+
+73
+00:05:37,580 --> 00:05:43,810
+هنوضحه في التعريف التاني، فأول تعريف اللي هو بيحددنا 
+
+74
+00:05:43,810 --> 00:05:46,230
+المعنى الاصطلاحي، لما نشوف احنا بيجينا نحكي كلمة
+
+75
+00:05:46,230 --> 00:05:48,810
+statement في هذا المساق ما هو المقصود بكلمة
+
+76
+00:05:48,810 --> 00:05:52,170
+statement؟ أه، فطبعًا زي ما قلنا هي قضية أو تقرير
+
+77
+00:05:52,170 --> 00:05:56,150
+التعريب تبعها statement، فما هي الـ statement زي ما
+
+78
+00:05:56,150 --> 00:05:59,270
+بتعرفه في 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
+الإنشائية، طبعًا الجملة الخبرية بيعرفها هي الجملة
+
+81
+00:06:06,750 --> 00:06:09,590
+اللي بتديني خبر أو معلومة، وهذه 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، وهذا الخبر طبعًا إذا كان رياضيًا 
+
+86
+00:06:25,210 --> 00:06:28,150
+وأنا ألمه بيكون صحيح أو بنحكم عليه أنه خطأ، و
+
+87
+00:06:28,150 --> 00:06:31,170
+بنصححه، فهذه الشكلة فاحنا بهمنا نتعامل مع الجمل
+
+88
+00:06:31,170 --> 00:06:34,630
+الخبرية، الجمل الإنشائية بتهم ناشِئِة 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 الـ statement is a declarative sentence
+
+91
+00:06:40,670 --> 00:06:44,500
+جملة خبرية، اللي هي ايش مالها، ايش 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 الـ statement هي جملة
+
+96
+00:06:58,560 --> 00:07:03,800
+خبرية، بيبقى الاحتمال واحد صحيح أو خطأ، طيب 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 ما عنديش أنا
+
+99
+00:07:07,700 --> 00:07:10,580
+المعلومات إني أحكم، لكن هي أي واحد، أنتو
+
+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
+بتدينا معلومة، بتدينا خبر، فهي جملة خبري، واضح؟ أي
+
+106
+00:07:31,790 --> 00:07:34,310
+أه، فطبعًا زي ما حكينا إن الـ statement في بعض الناس
+
+107
+00:07:34,310 --> 00:07:36,930
+بيسموها a proposition أو بيستخدموا الصلاحية a
+
+108
+00:07:36,930 --> 00:07:40,270
+proposition، خلينا نشوف أمثلة عشان نوضح ايش الفرق بين
+
+109
+00:07:40,270 --> 00:07:42,870
+الجملة الخبرية اللي هو الـ statement واللي هو 
+
+110
+00:07:42,870 --> 00:07:46,830
+الجملة الإنشائية اللي يـِِ statement، فطبعًا على سبيل
+
+111
+00:07:46,830 --> 00:07:50,970
+المثال ما يلي كلها عبارة عن statements وممكن
+
+112
+00:07:50,970 --> 00:07:53,890
+نناقشهم مع بعض true أو false، طبعًا مش كلنا ممكن
+
+113
+00:07:53,890 --> 00:07:56,590
+يعرف لكن بعضنا بيعرف، طبعًا احنا حاولنا نجيب أمثلة 
+
+114
+00:07:56,590 --> 00:08:01,010
+تكون معروفة وبسيطة، فلو قلنا غزة is a Palestinian
+
+115
+00:08:01,010 --> 00:08:05,650
+city، فهذا statement لأنه ادتنا خبر معلومة جغرافية، و
+
+116
+00:08:05,650 --> 00:08:08,730
+لا لأ؟ أه طبعًا كلنا .. احنا فلسطينيون عايشين في
+
+117
+00:08:08,730 --> 00:08:11,870
+غزة بنعرف إنها true، أه طبعًا أي واحد عنده معلومة
+
+118
+00:08:11,870 --> 00:08:14,930
+جغرافية بيعرف، طب واحد في أمريكا ما .. ما يعرفش 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 ادتنا 
+
+121
+00:08:19,250 --> 00:08:21,390
+معلومة ممكن تكون صحيحة ممكن تكون خاطئة، واحنا 
+
+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 statement، اثنين ناقص واحد بتساوي ثلاثة، 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، أه، فإنا statement
+
+126
+00:08:36,930 --> 00:08:39,430
+true or false، ايش تاني لإنهم تديني خبر تديني
+
+127
+00:08:39,430 --> 00:08:44,580
+معلومة، واضح؟ أه، فدي ايش statement، مثال آخر، Equation
+
+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 ادتني 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، طبعًا احنا بنعرف ممكن واحد في ابتدائي
+
+133
+00:09:01,080 --> 00:09:03,180
+ما يعرفش أو في اعدادي، لكن احنا عامة بنلاقي معلومات 
+
+134
+00:09:03,180 --> 00:09:05,560
+لكن هذا لما .. بالنسبة لأبن الاعدادي والابتدائي هذا
+
+135
+00:09:05,560 --> 00:09:06,720
+statement ولا statement؟ مش الـ statement ..
+
+136
+00:09:06,720 --> 00:09:10,420
+statement، واضح؟ 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، طبعًا احنا
+
+141
+00:09:25,180 --> 00:09:27,480
+بنعرف يمكن لو واحد في مصر ما يعرفش ولا واحد في
+
+142
+00:09:27,480 --> 00:09:29,900
+الصين ما يعرفش 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 الـ statement زي هيك تدينا معلومة نشوف
+
+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 you سؤال 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
+one هذه ولا ولا ايش مالاش معنى صحيح اه الحقيقة انه
+
+159
+00:10:32,400 --> 00:10:35,640
+هنا ايه أنا 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 أربعة زائد واحد إيش يعني ابدأ 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
+أو خاطئة طبعا لازم أنا بدي أكتب معلومة صحيحة زي ان
+
+165
+00:10:52,790 --> 00:10:55,670
+أنا بدي أكتب 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 week ممكن 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 أخوات comments
+
+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 سؤال نقطة 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
+الـ 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
+شفناها فالأمثلة 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 الرابط ما 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
+المعيار، يا أخي و هتنتبه إنه مش بتتكون من جزئين
+
+197
+00:12:52,110 --> 00:12:55,020
+أو من two statements، المعيار الأساسي وحتوى على
+
+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 الـ .. الـ .. الـ .. الـ
+
+202
+00:13:10,720 --> 00:13:10,980
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+203
+00:13:10,980 --> 00:13:11,300
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+204
+00:13:11,300 --> 00:13:11,340
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+205
+00:13:11,340 --> 00:13:11,480
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+206
+00:13:11,480 --> 00:13:11,520
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+207
+00:13:11,520 --> 00:13:11,600
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+208
+00:13:11,600 --> 00:13:15,380
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+209
+00:13:15,380 --> 00:13:20,680
+الـ
+
+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 statement الجملة 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 الـ 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
+Palestine 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 الـ compound statement لو رجعته للخمسة
+
+222
+00:14:02,850 --> 00:14:06,150
+مافيش أول واحد فيها and بصبوط؟ 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 الـ statement بالنسبة للأولى
+
+227
+00:14:21,550 --> 00:14:24,310
+الـ statement للأولى true ولا false true طيب
+
+228
+00:14:24,310 --> 00:14:27,780
+التانية الثانية 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 الخامس false
+
+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 then المثال
+
+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 آخر pi 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 المعيار في 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 الـ 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 الرمز اه طبعا هم تعرفوا انه 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
+و الناس 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 و بيدينا بالتعامل أفضل من رموز ليش؟ ع سبيل
+
+269
+00:17:00,820 --> 00:17:04,760
+المثال لو 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 فيه لأ، 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 انه 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 و بيقبل 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 الفهم، فاختيار الرمز المناسب في 
+
+283
+00:17:44,330 --> 00:17:48,510
+الرياضيات وده شيء من أساس تحصيلنا، بيساعد 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 نرمز 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 كتر ما احنا
+
+288
+00:18:00,530 --> 00:18:03,270
+متعودين، أول ما نشوف رمز بنعرف، نعيش بدول، لأنه متعارف 
+
+289
+00:18:03,270 --> 00:18:06,770
+عليه، طبعاً في اختلافات لكن بشكل عام في عرف 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
+الـcalculus 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 علينا
+
+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 و simple
+
+298
+00:18:31,640 --> 00:18:34,460
+و simple، فهنستخدم الرموز طبعا من كلمة proposition
+
+299
+00:18:34,460 --> 00:18:39,140
+هنبدأ بالحرف P 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، وال
+
+302
+00:18:44,140 --> 00:18:47,060
+compound جيد، نديها capital، ولا لأ، لأنه بدل ما 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 simple، 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 بيستعملنا 
+
+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
+و سلسله الحمد لله، نبدأ الآن، زي ما هو في العنوان احنا
+
+310
+00:19:13,110 --> 00:19:16,550
+قلنا الـstatements وعرفنا إيش معنى الـstatements
+
+311
+00:19:16,550 --> 00:19:19,710
+ونوعينهم، و عرفنا إيش وكان العنوان their connectives
+
+312
+00:19:19,710 --> 00:19:22,910
+الروابط، فنتحدث عن الروابط، و زي 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 ما ياش خمس اللي هم خمس
+
+315
+00:19:29,110 --> 00:19:32,100
+فهنبدأ ندرسهم بالتفصيل على عدة مراحل، فطبعا 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
+رابط، بنحددهم، اللي احنا قلنا هم خمسة في الأمثلة، لكن
+
+324
+00:20:01,300 --> 00:20:04,580
+الآن بنحط القاعدة بشكل عام، ان هم خمس روابط 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، or، 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 and، وهذا الرمز تبعه، الرابط التالت
+
+329
+00:20:21,740 --> 00:20:26,820
+الـand، و هنرمزه بالرمز ^، 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 جداً يا أخوات، لا يمكنني أن 
+
+334
+00:20:43,910 --> 00:20:47,850
+أستخدم أي رمز ما كان 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
+أن إيش نستخدم القواعد المتفق عليها، و كل رمز له 
+
+338
+00:20:58,150 --> 00:21:01,590
+أهميته، أستخدمه في المكان، وإيش والزمن 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 والأخير، 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 if، أي 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 تبعتها، جانب ما نبدأ ندرسهم في 
+
+346
+00:21:26,640 --> 00:21:30,000
+التفصيل، وندرس مثلاً، مثلاً في الأمثلة، لو قلت لنا
+
+347
+00:21:30,000 --> 00:21:32,860
+لأ، نهجل نحكم على الـstatement الـcompound، 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 الصدق، زي ما اتفقنا الـstatement 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
+false يا true، هذه القيمة لما بيقولها الـstatement
+
+355
+00:22:00,360 --> 00:22:04,220
+true بيسموها قيمة الصدق للـstatement، بيسموها truth
+
+356
+00:22:04,220 --> 00:22:09,260
+value، قيمة الصدق، إذا احنا مهتمين أن الـstatement
+
+357
+00:22:09,260 --> 00:22:12,040
+هذه في كثير من الحياة، ان نحكم عليها true أو false
+
+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؟ الـtruth table هي عبارة عن جداول 
+
+360
+00:22:18,780 --> 00:22:23,520
+رياضية أو جداول منطقية، بنستخدمها كأداة بتساعدنا في
+
+361
+00:22:23,520 --> 00:22:29,710
+تحديد قيمة الصدق للـstatement بشكل عام، طبعا 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
+جدول؟ 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 وبقول
+
+366
+00:22:39,970 --> 00:22:44,250
+true or false، لأ، بشكل عام يا أخوات، احنا مهتمين أن
+
+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 أي statement، اتفقنا بنرمز لها بـ P، مظبوط
+
+369
+00:22:52,070 --> 00:22:56,940
+و كمان statement Q، و P and Q مرموزة بالرادر رامز
+
+370
+00:22:56,940 --> 00:23:01,120
+مظبوط، فاحنا هنشوف انه في قاعدة، زي ما حكينا، لو أنا
+
+371
+00:23:01,120 --> 00:23:03,660
+بدأ أحكم على الـcompound statement اللي بتتكون من 
+
+372
+00:23:03,660 --> 00:23:07,120
+two statements و بينهم and، 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 أحل، إذا 
+
+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 و الثانية 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 تبعتها 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 compound، واضح؟ فهذه ما يُعرف بجدول
+
+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، وبدل false طبعا ممكن نستخدم
+
+387
+00:23:53,750 --> 00:24:00,410
+هذه أو هذه، و Capital F بدل false، أي سؤال؟ فالآن 
+
+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، negation
+
+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 احنا إيش نقراه؟ not، إيش بيسموه؟ إيش 
+
+394
+00:24:26,890 --> 00:24:29,730
+اسمه؟ طبعاً في احنا أي شيء بنحطه تعريف، فيه مصطلح
+
+395
+00:24:29,730 --> 00:24:33,130
+وفيه قواعد، و كيف أستخدمه في عملية الجمع، طب إيش هي
+
+396
+00:24:33,130 --> 00:24:35,630
+الجمع؟ إيش هي عملية؟ إيش هي عملية؟ إيش هي عملية؟ 
+
+397
+00:24:35,630 --> 00:24:38,350
+و إيها اسم؟ و إيها رمز؟ زي في عملية الجمع، إيش 
+
+398
+00:24:38,350 --> 00:24:41,870
+رمزها؟ الـcross، 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 أعمل منها compound باستخدام هذا الرابط، وأن
+
+402
+00:24:52,960 --> 00:24:58,420
+بحطها قبلها، بقول 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 قدامها، 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 P أو the negation of P، قراعتين التنتين
+
+407
+00:25:11,380 --> 00:25:14,920
+صح، اللي بتقولها، فإحنا بنقرعها not P أو the 
+
+408
+00:25:14,920 --> 00:25:18,800
+negation of P، 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، الـnegation، طيب هاي عرفنا اسم الرابط و رمزه
+
+411
+00:25:27,560 --> 00:25:30,720
+تمام، و كيف نلفظه، و كيف نتعرف، طيب لو أنا كيف
+
+412
+00:25:30,720 --> 00:25:33,360
+بتعامل معاه؟ إيش قواعد التعامل معاه؟ لو أنا 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
+أنا عندي معلومات عن الـP، كيف اجيب معلومات عن ال
+
+415
+00:25:38,940 --> 00:25:41,760
+compound not P؟ هاي القاعدة بتقوللي إنه إيه ده؟ 
+
+416
+00:25:41,760 --> 00:25:44,680
+النفي، بنعمل بعكس قيمة الصدق، إذا كانت الجملة
+
+417
+00:25:44,680 --> 00:25:47,860
+الأصلية true، فالنفي تبعها false، وإذا 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 أمامنا، أي سؤال
+
+420
+00:25:56,970 --> 00:25:59,370
+فهذه هي السياسة اللي احنا 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 للstatements 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
+جذر التربيع على اتنين هو عدد نسبي هذا statement
+
+430
+00:26:34,420 --> 00:26:37,060
+ولا لأ؟ اه وsimple 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 لجذر التنين؟ irrational، يعني
+
+433
+00:26:45,890 --> 00:26:48,410
+عدد غير نسبي، ده إيش النسبة؟ نحط بسط ومقام عدد
+
+434
+00:26:48,410 --> 00:26:51,290
+صحيح، لكن جزء ثاني لا يمكن وضعها على صورة عدد 
+
+435
+00:26:51,290 --> 00:26:55,610
+صحيح بسط ومقام 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 not a 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 أنه 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 وكيف نتعامل مع الرموز وكيف 
+
+445
+00:27:39,520 --> 00:27:41,580
+نتعامل من ناحية اللغوية وكيف نعكسها فاحنا بنتعلم
+
+446
+00:27:41,580 --> 00:27:44,980
+هذه الحاجة نحول من الرموز للغة والعكس 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 not 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 الجيب 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 بالتنفي، هذا داخل آليات، 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 قسمة اتنين فبنحن ننفيها
+
+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 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 الآن على الرابط الثاني وهو رابط الان
+
+468
+00:29:38,800 --> 00:29:42,260
+طبعا زي ما نقول إن 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
+الـ operands تبعه وكيف نحسب ال truth value لل
+
+474
+00:29:59,160 --> 00:30:03,170
+statement اللي بتحتوي على مين على الـ and بنقول اللي
+
+475
+00:30:03,170 --> 00:30:05,430
+هو الـ connective اللي هو هذا هو الرمز تبعه اللي هو
+
+476
+00:30:05,430 --> 00:30:08,770
+and بنقرأه إيش بيسموه؟ اسمه 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 بيجي two statements وبينهم بديجي .. 
+
+481
+00:30:23,960 --> 00:30:28,300
+بديجي واش؟ بينهم .. اه between two statements P
+
+482
+00:30:28,300 --> 00:30:30,820
+and Q وطبعا اللي هيكون compound statement اللي
+
+483
+00:30:30,820 --> 00:30:35,760
+هيحتوي على رابط طبعا كيف بنقرأها بي واكيو بسهولة
+
+484
+00:30:35,760 --> 00:30:39,720
+أو في طريقة أخرى نعم the conjunction من اسم of بي 
+
+485
+00:30:39,720 --> 00:30:44,980
+و اكيو اقتران بي و اكيو طبعا كيف نحسب ال truth
+
+486
+00:30:44,980 --> 00:30:51,310
+value بعدين نعمل الجدول في 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 هذه ال statement
+
+489
+00:30:57,350 --> 00:31:00,250
+تتكون من two false الآن لما يكون فيه أنا two
+
+490
+00:31:00,250 --> 00:31:03,390
+statements الحقيقة اللي بندور فيه أنا عدة احتمالات
+
+491
+00:31:03,390 --> 00:31:07,320
+أول احتمال تكون الأولى true والثانية false هي احتمالين طب
+
+492
+00:31:07,320 --> 00:31:10,120
+الأولى true والثانية false طب والأولى false 
+
+493
+00:31:10,120 --> 00:31:13,280
+والثانية true طب الترتيب مهم؟ في الشكل العام اه مهم 
+
+494
+00:31:13,280 --> 00:31:16,020
+في الرياضيات لإن تشوف أنه هل هو في .. في .. في ..
+
+495
+00:31:16,020 --> 00:31:20,880
+يعني لكل الروابط مهم طب لكل الروابط مش مهم مش خاضع
+
+496
+00:31:20,880 --> 00:31:22,960
+لكن تفحص أنا هذا الكلام فإذا في عندنا أربع
+
+497
+00:31:22,960 --> 00:31:26,040
+احتمالات فجدول الصدق اللي بده يكونه لازم يحتوي على 
+
+498
+00:31:26,040 --> 00:31:30,440
+الأربع احتمالات فبنلاحظ من جدول الصدق إنه 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
+الـ true فقط إذا 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 التنين مع بعض أو الأول أو الثاني
+
+503
+00:31:44,090 --> 00:31:47,290
+false فإذا كان واحد أو اثنين 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 التعريف طبعا هو هنا في الملاحظة بنؤكد على هذه 
+
+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 الـ components
+
+508
+00:32:03,840 --> 00:32:09,020
+true أو الـ two components are true بس نؤكد على 
+
+509
+00:32:09,020 --> 00:32:12,590
+ملاحظة اللي هو عدد اللي هو إيش الاحتمالات لو
+
+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 الثاني أو في التعريف الثاني كان أربعة طب لو 
+
+514
+00:32:23,370 --> 00:32:26,570
+كانوا ثلاثة بيصيروا ثمانية فالقاعدة العامة بتقول 
+
+515
+00:32:26,570 --> 00:32:29,450
+زي ما في عندي بتطلع على المركبات الأساسية إذا 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 N فلو كانوا ثلاثة بيكونوا اثنين أس
+
+518
+00:32:36,240 --> 00:32:38,600
+ثلاثة ثمانية لو كانوا أربعة اثنين أس أربعة ستة عشر 
+
+519
+00:32:38,600 --> 00:32:41,680
+وهكذا فهذه القاعدة كانت اثنين أس واحد واحد اثنين
+
+520
+00:32:41,680 --> 00:32:44,700
+أس اثنين أربعة وهكذا فهذه القاعدة العامة اللي
+
+521
+00:32:44,700 --> 00:32:51,330
+بتساعدنا في تكوين جداول الصورة خلينا نشوف مثال عشان
+
+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 القوانين 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 هذه 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 ما ينفعش تكون نصفها true ونصفها false أو كذا لأ
+
+531
+00:33:22,260 --> 00:33:25,940
+لازم كلها ككل أحكم عليها true or false كيف بتحكم
+
+532
+00:33:25,940 --> 00:33:29,760
+عليها؟ بتعيش في أي زاعة فعلنا هنا بنطلع إن في two
+
+533
+00:33:29,760 --> 00:33:36,440
+statements وبينهم and فالجزء الأول one and one plus
+
+534
+00:33:36,440 --> 00:33:41,300
+one equals two هي واحدة وهي 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 فإنا بدأ أحكم عليها كلها مش قادر أحكم عليها
+
+538
+00:33:54,160 --> 00:33:57,360
+مرة واحدة بحكم على العبارات وبخدم القاعدة وبحكم
+
+539
+00:33:57,360 --> 00:34:02,560
+على الكل وبحكم على الكل فهذا المثال الأول 
+
+540
+00:34:05,870 --> 00:34:11,690
+المثال الثاني الخمسة أو five is an integer هي
+
+541
+00:34:11,690 --> 00:34:18,460
+statement وهي true زي ما البعض بيحكوا 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 للعبارات
+
+545
+00:34:31,960 --> 00:34:35,940
+استخدمنا القاعدة التعريف وعرفنا نحدد إيش القيمة
+
+546
+00:34:35,940 --> 00:34:43,640
+لكل عرفنا نحدد القيمة للكل واضح تبين نشوف كمان 
+
+547
+00:34:43,640 --> 00:34:48,340
+مثال five 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 الـ false في الأول أو في الآخر ف ال
+
+550
+00:34:58,000 --> 00:35:01,100
+arguments of force فالكل false فإذا هذه 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
+مثال five 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 وبنعرف وبنطبق القاعدة بهذه
+
+556
+00:35:25,830 --> 00:35:31,570
+الصورة أتوقع إن هنا مناسب إن نوقف هنا عشان الوقت
+
+557
+00:35:31,570 --> 00:35:33,590
+إن شاء الله الساعة الثانية بنكمل 
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wUnjc84zu3o.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wUnjc84zu3o.srt
new file mode 100644
index 0000000000000000000000000000000000000000..10b362c1124158fe2c37f0352d9f5c27b463d0b3
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wUnjc84zu3o.srt
@@ -0,0 +1,2482 @@
+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 الاستدلالية اللي احنا شفناها عبارة عن نظريات
+
+3
+00:00:29,820 --> 00:00:33,240
+متعددة يمكن مر علينا تلت نظريات فيها أكثر من
+
+4
+00:00:33,240 --> 00:00:36,500
+قانون الحقيقة نظرية كان فيها قانونين أو أكثر تدينا
+
+5
+00:00:36,500 --> 00:00:39,970
+اللي هي قواعد المنطقية اللي هنعتمد عليها في 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 أن هو اللي هو صحيح أو 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 تبعنا أن هي صحيحة أو غير 
+
+10
+00:00:56,450 --> 00:01:00,560
+صحيحة. قبل ما نستكمل مع بعض نظرية هنمر على مصطلح
+
+11
+00:01:00,560 --> 00:01:04,680
+الحقيقة بنحتاجه في بعض الأحيان وهو ما يُعرب بالـ 
+
+12
+00:01:04,680 --> 00:01:07,720
+Denials. الـ Denials يمكن نقوله مثلاً ما روحناها من
+
+13
+00:01:07,720 --> 00:01:11,100
+ناحية لغوية هي النفي. طب ما احنا فيه إيه نقاش 
+
+14
+00:01:11,100 --> 00:01:15,280
+النفي؟ لأ. فالمعنى الاصطلاحي إيش الفرق بينهم؟ طبعاً
+
+15
+00:01:15,280 --> 00:01:18,320
+احنا النفي المباشر احنا كنا عايشين النفي ممكن نحط نط
+
+16
+00:01:18,320 --> 00:01:21,780
+نط أو نقول أن ليست هي الحالة كذا. it is not the
+
+17
+00:01:21,780 --> 00:01:26,190
+case. ممكن ننفي بهذا الشكل لكن احنا بنستخدم الـ Denial
+
+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 الـ
+
+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 Denial اللي هو
+
+23
+00:01:47,410 --> 00:01:50,450
+ممكن نسميه إيش؟ النفي المكافئ، النفي المكافئ.
+
+24
+00:01:50,450 --> 00:01:53,270
+فالمصطلح بيقول ليه denial of a statement الـ
+
+25
+00:01:53,270 --> 00:01:55,950
+denial of a statement بيعني is any statement
+
+26
+00:01:55,950 --> 00:01:59,190
+equivalent to not be. إذاً إن هي تكافئ مين؟ النفي. فالـ
+
+27
+00:01:59,190 --> 00:02:03,030
+denial statement تكافئ إيش؟ الـ negation statement.
+
+28
+00:02:03,030 --> 00:02:06,270
+تكافئ الـ negation أو النفي لمين؟ للجملة. طبعاً زي ما
+
+29
+00:02:06,270 --> 00:02:10,230
+حكينا الهدف من الـ denial إنه يحط النفي بصورة أبسط
+
+30
+00:02:10,230 --> 00:02:17,240
+بصورة أنسب للاستخدام، للاستخدام. أي سؤال؟ طبعاً اللي
+
+31
+00:02:17,240 --> 00:02:21,500
+هو الملاحظة الـ statement طبعاً 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 أحط له أداة نفي كما هو يستخدم في قواعد اللغة
+
+34
+00:02:28,080 --> 00:02:31,240
+الانجليزية. اه. فبيقول لي الـ statement has only one
+
+35
+00:02:31,240 --> 00:02:35,310
+negation. إن فيه واضح وحيد ومعروف. تبقى كم Denial
+
+36
+00:02:35,310 --> 00:02:38,870
+هيها؟ متعددين. اه. لكن إيش؟ but always has many
+
+37
+00:02:38,870 --> 00:02:41,130
+denials. لأن في statement بحطها بصورة مكافئة في
+
+38
+00:02:41,130 --> 00:02:44,190
+صورة مكافئة وممكن احطها بعدد صور مكافئة وبيعيش
+
+39
+00:02:44,190 --> 00:02:47,390
+دايماً إن أنا من ناحية عملية بختار الصورة الأنسب
+
+40
+00:02:47,390 --> 00:02:51,740
+إليه الأنسب للغرض التبعي للهدف التبعي. أي سؤال؟ واضح.
+
+41
+00:02:51,740 --> 00:02:54,700
+نشوف بعض الأمثلة ونشوف كيف.. كيف ممكن أن أحول
+
+42
+00:02:54,700 --> 00:02:57,180
+الـ statement negation للـ 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 مثال. إيش 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 مكافئ لكل statement من الـ statements اللي هي
+
+48
+00:03:18,820 --> 00:03:23,470
+التالية. الجملة الأولى أو السؤال الأول فرع إيه؟
+
+49
+00:03:23,470 --> 00:03:28,290
+ثلاثة is greater than or equal to three. three is is
+
+50
+00:03:28,290 --> 00:03:32,150
+greater than or equal to three. فهذه statement صح؟ بسيطة
+
+51
+00:03:32,150 --> 00:03:35,370
+ولا مركبة؟ مركبة.. مركبة.. مركبة.. إيه 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. وهي الـ solution. ونبدأ في إيه؟ فأول شيء نتحدث
+
+62
+00:04:11,350 --> 00:04:15,490
+عن الـ statement. statement ما هي الـ statement؟ الـ
+
+63
+00:04:15,490 --> 00:04:18,310
+three is greater than or equal to three. وعشان
+
+64
+00:04:18,310 --> 00:04:22,710
+أفسر وأتأكد أن هذه statement مركبة أقول هذه مش
+
+65
+00:04:22,710 --> 00:04:26,170
+تكافئ هادول كله، زي ما بنقرعها. ثلاثة أكبر من 
+
+66
+00:04:26,170 --> 00:04:32,500
+ثلاثة or ثلاثة تساوي ثلاثة. فدي جاية لمركبة بـ or مش
+
+67
+00:04:32,500 --> 00:04:37,620
+and. فإذا بقى بنقرأها ثلاثة أكبر أو مش و أكبر أو
+
+68
+00:04:37,620 --> 00:04:42,220
+تساوي ثلاثة. greater than or equal to three. واضح؟ فإذا
+
+69
+00:04:42,220 --> 00:04:44,540
+هذا الـ statement. الخطوة الثانية اللي احنا نعمل
+
+70
+00:04:44,540 --> 00:04:51,580
+ننفيها. negation. الـ negation وحيد. فإيش الـ negation
+
+71
+00:04:51,580 --> 00:04:55,460
+اللي هو نفي ثلاثة أكبر أو يساوي ثلاثة. بده كله
+
+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 وهتشوفوا إيه 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 بيقول لي؟
+
+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 the three أكبر من الـ three
+
+82
+00:05:34,190 --> 00:05:39,930
+and صح. الـ or صارت and وبعدين not the three تساوي الـ
+
+83
+00:05:39,930 --> 00:05:43,930
+three. واضح؟ 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 فعلاً 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 معتادين عليها. طبعاً هذا متعرف عليه أنه
+
+89
+00:05:58,050 --> 00:06:01,370
+إيش؟ ثلاثة لا تساوي ثلاثة، ننفي إيش؟ إيش لا تساوي؟
+
+90
+00:06:01,370 --> 00:06:04,770
+بحط هاي الرمز لا يساوي، وهذه ممكن نحطها ثلاثة ليست
+
+91
+00:06:04,770 --> 00:06:05,190
+أكبر.
+
+92
+00:06:11,640 --> 00:06:17,420
+السلام عليكم. هل نفي الأكبر أصغر؟ لأ، هنشوف مع بعض، 
+
+93
+00:06:17,420 --> 00:06:19,960
+شوف على الـ Gate. احنا نشوف القواعد، اه فعلاً، 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 أكثر، بس بدي يبسط بمعلومة
+
+98
+00:06:32,840 --> 00:06:37,660
+إضافية. معروف إنه من خواص الأعداد الحقيقية أن 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 الثاني، يا أصغر منه،
+
+101
+00:06:44,950 --> 00:06:48,190
+مافي احتمال ثالث. فانا هنا إيش نفيت؟ نفيت أن يكون 
+
+102
+00:06:48,190 --> 00:06:51,050
+الثلاثة أكبر من الثلاثة، ونفيت التساوي. ما بقاش
+
+103
+00:06:51,050 --> 00:06:54,490
+الاحتمال الوحيد أنه أصغر منه، أن الثلاثة أصغر من
+
+104
+00:06:54,490 --> 00:07:00,150
+الثلاثة. فإذاً الثلاثة أصغر من الثلاثة نافي لمن؟
+
+105
+00:07:00,150 --> 00:07:02,810
+نافي لهذه الجملة كلها، لثلاثة أكبر أو يساوي ثلاثة، 
+
+106
+00:07:02,810 --> 00:07:06,310
+مش نافي الأكبر بس، ثلاثة أصغر من ثلاثة هي مش نافي
+
+107
+00:07:06,310 --> 00:07:09,790
+الأكبر، وإنما نافي الأكبر مع اليساوي، واضح؟ اه. فإذا
+
+108
+00:07:09,790 --> 00:07:12,830
+لو احنا نعيش بيكون يتصرعنا بنقع في خطأ. طبعاً هنا
+
+109
+00:07:12,830 --> 00:07:15,730
+هذا هو الـ denial، مظبوط؟ شوفتوا احنا بدينا من
+
+110
+00:07:15,730 --> 00:07:18,990
+الصورة هي النفي المباشر، النفي المباشر هيها، لما
+
+111
+00:07:18,990 --> 00:07:21,690
+بسطناها حصلنا على denial. مين أفضل أتعامل معه هدي ولا
+
+112
+00:07:21,690 --> 00:07:24,990
+معها هدي؟ معها هدي. معها هدي كثير لو بدي أعمل عملية
+
+113
+00:07:24,990 --> 00:07:27,630
+حسابية بعمل معها هدي، 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 مفيد. واضح ياه؟ واضح الصورة
+
+116
+00:07:35,420 --> 00:07:37,260
+اللي بتعطيه؟ إيش معنى تعطيه؟ لو إيش فيودته، 
+
+117
+00:07:37,260 --> 00:07:40,220
+هأعطيه في صورة بسيطة جداً، بقدر أتعامل معها بكل
+
+118
+00:07:40,220 --> 00:07:43,500
+سهولة، اه. فلمّا أقول لها الـ three الـ greater than أصغر
+
+119
+00:07:43,500 --> 00:07:46,300
+من ثلاثة، إذاً إن هي ليست أكبر وليست أكبر، طبعاً
+
+120
+00:07:46,300 --> 00:07:49,460
+الـ state false هي، لأن الـ state ما بيقولها true الـ
+
+121
+00:07:49,460 --> 00:07:51,940
+statement الأولى true ولا لأ؟ ثلاثة أكبر يساوي ثلاثة
+
+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
+فجينا كل الأمور نعرف عن إيش 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 فعلاً اللي كنا نتعلمه
+
+126
+00:08:04,440 --> 00:08:08,440
+زمان صح مابتتنفيش مع ليش؟ قواعد المنطق اللي بنتعلمها
+
+127
+00:08:08,440 --> 00:08:11,680
+اليوم واضحة. إيش معنى الـ denial وإيش فائدته؟ فده هو
+
+128
+00:08:11,680 --> 00:08:14,220
+الـ denial. فإذاً هنا جينا هاي الـ statement هاي الـ
+
+129
+00:08:14,220 --> 00:08:18,460
+negation. فإذاً طبعاً ده كله تكافئ في denial أو a
+
+130
+00:08:18,460 --> 00:08:21,180
+useful denial. طبعاً 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 three أكبر أو يساوي three is three less than
+
+133
+00:08:35,440 --> 00:08:42,780
+three. 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
+وتزايدية. خليني أعلق عن خارج السؤال. الـ statement 
+
+138
+00:09:05,760 --> 00:09:08,520
+هذه مركبة ولا بسيطة؟ مركبة. مركبة. مركبة.
+
+139
+00:09:08,520 --> 00:09:08,800
+مركبة. مركبة. مركبة. مركبة. مركبة. مركبة.
+
+140
+00:09:08,800 --> 00:09:08,920
+مركبة. مركبة. مركبة. مركبة. مركبة. مركبة.
+
+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
+منحولها أفضل إذا كانت يعني عشانها طويلة هنا كانت
+
+147
+00:09:34,600 --> 00:09:36,900
+سهلة فما استخدمتش رموز لأنه سهلة الstatement 
+
+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
+increasing فدولة إيش 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 .. إيش نط بي؟ اللي
+
+170
+00:11:31,080 --> 00:11:34,760
+هي إيش؟ 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 either إن 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
+أقول لك 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 sign بقول 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 فدولة إيش 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 الممكن أي 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 إن 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 إيش 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
+الوحيدة كيف أدخل النافع على الان؟ واضح؟ فالان اللي 
+
+217
+00:15:59,030 --> 00:16:04,410
+هو الـ denial؟ اه 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
+have positive 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 إن 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 positive لو 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 فيها شايفين الخطوات كيف نجيب ال denial؟ ال
+
+241
+00:18:33,680 --> 00:18:37,780
+negation إيش 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 negation زي 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
+إيش 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 then لا ..
+
+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
+الإفدن لكن 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؟ النفي واضح؟ اه فانا
+
+260
+00:19:51,150 --> 00:19:54,810
+دايما إيش .. 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 إيش 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 قوس 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 ضياع بعض و انت فى بيت تبسيط أكتر من هيك مافيش 
+
+281
+00:21:28,380 --> 00:21:31,260
+تبسيط أكثر 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 نشوفه the 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 فضل إنه لما أنت عايز تتصيب
+
+294
+00:22:42,790 --> 00:22:46,570
+ال record ده إنه P نفيه وبعدين 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 ثانية 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 أكثر بساطة للاستخدام نرجع للقواعد النظرية
+
+303
+00:23:20,420 --> 00:23:25,430
+رقم أربع في شتر واحد نشوف بعض القوانين طبعا زي ما
+
+304
+00:23:25,430 --> 00:23:30,890
+تعلمنا أول statement فيها تمهيد للنظرية الهدف منه
+
+305
+00:23:30,890 --> 00:23:33,970
+إنه يقول لي أنا في هذه النظرية هأسخدم بعض الرموز
+
+306
+00:23:33,970 --> 00:23:37,670
+هذه الرموز لها شوف ترمز على statements فبقول لي let
+
+307
+00:23:37,670 --> 00:23:42,070
+b, q and r be an statement إذا إيش بفهم هذا ال
+
+308
+00:23:42,070 --> 00:23:46,430
+statement أن أي قانون حطه في هذه النظرية بينطبق
+
+309
+00:23:46,430 --> 00:23:50,030
+على أي 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
+بسيطة واضحة؟ فهذه اللي فيها نافي نافي نافي و لي
+
+316
+00:24:26,130 --> 00:24:29,350
+مافيش 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 كثير 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 على جزئين إنها تبدأ تتعرف على تلت أجزاء و
+
+322
+00:24:54,330 --> 00:24:58,150
+فأكثر تلت أجزاء فأكثر فإحنا لو شفنا اتذكرنا إحنا
+
+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 معهم كيف 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 اه 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 التجميع هذه 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؟ بقول لي ما أنت حر ابدأ من الأول
+
+338
+00:25:49,870 --> 00:25:53,250
+و الثاني و الناتج مع الثالث أو الثاني مع الثالث
+
+339
+00:25:53,250 --> 00:25:58,010
+و الناتج مع الأول أي سيئة وال or نفس الشيء و ال or نفس
+
+340
+00:25:58,010 --> 00:26:02,330
+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 الشيء نفس 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 سيان 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 الشيء هدول 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 أكثر 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 إحنا
+
+357
+00:27:07,860 --> 00:27:12,000
+مشهور في الحساب بنوزع الضرب على الجمع بنوزع الضرب
+
+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
+الضرب على الضرب لأ تجمع نفس القضية عشان هذا كمثال
+
+360
+00:27:18,640 --> 00:27:22,250
+متعودين عليه فهو بيقول له لو بدك توزع بتوزع زي
+
+361
+00:27:22,250 --> 00:27:26,030
+الجمع تماما هذا أسهل شيء أن نقارنه مع الضرب مع
+
+362
+00:27:26,030 --> 00:27:30,210
+الجمع هذا ليش ممكن نكتب حاجة مشابهة هي بي بدل
+
+363
+00:27:30,210 --> 00:27:33,570
+الآن خلينا نعملها ضرب و بدل ال or خلينا نعملها
+
+364
+00:27:33,570 --> 00:27:41,870
+مثلا جمع اه 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 التوزيع فوق؟ اه
+
+369
+00:28:05,190 --> 00:28:08,670
+طبعا 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 دائما 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 اه لكن إحنا بنحط دائما 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
+هتشوف كلها مفتوح طول العمليات إيش و القواعد صحيحة أي
+
+377
+00:28:30,570 --> 00:28:36,010
+سؤال؟ القانون الثالث في هذه النظرية الـ Transitive
+
+378
+00:28:36,010 --> 00:28:40,450
+law قانون التعدي قانون التعدي 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 و جواب التانية هو
+
+381
+00:28:50,430 --> 00:28:55,720
+شرط الأولى هو .. آسف جواب 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 الثانية إلى نتيجة الثانية
+
+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 بالضبط دول كلهم تكافؤوا 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
+الثاني بيكون مش صحيح في الغالب لأنه كان حطوا تكافؤ
+
+388
+00:29:17,200 --> 00:29:21,630
+هذا تعليق برضه 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 ال ألف 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 مكة مكة، 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 ما روحوا بالقاهرة transit فهي transitive
+
+399
+00:29:58,350 --> 00:30:04,370
+اللي ما هنقولهاش transit، قانون تعدي، إيش قاعدة
+
+400
+00:30:04,370 --> 00:30:08,720
+السلسلة؟ للتفاضل المختلفة مختلفة مش بالضبط هذه
+
+401
+00:30:08,720 --> 00:30:12,680
+خاصية التعدي هذه خاصية التعدي إنه أنا إيش بي تؤدي
+
+402
+00:30:12,680 --> 00:30:17,040
+إلى 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 أنت 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 و في 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
+ثالثة لكن الهدف الرئيسي إيش هو النهاية الثالثة
+
+408
+00:30:34,500 --> 00:30:37,180
+خليني أبرهن واحدة منهم لأن ممكن ما اديناش 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
+خليني 
+
+411
+00:30:45,040 --> 00:30:48,880
+أحل هنا عشان بدنا نوسع .. 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 يثبت إيش؟ C .. يثبت C
+
+414
+00:31:02,810 --> 00:31:06,850
+تمام ال statement اللي مطلوب إثباتها هي
+
+415
+00:31:06,850 --> 00:31:11,130
+implication تضمين كيف بتثبت التضمين؟ إيش معناه إيه
+
+416
+00:31:11,130 --> 00:31:14,090
+أثبت التضمين؟ إنه أثبت الجملة الشرطية ناشر
+
+417
+00:31:14,090 --> 00:31:17,510
+إنها tautology إنها tautology إذا اخذناها 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
+خليني 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 أن أُجل كتابتها أعملها
+
+423
+00:31:40,340 --> 00:31:48,640
+capital Q لليمين b and ايه أسف p then q if b then q
+
+424
+00:31:48,640 --> 00:31:58,370
+and FQ then R شمالها ايه ايه
+
+425
+00:31:58,370 --> 00:32:00,910
+شمالها ايه شمالها ايه شمالها ايه شمالها ايه
+
+426
+00:32:00,910 --> 00:32:01,130
+شمالها ايه شمالها ايه شمالها ايه شمالها
+
+427
+00:32:01,130 --> 00:32:01,390
+شمالها شمالها شمالها شمالها شمالها شمالها
+
+428
+00:32:01,390 --> 00:32:01,430
+شمالها شمالها شمالها شمالها شمالها شمالها
+
+429
+00:32:01,430 --> 00:32:01,890
+شمالها شمالها شمالها شمالها شمالها شمالها
+
+430
+00:32:01,890 --> 00:32:05,750
+شمالها شمالها شمالها شمالها شمالها 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 ما أندي اش اكتب عشان أنا طويل أبدأ أضع ال Q فجيت
+
+433
+00:32:11,810 --> 00:32:14,270
+أقول مكتوبة كابتنال Q ايش ترمز لل statement هذا
+
+434
+00:32:14,270 --> 00:32:16,990
+نثبت انها 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
+صياغته، 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
+table by the truth table أو تقنص بتدول الصدق نبدأ
+
+439
+00:32:33,840 --> 00:32:39,660
+عملية الحل خلّيني أحل هنا فالآن عشان يكون 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 إذا بدنا جدول تلت أعمدة رئيسية وكم
+
+442
+00:32:49,040 --> 00:32:53,120
+احتمال تمانية اتنين او ثلاثة تمانية فخلّيني أعمل
+
+443
+00:32:53,120 --> 00:33:01,120
+جدول أتوقع إن 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 الثاني 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 دائما
+
+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
+ثمانية هيكون أربعة true و بعدين التانين الأربعة
+
+451
+00:33:32,390 --> 00:33:36,760
+الأخرين false يعني بعدين في العمود الثاني 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
+الثاني بنفس الإسلوب true true false false العمود
+
+455
+00:33:48,760 --> 00:33:53,000
+الثالث 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
+أي 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 هذه true 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 اللي هي ايش q then a هدى مع هدى الـ 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 R أه 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 الباقي 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 true فهذا 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
+الـ b implies مين بيها فهذه مع هذه وسهم بالعكس بدنا
+
+490
+00:36:36,580 --> 00:36:42,690
+ننتبه true 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 الثاني ف true than true
+
+495
+00:36:56,550 --> 00:37:00,530
+true false فش مشاكل true true بنتطلع على الثاني
+
+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 tautology 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 سهلة 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 الخامسة النظرية 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 أو معضلات
+
+511
+00:38:32,810 --> 00:38:37,950
+مثبتة أو إيجابية بناء أو إيجابي constructive
+
+512
+00:38:37,950 --> 00:38:46,290
+dilemma معضلات بناء أو إيجابية طبعا 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 نفي 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 شرطيتين مستقلتين 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 الثانية 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 ايش بقول
+
+521
+00:39:17,890 --> 00:39:21,890
+نتيجة؟ إذا أخدت الشرط الأول أو الشرط الثاني بوصل
+
+522
+00:39:21,890 --> 00:39:25,670
+للنتيجة الأولى أو النتيجة الثانية، هيك معناها فعندي
+
+523
+00:39:25,670 --> 00:39:30,390
+جملتين شرطيتين إذا الشرط الأول اتحقق بوصل للتاني أو
+
+524
+00:39:30,390 --> 00:39:33,570
+إذا الشرط الثاني اتحقق بوصل للتاني 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 ايه and
+
+529
+00:39:51,570 --> 00:39:56,730
+بس أختلف الوضع هنا هنا أخدت مين؟ الشرطين مع بعض
+
+530
+00:39:56,730 --> 00:40:01,250
+والجوابين مع بعض وبينهم or في الثانية 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 بناء في
+
+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 الأشياء الطرف 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 هذه بيقدّي
+
+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 والتانية نفس العكس بس والعكس 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 اثنين أقصى أربعة ستة عشر احتمال ستة عشر ست
+
+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 أكثر شيء ممكن يكون مراهنة في
+
+552
+00:41:29,460 --> 00:41:34,540
+المصادر أربعة من ال statements المستقلين ف ال
+
+553
+00:41:34,540 --> 00:41:42,010
+proof كله هتركه exercise نظرية السادسة هنا 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
+ايش فينا قوانين؟ اه هنا فينا قانون مهم مهم جدا،
+
+556
+00:41:52,260 --> 00:41:58,060
+هنعتمد عليه كثيرا في البراهين Modus Ponens Modus
+
+557
+00:41:58,060 --> 00:42:01,740
+Ponens طبعا مش English اللغة مش عارف اللي هي غالب
+
+558
+00:42:01,740 --> 00:42:05,440
+لاتيني أو كذا المصطلح طبعا ايش ممكن نترجمها اللغة
+
+559
+00:42:05,440 --> 00:42:08,160
+الانجليزية ايش 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 إثبات بالإثبات
+ 
+564
+00:42:22,590 --> 00:42:25,810
+طيب نشوف احنا ده بس مجرد اسم القانون طب إيش
+ 
+565
+00:42:25,810 --> 00:42:30,850
+القانون بيقول أنا في عندي جملة شرطية if b then q و
+ 
+566
+00:42:30,850 --> 00:42:36,010
+الـ b صحيحة لازم الـ q تكون صحيحة بمعنى آخر إذا وعدت
+ 
+567
+00:42:36,010 --> 00:42:40,400
+أو في بالوعد 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، وإلا فيه
+ 
+571
+00:42:48,960 --> 00:42:51,700
+مشكلة ولا 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
+تتحقق، ده 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 الاسم 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
+Ponens 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 Modus the 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
+توعدش not 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 ماتوقعتش آه .. 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 إن شاء الله في
+ 
+595
+00:44:19,240 --> 00:44:26,290
+البراهين قانون تالت reduction and absurdance برضه
+ 
+596
+00:44:26,290 --> 00:44:29,830
+كل هذه مصطلحات ليست لغة إنجليزية 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
+النقيد آه 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 كثير 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 ليه if 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 ونخلف بالوعد، هذا تناقض، هذا تناقض فهذا 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 لا يحدث، هذا المفروض لا يحدث، 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، المنطقي 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 صحيحة، هذه عمرها ما بتكون صحيحة لأنه دائما
+ 
+617
+00:45:45,010 --> 00:45:49,030
+الشيء هو ضده وبينهم 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 ما فيش وقت خليني أنهي هنا إن شاء
+ 
+621
+00:46:03,090 --> 00:46:05,750
+الله المحاضرة القادمة بينكمل
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wUnjc84zu3o_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wUnjc84zu3o_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..246364be589ee3dc2ed03dba14347fc8de78bf96
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/wUnjc84zu3o_raw.srt
@@ -0,0 +1,2488 @@
+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 --> 00:32:01,890
+اشمالها اشمالها اشمالها اشمالها اشمالها اشمالها
+
+431
+00:32:01,890 --> 00:32:05,750
+اشمالها اشمالها اشمالها اشمالها اشمالها اشمهذا هو
+
+432
+00:32:05,750 --> 00:32:09,350
+المطلوب فاحنا بدنا نثبت أن هذا ال statement تتولجى
+
+433
+00:32:09,350 --> 00:32:11,810
+عشان مانديش اكتب عشان انا طويل ابدأ اوضع ال Q فجيت
+
+434
+00:32:11,810 --> 00:32:14,270
+قول مكتوبة كابتنال Q ايش ترمز لل statement هذا
+
+435
+00:32:14,270 --> 00:32:16,990
+نثبت ان انا تتولجى كيف؟ فاحنا ايش زي ما اتعلمنا
+
+436
+00:32:16,990 --> 00:32:20,130
+كيف بنحل المسائل؟ بنعيش .. بنفهم السؤال، بنعيد
+
+437
+00:32:20,130 --> 00:32:23,250
+صياخته، بنحطه بصورة مناسبة خطوة تانية بدنا القدرة،
+
+438
+00:32:23,250 --> 00:32:26,910
+طريقة، ماهي طريقة الحل؟ truth table، by truth
+
+439
+00:32:26,910 --> 00:32:33,840
+tableby the truth table او تقنص بتدول الصدق نبدأ
+
+440
+00:32:33,840 --> 00:32:39,660
+عملية الحل خلّيني أحل هنا فالآن عشان ايكون جدول
+
+441
+00:32:39,660 --> 00:32:44,860
+الصدق من أمور سهلة جدا باطلع أكمل statement أساسية
+
+442
+00:32:44,860 --> 00:32:49,040
+في الجملة تلاتة اذا بدنا جدول تلت أعمدة رئيسية وكم
+
+443
+00:32:49,040 --> 00:32:53,120
+احتمال تمانية اتنين او ثلاثة تمانية فخلّيني اعمل
+
+444
+00:32:53,120 --> 00:33:01,120
+جدول أتوقع ان شاء الله هيك بيكفيفعنا بي وعنا كيو
+
+445
+00:33:01,120 --> 00:33:06,320
+أساسيين وعنا ار تلت statement تلت أعمد رئيسية وفي
+
+446
+00:33:06,320 --> 00:33:13,090
+عنا تمان احتمالات ننصفوالنصف هنا و النصف الرابعة
+
+447
+00:33:13,090 --> 00:33:18,110
+نصف التاني و بعدين برضه كل جزء نصفه فهيك و نكون
+
+448
+00:33:18,110 --> 00:33:21,630
+حصلنا على تمان أجزاء واحد اتنين تلاتة أربعة خمسة
+
+449
+00:33:21,630 --> 00:33:25,550
+ستة سبعة تمانية طبعا بنبدأ .. اه .. بنبدأ دايما
+
+450
+00:33:25,550 --> 00:33:29,410
+العمود الأول بنجسمه نصين النص الأول true فعنا
+
+451
+00:33:29,410 --> 00:33:32,390
+تمانية هيكون أربعة true و بعدين التانين الأربعة
+
+452
+00:33:32,390 --> 00:33:36,760
+الأخرين falseيعني بعدين في العمود التاني ماببدأيش
+
+453
+00:33:36,760 --> 00:33:40,380
+نصف العملية بالعكس فالجيت هنا هناخد نصين كل نص
+
+454
+00:33:40,380 --> 00:33:44,540
+هنجسمله نصين ف true true false false و النصف
+
+455
+00:33:44,540 --> 00:33:48,760
+التاني بنفس الإسلوب true true false false العمود
+
+456
+00:33:48,760 --> 00:33:53,000
+التالت الآن بننصف عايش اللي جابله فإن true true
+
+457
+00:33:53,000 --> 00:33:58,260
+بيصير true false true false true false true false
+
+458
+00:33:58,900 --> 00:34:02,120
+أى سؤال فهذه الطريقة جد ما يكونوا تلات نين و
+
+459
+00:34:02,120 --> 00:34:05,340
+اتعلمنا تلاتة هيك و لو أربع نفس القضية بجسمه بيصير
+
+460
+00:34:05,340 --> 00:34:08,620
+ستة عشر تمانية الأول تمانية true تمانية false اللي
+
+461
+00:34:08,620 --> 00:34:12,800
+بعده أربعة أربعة أربعة أربع أربعات و هكذا التقسيم
+
+462
+00:34:12,800 --> 00:34:15,880
+بهذه الصورة فإذا احنا عايش نكون بننصف و بعدين ايش
+
+463
+00:34:15,880 --> 00:34:20,100
+أربع أقسام بنقسم و بعدين أيش تمان أقسام و هكذاأي
+
+464
+00:34:20,100 --> 00:34:24,400
+سؤال نبدأ بدنا نحسب في عندنا P then Q و Q then R و
+
+465
+00:34:24,400 --> 00:34:30,800
+P then R تلت جوبة شرطية بسيطة if P then Q و if Q
+
+466
+00:34:30,800 --> 00:34:36,760
+then R و if P then R و بعد هيك في عندنا الـQ كلها
+
+467
+00:34:36,760 --> 00:34:38,720
+فعشان هيك أنا حطت الرمز بدنا مكتوبة كلها مايصيحش
+
+468
+00:34:38,720 --> 00:34:45,810
+العمود بحط Q الآن بكون خلاصةفي N صحيح و هذا بي ..
+
+469
+00:34:45,810 --> 00:34:52,530
+أدعى أني أحط Q بعدين مش هتم وسع فعندي B then Q and
+
+470
+00:34:52,530 --> 00:34:59,990
+Q then R و بعدين Q فهذه طريقة إذا في statement
+
+471
+00:34:59,990 --> 00:35:03,690
+طويلة ممكن نحملها رمز عشان الوسع و نقدر نعمل
+
+472
+00:35:03,690 --> 00:35:07,710
+الجدول فنبدأ في العملية حساب قيام الصدق نبدأ
+
+473
+00:35:07,710 --> 00:35:12,670
+بالأولى هذه مع هذهtrue than true true true than
+
+474
+00:35:12,670 --> 00:35:16,990
+true true true than false false true than false
+
+475
+00:35:16,990 --> 00:35:20,190
+false الباقي كله true لأنه مافيش وعد مافيش شرط
+
+476
+00:35:20,190 --> 00:35:26,050
+false عطول بسهولة الآن خلصنا من الأولى نيجي
+
+477
+00:35:26,050 --> 00:35:32,540
+للتانية اللى هى ايش q then a هدى مع هدىالـ True ثم
+
+478
+00:35:32,540 --> 00:35:35,880
+الـ True، الـ True ثم الـ False، الـ False، الـ
+
+479
+00:35:35,880 --> 00:35:39,040
+False ثم الـ True، الـ True، الـ False ثم الـ
+
+480
+00:35:39,040 --> 00:35:42,800
+False، الـ True، الـ True ثم الـ True، الـ True ثم
+
+481
+00:35:42,800 --> 00:35:48,000
+الـ False، الـ False ثم الـ True، الـ True طبعا
+
+482
+00:35:48,000 --> 00:35:53,760
+عملية سهلة وبسيطة، الآن الـ B مع الـ Rأه true then
+
+483
+00:35:53,760 --> 00:35:58,760
+true true true false false true true true true
+
+484
+00:35:58,760 --> 00:36:02,800
+false false الباقى كله true لما اللي بيكون false
+
+485
+00:36:02,800 --> 00:36:07,860
+مافيش مشاكل أطلع أه الأن الأن بدنا mean هادي و
+
+486
+00:36:07,860 --> 00:36:13,380
+هادي هادي و هادي true و true true true false false
+
+487
+00:36:13,380 --> 00:36:18,520
+false true false false true false true true true
+
+488
+00:36:18,520 --> 00:36:26,060
+true false false true trueفهذا العمود قبل الأخير
+
+489
+00:36:26,060 --> 00:36:29,920
+لأن العمود الأخير هو الأهم بدنا اللي هو f اللي هو
+
+490
+00:36:29,920 --> 00:36:36,580
+ال b implies مين بيها فهذه مع هذه وسهم بالعكس بدنا
+
+491
+00:36:36,580 --> 00:36:42,690
+ننتبهtrue than true true false than true true
+
+492
+00:36:42,690 --> 00:36:47,330
+false فش مشكلة false فش مشكلة true انتبه بدنا
+
+493
+00:36:47,330 --> 00:36:50,750
+دايما دايما الجملة الشرطية إذا كانت الأول true
+
+494
+00:36:50,750 --> 00:36:53,610
+انتبهوا بدوا انتباه بدوا تدقيق إذا الأول false
+
+495
+00:36:53,610 --> 00:36:56,550
+خلاص على طول بنتطلعش على التاني ف true than true
+
+496
+00:36:56,550 --> 00:37:00,530
+true false فش مشاكل true true بنتطلع على التاني
+
+497
+00:37:00,530 --> 00:37:04,530
+true true true ففعلا كله true فده بيدل على ان ال Q
+
+498
+00:37:04,530 --> 00:37:07,630
+is datalogic وبالتالي الكلام صحي
+
+499
+00:37:10,500 --> 00:37:11,820
+So from the table,
+
+500
+00:37:16,080 --> 00:37:19,680
+we see
+
+501
+00:37:19,680 --> 00:37:24,960
+that if we say Q is a tautology, or if we say B
+
+502
+00:37:24,960 --> 00:37:36,760
+then Q and FQ then R implies FB then R. فهذا يعني
+
+503
+00:37:36,760 --> 00:37:44,680
+ما نريده هو F.أي سؤال فجدول الصدق فعلا سهله بهذا
+
+504
+00:37:44,680 --> 00:37:50,540
+الشكل إذا إتبعنا هذه الخطوات و هذه القواعد فإن شاء
+
+505
+00:37:50,540 --> 00:37:57,480
+الله بنقدر نعمل جدول صدق لأي استثناء نظرية
+
+506
+00:37:57,480 --> 00:38:02,950
+أخرى الخامسةالنظرية الخامسة في هذا الـ chapter
+
+507
+00:38:02,950 --> 00:38:07,650
+الآن على نفس المنهج، على نفس الطريقة، بس الآن فيه
+
+508
+00:38:07,650 --> 00:38:11,630
+أربع statements، هيستخدم القوانين أربع statements
+
+509
+00:38:11,630 --> 00:38:17,090
+بي كيو آر أس، هنرمزلهم، آه، فعنا بعض القواعد
+
+510
+00:38:19,050 --> 00:38:27,150
+القاعدة الأولى اسمها constructive dilemmas معضلات
+
+511
+00:38:27,150 --> 00:38:32,810
+بناء او معضلات
+
+512
+00:38:32,810 --> 00:38:37,950
+مثبتة او إيجابية بناء او إيجابي constructive
+
+513
+00:38:37,950 --> 00:38:46,290
+dilemma معضلات بناء او إيجابيةطبعا إيجابية لأن
+
+514
+00:38:46,290 --> 00:38:50,790
+فيها إثبات كله إثبات هنشوف واحدة اللي هي الهدامة
+
+515
+00:38:50,790 --> 00:38:53,530
+اللي فيها نفت بيادة المعنى المستخدمين المصطلح فهنا
+
+516
+00:38:53,530 --> 00:38:56,750
+بناها لأنه كله إثبات فطبعا اللي هنا قانون شوية
+
+517
+00:38:56,750 --> 00:39:02,550
+طويل في عندي جملتين شرطيتينمستقلتين عن بعض if B
+
+518
+00:39:02,550 --> 00:39:06,930
+then Q و if R then S تعرفوا إيش كانت؟ في حاجة
+
+519
+00:39:06,930 --> 00:39:10,490
+مشتركة بينهم جواب الأولى هو شرط التانية فصار
+
+520
+00:39:10,490 --> 00:39:13,910
+Transitive لكن الآن مستقلين عن بعض مستقلين عن
+
+521
+00:39:13,910 --> 00:39:17,890
+البعض الـB تؤدي للـQ و الـR تؤدي للـS إيش بقول
+
+522
+00:39:17,890 --> 00:39:21,890
+نتيجة؟ إذا أخدت الشرط الأول أو الشرط التاني بوصل
+
+523
+00:39:21,890 --> 00:39:25,670
+للنتيجة الأولى أو النتيجة التانية، هيك معناهافعندي
+
+524
+00:39:25,670 --> 00:39:30,390
+جملتين شرطيتين إذا الشرط الأول اتحقق بوصل لتاني أو
+
+525
+00:39:30,390 --> 00:39:33,570
+إذا الشرط التاني اتحقق بوصل لتاني فواحدة منهم
+
+526
+00:39:33,570 --> 00:39:36,770
+بيكون صحيحة فايق بالصحيحة فهي هياش بال ا فهو بيقول
+
+527
+00:39:36,770 --> 00:39:40,090
+ليه بيعدى الشكل implies طبعا مش تكافؤ فبقول ليه
+
+528
+00:39:40,090 --> 00:39:46,310
+اللي P then Q and R then S تؤدي أنه P or R تؤدي
+
+529
+00:39:46,310 --> 00:39:51,570
+إلى Q or S نفس القضية برضه ممكن أخد معاهم إيه and
+
+530
+00:39:51,570 --> 00:39:56,730
+بس أختلف الوضع هناهنا أخدت مين؟ الشرطين مع بعض
+
+531
+00:39:56,730 --> 00:40:01,250
+والجوابين مع بعض وبينهم or في التانية أخدت شرط
+
+532
+00:40:01,250 --> 00:40:04,550
+الأولى مع أيش؟ برضه الشرطين برضه الشرطين نفس الشيء
+
+533
+00:40:04,550 --> 00:40:08,450
+شرطين مع الجوابين بس مرة and ومرة or فدولة بيسموهم
+
+534
+00:40:08,450 --> 00:40:14,520
+constructive dilemmas قواعد اللي هو معضلات بناءفي
+
+535
+00:40:14,520 --> 00:40:19,800
+destructive dilemmas معضلات هدامة يعني إذا قولنا
+
+536
+00:40:19,800 --> 00:40:26,160
+بناءة أو إيجابية أو مثبتة هنا نافية لأن هنا في
+
+537
+00:40:26,160 --> 00:40:30,820
+نافية هنا في عملية نافية نفس الأشياءالطرف اليمين
+
+538
+00:40:30,820 --> 00:40:34,600
+نفسه زي اللي فوق، بس الاستنتاج فيه نفي، الاستنتاج
+
+539
+00:40:34,600 --> 00:40:39,760
+فيه نفي، اه فطبعا هنا الحقيقة هي عملية ليست الا
+
+540
+00:40:39,760 --> 00:40:43,420
+اللي هو contrapositive للي فوق، فاللي تحت هو
+
+541
+00:40:43,420 --> 00:40:46,100
+contrapositive للي فوق في الاستنتاج، اه فطبعا لو
+
+542
+00:40:46,100 --> 00:40:50,750
+بدي انا ايش ال contrapositive لهذه، نفي هذهبيقدّي
+
+543
+00:40:50,750 --> 00:40:54,630
+لنافية هذه طب نفلة هذه الشوة هيو ال or صارت and مع
+
+544
+00:40:54,630 --> 00:40:58,490
+نفلة و التانية نفس العكس بس و العكس فدولة بيسموهم
+
+545
+00:40:58,490 --> 00:41:02,370
+constructive dilemmas و destructive dilemmas طبعا
+
+546
+00:41:02,370 --> 00:41:05,690
+البرهان هنا في عندنا كام statement أساسية أربعة
+
+547
+00:41:05,690 --> 00:41:10,180
+نحتاج اتنين اقصى اربعة ستة عشر احتمال ستة عشرست
+
+548
+00:41:10,180 --> 00:41:15,300
+عشر احتمال اه طبعا مافيش حاجة جديدة فانا هتركهم
+
+549
+00:41:15,300 --> 00:41:19,200
+كلهم exercise لأنه بس مجرد عملية وقت يعني مش صعبة
+
+550
+00:41:19,200 --> 00:41:23,100
+لكن طويلة شوية لكن القواعد نفس الشيء فجيد انه
+
+551
+00:41:23,100 --> 00:41:26,720
+نعملها عشان نتمكن من عملية مين اللي هو ال truth
+
+552
+00:41:26,720 --> 00:41:29,460
+table و اللي يكون هذا اكتر شيء ممكن يكون مراهنة في
+
+553
+00:41:29,460 --> 00:41:34,540
+المصادر اربعة من ال statements المستقلين ف ال
+
+554
+00:41:34,540 --> 00:41:42,010
+proof كله هتركه exercise نظرية السادسةهنا two
+
+555
+00:41:42,010 --> 00:41:46,110
+statements نبيع let P and Q be any two statements،
+
+556
+00:41:46,110 --> 00:41:52,260
+إيش فينا قوانين؟ أه هنا فينا قانون مهممهم جدا،
+
+557
+00:41:52,260 --> 00:41:58,060
+هنعتمد عليه كثيرا في البراهين Modus Bonens Modus
+
+558
+00:41:58,060 --> 00:42:01,740
+Bonens طبعا مش English اللغة مش عارف اللي هي غالب
+
+559
+00:42:01,740 --> 00:42:05,440
+لاتيني او كذا المصطلح طبعا إيش ممكن نترجمها اللغة
+
+560
+00:42:05,440 --> 00:42:08,160
+الإنجليزية إيش تعني؟ بقول the way that affirms by
+
+561
+00:42:08,160 --> 00:42:12,600
+affirming الإثبات بالإثبات، الإثبات بالإثبات مر
+
+562
+00:42:12,600 --> 00:42:15,580
+علينا حاجة إيش اللي هو إيش؟ الإثبات بالنفي أو نفي
+
+563
+00:42:15,580 --> 00:42:18,420
+بالإثبات واحدة منها، فهذه إيش؟ الإثبات بالإثبات
+
+564
+00:42:18,710 --> 00:42:22,590
+that affirms by affirming ممكن نعمل اثبات بالاثبات
+
+565
+00:42:22,590 --> 00:42:25,810
+طيب نشوف احنا ده بس مجرد اسم القانون طب ايش
+
+566
+00:42:25,810 --> 00:42:30,850
+القانون بيقول انا في عندي جملة شرطية if b then q و
+
+567
+00:42:30,850 --> 00:42:36,010
+ال b صحيحة لازم ال q تكون صحيحة بمعنى اخر اذا وعدت
+
+568
+00:42:36,010 --> 00:42:40,400
+او في بالوعدو نفس القضية، إذا بدك توعد، بدك توفر
+
+569
+00:42:40,400 --> 00:42:42,500
+بقى، لازم الـQ تكون صحيحة، لازم يؤدي إلى الـQ،
+
+570
+00:42:42,500 --> 00:42:46,300
+فإذا كان عندي أنا، في عندي قاعدة B تؤدي إلى الـQ،
+
+571
+00:42:46,300 --> 00:42:48,960
+إذا الـB صحيحة، لازم الـQ تكون صحيحة، و إلا فيه
+
+572
+00:42:48,960 --> 00:42:51,700
+مشكلة و لا لأ؟ آه، فبقولي أنا في عندي قاعدة FB
+
+573
+00:42:51,700 --> 00:42:55,400
+تؤدي إلى الـQ، طب أنا الـB صح اتحققت، لازم الـQ
+
+574
+00:42:55,400 --> 00:43:00,090
+تتحققفده يسموه الواقعية .. طب ليش إثبات بالإثبات؟
+
+575
+00:43:00,090 --> 00:43:04,210
+لأن أنا أثبتت الـQ من الـB أخدت B صحيحة لأن إذا
+
+576
+00:43:04,210 --> 00:43:07,770
+الـB true فالـQ لازم تكون true فإن أنا إيش؟ أثبتت
+
+577
+00:43:07,770 --> 00:43:10,670
+الـQ عن طريق إثبات الـB إذا أثبتت الـB بتكون إيش
+
+578
+00:43:10,670 --> 00:43:14,610
+الـQ صحيحة فالمعنى تبعها ليش الإسم تبعها؟ أو
+
+579
+00:43:14,610 --> 00:43:17,150
+القاعدة بدا الشكل ممكن أخدها فدي بسموه Modus
+
+580
+00:43:17,150 --> 00:43:19,910
+Boninus Modus Modus Modus Modus Modus Modus Modus
+
+581
+00:43:19,910 --> 00:43:20,270
+Modus Modus Modus Modus Modus Modus Modus Modus
+
+582
+00:43:20,270 --> 00:43:22,410
+Modus Modus Modus Modus Modus Modus Modus Modus
+
+583
+00:43:22,410 --> 00:43:28,690
+Modus Modus Modus Modus Modus Modus Modusthe way
+
+584
+00:43:28,690 --> 00:43:34,030
+that denies by denying النفي بالنفي النفي بالنفي
+
+585
+00:43:34,030 --> 00:43:39,370
+فنفس الشيء برضه جملة شرطية إذا بتكاس توفي بالواعد
+
+586
+00:43:39,370 --> 00:43:44,670
+توعدشnot the Q عشان اثبت ان ال B انها false فبتبت
+
+587
+00:43:44,670 --> 00:43:47,830
+بي ليه ال true فإذا ال B false not B is true ف B
+
+588
+00:43:47,830 --> 00:43:51,230
+is false فبتكوناش not the Q اه فإذا كانت اللي
+
+589
+00:43:51,230 --> 00:43:54,850
+وقعتش نفي نفينا اللي هو ال B عن طريق انه ليهاش
+
+590
+00:43:54,850 --> 00:43:58,610
+نفينا ال Q فإذا كانت ال Q false مش هتقدر توفي
+
+591
+00:43:58,610 --> 00:44:03,180
+بالوعد ماتوقعتشأه .. اه .. انت مش جادر توفي بالوعد
+
+592
+00:44:03,180 --> 00:44:06,680
+متوقع انك ما توفيش بالوعد not Q ال Q of A يعني ال
+
+593
+00:44:06,680 --> 00:44:11,520
+Q is false ماتوعدش not B .. not B فإذا ال Q false
+
+594
+00:44:11,520 --> 00:44:15,480
+ال B بيكون false يعني not Q هي ال true واضح فهذا
+
+595
+00:44:15,480 --> 00:44:19,240
+قانونيا مهمين جدا هنستخدمهم ان شاء الله في
+
+596
+00:44:19,240 --> 00:44:26,290
+البراهينقانون تالت reduction and absordance برضه
+
+597
+00:44:26,290 --> 00:44:29,830
+كل هذه مصطلحات ليست لغة انجليزية فنقد النقيد ممكن
+
+598
+00:44:29,830 --> 00:44:33,490
+نعرفها نقد النقيد .. نقد النقيد .. نشوف ليش نقد
+
+599
+00:44:33,490 --> 00:44:37,140
+النقيدأه برضه كل التلات قوانين اللي هم علاقة
+
+600
+00:44:37,140 --> 00:44:39,920
+بالجملة الشرطية وهي الجملة الأكثر انتشارا في
+
+601
+00:44:39,920 --> 00:44:42,780
+الرياضيات هلاج أن معظم القوانين هنا فيها عايش جملة
+
+602
+00:44:42,780 --> 00:44:45,680
+شرطية if differentiable then continuous و هكذا
+
+603
+00:44:45,680 --> 00:44:49,980
+فأمور زي هيك if even divisible by two كتير من
+
+604
+00:44:49,980 --> 00:44:52,660
+القوانين من التعريفات من النظريات فالجملة الشرطية
+
+605
+00:44:52,660 --> 00:44:58,140
+مهمة جدا فبقول ليهif B then Q تكافئ الآن مش
+
+606
+00:44:58,140 --> 00:45:03,660
+implies إذا بدك توعد و تخلف بالوعد يؤدي إلى تناقض
+
+607
+00:45:03,660 --> 00:45:08,360
+إنك جيبت الشيء أو ضده Q and not Q هل يجتمعان؟
+
+608
+00:45:08,360 --> 00:45:11,160
+الشيء أو ضده بيجتمعوا؟ لأ، تناقض، عشان هي تناقض
+
+609
+00:45:11,160 --> 00:45:15,220
+النقيد، في تناقض هنا، حصلنا على تناقض، فبقولي B
+
+610
+00:45:15,220 --> 00:45:20,280
+and not Q تؤدي إلى جمع النقيدين مع بعض، بينفعش
+
+611
+00:45:20,280 --> 00:45:24,240
+نوعد و نخلف بالوعد، هذا تناقض، هذا تناقضفهذا ما
+
+612
+00:45:24,240 --> 00:45:28,920
+يسمى نقد النقيد، نقد النقيد، فعندك بي and not كيو،
+
+613
+00:45:28,920 --> 00:45:32,000
+هذا المفروض لايحدث، هذا المفروض لايحدث، لأنه يؤدي
+
+614
+00:45:32,000 --> 00:45:35,360
+إلى مشكلة، يؤدي إلى تناقض، يعني احنا بالمعنى العام
+
+615
+00:45:35,360 --> 00:45:38,900
+نقول بيؤدي إلى مشكلة، طبعا المعنى، المنطقى يؤدي
+
+616
+00:45:38,900 --> 00:45:41,560
+إلى تناقض، إلى إيش؟ إلى تناقض، يعني هذا عمره ما
+
+617
+00:45:41,560 --> 00:45:45,010
+بتكون صحيحةهذه عمرها ما بتكون صحيحة لأنه دايما
+
+618
+00:45:45,010 --> 00:45:49,030
+الشيء هو ضده و بينهم and إذا q true فننطق q false
+
+619
+00:45:49,030 --> 00:45:52,350
+فإذا نقل ال and false إذا ال q false فننطق q true
+
+620
+00:45:52,350 --> 00:45:56,770
+و ال and بتكون false فهذه بيسموه إيش تناقض فهذه هي
+
+621
+00:45:56,770 --> 00:46:03,090
+القوانين إذا حابين مافيش وقت خليني أنهي هنا إن شاء
+
+622
+00:46:03,090 --> 00:46:05,750
+الله المحاضرة القادمة بينكمل
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/xKzVbyXMocI_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/xKzVbyXMocI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d05cd044d606bbfc59d3e369beb7538614971376
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/xKzVbyXMocI_postprocess.srt
@@ -0,0 +1,2280 @@
+1
+00:00:21,580 --> 00:00:25,940
+بتصل مع ال internet 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 عرصة فتمها
+
+4
+00:00:35,500 --> 00:00:43,440
+لانهائية عرفنا أنه في عندنا ال Y بتساوي X ناقص ال
+
+5
+00:00:43,440 --> 00:00:48,860
+X0و ال X0 هو عنصر من عناصر ال capital X فهذه بنثبت
+
+6
+00:00:48,860 --> 00:00:51,840
+أنها infinite إذا كانت ال X infinite في حالة .. من
+
+7
+00:00:51,840 --> 00:00:54,300
+الحالة طبعا عشان نعرف دالة عشان إيش ال Y infinite
+
+8
+00:00:54,300 --> 00:00:58,380
+إيش معناته؟ هناك دالة one to one F من Y ل Y تكون
+
+9
+00:00:58,380 --> 00:01:01,780
+one to one و ليست unto فاحنا كلنا لازم ناخد حالتين
+
+10
+00:01:01,780 --> 00:01:06,480
+لو كانت ال X0 صورة عنصر من عناصر ال Y فيها مشكلة
+
+11
+00:01:06,480 --> 00:01:10,360
+فهذه اشتغلناها لحالة و لو ماكنتش صورة ناخد ال F
+
+12
+00:01:10,360 --> 00:01:13,340
+على طول بتسوء G اللي هي الدالة من و لا ويا من X ل
+
+13
+00:01:13,340 --> 00:01:20,860
+X احنا في عنا Gمن X ل 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 أنصر بينفعش لأن الـ X Zero خارج الـ Y فلو هي
+
+17
+00:01:33,460 --> 00:01:37,130
+صورة بذا سير أيش خارج الـ Y بينفعش بالنسبة للـ Fأه
+
+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 التانية إذا كانت صورة أعملنا trick بسيط
+
+20
+00:01:44,010 --> 00:01:49,910
+وعرفنا ال F إحنا في الحالة إن هذي X0 تنتمي لل G of
+
+21
+00:01:49,910 --> 00:01:56,710
+X هذي Case 2 احنا بنشتغل هنا فعرفنا ال F من Y ل Y
+
+22
+00:01:56,710 --> 00:02:05,280
+byF of X تساوي G of X إذا الـ X لا تساوي A طبعا
+
+23
+00:02:05,280 --> 00:02:09,400
+احنا عايش هذا معناته أن X0 تساوي G of A for some A
+
+24
+00:02:12,800 --> 00:02:18,300
+تنتمي لل X وإذا كانت من ال X بتساوي A أخدناها بيه
+
+25
+00:02:18,300 --> 00:02:23,880
+عنصر جديد واخترنا عنصر بيه 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 ال بيه أخدت ال بيه من هناأه 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 ال
+
+35
+00:02:55,020 --> 00:02:57,840
+one to one فاحنا اخترنا مادة شكلة طبعا بنا نثبت أن
+
+36
+00:02:57,840 --> 00:03:01,940
+هذه الـ F one to one وليست unto، مظبوط؟فأحنا أول
+
+37
+00:03:01,940 --> 00:03:08,240
+شي G أسف F is one to one وصلنا هنا ولا لأ؟ أه ال F
+
+38
+00:03:08,240 --> 00:03:12,940
+is one to one فكعادتنا في برهان ال one to one ناخد
+
+39
+00:03:12,940 --> 00:03:20,630
+عنصرين من ال domain تنتمي لل Y such thatF 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 ال one to
+
+42
+00:03:31,890 --> 00:03:35,910
+one بدايته على الأقل بداية بسيطة و بنتعلمها زي ما
+
+43
+00:03:35,910 --> 00:03:40,950
+اتعلمنا عدة مهارة بدنا نثبت أن X1 تساوي X2واتعلمنا
+
+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 واتاني في
+
+49
+00:03:59,930 --> 00:04:08,330
+الجزء التاني فهذا يؤدي لو كانت X واحدلاتساوي A و
+
+50
+00:04:08,330 --> 00:04:15,960
+X2 لاتساوي A إيش بيكون التعريف G of X1وبرضه g of
+
+51
+00:04:15,960 --> 00:04:21,740
+x2 مظبوط؟ امتبعين معاه؟ اه فلو كانوا لو x1 مش a
+
+52
+00:04:21,740 --> 00:04:25,240
+وx2 من a وين التعريف؟ بيقوللي اذا كانت ال x تسوى
+
+53
+00:04:25,240 --> 00:04:28,520
+ايش التعريف؟ g بيبقى تسوى g ناخد التاني لو كانوا
+
+54
+00:04:28,520 --> 00:04:33,340
+التنين بيسووا ايه؟ لو كانت x1 تسوى a تسوى x2 ايش
+
+55
+00:04:33,340 --> 00:04:37,620
+التعريف؟ b ايش التعريف؟ b اه طبعا ايش بينهم؟ or
+
+56
+00:04:37,620 --> 00:04:41,940
+لان احتمالاتالان الاحتمالين اللي تموا واحد هيك و
+
+57
+00:04:41,940 --> 00:04:44,880
+واحد هيك هتقول اتنين من نفس الاشي وقعوا مع بعض من
+
+58
+00:04:44,880 --> 00:04:51,300
+نفس الجزء الان or لو كانت x1 لا تساوي a لكن x2
+
+59
+00:04:51,300 --> 00:04:56,920
+بتساوي a اللي بتساويش ايش بتكون صورتها؟ g و اللي
+
+60
+00:04:56,920 --> 00:05:04,280
+بتساوي بيه احتمال الأخير بيه 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
+التالت و الرابع ممكن يدمجهم في احتمال واحد ليش؟
+
+64
+00:05:18,400 --> 00:05:21,860
+لأن ال X1 و X2 دي الترتيب ليه مش مهم ايش اختصارهم؟
+
+65
+00:05:21,860 --> 00:05:25,340
+ان واحد بيساوي ايه و واحد لا يساوي ايه فهم نفس
+
+66
+00:05:25,340 --> 00:05:29,580
+الاحتمال لكن هناخدهم بالتفصيل التكرار مافيش منه
+
+67
+00:05:29,580 --> 00:05:33,560
+ضرر لكن أحيانا حذف حالة بتكون أساسية ممكن يكون فيه
+
+68
+00:05:33,560 --> 00:05:36,620
+ضرر طبعا لكن هم هدول لو حذفنا واحدة فيهم مابنخسرش
+
+69
+00:05:36,620 --> 00:05:41,090
+اشي لكن خلينا نعمله تمام وين بدنا نوصل؟إن X1 يساوي
+
+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
+يساوي X2 ليش؟ لأن الـG one to one لأن الـG is one
+
+72
+00:05:51,110 --> 00:05:56,560
+to oneوالتانية بتقول بي تساوي بي، عدم أن 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 بي تساوي بي أحذفها؟ لأ، لأنها دي O، لكن
+
+75
+00:06:04,860 --> 00:06:07,720
+لو دقّقنا إيش معنات هدول، إيش معنهم؟ ماهم تساويين،
+
+76
+00:06:07,720 --> 00:06:12,760
+X1 تساوي X2 تساوي X2، فبرضه X1 تساوي X2or بقدر
+
+77
+00:06:12,760 --> 00:06:17,520
+أستنتج طيب اللي بعده contradiction التاني تاني ليش
+
+78
+00:06:17,520 --> 00:06:22,520
+لأنه لما يقول ال B صورة يعني ال B وين في صور ال G
+
+79
+00:06:22,520 --> 00:06:25,680
+و ال B من إيش خارج الصور مستحيل لما تقولي ال B
+
+80
+00:06:25,680 --> 00:06:29,260
+صورة عنصر ما يعني بالصور و ال B من وين اختارناها
+
+81
+00:06:29,260 --> 00:06:31,940
+من خارج الصور عشان هيك احنا لما أعرفنا ال 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 ال
+
+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، والتانية برضه
+
+87
+00:06:49,020 --> 00:06:51,400
+Contradiction زيها، ما احنا قولنا 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 Xواضح ال
+
+90
+00:07:00,340 --> 00:07:03,540
+contradiction ولا في حد مش واضح حاله؟ اه لأنه إيش
+
+91
+00:07:03,540 --> 00:07:08,240
+معناه أن ال 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 بي تنتمي لل G of X؟ يعني ال B تساوي صورة
+
+94
+00:07:17,420 --> 00:07:20,760
+عنصر من ال G of X اه فلو كانت ال B تلان ال X واحد
+
+95
+00:07:20,760 --> 00:07:24,100
+وين موجودة ال X واحدة دي؟ في ال X اه بي في ال Y و
+
+96
+00:07:24,100 --> 00:07:26,160
+ال Y جزء من ال X بتساويش X زيه فبتديني
+
+97
+00:07:26,160 --> 00:07:30,110
+contradiction طبعا الآن B or بي بيP or
+
+98
+00:07:30,110 --> 00:07:33,770
+contradiction P او P or contradiction P فهذا يقضي
+
+99
+00:07:33,770 --> 00:07:37,010
+ان ال P هي المين ل X واحد تساوي X اتنين فهذا يقضي
+
+100
+00:07:37,010 --> 00:07:40,870
+ان X واحد تساوي X اتنين و هذا يقضي ان ال F is one
+
+101
+00:07:40,870 --> 00:07:45,650
+to oneفزي 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
+تلاتة ممكن، لكن حتى لو كانوا أربعة، طبعا ماينفعش
+
+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 contradictionفهذا
+
+109
+00:08:10,910 --> 00:08:13,110
+المطلوب الأول نشوف المطلوب التاني انه proper
+
+110
+00:08:13,110 --> 00:08:18,710
+subset ليست onto ال F خلينا
+
+111
+00:08:18,710 --> 00:08:25,230
+هذه مؤقتا ان احنا نحتاجها اتنين F ال Y proper من
+
+112
+00:08:25,230 --> 00:08:31,190
+ال Yفبدنا عنصر موجود في الـY وغير موجود في الـF of
+
+113
+00:08:31,190 --> 00:08:35,910
+Y خلّينا نحسب الـF of Y، نحسب الـImage عشان نشوف
+
+114
+00:08:35,910 --> 00:08:40,650
+مين عنصر خارج الـImage، بدنا عنصر خارج الـImage، F
+
+115
+00:08:40,650 --> 00:08:48,360
+of Y إيش بتساوي؟ F ofكيف احسب الـ image لدالة
+
+116
+00:08:48,360 --> 00:08:55,200
+متعددة القاعدة كيف نحسب ال image لدالة متعددة
+
+117
+00:08:55,200 --> 00:08:58,920
+القاعدة ايش متعددة القاعدة ال domain مجسم فانا ايش
+
+118
+00:08:58,920 --> 00:09:03,600
+اعمل اجسم ال domain اجسم ال domain هذه ال Y عبارة
+
+119
+00:09:03,600 --> 00:09:06,080
+عن اصلا X ناقص X Zero
+
+120
+00:09:09,940 --> 00:09:14,820
+و احنا التعريف اذا X لا تساوي A لها تعريف و عند ال
+
+121
+00:09:14,820 --> 00:09:19,440
+A بتساوي تعريف فانا هجسم ال demand جزء من غير A و
+
+122
+00:09:19,440 --> 00:09:23,260
+الجزء اللي فيه ال A فدي كيف ممكن اكتبها بكتبها F
+
+123
+00:09:23,260 --> 00:09:31,520
+of X ناقص X0Aاتحاد الـ A لحال خلّيها 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 ال X0 والـ A اتحاد
+
+127
+00:09:49,760 --> 00:09:54,660
+F الـ A اللي هي على طول ممكن اكتبها مين مجموعة F
+
+128
+00:09:54,660 --> 00:10:01,530
+الـ Aمظبوط؟ انت باين؟ ولا اعيد؟ اه الآن بدي احسب
+
+129
+00:10:01,530 --> 00:10:07,930
+ال image طبعا مين اعوض عن F؟ اعوض G ولا B؟ لأ لازم
+
+130
+00:10:07,930 --> 00:10:11,650
+اجسم وين هي بتساوي B وين هي بتساوي G فاضطريت اجسم
+
+131
+00:10:11,650 --> 00:10:15,670
+ال domain وين هي بتساوي B عند ال A فخلت ال A لحالة
+
+132
+00:10:15,670 --> 00:10:20,130
+والباقي ايش تعرفه؟ G اه فالان من خواص ال F تتوزع
+
+133
+00:10:20,130 --> 00:10:26,550
+الاتحاد الآن هذي ايش بتساوي؟ Bمظبوط F of A بتساوي
+
+134
+00:10:26,550 --> 00:10:30,270
+B مظبوط هيك بنقرعها F of X لما ال 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 minus X0 و A أنا جيت بقى أقدر
+
+137
+00:10:43,190 --> 00:10:47,110
+أمحي هذا فعشان هيك جسمت ال 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 بديهامعروف أتوقع في أحد التمارين
+
+140
+00:10:55,760 --> 00:10:59,000
+الكتاب إذا تدالة one to one الصورة بتتوزع على ال
+
+141
+00:10:59,000 --> 00:11:02,340
+minus مش دائما 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 Yطيب أسأل نفسي ممكن
+
+146
+00:11:24,950 --> 00:11:29,310
+نكون تهنا احنا عايش بندور بدنا أنصر موجود في ال Y
+
+147
+00:11:29,310 --> 00:11:32,950
+مش موجود هنا طب هذا بيساوي هذا، بدي أنصر 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 أصلا في ال Y، بديها 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 الصورةموجودة 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 andWhy لا تنتمي
+
+158
+00:12:19,110 --> 00:12:23,270
+لمين للـF of Y؟ لأن هنا أخدناها من برا لأنه بالـ-C
+
+159
+00:12:23,270 --> 00:12:27,090
+طبعا 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 طبعا 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 التاليةبقول 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
+بالرنزة؟ 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 الواحداد من
+
+174
+00:13:23,430 --> 00:13:27,550
+واحد لعشر وها كذا 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
+الصورةبدنا 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
+تلاتةواحد و اتنين و تلاتة و هكذا واضح التعريف الان
+
+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 التاني خليني أسميها PM بلاش
+
+185
+00:14:29,590 --> 00:14:34,570
+PM تفرجش طبعا 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 sentenceمع 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 او من اي 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، طبعا 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
+طبعا، اللي هي هذه هي statement، اه open sentence
+
+197
+00:15:16,520 --> 00:15:19,520
+طبعا، بدي أثبت إنه هذه إيش، دايما 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 finiteإيش رأيكوا؟ هذي true ولا مش
+
+200
+00:15:31,140 --> 00:15:35,040
+true؟ لإيش؟ 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 trueأرجو إن هذا المثال يؤكد
+
+205
+00:15:59,710 --> 00:16:03,590
+أننا فاهمنا 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 وطبعا 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 finiteإيش 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 isبدنا 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
+طبعا 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 أه 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 assumeand 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
+أحنا 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
+البرهقة، 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 الا nk plus one مطوح
+
+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 البرهارةوانتهى البرهن فهنا دايما اروح من
+
+247
+00:19:21,820 --> 00:19:25,820
+الحالة او 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 بتامها infinite فمستحيل تكونها دي infinite
+
+251
+00:19:35,220 --> 00:19:44,960
+وانتهى البرهن فهذه حقيقة مهمة جدا 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 thatإذا 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 فعلا، 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، أه، بتكتسل هنا؟
+
+260
+00:20:24,900 --> 00:20:30,420
+إذا كانت هذه infinite حذفنا من 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 من عنصر بتامها 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 مالة؟ 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 تحتوى ال A و proper subset مش subset بقى
+
+277
+00:21:47,460 --> 00:21:52,340
+تحتوي proper subset إيش بيقدّي؟ يقدّي إن ال B is
+
+278
+00:21:52,340 --> 00:21:56,840
+infiniteلا لسه هذا المطلوب هذا كله مُعطَع 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 اثبت منه ايه
+
+282
+00:22:12,800 --> 00:22:17,380
+infinite we want to proveفدي 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 انا ايش افسر ايش 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 حطت implies هنا يعني ايش 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
+أخدنا أي proper لكل ال B اللي هي بتحتول A لازم ال
+
+293
+00:23:01,740 --> 00:23:07,400
+B تكون infiniteممكن، ممكن، بس هي بنفس المعنى، ففي
+
+294
+00:23:07,400 --> 00:23:12,500
+أحيان بكون أكتر من تفسير تمام، فإيش ممكن نعمل؟ إيش
+
+295
+00:23:12,500 --> 00:23:16,120
+ممكن نعمل؟ فاحنا مطلوب نثبت إن الـA 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 المؤتيات، بدي
+
+298
+00:23:21,920 --> 00:23:26,460
+أدور على مجموعة B بتكون أكبر من مين من الـA، و
+
+299
+00:23:26,460 --> 00:23:30,480
+تكون Infiniteأه و إيه علاقة مع ال A؟ إيه علاقة مع
+
+300
+00:23:30,480 --> 00:23:34,220
+ال A؟ إذا كنت تثبت أن ال B infinite فبقى .. آسف ال
+
+301
+00:23:34,220 --> 00:23:36,880
+B هتكون infinite و منها حسن تجي أن ال A infinite
+
+302
+00:23:36,880 --> 00:23:39,600
+لأنه بيقول ليه أي brother super set من ال A
+
+303
+00:23:39,600 --> 00:23:43,400
+infinite بدي أثبت أن ال A infinite أنا بعرففبدنا
+
+304
+00:23:43,400 --> 00:23:47,440
+علاقة نعملها زي ال trick الماضي بدنا مجموعة ما B
+
+305
+00:23:47,440 --> 00:23:51,100
+نطرح منها عنصر تدينا ال A واحنا عارفين أن ال B
+
+306
+00:23:51,100 --> 00:23:53,120
+infinite لأن بقول ال B إلى خلاص معايا بيكون
+
+307
+00:23:53,120 --> 00:23:56,440
+infinite وال A عبارة عن B ناقص عنصر بيصير ال A
+
+308
+00:23:56,440 --> 00:24:02,240
+infinite فكيف بنكوّنها؟ هنكوّنها مع بعض هقوله الآن
+
+309
+00:24:02,240 --> 00:24:09,240
+let B لا تنتمل ال A بدي أخد عنصر خارج ال A بدي أخد
+
+310
+00:24:09,240 --> 00:24:13,650
+عنصر خارج ال A بينفع أخد عنصر خارج ال A؟ليش؟ لأ مش
+
+311
+00:24:13,650 --> 00:24:17,530
+عارف الـB، بتكون الـB لسه لأن مافيش إيه بتحتوي كل
+
+312
+00:24:17,530 --> 00:24:20,750
+شيء فقدّيني أي مجموعة، في مجموعة عنصر أخرج، يا
+
+313
+00:24:20,750 --> 00:24:23,830
+خدنا عنصر معاه الآن هنكون الـB، انتبهوا على ال
+
+314
+00:24:23,830 --> 00:24:31,490
+trick اللي هنعمله أدلت B تساوي إيه اتحاد الـB ليش
+
+315
+00:24:31,490 --> 00:24:35,370
+بد الـB بالخارج؟ عشان لما أضيفه للـA تصير فعلا
+
+316
+00:24:35,370 --> 00:24:38,410
+أكبر لأن لو كان دي هو الـA كان مع اتحاده بتعمل
+
+317
+00:24:38,410 --> 00:24:44,970
+إيه؟ فانا بديها تكون proper الآن thenالـ B proper
+
+318
+00:24:44,970 --> 00:24:48,670
+super 6 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 إيش عندي
+
+322
+00:24:59,350 --> 00:25:03,190
+مقطع جالي كل proper super 6 إذا كانت الـ B proper
+
+323
+00:25:03,190 --> 00:25:05,970
+super 6 من إيش؟ مقلبة الـ B في infinite فهذا يؤدي
+
+324
+00:25:05,970 --> 00:25:12,830
+إن الـ B is infiniteطيب إيش علاقة الـ B مع الـ A
+
+325
+00:25:12,830 --> 00:25:21,870
+بط بي ناقص الـ B تساوي إيه؟ 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 المطلوبفهنا مرة
+
+328
+00:25:35,390 --> 00:25:37,770
+تانية كيف نستخدم النظرية فاحنا ايه 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 و طرحنا 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 ال criterion
+
+336
+00:26:25,190 --> 00:26:29,840
+for finite setsأه طبعاً احنا فيها إن التعريفات
+
+337
+00:26:29,840 --> 00:26:33,600
+وشوفنا إنه التعريفات مش دايماً 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 finiteكيف 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 ال finite و أعرف ال infinity اللي
+
+345
+00:26:56,890 --> 00:27:00,210
+عبارة عن ال negation و بعدين أوصل ل اللي 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 إيش 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
+إيش المجموعة بتكون finite بقول اللي asset X is
+
+350
+00:27:15,540 --> 00:27:20,560
+finite if and only if عشان هيه معيار if if and
+
+351
+00:27:20,560 --> 00:27:26,460
+only if either X is Phi يا فارغة or X is 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 تاوي اتحدثنا عنها والـ NK إيش
+
+354
+00:27:32,720 --> 00:27:35,780
+معناه دايما؟ دي finite فهي إيه إيش ال finite؟ ال
+
+355
+00:27:35,780 --> 00:27:40,450
+finite يا إمافارغة 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
+أشرين، مية يعني بتكافئ مين؟ NK ماودهش NK لما بقول
+
+361
+00:27:58,370 --> 00:28:01,770
+أناش بعدهم واحد، اتنين، تلاتة، K إذا رقم أنصر فيها
+
+362
+00:28:01,770 --> 00:28:07,210
+K من العناصر خلينا نشوف البرهان مع بعضخلّيني أبدأ
+
+363
+00:28:07,210 --> 00:28:11,690
+البرهان هنا Approve
+
+364
+00:28:11,690 --> 00:28:15,710
+طبعا هذه ال statement خلّيني أكتبها أول شي فعنا
+
+365
+00:28:15,710 --> 00:28:23,070
+هنا X يمكن جاب للبرهان نكتب ال statement X
+
+366
+00:28:23,070 --> 00:28:35,080
+is finite if and only ifx تساوي 5 او x in one to
+
+367
+00:28:35,080 --> 00:28:38,520
+one correspondence يعني ايش؟ there exists a
+
+368
+00:28:38,520 --> 00:28:47,000
+bijection نسميه f او g اللي بدنا يه جي من x لمين؟
+
+369
+00:28:47,000 --> 00:28:53,400
+للن كي for some k تمام؟ فهذه ال 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 التاني 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 فاي or there exist a bijection
+
+375
+00:29:30,440 --> 00:29:38,760
+J من X ل K ل NK طبعا for some K تنتمي
+
+376
+00:29:38,760 --> 00:29:47,000
+لل Z مظبوط for some NK طبعا خليها واضحة مش مشكلة
+
+377
+00:29:47,000 --> 00:29:55,580
+implies X is finite فهذا التجاه الأول تمام assume
+
+378
+00:29:55,580 --> 00:30:03,180
+X تسوى فAssume X تساوي فاي or there exists a
+
+379
+00:30:03,180 --> 00:30:07,060
+bijection
+
+380
+00:30:07,060 --> 00:30:14,220
+J من X لأنكي 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 التاني 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 Phi، 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
+تسوي Phi، then X is finite
+
+389
+00:30:57,400 --> 00:31:00,840
+الآن بدنا ناخد الاحتمال التاني فهذا هو يكون
+
+390
+00:31:00,840 --> 00:31:05,480
+proposition خمسة اتنين اتوقع proposition خمسة
+
+391
+00:31:05,480 --> 00:31:09,300
+اتنين خلصنا فالان بدنا ناخد الاحتمال التاني فإن
+
+392
+00:31:09,300 --> 00:31:16,240
+اذا ماكنتش five 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 إلىNK 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 تنتين finite
+
+397
+00:31:44,710 --> 00:31:48,010
+يا تنتين infinite أنا بعرف من المثال الماضي من
+
+398
+00:31:48,010 --> 00:31:51,890
+النتيجة أن ال NK is finite إذا لازم ال X تكون
+
+399
+00:31:51,890 --> 00:31:56,570
+finite أه فهنا by اللي هو ال corollary
+
+400
+00:32:00,900 --> 00:32:04,200
+خمسة واحد وخمسة اتنين خمسة واحد بتقول علاش انه
+
+401
+00:32:04,200 --> 00:32:09,520
+مافيش بيجيكشن اللاتنتين من finite and corollary
+
+402
+00:32:09,520 --> 00:32:17,430
+خمسة اتنين x is finite فهذا الجزء السهلفخلصنا، فلو
+
+403
+00:32:17,430 --> 00:32:20,750
+كانت five هي finite لأن فيها zero من العناصر، و
+
+404
+00:32:20,750 --> 00:32:23,710
+هذا أثبتناها قبل هيك، و لو كانت فيها bijection
+
+405
+00:32:23,710 --> 00:32:26,710
+بينها وبين N، NK، مانفعش يكون بيجيكشن لبين
+
+406
+00:32:26,710 --> 00:32:29,490
+مجموعتين من نفس الجنس، بما أن NK finite توي
+
+407
+00:32:29,490 --> 00:32:32,950
+أثبتناها بال induction، إذا لازم تاني تكون finite،
+
+408
+00:32:32,950 --> 00:32:39,120
+فأدا الاتجاه خلص، نيجي للاتجاه التانيبدنا الآن B
+
+409
+00:32:39,120 --> 00:32:41,760
+implies Q بس عشانها كبيرة مابديش اكتبها كمان مرة
+
+410
+00:32:41,760 --> 00:32:46,160
+مش هثبتها بشكل مباشر هثبت ال contrapositive تبعتها
+
+411
+00:32:46,160 --> 00:32:50,140
+ايش مطلوب نثبت ولا اكتب .. خليني اكتب يلّا اه هل
+
+412
+00:32:50,140 --> 00:33:00,380
+جيش بدنا نثبت ان X is finite implies X تساوي Phi
+
+413
+00:33:00,380 --> 00:33:05,880
+or there exists a bijection خليني اكتبها بشكل
+
+414
+00:33:05,880 --> 00:33:15,390
+مختصرمن X ل NK تكون one to one and unto واضحة؟ one
+
+415
+00:33:15,390 --> 00:33:20,170
+to one and unto اكتبه بهذا الشكل اختصارا اه تمام
+
+416
+00:33:20,170 --> 00:33:25,050
+فده مطلوب اه مش هنثبت هذه اليملة مباشرة هنثبت ال
+
+417
+00:33:25,050 --> 00:33:36,930
+contrapositive تبعدها او it's contrapositive نتذكر
+
+418
+00:33:38,300 --> 00:33:42,020
+شبتر واحد اه بيصير not Q implies not B يعني إيه ده
+
+419
+00:33:42,020 --> 00:33:48,240
+تكون هذا النفي تبعتها X لا تسوى فاي and their
+
+420
+00:33:48,240 --> 00:33:53,940
+existence هصيربتصير for all انه .. بس هو بيقول لي
+
+421
+00:33:53,940 --> 00:33:56,940
+there exists يعني مافيشش 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 بذا الشكل .. اه هي for all .. اي دالة من x
+
+424
+00:34:04,200 --> 00:34:08,500
+ل x and هتكون bijection .. اه بيصير أنه أي دالة من
+
+425
+00:34:08,500 --> 00:34:11,080
+x ل and 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 نثبتأه مرة تانية احنا
+
+431
+00:34:48,040 --> 00:34:53,500
+بنعمل هذه الجملة أثبتنا Q تكائط implies B ففي واحد
+
+432
+00:34:53,500 --> 00:34:58,500
+انهيش 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
+امتبعين باختصار شديد وده اللي عملنا تمام فالجملة
+
+435
+00:35:08,720 --> 00:35:11,580
+الشرطية اللي كترة 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 FI and there is no bijection between X
+
+438
+00:35:29,450 --> 00:35:38,100
+and NK ولا NK مستحيلكم اتمنواالبرهان 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 و بعدين نكتب أنا عندي مجموعة كبيرة بدي أثبت
+
+441
+00:35:48,420 --> 00:35:50,860
+إنها infinite اللي هنعملوا في طريقة البرهان إن
+
+442
+00:35:50,860 --> 00:35:54,900
+هدول العناصر هنرتبهم فنفترض إن إحنا في عندنا وعاء،
+
+443
+00:35:54,900 --> 00:35:59,130
+في عندنا كيس، في كرات مش عارفين عددهمهنبدأ ناخد كل
+
+444
+00:35:59,130 --> 00:36:01,990
+كورة ونعدّى عشان نصفد ان واحدة وانا 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 ال K صفضى إيش بيكون اتفيلها كورة واحدة؟ إيش
+
+447
+00:36:08,250 --> 00:36:12,250
+بيكون؟ بناقد 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
+كورةأمد إيدي واخد الكرة رقم اتنين ارقمها هي ايش
+
+451
+00:36:21,390 --> 00:36:26,490
+الكرة رقم اتنين طيب خلص ال case مستحيل لو انه خلصش
+
+452
+00:36:26,490 --> 00:36:30,530
+بيكون and two بينفعش فاخد ايش اخد كمان عنصر و هكذا
+
+453
+00:36:30,530 --> 00:36:33,570
+فدي الفكرة فدي الفكرة اللي حنمنها هنرقمها
+
+454
+00:36:36,520 --> 00:36:40,380
+X لا تساوي فاى، إيش معناته؟ 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
+أرقمه، مديت إيدي في الكيس، لاجيت أول كورة، لأنه مش
+
+457
+00:36:48,420 --> 00:36:51,580
+فاضي، هلاجي كورة و لا 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
+أه، اللي قاعد بالتأكيد أن الكيس مافضيش، لو أخدت
+
+460
+00:36:58,800 --> 00:37:02,520
+منه كورة بفضأ، بفضاش، أه، أه، 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 ال bijection؟ then g من n one
+
+463
+00:37:17,650 --> 00:37:22,880
+إلى x given by بدي أدريكيها بشكل صريحمين 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 والاكس واحد في بينهم one
+
+468
+00:37:41,370 --> 00:37:44,850
+to one correspondence ولا لأ الواحد اكس واحد هي
+
+469
+00:37:44,850 --> 00:37:47,710
+التنازف صح ولا لأ طبعا ايش مقالة ده contradiction
+
+470
+00:37:47,710 --> 00:37:50,630
+مستحيل اه اذا ايش مقالة اه اذا 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 ان اكس ناقص اكس one لا تساوي five بدل مكتبX
+
+474
+00:38:06,940 --> 00:38:13,560
+نقص واحد تسوى نفس المعنىفما 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 تانية،
+
+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؟ أه، فعشان
+
+482
+00:38:34,380 --> 00:38:36,860
+هي كان بيدي أخدياش عنصر من X ناقص X واحدة، ان
+
+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
+فانا عندي X ناقص X1 و X2 برضه لاتساوي 5فبعد ما خدت
+
+490
+00:39:29,730 --> 00:39:34,090
+الكورتين برضه ما فضيتش الكيس و لا 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
+أه 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، أه 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
+انعمم الفكرة ايش اللي كدبناها تعميم لجينا X1 لو
+
+500
+00:40:15,890 --> 00:40:21,570
+خلصت بينفعش اتخلص لجيت X2 بعد ما X2 ايش بلاجي X3
+
+501
+00:40:21,570 --> 00:40:26,490
+فكل مرة بعد ما خلص لما لاجي XN ايش بلاجي N plus
+
+502
+00:40:26,490 --> 00:40:29,490
+one واضحة ولا مش واضحة ال statement ها دي اه لأنه
+
+503
+00:40:29,490 --> 00:40:35,370
+انا ايش 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؟ لأ مابتجافش لو
+
+505
+00:40:38,770 --> 00:40:44,230
+وقفتلو هذا كان غلط، إيش معناته؟ إن هناك bijection
+
+506
+00:40:44,230 --> 00:40:48,150
+بين X و بين مين، N sub small n، صح؟ مستحيل، أه،
+
+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
+ال trick التالف let Y تساوي X N such that N تنتمي
+
+511
+00:41:07,310 --> 00:41:13,230
+للـ Nأيش اللي بده أعمله زي ما حكينا مرة تانية هي
+
+512
+00:41:13,230 --> 00:41:17,690
+الكيس فيه كورات مخربطين ومش عارفين إيش نوحهم 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 فالان طبعا إذا أثبت ان ال Y
+
+516
+00:41:28,950 --> 00:41:32,280
+infiniteكل عناصر الـ Y من أين واخدناها؟ 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، لأ 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 البرهة، فهي فكرة
+
+521
+00:41:44,540 --> 00:41:48,480
+البرهة طبعا، طب ليش الـ Y التعامل معها أسهل؟ لأنها
+
+522
+00:41:48,480 --> 00:41:52,140
+مرتبة، مرقمة، أه كيف ممكن أثبت أن الـ Y Infinite؟
+
+523
+00:41:52,140 --> 00:41:57,320
+ممكن نلاقي دالة one to one وليست أنتوا بسهولة then
+
+524
+00:42:02,100 --> 00:42:11,260
+Y subset من ال X and F من Y ل Y مين يثبت إن ال Y
+
+525
+00:42:11,260 --> 00:42:14,800
+Infinite؟ تدوني دالة one to one و ليست on two،
+
+526
+00:42:14,800 --> 00:42:22,330
+given byإيش نعمل؟ إيش عملنا بالـnatural number؟
+
+527
+00:42:22,330 --> 00:42:26,830
+لإن أحنا 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 الـand 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 أخدتF 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 one to less
+
+536
+00:43:08,560 --> 00:43:15,210
+فكروا فيها أوي المكتوب and F given byis one to one
+
+537
+00:43:15,210 --> 00:43:21,710
+and f of y برابر من ال 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 اتنين فصورة
+
+539
+00:43:25,230 --> 00:43:28,010
+من وين بتبدأ من x اتنين و طالع 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 البرهق خليني
+
+546
+00:44:06,960 --> 00:44:13,020
+بس ننهي بملاحظة لأن مافيش وقت كتير 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 ال 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 لأ هي أنا عنصر مقابل الأتنين في عنصرفإذا 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 ال X is a non-empty طبعا إذا empty ما
+
+555
+00:44:44,630 --> 00:44:46,870
+هي معروفة نيجي على ال 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
+منتهيةوغير 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 ال 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
+التنين أسميها X تنين فزا عناصر ال X ممكن إيش؟
+
+564
+00:45:17,590 --> 00:45:22,540
+أرقمهم ممكن نرقمهمإذا أي finite set يا إما Phi
+
+565
+00:45:22,540 --> 00:45:26,520
+وإذا ماكنتش Phi ممكن أرقمها من واحد لعدد العناصر ل
+
+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 ل X K for some K في
+
+569
+00:45:36,960 --> 00:45:40,860
+عدد K من العناصر وهذا متفق مع التعريف القدي نوجّف
+
+570
+00:45:40,860 --> 00:45:41,180
+هنا إن شاء الله
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/xKzVbyXMocI_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/xKzVbyXMocI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..8ded5a7dadffd246fcd0e70b1e27f8469f406d60
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/xKzVbyXMocI_raw.json
@@ -0,0 +1 @@
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فإذا بي of one is true thus بي of one is true", "tokens": [28814, 1829, 8592, 12602, 10721, 1829, 4117, 14407, 22807, 8032, 8848, 1829, 2074, 49429, 37893, 2074, 22807, 5296, 28814, 1829, 8592, 22807, 5296, 33456, 1867, 36764, 24401, 2167, 1756, 3714, 43500, 25894, 8315, 6156, 3224, 8315, 297, 472, 6055, 3794, 995, 45865, 3714, 7435, 2304, 2407, 27884, 2423, 472, 307, 19362, 24830, 16490, 2304, 3794, 3660, 1975, 2655, 1863, 9957, 5551, 12984, 3555, 2655, 8315, 8978, 3224, 2423, 1732, 4032, 2423, 1522, 14806, 2309, 366, 19362, 16490, 1211, 9381, 8315, 6156, 28814, 15730, 4724, 1829, 295, 472, 307, 2074, 8807, 4724, 1829, 295, 472, 307, 2074], "avg_logprob": -0.2731958664569658, "compression_ratio": 1.5660377358490567, "no_speech_prob": 0.0, "words": [{"start": 929.86, "end": 930.14, "word": "إيش", "probability": 0.7101643880208334}, {"start": 930.14, "end": 930.52, "word": " رأيكوا؟", "probability": 0.799072265625}, {"start": 930.52, "end": 930.66, "word": " هذي", "probability": 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بدي أثبت أنه أن كي plus one is finite we want to prove بي كي plus one is true يعني that is", "tokens": [28814, 1829, 8592, 20449, 8315, 3224, 4724, 1829, 9122, 1829, 39896, 3714, 4117, 2655, 37746, 3660, 37495, 22653, 14739, 9122, 1829, 307, 19362, 39896, 2423, 5629, 1975, 3224, 6156, 10721, 1829, 19446, 25961, 2655, 2423, 5629, 14739, 16254, 39896, 11203, 995, 28671, 6055, 3794, 995, 45865, 11203, 995, 28671, 44650, 3555, 995, 9957, 3660, 36632, 19446, 7251, 30544, 39896, 2423, 5629, 406, 2074, 4724, 16254, 5551, 12984, 3555, 2655, 14739, 3224, 4724, 1829, 9122, 1829, 1804, 472, 307, 2074, 37495, 22653, 4724, 16254, 5551, 12984, 3555, 2655, 14739, 3224, 14739, 9122, 1829, 1804, 472, 307, 19362, 321, 528, 281, 7081, 4724, 1829, 9122, 1829, 1804, 472, 307, 2074, 37495, 22653, 300, 307], "avg_logprob": -0.21944136535171913, "compression_ratio": 2.074626865671642, "no_speech_prob": 0.0, "words": [{"start": 1010.36, "end": 1010.68, "word": "إيش", "probability": 0.69964599609375}, {"start": 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0.93798828125}, {"start": 1036.08, "end": 1036.52, "word": " true", "probability": 0.94091796875}, {"start": 1036.52, "end": 1037.92, "word": " يعني", "probability": 0.94140625}, {"start": 1037.92, "end": 1038.62, "word": " that", "probability": 0.90966796875}, {"start": 1038.62, "end": 1039.1, "word": " is", "probability": 0.966796875}], "temperature": 1.0}, {"id": 44, "seek": 104942, "start": 1040.8, "end": 1049.42, "text": "بدنا نثبت ان NK plus one is finite is finite statement مش true تمام", "tokens": [44510, 8315, 8717, 12984, 3555, 2655, 16472, 426, 42, 1804, 472, 307, 19362, 307, 19362, 5629, 37893, 2074, 46811, 10943], "avg_logprob": -0.4378720124562581, "compression_ratio": 1.0246913580246915, "no_speech_prob": 0.0, "words": [{"start": 1040.8, "end": 1041.16, "word": "بدنا", "probability": 0.533294677734375}, {"start": 1041.16, "end": 1041.5, "word": " نثبت", "probability": 0.99560546875}, {"start": 1041.5, "end": 1041.64, "word": " ان", "probability": 0.400634765625}, 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"text": "طبعا كتابة هنا يمكن أشياء كثيرة لكن كلها سهلة ولا في عدى عنده صعوبة في اللي كتبناه واضح اللي كتبناه كله أمور سابقة أه إيش مطلوب أثبت n k plus one is finite هعملها بقى contradiction افترض إنها infinite اتفضل في سؤال تمام هنعملها بقى contradiction عشان بس نستخدم النظرية انتبهوا كيف نستخدم النظرية assume", "tokens": [9566, 3555, 3615, 995, 9122, 2655, 16758, 3660, 34105, 7251, 43020, 5551, 8592, 1829, 16606, 9122, 12984, 48923, 44381, 28242, 11296, 8608, 3224, 37977, 49429, 8978, 6225, 3215, 7578, 43242, 3224, 20328, 3615, 37746, 3660, 8978, 13672, 1829, 9122, 2655, 3555, 8315, 3224, 4032, 46958, 5016, 13672, 1829, 9122, 2655, 3555, 8315, 3224, 28242, 3224, 5551, 2304, 13063, 8608, 16758, 28671, 5551, 3224, 11933, 1829, 8592, 3714, 9566, 1211, 37746, 5551, 12984, 3555, 2655, 297, 350, 1804, 472, 307, 19362, 8032, 25957, 1211, 11296, 4724, 4587, 7578, 34937, 1975, 5172, 2655, 43042, 36145, 11296, 13785, 1975, 2655, 5172, 11242, 1211, 8978, 8608, 33604, 6027, 46811, 10943, 8032, 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"word": " العنصر", "probability": 0.9976806640625}, {"start": 1132.51, "end": 1133.35, "word": " الأخير،", "probability": 0.8675537109375}, {"start": 1133.35, "end": 1133.55, "word": " فانا", "probability": 0.8553059895833334}, {"start": 1133.55, "end": 1133.67, "word": " هنا", "probability": 0.60498046875}, {"start": 1133.67, "end": 1133.89, "word": " بدي", "probability": 0.60986328125}, {"start": 1133.89, "end": 1134.63, "word": " اكتبه،", "probability": 0.89208984375}, {"start": 1134.63, "end": 1134.87, "word": " هذه", "probability": 0.40185546875}, {"start": 1134.87, "end": 1135.01, "word": " إيش", "probability": 0.90087890625}, {"start": 1135.01, "end": 1135.73, "word": " بتساوي؟", "probability": 0.93466796875}, {"start": 1135.73, "end": 1136.03, "word": " هذه", "probability": 0.505859375}, {"start": 1136.03, "end": 1136.75, "word": " ناقص", "probability": 0.991943359375}, {"start": 1136.75, "end": 1137.57, "word": " أي", "probability": 0.64599609375}, {"start": 1137.57, "end": 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"end": 1334.22, "text": "لا لسه هذا المطلوب هذا كله مُعطَع كله ده assume is infinite اه فبقول ليه إذا كان عندنا مجموعة ما أخدنا أي مجموعة أكبر منها بتكون infinite أيش المطلوب اثبت منه ايه infinite we want to prove", "tokens": [15040, 5296, 3794, 3224, 23758, 9673, 9566, 1211, 37746, 23758, 28242, 3224, 3714, 10859, 3615, 9566, 6808, 3615, 28242, 3224, 11778, 3224, 6552, 307, 13785, 1975, 3224, 6156, 3555, 39648, 32239, 3224, 11933, 15730, 25961, 43242, 8315, 3714, 7435, 2304, 2407, 27884, 19446, 5551, 9778, 3215, 8315, 36632, 3714, 7435, 2304, 2407, 27884, 5551, 4117, 26890, 9154, 11296, 39894, 30544, 13785, 36632, 8592, 9673, 9566, 1211, 37746, 1975, 12984, 3555, 2655, 9154, 3224, 1975, 1829, 3224, 13785, 321, 528, 281, 7081], "avg_logprob": -0.2360899362985681, "compression_ratio": 1.6298342541436464, "no_speech_prob": 0.0, "words": [{"start": 1314.12, "end": 1314.38, "word": "لا", "probability": 0.2430419921875}, {"start": 1314.38, "end": 1314.68, "word": " لسه", "probability": 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1336.16, "end": 1354.4, "text": "فدي مش المطلوب اللي implies هذا كله بالمعطيات we want to prove بس حاولت انا ايش افسر ايش الشرط بعد يملة الشرطية اللي في السؤال we want to prove that a is infinite infinite", "tokens": [5172, 16254, 37893, 9673, 9566, 1211, 37746, 13672, 1829, 18779, 23758, 28242, 3224, 20666, 2304, 3615, 9566, 1829, 9307, 321, 528, 281, 7081, 4724, 3794, 11331, 995, 12610, 2655, 1975, 8315, 1975, 1829, 8592, 1975, 36178, 2288, 1975, 1829, 8592, 25124, 2288, 9566, 39182, 7251, 2304, 37977, 25124, 2288, 9566, 10632, 13672, 1829, 8978, 21136, 33604, 6027, 321, 528, 281, 7081, 300, 257, 307, 13785, 13785], "avg_logprob": -0.19064832623325176, "compression_ratio": 1.5617283950617284, "no_speech_prob": 0.0, "words": [{"start": 1336.16, "end": 1336.64, "word": "فدي", "probability": 0.571533203125}, {"start": 1336.64, "end": 1336.8, "word": " مش", "probability": 0.9892578125}, {"start": 1336.8, "end": 1337.24, "word": " المطلوب", "probability": 0.9720458984375}, {"start": 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"probability": 0.86875}, {"start": 1371.28, "end": 1371.48, "word": " بقول", "probability": 0.791259765625}, {"start": 1371.48, "end": 1371.78, "word": " ليه", "probability": 0.8505859375}, {"start": 1371.78, "end": 1373.06, "word": " every", "probability": 0.399658203125}, {"start": 1373.06, "end": 1373.56, "word": " proper", "probability": 0.29638671875}, {"start": 1373.56, "end": 1373.92, "word": " subset", "probability": 0.27783203125}, {"start": 1373.92, "end": 1374.34, "word": " of", "probability": 0.97705078125}, {"start": 1374.34, "end": 1374.56, "word": " A", "probability": 0.8349609375}, {"start": 1374.56, "end": 1374.96, "word": " is", "probability": 0.95556640625}, {"start": 1374.96, "end": 1375.58, "word": " infinite", "probability": 0.91796875}, {"start": 1375.58, "end": 1376.54, "word": " يعني", "probability": 0.7073974609375}, {"start": 1376.54, "end": 1376.74, "word": " لو", "probability": 0.91259765625}, {"start": 1376.74, "end": 1377.18, "word": " أخدنا", "probability": 0.9710693359375}, {"start": 1377.18, "end": 1377.42, "word": " أي", "probability": 0.873046875}, {"start": 1377.42, "end": 1377.94, "word": " proper", "probability": 0.272705078125}, {"start": 1377.94, "end": 1378.88, "word": " لكل", "probability": 0.9755859375}, {"start": 1378.88, "end": 1379.06, "word": " ال", "probability": 0.951171875}, {"start": 1379.06, "end": 1379.22, "word": " B", "probability": 0.56982421875}, {"start": 1379.22, "end": 1379.4, "word": " اللي", "probability": 0.86376953125}, {"start": 1379.4, "end": 1379.66, "word": " هي", "probability": 0.89013671875}, {"start": 1379.66, "end": 1380.7, "word": " بتحتول", "probability": 0.6244303385416666}, {"start": 1380.7, "end": 1380.92, "word": " A", "probability": 0.86767578125}, {"start": 1380.92, "end": 1381.64, "word": " لازم", "probability": 0.9762369791666666}, {"start": 1381.64, "end": 1381.74, "word": " ال", "probability": 0.97802734375}, {"start": 1381.74, "end": 1381.86, "word": " B", "probability": 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160598, "start": 1587.9, "end": 1605.98, "text": "أه طبعاً احنا فيها إن التعريفات وشوفنا إنه التعريفات مش دايماً سهلة أو فيها صعوبة فطبعاً النظرية تدينا بدائل كيف نثبت إن المجموعة finite أو infinite شوفنا الأمثلة الماضية كنا بنثبت infinite عن طريق نظرية معينة الآن هيدينا نظرية كيف نثبت إن المجموعة finite", "tokens": [10721, 3224, 23032, 3555, 3615, 995, 14111, 1975, 5016, 8315, 8978, 11296, 36145, 16712, 3615, 16572, 5172, 9307, 4032, 8592, 38688, 8315, 36145, 3224, 16712, 3615, 16572, 5172, 9307, 37893, 11778, 47302, 15042, 14111, 8608, 3224, 37977, 34051, 8978, 11296, 20328, 3615, 37746, 3660, 6156, 9566, 3555, 3615, 995, 14111, 28239, 19913, 2288, 10632, 6055, 16254, 8315, 47525, 16373, 1211, 9122, 33911, 8717, 12984, 3555, 2655, 36145, 9673, 7435, 2304, 2407, 27884, 19362, 34051, 13785, 13412, 38688, 8315, 16247, 2304, 12984, 37977, 9673, 46958, 10632, 9122, 8315, 44945, 12984, 3555, 2655, 13785, 18871, 23032, 16572, 4587, 8717, 19913, 2288, 10632, 20449, 9957, 3660, 6024, 48506, 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{"id": 67, "seek": 162769, "start": 1606.87, "end": 1627.69, "text": "كيف نثبت إن المجموعة finite؟ الحقيقة دي نظرية مهمة جدا في بعض الكتب تعتبر هذا هو التعريف يعني ممكن أنا أبدأ من النظرية أن هو التعريف ال finite و أعرف ال infinity اللي عبارة عن ال negation و بعدين أوصل ل اللي بدأت منه التعريف كأنه ياشهصي نظرية ممكن نعكس الترتيب فهذه مدارس وهذه آراء معينة إيش مجلد؟", "tokens": [4117, 33911, 8717, 12984, 3555, 2655, 36145, 9673, 7435, 2304, 45367, 3660, 19362, 22807, 21542, 38436, 28671, 11778, 1829, 8717, 19913, 2288, 10632, 3714, 16095, 3660, 10874, 28259, 8978, 45030, 11242, 33251, 2655, 3555, 6055, 34268, 26890, 23758, 31439, 16712, 3615, 16572, 5172, 37495, 22653, 3714, 43020, 41850, 5551, 44510, 10721, 9154, 28239, 19913, 2288, 10632, 14739, 31439, 16712, 3615, 16572, 5172, 2423, 19362, 4032, 5551, 3615, 28480, 2423, 13202, 13672, 1829, 6225, 3555, 9640, 3660, 18871, 2423, 2485, 399, 4032, 39182, 9957, 34051, 36520, 5296, 13672, 1829, 47525, 10721, 2655, 9154, 3224, 16712, 3615, 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"seek": 168489, "start": 1657.65, "end": 1684.89, "text": "فارغة يعني فيها Zero من العناصر يا فيها K من العناصر اللي يعيش عدد العناصر أشماله finite has infinitely many فهنا بيشبه التعريف القديم فده بتطابق مع التعريف القديم يعني يا إما فارغة فيها Zero من العناصر أو فيها عدد محدود عشرة، أشرين، مية يعني بتكافئ مين؟ NK ماودهش NK لما بقول أناش بعدهم واحد، اتنين، تلاتة، K إذا رقم أنصر فيها K من العناصر خلينا نشوف البرهان مع بعض", "tokens": [5172, 9640, 17082, 3660, 37495, 22653, 8978, 11296, 17182, 9154, 18863, 1863, 33546, 2288, 35186, 8978, 11296, 591, 9154, 18863, 1863, 33546, 2288, 13672, 1829, 37495, 1829, 8592, 6225, 3215, 3215, 18863, 1863, 33546, 2288, 5551, 8592, 2304, 6027, 3224, 19362, 575, 36227, 867, 6156, 3224, 8315, 4724, 1829, 8592, 3555, 3224, 16712, 3615, 16572, 5172, 25062, 16254, 2304, 6156, 3215, 3224, 39894, 9566, 16758, 4587, 20449, 16712, 3615, 16572, 5172, 25062, 16254, 2304, 37495, 22653, 35186, 11933, 15042, 6156, 9640, 17082, 3660, 8978, 11296, 17182, 9154, 18863, 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" a", "probability": 0.9267578125}, {"start": 1767.21, "end": 1768.03, "word": " bijection", "probability": 0.8172200520833334}], "temperature": 1.0}, {"id": 73, "seek": 179654, "start": 1770.44, "end": 1796.54, "text": "J من X ل K ل NK طبعا for some K تنتمي لل Z مظبوط for some NK طبعا خليها واضحة مش مشكلة implies X is finite فهذا التجاه الأول تمام assume X تسوى ف", "tokens": [41, 9154, 1783, 5296, 591, 5296, 426, 42, 23032, 3555, 3615, 995, 337, 512, 591, 6055, 29399, 2304, 1829, 24976, 1176, 3714, 19913, 3555, 2407, 9566, 337, 512, 426, 42, 23032, 3555, 3615, 995, 16490, 20292, 11296, 4032, 46958, 5016, 3660, 37893, 37893, 28820, 3660, 18779, 1783, 307, 19362, 6156, 3224, 15730, 16712, 7435, 40294, 16247, 12610, 46811, 10943, 6552, 1783, 6055, 3794, 2407, 7578, 6156], "avg_logprob": -0.24580223925078093, "compression_ratio": 1.320754716981132, "no_speech_prob": 0.0, "words": [{"start": 1770.44, "end": 1770.94, "word": "J", "probability": 0.461669921875}, {"start": 1770.94, "end": 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185285, "start": 1824.71, "end": 1852.85, "text": "لأ، نفترض إن الجزء التاني صحيح، نحن عندنا الـ Statement Main الـ Statement بـ if and only if Q بدأنا نثبت Main Q implies V فافترضنا إن الـ B صحيح، عدنا نثبت الـ B، إن الـ X finite تمام، أنا عندي الـ X، لو كانت Phi، نعرف بـ Proposition السابق إنها إيش؟ finite، فإن الاحتمال الأول، if X تسوي Phi، then X is finite", "tokens": [1211, 10721, 12399, 8717, 5172, 2655, 43042, 36145, 25724, 11622, 38207, 16712, 7649, 1829, 20328, 5016, 1829, 5016, 12399, 8717, 5016, 1863, 43242, 8315, 2423, 39184, 16249, 1712, 12383, 2423, 39184, 16249, 1712, 4724, 39184, 498, 293, 787, 498, 1249, 47525, 10721, 8315, 8717, 12984, 3555, 2655, 12383, 1249, 18779, 691, 6156, 31845, 2655, 43042, 8315, 36145, 2423, 39184, 363, 20328, 5016, 1829, 5016, 12399, 6225, 3215, 8315, 8717, 12984, 3555, 2655, 2423, 39184, 363, 12399, 36145, 2423, 39184, 1783, 19362, 46811, 10943, 12399, 41850, 18871, 16254, 2423, 39184, 1783, 12399, 45164, 25961, 2655, 41435, 12399, 8717, 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"seek": 191657, "start": 1887.83, "end": 1916.57, "text": "NK نشترك عليها مباشرة أم لا؟ أه تمام تمام هذا برهان مر علينا قبل هيك كان فينا نظرية ونتيجة قلنا إذا كان بيجيكشن بين two sets يا تنتين finite يا تنتين infinite أنا بعرف من المثال الماضي من النتيجة أن ال NK is finite إذا لازم ال X تكون finite أه فهنا by اللي هو ال corollary", "tokens": [45, 42, 8717, 8592, 2655, 31747, 25894, 11296, 3714, 3555, 33599, 25720, 5551, 2304, 20193, 22807, 5551, 3224, 46811, 10943, 46811, 10943, 23758, 4724, 2288, 3224, 7649, 3714, 2288, 25894, 8315, 12174, 36150, 39896, 4117, 25961, 8978, 8315, 8717, 19913, 2288, 10632, 4032, 29399, 1829, 7435, 3660, 12174, 1211, 8315, 11933, 15730, 25961, 4724, 1829, 7435, 1829, 4117, 8592, 1863, 49374, 732, 6352, 35186, 6055, 29399, 9957, 19362, 35186, 6055, 29399, 9957, 13785, 41850, 45030, 28480, 9154, 9673, 12984, 6027, 9673, 46958, 1829, 9154, 28239, 31371, 7435, 3660, 14739, 2423, 426, 42, 307, 19362, 11933, 15730, 5296, 31377, 2304, 2423, 1783, 6055, 30544, 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" بعرف", "probability": 0.9267578125}, {"start": 1906.69, "end": 1906.85, "word": " من", "probability": 0.9892578125}, {"start": 1906.85, "end": 1907.37, "word": " المثال", "probability": 0.9931640625}, {"start": 1907.37, "end": 1907.85, "word": " الماضي", "probability": 0.9811197916666666}, {"start": 1907.85, "end": 1908.01, "word": " من", "probability": 0.80810546875}, {"start": 1908.01, "end": 1909.55, "word": " النتيجة", "probability": 0.8885498046875}, {"start": 1909.55, "end": 1909.85, "word": " أن", "probability": 0.5791015625}, {"start": 1909.85, "end": 1909.99, "word": " ال", "probability": 0.865234375}, {"start": 1909.99, "end": 1910.39, "word": " NK", "probability": 0.6246337890625}, {"start": 1910.39, "end": 1910.57, "word": " is", "probability": 0.381103515625}, {"start": 1910.57, "end": 1910.93, "word": " finite", "probability": 0.98828125}, {"start": 1910.93, "end": 1911.13, "word": " إذا", "probability": 0.74951171875}, {"start": 1911.13, "end": 1911.37, "word": " لازم", "probability": 0.9108072916666666}, {"start": 1911.37, "end": 1911.43, "word": " ال", "probability": 0.79833984375}, {"start": 1911.43, "end": 1911.55, "word": " X", "probability": 0.7265625}, {"start": 1911.55, "end": 1911.89, "word": " تكون", "probability": 0.9345703125}, {"start": 1911.89, "end": 1912.49, "word": " finite", "probability": 0.97705078125}, {"start": 1912.49, "end": 1913.15, "word": " أه", "probability": 0.76611328125}, {"start": 1913.15, "end": 1913.65, "word": " فهنا", "probability": 0.9459635416666666}, {"start": 1913.65, "end": 1915.11, "word": " by", "probability": 0.7578125}, {"start": 1915.11, "end": 1915.79, "word": " اللي", "probability": 0.58282470703125}, {"start": 1915.79, "end": 1915.89, "word": " هو", "probability": 0.9736328125}, {"start": 1915.89, "end": 1916.07, "word": " ال", "probability": 0.347900390625}, {"start": 1916.07, "end": 1916.57, "word": " corollary", "probability": 0.7418619791666666}], "temperature": 1.0}, {"id": 78, "seek": 193456, "start": 1920.9, "end": 1934.56, "text": "خمسة واحد وخمسة اتنين خمسة واحد بتقول علاش انه مافيش بيجيكشن اللاتنتين من finite and corollary خمسة اتنين x is finite فهذا الجزء السهل", "tokens": [9778, 2304, 3794, 3660, 36764, 24401, 4032, 9778, 2304, 3794, 3660, 1975, 2655, 1863, 9957, 16490, 2304, 3794, 3660, 36764, 24401, 39894, 39648, 11203, 33599, 16472, 3224, 19446, 41185, 8592, 4724, 1829, 7435, 1829, 4117, 8592, 1863, 13672, 9307, 29399, 9957, 9154, 19362, 293, 1181, 1833, 822, 16490, 2304, 3794, 3660, 1975, 2655, 1863, 9957, 2031, 307, 19362, 6156, 3224, 15730, 25724, 11622, 38207, 21136, 3224, 1211], "avg_logprob": -0.2011718787252903, "compression_ratio": 1.4931506849315068, "no_speech_prob": 0.0, "words": [{"start": 1920.9, "end": 1921.52, "word": "خمسة", "probability": 0.8289794921875}, {"start": 1921.52, "end": 1921.86, "word": " واحد", "probability": 0.955078125}, {"start": 1921.86, "end": 1922.3, "word": " وخمسة", "probability": 0.87900390625}, {"start": 1922.3, "end": 1922.46, "word": " اتنين", "probability": 0.91259765625}, {"start": 1922.46, "end": 1922.74, "word": " خمسة", "probability": 0.81671142578125}, {"start": 1922.74, "end": 1922.88, "word": " واحد", "probability": 0.9658203125}, {"start": 1922.88, "end": 1923.14, "word": " بتقول", "probability": 0.825927734375}, {"start": 1923.14, "end": 1923.6, "word": " علاش", "probability": 0.453369140625}, {"start": 1923.6, "end": 1924.2, "word": " انه", "probability": 0.6474609375}, {"start": 1924.2, "end": 1924.56, "word": " مافيش", "probability": 0.9015299479166666}, {"start": 1924.56, "end": 1925.18, "word": " بيجيكشن", "probability": 0.8180803571428571}, {"start": 1925.18, "end": 1925.7, "word": " اللاتنتين", "probability": 0.7144775390625}, {"start": 1925.7, "end": 1925.88, "word": " من", "probability": 0.81396484375}, {"start": 1925.88, "end": 1926.38, "word": " finite", "probability": 0.72802734375}, {"start": 1926.38, "end": 1927.48, "word": " and", "probability": 0.810546875}, {"start": 1927.48, "end": 1929.52, "word": " corollary", "probability": 0.6709391276041666}, {"start": 1929.52, "end": 1931.26, "word": " خمسة", "probability": 0.9444580078125}, {"start": 1931.26, "end": 1931.78, "word": " اتنين", "probability": 0.9842529296875}, {"start": 1931.78, "end": 1932.22, "word": " x", "probability": 0.51806640625}, {"start": 1932.22, "end": 1932.52, "word": " is", "probability": 0.80810546875}, {"start": 1932.52, "end": 1932.88, "word": " finite", "probability": 0.98828125}, {"start": 1932.88, "end": 1933.8, "word": " فهذا", "probability": 0.9168294270833334}, {"start": 1933.8, "end": 1934.12, "word": " الجزء", "probability": 0.986328125}, {"start": 1934.12, "end": 1934.56, "word": " السهل", "probability": 0.9793294270833334}], "temperature": 1.0}, {"id": 79, "seek": 195579, "start": 1936.59, "end": 1955.79, "text": "فخلصنا، فلو كانت five هي finite لأن فيها zero من العناصر، و هذا أثبتناها قبل هيك، و لو كانت فيها bijection بينها وبين N، NK، مانفعش يكون بيجيكشن لبين مجموعتين من نفس الجنس، بما أن NK finite توي أثبتناها بال induction، إذا لازم تاني تكون finite، فأدا الاتجاه خلص، نيجي للاتجاه التاني", "tokens": [5172, 9778, 1211, 9381, 8315, 12399, 6156, 1211, 2407, 25961, 2655, 1732, 39896, 19362, 5296, 33456, 8978, 11296, 4018, 9154, 18863, 1863, 33546, 2288, 12399, 4032, 23758, 5551, 12984, 3555, 2655, 8315, 11296, 12174, 36150, 39896, 4117, 12399, 4032, 45164, 25961, 2655, 8978, 11296, 3228, 1020, 313, 49374, 11296, 46599, 9957, 426, 12399, 426, 42, 12399, 3714, 7649, 5172, 3615, 8592, 7251, 30544, 4724, 1829, 7435, 1829, 4117, 8592, 1863, 5296, 3555, 9957, 3714, 7435, 2304, 45367, 2655, 9957, 9154, 8717, 36178, 25724, 1863, 3794, 12399, 4724, 15042, 14739, 426, 42, 19362, 6055, 45865, 5551, 12984, 3555, 2655, 8315, 11296, 20666, 33371, 12399, 11933, 15730, 5296, 31377, 2304, 6055, 7649, 1829, 6055, 30544, 19362, 12399, 6156, 10721, 28259, 2423, 9307, 7435, 40294, 16490, 1211, 9381, 12399, 8717, 1829, 7435, 1829, 24976, 9307, 7435, 40294, 16712, 7649, 1829], "avg_logprob": -0.25000000842239545, "compression_ratio": 1.7984496124031009, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1936.5900000000001, "end": 1937.17, "word": "فخلصنا،", "probability": 0.8352457682291666}, {"start": 1937.17, "end": 1937.43, "word": " فلو", "probability": 0.9451497395833334}, {"start": 1937.43, "end": 1937.79, "word": " كانت", "probability": 0.95751953125}, {"start": 1937.79, "end": 1938.01, "word": " five", "probability": 0.12457275390625}, {"start": 1938.01, "end": 1938.25, "word": " هي", "probability": 0.353271484375}, {"start": 1938.25, "end": 1938.61, "word": " finite", "probability": 0.9638671875}, {"start": 1938.61, "end": 1939.19, "word": " لأن", "probability": 0.847900390625}, {"start": 1939.19, "end": 1939.43, "word": " فيها", "probability": 0.721923828125}, {"start": 1939.43, "end": 1939.67, "word": " zero", "probability": 0.468505859375}, {"start": 1939.67, "end": 1939.79, "word": " من", "probability": 0.98828125}, {"start": 1939.79, "end": 1940.69, "word": " العناصر،", "probability": 0.802294921875}, {"start": 1940.69, "end": 1940.75, "word": " و", "probability": 0.69482421875}, {"start": 1940.75, "end": 1940.91, "word": " هذا", "probability": 0.28466796875}, {"start": 1940.91, "end": 1941.57, "word": " أثبتناها", "probability": 0.9121907552083334}, {"start": 1941.57, "end": 1941.79, "word": " قبل", "probability": 0.979736328125}, {"start": 1941.79, "end": 1942.25, "word": " هيك،", "probability": 0.80859375}, {"start": 1942.25, "end": 1942.31, "word": " و", "probability": 0.63330078125}, {"start": 1942.31, "end": 1942.47, "word": " لو", "probability": 0.953125}, {"start": 1942.47, "end": 1942.91, "word": " كانت", "probability": 0.988525390625}, {"start": 1942.91, "end": 1943.13, "word": " فيها", "probability": 0.92333984375}, {"start": 1943.13, "end": 1943.71, "word": " bijection", "probability": 0.8133138020833334}, {"start": 1943.71, "end": 1943.97, "word": " بينها", "probability": 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finite،", "probability": 0.924560546875}, {"start": 1952.95, "end": 1953.21, "word": " فأدا", "probability": 0.5670572916666666}, {"start": 1953.21, "end": 1953.59, "word": " الاتجاه", "probability": 0.8778076171875}, {"start": 1953.59, "end": 1954.55, "word": " خلص،", "probability": 0.8828125}, {"start": 1954.55, "end": 1954.83, "word": " نيجي", "probability": 0.958251953125}, {"start": 1954.83, "end": 1955.33, "word": " للاتجاه", "probability": 0.9058837890625}, {"start": 1955.33, "end": 1955.79, "word": " التاني", "probability": 0.9676106770833334}], "temperature": 1.0}, {"id": 80, "seek": 198650, "start": 1958.16, "end": 1986.5, "text": "بدنا الآن B implies Q بس عشانها كبيرة مابديش اكتبها كمان مرة مش هثبتها بشكل مباشر هثبت ال contrapositive تبعتها ايش مطلوب نثبت ولا اكتب .. خليني اكتب يلّا اه هل جيش بدنا نثبت ان X is finite implies X تساوي Phi or there exists a bijection خليني اكتبها بشكل مختصر", "tokens": [44510, 8315, 6024, 48506, 363, 18779, 1249, 4724, 3794, 6225, 8592, 7649, 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2691.67, "text": "فإذا هذه العناصر ممكن أرقمها ممكن أرقمها فهنا الملاحظة بتقول لي إذا ال X is a non-empty طبعا إذا empty ما هي معروفة نيجي على ال non-empty بنشوف إيش كيف نتعامل معها is a non-empty finite set مجموعة منتهية", "tokens": [5172, 28814, 15730, 29538, 18863, 1863, 33546, 2288, 3714, 43020, 5551, 2288, 4587, 2304, 11296, 3714, 43020, 5551, 2288, 4587, 2304, 11296, 6156, 3224, 8315, 9673, 15040, 5016, 19913, 3660, 39894, 39648, 32239, 11933, 15730, 2423, 1783, 307, 257, 2107, 12, 4543, 88, 23032, 3555, 3615, 995, 11933, 15730, 6707, 19446, 39896, 20449, 32887, 5172, 3660, 8717, 1829, 7435, 1829, 15844, 2423, 2107, 12, 4543, 88, 44945, 8592, 38688, 11933, 1829, 8592, 9122, 33911, 8717, 2655, 3615, 10943, 1211, 20449, 11296, 307, 257, 2107, 12, 4543, 88, 19362, 992, 3714, 7435, 2304, 2407, 27884, 9154, 47395, 10632], "avg_logprob": -0.17426658741065434, "compression_ratio": 1.641025641025641, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 2676.49, "end": 2676.89, 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X", "probability": 0.90771484375}, {"start": 2716.91, "end": 2717.23, "word": " ممكن", "probability": 0.984619140625}, {"start": 2717.23, "end": 2717.59, "word": " إيش؟", "probability": 0.943603515625}, {"start": 2717.59, "end": 2718.27, "word": " أرقمهم", "probability": 0.9880859375}, {"start": 2718.27, "end": 2718.87, "word": " ممكن", "probability": 0.86767578125}, {"start": 2718.87, "end": 2719.51, "word": " نرقمهم", "probability": 0.87568359375}], "temperature": 1.0}, {"id": 112, "seek": 274118, "start": 2719.96, "end": 2741.18, "text": "إذا أي finite set يا إما Phi وإذا ماكنتش Phi ممكن أرقمها من واحد لعدد العناصر ل K هذه من نظري هيك بتقول فمن هنا وطالع هذا بيسهل علينا لو كل مجموعة finite ممكن أقولها إذا X تساوي إذا مش Phi بتساوي من X واحد ل X K for some K في عدد K من العناصر وهذا متفق مع التعريف القدي نوجّف هنا إن شاء الله", "tokens": [28814, 15730, 36632, 19362, 992, 35186, 11933, 15042, 41435, 4032, 28814, 15730, 19446, 19452, 2655, 8592, 41435, 3714, 43020, 5551, 2288, 4587, 2304, 11296, 9154, 36764, 24401, 5296, 22488, 3215, 18863, 1863, 33546, 2288, 5296, 591, 29538, 9154, 8717, 19913, 16572, 39896, 4117, 39894, 39648, 6156, 27842, 34105, 4032, 9566, 6027, 3615, 23758, 4724, 1829, 3794, 3224, 1211, 25894, 8315, 45164, 28242, 3714, 7435, 2304, 2407, 27884, 19362, 3714, 43020, 5551, 39648, 11296, 11933, 15730, 1783, 6055, 3794, 995, 45865, 11933, 15730, 37893, 41435, 39894, 3794, 995, 45865, 9154, 1783, 36764, 24401, 5296, 1783, 591, 337, 512, 591, 8978, 6225, 3215, 3215, 591, 9154, 18863, 1863, 33546, 2288, 37037, 15730, 44650, 5172, 4587, 20449, 16712, 3615, 16572, 5172, 25062, 16254, 8717, 2407, 7435, 11703, 5172, 34105, 36145, 13412, 16606, 21984], "avg_logprob": -0.20849236322723272, "compression_ratio": 1.800751879699248, "no_speech_prob": 1.7881393432617188e-06, "words": [{"start": 2719.96, "end": 2720.08, "word": "إذا", "probability": 0.53594970703125}, {"start": 2720.08, "end": 2720.36, "word": " أي", "probability": 0.65625}, {"start": 2720.36, "end": 2720.9, "word": " finite", "probability": 0.84375}, {"start": 2720.9, "end": 2721.32, "word": " set", "probability": 0.9033203125}, {"start": 2721.32, "end": 2721.8, "word": " يا", "probability": 0.33154296875}, {"start": 2721.8, "end": 2722.08, "word": " إما", "probability": 0.930908203125}, {"start": 2722.08, "end": 2722.54, "word": " Phi", "probability": 0.172119140625}, {"start": 2722.54, "end": 2723.04, "word": " وإذا", "probability": 0.8902994791666666}, {"start": 2723.04, "end": 2723.48, "word": " ماكنتش", "probability": 0.85211181640625}, {"start": 2723.48, "end": 2723.68, "word": " Phi", "probability": 0.94482421875}, {"start": 2723.68, "end": 2723.96, "word": " ممكن", "probability": 0.909423828125}, {"start": 2723.96, "end": 2724.52, "word": " أرقمها", "probability": 0.9232421875}, {"start": 2724.52, "end": 2724.72, "word": " من", "probability": 0.9775390625}, {"start": 2724.72, "end": 2725.18, "word": " واحد", "probability": 0.856201171875}, {"start": 2725.18, "end": 2725.92, "word": " لعدد", "probability": 0.9801432291666666}, {"start": 2725.92, "end": 2726.42, "word": " العناصر", "probability": 0.9456787109375}, {"start": 2726.42, "end": 2726.52, "word": " ل", "probability": 0.75830078125}, {"start": 2726.52, "end": 2726.72, "word": " K", "probability": 0.30078125}, {"start": 2726.72, "end": 2727.28, "word": " هذه", "probability": 0.293701171875}, {"start": 2727.28, "end": 2727.44, "word": " من", "probability": 0.92431640625}, {"start": 2727.44, "end": 2727.7, "word": " نظري", "probability": 0.8055013020833334}, {"start": 2727.7, "end": 2727.9, "word": " هيك", "probability": 0.707275390625}, {"start": 2727.9, "end": 2728.24, "word": " بتقول", "probability": 0.959228515625}, {"start": 2728.24, "end": 2728.74, "word": " فمن", "probability": 0.837158203125}, {"start": 2728.74, "end": 2728.88, "word": " هنا", "probability": 0.83251953125}, {"start": 2728.88, "end": 2729.18, "word": " وطالع", "probability": 0.7589111328125}, {"start": 2729.18, "end": 2729.32, "word": " هذا", "probability": 0.7607421875}, {"start": 2729.32, "end": 2729.64, "word": " بيسهل", "probability": 0.9623046875}, {"start": 2729.64, "end": 2729.98, "word": " علينا", "probability": 0.9345703125}, {"start": 2729.98, "end": 2730.38, "word": " لو", "probability": 0.93359375}, {"start": 2730.38, "end": 2730.6, "word": " كل", "probability": 0.6904296875}, {"start": 2730.6, "end": 2731.02, "word": " مجموعة", "probability": 0.94833984375}, {"start": 2731.02, "end": 2731.32, "word": " finite", "probability": 0.9091796875}, {"start": 2731.32, "end": 2731.6, "word": " ممكن", "probability": 0.9736328125}, {"start": 2731.6, "end": 2732.26, "word": " أقولها", "probability": 0.640625}, {"start": 2732.26, "end": 2732.64, "word": " إذا", "probability": 0.83203125}, {"start": 2732.64, "end": 2732.96, "word": " X", "probability": 0.7890625}, {"start": 2732.96, "end": 2733.42, "word": " تساوي", "probability": 0.83154296875}, {"start": 2733.42, "end": 2733.56, "word": " إذا", "probability": 0.956298828125}, {"start": 2733.56, "end": 2733.7, "word": " مش", "probability": 0.9775390625}, {"start": 2733.7, "end": 2734.06, "word": " Phi", "probability": 0.9658203125}, {"start": 2734.06, "end": 2734.58, "word": " بتساوي", "probability": 0.95068359375}, {"start": 2734.58, "end": 2734.74, "word": " من", "probability": 0.98876953125}, {"start": 2734.74, "end": 2734.94, "word": " X", "probability": 0.97119140625}, {"start": 2734.94, "end": 2735.24, "word": " واحد", "probability": 0.9326171875}, {"start": 2735.24, "end": 2735.36, "word": " ل", "probability": 0.5234375}, {"start": 2735.36, "end": 2735.6, "word": " X", "probability": 0.8662109375}, {"start": 2735.6, "end": 2735.88, "word": " K", "probability": 0.6728515625}, {"start": 2735.88, "end": 2736.1, "word": " for", "probability": 0.90478515625}, {"start": 2736.1, "end": 2736.36, "word": " some", "probability": 0.91943359375}, {"start": 2736.36, "end": 2736.58, "word": " K", "probability": 0.89990234375}, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/xKzVbyXMocI_raw.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/xKzVbyXMocI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d05cd044d606bbfc59d3e369beb7538614971376
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/xKzVbyXMocI_raw.srt
@@ -0,0 +1,2280 @@
+1
+00:00:21,580 --> 00:00:25,940
+بتصل مع ال internet 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 عرصة فتمها
+
+4
+00:00:35,500 --> 00:00:43,440
+لانهائية عرفنا أنه في عندنا ال Y بتساوي X ناقص ال
+
+5
+00:00:43,440 --> 00:00:48,860
+X0و ال X0 هو عنصر من عناصر ال capital X فهذه بنثبت
+
+6
+00:00:48,860 --> 00:00:51,840
+أنها infinite إذا كانت ال X infinite في حالة .. من
+
+7
+00:00:51,840 --> 00:00:54,300
+الحالة طبعا عشان نعرف دالة عشان إيش ال Y infinite
+
+8
+00:00:54,300 --> 00:00:58,380
+إيش معناته؟ هناك دالة one to one F من Y ل Y تكون
+
+9
+00:00:58,380 --> 00:01:01,780
+one to one و ليست unto فاحنا كلنا لازم ناخد حالتين
+
+10
+00:01:01,780 --> 00:01:06,480
+لو كانت ال X0 صورة عنصر من عناصر ال Y فيها مشكلة
+
+11
+00:01:06,480 --> 00:01:10,360
+فهذه اشتغلناها لحالة و لو ماكنتش صورة ناخد ال F
+
+12
+00:01:10,360 --> 00:01:13,340
+على طول بتسوء G اللي هي الدالة من و لا ويا من X ل
+
+13
+00:01:13,340 --> 00:01:20,860
+X احنا في عنا Gمن X ل 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 أنصر بينفعش لأن الـ X Zero خارج الـ Y فلو هي
+
+17
+00:01:33,460 --> 00:01:37,130
+صورة بذا سير أيش خارج الـ Y بينفعش بالنسبة للـ Fأه
+
+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 التانية إذا كانت صورة أعملنا trick بسيط
+
+20
+00:01:44,010 --> 00:01:49,910
+وعرفنا ال F إحنا في الحالة إن هذي X0 تنتمي لل G of
+
+21
+00:01:49,910 --> 00:01:56,710
+X هذي Case 2 احنا بنشتغل هنا فعرفنا ال F من Y ل Y
+
+22
+00:01:56,710 --> 00:02:05,280
+byF of X تساوي G of X إذا الـ X لا تساوي A طبعا
+
+23
+00:02:05,280 --> 00:02:09,400
+احنا عايش هذا معناته أن X0 تساوي G of A for some A
+
+24
+00:02:12,800 --> 00:02:18,300
+تنتمي لل X وإذا كانت من ال X بتساوي A أخدناها بيه
+
+25
+00:02:18,300 --> 00:02:23,880
+عنصر جديد واخترنا عنصر بيه 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 ال بيه أخدت ال بيه من هناأه 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 ال
+
+35
+00:02:55,020 --> 00:02:57,840
+one to one فاحنا اخترنا مادة شكلة طبعا بنا نثبت أن
+
+36
+00:02:57,840 --> 00:03:01,940
+هذه الـ F one to one وليست unto، مظبوط؟فأحنا أول
+
+37
+00:03:01,940 --> 00:03:08,240
+شي G أسف F is one to one وصلنا هنا ولا لأ؟ أه ال F
+
+38
+00:03:08,240 --> 00:03:12,940
+is one to one فكعادتنا في برهان ال one to one ناخد
+
+39
+00:03:12,940 --> 00:03:20,630
+عنصرين من ال domain تنتمي لل Y such thatF 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 ال one to
+
+42
+00:03:31,890 --> 00:03:35,910
+one بدايته على الأقل بداية بسيطة و بنتعلمها زي ما
+
+43
+00:03:35,910 --> 00:03:40,950
+اتعلمنا عدة مهارة بدنا نثبت أن X1 تساوي X2واتعلمنا
+
+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 واتاني في
+
+49
+00:03:59,930 --> 00:04:08,330
+الجزء التاني فهذا يؤدي لو كانت X واحدلاتساوي A و
+
+50
+00:04:08,330 --> 00:04:15,960
+X2 لاتساوي A إيش بيكون التعريف G of X1وبرضه g of
+
+51
+00:04:15,960 --> 00:04:21,740
+x2 مظبوط؟ امتبعين معاه؟ اه فلو كانوا لو x1 مش a
+
+52
+00:04:21,740 --> 00:04:25,240
+وx2 من a وين التعريف؟ بيقوللي اذا كانت ال x تسوى
+
+53
+00:04:25,240 --> 00:04:28,520
+ايش التعريف؟ g بيبقى تسوى g ناخد التاني لو كانوا
+
+54
+00:04:28,520 --> 00:04:33,340
+التنين بيسووا ايه؟ لو كانت x1 تسوى a تسوى x2 ايش
+
+55
+00:04:33,340 --> 00:04:37,620
+التعريف؟ b ايش التعريف؟ b اه طبعا ايش بينهم؟ or
+
+56
+00:04:37,620 --> 00:04:41,940
+لان احتمالاتالان الاحتمالين اللي تموا واحد هيك و
+
+57
+00:04:41,940 --> 00:04:44,880
+واحد هيك هتقول اتنين من نفس الاشي وقعوا مع بعض من
+
+58
+00:04:44,880 --> 00:04:51,300
+نفس الجزء الان or لو كانت x1 لا تساوي a لكن x2
+
+59
+00:04:51,300 --> 00:04:56,920
+بتساوي a اللي بتساويش ايش بتكون صورتها؟ g و اللي
+
+60
+00:04:56,920 --> 00:05:04,280
+بتساوي بيه احتمال الأخير بيه 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
+التالت و الرابع ممكن يدمجهم في احتمال واحد ليش؟
+
+64
+00:05:18,400 --> 00:05:21,860
+لأن ال X1 و X2 دي الترتيب ليه مش مهم ايش اختصارهم؟
+
+65
+00:05:21,860 --> 00:05:25,340
+ان واحد بيساوي ايه و واحد لا يساوي ايه فهم نفس
+
+66
+00:05:25,340 --> 00:05:29,580
+الاحتمال لكن هناخدهم بالتفصيل التكرار مافيش منه
+
+67
+00:05:29,580 --> 00:05:33,560
+ضرر لكن أحيانا حذف حالة بتكون أساسية ممكن يكون فيه
+
+68
+00:05:33,560 --> 00:05:36,620
+ضرر طبعا لكن هم هدول لو حذفنا واحدة فيهم مابنخسرش
+
+69
+00:05:36,620 --> 00:05:41,090
+اشي لكن خلينا نعمله تمام وين بدنا نوصل؟إن X1 يساوي
+
+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
+يساوي X2 ليش؟ لأن الـG one to one لأن الـG is one
+
+72
+00:05:51,110 --> 00:05:56,560
+to oneوالتانية بتقول بي تساوي بي، عدم أن 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 بي تساوي بي أحذفها؟ لأ، لأنها دي O، لكن
+
+75
+00:06:04,860 --> 00:06:07,720
+لو دقّقنا إيش معنات هدول، إيش معنهم؟ ماهم تساويين،
+
+76
+00:06:07,720 --> 00:06:12,760
+X1 تساوي X2 تساوي X2، فبرضه X1 تساوي X2or بقدر
+
+77
+00:06:12,760 --> 00:06:17,520
+أستنتج طيب اللي بعده contradiction التاني تاني ليش
+
+78
+00:06:17,520 --> 00:06:22,520
+لأنه لما يقول ال B صورة يعني ال B وين في صور ال G
+
+79
+00:06:22,520 --> 00:06:25,680
+و ال B من إيش خارج الصور مستحيل لما تقولي ال B
+
+80
+00:06:25,680 --> 00:06:29,260
+صورة عنصر ما يعني بالصور و ال B من وين اختارناها
+
+81
+00:06:29,260 --> 00:06:31,940
+من خارج الصور عشان هيك احنا لما أعرفنا ال 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 ال
+
+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، والتانية برضه
+
+87
+00:06:49,020 --> 00:06:51,400
+Contradiction زيها، ما احنا قولنا 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 Xواضح ال
+
+90
+00:07:00,340 --> 00:07:03,540
+contradiction ولا في حد مش واضح حاله؟ اه لأنه إيش
+
+91
+00:07:03,540 --> 00:07:08,240
+معناه أن ال 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 بي تنتمي لل G of X؟ يعني ال B تساوي صورة
+
+94
+00:07:17,420 --> 00:07:20,760
+عنصر من ال G of X اه فلو كانت ال B تلان ال X واحد
+
+95
+00:07:20,760 --> 00:07:24,100
+وين موجودة ال X واحدة دي؟ في ال X اه بي في ال Y و
+
+96
+00:07:24,100 --> 00:07:26,160
+ال Y جزء من ال X بتساويش X زيه فبتديني
+
+97
+00:07:26,160 --> 00:07:30,110
+contradiction طبعا الآن B or بي بيP or
+
+98
+00:07:30,110 --> 00:07:33,770
+contradiction P او P or contradiction P فهذا يقضي
+
+99
+00:07:33,770 --> 00:07:37,010
+ان ال P هي المين ل X واحد تساوي X اتنين فهذا يقضي
+
+100
+00:07:37,010 --> 00:07:40,870
+ان X واحد تساوي X اتنين و هذا يقضي ان ال F is one
+
+101
+00:07:40,870 --> 00:07:45,650
+to oneفزي 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
+تلاتة ممكن، لكن حتى لو كانوا أربعة، طبعا ماينفعش
+
+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 contradictionفهذا
+
+109
+00:08:10,910 --> 00:08:13,110
+المطلوب الأول نشوف المطلوب التاني انه proper
+
+110
+00:08:13,110 --> 00:08:18,710
+subset ليست onto ال F خلينا
+
+111
+00:08:18,710 --> 00:08:25,230
+هذه مؤقتا ان احنا نحتاجها اتنين F ال Y proper من
+
+112
+00:08:25,230 --> 00:08:31,190
+ال Yفبدنا عنصر موجود في الـY وغير موجود في الـF of
+
+113
+00:08:31,190 --> 00:08:35,910
+Y خلّينا نحسب الـF of Y، نحسب الـImage عشان نشوف
+
+114
+00:08:35,910 --> 00:08:40,650
+مين عنصر خارج الـImage، بدنا عنصر خارج الـImage، F
+
+115
+00:08:40,650 --> 00:08:48,360
+of Y إيش بتساوي؟ F ofكيف احسب الـ image لدالة
+
+116
+00:08:48,360 --> 00:08:55,200
+متعددة القاعدة كيف نحسب ال image لدالة متعددة
+
+117
+00:08:55,200 --> 00:08:58,920
+القاعدة ايش متعددة القاعدة ال domain مجسم فانا ايش
+
+118
+00:08:58,920 --> 00:09:03,600
+اعمل اجسم ال domain اجسم ال domain هذه ال Y عبارة
+
+119
+00:09:03,600 --> 00:09:06,080
+عن اصلا X ناقص X Zero
+
+120
+00:09:09,940 --> 00:09:14,820
+و احنا التعريف اذا X لا تساوي A لها تعريف و عند ال
+
+121
+00:09:14,820 --> 00:09:19,440
+A بتساوي تعريف فانا هجسم ال demand جزء من غير A و
+
+122
+00:09:19,440 --> 00:09:23,260
+الجزء اللي فيه ال A فدي كيف ممكن اكتبها بكتبها F
+
+123
+00:09:23,260 --> 00:09:31,520
+of X ناقص X0Aاتحاد الـ A لحال خلّيها 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 ال X0 والـ A اتحاد
+
+127
+00:09:49,760 --> 00:09:54,660
+F الـ A اللي هي على طول ممكن اكتبها مين مجموعة F
+
+128
+00:09:54,660 --> 00:10:01,530
+الـ Aمظبوط؟ انت باين؟ ولا اعيد؟ اه الآن بدي احسب
+
+129
+00:10:01,530 --> 00:10:07,930
+ال image طبعا مين اعوض عن F؟ اعوض G ولا B؟ لأ لازم
+
+130
+00:10:07,930 --> 00:10:11,650
+اجسم وين هي بتساوي B وين هي بتساوي G فاضطريت اجسم
+
+131
+00:10:11,650 --> 00:10:15,670
+ال domain وين هي بتساوي B عند ال A فخلت ال A لحالة
+
+132
+00:10:15,670 --> 00:10:20,130
+والباقي ايش تعرفه؟ G اه فالان من خواص ال F تتوزع
+
+133
+00:10:20,130 --> 00:10:26,550
+الاتحاد الآن هذي ايش بتساوي؟ Bمظبوط F of A بتساوي
+
+134
+00:10:26,550 --> 00:10:30,270
+B مظبوط هيك بنقرعها F of X لما ال 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 minus X0 و A أنا جيت بقى أقدر
+
+137
+00:10:43,190 --> 00:10:47,110
+أمحي هذا فعشان هيك جسمت ال 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 بديهامعروف أتوقع في أحد التمارين
+
+140
+00:10:55,760 --> 00:10:59,000
+الكتاب إذا تدالة one to one الصورة بتتوزع على ال
+
+141
+00:10:59,000 --> 00:11:02,340
+minus مش دائما 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 Yطيب أسأل نفسي ممكن
+
+146
+00:11:24,950 --> 00:11:29,310
+نكون تهنا احنا عايش بندور بدنا أنصر موجود في ال Y
+
+147
+00:11:29,310 --> 00:11:32,950
+مش موجود هنا طب هذا بيساوي هذا، بدي أنصر 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 أصلا في ال Y، بديها 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 الصورةموجودة 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 andWhy لا تنتمي
+
+158
+00:12:19,110 --> 00:12:23,270
+لمين للـF of Y؟ لأن هنا أخدناها من برا لأنه بالـ-C
+
+159
+00:12:23,270 --> 00:12:27,090
+طبعا 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 طبعا 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 التاليةبقول 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
+بالرنزة؟ 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 الواحداد من
+
+174
+00:13:23,430 --> 00:13:27,550
+واحد لعشر وها كذا 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
+الصورةبدنا 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
+تلاتةواحد و اتنين و تلاتة و هكذا واضح التعريف الان
+
+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 التاني خليني أسميها PM بلاش
+
+185
+00:14:29,590 --> 00:14:34,570
+PM تفرجش طبعا 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 sentenceمع 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 او من اي 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، طبعا 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
+طبعا، اللي هي هذه هي statement، اه open sentence
+
+197
+00:15:16,520 --> 00:15:19,520
+طبعا، بدي أثبت إنه هذه إيش، دايما 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 finiteإيش رأيكوا؟ هذي true ولا مش
+
+200
+00:15:31,140 --> 00:15:35,040
+true؟ لإيش؟ 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 trueأرجو إن هذا المثال يؤكد
+
+205
+00:15:59,710 --> 00:16:03,590
+أننا فاهمنا 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 وطبعا 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 finiteإيش 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 isبدنا 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
+طبعا 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 أه 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 assumeand 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
+أحنا 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
+البرهقة، 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 الا nk plus one مطوح
+
+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 البرهارةوانتهى البرهن فهنا دايما اروح من
+
+247
+00:19:21,820 --> 00:19:25,820
+الحالة او 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 بتامها infinite فمستحيل تكونها دي infinite
+
+251
+00:19:35,220 --> 00:19:44,960
+وانتهى البرهن فهذه حقيقة مهمة جدا 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 thatإذا 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 فعلا، 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، أه، بتكتسل هنا؟
+
+260
+00:20:24,900 --> 00:20:30,420
+إذا كانت هذه infinite حذفنا من 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 من عنصر بتامها 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 مالة؟ 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 تحتوى ال A و proper subset مش subset بقى
+
+277
+00:21:47,460 --> 00:21:52,340
+تحتوي proper subset إيش بيقدّي؟ يقدّي إن ال B is
+
+278
+00:21:52,340 --> 00:21:56,840
+infiniteلا لسه هذا المطلوب هذا كله مُعطَع 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 اثبت منه ايه
+
+282
+00:22:12,800 --> 00:22:17,380
+infinite we want to proveفدي 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 انا ايش افسر ايش 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 حطت implies هنا يعني ايش 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
+أخدنا أي proper لكل ال B اللي هي بتحتول A لازم ال
+
+293
+00:23:01,740 --> 00:23:07,400
+B تكون infiniteممكن، ممكن، بس هي بنفس المعنى، ففي
+
+294
+00:23:07,400 --> 00:23:12,500
+أحيان بكون أكتر من تفسير تمام، فإيش ممكن نعمل؟ إيش
+
+295
+00:23:12,500 --> 00:23:16,120
+ممكن نعمل؟ فاحنا مطلوب نثبت إن الـA 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 المؤتيات، بدي
+
+298
+00:23:21,920 --> 00:23:26,460
+أدور على مجموعة B بتكون أكبر من مين من الـA، و
+
+299
+00:23:26,460 --> 00:23:30,480
+تكون Infiniteأه و إيه علاقة مع ال A؟ إيه علاقة مع
+
+300
+00:23:30,480 --> 00:23:34,220
+ال A؟ إذا كنت تثبت أن ال B infinite فبقى .. آسف ال
+
+301
+00:23:34,220 --> 00:23:36,880
+B هتكون infinite و منها حسن تجي أن ال A infinite
+
+302
+00:23:36,880 --> 00:23:39,600
+لأنه بيقول ليه أي brother super set من ال A
+
+303
+00:23:39,600 --> 00:23:43,400
+infinite بدي أثبت أن ال A infinite أنا بعرففبدنا
+
+304
+00:23:43,400 --> 00:23:47,440
+علاقة نعملها زي ال trick الماضي بدنا مجموعة ما B
+
+305
+00:23:47,440 --> 00:23:51,100
+نطرح منها عنصر تدينا ال A واحنا عارفين أن ال B
+
+306
+00:23:51,100 --> 00:23:53,120
+infinite لأن بقول ال B إلى خلاص معايا بيكون
+
+307
+00:23:53,120 --> 00:23:56,440
+infinite وال A عبارة عن B ناقص عنصر بيصير ال A
+
+308
+00:23:56,440 --> 00:24:02,240
+infinite فكيف بنكوّنها؟ هنكوّنها مع بعض هقوله الآن
+
+309
+00:24:02,240 --> 00:24:09,240
+let B لا تنتمل ال A بدي أخد عنصر خارج ال A بدي أخد
+
+310
+00:24:09,240 --> 00:24:13,650
+عنصر خارج ال A بينفع أخد عنصر خارج ال A؟ليش؟ لأ مش
+
+311
+00:24:13,650 --> 00:24:17,530
+عارف الـB، بتكون الـB لسه لأن مافيش إيه بتحتوي كل
+
+312
+00:24:17,530 --> 00:24:20,750
+شيء فقدّيني أي مجموعة، في مجموعة عنصر أخرج، يا
+
+313
+00:24:20,750 --> 00:24:23,830
+خدنا عنصر معاه الآن هنكون الـB، انتبهوا على ال
+
+314
+00:24:23,830 --> 00:24:31,490
+trick اللي هنعمله أدلت B تساوي إيه اتحاد الـB ليش
+
+315
+00:24:31,490 --> 00:24:35,370
+بد الـB بالخارج؟ عشان لما أضيفه للـA تصير فعلا
+
+316
+00:24:35,370 --> 00:24:38,410
+أكبر لأن لو كان دي هو الـA كان مع اتحاده بتعمل
+
+317
+00:24:38,410 --> 00:24:44,970
+إيه؟ فانا بديها تكون proper الآن thenالـ B proper
+
+318
+00:24:44,970 --> 00:24:48,670
+super 6 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 إيش عندي
+
+322
+00:24:59,350 --> 00:25:03,190
+مقطع جالي كل proper super 6 إذا كانت الـ B proper
+
+323
+00:25:03,190 --> 00:25:05,970
+super 6 من إيش؟ مقلبة الـ B في infinite فهذا يؤدي
+
+324
+00:25:05,970 --> 00:25:12,830
+إن الـ B is infiniteطيب إيش علاقة الـ B مع الـ A
+
+325
+00:25:12,830 --> 00:25:21,870
+بط بي ناقص الـ B تساوي إيه؟ 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 المطلوبفهنا مرة
+
+328
+00:25:35,390 --> 00:25:37,770
+تانية كيف نستخدم النظرية فاحنا ايه 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 و طرحنا 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 ال criterion
+
+336
+00:26:25,190 --> 00:26:29,840
+for finite setsأه طبعاً احنا فيها إن التعريفات
+
+337
+00:26:29,840 --> 00:26:33,600
+وشوفنا إنه التعريفات مش دايماً 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 finiteكيف 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 ال finite و أعرف ال infinity اللي
+
+345
+00:26:56,890 --> 00:27:00,210
+عبارة عن ال negation و بعدين أوصل ل اللي 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 إيش 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
+إيش المجموعة بتكون finite بقول اللي asset X is
+
+350
+00:27:15,540 --> 00:27:20,560
+finite if and only if عشان هيه معيار if if and
+
+351
+00:27:20,560 --> 00:27:26,460
+only if either X is Phi يا فارغة or X is 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 تاوي اتحدثنا عنها والـ NK إيش
+
+354
+00:27:32,720 --> 00:27:35,780
+معناه دايما؟ دي finite فهي إيه إيش ال finite؟ ال
+
+355
+00:27:35,780 --> 00:27:40,450
+finite يا إمافارغة 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
+أشرين، مية يعني بتكافئ مين؟ NK ماودهش NK لما بقول
+
+361
+00:27:58,370 --> 00:28:01,770
+أناش بعدهم واحد، اتنين، تلاتة، K إذا رقم أنصر فيها
+
+362
+00:28:01,770 --> 00:28:07,210
+K من العناصر خلينا نشوف البرهان مع بعضخلّيني أبدأ
+
+363
+00:28:07,210 --> 00:28:11,690
+البرهان هنا Approve
+
+364
+00:28:11,690 --> 00:28:15,710
+طبعا هذه ال statement خلّيني أكتبها أول شي فعنا
+
+365
+00:28:15,710 --> 00:28:23,070
+هنا X يمكن جاب للبرهان نكتب ال statement X
+
+366
+00:28:23,070 --> 00:28:35,080
+is finite if and only ifx تساوي 5 او x in one to
+
+367
+00:28:35,080 --> 00:28:38,520
+one correspondence يعني ايش؟ there exists a
+
+368
+00:28:38,520 --> 00:28:47,000
+bijection نسميه f او g اللي بدنا يه جي من x لمين؟
+
+369
+00:28:47,000 --> 00:28:53,400
+للن كي for some k تمام؟ فهذه ال 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 التاني 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 فاي or there exist a bijection
+
+375
+00:29:30,440 --> 00:29:38,760
+J من X ل K ل NK طبعا for some K تنتمي
+
+376
+00:29:38,760 --> 00:29:47,000
+لل Z مظبوط for some NK طبعا خليها واضحة مش مشكلة
+
+377
+00:29:47,000 --> 00:29:55,580
+implies X is finite فهذا التجاه الأول تمام assume
+
+378
+00:29:55,580 --> 00:30:03,180
+X تسوى فAssume X تساوي فاي or there exists a
+
+379
+00:30:03,180 --> 00:30:07,060
+bijection
+
+380
+00:30:07,060 --> 00:30:14,220
+J من X لأنكي 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 التاني 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 Phi، 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
+تسوي Phi، then X is finite
+
+389
+00:30:57,400 --> 00:31:00,840
+الآن بدنا ناخد الاحتمال التاني فهذا هو يكون
+
+390
+00:31:00,840 --> 00:31:05,480
+proposition خمسة اتنين اتوقع proposition خمسة
+
+391
+00:31:05,480 --> 00:31:09,300
+اتنين خلصنا فالان بدنا ناخد الاحتمال التاني فإن
+
+392
+00:31:09,300 --> 00:31:16,240
+اذا ماكنتش five 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 إلىNK 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 تنتين finite
+
+397
+00:31:44,710 --> 00:31:48,010
+يا تنتين infinite أنا بعرف من المثال الماضي من
+
+398
+00:31:48,010 --> 00:31:51,890
+النتيجة أن ال NK is finite إذا لازم ال X تكون
+
+399
+00:31:51,890 --> 00:31:56,570
+finite أه فهنا by اللي هو ال corollary
+
+400
+00:32:00,900 --> 00:32:04,200
+خمسة واحد وخمسة اتنين خمسة واحد بتقول علاش انه
+
+401
+00:32:04,200 --> 00:32:09,520
+مافيش بيجيكشن اللاتنتين من finite and corollary
+
+402
+00:32:09,520 --> 00:32:17,430
+خمسة اتنين x is finite فهذا الجزء السهلفخلصنا، فلو
+
+403
+00:32:17,430 --> 00:32:20,750
+كانت five هي finite لأن فيها zero من العناصر، و
+
+404
+00:32:20,750 --> 00:32:23,710
+هذا أثبتناها قبل هيك، و لو كانت فيها bijection
+
+405
+00:32:23,710 --> 00:32:26,710
+بينها وبين N، NK، مانفعش يكون بيجيكشن لبين
+
+406
+00:32:26,710 --> 00:32:29,490
+مجموعتين من نفس الجنس، بما أن NK finite توي
+
+407
+00:32:29,490 --> 00:32:32,950
+أثبتناها بال induction، إذا لازم تاني تكون finite،
+
+408
+00:32:32,950 --> 00:32:39,120
+فأدا الاتجاه خلص، نيجي للاتجاه التانيبدنا الآن B
+
+409
+00:32:39,120 --> 00:32:41,760
+implies Q بس عشانها كبيرة مابديش اكتبها كمان مرة
+
+410
+00:32:41,760 --> 00:32:46,160
+مش هثبتها بشكل مباشر هثبت ال contrapositive تبعتها
+
+411
+00:32:46,160 --> 00:32:50,140
+ايش مطلوب نثبت ولا اكتب .. خليني اكتب يلّا اه هل
+
+412
+00:32:50,140 --> 00:33:00,380
+جيش بدنا نثبت ان X is finite implies X تساوي Phi
+
+413
+00:33:00,380 --> 00:33:05,880
+or there exists a bijection خليني اكتبها بشكل
+
+414
+00:33:05,880 --> 00:33:15,390
+مختصرمن X ل NK تكون one to one and unto واضحة؟ one
+
+415
+00:33:15,390 --> 00:33:20,170
+to one and unto اكتبه بهذا الشكل اختصارا اه تمام
+
+416
+00:33:20,170 --> 00:33:25,050
+فده مطلوب اه مش هنثبت هذه اليملة مباشرة هنثبت ال
+
+417
+00:33:25,050 --> 00:33:36,930
+contrapositive تبعدها او it's contrapositive نتذكر
+
+418
+00:33:38,300 --> 00:33:42,020
+شبتر واحد اه بيصير not Q implies not B يعني إيه ده
+
+419
+00:33:42,020 --> 00:33:48,240
+تكون هذا النفي تبعتها X لا تسوى فاي and their
+
+420
+00:33:48,240 --> 00:33:53,940
+existence هصيربتصير for all انه .. بس هو بيقول لي
+
+421
+00:33:53,940 --> 00:33:56,940
+there exists يعني مافيشش 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 بذا الشكل .. اه هي for all .. اي دالة من x
+
+424
+00:34:04,200 --> 00:34:08,500
+ل x and هتكون bijection .. اه بيصير أنه أي دالة من
+
+425
+00:34:08,500 --> 00:34:11,080
+x ل and 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 نثبتأه مرة تانية احنا
+
+431
+00:34:48,040 --> 00:34:53,500
+بنعمل هذه الجملة أثبتنا Q تكائط implies B ففي واحد
+
+432
+00:34:53,500 --> 00:34:58,500
+انهيش 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
+امتبعين باختصار شديد وده اللي عملنا تمام فالجملة
+
+435
+00:35:08,720 --> 00:35:11,580
+الشرطية اللي كترة 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 FI and there is no bijection between X
+
+438
+00:35:29,450 --> 00:35:38,100
+and NK ولا NK مستحيلكم اتمنواالبرهان 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 و بعدين نكتب أنا عندي مجموعة كبيرة بدي أثبت
+
+441
+00:35:48,420 --> 00:35:50,860
+إنها infinite اللي هنعملوا في طريقة البرهان إن
+
+442
+00:35:50,860 --> 00:35:54,900
+هدول العناصر هنرتبهم فنفترض إن إحنا في عندنا وعاء،
+
+443
+00:35:54,900 --> 00:35:59,130
+في عندنا كيس، في كرات مش عارفين عددهمهنبدأ ناخد كل
+
+444
+00:35:59,130 --> 00:36:01,990
+كورة ونعدّى عشان نصفد ان واحدة وانا 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 ال K صفضى إيش بيكون اتفيلها كورة واحدة؟ إيش
+
+447
+00:36:08,250 --> 00:36:12,250
+بيكون؟ بناقد 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
+كورةأمد إيدي واخد الكرة رقم اتنين ارقمها هي ايش
+
+451
+00:36:21,390 --> 00:36:26,490
+الكرة رقم اتنين طيب خلص ال case مستحيل لو انه خلصش
+
+452
+00:36:26,490 --> 00:36:30,530
+بيكون and two بينفعش فاخد ايش اخد كمان عنصر و هكذا
+
+453
+00:36:30,530 --> 00:36:33,570
+فدي الفكرة فدي الفكرة اللي حنمنها هنرقمها
+
+454
+00:36:36,520 --> 00:36:40,380
+X لا تساوي فاى، إيش معناته؟ 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
+أرقمه، مديت إيدي في الكيس، لاجيت أول كورة، لأنه مش
+
+457
+00:36:48,420 --> 00:36:51,580
+فاضي، هلاجي كورة و لا 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
+أه، اللي قاعد بالتأكيد أن الكيس مافضيش، لو أخدت
+
+460
+00:36:58,800 --> 00:37:02,520
+منه كورة بفضأ، بفضاش، أه، أه، 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 ال bijection؟ then g من n one
+
+463
+00:37:17,650 --> 00:37:22,880
+إلى x given by بدي أدريكيها بشكل صريحمين 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 والاكس واحد في بينهم one
+
+468
+00:37:41,370 --> 00:37:44,850
+to one correspondence ولا لأ الواحد اكس واحد هي
+
+469
+00:37:44,850 --> 00:37:47,710
+التنازف صح ولا لأ طبعا ايش مقالة ده contradiction
+
+470
+00:37:47,710 --> 00:37:50,630
+مستحيل اه اذا ايش مقالة اه اذا 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 ان اكس ناقص اكس one لا تساوي five بدل مكتبX
+
+474
+00:38:06,940 --> 00:38:13,560
+نقص واحد تسوى نفس المعنىفما 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 تانية،
+
+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؟ أه، فعشان
+
+482
+00:38:34,380 --> 00:38:36,860
+هي كان بيدي أخدياش عنصر من X ناقص X واحدة، ان
+
+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
+فانا عندي X ناقص X1 و X2 برضه لاتساوي 5فبعد ما خدت
+
+490
+00:39:29,730 --> 00:39:34,090
+الكورتين برضه ما فضيتش الكيس و لا 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
+أه 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، أه 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
+انعمم الفكرة ايش اللي كدبناها تعميم لجينا X1 لو
+
+500
+00:40:15,890 --> 00:40:21,570
+خلصت بينفعش اتخلص لجيت X2 بعد ما X2 ايش بلاجي X3
+
+501
+00:40:21,570 --> 00:40:26,490
+فكل مرة بعد ما خلص لما لاجي XN ايش بلاجي N plus
+
+502
+00:40:26,490 --> 00:40:29,490
+one واضحة ولا مش واضحة ال statement ها دي اه لأنه
+
+503
+00:40:29,490 --> 00:40:35,370
+انا ايش 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؟ لأ مابتجافش لو
+
+505
+00:40:38,770 --> 00:40:44,230
+وقفتلو هذا كان غلط، إيش معناته؟ إن هناك bijection
+
+506
+00:40:44,230 --> 00:40:48,150
+بين X و بين مين، N sub small n، صح؟ مستحيل، أه،
+
+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
+ال trick التالف let Y تساوي X N such that N تنتمي
+
+511
+00:41:07,310 --> 00:41:13,230
+للـ Nأيش اللي بده أعمله زي ما حكينا مرة تانية هي
+
+512
+00:41:13,230 --> 00:41:17,690
+الكيس فيه كورات مخربطين ومش عارفين إيش نوحهم 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 فالان طبعا إذا أثبت ان ال Y
+
+516
+00:41:28,950 --> 00:41:32,280
+infiniteكل عناصر الـ Y من أين واخدناها؟ 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، لأ 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 البرهة، فهي فكرة
+
+521
+00:41:44,540 --> 00:41:48,480
+البرهة طبعا، طب ليش الـ Y التعامل معها أسهل؟ لأنها
+
+522
+00:41:48,480 --> 00:41:52,140
+مرتبة، مرقمة، أه كيف ممكن أثبت أن الـ Y Infinite؟
+
+523
+00:41:52,140 --> 00:41:57,320
+ممكن نلاقي دالة one to one وليست أنتوا بسهولة then
+
+524
+00:42:02,100 --> 00:42:11,260
+Y subset من ال X and F من Y ل Y مين يثبت إن ال Y
+
+525
+00:42:11,260 --> 00:42:14,800
+Infinite؟ تدوني دالة one to one و ليست on two،
+
+526
+00:42:14,800 --> 00:42:22,330
+given byإيش نعمل؟ إيش عملنا بالـnatural number؟
+
+527
+00:42:22,330 --> 00:42:26,830
+لإن أحنا 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 الـand 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 أخدتF 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 one to less
+
+536
+00:43:08,560 --> 00:43:15,210
+فكروا فيها أوي المكتوب and F given byis one to one
+
+537
+00:43:15,210 --> 00:43:21,710
+and f of y برابر من ال 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 اتنين فصورة
+
+539
+00:43:25,230 --> 00:43:28,010
+من وين بتبدأ من x اتنين و طالع 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 البرهق خليني
+
+546
+00:44:06,960 --> 00:44:13,020
+بس ننهي بملاحظة لأن مافيش وقت كتير 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 ال 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 لأ هي أنا عنصر مقابل الأتنين في عنصرفإذا 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 ال X is a non-empty طبعا إذا empty ما
+
+555
+00:44:44,630 --> 00:44:46,870
+هي معروفة نيجي على ال 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
+منتهيةوغير 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 ال 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
+التنين أسميها X تنين فزا عناصر ال X ممكن إيش؟
+
+564
+00:45:17,590 --> 00:45:22,540
+أرقمهم ممكن نرقمهمإذا أي finite set يا إما Phi
+
+565
+00:45:22,540 --> 00:45:26,520
+وإذا ماكنتش Phi ممكن أرقمها من واحد لعدد العناصر ل
+
+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 ل X K for some K في
+
+569
+00:45:36,960 --> 00:45:40,860
+عدد K من العناصر وهذا متفق مع التعريف القدي نوجّف
+
+570
+00:45:40,860 --> 00:45:41,180
+هنا إن شاء الله
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yaE-rza0wfU_postprocess.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yaE-rza0wfU_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3753ba6402e085b4d67d64d196bcef77947179c3
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yaE-rza0wfU_postprocess.srt
@@ -0,0 +1,2096 @@
+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
+00:02:00,430 --> 00:02:05,470
+بكون لهم علاقة مع بعض إذا وقعها في نفس الجزء هاي X
+
+30
+00:02:05,470 --> 00:02:11,190
+وهاي Y وهاي Y وماكنتش لهم علاقة مع بعض إذا وقعها
+
+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
+تالت Z هنافي 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 وقعها 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 التعريففبقول لي we
+
+38
+00:02:39,010 --> 00:02:42,910
+define a relation ايش .. ايش الرمز تبعها؟ X على B
+
+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 B .. X على B
+
+43
+00:02:58,150 --> 00:03:01,690
+طيب هي relation من وين لوين؟ من X لX لأن منصوبة ان
+
+44
+00:03:01,690 --> 00:03:05,600
+هي علاقة تكافأطيب كيف بنعرفها؟ بيقولّي 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
+لأنه 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
+إيش عناصرها؟ أزواج مرتبةsuch that X في الـ A والـ
+
+50
+00:03:27,560 --> 00:03:31,200
+Y في الـ A for some A للـ B فالـ X والـ Y ليش انهم
+
+51
+00:03:31,200 --> 00:03:34,540
+علاقة مع بعض؟ لأنهم مقعوا في جزء انما لو في عندنا
+
+52
+00:03:34,540 --> 00:03:37,920
+هنا A و B ليش انهم علاقة مع بعض؟ لأنهم مقعوا في
+
+53
+00:03:37,920 --> 00:03:41,160
+جزء معين مش دارون نفس الجزء فكل أنصرين في نفس
+
+54
+00:03:41,160 --> 00:03:46,020
+الجزء لكن كل جزء بيكوّل لأزواج مرتبة أزواج مرتبة
+
+55
+00:03:46,020 --> 00:03:48,980
+واضح التعريف؟ اه ان شاء الله هنشوف الأمثلة و ان
+
+56
+00:03:48,980 --> 00:03:55,700
+شاء الله الأمور بتكون أفضل نشوف المثال الأولطبعا
+
+57
+00:03:55,700 --> 00:03:58,660
+دائما بنبدأ بالأمثلة البسيطة عشان دائما الإنسان
+
+58
+00:03:58,660 --> 00:04:02,000
+بيبدأ من المرحلة الدنيا و بيبنيه و بيطلع و بتساعد
+
+59
+00:04:02,000 --> 00:04:05,100
+في المفهوم نبدأ مجموعة صغيرة طبعا هذا أسهل في
+
+60
+00:04:05,100 --> 00:04:09,600
+الفهم من تلت عناصر و معوونها partition كيف ال
+
+61
+00:04:09,600 --> 00:04:13,440
+partition ال zero مع التانين جزء و الواحد لحاله لو
+
+62
+00:04:13,440 --> 00:04:19,480
+رسمنا صورة هي جزء ايه فيها الواحد لحاله و ال zero
+
+63
+00:04:19,480 --> 00:04:23,800
+و التانين لحاله اللي مع بعضzero و اتنين و الواحد
+
+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 و بعدين
+
+67
+00:04:34,120 --> 00:04:38,800
+بدنا نجاوب هل العلاقة المتولدة هي علاقة تكافئ ولا
+
+68
+00:04:38,800 --> 00:04:43,100
+لأ فنبدأ الحل solution فطبعا ايش الجزء الاول من
+
+69
+00:04:43,100 --> 00:04:48,180
+الحل بدنا نحسب X على B اللي انا ممكن اسميها Q
+
+70
+00:04:48,180 --> 00:04:53,740
+اختصارا اذا حبيت نسميها Qتساوي عشان R طيب ماشي
+
+71
+00:04:53,740 --> 00:04:59,100
+اشملها دي من التعريف أيه فوق؟ بدنا الأزواج المرتبة
+
+72
+00:04:59,100 --> 00:05:02,140
+ليش يكون الأحداث 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
+لأن هي و نفسها بيقعوا في نفس الجزء إذا أول زوج
+
+75
+00:05:10,700 --> 00:05:14,600
+عندي الواحد و واحد بنفس الأسلوب ال zero و ال zero
+
+76
+00:05:14,600 --> 00:05:18,790
+بنفس الأسلوب التنين و التنين ولا لأ؟لازم يكون لأن
+
+77
+00:05:18,790 --> 00:05:22,690
+الواحد باتجاه هي في جزء و نفسها في جزء آخر،
+
+78
+00:05:22,690 --> 00:05:25,470
+مانفعش، و الـ zero نفس الشياء و الـ two نفس الجزء،
+
+79
+00:05:25,470 --> 00:05:29,310
+إذا حسبناها، إذا واضح على طول إن هذه علاقة شمالها،
+
+80
+00:05:29,310 --> 00:05:32,350
+علاقة انعكاس، reflexive، واضح؟ كل أنصف دي قاعمة
+
+81
+00:05:32,350 --> 00:05:36,190
+نفسه، تمام، طيب، إيش كمان؟ هل الواحد لعلاقة مع أي
+
+82
+00:05:36,190 --> 00:05:39,810
+حد آخر؟ لأ، لأن في جزء لحالة، إذا الواحد خلصنا،
+
+83
+00:05:39,810 --> 00:05:43,590
+طيب الـ zero إيه العلاقة مع حد آخر؟ مع التنين، لأن
+
+84
+00:05:43,590 --> 00:05:50,030
+هي و التنين بيقع في نفس الجزءطب والتنين و Zero و
+
+85
+00:05:50,030 --> 00:05:53,490
+خلصنا .. اه .. و خلصنا .. لأ .. طب ليش؟ لأنه زي ما
+
+86
+00:05:53,490 --> 00:05:57,530
+تشوفين التعريف بيقول يقعاه في نفس الجزء الترتيب
+
+87
+00:05:57,530 --> 00:06:01,550
+مهم؟ لأ .. اذا زوج موجود عكسه لازم يكون موجود لأنه
+
+88
+00:06:01,550 --> 00:06:04,030
+الان commutative التعريف .. اه .. commutative ..
+
+89
+00:06:04,030 --> 00:06:07,410
+اه فياك 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 و التنين مع ال Zero و Zero مع ال
+
+92
+00:06:14,070 --> 00:06:15,990
+Zero و التنين مع التنين طب هذا الجزء الأول
+
+93
+00:06:17,840 --> 00:06:21,220
+التكافأة؟ لأن الـ reflexive واضح من أول شيء
+
+94
+00:06:21,220 --> 00:06:25,680
+الـsymmetric كل زوج عكسه موجود لأنها and والand
+
+95
+00:06:25,680 --> 00:06:28,240
+دائما committed الترتيب مش مهم طب هل هذه
+
+96
+00:06:28,240 --> 00:06:30,260
+transitive؟ لو فحصنا من اللي جاها فعلا أنها
+
+97
+00:06:30,260 --> 00:06:33,980
+transitive لأن 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 إلى زيرو، خلصنا، فبنكون احنا فحصناه،
+
+102
+00:06:47,890 --> 00:06:51,450
+فهذه إيش 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 ان كلهم متحققين، بنلاقي
+
+105
+00:07:00,530 --> 00:07:05,010
+هي علاقة انعكاس، علاقة تماثل، وعي فيها خاصية
+
+106
+00:07:05,010 --> 00:07:08,130
+التعجل، ففعلًا هذه علاقة تكافأ
+
+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
+طبعاً 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 طبعا في X cross X طبعا لأن وين هي relation علي
+
+118
+00:08:23,760 --> 00:08:29,040
+ال X ممكن نكتبها للتأكيد هي in Z cross Z لأنها 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 طبعا لأنها عراقة علي ال X طبعا
+
+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 للـ A for some A تنتمي لل partition اللي
+
+124
+00:08:54,210 --> 00:09:02,130
+في هذا السؤال هو إيه؟ هو E و D هو E و D متابعين؟
+
+125
+00:09:03,680 --> 00:09:08,460
+في أي حد عنده استفسار واضح تقريب انا 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 ان صحيح العناصر كتيرة لكن الأجزاء
+
+129
+00:09:21,980 --> 00:09:25,480
+قليلة جزءين لما بقوله for some ايه تنتمي لل
+
+130
+00:09:25,480 --> 00:09:29,180
+partition ايش احتمالات الـA؟ ياد E ياد D مافيش
+
+131
+00:09:29,180 --> 00:09:33,780
+الاحتمالين فخلينا نكتب هذا الكلام فهذا تساويX of Y
+
+132
+00:09:33,780 --> 00:09:36,680
+طبعا في الـ Z cross الـ Z بدي اكتب .. بديش اكتب
+
+133
+00:09:36,680 --> 00:09:42,140
+اختصار لإنه واضح بحيث ال X تنتمي ليا 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 او احتمال تاني لإن 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 Dممكن اكتب بهذا الشكل هذا اليوم اللي اترجمه هيك
+
+138
+00:10:02,090 --> 00:10:05,050
+و لا لأ؟ لان انا بقول for some ايه؟ ايش احتمالات
+
+139
+00:10:05,050 --> 00:10:09,430
+الـA؟ الـA يا E يا O يا R فور some ايش معناته؟
+
+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
+اوصل الـquadration، بدي اكتبها بشكل حتى تكون انتوا
+
+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 اتنين يعني ايش بكتوبها
+
+145
+00:10:31,690 --> 00:10:36,290
+اتنين في N او اتنين في M فهذا معناته ان X تساوي
+
+146
+00:10:36,290 --> 00:10:41,890
+اتنين N و Y تساوي اتنين M for some N و M انتجة
+
+147
+00:10:41,890 --> 00:10:44,970
+لانه مضاعفات اتنين بس بدي اكتوبها بالاخر بدي أجلها
+
+148
+00:10:44,970 --> 00:10:51,100
+شوية عشان اختصر في الكتاب orإيش معنات فردي؟ 2n
+
+149
+00:10:51,100 --> 00:10:57,880
+زياد 1 فال X تساوي 2n زياد 1 and Y تساوي 2m زياد 1
+
+150
+00:10:57,880 --> 00:11:01,120
+طبعا هدول ال N و ال M إيه 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 ان الاحداث الأول
+
+154
+00:11:17,270 --> 00:11:20,890
+والتاني يقع في نفس الجزء بما ان ال partition جزءين
+
+155
+00:11:20,890 --> 00:11:24,090
+اذا هدول هيكون في الجزء الأول او الجزء التانيالان
+
+156
+00:11:24,090 --> 00:11:27,690
+من معلوماتنا الجزء الاول هو الاعداد الزوجية كيف
+
+157
+00:11:27,690 --> 00:11:31,110
+صورتهم اتنين في N او اتنين في M من ضعفات التنين
+
+158
+00:11:31,110 --> 00:11:34,510
+طباش الفردي اللي هو عيش مش زوجي يعني زائد واحد او
+
+159
+00:11:34,510 --> 00:11:37,850
+ناقص واحد لان كل اعداد 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
+الان بس عشان انا بيدوصل كل صورة مألوفة اه يساوي XY
+
+162
+00:11:49,560 --> 00:11:56,100
+لو طرحنا X ناقص Y في الحالتين X ناقص Y إيش بتديني؟
+
+163
+00:11:56,100 --> 00:12:03,340
+2N ناقص M وفي التاني برضه 2N ناقص M الواحد بتروح
+
+164
+00:12:03,340 --> 00:12:10,080
+مع الواحد اللي هي إيش بتساوي؟اتنين في K for some K
+
+165
+00:12:10,080 --> 00:12:15,260
+from N to Z لأن الـ N و الـ M أعداد صحيحة فالفرق
+
+166
+00:12:15,260 --> 00:12:20,560
+بينهم أعداد صحيحة بدي أسميه K الـ N ال relation لو
+
+167
+00:12:20,560 --> 00:12:25,230
+تخبينا هذا مقلوفة الكل مش مقلوفةاللي سمناها Mode M
+
+168
+00:12:25,230 --> 00:12:28,230
+تذكروا؟ احنا أخدناها Mode 3 كمثال بالتفصيل
+
+169
+00:12:28,230 --> 00:12:31,850
+وقلنالكم أي عدد صحيح غير التلاتة بيقدر الغرض واحد
+
+170
+00:12:31,850 --> 00:12:35,390
+اتنين تلاتة اربع وهاكذا ويمكن نشوف الاربعة كمثال
+
+171
+00:12:35,390 --> 00:12:39,250
+لما حسبنا صفوف التكافأة و لا لأ فدياش relation فهي
+
+172
+00:12:39,250 --> 00:12:41,670
+شايفين ان ال relation مشهورة هي عندي بدأت بال
+
+173
+00:12:41,670 --> 00:12:45,050
+partition وولدت relation و relation معروفة فهي
+
+174
+00:12:45,050 --> 00:12:48,880
+relation relation معروفة طبعاواحد يقول لك ضروري
+
+175
+00:12:48,880 --> 00:12:51,600
+نعمل كل حسابات لو المثال جالك ال relation و كده
+
+176
+00:12:51,600 --> 00:12:55,320
+اول تعريف يكفي عندي لكن هناكش كان الهدف ان 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 لان 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 فالان الحقيقة ان هو اللي صار في دول
+
+181
+00:13:10,060 --> 00:13:14,720
+المثالينبدأنا 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 دايما صحيح
+
+184
+00:13:21,620 --> 00:13:24,620
+و لا بس كانت من الصدفة المثالين الحقيقة دايما صحيح
+
+185
+00:13:24,620 --> 00:13:27,440
+زي ما حد شوفه في النظرية فنظرية تلاتة خمسة بيقول
+
+186
+00:13:27,440 --> 00:13:32,900
+دايماEQ هذي اللي هي X على B، إيش معناه X على B؟ ال
+
+187
+00:13:32,900 --> 00:13:36,060
+relation اللي بعرفها ال partition دايما
+
+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 Xthen 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 بيساعدناش بيقولني
+
+192
+00:13:51,710 --> 00:13:55,110
+the relation X على B هاد رمزة لإن معناته إيش؟ 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 بعضطبعا كيف بنسميها الـ
+
+196
+00:14:07,750 --> 00:14:11,670
+equivalence relation؟ تلات شروط إنها reflexive،
+
+197
+00:14:11,670 --> 00:14:19,310
+transitive و symmetric فهذه نظرية تلاتة خمسة وهذه
+
+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 Bخلينا نرمز اللي احنا بالرمز Q
+
+200
+00:14:30,800 --> 00:14:34,000
+أسهلنا طبعا انا مااخد الـ Q لأن زي هي واضحة علينا
+
+201
+00:14:34,000 --> 00:14:37,740
+زي قسمة قوشن فبدي اخد الـ Q اه بدي اثبت ان الـ Q
+
+202
+00:14:37,740 --> 00:14:40,900
+is an equivalent relation فأول شيء بدي اثبت ان 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 عصره علاقة مع نفسهوزي ما شوفنا بالامثلة طبعا كل
+
+205
+00:14:53,220 --> 00:14:55,660
+عنصر زوجي ما هو بيبغى يقع مع الزوج في المثال
+
+206
+00:14:55,660 --> 00:14:58,140
+الأخير وكل شوفنا ان الواحد لعقله في المثال اللي
+
+207
+00:14:58,140 --> 00:15:01,780
+جابله وها كذا طب كيف بنثبت ان كل عنصر يقع مع نفسه
+
+208
+00:15:01,780 --> 00:15:06,820
+انه علاقة مع نفسه انه كل عنصر يقع بنفس الجزء من
+
+209
+00:15:06,820 --> 00:15:09,420
+البرتش احنا ايش عندنا معطيات؟إن الـ P partition
+
+210
+00:15:09,420 --> 00:15:12,460
+وهي relation ومعروف كيف تعريفها الـ 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
+إيش بدنا نثبت؟ for all X، مظبوط؟ إيش تعريف
+
+213
+00:15:19,640 --> 00:15:24,240
+reflexive؟ for all X in capital X XX في الـ Q، صح؟
+
+214
+00:15:24,240 --> 00:15:27,380
+طب ما زال for all إيش 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 elementطبعا طريقة الكتابة
+
+217
+00:15:38,890 --> 00:15:41,670
+والتقنيم والتأخير 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 اثبت ان ال X تقع مع نفسها
+
+220
+00:15:49,090 --> 00:15:55,490
+بنفس الجزء طب هل ال X بتقع بجزء أصلا؟ وليش؟ 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 اذكركوا ان 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 انا من الخاصية رقم اتنينفي 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
+لضمن الكلام وخاصية رقم واحد وخاصية رقم اتنين فهذه
+
+228
+00:16:24,160 --> 00:16:27,640
+خاصية رقم اتنين 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 بدناية فده بيقوللي 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 نيجي للخاصية رقم اتنين بس خليني
+
+234
+00:16:55,530 --> 00:17:03,910
+اكتف ال Q is symmetric بدنا نثبت انه ان ال Q is
+
+235
+00:17:03,910 --> 00:17:09,220
+symmetricوالبرهان الحقيقة زي ما شرحنا من التعريف
+
+236
+00:17:09,220 --> 00:17:11,860
+طبعا إيش معناه 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
+إيش let x,y تنتمي لـQ طيب إيش معناه الـQ إن الـx و
+
+239
+00:17:21,880 --> 00:17:27,220
+الـy في نفس الجزء فده implies اللي هو إيش x تنتمي
+
+240
+00:17:27,220 --> 00:17:33,660
+لـA و y تنتمي لـA for some a في ال partition
+
+241
+00:17:33,660 --> 00:17:37,620
+التعريفأنا قلتلكم 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
+أه 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
+تاني ما هذي بتساوي هذي إيش ماله؟ أبدل لإن 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 البرتش أه الآن اتبدلت دور هذا أيه
+
+248
+00:18:02,400 --> 00:18:09,100
+معناته أن Y Xفي الـ 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 التالتة والاخيرة بدنا نثبت ان الـ Q is
+
+251
+00:18:24,720 --> 00:18:32,020
+transitive الـ Q is transitive هذه تلاتة
+
+252
+00:18:37,700 --> 00:18:42,020
+تمام ايه الشرط الـ Transitive؟ بدنا زوجين بترتيب
+
+253
+00:18:42,020 --> 00:18:46,780
+معين موجودين لازم المكمل تبعهم التالت يكون موجود
+
+254
+00:18:46,780 --> 00:18:53,210
+فبرضه بنبدأ ايش assume او letlet x,y في الـ Q and
+
+255
+00:18:53,210 --> 00:18:58,470
+y,z في الـ Q بدنا نثبت إنه x,z في الـ Q إيش نعمل؟
+
+256
+00:18:58,470 --> 00:19:02,650
+نستخدم التعريف ماذا يعني x,y في الـ 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 للـ partition بحيث x في الـ A and y
+
+259
+00:19:11,770 --> 00:19:15,770
+في الـ A هيك معناته الـ x والـ y اللي ملاقة مع بعض
+
+260
+00:19:15,770 --> 00:19:20,360
+إنه من نفس الجزء andكفي كمان قاندة كبيرة، إيش
+
+261
+00:19:20,360 --> 00:19:24,140
+معناة Y و Z في الـQ 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
+أه، فانا بقول there exist .. إيش أسميها؟ A ولا
+
+264
+00:19:29,780 --> 00:19:32,900
+إيش؟ ولا أغير اسم؟ بنغير بيه، لإنهم مش عارفين و
+
+265
+00:19:32,900 --> 00:19:38,560
+متساويين، there exist B in partition بحيث أنه إيش؟
+
+266
+00:19:38,560 --> 00:19:41,520
+Y في الـB و Z في الـB
+
+267
+00:19:44,880 --> 00:19:48,180
+تمام الآن أنا إيش 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 أنتيش 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 مشترك و من خلاص ال partition يا كل عناصر
+
+272
+00:20:04,760 --> 00:20:07,580
+مشتركة يا مافيش مشترك إذا واحد مشترك 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
+followsthat Y تنتمي لـ A تقاطع الـ B الـ Y مشترك
+
+275
+00:20:17,970 --> 00:20:25,190
+وبالتالي الـ A تقاطع الـ 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 الـ B partition تمام مازال 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 بقول إيه Xو Z تنتمي الـ A تساوي الـ B
+
+280
+00:20:41,050 --> 00:20:49,090
+وهذا 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 تكافئة واضح فإحنا
+
+283
+00:20:59,950 --> 00:21:04,870
+الأمثلة الماضية كانت مش حاجة نادرة إنما هي دايما
+
+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 جالب 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 الجزءنقطة 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 التاليةبدأنا 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 متساويفدى 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 زى
+
+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 زى 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 بادة 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 و لا نفس اللي بدأت منه و نفس
+
+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 partitionوال 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
+partitionو هيعندي 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 التكافأة
+
+322
+00:23:47,700 --> 00:23:50,320
+اللي ولد و تولد relation طيب هذا ال equivalent
+
+323
+00:23:50,320 --> 00:23:54,360
+class عبارة عن partition ايش 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 طبعا 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 Aهذه 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 و أصله 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
+elementطبعا ممكن تلاقوا في الكتب المتقدمة مابكتبش
+
+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 ان ال Y في صف ال X؟ ايش تعريف
+
+354
+00:26:03,520 --> 00:26:07,220
+الصف؟ يعني ال X و ال Y لملاقا مع بعض، فهذا يؤدي ان
+
+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 Qصحيح؟ 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
+إنه 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 و ال 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 و ال 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 bإذا الـ
+
+374
+00:27:27,600 --> 00:27:30,880
+A بتسوى ال B إيش صار الصورة نقرأ مع بعض و ده ممكن
+
+375
+00:27:30,880 --> 00:27:34,380
+أحنا 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 و ال B
+
+379
+00:27:48,060 --> 00:27:53,790
+تسوى ال A إذا ال Y وين؟ في ال A and henceY تنتمي
+
+380
+00:27:53,790 --> 00:27:59,790
+للـA فإيش وصلنا بدأنا من X على Q وصلناها للـA 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 الـA الآن let Y
+
+384
+00:28:15,470 --> 00:28:22,950
+تنتمي للـA be any elementو أرجو نتعود نقرأ صح واحد
+
+385
+00:28:22,950 --> 00:28:26,390
+يقولي طب ايه و انا ا 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 على2 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 ان 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
+فارجو أن نستخدم الرموز بشكل صحيح و عشان نكون
+
+399
+00:29:33,170 --> 00:29:39,590
+برهاننا كامل و صحيح 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
+partitionthen 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 partitionوولد
+
+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 مقلوفة عليك وإذا عملت جسمها X على X
+
+410
+00:30:25,500 --> 00:30:28,460
+على B مقام المقام بيصيح ال bus و ال 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 انه قسم زي القسمة واضحة فهي إيش
+
+414
+00:30:40,600 --> 00:30:44,800
+ال X على Q فهي نفس الكلام بدأت من partitionعرفت
+
+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 فانا 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
+لانها ساعدنا في ان 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 خلّينا 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 ال 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 صفوق في التكافئة 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 القراة 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 اليسارlet هاخد عنصر هان واتعلمنا انه
+
+437
+00:32:30,870 --> 00:32:35,110
+في الاصل اخد عنصر عشوائي صحيح طب انا دي انا 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
+انا 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
+letA 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 ممتازالـ X على الـ Q تمام
+
+447
+00:33:20,620 --> 00:33:24,520
+بدنا نستخدم اللي ما الحقيقة هلجيت 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 فالان now small x تنتمي لل capital Xوما
+
+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؟تلاتة واحد ايش 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 اذا اول شيء بدأت من عنصر في X على Q
+
+462
+00:34:32,500 --> 00:34:38,620
+وصلته لل partition اذا اثبتنا ان ال capital X على
+
+463
+00:34:38,620 --> 00:34:44,440
+Q هي subset من ال partition فالاتجاه الاول فده هو
+
+464
+00:34:44,440 --> 00:34:52,400
+الاتجاه الاول نعمل اتجاه التانيlet ايش؟ بدنا ناخد
+
+465
+00:34:52,400 --> 00:34:56,000
+جزء من .. أنصر 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 تكافر، طيب، ممتاز، هل جيت؟بدنا
+
+470
+00:35:14,780 --> 00:35:19,540
+نستخدم برضه اللي مّا 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 مابتقول طب مين بيقوللي 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 بيقوللي 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 Aبالنسبة لما إذا X تنتمي لصف X في شمال A بيسوء
+
+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 تسوى صف ال X وصف ال X موجود في الصفوفمازال الـ A
+
+479
+00:36:04,330 --> 00:36:07,870
+صفف 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 اتنين
+
+483
+00:36:24,790 --> 00:36:31,210
+طبعا واحد واتنين بيقول البرهان انتهى أي سؤال تمام؟
+
+484
+00:36:34,250 --> 00:36:39,130
+خلّينا ننهي ال 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، فخلّينا 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 التلاتة التانية مع بعض
+
+492
+00:37:13,590 --> 00:37:17,490
+حطينا طالب في شعبة و تلات طلاب في شعبة جسمناهم هيك
+
+493
+00:37:17,490 --> 00:37:21,250
+تجسيم بيد الصورة بقول يوجد ال partition يوجد ال Q
+
+494
+00:37:21,250 --> 00:37:25,030
+ويوجد X على ال Q بهذا المعنى عشان نوصل لبدنيا
+
+495
+00:37:25,030 --> 00:37:31,530
+solution فخلينا نحسب Q تساوي X على ال partition
+
+496
+00:37:31,530 --> 00:37:36,150
+تمامبتتكون من أزواج مرتبة إشمالها كل اللي حصلناها
+
+497
+00:37:36,150 --> 00:37:39,390
+في بداية المحاضرة، مش ذاكرين؟ فهي عند ال 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
+والتانين مع نفسها، والتلاتة مع نفسها، والاربعة مع
+
+500
+00:37:46,690 --> 00:37:51,920
+نفسها، تمام، هذه النقطة السهلةهل الواحد لعلاقة مع
+
+501
+00:37:51,920 --> 00:37:55,260
+حد غير نفسه؟ لا لأنه موجود في جزء لحاله لكن التنين
+
+502
+00:37:55,260 --> 00:37:58,540
+لعلاقة مع التلاتة وبالتالي التلاتة لعلاقة مع
+
+503
+00:37:58,540 --> 00:38:02,180
+التنين لأنه symmetric مظبوط والتنين لعلاقة مع
+
+504
+00:38:02,180 --> 00:38:05,620
+الأربعة والاربعة لعلاقة مع التنين لأنه symmetric
+
+505
+00:38:05,620 --> 00:38:12,590
+وتلاتة واربعةوالاربعة والتلاتة في تمشي خلصت ال
+
+506
+00:38:12,590 --> 00:38:15,290
+relation اه فانا في ضوء النظرية انا عارف ان ال
+
+507
+00:38:15,290 --> 00:38:18,470
+relation هي Q لنا و بقدر احسب بيبقى ده الشكل تمام
+
+508
+00:38:18,470 --> 00:38:22,930
+فهي partition بي ده نيا وولدنا relation انشوف ال
+
+509
+00:38:22,930 --> 00:38:26,050
+relation ده ايش ملها بتتولد مين partition نحسبه
+
+510
+00:38:26,050 --> 00:38:30,430
+ايش .. ايش .. ايش رمزه X على Q مظبوط ايش بيساوي
+
+511
+00:38:30,430 --> 00:38:34,890
+الصفوفالـ X أكمل عنصر فيها أربع، ففيدنا يكون فيها
+
+512
+00:38:34,890 --> 00:38:39,330
+أربع صفوف صف الواحد، صف التنين، بس ممكن يكون بعضه
+
+513
+00:38:39,330 --> 00:38:43,830
+متساوي، صف التلاتة وصف الأربع، مظبوط؟ أه، الأن
+
+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 الشيء للواحدلأن
+
+517
+00:38:57,480 --> 00:39:00,360
+الواحد بس لإنه يقول مافيش هو صف فاضي و أول عنصر في
+
+518
+00:39:00,360 --> 00:39:04,300
+صف ال X هو ال X في غيره مافيش طيب مين صف التنين؟
+
+519
+00:39:04,300 --> 00:39:08,640
+التنين و التلاتة و الأربعة و هو بيسوي صف التلاتة و
+
+520
+00:39:08,640 --> 00:39:11,060
+بيسوي صف الأربعة لإنهم ملقا 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 اي سؤال
+
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yaE-rza0wfU_raw.json b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yaE-rza0wfU_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..1abc3c3c76151aa93eb27961158396d098f5879d
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/yaE-rza0wfU_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4283, "start": 19.67, "end": 42.83, "text": "بسم الله الرحمن الرحيم ان شاء الله احنا هنكمل مع ال relations وبشكل خاص مع ال equivalence relations و علاقتها مع ال partition في المحاضرات الماضية شفنا إذا في عندنا equivalence relation أبسلون فصفوف التكافؤ اللي بتولدها هذه ال relation is a partition", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 16472, 13412, 16606, 21984, 1975, 5016, 8315, 8032, 1863, 24793, 1211, 20449, 2423, 2299, 46599, 8592, 28820, 16490, 33546, 20449, 2423, 9052, 655, 2299, 4032, 11203, 995, 38149, 11296, 20449, 2423, 24808, 8978, 9673, 5016, 46958, 2288, 9307, 9673, 46958, 10632, 13412, 5172, 8315, 11933, 15730, 8978, 43242, 8315, 9052, 655, 9721, 5551, 3555, 3794, 1211, 11536, 6156, 9381, 5172, 38688, 16712, 4117, 31845, 33604, 13672, 1829, 39894, 12610, 3215, 11296, 29538, 2423, 9721, 307, 257, 24808], "avg_logprob": -0.12526939552405786, "compression_ratio": 1.7971698113207548, "no_speech_prob": 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"probability": 0.9693603515625}, {"start": 40.05, "end": 40.43, "word": " هذه", "probability": 0.80908203125}, {"start": 40.43, "end": 40.55, "word": " ال", "probability": 0.93115234375}, {"start": 40.55, "end": 41.09, "word": " relation", "probability": 0.98974609375}, {"start": 41.09, "end": 42.25, "word": " is", "probability": 0.8994140625}, {"start": 42.25, "end": 42.45, "word": " a", "probability": 0.90576171875}, {"start": 42.45, "end": 42.83, "word": " partition", "probability": 0.98193359375}], "temperature": 1.0}, {"id": 2, "seek": 6563, "start": 46.17, "end": 65.63, "text": "هو partition مظبوط شفنا انه ولا صف فاضي و الصفين يا متطابقين يا تقاط عفاي واتحاد كل الصفوف بدينا كل ال X اليوم ان شاء الله هنشوف العكس لو بدأنا من ال partition هل ممكن اولد علاق التكافؤ الجواب برضه نعم", "tokens": [3224, 2407, 24808, 3714, 19913, 3555, 2407, 9566, 13412, 5172, 8315, 16472, 3224, 49429, 20328, 5172, 6156, 46958, 1829, 4032, 31767, 5172, 9957, 35186, 44650, 9566, 16758, 4587, 9957, 35186, 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partition هل ممكن نوصل ل equivalence relation؟ هنشوف أن الجواب نعم طبعا هنمشي واحدة واحدة أولا كيف من partition بعرف equivalence relation كيف نعرف أولا relation وكيف تكون equivalence relation فطبعا العنوان relations induced by partitions", "tokens": [5172, 28814, 15730, 47525, 10721, 8315, 9154, 9052, 655, 9721, 4032, 36520, 8315, 5296, 24808, 23758, 6225, 3555, 9640, 3660, 18871, 430, 24808, 6024, 48506, 18863, 4117, 3794, 8717, 44510, 10721, 9154, 2423, 24808, 8032, 1211, 3714, 43020, 8717, 2407, 36520, 5296, 9052, 655, 9721, 22807, 8032, 1863, 8592, 38688, 14739, 25724, 14407, 3555, 8717, 25957, 23032, 3555, 3615, 995, 8032, 1863, 2304, 8592, 1829, 36764, 24401, 3660, 36764, 24401, 3660, 5551, 12610, 995, 9122, 33911, 9154, 24808, 45030, 28480, 9052, 655, 9721, 9122, 33911, 8717, 3615, 28480, 5551, 12610, 995, 9721, 4032, 4117, 33911, 6055, 30544, 9052, 655, 9721, 6156, 9566, 3555, 3615, 995, 18863, 1863, 2407, 7649, 2299, 33991, 538, 644, 2451], "avg_logprob": -0.1725543543048527, 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{"id": 24, "seek": 62829, "start": 599.67, "end": 628.29, "text": "ممكن اكتب بهذا الشكل هذا اليوم اللي اترجمه هيك و لا لأ؟ لان انا بقول for some ايه؟ ايش احتمالات الـA؟ الـA يا E يا O يا R فور some ايش معناته؟ there exist و there exist ايش تقابل؟ R شوفتوا كيف الأمور متسايمة؟ تمام؟ تمام، نمشي كمان خطوة، بدي اوصل الـquadration، بدي اكتبها بشكل حتى تكون انتوا متعودين عليه، what is that? 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{"start": 800.18, "end": 800.66, "word": " الكلام", "probability": 0.9658203125}, {"start": 800.66, "end": 801.12, "word": " دايما", "probability": 0.8815104166666666}, {"start": 801.12, "end": 801.62, "word": " صحيح", "probability": 0.988037109375}, {"start": 801.62, "end": 801.74, "word": " و", "probability": 0.390869140625}, {"start": 801.74, "end": 801.82, "word": " لا", "probability": 0.98486328125}, {"start": 801.82, "end": 802.04, "word": " بس", "probability": 0.897216796875}, {"start": 802.04, "end": 802.26, "word": " كانت", "probability": 0.95947265625}, {"start": 802.26, "end": 802.34, "word": " من", "probability": 0.4306640625}, {"start": 802.34, "end": 802.58, "word": " الصدفة", "probability": 0.848876953125}, {"start": 802.58, "end": 803.14, "word": " المثالين", "probability": 0.9310302734375}, {"start": 803.14, "end": 803.88, "word": " الحقيقة", "probability": 0.8541666666666666}, {"start": 803.88, "end": 804.16, "word": " دايما", "probability": 0.947265625}, {"start": 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82178, "start": 809.32, "end": 821.78, "text": "EQ هذي اللي هي X على B، إيش معناه X على B؟ ال relation اللي بعرفها ال partition دايما equivalence relation فهنا النظرية let B be a partition of a non-empty set X", "tokens": [36, 48, 8032, 8848, 1829, 13672, 1829, 39896, 1783, 15844, 363, 12399, 11933, 1829, 8592, 20449, 8315, 3224, 1783, 15844, 363, 22807, 2423, 9721, 13672, 1829, 45030, 28480, 11296, 2423, 24808, 11778, 47302, 15042, 9052, 655, 9721, 6156, 3224, 8315, 28239, 19913, 2288, 10632, 718, 363, 312, 257, 24808, 295, 257, 2107, 12, 4543, 88, 992, 1783], "avg_logprob": -0.2707435267752615, "compression_ratio": 1.3584905660377358, "no_speech_prob": 0.0, "words": [{"start": 809.32, "end": 809.86, "word": "EQ", "probability": 0.588623046875}, {"start": 809.86, "end": 810.24, "word": " هذي", "probability": 0.4676920572916667}, {"start": 810.24, "end": 810.32, "word": " اللي", "probability": 0.60888671875}, {"start": 810.32, "end": 810.46, "word": " هي", "probability": 0.755859375}, {"start": 810.46, "end": 810.66, "word": " X", "probability": 0.69091796875}, {"start": 810.66, "end": 810.84, "word": " على", "probability": 0.576171875}, {"start": 810.84, "end": 811.48, "word": " B،", "probability": 0.5711669921875}, {"start": 811.48, "end": 811.64, "word": " إيش", "probability": 0.8164876302083334}, {"start": 811.64, "end": 811.86, "word": " معناه", "probability": 0.8155924479166666}, {"start": 811.86, "end": 812.02, "word": " X", "probability": 0.8994140625}, {"start": 812.02, "end": 812.16, "word": " على", "probability": 0.8779296875}, {"start": 812.16, "end": 812.7, "word": " B؟", "probability": 0.976806640625}, {"start": 812.7, "end": 812.9, "word": " ال", "probability": 0.828125}, {"start": 812.9, "end": 813.48, "word": " relation", "probability": 0.919921875}, {"start": 813.48, "end": 814.12, "word": " اللي", "probability": 0.96875}, {"start": 814.12, "end": 814.76, "word": " بعرفها", "probability": 0.8663736979166666}, {"start": 814.76, "end": 814.88, "word": " ال", "probability": 0.94384765625}, {"start": 814.88, "end": 815.34, "word": " partition", "probability": 0.63232421875}, {"start": 815.34, "end": 816.06, "word": " دايما", "probability": 0.77734375}, {"start": 816.06, "end": 816.66, "word": " equivalence", "probability": 0.7763671875}, {"start": 816.66, "end": 817.08, "word": " relation", "probability": 0.98779296875}, {"start": 817.08, "end": 817.76, "word": " فهنا", "probability": 0.8927408854166666}, {"start": 817.76, "end": 818.4, "word": " النظرية", "probability": 0.9625244140625}, {"start": 818.4, "end": 818.72, "word": " let", "probability": 0.76904296875}, {"start": 818.72, "end": 819.4, "word": " B", "probability": 0.54150390625}, {"start": 819.4, "end": 819.6, "word": " be", "probability": 0.73974609375}, {"start": 819.6, "end": 819.8, "word": " a", "probability": 0.93994140625}, {"start": 819.8, "end": 820.26, "word": " partition", "probability": 0.9736328125}, {"start": 820.26, "end": 820.58, "word": " of", "probability": 0.96923828125}, {"start": 820.58, "end": 820.72, "word": " a", "probability": 0.43212890625}, {"start": 820.72, "end": 820.86, "word": " non", "probability": 0.85595703125}, {"start": 820.86, "end": 821.24, "word": "-empty", "probability": 0.6189778645833334}, {"start": 821.24, "end": 821.48, "word": " set", "probability": 0.97705078125}, {"start": 821.48, "end": 821.78, "word": " X", "probability": 0.9736328125}], "temperature": 1.0}, {"id": 35, "seek": 84473, "start": 822.99, "end": 844.73, "text": "then the relation X على B is an equivalence relation on X طبعا يمكن الرمز شوية غريب و بس احنا شايفين بيساعدناش بيقولني the relation X على B هاد رمزة لإن معناته إيش؟ هي العلاقة المتولدة من ال partition B على المجموعة X على المجموعة X خليني أشوف البرهان مع بعض خليني أشوف البرهان مع بعض", "tokens": [19096, 264, 9721, 1783, 15844, 363, 307, 364, 9052, 655, 9721, 322, 1783, 23032, 3555, 3615, 995, 7251, 43020, 34892, 2304, 11622, 13412, 2407, 10632, 32771, 16572, 3555, 4032, 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"probability": 0.76220703125}, {"start": 838.17, "end": 838.63, "word": " على", "probability": 0.8916015625}, {"start": 838.63, "end": 839.13, "word": " المجموعة", "probability": 0.91103515625}, {"start": 839.13, "end": 839.45, "word": " X", "probability": 0.99365234375}, {"start": 839.45, "end": 839.87, "word": " على", "probability": 0.39697265625}, {"start": 839.87, "end": 840.41, "word": " المجموعة", "probability": 0.96083984375}, {"start": 840.41, "end": 840.71, "word": " X", "probability": 0.986328125}, {"start": 840.71, "end": 841.13, "word": " خليني", "probability": 0.7808837890625}, {"start": 841.13, "end": 841.35, "word": " أشوف", "probability": 0.84716796875}, {"start": 841.35, "end": 841.77, "word": " البرهان", "probability": 0.91455078125}, {"start": 841.77, "end": 841.95, "word": " مع", "probability": 0.99755859375}, {"start": 841.95, "end": 842.27, "word": " بعض", "probability": 0.9912109375}, {"start": 842.27, "end": 843.09, "word": " خليني", "probability": 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{"start": 994.88, "end": 995.24, "word": " Q", "probability": 0.81396484375}, {"start": 995.24, "end": 996.44, "word": " وبالتالي", "probability": 0.89501953125}, {"start": 996.44, "end": 996.94, "word": " and", "probability": 0.6015625}, {"start": 996.94, "end": 997.44, "word": " hence", "probability": 0.85498046875}, {"start": 997.44, "end": 998.48, "word": " ال", "probability": 0.49658203125}, {"start": 998.48, "end": 998.74, "word": " Q", "probability": 0.56298828125}, {"start": 998.74, "end": 999.24, "word": " is", "probability": 0.9443359375}, {"start": 999.24, "end": 1000.22, "word": " reflexive", "probability": 0.98388671875}, {"start": 1000.22, "end": 1001.3, "word": " فخاصية", "probability": 0.9766845703125}, {"start": 1001.3, "end": 1001.46, "word": " ال", "probability": 0.8515625}, {"start": 1001.46, "end": 1001.94, "word": " reflexive", "probability": 0.76953125}, {"start": 1001.94, "end": 1002.56, "word": " أثبتت", "probability": 0.9416015625}, {"start": 1002.56, "end": 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"probability": 0.96630859375}, {"start": 1368.82, "end": 1369.22, "word": " من", "probability": 0.90087890625}, {"start": 1369.22, "end": 1369.46, "word": " أي", "probability": 0.75537109375}, {"start": 1369.46, "end": 1369.82, "word": " نقطة", "probability": 0.9871419270833334}, {"start": 1369.82, "end": 1370.08, "word": " ابتدى", "probability": 0.69305419921875}, {"start": 1370.08, "end": 1370.4, "word": " بترجع", "probability": 0.8079427083333334}, {"start": 1370.4, "end": 1370.76, "word": " لمين", "probability": 0.876953125}, {"start": 1370.76, "end": 1371.28, "word": " لنفس", "probability": 0.9246419270833334}, {"start": 1371.28, "end": 1371.72, "word": " النقطة", "probability": 0.9845377604166666}], "temperature": 1.0}, {"id": 57, "seek": 139886, "start": 1375.34, "end": 1398.86, "text": "مش بالظبط يعني لأ بس هي بادة الصورة إذا بدأنا من partition كل partition بيولد equivalence relation كل equivalence relation بتولد partition هل ال partition هذا جديد و لا نفس اللي بدأت منه و نفس اللي بدأت منه فهي صورها فطبعا عشان أوصل لعدي نظرية بس عندي اللي هو نظرية تمهيدية لما بيقوللي إذا كان عندي partition", "tokens": [2304, 8592, 20666, 19913, 3555, 9566, 37495, 22653, 5296, 10721, 4724, 3794, 39896, 4724, 18513, 3660, 31767, 13063, 3660, 11933, 15730, 47525, 10721, 8315, 9154, 24808, 28242, 24808, 4724, 1829, 12610, 3215, 9052, 655, 9721, 28242, 9052, 655, 9721, 39894, 12610, 3215, 24808, 8032, 1211, 2423, 24808, 23758, 10874, 16254, 3215, 4032, 20193, 8717, 36178, 13672, 1829, 47525, 10721, 2655, 9154, 3224, 4032, 8717, 36178, 13672, 1829, 47525, 10721, 2655, 9154, 3224, 6156, 3224, 1829, 20328, 13063, 11296, 6156, 9566, 3555, 3615, 995, 6225, 8592, 7649, 34051, 36520, 5296, 3615, 16254, 8717, 19913, 2288, 10632, 4724, 3794, 18871, 16254, 13672, 1829, 31439, 8717, 19913, 2288, 10632, 46811, 3224, 25708, 10632, 5296, 15042, 4724, 1829, 39648, 20292, 11933, 15730, 25961, 18871, 16254, 24808], "avg_logprob": -0.18635671240527454, "compression_ratio": 1.9710743801652892, 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"word": " اللي", "probability": 0.6314697265625}, {"start": 1393.36, "end": 1393.46, "word": " هو", "probability": 0.92626953125}, {"start": 1393.46, "end": 1393.9, "word": " نظرية", "probability": 0.987060546875}, {"start": 1393.9, "end": 1394.46, "word": " تمهيدية", "probability": 0.9736328125}, {"start": 1394.46, "end": 1394.82, "word": " لما", "probability": 0.33135986328125}, {"start": 1394.82, "end": 1396.46, "word": " بيقوللي", "probability": 0.8123779296875}, {"start": 1396.46, "end": 1397.26, "word": " إذا", "probability": 0.951904296875}, {"start": 1397.26, "end": 1397.56, "word": " كان", "probability": 0.98291015625}, {"start": 1397.56, "end": 1398.08, "word": " عندي", "probability": 0.832275390625}, {"start": 1398.08, "end": 1398.86, "word": " partition", "probability": 0.96240234375}], "temperature": 1.0}, {"id": 58, "seek": 141374, "start": 1399.64, "end": 1413.74, "text": "وال partition ايش ماله؟ وولد علاقة تكافؤ، كل علاقة تكافؤ إيش بتعرف؟ صفوف تكافؤ، فبقول الصف اللي بتعرفه هذه العلاقة X أنا عندي .. هي عندي partition", "tokens": [2407, 6027, 24808, 1975, 1829, 8592, 3714, 6027, 3224, 22807, 4032, 12610, 3215, 11203, 995, 28671, 6055, 4117, 31845, 33604, 12399, 28242, 11203, 995, 28671, 6055, 4117, 31845, 33604, 11933, 1829, 8592, 39894, 3615, 28480, 22807, 20328, 5172, 38688, 6055, 4117, 31845, 33604, 12399, 6156, 3555, 39648, 31767, 5172, 13672, 1829, 39894, 3615, 28480, 3224, 29538, 18863, 15040, 28671, 1783, 41850, 18871, 16254, 4386, 39896, 18871, 16254, 24808], "avg_logprob": -0.21931612491607666, "compression_ratio": 1.6013071895424837, "no_speech_prob": 0.0, "words": [{"start": 1399.64, "end": 1400.0, "word": "وال", "probability": 0.7119140625}, {"start": 1400.0, "end": 1400.6, "word": " partition", "probability": 0.353759765625}, {"start": 1400.6, "end": 1401.14, "word": " ايش", "probability": 0.6180013020833334}, {"start": 1401.14, "end": 1401.6, "word": " ماله؟", "probability": 0.83154296875}, {"start": 1401.6, "end": 1402.16, "word": " 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2324.25, "end": 2324.43, "word": " أن", "probability": 0.6337890625}, {"start": 2324.43, "end": 2324.79, "word": " علاقة", "probability": 0.78173828125}, {"start": 2324.79, "end": 2325.91, "word": " التكافؤ،", "probability": 0.766796875}, {"start": 2325.91, "end": 2326.35, "word": " درسنا", "probability": 0.878662109375}, {"start": 2326.35, "end": 2326.73, "word": " علاقات", "probability": 0.9793701171875}, {"start": 2326.73, "end": 2327.31, "word": " التكافؤ", "probability": 0.9827880859375}, {"start": 2327.31, "end": 2327.81, "word": " وكيف", "probability": 0.8912760416666666}, {"start": 2327.81, "end": 2328.15, "word": " نحسب", "probability": 0.99609375}, {"start": 2328.15, "end": 2328.53, "word": " صفوف", "probability": 0.9928385416666666}, {"start": 2328.53, "end": 2329.31, "word": " التكافؤ،", "probability": 0.9125}, {"start": 2329.31, "end": 2329.43, "word": " بس", "probability": 0.99658203125}, {"start": 2329.43, "end": 2329.61, "word": " عشان", "probability": 0.9562174479166666}, {"start": 2329.61, "end": 2329.83, "word": " ليش", "probability": 0.4815673828125}, {"start": 2329.83, "end": 2330.17, "word": " نوضح", "probability": 0.939453125}, {"start": 2330.17, "end": 2330.69, "word": " النظرية", "probability": 0.9736328125}, {"start": 2330.69, "end": 2331.77, "word": " تمام،", "probability": 0.8610026041666666}, {"start": 2331.77, "end": 2332.05, "word": " بدأ", "probability": 0.6658935546875}, {"start": 2332.05, "end": 2332.37, "word": " جاود", "probability": 0.7819010416666666}, {"start": 2332.37, "end": 2333.35, "word": " مباشرة،", "probability": 0.96181640625}, {"start": 2333.35, "end": 2333.53, "word": " مين", "probability": 0.952880859375}, {"start": 2333.53, "end": 2333.79, "word": " صف", "probability": 0.9951171875}, {"start": 2333.79, "end": 2334.65, "word": " الواحد؟", "probability": 0.9739990234375}, {"start": 2334.65, "end": 2335.23, "word": " في", "probability": 0.3603515625}, {"start": 2335.23, "end": 2335.41, "word": " 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16247, 25513, 27884, 5296, 28814, 1863, 16095, 3714, 1211, 4587, 995, 20449, 45030, 11242, 9154, 16490, 2407, 33546, 31767, 5172, 38688, 6156, 28814, 1829, 8592, 12602, 7435, 3615, 8315, 22807], "avg_logprob": -0.20608836463813124, "compression_ratio": 2.0, "no_speech_prob": 1.0728836059570312e-06, "words": [{"start": 2337.2, "end": 2337.48, "word": "لأن", "probability": 0.874267578125}, {"start": 2337.48, "end": 2337.82, "word": " الواحد", "probability": 0.7928873697916666}, {"start": 2337.82, "end": 2338.02, "word": " بس", "probability": 0.954345703125}, {"start": 2338.02, "end": 2338.26, "word": " لإنه", "probability": 0.573883056640625}, {"start": 2338.26, "end": 2338.34, "word": " يقول", "probability": 0.621826171875}, {"start": 2338.34, "end": 2338.58, "word": " مافيش", "probability": 0.8701171875}, {"start": 2338.58, "end": 2338.66, "word": " هو", "probability": 0.66748046875}, {"start": 2338.66, "end": 2338.98, "word": " صف", "probability": 0.92822265625}, {"start": 2338.98, "end": 2339.28, "word": " فاضي", "probability": 0.9342447916666666}, {"start": 2339.28, "end": 2339.58, "word": " و", "probability": 0.440673828125}, {"start": 2339.58, "end": 2339.84, "word": " أول", "probability": 0.7529296875}, {"start": 2339.84, "end": 2340.22, "word": " عنصر", "probability": 0.9903971354166666}, {"start": 2340.22, "end": 2340.36, "word": " في", "probability": 0.9609375}, {"start": 2340.36, "end": 2340.78, "word": " صف", "probability": 0.9560546875}, {"start": 2340.78, "end": 2340.88, "word": " ال", "probability": 0.95849609375}, {"start": 2340.88, "end": 2341.06, "word": " X", "probability": 0.8046875}, {"start": 2341.06, "end": 2341.22, "word": " هو", "probability": 0.97509765625}, {"start": 2341.22, "end": 2341.32, "word": " ال", "probability": 0.9619140625}, {"start": 2341.32, "end": 2341.48, "word": " X", "probability": 0.97021484375}, {"start": 2341.48, "end": 2341.82, "word": " في", "probability": 0.599609375}, {"start": 2341.82, "end": 2342.16, "word": " غيره", "probability": 0.9581705729166666}, {"start": 2342.16, "end": 2342.58, "word": " مافيش", "probability": 0.9415690104166666}, {"start": 2342.58, "end": 2343.02, "word": " طيب", "probability": 0.7659505208333334}, {"start": 2343.02, "end": 2343.2, "word": " مين", "probability": 0.9638671875}, {"start": 2343.2, "end": 2343.46, "word": " صف", "probability": 0.95751953125}, {"start": 2343.46, "end": 2344.3, "word": " التنين؟", "probability": 0.7552490234375}, {"start": 2344.3, "end": 2345.64, "word": " التنين", "probability": 0.9239908854166666}, {"start": 2345.64, "end": 2345.74, "word": " و", "probability": 0.5048828125}, {"start": 2345.74, "end": 2346.24, "word": " التلاتة", "probability": 0.9298095703125}, {"start": 2346.24, "end": 2346.34, "word": " و", "probability": 0.93701171875}, {"start": 2346.34, "end": 2346.82, "word": " الأربعة", "probability": 0.953125}, {"start": 2346.82, "end": 2347.4, "word": " و", "probability": 0.509765625}, {"start": 2347.4, "end": 2347.56, "word": " هو", "probability": 0.98779296875}, {"start": 2347.56, "end": 2347.96, "word": " بيسوي", "probability": 0.781982421875}, {"start": 2347.96, "end": 2348.18, "word": " صف", "probability": 0.982421875}, {"start": 2348.18, "end": 2348.56, "word": " التلاتة", "probability": 0.978515625}, {"start": 2348.56, "end": 2348.64, "word": " و", "probability": 0.96923828125}, {"start": 2348.64, "end": 2348.82, "word": " بيسوي", "probability": 0.917724609375}, {"start": 2348.82, "end": 2349.02, "word": " صف", "probability": 0.93994140625}, {"start": 2349.02, "end": 2349.3, "word": " الأربعة", "probability": 0.9676106770833334}, {"start": 2349.3, "end": 2349.54, "word": " لإنهم", "probability": 0.82177734375}, {"start": 2349.54, "end": 2349.82, "word": " ملقا", "probability": 0.4481201171875}, {"start": 2349.82, "end": 2349.94, "word": " مع", "probability": 0.74755859375}, {"start": 2349.94, "end": 2350.24, "word": " بعض", "probability": 0.99365234375}, {"start": 2350.24, "end": 2350.34, "word": " من", "probability": 0.88037109375}, {"start": 2350.34, "end": 2350.64, "word": " خواص", "probability": 0.8245442708333334}, {"start": 2350.64, "end": 2351.06, "word": " الصفوف", "probability": 0.98291015625}, {"start": 2351.06, "end": 2351.58, "word": " فإيش", "probability": 0.9019775390625}, {"start": 2351.58, "end": 2352.22, "word": " رجعنا؟", "probability": 0.774072265625}], "temperature": 1.0}, {"id": 98, "seek": 236921, "start": 2356.49, "end": 2369.21, "text": "النظرية بتقول ابدأي من partition عارفي equivalence relation من ال partition احصي بتقع فوق ترجع لنقطة اللي بدأتي منها اي سؤال", "tokens": [6027, 1863, 19913, 2288, 10632, 39894, 39648, 1975, 44510, 10721, 1829, 9154, 24808, 6225, 9640, 41185, 9052, 655, 9721, 9154, 2423, 24808, 1975, 5016, 9381, 1829, 39894, 4587, 3615, 6156, 30543, 6055, 47341, 3615, 5296, 1863, 47432, 3660, 13672, 1829, 47525, 10721, 31371, 9154, 11296, 1975, 1829, 8608, 33604, 6027], "avg_logprob": -0.3851102847678989, "compression_ratio": 1.3642857142857143, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2356.49, "end": 2357.37, "word": "النظرية", "probability": 0.65782470703125}, {"start": 2357.37, "end": 2357.73, "word": " بتقول", "probability": 0.838134765625}, {"start": 2357.73, "end": 2358.79, "word": " ابدأي", "probability": 0.63543701171875}, {"start": 2358.79, "end": 2358.91, "word": " من", "probability": 0.96728515625}, {"start": 2358.91, "end": 2359.41, "word": " partition", "probability": 0.35400390625}, {"start": 2359.41, "end": 2360.63, "word": " عارفي", "probability": 0.8069661458333334}, {"start": 2360.63, "end": 2361.25, "word": " equivalence", "probability": 0.806640625}, {"start": 2361.25, "end": 2361.71, "word": " relation", "probability": 0.99072265625}, {"start": 2361.71, "end": 2361.85, "word": " من", "probability": 0.97265625}, {"start": 2361.85, "end": 2361.97, "word": " ال", "probability": 0.81494140625}, {"start": 2361.97, "end": 2362.47, "word": " partition", "probability": 0.74365234375}, {"start": 2362.47, "end": 2363.51, "word": " احصي", "probability": 0.7322998046875}, {"start": 2363.51, "end": 2363.95, "word": " بتقع", "probability": 0.5042317708333334}, {"start": 2363.95, "end": 2364.85, "word": " فوق", "probability": 0.5615234375}, {"start": 2364.85, "end": 2365.25, "word": " ترجع", "probability": 0.734619140625}, {"start": 2365.25, "end": 2365.63, "word": " لنقطة", "probability": 0.78717041015625}, {"start": 2365.63, "end": 2365.71, "word": " اللي", "probability": 0.79931640625}, {"start": 2365.71, "end": 2365.99, "word": " بدأتي", "probability": 0.8108723958333334}, {"start": 2365.99, "end": 2366.29, "word": " منها", "probability": 0.990478515625}, {"start": 2366.29, "end": 2368.87, "word": " اي", "probability": 0.6014404296875}, {"start": 2368.87, "end": 2369.21, "word": " سؤال", "probability": 0.9921875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2369.2480625, "duration_after_vad": 2258.8199999999924}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/zP0kNk_tTIE.srt b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/zP0kNk_tTIE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..54a5102e3335086f8de45649640e915baa06108b
--- /dev/null
+++ b/PL9fwy3NUQKwZ_fogpdAdMdObPzyKLyONA/zP0kNk_tTIE.srt
@@ -0,0 +1,2707 @@
+1
+00:00:20,100 --> 00:00:23,340
+بسم الله الرحمن الرحيم، الآن إن شاء الله هنبدأ في
+
+2
+00:00:23,340 --> 00:00:27,380
+دراسة الدوال أو functions، طبعًا هنعرف الـ function
+
+3
+00:00:27,380 --> 00:00:32,540
+كحالة خاصة من العلاقات، فدول مرتبطين في بعض، موضوع 
+
+4
+00:00:32,540 --> 00:00:37,280
+الدوال أو الإختيارات كما تعرف،  أي علاقة مع اللي
+
+5
+00:00:37,280 --> 00:00:42,120
+هي العلاقات أو الـ relations؟ فطبعًا مفهوم الـ
+
+6
+00:00:42,120 --> 00:00:46,500
+function كمفهوم رياضي مفهوم أساسي صعب إنه نلاقي
+
+7
+00:00:46,500 --> 00:00:49,860
+فيه فرع من فروع الرياضيات لا يستخدم مفهوم الدالة
+
+8
+00:00:49,860 --> 00:00:53,600
+أو الاقتران فمفهوم الـ function is one of the most
+
+9
+00:00:53,600 --> 00:00:57,220
+basic ideas in every branch of mathematics فهذا
+
+10
+00:00:57,220 --> 00:01:02,140
+المفاهيم الأساسية اللي بتقابلنا في أي تخصص أو في 
+
+11
+00:01:02,140 --> 00:01:07,640
+أي فرع من فروع الرياضيات التعريف نشوف كيف التعريف اه
+
+12
+00:01:07,640 --> 00:01:10,800
+طبعًا احنا متحدث عن function بين مجموعتين كما هو
+
+13
+00:01:10,800 --> 00:01:14,440
+معروف يعني ده مفهوم مرة علينا لكن بدنا نشوف احنا
+
+14
+00:01:14,440 --> 00:01:19,140
+كيف بدنا ندرسه بشكل عام و بشكل مجرد فاحنا في عندنا
+
+15
+00:01:19,140 --> 00:01:23,420
+مجموعتين let x and y be sets فدي هي نقطة البداية 
+
+16
+00:01:23,420 --> 00:01:27,400
+عشان نعرف اللي هو الـ function تمام ما هي الـ
+
+17
+00:01:27,400 --> 00:01:30,340
+function اللي هي الدالة أو الاقتران a function
+
+18
+00:01:30,340 --> 00:01:34,740
+from X to Y فالآن احنا هنا الترتيب مهم من إلى فهم
+
+19
+00:01:34,740 --> 00:01:39,180
+نتحدث عن function اللي يحمل مظلة بالرمز F من X لـ Y
+
+20
+00:01:39,180 --> 00:01:43,640
+ما هي الـ function بيقول عبارة عن الـ triple من تلت 
+
+21
+00:01:43,640 --> 00:01:46,480
+أشياء يعني الـ triple يعني الثلاثة مما تتكون الـ
+
+22
+00:01:46,480 --> 00:01:51,490
+function من تلت أشياء إيش هما؟ مجموعة أولى مجموعة
+
+23
+00:01:51,490 --> 00:01:55,870
+ثانية و relation و relation فهي triple اه الـ
+
+24
+00:01:55,870 --> 00:01:58,650
+relation اللي هتكون function طبعًا هنشوف الشروط
+
+25
+00:01:58,650 --> 00:02:02,450
+اللي عليها و مجموعتين مجموعة ابتداء و مجموعة
+
+26
+00:02:02,450 --> 00:02:07,110
+انتهاء X و Y where F is a relation from X to Y فالـ
+
+27
+00:02:07,110 --> 00:02:10,670
+F عبارة عن relation إيش معنى relation يعني الـ F هي
+
+28
+00:02:10,670 --> 00:02:15,010
+subset من X across الـ Y هذا ايه إيش هذا مبدئيًا 
+
+29
+00:02:16,690 --> 00:02:20,830
+الكلام ممكن يجي سؤال يتبادل للذهن هل الـ
+
+30
+00:02:20,830 --> 00:02:24,130
+correlation function طبعًا لا فهي الـ relation عليها
+
+31
+00:02:24,130 --> 00:02:28,750
+شروط إضافية عليها شروط إضافية أول شرط بدنا الـ
+
+32
+00:02:28,750 --> 00:02:32,970
+domain لهذه الـ relation يكون بيغطي كل المجموعة
+
+33
+00:02:32,970 --> 00:02:37,070
+الأولى X بدنا الـ domain يغطي كل المجموعة الأولى
+
+34
+00:02:37,070 --> 00:02:40,670
+طبعًا الـ relation كنا عرفناها هي أي subset من الـ X 
+
+35
+00:02:40,670 --> 00:02:44,590
+cross الـ Y أو الـ A cross الـ B لكن مافيش شرط أنه 
+
+36
+00:02:44,590 --> 00:02:46,570
+مين يغطي المهم يكون subset الـ relation كلها
+
+37
+00:02:46,570 --> 00:02:49,810
+تعريفها بسيط جدًا فأي subset من الكارتيسة هي
+
+38
+00:02:49,810 --> 00:02:52,310
+relation لكن الآن الـ functions هي الـ relation
+
+39
+00:02:52,310 --> 00:02:56,490
+عليها شروط أول شرط بدنا الـ domain يغطي كل المجموعة
+
+40
+00:02:56,490 --> 00:03:03,000
+الأولى الشرط الثاني المهم كما هو معروف بدنا العنصر
+
+41
+00:03:03,000 --> 00:03:07,100
+ما يكونوش أكثر من صورة بدنا كل عنصر كل صورة واحدة 
+
+42
+00:03:07,100 --> 00:03:12,640
+أنا باخد عنصر small x من الـ capital X بدي أوديله 
+
+43
+00:03:12,640 --> 00:03:16,940
+small y في الـ Y ما ينفعش زي ما بقول يطلع سهمين من
+
+44
+00:03:16,940 --> 00:03:21,520
+هذه الـ X لازم بس سهم واحد بس سهم واحد كيف بنعبر عن
+
+45
+00:03:21,520 --> 00:03:25,380
+هذا الشرط؟ بنقول لو كان أنا عندي X و Y في الـ F ما 
+
+46
+00:03:25,380 --> 00:03:28,180
+هي الـ F ع صورة relation فهي أزواج مرتبة وعندي 
+
+47
+00:03:28,180 --> 00:03:31,020
+كمان X و Z في الـ F يعني الـ X إلها صورتين Z 
+
+48
+00:03:31,020 --> 00:03:34,680
+ما ينفعش أكون الـ Z و X و الـ Y و الـ Z مختلفين لازم 
+
+49
+00:03:34,680 --> 00:03:38,540
+Y تساوي Z فلو كانت الـ X بتروح لصورتين لازم صورتين 
+
+50
+00:03:38,540 --> 00:03:42,060
+يتطابقوا ما ينفعش يكون صورتين مختلفتين فهذا هو 
+
+51
+00:03:42,060 --> 00:03:46,000
+التعريف واضح؟ طبعًا تعريف قديم ومر عليكم كثير لكن
+
+52
+00:03:46,000 --> 00:03:48,960
+هذه هي صياغته بشكل عام فاحنا بدنا كل function هي 
+
+53
+00:03:48,960 --> 00:03:53,180
+relation عليها شرطين الشرط الأول أن يكون الـ domain
+
+54
+00:03:53,180 --> 00:03:56,300
+بيغطي كل المجموعة الأولى الشرط الثاني لكل عنصر 
+
+55
+00:03:56,300 --> 00:04:01,840
+صورة واحدة بنعبر عنهم بهذه الطريقة خليني نبدأ نشوف
+
+56
+00:04:01,840 --> 00:04:06,780
+بعض الأمثلة أو كالعادة نبدأ بالأمثلة البسيطة نأخذ
+
+57
+00:04:06,780 --> 00:04:10,800
+مجموعة صغيرة X تتكون من عنصرين الواحد والسالب واحد 
+
+58
+00:04:10,800 --> 00:04:16,000
+و الـ Y تتكون من عنصر واحد وهو الـ zero وعرفنا الـ 
+
+59
+00:04:16,000 --> 00:04:18,960
+relation طبعًا بدي أنا relation من X cross الـ Y 
+
+60
+00:04:18,960 --> 00:04:23,680
+طبعًا X cross الـ Y إيش بتساوي طبعًا هيكون فيها
+
+61
+00:04:23,680 --> 00:04:27,160
+الاحتمالات إنه الواحد مع الـ zero والسالب واحد مع
+
+62
+00:04:27,160 --> 00:04:31,100
+الـ zero أخذتها كلها أخذت x cross y كلها كـ relation
+
+63
+00:04:31,100 --> 00:04:33,320
+أي subset من الكارتية الـ subproduct هي relation 
+
+64
+00:04:33,320 --> 00:04:36,980
+فالسؤال هل هذه الـ relation f المعرفة في هذه الصورة 
+
+65
+00:04:36,980 --> 00:04:40,720
+هي function؟ طبعًا دائمًا احنا بدنا نستخدمه بدنا 
+
+66
+00:04:40,720 --> 00:04:43,700
+نكون .. إذا function ليش هي function؟ وإذا مش
+
+67
+00:04:43,700 --> 00:04:45,880
+function ليش مش function؟ إيش اختل من الشروط؟
+
+68
+00:04:45,880 --> 00:04:48,380
+بخلّهاش function؟ وهل الشروط كلها تتحقق؟ هتخلّها 
+
+69
+00:04:48,380 --> 00:04:51,420
+تكون function؟ آه فطبعًا بدنا نشوف طبعًا هذه عبارة
+
+70
+00:04:51,420 --> 00:04:54,620
+عن إيش؟ زي ما احنا شايفين هي relation طب إيش
+
+71
+00:04:54,620 --> 00:04:57,740
+الشروط؟ بدنا الـ domain يكون كل الـ X فده المثال
+
+72
+00:04:57,740 --> 00:05:02,750
+الأول في المثال الأول solution فهل الـ domain بيساوي
+
+73
+00:05:02,750 --> 00:05:08,710
+كل الـ X؟ نعم فطبعًا domain الـ F ايه كيف نجيب domain 
+
+74
+00:05:08,710 --> 00:05:11,650
+لأي relation؟ بناخذ الإحداثيات الأولى فالواحد
+
+75
+00:05:11,650 --> 00:05:15,790
+والسالب واحد وهو يساوي مين؟ الـ capital X فده صح
+
+76
+00:05:15,790 --> 00:05:21,570
+الشرط الأول فأول شرط تحقق طيب اثنين .. اثنين هل في
+
+77
+00:05:21,570 --> 00:05:26,450
+عنصر له أكثر من صورة؟ لأ الواحد صورته صفر والسالب
+
+78
+00:05:26,450 --> 00:05:30,490
+واحد صورته صفر طب لو طلعنا كيف نص .. نص اللي .. 
+
+79
+00:05:30,490 --> 00:05:34,910
+اللي هو الشرط في التعريف جالي شوف ما شرطية إذا كان
+
+80
+00:05:34,910 --> 00:05:37,790
+في عنصر له صورتين لازم الصورتين يتساوى طب في عنصر 
+
+81
+00:05:37,790 --> 00:05:41,530
+له صورتين؟ لأ إذا الشرط تحقق ولا لأ؟ ليش؟ لأنه ما 
+
+82
+00:05:41,530 --> 00:05:45,050
+زال ما فيش شرط إذا false إيش implies anything آه
+
+83
+00:05:45,050 --> 00:05:48,120
+فهنا بنعد الكلام آه كيف نعبر عنه؟ بنعبر عنه بأي
+
+84
+00:05:48,120 --> 00:05:52,080
+طريقة ممكن لكن هو أي كل كلام ما زال اللي هو بي
+
+85
+00:05:52,080 --> 00:05:55,440
+then q إذا بيه false فإيش؟ الجملة الشرطية دائمًا 
+
+86
+00:05:55,440 --> 00:05:59,080
+صحيحة دائمًا true فكيف نعبر عنه؟ إحنا مش لاقيين
+
+87
+00:05:59,080 --> 00:06:02,180
+إنه نقوله صورتين وندور إنه صورتين مطابقتين ولا لأ
+
+88
+00:06:02,180 --> 00:06:06,680
+فنقوله إنه فش لأ إن لا اللي هو اثنين فش لأ only
+
+89
+00:06:06,680 --> 00:06:11,360
+إيش في صورة الواحد؟ Zero تنتمي للأفر فالواحد
+
+90
+00:06:11,360 --> 00:06:16,230
+ما لهوش إلا صورة واحدي ده الصفر وأيضًا and سالب واحد
+
+91
+00:06:16,230 --> 00:06:20,010
+ايه صورته الـ F بس فإذا أنا أدي فعل انياش a
+
+92
+00:06:20,010 --> 00:06:26,730
+function Thus F is a function طبعًا a function from
+
+93
+00:06:26,730 --> 00:06:27,350
+X to Y
+
+94
+00:06:30,210 --> 00:06:34,750
+واضح؟ لأ فهذه function بتنطبق عليها شروط لأن الـ
+
+95
+00:06:34,750 --> 00:06:37,830
+domain غطى كل المجموعة الأولى وكل عنصر في الـ
+
+96
+00:06:37,830 --> 00:06:40,990
+domain له صورة واحدة .. له صورة واحدة .. طبعًا جالي
+
+97
+00:06:40,990 --> 00:06:42,890
+العنصرين راحوا لنفس الصورة ما لاش دعوة .. ما لاش
+
+98
+00:06:42,890 --> 00:06:48,550
+شروط .. هذا إشي موضوع آخر .. موضوع آخر خليني أشوف
+
+99
+00:06:48,550 --> 00:06:49,390
+كمان مثال
+
+100
+00:06:54,600 --> 00:07:00,400
+نكبر المجموعة شوية نأخذ مجموعة X من 3 عناصر ونأخذ 
+
+101
+00:07:00,400 --> 00:07:06,460
+Y من 4 عناصر ونأخذ الـ relation طبعًا subset 1 5 و
+
+102
+00:07:06,460 --> 00:07:10,860
+نأخذ الـ 2 مع الـ 20 هل هذه الدالة هل هذه العلاقة
+
+103
+00:07:10,860 --> 00:07:14,800
+function؟ لأ ليش؟ لأن الـ domain ما غطّاش الكل فهذا 
+
+104
+00:07:14,800 --> 00:07:19,780
+المثال رقم 2 اختل شرط من الشروط solution فعنا 
+
+105
+00:07:19,780 --> 00:07:27,460
+domain الـ F بيساوي إيش؟ بس الواحد والاثنين الواحد
+
+106
+00:07:27,460 --> 00:07:30,200
+والاثنين لا يساوي X فإذا أنا دي ليست أ function
+
+107
+00:07:34,120 --> 00:07:36,840
+الـ domain دائمًا من الـ X واحنا عرفنا الـ domain 
+
+108
+00:07:36,840 --> 00:07:40,600
+لأي relation وكل function هي relation وكل
+
+109
+00:07:40,600 --> 00:07:43,560
+function هي relation كيف نعمل الـ domain؟ نأخذ
+
+110
+00:07:43,560 --> 00:07:48,500
+الإحداثي الأول من كل زوج مرتب، صح؟ نتذكر، آه فإذن F
+
+111
+00:07:48,500 --> 00:07:51,540
+is not a function
+
+112
+00:07:55,970 --> 00:08:00,010
+فاحنا عرفنا الـ domain لأي relation فكأي relation
+
+113
+00:08:00,010 --> 00:08:02,810
+بقدر أحصل بالـ domain كيف من كل زوج مرتب بأخذ
+
+114
+00:08:02,810 --> 00:08:08,010
+الأحداث الأول وقلنا المادة كيف نأخذ الأحداث الثاني
+
+115
+00:08:08,010 --> 00:08:11,690
+فاحنا حصلناها فاحنا عادة بدنا يشعر فهذا مش function
+
+116
+00:08:11,690 --> 00:08:19,100
+خليني أشوف كمان مثال المثال هنأخذ نفس المجموعتين
+
+117
+00:08:19,100 --> 00:08:24,060
+نفس المجموعتين لكن هنغير الـ relation اه هنغير الـ
+
+118
+00:08:24,060 --> 00:08:28,580
+relation واحد خمسة واثنين عشرين زي ما احنا طب ضفنا 
+
+119
+00:08:28,580 --> 00:08:33,860
+كمان زوجين ثلاثة خمسة عشر وثلاثة عشرة مش function
+
+120
+00:08:33,860 --> 00:08:37,260
+لأن الثلاثة صار لها صورتين غطينا الـ domain لكن في 
+
+121
+00:08:37,260 --> 00:08:41,060
+عندنا عنصر قاله صورتين وهذا بيخالف شرط الـ function 
+
+122
+00:08:41,060 --> 00:08:47,440
+فإذا هذا solution F is not a function not a
+
+123
+00:08:47,440 --> 00:08:51,740
+function ليش؟ لأن في عندي الثلاثة اللي هي صورتين 
+
+124
+00:08:51,740 --> 00:08:56,660
+فعندي الثلاثة بتروح للخمسة عشر والثلاثة بتروح للعشرة
+
+125
+00:08:56,660 --> 00:09:03,160
+لكوا لكن but العشرة لا تساوي خمسة عشر فصورتين
+
+126
+00:09:03,160 --> 00:09:08,360
+مختلفتين فهذا بشكل بسيط إيش التعريف فإذا اختل أي 
+
+127
+00:09:08,360 --> 00:09:12,220
+شرط من الشرطين الـ domain ما غطّاش المجموعة الأولى أو 
+
+128
+00:09:12,220 --> 00:09:15,180
+صار في عندي عنصر من عناصر مش كل عناصر لو بس عنصر
+
+129
+00:09:15,180 --> 00:09:18,100
+واحد له أكثر من صورة بتبطل الـ function لكن هي الـ
+
+130
+00:09:18,100 --> 00:09:24,640
+relation تمام أي سؤال تمام آه فإذا هذه هي نقطة
+
+131
+00:09:24,640 --> 00:09:28,760
+الانطلاق فكل الـ function هي relation عليها شرطين
+
+132
+00:09:28,760 --> 00:09:31,960
+الـ domain بيساوي كل المجموعة الأولى ولكل عنصر 
+
+133
+00:09:31,960 --> 00:09:35,560
+صورة واحدة هذا هو النقطة تمام يمكن احنا مش متعودين
+
+134
+00:09:35,560 --> 00:09:37,900
+نكتب الـ function على صورة relation متعودين نقول y
+
+135
+00:09:37,900 --> 00:09:41,140
+تساوي f of x وهكذا الآن بدنا نتحدث عن هذا الكلام
+
+136
+00:09:41,140 --> 00:09:46,240
+كـ notation كيف الصورة أو الرموز المشهورة في 
+
+137
+00:09:46,240 --> 00:09:49,590
+التعامل مع الـ function فطبعًا احنا ذكرنا بالتعريف إن
+
+138
+00:09:49,590 --> 00:09:53,110
+الـ function هي تتكون من تلت أشياء triple في علاقة
+
+139
+00:09:53,110 --> 00:09:56,570
+F في مجموعة أولى اللي بتحتوي الـ domain وفي مجموعة 
+
+140
+00:09:56,570 --> 00:10:00,530
+ثانية بتحتوي مين المدى اه فبيقول لي if Fxy is a
+
+141
+00:10:00,530 --> 00:10:04,030
+function هاي ثلاث أشياء from X to Y then we write
+
+142
+00:10:04,030 --> 00:10:07,590
+إيش الطريقة الأشهر في الكتاب الأشهر F نخطين فوق
+
+143
+00:10:07,590 --> 00:10:11,090
+بعض من X ل Y وهي السهل فهي الطريقة الأشهر فبعد ما
+
+144
+00:10:11,090 --> 00:10:14,190
+نكتب هذه الصورة نقول هذه a function نكتب هذا الشكل
+
+145
+00:10:14,190 --> 00:10:18,630
+هذا هو الرمز المشهور الرمز الشائع الانتشار فهذه هي 
+
+146
+00:10:18,630 --> 00:10:24,090
+الطريقة ملاحظة الأولى، الملاحظة الثانية احنا بنقول
+
+147
+00:10:24,090 --> 00:10:28,370
+الـ F هي إيش relation فبنقول x y تنتمي للـ F لكن مش 
+
+148
+00:10:28,370 --> 00:10:31,910
+هذه الطريقة الأشهر إيش بنكتب y تساوي f of x؟ y
+
+149
+00:10:31,910 --> 00:10:35,850
+تساوي f of x فبقول لي إذا كانت x و y في الـ F والـ F 
+
+150
+00:10:35,850 --> 00:10:40,870
+function بنكتب y تساوي f of x أه هنا يمكن في نقطة
+
+151
+00:10:40,870 --> 00:10:44,550
+تكون جيدة ننتبه لها طب لو كانت الـ F هذه relation
+
+152
+00:10:44,550 --> 00:10:48,490
+ليش ما كتبناش مثلا إن في عندي R relation والـ X والـ
+
+153
+00:10:48,490 --> 00:10:52,260
+Y في الـ R؟ ليش ما كتبناش y تساوي R of X؟ لأ لأ
+
+154
+00:10:52,260 --> 00:10:55,380
+احنا جينا في الـ function استخدمنا هذا الرمز اه
+
+155
+00:10:55,380 --> 00:10:58,280
+عندي function إذا الـ F function في هذا الرمز صحيح
+
+156
+00:10:58,280 --> 00:11:03,360
+طب لو كانت هذه relation مش function X Y تنتمي للـ R
+
+157
+00:11:03,360 --> 00:11:10,600
+ليش ما بكتبش أنه Y تساوي R of X؟ في حد عنده تفسير؟
+
+158
+00:11:10,600 --> 00:11:10,880
+اه
+
+159
+00:11:14,460 --> 00:11:19,020
+لأ لأنه هنا أنا أخذت عنصر X ممكن يكونوا أكثر من 
+
+160
+00:11:19,020 --> 00:11:22,360
+صورة فبعرفش مين الصورة الوحيدة لكن في الـ
+
+161
+00:11:22,360 --> 00:11:24,220
+function عشان الصورة الوحيدة بقدر أعرف بعد الصورة
+
+162
+00:11:24,220 --> 00:11:29,680
+لأن هو يعني هاي المثال وين المثال تبعته هي عندي 
+
+163
+00:11:29,680 --> 00:11:34,180
+relation بده يكتب هل الخمستاش هي F في ثلاثة ولا
+
+164
+00:11:34,180 --> 00:11:37,300
+العصر F في ثلاثة ففي صعوبة لكن لما تكون function
+
+165
+00:11:37,300 --> 00:11:39,700
+لأني عارف أن الصورة واحدة فأكيد بـ y تساوي F في X
+
+166
+00:11:39,700 --> 00:11:43,540
+أه فهنا أن هذا رمز خاص بالدوال بينفعش لأي relation
+
+167
+00:11:43,540 --> 00:11:48,180
+اللي بينفعش لأي relation فإن هدول الرموز المشهور
+
+168
+00:11:48,180 --> 00:11:51,960
+اللي متعرفين عليها هنستخدمها بدأنا احنا من الـ
+
+169
+00:11:51,960 --> 00:11:55,240
+relation والآن اتعرفنا على الرموز العادية اللي 
+
+170
+00:11:55,240 --> 00:12:00,580
+ممكن استخدامها تمام ننتقل لنقطة أخرى في عندنا
+
+171
+00:12:00,580 --> 00:12:07,380
+مصطلحات مهمة تستخدم الـ image اللي هو الصورة والـ
+
+172
+00:12:07,380 --> 00:12:12,740
+pre image والـ range وهنا بدنا ننبه مصطلح الـ
+
+173
+00:12:12,740 --> 00:12:15,000
+range هنا يستخدم غير ما استخدمناه في الـ calculus
+
+174
+00:12:15,000 --> 00:12:18,360
+في هذا الكتاب بيعني بالـ range المجال المقابل الـ
+
+175
+00:12:18,360 --> 00:12:22,500
+codomain الـ codomain هنشوف إيش التعريفة طبعا
+
+176
+00:12:22,500 --> 00:12:25,900
+الـ image بيقول هنا لو في عندنا function كتبناها
+
+177
+00:12:25,900 --> 00:12:31,140
+بالطريقة المشهورة الطريقة الجديدة if y تساوي f of x
+
+178
+00:12:31,140 --> 00:12:34,540
+إيش بنقول؟ احنا هنا مجرد مصطلحات تسميات فاحنا
+
+179
+00:12:34,540 --> 00:12:38,740
+بنقول على الـ y صورة الـ x تحت الـ F، مظبوط؟ طب الـ X
+
+180
+00:12:38,740 --> 00:12:42,180
+إيش بنقول عنها؟ بقول عنها الـ preimage للـ Y الـ
+
+181
+00:12:42,180 --> 00:12:44,500
+preimage للـ Y، هي إيش؟ يعني .. بنقول الصورة
+
+182
+00:12:44,500 --> 00:12:47,140
+المسبقة الـ preimage يعني الصورة المسبقة أو الأصل،
+
+183
+00:12:47,140 --> 00:12:50,480
+يعني بنقول هذه أنا عندي Y، هذه الـ Y هي F of X، طب
+
+184
+00:12:50,480 --> 00:12:53,120
+الـ Y إيش علاقتها بالـ X؟ هي .. إيش؟ الـ Y هي صورة الـ
+
+185
+00:12:53,120 --> 00:12:55,880
+X، طب إيش علاقة الـ X بالنسبة للـ Y؟ هي الـ preimage
+
+186
+00:12:55,880 --> 00:12:59,510
+للـ Y، هيك بيسمون، كمصطلح، كمصطلح أه فهيبقى نقول
+
+187
+00:12:59,510 --> 00:13:03,970
+عليهاش أن الـ Y is the image of X under F and X is
+
+188
+00:13:03,970 --> 00:13:09,050
+the pre image of Y under F ف أنا في عندي نقطتين هي
+
+189
+00:13:09,050 --> 00:13:15,440
+في عندنا نقطة X وهي راحت بطريقة الـ F لمين للـ Y
+
+190
+00:13:15,440 --> 00:13:19,440
+فطبعا المصطلح الأشهر Y صورة الـ X تحت الـ F طب الـ X
+
+191
+00:13:19,440 --> 00:13:22,460
+هي الـ pre image يعني من وين جاية وين المصدر وين 
+
+192
+00:13:22,460 --> 00:13:26,040
+الأصل قبل ما تصير صورة مين كانت وين كانت جاية من X
+
+193
+00:13:26,040 --> 00:13:31,480
+بيدّي المعنى فدول المصطلحين يستخدموا الـ range ما هو
+
+194
+00:13:31,480 --> 00:13:34,960
+الـ range هو المجال المقابل بالعربي المجال المقابل
+
+195
+00:13:34,960 --> 00:13:38,280
+بقول إذا كانت الـ F دالة من X ل Y is a function
+
+196
+00:13:38,280 --> 00:13:42,200
+طبعا هذا بنحسبش هذا معطى على طول دالة من X ل Y فالـ
+
+197
+00:13:42,200 --> 00:13:45,560
+Y بيسميها إيش المجال المقابل فالـ X هي دائما المجال
+
+198
+00:13:45,560 --> 00:13:48,320
+هي الـ domain والـ Y بيسموها المجال المقابل أو الـ
+
+199
+00:13:48,320 --> 00:13:51,120
+range الـ codomain أو range هنا مصطلح في الكتابة
+
+200
+00:13:51,160 --> 00:13:54,700
+هنستخدم الصلحة range of F طبعا هنا في شوية اللي هو 
+
+201
+00:13:54,700 --> 00:13:58,200
+تداخل في بعض الناس بيستخدموا range بمعنى المدى لكن
+
+202
+00:13:58,200 --> 00:14:01,960
+في الكتاب بيستخدموا المجال المقابل هنتظم بهذا
+
+203
+00:14:01,960 --> 00:14:09,910
+التعريف أو هذا الاستخدام تمام أه فطبعا دائما الـ
+
+204
+00:14:09,910 --> 00:14:12,470
+Codomain اللي هو الـ Range هنا المجال المقابل
+
+205
+00:14:12,470 --> 00:14:16,630
+بالعربي المتفقين طبعا المجال المقابل دوره ليس
+
+206
+00:14:16,630 --> 00:14:19,950
+إلا وعاء يحتوي الصور طبعا هذا الوعاء ممكن يكون
+
+207
+00:14:19,950 --> 00:14:23,310
+على الجد بس بيحتوي الصور بالظبط ممكن يكون أكبر
+
+208
+00:14:23,310 --> 00:14:27,070
+فبدنا أي وعاء يسع الصور يسعهم بالظبط أو أكثر
+
+209
+00:14:27,070 --> 00:14:29,630
+بيقدي الغرض ف أنا طبعا ملاحظة العالم يقول لي 
+
+210
+00:14:29,630 --> 00:14:33,120
+دائما احنا إيش قلنا الـ image هو المدى الـ image الـ
+
+211
+00:14:33,120 --> 00:14:35,380
+image الـ function زي الـ relation طبعا هو المدى
+
+212
+00:14:35,380 --> 00:14:38,680
+فهو بيقول لي كل Y في الـ Y بحيث تكون لها علاقة مع
+
+213
+00:14:38,680 --> 00:14:42,320
+عنصر ما يعني تكون صورة .. صورة ما أشمله دائما
+
+214
+00:14:42,320 --> 00:14:46,060
+المدى subset من المجال المقابل subset من المجال
+
+215
+00:14:46,060 --> 00:14:49,960
+المقابل أو من الـ range طبعا in general بشكل عام
+
+216
+00:14:49,960 --> 00:14:53,140
+دائما الـ range ممكن يكون كبير المجال المقابل أكبر
+
+217
+00:14:53,140 --> 00:14:56,040
+لكن هو احنا بيقول subset أو يساوي ممكن يكون على
+
+218
+00:14:56,040 --> 00:15:00,080
+الجد بيساوي أو أكبر أو أكبر فدي ملاحظة عامة بس أرجو
+
+219
+00:15:00,080 --> 00:15:02,240
+الانتباه لكلمة range لأنه متعودين عليها من الـ
+
+220
+00:15:02,240 --> 00:15:07,820
+calculus اللي هي إيش بتتردد بمختلفة خليني أنا أكد
+
+221
+00:15:07,820 --> 00:15:10,840
+على هذه المعلومة ناخد برضه دالة من الـ calculus
+
+222
+00:15:10,840 --> 00:15:14,460
+مشهورة لـ greatest integer ليه أصغر أو يساوي X الـ
+
+223
+00:15:14,460 --> 00:15:16,600
+greatest اللي بيسموه floor function الدالة إيش
+
+224
+00:15:16,600 --> 00:15:19,160
+اللي بتاخد الـ integer الـ A أول integer قبلك من تحت
+
+225
+00:15:19,160 --> 00:15:22,880
+أي يكون أصغر من مين من الـ X فني وجيت خلينا نحسب
+
+226
+00:15:22,880 --> 00:15:27,680
+الـ range والـ image عشان نأكد على المعلومة فدي مثال
+
+227
+00:15:27,680 --> 00:15:32,320
+solution أه طبعا بالنسبة للـ range بدوش حساب بنحسبش
+
+228
+00:15:32,320 --> 00:15:36,820
+من المعطيات من المثال مباشرة فالـ range إيش بيساوي
+
+229
+00:15:36,820 --> 00:15:43,140
+A فـ range الـ F هو الـ A دالة من X ل Y من الـ range
+
+230
+00:15:43,140 --> 00:15:46,680
+تبقى Hawaii على طول معطى بنحسبش ف دائما المجال
+
+231
+00:15:46,680 --> 00:15:50,640
+المقابل معطى بيكون ما بينحسبش طيب مين الـ MH هذا بده
+
+232
+00:15:50,640 --> 00:15:56,370
+حساب اللي هو المدى بيساوي Z لأن هذه الدالة تديناش
+
+233
+00:15:56,370 --> 00:15:59,950
+الأعداد الصحيحة وبتغطي كل الأعداد الصحيحة بتغطي كل
+
+234
+00:15:59,950 --> 00:16:05,530
+الأعداد الصحيحة فأرجو أنه ننتبه لهذه المصطلحات
+
+235
+00:16:05,530 --> 00:16:11,790
+والتعريفات تمام واضح فهذه بداية أتوقع أمور كلها
+
+236
+00:16:11,790 --> 00:16:16,450
+مرت عليكم لكن احنا بنأكد عليها وبنحاول ممكن يكون 
+
+237
+00:16:16,450 --> 00:16:19,670
+في بعض الإضافات البسيطة فضل
+
+238
+00:16:22,040 --> 00:16:24,580
+الآن مش هذا بده حساب، مين الانمش؟ مين الصور
+
+239
+00:16:24,580 --> 00:16:27,420
+الممكنة؟ طبعا الدالة الشمال هي greatest integer،
+
+240
+00:16:27,420 --> 00:16:31,160
+إيش تاخد إيش؟ عدد صحيح، هي بتاخد أول عدد صحيح
+
+241
+00:16:31,160 --> 00:16:34,560
+بيقابلك من اليسار، اللي بيسموه إيش؟ أكبر عدد صحيح
+
+242
+00:16:34,560 --> 00:16:38,160
+أصغر أو يساوي الـ X، أه، فيعني احنا بيكون هنا إيش؟
+
+243
+00:16:38,160 --> 00:16:41,640
+ماشيين على خط الأعداد، أذكركوا في الدالة بساه هي 
+
+244
+00:16:41,640 --> 00:16:45,240
+الصفر وهي الواحد هي السالبة واحد فبتاخد الـ X إذا الـ
+
+245
+00:16:45,240 --> 00:16:50,180
+X واقع هان وين بتروح؟ صفر الـ X واقع هان الواحد وها
+
+246
+00:16:50,180 --> 00:16:53,640
+كذا تاخد أول عدد صحيح بيقابلك من اليسار أول عدد
+
+247
+00:16:53,640 --> 00:16:55,880
+صحيح بيقابلك من اليسار طب العدد الصحيح بيطلع زي ما
+
+248
+00:16:55,880 --> 00:16:58,780
+هو بيطلع زي ما هو تمام فدي هي الدالة
+
+249
+00:17:02,780 --> 00:17:07,640
+في هذه نظرية، نظرية 3-6 بدي أتأكد على معلومة أو
+
+250
+00:17:07,640 --> 00:17:12,800
+الحقيقة أن المجال المقابل ليس إلا وعاء يحتوي
+
+251
+00:17:12,800 --> 00:17:17,500
+الصور، بدنا وعاء يكون كبير بشكل كافي يحتوي الصور،
+
+252
+00:17:17,500 --> 00:17:21,540
+فإيه بتقول each set containing the image can be
+
+253
+00:17:21,540 --> 00:17:24,920
+arranged يعني احنا إيش دور المجال المقابل؟ بدنا
+
+254
+00:17:24,920 --> 00:17:28,660
+مجموعة تقدر تحتوي كل إيش المدى، تكون جد المدى 
+
+255
+00:17:28,660 --> 00:17:32,060
+بالظبط يؤدي، لو كبرتها زيادة، فإيش عندي مشكلة أه
+
+256
+00:17:32,060 --> 00:17:36,060
+فهي النظرية بتقول لي أنا لو استبدلت المجال المقابل
+
+257
+00:17:36,060 --> 00:17:40,920
+بأي مجموعة كبيرة تحتوي المهم إيش الشرط تحتوي الاش
+
+258
+00:17:40,920 --> 00:17:44,860
+المدى تحتوي المدى فبتتمها دالة دالة بتتغيرش بتتمها
+
+259
+00:17:44,860 --> 00:17:49,910
+دالة فبيقول لي let f from x y be a function and let W
+
+260
+00:17:49,910 --> 00:17:53,590
+be a set containing the image، هذه المهمة، المهم
+
+261
+00:17:53,590 --> 00:17:57,250
+أنها تكون توسع من الصور، اللي هو المدى، توسع
+
+262
+00:17:57,250 --> 00:18:00,770
+الصور، بيعد المعنى، أه that is image الـ F subset
+
+263
+00:18:00,770 --> 00:18:04,930
+من W، then F from X to W is a function أه فدي كل
+
+264
+00:18:04,930 --> 00:18:09,510
+القضية احنا كل مطلوب من المجال مقابل مجموعة تحتوي
+
+265
+00:18:09,510 --> 00:18:13,090
+الصور تحتوي الـ image أه هاي البرهان مش هتطرقله
+
+266
+00:18:13,090 --> 00:18:16,830
+لأنه أتوقع نظرية واضحة والبرهان ممكن اللي حابه
+
+267
+00:18:16,830 --> 00:18:20,390
+يقرأه من الكتاب يعني مش كثير مهم البرهان فاحنا
+
+268
+00:18:20,390 --> 00:18:27,790
+هنتركه خلينا ندي مثال على هذا الموضوع ندي مثال على
+
+269
+00:18:27,790 --> 00:18:32,050
+هذا الموضوع ونرجع لنفس الدالة الـ greatest integer
+
+270
+00:18:32,050 --> 00:18:32,630
+function
+
+271
+00:18:35,130 --> 00:18:42,350
+نرجع لنفس الدالة تابعة التوة وهذا ناخده كمثال طبعا 
+
+272
+00:18:42,350 --> 00:18:46,470
+هو مثال توضيحي طبعا هنا الـ F قلنا فو درسناها قلنا
+
+273
+00:18:46,470 --> 00:18:50,830
+هي من R ل R من R ل R طب الـ R هنا المجال المقابل
+
+274
+00:18:50,830 --> 00:18:53,910
+أنا بأهتم أن الـ Y بتساوي R كبيرة كتير طب لو زغرتها
+
+275
+00:18:53,910 --> 00:18:58,010
+بنفع أزغرها ممكن أخدها Q بتتمها function ليش؟ لأن
+
+276
+00:18:58,010 --> 00:19:03,310
+الـ M مش Z ممكن أخد المجال المقابل Z ممكن فبتتمها 
+
+277
+00:19:03,310 --> 00:19:07,830
+function فهي function من R ل R صح من R ل Q صح من R
+
+278
+00:19:07,830 --> 00:19:12,440
+لـ Z صح طب من R لـ N تظبطش لأن الـ N بتحتويش كل الصور
+
+279
+00:19:12,440 --> 00:19:16,940
+فأنا لما أخد المجال المقابل أخدته A بتمشي الحالة
+
+280
+00:19:16,940 --> 00:19:20,720
+أخدته Q أخدته Z كله بيقدر الغرض طول ما أن المجال 
+
+281
+00:19:20,720 --> 00:19:23,740
+المقابل الشمالي احتوى ال image اللي هو ال Z واضح
+
+282
+00:19:23,740 --> 00:19:27,520
+فهي كل القضية فنظرية بسيطة وهي الهدف تبعها فأنا 
+
+283
+00:19:27,520 --> 00:19:32,100
+المجال المقابل كل دوره انه مجموعة تحتوي الصور
+
+284
+00:19:32,100 --> 00:19:39,430
+تحتوي الصور تمام ننتقل لنقطة أخرى مهمة نظرية سبعة
+
+285
+00:19:39,430 --> 00:19:43,770
+تساوى دوال equality of functions واقتصر بقول على
+
+286
+00:19:43,770 --> 00:19:47,970
+دالتين ان هم متساويتين الدالة دالة أولى F وكمان
+
+287
+00:19:47,970 --> 00:19:51,610
+دالة G واقتصر بحكم عليهم ان هم متساويتين طبعا أو
+
+288
+00:19:51,610 --> 00:19:54,730
+غير متساويتين لأن اذا مش هتروا بده تكون false اه
+
+289
+00:19:54,730 --> 00:19:59,090
+let F from X to Y and G from X to Y be functions
+
+290
+00:19:59,740 --> 00:20:05,980
+then f تساوي g كدوال if and only if f of x تساوي g 
+
+291
+00:20:05,980 --> 00:20:09,620
+of x for all x تنتمي لـ X طبعا النص وممكن
+
+292
+00:20:09,620 --> 00:20:14,850
+واضح بس بنحاول نوضحه ونشوف النقاط المهمة فيه تساوي
+
+293
+00:20:14,850 --> 00:20:18,270
+الدوال يعني اللي بدنا نتساوي الصور لكل عناصر ال
+
+294
+00:20:18,270 --> 00:20:21,950
+domain بدنا لكل عنصر في ال domain الصور تكون تحت
+
+295
+00:20:21,950 --> 00:20:25,690
+الـ F تساوي الصورة تحت الـ G هنا في كمان شرط خفي
+
+296
+00:20:25,690 --> 00:20:29,170
+الحقيقة بدنا ننتبه له هو يعني الـ F دالة من وين؟ من
+
+297
+00:20:29,170 --> 00:20:33,550
+X لـ Y والـ G دالة من X لـ Y فهنا في نفس الشرط لازم
+
+298
+00:20:33,550 --> 00:20:36,750
+الـ domain يتساوى لأنه إيش معناه أنه هذا الشرط؟
+
+299
+00:20:36,750 --> 00:20:39,590
+أنه ما زال function من X لـ Y إذا الـ domain الـ F
+
+300
+00:20:39,590 --> 00:20:43,450
+إيش بيساوي؟ Xو domain الجي بيساوي X طب هو أي واحد
+
+301
+00:20:43,450 --> 00:20:47,930
+تقول طب ما هي برضه مثبت الـ Y طب لو غير الـ Y تفرقش
+
+302
+00:20:47,930 --> 00:20:51,970
+كتير ليش؟ اه لأ لأنه من النظرية السابقة تفرقش
+
+303
+00:20:51,970 --> 00:20:55,590
+فاحنا أهم شرطين عشان تتساوى الدوال الـ domain تبعهم
+
+304
+00:20:55,590 --> 00:20:59,850
+يتساوى وصورهم تتساوى كل عنصر نتجه لل domain نفس
+
+305
+00:20:59,850 --> 00:21:02,690
+الصورة بيقول على الدالتين دول ليش متساوية يعني خليني
+
+306
+00:21:02,690 --> 00:21:06,600
+أشوف البرهان مع بعض خلينا نشوف البرهان مع بعض فهنا
+
+307
+00:21:06,600 --> 00:21:13,860
+محتاجناش نكتب نشوف نظرية ثلاثة سبعة theorem ثلاثة
+
+308
+00:21:13,860 --> 00:21:19,740
+سبعة prove خلينا نحللها بطريقتنا العادية طبعا let
+
+309
+00:21:19,740 --> 00:21:23,840
+f and g be functions هذول مواطين نفترض إن هذول هي
+
+310
+00:21:23,840 --> 00:21:26,400
+ممكن أكتبهم وممكن ما أكتبش واضح في أي سؤال لما
+
+311
+00:21:26,400 --> 00:21:29,000
+يقول let هدول يعتبروا مواطين ممكن في البداية أقول
+
+312
+00:21:29,000 --> 00:21:34,020
+let أو assume نفس المعنى تمام then f تساوي g إيش
+
+313
+00:21:34,020 --> 00:21:41,380
+بدنا نثبت أن f تساوي g if and only if F of X تساوي 
+
+314
+00:21:41,380 --> 00:21:46,300
+G of X for all X in X هذا المطلوب عادة صياغته
+
+315
+00:21:46,300 --> 00:21:52,040
+تمام؟ مش هيك؟ هي المطلوب فالمطلوب جملة مركبة فيها
+
+316
+00:21:52,040 --> 00:21:55,340
+if and only if عشان أثبتها بدي أعمل two parts if
+
+317
+00:21:55,340 --> 00:21:58,620
+proof فاحنا هنعمل two parts if proof فنبدأ
+
+318
+00:21:58,620 --> 00:22:04,760
+بالاتجاه الأول واحد اللي هو F تساوي G implies ال
+
+319
+00:22:04,760 --> 00:22:07,800
+for all X تنتمي لـ X خلينا نكتبه بالطريقة
+
+320
+00:22:10,250 --> 00:22:16,770
+العادية أو الرسمية فهذا الاتجاه الأول اه فبدأ أثبت
+
+321
+00:22:16,770 --> 00:22:21,950
+إذا كانوا الدوال متساويتين فإذا الصور كلها متساوية
+
+322
+00:22:21,950 --> 00:22:27,960
+كالعادة إيش بدأ أقول assume F تساوي G طبعا كله
+
+323
+00:22:27,960 --> 00:22:31,940
+بشتغل تحت كلمة let المواطيات العامة اه اه بدي أثبت
+
+324
+00:22:31,940 --> 00:22:36,480
+إن هذا الكلام صحيح تمام إذا هذا إيش بنفترضه لأن
+
+325
+00:22:36,480 --> 00:22:40,440
+هذا إيش الشرط بنثبت جواب الشرط نيجي لجواب الشرط
+
+326
+00:22:40,440 --> 00:22:43,880
+أول شيء عبارة عن for all كيف بدي أعمله بقوله
+
+327
+00:22:43,880 --> 00:22:48,640
+let x تنتمي لـ X let x تنتمي لـ X be 
+
+328
+00:22:48,640 --> 00:22:52,850
+an element لو ما كتبتش any element مفهومة be any
+
+329
+00:22:52,850 --> 00:22:58,050
+element اسم المطلوب بدي F of x تساوي G of x تساوي
+
+330
+00:22:58,050 --> 00:23:05,220
+تساوي إيش صورها تساوي صورها والصور يعني إيش؟ يعني عناصر
+
+331
+00:23:05,220 --> 00:23:09,080
+انتبه مش مجموعات فابد أثبت أن F of X تساوي G of X
+
+332
+00:23:09,080 --> 00:23:12,060
+ممتاز بدنا نشوف كيف بدنا نمشي فهنا مهم جدا احنا
+
+333
+00:23:12,060 --> 00:23:16,040
+كنا نقول تساوي مجموعات تساوي علاقات تساوي دوال
+
+334
+00:23:16,040 --> 00:23:19,640
+تساوي عناصر تساوي أرقام فدائما لازم نحلل إيش اللي
+
+335
+00:23:19,640 --> 00:23:23,090
+بدنا ياه ونمشي واحدة واحدة فاحنا بدنا في عندنا مظلة
+
+336
+00:23:23,090 --> 00:23:27,290
+عامة معطيات الـ F والـ G دوال من X لـ Y بعدين بدنا
+
+337
+00:23:27,290 --> 00:23:30,610
+مطلوب إيش .. بإيش ال statement اللي هي صحيحة تكون
+
+338
+00:23:30,610 --> 00:23:34,710
+by conditional if and only if كيف نثبتها؟ two
+
+339
+00:23:34,710 --> 00:23:37,810
+parts of proof وبعدين نشتغل بالاتجاه الأول ممتاز
+
+340
+00:23:37,810 --> 00:23:42,990
+بدأ أوصل أن F of X تساوي G of X كيف ممكن نروح؟ لأن
+
+341
+00:23:42,990 --> 00:23:45,330
+هي طبعا .. يمكن هذا أول مثال بنعمل proof مع
+
+342
+00:23:45,330 --> 00:23:48,830
+النظرية .. مع ال .. مع ال .. مع الدوال اه .. الآن
+
+343
+00:23:48,830 --> 00:23:52,340
+احنا إيش عندنا معلومات؟ إن الـ X هي domain
+
+344
+00:23:52,340 --> 00:23:55,640
+الـ F فكل عنصر في الـ F إيش ما له، له صورة لازم
+
+345
+00:23:55,640 --> 00:23:58,240
+يكون، هيك معناه في ال domain إيش معناه التعريف
+
+346
+00:23:58,240 --> 00:24:00,300
+ال domain؟ إيش ما هو ال domain؟ ال domain قال لي
+
+347
+00:24:00,300 --> 00:24:06,220
+هو كل X such that XY تنتمي لل relation أو لل F for 
+
+348
+00:24:06,220 --> 00:24:14,870
+some Y فهنا على طول هذا يؤدي إن X Y تنتمي لمن؟ نبدأ
+
+349
+00:24:14,870 --> 00:24:17,710
+بواحدة فيهم لأن X هو الـDomain الاتنين للـF هو
+
+350
+00:24:17,710 --> 00:24:21,710
+الاتنين صح لأن X هو الـDomain الاتنين الـXY for
+
+351
+00:24:21,710 --> 00:24:29,370
+some Y تنتمي لـ Y من أين جبته هذا؟ لأن الـ X تساوي
+
+352
+00:24:29,370 --> 00:24:32,550
+domain الـ F وهذا تعريف ال domain لأن X تساوي
+
+353
+00:24:32,550 --> 00:24:36,230
+domain الـ F لو رجعتوا لتعريف ال domain بتلاقوه
+
+354
+00:24:36,230 --> 00:24:40,650
+هكذا تعريف ال domain هو كل X such that إن X إحداثي
+
+355
+00:24:40,650 --> 00:24:44,450
+أول توي حكينا عنها من زوج مرتب، عامي مكان، مهمنيش
+
+356
+00:24:44,450 --> 00:24:48,880
+الإحداثي التاني، somewhere، somewhere، ممتاز أنا بدي 
+
+357
+00:24:48,880 --> 00:24:57,200
+أثبت أن F of x تساوي G of x بنفس الإسلوب أيضا and
+
+358
+00:24:57,200 --> 00:25:03,760
+implies and x y أو مش مش y أنا إيش بدي أثبت أن F
+
+359
+00:25:03,760 --> 00:25:12,360
+of x ألاقيت أن ال x تنتمي لـ  أ لأ بس for some تمام
+
+360
+00:25:12,360 --> 00:25:19,310
+لأن احنا تمام ممتاز لأ مافيش داعي بدي أستخدم .. لو
+
+361
+00:25:19,310 --> 00:25:22,610
+قلت .. لو قلت بدي أقول إيش؟ لو الـ X تنتمي لـ 
+
+362
+00:25:22,610 --> 00:25:25,830
+domain الـ G إذا الـ X لها صورة ما مش ضروري تكون Y
+
+363
+00:25:25,830 --> 00:25:28,890
+بقى ممكن تكون for some لأنه لكن مش محتاجة الحقيقة
+
+364
+00:25:28,890 --> 00:25:33,090
+الحل هنا ما زال XY في الـ F والـ F تساوي G هذول
+
+365
+00:25:33,090 --> 00:25:36,990
+إيش relations يعني مجموعات إذا لازم XY تنتمي للـ G
+
+366
+00:25:36,990 --> 00:25:44,210
+تنتمي للـ G اه فطبعا هذا معناه إن X Y تنتمي للـ G
+
+367
+00:25:44,210 --> 00:25:49,790
+لأن الـ F تساوي G الـ F والـ G كرموز عبارة عن
+
+368
+00:25:49,790 --> 00:25:54,490
+علاقات يعني مجموعات من أزواج مرتبة طبعا خلصنا الآن
+
+369
+00:25:54,490 --> 00:25:58,250
+إيش معناه إن X Y في الـ F يعني Y تساوي F في X
+
+370
+00:26:02,390 --> 00:26:07,690
+Y تساوي F of X وبنفس الوقت Y بتساوي G of X خلينا
+
+371
+00:26:07,690 --> 00:26:14,950
+نكتبها بشكل أوضح Y تساوي F of X وY تساوي G of X
+
+372
+00:26:14,950 --> 00:26:19,650
+هذا إيش جليلي هنا ليس إلا notation هذه مجرد ما
+
+373
+00:26:19,650 --> 00:26:23,410
+كتبناها إيش معناه XY في ال F مهمة جدا يعني Y تساوي
+
+374
+00:26:23,410 --> 00:26:27,110
+F of X بمعنى الدوال مش لو شرحناها برموز وإيش معناه 
+
+375
+00:26:27,110 --> 00:26:31,030
+XY في ال G يعني Y تساوي G of X هذه مجرد notation
+
+376
+00:26:34,370 --> 00:26:37,490
+تمام؟ أنا إيش بده أثبت؟ بده أثبت إن F of X تساوي G
+
+377
+00:26:37,490 --> 00:26:41,090
+of X إسمالهم بيساوي قيمة مشتركة واحد، اه فدا إيش
+
+378
+00:26:41,090 --> 00:26:48,230
+بيكون انتهت؟
+
+379
+00:26:48,230 --> 00:26:54,150
+اه implies F of X تساوي G of X وهو المطلوب فاحنا 
+
+380
+00:26:54,150 --> 00:26:57,310
+بدينا وشوفنا إيش اللي .. اللي بدنا نتعامل وإيش
+
+381
+00:26:57,310 --> 00:27:00,150
+المواقعيات اللي ممكن نعملها لعد ما وصلنا للمطلوب،
+
+382
+00:27:00,150 --> 00:27:08,300
+الآن لتجاه الثاني for all x تنتمي لـ X f of x تساوي
+
+383
+00:27:08,300 --> 00:27:17,620
+g of x implies f تساوي g فطبعا كالعادة let for all
+
+384
+00:27:17,620 --> 00:27:28,580
+x أو assume كله نفس الكلام for all x تنتمي 
+
+385
+00:27:28,580 --> 00:27:37,020
+لـ X F of X تساوي G of X فهذه الأمور أتوقع مع
+
+386
+00:27:37,020 --> 00:27:40,200
+التكرار صارت الأمور يعنيئبة دي هيية أنا عندي 
+
+387
+00:27:40,200 --> 00:27:43,060
+statement شرطية على طول ببدأ أني أفترض أن الشرط 
+
+388
+00:27:43,060 --> 00:27:49,140
+صحيح تمام ماشي إيش بده أثبت F تساوي G تساوي تساوي
+
+389
+00:27:49,140 --> 00:27:55,770
+إيش مش عناصر هذه، لأ، فين نميز، مجموعات اللي هي 
+
+390
+00:27:55,770 --> 00:27:59,550
+عبارة عن relations اللي هي مجموعة من أزواج مرتبة، 
+
+391
+00:27:59,550 --> 00:28:02,390
+functions اللي هي ال relation يعني كيف عناصرها
+
+392
+00:28:02,390 --> 00:28:05,870
+أزواج مرتبة، ده ما كنش طلعناه، لكن لما قال لي F of X
+
+393
+00:28:05,870 --> 00:28:08,420
+سوجوا في X صورة عشان هيك أحيانا طبعا احنا ممكن
+
+394
+00:28:08,420 --> 00:28:11,700
+أحيانا التجاوز عشان نقول ال function f of x 
+
+395
+00:28:11,700 --> 00:28:14,220
+الحقيقة بيقول ال function f فيها، f of x صورة،
+
+396
+00:28:14,220 --> 00:28:19,760
+عنصر، بدنا نميز بينهم، أحيانا نتجاوز، بيصير عملية
+
+397
+00:28:19,760 --> 00:28:22,680
+تجاوز عشان المفهومة تكون الصورة، ففي فرق بين f ك
+
+398
+00:28:22,680 --> 00:28:26,180
+function وبين f of x كصورة فالناس أحيانًا بيدقق
+
+399
+00:28:26,180 --> 00:28:28,680
+عليها كتير لكن إذا كان السياق واضح فإيش عندنا
+
+400
+00:28:28,680 --> 00:28:33,100
+مشكلة فدول عبارة عن تساوي relations يعني مجموعات
+
+401
+00:28:33,100 --> 00:28:37,600
+من أزواج مرتبة كيف بدأ أثبت التساوي؟ بدأ عنصر من
+
+402
+00:28:37,600 --> 00:28:42,380
+طرف وامشي للطرف الثاني إذا مشيت تكافؤ خلص التساوي
+
+403
+00:28:42,380 --> 00:28:47,960
+امشي من الطرف للاتجاه فحنقوله الآن let أسع نصبرها 
+
+404
+00:28:47,960 --> 00:28:55,200
+أزواج مرتبة تنتمي للـ F be any element 
+
+405
+00:28:58,090 --> 00:29:01,510
+فمبادئنا ما بتتغيرش، اه التفاصيل ممكن تتغير، ممتاز
+
+406
+00:29:01,510 --> 00:29:05,070
+اه الآن بده أوصل انه x y في main في ال G، إذا مشيت
+
+407
+00:29:05,070 --> 00:29:09,770
+تكافؤ خلص تمام، الآن بده يحاول يستفيد من المعطيات،
+
+408
+00:29:09,770 --> 00:29:14,910
+إيش المعطيات؟ إنه الـ F تساوي G كيف ممكن أعمل؟ بدنا 
+
+409
+00:29:14,910 --> 00:29:20,450
+نشوف كيف نروح من الرمزين المتكافئين، x y في الـ F
+
+410
+00:29:20,450 --> 00:29:24,930
+يعني y تساوي F of X فهذا يؤدي أن y تساوي F of X،
+
+411
+00:29:24,930 --> 00:29:29,210
+فهذا ليس إلا notation فده ليس إلا notation هي ده هو 
+
+412
+00:29:29,210 --> 00:29:34,270
+المفتاح implies طبعا implies طب ولا تكافؤ تكافؤ
+
+413
+00:29:34,270 --> 00:29:38,530
+لأنه ده بس مجرد notation نفس المعنى طبعا كيف بدك 
+
+414
+00:29:38,530 --> 00:29:40,930
+تعرف إنه implies ولا نفس المعنى هالجيت إذا هذي صح
+
+415
+00:29:40,930 --> 00:29:44,590
+هذي صح implies ممتاز طب لو هذي صح هذي مش صح بقدرش
+
+416
+00:29:44,590 --> 00:29:47,710
+أرجع وجوع لو أنا بديت منها أنا بقدرش أعيش تكافؤ من 
+
+417
+00:29:47,710 --> 00:29:50,870
+أين؟ 
+
+418
+00:29:50,870 --> 00:29:55,930
+أنا الجيت بديت من هنا هي .. هي .. هي .. لا ما ليش
+
+419
+00:29:55,930 --> 00:29:59,570
+أنا دي assumption .. دي ال unwise أنا بدي أثبت هذا
+
+420
+00:29:59,570 --> 00:30:03,530
+المطلوب اه .. أنا إيش بحكي .. هذه ال statement إيش 
+
+421
+00:30:03,530 --> 00:30:08,260
+علاقتها مع هذه؟ تكافؤ واضحة؟ أنا بدل الـ statement
+
+422
+00:30:08,260 --> 00:30:12,960
+مع علاقة ما حد يتكافأ، طبعًا، اه الآن .. اه يعني مش 
+
+423
+00:30:12,960 --> 00:30:15,480
+عارف .. مش حابع أعملها بذا الشكل، بدي أكتبها بذا
+
+424
+00:30:15,480 --> 00:30:18,700
+الشكل، ليش؟ عشان ما نخربطش بينه و بين اللي يساوي،
+
+425
+00:30:18,700 --> 00:30:20,520
+واحدة تنسى الشرطة تقول لك يساوي و يساوي و صارت
+
+426
+00:30:20,520 --> 00:30:23,620
+مشكلة، فنعملها بذا الشكل، أنا ملاجيء هيك answer، اه
+
+427
+00:30:23,620 --> 00:30:26,720
+هي بتحطها قواز، تمام؟ الآن أنا أول ما بدي أروح،
+
+428
+00:30:26,720 --> 00:30:32,210
+بدي أوصلها للـ G، طب إيش عندي معطيات؟ لأ لسه مش Y لأ 
+
+429
+00:30:32,210 --> 00:30:35,410
+لأن الـ F بقدر أبدلها بـ G بقدر أبدلها بـ G if and 
+
+430
+00:30:35,410 --> 00:30:40,650
+only if Y تساوي G of X ليش؟ لأن F of X تساوي G of 
+
+431
+00:30:40,650 --> 00:30:46,060
+X هي المعبرة و برضه تكافؤ لإيش؟ بدلت قيمة بقيمة 
+
+432
+00:30:46,060 --> 00:30:50,660
+مساوية فهذا كلام صحيح لو أنا عندي G بقدر أبدلها بـ
+
+433
+00:30:50,660 --> 00:30:54,240
+F لو عندي F بقدر أبدلها بـ G لأنهم متساويين أنت عندك
+
+434
+00:30:54,240 --> 00:30:57,780
+اتنين كتاب ديها واحد زائد واحد إذا بدأت من واحد
+
+435
+00:30:57,780 --> 00:31:00,640
+لواحد بتوضيها باتنين أو اتنين واحد وبواحد نفس
+
+436
+00:31:00,640 --> 00:31:04,460
+المعنى طيب هذا إيش معناته؟ بـ notation إنه XY في
+
+437
+00:31:04,460 --> 00:31:08,900
+الـ G وهو المطلوب if and only if XY تنتمي للـ G هذا
+
+438
+00:31:08,900 --> 00:31:10,320
+عبارة عن إيش؟ برضه notation
+
+439
+00:31:13,390 --> 00:31:17,110
+بدأت من عنصر في الـ F كـ relation وصلته للـ G
+
+440
+00:31:17,110 --> 00:31:26,770
+تكافؤ فأثبتت التساوية Thus F تساوي G فهذه الأمور
+
+441
+00:31:26,770 --> 00:31:31,270
+يمكن تبدو بسيطة و إحنا من حياتنا ممكن نحاول نقفز
+
+442
+00:31:31,270 --> 00:31:34,870
+عنها لكن أنا في رأيها أساسية إنه أعرف أنا طبعًا
+
+443
+00:31:34,870 --> 00:31:37,750
+ببدأ من الخارج أيش الـ statement أيش المواطيات أيش
+
+444
+00:31:37,750 --> 00:31:40,990
+المطلوب نقع الـ statement كمطلوب و كيه بحللها و
+
+445
+00:31:40,990 --> 00:31:44,590
+بعدين و أنا بحلل أيش العلاقة علاقة أيش اللي بده
+
+446
+00:31:44,590 --> 00:31:47,130
+أثبتها و هكذا فهذه الأمور بنمشي فيها واحدة واحدة
+
+447
+00:31:47,130 --> 00:31:51,230
+بدنا نوصل هذا الاتجاه الأول و لا خلصنا خلصنا اتجاه 
+
+448
+00:31:51,230 --> 00:32:01,060
+التالي وهو المطلوب تمام نشوف أمثلة المثال الأول
+
+449
+00:32:02,750 --> 00:32:06,910
+بنجيب نفس مثال بسيط على التساوي مديني مجموعتين
+
+450
+00:32:06,910 --> 00:32:12,150
+طبعًا جالي من X لـ Y دلتين 1 2 3 و الـ Y سالب 1 سالب
+
+451
+00:32:12,150 --> 00:32:17,410
+2 3 معرف الـ function ع صورة أزواج مرتبة 1 سالب 1 2
+
+452
+00:32:17,410 --> 00:32:23,190
+سالب 2 3 سالب 3 و معرف الـ G بقاعدة علاش قاعدة عامة
+
+453
+00:32:23,190 --> 00:32:26,290
+للتعريف G of X يساوي سالب X هل هدولة دلتين
+
+454
+00:32:26,290 --> 00:32:30,330
+متساويتين؟ اه طبعًا صحيح اه لأنه بس هنا أحكي أس
+
+455
+00:32:30,330 --> 00:32:35,150
+طريقة الكتابة مختلفة طريقة كتابة مختلفة طبعًا بدنا
+
+456
+00:32:35,150 --> 00:32:41,220
+نشوف الشروط بس خلينا نمشي على الشروط هذا مثالأه
+
+457
+00:32:41,220 --> 00:32:46,520
+طبعًا هيهم الـ F و الـ G دلتين من X لـ Y F by .. هو 
+
+458
+00:32:46,520 --> 00:32:49,900
+مديناياهم بس بنحقق الشروط فإيش الشروط؟ بدنا for
+
+459
+00:32:49,900 --> 00:32:54,020
+all X تنتمي لـ X بدنا نفحص F of X يساوي G of
+
+460
+00:32:54,020 --> 00:32:59,620
+X هاي ده هو الشرط solution فـ F of واحد إيش بتساوي
+
+461
+00:32:59,620 --> 00:33:02,860
+في هذه القضية؟ سالب واحد ايه لإن واحد سالب واحد
+
+462
+00:33:02,860 --> 00:33:07,160
+تنتمي للـ F من هذه إيش بفهم؟ إن صورة الواحد سالب
+
+463
+00:33:07,160 --> 00:33:13,260
+واحد و هذه تساوي مين؟ G of واحد من التعريف F التنين
+
+464
+00:33:13,260 --> 00:33:18,960
+سالب اتنين تساوي G of اتنين F التلاتة سالب تلاتة
+
+465
+00:33:18,960 --> 00:33:23,220
+تساوي G of تلاتة هي فحصها فلكل عناصر الـ X
+
+466
+00:33:23,220 --> 00:33:27,540
+صور كل عنصر في الـ F والـ G نفس الكلمة فإذن
+
+467
+00:33:27,540 --> 00:33:31,100
+فعلاً هدولة دالتين متساويتين
+
+468
+00:33:33,050 --> 00:33:36,730
+اه طبعًا أيضًا لو أنا روحت كتبت الـ G بنفس الاسلوب
+
+469
+00:33:36,730 --> 00:33:40,630
+هلاجيها نفس الأزواج للدينة ولا لأ لو حسبك فإن بس
+
+470
+00:33:40,630 --> 00:33:45,170
+هذا هو القضية فقد يكون واضحة فقد يكون واضحة و هذه
+
+471
+00:33:45,170 --> 00:33:51,610
+هي النظرية اللي بتحكم الموضوع تمام؟
+
+472
+00:33:52,990 --> 00:33:56,310
+فأتوقع إن هي كل أيام كتير من الأمور متعودين عليها
+
+473
+00:33:56,310 --> 00:34:01,150
+لكن بدنا نحطها في الصياق العام و في اللي هو الصورة
+
+474
+00:34:01,150 --> 00:34:05,410
+العام الآن هيتحدث عن بعض الدوال المشهورة و الخاصة
+
+475
+00:34:05,410 --> 00:34:07,970
+some special functions في بعض الدوال اللي بتمر
+
+476
+00:34:07,970 --> 00:34:10,730
+علينا وين ما كان بغض النظر من المجموعات اللي
+
+477
+00:34:10,730 --> 00:34:13,850
+بتعامل معاهم اه طبعًا إحنا متعودين على الدوال كلها
+
+478
+00:34:13,850 --> 00:34:17,370
+من الـ calculus أنه نتحدث انه المجال من الـ .. من الـ
+
+479
+00:34:17,370 --> 00:34:19,730
+real numbers و المجال المقابل من الـ real numbers
+
+480
+00:34:19,730 --> 00:34:21,910
+طبعًا إحنا هنا هندرس الدوال بشكل عام لأنه هنا
+
+481
+00:34:21,910 --> 00:34:25,110
+ما شرطش جالي أي مجموعتين X و Y مش ضروري يكونوا
+
+482
+00:34:25,110 --> 00:34:28,370
+أعداد اه فالصورة هنا متعرفة على إيش .. أي علاقة
+
+483
+00:34:28,370 --> 00:34:31,470
+بين مجموعتين بتحقق الشرطين الدماني غطي المجموعة
+
+484
+00:34:31,470 --> 00:34:34,350
+الأولى و لكل عنصر صورة واحدة مش ضروري تكون الدالة
+
+485
+00:34:34,350 --> 00:34:39,130
+تودي عدد لعدد لأ مش ضروري بنتحدث عن إيش أي علاقة
+
+486
+00:34:39,130 --> 00:34:42,310
+بين أي مجموعتين بغض النظر أيش العناصر كلام عام
+
+487
+00:34:42,310 --> 00:34:47,670
+بس إيش راح بقول let X be a non-empty set فإحنا شفنا
+
+488
+00:34:47,670 --> 00:34:50,490
+الـ diagonal relation بتذكروها؟ اللي هي إيش؟ هذه
+
+489
+00:34:50,490 --> 00:34:53,670
+أصغر علاقة التكافؤ، اللي هي delta X، اللي هي
+
+490
+00:34:53,670 --> 00:34:57,850
+بتتكون من XX عناصر، هذه برضه كإيش بتكون function،
+
+491
+00:34:57,850 --> 00:35:01,170
+هي عبارة عن علاقة التكافؤ و بنفس الوقت هي دالة،
+
+492
+00:35:01,170 --> 00:35:03,990
+ليش؟ لأن بتتغطي كل الـ domain و كل عنصر ما له ولا
+
+493
+00:35:03,990 --> 00:35:06,530
+صورة واحدة، لو إننا صورة نفسنا، فهذه بيسموها
+
+494
+00:35:06,530 --> 00:35:09,920
+الـ Dial ليش؟ الدالة المحايدة لأنهم برضه
+
+495
+00:35:09,920 --> 00:35:12,740
+بيسمونها identity relation فهي عبارة عن function و
+
+496
+00:35:12,740 --> 00:35:16,040
+هي الـ identity function فأنا أديني أي مجموعة غير
+
+497
+00:35:16,040 --> 00:35:19,320
+فارغة بديله مثال في دالة ملائمة معروفة هي الدالة
+
+498
+00:35:19,320 --> 00:35:22,840
+المحايدة F of X يساوي X الدالة المحايدة الـ X تروح
+
+499
+00:35:22,840 --> 00:35:27,320
+لنفسها فبيسمونها identity function طب أنا هسمونها
+
+500
+00:35:27,320 --> 00:35:29,600
+diagonal relation لكن مسموهاش diagonal function
+
+501
+00:35:29,600 --> 00:35:33,080
+بيسمونها identity function الدالة المحايدة مثال
+
+502
+00:35:33,080 --> 00:35:37,480
+آخر برضه فطبعًا هذه الـ function من وين لوين الـ 
+
+503
+00:35:37,480 --> 00:35:41,100
+delta X من X لنفسها من X لنفسها فعند المجال و
+
+504
+00:35:41,100 --> 00:35:43,800
+المجال المقابل متساويين في هذه الحالة و المدى
+
+505
+00:35:43,800 --> 00:35:47,420
+الحقيقة هو المدى كمان هو المدى بيساويه لأنه كلهم 
+
+506
+00:35:47,420 --> 00:35:52,480
+صحيح مثال آخر بيقول لو أخذنا أي دالة T أي مجموعتين
+
+507
+00:35:52,480 --> 00:35:58,160
+غير فارغتين X و Y اه B2 sets و ناخد الـ B بـ N fixed
+
+508
+00:35:58,160 --> 00:36:02,700
+element of Y ناخد أي عنصر ثابت من الـ Y و نخلي كل
+
+509
+00:36:02,700 --> 00:36:05,940
+العناصر تروح للـ B هذه بيسميها الدالة الثابتة كل
+
+510
+00:36:05,940 --> 00:36:09,500
+العناصر بتروح لنفس الصورة اه فانا عايش في عندي ..
+
+511
+00:36:09,500 --> 00:36:15,630
+في عندي X كله بده يودي لعنصر واحد وهي Y
+
+512
+00:36:15,630 --> 00:36:22,070
+روحت اختارت عنصر من الـ Y عنصر B و روحت كل العناصر
+
+513
+00:36:22,070 --> 00:36:26,210
+اللي أنا وديتهم على B كله وديته على B هذه الدالة
+
+514
+00:36:26,210 --> 00:36:28,310
+الثابتة هي الدالة الثابتة لما نقول f of x equal to
+
+515
+00:36:28,310 --> 00:36:33,550
+1 يعني في الـ calculus يعني f في الـ zero واحد لأن
+
+516
+00:36:33,550 --> 00:36:36,150
+كل عناصر صورهم واحد نفس الشيء معاها فطبعًا هذه هي
+
+517
+00:36:36,150 --> 00:36:38,530
+طريقة تعريف الدالة الثابتة فبقول لي هذه الـ
+
+518
+00:36:38,530 --> 00:36:42,030
+function بدرمزها من كلمة constant C sub P
+
+519
+00:36:42,030 --> 00:36:46,210
+طبعًا بالنسبة للصورة الثابتة الوحيدة فهذه بسموها
+
+520
+00:36:46,210 --> 00:36:49,710
+constant function بسموها constant function فهي
+
+521
+00:36:49,710 --> 00:36:54,620
+طريقتين كيف أكون function بسهولة المثال الأول
+
+522
+00:36:54,620 --> 00:36:57,400
+function من مجموعة لنفسها المثال التاني function
+
+523
+00:36:57,400 --> 00:37:00,500
+من أي مجموعة لمجموعة أخرى مش لازم تكون نفسها
+
+524
+00:37:00,500 --> 00:37:06,080
+المثال التالت برضه دوال مشهورة و دوال خاصة بيسموها
+
+525
+00:37:06,080 --> 00:37:10,620
+الـ characteristic function الدالة المميزة بقول let
+
+526
+00:37:10,620 --> 00:37:17,140
+A be a subset of non empty set X and define هنعرف
+
+527
+00:37:17,140 --> 00:37:22,320
+function بالشكل التالي خلينا نحاول نشرحها و نفهمها
+
+528
+00:37:24,460 --> 00:37:29,140
+أول شيء الـ function هي function بيكتبوها .. هذا
+
+529
+00:37:29,140 --> 00:37:35,220
+الرمز X مائلة اللي بيسموها K sub A من وين لوين الـ
+
+530
+00:37:35,220 --> 00:37:41,560
+function من مجموعة X لـ 0,1 فالـ Y بتساوي 0
+
+531
+00:37:41,560 --> 00:37:48,800
+,1 هذه أول ملاحظة كيف تتعرف هي أنا عندي الـ X و
+
+532
+00:37:48,800 --> 00:37:56,560
+باخد subset A جوا الـ X و بدلالتها أعرف الدالة لكل
+
+533
+00:37:56,560 --> 00:38:00,140
+subset من الـ domain بعرف الدالة دي اللي يسموها الـ
+
+534
+00:38:00,140 --> 00:38:05,260
+characteristic function of A دالة مميزة للـ A in X
+
+535
+00:38:05,260 --> 00:38:08,830
+إيش بتعملها دي؟ الحقيقة هذه بس بتقول العنصر هل
+
+536
+00:38:08,830 --> 00:38:13,110
+موجود في الـ A أو خارج الـ A بس هي بتعملية بتقول إذا
+
+537
+00:38:13,110 --> 00:38:16,370
+كان الـ X في الـ A بتديني واحد يعني موجود يعني زي
+
+538
+00:38:16,370 --> 00:38:19,110
+true في الكمبيوتر أحيان بدي ما تقول true بحط واحد
+
+539
+00:38:19,110 --> 00:38:21,930
+و إذا كانت مش موجودة يعني في الخارج بتديني false،
+
+540
+00:38:21,930 --> 00:38:25,530
+zero، بتديني zero فعشان هيك بتتميز، بتتميز العناصر
+
+541
+00:38:25,530 --> 00:38:28,950
+اللي في الـ A و اللي خارج الـ A فهذه دالة، تعتبر دالة
+
+542
+00:38:28,950 --> 00:38:33,650
+لأي عنصر، للعنصر اللي احتماليًا، يا يكون جوا هنا هنا
+
+543
+00:38:33,650 --> 00:38:38,430
+أو برا إذا كان جوا قيمة صورته واحد و إذا كان برا
+
+544
+00:38:38,430 --> 00:38:41,430
+صورته صفر فدول الاحتمالية فانسموها characteristic
+
+545
+00:38:41,430 --> 00:38:45,430
+function characteristic function of A in X بتميز
+
+546
+00:38:45,430 --> 00:38:48,550
+عناصر الـ domain بتقسم من نصها عناصر جوا الـ subset
+
+547
+00:38:48,550 --> 00:38:53,230
+و عناصر خارج الـ subset فهذه دالة معروفة برضه
+
+548
+00:38:53,230 --> 00:39:01,480
+مشهورة تمام مثال الرابع دالة الإسقاط projection اه
+
+549
+00:39:01,480 --> 00:39:06,280
+فأنا لو عندي مجموعتين و ممكن أنا أعمل إسقاط على
+
+550
+00:39:06,280 --> 00:39:09,740
+محور السينات أو محور الصادات كل هذه تعتبر function
+
+551
+00:39:09,740 --> 00:39:14,710
+فبقولي the X projection function PX من XY لـ X من هون
+
+552
+00:39:14,710 --> 00:39:18,170
+بتودي للـ X باخد الإحداث الأول عملية إسقاط is given
+
+553
+00:39:18,170 --> 00:39:22,110
+by الرمز تبعها من كلمته projection P sub X إسقاط
+
+554
+00:39:22,110 --> 00:39:25,710
+على محور السينات of X and Y باخد الإحداث الأول
+
+555
+00:39:25,710 --> 00:39:29,570
+عملية إسقاط و الـ Y projection إسقاط على محور
+
+556
+00:39:29,570 --> 00:39:33,150
+الصادات بتدالة من وين لوين من X cross Y، انتبهوا
+
+557
+00:39:33,150 --> 00:39:37,310
+هنا، مهم جدًا، هي هذه الدالة بتاخد زوج مرتب و الصورة
+
+558
+00:39:37,310 --> 00:39:41,470
+عنصر إحداثي يا الأول يا الثاني، اه فهنا هذه من XY
+
+559
+00:39:41,470 --> 00:39:46,470
+لـ X أو من XY لـ Y، بتاخد زوج مرتب تديله إحداثي
+
+560
+00:39:46,470 --> 00:39:49,110
+الأول أو الثاني، بدي أسقط على محور الصادات باخد
+
+561
+00:39:49,110 --> 00:39:51,870
+الإحداث الأول، أسقط على محور السينات بآخذ الإحداث
+
+562
+00:39:51,870 --> 00:39:55,450
+الثاني، فهذه بيسموها projection function، وفيه يا
+
+563
+00:39:55,450 --> 00:39:59,750
+بعمل إسقاط على الـ X أو إسقاط على الـ Y، فدولة دوال
+
+564
+00:39:59,750 --> 00:40:04,590
+مشهورة، بقدر أعرفهم على أي مجموعة، ليش هذا الكلام
+
+565
+00:40:04,590 --> 00:40:08,110
+مهم؟ لأن حد يقول لي طب أنا بقدر أعرف الدالة 
+
+566
+00:40:08,110 --> 00:40:12,510
+الـabsolute value على مجموعة عامة؟ لأ، الـabsolute
+
+567
+00:40:12,510 --> 00:40:15,490
+value خاص بالـreal numbers، مثلًا عملية التربيع،
+
+568
+00:40:15,490 --> 00:40:18,490
+بنفع أعرف التربيع على حاجة مش عدد؟ ما بنفعش، فهي
+
+569
+00:40:18,490 --> 00:40:21,450
+المقضية، لكن دولة الدوال الأربعة بقدر أعرفهم لأي
+
+570
+00:40:21,450 --> 00:40:24,910
+مجموعة، واضح الفرق، ليش درسناهم؟ لأن في دوال احنا
+
+571
+00:40:24,910 --> 00:40:27,940
+مشهورين، متعاملين عليها، ومتعرفين عليها من الـ calculus
+
+572
+00:40:27,940 --> 00:40:30,780
+ما بنفعش أعرفهم على أي مجموعة، لكن هدول الدوال بينفع
+
+573
+00:40:30,780 --> 00:40:33,360
+أعرفهم على أي مجموعات، ما جليش الـ X والـ Y دولة
+
+574
+00:40:33,360 --> 00:40:39,540
+numbers ولا sets ولا ... ولا أي حاجة، لأ، جلي أي
+
+575
+00:40:39,540 --> 00:40:47,700
+مجموعات، أي عناصر، تمام، ننتقل لنقطة أخرى، unions of
+
+576
+00:40:47,700 --> 00:40:53,840
+functions، اتحاد الدوال، يمكن المصطلح يكون غريب، واحد
+
+577
+00:40:53,840 --> 00:40:58,220
+يقول كيف الدول اللي بيعملوا عليهم اتحاد؟ عشان نزيل
+
+578
+00:40:58,220 --> 00:41:00,900
+هذا الـ lapse، نتذكر الـ function هي إيش؟ هي الـ
+
+579
+00:41:00,900 --> 00:41:04,340
+relation، والـ relation subset مجموعة من أزواج
+
+580
+00:41:04,340 --> 00:41:08,040
+مرتبة، إذا بقدر أتحدث عن اتحاد الـ relations، عن
+
+581
+00:41:08,040 --> 00:41:10,660
+تقاطع الـ relations، عن الـ difference للـ relation،
+
+582
+00:41:10,660 --> 00:41:13,120
+عن الـ complement للـ relation، فالمصطلح أولًا مش 
+
+583
+00:41:13,120 --> 00:41:16,030
+غريب، واحد أحداث مش غريب؟ لأن الـ function رجعناها
+
+584
+00:41:16,030 --> 00:41:18,530
+لأصلها، هي الـ relation، والـ relation هي مجموعة من
+
+585
+00:41:18,530 --> 00:41:21,690
+أزواج مرتبة، إذا أنا ممكن أتحدث عن الـ unions طبعًا
+
+586
+00:41:21,690 --> 00:41:25,210
+السؤال أنا عندي دالتين أخدت اتحادهم، تمام، دالة ولا
+
+587
+00:41:25,210 --> 00:41:27,990
+ما تمام؟ هذا سؤال آخر، لأن الاتحاد ده عملية على
+
+588
+00:41:27,990 --> 00:41:31,450
+المجموعات، فالمجموعة الجديدة الكبيرة بتامها
+
+589
+00:41:31,450 --> 00:41:35,510
+function ولا لأ؟ هذا سؤال آخر، واضح؟ استمعنا نشوف
+
+590
+00:41:35,510 --> 00:41:40,400
+بعض الأمثلة التمهيدية، الأمثلة التمهيدية، الحقيقة
+
+591
+00:41:40,400 --> 00:41:43,920
+الموضوع أقرب شيء احنا طبعًا مر علينا الـ university
+
+592
+00:41:43,920 --> 00:41:48,180
+جاب الـ هيك في دراستكم، اتحاد الدوال مر عليكم، جاب الـ
+
+593
+00:41:48,180 --> 00:41:54,790
+هيك في الدراسة، مر عليكم بس بشكل مختلف، لأ، هي عبارة
+
+594
+00:41:54,790 --> 00:41:58,510
+عن الدالة المعرفة بالتجزئة، هي أقرب شيء لها، لدالة
+
+595
+00:41:58,510 --> 00:42:01,310
+ما يكون الدالة معرفة بالتجزئة، زي الـ absolute
+
+596
+00:42:01,310 --> 00:42:03,930
+value، الـ absolute value عبارة عن اتحاد دالتين
+
+597
+00:42:03,930 --> 00:42:07,170
+الدالة المحايدة والدالة دو طول بفصيلة بواحد، فهي
+
+598
+00:42:07,170 --> 00:42:10,230
+أقرب شيء له، تعدد الدالة بالتجزئة، نشوف مثال، خدي
+
+599
+00:42:10,230 --> 00:42:16,240
+نشوف مثال، let f from one two to zerofrom one to
+
+600
+00:42:16,240 --> 00:42:22,120
+zero، اه صحيح، هو الدوال المتعددة القاعدة، الدالة
+
+601
+00:42:22,120 --> 00:42:24,980
+المعرفة بالتجزئة أو الاقتران أو الدالة المتعددة
+
+602
+00:42:24,980 --> 00:42:29,520
+القاعدة، صحيح، فهذا
+
+603
+00:42:29,520 --> 00:42:34,140
+أقرب موضوع له أو يمكن هو بالظبط يعني الدالة متعددة
+
+604
+00:42:34,140 --> 00:42:34,760
+القاعدة
+
+605
+00:42:38,870 --> 00:42:44,310
+ففي المثال هيدينا دلتين وبدنا نحسب الاتحاد
+
+606
+00:42:44,310 --> 00:42:47,770
+بدنا نحسب الاتحاد وبعدين نشوف هل الاتحاد بيتم
+
+607
+00:42:47,770 --> 00:42:50,290
+function ولا بيتمش؟ لأن الاتحاد كلنا عملية على
+
+608
+00:42:50,290 --> 00:42:54,690
+مجموعات ونتعامل كمجموعات، هل بنحافظ عليها تكون دالة
+
+609
+00:42:54,690 --> 00:43:04,370
+ولا لأ؟ فعنا مثال في عندنا دلتين الـ F مديناها أزواج
+
+610
+00:43:04,370 --> 00:43:17,830
+مرتبة (1,0)، (2,0) والـ G (2,5)، (3,5)، طبعًا بقول
+
+611
+00:43:17,830 --> 00:43:21,870
+جيب الاتحاد بقولي find the union وبعدين بقولي هل
+
+612
+00:43:21,870 --> 00:43:26,230
+هو function ولا لأ؟ طبعًا الاتحاد مش أسهل من هيك، إيش
+
+613
+00:43:26,230 --> 00:43:32,860
+عليا احطهم مع بعض، أجمّعهم، فطبعًا بالدبدبة (1,0) و (2,0) و
+
+614
+00:43:32,860 --> 00:43:35,840
+هذا الـ answer موجود ومش موجود بكتبه، ولو الطابق
+
+615
+00:43:35,840 --> 00:43:40,680
+الشمالي بكتبه (2,5) و (3,5)، فالاتحاد كان اتحاد
+
+616
+00:43:40,680 --> 00:43:46,440
+مجموعات تمامًا، ما فيش أي اختلاف، تمام؟ فالسؤال هل هذه
+
+617
+00:43:46,440 --> 00:43:51,180
+function؟ لأ، لأن الاتنين مرتبطة ببعض، تاني، اه هذه هي
+
+618
+00:43:51,180 --> 00:43:55,240
+هي الاختلاف، فالاتحاد فشل، فداش، it is not a
+
+619
+00:43:55,240 --> 00:44:05,540
+function، it is not a function، ليش؟ since عنا اتنين
+
+620
+00:44:05,540 --> 00:44:10,100
+زيرو تنتمي للـ F Union G اللي ممكن نسميها H and
+
+621
+00:44:10,100 --> 00:44:17,260
+(2,5) تنتمي للـ F Union G، لكن طبعًا إيش الـ zero
+
+622
+00:44:17,260 --> 00:44:22,140
+لا تساوي خمسة، اه فهنا احنا أخدنا اتحاد أي دلتين
+
+623
+00:44:22,140 --> 00:44:25,180
+بقدر أجيب بالاتحاد تبعه لأنه كمجموعات لكن هل بتبقى
+
+624
+00:44:25,180 --> 00:44:32,040
+function ولا لأ؟ هذا سؤال آخر، وهنا فشل الاتحاد، و
+
+625
+00:44:32,040 --> 00:44:37,560
+طبعًا هذا هو دالة من وين؟ لو أخدت اتحاد المجموعة الـ
+
+626
+00:44:37,560 --> 00:44:42,940
+dominant، اه اتحاد التاني مع بعض، طلعت الـ dominant
+
+627
+00:44:42,940 --> 00:44:46,460
+طبعًا 1 و 2 و 3 وبيساوى اتحاد المجموعة
+
+628
+00:44:46,460 --> 00:44:49,760
+الثانية، مش مش مش مشكلة، هذا الشرط مش هو المهم، أتوقع أنه
+
+629
+00:44:49,760 --> 00:44:56,360
+مش هذا الأساس، تمام؟ نشوف كمان مثال، نشوف كمان مثال
+
+630
+00:44:56,360 --> 00:45:00,280
+نشوف
+
+631
+00:45:00,280 --> 00:45:07,440
+مثال ثاني، هذا المثال الأول برضه مدينا function، كبّر
+
+632
+00:45:07,440 --> 00:45:14,400
+الأمور شوية، وهي (1,1)، (2,4)، والـ G (3,5)، (4,5)، نوجد اتحاد
+
+633
+00:45:14,400 --> 00:45:19,420
+بدون مشاكل، هذه عملية سهلة، F Union G، ما علينا إلا
+
+634
+00:45:19,420 --> 00:45:30,240
+أن نجمّع العناصر مع بعض، (1,1)، (2,4)، صح؟ و (3,5)، (4,5)، (3,5)، (4,5)
+
+635
+00:45:30,240 --> 00:45:35,400
+هل هذه function؟ اه، هي function بس من وين لوين؟
+
+636
+00:45:35,400 --> 00:45:43,300
+من اتحادهم، اه، it is a function from من وين لوين؟
+
+637
+00:45:44,060 --> 00:45:50,020
+من 1، 2، 3، 4 إلى وين؟ 1، 4، 5، طبعًا تفرّجش
+
+638
+00:45:50,020 --> 00:45:54,300
+احنا ممكن نآخد اتحاد، احنا كانت من 1 لـ 4 وإيش؟
+
+639
+00:45:54,300 --> 00:45:58,300
+لخمسة، هي إيش تزداد الصور؟ تدي 1، 4، الصور و 5، 
+
+640
+00:45:58,300 --> 00:46:02,340
+و 5، فعلا من اتحادها، فهي فعلا function، حافظنا على
+
+641
+00:46:02,340 --> 00:46:07,260
+إنها function، فهنا اه، طبعًا ما فيش مشكلة إن عنصرين
+
+642
+00:46:07,260 --> 00:46:10,560
+يروحوا لنفس الصورة، أشهر مثال الدالة التربيعية، تديك
+
+643
+00:46:10,560 --> 00:46:12,220
+السالب والموجب، نفس الصورة.
+
+644
+00:46:16,090 --> 00:46:21,050
+فإذا الشاهد من المثالين أن الاتحاد بقدر أحسبه بشكل
+
+645
+00:46:21,050 --> 00:46:24,110
+عام، لكن هل بيتم function أو لا، ده سؤال آخر، ممكن
+
+646
+00:46:24,110 --> 00:46:28,970
+يبقى وممكن لأ، خلينا نآخد مثال أشهر من الـ calculus
+
+647
+00:46:30,770 --> 00:46:34,990
+من الـ calculus، الـ F function من الفترة المفتوحة
+
+648
+00:46:34,990 --> 00:46:38,310
+سالب infinity لـ 1 للـ R، ومدينا إياها هي بتعدد
+
+649
+00:46:38,310 --> 00:46:41,370
+القاعدة، نحن نديكوا المثال الأقرب اللي بتعودين عليه
+
+650
+00:46:41,370 --> 00:46:46,810
+والتعريف الدالة 2X + 1، والـ G، فانا إيش هي؟ عند
+
+651
+00:46:46,810 --> 00:46:49,650
+الـ R قصّيتها نصين، عرفت على الجزء الأول من سالب
+
+652
+00:46:49,650 --> 00:46:53,870
+infinity لـ 1 بـ F ومن الـ G من 1 لـ infinity
+
+653
+00:46:53,870 --> 00:46:58,630
+given by X - 2، أوجد الاتحاد وهل بتكون function
+
+654
+00:46:58,630 --> 00:47:00,230
+ولا لأ
+
+655
+00:47:02,670 --> 00:47:05,970
+Solution، فطبعًا هنا صعب إن أكتب بنفس الطريقة واحنا
+
+656
+00:47:05,970 --> 00:47:11,190
+زي ما حكينا إن الواحد إيش هو؟ ليس إلا إيش؟ للدالة
+
+657
+00:47:11,190 --> 00:47:15,910
+المعرفة بمتعددة القاعدة، أول شيء F Union G بيصير
+
+658
+00:47:15,910 --> 00:47:20,950
+دالة من وين لوين؟ من اتحاد المجالين، من كل R إلى كل
+
+659
+00:47:20,950 --> 00:47:24,510
+R، أو إيش كمان؟ بدنا نشوف انا هذه من وين لوين؟ أو إيش
+
+660
+00:47:24,510 --> 00:47:27,170
+بدنا بدنا نعرف الدالة، بدنا الـ domain وبدنا المجال
+
+661
+00:47:27,170 --> 00:47:32,870
+المقابل، بدنا القاعدة، فبدنا نكتب F Union G of X إيش
+
+662
+00:47:32,870 --> 00:47:38,690
+بتساوي؟ لها قاعدتين، فهي متعددة القاعدة، فهي بتتعرف
+
+663
+00:47:38,690 --> 00:47:45,390
+2X + 1 إذا الـ X شمالها أصغر من 1، اللي هي تنتمي
+
+664
+00:47:45,390 --> 00:47:50,390
+من سالب infinity لـ 1، مظبوط؟ وتعريفها X - 2
+
+665
+00:47:50,390 --> 00:47:55,290
+إذا كانت الـ X شمالها في الفترة من 1 إلى ما
+
+666
+00:47:55,290 --> 00:48:00,970
+لا نهاية، من 1 إلى ما لا نهاية، نتأكد بس، نتأكد
+
+667
+00:48:06,530 --> 00:48:12,110
+اه، هذه function مباشرة، هذه function، وكل عنصر له
+
+668
+00:48:12,110 --> 00:48:16,430
+صورة واحدة، لأن الـ F والـ G functions، طب هل في عنصر
+
+669
+00:48:16,430 --> 00:48:20,350
+كان مشترك بينهم ليصله صورتين؟ لأ، بما أنه أخذ أي
+
+670
+00:48:20,350 --> 00:48:23,350
+عنصر، إذا كان في domain الـ F فله صورة واحدة، وإذا
+
+671
+00:48:23,350 --> 00:48:25,230
+كان في domain الـ G فله صورة واحدة، فهذه فعلا
+
+672
+00:48:25,230 --> 00:48:32,420
+function، it is a function، it is a function، اه، فهنا
+
+673
+00:48:32,420 --> 00:48:37,340
+زي ما حكينا الشاهد إن كاتحاد ما فيش مشاكل بقدر
+
+674
+00:48:37,340 --> 00:48:40,800
+أجيب اتحاد أي دالتين كمجموعات أو كـ relation، لكن
+
+675
+00:48:40,800 --> 00:48:43,940
+السؤال هل بدأ بالدب،  become function ولا لأ؟ واضح
+
+676
+00:48:43,940 --> 00:48:48,380
+أنه مش دائمًا، بدنا شروط إضافية، تمام؟ نوقف هنا إن شاء
+
+677
+00:48:48,380 --> 00:48:49,220
+الله، المرة الجاية بنكمل
diff --git a/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/1HKBtNyYh7U_raw.srt b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/1HKBtNyYh7U_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2d16cddc36efb4ae09c738089d298fee9541e99c
--- /dev/null
+++ b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/1HKBtNyYh7U_raw.srt
@@ -0,0 +1,1248 @@
+1
+00:00:05,210 --> 00:00:07,870
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:07,870 --> 00:00:12,190
+وبركاته هنكمل في مادة تصميم الألات اتنين هنكمل
+
+3
+00:00:12,190 --> 00:00:19,430
+chapter ال wire rope احنا استعرضنا طريقة الحسابات
+
+4
+00:00:19,430 --> 00:00:28,710
+و تصميم ال wire ropes هنحل example ال
+
+5
+00:00:28,710 --> 00:00:37,090
+example given 6 في 19 monitor steelيعني عندي ال
+
+6
+00:00:37,090 --> 00:00:42,750
+standard عندي ستة في
+
+7
+00:00:42,750 --> 00:00:51,330
+تسعتاش monitor monitor
+
+8
+00:00:51,330 --> 00:00:56,890
+steel ماعطيني
+
+9
+00:00:56,890 --> 00:01:01,210
+ال strength ال SU متين
+
+10
+00:01:01,210 --> 00:01:04,310
+و أربعين KPSI
+
+11
+00:01:07,300 --> 00:01:13,980
+wire rope develop expressions for the rope tension
+
+12
+00:01:13,980 --> 00:01:23,540
+fatigue
+
+13
+00:01:23,540 --> 00:01:25,860
+tension
+
+14
+00:01:37,050 --> 00:01:50,530
+equivalent bending tension FB and
+
+15
+00:01:50,530 --> 00:01:52,430
+fatigue factor of safety
+
+16
+00:02:02,610 --> 00:02:06,210
+four five hundred three hundred five three one
+
+17
+00:02:06,210 --> 00:02:21,950
+point five foot يعني طول الحبل one
+
+18
+00:02:21,950 --> 00:02:26,690
+ton cash and load mine host الوزن W capital
+
+19
+00:02:31,300 --> 00:02:36,440
+واحد طن With
+
+20
+00:02:36,440 --> 00:02:42,300
+a
+
+21
+00:02:42,300 --> 00:02:45,080
+starting acceleration of two feet per second
+
+22
+00:02:45,080 --> 00:02:55,300
+squared ال A The
+
+23
+00:02:55,300 --> 00:02:57,380
+chief diameter دي capital
+
+24
+00:03:01,660 --> 00:03:11,380
+بتساوي نينو سبعين انش بدو
+
+25
+00:03:11,380 --> 00:03:20,020
+expression لل F T عندنا
+
+26
+00:03:20,020 --> 00:03:27,480
+اول شهومة اعطينا ال N F بساوي بساوي
+
+27
+00:03:27,480 --> 00:03:28,120
+F F
+
+28
+00:03:32,040 --> 00:03:39,180
+minus FB على
+
+29
+00:03:39,180 --> 00:03:48,440
+FT وال
+
+30
+00:03:48,440 --> 00:03:55,000
+FB بتساوي
+
+31
+00:03:55,000 --> 00:03:56,060
+ER
+
+32
+00:04:00,530 --> 00:04:09,170
+فى D ال wire فى ال AM على
+
+33
+00:04:09,170 --> 00:04:15,910
+D capital وال
+
+34
+00:04:15,910 --> 00:04:21,010
+FF بالساوية
+
+35
+00:04:21,010 --> 00:04:24,430
+P
+
+36
+00:04:24,430 --> 00:04:26,770
+على SU
+
+37
+00:04:30,990 --> 00:04:43,190
+فى S U D Capital D Small على اتنين وال
+
+38
+00:04:43,190 --> 00:04:52,230
+F T سوى
+
+39
+00:04:52,230 --> 00:04:57,050
+W على
+
+40
+00:04:57,050 --> 00:05:00,190
+M زائد
+
+41
+00:05:10,720 --> 00:05:27,720
+وال جي عندى سواء 32 الأهم
+
+42
+00:05:27,720 --> 00:05:34,820
+عدد الإحبال طيب
+
+43
+00:05:34,820 --> 00:05:37,820
+خلنا نضع الموضوع تهدأ على ال excel sheet اللى
+
+44
+00:05:37,820 --> 00:05:38,360
+عملناها
+
+45
+00:05:49,670 --> 00:05:54,130
+احنا أولش عندنا ستة وتسعتاش ال standard صح؟ معناته
+
+46
+00:05:54,130 --> 00:06:12,470
+هحكي هذا كان input عندي صح؟ هذا إيش input الآن
+
+47
+00:06:12,470 --> 00:06:17,650
+ال weight of wire rope per foot من ال table سبعتاش
+
+48
+00:06:17,650 --> 00:06:24,160
+أربع عشرين هذا حسابهذا المفروض يكون ال diameter of
+
+49
+00:06:24,160 --> 00:06:33,140
+rope قرار صح قرار مصمم خلّيني أعطيه لون لون تاني
+
+50
+00:06:33,140 --> 00:06:37,220
+هذا قرار لأن هذا معلومات مستخرجة عندك weight of
+
+51
+00:06:37,220 --> 00:06:46,720
+wire rope 6 في 19 6 في 19 1.6 D تربيع
+
+52
+00:06:49,640 --> 00:06:53,000
+انا هنفرض القطر مثلا واحد انش هتكون واحد ستة وان
+
+53
+00:06:53,000 --> 00:07:02,180
+عشرة هذه المعادلة في دي تربيع هذه تحسب من تابل
+
+54
+00:07:02,180 --> 00:07:11,420
+سبعتاش أربعة وعشرين ال minimum chief diameter من
+
+55
+00:07:11,420 --> 00:07:16,530
+أربعة وعشرينأو سبعة و عشرين صح؟ الأربعة و عشرين
+
+56
+00:07:16,530 --> 00:07:19,410
+بيحكي من أربعة و عشرين لأربعة .. من ستة و عشرين
+
+57
+00:07:19,410 --> 00:07:23,890
+لأربعة و تلاتين يعني تلاتين دي نروح على سبعة و
+
+58
+00:07:23,890 --> 00:07:33,630
+عشرين تطلع كام؟ تلاتين دي معناته احنا هنكون عنده
+
+59
+00:07:33,630 --> 00:07:37,850
+تلاتين في الواحد تلاتين
+
+60
+00:07:39,910 --> 00:07:47,850
+ال بترشيف ديامتر من تابل سبعتاش سبعة و عشرين خمس و
+
+61
+00:07:47,850 --> 00:07:51,490
+أربعين بس هو معطين ال .. معطين ال دي كابتا اللي هو
+
+62
+00:07:51,490 --> 00:07:56,390
+ال بترشيف دي خمس و أربعين اه هذا معلوم مستخرج من
+
+63
+00:07:56,390 --> 00:08:01,470
+تابل سبعة و عشرين اللي هي خمس و أربعين الدي
+
+64
+00:08:12,900 --> 00:08:20,960
+طيب ال material monitor steel الان ال size of
+
+65
+00:08:20,960 --> 00:08:23,720
+outer wires بنروح على ال table سبعتاشر أربعة و
+
+66
+00:08:23,720 --> 00:08:30,200
+عشرين ال
+
+67
+00:08:30,200 --> 00:08:35,380
+size of outer wires D على تسعة لل monitor steel
+
+68
+00:08:39,710 --> 00:08:45,410
+ال D عندي تتراوح بين ربع ل واحد و نص انش يعني في
+
+69
+00:08:45,410 --> 00:08:50,050
+حالة .. لأ ستة لتسعتاش هتكون بين ربع لاتنين و تلت
+
+70
+00:08:50,050 --> 00:08:56,550
+ارباع انش مظبوط ال monitor steel هتكون D على
+
+71
+00:08:56,550 --> 00:09:04,190
+التلتاش ل D على ستاش يعني هتكون تقريبا ستاش نقش
+
+72
+00:09:04,190 --> 00:09:09,430
+تلت تلتاش اكمتلاتة و احد و نص يعني دي على اربتاش و
+
+73
+00:09:09,430 --> 00:09:17,310
+نص تطلع المفروض monitor steel ال d wire point zero
+
+74
+00:09:17,310 --> 00:09:33,930
+six ستة سبعة table سبعتاش اربع و عشرين نتأكد طب
+
+75
+00:09:33,930 --> 00:09:36,210
+نشوف table سبعتاش سبعة و عشرين
+
+76
+00:09:39,450 --> 00:09:44,890
+أنا باخدها من سبعة و عشرين باسم point o67d small
+
+77
+00:09:44,890 --> 00:09:59,970
+يعني هذه هتكون ال table هذه طيب
+
+78
+00:09:59,970 --> 00:10:06,290
+ال modulus of elasticity للروب نشوف ال table
+
+79
+00:10:06,290 --> 00:10:07,430
+سبعتاشر أربعة و عشرين
+
+80
+00:10:13,460 --> 00:10:17,960
+أتناشر ميجا باون per square inch إذا أروح على سبعة
+
+81
+00:10:17,960 --> 00:10:25,580
+و عشرين برضه اتناش نفس الشيء
+
+82
+00:10:25,580 --> 00:10:30,700
+فهتكون عندي هذي برضه ال table سبعتاش أربعة و عشرين
+
+83
+00:10:30,700 --> 00:10:38,260
+ال strength of rope table
+
+84
+00:10:38,260 --> 00:10:39,760
+سبعتاش أربعة و عشرين
+
+85
+00:10:45,620 --> 00:10:57,160
+مية و ستة خلنا نشوف اللي هو سبعة
+
+86
+00:10:57,160 --> 00:11:00,620
+و عشرين ماتيني ال weight ال weight sheeter ال
+
+87
+00:11:00,620 --> 00:11:07,120
+diameter مش ماتينا اربع و عشرين هذا
+
+88
+00:11:07,120 --> 00:11:14,220
+لل rope اللي ماتينا احنا في السؤال متأكد
+
+89
+00:11:16,250 --> 00:11:20,110
+شكت ال wire ال
+
+90
+00:11:20,110 --> 00:11:23,970
+C ل ال wire
+
+91
+00:11:23,970 --> 00:11:27,130
+ال
+
+92
+00:11:27,130 --> 00:11:30,890
+R تسرق ل ال wire غير ال روب اللي يعطينا ال 300
+
+93
+00:11:41,560 --> 00:11:48,460
+طيب خلينا هذه تسعة نرجعلها بعد شوية هذه خليها شوية
+
+94
+00:11:48,460 --> 00:11:54,980
+هنعملها ash bold طيب
+
+95
+00:11:54,980 --> 00:12:05,480
+ال am table 1727 اللي
+
+96
+00:12:05,480 --> 00:12:10,600
+هي point 4D square point 4D
+
+97
+00:12:13,410 --> 00:12:19,470
+square الـ actual shift meter هذا أيه؟ معطو، هذا
+
+98
+00:12:19,470 --> 00:12:26,070
+input 72
+
+99
+00:12:26,070 --> 00:12:32,130
+انش ال
+
+100
+00:12:32,130 --> 00:12:36,230
+FB ال
+
+101
+00:12:36,230 --> 00:12:43,310
+FB اللي هو بيساوي ER D للwireفي ال AM على D
+
+102
+00:12:43,310 --> 00:12:47,630
+capital يعني ال FB هتكون تساوي ال ER هي ال ER
+
+103
+00:12:47,630 --> 00:12:55,050
+اتناش مظبوط و ال D wire هيها و ال AM هيها و ال D
+
+104
+00:12:55,050 --> 00:13:03,590
+capital اتنين و سبعين بحسب ال FB بحسب ال FB ال
+
+105
+00:13:03,590 --> 00:13:08,110
+weight at end of rope معطيني اكم واحد طن يعني
+
+106
+00:13:08,110 --> 00:13:12,160
+الفين pound هذا طن انجليزيالطن العادي بيسموه
+
+107
+00:13:12,160 --> 00:13:19,340
+metric ton metric ton هي ده الفين الفين pound هد
+
+108
+00:13:19,340 --> 00:13:28,380
+ايش معلوم input صح number
+
+109
+00:13:28,380 --> 00:13:36,700
+via ropes هد قرار صح عدد الإحبال انت هتتخذوا هد
+
+110
+00:13:36,700 --> 00:13:37,100
+قرار
+
+111
+00:13:47,600 --> 00:13:50,300
+ال maximum suspended length of rope هو ماعطيني يا
+
+112
+00:13:50,300 --> 00:13:59,160
+عياش خمسمية واحد تلاتين و نص خمسمية واحد تلاتين و
+
+113
+00:13:59,160 --> 00:14:02,800
+نص هذا
+
+114
+00:14:02,800 --> 00:14:10,940
+يا عياش input وال
+
+115
+00:14:10,940 --> 00:14:15,740
+acceleration input
+
+116
+00:14:15,740 --> 00:14:16,440
+صح؟
+
+117
+00:14:19,320 --> 00:14:29,000
+وهذه برضه input بحسب
+
+118
+00:14:29,000 --> 00:14:36,860
+ال Ft Ft بيسوى W على M زي ال WL في واحد زي A على G
+
+119
+00:14:36,860 --> 00:14:43,540
+بلزم نقاش أحسب W ال weight of wire اللي هي من ال
+
+120
+00:14:43,540 --> 00:14:46,060
+table سبعتاش أربعة و عشرين W
+
+121
+00:14:59,520 --> 00:15:03,700
+واحد بون ستة في دي square واحد بون ستة في دي
+
+122
+00:15:03,700 --> 00:15:09,220
+square نشوف سبعة وعشرين واحد بون ستة في دي ايش
+
+123
+00:15:09,220 --> 00:15:16,560
+square معناته هذي من ال table هذي اربعة وعشرين او
+
+124
+00:15:16,560 --> 00:15:25,520
+سبعة وعشرين هذي ايش ال D ال W بدك تحسب ال FT ال W
+
+125
+00:15:25,520 --> 00:15:29,030
+اللي هو خمسين واحد تلاتين ونصو ال M هي واحد او
+
+126
+00:15:29,030 --> 00:15:32,870
+اتنين او تلت عدد الإحبال و ال W اللي هي واحد point
+
+127
+00:15:32,870 --> 00:15:37,450
+ستة ال
+
+128
+00:15:37,450 --> 00:15:41,950
+W .. ال W هذه للألفين ton ألفين pound ألفين pound
+
+129
+00:15:41,950 --> 00:15:47,230
+و ال M عدد الإحبال ال W اللي هو ال weight per foot
+
+130
+00:15:47,230 --> 00:15:53,890
+للحبل و ال L طول الحبل فى واحد زاد ا على جيب انا
+
+131
+00:15:53,890 --> 00:15:57,310
+بتقدر انا عندى كل بيانات عشان احسب اياش ال FT مظبط
+
+132
+00:16:10,010 --> 00:16:14,690
+طيب ال minimum factor of state for wire ropes في
+
+133
+00:16:14,690 --> 00:16:20,630
+حالة .. هو احنا حاكينا أياش انه
+
+134
+00:16:20,630 --> 00:16:24,770
+الشغل
+
+135
+00:16:24,770 --> 00:16:28,670
+المناجم هذا هنرجع على tables لوراه
+
+136
+00:16:40,920 --> 00:16:45,880
+الـ hoisting خمسة minimum ده تقول ان انا عندي ال
+
+137
+00:16:45,880 --> 00:16:58,580
+fact minimum خمسة table سبعتاش خمسة و عشرين اللي
+
+138
+00:16:58,580 --> 00:17:04,540
+هو أيه؟ يعني انا ده هيكون ايهاش؟ قرار صح؟
+
+139
+00:17:12,870 --> 00:17:21,010
+طيب ال chief material هختار البكرة خلينا نعتبرها
+
+140
+00:17:21,010 --> 00:17:26,850
+cast steel خلينا نشوف
+
+141
+00:17:37,150 --> 00:17:42,330
+ع الأوزان هذه لأ همس مانفعش خشب لشغل لعبة لشغل و
+
+142
+00:17:42,330 --> 00:17:56,490
+بدك تشيل جرد المي حاجات زي هيك بس اه
+
+143
+00:17:56,490 --> 00:18:05,240
+انا خدت cast steelال .. ال .. ال maximum اللي هو
+
+144
+00:18:05,240 --> 00:18:08,300
+ال bearing pressure تسعمية ال maximum اللي هو ال
+
+145
+00:18:08,300 --> 00:18:17,860
+pressure تسعمية PSI كأس
+
+146
+00:18:17,860 --> 00:18:25,160
+steel أنا عامله كأس steel هذا برضه ايش قرار
+
+147
+00:18:31,450 --> 00:18:39,410
+الـ maximum اللي هو ال pressure في الكاس ستيل ستة
+
+148
+00:18:39,410 --> 00:18:53,870
+في تسعتاش تسعمائة أنا مقارنه بتسعمائة ال
+
+149
+00:18:53,870 --> 00:19:01,290
+ultimate tensile strength of wireاللي احنا حاكينا
+
+150
+00:19:01,290 --> 00:19:04,430
+سواء ال read ما أعطيانا عشان كده بطلت اللي لازمها
+
+151
+00:19:04,430 --> 00:19:11,550
+ده ماكناش شايفين هو صبوط هاي بيعطيني ال SEO اتين
+
+152
+00:19:11,550 --> 00:19:21,790
+و اربعين ولا تلاتمية؟ اتين و اربعين صح؟ اه
+
+153
+00:19:21,790 --> 00:19:23,210
+ال wire أكبر من ال rock
+
+154
+00:19:26,470 --> 00:19:33,250
+لأن جزء من ال strength بيصير بتروح بال friction
+
+155
+00:19:33,250 --> 00:19:37,890
+بينهم لأن في strength وفي stress، مين بيشيل ال
+
+156
+00:19:37,890 --> 00:19:43,310
+stress أكتر؟ ال wire ولا الحبل؟ الحبل أكتر، بس ال
+
+157
+00:19:43,310 --> 00:19:47,850
+strength لو عملتله tensile test ال strength .. ال
+
+158
+00:19:47,850 --> 00:19:50,670
+strength بتاعة اللي انت ماتيده properly هتكون ال
+
+159
+00:19:50,670 --> 00:19:51,890
+rope أقل من ال wire
+
+160
+00:20:06,010 --> 00:20:11,470
+هو تنساش فيه twisting effect، twisting effect هذا
+
+161
+00:20:11,470 --> 00:20:17,070
+بضعف، يعني فيه هو إردق إجهدات مخزنة، فيه إردق
+
+162
+00:20:17,070 --> 00:20:18,410
+إجهدات مخزنة نتيجة لل twisting
+
+163
+00:20:22,190 --> 00:20:24,890
+طيب ال .. ال ultra tensile strength هذه كانت عندي
+
+164
+00:20:24,890 --> 00:20:30,530
+ايش input صح
+
+165
+00:20:30,530 --> 00:20:35,330
+ال
+
+166
+00:20:35,330 --> 00:20:36,630
+number of pins to failure
+
+167
+00:20:55,040 --> 00:21:05,620
+أنا عندى ستة فى تسعة عشر يعنى
+
+168
+00:21:05,620 --> 00:21:14,360
+لو أخدت هنطلع تقريبا
+
+169
+00:21:14,360 --> 00:21:19,380
+ل point تمانية ما هو ال life بتحدد إيهاش point
+
+170
+00:21:19,380 --> 00:21:22,200
+تمانية مليون
+
+171
+00:21:24,260 --> 00:21:33,900
+الان هتعطيني P على SU واحد و نص على ألف ال life
+
+172
+00:21:33,900 --> 00:21:37,280
+انا بدي ال life مثلا تمام عشرة لو بدي ال life مثلا
+
+173
+00:21:37,280 --> 00:21:44,060
+تلاتة من عشرة انه ستة و ستاش هي تلاتة من عشرة بس
+
+174
+00:21:44,060 --> 00:21:48,320
+يعني دي هاي ايش ال P على SU خلينا نحكي اللي انا
+
+175
+00:21:48,320 --> 00:21:52,960
+بدي اعتبرها تمام من عشرة فبدي هتكون واحد و نص على
+
+176
+00:21:52,960 --> 00:21:53,340
+ألف
+
+177
+00:22:00,150 --> 00:22:07,710
+خلّيني أحكي هنا zero point eight هتكون
+
+178
+00:22:07,710 --> 00:22:12,170
+هذه واحد و نص على
+
+179
+00:22:12,170 --> 00:22:17,550
+الف هذه
+
+180
+00:22:17,550 --> 00:22:24,710
+فمن
+
+181
+00:22:24,710 --> 00:22:28,550
+pressure strength ratio اللي هيكون point o o واحد
+
+182
+00:22:28,550 --> 00:22:33,680
+خمسةطبيعي انت تفضل .. نعم .. اقنع معاك لبس الاول
+
+183
+00:22:33,680 --> 00:22:41,700
+واحد بصر واحد على الفرشان هاي
+
+184
+00:22:41,700 --> 00:22:46,780
+عندك تمانية من عشرة ومفقود بالاتنين .. صحيح .. نزل
+
+185
+00:22:46,780 --> 00:22:52,640
+على ستة على اتناش يعني عندك هنا واحد و نص .. واحد
+
+186
+00:22:52,640 --> 00:22:55,240
+point اربع .. يعني في الأول كان صح .. اه بصورة
+
+187
+00:22:55,240 --> 00:22:59,260
+مفقود .. اه اه .. ستة اتناش .. اه احنا هو اربعتاش
+
+188
+00:22:59,260 --> 00:23:10,340
+هو الصحاللي هو كانت الواحد
+
+189
+00:23:10,340 --> 00:23:15,000
+و نص طبعا طيب
+
+190
+00:23:15,000 --> 00:23:19,720
+اللي هو ال fatigue tension as well is a flexed
+
+191
+00:23:19,720 --> 00:23:27,980
+number of times ال FF هذا
+
+192
+00:23:27,980 --> 00:23:33,130
+ال FTحسبنا ال FB حسبنا ال FD و حسبنا ال FT لنحسب
+
+193
+00:23:33,130 --> 00:23:38,330
+ال FF ال FF اللي هي P على S U ال رد جيبناها في ال
+
+194
+00:23:38,330 --> 00:23:50,710
+S U فدي small دي capital على اتنين هذه ال FF هذي
+
+195
+00:23:50,710 --> 00:23:55,570
+ال number بالنسبالي هذي طبعا هذي إيش كانت قرار صح؟
+
+196
+00:24:01,560 --> 00:24:09,260
+طيب ال pressure ratio P على Su point 0014 ال FF
+
+197
+00:24:09,260 --> 00:24:13,560
+حسبناها من المعادلة هذه ال P على Su معروفة و ال Su
+
+198
+00:24:13,560 --> 00:24:19,300
+معروفة و D small و D cut على اتنين حسبناش ال
+
+199
+00:24:19,300 --> 00:24:25,180
+pressure ratio اللي حسبناه ال FF ال
+
+200
+00:24:25,180 --> 00:24:32,610
+NF اللي هو FF- FB على FT تطلع اتنين و نص معناته
+
+201
+00:24:32,610 --> 00:24:35,970
+لسه
+
+202
+00:24:35,970 --> 00:24:39,270
+مش
+
+203
+00:24:39,270 --> 00:24:43,770
+ايش ماوصلناش خمس معناته خليني ازود عدد الإحبال ال
+
+204
+00:24:43,770 --> 00:24:49,630
+M هاي نشوف هاي اتنين نشوف ايش بيصير معناها انا
+
+205
+00:24:49,630 --> 00:24:53,650
+طبعا الشغلات اللي عندي هلعب فيها ال rock diameter
+
+206
+00:24:53,650 --> 00:24:58,670
+دي small و عدد الإحبالهيصار تلاتة بقون تمانية
+
+207
+00:24:58,670 --> 00:25:09,330
+تمانية اتنين طب خلي تلاتة حبال اربعة
+
+208
+00:25:09,330 --> 00:25:18,070
+بقون سبعة اربعة يعني هتغير
+
+209
+00:25:18,070 --> 00:25:22,690
+شغلاتك كتير عندك او ممكن تغير اتنينبس انا حاليا
+
+210
+00:25:22,690 --> 00:25:26,450
+اسلب اغير ايش نفس الفكرة هتكون بس تنتبه لكل
+
+211
+00:25:26,450 --> 00:25:34,210
+الخطوات هكون اربعة لخمسة point تلاتة واحد تسعة
+
+212
+00:25:34,210 --> 00:25:43,640
+معناته انا لو اخترت robe اللي هو ستة في تسعة عشرال
+
+213
+00:25:43,640 --> 00:25:54,260
+روب ديامتر واحد انش بالزمن اربع احبال اربع احبال
+
+214
+00:25:54,260 --> 00:26:03,280
+في
+
+215
+00:26:03,280 --> 00:26:07,480
+الكتاب ايش بنسوي بنخلي
+
+216
+00:26:07,480 --> 00:26:08,020
+ال FB
+
+217
+00:26:14,640 --> 00:26:21,660
+بدلالة اللي هو ال rope diameter خلّي ال fb و ال ft
+
+218
+00:26:21,660 --> 00:26:30,320
+و ال ff و ال nf بدلالة number of ropes و قطر ال
+
+219
+00:26:30,320 --> 00:26:34,900
+rope two variables و حاطط for different rope
+
+220
+00:26:34,900 --> 00:26:44,260
+diameters حاطط ايش اللي هواعداد مختلفة ل .. لل
+
+221
+00:26:44,260 --> 00:26:48,920
+ropes و جايب كذا خيار يعني انا بأحكيلك لو كان
+
+222
+00:26:48,920 --> 00:26:52,740
+القطر كذا بيطلع عدد الإحبال كذا لو كان القطر اشي
+
+223
+00:26:52,740 --> 00:26:56,220
+تاني بيطلع عدد الإحبال كذا عشان ت satisfy اللي هو
+
+224
+00:26:56,220 --> 00:27:00,960
+factor of safety معين يعني
+
+225
+00:27:00,960 --> 00:27:08,180
+في .. اه في زيادة .. زيادة غريبة لإن كنت دايما 25
+
+226
+00:27:08,180 --> 00:27:13,140
+من 100 ال factor of safetyبيصل ال maximum .. بيصل
+
+227
+00:27:13,140 --> 00:27:17,780
+ال maximum و بعدين بنزل factor of safety بيصل ال
+
+228
+00:27:17,780 --> 00:27:25,220
+maximum و بعدين بنزل انا مش عند ال .. ال .. الكتاب
+
+229
+00:27:25,220 --> 00:27:30,100
+على الجهاز كمار جيتكوا يا اه طبعا مش linear اما
+
+230
+00:27:30,100 --> 00:27:32,900
+انت شايف المعادلات المعادلات مقتلان بعض مش linear
+
+231
+00:27:32,900 --> 00:27:36,880
+بيصل ال maximum و ال factor of safety و بعدين بنزل
+
+232
+00:27:39,950 --> 00:27:45,810
+التنين دي او و ال number of يعني انت ممكن تعمل
+
+233
+00:27:45,810 --> 00:27:51,190
+surface plot three-D plot تعمل محور ال X ال number
+
+234
+00:27:51,190 --> 00:27:56,190
+of ropes و المحور ال Y ال diameter .. ال rope ال
+
+235
+00:27:56,190 --> 00:28:02,710
+diameter و المحور Z ك indicator بتحكي الانقف بتطلع
+
+236
+00:28:02,710 --> 00:28:10,180
+عندك إياش surface three-D surfaceهو عشان ايه بيعمل
+
+237
+00:28:10,180 --> 00:28:15,420
+gradual و بيعطي مثلا ل .. مثلا لقطر معين عدد مختلف
+
+238
+00:28:15,420 --> 00:28:22,680
+من الحبال حد مع الكتاب على فلاشة هو لو .. لو غيرنا
+
+239
+00:28:22,680 --> 00:28:26,340
+في درامتها ال achieve بيصير العلاقة هتختلف لو صارت
+
+240
+00:28:26,340 --> 00:28:28,920
+تغيير في ال achieve يعني كل ما ازيد ال D ل small
+
+241
+00:28:28,920 --> 00:28:35,240
+او ازيد ال D كتير هتختلفما بحكيلك انك مش بضروري
+
+242
+00:28:35,240 --> 00:28:39,220
+تزود ده ممكن ان انت تزود الاشي و تكلفك كتير و ال
+
+243
+00:28:39,220 --> 00:28:43,080
+factor of safety ينزل صحيح بيصير تأثيره سلبي اه
+
+244
+00:28:43,080 --> 00:28:46,680
+بيصير تأثيره سلبي فبيصل ال maximum يعني ان انا
+
+245
+00:28:46,680 --> 00:28:48,360
+تزيد من ال maximum يعني ان انا قبل ال maximum
+
+246
+00:28:48,360 --> 00:28:54,260
+بيكون اقل بعد ال maximum بيكون ايش اقل برضه ازاي
+
+247
+00:28:54,260 --> 00:28:59,840
+عندك تطلع على عنصر التكلفة عندك تعمل عنصر التكلفة
+
+248
+00:29:00,620 --> 00:29:04,940
+يعني مين أرخص لأجيب كتر وير كبير و لا عدد أكبر عدد
+
+249
+00:29:04,940 --> 00:29:08,500
+الحبال لإنه هتعمل ال achieve بده تعمل إيش مجاري لل
+
+250
+00:29:08,500 --> 00:29:18,640
+.. للحبال بالظبط بالظبط
+
+251
+00:29:18,640 --> 00:29:25,180
+هيك و كم خلصنا ال .. الشبطر المحاضرة جاية في أي
+
+252
+00:29:25,180 --> 00:29:33,940
+سؤال واضح كيف ال processيعني ممكن احنا هنا عندك في
+
+253
+00:29:33,940 --> 00:29:38,840
+المعادلات ا
+
+254
+00:29:38,840 --> 00:29:55,600
+دي ا دي و function of دي صح؟ P على Su عندك هاي دي
+
+255
+00:29:55,600 --> 00:30:01,040
+عندك Fb وال D wire
+
+256
+00:30:03,820 --> 00:30:08,360
+برضه function of D some function of D و ال A M
+
+257
+00:30:08,360 --> 00:30:17,780
+function of D و التالي NF هكون some function of D
+
+258
+00:30:17,780 --> 00:30:27,780
+and M عشانك
+
+259
+00:30:27,780 --> 00:30:35,110
+يعني بتعمل جدول table بتحكي هي ال Dهي different
+
+260
+00:30:35,110 --> 00:30:40,350
+values of D هى
+
+261
+00:30:40,350 --> 00:30:51,350
+different values of M واحد
+
+262
+00:30:51,350 --> 00:31:02,910
+اتنين تلاتة اربع خمسة و بتعطي ايش بتعمل جدول ايش
+
+263
+00:31:02,910 --> 00:31:03,730
+بيسوي هو
+
+264
+00:31:07,930 --> 00:31:16,090
+احنا حكينا ال D ال D احنا حكينا واحد انش وعدد
+
+265
+00:31:16,090 --> 00:31:19,210
+الإحبال أربعة كم طلعنا ال factor of safety خمسة
+
+266
+00:31:19,210 --> 00:31:23,390
+point تلت اتنين بس خلينا نطلع لو كان عدد الإحبال
+
+267
+00:31:23,390 --> 00:31:29,490
+واحد و بدى يزود القطر factor of safety بزيد اتنين
+
+268
+00:31:29,490 --> 00:31:31,830
+point اتنين point سبعة و بعدين ببدى ينزل يعني وصل
+
+269
+00:31:31,830 --> 00:31:36,450
+ال maximum لو كان العدد اتنين
+
+270
+00:31:40,120 --> 00:31:47,100
+بصر ال maximum و بعدين بنزل لو كان عدد تلاتة بصر
+
+271
+00:31:47,100 --> 00:31:52,200
+ال maximum و بعدين بنزل لو العدد أربع هى maximum و
+
+272
+00:31:52,200 --> 00:31:59,160
+بعدين بنزل معناته لو أنا بدي مثلا يكون خمسة يعني
+
+273
+00:31:59,160 --> 00:32:08,940
+بظبطش ولا واحد يعني لأن بعد تالتة حبال يعني بظبط
+
+274
+00:32:08,940 --> 00:32:16,290
+عندكواحد، اتنين، تلاتة، اربعة، خمسة، احساس factor
+
+275
+00:32:16,290 --> 00:32:19,130
+of safety ايش؟ خمسة، فوق في الكتاب بنتبر factor of
+
+276
+00:32:19,130 --> 00:32:24,370
+safety ستة، ستة ال minimum ماخده، لو بدي احكي ستة
+
+277
+00:32:24,370 --> 00:32:27,070
+معناته هذا مظبوطش، هذا مظبوطش ع ال range اللي هو
+
+278
+00:32:27,070 --> 00:32:35,750
+عامله عند هنا هاي واحد، واحد، اتنين، تلاتة، اربعة،
+
+279
+00:32:35,750 --> 00:32:40,580
+خمسة، ستة، احساس factor of safety ستةيعني لو كنا
+
+280
+00:32:40,580 --> 00:32:49,580
+هنا هتختار قطر .. قطر وان ست اتنين خمسة و تلت
+
+281
+00:32:49,580 --> 00:32:58,480
+احبال او شكله زي هيك او قطر وان تلت سواء خمسة
+
+282
+00:32:58,480 --> 00:33:04,480
+واربع احبال طبعا
+
+283
+00:33:04,480 --> 00:33:08,420
+مافيش داعي اكمل هنا لان انا هزيد القطر و انا اتوقع
+
+284
+00:33:08,420 --> 00:33:17,850
+احسن خيارأو الخيارات المتعددة اي خيار هي اتنين
+
+285
+00:33:17,850 --> 00:33:23,950
+هو
+
+286
+00:33:23,950 --> 00:33:31,830
+طبعا عامل على شكل معدلات هي ال
+
+287
+00:33:31,830 --> 00:33:38,270
+FF as a function of D و FB as a function of Dو ال
+
+288
+00:33:38,270 --> 00:33:49,750
+Ft عملها ال Ft هي 224
+
+289
+00:33:49,750 --> 00:33:53,090
+على M زي ال point 903 دي square يعني عملها بتلاتة
+
+290
+00:33:53,090 --> 00:33:57,850
+ال D و M و
+
+291
+00:33:57,850 --> 00:34:10,350
+بعدين طلع ال N F بطلع المعادلة هذه D و Fو M D و M
+
+292
+00:34:10,350 --> 00:34:13,610
+لو بدي ايه وجبدي اللي هو اللي بيكون عندها maximum
+
+293
+00:34:13,610 --> 00:34:19,590
+باخد ال partial ال .. بالنسبة ل D و ال partial
+
+294
+00:34:19,590 --> 00:34:24,470
+بالنسبة ل M بس بعمل .. بعمل .. بحل معادلتين ال
+
+295
+00:34:24,470 --> 00:34:28,330
+partial بالنسبة ل D و ال partial بالنسبة ل M اول
+
+296
+00:34:28,330 --> 00:34:30,530
+معادل بيسوء لل صفر و المعادل تاني بيسوء لل صفر
+
+297
+00:34:30,530 --> 00:34:35,700
+بيكون عندى معادلتين ب D و Mبحسب D و M طبعا هتطلع
+
+298
+00:34:35,700 --> 00:34:40,420
+كثورة دي مظلوط يعني مش ال standard باخد اقرش او في
+
+299
+00:34:40,420 --> 00:34:44,500
+شي ده اعمل زيك بعمل جدول و خلاص عشان تجيب ال
+
+300
+00:34:44,500 --> 00:34:48,340
+maximum factor of safety لأ مش ال maximum factor
+
+301
+00:34:48,340 --> 00:34:51,500
+of safety انا عشان أجيب ال factor of safety اللي
+
+302
+00:34:51,500 --> 00:34:55,860
+بلبّي الاحتياج اللي انا او انا ال criteria انا
+
+303
+00:34:55,860 --> 00:34:57,740
+حاططها انا حاكي والله من دي factor of safety
+
+304
+00:34:57,740 --> 00:35:01,900
+minimum ستة يعني
+
+305
+00:35:01,900 --> 00:35:02,680
+الخيارات هذه
+
+306
+00:35:05,940 --> 00:35:11,960
+هذه كلها بتحقق بس بالزيادة
+
+307
+00:35:11,960 --> 00:35:18,680
+اللي هو
+
+308
+00:35:18,680 --> 00:35:21,660
+هذا ممكن هي هذا عساس factor of 36 لكن لو حكى والله
+
+309
+00:35:21,660 --> 00:35:25,620
+لأ انا من ال factor of 67 مينفعش يعني يا هذا يا
+
+310
+00:35:25,620 --> 00:35:30,460
+هذا يعني حسب انا ايش بده
+
+311
+00:35:36,440 --> 00:35:41,360
+في سؤال تانى هل لازم تحلوا مثال عشان تتعودوا عليه
+
+312
+00:35:41,360 --> 00:35:46,660
+بنتثأ بسرعة؟ هعطيكوا لعبكات تنكون خلصنا
+
diff --git a/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/20rGnqdh2-Y_postprocess.srt b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/20rGnqdh2-Y_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..129d3f6c08347bccc23c76b683ab45c5506c3d4e
--- /dev/null
+++ b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/20rGnqdh2-Y_postprocess.srt
@@ -0,0 +1,1556 @@
+1
+00:00:06,010 --> 00:00:09,030
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:09,030 --> 00:00:13,150
+وبركاته، هنكمل في مادة تصميم الألات، المحاضرة
+
+3
+00:00:13,150 --> 00:00:18,690
+الفاترة بدأنا نحكي عن ال design of flat built
+
+4
+00:00:18,690 --> 00:00:21,970
+drives، اتعرفنا على أنواع ال built drives، حكينا
+
+5
+00:00:21,970 --> 00:00:25,970
+عندنا أربع أنواع اللي هي flat built، عندنا round
+
+6
+00:00:25,970 --> 00:00:32,340
+built، عندنا V built و عندنا timing builtاتعرفنا
+
+7
+00:00:32,340 --> 00:00:35,020
+على ال geometric parameters لل flat built drives،
+
+8
+00:00:35,020 --> 00:00:37,620
+ال flat built drives مكوّن من بكرتين، واحد driver
+
+9
+00:00:37,620 --> 00:00:42,420
+واحد driven، وفي ال built اتعرفنا على ال center
+
+10
+00:00:42,420 --> 00:00:47,640
+distance، ال .. ال .. ال tangency point، الزوايا،
+
+11
+00:00:47,640 --> 00:00:50,580
+ال contact angle عند driver و ال contact angle عند
+
+12
+00:00:50,580 --> 00:00:54,000
+ال driven، في الحالتين، في حالة open built و في
+
+13
+00:00:54,000 --> 00:00:59,710
+حالة crossed builtأنا كان ممكن نعمل arrangement لل
+
+14
+00:00:59,710 --> 00:01:03,610
+.. لل police و ال built بحيث يكونوا ال driver او
+
+15
+00:01:03,610 --> 00:01:06,970
+ال driven يدوروا في نفس الاتجاه او في عكس الاتجاه
+
+16
+00:01:06,970 --> 00:01:10,070
+الحالة اللي احنا شايفينا فيها انها non-reversing
+
+17
+00:01:10,070 --> 00:01:12,190
+open built يعني ال driver و ال driven بدوروا في
+
+18
+00:01:12,190 --> 00:01:16,170
+نفس الاتجاه عند الحالة هذه crossed .. reversing
+
+19
+00:01:16,170 --> 00:01:20,330
+crossed built ال driver بدور عكس ال driven عند هنا
+
+20
+00:01:20,330 --> 00:01:24,370
+reversing open to drive ال driver بدور عكس ال ..
+
+21
+00:01:24,370 --> 00:01:31,490
+ال drivenمش بالضروري يكون عندي اللي هو ال two
+
+22
+00:01:31,490 --> 00:01:35,010
+poles في نفس المستوى، عندي عاملين ال two poles
+
+23
+00:01:35,010 --> 00:01:36,510
+زاوية 90 درجة
+
+24
+00:01:43,070 --> 00:01:47,570
+حكينا إنه ال .. ال .. نتيجة ال friction بتولد بين
+
+25
+00:01:47,570 --> 00:01:54,550
+ال built و ال pulley بيصير تغير في ال .. ال force
+
+26
+00:01:54,550 --> 00:01:58,330
+أو ال tension في الحبل اللي طبعا ال tension في
+
+27
+00:01:58,330 --> 00:02:04,470
+الحبل بيكون في ال .. نحكي ال tight side اللي هو F1
+
+28
+00:02:04,470 --> 00:02:07,810
+أكبر من ال slag side F2
+
+29
+00:02:10,020 --> 00:02:14,740
+و ال velocity ال V ال velocity في ال slack side
+
+30
+00:02:14,740 --> 00:02:18,100
+اقل من ال velocity في ال اش في ال tight side
+
+31
+00:02:23,000 --> 00:02:28,440
+أخدنا المرة الفاتتة segment من ال build ملامس لل
+
+32
+00:02:28,440 --> 00:02:35,280
+pulley segment عامل زاوية d theta فيه بتأثير لل
+
+33
+00:02:35,280 --> 00:02:39,160
+force DS اللي هي centrifugal force في عندى DN اللي
+
+34
+00:02:39,160 --> 00:02:43,120
+هي normal force من ال pulley على ال build في عندى
+
+35
+00:02:43,120 --> 00:02:47,280
+traction او friction اللي هي FDN في الشد في الحبل
+
+36
+00:02:48,090 --> 00:02:53,270
+اللي هو F و بعد زاوية D θ بتتغير بيصير F زائد D F
+
+37
+00:02:53,270 --> 00:02:59,190
+أخدنا summation لل forces باتجاه ال radial
+
+38
+00:02:59,190 --> 00:03:13,210
+direction وال
+
+39
+00:03:13,210 --> 00:03:19,360
+forces باتجاهالـ tangential direction باتجاه الـ
+
+40
+00:03:19,360 --> 00:03:27,280
+tangential direction أنا عندي هذه
+
+41
+00:03:27,280 --> 00:03:33,360
+ال radial وهذه
+
+42
+00:03:33,360 --> 00:03:33,980
+ال tangential
+
+43
+00:03:43,360 --> 00:03:55,820
+هذه F هذه F زائد DF وهذه DS وهذه
+
+44
+00:03:55,820 --> 00:04:02,240
+DN وهذه ال
+
+45
+00:04:02,240 --> 00:04:05,300
+element
+
+46
+00:04:20,310 --> 00:04:28,170
+هذه الزاوية دي ثيتا وهذه
+
+47
+00:04:28,170 --> 00:04:40,770
+دي ثيتا على اتنين اكيد
+
+48
+00:04:40,770 --> 00:04:44,390
+الصماش من تجاه ال radial direction الصماش لل
+
+49
+00:04:44,390 --> 00:04:47,830
+forces من تجاه ال radial direction يستوى ال zero
+
+50
+00:04:49,520 --> 00:04:55,240
+بالساوية DS زائد
+
+51
+00:04:55,240 --> 00:05:01,380
+DN ناقص
+
+52
+00:05:01,380 --> 00:05:04,600
+F
+
+53
+00:05:04,600 --> 00:05:22,350
+التي هي Dθ على 2 minus F زائد DF Dθ على 2تطلع ان
+
+54
+00:05:22,350 --> 00:05:28,690
+DN بتساوي
+
+55
+00:05:28,690 --> 00:05:32,850
+F
+
+56
+00:05:32,850 --> 00:05:38,790
+Dθ minus DS
+
+57
+00:05:45,310 --> 00:05:49,490
+طيب لو خدنا summation forces بتجاه ال tangential
+
+58
+00:05:49,490 --> 00:05:53,150
+summation summation
+
+59
+00:05:53,150 --> 00:05:59,730
+forces بتجاه ال tangential بالساوية
+
+60
+00:05:59,730 --> 00:06:09,970
+zero هتساوي F
+
+61
+00:06:09,970 --> 00:06:23,390
+زي دي Fcos dθ على اتنين minus
+
+62
+00:06:23,390 --> 00:06:35,370
+F cos dθ على اتنين minus
+
+63
+00:06:35,370 --> 00:06:39,990
+F dN
+
+64
+00:06:47,390 --> 00:06:53,830
+يعني انا هسير عنده zero ال .. دي theta على اتنين
+
+65
+00:06:53,830 --> 00:06:59,110
+صغيرة كتير فكل كوسين واحد كوسينها تقريبا واحد يعني
+
+66
+00:06:59,110 --> 00:07:03,230
+انا هكون عندي بتروح
+
+67
+00:07:03,230 --> 00:07:18,850
+عندي F cosine F F زائد DF minus F minus F DNيعني
+
+68
+00:07:18,850 --> 00:07:33,610
+هصفه دي اف بالساوية اف دي ان هذا معادلة واحد هذا
+
+69
+00:07:33,610 --> 00:07:37,190
+معادلة اتنين بنعود عن دي ان في المعادلة واحد بس
+
+70
+00:07:37,190 --> 00:07:41,470
+يعني دي اف بالساوية
+
+71
+00:07:41,470 --> 00:07:44,810
+اف
+
+72
+00:07:44,810 --> 00:07:47,930
+اف دي ثيتا
+
+73
+00:07:52,950 --> 00:08:02,650
+minus FDS احنا DS سابق انحكيه انا اشو الساوي M
+
+74
+00:08:02,650 --> 00:08:14,390
+R Square Omega Square minus FM R Square Omega
+
+75
+00:08:14,390 --> 00:08:14,830
+Square
+
+76
+00:08:18,620 --> 00:08:31,140
+الان نقسم على دي ثيتا يعني دي F على دي ثيتا ناقص F
+
+77
+00:08:31,140 --> 00:08:38,560
+F so minus F M R Square Omega Square
+
+78
+00:08:50,820 --> 00:09:01,900
+هذه اللي هي هذه يعني طيب
+
+79
+00:09:01,900 --> 00:09:09,260
+هذه معادلة تفاضلية خطية
+
+80
+00:09:09,260 --> 00:09:16,520
+من الدرجة الأولىnon homogeneous يعني
+
+81
+00:09:16,520 --> 00:09:21,160
+هتكون ال total solution هو ال homogeneous solution
+
+82
+00:09:21,160 --> 00:09:24,720
+زاد ال particular solution او ال non homogeneous
+
+83
+00:09:24,720 --> 00:09:31,720
+يعني هتكون المعادلة حالها اللي هي F او A
+
+84
+00:09:31,720 --> 00:09:38,300
+exponential لل F theta
+
+85
+00:09:43,760 --> 00:09:50,680
+زائد M R Square Omega Square هدا ال solution بتاع
+
+86
+00:09:50,680 --> 00:10:03,040
+المعادلة عن
+
+87
+00:10:03,040 --> 00:10:08,800
+حيث ثيتا عند ثيتا وستاوة سفر at
+
+88
+00:10:13,690 --> 00:10:19,490
+ثيتا بيستوا صفر بتكون ان دي ال F بيستوا ايش ال F2
+
+89
+00:10:19,490 --> 00:10:27,330
+بنعود غير ان بثيتا صفر بيستوا ان دي F2 ال
+
+90
+00:10:27,330 --> 00:10:34,670
+exponential ل 0 و 1 صح؟ بيستوا A زاد MR Square
+
+91
+00:10:34,670 --> 00:10:42,450
+Omega Square يعني ال A بتكون F2 minus MR Square
+
+92
+00:10:43,980 --> 00:10:49,240
+وميجا سكوير يعني
+
+93
+00:10:49,240 --> 00:10:54,720
+بالصورة ال F بالساوية
+
+94
+00:10:54,720 --> 00:11:01,340
+اللي هي F اتنين minus MR square اوميجا سكوير
+
+95
+00:11:01,340 --> 00:11:09,380
+exponential لل F ثاتا زائد
+
+96
+00:11:11,960 --> 00:11:33,060
+م ر سكوير اوميجا سكوير طيب
+
+97
+00:11:33,060 --> 00:11:43,570
+لما ال theta تسوى fiveبتكون ال F بساوية F واحد صح؟
+
+98
+00:11:43,570 --> 00:11:52,650
+لما ال theta بساوية فاي بتكون ال F بساوية F واحد
+
+99
+00:11:52,650 --> 00:11:58,290
+يعني مثلا دي F واحد خلينا ال let نخلي نسمي ال
+
+100
+00:11:58,290 --> 00:12:04,730
+central for F C بساوية M R Square Omega Square
+
+101
+00:12:04,730 --> 00:12:17,760
+هتكون F واحدف اف اتنين فاف
+
+102
+00:12:17,760 --> 00:12:31,820
+اتنين ماينوس اف سي في ال exponential للف فاي زاد
+
+103
+00:12:31,820 --> 00:12:32,500
+الف سي
+
+104
+00:12:37,620 --> 00:12:41,880
+يعني لجهة ال Fc على الجهة التانية بيصير F1 minus
+
+105
+00:12:41,880 --> 00:12:46,260
+Fc
+
+106
+00:12:46,260 --> 00:12:58,540
+عندي هنا F1 minus Fc بيستوى F2 minus Fc في ال
+
+107
+00:12:58,540 --> 00:13:00,980
+exponential لل F
+
+108
+00:13:03,720 --> 00:13:09,220
+يعني انا هكون عندى F1 اقسم الطرفين على F2-Fc فانا
+
+109
+00:13:09,220 --> 00:13:21,900
+عندى F1-Fc على F2-Fc ساوى ال exponential لل F5
+
+110
+00:13:42,720 --> 00:13:59,160
+المعادلة هذه هذه
+
+111
+00:13:59,160 --> 00:14:05,300
+المعادلة لو طرحت منها أف اتنين طرحت من هنا أف
+
+112
+00:14:05,300 --> 00:14:10,020
+اتنين و من هنا أف اتنين بأثر؟ بأثرش يعني انا هاكل
+
+113
+00:14:10,020 --> 00:14:10,480
+عندي هنا
+
+114
+00:14:16,240 --> 00:14:22,240
+ف1-ف2 بالساوية
+
+115
+00:14:22,240 --> 00:14:26,280
+ف2
+
+116
+00:14:26,280 --> 00:14:35,580
+-فC في الـ exponential ففاي
+
+117
+00:14:39,520 --> 00:14:51,160
+زائد fc minus f2 يعني
+
+118
+00:14:51,160 --> 00:14:57,020
+هتكون اخليها بصيغة يعنى f2
+
+119
+00:14:57,020 --> 00:15:05,720
+minus fc في ال exponential لل FI minus
+
+120
+00:15:08,190 --> 00:15:18,010
+ف2-فC واخد
+
+121
+00:15:18,010 --> 00:15:30,230
+ف2-فC عام مشترك and exponential للف5
+
+122
+00:15:30,230 --> 00:15:36,850
+-1 ومن
+
+123
+00:15:36,850 --> 00:15:47,540
+هذهعندي ال F2 minus ال Fc بالسواء
+
+124
+00:15:47,540 --> 00:15:56,820
+F1 minus Fc على ال exponential لل F فاين من هذه
+
+125
+00:15:56,820 --> 00:16:05,950
+المعادلة اعوض هنا يعني حسينا عندي F1- F2 هتكون سوى
+
+126
+00:16:05,950 --> 00:16:10,130
+F1
+
+127
+00:16:10,130 --> 00:16:20,370
+- Fc في الاكسبونانشال
+
+128
+00:16:20,370 --> 00:16:31,710
+لل F5-1 على الاكسبونانشال F5
+
+129
+00:16:34,340 --> 00:16:40,180
+ليه هذه العلاقة؟ هذه بنسميها ال bending equation
+
+130
+00:16:40,180 --> 00:16:52,400
+هذه ال bending equation إذا
+
+131
+00:16:52,400 --> 00:16:58,460
+كانت البكرة اللي قطرة دي small بتدور بسرعة زاوية N
+
+132
+00:16:58,460 --> 00:17:06,790
+لأن هي وحدتها بال RPMان روتيشن سبيد بالار بي ام
+
+133
+00:17:06,790 --> 00:17:15,670
+وال دي وحدتها بالإنش سرعة اللي بنحطيها هتكون إيش
+
+134
+00:17:15,670 --> 00:17:20,250
+ساوية سرعة
+
+135
+00:17:20,250 --> 00:17:23,430
+اللي بنحطيها هتكون إيش ساوية سرعة اللي بنحطيها
+
+136
+00:17:23,430 --> 00:17:23,750
+هتكون إيش ساوية سرعة اللي بنحطيها هتكون إيش ساوية
+
+137
+00:17:27,280 --> 00:17:34,760
+ال foot permanent اللي هو هضرب اللي هتكون ال n طب
+
+138
+00:17:34,760 --> 00:17:38,740
+ال n وحدتها إيه؟ revolution permanent دي يعني
+
+139
+00:17:38,740 --> 00:17:45,680
+radian permanent هضربها في إيه؟ في اتنين باي
+
+140
+00:17:45,680 --> 00:17:50,560
+permanent لأ
+
+141
+00:17:50,560 --> 00:17:54,020
+هخليها permanent انا هكذا اه
+
+142
+00:17:56,830 --> 00:18:02,330
+بدي اضغط في ال D على اتنين ال radius في ال D على
+
+143
+00:18:02,330 --> 00:18:10,790
+اتنين هذي وقتتها inch بدي احولها لقدم هضغط في واحد
+
+144
+00:18:10,790 --> 00:18:24,550
+على اتناش هسكن سواء by DN by
+
+145
+00:18:24,550 --> 00:18:30,930
+DN smallعلى ات ماشي يعني انا هوض عن ال D بال انش و
+
+146
+00:18:30,930 --> 00:18:35,590
+ال N small بال بال RPM و بتعطيني وحدات لسرعة اللي
+
+147
+00:18:35,590 --> 00:18:43,550
+هي foot per minute يعني هذا سرعة بال foot per
+
+148
+00:18:43,550 --> 00:18:51,130
+minute الان
+
+149
+00:19:03,260 --> 00:19:08,460
+لأن هنجيب الوزن الوزن
+
+150
+00:19:08,460 --> 00:19:15,600
+وزن
+
+151
+00:19:15,600 --> 00:19:19,680
+القدم الواحد وزن القدم الواحد يعني الوزن هذه
+
+152
+00:19:19,680 --> 00:19:26,440
+وحدتها pound لكل foot
+
+153
+00:19:30,940 --> 00:19:39,740
+فاندي ال specific weight جامع هو ال weight density
+
+154
+00:19:39,740 --> 00:19:49,340
+وحدتها pound لكل انش مكعب
+
+155
+00:19:49,340 --> 00:19:57,500
+معناته
+
+156
+00:19:57,500 --> 00:19:58,140
+ال W
+
+157
+00:20:01,580 --> 00:20:06,380
+هتكون تساوي الحجم
+
+158
+00:20:06,380 --> 00:20:10,980
+لأ هتكون بدون الطول لإن انا bare foot معناته
+
+159
+00:20:10,980 --> 00:20:17,820
+بمساحة المقطع اللي هو عندي ال B ال B و ال T وحدتها
+
+160
+00:20:17,820 --> 00:20:22,100
+بال انش مظبوط
+
+161
+00:20:22,100 --> 00:20:25,680
+القامة
+
+162
+00:20:25,680 --> 00:20:36,540
+اللي هي وحدتها بال poundعلى انش تكيب في
+
+163
+00:20:36,540 --> 00:20:50,480
+ال B اللي هي انش في ال T اللي هي انش صح؟ هيروح هاي
+
+164
+00:20:50,480 --> 00:20:56,720
+انش و انش و هين بيصير انش تحت الانش عشان احولها
+
+165
+00:20:56,720 --> 00:20:58,620
+لقدم
+
+166
+00:21:00,800 --> 00:21:04,220
+حضروه في واحد على اتناش تحت بيصير اتناش يعني حضروه
+
+167
+00:21:04,220 --> 00:21:12,920
+في اش و اتناش و هصير ال W اتناشر جاما بي تي و
+
+168
+00:21:12,920 --> 00:21:26,520
+لوحدتها بتكون pound force لكل foot ال
+
+169
+00:21:26,520 --> 00:21:28,480
+FC اللي هي centrifugal force
+
+170
+00:21:32,180 --> 00:21:42,260
+أكيد M Omega Square R Square ال M اللي هي وزن على
+
+171
+00:21:42,260 --> 00:21:49,920
+جيه W على جيه
+
+172
+00:21:49,920 --> 00:21:56,260
+يعني احنا هى ممكن نحكي السواء M بتربيه
+
+173
+00:21:56,260 --> 00:22:00,480
+صح؟ هتكون
+
+174
+00:22:01,700 --> 00:22:11,160
+ال V ايش وحداتها ال V فوت بير منت فوت بير منت يعني
+
+175
+00:22:11,160 --> 00:22:18,360
+انا هضربها ال V عشان احولها per second اقسم على
+
+176
+00:22:18,360 --> 00:22:23,540
+ستين الكلتر
+
+177
+00:22:23,540 --> 00:22:29,470
+يعنيإذا بعود عن جي اللي هو ال gravity ال
+
+178
+00:22:29,470 --> 00:22:31,550
+extraction of gravity اللي هي اتنين و تلاتين point
+
+179
+00:22:31,550 --> 00:22:39,270
+واحد سبعة foot per second يعني هتكون W على جي اللي
+
+180
+00:22:39,270 --> 00:22:45,130
+هي اتنين و تلاتين point واحد سبعة قدم على الثانية
+
+181
+00:22:45,130 --> 00:22:49,850
+في V على ستين الكل تربية
+
+182
+00:22:54,230 --> 00:23:14,970
+بتطلع ال force بال pound طيب
+
+183
+00:23:24,490 --> 00:23:28,190
+احنا حكينا هاي ال tight side هذا هو ال tight side
+
+184
+00:23:28,190 --> 00:23:32,510
+هذا
+
+185
+00:23:32,510 --> 00:23:37,250
+الجزء المشدود وهذا الجزء المرتقي هذا F1 أكبر من F2
+
+186
+00:23:37,250 --> 00:23:43,530
+الآن الحبل لما يكون راكب على البكرات بيكون راكب
+
+187
+00:23:43,530 --> 00:23:49,690
+بالظبط ولا بكون أنا شده؟ شد بيكون مشدود والبكرات
+
+188
+00:23:49,690 --> 00:23:52,910
+بتدورش بيكون فيه شد المعنية بيكون فيه initial
+
+189
+00:23:54,220 --> 00:23:59,880
+Tension ال اف اي هي ال initial tension والبقرة ما
+
+190
+00:23:59,880 --> 00:24:08,620
+بتدور طيب وفي tension due to centrifugal force
+
+191
+00:24:08,620 --> 00:24:13,780
+خلال
+
+192
+00:24:13,780 --> 00:24:17,520
+ال rotation بيصير centrifugal effect ففي عندي
+
+193
+00:24:17,520 --> 00:24:22,890
+tension due لل initial tension والبقرة مابتدورشو
+
+194
+00:24:22,890 --> 00:24:25,850
+خلال الدوران فى عندى tension due to centrifugal
+
+195
+00:24:25,850 --> 00:24:33,410
+force Fc وحنا حكينا ال F1 أكبر
+
+196
+00:24:33,410 --> 00:24:42,450
+من F2 معناته ال F1 هضفلها Delta F على 2 increment
+
+197
+00:24:42,450 --> 00:24:51,090
+زيادة وال F2 هترح منها increment Delta F على 2
+
+198
+00:24:54,030 --> 00:25:00,750
+وبالتالي هتكون ال force على ال tension side F1 في
+
+199
+00:25:00,750 --> 00:25:07,110
+جزء due to initial tension و جزء due to
+
+200
+00:25:07,110 --> 00:25:12,670
+centrifugal force و جزء لأن ال tension side ال
+
+201
+00:25:12,670 --> 00:25:17,070
+force عليه أعلى delta F على اتنين على الجزء
+
+202
+00:25:17,070 --> 00:25:22,720
+المرتخع F2 في جزء due to initial tension Fiجزء due
+
+203
+00:25:22,720 --> 00:25:26,480
+to centrifugal force minus لان هو اقل من F2 minus
+
+204
+00:25:26,480 --> 00:25:33,680
+delta F على 2 الفرق بينهم اترح اترح F1 ناقص F2
+
+205
+00:25:33,680 --> 00:25:37,040
+بيطلع
+
+206
+00:25:37,040 --> 00:25:43,920
+delta F مظبوط F1 ناقص F2 delta F delta F هي اللي
+
+207
+00:25:43,920 --> 00:25:46,400
+بتعمل ال torque ال torque هيكون
+
+208
+00:25:49,980 --> 00:26:00,540
+الـ Torque هيكون Force Delta F في الـ D على 2 صح؟
+
+209
+00:26:00,540 --> 00:26:13,420
+يعني Delta F هيكون تساوي 2T على D يعني Delta F على
+
+210
+00:26:13,420 --> 00:26:17,060
+2 سوى T على D
+
+211
+00:26:20,610 --> 00:26:27,190
+فبالصير ان دي ال F واحد بيسوا F I زي F C زي T
+
+212
+00:26:27,190 --> 00:26:31,710
+capital هي ال torque على دي وال F اتنين بيسوا F I
+
+213
+00:26:31,710 --> 00:26:37,250
+زي F C minus T على دي اذا باطرح بحكي F واحد مانقس
+
+214
+00:26:37,250 --> 00:26:43,610
+F اتنين هتروح ال F I مع ال F I و ال F C مع ال F C
+
+215
+00:26:45,440 --> 00:26:54,060
+فبصير F1-F2 بيسوا 2T على D إذا باجبعهم مع بعض اجبع
+
+216
+00:26:54,060 --> 00:27:04,240
+F1 مع F2 هتروح plus T على D مع minus T على D بلغوا
+
+217
+00:27:04,240 --> 00:27:11,000
+بعض وحيكون دي FI زاد FI و FC زاد FC بيعنى F1 زاد
+
+218
+00:27:11,000 --> 00:27:14,420
+F2 بيسوا 2FI زاد 2
+
+219
+00:27:18,000 --> 00:27:29,240
+F1-F2 F1
+
+220
+00:27:29,240 --> 00:27:37,360
+-F2 F1-F2 F1-F2 F1-F2 F1-F2 F1-F2 F1-F2 F1-F2 F1
+
+221
+00:27:37,360 --> 00:27:37,580
+-F2 F1-F2 F1-F2 F1-F2 F1-F2 F1-F2 F1-F2 F1-F2 F1
+
+222
+00:27:37,580 --> 00:27:40,340
+-F2 F1-F2 F1-F2 F1-F2 F1-F2 F1-F2 F1-F2 F1-F2 F1
+
+223
+00:27:40,340 --> 00:27:40,700
+-F2 F1-F2 F1-F2 F1-F
+
+224
+00:27:46,100 --> 00:27:53,300
+يعني ال FI ال initial tension هيكون
+
+225
+00:27:53,300 --> 00:27:57,760
+الساوية F1
+
+226
+00:27:57,760 --> 00:28:09,840
+زائد F2 minus 2 Fc على 2 يعني
+
+227
+00:28:09,840 --> 00:28:13,860
+ممكن اعمل التالت F1
+
+228
+00:28:15,060 --> 00:28:21,640
+-FC-F2
+
+229
+00:28:21,640 --> 00:28:25,460
+أو
+
+230
+00:28:25,460 --> 00:28:31,660
+زائد F2
+
+231
+00:28:31,660 --> 00:28:39,520
+-FC على اتنين طيب
+
+232
+00:28:39,520 --> 00:28:41,980
+احنا سابقا عرفنا
+
+233
+00:29:07,040 --> 00:29:19,280
+في عند هنا علاقة F1 ناقص Fc على F2 ناقص Fc بستوى
+
+234
+00:29:19,280 --> 00:29:24,540
+exponential لل Ff هذا هنستخدمها هنا
+
+235
+00:29:32,630 --> 00:29:39,190
+هنستخلع العلاقة اللي هي F1-Fc العلاقة السابقة على
+
+236
+00:29:39,190 --> 00:29:44,410
+F2-Fc بستوى exponential لل FI بنعوضها بالعلاقة هذه
+
+237
+00:29:44,410 --> 00:29:47,510
+و
+
+238
+00:29:47,510 --> 00:29:51,750
+في عندك كمان F1-F2 بستوى 2T على D بصفح .. انا بحل
+
+239
+00:29:51,750 --> 00:29:56,730
+المعادلة هذه بصفح عندي FI بستوى T على D مضروبة في
+
+240
+00:29:56,730 --> 00:30:04,470
+كل هذاExponential of FI زاد واحد على Exponential
+
+241
+00:30:04,470 --> 00:30:11,690
+of FI ناقص واحد طيب معناته انا عرفت ال initial
+
+242
+00:30:11,690 --> 00:30:16,510
+tension بالعلاقة اللي هي FI سواء T capital على D
+
+243
+00:30:16,510 --> 00:30:22,530
+small في كله Exponential of FI FF زاد واحد على
+
+244
+00:30:22,530 --> 00:30:24,770
+Exponential of FI ناقص واحد
+
+245
+00:30:33,250 --> 00:30:42,730
+لأن برجع بعوض عند ال F1 بيستوى ال FI زاد FC زاد T
+
+246
+00:30:42,730 --> 00:30:47,890
+على D capital بعوض عن ال FI في المعادلة هذه في هذه
+
+247
+00:30:47,890 --> 00:30:56,960
+المعادلة بحصل على علاقة ليش لل F1و ال F2 يعني F1
+
+248
+00:30:56,960 --> 00:31:02,400
+بيستوى Fc زي FI فتنين exponential لل F Phi على
+
+249
+00:31:02,400 --> 00:31:06,700
+exponential F Phi زي واحد و F2 بيستوى Fc زي FI
+
+250
+00:31:06,700 --> 00:31:14,140
+فتنين على exponential F Phi زي واحد طيب الآن بدي
+
+251
+00:31:14,140 --> 00:31:21,480
+اعمل plot لل F1 طبعا لاحظوا ال F و ال Phi اشمع لما
+
+252
+00:31:21,480 --> 00:31:23,960
+دول constant
+
+253
+00:31:24,990 --> 00:31:32,330
+صح هدى ال contact angle بين ال pulley و ال build و
+
+254
+00:31:32,330 --> 00:31:36,830
+ال F معامل الاحتكار و ال Fc اللى هى centrifugal
+
+255
+00:31:36,830 --> 00:31:43,130
+force بتدرسوهم مع Fi بدى انا اغير ال initial
+
+256
+00:31:43,130 --> 00:31:49,030
+tension بعمل plot لل F1 مع ال Fi و ال F2 مع ال Fi
+
+257
+00:31:49,030 --> 00:31:54,170
+لان لو فىش initial tension عندى يعني Fi بستوى سفر
+
+258
+00:31:55,820 --> 00:32:03,640
+بتكون ال F1 بيستوي Fc و ال F2 بيستوي Fc يعني لو F
+
+259
+00:32:03,640 --> 00:32:09,020
+هي عندي على المحور الوثقي Fi على المحور الرأسي F1
+
+260
+00:32:09,020 --> 00:32:19,580
+و F2 هذا المنحنة احنا حاكينا دايما F2 F1 أكبر من
+
+261
+00:32:19,580 --> 00:32:28,010
+F2 صح؟ معناتههذا يمثل ال slope اللي هو ال slope
+
+262
+00:32:28,010 --> 00:32:32,250
+هذا linear العلاقة بين ال F1 و ال FI linear و ال
+
+263
+00:32:32,250 --> 00:32:37,250
+slope هو هذا صح؟ و هذا علاقة linear بين F2 و FI و
+
+264
+00:32:37,250 --> 00:32:41,350
+هذا ال slope بتاع المعادلة التانية هذا ال term
+
+265
+00:32:41,350 --> 00:32:46,070
+أكبر من هذا ال term و لما ال FI بيستوى سفر بيبدو
+
+266
+00:32:46,070 --> 00:32:51,650
+مع بعض يعني هاي عندي ال curve بتاع F1 و هذا ال
+
+267
+00:32:51,650 --> 00:33:00,300
+curve بتاعF2 and for a given initial tension Fi
+
+268
+00:33:00,300 --> 00:33:08,100
+هذه المسافة من هنا إلى هنا بتمثل الفرق بين F1 و F2
+
+269
+00:33:08,100 --> 00:33:17,640
+يعني هذه المسافة من هنا إلى هنا بتمثل F1-F2 F1-F2
+
+270
+00:33:17,640 --> 00:33:24,790
+ال nominal power nominal powerيعني النمو ال power
+
+271
+00:33:24,790 --> 00:33:30,850
+يعني ال power ال calculated as is بدون ما احنا
+
+272
+00:33:30,850 --> 00:33:34,810
+بنعمل احتياطات، الاختلافات، ال load، ال .. ال ..
+
+273
+00:33:34,810 --> 00:33:37,970
+اذا .. اذا فيه احتزازات، فيش احتزازات، يعني هذا ال
+
+274
+00:33:37,970 --> 00:33:42,290
+nominal يعني ال ideal ال nominal power بتكون اتش
+
+275
+00:33:42,290 --> 00:33:49,950
+السواء F1 نقص F2 في V على 33000 احنا طبعا معوض عن
+
+276
+00:33:49,950 --> 00:33:56,730
+ال F1 و F2 بال poundو ال V بال foot per minute
+
+277
+00:33:56,730 --> 00:34:01,650
+يعني عادة معادلة جاهزة بس تاك تعود ال V بال foot
+
+278
+00:34:01,650 --> 00:34:04,130
+per minute و ال F واحد و الف اتنين بال pound
+
+279
+00:34:04,130 --> 00:34:12,170
+المصنعين
+
+280
+00:34:12,170 --> 00:34:18,490
+بيزودونا بمصنعين ال bells و ال bullies بيزودونا
+
+281
+00:34:18,490 --> 00:34:25,380
+بمواصفاتلل builds اللي بنتجوها هذه المواصفات تتضمن
+
+282
+00:34:25,380 --> 00:34:33,020
+allow tension of a يديش ال tension المسموح مسموح
+
+283
+00:34:33,020 --> 00:34:39,640
+لك طبعا هذا بيقول لك force per unit width يعني مش
+
+284
+00:34:39,640 --> 00:34:43,660
+per unit length هاي ال width هذا هو ايش ال width
+
+285
+00:34:43,660 --> 00:34:50,390
+هذا ايشالـ length و بيحكي four per unit width اللي
+
+286
+00:34:50,390 --> 00:34:56,590
+هي F A small و بيعطينا ال built life عمر ال built
+
+287
+00:34:56,590 --> 00:35:03,050
+بالسنوات و بيعطينا اللي هي severity of flexing at
+
+288
+00:35:03,050 --> 00:35:06,270
+the pulley and its effect on life is reflected in
+
+289
+00:35:06,270 --> 00:35:09,630
+a pulley correction factors بيقشنة ال severity of
+
+290
+00:35:09,630 --> 00:35:15,500
+flexing فقلت لو انا عندي بكرة قطرة كبيرةهذه حالة
+
+291
+00:35:15,500 --> 00:35:28,280
+يعني هذه بكرة كبيرة الآن
+
+292
+00:35:28,280 --> 00:35:34,660
+و هي تلف ال flexing بيكون
+
+293
+00:35:34,660 --> 00:35:41,400
+أقل لو كانت ال بكرة صغيرة أضغط
+
+294
+00:35:42,740 --> 00:35:46,060
+فال flexing التاني في الصغيرة أكتر فبتكون more
+
+295
+00:35:46,060 --> 00:35:51,160
+severe أكتر أو أسوأ فبيعطيني برضه اللي هو poly
+
+296
+00:35:51,160 --> 00:36:06,740
+correction factor for severity of flexing speed
+
+297
+00:36:06,740 --> 00:36:09,480
+in axis of 600 feet per minute
+
+298
+00:36:13,950 --> 00:36:18,670
+بكون هي مصممة او بعطينا بيانات على سرعة ستمية سرعة
+
+299
+00:36:18,670 --> 00:36:24,550
+محيطية ستمية قدم في الدقيقة اذا اختلفت عن ستمية
+
+300
+00:36:24,550 --> 00:36:28,750
+معناته محتاج velocity correction factor CV محتاج
+
+301
+00:36:28,750 --> 00:36:33,110
+velocity correction factor CV لان هو كل حساباته
+
+302
+00:36:33,110 --> 00:36:40,930
+عند ستمية قدم في الدقيقةإذا كانت الحبل مصنوعة من
+
+303
+00:36:40,930 --> 00:36:46,230
+بدة ال polyamide أو اليوريثين في كل حوال بيعتبر ال
+
+304
+00:36:46,230 --> 00:36:52,550
+CV بالساوية واحد for liver pills يعني مش polyamide
+
+305
+00:36:52,550 --> 00:36:58,090
+ولا يوريثين بنتطلع على figure 17 9 figure 17 9
+
+306
+00:36:58,090 --> 00:37:05,150
+معطين الصراعات ال builtطبعا هنا قسم على الف، هنا
+
+307
+00:37:05,150 --> 00:37:11,210
+الف foot per minute، هنا الفين، هنا تلت تلاف، اربع
+
+308
+00:37:11,210 --> 00:37:15,730
+تلاف، خمس تلاف، ست تلاف و هنا معطيني four
+
+309
+00:37:15,730 --> 00:37:20,030
+different built thicknesses يعني مثلا هذه احداشر
+
+310
+00:37:20,030 --> 00:37:23,950
+على اربع ستين ال thickness، هذا خمسة و عشرين على
+
+311
+00:37:23,950 --> 00:37:29,960
+اربع ستينهذا تلتاش على اربع و ستين هذا تمانتاش على
+
+312
+00:37:29,960 --> 00:37:33,860
+اربع و ستين for different build thicknesses معطيني
+
+313
+00:37:33,860 --> 00:37:37,440
+ال velocity correction factor as a function of
+
+314
+00:37:37,440 --> 00:37:43,980
+built velocity بالذبنة
+
+315
+00:37:43,980 --> 00:37:52,320
+service factor Ks عشان ياخد في الحسبان الاختلاف عن
+
+316
+00:37:52,320 --> 00:37:55,700
+ال nominal powerلأن ليش بيصير اختلاف عن nominal
+
+317
+00:37:55,700 --> 00:38:01,380
+وال power؟ في اهتزازات في shocks في عدم دقت في
+
+318
+00:38:01,380 --> 00:38:06,280
+التصنيع وفي كتير تفاصيل فلازم اخد ايه اش فاللي هو
+
+319
+00:38:06,280 --> 00:38:13,000
+service factor ال HD او ال design ال design power
+
+320
+00:38:13,000 --> 00:38:16,880
+او ال allowable power so مثلا ال design power او
+
+321
+00:38:16,880 --> 00:38:23,120
+ال allowable power بيستوى ال H nominal في KS في ND
+
+322
+00:38:24,310 --> 00:38:37,770
+ال KS مُعطى في جدول سبعتاش خمستاش معطيني
+
+323
+00:38:37,770 --> 00:38:44,270
+في حالة عندي source of powerعندي ال driven
+
+324
+00:38:44,270 --> 00:38:47,650
+machinery uniform, light shock, medium shock,
+
+325
+00:38:48,270 --> 00:38:51,310
+heavy shock وعندي هنا normal torque
+
+326
+00:38:51,310 --> 00:38:53,730
+characteristics source of power اللي هو على البكرة
+
+327
+00:38:53,730 --> 00:38:58,830
+اللي هي عليها ال driver وعندي high or non uniform
+
+328
+00:38:58,830 --> 00:39:03,690
+torque يعني ممكن تكون عندى ال uniformity او ال non
+
+329
+00:39:03,690 --> 00:39:11,520
+uniformity على ال input و او ال outputواضح؟ يعني
+
+330
+00:39:11,520 --> 00:39:18,480
+ال uniformity أو ال non uniformity ممكن تكون على
+
+331
+00:39:18,480 --> 00:39:25,060
+ال input أو و ال output واضح؟ فهم يعطينا ال
+
+332
+00:39:25,060 --> 00:39:33,180
+service factor و
+
+333
+00:39:33,180 --> 00:39:34,900
+الأن دي design factor
+
+334
+00:39:37,790 --> 00:39:44,210
+these effects اللي هي severity of flexing واختلاف
+
+335
+00:39:44,210 --> 00:39:50,890
+السرعة عن ستمية قدم في الدقيقة بحسب
+
+336
+00:39:50,890 --> 00:39:59,010
+بانقسين F1A بسوء BFA CBCB ال B اللي هي ال built
+
+337
+00:39:59,010 --> 00:40:06,210
+width بال انش هذا هو ال built width بال انشال F.A
+
+338
+00:40:06,210 --> 00:40:09,150
+ال manufacturers allow tension pound force per
+
+339
+00:40:09,150 --> 00:40:14,790
+inch ال F.A اللي هو بيحكي للمصنع اللي هي الشد
+
+340
+00:40:14,790 --> 00:40:19,290
+المسموح لك فيه اللي هو طبق للمصنع ال C.P poly
+
+341
+00:40:19,290 --> 00:40:23,550
+correction factor for
+
+342
+00:40:23,550 --> 00:40:26,990
+flexing ال C.V ballistic correction factor اذا
+
+343
+00:40:26,990 --> 00:40:32,850
+السرعة اختلفت عن ستمية قدم في الدقيقةو ال F1A ال
+
+344
+00:40:32,850 --> 00:40:35,830
+law of largest tension بعد ما أخدنا في الحسبان
+
+345
+00:40:35,830 --> 00:40:44,170
+اللي هي severity of flexing والاختلاف الصراعي
+
+346
+00:40:44,170 --> 00:40:52,210
+الان طبعا هذه المعادلات كلها بدها ترتيب بدها تعمل
+
+347
+00:40:52,210 --> 00:40:56,470
+إيش؟ زي code للحسباتالخطوة اللي حسيبها الـ steps
+
+348
+00:40:56,470 --> 00:40:59,330
+لازم تبقى built flat بال drive أول شي find
+
+349
+00:40:59,330 --> 00:41:05,370
+exponential f phi from built geometry فاكرين الشكل
+
+350
+00:41:05,370 --> 00:41:10,490
+في أول ال chapter لما حسبنا ال gamma بالساوية sin
+
+351
+00:41:10,490 --> 00:41:14,610
+inverse اللي هو D capital minus D small على 2C و
+
+352
+00:41:14,610 --> 00:41:19,570
+بعدين حسبنا فا دي small و فا دي capital لنحصل فا
+
+353
+00:41:19,570 --> 00:41:24,430
+دي small و بعدين من table 17-2
+
+354
+00:41:28,620 --> 00:41:32,280
+معطيني معامل احتكاك بجيب معامل احتكاك يعني من
+
+355
+00:41:32,280 --> 00:41:38,560
+figure سبعتاش واحد بحسب ال في في دي و من table
+
+356
+00:41:38,560 --> 00:41:43,440
+سبعتاش اتنين بطلع اللي هو معامل الاحتكاك معامل
+
+357
+00:41:43,440 --> 00:41:49,940
+الاحتكاك و
+
+358
+00:41:49,940 --> 00:41:55,530
+بحسب exponential لل F file لان صارت F معروفةمن
+
+359
+00:41:55,530 --> 00:42:00,830
+تابل سبعتاش اتنين و في من figure سبعتاش واحد بحث
+
+360
+00:42:00,830 --> 00:42:05,830
+ال exponential لل F في برضه
+
+361
+00:42:05,830 --> 00:42:16,230
+من figure سبعتاش واحد و table سبعتاش اتنين
+
+362
+00:42:16,230 --> 00:42:23,050
+طبعا نرجع لtable سبعتاش اتنين بلزام نقاش
+
+363
+00:42:25,790 --> 00:42:32,890
+بالزمنة اللي هو ال .. ال .. ال gamma عشان تست ال W
+
+364
+00:42:32,890 --> 00:42:36,710
+ماشي خلينا نروح نشوف على table سبعتاشر اتنين
+
+365
+00:42:36,710 --> 00:42:40,770
+معطيني ال material ال built ال specification ال
+
+366
+00:42:40,770 --> 00:42:46,170
+size في ال inch ال thickness تبعها و معطيني ال
+
+367
+00:42:46,170 --> 00:42:53,140
+minimum .. ال minimumمعطيني ال F A ال F A عنده
+
+368
+00:42:53,140 --> 00:42:56,420
+اللي هي allow tension per unit width at six
+
+369
+00:42:56,420 --> 00:43:00,600
+hundred feet per minute معطيني ال allowable
+
+370
+00:43:00,600 --> 00:43:04,540
+tension pound force per inch معطيني ال specific
+
+371
+00:43:04,540 --> 00:43:06,760
+weight اللي هي الجامعة معطيني ال specific weight
+
+372
+00:43:06,760 --> 00:43:14,280
+الجامعة ومعطيني ايش معامل احتكاك يعني برضه من تلو
+
+373
+00:43:14,280 --> 00:43:23,400
+سبعتاش اتنين باخد ايش الجامعةو منها بحسب ايش ال W
+
+374
+00:43:23,400 --> 00:43:28,000
+اللي هي اتناشر جاما بي تي ال B اللي هي ال built
+
+375
+00:43:28,000 --> 00:43:36,360
+width و ال T ال built thickness و ال V بحسبها من
+
+376
+00:43:36,360 --> 00:43:42,960
+by DN على اتناشر ال D اللي هي قطر البكرة الصغيرة و
+
+377
+00:43:42,960 --> 00:43:48,280
+ال N اللي هي سرعة البكرة بال RPMبعدين بعوض في
+
+378
+00:43:48,280 --> 00:43:58,080
+المعادلة هذه باحسب ال Fc هذه الخطوة التانية خطوة
+
+379
+00:43:58,080 --> 00:44:02,140
+تالتة بحسب
+
+380
+00:44:02,140 --> 00:44:05,580
+ال design power أو ال allow power بيستوى H nominal
+
+381
+00:44:05,580 --> 00:44:11,180
+في K S and D ال KS حكينا من ال table سبعتاش و
+
+382
+00:44:11,180 --> 00:44:16,910
+خمستاشو ال N دي انا ك designer كمصمم بحطه له عامل
+
+383
+00:44:16,910 --> 00:44:22,390
+امان و ال H nominal اذا فاكرين F1-F2 او بيكون
+
+384
+00:44:22,390 --> 00:44:30,270
+معطنية هو F1-F2 في V على تلات و تلاتين الف و منها
+
+385
+00:44:30,270 --> 00:44:33,970
+بحسب ال torque ال torque يستوى تلات و ستين الف و
+
+386
+00:44:33,970 --> 00:44:39,030
+خمسة و عشرين في ال HD على N هو معون على ال HD في
+
+387
+00:44:39,030 --> 00:44:46,280
+ال HD هذه كلها ايش ال HD في ال HDعلى N بعدين بأحسب
+
+388
+00:44:46,280 --> 00:44:56,940
+بين قسين F1A-F2 بيستوى اتنين T على D المحاضرة
+
+389
+00:44:56,940 --> 00:44:59,000
+الجاية بنكمل الخطوات
+
diff --git a/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/6iOKfNH0QyQ_raw.srt b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/6iOKfNH0QyQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5a01474f4a7c729b7bc5d7469aa0a062a3ef3093
--- /dev/null
+++ b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/6iOKfNH0QyQ_raw.srt
@@ -0,0 +1,1804 @@
+1
+00:00:05,040 --> 00:00:08,060
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:08,060 --> 00:00:12,500
+وبركاته هنكمل في مادة تصميم الألات اتنين احنا كنا
+
+3
+00:00:12,500 --> 00:00:18,060
+بدأنا chapter ل design of flat built drives حكينا
+
+4
+00:00:18,060 --> 00:00:21,780
+على ال mathematical formulation الجيومتري كل
+
+5
+00:00:21,780 --> 00:00:26,720
+حسابات التصميم الآن هنرتبه بخطوات كأنها code كأنها
+
+6
+00:00:26,720 --> 00:00:30,520
+code تتمشي عليه فهنحكي عن ال steps in analyzing
+
+7
+00:00:30,520 --> 00:00:46,600
+flat built drives أول شيfind exponential find
+
+8
+00:00:46,600 --> 00:00:50,580
+exponential FI from built drive geometry من شكل 17
+
+9
+00:00:50,580 --> 00:00:57,470
+واحد فاكرين شكل 17 واحداللي بإنه بنوجد اللي هي ال
+
+10
+00:00:57,470 --> 00:01:00,710
+gamma اللي هي ال sign inverse D capital minus D
+
+11
+00:01:00,710 --> 00:01:05,830
+small على اتنين D و بنحسب ال five D small و ال
+
+12
+00:01:05,830 --> 00:01:13,810
+five D capital و من table سبعتاشر اتنين .. table
+
+13
+00:01:13,810 --> 00:01:18,670
+سبعتاشر اتنين بنطلع احنا عندنا ال material معروفة
+
+14
+00:01:18,670 --> 00:01:24,460
+بتكون materialال thickness بتاع ال built ال
+
+15
+00:01:24,460 --> 00:01:28,060
+minimum poly diameter اللي هو ال tension per width
+
+16
+00:01:28,060 --> 00:01:33,260
+at 600 feet per minute pound force per inch اللي
+
+17
+00:01:33,260 --> 00:01:38,600
+هي FA و بنطلع الجامعة اللي هي ال specific weight و
+
+18
+00:01:38,600 --> 00:01:45,560
+بنطلع معامل الاحتكاك هذا من table 17 اتنين
+
+19
+00:01:48,760 --> 00:01:52,480
+الان صار عندى معروف بنحسب الفاى و بنحسب الاف منها
+
+20
+00:01:52,480 --> 00:01:58,340
+بنحسب اكسبلانشها لل F فاى الان
+
+21
+00:01:58,340 --> 00:02:05,280
+بعدين بنيجي نحسب احنا already بنحسب ال W ال W
+
+22
+00:02:05,280 --> 00:02:08,920
+بيستوى اتناشر جاما BT الجاما هى ال specific weight
+
+23
+00:02:08,920 --> 00:02:14,900
+من table سبعتاشر اتنين و ال B هي ال built width و
+
+24
+00:02:14,900 --> 00:02:20,530
+ال T ال thickness بتاع ال builtو ال V اللي هي
+
+25
+00:02:20,530 --> 00:02:24,770
+الصراع المحيطية بالسواء PIE DN على اتناش ال D هو
+
+26
+00:02:24,770 --> 00:02:29,730
+القطر ال .. ال .. ال .. البولي الصغيرة و ال N اللي
+
+27
+00:02:29,730 --> 00:02:34,150
+هي صراعتها بال RPM بعدين نحسب ال FC بالسواء W على
+
+28
+00:02:34,150 --> 00:02:37,770
+اتنين و تلاتين point واحد سبعة في ال V على ستين
+
+29
+00:02:37,770 --> 00:02:41,650
+الكل تربيع بتطلع وحدتها بال pound
+
+30
+00:02:44,530 --> 00:02:48,590
+بعدين بنحسب ال H design أو ال H allowable اللي هي
+
+31
+00:02:48,590 --> 00:02:52,350
+بتساوي H nominal اللي هي nominal power في ال KS في
+
+32
+00:02:52,350 --> 00:02:57,270
+ال ND ال .. ال KS اللي هو service factor من table
+
+33
+00:02:57,270 --> 00:03:03,430
+سبعتاش خمستاش و ال ND design factor و منهم بحسب
+
+34
+00:03:03,430 --> 00:03:07,430
+اللي هي ال T بالساوية تلات ستين ألف و خمس عشرين
+
+35
+00:03:07,430 --> 00:03:09,410
+ممكن أعملها بالشكل هذا
+
+36
+00:03:15,600 --> 00:03:25,140
+زيك بس اتش ديزاين ما هي هي فبتطلع التورك يستوي
+
+37
+00:03:25,140 --> 00:03:29,740
+تلاثين الف و خمس و عشرين design ال power او ال
+
+38
+00:03:29,740 --> 00:03:35,220
+allow ال power على ال factor of safety على ال RPM
+
+39
+00:03:35,220 --> 00:03:38,540
+بعدين
+
+40
+00:03:38,540 --> 00:03:46,370
+من حسابنا للتورك بنحسب F1F1 بينقصين A-F2 بيسوا
+
+41
+00:03:46,370 --> 00:03:55,910
+اتنين T على D رقم خمسة بنحسب F1 A A بيسوا B في F A
+
+42
+00:03:55,910 --> 00:04:01,750
+C B C D ال B اللي هي ال width بتاع ال built و ال F
+
+43
+00:04:01,750 --> 00:04:07,090
+A من table سبعتاشر اتنين و ال CP correction factor
+
+44
+00:04:07,090 --> 00:04:13,490
+for flexing and bending of the builtمن table 17-4
+
+45
+00:04:13,490 --> 00:04:18,590
+و ال CV اللي هي correction for speed other other
+
+46
+00:04:18,590 --> 00:04:22,350
+other اللي هو اللي مختلف عن ستمية قدم في الدقيقة
+
+47
+00:04:22,350 --> 00:04:25,510
+بعدين
+
+48
+00:04:25,510 --> 00:04:27,530
+هنكمل هذا شوية
+
+49
+00:04:42,090 --> 00:04:53,950
+بعدين احنا حسبنا F1A سابقا حسبنا F1A-F2 بنطرح F1A
+
+50
+00:04:53,950 --> 00:05:03,330
+-F2 F1A-F2 بتعطينا F2، مظبوط؟ لأن هذه هتروح مع هذه
+
+51
+00:05:03,330 --> 00:05:07,970
+بتعطينا F2بعدين نحسب ال initial tension في ال
+
+52
+00:05:07,970 --> 00:05:12,330
+built اللي هي FI بسوء F1A زياد F2 على 2 minus Fc
+
+53
+00:05:12,330 --> 00:05:15,410
+Fc already حسبناها من رقم 2
+
+54
+00:05:18,460 --> 00:05:21,340
+تمانية بدنا نشوف ال check .. ال check على ال
+
+55
+00:05:21,340 --> 00:05:23,680
+friction coefficient هل بيصير انزلاق و لا بيصيرش
+
+56
+00:05:23,680 --> 00:05:27,140
+انزلاق نحسب ما يسمى F prime بيستوى واحد على فايل
+
+57
+00:05:27,140 --> 00:05:32,040
+لإن ال F1 A minus F C على F2 minus F C لازم يكون F
+
+58
+00:05:32,040 --> 00:05:36,720
+prime أقل من ال F و إلا بيصير انزلاق بعدين نتأكد
+
+59
+00:05:36,720 --> 00:05:41,340
+من ال factor of safety بيستوى H A على H nominal
+
+60
+00:05:41,340 --> 00:05:42,720
+على K S
+
+61
+00:05:50,900 --> 00:05:55,240
+طيب هنحكي هنا ال serious factor KS نجيه و نتابر
+
+62
+00:05:55,240 --> 00:06:02,260
+سبعتاش، خمس، اتاش ال .. ال poly correction factor
+
+63
+00:06:02,260 --> 00:06:06,200
+اللي هو ال CP accounts for amount of bending or
+
+64
+00:06:06,200 --> 00:06:09,320
+flexing يعني هو .. بو أرجينيا ديش عندي إيش؟
+
+65
+00:06:09,320 --> 00:06:12,920
+bending و flexing كل ما كانت ال poly قطرة كبيرة كل
+
+66
+00:06:12,920 --> 00:06:16,980
+ما كانت كمية ال bending و flexing أقل، مظبوط؟
+
+67
+00:06:18,130 --> 00:06:23,970
+بنستخدم CP بسواحد في حالة urethane builds هال
+
+68
+00:06:23,970 --> 00:06:29,510
+table 17-5 ال table 17-4 اللي هي ال poly
+
+69
+00:06:29,510 --> 00:06:34,950
+correction factor ال CP بعتمد على ال material و
+
+70
+00:06:34,950 --> 00:06:42,190
+القطر بتاع ال build الآن
+
+71
+00:06:42,190 --> 00:06:49,190
+ال ال ال polys ما بتكون مخلوطة عدليعني ازاي ما
+
+72
+00:06:49,190 --> 00:07:00,430
+انتوا شايفين ممكن
+
+73
+00:07:00,430 --> 00:07:11,690
+تيجي زي هيك ممكن
+
+74
+00:07:11,690 --> 00:07:12,210
+تيجي
+
+75
+00:07:25,130 --> 00:07:34,930
+ممكن تيجي ممكن
+
+76
+00:07:34,930 --> 00:07:47,210
+تيجي طبعا
+
+77
+00:07:47,210 --> 00:07:51,030
+في كل حوال بيسموها ال crown height
+
+78
+00:07:58,440 --> 00:08:11,660
+هذا ال crown height هذا ال crown height وهذا
+
+79
+00:08:11,660 --> 00:08:12,660
+ال crown height
+
+80
+00:08:20,220 --> 00:08:27,480
+طبعا وجود ال crown أو القمة أو التاج تمنع زلاق ال
+
+81
+00:08:27,480 --> 00:08:30,880
+build في هذا الاتجاه فبضلها في مكانها ال build
+
+82
+00:08:30,880 --> 00:08:35,280
+ومهم كتير بضلها في مكانها table
+
+83
+00:08:35,280 --> 00:08:39,000
+السبعتاشر الآن if only one pulley is crowned اذا
+
+84
+00:08:39,000 --> 00:08:43,600
+كانت واحدة فيها crown لازم تكون البقرة الكبيرة اذا
+
+85
+00:08:43,600 --> 00:08:46,940
+انت مش عامل تنتيني crowning لازم الكبيرة تكون هي
+
+86
+00:08:46,940 --> 00:08:47,300
+ال crown
+
+87
+00:08:51,160 --> 00:08:53,960
+إذا ماكانوش البكرتين في نفس المستوى، يعني هاي
+
+88
+00:08:53,960 --> 00:08:58,540
+المستوى الأفقي، هاي وضع الطبيعي، هاي بكره، هاي
+
+89
+00:08:58,540 --> 00:09:11,280
+بكره لو كان إشي زي هيك مثلا لازم
+
+90
+00:09:11,280 --> 00:09:14,940
+البكرتين يكون فيهم crown
+
+91
+00:09:17,480 --> 00:09:22,780
+شوف ال table سبعتاشر خمسة for crown height فانا ده
+
+92
+00:09:22,780 --> 00:09:29,880
+باضح ايش ال crown زي ما انتوا شايفين بيكون فيه
+
+93
+00:09:29,880 --> 00:09:35,980
+تحدب او عندى بيكون ايش table يعني هنا عرض بس
+
+94
+00:09:35,980 --> 00:09:41,700
+حالتين لان ال table سبعتاشر خمسة معطيني ال crown
+
+95
+00:09:41,700 --> 00:09:44,100
+height بدلالة
+
+96
+00:09:45,830 --> 00:09:48,190
+ال poly diameter اذا انا عارف ال poly diameter
+
+97
+00:09:48,190 --> 00:09:55,690
+بحدد ال crown height يعني لو كانت عندي قطر
+
+98
+00:09:55,690 --> 00:09:58,010
+البكرة تمانية انش تمانية انش يعني حوالي عشرين
+
+99
+00:09:58,010 --> 00:10:05,110
+صنطة، مظبوط؟ تقريبا ال crown height point O to
+
+100
+00:10:05,110 --> 00:10:07,310
+four يعني انا انا احسبه بالmillimeter
+
+101
+00:10:21,220 --> 00:10:31,920
+وان ال calculator بيطلع
+
+102
+00:10:31,920 --> 00:10:36,040
+حوالي ستة من عشرة ملي الارتفاع يعني صغير الصعب
+
+103
+00:10:36,040 --> 00:10:47,920
+تلاحظه طيب
+
+104
+00:10:47,920 --> 00:10:48,740
+نشوف مثال
+
+105
+00:11:06,350 --> 00:11:12,090
+Polyamide A3 flat built انا ملخص المثلة وانا
+
+106
+00:11:12,090 --> 00:11:19,130
+عندهين polyamide A3 flat built six
+
+107
+00:11:19,130 --> 00:11:27,350
+inch wide يعني ال B ستة انش ال
+
+108
+00:11:27,350 --> 00:11:30,230
+U ت transmit fifteen horsepower يعني ال nominal
+
+109
+00:11:30,230 --> 00:11:33,750
+power H nominal خمس عشر حصان
+
+110
+00:11:37,530 --> 00:11:41,770
+Under light shock conditions where Ks يساو 1.25
+
+111
+00:11:41,770 --> 00:11:52,030
+And in light shock conditions Kc يساو 1.25 And
+
+112
+00:11:52,030 --> 00:11:55,530
+the factor of safety equal to or greater than 1.1
+
+113
+00:11:55,530 --> 00:12:03,230
+Lns أكبر أو يساوي 1.1 The
+
+114
+00:12:03,230 --> 00:12:07,420
+poly rotational axes are paralleland in the
+
+115
+00:12:07,420 --> 00:12:11,980
+horizontal plane the shafts are eight feet apart
+
+116
+00:12:11,980 --> 00:12:15,600
+يعني ال center distance ال pulley rotation axis
+
+117
+00:12:15,600 --> 00:12:18,160
+are parallel and in the horizontal plane ال center
+
+118
+00:12:18,160 --> 00:12:26,640
+distance تمانية قدم ال
+
+119
+00:12:26,640 --> 00:12:29,880
+shafts are eight .. the six inch driving pulley
+
+120
+00:12:29,880 --> 00:12:33,540
+rotates at seventeen hundred fifty rpm
+
+121
+00:12:36,440 --> 00:12:41,180
+عندي قطر البكر صغيره ستة انش وبدوره سرعة ألف
+
+122
+00:12:41,180 --> 00:12:46,860
+سبعمائة وخمسين rpm in such a way that the load
+
+123
+00:12:46,860 --> 00:12:50,360
+site is on the top the driven pulley is eighteen
+
+124
+00:12:50,360 --> 00:12:59,860
+inch in diameter دي capital تمانتاشر انش طيب
+
+125
+00:12:59,860 --> 00:13:04,580
+هيك لخصنا المثال احنا عندي فرصة مبين
+
+126
+00:13:29,840 --> 00:13:34,620
+center distance تمانية قدم يعني بال انش تمانية في
+
+127
+00:13:34,620 --> 00:13:49,040
+اتناش ستة و تسعين C ستة و ستة و تسعين انش طبعا
+
+128
+00:13:49,040 --> 00:13:51,480
+اذا هذا ال low side ال rotation هيكون بهذا الاتجاه
+
+129
+00:13:51,480 --> 00:14:02,300
+عند ال N ماتينها الف سبعة مية و خمسينRPM وهذه
+
+130
+00:14:02,300 --> 00:14:06,940
+كترها ستة
+
+131
+00:14:06,940 --> 00:14:11,500
+انش وهذه
+
+132
+00:14:11,500 --> 00:14:19,240
+كترها تمنتاشر
+
+133
+00:14:19,240 --> 00:14:19,660
+انش
+
+134
+00:14:26,330 --> 00:14:31,030
+estimate the centrial force FC بده ال FC و ال
+
+135
+00:14:31,030 --> 00:14:36,630
+torque بده ال FC و
+
+136
+00:14:36,630 --> 00:14:43,050
+ال torque نرجع
+
+137
+00:14:43,050 --> 00:14:43,610
+الخطوات
+
+138
+00:14:56,080 --> 00:15:01,280
+طيب ممكن امشي على الخطوات او امشي ابدأ من الآخر
+
+139
+00:15:01,280 --> 00:15:07,900
+يعني احكي Fc Fc
+
+140
+00:15:07,900 --> 00:15:21,960
+بالساوية W على 32 point واحد سبعة V على ستين لكل
+
+141
+00:15:21,960 --> 00:15:22,420
+تربيع
+
+142
+00:15:25,310 --> 00:15:31,810
+طيب ال W شو الساوية اتناش
+
+143
+00:15:31,810 --> 00:15:35,510
+جاما
+
+144
+00:15:35,510 --> 00:15:41,470
+بي تي مظبوط طيب
+
+145
+00:15:41,470 --> 00:15:49,750
+ال B موطعنا صح ال B موطعنا بدنا الجامعة بنروح على
+
+146
+00:15:49,750 --> 00:15:53,910
+ال table سبعتاش اتنين عشان نحسب الجامعة table
+
+147
+00:15:53,910 --> 00:15:55,030
+سبعتاش اتنين
+
+148
+00:16:02,420 --> 00:16:08,260
+table سبعتاشر اتنين ال material عندي اللي هي
+
+149
+00:16:08,260 --> 00:16:22,320
+polyamide A3 polyamide A3A فممكن
+
+150
+00:16:22,320 --> 00:16:26,460
+اطلع نحكي واحد اتنين تلاتة خلنا نطلع معامل احتكاك
+
+151
+00:16:28,220 --> 00:16:33,440
+فمعامل احتكاك اكم
+
+152
+00:16:33,440 --> 00:16:42,900
+بالساوية point تمانية point تمانية ومعطيني
+
+153
+00:16:42,900 --> 00:16:47,000
+gamma اكم
+
+154
+00:16:47,000 --> 00:16:52,340
+بالساوية point zero four اتنين
+
+155
+00:16:57,900 --> 00:17:08,360
+pound لكل انش مكعب صح؟ ال .. وال F A ماعطينا ال F
+
+156
+00:17:08,360 --> 00:17:13,340
+A خدنا نطلع F A
+
+157
+00:17:13,340 --> 00:17:18,700
+بتساوي مية
+
+158
+00:17:18,700 --> 00:17:28,250
+pound force per unit weight وال F A ميةpound force
+
+159
+00:17:28,250 --> 00:17:37,550
+per inch ومعطينا
+
+160
+00:17:37,550 --> 00:17:44,870
+ايش thickness point one thickness T point one
+
+161
+00:17:44,870 --> 00:17:50,030
+three inch معناه
+
+162
+00:17:50,030 --> 00:17:59,720
+ال W هتساوي اتناش في جامعةاللي هي point O أربعة
+
+163
+00:17:59,720 --> 00:18:07,420
+اتنين في ال thickness point واحد تلاتة
+
+164
+00:18:07,420 --> 00:18:10,540
+تطلع
+
+165
+00:18:10,540 --> 00:18:14,380
+حسبنا
+
+166
+00:18:14,380 --> 00:18:21,720
+ال W هنحسب ال V ال
+
+167
+00:18:21,720 --> 00:18:26,160
+V بالساوية by
+
+168
+00:18:27,880 --> 00:18:37,300
+D N على اتناش باى
+
+169
+00:18:37,300 --> 00:18:42,360
+ال D اللى هى ستة انش فى ال N ألف سبعمائه و خمسين
+
+170
+00:18:42,360 --> 00:18:55,680
+على اتناش اكتم تطلع ال W فى ال B اللى
+
+171
+00:18:55,680 --> 00:18:57,140
+هى تلاتة صح
+
+172
+00:19:00,480 --> 00:19:06,280
+في تلاتة مظبوط تلاتة
+
+173
+00:19:06,280 --> 00:19:16,600
+اش بنحسب
+
+174
+00:19:16,600 --> 00:19:24,820
+ال V ال W و بعدين بنحسب ال Fc point
+
+175
+00:19:24,820 --> 00:19:28,440
+واحد تسعة سبعة
+
+176
+00:19:31,280 --> 00:19:44,540
+ال بي ستة ال
+
+177
+00:19:44,540 --> 00:19:53,980
+بي ستة اكم point تلاتة تسعة point
+
+178
+00:19:53,980 --> 00:19:56,000
+تلاتة تسعة كمان رقم
+
+179
+00:19:59,030 --> 00:20:07,850
+الى bound force لكل foot و
+
+180
+00:20:07,850 --> 00:20:18,210
+ال V اكم تطلع طيب
+
+181
+00:20:18,210 --> 00:20:21,810
+هذا المنطوب الاول عشان احسب ال torque
+
+182
+00:20:27,190 --> 00:20:33,090
+الفين سبعمية و تسعة و أربعين foot per minute وال
+
+183
+00:20:33,090 --> 00:20:40,450
+Fc هتكون تستاوي اللي هي point تلاتة تسعة تلاتة على
+
+184
+00:20:40,450 --> 00:20:44,790
+اتنين و تلاتين point واحد سبعة في ال V اللي هي
+
+185
+00:20:44,790 --> 00:20:51,290
+الفين سبعمية و تسعة و أربعين على ستين لكل تربية
+
+186
+00:21:01,240 --> 00:21:10,320
+خمسة و عشرين point six اربعة pound force عشان احسب
+
+187
+00:21:10,320 --> 00:21:22,720
+ال torque ال
+
+188
+00:21:22,720 --> 00:21:23,700
+torque شو تساوي؟
+
+189
+00:21:30,380 --> 00:21:37,660
+كلاتة ستين ألف HD
+
+190
+00:21:37,660 --> 00:21:45,160
+على N طيب
+
+191
+00:21:45,160 --> 00:21:55,860
+ال HD ايه في الساوية ال HD بتساوي H nominal في
+
+192
+00:21:55,860 --> 00:21:56,860
+KS
+
+193
+00:22:00,300 --> 00:22:06,260
+في ND اكتشنوم الأكل عندنا خمس استاش في ال KS واحد
+
+194
+00:22:06,260 --> 00:22:20,740
+وربع في ال ND واحد point واحد عشرين
+
+195
+00:22:20,740 --> 00:22:22,240
+horse power
+
+196
+00:22:26,930 --> 00:22:31,250
+معناة ال torque هتكون سوى تلات ستين الف خمسة و
+
+197
+00:22:31,250 --> 00:22:37,530
+عشرين في عشرين bond ستة تلاتة على الف سبعمية و
+
+198
+00:22:37,530 --> 00:22:38,570
+خمسين
+
+199
+00:23:09,790 --> 00:23:21,670
+المطلوب بعدك بده بده F1 بده
+
+200
+00:23:21,670 --> 00:23:28,530
+F1 F2
+
+201
+00:23:28,530 --> 00:23:34,630
+FI
+
+202
+00:23:38,310 --> 00:23:59,850
+و ال H قال لا وقبل طيب
+
+203
+00:23:59,850 --> 00:24:04,190
+عشان
+
+204
+00:24:04,190 --> 00:24:07,310
+احسب F1 و F2 و FI
+
+205
+00:24:10,270 --> 00:24:14,290
+لازم امشي على الفطوات المعنى هو لازم احسب F1A
+
+206
+00:24:14,290 --> 00:24:20,630
+minus
+
+207
+00:24:20,630 --> 00:24:29,690
+F2 ايش تساوي اتنين T على
+
+208
+00:24:29,690 --> 00:24:36,250
+D هتكون
+
+209
+00:24:36,250 --> 00:24:38,730
+تساوي اتنين
+
+210
+00:24:40,560 --> 00:24:46,980
+في سبعمية و اتنين و اربعين point تمانية على دي
+
+211
+00:24:46,980 --> 00:24:53,880
+اللي هي ستة
+
+212
+00:24:53,880 --> 00:24:58,040
+اتنين
+
+213
+00:24:58,040 --> 00:25:04,040
+و سبعة و اربعين يبدو
+
+214
+00:25:04,040 --> 00:25:06,660
+هذه انش
+
+215
+00:25:16,410 --> 00:25:25,610
+طيب بعدين هحسب F1A بتساوي
+
+216
+00:25:25,610 --> 00:25:29,450
+BFA
+
+217
+00:25:29,450 --> 00:25:36,750
+CB CV ال
+
+218
+00:25:36,750 --> 00:25:43,500
+B معروف هنا six inch طلعناها وال F A ميةبندن طلع
+
+219
+00:25:43,500 --> 00:26:01,480
+ال CP CP بنروح تابر سبعتاش أربعة CP هستخدم
+
+220
+00:26:01,480 --> 00:26:08,920
+هنا polyamide A3 القطر أنا عندي جاي ستانش يعني بين
+
+221
+00:26:08,920 --> 00:26:20,250
+أربعة و نص و تمانيةمعناته هتكون ال CP point 7 ال
+
+222
+00:26:20,250 --> 00:26:27,510
+V
+
+223
+00:26:27,510 --> 00:26:29,210
+عنده ال CV
+
+224
+00:26:46,510 --> 00:26:51,250
+طيب نروح لل CV و نجيبها table سبعتاشر لأ figure
+
+225
+00:26:51,250 --> 00:27:03,710
+طيب
+
+226
+00:27:03,710 --> 00:27:09,480
+ال built business خلينا نرجع لل CVهذه بيحكي لي
+
+227
+00:27:09,480 --> 00:27:12,720
+four polyamide and urethane builds you CV واحد
+
+228
+00:27:12,720 --> 00:27:18,700
+بسوط CV بساوة
+
+229
+00:27:18,700 --> 00:27:28,080
+واحد معناته F1A بساوة P اللي هي ستة في FA مية في
+
+230
+00:27:28,080 --> 00:27:31,340
+CP اللي هي سبعة عشرة في واحد
+
+231
+00:27:41,220 --> 00:27:44,180
+تطلع مائة و عشرين اربعة مائة و عشرين اربعة مائة و
+
+232
+00:27:44,180 --> 00:27:55,460
+عشرين اربعة
+
+233
+00:27:55,460 --> 00:27:55,460
+مائة و عشرين اربعة مائة و عشرين اربعة مائة و عشرين
+
+234
+00:27:55,460 --> 00:27:59,940
+اربعة مائة و عشرين اربعة مائة و عشرين اربعة مائة و
+
+235
+00:27:59,940 --> 00:28:01,020
+عشرين اربعة مائة و عشرين اربعة مائة و عشرين اربعة
+
+236
+00:28:01,020 --> 00:28:01,020
+مائة و عشرين اربعة مائة و عشرين اربعة مائة و عشرين
+
+237
+00:28:01,020 --> 00:28:01,040
+اربعة مائة و عشرين اربعة مائة و عشرين اربعة مائة و
+
+238
+00:28:01,040 --> 00:28:02,140
+عشرين اربعة مائة و عشرين اربعة مائة و عشرين اربعة
+
+239
+00:28:02,140 --> 00:28:04,980
+مائة و عشرين اربعة مائة و عشرين اربعة مائة و عشرين
+
+240
+00:28:04,980 --> 00:28:10,280
+اربعة
+
+241
+00:28:11,460 --> 00:28:17,780
+اللي هو F1A minus
+
+242
+00:28:17,780 --> 00:28:29,440
+F2 هتساوي F1A اللي هي أربعمائة و عشرين minus متين
+
+243
+00:28:29,440 --> 00:28:35,460
+و سبعة و أربعين بن ستة أكم
+
+244
+00:28:45,330 --> 00:28:50,970
+ال F I بتساوي
+
+245
+00:28:50,970 --> 00:29:06,950
+F 1 A زاد F 2 على 2 minus ال F C يعني هتساوي F 1 A
+
+246
+00:29:06,950 --> 00:29:08,310
+أربعمائة و عشرين
+
+247
+00:29:11,610 --> 00:29:18,570
+زاد F2 اللي هي مية و اتنين و سبعين bond four على
+
+248
+00:29:18,570 --> 00:29:25,490
+اتنين minus ال Fc حسبناها ال Fc اللي هي خمس و
+
+249
+00:29:25,490 --> 00:29:34,870
+عشرين bond ست اربعة اتنين
+
+250
+00:29:34,870 --> 00:29:38,390
+و سبعين bond
+
+251
+00:29:45,370 --> 00:29:52,170
+الـ HM هي الـ H Design ليه هذا؟
+
+252
+00:29:52,170 --> 00:29:56,010
+خلّيني
+
+253
+00:29:56,010 --> 00:30:01,070
+أتأكد من الأرقام أنا
+
+254
+00:30:01,070 --> 00:30:01,990
+عامل Excel Sheet
+
+255
+00:30:17,860 --> 00:30:23,040
+الأول الشي عندى type of built open built drive ال
+
+256
+00:30:23,040 --> 00:30:29,160
+built material عندى polyamide a3 المصدر 17.2 لازم
+
+257
+00:30:29,160 --> 00:30:34,360
+يرجع تابل 17.2 ال built thickness ال T عندى point
+
+258
+00:30:34,360 --> 00:30:39,200
+واحد تلاتة ال minimum poly diameter مش لازم يكون
+
+259
+00:30:39,200 --> 00:30:45,070
+أقل اللي هو تابل 17.24 point threeال F A طلعناها
+
+260
+00:30:45,070 --> 00:30:49,870
+مية مظبوط عندي ال specific weight point O for two
+
+261
+00:30:49,870 --> 00:30:53,470
+تابع سبعتاشر اتنين ال coefficient of friction
+
+262
+00:30:53,470 --> 00:30:57,790
+point تمانية تابع سبعتاشر اتنين ال built width ستة
+
+263
+00:30:57,790 --> 00:31:02,170
+انش ال diameter of a small pulley ستة انش ال speed
+
+264
+00:31:02,170 --> 00:31:05,890
+ratio تلاتة ال diameter of a large pulley تمانتاشر
+
+265
+00:31:05,890 --> 00:31:10,590
+انش ال center distance اللي هي تمانية في اتناش ستة
+
+266
+00:31:10,590 --> 00:31:18,840
+و ستين انشrotation speed small poly 1950 rpm الرب
+
+267
+00:31:18,840 --> 00:31:29,340
+انجل اللى هى معادلة فى دى حسبناها هى معادلتها اللى
+
+268
+00:31:29,340 --> 00:31:34,340
+هى πى ناقص اتنين sin inverse لدى capital minus d
+
+269
+00:31:34,340 --> 00:31:39,500
+small على اتنين على
+
+270
+00:31:39,500 --> 00:31:45,640
+اتنين c على اتنين ال center distanceتطلع تلات هذه
+
+271
+00:31:45,640 --> 00:31:52,920
+radians radians هذا ال small بتكون أقل من 180 ال
+
+272
+00:31:52,920 --> 00:31:57,420
+pi أكملت تلاتة point واحد أربعة، مظبوط؟ يعني هذا
+
+273
+00:31:57,420 --> 00:32:02,920
+أقل من pi بعد ان exponential في اف في احداشر point
+
+274
+00:32:02,920 --> 00:32:08,480
+واحد سبعة اللي هو w حسبناه طلع point تلات ساعة
+
+275
+00:32:08,480 --> 00:32:14,030
+تلاتة صحيح، مظبوط؟ الرقم صح بناتهوالسرعة المحيطية
+
+276
+00:32:14,030 --> 00:32:17,490
+V capital طلعت ألفين سبعمائة وتسعة واربعين، مظبوط
+
+277
+00:32:17,490 --> 00:32:26,070
+الرقم ال Fc طلعت ستة عشرين و نص، مظبوط، صح؟
+
+278
+00:32:30,970 --> 00:32:33,790
+ما انا اتولد غلط اتكون عندك نوع ال horse power
+
+279
+00:32:33,790 --> 00:32:37,470
+خمسة استاش condition driver normal torque medium
+
+280
+00:32:37,470 --> 00:32:41,650
+shock ال KS 1.25 من ال table سبتاشر خمسة ستاشر هو
+
+281
+00:32:41,650 --> 00:32:47,210
+ماعطينيها على اي حال ال ND 1.1 ال design horse
+
+282
+00:32:47,210 --> 00:32:51,110
+power عشرين point ستة زي ما حسبتها عند ال design
+
+283
+00:32:51,110 --> 00:32:53,210
+torque سبعمية تلاتة واربين صح الرقم
+
+284
+00:32:57,230 --> 00:33:05,910
+طيب ال f1 a minus f2 تطلع 248 ال poly correction
+
+285
+00:33:05,910 --> 00:33:10,550
+factor cv point 7 اللي هي ال table 17 اربعة عندك
+
+286
+00:33:10,550 --> 00:33:14,050
+speed connection اللي هو cv بالساوية ايه؟ واحد
+
+287
+00:33:14,050 --> 00:33:22,990
+allowed largest tension f1 a 420، مظبوط عند ال f2
+
+288
+00:33:22,990 --> 00:33:23,930
+تطلع 172
+
+289
+00:33:26,500 --> 00:33:32,920
+عندي ال initial tension fy ميتين و سبعين عندي ال
+
+290
+00:33:32,920 --> 00:33:38,400
+actual اللي هو F برايم بالثوبون تلاتة اتنين تسعة
+
+291
+00:33:38,400 --> 00:33:43,080
+هنا انا عامل F statement اذا كان اقل من F هو اقل
+
+292
+00:33:43,080 --> 00:33:46,220
+من تمانية و عاشرة مانا انا مش عندى slip danger of
+
+293
+00:33:46,220 --> 00:33:50,500
+slipping no ده
+
+294
+00:33:50,500 --> 00:33:54,780
+حساب التانية مانت
+
+295
+00:33:54,780 --> 00:33:56,220
+شغلنياش صحيح
+
+296
+00:34:18,060 --> 00:34:25,040
+طيب في طرق لتحكم بال initial tension ممكن احط عند
+
+297
+00:34:25,040 --> 00:34:29,960
+هاي .. عند هاي .. هاي بكرة ال driver هذا ال driven
+
+298
+00:34:29,960 --> 00:34:35,880
+احط اللي هو بكرة وزن عشان تعمل شد بالشكل هذا زي ما
+
+299
+00:34:35,880 --> 00:34:41,470
+انتوا شايفينه اللي هي weighted idler pulleyفي عندى
+
+300
+00:34:41,470 --> 00:34:46,250
+pivoted motor pulley انا عندى هاي ال motor و راكب
+
+301
+00:34:46,250 --> 00:34:49,390
+عليه البكرة الصغيرة بتكون ان في عندى بكرة كبيرة و
+
+302
+00:34:49,390 --> 00:34:54,530
+في عندهين محور دوران فوزن ال motor لتحت زي ما انت
+
+303
+00:34:54,530 --> 00:35:01,590
+شايف وزن ال motor لتحت ايش بيعمل؟ بيشد ال ..
+
+304
+00:35:01,590 --> 00:35:05,290
+كيف بنرقص ال tension؟ نعم كيف بنرقص ال tension؟
+
+305
+00:35:08,110 --> 00:35:14,850
+انت عندك تقريبا .. هتيجي تحكي ال .. ال initial
+
+306
+00:35:14,850 --> 00:35:18,030
+tension طبعا تحكي انت في ال .. في ال initial
+
+307
+00:35:18,030 --> 00:35:21,090
+tension و ليش في ال .. في ال .. يعني ان هو .. هو
+
+308
+00:35:21,090 --> 00:35:25,730
+الجسم بدورش بيكون .. بيكون F1 بيستوي F2، هو بدورش
+
+309
+00:35:29,690 --> 00:35:32,550
+ما هدا هي .. ما هدا بتعمل .. بتعمل عزيزي بحوالي
+
+310
+00:35:32,550 --> 00:35:34,630
+النقطة ها دي ال summation فوق ال summation of
+
+311
+00:35:34,630 --> 00:35:36,630
+moment بساوة zero بس ببساطة
+
+312
+00:35:41,220 --> 00:35:45,240
+طيب اللي في عندي اللي هو catenary induced tension
+
+313
+00:35:45,240 --> 00:35:48,000
+نتيجة لما تكون طبعا في حالة البكارات الكبيرة و
+
+314
+00:35:48,000 --> 00:35:52,960
+الخميلة بيكون هنا وزن هذه بتساعد ان تحدث initial
+
+315
+00:35:52,960 --> 00:35:58,280
+tension الان بيصير فيها انزول نتيجة وزنها اللي هو
+
+316
+00:35:58,280 --> 00:36:03,720
+بيسموها ال dip ال dip يستوي C2W على 96Fiيعني في
+
+317
+00:36:03,720 --> 00:36:07,720
+علاقة من ال initial tension و المسافة هذه ال C
+
+318
+00:36:07,720 --> 00:36:11,560
+اللي هي ال center distance و ال W اللي هي weight
+
+319
+00:36:11,560 --> 00:36:15,520
+per feet of the build اللي هي بالثورة و اتناشر
+
+320
+00:36:15,520 --> 00:36:25,520
+جاما بي تي و ال FI اللي هو ال initial tension
+
+321
+00:36:25,520 --> 00:36:31,520
+لأن لو اتبعنا تغير ال tension و البكرات بدورهنبدأ
+
+322
+00:36:31,520 --> 00:36:39,660
+من نقطة A نقطة A لأن عندهاي محور الدوران هتكون F1
+
+323
+00:36:39,660 --> 00:36:45,640
+أعلى من F2 يعني في البداية الشد
+
+324
+00:36:45,640 --> 00:36:50,740
+عند A بيكون قيمته F1 من A ل B بيضلوا F1 يعني هاي A
+
+325
+00:36:50,740 --> 00:36:57,110
+ل B بيضلوا إيش قيمته F1الان في الفترة من D ل C
+
+326
+00:36:57,110 --> 00:37:07,450
+ببدأ ينزل عند C بيصير H F2 بنزل لحد H F2 من C ل E
+
+327
+00:37:07,450 --> 00:37:13,350
+بيضلوا F2 هي C دي E بيضلوا H F2 بعدين من E ل F
+
+328
+00:37:13,350 --> 00:37:17,870
+ببدأ يرتفع ل H ل F1 بعدين بتتكرر العملية
+
+329
+00:37:21,560 --> 00:37:28,000
+طبعا هذه F2 وهذه F1 حكينا F1 بالساوية ال initial
+
+330
+00:37:28,000 --> 00:37:32,200
+tension بالساوية ال Fc اللي هو due to centrifugal
+
+331
+00:37:32,200 --> 00:37:36,520
+force زائد ال initial tension زي دلتة F على اتنين
+
+332
+00:37:36,520 --> 00:37:45,540
+و F2 ايش بالساوية بالساوية اللي هو Fi هذه زي Fc
+
+333
+00:37:45,540 --> 00:37:51,720
+ناقص دلتة F على اتنين اللي هي هذهواضح؟ معناه ان
+
+334
+00:37:51,720 --> 00:37:56,460
+هاي عندى F1 و F2 الفرق بينهم Delta F
+
+335
+00:38:03,950 --> 00:38:07,250
+الان عادة ال decision set اللي هي قائمة الشغلات
+
+336
+00:38:07,250 --> 00:38:11,190
+اللي ممكن تاخذ فيها قرار لتصميم ال flat build ملزم
+
+337
+00:38:11,190 --> 00:38:15,210
+ان نعرف ال power و ال speed و ال reduction ratio و
+
+338
+00:38:15,210 --> 00:38:18,610
+ال serious factor و ال center distance و ال design
+
+339
+00:38:18,610 --> 00:38:23,550
+factor ND و ال initial tension و ال built material
+
+340
+00:38:23,550 --> 00:38:27,330
+و ال drive geometry دي small و دي capital و ال
+
+341
+00:38:27,330 --> 00:38:29,490
+built thickness و ال built width
+
+342
+00:38:32,770 --> 00:38:38,290
+نشوف مثال سبعتاش اتنين design
+
+343
+00:38:38,290 --> 00:38:42,970
+a flat built drive اكتبوا المعلومات او هتلذبناه
+
+344
+00:38:42,970 --> 00:38:46,390
+design a flat built drive to connect horizontal
+
+345
+00:38:46,390 --> 00:38:49,570
+shafts on sixteen feet centers معناه ال center ال
+
+346
+00:38:49,570 --> 00:38:56,070
+distance ايش ستاشر قدم ال value of this ratio is
+
+347
+00:38:56,070 --> 00:38:59,330
+to be two point two five value of this ratio اتنين
+
+348
+00:38:59,330 --> 00:38:59,670
+وربع
+
+349
+00:39:02,990 --> 00:39:06,050
+السرعة الكبيرة للسيارة الصغيرة هي تقريبا تقريبا
+
+350
+00:39:06,050 --> 00:39:08,510
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+351
+00:39:08,510 --> 00:39:15,970
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+352
+00:39:15,970 --> 00:39:15,970
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+353
+00:39:15,970 --> 00:39:15,990
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+354
+00:39:15,990 --> 00:39:15,990
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+355
+00:39:15,990 --> 00:39:31,090
+تقريبا تقريبا تقريبا تقريبا تقري
+
+356
+00:39:31,970 --> 00:39:36,170
+معروف عند ال RPM عند ال small pulley معروف في ال
+
+357
+00:39:36,170 --> 00:39:39,970
+power اللي هنقلها معروف عند ال shock condition
+
+358
+00:39:39,970 --> 00:39:44,490
+very light shock condition انا عملتها على اكسل شيت
+
+359
+00:39:44,490 --> 00:39:56,630
+خليني
+
+360
+00:39:56,630 --> 00:39:58,790
+اعرف الشغلات انا بدي اعلم شغلات اللي هو معطينيها
+
+361
+00:39:58,790 --> 00:40:06,620
+بالأصفرمعطينا ال center distance و
+
+362
+00:40:06,620 --> 00:40:19,100
+ال velocity ratio ال speed ratio اللي هي هذه نعم
+
+363
+00:40:19,100 --> 00:40:27,420
+و ال N طيب
+
+364
+00:40:27,420 --> 00:40:30,200
+و ال H nominal
+
+365
+00:40:41,410 --> 00:40:48,170
+السنتر دلس نساقى بيعطينيها و ال ks ال ks اللي هي
+
+366
+00:40:48,170 --> 00:40:59,090
+table سبعتاش خمستاش يعني
+
+367
+00:40:59,090 --> 00:41:01,990
+تقريبا انا أخدتها very light يعني من four تقريبا
+
+368
+00:41:01,990 --> 00:41:07,010
+يعني one point fifty انا أخدتها في النص بيعطيني
+
+369
+00:41:07,010 --> 00:41:09,630
+ال ks هو ان ال ks
+
+370
+00:41:14,920 --> 00:41:20,180
+هذه المعلومات عن DH المعطار في
+
+371
+00:41:20,180 --> 00:41:28,000
+شي تاني طيب أول شئ بدي أحدد نوع ال drive هل هو
+
+372
+00:41:28,000 --> 00:41:33,560
+open ولا crossed أنا حكيت open بدي أختار material
+
+373
+00:41:33,560 --> 00:41:38,680
+لل build حكيت ال material انا polyamide A3 او اي
+
+374
+00:41:38,680 --> 00:41:43,380
+material تانية يعني هذا الاختيار اللي عملتهطيب
+
+375
+00:41:43,380 --> 00:41:47,820
+based on selection of built material هروح من ال
+
+376
+00:41:47,820 --> 00:41:50,440
+tier 17 ال 2 أطلع اللي هو ال build thickness اللي
+
+377
+00:41:50,440 --> 00:41:54,840
+هو point واحد تلاتة و بحكي ال minimum poly
+
+378
+00:41:54,840 --> 00:41:56,320
+diameter لسه مااخترتش و بحكي ال minimum poly
+
+379
+00:41:56,320 --> 00:41:59,660
+diameter أربع point three لازم تكون ماتقلش عن أربع
+
+380
+00:41:59,660 --> 00:42:04,200
+point three لسه مااخترتش ال diameter بتاعها و
+
+381
+00:42:04,200 --> 00:42:08,770
+بعطيني ال fa اللي هو ميةوال Gamma ل specific
+
+382
+00:42:08,770 --> 00:42:15,030
+weight point 042 ومعامل احتكاك تمانية من عشرة الآن
+
+383
+00:42:15,030 --> 00:42:18,550
+هذا
+
+384
+00:42:18,550 --> 00:42:22,310
+يعني هو .. هذا معطيني معلومات يعني خلاص ثابتة بس
+
+385
+00:42:22,310 --> 00:42:25,170
+لسه انا ماعملتش decisions يعني ال decision اللي
+
+386
+00:42:25,170 --> 00:42:28,810
+عملته هاد ال decision بتحكي هاد ال first decision
+
+387
+00:42:28,810 --> 00:42:30,950
+هاد القرار الأول
+
+388
+00:42:34,080 --> 00:42:38,380
+هذا القرار الأول بناء القرار هذا طلعت استخلاص
+
+389
+00:42:38,380 --> 00:42:46,700
+معلومات هي واحدة اتنين تلاتة اربع خمسة بتاخد
+
+390
+00:42:46,700 --> 00:42:57,540
+decision ال built width فيه
+
+391
+00:42:57,540 --> 00:43:01,480
+بتهيألي عند هنا نرجع لورا شوية
+
+392
+00:43:28,360 --> 00:43:35,100
+طيب انا اللي سويته يعني حكيت بدي فيه عشان عشرة
+
+393
+00:43:35,100 --> 00:43:39,700
+يعني هاي decision هحضيها هادي decision ال minimum
+
+394
+00:43:39,700 --> 00:43:43,480
+polydynamic الاربعة point تلاتة يعني لازم تكون
+
+395
+00:43:43,480 --> 00:43:47,280
+اكبر انا حكيت بديها تكون ايهاش ستاشر ممكن اغير و
+
+396
+00:43:47,280 --> 00:43:50,420
+اشوف ايش اللي بيصير معناها هاي ستاشر يعني خلاني
+
+397
+00:43:50,420 --> 00:43:55,730
+أشوف اللي هو طبعا مستحيل اجيبه من اول مرةماشي بس
+
+398
+00:43:55,730 --> 00:43:58,250
+خنشوف النتيجة النهائية و بعدين نلعب في الأرقام
+
+399
+00:43:58,250 --> 00:44:04,990
+الان الان الان اذا انا عارف ال .. ال .. ال speed
+
+400
+00:44:04,990 --> 00:44:07,350
+ratio اتنين و ربوع عارف قطر اللي صغيرة هذي مش
+
+401
+00:44:07,350 --> 00:44:11,930
+decision هذي محسوبة هتكون اتنين و ربوع في ستاش
+
+402
+00:44:11,930 --> 00:44:17,890
+يعني اكام ستة و تلاتين انش ال
+
+403
+00:44:17,890 --> 00:44:25,160
+Phi D اللي هي exponential لل F Phiأخدت ال F عرفي
+
+404
+00:44:25,160 --> 00:44:30,400
+أنا و ال Phi ال Phi لما أنا عارف ال center
+
+405
+00:44:30,400 --> 00:44:33,260
+distance already سرتي أعرف دي small و دي capital
+
+406
+00:44:33,260 --> 00:44:39,820
+مظبوط لما أنا ببحث بال Phi دي بحث بال Phi دي و
+
+407
+00:44:39,820 --> 00:44:43,680
+منها بحث ال exponential لإفعيانات هذه كمية محسوبة
+
+408
+00:44:43,680 --> 00:44:51,610
+ال W تعتمد على ال B و ال T و الجامعةalready هدول
+
+409
+00:44:51,610 --> 00:44:57,830
+طلعتهم معناته كمية محسوبة السرعة المحيطية بي دي ان
+
+410
+00:44:57,830 --> 00:45:03,490
+small على اتناش معناته برضه كمية محسوبة هذه صارت
+
+411
+00:45:03,490 --> 00:45:13,570
+ايش كمية محسوبة بعدين ال Fc برضه
+
+412
+00:45:13,570 --> 00:45:16,290
+كمية محسوبة الى W على اتنين و تلاتين مو اتواحد
+
+413
+00:45:16,290 --> 00:45:20,470
+سبعة في V على ستين كل تربيع مظبوط ال Fc
+
+414
+00:45:26,280 --> 00:45:32,920
+طيب ال design factor انا بقرر بديها اللي بديها انا
+
+415
+00:45:32,920 --> 00:45:38,940
+هذا decision معناته هذا قرار للمصمم حتى انا حاططه
+
+416
+00:45:38,940 --> 00:45:43,780
+one point oh fiveال design horsepower ايش بتستوي
+
+417
+00:45:43,780 --> 00:45:50,320
+اللي هي ND في ال KS في ال H nominal انا already
+
+418
+00:45:50,320 --> 00:45:53,780
+اختارت ال ND و ال KS اللي عارفه و ال H nominal
+
+419
+00:45:53,780 --> 00:46:00,060
+عارفها معناته كمية محسوبة ال
+
+420
+00:46:00,060 --> 00:46:05,900
+design torque اللي هو تلات ستين الف و خمس و عشرين
+
+421
+00:46:05,900 --> 00:46:14,840
+في HD على N معناته كمية محسوبة هذهبعدين ال F1A
+
+422
+00:46:14,840 --> 00:46:21,020
+ناقص F2 سواء 2T على D كمية محسوبة ال poly
+
+423
+00:46:21,020 --> 00:46:26,520
+correction factor بيتم دي حسب إيش قطر ال poly صح
+
+424
+00:46:26,520 --> 00:46:29,960
+قطر ال poly أنا حكيت ستاشر إنش بيدوروا على ال
+
+425
+00:46:29,960 --> 00:46:33,920
+table سبعتاشر
+
+426
+00:46:33,920 --> 00:46:38,900
+أربعة صح ستاشر
+
+427
+00:46:38,900 --> 00:46:49,220
+إنشيعني لأ polyamide bond تسعة أربعة مظبط هذه
+
+428
+00:46:49,220 --> 00:46:53,500
+معناه كمية مستخرجة او يعني مستخرج محسب نفس الشيء
+
+429
+00:46:53,500 --> 00:47:01,800
+ال CV يعني دي polyamide واحد مستخرجة ال F1A بساولة
+
+430
+00:47:01,800 --> 00:47:11,120
+هو F1A في B في T في CB صح؟QCV المهم هذه كمية
+
+431
+00:47:11,120 --> 00:47:17,620
+محسوبة عندي بعدين ال F2 كمية محسوبة ال initial
+
+432
+00:47:17,620 --> 00:47:23,920
+tension برضه كمية محسوبة ال F prime برضه كمية
+
+433
+00:47:23,920 --> 00:47:33,540
+محسوبة ماشي احنا عرفنا ايش الشغلات ال input اللي
+
+434
+00:47:33,540 --> 00:47:41,300
+هو الأصفرو الأصفر هو قرارات المصمم و عندي ال
+
+435
+00:47:41,300 --> 00:47:44,760
+otherwise اللي هو كمية محسوبة معناته خليني احكي
+
+436
+00:47:44,760 --> 00:47:49,340
+انا طرت اللي هو polyamide A3 decision والله حكيت
+
+437
+00:47:49,340 --> 00:47:56,160
+ال built with خليني احكي مثلا تماني انش خليني اشوف
+
+438
+00:47:56,160 --> 00:48:00,020
+ايش بيصير عندى ال
+
+439
+00:48:00,020 --> 00:48:01,320
+factor of safety
+
+440
+00:48:04,750 --> 00:48:09,970
+فى danger of slip المفروض أحسن ال factor ستة كم
+
+441
+00:48:09,970 --> 00:48:13,570
+مرة انا فين danger of slip انا تبقى كفيش اللي هو
+
+442
+00:48:13,570 --> 00:48:23,650
+ايش تمانية هاي عشرة طب خلينا نحط ال D عشرة او
+
+443
+00:48:23,650 --> 00:48:24,770
+تمانية تمانية يعنيش
+
+444
+00:48:32,690 --> 00:48:42,470
+بطلعشوش منطقي ايش ايه؟ رياضيا مش صح طيب خليني
+
+445
+00:48:42,470 --> 00:48:51,390
+احطها عشرة اشوف شو يصير معاه، هاي عشرة لسه،
+
+446
+00:48:51,390 --> 00:48:59,390
+هاي اتناش بس
+
+447
+00:48:59,390 --> 00:49:08,110
+فيه .. فيه slavageهنحطها اربعتاش هاي اربعتاش فى
+
+448
+00:49:08,110 --> 00:49:11,410
+حاجات بتاعت مدعومة على السرعة فى حاجات انا already
+
+449
+00:49:11,410 --> 00:49:17,750
+كاتب يعنى no لان برضه ايش تظبط ايش اتناشر انش تظبط
+
+450
+00:49:17,750 --> 00:49:24,790
+اتناشر انش واضح؟
+
+451
+00:49:24,790 --> 00:49:28,870
+طب ياك ممكن خلصنا اعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/7NsmsovxXi0_raw.srt b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/7NsmsovxXi0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6d192374621c95943e0b6d74155e39c994fd551f
--- /dev/null
+++ b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/7NsmsovxXi0_raw.srt
@@ -0,0 +1,1460 @@
+1
+00:00:05,130 --> 00:00:07,770
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:07,770 --> 00:00:11,750
+وبركاته، هنكمل في مادة تصيم الألات، احنا كنا
+
+3
+00:00:11,750 --> 00:00:16,110
+الموضوع الفصد الحالي اللي هو design of flat
+
+4
+00:00:16,110 --> 00:00:20,750
+builds، حكينا عن ال flat builds،
+
+5
+00:00:20,750 --> 00:00:24,290
+حكينا عن flat metal builds، و بعدين المرفعات نحكي
+
+6
+00:00:24,290 --> 00:00:31,450
+عن ال V buildsالان عشان احدد flat built باختار
+
+7
+00:00:31,450 --> 00:00:35,110
+طبعا فيه succession .. فيه succession من a,b,c,d,e
+
+8
+00:00:35,110 --> 00:00:39,570
+.. table سبعة تسعة موجينة ال .. ال .. نحكي ال ..
+
+9
+00:00:39,570 --> 00:00:45,070
+ال basic dimensions لل .. لل ..الستاندرد V Builds
+
+10
+00:00:45,070 --> 00:00:49,590
+يعني ماعطيني ال width ال A و ال thickness B و ال
+
+11
+00:00:49,590 --> 00:00:53,390
+minimum sheath diameter و ال horsepower range يعني
+
+12
+00:00:53,390 --> 00:00:56,390
+لو أخدنا B ال A تعيطة تكون واحد و اشرين على اتنين
+
+13
+00:00:56,390 --> 00:01:00,010
+و تلاتين و ال B سبعة ستاشر و ال minimum sheath
+
+14
+00:01:00,010 --> 00:01:03,390
+diameter خمسة point اربع انش و بتغطي ال power
+
+15
+00:01:03,390 --> 00:01:07,690
+range سواء كانت one built او اكتر من built من واحد
+
+16
+00:01:07,690 --> 00:01:10,470
+لخمس و عشرين حصان يعني لو اتجوزت انك ال power لخمس
+
+17
+00:01:10,470 --> 00:01:12,590
+و عشرين حصان بدك تروح على ايش على ال C على اللي
+
+18
+00:01:12,590 --> 00:01:12,870
+بعدها
+
+19
+00:01:15,620 --> 00:01:21,340
+فى شكل سبعتاشر عشرة او فى table سبعتاشر عشرة
+
+20
+00:01:21,340 --> 00:01:27,800
+ماطيني ال list ال .. ال succession A, B, C, D ال
+
+21
+00:01:27,800 --> 00:01:33,720
+standard و ماطيني ال standard المحيط الداخلياللي
+
+22
+00:01:33,720 --> 00:01:37,780
+هي بتيجي مقاسات معيارية، يعني عندي خمس تلاتين،
+
+23
+00:01:37,780 --> 00:01:42,100
+تمنع تلاتين، عندي مية وعشرين، مية وعشرين انش طبعا،
+
+24
+00:01:42,100 --> 00:01:45,480
+تلت مية انش وعكس هذه اللي هي المقاسات standard في
+
+25
+00:01:45,480 --> 00:01:46,240
+ال B section
+
+26
+00:01:50,600 --> 00:01:53,840
+طبعا احنا في الحسابات باهبنا اللي هو ال pitch
+
+27
+00:01:53,840 --> 00:01:58,700
+length مش ال inside مش المحيط الداخلي عشان يكتب ال
+
+28
+00:01:58,700 --> 00:02:03,560
+17 11 يعطينا correction factor
+
+29
+00:02:03,560 --> 00:02:09,580
+يختلف باختلاف المقطع مثلا انا كنت بختار B 75 ال
+
+30
+00:02:09,580 --> 00:02:12,500
+correction factor عشان اجيب ال pitch length بدي
+
+31
+00:02:12,500 --> 00:02:19,260
+اضيف 1.8 فبصير ال pitch length 75 زياد 1.8 بصير 76
+
+32
+00:02:19,260 --> 00:02:22,860
+.8طبعا كل ال calculations الحسابات لل
+
+33
+00:02:22,860 --> 00:02:26,820
+Velociraptors تعتمد على ال pitch diameters مش ال
+
+34
+00:02:26,820 --> 00:02:27,740
+inside diameters
+
+35
+00:02:32,870 --> 00:02:37,810
+ال groove angle على البكرة نفسها بتكون عادة أصغر
+
+36
+00:02:37,810 --> 00:02:44,010
+شويه من .. من .. من اللي هو زاوية ميل ال build ..
+
+37
+00:02:44,010 --> 00:02:49,010
+زاوية ميل اللي هي المقطع تاع ال V build طبعا هذا
+
+38
+00:02:49,010 --> 00:02:55,170
+لازم عشان يولد احتكاك كافي طبعا إذا كان الأصغر
+
+39
+00:02:55,170 --> 00:02:58,990
+بكتير بتعمل مشكلة بتصير عملية نزع ال build من ال
+
+40
+00:02:58,990 --> 00:03:01,290
+.. ال pulley بتصير بتعمله صعوبة
+
+41
+00:03:05,560 --> 00:03:08,640
+for best results v build should run quite fast
+
+42
+00:03:08,640 --> 00:03:13,440
+عشان نحصل على نتائج كفاءة عالية لازت تكون نسبيا
+
+43
+00:03:13,440 --> 00:03:19,200
+سرعة ال v build سريعة فاربع تلاف foot per minute
+
+44
+00:03:19,200 --> 00:03:21,520
+يعني ممكن نعطيها سرعة مناسبة و تكون ال efficiency
+
+45
+00:03:21,520 --> 00:03:25,700
+عندها عالية الان typically ال v build drivers
+
+46
+00:03:25,700 --> 00:03:28,880
+بيشتغلوا على سرعة محطية بين الف foot per minute
+
+47
+00:03:28,880 --> 00:03:35,820
+لخمس تلاف foot per minute ال pitch lengthفي علاقة
+
+48
+00:03:35,820 --> 00:03:41,540
+بين ال pitch length و ال center distance اللي هي
+
+49
+00:03:41,540 --> 00:03:46,700
+هذه العلاقة او اذا انا بكون عارف ال pitch length
+
+50
+00:03:46,700 --> 00:03:50,910
+انا في النهاية انا بختار ايه ايشبختار انا .. انا
+
+51
+00:03:50,910 --> 00:03:52,890
+بعمل calculation لل pitch length طبعا ال pitch
+
+52
+00:03:52,890 --> 00:03:58,350
+length لما اعمل حسابات اكيد هتختلف عن ال standard
+
+53
+00:03:58,350 --> 00:04:01,870
+بختار standard قريب و بعد ما اختار ال standard
+
+54
+00:04:01,870 --> 00:04:06,550
+قريب برجع بحسب ال center distance كمان مرة ال
+
+55
+00:04:06,550 --> 00:04:10,610
+center distance typical تتراوح بين D capital ل 3
+
+56
+00:04:10,610 --> 00:04:13,390
+في D plus .. D capital زائد D small
+
+57
+00:04:17,510 --> 00:04:21,170
+التابل سبعتاشر اتناش ميقين ال horse power ratings
+
+58
+00:04:21,170 --> 00:04:28,550
+of standard v builds يعني لو أخدنا a
+
+59
+00:04:28,550 --> 00:04:32,430
+built ال
+
+60
+00:04:32,430 --> 00:04:36,570
+shift data مثلا لو كان four point two و الصراع تلت
+
+61
+00:04:36,570 --> 00:04:41,590
+تلافبتكون ال .. ال .. ال .. ال power rating ال
+
+62
+00:04:41,590 --> 00:04:46,310
+power rating اتنين point two احصان طبعا هذا ال
+
+63
+00:04:46,310 --> 00:04:50,070
+rating is based on running on equal diameter
+
+64
+00:04:50,070 --> 00:04:53,370
+sheaves يعني دي small بالساوية دي capital يعني ال
+
+65
+00:04:53,370 --> 00:04:57,370
+wrap angle بالساوية مية و تمانين درجة ال length
+
+66
+00:04:57,370 --> 00:05:03,250
+بتاع ال built moderate length و بمشي steady load
+
+67
+00:05:03,250 --> 00:05:05,570
+يعني الكأس بالساوية واحد
+
+68
+00:05:08,360 --> 00:05:12,120
+عشان هيك عشان احسب ال allowable power per built
+
+69
+00:05:12,120 --> 00:05:18,120
+لازم اخد في الاعتبار ان قطر البكرتين مش بدار يكون
+
+70
+00:05:18,120 --> 00:05:25,260
+نفس الشي هاي واحد اتنين ال .. ال .. ال .. ال .. ال
+
+71
+00:05:25,260 --> 00:05:29,600
+.. في correction factor لل built length فهيكون دي
+
+72
+00:05:29,600 --> 00:05:32,100
+ال allowable power بستوى K واحد K اتنين H
+
+73
+00:05:32,100 --> 00:05:39,540
+tabulatedالـ H Tabulated من الـ Table 17-12 اللي
+
+74
+00:05:39,540 --> 00:05:45,340
+هو هذا و الـ K واحد correction factor لل angle of
+
+75
+00:05:45,340 --> 00:05:51,840
+wrap Table 17-13 لان عندي دي capital minus دي اسمه
+
+76
+00:05:51,840 --> 00:05:57,160
+على C او ال angle of wrap منها بحسب ال K واحد طبعا
+
+77
+00:05:57,160 --> 00:06:04,110
+المقطوع عندي VVو V flat ال V V يعني بيكون البكرتين
+
+78
+00:06:04,110 --> 00:06:12,710
+V type البكرتين بيكونوا إيش V type ال V flat واحدة
+
+79
+00:06:12,710 --> 00:06:17,810
+منهم تكون V واحدة إيش flat البكرتين بيصير بس عادة
+
+80
+00:06:17,810 --> 00:06:20,910
+بتكون ال flat هي البكرة إيش الكبيرة
+
+81
+00:06:25,150 --> 00:06:29,290
+الـ key to built length correction factor table
+
+82
+00:06:29,290 --> 00:06:36,270
+1714 لأن
+
+83
+00:06:36,270 --> 00:06:39,350
+مايعطيني هنا ال .. انا بتطلع ان هو ال build لو
+
+84
+00:06:39,350 --> 00:06:47,210
+كانت بي build بي build و ال length بتاعها بين 48 ل
+
+85
+00:06:47,210 --> 00:06:52,730
+60 انش بكون عندي ال length factor point 9
+
+86
+00:06:55,950 --> 00:06:58,690
+و ال H اللي هو ابو ال K واحد K اتنين في ال H
+
+87
+00:06:58,690 --> 00:07:03,010
+tabulated .. ال H tabulated من ال table سبعتاش
+
+88
+00:07:03,010 --> 00:07:03,690
+اتناش
+
+89
+00:07:07,020 --> 00:07:11,240
+في شركة اسمها Gates rubber company declares its
+
+90
+00:07:11,240 --> 00:07:13,940
+effective coefficient of friction يعني حكت انا في
+
+91
+00:07:13,940 --> 00:07:18,900
+ال V built بنستخدم معامر احتكاك قيمته point خمسة
+
+92
+00:07:18,900 --> 00:07:24,380
+واحد اتنين تلاتة فالمعادلة تستخدم F واحد minus F
+
+93
+00:07:24,380 --> 00:07:27,200
+centrifugal على F اتنين minus F centrifugal بصورة
+
+94
+00:07:27,200 --> 00:07:31,640
+exponential ل point خمسة واحد اتنين تلاتة الفايةال
+
+95
+00:07:31,640 --> 00:07:36,400
+F1 هى ال force ال tension فى الحبل فى الطرف
+
+96
+00:07:36,400 --> 00:07:41,460
+المجدود ال tight side وال F2 هى ال tension فى
+
+97
+00:07:41,460 --> 00:07:46,180
+الحبل فى الجزء المرتخى نسبيا و ال Fc ال force due
+
+98
+00:07:46,180 --> 00:07:51,460
+to the centrifugal effectالقالة design power دي
+
+99
+00:07:51,460 --> 00:07:54,520
+لإن في عشان تكون في عندي ال allow power per built
+
+100
+00:07:54,520 --> 00:07:59,760
+اللي هي HA وفي design power لكل ال poly drive
+
+101
+00:07:59,760 --> 00:08:04,660
+system ال poly drive system ممكن يكون حبل أو أكتر
+
+102
+00:08:04,660 --> 00:08:10,360
+فال H design بتستوى ال nominal power في ال KS في
+
+103
+00:08:10,360 --> 00:08:16,140
+ال ND ال nominal power مش هي تبيلة ال powerالـ KS
+
+104
+00:08:16,140 --> 00:08:19,120
+service factor والان دي design factor of safety
+
+105
+00:08:19,120 --> 00:08:22,820
+طبعا
+
+106
+00:08:22,820 --> 00:08:27,800
+لما أقسم ال H design على ال H A أكيد هتكون أكبر أو
+
+107
+00:08:27,800 --> 00:08:34,660
+يساوي واحد لو طلعت واحد و نص منها بقى أحسب عدد إيش
+
+108
+00:08:34,660 --> 00:08:40,960
+ال builds لأن ال H اللي هو أقول لل build الواحدةال
+
+109
+00:08:40,960 --> 00:08:44,880
+H design لكل ال system معناته ال number of builds
+
+110
+00:08:44,880 --> 00:08:51,040
+بساوي ال H design على ال H ال level و انا بقرب
+
+111
+00:08:51,040 --> 00:08:55,120
+يعني برفع الرقم لو كان one point two بصير اتنين لو
+
+112
+00:08:55,120 --> 00:08:57,620
+one point three برضه بصير اتنين لو one point six
+
+113
+00:08:57,620 --> 00:09:00,560
+برضه بصير اش اتنين اتنين point واحد بصير تلاتة
+
+114
+00:09:00,560 --> 00:09:05,900
+builds و هكذا طيب
+
+115
+00:09:09,040 --> 00:09:12,940
+الـ centrifugal tension Fc يُعطي العلاقة Fc بساوية
+
+116
+00:09:12,940 --> 00:09:18,500
+Kc في V على الف لكل تربيع و Delta F اللي هي الفرق
+
+117
+00:09:18,500 --> 00:09:23,400
+بين ال tight side و ال tension side بساوية تلات
+
+118
+00:09:23,400 --> 00:09:30,860
+سنين الف و خمسة و عشرين في HD على NPعلى N في D على
+
+119
+00:09:30,860 --> 00:09:36,260
+2 N small اللى هى ال RPM و ال HD اللى هى ال design
+
+120
+00:09:36,260 --> 00:09:40,180
+power و ال N بيه ال number of builds هان فى ال
+
+121
+00:09:40,180 --> 00:09:45,920
+table سبعتاش ستاش ماطينى ال KB ال KB هنجيله بعد
+
+122
+00:09:45,920 --> 00:09:49,200
+شوية ال KB و الكاسي حاليا بيبنى الكاسي for
+
+123
+00:09:49,200 --> 00:09:53,100
+different build sections مثلا ال B لل B build
+
+124
+00:09:53,100 --> 00:09:58,000
+section بتكون الكاسي بسببه تسعة ستة خمسة
+
+125
+00:10:02,970 --> 00:10:09,210
+الملخص احنا بنحسب الـ delta F بتساوي تلت ستين الف
+
+126
+00:10:09,210 --> 00:10:13,190
+و خمس و عشرين في H design على N D على N small D
+
+127
+00:10:13,190 --> 00:10:17,790
+على اتنين وال F واحد بيساوي F C زي delta F
+
+128
+00:10:17,790 --> 00:10:23,170
+exponential F prime Phi على exponential F prime
+
+129
+00:10:23,170 --> 00:10:27,710
+Phi minus واحد وال F two بيساوي F واحد minus delta
+
+130
+00:10:27,710 --> 00:10:30,950
+F وال F I بيساوي F واحد زي F اتنين على اتنين minus
+
+131
+00:10:30,950 --> 00:10:31,470
+F C
+
+132
+00:10:37,080 --> 00:10:40,460
+الان ال derivative او ال life correlations علاقات
+
+133
+00:10:40,460 --> 00:10:49,680
+الحياة بتاعة ال .. او عمر ال bills بتكون معقدة
+
+134
+00:10:49,680 --> 00:10:53,860
+شوية لأنه احنا نفترض ان في عندي بس F واحد و F
+
+135
+00:10:53,860 --> 00:11:01,340
+اتنين، F واحد، الان مع ال flexing effectهيكون في
+
+136
+00:11:01,340 --> 00:11:03,820
+stress component due to bending في stress
+
+137
+00:11:03,820 --> 00:11:07,720
+component due to bending يعني هده هتكون equivalent
+
+138
+00:11:07,720 --> 00:11:13,240
+ل some يعني انا ممكن احول في الآخر ال bending
+
+139
+00:11:13,240 --> 00:11:19,220
+بيعمل إيهاش normal stress و الشد برضه بيعمل normal
+
+140
+00:11:19,220 --> 00:11:23,320
+stress معناته جزئية ال building اللي بتعمل normal
+
+141
+00:11:23,320 --> 00:11:29,320
+stress ممكن احول ل equivalentاللي هو axial أو
+
+142
+00:11:29,320 --> 00:11:37,300
+tensile stress فبيصير عندى .. عندى two forces T1
+
+143
+00:11:37,300 --> 00:11:43,160
+بيصير F1 زي FB1 بيصير F1 زي KB على D و ال tension
+
+144
+00:11:43,160 --> 00:11:49,760
+ال cooling tension T2 بيصير F1 زي FB2 ليه F1 زي KB
+
+145
+00:11:49,760 --> 00:11:56,570
+على Dالان في ال built drives خان اتبع عند النقاط a
+
+146
+00:11:56,570 --> 00:12:06,130
+,b,c,d,e,f عند a .. عند a ال force ايش بتكون
+
+147
+00:12:06,130 --> 00:12:14,210
+قمتها؟ F1 صح؟ بتكون ايه ايش؟ F1 حضلها F1 لحد ما
+
+148
+00:12:14,210 --> 00:12:22,610
+نصل لنقطة B هاي عندي من A ل B حضلها ايه ايش؟ F1من
+
+149
+00:12:22,610 --> 00:12:29,170
+B ل C ببدأ يصير ال bending effect يشتغل ببدأ يصير
+
+150
+00:12:29,170 --> 00:12:35,350
+bending effect معناته ال tension في الحبل هيكون
+
+151
+00:12:35,350 --> 00:12:39,290
+due لل tension الأصلي اللي هو F1 و due to
+
+152
+00:12:39,290 --> 00:12:43,270
+equivalent due to ال bending effect فهيصير عندي
+
+153
+00:12:43,270 --> 00:12:48,130
+اضيف هنا component اللي هي FB1 اللي هي المعادلة
+
+154
+00:12:48,130 --> 00:12:50,090
+هذه زاد FB
+
+155
+00:12:52,900 --> 00:13:02,400
+بتعطيني T1 هذا من B ل C طبعا من B ل C ببدأ يش يقل
+
+156
+00:13:02,400 --> 00:13:10,160
+لأن ال tension F2 هنا أقل فعندي
+
+157
+00:13:10,160 --> 00:13:13,000
+هذه اللي هي نقطة C
+
+158
+00:13:15,770 --> 00:13:24,870
+أو قبل C بنزل فجأة لإيش؟ ل F2 بنزل فجأة ل F2 طيب
+
+159
+00:13:24,870 --> 00:13:36,090
+الآن من C ل إيه؟ بتظل ل إيش؟ F2 بعدين
+
+160
+00:13:36,090 --> 00:13:43,630
+مجرد مدخل هنا فجأة بقفز ل .. شوية .. هنا بقفز فجأة
+
+161
+00:13:43,630 --> 00:13:51,900
+بدخل يعني إش تانيبعدين من E ل F ببدأ اش ازيد ل F
+
+162
+00:13:51,900 --> 00:14:00,100
+واحد بعدين بنزل FB2 فانا هنا انا اش هاد البقرة
+
+163
+00:14:00,100 --> 00:14:03,900
+الكبيرة، تنسوش، فهتكون عندى ال tension على البقرة
+
+164
+00:14:03,900 --> 00:14:06,620
+الكبيرة اللي هو T2
+
+165
+00:14:11,850 --> 00:14:16,030
+الان number of passes أكاب لف number of passes
+
+166
+00:14:16,030 --> 00:14:22,110
+للحبل يُعطى بالعلاقة اللي هي k على t واحد أس ناقص
+
+167
+00:14:22,110 --> 00:14:27,510
+بي زائد k على t اتنين أس ناقص بي لكل أس ناقص واحد
+
+168
+00:14:27,510 --> 00:14:32,030
+طبعا هذه بيحكي عن عدد عن passes ممكن أحولها لإيش
+
+169
+00:14:32,030 --> 00:14:39,830
+لساعاتالان ال lifetime in hours يُعطي للقى n بي ال
+
+170
+00:14:39,830 --> 00:14:43,490
+number of passes ال T هتكون اللي هي ال number of
+
+171
+00:14:43,490 --> 00:14:47,530
+passes في ال pitch length على سبمائة و عشرين V
+
+172
+00:14:47,530 --> 00:14:50,990
+الصراع ال V اللي هي إيش الصراع المحيطية و ال T
+
+173
+00:14:50,990 --> 00:14:53,150
+اللي هو ال time العمر في الساعة
+
+174
+00:14:57,230 --> 00:15:02,770
+ال K و ال B طبعا بنجيبه من table سبعتاش .. سبعتاش
+
+175
+00:15:02,770 --> 00:15:08,950
+يختلف باختلاف ايش؟ ال section بتاع B built و بال
+
+176
+00:15:08,950 --> 00:15:13,680
+life expectancy التواقع العمرمن عشرة أقصد تمانية
+
+177
+00:15:13,680 --> 00:15:17,860
+لعشر أقصد تسعة بيكون فيه قيم ل K و B من عشر أقصد
+
+178
+00:15:17,860 --> 00:15:22,820
+تسعة لعشر أسعاشرة passes بيكون برضه فيه قيم ل K و
+
+179
+00:15:22,820 --> 00:15:29,460
+B لحظة عندي ال A و ال B و ال C و ال D و ال E مصممة
+
+180
+00:15:29,460 --> 00:15:32,620
+تعيش من عشر أقصد تمانية لعشر أقصد تسعة فبتالي ال K
+
+181
+00:15:32,620 --> 00:15:37,940
+و ال B جاي في المنطقة هذهالتلاتة V في تلاتة V
+
+182
+00:15:37,940 --> 00:15:42,220
+والخامسة V ممكن تعيش في ال two ranges في العشرة أس
+
+183
+00:15:42,220 --> 00:15:45,040
+تلانية العشرة أس تسعة أو عشرة أقص تسعة عشرة أقص
+
+184
+00:15:45,040 --> 00:15:50,160
+عشرة أقص عشرة طيب
+
+185
+00:15:52,520 --> 00:15:55,960
+لان ملخص ال analysis ل V built drive اول شي لازم
+
+186
+00:15:55,960 --> 00:16:01,720
+نحسب السرعة المحيطية ال pitch length و ال center
+
+187
+00:16:01,720 --> 00:16:06,320
+distance و ال angle of wrap و ال exponential لل F
+
+188
+00:16:06,320 --> 00:16:12,080
+فاين واحد اتنين هنحسب ال design power و ال
+
+189
+00:16:12,080 --> 00:16:18,200
+allowable power و ال number of buildsو ال number
+
+190
+00:16:18,200 --> 00:16:21,760
+of bills نحصل من ND بالساوية HDE على HA و نعمل
+
+191
+00:16:21,760 --> 00:16:28,040
+round upبعدين بنحسب ال Fc و ال delta F و ال F1 و
+
+192
+00:16:28,040 --> 00:16:32,860
+ال F2 و ال Fi و ال factor of safety وبعدين بنحسب
+
+193
+00:16:32,860 --> 00:16:41,340
+عمر ال build ال number و ال passes او الساعات هذا
+
+194
+00:16:41,340 --> 00:16:47,580
+الملخص اللي هو الحسابات نشوف مثال مثلا انا طبعا
+
+195
+00:16:47,580 --> 00:16:48,580
+عامل excel sheet
+
+196
+00:16:53,340 --> 00:16:59,160
+أنا عندي هنا a ten horsepower الموتور عشرة أحصان
+
+197
+00:16:59,160 --> 00:17:03,820
+يعني
+
+198
+00:17:03,820 --> 00:17:11,120
+هذه هتكون H nominal عشرة
+
+199
+00:17:11,120 --> 00:17:15,900
+horsepower a ten horsepower split-phase motor
+
+200
+00:17:15,900 --> 00:17:20,600
+running at seventeen hundred fifty rpm الآن
+
+201
+00:17:22,920 --> 00:17:30,660
+ألف سبعمائة و خمسين rpm is
+
+202
+00:17:30,660 --> 00:17:34,960
+used to drive a rotary pump تستخدم عشان أشجع
+
+203
+00:17:34,960 --> 00:17:39,280
+المضخة which operates twenty four hours per day
+
+204
+00:17:39,280 --> 00:17:47,600
+يعني ال operation أربع
+
+205
+00:17:47,600 --> 00:17:49,640
+و عشرين hour
+
+206
+00:17:51,860 --> 00:17:58,400
+per day شغالة على طول يعني an engineer has
+
+207
+00:17:58,400 --> 00:18:06,820
+specified a 7.4 inch small shape دي small سواء
+
+208
+00:18:06,820 --> 00:18:16,800
+7.4 inch و دي capital سواء 11 inch هو
+
+209
+00:18:16,800 --> 00:18:25,400
+مستخدم تلاتة bills تلاتة three ال NBساوت تلاتة و
+
+210
+00:18:25,400 --> 00:18:33,360
+ال section اللي هو B مية و اتناش service
+
+211
+00:18:33,360 --> 00:18:38,280
+factor one point three يعني
+
+212
+00:18:38,280 --> 00:18:40,520
+هو شرح لك ليش one point two تضيف عليها كمان واحد
+
+213
+00:18:40,520 --> 00:18:47,040
+point one one point three analyze
+
+214
+00:18:47,040 --> 00:18:50,000
+the drive and estimate the built life in past and
+
+215
+00:18:50,000 --> 00:18:51,520
+hour اعمل analysis ده لل drive
+
+216
+00:19:01,730 --> 00:19:05,970
+انا هنعمل اللي هو excel sheet اللي باللون أصفر
+
+217
+00:19:05,970 --> 00:19:10,690
+يعني هذا ال input لان
+
+218
+00:19:10,690 --> 00:19:14,130
+ال input عندي أنا معروف ال built drive نوع open
+
+219
+00:19:14,130 --> 00:19:20,970
+built drive و انا عارف انه .. انه ال section is B,
+
+220
+00:19:21,630 --> 00:19:22,390
+B section
+
+221
+00:19:25,250 --> 00:19:28,830
+من تابل سبعتاش تسعة ما زال بيه اخدت ال width اللي
+
+222
+00:19:28,830 --> 00:19:34,630
+هو اخدت ال a واخدت ال thickness ال b ماشي و ال
+
+223
+00:19:34,630 --> 00:19:39,270
+minimum sheath diameter خمسة point اربعة انش و ال
+
+224
+00:19:39,270 --> 00:19:46,950
+power range ال power range من واحد لخمسة و .. من
+
+225
+00:19:46,950 --> 00:19:51,590
+واحد لخمسة و عشرين هذا
+
+226
+00:19:51,590 --> 00:19:54,410
+كله من تابل سبعتاش تسعة
+
+227
+00:19:59,840 --> 00:20:03,800
+الان هو ماعطيني .. حكيلي ال section 112 معناته هو
+
+228
+00:20:03,800 --> 00:20:09,620
+ماعطيني إيش ال inside circumference مظبوط باروح
+
+229
+00:20:09,620 --> 00:20:14,040
+على ال table 1711 هي بيب 112 موجود هي بيب 112
+
+230
+00:20:14,040 --> 00:20:25,920
+table 1710 الان باروح على ال table 1711 وبجيب
+
+231
+00:20:25,920 --> 00:20:29,300
+ال correction factor اللي هي عندك
+
+232
+00:20:32,110 --> 00:20:36,290
+اللي هو length conversion dimension one point
+
+233
+00:20:36,290 --> 00:20:40,050
+eight من سبعتاش احداش بحسب pitch length اللي هو
+
+234
+00:20:40,050 --> 00:20:42,510
+مائة و اتناش زاد one point تمانية بيطلع مائة و
+
+235
+00:20:42,510 --> 00:20:48,210
+تلتاش point تمانية انش هو معطين ال diameter of
+
+236
+00:20:48,210 --> 00:20:52,570
+small pulley سبعة point اربعة انش و ال diameter of
+
+237
+00:20:52,570 --> 00:20:56,290
+large pulley حداشر انش معناه و ال speed ratio تكون
+
+238
+00:20:56,290 --> 00:20:58,630
+حد كل احداش ع السبعة point اربعة بتطلع one point
+
+239
+00:20:58,630 --> 00:20:59,790
+four eight six five
+
+240
+00:21:04,020 --> 00:21:11,660
+الأن طالما هو معطين عرفت انا .. انا حاليا عارف ال
+
+241
+00:21:11,660 --> 00:21:16,020
+.. ال pitch length و اعرف دي capital و اذا عارف دي
+
+242
+00:21:16,020 --> 00:21:18,540
+small بحسب ال centered instance من العلاقة هذه
+
+243
+00:21:24,590 --> 00:21:30,030
+هذه حسبنا ال center distance تطلع 42.41 انش خليني
+
+244
+00:21:30,030 --> 00:21:33,190
+اعمل تشيكة احنا حكينا ال center distance تتروح بين
+
+245
+00:21:33,190 --> 00:21:37,610
+D capital و 3 D capital زي D small صح؟ معناه
+
+246
+00:21:37,610 --> 00:21:39,810
+تلمينه ال center distance هتكون D capital اللي هي
+
+247
+00:21:39,810 --> 00:21:45,520
+11 انش صح؟و ال max center distance هتكون تلاتة في
+
+248
+00:21:45,520 --> 00:21:50,000
+D capital زي D small دي capital اللي هي 11 و D
+
+249
+00:21:50,000 --> 00:21:56,700
+small 7.4 يعني 18.4 في تلاتة تطلع 55.2 و ال center
+
+250
+00:21:56,700 --> 00:22:04,760
+distance بتاعتنا جاية بناته مش مشكلة هو معطيني ال
+
+251
+00:22:04,760 --> 00:22:10,520
+rotation speed لل small pulley and small 1750 rpm
+
+252
+00:22:12,650 --> 00:22:15,610
+لأن طالما انا عارف دي capital و دي small ممكن احسب
+
+253
+00:22:15,610 --> 00:22:22,990
+ال angle of wrap اللي هي هتكون by minus
+
+254
+00:22:22,990 --> 00:22:27,050
+اتنين sin inverse لدي capital minus d small على
+
+255
+00:22:27,050 --> 00:22:29,430
+اتنين C، مظهور؟
+
+256
+00:22:35,260 --> 00:22:40,840
+و منها بحسب ال exponential ل ال fy ال .. ال .. ال
+
+257
+00:22:40,840 --> 00:22:45,420
+.. ال F هو معطينيه أنا already بداخلها عادي point
+
+258
+00:22:45,420 --> 00:22:51,580
+خمس واحد اتنين تلاتة عصب الشركة ال built speed
+
+259
+00:22:51,580 --> 00:22:57,640
+اللي هي by .. by d small n small على اتناش اللي هي
+
+260
+00:22:57,640 --> 00:23:03,120
+سرعة بال foot per minute هذه بتطلع تلت تلف و تلت
+
+261
+00:23:03,120 --> 00:23:04,260
+مية و تسعين
+
+262
+00:23:06,720 --> 00:23:16,160
+من table من ألف لخمس تلاف يعني تقريبا
+
+263
+00:23:16,160 --> 00:23:21,700
+من أربع تلاف احسن لفشان الـ H tabulated هنجيهه من
+
+264
+00:23:21,700 --> 00:23:28,540
+table سبعتاش اتناش based هاي ال table سبعتاش اتناش
+
+265
+00:23:28,540 --> 00:23:33,280
+انا عند بي بي
+
+266
+00:23:33,280 --> 00:23:40,960
+و ال shift diameter7.4 يعني هي هتكون السبعة and up
+
+267
+00:23:40,960 --> 00:23:46,900
+و ال build speed 3000 و 1390 يعني جاي بين 3000 و
+
+268
+00:23:46,900 --> 00:23:51,860
+4000 جاي بين هذه القيمة و هذه القيمة و أنا هتعمل
+
+269
+00:23:51,860 --> 00:24:02,420
+interpolation يعني جاي بين 4.49 و 5.01 فبعمل
+
+270
+00:24:02,420 --> 00:24:04,340
+interpolation
+
+271
+00:24:06,440 --> 00:24:15,440
+بتطلع عندك ال H tabulated 4.693 من ال table 17 12
+
+272
+00:24:15,440 --> 00:24:21,980
+انا عملتها خارجي طيب هو بيعطينا ال condition of a
+
+273
+00:24:21,980 --> 00:24:25,320
+drive اللي هو normal torque او medium انا مش
+
+274
+00:24:25,320 --> 00:24:29,940
+بغيرها حط ال Ks على طول 1.3 من ال table 17 15
+
+275
+00:24:32,870 --> 00:24:36,650
+الان عشان احسب ال H allowable H allowable بيستوي K
+
+276
+00:24:36,650 --> 00:24:42,550
+واحد في K اتنين في H tabulated صح؟ ملزم نحسب K
+
+277
+00:24:42,550 --> 00:24:47,030
+واحد angle of wrap correction factor من ال table
+
+278
+00:24:47,030 --> 00:24:55,690
+سبعتاش تلتاش الفاي
+
+279
+00:24:55,690 --> 00:25:01,290
+الفاي اكتر ما هنطلع تبقى معنا ال
+
+280
+00:25:01,290 --> 00:25:01,990
+angle of wrap
+
+281
+00:25:10,060 --> 00:25:12,780
+أيه؟ انا خليني احكيها هادي، اللي بدي أحولها ..
+
+282
+00:25:12,780 --> 00:25:15,840
+اللي بدي أجيبها أنا أبسط على السريع، في مية و
+
+283
+00:25:15,840 --> 00:25:17,540
+تمانين على باي
+
+284
+00:25:43,270 --> 00:25:56,030
+أنا هتكون تساوي هذه في مية و تمانين على باقي تطلع
+
+285
+00:25:56,030 --> 00:26:00,010
+مية و خمس سبعين point واحد تلاتة خمسة مظبوط اللي
+
+286
+00:26:00,010 --> 00:26:08,750
+هنروح على ال table السبعتاش تلاتاش يعني
+
+287
+00:26:08,750 --> 00:26:15,990
+تقريبا هتطلعفي حالة انا هنا VV V to V built drive
+
+288
+00:26:15,990 --> 00:26:24,650
+هتطلع بون تسعة تسعة اللي هي ال K واحد ال K واحد ال
+
+289
+00:26:24,650 --> 00:26:30,150
+K two اللي هي built length correction factor انا
+
+290
+00:26:30,150 --> 00:26:34,910
+ال built length أكتر من طلعت عندي مائة
+
+291
+00:26:34,910 --> 00:26:40,530
+و تلتاش هتكون table سبعتاش اربعتاش
+
+292
+00:26:46,020 --> 00:26:52,220
+اربعتاشر ال B .. ال built نوعها B احنا في ال range
+
+293
+00:26:52,220 --> 00:26:56,840
+.. في ال range هذا صح؟ واحد فاصل صفر خمس
+
+294
+00:27:00,830 --> 00:27:06,090
+ال K2 بتطلع واحد صفر خمسة بعدين بحسب ال HA بتساوي
+
+295
+00:27:06,090 --> 00:27:09,110
+H tabulated اللي انا طلعتها من ال table سبتاشر
+
+296
+00:27:09,110 --> 00:27:13,170
+اتناش في K1 في K2 بتطلع اربع بوان تمانية سبعة سبعة
+
+297
+00:27:13,170 --> 00:27:19,770
+هذي اللي قاله هو ال power لكل build افترض ان انا
+
+298
+00:27:19,770 --> 00:27:24,210
+حاطط هنا design factor of safety بتساوي واحد اللي
+
+299
+00:27:24,210 --> 00:27:34,260
+انا design horsepower بتساوي ال NDفي ال KS في ال
+
+300
+00:27:34,260 --> 00:27:37,980
+nominal اللي هي عشرة nominal power انا عشرة احصان
+
+301
+00:27:37,980 --> 00:27:44,080
+تطلع عندى ايش تلتاشة احصان ال number of bills انا
+
+302
+00:27:44,080 --> 00:27:48,180
+هقسم تلتاشة على اربعة point تمانية سبعة سبعة و
+
+303
+00:27:48,180 --> 00:27:54,040
+اعملها round up هاي
+
+304
+00:27:54,040 --> 00:27:59,740
+round up اللي هي H design على H اللابلانا round up
+
+305
+00:27:59,740 --> 00:28:04,880
+فبتطلع عياش فعلا تلاتة تلاتة صحيح اللي عامله هو
+
+306
+00:28:04,880 --> 00:28:14,260
+طيب من ال table 17 16 هحسب ال KB و ال KC نشوف ال
+
+307
+00:28:14,260 --> 00:28:16,180
+table 17 16
+
+308
+00:28:21,180 --> 00:28:25,800
+أنا عندي بيلت بي بيلت درايف ال KB خمسمية و ستة و
+
+309
+00:28:25,800 --> 00:28:33,240
+سبعين و ال KC point تسعة و ستة و خمسة هى
+
+310
+00:28:33,240 --> 00:28:43,900
+ال KB و الكاسي مظبط هحسب ال central force FC FC
+
+311
+00:28:43,900 --> 00:28:47,220
+بستوى KC في V على الف كل ترابع لأن KC معروفة عندي
+
+312
+00:28:47,220 --> 00:28:56,740
+و V عياش معروفةهي حسبنياش ال Fc بعدين هحسب delta F
+
+313
+00:28:56,740 --> 00:29:00,320
+بستوى
+
+314
+00:29:00,320 --> 00:29:06,340
+تلتة ستين الف في ال H design على number of belts
+
+315
+00:29:06,340 --> 00:29:11,740
+على N small على D على اتنين تطلع delta F عندى
+
+316
+00:29:11,740 --> 00:29:15,340
+اتنين واربعين point two بعدين هحسب tension side
+
+317
+00:29:15,340 --> 00:29:21,850
+force ال F واحد و F اتنينالـ F1 بيستوى Fc اللي
+
+318
+00:29:21,850 --> 00:29:25,870
+صارت معروفة زائد Delta F صارت معروفة في الـ
+
+319
+00:29:25,870 --> 00:29:27,810
+exponential للـ F الـ prime F على exponential F
+
+320
+00:29:27,810 --> 00:29:32,490
+prime F minus 1 والـ F2 بيستوى F1 minus Delta F
+
+321
+00:29:32,490 --> 00:29:38,650
+حسبنا F1 F2 بحسب بعدين ال initial tension Fi
+
+322
+00:29:42,830 --> 00:29:49,650
+initial tension بس هو F1 زي F2 على 2 minus FC F1
+
+323
+00:29:49,650 --> 00:29:56,390
+معروف F2 معروف و FC صار ايه؟ معروف بعد ال factor
+
+324
+00:29:56,390 --> 00:30:02,070
+of safety لأ
+
+325
+00:30:02,070 --> 00:30:03,110
+على كلهم
+
+326
+00:30:10,950 --> 00:30:13,850
+طيب بعدين بحث ال factors احنا البداية حكينا ال
+
+327
+00:30:13,850 --> 00:30:15,630
+factors of safety بيستوى واحد ال design factors of
+
+328
+00:30:15,630 --> 00:30:19,590
+safety لكن انا لما كانت على حساب انه عدد ال builds
+
+329
+00:30:19,590 --> 00:30:22,370
+قصور لكن انا عملت round up بمعنى ان ال factors
+
+330
+00:30:22,370 --> 00:30:26,350
+بتاعي يكون اكبر من واحد اللي انا نفسي بيستوأتش ايه
+
+331
+00:30:26,350 --> 00:30:32,150
+في ال number of builds علقتش نمنا على ال KS بيطلع
+
+332
+00:30:32,150 --> 00:30:37,530
+ال NFS 1.13 مظبوط؟ لما كانش فيه داعي اخد design
+
+333
+00:30:37,530 --> 00:30:45,840
+factorsلأ مش هيك انا حكيت انت ممكن تاخد design
+
+334
+00:30:45,840 --> 00:30:49,620
+factor اكتر و هتحكي one point two و لما تحسب ممكن
+
+335
+00:30:49,620 --> 00:30:53,780
+يطلع اكتر ع الأقل هتطلع اكتر one point two بغض
+
+336
+00:30:53,780 --> 00:30:56,140
+النظر اخدت واحد ولا one point two ولا واحد و نص
+
+337
+00:30:56,140 --> 00:31:01,680
+هتعمل round up لل number of bills اذا زودت ال
+
+338
+00:31:01,680 --> 00:31:04,480
+factor في ال safety مثلا خلته اتنين مثلا ممكن يطلع
+
+339
+00:31:04,480 --> 00:31:08,040
+العدد عندي مش تلاتة اربعة bills لان انا بدي safety
+
+340
+00:31:08,040 --> 00:31:08,420
+اكتر
+
+341
+00:31:11,140 --> 00:31:17,720
+طيب ال .. فعندى priority parameter k و ال b من ال
+
+342
+00:31:17,720 --> 00:31:24,840
+table 17 17 هاي ال table 17 17 انا عند b built
+
+343
+00:31:24,840 --> 00:31:29,340
+drive هتكون ال k ألف و مئة و تلات تسعين و ال b
+
+344
+00:31:29,340 --> 00:31:35,900
+عشرة بون تسعة اتنين ستة هاي
+
+345
+00:31:35,900 --> 00:31:41,010
+ال table 17 هاي جيبناها من ال table 17 17بعدين
+
+346
+00:31:41,010 --> 00:31:50,550
+هحسب T1 هاي T1 و احسب ايش؟ T2 T1 بيستوى F1 زي KB
+
+347
+00:31:50,550 --> 00:31:58,950
+على D و T2 بيستوى F1 زي KB على D بحسب
+
+348
+00:31:58,950 --> 00:32:04,930
+اللي هو T1 و T2 بعدين بحسب number of passes
+
+349
+00:32:08,140 --> 00:32:12,460
+من العلاقة هذه K على T واحد اصناق بي زاد K على T
+
+350
+00:32:12,460 --> 00:32:17,320
+اتنين اصناق بي كله اصناق واحد الان K معروفة و T
+
+351
+00:32:17,320 --> 00:32:20,420
+واحد معروفة و T اتنين معروفة بعدين بحسب العمر
+
+352
+00:32:20,420 --> 00:32:24,220
+بالساعة اللي هي number of passes في ال pitch
+
+353
+00:32:24,220 --> 00:32:29,620
+length على 720 ال V capital تطلع هذه ال lifetime
+
+354
+00:32:29,620 --> 00:32:38,040
+بتعيش ستة واربين ألف و ..و ستمية و عشرين ساعة لو
+
+355
+00:32:38,040 --> 00:32:44,520
+دي احكي ال lifetime ال ..
+
+356
+00:32:44,520 --> 00:32:53,400
+مش بالساعات بال year او بال days هتكون
+
+357
+00:32:53,400 --> 00:32:59,520
+متساوى هذه على
+
+358
+00:32:59,520 --> 00:33:03,980
+اربعة و عشرينيعني بتعيش ألف و سنتين و أربع مليون
+
+359
+00:33:03,980 --> 00:33:10,380
+لو ده حوّلها ل year على .. هي بتشتغل بعد 24 ساعة
+
+360
+00:33:10,380 --> 00:33:19,900
+على 365 يعني خمس سنين bond تلادة خمس سنين و أشهر
+
+361
+00:33:19,900 --> 00:33:24,900
+على نفس واحد تكون شغالة طبعا على فرض برضه أن ال
+
+362
+00:33:24,900 --> 00:33:30,220
+bearings ذاتها كل شغالة فيش مشاكل يعني
+
+363
+00:33:30,220 --> 00:33:31,800
+بتعمل كويس يعني
+
+364
+00:33:34,790 --> 00:33:42,650
+هذا شغل متواصل، في
+
+365
+00:33:42,650 --> 00:33:46,550
+أي سؤال اكمل خلاص المحاضرة اعطيكوا العاشر
+
diff --git a/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/7peQqkxODFs_raw.json b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/7peQqkxODFs_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..94e17f734be69955054e2d1c18c6e3a8129e56e4
--- /dev/null
+++ b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/7peQqkxODFs_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2209, "start": 5.01, "end": 22.09, "text": "بسم الله الرحمن الرحيم السلام عليكم ورحمة الله وبركاته هنبدأ مادة تصميم الألوان هنبدأ ب chapter 17 اللي هو design flexible mechanical elements اللي flexible mechanical elements تتضمن ل flat built drives بأنواعها", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21136, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224, 8032, 1863, 44510, 10721, 3714, 18513, 3660, 6055, 9381, 2304, 32640, 16247, 1211, 2407, 7649, 8032, 1863, 44510, 10721, 4724, 7187, 3282, 13672, 1829, 31439, 1715, 11358, 12070, 4959, 13672, 1829, 11358, 12070, 4959, 6055, 2655, 11242, 27842, 5296, 4962, 3094, 11754, 4724, 33456, 14407, 3615, 11296], "avg_logprob": -0.13809419223960018, "compression_ratio": 1.664864864864865, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 5.01, "end": 5.41, "word": "بسم", "probability": 0.901611328125}, {"start": 5.41, "end": 5.61, "word": " 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"end": 1128.7, "text": "عندى البكره الكبيرة", "tokens": [3615, 41260, 7578, 29739, 37983, 3224, 33251, 3555, 48923], "avg_logprob": -0.26113281548023226, "compression_ratio": 0.8571428571428571, "no_speech_prob": 0.0, "words": [{"start": 1127.54, "end": 1127.92, "word": "عندى", "probability": 0.6162109375}, {"start": 1127.92, "end": 1128.32, "word": " البكره", "probability": 0.8046875}, {"start": 1128.32, "end": 1128.7, "word": " الكبيرة", "probability": 0.92236328125}], "temperature": 1.0}, {"id": 38, "seek": 117061, "start": 1156.32, "end": 1170.62, "text": "هذه المسافة اللي هي ال center distance بين البكارتين هذا الحبل", "tokens": [3224, 24192, 9673, 3794, 31845, 3660, 13672, 1829, 39896, 2423, 3056, 4560, 49374, 29739, 4117, 9640, 2655, 9957, 23758, 21542, 36150], "avg_logprob": -0.2887073944915425, "compression_ratio": 1.1363636363636365, "no_speech_prob": 0.0, "words": [{"start": 1156.32, "end": 1156.66, "word": "هذه", "probability": 0.73388671875}, {"start": 1156.66, "end": 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هذه", "tokens": [3224, 24192, 6055, 1863, 7435, 1863, 3794, 1829, 935, 15844, 29739, 37983, 31767, 17082, 48923, 18871, 16254, 6055, 1863, 7435, 1863, 3794, 1829, 935, 18871, 16254, 6055, 1863, 7435, 1863, 3794, 1829, 935, 34105, 4032, 3615, 1863, 16254, 6055, 1863, 7435, 1863, 3794, 1829, 935, 34105, 30767, 995, 2407, 10632, 29538], "avg_logprob": -0.26832932463059056, "compression_ratio": 1.7959183673469388, "no_speech_prob": 0.0, "words": [{"start": 1206.49, "end": 1206.89, "word": "هذه", "probability": 0.6136474609375}, {"start": 1206.89, "end": 1207.55, "word": " تنجنسي", "probability": 0.698486328125}, {"start": 1207.55, "end": 1207.89, "word": " point", "probability": 0.482666015625}, {"start": 1207.89, "end": 1209.57, "word": " على", "probability": 0.60302734375}, {"start": 1209.57, "end": 1211.75, "word": " البكر", "probability": 0.664306640625}, {"start": 1211.75, "end": 1212.27, "word": " الصغيرة", "probability": 0.86474609375}, {"start": 1212.27, "end": 1213.59, "word": " 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"seek": 241298, "start": 2390.9, "end": 2412.98, "text": "معنى انتوا هيكون في عندى normal force او centrifugal force اللي هي ال mass في ال normal acceleration و ال normal acceleration هي عبارة عن omega square في ال radius صح ف ال DS هي centrifugal force في عندى normal force من البكرة على الحبل اللي هي DN", "tokens": [2304, 3615, 1863, 7578, 16472, 2655, 14407, 39896, 30544, 8978, 43242, 7578, 2710, 3464, 1975, 2407, 44828, 17812, 3464, 13672, 1829, 39896, 2423, 2758, 8978, 2423, 2710, 17162, 4032, 2423, 2710, 17162, 39896, 6225, 3555, 9640, 3660, 18871, 10498, 3732, 8978, 2423, 15845, 20328, 5016, 6156, 2423, 15816, 39896, 44828, 17812, 3464, 8978, 43242, 7578, 2710, 3464, 9154, 29739, 4117, 25720, 15844, 21542, 36150, 13672, 1829, 39896, 21500], "avg_logprob": -0.27762680468351947, "compression_ratio": 1.814207650273224, "no_speech_prob": 0.0, "words": [{"start": 2390.9, "end": 2391.2, "word": "معنى", "probability": 0.72637939453125}, {"start": 2391.2, "end": 2391.32, "word": " 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على الحبل يعني FDN وفي شد في الحبل F و بعد زاوية D θ بتغير بيصير F زائد DF بيصير F زائد DF و هو يعني مستخدم اللي هو normal cord .. normal antangelical cord and system يعني هي هذي بيسميها R او ال normal", "tokens": [2407, 8978, 17710, 3464, 1975, 2407, 23558, 3464, 9154, 21542, 36150, 15844, 4386, 9154, 29739, 4117, 25720, 15844, 21542, 36150, 37495, 22653, 479, 35, 45, 4032, 41185, 13412, 3215, 8978, 21542, 36150, 479, 4032, 39182, 30767, 995, 2407, 10632, 413, 12622, 39894, 17082, 13546, 4724, 1829, 9381, 13546, 479, 30767, 16373, 3215, 48336, 4724, 1829, 9381, 13546, 479, 30767, 16373, 3215, 48336, 4032, 31439, 37495, 22653, 3714, 14851, 9778, 40448, 13672, 1829, 31439, 2710, 12250, 4386, 2710, 2511, 656, 338, 804, 12250, 293, 1185, 37495, 22653, 39896, 8032, 8848, 1829, 4724, 1829, 38251, 1829, 11296, 497, 1975, 2407, 2423, 2710], "avg_logprob": -0.27057549150863497, "compression_ratio": 1.7066666666666668, "no_speech_prob": 0.0, "words": [{"start": 2413.95, "end": 2414.17, "word": 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"probability": 0.85400390625}, {"start": 2733.35, "end": 2733.35, "word": " θ", "probability": 0.90869140625}, {"start": 2733.35, "end": 2733.37, "word": " على", "probability": 0.97265625}, {"start": 2733.37, "end": 2733.55, "word": " اتنين", "probability": 0.982421875}, {"start": 2733.55, "end": 2734.49, "word": " FD", "probability": 0.8544921875}, {"start": 2734.49, "end": 2734.49, "word": " θ", "probability": 0.90771484375}, {"start": 2734.49, "end": 2734.49, "word": " على", "probability": 0.97314453125}, {"start": 2734.49, "end": 2734.49, "word": " اتنين", "probability": 0.982177734375}, {"start": 2734.49, "end": 2734.49, "word": " FD", "probability": 0.86083984375}, {"start": 2734.49, "end": 2734.49, "word": " θ", "probability": 0.90771484375}, {"start": 2734.49, "end": 2734.49, "word": " على", "probability": 0.97314453125}, {"start": 2734.49, "end": 2734.49, "word": " اتنين", "probability": 0.98095703125}, {"start": 2734.49, "end": 2734.49, "word": " FD", "probability": 0.866455078125}, {"start": 2734.49, "end": 2734.49, "word": " θ", "probability": 0.9052734375}, {"start": 2734.49, "end": 2734.49, "word": " على", "probability": 0.97265625}, {"start": 2734.49, "end": 2734.49, "word": " اتنين", "probability": 0.9798583984375}, {"start": 2734.49, "end": 2734.53, "word": " FD", "probability": 0.871826171875}, {"start": 2734.53, "end": 2734.53, "word": " θ", "probability": 0.9052734375}, {"start": 2734.53, "end": 2734.53, "word": " على", "probability": 0.97314453125}, {"start": 2734.53, "end": 2734.53, "word": " اتنين", "probability": 0.9793701171875}, {"start": 2734.53, "end": 2734.65, "word": " FD", "probability": 0.8798828125}, {"start": 2734.65, "end": 2734.65, "word": " θ", "probability": 0.89990234375}, {"start": 2734.65, "end": 2734.65, "word": " على", "probability": 0.97265625}, {"start": 2734.65, "end": 2734.65, "word": " اتنين", "probability": 0.9788818359375}, {"start": 2734.65, "end": 2734.65, "word": " FD", "probability": 0.884521484375}, {"start": 2734.65, "end": 2734.69, "word": " θ", "probability": 0.8935546875}, {"start": 2734.69, "end": 2734.69, "word": " على", "probability": 0.97216796875}, {"start": 2734.69, "end": 2734.69, "word": " اتنين", "probability": 0.978515625}, {"start": 2734.69, "end": 2734.69, "word": " FD", "probability": 0.88525390625}, {"start": 2734.69, "end": 2734.69, "word": " θ", "probability": 0.8876953125}, {"start": 2734.69, "end": 2734.69, "word": " على", "probability": 0.97216796875}, {"start": 2734.69, "end": 2734.69, "word": " اتنين", "probability": 0.97802734375}, {"start": 2734.69, "end": 2734.69, "word": " FD", "probability": 0.890380859375}, {"start": 2734.69, "end": 2734.69, "word": " θ", "probability": 0.88134765625}, {"start": 2734.69, "end": 2734.69, "word": " على", "probability": 0.97119140625}, {"start": 2734.69, "end": 2734.69, "word": " اتنين", "probability": 0.9771728515625}, {"start": 2734.69, "end": 2734.69, "word": " FD", "probability": 0.892578125}, {"start": 2734.69, "end": 2734.69, "word": " θ", "probability": 0.87060546875}, {"start": 2734.69, "end": 2734.69, "word": " على", "probability": 0.970703125}, {"start": 2734.69, "end": 2734.69, "word": " اتنين", "probability": 0.9769287109375}, {"start": 2734.69, "end": 2734.69, "word": " FD", "probability": 0.893310546875}, {"start": 2734.69, "end": 2734.75, "word": " θ", "probability": 0.8583984375}, {"start": 2734.75, "end": 2734.93, "word": " على", "probability": 0.970703125}, {"start": 2734.93, "end": 2734.93, "word": " اتنين", "probability": 0.97607421875}, {"start": 2734.93, "end": 2736.07, "word": " FD", "probability": 0.89208984375}, {"start": 2736.07, "end": 2736.07, "word": " θ", "probability": 0.84375}, {"start": 2736.07, "end": 2736.27, "word": " على", "probability": 0.97021484375}, {"start": 2736.27, "end": 2736.67, "word": " اتنين", "probability": 0.9759521484375}, {"start": 2736.67, "end": 2737.37, "word": " FD", "probability": 0.89111328125}, {"start": 2737.37, "end": 2737.83, "word": " θ", "probability": 0.8232421875}, {"start": 2737.83, "end": 2737.83, "word": " على", "probability": 0.96923828125}, {"start": 2737.83, "end": 2737.89, "word": " اتنين", "probability": 0.9759521484375}, {"start": 2737.89, "end": 2739.65, "word": " FD", "probability": 0.8916015625}, {"start": 2739.65, "end": 2740.13, "word": " θ", "probability": 0.80517578125}, {"start": 2740.13, "end": 2740.13, "word": " على", "probability": 0.96875}, {"start": 2740.13, "end": 2740.13, "word": " اتن", "probability": 0.9659830729166666}], "temperature": 1.0}, {"id": 91, "seek": 276371, "start": 2741.33, "end": 2763.71, "text": "بتصفى عند ال DN بتساوي FD θ minus DS الحاضرة الجاية ونكمل ..", "tokens": [3555, 2655, 9381, 5172, 7578, 43242, 2423, 21500, 39894, 3794, 995, 45865, 479, 35, 12622, 3175, 15816, 21542, 46958, 25720, 25724, 995, 10632, 4032, 1863, 24793, 1211, 4386], "avg_logprob": -0.3798491420416996, "compression_ratio": 1.0326086956521738, "no_speech_prob": 0.0, "words": [{"start": 2741.33, "end": 2741.93, "word": "بتصفى", "probability": 0.85361328125}, {"start": 2741.93, "end": 2742.13, "word": " عند", "probability": 0.90966796875}, {"start": 2742.13, "end": 2742.31, "word": " ال", "probability": 0.951171875}, {"start": 2742.31, "end": 2742.79, "word": " DN", "probability": 0.455810546875}, {"start": 2742.79, "end": 2746.59, "word": " بتساوي", "probability": 0.78912353515625}, {"start": 2746.59, "end": 2750.31, "word": " FD", "probability": 0.771728515625}, {"start": 2750.31, "end": 2750.65, "word": " θ", "probability": 0.260498046875}, {"start": 2750.65, "end": 2755.35, "word": " minus", "probability": 0.476318359375}, {"start": 2755.35, "end": 2756.21, "word": " DS", "probability": 0.92724609375}, {"start": 2756.21, "end": 2762.69, "word": " الحاضرة", "probability": 0.623046875}, {"start": 2762.69, "end": 2763.05, "word": " الجاية", "probability": 0.822265625}, {"start": 2763.05, "end": 2763.61, "word": " ونكمل", "probability": 0.70751953125}, {"start": 2763.61, "end": 2763.71, "word": " ..", "probability": 0.3359375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2764.3125, "duration_after_vad": 2316.1099999999915}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/7peQqkxODFs_raw.srt b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/7peQqkxODFs_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..883a1f5c9b450cf558c1987fecb79f159a9587aa
--- /dev/null
+++ b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/7peQqkxODFs_raw.srt
@@ -0,0 +1,1580 @@
+1
+00:00:05,010 --> 00:00:07,690
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:07,690 --> 00:00:11,770
+وبركاته هنبدأ مادة تصميم الألوان هنبدأ ب chapter
+
+3
+00:00:11,770 --> 00:00:16,170
+17 اللي هو design flexible mechanical elements
+
+4
+00:00:16,170 --> 00:00:19,730
+اللي flexible mechanical elements تتضمن ل flat
+
+5
+00:00:19,730 --> 00:00:25,400
+built drives بأنواعهاتتضمن ال chain ال sprocket
+
+6
+00:00:25,400 --> 00:00:30,400
+and chain تتضمن ال ropes و ال flexible shirts
+
+7
+00:00:30,400 --> 00:00:36,600
+هنبدأ طبعا في ال built ال built ال built drives ال
+
+8
+00:00:36,600 --> 00:00:43,780
+built drives فيه تيجي على أربع أنواع في
+
+9
+00:00:43,780 --> 00:00:49,720
+عندي ال flat built drive طبعا في كل حوالي بيكون
+
+10
+00:00:49,720 --> 00:00:53,760
+عندي بكرة و بكرةو واحدة منهم driver و واحدة منهم
+
+11
+00:00:53,760 --> 00:00:58,600
+driven في عندي ال flat built drive بيجي ال built
+
+12
+00:00:58,600 --> 00:01:07,340
+يعني مقطع مستطيل في عندي ال round built drive و في
+
+13
+00:01:07,340 --> 00:01:12,920
+عندي ال v built drive و في عندي اللي هو timing
+
+14
+00:01:12,920 --> 00:01:16,880
+built drive ال flat built drive زي ما أنتوا شايفين
+
+15
+00:01:16,880 --> 00:01:18,980
+هذا هو flat built drive
+
+16
+00:01:22,920 --> 00:01:29,740
+هذا ال V .. هذا ال V built drive جاية المقطع في
+
+17
+00:01:29,740 --> 00:01:37,040
+عنده سلبة فيه زاوية أو flat build فعندي ال timing
+
+18
+00:01:37,040 --> 00:01:41,900
+.. ال timing نفس ال built بيكون فيه عياش أسنان و
+
+19
+00:01:41,900 --> 00:01:44,540
+الأسنان تركب على أسنان البكرة نفسها
+
+20
+00:01:48,690 --> 00:01:52,850
+إذا بنعمل مقارنة سريعة بين ال flat و ال round و ال
+
+21
+00:01:52,850 --> 00:02:00,410
+V و ال timing ال flat المقطع مستطيل عرضه بسماكة T
+
+22
+00:02:00,410 --> 00:02:05,690
+بيجي بالطول اللي بدك هيه معناته لازم توصله لازم
+
+23
+00:02:05,690 --> 00:02:12,330
+ينوصل فيه طرق وصل فهو بيجي الشريط و بتختار الطول
+
+24
+00:02:12,330 --> 00:02:14,730
+اللي بدك هيه و بنوصل بسيراش مغلق
+
+25
+00:02:17,450 --> 00:02:20,550
+ال thickness range بتتراوح بين .. السماعة بتتراوح
+
+26
+00:02:20,550 --> 00:02:23,630
+بين bones تبقى خمسة millimeter لخمسة millimeter
+
+27
+00:02:23,630 --> 00:02:29,950
+الآن مافيش حدود لمسافة بين مركزي البكرتين ال
+
+28
+00:02:29,950 --> 00:02:33,090
+center distance لأنه انا باخد الطول بالديها و بسكر
+
+29
+00:02:33,090 --> 00:02:39,910
+في ال round built
+
+30
+00:02:39,910 --> 00:02:46,810
+المقطع مدورهل محتاج وصله؟ محتاج وصله بيجي هو بيجي
+
+31
+00:02:46,810 --> 00:02:50,890
+يعني بيجي على شكل حبل و باخد الطول بديه و باوصله
+
+32
+00:02:50,890 --> 00:02:56,090
+القطر اتراح بين تمان انش و تلت اربان انش يعني
+
+33
+00:02:56,090 --> 00:03:01,190
+حوالي تلت مل و ربع لحوالي عشرين ملي في limit على
+
+34
+00:03:01,190 --> 00:03:04,270
+center distance؟ لأ لأن انا باخد الطول بديه و
+
+35
+00:03:04,270 --> 00:03:10,530
+باوصله ال V built ال V built بتيجي بال standards A
+
+36
+00:03:10,530 --> 00:03:19,600
+,B,C,D بتيجي مغلقةمعناته انت مقيد ب standard sizes
+
+37
+00:03:19,600 --> 00:03:27,000
+او بالتالي ال standard distance is limited المقطع
+
+38
+00:03:27,000 --> 00:03:31,540
+بتاعه بيكون بشكل هدفي عنده H في عنده زاوية ارتفاع
+
+39
+00:03:31,540 --> 00:03:36,900
+B ال B اتراح بين تمانية لتسعتاشر ميلي في عند ال
+
+40
+00:03:36,900 --> 00:03:41,160
+timing built بار timing built بتيجي standard sizes
+
+41
+00:03:41,160 --> 00:03:41,900
+بتيجي مغلقة
+
+42
+00:03:44,520 --> 00:03:49,760
+الخطوة بين sin و sin اللي هي P بتكون اتنين ملي
+
+43
+00:03:49,760 --> 00:03:54,160
+اقلش اتنين ملي و اطلع في limitation في ال center
+
+44
+00:03:54,160 --> 00:03:56,560
+distance اه في limitation في ال center distance
+
+45
+00:03:56,560 --> 00:04:03,060
+طيب
+
+46
+00:04:03,060 --> 00:04:10,280
+ممكن
+
+47
+00:04:10,280 --> 00:04:16,240
+ال build تيجي open build driveهذا يسمى open يعني
+
+48
+00:04:16,240 --> 00:04:23,940
+الطريقة التقليدية مافيش crossing بين الإحبال ممكن
+
+49
+00:04:23,940 --> 00:04:31,640
+تيجي crossed built drive زي
+
+50
+00:04:31,640 --> 00:04:35,300
+الحالة اللي احنا شايفينها طبعا عشان مايصيرش اهتكاك
+
+51
+00:04:35,300 --> 00:04:40,720
+بين الإحبال بيكون في مسافة خفيفة بين الحبلين
+
+52
+00:04:46,810 --> 00:04:50,910
+ال build قد تكون non-reversing open build non
+
+53
+00:04:50,910 --> 00:04:56,550
+-reversing يعني اتجاه ال driver و ال driven نفس
+
+54
+00:04:56,550 --> 00:04:59,870
+الدور و نفس الاتجاه اذا هذا باتجاه عقارب الساعة
+
+55
+00:04:59,870 --> 00:05:03,430
+هذا بدور اتجاه عقارب الساعة هذا open .. non
+
+56
+00:05:03,430 --> 00:05:09,470
+-reversing open built drive او قد يكون reversing
+
+57
+00:05:09,470 --> 00:05:14,470
+cross built drive لحظة انا عندي ال driver بدور
+
+58
+00:05:14,470 --> 00:05:14,870
+clockwise
+
+59
+00:05:19,270 --> 00:05:24,110
+معناته عندي هين ال driven بدور counter clockwise
+
+60
+00:05:24,110 --> 00:05:27,630
+يعني اتجاه عكس ال driver ال driver اتجاه دورانه
+
+61
+00:05:27,630 --> 00:05:33,070
+عكس دوران ال driven هذا بيسميه reversing cross
+
+62
+00:05:33,070 --> 00:05:39,730
+built في reversing open built drive reversing open
+
+63
+00:05:39,730 --> 00:05:44,830
+built drive هاي ال driver إذا بنتبعاللي طلعت سرعة
+
+64
+00:05:44,830 --> 00:05:54,570
+الحبل هاي اتجاه سرعة الحبل انا ماشي بالماوس لاحظوا
+
+65
+00:05:54,570 --> 00:05:59,290
+البكر هدا هتدور بعكس عقارب السيعة ال driver ايش ده
+
+66
+00:05:59,290 --> 00:06:04,350
+بدور مع عقارب السيعة هذا reversing open built
+
+67
+00:06:04,350 --> 00:06:10,290
+drive هي open type و ال driver اتجاه دورانه عكس
+
+68
+00:06:10,290 --> 00:06:12,110
+اتجاه دوران ال driven
+
+69
+00:06:17,120 --> 00:06:21,720
+مش ضروري يكون ال two poles في نفس المستوى يعني
+
+70
+00:06:21,720 --> 00:06:27,780
+ممكن يكون بينهم زاوية تسعين درجة زي ما احنا شايفين
+
+71
+00:06:27,780 --> 00:06:34,780
+في الحلقة السابقة quarter twist built drive لأن
+
+72
+00:06:34,780 --> 00:06:39,100
+هنحكي عن ال flat and
+
+73
+00:06:39,100 --> 00:06:43,980
+round built drives ال flat built drive تتكون من
+
+74
+00:06:43,980 --> 00:06:50,910
+strong elastic coreيعني من جوه ال core بتاعها مادة
+
+75
+00:06:50,910 --> 00:06:59,350
+فيها elasticity و strong محاطة به elastomer ال
+
+76
+00:06:59,350 --> 00:07:02,770
+flat plate drive الكفاءة بتاعتها قد تصل تمانية
+
+77
+00:07:02,770 --> 00:07:05,470
+وتسعين في المية أنا قريبا من ال efficiency بتاعة
+
+78
+00:07:05,470 --> 00:07:10,190
+ال gear drive لكن ال efficiency في حالة ال V built
+
+79
+00:07:10,190 --> 00:07:13,690
+drive تتراه بين سبعين لستة وتسعين في المية
+
+80
+00:07:16,860 --> 00:07:24,140
+ال flat belted rise بنتج عنها ضجيج أقل و تمتص
+
+81
+00:07:24,140 --> 00:07:28,340
+الاحتزازات اللى ناتجة عن ال shaft و ال rotation
+
+82
+00:07:28,340 --> 00:07:34,360
+بتاع ال shaft لأن هى flexible و في مجال say some
+
+83
+00:07:34,360 --> 00:07:38,120
+sliding فتمتص الاحتزازات
+
+84
+00:07:45,070 --> 00:07:48,670
+الان خلينا نشوف اللي هو ال geometry لل built drive
+
+85
+00:07:48,670 --> 00:07:52,470
+اول شحن في ال geometry لل open built drive بعد
+
+86
+00:07:52,470 --> 00:07:58,350
+نشوف ال geometry لل crossed built drive خلينا نعرف
+
+87
+00:07:58,350 --> 00:08:07,990
+ال terms طبعا
+
+88
+00:08:07,990 --> 00:08:12,270
+المسافة بين ال two centers مثلا بين ال center هذا
+
+89
+00:08:12,270 --> 00:08:14,250
+ال center بسميها ال center distance C
+
+90
+00:08:23,730 --> 00:08:25,130
+هذه الـ Center Distance
+
+91
+00:08:51,920 --> 00:08:59,180
+هذا الحبل او ال built الواصل
+
+92
+00:08:59,180 --> 00:09:06,840
+بين البكرتين طبعا
+
+93
+00:09:06,840 --> 00:09:11,700
+فين ال tengency point هذا المركز
+
+94
+00:09:41,120 --> 00:09:48,280
+عندى نقطة تماث هنا بتعمل
+
+95
+00:09:48,280 --> 00:09:55,600
+زاوية أنا ساميها gamma عندى
+
+96
+00:09:55,600 --> 00:10:02,120
+برضه نقطة تماث هنا برضه
+
+97
+00:10:02,120 --> 00:10:06,000
+بتعمل زاوية gamma
+
+98
+00:10:33,060 --> 00:10:44,760
+هذه gamma ال
+
+99
+00:10:44,760 --> 00:10:51,240
+contact angle بين البكرة الصغيرة والحبل هذه هي
+
+100
+00:10:51,240 --> 00:10:58,300
+زاوية التلامس بين
+
+101
+00:10:58,300 --> 00:11:16,790
+البكرة والحبل في دي smallو هذه زاوية التلامس فاي
+
+102
+00:11:16,790 --> 00:11:29,430
+دي capital بين البكرة الكبيرة و الحبل لو
+
+103
+00:11:29,430 --> 00:11:36,650
+أخد من المركز هذاطبعا هذا جنسي point بناته نصف قطر
+
+104
+00:11:36,650 --> 00:11:40,670
+هيكون عمودي عند زواها 90 درجة صح عند زواها 90 درجة
+
+105
+00:11:40,670 --> 00:11:57,850
+لو أخدنا موازن الحبل خلنا
+
+106
+00:11:57,850 --> 00:11:58,870
+نسمي النقطة هذه a
+
+107
+00:12:03,700 --> 00:12:13,140
+C واخدنا المثلث ABC مثلث ABC
+
+108
+00:12:13,140 --> 00:12:17,380
+هذه
+
+109
+00:12:17,380 --> 00:12:22,020
+المسافة ايش دي على اتنين دي اسمها على اتنين معناته
+
+110
+00:12:22,020 --> 00:12:26,980
+هذه هتكون خدنا نسمي هذه دي الان BD
+
+111
+00:12:33,740 --> 00:12:39,760
+هتكون دي على اتنين صح؟
+
+112
+00:12:39,760 --> 00:12:48,660
+و CD دي capital على اتنين، مظبوط؟
+
+113
+00:12:48,660 --> 00:12:52,200
+معناته
+
+114
+00:12:52,200 --> 00:12:58,120
+بي سي ايش تساوي؟
+
+115
+00:12:58,120 --> 00:13:02,500
+بتساوي CD minus
+
+116
+00:13:02,500 --> 00:13:10,170
+BDيعني هيكون الساوية D capital minus D small على
+
+117
+00:13:10,170 --> 00:13:19,930
+اتنين الزاوية ده فاهم كمية هتكون هذه الزاوية برضه
+
+118
+00:13:19,930 --> 00:13:29,410
+جامعة طيب sign جامعة شو الساوية ساوية
+
+119
+00:13:29,410 --> 00:13:29,830
+بي سي
+
+120
+00:13:33,220 --> 00:13:41,660
+على AC ب C اللي هي D capital minus D small على
+
+121
+00:13:41,660 --> 00:13:47,800
+اتنين و AC اللي هو ال center distance C معناته
+
+122
+00:13:47,800 --> 00:13:54,260
+جامعة سوى sign inverse ل D capital minus D small
+
+123
+00:13:54,260 --> 00:13:59,560
+على اتنين C معناته ال five D small شو يستوي
+
+124
+00:14:04,340 --> 00:14:07,860
+بالساوة مائة و اتنين درجة ناقص gamma ناقص gamma صح
+
+125
+00:14:07,860 --> 00:14:14,960
+يعني هتكون ساوة by minus اتنين gamma و ال fi d
+
+126
+00:14:14,960 --> 00:14:21,340
+capital بالساوة مائة و اتنين زائد gamma زائد gamma
+
+127
+00:14:21,340 --> 00:14:28,280
+يعني هتكون by زائد اتنين gamma
+
+128
+00:14:31,370 --> 00:14:38,070
+هذا ينسى لفاي دي والفاي لان بدنا نحسب طول الحبل
+
+129
+00:14:38,070 --> 00:14:42,770
+طول
+
+130
+00:14:42,770 --> 00:14:46,430
+الحبل مكوّن الحبل مكوّن من عنده من الجزء المستقيم
+
+131
+00:14:46,430 --> 00:14:53,550
+هذا من تنجنسي للتنجنسي زاد الارك هذا زاد
+
+132
+00:14:53,550 --> 00:14:59,700
+ال line من تنجنسي لتنجنسي زاد الارك هذاصح فانا
+
+133
+00:14:59,700 --> 00:15:06,160
+هتقول ال L هتكون تساوي طول
+
+134
+00:15:06,160 --> 00:15:12,860
+ال arc اللي على البكرة الصغيرة الزاوية بتاعته اكم
+
+135
+00:15:12,860 --> 00:15:19,220
+فاي دي نص القطر دي على اتنين هتكون طوله اكم دي على
+
+136
+00:15:19,220 --> 00:15:22,940
+اتنين فاي دي small
+
+137
+00:15:28,220 --> 00:15:35,600
+والارك هذا شو يستوي زائد دي capital على اتنين في
+
+138
+00:15:35,600 --> 00:15:41,220
+في دي capital زاد
+
+139
+00:15:41,220 --> 00:15:50,400
+الطول هذا اللي هو بيستوي a b احنا
+
+140
+00:15:50,400 --> 00:15:53,340
+a b من فيثا غورث شو يستوي زائد
+
+141
+00:15:56,100 --> 00:16:02,960
+هذا هيكون الهو a c تربيع minus b c تربيع اللي هكون
+
+142
+00:16:02,960 --> 00:16:07,620
+جزر التربيع اللي
+
+143
+00:16:07,620 --> 00:16:13,800
+هو لل c تربيع minus ال b c تربيع اللي هي بقرا عن d
+
+144
+00:16:13,800 --> 00:16:24,860
+capital minus d small على اتنين لكل تربيع يعني
+
+145
+00:16:24,860 --> 00:16:25,340
+هيكون
+
+146
+00:16:29,280 --> 00:16:39,700
+نص في دي small فا دي small زاد دي capital فا دي
+
+147
+00:16:39,700 --> 00:16:49,580
+capital زاد صحيح
+
+148
+00:16:49,580 --> 00:16:52,080
+هدف ايش هدي هدف اتنين
+
+149
+00:16:58,170 --> 00:17:02,350
+الاتنين هدخلها برا بيصير أربعة صح زاد الجزر
+
+150
+00:17:02,350 --> 00:17:12,990
+التربيعي لأربعة C تربيع minus D capital minus D
+
+151
+00:17:12,990 --> 00:17:22,330
+small لكل تربيع هيك وصفنا كل الجيومتري لل built
+
+152
+00:17:22,330 --> 00:17:28,290
+drive يعنيعرفنا ال contact angle على ال small poly
+
+153
+00:17:28,290 --> 00:17:34,930
+ال contact angle على ال large poly وعرفنا طول
+
+154
+00:17:34,930 --> 00:17:41,290
+الحبل المطلوب بدلالة ال center distance و أكتر قطر
+
+155
+00:17:41,290 --> 00:17:49,610
+ال poly الصغيرة و قطر ال poly الكبيرة النوع
+
+156
+00:17:49,610 --> 00:17:53,790
+التاني اللي هو ال crossed
+
+157
+00:18:09,700 --> 00:18:20,840
+الكروست بيلت درايف عندي
+
+158
+00:18:20,840 --> 00:18:21,980
+البكره الصغيرة
+
+159
+00:18:47,540 --> 00:18:48,700
+عندى البكره الكبيرة
+
+160
+00:19:16,320 --> 00:19:20,820
+هذه المسافة اللي هي ال center distance بين
+
+161
+00:19:20,820 --> 00:19:30,140
+البكارتين هذا
+
+162
+00:19:30,140 --> 00:19:30,620
+الحبل
+
+163
+00:20:06,490 --> 00:20:14,010
+هذه تنجنسي point على البكر الصغيرة عندي تنجنسي
+
+164
+00:20:14,010 --> 00:20:24,190
+point عندي تنجنسي point هنا وعندي
+
+165
+00:20:24,190 --> 00:20:28,270
+تنجنسي point هنا
+
+166
+00:20:28,270 --> 00:20:35,150
+زاوية
+
+167
+00:20:35,150 --> 00:20:35,450
+هذه
+
+168
+00:20:41,140 --> 00:20:49,960
+و هاد نسميها برضه gamma وهدي نفسها gamma
+
+169
+00:20:49,960 --> 00:20:53,320
+وهدي
+
+170
+00:20:53,320 --> 00:20:56,760
+gamma
+
+171
+00:20:56,760 --> 00:21:02,700
+gamma
+
+172
+00:21:10,700 --> 00:21:15,760
+لاحظوا في الحالتين البكر الصغيرة والبكر الكبيرة ال
+
+173
+00:21:15,760 --> 00:21:19,920
+arc of contact زاوية ال arc of contact على البكر
+
+174
+00:21:19,920 --> 00:21:25,600
+الصغيرة نفسها هي زاوية ال arc of contact على البكر
+
+175
+00:21:25,600 --> 00:21:29,200
+الكبيرة والزاويتين بيكونوا أكبر من مية و تمانين
+
+176
+00:21:29,200 --> 00:21:33,060
+هذه هنسميها معناته
+
+177
+00:21:42,420 --> 00:21:49,100
+فاي وهذه برضه
+
+178
+00:21:49,100 --> 00:21:55,260
+فاي
+
+179
+00:21:55,260 --> 00:22:02,680
+خلنا
+
+180
+00:22:02,680 --> 00:22:07,780
+نسمي المسافر من هنا إلى هنا x
+
+181
+00:22:07,780 --> 00:22:08,300
+مثلا
+
+182
+00:22:13,110 --> 00:22:25,430
+المسافة هذه y
+
+183
+00:22:25,430 --> 00:22:31,850
+طيب
+
+184
+00:22:31,850 --> 00:22:38,170
+خلنا
+
+185
+00:22:38,170 --> 00:22:40,170
+نسمي هذه a
+
+186
+00:22:46,880 --> 00:22:57,560
+B C D A أول
+
+187
+00:22:57,560 --> 00:23:07,880
+شي عند X زائد Y بتساوي C X زائد Y بتساوي C
+
+188
+00:23:13,160 --> 00:23:20,180
+طبعا هذه الزاوية هتكون هذه هذي برضه gamma و هذي
+
+189
+00:23:20,180 --> 00:23:27,460
+ايش gamma لو
+
+190
+00:23:27,460 --> 00:23:33,200
+أخدت المثلث ABC
+
+191
+00:23:33,200 --> 00:23:37,960
+هتكون
+
+192
+00:23:37,960 --> 00:23:40,100
+sin gamma
+
+193
+00:23:47,710 --> 00:23:55,350
+AB على AC صح AB
+
+194
+00:23:55,350 --> 00:24:00,690
+اللي هو دي سمون على اتنين وال
+
+195
+00:24:00,690 --> 00:24:08,870
+AC اكس صح فاخدت المثلث EDC
+
+196
+00:24:08,870 --> 00:24:11,910
+EDC
+
+197
+00:24:11,910 --> 00:24:15,730
+هتكون sign gamma
+
+198
+00:24:20,490 --> 00:24:26,690
+بتساوى دي اي على سي اي
+
+199
+00:24:26,690 --> 00:24:34,650
+دي اي اللي هي دي كابيتال على اتنين Y معناه تحسر ان
+
+200
+00:24:34,650 --> 00:24:39,970
+ال دي على اتنين X دي اسمه على اتنين X سواء دي
+
+201
+00:24:39,970 --> 00:24:45,430
+كابيتال على اتنين Y يعني
+
+202
+00:24:48,630 --> 00:24:55,730
+ممكن احكي x small على d small يسوى y على d capital
+
+203
+00:24:55,730 --> 00:25:02,510
+معناته y بيسوى
+
+204
+00:25:02,510 --> 00:25:10,010
+x في d capital على d small صح؟ خلينا نسميها دي
+
+205
+00:25:10,010 --> 00:25:15,170
+بمعادلة واحد عوض عن y في معادلة واحد بيصير ان دي x
+
+206
+00:25:15,170 --> 00:25:17,350
+زائد
+
+207
+00:25:18,900 --> 00:25:29,020
+X في D capital على D small سوى C يعني ناخد X ع
+
+208
+00:25:29,020 --> 00:25:37,320
+المشترك وD small تحت هيكون
+
+209
+00:25:37,320 --> 00:25:49,360
+D small زي D capital سوى C يعني Xهتكون تساوي سي دي
+
+210
+00:25:49,360 --> 00:25:57,040
+small على دي small زائد دي capital معناه تواجه
+
+211
+00:25:57,040 --> 00:26:03,920
+هتساوي نعود عن اكسر اللي هي سي دي small على دي
+
+212
+00:26:03,920 --> 00:26:09,680
+small زائد دي capital في دي capital على دي small
+
+213
+00:26:11,280 --> 00:26:24,800
+يعني هتكون تساوي D capital C على D زائد D يعني
+
+214
+00:26:24,800 --> 00:26:31,320
+ال sign جامعة هتطلع عندي D
+
+215
+00:26:31,320 --> 00:26:38,240
+على 2X D small هتكون D
+
+216
+00:26:40,460 --> 00:26:50,360
+على اتنين X اللي هي في CD وعندهين
+
+217
+00:26:50,360 --> 00:26:58,900
+D Small زي D Capital يعني هتكون تساوي D
+
+218
+00:26:58,900 --> 00:27:03,800
+Small زي D Capital على اتنين C
+
+219
+00:27:10,070 --> 00:27:16,490
+يعني عرفنا الجامعة معناته الفاي هتكون تساوي اللي
+
+220
+00:27:16,490 --> 00:27:28,650
+هو باي زاد اتنين جامعة طب
+
+221
+00:27:28,650 --> 00:27:34,870
+طول الحبل كله عند هذا الحبل من هنا لهنا زاد هذا من
+
+222
+00:27:34,870 --> 00:27:40,300
+هنا لهنا بعدين الار كده بعدين الحبل من هنا لهنامن
+
+223
+00:27:40,300 --> 00:27:48,480
+هنا الى هنا و بعدها ال arc هذا ال a ليش هتساوي؟
+
+224
+00:27:48,480 --> 00:27:53,120
+بيكون بي
+
+225
+00:27:53,120 --> 00:28:05,060
+سي في اتنين صح؟ اتنين بي سي هلأ
+
+226
+00:28:05,060 --> 00:28:06,100
+سامع هذه F
+
+227
+00:28:08,800 --> 00:28:15,140
+زاد اتنين CD زاد اتنين CD
+
+228
+00:28:15,140 --> 00:28:20,820
+زاد طول ال arc على البكر الصغير اللي هو D على
+
+229
+00:28:20,820 --> 00:28:24,500
+اتنين فاي
+
+230
+00:28:24,500 --> 00:28:32,540
+زاد طول ال arc على البكر الكبير دي capital هيكون
+
+231
+00:28:32,540 --> 00:28:34,300
+عنده هي ان اتنين في
+
+232
+00:28:40,020 --> 00:28:45,120
+الـ BC هيكون
+
+233
+00:28:45,120 --> 00:28:58,400
+الجزر التربية ل X تربية جزر التربية ل X تربية ناقص
+
+234
+00:28:58,400 --> 00:29:02,740
+D على 2 للتربية، صح؟
+
+235
+00:29:02,740 --> 00:29:07,920
+ناقص D تربية
+
+236
+00:29:07,920 --> 00:29:08,440
+على 4
+
+237
+00:29:11,170 --> 00:29:19,410
+زائد CD الجزر التربيعي
+
+238
+00:29:19,410 --> 00:29:24,270
+ل
+
+239
+00:29:24,270 --> 00:29:32,190
+Y تربيع ناقص
+
+240
+00:29:32,190 --> 00:29:39,750
+D capital تربيع على أربعة زائد
+
+241
+00:29:41,290 --> 00:29:48,810
+فاي على اتنين في دي small زائد دي capital هنعوض عن
+
+242
+00:29:48,810 --> 00:29:52,530
+X هنعوض
+
+243
+00:29:52,530 --> 00:30:01,710
+عن X في
+
+244
+00:30:01,710 --> 00:30:05,570
+الجزر التربيعي ل
+
+245
+00:30:09,490 --> 00:30:19,090
+X تربيع اللي هي C تربيع D تربيع على D small زي D
+
+246
+00:30:19,090 --> 00:30:24,950
+capital كل تربيع ناقص
+
+247
+00:30:24,950 --> 00:30:34,470
+D تربيع دخل اتنين جوا سير
+
+248
+00:30:34,470 --> 00:30:35,890
+اربع هذه صح؟
+
+249
+00:30:40,180 --> 00:30:47,540
+زائد الجزر التربيعي لاربع
+
+250
+00:30:47,540 --> 00:30:54,600
+C تربيع D capital تربيع على D small زائد D capital
+
+251
+00:30:54,600 --> 00:31:05,400
+كل تربيع ناقص D capital تربيع زائد في على اتنين في
+
+252
+00:31:05,400 --> 00:31:07,920
+D small زائد D capital
+
+253
+00:31:12,350 --> 00:31:31,610
+هطلع دي small دي capital برا حاسس اللي عنده الجزر
+
+254
+00:31:31,610 --> 00:31:32,190
+التربي يعني
+
+255
+00:31:41,690 --> 00:31:45,050
+يعني ممكن ابسطها او اخليها زي ما هي يعني في الآخر
+
+256
+00:31:45,050 --> 00:31:50,510
+طب
+
+257
+00:31:50,510 --> 00:31:53,890
+ممكن من فوق انت قبل ما تعمل كلش ال X تربيه زي فوق
+
+258
+00:31:53,890 --> 00:31:56,930
+و خارج انت ترمى على ال X تربيه زي ال Y تربيه و ليه
+
+259
+00:31:56,930 --> 00:32:05,050
+مش ال C تربيه؟ لأ لأ هيك صحية هيك صحية انا عارف اه
+
+260
+00:32:05,050 --> 00:32:08,510
+بس مثلا انت لو جسميه X تربيه زي ال Y تربيه يعني
+
+261
+00:32:08,510 --> 00:32:12,280
+عبارة عن ال C تربيهبنفعش أحط هدول مع بعض، أشبههم
+
+262
+00:32:12,280 --> 00:32:16,520
+مع بعض، ما بنفع طيب، على أي حال، على أي حال،
+
+263
+00:32:16,520 --> 00:32:20,200
+بحيطلع لما نعمل تصفيات، حيطلع أشهر مشترك، حيطلع
+
+264
+00:32:20,200 --> 00:32:24,740
+أشهر مشترك بالإتنين بتصف المعادلة عندنا اللي هي L
+
+265
+00:32:24,740 --> 00:32:36,620
+اللي هو الجزر التربيعي ل 4C تربيع ناقص D small زي
+
+266
+00:32:36,620 --> 00:32:38,740
+D capital لكل تربيع
+
+267
+00:32:42,760 --> 00:32:50,680
+زائد في على اتنين في دي small زائد دي capital
+
+268
+00:32:50,680 --> 00:32:55,000
+انتبهوا
+
+269
+00:32:55,000 --> 00:32:59,360
+اللي حيصير عندهين تشابهات هيطلع أشهر مشترك و تختصر
+
+270
+00:32:59,360 --> 00:33:01,380
+المعادلة طيب
+
+271
+00:33:27,340 --> 00:33:37,380
+الان ال built فين دي driver و فينا driven الان
+
+272
+00:33:37,380 --> 00:33:43,160
+هيكون في احتكاك بين ال pulley و
+
+273
+00:33:43,160 --> 00:33:48,800
+بين ال built نفسها
+
+274
+00:33:48,800 --> 00:33:53,640
+طبعا ال .. اذا كان اللي على الشمال هو ال driver
+
+275
+00:33:55,330 --> 00:33:59,390
+هيكون الجزء التحتاني الحاجب مجدود او اكتر الشد فيه
+
+276
+00:33:59,390 --> 00:34:03,830
+اكتر من الجزء ايش العلوي يعني بسميه التحتاني الجزء
+
+277
+00:34:03,830 --> 00:34:07,870
+المجدود tight side والجزء العلوي اللي هو slack
+
+278
+00:34:07,870 --> 00:34:12,930
+side يعني ال tension تحت طبعا
+
+279
+00:34:12,930 --> 00:34:18,590
+اول ما بدأ يدخل بدخل بسرعة V واحد و force F واحد
+
+280
+00:34:18,590 --> 00:34:21,290
+لان في احتكاك
+
+281
+00:34:24,330 --> 00:34:28,010
+مش مباشرة بيبدأ يتغير لإن بيبدأ الاحتكاك يعني
+
+282
+00:34:28,010 --> 00:34:34,470
+build up بيصير شوية شوية لحد ما يصير إياش يبدأ
+
+283
+00:34:34,470 --> 00:34:38,170
+يصير sliding
+
+284
+00:34:38,170 --> 00:34:43,450
+نتيجة إنه ال build فيها مرونة ال build فيها إياش
+
+285
+00:34:43,450 --> 00:34:49,350
+مرونة بيصير فيها elongated contract و مجرد صارت
+
+286
+00:34:49,350 --> 00:34:52,470
+elongated contract معناه تصار في حركة نسبية بين ال
+
+287
+00:34:52,470 --> 00:34:58,430
+build و بينالـ pulley معناته we develop friction
+
+288
+00:34:58,430 --> 00:35:04,770
+وبالتالي الصراع عند ال exit نهاية ال arc بتكون
+
+289
+00:35:04,770 --> 00:35:09,430
+الصراع المحيطية للحبل أقل من الصراع المحيطية
+
+290
+00:35:09,430 --> 00:35:13,850
+للبكرة نفسها أقل من الصراع المحيطية للبكرة نفسها
+
+291
+00:35:13,850 --> 00:35:18,650
+عشانك ال arc of contact بتجزئه لجزئين
+
+292
+00:35:21,540 --> 00:35:26,680
+في ال ideal arc يعني ماصار فيه تغير لا بالسرعة ولا
+
+293
+00:35:26,680 --> 00:35:30,840
+بال force ال friction force وفي ال effective او ال
+
+294
+00:35:30,840 --> 00:35:35,760
+active arc اللي بيبدأ يصير فيه sliding effect و
+
+295
+00:35:35,760 --> 00:35:41,460
+بيصير فيه تغير في السرعة المحيطية لل built و ال
+
+296
+00:35:41,460 --> 00:35:42,660
+tension في الحبل
+
+297
+00:35:55,770 --> 00:36:01,510
+طيب انا ببقى ان عندي اعمل .. باخد ال free path
+
+298
+00:36:01,510 --> 00:36:05,990
+diagram اعمل cut و cut و باخد ال driving poly هاد
+
+299
+00:36:05,990 --> 00:36:13,370
+ال driving poly لكن الشد هنا F1 هيكون اعلى F2
+
+300
+00:36:13,370 --> 00:36:17,890
+معناه ان هنا هاد ال tight side و هاد ال slag side
+
+301
+00:36:17,890 --> 00:36:25,770
+F1 أكبر من F2والزاوية في هذه هتكون جزءين جزء
+
+302
+00:36:25,770 --> 00:36:31,030
+ايديال مافيه تغيير في ال velocity ولا تغيير في ال
+
+303
+00:36:31,030 --> 00:36:35,390
+tension او ال friction عندي هنا اللي هو ال
+
+304
+00:36:35,390 --> 00:36:38,890
+effective او ال active arc اللي هو جزء من ال arc
+
+305
+00:36:38,890 --> 00:36:39,270
+الكلي
+
+306
+00:36:43,080 --> 00:36:46,420
+زي ما احكي ان انا for the driving pulley the built
+
+307
+00:36:46,420 --> 00:36:48,920
+first contacts the pulley with a tight side
+
+308
+00:36:48,920 --> 00:36:53,320
+tension F1 لان تبدأ هنا تدخل ..اللي حابب يدخل في
+
+309
+00:36:53,320 --> 00:37:01,520
+البكرة بال tension F1 والسرعة ابتدائية V1 طبعا V1
+
+310
+00:37:01,520 --> 00:37:09,440
+هي نفس السرعة المحطية للبكرة طبعا
+
+311
+00:37:10,160 --> 00:37:13,280
+ال build زي ما حكينا ال arc بجزء ايش؟ جزء ايديال
+
+312
+00:37:13,280 --> 00:37:22,500
+وجزء ايش؟ active في فترة ال ideal arc ما بتتغير
+
+313
+00:37:22,500 --> 00:37:33,540
+قيمة ال tension F1 ولا قيمة الصراحة المحيطية مجرد
+
+314
+00:37:33,540 --> 00:37:35,560
+ما ندخل ال active
+
+315
+00:37:37,570 --> 00:37:41,570
+أو ال effective arc بيبدأ يصير عندى إيش sliding
+
+316
+00:37:41,570 --> 00:37:45,330
+بيصير في عندى elongation و contraction يعني بيصير
+
+317
+00:37:45,330 --> 00:37:50,810
+تمدد و انكماش في و استطالة في الحبل فبيبدأ يصير
+
+318
+00:37:50,810 --> 00:37:54,510
+عندى sliding contact و التالي ال sliding contact
+
+319
+00:37:54,510 --> 00:38:00,970
+بيعمل تغير في قيمة اللي هو ال tension في الحبل و
+
+320
+00:38:00,970 --> 00:38:01,930
+ال velocity
+
+321
+00:38:06,460 --> 00:38:11,080
+في نهاية ال effective يعني هنا لما يجي يطلع الحبل
+
+322
+00:38:11,080 --> 00:38:15,420
+في نهاية ال effective أو ال active arc الحبل بيسيب
+
+323
+00:38:15,420 --> 00:38:21,540
+البكرة بتension F2 أقل من ال tension اللي دخل فيه
+
+324
+00:38:21,540 --> 00:38:27,920
+أقل من F1 و بسرعة محيطية V2 أقل من السرعة المحيطية
+
+325
+00:38:27,920 --> 00:38:28,580
+للبكرة
+
+326
+00:38:36,200 --> 00:38:42,920
+typically في حالة built مصنوعة الكورتع من النيلون
+
+327
+00:38:42,920 --> 00:38:48,240
+والسطح الخارج من ال leather ومعامل احتكالات تقريبا
+
+328
+00:38:48,240 --> 00:38:54,960
+في حدود سبعة عشر بيكون طيب
+
+329
+00:38:54,960 --> 00:39:02,100
+هاخد جزء من الحبل الحبل احنا هي الحبلحبل هاخد جزء
+
+330
+00:39:02,100 --> 00:39:06,000
+infinitesimal element من الحبل الملامس للبقرة
+
+331
+00:39:06,000 --> 00:39:11,560
+واشوف ايش ال forces اللي بتأثر عليه زي ما انتوا
+
+332
+00:39:11,560 --> 00:39:15,140
+شايفين ماخد element at an angle theta ال theta
+
+333
+00:39:15,140 --> 00:39:20,520
+عشان تكون الصورة هي ال theta جامن
+
+334
+00:39:20,520 --> 00:39:24,520
+عند F2 و بعدين ماخد infinitesimal element delta
+
+335
+00:39:24,520 --> 00:39:24,960
+theta
+
+336
+00:39:29,250 --> 00:39:37,010
+الان ال element هذا اللي هو زوية و دي ثيتا بتأثى
+
+337
+00:39:37,010 --> 00:39:40,210
+عليه اللي هو DS اللي هي centrifugal force ال force
+
+338
+00:39:40,210 --> 00:39:48,290
+due لكتلة الحبل في عندي force لإنه بيكون فيه
+
+339
+00:39:48,290 --> 00:39:51,200
+rotation معناته فيه neuron acceleration صح؟معنى
+
+340
+00:39:51,200 --> 00:39:54,180
+انتوا هيكون في عندى normal force او centrifugal
+
+341
+00:39:54,180 --> 00:40:00,500
+force اللي هي ال mass في ال normal acceleration و
+
+342
+00:40:00,500 --> 00:40:03,840
+ال normal acceleration هي عبارة عن omega square في
+
+343
+00:40:03,840 --> 00:40:09,400
+ال radius صح ف ال DS هي centrifugal force في عندى
+
+344
+00:40:09,400 --> 00:40:14,330
+normal force من البكرة على الحبل اللي هي DNو في
+
+345
+00:40:14,330 --> 00:40:19,190
+friction force او traction force من الحبل على ..
+
+346
+00:40:19,190 --> 00:40:27,010
+من البكرة على الحبل يعني FDN وفي شد في الحبل F و
+
+347
+00:40:27,010 --> 00:40:33,050
+بعد زاوية D θ بتغير بيصير F زائد DF بيصير F زائد
+
+348
+00:40:33,050 --> 00:40:37,530
+DF و هو يعني مستخدم اللي هو normal cord .. normal
+
+349
+00:40:37,530 --> 00:40:40,690
+antangelical cord and system يعني هي هذي بيسميها R
+
+350
+00:40:40,690 --> 00:40:46,920
+او ال normalو هاي ال tangential بهذا الاتجاه R و T
+
+351
+00:40:46,920 --> 00:40:58,900
+ال B يمثل عرض ال built هذا هو ال B عرض ال T الصمق
+
+352
+00:40:58,900 --> 00:41:06,500
+ال M ال built mass per unit length اللي هي الكتلة
+
+353
+00:41:06,500 --> 00:41:10,820
+كل وحدة طول الكتلة كل وحدة طول
+
+354
+00:41:14,080 --> 00:41:16,780
+إذا باخد summation of forces بتجاه ال radial
+
+355
+00:41:16,780 --> 00:41:19,960
+direction أو ال normal direction و summation of
+
+356
+00:41:19,960 --> 00:41:26,840
+forces بتجاه ال tangential direction يعني
+
+357
+00:41:26,840 --> 00:41:38,760
+لو قعدت عندي هاي هذا ال radial direction وهذا
+
+358
+00:41:46,680 --> 00:41:59,480
+تنجينشال داريكشن هذا
+
+359
+00:41:59,480 --> 00:42:09,460
+زي ماشي حتكون دي ثتا على اتنين صح وهذا دي ثتا على
+
+360
+00:42:09,460 --> 00:42:09,960
+اتنين
+
+361
+00:42:17,610 --> 00:42:28,950
+و هذه دي ثيتا هذه
+
+362
+00:42:28,950 --> 00:42:33,210
+دي اس وهذه
+
+363
+00:42:33,210 --> 00:42:38,970
+دي ان وهذه
+
+364
+00:42:38,970 --> 00:42:43,410
+اف
+
+365
+00:42:43,410 --> 00:42:50,100
+دي انماصطمش اللي ال DS اللي هي centrifugal force
+
+366
+00:42:50,100 --> 00:43:01,340
+ال
+
+367
+00:43:01,340 --> 00:43:08,160
+DS
+
+368
+00:43:08,160 --> 00:43:11,980
+centrifugal force بالساوية
+
+369
+00:43:16,030 --> 00:43:23,470
+A Normal في الـ D تاعة الـ Mass صح الـ A Normal
+
+370
+00:43:23,470 --> 00:43:32,110
+عبارة عن Omega Square R الـ D M فين دي الكتلة لكل
+
+371
+00:43:32,110 --> 00:43:38,610
+واحدة الطول اللي هي M الطول الواحدة الطول اللي هي
+
+372
+00:43:38,610 --> 00:43:46,820
+هذا الطول اللي هو عبارة عن R D Theta صح عن RD ثتا
+
+373
+00:43:46,820 --> 00:44:01,560
+بتصف هذه omega square R square M D ثتا ال omega في
+
+374
+00:44:01,560 --> 00:44:10,460
+R سرعة المحيطية صح؟ يعني هتكون V square M D ثتا
+
+375
+00:44:10,460 --> 00:44:22,360
+هذه كلها سميها centrifugal forceD ثتا Fc D ثتا لان
+
+376
+00:44:22,360 --> 00:44:24,540
+انا ما اصمش ال force اتجاه ال radial انا ما اصمش
+
+377
+00:44:24,540 --> 00:44:35,520
+ال force اتجاه ال radial direction عندنا ال DS ال
+
+378
+00:44:35,520 --> 00:44:43,300
+DS زائد ال DN عند
+
+379
+00:44:43,300 --> 00:45:00,330
+مناقص F sin dθ على اتنين minus F زائد dF sin dθ
+
+380
+00:45:00,330 --> 00:45:08,430
+على اتنين يعني هكون عندى dS زائد بسواة زيرو طبعا
+
+381
+00:45:08,430 --> 00:45:10,890
+زائد dN
+
+382
+00:45:16,270 --> 00:45:24,430
+- FD θ على اتنين FD
+
+383
+00:45:24,430 --> 00:45:30,670
+θ على اتنين FD θ على اتنين FD θ على اتنين FD θ على
+
+384
+00:45:30,670 --> 00:45:33,150
+اتنين FD θ على اتنين FD θ على اتنين FD θ على اتنين
+
+385
+00:45:33,150 --> 00:45:33,330
+FD θ على اتنين FD θ على اتنين FD θ على اتنين FD θ
+
+386
+00:45:33,330 --> 00:45:33,370
+على اتنين FD θ على اتنين FD θ على اتنين FD θ على
+
+387
+00:45:33,370 --> 00:45:34,490
+اتنين FD θ على اتنين FD θ على اتنين FD θ على اتنين
+
+388
+00:45:34,490 --> 00:45:34,690
+FD θ على اتنين FD θ على اتنين FD θ على اتنين FD θ
+
+389
+00:45:34,690 --> 00:45:34,930
+على اتنين FD θ على اتنين FD θ على اتنين FD θ على
+
+390
+00:45:34,930 --> 00:45:40,130
+اتنين FD θ على اتنين FD θ على اتنين FD θ على اتن
+
+391
+00:45:41,330 --> 00:45:46,590
+بتصفى عند ال DN بتساوي
+
+392
+00:45:46,590 --> 00:45:50,310
+FD
+
+393
+00:45:50,310 --> 00:45:55,350
+θ minus
+
+394
+00:45:55,350 --> 00:46:02,690
+DS الحاضرة
+
+395
+00:46:02,690 --> 00:46:03,710
+الجاية ونكمل ..
+
diff --git a/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/eDuly-EiEE0_postprocess.srt b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/eDuly-EiEE0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ccc94e96451da37ef22378b0cfc314cc26add839
--- /dev/null
+++ b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/eDuly-EiEE0_postprocess.srt
@@ -0,0 +1,1452 @@
+1
+00:00:05,260 --> 00:00:08,080
+طيب بسم الله الرحمن الرحيم السلام عليكم و رحمة
+
+2
+00:00:08,080 --> 00:00:10,920
+الله وبركاته و هنكمل في مادة تصميم الألات اتنين
+
+3
+00:00:10,920 --> 00:00:14,800
+بدأنا في ال design of flat belts خلصنا اللي هو ال
+
+4
+00:00:14,800 --> 00:00:19,620
+flat belts اللي هي non-metal بتكون يوريثين يعني
+
+5
+00:00:19,620 --> 00:00:25,120
+مطات أو أنواع غير معدنية اليوم هنحكي عن ال belts
+
+6
+00:00:25,120 --> 00:00:29,000
+ال flat built او ال flat metal built يعني ال built
+
+7
+00:00:29,000 --> 00:00:36,530
+بتكون معدن نفس الفكرة ان انا بكون في عندىtight
+
+8
+00:00:36,530 --> 00:00:41,990
+side لو هي ال rotation بيكون عندي F1 أكبر من F2 و
+
+9
+00:00:41,990 --> 00:00:46,350
+F1 ناقص F2 بيستوى 2T على D و في عندي initial
+
+10
+00:00:46,350 --> 00:00:49,690
+tension نفس العلاقة يُعطى بالعلاقة ال T على D
+
+11
+00:00:49,690 --> 00:00:53,110
+بيستوى exponential لل FI زياد واحد على ال
+
+12
+00:00:53,110 --> 00:00:58,050
+exponential لل FI minus 2 و ال F1 بيستوى Fc زياد
+
+13
+00:00:58,050 --> 00:01:00,470
+Fi في 2 exponential F
+
+14
+00:01:13,820 --> 00:01:20,950
+الخطوات لاختيار flat metalأولش احنا بنحسب ال
+
+15
+00:01:20,950 --> 00:01:24,250
+exponential لل F فاي من ال geometry اللي هو شكل
+
+16
+00:01:24,250 --> 00:01:32,670
+سبعتاش واحد بنحسب اللي هو الفاي مظبوط وال F من
+
+17
+00:01:32,670 --> 00:01:39,260
+الجداول الآن نحكي احنا عن معادنfor بالذبنة طبعا
+
+18
+00:01:39,260 --> 00:01:42,460
+احنا فينا rotation معناته بنحكي في endurance او
+
+19
+00:01:42,460 --> 00:01:45,940
+بنحكي عن fatigue design فبالذبنة ال endurance
+
+20
+00:01:45,940 --> 00:01:51,140
+strength يعني ال strength يعني تحسب من العلاقة SF
+
+21
+00:01:51,140 --> 00:01:55,620
+بالساوية خمساش point واحد ستة في عشرة وستة NV
+
+22
+00:01:55,620 --> 00:01:59,040
+أصلاق سبونت اربع واحد اتنين في حالة تلاتمية واحد
+
+23
+00:01:59,040 --> 00:02:04,720
+تلاتمية اتنين stainless steelأو ال fatigue
+
+24
+00:02:04,720 --> 00:02:06,900
+strength أو ال yield strength بالسواء أسوأ على
+
+25
+00:02:06,900 --> 00:02:13,500
+تلاتة الأسوأ هي اللي هي ال yield strength ال NP هي
+
+26
+00:02:13,500 --> 00:02:16,640
+number of passes أكام لفة بالدورة ع مدار حياتها
+
+27
+00:02:16,640 --> 00:02:22,960
+number of passes ال table سبعتاشر تمانية معطيني
+
+28
+00:02:22,960 --> 00:02:29,400
+typical material properties لمعدن مختلفةمعطين ال
+
+29
+00:02:29,400 --> 00:02:33,100
+yield strength و ال young modulus و ال poison
+
+30
+00:02:33,100 --> 00:02:36,780
+ratio مثلا إذا كان عندك ال flat built مصنوع من ال
+
+31
+00:02:36,780 --> 00:02:42,500
+stainless steel 301 او 302 جليد عند 175 Kps I و ال
+
+32
+00:02:42,500 --> 00:02:47,640
+E capital 28 Mega pound per square inch فيها نوع
+
+33
+00:02:47,640 --> 00:02:52,640
+مختلفة طبعا في inc و nel لأن ال 1075 او 1050
+
+34
+00:02:52,640 --> 00:02:55,280
+carbon steel
+
+35
+00:02:57,710 --> 00:03:03,970
+طيب بعدين بنحسب ال allowal tension F1A
+
+36
+00:03:03,970 --> 00:03:09,610
+بسوء SF minus E capital اللي هي T على واحدة ناقص
+
+37
+00:03:09,610 --> 00:03:16,410
+new square في D capital في TB وكل ال term اللي هو
+
+38
+00:03:16,410 --> 00:03:20,450
+بين الأقواص مضروف ال thickness بيسميه A
+
+39
+00:03:23,190 --> 00:03:26,710
+عندنا ال E capital هي ال modulus of ال الستي ال T
+
+40
+00:03:26,710 --> 00:03:30,630
+هي ال thickness لل new اللي هي ال Poisson ratio ال
+
+41
+00:03:30,630 --> 00:03:33,250
+D capital قطر البكرة الكبيرة
+
+42
+00:03:40,280 --> 00:03:46,520
+التابل 17 7 يعطينا ال minimum يعطينا ال build
+
+43
+00:03:46,520 --> 00:03:50,520
+thickness مقابل ال minimum poly diameter مثلا ال
+
+44
+00:03:50,520 --> 00:04:00,460
+build thickness 0.002 أقل قطر للبكرة 1.2 انش لو
+
+45
+00:04:00,460 --> 00:04:06,220
+أخدنا ال thickness 0.04 انش أقل أقل قطر للبكرة 25
+
+46
+00:04:06,220 --> 00:04:13,920
+انشطيب خلينا نقسم ال poly diameter على ال
+
+47
+00:04:13,920 --> 00:04:18,760
+thickness one point two على point 002 أكم تطلع
+
+48
+00:04:18,760 --> 00:04:27,140
+ستمية صح؟ one point eight على point 003 ستمية
+
+49
+00:04:27,140 --> 00:04:36,860
+تلاتة على point 005 أكم ستمية خمسة على point 008
+
+50
+00:04:36,860 --> 00:04:38,400
+بتطلع ستمية و إشي
+
+51
+00:04:41,580 --> 00:04:48,040
+ستمية و ستمية و خمسة و عشرين مظبوط طيب ستة على
+
+52
+00:04:48,040 --> 00:04:56,360
+point o one ستمية عشر على point o one five سبوليها
+
+53
+00:04:56,360 --> 00:05:02,000
+طيب
+
+54
+00:05:02,000 --> 00:05:04,920
+اتناشر و نص على point o two ستمية و خمسة و عشرين
+
+55
+00:05:04,920 --> 00:05:09,950
+عندك خمسة و عشرين على point o fourستمية و خمسة و
+
+56
+00:05:09,950 --> 00:05:14,290
+عشرين يعني ال range .. ستمية لستمية و خمسة يعني في
+
+57
+00:05:14,290 --> 00:05:17,990
+ال range مش أقل من ستمية بيكون ال relation بين ال
+
+58
+00:05:17,990 --> 00:05:21,670
+poly diameter و ال thickness هذا ال minimum، هدا
+
+59
+00:05:21,670 --> 00:05:28,430
+ياش ال minimum ال ..
+
+60
+00:05:28,430 --> 00:05:34,430
+ل ..
+
+61
+00:05:34,430 --> 00:05:36,010
+للصغيرة
+
+62
+00:05:40,670 --> 00:05:47,230
+وين ال D capital كتبت؟ اه صحيح D capital صحيح صحيح
+
+63
+00:05:47,230 --> 00:05:50,390
+ال built life for stainless steel friction rises
+
+64
+00:05:50,390 --> 00:05:54,470
+اذا كان عندى stainless steel ال built ال D على ال
+
+65
+00:05:54,470 --> 00:06:01,270
+T بتكون ستمية و خمسة و عشرين ال .. ال built passes
+
+66
+00:06:01,270 --> 00:06:06,830
+عمرها هتعمر لأكتر من مليون pass اذا ال D على ال T
+
+67
+00:06:06,830 --> 00:06:11,790
+صارت أربعمية قلتهتعيش نص في عشر عقل ستة يعني
+
+68
+00:06:11,790 --> 00:06:17,150
+الحياة بتاعتها ايش بتقل اذا كانت D على T ratio
+
+69
+00:06:17,150 --> 00:06:23,610
+تلاتين تلات تلاتين ال build passes بتساوي
+
+70
+00:06:23,610 --> 00:06:27,950
+point واحد ستة خمس عشر عقل ستة اذا متين بتساوي
+
+71
+00:06:27,950 --> 00:06:31,570
+point oh eight five عشر عشر ستة لحظة كله بتقلي ال
+
+72
+00:06:31,570 --> 00:06:35,010
+ratio بتقلي ال life لان ال flexing ال bending بزيد
+
+73
+00:06:38,060 --> 00:06:41,100
+طب هل سألتوا نوصل ال .. ال .. ال .. ال .. ال .. ال
+
+74
+00:06:41,100 --> 00:06:42,160
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+75
+00:06:42,160 --> 00:06:42,600
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+76
+00:06:42,600 --> 00:06:43,440
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+77
+00:06:43,440 --> 00:06:44,100
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+78
+00:06:44,100 --> 00:06:45,580
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+79
+00:06:45,580 --> 00:06:46,480
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+80
+00:06:46,480 --> 00:06:52,920
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+81
+00:06:52,920 --> 00:06:53,260
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+82
+00:06:53,260 --> 00:06:53,640
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+83
+00:06:53,640 --> 00:06:58,800
+ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+84
+00:07:05,300 --> 00:07:09,180
+يعني انت خد مثلا ال point OO2 اضغط عليه في خمسة و
+
+85
+00:07:09,180 --> 00:07:21,240
+عشرين اكتر تطلع ال point OO2 في خمسة و عشرين point
+
+86
+00:07:21,240 --> 00:07:27,020
+point O05 ميلي متر اضغط بال point O4 في خمسة و
+
+87
+00:07:27,020 --> 00:07:31,640
+عشرين واحد
+
+88
+00:07:31,640 --> 00:07:34,300
+اضغط
+
+89
+00:07:35,370 --> 00:07:38,210
+يعني عندك من point O5 اللي هو واحد من اللي بس طالع
+
+90
+00:07:38,210 --> 00:07:42,570
+على القطر ال minimum diameter خمسة و عشرين انش
+
+91
+00:07:42,570 --> 00:07:48,130
+يعني حوالي ستمية و تلاتين ميلي تلات ستين صنطة قطر
+
+92
+00:07:48,130 --> 00:07:52,170
+البكرة انا
+
+93
+00:07:52,170 --> 00:07:55,210
+بعتقد في عنده خربطة يعني دي capital هي البكرة
+
+94
+00:07:55,210 --> 00:08:03,170
+الصغيرة بس هي بس حكاية رموزطيب ممكن نعمل ما هو
+
+95
+00:08:03,170 --> 00:08:06,730
+يكون عبارة زي اكشاف المخبز يكون يعني فيه فصلات
+
+96
+00:08:06,730 --> 00:08:12,890
+ممكن تعمل فيه فصلات اه طبعا رقم
+
+97
+00:08:12,890 --> 00:08:16,870
+اربعة بتحسب delta F بيستوى اتنين T capital على D
+
+98
+00:08:16,870 --> 00:08:22,990
+ال F2 بيستوى F1A minus delta F ال F1A احنا حاكيه
+
+99
+00:08:22,990 --> 00:08:28,610
+بيستوى AB minus delta Fوالـ FI بيسوء F1A زي F2 على
+
+100
+00:08:28,610 --> 00:08:33,830
+2 بيسوء AB زي AB minus delta F على 2 يعني بيسوء AB
+
+101
+00:08:33,830 --> 00:08:38,570
+minus delta F على 2 وفيه ان ال minimum built with
+
+102
+00:08:38,570 --> 00:08:42,650
+معطل علاقة delta F على A في exponential ال FY على
+
+103
+00:08:42,650 --> 00:08:46,780
+exponential FY minus 1دائما اختار b أكبر من b
+
+104
+00:08:46,780 --> 00:08:54,260
+minimum و بعدين ارجع احسب اللي هي f1 a و f2 و fi و
+
+105
+00:08:54,260 --> 00:08:59,180
+t و check for friction development احسب f prime
+
+106
+00:08:59,180 --> 00:09:05,500
+let's go أقل من f نشوف
+
+107
+00:09:05,500 --> 00:09:09,680
+مثال a
+
+108
+00:09:09,680 --> 00:09:14,230
+friction drive stainless steel metal builtأولا
+
+109
+00:09:14,230 --> 00:09:18,790
+الشيء المثالي بتاعة البلدياش steel steel runs over
+
+110
+00:09:18,790 --> 00:09:29,270
+two four-inch metal pulleys يعني
+
+111
+00:09:29,270 --> 00:09:30,810
+عندي هذه pulley
+
+112
+00:09:46,740 --> 00:09:53,160
+high poly ال
+
+113
+00:09:53,160 --> 00:10:05,940
+D هو الفاي اربع انش يعني ال D اربع انش ال material
+
+114
+00:10:05,940 --> 00:10:12,810
+stainless steelمعامل الاحتكاك ال friction
+
+115
+00:10:12,810 --> 00:10:19,410
+coefficient point تلاتة خمسة ال build thickness is
+
+116
+00:10:19,410 --> 00:10:25,230
+to be point o o تلاتة انش ال build thickness point
+
+117
+00:10:25,230 --> 00:10:31,850
+o o تلاتة انشfor a life exceeding عشرة او ستة
+
+118
+00:10:31,850 --> 00:10:38,870
+built passes يعني ن بيه يساوي عشرة او ستة اكبر أو
+
+119
+00:10:38,870 --> 00:10:46,870
+يساوي passes with
+
+120
+00:10:46,870 --> 00:10:52,410
+a smooth torque الكياس بيعطيليه واحد
+
+121
+00:10:56,910 --> 00:11:00,050
+select the belt if the torque is to be 30 pound
+
+122
+00:11:00,050 --> 00:11:05,730
+force احسب اللي هو اختار ال belt اذا كان ال torque
+
+123
+00:11:05,730 --> 00:11:08,830
+تلاتين
+
+124
+00:11:08,830 --> 00:11:19,330
+pound force في انش و find ال initial يعني select
+
+125
+00:11:19,330 --> 00:11:23,650
+ال belt find ال initial tension
+
+126
+00:11:32,720 --> 00:11:49,160
+انا هنا عملت اكسل شيط الان
+
+127
+00:11:49,160 --> 00:11:56,060
+نوع ال built انا اختارته open منعت هذا القرار انا
+
+128
+00:11:56,060 --> 00:12:01,260
+اعطيت اللون الكرمي دي ال built material
+
+129
+00:12:04,560 --> 00:12:07,840
+stay in the scene تلاتي واحد او تلاتي و اتنين طبعا
+
+130
+00:12:07,840 --> 00:12:12,000
+هرجع على ال table سبعتاش تمانية هذا ياش قرار برضه
+
+131
+00:12:12,000 --> 00:12:16,140
+من البناء على القرار هذا هاجيب ال yield strength
+
+132
+00:12:16,140 --> 00:12:19,540
+من ال table سبعتاش تمانية تطلع مية خمسة سبعين
+
+133
+00:12:19,540 --> 00:12:23,880
+الأسواي و ال modulus of the CTE capital تطلع
+
+134
+00:12:23,880 --> 00:12:27,400
+تمانية و عشرين ميجاباون في ال square inch و ال
+
+135
+00:12:27,400 --> 00:12:29,740
+poison ratio point اتنين تمانية خمسة هذا كله من ال
+
+136
+00:12:29,740 --> 00:12:42,580
+table السبعتاش تمانية175.28.285 number
+
+137
+00:12:42,580 --> 00:12:50,880
+of built passes هذي input هو ماعطينيها مليون الان
+
+138
+00:12:50,880 --> 00:12:56,620
+ال endurance strength sf
+
+139
+00:12:56,620 --> 00:13:00,300
+بالثورة خمس تاش point واحد ستة في عشر او ستة and P
+
+140
+00:13:00,300 --> 00:13:05,370
+أس minus point four واحد اتنينمن المعادلة هذه بحث
+
+141
+00:13:05,370 --> 00:13:10,410
+في ال NP ال SF نه
+
+142
+00:13:10,410 --> 00:13:17,910
+مضتين ال NP بتطلع واحد و خمسين point one Kpsi ال
+
+143
+00:13:17,910 --> 00:13:21,790
+build thickness ماتينيها ده هو point O O تلاتة هذه
+
+144
+00:13:21,790 --> 00:13:28,570
+input ال minimum poly diameter من ال table سبعتاش
+
+145
+00:13:28,570 --> 00:13:33,470
+سبعة هاي ال table سبعتاش سبعةالـ Pelt thickness هو
+
+146
+00:13:33,470 --> 00:13:38,430
+0.003 المنهم poly diameter 1.8 هاي المنهم poly
+
+147
+00:13:38,430 --> 00:13:44,850
+diameter 1.8 تابر سبعتاش سبعة معامل احتكالة كال F
+
+148
+00:13:44,850 --> 00:13:49,370
+هو معطينيها 0.35 ال diameter ب small poly هو
+
+149
+00:13:49,370 --> 00:13:54,350
+معطينيها لو انا اخترتها بيصير long تانية أربع انش
+
+150
+00:13:54,350 --> 00:13:58,630
+والتنتين نفس القطر معناته ال speed ratio شو يساويه
+
+151
+00:13:58,630 --> 00:14:05,670
+واحدو ال diameter of large poly اربعة انش ال
+
+152
+00:14:05,670 --> 00:14:10,050
+center distance انا
+
+153
+00:14:10,050 --> 00:14:15,470
+اتخذ قرار ان تكون في بتهيألة نرجع هنا نشوف اذا
+
+154
+00:14:15,470 --> 00:14:24,510
+عندنا معلومة عن ال center distance القطر
+
+155
+00:14:24,510 --> 00:14:27,570
+اربعة انش يعني
+
+156
+00:14:28,710 --> 00:14:31,790
+يعني مافيش في ال open احنا فحكينا في ال open built
+
+157
+00:14:31,790 --> 00:14:38,730
+فيه limit على ال center distance مافيش اه يعني انا
+
+158
+00:14:38,730 --> 00:14:41,650
+مش شايف اشي مافيش limitation اذا فاكد سبتاشر تابع
+
+159
+00:14:41,650 --> 00:14:45,210
+سبتاشر واحد بيحكينا ان مافيش limitation على ال
+
+160
+00:14:45,210 --> 00:14:52,070
+center distance انا اختارتها عشرة inch يعني
+
+161
+00:14:52,070 --> 00:14:54,010
+ده حكيه decision خدته انا
+
+162
+00:15:01,600 --> 00:15:10,860
+الـ rotational speed مش ماتيني اهو صح 860 rpm ال
+
+163
+00:15:10,860 --> 00:15:14,080
+wrap angle هتكون 180 درجة اكيد هطلع في حالة هذه بس
+
+164
+00:15:14,080 --> 00:15:20,280
+هي محسوبة حساب هطلع 180 درجة ال exponential لل FI
+
+165
+00:15:20,280 --> 00:15:27,740
+هذه المحسوبة اللي هي بعدين السرعة المحيطية V
+
+166
+00:15:27,740 --> 00:15:33,760
+capital اللي هي πايدين علىأتناش وتسعمائة واحد قدم
+
+167
+00:15:33,760 --> 00:15:44,460
+في الدقيقة الان ال KS معطينيها واحد الان
+
+168
+00:15:44,460 --> 00:15:49,440
+دي انا مختاره one point five هاي هذه ال decision
+
+169
+00:15:49,440 --> 00:15:54,580
+طيب
+
+170
+00:15:54,580 --> 00:15:58,740
+هو معطيني ال torque معطيني اياه تلاتين pound
+
+171
+00:16:01,610 --> 00:16:06,750
+inch ال a اللي هو ال parameter هذا ال a اللي هو
+
+172
+00:16:06,750 --> 00:16:13,830
+بين ال cosine في ال T هذا عيش ال a هذا معسوب حساب
+
+173
+00:16:13,830 --> 00:16:21,130
+يطلع خمس و تمانين ال delta F بيستوى اتنين T على D
+
+174
+00:16:21,130 --> 00:16:24,290
+اتنين T على D
+
+175
+00:16:34,430 --> 00:16:40,030
+هي دلت اف اتنين ت على دي ال minimum built
+
+176
+00:16:40,030 --> 00:16:45,250
+thickness ال بيه minimum دلت
+
+177
+00:16:45,250 --> 00:16:48,110
+اف على ايه في exponent of في على exponent of في
+
+178
+00:16:48,110 --> 00:16:55,810
+minus واحد حسبت ال بيه ال بيه minimum ال built
+
+179
+00:16:55,810 --> 00:16:58,670
+width انا عرفت ال minimum انا كنت بيكون اكبر من
+
+180
+00:16:58,670 --> 00:17:04,090
+هذا اخترت قيمة ايش قلتلك تربع انشيعني هتكون ال
+
+181
+00:17:04,090 --> 00:17:08,830
+build تقريبا اكام عرضها تلت اربع انش يعني حوالي
+
+182
+00:17:08,830 --> 00:17:13,090
+عشرين مليون مظبوط تين سنة هي دور هتكون رفيعة كتير
+
+183
+00:17:13,090 --> 00:17:23,710
+فاختارتها تلت اربع انش بعدين حسب ال F1A F1A ضربت A
+
+184
+00:17:23,710 --> 00:17:34,740
+في B ضربت A في B حسبت ال F1A بعدين ال F2بالساوية
+
+185
+00:17:34,740 --> 00:17:41,200
+اللى هو F1A-Delta F انا برضه حاسب F1A وDelta F هاد
+
+186
+00:17:41,200 --> 00:17:48,620
+ال F2 تطلع 48 من 6 ال initial tension FI بالساوية
+
+187
+00:17:48,620 --> 00:17:58,500
+F1A زي F2 على 2 F1A زي F2 على 2 هاد ال FI طلعت 56
+
+188
+00:17:58,500 --> 00:18:05,630
+poundالان الـ actual friction coefficient F prime
+
+189
+00:18:05,630 --> 00:18:12,110
+من المعادلة هذه بس واحدة على فاية لين F one A على
+
+190
+00:18:12,110 --> 00:18:17,450
+F اتنين هعندى
+
+191
+00:18:17,450 --> 00:18:22,150
+ال F primeالان danger of slip لازم تكون ال F prime
+
+192
+00:18:22,150 --> 00:18:29,270
+أصغر من ال F يعني هذه point او تبني خمسة أصغر من
+
+193
+00:18:29,270 --> 00:18:33,070
+ال point تلاتة خمسة خلنا نخلي هذه مثلا نص انش شوف
+
+194
+00:18:33,070 --> 00:18:39,650
+ايش يصير معاها هاي نص انش خلنا نحكي مثلا point
+
+195
+00:18:39,650 --> 00:18:47,260
+تلاتة انشمافيش عندى اي danger of slip مافي
+
+196
+00:18:47,260 --> 00:18:58,120
+اي danger of slip point سبعة خمسة رجعها طيب
+
+197
+00:18:58,120 --> 00:19:07,780
+خليني خاطر نحفظ شغلة احنا حكينا ال B ال
+
+198
+00:19:07,780 --> 00:19:08,060
+B
+
+199
+00:19:26,870 --> 00:19:31,030
+بدي احسب .. بدي احسب ال stresses اشوف ايش .. انا
+
+200
+00:19:31,030 --> 00:19:37,690
+اكبر ايش عندي F1A اللي هي تلاتة و ستين و نص مظبوط
+
+201
+00:19:37,690 --> 00:19:45,370
+و ال .. خلنا نحسب ال stress أول واحدة هيكون
+
+202
+00:19:45,370 --> 00:19:53,890
+الساوية هذا على ال thickness على .. على B على ال
+
+203
+00:19:53,890 --> 00:19:54,350
+thickness
+
+204
+00:19:57,580 --> 00:20:04,540
+وين ال thickness على
+
+205
+00:20:04,540 --> 00:20:13,260
+الف هحكي على الف عشان نطلعها KPSI تمانية
+
+206
+00:20:13,260 --> 00:20:20,220
+و عشرين point اتنين سبعة الليل دي انا كام عنده ال
+
+207
+00:20:20,220 --> 00:20:30,670
+ASI مية خمسة و سبعينبعيد كتير، بعيد كتير، صح؟ يعني
+
+208
+00:20:30,670 --> 00:20:34,410
+مابش حاسيه real دنيا خليني أحكي ال B ال B خليني
+
+209
+00:20:34,410 --> 00:20:41,290
+أغير ال B ال B و اين ال B؟
+
+210
+00:20:41,290 --> 00:20:48,290
+هيا خليني أحكي 0.3 لحظة
+
+211
+00:20:48,290 --> 00:20:54,650
+مصممة، هتبقى لها نفس الأشياءال ratio لما تتغير
+
+212
+00:20:54,650 --> 00:20:58,730
+قيمة ال F1A فانا بحكي انه انا قللت العرض معناته
+
+213
+00:20:58,730 --> 00:21:05,710
+هذا المفروض ال maximum allowable force تظل ثابتة
+
+214
+00:21:05,710 --> 00:21:10,150
+ال maximum allowable force تظل ثابتة معناته انا
+
+215
+00:21:10,150 --> 00:21:13,970
+روحت قللت العرض راح قلل .. انت مسموح لك خلاص مازال
+
+216
+00:21:13,970 --> 00:21:18,710
+قللت العرض المسموح لك برضه هينزل خلنا نحكي القطر
+
+217
+00:21:18,710 --> 00:21:30,750
+مثلا خلنا ال B ال Bالبيخ انا احكيه واحد انش لاعزاش
+
+218
+00:21:30,750 --> 00:21:42,270
+اللي بيصير خليا واحد و نص يعني
+
+219
+00:21:42,270 --> 00:21:47,670
+هو ال control اللي هو مش ال .. يعني حقيقة ال
+
+220
+00:21:47,670 --> 00:21:52,530
+control مثبت ال stress مثبت ايه اش؟ ال stress
+
+221
+00:22:01,270 --> 00:22:04,330
+لأ هذا ال factor .. هذا ال factor against كل عملية
+
+222
+00:22:04,330 --> 00:22:07,670
+ال design هذا ال factor saved against yielding
+
+223
+00:22:07,670 --> 00:22:16,370
+اللي انا .. انا نبدأ أحسبه save طيب هيك نكون احنا
+
+224
+00:22:23,620 --> 00:22:28,240
+فاهم ان ايش design flat metal ايش اقل الصمم ممتاح
+
+225
+00:22:28,240 --> 00:22:37,160
+في غزاينة في الحديد الصاجي صفر اربعة مش هتقدر تعمل
+
+226
+00:22:37,160 --> 00:22:40,700
+اقل من صفر اربعة صفر اربعة قسموها على خمسة وعشرين
+
+227
+00:22:40,700 --> 00:22:47,620
+ده كام تطلع point
+
+228
+00:22:47,620 --> 00:22:52,340
+هو واحد خمسة تقريبا مظبوط
+
+229
+00:22:54,430 --> 00:23:04,710
+point o o point 0 4 على 25 point
+
+230
+00:23:04,710 --> 00:23:13,870
+o 1 6 يعني تقريبا انت جاين احنا هنا في المنطقة هذه
+
+231
+00:23:13,870 --> 00:23:21,670
+هنا عم تحكي عن بكر أقل شي 11 انش عن بكر أقل شي 11
+
+232
+00:23:21,670 --> 00:23:22,290
+انش
+
+233
+00:23:25,890 --> 00:23:30,990
+يعني ممكن تعمل في ال bond سفر أربعة، هل ممكن اللي
+
+234
+00:23:30,990 --> 00:23:33,750
+حامها فيها اللي حاموها في غزة ال bond four .. ال
+
+235
+00:23:33,750 --> 00:23:39,170
+bond four؟ اللي حاموها اللي حام .. لأ لأ ال bond
+
+236
+00:23:39,170 --> 00:23:44,730
+هو مينفعش، مينفعش، اه مينفعش ال bond طيب
+
+237
+00:23:45,800 --> 00:23:49,220
+نخش على نوع تاني من ال builds اللي هو ال V builds
+
+238
+00:23:49,220 --> 00:23:55,920
+ال V build زي ما انتوا شايفين بيكون مقطع ال build
+
+239
+00:23:55,920 --> 00:24:02,820
+نفسه في عندى زاوية العرطة هي A والارتفاع B
+
+240
+00:24:02,820 --> 00:24:09,170
+والزاوية بتاعة ال build بتكون اربعين درجةالان تيجي
+
+241
+00:24:09,170 --> 00:24:14,850
+انواع build section تيجي A B C D E طبعا اصغر حجم
+
+242
+00:24:14,850 --> 00:24:19,270
+اللي هو A بعدين B بعدين C بعدين D بعدين E معطينا
+
+243
+00:24:19,270 --> 00:24:24,510
+طبعا ال A و ال B في كل حالة مثلا اذا كانت A بيكون
+
+244
+00:24:24,510 --> 00:24:32,210
+المقطع نصف و 11 ع 32 و ال minimum sheath diameter
+
+245
+00:24:32,210 --> 00:24:39,920
+اقل قطر كرة تلاتة انشو ال horse power range ل
+
+246
+00:24:39,920 --> 00:24:43,280
+built او اكتر ممكن تكون البكرة multiple built
+
+247
+00:24:43,280 --> 00:24:50,800
+يتراوح من .. من ربع لعشرة حصان .. ربع لعشرة حصان
+
+248
+00:24:50,800 --> 00:24:55,120
+يعني حتى لو استخدمت مثلا تلاتة built جانب بعض مش
+
+249
+00:24:55,120 --> 00:24:58,620
+.. ما تتخططش لعشرة حصان إذا تخططت لعشرة حصان روح
+
+250
+00:24:58,620 --> 00:25:04,580
+على ال size اللي بعده طيب
+
+251
+00:25:08,690 --> 00:25:14,270
+to specify a v built give a built section letter
+
+252
+00:25:14,270 --> 00:25:17,330
+هتاخد section letter يا a يا b يا c يا d يا a
+
+253
+00:25:17,330 --> 00:25:23,330
+followed by inside circumference images مطبوعة
+
+254
+00:25:23,330 --> 00:25:26,910
+بالمحيط الداخل للbuilt المحيط اللي انا من ال table
+
+255
+00:25:26,910 --> 00:25:31,790
+17 يعني عندي هنا مثلا في ال Bالمحيط الداخلي ال
+
+256
+00:25:31,790 --> 00:25:35,870
+standard المتاح يتروح بين خمسة و تلاتين انش
+
+257
+00:25:35,870 --> 00:25:43,010
+لتلاتميت انش في ال A في ال A من ستة و عشرين انش
+
+258
+00:25:43,010 --> 00:25:48,590
+لمية و تمانية و عشرين انش في ال C من واحد و خمسين
+
+259
+00:25:48,590 --> 00:25:53,620
+انش لاربع مية و عشرين انشطبعا مافيش كثور يعني
+
+260
+00:25:53,620 --> 00:25:59,420
+بتختار في حالة ال B يا 35 يا 38 يا 42 يا 380 يا
+
+261
+00:25:59,420 --> 00:26:04,880
+180 يا 270 يا 300 تحكي هذه ال standard المتاع في
+
+262
+00:26:04,880 --> 00:26:10,780
+ال D طبعا واحد بين 120 انش و 660 انش ال E بين 180
+
+263
+00:26:10,780 --> 00:26:13,800
+انش و 660 انش
+
+264
+00:26:16,060 --> 00:26:20,180
+في كل حوال مش هتلاقي V built المحيط الداخلي لها
+
+265
+00:26:20,180 --> 00:26:27,000
+بزيادة عن 660 انش مثلا
+
+266
+00:26:27,000 --> 00:26:33,480
+لو حكيت V 75 هي B section والمحيط الداخلي لها 75
+
+267
+00:26:33,480 --> 00:26:43,200
+انش موجود عند V 75 هي موجودة for
+
+268
+00:26:43,200 --> 00:26:49,050
+any given built sectionالان عندى المحيط الداخلي
+
+269
+00:26:49,050 --> 00:26:55,290
+وفي عندى اللى هو ال pitch length ال pitch length
+
+270
+00:26:55,290 --> 00:27:04,150
+جاى أكبر شوية بيكون من ال .. من ال .. المحيط اللى
+
+271
+00:27:04,150 --> 00:27:10,250
+هو تعالى بدسم اللى هو ال pitch profile أكبر من ال
+
+272
+00:27:10,250 --> 00:27:14,090
+inside circumferenceفلازم اعمل correction هو عمل
+
+273
+00:27:14,090 --> 00:27:18,730
+correction مثلا لو كان بي سكتشن باضيف one point
+
+274
+00:27:18,730 --> 00:27:22,010
+eight يعني لو حكيت بي خمس سبعين حيكون محيط ال
+
+275
+00:27:22,010 --> 00:27:27,310
+pitch ال pitch circumference حيكون خمس سبعين زائد
+
+276
+00:27:27,310 --> 00:27:31,130
+one point تمانية حيصير ستة سبعين point تمانية ليش
+
+277
+00:27:31,130 --> 00:27:35,150
+لأن ال calculations of velocity ratios are based
+
+278
+00:27:35,150 --> 00:27:38,210
+on pitch diameters of the sheaves انا لما احسب
+
+279
+00:27:39,000 --> 00:27:48,920
+بالاستراشيز بعتمد على ال pitch ديامتر طيب
+
+280
+00:27:48,920 --> 00:27:53,160
+الان
+
+281
+00:27:53,160 --> 00:27:57,960
+عندي اللي هو زر بتاعة ال build
+
+282
+00:28:11,630 --> 00:28:19,010
+هي ال build النقطة تاع ال build وهي
+
+283
+00:28:19,010 --> 00:28:30,490
+البكرة هذه
+
+284
+00:28:30,490 --> 00:28:32,130
+Alpha تاعة ال build
+
+285
+00:28:40,960 --> 00:28:48,440
+البكرة نفسها بيسموها Alpha S Alpha S Alpha S بتكون
+
+286
+00:28:48,440 --> 00:28:54,860
+أقل شوية Alpha S أقل
+
+287
+00:28:54,860 --> 00:29:00,900
+شويةمن ال alpha بتاعة ال build عشان تحشر عشان تحشر
+
+288
+00:29:00,900 --> 00:29:04,920
+بس تكونش أقل كتير اذا كانت أقل كتير بتحشر كتير
+
+289
+00:29:04,920 --> 00:29:08,800
+بتقطس كتير بتحشر كتير فلما تلف .. ما هي بتلف يعني
+
+290
+00:29:08,800 --> 00:29:12,360
+.. يعني تمسك و بتنزع ماسك و نزع ماسك و نزع من ال
+
+291
+00:29:12,360 --> 00:29:16,420
+.. من ال .. من ال poly بيصير نزعها صعب بيصير صعب
+
+292
+00:29:16,420 --> 00:29:19,820
+فبتكون ال alpha أس عشان .. عشان ليش لازت تكون أصغر
+
+293
+00:29:19,820 --> 00:29:25,840
+عشان تولد احتكاك لازت عشان تولد احتكاك كافي
+
+294
+00:29:32,820 --> 00:29:38,240
+طيب إذا كانت أصغر بكتير الفرق واضح بتولد يعني
+
+295
+00:29:38,240 --> 00:29:42,720
+بيصير نزعها من ال grooves الصعبة إذا كانت قليل جدا
+
+296
+00:29:42,720 --> 00:29:49,580
+الفرق بتولدش احتكاك كافي for
+
+297
+00:29:49,580 --> 00:29:54,390
+best resultsa v built should be run quite fast
+
+298
+00:29:54,390 --> 00:29:58,990
+four thousand foot per minute is a good speed يعني
+
+299
+00:29:58,990 --> 00:30:04,030
+ال average سرعة كويسة سرعة محيطيةمناسب اربع تلاف
+
+300
+00:30:04,030 --> 00:30:07,670
+قدم في الدقيقة عشان تحصل على احسن نتاج او احسن
+
+301
+00:30:07,670 --> 00:30:11,830
+efficiency من ال ايش ال V built اتفاكرين احنا
+
+302
+00:30:11,830 --> 00:30:16,010
+حكينا تتراوح ال efficiency لل V built من خمس و
+
+303
+00:30:16,010 --> 00:30:20,330
+سبعين لست و تسعين اظن مظبوط for best results يعني
+
+304
+00:30:20,330 --> 00:30:24,630
+for best efficiencies اربع تلاف feet per minute is
+
+305
+00:30:24,630 --> 00:30:29,810
+a good choice trouble may be encountered ممكن
+
+306
+00:30:29,810 --> 00:30:35,070
+تواجهنا مشاكلif built runs much faster than خمس
+
+307
+00:30:35,070 --> 00:30:38,410
+تلاف إذا كانت أسرع بكتير من خمس تلاف ممكن يكون في
+
+308
+00:30:38,410 --> 00:30:42,050
+مشاكل في ال design بتاع ال build أو إذا كانت أقل
+
+309
+00:30:42,050 --> 00:30:47,670
+بكتير من ألف يعني ال range عندك بين ألف السرعة
+
+310
+00:30:47,670 --> 00:30:52,690
+المحيطية بين ألف قدم permanent لخمس تلاف دايما
+
+311
+00:30:52,690 --> 00:30:56,910
+أشتغل على ال range هذا best results عند الأربعة
+
+312
+00:30:56,910 --> 00:31:00,830
+تلاف ال
+
+313
+00:31:00,830 --> 00:31:08,900
+pitch lengthاللي هو المحيط يُعطيه
+
+314
+00:31:08,900 --> 00:31:10,960
+العلاقة قلبي بيعتمد على ال center distance يستوى
+
+315
+00:31:10,960 --> 00:31:13,880
+اتنين C زائد باعف D capital زائد D small على اتنين
+
+316
+00:31:13,880 --> 00:31:17,860
+زائد D capital minus D الكل تربيه على اربع C ال C
+
+317
+00:31:17,860 --> 00:31:21,780
+هي ال center distance بين ال two poles ال D
+
+318
+00:31:21,780 --> 00:31:27,240
+capital قطر البكرة الكبيرة D small قطر البكرة
+
+319
+00:31:27,240 --> 00:31:31,720
+الصغيرة او انا بكون عارف
+
+320
+00:31:35,530 --> 00:31:39,870
+عارف ايش اللي بيصير انا بكون في الأول بختار center
+
+321
+00:31:39,870 --> 00:31:46,650
+distance و بحسب القلبي القلبي بروح على الجدول
+
+322
+00:31:46,650 --> 00:31:50,690
+بختار section و انا عندي standard بختار اشي قريب
+
+323
+00:31:50,690 --> 00:31:56,170
+منه standard معناه تصير تعرف القلبي بتاعتها بعدين
+
+324
+00:31:56,170 --> 00:31:59,710
+بعمل recalculation بعمل عدة حساب ليش ل center
+
+325
+00:31:59,710 --> 00:32:04,660
+distance لأن في النهاية انا هاختارهختار من هنا
+
+326
+00:32:04,660 --> 00:32:06,740
+هختار ال standard لازم اختار ال standard انا اعرف
+
+327
+00:32:06,740 --> 00:32:10,540
+المحيط لكن في البداية انا ماكنش عارف بحسب ال LPE
+
+328
+00:32:10,540 --> 00:32:19,100
+based on center distance و بعدين بختار
+
+329
+00:32:19,100 --> 00:32:22,580
+ال LPE الحقيقية و بعدين بعد بعدد ال center
+
+330
+00:32:22,580 --> 00:32:27,060
+distance typically ال center distance تتراح بين D
+
+331
+00:32:27,060 --> 00:32:32,500
+capital لتلاتة في D capital زي D small اللي هي ال
+
+332
+00:32:32,500 --> 00:32:33,260
+center distance
+
+333
+00:32:37,630 --> 00:32:41,450
+الان عندى ال horse power ratings of standard v
+
+334
+00:32:41,450 --> 00:32:46,230
+builds طبعا هدى partial list هدى مش كل ال list
+
+335
+00:32:46,230 --> 00:32:49,090
+عندى ال a و ال b و ال c و ال d و ال e انا مارجة ال
+
+336
+00:32:49,090 --> 00:32:55,310
+a بس يعنى ماعطينى يعنى ال build speed بالقدم على
+
+337
+00:32:55,310 --> 00:32:58,530
+الدقيقة عندهين ألف ألفين تلت تلات أربع تلات خمس
+
+338
+00:32:58,530 --> 00:33:02,710
+تلات هو مش نازع عن ألف و مش طالع عن خمس تلات خلاص
+
+339
+00:33:02,710 --> 00:33:08,090
+احكيلك اشتغل في ال range هذاالان لو كان ال shift
+
+340
+00:33:08,090 --> 00:33:17,990
+diameter تلاتة انش تلاتة انش والسرعة تلت تلاف ممكن
+
+341
+00:33:17,990 --> 00:33:21,030
+هذه ال power اللي هي تبقى .. ال .. تبقى ليها ال
+
+342
+00:33:21,030 --> 00:33:25,610
+power تكون one point one two horsepower اذا كانت
+
+343
+00:33:25,610 --> 00:33:30,070
+ايه؟ اذا كانت القطر مثلا اربع point ستة انش
+
+344
+00:33:30,070 --> 00:33:35,360
+والسرعة مثلا اربع تلافال power rating بتكون ايه اش
+
+345
+00:33:35,360 --> 00:33:38,160
+اتنين point ستة تسعة horse power بتاعة ال build
+
+346
+00:33:38,160 --> 00:33:41,800
+rating
+
+347
+00:33:41,800 --> 00:33:48,220
+اللي هى hours or built or built passes is for a
+
+348
+00:33:48,220 --> 00:33:52,860
+built running on equal diameter sheaves يعني هذه
+
+349
+00:33:52,860 --> 00:33:58,820
+ال ratings معمولة على اساس البكرتين اللي هو نفس
+
+350
+00:33:58,820 --> 00:34:00,340
+القطر
+
+351
+00:34:01,920 --> 00:34:06,820
+يعني بتكون ال rap angle مية و تمانين درجة of
+
+352
+00:34:06,820 --> 00:34:10,260
+moderate length and transmitting steady load
+
+353
+00:34:10,260 --> 00:34:15,860
+otherwise هنحتاج correction هنحتاج correction يعني
+
+354
+00:34:15,860 --> 00:34:20,020
+لو كانت البكر بين بكرتين متساوتين و ال length
+
+355
+00:34:20,020 --> 00:34:26,320
+متوسط و ال load steady طول باخد الرقم يعني لكن
+
+356
+00:34:26,320 --> 00:34:33,060
+مضطر ايش اعملالـ allow bar per built is given by
+
+357
+00:34:33,060 --> 00:34:36,900
+K1, K2, H tablet H tablet اللي هي .. اللي هي من ال
+
+358
+00:34:36,900 --> 00:34:43,320
+table السابق ال .. ال K1 correction factor لل
+
+359
+00:34:43,320 --> 00:34:45,700
+angle of wrap ال angle of wrap احنا ال standard هو
+
+360
+00:34:45,700 --> 00:34:48,380
+اللي هي ال table السابق على مية و تمانين درجة
+
+361
+00:34:48,380 --> 00:34:50,780
+اختلف من مية و تمانين درجة يعني انا محتاج اعمل
+
+362
+00:34:50,780 --> 00:34:56,380
+correctionالـ K2 بيلت لينكس كوركشن فاكتور بيلت
+
+363
+00:34:56,380 --> 00:34:58,820
+لينكس كوركشن فاكتور حاضرش ده بالكامل
+
diff --git a/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/eDuly-EiEE0_raw.json b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/eDuly-EiEE0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..e99e21d84d22d145a2d7b61404b611b45be6cddb
--- /dev/null
+++ b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/eDuly-EiEE0_raw.json
@@ -0,0 +1 @@
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"probability": 0.9150390625}, {"start": 625.23, "end": 625.65, "word": " o", "probability": 0.9111328125}, {"start": 625.65, "end": 626.05, "word": " o", "probability": 0.984375}, {"start": 626.05, "end": 627.53, "word": " تلاتة", "probability": 0.9835205078125}, {"start": 627.53, "end": 628.03, "word": " انش", "probability": 0.936767578125}], "temperature": 1.0}, {"id": 25, "seek": 65241, "start": 629.49, "end": 652.41, "text": "for a life exceeding عشرة او ستة built passes يعني ن بيه يساوي عشرة او ستة اكبر أو يساوي passes with a smooth torque الكياس بيعطيليه واحد", "tokens": [2994, 257, 993, 14048, 278, 6225, 8592, 25720, 1975, 2407, 8608, 2655, 3660, 3094, 11335, 37495, 22653, 8717, 4724, 1829, 3224, 7251, 3794, 995, 45865, 6225, 8592, 25720, 1975, 2407, 8608, 2655, 3660, 1975, 4117, 26890, 34051, 7251, 3794, 995, 45865, 11335, 365, 257, 5508, 16437, 33251, 1829, 32277, 4724, 40228, 9566, 1829, 20292, 3224, 36764, 24401], "avg_logprob": -0.3289331942796707, "compression_ratio": 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2084.42, "end": 2084.64, "word": " احنا", "probability": 0.9261067708333334}, {"start": 2084.64, "end": 2084.98, "word": " ال", "probability": 0.81787109375}, {"start": 2084.98, "end": 2085.4, "word": " standard", "probability": 0.947265625}, {"start": 2085.4, "end": 2085.7, "word": " هو", "probability": 0.70068359375}, {"start": 2085.7, "end": 2086.08, "word": " اللي", "probability": 0.96435546875}, {"start": 2086.08, "end": 2086.28, "word": " هي", "probability": 0.8271484375}, {"start": 2086.28, "end": 2086.72, "word": " ال", "probability": 0.86376953125}, {"start": 2086.72, "end": 2086.98, "word": " table", "probability": 0.9130859375}, {"start": 2086.98, "end": 2087.48, "word": " السابق", "probability": 0.9938151041666666}, {"start": 2087.48, "end": 2087.64, "word": " على", "probability": 0.9072265625}, {"start": 2087.64, "end": 2087.82, "word": " مية", "probability": 0.357421875}, {"start": 2087.82, "end": 2087.88, "word": " و", "probability": 0.8642578125}, {"start": 2087.88, "end": 2088.04, "word": " تمانين", "probability": 0.7861328125}, {"start": 2088.04, "end": 2088.38, "word": " درجة", "probability": 0.9915364583333334}, {"start": 2088.38, "end": 2088.64, "word": " اختلف", "probability": 0.8642578125}, {"start": 2088.64, "end": 2088.78, "word": " من", "probability": 0.5478515625}, {"start": 2088.78, "end": 2089.26, "word": " مية", "probability": 0.840576171875}, {"start": 2089.26, "end": 2089.34, "word": " و", "probability": 0.99365234375}, {"start": 2089.34, "end": 2089.46, "word": " تمانين", "probability": 0.9814453125}, {"start": 2089.46, "end": 2089.72, "word": " درجة", "probability": 0.9860026041666666}, {"start": 2089.72, "end": 2089.82, "word": " يعني", "probability": 0.59832763671875}, {"start": 2089.82, "end": 2090.02, "word": " انا", "probability": 0.52490234375}, {"start": 2090.02, "end": 2090.42, "word": " محتاج", "probability": 0.7794596354166666}, {"start": 2090.42, "end": 2090.78, "word": " اعمل", "probability": 0.9313151041666666}, {"start": 2090.78, "end": 2091.28, "word": " correction", "probability": 0.94140625}], "temperature": 1.0}, {"id": 77, "seek": 209882, "start": 2092.08, "end": 2098.82, "text": "الـ K2 بيلت لينكس كوركشن فاكتور بيلت لينكس كوركشن فاكتور حاضرش ده بالكامل", "tokens": [6027, 39184, 591, 17, 4724, 26895, 2655, 5296, 9957, 4117, 3794, 9122, 13063, 4117, 8592, 1863, 6156, 995, 4117, 2655, 13063, 4724, 26895, 2655, 5296, 9957, 4117, 3794, 9122, 13063, 4117, 8592, 1863, 6156, 995, 4117, 2655, 13063, 11331, 46958, 2288, 8592, 11778, 3224, 20666, 4117, 10943, 1211], "avg_logprob": -0.2989477040816326, "compression_ratio": 1.5903614457831325, "no_speech_prob": 0.0, "words": [{"start": 2092.08, "end": 2092.42, "word": "الـ", "probability": 0.6392822265625}, {"start": 2092.42, "end": 2092.7, "word": " K2", "probability": 0.806640625}, {"start": 2092.7, "end": 2093.64, "word": " بيلت", "probability": 0.5382486979166666}, {"start": 2093.64, "end": 2095.04, "word": " لينكس", "probability": 0.795654296875}, {"start": 2095.04, "end": 2095.64, "word": " كوركشن", "probability": 0.782470703125}, {"start": 2095.64, "end": 2096.04, "word": " فاكتور", "probability": 0.825390625}, {"start": 2096.04, "end": 2096.38, "word": " بيلت", "probability": 0.5889892578125}, {"start": 2096.38, "end": 2096.68, "word": " لينكس", "probability": 0.9822998046875}, {"start": 2096.68, "end": 2097.1, "word": " كوركشن", "probability": 0.9849609375}, {"start": 2097.1, "end": 2097.54, "word": " فاكتور", "probability": 0.98212890625}, {"start": 2097.54, "end": 2098.28, "word": " حاضرش", "probability": 0.6182861328125}, {"start": 2098.28, "end": 2098.4, "word": " ده", "probability": 0.873046875}, {"start": 2098.4, "end": 2098.82, "word": " بالكامل", "probability": 0.82171630859375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2099.38575, "duration_after_vad": 1905.2012499999942}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/gJkf9bF_pgg.srt b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/gJkf9bF_pgg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a0093c05f3db1f116d5fcf5a8dd456b5a96a99a4
--- /dev/null
+++ b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/gJkf9bF_pgg.srt
@@ -0,0 +1,1855 @@
+1
+00:00:05,280 --> 00:00:07,560
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:07,560 --> 00:00:10,520
+وبركاته هنتكمل في مادة تصمييم الآلات هنحكي لك عن 
+
+3
+00:00:10,520 --> 00:00:16,500
+موضوع جديد اللي هي الحبل wire rope طبعًا أول شيء أن 
+
+4
+00:00:16,500 --> 00:00:20,940
+نتعرف على تسميات الحبل
+
+5
+00:00:20,940 --> 00:00:26,100
+بيكون متكون من شكل أساسي من جدائل مجموعة من جدائل
+
+6
+00:00:26,100 --> 00:00:31,940
+وقلب core  الجديلة الواحدة يعني هذه الجديلة الجديلة
+
+7
+00:00:31,940 --> 00:00:36,090
+متكونة من مجموعة من إيش؟ من الأسلاك لأن مجموع
+
+8
+00:00:36,090 --> 00:00:46,190
+الجدائل والقلب بيشكل ليها الـ wire rope الـ 
+
+9
+00:00:46,190 --> 00:00:52,270
+wire rope ممكن يجي right hand ordinary بيكون 
+
+10
+00:00:52,270 --> 00:00:58,370
+الجدائل بتروح زي البرج بتروح باتجاه اليمين والأسلاك
+
+11
+00:00:58,370 --> 00:01:02,470
+بتروح على الشمال عكس بعض يعني عندكوا
+
+12
+00:01:02,470 --> 00:01:08,910
+الـ strand رايحة على الجهة اليمين على اليمين الـ
+
+13
+00:01:08,910 --> 00:01:15,910
+strand والحبل على الشمال هذا إيش؟ right hand 
+
+14
+00:01:15,910 --> 00:01:24,270
+ordinary في عندي right hand langth الـ 
+
+15
+00:01:24,270 --> 00:01:29,860
+strand رايح على اليمين والخيوط أو الـ ... الـ ... الـ 
+
+16
+00:01:29,860 --> 00:01:34,540
+الخيوط نفسها يا ريت رايحة برضه على اليمين في left
+
+17
+00:01:34,540 --> 00:01:41,060
+hand الجدائل اللي رايحة يا ريت الشمال والخيوط رايحة
+
+18
+00:01:41,060 --> 00:01:47,320
+يا ريت يمين left hand ordinary وفي left hand langth
+
+19
+00:01:47,320 --> 00:01:54,720
+الجدائل اللي رايحة الشمال والخيوط الشمال في حالة
+
+20
+00:01:54,720 --> 00:01:55,440
+الـ ...
+
+21
+00:01:59,420 --> 00:02:02,700
+الـ right hand ordinary أو left hand ordinary 
+
+22
+00:02:02,700 --> 00:02:07,580
+تقريبًا الخيوط والأسلاك بتكون موازية لمحور لمحور
+
+23
+00:02:07,580 --> 00:02:13,760
+الرب في حالة الـ right hand langth أو left hand
+
+24
+00:02:13,760 --> 00:02:20,680
+langth بتكون الخيوط عاملة زي قطر ميلة بيكون فيها 
+
+25
+00:02:20,680 --> 00:02:31,180
+ميل عاملة زاوية مع محور الرب طبعًا الـ regular ليه؟
+
+26
+00:02:31,180 --> 00:02:35,700
+اللي هو سواء كان right hand ordinary أو left hand
+
+27
+00:02:35,700 --> 00:02:41,120
+ordinary هو الـ accepted standard بغض
+
+28
+00:02:41,120 --> 00:02:45,110
+النظر هو right hand أو left hand بيكون إذا الـ
+
+29
+00:02:45,110 --> 00:02:50,370
+strand رايح يمين بيكون السلك رايح الشمال أو إذا الـ
+
+30
+00:02:50,370 --> 00:02:57,630
+strand رايح الشمال بيكون السلك رايح يمين الأسلاك
+
+31
+00:02:57,630 --> 00:03:01,050
+اللي احنا بكون شايفينها بتكون تقريبًا موازية لمحور
+
+32
+00:03:01,050 --> 00:03:07,810
+الحبل طبعًا بتفسخش
+
+33
+00:03:07,810 --> 00:03:12,590
+هذا اللي هي kink بتفسخش في الاستخدام يعني بيفتحش
+
+34
+00:03:12,590 --> 00:03:13,550
+معاك الحبل
+
+35
+00:03:16,660 --> 00:03:23,160
+في long lay سواء كان يمين أو كان شمال دائمًا الـ
+
+36
+00:03:23,160 --> 00:03:26,260
+strand والخيوط في نفس الاتجاه إذا كان الـ strand
+
+37
+00:03:26,260 --> 00:03:30,040
+رايحين يمين برضه الخيوط بتكون رايحة يمين وإذا كان
+
+38
+00:03:30,040 --> 00:03:35,180
+الـ strand رايحة شمال برضه الخيوط الشمال الـ outer
+
+39
+00:03:35,180 --> 00:03:41,640
+wires بتكون diagonal يعني عاملة زاوية مع محور الحبل
+
+40
+00:03:43,410 --> 00:03:47,970
+احتمالية أن... أن تفتح أو يعني تفسخ معه أكبر
+
+41
+00:03:47,970 --> 00:03:50,510
+من الـ ... الـ regular
+
+42
+00:03:56,790 --> 00:04:00,050
+الـ standard drops are made with a hemp core which
+
+43
+00:04:00,050 --> 00:04:02,950
+supports and lubricates the strands يعني بيكون
+
+44
+00:04:02,950 --> 00:04:08,950
+عندي الطلع عند الجدائل الخارجية وفي core وفي hemp
+
+45
+00:04:08,950 --> 00:04:12,990
+أنا حاطط صورة الـ hemp اللي هي نبات القنب بيكون شكله
+
+46
+00:04:12,990 --> 00:04:16,090
+طالع كيف شكله طالع الشكل في النص هنا
+
+47
+00:04:18,960 --> 00:04:23,780
+نفس شكل النباتة طالع النباتة طالع العادي من الـ top
+
+48
+00:04:23,780 --> 00:04:30,100
+view هتشوف زي إيش زي نجم كأنه نجم فعشان هيك يسموه
+
+49
+00:04:30,100 --> 00:04:37,580
+hemp core hemp core ففي عندي الـ strands وفي عندي إيش
+
+50
+00:04:37,580 --> 00:04:41,920
+الـ core إذا كان الحبل بيتعرض للحرارة
+
+51
+00:04:45,080 --> 00:04:53,380
+يعني نستخدم الـ ... المركز أو الـ core حديد أو wire
+
+52
+00:04:53,380 --> 00:05:00,120
+strand ... strand center must be used الـ
+
+53
+00:05:00,120 --> 00:05:04,020
+wire rope designation هنا هي مقطع ... يعني دي مقطع
+
+54
+00:05:04,020 --> 00:05:05,800
+للحبل
+
+55
+00:05:07,800 --> 00:05:13,640
+من هنا إلى هنا هو الـ rope diameter الـ rope مكون
+
+56
+00:05:13,640 --> 00:05:17,360
+من مجموع من strands ها هي strand واحدة اثنين ثلاثة
+
+57
+00:05:17,360 --> 00:05:23,960
+أربعة خمسة ستة والـ core مثلًا عندي واحد على ثمانية 
+
+58
+00:05:23,960 --> 00:05:28,020
+إنش ستة في سبعة haulage rope واحد من إنش اللي هو
+
+59
+00:05:28,020 --> 00:05:30,800
+القطر الـ rope واحد من إنش القطر الـ rope اللي هو من 
+
+60
+00:05:30,800 --> 00:05:36,090
+هنا إلى هنا ستة يعني ست جدائل واحدة اثنين ثلاثة
+
+61
+00:05:36,090 --> 00:05:40,950
+أربعة خمس ست جدائل سبعة في كل جديلة فيها سبعة سلك
+
+62
+00:05:40,950 --> 00:05:48,670
+هنعد هنا واحد اثنين ثلاثة أربعة خمسة ستة سبعة الـ 
+
+63
+00:05:48,670 --> 00:05:53,710
+area of metal in standard hosting الـ AM اللي هي 
+
+64
+00:05:53,710 --> 00:05:59,710
+مساحة المقطع بالسنتيمتر 3.8 D square جدول
+
+65
+00:05:59,710 --> 00:06:05,100
+سبعة عشر أربعة عشر معطين اللي هو الـ rope standards
+
+66
+00:06:05,100 --> 00:06:10,300
+عند ستة في سبعة ... ستة في سبعة يعني إيش؟ ست جدائل
+
+67
+00:06:10,300 --> 00:06:17,490
+كل جديلة في سبعة سلك ستة في تسعة عشر ست جدائل كل
+
+68
+00:06:17,490 --> 00:06:23,110
+جديلة فيها تسعة عشر سلك ستة في سبعة وثلاثين ست
+
+69
+00:06:23,110 --> 00:06:28,190
+جدائل كل جديلة فيها سبعة وثلاثين سلك ثمانية في 
+
+70
+00:06:28,190 --> 00:06:32,770
+تسعة عشر ثمانية جدائل كل جديلة تسعة عشر سلك سبعة في 
+
+71
+00:06:32,770 --> 00:06:37,550
+سبعة سبع جدائل كل جديلة فيها سبعة سلاك سبعة في 
+
+72
+00:06:37,550 --> 00:06:42,810
+تسعة تسعة عشر aircraft طيب معطيل العمود الثاني الـ 
+
+73
+00:06:42,810 --> 00:06:49,110
+weight per foot الـ weight per foot بيساوي واحد بس
+
+74
+00:06:49,110 --> 00:06:54,170
+في الحالة ستة في سبعة واحد ونصف دي square minimum 
+
+75
+00:06:54,170 --> 00:06:57,230
+sheaf diameter البكرة الأقل قطر منك ممكن يركب
+
+76
+00:06:57,230 --> 00:07:01,790
+عليها اللي هي بيساوي اثنين وأربعين دي اثنين و
+
+77
+00:07:01,790 --> 00:07:07,290
+أربعين قطر الربع الـ standard size الـ size ستة في 
+
+78
+00:07:07,290 --> 00:07:13,930
+سبعة بيجي من ربع إنش لواحد ونصف إنش الـ material دي
+
+79
+00:07:13,930 --> 00:07:16,870
+أنواع مختلفة من الـ steel تسمية monitor steel, plow
+
+80
+00:07:16,870 --> 00:07:21,570
+steel, mild plow steel الـ size of outer wires هذه
+
+81
+00:07:21,570 --> 00:07:25,810
+الـ outer wires هي هذه مش القلب بيكون D على تسعة دي 
+
+82
+00:07:25,810 --> 00:07:30,530
+اللي هي قطر الروب يعني D على تسعة الـ modulus of
+
+83
+00:07:30,530 --> 00:07:35,050
+elasticity أربعة عشر ميجا pound per square inch الـ 
+
+84
+00:07:35,050 --> 00:07:38,450
+strength في الـ kilo pound per square inch مئة
+
+85
+00:07:41,830 --> 00:07:46,590
+السلك الصغير نفسه المجدل يعني، هل التجديل بيقلل الـ
+
+86
+00:07:46,590 --> 00:07:50,390
+tensile strength له؟ يعني هل المجدل نفس الـ tensile
+
+87
+00:07:50,390 --> 00:07:55,090
+strength للمجدل ولا لا؟ لأ التجديل بيخليه شيء أكثر 
+
+88
+00:07:55,990 --> 00:08:00,030
+أنت ... أنت ... اه طبعًا اه لإنه بيصير فيه friction 
+
+89
+00:08:00,030 --> 00:08:05,030
+بينهم كثير، تخيل سلك مش مجدل على عدل، بيشدّه، صح؟
+
+90
+00:08:05,030 --> 00:08:08,390
+صحيح وبالتالي تقليل الـ ... الـ friction minimized،
+
+91
+00:08:08,390 --> 00:08:11,650
+فالتجديل بيعمل friction، الـ friction بيساعد
+
+92
+00:08:17,270 --> 00:08:23,350
+الآن نخش على اللي هو المصطلحات المعدلة والمعدلات
+
+93
+00:08:23,350 --> 00:08:27,670
+المستخدمة أول شيء هنا الـ equivalent bending load FB
+
+94
+00:08:27,670 --> 00:08:32,370
+الحبل
+
+95
+00:08:32,370 --> 00:08:36,230
+بيكون على بكرة وهو يلف على البكرة بيكون لابس عليه 
+
+96
+00:08:36,230 --> 00:08:38,390
+إيه؟ twisting
+
+97
+00:08:40,000 --> 00:08:45,700
+الـ twisting بيعمل إيه؟ normal stress الـ 
+
+98
+00:08:45,700 --> 00:08:48,960
+equivalent bending load هو الـ equivalent tensile 
+
+99
+00:08:48,960 --> 00:08:52,520
+load اللي بيعطيني نفس الـ bending effect يعني لو
+
+100
+00:08:52,520 --> 00:08:59,270
+شديت زي هيك وحسبت الـ stress في الحبل الـ FB هو نفس 
+
+101
+00:08:59,270 --> 00:09:04,470
+الـ FB بيعطيه نفس الـ normal stress الناتج عن عملية
+
+102
+00:09:04,470 --> 00:09:07,890
+الـ bending معناته الـ equivalent bending load هو الـ
+
+103
+00:09:07,890 --> 00:09:11,390
+wire rope tension giving the same tensile stress
+
+104
+00:09:11,390 --> 00:09:17,530
+as أو due to bending الـ 
+
+105
+00:09:17,530 --> 00:09:23,990
+FB بيساوي الـ sigma في الـ A metal بيساوي E R في D W A 
+
+106
+00:09:23,990 --> 00:09:28,070
+M على D E R هي الـ modulus of الـ steel للروم مش
+
+107
+00:09:28,070 --> 00:09:32,030
+لسلك في modulus of الـ steel للروم الروم كوا من 
+
+108
+00:09:32,030 --> 00:09:39,030
+مجموع من الجدايا صح؟ وفي لسلك كل جديلة فيها أسلاك
+
+109
+00:09:39,030 --> 00:09:42,410
+الـ E R معناته الـ modulus of الـ steel للروم مش لسلك
+
+110
+00:09:42,410 --> 00:09:46,550
+الـ D W اللي هي الـ wire الـ diameter والـ D قطر
+
+111
+00:09:46,550 --> 00:09:47,710
+البكرة الـ sheave الـ diameter
+
+112
+00:09:55,060 --> 00:09:58,300
+الـ first consideration لاعتبار الأول في اختيار
+
+113
+00:09:58,300 --> 00:10:03,140
+wire rope أن نحسب الـ static load نحسب الـ static
+
+114
+00:10:03,140 --> 00:10:08,460
+load الـ static load يتكون من الـ dead weight الوزن
+
+115
+00:10:08,460 --> 00:10:13,180
+اللي هيشيله الـ dead weight additional load caused
+
+116
+00:10:13,180 --> 00:10:19,220
+by sudden stop or start لما أكبس start بتعمل إيش 
+
+117
+00:10:19,220 --> 00:10:22,580
+load ما أعرف عندي الـ static load زاد الـ load due to
+
+118
+00:10:22,580 --> 00:10:27,270
+sudden stop start والـ shock loads أنا بكون أطلع
+
+119
+00:10:27,270 --> 00:10:32,670
+فيه ممكن يصير عنده shock وعنده achieve bearing 
+
+120
+00:10:32,670 --> 00:10:36,470
+friction هو ماشي على البكرة بيكون فيه عنده احتكاك
+
+121
+00:10:36,470 --> 00:10:40,530
+يعني في الآخر أنا ... أنا بده أقاوم الوزن اللي أنا
+
+122
+00:10:40,530 --> 00:10:47,180
+شايله والـ start أو start stop والـ shock loads و
+
+123
+00:10:47,180 --> 00:10:51,300
+الـ friction بين الحبل والبكرة هذا هو الـ static 
+
+124
+00:10:51,300 --> 00:10:54,960
+load كونه أربع شغلات الـ dead load والـ load due to
+
+125
+00:10:54,960 --> 00:10:59,200
+sudden stop start والـ shock loads والـ sheave
+
+126
+00:10:59,200 --> 00:11:04,760
+bearing friction some 
+
+127
+00:11:04,760 --> 00:11:09,160
+of these loads اللي هي الـ loads المكون للـ static
+
+128
+00:11:09,160 --> 00:11:14,960
+load is compared with the ultimate strength of the 
+
+129
+00:11:14,960 --> 00:11:18,920
+rope بنقارنها في الـ ultimate strength للإيش؟ للحبل
+
+130
+00:11:22,070 --> 00:11:25,110
+الـ ultimate strength must be reduced by strength
+
+131
+00:11:25,110 --> 00:11:28,250
+loss that occurs when the rope passes over a
+
+132
+00:11:28,250 --> 00:11:35,710
+cursor لأن لما الحبل يمر على البكرة البكرة منحنية
+
+133
+00:11:35,710 --> 00:11:43,010
+بيصير الـ loss في الـ tensile strength due to bending
+
+134
+00:11:43,010 --> 00:11:45,210
+شكل سبعة عشر عشرين
+
+135
+00:11:49,150 --> 00:11:52,550
+معطين الـ D capital على الـ D ratio D capital هي قطر 
+
+136
+00:11:52,550 --> 00:12:05,170
+البكرة والـ D small قطر الحبل الآن كل ما قطر البكرة
+
+137
+00:12:05,170 --> 00:12:08,830
+كبر كثير ونفسه لا قطر الحبل الـ bending effect إيش 
+
+138
+00:12:08,830 --> 00:12:15,920
+معلومة بيقل صح؟ معناته الـ loss إيش؟ معلومة بيصير أقل يعني
+
+139
+00:12:15,920 --> 00:12:21,020
+كل ما زادت الـ ratio اللص أشملّه بيقل كل ما كان حجم 
+
+140
+00:12:21,020 --> 00:12:27,820
+البكرة صغير بالمقارنة مع قطر الحبل بيكون الـ loss 
+
+141
+00:12:27,820 --> 00:12:33,180
+أكبر يعني مثلا لو كان عندي الـ D على D ratio مثلا
+
+142
+00:12:33,180 --> 00:12:39,700
+أربعين تقريبا الـ loss بيكون خمسة في المية لو كان
+
+143
+00:12:39,700 --> 00:12:45,530
+عندي الـ D capital على D small ratio عشرة الـ loss
+
+144
+00:12:45,530 --> 00:12:50,850
+تقريبا يكون حوالي أربعة عشر أربع عشرة تلات عشرة لو
+
+145
+00:12:50,850 --> 00:12:55,710
+كانت أربعة الـ D capital على D small ratio الـ loss
+
+146
+00:12:55,710 --> 00:13:00,470
+بيكون خمسة وعشرين في المية لو كان عند D capital
+
+147
+00:13:00,470 --> 00:13:05,550
+على D small ratio اتنين بيكون الـ loss حوالي ستة و
+
+148
+00:13:05,550 --> 00:13:06,910
+ثلاثين وسبعة وثلاثين في المية
+
+149
+00:13:13,240 --> 00:13:18,780
+الـ factor of safety بيساوي F U على F T الـ F U اللي
+
+150
+00:13:18,780 --> 00:13:26,500
+هي الـ ultimate wire load على الـ F T الـ largest 
+
+151
+00:13:26,500 --> 00:13:34,220
+working tension هنشتغلهم بعد شوية الآن تابل سبعة عشر
+
+152
+00:13:34,220 --> 00:13:37,180
+خمسة وعشرين معطيني minimum factors of safety for
+
+153
+00:13:37,180 --> 00:13:40,980
+wire ropes يعني عند الـ track .. في عند الـ track
+
+154
+00:13:40,980 --> 00:13:44,060
+cables أنا ببين معاهم شغلات الـ track cables زي
+
+155
+00:13:44,060 --> 00:13:49,580
+هدول .. هدول الـ track cables بوصل
+
+156
+00:13:49,580 --> 00:13:53,620
+ممكن الـ factor of safety three upon two الـ guy
+
+157
+00:13:53,620 --> 00:13:59,600
+ropes أو الـ guy cable زي هدول مشدات ده العمدان و
+
+158
+00:13:59,600 --> 00:14:07,020
+الجزاية أو الخيام الكبيرة بوصل ثلاثة ونص عندنا الـ
+
+159
+00:14:07,020 --> 00:14:13,280
+hosting .. hosting زي هذا ممكن نصف الخمسة عندنا الـ
+
+160
+00:14:13,280 --> 00:14:19,850
+passenger Elevators اللي هو المصاعد للركاب factor
+
+161
+00:14:19,850 --> 00:14:22,730
+of six بيكون حسب سرعة المصعد، يعني لو كان سرعة
+
+162
+00:14:22,730 --> 00:14:27,390
+المصعد سبعة وستة عشر foot per minute يعني أكام
+
+163
+00:14:27,390 --> 00:14:33,050
+متر في الثانية،
+
+164
+00:14:33,050 --> 00:14:35,510
+السرعة .. السرعة خمسين 
+
+165
+00:14:45,160 --> 00:14:49,120
+يعني حوالي 15 متر في الثانية مظبوط؟ يعني على سرعة
+
+166
+00:14:49,120 --> 00:14:54,720
+خمسين قدم في الدقيقة لأ على ستين على ستين يعني ربع
+
+167
+00:14:54,720 --> 00:15:01,820
+متر في الثانية لو كانت السرعة خمسين قدم في الدقيقة
+
+168
+00:15:01,820 --> 00:15:06,280
+عادة بضعه factor of safety 7.6 كل ما كانت السرعة
+
+169
+00:15:06,280 --> 00:15:10,980
+أكثر المفروض الـ factor of safety أعلى فلو كانت
+
+170
+00:15:10,980 --> 00:15:16,920
+1500 قدم في الدقيقة بتكون وص الفاكتوره ستة عشر
+
+171
+00:15:16,920 --> 00:15:24,180
+point تسعة اه فاكتوره ستة هنا لإنه فيه هامش خاطر في
+
+172
+00:15:24,180 --> 00:15:27,830
+الحسابات ولا بس أمانة على book cap أمان يعني ..
+
+173
+00:15:27,830 --> 00:15:31,870
+أمان طبعا .. ممكن .. ممكن .. لأ هو الـ factor six
+
+174
+00:15:31,870 --> 00:15:38,390
+مش عشان .. عشان أنه أمان وبس .. عشان في طبعا ممكن
+
+175
+00:15:38,390 --> 00:15:41,850
+يكونها مش خطأ وبعدين كلها .. كلها أنت هذه نماذج
+
+176
+00:15:41,850 --> 00:15:46,990
+رياضية لا تمثل واقع مائة في المية، هي بتمثل الواقع
+
+177
+00:15:46,990 --> 00:15:48,830
+بنسبة معينة، مش مائة في المية
+
+178
+00:15:52,340 --> 00:15:56,800
+فأنت طبعا هذا الـ .. يعني زي .. يعني guide لاختيارك 
+
+179
+00:15:56,800 --> 00:15:58,280
+للـ factor of safety
+
+180
+00:16:03,210 --> 00:16:06,390
+once you select a rope based on static strength
+
+181
+00:16:06,390 --> 00:16:11,170
+مجرد ما اخترت حبل بناء على الـ static strength
+
+182
+00:16:11,170 --> 00:16:15,770
+ensure that the wear life of the rope and the
+
+183
+00:16:15,770 --> 00:16:18,930
+sheep meets certain requirements، بنتأكد إنه لأن
+
+184
+00:16:18,930 --> 00:16:22,330
+هو بتعرض لـ fatigue loading و wear، wear اللي هو
+
+185
+00:16:22,330 --> 00:16:26,710
+الهريان نتيجة الاحتكاك بين الحبل والبكرة
+
+186
+00:16:32,420 --> 00:16:38,640
+when a load is bent over a sheave لما عندي .. when
+
+187
+00:16:38,640 --> 00:16:41,520
+a load drop is bent over a sheave يعني عندي حبل
+
+188
+00:16:41,520 --> 00:16:49,120
+عليه وزن عليه تحميل لما ينتنع على يتني على البكرة
+
+189
+00:16:49,120 --> 00:16:51,060
+drop
+
+190
+00:16:53,270 --> 00:16:57,390
+stretches بمغطي فعليا بيصير فيه إيش deformation
+
+191
+00:16:57,390 --> 00:17:02,730
+rubs against the sheath برضه rubbing هذا rubbing
+
+192
+00:17:02,730 --> 00:17:08,330
+يعني ضغط مع  احتكاك and cause wear to both the
+
+193
+00:17:08,330 --> 00:17:11,210
+robe and sheath بيعني الـ stretching و الـ rubbing
+
+194
+00:17:11,210 --> 00:17:15,810
+effect بيعمللي هريان في الحبل وفي البكرة
+
+195
+00:17:18,450 --> 00:17:24,830
+amount of weir كمية الوير أو الهريان تعتمد على
+
+196
+00:17:24,830 --> 00:17:32,740
+الضغط من الحبل على البكرة لإن في البكرة بيكون فيها
+
+197
+00:17:32,740 --> 00:17:37,720
+إيش؟ groove مجاري لإن الحبل بيكون ضغط عليها كل ما
+
+198
+00:17:37,720 --> 00:17:41,280
+أزيد الضغط بأزيد الـ normal force صح؟ بتزيد الـ
+
+199
+00:17:41,280 --> 00:17:45,280
+normal force الاحتكاك بالسواء معامل احتكاك من احنا
+
+200
+00:17:45,280 --> 00:17:50,040
+البداية بالسواء normal force ومعامل احتكاك مظبوط؟
+
+201
+00:17:50,040 --> 00:17:54,820
+فكل ما أزيد الضغط كل .. الاحتكاك بيزيد بيزيد اللي هو
+
+202
+00:17:54,820 --> 00:18:01,130
+كمية الهريان بين الـ rope وبين الـ sheep this
+
+203
+00:18:01,130 --> 00:18:03,590
+pressure is called the bearing pressure هذا الضغط
+
+204
+00:18:03,590 --> 00:18:08,390
+نسميه الـ bearing pressure ويُعطى بالعلاقة اللي هي
+
+205
+00:18:08,390 --> 00:18:13,550
+P سوا اثنين F على D small D capital F اللي هي ten
+
+206
+00:18:13,550 --> 00:18:18,730
+style force on the rope قوة الشد في الحبل الـ D
+
+207
+00:18:18,730 --> 00:18:23,630
+اللي هو قطر الحبل الـ D capital قطر البكرة
+
+208
+00:18:28,580 --> 00:18:31,900
+الـ table سبعة عشر ستة عشرين ما أعطيني الـ maximum اللي
+
+209
+00:18:31,900 --> 00:18:36,000
+هو bearing pressures of ropes on sheaves ما أعطينها
+
+210
+00:18:36,000 --> 00:18:42,000
+هنا إيش الـ bearing pressure المسموح فيه بحسب الـ
+
+211
+00:18:42,000 --> 00:18:47,860
+standard بتاع الحبل وبحسب الـ material بتاعة
+
+212
+00:18:47,860 --> 00:18:50,400
+البكرة يعني لو كان أنا عندي هنا ستة في سبعة يعني
+
+213
+00:18:50,400 --> 00:18:55,640
+ست جدائل كل جديدة فيها سبعة والبكرة كانت مائة و
+
+214
+00:18:55,640 --> 00:18:56,160
+خمسين
+
+215
+00:18:58,880 --> 00:19:04,220
+وكانت خشب الـ .. الـ .. الـ bearing pressure المسموح
+
+216
+00:19:04,220 --> 00:19:10,840
+فيه الأقصى مائة وخمسين .. مائة وخمسين PSI الـ
+
+217
+00:19:10,840 --> 00:19:16,560
+cast iron ثلاثمائة أكثر الـ cast steel خمسمائة و
+
+218
+00:19:16,560 --> 00:19:22,560
+خمسين الـ chilled cast iron ستمائة وخمسين مانجانيزي
+
+219
+00:19:22,560 --> 00:19:30,210
+steel ألف وأربعمائة وسبعين PSI فواضح إنه المواد
+
+220
+00:19:30,210 --> 00:19:33,870
+القاسية بتتحمل bearing pressure أكثر مثلا زي الخشب
+
+221
+00:19:33,870 --> 00:19:42,210
+مثلا طبعا لو طلعنا لو إحنا ستة في تسعة عشر ست
+
+222
+00:19:42,210 --> 00:19:47,090
+جدائل كل جدائل فيها تسعة عشر سلك طبعا الـ bearing
+
+223
+00:19:47,090 --> 00:19:49,610
+pressure مصروف فيه إيش بيزيدي
+
+224
+00:20:03,730 --> 00:20:13,250
+طيب figure seventeen واحد وعشرون احكي
+
+225
+00:20:13,250 --> 00:20:18,030
+إن الـ pressure إيش معطاه P بالساوية من F على D
+
+226
+00:20:18,030 --> 00:20:24,630
+small D capital figure
+
+227
+00:20:24,630 --> 00:20:26,110
+سبعة عشر واحد وعشرون
+
+228
+00:20:32,580 --> 00:20:39,880
+هأعمل plot للـ ratio بين الـ P على Su طبعا هذا الـ
+
+229
+00:20:39,880 --> 00:20:43,460
+ratio إيش معناه مضروبة في ألف يعني لما أحكي واحد
+
+230
+00:20:43,460 --> 00:20:48,640
+هذا مضروبة في ألف يعني هتكون point O O واحد الـ
+
+231
+00:20:48,640 --> 00:20:53,200
+ratio لما أحكي أربعة هذا مضروبة في ألف يعني هتكون
+
+232
+00:20:53,200 --> 00:20:58,120
+الـ ratio point O O أربعة هذا على الـ Y هنا عندي
+
+233
+00:20:58,120 --> 00:21:03,530
+number of pins to failure in millions يعني عندي هين
+
+234
+00:21:03,530 --> 00:21:10,710
+واحد مليون، هين عندي أكام؟ مائة ألف، هين تسعمائة
+
+235
+00:21:10,710 --> 00:21:16,950
+ألف بند، تسعمائة ألف بند وهين معطينا لـ different
+
+236
+00:21:16,950 --> 00:21:20,750
+standards، هين عندي ستة في أربعة وعشرين، يعني الـ
+
+237
+00:21:20,750 --> 00:21:26,470
+strands ستة وأربعة وعشرون سلك في الجديدة الواحدة
+
+238
+00:21:29,340 --> 00:21:33,540
+الستة وارتين الثاني الأولان ستة في أطماش الثالث
+
+239
+00:21:33,540 --> 00:21:41,300
+ستة في تسعة وعشرين الرابع ستة في سبعة وثلاثين واضح
+
+240
+00:21:41,300 --> 00:21:49,320
+كل ما بتزيد الـ life لازم تقلل الـ ratio لازم تقلل
+
+241
+00:21:49,320 --> 00:21:52,100
+الـ ratio بين الـ benign pressure والـ ultimate
+
+242
+00:21:52,100 --> 00:21:54,160
+strength الـ P على SU
+
+243
+00:21:57,240 --> 00:22:05,700
+إذا الـ life قليلة ممكن ترفع الـ ratio P على S U الـ
+
+244
+00:22:05,700 --> 00:22:08,820
+S U هي الـ ultimate strength of the wire not the
+
+245
+00:22:08,820 --> 00:22:13,080
+rope انتبهوا الـ S U هي الـ ultimate strength للسلك
+
+246
+00:22:13,080 --> 00:22:19,660
+مش للحبل للسلك مش للحبل wire
+
+247
+00:22:19,660 --> 00:22:23,960
+rope will eventually fail in fatigue or will
+
+248
+00:22:23,960 --> 00:22:30,520
+الأسلاك ممكن سيلف failure by fatigue failure أو
+
+249
+00:22:30,520 --> 00:22:36,100
+تتاكل by wear the graph show that the rope will
+
+250
+00:22:36,100 --> 00:22:39,160
+have a long life if the ratio P على S U أقل من
+
+251
+00:22:39,160 --> 00:22:43,380
+point one لحظة عند الواحد تقريبا إذا كانت الـ ratio
+
+252
+00:22:43,380 --> 00:22:49,400
+أقل من واحد هأعيش فترة طويلة هأعيش الحبل فترة طويلة
+
+253
+00:22:56,880 --> 00:23:01,200
+الآن إحنا حكينا افترض إننا بدنا نصمم الـ P على SU
+
+254
+00:23:01,200 --> 00:23:07,180
+بالساوية 0.01 يعني أنا عند المعادلة الـ
+
+255
+00:23:07,180 --> 00:23:13,660
+P بالساوية
+
+256
+00:23:13,660 --> 00:23:24,500
+2F على D D لو
+
+257
+00:23:24,500 --> 00:23:25,700
+قسمت على SU
+
+258
+00:23:29,150 --> 00:23:37,590
+ضربت بـ S U بس حكيت إن ده الـ design بتاع P على S U
+
+259
+00:23:37,590 --> 00:23:40,990
+بساوي
+
+260
+00:23:40,990 --> 00:23:50,210
+point O O واحد فحسي عندي S U في point O O واحد
+
+261
+00:23:50,210 --> 00:23:59,330
+بساوي اثنين F على دي دي أدور الطرفين في الفيرين دي
+
+262
+00:23:59,330 --> 00:24:10,750
+الـ SU بيصير الفين F على دي دي اللي أنت معادلة
+
+263
+00:24:10,750 --> 00:24:11,130
+شايفينه
+
+264
+00:24:24,820 --> 00:24:27,840
+الآن dividing both sides of equation سبعة عشر و
+
+265
+00:24:27,840 --> 00:24:33,700
+اثنين وأربعين يعني هذه المعادلة P بالساوية P
+
+266
+00:24:33,700 --> 00:24:44,060
+ساوية اثنين F على D D أضرب طرفين على SU
+
+267
+00:24:52,460 --> 00:25:00,660
+معناته هتكون عند الـ F بيساوي
+
+268
+00:25:00,660 --> 00:25:06,160
+P على SU في
+
+269
+00:25:06,160 --> 00:25:15,080
+D small D capital في SU على 2
+
+270
+00:25:22,140 --> 00:25:25,280
+بيعطيني ما يسمى الـ FF الـ FF اللي هي allowable
+
+271
+00:25:25,280 --> 00:25:29,680
+fatigue tension as the wire is flexed a number of
+
+272
+00:25:29,680 --> 00:25:35,260
+times corresponding to P على SU for a particular
+
+273
+00:25:35,260 --> 00:25:40,060
+rope and life expectancy عند الـ FF اللي هو الـ
+
+274
+00:25:40,060 --> 00:25:42,260
+fatigue tension allowable fatigue tension مسموح
+
+275
+00:25:42,260 --> 00:25:48,780
+بالسلك بحيث السلك يعيش لعدد مرات من الـ .. الـ .. الـ
+
+276
+00:25:48,780 --> 00:25:52,380
+.. الـ .. الـ bending لعدد معين من الـ bending عدد
+
+277
+00:25:52,380 --> 00:25:56,200
+المرات الـ bending اللي هو من خلال إيهاش الـ P على S
+
+278
+00:25:56,200 --> 00:26:01,120
+U P على S U الـ P على S U من شكل سبعة عشر واحد و
+
+279
+00:26:01,120 --> 00:26:06,240
+عشرين يعني إذا أنا بدي أعيش point one الـ P على S U
+
+280
+00:26:06,240 --> 00:26:08,900
+بتكون أكام؟ اثنين ونصف على ألف 
+
+281
+00:26:17,390 --> 00:26:21,810
+الـ fatigue factor of safety نف بيساوي Ff ماينص F
+
+282
+00:26:21,810 --> 00:26:29,870
+بي Ff اللي هي من المعادلة السابقة وال FT 
+
+283
+00:26:34,520 --> 00:26:40,400
+الشد في الحبل في المنطقة اللي بيكون متن فيها الحبل
+
+284
+00:26:40,400 --> 00:26:46,480
+بيكون متن فيها الحبل وال FB الـ rope tension that
+
+285
+00:26:46,480 --> 00:26:50,060
+would induce the same outer wire stress as that
+
+286
+00:26:50,060 --> 00:26:55,800
+given by الـ equation FB بيساوي E R D W A M على D
+
+287
+00:26:55,800 --> 00:27:00,240
+كابتن الـ FB هو الـ equivalent tensile stress الذي
+
+288
+00:27:00,240 --> 00:27:12,260
+يكافئ الـ effect بتاع الـ bending stress designer
+
+289
+00:27:12,260 --> 00:27:15,960
+often has vendor of information عادة المصنعين 
+
+290
+00:27:15,960 --> 00:27:22,730
+بياخدوا المعلومات من المصنعين بتاعة الحبل هذه الـ ..
+
+291
+00:27:22,730 --> 00:27:29,290
+المعلومات اللي بيزودها المصنع بتكون عاملة جدوى للـ
+
+292
+00:27:29,290 --> 00:27:34,130
+ultimate rope tension ميعطينى الـ rope tension الـ
+
+293
+00:27:34,130 --> 00:27:38,550
+ultimate strength للروب مش للسلك and gives no
+
+294
+00:27:38,550 --> 00:27:40,910
+ultimate strength as you information concerning
+
+295
+00:27:40,910 --> 00:27:44,290
+one مابيعطى معلومات على الـ tensile strength
+
+296
+00:27:44,290 --> 00:27:49,850
+للأسلاك المكونة للحبل طبعا
+
+297
+00:27:49,850 --> 00:27:56,890
+في ممكن as a guide نحسب الـ tensile strength للـ
+
+298
+00:27:56,890 --> 00:28:01,850
+individual wires اذا كان عندي الحديد تاع الحجلالـ
+
+299
+00:28:01,850 --> 00:28:06,210
+Plus Steel بيسموه Monitor Steel الـ SU للأسلاك
+
+300
+00:28:06,210 --> 00:28:11,010
+اللي بيكون الحبل يتطرح بين 240 و 280 Kps I إذا كان
+
+301
+00:28:11,010 --> 00:28:17,110
+الـ Plus Steel SU بتطرح بين 210 و 240 Kps I إذا كان 
+
+302
+00:28:17,110 --> 00:28:22,530
+الـ mild plus steel الـ SU بتطرح بين 180 و 210 Kps I
+
+303
+00:28:31,980 --> 00:28:34,440
+لأن طبعا في static factor of safety، الـ static
+
+304
+00:28:34,440 --> 00:28:39,880
+factor of safety ممعطل علاقة فيو ماينص F بي على F
+
+305
+00:28:39,880 --> 00:28:43,260
+تي، F بي حاكي ان الـ rope tension that would induce
+
+306
+00:28:43,260 --> 00:28:46,680
+the same outer wire stress as that given by
+
+307
+00:28:46,680 --> 00:28:49,580
+equation اللي هي سيجمع السواء ار دي في دي 
+
+308
+00:28:49,580 --> 00:28:51,640
+دابوليو على دي كابيتال اللي هي المعادلة هذه
+
+309
+00:29:04,180 --> 00:29:13,440
+فجر سبعة عشر اتنين و عشرين معطيني على 
+
+310
+00:29:13,440 --> 00:29:19,360
+الـ X axis الـ D capital على D small D capital هي
+
+311
+00:29:19,360 --> 00:29:23,760
+إيش الـ chief diameter و D small اللي هي الـ rope
+
+312
+00:29:23,760 --> 00:29:31,760
+diameter and in relative service life يعني اللي
+
+313
+00:29:31,760 --> 00:29:36,200
+اعتبرت life معينة هي الـ .. الـ ultimate مية فعندي
+
+314
+00:29:36,200 --> 00:29:40,520
+كل ما زيدت الـ D cavity على الـ D small ratio كل ما 
+
+315
+00:29:40,520 --> 00:29:47,340
+كانت كتر البكرة كبير كتير بالنسبة للحبل متوقع أعيش
+
+316
+00:29:47,340 --> 00:29:53,680
+أكثر ولا أقل أكثر هعيش، كل ما قطر البكرة صغير
+
+317
+00:29:53,680 --> 00:29:57,540
+بالنسبة له قطر الحبل هتعيش أقل يعني إذا أنا بقترب
+
+318
+00:29:57,540 --> 00:30:01,420
+من الـ zero يعني حوالي بدي أكسره الحبل مش هعيش،
+
+319
+00:30:01,420 --> 00:30:10,110
+مظبوط؟ فبشكل عام كل ما d capital على d small بتقل
+
+320
+00:30:10,110 --> 00:30:18,450
+الـ life بتقل .. الـ life بتقل لحظة الـ life لما أنا
+
+321
+00:30:18,450 --> 00:30:21,710
+.. لما أخذنا d capital على d small حوالي ثمانية و
+
+322
+00:30:21,710 --> 00:30:27,190
+أربعين في المية هي حالة والحالة الثانية ان تكون
+
+323
+00:30:27,190 --> 00:30:30,510
+عند الـ d capital على d small هي تلات و تلاتين في
+
+324
+00:30:30,510 --> 00:30:37,860
+المية الـ life بتنزل للنصلو نزلت من 48 الـ ratio لـ
+
+325
+00:30:37,860 --> 00:30:44,260
+33 الـ life تنزل لـ نص الـ
+
+326
+00:30:44,260 --> 00:30:50,840
+table 17 و 27 بيعطينا some useful properties of
+
+327
+00:30:50,840 --> 00:30:57,760
+6x7 6x19 و 6x37 wire ropes بيعطينا العمود الأول الـ
+
+328
+00:30:57,760 --> 00:31:01,950
+wire rope مثلا يعني ستة في سبعة يعني ست جدائل كل
+
+329
+00:31:01,950 --> 00:31:08,690
+جديلة فيها سبعة أسلاك الـ weight per foot مثلا
+
+330
+00:31:08,690 --> 00:31:11,350
+خلّيني أخذ أتانى ستة في تسعتاش واحد one ستة في دي 
+
+331
+00:31:11,350 --> 00:31:15,490
+square الـ weight per foot including core طبعا الـ
+
+332
+00:31:15,490 --> 00:31:24,490
+weight per foot بدون القلب هي المعيش مع القلب لأن
+
+333
+00:31:24,490 --> 00:31:32,680
+في الحالة الأولى الفراغ هذه يعني أحد شغل تاني انه
+
+334
+00:31:32,680 --> 00:31:36,360
+فشله .. فشله قلب أساسا هو وبالتالي فشيده على
+
+335
+00:31:36,360 --> 00:31:42,100
+المعلومة هذه أو مافيش عند بيانات بس على أغلب هي
+
+336
+00:31:42,100 --> 00:31:47,240
+الاحتمال ايه أش؟ الأولهي ان الـ minimum sheave
+
+337
+00:31:47,240 --> 00:31:48,960
+diameter مثلا ست و ست عشان تعرف الـ minimum sheave
+
+338
+00:31:48,960 --> 00:31:51,860
+diameter بيكون تلاتين دي يعني لو كان قطر الحبل
+
+339
+00:31:51,860 --> 00:31:58,600
+واحد inch الـ minimum sheave diameter تلاتين هكون
+
+340
+00:31:58,600 --> 00:32:04,160
+تلاتين inch فهي عندي better sheave diameter يعني
+
+341
+00:32:04,160 --> 00:32:07,540
+هو الـ minimum تلاتين بس المفضل اكم يكون خمس و
+
+342
+00:32:07,540 --> 00:32:07,880
+أربعين
+
+343
+00:32:17,570 --> 00:32:21,050
+بتلاحظوا كتير في نظام الإحبال، انها بالتزموش في
+
+344
+00:32:21,050 --> 00:32:24,210
+الأقطار هذه، عشانك بتلاحظوا ان الحبل بيفسخ معاهم
+
+345
+00:32:24,210 --> 00:32:30,750
+كتير، بتكون الأقطار الحبل اللي بتحس انه فعلا بيفسخ
+
+346
+00:32:30,750 --> 00:32:36,660
+معاك لان القطر دي capital، اه ففيه مش مشكلة يعني الـ
+
+347
+00:32:36,660 --> 00:32:41,240
+diameter of wires DW بيساوي point O في الحالة point
+
+348
+00:32:41,240 --> 00:32:47,180
+O ستة سبعة دي small الـ AM point أربعة دي square الـ
+
+349
+00:32:47,180 --> 00:32:52,500
+rope young's modulus يعني الـ E للروب مش للـ .. مش
+
+350
+00:32:52,500 --> 00:32:58,740
+.. مش .. مش للأسلاك اتناشر في عشر الستة PSI او
+
+351
+00:32:58,740 --> 00:33:00,320
+اتناشر ميجا PSI
+
+352
+00:33:07,590 --> 00:33:16,550
+الـ main host problem الـ main إيش يعني؟ منجم، المنجم
+
+353
+00:33:16,550 --> 00:33:23,490
+بيستخدم فيه لحبال كتير، فالمنجم عادة بيكون عنده
+
+354
+00:33:23,490 --> 00:33:31,170
+هاي 
+
+355
+00:33:31,170 --> 00:33:31,710
+بكرة
+
+356
+00:33:40,000 --> 00:33:48,160
+و هاي الوزن اللي هشيله الـ wire rope tension due to
+
+357
+00:33:48,160 --> 00:33:53,580
+load and acceleration is given الـ Ft بيساوي الـ W
+
+358
+00:33:53,580 --> 00:34:02,640
+capital على M زائد W small في الف واحد زائد A على
+
+359
+00:34:02,640 --> 00:34:07,860
+G الـ W capital wind at end الـ weight at end of
+
+360
+00:34:07,860 --> 00:34:16,210
+rope الوزن اللي أنا شايله الـ 
+
+361
+00:34:16,210 --> 00:34:21,890
+M عدد لحبال يعني بكره هذه ممكن تكون حبل او ممكن
+
+362
+00:34:21,890 --> 00:34:28,390
+تكون مجموعة من لحبال عدد لحبال الـ
+
+363
+00:34:28,390 --> 00:34:38,690
+W small الـ weight of wirerope لكل foot وزن
+
+364
+00:34:38,690 --> 00:34:42,810
+الحبل لكل 
+
+365
+00:34:42,810 --> 00:34:49,270
+قدم الـ L الـ maximum suspended length of rope الـ
+
+366
+00:34:49,270 --> 00:34:58,890
+ايه
+
+367
+00:34:58,890 --> 00:35:04,380
+الـ acceleration؟ الـ g الـ acceleration of gravity
+
+368
+00:35:04,380 --> 00:35:12,160
+طبعا إذا في acceleration هيزيد إيش الـ load rope
+
+369
+00:35:12,160 --> 00:35:19,640
+tension الماس الكلية جزء من الماس جاي من الوزن اللي
+
+370
+00:35:19,640 --> 00:35:29,430
+أنا شايله جزء من الماس إيش جاي من الحبل نفسه جزء
+
+371
+00:35:29,430 --> 00:35:33,150
+من الـ load جاية due to static load اللي هي الواحد
+
+372
+00:35:33,150 --> 00:35:39,410
+و جزء تاني due to dynamic load نتيجة ايه؟ الـ
+
+373
+00:35:39,410 --> 00:35:40,850
+acceleration اللي هي a على g
+
+374
+00:35:53,220 --> 00:35:57,080
+الـ fatigue tension الـ strength in pounds for a specified
+
+375
+00:35:57,080 --> 00:36:04,420
+life is given by الـ FF بيساوي P على SU في SU في دي
+
+376
+00:36:04,420 --> 00:36:06,780
+capital دي small على اتنين مرة يعني المعادلة بن
+
+377
+00:36:06,780 --> 00:36:12,940
+شويه بس احنا عاملين لمشألة ايش المناجم الـ P على SU
+
+378
+00:36:14,800 --> 00:36:18,180
+الـ PSU ما انا اختارتها بناء على specified life صح
+
+379
+00:36:18,180 --> 00:36:23,700
+من figure 17 و 21 مثلا أنا حاكيها عشان يكون عندي 
+
+380
+00:36:23,700 --> 00:36:33,000
+الـ life مثلا مصممين بند حيكون عند الـ PSU تقريبا
+
+381
+00:36:33,000 --> 00:36:39,120
+point يعني تقريبا 13 من الف 13 على الف او one
+
+382
+00:36:39,120 --> 00:36:40,160
+point three على الف
+
+383
+00:36:46,890 --> 00:36:51,290
+الـ SU اللي هي الـ ultimate strength of wire مش ..
+
+384
+00:36:51,290 --> 00:36:57,830
+مش الـ rope الـ D capital هو الشيف ديميتر الـ D small
+
+385
+00:36:57,830 --> 00:37:05,670
+nominal wire rope size يعني قطر الحبل بالإنش
+
+386
+00:37:05,670 --> 00:37:12,650
+فأنا بحسب الـ fatigue tension strength in pounds بعدين بحث
+
+387
+00:37:12,650 --> 00:37:18,110
+الـ equivalent bending load FB FB بيساوي ERDWAM على
+
+388
+00:37:18,110 --> 00:37:22,330
+D capital الـ ER لـ young's modulus of rope يعني ما
+
+389
+00:37:22,330 --> 00:37:24,990
+بياخد من الـ table سبعة عشر سبعه و عشرين او سبعة عشر
+
+390
+00:37:24,990 --> 00:37:30,730
+سبعة و عشرين هاي سبعة عشر سبعة و عشرين
+
+391
+00:37:30,730 --> 00:37:34,870
+هاي
+
+392
+00:37:34,870 --> 00:37:38,110
+سبعة عشر سبعه و عشرين ماعطيني الـ young's modulus أخر
+
+393
+00:37:38,110 --> 00:37:40,530
+عمود او اربع و عشرين
+
+394
+00:37:46,500 --> 00:37:49,800
+برضه بيعطينا إيش الـ modulus of elasticity هي اربع 
+
+395
+00:37:49,800 --> 00:37:56,100
+عشرين او سبعة عشرين الـ
+
+396
+00:37:56,100 --> 00:38:04,120
+DW
+
+397
+00:38:04,120 --> 00:38:09,780
+الـ diameter of wire Diameter of wire برضه given في
+
+398
+00:38:09,780 --> 00:38:15,940
+table 1724 او 27 الام الـ middle cross section
+
+399
+00:38:15,940 --> 00:38:24,580
+table 1727 الـ D capital achieve diameter بحسب الـ 
+
+400
+00:38:24,580 --> 00:38:29,200
+static factor of safety فهو F U ماينص F B على F T
+
+401
+00:38:29,200 --> 00:38:33,680
+و الـ fatigue factor of safety F F ماينص F B على F
+
+402
+00:38:33,680 --> 00:38:39,090
+T الان أنا عامل excel sheet
+
+403
+00:39:09,710 --> 00:39:14,670
+أول شيء هحط الـ rope designation بحط
+
+404
+00:39:14,670 --> 00:39:17,610
+الـ rope designation ست في ستة عشر، ست في سبعة، ست 
+
+405
+00:39:17,610 --> 00:39:24,050
+في ثمانية، سبعة، ست، ستة عشر وهكذا الست ايش هي؟
+
+406
+00:39:24,050 --> 00:39:31,010
+هتتسعة عشر سلك الان طبعا بروح اتقبل سبعة عشر أربعة و
+
+407
+00:39:31,010 --> 00:39:35,570
+عشرين ها 
+
+408
+00:39:35,570 --> 00:39:41,570
+سبعة عشر أربعة و عشرين معطيني الـ weight per foot الـ
+
+409
+00:39:41,570 --> 00:39:46,310
+minimum sheath diameter الـ standard size D الـ
+
+410
+00:39:46,310 --> 00:39:52,090
+material الـ size of outer wires الـ modulus 
+
+411
+00:39:52,090 --> 00:39:59,510
+والاستثناء الـ strength دي
+
+412
+00:39:59,510 --> 00:40:04,750
+عندي الـ diameter of rope DR مثلا انا بختار واحد
+
+413
+00:40:04,750 --> 00:40:13,160
+انش الـ weight of wire rope per foot table سبعة عشر
+
+414
+00:40:13,160 --> 00:40:21,300
+أربعة و عشرين واحد
+
+415
+00:40:21,300 --> 00:40:30,780
+وان ستة إيش دي square واحد وان ستة دي square عند
+
+416
+00:40:30,780 --> 00:40:33,040
+الـ minimum sheave في ديامتر
+
+417
+00:40:49,840 --> 00:40:54,180
+تلاتين يعني هيكون ان هو طلع هو ستة و عشرين أنا
+
+418
+00:40:54,180 --> 00:40:58,240
+ماخد واحد انش ستة و عشرين في واحد ستة و عشرين
+
+419
+00:40:58,240 --> 00:41:00,640
+لأربعة و تلاتين في واحد اربعة و تلاتين زي الستة و
+
+420
+00:41:00,640 --> 00:41:04,700
+عشرين الـ average بتاعهم إيش تلاتين روح على الـ 
+
+421
+00:41:04,700 --> 00:41:09,340
+table سبعة وعشرين هذه ستة في تسعة عشر معتين ال
+
+422
+00:41:09,340 --> 00:41:11,880
+minimum sheave diameter ليش تلاتي نفس الأشياء
+
+423
+00:41:11,880 --> 00:41:18,320
+بتطلعوا ال minimum sheave diameter عند ال bitter
+
+424
+00:41:18,320 --> 00:41:23,180
+sheave diameter من تابر سبعة عشر سبعة وعشرين حكى ليش
+
+425
+00:41:23,180 --> 00:41:28,700
+خمسة وأربعين ال material اللي هي monitor steel
+
+426
+00:41:28,700 --> 00:41:33,520
+تابر سبعة عشر أربع وعشرين فيه ثلاث أنواع في عند
+
+427
+00:41:33,520 --> 00:41:35,960
+monitor steel و عند plus steel و عند mild steel
+
+428
+00:41:35,960 --> 00:41:39,340
+أنا اخترت مثلاً monitor steel و بينها المطالع اللي
+
+429
+00:41:39,340 --> 00:41:47,920
+هو modulus of elasticity و strength طيب
+
+430
+00:41:51,420 --> 00:41:57,500
+الـ size of outer wires من table 1724.067 ال
+
+431
+00:41:57,500 --> 00:42:01,580
+modulus of the slur rope اللي هو من الجدول 24 اللي
+
+432
+00:42:01,580 --> 00:42:06,140
+هو 12 megapound per square inch ال strength of
+
+433
+00:42:06,140 --> 00:42:11,600
+rope 106 pound per square inch table 1724
+
+434
+00:42:16,700 --> 00:42:20,200
+ال area of metal in standard housing and haulage
+
+435
+00:42:20,200 --> 00:42:34,860
+ال area اللي هي اللي هي ال a m ال a m هي
+
+436
+00:42:34,860 --> 00:42:38,960
+bond أربعة دي square bond أربعة دي square السبعة
+
+437
+00:42:38,960 --> 00:42:42,080
+وعشرين معناته هي دي هتكون سبعة عشر
+
+438
+00:42:48,420 --> 00:42:52,520
+الـ 27 الـ
+
+439
+00:42:52,520 --> 00:42:58,760
+actual shape diameter طبعاً في عند ال beta وفي
+
+440
+00:42:58,760 --> 00:43:05,080
+ال actual يعني هذا دي minimum دي beta في دي
+
+441
+00:43:05,080 --> 00:43:09,920
+capital هو دي ال actual أنا اخترت مثلاً 72 انش 72
+
+442
+00:43:09,920 --> 00:43:11,540
+انش أكمل ملي متر
+
+443
+00:43:18,980 --> 00:43:27,600
+بطلع مية واتنين وثمانين ملي متر على عشرة كم
+
+444
+00:43:27,600 --> 00:43:34,040
+بطلع اثنين
+
+445
+00:43:34,040 --> 00:43:38,660
+وسبعين في خمسة وعشرين point four على أدق ميلي
+
+446
+00:43:38,660 --> 00:43:45,120
+متر على عشرة ميتر يعني هيطلع متر ثانية يعني هيكون
+
+447
+00:43:45,120 --> 00:43:51,680
+sheave كبيرة كثير يعني مش هتكون يعني لو أخذنا
+
+448
+00:43:51,680 --> 00:43:57,220
+البتر خمسة وأربعين في خمسة وعشرين point four يعني
+
+449
+00:43:57,220 --> 00:44:01,540
+بتطلع أكبر من متر عشان إيه أنا بحكيكوا إن معظم ال
+
+450
+00:44:01,540 --> 00:44:05,820
+sheaves اللي بيستخدموها هنا مش مطابق للمواصفات يعني
+
+451
+00:44:05,820 --> 00:44:10,240
+حتى لو أخذت الثلاثين لو أخدت أخدت الثلاثين في خمسة
+
+452
+00:44:10,240 --> 00:44:11,180
+وعشرين point four
+
+453
+00:44:14,010 --> 00:44:17,870
+يعني بتحكي عن ستة وسبعين صنطة، زي ارتفاع الطاولة،
+
+454
+00:44:17,870 --> 00:44:25,770
+القطر البكرة، كبير، هذا ال minimum فواضح أنا بحكي
+
+455
+00:44:25,770 --> 00:44:30,970
+على قطر واحد انش، فواضح الموجود هنا المعظم مش
+
+456
+00:44:30,970 --> 00:44:35,810
+مطابق للمواصفات، فعلى فرض أنه أنا اخترت اثنين و
+
+457
+00:44:35,810 --> 00:44:39,360
+سبعين أو ثلاثين أو خمسة وأربعين بعدين بحسب ال
+
+458
+00:44:39,360 --> 00:44:43,640
+equivalent bending load من المعادلة هذه صار عندي
+
+459
+00:44:43,640 --> 00:44:47,380
+AR معروفة و DR معروف و AL معروف و D كلمة المعروف
+
+460
+00:44:47,380 --> 00:44:52,220
+بحسب ال equivalent bending load بعدين ال weight at
+
+461
+00:44:52,220 --> 00:44:58,840
+end of rope خلينا طبعاً بكمل حسابات بحسب اللي هو ال
+
+462
+00:44:58,840 --> 00:45:04,340
+FB و ال W و ال M و ال L و ال A و ال G و ال FT و ال
+
+463
+00:45:04,340 --> 00:45:08,780
+factor of safety يعني بقى أكمل الحسابات محاضرة جاي
+
+464
+00:45:08,780 --> 00:45:10,580
+بنكمل أعطيكوا العفو 
diff --git a/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/gJkf9bF_pgg_postprocess.srt b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/gJkf9bF_pgg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..829781d60186cc35e12349f0d407bc19d3250783
--- /dev/null
+++ b/PL9fwy3NUQKwa9i_AhTzo8vc87vEWBVzRv/gJkf9bF_pgg_postprocess.srt
@@ -0,0 +1,1856 @@
+1
+00:00:05,280 --> 00:00:07,560
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:07,560 --> 00:00:10,520
+وبركاته هنتكمل في مادة تصييم الألات هنحكي لك عن
+
+3
+00:00:10,520 --> 00:00:16,500
+موضوع جديد اللي هي الحبل wire rope طبعا أولش أن
+
+4
+00:00:16,500 --> 00:00:20,940
+نتعرف على التسميات الحبل
+
+5
+00:00:20,940 --> 00:00:26,100
+بيكون متكون من شكل أساسي من جدائل مجموعة من جدائل
+
+6
+00:00:26,100 --> 00:00:31,940
+وقلب core الجديلة الواحدة يعني هذه الجديلة الجديلة
+
+7
+00:00:31,940 --> 00:00:36,090
+متكونة من مجموعة من إيش؟ من الأسلاكلأن مجموع
+
+8
+00:00:36,090 --> 00:00:46,190
+الجدائل والقلب بيشكل ليهاش ال rope ال wire rope ال
+
+9
+00:00:46,190 --> 00:00:52,270
+wire rope ممكن يجي right hand ordinary بيكون
+
+10
+00:00:52,270 --> 00:00:58,370
+الجدائل بت .. زي البرج بتروح بتجاه اليمينو الأسلاك
+
+11
+00:00:58,370 --> 00:01:02,470
+طلعوا الأسلاك بتروح على الشمال عكس بعض يعني عندكوا
+
+12
+00:01:02,470 --> 00:01:08,910
+ال strand رايحة على الجهة اليمين على اليمين ال
+
+13
+00:01:08,910 --> 00:01:15,910
+strand و الحبل على الشمال هذا إيش right hand
+
+14
+00:01:15,910 --> 00:01:24,270
+ordinary في عندي right hand length ال
+
+15
+00:01:24,270 --> 00:01:29,860
+strand رايح على اليمينوالخيوط او ال .. ال .. ال ..
+
+16
+00:01:29,860 --> 00:01:34,540
+الخيوط نفسها ياش رايحة برضه على اليمين في left
+
+17
+00:01:34,540 --> 00:01:41,060
+hand الجدائق اللي رايحة ياش الشمال و الخيوط رايحة
+
+18
+00:01:41,060 --> 00:01:47,320
+ياش يمين left hand ordinary و في left hand lungs
+
+19
+00:01:47,320 --> 00:01:54,720
+الجدائق اللي رايحة الشمال و الخيوط الشمال في حالة
+
+20
+00:01:54,720 --> 00:01:55,440
+ال ..
+
+21
+00:01:59,420 --> 00:02:02,700
+ال right hand ordinary او left hand ordinary
+
+22
+00:02:02,700 --> 00:02:07,580
+تقريبا الخيوط والاسلاك بتكون موازية لمحور لمحور
+
+23
+00:02:07,580 --> 00:02:13,760
+الرب في حالة ال right hand length او left hand
+
+24
+00:02:13,760 --> 00:02:20,680
+length بتكون الخيوط عاملة زي قطر ميلة بيكون فيها
+
+25
+00:02:20,680 --> 00:02:31,180
+ميل عاملة زاوية مع محور الرب طبعا ال regularليه؟
+
+26
+00:02:31,180 --> 00:02:35,700
+اللي هو سواء كان right hand ordinary او left hand
+
+27
+00:02:35,700 --> 00:02:41,120
+ordinary هو ال accepted standard بغض
+
+28
+00:02:41,120 --> 00:02:45,110
+النظر هو right hand او left hand بيكونإذا ال
+
+29
+00:02:45,110 --> 00:02:50,370
+strand رايح يمين بيكون السلك رايح الشمال أو إذا ال
+
+30
+00:02:50,370 --> 00:02:57,630
+strand رايح الشمال بيكون السلك رايح يمين الأسلاك
+
+31
+00:02:57,630 --> 00:03:01,050
+اللي احنا بكون شايفينها بتكون تقريبا موازية لمحور
+
+32
+00:03:01,050 --> 00:03:07,810
+الحبل طبعا بتفسخش
+
+33
+00:03:07,810 --> 00:03:12,590
+هذا اللي هي kink بتفسخش في الاستخدام يعني بيفتحش
+
+34
+00:03:12,590 --> 00:03:13,550
+معاك الحبل
+
+35
+00:03:16,660 --> 00:03:23,160
+في long lay سواء كان يمين او كان شمال دايما ال
+
+36
+00:03:23,160 --> 00:03:26,260
+strand و الخيوط في نفس الاتجاه اذا كان ال strand
+
+37
+00:03:26,260 --> 00:03:30,040
+رايحين يمين برضه الخيوط بتكون رايحة يمين و اذا كان
+
+38
+00:03:30,040 --> 00:03:35,180
+ال strand رايحة شمال برضه الخيوط الشمال ال outer
+
+39
+00:03:35,180 --> 00:03:41,640
+wires بتكون diagonal يعني عامل زاوية مع محور الحبل
+
+40
+00:03:43,410 --> 00:03:47,970
+احتمالية انها .. انها تفتح او يعني تفسخ معاه اكبر
+
+41
+00:03:47,970 --> 00:03:50,510
+من ال .. ال regular
+
+42
+00:03:56,790 --> 00:04:00,050
+ال standard drops are made with a hem core which
+
+43
+00:04:00,050 --> 00:04:02,950
+supports and lubricates the strands يعني بيكون
+
+44
+00:04:02,950 --> 00:04:08,950
+عندى الطلع عند الهجداء الخارجية و فيه core و hem
+
+45
+00:04:08,950 --> 00:04:12,990
+انا حاطس صورة ال hem اللى هى نبات القنب بيكون شكله
+
+46
+00:04:12,990 --> 00:04:16,090
+طلع كيف شكله طلع الشكل فى النص هنا
+
+47
+00:04:18,960 --> 00:04:23,780
+نفس شكل النباتة طلع النباتة طلع العادى من ال top
+
+48
+00:04:23,780 --> 00:04:30,100
+view هتشوف زي إيش زي نجم كأنه نجم فعشان هيك يسموه
+
+49
+00:04:30,100 --> 00:04:37,580
+hem core hem core ففي عندي ال strands وفي عندي إيش
+
+50
+00:04:37,580 --> 00:04:41,920
+ال core إذا كان الحبل بتعرض للحرارة
+
+51
+00:04:45,080 --> 00:04:53,380
+يعني نستخدم ال .. المركز او ال core حديد او wire
+
+52
+00:04:53,380 --> 00:05:00,120
+strand .. strand center must be used ال
+
+53
+00:05:00,120 --> 00:05:04,020
+wire rope designation هنا هي مقطع .. يعني دي مقطع
+
+54
+00:05:04,020 --> 00:05:05,800
+للحبل
+
+55
+00:05:07,800 --> 00:05:13,640
+من هنا إلى هنا هو ال rope diameter ال rope مكوّم
+
+56
+00:05:13,640 --> 00:05:17,360
+من مجموع من strands هايستراند واحدة اتنين تلاتة
+
+57
+00:05:17,360 --> 00:05:23,960
+اربعة خمسة ستة وال core مثلا عندي واحد على تمانية
+
+58
+00:05:23,960 --> 00:05:28,020
+انش ستة في سبعة haulage rope واحد من انش اللي هو
+
+59
+00:05:28,020 --> 00:05:30,800
+القطر ال rope واحد من انش القطر ال rope اللي هو من
+
+60
+00:05:30,800 --> 00:05:36,090
+هنا إلى هناستة يعني ست جدائل واحدة تنتين تلاتة
+
+61
+00:05:36,090 --> 00:05:40,950
+اربعة خمس ست جدائل سبعة في كل جديلة فيها سبعة سلاك
+
+62
+00:05:40,950 --> 00:05:48,670
+هنعد هنا واحد اتنين تلاتة اربعة خمس ستة سبعة ال
+
+63
+00:05:48,670 --> 00:05:53,710
+area of metal in standard hosting ال AM اللي هي
+
+64
+00:05:53,710 --> 00:05:59,710
+مساحة المقطع بالسوقون تلات تمانية D square جدول
+
+65
+00:05:59,710 --> 00:06:05,100
+سبعتاش اربعة عشرينمعطين اللي هو ال rope standards
+
+66
+00:06:05,100 --> 00:06:10,300
+عند ستة في سبعة .. ستة في سبعة يعني إيش؟ ست جدائل
+
+67
+00:06:10,300 --> 00:06:17,490
+كل جديدة في سبعة سلاكستة في تسعتاش ست جدائل كل
+
+68
+00:06:17,490 --> 00:06:23,110
+جديلة فيها تسعتاشر سلك ستة في سبعة وتلاتين ست
+
+69
+00:06:23,110 --> 00:06:28,190
+جدائل كل جديلة فيها سبعة تلاتين سلك تماني في
+
+70
+00:06:28,190 --> 00:06:32,770
+تسعتاش تماني جدائل كل جديلة تسعتاشر سلك سبعة في
+
+71
+00:06:32,770 --> 00:06:37,550
+سبعة سبع جدائل كل جديلة فيها سبعة سلاك سبعة في
+
+72
+00:06:37,550 --> 00:06:42,810
+تسعة تسعتاشر aircraft طيبمعطيل العمود التاني ال
+
+73
+00:06:42,810 --> 00:06:49,110
+weight per foot ال weight per foot بيساوة واحد بس
+
+74
+00:06:49,110 --> 00:06:54,170
+في الحالة ستة في سبعة واحد و نص دي square minimum
+
+75
+00:06:54,170 --> 00:06:57,230
+sheaf diameter البكرة الأقل القطر منك ممكن يركب
+
+76
+00:06:57,230 --> 00:07:01,790
+عليها اللي هي بيساوة اتنين و اربعين دي اتنين و
+
+77
+00:07:01,790 --> 00:07:07,290
+اربعين قطر الربع ال standard size ال size ستة في
+
+78
+00:07:07,290 --> 00:07:13,930
+سبعة بيجي من ربع انش لواحدو نص انش ال material دي
+
+79
+00:07:13,930 --> 00:07:16,870
+أنواع مختلفة من ال steel تسمية monitor steel, plow
+
+80
+00:07:16,870 --> 00:07:21,570
+steel, mild plow steel ال size of outer wires هذه
+
+81
+00:07:21,570 --> 00:07:25,810
+ال outer wires هي هذه مش القلب بيكون D على تسعة دي
+
+82
+00:07:25,810 --> 00:07:30,530
+اللي هي قطر الروب يعني D على تسعة ال modulus of
+
+83
+00:07:30,530 --> 00:07:35,050
+elasticity اربتاشر ميجا pound per square inch ال
+
+84
+00:07:35,050 --> 00:07:38,450
+strength في ال kilo pound per square inch مية
+
+85
+00:07:41,830 --> 00:07:46,590
+السلف صغير نفسه المجدل يعني، هل التجديد بقلل ال
+
+86
+00:07:46,590 --> 00:07:50,390
+tensile strength له؟ يعني هل المجدل نفس ال tensile
+
+87
+00:07:50,390 --> 00:07:55,090
+strength للمجدل ولا لا؟ لأ التجديد بيخليه شيء أكتر
+
+88
+00:07:55,990 --> 00:08:00,030
+انت .. انت .. اه طبعا اه لإنه بيصير فيه friction
+
+89
+00:08:00,030 --> 00:08:05,030
+بينهم كتير، تخيل أسلوب مش مجدد على عدل، بيشده، صح؟
+
+90
+00:08:05,030 --> 00:08:08,390
+صحيح وبالتالي تقريروا ال .. ال friction minimized،
+
+91
+00:08:08,390 --> 00:08:11,650
+فالتجديد بيعمل friction، ال friction بيساعد
+
+92
+00:08:17,270 --> 00:08:23,350
+الان نخش على اللي هو المصطلحات المعدلة و المعدلات
+
+93
+00:08:23,350 --> 00:08:27,670
+المستخدمة أول شي هنا ال equivalent bending load FB
+
+94
+00:08:27,670 --> 00:08:32,370
+الحبل
+
+95
+00:08:32,370 --> 00:08:36,230
+بيكون على بكرة و هو يلف على البكرة بيكون لبسي على
+
+96
+00:08:36,230 --> 00:08:38,390
+إيه؟ twisting
+
+97
+00:08:40,000 --> 00:08:45,700
+الـ twisting بيعمل أيه؟ normal stress ال
+
+98
+00:08:45,700 --> 00:08:48,960
+equivalent bending load هو ال equivalent tensile
+
+99
+00:08:48,960 --> 00:08:52,520
+load اللي بيعطيني نفس ال bending effect يعني لو
+
+100
+00:08:52,520 --> 00:08:59,270
+شديت زي هيكوحسبت ال stress في الحبل ال FB هو نفس
+
+101
+00:08:59,270 --> 00:09:04,470
+ال FB بيعطيه نفس ال normal stress الناتج عن عملية
+
+102
+00:09:04,470 --> 00:09:07,890
+ال bending معناته ال equivalent bending load هو ال
+
+103
+00:09:07,890 --> 00:09:11,390
+wire rope tension giving the same tensile stress
+
+104
+00:09:11,390 --> 00:09:17,530
+as او due to bending ال
+
+105
+00:09:17,530 --> 00:09:23,990
+FB بستوى ال sigma في ال A metalبيستوى E R في D W A
+
+106
+00:09:23,990 --> 00:09:28,070
+M على D E R هي ال modulus of ال steel للروم مش
+
+107
+00:09:28,070 --> 00:09:32,030
+لسلك في modulus of ال steel للروم الروم كوا من
+
+108
+00:09:32,030 --> 00:09:39,030
+مجموع من الجدايا صح؟ وفي لسلك كل جديدة فيها أسلاك
+
+109
+00:09:39,030 --> 00:09:42,410
+ال E R معناته ال modulus of ال steel للروم مش لسلك
+
+110
+00:09:42,410 --> 00:09:46,550
+ال D W اللي هي ال wire ال diameter و ال D قطر
+
+111
+00:09:46,550 --> 00:09:47,710
+البكرة ال sheave ال diameter
+
+112
+00:09:55,060 --> 00:09:58,300
+الـ first consideration لاعتبار الأول في اختيار
+
+113
+00:09:58,300 --> 00:10:03,140
+wire rope ان نحسب ال static load نحسب ال static
+
+114
+00:10:03,140 --> 00:10:08,460
+load ال static load يتكون من ال dead weight الوزن
+
+115
+00:10:08,460 --> 00:10:13,180
+اللي هيشيله ال dead weight additional load caused
+
+116
+00:10:13,180 --> 00:10:19,220
+by sudden stop or start لما اكبس start بتعمل ايش
+
+117
+00:10:19,220 --> 00:10:22,580
+load ماعرف عندي ال static load زاد ال load due to
+
+118
+00:10:22,580 --> 00:10:27,270
+sudden stop startو ال shock closed انا بكون اطلع
+
+119
+00:10:27,270 --> 00:10:32,670
+فيه ممكن يصير عنده shock و عنده achieve bearing
+
+120
+00:10:32,670 --> 00:10:36,470
+friction هو ماشي على البكرة بكون فيه عنده احتكاك
+
+121
+00:10:36,470 --> 00:10:40,530
+يعني في الآخر انا .. انا بده اقاوم الوزن اللي انا
+
+122
+00:10:40,530 --> 00:10:47,180
+شايله و ال startأو start stop و ال shock loads و
+
+123
+00:10:47,180 --> 00:10:51,300
+ال friction بين الحبل و البكره هذا هو ال static
+
+124
+00:10:51,300 --> 00:10:54,960
+load كونه أربع شغلات ال dead load و ال load due to
+
+125
+00:10:54,960 --> 00:10:59,200
+sudden stop start و ال shock loads و ال sheave
+
+126
+00:10:59,200 --> 00:11:04,760
+bearing friction some
+
+127
+00:11:04,760 --> 00:11:09,160
+of these loads اللي هي ال loads المكون لل static
+
+128
+00:11:09,160 --> 00:11:14,960
+loadis compared with the ultimate strength of the
+
+129
+00:11:14,960 --> 00:11:18,920
+rope بنقارنها في ال ultimate strength للإيش للحبل
+
+130
+00:11:22,070 --> 00:11:25,110
+ال ultimate strength must be reduced by strength
+
+131
+00:11:25,110 --> 00:11:28,250
+loss that occurs when the rope passes over a
+
+132
+00:11:28,250 --> 00:11:35,710
+cursor لان لما الحبل يمر على البكرة البكرة منحنة
+
+133
+00:11:35,710 --> 00:11:43,010
+بصير ال loss في ال tensile strength due to bending
+
+134
+00:11:43,010 --> 00:11:45,210
+شكل سبعتاشر عشرين
+
+135
+00:11:49,150 --> 00:11:52,550
+معطين ال D capital على ال D ratio D capital هي قطر
+
+136
+00:11:52,550 --> 00:12:05,170
+البكرة وال D small قطر الحبل الان كل ما قطر البكرة
+
+137
+00:12:05,170 --> 00:12:08,830
+كبر كتير و نفسه لا قطر الحبل ال bending effect ايش
+
+138
+00:12:08,830 --> 00:12:15,920
+معلوه بقل صح معناته ال loss ايش معلوهبصير أقل يعني
+
+139
+00:12:15,920 --> 00:12:21,020
+كل ما زادت ال ratio اللص أشماله بقل كل ما كان حجم
+
+140
+00:12:21,020 --> 00:12:27,820
+البكرة صغير بالمقارنة مع قطرس الحبل بيكون ال loss
+
+141
+00:12:27,820 --> 00:12:33,180
+أكبر يعني مثلا لو كان عندي ال D على D ratio مثلا
+
+142
+00:12:33,180 --> 00:12:39,700
+اربعين تقريبا ال loss بيكون خمسة في المية لو كان
+
+143
+00:12:39,700 --> 00:12:45,530
+عنديال D capital على D small ratio عشرة اللص
+
+144
+00:12:45,530 --> 00:12:50,850
+تقريبا يكون حوالي اربعة عشرة اربع تاش تلات تاش لو
+
+145
+00:12:50,850 --> 00:12:55,710
+كانت اربعة ال D capital على D small ratio اللص
+
+146
+00:12:55,710 --> 00:13:00,470
+بيكون خمسة و عشرين في المية لو كان عند D capital
+
+147
+00:13:00,470 --> 00:13:05,550
+على D small ratio اتنين بيكون اللص حوالي ستة و
+
+148
+00:13:05,550 --> 00:13:06,910
+تلاتين و سبعة و تلاتين في المية
+
+149
+00:13:13,240 --> 00:13:18,780
+ال factor of safety بيساوي F U على F T ال F U اللي
+
+150
+00:13:18,780 --> 00:13:26,500
+هي ال ultimate wire load على ال F T ال largest
+
+151
+00:13:26,500 --> 00:13:34,220
+working tension هنشتجلهم بعد شويةالان تابل سبعتاشر
+
+152
+00:13:34,220 --> 00:13:37,180
+خمسة و عشرين معطيني minimum factors of safety for
+
+153
+00:13:37,180 --> 00:13:40,980
+wire ropes يعني عند ال track .. في عند ال track
+
+154
+00:13:40,980 --> 00:13:44,060
+cables انا ببين معاهم شغلات ال track cables زي
+
+155
+00:13:44,060 --> 00:13:49,580
+هدول .. هدول ال track cables بوصل
+
+156
+00:13:49,580 --> 00:13:53,620
+ممكن ال factor of safety three upon two ال guy
+
+157
+00:13:53,620 --> 00:13:59,600
+ropes او ال guy cable زي هدولمشدات ده العمدان و
+
+158
+00:13:59,600 --> 00:14:07,020
+الجزاية او الخيام الكبيرة بوصل تلاتة و نص عندنا ال
+
+159
+00:14:07,020 --> 00:14:13,280
+hosting .. hosting زي هذا ممكن نص الخمسة عندنا ال
+
+160
+00:14:13,280 --> 00:14:19,850
+passengerElevators اللي هو المصاعد للركاب factor
+
+161
+00:14:19,850 --> 00:14:22,730
+of six بيكون حسب سرعة المصعد، يعني لو كان سورة
+
+162
+00:14:22,730 --> 00:14:27,390
+المصعد سبعة و ستة و عشرة foot per minute يعني أكام
+
+163
+00:14:27,390 --> 00:14:33,050
+متر في الثانية،
+
+164
+00:14:33,050 --> 00:14:35,510
+السرعة .. السرعة خمسين
+
+165
+00:14:45,160 --> 00:14:49,120
+يعني حوالي 15 متر في الثانية مظلوط؟ يعني على سرعة
+
+166
+00:14:49,120 --> 00:14:54,720
+خمسين قدم في الدقيقة لأ على ستين على ستين يعني ربع
+
+167
+00:14:54,720 --> 00:15:01,820
+متر في الثانية لو كانت السرعة خمسين قدم في الدقيقة
+
+168
+00:15:01,820 --> 00:15:06,280
+عادة بحطه factor of safety 7.6 كل ما كانت السرعة
+
+169
+00:15:06,280 --> 00:15:10,980
+أكتر المفروض ال factor of safety أعلى فلو كانت
+
+170
+00:15:10,980 --> 00:15:16,920
+1500 قدم في الدقيقةبتكون وص الفاكتوره ستة أحداشر
+
+171
+00:15:16,920 --> 00:15:24,180
+point تسعة اه فاكتوره ستة هنا لإنه فيه همش خاطر في
+
+172
+00:15:24,180 --> 00:15:27,830
+الحسابات ولا بس أمانة على book capأمان يعني ..
+
+173
+00:15:27,830 --> 00:15:31,870
+أمان طبعا .. ممكن .. ممكن .. لأ هو ال factor six
+
+174
+00:15:31,870 --> 00:15:38,390
+مش عشان .. عشان أنه أمان و بس .. عشان في طبعا ممكن
+
+175
+00:15:38,390 --> 00:15:41,850
+يكونها مش خطأ و بعدين كلها .. كلها انت هذه نماذج
+
+176
+00:15:41,850 --> 00:15:46,990
+رياضية لا تمثل واقع مية في المية، هي بتمثل الواقع
+
+177
+00:15:46,990 --> 00:15:48,830
+بنسبة معينة، مش مية في المية
+
+178
+00:15:52,340 --> 00:15:56,800
+فانت طبعا هذا ال .. يعني زي .. يعني guide لاختيارك
+
+179
+00:15:56,800 --> 00:15:58,280
+لل factor of safety
+
+180
+00:16:03,210 --> 00:16:06,390
+once you select a rope based on static strength
+
+181
+00:16:06,390 --> 00:16:11,170
+مجرد ما اختارت حبل بناء على ال static strength
+
+182
+00:16:11,170 --> 00:16:15,770
+ensure that the wear life of the rope and the
+
+183
+00:16:15,770 --> 00:16:18,930
+sheep meets certain requirements، بنتأكد انه لإن
+
+184
+00:16:18,930 --> 00:16:22,330
+هو بتعرض ل fatigue loading و wear، wear اللي هو
+
+185
+00:16:22,330 --> 00:16:26,710
+الهريان نتيجة الاحتكاك بين الحبل و البكرة
+
+186
+00:16:32,420 --> 00:16:38,640
+when a load is bent over a sheave لما عندي .. when
+
+187
+00:16:38,640 --> 00:16:41,520
+a load drop is bent over a sheave يعني عندي حبل
+
+188
+00:16:41,520 --> 00:16:49,120
+عليه وزن عليه تحميل لما ينتنع على يتني على البكرة
+
+189
+00:16:49,120 --> 00:16:51,060
+drop
+
+190
+00:16:53,270 --> 00:16:57,390
+stretches بمغطي فعليا بيصير فيه ايش deformation
+
+191
+00:16:57,390 --> 00:17:02,730
+rubs against the sheath برضه rubbing هذا rubbing
+
+192
+00:17:02,730 --> 00:17:08,330
+يعني ضغط معاش مع احتكاك and cause wear to both the
+
+193
+00:17:08,330 --> 00:17:11,210
+robe and sheath بيعني ال stretching و ال rubbing
+
+194
+00:17:11,210 --> 00:17:15,810
+effect بيعمللي هريان في الحبل و في البكرة
+
+195
+00:17:18,450 --> 00:17:24,830
+amount of weir كمية الوير أو الهريان تعتمد على
+
+196
+00:17:24,830 --> 00:17:32,740
+الضغط من الحبل علاهالبكرة لإن في البكرة بيكون فيها
+
+197
+00:17:32,740 --> 00:17:37,720
+ايش؟ groove مجاري لإن الحبل بيكون ضغط عليها كل ما
+
+198
+00:17:37,720 --> 00:17:41,280
+ازود الضغط بزود ال normal force صح؟ بتزيد ال
+
+199
+00:17:41,280 --> 00:17:45,280
+normal force الاحتكاك بالسواء معامل احتكاك من احنا
+
+200
+00:17:45,280 --> 00:17:50,040
+البداية بالسواء normal force و معامل احتكاك مظلوط؟
+
+201
+00:17:50,040 --> 00:17:54,820
+فكل ما ازيد الضغط كل .. الاحتكاك بزيد بزيد اللي هو
+
+202
+00:17:54,820 --> 00:18:01,130
+كمية الهريان بين ال rope و بين ال sheepthis
+
+203
+00:18:01,130 --> 00:18:03,590
+pressure is called the bearing pressure هذا الضغط
+
+204
+00:18:03,590 --> 00:18:08,390
+نسميه ال bearing pressure ويُعطى بالعلاقة اللي هي
+
+205
+00:18:08,390 --> 00:18:13,550
+P سوا اتنين F على D small D capital F اللي هي ten
+
+206
+00:18:13,550 --> 00:18:18,730
+style force on the rope قوت الشد في الحبل ال D
+
+207
+00:18:18,730 --> 00:18:23,630
+اللي هو قطر الحبل ال D capital قطر البكرة
+
+208
+00:18:28,580 --> 00:18:31,900
+ال table سبعتاشر ستة عشرين ماعطيني ال maximum اللي
+
+209
+00:18:31,900 --> 00:18:36,000
+هو bearing pressures of ropes on sheaves ماعطينها
+
+210
+00:18:36,000 --> 00:18:42,000
+هنا إيش ال bearing pressure المسموح فيه بحسب ال
+
+211
+00:18:42,000 --> 00:18:47,860
+standard بتاع الحبل و بحسب ال material بتاعة
+
+212
+00:18:47,860 --> 00:18:50,400
+البكرة يعني لو كان أنا عندي هنا ستة في سبعة يعني
+
+213
+00:18:50,400 --> 00:18:55,640
+ست جدائل كل جديدة فيها سبعة و البكرة كانت مية و
+
+214
+00:18:55,640 --> 00:18:56,160
+خمسين
+
+215
+00:18:58,880 --> 00:19:04,220
+وكانت خشب ال .. ال .. ال bearing pressure المسموح
+
+216
+00:19:04,220 --> 00:19:10,840
+فيه الأقصى مائة و خمسين .. مائة و خمسين PSI ال
+
+217
+00:19:10,840 --> 00:19:16,560
+cast iron تلاتمية اكتر ال cast steel خمسمية و
+
+218
+00:19:16,560 --> 00:19:22,560
+خمسين ال chilled cast iron ستمية و خمسين مانجانيزي
+
+219
+00:19:22,560 --> 00:19:30,210
+steel الف و اربعمائة و سبعين PSIفواضح انه المواد
+
+220
+00:19:30,210 --> 00:19:33,870
+القاسية بتتحمل bearing pressure اكتر مثلا زي الخشب
+
+221
+00:19:33,870 --> 00:19:42,210
+مثلا طبعا لو اطلعنا لو احنا ستة في تسعة عشر ست
+
+222
+00:19:42,210 --> 00:19:47,090
+جدائل كل جدائل فيها تسعة عشر سلك طبعا ال bearing
+
+223
+00:19:47,090 --> 00:19:49,610
+pressure مصروف فيه إيش بزيدي
+
+224
+00:20:03,730 --> 00:20:13,250
+طيب figure seventeen واحد وعشرين احكي
+
+225
+00:20:13,250 --> 00:20:18,030
+ان ال pressure ايش معطاه P بالساوية من F على D
+
+226
+00:20:18,030 --> 00:20:24,630
+small D capital figure
+
+227
+00:20:24,630 --> 00:20:26,110
+سبعتاش واحد وعشرين
+
+228
+00:20:32,580 --> 00:20:39,880
+هعمل plot لل ratio بين ال P على Su طبعا هذا ال
+
+229
+00:20:39,880 --> 00:20:43,460
+ratio إيش معناه مضروة في ألف يعني لما أحكي واحد
+
+230
+00:20:43,460 --> 00:20:48,640
+هذا مضروة في ألف يعني هتكون point O O واحد ال
+
+231
+00:20:48,640 --> 00:20:53,200
+ratio لما أحكي أربعة هذا مضروة في ألف يعني هتكون
+
+232
+00:20:53,200 --> 00:20:58,120
+ال ratio point O O أربعة هذا على ال Y هنا عندي
+
+233
+00:20:58,120 --> 00:21:03,530
+number of pins to failurein millions يعني عندي هين
+
+234
+00:21:03,530 --> 00:21:10,710
+واحد مليون، هين عندي أكام؟ ميت ألف، هين تسعمائة
+
+235
+00:21:10,710 --> 00:21:16,950
+ألف بند، تسعمائة ألف بند و هين معطينا ل different
+
+236
+00:21:16,950 --> 00:21:20,750
+standards، هين عندي ستة في أربع وعشرين، يعني ال
+
+237
+00:21:20,750 --> 00:21:26,470
+strands ستة و أربع و عشرين سلك في الجديدة الواحدة
+
+238
+00:21:29,340 --> 00:21:33,540
+الستة وارتين التاني الأولان ستة في أطماش التالت
+
+239
+00:21:33,540 --> 00:21:41,300
+ستة في تسعة واتاش الرابع ستة في سبعة و تلاتين واضح
+
+240
+00:21:41,300 --> 00:21:49,320
+كل ما بتزيد ال life لازم تقلل ال ratio لازم تقلل
+
+241
+00:21:49,320 --> 00:21:52,100
+ال ratio بين ال benign pressure و ال ultimate
+
+242
+00:21:52,100 --> 00:21:54,160
+strength ال P على SU
+
+243
+00:21:57,240 --> 00:22:05,700
+إذا ال life قليلة ممكن ترفع ال ratio P على S U ال
+
+244
+00:22:05,700 --> 00:22:08,820
+S U هي ال ultimate strength of the wire not the
+
+245
+00:22:08,820 --> 00:22:13,080
+rope انتبهوا ال S U هي ال ultimate strength للسلك
+
+246
+00:22:13,080 --> 00:22:19,660
+مش للحبل لسلك مش للحبل wire
+
+247
+00:22:19,660 --> 00:22:23,960
+rope will eventually fail in fatigue or will
+
+248
+00:22:23,960 --> 00:22:30,520
+الأسلاكممكن سيلف failure by fatigue failure او
+
+249
+00:22:30,520 --> 00:22:36,100
+تتاكل by wear the graph show that the rope will
+
+250
+00:22:36,100 --> 00:22:39,160
+have a long life if the ratio P على S U اقل من
+
+251
+00:22:39,160 --> 00:22:43,380
+point one لحظة عند الواحد تقريبا اذا كانت ال ratio
+
+252
+00:22:43,380 --> 00:22:49,400
+اقل من واحد هعيش فترة طويلة هعيش الحبل فترة طويلة
+
+253
+00:22:56,880 --> 00:23:01,200
+الان احنا حكينا افترض اننا بدنا نصمم ال P على SU
+
+254
+00:23:01,200 --> 00:23:07,180
+بالساوية 0.01 يعني انا عند المعادلة ال
+
+255
+00:23:07,180 --> 00:23:13,660
+P بالساوية
+
+256
+00:23:13,660 --> 00:23:24,500
+2F على D D لو
+
+257
+00:23:24,500 --> 00:23:25,700
+قسمت على SU
+
+258
+00:23:29,150 --> 00:23:37,590
+ضربت ب S U بس حكيت ان ده ال design بتاع P على S U
+
+259
+00:23:37,590 --> 00:23:40,990
+بسوى
+
+260
+00:23:40,990 --> 00:23:50,210
+point O O واحد فحسي عندي S U في point O O واحد
+
+261
+00:23:50,210 --> 00:23:59,330
+بسوا اتنين Fعلى دي دي ادور الطرفين في الف سيرين دي
+
+262
+00:23:59,330 --> 00:24:10,750
+ال SU بيصير الفين F على دي دي اللي انت معادل
+
+263
+00:24:10,750 --> 00:24:11,130
+شايفينه
+
+264
+00:24:24,820 --> 00:24:27,840
+الان dividing both sides of equation سبعتاشر و
+
+265
+00:24:27,840 --> 00:24:33,700
+اتنين و اربعين يعني هذه المعادلة P بالساوية P
+
+266
+00:24:33,700 --> 00:24:44,060
+ساوية اتنين F على D D اكسن طرفيا على SU
+
+267
+00:24:52,460 --> 00:25:00,660
+معناته هتكون عنده ال F بستوى
+
+268
+00:25:00,660 --> 00:25:06,160
+P على SU في
+
+269
+00:25:06,160 --> 00:25:15,080
+D small D capital في SU على 2
+
+270
+00:25:22,140 --> 00:25:25,280
+بيعطيني ما يسمى ال FF ال FF اللي هي allowable
+
+271
+00:25:25,280 --> 00:25:29,680
+fatigue tension as the wire is flexed a number of
+
+272
+00:25:29,680 --> 00:25:35,260
+times corresponding to P على SU for a particular
+
+273
+00:25:35,260 --> 00:25:40,060
+rope and life expectancy عند ال FF اللي هو ال
+
+274
+00:25:40,060 --> 00:25:42,260
+fatigue tension allowable fatigue tension مسموح
+
+275
+00:25:42,260 --> 00:25:48,780
+بالسلكبحيث السلك يعيش لعدد مرات من ال .. ال .. ال
+
+276
+00:25:48,780 --> 00:25:52,380
+.. ال .. ال bending لعدد معين من ال bending عدد
+
+277
+00:25:52,380 --> 00:25:56,200
+المرات ال bending اللي هو من خلال إيهاش ال P على S
+
+278
+00:25:56,200 --> 00:26:01,120
+U P على S U ال P على S U من شكل سبعتاش واحد و
+
+279
+00:26:01,120 --> 00:26:06,240
+عشرين يعني إذا أنا بدي عيش point one ال P على S U
+
+280
+00:26:06,240 --> 00:26:08,900
+بتكون أكام نين و نص على ألف
+
+281
+00:26:17,390 --> 00:26:21,810
+الـ fatigue factor of safety نف بيساوي فف ماينوس ف
+
+282
+00:26:21,810 --> 00:26:29,870
+بي فف اللي هي من المعادلة السابقة وال FT
+
+283
+00:26:34,520 --> 00:26:40,400
+الشد في الحبل في المنطقة اللي بيكون متن فيها الحبل
+
+284
+00:26:40,400 --> 00:26:46,480
+بيكون متن فيها الحبل وال FB ال rope tension that
+
+285
+00:26:46,480 --> 00:26:50,060
+would induce the same outer wire stress as that
+
+286
+00:26:50,060 --> 00:26:55,800
+given byالـ equation FB بيستوى E R D W A M على D
+
+287
+00:26:55,800 --> 00:27:00,240
+كابتن ال FB هو ال equivalent tensile stress الذي
+
+288
+00:27:00,240 --> 00:27:12,260
+يكافئ ال effect بتاع ال bending stress designer
+
+289
+00:27:12,260 --> 00:27:15,960
+often has vendor of information عادتها المصنعين
+
+290
+00:27:15,960 --> 00:27:22,730
+بياخدوا المعلومات من المصنعين بتاعة الحبل هذهال ..
+
+291
+00:27:22,730 --> 00:27:29,290
+المعلومات اللى بيزودها المصنع بتكون عاملة جدوى لل
+
+292
+00:27:29,290 --> 00:27:34,130
+ultimate rope tension ميعطنى ال rope tension ال
+
+293
+00:27:34,130 --> 00:27:38,550
+ultimate strength للروب مش للسلك and gives no
+
+294
+00:27:38,550 --> 00:27:40,910
+ultimate strength as you information concerning
+
+295
+00:27:40,910 --> 00:27:44,290
+one مابيعطى معلومات على ال tensile strength
+
+296
+00:27:44,290 --> 00:27:49,850
+للأسلاك المكونة للحبل طبعا
+
+297
+00:27:49,850 --> 00:27:56,890
+فى ممكنas a guide نحسب ال tensile strength لل
+
+298
+00:27:56,890 --> 00:28:01,850
+individual wires اذا كان عندى الحديد تاع الحجلالـ
+
+299
+00:28:01,850 --> 00:28:06,210
+Plus Steel بيسموه Monitor Steel الـ SU للأسلاك
+
+300
+00:28:06,210 --> 00:28:11,010
+اللي بيكون الحب يتطرح بين 240 و 280 Kps I إذا كان
+
+301
+00:28:11,010 --> 00:28:17,110
+ال Plus Steel SU بتترح بين 210 و 240 Kps I إذا كان
+
+302
+00:28:17,110 --> 00:28:22,530
+ال mild plus steel ال SU تترح بين 180 و 210 Kps I
+
+303
+00:28:31,980 --> 00:28:34,440
+لأن طبعا في static factor of safety، ال static
+
+304
+00:28:34,440 --> 00:28:39,880
+factor of safety ممعطل علاقة فيو minus ف بي على ف
+
+305
+00:28:39,880 --> 00:28:43,260
+تي، ف بي حاكي ان ال rope tension that would induce
+
+306
+00:28:43,260 --> 00:28:46,680
+the same outer wire stress as that given by
+
+307
+00:28:46,680 --> 00:28:49,580
+equation اللي هي سيجمع السواء ا ار دي في دي
+
+308
+00:28:49,580 --> 00:28:51,640
+دابوليو على دي كابيتال اللي هي المعادلة هذه
+
+309
+00:29:04,180 --> 00:29:13,440
+فجر سبعتاش اتنين و عشرين معطيني على
+
+310
+00:29:13,440 --> 00:29:19,360
+ال X axis ال D capital على D small D capital هي
+
+311
+00:29:19,360 --> 00:29:23,760
+إيش ال chief diameter و D small اللي هي ال rope
+
+312
+00:29:23,760 --> 00:29:31,760
+diameter and in relative service life يعنياللي
+
+313
+00:29:31,760 --> 00:29:36,200
+اعتبرت life معينة هي ال .. ال ultimate مية فعندي
+
+314
+00:29:36,200 --> 00:29:40,520
+كل ما زيدت ال D cavity على ال D small ratio كل ما
+
+315
+00:29:40,520 --> 00:29:47,340
+كانت كتر البكر كبير كتير بالنسبة للحبل متوقع أعيش
+
+316
+00:29:47,340 --> 00:29:53,680
+أكتر ولا أقلاكتر هعيش، كل ما قطر البكرة صغير
+
+317
+00:29:53,680 --> 00:29:57,540
+بالنسبة له قطر الحبل هتعيش اقل يعني اذا انا بقترب
+
+318
+00:29:57,540 --> 00:30:01,420
+من ال zero يعني حوالي بدي اكسره الحبل مش هعيش،
+
+319
+00:30:01,420 --> 00:30:10,110
+مظبوط؟ فبشكل عامكل ما d capital على d small بتقل
+
+320
+00:30:10,110 --> 00:30:18,450
+ال life بتقل .. ال life بتقل لحظة ال life لما انا
+
+321
+00:30:18,450 --> 00:30:21,710
+.. لما أخدنا d capital على d small حوالي تمانية و
+
+322
+00:30:21,710 --> 00:30:27,190
+اربعين في المية هي حالة و الحالة التانية ان تكون
+
+323
+00:30:27,190 --> 00:30:30,510
+عند ال d capital على d small هي تلات و تلاتين في
+
+324
+00:30:30,510 --> 00:30:37,860
+المية ال life بتنزل للنصلو نزلت من 48 ال ratio ل
+
+325
+00:30:37,860 --> 00:30:44,260
+33 ال life تنزل ل نص ال
+
+326
+00:30:44,260 --> 00:30:50,840
+table 17 و 27 بيعطينا some useful properties of
+
+327
+00:30:50,840 --> 00:30:57,760
+6x7 6x19 و 6x37 wire ropes بيعطينا العمود الأول ال
+
+328
+00:30:57,760 --> 00:31:01,950
+wire ropeمثلا يعني ستة في سبعة يعني ست جدائل كل
+
+329
+00:31:01,950 --> 00:31:08,690
+جديلة فيها سبعة أسلاك ال weight per foot مثلا
+
+330
+00:31:08,690 --> 00:31:11,350
+خلّيني أخد أتانى ستة في تسعتاش واحد one ستة في دي
+
+331
+00:31:11,350 --> 00:31:15,490
+square ال weight per foot including core طبعا ال
+
+332
+00:31:15,490 --> 00:31:24,490
+weight per foot بدون القلب هي المعيش مع القلب لأن
+
+333
+00:31:24,490 --> 00:31:32,680
+في الحالة الأولىالفراغ هده يعني أحد شغل تاني انه
+
+334
+00:31:32,680 --> 00:31:36,360
+فشله .. فشله قلب أساسا هو وبالتالي فشيده على
+
+335
+00:31:36,360 --> 00:31:42,100
+المعلومة هدى أو مافيش عند بيانات بس على أغلب هي
+
+336
+00:31:42,100 --> 00:31:47,240
+الاحتمال إيه أش؟ الأولهي ان ال minimum sheave
+
+337
+00:31:47,240 --> 00:31:48,960
+diameter مثلا ست و ست عشان تعرف ال minimum sheave
+
+338
+00:31:48,960 --> 00:31:51,860
+diameter بيكون تلاتين دي يعني لو كان قطر الحبل
+
+339
+00:31:51,860 --> 00:31:58,600
+واحد inch ال minimum sheave diameter تلاتين هكون
+
+340
+00:31:58,600 --> 00:32:04,160
+تلاتين inch فهي عندي better sheave diameter يعني
+
+341
+00:32:04,160 --> 00:32:07,540
+هو ال minimum تلاتين بس المفضل أكم يكون خمس و
+
+342
+00:32:07,540 --> 00:32:07,880
+أربعين
+
+343
+00:32:17,570 --> 00:32:21,050
+بتلاحظوا كتير في نظام الإحبال، انها بالتزموش في
+
+344
+00:32:21,050 --> 00:32:24,210
+الأقطار هذه، عشانك بتلاحظوا ان الحب بيفسخ معاهم
+
+345
+00:32:24,210 --> 00:32:30,750
+كتير، بتكون الأقطار الحب اللي بتحس انه فعلا بيفسخ
+
+346
+00:32:30,750 --> 00:32:36,660
+معاك لان القطر دي capital، اه ففيه مش مشكلةيعني ال
+
+347
+00:32:36,660 --> 00:32:41,240
+diameter of wires DW بيسوى point O في الحالة point
+
+348
+00:32:41,240 --> 00:32:47,180
+O ستة سبعة دي small ال AM point أربعة دي square ال
+
+349
+00:32:47,180 --> 00:32:52,500
+rope young's modulus يعني ال E للروب مش لل .. مش
+
+350
+00:32:52,500 --> 00:32:58,740
+.. مش .. مش لل أسلاك اتناش في عشر الستة PSI او
+
+351
+00:32:58,740 --> 00:33:00,320
+اتناشر ميجا PSI
+
+352
+00:33:07,590 --> 00:33:16,550
+المين host problem المين إيش يعني؟ منجم، المنجم
+
+353
+00:33:16,550 --> 00:33:23,490
+بيستخدم فيه لحبال كتير، فالمنجم عادة بيكون عنده
+
+354
+00:33:23,490 --> 00:33:31,170
+هاي
+
+355
+00:33:31,170 --> 00:33:31,710
+بكرة
+
+356
+00:33:40,000 --> 00:33:48,160
+و هاي الوزن اللي هشيله ال wire rope tension due to
+
+357
+00:33:48,160 --> 00:33:53,580
+load and acceleration is given ال Ft بالساوية ال W
+
+358
+00:33:53,580 --> 00:34:02,640
+capital على M زائد W small في الف واحد زائد A على
+
+359
+00:34:02,640 --> 00:34:07,860
+G ال W capital wind at end ال weight at end of
+
+360
+00:34:07,860 --> 00:34:16,210
+ropeالوزن اللي أنا شايله ال
+
+361
+00:34:16,210 --> 00:34:21,890
+M عدد لحبال يعني بكره هذه ممكن تكون حبل او ممكن
+
+362
+00:34:21,890 --> 00:34:28,390
+تكون مجموعة من لحبال عدد لحبال ال
+
+363
+00:34:28,390 --> 00:34:38,690
+W small ال weight of wirerope لكل foot وزن
+
+364
+00:34:38,690 --> 00:34:42,810
+الحبل لكل
+
+365
+00:34:42,810 --> 00:34:49,270
+قدم ال L ال maximum suspended length of rope ال
+
+366
+00:34:49,270 --> 00:34:58,890
+ايه
+
+367
+00:34:58,890 --> 00:35:04,380
+ال acceleration؟ال جيه ال acceleration of gravity
+
+368
+00:35:04,380 --> 00:35:12,160
+طبعا إذا في acceleration هزيد إيش ال load روب
+
+369
+00:35:12,160 --> 00:35:19,640
+تنشن الماس الكلية جزء من الماس جاي من الوزن اللي
+
+370
+00:35:19,640 --> 00:35:29,430
+أنا أشايله جزء من الماس إيش جاي من الحبل نفسهجزء
+
+371
+00:35:29,430 --> 00:35:33,150
+من ال load جاية due to static load اللي هي الواحد
+
+372
+00:35:33,150 --> 00:35:39,410
+و جزء تاني due to dynamic load نتيجة ايه؟ ال
+
+373
+00:35:39,410 --> 00:35:40,850
+acceleration اللي هي a على g
+
+374
+00:35:53,220 --> 00:35:57,080
+الفتيك تنصي ال strength in pounds for a specified
+
+375
+00:35:57,080 --> 00:36:04,420
+life is given by ال FF بستوى P على SU في SU في دي
+
+376
+00:36:04,420 --> 00:36:06,780
+capital دي small على اتنين مرة يعني المعادلة بن
+
+377
+00:36:06,780 --> 00:36:12,940
+شويه بس احنا عاملين لمشألة ايش المناجم ال P على SU
+
+378
+00:36:14,800 --> 00:36:18,180
+ال PSU ما انا اختارتها بناء على specified life صح
+
+379
+00:36:18,180 --> 00:36:23,700
+من figure 17 و 21 مثلا انا حاكيها عشان يكون عندى
+
+380
+00:36:23,700 --> 00:36:33,000
+ال life مثلا مصمليون بند حيكون عند ال PSU تقريبا
+
+381
+00:36:33,000 --> 00:36:39,120
+point يعني تقريبا 13 من الف 13 على الف او one
+
+382
+00:36:39,120 --> 00:36:40,160
+point three على الف
+
+383
+00:36:46,890 --> 00:36:51,290
+ال SU اللي هي ال ultimate strength of wire مش ..
+
+384
+00:36:51,290 --> 00:36:57,830
+مش ال rope ال D capital هو الشيف ديميتر ال D small
+
+385
+00:36:57,830 --> 00:37:05,670
+nominal wire rope size يعني قطر الحبل بالإنش
+
+386
+00:37:05,670 --> 00:37:12,650
+فانا بحسب الفتيك تنصير strength in poundsبعدين بحث
+
+387
+00:37:12,650 --> 00:37:18,110
+ال equivalent bending load FB FB بستوي ERDWAM على
+
+388
+00:37:18,110 --> 00:37:22,330
+D capital ال ER ل young's modulus of rope يعني ما
+
+389
+00:37:22,330 --> 00:37:24,990
+بياخد من ال table سبعتاش سابعة و عشرين او سبعتاش
+
+390
+00:37:24,990 --> 00:37:30,730
+سابعة و عشرين هاي سبعتاش سابعة و عشرين
+
+391
+00:37:30,730 --> 00:37:34,870
+هاي
+
+392
+00:37:34,870 --> 00:37:38,110
+سبعتاش سابعة و عشرين ماعطين ال young's modulus اخر
+
+393
+00:37:38,110 --> 00:37:40,530
+عمود او اربع و عشرين
+
+394
+00:37:46,500 --> 00:37:49,800
+برضه بيعطينا ايش ال modulus of elasticity هي اربع
+
+395
+00:37:49,800 --> 00:37:56,100
+عشرين او سبع عشرين ال
+
+396
+00:37:56,100 --> 00:38:04,120
+DW
+
+397
+00:38:04,120 --> 00:38:09,780
+ال diameter of wireDiameter of wire برضه given فى
+
+398
+00:38:09,780 --> 00:38:15,940
+table 1724 او 27 الام ال middle cross section
+
+399
+00:38:15,940 --> 00:38:24,580
+table 1727 ال D capital achieve diameter بحسم ال
+
+400
+00:38:24,580 --> 00:38:29,200
+static factor of safety فهو F U minus F B على F T
+
+401
+00:38:29,200 --> 00:38:33,680
+و ال fatigue factor of safety F F minus F B على F
+
+402
+00:38:33,680 --> 00:38:39,090
+Tالان انا عامل excel sheet
+
+403
+00:39:09,710 --> 00:39:14,670
+أولش هحط ال rope designation بحط
+
+404
+00:39:14,670 --> 00:39:17,610
+ال rope designation ست في سنتاشر، ست في سبعة، ست
+
+405
+00:39:17,610 --> 00:39:24,050
+في تمانية، سبعة، ست، سنتاشر و هكذا الست ايش هي؟
+
+406
+00:39:24,050 --> 00:39:31,010
+هتتسعتاشر سلك الآن طبعا بروح اتقبل سبعتاشر أربعة و
+
+407
+00:39:31,010 --> 00:39:35,570
+عشرين ها
+
+408
+00:39:35,570 --> 00:39:41,570
+سبعتاشر أربعة و عشرينمعطني ال weight per foot ال
+
+409
+00:39:41,570 --> 00:39:46,310
+minimum sheath diameter ال standard size D ال
+
+410
+00:39:46,310 --> 00:39:52,090
+material ال size of outer wires ال modulus
+
+411
+00:39:52,090 --> 00:39:59,510
+والاستثناء ال strength دي
+
+412
+00:39:59,510 --> 00:40:04,750
+عندى ال diameter of rope DR مثلا انا بختار واحد
+
+413
+00:40:04,750 --> 00:40:13,160
+انشالـ weight of wire rope per foot table سبعتاش
+
+414
+00:40:13,160 --> 00:40:21,300
+أربعة و عشرين واحد
+
+415
+00:40:21,300 --> 00:40:30,780
+وان ستة ايش دي square واحد وان ستة دي square عند
+
+416
+00:40:30,780 --> 00:40:33,040
+ال minimum sheave في ديامتر
+
+417
+00:40:49,840 --> 00:40:54,180
+تلاتين يعني هيكون ان هو طلع هو ستة و عشرين انا
+
+418
+00:40:54,180 --> 00:40:58,240
+ماخد واحد انش ستة و عشرين في واحد ستة و عشرين
+
+419
+00:40:58,240 --> 00:41:00,640
+لأربعة و تلاتين في واحد اربعة و تلاتين زي الستة و
+
+420
+00:41:00,640 --> 00:41:04,700
+عشرين ال average بتاعهم ايش تلاتين روح على ال
+
+421
+00:41:04,700 --> 00:41:09,340
+table سبعة و عشرينهذه ستة في تسعة عشر معتين ال
+
+422
+00:41:09,340 --> 00:41:11,880
+minimum sheave diameter ليش تلاتي نفس الاشياء
+
+423
+00:41:11,880 --> 00:41:18,320
+بتطلعوا ال minimum sheave diameter عند ال bitter
+
+424
+00:41:18,320 --> 00:41:23,180
+sheave diameter من تابر سبعتاش سبعة عشرين حكى ليش
+
+425
+00:41:23,180 --> 00:41:28,700
+خمسة واربعين ال material اللي هي monitor steel
+
+426
+00:41:28,700 --> 00:41:33,520
+تابر سبعتاش أربع عشرينفيه ثلاث أنواع في عند
+
+427
+00:41:33,520 --> 00:41:35,960
+monitor steel و عند plus steel و عند mild steel
+
+428
+00:41:35,960 --> 00:41:39,340
+انا اختارت مثلا monitor steel و بينها المطالع اللي
+
+429
+00:41:39,340 --> 00:41:47,920
+هو modulus of elasticity و strength طيب
+
+430
+00:41:51,420 --> 00:41:57,500
+الـ size of outer wires من table 1724.067 ال
+
+431
+00:41:57,500 --> 00:42:01,580
+modulus of the slur rope اللي هو من الجدول 24 اللي
+
+432
+00:42:01,580 --> 00:42:06,140
+هو 12 megapound per square inch ال strength of
+
+433
+00:42:06,140 --> 00:42:11,600
+rope 106 pound per square inch table 1724
+
+434
+00:42:16,700 --> 00:42:20,200
+ال area of metal in standard housing and haulage
+
+435
+00:42:20,200 --> 00:42:34,860
+ال area اللي هي اللي هي ال a m ال a m هي
+
+436
+00:42:34,860 --> 00:42:38,960
+bond أربعة دي square bond أربعة دي square السبعة
+
+437
+00:42:38,960 --> 00:42:42,080
+عشرين معناته هي دي هتكون سبعتاش
+
+438
+00:42:48,420 --> 00:42:52,520
+الـ 27 الـ
+
+439
+00:42:52,520 --> 00:42:58,760
+actual shape diameter طبعا في عند ال beta وفي
+
+440
+00:42:58,760 --> 00:43:05,080
+ال actual يعني هذا دي minimum دي beta في دي
+
+441
+00:43:05,080 --> 00:43:09,920
+capital هو دي ال actual انا اختار مثلا 72 انش 72
+
+442
+00:43:09,920 --> 00:43:11,540
+انش اكمل ملي متر
+
+443
+00:43:18,980 --> 00:43:27,600
+بطلع مية و اتنين و ثمانين ميلي متر على عشرة كم
+
+444
+00:43:27,600 --> 00:43:34,040
+بطلع اتنين
+
+445
+00:43:34,040 --> 00:43:38,660
+و سبعين في خمسة و عشرين point four على ادق ميلي
+
+446
+00:43:38,660 --> 00:43:45,120
+متر على عشرةميتر يعني هيطلع متر تانية يعني هيكون
+
+447
+00:43:45,120 --> 00:43:51,680
+sheave كبيرة كتير يعني مش هتكون يعني لو أخدنا
+
+448
+00:43:51,680 --> 00:43:57,220
+البتر خمسة واربعين في خمسة وعشرين point four يعني
+
+449
+00:43:57,220 --> 00:44:01,540
+بتطلع أكبر من متر عشان ايه انا بحكيكوا ان معظم ال
+
+450
+00:44:01,540 --> 00:44:05,820
+sheaves اللي بيستخدموها هنا مش مطابق المعصفات يعني
+
+451
+00:44:05,820 --> 00:44:10,240
+حتى لو أخدت التلاتين لو أخدت أخدت التلاتين في خمسة
+
+452
+00:44:10,240 --> 00:44:11,180
+وعشرين point four
+
+453
+00:44:14,010 --> 00:44:17,870
+يعني بتحكي عن ستة و سبعين صنطة، زي ارتفاع الطاولة،
+
+454
+00:44:17,870 --> 00:44:25,770
+القطر البكرة، كبير، هذا ال minimum فواضح أنا بحكي
+
+455
+00:44:25,770 --> 00:44:30,970
+على قطر واحد انش، فواضح الموجود هنا المعظم مش
+
+456
+00:44:30,970 --> 00:44:35,810
+مطابق للمواصفات، فعلى فرض انه انا اختارت اتنين و
+
+457
+00:44:35,810 --> 00:44:39,360
+سبعين او تلاتين او خمس و اربعينبعدين بحسب ال
+
+458
+00:44:39,360 --> 00:44:43,640
+equivalent bending load من المعادلة هذه صار عندي
+
+459
+00:44:43,640 --> 00:44:47,380
+AR معروفة و DR معروف و AL معروف و D كلمة المعروف
+
+460
+00:44:47,380 --> 00:44:52,220
+بحسب ال equivalent bending loadبعدين ال weight at
+
+461
+00:44:52,220 --> 00:44:58,840
+end of rope خلينا طبعا بكمل حسابات بحسب اللي هو ال
+
+462
+00:44:58,840 --> 00:45:04,340
+FB و ال W و ال M و ال L و ال A و ال G و ال FT و ال
+
+463
+00:45:04,340 --> 00:45:08,780
+factor of safety يعني بقى أكمل الحسابات محاضرة جاي
+
+464
+00:45:08,780 --> 00:45:10,580
+بنكمل اعطيكوا العفو
+
diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/MdYlKYcQfdg.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/MdYlKYcQfdg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fe41112b89801eda4671842679fc6f6071d05d11
--- /dev/null
+++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/MdYlKYcQfdg.srt
@@ -0,0 +1,4011 @@
+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 بـ chapter الـ 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
+الـ delta H للـ reaction فاتكلمنا عن الـ calorimetry
+
+5
+00:00:37,840 --> 00:00:42,360
+واتكلمنا في البداية عن الـ coffee cup
+
+6
+00:00:51,110 --> 00:00:54,990
+النوع الثاني 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 الـ Constant Volume
+
+9
+00:01:02,530 --> 00:01:06,930
+Calorimeter بس في البداية بدي 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
+أساسي لتعيين الـ Delta H للـ combustion reactions
+
+12
+00:01:17,170 --> 00:01:21,190
+للـ combustion reactions فالـ reactants عادة اللي هي
+
+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 في وعاء بنسميه
+
+15
+00:01:32,150 --> 00:01:38,920
+Bomb كويس هنشوفه بعد شوية فهدول والله يعني إذا كان
+
+16
+00:01:38,920 --> 00:01:43,900
+.. كان في عندي شرارة كهربية في هذا الوعاء
+
+17
+00:01:43,900 --> 00:01:48,700
+فهيتفاعلوا هيتفاعلوا فهيحترق الـ hydrocarbon بالـ
+
+18
+00:01:48,700 --> 00:01:53,570
+oxygen ويكون CO2 وميه عادة ونتيجة التفاعل طبعا راح
+
+19
+00:01:53,570 --> 00:01:57,990
+يطلع حرارة الـ bomb هيكون محط بكمية من الماء الماء
+
+20
+00:01:57,990 --> 00:02:02,030
+هذا راح يسخن والـ bomb نفسه راح تسخن فممكن بمعلومية
+
+21
+00:02:02,030 --> 00:02:07,550
+الـ heat capacity للـ calorie meter ممكن نعرف والله
+
+22
+00:02:07,550 --> 00:02:12,910
+جداش كمية الـ heat evolved وبالتالي بنقدر نعين الـ
+
+23
+00:02:12,910 --> 00:02:18,590
+heat flow فنشوف هذه
+
+24
+00:02:18,590 --> 00:02:19,870
+هي الـ bomb
+
+25
+00:02:22,090 --> 00:02:27,190
+و واضح أن فيها وعاء صغير جوا بنحط فيه الـ reactants
+
+26
+00:02:27,190 --> 00:02:32,730
+سواء كان liquid أو solid و بيتم ضخ كمية من الـ
+
+27
+00:02:32,730 --> 00:02:38,910
+oxygen علشان تكون كافية لتفاعل يتم بشكل تام في
+
+28
+00:02:38,910 --> 00:02:42,190
+عندي سلكين كهرباء هان بيقدروا يعطوا فيه زي
+
+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 الـ fuel والـ oxidant وهان في عندي زي ما
+
+31
+00:02:50,310 --> 00:02:55,150
+احنا شايفين ميّه وهذا شيء عازل فبنقدر نقول احنا
+
+32
+00:02:55,150 --> 00:02:58,390
+بشكل عام وهذا طبعا الـ tiller عشان يخلي الحرارة
+
+33
+00:02:58,390 --> 00:03:03,830
+داخل الميّه كلها تجربة تاخد نفس الحرارة وطبعا الـ
+
+34
+00:03:03,830 --> 00:03:08,390
+thermometer عشان يجس لفرق درجات الحرارة واضح
+
+35
+00:03:08,390 --> 00:03:12,170
+بالنسبة لي أنه إذا 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 الناشئة عن الـ reaction هتسخن الـ bomb و
+
+38
+00:03:23,810 --> 00:03:28,010
+هتسخن أيضا الميه فعادة بتكون يعني ممكن اقول انا أن
+
+39
+00:03:28,010 --> 00:03:35,890
+الـ Q للـ reaction هتساوي الـ Q أو minus Q لأن طبعا
+
+40
+00:03:35,890 --> 00:03:41,050
+هي هتعطي minus Q للـ bomb زائد الـ calorie meter اللي
+
+41
+00:03:41,050 --> 00:03:44,710
+هو عبارة عن الميه اللي في الـ calorie meter في 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 الـ calorie meter معين والـ bomb تبعته معروفة
+
+44
+00:03:50,790 --> 00:03:53,390
+فبتكون الـ heat capacity للـ calorie meter ككل
+
+45
+00:03:53,390 --> 00:03:56,630
+معروفة اللي هي عبارة عن الـ bomb زائد الـ ايه؟ الميه
+
+46
+00:03:56,630 --> 00:03:59,390
+فممكن نلاقي بعض الأسئلة بتقولنا والله الـ heat
+
+47
+00:03:59,390 --> 00:04:02,670
+capacity للميه هل جد أو هل جد في عيننا ميه؟ والـ
+
+48
+00:04:02,670 --> 00:04:05,890
+bomb الـ heat capacity لها يعني قيمة معينة وفي بعض
+
+49
+00:04:05,890 --> 00:04:08,550
+الأسئلة الأخرى ممكن تقولنا والله الـ heat capacity
+
+50
+00:04:08,550 --> 00:04:12,450
+للـ calorie meter ككل هل جد فتعني يعني أن والله الـ
+
+51
+00:04:12,450 --> 00:04:18,500
+bomb زائد الميّه اللي موجودة فهذه الفكرة العامة
+
+52
+00:04:18,500 --> 00:04:26,200
+للجهاز فكرة كتير بسيطة وفكرة كتير سهلة وأفضل
+
+53
+00:04:26,200 --> 00:04:29,460
+طريقة في الحقيقة لتعيين الـ heat flow لمثل هذه الـ
+
+54
+00:04:29,460 --> 00:04:34,700
+reactions هي أن نعملها بـ bomb calorimeter الكلولة الـ
+
+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 فـ C للكالوريمتر اللي هي عبارة عن الـ heat
+
+58
+00:04:46,860 --> 00:04:53,920
+capacity للميّه في كتلة الميّه هذا الـ heat .. هذا
+
+59
+00:04:53,920 --> 00:04:58,600
+عبارة عن الـ C للميّه وكمان الـ bomb الـ heat
+
+60
+00:04:58,600 --> 00:05:01,920
+capacity للـ bomb والـ C للـ .. والـ heat capacity
+
+61
+00:05:01,920 --> 00:05:06,920
+للـ .. CS للـ bomb مضروبة في الـ mass للـ bomb بأي
+
+62
+00:05:06,920 --> 00:05:10,360
+material معمولة يعني والـ delta T طبعا للاتنين
+
+63
+00:05:10,360 --> 00:05:13,420
+بتعطين الـ C .. للـ .. الـ C calorie meter ككل الـ
+
+64
+00:05:13,420 --> 00:05:15,980
+heat capacity للـ calorie meter ككل في الـ delta T
+
+65
+00:05:15,980 --> 00:05:20,670
+اللي هو الـ change in temperature فخلينا نطلع على
+
+66
+00:05:20,670 --> 00:05:28,370
+مثال كتير بسيط كيف نعين الـ Q للـ 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
+الـ methylhydrazine the temperature of the
+
+74
+00:06:00,260 --> 00:06:03,660
+calorimeter increases from خمسة و عشرين لتسعة و
+
+75
+00:06:03,660 --> 00:06:08,160
+ثلاثين point five degrees c حلو بيقول in a
+
+76
+00:06:08,160 --> 00:06:12,130
+separate experiment في تجربة منفصلة تماما The 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 الـ heat capacity
+
+79
+00:06:18,810 --> 00:06:24,410
+للـ calorimeter 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؟ للـ one mole بقول حلو كتير
+
+83
+00:06:36,670 --> 00:06:39,270
+خلينا نشوف في الأول الـ heat evolved من الأربعة
+
+84
+00:06:39,270 --> 00:06:43,270
+جرام وبعدين بنحوّل الأربعة جرام لمول فبقول أنا الـ
+
+85
+00:06:43,270 --> 00:06:48,210
+Q للـ reaction بتساوي minus Q للميّه زائد Q للـ bomb
+
+86
+00:06:48,210 --> 00:06:53,110
+بالتان تان مع بعض لـ Q ككل بتساوي minus Q بتساوي
+
+87
+00:06:53,110 --> 00:06:56,730
+minus Q للكالوريمتر يعني minus C للكالوريمتر في الـ
+
+88
+00:06:56,730 --> 00:07:00,380
+Delta T الـ 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 للـ reaction بتساوي سالب الـ C للكالوريمتر
+
+95
+00:07:21,520 --> 00:07:29,540
+معايا 7.794 في الـ Delta T اللي هي هي 7.794 في 39.5
+
+96
+00:07:29,540 --> 00:07:35,260
+minus 25 تعطيني سالب 113 kilojoule بس هذا الـ .. أو
+
+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 لـ مول بدي احوّل الاربعة جرام لمول عدد
+
+99
+00:07:43,560 --> 00:07:46,940
+مولاتل مثل الهيدرزين جال والله الـ mass على الـ
+
+100
+00:07:46,940 --> 00:07:49,920
+formula weight بتعطينا عدد المولات وهي عدد المولات
+
+101
+00:07:49,920 --> 00:07:55,020
+إذا والله انا بدي الـ Q للـ reaction للمول إذا بدي
+
+102
+00:07:55,020 --> 00:07:58,520
+أجسم هذه على عدد المولات فبتعطيني one point three
+
+103
+00:07:58,520 --> 00:08:02,120
+فعشرة أقصى تلاتة one point three فعشرة أقصى تلاتة
+
+104
+00:08:02,120 --> 00:08:07,150
+يعني حوالي ألف وتلاتمية kilo joule per mole الـ
+
+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 H At
+
+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 أن بجيسي الـ delta E هان مش الـ
+
+112
+00:08:36,680 --> 00:08:40,450
+delta H وصحيح أنا بجيث الـ Delta E at constant
+
+113
+00:08:40,450 --> 00:08:44,030
+volume لكن يا بنات احنا ايش قلنا؟ قلنا أن الفرق
+
+114
+00:08:44,030 --> 00:08:47,490
+بين الـ Delta E و Delta H قليل جدا هو الـ PDV اللي
+
+115
+00:08:47,490 --> 00:08:51,370
+هو الـ Expansion Work وهذا قليل جدا يعني لو اجينا
+
+116
+00:08:51,370 --> 00:08:55,310
+شوفنا في الواقع جداش الفرق بين الـ 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 عندي
+
+119
+00:09:04,550 --> 00:09:08,260
+لو بدي اقول أن أنا اللي حسبته هذا Delta H نسبة خطأ
+
+120
+00:09:08,260 --> 00:09:12,500
+point one percent تقريبا ولا إشي فممكن نعبر عن الـ
+
+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 الـ delta H للـ reaction
+
+123
+00:09:19,680 --> 00:09:23,480
+على أي حال في كتب الـ thermodynamics والجداو اللي
+
+124
+00:09:23,480 --> 00:09:28,020
+احنا بنحطها الـ delta H مصححة يعني عند الـ delta E
+
+125
+00:09:28,020 --> 00:09:31,780
+بنحصل على الـ delta E at constant volume وبنصححها
+
+126
+00:09:31,780 --> 00:09:36,630
+عشان نحصل على الـ delta H at constant pressure لكن
+
+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 الـ bomb calorimeter كـ
+
+131
+00:09:53,970 --> 00:09:59,670
+heat of reaction ممكن نعتبرها delta H تمام فهنا
+
+132
+00:09:59,670 --> 00:10:03,450
+بنقول delta H للـ 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 الـ lactic acid وحرجناه في
+
+137
+00:10:25,270 --> 00:10:30,930
+bomb calorimeter هو heat capacity is 4.812
+
+138
+00:10:30,930 --> 00:10:33,450
+kilojoules per degree c برضه الـ heat capacity
+
+139
+00:10:33,450 --> 00:10:39,630
+للـ bomb كله معروفة يعني الميه زائد الـ bomb كله معروف
+
+140
+00:10:39,630 --> 00:10:45,290
+قيمته كله 4.812 kilojoules per degree c بيقول الـ 
+
+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 gram حلو 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 للكالوريمتر 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 للكالوريمتر الـ 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 للكالوريمتر بتساوي
+
+152
+00:11:34,990 --> 00:11:39,670
+minus C للكالوريمتر في ال Delta T طيب بدنا نعوض عن
+
+153
+00:11:39,670 --> 00:11:44,230
+الـ C للكالوريمتر و الـ 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 أو هذه مقدار الطاقة أو ال heat evolved من
+
+158
+00:12:02,210 --> 00:12:08,730
+أيه؟ من 0.5865 gram طب أنا بدي من ال gram كله بدي
+
+159
+00:12:08,730 --> 00:12:13,880
+أقسم عليها كويس فبتطلع
+
+160
+00:12:13,880 --> 00:12:17,360
+عندي سالب fifteen point one eight kilo joule per
+
+161
+00:12:17,360 --> 00:12:25,040
+gram لو بدي أجيب ال heat evolved أو ال heat of
+
+162
+00:12:25,040 --> 00:12:28,780
+combustion يعني per mole معناته بدي أحول هذه
+
+163
+00:12:28,780 --> 00:12:36,660
+القيمة لمول وبعدين بدي أقول والله بدي أقسم على
+
+164
+00:12:36,660 --> 00:12:42,710
+عدد المولات فبيطلع عندي الـ 8.902 KJ اللي هي point
+
+165
+00:12:42,710 --> 00:12:45,930
+eight five بتنقسمها على عدد المولات 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
+المولات بتطلع عندي سالب one point three seven فعشرة
+
+168
+00:12:50,810 --> 00:12:54,170
+أقصى تلاتة لإنه عندي عدد المولات 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 C الكالوريمتر يحتوي على
+
+175
+00:13:32,240 --> 00:13:35,720
+1200 جرام ماء ماء ماء ماء ماء ماء 
+
+176
+00:13:35,720 --> 00:13:37,320
+ماء ماء ماء ماء ماء ماء ماء ماء
+
+177
+00:13:37,320 --> 00:13:40,640
+ماء ماء ماء ماء ماء ماء ماء ماء
+
+178
+00:13:40,640 --> 00:13:46,240
+ماءيعني أعطاني ال heat capacity للبومب و
+
+179
+00:13:46,240 --> 00:13:51,100
+أعطاني ال mass للمية من ال mass للمية و من ال
+
+180
+00:13:51,100 --> 00:13:55,580
+specific heat للمية اللي هي معروفة 4.18 كويس و ال
+
+181
+00:13:55,580 --> 00:14:00,760
+delta T بقدر أجيب ال Q للمية إذا كان أنا حبيت طب
+
+182
+00:14:00,760 --> 00:14:05,500
+على أي حال هي عندي التفاعل أنا 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 للمية زائد ال heat capacity لل pump فال q
+
+186
+00:14:17,360 --> 00:14:23,810
+لل water هي عبارة عن ال heat capacity لل water في
+
+187
+00:14:23,810 --> 00:14:26,870
+ال mass لل water في ال delta T مفهومة شفناها
+
+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 هنا مضروبة في ال
+
+193
+00:14:46,930 --> 00:14:51,930
+delta T بتعطيني ال Q لل bomb إذا الـ Q للـ water
+
+194
+00:14:51,930 --> 00:14:55,290
+زائد الـ Q للبوم مجموعهم حلو كتير الـ Q لل
+
+195
+00:14:55,290 --> 00:15:00,520
+reaction minus Q للcalorimeter أنا 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 إكسوثيرميك ال Q اللي هو بالسالب 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 ثمانية وأربعين تقريبا كيلوجول ثمانية
+
+200
+00:15:16,840 --> 00:15:20,240
+وأربعين كيلوجول يعني التفاعل طارد للحرارة بيعطي
+
+201
+00:15:20,240 --> 00:15:22,240
+ثمانية 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 و أنا عندي هاي النتيجة ال
+
+204
+00:15:33,350 --> 00:15:38,550
+one gram إن الحرارة تفاعت من 25 ل 33.2 من 10 طيب
+
+205
+00:15:38,550 --> 00:15:44,090
+الآن يبقى صار بإمكاني أن أحسب ال delta H باستخدام
+
+206
+00:15:44,810 --> 00:15:49,250
+إما coffee cup calorimeter أو 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
+أو 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 أفضل 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 كويسة
+
+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 إنه لل combustion
+
+217
+00:16:31,650 --> 00:16:36,290
+reactions أفضل كالوريمتر أو أفضل طريقة لحساب ال
+
+218
+00:16:36,290 --> 00:16:40,700
+delta H لها هي استخدام ال bomb calorimeter للـ
+
+219
+00:16:40,700 --> 00:16:44,220
+Combustion Reactions تحديدا الآن دعوني أطلع 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
+جدا ومفيد جدا لنا في الكيمياء لأنه بيقول كلام
+
+222
+00:16:57,300 --> 00:17:02,780
+كتير بسيط بيقول احنا مش مضطرين إنه نحسب ال heat of
+
+223
+00:17:02,780 --> 00:17:06,410
+reaction تجريبياً ممكن نحسب ال heat of reaction
+
+224
+00:17:06,410 --> 00:17:09,990
+أيه؟ نظريا من ال heat of reactions ل other
+
+225
+00:17:09,990 --> 00:17:14,130
+reactions ليش هذا الكلام؟ 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 بدأت أروح لل final state إذا أنا بحاجة
+
+229
+00:17:24,910 --> 00:17:28,570
+لكمية من الطاقة أو أنا بحاجة لأني أخد كمية من
+
+230
+00:17:28,570 --> 00:17:32,650
+الطاقة أما أن التفاعل يحرر أو أما التفاعل يستلزم
+
+231
+00:17:32,650 --> 00:17:37,390
+يأخذ بغض النظر عن ال route بغض النظر عن ايه عن
+
+232
+00:17:37,390 --> 00:17:44,190
+الطريق حولت مثلا عندي أنا حولت بدي أروح من A ل D
+
+233
+00:17:44,190 --> 00:17:50,390
+قال والله أنا A ل D بدي أجيب ال hot delta H فقول
+
+234
+00:17:50,390 --> 00:17:55,850
+حلو كتير خليني أدور على أي route أي طريق أي طريق
+
+235
+00:17:55,850 --> 00:18:00,790
+بوصلني من A ل D فمثلا قلت والله اه من A بدي أروح ل
+
+236
+00:18:00,790 --> 00:18:05,770
+B هذا معروف الـ delta H تبعته في ال literature،
+
+237
+00:18:05,770 --> 00:18:10,310
+معروفة في الجداول، معروف جدا، طب من B ل C، معروف
+
+238
+00:18:10,310 --> 00:18:15,230
+جدا، delta H تبعته، طب من C ل D، معروف جدا، أنا
+
+239
+00:18:15,230 --> 00:18:20,030
+وصلت، إذا أنا روحت من A ل E ل D، معنى الكلام ال
+
+240
+00:18:20,030 --> 00:18:22,390
+delta H، أنا ساوي ال delta H هذه، زائد هذه، زائد
+
+241
+00:18:22,390 --> 00:18:26,190
+هذه ليه؟ لأن هذا state function، لا يمكن أن يكون
+
+242
+00:18:26,190 --> 00:18:30,970
+أكثر أو أقل، عارفين لو كان أكثر أو أقل، يعني ممكن
+
+243
+00:18:30,970 --> 00:18:35,170
+نقول إن الكون بيختل، ليه؟ لأنه أنا بأخذ 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 أصلت له، إذا بخليه يتحول لتاني و يعطينا طاقة
+
+246
+00:18:44,630 --> 00:18:49,380
+أكثر بقي بوصل له طاقة أقل و بأخذ منه طاقة أكثر ..
+
+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 perpetual 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
+ما بينفعش .. ما بينفع .. ال thermodynamics ليه؟ لأن
+
+251
+00:19:01,260 --> 00:19:05,740
+ال energy is conserved الإنيرجي هي مفهوم القانون
+
+252
+00:19:05,740 --> 00:19:10,260
+الأول للـ Thermodynamics ف أنا لأ ما بقدرش مدام
+
+253
+00:19:10,260 --> 00:19:13,900
+وصلت من A ل D بروت معين إذا الـ Delta H هتساوى
+
+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 إذا بعرف قد ايه
+
+257
+00:19:27,780 --> 00:19:32,660
+A ل D هذا كلام السيد Hess مش بس هيك في أحيان .. في
+
+258
+00:19:32,660 --> 00:19:36,600
+بعض الأحيان بعض التفاعلات ما بقدرش أعملها مباشرة
+
+259
+00:19:36,600 --> 00:19:41,760
+ما بقدرش أعملها لأسباب مختلفة هنشوف بعضها يعني لأسباب
+
+260
+00:19:41,760 --> 00:19:45,860
+مختلفة طيب هذه إيش بدي أعمل فيها ما 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 route ممكن هذا بدل ما إن 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 أكثر من هيك أو أقل من هيك يعني عرض الخطوات مش
+
+265
+00:20:07,190 --> 00:20:11,290
+مهم المهم في النهاية مدام بدأت من a ال initial
+
+266
+00:20:11,290 --> 00:20:18,430
+ووصلت ل bd ال final يبقى 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
+Hess'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 reaction equals 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 ايه؟ إلى النواتج فأخدني
+
+277
+00:21:16,030 --> 00:21:21,820
+هذه عدة خطوات قلت Delta H للتفاعل الخطوة الواحدة
+
+278
+00:21:21,820 --> 00:21:26,600
+الـ Over all reaction بيساوي 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
+ΔH ΔH ΔH ΔH ΔH ΔH ΔH
+
+282
+00:21:44,440 --> 00:21:52,050
+ΔH ΔH معادلة تبين فيها ال states
+
+283
+00:21:52,050 --> 00:21:57,130
+طبعًا التفاهم يكون موزون بداية وبعدين ال states هل
+
+284
+00:21:57,130 --> 00:22:03,180
+هي كل مادة gas أو liquid أو solid لازم تكون مبينة
+
+285
+00:22:03,180 --> 00:22:07,720
+لأن هذا كله مهم وبعدين كمان الـ ΔH بنسمي هذه الـ
+
+286
+00:22:07,720 --> 00:22:13,340
+Thermochemical equation فعلشان نشتغل احنا ونطبق
+
+287
+00:22:13,340 --> 00:22:18,900
+قانون السيد Hess بشكل جيد وبطريقة مختصرة كثير 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 أنا بدي أحسبه الـ ΔH طبعًا بتكون من 
+
+290
+00:22:27,380 --> 00:22:35,220
+متفاعلات ونواتج بمسك واحدة واحدة وبشوف إيش أو كيف
+
+291
+00:22:35,220 --> 00:22:39,480
+بدي أحصل عليها من التفاعلات أو ال steps المختلفة
+
+292
+00:22:39,480 --> 00:22:43,280
+اللي برضه موجودة معايا وموجودة في ال literature لكن
+
+293
+00:22:43,280 --> 00:22:47,040
+إذا كان في عندي مكون من المكونات بتكرر في أكثر من
+
+294
+00:22:47,040 --> 00:22:53,160
+معادلة بسيبه بتعاملش معاها بسيبه للاخر هفرجيكم 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 وأشوف إيش مكوناتها
+
+297
+00:23:00,880 --> 00:23:05,140
+وبدي أطلع إذا كان في عندي شغلات بتتكرر في
+
+298
+00:23:05,140 --> 00:23:08,300
+المعادلات الأخرى بدي أقول لأ هذا والله ما 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 المعطاة معايا نشوف 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 يشوف أي معادلة بده يحصل منها على 
+
+305
+00:23:31,880 --> 00:23:35,020
+إما واحد من المتفاعلات وإما واحد من النواتج بما
+
+306
+00:23:35,020 --> 00:23:39,640
+في ذلك عدد المولات يعني إذا كان في المتفاعلات
+
+307
+00:23:39,640 --> 00:23:43,040
+اثنين مول وأنا عندي في ال target equation واحد مول
+
+308
+00:23:43,040 --> 00:23:46,730
+بده يضرب ال target equation في اثنين إذا كان الـ
+
+309
+00:23:46,730 --> 00:23:51,170
+target equation المادة هذه في النواتج بينما الـ
+
+310
+00:23:51,170 --> 00:23:54,150
+target equation في النواتج المادة بينما المعطاة
+
+311
+00:23:54,150 --> 00:23:57,030
+في المتفاعلات في أحد المعادلات بدي أجيب 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
+الكلام بعد ما نعمل ونطلع كل المواد اللي موجودة في
+
+314
+00:24:07,350 --> 00:24:10,630
+المعادلة target equation بنكون جاهزين إنه نجمع
+
+315
+00:24:10,630 --> 00:24:13,950
+المعادلات ونطلع قيمة الـ ΔH 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 وماء can be thought
+
+318
+00:24:25,030 --> 00:24:32,530
+of as occurring in one step هي CH4 زائد 2 O2 هذا هو
+
+319
+00:24:33,150 --> 00:24:36,990
+بيعطينا CO2 زائد اثنين ماء ΔH تبعته مجهولة مش
+
+320
+00:24:36,990 --> 00:24:45,570
+عارفينها طيب أو ممكن نفكر فيه زي هيك or in two
+
+321
+00:24:45,570 --> 00:24:50,670
+steps ال CH4 زائد 2 O2 بتعطينا CO2 زائد 2
+
+322
+00:24:50,670 --> 00:24:54,330
+H2O جاهز هنقلب إيه عشان اللي عندي أنا 2 H2O
+
+323
+00:24:54,330 --> 00:24:58,040
+liquid إذا هذه المعادلة مش هي هذه وكمان معادلة
+
+324
+00:24:58,040 --> 00:25:02,920
+2 H2O gas تتحول لـ 2 H2O liquid الـ delta H
+
+325
+00:25:02,920 --> 00:25:06,260
+لها سالب ثمانية وثمانين كيلوجول مثلًا يعني هي
+
+326
+00:25:06,260 --> 00:25:10,660
+عندي هذول المعادلتين هذول المعادلتين كيف بدي أحصل
+
+327
+00:25:10,660 --> 00:25:15,760
+منهم على هذه المعادلة بقول CH4 هذه CH4 حلو يبقى
+
+328
+00:25:15,760 --> 00:25:22,000
+هذه خلصنا منه خلصنا منه باجي لـ مثلًا ال H2O
+
+329
+00:25:23,910 --> 00:25:28,810
+هذا البرنامج موجود زي ما هي H2O gas بتحول لـ 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 الـ 2 H2O راحت مع الـ 2 H2O نتيجة
+
+332
+00:25:44,850 --> 00:25:48,670
+الجمع إيش أعطتني؟ الـ Target Equation بالظبط إذا
+
+333
+00:25:48,670 --> 00:25:52,810
+الـ Delta H لهذا التفاعل هذه مخبيها تساوي الـ Delta
+
+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
+أعطاني زي هذا هي هذه يعني هفرجيكم في عندي slide
+
+336
+00:26:02,850 --> 00:26:07,040
+اللي أقول لكم لما جمعنا المعادلتين أعطتني المعادلة الـ
+
+337
+00:26:07,040 --> 00:26:09,720
+target إذا الـ delta H للمعادلة الـ target الـ
+
+338
+00:26:09,720 --> 00:26:12,460
+over all reaction يساوي مجموعة delta H values
+
+339
+00:26:12,460 --> 00:26:16,240
+للمعادلتين فانا عندي سالب ثمانية وثمانين زائد سالب
+
+340
+00:26:16,240 --> 00:26:18,660
+ثمانية وتسعين يبقى سالب ثمانية وتسعين kilo
+
+341
+00:26:18,660 --> 00:26:27,440
+joules هذا يعني consequence لـ 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 CH4 2 O2 إلى CH4 2 O2
+
+345
+00:26:43,940 --> 00:26:46,080
+إلى CH4 2 O2 إلى CH4 2 O2 إلى CH4 2 O2 إلى CH4 2 O2
+
+346
+00:26:46,080 --> 00:26:48,180
+إلى CH4 2 O2 إلى CH4 2 O2 إلى CH4 2 O2 إلى CH4 2 O2
+
+347
+00:26:48,180 --> 00:26:50,940
+إلى CH4 2 O2 إلى CH4 2 O2 إلى CH4 2 O2 إلى CH4 2 O2
+
+348
+00:26:50,940 --> 00:26:51,520
+إلى CH4 2 O2 إلى CH4 2 O2 إلى CH4 2 O2 إلى CH4 2 O2
+
+349
+00:26:51,520 --> 00:26:51,540
+إلى CH4 2 O2 إلى CH4 2 O2 إلى CH4 2 O2 إلى CH4 2 O2
+
+350
+00:26:51,540 --> 00:26:54,560
+إلى CH4 2 O2 إلى CH4 2 O2 إلى CH4 2 O2 إلى CH4 2 O2
+
+351
+00:26:54,560 --> 00:27:00,610
+إلى CH4 2 O2 إلى CH4 بعدين 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 ثمانية وثمانين كيلوجول بما أنه أنا روحت من المتفاعلات،
+
+354
+00:27:09,730 --> 00:27:13,170
+لـ نواتج، يعني هذا كله أيها السهم الأزرق، إذا
+
+355
+00:27:13,170 --> 00:27:16,370
+السهم الأزرق 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 حبينا، يعني حاجة ثالثة مثلًا وأقول
+
+358
+00:27:23,940 --> 00:27:28,520
+ثلاثة أو أربعة أو خمسة ما فيش عندي مشكلة ممكن أروح
+
+359
+00:27:28,520 --> 00:27:34,760
+لهنا وأعود أرجع ثاني مثلًا يعني المهم في النهاية
+
+360
+00:27:34,760 --> 00:27:39,440
+في النهاية لابد إلا أن أحصل 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 أدور على route ثاني هذا another route انتبهوا
+
+363
+00:27:49,000 --> 00:27:53,980
+شوية تبه 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 ΔH2 اللي هي CO زائد .. بتعطينا
+
+367
+00:28:08,100 --> 00:28:14,800
+CO زائد 2 H2O Liquid زائد نصف O2 Gas هذا تفاعل من
+
+368
+00:28:14,800 --> 00:28:20,620
+hand ل hand هيو CH4 زائد 2 O2 بيعطيني CO gas 2 H2O
+
+369
+00:28:20,620 --> 00:28:25,260
+liquid نصف O2 gas الـ ΔH سالب 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 gas زائد
+
+372
+00:28:33,580 --> 00:28:38,800
+2 H2O liquid زائد نصف O2 بيعطيني CO2 زائد 2 H2O liquid
+
+373
+00:28:38,800 --> 00:28:45,070
+ΔH سالب 283 KJ المهم روحنا من هنا لهنا إذا الـ
+
+374
+00:28:45,070 --> 00:28:48,890
+delta H هذه زائد الـ delta H هذه لازم يطلع 890
+
+375
+00:28:48,890 --> 00:28:52,680
+negative لازم التفاعلين مختلفين خالص اللي
+
+376
+00:28:52,680 --> 00:28:57,060
+استخدمناهم، لكن ما ينفعش يعطينا حاجة ثانية،
+
+377
+00:28:57,060 --> 00:29:00,840
+ما بينفعش، 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 قلت لكم سابقًا، ممكن أستخدم تفاعل
+
+380
+00:29:08,360 --> 00:29:11,800
+مرارا وتكرارًا عشان أتمنى إيه، أخليه يولد الطاقة
+
+381
+00:29:11,800 --> 00:29:17,490
+وهذا الكلام، مستحيل، ما بينفعش يعني طيب نتطلع على
+
+382
+00:29:17,490 --> 00:29:23,270
+حاجة يعني كتير جميلة في Hess law قلت أنا إنه Hess
+
+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 بيكون شبه مستحيل فمثلًا لو أنا بدي أجيب ال
+
+385
+00:29:32,890 --> 00:29:38,690
+heat of combustion لل carbon إلى CO مش CO إلى CO
+
+386
+00:29:38,690 --> 00:29:41,070
+فما أجيب أحط والله carbon solid
+
+387
+00:29:44,850 --> 00:29:50,390
+زائد نصف O2 بتعطينا CO، بقول هذا التفاعل ما يحصلش،
+
+388
+00:29:50,390 --> 00:29:58,710
+ما يحصلش هيك، هذا التفاعل هيعطينا COA وهيعطي CO2 و
+
+389
+00:29:58,710 --> 00:30:05,890
+هيزيد هنا شوية C solid، مش هيتحول الكربون للـ CO بس
+
+390
+00:30:06,790 --> 00:30:11,910
+مجرد وجود Oxygen هيتحول جزء منه للـ CO2 وجزء منه
+
+391
+00:30:11,910 --> 00:30:17,230
+للـ CO وحيزيد شوية إيه؟ حيزيد شوية C solid طب أنا
+
+392
+00:30:17,230 --> 00:30:21,170
+بدي أجيب الـ Delta H للتفاعل هذا أنا بدي أجيب الـ
+
+393
+00:30:21,170 --> 00:30:24,930
+Delta H لهذا التفاعل يا جماعة إيش الـ Delta H له؟
+
+394
+00:30:24,930 --> 00:30:32,310
+قال ما بقدرش أوصله بشكل مباشر لازم أدور لي على لفة آه
+
+395
+00:30:32,310 --> 00:30:36,690
+لازم أدور على لفة أدور على steps أخرى ممكن جدًا إنه
+
+396
+00:30:36,690 --> 00:30:41,250
+تعطيني في النهاية delta H لهذا التفاعل وهذا يعني شيء
+
+397
+00:30:41,250 --> 00:30:50,290
+عظيم في فوائد الشغل باستخدام Hess law شيء عظيم جدًا
+
+398
+00:30:50,290 --> 00:30:50,930
+في الحقيقة
+
+399
+00:30:55,020 --> 00:30:58,780
+طيب نتطلع كيف ممكن نعملها؟ قال والله مثلًا بيقول
+
+400
+00:30:58,780 --> 00:31:01,040
+الـ the enthalpy of reaction for the combustion of
+
+401
+00:31:01,040 --> 00:31:07,160
+C is to CO2 is .. هذا معروف معروف احتراق كامل للـ C
+
+402
+00:31:07,160 --> 00:31:11,380
+للـ CO2 معروف excess oxygen كل الكربون بيحترق للـ CO2
+
+403
+00:31:11,380 --> 00:31:17,690
+سالب 393.5 kilojoule per mole degrees Kelvin طيب،
+
+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 جبت CO وحطيت عليها Oxygen، هيتحول
+
+406
+00:31:26,030 --> 00:31:30,870
+لـ CO2؟ طبعًا، هذا برضه تفاعل معروف، جداش باطين بيقول
+
+407
+00:31:30,870 --> 00:31:33,510
+سالب مائتين وثلاثة وثمانين كيلوجول برمول، أنا مش
+
+408
+00:31:33,510 --> 00:31:35,890
+مهتم فيهم، لأن هذول معروفين في ال literature، أنا
+
+409
+00:31:35,890 --> 00:31:41,530
+مهتم بالـ CS زائد نصف O2، بده يتحول للـ CO، اللي قلنا
+
+410
+00:31:41,530 --> 00:31:45,930
+مباشرة، بينفعش ينعمل مباشرة ما ينفعش 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
+ما فيش مشكلة CO هنا في النواتج هنا وين إذا واحد مول
+
+414
+00:31:59,890 --> 00:32:03,510
+بدي أجلبها لما أجلبها إيش بجيب على طول الإشارة
+
+415
+00:32:03,510 --> 00:32:06,630
+إذا أنهينا المعادلة الأولى خليناها زي ما هي
+
+416
+00:32:06,630 --> 00:32:10,990
+المعادلة الثانية إيش عملناها reverse فـ delta H إيش
+
+417
+00:32:10,990 --> 00:32:15,050
+صارت موجبة لكن لما اجيت لغاية الـ CO2 ووقفت عند ال
+
+418
+00:32:15,050 --> 00:32:19,390
+CS زائد هنا نصف O2 في النواتج هنا O2 في المتفاعلات
+
+419
+00:32:19,390 --> 00:32:23,090
+إذا نصف O2 بيعطينا CO هي المعادلة اللي أنا كنت
+
+420
+00:32:23,090 --> 00:32:26,580
+بديها وما عارف أوصل لها جداشل 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 التفاعل بيقول 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
+لهم 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 بمعلومية هذه 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 تسيل المعادلة
+
+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 هي هي وين؟ H2 هي هي هي بتنضرب في
+
+433
+00:33:41,910 --> 00:33:48,210
+اثنين إذا هذه في اثنين طب C2H6 هذه موجودة وين؟
+
+434
+00:33:48,810 --> 00:33:56,030
+نجلبها بس نجلبها و نضربها في اثنين معايا يا بنات
+
+435
+00:33:56,030 --> 00:34:00,130
+كمان مرة نقولهم ابصرها بقول كيف بفكر أنا في حل
+
+436
+00:34:00,130 --> 00:34:03,270
+المسألة باستخدام Hess Law بمسك ال target equation
+
+437
+00:34:03,270 --> 00:34:06,170
+على فكرة هذا كله بتنسقله فيه كثير في الامتحان يعني
+
+438
+00:34:06,170 --> 00:34:12,050
+بيجي دائماً سؤال على Hess Law فإيش بنقول؟ طلع معايا
+
+439
+00:34:12,050 --> 00:34:16,430
+بقول بتطلع على ال target equation إيش أول حاجة فيها
+
+440
+00:34:16,430 --> 00:34:21,210
+C2H2 هيني بلاقيه هين في أول معادلة إذا هذا واحد هذا
+
+441
+00:34:21,210 --> 00:34:24,050
+اثنين بدي اضرب المعادلة في اثنين و ال delta H
+
+442
+00:34:24,050 --> 00:34:27,150
+بضربها في اثنين مش بس المعادلة المعادلة و ال
+
+443
+00:34:27,150 --> 00:34:34,650
+delta H هذا عندي H2 اثنين H2 هذا H2 واحدة بس one
+
+444
+00:34:34,650 --> 00:34:37,250
+more إذا بدي اضرب هذه المعادلة في اثنين و ال delta
+
+445
+00:34:37,250 --> 00:34:41,230
+H بدي اضربها في اثنين طيب الـ C2H6 جال هدف
+
+446
+00:34:41,230 --> 00:34:45,590
+النواتج هي هنا ظاهرة إذا بدي أجلب المعادلة و
+
+447
+00:34:45,590 --> 00:34:50,690
+اضربها في اثنين و ما أنسا الشارة لما نعمل هيك
+
+448
+00:34:50,690 --> 00:34:54,650
+بقى لاحظ انه لما نجمع بنبحث على ال target equation
+
+449
+00:34:54,650 --> 00:34:58,590
+عن طريق جمع delta H1, delta H2 و delta H3 اللي
+
+450
+00:34:58,590 --> 00:35:03,630
+حنعملهم delta H4, delta H5, delta H6 ماشي يا جماعة
+
+451
+00:35:03,630 --> 00:35:07,150
+هو أنا عامل لكم هذا نفس اللون في المعادلة السابقة
+
+452
+00:35:07,150 --> 00:35:09,170
+يعني لو جئتم و طلعتوا المعادلة السابقة نفس
+
+453
+00:35:09,170 --> 00:35:12,010
+الألوان عاملها على أساس انه تعرفوا إيش 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 reaction اثنين FE Solid زي الثلاثه على اثنين
+
+456
+00:35:22,320 --> 00:35:27,360
+O2 Gas بتعطينا FE اثنين O ثلاثة Solid Given هاي
+
+457
+00:35:27,360 --> 00:35:30,340
+اعطاني المعادلة اللي هستخدمها FE اثنين O ثلاثة
+
+458
+00:35:30,340 --> 00:35:33,960
+Solid زي الثلاثه CO Gas بتعطينا اثنين FE Solid زي
+
+459
+00:35:33,960 --> 00:35:38,600
+الثلاثه CO2 Gas واللي عندنا دلتة H دلتة H معينة
+
+460
+00:35:38,600 --> 00:35:43,400
+الـCO زي نصف O2 بتعطينا CO2 برضه دلتة H معينة باجي
+
+461
+00:35:43,400 --> 00:35:48,390
+أنا لل target equation اثنين FE Solid طب إذا هذه
+
+462
+00:35:48,390 --> 00:35:52,610
+وين مش هذا في النواتج؟ بدي أجلبها و بدي إيه؟ أغير
+
+463
+00:35:52,610 --> 00:35:58,910
+الإشارة طب حلو كثير طب ال F E اثنين او ثلاثة؟ 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 ثلاثة CO يعني هذه المعادلة ما فيش منها
+
+467
+00:36:09,430 --> 00:36:12,910
+فائدة كبيرة هالجزء إلا بس عشان أضايق ال CO لأن هذا
+
+468
+00:36:13,770 --> 00:36:18,330
+و هذا صاروا موجودين هنا يعني هذا صار موجود و هذا صار
+
+469
+00:36:18,330 --> 00:36:22,150
+موجود الآن هذه المعادلة لو جيت طلعت عليها بلاجأ
+
+470
+00:36:22,150 --> 00:36:25,850
+انه لازم ال CO تروح مع ال CO فبتضرب هذه في ثلاثة
+
+471
+00:36:25,850 --> 00:36:30,590
+و الدلتا H بيتضرب في ثلاثة في النهاية في 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 حتساوي مجموع الـ delta H
+
+474
+00:36:41,530 --> 00:36:48,560
+values للمعادلتين اللي عندي طيب برضه نطلع هنا 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 اثنين N O two بتحولت N
+
+477
+00:36:55,800 --> 00:36:59,240
+two O أربعة جاز اثنين N O two جاز تحولت N two O
+
+478
+00:36:59,240 --> 00:37:05,720
+أربعة جاز أحد بيقدر يسميلي هذا المركب binary
+
+479
+00:37:05,720 --> 00:37:11,370
+compound بنفع نقول mono nitrogen ولا ما بنفعش؟ ما 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 ما بنفعش
+
+482
+00:37:20,310 --> 00:37:23,430
+نقول mono nitrogen هذا dinitrogen tetroxide
+
+483
+00:37:23,430 --> 00:37:27,290
+dinitrogen tetroxide ما لازم ننسيها، أنا 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 أنا عندي هدول ال two equations
+
+486
+00:37:34,010 --> 00:37:40,250
+باشي بقول ال N O two بدي ياها وين اه بدي ياها على
+
+487
+00:37:40,250 --> 00:37:45,310
+اليسار بجيب أطلع وين هو وهي موجودة هنا ال N O2 ال
+
+488
+00:37:45,310 --> 00:37:48,910
+N O2 موجودة هنا اثنين و اثنين اه حلو كثير 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
+الشاره ليه لأن ال N O2 هنا وين في ال reactants هنا
+
+491
+00:37:56,550 --> 00:38:01,910
+في 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 كثير 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
+إيش رأيكم .. طيب .. ناخذ 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، الاثنين كربون، الاثنين 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 mole المعادلة 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 طبعاً لأنه ثاني كربون ديلتا
+
+503
+00:38:51,850 --> 00:38:55,830
+اتش سالب ثلاثمية جرى  كثير 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 حتروح للـ CA
+
+506
+00:39:02,690 --> 00:39:07,310
+diamond ماشي يا جماعة إيش الـ delta H لها؟ بنفس
+
+507
+00:39:07,310 --> 00:39:11,490
+الطريقة بنفس الطريقة بدي أدريغرافيت 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 بيأتي كل عن ناحية الثانية 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 جدش قليلة قليلة و التفاعل
+
+512
+00:39:31,010 --> 00:39:36,880
+endothermic يعني التفاعل يعني endothermic لكن 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؟ ما لهاش دعوة، ما لهاش دعوة عادة يا
+
+515
+00:39:46,020 --> 00:39:49,820
+فَنّات الـ Thermodynamics مش هذا 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
+ما بيعطيني فكرة السرعة بندرسها في حاجة اسمها
+
+521
+00:40:11,960 --> 00:40:16,920
+chemical kinetics فيعني مش شرط انه والله أعطاني
+
+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 إلا كان ال mass لجنائه سعر
+
+524
+00:40:24,420 --> 00:40:29,270
+الفحم يعني و هذا مستحيل  calculate delta H for the
+
+525
+00:40:29,270 --> 00:40:36,190
+reaction اثنين CS زائد H2 بتعطينا C2H2 gas و معطيني
+
+526
+00:40:36,190 --> 00:40:41,430
+المعادلات التالية ثلاثة
+
+527
+00:40:41,430 --> 00:40:44,070
+معادلات بقول كيف بدي أفكر في هذا المثال أهم
+
+528
+00:40:44,070 --> 00:40:47,630
+بالنسبة لي carbon solid بدور وين موجودة هي موجودة
+
+529
+00:40:47,630 --> 00:40:52,290
+هنا لكن إيش أش مالها؟ بنضربها في اثنين 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
+حيعطيني Delta H لل reaction بيتهيأ لي 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 حلو
+
+535
+00:41:22,140 --> 00:41:25,020
+حالكم في ال notes أنا حابب أن أعطي أمثلة كثير 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
+يتنسقلي فيه و يعني و فيه varieties في الحقيقة يعني في
+
+538
+00:41:32,200 --> 00:41:35,860
+عنا أسئلة كثير ممكن أن الواحد يتعرض لها في هذا
+
+539
+00:41:35,860 --> 00:41:38,200
+الباب فأنا 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
+formation الـ 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 formation في البداية يعني لازم نعرف انه
+
+544
+00:42:00,320 --> 00:42:09,920
+في عندنا كمية هائلة من ال constants لتغيرات
+
+545
+00:42:09,920 --> 00:42:13,600
+متعددة في ال thermodynamics فممكن نلاقي مثلاً
+
+546
+00:42:13,600 --> 00:42:17,870
+تقريباً عدد هائل من الـ tables لـ Delta H
+
+547
+00:42:17,870 --> 00:42:23,710
+Vaporization يعني Delta H لتحويل ال liquid إلى gas
+
+548
+00:42:23,710 --> 00:42:34,270
+Delta H ل refusion أو ال melting لل solid لل liquid ممكن
+
+549
+00:42:34,270 --> 00:42:39,580
+Delta H Sublimation تحول ال solid إلى gas فحنلاقي
+
+550
+00:42:39,580 --> 00:42:44,640
+جداول كثيرة جداً 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 أكون مادة،
+
+553
+00:42:53,620 --> 00:43:01,130
+بدي أكون مادة فالمادة هذه بدي أكونها من .. ما 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 مثلاً 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 الـ C Graphite زائد
+
+560
+00:43:29,910 --> 00:43:36,490
+Oxygen Gas فانا بدي أكون المادة من إيه؟ من عناصرها 
+
+561
+00:43:36,490 --> 00:43:40,750
+الأساسية اللي أنا بدي أتكلم عنه هو تكوين المادة من
+
+562
+00:43:40,750 --> 00:43:46,550
+عناصرها الأساسية، مش بس هيك أنا مهتم أكثر في أن أكون
+
+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 بدّه يكون
+
+565
+00:43:57,810 --> 00:44:01,430
+هو غاز مش Liquid لأن عادة الـCO2 ايش بيكون؟ غاز
+
+566
+00:44:01,430 --> 00:44:07,250
+بدّه يكون من عناصره الأولية في حالتها القياسية ايش
+
+567
+00:44:07,250 --> 00:44:10,150
+هي الحالة القياسية اللي أنا بأتكلم عنها الحالة
+
+568
+00:44:10,150 --> 00:44:14,250
+القياسية اللي أنا بأتكلم عنها هي 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 المية 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 Gas لكن المية اللي بدي أحصل 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 وقلنا ل Standard State
+
+578
+00:45:06,160 --> 00:45:10,440
+أنا بشتغل عند حرارة خمسة و عشرين ديجري سي أو 298
+
+579
+00:45:10,440 --> 00:45:15,950
+كيلفن وبشتغل اه وبشتغل عند ايه؟ و بشتغل واحد
+
+580
+00:45:15,950 --> 00:45:19,710
+أتموسفير ولازم المادة تكون ايه؟ في حالتها
+
+581
+00:45:19,710 --> 00:45:23,930
+الطبيعية ولما يكون في عندي أكثر من حالة طبيعية
+
+582
+00:45:23,930 --> 00:45:29,150
+للمادة بقول باخد الحالة اللي 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 غاز، طب Ozone ولا Oxygen؟
+
+586
+00:45:41,350 --> 00:45:45,820
+قال لأ ال Oxygen هو الحالة الطبيعية ليه؟ لأنه أكثر
+
+587
+00:45:45,820 --> 00:45:49,500
+استقرارًا فباخد الحالة المستقرة، أكثر استقرارًا
+
+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
+استقرارًا بعدين واحد أتموسفير 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 ومن خلال القراءات ناس كان مشوفناش الأنصار
+
+593
+00:46:10,660 --> 00:46:14,760
+قبل هيك فلأ 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 استقرارًا الكربون ايه 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 حلقي مثلا P4 مثلا ال Sulfur، Rhombic Sulfur
+
+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 نشوف كيف ممكن نستخدم ال heat
+
+604
+00:46:58,710 --> 00:47:05,530
+of formation وبالفعل 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 كثيرة في الحقيقة لحساب
+
+607
+00:47:14,630 --> 00:47:17,800
+ال heat of reaction إذا كنت أنا عارف الـ 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 ونواتج
+
+610
+00:47:24,280 --> 00:47:28,040
+ودائما الـ ΔH لل reaction هي عبارة عن إن الـ H
+
+611
+00:47:28,040 --> 00:47:31,020
+للنواتج ناقص الـ H للمتفاعلات هي الـ ΔH لل
+
+612
+00:47:31,020 --> 00:47:35,920
+reaction وبما إن الـ ΔH لل reaction واحدة إذا أنا
+
+613
+00:47:35,920 --> 00:47:38,560
+عندي المتفاعلات والنواتج لو أنا عارف الـ ΔH F
+
+614
+00:47:38,560 --> 00:47:41,900
+لهن 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 كثيرة زي هيك هذه الـ Standard Enthalpies 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 كثير بتكون
+
+620
+00:48:07,450 --> 00:48:12,710
+من ايش؟ جال C Graphite زائد H .. اثنين 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 عندي .. يبقى معادلة التكوين دائما
+
+623
+00:48:21,820 --> 00:48:28,680
+عناصر في حالتها القياسية عند 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
+Celsius فنلاقي جداول زي هيك كثيرة خالص وبنستفيد
+
+626
+00:48:40,090 --> 00:48:43,870
+منها في الحقيقة في حل الأسئلة وإذا كان ما لاقيناش
+
+627
+00:48:43,870 --> 00:48:46,650
+المادة اللي بدناها بنرجع في آخر الكتاب برا وب
+
+628
+00:48:46,650 --> 00:48:51,010
+نلاقي 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 وغيره بس بدي
+
+631
+00:49:00,910 --> 00:49:05,770
+ألفت انتباهكم أنا 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 أجيب 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 فيها أي 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 بدّه يحوّله 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؟ جدّاش ما عوز طاقة؟ zero ما عوزش شيء عشان
+
+643
+00:49:57,690 --> 00:50:02,690
+هيك دائما بنقول إن العناصر اللي 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
+بتساوي صفر، فمثلا الأكسجين الـ delta H0FL هو جدّاش
+
+646
+00:50:11,110 --> 00:50:14,490
+صفر لأنه بدّه يكون أكسجين من نفسه في حالته الطبيعية
+
+647
+00:50:14,490 --> 00:50:17,070
+وهو أصلا موجود في حالته الطبيعية، لذا ايش بدّه
+
+648
+00:50:17,070 --> 00:50:21,670
+طاقة؟ ولا ايش، ما بدّيش حاجة، ما بدّي نتذكر إنه أي
+
+649
+00:50:21,670 --> 00:50:26,710
+عنصر من العناصر موجود في حالته الطبيعية بنقولش 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 أتموسفير 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 بدّه يكونه من ذاته عند نفس ظروفه لأنه
+
+654
+00:50:47,110 --> 00:50:50,140
+في الحاجة القياسية وأصلا موجود فما بدّه طاقة في
+
+655
+00:50:50,140 --> 00:50:53,440
+حالته الطبيعية والله بتفرض عليّ أن أقول Delta H not
+
+656
+00:50:53,440 --> 00:51:02,720
+F لّه هي عبارة عن صفر ال H2 نفس الكلام ال H2 نفس
+
+657
+00:51:02,720 --> 00:51:08,550
+الكلام صفر الـC Graphite صفر بدّه يكونه من نفسه الـC
+
+658
+00:51:08,550 --> 00:51:11,050
+Graphite بدّه يكونه من الـC Graphite عند خمسة و
+
+659
+00:51:11,050 --> 00:51:14,830
+عشرين ديجريات C وعند واحد اتنسيت بحجر طاقة جدّاش
+
+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 الامتحان لما 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 إنه تفهم
+
+665
+00:51:35,130 --> 00:51:40,390
+هذا الكلام وما تسألي عنه نهائيًا 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 اثنين NA Solid زائد نصف
+
+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
+هدول المتفاعلات هي عبارة عن elements في حالتها
+
+677
+00:52:32,180 --> 00:52:38,260
+القياسية كويس ولا لأ فال NA Solid صحيح ال O2 Gas
+
+678
+00:52:38,260 --> 00:52:45,760
+صحيح كمان NA2O هذا ملح صلب 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 صلب يبقى 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 الثانية 2K Liquid زائد Cl2 Gas
+
+684
+00:53:10,850 --> 00:53:15,490
+2K Cl Solid نيجي هنا 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 Formation لأن 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 الثانية ال delta HF دائما بتكون المول واحد
+
+691
+00:53:45,600 --> 00:53:50,240
+مش لاثنين مول او لثلاثة مول او لنصف مول معنى الكلام
+
+692
+00:53:50,240 --> 00:53:54,780
+لازم المعادلة هذه كمان تنقسم على اثنين لازم
+
+693
+00:53:54,780 --> 00:53:58,800
+المعادلة هذه تنقسم على اثنين 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 عناصرها الأساسية في الحاجة القياسية
+
+696
+00:54:11,980 --> 00:54:16,780
+واحد مول مش أكثر إذا هنا لأ بنفعش اثنين بنفعش هد
+
+697
+00:54:16,780 --> 00:54:20,120
+على اثنين هد على اثنين هد على اثنين هيك بتصير
+
+698
+00:54:20,120 --> 00:54:28,990
+صحيحة طب C6H12O6 صلب بتتحول 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 الطبيعي هذا
+
+704
+00:54:46,570 --> 00:54:50,920
+حالته الطبيعي صحيح يعني بدها نجلبها و الـ C بدها تكون
+
+705
+00:54:50,920 --> 00:54:55,160
+مش دايمون بدها تكون جرافيت 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 إذا
+
+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 equation اتنين 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 summation 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
+reactants كويس؟ 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 product عنصر 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
+reaction 2C6H6 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 اتناش في 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
+تلاتة هذه 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 بتساوي البرودكس 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 يعني طب هيها هيك خلاص زائد صفر صفر
+
+781
+01:01:05,740 --> 01:01:09,910
+طبعا ال auto فممكن نعملها زي هيك وخلاص معايا 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 F هي 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 اتعلمت إيش 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 أسهل لي 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
+مثال بيقول 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 O2 H2O 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 compound بنفعش 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 S سلفر 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 اليمين لأنه
+
+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 اه ممكن 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
+لأنه المادة 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 دلتا H  هي طبعا هي نفسها
+
+844
+01:06:00,900 --> 01:06:04,800
+لهذا التفاعل، 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 ما بتبطل 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 أنا بدي إياها بيقول in the
+
+849
+01:06:22,050 --> 01:06:27,670
+reaction اتنين Sodium Bicarbonate بتتحول لـ Sodium
+
+850
+01:06:27,670 --> 01:06:31,010
+Solid بتتحول لـ Sodium Carbonate Solid زائد H2O Gas
+
+851
+01:06:31,010 --> 01:06:35,290
+زائد CO2 Gas بيقول find Delta H not للـ 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 للـ H2O
+
+854
+01:06:44,800 --> 01:06:49,760
+برضه معايا Delta Hnot F للـ CO2 معايا طب خلاص يفجأت
+
+855
+01:06:49,760 --> 01:06:53,320
+Delta Hnot F للـ reaction هي عبارة عن ايش نقول مع بعض
+
+856
+01:06:53,320 --> 01:06:56,220
+Delta Hnot F للـ reaction ايش بتساوي الـ products
+
+857
+01:06:56,220 --> 01:07:02,980
+يللا هذا هي الـ products 1 في Delta Hnot F للصوديوم
+
+858
+01:07:02,980 --> 01:07:14,000
+كربونيت زائد Delta H0 F واحد بس للـ H2O جاز زائد
+
+859
+01:07:14,000 --> 01:07:24,280
+Delta H0 F للـ CO2 جاز هذا كله ناقص اتنين فيه Delta
+
+860
+01:07:24,280 --> 01:07:31,170
+H0 F للـ Sodium Bicarbonate خلاص وكلهم معايا بس
+
+861
+01:07:31,170 --> 01:07:35,350
+بنعوض تعويض مباشر بيطلع عندي موجبة بـ 128 و
+
+862
+01:07:35,350 --> 01:07:38,350
+طبيعي لأنه الـ Sodium b carbonate بيبقى تنحرج عشان
+
+863
+01:07:38,350 --> 01:07:44,050
+تتحول لـ 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 الـ Delta H ايش تكون موجبة بقى أقول
+
+866
+01:07:55,130 --> 01:07:57,230
+هذا يعني مثلاً آخر مثال معايا
+
+867
+01:08:01,010 --> 01:08:06,750
+بيقول calculate Delta H0 للـ 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 Peroxide  مراكب أيونية طبعًا زائد
+
+870
+01:08:18,820 --> 01:08:23,400
+اتنين H2O liquid بتعطينا أربع NAOH solid زائد O2
+
+871
+01:08:23,400 --> 01:08:27,020
+gas بيقول بده يحسب الـ Delta H للـ reaction provided
+
+872
+01:08:27,020 --> 01:08:35,140
+that Delta H not if للـ NA2O2 معايا Delta H not if
+
+873
+01:08:35,140 --> 01:08:39,920
+للـ Sodium Hydroxide معايا Delta H not if للميه
+
+874
+01:08:39,920 --> 01:08:44,870
+معايا طب الأكسجين ما تهمنيّش لأنها لأنها نصفها طب خلاص
+
+875
+01:08:44,870 --> 01:08:50,170
+يفجر المسألة المحلولة لأنها هي الـ 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
+الـ Delta H نوت F للـ Sodium Hydroxide ناقص هي فتحنا
+
+878
+01:09:01,350 --> 01:09:10,420
+جوس كبير اتنين في Delta H نوت F للـ NA2O2 زائد اتنين
+
+879
+01:09:10,420 --> 01:09:17,380
+في دلتا H نوت F للـ H2O اللي هي الـ liquid و خلاص و
+
+880
+01:09:17,380 --> 01:09:20,180
+لاحظوا أن الأكسجين ما حطيناهاش ولا أعطاناها أي
+
+881
+01:09:20,180 --> 01:09:23,100
+اهتمام لأنها طبعًا 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 يوم 178 و 11 كيلو جول 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 أنا بقول هذا معايا اللي هو الـ
+
+888
+01:09:49,040 --> 01:09:55,800
+Delta H0 للـ reaction 178.1 بدها تساوي النواتج الـ
+
+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 الـ solid، هدول ناقص Delta H0F للـ Calcium
+
+891
+01:10:11,160 --> 01:10:15,440
+Carbonate هو طالب الـ ΔH نوت F للكالسيوم 
+
+892
+01:10:15,440 --> 01:10:18,400
+الكربونات وبدأ أبحث في الجداول على الـ Calcium
+
+893
+01:10:18,400 --> 01:10:22,000
+Oxide و الـ CO2 الجداول موجودة فيها كل هذه 
+
+894
+01:10:22,000 --> 01:10:27,360
+المركبات فهي الـ Calcium Oxide وهي الـ CO2 هذه 
+
+895
+01:10:27,360 --> 01:10:31,570
+مجهولة بقدر أحسبها مباشرة فسواء جلد Delta H للـ
+
+896
+01:10:31,570 --> 01:10:35,250
+reaction أو جالي أعطاني الـ reaction وجالي بده 
+
+897
+01:10:35,250 --> 01:10:40,510
+والله Delta H not F لمادة من المواد سهل جداً أن 
+
+898
+01:10:40,510 --> 01:10:46,230
+أوُصل لها ليه؟ لأنه السطر هذا أو المعادلة المعادلة 
+
+899
+01:10:46,230 --> 01:10:50,770
+سهلة بسيطة خالص وجدامي موجودة الـ Delta H not للـ
+
+900
+01:10:50,770 --> 01:10:54,430
+reaction بتساوي summation Delta H not F للـ products
+
+901
+01:10:54,430 --> 01:10:58,320
+minus reactants وبالتالي 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 الـ
+
+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 للـ food و الـ fuels عموماً، القيمة الغذائية
+
+906
+01:11:15,180 --> 01:11:20,520
+للـ food كـ energy، كـ energy، وللـ fuel برضه قيمة الـ
+
+907
+01:11:20,520 --> 01:11:25,480
+energy اللي موجودة فيه فبنقول بشكل أساسي يمكن الـ
+
+908
+01:11:25,480 --> 01:11:29,960
+energy في أجسامنا بتيجي من حاجتين الـ carbohydrates
+
+909
+01:11:29,960 --> 01:11:31,300
+و الـ fats
+
+910
+01:11:34,470 --> 01:11:38,490
+الـ carbohydrates أساساً يعني بتكون موجودة على هيئة
+
+911
+01:11:38,490 --> 01:11:43,850
+سكريات و starches وهذه بتتكسر في الـ intestines في 
+
+912
+01:11:43,850 --> 01:11:47,390
+الأمعاء يعني بتتحول لـ glucose، اللي هو اللي احنا 
+
+913
+01:11:47,390 --> 01:11:53,720
+بنستفيد منه كمصدر للطاقة لأنه بيتحول لـ CO2 و H2O يا
+
+914
+01:11:53,720 --> 01:11:58,220
+سلام، بتحول لـ CO2 و H2O؟ آه، زي ما تنحرج 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
+لـ CO2 و مياه، نفس الكلام، طاقة طاقة، كله طاقة،
+
+917
+01:12:05,720 --> 01:12:11,630
+فالجسم برضه لما ينحرج للجلوكوز، بتحول لـ CO2 و H2O 
+
+918
+01:12:11,630 --> 01:12:15,830
+يطلعوا كمية طاقة فظيعة المول من الـ 180 جرام يعني
+
+919
+01:12:15,830 --> 01:12:22,810
+المول من الـ glucose بيعطيني 2803 kilo joules شيء
+
+920
+01:12:22,810 --> 01:12:27,350
+كتير خالص يعني كمية رهيبة جداً 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 الـ caloric content
+
+923
+01:12:36,750 --> 01:12:41,970
+في أي كمية من الـ food، هذا بداية، فبنقول إنه كل 
+
+924
+01:12:41,970 --> 01:12:46,610
+gram من الـ carbohydrates موجود فيه 17 أو بقدر
+
+925
+01:12:46,610 --> 01:12:50,990
+يعطينا 17 kilojoule كل جرام Carbohydrate بيعطينا 
+
+926
+01:12:50,990 --> 01:12:55,630
+السبعة عشر كيلو جول أو يعني تقريباً أربعة كيلو
+
+927
+01:12:55,630 --> 01:13:00,930
+كالوري لأن احنا بنعرف إنه يعني
+
+928
+01:13:00,930 --> 01:13:06,330
+العلاقة بين الجول و الكالوري 4.18 شفناها سابقاً
+
+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
+تخيلوا كيف بده يكون التركيب وهذا فظيع جداً 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 ثمانية و ثلاثين كيلو جول ضعف السكر ثمانية و
+
+935
+01:13:33,550 --> 01:13:38,710
+ثلاثين كيلو جول تقريباً يعني وهاي 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  الـ fat 38 KJ طبعاً 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 17 برضه كيلو زي تقريباً زي الـ
+
+942
+01:14:08,620 --> 01:14:14,220
+carbohydrates الـ .. الـ apples موجودة فيها 
+
+943
+01:14:14,220 --> 01:14:17,300
+carbohydrates وموجودة فيها fat وموجودة فيها protein
+
+944
+01:14:17,300 --> 01:14:20,700
+لما نيجي نحسبها تطلع تقريباً اتنين و نص kilo joule 
+
+945
+01:14:20,700 --> 01:14:25,460
+per gram الـ bread طبعاً موجود فيه كمية كبيرة من الـ
+
+946
+01:14:25,460 --> 01:14:29,060
+carbohydrates كمية من الـ fat كمية .. بتحول لـ اتناشر
+
+947
+01:14:29,060 --> 01:14:35,890
+kilo joule per gram فهذه بتعبرلي عن الـ .. 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 فخليني آخد مثال نحسب فيه جداش مثلاً الـ
+
+950
+01:14:49,250 --> 01:14:54,550
+Caloric Content لـ One Serving ففيه عندي 28 جرام، 1
+
+951
+01:14:54,550 --> 01:14:59,910
+أنص، أنصة يعني طبعاً الأنصة دي بنستخدمها في بريطانيا
+
+952
+01:14:59,910 --> 01:15:03,680
+أو في أمريكا يعني البلدان اللي بستخدم الـ foot و الـ
+
+953
+01:15:03,680 --> 01:15:08,000
+inch برضه بستخدموا الأنص اللي لهم نظام خاص يعني اه
+
+954
+01:15:08,000 --> 01:15:13,520
+تبانية و عشرين جرام تقريباً واحد أنص تقريباً واحد
+
+955
+01:15:13,520 --> 01:15:16,520
+أنص يعني تبانية و عشرين جرام serving of a popular
+
+956
+01:15:16,520 --> 01:15:19,540
+breakfast cereal تعرفوه الـ 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 منزوع
+
+959
+01:15:27,900 --> 01:15:33,610
+الدسم ميه و عشرين مل provides 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 الـ skim milk موجودة 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
+الجدول اللي شفناه قبل شوي عشان نحسب جداش الـ
+
+964
+01:15:54,390 --> 01:15:59,730
+calorie content لهذا الواجبة نقول energy 8 gram
+
+965
+01:15:59,730 --> 01:16:04,510
+protein كل جرام 17 kilo joule 26 gram carbohydrate
+
+966
+01:16:04,510 --> 01:16:09,170
+برضه كل جرام 17 kilo joule 2 gram fat كل جرام 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
+نحولها لـ calorie نقسمها لـ 4.18 ميه بيطلع حوالي 156
+
+969
+01:16:18,150 --> 01:16:23,720
+kilo calorie ما في أو ارا كتابة calorie C كبيرة C
+
+970
+01:16:23,720 --> 01:16:25,420
+كبيرة يعني إيه 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 جداً، طبعاً الكاتب بيذكر إنه يعني هال
+
+974
+01:16:46,540 --> 01:16:48,860
+petrol اللي احنا بنستخدمه اللي هو الـ fossil fuels
+
+975
+01:16:48,860 --> 01:16:53,910
+هذا تكون خلال ملايين السنين الله أعلم يعني لكن 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 جداً يعني عشان .. وظروف كمان صعبة جداً 
+
+981
+01:17:14,250 --> 01:17:19,970
+عشان يتكون خاصة بالكميات هذه فهو بيقول يعني أن هذه
+
+982
+01:17:19,970 --> 01:17:25,350
+كلها يعني بتختلف في قدرتها على إمدادنا بالطاقة فمثلا
+
+983
+01:17:25,350 --> 01:17:28,130
+يعني الـ natural gas اللي هو بتكون أساسا من الـ
+
+984
+01:17:28,130 --> 01:17:32,070
+methane لكن مخلوط معاه طبعا ethane و propane و
+
+985
+01:17:32,070 --> 01:17:37,770
+butane كميات متفاوتة مش زي الـ hydrogen ولا زي الـ
+
+986
+01:17:37,770 --> 01:17:41,770
+البنزين اللي إحنا بنستخدمه في السيارات ولا زي الـ
+
+987
+01:17:41,770 --> 01:17:46,550
+solar لأ كل واحد منهم فيه له يعني إمكانية إنه
+
+988
+01:17:46,550 --> 01:17:51,770
+يُمدّنا بقدرة معينة فمثلا الـ wood الـ fuel value له
+
+989
+01:17:51,770 --> 01:17:59,010
+18 kilo joule per gram الـ wood الـ 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 48 natural gas 49 قريب منه
+
+992
+01:18:11,250 --> 01:18:15,470
+الهيدروجين أو كتير خالص per gram ليه؟ لأن إذا كانت
+
+993
+01:18:15,470 --> 01:18:18,570
+تلاحظوا الهيدروجين الـ gram تبعه عبارة عن نص مول
+
+994
+01:18:18,570 --> 01:18:22,350
+كمية هائلة الـ gram تبع الهيدروجين عبارة عن إيه؟
+
+995
+01:18:22,350 --> 01:18:26,670
+عبارة عن نص مول فبيعطيني 142 جرام مش المفروض مني
+
+996
+01:18:26,670 --> 01:18:29,930
+أن أحفظ هذا الكلام لكن المفروض إنه إذا كان إعتمدنا
+
+997
+01:18:30,420 --> 01:18:37,180
+قيم الـ .. يعني الـ fuel value لبعض الـ .. الـ
+
+998
+01:18:37,180 --> 01:18:40,620
+components من مثلا وجبة غذائية أو غيرها وممكن إنه
+
+999
+01:18:40,620 --> 01:18:44,080
+والله آه لازم نقدر نحسب قد إيش الـ calorie content
+
+1000
+01:18:44,080 --> 01:18:51,570
+لها بس مش أكثر بتمنى إنه يعني نكون إن نكون يعني
+
+1001
+01:18:51,570 --> 01:18:54,410
+استفدنا من هذا الـ chapter و بتمنى إنه 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 رايد الحصة الجاية 
diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/Sp8Q6FPQZTc_raw.json b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/Sp8Q6FPQZTc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..898b0b1cb46bf8fa07be7c2e79419daae7ce0dec
--- /dev/null
+++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/Sp8Q6FPQZTc_raw.json
@@ -0,0 +1 @@
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0.58837890625}, {"start": 152.09, "end": 152.83, "word": " occurring", "probability": 0.9150390625}, {"start": 152.83, "end": 153.35, "word": " هنلاحظ", "probability": 0.96474609375}, {"start": 153.35, "end": 153.51, "word": " أن", "probability": 0.77490234375}, {"start": 153.51, "end": 153.85, "word": " كل", "probability": 0.904296875}, {"start": 153.85, "end": 155.79, "word": " ذره", "probability": 0.434814453125}, {"start": 155.79, "end": 155.91, "word": " من", "probability": 0.92431640625}, {"start": 155.91, "end": 156.21, "word": " ذرات", "probability": 0.8533528645833334}, {"start": 156.21, "end": 156.55, "word": " حوالى", "probability": 0.7525634765625}, {"start": 156.55, "end": 156.95, "word": " 6", "probability": 0.6240234375}, {"start": 156.95, "end": 157.79, "word": " بروتونات", "probability": 0.93603515625}], "temperature": 1.0}, {"id": 6, "seek": 17842, "start": 158.1, "end": 178.42, "text": "لكن عدد النيوترونات ممكن يختلف وهذا اللي بيعطينا النظائر فمجموع عدد البروتونز و النيوترونز سمناه ال mass number ففي عندي كل عنصر من العناصر فيه إله أو كل ذره من ذرات العنصر موجود في ..الها atomic", "tokens": [1211, 19452, 6225, 3215, 3215, 2423, 22653, 35473, 2288, 11536, 9307, 3714, 43020, 7251, 46456, 46538, 37037, 15730, 13672, 1829, 4724, 40228, 9566, 1829, 8315, 28239, 19913, 16373, 2288, 6156, 2304, 7435, 2304, 45367, 6225, 3215, 3215, 2423, 26890, 35473, 11536, 11622, 4032, 2423, 22653, 35473, 2288, 11536, 11622, 8608, 2304, 8315, 3224, 2423, 2758, 1230, 6156, 41185, 18871, 16254, 28242, 18871, 9381, 2288, 9154, 18863, 1863, 33546, 2288, 8978, 3224, 11933, 43761, 34051, 28242, 29910, 2288, 3224, 9154, 29910, 2288, 9307, 18863, 1863, 9381, 2288, 3714, 29245, 23328, 8978, 4386, 6027, 11296, 22275], "avg_logprob": -0.26282894736842105, "compression_ratio": 1.6683168316831682, "no_speech_prob": 0.0, "words": [{"start": 158.1, "end": 158.66, "word": "لكن", "probability": 0.6983642578125}, {"start": 158.66, "end": 159.22, "word": " عدد", "probability": 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الواحد ال atomic number اللي هو واحد فعادة ما بنكتبش ال atomic number بنكتب ال mass number فبنقول مثلا ال carbon اللي بيحتوي على ستة بروتونز وستة نيوترونز بنقوله carbon twelve فقط", "tokens": [41261, 13672, 1829, 31439, 6225, 3215, 3215, 2423, 26890, 35473, 11536, 11622, 4032, 2304, 29245, 23328, 5296, 11296, 36632, 11242, 995, 2758, 1230, 13672, 1829, 31439, 3714, 7435, 2304, 45367, 6225, 3215, 3215, 2423, 26890, 35473, 11536, 11622, 4032, 6027, 22653, 35473, 2288, 11536, 11622, 4032, 1211, 33456, 3224, 11778, 16373, 15042, 18863, 1863, 9381, 2288, 2423, 14407, 24401, 2423, 22275, 1230, 13672, 1829, 31439, 36764, 24401, 6156, 3615, 18513, 3660, 19446, 44945, 4117, 2655, 3555, 8592, 2423, 22275, 1230, 44945, 4117, 2655, 3555, 2423, 2758, 1230, 6156, 3555, 1863, 39648, 50113, 15040, 2423, 5954, 13672, 1829, 4724, 1829, 33753, 45865, 15844, 8608, 2655, 3660, 4724, 32887, 2655, 11536, 11622, 4032, 14851, 3660, 8717, 1829, 35473, 2288, 11536, 11622, 44945, 39648, 3224, 5954, 14390, 6156, 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"probability": 0.98583984375}, {"start": 191.65, "end": 191.85, "word": " اللي", "probability": 0.7186279296875}, {"start": 191.85, "end": 191.95, "word": " هو", "probability": 0.921875}, {"start": 191.95, "end": 192.23, "word": " واحد", "probability": 0.93359375}, {"start": 192.23, "end": 192.69, "word": " فعادة", "probability": 0.836669921875}, {"start": 192.69, "end": 192.77, "word": " ما", "probability": 0.7626953125}, {"start": 192.77, "end": 193.43, "word": " بنكتبش", "probability": 0.95966796875}, {"start": 193.43, "end": 194.05, "word": " ال", "probability": 0.96435546875}, {"start": 194.05, "end": 194.37, "word": " atomic", "probability": 0.98193359375}, {"start": 194.37, "end": 194.69, "word": " number", "probability": 0.98974609375}, {"start": 194.69, "end": 195.05, "word": " بنكتب", "probability": 0.8592529296875}, {"start": 195.05, "end": 195.17, "word": " ال", "probability": 0.8447265625}, {"start": 195.17, "end": 195.51, "word": " mass", "probability": 0.908203125}, {"start": 195.51, "end": 195.95, "word": " number", "probability": 0.98291015625}, {"start": 195.95, "end": 196.37, "word": " فبنقول", "probability": 0.9488525390625}, {"start": 196.37, "end": 196.79, "word": " مثلا", "probability": 0.9873046875}, {"start": 196.79, "end": 197.63, "word": " ال", "probability": 0.7763671875}, {"start": 197.63, "end": 198.09, "word": " carbon", "probability": 0.90380859375}, {"start": 198.09, "end": 198.39, "word": " اللي", "probability": 0.9794921875}, {"start": 198.39, "end": 198.89, "word": " بيحتوي", "probability": 0.940673828125}, {"start": 198.89, "end": 199.25, "word": " على", "probability": 0.90478515625}, {"start": 199.25, "end": 200.49, "word": " ستة", "probability": 0.8484700520833334}, {"start": 200.49, "end": 201.47, "word": " بروتونز", "probability": 0.83935546875}, {"start": 201.47, "end": 202.55, "word": " وستة", "probability": 0.8971354166666666}, {"start": 202.55, "end": 203.83, "word": " نيوترونز", "probability": 0.9234212239583334}, {"start": 203.83, "end": 204.23, "word": " بنقوله", "probability": 0.6863606770833334}, {"start": 204.23, "end": 204.53, "word": " carbon", "probability": 0.8642578125}, {"start": 204.53, "end": 204.95, "word": " twelve", "probability": 0.63916015625}, {"start": 204.95, "end": 205.47, "word": " فقط", "probability": 0.9921875}], "temperature": 1.0}, {"id": 8, "seek": 21982, "start": 206.08, "end": 219.82, "text": "مش carbon 612 ممكن نكتبه carbon 612 لكن هو carbon 12 بيقال لو كان بيحتوي على سبعة نيوترون و لازم بالضرورة يحتوي على ستة protons فمعناته ده carbon 13 سبعة و ستة تلتاشر", "tokens": [2304, 8592, 5954, 1386, 4762, 3714, 43020, 8717, 4117, 2655, 3555, 3224, 5954, 1386, 4762, 44381, 31439, 5954, 2272, 4724, 1829, 4587, 6027, 45164, 25961, 4724, 1829, 33753, 45865, 15844, 8608, 3555, 27884, 8717, 1829, 35473, 2288, 11536, 4032, 5296, 31377, 2304, 20666, 11242, 2288, 13063, 3660, 7251, 33753, 45865, 15844, 8608, 2655, 3660, 40270, 6156, 2304, 3615, 8315, 47395, 11778, 3224, 5954, 3705, 8608, 3555, 27884, 4032, 8608, 2655, 3660, 6055, 1211, 2655, 33599, 2288], "avg_logprob": -0.16416396723165141, "compression_ratio": 1.61875, "no_speech_prob": 0.0, "words": [{"start": 206.08, "end": 206.36, "word": "مش", "probability": 0.67333984375}, {"start": 206.36, "end": 206.66, "word": " carbon", "probability": 0.61474609375}, {"start": 206.66, "end": 207.3, "word": " 612", "probability": 0.749267578125}, {"start": 207.3, "end": 207.56, "word": " ممكن", "probability": 0.779296875}, {"start": 207.56, "end": 207.96, "word": " نكتبه", "probability": 0.93212890625}, {"start": 207.96, "end": 208.16, "word": " carbon", "probability": 0.91845703125}, {"start": 208.16, "end": 208.78, "word": " 612", "probability": 0.9599609375}, {"start": 208.78, "end": 209.06, "word": " لكن", "probability": 0.7646484375}, {"start": 209.06, "end": 209.24, "word": " هو", "probability": 0.93994140625}, {"start": 209.24, "end": 209.6, "word": " carbon", "probability": 0.9423828125}, {"start": 209.6, "end": 210.04, "word": " 12", "probability": 0.73486328125}, {"start": 210.04, "end": 210.56, "word": " بيقال", "probability": 0.8992919921875}, {"start": 210.56, "end": 211.3, "word": " لو", "probability": 0.74169921875}, {"start": 211.3, "end": 211.54, "word": " كان", "probability": 0.98828125}, {"start": 211.54, "end": 211.98, "word": " بيحتوي", "probability": 0.9539794921875}, {"start": 211.98, "end": 212.28, "word": " على", "probability": 0.8974609375}, {"start": 212.28, "end": 213.38, "word": " سبعة", "probability": 0.72607421875}, {"start": 213.38, "end": 213.94, "word": " نيوترون", "probability": 0.8966796875}, {"start": 213.94, "end": 214.08, "word": " و", "probability": 0.390869140625}, {"start": 214.08, "end": 214.44, "word": " لازم", "probability": 0.9441731770833334}, {"start": 214.44, "end": 214.84, "word": " بالضرورة", "probability": 0.823583984375}, {"start": 214.84, "end": 215.1, "word": " يحتوي", "probability": 0.923828125}, {"start": 215.1, "end": 215.26, "word": " على", "probability": 0.90966796875}, {"start": 215.26, "end": 216.02, "word": " ستة", "probability": 0.9541015625}, {"start": 216.02, "end": 216.7, "word": " protons", "probability": 0.8310546875}, {"start": 216.7, "end": 217.2, "word": " فمعناته", "probability": 0.9734375}, {"start": 217.2, "end": 217.42, "word": " ده", "probability": 0.7379150390625}, {"start": 217.42, "end": 217.74, "word": " carbon", "probability": 0.95458984375}, {"start": 217.74, "end": 218.32, "word": " 13", "probability": 0.7529296875}, {"start": 218.32, "end": 218.68, "word": " سبعة", "probability": 0.8802083333333334}, {"start": 218.68, "end": 218.76, "word": " و", "probability": 0.9208984375}, {"start": 218.76, "end": 219.08, "word": " ستة", "probability": 0.85595703125}, {"start": 219.08, "end": 219.82, "word": " تلتاشر", "probability": 0.87763671875}], "temperature": 1.0}, {"id": 9, "seek": 23658, "start": 220.34, "end": 236.58, "text": "ولو كان بيحتوي على تمانية الـ neutrons و طبعا ستة ال protons فبنسميه carbon 14 وهذه كلها ال carbon 12 و 13 و 14 تعتبر isotopes أو نظائر", "tokens": [12610, 2407, 25961, 4724, 1829, 33753, 45865, 15844, 46811, 7649, 10632, 2423, 39184, 7989, 13270, 4032, 23032, 3555, 3615, 995, 8608, 2655, 3660, 2423, 40270, 6156, 3555, 1863, 38251, 1829, 3224, 5954, 3499, 37037, 24192, 28242, 11296, 2423, 5954, 2272, 4032, 3705, 4032, 3499, 6055, 34268, 26890, 38018, 30545, 34051, 8717, 19913, 16373, 2288], "avg_logprob": -0.21136363473805514, "compression_ratio": 1.3157894736842106, "no_speech_prob": 0.0, "words": [{"start": 220.34, "end": 220.68, "word": "ولو", "probability": 0.81494140625}, {"start": 220.68, "end": 220.86, "word": " كان", "probability": 0.9833984375}, {"start": 220.86, "end": 221.28, "word": " بيحتوي", "probability": 0.9202880859375}, {"start": 221.28, "end": 221.6, "word": " على", "probability": 0.81298828125}, {"start": 221.6, "end": 224.42, "word": " تمانية", "probability": 0.9285481770833334}, {"start": 224.42, "end": 224.78, "word": " الـ", 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"probability": 0.9599609375}, {"start": 260.24, "end": 260.9, "word": " فبداروا", "probability": 0.5733642578125}, {"start": 260.9, "end": 261.86, "word": " البروتونز", "probability": 0.9482421875}, {"start": 261.86, "end": 262.36, "word": " شفنا", "probability": 0.8873697916666666}, {"start": 262.36, "end": 262.68, "word": " إنه", "probability": 0.848388671875}, {"start": 262.68, "end": 263.16, "word": " plus", "probability": 0.96826171875}, {"start": 263.16, "end": 263.68, "word": " one", "probability": 0.955078125}, {"start": 263.68, "end": 264.06, "word": " وطبعا", "probability": 0.94443359375}, {"start": 264.06, "end": 264.24, "word": " هذا", "probability": 0.724609375}, {"start": 264.24, "end": 264.86, "word": " بوحدات", "probability": 0.9453125}], "temperature": 1.0}, {"id": 11, "seek": 29285, "start": 265.51, "end": 292.85, "text": "المفروض إنه مضروبة في شحنة الإلكترون الحقيقية اللي هي 1.602×10¹19 كلهم الآن من الـisotopes و ال abundance تبعها يعني جداش النسبة المقوية إلها في الطبيعة اقدرنا نحسب ال average atomic weight أو atomic mass للعناصر المختلفة للذرات المختلفة فشوفنا الحصة الماضية أيضا", "tokens": [45340, 5172, 32887, 11242, 36145, 3224, 3714, 11242, 32887, 49401, 8978, 13412, 5016, 1863, 3660, 33688, 23275, 2655, 2288, 11536, 21542, 38436, 4587, 10632, 13672, 1829, 39896, 502, 13, 4550, 17, 37550, 3279, 126, 117, 3405, 28242, 16095, 6024, 48506, 9154, 2423, 39184, 271, 310, 30545, 4032, 2423, 23391, 6055, 3555, 3615, 11296, 37495, 22653, 10874, 3215, 33599, 28239, 35457, 3660, 9673, 4587, 2407, 10632, 11933, 1211, 11296, 8978, 41950, 21292, 27884, 1975, 28543, 2288, 8315, 8717, 5016, 35457, 2423, 4274, 22275, 3364, 34051, 22275, 2758, 24976, 3615, 1863, 33546, 2288, 9673, 46456, 46538, 3660, 24976, 8848, 2288, 9307, 9673, 46456, 46538, 3660, 6156, 8592, 38688, 8315, 21542, 9381, 3660, 9673, 46958, 10632, 36632, 11242, 995], "avg_logprob": -0.18135684117292747, "compression_ratio": 1.5867158671586716, "no_speech_prob": 0.0, "words": [{"start": 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في", "probability": 0.96923828125}, {"start": 282.49, "end": 283.03, "word": " الطبيعة", "probability": 0.9864908854166666}, {"start": 283.03, "end": 283.89, "word": " اقدرنا", "probability": 0.8009033203125}, {"start": 283.89, "end": 284.25, "word": " نحسب", "probability": 0.9825846354166666}, {"start": 284.25, "end": 284.41, "word": " ال", "probability": 0.96630859375}, {"start": 284.41, "end": 284.89, "word": " average", "probability": 0.50927734375}, {"start": 284.89, "end": 285.41, "word": " atomic", "probability": 0.8857421875}, {"start": 285.41, "end": 285.87, "word": " weight", "probability": 0.92431640625}, {"start": 285.87, "end": 286.13, "word": " أو", "probability": 0.73388671875}, {"start": 286.13, "end": 286.59, "word": " atomic", "probability": 0.9140625}, {"start": 286.59, "end": 287.35, "word": " mass", "probability": 0.8115234375}, {"start": 287.35, "end": 288.47, "word": " للعناصر", "probability": 0.89814453125}, {"start": 288.47, "end": 289.27, "word": " المختلفة", "probability": 0.996826171875}, {"start": 289.27, "end": 290.17, "word": " للذرات", "probability": 0.9183349609375}, {"start": 290.17, "end": 290.95, "word": " المختلفة", "probability": 0.9974365234375}, {"start": 290.95, "end": 291.69, "word": " فشوفنا", "probability": 0.9310302734375}, {"start": 291.69, "end": 292.05, "word": " الحصة", "probability": 0.9186197916666666}, {"start": 292.05, "end": 292.45, "word": " الماضية", "probability": 0.9962565104166666}, {"start": 292.45, "end": 292.85, "word": " أيضا", "probability": 0.9521484375}], "temperature": 1.0}, {"id": 12, "seek": 31110, "start": 293.44, "end": 311.1, "text": "إن الـ Atomic Weight أو الـ Average Atomic Weight هو عبارة عن summation للـ Isotope Mass معبر عنها بالـ AMU في ال fraction لل Isotope Abundance يعني النسبة المئوية لوجوده في الطبيعة وحلنا هذا المثال فقولنا إنه", "tokens": [28814, 1863, 2423, 39184, 1711, 21401, 44464, 34051, 2423, 39184, 316, 3623, 1711, 21401, 44464, 31439, 6225, 3555, 9640, 3660, 18871, 28811, 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"probability": 0.936767578125}, {"start": 301.08, "end": 301.66, "word": " AMU", "probability": 0.773681640625}, {"start": 301.66, "end": 302.32, "word": " في", "probability": 0.62109375}, {"start": 302.32, "end": 302.4, "word": " ال", "probability": 0.57275390625}, {"start": 302.4, "end": 302.9, "word": " fraction", "probability": 0.77001953125}, {"start": 302.9, "end": 303.86, "word": " لل", "probability": 0.84521484375}, {"start": 303.86, "end": 304.5, "word": " Isotope", "probability": 0.7801920572916666}, {"start": 304.5, "end": 305.22, "word": " Abundance", "probability": 0.9147135416666666}, {"start": 305.22, "end": 305.44, "word": " يعني", "probability": 0.763427734375}, {"start": 305.44, "end": 305.78, "word": " النسبة", "probability": 0.9514973958333334}, {"start": 305.78, "end": 306.32, "word": " المئوية", "probability": 0.83758544921875}, {"start": 306.32, "end": 307.42, "word": " لوجوده", "probability": 0.8748779296875}, {"start": 307.42, "end": 307.64, "word": " في", 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382.58, "end": 382.9, "word": " ف", "probability": 0.72216796875}, {"start": 382.9, "end": 383.22, "word": " point", "probability": 0.53369140625}, {"start": 383.22, "end": 383.7, "word": " nine", "probability": 0.7822265625}, {"start": 383.7, "end": 384.54, "word": " eight", "probability": 0.8681640625}, {"start": 384.54, "end": 385.44, "word": " nine", "probability": 0.927734375}, {"start": 385.44, "end": 385.92, "word": " three", "probability": 0.77783203125}], "temperature": 1.0}, {"id": 16, "seek": 40613, "start": 386.93, "end": 406.13, "text": "مجموع الها الـisotope التاني 13.00335 AMU اللي هو الكربون 13 في النسبة المقوية تبعته ك fraction بيطلع عند 12.01 عشان هيك لما نيجي نقول والله جديش ال atomic weight للكربون اللي موجود في الجدول الدوري بنقول 12.01", "tokens": [2304, 7435, 2304, 45367, 2423, 11296, 2423, 39184, 271, 310, 1114, 16712, 7649, 1829, 3705, 13, 628, 18, 8794, 6475, 52, 13672, 1829, 31439, 33251, 25513, 11536, 3705, 8978, 28239, 35457, 3660, 9673, 4587, 2407, 10632, 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atomic number أعلى بواحد لكن هنلاحظ أنه مثلا كان مشابه في خصائصه لأول عنصر حنطلع تحت أول عنصر ونبدأ من أول و جديد", "tokens": [5016, 35457, 2423, 22275, 1230, 4032, 24793, 7649, 11331, 26108, 3660, 50239, 4032, 24793, 7649, 47525, 8315, 8717, 5016, 995, 12610, 8717, 5016, 9566, 18863, 1863, 33546, 2288, 9673, 2655, 8592, 16758, 3224, 3660, 6055, 33753, 45030, 11242, 11296, 37495, 22653, 45164, 5551, 12984, 1863, 16606, 6055, 2288, 31371, 3555, 8315, 24976, 3615, 1863, 33546, 2288, 11331, 35457, 2423, 22275, 1230, 4032, 36520, 8315, 5296, 3615, 1863, 9381, 2288, 20449, 9957, 39182, 9957, 18863, 1863, 9381, 2288, 13672, 1829, 39182, 3224, 2423, 22275, 1230, 5551, 3615, 23942, 4724, 14407, 24401, 44381, 8032, 1863, 15040, 5016, 19913, 14739, 3224, 50113, 15040, 25961, 37893, 16758, 3224, 8978, 16490, 9381, 16373, 9381, 3224, 5296, 10721, 12610, 18871, 9381, 2288, 11331, 1863, 9566, 1211, 3615, 6055, 33753, 5551, 12610, 18871, 9381, 2288, 4032, 1863, 44510, 10721, 9154, 5551, 12610, 4032, 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احنا بنعيشها لكن ضمن ظروف تانية ممكن انه يتفاعل فهو ليش نقول عنه خامل برضه بالعقل يعني فاحنا ممكن نسميها rare gases ايش يعني؟", "tokens": [3224, 24192, 9673, 7435, 2304, 2407, 27884, 39896, 3714, 7435, 2304, 2407, 27884, 6024, 118, 31377, 9307, 33962, 10943, 37977, 1975, 2407, 8978, 45030, 11242, 13672, 1829, 1975, 5016, 8315, 8717, 39648, 32771, 31377, 9307, 8717, 18513, 25720, 5296, 33456, 3224, 8978, 33251, 32640, 25528, 1975, 5016, 8315, 37495, 22653, 6225, 2304, 2407, 15042, 19446, 19446, 41185, 8592, 6225, 8315, 1975, 8592, 1829, 16490, 10943, 1211, 31439, 16490, 10943, 1211, 48812, 27842, 6024, 116, 32887, 5172, 13672, 1829, 1975, 5016, 8315, 44945, 3615, 1829, 8592, 11296, 44381, 48812, 27842, 1357, 116, 32887, 5172, 6055, 7649, 10632, 3714, 43020, 16472, 3224, 7251, 2655, 5172, 995, 30241, 6156, 3224, 2407, 32239, 8592, 8717, 39648, 18871, 3224, 16490, 10943, 1211, 4724, 43042, 3224, 20666, 3615, 4587, 1211, 37495, 22653, 6156, 39319, 8315, 3714, 43020, 8717, 38251, 1829, 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element لكنه بما أنه أكتر من ذرة فهو جزء لذا هذا molecular element ال O2 ال N2 ال Cl2 Br2 F2 I2 هذه كلها عبارة عن molecular", "tokens": [4587, 1211, 8315, 50113, 15040, 30767, 1829, 2423, 9169, 422, 17, 23758, 19046, 4478, 2423, 422, 39896, 6225, 3555, 9640, 3660, 18871, 2423, 422, 17, 39896, 4478, 44381, 3224, 4724, 15042, 14739, 3224, 5551, 4117, 2655, 2288, 9154, 29910, 25720, 6156, 3224, 2407, 10874, 11622, 38207, 5296, 15730, 23758, 19046, 4478, 2423, 422, 17, 2423, 426, 17, 2423, 2033, 17, 1603, 17, 479, 17, 286, 17, 29538, 28242, 11296, 6225, 3555, 9640, 3660, 18871, 19046], "avg_logprob": -0.1839021318837216, "compression_ratio": 1.5977011494252873, "no_speech_prob": 0.0, "words": [{"start": 2388.03, "end": 2388.61, "word": "قلنا", "probability": 0.7228190104166666}, {"start": 2388.61, "end": 2390.11, "word": " مثلا", "probability": 0.929443359375}, {"start": 2390.11, "end": 2390.59, "word": " زي", "probability": 0.8486328125}, {"start": 2390.59, "end": 2390.91, "word": " ال", 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0.77294921875}, {"start": 2400.81, "end": 2401.19, "word": " molecular", "probability": 0.6123046875}, {"start": 2401.19, "end": 2401.69, "word": " element", "probability": 0.978515625}, {"start": 2401.69, "end": 2402.47, "word": " ال", "probability": 0.90966796875}, {"start": 2402.47, "end": 2403.25, "word": " O2", "probability": 0.97900390625}, {"start": 2403.25, "end": 2403.63, "word": " ال", "probability": 0.85009765625}, {"start": 2403.63, "end": 2404.43, "word": " N2", "probability": 0.955810546875}, {"start": 2404.43, "end": 2405.21, "word": " ال", "probability": 0.939453125}, {"start": 2405.21, "end": 2407.35, "word": " Cl2", "probability": 0.861328125}, {"start": 2407.35, "end": 2408.33, "word": " Br2", "probability": 0.726806640625}, {"start": 2408.33, "end": 2409.51, "word": " F2", "probability": 0.982421875}, {"start": 2409.51, "end": 2410.61, "word": " I2", "probability": 0.984619140625}, {"start": 2410.61, "end": 2410.97, "word": " هذه", "probability": 0.68798828125}, {"start": 2410.97, "end": 2411.31, "word": " كلها", "probability": 0.876708984375}, {"start": 2411.31, "end": 2411.71, "word": " عبارة", "probability": 0.998291015625}, {"start": 2411.71, "end": 2412.05, "word": " عن", "probability": 0.97802734375}, {"start": 2412.05, "end": 2412.83, "word": " molecular", "probability": 0.76611328125}], "temperature": 1.0}, {"id": 102, "seek": 242834, "start": 2413.64, "end": 2428.34, "text": "Elements و ال P4 و ال S8 هذي كلها molecular elements ليه؟ لأنه بتتكون من نوع واحد من الذرات وهي في نفس الوجه اكتر من ذرة، مدام اكتر من ذرة، اذا molecular element", "tokens": [36, 17988, 4032, 2423, 430, 19, 4032, 2423, 318, 23, 8032, 8848, 1829, 28242, 11296, 19046, 4959, 32239, 3224, 22807, 5296, 33456, 3224, 39894, 2655, 30544, 9154, 8717, 45367, 36764, 24401, 9154, 32545, 2288, 9307, 37037, 1829, 8978, 8717, 36178, 2423, 29245, 3224, 1975, 4117, 2655, 2288, 9154, 29910, 25720, 12399, 3714, 3215, 10943, 1975, 4117, 2655, 2288, 9154, 29910, 25720, 12399, 1975, 15730, 19046, 4478], "avg_logprob": -0.2800839596719884, "compression_ratio": 1.53125, "no_speech_prob": 0.0, "words": [{"start": 2413.64, "end": 2414.4, "word": "Elements", "probability": 0.4546661376953125}, {"start": 2414.4, "end": 2414.62, "word": " و", "probability": 0.416259765625}, {"start": 2414.62, "end": 2414.74, "word": " ال", "probability": 0.5595703125}, {"start": 2414.74, "end": 2415.3, "word": " P4", "probability": 0.7958984375}, {"start": 2415.3, "end": 2415.5, "word": " و", "probability": 0.7001953125}, {"start": 2415.5, "end": 2415.62, "word": " ال", "probability": 0.6123046875}, {"start": 2415.62, "end": 2416.16, "word": " S8", "probability": 0.984619140625}, {"start": 2416.16, "end": 2416.88, "word": " هذي", "probability": 0.4905598958333333}, {"start": 2416.88, "end": 2417.1, "word": " كلها", "probability": 0.968017578125}, {"start": 2417.1, "end": 2417.48, "word": " molecular", "probability": 0.457763671875}, {"start": 2417.48, "end": 2418.1, "word": " elements", "probability": 0.85107421875}, {"start": 2418.1, "end": 2418.42, "word": " ليه؟", "probability": 0.7779947916666666}, {"start": 2418.42, "end": 2418.62, "word": " لأنه", "probability": 0.8349609375}, {"start": 2418.62, "end": 2419.16, "word": " بتتكون", "probability": 0.9352213541666666}, {"start": 2419.16, "end": 2419.54, "word": " من", "probability": 0.99609375}, {"start": 2419.54, "end": 2421.3, "word": " نوع", "probability": 0.9931640625}, {"start": 2421.3, "end": 2421.76, "word": " واحد", "probability": 0.989501953125}, {"start": 2421.76, "end": 2421.94, "word": " من", "probability": 0.9921875}, {"start": 2421.94, "end": 2422.34, "word": " الذرات", "probability": 0.94482421875}, {"start": 2422.34, "end": 2422.54, "word": " وهي", "probability": 0.81494140625}, {"start": 2422.54, "end": 2422.6, "word": " في", "probability": 0.9326171875}, {"start": 2422.6, "end": 2422.76, "word": " نفس", "probability": 0.9970703125}, {"start": 2422.76, "end": 2423.02, "word": " الوجه", 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الهالوجينات هي عبارة عن هذا جاز وهذا جاز ال PR2 Liquid في الحقيقة ال I2 يعني ال solid و ال sub-limes يعني بيتبخر بتحول لجاز مباشرة ال hydrogen طبعا برضه molecular element يبقى هيها ال hydrogen", "tokens": [15040, 5016, 19913, 14407, 16472, 3224, 28242, 3714, 7435, 2304, 2407, 27884, 2423, 4386, 33599, 4724, 1829, 38251, 2407, 11296, 2423, 3224, 6027, 29245, 1829, 8315, 2655, 39896, 6225, 3555, 9640, 3660, 18871, 23758, 10874, 31377, 37037, 15730, 10874, 31377, 2423, 11568, 17, 38943, 8978, 21542, 38436, 28671, 2423, 286, 17, 37495, 22653, 2423, 5100, 4032, 2423, 1422, 12, 75, 1532, 37495, 22653, 4724, 36081, 3555, 34740, 39894, 5016, 12610, 5296, 7435, 31377, 3714, 3555, 33599, 25720, 2423, 12697, 23032, 3555, 3615, 995, 4724, 43042, 3224, 19046, 4478, 7251, 3555, 4587, 7578, 39896, 11296, 2423, 12697], "avg_logprob": -0.24017396907216496, "compression_ratio": 1.5387931034482758, "no_speech_prob": 0.0, "words": [{"start": 2430.55, "end": 2431.55, "word": "لاحظوا", "probability": 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{"start": 2443.19, "end": 2443.83, "word": " و", "probability": 0.89501953125}, {"start": 2443.83, "end": 2444.25, "word": " ال", "probability": 0.51171875}, {"start": 2444.25, "end": 2444.41, "word": " sub", "probability": 0.90283203125}, {"start": 2444.41, "end": 2444.73, "word": "-limes", "probability": 0.6092122395833334}, {"start": 2444.73, "end": 2445.03, "word": " يعني", "probability": 0.876220703125}, {"start": 2445.03, "end": 2446.21, "word": " بيتبخر", "probability": 0.905517578125}, {"start": 2446.21, "end": 2446.65, "word": " بتحول", "probability": 0.6868489583333334}, {"start": 2446.65, "end": 2446.97, "word": " لجاز", "probability": 0.83740234375}, {"start": 2446.97, "end": 2447.57, "word": " مباشرة", "probability": 0.9915771484375}, {"start": 2447.57, "end": 2449.21, "word": " ال", "probability": 0.90673828125}, {"start": 2449.21, "end": 2450.61, "word": " hydrogen", "probability": 0.61865234375}, {"start": 2450.61, "end": 2451.29, "word": " طبعا", "probability": 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4032, 23032, 3555, 3615, 995, 12174, 1211, 2655, 23275, 2304, 2423, 430, 19, 4032, 2423, 318, 23, 4724, 43042, 3224, 39894, 3615, 9566, 9957, 1829, 19046, 4959, 8032, 1211, 48812, 2288, 13063, 1829, 16472, 3224, 1975, 15730, 25961, 29910, 25720, 20449, 9957, 3660], "avg_logprob": -0.15897254262006644, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 2456.61, "end": 2456.79, "word": "و", "probability": 0.83544921875}, {"start": 2456.79, "end": 2457.17, "word": " هذه", "probability": 0.27197265625}, {"start": 2457.17, "end": 2458.23, "word": " المجموعة", "probability": 0.8837890625}, {"start": 2458.23, "end": 2458.57, "word": " هيك", "probability": 0.815185546875}, {"start": 2458.57, "end": 2458.75, "word": " هذه", "probability": 0.302978515625}, {"start": 2458.75, "end": 2459.03, "word": " كلها", "probability": 0.925537109375}, {"start": 2459.03, "end": 2459.81, "word": " بتعطيني", "probability": 0.880078125}, {"start": 2459.81, "end": 2461.33, "word": " molecular", "probability": 0.7255859375}, {"start": 2461.33, "end": 2462.41, "word": " elements", "probability": 0.900390625}, {"start": 2462.41, "end": 2462.87, "word": " عادة", "probability": 0.9840494791666666}, {"start": 2462.87, "end": 2462.99, "word": " و", "probability": 0.57763671875}, {"start": 2462.99, "end": 2463.23, "word": " طبعا", "probability": 0.9586181640625}, {"start": 2463.23, "end": 2463.85, "word": " قلتلكم", "probability": 0.90771484375}, {"start": 2463.85, "end": 2464.21, "word": " ال", "probability": 0.8984375}, {"start": 2464.21, "end": 2464.81, "word": " P4", "probability": 0.91162109375}, {"start": 2464.81, "end": 2465.13, "word": " و", "probability": 0.59521484375}, {"start": 2465.13, "end": 2465.43, "word": " ال", "probability": 0.78076171875}, {"start": 2465.43, "end": 2466.69, "word": " S8", "probability": 0.9677734375}, {"start": 2466.69, "end": 2467.57, "word": " برضه", "probability": 0.9671223958333334}, {"start": 2467.57, "end": 2468.15, "word": " بتعطيني", "probability": 0.94794921875}, {"start": 2468.15, "end": 2468.49, "word": " molecular", "probability": 0.82568359375}, {"start": 2468.49, "end": 2470.13, "word": " elements", "probability": 0.92333984375}, {"start": 2470.13, "end": 2474.81, "word": " هل", "probability": 0.96484375}, {"start": 2474.81, "end": 2475.71, "word": " ضروري", "probability": 0.970458984375}, {"start": 2475.71, "end": 2476.63, "word": " انه", "probability": 0.7025146484375}, {"start": 2476.63, "end": 2477.15, "word": " اذا", "probability": 0.901123046875}, {"start": 2477.15, "end": 2477.69, "word": " كان", "probability": 0.99609375}, {"start": 2477.69, "end": 2480.35, "word": " ذرة", "probability": 0.662109375}, {"start": 2480.35, "end": 2481.05, "word": " معينة", "probability": 0.9855143229166666}], "temperature": 1.0}, {"id": 105, "seek": 250798, "start": 2482.18, "end": 2507.98, "text": "بتعطينى او ذرات معينة من نفس النوع بتعطينى molecular element هل ضرورى ان ال molecular elements هذه تكون متشابهة في الخصائص مثلا يعني في عند ال oxygen ممكن يكون O2 بنسميه oxygen و O3 ozone هل خصائصهم متشابه لأنه بيتكونوا من ال oxygen فقط بنقول أبدا أبدا", "tokens": [3555, 2655, 3615, 9566, 9957, 7578, 1975, 2407, 29910, 2288, 9307, 20449, 9957, 3660, 9154, 8717, 36178, 28239, 45367, 39894, 3615, 9566, 9957, 7578, 19046, 4478, 8032, 1211, 48812, 2288, 13063, 7578, 16472, 2423, 19046, 4959, 29538, 6055, 30544, 44650, 8592, 16758, 3224, 3660, 8978, 33962, 9381, 16373, 9381, 50113, 15040, 37495, 22653, 8978, 43242, 2423, 9169, 3714, 43020, 7251, 30544, 422, 17, 44945, 38251, 1829, 3224, 9169, 4032, 422, 18, 46769, 8032, 1211, 16490, 9381, 16373, 9381, 16095, 44650, 8592, 16758, 3224, 5296, 33456, 3224, 4724, 36081, 30544, 14407, 9154, 2423, 9169, 6156, 47432, 44945, 39648, 5551, 3555, 28259, 5551, 3555, 28259], "avg_logprob": -0.16346153444968736, "compression_ratio": 1.7304347826086957, "no_speech_prob": 0.0, "words": [{"start": 2482.18, "end": 2483.1, "word": "بتعطينى", "probability": 0.7883707682291666}, 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0.98681640625}, {"start": 2496.2, "end": 2496.34, "word": " ال", "probability": 0.9150390625}, {"start": 2496.34, "end": 2496.64, "word": " oxygen", "probability": 0.7578125}, {"start": 2496.64, "end": 2496.9, "word": " ممكن", "probability": 0.953857421875}, {"start": 2496.9, "end": 2497.1, "word": " يكون", "probability": 0.861572265625}, {"start": 2497.1, "end": 2497.56, "word": " O2", "probability": 0.7261962890625}, {"start": 2497.56, "end": 2498.22, "word": " بنسميه", "probability": 0.9058837890625}, {"start": 2498.22, "end": 2498.72, "word": " oxygen", "probability": 0.76220703125}, {"start": 2498.72, "end": 2499.54, "word": " و", "probability": 0.4609375}, {"start": 2499.54, "end": 2500.0, "word": " O3", "probability": 0.879638671875}, {"start": 2500.0, "end": 2500.56, "word": " ozone", "probability": 0.3154296875}, {"start": 2500.56, "end": 2501.72, "word": " هل", "probability": 0.91943359375}, {"start": 2501.72, "end": 2502.46, "word": " خصائصهم", "probability": 0.9916015625}, 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على طبيعة الذرات وهي نفس النوع لكن طبيعة بتربطها بتعطيني خصائص مختلفة للغاية فبنلاحظ أن الـ Oxygen ممتاز جدا، بنتنفسه، مقدرش نعيش من غيره، ضروري للنبات والحيوان والحياة بشكل عام", "tokens": [45340, 10859, 31747, 11703, 3555, 16490, 9381, 16373, 9381, 3224, 4386, 5551, 5172, 2407, 7649, 4386, 37495, 22653, 2423, 39184, 15582, 16490, 9381, 16373, 9381, 3224, 39894, 2655, 30543, 5172, 15844, 23032, 21292, 27884, 32545, 2288, 9307, 37037, 1829, 8717, 36178, 28239, 45367, 44381, 23032, 21292, 27884, 39894, 25513, 9566, 11296, 39894, 3615, 9566, 9957, 1829, 16490, 9381, 16373, 9381, 3714, 46456, 46538, 3660, 24976, 17082, 995, 10632, 6156, 3555, 1863, 15040, 5016, 19913, 14739, 2423, 39184, 16489, 8647, 3714, 2304, 2655, 31377, 10874, 28259, 12399, 44945, 2655, 1863, 36178, 3224, 12399, 3714, 28543, 2288, 8592, 8717, 3615, 1829, 8592, 9154, 32771, 13546, 3224, 12399, 48812, 2288, 13063, 1829, 24976, 1863, 3555, 9307, 16070, 5016, 1829, 2407, 7649, 16070, 5016, 25528, 3660, 4724, 8592, 28820, 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S2 في عندي بس عنصر molecular element بتكون من عنصر .. ذرتين من ال sulfur و S8 بتكون من تمانية من ال sulfur بيقول هذا عبارة عن Allotropes وهذا نفس الكلام ال O2 و ال O3 عبارة عن Allotropes يبقى ال Allotropes نفس نوع الذرات لكن different molecules نفس نوع الذرات لكن different", "tokens": [39237, 10943, 22807, 37495, 22653, 50113, 15040, 318, 17, 4032, 318, 23, 4724, 1829, 39648, 16070, 43761, 8032, 3215, 12610, 3660, 1057, 310, 1513, 279, 318, 17, 8978, 18871, 16254, 4724, 3794, 18871, 9381, 2288, 19046, 4478, 39894, 30544, 9154, 18871, 9381, 2288, 4386, 29910, 43500, 9957, 9154, 2423, 33831, 4032, 318, 23, 39894, 30544, 9154, 46811, 7649, 10632, 9154, 2423, 33831, 4724, 1829, 39648, 23758, 6225, 3555, 9640, 3660, 18871, 1057, 310, 1513, 279, 37037, 15730, 8717, 36178, 2423, 28820, 10943, 2423, 422, 17, 4032, 2423, 422, 18, 6225, 3555, 9640, 3660, 18871, 1057, 310, 1513, 279, 7251, 3555, 4587, 7578, 2423, 1057, 310, 1513, 279, 8717, 36178, 8717, 45367, 32545, 2288, 9307, 44381, 819, 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ال molecular formula ليه؟ لأنه بتتبسطش الاتنين و الواحد بتتبسطش أبسط من هيك", "tokens": [7435, 47302, 11622, 25062, 38251, 3660, 20328, 13546, 23097, 8032, 995, 11778, 1829, 31886, 8513, 9673, 10632, 389, 17, 46, 8032, 995, 11778, 1829, 19046, 8513, 23032, 3555, 2423, 31886, 8513, 39894, 9566, 1211, 3615, 15844, 11933, 1829, 8592, 18863, 10943, 1211, 37893, 2655, 31747, 49374, 16095, 36764, 24401, 11778, 1211, 2655, 30767, 1829, 3714, 10632, 389, 17, 46, 2423, 31886, 8513, 8032, 7649, 30767, 1829, 2423, 19046, 8513, 32239, 3224, 22807, 5296, 33456, 3224, 39894, 2655, 3555, 3794, 9566, 8592, 2423, 9307, 1863, 9957, 4032, 2423, 14407, 24401, 39894, 2655, 3555, 3794, 9566, 8592, 5551, 3555, 3794, 9566, 9154, 39896, 4117], "avg_logprob": -0.2806432009900658, "compression_ratio": 1.8269230769230769, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2832.92, "end": 2833.42, "word": "جايز", "probability": 0.5411376953125}, {"start": 2833.42, "end": 2834.06, "word": " القسمة", 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بتعبر تعبير صحيح عن عدد الذرات الموجودة من كل نوع من أنواع الذرات عدد الذرات الموجودة في الجزائع من كل نوع من أنواع الذرات هيا في عندى ذرتيل كربون أربعة هيدروجين هذه molecular formula هيك المركب بيحتوي كل مركب لو مسكنها واحد واحد كل واحد في حاليك بيحتوي على C2H4 لكن ال empirical formula الأولية اللي هي بنجسم على العامل المشترك", "tokens": [5172, 41185, 43242, 7578, 19046, 8513, 39894, 3615, 3555, 2288, 37279, 3555, 13546, 20328, 5016, 1829, 5016, 18871, 6225, 3215, 3215, 32545, 2288, 9307, 9673, 29245, 23328, 3660, 9154, 28242, 8717, 45367, 9154, 14739, 14407, 3615, 32545, 2288, 9307, 6225, 3215, 3215, 32545, 2288, 9307, 9673, 29245, 23328, 3660, 8978, 25724, 11622, 16373, 3615, 9154, 28242, 8717, 45367, 9154, 14739, 14407, 3615, 32545, 2288, 9307, 8032, 25528, 8978, 43242, 7578, 29910, 2288, 31371, 1211, 9122, 25513, 11536, 5551, 25513, 27884, 8032, 25708, 2288, 29245, 9957, 29538, 19046, 8513, 39896, 4117, 9673, 31747, 3555, 4724, 1829, 33753, 45865, 28242, 3714, 31747, 3555, 45164, 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في حالة زي الميه ال empirical formula هي ال ال ال ال molecular formula هي ال empirical formula طب ال CO2 ال CO2 هذي molecular formula carbon dioxide تانيكسيل كربون طب ايش ال empirical formula اللي له؟", "tokens": [5172, 3555, 2655, 3615, 9566, 9957, 1829, 5995, 1975, 2655, 1863, 9957, 8032, 8848, 1829, 31886, 8513, 4032, 30767, 1829, 19446, 12174, 1211, 8315, 50113, 15040, 8978, 11331, 6027, 3660, 30767, 1829, 9673, 1829, 3224, 2423, 31886, 8513, 39896, 2423, 2423, 2423, 2423, 19046, 8513, 39896, 2423, 31886, 8513, 23032, 3555, 2423, 3002, 17, 2423, 3002, 17, 8032, 8848, 1829, 19046, 8513, 5954, 19590, 6055, 7649, 1829, 4117, 3794, 26895, 9122, 25513, 11536, 23032, 3555, 1975, 1829, 8592, 2423, 31886, 8513, 13672, 1829, 46740, 22807], "avg_logprob": -0.30523255467414856, "compression_ratio": 1.8526315789473684, "no_speech_prob": 0.0, "words": [{"start": 2936.13, "end": 2936.87, "word": "فبتعطيني", "probability": 0.6565290178571429}, {"start": 2936.87, "end": 2937.39, "word": " CH", 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مافيش تتبسطش اكتر من هيك طيب هنشوفه بعد شوية مثال لجلوكوز C6 H12 O6 هى الملوك ده ال formula CH2O أه سهل جدا سهل جدا طيب", "tokens": [1863, 36178, 11296, 5296, 33456, 19446, 41185, 8592, 6055, 2655, 3555, 3794, 9566, 8592, 1975, 4117, 2655, 2288, 9154, 39896, 4117, 23032, 1829, 3555, 8032, 1863, 8592, 38688, 3224, 39182, 13412, 2407, 10632, 50113, 6027, 5296, 7435, 1211, 2407, 4117, 2407, 11622, 383, 21, 389, 4762, 422, 21, 8032, 7578, 9673, 1211, 2407, 4117, 11778, 3224, 2423, 8513, 5995, 17, 46, 5551, 3224, 8608, 3224, 1211, 10874, 28259, 8608, 3224, 1211, 10874, 28259, 23032, 1829, 3555], "avg_logprob": -0.26278410329447166, "compression_ratio": 1.356687898089172, "no_speech_prob": 0.0, "words": [{"start": 2962.64, "end": 2963.3, "word": "نفسها", "probability": 0.85546875}, {"start": 2963.3, "end": 2963.58, "word": " لأن", "probability": 0.657470703125}, {"start": 2963.58, "end": 2963.96, "word": " مافيش", "probability": 0.7010091145833334}, {"start": 2963.96, "end": 2964.96, "word": 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بتعطيني بس ال empirical formula لكن في تجارب أخرى بتعمل علاقة بين ال empirical formula و ال molecular formula فبستخدم هذه العلاقة عشان أقدر أوصل من ال empirical ل", "tokens": [5172, 7649, 995, 45030, 9957, 2423, 31886, 8513, 4032, 4724, 25957, 1211, 6055, 7435, 9640, 3555, 5551, 34740, 7578, 39894, 9778, 20292, 8978, 11203, 995, 28671, 49374, 2423, 31886, 4032, 2423, 19046, 6156, 27842, 18863, 15040, 28671, 29538, 4724, 28543, 2288, 34051, 36520, 5296, 19046, 8513, 7251, 3555, 4587, 7578, 8978, 18871, 16254, 23032, 2288, 4587, 3714, 2304, 2655, 31377, 3660, 5296, 2655, 3615, 9957, 11296, 34051, 9122, 12984, 13546, 9154, 41950, 2288, 4587, 33251, 32640, 10632, 39894, 3615, 9566, 9957, 1829, 4724, 3794, 2423, 31886, 8513, 44381, 8978, 6055, 7435, 9640, 3555, 5551, 34740, 7578, 39894, 25957, 1211, 11203, 995, 28671, 49374, 2423, 31886, 8513, 4032, 2423, 19046, 8513, 6156, 3555, 14851, 9778, 40448, 29538, 18863, 15040, 28671, 6225, 8592, 7649, 5551, 28543, 2288, 34051, 36520, 9154, 2423, 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"end": 4155.31, "text": "قلنا جداش الـ 34 تسعة و سبعين هذا متعادل طب لما يكون سيلينيام اتنين سالب اذا بدي يكون عندي هنا ستة و تلاتين ليش لأن هن في عندي اربعة و تلاتين الكترون و كان متعادل حطيت عليه كمان هذه بتبقى طبعا اربعة و تلاتين ال atomic number عدد البروتونات", "tokens": [4587, 1211, 8315, 10874, 3215, 33599, 2423, 39184, 12790, 6055, 3794, 27884, 4032, 8608, 3555, 3615, 9957, 23758, 44650, 3615, 18513, 1211, 23032, 3555, 5296, 15042, 7251, 30544, 8608, 26895, 9957, 1829, 10943, 1975, 2655, 1863, 9957, 8608, 6027, 3555, 1975, 15730, 4724, 16254, 7251, 30544, 43242, 1829, 34105, 8608, 2655, 3660, 4032, 6055, 1211, 9307, 9957, 32239, 8592, 5296, 33456, 8032, 1863, 8978, 43242, 1829, 1975, 25513, 27884, 4032, 6055, 1211, 9307, 9957, 2423, 4117, 2655, 2288, 11536, 4032, 25961, 44650, 3615, 18513, 1211, 11331, 9566, 36081, 47356, 9122, 2304, 7649, 29538, 39894, 3555, 4587, 7578, 23032, 3555, 3615, 995, 1975, 25513, 27884, 4032, 6055, 1211, 9307, 9957, 2423, 22275, 1230, 6225, 3215, 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{"start": 4139.87, "end": 4140.05, "word": " لما", "probability": 0.91845703125}, {"start": 4140.05, "end": 4140.39, "word": " يكون", "probability": 0.935302734375}, {"start": 4140.39, "end": 4140.91, "word": " سيلينيام", "probability": 0.665771484375}, {"start": 4140.91, "end": 4141.75, "word": " اتنين", "probability": 0.87744140625}, {"start": 4141.75, "end": 4143.03, "word": " سالب", "probability": 0.857421875}, {"start": 4143.03, "end": 4143.25, "word": " اذا", "probability": 0.718017578125}, {"start": 4143.25, "end": 4143.53, "word": " بدي", "probability": 0.6009521484375}, {"start": 4143.53, "end": 4143.83, "word": " يكون", "probability": 0.705322265625}, {"start": 4143.83, "end": 4144.17, "word": " عندي", "probability": 0.5400390625}, {"start": 4144.17, "end": 4144.47, "word": " هنا", "probability": 0.91748046875}, {"start": 4144.47, "end": 4145.29, "word": " ستة", "probability": 0.9129231770833334}, {"start": 4145.29, "end": 4145.37, "word": " و", "probability": 0.53515625}, 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{"start": 4149.53, "end": 4150.07, "word": " متعادل", "probability": 0.9705810546875}, {"start": 4150.07, "end": 4150.55, "word": " حطيت", "probability": 0.7639973958333334}, {"start": 4150.55, "end": 4150.73, "word": " عليه", "probability": 0.96826171875}, {"start": 4150.73, "end": 4151.13, "word": " كمان", "probability": 0.9817708333333334}, {"start": 4151.13, "end": 4152.03, "word": " هذه", "probability": 0.720703125}, {"start": 4152.03, "end": 4152.31, "word": " بتبقى", "probability": 0.7689208984375}, {"start": 4152.31, "end": 4152.69, "word": " طبعا", "probability": 0.92236328125}, {"start": 4152.69, "end": 4152.97, "word": " اربعة", "probability": 0.91357421875}, {"start": 4152.97, "end": 4153.07, "word": " و", "probability": 0.97607421875}, {"start": 4153.07, "end": 4153.33, "word": " تلاتين", "probability": 0.986328125}, {"start": 4153.33, "end": 4153.45, "word": " ال", "probability": 0.31591796875}, {"start": 4153.45, "end": 4153.67, "word": " atomic", "probability": 0.68310546875}, {"start": 4153.67, "end": 4154.03, "word": " number", "probability": 0.9833984375}, {"start": 4154.03, "end": 4154.57, "word": " عدد", "probability": 0.9259440104166666}, {"start": 4154.57, "end": 4155.31, "word": " البروتونات", "probability": 0.8027750651041666}], "temperature": 1.0}, {"id": 176, "seek": 416362, "start": 4156.06, "end": 4163.62, "text": "لكن اتنين سالب معناته بيصير ستة وتلاتين إلكترون وهذا طبعا زي ما هي تسعة وسبعين", "tokens": [1211, 19452, 1975, 2655, 1863, 9957, 8608, 6027, 3555, 20449, 8315, 47395, 4724, 1829, 9381, 13546, 8608, 2655, 3660, 34683, 1211, 9307, 9957, 11933, 23275, 2655, 2288, 11536, 37037, 15730, 23032, 3555, 3615, 995, 30767, 1829, 19446, 39896, 6055, 3794, 27884, 4032, 35457, 3615, 9957], "avg_logprob": -0.2102581460190856, "compression_ratio": 1.4343434343434343, "no_speech_prob": 0.0, "words": [{"start": 4156.06, "end": 4156.72, "word": "لكن", "probability": 0.7294921875}, {"start": 4156.72, "end": 4157.64, "word": " اتنين", "probability": 0.7977294921875}, {"start": 4157.64, "end": 4158.04, "word": " سالب", "probability": 0.9073893229166666}, {"start": 4158.04, "end": 4158.36, "word": " معناته", "probability": 0.6676839192708334}, {"start": 4158.36, "end": 4158.66, "word": " بيصير", "probability": 0.8619384765625}, {"start": 4158.66, "end": 4159.0, "word": " ستة", "probability": 0.9345703125}, {"start": 4159.0, "end": 4159.44, "word": " وتلاتين", "probability": 0.860107421875}, {"start": 4159.44, "end": 4160.08, "word": " إلكترون", "probability": 0.8106201171875}, {"start": 4160.08, "end": 4160.44, "word": " وهذا", "probability": 0.717041015625}, {"start": 4160.44, "end": 4161.22, "word": " طبعا", "probability": 0.974609375}, {"start": 4161.22, "end": 4161.54, "word": " زي", "probability": 0.91552734375}, {"start": 4161.54, "end": 4161.6, "word": " ما", "probability": 0.9375}, {"start": 4161.6, "end": 4161.8, "word": " هي", "probability": 0.8642578125}, {"start": 4161.8, "end": 4162.36, "word": " تسعة", 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"avg_logprob": -0.20950941116579117, "compression_ratio": 1.7391304347826086, "no_speech_prob": 0.0, "words": [{"start": 4180.89, "end": 4181.77, "word": "خلّيني", "probability": 0.752734375}, {"start": 4181.77, "end": 4182.17, "word": " اتطلع", "probability": 0.70732421875}, {"start": 4182.17, "end": 4182.45, "word": " على", "probability": 0.73828125}, {"start": 4182.45, "end": 4182.85, "word": " كيف", "probability": 0.973876953125}, {"start": 4182.85, "end": 4183.23, "word": " الأيونات", "probability": 0.800146484375}, {"start": 4183.23, "end": 4183.69, "word": " تتكون", "probability": 0.8154296875}, {"start": 4183.69, "end": 4184.35, "word": " كيف", "probability": 0.56195068359375}, {"start": 4184.35, "end": 4185.69, "word": " الأيونات", "probability": 0.9009765625}, {"start": 4185.69, "end": 4187.77, "word": " بتتكون", "probability": 0.916015625}, {"start": 4187.77, "end": 4188.91, "word": " فانا", "probability": 0.5535481770833334}, {"start": 4188.91, "end": 4189.27, "word": " اتطلع", "probability": 0.9341796875}, {"start": 4189.27, "end": 4189.49, "word": " على", "probability": 0.90380859375}, {"start": 4189.49, "end": 4190.11, "word": " picturing", "probability": 0.607177734375}, {"start": 4190.11, "end": 4190.53, "word": " ionic", "probability": 0.9033203125}, {"start": 4190.53, "end": 4191.13, "word": " charges", "probability": 0.93701171875}, {"start": 4191.13, "end": 4194.09, "word": " مثلا", "probability": 0.93408203125}, {"start": 4194.09, "end": 4194.97, "word": " كل", "probability": 0.734375}, {"start": 4194.97, "end": 4195.45, "word": " هذا", "probability": 0.84716796875}, {"start": 4195.45, "end": 4195.97, "word": " اشتقاق", "probability": 0.8531901041666666}, {"start": 4195.97, "end": 4196.11, "word": " من", "probability": 0.98876953125}, {"start": 4196.11, "end": 4196.43, "word": " الجد", "probability": 0.8955078125}, {"start": 4196.43, "end": 4196.57, "word": " من", "probability": 0.77197265625}, {"start": 4196.57, "end": 4196.81, "word": " 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178, "seek": 421238, "start": 4201.5, "end": 4212.38, "text": "أيش هو الجدول الدوري؟ وبنتاش نحفظ عادة الجدول الدوري اللي بتاخدوه في الامتحان أو بنكتبلكم المعلومات اللي لازمكم كتابة فبقول predict the charge expected", "tokens": [10721, 1829, 8592, 31439, 25724, 3215, 12610, 32748, 13063, 1829, 22807, 46599, 29399, 33599, 8717, 5016, 5172, 19913, 6225, 18513, 3660, 25724, 3215, 12610, 32748, 13063, 1829, 13672, 1829, 39894, 47283, 3215, 2407, 3224, 8978, 2423, 10943, 2655, 5016, 7649, 34051, 44945, 4117, 2655, 3555, 23275, 2304, 9673, 30241, 20498, 9307, 13672, 1829, 5296, 31377, 2304, 24793, 9122, 2655, 16758, 3660, 6156, 3555, 39648, 6069, 264, 4602, 5176], "avg_logprob": -0.2814764423646789, "compression_ratio": 1.5644171779141105, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 4201.5, "end": 4201.88, "word": "أيش", "probability": 0.5649312337239584}, {"start": 4201.88, "end": 4201.98, "word": " هو", "probability": 0.8369140625}, {"start": 4201.98, "end": 4202.34, 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4205.84, "end": 4206.56, "word": " بنكتبلكم", "probability": 0.933349609375}, {"start": 4206.56, "end": 4207.2, "word": " المعلومات", "probability": 0.9600830078125}, {"start": 4207.2, "end": 4207.8, "word": " اللي", "probability": 0.96240234375}, {"start": 4207.8, "end": 4208.4, "word": " لازمكم", "probability": 0.79132080078125}, {"start": 4208.4, "end": 4208.96, "word": " كتابة", "probability": 0.9884033203125}, {"start": 4208.96, "end": 4209.7, "word": " فبقول", "probability": 0.7272135416666666}, {"start": 4209.7, "end": 4210.46, "word": " predict", "probability": 0.232666015625}, {"start": 4210.46, "end": 4211.06, "word": " the", "probability": 0.888671875}, {"start": 4211.06, "end": 4211.66, "word": " charge", "probability": 0.9716796875}, {"start": 4211.66, "end": 4212.38, "word": " expected", "probability": 0.93798828125}], "temperature": 1.0}, {"id": 179, "seek": 423774, "start": 4213.58, "end": 4237.74, "text": "for the most stable ion of barium and the most stable ion of oxygen ايش اكتر ايون مستقر للباريوم و ايش اكتر ايون مستقر للأكسجين لو بدنا نجاوب على هذا السؤال بشكل عام بنقول هو ايون اللي بيعطيني تركيب النوبلجاز القريب منه", "tokens": [2994, 264, 881, 8351, 17437, 295, 2159, 2197, 293, 264, 881, 8351, 17437, 295, 9169, 1975, 1829, 8592, 1975, 4117, 2655, 2288, 1975, 1829, 11536, 3714, 14851, 4587, 2288, 24976, 3555, 9640, 1829, 20498, 4032, 1975, 1829, 8592, 1975, 4117, 2655, 2288, 1975, 1829, 11536, 3714, 14851, 4587, 2288, 24976, 10721, 4117, 3794, 7435, 9957, 45164, 47525, 8315, 8717, 7435, 995, 37746, 15844, 23758, 21136, 33604, 6027, 4724, 8592, 28820, 6225, 10943, 44945, 39648, 31439, 1975, 1829, 11536, 13672, 1829, 4724, 40228, 9566, 1829, 22653, 6055, 31747, 1829, 3555, 28239, 2407, 36150, 7435, 31377, 25062, 16572, 3555, 9154, 3224], "avg_logprob": -0.1596875050663948, "compression_ratio": 1.758974358974359, "no_speech_prob": 0.0, "words": [{"start": 4213.58, "end": 4213.9, "word": "for", "probability": 0.36181640625}, {"start": 4213.9, 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4612.52, "end": 4613.6, "word": " اذا", "probability": 0.79443359375}, {"start": 4613.6, "end": 4613.86, "word": " الله", "probability": 0.9345703125}, {"start": 4613.86, "end": 4614.3, "word": " راد", "probability": 0.5689697265625}, {"start": 4614.3, "end": 4615.26, "word": " بنكتفي", "probability": 0.82598876953125}, {"start": 4615.26, "end": 4615.72, "word": " اليوم", "probability": 0.96630859375}, {"start": 4615.72, "end": 4615.9, "word": " و", "probability": 0.52978515625}, {"start": 4615.9, "end": 4616.32, "word": " الحصة", "probability": 0.9599609375}, {"start": 4616.32, "end": 4616.84, "word": " الجاية", "probability": 0.9051106770833334}, {"start": 4616.84, "end": 4618.6, "word": " بنكملها", "probability": 0.9166259765625}], "temperature": 1.0}, {"id": 198, "seek": 462010, "start": 4619.23, "end": 4620.11, "text": "يعطيكم العافية", "tokens": [40228, 9566, 1829, 24793, 18863, 31845, 10632], "avg_logprob": -0.1239013671875, "compression_ratio": 0.7714285714285715, "no_speech_prob": 0.0, "words": [{"start": 4619.23, "end": 4619.71, "word": "يعطيكم", "probability": 0.8748779296875}, {"start": 4619.71, "end": 4620.11, "word": " العافية", "probability": 0.9495442708333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 4620.4225, "duration_after_vad": 4445.286249999997}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/YJXI0wt-r6g_postprocess.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/YJXI0wt-r6g_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a42f05ddae5fc2f1e04b22d65401c9eb0c7700cb
--- /dev/null
+++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/YJXI0wt-r6g_postprocess.srt
@@ -0,0 +1,3772 @@
+1
+00:00:20,770 --> 00:00:23,730
+بسم الله الرحمن الرحيم دقيقة الله راضي اليوم نتكلم
+
+2
+00:00:23,730 --> 00:00:26,410
+عن آخر محاضرة في هذا ال chapter بتحدث عن ال
+
+3
+00:00:26,410 --> 00:00:29,670
+elements وال molecules وال ions وجفنا الحصة
+
+4
+00:00:29,670 --> 00:00:36,290
+الماضية عند ال ionic compounds كيف ممكن في البداية
+
+5
+00:00:36,290 --> 00:00:40,370
+نعرف الأيون إذا كان عليه شحنة موجبة أو شحنة سالبة
+
+6
+00:00:40,890 --> 00:00:44,670
+طيب أكم شحنة موجبة تبقى أكم شحنة سالبة؟ شفنا إنه
+
+7
+00:00:44,670 --> 00:00:47,750
+هذا كلام سهولة بنقدر نحصل عليه من الجدول الدوري
+
+8
+00:00:47,750 --> 00:00:53,190
+فشفنا إنه مثلا عناصر المجموعة الأولى اللي هي
+
+9
+00:00:53,190 --> 00:00:56,510
+الـalkali metals دائما عليها شحنة موجبة لأنها
+
+10
+00:00:56,510 --> 00:00:59,810
+بتروح على الغاز الخامل اللي جابلها تركيب الغاز
+
+11
+00:00:59,810 --> 00:01:04,160
+الخامل اللي جابلها وبالتالي تفقد إلكترونالمجموعة
+
+12
+00:01:04,160 --> 00:01:07,300
+التانية اللي هي الـ alkaline earth metals كانت
+
+13
+00:01:07,300 --> 00:01:11,280
+تفقد 2 إلكترون علشان توصل لتركيب الغاز الخامل على
+
+14
+00:01:11,280 --> 00:01:16,060
+سبيل المثال أيضا مجموعة الـ halogens المجموعة
+
+15
+00:01:16,060 --> 00:01:21,480
+السابعة من الـ representative elements هذه
+
+16
+00:01:21,480 --> 00:01:25,220
+المجموعة بتكتسب إلكترون علشان توصل لتركيب الغاز
+
+17
+00:01:25,220 --> 00:01:28,880
+الخامل جانبها على طول المجموعة السادسة اللي جابلها
+
+18
+00:01:28,880 --> 00:01:34,130
+تكتسب 2 إلكترونعشان توصل برضه لتركيبة الغاز الخامل
+
+19
+00:01:34,130 --> 00:01:41,610
+اللي على يمينها ايضا فبالتالي يعني بسهولة بنقدر
+
+20
+00:01:41,610 --> 00:01:49,040
+نعرف ال ion او ال atom لأي elementهل هتاخد شحنة
+
+21
+00:01:49,040 --> 00:01:51,940
+موجبة او شحنة سالبة جثة من الجدول الدوري لجسمين
+
+22
+00:01:51,940 --> 00:01:56,820
+تقريبا يعني جسم metals دايما بيكون يعني ايوناته
+
+23
+00:01:56,820 --> 00:02:02,080
+موجبة و جسم non metals ايوناته سالبة ال metals وان
+
+24
+00:02:02,080 --> 00:02:06,680
+ال metalloids او العناصر اللي خاليا نقول متوسطة
+
+25
+00:02:06,680 --> 00:02:10,730
+خصائصها بين ال metals و ال non metalsهذه تفصل
+
+26
+00:02:10,730 --> 00:02:13,430
+الـmetals عن الـnon-metals فمعظم العلاقات اللي
+
+27
+00:02:13,430 --> 00:02:17,370
+عندي متالز وقليل منها non-metals برضه اليوم
+
+28
+00:02:17,370 --> 00:02:23,030
+هنشوفها مرة تانية نتكلم عن الـionic compounds ايش
+
+29
+00:02:23,030 --> 00:02:29,490
+بيحصل اذا كان ايون موجبالتقب ايون سالب طبعا احنا
+
+30
+00:02:29,490 --> 00:02:32,750
+بنقول انه راح يتكون رابطة، الرابطة هذه رابطة
+
+31
+00:02:32,750 --> 00:02:36,930
+ايونية نتجة عن ال electrostatic interaction او
+
+32
+00:02:36,930 --> 00:02:41,890
+attraction ما بين الشحنة الموجبة والشحنة السالبة
+
+33
+00:02:43,580 --> 00:02:48,400
+وفي الحقيقة يعني انتقال الالكترونات من ال .. الـ
+
+34
+00:02:48,400 --> 00:02:52,060
+atom عشان تصبح ايون او من ايه سواء ايون موجب او
+
+35
+00:02:52,060 --> 00:02:55,160
+ايون سالف هذا بعطيها activity كبيرة خالص لأنه
+
+36
+00:02:55,160 --> 00:02:57,920
+نتيجة مباشرة لل activity انه اه والله الايون
+
+37
+00:02:57,920 --> 00:03:02,160
+الموجب راح يتحد بالايون السالف فهذا يعني بعطيه نوع
+
+38
+00:03:02,160 --> 00:03:09,320
+منال activity فمثلا عند ال sodium plus ممكن يتفاعل
+
+39
+00:03:09,320 --> 00:03:13,920
+معه او على طول ينجذب الى اكلورين سالب او اي في
+
+40
+00:03:13,920 --> 00:03:19,840
+الحقيقة انايون او اي ايون سالب بنقوله انايون اي
+
+41
+00:03:19,840 --> 00:03:23,480
+انايون عشان يكون المركب المركب في النهاية خلينا
+
+42
+00:03:23,480 --> 00:03:28,060
+نقول بده يكون متعادلبدي يكون متعادل ما يميز
+
+43
+00:03:28,060 --> 00:03:34,660
+المراكبات الايونية انه دائما ال formula لإلها هي
+
+44
+00:03:34,660 --> 00:03:39,560
+عبارة عن empirical formula يعني مثلا بتكون NACL
+
+45
+00:03:39,560 --> 00:03:45,700
+بنفعش اقول NA2CL2 او NA3CL3 لأ دائما بعبر عن
+
+46
+00:03:45,700 --> 00:03:50,220
+المراكبات الايونية بال empirical formula مش ال
+
+47
+00:03:50,220 --> 00:03:53,180
+molecular formula لأن في الحقيقة المراكبات
+
+48
+00:03:53,180 --> 00:03:58,470
+الايونية ماهياش moleculesيعني ماقدرش أخد جزء واحد
+
+49
+00:03:58,470 --> 00:04:03,170
+من ال NACL أو جزء واحد من مثلا ال Sodium Carbonate
+
+50
+00:04:03,170 --> 00:04:07,270
+لأ هذه عبارة عن crystal lattice موجود فيها كل
+
+51
+00:04:07,270 --> 00:04:11,250
+الايونات الموجبة والايونات السالبة في crystal
+
+52
+00:04:11,250 --> 00:04:15,910
+تركيبة معينة لكن ال net charge إليها صفر مافيش
+
+53
+00:04:15,910 --> 00:04:19,730
+عنده charge وبالتالي دائما ال empirical formula
+
+54
+00:04:19,730 --> 00:04:23,770
+بتعبر عن ال ionic compounds
+
+55
+00:04:26,590 --> 00:04:33,810
+دائما ال ionic bond بتكون ما بين حاجتين metal ion
+
+56
+00:04:33,810 --> 00:04:37,830
+وهذا دائما بياخد شحنة مجباه و nonmetal بياخد شحنة
+
+57
+00:04:37,830 --> 00:04:41,490
+سالبه ال metal ion على يسار الجدول الدوري و ال
+
+58
+00:04:41,490 --> 00:04:48,770
+nonmetal على يمين الجدول الدوري طبعا يعني مش معناه
+
+59
+00:04:48,770 --> 00:04:52,250
+كلام انه دائما المركبات اللي بتكون انها مركبات
+
+60
+00:04:52,250 --> 00:04:58,980
+ايونية بالعكس ممكن جدا انهTwo non-metals يتفاعلوا
+
+61
+00:04:58,980 --> 00:05:01,840
+مع بعض وبالتالي بحصل على مركب لكن المركب اللي بحصل
+
+62
+00:05:01,840 --> 00:05:06,880
+ليه مش ايوني مدام non-metals فبحصل على molecular
+
+63
+00:05:06,880 --> 00:05:12,740
+compound مولكيول زي مثلا الميه H2O زي السكر زي
+
+64
+00:05:12,740 --> 00:05:16,700
+المركبات العضوية كلها كويسة عبارة عن مولكيول ليه؟
+
+65
+00:05:16,700 --> 00:05:25,760
+لأنهعناصر من المجموعة السابعة والسادسة والخامسة
+
+66
+00:05:25,760 --> 00:05:30,680
+خلانا نقول جزء مهم منها والربعة يعني الكاربون على
+
+67
+00:05:30,680 --> 00:05:34,320
+سبيل المثال هذه العناصر ممكن تتحد مع بعضها البعض
+
+68
+00:05:34,320 --> 00:05:38,340
+وتعطيني مركبات مادام non-metals اتحدت مع بعضها
+
+69
+00:05:38,340 --> 00:05:44,560
+البعض وعطتني مركب الأصل أن هذا مركب هو مركبجزئي مش
+
+70
+00:05:44,560 --> 00:05:48,760
+ايوني عشان يكون مركب ايوني لازم يكون فيه عندى
+
+71
+00:05:48,760 --> 00:05:55,180
+metal و non-metal metal ايون عليه شحنة موجبة non
+
+72
+00:05:55,180 --> 00:05:57,260
+-metal عليه شحنة سالبة
+
+73
+00:06:00,820 --> 00:06:06,840
+بجمعنا الكلام لو اتطلعنا هنا هذه العناصر اللي
+
+74
+00:06:06,840 --> 00:06:13,220
+تقريبا باللون بين العناصر ككل هذه العناصر هي عبارة
+
+75
+00:06:13,220 --> 00:06:18,760
+عن متالويديعني خصائصها بين خصائص ال metals و ال
+
+76
+00:06:18,760 --> 00:06:21,920
+non metals مش كتير بنحكي عنها هان بستفيدوا كتير
+
+77
+00:06:21,920 --> 00:06:25,200
+منها في ال semiconductors بستفيدوا كتير منها في
+
+78
+00:06:25,200 --> 00:06:28,900
+ايه؟ في صناعات ال semiconductors معظم صناعات ال
+
+79
+00:06:28,900 --> 00:06:33,080
+semiconductors يعني بتتركز باستخدام هذه العناصر
+
+80
+00:06:33,080 --> 00:06:37,610
+بشكل او باخرلكن لو طلعنا على الـ non-metals فهي هي
+
+81
+00:06:37,610 --> 00:06:41,190
+الـ non-metals يعني الهالوجينات وبعدين هي
+
+82
+00:06:41,190 --> 00:06:44,970
+السيلينيوم والسلفر والأكسجين والنيتروجين الفوسفروس
+
+83
+00:06:44,970 --> 00:06:50,910
+والكاربون قلال جداً قلال بينما الـ metals هي عبارة
+
+84
+00:06:50,910 --> 00:06:54,390
+عن أيه؟ عن معظم الجدول الدوري قلنا إن الـ group
+
+85
+00:06:54,390 --> 00:07:00,060
+الأولىفي عندي شحنة موجبة واحدة لجروب التانية
+
+86
+00:07:00,060 --> 00:07:04,260
+شحنتين موجبتين الهيدروجين هذا محطوط هنا بس عشان
+
+87
+00:07:04,260 --> 00:07:07,240
+نقول هذا واحد لكن في الحقيقة الهيدروجين ممكن ياخد
+
+88
+00:07:07,240 --> 00:07:11,900
+شحنة موجبة او شحنة سالبة شحنة موجبة بنقوله
+
+89
+00:07:11,900 --> 00:07:16,960
+هيدرونيام او يعني بنقوله هيدروجين ايون كويس اما
+
+90
+00:07:16,960 --> 00:07:21,880
+الشحنة السالبة بنقوله هيدرايدهيدرايد هنشوفه يمر
+
+91
+00:07:21,880 --> 00:07:25,820
+معنا بعد شوية في المركبات الايونة بيشكل مركب ايوني
+
+92
+00:07:25,820 --> 00:07:30,240
+مع أي مثل ايون اذا كان كان على صورة هيدرايد بينما
+
+93
+00:07:30,240 --> 00:07:34,240
+العناصر اللي بين ال representative elements هذه من
+
+94
+00:07:34,240 --> 00:07:40,400
+هالهال المجموعات هذه من 3A ل7A و 1A و 2A هدول
+
+95
+00:07:40,400 --> 00:07:43,900
+representative elements او ال elements يعني
+
+96
+00:07:43,900 --> 00:07:49,640
+الأساسية المكونة للجدول الدوري لكن في بينهاأه اللي
+
+97
+00:07:49,640 --> 00:07:51,960
+هي ال transition elements ال transition elements
+
+98
+00:07:51,960 --> 00:07:55,440
+ما يميزها انه ممكن تاخد و مش بس ال transition
+
+99
+00:07:55,440 --> 00:07:58,480
+elements في الحقيقة بعض ال non transition elements
+
+100
+00:07:58,480 --> 00:08:02,840
+ممكن تاخد تكافؤ اكتر من واحد يعني عدد الشحنات اللي
+
+101
+00:08:02,840 --> 00:08:07,340
+فيها مش حسب عدد او موضعها ك group يعني هان مثلا
+
+102
+00:08:07,340 --> 00:08:11,720
+واحد اه عليه شحنة موجبة هان اتنين عليه شحنة شحنتين
+
+103
+00:08:11,720 --> 00:08:15,800
+موجبتين هان ال aluminum عليه تلاتة غالبا هدول
+
+104
+00:08:15,800 --> 00:08:20,400
+غالبا عليهم تلاتة غالبا بس مش دائمامش دائماً كويس
+
+105
+00:08:20,400 --> 00:08:25,840
+هدول عليها شحنة سالبة واحدة ماشي شحنتين سالبتين
+
+106
+00:08:25,840 --> 00:08:30,120
+تلت شحنات سالبة خلاني أقول أربع موجبة أو سالبة
+
+107
+00:08:30,120 --> 00:08:34,740
+يعني الله أعلم لإنه بين بين لكن ال .. بشكل أساسي
+
+108
+00:08:34,740 --> 00:08:39,140
+ال transition elements لأ ممكن يكون في عندي أكتر
+
+109
+00:08:39,140 --> 00:08:43,760
+من شحنة ل ال metal ion موجبة طبعا موجبة لأنها
+
+110
+00:08:43,760 --> 00:08:48,750
+metalsكويس لكن مش شرط ان يكون في عنده فقط يعني
+
+111
+00:08:48,750 --> 00:08:51,890
+مثلا هان يكون في عنده تلاتة هان اربعة هان خمسة هان
+
+112
+00:08:51,890 --> 00:08:55,270
+ستة هان سبعة لأ مصيرش هيك ممكن يكون حاجة زي
+
+113
+00:08:55,270 --> 00:09:00,710
+المنجانيز شحنتين موجبتين او تلاتة او اربعة او خمسة
+
+114
+00:09:00,710 --> 00:09:06,080
+او ستة او سبعةعلشان هيك بنعبر عن عدد الشحنات
+
+115
+00:09:06,080 --> 00:09:13,520
+الموجبة في العناصر اللي قد تأخذ أكتر من شحنة موجبة
+
+116
+00:09:13,520 --> 00:09:16,460
+أو عدد معين من شحنات الموجبة، بنعبر عنها رغم
+
+117
+00:09:16,460 --> 00:09:20,120
+الـNumerals يعني اللي هي واحد بنقوله Iالاتنين
+
+118
+00:09:20,120 --> 00:09:24,460
+بنقولها I و I جانبها تلاتة تلاتة I أربعة أربعة I
+
+119
+00:09:24,460 --> 00:09:29,500
+مثلا خمسة V و جابلها I و هكذا هذه بنحطها بين دوسين
+
+120
+00:09:29,500 --> 00:09:35,760
+عشان نعرف ايه عدد ال charges او ال valency للذرع
+
+121
+00:09:35,760 --> 00:09:39,340
+من ال transition elements و اي ذرع اخر احنا شكين
+
+122
+00:09:39,340 --> 00:09:44,490
+بانه والله ممكن يكون لها اكتر من valencyكويس هذا
+
+123
+00:09:44,490 --> 00:09:48,890
+كلام هذا مهم لأنه بعد شوية هنستخدمه مهم كتير يبقى
+
+124
+00:09:48,890 --> 00:09:52,550
+هنا المجموعة الأولى plus one المجموعة التانية plus
+
+125
+00:09:52,550 --> 00:09:56,690
+two المجموعة الأخيرة الجابن الأخيرة سالب سالب
+
+126
+00:09:56,690 --> 00:10:00,170
+واحدها سالب اتنين كويس نذكر ان نيتروجين وفسفر
+
+127
+00:10:00,170 --> 00:10:04,370
+السالب تلاتة اذا كان كونه مركبات ال carbon عادة
+
+128
+00:10:04,370 --> 00:10:13,460
+مابنحكيش عنه كتيرممكن يكون يعني plus or minus
+
+129
+00:10:13,460 --> 00:10:17,980
+لكن عادة هو يكون مراكبات تساهمية تعرفوا كلكم الـ
+
+130
+00:10:17,980 --> 00:10:22,120
+hydrocarbons كربون، هيدروجين، أكسوجين، في بعض
+
+131
+00:10:22,120 --> 00:10:25,600
+الأحيان نيتروجين، في بعض الأحيان عناصر أخرى، بس مش
+
+132
+00:10:25,600 --> 00:10:29,740
+metal ions بس هذه مراكبات تساهمية الـ carbon يعني
+
+133
+00:10:29,740 --> 00:10:36,260
+جزء مهم منها عشان هي تسمى hydrocarbons فمثلاعنا
+
+134
+00:10:36,260 --> 00:10:40,680
+الـ Sodium شايفين ذرة كبيرة في التلاتة اس و احنا
+
+135
+00:10:40,680 --> 00:10:42,440
+مش ضروري نعرف هذا الكلام لأنه في هذا المساك ده
+
+136
+00:10:42,440 --> 00:10:46,660
+لأسف نتعرضش لتركيب الإلكتروني بتفصيل يعني فهو في
+
+137
+00:10:46,660 --> 00:10:52,000
+إلكترون في المدار الخارجي الإلكترون بنتقل لchlor
+
+138
+00:10:52,350 --> 00:10:56,490
+الكلورين الكلورين 17 عشان ياخد تركيبة الارجون اللى
+
+139
+00:10:56,490 --> 00:11:00,510
+جانبه بده يصير 18 فبده إلكترون عشان إن الصوديوم
+
+140
+00:11:00,510 --> 00:11:02,510
+ياخد تركيبة الغاز الخامل اللى جابه اللى هو النيون
+
+141
+00:11:02,510 --> 00:11:06,030
+العشرة بده يفقد إلكترون فالصوديوم بيعطي إلكترون
+
+142
+00:11:06,030 --> 00:11:09,790
+للكلورين الكلورين لحظه كبر لإن الصوديوم صار موجود
+
+143
+00:11:09,790 --> 00:11:14,070
+في المدار فعمل تنافر مع الإلكترون التاني فكبر شوية
+
+144
+00:11:14,070 --> 00:11:19,680
+تسع بينما الصوديوم فقدالألكترون وبالتالي انكمش وفي
+
+145
+00:11:19,680 --> 00:11:23,640
+الواقع انكمش كتير لأنه فقد مدار كامل لأن الالكترون
+
+146
+00:11:23,640 --> 00:11:27,500
+كان موجود في المدار لحاله فصار في عندي Sodium Plus
+
+147
+00:11:27,500 --> 00:11:31,580
+وChlorine سالب بتجمعه مش بس واحد مع واحد لأ
+
+148
+00:11:31,580 --> 00:11:35,240
+بيعطيني crystal structure تمام زي اللي قدامي هان
+
+149
+00:11:35,740 --> 00:11:39,380
+الـ Empirical Formula لها بتعبّر عن الـ formula
+
+150
+00:11:39,380 --> 00:11:44,980
+للـ NaCl واللي هي NaCl ممنوع أن احط Na2 Cl2 أو Na3
+
+151
+00:11:44,980 --> 00:11:48,720
+Cl3 لأنه زي ما قلت الـ Empirical Formula راح تعبّر
+
+152
+00:11:48,720 --> 00:11:54,840
+عن تركيبة ال .. او ال chemical composition لل
+
+153
+00:11:54,840 --> 00:11:58,020
+Ionic compound ممنوع استخدم molecular formula لأنه
+
+154
+00:11:58,020 --> 00:12:04,100
+ال Ionic compounds ماهياش molecules اكويس هيكطيب
+
+155
+00:12:04,100 --> 00:12:10,070
+نفس ال ..الطريقة الآن بنقدر نقول حاجة مدام عرفت
+
+156
+00:12:10,070 --> 00:12:13,490
+انا انه المجموعة الاولى plus one المجموعة التانية
+
+157
+00:12:13,490 --> 00:12:16,730
+plus two المجموعة او one plus المجموعة التانية two
+
+158
+00:12:16,730 --> 00:12:20,010
+plus المجموعة الأخيرة سالب واحد ال nitrogen قلنا
+
+159
+00:12:20,010 --> 00:12:24,350
+عنه توي قبل شوية سالب تلاتة المجنيزيام في المجموعة
+
+160
+00:12:24,350 --> 00:12:28,410
+التانية موجب اتنين اذا بقدر اقول انا المجنيزيام
+
+161
+00:12:28,410 --> 00:12:35,380
+كتايون كتايون يعني ايون موجب ال nitrogenان ايون
+
+162
+00:12:35,380 --> 00:12:40,140
+يعني ايون سالب بنسميه احنا نيتريد هنشوفه بعد شوية
+
+163
+00:12:40,140 --> 00:12:43,320
+نيتريد نيتروجين بنسميه نيتريد و هنقولكم ليش ايش ال
+
+164
+00:12:43,320 --> 00:12:47,060
+convention ورا التسمية فهدول على طول بيكونوا مركب
+
+165
+00:12:47,060 --> 00:12:50,300
+ايوني لإن واحد موجب و واحد سالب بهمناش ايش هو
+
+166
+00:12:50,300 --> 00:12:52,840
+الموجب و ايش هو السالب مادام عندى موجب سالب خلاص
+
+167
+00:12:52,840 --> 00:12:57,460
+بتكون عندى مركب ايوني طيب هن الشحنة بتختلفوا
+
+168
+00:12:57,460 --> 00:13:03,000
+المركب الايوني دائما ايش ماله؟لأ نانت شارج لأنه
+
+169
+00:13:03,000 --> 00:13:06,080
+مُركّب مافيش عليه شحنة فالشحنة الكلية إله صفر
+
+170
+00:13:06,080 --> 00:13:12,420
+فياشبن عمال قال آه بننزل هذهان و بننزل هذهان و
+
+171
+00:13:12,420 --> 00:13:16,640
+هذهان بتبادلوا ال إيه؟ بتبادلوا الشحنات وبالتالي
+
+172
+00:13:16,640 --> 00:13:21,080
+بيكون فيه عندنا تلت أيونات من المجنيزيوم مع أيونين
+
+173
+00:13:21,080 --> 00:13:24,080
+من الصوديوم تلت أيونات من المجنيزيوم معنات تلاتة
+
+174
+00:13:24,080 --> 00:13:29,390
+فيهيموجة باثنين فيهيموجة بستةأيونين من الـ .. من
+
+175
+00:13:29,390 --> 00:13:33,310
+الـ Nitrogen الـ Nitrite اتنين في سالب تلاتة معناه
+
+176
+00:13:33,310 --> 00:13:37,530
+تسالب ستة اه موجة بستة سالب ستة اذا مركب متعدل هيك
+
+177
+00:13:37,530 --> 00:13:42,450
+بنكون المركبات يبقى شحنة كل أيون بتروح للاخر كعدد
+
+178
+00:13:42,450 --> 00:13:47,410
+درّات وانتهينا هيك بيكون المركب ايه non charged
+
+179
+00:13:47,410 --> 00:13:50,110
+مافيش عليه اي شحنة
+
+180
+00:13:52,480 --> 00:13:55,680
+بنشوف بعض الأمثلة، لو قال لي مثلا، which of these
+
+181
+00:13:55,680 --> 00:13:59,120
+compounds would you expect to be ionic؟ أنه واحد
+
+182
+00:13:59,120 --> 00:14:02,620
+من هدول ممكن نتوقع أنه يكون ionic، بنعرف، إيش
+
+183
+00:14:02,620 --> 00:14:06,300
+المراكب عشان يكون ionic؟ إيش لازم يكون إشي أساسي
+
+184
+00:14:06,300 --> 00:14:11,880
+فيه؟ قال، بتكون من metal و non-metal، يعني واحد من
+
+185
+00:14:11,880 --> 00:14:16,680
+المجموعات الأخيرة وواحد من المجموعات المتقدمة، فلو
+
+186
+00:14:16,680 --> 00:14:21,870
+أجينا له N2Oوالله الـ Nitrogen بالاستعانة بالجدول
+
+187
+00:14:21,870 --> 00:14:24,510
+الدوري مافي مشكلة هاي الـ Nitrogen وهي الأكسجين
+
+188
+00:14:24,510 --> 00:14:29,230
+وين الـTen موجودين؟ آه Non-metals بينفع يعطون أيه؟
+
+189
+00:14:29,230 --> 00:14:32,990
+Ionic compound؟ لأ مابينفع يعطون Ionic compound طب
+
+190
+00:14:32,990 --> 00:14:37,450
+نيجي نتطلع على Na2O الصوديوم موجود في المجموعة
+
+191
+00:14:37,450 --> 00:14:41,070
+الأولى الأكسجين في المجموعة السادسة الأكسجين Non
+
+192
+00:14:41,070 --> 00:14:48,650
+-metal الصوديوم Metal آه إذا هايها الأكسجينO عليه
+
+193
+00:14:48,650 --> 00:14:54,370
+اتنين سالب لأنه nonmetal طب وش ال Sodium عليه موجب
+
+194
+00:14:54,370 --> 00:15:01,290
+واحد اذا لما بدى كون مركب بيصير NA ه معايا NA
+
+195
+00:15:01,290 --> 00:15:07,410
+اتنين O بكتبش واحد انا اسمها Sodium Oxide Sodium
+
+196
+00:15:07,410 --> 00:15:11,810
+Oxide طب نيجي لأ اللي بعدها Calcium Chloride
+
+197
+00:15:12,850 --> 00:15:15,990
+الكالسيوم من المجموعة التانية الكلورايد من
+
+198
+00:15:15,990 --> 00:15:19,430
+المجموعة القبل الأخيرة زي قبل النوبل جازيز حلو
+
+199
+00:15:19,430 --> 00:15:25,170
+كتير الكلورايد هيها مفهومة طب وهي الكلسيوم اه هذه
+
+200
+00:15:25,170 --> 00:15:30,490
+باتي جهان وهذه باتي جهان اذا الكلسيوم CL2 هذا مركب
+
+201
+00:15:30,490 --> 00:15:34,370
+ايه مركب ايوني طبعا مركب ايوني لانه بتكون من متل
+
+202
+00:15:34,370 --> 00:15:39,270
+كالسيوم ونون متل الكلورايد ال SF4 السلفر في
+
+203
+00:15:39,270 --> 00:15:41,210
+المجموعة السادسة
+
+204
+00:15:42,690 --> 00:15:47,750
+هذه الـ Sulphur وهذه الـ Oxygen لأ الـ F بده هذه
+
+205
+00:15:47,750 --> 00:15:51,170
+الـ F الاتنين ايش مالهم؟ Non metals لأنهم مش
+
+206
+00:15:51,170 --> 00:15:54,950
+مركّفات ايونية ونفس الـ K هذا مركّب تساهمي نحكيش
+
+207
+00:15:54,950 --> 00:16:00,990
+عنه SF4 هذا مركّب تساهمي molecular compound طبعا
+
+208
+00:16:00,990 --> 00:16:04,010
+احنا بهمناش كتير التسميات هل جيت لأن مش هناخد
+
+209
+00:16:04,010 --> 00:16:07,010
+المركّبات التساهمية برضه بالتفصيل بس بهمنا انه
+
+210
+00:16:07,010 --> 00:16:12,620
+نقول والله ان هذا مركّب جزائي مش مركّب ايونيإذا
+
+211
+00:16:12,620 --> 00:16:17,260
+اللي عندي أنا بسهولة بقدر أقول إنه أه والله هذا
+
+212
+00:16:17,260 --> 00:16:21,360
+مركب مش أيوني، هذا مركب أيوني، هذا مركب أيوني، هذا
+
+213
+00:16:21,360 --> 00:16:25,960
+مركب جزئي حلو؟ طب لو جينا نطلعلها، which of these
+
+214
+00:16:25,960 --> 00:16:31,830
+compounds are molecular؟بنطلع سي بي أربعة بي ار
+
+215
+00:16:31,830 --> 00:16:35,930
+أربعة البروميد في المجموعة الأفهاد الهالوجين في
+
+216
+00:16:35,930 --> 00:16:39,410
+المجموعة الأخيرة قبل النوبل جازيز والكاربون نان
+
+217
+00:16:39,410 --> 00:16:46,430
+متال اذا نان متل مع نان متل هذا عبارة عنموليكولار
+
+218
+00:16:46,430 --> 00:16:51,630
+كمباود يبقى هذا موليكولار كمباود FES الايرون موجود
+
+219
+00:16:51,630 --> 00:16:54,910
+متل كلنا نعرف ان الايرون متل هو من ال transition
+
+220
+00:16:54,910 --> 00:16:59,710
+متل عموما الايرون متل يبقى مجموعة من ضمن المتل طب
+
+221
+00:16:59,710 --> 00:17:05,490
+والسلفر non-metal إذا هذا مركبايوني هذا مش
+
+222
+00:17:05,490 --> 00:17:08,990
+موليكولار اذا لأ هذا مش مش موليكولار طب نيجي نطلع
+
+223
+00:17:08,990 --> 00:17:14,570
+على ال P4O6 هاي الفوسفورس حلو نزل كلهم اكم من اكم
+
+224
+00:17:14,570 --> 00:17:19,810
+من element نذكرهم حلوين كتير P و O اتنين ايه
+
+225
+00:17:19,810 --> 00:17:24,830
+اشمالهم nonmetal هذا مركب ايه موليكولر موليكولر
+
+226
+00:17:24,830 --> 00:17:31,650
+طيب PPF2 نيجي نطلع وين الرصاص ايش مركب الرصاص متل
+
+227
+00:17:31,650 --> 00:17:36,400
+ولا nonmetalميتال الرصاص .. الرصاص متال .. كل ال
+
+228
+00:17:36,400 --> 00:17:40,640
+.. يعني هي خصائص الـ metals بتوصل للكهربا .. ده
+
+229
+00:17:40,640 --> 00:17:46,220
+اكتبه بسهولة لو كان شكلها .. بتوصل لحرارة .. فهذا
+
+230
+00:17:46,220 --> 00:17:49,480
+معروف الرصاص من ضمنها .. لكن برضه خلينا نطلع على
+
+231
+00:17:49,480 --> 00:17:52,940
+الجدول الدوري .. هاي الرصاص من ضمن ايه؟ من ضمن ال
+
+232
+00:17:52,940 --> 00:17:56,640
+metals .. لأن هاي ال metals كلها ده metalsهي الـ
+
+233
+00:17:56,640 --> 00:18:01,060
+non-metals بعد الـ what؟ بعد الـ metalloids
+
+234
+00:18:01,060 --> 00:18:08,780
+وبالتالي ال P P إيش معاها قلناها F هاي ال F ها ال
+
+235
+00:18:08,780 --> 00:18:13,240
+F non-metal وال P P إيه؟ آه وال P P متل إذا هذا
+
+236
+00:18:13,240 --> 00:18:17,120
+مركّب أيوني يبقى عارفنا إيش من المركّبات ممكن يكون
+
+237
+00:18:17,120 --> 00:18:21,280
+مركّب أيوني وإيش من المركّبات ممكن يكون مركّب جزئي
+
+238
+00:18:23,570 --> 00:18:26,870
+ممكن نستخدم الـ Ionic Charge عشان نكتب الـ
+
+239
+00:18:26,870 --> 00:18:30,910
+Empirical Formula زي ما حكيت معاكم و كمان بنأكد
+
+240
+00:18:30,910 --> 00:18:34,510
+على هذا الكلام مثلا الومنام مع كلورايد هاي الومنام
+
+241
+00:18:34,510 --> 00:18:39,210
+تلاتة وهاي كلورايد بدي اكتب المركب اللي بتكون من
+
+242
+00:18:39,210 --> 00:18:44,870
+ال الومنام مع الكلورايد ايش بده يكون ALCL
+
+243
+00:18:44,870 --> 00:18:49,970
+تلعب تصريح طب اللي بعده الومنام مع ال O2 الومنام
+
+244
+00:18:49,970 --> 00:18:57,220
+وهاي O2 سالب هذهبتنزل او ها دي بتنزل اذا aluminum
+
+245
+00:18:57,220 --> 00:19:03,440
+اتنين او تلاتة aluminum اكسيد اسمه طيب magnesium
+
+246
+00:19:03,440 --> 00:19:09,050
+هانتبه شويةمع Nitrate الـ Nitrate كلها عليها شحنة
+
+247
+00:19:09,050 --> 00:19:13,850
+سالبة هذا اسمه Molecular Ion Molecular يعني لأنه
+
+248
+00:19:13,850 --> 00:19:17,570
+مش عبارة عن درّة واحدة لأ عبارة عن درتين N O
+
+249
+00:19:17,570 --> 00:19:22,790
+فبنقوله Molecular Ion Anion Molecular Ion هو Anion
+
+250
+00:19:22,790 --> 00:19:26,170
+فبنقول هذه الشحنة شحنة على مين؟ مش على الأكسيد
+
+251
+00:19:26,170 --> 00:19:30,670
+شحنة على كل هذا فهذه الشحنة بتنزل وهذا هي بتنزل
+
+252
+00:19:30,670 --> 00:19:36,050
+يبقى Magnesiumن أو تلاتة هي اتنين حطيناها وين كلها
+
+253
+00:19:36,050 --> 00:19:39,930
+في جوس لأن كلها عليها شحنة سالبة واحدة بدنا تسير
+
+254
+00:19:39,930 --> 00:19:43,510
+تنتين عشان المجنيزة تنتين بنحط تنين في جوس بنحطها
+
+255
+00:19:43,510 --> 00:19:48,630
+ماشي يا جماعة يبجي احنا بنقدر نكتب ايش هي ال
+
+256
+00:19:48,630 --> 00:19:53,130
+empirical formula للمركب الايوني اذا كان عارفنا ال
+
+257
+00:19:53,130 --> 00:19:57,010
+charges اللي على الايونات سواء كانت الايونات mono
+
+258
+00:19:57,010 --> 00:20:02,930
+atomic تتكون منظرّة واحدة أو كانت polyatomic او
+
+259
+00:20:02,930 --> 00:20:06,730
+molecular ion زي ال nitrate زي الصلفات الاخرى
+
+260
+00:20:06,730 --> 00:20:15,450
+ونتطلع على كمان مثال بقول
+
+261
+00:20:15,450 --> 00:20:18,430
+write the empirical formula for the compound
+
+262
+00:20:18,430 --> 00:20:24,330
+formed by a sodium and phosphate هاي ال sodium وهي
+
+263
+00:20:24,330 --> 00:20:29,870
+ال phosphateلاحظوا ان كل PO فرقها مدام فيه شحنة
+
+264
+00:20:29,870 --> 00:20:33,750
+على كلها فهذه عبارة عن شحنة على الكل يبقى معنا
+
+265
+00:20:33,750 --> 00:20:39,750
+الكلام بدي أدخلها دهان و أدخلها دهان واحد يعني هاي
+
+266
+00:20:39,750 --> 00:20:45,230
+NA إيش بتصير؟ NA تلاتة PO أربعة صوت ينفذ سويت سهل
+
+267
+00:20:45,230 --> 00:20:48,570
+كتير يعني حاجة بسيطة زي هذه بتجيكي في الامتحان بس
+
+268
+00:20:48,570 --> 00:20:55,020
+تكتبيها بتاخد عليها درجة سهل خالصسوديو انفسفيت ايش
+
+269
+00:20:55,020 --> 00:21:01,500
+بده زينك او صلفيت هاي زينك two plus او صلفيت اتنين
+
+270
+00:21:01,500 --> 00:21:07,500
+سالب بدي اعمل المركب الصيغة الايونية لهذا المركب
+
+271
+00:21:07,500 --> 00:21:12,690
+فبقول هاد اتنين وهاد اتنين يعني زينك ايهبدا اقول
+
+272
+00:21:12,690 --> 00:21:17,730
+زنك اتنين و صلفيت اتنين غلط ممنوع ليه؟ لأنها دائما
+
+273
+00:21:17,730 --> 00:21:22,510
+empirical يبجى لأ بدي اقول بس زنك صلفيت بدون اي
+
+274
+00:21:22,510 --> 00:21:26,630
+coefficients ماشي يا جماعة يبجى هذه زنك صلفيت
+
+275
+00:21:26,630 --> 00:21:32,790
+بيقول ليه؟ اخر واحدة اللي هو ال iron مع الكربونيت
+
+276
+00:21:32,790 --> 00:21:41,370
+نطلع عليها برضه بنفس المنطق ironتلاتة و carbonate
+
+277
+00:21:41,370 --> 00:21:44,990
+اتنين سالب انا بدي الاتنين هذي بتنزل والتلاتة هذي
+
+278
+00:21:44,990 --> 00:21:51,910
+بتنزل اذا ال iron اتنين وهي ال carbonate تلاتة بس
+
+279
+00:21:51,910 --> 00:21:54,890
+لاحظوا لازم نحط ال carbonate في ايه؟ في ghost عشان
+
+280
+00:21:54,890 --> 00:21:58,750
+نقول تلاتة في اتنين سالب ستة سالب اتنين في تلاتة
+
+281
+00:21:58,750 --> 00:22:04,410
+موجب ستة موجب اه متعادل لازم الصيغة الايونية تكون
+
+282
+00:22:04,410 --> 00:22:08,070
+متعادلة طيب
+
+283
+00:22:11,640 --> 00:22:15,080
+الان بننتقل للموضوع الأساسي في هذه المحاضرة
+
+284
+00:22:15,080 --> 00:22:19,220
+الموضوع الأساسي في هذه المحاضرة كيف ممكن نسمي
+
+285
+00:22:19,220 --> 00:22:25,440
+المراكبات المختلفة اللي دائما بنشوفها في الحياة
+
+286
+00:22:25,440 --> 00:22:30,080
+العملية كيف ممكن نسميها؟ بقول في الحقيقة يعني ممكن
+
+287
+00:22:30,080 --> 00:22:32,180
+قسمة المراكبات لقسمين
+
+288
+00:22:34,810 --> 00:22:39,350
+عموما يعني فكرة أو مصطلح التسمية بنقوله chemical
+
+289
+00:22:39,350 --> 00:22:43,830
+nomenclature chemical nomenclature التسمية وتعتبر
+
+290
+00:22:43,830 --> 00:22:48,630
+من يعني بديهيات الكيميا الاشي الأساسي في الكيميا
+
+291
+00:22:48,630 --> 00:22:52,090
+يعني اللي ماعرفش يسمي المراكبات في عنده مشكلة
+
+292
+00:22:52,090 --> 00:22:55,770
+أساسية عشان هيك دائما تسمية المراكبات لازم يجيلنا
+
+293
+00:22:55,770 --> 00:22:58,950
+منها حاجة في الامتحان النصفي والامتحان النهائي
+
+294
+00:22:58,950 --> 00:23:04,350
+دائما ليه؟ لأنه تعتبر زي بفرداتالكيميا تسمية زي
+
+295
+00:23:04,350 --> 00:23:08,430
+المفردات أو زي الحروف الأبجدية لازم نعرف نسمي
+
+296
+00:23:08,430 --> 00:23:14,030
+المراكبات بشكل صحيح فانا في عندي في الحقيقة يعني
+
+297
+00:23:14,030 --> 00:23:18,530
+يمكن يعني تقديرات خمسين مليون مراكب كيميائي معروف
+
+298
+00:23:18,530 --> 00:23:23,930
+حاليا لو كل مراكب كيميائي بدي أسميه زي أسماءنا اسم
+
+299
+00:23:23,930 --> 00:23:28,330
+يعني عام يعني من الأسماء الشائعة كويس كيف بدي
+
+300
+00:23:28,330 --> 00:23:34,000
+أتذكر أنا خمسين مليون اسم؟لا انا احسن لما ان اعطي
+
+301
+00:23:34,000 --> 00:23:40,640
+لكل مُركّب اسم معين غير مبني على يعني طبيعته
+
+302
+00:23:40,640 --> 00:23:44,040
+وطبيعة تركيبه الكيميائي بس انه والله ها دي اسم
+
+303
+00:23:44,040 --> 00:23:46,700
+فلانة وها دي اسم فلانة وها دي اسم فلانة هيك واحفظ
+
+304
+00:23:46,700 --> 00:23:51,190
+اسامي خمسين مليون مثلالا بدنا نحاول ناخد بعض
+
+305
+00:23:51,190 --> 00:23:55,170
+القوانين البسيطة اللى بتساعدنا على التسمية بعض
+
+306
+00:23:55,170 --> 00:23:58,130
+القوانين البسيطة اللى ممكن انها تساعدنا على
+
+307
+00:23:58,130 --> 00:24:03,710
+التسمية مع العلم انه بعض المركبات الشائعة زى مثلا
+
+308
+00:24:03,710 --> 00:24:12,310
+الميه water H2O هذا تسمية شائعة زى الأمونيا تسمية
+
+309
+00:24:12,310 --> 00:24:17,930
+شائعة in H3 نحكيش عنهايعني مراكبات قليلة إلها
+
+310
+00:24:17,930 --> 00:24:21,130
+تسمية شائعة، ماشي الحال، لكن إحنا بنتكلم عن تسمية
+
+311
+00:24:21,130 --> 00:24:25,710
+المراكبات ككل، كليتها، وبعدين ممكن إحنا لو حبينا
+
+312
+00:24:25,710 --> 00:24:28,730
+إنه نسمي هذه المراكبات تسمية علمية، ممكن نسميها
+
+313
+00:24:28,730 --> 00:24:32,330
+تسمية علمية، لكن إحنا راضين بالتسمية الشائعة
+
+314
+00:24:32,330 --> 00:24:36,480
+بالنسبالها، لأنه عارفينها واتقالفنا معاهاطول
+
+315
+00:24:36,480 --> 00:24:41,760
+حياتنا يعني وبالتالي مافيش عنا مشكلة في التسميات
+
+316
+00:24:41,760 --> 00:24:46,140
+للمراكبات الشائعة زي على سبيل المثال الميه
+
+317
+00:24:46,140 --> 00:24:54,700
+والأمونيا لأنه من زمان احنا بنعرفهم هيك طبعا ممكن
+
+318
+00:24:54,700 --> 00:24:59,340
+نجسم المراكبات لمراكبات عضوية وهذه بدناش نتكلم عن
+
+319
+00:24:59,340 --> 00:25:03,510
+التسمية تبعتهامُركّبات عضوية هي المُركّبات اللي
+
+320
+00:25:03,510 --> 00:25:08,130
+بتحتوي على الكاربون والهيدروجين وفي أحيان كتيرة
+
+321
+00:25:08,130 --> 00:25:13,010
+الأكسجين وفي بعض الأحيان نيتروجين وفي أحيان يعني
+
+322
+00:25:13,010 --> 00:25:18,090
+قليلة يعني عناصر أخرى لكن مش metal ions لكن
+
+323
+00:25:18,090 --> 00:25:21,790
+تركيبها الجوهر كاربون وهيدروجين لازم يكون موجود
+
+324
+00:25:21,790 --> 00:25:24,350
+فيها عشان تقول والله هذه hydrocarbon أو كاربون
+
+325
+00:25:24,350 --> 00:25:28,920
+لوحده في بعض الأحيان يعنيوفي هذه الحالة بيكون
+
+326
+00:25:28,920 --> 00:25:39,620
+element يعني مش مش مركب يعني مش مركب لأنه المركب
+
+327
+00:25:39,620 --> 00:25:43,100
+احنا تفاجأنا عنه بتكون من أكتر من نوع من أنواع
+
+328
+00:25:43,100 --> 00:25:45,620
+الذرات
+
+329
+00:25:46,880 --> 00:25:51,020
+فخلّيني أتطلع بداية بدي أتكلم عن الجدول الدوري و
+
+330
+00:25:51,020 --> 00:25:54,660
+أشوف كيف بسمي ال cations كيف بسمي ال anions في بعض
+
+331
+00:25:54,660 --> 00:26:00,680
+الأحيان ال cations بتكون خلّيني أقول مركبة مش بس
+
+332
+00:26:00,680 --> 00:26:05,360
+mono atomic وال anions برضه بتكون مركبة مش mono
+
+333
+00:26:06,930 --> 00:26:10,350
+ionic او atomic يعني مش mono atomic ممكن تكون
+
+334
+00:26:10,350 --> 00:26:13,430
+مركبة زي ال nitrate زي الصلفات اللي تاوى شوفناها
+
+335
+00:26:13,430 --> 00:26:18,490
+فخلينا نشوف اشي اشي فبنطلع على ال cations بقول
+
+336
+00:26:18,490 --> 00:26:27,850
+عادة ال metal ion كويس بياخد نفس التسمية زي ال
+
+337
+00:26:27,850 --> 00:26:32,500
+metal يعني مثلا بدي اقول Sodiumplus بقول صديم ايون
+
+338
+00:26:32,500 --> 00:26:37,880
+زينك 2 plus زينك ايون الومنام 3 plus الومنام ايون
+
+339
+00:26:37,880 --> 00:26:43,600
+ولاحظوا ان هذه الصديم الزينك هو من ال transition
+
+340
+00:26:43,600 --> 00:26:48,140
+لكن الشحنة تبعته دائما 2 plus ال الومنام دائما
+
+341
+00:26:48,140 --> 00:26:50,460
+الشحنة تبعته تلاتة من ال representative elements
+
+342
+00:26:50,460 --> 00:26:53,720
+الشحنة تبعته تلاتة plus يعني مش transition
+
+343
+00:26:53,720 --> 00:26:58,300
+وبالتالي ماحطناش اي اشي بين جوسين على اي حال يعني
+
+344
+00:26:58,300 --> 00:26:59,040
+مش مشكلة
+
+345
+00:27:02,730 --> 00:27:09,330
+طيب، إذا كان الـmetal ممكن يكون أكتر من الـcharged
+
+346
+00:27:09,330 --> 00:27:15,110
+ion، يعني ممكن يكون فيه عنده أكتر من الـcharge،
+
+347
+00:27:15,110 --> 00:27:22,050
+فمثلا الـiron ممكن يكون iron 2 plus أو iron 3 plus
+
+348
+00:27:23,130 --> 00:27:26,890
+فكيف بدنا نقول iron ion؟ بنفعش iron ion يعني موجة
+
+349
+00:27:26,890 --> 00:27:31,010
+بتنين ولا موجة بتلاتة مافهمناش ال cover يكون plus
+
+350
+00:27:31,010 --> 00:27:34,670
+one أو يكون plus two علشان هيك قلنا إنه في حالة
+
+351
+00:27:34,670 --> 00:27:38,650
+هذه ال metals اللي عادة هي ال transition elements
+
+352
+00:27:38,650 --> 00:27:41,910
+بالإضافة ل metals قليلة بدناش يعني نلخم حالنا فيها
+
+353
+00:27:41,910 --> 00:27:46,110
+بس المهم عادة ال transition elements هذه لازم نحط
+
+354
+00:27:46,110 --> 00:27:50,270
+ل charge على هيئة numberals رغم ال numberals بين
+
+355
+00:27:50,270 --> 00:28:01,090
+جثين فمثلاالايرون اتنين والكابر وان الايرون
+
+356
+00:28:01,090 --> 00:28:04,250
+اتنين ايون هو عبارة عن الايرون اتنين ايون هو عبارة
+
+357
+00:28:04,250 --> 00:28:05,010
+ايون هو عبارة عن الايرون اتنين ايون هو عبارة عن
+
+358
+00:28:05,010 --> 00:28:06,150
+الايرون اتنين ايون هو عبارة عن الايرون اتنين ايون
+
+359
+00:28:06,150 --> 00:28:06,950
+هو عبارة عن الايرون اتنين ايون هو عبارة عن الايرون
+
+360
+00:28:06,950 --> 00:28:12,250
+اتنين ايون هو عبارة عن الايرون اتنين ايون هو عبارة
+
+361
+00:28:12,250 --> 00:28:18,150
+عن الايرون اتنين ايون هو عبارة عن الايرون اتنين
+
+362
+00:28:18,150 --> 00:28:20,990
+ايون هو عبارة عن الايرون اتنين ايون هو عبارة عن
+
+363
+00:28:20,990 --> 00:28:25,820
+الايركبر اتنين ايون يعني كبر اتنين plus مانجانيز
+
+364
+00:28:25,820 --> 00:28:33,680
+سبعة موجة بده اقول لهم مانجانيز ايون
+
+365
+00:28:33,680 --> 00:28:38,300
+مانجانيز ايون بس يبقى بده احط ل charge بين جثين و
+
+366
+00:28:38,300 --> 00:28:43,800
+احطها ايه نوميرل رومان نوميرل رومان نوميرل طب حلو
+
+367
+00:28:43,800 --> 00:28:44,100
+كتير
+
+368
+00:28:49,720 --> 00:28:56,700
+في الحقيقة الـmetal ions اللي إلها شحنات مختلفة قد
+
+369
+00:28:56,700 --> 00:29:00,760
+تختلف كثيرا جدا في خصائصها مش معناه كلمة مثلا iron
+
+370
+00:29:00,760 --> 00:29:06,220
+2 iron 2 تقريبا colorless very faint green very
+
+371
+00:29:06,220 --> 00:29:09,880
+faint يعني طب اللي شايفينه ان هو مخترق قليلا جدا
+
+372
+00:29:09,880 --> 00:29:17,340
+جدا جدا لكن ال iron 3 dark yellowأصفر إيه شماله
+
+373
+00:29:17,340 --> 00:29:23,820
+فاقع أصفر يعني شديد الصفرة مثلاً فبنلاحظ إنه في قد
+
+374
+00:29:23,820 --> 00:29:28,180
+تختلف خصائصهم اختلاف كبير خالص ال iron تلاتة عامل
+
+375
+00:29:28,180 --> 00:29:32,400
+مؤكسد ال iron اتنين عامل مختزل فمش شرط إنه هذا
+
+376
+00:29:32,400 --> 00:29:35,740
+iron و هذا iron اختلفت الشحنة يعني و الله خصائصهم
+
+377
+00:29:35,740 --> 00:29:40,000
+نقول يعني مثلا لأ خصائصهم قد تختلف جذرياً عشان هيك
+
+378
+00:29:40,000 --> 00:29:44,110
+يجب الاتمام بالتسمية بشكل سليم لأن التسميةلو
+
+379
+00:29:44,110 --> 00:29:48,330
+عرفناها إن هذا Iron 3، هنعرف إنه عامل مؤكسد، Iron
+
+380
+00:29:48,330 --> 00:29:54,150
+2 عامل مختزل مثلاً، Iron 3 لونه أصفر غامق، Iron 2
+
+381
+00:29:54,150 --> 00:29:58,190
+لونه Very Faint Green، Very Faint، يدوم اللي
+
+382
+00:29:58,190 --> 00:30:02,710
+شايفين اللون، فخصائصهم بتختلف بشكل جذري، عشان هي
+
+383
+00:30:02,710 --> 00:30:08,430
+التسميات تبعتهم لازم تكون يعني صحيحةهذه الايونات
+
+384
+00:30:08,430 --> 00:30:11,010
+الموجباها اه شفناها قبل هيك نفس الكلام اللي
+
+385
+00:30:11,010 --> 00:30:13,330
+اتحدثنا عنه في الايون الكمباز والايونات السالبة
+
+386
+00:30:13,330 --> 00:30:18,010
+نفس الكلام اللي اتحدثنا عنها برضه في السابق قلنا
+
+387
+00:30:18,010 --> 00:30:21,550
+مدام ال .. الايون بياخد نفس اسم المعنى بس ايه
+
+388
+00:30:21,550 --> 00:30:28,070
+بنضفله ال word الكلمة ion وإذا كان الايون
+
+389
+00:30:28,070 --> 00:30:32,550
+transition يبقى لازم نحدد ال charge اللي عليه ونحط
+
+390
+00:30:32,550 --> 00:30:39,500
+هاش بين جثينهمن الـ Transition elements فى عندي
+
+391
+00:30:39,500 --> 00:30:43,820
+تلت عناصر دائما شحنتهم واحدة وعشان هيك بنهتم عشان
+
+392
+00:30:43,820 --> 00:30:47,900
+نحط بين جثين النوميرالز أول واحد ال silver دائما
+
+393
+00:30:47,900 --> 00:30:52,220
+plus one silver plus عشان هيك بنكتبش silver جثين
+
+394
+00:30:52,220 --> 00:30:57,150
+فيها I أو يعني واحد بالرومان نوميرالزهذه واحدة من
+
+395
+00:30:57,150 --> 00:31:00,830
+المعادن الحاجة التانية اللى هو الـ Zinc قطعه
+
+396
+00:31:00,830 --> 00:31:05,290
+شفناها Zinc 2 plus دائما 2 plus والكادميوم برضه 2
+
+397
+00:31:05,290 --> 00:31:10,610
+plus والباجين لأ الباجين ممكن ياخدوا ايه ال charge
+
+398
+00:31:10,610 --> 00:31:13,870
+علشان هيك يعني ممكن يكون لهم اكتر من ال charge
+
+399
+00:31:13,870 --> 00:31:16,770
+ممكن ياخدوا اي charge لكن ممكن يكون لهم اكتر من
+
+400
+00:31:16,770 --> 00:31:19,770
+oxidation number
+
+401
+00:31:21,760 --> 00:31:25,700
+عندي تلاتة ال silver دائما واحد ال zinc دائما
+
+402
+00:31:25,700 --> 00:31:31,600
+اتنين ال cadmium CD بنكتب C capital دي صغيرة دائما
+
+403
+00:31:31,600 --> 00:31:33,600
+اتنين هدول التلات عناصر فقط
+
+404
+00:31:42,920 --> 00:31:46,860
+الألومنام دائما تلاتة لأنها جروب 3A من الـ
+
+405
+00:31:46,860 --> 00:31:50,040
+representative elements لا تتغير الشحنة
+
+406
+00:31:54,110 --> 00:31:57,370
+يعني الكاتب بيقول مش كتير هذا كلام مشهور لكن
+
+407
+00:31:57,370 --> 00:32:00,890
+الكاتب بيقول اذا كان .. كان فيه انا شك انه هذا
+
+408
+00:32:00,890 --> 00:32:03,050
+transition element او مش transition .. او ان ال
+
+409
+00:32:03,050 --> 00:32:07,890
+element هذا ممكن يكون له اكتر من شحنة فيمكن بلا
+
+410
+00:32:07,890 --> 00:32:11,670
+حرج انه نحط الشحنة تبعته بين ايه؟ بين جثين عشان
+
+411
+00:32:11,670 --> 00:32:15,910
+نعرفه يعني حتى لو انسينا ان ال silver دائما plus
+
+412
+00:32:15,910 --> 00:32:21,970
+oneهو يقول انه اعطاه اللى هو .. خليني اقول موجب
+
+413
+00:32:21,970 --> 00:32:25,490
+واحد هو موجود في ال .. ايش بيسموه؟ في الجدول
+
+414
+00:32:25,490 --> 00:32:27,870
+الدوري في ال transition elements او ممكن تحطيه بين
+
+415
+00:32:27,870 --> 00:32:33,130
+جثين يعني مش غلط لكن هذا مش مشهور المشهور دائما بس
+
+416
+00:32:33,130 --> 00:32:36,230
+ال transition elements عدا هدول التلاتة هم اللي
+
+417
+00:32:36,230 --> 00:32:40,090
+بنحط ال oxidation number تبعهم او ال charge تبعتهم
+
+418
+00:32:40,090 --> 00:32:46,590
+بين جثينلكن هو الغرب من التسمية أنه نسمي بشكل سليم
+
+419
+00:32:46,590 --> 00:32:50,630
+يعني أنا بلاقي الكتاب أو الكاتب محق يعني ماعندي
+
+420
+00:32:50,630 --> 00:32:58,050
+مشكلة في الكلام تبعه كان في تسمية أخرى لل
+
+421
+00:32:58,050 --> 00:33:02,890
+translation elements عشان نعبر عن ال lower
+
+422
+00:33:02,890 --> 00:33:06,590
+oxidation state يعني الشحنة القليلة وال higher
+
+423
+00:33:06,590 --> 00:33:10,590
+oxidation state يعني الشحنة الأعلىLower oxidation
+
+424
+00:33:10,590 --> 00:33:16,570
+state يعني الحالة اللي خلّيني أقول حالة الأكسدة
+
+425
+00:33:16,570 --> 00:33:22,310
+تبعتها المنخفضة اتنين plus مثلا لل iron وال higher
+
+426
+00:33:22,310 --> 00:33:25,970
+oxidation state لل iron تلاتة plus فجالوا انه ال
+
+427
+00:33:25,970 --> 00:33:29,770
+iron اتنين او ال low oxidation state بنقوله بنحطله
+
+428
+00:33:29,770 --> 00:33:36,750
+أس فرس لأن هو فرس هو ال iron اسم يعني خلّيني أقول
+
+429
+00:33:36,750 --> 00:33:41,720
+لاتينيالـ Ferrous بنقوله بينما الـ Fe ثلاثة لأنه
+
+430
+00:33:41,720 --> 00:33:45,500
+Higher Oxidation بنقوله Ferric نفس الكلام الـ
+
+431
+00:33:45,500 --> 00:33:50,020
+Copper Plus بنقوله Capras بينما الـ Higher
+
+432
+00:33:50,020 --> 00:33:53,240
+Oxidation State يعني التشارج الأعلى بنقوله Cupric
+
+433
+00:33:53,240 --> 00:33:56,740
+نفس
+
+434
+00:33:56,740 --> 00:34:01,140
+الكلام الـ Mercury One بنقوله Mercurous الـ
+
+435
+00:34:01,140 --> 00:34:05,740
+Mercury Two بنقوله Mercurek فدائما الشحن الأقل Us
+
+436
+00:34:05,740 --> 00:34:09,820
+والشحن الأعلى Xالكويتس هذا كلام برضه يستخدم لكن
+
+437
+00:34:09,820 --> 00:34:14,140
+علميا يعني مش كتير هذا كلام مهم المهم اه والله نحط
+
+438
+00:34:14,140 --> 00:34:17,300
+بين دوسين هذا افضل لنا لكن و احنا بنقرأ لابد الا
+
+439
+00:34:17,300 --> 00:34:21,300
+انه تصادفنا شغلات زي هيك فنفهم ايش معناها أس يعني
+
+440
+00:34:21,300 --> 00:34:23,940
+lower oxidation state اك يعني higher oxidation
+
+441
+00:34:23,940 --> 00:34:31,740
+state طيب لازم نتذكر ان في عندي ايونين
+
+442
+00:34:33,630 --> 00:34:36,310
+مش هنستخدمهم في التسمية، هنستخدم مادة في التسمية
+
+443
+00:34:36,310 --> 00:34:40,210
+بس يعني، أما الميه، لأ الهيدرونيا مش هنستخدمها في
+
+444
+00:34:40,210 --> 00:34:46,120
+التسمية، لكن هدول الأيونين بينتهوا بالإنديوميوم
+
+445
+00:34:46,120 --> 00:34:51,720
+يوم فهد اسمه ammonium ايون هد اسمه هيدرونيوم
+
+446
+00:34:51,720 --> 00:34:58,440
+هيدرونيوم ايون فهدول بدنا نتذكرهم احنا هنستخدم بس
+
+447
+00:34:58,440 --> 00:35:01,220
+ال ammonium الهيدرونيوم مش هنستخدمه في التسمية
+
+448
+00:35:01,220 --> 00:35:03,740
+تبعتنا وبالتالي كان ممكن اني ألغي هذا الكلام
+
+449
+00:35:03,740 --> 00:35:09,640
+ماجلهوش لكن بس حبيت اني امشي مع الكتاب تقريبا يعني
+
+450
+00:35:09,640 --> 00:35:11,360
+لكن احنا هنستخدم ال ammonium
+
+451
+00:35:14,300 --> 00:35:21,240
+خلّيني أتطلع على بعض الأيونات من الجدول اللي موجود
+
+452
+00:35:21,240 --> 00:35:25,460
+قدامنا، متاحة طبعا من الجدول الدوري، فنتطلع على
+
+453
+00:35:25,460 --> 00:35:30,420
+الأيونات الموجبة، بنقول plus one يعني أيونات
+
+454
+00:35:30,420 --> 00:35:34,540
+المجموعة الأولى، ليثيوم، صوديوم، بوتاسيوم، سيزيوم،
+
+455
+00:35:34,540 --> 00:35:38,420
+فرانسيوم، مش كاتبينو، كويس، زائد السلفر زائد
+
+456
+00:35:38,420 --> 00:35:42,040
+الأمونيامهدول عليهم شحنة موجبة دائما، شحنة واحدة،
+
+457
+00:35:42,040 --> 00:35:47,600
+تتغيرش، شحنة واحدة، بالاضافة اليهم LH، H plus،
+
+458
+00:35:47,600 --> 00:35:52,700
+hydrogen ion، hydrogen ion، فلاحظوا الأسماء
+
+459
+00:35:52,700 --> 00:35:55,280
+lithium، اه lithium ion، sodium، sodium ion،
+
+460
+00:35:55,280 --> 00:35:58,630
+بوتاسيام، بوتاسيام، نفس التسمية بالظبططيب نيجي
+
+461
+00:35:58,630 --> 00:36:03,270
+نتطلع على two charges المجموعات التانية مجنيزيام
+
+462
+00:36:03,270 --> 00:36:07,250
+كالسيام سرانشيام باريام اه اضافتلهم الذنك و ال
+
+463
+00:36:07,250 --> 00:36:10,210
+cadmium لأن هدول من ال transition element صحيح لكن
+
+464
+00:36:10,210 --> 00:36:14,970
+دائما شحنتهم two plus الموجة بتنين الموجة بتلاتة
+
+465
+00:36:14,970 --> 00:36:19,290
+ال aluminum الموجة بتلاتة اللي هو ال aluminum طيب
+
+466
+00:36:19,290 --> 00:36:27,910
+في عندي اه ..بعض الـ Transition elements plus two
+
+467
+00:36:27,910 --> 00:36:32,810
+مثلًا كوبلت بين جثين
+
+468
+00:36:35,990 --> 00:36:39,130
+يعني مش ضروري تعرفوا الاص هذه لأنه مايعرفوش انتوا
+
+469
+00:36:39,130 --> 00:36:42,590
+ان الكوبلت في كوبلت اتنين و كوبلت تلاتة فاسيبونا
+
+470
+00:36:42,590 --> 00:36:45,390
+من ال .. من ال .. من التسمية بعد الجثين هنا
+
+471
+00:36:45,390 --> 00:36:50,170
+بلزمكمش لأن انتوا مش عارفين ان في عندنا كوبلت
+
+472
+00:36:50,170 --> 00:36:54,230
+اتنين و كوبلت تلاتة الكوبلت تلاتة اك الكوبلت اتنين
+
+473
+00:36:54,230 --> 00:36:57,510
+اصلا انه اقل تعرفوش انتوا هذا الكلام لكن بس اللي
+
+474
+00:36:57,510 --> 00:37:01,210
+بيهمني الجزء الاول كابر اتنين plus كابر في عندي
+
+475
+00:37:01,210 --> 00:37:06,440
+بين جثيناتنين ايرون اتنين بلس ايرون بين جثين اتنين
+
+476
+00:37:06,440 --> 00:37:10,920
+مانجانيز مانجانيز اتنين هايو مانجانيز اتنين كله
+
+477
+00:37:10,920 --> 00:37:15,080
+هان ميركوري بس بدكم اتلاحظوا هذه اللي ممكن تجيبكم
+
+478
+00:37:15,080 --> 00:37:18,120
+في الامتحان في بعض الأحيان هذه ميركور اتنين اتنين
+
+479
+00:37:18,120 --> 00:37:23,260
+بلس يبقى الميركور الواحدة ايه؟ واحدة ذرتين ميركوري
+
+480
+00:37:23,260 --> 00:37:27,840
+عليهم ايه؟ اتنين اتنين وبرضه اتذكروا هذا بنقوله
+
+481
+00:37:27,840 --> 00:37:34,660
+ميركوراستذكروا بس بس هذا ميركوراس تمام لأن ايه؟
+
+482
+00:37:34,660 --> 00:37:39,360
+الاتنين عليهم اتنين اذا mercury one لأن الظرتين
+
+483
+00:37:39,360 --> 00:37:43,560
+عليهم شحنتين يبقى الظرة عليها شحنة mercury اتنين
+
+484
+00:37:43,560 --> 00:37:49,220
+plus اه عادي mercury اتنين nickel led10 كله نفس
+
+485
+00:37:49,220 --> 00:37:53,400
+الكلام نفس الصورة بالظبط plus three اللي هو
+
+486
+00:37:53,400 --> 00:37:57,160
+اكروبيام تلاتة مثلا يعني في علاصر كتير بس هو
+
+487
+00:37:57,160 --> 00:38:00,280
+ماتينا أمثل اكروبيام تلاتة ايرون تلاتة اكروبيام
+
+488
+00:38:00,280 --> 00:38:06,800
+تلاتة ايرون تلاتة طبعا مش ضروري انه نعرف الجزء
+
+489
+00:38:06,800 --> 00:38:10,430
+التاني من التسمية لأنهأنتم ما بتعرفوش الـ
+
+490
+00:38:10,430 --> 00:38:16,050
+oxidation states للعناصر و هل هذه الـ charge هي
+
+491
+00:38:16,050 --> 00:38:19,560
+الأعلى ولا مش الأعلى، ما بتعرفوا هذا الكلامبدي
+
+492
+00:38:19,560 --> 00:38:22,240
+اتكلم الان عن ال .. اتكلمنا عن ال cations سهلة
+
+493
+00:38:22,240 --> 00:38:27,760
+خالص ال cations تاخد نفس الاسم الشحنات تبعيتها
+
+494
+00:38:27,760 --> 00:38:31,680
+ثابتة المجموعة الأولى و التانية مش مشكلة بالاضافة
+
+495
+00:38:31,680 --> 00:38:35,940
+لها التلات عناصر ال silver او الأربعة ال ammonium
+
+496
+00:38:35,940 --> 00:38:41,740
+و هم مش عنصر ال ammonium ال silver ال zinc ال
+
+497
+00:38:41,740 --> 00:38:47,160
+cadmium هدوة انضموا اليهم و بتاخد نفس الاسمتماما
+
+498
+00:38:47,160 --> 00:38:49,660
+لكن في حالة ال Transient elements بدنا نحط ال
+
+499
+00:38:49,660 --> 00:38:54,040
+charge ايه العدد تبع ال charge بين جثين ك Roman
+
+500
+00:38:54,040 --> 00:38:58,260
+numerals و خلاص انتهى لكن نفس اسم العنصر تماما
+
+501
+00:38:58,260 --> 00:39:02,520
+بنيجي و بنطلع الآن على ال anions و ال oxyanions ال
+
+502
+00:39:02,520 --> 00:39:05,780
+anions اللي هي الأيونات السالبة ال oxyanions
+
+503
+00:39:05,780 --> 00:39:08,960
+الأيونات السالبة اللي بتحتوي كمان على أكسجين
+
+504
+00:39:08,960 --> 00:39:13,640
+oxyanions زي ال nitrate زي ال sulfate هذه أكسجين و
+
+505
+00:39:13,640 --> 00:39:18,600
+عنصر آخر صار اسمها oxyanionsطيب نتطلع على الانيوز
+
+506
+00:39:18,600 --> 00:39:25,560
+و نشوف كيف بنتعامل معاها جال هي نفس الأنصر لكن
+
+507
+00:39:25,560 --> 00:39:30,480
+الجزء الأخير من الأنصر بنحت فوق الحط ايد يعني
+
+508
+00:39:30,480 --> 00:39:36,640
+كلوريين جال كلورايد فلوريين فلورايد سالفر سالفايد
+
+509
+00:39:37,150 --> 00:39:41,470
+اكسيجن اكسايد نيتروجين نيترايد اللى شوفناها قبل
+
+510
+00:39:41,470 --> 00:39:47,070
+شوية وقلنا بنقولها نيترايد نيترايد اذا مدام العنصر
+
+511
+00:39:47,070 --> 00:39:52,090
+اخد شحنة سالبة العنصرها مدام اخد شحنة سالبة على
+
+512
+00:39:52,090 --> 00:39:59,490
+طول بدي اجلب اخر جزء منه كايد بدي اخليه ايد ارزنك
+
+513
+00:39:59,490 --> 00:40:06,290
+ارزنايدالاخره فهي Hydride هه هانجتني الهيدروجين طب
+
+514
+00:40:06,290 --> 00:40:08,330
+متابعي اقول عنها موجة بقى اه ممكن تكون موجة وممكن
+
+515
+00:40:08,330 --> 00:40:12,990
+تكون سالبة فهن بتاخد شحنه سالبة Hydride اذا كانت
+
+516
+00:40:12,990 --> 00:40:19,230
+تاخد شحنه سالبة فيجب ان تتحد مع metal ion علشان
+
+517
+00:40:19,230 --> 00:40:26,570
+تعطينا ion ال compound زي مثلا Sodium H سالب اه
+
+518
+00:40:26,570 --> 00:40:32,250
+هذا Sodium Hydride واحد واحد كويس مثلا يعنيهذا
+
+519
+00:40:32,250 --> 00:40:40,150
+للأيونات العادة للـ Ionic compounds أكسجين صارت
+
+520
+00:40:40,150 --> 00:40:42,910
+Oxide أكسجين على شحنتين سلبتين على المجموعة
+
+521
+00:40:42,910 --> 00:40:46,210
+السادسة نيتروجين في المجموعة الخامسة عليها تلات
+
+522
+00:40:46,210 --> 00:40:53,110
+نيترايد سلفر سلفايد سيلينيوم سيلينايد تيلوريوم
+
+523
+00:40:53,110 --> 00:40:58,230
+تيلورايدالسيلينيوم والتيلوريوم هذه من العناصر
+
+524
+00:40:58,230 --> 00:41:01,190
+المهمة اللي هتواجهوها في حياتكم العملية لأنه
+
+525
+00:41:01,190 --> 00:41:07,750
+تستخدم بشكل كبير في الخلايا الشمسية ال solar cells
+
+526
+00:41:07,750 --> 00:41:12,290
+حاليا يعني فتستخدم بشكل كبير هتشوفوها خلايا تستخدم
+
+527
+00:41:12,290 --> 00:41:17,250
+السيلينيوم وخلايا تستخدم التيلوريوم ومراكباتهم
+
+528
+00:41:17,250 --> 00:41:21,710
+فهدول من العناصر المهمين جدا في الخلايا هذه الأيام
+
+529
+00:41:22,430 --> 00:41:27,930
+بنقول some binary atomic anions بيناري اتوميك
+
+530
+00:41:27,930 --> 00:41:32,450
+بيناري يعني اتنين ثنائي بيناري يعني اتنين يتكون من
+
+531
+00:41:32,450 --> 00:41:36,290
+ايه؟ من ذرتين بيناري اتوميك لما نقول بيناري اتوميك
+
+532
+00:41:36,290 --> 00:41:46,970
+يعني بتكون من ذرتينزي مثلا CUN OH OO OO صارت O2
+
+533
+00:41:46,970 --> 00:41:53,530
+كويس فهذه برضه كمان بتاخد ايد الجزء الأخير منها
+
+534
+00:41:53,530 --> 00:41:59,630
+بياخد ايد فمثلا CN بنقول cyanideOH هايدروكسايد
+
+535
+00:41:59,630 --> 00:42:04,130
+هايدروكسايد في آخرها ايه؟ لازم نحفظهم هدول هذه
+
+536
+00:42:04,130 --> 00:42:09,210
+ساينايد هذه هايدروكسايد ال O2 اتنين سالب مش أكسايد
+
+537
+00:42:09,210 --> 00:42:13,970
+عشان أجهها كمان و بنقول peroxide أكتر من أكسايد
+
+538
+00:42:13,970 --> 00:42:19,090
+فوق الأكسيد فوقففي أحد الألفات اللي بنقول peroxide
+
+539
+00:42:19,090 --> 00:42:23,490
+المهم في آخرها أيضا ايد بس كانت binary atomic
+
+540
+00:42:23,490 --> 00:42:28,630
+بنقولها أيه برضه بتاخد ايد في الآخر binary atomic
+
+541
+00:42:28,630 --> 00:42:32,930
+بتاخد ايد هتلاقوا
+
+542
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+بنقولها
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+بقول reference ايون فمثلا ال boron carbon نيتروجين
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+في المجموعات يعني هذه سالب واحد سالب اتنين سالب
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+590
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+تلاتة PO أربعة طب الأرذنيك ASO أربعة هذا ال
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+reference طيب ال sulfur SO أربعة ال selenium SEO
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+أربعة اتنين سالب لأنه سالب واحد سالب اتنين
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+00:47:04,350 --> 00:47:12,040
+التلوريام TEO أربعة طب لو أخد أجلمثلا قول لهان ال
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+594
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+reference جداش هان أربعة تذكروها هان تلاتة هان
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+00:47:20,280 --> 00:47:29,960
+طيب الان لو اجا مثلا ال sulfur بدأ .. ال sulfur
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+597
+00:47:29,960 --> 00:47:33,040
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+598
+00:47:35,270 --> 00:47:43,430
+بنصير اسمه Sulphite هذا Sulphate الات إيش اتحولت؟
+
+599
+00:47:43,430 --> 00:47:51,030
+لأ Sulphite لإنه جلب واحد كويس ال سيلينيوم هي SEO4
+
+600
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+هذا Selinate طيب
+
+601
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+ال SEO3 نفس الشحنة هاخدوا بالكم سيلين مش ات ايت
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+أكسجينة واحدة سيلينايت و هكذا إذا هاي المجموعتين
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+الـNitrogen، هاي بنشوفها مع بعض الأناص اللي هفرجها
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+لكم بعد شوية، طب الهالوجينات جال ال reference I دي
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+607
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+برضه إيه؟ تلاتة، يبقى CL
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+608
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+أو تلاتة سالب هذه كل مجموعة سالب الشحنة تبعتها سيل
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+609
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+او تلاتة هذا اسمه اكلور لا اكلوريت لأن هو ايش قلنا
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+610
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+قلنا الاصل تلاتة فالاصل بياخد ال eight التلاتة
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+00:48:46,120 --> 00:48:49,700
+بتاخد ال اربع الاصل الاصل بياخد ال eight ال
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+00:48:49,700 --> 00:48:52,420
+reference المرجع هو ايه تلاتة بياخد ال eight
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+613
+00:48:52,420 --> 00:48:54,820
+اكلوريت طيب
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+614
+00:48:58,300 --> 00:49:06,220
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+615
+00:49:06,220 --> 00:49:11,340
+CLO4 أخد أكتر قال أخد pair أكتر زيادة pair
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+616
+00:49:11,340 --> 00:49:16,820
+اكلورايت زي ما هي بس ايه حطلها pair يعني أكتر بس
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+617
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+619
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+يعني هان جلت واحدة صارت اكلورايت طب جلت صارت CLO
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+الكلام هذا و
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+625
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+أضحي الصورة بشكل أحسن
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+طيب نتطلع على ال Oxyanions ل .. لchlorine لبرومين
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+627
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+ال A في المستطيل اللي انا حاطه جال ايش بنقول؟
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+629
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+الاصل اين دي اكم؟ ايش ال reference compound؟ تلاتة
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+.. تلاتة بتاخد ال eight هدا هي .. هدا هو ال
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+referenceهذا هو ال reference اكلور اكلوريت ايودين
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+أقل من الكلوريت بواحدة صار اسمها اكتر من الكلوريت
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+638
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+باكتر من واحدة hypochlorite نفس الكلام ايوديت
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+639
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+Iodate هي الأصل تلاتة طيب أكتر pair Iodate أجل
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+بواحدة Iodite أجل كمان بواحدة من Iodite Hypo
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+641
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+Iodite ماشي يا جماعة طيب هذه أول ملاحظة يعني ال
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+reference أو ال most common هنا
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+قلنا مجموعة بورون، كاربون، نيتروجين، بوريت
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+Carbonate Nitrate مجموعة الهالوجينات الchlorate
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+كلها ايه؟ مجموعة الفوسفورس والارزنك والسليم مجموعة
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+سالب مادام ال Oxygen جال عن ال reference بدي يكون
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+673
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+ايت فسف بدل ايت فسفايت هي هي هي الأصل Phosphate
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+ال
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+675
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+أكسجين لكنلكن بنسمي ال MnO4 سالب بنسميها
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+682
+00:55:04,940 --> 00:55:10,040
+permanganate permanganate كويس؟ permanganate على
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+683
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+طول permanganate فتذكروا ال MnO4 لأنها مركب مشهور
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+
+685
+00:55:21,140 --> 00:55:22,460
+اسمه permanganate
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+686
+00:55:24,740 --> 00:55:29,420
+بدنا نحاول نحصل على ال formula من الإسم تدريب
+
+687
+00:55:29,420 --> 00:55:36,490
+نحاول نحصل على ال formula من الإسمبسيطة على الواقع
+
+688
+00:55:36,490 --> 00:55:39,930
+الموجود في الـ Sulphate Ion اتخيل الواقع الموجود
+
+689
+00:55:39,930 --> 00:55:42,810
+في الـ Sulphate Ion اول حاجة السيلينيت ايون
+
+690
+00:55:42,810 --> 00:55:47,330
+والسيلينايت وبيقول هو ان السلفر والسلينيام في نفس
+
+691
+00:55:47,330 --> 00:55:54,670
+المجموعة ويكونوا اكسي انايون متناضرة
+
+692
+00:55:54,670 --> 00:55:58,530
+زيها بالظبط يعني فانا عندي ال Sulphate SO4 نفس
+
+693
+00:55:58,530 --> 00:56:05,290
+الكلام اللي قلناه SO4إذا لو بدى أقول سيلينيت SEO4
+
+694
+00:56:05,290 --> 00:56:12,810
+سيلينيوم O4 الصلفيت sulfur متحد مع هي الصلفيت SO4
+
+695
+00:56:12,810 --> 00:56:17,930
+2 سالم إذا السيلينيت المناظرة إليها سيلينيوم O4 2
+
+696
+00:56:17,930 --> 00:56:23,910
+سالم سؤال بسيط كتير عشان هيك احنايعني بيقول ليش
+
+697
+00:56:23,910 --> 00:56:30,890
+بيسأل هذا السؤال طيب هذه الصلفات بد هو selenate و
+
+698
+00:56:30,890 --> 00:56:34,170
+بيه بده selenite selenite معناته بده يجلب مقدار
+
+699
+00:56:34,170 --> 00:56:40,710
+ايه س ا و تلاتة هاي ال selenite طيب بيقول لي write
+
+700
+00:56:40,710 --> 00:56:46,110
+the formula for the hybromite and bromite ions بده
+
+701
+00:56:46,110 --> 00:56:51,690
+ال formula للhybromite انا بعرف ال bromate اكمأكم
+
+702
+00:56:51,690 --> 00:56:59,070
+أكسجينة لبروميت الـ representative بي آر أو تلاتة
+
+703
+00:56:59,070 --> 00:57:07,490
+سالب هذه إيه لبروميت طب إيش لبروميت صحيح هذه
+
+704
+00:57:07,490 --> 00:57:14,470
+بروميت طب إيش ال .. إيش ال hypobromite بي آر أو
+
+705
+00:57:14,470 --> 00:57:18,230
+سالف هذا hypo طبعا لبروميت
+
+706
+00:57:21,590 --> 00:57:25,530
+تمام؟ سهل جدا جدا سهل دائما يروحوا لل reference
+
+707
+00:57:25,530 --> 00:57:30,670
+ومنه ينطلقوا بتزودوا pair بتجلله it بتجلله اكتر
+
+708
+00:57:30,670 --> 00:57:36,250
+hypo it طيب اذا
+
+709
+00:57:36,250 --> 00:57:41,410
+كمان ال oxy anions حاجة مش صعبة بالمرة سهلة خالص
+
+710
+00:57:41,410 --> 00:57:48,140
+وقانونها سهل كتيرفي قندي في بعض الأحيان ممكن انه
+
+711
+00:57:48,140 --> 00:57:53,200
+يرتبط هيدروجين بالاوكسي انايون ممكن يرتبط هيدروجين
+
+712
+00:57:53,200 --> 00:57:56,280
+بالاوكسي انايون يظلوا انايون لكن يرتبط معاه
+
+713
+00:57:56,280 --> 00:58:00,860
+هيدروجين من المحلول فكيف بنسمي مثلا كربونيت لو
+
+714
+00:58:00,860 --> 00:58:06,540
+رتبط معها هيدروجين صارت HCO3بس بنقول هايدروجين
+
+715
+00:58:06,540 --> 00:58:10,220
+هادي كربونيت صار اسمها هايدروجين كربونيت ولا حاجة
+
+716
+00:58:10,220 --> 00:58:14,120
+بس حطينا كلمة هايدروجين قبلها طيب هادي فوسفيت
+
+717
+00:58:14,120 --> 00:58:18,900
+ارتبط معها هايدروجين صارت HPO اربع سنة هايدروجين
+
+718
+00:58:18,900 --> 00:58:24,670
+فوسفيت طب ارتبط معها اتنين هايدروجينباي هيدروجين
+
+719
+00:58:24,670 --> 00:58:29,630
+فوسفيت لأنه والله في عندنا اتنين هيدروجين ارتبطوا
+
+720
+00:58:29,630 --> 00:58:35,510
+مع ال P offer فصارت ايه؟ باي هيدروجين عشان نفرجها
+
+721
+00:58:35,510 --> 00:58:39,790
+عن اللي جاملها اللي جاملها هيدروجين فوسفيت لأنها
+
+722
+00:58:39,790 --> 00:58:43,610
+دي ايه؟ فيها اتنين هيدروجين باي هيدروجين فوسفيت
+
+723
+00:58:43,610 --> 00:58:48,050
+فبعض الأحيان لما تكون مرتبطة بس مع H واحدة بدل ما
+
+724
+00:58:48,050 --> 00:58:51,130
+يقولوا هيدروجين كربونيت بيقولها باي
+
+725
+00:58:54,370 --> 00:59:00,630
+by ممكن نقول لهذه برضه كمان by فبقولها by يعني بدل
+
+726
+00:59:00,630 --> 00:59:02,930
+ما نقوله hydrogen carbonate نسمع المصطلح by
+
+727
+00:59:02,930 --> 00:59:06,070
+carbonate by carbonate معناته فيه هيدروجينة مرتبطة
+
+728
+00:59:06,070 --> 00:59:09,290
+مع الكربونيت ماشي يا جماعة برضه هذا من ضمن
+
+729
+00:59:09,290 --> 00:59:17,950
+التسميات حلو انه نكون على دراية كويسة فيه الآن بده
+
+730
+00:59:17,950 --> 00:59:22,690
+نيجي لكيف مدى شفناالـCations وكيف بنسميها
+
+731
+00:59:22,690 --> 00:59:27,070
+والـAnions وكيف بنسميها تعالوا الآن نجمع
+
+732
+00:59:27,070 --> 00:59:30,310
+الـCations والـAnions تعطينا Ionic compound نشوف
+
+733
+00:59:30,310 --> 00:59:33,530
+كيف بنسمي الـIonic compound اتطلعنا على كيفية
+
+734
+00:59:33,530 --> 00:59:38,470
+تسمية الـCations واطلعنا على كيفية تسمية الـAnions
+
+735
+00:59:38,470 --> 00:59:43,550
+الآن بدنا نحاول نجمع الـCations والـAnions ونسمي
+
+736
+00:59:43,550 --> 00:59:49,850
+المركبات الايونية فمثلا CACl2
+
+737
+00:59:50,980 --> 00:59:56,400
+جال فى التسمية دائما ياريت عندي الجدول متأخر شوية
+
+738
+00:59:56,400 --> 01:00:02,500
+ليش هيك طب مش مشكلة دائما فى التسمية ال metal ion
+
+739
+01:00:02,500 --> 01:00:05,560
+فى الأول لحظة ان ال ion ال compound فى عندي metal
+
+740
+01:00:05,560 --> 01:00:09,900
+ion و nonmetal ion كويس فى عندي metal و nonmetal
+
+741
+01:00:09,900 --> 01:00:14,120
+او فى عندي group ماشي برضه union unionic group
+
+742
+01:00:14,120 --> 01:00:18,340
+فكيف بدى أسمي جال ال metal فى الأول و بكبه زى ما
+
+743
+01:00:18,340 --> 01:00:23,680
+هومثلا هذه CA يعني كالسيوم يقول كالسيوم اكلور
+
+744
+01:00:23,680 --> 01:00:28,180
+قولنا كده كيف بنسمي الكلور بنحطله ايد اكلور ايد
+
+745
+01:00:28,180 --> 01:00:31,620
+كالسيوم اكلور ايد طب ليش يا أستاذ محطتش هنا
+
+746
+01:00:31,620 --> 01:00:36,580
+الكلسيوم ليش محطتش هنا اتنين لأنه معروف ان
+
+747
+01:00:36,580 --> 01:00:40,540
+الكلسيوم في المجموعة التانية مش من اللي معروف انه
+
+748
+01:00:40,540 --> 01:00:46,240
+دائما الشحنة تبعت ب two plus شحنتين و جبتين فبنفعش
+
+749
+01:00:46,240 --> 01:00:54,500
+نحطلهنوميرال رومان نوميرال طيب خدوا بالكم ألومنام
+
+750
+01:00:54,500 --> 01:01:03,190
+ALNO 3 3 حلو هذا ألومنام حطوا ألومنام نفسههذه الـ
+
+751
+01:01:03,190 --> 01:01:07,770
+NO تلاتة جال اسمها Nitrate اذا Aluminum Nitrate طب
+
+752
+01:01:07,770 --> 01:01:13,110
+نفس الكلام ليش عرفنا ان هنا ال Nitrate تلاتة مثلا
+
+753
+01:01:13,110 --> 01:01:18,410
+يعني بقى هاي ال Aluminum تلاتة وهي ال Nitrate سالب
+
+754
+01:01:18,410 --> 01:01:22,690
+واحد هذه بتيجي هنا وهذه بتيجي هنا وهي ال Aluminum
+
+755
+01:01:22,690 --> 01:01:28,900
+NO تلاتة تلاتةلأن الـ Aluminum من الـ
+
+756
+01:01:28,900 --> 01:01:32,820
+representative elements ال .. ال charge اللي عليه
+
+757
+01:01:32,820 --> 01:01:37,860
+لا تتغير ال charge اللي عليه لا تتغير بتبالها
+
+758
+01:01:37,860 --> 01:01:45,320
+تلاتة موجب طيب .. هان عندي cover CLO4 أنا متحير
+
+759
+01:01:45,320 --> 01:01:49,080
+CLO4 هذه في طباعة الهالوجينات أكم أكسجينة معها
+
+760
+01:01:49,080 --> 01:01:58,120
+الأصل تلاتة واسمها Eclorate لكن هذه إيش فيها؟CLO4
+
+761
+01:01:58,120 --> 01:02:04,180
+اذا ايش بدها تصير؟ Pair Clorate اذا انا عرفت هذا
+
+762
+01:02:04,180 --> 01:02:08,460
+الايون مباشرة يبجى هذا cover لكن ال cover فيه ل
+
+763
+01:02:08,460 --> 01:02:10,740
+transition elements مش من المجموع الاولى ولا
+
+764
+01:02:10,740 --> 01:02:15,120
+التانية اذا بدنا نحط بين دوسين بدنا نحط الشحنة
+
+765
+01:02:15,120 --> 01:02:19,300
+تبعته هان هو متحد مع ايه؟ مع اتنين Clorate يبجى
+
+766
+01:02:19,300 --> 01:02:23,900
+الاصل انه هاي ال coverوهاي الـ Chlorate هذا على
+
+767
+01:02:23,900 --> 01:02:27,340
+شحنة سالبة إذا كان هذا اتنين موجب يبقى معناه
+
+768
+01:02:27,340 --> 01:02:31,960
+الكلام المداجي أقوله بقول كبر اتنين perchlorate
+
+769
+01:02:31,960 --> 01:02:36,840
+كبر اتنين ليش كبر اتنين لأن في عندنا اتنين من ال
+
+770
+01:02:36,840 --> 01:02:40,000
+perchlorate متحدة معاه عشان نفرجه عن لو جالك كبر
+
+771
+01:02:40,000 --> 01:02:47,040
+CLO4 هذا كبر واحد
+
+772
+01:02:47,040 --> 01:02:48,960
+perchlorate
+
+773
+01:02:50,770 --> 01:02:55,030
+كويس فعنا لازم نعرف ال charge اللي عليه من وين
+
+774
+01:02:55,030 --> 01:02:58,890
+بنعرفها بنستعين بال group اللي هو متصل فيها كل
+
+775
+01:02:58,890 --> 01:03:04,570
+المجموعة الأخيرة سالب واحد فمدام سالب واحد وفيها
+
+776
+01:03:04,570 --> 01:03:08,070
+اتنين منها اذا هذا موجب اتنين اذا لازم نحط اتنين
+
+777
+01:03:08,070 --> 01:03:11,850
+لأن هذا من ال transition elements ليش من ال
+
+778
+01:03:11,850 --> 01:03:14,230
+transition elements؟ جال لأنه مش من المجموعة
+
+779
+01:03:14,230 --> 01:03:15,990
+الأولى ولا التانية
+
+780
+01:03:18,610 --> 01:03:21,670
+و برضه بالاستعانة بالجدول الدوري ممكن اني ألاجيه
+
+781
+01:03:21,670 --> 01:03:29,430
+على طول بيقول لي name the ionic compounds K2SO4
+
+782
+01:03:29,430 --> 01:03:34,190
+و Barium Hydroxide مثلا و Iron اكلورايد انا سميتهم
+
+783
+01:03:34,190 --> 01:03:43,390
+انا باجسم لجسمين الميتال لحاله والايهاو الايون
+
+784
+01:03:43,390 --> 01:03:46,770
+الاول لحاله والايون التاني لحاله الكاتايون لحاله
+
+785
+01:03:46,770 --> 01:03:51,650
+والايون الا انايون لحاله فهنا هذا ايش هو بكتب
+
+786
+01:03:51,650 --> 01:03:54,190
+potassium لانه معروف انه بكتب زي ما هو لانه هذا
+
+787
+01:03:54,190 --> 01:04:00,210
+موجب potassium وهذه ايش المجموعة صلفيت
+
+788
+01:04:00,210 --> 01:04:06,770
+SO4 كبريتات SO4 مافيقول سالفر تترا اكسجين لأ هذه
+
+789
+01:04:06,770 --> 01:04:11,110
+مجموعة كاملة لانه هيهلو بدنا نفصله نكتب كتابة
+
+790
+01:04:11,110 --> 01:04:12,910
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+791
+01:04:12,910 --> 01:04:14,150
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+792
+01:04:14,150 --> 01:04:16,550
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+793
+01:04:16,550 --> 01:04:22,750
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+794
+01:04:22,750 --> 01:04:24,490
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+795
+01:04:24,490 --> 01:04:25,090
+كتابة كتابة كتابة كتابة كتابة كتابة كتابة كتابة
+
+796
+01:04:25,090 --> 01:04:35,070
+كتابة كتابة كتابة كتابة
+
+797
+01:04:36,050 --> 01:04:39,690
+الاسم باريوم هيدروكسايت ال ايرون كلورايت هذا ايرون
+
+798
+01:04:39,690 --> 01:04:45,050
+مفهوم وهذا كلور CL حصلنا على الفورمولا بإنه نزلنا
+
+799
+01:04:45,050 --> 01:04:48,390
+ها دي هان وها دي هان حصلنا على الفورمولا فوق فهذا
+
+800
+01:04:48,390 --> 01:04:53,350
+اسمه على طول ايرون لكن لكن لأن ال ايرون من ال
+
+801
+01:04:53,350 --> 01:04:57,670
+transition elements لازم أحط بين جثين الشحن اللي
+
+802
+01:04:57,670 --> 01:05:02,400
+عليه فهو ايرون تلاتة و احط ايرون تلاتة كلورايتلازم
+
+803
+01:05:02,400 --> 01:05:06,360
+أحط الشحن اللي عليه بين جثين على هيئة roman
+
+804
+01:05:06,360 --> 01:05:11,320
+numerals من
+
+805
+01:05:11,320 --> 01:05:17,000
+أبسط ما يكن بسيط جدا مثلا
+
+806
+01:05:17,000 --> 01:05:19,480
+قال لي write the chemical formula هذا أعطاني الاسم
+
+807
+01:05:19,480 --> 01:05:23,080
+وقال لي اكتب ال formula ناخد واحد واحد potassium
+
+808
+01:05:23,080 --> 01:05:29,070
+sulfide هاي ال potassium وهي ال sulfideطب بدنا
+
+809
+01:05:29,070 --> 01:05:32,150
+نكتب الفورمولة قال هذه بتيجي هنا وهذه بتيجي هنا
+
+810
+01:05:32,150 --> 01:05:37,630
+يعني كتو اس ايفون انا بتكتب زي ما هو زي ما بيقوليا
+
+811
+01:05:37,630 --> 01:05:42,310
+بوتاسيوم سالفايت طب قاللي كالسيوم هيدروجين كربونيت
+
+812
+01:05:42,310 --> 01:05:49,370
+هاي الكربونيت وهي الهيدروجين حطيته رفعت شحنة سالبة
+
+813
+01:05:49,370 --> 01:05:52,770
+لازم لأن الهيدروجين بيجي هاي h plus برفع شحنة
+
+814
+01:05:52,770 --> 01:05:58,520
+سالبة على طولهيدروجين كربونات ايش قال ليه؟ قال لي
+
+815
+01:05:58,520 --> 01:06:03,460
+كالسيوم هيدروجين كالسيوم اتنين موجب اذا اتنين موجب
+
+816
+01:06:03,460 --> 01:06:07,580
+هذه بقى تيجي هان وهذه بقى تيجي هان يبقى الكالسيوم
+
+817
+01:06:07,580 --> 01:06:14,490
+HCO3 اتنينفيعني انا مش عارف ايش يعني hydrogen
+
+818
+01:06:14,490 --> 01:06:17,730
+كربونات بكتب الكربونات بحطلها الهيدروجين بتجل
+
+819
+01:06:17,730 --> 01:06:20,950
+الشحن السلبى المقدار واحد صارت شحن السلبى واحد اقل
+
+820
+01:06:20,950 --> 01:06:24,770
+كالسيوم شحنتين موجبتين بحاول اجمع هاي الشحن السلبى
+
+821
+01:06:24,770 --> 01:06:29,090
+بتنزل الاتنين بتنزل ك coefficient فمعنى الكلام
+
+822
+01:06:29,090 --> 01:06:31,690
+calcium hydrogen carbonate طب ال nickel
+
+823
+01:06:31,690 --> 01:06:35,270
+perichlorate انسيت ايش يعني perichlorate بس بتذكر
+
+824
+01:06:35,270 --> 01:06:40,510
+انا ان الchlorate perichlorate معناتها اربع حلو
+
+825
+01:06:40,510 --> 01:06:45,000
+كتير وهي ال nickelالنكل هان ايش فيه عنده نكل اتنين
+
+826
+01:06:45,000 --> 01:06:48,860
+هذا هي نكل اتنين يبقى معنا الكلام بدي اكتب ال ..
+
+827
+01:06:48,860 --> 01:06:54,280
+هاي ال nickel CLO4 الكل اتنين لإن هذه بتنزل هان
+
+828
+01:06:54,280 --> 01:06:59,980
+وهذه بتنزل هان واحد آه يا بنات شوية تدريب بسيط جدا
+
+829
+01:06:59,980 --> 01:07:02,900
+أول حاجة نحلي الأمثلة اللي أخدناها وبعدين نتدرب
+
+830
+01:07:02,900 --> 01:07:06,420
+شوية صغيرة بيكون مافيش عيننا اي مشكلة فيها هذا
+
+831
+01:07:06,420 --> 01:07:11,950
+الكلاملأنه كلام كتير كتير سهل و مباشر بقول name
+
+832
+01:07:11,950 --> 01:07:16,530
+the ionic compounds NH4 bromide بجسم على طول
+
+833
+01:07:16,530 --> 01:07:21,610
+السالب ع شجة والموجب ع شجة NH4 يعني ammonium
+
+834
+01:07:21,610 --> 01:07:29,710
+قلتلكم تذكروها ammonium brom bromide لأنها ال
+
+835
+01:07:29,710 --> 01:07:34,500
+ammoniumالمُركّب الأيوني بتكون من أيون موجب كتاين
+
+836
+01:07:34,500 --> 01:07:38,320
+و أيون سالب أنيون الأيون السالب بده ينتهي بال ..
+
+837
+01:07:38,320 --> 01:07:46,300
+بالعيد إذا كانوا يعني mono-atomic أو di-atomic
+
+838
+01:07:46,300 --> 01:07:50,540
+عندي
+
+839
+01:07:50,540 --> 01:07:58,860
+هان إيش بده .. بده أسمي هذا chromium و
+
+840
+01:07:58,860 --> 01:08:05,680
+هذه oxygen يعني oxideحلو كتير لكن بدي اعرف انا ايش
+
+841
+01:08:05,680 --> 01:08:13,200
+بدي احط هنا فهي الكروم ت الكوبلت برضه كمان عنصر
+
+842
+01:08:13,200 --> 01:08:15,140
+انتقالي لانه مش معناه عنصر مش معناه نقول لا ولا
+
+843
+01:08:15,140 --> 01:08:24,160
+تانية هي الكوبلت هي اتنين نيتريت برضه مباشر كوبلت
+
+844
+01:08:24,160 --> 01:08:28,960
+اتنين نيتريتGive the chemical formula for A
+
+845
+01:08:28,960 --> 01:08:35,820
+مجنيزيام صلفيت هاي مجنيزيام و هاي الصلفيت اتنين و
+
+846
+01:08:35,820 --> 01:08:40,680
+اتنين اذا مجنيزيام صلفيت بدون اي coefficients طب
+
+847
+01:08:40,680 --> 01:08:45,560
+اللي بعده silver sulfide هاي ال silver لأنه عليه
+
+848
+01:08:45,560 --> 01:08:49,940
+شحن موجة بتذكرناها و هاي ال sulfide شحنتين سلبتين
+
+849
+01:08:49,940 --> 01:08:54,600
+اذا هاد بيعطيني ال silver اتنين S صح؟
+
+850
+01:08:56,080 --> 01:09:02,760
+طب led nitrate هاي ال led لأنه جاله led اتنين وهاي
+
+851
+01:09:02,760 --> 01:09:07,320
+ال nitrate طب هذا هذا هو بده يصير led هاي ها دي
+
+852
+01:09:07,320 --> 01:09:15,120
+هان وها دي هان led n o تلاتة كل اتنين ليه لأن ال
+
+853
+01:09:15,120 --> 01:09:20,660
+led عين دي فيه اتنين يبقى سهل جدا انه
+
+854
+01:09:24,600 --> 01:09:30,180
+أطلّع الاسم من الـ structure من الفورمولة أو أطلّع
+
+855
+01:09:30,180 --> 01:09:33,300
+الفورمولة
+
+856
+01:09:33,300 --> 01:09:41,280
+من الاسم سيّن سهل كتير الآن يعني بدأ اطلع لنقطة
+
+857
+01:09:41,280 --> 01:09:45,360
+صغيرة كتير اللي هي تسمية ال acids تسمية ال acids
+
+858
+01:09:45,360 --> 01:09:51,220
+ال acids تسميتها كتير كتير بسيطة وين في عندي Ion
+
+859
+01:09:52,100 --> 01:10:01,320
+كويس ايد بحطه اك و باسبقه بهيدرو اذا كان عندى ايون
+
+860
+01:10:01,320 --> 01:10:11,540
+ايد مونو اتوميك يعني مش مشكلة ايد اي ايد بحولها
+
+861
+01:10:11,540 --> 01:10:21,820
+لاك و في الاول هايدرو فمثلا اكلور ايدكويس بيصير
+
+862
+01:10:21,820 --> 01:10:28,200
+Chloric وفيه إيش هنجملها Hydro يبقى Hydrochloric
+
+863
+01:10:28,200 --> 01:10:39,640
+acid كويس Sulfide بقول Sulfuric بدك تتذكري هذا
+
+864
+01:10:39,640 --> 01:10:43,760
+Sulfuric Sulfuric Sulfuric Sulfuric Sulfuric
+
+865
+01:10:43,760 --> 01:10:44,640
+Sulfuric Sulfuric Sulfuric Sulfuric Sulfuric
+
+866
+01:10:52,830 --> 01:10:57,530
+Hydro طبعاً بيها تسبق الـ sulphuric acid اللي هي
+
+867
+01:10:57,530 --> 01:11:01,670
+اللي عبارة عن ال sulphide طبعاً بيوضف ال Hannah H
+
+868
+01:11:01,670 --> 01:11:07,430
+عشان تصير acid مش لحالها يعني Hannah HC ال Hannah
+
+869
+01:11:07,430 --> 01:11:14,010
+H2S كويس H2 ليه؟ لأن ال sulphur عليه شحنتين
+
+870
+01:11:14,010 --> 01:11:22,180
+سالبتين و هكذاهذا لو كان ال ايون السالب اللى عندى
+
+871
+01:11:22,180 --> 01:11:29,900
+بينتهي بايد مثلا هى CN اسمه cyanide اه لو بدى
+
+872
+01:11:29,900 --> 01:11:33,880
+احطله لو بدى اخليه اثيد بدى ارفع هذا و احط H HCN
+
+873
+01:11:33,880 --> 01:11:38,900
+ايش بدى يصير؟ Hydrocyanide
+
+874
+01:11:38,900 --> 01:11:44,560
+سرقت cyanic بدل ايه بدى احط ايك؟ Hydrocyanic acid
+
+875
+01:11:44,560 --> 01:11:51,000
+طيبفى ما لو كان يبقى اذا كان عندى ايد على طول بدي
+
+876
+01:11:51,000 --> 01:11:56,260
+احوله ل ايك تمام اضيف اتش طبعا او اتش كافى لإنه
+
+877
+01:11:56,260 --> 01:12:02,160
+يحصل عندى مركب متعدل فبدي احول الايد ل ايك و احط
+
+878
+01:12:02,160 --> 01:12:09,140
+جابلها هيدرو طيب فى ما لو كان اكسي انايون لو كان
+
+879
+01:12:09,140 --> 01:12:11,820
+اكسي انايون هان بدي نتطلع شوية
+
+880
+01:12:15,100 --> 01:12:25,780
+ال إيت بدي أحولها ل إيك ال إيت بدي أحولها ل إيك ال
+
+881
+01:12:25,780 --> 01:12:32,060
+ايت بدي أحولها ل أص ال
+
+882
+01:12:32,060 --> 01:12:38,100
+ايت بدي أحولها ل أص ناخد في الأول بعض الأمثلة على
+
+883
+01:12:38,100 --> 01:12:44,620
+ال إيت فمثلا لو جالي sulfateده والله بتحطها ..
+
+884
+01:12:44,620 --> 01:12:50,220
+بتخليها asset بتصير H2SO4 هذه الـ Sulphate جال
+
+885
+01:12:50,220 --> 01:12:57,760
+بتصير Sulphuric حولت ال A تلاقيش لإك Sulphuric
+
+886
+01:12:57,760 --> 01:13:08,300
+بينما لو كان SO3 هذا عبارة عن Sulphite لو بده أقول
+
+887
+01:13:08,300 --> 01:13:12,460
+H2SO3 Sulphurous
+
+888
+01:13:14,550 --> 01:13:18,690
+القاعدة ايش بتصير اث سالفوراس عشان نقراها مش
+
+889
+01:13:18,690 --> 01:13:22,070
+سالفوس سالفوراس يعني عشان نقراها ان هي سالفر يعني
+
+890
+01:13:22,070 --> 01:13:29,690
+عشان نعرف نقراها بس مش اكتر سالفوراس تمام طيب لو
+
+891
+01:13:29,690 --> 01:13:38,810
+اجينا اخدنا حاجة زي هذه ايش يا فنات perichloride
+
+892
+01:13:42,370 --> 01:13:51,870
+HClO4 سارك بير اكلوريك اكلوريك
+
+893
+01:13:51,870 --> 01:13:58,410
+اكلوريك اكلوريك اكلوريك
+
+894
+01:13:58,410 --> 01:14:03,170
+اكلوريك اكلوريك
+
+895
+01:14:08,560 --> 01:14:21,340
+العيط ايش تحول ل أث أث يصير أكلوراس أسد طب ال CLO
+
+896
+01:14:21,340 --> 01:14:32,920
+هيبو عيط بيصير هيبو أكلوراس أسد لأنها أكلوراس أسد
+
+897
+01:14:32,920 --> 01:14:35,500
+فالهايبو أقل من هيبو أكلوراس أسد
+
+898
+01:14:48,480 --> 01:14:58,720
+نشوف كمان يعني بعض الأمثلة او
+
+899
+01:14:58,720 --> 01:15:04,980
+قال لي مثلا name the acids HCN باخد على طول لما
+
+900
+01:15:04,980 --> 01:15:07,600
+نقول name the acid ايش بساوي بروح على طول للانيون
+
+901
+01:15:07,600 --> 01:15:12,900
+ال هو بتحدى اسم ال acid الانيون ايش الانيون؟ CNN
+
+902
+01:15:12,900 --> 01:15:14,760
+متذكرين ايش يعني ال CNN؟
+
+903
+01:15:17,950 --> 01:15:25,850
+cyanide حلو الايد ايش بنعمله hydrocyanic
+
+904
+01:15:25,850 --> 01:15:30,450
+acid قولنا بنحوط قبله hydro بنحوّل الايد لا ايه اك
+
+905
+01:15:30,450 --> 01:15:36,210
+قولنا لازم نتذكر يعني صح كان صعب عليكم عشان يعني
+
+906
+01:15:36,210 --> 01:15:42,830
+كله في حصة واحدة لكن طيب نيتريت هيا أخدنا الايه ال
+
+907
+01:15:42,830 --> 01:15:50,500
+nitrate هذا cyanideهذه نيتريت ايش بنعمل ال nitrate
+
+908
+01:15:50,500 --> 01:15:55,840
+يالا على طول ايت نيتريك acid ال nitrate فورا مدام
+
+909
+01:15:55,840 --> 01:16:02,200
+اكسي انايون ال ايت بتصير ايك و خلاص طيب ال H2SO4
+
+910
+01:16:02,200 --> 01:16:08,940
+هاي الانيون صلفيت على
+
+911
+01:16:08,940 --> 01:16:10,700
+طول اذا صلفيوريك
+
+912
+01:16:14,350 --> 01:16:22,950
+طبعا هذا شفناه برضه ال H2SO3 هذا sulphite اذا
+
+913
+01:16:22,950 --> 01:16:27,390
+بده اقول sulphurous
+
+914
+01:16:27,390 --> 01:16:36,570
+acid ماشي يا جماعة يعني لما يتراجعوا هذا الكلام ان
+
+915
+01:16:36,570 --> 01:16:41,470
+شاء الله بتلاقوه سهل للغايةبس هذا هو المعطق وراء
+
+916
+01:16:41,470 --> 01:16:57,790
+التسمية هيك أي مركّب بنقدر نسميه بسهولة للغاية عكس
+
+917
+01:16:57,790 --> 01:17:01,730
+هذا الكلام بالظبط ثواني بس عكسه بالظبط فيه ملوى
+
+918
+01:17:01,730 --> 01:17:05,670
+أعطاني اسم ال acid و جالي هات ال structure تبعه
+
+919
+01:17:05,670 --> 01:17:12,600
+برضه ممكن فجالي hydrobromic acidهيدروبروميك أسد
+
+920
+01:17:12,600 --> 01:17:18,380
+ماذا فيه هيدرو و ايك اذا اعيد اعيد اصلا برومايد
+
+921
+01:17:18,380 --> 01:17:23,330
+يفجأة HPRيبجى اصله ايه؟ مدام جالي هايدرو هذه تضعف
+
+922
+01:17:23,330 --> 01:17:28,430
+للعيد فاصل ال .. اه هذه برومايد فهيبجى هذا كلام
+
+923
+01:17:28,430 --> 01:17:34,850
+HBR طب كربونيك أسد هذا على طول كربونيت كربونيك أسد
+
+924
+01:17:34,850 --> 01:17:43,190
+جاء من الكربونيت يبجى H2CO3 H2CO3 ليه؟ لأن أصلها
+
+925
+01:17:43,190 --> 01:17:50,120
+كربونيت هي H2CO3 تعالوا نسمي الـ Acid هذه
+
+926
+01:17:50,120 --> 01:17:55,400
+Carbonate بتصير Carbonic Acid على طول لأنها
+
+927
+01:17:55,400 --> 01:18:01,880
+Oxyanion فوسفوريك Acid نفس الكلام هذه أصلها فوسفيت
+
+928
+01:18:01,880 --> 01:18:08,080
+اذا H اه PO4 نحط لها الـ H اللازم لها H3 PO4
+
+929
+01:18:08,080 --> 01:18:15,300
+Nitrous Acidأيت كانت لأ لو نيتريت كانت نيتريك أسد
+
+930
+01:18:15,300 --> 01:18:20,680
+هذه ن او اتنين نيتراس نيتريت أصلها لأن ال ايت هي
+
+931
+01:18:20,680 --> 01:18:28,160
+اللي بتجلب لأس ال ايت اللي بتجلب لأس فالنيتراس أسد
+
+932
+01:18:28,160 --> 01:18:32,800
+معناته HNO2 لأنه فيه أنه نيتريت ليه؟ لأنه ال
+
+933
+01:18:32,800 --> 01:18:39,680
+representativeأكسيانيوم بياخد تلاتة oxygens في ال
+
+934
+01:18:39,680 --> 01:18:43,480
+period اتنين اللى فيها ال boron و ال carbon و ال
+
+935
+01:18:43,480 --> 01:18:47,060
+nitrogen يبجى هان لما تقول هات اتنين مش تلاتة ايت
+
+936
+01:18:47,060 --> 01:18:54,640
+قولنا ن اتنين يعني ايت وبالتالي hno اتنين هدعب عن
+
+937
+01:18:54,640 --> 01:19:01,560
+ال nitrous acidطيب يا جماعة ضايل علينا للأسف يعني
+
+938
+01:19:01,560 --> 01:19:05,480
+نقطة صغيرة خالص تاخد لها خمس دقايق لكن فاش معنوقة
+
+939
+01:19:05,480 --> 01:19:09,960
+جدا انكملها الحصة الجاية إذا الله راد الحصة الجاية
+
+940
+01:19:09,960 --> 01:19:18,540
+بنكمل تسمية ال binary molecular compounds فيعني مش
+
+941
+01:19:18,540 --> 01:19:21,740
+هتاخد معنوقة كتير نقطة صغيرة خالص لكنها مهمة جدا
+
+942
+01:19:21,740 --> 01:19:25,660
+وبرضه دائما بنسل عنها في الامتحانات فبنشوفكم إذا
+
+943
+01:19:25,660 --> 01:19:26,680
+الله راد الحصة الجاية
+
diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ioVHzgIc_40.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ioVHzgIc_40.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e412bdfff07cecd6b3e8bd5560f3cbb4549602be
--- /dev/null
+++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/ioVHzgIc_40.srt
@@ -0,0 +1,4187 @@
+1
+00:00:20,870 --> 00:00:24,310
+بسم الله الرحمن الرحيم إذا الله راضٍ اليوم نتكلم
+
+2
+00:00:24,310 --> 00:00:28,510
+عن آخر محاضرة في الـ chapter اللي بتحدث عن الـ
+
+3
+00:00:28,510 --> 00:00:31,950
+properties of solutions فكنا في الحصة الماضية 
+
+4
+00:00:31,950 --> 00:00:35,810
+تكلمنا عن بعض الـ qualitative properties تكلمنا
+
+5
+00:00:35,810 --> 00:00:39,890
+عن الـ vapor pressure lowering تكلمنا عن الـ
+
+6
+00:00:39,890 --> 00:00:43,330
+Boiling Point Elevation والـ Freezing Point 
+
+7
+00:00:43,330 --> 00:00:46,730
+Depression ففيما يتعلق بالـ Boiling Point
+
+8
+00:00:46,730 --> 00:00:50,890
+Elevation والـ Freezing Point Depression قلنا إن
+
+9
+00:00:50,890 --> 00:00:54,490
+الـ Depression في الـ Freezing Point بيساوي Kf في 
+
+10
+00:00:54,490 --> 00:00:58,850
+M وشفنا إحنا إن الـ Kf هو الـ Molal Freezing
+
+11
+00:00:58,850 --> 00:01:04,210
+Point Constant وشفنا برضه إن هو خاص بكل solvent والـ
+
+12
+00:01:04,210 --> 00:01:07,990
+M هي الـ Molality وبنفس الطريقة تمامًا الـ
+
+13
+00:01:07,990 --> 00:01:08,830
+Delta Tb
+
+14
+00:01:12,680 --> 00:01:17,700
+مولال الـ boiling point constant مولال الـ M مولال
+
+15
+00:01:17,700 --> 00:01:21,860
+الـ T مولال الـ M مولال الـ T مولال الـ M مولال 
+
+16
+00:01:21,860 --> 00:01:24,980
+الـ T مولال الـ M مولال الـ T مولال الـ T مولال 
+
+17
+00:01:24,980 --> 00:01:27,680
+الـ M مولال الـ T مولال الـ T مولال الـ T مولال
+
+18
+00:01:27,680 --> 00:01:28,860
+الـ T مولال الـ T مولال الـ T مولال الـ T مولال
+
+19
+00:01:28,860 --> 00:01:36,780
+الـ T مولال الـ T مولال
+
+20
+00:01:36,780 --> 00:01:44,150
+الـ T فخلينا نتطلع على بعض الأمثلة بهذا الـ قصص بقول
+
+21
+00:01:44,150 --> 00:01:47,850
+لي مثلًا what's the molecular mass of a solute if 
+
+22
+00:01:47,850 --> 00:01:51,790
+250 grams of the solute are dissolved in 1000
+
+23
+00:01:51,790 --> 00:01:55,990
+grams of water and the temperature rose by 3.5 
+
+24
+00:01:55,990 --> 00:02:03,670
+degrees c يعني لما دوبنا 250 gram من solute ما في
+
+25
+00:02:03,670 --> 00:02:07,690
+الألف جرام من الميه لاحظنا إنه في عندي boiling point
+
+26
+00:02:07,690 --> 00:02:12,010
+elevation بمقدار ثلاثة ونصف ديجري سي الـ KB point
+
+27
+00:02:12,010 --> 00:02:18,130
+five one ديجري سي طبعًا هذا خاص بالميه طريقة الحل 
+
+28
+00:02:18,130 --> 00:02:22,090
+كتير سهلة في البداية أنا بقدر أجيب الـ molality من
+
+29
+00:02:22,090 --> 00:02:27,230
+الـ boiling point elevation لأن هذا الـ constant معروف
+
+30
+00:02:27,230 --> 00:02:31,010
+والـ delta Tb معايا فبقدر أجيب الـ molality الـ
+
+31
+00:02:31,010 --> 00:02:33,890
+molality تعريفها والله mol solute على الـ kilogram 
+
+32
+00:02:33,890 --> 00:02:37,710
+solvent وأنا عندي kilogram solvent أصلًا فبقدر أجيب 
+
+33
+00:02:37,710 --> 00:02:41,710
+أنا الـ mol solute هي عبارة عن الـ molality في الـ
+
+34
+00:02:41,710 --> 00:02:47,780
+kilogram solvent فالمolality اللي أنا حسبتها بقدر
+
+35
+00:02:47,780 --> 00:02:52,300
+أقول مباشرة بضربها في وزن الـ solvent بالكيلوجرام 
+
+36
+00:02:52,300 --> 00:02:55,500
+باعطيني number of moles مادام جبت number of moles
+
+37
+00:02:55,500 --> 00:02:58,840
+أنا بعرف إن الـ moles number of moles بتساوي الـ massع 
+
+38
+00:02:58,840 --> 00:03:02,040
+الفورمولوية أو يعني الفورمولوية دي عبارة عن الـ mass ع
+
+39
+00:03:02,040 --> 00:03:06,060
+عدد المولات فبحلول المسألة كل المسألة بهذه
+
+40
+00:03:06,060 --> 00:03:10,740
+الطريقة يبقى مفتاح الحل عندي إن أوجد الـ molality و
+
+41
+00:03:10,740 --> 00:03:13,640
+أعرف هذه الـ molality كيف أنا حصلت عليها عشان أجيب 
+
+42
+00:03:13,640 --> 00:03:17,710
+number of moles بطريقة صحيحة ففي البداية delta Tb 
+
+43
+00:03:17,710 --> 00:03:21,130
+بتساوي Kb في M ثلاثة ونصف ديجري الـC point five
+
+44
+00:03:21,130 --> 00:03:25,930
+one اللي هو الـKb في M  M فقط هي المجهولة تطلع 6.86 
+
+45
+00:03:25,930 --> 00:03:29,890
+لكن الـ modality بتساوي عدد المولات من الـ solute ع الـ
+
+46
+00:03:29,890 --> 00:03:34,430
+kilogram solvent عدد المولات من الـ solute بده يساوي 
+
+47
+00:03:34,430 --> 00:03:37,870
+الـ modality اللي هي 6.86 في واحد kilogram solvent
+
+48
+00:03:37,870 --> 00:03:44,140
+لأنه جلي ألف gram معنى الكلام 6.86 moles طيب الـ
+
+49
+00:03:44,140 --> 00:03:47,000
+molecular mass الآن اللي هي عن الـ formula weight
+
+50
+00:03:47,000 --> 00:03:50,720
+هي عبارة عن الـ formula تساوي الـ mass على عدد
+
+51
+00:03:50,720 --> 00:03:55,810
+المولات الـ mass اللي عندي 250 gram اللي أعطاني إياها هذه
+
+52
+00:03:55,810 --> 00:04:01,270
+الـ molality 250 جرام على الـ number of moles 6.86 
+
+53
+00:04:01,270 --> 00:04:05,530
+بيطلع عندي الـ molecular mass 36 و4 من 10 في
+
+54
+00:04:05,530 --> 00:04:08,110
+الحقيقة طريقة سهلة كثير لتعيين الـ molecular mass
+
+55
+00:04:08,110 --> 00:04:16,330
+وإن كانت يعني مش دائمًا بتكون دقيقة جدًا لأن تعيين
+
+56
+00:04:16,330 --> 00:04:20,070
+درجة الحرارة أو التغير في درجة الحرارة ممكن 
+
+57
+00:04:20,070 --> 00:04:24,330
+ما يكونش يعني كبير كثير فممكن يكون فيها شوية عدم دقة
+
+58
+00:04:24,330 --> 00:04:28,730
+في طرق أفضل منها برضه في في ما يتعلق بالـ
+
+59
+00:04:28,730 --> 00:04:32,430
+properties الـ Collegate في أحسن من الـ boiling
+
+60
+00:04:32,430 --> 00:04:37,830
+point elevation نطلع على كمان مثال بيقول اللي هي
+
+61
+00:04:37,830 --> 00:04:40,610
+solution of an unknown non volatile non
+
+62
+00:04:40,610 --> 00:04:44,670
+electrolyte was prepared by dissolving 0.25 gram
+
+63
+00:04:44,670 --> 00:04:47,590
+of the substance in 40 gram of carbon
+
+64
+00:04:47,590 --> 00:04:51,210
+tetrachloride إذا هذا محلول مش شرط يكون ماء يمكن 
+
+65
+00:04:51,210 --> 00:04:55,530
+يكون أي محلول مش شرط يكون الألف جرام في أي وزن من
+
+66
+00:04:55,530 --> 00:04:59,430
+الـ solvent فشي عين دي مشكلة بيقول the boiling point
+
+67
+00:04:59,430 --> 00:05:05,020
+of the resulting solution was 0.357 degree c 0.357 
+
+68
+00:05:05,020 --> 00:05:09,300
+degree c higher than that of pure solvent يعني الـ
+
+69
+00:05:09,300 --> 00:05:14,200
+delta Tb 0.357 لأنه لاقينا إنه الـ boiling point
+
+70
+00:05:14,200 --> 00:05:19,440
+elevation 0.357 فبيقول ليه؟ find the molar mass of 
+
+71
+00:05:19,440 --> 00:05:25,280
+the solute إذا كان الـ Kb للسولفن 5.02 degree c per 
+
+72
+00:05:25,280 --> 00:05:30,710
+molar فبيقول delta Tb اللي هي 3.57 تساوي الـ Kb معايا 5 
+
+73
+00:05:30,710 --> 00:05:36,110
+.8 وفي الـ molality الـ molality 0.071 مباشر جدًا لكن 
+
+74
+00:05:36,110 --> 00:05:38,370
+الـ molality هي الـ more solute على الـ kilogram
+
+75
+00:05:38,370 --> 00:05:43,750
+solvent فمعنى الكلام الـ more solute تساوي الـ 
+
+76
+00:05:43,750 --> 00:05:47,570
+molality في الـ kilogram solvent المolality حسبته 0 
+
+77
+00:05:47,570 --> 00:05:52,390
+.0711 الـ kilogram solvent أربعين جرام يعني 0.040 
+
+78
+00:05:52,390 --> 00:05:57,220
+kilogram أربعين في عشرة أس سالب تلاتة معناه الكلام 
+
+79
+00:05:57,220 --> 00:06:01,160
+point o o two eight moles الآن بنعرف إن عدد 
+
+80
+00:06:01,160 --> 00:06:03,080
+المولات الـ mass على الـ formula weight يبقى الـ 
+
+81
+00:06:03,080 --> 00:06:06,540
+formula weight الـ mass على عدد المولات يعني point 
+
+82
+00:06:06,540 --> 00:06:10,720
+two five zero اللي هي وزن المادة الـ unknown على
+
+83
+00:06:10,720 --> 00:06:17,400
+عدد مولاتها بنلاقي eighty eight grams per mole هذه
+
+84
+00:06:17,400 --> 00:06:23,280
+هي الـ molecular mass طب من الـ freezing point
+
+85
+00:06:23,280 --> 00:06:27,700
+depression نفس المنطق بالظبط بقول مثلًا five point 
+
+86
+00:06:27,700 --> 00:06:33,140
+five grams of a newly synthesized compound was 
+
+87
+00:06:33,140 --> 00:06:39,980
+dissolved يعني مركب حضرناه بطريقة مركب جديد يعني 
+
+88
+00:06:40,630 --> 00:06:45,230
+كويس يعني حضرناه تجريبيًا إحنا بنقول .. ما بدناش نقول 
+
+89
+00:06:45,230 --> 00:06:48,150
+خلقناه يعني عارفة في اللغة العربية بيقولوا خلقناه 
+
+90
+00:06:48,150 --> 00:06:52,310
+لكن إحنا بيقولوا حضرناه يعني نفس الحاجة عشان ما ..
+
+91
+00:06:52,310 --> 00:06:55,550
+يعني مش .. يعني ما عملناهاش من لا شيء يعني عشان
+
+92
+00:06:55,550 --> 00:06:58,630
+نقول خلقناه يعني مع إنه في الـ .. الـ .. الـ .. الـ 
+
+93
+00:06:58,630 --> 00:07:01,770
+كيمياء العضوية بيقولوا هذا المصطلح يعني لكن يعني
+
+94
+00:07:01,770 --> 00:07:06,250
+حضرناه بطريقة ما يعني لكن مش عارفين إيش الـ motor
+
+95
+00:07:06,250 --> 00:07:12,420
+mass تبعته 5.5 جرام منه ودورناهم في 250 جرام من 
+
+96
+00:07:12,420 --> 00:07:18,580
+البنزين البنزين الكاف له 5.12 ديجري سي برمولد حلو
+
+97
+00:07:18,580 --> 00:07:22,060
+بيقول and the freezing point depression was found
+
+98
+00:07:22,060 --> 00:07:26,080
+to be 1.2 ديجري سي is in the delta TF freezing
+
+99
+00:07:26,080 --> 00:07:30,610
+point depression خلينا Delta TF واحد واثنين من عشرة 
+
+100
+00:07:30,610 --> 00:07:33,450
+ديجري الـC بيقول find the molecular mass of the 
+
+101
+00:07:33,450 --> 00:07:36,410
+compound بيقول Delta TF اللي هي واحد واثنين من 
+
+102
+00:07:36,410 --> 00:07:40,410
+ديجري الـC كان ممكن يعقّلنا إنه والله الحرارة اللي
+
+103
+00:07:40,410 --> 00:07:44,230
+لاقينا إنه الـ freezing point صارت هلجد والـ pure 
+
+104
+00:07:44,230 --> 00:07:47,190
+salt بتقوله freezing point هلجد فبتجيب الفرق هو
+
+105
+00:07:47,190 --> 00:07:49,850
+عبارة عن دلتا لكن لا هو ده اللي أنا على طول إنه الـ
+
+106
+00:07:49,850 --> 00:07:53,350
+freezing point depression was found to be واحد 
+
+107
+00:07:53,350 --> 00:07:58,920
+واثنين من عشرة ديجري الـC فبتساوي Kf اللي هو degree 
+
+108
+00:07:58,920 --> 00:08:02,900
+c per mol في الـ molality إذا الـ molality 0.199
+
+109
+00:08:02,900 --> 00:08:07,000
+mol حلو كثير، مادام جبنا الـ molality على طول بجيب
+
+110
+00:08:07,000 --> 00:08:11,080
+الـ moles الـ moles بتساوي الـ molality في الـ
+
+111
+00:08:11,080 --> 00:08:14,040
+kilogram solvent شفنا هذا الكلام سابقًا الـ
+
+112
+00:08:14,040 --> 00:08:18,200
+molality 0.199 الـ kilogram solvent جعل 250 gram
+
+113
+00:08:18,200 --> 00:08:25,200
+بنزين إذا 0.250 kilogram بنزين يبقى point two five 
+
+114
+00:08:25,200 --> 00:08:28,380
+zero كل إيه بيطلع عند العدد المولات point oh four
+
+115
+00:08:28,380 --> 00:08:33,820
+nine eight كمان مرة العدد المولات هو عبارة عن الـ
+
+116
+00:08:33,820 --> 00:08:37,280
+mass بالإجرام على الـ formula weight أو الـ formula 
+
+117
+00:08:37,280 --> 00:08:39,860
+weight هي عبارة عن الـ mass بالإجرام على عدد المولات 
+
+118
+00:08:39,860 --> 00:08:45,900
+ترتيب فالـ mass خمسة ونصي grams عدد المولات point oh 
+
+119
+00:08:45,900 --> 00:08:49,260
+four nine eight إذن بيطلع عند مئة وعشرة إجرام
+
+120
+00:08:49,260 --> 00:08:51,720
+المل هاد هي الـ formula weight 
+
+121
+00:08:54,330 --> 00:08:58,050
+كمان مسألة بيقول لإيه solution of point eight five
+
+122
+00:08:58,050 --> 00:09:02,750
+grams of a compound in
+
+123
+00:09:02,750 --> 00:09:05,930
+hundred grams of بنزين has a freezing point of
+
+124
+00:09:05,930 --> 00:09:08,530
+five point one six degrees c إذا أعطاني الـ
+
+125
+00:09:08,530 --> 00:09:13,090
+freezing point للـ solution what are the molality
+
+126
+00:09:13,090 --> 00:09:14,930
+and the molar mass
+
+127
+00:09:24,090 --> 00:09:29,090
+على طول بقول والله المولاليتي بدها تساوي الـ delta 
+
+128
+00:09:29,090 --> 00:09:34,670
+TF على الـ KF دلتا TF خمسة ونص كانت صارت خمسة وستة
+
+129
+00:09:34,670 --> 00:09:40,460
+عشر مية قلت طبعًا freezing point depression على الـ 
+
+130
+00:09:40,460 --> 00:09:47,160
+KF  0512 بيطلع عندي 0.066 مول لكل جرام لكل كيلو جرام
+
+131
+00:09:47,160 --> 00:09:50,820
+هذا عبارة عن الـ molality اللي بنحسبها كل مرة زي ما
+
+132
+00:09:50,820 --> 00:09:54,000
+شوفنا سابقًا لكن الـ molality هي المول solute على الـ 
+
+133
+00:09:54,000 --> 00:09:57,620
+kilogram solvent أو المول solute بنساوي الـ molality 
+
+134
+00:09:57,620 --> 00:10:03,390
+في الـ kilogram solvent المولالية حسبناها 0.066 في
+
+135
+00:10:03,390 --> 00:10:08,910
+جدّاش وزن الـ solvent بالكيلو جرام مائة جرام في 
+
+136
+00:10:08,910 --> 00:10:11,870
+عشرة أس سالب تلاتة يعني واحد من عشرة كيلو جرام
+
+137
+00:10:11,870 --> 00:10:16,010
+فبيطلع عندي six point six في عشرة أس سالب تلاتة
+
+138
+00:10:16,010 --> 00:10:19,810
+moles وبنفس الطريقة الـ moles هي عبارة عن الـ mass على 
+
+139
+00:10:19,810 --> 00:10:22,730
+الـ formulate أو الـ formulate mass على المول الـ mass 
+
+140
+00:10:22,730 --> 00:10:26,430
+point eight five gram من الـ compound على عدد 
+
+141
+00:10:26,430 --> 00:10:29,530
+مولاته six point six في عشرة أس سالب تلاتة بتطلع
+
+142
+00:10:29,530 --> 00:10:31,430
+عندي مية تمانية وعشرين
+
+143
+00:10:33,810 --> 00:10:37,970
+آخر مثال بس اللي أنا بدي أبين فكرة معينة فيه بيقول
+
+144
+00:10:37,970 --> 00:10:45,290
+كامفور هيك رمزه melts at 179.8 degree c melts يعني
+
+145
+00:10:45,290 --> 00:10:50,590
+هي نفس درجة ال freezing مدام هو بيدوب زي التلج هو 
+
+146
+00:10:50,590 --> 00:10:54,090
+نفس الدرجة لأن ال melting و ال freezing نفس الشيء
+
+147
+00:10:54,090 --> 00:10:57,330
+نفس الشيء واحدة يعني عكس الثانية لكن بتمثل نفس
+
+148
+00:10:57,330 --> 00:11:03,680
+درجة الحرارة and has a high Kf value عادة ال Kf 
+
+149
+00:11:03,680 --> 00:11:07,820
+اللي هو جدّيش مش خمسة ولا point five point five one
+
+150
+00:11:07,820 --> 00:11:11,580
+ولا one point eight six لا أربعين degree c لكل
+
+151
+00:11:11,580 --> 00:11:16,240
+مولال علشان هيك استخدامه بيعطينا نتائج أدق لأن
+
+152
+00:11:16,240 --> 00:11:21,520
+الفرق فيه خليني أقول درجة الحرارة بيكون أحسن عادة 
+
+153
+00:11:23,050 --> 00:11:26,410
+أربعين ديجريسي و point one eight six gram of an
+
+154
+00:11:26,410 --> 00:11:28,690
+unknown إذا وزن ال unknown point one eight six
+
+155
+00:11:28,690 --> 00:11:32,770
+gram بقدر آخذ كمية قليلة منه مش خمسة و نص جرام ولا
+
+156
+00:11:32,770 --> 00:11:36,690
+عشرة جرام لا point one eight six gram ده واخدت 
+
+157
+00:11:36,690 --> 00:11:42,030
+أكثر كان فرق درجات الحرارة كان أكبر لكن فقط كمية 
+
+158
+00:11:42,030 --> 00:11:48,190
+قليلة جدًّا من ال unknown in twenty point one grams
+
+159
+00:11:48,190 --> 00:11:53,400
+of liquid camphor إذا هاي وزن الكامفور اللي هو ال
+
+160
+00:11:53,400 --> 00:11:56,040
+solvent the freezing point of the mixture was
+
+161
+00:11:56,040 --> 00:12:00,620
+found to be 176.7 degree c what's the molar mass
+
+162
+00:12:00,620 --> 00:12:04,800
+of the solute نفس الكلام delta TF KF في ال M Delta 
+
+163
+00:12:04,800 --> 00:12:16,360
+TF الأصلية 179.8 minus 176.7 كويس بدها تساوي
+
+164
+00:12:16,360 --> 00:12:20,980
+ال KF أربعين ديجري سي بر مولال في ال M ال M نحسبها
+
+165
+00:12:20,980 --> 00:12:26,060
+point 0.0775 نفس الكلام المولالية مول ع ال 
+
+166
+00:12:26,060 --> 00:12:29,500
+kilogram solvent مول صليوت إذا المول صليوت مولالتي 
+
+167
+00:12:29,500 --> 00:12:33,560
+في ال kilogram solvent أو point 0.0775 في point 0
+
+168
+00:12:33,560 --> 00:12:38,120
+.02201 اللي هو هذا ال volume اتنين و عشرين و شوية 
+
+169
+00:12:38,120 --> 00:12:44,490
+mil يعني point 0.022 أول لتر بتساوي one point seven
+
+170
+00:12:44,490 --> 00:12:48,950
+one في عشرة أس سالب تلاتة إذا عدد المولات الماس
+
+171
+00:12:48,950 --> 00:12:51,590
+على ال formula weight أو ال formula weight تساوي الماس على
+
+172
+00:12:51,590 --> 00:12:55,690
+عدد المولات الماس point one eight six على عدد
+
+173
+00:12:55,690 --> 00:12:57,950
+المولات one point seven one في عشرة أس سالب تلاتة 
+
+174
+00:12:57,950 --> 00:13:01,030
+بتطلع عندي مية وتسعة إذا ال formula weight أو ال
+
+175
+00:13:01,030 --> 00:13:06,460
+molecular mass مية وتسعة بنلاحظ أنه كل الأسئلة في 
+
+176
+00:13:06,460 --> 00:13:09,860
+هذا المجال بتدور حوالين نفس الشيء يعني هذه أسئلة
+
+177
+00:13:09,860 --> 00:13:13,820
+كلها مهمة و ممكن أنه نسأل عنها في الامتحان يعني
+
+178
+00:13:13,820 --> 00:13:19,600
+هذا سؤال سهل سؤال بسيط من خلاله بنحسب حاجتين
+
+179
+00:13:19,600 --> 00:13:22,560
+بنحسب ال morality وهذا شيء كويس وكمان بنحسب
+
+180
+00:13:22,560 --> 00:13:25,200
+ال molecular mass هذا شيء ممتاز بالنسبة لنا يعني
+
+181
+00:13:25,200 --> 00:13:29,420
+السؤال بعطيني معلومتين مهمات للغاية عشان هيك بنحب
+
+182
+00:13:29,420 --> 00:13:33,380
+احنا عمومًا يعني في الامتحانات أنه نسأل أسئلة بسيطة
+
+183
+00:13:33,690 --> 00:13:38,230
+زي هيك لكن في نفس الوقت بتعطيني أكثر من مفهوم 
+
+184
+00:13:38,230 --> 00:13:41,270
+دكتور فيه بيانات اللي هيحسب فيها ال formula weight؟
+
+185
+00:13:41,270 --> 00:13:48,610
+آه من المعطيات هذه والله يعني ال formula weight أنا
+
+186
+00:13:48,610 --> 00:13:53,670
+أعتقد أنه لا من المعطيات هذه لا
+
+187
+00:13:53,670 --> 00:13:56,430
+لو معك ال density بتقدر تجيب ال molar mass وممكن يعني 
+
+188
+00:13:56,430 --> 00:14:01,550
+مثلًا آه ممكن يعني لكن من غير ال density لا لازم
+
+189
+00:14:01,550 --> 00:14:06,340
+يكون معك معلومات أخرى الآن نتكلم عن مفهوم ال 
+
+190
+00:14:06,340 --> 00:14:10,980
+Osmosis Osmosis وضغط ال Osmosis يمكن سمعته عنه
+
+191
+00:14:10,980 --> 00:14:21,260
+أكيد في المدرسة فبنقول أن بعض ال بعض الجزيئات
+
+192
+00:14:21,260 --> 00:14:25,920
+طبعًا تتفاوت في البداية بال size تبعها تتفاوت بال 
+
+193
+00:14:25,920 --> 00:14:29,960
+size تبعها فممكن يكون في عندي 
+
+194
+00:14:32,350 --> 00:14:38,710
+خليني أقول membranes أغشية ال membranes هذه فيها فتحات 
+
+195
+00:14:38,710 --> 00:14:45,870
+فيها pores فيها مسامات كويس فيها مسامات المسامات 
+
+196
+00:14:45,870 --> 00:14:51,310
+هذه قد تكون تتسع لجزء صغير لكن لا تتسع لجزء أكبر
+
+197
+00:14:51,310 --> 00:14:55,930
+منه فالجزء الكبير مؤكد أنه مش راح يدخل بينما الجزء 
+
+198
+00:14:55,930 --> 00:14:59,980
+الصغير في عنده خيار الجزيء الصغير آه مدام فيه ثقب 
+
+199
+00:14:59,980 --> 00:15:04,800
+واسع أنه ينتقل على طرفي ال membrane فبيمكنه أن 
+
+200
+00:15:04,800 --> 00:15:09,740
+ينتقل فبنقول احنا ال semi permeable membranes اللي 
+
+201
+00:15:09,740 --> 00:15:14,840
+هي الأغشية شبه المنفذة كويس يعني اللي لها مسامات
+
+202
+00:15:14,840 --> 00:15:19,020
+في range معين allow some smaller particles to pass
+
+203
+00:15:19,020 --> 00:15:24,610
+through بتسمح لبعض الجزيئات الصغيرة أنها إيه؟ تعدّي
+
+204
+00:15:24,610 --> 00:15:28,410
+في الاتجاهين في الحقيقة but they block other
+
+205
+00:15:28,410 --> 00:15:33,980
+larger particles ليه؟ لأن المسام لا يتسع لمرور ال 
+
+206
+00:15:33,980 --> 00:15:37,080
+particle الكبير فال particle الصغير آه عنده حرية
+
+207
+00:15:37,080 --> 00:15:40,580
+هذا بداية يعني ال semipermeable membranes كثيرة
+
+208
+00:15:40,580 --> 00:15:45,780
+خالص وتتفوّت في ال porosity تتفاوت في ال poor size
+
+209
+00:15:45,780 --> 00:15:51,340
+تتفاوت في حجم أو يعني حجم المسام تبعه وبالتالي لا
+
+210
+00:15:51,340 --> 00:15:56,980
+شك أنها بتسمح لبعض الجزيئات اللي أصغر من المسام 
+
+211
+00:15:56,980 --> 00:16:01,360
+أن تدخل لكن الجزيئات الأكبر من المسام مستحيل أنها
+
+212
+00:16:01,360 --> 00:16:07,160
+تدخل ما تقدرش هذا وضع طبيعي في ال biological
+
+213
+00:16:07,160 --> 00:16:11,200
+systems في جسم الإنسان والحيوانات وغيره كويس
+
+214
+00:16:11,200 --> 00:16:17,520
+بنلاحظ أن ال most semi permeable membranes كل
+
+215
+00:16:17,520 --> 00:16:21,640
+الأغشية اللي موجودة طبعًا كل الإنسان أغشية في
+
+216
+00:16:21,640 --> 00:16:25,920
+الخلايا في غيره معظم الأغشية هذه تسمح فقط بمرور
+
+217
+00:16:25,920 --> 00:16:31,040
+الماء ليه؟ لأن ال poor size تبعها فقط كافي لمرور
+
+218
+00:16:31,040 --> 00:16:36,280
+المياه أي شيء أكبر من المياه مسموحلهش عادة في
+
+219
+00:16:36,280 --> 00:16:40,860
+بتسمح لحاجات ثانية؟ في، لكن عادة في ال يعني
+
+220
+00:16:40,860 --> 00:16:46,780
+خليني أقول النسبة القريبة من 100% لها بتسمح فقط 
+
+221
+00:16:46,780 --> 00:16:50,860
+بمرور الايه؟ المياه يعني ال poor size تبعها قليل و
+
+222
+00:16:50,860 --> 00:16:55,880
+هنشوف هذا الكلام بعد شوية طب إيش هو ال osmosis؟ اللي
+
+223
+00:16:55,880 --> 00:16:58,180
+بتتكلم عنه واحنا قلنا هذه ال Semi-permeable
+
+224
+00:16:58,180 --> 00:17:01,260
+membranes طب إيه هو ال Osmosis؟ جال ال Osmosis هو
+
+225
+00:17:01,260 --> 00:17:07,820
+عبارة عن عملية من خلالها جزيئات ال solvent بتنتقل
+
+226
+00:17:07,820 --> 00:17:11,980
+خلال ال Semi-permeable membrane من المنطقة اللي 
+
+227
+00:17:11,980 --> 00:17:17,020
+ال solvent فيها كثير مركز أكثر تركيز ال solvent مش
+
+228
+00:17:17,020 --> 00:17:22,660
+ال solute أكبر إلى المنطقة اللي تركيز ال solvent
+
+229
+00:17:22,660 --> 00:17:27,180
+فيها أقل بمعنى آخر من المنطقة الأقل تركيز فيما
+
+230
+00:17:27,180 --> 00:17:31,660
+يتعلق بال solute إلى المنطقة الأعلى تركيز إيش اللي 
+
+231
+00:17:31,660 --> 00:17:35,400
+بتنتقل مش ال solute الـ water فالمياه بتنتقل من
+
+232
+00:17:35,400 --> 00:17:39,810
+إذا كنا بنأخذ باعتبار ال solvent  السولفان الأعلى
+
+233
+00:17:39,810 --> 00:17:43,370
+الأكثر يعني اللي خلينا نقول المحلول بيكون أقل 
+
+234
+00:17:43,370 --> 00:17:48,790
+تركيز من المحلول الأقل تركيز إلى المحلول الأعلى
+
+235
+00:17:48,790 --> 00:17:53,250
+تركيز فال Osmosis is a process by which molecules
+
+236
+00:17:53,250 --> 00:17:57,910
+of a solvent tend to pass through a semi permeable
+
+237
+00:17:57,910 --> 00:18:02,090
+membrane from a less concentrated solution يعني
+
+238
+00:18:02,090 --> 00:18:06,510
+السولفان فيه مركز أكثر less concentrated solution
+
+239
+00:18:07,310 --> 00:18:11,750
+ال Concentration بنجيصه بكمية ال Solute المدابة
+
+240
+00:18:11,750 --> 00:18:15,110
+فهذا إيه؟ يعني معناته فيه مياه إيه أكثر ال Less
+
+241
+00:18:15,110 --> 00:18:19,470
+Concentrated Solution تركيز المياه فيه إيه؟ أعلى
+
+242
+00:18:19,470 --> 00:18:23,870
+تركيز ال Solvent أعلى Into a More Concentrated
+
+243
+00:18:23,870 --> 00:18:28,930
+One فيه Solute كثير يعني فيه Solvent أقل يعني ال 
+
+244
+00:18:28,930 --> 00:18:34,310
+Solvent هو اللي بينتقل لو جينا طلعنا هذا Semi
+
+245
+00:18:34,310 --> 00:18:41,450
+-permeable membrane لحظة لو كان عندي مثلًا particle
+
+246
+00:18:41,450 --> 00:18:49,930
+هالجد حجمه يعدّي على طول من هذه pores كويس؟ هذا
+
+247
+00:18:49,930 --> 00:18:52,790
+عبارة عن مسامات لو كان هالجد حجمه يعدّي على طول
+
+248
+00:18:52,790 --> 00:18:57,330
+الأحمر هذا أي عامل إيش بيسوي بيقدر ينتقل لأن هذا
+
+249
+00:18:57,330 --> 00:19:02,590
+الوسع اللي موجود بيساعد لكن الأزرق شايفين بيقدر 
+
+250
+00:19:02,590 --> 00:19:06,570
+يعدّي من هذه الفتحة ما بيقدرش يعدّي إذاً هذا semi
+
+251
+00:19:06,570 --> 00:19:11,350
+permeable membrane يسمح فقط بمرور في الرسم اللي 
+
+252
+00:19:11,350 --> 00:19:16,890
+عنده يسمح فقط بمرور الجزيئات الحمراء بنلاحظ أن
+
+253
+00:19:16,890 --> 00:19:22,990
+الجزيئات الحمراء هنا هذا هو تركيز ال solvent كبير 
+
+254
+00:19:22,990 --> 00:19:27,870
+تركيز ال solvent اللي هو الأحمر أقل مثلًا يعني هنا
+
+255
+00:19:27,870 --> 00:19:34,090
+تركيز المحلول مخفف جدًّا هنا تركيز المحلول مركز لأن 
+
+256
+00:19:34,090 --> 00:19:36,650
+هي ال solute أزرق كمية كبيرة من ال solute فهذا
+
+257
+00:19:36,650 --> 00:19:40,750
+محلول مركز هذا محلول dilute بلاحظ أن جزيئات ال 
+
+258
+00:19:40,750 --> 00:19:45,610
+solvent بتيجي بتعدّي من هذه الفتحات وبتيجي على
+
+259
+00:19:45,610 --> 00:19:50,130
+الناحية هنا للمحلول المركز من المحلول المخفف إلى 
+
+260
+00:19:50,130 --> 00:19:56,470
+المحلول المركز مش معنى الكلام أن المياه بتنتقلش من 
+
+261
+00:19:56,470 --> 00:19:59,890
+المحلول المركز إلى المحلول المخفف لا بتنتقل لكن 
+
+262
+00:19:59,890 --> 00:20:04,730
+معدّل الانتقال من المحلول المخفف إلى المركز أعلى 
+
+263
+00:20:04,730 --> 00:20:10,470
+كثير ففي النهاية ال net ال net tendency القابلية
+
+264
+00:20:10,470 --> 00:20:17,030
+يعني ال net أن والله احنا بنلاحظ أن جزيئات ال
+
+265
+00:20:17,030 --> 00:20:20,650
+solvent بتنتقل من المحلول المخفف للمحلول الأكثر
+
+266
+00:20:20,650 --> 00:20:26,860
+تركيز تمام؟ وزي ما شوفنا هنا كل الجزيئات الزرقاء
+
+267
+00:20:26,860 --> 00:20:30,840
+لأنها أكبر من حجم المسام ال poor size ما تقدرش 
+
+268
+00:20:30,840 --> 00:20:36,220
+تعدّي بنقدر نترجم هذا الكلام برضه هذا واضح هنا عندي
+
+269
+00:20:36,220 --> 00:20:40,900
+هذا محلول خليني أقول solvent pure solvent لأن
+
+270
+00:20:40,900 --> 00:20:43,960
+مافيش فيه ولا solute وهذا محلول فيه شوية solute
+
+271
+00:20:43,960 --> 00:20:47,240
+إذا هذا محلول اللي على اليمين محلول إيه؟ بنقول 
+
+272
+00:20:47,240 --> 00:20:51,460
+مركز اللي على اليسار محلول إيه؟ مخفف أو بالأخرى
+
+273
+00:20:51,460 --> 00:20:56,820
+pure solvent فبلاحظ أن جزيئات ال solvent بتعدّي من
+
+274
+00:20:56,820 --> 00:21:01,740
+اليسار إلى اليمين من اليسار إلى اليمين مش معنى 
+
+275
+00:21:01,740 --> 00:21:03,360
+الكلام اللي هو بتعدّي من اليسار إلى اليمين ما فيش
+
+276
+00:21:03,360 --> 00:21:08,440
+ولا واحد جاي من اليمين لا فيه لكن ال net transfer
+
+277
+00:21:08,440 --> 00:21:15,960
+الانتقال يعني ال net الصافي يعني هو من اليسار إلى 
+
+278
+00:21:15,960 --> 00:21:19,900
+اليمين لكن في نفس الوقت لو اتطلعنا على جزيئات ال
+
+279
+00:21:19,900 --> 00:21:23,360
+solute هل تستطيع العبور؟ هل تستطيع الانتقال؟ لا
+
+280
+00:21:23,360 --> 00:21:27,880
+لأن هذه ال poor size المتاحة لها وهي واضح الأحمر 
+
+281
+00:21:27,880 --> 00:21:32,600
+هذا أكبر من الـ poor size لا تستطيع معنى الكلام في
+
+282
+00:21:32,600 --> 00:21:38,720
+البداية لما نقاش أحط محلول مركز concentrated وهذا 
+
+283
+00:21:38,720 --> 00:21:43,900
+dilute أول ما أحطه before equilibrium before
+
+284
+00:21:43,900 --> 00:21:47,200
+equilibrium هيكون هدول جت بعض على طول لسه هذا semi
+
+285
+00:21:47,200 --> 00:21:51,740
+permeable membrane هذا ايش ماله غشاء شبه منفذ
+
+286
+00:21:51,740 --> 00:21:56,580
+يعني بيقدر يدخل بس جزيقات الـ ايه الـ solvent والـ
+
+287
+00:21:56,580 --> 00:22:01,400
+solute لأ طب حلو الآن الـ solute الآن أول ما حطهم
+
+288
+00:22:01,400 --> 00:22:06,550
+يكون هدول في ارتفاع بعض بالظبط الآن بعد فترة بعد
+
+289
+00:22:06,550 --> 00:22:12,070
+فترة سبته يحصله اتزان ايش عمال بيحصل جزيئات الـ
+
+290
+00:22:12,070 --> 00:22:15,210
+solvent بتعدى من اليسار لليمين من اليسار لليمين من
+
+291
+00:22:15,210 --> 00:22:20,410
+اليسار لليمين من اليسار لليمين لغاية ما نوصل
+
+292
+00:22:20,410 --> 00:22:27,010
+لمرحلة صار في عندها ارتفاع المحلول أكبر منها ليه؟
+
+293
+00:22:27,010 --> 00:22:30,310
+لأنه كمان مرة جزيئات الـ solvent عمال بتنتقل من
+
+294
+00:22:30,310 --> 00:22:38,240
+اليسار لليمين تمام ليه؟ لأنه تركيز الـ solvent على
+
+295
+00:22:38,240 --> 00:22:42,420
+اليسار أكبر من تركيز الـ solvent على اليمين فالـ
+
+296
+00:22:42,420 --> 00:22:46,920
+solvent molecules بتنتقل فبنلاحظ فيها أن عندي صار
+
+297
+00:22:46,920 --> 00:22:53,760
+ارتفاع الـ solution أعلى في المنطقة المركز من
+
+298
+00:22:53,760 --> 00:22:58,270
+المخفف هذا عبارة عن الـ Osmotic Pressure، هذا عبارة
+
+299
+00:22:58,270 --> 00:23:01,670
+عن الـ Osmotic Pressure، تمام؟ يعني هذا هو اللي
+
+300
+00:23:01,670 --> 00:23:04,370
+بعطيني الـ pressure، Osmotic، اللي هي صار واحد أعلى
+
+301
+00:23:04,370 --> 00:23:06,710
+من الثاني، ليش أعلى جال ناتج عن الـ Osmotic
+
+302
+00:23:06,710 --> 00:23:12,470
+Pressure؟ ناتج عن الـ Osmotic Pressure، في فرق في
+
+303
+00:23:12,470 --> 00:23:18,060
+الحقيقة بين الـ Osmosis و الـ diffusion لو كان في
+
+304
+00:23:18,060 --> 00:23:20,880
+عنده هنا barrier و في عنده هنا solvent و في عنده
+
+305
+00:23:20,880 --> 00:23:25,940
+هنا solution مركز هان بس solvent هان solution مركز
+
+306
+00:23:25,940 --> 00:23:29,620
+و روحت رفعت الـ barrier جال بحصل عندي diffusion في
+
+307
+00:23:29,620 --> 00:23:33,900
+اختلاط اختلاط للجزيئات لما في كل المحلول يكون
+
+308
+00:23:33,900 --> 00:23:38,300
+تركيز الـ solute و الـ solvent نفس الشيء هذا اسمه
+
+309
+00:23:38,300 --> 00:23:42,740
+diffusion زي ما نجيب نقطة حبر و نحطها في ايه؟ في
+
+310
+00:23:42,740 --> 00:23:46,040
+مية و نسرقها فترة الحبر بنتقل في ايه؟ في كل
+
+311
+00:23:46,040 --> 00:23:49,660
+المحلول لغاية ما يحصل عندي اتزان لكن لو كان في
+
+312
+00:23:49,660 --> 00:23:55,580
+عندي semi permeable barrier بلاحظ أنه لأ بحصلش هيك
+
+313
+00:23:55,580 --> 00:23:59,260
+هان هذا بدي يبدأ جزيئات الـ solvent تمتقل من هان
+
+314
+00:23:59,260 --> 00:24:02,400
+لهان تمتقل من هان لهان تمتقل من هان لهان وبالتالي
+
+315
+00:24:02,400 --> 00:24:07,550
+عمال الـ solvent هان بيجل لأنه بينتقل لليسركويس
+
+316
+00:24:07,550 --> 00:24:12,130
+لغاية بيحصل عنده اتزان ايش اللي بيعمل الاتزان هان
+
+317
+00:24:12,130 --> 00:24:15,890
+الـ Osmotic pressure واحدة أعلى من الثانية خلاص
+
+318
+00:24:15,890 --> 00:24:19,730
+البطل ينتقل واحدة أعلى من الثانية تضغط عليها وبطل
+
+319
+00:24:19,730 --> 00:24:24,170
+ينتقل إذا هذا هو الـ Osmosis و هذا هو الـ diffusion
+
+320
+00:24:24,170 --> 00:24:28,490
+صرق كبير مافيش شبه بينهم هذه ظاهرة و الثانية ظاهرة
+
+321
+00:24:28,490 --> 00:24:32,050
+أو عملية و الثانية عملية مختلفة تماما
+
+322
+00:24:35,620 --> 00:24:42,720
+الآن لو جينا تطلعنا كمان مرة بقول أول يعني هان في
+
+323
+00:24:42,720 --> 00:24:48,520
+عندي semi permeable membrane فعبيت هان الـ glucose
+
+324
+00:24:48,520 --> 00:24:52,520
+solution concentrated وعبيت هان مية بحيث أن هذا
+
+325
+00:24:52,520 --> 00:24:56,490
+بالظبط بسوي هذا قبل الإتزان صحيح بيكونوا زي هيك أول
+
+326
+00:24:56,490 --> 00:24:59,890
+ما اعمل العملية بيكونوا زي هيك بالظبط لكن لو سيبت
+
+327
+00:24:59,890 --> 00:25:04,150
+هذه الـ tube الـ YouTube فترة بنلاحظ أن المية راح
+
+328
+00:25:04,150 --> 00:25:08,410
+يتعدي من اليسار لليمين ليه؟ لأن اليمين مركز أكتر
+
+329
+00:25:08,410 --> 00:25:12,330
+عامل هذه بتجلق وهذه بتزيد ارتفاعها هذه بتجلق وهذه
+
+330
+00:25:12,330 --> 00:25:15,970
+بتزيد لغاية ما ايه لغاية ما يعني يصير في عندي
+
+331
+00:25:15,970 --> 00:25:20,310
+اتزان الاتزان بيصير هدول جت بعض مانو مابتاش بيصير
+
+332
+00:25:20,310 --> 00:25:25,180
+الاتزانلاحظ هان طلع السهم هذا أكتر انتقال أكتر في
+
+333
+00:25:25,180 --> 00:25:28,640
+انتقال هان بس قليل هان بحصل اتزان وقتي اشتمر يكون
+
+334
+00:25:28,640 --> 00:25:33,840
+هذه أعلى المحلول المركز أعلى من المحلول المخفف
+
+335
+00:25:33,840 --> 00:25:40,580
+بكمية معينة علاقة بالـ Osmotic pressure الآن لو
+
+336
+00:25:40,580 --> 00:25:47,400
+أنا اجيت طبقت ضغط خارجي بحيث أني أخلي ارتفاع
+
+337
+00:25:47,400 --> 00:25:53,480
+المحلول هان و هان واحد طبقت ضغط خارجي يعني ضغطت على
+
+338
+00:25:53,480 --> 00:25:57,180
+اليوتيوب هذه طبعا المحلول هيعدي هيرجع صح ولا لأ
+
+339
+00:25:57,180 --> 00:25:59,640
+لغاية ما يصير الاثنين جت بعض يعني الضغط اللي أنا
+
+340
+00:25:59,640 --> 00:26:05,820
+بطبقه يساوي الـ osmotic pressure عشان أخلي المحلول
+
+341
+00:26:05,820 --> 00:26:09,120
+ارتفاع المحلول في الـ youtube في الذراعين تبعونها نفس
+
+342
+00:26:09,120 --> 00:26:13,220
+الاشياء الضغط اللي بقى طبقه بيساوي الـ osmotic
+
+343
+00:26:13,220 --> 00:26:16,920
+pressure فهيك بقدر أجيس أنا الـ osmotic pressure
+
+344
+00:26:16,920 --> 00:26:20,680
+يبقى هو عبارة عن الـ pressure اللي راح يوجف الـ
+
+345
+00:26:20,680 --> 00:26:24,860
+osmosis الـ osmotic pressure in osmosis there is
+
+346
+00:26:24,860 --> 00:26:29,160
+net movement of solvent from the area of higher
+
+347
+00:26:29,160 --> 00:26:33,560
+solvent concentration يعني lower solute
+
+348
+00:26:33,560 --> 00:26:36,800
+concentration to the area of lower solvent
+
+349
+00:26:36,800 --> 00:26:41,080
+concentration يعني higher solute concentration طيب،
+
+350
+00:26:41,080 --> 00:26:48,590
+الآن أتيت أنا طبقت ضغط على الـ solution في الـ more
+
+351
+00:26:48,590 --> 00:26:53,270
+concentrated arm أو الذراع للـ YouTube بحيث أنه
+
+352
+00:26:53,270 --> 00:26:57,690
+يخسر ارتفاع الـ solution في الذراعين واحد بقول
+
+353
+00:26:57,690 --> 00:27:01,170
+الضغط المطبق الآن يساوي الـ osmotic pressure يعني
+
+354
+00:27:01,170 --> 00:27:05,550
+وكأنه الـ osmotic pressure هو عبارة عن الـ pressure
+
+355
+00:27:05,550 --> 00:27:09,830
+اللازم لوقف الـ osmosis يعني هل جيت لملأ طبق هذا الـ
+
+356
+00:27:09,830 --> 00:27:13,170
+pressure؟ في عنده osmosis رايح في هذا الاتجاه؟ لأ
+
+357
+00:27:13,170 --> 00:27:19,200
+خلاص وقف السهمين صاروا ايه؟ جت بعض الانتقال اه
+
+358
+00:27:19,200 --> 00:27:23,940
+وعملت انتقال الـ solvent molecules من الـ less
+
+359
+00:27:23,940 --> 00:27:26,840
+concentrated أو الـ dilute solution إلى الـ more
+
+360
+00:27:26,840 --> 00:27:29,940
+concentrated solution الآن بلاحظ مافيش عندي أي
+
+361
+00:27:29,940 --> 00:27:34,120
+انتقال يعني الـ osmotic pressure هو عبارة عن الـ
+
+362
+00:27:34,120 --> 00:27:39,600
+pressure اللازم لوقف الـ osmosis يفجر الـ osmotic
+
+363
+00:27:39,600 --> 00:27:42,820
+pressure هو عبارة عن الـ pressure اللازم لوقف الـ
+
+364
+00:27:42,820 --> 00:27:48,640
+osmosis طيب حلو كثير الـ osmotic pressure هي تعريفه
+
+365
+00:27:48,640 --> 00:27:53,100
+أجانب على طول طيب بقول هو عبارة عن الـ pressure
+
+366
+00:27:53,100 --> 00:27:58,140
+required to stop osmosis شفنا كيف to stop osmosis
+
+367
+00:27:58,140 --> 00:28:02,870
+known as osmotic pressure يعني الـ pressure required
+
+368
+00:28:02,870 --> 00:28:06,570
+to stop osmosis is known as osmotic pressure أو
+
+369
+00:28:06,570 --> 00:28:09,350
+الـ osmotic pressure if the pressure required to
+
+370
+00:28:09,350 --> 00:28:15,790
+stop osmosis، ابنه رمزله بالرمز π وهذا شيء جميل جدا
+
+371
+00:28:15,790 --> 00:28:19,310
+احنا بنعرف أن الـ pv بتساوي nRT طبعا هذه للغازات
+
+372
+00:28:19,310 --> 00:28:21,930
+لكن هنستخدمها لإنه بتساوم pressure عمال
+
+373
+00:28:21,930 --> 00:28:27,290
+فهنستخدمها كمان للـ osmotic pressure فبقول pv
+
+374
+00:28:27,290 --> 00:28:33,030
+بتساوي nRT أو الـ p بتساوي n على v في الـ RT الـ P
+
+375
+00:28:33,030 --> 00:28:35,850
+الآن لو بده اقول osmotic pressure بقول والله Pi
+
+376
+00:28:44,300 --> 00:28:51,560
+يبقى الـ Pi بتساوي MRT الـ Pi بتساوي MRT where M is
+
+377
+00:28:51,560 --> 00:28:56,320
+the molarity of the solution if the osmotic
+
+378
+00:28:56,320 --> 00:29:00,620
+pressure is the same on both sides of a membrane
+
+379
+00:29:00,620 --> 00:29:08,500
+لو كان الـ osmotic pressure كويس على الـ two sides
+
+380
+00:29:08,500 --> 00:29:14,970
+واحد بنقول عن المحلول isotonic اسمه ايزوتونيك اتعلم
+
+381
+00:29:14,970 --> 00:29:21,210
+بعض المصطلحات ايزوتونيك يعني ماعندي ازموزز ماعندي
+
+382
+00:29:21,210 --> 00:29:25,570
+انتقال للسولفان من جهة الى جهة اخرى ليه؟ لان الـ
+
+383
+00:29:25,570 --> 00:29:28,830
+ازموتكي pressure is the same الـ ازموتكي pressure
+
+384
+00:29:28,830 --> 00:29:31,890
+للمحلول للمحلولين اللي موجودين المحلول اللي ع
+
+385
+00:29:31,890 --> 00:29:35,350
+اليمين و المحلول اللي ع اليسار نفس الشيء اذا
+
+386
+00:29:35,350 --> 00:29:40,110
+ماعندي انتقال فيش انتقال للـ solvent من جهة إلى جهة
+
+387
+00:29:40,110 --> 00:29:43,770
+اخرى وقت ايش بيكون في عندي انتقال جال لما يكون فيه
+
+388
+00:29:43,770 --> 00:29:47,550
+فرق في الـ osmotic pressure لكن إذا كان فيش فرق
+
+389
+00:29:47,550 --> 00:29:49,930
+متساوي الـ osmotic pressure على الناحيتين معناته
+
+390
+00:29:49,930 --> 00:29:54,690
+فيش عندي انتقال ل الـ molecules للـ solvent
+
+391
+00:29:54,690 --> 00:29:58,910
+molecules من جهة إلى جهة أخرى وبالتالي هذا النوع
+
+392
+00:29:58,910 --> 00:30:05,140
+من المحاليل اللي بيحصلش فيه osmosis نظرا لتساوي الـ
+
+393
+00:30:05,140 --> 00:30:10,560
+osmotic pressure بقول عنه isotonic مصطلحات لازم
+
+394
+00:30:10,560 --> 00:30:14,060
+نتعلمها يعني ممكن يجيكي في الامتحان للأسف يعني
+
+395
+00:30:14,060 --> 00:30:18,140
+حاجة زي هيك باعتبرها سؤال صح و غلط يعني أو يعني
+
+396
+00:30:18,140 --> 00:30:22,720
+بجيبلي خيارات تختار اللفظ الصحيح ف isotonic هذه
+
+397
+00:30:22,720 --> 00:30:26,900
+عبارة عن أن المحلولين يلهم نفس الـ osmotic pressure
+
+398
+00:30:29,670 --> 00:30:33,970
+يعني يعتبر الحسابات الـ Molecular Mass من الـ
+
+399
+00:30:33,970 --> 00:30:37,410
+Osmotic Pressure من أدق الحسابات الـ Osmotic
+
+400
+00:30:37,410 --> 00:30:45,270
+Pressure هو عبارة عن يعني .. يعني خاصية مهمة جدا
+
+401
+00:30:45,270 --> 00:30:48,490
+من خلالها بنقدر نجيب الـ Molecular Mass والـ
+
+402
+00:30:48,490 --> 00:30:50,670
+Molecular Mass المحسوبة من الـ Osmotic Pressure
+
+403
+00:30:50,670 --> 00:30:54,850
+بتكون يعني إلها قيمة مهمة جدا لأنه تعتبر دقتها
+
+404
+00:30:54,850 --> 00:31:02,060
+عالية من وين بتيجي الدقة العالية جال لأن المحليل
+
+405
+00:31:02,060 --> 00:31:05,500
+حتى لو كانت مخففة التغير في الـ osmotic pressure
+
+406
+00:31:05,500 --> 00:31:10,500
+فيها كبير فالـ osmotic pressure يعني ظاهرة مهمة جدا
+
+407
+00:31:10,500 --> 00:31:14,220
+من خلالها ممكن أنه نحسب الـ molecular mass خليني
+
+408
+00:31:14,220 --> 00:31:19,360
+أقول يعني بشكل ممتاز وحنشوف مثال على هذا الكلام
+
+409
+00:31:19,360 --> 00:31:24,080
+بعد شوية لأن نتطلع كيف ممكن نحسب الـ polarity أو الـ
+
+410
+00:31:24,080 --> 00:31:26,920
+πاي لأن في عندي الـ πاي بتساوي
+
+411
+00:31:30,640 --> 00:31:34,220
+مرت فهذا ثابت وهذا ثابت إذا و لو أعطاني الـ M بحسب
+
+412
+00:31:34,220 --> 00:31:38,300
+الـ Pi لو اعطاني الـ Pi بحسب الـ M فش غير هيك لأن الـ
+
+413
+00:31:38,300 --> 00:31:43,680
+R و T عبارة عن ثوابت فبقدر احسب الـ M إذا معايا الـ
+
+414
+00:31:43,680 --> 00:31:46,580
+Pi أو بحسب الـ Pi إذا معايا الـ M فأنت طلع هال
+
+415
+00:31:46,580 --> 00:31:49,320
+بيقول الـ The average osmotic pressure of blood
+
+416
+00:31:49,320 --> 00:31:52,600
+السبعة وسبعة من عشرة أتمسفير at خمسة وعشرين ديجري
+
+417
+00:31:52,600 --> 00:31:57,200
+C what molarity of glucose will be isotonic with
+
+418
+00:31:57,200 --> 00:32:01,400
+this blood
+
+419
+00:32:01,400 --> 00:32:06,380
+solution؟ كويس يعني ايش تركيز الـ glucose solution
+
+420
+00:32:06,380 --> 00:32:11,560
+اللي عنده بحصلش net transfer للمية من الـ blood الى 
+
+421
+00:32:11,560 --> 00:32:14,500
+من الـ glucose أو من الـ glucose solution إلى الـ blood
+
+422
+00:32:14,500 --> 00:32:20,080
+فبقول أن الـ π بتساوي m RT ، الـ m بتساوي π على الـ 
+
+423
+00:32:20,080 --> 00:32:26,770
+RT ، على 0.0821 ليش استخدمنا هذا؟ ثانوية لأن PV بتساوي
+
+424
+00:32:26,770 --> 00:32:29,630
+nRT ، عوضنا عن الـ n بالـ number of moles والـ
+
+425
+00:32:29,630 --> 00:32:34,270
+volume بالـ liter والـ π بالـ atmosphere إذا 
+
+426
+00:32:34,270 --> 00:32:41,710
+هذه 0.0821 مش energy في 298 لـ 25 زائد بعتيني 0.31
+
+427
+00:32:41,710 --> 00:32:46,370
+يعني إذا كان تركيز الـ glucose solution عندي 0.31 و
+
+428
+00:32:46,370 --> 00:32:52,960
+حطينا غشاء شبه منفذ كويس مابينه مابين الـ blood اللي 
+
+429
+00:32:52,960 --> 00:32:55,680
+هذه خصائصه، 7 و 7 و 10 أتموسفير، 5 و
+
+430
+00:32:55,680 --> 00:32:58,900
+10 degrees C، بنلاحظ أنه ما فيش أي net transfer 
+
+431
+00:32:58,900 --> 00:33:02,600
+للميه لا ناحية الـ blood ولا من الـ blood ناحية الـ
+
+432
+00:33:02,600 --> 00:33:06,960
+glucose، ليه؟ لأن المحلولين أشمالهم isotonic، في
+
+433
+00:33:06,960 --> 00:33:10,280
+الـ isotonic solution ما فيش عندي net transfer للـ
+
+434
+00:33:10,280 --> 00:33:14,990
+solvent molecules من واحد للاخر، طيب بيقول لي what
+
+435
+00:33:14,990 --> 00:33:20,450
+is the osmotic pressure in tor of a 0.002 molar
+
+436
+00:33:20,450 --> 00:33:26,090
+sucrose at 20 degrees C؟ عادي جدا بده الـ osmotic
+
+437
+00:33:26,090 --> 00:33:30,210
+pressure ، أنا مش عندي لغير π تساوي MRT فبحسب الـ
+
+438
+00:33:30,210 --> 00:33:36,610
+... الـ molarity معايا بحسب الـ π ، الـ π طبعا نتذكر 
+
+439
+00:33:36,610 --> 00:33:41,310
+كلنا أن الـ molarity n number of moles على V liter
+
+440
+00:33:41,310 --> 00:33:48,570
+والـ R 0.0821 liter أتمسفير على الـ mole Kelvin ، الـ
+
+441
+00:33:48,570 --> 00:33:52,130
+T Kelvin إذا معنى الكلام الـ π أتمسفير اللي راح
+
+442
+00:33:52,130 --> 00:33:55,930
+أحسبها، الـ π بالاتمسفير فبحسب الـ π، يطلع عندي
+
+443
+00:33:55,930 --> 00:33:59,650
+0.048 atmosphere بدي أحولها لـ tor بدي اضرب في
+
+444
+00:33:59,650 --> 00:34:06,570
+760 لأن كل atmosphere 760 tor فيها، فبيطلع 37 tor 
+
+445
+00:34:09,990 --> 00:34:13,010
+لتطلع هذه المثالة هي اللي حكيتلكم عنها قبل شوية
+
+446
+00:34:13,010 --> 00:34:16,610
+مهمة كتير بالنسبة لي أنا، فبقول a solution is
+
+447
+00:34:16,610 --> 00:34:21,010
+prepared by dissolving 2.47 grams of an organic
+
+448
+00:34:21,010 --> 00:34:26,510
+polymer in 202 ml of بنزين، اللي عندها الـ notes 
+
+449
+00:34:26,510 --> 00:34:31,410
+موجودة من الـ net هذا الجواب في خطأ بتصلحي يعني مش 
+
+450
+00:34:31,410 --> 00:34:37,500
+ضرب في 10 أس -4 أو يعنيفدوّبنا هذه الكمية في 
+
+451
+00:34:37,500 --> 00:34:42,740
+البنزين 202 مل من البنزين، بيقول the solution has
+
+452
+00:34:42,740 --> 00:34:45,980
+an osmotic pressure of 8.3 من 10 ملي
+
+453
+00:34:45,980 --> 00:34:51,240
+متر زئبق at 21 degree الـ C، find the polar
+
+454
+00:34:51,240 --> 00:34:55,900
+mass of the polymer، فهو إيش اللي عمله؟ هو حضر 
+
+455
+00:34:55,900 --> 00:35:00,700
+محلول سهل جدا، دوب كمية من organic solvent في إيه؟
+
+456
+00:35:00,700 --> 00:35:04,160
+في بنزين، في كمية من البنزين، عمل محلول، gas non
+
+457
+00:35:04,160 --> 00:35:09,260
+osmotic pressure، حطه جنب بنزين صافي، كويس، هاي ها
+
+458
+00:35:09,260 --> 00:35:17,620
+ممكن نطلع هذا
+
+459
+00:35:17,620 --> 00:35:19,140
+semi permeable membrane
+
+460
+00:35:26,000 --> 00:35:33,980
+وهي محلول الـ إيه؟ محلول الـ إيه؟ إيش سميناه؟ بنزين صافي
+
+461
+00:35:33,980 --> 00:35:40,300
+وهي الـ solution اللي هو عبارة عن البنزين زائد الـ 
+
+462
+00:35:40,300 --> 00:35:48,760
+solute الـ polymer يعني وحط هنا الـ pressure فلما
+
+463
+00:35:48,760 --> 00:35:53,060
+صار هدول اثنين جت بعض بالظبط الـ pressure هذا 
+
+464
+00:35:53,060 --> 00:35:59,970
+بيساوي π الـ Osmotic Pressure كويس، فلاحظ أنه الـ 
+
+465
+00:35:59,970 --> 00:36:06,550
+π هادي 8.3 ملي متر زئبق at 21 degree C، بده الموليك
+
+466
+00:36:06,550 --> 00:36:09,790
+ولار، بنرمز بقول الـ ... الـ ... الـ molarity في البداية بقدر 
+
+467
+00:36:09,790 --> 00:36:15,290
+أجيب الـ π بتساوي M RT ، الـ π يبقى الـ M بتساوي RT
+
+468
+00:36:15,290 --> 00:36:25,230
+... π على الـ RT ، الـ M ما بنفعش أن أعوض مليمتر زيبا لأن 
+
+469
+00:36:25,230 --> 00:36:30,750
+أنا بعرف أن هذه العلاقة الـ π فيها أتمسفير
+
+470
+00:36:43,670 --> 00:36:51,970
+الـ R والـ T هي الـ π بتساوي الـ M بتساوي عفوا الـ π
+
+471
+00:36:51,970 --> 00:36:57,130
+على الـ RT فهي الـ π الـ R 0.0821 لتر أتمسفير على مول
+
+472
+00:36:57,130 --> 00:37:01,910
+كيلفين في الـ T 294 لأنه 21 زائد 273
+
+473
+00:37:01,910 --> 00:37:05,310
+وبيعطينا 4.5 × 10 أس -4 مولر 
+
+474
+00:37:06,220 --> 00:37:12,620
+إذا التركيز بالمولار طلع 4.5 × 10 أس -4 مولر 
+
+475
+00:37:16,900 --> 00:37:24,640
+قال والله اه عدد اه في عندي الـ molarity في الـ 
+
+476
+00:37:24,640 --> 00:37:28,360
+volume بالـ liter بتعطينا عدد المولات 9.1 × 10 أس -5
+
+477
+00:37:28,360 --> 00:37:33,460
+لأن الـ molarity بتساوي الـ moles على الـ volume بالـ liter إذا الـ moles بتساوي الـ 
+
+478
+00:37:33,460 --> 00:37:36,840
+molarity اللي أنا حسبتها في الـ volume بالـ liter 
+
+479
+00:37:36,840 --> 00:37:40,400
+أنا عندي 202 مل يعني 0.202 
+
+480
+00:37:40,400 --> 00:37:43,640
+liter 
+
+481
+00:37:43,640 --> 00:37:44,060
+liter
+
+482
+00:37:48,560 --> 00:37:53,560
+معنى الكلام في عندي 9.1 × 10 أس -5 
+
+483
+00:37:53,560 --> 00:37:57,740
+مول بتجيب الـ molar mass عبارة عن الـ gram polymer 
+
+484
+00:37:57,740 --> 00:38:03,860
+على number of moles لأنه كمان مرة العدد المولات الـ 
+
+485
+00:38:03,860 --> 00:38:08,640
+moles بده يساوي جرام على الـ formula weight يبقى 
+
+486
+00:38:08,640 --> 00:38:15,440
+عندي الـ formula weight بتساوي جرام جرام على الـ 
+
+487
+00:38:15,440 --> 00:38:20,020
+mole جرام على المول، هاي الجرامات 2.47
+
+488
+00:38:20,020 --> 00:38:25,360
+و40 على 9.1 × 10 أس -5
+
+489
+00:38:25,360 --> 00:38:29,740
+بتعطيني 2.7 × 10 أس -4 
+
+490
+00:38:29,740 --> 00:38:36,760
+جرام على المول، فيعني هذا هو الـ molecular mass للـ 
+
+491
+00:38:36,760 --> 00:38:40,280
+polymer اللي أنا دوبته في البنزين واللي أعطاني 
+
+492
+00:38:40,280 --> 00:38:43,780
+الـ osmotic pressure 8.3 من 10 مليمتر
+
+493
+00:38:43,780 --> 00:38:48,950
+زئبق، فهذه مسألة كتير كتير بسيطة كتير سهلة، وأيضا من 
+
+494
+00:38:48,950 --> 00:38:52,690
+خلالها بنقدر نحسب الـ molecular mass لـ compound 
+
+495
+00:38:52,690 --> 00:38:58,650
+مجهول بسهولة، بالذات لو كان polymer الطرق العادية 
+
+496
+00:38:58,650 --> 00:39:04,930
+المشكلة لما ناخد polymer بدي يكون يعني التغير في 
+
+497
+00:39:04,930 --> 00:39:10,900
+الـ freezing point أو الـ ... الـ boiling point قليل
+
+498
+00:39:10,900 --> 00:39:15,420
+جدا جدا لأنه الـ molality إله هتكون قليلة جدا لأن 
+
+499
+00:39:15,420 --> 00:39:18,760
+الـ molar mass تبعته كبيرة خالص، فلما بتاخد وزنة 
+
+500
+00:39:18,760 --> 00:39:22,500
+بسيطة منه بتعطيني molality زي ما شوفنا 10 أس -4 
+
+501
+00:39:22,500 --> 00:39:26,280
+هذه مثلا قريبة، الـ molality هتكون قريبة من هيك
+
+502
+00:39:26,280 --> 00:39:30,480
+فهذه مش سهل إنه بتعطيني تغير في درجة الحرارة سواء 
+
+503
+00:39:30,480 --> 00:39:32,720
+boiling point elevation أو freezing point
+
+504
+00:39:32,720 --> 00:39:37,740
+depression لكن مع إنه المحلول مخفف جدا أعطاني ومن 
+
+505
+00:39:37,740 --> 00:39:41,800
+الـ osmotic pressure قدرت أعرف الـ molecular mass
+
+506
+00:39:41,800 --> 00:39:45,380
+فهذه طريقة ممتازة جدا في الحقيقة لحساب الـ
+
+507
+00:39:45,380 --> 00:39:52,880
+molecular mass فيما يتعلق أيضا بالـ osmosis يعني 
+
+508
+00:39:52,880 --> 00:39:56,640
+أنا حبيت أن أقولكم بعض الحاجات الإضافية
+
+509
+00:40:00,160 --> 00:40:03,860
+بقولنا أنه لما يكون في عندي محلول مخفف وفي عندي
+
+510
+00:40:03,860 --> 00:40:08,240
+semi permeable membrane ومحلول مركز، جزيئات الـ 
+
+511
+00:40:08,240 --> 00:40:10,960
+solvent في المحلول المخفف بتنتقل للمحلول المركز 
+
+512
+00:40:10,960 --> 00:40:16,940
+فبيصير في عندي ارتفاع في الـ solution ارتفاع في عمود 
+
+513
+00:40:16,940 --> 00:40:22,140
+الـ solution في المحلول المركز، والآن لو طبقنا ضغط
+
+514
+00:40:22,140 --> 00:40:24,500
+لما هدول اثنين يكونوا متساويين
+
+515
+00:40:26,650 --> 00:40:30,990
+كويس؟ بنقول هذا هو عبارة عن الضغط بيساوي الـ 
+
+516
+00:40:30,990 --> 00:40:37,510
+osmotic pressure طيب إيش بيحصل لو أنا طبقت ضغط أكبر
+
+517
+00:40:37,510 --> 00:40:44,770
+من هيك؟ ضغط أكبر من هيك؟ كويس؟ هو هذا يعني لمفهوم
+
+518
+00:40:44,770 --> 00:40:47,330
+هذا ضغط كهلي بس لو طبقت ضغط أكبر من هيك إيش بدي
+
+519
+00:40:47,330 --> 00:40:52,650
+يحصل؟ بيقول بتصير جزيئات الميه تنتقل من هنا لهان، من 
+
+520
+00:40:52,650 --> 00:40:58,110
+هنا لهان يعني الـ ... الـ osmosis بيصير إيه؟ عكسي اه 
+
+521
+00:40:58,110 --> 00:41:01,230
+هذا بنقوله reverse osmosis وفي الحقيقة لما آجي
+
+522
+00:41:01,230 --> 00:41:04,930
+أطبق الضغط هنا، حطيت الـ pistol هنا وبديت بدي أطبق
+
+523
+00:41:04,930 --> 00:41:09,610
+ضغط إيش اللي بيحصل؟ ليش هذا بينزل؟ بيقول لأن جزيئات 
+
+524
+00:41:09,610 --> 00:41:14,290
+الميه بت ... بت ... بت ... يعني بتنتقل من المركز إلى
+
+525
+00:41:14,290 --> 00:41:18,510
+المخفف عكس الـ osmosis فهذا إيش اسمه؟ reverse 
+
+526
+00:41:18,510 --> 00:41:26,440
+osmosis Reverse osmosis أو بنقول رو رو reverse
+
+527
+00:41:26,440 --> 00:41:31,800
+osmosis يعني الـ osmosis بنعكس بنقدر نعكس واحنا اه 
+
+528
+00:41:31,800 --> 00:41:38,980
+يعني مثلا لو أنا عندي ميه بحر تنشرب؟ لأ ما تنشربش، لو
+
+529
+00:41:38,980 --> 00:41:44,160
+حطيتها في الـ youtube هذه وضغط عليها وهنا في عندي
+
+530
+00:41:44,160 --> 00:41:51,530
+fresh water هذا fresh water وهادي salt أو brine ميه
+
+531
+00:41:51,530 --> 00:41:57,950
+البحر بنقولها brine برضه لو جت ضغطت عليها طبقت ضغط
+
+532
+00:41:57,950 --> 00:42:01,770
+بلاحظ أنه هذا الانتقال بس يعني ميه البحر الـ ... الـ 
+
+533
+00:42:01,770 --> 00:42:06,170
+... الميه اللي فيها بس هي اللي بتنتقل لليسار و
+
+534
+00:42:06,170 --> 00:42:09,750
+بيصير ميه صالحة على الشرب ممتازة جدا بينما الـ salts
+
+535
+00:42:09,750 --> 00:42:14,390
+كلها بتضل فين؟ على اليمين، هذا اسمه reverse osmosis 
+
+536
+00:42:14,390 --> 00:42:20,040
+هو بالظبط التكنيك المستخدم في تحلية الميه في 
+
+537
+00:42:20,040 --> 00:42:25,840
+البيوت، الفلاتر، نعرف الفلاتر أو شفناها أو سمعنا
+
+538
+00:42:25,840 --> 00:42:30,620
+عنها، لكن ناس كتير بيستخدموها الميه في غزة يعني
+
+539
+00:42:30,620 --> 00:42:36,980
+مالحة نسبيا يعني في أغلب المناطق فالناس بتستخدم
+
+540
+00:42:36,980 --> 00:42:41,580
+إما فلاتر اللي هي reverse osmosis في الحقيقة أو
+
+541
+00:42:41,580 --> 00:42:44,640
+بتشتري مياه شرب يعني من الناس اللي بيلفوا
+
+542
+00:42:44,640 --> 00:42:48,900
+بيبيعوا مياه فهذا هو الـ reverse osmosis بالظبط
+
+543
+00:42:48,900 --> 00:42:54,340
+اللي بيحصل هو كالتالي في الـ reverse osmosis أنا 
+
+544
+00:42:54,340 --> 00:42:59,560
+عندي الاصل أنه إذا كان هذا fresh water وهذا salt 
+
+545
+00:42:59,560 --> 00:43:05,300
+water الاصل أنه الميه تنتقل من اليمين لليسار في
+
+546
+00:43:05,300 --> 00:43:14,980
+هذا الاتجاه صح لازم تنتقل في هذا الاتجاه مظبوط 
+
+547
+00:43:14,980 --> 00:43:18,620
+ليه؟ لأنه من المخفف للمركز، لكن لو أنا طبقت
+
+548
+00:43:18,620 --> 00:43:24,510
+pressure على هذا الجانب بيحصل العكس بيحصل أنه 
+
+549
+00:43:24,510 --> 00:43:32,610
+المياه راح تنتقل من اليسار لليمين طبعا هذا بشرط
+
+550
+00:43:32,610 --> 00:43:36,650
+أنه ما يكونش مسموح للمحلولين أن يحصل فيهم
+
+551
+00:43:36,650 --> 00:43:41,550
+diffusion يعني الـ ... الـ membrane الـ semi permeable
+
+552
+00:43:41,550 --> 00:43:45,930
+membrane تكون الـ porosity تبعته أو الـ pore size 
+
+553
+00:43:45,930 --> 00:43:51,290
+تبعته غير كافي لمرور الايونات الـ salt لأن لو كان 
+
+554
+00:43:51,290 --> 00:43:55,210
+كافي لمرور الايونات مش هيحصل عندنا Osmosis هيحصل
+
+555
+00:43:55,210 --> 00:43:58,310
+تبادله، بعد شوية حيصير في عندي diffusion انتشر
+
+556
+00:43:58,310 --> 00:44:03,750
+عادي، يعني لو أنا جبت والله طلعولي
+
+557
+00:44:03,750 --> 00:44:04,870
+عليها الـ ...
+
+558
+00:44:07,420 --> 00:44:12,020
+هذه المنبران وهذه الفتحة تبعته هل هذه الفتحة بتمنع 
+
+559
+00:44:12,020 --> 00:44:15,680
+هذا أن يعدي جوا؟ لأ، هذا محدد diffusion مش osmosis
+
+560
+00:44:15,680 --> 00:44:19,280
+الـ osmosis شرط أن يكون المنبران semi permeable 
+
+561
+00:44:19,280 --> 00:44:24,740
+بمعنى أنه يسمح فقط لجزيئات الـ solvent تقريباً يعني
+
+562
+00:44:24,740 --> 00:44:29,320
+لجزيئات الـ solvent أن هو اللي يحصل transfer ما بين
+
+563
+00:44:29,320 --> 00:44:34,280
+الـ two sides لإيه؟ للـ membrane وبالتالي الماء بنلاحظ
+
+564
+00:44:34,280 --> 00:44:37,500
+أن لو طبقنا high ضغط وهي اللي بيحصل بالظبط لو
+
+565
+00:44:37,500 --> 00:44:41,660
+طبقنا high ضغط فالمياه بتنتقل من المركز إلى المخفف
+
+566
+00:44:41,660 --> 00:44:45,420
+يعني high على اليمين بيصير في عندي fresh water أو
+
+567
+00:44:45,420 --> 00:44:49,360
+pure water يمكن أن تكون صالحة طبعاً هي صالحة للشرب 
+
+568
+00:44:49,360 --> 00:44:52,000
+لأن بيستخدموها في البيوت فشعرنا بمشكلة في هذا الكلام
+
+569
+00:44:52,000 --> 00:44:57,600
+كمان مرة هاي salt water أو sea water طبق ضغط
+
+570
+00:44:57,600 --> 00:45:03,950
+تعطيني fresh waterوفي الحقيقة في أدوات صغيرة بتنبع
+
+571
+00:45:03,950 --> 00:45:08,310
+يعني تحطها في مياه البحر وبالشفط مثلاً يعني فبتطلع
+
+572
+00:45:08,310 --> 00:45:11,470
+لنا مياه صالحة للشرب لأن الضغط اللي احنا بنطبقه 
+
+573
+00:45:11,470 --> 00:45:19,270
+كافي يعني ضغط من هنا كافي أنه يعطيني reverse
+
+574
+00:45:19,270 --> 00:45:24,090
+osmosis وبالتالي برضه هذه حاجة تعتبر يعني مفيدة
+
+575
+00:45:24,090 --> 00:45:27,780
+للغايةاللي عندنا الفلاتر اللي في البيوت، يمكن
+
+576
+00:45:27,780 --> 00:45:33,500
+بعضكم بيشوف علب مسكرة، في طبعاً العلب بتختلف، في علب 
+
+577
+00:45:33,500 --> 00:45:39,160
+لتنقية الـ particles، في علب لتنقية الروائح وما 
+
+578
+00:45:39,160 --> 00:45:47,630
+شابه، carbon بتكونلكن في علبة أو سيلندر خاص هذا للـ
+
+579
+00:45:47,630 --> 00:45:53,610
+reverse osmosis هذا هو الـ heart للـ reverse osmosis
+
+580
+00:45:53,610 --> 00:45:57,330
+system اللي عندي ففي الـ reverse osmosis system في
+
+581
+00:45:57,330 --> 00:46:03,260
+عندي غشاء شبه منفذ ملفوف بالطريقة هذه لفينه وهي
+
+582
+00:46:03,260 --> 00:46:07,280
+أخره لفينه كثير يعني لفات كثير بيكون موجود داخل
+
+583
+00:46:07,280 --> 00:46:13,540
+أنبوبة cylindrical tube كويس فالمحلول
+
+584
+00:46:13,540 --> 00:46:22,420
+العادي بيمر من هنا بيصير يلف وطبعاً خدوا بالكم الـ
+
+585
+00:46:22,420 --> 00:46:26,600
+membrane هذا موجود فيه فتحات ضيقة للغاية عشان يطلع 
+
+586
+00:46:26,600 --> 00:46:30,890
+بده يطلع من هنا بس فبيكون بدهوا مرة على عدد كبير
+
+587
+00:46:30,890 --> 00:46:34,950
+جداً من الـ pores دائماً بس الماء هي اللي بتطلع الماء
+
+588
+00:46:34,950 --> 00:46:37,370
+اللي بتطلع الماء اللي بتطلع الماء وبالتالي هنا
+
+589
+00:46:37,370 --> 00:46:41,170
+بطلع ليّ ماء والـ concentrated بيطلع أنا من هنا
+
+590
+00:46:41,170 --> 00:46:47,360
+بدخل الـ feed waterكويس هنا الـ feed water دخلت من
+
+591
+00:46:47,360 --> 00:46:50,440
+واحد مكان لكن في النهاية عشان تطلع بتطلع من هنا
+
+592
+00:46:50,440 --> 00:46:54,900
+بمر من هنا إلا بس لـ pure water لكن الـ
+
+593
+00:46:54,900 --> 00:46:58,200
+concentrate أو المحلول المركزي اللي أتركز فيه الملح 
+
+594
+00:46:58,200 --> 00:47:04,090
+بيطلع من مكان آخر وبروح للـ disposal يعني في ما 
+
+595
+00:47:04,090 --> 00:47:09,830
+يتعلق بالبرميات بنلاحظ أنه مش 100% ماء يعني حتى في
+
+596
+00:47:09,830 --> 00:47:14,010
+الـ systems بتاعتنا لأن في عندنا قليل فيه مش كثير في
+
+597
+00:47:14,010 --> 00:47:17,030
+عندنا خلّيني أقول imperfections في التصنيع يعني
+
+598
+00:47:17,030 --> 00:47:20,930
+مايقدرش نصنع membrane يعني صح 100% بس الماء اللي
+
+599
+00:47:20,930 --> 00:47:24,050
+بتعدي له ممكن في بعض الأحيان يكون غلطان في pore
+
+600
+00:47:24,050 --> 00:47:27,790
+واسع شويّة ممكن يدخل صوديوم شويّة صوديومبتر أشياء قليلة
+
+601
+00:47:27,790 --> 00:47:32,910
+شويّة chloride أشياء قليلة لكن في شكل عام اللي خارج هو
+
+602
+00:47:32,910 --> 00:47:41,770
+عبارة عن pure water كمان مرة هاي عندي أنا اللي
+
+603
+00:47:41,770 --> 00:47:47,600
+داخل دخل فدخل منها لحظة اللي هو عمل بس الماء اللي 
+
+604
+00:47:47,600 --> 00:47:50,160
+بسمح لها أنها تعدي الماء بتعدي الماء بتعدي الماء
+
+605
+00:47:50,160 --> 00:47:51,640
+بتعدي الماء بتعدي الماء بتعدي الماء بتعدي الماء
+
+606
+00:47:51,640 --> 00:47:56,680
+بتعدي الماء بتعدي الماء بتعدي الماء بتعدي الماء
+
+607
+00:47:56,680 --> 00:48:00,840
+بتعدي الماء بتعدي الماء بتعدي الماء بتعدي الماء
+
+608
+00:48:00,840 --> 00:48:02,640
+بتعدي الماء بتعدي الماء بتعدي الماء بتعدي الماء
+
+609
+00:48:02,640 --> 00:48:03,160
+بتعدي الماء بتعدي الماء بتعدي الماء بتعدي الماء
+
+610
+00:48:03,160 --> 00:48:03,620
+بتعدي الماء بتعدي الماء بتعدي الماء بتعدي الماء
+
+611
+00:48:03,620 --> 00:48:10,580
+بتعدي الماء نفس الكلام هي هي ده هو عبارة عن الـ
+
+612
+00:48:10,580 --> 00:48:18,900
+reverse osmosis cylinder يعني أو tube هي
+
+613
+00:48:18,900 --> 00:48:22,320
+اللي يعني على سبيل المثال بنلفه بالطريقة هذه 
+
+614
+00:48:22,320 --> 00:48:27,500
+فالممكن الماء أو المحلول يعدي منها لكن اللي بيعدي
+
+615
+00:48:27,500 --> 00:48:32,060
+لجوه بس هو الماء فقط لأن هي المسموحة تعدي من الـ
+
+616
+00:48:32,060 --> 00:48:38,610
+pores اللي موجودة هذا نفس الكلام أن الـ calcium مثلاً
+
+617
+00:48:38,610 --> 00:48:41,630
+أكبر من الـ pore size، الـ sodium أكبر من الـ pore
+
+618
+00:48:41,630 --> 00:48:44,810
+size، الـ chloride أكبر من الـ pore size، لكن أيش
+
+619
+00:48:44,810 --> 00:48:48,210
+اللي بقدر يعدي بس الماء؟ وهذا نفس الكلام، الـ
+
+620
+00:48:48,210 --> 00:48:51,030
+magnesium أكبر من الـ pore size، الـ calcium أكبر،
+
+621
+00:48:51,030 --> 00:48:53,430
+الـ sodium أكبر، فبس اللي بده يعدي الماء، وفي
+
+622
+00:48:53,430 --> 00:48:58,460
+النهاية بنحصل فقط على الماء هذا هو مبدأ الـ reverse
+
+623
+00:48:58,460 --> 00:49:06,120
+osmosis تطبيقاته الصناعية كثير يعني ممتازة ويعتبر
+
+624
+00:49:06,120 --> 00:49:11,260
+من يمكن أفضل الـ water purification techniques
+
+625
+00:49:11,260 --> 00:49:13,360
+الموجودة حالياً
+
+626
+00:49:16,280 --> 00:49:19,400
+بدي أطلع على بعض المصطلحات الـ osmosis in blood
+
+627
+00:49:19,400 --> 00:49:23,860
+cells الـ osmosis in blood cells طبعاً كل blood
+
+628
+00:49:23,860 --> 00:49:27,920
+cells وكل يعني الخلايا اللي في الجسم دائماً موجود
+
+629
+00:49:27,920 --> 00:49:32,020
+على الخلية membrane خارجي membrane هذا الـ membrane
+
+630
+00:49:32,020 --> 00:49:35,220
+semi permeable مافيش يكون مصمت ماهو مش permeable
+
+631
+00:49:35,220 --> 00:49:43,790
+بتموت الخلية بده تاخد غذاء وبده ترمي الفضلات
+
+632
+00:49:43,790 --> 00:49:47,630
+أو غيره عمليات معقدة بتتم في الخلية فدائماً في عندي
+
+633
+00:49:47,630 --> 00:49:53,030
+semi permeable membrane فبنقول if the solute
+
+634
+00:49:53,030 --> 00:49:57,090
+concentration outside the cell is greater than 
+
+635
+00:49:57,090 --> 00:50:01,030
+that inside the cell the solution is hypertonic
+
+636
+00:50:01,030 --> 00:50:06,350
+اسمه أو بنطلق عليه hypertonic يعني في عندي high
+
+637
+00:50:06,350 --> 00:50:10,470
+concentration برا وlow concentration جوا and low
+
+638
+00:50:10,470 --> 00:50:17,690
+concentration يعني الماء high water
+
+639
+00:50:21,120 --> 00:50:24,060
+concentration low concentration يعني low solute
+
+640
+00:50:24,060 --> 00:50:27,420
+concentration يعني high water .. إيش طب بده يحصل
+
+641
+00:50:27,420 --> 00:50:32,340
+للماء في هذه الحالة؟ بتعدي جوه ولا تطلع برا؟ أنا
+
+642
+00:50:32,340 --> 00:50:35,120
+عندي high water concentration داخل الخلية، هي
+
+643
+00:50:35,120 --> 00:50:39,400
+الخلية طبعاً راح يطلع برا لأن اللي برا high solute
+
+644
+00:50:39,400 --> 00:50:43,140
+concentration يبقى .. هذا المحلول إيش بنقوله؟
+
+645
+00:50:43,140 --> 00:50:48,350
+hypertonichypertonic the solution is hypertonic
+
+646
+00:50:48,350 --> 00:50:53,690
+وبالتالي water will flow out of the cell وحاجة
+
+647
+00:50:53,690 --> 00:50:57,530
+نقولها creation process creation يعني shrinkage
+
+648
+00:50:57,530 --> 00:51:03,470
+الخلية عمال اه بتتقلص بتمكمش لأنها بتفقد الماء 
+
+649
+00:51:03,470 --> 00:51:08,390
+عمال فبتمكمش shrinkage results فهذه إيه؟ hypertonic
+
+650
+00:51:08,390 --> 00:51:12,970
+solution معناته على طول shrinkage للخلية أو يعني
+
+651
+00:51:12,970 --> 00:51:19,910
+crenation للخلية عكس هذا الكلام if the solute
+
+652
+00:51:19,910 --> 00:51:24,590
+concentration outside the cell is less than that 
+
+653
+00:51:24,590 --> 00:51:29,570
+inside the cell يعني هنا low concentration هنا high
+
+654
+00:51:29,570 --> 00:51:32,950
+concentration
+
+655
+00:51:32,950 --> 00:51:42,560
+يعني بده أقول low water concentration وهنا high
+
+656
+00:51:42,560 --> 00:51:49,660
+water concentration، إذا الماء أيش اللي هتسوي؟
+
+657
+00:51:49,660 --> 00:51:54,530
+تعدي جوه، إيش اللي .. هذا اسمه hypotonic solution
+
+658
+00:51:54,530 --> 00:51:59,390
+هيبوتونيك solution طيب water will flow into the cell
+
+659
+00:51:59,390 --> 00:52:02,710
+and hemolysis يعني rapture راح تفجع الخلية راح
+
+660
+00:52:02,710 --> 00:52:07,870
+يعني تتكسر كويس rapture عمالي بتنفخ بتنفخ طب 
+
+661
+00:52:07,870 --> 00:52:15,070
+وبعدين اه بيحصل rapture الغشاء اللي حاميها بيتهتك
+
+662
+00:52:15,070 --> 00:52:17,790
+خلاص بتخرب الخلية هذا عمالي بيقولها hemolysis
+
+663
+00:52:18,410 --> 00:52:22,790
+Hemolysis يعني Rapture Results إذا إذا كان المحلول
+
+664
+00:52:22,790 --> 00:52:28,650
+Hypotonic ففي عنده Hemolysis طب لو كان النوع 
+
+665
+00:52:28,650 --> 00:52:32,210
+الثالث أن يكون Isotonic طبعاً احنا فهمنا إنه في جسم 
+
+666
+00:52:32,210 --> 00:52:36,430
+الإنسان ما يحصلش shrinkage يعني Crenation ولا يحصل
+
+667
+00:52:36,430 --> 00:52:40,510
+Hemolysis ليه؟ ما بدناش الخلايا والله تنكمش أو
+
+668
+00:52:40,510 --> 00:52:44,470
+الخلايا تتكسر المحلول اللي بدنا إياه إيش بده 
+
+669
+00:52:44,470 --> 00:52:49,300
+يكون؟ Isotonic ففي عندنا isotonic اه هذا هو الممتاز
+
+670
+00:52:49,300 --> 00:52:52,460
+بالنسبة لنا لكن في عندنا على الناحية الأخرى في 
+
+671
+00:52:52,460 --> 00:52:58,100
+عندنا اه hypertonic وhypotonic solutions هي خلية
+
+672
+00:52:58,100 --> 00:53:01,420
+حلوة خالص للأسف مش مبينة منيح الرسم اللي عندكم في 
+
+673
+00:53:01,420 --> 00:53:06,460
+الـ notes مبينة أحسن فلما يكون يعني عندنا التركيز
+
+674
+00:53:07,040 --> 00:53:10,860
+تركيز الماء خلّيني أقول أو تركيز المحلول داخل وخارج
+
+675
+00:53:10,860 --> 00:53:14,400
+الخلية نفس الشيء يعني isotonic بنلاحظ أن في
+
+676
+00:53:14,400 --> 00:53:16,720
+عندي equilibrium الماء اللي داخلة ساهي الماء
+
+677
+00:53:16,720 --> 00:53:20,400
+اللي خارجها يبقى في عندي الخلية بتحافظ حالها
+
+678
+00:53:20,400 --> 00:53:30,280
+ممتازة جداً لا هي created ولا هي يعني swollen لأ 
+
+679
+00:53:30,280 --> 00:53:35,940
+بتحافظ على حالها في الـ hypotonic solution اه في
+
+680
+00:53:35,940 --> 00:53:39,340
+عندي high محدود مخفف high مركز إذا شايفين الأسهم 
+
+681
+00:53:39,340 --> 00:53:43,920
+السهمين وين جايين كل الماء عمال بتعدي جوه هذا
+
+682
+00:53:43,920 --> 00:53:47,340
+الكلام swollen red blood cells وهذا بيقدر له
+
+683
+00:53:47,340 --> 00:53:52,680
+hemolysis rupture الحالة الثالثة الـ hypertonic
+
+684
+00:53:52,680 --> 00:53:57,260
+solution في عندي concentrated solution وفي عندها
+
+685
+00:53:57,260 --> 00:54:00,960
+dilute solution فالمياه بتنتقل من الـ dilute
+
+686
+00:54:00,960 --> 00:54:04,220
+solution اللي في يعني high water concentration إلى 
+
+687
+00:54:04,220 --> 00:54:08,140
+الخارج فمعناه كلام في عندي crenation أو shrunken
+
+688
+00:54:08,140 --> 00:54:08,620
+cell
+
+689
+00:54:12,150 --> 00:54:20,070
+هذه الصورة يبدو أنها تحت مجهر حلو جداً فهنا cells in
+
+690
+00:54:20,070 --> 00:54:24,250
+dilute salt solution يعني عايزو tonic solution هاي
+
+691
+00:54:24,250 --> 00:54:32,510
+شكل الخلايا اللي عندي هنا حطينا الـ cells في
+
+692
+00:54:32,510 --> 00:54:36,740
+distilled water distilled water يعني المياه في
+
+693
+00:54:36,740 --> 00:54:46,160
+الخارج مركزة ومقطرة فبنلاحظ
+
+694
+00:54:46,160 --> 00:54:48,680
+أن المياه ستتعدي لجوه وهذا ما سيحصل فيه هو
+
+695
+00:54:48,680 --> 00:54:54,470
+Hemolysis لكن أطلعوا على شكل الخلايا كيف صار لما
+
+696
+00:54:54,470 --> 00:54:58,150
+يكون فيه عندي cells in concentrated salt solution
+
+697
+00:54:58,150 --> 00:55:02,730
+الماء راح تطلع من الخلية كويس وتروح للمحلول
+
+698
+00:55:02,730 --> 00:55:05,490
+المركز يبقى عمال بيحصلها shrinkage تطلع شكل 
+
+699
+00:55:05,490 --> 00:55:10,210
+الخلايا كثير فظيعة خلايا صارلها shrinkage بشكل
+
+700
+00:55:10,210 --> 00:55:15,250
+يعني عجيب للغاية هنا أسأل أسأل الـ cells بينما 
+
+701
+00:55:15,250 --> 00:55:18,810
+هان هذا isotonic solution معناته الـ cells normal
+
+702
+00:55:18,810 --> 00:55:25,900
+طيب الآن شوفنا احنا يبقى أربع أنواع من الـ cells
+
+703
+00:55:25,900 --> 00:55:30,220
+properties سمنها colligative properties لأنها 
+
+704
+00:55:30,220 --> 00:55:36,320
+ببساطة تتوقف على عدد الجزيئات من الـ solute
+
+705
+00:55:36,320 --> 00:55:41,180
+الموجودة في المحلول ولا تتوقف على طبيعة هذه
+
+706
+00:55:41,180 --> 00:55:47,200
+الجزيئات لا تتوقف على طبيعتها تتوقف دائماً على عددها
+
+707
+00:55:47,200 --> 00:55:51,560
+يعني التركيز سواء كان مولاليتي أو مولاريتي كانت الـ
+
+708
+00:55:51,560 --> 00:55:56,760
+vapor pressure lowering وكانت P<sub>A</sub> بتساوي X<sub>A</sub> P<sup>0</sup><sub>A</sub>
+
+709
+00:55:56,760 --> 00:56:02,220
+رؤولتس لوالـ Boiling Point Elevation ΔT<sub>b</sub>
+
+710
+00:56:02,220 --> 00:56:05,700
+بتساوي K<sub>b</sub> في M والـ Freezing Point Depression
+
+711
+00:56:05,700 --> 00:56:10,200
+ΔT<sub>f</sub> بتساوي K<sub>f</sub> في M والـ Osmotic Pressure Π
+
+712
+00:56:10,200 --> 00:56:14,980
+بتساوي M R T هذه الأربع خصائص اللي سمنها الـ
+
+713
+00:56:14,980 --> 00:56:17,700
+Colligative Properties اللي درسنا كل واحدة منها
+
+714
+00:56:17,700 --> 00:56:23,280
+بالتفصيل الآن خلينا ننتقل للـ Colligative
+
+715
+00:56:23,280 --> 00:56:27,640
+Properties للـ Electrolyte Solutions في عندي ..
+
+716
+00:56:27,640 --> 00:56:33,400
+لما نكون الـ ..المادة non-electrolyte معناته لا
+
+717
+00:56:33,400 --> 00:56:38,460
+تتفكك .. لا تتفكك طب أنا عندي الـ colligative
+
+718
+00:56:38,460 --> 00:56:43,920
+properties تعتمد على عدد الـ species مش نوعها طب
+
+719
+00:56:43,920 --> 00:56:47,380
+لما يكون عندي electrolyte solutions معناته الـ
+
+720
+00:56:47,380 --> 00:56:53,890
+electrolyte يحصل له تفكك يبقى أنا لازم لما بدي أحسب
+
+721
+00:56:53,890 --> 00:56:59,190
+الـ ΔT<sub>f</sub> أو أحسب الـ ΔT<sub>b</sub> تحديدا يعني لازم
+
+722
+00:56:59,190 --> 00:57:06,050
+في البداية أعرف قد ايش عدد الجزيئات وبالتالي أحسب الـ
+
+723
+00:57:06,050 --> 00:57:09,090
+molality أو الـ molarity بشكل صحيح لأن اللي بيهمني
+
+724
+00:57:09,090 --> 00:57:15,670
+عدد الجزيئات تركيز الجزيئات كـ species مش كـ full مش
+
+725
+00:57:15,670 --> 00:57:19,450
+كحاجة يعني إيه ما هيّا مش متأينة اللي بتأين خليها تتأين
+
+726
+00:57:19,450 --> 00:57:24,330
+هيك التركيز بيزيد فلازم نأخذ بالنا
+
+727
+00:57:29,370 --> 00:57:33,390
+نأخذ بالنا من هذه الأمور طبعاً لما يكون في عندي
+
+728
+00:57:33,390 --> 00:57:36,730
+electrolyte على طول بدرب مثلاً لو كان عندي واحد
+
+729
+00:57:36,730 --> 00:57:44,790
+molar solution NaCl وأنا بدي ΔT<sub>f</sub> بتساوي K<sub>f</sub> في
+
+730
+00:57:44,790 --> 00:57:50,190
+M فبقولي الـ molality لما نقولي واحد molar solution
+
+731
+00:57:50,190 --> 00:57:58,950
+من الـ NaCl معناته الـ molality للـ solution بتساوي
+
+732
+00:57:58,950 --> 00:58:06,910
+اثنين في واحد تساوي اثنين ليش؟ لأنه عند الـ NaCl في
+
+733
+00:58:06,910 --> 00:58:09,690
+الماء ايش بيحصل له؟ هاد الـ electrolyte بيصير Na
+
+734
+00:58:09,690 --> 00:58:13,490
+<sup>+</sup> والـ Cl <sup>-</sup> يبقى عند أي عدد الـ species
+
+735
+00:58:13,490 --> 00:58:16,830
+اثنين يبقى بتضرب التركيز في اثنين التركيز الذات
+
+736
+00:58:16,830 --> 00:58:19,170
+بينما لو كان عندي مثلاً الميثانول
+
+737
+00:58:22,170 --> 00:58:26,530
+واحد مولار بيبقى واحد لأن مثلها مولار بيتفككش لو
+
+738
+00:58:26,530 --> 00:58:29,770
+كان عندي جلوكوز واحد مولار بتفككش لو كان عندي
+
+739
+00:58:29,770 --> 00:58:35,390
+بنزين واحد مولار بتفككش تمام؟ لكن إذا كان في عندي
+
+740
+00:58:35,390 --> 00:58:39,130
+electrolyte في ايش بدي أضرب؟ في عدد الـ species
+
+741
+00:58:39,130 --> 00:58:45,170
+يعني مثلاً calcium chloride واحد من عشرة مولار لما
+
+742
+00:58:45,170 --> 00:58:49,330
+بدي أجي أحسب واحد من عشرة مولار خليني أقول لما بدي
+
+743
+00:58:49,330 --> 00:58:54,750
+أجي أحسب الـ molality بقول ثلاثة من عشرة أو ثلاثة في
+
+744
+00:58:54,750 --> 00:58:58,390
+واحد من عشرة ليه؟ لأن الكالسيوم يبقى يعطيني
+
+745
+00:58:58,390 --> 00:59:03,410
+كالسيوم <sup>+2</sup> واثنين Cl <sup>-</sup> عادل سويس واحد و
+
+746
+00:59:03,410 --> 00:59:08,690
+اثنين ثلاثة يبقى الملائكة الكلية للـ species لأنه
+
+747
+00:59:08,690 --> 00:59:12,770
+ما يهمّني ايش هي الـ species أنا يهمّني عددها فعندي
+
+748
+00:59:12,770 --> 00:59:18,830
+ثلاثة تمام؟ يبقى ثلاثة في التركيز اللي هي واحد من
+
+749
+00:59:18,830 --> 00:59:22,430
+عشرة مول يبقى ثلاثة من عشرة مولال وهكذا لما بدي
+
+750
+00:59:22,430 --> 00:59:28,530
+أحسب الـ ΔT<sub>f</sub> والـ ΔT<sub>b</sub> وحتى الـ polarity
+
+751
+00:59:28,530 --> 00:59:34,030
+بدي أقول والله في عدد الـ species ليه؟ لأن الـ
+
+752
+00:59:34,030 --> 00:59:38,170
+colligative properties تتوقف على عدد الـ species مش
+
+753
+00:59:38,170 --> 00:59:44,370
+على نوع المركب نفسه، فإذا كان non-volatile، non
+
+754
+00:59:44,370 --> 00:59:47,670
+-electrolyte، مش فيه مشكلة، لأنه إيه؟ مش راح
+
+755
+00:59:47,670 --> 00:59:50,770
+يتفكك، فدائماً الـ molarity، وهذا الكلام اللي احنا
+
+756
+00:59:50,770 --> 00:59:53,610
+شفناه، الـ molarity له دائماً، الـ molarity له
+
+757
+00:59:53,610 --> 00:59:56,390
+واحدة، بتتغيّر، لأنه مش راح .. لكن لو كان
+
+758
+00:59:56,390 --> 01:00:00,710
+electrolyte، راح يتفكك، بدنا نشوف قد ايش عدد الـ
+
+759
+01:00:00,710 --> 01:00:08,300
+species، تمام؟ لكن السؤال من ناحية عملية مثلاً بيقول
+
+760
+01:00:08,300 --> 01:00:11,260
+however a one molar solution of sodium chloride
+
+761
+01:00:11,260 --> 01:00:14,340
+does not show twice the change in freezing point
+
+762
+01:00:14,340 --> 01:00:22,720
+يعني وكأنه مش اثنين مش اثنين بلجي مش اثنين ضرب هو
+
+763
+01:00:22,720 --> 01:00:27,000
+الأصل يكون زي هيك لكن بلجي انه لأ مش اثنين ممكن
+
+764
+01:00:27,000 --> 01:00:31,760
+يكون أقل من اثنين الميثانول دائماً واحد، الميثانول
+
+765
+01:00:31,760 --> 01:00:35,740
+ما في مشكلة، الميثانول مثلاً دائماً واحد، ما في مشكلة،
+
+766
+01:00:35,740 --> 01:00:40,700
+لكن الـ Electrolyte يعني الأصل انه يكون عدد الـ
+
+767
+01:00:40,700 --> 01:00:44,860
+species في ايه؟ في التركيز، لكن بلاحظ انه لأ دائماً
+
+768
+01:00:44,860 --> 01:00:51,290
+أقل، أقل، أقل، هفرجيكم ليش هان بدنا نتحدث عن حاجة
+
+769
+01:00:51,290 --> 01:00:56,570
+بنقولها van't Hoff factor هذا الـ factor الاثنين أو
+
+770
+01:00:56,570 --> 01:00:59,470
+الثلاثة أو كذا هذا اسمه van't Hoff factor تعالوا
+
+771
+01:00:59,470 --> 01:00:59,930
+نشوفه
+
+772
+01:01:08,810 --> 01:01:16,130
+بقول أنا عندي NaCl مثلاً واحد من عشرة NaCl لو أجهل
+
+773
+01:01:16,130 --> 01:01:22,850
+مولاليتي total molality بقول والله M في M في اثنين
+
+774
+01:01:22,850 --> 01:01:29,110
+يعني لأن هذا واحد وهذا واحد two species يعني هي N
+
+775
+01:01:29,110 --> 01:01:32,870
+a <sup>+</sup> وCl <sup>-</sup> اثنين يعني هذا الواحد الـ mole
+
+776
+01:01:32,870 --> 01:01:37,570
+أعطاني اثنين moles الأصل هيك الأصل انه يعطيني ضعف
+
+777
+01:01:37,570 --> 01:01:43,640
+اثنين من عشرة لكن بقول ايه؟ some Na<sup>+</sup> وCl<sup>-</sup>
+
+778
+01:01:43,640 --> 01:01:46,840
+اللي المفروض يتفككوا بشكل مئة في المئة بتفككوا مئة في
+
+779
+01:01:46,840 --> 01:01:49,460
+المئة لأن المحلول الأيوني بتفكك مئة في المئة في
+
+780
+01:01:49,460 --> 01:01:54,120
+المحلول NaCl لكن بعض الـ Na<sup>+</sup> والـ Cl<sup>-</sup> re
+
+781
+01:01:54,120 --> 01:01:58,090
+-associate momentarily في أي لحظة ممكن يجربوا على
+
+782
+01:01:58,090 --> 01:02:01,270
+بعض ويلاقيهم ايش مسكوا في بعض لحظياً بعدين بيسيبوا
+
+783
+01:02:01,270 --> 01:02:05,570
+بعض تعيون عادي for a short time so the true
+
+784
+01:02:05,570 --> 01:02:09,290
+concentration of particles is somewhat less than
+
+785
+01:02:09,290 --> 01:02:13,490
+two times the concentration of NaCl ليه؟ لأنه في
+
+786
+01:02:13,490 --> 01:02:18,970
+أي ثانية أو في أي جزء من الثانية هنلاقي انه بعض الـ
+
+787
+01:02:18,970 --> 01:02:22,010
+Na<sup>+</sup> والـ Cl<sup>-</sup> ايش حصل لهم؟ Re
+
+788
+01:02:22,010 --> 01:02:26,550
+-association يجمعنا الكلام مش اثنين في التركيز،
+
+789
+01:02:26,550 --> 01:02:30,850
+لأ، أقل شوية، أقل شوية، لازم نأخذ هذا الكلام بعين
+
+790
+01:02:30,850 --> 01:02:35,410
+الاعتبار، فهي احنا شايفين، هاي Cl<sup>-</sup> وهي Na
+
+791
+01:02:35,410 --> 01:02:38,510
+<sup>+</sup>، ما فيش مشكلة، هدول ابعد عن بعض، هد بتنعد
+
+792
+01:02:38,510 --> 01:02:42,570
+واحد وهد واحد، لكن هان جربوا على بعض عملوا ايه؟
+
+793
+01:02:42,570 --> 01:02:46,670
+Ion Pair، وكأنها NaCl Molecule، لكن هو مش
+
+794
+01:02:46,670 --> 01:02:52,270
+Molecule بس association لـ very short time تبقى معنى
+
+795
+01:02:52,270 --> 01:02:57,010
+الكلام في أي لحظة مش هيكون اثنين في التركيز لأ
+
+796
+01:02:57,010 --> 01:03:02,270
+لأنه هذه مش يعني الـ Na<sup>+</sup> مش منفصلة تماماً عن الـ
+
+797
+01:03:02,270 --> 01:03:03,030
+Cl<sup>-</sup>
+
+798
+01:03:06,340 --> 01:03:10,360
+بقول thus, one mole of NaCl in water does not
+
+799
+01:03:10,360 --> 01:03:13,900
+really give rise to two moles of ions أقل شوية
+
+800
+01:03:13,900 --> 01:03:17,460
+لأنه في أي لحظة لازم يكون في عنده reassociation
+
+801
+01:03:17,460 --> 01:03:23,150
+لبعض الايه؟ لبعض أيوناته هذا يعتمد أكثر على نوع
+
+802
+01:03:23,150 --> 01:03:26,190
+الماء والتركيز اللي هو الماء والتركيز اللي هو
+
+803
+01:03:26,190 --> 01:03:28,030
+الماء والتركيز اللي هو الماء والتركيز اللي هو
+
+804
+01:03:28,030 --> 01:03:28,890
+الماء والتركيز اللي هو الماء والتركيز اللي هو
+
+805
+01:03:28,890 --> 01:03:29,730
+الماء والتركيز اللي هو الماء والتركيز اللي هو
+
+806
+01:03:29,730 --> 01:03:31,350
+الماء والتركيز اللي هو الماء والتركيز اللي هو
+
+807
+01:03:31,350 --> 01:03:33,810
+الماء والتركيز اللي هو الماء والتركيز اللي هو
+
+808
+01:03:33,810 --> 01:03:38,790
+الماء والتركيز اللي هو الماء والتركيز اللي هو
+
+809
+01:03:38,790 --> 01:03:40,970
+الماء والتركيز اللي هو الماء والتركيز اللي هو
+
+810
+01:03:40,970 --> 01:03:45,350
+الماء و
+
+811
+01:03:45,370 --> 01:03:49,110
+وين لما اثنين يلاجوا بعض ويحصل .. فهان اه لما
+
+812
+01:03:49,110 --> 01:03:53,790
+نكون مخفف كثير معناته هذا الظاهرة ما فيش لها خليني
+
+813
+01:03:53,790 --> 01:03:58,230
+أقول importance أو أهمية عالية بينما لما نزيد
+
+814
+01:03:58,230 --> 01:04:03,970
+التركيز اه احتمال بيكون أكبر as concentrations of
+
+815
+01:04:03,970 --> 01:04:08,310
+electrolyte gets smaller behavior becomes closer
+
+816
+01:04:08,310 --> 01:04:13,690
+to ideal ideal يعني الاثنين يعطون اثنين هذه الـ
+
+817
+01:04:13,690 --> 01:04:17,370
+Ideal، الثلاثة يعطوني ثلاثة، مش اثنين إلا شوية أو
+
+818
+01:04:17,370 --> 01:04:21,050
+ثلاثة إلا شوية، تمام؟ هذا Ideal، تمام؟ لكن هذا
+
+819
+01:04:21,050 --> 01:04:27,470
+ما بتبدأ نحصل عليه لما المحلول يكون very dilute، كل
+
+820
+01:04:27,470 --> 01:04:32,770
+ما الـ .. كل ما التركيز قل، بنروح ناحية الـ
+
+821
+01:04:32,770 --> 01:04:36,290
+Ideality، كل ما التركيز قل، بنروح ناحية الـ
+
+822
+01:04:36,290 --> 01:04:43,230
+Ideality هذه الصورة جميلة جداً لحظة يعني هذا حصل له
+
+823
+01:04:43,230 --> 01:04:45,730
+hydration وهذا حصل له hydration لكن جربوا على بعض
+
+824
+01:04:45,730 --> 01:04:52,150
+كثير فحصل عندي ion pair يبقى عدد الـ Na<sup>+</sup> والـ
+
+825
+01:04:52,150 --> 01:04:56,680
+Cl<sup>-</sup> اللي في المحلول قل ليه؟ لأنه صار فيهم
+
+826
+01:04:56,680 --> 01:05:00,640
+بعضهم ion pairs هذه الـ ion pairs بتزيد بزيادة
+
+827
+01:05:00,640 --> 01:05:04,860
+التركيز لأن الـ Na<sup>+</sup> والـ Cl<sup>-</sup> بيقتربوا
+
+828
+01:05:04,860 --> 01:05:12,680
+على بعض بشكل فعال للغاية كل ما زاد التركيز لو جينا
+
+829
+01:05:12,680 --> 01:05:19,560
+طلعنا بعض
+
+830
+01:05:19,560 --> 01:05:26,010
+مثلاً الـ sucrose هن 0.1 molal 0.1 molal
+
+831
+01:05:26,010 --> 01:05:29,330
+0.1 molal 0.1 molal 0.1 molal
+
+832
+01:05:29,330 --> 01:05:29,370
+0.1 molal 0.1 molal 0.1 molal
+
+833
+01:05:29,370 --> 01:05:31,990
+0.1 molal 0.1 molal 0.1 molal
+
+834
+01:05:31,990 --> 01:05:33,830
+0.1 molal 0.1 molal 0.1 molal
+
+835
+01:05:33,830 --> 01:05:41,070
+0.1 molal 0.1 molal 0.1 molal
+
+836
+01:05:41,070 --> 01:05:43,810
+0.1 molal 0.1 molal 0.1 molal
+
+837
+01:05:43,810 --> 01:05:44,830
+0.1 molal 0.1 molal 0.1 molal
+
+838
+01:05:44,830 --> 01:05:46,610
+0.1 molal 0.1 molal 0.1 molal
+
+839
+01:05:46,610 --> 01:05:47,210
+0.1 molal 0.1 molal 0.1 molal
+
+840
+01:05:47,210 --> 01:05:47,250
+0.1 molal 0.1 molal 0.1 molal
+
+841
+01:05:47,250 --> 01:05:47,430
+point one molal point one molal point one molal
+
+842
+01:05:47,430 --> 01:05:51,790
+point one molal point one molal point one الفاكتور
+
+843
+01:05:51,790 --> 01:05:54,470
+عين دي واحد يعني الـ واحد من عشرة بيبقى واحد من
+
+844
+01:05:54,470 --> 01:05:58,850
+عشرة طب في الـ point one طبعا الـ واحد من .. الـ واحد
+
+845
+01:05:58,850 --> 01:06:00,590
+من واحد بيبقى واحد من واحد الفاكتور عين دي واحد
+
+846
+01:06:00,590 --> 01:06:04,010
+يعني الـ morality اللي هي واحد من عشرة بضربها في جد
+
+847
+01:06:04,010 --> 01:06:09,170
+ياش واحد ليه؟ لأن هذا ما بيتفككش هذا ما بيحصلش مش 
+
+848
+01:06:09,170 --> 01:06:12,350
+electrolyte فبتبقى نفسي .. يبقى الفاكتور اللي بدي
+
+849
+01:06:12,350 --> 01:06:18,670
+أضرب فيه يعني لو قلنا مثلا Delta TB بتساوي خليني
+
+850
+01:06:18,670 --> 01:06:26,910
+أقول I فيهكي اف في ام هاد الـ I هي vant Hoff factor
+
+851
+01:06:26,910 --> 01:06:32,490
+فبما أن السكروز non volatile non electrolyte
+
+852
+01:06:32,490 --> 01:06:37,010
+فدائما هاد الـ I بواحد يعني عندي كي اف في ام كي اف
+
+853
+01:06:37,010 --> 01:06:41,870
+في ام على طول طيب لو كان عندي NACL بتوقع الـ I بإيش
+
+854
+01:06:41,870 --> 01:06:46,470
+بدرجة من M في إيش في اتنين لإن الـ 1 من عشرة
+
+855
+01:06:46,470 --> 01:06:51,610
+هتعطيني إيه؟ اتنين من عشرة لكن بلاجيها لأ مضروبة في
+
+856
+01:06:51,610 --> 01:06:56,370
+one point eight seven يفجل واحد اه I هي one point
+
+857
+01:06:56,370 --> 01:06:59,470
+eight seven لما كان إيش التركيز واحد من عشرة طب
+
+858
+01:06:59,470 --> 01:07:02,630
+لما انجلّت التركيز one point اقتربت من الـ ideality
+
+859
+01:07:02,630 --> 01:07:06,270
+طب لما انجلّت التركيز كتير one point اتقربت من
+
+860
+01:07:06,270 --> 01:07:09,210
+الاتنين الـ limiting factor هي اتنين الـ limiting
+
+861
+01:07:09,210 --> 01:07:18,410
+value هي اتنين طيب الـ K2SO4 قال والله هان لما كان
+
+862
+01:07:18,410 --> 01:07:23,090
+point one مولل المفروض إنه يعطيني تلاتة اتنين
+
+863
+01:07:23,090 --> 01:07:25,770
+للبوتاسيم واحد للكبريتية لكن أنا اتنين واتنين و
+
+864
+01:07:25,770 --> 01:07:29,950
+تلاتين لما كان point one جال two point seven لما
+
+865
+01:07:29,950 --> 01:07:34,030
+كان point one two point eight four لحظة لما نكون
+
+866
+01:07:34,030 --> 01:07:40,450
+في عندها شحنات ثنائية يعني أو poly charges يعني
+
+867
+01:07:40,450 --> 01:07:44,510
+اتنين تلاتة اربعة الكبريتات طبعا عليها اتنين فبنلاحظ
+
+868
+01:07:44,510 --> 01:07:50,090
+إن هذه الأرقام بتنزل بشكل ملحوظ الـ I قيمتها بتقل عن
+
+869
+01:07:50,090 --> 01:07:54,710
+الـ limiting value بشكل ملحوظ مجنيزة أو كبريتية لحظة
+
+870
+01:07:54,710 --> 01:08:00,330
+بس لو بدنا نقارن بينها وبين الـ NACL لان هذه واحد من
+
+871
+01:08:00,330 --> 01:08:04,090
+عشرة مولل وهذه واحد من عشرة مولل وهذه واحد إلى
+
+872
+01:08:04,090 --> 01:08:07,370
+واحد يعني بتضرب في اتنين الـ limiting factor هيها
+
+873
+01:08:07,370 --> 01:08:10,290
+اتنين وهيها اتنين هذه limiting factor يعني إذا كان
+
+874
+01:08:10,290 --> 01:08:14,190
+عندي واحد من عشرة مولل مجنيزة كبريتية يعني I باتنين
+
+875
+01:08:14,190 --> 01:08:19,170
+بدها تكون لكن تعالوا نلاحظ الـ NAC 1.87 بينما هي 1
+
+876
+01:08:19,170 --> 01:08:23,570
+.21 التنتين تركيزهم 1 من 10 مولل لكن لاحظوا إنه
+
+877
+01:08:23,570 --> 01:08:27,650
+إيه فرق كبير ليه؟ لأن الـ charges هدف ثنائي و هدف
+
+878
+01:08:27,650 --> 01:08:31,890
+ثنائي فرصة إن يحصل ايون بير أكبر لأن الـ charges
+
+879
+01:08:31,890 --> 01:08:39,990
+أعلى الـ charges أعلى 1.21 1.53 1.82
+
+880
+01:08:43,620 --> 01:08:49,560
+لازم ناخد معامل فان هوف بعين الاعتبار لازم
+
+881
+01:08:49,560 --> 01:08:55,840
+ناخد معامل فان هوف بعين الاعتبار فعشان هيك
+
+882
+01:08:55,840 --> 01:09:01,140
+عملت التعديل Delta TF KF M I I صغيرة يعني اكتبوها
+
+883
+01:09:01,140 --> 01:09:09,020
+يعني هدا هي I i و الـ KB برضه نفس الكلام في M في I
+
+884
+01:09:09,020 --> 01:09:14,850
+عشان نجيب الـ Delta TBيعني لازم ناخد vant Hoff
+
+885
+01:09:14,850 --> 01:09:20,530
+factor بعين الاعتبار طيب
+
+886
+01:09:20,530 --> 01:09:24,410
+نتطلع
+
+887
+01:09:24,410 --> 01:09:26,930
+على الـ freeze نفس الكلام اللي شوفناه لكن بدأ ناخد
+
+888
+01:09:26,930 --> 01:09:29,290
+vant Hoff factor بعين الاعتبار بقول at what
+
+889
+01:09:29,290 --> 01:09:33,390
+temperature will a 5.4 molar solution of NaCl
+
+890
+01:09:33,390 --> 01:09:39,050
+freeze assume I بتساوي 2 طبعا الـ NaCl المفروض إنه
+
+891
+01:09:39,050 --> 01:09:45,020
+يعني الـ limiting value هي 2لأن الـ NACL واحد و واحد
+
+892
+01:09:45,020 --> 01:09:48,360
+لكن لو بالي أي حاجة جالي الـ value of factor واحد و
+
+893
+01:09:48,360 --> 01:09:51,700
+ثمانية من عشرة بيضرب واحد و ثمانية من عشرة معي
+
+894
+01:09:51,700 --> 01:09:53,100
+واحد و ثمانية من عشرة بيضرب واحد و ثمانية من
+
+895
+01:09:53,100 --> 01:09:58,120
+عشرة فبيقولوا delta F تساوي KF M في I الـ delta TF
+
+896
+01:09:58,120 --> 01:10:02,410
+1.86 اللي هو الـ freezing الـ freezing point
+
+897
+01:10:02,410 --> 01:10:08,370
+constant في 5.4 مولال في 2 اللي هي I فبيطلع عندي
+
+898
+01:10:08,370 --> 01:10:14,730
+21 من 10 ديجريز C لحظة لو إنه كان هذا non
+
+899
+01:10:14,730 --> 01:10:18,870
+electrolyte كان ضربت في واحد بس يعني الـ freezing
+
+900
+01:10:18,870 --> 01:10:22,550
+point إيش بتكون النص الـ freezing point دي بتكون
+
+901
+01:10:22,550 --> 01:10:27,590
+عشرة لكن لأنه صار عندي two species اه هذه ضربت في
+
+902
+01:10:27,590 --> 01:10:33,340
+اتنين الـ Delta TF تنضرب في اتنين بيقول لي what is
+
+903
+01:10:33,340 --> 01:10:36,660
+the freezing point depression of a 0.15 mol
+
+904
+01:10:36,660 --> 01:10:41,540
+aqueous solution of aluminum sulfate KF 1.86
+
+905
+01:10:46,200 --> 01:10:52,060
+1.86 degrees c per mole طيب بقول .. بقول هذا بيتفكك
+
+906
+01:10:52,060 --> 01:10:55,420
+اتنين aluminum و تلاتة كبريتية يعني بتضرب في قداش؟
+
+907
+01:10:55,420 --> 01:11:02,830
+في خمسة بدها الشطارة طيب في خمسة هذا الاصل انهدلتا
+
+908
+01:11:02,830 --> 01:11:07,570
+T F 1.86 في خمسة في point one five اللي هو التركيز
+
+909
+01:11:07,570 --> 01:11:11,530
+فبيعطيني one point four degree C لكن هذا على فرض
+
+910
+01:11:11,530 --> 01:11:16,330
+إنه الـ I عندي limiting value لكن لو اعطاني قيمة
+
+911
+01:11:16,330 --> 01:11:23,270
+جالي مثلا the van't Hoff factor
+
+912
+01:11:23,270 --> 01:11:29,690
+is مثلا three point eight seventy بجامعة اللي
+
+913
+01:11:29,690 --> 01:11:34,000
+الخمسة بدي اضرب في three point لانه مش كله
+
+914
+01:11:34,000 --> 01:11:39,720
+dissociated معايا فلازم اخد van't Hoff factor بعين
+
+915
+01:11:39,720 --> 01:11:44,860
+الاعتبار إذا كان اعطاني قيمته لكن لو ما اعطانيش
+
+916
+01:11:44,860 --> 01:11:48,160
+قيمته بعتبر إنه هو electrolyte وبعامله على إنه
+
+917
+01:11:48,160 --> 01:11:51,440
+limiting value limiting value عبارة عن عدد
+
+918
+01:11:51,440 --> 01:11:56,560
+الايونات مضروبة في الملالة بجيب الملالة لالمحلول
+
+919
+01:11:57,110 --> 01:12:00,290
+الـ Boiling point elevation نطلع على هذا المثال
+
+920
+01:12:00,290 --> 01:12:02,770
+نقول find the boiling point elevation of a 0.1
+
+921
+01:12:02,770 --> 01:12:06,970
+molar magnesium sulfate أكبر solution Kb 0.51
+
+922
+01:12:06,970 --> 01:12:11,970
+degree c و I واحد اعطاني I بقداش هي الـ I الاصل
+
+923
+01:12:11,970 --> 01:12:17,570
+انها تكون إيه لأ اتنين واحد magnesium يا بنتي واحد
+
+924
+01:12:17,570 --> 01:12:21,350
+sulfate اتنين لكن إيه اعطاني I واحد وطبقه حلو كتير
+
+925
+01:12:21,350 --> 01:12:29,470
+Delta T بتساوي Iفي KB في M Delta T بواحد و تلاتة
+
+926
+01:12:29,470 --> 01:12:33,490
+الـ I مش اتنين لإنه أعطاني هدقنة الـ Van't Hoff
+
+927
+01:12:33,490 --> 01:12:38,350
+factor في 0.51 degree C per molar في 0.1 بتعطيني 0
+
+928
+01:12:38,350 --> 01:12:42,330
+.066 if magnesium sulfate was not an electrolyte
+
+929
+01:12:42,330 --> 01:12:47,070
+إذا مافيش in the I في واحد على طول لو كانت بس هي
+
+930
+01:12:47,070 --> 01:12:49,310
+لأ هي طبعا electrolyte
+
+931
+01:12:52,720 --> 01:12:58,460
+آخر فقرة في هذا الـ chapter اتحدث فيها عن حاجة
+
+932
+01:12:58,460 --> 01:13:04,080
+بنقولها colloids الـ colloids هي الغرويات المحلول
+
+933
+01:13:04,080 --> 01:13:07,820
+الغروية يعني أو الـ suspensions suspensions of
+
+934
+01:13:07,820 --> 01:13:11,460
+particles larger than individual ions or molecules
+
+935
+01:13:11,460 --> 01:13:15,460
+but too small to be settled out يعني بنلاحظ إنه
+
+936
+01:13:15,460 --> 01:13:20,640
+بتترسبش بتضلها معلقة في المحلول too small to be
+
+937
+01:13:20,640 --> 01:13:23,060
+settled out by gravity يعني لو سبناها في المحلوق
+
+938
+01:13:23,060 --> 01:13:26,040
+تمها معلقة زي الحليب الحليب يحتوي على كمية هائلة
+
+939
+01:13:26,040 --> 01:13:30,360
+من الـ particles كل particles لكن لو سبنا الحليب
+
+940
+01:13:30,360 --> 01:13:33,700
+في التلاجة برا التلاجة بيبقى حليب طب إيش معناه
+
+941
+01:13:33,700 --> 01:13:39,080
+الجزيئات بتترسبش جال لأنه الجزيئات يعني خلينا نقول
+
+942
+01:13:39,080 --> 01:13:44,340
+أصغر من إنه يحصلها precipitation by gravity هذه
+
+943
+01:13:44,340 --> 01:13:48,200
+المحلوق اللي تسمى colloids محلوق غروية عادةً الـ
+
+944
+01:13:48,200 --> 01:13:51,160
+particle size أو الـ molecular size الـ dimension
+
+945
+01:13:51,160 --> 01:13:54,320
+للمولكولات اللي فيها أو الـ particles اللي فيها
+
+946
+01:13:54,320 --> 01:13:57,840
+بيقع في الـ micro meter range يعني يمكن من واحد من
+
+947
+01:13:57,840 --> 01:14:01,380
+عشرة micro meter لواحد micro meter في هذا الـ range
+
+948
+01:14:02,670 --> 01:14:07,070
+أنواعها متعددة للغاية .. أنواعها متعددة للغاية
+
+949
+01:14:07,070 --> 01:14:12,970
+ممكن نتطلع على هذا الجدول لكن ما بديش ألخمكم فيه ما
+
+950
+01:14:12,970 --> 01:14:18,230
+يهمني في الـ .. الـ colloids أو المحالي الغروية إنه
+
+951
+01:14:18,230 --> 01:14:21,910
+هذه الـ colloids لو أسقطنا عليها شعاع لاحظوا إنه
+
+952
+01:14:21,910 --> 01:14:25,930
+هذه الـ colloids طبعا ممكن تكون مبينة واضحة زي
+
+953
+01:14:25,930 --> 01:14:29,690
+الحليب وممكن ما تكونش واضحة .. تشوف فيها ميه مجترة
+
+954
+01:14:30,520 --> 01:14:35,000
+لكن على فرض إن هذه محلول الميه دايما فيه بروتين،
+
+955
+01:14:35,000 --> 01:14:38,940
+أنت ما تعرفش إنه فيه بروتين، بتشوفيه ميه صافية،
+
+956
+01:14:38,940 --> 01:14:45,010
+البروتين صح جزء كبير، لكنه معلق إيش بدي يعرفك إنه
+
+957
+01:14:45,010 --> 01:14:49,470
+فيها إشي ولا لأ؟ قال لو أسقطنا شعاع ضوء ويضل
+
+958
+01:14:49,470 --> 01:14:54,050
+يكون ملون عشان نشوفه بنلاحظ إنه هذه الأجسام
+
+959
+01:14:54,050 --> 01:14:57,470
+المعلقة أو الـ particles المعلقة الـ suspended
+
+960
+01:14:57,470 --> 01:15:02,290
+particles أو molecules بتعمل scattering للضوء
+
+961
+01:15:02,290 --> 01:15:07,470
+تشتيت للضوء فهيها لو سقط شعاع من هنا هذه الـ tube
+
+962
+01:15:07,470 --> 01:15:12,140
+ما فيها ولا إشي مادة ملونة نفس اللون اللي هنا مادة
+
+963
+01:15:12,140 --> 01:15:18,120
+ملونة نفس اللون اللي هنا ماشي يا جماعة لكن هذه الـ
+
+964
+01:15:18,120 --> 01:15:23,240
+tube موجود فيها المادة المعلقة اللي هي الـ Colloid
+
+965
+01:15:23,240 --> 01:15:27,140
+لاحظوا حصل scattering وكأنه ضوت مكانها وإن سقط
+
+966
+01:15:27,140 --> 01:15:33,400
+الشعاع شوفنا ضوء هذا اسمه scattering أو تشتت فما
+
+967
+01:15:33,400 --> 01:15:37,400
+يهمنا فيه الـ Colloids إن لو سقط عليها شعاع ضوئي
+
+968
+01:15:37,400 --> 01:15:42,580
+بيحصله تشتت هذه الظاهرة، ظاهرة تشتت الضوء عند
+
+969
+01:15:42,580 --> 01:15:47,100
+سقوطه على محلول غروي colloidal solution هذه
+
+970
+01:15:47,100 --> 01:15:51,820
+الظاهرة بتقولها تندال effect تندال الـ effect يبقى
+
+971
+01:15:51,820 --> 01:15:56,200
+أي شي تندال effect ظاهرة التشتت الضوء عند سقوطه
+
+972
+01:15:56,200 --> 01:16:02,120
+على محلول غروي يبقى الـ scattering of light hitting
+
+973
+01:16:02,120 --> 01:16:09,300
+a colloidal solution في الجسم الـ .. في الـ
+
+974
+01:16:09,300 --> 01:16:13,220
+biological systems عموما الـ colloids منتشرة للغاية
+
+975
+01:16:13,220 --> 01:16:17,380
+كتير منها colloids يعني مثلا الـ cholesterol بدوبش
+
+976
+01:16:17,380 --> 01:16:23,000
+في الـ .. طب كيف بيمشي؟ يعني ليش بتجمدش في نقطة
+
+977
+01:16:23,000 --> 01:16:26,800
+معينة وبيسد الشرايين؟ مثلا يعني الـ triglycerides
+
+978
+01:16:26,800 --> 01:16:30,220
+الدهون طب هي بتدوبش في الميه واحدة جسم الإنسان ميه
+
+979
+01:16:30,220 --> 01:16:36,940
+طب إيش معناه؟ بتدوبش يعني ما بتتكومش طب وإن بتروح؟
+
+980
+01:16:36,940 --> 01:16:41,720
+كيف الجسم بتتعامل معاها؟ الاصل إنها يعني خليني 
+
+981
+01:16:41,720 --> 01:16:47,860
+أقول غرويات و بتدوبش فاتس فالأصل إنه تتكوم تتجمع
+
+982
+01:16:48,530 --> 01:16:56,330
+وبالتالي جسم الإنسان ما يقدرش يعني .. يعني يقوم 
+
+983
+01:16:56,330 --> 01:17:01,830
+بعملياته بشكل مرضي هذه حاجة و الحاجة الثانية معظم
+
+984
+01:17:01,830 --> 01:17:07,510
+الأدوية تعتبر بدوبش دوبان كامل خليني أقول في المئة
+
+985
+01:17:07,510 --> 01:17:09,970
+كتير من الأدوية بدوبش دوبان كامل في المئة طب كيف
+
+986
+01:17:09,970 --> 01:17:15,810
+تنتقل مع الدم اللي هو مية كويسة وبتروح للخلايا
+
+987
+01:17:15,810 --> 01:17:19,130
+المختلفة وبتعدي وبتعمل ال function أو الوظيفة
+
+988
+01:17:19,130 --> 01:17:27,750
+بتاعتها كيف ده كلام بيحصل؟ قال عادة الجزيئات الممكن
+
+989
+01:17:27,750 --> 01:17:32,570
+يكون في إلها طبيعتين طبيعة polar وطبيعة non polar
+
+990
+01:17:32,570 --> 01:17:37,130
+طبيعة polar وطبيعة non polar زي مثلا زي هيك هذا
+
+991
+01:17:37,130 --> 01:17:41,290
+fatty acid موجود في جسم الإنسان fatty acid CH2 CH2
+
+992
+01:17:41,290 --> 01:17:47,250
+CH2 CH2 CH2 وفي الآخر COOH هذي polar بينما هذي non 
+
+993
+01:17:47,250 --> 01:17:51,030
+polar بنسمي الجزيئات بهذه الصيغة أو بهذه الشكل
+
+994
+01:17:51,030 --> 01:17:56,930
+اللي فيها non polar tail ذيل طويل non polar و
+
+995
+01:17:56,930 --> 01:18:01,470
+polar بنقول head group بنسميها surfactants surface
+
+996
+01:18:01,470 --> 01:18:09,930
+active agents كيف وجودها في الجسم
+
+997
+01:18:09,930 --> 01:18:14,570
+طبعا ال non polar بتحبش الميه طب كيف هي تبعد عن
+
+998
+01:18:14,570 --> 01:18:18,970
+الميه؟ جال بتكون حاجة شبيهة بهذا الشكل بنقولها
+
+999
+01:18:18,970 --> 01:18:23,990
+micelle ال polar head group وين بتكون؟ على السطح
+
+1000
+01:18:23,990 --> 01:18:28,590
+وال tail وين بيكون؟ جوا فهنا ال tail كله non polar
+
+1001
+01:18:29,340 --> 01:18:33,560
+لكن السطح إيش ماله؟ Polar هذه بتمشي في الدم زي ما
+
+1002
+01:18:33,560 --> 01:18:37,140
+هي طب لو في عينة non-polar material جاية بتيجي هان
+
+1003
+01:18:37,140 --> 01:18:41,640
+بيحملها وين في نصها لأن هاد ال polar هي اللي في 
+
+1004
+01:18:41,640 --> 01:18:44,900
+الميه على احتكاك مع الميه مافيش مشكلة طب و ال non
+
+1005
+01:18:44,900 --> 01:18:48,100
+-polar جاية في النص بيحملها تمام فبتنتقل وين ما
+
+1006
+01:18:48,100 --> 01:18:59,360
+بدنا مش بس هيك نتطلع هذا خلينا نقول membrane من ايش
+
+1007
+01:18:59,360 --> 01:19:03,520
+بيتكون؟ ال membrane طبعا بتدوبش في الميه و ال
+
+1008
+01:19:03,520 --> 01:19:05,740
+membranes اللي في الداخل بتدوبش في الميه لكن طب من
+
+1009
+01:19:05,740 --> 01:19:09,680
+ايش بيتكونها؟ جال polar head زيها و non polar
+
+1010
+01:19:09,680 --> 01:19:11,780
+tails polar head و non polar tails هذا ال polar
+
+1011
+01:19:11,780 --> 01:19:17,920
+بيكون على تماث مع الميه و الدم و غيره و ال non
+
+1012
+01:19:17,920 --> 01:19:22,920
+polar head لا هذا مختفي تماما جوا و هذا polar
+
+1013
+01:19:24,500 --> 01:19:27,240
+فالمادة .. وطبعا هذا ما نستطيع أن نقوله ثابت يوما
+
+1014
+01:19:27,240 --> 01:19:32,960
+لأ في عندنا fluidity معينة فلو في حاجة بدها تنتقل
+
+1015
+01:19:32,960 --> 01:19:37,200
+.. بتنتقل جوا يعني .. يعني بتنتقل المواد ال non
+
+1016
+01:19:37,200 --> 01:19:44,100
+polar من خلال ال non polar sheet اللي موجود عندها
+
+1017
+01:19:44,100 --> 01:19:48,600
+هذا نوع شكل .. شكل آخر هذا شكل .. هذا شكل ثالث
+
+1018
+01:19:49,240 --> 01:19:53,800
+هذه كلها بتكون موجودة بأشكال مختلفة وبتخلي المواد
+
+1019
+01:19:53,800 --> 01:19:59,700
+الغير ذائبة في الميّه تتمها موجودة وتنتقل من مكان
+
+1020
+01:19:59,700 --> 01:20:03,060
+لآخر داخل جسم الناس لكن بدون ما ايه يحصلها
+
+1021
+01:20:03,060 --> 01:20:09,370
+accumulation لأنها محمولة ومحمية داخل أوعية ممكن
+
+1022
+01:20:09,370 --> 01:20:13,050
+يكون هيك شكلها، ممكن هو هيك يكون شكلها، هذا polar،
+
+1023
+01:20:13,050 --> 01:20:16,230
+هذا non-polar، هذا polar، يعني هنا جوا الشغلات
+
+1024
+01:20:16,230 --> 01:20:19,270
+ممكن تكون polar، بينما هنا طبعا تبقى الشغلات non
+
+1025
+01:20:19,270 --> 01:20:25,150
+-polar وهكذا، فال colloids في ال biological
+
+1026
+01:20:25,150 --> 01:20:31,110
+systems تساعد على عمل emulsification of fats and
+
+1027
+01:20:31,110 --> 01:20:35,510
+oils in aqua solution emulsification يعني زي
+
+1028
+01:20:35,510 --> 01:20:40,370
+ذوبانة بتدوبها لأن ال non polar بدوب في ال non
+
+1029
+01:20:40,370 --> 01:20:44,810
+polar هي هذه non polar من جوا وين ال polar head
+
+1030
+01:20:44,810 --> 01:20:49,230
+groups هيها برا فعندي انا لو فاندي oily droplets
+
+1031
+01:20:49,230 --> 01:20:53,780
+ال oil بيجي هانطب هذا اللي خارجي كله عبارة عن ايه؟
+
+1032
+01:20:53,780 --> 01:20:58,180
+عبارة عن ميه وهيك بتعمل لكريمات اللي بنحطها على
+
+1033
+01:20:58,180 --> 01:21:02,900
+ادينا او الشامبوهات او شغلات كتير بنفس الطريقة
+
+1034
+01:21:02,900 --> 01:21:05,960
+بالظبط كيف بتحمل ال oil الشامبو كيف بحمل ال oil
+
+1035
+01:21:05,960 --> 01:21:09,660
+علشان يكون مناسب مثلا للشعر قال اه لازم يكون في
+
+1036
+01:21:09,660 --> 01:21:14,960
+شيء زي هيك فال شامبو أكوس فلازم يكون السطح عندي
+
+1037
+01:21:14,960 --> 01:21:23,180
+polar لكن جواتهداخل نظامه يوجد نانبولار ريجون وهو
+
+1038
+01:21:23,180 --> 01:21:30,020
+يتدوّب الفاتس والريحة في بعض الأحيان فهذا الكلام
+
+1039
+01:21:30,020 --> 01:21:36,210
+يعني يعتبر شيء مفيد جدا فيما يتعلق بـالـ
+
+1040
+01:21:36,210 --> 01:21:41,030
+emulsification of biological substances في جسم
+
+1041
+01:21:41,030 --> 01:21:45,910
+الإنسان هذا طبعا يعني لو حبيته تقوله والله هذا
+
+1042
+01:21:45,910 --> 01:21:49,390
+عبارة عن ما عايزي اللحظة انه جوا very non polar
+
+1043
+01:21:49,390 --> 01:21:56,450
+لكن برا very polar تمشي في الدم بسهولة خالص بعتقد
+
+1044
+01:21:56,450 --> 01:22:01,830
+أنا أنه هيك كفاية على هذا ال chapter بتمنى أنه إن
+
+1045
+01:22:01,830 --> 01:22:04,370
+شاء الله نكون استفدنا منه ال chapter الجاية هنتحدث
+
+1046
+01:22:04,370 --> 01:22:08,360
+عن الـ Chemistry of the Environment Chapter كتير
+
+1047
+01:22:08,360 --> 01:22:12,540
+كتير بسيط وسهل فبنشوفكم إذا الله راد الحصة الجاية
diff --git a/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/vDFGj4jYkGY.srt b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/vDFGj4jYkGY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8ff381160dd98ff6074c85a2e64be078605bc76d
--- /dev/null
+++ b/PL9fwy3NUQKwbMCDx86wSN33qITCXfwocY/vDFGj4jYkGY.srt
@@ -0,0 +1,3900 @@
+1
+00:00:20,860 --> 00:00:25,000
+بسم الله الرحمن الرحيم إذا الله راضٍ اليوم بنكمل
+
+2
+00:00:25,000 --> 00:00:29,660
+في chapter الغازات آخر chapter آخر الـ chapter 
+
+3
+00:00:29,660 --> 00:00:36,420
+تقريباً ففضل عدة جزئية نتكلم عن الـ molecular theory
+
+4
+00:00:36,420 --> 00:00:39,900
+للـ gases أو الـ kinetic molecular theory للـ gases
+
+5
+00:00:39,900 --> 00:00:44,740
+في الحقيقة احنا شفنا كيف الغازات بتتأثر عند تغير
+
+6
+00:00:44,740 --> 00:00:49,520
+بعض الظروف فمثلاً لما يتغير الضغط لما يتغير الحجم
+
+7
+00:00:49,520 --> 00:00:53,630
+لما يتغير الحرارة شفنا إيش بيحصل لكن ما جوابناش
+
+8
+00:00:53,630 --> 00:00:58,890
+على السؤال ليش بيحصل هيك تمام فاحنا شفنا الظاهرة
+
+9
+00:00:58,890 --> 00:01:03,490
+لكن ما عرفناش السبب الحقيقي وراها فالعلماء حاولوا
+
+10
+00:01:03,490 --> 00:01:09,770
+إنهم يفسروا إيش الأسباب اللي بتؤدي لهذه الظواهر أو
+
+11
+00:01:09,770 --> 00:01:13,510
+المشاهدات اللي احنا بنشاهدها مثلاً زودنا الضغط
+
+12
+00:01:13,510 --> 00:01:17,750
+الحجم بيقل زودنا الحرارة الـ volume بيزيد الضغط 
+
+13
+00:01:17,750 --> 00:01:24,090
+بيزيد زودنا عدد المولات الضغط بيزيد الحجم بيزيد مثلاً
+
+14
+00:01:24,090 --> 00:01:28,030
+يعني فليش هذا الكلام بيحصل؟ فالعلماء حاولوا يحطوا
+
+15
+00:01:28,030 --> 00:01:33,190
+يعني زي مضل يعني نموذج يشوفوا فيه يعني إيش الأسباب
+
+16
+00:01:33,190 --> 00:01:37,930
+الحقيقية وراء هذه التغيرات اللي بتحصل عندما نغير
+
+17
+00:01:37,930 --> 00:01:42,190
+أحد المتغيرات زي الـ pressure الـ volume الـ N اللي 
+
+18
+00:01:42,190 --> 00:01:47,030
+هي number of moles أو الحرارة في الحقيقة هذه
+
+19
+00:01:47,030 --> 00:01:50,750
+النظرية أو بناء هذا الـ Model أخذ وقت طويل يعني
+
+20
+00:01:50,750 --> 00:01:55,050
+يمكن حسب ما الكاتب بيقول يتجاوز 100 سنة لغاية ما
+
+21
+00:01:55,050 --> 00:02:00,970
+جدر كلازيوس تقريباً في الـ 1857 يعطي خدنا نقول
+
+22
+00:02:00,970 --> 00:02:04,150
+ملامح واضحة للنظرية اللي سميناها الـ kinetic
+
+23
+00:02:04,150 --> 00:02:07,470
+molecular theory اللي راح تفسر لنا ليش الظواهر
+
+24
+00:02:07,470 --> 00:02:11,210
+المختلفة اللي كنا بنشوفها في الغازات ليش بتحصل
+
+25
+00:02:11,210 --> 00:02:14,570
+بشكل أساسي
+
+26
+00:02:15,840 --> 00:02:22,320
+ففي هذه النظرية عموماً في عندي بعض المكونات
+
+27
+00:02:22,320 --> 00:02:27,880
+الأساسية أو بعض الـ .. خليني أقول الفروض الأساسية
+
+28
+00:02:27,880 --> 00:02:35,060
+في النظرية فأول مكون من مكونات النظرية بيقول فيه
+
+29
+00:02:35,060 --> 00:02:39,750
+أنّ الغازات عموماً بتتكون من large number of
+
+30
+00:02:39,750 --> 00:02:45,610
+molecules هنلاحظ أن معظم يعني مكونات هذه النظرية
+
+31
+00:02:45,610 --> 00:02:50,090
+احنا يعني يمكن نعرفها by intuition يعني بالفهم
+
+32
+00:02:50,090 --> 00:02:53,550
+البسيط تبعنا فطبعاً يعني الغازات لازم تكون بتتكون
+
+33
+00:02:53,550 --> 00:02:57,990
+من large number of molecules طبيعي هي غازات فتتكون
+
+34
+00:02:57,990 --> 00:03:01,810
+من جزيئات طبعاً لما نقول جزيئات هذه ينطبق على كمان
+
+35
+00:03:01,810 --> 00:03:07,470
+الـ .. يعني الذرات الغازية مش جزيئات لازم يكون أكثر 
+
+36
+00:03:07,470 --> 00:03:10,990
+من ذرة لأ فينطبق أيضاً على الذرات الغازية زي مثلاً
+
+37
+00:03:10,990 --> 00:03:16,450
+الارجون النيون الهيليوم هذه عبارة عن ذرات غازية
+
+38
+00:03:16,450 --> 00:03:19,890
+لكن برضه ينطبق عليها أنها يعني هان داخلة تحت كلمة
+
+39
+00:03:19,890 --> 00:03:23,410
+molecules طيب فبيقول أنه بيتكون من عدد كبير من
+
+40
+00:03:23,410 --> 00:03:28,430
+الجزيئات لكن هذه ها هذه الجزيئات اللي بتكلم عنها in
+
+41
+00:03:28,430 --> 00:03:33,490
+continuous random motion يعني آه هذه الجزيئات مش
+
+42
+00:03:33,490 --> 00:03:37,130
+قاعدة كل واحد في مكانه لأ هي بتتحرك وفي الحقيقة
+
+43
+00:03:37,130 --> 00:03:44,670
+بتتحرك بسرعة كبيرة بتتحرك بشكل مستمر بشكل مستمر و
+
+44
+00:03:44,670 --> 00:03:49,710
+أيّه و عشوائي مش في اتجاه واحد لأ والله هنشوف بعد
+
+45
+00:03:49,710 --> 00:03:53,230
+شوية كيف بتتحرك جزيئات الغاز
+
+46
+00:03:56,030 --> 00:04:01,450
+خليني أقول إن الجزء نفسه فيه حجم، جزء الغاز نفسه
+
+47
+00:04:01,450 --> 00:04:05,450
+فيه حجم، جويس، لو حطينا جزء واحد بس في لتر، قلنا
+
+48
+00:04:05,450 --> 00:04:08,950
+بيشغل اللتر هذا، لأنّ أنا بتحرك، فبيشغل اللتر، لو
+
+49
+00:04:08,950 --> 00:04:11,650
+حطينا جزئين، بيشغلوا اللتر، لو حطينا في 100 لتر،
+
+50
+00:04:11,650 --> 00:04:15,490
+بيشغل الـ 100 لتر، لكن نفس الجزء هذا إيش فيه له؟ فيه
+
+51
+00:04:15,490 --> 00:04:24,250
+حجم، بنقول إن حجمه هذا عبارة عن قيمة مهملة يبقى حجم
+
+52
+00:04:24,250 --> 00:04:29,330
+الجزيئات نفسها هي عبارة عن إيه؟ عن قيمة مهملة إذا
+
+53
+00:04:29,330 --> 00:04:34,190
+ما قورنت بالحجم اللي بتشغله يعني مثلاً لو عندنا 3
+
+54
+00:04:34,190 --> 00:04:37,450
+4 جزيئات في هذه الغرفة حجمهم بالنسبة لحجم
+
+55
+00:04:37,450 --> 00:04:40,710
+الغرفة اللي بيشغلوا مهمل فبنقول آه يبقى الـ
+
+56
+00:04:40,710 --> 00:04:44,990
+combined volume of all the molecules of the gas is
+
+57
+00:04:44,990 --> 00:04:48,330
+negligible relative to the total volume in which
+
+58
+00:04:48,330 --> 00:04:55,470
+the gas is contained تمام طيب هل توجد روابط ..
+
+59
+00:04:55,470 --> 00:05:00,710
+خليني أقول تجاذبات attractive forces أو repulsive
+
+60
+00:05:00,710 --> 00:05:03,430
+forces ما بين الجزيئات المختلفة؟ بنقول لأ حسب
+
+61
+00:05:03,430 --> 00:05:06,070
+النظرية، النظرية بتقول attractive and repulsive
+
+62
+00:05:06,070 --> 00:05:09,250
+forces between gas molecules are negligible، مهملة
+
+63
+00:05:09,250 --> 00:05:15,270
+لأ، بدليل إنه لو كانت قوية لكن لاجناه صار liquid و
+
+64
+00:05:15,270 --> 00:05:19,230
+لو كانت أقوى كان صار solid لكن لأ هذا كل واحد
+
+65
+00:05:19,230 --> 00:05:25,150
+بيتحرك بحرية و دائماً بملء الحيز اللي بيشغله فمش ممكن
+
+66
+00:05:25,150 --> 00:05:28,790
+تكون الـ attractive أو الـ repulsive forces يعني
+
+67
+00:05:28,790 --> 00:05:33,010
+خليني أقول بالذات الـ attractive خليني أقول موجودة
+
+68
+00:05:33,010 --> 00:05:37,500
+بشكل كبير ليه؟ لأن لو كانت موجودة بشكل كبير كان
+
+69
+00:05:37,500 --> 00:05:41,840
+والله الجزيئات الغاز تحولت إلى liquid أو إلى solid
+
+70
+00:05:41,840 --> 00:05:46,480
+ليه؟ لأن اللي بيحول الـ gas إلى liquid أحد خصائص الـ
+
+71
+00:05:46,480 --> 00:05:48,280
+liquid آه الـ intermolecular forces زي ما هنشوف
+
+72
+00:05:48,280 --> 00:05:52,420
+الـ chapter الجاي لكن هنّ بنقول إيه الـ attractive و الـ
+
+73
+00:05:52,420 --> 00:05:55,360
+repulsive forces between gas molecules are
+
+74
+00:05:55,360 --> 00:05:59,880
+negligible حاجة مهملة للغاية الآن في هدول الـ two
+
+75
+00:05:59,880 --> 00:06:04,080
+postulates أو الـ two statements بنتكلم عن الحرارة
+
+76
+00:06:04,900 --> 00:06:08,480
+وبنقول الـ energy can be transferred between
+
+77
+00:06:08,480 --> 00:06:14,720
+molecules during collisions الـ energy الطاقة يمكن
+
+78
+00:06:14,720 --> 00:06:20,840
+أن تنتقل ما بين الجزيئات نتيجة إيه التصادمات في
+
+79
+00:06:20,840 --> 00:06:25,090
+حالة التصادم ممكن جداً أنه يعني جزاء يكون سريع جداً
+
+80
+00:06:25,090 --> 00:06:29,410
+يضرب في جزاء آخر الجزاء السريع جداً هذا يوصل
+
+81
+00:06:29,410 --> 00:06:35,330
+لتقريباً سرعة التوقف بينما الجزاء الآخر ياخذ الطاقة
+
+82
+00:06:35,330 --> 00:06:38,810
+و يسير بسرعة لكن الـ energy دائماً conserved يعني
+
+83
+00:06:38,810 --> 00:06:42,330
+إذا كان الأول يعطي طاقة فالثاني لازم ياخذها فالـ
+
+84
+00:06:42,330 --> 00:06:47,510
+energy عندي دائماً conserved بقول ها أنا أقول لك هدول
+
+85
+00:06:47,510 --> 00:06:49,650
+اثنين اتكلم فيهم على الحرارة بقول as long as
+
+86
+00:06:49,650 --> 00:06:53,490
+temperature remains constant مدام الحرارة ثابتة
+
+87
+00:06:53,490 --> 00:06:56,690
+then the average kinetic energy of molecules does
+
+88
+00:06:56,690 --> 00:06:59,570
+not change الـ average kinetic energy للمولكولات
+
+89
+00:06:59,570 --> 00:07:03,910
+does not change طب هيش بتعمل الحرارة؟ أيش بتعمل
+
+90
+00:07:03,910 --> 00:07:08,910
+يعني؟ طب كيف الطاقة الحركية المتوسط طاقة الحركية
+
+91
+00:07:08,910 --> 00:07:13,070
+للجزيئات جالها تتغير؟ طب حلو طب خليني أشوف بقول
+
+92
+00:07:13,070 --> 00:07:16,670
+the average kinetic energy of the molecules is
+
+93
+00:07:16,670 --> 00:07:19,830
+proportional to the absolute temperature يعني
+
+94
+00:07:19,830 --> 00:07:23,970
+بمعنى إذا كان زادت درجة الحرارة الـ average kinetic
+
+95
+00:07:23,970 --> 00:07:26,710
+energy هذه statements مهمة جداً بالنسبة لنا لأنّ
+
+96
+00:07:26,710 --> 00:07:31,290
+عليها بتنبني النظرية كويس بقول إذا كان زادت الـ
+
+97
+00:07:31,290 --> 00:07:34,450
+absolute temperature فالـ average kinetic energy
+
+98
+00:07:34,450 --> 00:07:39,270
+بتزيد إذا زادت الـ absolute temperature فالـ average
+
+99
+00:07:39,270 --> 00:07:45,700
+kinetic energy بتزيد طيب إذا كان عندي نفس الجزيئات،
+
+100
+00:07:45,700 --> 00:07:49,340
+طب الجزيئ إله mass معينة، و الـ kinetic energy إيش
+
+101
+00:07:49,340 --> 00:07:53,600
+هي؟ جال نص M في V squared، معناه الكلام إذا كان
+
+102
+00:07:53,600 --> 00:07:58,600
+للجزيئات نفسها، للجزيئات نفسها، إيش اللي بيحصل؟
+
+103
+00:07:58,600 --> 00:08:04,040
+نفس الكتلة، نفس الكتلة، طيب الطاقة زادت، يبقى إيش
+
+104
+00:08:04,040 --> 00:08:08,010
+اللي بده يزيد بشكل كبير؟ السرعة آه طب إيش تأثير
+
+105
+00:08:08,010 --> 00:08:11,190
+زيادة السرعة؟ آه هذا تأثير مهم جداً، collisions
+
+106
+00:08:11,190 --> 00:08:15,690
+أكثر وهذا كلام له تأثير زي ما هنشوف على الضغط فهذه
+
+107
+00:08:15,690 --> 00:08:16,590
+هي الـ statements
+
+108
+00:08:19,000 --> 00:08:23,740
+اللي انبنت عليها النظرية، بدنا ننتبه، زي ما حكينا
+
+109
+00:08:23,740 --> 00:08:27,320
+في البداية، طبعاً تتحرك أو هي اسمها kinetic يعني
+
+110
+00:08:27,320 --> 00:08:31,080
+هي نظرية الحركة، نظرية حركية، kinetic، كويس؟
+
+111
+00:08:31,080 --> 00:08:35,060
+اتكلموا عن الـ motion، فالجزيئة تتحرك بشكل مستمر
+
+112
+00:08:35,060 --> 00:08:40,380
+وعشوائي حلو كتير، بنقول إن الـ volume للجزيئات بحد
+
+113
+00:08:40,380 --> 00:08:43,900
+ذاتها مهمل بالنسبة للحجم اللي بتشغله، طيب الـ
+
+114
+00:08:43,900 --> 00:08:47,220
+attractive و الـ repulsive forces مهملة، مهملة،
+
+115
+00:08:47,220 --> 00:08:53,140
+بعدين بنتكلم عن الحرارة، فبنقول إذا كان الحرارة
+
+116
+00:08:53,140 --> 00:08:56,480
+ثابتة، فالـ average kinetic energy ثابتة، يعني كل
+
+117
+00:08:56,480 --> 00:09:00,300
+مهما كان نوع الجزيئ، مهما كان نوع الغاز، مدام
+
+118
+00:09:00,300 --> 00:09:03,580
+الحرارة ثابتة، الـ average kinetic energy له إيه؟
+
+119
+00:09:03,580 --> 00:09:07,180
+ثابتة طب إذا كان الحرارة زادت أو الـ average kinetic
+
+120
+00:09:07,180 --> 00:09:10,340
+energy تناسب مع الـ absolute temperature يعني لو
+
+121
+00:09:10,340 --> 00:09:13,300
+زادت الحرارة الـ average kinetic energy بدها تزيد
+
+122
+00:09:13,300 --> 00:09:17,140
+للغاز الواحد إيش معنى إنها تزيد؟ معناته السرعة هي
+
+123
+00:09:17,140 --> 00:09:20,260
+اللي بدها تزيد معناته راح يكون في عندي collisions
+
+124
+00:09:20,260 --> 00:09:25,900
+أكثر وهذا لأنه أثر على مثلاً الضغط بشكل أساسي
+
+125
+00:09:25,900 --> 00:09:30,880
+تعالوا نتطلع بقول إيش علاقة الـ kinetic molecular
+
+126
+00:09:30,880 --> 00:09:36,920
+theory مع الـ pressure؟ الكاينيتيك موليكيالر ثيوري
+
+127
+00:09:36,920 --> 00:09:41,080
+يشرح كلا الانتشار والانضغاط على مستوى الموليكيالر،
+
+128
+00:09:41,080 --> 00:09:44,240
+ليس فقط بتعطينا الظاهرة إنه والله آه الـ volume
+
+129
+00:09:44,240 --> 00:09:48,020
+بيزيد بزيادة الحرارة أو الضغط بيزيد بزيادة الحرارة
+
+130
+00:09:48,020 --> 00:09:54,780
+مثلاً، بقول لي ليش، بدنا نشوف ليش احنا فبدي أفهم
+
+131
+00:09:54,780 --> 00:09:59,140
+بداية أن ضغط الغاز ما هو إلا عبارة عن تصادمات
+
+132
+00:09:59,140 --> 00:10:03,100
+جزيئات الغاز مع الجدار هذا اللي بيحدد ضغط تصادمات
+
+133
+00:10:03,100 --> 00:10:06,540
+جزيئات الغاز مع الجدار في عندي حاجتين بدي
+
+134
+00:10:06,540 --> 00:10:11,680
+أنتبه لهم والله لو عدد التصادمات زاد كويس طبعاً الـ
+
+135
+00:10:11,680 --> 00:10:16,820
+pressure بده يزيد هذا إذا كان الحجم خلينا نقول ثابت
+
+136
+00:10:16,820 --> 00:10:21,740
+لو زاد عدد التصادمات الـ pressure بده يزيد طيب لو
+
+137
+00:10:21,740 --> 00:10:27,100
+قلّ الحجم بتصير عندي أنا كمان حاجة أنه per unit
+
+138
+00:10:27,100 --> 00:10:31,580
+area عدد التصادمات بيزيد يعني وكأنه الحجم يتناسب
+
+139
+00:10:31,580 --> 00:10:35,600
+عكس مع الـ volume طيب the magnitude of the pressure
+
+140
+00:10:35,600 --> 00:10:42,220
+is determined by how often عدد المرات and how
+
+141
+00:10:42,220 --> 00:10:46,500
+forcefully the molecules strike the walls اه يبقى
+
+142
+00:10:46,500 --> 00:10:51,320
+عندي التصادمات هي الأصل في الضغط طب ايش اللي بيحدد
+
+143
+00:10:51,860 --> 00:10:56,640
+كمية الضغط أو مقدار الضغط؟ جال عدد التصادمات هذه
+
+144
+00:10:56,640 --> 00:11:00,980
+واحدة وكمان القوة اللي بت .. اللي بت .. بيصدم فيها
+
+145
+00:11:00,980 --> 00:11:06,520
+الجزيء الـ walls اللي موجودة فهدول الحاجتين لازم
+
+146
+00:11:06,520 --> 00:11:09,540
+آخذ بالي منهم ولازم الـ kinetic molecular theory
+
+147
+00:11:09,540 --> 00:11:14,380
+تفسرهم ليه؟ فبقول أنا ايه؟ أنا عندي الـ absolute
+
+148
+00:11:14,380 --> 00:11:18,080
+temperature زي ما شفناه هي عبارة عن أو تتناسب مع
+
+149
+00:11:18,080 --> 00:11:22,450
+الـ kinetic energy of molecules فلو قلنا إن two
+
+150
+00:11:22,450 --> 00:11:26,150
+gases are at the same temperature المفروض إن
+
+151
+00:11:26,150 --> 00:11:31,770
+الاتنين لهم same average kinetic energy مادام
+
+152
+00:11:31,770 --> 00:11:35,310
+الاتنين عند نفس الحرارة يبقى الاتنين لهم ايه؟ same
+
+153
+00:11:35,310 --> 00:11:39,490
+average kinetic energy طبعًا إذا كان زادت الـ
+
+154
+00:11:39,490 --> 00:11:43,350
+absolute temperature زي ما شفنا مثلًا لو صارت
+
+155
+00:11:43,350 --> 00:11:47,200
+doubled لو ضربناها في اثنين على طول الـ average
+
+156
+00:11:47,200 --> 00:11:51,920
+kinetic energy تنضرب في اثنين تتضاعف وقلنا إنه لنفس
+
+157
+00:11:51,920 --> 00:11:56,460
+الغاز معناته هذا يعني ايش؟ انعكاسه جال ورا السرعة
+
+158
+00:11:56,460 --> 00:12:01,400
+بتزيد عشان هيك بنقول الـ molecular motion increases
+
+159
+00:12:01,400 --> 00:12:05,140
+with increasing temperature and thus pressure as
+
+160
+00:12:05,140 --> 00:12:08,000
+well ليه؟ لأن الـ molecular motion بتزيد فمعناه
+
+161
+00:12:08,000 --> 00:12:10,680
+كلام تصادمات هتزيد ويبقى ال pressure أيضًا هيزيد
+
+162
+00:12:10,680 --> 00:12:17,530
+وهنرجع عليه هذا الكلام بعد شوية الآن ايش علاقة الـ
+
+163
+00:12:17,530 --> 00:12:21,790
+molecular speeds؟ في عندي جزيئات مختلفة، كلها لها
+
+164
+00:12:21,790 --> 00:12:24,950
+نفس السرعة؟ لأ، كل جزيء له سرعة، لأن حاليًا في
+
+165
+00:12:24,950 --> 00:12:29,230
+تصادمات، وتصادمات يعني مش حاجة سهلة، يعني تصادمات
+
+166
+00:12:29,230 --> 00:12:34,210
+بالملايين في الثانية، بالملايين، كويس؟ لأن سرعة
+
+167
+00:12:34,210 --> 00:12:38,870
+الجزيئات عالية كثير جزيئات الغازات عالية كثير فعندي
+
+168
+00:12:38,870 --> 00:12:45,530
+تصادمات بالملايين فمع ذلك لما في جزيء كان  تلجأ سرعته عالية بعد شوية ضرب في جزيء آخر صارت سرعته من
+
+169
+00:12:45,530 --> 00:12:49,090
+الخفضة الجزيء الآخر اللي كان سرعته منخفضة صارت
+
+170
+00:12:49,090 --> 00:12:51,750
+سرعته عالية في جزيء .. جزيء .. كمان ضرب في جزيء
+
+171
+00:12:51,750 --> 00:12:55,050
+آخر اتغيرت سرعته وهكذا فمقدر أقول أنا إن ال ..
+
+172
+00:12:55,050 --> 00:12:59,350
+السرعات الـ molecular speeds بتتفاوت تتفاوت ففي عندي
+
+173
+00:12:59,350 --> 00:13:05,230
+دائمًا range من السرعات ممكن أقول زي curve في مثلًا
+
+174
+00:13:05,230 --> 00:13:11,110
+جزيئات كثير اللهم سرعة معينة جزيئات اللهم سرعة أقل
+
+175
+00:13:11,110 --> 00:13:13,930
+وجزيئات اللهم سرعة أكبر
+
+176
+00:13:13,930 --> 00:13:16,830
+وجزيئات اللهم سرعة أكبر
+
+177
+00:13:18,790 --> 00:13:23,070
+هذا الكلام كله بيتوقف على خلّيني أقول يعني الـ
+
+178
+00:13:23,070 --> 00:13:25,610
+kinetic energy حاجة اللي هي leverage kinetic
+
+179
+00:13:25,610 --> 00:13:28,930
+energy اللي هي الحرارة برضه كمان يعني بتأثر تأثير
+
+180
+00:13:28,930 --> 00:13:34,250
+كبير على السرعات فتعالوا نشوف للـ nitrogen gas at
+
+181
+00:13:34,250 --> 00:13:39,670
+zero و hundred degrees C ايش في عندي؟ هان هذا
+
+182
+00:13:39,670 --> 00:13:47,540
+الأسراج عند zero degrees C لاحظوا إنه يعنيهان
+
+183
+00:13:47,540 --> 00:13:52,200
+الموليكو در السبيت لاحظوا إنه يعني عند zero
+
+184
+00:13:52,200 --> 00:13:56,300
+degrees c خليني أقول كانت ال .. ال .. ايش بيسموها
+
+185
+00:13:56,300 --> 00:14:00,020
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+186
+00:14:00,020 --> 00:14:00,600
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+187
+00:14:00,600 --> 00:14:00,640
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+188
+00:14:00,640 --> 00:14:00,760
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+189
+00:14:00,760 --> 00:14:00,880
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+190
+00:14:00,880 --> 00:14:01,580
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+191
+00:14:01,580 --> 00:14:02,200
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+192
+00:14:02,200 --> 00:14:10,640
+ال .. ال .. ال ..
+
+193
+00:14:10,640 --> 00:14:12,340
+ال .. ال ..
+
+194
+00:14:17,200 --> 00:14:23,520
+لكن لما صار الغاز عند مائة
+
+195
+00:14:23,520 --> 00:14:28,520
+درجة، لاحظوا الـ maximum وين؟ وصل خمسة في عشر أقصى
+
+196
+00:14:28,520 --> 00:14:34,960
+اثنين، زادت، يعني عدد الجزيئات اللي بيحمل كينتك
+
+197
+00:14:34,960 --> 00:14:40,160
+energy أكبر بيزيد بزيادة درجة الحرارة أو إن الـ
+
+198
+00:14:40,160 --> 00:14:44,640
+molecular speeds بتزيد
+
+199
+00:14:44,640 --> 00:14:47,520
+بزيادة درجة الحرارة الـ molecular speeds بتزيد
+
+200
+00:14:47,520 --> 00:14:48,020
+بزيادة درجة الحرارة الـ molecular speeds بتزيد
+
+201
+00:14:48,020 --> 00:14:49,820
+بزيادة درجة الحرارة الـ molecular speeds بتزيد
+
+202
+00:14:49,820 --> 00:14:50,340
+بزيادة درجة الحرارة الـ molecular speeds بتزيد
+
+203
+00:14:50,340 --> 00:14:51,560
+بزيادة درجة الحرارة الـ molecular speeds بتزيد
+
+204
+00:14:51,560 --> 00:14:52,620
+بزيادة درجة الحرارة الـ molecular speeds بتزيد
+
+205
+00:14:52,620 --> 00:14:52,640
+بزيادة درجة الحرارة الـ molecular speeds بتزيد
+
+206
+00:14:52,640 --> 00:14:52,660
+بزيادة درجة الحرارة الـ molecular speeds بتزيد ب
+
+207
+00:14:53,060 --> 00:14:57,160
+هذه الـ speed اللي عنده الـ maximum بنقولها ميو أو 
+
+208
+00:14:57,160 --> 00:15:00,480
+speed most probable وهذه الـ speed هي الـ average
+
+209
+00:15:00,480 --> 00:15:06,620
+speed وهذه الـ URMS root mean square مرة معاكم
+
+210
+00:15:06,620 --> 00:15:08,960
+يعني حاجزي الـ root mean square اسمها الـ root mean
+
+211
+00:15:08,960 --> 00:15:09,940
+square speed
+
+212
+00:15:13,190 --> 00:15:16,790
+الـ Speed للجزيئات اللي لها الـ Average Kinetic
+
+213
+00:15:16,790 --> 00:15:20,290
+Energy
+
+214
+00:15:20,290 --> 00:15:26,190
+الـ
+
+215
+00:15:26,190 --> 00:15:33,170
+UMP اللي هي الـ Most Probable Speed وهذه بتتوقف
+
+216
+00:15:33,170 --> 00:15:37,550
+على درجة الحرارة طبعًا بيحصلها shift كل ما زودنا الـ
+
+217
+00:15:37,550 --> 00:15:40,090
+Absolute Temperature بتروح على اليمين يعني بتزيد
+
+218
+00:15:40,090 --> 00:15:41,690
+قيمتها
+
+219
+00:15:46,260 --> 00:15:51,280
+الشيء اللي حكينا عنه هو إن تطلع على effect of
+
+220
+00:15:51,280 --> 00:15:55,330
+temperature on the RMS وهذا كلام برضه شفناه شوفنا
+
+221
+00:15:55,330 --> 00:15:58,930
+احنا إن الحرارة اللي بنتكلم عن نفس نوع الغاز
+
+222
+00:15:58,930 --> 00:16:04,390
+الحرارة وضع طبيعي إنها يعني مدام زودنا الحرارة
+
+223
+00:16:04,390 --> 00:16:06,690
+يبقى الـ average kinetic energy هذا بنص النظرية
+
+224
+00:16:06,690 --> 00:16:09,850
+احنا بنحاول نستخدم دائمًا نصوص النظرية مش تفسيراتنا
+
+225
+00:16:09,850 --> 00:16:14,270
+فبقول ايه؟ بقول إن الـ average kinetic energy تتناسب
+
+226
+00:16:14,270 --> 00:16:17,590
+مع الـ absolute temperature طب ايش بيحصل لما نزود
+
+227
+00:16:17,590 --> 00:16:21,110
+درجة الحرارة؟ جال والله يبقى الـ average kinetic
+
+228
+00:16:21,110 --> 00:16:27,440
+energy بتزيد لو ضعفناها بتضعف نفس نوع الغاز إذا نفس
+
+229
+00:16:27,440 --> 00:16:31,880
+الكتلة للغاز هي الـ kinetic energy نص M U R M S
+
+230
+00:16:31,880 --> 00:16:37,740
+squared ليش M U R M S squared؟ لأن هذه الـ root
+
+231
+00:16:37,740 --> 00:16:42,560
+mean square speed قلنا هذه عبارة عن الـ speed
+
+232
+00:16:42,560 --> 00:16:46,420
+للمولكولات اللي لها الـ average kinetic energy وهذا
+
+233
+00:16:46,420 --> 00:16:50,300
+هو الـ average kinetic energy تمام فدايمًا الميو في
+
+234
+00:16:50,300 --> 00:16:54,880
+هذه العلاقة RMS لأن تعريفها هي عبارة عن الـ speed
+
+235
+00:16:54,880 --> 00:16:59,360
+لـ الجزئية اللي لها نفس الـ average kinetic energy
+
+236
+00:16:59,360 --> 00:17:02,800
+للـ molecules طب إذا كان الـ M ثابتة، ايش بده يحصل؟
+
+237
+00:17:02,800 --> 00:17:06,720
+وزادت درجة الحرارة، ما هي كلام الميو RMS بدها
+
+238
+00:17:06,720 --> 00:17:13,800
+تزيد وهذا الكلام يعني هذا هو تأثير الحرارة على الـ
+
+239
+00:17:13,800 --> 00:17:18,670
+RMS speed تأثير إن والله اه الحرارة بتزود السرعة،
+
+240
+00:17:18,670 --> 00:17:22,130
+ليش بنقول هذا الكلام؟ إن هنستخدم هذه المعلومة في
+
+241
+00:17:22,130 --> 00:17:27,950
+تفسير ايش علاقة الضغط، ايش علاقة الحرارة بالـ
+
+242
+00:17:27,950 --> 00:17:34,130
+volume أو ايش علاقة الحرارة بالضغط، فهنستخدم هذه
+
+243
+00:17:34,130 --> 00:17:40,510
+المعلومة تعالوا نتطلع على كيف الـ kinetic molecular
+
+244
+00:17:40,510 --> 00:17:47,310
+theory يمكن تطبيقها علشان نفهم الـ gas laws وهذا هو
+
+245
+00:17:47,310 --> 00:17:50,990
+السبب حديثنا عن الـ kinetic molecular theory كيف
+
+246
+00:17:50,990 --> 00:17:53,990
+نحاول نستخدم الـ kinetic theory علشان الـ kinetic
+
+247
+00:17:53,990 --> 00:17:57,450
+molecular theory علشان نقدر نفسر الـ gas laws ايش
+
+248
+00:17:57,450 --> 00:18:00,230
+الـ gas laws؟ اللي هو بويلز لو، تشارلز لو، إلى آخره
+
+249
+00:18:00,230 --> 00:18:04,730
+يعني الـ P تتناسب مع 1 على V أو P تتناسب مع T إلى
+
+250
+00:18:04,730 --> 00:18:05,170
+آخره
+
+251
+00:18:08,590 --> 00:18:16,130
+طيب نتطلع في البداية على الـ boils law فبقول أنا an
+
+252
+00:18:16,130 --> 00:18:19,910
+increase in volume at constant temperature causes
+
+253
+00:18:20,520 --> 00:18:26,400
+pressure to decrease لو يعني لو زودنا الحجم الضغط
+
+254
+00:18:26,400 --> 00:18:29,420
+ايش بده يجي له؟ بده يقل طب ليش الضغط بيزيد؟ ماذا
+
+255
+00:18:29,420 --> 00:18:32,440
+السؤال؟ هذه ملاحظة بالنسبة للعارفينها احنا هذه
+
+256
+00:18:32,440 --> 00:18:35,480
+لاحظناها وكتبناها في قانون P تتنسب مع واحد على V
+
+257
+00:18:35,480 --> 00:18:39,600
+أو V تتنسب مع واحد على P كتبناها طب السؤال ليش؟
+
+258
+00:18:39,600 --> 00:18:45,740
+جال اه لما الحجم يزيد الجزيئات بتتباعد عن بعضها
+
+259
+00:18:45,740 --> 00:18:53,410
+البعض فبتصير يعني الـ collisions لازم يمشي الجزيء
+
+260
+00:18:53,410 --> 00:18:56,190
+مسافة أكبر عشان يعمل collisions لأنه صار حجم كبير
+
+261
+00:18:56,190 --> 00:19:00,650
+بدّه يمشي مسافة أكبر معناته عدد الـ collisions للـ
+
+262
+00:19:00,650 --> 00:19:05,870
+unit area per second بيقل إذا الضغط بيقل هذا تفسير
+
+263
+00:19:05,870 --> 00:19:10,570
+الـ kinetic molecular theory لإيش تأثير والله مثلًا
+
+264
+00:19:10,570 --> 00:19:15,150
+هنا an increase in volume أي constant temperature
+
+265
+00:19:15,150 --> 00:19:18,630
+means that the average kinetic energy of the
+
+266
+00:19:18,630 --> 00:19:22,730
+molecules remains constant بتتغيرش مدام الحرارة
+
+267
+00:19:22,730 --> 00:19:26,510
+ثابتة إذا الـ average kinetic energy عندي ثابتة
+
+268
+00:19:26,510 --> 00:19:32,950
+طيب ايش مدلوله هذا؟ this means that the RMS speed
+
+269
+00:19:32,950 --> 00:19:36,690
+of the molecules remains unchanged إذا سرعة
+
+270
+00:19:36,690 --> 00:19:40,570
+الجزيئات بتبقى ثابتة لأن الحرارة ثابتة ما دام
+
+271
+00:19:40,570 --> 00:19:42,870
+الحرارة ثابتة إذا الـ average kinetic energy
+
+272
+00:19:42,870 --> 00:19:46,230
+ثابتة ما دام الـ average kinetic energy ثابتة
+
+273
+00:19:46,230 --> 00:19:51,950
+معناته ما فيش تغيير في السرعة نص MRMS كلها squared
+
+274
+00:19:51,950 --> 00:19:55,610
+بتبقى زي ما هي ثابتة ما دام ما فيش تغيير في الـ
+
+275
+00:19:55,610 --> 00:19:58,990
+average kinetic energy ما فيش تغيير في الحرارة
+
+276
+00:19:58,990 --> 00:20:03,390
+كويس معناته السرعة دي ثابتة because when the
+
+277
+00:20:03,390 --> 00:20:06,790
+volume is increased the molecules must move a
+
+278
+00:20:06,790 --> 00:20:11,330
+longer distance between collisions عشان تعمل
+
+279
+00:20:11,330 --> 00:20:14,090
+collisions تمشي في مسافة طويلة لأن الحجم زاد
+
+280
+00:20:14,090 --> 00:20:17,450
+Consequently there are fewer collisions per unit
+
+
+281
+00:20:17,450 --> 00:20:23,830
+time with the container walls في عندي عدد أقل من
+
+282
+00:20:23,830 --> 00:20:28,270
+ال collisions في الوقت في ال unit time في وحدة 
+
+283
+00:20:28,270 --> 00:20:29,010
+الوقت يعني
+
+284
+00:20:32,240 --> 00:20:36,440
+على جدار الـ containers الداخلية وبالتالي الضغط في
+
+285
+00:20:36,440 --> 00:20:40,080
+أكيد لازم يقل لأن احنا عرفنا الضغط على أنه
+
+286
+00:20:40,080 --> 00:20:43,800
+حاجتين أول حاجة ال frequency لـ ال collisions و
+
+287
+00:20:43,800 --> 00:20:47,580
+ثاني حاجة how forceful  قد إيش قوية ال collisions
+
+288
+00:20:47,580 --> 00:20:53,340
+فهنا شوفنا إيه أول ظاهرة اللي هي إيه اللي هي يعني
+
+289
+00:20:53,340 --> 00:20:55,620
+عدد ال collisions فوجدنا أن عدد ال collisions
+
+290
+00:20:55,620 --> 00:20:59,480
+بيقل لما الحجم يزيد إذن أكيد ال pressure راح يقل
+
+291
+00:21:01,340 --> 00:21:07,820
+طيب نتطلع على كمان حاجة كثيرة مهمة بقول a
+
+292
+00:21:07,820 --> 00:21:10,800
+temperature increase at constant volume causes
+
+293
+00:21:10,800 --> 00:21:14,260
+pressure to increase حلو لما نزود الحرارة إيش
+
+294
+00:21:14,260 --> 00:21:18,380
+بيحصل؟ ال pressure بيزيد طيب لما نزود الحرارة إيش
+
+295
+00:21:18,380 --> 00:21:20,560
+بيحصل من الـ molecular من الـ kinetic molecular
+
+296
+00:21:20,560 --> 00:21:25,380
+theory لما نزود الحرارة بتزيد الـ average هيك بدنا
+
+297
+00:21:25,380 --> 00:21:28,520
+نقول بتزيد الـ average kinetic energy يعني بتزيد الـ
+
+298
+00:21:28,520 --> 00:21:34,460
+RMS speed طب مدام زادت الـ RMS Speed إيش اللي بيحصل؟
+
+299
+00:21:34,460 --> 00:21:37,840
+بتتحرك بسرعة، إذن عدد ال collisions عدد ال
+
+300
+00:21:37,840 --> 00:21:41,520
+collisions راح تزيد، يبقى الضغط إيش بده يجرى له؟ بده
+
+301
+00:21:41,520 --> 00:21:45,160
+يزيد، تمام؟ يبقى عدد ال collisions بدها تزيد، يبقى
+
+302
+00:21:45,160 --> 00:21:49,480
+معناه كلام الضغط بده يزيد، طبعا إذا كان حافظنا على
+
+303
+00:21:49,480 --> 00:21:56,620
+ال volume ثابت وأكثر من هيك كمان، بيقول ال momentum
+
+304
+00:21:56,620 --> 00:22:01,080
+in each collision increases  الجزيئات بتطلع في
+
+305
+00:22:01,080 --> 00:22:06,840
+الجدار بشكل أقوى لأن السرعة زادت ال momentum M في ال
+
+306
+00:22:06,840 --> 00:22:11,820
+V فمدام السرعة زادت يبقى ال momentum زاد يبقى هتضرب
+
+307
+00:22:11,820 --> 00:22:16,160
+في الجدار بشكل أقوى وهذا الكلام بيخلي كمان الضغط
+
+308
+00:22:16,160 --> 00:22:21,210
+يزيد إذا زيادة درجة الحرارة بتزود الـ .. الـ average
+
+309
+00:22:21,210 --> 00:22:25,090
+kinetic energy للجزيئات وهذا بينشأ عنه زيادة في
+
+310
+00:22:25,090 --> 00:22:28,750
+الـ RMS Speed وهذا بينشأ عنه more collisions وفي
+
+311
+00:22:28,750 --> 00:22:33,550
+نفس الوقت بينشأ عنه more forceful collisions معنى
+
+312
+00:22:33,550 --> 00:22:38,000
+الكلام الضغط بيزيد بشكل أوضح نفس الكلام احنا قلنا
+
+313
+00:22:38,000 --> 00:22:41,500
+الـ P تتناسب مع الـ T و الـ V تتناسب عكسياً و الـ V تتناسب
+
+314
+00:22:41,500 --> 00:22:45,440
+عكسياً طب نشوف increasing the number of moles at
+
+315
+00:22:45,440 --> 00:22:49,340
+constant volume and pressure إيش بيحصل لما نزود عدد
+
+316
+00:22:49,340 --> 00:22:55,160
+الجزيئات؟ هل زادت؟ خلينا نقول
+
+317
+00:22:57,640 --> 00:23:00,860
+لما حفظنا على الـ volume constant volume و الـ
+
+318
+00:23:00,860 --> 00:23:05,780
+temperature constant and temperature increases at
+
+319
+00:23:05,780 --> 00:23:08,640
+constant volume ماشي و ال temperature increases
+
+320
+00:23:08,640 --> 00:23:13,840
+إيش بيحصل لما ال temperature اتزودت خليني كمان مرة
+
+321
+00:23:13,840 --> 00:23:16,820
+نقول increasing the number of moles at constant
+
+322
+00:23:16,820 --> 00:23:21,880
+volume and temperature اه ثابتة الحرارة ثابتة إيش
+
+323
+00:23:21,880 --> 00:23:26,870
+لما الحرارة تكون ثابتة؟ هذا هو الـ Average Kinetic
+
+324
+00:23:26,870 --> 00:23:32,390
+Energy ثابتة إذا الـ RMSA speed ثابتة بيقول بيزود
+
+325
+00:23:32,390 --> 00:23:38,170
+عدد جزيئات الغاز بيزود عدد جزيئات الغاز فيش جدال
+
+326
+00:23:38,170 --> 00:23:42,110
+في هذا الكلام طيب without change in kinetic energy
+
+327
+00:23:42,680 --> 00:23:46,200
+الـ RMS Speed هي اللي ثابتة which reflects more
+
+328
+00:23:46,200 --> 00:23:51,480
+collisions لأن صار عدد الجزيئات زادت يبقى مدام
+
+329
+00:23:51,480 --> 00:23:54,560
+زادت عدد الجزيئات في نفس الحجم يبقى عدد ال
+
+330
+00:23:54,560 --> 00:23:57,980
+collisions في الجدار إيه؟ راح تزيد يبقى ال
+
+331
+00:23:57,980 --> 00:24:01,920
+pressure إيش بده يجرى له؟ بده يزيد يبقى خلينا نقول
+
+332
+00:24:01,920 --> 00:24:06,300
+أن الـ kinetic molecular theory بتفسر قوانين
+
+333
+00:24:06,300 --> 00:24:10,460
+الغازات المختلفة ببساطة خالص بدنا نرجع دائما لل
+
+334
+00:24:10,460 --> 00:24:17,540
+average kinetic energy حلو؟ ونشوف إيش علاقتها بإذا
+
+335
+00:24:17,540 --> 00:24:21,360
+كان الحرارة عندي ثابتة ولا متغيرة هذا طبعا بفرق
+
+336
+00:24:21,360 --> 00:24:27,540
+كثير خالص ثابتة معناته الـ RMS Speed ثابتة وبتدور
+
+337
+00:24:27,540 --> 00:24:31,680
+على يعني إيش مدلول إن الـ RMS Speed كون ثابتة أو
+
+338
+00:24:31,680 --> 00:24:36,720
+الحرارة بتزيد و الـ RMS Speed فده الحالة بدها تزيد
+
+339
+00:24:36,720 --> 00:24:44,350
+أو وإيش مدلولها أو إن الحرارة تقل، يبقى الـRMS
+
+340
+00:24:44,350 --> 00:24:50,250
+Speed تقل، يبقى الـRMS Speed تقل، طب إيش مدلولها؟
+
+341
+00:24:50,250 --> 00:24:55,770
+الـcollisions هتقل مثلا؟ هذا هو تفسير قوانين
+
+342
+00:24:55,770 --> 00:25:00,430
+الغازات at the molecular level مش بس مجرد
+
+343
+00:25:00,430 --> 00:25:04,390
+ملاحظاتنا، لا هذا هو التفسير بنسميه احنا at the
+
+344
+00:25:04,390 --> 00:25:08,130
+molecular level، فال kinetic molecular theory
+
+345
+00:25:08,130 --> 00:25:14,730
+بالفعل فسرت قوانين الغازات بشكل بسيط للغاية نأخذ
+
+346
+00:25:14,730 --> 00:25:19,290
+بعض الأمثلة خليني أقول يعني عشان تترسخ المفاهيم
+
+347
+00:25:19,290 --> 00:25:24,670
+الأساسية اللي ذكرناها قبل شوية فقط مش إنها والله
+
+348
+00:25:24,670 --> 00:25:28,790
+يعني حاجة صعبة أو .. لا بس تترسخ المفاهيم الأساسية
+
+349
+00:25:28,790 --> 00:25:32,350
+اللي أخذناها فبقول a sample of O2 gas initially at
+
+350
+00:25:32,350 --> 00:25:37,430
+STP is compressed to a smaller volume at constant
+
+351
+00:25:37,430 --> 00:25:42,220
+temperature مهم جدا أن يقول لي هذا الكلام ال
+
+352
+00:25:42,220 --> 00:25:48,020
+constant temperature قل الحجم قل لكن الحرارة إيش
+
+353
+00:25:48,020 --> 00:25:50,980
+مالها؟ ثابتة إيش يعني الحرارة ثابتة؟ بفهم من ال
+
+354
+00:25:50,980 --> 00:25:54,200
+kinetic molecule theory اه بس بدي أقول الـ average
+
+355
+00:25:54,200 --> 00:26:00,680
+kinetic energy معنى الكلام لم تتغير وبالتالي ثابتة
+
+356
+00:26:00,680 --> 00:26:03,380
+ثابتة ما لها تتغير طب بيقول لي إيه؟ بيقول لي what
+
+357
+00:26:03,380 --> 00:26:07,240
+effect does this change have on a the average
+
+358
+00:26:07,240 --> 00:26:08,700
+kinetic energy of the molecules
+
+359
+00:26:11,720 --> 00:26:17,540
+بتزيد التصادمات فبتزيد الضغط .. بقولش الضغط أنا
+
+360
+00:26:17,540 --> 00:26:21,860
+إيش بقول؟ بقول الـ average بدي تأثير .. اه بدي
+
+361
+00:26:21,860 --> 00:26:24,340
+تأثير الـ average .. تأثيرها على الـ average kinetic
+
+362
+00:26:24,340 --> 00:26:28,000
+energy أنا غيرت الحرارة؟ لا إذا الـ average kinetic
+
+363
+00:26:28,000 --> 00:26:30,980
+energy بيبقى ثابتة الـ average kinetic energy بيبقى
+
+364
+00:26:30,980 --> 00:26:35,940
+ثابتة مهما كان الغاز طيب their average speed من
+
+365
+00:26:35,940 --> 00:26:41,020
+الحرارة حرارة ثابتة is in rms ثابتة طيب the number
+
+366
+00:26:41,020 --> 00:26:44,360
+of collisions they make with the container walls
+
+367
+00:26:44,360 --> 00:26:50,100
+per unit time أنا قلت الحجم بتزيد التصادمات بتزيد
+
+368
+00:26:50,100 --> 00:26:54,140
+.. قلت الحجم يبقى بتزيد التصادمات طب دي the
+
+369
+00:26:54,140 --> 00:26:57,180
+number of collisions they make with a unit area of
+
+370
+00:26:57,180 --> 00:27:00,680
+container wall per unit time the number of
+
+371
+00:27:00,680 --> 00:27:02,900
+collisions
+
+372
+00:27:04,340 --> 00:27:07,020
+خليني أشوف number of collisions they make with
+
+373
+00:27:07,020 --> 00:27:10,820
+the container walls per unit time نفسها number of
+
+374
+00:27:10,820 --> 00:27:15,800
+collisions with unit time area of wall unit time
+
+375
+00:27:15,800 --> 00:27:20,940
+decreased نفس الحاجة أنا شايفها في فرق بين التنتين
+
+376
+00:27:20,940 --> 00:27:24,850
+ولا لا؟ نفس الـ .. نفس الـ issue المهم إنه تطبيق
+
+377
+00:27:24,850 --> 00:27:28,650
+مباشر على ال إيه؟ على الـ kinetic molecular theory
+
+378
+00:27:28,650 --> 00:27:33,230
+طب نيجي نطلعها يعني بيقول how is the RMS speed of
+
+379
+00:27:33,230 --> 00:27:38,130
+nitrogen molecules in a gas sample it changed by
+
+380
+00:27:38,130 --> 00:27:43,010
+إيه؟ كيف اتغير الـ RMS؟ an increase in temperature
+
+381
+00:27:43,010 --> 00:27:46,970
+بتزيد أكيد اه بتزيد ليه؟ لأن والله الـ average ..
+
+382
+00:27:46,970 --> 00:27:52,000
+الـ kinetic average بتزيد an increase in volume عند
+
+383
+00:27:52,000 --> 00:27:53,900
+زيادة المزيد من المزيد من المزيد من المزيد من
+
+384
+00:27:53,900 --> 00:27:56,380
+المزيد من المزيد من المزيد من المزيد من المزيد من
+
+385
+00:27:56,380 --> 00:27:58,580
+المزيد من المزيد من المزيد من المزيد من المزيد من
+
+386
+00:27:58,580 --> 00:28:00,440
+المزيد من المزيد من المزيد من المزيد من المزيد من
+
+387
+00:28:00,440 --> 00:28:01,660
+المزيد من المزيد من المزيد من المزيد من المزيد من
+
+388
+00:28:01,660 --> 00:28:01,740
+المزيد من المزيد من المزيد من المزيد من المزيد من
+
+389
+00:28:01,740 --> 00:28:01,820
+المزيد من المزيد من المزيد من المزيد من المزيد من
+
+390
+00:28:01,820 --> 00:28:02,520
+المزيد من المزيد من المزيد من المزيد من المزيد من
+
+391
+00:28:02,520 --> 00:28:03,820
+المزيد من المزيد من المزيد من المزيد من المزيد من
+
+392
+00:28:03,820 --> 00:28:08,220
+المزيد من المزيد من المزيد من المزيد من المزيد من
+
+393
+00:28:08,220 --> 00:28:13,060
+بقول والله الـ RMS من الـ Kinetic Energy إذا
+
+394
+00:28:13,060 --> 00:28:15,180
+كانت الـ Kinetic Energy ثابتة فهي ثابتة الـ Kinetic
+
+395
+00:28:15,180 --> 00:28:18,240
+Energy زادت فهي بتزيد الـ Kinetic Energy قلت فهي
+
+396
+00:28:18,240 --> 00:28:21,960
+بتقل فمع هذا الكلام بدي أرجع للحرارة الحرارة ثابتة
+
+397
+00:28:21,960 --> 00:28:26,500
+ما لهاش دعوة في الـ increase in volume الـ RMS ما لهاش
+
+398
+00:28:26,500 --> 00:28:29,780
+دعوة في الـ increase in volume طب فيما يتعلق بـ
+
+399
+00:28:29,780 --> 00:28:34,460
+mixing with a sample of argon at the same
+
+400
+00:28:34,460 --> 00:28:37,020
+temperature مدام at the same temperature الأرقام
+
+401
+00:28:37,020 --> 00:28:43,440
+الثابتة ليه؟ لأنه كل غاز بيتصرف وكأنه لوحده موجود
+
+402
+00:28:43,440 --> 00:28:47,360
+في ال container بيهموش إيش فيه عنده غازات ماشي؟ كل
+
+403
+00:28:47,360 --> 00:28:50,500
+غاز بيصرف وإله ضغط الـ partial pressure لوحده لكن لو
+
+404
+00:28:50,500 --> 00:28:53,720
+بدنا نجمع بس الـ partial pressure نجمع الـ partial
+
+405
+00:28:53,720 --> 00:28:58,120
+pressure للغازات المختلفة الـ RMS علاقتها بإيه فقط
+
+406
+00:28:58,120 --> 00:29:00,980
+بالـ temperature لأنها بتعبر عن الـ average
+
+407
+00:29:00,980 --> 00:29:03,380
+kinetic energy أو علاقة بالـ average kinetic
+
+408
+00:29:03,380 --> 00:29:08,920
+energy طيب الآن هذا نحطه على شجة و نحاول أن نتطلع
+
+409
+00:29:08,920 --> 00:29:15,360
+على بعض الاستنتاجات اللي إيه علاقة بهذا الكلام
+
+410
+00:29:15,360 --> 00:29:18,780
+وهذه استنتاجات مهمة جدا في واقعنا وفي حياتنا
+
+411
+00:29:18,780 --> 00:29:22,960
+فلازم ننتبه لها يعني ففي البداية نتكلم عن ال
+
+412
+00:29:22,960 --> 00:29:27,600
+molecular speeds قلت سابقا إن الـ molecular speeds
+
+413
+00:29:27,600 --> 00:29:34,420
+in general بتزيد بزيادة درجة الحرارة، بالظبط إذا
+
+414
+00:29:34,420 --> 00:29:39,960
+أتكلم عن جزيء معين فعند الـ kinetic energy بتزيد
+
+415
+00:29:39,960 --> 00:29:44,140
+بزيادة درجة الحرارة، بما أن الـM ثابتة، فالـ U RMS
+
+416
+00:29:44,140 --> 00:29:51,420
+بتكون أكبر لو جئنا حسابيا بنقول ميو RMS اللي هو ال
+
+417
+00:29:51,420 --> 00:29:57,800
+RMS Speed بتساوي الجذر التربيعي ل 3RT على M وهنا
+
+418
+00:29:57,800 --> 00:30:01,760
+بقول الـ M هي الـ formula weight الـ molecular mass
+
+419
+00:30:01,760 --> 00:30:05,160
+الـ M هي الـ formula weight أو الـ molecular mass الـ
+
+420
+00:30:05,160 --> 00:30:09,180
+T هي الـ absolute temperature طيب ميو RMS طبعا
+
+421
+00:30:09,180 --> 00:30:14,480
+معروف هاد الـ speed طب وإيش الـ R؟ معروفة الـ gas
+
+422
+00:30:14,480 --> 00:30:19,380
+كونستانت لكن بدنا ننتبه للوحدات الـ gas كونستانت هذا
+
+423
+00:30:19,380 --> 00:30:25,460
+بالـ جول per kelvin per mole يعني كيلو جرام متر
+
+424
+00:30:25,460 --> 00:30:31,900
+تربيع على الثانية تربيع يعني الـ R 8.314 مش 0.0821
+
+425
+00:30:31,900 --> 00:30:38,530
+في الـ PV بتساوي n RT لكن هلأ هنقش الوحدة تبعها 
+
+426
+00:30:38,530 --> 00:30:44,810
+المستخدمة عشان نطلع الـ RMS Speed أنا بتعود عن
+
+427
+00:30:44,810 --> 00:30:47,590
+الـ R أتذكره ليش بتعود عنها جول per mole per 
+
+428
+00:30:47,590 --> 00:30:52,870
+kilogram لإن الـ جول متر تربيع كيلو جرام متر تربيع
+
+429
+00:30:52,870 --> 00:30:56,050
+على ثانية تربيع فأنا بتكلم عن متر بتكلم عن إيه؟ عن
+
+430
+00:30:56,050 --> 00:31:00,410
+أطول وغيره فالـ جول هان الـ R بتكون eight point three
+
+431
+00:31:00,410 --> 00:31:09,010
+one four 8.314 فبتنذكر الوحدة لما نشتغل علشان نطلع
+
+432
+00:31:09,010 --> 00:31:14,270
+الـ molecular speeds في الـ R مش 0.0821 الـ 0.0821
+
+433
+00:31:14,270 --> 00:31:18,690
+بتقول لليتر أتمسفير على المول في كيلوفر لكن هنا لأ
+
+434
+00:31:18,690 --> 00:31:23,750
+كيلو جرام متر تربيع لهذه اللي هي اللي بيهمني في الـ ...
+
+435
+00:31:23,750 --> 00:31:28,010
+في سواء الـ kinetic energy أو في ... أتذكروا أن الـ
+
+436
+00:31:28,010 --> 00:31:30,530
+U<sub>RMS</sub> اللي علاقة بالـ temperature و الـ temperature 
+
+437
+00:31:30,530 --> 00:31:33,210
+علاقة بالـ kinetic energy و الـ kinetic energy جول
+
+438
+00:31:33,210 --> 00:31:41,110
+يبقَ عيش متعود عن الـ R 8.314 ماشي يا جماعة نتذكر هذه
+
+439
+00:31:41,110 --> 00:31:49,690
+الملاحظة إيه كويس؟ بما أن U<sub>RMS</sub> بتساوي الجزر التربيع
+
+440
+00:31:49,690 --> 00:31:54,070
+على 3RT على M، إذا لو في عندي غازين، غاز واحد وغاز
+
+441
+00:31:54,070 --> 00:31:59,410
+اثنين، يبقى U<sub>RMS</sub> للغاز الأول على U<sub>RMS</sub> للغاز الثاني
+
+442
+00:31:59,410 --> 00:32:04,350
+ساوي الجزر التربيع على M2 على M1، لأن السرعة
+
+443
+00:32:04,350 --> 00:32:09,280
+تتناسب عكسيا مع الـ formula weight وهذا طبيعي
+
+444
+00:32:09,280 --> 00:32:11,980
+لأنه كل ما زاد الـ formula weight كل ما كبر الـ
+
+445
+00:32:11,980 --> 00:32:15,020
+formula weight السرعة بدها تقل طبيعي هذا الكلام
+
+446
+00:32:15,020 --> 00:32:19,980
+فبالتالي التناسب عكسي لكن لاحظنا أن الـ 3RT راحت مع
+
+447
+00:32:19,980 --> 00:32:25,920
+الـ 3RT فضل M2 على M1 هذا قانون نستخدمه كثير علشان
+
+448
+00:32:25,920 --> 00:32:30,580
+نعرف سرعة الغازات لأنه مفيد بالنسبة لنا في تحديد
+
+449
+00:32:30,580 --> 00:32:34,400
+مفهوم الـ effusion و الـ diffusion زي ما هنشوف بعد
+
+450
+00:32:34,400 --> 00:32:35,980
+شوية لاحظوا معايا
+
+451
+00:32:38,810 --> 00:32:47,010
+إيش تأثير الـ formula weight على الـ RMS speed؟ عكسي
+
+452
+00:32:47,010 --> 00:32:54,130
+فلما ألاقي مثلًا عدة غازات بلاحظ أن الـ H2 لأنه له
+
+453
+00:32:54,130 --> 00:32:59,570
+very small formula weight أو molecular mass سموها
+
+454
+00:32:59,570 --> 00:33:02,530
+زي ما بدكم formula weight أو molecular mass بلاحظ
+
+455
+00:33:02,530 --> 00:33:05,870
+أن الـ average speed إيش مالها؟ الـ Molecular Speed
+
+456
+00:33:05,870 --> 00:33:10,130
+عالية بينما هي دي اثنين، هي دي أربعة، قلت الـ
+
+457
+00:33:10,130 --> 00:33:14,590
+Oxygen .. طب هي المية 18 قلت، الـ Nitrogen 28 قلت،
+
+458
+00:33:14,590 --> 00:33:18,790
+الـ Oxygen 32 قلت وبالتالي وضع طبيعي يعني حسب
+
+459
+00:33:18,790 --> 00:33:22,290
+القانون اللي شفناها قبل شوية أن واه والله عند الـ
+
+460
+00:33:22,290 --> 00:33:26,180
+Molecular Speed بتزيد كل ما قلت الـ molecular mass
+
+461
+00:33:26,180 --> 00:33:32,480
+لكن .. لكن التناسب مع واحد على الجزر التربيعي، مش
+
+462
+00:33:32,480 --> 00:33:35,880
+مباشرة، مش واحد على الـ formula weight، واحد على
+
+463
+00:33:35,880 --> 00:33:40,860
+الجزر التربيعي للـ formula weight نتطلع على هذا
+
+464
+00:33:40,860 --> 00:33:44,360
+المثال، نقول calculate the RMS speed of the
+
+465
+00:33:44,360 --> 00:33:48,040
+molecules in a sample of nitrogen gas at 25
+
+466
+00:33:48,040 --> 00:33:54,290
+degrees C بدي أحسب الـ RMS speed للنيتروجين gas at 25
+
+467
+00:33:54,290 --> 00:33:58,390
+degrees C بقول الـ T بدها تساوي طبعًا الـ T Kelvin
+
+468
+00:33:58,390 --> 00:34:03,790
+شفناها الـ molecular mass 28 gram per mole يعني آه
+
+469
+00:34:03,790 --> 00:34:09,100
+بدها 28 في 10 أس سالب تلاتة كيلو جرام per mole ليه؟ لأن الـ
+
+470
+00:34:09,100 --> 00:34:13,600
+Joule الـ R كيلو جرام متر تربيع على ثانية تربيع
+
+471
+00:34:13,600 --> 00:34:17,380
+فبالكيلو جرام برضه الـ units عشان هي كاتبة الـ units
+
+472
+00:34:17,380 --> 00:34:23,260
+units انتبهوا للـ units انتبهوا للـ units الـ R 8.314
+
+473
+00:34:23,260 --> 00:34:27,840
+Joule على المول كيلوفر يعني 8.314 كيلو جرام متر تربيع
+
+474
+00:34:27,840 --> 00:34:32,880
+على ثانية تربيع فهو بتكلم عن كيلو جرام و بتكلم عن
+
+475
+00:34:32,880 --> 00:34:38,450
+متر كويس لأن كل واحد جول عبارة عن واحد kilogram متر
+
+476
+00:34:38,450 --> 00:34:44,650
+تربيع على ثانية تربيع الآن لو عوضت U<sub>RMS</sub> اللي هو الـ
+
+477
+00:34:44,650 --> 00:34:46,950
+route من الـ square speed بتساوي الجزر التربيع إلى
+
+478
+00:34:46,950 --> 00:34:52,910
+ثلاثة في الـ R كويس ولاحظوا كيلو جرام متر تربيع
+
+479
+00:34:52,910 --> 00:35:00,550
+ثانية تربيع على الـ mol Kelvin في 298 على 28 في
+
+480
+00:35:00,550 --> 00:35:04,150
+10 أس سالب تلاتة كيلو جرام عشان الـ كيلو جرام مع الـ كيلو جرام ماشي
+
+481
+00:35:04,150 --> 00:35:08,210
+يا جماعة فلازم ننتبه للوحدات بشكل كبير المخيف أنه
+
+482
+00:35:08,210 --> 00:35:13,430
+لما نيجي نتطلع جداش الـ RMS جال خمسة و خمسة عشر مية
+
+483
+00:35:13,430 --> 00:35:16,910
+فعشرة أس سالب اثنين متر في الثانية يعني خمس مية و
+
+484
+00:35:16,910 --> 00:35:20,750
+خمسة عشر متر في الثانية حركة الغاز عند خمسة و عشرين
+
+485
+00:35:20,750 --> 00:35:25,310
+درجة خمس مية و خمسة عشر متر في الثانية علشان هيك لما
+
+486
+00:35:25,310 --> 00:35:32,000
+مثلًا خلينا أقول ولو إنه يعني حاجة مش كتير خليني
+
+487
+00:35:32,000 --> 00:35:35,700
+أقول بتنطبق اجتماعنا زي ما هنشوف لو مثلًا رشينا شوية
+
+488
+00:35:35,700 --> 00:35:39,320
+ريحة هنا بعد شوية بنلاحظ أن الريحة بتوصل لآخر
+
+489
+00:35:39,320 --> 00:35:43,800
+الغرفة صحيح؟ ليش؟ لأن الجزيئات بتتحرك بسرعة
+
+490
+00:35:43,800 --> 00:35:47,460
+إيش مالها؟ كبيرة الجزيئات الـ gas بتتحرك بسرعة كبيرة
+
+491
+00:35:47,460 --> 00:35:50,360
+وإن كان طبعًا لو خمس مية أو خمسة عشر متر في الثانية
+
+492
+00:35:50,360 --> 00:35:54,280
+لازم توصل في نفس الوجد لكن لأ هي بتمشي شهيدل لأ هي
+
+493
+00:35:54,280 --> 00:36:00,850
+بتمشي آه يعني هفرجيكم إياها بعد شوية طيب سؤال ثاني
+
+494
+00:36:00,850 --> 00:36:04,990
+بيقول what's the RMS speed of an atom in a sample
+
+495
+00:36:04,990 --> 00:36:09,970
+of helium gas at 25 degrees C؟ لحظة الـ helium غير
+
+496
+00:36:09,970 --> 00:36:14,550
+عن الـ nitrogen الـ helium الـ M تبعته أقل فالمفروض
+
+497
+00:36:14,550 --> 00:36:21,330
+أن السرعة تبعته تكون أعلى بتكون أعلى طيب U<sub>RMS</sub> 3 في 
+
+498
+00:36:21,330 --> 00:36:24,930
+8.314
+
+499
+00:36:24,930 --> 00:36:29,650
+في 298 على 4 في 10 أس سالب تلاتة اللي هو كيلو جرام
+
+500
+00:36:29,650 --> 00:36:34,650
+per mole يعني تحت الجزر بحطين 136 في 10 أس سالب 2 أو 
+
+501
+00:36:34,650 --> 00:36:40,150
+136 في 10 أس سالب 2 136 يعني 13 عفوا في 10 أس سالب 2
+
+502
+00:36:40,150 --> 00:36:44,710
+تلاتة عشان خمسة و خمسة عشان يعني هنزلت تقريبًا مرتين
+
+503
+00:36:44,710 --> 00:36:49,510
+و نصف مرتين ونصف ليه؟ لأن الـ helium الـ molecular mass
+
+504
+00:36:49,510 --> 00:36:52,970
+تبعته أوي يعني الـ atomic mass له أقل من الـ
+
+505
+00:36:52,970 --> 00:36:57,290
+molecular mass للنيتروجين أربعة الـ helium بينما الـ
+
+506
+00:36:57,290 --> 00:37:01,450
+nitrogen ثمانية و عشرين عشان هيك بنلاحظ أن الـ RMS
+
+507
+00:37:01,450 --> 00:37:07,550
+speed للهيليوم أعلى حوالي مرتين ونصف الكمية حرزانة
+
+508
+00:37:07,550 --> 00:37:12,710
+الآن نتطلع على مفهومين مفهوم بنقوله diffusion و
+
+509
+00:37:12,710 --> 00:37:17,460
+مفهوم بنقوله effusion الـ effusion في الحقيقة
+
+510
+00:37:17,460 --> 00:37:22,520
+كتعريف بختلف كلية عن الـ diffusion فلازم نعرف إيش
+
+511
+00:37:22,520 --> 00:37:30,280
+تعريف هذا وإيش تعريف هذا فالـ ... بالنسبة للـ
+
+512
+00:37:30,280 --> 00:37:32,620
+effusion هو عبارة عن
+
+513
+00:37:36,240 --> 00:37:43,060
+سرعة تسرب .. سرعة تسرب الغاز من pin hole يعني في
+
+514
+00:37:43,060 --> 00:37:47,440
+عندي وعاء موجود فيه غاز الوعاء هذا فيه pin hole
+
+515
+00:37:47,440 --> 00:37:52,500
+فتحة ضيقة جدا جدا فالغاز بده يتسرب من خلالها هذا
+
+516
+00:37:52,500 --> 00:37:57,080
+التسرب أو الـ escape كويس للغاز من هذه الفتحة اسمه
+
+517
+00:37:57,080 --> 00:38:03,530
+effusion اسمه effusion تمام؟ طب كيف بيحصل؟ من الـ 
+
+518
+00:38:03,530 --> 00:38:06,750
+kinetic theory ها، كيف بيحصل؟ احنا بنعرف أنه موجود
+
+519
+00:38:06,750 --> 00:38:09,850
+لأنه لو كان في فتحة ضيقة جدا بعد فترة من اللي لاجي
+
+520
+00:38:09,850 --> 00:38:13,590
+الغاز، آه بتسرب، مش هيك؟ بنعرف أنه تسرب الغاز، طب
+
+521
+00:38:13,590 --> 00:38:16,990
+كيف بيحصل؟ حسب الـ kinetic molecular theory قال
+
+522
+00:38:16,990 --> 00:38:20,790
+لازم تيجي التصادم مش في عند الجذائكات بتتحرك و
+
+523
+00:38:20,790 --> 00:38:24,430
+بتتصادم مع الجدار، لازم تيجي تصادم أين؟ في الفتحة
+
+524
+00:38:24,430 --> 00:38:28,740
+بالضبط عشان يطلع الفتحة بالضبط فكل ما كانت الفتحة
+
+525
+00:38:28,740 --> 00:38:32,760
+ضيقة كل ما كان صعب أن الغاز إيه يتسرب ولما تكون
+
+526
+00:38:32,760 --> 00:38:36,360
+الفتحة أوسع بيكون أسهل أنه يتسرب لكن احنا بنتكلم
+
+527
+00:38:36,360 --> 00:38:41,120
+عن التسرب من خلال فتحة ضيقة جدا بنقولها pin hole
+
+528
+00:38:41,120 --> 00:38:45,360
+يعني زي خرم الإبرة pin hole أو very tiny hole يعني
+
+529
+00:38:45,360 --> 00:38:48,840
+زي خرم الإبرة بيقول الـ effusion which is the
+
+530
+00:38:48,840 --> 00:38:52,960
+escape of gas molecules through a very small hole
+
+531
+00:38:52,960 --> 00:38:57,450
+الـ very small hole هذا بيقولها a pin hole Pinhole
+
+532
+00:38:57,450 --> 00:39:03,730
+هيك هي في اللغة يعني كلمة
+
+533
+00:39:03,730 --> 00:39:10,970
+واحدة فالـ escape أو التسرب للـ gas molecules من
+
+534
+00:39:10,970 --> 00:39:16,050
+خلال هذه الفتحة الضيقة اسمه إيه؟ effusion طيب إيش
+
+535
+00:39:16,050 --> 00:39:20,980
+مفرج عن الـ diffusion؟ الـ diffusion الانتشار مش
+
+536
+00:39:20,980 --> 00:39:24,980
+التسرب الانتشار زي ما قلت والله بدي أرش ريحة هان
+
+537
+00:39:24,980 --> 00:39:29,420
+وأنا واقف رشيت شوية ريحة بالـ diffusion بتوصل لآخر
+
+538
+00:39:29,420 --> 00:39:34,360
+الغرفة مش الـ diffusion لإيه؟ هتنتشر الريحة هتنتشر
+
+539
+00:39:34,360 --> 00:39:40,900
+شوية شوية والله كل مكان الوسط كثيف أكثر الانتشار
+
+540
+00:39:40,900 --> 00:39:45,260
+بيقل كل مكان الوسط كثيف يعني فيه عدد جزيئات أكبر
+
+541
+00:39:45,260 --> 00:39:50,690
+الـ diffusion بيقلي يعني مثلًا لو قلت والله الـ
+
+542
+00:39:50,690 --> 00:39:54,570
+diffusion في الهواء آه سهل كثير بسهولة والله لو
+
+543
+00:39:54,570 --> 00:39:57,910
+رشينا شوية ريحة هان بتوصل آخر الغرفة يعني بعد
+
+544
+00:39:57,910 --> 00:40:01,870
+دقيقة ولا دقيقتين ولا few minutes لكن وهذا كلام
+
+545
+00:40:01,870 --> 00:40:07,070
+اللي يام يعني مثلًا الشرطة لما تيجي تضرب على الناس
+
+546
+00:40:07,070 --> 00:40:11,170
+غاز فبتلاحظ أن الغاز على طول بينتشر يعني مش بالله
+
+547
+00:40:11,170 --> 00:40:13,430
+يبقى قاعدة للساعتين تلاتة واللي كان الناس راحت
+
+548
+00:40:13,430 --> 00:40:16,830
+عملت مظاهرتها و راحت لكن لأ باللحظة اللي اتول خلال
+
+549
+00:40:16,830 --> 00:40:21,230
+يعني دقائق بسيطة بكون انتشر في مساحة إيه واسعة هذا
+
+550
+00:40:21,230 --> 00:40:27,510
+انتشار لكن لو قلنا والله بدنا في عيننا وعاء من المية
+
+551
+00:40:27,510 --> 00:40:33,250
+ضخم وحطيت عليه لبطة حبر في جانبه هتأخذ وجهة أطول
+
+552
+00:40:33,250 --> 00:40:37,990
+علشان تنتشر وتكون انتشار تام في كل الوعاء فلما
+
+553
+00:40:37,990 --> 00:40:42,370
+نكون الجزيئات denser يعني عددها أكبر كثير انتشار
+
+554
+00:40:42,370 --> 00:40:44,750
+عندي عادة بيقل
+
+555
+00:40:48,590 --> 00:40:52,910
+طيب هي الـ pin hole فتحة ضيقة جدا مش مبينة في
+
+556
+00:40:52,910 --> 00:40:56,950
+الحقيقة والله إذا كان حصل وتصادم الجزيق هيأ يجي
+
+557
+00:40:56,950 --> 00:40:59,310
+بده يتصادم مع الجدار فهيأ نصيبه أن يجي على
+
+558
+00:40:59,310 --> 00:41:04,370
+الفتحة بالضبط هيأ يجي نصيبه على الفتحة بالضبط إيه؟
+
+559
+00:41:04,370 --> 00:41:07,910
+بدخل منها، بتسرب، ماجاش نصيبه يجي جانبها هنا أو
+
+560
+00:41:07,910 --> 00:41:11,990
+هنا أو هنا أو حواليها، بتطلعش، فغير لازم يعني 
+
+561
+00:41:11,990 --> 00:41:16,370
+الجزء يصطدم تماما بال .. بالـ pinhole، بلاقيش جدار
+
+562
+00:41:16,370 --> 00:41:20,390
+فبتم طالع على إيه؟ على هذا المكان، طب حلو كتير، طب
+
+563
+00:41:20,390 --> 00:41:28,980
+إيش علاقة التسرب بالـ molecular mass؟ إيش علاقته؟ أه
+
+564
+00:41:28,980 --> 00:41:32,120
+هو هضع طبيعي جدا يعني، يعني لو شوفنا مثلا هنا ال
+
+565
+00:41:32,120 --> 00:41:35,720
+helium، أه والله الـ helium أول حاجة أسرع يبقى على
+
+566
+00:41:35,720 --> 00:41:40,500
+التصادمات أكثر، الـ RMS أسرع تصادمات أكثر، معنى
+
+567
+00:41:40,500 --> 00:41:44,700
+الكلام في فرصته أنه يضرب في الـ pin hole ويخرج
+
+568
+00:41:44,700 --> 00:41:48,220
+منها أكبر، بينما حاجة زي الـ ethylene oxide مثلا
+
+569
+00:41:48,220 --> 00:41:56,520
+يعني قال والله هذا جزء كبير سرعته أقل عن نفس الظروف
+
+570
+00:41:56,520 --> 00:42:01,460
+سرعته أقل معناه كلام يعني احتمالية أنه يلاقي ال
+
+571
+00:42:01,460 --> 00:42:05,180
+pin hole ويطلع منها احتمالية أقل علشان هيك بيكون
+
+572
+00:42:05,180 --> 00:42:11,380
+خليني أقول الـ effusion  لقاله أقل نفس الكلام بنلاحظه
+
+573
+00:42:11,380 --> 00:42:15,580
+لو عندي بلونين بلون مليان argon وبلون مليان
+
+574
+00:42:15,580 --> 00:42:19,860
+helium الـ helium أصغر كتير من الـ argon أصغر كمان
+
+575
+00:42:19,860 --> 00:42:25,860
+في الـ molecular mass أقل كتير من الـ argon فبنلاحظ
+
+576
+00:42:25,860 --> 00:42:31,080
+أن المسامات اللي موجودة في البلون هي نفس البلون
+
+577
+00:42:31,080 --> 00:42:35,420
+وقال إنه نفخنا لنفس الدرجة فالمسامات اللي موجودة
+
+578
+00:42:35,420 --> 00:42:40,040
+هنا هي نفس المسامات اللي موجودة هنا لكن بما أنه
+
+579
+00:42:40,040 --> 00:42:46,740
+الـ helium حجم الذرة أصغر وسرعتها أكبر فهيروح نتيجة
+
+580
+00:42:46,740 --> 00:42:50,000
+الخطاط هيلاقي المسامات بسرعة ويطلع فبنلاحظ بعد
+
+581
+00:42:50,000 --> 00:42:53,720
+فترة لسه ضايل الـ argon خف شوية جل شوية صغيرة لكن
+
+582
+00:42:53,720 --> 00:42:58,020
+بالنسبة للهيليوم إيش ماله جل بشكل أكبر فهذا الكلام
+
+583
+00:42:58,020 --> 00:43:06,810
+كله ناتج عن الـ effusion السيد جرام حطيلنا قانون
+
+584
+00:43:06,810 --> 00:43:10,850
+للـ effusion، إيش قال فيه؟ قال فيه كلام بسيط كتير،
+
+585
+00:43:10,850 --> 00:43:15,350
+قال الـ rate of effusion للغاز الأول على ال
+
+586
+00:43:15,350 --> 00:43:19,470
+rate of effusion للغاز الثاني قال بيتناسب مع ال
+
+587
+00:43:19,470 --> 00:43:25,050
+RMS speed ولاحظوا الـ RMS speed بتناسب مع الـ mass عكسيا
+
+588
+00:43:25,050 --> 00:43:29,910
+تحت الجذر فقال بما أن الـ rate للـ effusion للغاز
+
+589
+00:43:29,910 --> 00:43:36,790
+الأول بيتناسب مع U RMS للغاز الأول وR2 اللي هو ال
+
+590
+00:43:36,790 --> 00:43:42,000
+rate للـ effusion للغاز الثاني يتناسب مع ال U RMS
+
+591
+00:43:42,000 --> 00:43:45,060
+للغاز الثاني إذا هدى على هدى بتساوي هدى على هدى
+
+592
+00:43:45,060 --> 00:43:51,480
+لكن الـ U RMS كنا بنساوي والله 3 RT على M هدى
+
+593
+00:43:51,480 --> 00:43:59,150
+على M واحد ماشي هدى هي هدى و ال RMS2 هدى هي هدى
+
+594
+00:43:59,150 --> 00:44:02,790
+فالتلاتة R بتروح مع بعض الـ T بتروح مع بعض والـ M
+
+595
+00:44:02,790 --> 00:44:05,890
+هدى تحت تطلع فوق والـ M2 بتنزل تحت ويصير جذر ال
+
+596
+00:44:05,890 --> 00:44:10,870
+M2 على M1 معنى الكلام R1 على R2 هي نفس اللي شفناها
+
+597
+00:44:10,870 --> 00:44:15,050
+سابقا هي نفسها جذر الـ M2 على الـ M1 نفس العلاقة
+
+598
+00:44:15,050 --> 00:44:19,090
+اللي شفناها سابقا باسم الـ RMS هي هي نفس العلاقة
+
+599
+00:44:19,090 --> 00:44:23,090
+يبقى معنى الكلام الـ rate of effusion يتناسب عكسيا
+
+600
+00:44:23,090 --> 00:44:28,140
+مع الـ mass تحت الجذر وبالتالي هذه العلاقة ممكن
+
+601
+00:44:28,140 --> 00:44:31,740
+منها حساب الـ rate of effusion أو حساب الـ mass لو
+
+602
+00:44:31,740 --> 00:44:34,620
+عند الـ rate of effusion يعني لو أنا في عندي وعاء
+
+603
+00:44:34,620 --> 00:44:37,940
+وفي pin hole وحطيت فيه أكثر من غاز وعرفت الـ rate
+
+604
+00:44:37,940 --> 00:44:39,940
+of effusion لكل واحد فيهم بقدر أحسب الـ molecular
+
+605
+00:44:39,940 --> 00:44:42,440
+mass والعكس صحيح لو عندي الـ molecular mass بقدر
+
+606
+00:44:42,440 --> 00:44:46,060
+أحسب الـ rate of effusion هذا القانون اسمه Gram's
+
+607
+00:44:46,060 --> 00:44:47,300
+law of effusion
+
+608
+00:44:49,920 --> 00:44:53,760
+فاللي هو القانون بينص على إنه الـ effusion rate of
+
+609
+00:44:53,760 --> 00:44:57,980
+a gas is inversely proportional to the square root
+
+610
+00:44:57,980 --> 00:45:02,360
+of its molar mass يعني الـ effusion rate لأي غاز
+
+611
+00:45:02,360 --> 00:45:05,580
+يتناسب عكسيا مع الجذر التربيعي لـ molar mass
+
+612
+00:45:05,580 --> 00:45:09,160
+للغاز وطبعا هذا لو في عندي two gases بده أقارن
+
+613
+00:45:09,160 --> 00:45:14,240
+بينهم هذا القانون أو هذه العلاقة ممتازة نطلع على
+
+614
+00:45:14,240 --> 00:45:20,540
+مثال كيف نستخدم قانون السيد جرام بيقول an unknown
+
+615
+00:45:20,540 --> 00:45:26,420
+gas composed of homonuclear يعني نفس نوع الذرات
+
+616
+00:45:26,420 --> 00:45:30,300
+تبعته، diatomic molecules يعني زي أكسجين،
+
+617
+00:45:30,300 --> 00:45:33,740
+هيدروجين، نيتروجين، homonuclear يعني نفس نوع
+
+618
+00:45:33,740 --> 00:45:39,020
+الذرات An unknown gas composed of homonuclear
+
+619
+00:45:39,020 --> 00:45:44,400
+diatomic molecules effuses at a rate that is 0.355
+
+620
+00:45:44,400 --> 00:45:49,000
+times the rate at which oxygen effuses يعني أنا
+
+621
+00:45:49,000 --> 00:45:56,140
+عارف أن الغاز بيعمل effusion أقل من الأكسجين 0.355
+
+622
+00:45:56,140 --> 00:46:02,280
+0.355 times يعني أقل من الأكسجين طيب إيش بيقول ليه؟
+
+623
+00:46:02,280 --> 00:46:04,940
+at the same temperature طبيعي لازم يقول لي at the
+
+624
+00:46:04,940 --> 00:46:07,760
+same temperature لأنه لو تغيرت الحرارة ما أقدرش
+
+625
+00:46:07,760 --> 00:46:12,760
+أقارن بينهم مباشرة لأن الـ RMS هتتغير وأنا بدي
+
+626
+00:46:12,760 --> 00:46:17,040
+الاتنين العلاقة بينهم الـ RMS ثابتة بيقول calculate
+
+627
+00:46:17,040 --> 00:46:21,120
+the molar mass of the unknown gas بقول والله
+
+628
+00:46:21,120 --> 00:46:25,100
+ببساطة خالص RX على الـ R للـ O2 الـ rate للـ unknown
+
+629
+00:46:25,100 --> 00:46:29,310
+gas على الـ rate of effusion للأكسجين تساوي جذر
+
+630
+00:46:29,310 --> 00:46:31,730
+التربيعي للموليكولر ماس للأكسجين على الموليكولر
+
+631
+00:46:31,730 --> 00:46:35,530
+الماس للـ unknown gas بعوض بقول هدول اثنين جالي
+
+632
+00:46:35,530 --> 00:46:39,490
+point three five five هاي thirty two على MX اللي
+
+633
+00:46:39,490 --> 00:46:42,690
+بيطلع إنه لو ربعنا الطرفين اللي بيطلع إن الـ MX
+
+634
+00:46:42,690 --> 00:46:46,830
+254 هو في السؤال بيقول كمان تعرف
+
+635
+00:46:46,830 --> 00:46:49,610
+عليه أنا رفعت كلمة تعرف عليه لأن أنتم مابتعرفوش
+
+636
+00:46:49,610 --> 00:46:53,990
+يعني هاد الـ molecular الـ molecular masses لمين
+
+637
+00:46:53,990 --> 00:46:58,610
+254 يعني ايودين الايودين صلب يا بنات
+
+638
+00:46:58,610 --> 00:47:03,410
+عشان هيك بنقول ايودين at مثلا high temperature
+
+639
+00:47:03,410 --> 00:47:06,110
+some high temperature اللي يكون gas لأن ما ينفعش
+
+640
+00:47:06,110 --> 00:47:10,190
+ايودين صلب ما ينفعش أنا الـ fusion للغازات مش للمواد
+
+641
+00:47:10,190 --> 00:47:17,670
+الصلبة وبالتالي يعني الـ .. الـ .. الغاز تبعي 254 هو
+
+642
+00:47:17,670 --> 00:47:22,410
+عبارة عن الايودين لكن الايودين بدي يكون gas معناه
+
+643
+00:47:22,410 --> 00:47:25,700
+كلمة أنا .. أنا مستخدم حرارة عالية بحيث إنه نفس
+
+644
+00:47:25,700 --> 00:47:29,060
+الحرارة، نفس الحرارة للـ Oxygen ونفس الحرارة للـ
+
+645
+00:47:29,060 --> 00:47:33,480
+Iodine لكن هي حرارة كافية إنه يتخلى الـ Iodine Gas
+
+646
+00:47:33,480 --> 00:47:36,940
+أما هو في الواقع الـ Iodine عبارة عن Solid
+
+647
+00:47:36,940 --> 00:47:41,600
+وبالمناسبة هو بـ Ceres Liquid بيحصل له Sublimation
+
+648
+00:47:41,600 --> 00:47:46,740
+للغاز مباشرة، تسامي يعني آه تسامي بنقوله، بيطلع من
+
+649
+00:47:46,740 --> 00:47:51,430
+الـ Solid للغاز مباشرة طيب، نتطلع على بعض الأمثلة
+
+650
+00:47:51,430 --> 00:47:54,630
+الأخرى، بيقول لي which will effuse faster؟ أمونيا
+
+651
+00:47:54,630 --> 00:47:59,470
+ولا CO2؟ نجاوب على هذه الجزئية، الأمونيا الـ 4 و
+
+652
+00:47:59,470 --> 00:48:04,050
+17، الـ CO2 الـ 4 و 44، مين بده يحصل له effusion أسرع؟
+
+653
+00:48:04,050 --> 00:48:07,590
+طبعا الأمونيا أسرع، لأنها الـ molecular mass أقل،
+
+654
+00:48:07,590 --> 00:48:10,630
+وقانون السيد اي جرام بيقول إن الـ effusion rate
+
+655
+00:48:10,630 --> 00:48:14,690
+عكسيا مع الجذر التربيعي للـ molecular mass، إذا والله
+
+656
+00:48:14,690 --> 00:48:21,070
+آه، الأمونيا effuses faster لأنها إلها smaller
+
+657
+00:48:21,070 --> 00:48:25,550
+molecular mass طيب بكمل بيقول ليه what are their
+
+658
+00:48:25,550 --> 00:48:29,970
+relative rates of effusion حلو بقول والله الـ R لل
+
+659
+00:48:29,970 --> 00:48:35,790
+أمونيا الـ R للـ أمونيا وين الـ .. آه الـ R للـ أمونيا
+
+660
+00:48:35,790 --> 00:48:38,450
+بقول الـ rate of effusion للـ أمونيا على الـ rate of
+
+661
+00:48:38,450 --> 00:48:43,610
+effusion للـ CO2 هو عبارة عن الـ M للـ CO2 على الـ M
+
+662
+00:48:43,610 --> 00:48:48,160
+للـ أمونيا تحت الجذر فبيطلع 1.6 يعني الـ ammonia
+
+663
+00:48:48,160 --> 00:48:52,960
+effuses 1.6 times faster than carbon dioxide وهذا
+
+664
+00:48:52,960 --> 00:48:59,400
+وضع طبيعي لأن الـ molecular mass للـ ammonia أقل من
+
+665
+00:48:59,400 --> 00:49:03,920
+الـ molecular mass للـ CO2 نفس المنطق، calculate the
+
+666
+00:49:03,920 --> 00:49:09,240
+ratio of the effusion rates of nitrogen gas and O2
+
+667
+00:49:09,240 --> 00:49:14,000
+gas بدو الـ ratio للـ effusion race نيتروجين جاس لل
+
+668
+00:49:14,000 --> 00:49:19,880
+O2 طيب R للـ N2 على R للـ O2 الـ M للـ O2 على M للـ N2
+
+669
+00:49:19,880 --> 00:49:25,620
+تحت الجذر فبيطلع 1.07 طبعا الـ nitrogen effuses
+
+670
+00:49:25,620 --> 00:49:31,480
+faster لأنه 28 بينما الـ oxygen 32 لاحظوا جرام على
+
+671
+00:49:31,480 --> 00:49:36,520
+بعض عشان هيك كانت الـ ratio 1.07 يعني إيه لحد ما
+
+672
+00:49:36,520 --> 00:49:41,440
+فل لكن الـ nitrogen will diffuse 1.07 times faster
+
+673
+00:49:41,440 --> 00:49:46,960
+than O2 مثال
+
+674
+00:49:46,960 --> 00:49:51,220
+آخر بيقول determine the relative rate of diffusion
+
+675
+00:49:51,220 --> 00:49:57,080
+for krypton هذا عبارة عن غاز خامل and bromine
+
+676
+00:49:57,080 --> 00:50:03,880
+طبعا لبرومين liquid لبرومين إيش ماله؟ liquid طيب
+
+677
+00:50:03,880 --> 00:50:06,040
+احنا بنقول هذا ينطبق على الغازات يبقى احنا
+
+678
+00:50:06,040 --> 00:50:10,200
+مستخدمين إيه ناد مستخدمين درجة حرارة للاتنين بحيث
+
+679
+00:50:10,200 --> 00:50:14,260
+إن الدرجة يعني سمحت للاتنين إن يكونوا غازات
+
+680
+00:50:17,100 --> 00:50:20,380
+فانديبرومين at a temperature where both are gases
+
+681
+00:50:20,380 --> 00:50:23,520
+أنا كتبت لكم هذه من اندي لأنه يعني ما كانتش موجودة
+
+682
+00:50:23,520 --> 00:50:29,440
+طيب U للكريبتون أو الـ rate R للكريبتون على R
+
+683
+00:50:29,440 --> 00:50:34,080
+لبرومين هذه نفسها بتساوي M لبرومين على M لكريبتون
+
+684
+00:50:34,080 --> 00:50:38,800
+بيطلع عندي 1.381 معنى الكلام لكريبتون طبعا لأنه له
+
+685
+00:50:38,800 --> 00:50:45,200
+atomic mass أقل effuses مش diffuses effuses 1
+
+686
+00:50:45,200 --> 00:50:51,280
+point three eight one times faster than هو اللي
+
+687
+00:50:51,280 --> 00:50:55,240
+يعني احنا بنتكلم عن هذا القانون كـ effusion مش
+
+688
+00:50:55,240 --> 00:50:58,480
+diffusion يعني حتى الـ .. الـ .. هذه بدنا نقول
+
+689
+00:50:58,480 --> 00:51:00,940
+effusion
+
+690
+00:51:01,540 --> 00:51:05,640
+هو الـ diffusion والـ .. والـ effusion برضه يعني
+
+691
+00:51:05,640 --> 00:51:11,920
+بينطبق عليهم نفس القوانين من ناحية إيش بيسموه يعني
+
+692
+00:51:11,920 --> 00:51:18,000
+سرعة التدفق يعني سرعة التدفق نفس القوانين فهي لكن
+
+693
+00:51:18,000 --> 00:51:20,580
+احنا بنتكلم الـ grams دول بنتكلم عن الـ effusion مش
+
+694
+00:51:20,580 --> 00:51:25,330
+عن الـ diffusion نفس الكلام بيقول إن unknown gas if
+
+695
+00:51:25,330 --> 00:51:28,670
+uses خليني أقول four times faster than O2 find
+
+696
+00:51:28,670 --> 00:51:32,790
+its molar mass نفس الكلام يعني عندي هذه أربعة
+
+697
+00:51:32,790 --> 00:51:41,390
+بتساوي عن الـ oxygen عن الـ molar mass للغاز
+
+698
+00:51:41,390 --> 00:51:45,190
+الآخر فالـ molar mass للغاز الآخر بقدر أجيبه طلع
+
+699
+00:51:45,190 --> 00:51:49,470
+عندي 2 يعني هيدروجين الـ molar mass للغاز الآخر
+
+700
+00:51:49,470 --> 00:51:58,020
+هو عبارة عن الـ Hydrogen طيب هذا سؤال بس حبيت إني 
+
+701
+00:51:58,020 --> 00:52:01,920
+ألفت انتباهكم له موجود في الكتاب يعني ففيه يعني
+
+702
+00:52:01,920 --> 00:52:05,140
+معلومة بنتسلى فيها عشان غازات يعني وفصل غازات
+
+703
+00:52:05,140 --> 00:52:09,380
+وغيره فبيقول during world war two أثناء الحرب
+
+704
+00:52:09,380 --> 00:52:12,140
+العالمية الثانية scientists working on the first
+
+705
+00:52:12,620 --> 00:52:15,720
+Atomic bomb were faced with the challenge of
+
+706
+00:52:15,720 --> 00:52:19,320
+finding a way to obtain large amounts of uranium
+
+707
+00:52:19,320 --> 00:52:25,540
+235 لأن اليورانيوم 235 هو الفيشينابل هو اللي بينشطر
+
+708
+00:52:25,540 --> 00:52:32,980
+أغلب اليورانيوم اللي في الطبيعة هو اليورانيوم 238
+
+709
+00:52:32,980 --> 00:52:39,890
+حوالي 99.8% لا ينشطر تسمعوا عن تخصيب اليورانيوم بدنا
+
+710
+00:52:39,890 --> 00:52:45,650
+ناخد اليورانيوم 235 اللي موجود في اليورانيوم اللي
+
+711
+00:52:45,650 --> 00:52:48,490
+في الطبيعة اللي هو جداش نسبته 0.72
+
+712
+00:52:48,490 --> 00:52:52,250
+تقريبا في المية فبدنا ناخده عشان نعمله enrichment أو
+
+713
+00:52:52,250 --> 00:52:56,530
+تخصيب يعني نزود كمية اليورانيوم 235 لأن هو اللي
+
+714
+00:52:56,530 --> 00:53:00,710
+بيستخدم عسكريا بدنا نقول عسكريا يعني في صناعة ال
+
+715
+00:53:00,710 --> 00:53:05,630
+atomic bombs أو سلميا يعني في محطات الوقود وغيره 
+
+716
+00:53:05,980 --> 00:53:10,020
+الوقود النووي يعني فهم لازم ياخدوا هذا النوع من
+
+717
+00:53:10,020 --> 00:53:13,560
+اليورانيوم يورانيوم 235 من اليورانيوم الموجود في
+
+718
+00:53:13,560 --> 00:53:19,300
+الطبيعة اللي أغلب 238 وللأسف كمان الـ 238 مش بس
+
+719
+00:53:19,300 --> 00:53:26,120
+أنه لا ينشطر لأ وكمان بعمل poisoning لعملية 
+
+720
+00:53:26,120 --> 00:53:32,380
+الانشطار يعني بيخربها يورانيوم
+
+721
+00:53:32,380 --> 00:53:38,880
+هو يعني خامات اليورانيوم قامات فهو موجود لكن زي
+
+722
+00:53:38,880 --> 00:53:41,920
+الكربون الكربون حوالي تسعة وتسعين في المية
+
+723
+00:53:41,920 --> 00:53:46,320
+كربون 12 واحد في المية كربون 13 فهذه
+
+724
+00:53:46,320 --> 00:53:50,580
+نظائر فهذه نظير فهم موجودين مع بعض في الطبيعة لكن
+
+725
+00:53:50,580 --> 00:53:55,020
+أغلب اللي موجود هو إيه اليورانيوم 238 و
+
+726
+00:53:55,020 --> 00:53:59,030
+30 لكن احنا بدنا اليورانيوم إيه؟ 235 جداش ما هو
+
+727
+00:53:59,030 --> 00:54:02,230
+0.72% فبدنا ناخد هالـ 0.72 
+
+728
+00:54:02,230 --> 00:54:05,370
+هذا من كمية كبيرة أغلب بنرميه و نتخلص منه لكن
+
+729
+00:54:05,370 --> 00:54:13,630
+إذا ناخد الـ uranium 235 طيب كيف بدهم يفصلوا؟ إيش
+
+730
+00:54:13,630 --> 00:54:17,670
+فكروا أيام زمان يعني في الحرب العالمية الثانية؟
+
+731
+00:54:17,840 --> 00:54:23,100
+لجوا أن فصلوا كيميائيا مستحيل لأن تفاعلاتهم نفسها
+
+732
+00:54:23,100 --> 00:54:27,700
+ففيش فصل كيميائي مش ممكن يعني فاطلوا على تحويل
+
+733
+00:54:27,700 --> 00:54:31,740
+اليورانيوم لغاز استخدموا الفلورين فحولوا
+
+734
+00:54:31,740 --> 00:54:36,190
+اليورانيوم هكسافلورايد اليورانيوم هكسا فلوريد ال
+
+735
+00:54:36,190 --> 00:54:42,810
+boiling point تبعه 56 56 لجوا
+
+736
+00:54:42,810 --> 00:54:47,590
+أنه بما إنه هذا بيختلف في الكتلة الـ 235 حولوه في
+
+737
+00:54:47,590 --> 00:54:51,510
+الأول لليورانيوم UF6 حولوه لغاز لأنه هنا 56
+
+738
+00:54:51,510 --> 00:54:56,550
+ساخنة لـ 57 58 بصير غاز بس حرارة بسيطة
+
+739
+00:54:56,550 --> 00:55:03,690
+فهنا هذا الـ 235 ممكن نقول لكم جداش الـ formula تبقى
+
+740
+00:55:03,690 --> 00:55:07,870
+تبقى شوية وهذا 238 إذا في فرق في الـ molecular
+
+741
+00:55:07,870 --> 00:55:12,530
+mass يبقى لو خلينا الاتنين يحصلهم effusion مين اللي
+
+742
+00:55:12,530 --> 00:55:18,660
+حصله effusion أسرع؟ الـ 235 إذا بنجمّه وبعدين
+
+743
+00:55:18,660 --> 00:55:21,800
+بنعمله كمان بناخده أول دورة وبنعمله تخصيب كمان
+
+744
+00:55:21,800 --> 00:55:26,360
+دورة بناخد منه الـ A وهكذا عدة مرات لغاية ما نحصل
+
+745
+00:55:26,360 --> 00:55:34,450
+على تخصيب يفوق الـ 99% صعبة لكن مش مستحيلة فحولنا
+
+746
+00:55:34,450 --> 00:55:39,630
+المركبات الاتنين لليورانيوم hexafluoride وبعدين
+
+747
+00:55:39,630 --> 00:55:43,870
+قولنا والله خلينا نشوف الـ rate of effusion فالـ
+
+748
+00:55:43,870 --> 00:55:48,210
+rate of effusion لليورانيوم UF6 235 على الـ rate of
+
+749
+00:55:48,210 --> 00:55:56,600
+effusion لليورانيوم 238 UF6 بيقول بيساوي الـ 238
+
+750
+00:55:56,600 --> 00:56:00,500
+على 235 الفورمولا ويتقلّه أو الـ molecular mass
+
+751
+00:56:00,500 --> 00:56:09,620
+اليورانيوم 235 على 349 بيطلع عندي فرق لصالح الايه؟ الـ
+
+752
+00:56:09,620 --> 00:56:17,080
+UF6 235 1.0043 يعني أكثر شوية صغيرة فقط من إيه من
+
+753
+00:56:17,080 --> 00:56:21,360
+اليورانيوم 238 طبعا بيكرروا هذه العملية لو كرروها
+
+754
+00:56:21,360 --> 00:56:26,020
+حوالي 1150 مرة لو كرروا هذه العملية طبعا بتطول
+
+755
+00:56:26,020 --> 00:56:29,560
+تروح عشانك بيقعدوا سنين وهم بيحاولوا أن هم يعملوا
+
+756
+00:56:29,560 --> 00:56:38,160
+تخصيب فلو قرروها 1150 مرة بيحصلوا على 99% يورانيوم
+
+757
+00:56:38,160 --> 00:56:43,880
+235 طبعا هذا كان زمان بس حاليا صاروا يستخدموا
+
+758
+00:56:43,880 --> 00:56:47,680
+أسلوب آخر زمان كانت هذه الطريقة هي المعتمدة لكن
+
+759
+00:56:47,680 --> 00:56:52,860
+حالياً بيستخدموا أجهزة الطرد المركزي تسمعوا عنها و
+
+760
+00:56:52,860 --> 00:56:55,980
+بتعرفوا يعني في الأخبار أجت كتير في الفترة الأخيرة
+
+761
+00:56:55,980 --> 00:57:01,760
+في موضوع إيران على سبيل المثال فيعني في أجهزة
+
+762
+00:57:01,760 --> 00:57:07,860
+الطرد المركزي طبعا يتم فصل الـ .. اليورانيوم 235 عن
+
+763
+00:57:07,860 --> 00:57:11,560
+اليورانيوم 238 بالطرد المركزي لأن في فرق في الكتلة
+
+764
+00:57:11,560 --> 00:57:16,120
+بينهم فبالتالي لو عندنا أجهزة طارد مركزي يعني خلّوا
+
+765
+00:57:16,120 --> 00:57:19,840
+.. خلّنا نقول يعني عالية الكفاءة آه والله كل ما
+
+766
+00:57:19,840 --> 00:57:23,640
+الكتلة كانت أكثر كل ما جاعدت في الجاع أكثر وهكذا
+
+767
+00:57:23,640 --> 00:57:30,760
+فبرضه عملية مضنية جدا وخطواتها يعني متعددة كتير
+
+768
+00:57:30,760 --> 00:57:33,580
+لكن في النهاية بيقدروا يخصبوا اليورانيوم لمثلا
+
+769
+00:57:33,580 --> 00:57:39,530
+تسعة وتسعة أو للكمية الـ .. للنسبة الصالحة اللي عمل
+
+770
+00:57:39,530 --> 00:57:44,590
+يعني يورانيوم إما لأغراض عسكرية أو لأغراض مدنية
+
+771
+00:57:44,590 --> 00:57:49,090
+المهم أنه في نهاية اليورانيوم و pure لأنه لازم يرفع
+
+772
+00:57:49,090 --> 00:57:53,010
+عمل اليورانيوم 238 لأنه أصلا بيسمم عملية الانشطار
+
+773
+00:57:53,010 --> 00:57:54,930
+طيب
+
+774
+00:57:56,030 --> 00:58:00,050
+خلّيني أتكلم الآن عن الـ Diffusion والـ Mean Free
+
+775
+00:58:00,050 --> 00:58:07,210
+Path أنا قلت إن سرعة الغاز يعني العادي مثلا خلّيني
+
+776
+00:58:07,210 --> 00:58:12,110
+أقول زي ما حسبناها بنلاقي سرعة مثلا 500 متر في
+
+777
+00:58:12,110 --> 00:58:19,050
+الثانية 1000 متر في ثانية كويس طيب ليش لما نجيجي
+
+778
+00:58:19,050 --> 00:58:22,350
+أرش ريحة هان فاش إلى 500 متر وعشرة متر من
+
+779
+00:58:22,350 --> 00:58:26,700
+هالأخر تقعد عدي الدجاج إيش معنى؟ إيش فانا يعني؟ جال
+
+780
+00:58:26,700 --> 00:58:33,240
+لأنه الغازات اللي موجودة عندي بتمشيش بشكل في اتجاه
+
+781
+00:58:33,240 --> 00:58:37,000
+واحد فقط يعني، لأ بتمشي بشكل عشوائي زي ما شوفنا في
+
+782
+00:58:37,000 --> 00:58:40,780
+النظرية عشوائي وبتتصادم مع بعض البعض، لدرجة إن
+
+783
+00:58:40,780 --> 00:58:45,780
+التصادمات ممكن توصل لـ 10 قصر 10، تصادم يعني 100،
+
+784
+00:58:45,780 --> 00:58:50,970
+عشر تلاف مليون مرة عشرة بليون مرة في الثانية يعني
+
+785
+00:58:50,970 --> 00:58:55,290
+أش كتير يعني سرعتها عالية آه لكن أش فيه مش فضل
+
+786
+00:58:55,290 --> 00:58:59,490
+الواحد مثلا يمشيله 500 متر لأ بدها تتصادم
+
+787
+00:58:59,490 --> 00:59:06,150
+وبالتالي بنلاحظ أنه
+
+788
+00:59:06,150 --> 00:59:12,530
+الـ diffusion rate أقل كتير من سرعة الـ إيه سرعة
+
+789
+00:59:12,530 --> 00:59:20,560
+الغاز هي التصادم هذا ماشي من هالهالخبطة في جزء آخر
+
+790
+00:59:20,560 --> 00:59:23,820
+.. مش هيك .. خبط في جزء آخر .. مش هيك .. مش هيك ..
+
+791
+00:59:23,820 --> 00:59:26,680
+إذا كانت تبعته .. مش هيك .. خبط في جزء .. كل .. كل
+
+792
+00:59:26,680 --> 00:59:31,460
+انحناء آهان أو كل زاوية هي عبارة عن تصادم فـ ..
+
+793
+00:59:31,460 --> 00:59:36,560
+مئات .. الملايين اتصادوا مات .. لكن في النهاية ..
+
+794
+00:59:36,560 --> 00:59:40,220
+في النهاية وصل من إيه لبيه؟ وصل من أول غرفة آهانها
+
+795
+00:59:40,220 --> 00:59:43,160
+.. رشينا ريحة .. وصلت لبيه هناك .. آه شمنا الريحة
+
+796
+00:59:43,160 --> 00:59:48,810
+.. ماشي .. لكن جداش مش هيك مش .. مش مسافة فقط من
+
+797
+00:59:48,810 --> 00:59:53,550
+hand لأول غرفة بشكل مباشر ممكن نجيسها مثلا من hand
+
+798
+00:59:53,550 --> 00:59:57,490
+لـ hand على سبيل المثال لأ مش هيك هو مش مسافة طويلة
+
+799
+00:59:57,490 --> 01:00:02,770
+جدا جدا جدا جدا أخد مسافة هائلة نتيجة التصادمات
+
+800
+01:00:02,770 --> 01:00:07,030
+اللي بيقبلها في الطريق هذا اللي بنقوله mean free
+
+801
+01:00:07,030 --> 01:00:12,830
+path .. mean free path .. mean free path هذا هو
+
+802
+01:00:12,830 --> 01:00:17,940
+عبارة عن path of a single molecule in a gas sample
+
+803
+01:00:17,940 --> 01:00:24,480
+كويس فهي عبارة عن حركة random لأن في النهاية هي
+
+804
+01:00:24,480 --> 01:00:28,620
+عبارة عن تصادمات إما تصادمات مع الجدار في بعض
+
+805
+01:00:28,620 --> 01:00:33,560
+الأحيان تصادمات مع الجزيئات المهم عدد هائل جدا جدا
+
+806
+01:00:33,560 --> 01:00:37,420
+من التصادمات في الثانية الواحدة
+
+807
+01:00:40,850 --> 01:00:45,830
+فبنقول الـ molecular collisions بتؤدي إلى تغيير الـ
+
+808
+01:00:45,830 --> 01:00:49,930
+direction of motion الـ molecular collisions بتؤدي
+
+809
+01:00:49,930 --> 01:00:55,090
+إلى تغيير الـ direction of motion بشكل مستمر علشان
+
+810
+01:00:55,090 --> 01:00:59,730
+هيك الـ diffusion للجزيء من نقطة إلى أخرى هياخد
+
+811
+01:00:59,730 --> 01:01:05,750
+يعني عدد هائل من الـ short straight line segments
+
+812
+01:01:05,750 --> 01:01:07,470
+اللي هي هيها short
+
+813
+01:01:19,570 --> 01:01:22,470
+النتيجة الـ collisions طبعا وهذا كلام هياخد وجهته
+
+814
+01:01:22,470 --> 01:01:25,230
+ويمشي مسافة أطول كتير من المتوقع
+
+815
+01:01:34,020 --> 01:01:38,080
+ممكن تكون طويلة ممكن تكون قصيرة لكن في المعدل يعني
+
+816
+01:01:38,080 --> 01:01:44,620
+هي صغيرة جدا جدا يعني عادة في الـ sea level بتكون في
+
+817
+01:01:44,620 --> 01:01:49,420
+الـ nanometer range يعني بيمشي جداش في العشرة أسالت
+
+818
+01:01:49,420 --> 01:01:52,880
+تسعة من المتر يعني إشي قليل خالص لكن كل ما ارتفعنا
+
+819
+01:01:52,880 --> 01:01:56,480
+إلى طبقات الهواء العليا لما الجزيئات تبعد عن بعض
+
+820
+01:01:56,480 --> 01:02:01,900
+كتير لأن الضغط بيقل فبتزيد ممكن توصل لعشرة سم طب
+
+821
+01:02:01,900 --> 01:02:08,640
+التنين جلال معايا يعني الـ free free من path الـ الـ
+
+822
+01:02:08,640 --> 01:02:13,900
+mean free path بقول أنا إذا كان في الـ at sea level
+
+823
+01:02:14,500 --> 01:02:17,520
+في حدود العشرة نانومتر تقريبا يعني إشي قليل
+
+824
+01:02:17,520 --> 01:02:20,040
+بالنانومتر عشرة أس سالب تسعة من المتر يعني جداش
+
+825
+01:02:20,040 --> 01:02:22,260
+بالحاجة الشمس اللي هو خابط بالحاجة الشمس اللي هو
+
+826
+01:02:22,260 --> 01:02:25,900
+خابط إشي مش مبين يعني فوقتها مش بده يوصل لآخر
+
+827
+01:02:25,900 --> 01:02:30,060
+الغرفة بده ده جايج يعني مع إنه سرعته عالية جدا
+
+828
+01:02:30,060 --> 01:02:34,860
+بينما لو طلعنا لـ higher elevations ممكن نلاقي يعني
+
+829
+01:02:34,860 --> 01:02:41,060
+أنه بتوصل لعشرة سنتيمتر على سبيل المثال بس هذا
+
+830
+01:02:41,060 --> 01:02:44,340
+الكلام ليه؟ لأنه الضغط عندي قليل كتير وبالتالي
+
+831
+01:02:44,340 --> 01:02:47,940
+الجزيئات بتكون أبعد عن بعضها البعض وبالتالي الـ
+
+832
+01:02:47,940 --> 01:02:51,900
+mean free path بيكون أطول لكن أطول جداش يعني لو
+
+833
+01:02:51,900 --> 01:02:55,180
+قلنا هانفد دي مش عشرة سم، هفرض عشرة سم، عشرة
+
+834
+01:02:55,180 --> 01:02:57,780
+سم، خبط عشرة سم، عشرة سم، عشرة سم،
+
+835
+01:02:57,780 --> 01:03:04,040
+عشرة سم، عشرة سم، عشرة سم، عشرة سم،
+
+836
+01:03:04,040 --> 01:03:04,180
+عشرة سم، عشرة سم، عشرة سم، عشرة سم،
+
+837
+01:03:04,180 --> 01:03:04,760
+عشرة سم، عشرة سم، عشرة سم، عشرة سم،
+
+838
+01:03:04,760 --> 01:03:08,680
+عشرة سم، عشرة سم، عشرة سم، عشرة سم،
+
+839
+01:03:08,680 --> 01:03:11,780
+عشرة
+
+840
+01:03:11,780 --> 01:03:20,480
+سم، عشرة سم، عشرة 
+
+841
+01:03:20,480 --> 01:03:26,980
+سانتي، هل هذه الغازات هي بالفعل غازات مثالية زي ما 
+
+842
+01:03:26,980 --> 01:03:33,940
+احنا شفناها الـ PV بتساوي NRT؟ طيب علشان نوجد هذه 
+
+843
+01:03:33,940 --> 01:03:38,920
+العلاقة احنا افترضنا افتراضات في الحقيقة يعني ليست 
+
+844
+01:03:38,920 --> 01:03:44,480
+منطقية كيف؟ يعني مثلا افترضنا أن الجزيئات الجزيئات
+
+845
+01:03:44,480 --> 01:03:50,210
+الغازات ليس لها حجم لكن هل هذا كلام صحيح؟ والله 
+
+846
+01:03:50,210 --> 01:03:54,710
+ممكن يكون صحيح إذا كان الضغط كان قليل جدا جدا 
+
+847
+01:03:54,710 --> 01:03:58,380
+يقترب من الصفر يَقترب من الصفر يعني ما فيش عندي
+
+848
+01:03:58,380 --> 01:04:02,020
+جزيئات يعني ممكن يكون ثلاث أربع جزيئات في هذه الغرفة
+
+849
+01:04:02,020 --> 01:04:06,920
+هذه بنقول والله آه يعني الحجم الكلي للغرفة كويس هو
+
+850
+01:04:06,920 --> 01:04:14,220
+عبارة عن حجم الغاز نفسه يعني الكلي كويس اللي هو 
+
+851
+01:04:14,220 --> 01:04:20,520
+عبارة عن الـ V measured هو عبارة عن الـ V للـ ideal
+
+852
+01:04:20,520 --> 01:04:24,900
+gasكويس، ليش هذا كلام؟ لأنه هيكون أكوام من جزيئات
+
+853
+01:04:24,900 --> 01:04:28,880
+والفراغ اللي هم بالفعل يعني خلينا نقول إنه حجمهم 
+
+854
+01:04:28,880 --> 01:04:33,160
+قليل للغاية لكن طب إيش بيحصل لما أنا آجي أستخدم
+
+855
+01:04:33,160 --> 01:04:37,280
+ضغط؟ طب ضغط الغاز طب بعد فترة من الضغط بتتحول ل
+
+856
+01:04:37,280 --> 01:04:42,700
+liquid طب هذا الـ liquid فيه له حجم يبقى أنا يعني
+
+857
+01:04:42,700 --> 01:04:47,080
+إذا كان .. ما بديش أقول حولته لـ liquid لغاز بس تحت
+
+858
+01:04:47,080 --> 01:04:51,840
+ضغط يبقى فيه حجم مهم للي بعده هيتحول لـ liquid ماشي 
+
+859
+01:04:51,840 --> 01:04:55,780
+إيه بيجي هiaخد إيه؟ هياخد حجم مهم فمعنى الكلام الـ
+
+860
+01:04:55,780 --> 01:05:01,540
+particles أو الـ molecules للغاز مش صح إنه نقول إنه 
+
+861
+01:05:01,540 --> 01:05:05,660
+والله فاضي إلا حجم لأ هي لها finite volume لكن 
+
+862
+01:05:05,660 --> 01:05:10,760
+احنا فقط نستطيع إنه مثلا نهمل هذا الحجم إذا كان 
+
+863
+01:05:11,420 --> 01:05:17,740
+عندي الضغط قليل للغاية لما نكون الضغط قليل للغاية
+
+864
+01:05:17,740 --> 01:05:22,440
+بيكون عدد الجزيئات اللي موجودة في الوعاء لها إكاد
+
+865
+01:05:22,440 --> 01:05:27,440
+يُذكر مثلا في الـ 100 لتر يكون في عندي ثلاثة
+
+866
+01:05:27,440 --> 01:05:30,860
+أربع جزيئات مثلا يعني الثلاث أربع جزيئات طب و
+
+867
+01:05:30,860 --> 01:05:33,120
+إيش حجمهم؟ ولا شيء بالنسبة لي لما أقول 100 لتر هو 
+
+868
+01:05:33,120 --> 01:05:36,060
+إيش حجم الجزيئة؟ ولا حاجة جزء من الـ .. من الـ 
+
+869
+01:05:36,060 --> 01:05:40,820
+nanometer يعني ولا شيء وحجم الوعاء مثلا 100 لتر
+
+870
+01:05:40,820 --> 01:05:43,840
+لما أبدأ أقول والله nanometers للمتر مش مشكلة لكن 
+
+871
+01:05:43,840 --> 01:05:49,990
+لما آجي أضغط هذول الـ 100 لتر أضغطهم ويصير حجمهم
+
+872
+01:05:49,990 --> 01:05:55,450
+مثلا عشرة micro liters أو خمسة micro liters
+
+873
+01:05:55,450 --> 01:06:01,310
+ساعتها بيكون لحجم الغازات أهمية هذه حاجة الحاجة 
+
+874
+01:06:01,310 --> 01:06:06,710
+الثانية يبقى الـ P اللي هي الـ V اللي هي measured
+
+875
+01:06:06,710 --> 01:06:13,750
+هذه مش حقيقية مش حقيقية إلا at very low at very
+
+876
+01:06:13,750 --> 01:06:18,340
+low pressures الحاجة الثانية احنا افترضنا أنه 
+
+877
+01:06:18,340 --> 01:06:24,380
+الجزيئات ما فيش بينها لا repulsive ولا attractive
+
+878
+01:06:24,380 --> 01:06:27,800
+forces لكن هل هذا كلام صحيح؟ بقول مستحيل يكون صحيح
+
+879
+01:06:27,800 --> 01:06:33,340
+ليش مستحيل يكون صحيح؟ قال لأنه أنا إيش بخلي الـ
+
+880
+01:06:33,340 --> 01:06:38,580
+liquid liquid؟ قال والله إنه في ترابط بين جزيئاته
+
+881
+01:06:38,580 --> 01:06:41,900
+بحيث إنه الجزيء بده يـ flip بده يطلع بده يسيب لكن 
+
+882
+01:06:41,900 --> 01:06:46,540
+الرابطة أقوى تمام؟ يبقى فيه .. فيه ترابط، هي اللي 
+
+883
+01:06:46,540 --> 01:06:49,240
+بيخلي الـ .. الـ liquid liquid وأيضا اللي بيخلي 
+
+884
+01:06:49,240 --> 01:06:53,500
+الـ gas gas وبيخلي الـ .. حتى الجزء ما يتحركش قال 
+
+885
+01:06:53,500 --> 01:06:57,520
+هو ترابط أقوى، يخليه solid طب أنا ممكن أحول الـ gas 
+
+886
+01:06:57,520 --> 01:07:01,600
+ده لـ liquid وممكن أحول الـ gas أيضا لـ solid عن طريق 
+
+887
+01:07:01,600 --> 01:07:07,000
+الضغط كويس يبقى معنى الكلام ليش ممكن الغاز يصير 
+
+888
+01:07:07,000 --> 01:07:10,860
+liquid قال لأنه فيه attractive forces ليش ممكن 
+
+889
+01:07:10,860 --> 01:07:14,000
+الغاز يصير solid قال لأنه فيه attractive forces
+
+890
+01:07:14,000 --> 01:07:17,840
+إذا كيف أنا بدي ألغي الـ attractive forces هذه لأ 
+
+891
+01:07:17,840 --> 01:07:22,680
+لازم أخدها بعين الاعتبار برضه عند ما تكون عندي 
+
+892
+01:07:22,680 --> 01:07:29,400
+الضغوط يعني عالية أو مرتفعة بشكل عام لهذا السبب
+
+893
+01:07:29,400 --> 01:07:34,560
+بقدر أقول أنا إنه عادةً الـ V measured اللي هو
+
+894
+01:07:34,560 --> 01:07:37,520
+الحجم الكلي هو عبارة عن الـ V ideal اللي أنا 
+
+895
+01:07:37,520 --> 01:07:43,760
+بستخدمه في الـ PV بتساوي NRT زائد NB يعني هذا مش 
+
+896
+01:07:43,760 --> 01:07:46,480
+المفروض يكون V لحاله في العلاقة PV بتساوي NRT، لأ،
+
+897
+01:07:46,480 --> 01:07:54,020
+المفروض يكون V ideal زائد NB فبتكون V ideal عبارة
+
+898
+01:07:54,020 --> 01:07:57,020
+عن الـ V measured اللي هو حجم الوعاء ناقص الـ A
+
+899
+01:08:02,210 --> 01:08:06,850
+نفس الكلام بالنسبة للحجم P نفس الكلام بالنسبة للـ
+
+900
+01:08:06,850 --> 01:08:07,490
+P
+
+901
+01:08:12,710 --> 01:08:16,070
+هي عبارة عن الـ P measured زائد correction factor
+
+902
+01:08:16,070 --> 01:08:20,410
+خاص بالـ attractive forces لأنه مجرد وجود
+
+903
+01:08:20,410 --> 01:08:25,270
+attractive forces مش هتخلي الجزيئات حرة بأنها 
+
+904
+01:08:25,270 --> 01:08:28,110
+تنتشر زي ما هي وتعطينا الضغط، لأ هي بدها تضرب لكن 
+
+905
+01:08:28,110 --> 01:08:31,480
+في attractive forces بتعمل كل جيل لكن فيه
+
+906
+01:08:31,480 --> 01:08:35,020
+attractive forces فبالتالي بدي أضيف term تصحيح إيه
+
+907
+01:08:35,020 --> 01:08:40,820
+بقول N squared A على V squared V هذا اللي دعا
+
+908
+01:08:40,820 --> 01:08:44,700
+بالحجم يعني و A هذا عبارة عن factor فبتصير العلاقة
+
+909
+01:08:44,700 --> 01:08:46,180
+الكلية دي
+
+910
+01:08:51,360 --> 01:08:55,320
+الـ PV بتساوي NRT، الآن الـ P هي عبارة عن الـ P 
+
+911
+01:08:55,320 --> 01:09:00,260
+measured زائد N squared A على الـ V squared، الـ A 
+
+912
+01:09:00,260 --> 01:09:03,600
+هي عبارة عن الـ factor علاقة بالـ attractive forces 
+
+913
+01:09:03,600 --> 01:09:07,080
+و الـ N number of moles و الـ V هي الحجم، طب الـ V 
+
+914
+01:09:07,080 --> 01:09:12,930
+صارت V measured ناقص NB بتساوي NRT في الحقيقة لو 
+
+915
+01:09:12,930 --> 01:09:18,290
+اجينا رسمنا هذه العلاقة بقول الـ Ideal gas PV
+
+916
+01:09:18,290 --> 01:09:24,810
+بتساوي nRT PV بتساوي nRT يعني لو اجينا استخدمنا 
+
+917
+01:09:24,810 --> 01:09:31,810
+ضغوط مختلفة فبنلاحظ أن الـ Ideal gas هيعطيني شيء زي 
+
+918
+01:09:31,810 --> 01:09:36,050
+هيك ثابتة PV على nRT هتكون دائما ثابتة PV على nRT
+
+919
+01:09:36,050 --> 01:09:43,090
+هتكون إيه ثابتة لكن لكن حقيقة إيش اللي بيحصل خلينا 
+
+920
+01:09:43,090 --> 01:09:51,230
+ناخد عند مثلا عند 173 Kelvin لحظة أو عند 286 أو
+
+921
+01:09:51,230 --> 01:09:57,270
+عند 873 وين كلهم بيلتقوا يلتقون عند الصفر إيش معنى
+
+922
+01:09:57,270 --> 01:10:01,870
+عند الصفر يعني PV بتساوي nRT يعني هذه PV على nRT
+
+923
+01:10:01,870 --> 01:10:06,610
+بتساوي واحد وكثير بتكون واحد صحيح لكل الغازات عند
+
+924
+01:10:06,610 --> 01:10:10,970
+ضغط إيش ماله قليل جدا قريب جدا من الصفر لإيه؟ لأن
+
+925
+01:10:10,970 --> 01:10:13,950
+عدد الغازات اللي موجودة عدد جزيئات الغاز اللي 
+
+926
+01:10:13,950 --> 01:10:18,150
+موجودة بتكون قليلة للغاية وبالتالي لأ صح ما فيش
+
+927
+01:10:18,150 --> 01:10:21,490
+attractive فأفرض أن عندي غاز واحد جزيء واحد من
+
+928
+01:10:21,490 --> 01:10:25,450
+الغاز ما فيش عندي attractive forces وأيضا الحجم 
+
+929
+01:10:25,450 --> 01:10:28,770
+بالنسبة للحجم المشغول حجم الغاز نفسه حجم الجزيء
+
+930
+01:10:28,770 --> 01:10:32,370
+نفسه بالنسبة للحجم المشغول لها كانت يُذكر بس هي
+
+931
+01:10:32,370 --> 01:10:38,760
+كلها كله فقط عند تقريبا يعني قريب جدا جدا جدا من 
+
+932
+01:10:38,760 --> 01:10:42,860
+الصفر أن صفر بدأ يكون هذا صفر مش واحد أن صفر يعني
+
+933
+01:10:42,860 --> 01:10:48,320
+فهو مش صفر بالظبط يعني قريب جدا من الصفر لكن 
+
+934
+01:10:48,320 --> 01:10:53,280
+لاحظوا أنه يعني هذا عند 173 شكل
+
+935
+01:10:53,280 --> 01:10:59,580
+غريب لكن مختلف جدا عن إيه عن المثالي مختلف جدا طيب
+
+936
+01:10:59,580 --> 01:11:03,240
+لو أخدنا مثلا عند 286 لاحظوا معاه 
+
+937
+01:11:03,240 --> 01:11:09,010
+طلعوا يلتقون كله مثالي مثالي مش مشكلة عنده غوط حلوة 
+
+938
+01:11:09,010 --> 01:11:13,050
+يعني آه عنده غوط حلوة مش فارق يعني عند الحرارة هنا
+
+939
+01:11:13,050 --> 01:11:20,030
+298 في عند يعني يعني اختلاف لكن بسيط مش كثير يعني
+
+940
+01:11:20,030 --> 01:11:23,590
+ممكن نقول تقريبا آه والله عند الحرارة العادية PV 
+
+941
+01:11:23,590 --> 01:11:29,400
+بتساوي NRTPV بتساوي NRT لكن لما نروح لـ very high
+
+942
+01:11:29,400 --> 01:11:33,260
+temperatures على سبيل المثال فنتطلع على طول بدت 
+
+943
+01:11:33,260 --> 01:11:41,660
+إيه الـ PV بطلت تساوي NRT لاحظنا فيه يعني زيادة 
+
+944
+01:11:41,660 --> 01:11:46,960
+مستمرة إذا كانت طلعنا على الخط الأحمر وطلعنا على 
+
+945
+01:11:46,960 --> 01:11:48,460
+الخط الفسفوري يعني
+
+946
+01:11:56,430 --> 01:12:01,490
+الخط الأحمر لأ زيادة، بينما الـ low temperatures 
+
+947
+01:12:01,490 --> 01:12:06,910
+لأن الغاز سيصبح سائلالـ low temperatures واللي هيبقى
+
+948
+01:12:06,910 --> 01:12:13,930
+بيصير الغاز حجمه قليل كثير وبالتالي يعني في عندي 
+
+949
+01:12:13,930 --> 01:12:19,710
+اختلاف كبير بين الـ ideal وبين الـ real gases ففي
+
+950
+01:12:19,710 --> 01:12:24,760
+الحقيقة يعني اللي بدنا نقوله إنه في أغلب الأحيان
+
+951
+01:12:24,760 --> 01:12:30,240
+المعادلة
+
+952
+01:12:30,240 --> 01:12:35,220
+الـ Ideal Gas Equation بتعطي نتائج ممتازة في أغلب
+
+953
+01:12:35,220 --> 01:12:40,680
+الأحيان في الظروف العادية معادلة الـ Ideal Gas
+
+954
+01:12:40,680 --> 01:12:45,620
+Equation بتعطي نتائج ممتازة لكن إذا كان عندي high
+
+955
+01:12:45,620 --> 01:12:48,680
+temperatures أو low temperatures high pressures
+
+956
+01:12:49,640 --> 01:12:53,120
+بشكل عام دائما في الـ high pressures مشكلة عويصة
+
+957
+01:12:53,120 --> 01:12:55,460
+كلهم في الـ high pressures لاحظوا إيش اللي بيحصل
+
+958
+01:12:55,460 --> 01:12:59,580
+فيهم في انحراف أو تغير كبير عن الـ ideal gas
+
+959
+01:12:59,580 --> 01:13:03,140
+equation لو طلعنا على الجدول هذا منلاحظ قيم 
+
+960
+01:13:03,140 --> 01:13:07,900
+مختلفة للـ a اللي هو الـ correction factor للـ
+
+961
+01:13:07,900 --> 01:13:14,000
+attractive والـ repulsive forces وايضا للـ b اللي هي
+
+962
+01:13:14,000 --> 01:13:19,620
+الـ correction factor للـ volume للـ gases فهذا 
+
+963
+01:13:19,620 --> 01:13:23,020
+الكلام يستخدم هذا للغازات المختلفة في هذه الـ
+
+964
+01:13:23,020 --> 01:13:26,020
+correction factors يجب أن نأخذها بعين الاعتبار إذا
+
+965
+01:13:26,020 --> 01:13:32,760
+بدنا نشتغل شغل صحيح بالذات at high temperatures at 
+
+966
+01:13:32,760 --> 01:13:37,400
+high pressures لكن معادلة الـ ideal gas equation
+
+967
+01:13:37,400 --> 01:13:42,460
+بتكون مثالية وصحيحة جدا يعني خلينا نقول at 
+
+968
+01:13:42,460 --> 01:13:47,870
+pressures close to zero وممكن نقول يعني .. يعني 
+
+969
+01:13:47,870 --> 01:13:51,010
+حتى لو زاد الـ pressure شوية والـ temperatures يعني
+
+970
+01:13:51,010 --> 01:13:55,450
+برضه يعني خلينا نقول معقولة يعني لكن لو زاد الـ
+
+971
+01:13:55,450 --> 01:14:01,890
+pressure شوية مش .. يعني بتضلها إلى حد كبير قريبة
+
+972
+01:14:01,890 --> 01:14:06,610
+جدا من المثالية هيك بنكون خلصنا الشابتر المتعلق
+
+973
+01:14:06,610 --> 01:14:11,730
+بالغازات إذا الله راضٍ الحصة اللي جاية بنتكلم عن الـ
+
+974
+01:14:11,730 --> 01:14:17,260
+liquids وأيضا الـ Intermolecular Forces فبنشوفكوا 
+
+975
+01:14:17,260 --> 01:14:18,400
+الحصة الجاية إذا الله رغب