diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/1BvFOhgJTvk_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/1BvFOhgJTvk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..82bf27c276e9dbb93944a04877592ac5826f7560
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+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/1BvFOhgJTvk_postprocess.srt
@@ -0,0 +1,1296 @@
+1
+00:00:05,250 --> 00:00:07,890
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,890 --> 00:00:10,650
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,650 --> 00:00:15,990
+أهلي وصحابي أجمعين هذه هي المحاضرة رقم 23 مساق
+
+4
+00:00:15,990 --> 00:00:20,050
+تحليل اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:20,050 --> 00:00:25,670
+الإسلامية قسم الرياضيات للماجستير اليوم هنحكي عن
+
+6
+00:00:25,670 --> 00:00:30,550
+تلاتة تمانية اللي هو representation of functional
+
+7
+00:00:30,550 --> 00:00:36,850
+on Hilbert spaces اللي بدنا نسويهإنه اللي هو عادة
+
+8
+00:00:36,850 --> 00:00:40,770
+لما الناس يقولكم بدأ أعمل تمثيل لشغلها بوسط شغلها
+
+9
+00:00:40,770 --> 00:00:44,970
+أكيد اللي بده يعملها الشغل الجديد اللي يعملها أحد
+
+10
+00:00:44,970 --> 00:00:48,730
+عمرين إما تكون أسهل أو إما تكون يعني الصيغة اللي
+
+11
+00:00:48,730 --> 00:00:51,990
+بده يعملها بتستخدم في أمور أخرى حتى لو كانت معقدة
+
+12
+00:00:52,240 --> 00:00:56,220
+ماشي الحال الان هذه لحسن الحظ انا بقى انا هيك وجه
+
+13
+00:00:56,220 --> 00:00:59,340
+نظري ان احنا بدنا نروح باتجاه اللي هو ناخد ال
+
+14
+00:00:59,340 --> 00:01:04,440
+functional ونوصله الى صيغة معينة الصيغة سهلة اللي
+
+15
+00:01:04,440 --> 00:01:06,640
+هو بالدكتب اللي هو ال functional بصورة inner
+
+16
+00:01:06,640 --> 00:01:09,720
+productيعني اي linear functional يعني ده اللي
+
+17
+00:01:09,720 --> 00:01:13,080
+linear functional بدك تكتبها على صورة ايش بتساوي
+
+18
+00:01:13,080 --> 00:01:16,020
+inner product و inner product لطيف يعني و الناس
+
+19
+00:01:16,020 --> 00:01:19,720
+بتحب تتعامل معاه نيجي الآن نيجي اللي هي اول نظرية
+
+20
+00:01:19,720 --> 00:01:23,920
+بنحكي فيها اللي هي دي النظرية Ray's theorem بقولك
+
+21
+00:01:23,920 --> 00:01:27,400
+every bounded linear functional on a Hilbert space
+
+22
+00:01:28,290 --> 00:01:31,710
+H can be represented in terms of inner product
+
+23
+00:01:31,710 --> 00:01:36,390
+يعني كل linear functional اللي هو of Hilbert space
+
+24
+00:01:36,390 --> 00:01:39,610
+كان بيه إيش ما لها بنقدر نكتبها على صورة inner
+
+25
+00:01:39,610 --> 00:01:43,830
+product بالظبط لو F bounded linear functional بقدر
+
+26
+00:01:43,830 --> 00:01:46,730
+أقولك أكتب لك F of X بيساوي ال inner product بين X
+
+27
+00:01:46,730 --> 00:01:52,330
+و Z حيث Z depends on F اللي بتحكي عنها أكيد لأن كل
+
+28
+00:01:52,330 --> 00:01:55,070
+واحدة بده يكونها Z معينةوالـ F is uniquely
+
+29
+00:01:55,070 --> 00:01:59,210
+determined by F with norm كمان هيطلع نورم الـ Z
+
+30
+00:01:59,210 --> 00:02:03,490
+هذا هو normية نورم الـ F هذه النظرية اللي عندنا
+
+31
+00:02:03,490 --> 00:02:07,600
+ماشي الحال اطلع خلينا نشوف ال proofالشيء الذي يظهر
+
+32
+00:02:07,600 --> 00:02:10,880
+في حالة f يتساوي 0 هو حالة الـ Z لأنه على طول
+
+33
+00:02:10,880 --> 00:02:14,280
+تلاقي الـ Z يتساوي 0 بيصير f of x يتساوي x و 0
+
+34
+00:02:14,280 --> 00:02:17,760
+بيصير الهي الهي الهي الهي الهي الهي الهي الهي الهي
+
+35
+00:02:17,760 --> 00:02:18,600
+الهي الهي الهي الهي الهي الهي الهي الهي الهي الهي
+
+36
+00:02:18,600 --> 00:02:19,440
+الهي الهي الهي الهي الهي الهي الهي الهي الهي الهي
+
+37
+00:02:19,440 --> 00:02:21,680
+الهي الهي الهي الهي الهي الهي الهي الهي الهي الهي
+
+38
+00:02:21,680 --> 00:02:22,240
+الهي الهي الهي الهي ال
+
+39
+00:02:27,870 --> 00:02:32,850
+بما أن F لا تساوي سفر إذا يعني مافيش حاجة تقول لي
+
+40
+00:02:32,850 --> 00:02:37,230
+إن كل العناصر هتروح للسفر يعني ال null F مش هيكون
+
+41
+00:02:37,230 --> 00:02:40,330
+ال H اللي هو ال null space ال null space هو عبارة
+
+42
+00:02:40,330 --> 00:02:44,690
+عن super zero مدان فيه صورة مش zero إذا أكيد مالها
+
+43
+00:02:44,690 --> 00:02:48,840
+ال null F في شمالها مش كل ال H كاملةطيب لكن احنا
+
+44
+00:02:48,840 --> 00:02:52,540
+قبل هيك قلنا N of S from null space is a closed
+
+45
+00:02:52,540 --> 00:02:55,980
+subspace of H طيب ماذا يعمل closed subspace لـ H
+
+46
+00:02:55,980 --> 00:02:59,440
+ده الأمور حلوة في الدنيا بالصحيحة إذا من theorem
+
+47
+00:02:59,440 --> 00:03:04,080
+334 بقدر اكتب H اللي هي ال complete على صورة
+
+48
+00:03:04,080 --> 00:03:07,240
+closed subspace N of S و ال orthogonal complement
+
+49
+00:03:07,240 --> 00:03:11,580
+له اللي هو N of إيه أش orthogonal كتبت على صورة
+
+50
+00:03:11,580 --> 00:03:17,890
+direct sum من الـ Hطبعا هنا ال N of F مش H إذا ال
+
+51
+00:03:17,890 --> 00:03:21,770
+N of F Orthogonal مش Zero إذا ال N of F Orthogonal
+
+52
+00:03:21,770 --> 00:03:25,330
+ليسوا Zero فما دام هيك ما دام مش Zero إذا بقدر
+
+53
+00:03:25,330 --> 00:03:29,830
+أجيلي اللي هو Z not لات سوى سفر و Z not وين موجودة
+
+54
+00:03:29,830 --> 00:03:35,340
+في ال N of F Orthogonal طيبطيب الآن منها هذه بدي
+
+55
+00:03:35,340 --> 00:03:38,820
+أصنع اللي بدي .. اللي بدي أصل لمين للـ z اللي فوق
+
+56
+00:03:38,820 --> 00:03:42,220
+ماشي الحالة بواسطة هذه و بواسطة ال F اللي هي اللي
+
+57
+00:03:42,220 --> 00:03:46,380
+عندي المعتار الآن صارت عندي z note بين إيديا و ال
+
+58
+00:03:46,380 --> 00:03:52,340
+F عندي معتار بقولك 6 الآن أو اللي هو ركّب التركيبة
+
+59
+00:03:52,340 --> 00:03:57,880
+التالية ضرب ل z note في F of X X arbitrary fixed
+
+60
+00:03:57,880 --> 00:04:02,800
+pointو X في مين في أفه في Z نوت و حاصل الطرح سميه
+
+61
+00:04:02,800 --> 00:04:06,980
+مين هنا V و مقصودة ان هذي هذي Z نوت وهنا X وهنا X
+
+62
+00:04:06,980 --> 00:04:10,790
+وهنا Z نوت مقصودة على الطرحWhere X is an arbitrary
+
+63
+00:04:10,790 --> 00:04:16,690
+element in H since F is linear إذا لو جيت حسبت ال
+
+64
+00:04:16,690 --> 00:04:21,290
+F of V هذي بيصير عدد بتطلع براها فبصير F of Z0 في
+
+65
+00:04:21,290 --> 00:04:25,310
+F of X و هذي بيصير عدد بتطلع برا ال F بيصير ناقص F
+
+66
+00:04:25,310 --> 00:04:29,250
+of X في F of Z0 حصلت رحلنا إيش بيساوي؟ بيساوي 0
+
+67
+00:04:29,250 --> 00:04:34,370
+صارت ال V هذه اللي اخترتها هذه where موجودة في ال
+
+68
+00:04:34,370 --> 00:04:39,200
+null في ال null of Fإذا صارت الـ V عمودية على مين؟
+
+69
+00:04:39,200 --> 00:04:41,400
+على الـ Z note اللي هي اللي موجودة في الـ N of
+
+70
+00:04:41,400 --> 00:04:45,160
+orthogonal إذا صار عندي مدام عمودية عليها إذا صار
+
+71
+00:04:45,160 --> 00:04:48,580
+عندي ال inner product بين ال V و Z note صفر ال V
+
+72
+00:04:48,580 --> 00:04:52,380
+حقق اللي قيمتها اللي هي Z note و F of X ناقص X في
+
+73
+00:04:52,380 --> 00:04:56,640
+F و Z note و Z note استخدم خلاص ال inner product و
+
+74
+00:04:56,640 --> 00:05:00,460
+طلعلي هدولة برا و ارتبليياه فبصير F of X في Z note
+
+75
+00:05:00,460 --> 00:05:04,770
+و Z يعني هادي مع هادي ناقص هادي مع هاديبصير عندى F
+
+76
+00:05:04,770 --> 00:05:09,190
+of X فى Z0 و Z ناقص اللى هى F of Z0 بتطلع و X و
+
+77
+00:05:09,190 --> 00:05:13,770
+مين و Z0 معايا الآن صار عندى أي واجهة عندها دى
+
+78
+00:05:13,770 --> 00:05:18,970
+صارت عندى هذا المقدار بساوي سفر انجللي هذا على
+
+79
+00:05:18,970 --> 00:05:23,890
+الطرف التانى ماشي الحال و اجسملي اللى هو على Z و
+
+80
+00:05:23,890 --> 00:05:28,450
+Z0 فبصير F of X إيش هتساوي اللى هو هذا المقدار على
+
+81
+00:05:28,450 --> 00:05:32,890
+Z و Z0 بصير اللى هى F of Z0 على Z و Z0 فى X و مين
+
+82
+00:05:32,890 --> 00:05:39,340
+و Z0واضح معايا
+
+83
+00:05:39,340 --> 00:05:43,760
+يا جماعة إذا F of X صارت عبارة عن F of Z note على
+
+84
+00:05:43,760 --> 00:05:47,920
+Z of Z note في X of Z note واضحة اتها وبيساوي الان
+
+85
+00:05:47,920 --> 00:05:52,300
+دخلوليها دي علي بعيد عشان بتاخد Z انا بتلاحظ ال Z
+
+86
+00:05:52,300 --> 00:05:57,900
+فبصير X of F of Z note على اللي هو Z note و Z note
+
+87
+00:05:57,900 --> 00:06:04,490
+و main و Z noteماشي الان عندي X was arbitrary اذا
+
+88
+00:06:04,490 --> 00:06:07,530
+لو اجينا اخدنا صارت الان F of X بالساوية القيمة
+
+89
+00:06:07,530 --> 00:06:12,350
+هذه هذه صارت بين إيديا مبنية ال Z note وهذه بين
+
+90
+00:06:12,350 --> 00:06:18,270
+إيديا ماشي الحال كل هذه كل هذه هي اللي سميه ليهاش
+
+91
+00:06:18,270 --> 00:06:23,910
+Z إذا صار عندى الآن حصلنا F of X بالساوية X ومين
+
+92
+00:06:23,910 --> 00:06:30,620
+وZ هاي واحدالآن بدي أثبتلك اللي هو عندي بدي أثبتلك
+
+93
+00:06:30,620 --> 00:06:33,420
+أنه وحيدة و بعدين بدي أثبتلك norm هذه بيسوي normين
+
+94
+00:06:33,420 --> 00:06:36,760
+الـ z خلّيني واحدة واحدة to prove the uniqueness
+
+95
+00:06:36,760 --> 00:06:40,840
+of z suppose that there are z واحد and z اتنين
+
+96
+00:06:40,840 --> 00:06:44,940
+such that f of x بيسوي x و z واحد و f of x بيسوي x
+
+97
+00:06:44,940 --> 00:06:48,940
+و z اتنين وهذه سهلة for all x المتناشر إذا جيب هنا
+
+98
+00:06:48,940 --> 00:06:51,440
+دولة جانب بعض و اترحى من بعض بيطلع من ساوي سفر
+
+99
+00:06:51,440 --> 00:06:56,950
+اترحى انش هيكون x و z واحد ناقص 2 z اتنينالآن عندي
+
+100
+00:06:56,950 --> 00:07:00,570
+هذا الكلام صحيح لكل x والتي موجودة في الـ H مضمنها
+
+101
+00:07:00,570 --> 00:07:06,770
+هي z1-z2 في الـ H إذا صار z1-z2 إذا z1-z2 بيساوي 0
+
+102
+00:07:06,770 --> 00:07:10,370
+إذا ال norm هنا بيساوي 0 إذا z1 بيساوي z0 وهذا
+
+103
+00:07:10,370 --> 00:07:13,890
+بيثبت ال uniqueness الآن أنزلوا شوية، أنزلوا،
+
+104
+00:07:13,890 --> 00:07:18,510
+أنزلوا، بنرجع نثبت مين الآن عندي اللي هو normal F
+
+105
+00:07:18,510 --> 00:07:25,890
+بيساوي normal z، normal Fبساوي norm الـ z احنا
+
+106
+00:07:25,890 --> 00:07:29,890
+قلنا f of x ايش هتساوي ال inner product بين x و z
+
+107
+00:07:29,890 --> 00:07:34,110
+صح ولا لأ؟ لأن خدولي ال absolute value للجهتين او
+
+108
+00:07:34,110 --> 00:07:38,530
+ال modulus هذا بشوارز ال quality بصير اصغر هو
+
+109
+00:07:38,530 --> 00:07:44,190
+يساوي norm ال x في norm main ال z لأن اجسمول
+
+110
+00:07:44,190 --> 00:07:46,170
+الجهتين على norm ال x اللي هي ال xات اللي بيساوي
+
+111
+00:07:46,170 --> 00:07:52,230
+نش سفر فبصير f of xعلى نورم الـ x أصغر شوه نورم
+
+112
+00:07:52,230 --> 00:07:55,730
+مين الـ z صارت هذه upper bound لهذه إذا أكيد ال
+
+113
+00:07:55,730 --> 00:07:57,730
+suprem لهادي أصغر شوه هذه اللي هو اللي is upper
+
+114
+00:07:57,730 --> 00:08:03,410
+bound إذا ال suprem لهادي over x element أتش و x
+
+115
+00:08:03,410 --> 00:08:08,810
+لا تشوه سفر بيصير عندي هذا كله اسمه مين نورم ال F
+
+116
+00:08:08,810 --> 00:08:12,950
+إذا صار نورم ال F أصغر شوه مين نورم ال Z هاي واحدة
+
+117
+00:08:12,950 --> 00:08:18,170
+الان الاتجاه الثاني الاتجاه الثاني خدوا الآن عندي
+
+118
+00:08:18,170 --> 00:08:27,860
+F of Xبساوي ايش يا جماعة X و Z صح ولا لأن
+
+119
+00:08:27,860 --> 00:08:33,220
+F of Z ايش بساوي اللي انها ال product بين Z و مين
+
+120
+00:08:33,220 --> 00:08:46,220
+و Z صح و يساوي مين نورم Z تربيه باشي الحال عند
+
+121
+00:08:46,220 --> 00:08:50,110
+نورم ال Fأكيد اللي عندي absolute value of f of z
+
+122
+00:08:50,110 --> 00:08:55,790
+بساوي نورم الـ z تربيع صح ولا لأ؟ باين هاه؟ باين
+
+123
+00:08:55,790 --> 00:09:04,090
+هاه؟ هذه الآن أكبر أو يساوي اللي هو norm of f of a
+
+124
+00:09:04,090 --> 00:09:05,830
+من norm of f نفسها
+
+125
+00:09:09,670 --> 00:09:14,410
+ماشي الحال عند نورم ال F أصغر أو يشاوي نورم ال ..
+
+126
+00:09:14,410 --> 00:09:20,810
+ال .. الأكبر آسف شو هو هذي اللي هي السبرما نورم ال
+
+127
+00:09:20,810 --> 00:09:25,470
+F السبرما وهذه نقطة منها بيصير نورم ال F أكبر
+
+128
+00:09:25,470 --> 00:09:29,630
+شاومين نورم ال Z هي أكبر شاومين نورم ال Z وهي أصغر
+
+129
+00:09:29,630 --> 00:09:34,290
+أو يشاوي نورم ال Z من التنتين مع بعض اشمالهمعايا
+
+130
+00:09:34,290 --> 00:09:37,670
+يا جماعة هاد نورم ال F أصغر و ساوي و هاد نورم ال F
+
+131
+00:09:37,670 --> 00:09:40,770
+أكبر و ساوي التنتين مع بعض اللي هو بيصير نورم ال F
+
+132
+00:09:40,770 --> 00:09:47,010
+ساوي نورم ال Z يلا اللي بعدها نيجي الأن لما هاد
+
+133
+00:09:47,010 --> 00:09:47,770
+المم سهلة
+
+134
+00:09:50,440 --> 00:09:54,320
+ف V1 و W .. مش عارف ايش كتبها اصلا V2 و W for all
+
+135
+00:09:54,320 --> 00:09:58,980
+W in inner product space X then V1 بيساوي V2 in
+
+136
+00:09:58,980 --> 00:10:02,180
+particular V1 و W بيساوي 0 for all W المتن X
+
+137
+00:10:02,180 --> 00:10:06,100
+implies that V1 بيساوي مين؟ سفر هذا exercise بسيط
+
+138
+00:10:06,100 --> 00:10:13,320
+يعني .. طب و في أثناء البرهان اللي برهنناها اللي
+
+139
+00:10:13,320 --> 00:10:28,520
+قبل و شوية هنشوفها عند ما أعطيني V1و V2 و V1
+
+140
+00:10:28,520 --> 00:10:32,800
+و V2 في ال Xبقول إذا كان هذا بساوة داك معناته V1
+
+141
+00:10:32,800 --> 00:10:36,700
+بساوة V2 فكي ترجله هذا على الجهة تاني بيصيح V1 نقص
+
+142
+00:10:36,700 --> 00:10:40,680
+V2 و W عملتها قبل شوية بساوة سفر هذا لكل W من ضمن
+
+143
+00:10:40,680 --> 00:10:47,340
+هم مين V1 نقص V2 لأن V1 نقص V2 و V1 نقص V2 بساوة
+
+144
+00:10:47,340 --> 00:10:52,160
+سفر أو منه اللي هو V1 بساوة V2 لأنه ال norm تربيعي
+
+145
+00:10:52,160 --> 00:10:55,800
+بساوة سفر لأن V1 بساوة V2 إلى اللي بعدها حالة خاصة
+
+146
+00:10:55,800 --> 00:11:00,730
+منها إذا كانت V1 و W بساوة سفر لكل W في ال Xإذا
+
+147
+00:11:00,730 --> 00:11:04,530
+سأكون من ضمن الـ W V1 يصبح V1 و V1 بالساعة و سفر و
+
+148
+00:11:04,530 --> 00:11:06,370
+V1 بالساعة و سفر وهو المطلوب
+
+149
+00:11:11,800 --> 00:11:16,200
+حكينا كان عن ال linear .. اطلع لفوق شوية حكينا عن
+
+150
+00:11:16,200 --> 00:11:20,000
+ال linear functional الآن عرفنا احنا قبل هيك ال
+
+151
+00:11:20,000 --> 00:11:23,900
+bilinear بتكون linear في الجهتين اه يعني function
+
+152
+00:11:23,900 --> 00:11:25,800
+of two variables بتكون linear في الأولى و linear
+
+153
+00:11:25,800 --> 00:11:29,120
+في التانية sesquilinear بتكون linear في الأولى و
+
+154
+00:11:29,120 --> 00:11:31,880
+التانية conjugate linear يعني مش linear .. زي اللي
+
+155
+00:11:31,880 --> 00:11:34,980
+انار ال product .. زي اللي بنار ال productالـ
+
+156
+00:11:34,980 --> 00:11:37,860
+Liner Product Linear في الأولى لكن في الـ Inter
+
+157
+00:11:37,860 --> 00:11:40,560
+التاني هي إيش ماله Conjugate Linear لما يطلع يطلع
+
+158
+00:11:40,560 --> 00:11:44,180
+يبقى إيش و Conjugate فعشان هيك بنسميه Cisco Linear
+
+159
+00:11:44,180 --> 00:11:49,300
+إذا نقول بالظبط إيش اللي بتحكيه هذا بقول الآن let
+
+160
+00:11:49,300 --> 00:11:53,920
+X and Y be vector spaces over a field K تنين over
+
+161
+00:11:53,920 --> 00:11:59,420
+the same fieldلأن a sesquilinear form أو
+
+162
+00:11:59,420 --> 00:12:04,320
+sesquilinear functional H هو عبارة عن ده لمن X
+
+163
+00:12:04,320 --> 00:12:09,700
+cross Y لمين للـ scalar field تبع حينكي إيش بيحقق؟
+
+164
+00:12:09,700 --> 00:12:14,240
+بيحقق إنه linear في الأولى و conjugate linear في
+
+165
+00:12:14,240 --> 00:12:19,920
+التانية، ماشي؟إيش يعني أنه لكل X1 و X2 و X في الـ
+
+166
+00:12:19,920 --> 00:12:24,280
+X و Y1 و Y2 نقوله بـ Y و كل Scale as Alpha Beta
+
+167
+00:12:24,280 --> 00:12:31,360
+تحقق مالي H of X1 زاد X2 و Y بتساوي H of X1 و Y
+
+168
+00:12:31,360 --> 00:12:36,440
+زاد H of X2 و Y زي ال inner productالان اتشوف x و
+
+169
+00:12:36,440 --> 00:12:39,720
+y واحد زي اضاءة y اتنين بالساوية اتشوف x واحد و y
+
+170
+00:12:39,720 --> 00:12:44,960
+واحد زي اتشوف x و y اتنين اللي نهار اتعادى بس لان
+
+171
+00:12:44,960 --> 00:12:47,280
+لما ندخل ال scalar بصير انا conjugate و انا مش
+
+172
+00:12:47,280 --> 00:12:50,620
+conjugateلأن H في Alpha X و Y بيسوي Alpha H X و Y
+
+173
+00:12:50,620 --> 00:12:53,800
+إذا ال linear صارت في ال entry الأول في ال entry
+
+174
+00:12:53,800 --> 00:12:57,020
+التاني بتطلع بيه conjugate يعني اللي هو conjugate
+
+175
+00:12:57,020 --> 00:13:01,720
+linear هذا كله مع بعض بنسميه Cisco linear لو لو
+
+176
+00:13:01,720 --> 00:13:06,200
+كانت K بيتساوي R ال above بنسميه إيش ماله bilinear
+
+177
+00:13:06,200 --> 00:13:08,800
+لإن مافيش حاجة اسمها conjugate حيصير إيش ماله اللي
+
+178
+00:13:08,800 --> 00:13:11,900
+هو ال conjugate هو نفسه في حالة ال real
+
+179
+00:13:14,640 --> 00:13:19,060
+أطلع لفوق، بدنا نعرف الـNormally، if X and Y are
+
+180
+00:13:19,060 --> 00:13:22,940
+normed spaces, then is C أكبر من 0 such that for
+
+181
+00:13:22,940 --> 00:13:26,660
+all X element in X and all Y element in Y، احسبلي
+
+182
+00:13:26,660 --> 00:13:30,720
+الـabsolute value of H of X وY، ماشي؟ الـabsolute
+
+183
+00:13:30,720 --> 00:13:35,790
+value of H of X وY، لأ مش حسب، بدنا نعرففإن X وY
+
+184
+00:13:35,790 --> 00:13:39,170
+هم مجموعات عادية وكان هناك C أكبر من 0 إذا كان
+
+185
+00:13:39,170 --> 00:13:42,770
+عندي
+
+186
+00:13:42,770 --> 00:13:46,190
+H بX وY أصغر سواء C في عادية X وعادية Y إذا كان
+
+187
+00:13:46,190 --> 00:13:52,100
+هذا حدث إذا كان هذا حدث بنسميه H is boundand the
+
+188
+00:13:52,100 --> 00:13:55,980
+number normal h نفس اللي قمناها قبل اللي هو
+
+189
+00:13:55,980 --> 00:13:59,680
+supremum لهذا المقدار على norm ال X و norm ال Y ال
+
+190
+00:13:59,680 --> 00:14:02,580
+Xات اللي بيساوي نش سفر و ال Yات اللي بيساوي نش سفر
+
+191
+00:14:02,580 --> 00:14:06,700
+أو ال supremum عليهم نفسهم ال H of X و Y و هدول
+
+192
+00:14:06,700 --> 00:14:11,520
+نوماتهم ايش بيساوي بساوي واحد الان هذا بسميه اللي
+
+193
+00:14:11,520 --> 00:14:14,680
+هو norm cisquilinear اللي هو H
+
+194
+00:14:18,360 --> 00:14:22,520
+الان واضح أنه لو جيت أخدت ال H في X و Y هتصير
+
+195
+00:14:22,520 --> 00:14:25,140
+الأصغر يساوي نورم ال H في نورم ال X في نورم ال Y
+
+196
+00:14:25,140 --> 00:14:30,740
+لإنه هذه نورم ال H أكبر أو يساوي هذا على هذا لأن
+
+197
+00:14:30,740 --> 00:14:34,410
+نورم ال H هي ال supremumفأكيد h و في x و y أصغر
+
+198
+00:14:34,410 --> 00:14:38,870
+سواء normal h في normal x في normal y for all x و
+
+199
+00:14:38,870 --> 00:14:42,310
+y عندي the inner product is sesquilinear and
+
+200
+00:14:42,310 --> 00:14:46,210
+bounded و هذا طبعا أخدناه هو ولا مش هو كله أخدناه
+
+201
+00:14:46,210 --> 00:14:49,530
+أنه أصلا هو اللي قلنا عنه مثال عالمين على ال
+
+202
+00:14:49,530 --> 00:14:55,530
+sesquilinear طيب نيجي للنظرية الأخيرة عندناأطلع
+
+203
+00:14:55,530 --> 00:14:59,610
+لفظ الان الـ Raise Representation Theorem زي
+
+204
+00:14:59,610 --> 00:15:03,370
+الأولى تبع الـ Linear Functional بدنا نعمل لنين؟
+
+205
+00:15:03,370 --> 00:15:06,830
+لأ اللي هو Cisco Linear Form أو Cisco Linear
+
+206
+00:15:06,830 --> 00:15:09,490
+Functional اللي انا بقوله اذا الـ Raise
+
+207
+00:15:09,490 --> 00:15:12,910
+Representation Theorem ليه اتقدش واحد؟ انا اتقدش
+
+208
+00:15:12,910 --> 00:15:17,520
+اتنين مالهن الـ Hilbert spaces كاملة يعنيover a
+
+209
+00:15:17,520 --> 00:15:23,440
+failed mean K and H من H واحد cross H اتنين لعند K
+
+210
+00:15:23,440 --> 00:15:28,320
+فرضي أنه احنا a bounded CISC وlinear form then H
+
+211
+00:15:28,320 --> 00:15:32,100
+can be written او has a representation H of X وY
+
+212
+00:15:32,100 --> 00:15:35,300
+اش بتساوي برضه بدات يطبع على صورة mean inner
+
+213
+00:15:35,300 --> 00:15:41,430
+productاللي هي Sx دلة في الـ H واحد والـ Y where S
+
+214
+00:15:41,430 --> 00:15:44,870
+من H واحد لعند H اتنين function من H واحد لعند H
+
+215
+00:15:44,870 --> 00:15:50,490
+اتنين الان is a bounded linear operator ماشي
+
+216
+00:15:50,490 --> 00:15:55,410
+moreover normal Sاللي هو حيساو الـH و الـS is
+
+217
+00:15:55,410 --> 00:15:58,790
+uniquely determined by H and has the norm اللي هو
+
+218
+00:15:58,790 --> 00:16:01,430
+norm الـS بيساوي norm الـH إذا نفس الأولى، نفس
+
+219
+00:16:01,430 --> 00:16:07,370
+النص تقريبا بس بما يلائم اللي هو من الـH اللي هي
+
+220
+00:16:07,370 --> 00:16:10,630
+ال-cisquilinear form اللي عندي إذا الان ال
+
+221
+00:16:10,630 --> 00:16:13,610
+-cisquilinear form can be written as an inner
+
+222
+00:16:13,610 --> 00:16:17,490
+product هذا اللي هذا و الكتابة اللي هي أشمالها
+
+223
+00:16:17,490 --> 00:16:26,450
+وحيدة اطلع لفوقالان بدنا نحصل على ال S ونحصل على
+
+224
+00:16:26,450 --> 00:16:31,170
+ال H as inner product بين ال S X وY ونثبت ان norm
+
+225
+00:16:31,170 --> 00:16:37,010
+S هو norm H واحدةconsider الان f of x y conjugate
+
+226
+00:16:37,010 --> 00:16:43,030
+which is linear in y لأنها
+
+227
+00:16:43,030 --> 00:16:46,290
+كانت لحالها بدون ال conjugate اللي هي linear في
+
+228
+00:16:46,290 --> 00:16:50,870
+الأولى و conjugate linear في الثانية لما أخدناها
+
+229
+00:16:50,870 --> 00:16:54,910
+صارت اللي هي linear في مين في ال y خلينا نثبت x و
+
+230
+00:16:54,910 --> 00:16:58,610
+نشتغل على مين و كأنها صارت هذه function f of x y
+
+231
+00:16:58,610 --> 00:17:02,870
+function في مين بس في y و x arbitrary لكن fixed
+
+232
+00:17:03,740 --> 00:17:07,680
+الآن إذا هذه صارت عبارة عن linear function in Y
+
+233
+00:17:07,680 --> 00:17:12,180
+الشكل اللي بدي استخدمه من نظرية قبل شوية اللي كانت
+
+234
+00:17:12,180 --> 00:17:15,720
+.. اللي هي تحكي عن من لجيلها inner product بواسطة
+
+235
+00:17:15,720 --> 00:17:20,660
+مين اللي هتكون F linear، ماشي؟ إذا now for any
+
+236
+00:17:20,660 --> 00:17:25,220
+fixed x element in H we have a ply theorem 381
+
+237
+00:17:25,220 --> 00:17:29,880
+اللي أخدناهاto get a unique Z element in H2 that
+
+238
+00:17:29,880 --> 00:17:35,940
+depends on X لأن احنا أخدنا الآن ثبتنا X صارت عند
+
+239
+00:17:35,940 --> 00:17:40,880
+H of X معينة و Y واخدناها كونتجة صارت function في
+
+240
+00:17:40,880 --> 00:17:46,880
+مين في Y يعني حتي تاخد من H2 وترمي في مين في K في
+
+241
+00:17:46,880 --> 00:17:50,590
+ال scalar fieldماشي الحال إلى أن أنا بحكي عن X
+
+242
+00:17:50,590 --> 00:17:55,810
+محددة بين ديها هذه الآن صارت linear في ال Y مدام
+
+243
+00:17:55,810 --> 00:17:59,290
+linear في ال Y إذا بقدر ألاقي حسب النظرية اللي قبل
+
+244
+00:17:59,290 --> 00:18:02,350
+و شوية بلاقي Z بحيث أن هذه بتساوي ال inner product
+
+245
+00:18:02,350 --> 00:18:05,670
+بين اللي هو ال Y و ال Z أو ال Z و ال Y ماشي الحال
+
+246
+00:18:06,490 --> 00:18:10,530
+طيب هذه لمن؟ لـ X المحددة هذه إذا كل X هجي لها من؟
+
+247
+00:18:10,530 --> 00:18:13,910
+Z معينة أه لإن ما أضمنش كل .. هذه احنا حكيت عن X
+
+248
+00:18:13,910 --> 00:18:17,470
+معينة لو غيرت ال X هجي Z تاني و هكذا إذا صارت اللي
+
+249
+00:18:17,470 --> 00:18:21,910
+هي ال Z هذه بتعتمد على من؟ على ال X اللي عنده طيب
+
+250
+00:18:21,910 --> 00:18:28,200
+إذا و كأنه صح بده يصير ده لأ الآنقلنا to get a
+
+251
+00:18:28,200 --> 00:18:32,180
+unique z وحيدة element in h2 that depends on x
+
+252
+00:18:32,180 --> 00:18:36,380
+element in h1 such that h of x,y هذه الـ function
+
+253
+00:18:36,380 --> 00:18:40,360
+اللي عندي f of a كنا نسميها f of y بتساوي ال y و
+
+254
+00:18:40,360 --> 00:18:44,060
+ال z اللي لجيتها، معايا؟ لكن ال z تعتمد عالميا على
+
+255
+00:18:44,060 --> 00:18:49,400
+x for all y element in h2and so رجع الأمور لنصابها
+
+256
+00:18:49,400 --> 00:18:52,940
+بيصير h of x و y بتساوي ال inner product أخدت
+
+257
+00:18:52,940 --> 00:18:55,920
+الكون جيجتله الجهتين أخدت الكون جيجتله هذه و الكون
+
+258
+00:18:55,920 --> 00:19:00,120
+جيجتله هذه هذي رجعت لنفسها و هذي صارت z و y ماشي
+
+259
+00:19:00,120 --> 00:19:05,100
+الحال hence الأن الاسم h واحد أدش اتنين ايش هي
+
+260
+00:19:05,100 --> 00:19:08,940
+given by مين زي ما قولنا كل x بتلاقي لها مين z as
+
+261
+00:19:08,940 --> 00:19:13,200
+x أيش بتساوي z is an operator and h of x و y
+
+262
+00:19:13,200 --> 00:19:17,840
+بتساوياللي هو Z و Y اللي سميتها دي إيش ما لها S X
+
+263
+00:19:17,840 --> 00:19:24,560
+and for عندي أثبتت إنه أتشوف X و Y بيساوي S X و Y
+
+264
+00:19:24,560 --> 00:19:28,480
+بدنا الأن نثبت إنه هذه الأس اللي لقيناها is linear
+
+265
+00:19:28,480 --> 00:19:35,550
+ماشي طيبخدوا الأن for all x1 و x2 in element h1 و
+
+266
+00:19:35,550 --> 00:19:39,530
+y element in h2 and all scalars α احسبلي الأن ال
+
+267
+00:19:39,530 --> 00:19:44,430
+inner product S α x1 زي x2 و y بتساوي حسب اللي ..
+
+268
+00:19:44,430 --> 00:19:49,330
+اللي عرفته فوق حسب اللي أوجدته هان ايش هيساوي H of
+
+269
+00:19:49,330 --> 00:19:55,550
+اللي هي α x .. هيها من Sxy بيساوي H of xy ماشي
+
+270
+00:19:55,550 --> 00:20:02,620
+الان S of α x1 زي x2 و y بيساوي H هيهابعد هذه of α
+
+271
+00:20:02,620 --> 00:20:08,220
+X1 زي X2 أو Y Y ساوي الـ H ما هي Sys collinear
+
+272
+00:20:08,220 --> 00:20:12,620
+اللي هنا في الأولى إذا تطلع الـ Alpha H of X1 Y زي
+
+273
+00:20:12,620 --> 00:20:18,600
+H of X2 X2 أو Y هذه اللي هي مين بتمثل اللي هي
+
+274
+00:20:18,600 --> 00:20:24,760
+Alpha في S X1 أو Y وهذه بتمثل مين التانية H of X2
+
+275
+00:20:24,760 --> 00:20:31,320
+اللي هي عبارة عن S X2 ومين أو Y من هذا التعريفالان
+
+276
+00:20:31,320 --> 00:20:39,000
+صار عندي اللي هو S α X1 زي X2 وY بيساوي هذا
+
+277
+00:20:39,000 --> 00:20:43,880
+المقدار ماشي رجعوهم لبعض هيك في ال inner product
+
+278
+00:20:43,880 --> 00:20:48,380
+inner product هي Y و هي Y مظبوط هذه بندخلها هنا و
+
+279
+00:20:48,380 --> 00:20:53,280
+بنجمع هذه اللي هذه بيصير α S X1 و S X2 و Y صار هذا
+
+280
+00:20:53,280 --> 00:20:57,160
+المقدار بيساوي هذا المقدار لكل Yحسب النظرية اللي
+
+281
+00:20:57,160 --> 00:21:03,300
+قبله شوية لما قلنا اللي هو V1 و V2 و W متساويات
+
+282
+00:21:03,300 --> 00:21:07,960
+دائما إذا لازم اللي هو ال V1 سوى V2 هذه و هذه
+
+283
+00:21:07,960 --> 00:21:11,980
+بساوي هذه و هذه لكل Y إذا اللي جوا هذا بساوي اللي
+
+284
+00:21:11,980 --> 00:21:15,860
+جوا هذاإذا أصبح بايلمة تلاتة تمانين قبل بشوية
+
+285
+00:21:15,860 --> 00:21:20,740
+هيطلع S of Alpha X واحد زايد X اتنين بسوء Alpha S
+
+286
+00:21:20,740 --> 00:21:25,840
+X واحد زايد S X اتنين وهذه تعني أن الـ S is linear
+
+287
+00:21:25,840 --> 00:21:30,720
+الآن نثبت ال boundedness إذا كانت S بتساوي سفر
+
+288
+00:21:30,720 --> 00:21:34,880
+then it is bounded automatic ما أنتوا عارفين إذا
+
+289
+00:21:34,880 --> 00:21:38,460
+كانت الـ S لا تساوي سفر then احسبلي الانونومرة
+
+290
+00:21:38,460 --> 00:21:43,050
+الاتش إيش بيساوي السبريماللـ h of x و y اللي هو
+
+291
+00:21:43,050 --> 00:21:46,890
+ليش h of x و y بيساوي sxy ع normal x في normal y
+
+292
+00:21:46,890 --> 00:21:50,510
+ماشي الحال وشيل ال xات طبعا over ال xات و ال yات
+
+293
+00:21:50,510 --> 00:21:54,390
+اللي مش سفر هذه أكيد أكبر أو يساوي ال supremum لل
+
+294
+00:21:54,390 --> 00:21:59,130
+sx و لل sx normal x و normal sx x limiting h1ليش
+
+295
+00:21:59,130 --> 00:22:03,330
+هذه أكبر يساوي هذه لأن هذه المجموعة هذه المجموعة
+
+296
+00:22:03,330 --> 00:22:08,150
+اللي موخوذة على كل ال inner product S X وY وهذه
+
+297
+00:22:08,150 --> 00:22:11,770
+المجموعة هذه المجموعة بتحتوي هذه لأنها حالة خاصة
+
+298
+00:22:11,770 --> 00:22:17,270
+من هذهك بس على خدة ال Y التي عصورة من S X فأكيد ال
+
+299
+00:22:17,270 --> 00:22:20,170
+super مملال كبيرة أكبر أو يساوي ال super مملال
+
+300
+00:22:20,170 --> 00:22:25,770
+صغيرة كمجموعاتالان هذه الان بتساوي بتعمل اختصارات
+
+301
+00:22:25,770 --> 00:22:29,170
+هذه مع هذه فبصير supremum لل S X ع Normal X
+
+302
+00:22:29,170 --> 00:22:34,790
+فاهمين؟ اه و يساوي هذه اصلا تعريف مين تعريف Normal
+
+303
+00:22:34,790 --> 00:22:41,430
+S إذا صارت Normal H أكبر أو يساوي Normal S ال S
+
+304
+00:22:41,430 --> 00:22:49,010
+إذا Normal Hأكبر أو يساوي norm الـ S يعني مكاني
+
+305
+00:22:49,010 --> 00:22:54,090
+بقولي الـ S صارت bounded طيب ناخد الجهة الثانية
+
+306
+00:22:54,090 --> 00:22:57,670
+hence S is bounded and normal H أكبر يساوي normal
+
+307
+00:22:57,670 --> 00:23:02,490
+H but normal H إيش بيساوي ال superman S X was Y ع
+
+308
+00:23:02,490 --> 00:23:07,070
+normal X normal Yوهذا أصغر أو يساوي الـ Supremum،
+
+309
+00:23:07,070 --> 00:23:11,230
+بتاخد مين الآن؟ الشوارز in quality الان هذه نفسها
+
+310
+00:23:11,230 --> 00:23:14,250
+absolute value لها أصغر أو يساوي norm هذه في norm
+
+311
+00:23:14,250 --> 00:23:17,070
+هذه، لذا ال supremum على هذه هيكون أصغر أو يساوي
+
+312
+00:23:17,070 --> 00:23:21,580
+ال supremum على هذهإن هدولة هدى أكبر أو يساوي هدى
+
+313
+00:23:21,580 --> 00:23:25,500
+ما هي الان اقوم بالاختصارات هدى مح هدى فبصير SX
+
+314
+00:23:25,500 --> 00:23:29,380
+على مين على ال X وهى norm بيهن ال S إذا صارت norm
+
+315
+00:23:29,380 --> 00:23:33,420
+ال H أصغر أو يساوي norm ال S التنتين مع بعض norm
+
+316
+00:23:33,420 --> 00:23:38,990
+ال H إيش بيساوي norm ال S نثبت إنه الوحيدTo prove
+
+317
+00:23:38,990 --> 00:23:41,510
+the uniqueness, suppose that there is a linear
+
+318
+00:23:41,510 --> 00:23:46,610
+operator T تاني من H1 إلى H2 بحيث أن Hxy بيساوي
+
+319
+00:23:46,610 --> 00:23:51,610
+Sxy الأولاني و بيساوي Txy الأولاني بفرضنا جديد for
+
+320
+00:23:51,610 --> 00:23:55,670
+all x element in H1 و all y element in H2إذاً by
+
+321
+00:23:55,670 --> 00:23:59,750
+لمّا طلعت الـ 82 لقبل بشوية مزام هذا بيساوي هذا
+
+322
+00:23:59,750 --> 00:24:02,730
+لكل الوايات اللي في الدنيا إذاً هذه بتساوي هذه لكل
+
+323
+00:24:02,730 --> 00:24:06,510
+ال Xات وهذا يعني أن T بتساوي S معناته S is unique
+
+324
+00:24:06,510 --> 00:24:09,150
+وبارك الله فيكم وإلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/1BvFOhgJTvk_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/1BvFOhgJTvk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ad275f42a1befdcd241377fc5043fb42d4aebe1a
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/1BvFOhgJTvk_raw.json
@@ -0,0 +1 @@
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هذه في norm هذه، لذا ال supremum على هذه هيكون أصغر أو يساوي ال supremum على هذه", "tokens": [2407, 3224, 15730, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 2423, 39184, 9141, 2579, 449, 12399, 39894, 47283, 3215, 3714, 9957, 6024, 48506, 22807, 25124, 2407, 9640, 11622, 294, 3125, 2423, 7649, 29538, 8717, 36178, 11296, 8236, 2158, 5296, 11296, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 2026, 29538, 8978, 2026, 29538, 12399, 5296, 15730, 2423, 23710, 449, 15844, 29538, 39896, 30544, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 2423, 23710, 449, 15844, 29538], "avg_logprob": -0.30806326571805975, "compression_ratio": 1.7514124293785311, "no_speech_prob": 2.6226043701171875e-06, "words": [{"start": 1383.85, "end": 1384.33, "word": "وهذا", "probability": 0.8172200520833334}, {"start": 1384.33, "end": 1384.79, "word": " أصغر", "probability": 0.9169921875}, {"start": 1384.79, "end": 1384.95, "word": " أو", "probability": 0.87890625}, {"start": 1384.95, 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"temperature": 1.0}, {"id": 64, "seek": 141782, "start": 1398.7, "end": 1417.82, "text": "إن هدولة هدى أكبر أو يساوي هدى ما هي الان اقوم بالاختصارات هدى مح هدى فبصير SX على مين على ال X وهى norm بيهن ال S إذا صارت norm ال H أصغر أو يساوي norm ال S التنتين مع بعض norm ال H إيش بيساوي norm ال S نثبت إنه الوحيد", "tokens": [28814, 1863, 8032, 3215, 12610, 3660, 8032, 3215, 7578, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 8032, 3215, 7578, 19446, 39896, 2423, 7649, 1975, 4587, 20498, 20666, 47283, 2655, 9381, 9640, 9307, 8032, 3215, 7578, 3714, 5016, 8032, 3215, 7578, 6156, 3555, 9381, 13546, 318, 55, 15844, 3714, 9957, 15844, 2423, 1783, 37037, 7578, 2026, 4724, 1829, 3224, 1863, 2423, 318, 11933, 15730, 20328, 9640, 2655, 2026, 2423, 389, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 2026, 2423, 318, 16712, 29399, 9957, 20449, 45030, 11242, 2026, 2423, 389, 11933, 1829, 8592, 4724, 1829, 3794, 995, 45865, 2026, 2423, 318, 8717, 12984, 3555, 2655, 36145, 3224, 2423, 2407, 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" يساوي", "probability": 0.96923828125}, {"start": 1411.2, "end": 1411.46, "word": " norm", "probability": 0.625}, {"start": 1411.46, "end": 1411.6, "word": " ال", "probability": 0.58251953125}, {"start": 1411.6, "end": 1411.88, "word": " S", "probability": 0.9951171875}, {"start": 1411.88, "end": 1412.64, "word": " التنتين", "probability": 0.8167317708333334}, {"start": 1412.64, "end": 1412.8, "word": " مع", "probability": 0.99365234375}, {"start": 1412.8, "end": 1413.18, "word": " بعض", "probability": 0.9921875}, {"start": 1413.18, "end": 1413.42, "word": " norm", "probability": 0.63671875}, {"start": 1413.42, "end": 1413.54, "word": " ال", "probability": 0.90478515625}, {"start": 1413.54, "end": 1413.68, "word": " H", "probability": 0.919921875}, {"start": 1413.68, "end": 1413.84, "word": " إيش", "probability": 0.7422688802083334}, {"start": 1413.84, "end": 1414.34, "word": " بيساوي", "probability": 0.860498046875}, {"start": 1414.34, "end": 1414.92, "word": " norm", "probability": 0.5380859375}, {"start": 1414.92, "end": 1415.04, "word": " ال", "probability": 0.80712890625}, {"start": 1415.04, "end": 1415.32, "word": " S", "probability": 0.990234375}, {"start": 1415.32, "end": 1417.04, "word": " نثبت", "probability": 0.740234375}, {"start": 1417.04, "end": 1417.28, "word": " إنه", "probability": 0.692138671875}, {"start": 1417.28, "end": 1417.82, "word": " الوحيد", "probability": 0.9212646484375}], "temperature": 1.0}, {"id": 65, "seek": 143471, "start": 1418.43, "end": 1434.71, "text": "To prove the uniqueness, suppose that there is a linear operator T تاني من H1 إلى H2 بحيث أن Hxy بيساوي Sxy الأولاني و بيساوي Txy الأولاني بفرضنا جديد for all x element in H1 و all y element in H2", "tokens": [13342, 7081, 264, 48294, 11, 7297, 300, 456, 307, 257, 8213, 12973, 314, 6055, 7649, 1829, 9154, 389, 16, 30731, 389, 17, 4724, 5016, 1829, 12984, 14739, 389, 12876, 4724, 1829, 3794, 995, 45865, 318, 12876, 16247, 12610, 7649, 1829, 4032, 4724, 1829, 3794, 995, 45865, 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"probability": 0.8455403645833334}, {"start": 1436.75, "end": 1436.93, "word": " الـ", "probability": 0.551025390625}, {"start": 1436.93, "end": 1437.15, "word": " 82", "probability": 0.6181640625}, {"start": 1437.15, "end": 1437.73, "word": " لقبل", "probability": 0.6849772135416666}, {"start": 1437.73, "end": 1438.25, "word": " بشوية", "probability": 0.8798828125}, {"start": 1438.25, "end": 1438.93, "word": " مزام", "probability": 0.8131510416666666}, {"start": 1438.93, "end": 1439.21, "word": " هذا", "probability": 0.9716796875}, {"start": 1439.21, "end": 1439.55, "word": " بيساوي", "probability": 0.72919921875}, {"start": 1439.55, "end": 1439.75, "word": " هذا", "probability": 0.98291015625}, {"start": 1439.75, "end": 1440.09, "word": " لكل", "probability": 0.9560546875}, {"start": 1440.09, "end": 1440.45, "word": " الوايات", "probability": 0.7327880859375}, {"start": 1440.45, "end": 1440.57, "word": " اللي", "probability": 0.963623046875}, {"start": 1440.57, "end": 1440.65, "word": " في", "probability": 0.869140625}, {"start": 1440.65, "end": 1441.09, "word": " الدنيا", "probability": 0.9892578125}, {"start": 1441.09, "end": 1441.59, "word": " إذاً", "probability": 0.6417643229166666}, {"start": 1441.59, "end": 1441.81, "word": " هذه", "probability": 0.65625}, {"start": 1441.81, "end": 1442.21, "word": " بتساوي", "probability": 0.912353515625}, {"start": 1442.21, "end": 1442.43, "word": " هذه", "probability": 0.92724609375}, {"start": 1442.43, "end": 1442.73, "word": " لكل", "probability": 0.9736328125}, {"start": 1442.73, "end": 1442.83, "word": " ال", "probability": 0.8740234375}, {"start": 1442.83, "end": 1443.25, "word": " Xات", "probability": 0.580810546875}, {"start": 1443.25, "end": 1443.81, "word": " وهذا", "probability": 0.82373046875}, {"start": 1443.81, "end": 1444.15, "word": " يعني", "probability": 0.970703125}, {"start": 1444.15, "end": 1444.33, "word": " أن", "probability": 0.46533203125}, {"start": 1444.33, "end": 1444.63, "word": " T", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/1BvFOhgJTvk_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/1BvFOhgJTvk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a2e24f5a30a732b528af06e20ddf6a76fbb3fb7e
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/1BvFOhgJTvk_raw.srt
@@ -0,0 +1,1300 @@
+1
+00:00:05,250 --> 00:00:07,890
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,890 --> 00:00:10,650
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,650 --> 00:00:15,990
+أهلي وصحابي أجمعين هذه هي المحاضرة رقم 23 مساق
+
+4
+00:00:15,990 --> 00:00:20,050
+تحليل اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:20,050 --> 00:00:25,670
+الإسلامية قسم الرياضيات للماجستير اليوم هنحكي عن
+
+6
+00:00:25,670 --> 00:00:30,550
+تلاتة تمانية اللي هو representation of functional
+
+7
+00:00:30,550 --> 00:00:36,850
+on Hilbert spaces اللي بدنا نسويهإنه اللي هو عادة
+
+8
+00:00:36,850 --> 00:00:40,770
+لما الناس يقولكم بدأ أعمل تمثيل لشغلها بوسط شغلها
+
+9
+00:00:40,770 --> 00:00:44,970
+أكيد اللي بده يعملها الشغل الجديد اللي يعملها أحد
+
+10
+00:00:44,970 --> 00:00:48,730
+عمرين إما تكون أسهل أو إما تكون يعني الصيغة اللي
+
+11
+00:00:48,730 --> 00:00:51,990
+بده يعملها بتستخدم في أمور أخرى حتى لو كانت معقدة
+
+12
+00:00:52,240 --> 00:00:56,220
+ماشي الحال الان هذه لحسن الحظ انا بقى انا هيك وجه
+
+13
+00:00:56,220 --> 00:00:59,340
+نظري ان احنا بدنا نروح باتجاه اللي هو ناخد ال
+
+14
+00:00:59,340 --> 00:01:04,440
+functional ونوصله الى صيغة معينة الصيغة سهلة اللي
+
+15
+00:01:04,440 --> 00:01:06,640
+هو بالدكتب اللي هو ال functional بصورة inner
+
+16
+00:01:06,640 --> 00:01:09,720
+productيعني اي linear functional يعني ده اللي
+
+17
+00:01:09,720 --> 00:01:13,080
+linear functional بدك تكتبها على صورة ايش بتساوي
+
+18
+00:01:13,080 --> 00:01:16,020
+inner product و inner product لطيف يعني و الناس
+
+19
+00:01:16,020 --> 00:01:19,720
+بتحب تتعامل معاه نيجي الآن نيجي اللي هي اول نظرية
+
+20
+00:01:19,720 --> 00:01:23,920
+بنحكي فيها اللي هي دي النظرية Ray's theorem بقولك
+
+21
+00:01:23,920 --> 00:01:27,400
+every bounded linear functional on a Hilbert space
+
+22
+00:01:28,290 --> 00:01:31,710
+H can be represented in terms of inner product
+
+23
+00:01:31,710 --> 00:01:36,390
+يعني كل linear functional اللي هو of Hilbert space
+
+24
+00:01:36,390 --> 00:01:39,610
+كان بيه إيش ما لها بنقدر نكتبها على صورة inner
+
+25
+00:01:39,610 --> 00:01:43,830
+product بالظبط لو F bounded linear functional بقدر
+
+26
+00:01:43,830 --> 00:01:46,730
+أقولك أكتب لك F of X بيساوي ال inner product بين X
+
+27
+00:01:46,730 --> 00:01:52,330
+و Z حيث Z depends on F اللي بتحكي عنها أكيد لأن كل
+
+28
+00:01:52,330 --> 00:01:55,070
+واحدة بده يكونها Z معينةوالـ F is uniquely
+
+29
+00:01:55,070 --> 00:01:59,210
+determined by F with norm كمان هيطلع نورم الـ Z
+
+30
+00:01:59,210 --> 00:02:03,490
+هذا هو normية نورم الـ F هذه النظرية اللي عندنا
+
+31
+00:02:03,490 --> 00:02:07,600
+ماشي الحال اطلع خلينا نشوف ال proofالشيء الذي يظهر
+
+32
+00:02:07,600 --> 00:02:10,880
+في حالة f يتساوي 0 هو حالة الـ Z لأنه على طول
+
+33
+00:02:10,880 --> 00:02:14,280
+تلاقي الـ Z يتساوي 0 بيصير f of x يتساوي x و 0
+
+34
+00:02:14,280 --> 00:02:17,760
+بيصير الهي الهي الهي الهي الهي الهي الهي الهي الهي
+
+35
+00:02:17,760 --> 00:02:18,600
+الهي الهي الهي الهي الهي الهي الهي الهي الهي الهي
+
+36
+00:02:18,600 --> 00:02:18,600
+الهي الهي الهي الهي الهي الهي الهي الهي الهي الهي
+
+37
+00:02:18,600 --> 00:02:19,440
+الهي الهي الهي الهي الهي الهي الهي الهي الهي الهي
+
+38
+00:02:19,440 --> 00:02:21,680
+الهي الهي الهي الهي الهي الهي الهي الهي الهي الهي
+
+39
+00:02:21,680 --> 00:02:22,240
+الهي الهي الهي الهي ال
+
+40
+00:02:27,870 --> 00:02:32,850
+بما أن F لا تساوي سفر إذا يعني مافيش حاجة تقول لي
+
+41
+00:02:32,850 --> 00:02:37,230
+إن كل العناصر هتروح للسفر يعني ال null F مش هيكون
+
+42
+00:02:37,230 --> 00:02:40,330
+ال H اللي هو ال null space ال null space هو عبارة
+
+43
+00:02:40,330 --> 00:02:44,690
+عن super zero مدان فيه صورة مش zero إذا أكيد مالها
+
+44
+00:02:44,690 --> 00:02:48,840
+ال null F في شمالها مش كل ال H كاملةطيب لكن احنا
+
+45
+00:02:48,840 --> 00:02:52,540
+قبل هيك قلنا N of S from null space is a closed
+
+46
+00:02:52,540 --> 00:02:55,980
+subspace of H طيب ماذا يعمل closed subspace لـ H
+
+47
+00:02:55,980 --> 00:02:59,440
+ده الأمور حلوة في الدنيا بالصحيحة إذا من theorem
+
+48
+00:02:59,440 --> 00:03:04,080
+334 بقدر اكتب H اللي هي ال complete على صورة
+
+49
+00:03:04,080 --> 00:03:07,240
+closed subspace N of S و ال orthogonal complement
+
+50
+00:03:07,240 --> 00:03:11,580
+له اللي هو N of إيه أش orthogonal كتبت على صورة
+
+51
+00:03:11,580 --> 00:03:17,890
+direct sum من الـ Hطبعا هنا ال N of F مش H إذا ال
+
+52
+00:03:17,890 --> 00:03:21,770
+N of F Orthogonal مش Zero إذا ال N of F Orthogonal
+
+53
+00:03:21,770 --> 00:03:25,330
+ليسوا Zero فما دام هيك ما دام مش Zero إذا بقدر
+
+54
+00:03:25,330 --> 00:03:29,830
+أجيلي اللي هو Z not لات سوى سفر و Z not وين موجودة
+
+55
+00:03:29,830 --> 00:03:35,340
+في ال N of F Orthogonal طيبطيب الآن منها هذه بدي
+
+56
+00:03:35,340 --> 00:03:38,820
+أصنع اللي بدي .. اللي بدي أصل لمين للـ z اللي فوق
+
+57
+00:03:38,820 --> 00:03:42,220
+ماشي الحالة بواسطة هذه و بواسطة ال F اللي هي اللي
+
+58
+00:03:42,220 --> 00:03:46,380
+عندي المعتار الآن صارت عندي z note بين إيديا و ال
+
+59
+00:03:46,380 --> 00:03:52,340
+F عندي معتار بقولك 6 الآن أو اللي هو ركّب التركيبة
+
+60
+00:03:52,340 --> 00:03:57,880
+التالية ضرب ل z note في F of X X arbitrary fixed
+
+61
+00:03:57,880 --> 00:04:02,800
+pointو X في مين في أفه في Z نوت و حاصل الطرح سميه
+
+62
+00:04:02,800 --> 00:04:06,980
+مين هنا V و مقصودة ان هذي هذي Z نوت وهنا X وهنا X
+
+63
+00:04:06,980 --> 00:04:10,790
+وهنا Z نوت مقصودة على الطرحWhere X is an arbitrary
+
+64
+00:04:10,790 --> 00:04:16,690
+element in H since F is linear إذا لو جيت حسبت ال
+
+65
+00:04:16,690 --> 00:04:21,290
+F of V هذي بيصير عدد بتطلع براها فبصير F of Z0 في
+
+66
+00:04:21,290 --> 00:04:25,310
+F of X و هذي بيصير عدد بتطلع برا ال F بيصير ناقص F
+
+67
+00:04:25,310 --> 00:04:29,250
+of X في F of Z0 حصلت رحلنا إيش بيساوي؟ بيساوي 0
+
+68
+00:04:29,250 --> 00:04:34,370
+صارت ال V هذه اللي اخترتها هذه where موجودة في ال
+
+69
+00:04:34,370 --> 00:04:39,200
+null في ال null of Fإذا صارت الـ V عمودية على مين؟
+
+70
+00:04:39,200 --> 00:04:41,400
+على الـ Z note اللي هي اللي موجودة في الـ N of
+
+71
+00:04:41,400 --> 00:04:45,160
+orthogonal إذا صار عندي مدام عمودية عليها إذا صار
+
+72
+00:04:45,160 --> 00:04:48,580
+عندي ال inner product بين ال V و Z note صفر ال V
+
+73
+00:04:48,580 --> 00:04:52,380
+حقق اللي قيمتها اللي هي Z note و F of X ناقص X في
+
+74
+00:04:52,380 --> 00:04:56,640
+F و Z note و Z note استخدم خلاص ال inner product و
+
+75
+00:04:56,640 --> 00:05:00,460
+طلعلي هدولة برا و ارتبليياه فبصير F of X في Z note
+
+76
+00:05:00,460 --> 00:05:04,770
+و Z يعني هادي مع هادي ناقص هادي مع هاديبصير عندى F
+
+77
+00:05:04,770 --> 00:05:09,190
+of X فى Z0 و Z ناقص اللى هى F of Z0 بتطلع و X و
+
+78
+00:05:09,190 --> 00:05:13,770
+مين و Z0 معايا الآن صار عندى أي واجهة عندها دى
+
+79
+00:05:13,770 --> 00:05:18,970
+صارت عندى هذا المقدار بساوي سفر انجللي هذا على
+
+80
+00:05:18,970 --> 00:05:23,890
+الطرف التانى ماشي الحال و اجسملي اللى هو على Z و
+
+81
+00:05:23,890 --> 00:05:28,450
+Z0 فبصير F of X إيش هتساوي اللى هو هذا المقدار على
+
+82
+00:05:28,450 --> 00:05:32,890
+Z و Z0 بصير اللى هى F of Z0 على Z و Z0 فى X و مين
+
+83
+00:05:32,890 --> 00:05:39,340
+و Z0واضح معايا
+
+84
+00:05:39,340 --> 00:05:43,760
+يا جماعة إذا F of X صارت عبارة عن F of Z note على
+
+85
+00:05:43,760 --> 00:05:47,920
+Z of Z note في X of Z note واضحة اتها وبيساوي الان
+
+86
+00:05:47,920 --> 00:05:52,300
+دخلوليها دي علي بعيد عشان بتاخد Z انا بتلاحظ ال Z
+
+87
+00:05:52,300 --> 00:05:57,900
+فبصير X of F of Z note على اللي هو Z note و Z note
+
+88
+00:05:57,900 --> 00:06:04,490
+و main و Z noteماشي الان عندي X was arbitrary اذا
+
+89
+00:06:04,490 --> 00:06:07,530
+لو اجينا اخدنا صارت الان F of X بالساوية القيمة
+
+90
+00:06:07,530 --> 00:06:12,350
+هذه هذه صارت بين إيديا مبنية ال Z note وهذه بين
+
+91
+00:06:12,350 --> 00:06:18,270
+إيديا ماشي الحال كل هذه كل هذه هي اللي سميه ليهاش
+
+92
+00:06:18,270 --> 00:06:23,910
+Z إذا صار عندى الآن حصلنا F of X بالساوية X ومين
+
+93
+00:06:23,910 --> 00:06:30,620
+وZ هاي واحدالآن بدي أثبتلك اللي هو عندي بدي أثبتلك
+
+94
+00:06:30,620 --> 00:06:33,420
+أنه وحيدة و بعدين بدي أثبتلك norm هذه بيسوي normين
+
+95
+00:06:33,420 --> 00:06:36,760
+الـ z خلّيني واحدة واحدة to prove the uniqueness
+
+96
+00:06:36,760 --> 00:06:40,840
+of z suppose that there are z واحد and z اتنين
+
+97
+00:06:40,840 --> 00:06:44,940
+such that f of x بيسوي x و z واحد و f of x بيسوي x
+
+98
+00:06:44,940 --> 00:06:48,940
+و z اتنين وهذه سهلة for all x المتناشر إذا جيب هنا
+
+99
+00:06:48,940 --> 00:06:51,440
+دولة جانب بعض و اترحى من بعض بيطلع من ساوي سفر
+
+100
+00:06:51,440 --> 00:06:56,950
+اترحى انش هيكون x و z واحد ناقص 2 z اتنينالآن عندي
+
+101
+00:06:56,950 --> 00:07:00,570
+هذا الكلام صحيح لكل x والتي موجودة في الـ H مضمنها
+
+102
+00:07:00,570 --> 00:07:06,770
+هي z1-z2 في الـ H إذا صار z1-z2 إذا z1-z2 بيساوي 0
+
+103
+00:07:06,770 --> 00:07:10,370
+إذا ال norm هنا بيساوي 0 إذا z1 بيساوي z0 وهذا
+
+104
+00:07:10,370 --> 00:07:13,890
+بيثبت ال uniqueness الآن أنزلوا شوية، أنزلوا،
+
+105
+00:07:13,890 --> 00:07:18,510
+أنزلوا، بنرجع نثبت مين الآن عندي اللي هو normal F
+
+106
+00:07:18,510 --> 00:07:25,890
+بيساوي normal z، normal Fبساوي norm الـ z احنا
+
+107
+00:07:25,890 --> 00:07:29,890
+قلنا f of x ايش هتساوي ال inner product بين x و z
+
+108
+00:07:29,890 --> 00:07:34,110
+صح ولا لأ؟ لأن خدولي ال absolute value للجهتين او
+
+109
+00:07:34,110 --> 00:07:38,530
+ال modulus هذا بشوارز ال quality بصير اصغر هو
+
+110
+00:07:38,530 --> 00:07:44,190
+يساوي norm ال x في norm main ال z لأن اجسمول
+
+111
+00:07:44,190 --> 00:07:46,170
+الجهتين على norm ال x اللي هي ال xات اللي بيساوي
+
+112
+00:07:46,170 --> 00:07:52,230
+نش سفر فبصير f of xعلى نورم الـ x أصغر شوه نورم
+
+113
+00:07:52,230 --> 00:07:55,730
+مين الـ z صارت هذه upper bound لهذه إذا أكيد ال
+
+114
+00:07:55,730 --> 00:07:57,730
+suprem لهادي أصغر شوه هذه اللي هو اللي is upper
+
+115
+00:07:57,730 --> 00:08:03,410
+bound إذا ال suprem لهادي over x element أتش و x
+
+116
+00:08:03,410 --> 00:08:08,810
+لا تشوه سفر بيصير عندي هذا كله اسمه مين نورم ال F
+
+117
+00:08:08,810 --> 00:08:12,950
+إذا صار نورم ال F أصغر شوه مين نورم ال Z هاي واحدة
+
+118
+00:08:12,950 --> 00:08:18,170
+الان الاتجاه الثاني الاتجاه الثاني خدوا الآن عندي
+
+119
+00:08:18,170 --> 00:08:27,860
+F of Xبساوي ايش يا جماعة X و Z صح ولا لأن
+
+120
+00:08:27,860 --> 00:08:33,220
+F of Z ايش بساوي اللي انها ال product بين Z و مين
+
+121
+00:08:33,220 --> 00:08:46,220
+و Z صح و يساوي مين نورم Z تربيه باشي الحال عند
+
+122
+00:08:46,220 --> 00:08:50,110
+نورم ال Fأكيد اللي عندي absolute value of f of z
+
+123
+00:08:50,110 --> 00:08:55,790
+بساوي نورم الـ z تربيع صح ولا لأ؟ باين هاه؟ باين
+
+124
+00:08:55,790 --> 00:09:04,090
+هاه؟ هذه الآن أكبر أو يساوي اللي هو norm of f of a
+
+125
+00:09:04,090 --> 00:09:05,830
+من norm of f نفسها
+
+126
+00:09:09,670 --> 00:09:14,410
+ماشي الحال عند نورم ال F أصغر أو يشاوي نورم ال ..
+
+127
+00:09:14,410 --> 00:09:20,810
+ال .. الأكبر آسف شو هو هذي اللي هي السبرما نورم ال
+
+128
+00:09:20,810 --> 00:09:25,470
+F السبرما وهذه نقطة منها بيصير نورم ال F أكبر
+
+129
+00:09:25,470 --> 00:09:29,630
+شاومين نورم ال Z هي أكبر شاومين نورم ال Z وهي أصغر
+
+130
+00:09:29,630 --> 00:09:34,290
+أو يشاوي نورم ال Z من التنتين مع بعض اشمالهمعايا
+
+131
+00:09:34,290 --> 00:09:37,670
+يا جماعة هاد نورم ال F أصغر و ساوي و هاد نورم ال F
+
+132
+00:09:37,670 --> 00:09:40,770
+أكبر و ساوي التنتين مع بعض اللي هو بيصير نورم ال F
+
+133
+00:09:40,770 --> 00:09:47,010
+ساوي نورم ال Z يلا اللي بعدها نيجي الأن لما هاد
+
+134
+00:09:47,010 --> 00:09:47,770
+المم سهلة
+
+135
+00:09:50,440 --> 00:09:54,320
+ف V1 و W .. مش عارف ايش كتبها اصلا V2 و W for all
+
+136
+00:09:54,320 --> 00:09:58,980
+W in inner product space X then V1 بيساوي V2 in
+
+137
+00:09:58,980 --> 00:10:02,180
+particular V1 و W بيساوي 0 for all W المتن X
+
+138
+00:10:02,180 --> 00:10:06,100
+implies that V1 بيساوي مين؟ سفر هذا exercise بسيط
+
+139
+00:10:06,100 --> 00:10:13,320
+يعني .. طب و في أثناء البرهان اللي برهنناها اللي
+
+140
+00:10:13,320 --> 00:10:28,520
+قبل و شوية هنشوفها عند ما أعطيني V1و V2 و V1
+
+141
+00:10:28,520 --> 00:10:32,800
+و V2 في ال Xبقول إذا كان هذا بساوة داك معناته V1
+
+142
+00:10:32,800 --> 00:10:36,700
+بساوة V2 فكي ترجله هذا على الجهة تاني بيصيح V1 نقص
+
+143
+00:10:36,700 --> 00:10:40,680
+V2 و W عملتها قبل شوية بساوة سفر هذا لكل W من ضمن
+
+144
+00:10:40,680 --> 00:10:47,340
+هم مين V1 نقص V2 لأن V1 نقص V2 و V1 نقص V2 بساوة
+
+145
+00:10:47,340 --> 00:10:52,160
+سفر أو منه اللي هو V1 بساوة V2 لأنه ال norm تربيعي
+
+146
+00:10:52,160 --> 00:10:55,800
+بساوة سفر لأن V1 بساوة V2 إلى اللي بعدها حالة خاصة
+
+147
+00:10:55,800 --> 00:11:00,730
+منها إذا كانت V1 و W بساوة سفر لكل W في ال Xإذا
+
+148
+00:11:00,730 --> 00:11:04,530
+سأكون من ضمن الـ W V1 يصبح V1 و V1 بالساعة و سفر و
+
+149
+00:11:04,530 --> 00:11:06,370
+V1 بالساعة و سفر وهو المطلوب
+
+150
+00:11:11,800 --> 00:11:16,200
+حكينا كان عن ال linear .. اطلع لفوق شوية حكينا عن
+
+151
+00:11:16,200 --> 00:11:20,000
+ال linear functional الآن عرفنا احنا قبل هيك ال
+
+152
+00:11:20,000 --> 00:11:23,900
+bilinear بتكون linear في الجهتين اه يعني function
+
+153
+00:11:23,900 --> 00:11:25,800
+of two variables بتكون linear في الأولى و linear
+
+154
+00:11:25,800 --> 00:11:29,120
+في التانية sesquilinear بتكون linear في الأولى و
+
+155
+00:11:29,120 --> 00:11:31,880
+التانية conjugate linear يعني مش linear .. زي اللي
+
+156
+00:11:31,880 --> 00:11:34,980
+انار ال product .. زي اللي بنار ال productالـ
+
+157
+00:11:34,980 --> 00:11:37,860
+Liner Product Linear في الأولى لكن في الـ Inter
+
+158
+00:11:37,860 --> 00:11:40,560
+التاني هي إيش ماله Conjugate Linear لما يطلع يطلع
+
+159
+00:11:40,560 --> 00:11:44,180
+يبقى إيش و Conjugate فعشان هيك بنسميه Cisco Linear
+
+160
+00:11:44,180 --> 00:11:49,300
+إذا نقول بالظبط إيش اللي بتحكيه هذا بقول الآن let
+
+161
+00:11:49,300 --> 00:11:53,920
+X and Y be vector spaces over a field K تنين over
+
+162
+00:11:53,920 --> 00:11:59,420
+the same fieldلأن a sesquilinear form أو
+
+163
+00:11:59,420 --> 00:12:04,320
+sesquilinear functional H هو عبارة عن ده لمن X
+
+164
+00:12:04,320 --> 00:12:09,700
+cross Y لمين للـ scalar field تبع حينكي إيش بيحقق؟
+
+165
+00:12:09,700 --> 00:12:14,240
+بيحقق إنه linear في الأولى و conjugate linear في
+
+166
+00:12:14,240 --> 00:12:19,920
+التانية، ماشي؟إيش يعني أنه لكل X1 و X2 و X في الـ
+
+167
+00:12:19,920 --> 00:12:24,280
+X و Y1 و Y2 نقوله بـ Y و كل Scale as Alpha Beta
+
+168
+00:12:24,280 --> 00:12:31,360
+تحقق مالي H of X1 زاد X2 و Y بتساوي H of X1 و Y
+
+169
+00:12:31,360 --> 00:12:36,440
+زاد H of X2 و Y زي ال inner productالان اتشوف x و
+
+170
+00:12:36,440 --> 00:12:39,720
+y واحد زي اضاءة y اتنين بالساوية اتشوف x واحد و y
+
+171
+00:12:39,720 --> 00:12:44,960
+واحد زي اتشوف x و y اتنين اللي نهار اتعادى بس لان
+
+172
+00:12:44,960 --> 00:12:47,280
+لما ندخل ال scalar بصير انا conjugate و انا مش
+
+173
+00:12:47,280 --> 00:12:50,620
+conjugateلأن H في Alpha X و Y بيسوي Alpha H X و Y
+
+174
+00:12:50,620 --> 00:12:53,800
+إذا ال linear صارت في ال entry الأول في ال entry
+
+175
+00:12:53,800 --> 00:12:57,020
+التاني بتطلع بيه conjugate يعني اللي هو conjugate
+
+176
+00:12:57,020 --> 00:13:01,720
+linear هذا كله مع بعض بنسميه Cisco linear لو لو
+
+177
+00:13:01,720 --> 00:13:06,200
+كانت K بيتساوي R ال above بنسميه إيش ماله bilinear
+
+178
+00:13:06,200 --> 00:13:08,800
+لإن مافيش حاجة اسمها conjugate حيصير إيش ماله اللي
+
+179
+00:13:08,800 --> 00:13:11,900
+هو ال conjugate هو نفسه في حالة ال real
+
+180
+00:13:14,640 --> 00:13:19,060
+أطلع لفوق، بدنا نعرف الـNormally، if X and Y are
+
+181
+00:13:19,060 --> 00:13:22,940
+normed spaces, then is C أكبر من 0 such that for
+
+182
+00:13:22,940 --> 00:13:26,660
+all X element in X and all Y element in Y، احسبلي
+
+183
+00:13:26,660 --> 00:13:30,720
+الـabsolute value of H of X وY، ماشي؟ الـabsolute
+
+184
+00:13:30,720 --> 00:13:35,790
+value of H of X وY، لأ مش حسب، بدنا نعرففإن X وY
+
+185
+00:13:35,790 --> 00:13:39,170
+هم مجموعات عادية وكان هناك C أكبر من 0 إذا كان
+
+186
+00:13:39,170 --> 00:13:42,770
+عندي
+
+187
+00:13:42,770 --> 00:13:46,190
+H بX وY أصغر سواء C في عادية X وعادية Y إذا كان
+
+188
+00:13:46,190 --> 00:13:52,100
+هذا حدث إذا كان هذا حدث بنسميه H is boundand the
+
+189
+00:13:52,100 --> 00:13:55,980
+number normal h نفس اللي قمناها قبل اللي هو
+
+190
+00:13:55,980 --> 00:13:59,680
+supremum لهذا المقدار على norm ال X و norm ال Y ال
+
+191
+00:13:59,680 --> 00:14:02,580
+Xات اللي بيساوي نش سفر و ال Yات اللي بيساوي نش سفر
+
+192
+00:14:02,580 --> 00:14:06,700
+أو ال supremum عليهم نفسهم ال H of X و Y و هدول
+
+193
+00:14:06,700 --> 00:14:11,520
+نوماتهم ايش بيساوي بساوي واحد الان هذا بسميه اللي
+
+194
+00:14:11,520 --> 00:14:14,680
+هو norm cisquilinear اللي هو H
+
+195
+00:14:18,360 --> 00:14:22,520
+الان واضح أنه لو جيت أخدت ال H في X و Y هتصير
+
+196
+00:14:22,520 --> 00:14:25,140
+الأصغر يساوي نورم ال H في نورم ال X في نورم ال Y
+
+197
+00:14:25,140 --> 00:14:30,740
+لإنه هذه نورم ال H أكبر أو يساوي هذا على هذا لأن
+
+198
+00:14:30,740 --> 00:14:34,410
+نورم ال H هي ال supremumفأكيد h و في x و y أصغر
+
+199
+00:14:34,410 --> 00:14:38,870
+سواء normal h في normal x في normal y for all x و
+
+200
+00:14:38,870 --> 00:14:42,310
+y عندي the inner product is sesquilinear and
+
+201
+00:14:42,310 --> 00:14:46,210
+bounded و هذا طبعا أخدناه هو ولا مش هو كله أخدناه
+
+202
+00:14:46,210 --> 00:14:49,530
+أنه أصلا هو اللي قلنا عنه مثال عالمين على ال
+
+203
+00:14:49,530 --> 00:14:55,530
+sesquilinear طيب نيجي للنظرية الأخيرة عندناأطلع
+
+204
+00:14:55,530 --> 00:14:59,610
+لفظ الان الـ Raise Representation Theorem زي
+
+205
+00:14:59,610 --> 00:15:03,370
+الأولى تبع الـ Linear Functional بدنا نعمل لنين؟
+
+206
+00:15:03,370 --> 00:15:06,830
+لأ اللي هو Cisco Linear Form أو Cisco Linear
+
+207
+00:15:06,830 --> 00:15:09,490
+Functional اللي انا بقوله اذا الـ Raise
+
+208
+00:15:09,490 --> 00:15:12,910
+Representation Theorem ليه اتقدش واحد؟ انا اتقدش
+
+209
+00:15:12,910 --> 00:15:17,520
+اتنين مالهن الـ Hilbert spaces كاملة يعنيover a
+
+210
+00:15:17,520 --> 00:15:23,440
+failed mean K and H من H واحد cross H اتنين لعند K
+
+211
+00:15:23,440 --> 00:15:28,320
+فرضي أنه احنا a bounded CISC وlinear form then H
+
+212
+00:15:28,320 --> 00:15:32,100
+can be written او has a representation H of X وY
+
+213
+00:15:32,100 --> 00:15:35,300
+اش بتساوي برضه بدات يطبع على صورة mean inner
+
+214
+00:15:35,300 --> 00:15:41,430
+productاللي هي Sx دلة في الـ H واحد والـ Y where S
+
+215
+00:15:41,430 --> 00:15:44,870
+من H واحد لعند H اتنين function من H واحد لعند H
+
+216
+00:15:44,870 --> 00:15:50,490
+اتنين الان is a bounded linear operator ماشي
+
+217
+00:15:50,490 --> 00:15:55,410
+moreover normal Sاللي هو حيساو الـH و الـS is
+
+218
+00:15:55,410 --> 00:15:58,790
+uniquely determined by H and has the norm اللي هو
+
+219
+00:15:58,790 --> 00:16:01,430
+norm الـS بيساوي norm الـH إذا نفس الأولى، نفس
+
+220
+00:16:01,430 --> 00:16:07,370
+النص تقريبا بس بما يلائم اللي هو من الـH اللي هي
+
+221
+00:16:07,370 --> 00:16:10,630
+ال-cisquilinear form اللي عندي إذا الان ال
+
+222
+00:16:10,630 --> 00:16:13,610
+-cisquilinear form can be written as an inner
+
+223
+00:16:13,610 --> 00:16:17,490
+product هذا اللي هذا و الكتابة اللي هي أشمالها
+
+224
+00:16:17,490 --> 00:16:26,450
+وحيدة اطلع لفوقالان بدنا نحصل على ال S ونحصل على
+
+225
+00:16:26,450 --> 00:16:31,170
+ال H as inner product بين ال S X وY ونثبت ان norm
+
+226
+00:16:31,170 --> 00:16:37,010
+S هو norm H واحدةconsider الان f of x y conjugate
+
+227
+00:16:37,010 --> 00:16:43,030
+which is linear in y لأنها
+
+228
+00:16:43,030 --> 00:16:46,290
+كانت لحالها بدون ال conjugate اللي هي linear في
+
+229
+00:16:46,290 --> 00:16:50,870
+الأولى و conjugate linear في الثانية لما أخدناها
+
+230
+00:16:50,870 --> 00:16:54,910
+صارت اللي هي linear في مين في ال y خلينا نثبت x و
+
+231
+00:16:54,910 --> 00:16:58,610
+نشتغل على مين و كأنها صارت هذه function f of x y
+
+232
+00:16:58,610 --> 00:17:02,870
+function في مين بس في y و x arbitrary لكن fixed
+
+233
+00:17:03,740 --> 00:17:07,680
+الآن إذا هذه صارت عبارة عن linear function in Y
+
+234
+00:17:07,680 --> 00:17:12,180
+الشكل اللي بدي استخدمه من نظرية قبل شوية اللي كانت
+
+235
+00:17:12,180 --> 00:17:15,720
+.. اللي هي تحكي عن من لجيلها inner product بواسطة
+
+236
+00:17:15,720 --> 00:17:20,660
+مين اللي هتكون F linear، ماشي؟ إذا now for any
+
+237
+00:17:20,660 --> 00:17:25,220
+fixed x element in H we have a ply theorem 381
+
+238
+00:17:25,220 --> 00:17:29,880
+اللي أخدناهاto get a unique Z element in H2 that
+
+239
+00:17:29,880 --> 00:17:35,940
+depends on X لأن احنا أخدنا الآن ثبتنا X صارت عند
+
+240
+00:17:35,940 --> 00:17:40,880
+H of X معينة و Y واخدناها كونتجة صارت function في
+
+241
+00:17:40,880 --> 00:17:46,880
+مين في Y يعني حتي تاخد من H2 وترمي في مين في K في
+
+242
+00:17:46,880 --> 00:17:50,590
+ال scalar fieldماشي الحال إلى أن أنا بحكي عن X
+
+243
+00:17:50,590 --> 00:17:55,810
+محددة بين ديها هذه الآن صارت linear في ال Y مدام
+
+244
+00:17:55,810 --> 00:17:59,290
+linear في ال Y إذا بقدر ألاقي حسب النظرية اللي قبل
+
+245
+00:17:59,290 --> 00:18:02,350
+و شوية بلاقي Z بحيث أن هذه بتساوي ال inner product
+
+246
+00:18:02,350 --> 00:18:05,670
+بين اللي هو ال Y و ال Z أو ال Z و ال Y ماشي الحال
+
+247
+00:18:06,490 --> 00:18:10,530
+طيب هذه لمن؟ لـ X المحددة هذه إذا كل X هجي لها من؟
+
+248
+00:18:10,530 --> 00:18:13,910
+Z معينة أه لإن ما أضمنش كل .. هذه احنا حكيت عن X
+
+249
+00:18:13,910 --> 00:18:17,470
+معينة لو غيرت ال X هجي Z تاني و هكذا إذا صارت اللي
+
+250
+00:18:17,470 --> 00:18:21,910
+هي ال Z هذه بتعتمد على من؟ على ال X اللي عنده طيب
+
+251
+00:18:21,910 --> 00:18:28,200
+إذا و كأنه صح بده يصير ده لأ الآنقلنا to get a
+
+252
+00:18:28,200 --> 00:18:32,180
+unique z وحيدة element in h2 that depends on x
+
+253
+00:18:32,180 --> 00:18:36,380
+element in h1 such that h of x,y هذه الـ function
+
+254
+00:18:36,380 --> 00:18:40,360
+اللي عندي f of a كنا نسميها f of y بتساوي ال y و
+
+255
+00:18:40,360 --> 00:18:44,060
+ال z اللي لجيتها، معايا؟ لكن ال z تعتمد عالميا على
+
+256
+00:18:44,060 --> 00:18:49,400
+x for all y element in h2and so رجع الأمور لنصابها
+
+257
+00:18:49,400 --> 00:18:52,940
+بيصير h of x و y بتساوي ال inner product أخدت
+
+258
+00:18:52,940 --> 00:18:55,920
+الكون جيجتله الجهتين أخدت الكون جيجتله هذه و الكون
+
+259
+00:18:55,920 --> 00:19:00,120
+جيجتله هذه هذي رجعت لنفسها و هذي صارت z و y ماشي
+
+260
+00:19:00,120 --> 00:19:05,100
+الحال hence الأن الاسم h واحد أدش اتنين ايش هي
+
+261
+00:19:05,100 --> 00:19:08,940
+given by مين زي ما قولنا كل x بتلاقي لها مين z as
+
+262
+00:19:08,940 --> 00:19:13,200
+x أيش بتساوي z is an operator and h of x و y
+
+263
+00:19:13,200 --> 00:19:17,840
+بتساوياللي هو Z و Y اللي سميتها دي إيش ما لها S X
+
+264
+00:19:17,840 --> 00:19:24,560
+and for عندي أثبتت إنه أتشوف X و Y بيساوي S X و Y
+
+265
+00:19:24,560 --> 00:19:28,480
+بدنا الأن نثبت إنه هذه الأس اللي لقيناها is linear
+
+266
+00:19:28,480 --> 00:19:35,550
+ماشي طيبخدوا الأن for all x1 و x2 in element h1 و
+
+267
+00:19:35,550 --> 00:19:39,530
+y element in h2 and all scalars α احسبلي الأن ال
+
+268
+00:19:39,530 --> 00:19:44,430
+inner product S α x1 زي x2 و y بتساوي حسب اللي ..
+
+269
+00:19:44,430 --> 00:19:49,330
+اللي عرفته فوق حسب اللي أوجدته هان ايش هيساوي H of
+
+270
+00:19:49,330 --> 00:19:55,550
+اللي هي α x .. هيها من Sxy بيساوي H of xy ماشي
+
+271
+00:19:55,550 --> 00:20:02,620
+الان S of α x1 زي x2 و y بيساوي H هيهابعد هذه of α
+
+272
+00:20:02,620 --> 00:20:08,220
+X1 زي X2 أو Y Y ساوي الـ H ما هي Sys collinear
+
+273
+00:20:08,220 --> 00:20:12,620
+اللي هنا في الأولى إذا تطلع الـ Alpha H of X1 Y زي
+
+274
+00:20:12,620 --> 00:20:18,600
+H of X2 X2 أو Y هذه اللي هي مين بتمثل اللي هي
+
+275
+00:20:18,600 --> 00:20:24,760
+Alpha في S X1 أو Y وهذه بتمثل مين التانية H of X2
+
+276
+00:20:24,760 --> 00:20:31,320
+اللي هي عبارة عن S X2 ومين أو Y من هذا التعريفالان
+
+277
+00:20:31,320 --> 00:20:39,000
+صار عندي اللي هو S α X1 زي X2 وY بيساوي هذا
+
+278
+00:20:39,000 --> 00:20:43,880
+المقدار ماشي رجعوهم لبعض هيك في ال inner product
+
+279
+00:20:43,880 --> 00:20:48,380
+inner product هي Y و هي Y مظبوط هذه بندخلها هنا و
+
+280
+00:20:48,380 --> 00:20:53,280
+بنجمع هذه اللي هذه بيصير α S X1 و S X2 و Y صار هذا
+
+281
+00:20:53,280 --> 00:20:57,160
+المقدار بيساوي هذا المقدار لكل Yحسب النظرية اللي
+
+282
+00:20:57,160 --> 00:21:03,300
+قبله شوية لما قلنا اللي هو V1 و V2 و W متساويات
+
+283
+00:21:03,300 --> 00:21:07,960
+دائما إذا لازم اللي هو ال V1 سوى V2 هذه و هذه
+
+284
+00:21:07,960 --> 00:21:11,980
+بساوي هذه و هذه لكل Y إذا اللي جوا هذا بساوي اللي
+
+285
+00:21:11,980 --> 00:21:15,860
+جوا هذاإذا أصبح بايلمة تلاتة تمانين قبل بشوية
+
+286
+00:21:15,860 --> 00:21:20,740
+هيطلع S of Alpha X واحد زايد X اتنين بسوء Alpha S
+
+287
+00:21:20,740 --> 00:21:25,840
+X واحد زايد S X اتنين وهذه تعني أن الـ S is linear
+
+288
+00:21:25,840 --> 00:21:30,720
+الآن نثبت ال boundedness إذا كانت S بتساوي سفر
+
+289
+00:21:30,720 --> 00:21:34,880
+then it is bounded automatic ما أنتوا عارفين إذا
+
+290
+00:21:34,880 --> 00:21:38,460
+كانت الـ S لا تساوي سفر then احسبلي الانونومرة
+
+291
+00:21:38,460 --> 00:21:43,050
+الاتش إيش بيساوي السبريماللـ h of x و y اللي هو
+
+292
+00:21:43,050 --> 00:21:46,890
+ليش h of x و y بيساوي sxy ع normal x في normal y
+
+293
+00:21:46,890 --> 00:21:50,510
+ماشي الحال وشيل ال xات طبعا over ال xات و ال yات
+
+294
+00:21:50,510 --> 00:21:54,390
+اللي مش سفر هذه أكيد أكبر أو يساوي ال supremum لل
+
+295
+00:21:54,390 --> 00:21:59,130
+sx و لل sx normal x و normal sx x limiting h1ليش
+
+296
+00:21:59,130 --> 00:22:03,330
+هذه أكبر يساوي هذه لأن هذه المجموعة هذه المجموعة
+
+297
+00:22:03,330 --> 00:22:08,150
+اللي موخوذة على كل ال inner product S X وY وهذه
+
+298
+00:22:08,150 --> 00:22:11,770
+المجموعة هذه المجموعة بتحتوي هذه لأنها حالة خاصة
+
+299
+00:22:11,770 --> 00:22:17,270
+من هذهك بس على خدة ال Y التي عصورة من S X فأكيد ال
+
+300
+00:22:17,270 --> 00:22:20,170
+super مملال كبيرة أكبر أو يساوي ال super مملال
+
+301
+00:22:20,170 --> 00:22:25,770
+صغيرة كمجموعاتالان هذه الان بتساوي بتعمل اختصارات
+
+302
+00:22:25,770 --> 00:22:29,170
+هذه مع هذه فبصير supremum لل S X ع Normal X
+
+303
+00:22:29,170 --> 00:22:34,790
+فاهمين؟ اه و يساوي هذه اصلا تعريف مين تعريف Normal
+
+304
+00:22:34,790 --> 00:22:41,430
+S إذا صارت Normal H أكبر أو يساوي Normal S ال S
+
+305
+00:22:41,430 --> 00:22:49,010
+إذا Normal Hأكبر أو يساوي norm الـ S يعني مكاني
+
+306
+00:22:49,010 --> 00:22:54,090
+بقولي الـ S صارت bounded طيب ناخد الجهة الثانية
+
+307
+00:22:54,090 --> 00:22:57,670
+hence S is bounded and normal H أكبر يساوي normal
+
+308
+00:22:57,670 --> 00:23:02,490
+H but normal H إيش بيساوي ال superman S X was Y ع
+
+309
+00:23:02,490 --> 00:23:07,070
+normal X normal Yوهذا أصغر أو يساوي الـ Supremum،
+
+310
+00:23:07,070 --> 00:23:11,230
+بتاخد مين الآن؟ الشوارز in quality الان هذه نفسها
+
+311
+00:23:11,230 --> 00:23:14,250
+absolute value لها أصغر أو يساوي norm هذه في norm
+
+312
+00:23:14,250 --> 00:23:17,070
+هذه، لذا ال supremum على هذه هيكون أصغر أو يساوي
+
+313
+00:23:17,070 --> 00:23:21,580
+ال supremum على هذهإن هدولة هدى أكبر أو يساوي هدى
+
+314
+00:23:21,580 --> 00:23:25,500
+ما هي الان اقوم بالاختصارات هدى مح هدى فبصير SX
+
+315
+00:23:25,500 --> 00:23:29,380
+على مين على ال X وهى norm بيهن ال S إذا صارت norm
+
+316
+00:23:29,380 --> 00:23:33,420
+ال H أصغر أو يساوي norm ال S التنتين مع بعض norm
+
+317
+00:23:33,420 --> 00:23:38,990
+ال H إيش بيساوي norm ال S نثبت إنه الوحيدTo prove
+
+318
+00:23:38,990 --> 00:23:41,510
+the uniqueness, suppose that there is a linear
+
+319
+00:23:41,510 --> 00:23:46,610
+operator T تاني من H1 إلى H2 بحيث أن Hxy بيساوي
+
+320
+00:23:46,610 --> 00:23:51,610
+Sxy الأولاني و بيساوي Txy الأولاني بفرضنا جديد for
+
+321
+00:23:51,610 --> 00:23:55,670
+all x element in H1 و all y element in H2إذاً by
+
+322
+00:23:55,670 --> 00:23:59,750
+لمّا طلعت الـ 82 لقبل بشوية مزام هذا بيساوي هذا
+
+323
+00:23:59,750 --> 00:24:02,730
+لكل الوايات اللي في الدنيا إذاً هذه بتساوي هذه لكل
+
+324
+00:24:02,730 --> 00:24:06,510
+ال Xات وهذا يعني أن T بتساوي S معناته S is unique
+
+325
+00:24:06,510 --> 00:24:09,150
+وبارك الله فيكم وإلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/2kTCGkbdyVU_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/2kTCGkbdyVU_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6deec4552edb129a38c329a332b16faa2ac48ce4
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/2kTCGkbdyVU_postprocess.srt
@@ -0,0 +1,376 @@
+1
+00:00:05,500 --> 00:00:07,980
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,980 --> 00:00:10,740
+والصلاة والسلام على سيدنا محمد وعلى آله والصحابي
+
+3
+00:00:10,740 --> 00:00:15,440
+الجماعين هذه هي المحاضرة رقم 12 مساق تحليل إقتراني
+
+4
+00:00:15,440 --> 00:00:19,000
+أو تحليل دالي طلاب وطالبات الجامعة الإسلامية
+
+5
+00:00:19,000 --> 00:00:24,620
+ماجستير الرياضياتان شاء الله هنحكي اليوم عن اللي
+
+6
+00:00:24,620 --> 00:00:28,340
+هو section قصير وسريع اللي هو اتنين ستة linear
+
+7
+00:00:28,340 --> 00:00:31,400
+operators المفروض هذا يكون انتوا يعني خليني اقول
+
+8
+00:00:31,400 --> 00:00:36,200
+عارفينه من الجبر الخطي ولكن حبيت ان احكيه على اساس
+
+9
+00:00:36,200 --> 00:00:39,100
+انه نذكركم فيه على اقل يعني ونشوف ال notations
+
+10
+00:00:39,100 --> 00:00:42,300
+اللي بدنا نستخدمها عشان اللي هو للمرات القادمة
+
+11
+00:00:43,210 --> 00:00:48,330
+definition a linear operator T is a mapping such
+
+12
+00:00:48,330 --> 00:00:53,070
+that عندي بنقول عن T إنه linear operator إذا بحقق
+
+13
+00:00:53,070 --> 00:00:56,590
+مالي أول حاجة ال domain D of T of T is a vector
+
+14
+00:00:56,590 --> 00:01:00,090
+space and the range R of T lies in a vector space
+
+15
+00:01:00,090 --> 00:01:04,740
+over the same field اتنين على نفس ال fieldFor all
+
+16
+00:01:04,740 --> 00:01:08,500
+x و y limited in D of T and all scalars α T x زائد
+
+17
+00:01:08,500 --> 00:01:15,060
+y بيسوا T x زائد T y and T α x بيسوا α T x اللي
+
+18
+00:01:15,060 --> 00:01:20,140
+بالظبط اللي هو عندي بكل سهولة T من عند domain of T
+
+19
+00:01:20,810 --> 00:01:26,490
+لعند X أو لعند Y هذا اللي هو عبارة عن اللي هي
+
+20
+00:01:26,490 --> 00:01:33,850
+domain of T نفسه lies بعملني اللي هو vector space
+
+21
+00:01:33,850 --> 00:01:39,930
+vector space و ال range إيه له هذا اللي هو lies in
+
+22
+00:01:39,930 --> 00:01:42,830
+a vector space يعني Y vector space و D of T vector
+
+23
+00:01:42,830 --> 00:01:50,290
+space domain of Tالان اتنين شرط ان نكون ناشمال هنا
+
+24
+00:01:50,290 --> 00:01:53,990
+over the same field لأنه عشان نسميه Linear لازم
+
+25
+00:01:53,990 --> 00:01:59,590
+يكون T of Alpha X زائد Y بساوية Alpha TX زائد TY
+
+26
+00:01:59,590 --> 00:02:07,090
+او زي ما قلنا ان TX زائد Y بساوية TX زائد TY
+
+27
+00:02:07,090 --> 00:02:12,670
+بالاضافة T Alpha X بساوية Alpha TXهذولا مع بعض او
+
+28
+00:02:12,670 --> 00:02:16,710
+هذا التنين اللي هو C يان بنقول عنه linear لاحظ ليش
+
+29
+00:02:16,710 --> 00:02:18,810
+هو بيقول over the same field بس هذي اللي بتحكيها
+
+30
+00:02:18,810 --> 00:02:21,790
+ليش التنين over the same field يعني هذا لازم يكون
+
+31
+00:02:21,790 --> 00:02:27,900
+over R مثلا وهذا over Rلأنه .. لأنه الآن .. عشان
+
+32
+00:02:27,900 --> 00:02:29,760
+ال .. هذه اللي .. ال .. ال .. ال .. ال .. ال .. ال
+
+33
+00:02:29,760 --> 00:02:30,500
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+34
+00:02:30,500 --> 00:02:31,500
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+35
+00:02:31,500 --> 00:02:34,340
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+36
+00:02:34,340 --> 00:02:35,940
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+37
+00:02:35,940 --> 00:02:37,300
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+38
+00:02:37,300 --> 00:02:39,440
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+39
+00:02:39,440 --> 00:02:42,980
+.. ال ..
+
+40
+00:02:42,980 --> 00:02:44,800
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+41
+00:02:44,800 --> 00:02:50,850
+.. ال .. الما هي Alpha وين في ال .. في ال .. في ال
+
+42
+00:02:50,850 --> 00:02:54,590
+complex وهذه over R مش ذابطة هنا مع حد فلازم يكون
+
+43
+00:02:54,590 --> 00:02:59,270
+التنين اشماله over the same field طيب اللي قال ال
+
+44
+00:02:59,270 --> 00:03:02,570
+null space او ال kernel كله نقول عنه في احيانا ال
+
+45
+00:03:02,570 --> 00:03:05,990
+N of T ايش بيساوي؟ هي عبارة عن كل ال Excel من ال
+
+46
+00:03:05,990 --> 00:03:11,370
+domain of T اللي صورها ايش بتساوي السفر هذه اللي
+
+47
+00:03:11,370 --> 00:03:15,960
+بنسميها اشمالها ال null spaceنيدي لبعض النظريات
+
+48
+00:03:15,960 --> 00:03:19,220
+النظرية الأولى هذه طبعا نظرية من الجبر الخطي
+
+49
+00:03:19,220 --> 00:03:24,100
+وبرهانها لكم لإنه شغلات بسيطة ومش وخلينا نقول
+
+50
+00:03:24,100 --> 00:03:28,080
+متطلب سابق للمادة أكثر من إنها هي المادة let T
+
+51
+00:03:28,080 --> 00:03:33,320
+بيقى linear operator then لأن لو T linear operator
+
+52
+00:03:33,320 --> 00:03:38,480
+معناته range of T نفسه إيش هيطلع vector spaceوإذا
+
+53
+00:03:38,480 --> 00:03:41,180
+كان ال dimension للـ T بيساوي N هيكون ال dimension
+
+54
+00:03:41,180 --> 00:03:44,960
+لل range of T اللي هو ال .. ال .. ال .. ال range
+
+55
+00:03:44,960 --> 00:03:50,360
+أصغر أو يساوي مين أثر أو يساوي N ال N null space
+
+56
+00:03:50,360 --> 00:03:53,860
+نفسه هيطلعيش مرضه vector space مبرهين انسهلات يعني
+
+57
+00:03:53,860 --> 00:03:57,800
+مبرهين جبر خط عاديات ما .. مافيش فيه مشكلة عشان
+
+58
+00:03:57,800 --> 00:04:01,920
+هيك left to the reader ال .. ال theorem التانيلت X
+
+59
+00:04:01,920 --> 00:04:06,120
+and Y be vector spaces, both real or إيه شمال هين،
+
+60
+00:04:06,120 --> 00:04:09,360
+both complex، التنين، يا الريال يا إياش يا كمplex،
+
+61
+00:04:09,360 --> 00:04:14,550
+لت يعني التنين over the same fieldلت من domain of
+
+62
+00:04:14,550 --> 00:04:17,130
+T لعند Y بي a linear operator with domain of T
+
+63
+00:04:17,130 --> 00:04:20,210
+subset من مين من ال X اللي هو عبارة عن vector
+
+64
+00:04:20,210 --> 00:04:24,730
+space and range of T subset من مين من Y then T من
+
+65
+00:04:24,730 --> 00:04:27,950
+inverse من R of T لعند E of T exists if and only
+
+66
+00:04:27,950 --> 00:04:31,550
+if ال T X بساوة سفر implies مين X بساوة سفر يعني
+
+67
+00:04:31,550 --> 00:04:34,900
+نبقى ناخر one to oneTX بتساوة و سفرة تقع تقع تقع
+
+68
+00:04:34,900 --> 00:04:36,440
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+69
+00:04:36,440 --> 00:04:37,740
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+70
+00:04:37,740 --> 00:04:44,660
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+71
+00:04:44,660 --> 00:04:47,540
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+72
+00:04:47,540 --> 00:04:48,100
+تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع تقع
+
+73
+00:04:48,100 --> 00:04:57,900
+تقع تقع تقع تقع تقع تقع تقع
+
+74
+00:04:57,900 --> 00:05:03,320
+تق
+
+75
+00:05:03,900 --> 00:05:08,780
+واضح؟ طيب إذا كان ال dimension لـ T بيساوي N و T
+
+76
+00:05:08,780 --> 00:05:12,020
+inverse exist إذا ال dimension ل domain of T إيش
+
+77
+00:05:12,020 --> 00:05:16,860
+هيساوي؟ ال dimension لمين؟ لل R of T ماشي الحال
+
+78
+00:05:16,860 --> 00:05:20,800
+إذا كان ال dimension ل domain of T بيساوي N و T
+
+79
+00:05:20,800 --> 00:05:24,000
+inverse exist صارت بين ال domain و T أصلا و ال
+
+80
+00:05:24,000 --> 00:05:26,980
+range of T one to one onto أصلا هيكون ال dimension
+
+81
+00:05:26,980 --> 00:05:30,340
+ل domain of T هو نفس ال dimension لمين؟ لل range
+
+82
+00:05:30,340 --> 00:05:34,440
+of Tبرضه ال .. ال .. left to the reader اللي هو
+
+83
+00:05:34,440 --> 00:05:42,040
+جابه الخط بحت نيجي لان لنظرية اللمم الأخيرة let X,
+
+84
+00:05:42,220 --> 00:05:46,480
+Y and Z be vector spaces and let T من X لعند Y and
+
+85
+00:05:46,480 --> 00:05:49,520
+S من عند Y لعند B لعند Z بده يعمل combination of
+
+86
+00:05:49,520 --> 00:05:54,990
+functions إذا كان T اللي هوBijective و Linear
+
+87
+00:05:54,990 --> 00:05:59,010
+Operators يعني اتنين وانت وان وانت واش و Linear
+
+88
+00:05:59,010 --> 00:06:01,970
+عشان يقدر يعرف يعرف ايش ال inverse بده يجيب ال
+
+89
+00:06:01,970 --> 00:06:06,970
+inverse then S T inverse exist و ال S T inverse
+
+90
+00:06:06,970 --> 00:06:10,610
+بيساوي ايش T inverse composite S inverse طبعا S في
+
+91
+00:06:10,610 --> 00:06:13,490
+T هنا composition يعني S composition T لكل inverse
+
+92
+00:06:13,490 --> 00:06:15,950
+هو عبارة عن T inverse composition من مين لل S
+
+93
+00:06:15,950 --> 00:06:18,610
+inverse و هذا برضه left to the reader و هيك بتكون
+
+94
+00:06:18,610 --> 00:06:21,430
+خلصت المحاضرة و السلام عليكم و رحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/4GZHS19Cyqk_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/4GZHS19Cyqk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..32605caedee4d6a9c6d8fcfe02e337f6e550e6a4
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/4GZHS19Cyqk_postprocess.srt
@@ -0,0 +1,1776 @@
+1
+00:00:05,040 --> 00:00:07,760
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,760 --> 00:00:10,580
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,580 --> 00:00:16,840
+أهله وصحبه أجمعين المحاضرة رقم 17 مساق تحليل
+
+4
+00:00:16,840 --> 00:00:20,560
+اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:20,560 --> 00:00:25,590
+الإسلامية ماجستير رياضياتأحنا المحاضرة الماضية
+
+6
+00:00:25,590 --> 00:00:29,830
+أنهينا Chapter 2 اللي هو Normed Spaces الآن بدنا
+
+7
+00:00:29,830 --> 00:00:35,410
+ندخل للحلقة اللي داخل Normed Spaces اللي هي Inner
+
+8
+00:00:35,410 --> 00:00:41,050
+and Product Space ومن ثم الاشي المكتمل منه اسمه
+
+9
+00:00:41,050 --> 00:00:45,880
+Hilbert Spaceالتلاتة واحد اللي هو تحت عنوان inner
+
+10
+00:00:45,880 --> 00:00:49,960
+product space و Hilbert space الكلام يعني هذا أنا
+
+11
+00:00:49,960 --> 00:00:53,160
+بتذكر أعطيته في الجبر الخطي الجبر الخطي للطلاب
+
+12
+00:00:53,160 --> 00:00:56,940
+الجبر الخطي 2 كنا نعطيه في الجامعة ال inner
+
+13
+00:00:56,940 --> 00:00:59,740
+product space وحتى ال Hilbert space حكينا فيه يعني
+
+14
+00:00:59,740 --> 00:01:04,300
+زي ما قلنا في البداية عنده اللي هو topological
+
+15
+00:01:04,300 --> 00:01:09,800
+spaces وفي داخله اللي هو metric spacesوفي داخله
+
+16
+00:01:09,800 --> 00:01:14,260
+اللي هو Normed Spaces ومن ثم اليوم بنحكي عن اللي
+
+17
+00:01:14,260 --> 00:01:18,100
+هو Inner Product Spaces أو اللي هو المكتمل منه الـ
+
+18
+00:01:18,100 --> 00:01:21,720
+Hilbert Spaces وأنفلة عليه اللي هو الـR تربيع
+
+19
+00:01:21,720 --> 00:01:26,580
+والـC تربيع والـC والـR إلى أخرى وكل ما يتعلق بهذه
+
+20
+00:01:26,580 --> 00:01:29,600
+الأمور اللي احنا مشتغل فيها في حياتنا فخلينا احنا
+
+21
+00:01:29,600 --> 00:01:32,740
+نبدأ الآن اللي هو نعرف شو معناته Inner Product
+
+22
+00:01:34,300 --> 00:01:39,080
+الحديث الآن خلّيني أقول أقرب إلى الاشي الجبري ومن
+
+23
+00:01:39,080 --> 00:01:42,320
+فمّا بندخل إلى اللي هو اندخل الـ topology أو الـ
+
+24
+00:01:42,320 --> 00:01:46,780
+norm اللي بتولد من الـ inner product an inner
+
+25
+00:01:46,780 --> 00:01:49,960
+product space is a vector space إذا إحنا شغلنا
+
+26
+00:01:49,960 --> 00:01:52,520
+over vector space زي ما كنا نشتغل في normed space
+
+27
+00:01:52,520 --> 00:01:56,100
+اللي هي أرضيتنا vector space with an inner product
+
+28
+00:01:56,100 --> 00:01:58,780
+defined on X يعني inner product space هو عبارة عن
+
+29
+00:01:58,780 --> 00:02:01,320
+vector space معرف عليه حاجة اسمها inner product
+
+30
+00:02:02,200 --> 00:02:05,820
+ماشي الان a Hilbert space is a complete inner
+
+31
+00:02:05,820 --> 00:02:08,920
+product space ال Hilbert space هو أشمله complete
+
+32
+00:02:08,920 --> 00:02:14,420
+inner product وكأنه من تحت بطن بقولكم ان ال inner
+
+33
+00:02:14,420 --> 00:02:17,540
+product بيعمل topology هو في الواقع ال inner
+
+34
+00:02:17,540 --> 00:02:21,800
+product بيعمل norm مباشرة و ال norm بيعمل اللي هو
+
+35
+00:02:21,800 --> 00:02:25,240
+اللي هي topology و بيسير عندنا اللي هي او بيعمل
+
+36
+00:02:25,240 --> 00:02:29,830
+metric space و ثم بيعملنا topologyالحديث عن ال
+
+37
+00:02:29,830 --> 00:02:34,090
+part أو complete inner product space اللي هو مبرر
+
+38
+00:02:34,090 --> 00:02:37,630
+لأن an inner product لأن شو معناه inner product on
+
+39
+00:02:37,630 --> 00:02:41,310
+X is a mapping of X cross X onto the scalar field
+
+40
+00:02:41,310 --> 00:02:46,210
+K of X such that يحقق مالي إذا ال inner product ال
+
+41
+00:02:46,210 --> 00:02:51,340
+inner product ما هو ال inner product عبارةعن دالة
+
+42
+00:02:51,340 --> 00:02:56,880
+من اللي هو X across X من X across X هي الدالة دي
+
+43
+00:02:56,880 --> 00:02:59,400
+بس ده الروج اللي برهزها ده الروج اللي أقف ده مضايق
+
+44
+00:02:59,400 --> 00:03:02,960
+منها لعند ال scalar field mean كي ال scalar field
+
+45
+00:03:02,960 --> 00:03:08,860
+اللي أمامي حسب اللي هو ال field اتبع من ال X اللي
+
+46
+00:03:08,860 --> 00:03:13,780
+نفسها يا real يا إياش يا complex يحقق الشروط
+
+47
+00:03:13,780 --> 00:03:18,660
+الآتيةاللي هو التعميم عموما هو للـ dot product
+
+48
+00:03:18,660 --> 00:03:24,280
+اللي بيكونوا ياخدوا في المتجهات شوفوا الآن ال X
+
+49
+00:03:24,280 --> 00:03:31,120
+زائد Y و ال Z بساوي X و Z زائد mean Y و Z يعني و
+
+50
+00:03:31,120 --> 00:03:37,560
+كأنه linear in the first entry ماشي؟ الآن طبعا هذه
+
+51
+00:03:37,560 --> 00:03:40,780
+دالة زي ما قلنا دالة من X cross X هذا من ال X
+
+52
+00:03:40,780 --> 00:03:45,090
+الأولى وهذا من X الثانيةماشي الان ال alpha x
+
+53
+00:03:45,090 --> 00:03:49,410
+بيساوي ال alpha بتطلع منه الجريب alpha في x و main
+
+54
+00:03:49,410 --> 00:03:54,310
+و y اذا و كأنه مش additive بس linear كاملة في اللي
+
+55
+00:03:54,310 --> 00:03:58,870
+هو the first entry الان x و y بيساوي ال y و x ايش
+
+56
+00:03:58,870 --> 00:04:02,390
+ما لها conjugate يعني لما بدك ايش علاقة ال x و y
+
+57
+00:04:02,390 --> 00:04:07,130
+بيه اللي هي y و x اللي هي هذه conjugate لهذه ماشي
+
+58
+00:04:07,130 --> 00:04:11,510
+الحال طيب the complex conjugate of a y و xلو كان
+
+59
+00:04:11,510 --> 00:04:14,310
+ريال بيصير إيش مالهم هو الـ conjugate ولادك زي بعض
+
+60
+00:04:14,310 --> 00:04:20,410
+بصير نفسه بساوي معايا إيه الآن X و X هيطلع ريال
+
+61
+00:04:20,410 --> 00:04:25,230
+هيطلع أكبر أوي ساوي سفر و X و X بيساوي سفر إذا و
+
+62
+00:04:25,230 --> 00:04:30,110
+فقط X إيش مالها تساوي إيش سفر بعد شوية حلاجة هذا
+
+63
+00:04:30,110 --> 00:04:32,290
+هو اللي بيطلع اللي بيولد لنا norm أو بيطلع لنا
+
+64
+00:04:32,290 --> 00:04:36,630
+norm إيه الآن اطلع لفوق an inner product on X
+
+65
+00:04:36,630 --> 00:04:42,760
+defines a normالادعاء كان التالي الان ال product
+
+66
+00:04:42,760 --> 00:04:47,480
+هذا بنقدر منه انعرف منه norm ال norm كيف بتعرفه
+
+67
+00:04:47,480 --> 00:04:50,880
+على ال X اللي هو عبارة عن norm ال X بساوي هذا جول
+
+68
+00:04:50,880 --> 00:04:54,380
+الأكبر شو سفر فالجدر التابع هو مشروع فبتاخد الجدر
+
+69
+00:04:54,380 --> 00:04:59,820
+التابع له هذا هيعمل ليه norm يعني هيحقق لكل شروط
+
+70
+00:04:59,820 --> 00:05:05,260
+norm اللي احنا بنعرفها او تحقيقها مش صعبand a
+
+71
+00:05:05,260 --> 00:05:08,740
+metric on X والمتريك ما دام جيبنا norm نجيب metric
+
+72
+00:05:08,740 --> 00:05:12,880
+المتريك ايش هو المسافة بين X و Y هو عبارة عن norm
+
+73
+00:05:12,880 --> 00:05:16,000
+X minus Y عرفناها زمان هذه اللي هي عبارة حسب
+
+74
+00:05:16,000 --> 00:05:18,060
+التعريف اللي فوق يبقى عبارة عن جدر الترميه لل
+
+75
+00:05:18,060 --> 00:05:23,160
+inner product بين X minus Y و X minus Y الان ال
+
+76
+00:05:23,160 --> 00:05:27,620
+inner product spacesare normed spaces لأنه جيبناها
+
+77
+00:05:27,620 --> 00:05:33,140
+من وين ال norm هذا اللي جيبناها جيبناها من مين؟ من
+
+78
+00:05:33,140 --> 00:05:37,240
+inner product صار كل inner product يجيبله نور فال
+
+79
+00:05:37,240 --> 00:05:40,400
+inner product spaces are normed spaces لكن ال
+
+80
+00:05:40,400 --> 00:05:43,680
+normed spaces مش شرط يكون شمالين inner product
+
+81
+00:05:43,680 --> 00:05:55,740
+spaces وحناخد بعد شوية مثلةHilbert spaces هم
+
+82
+00:05:55,740 --> 00:06:00,940
+بنخ الاسباسالأن بعض الخواص الأخرى اللي بنستقيها من
+
+83
+00:06:00,940 --> 00:06:07,520
+الخواص اللي فوق و استقاها سهل for all x, y and z
+
+84
+00:06:07,520 --> 00:06:11,700
+in an inner product space and an scalar α لو جيت
+
+85
+00:06:11,700 --> 00:06:18,120
+حسبة α x زائد y و z بساوي اللي هو α في x و z زائد
+
+86
+00:06:18,120 --> 00:06:22,460
+y و zفبنعملنا خطوتين أول شي Alpha X ككولة واحدة و
+
+87
+00:06:22,460 --> 00:06:26,460
+Z زاد Y على Z من الخاصية الأولى و ال Alpha بتطلحها
+
+88
+00:06:26,460 --> 00:06:28,960
+من الخاصية التانية X و Y بتطلع اللي هي بالشكل هذه
+
+89
+00:06:28,960 --> 00:06:33,480
+الآن هذه X و Alpha Y لما تطلع من اللي بعيد بتطلع
+
+90
+00:06:33,480 --> 00:06:37,220
+من ال conjugate كيف بجيبها Alpha X و Alpha Y
+
+91
+00:06:37,220 --> 00:06:41,680
+بتساوي اللي هو Alpha Y و X conjugate الآن من
+
+92
+00:06:41,680 --> 00:06:46,290
+الخاصية اللي بقى بنتجيب الخاصية هلجيت Xو α y
+
+93
+00:06:46,290 --> 00:06:49,890
+بيساوم الخاصية التالتة اظن انه بتساوم ال conjugate
+
+94
+00:06:49,890 --> 00:06:54,430
+لها α y و x صح ولا لأ الان ال alpha بتطلع من
+
+95
+00:06:54,430 --> 00:07:01,230
+الجريم مباشرة بيساوم ال alpha في ال y و x و الكل
+
+96
+00:07:01,230 --> 00:07:05,070
+ما له ال conjugate ال alpha conjugate هذه في هذه
+
+97
+00:07:05,070 --> 00:07:08,790
+بتطلع انه alpha conjugate في ال y و x conjugate
+
+98
+00:07:08,790 --> 00:07:13,450
+ماشي هذه اللي هي بتساوم ال alpha conjugate في x و
+
+99
+00:07:13,450 --> 00:07:19,450
+y ما هو المطلوبطيب إذا الآن عندي هذه اللي هي سهلة
+
+100
+00:07:19,450 --> 00:07:24,110
+نيجي للي بعيدها هذه برضه اللي عملناها نيجي للي
+
+101
+00:07:24,110 --> 00:07:27,450
+بعيدها هذه بناء على الحالتين اللي فوق أو الحالة
+
+102
+00:07:27,450 --> 00:07:29,930
+هذه و الـ Linearية الأولى و الـ Additiveية الأولى
+
+103
+00:07:29,930 --> 00:07:34,750
+X و Alpha Y زائد Z بتساوي اللي هو Alpha conjugate
+
+104
+00:07:34,750 --> 00:07:40,730
+Alpha conjugate XY زائد اللي هو Y X و مين و Z الآن
+
+105
+00:07:40,730 --> 00:07:46,140
+بعملها conjugationبتصير هذه عبارة عن α y زائد z و
+
+106
+00:07:46,140 --> 00:07:49,660
+x conjugate وإن جريبه بعملها زي اللي ملمنت اللي
+
+107
+00:07:49,660 --> 00:07:52,340
+فوق و بتطلع و تضال تحت ال conjugate و بعدين
+
+108
+00:07:52,340 --> 00:07:55,740
+برجّولها للأصل فاهمين؟ مافيش داعي أن أعملها سوى
+
+109
+00:07:55,740 --> 00:08:00,340
+نفس اللي هي اللي عاملة إذا وكأنه اللي هو في الجريب
+
+110
+00:08:00,340 --> 00:08:03,630
+في الجريب في الـinter الجريب linearفي الـ .. في
+
+111
+00:08:03,630 --> 00:08:06,590
+الـ .. في الـ .. في الـ .. في الجريب .. في ال ..
+
+112
+00:08:06,590 --> 00:08:10,450
+في البعيد مش linear خلّينا نقول conjugate linear
+
+113
+00:08:10,450 --> 00:08:13,590
+ده صح التعبير يعني بتطلع من برا الألف ألف
+
+114
+00:08:13,590 --> 00:08:17,850
+conjugate أما ال additive additive additiveفاهمين؟
+
+115
+00:08:17,850 --> 00:08:21,650
+لأن the inner product is sesquilinear بناء عن اللي
+
+116
+00:08:21,650 --> 00:08:25,570
+حكيته إيش معنى sesquilinear؟ linear in the first
+
+117
+00:08:25,570 --> 00:08:30,990
+factor and conjugate linear in the second factor
+
+118
+00:08:30,990 --> 00:08:36,070
+وكأنه بيقولّي إحنا بنعرف ال sesquilinear أصلا هو
+
+119
+00:08:36,070 --> 00:08:42,170
+عبارة عن إيش؟ إنه عدالة من X cross Xبترمى فى كده
+
+120
+00:08:42,170 --> 00:08:45,390
+انه لو كانت فى الأولى Linear وفى التانى يكون Digit
+
+121
+00:08:45,390 --> 00:08:47,670
+Linear بنسمي اللى هى الدالة فى هذه الحالة
+
+122
+00:08:47,670 --> 00:08:52,170
+Sesquilinear Function ماشى الان مثال على
+
+123
+00:08:52,170 --> 00:08:55,030
+Sesquilinear اللى هو inner product inner product
+
+124
+00:08:55,030 --> 00:08:58,370
+إذا sesquilinear ال general حكيته وده inner
+
+125
+00:08:58,370 --> 00:09:01,410
+product ducked مثال عليه الان نيجى لل
+
+126
+00:09:01,410 --> 00:09:07,150
+parallelogram equality اللى هى Fx is an inner
+
+127
+00:09:07,150 --> 00:09:15,530
+product space ضمنfor all x of y element in x هيكون
+
+128
+00:09:15,530 --> 00:09:17,950
+عندي normal x زاد y تربيع زاد normal x minus y
+
+129
+00:09:17,950 --> 00:09:21,270
+تربيع بيساوي 2 for normal x تربيع زاد normal mean
+
+130
+00:09:21,270 --> 00:09:26,610
+ال y تربيع البرهانة
+
+131
+00:09:26,610 --> 00:09:30,870
+سهل خلّيني أعملكم إياها نحسبلكم إياها عشان تتعلم
+
+132
+00:09:30,870 --> 00:09:33,150
+.. خلّيني أقول ندرع على الحسابات و بعدين تصير
+
+133
+00:09:33,150 --> 00:09:38,450
+الشغلات هذه إليكم على السريع هنيجي اللي هو normal
+
+134
+00:09:38,450 --> 00:09:45,190
+x زاد ynorm x زاد y الكل تربيع زاد norm x minus y
+
+135
+00:09:45,190 --> 00:09:54,710
+x minus y الكل تربيع عندي
+
+136
+00:09:54,710 --> 00:10:00,870
+اللي هو لو كان المستطيل هذا هاي ال vector هذا x
+
+137
+00:10:01,980 --> 00:10:06,200
+والـ vector هذا Y هذا إيه شماله؟ هذا X زيدي Y
+
+138
+00:10:06,200 --> 00:10:12,140
+مظبوط هذا الان Y بالشكل هذا وهذا اللي هو X بالشكل
+
+139
+00:10:12,140 --> 00:10:19,620
+هذا الآن اللي بيسكر في الاتجاه المخالف اللي هو
+
+140
+00:10:19,620 --> 00:10:24,140
+سلبهم فبصير هذا طول هذا زي الطول التاني بيساوي هذا
+
+141
+00:10:24,140 --> 00:10:28,280
+زائد هذا زائد هذاماشي فطول فعشان هيك بيسموها
+
+142
+00:10:28,280 --> 00:10:32,440
+program law طيب شوفوا صلى الله عليه وسلم الحسابات
+
+143
+00:10:32,440 --> 00:10:37,480
+لان نيجي للحسابات نيجي للحسابات ويساوي X زائد Y و
+
+144
+00:10:37,480 --> 00:10:40,280
+X زائد Y هذا ال inner product .. ال X زائد Y الكتر
+
+145
+00:10:40,280 --> 00:10:43,700
+بيه اتعرفنا ال inner product و .. و .. و مع ال law
+
+146
+00:10:43,700 --> 00:10:50,160
+زائد X minus Y و X minus Y بنفكل الآن ويساوي X مع
+
+147
+00:10:50,160 --> 00:10:59,160
+ال X فاهمين؟ و X مع ال Yو ال y مع ال x و ال y مع
+
+148
+00:10:59,160 --> 00:11:08,080
+ال y تحتيها ال x مع ال x اه لان ال x مع ناقص y
+
+149
+00:11:08,080 --> 00:11:13,660
+بطلع النقص برا تسيي ال x و ال y فاهمين؟ و لان خلاص
+
+150
+00:11:13,660 --> 00:11:18,040
+من ال x مع التنتين لان ناقص y ناقص y مع ال x بطلع
+
+151
+00:11:18,040 --> 00:11:22,880
+ناقص y مع ال xو ناقص Y معاه ناقص Y ناقصين بيطلعين
+
+152
+00:11:22,880 --> 00:11:25,880
+بيطلعين زائد ناقص واحد ناقص واحد بيطلع من برا ناقص
+
+153
+00:11:25,880 --> 00:11:32,680
+واحد نفسه و ناقص واحد نفسه نفسه نفسه نفسه نفسه
+
+154
+00:11:32,680 --> 00:11:37,380
+نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه
+
+155
+00:11:37,380 --> 00:11:37,580
+نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه
+
+156
+00:11:37,580 --> 00:11:37,640
+نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه
+
+157
+00:11:37,640 --> 00:11:45,080
+نفسه نفسه نفسه نفسه نفسه نفسه
+
+158
+00:11:45,080 --> 00:11:54,920
+نفساللي هي هذه البرنامج equality is true الان
+
+159
+00:11:54,920 --> 00:12:01,620
+شوفوا الان بس هذا كلام مهم انت باهم if xis an
+
+160
+00:12:01,620 --> 00:12:05,940
+inner product space عشان نفهم النص كويس لإن
+
+161
+00:12:05,940 --> 00:12:09,800
+استعمالته مهمة if x is an inner product space إذا
+
+162
+00:12:09,800 --> 00:12:13,920
+كان عند inner product space مضمون مية في المية
+
+163
+00:12:13,920 --> 00:12:19,650
+then for all x هذه متحققةالأن الـ Contraposition
+
+164
+00:12:19,650 --> 00:12:23,810
+لها لو مش متحققة مش هيكون inner product space
+
+165
+00:12:23,810 --> 00:12:28,870
+وكأنها tool أو أداة لإثبات إن ال space اللي عندك
+
+166
+00:12:28,870 --> 00:12:33,110
+ماله مش inner product إنه نجيب اللي هو vectors
+
+167
+00:12:33,110 --> 00:12:36,870
+بحيث إنه هذا لا يساوي هذا كل سنة من تسلميه ميكونش
+
+168
+00:12:36,870 --> 00:12:39,770
+اللي هو main inner product يعني ال normed space
+
+169
+00:12:39,770 --> 00:12:46,040
+ليس مولد من inner product definitionElement X in
+
+170
+00:12:46,040 --> 00:12:48,820
+an inner product space X is said to be orthogonal
+
+171
+00:12:48,820 --> 00:12:54,360
+to Yإذا كان الـ inner product بين X وY بساوية 0 و
+
+172
+00:12:54,360 --> 00:12:57,160
+كنا نكتب X أرثجونال لـ Y بساوية 100 لما كنا نعمل
+
+173
+00:12:57,160 --> 00:12:59,700
+زمان في ال .. في ال .. في ال vectors العادية لما
+
+174
+00:12:59,700 --> 00:13:02,900
+يكون عندي اللي هو اللي بنقول عن ال .. ال .. ال ..
+
+175
+00:13:02,900 --> 00:13:04,940
+ال vector عمودي على التاني إذا كان اللي هو ال
+
+176
+00:13:04,940 --> 00:13:08,600
+inner product بينهم مش بساوية 0 ماشي الحال الآن
+
+177
+00:13:08,600 --> 00:13:13,080
+هذا بنسميه orthogonal elements وعنا علم كامل في ال
+
+178
+00:13:13,080 --> 00:13:16,200
+orthogonality فيه حتى مش في ال inner product سر
+
+179
+00:13:16,200 --> 00:13:21,430
+نعرف ال orthogonalityفى ال north spaces فى ال
+
+180
+00:13:21,430 --> 00:13:27,810
+north اه اه طبعا فى ال inner and product طبعا بشكل
+
+181
+00:13:27,810 --> 00:13:34,100
+معين FA و PR subsetsof X بنقول إن X عمودية على Y
+
+182
+00:13:34,100 --> 00:13:36,660
+إذا كانت X عمودية على كل element منها على نصره
+
+183
+00:13:36,660 --> 00:13:39,560
+يعني X ارتجون على كل element يعني ال inner product
+
+184
+00:13:39,560 --> 00:13:42,600
+بين X و أي element في ال A بيساوي سفر بنقول two
+
+185
+00:13:42,600 --> 00:13:45,240
+sets عموديات على بعض إذا كان كل element هنا عمودي
+
+186
+00:13:45,240 --> 00:13:48,140
+على ثاني يعني ال inner product بين A وB بيساوي سفر
+
+187
+00:13:48,140 --> 00:13:52,480
+لكل A وB كل A المتن A وB المتن B اطلع لفوق كلام
+
+188
+00:13:52,480 --> 00:13:55,660
+جميل وسهلالآن included in space around is a
+
+189
+00:13:55,660 --> 00:13:57,700
+Hilbert space with inner product defined by inner
+
+190
+00:13:57,700 --> 00:14:00,700
+product بين x و y بسبب summation x i i في مين في
+
+191
+00:14:00,700 --> 00:14:04,320
+Gamma I الآن هو هذا عبارة زي ما قلنا قبل شوية
+
+192
+00:14:04,320 --> 00:14:08,160
+عبارة عن ال x و ال y عبارة عن تعميم لمين لل dot
+
+193
+00:14:08,160 --> 00:14:11,020
+product ال dot product زي ما قلنا لو جينا في ال R
+
+194
+00:14:11,020 --> 00:14:14,980
+تنين اللي كنا لو كان ال vector A بيساوي x i زائد y
+
+195
+00:14:14,980 --> 00:14:19,220
+j و B بيساوي x prime i زائد y prime j إيش بيكون ال
+
+196
+00:14:19,220 --> 00:14:22,740
+dot product A dot B عبارة عن x في x prime زائد y
+
+197
+00:14:22,740 --> 00:14:26,670
+في y primeالآن هذا إذا اللي معرفه هنا ما هو اللي
+
+198
+00:14:26,670 --> 00:14:29,430
+عبارة عن تعميم للـ inner product للـ dot product
+
+199
+00:14:29,430 --> 00:14:32,610
+اللي إحنا بنعرفه في الأصل في ال calculus gene هذا
+
+200
+00:14:32,610 --> 00:14:35,370
+هيعمل inner product كيف ده يثبت إنه inner product
+
+201
+00:14:35,370 --> 00:14:38,190
+بثبت إنه inner product إنه بيحقق الشروط اللي عندي
+
+202
+00:14:38,190 --> 00:14:41,150
+الأربعة أو الخمسة اللي موجودة عندي الان كيف معرفي
+
+203
+00:14:41,150 --> 00:14:43,350
+إنه إحنا X اللي هي إكساية واحد إكساية اتنين إكساية
+
+204
+00:14:43,350 --> 00:14:46,070
+تلتة وتلتة إكساية وY بيساوي Gamma واحد Gamma اتنين
+
+205
+00:14:46,070 --> 00:14:48,810
+Gamma تلتة Gamma and عناصر في الأرقام ال inner
+
+206
+00:14:48,810 --> 00:14:51,330
+product بيانين اللي هو ال entry الأول زي ما عملنا
+
+207
+00:14:51,330 --> 00:14:54,020
+في ال .. في ال .. في ال .. في ال ..في ال .. ال
+
+208
+00:14:54,020 --> 00:14:57,820
+vector اللي هو ال dot .. ال dot من ال vectors اللي
+
+209
+00:14:57,820 --> 00:15:01,120
+بنعرفها في الcalculus gene اللي هو xi واحد ماجاما
+
+210
+00:15:01,120 --> 00:15:03,640
+واحد زاد xi اتنين ماجاما اتنين لما اصل xi ان جاما
+
+211
+00:15:03,640 --> 00:15:07,220
+ان هذا بيعمل ال inner product ال ال inner product
+
+212
+00:15:07,220 --> 00:15:10,120
+بيقول لي اللي هو induce the norm ال norm اللي
+
+213
+00:15:10,120 --> 00:15:14,020
+بيطلع منه x و x زي ما احنا عارفين اللي هو x و x
+
+214
+00:15:14,020 --> 00:15:17,720
+اللي هو ده بيطلع norm تربيةبيصير Xi I في Xi I
+
+215
+00:15:17,720 --> 00:15:21,760
+بيصير Xi I تربيع إذن بيصير نورم الـ X لحاله اللي
+
+216
+00:15:21,760 --> 00:15:24,120
+هو الجدر التربيعي لهذا اللي هو Xi I تربيعه اللي هو
+
+217
+00:15:24,120 --> 00:15:28,460
+ال norm اللي احنا عارفينه في القرأن وهذا أثبتناه
+
+218
+00:15:28,460 --> 00:15:31,840
+في المرة الماضية إن إيش ماله هذا بيعمل لي complete
+
+219
+00:15:31,840 --> 00:15:36,780
+normed space إذن ال inner product اللي ولد هذا ال
+
+220
+00:15:36,780 --> 00:15:39,720
+norm هو complete يعني بمعنى آخر ال inner product
+
+221
+00:15:39,720 --> 00:15:45,160
+مع هذا is a Hilbert spaceومش هيك وبنطلع منه الـ
+
+222
+00:15:45,160 --> 00:15:49,120
+Metrical تالي DXY بيساوي ال norm لل X minus Y اللي
+
+223
+00:15:49,120 --> 00:15:53,560
+هو هذا XII نقص غامعي تربيع لكل إيه شماله لكل نص
+
+224
+00:15:53,560 --> 00:15:58,280
+وهذا برضه أثبتنا عبارة عن Metric على اللي هو ال
+
+225
+00:15:58,280 --> 00:16:00,400
+space الأخرى يعني هي أول من التالي يلا اللي بعد
+
+226
+00:16:02,630 --> 00:16:05,790
+الأن الـ Unitary space نفس اللي توّى نفس اللي توّى
+
+227
+00:16:05,790 --> 00:16:07,770
+الـ Unitary space اللي هو الكمبليكس بدل الـ R اللي
+
+228
+00:16:07,770 --> 00:16:11,410
+هي الـ UNC الان بس بدنا ناخد بعين الاعتبار ان الـ
+
+229
+00:16:11,410 --> 00:16:14,770
+inner product هيصير ايش ماله الـ Psi I في ال
+
+230
+00:16:14,770 --> 00:16:17,850
+conjugate تبع حاجة ده مش فيه في ال conjugate سواء
+
+231
+00:16:17,850 --> 00:16:21,080
+ما I اللي هو conjugateالان هذا لما صار في ال
+
+232
+00:16:21,080 --> 00:16:25,320
+conjugate لما بتحسب ال X و ال X فبصير Xi I في Xi I
+
+233
+00:16:25,320 --> 00:16:29,200
+conjugate فبتطلع الموضوع للتربيع ماشي الحال فبصير
+
+234
+00:16:29,200 --> 00:16:34,120
+الان ال norm اللي هو عبارة عن جدر التربيع ل X و X
+
+235
+00:16:34,120 --> 00:16:38,850
+بساوة ال summation هذا لكل أص نصهذا بيصير اللي جوا
+
+236
+00:16:38,850 --> 00:16:41,850
+زي ما تقولنا المدرس تربيع أس نص اللي هو ال norm
+
+237
+00:16:41,850 --> 00:16:45,050
+اللي احنا عارفينه من الاصل على ال CN واحنا عارفين
+
+238
+00:16:45,050 --> 00:16:47,330
+ان ال norm على ال CN is complete اذا هذا ال inner
+
+239
+00:16:47,330 --> 00:16:50,670
+product عملي complete normed space اللي هو هيطلع
+
+240
+00:16:50,670 --> 00:16:53,530
+عليه في الهش ماله complete inner product space
+
+241
+00:16:53,530 --> 00:16:58,270
+يعني Hilbert space و ال metric تبعه دي x و y نفس
+
+242
+00:16:58,270 --> 00:17:01,530
+اللي قبل بشوية summation x I I نبسغام I تربيع اللي
+
+243
+00:17:01,530 --> 00:17:04,330
+كل أس نص عاملة واحدة عند N لكل ال X و ال Y
+
+244
+00:17:04,330 --> 00:17:09,100
+الموجودة في ال CNاللي بعده الان اول مرة نحكي عن
+
+245
+00:17:09,100 --> 00:17:14,570
+حاجة اسمها L2VABقبل هيك عرفنا نورم نورم اللي هو
+
+246
+00:17:14,570 --> 00:17:17,990
+نورم الـ X كفانكشن لما أخدنا ال space of all
+
+247
+00:17:17,990 --> 00:17:20,210
+continuous functions ال space of all continuous
+
+248
+00:17:20,210 --> 00:17:24,730
+functions X تربيع of T DT كل إيش ماله أص نص هذا
+
+249
+00:17:24,730 --> 00:17:28,470
+اللي هو خليني نقول نورم اللي عرفناه قبل هيك قلنا
+
+250
+00:17:28,470 --> 00:17:31,430
+هذا النورم إيه ماله مش complete بيعملليش complete
+
+251
+00:17:31,430 --> 00:17:34,230
+space و جبنا الرسمات و جبناكم مثال و قلنا مش
+
+252
+00:17:34,230 --> 00:17:39,010
+complete الان اكملوا احنا و قلنا قبل هيك أنه أنا
+
+253
+00:17:40,730 --> 00:17:43,970
+متريك الـ space أو any normed space can be
+
+254
+00:17:43,970 --> 00:17:50,010
+completed الكمبليشن اللي هو الكمبليشن اللي هو
+
+255
+00:17:50,010 --> 00:17:51,810
+الكمبليشن اللي هو الكمبليشن اللي هو الكمبليشن اللي
+
+256
+00:17:51,810 --> 00:17:52,270
+هو الكمبليشن اللي هو الكمبليشن اللي هو الكمبليشن
+
+257
+00:17:52,270 --> 00:17:52,770
+اللي هو الكمبليشن اللي هو الكمبليشن اللي هو
+
+258
+00:17:52,770 --> 00:17:54,290
+الكمبليشن اللي هو الكمبليشن اللي هو الكمبليشن اللي
+
+259
+00:17:54,290 --> 00:17:55,150
+هو الكمبليشن اللي هو الكمبليشن اللي هو الكمبليشن
+
+260
+00:17:55,150 --> 00:17:55,210
+اللي هو الكمبليشن اللي هو الكمبليشن اللي هو
+
+261
+00:17:55,210 --> 00:17:56,030
+الكمبليشن اللي هو الكمبليشن اللي هو الكمبليشن اللي
+
+262
+00:17:56,030 --> 00:17:57,710
+هو الكمبليشن اللي هو الكمبليشن اللي هو الكمإذا ال
+
+263
+00:17:57,710 --> 00:18:02,010
+L of 2 of A وB the completion of the space of all
+
+264
+00:18:02,010 --> 00:18:05,630
+continuous real valid functions on A وB with norm
+
+265
+00:18:05,630 --> 00:18:09,450
+defined بهذا عند ال inner product في هذه الحالة
+
+266
+00:18:09,450 --> 00:18:12,750
+مين هو هناخده ال inner product هو عبارة عن ال X of
+
+267
+00:18:12,750 --> 00:18:16,770
+T في مين في Y of T من A لعند B لو بداش تشغل على ال
+
+268
+00:18:16,770 --> 00:18:20,230
+C باخد بس ال conjugate ماشي الحال سمونا احنا بنحكي
+
+269
+00:18:20,230 --> 00:18:24,030
+عالمين على ال R لأنه على فترة من A لعند B و بترمي
+
+270
+00:18:24,030 --> 00:18:29,140
+برضه في Rلو جيت أخدت اللي هو ال norm من هنا X و X
+
+271
+00:18:29,140 --> 00:18:32,320
+هتطلع X of T و Y of T مضربات في بعض X of T و X of
+
+272
+00:18:32,320 --> 00:18:36,020
+T بتصير تربيع الآن و هذا norm تربيع فبتطلع أقلص نص
+
+273
+00:18:36,020 --> 00:18:39,540
+فعلا هذا ال inner بولد ال norm هذا إذا هذا عبارة
+
+274
+00:18:39,540 --> 00:18:43,560
+عن inner product space اللي قالته الآن على اللي هي
+
+275
+00:18:43,560 --> 00:18:46,780
+هذه اللي هي ال continuous ده حالها مش complete لكن
+
+276
+00:18:46,780 --> 00:18:51,380
+لما حكيناها بصورة عامة على ال completion إيه له
+
+277
+00:18:51,380 --> 00:18:55,960
+صار completeأي سؤال؟ طيب، قل لبعدي The function X
+
+278
+00:18:55,960 --> 00:18:58,640
+of T can be accepted to be complex-valid وزي ما
+
+279
+00:18:58,640 --> 00:19:01,300
+قلت أن A و B and the corresponding inner product
+
+280
+00:19:01,300 --> 00:19:04,960
+is a norm لأن ال inner product بين X و Y هي نفسها
+
+281
+00:19:04,960 --> 00:19:07,800
+بس بتنحط conjugate و ال norm في هذه الحالة بتطلع
+
+282
+00:19:07,800 --> 00:19:12,360
+أشماله modulus تربيع الكل أص نص و then L2 of A و B
+
+283
+00:19:12,360 --> 00:19:15,640
+becomes the completion of the space of all
+
+284
+00:19:15,640 --> 00:19:19,760
+continuous complexvalued functions يعني بترمي في
+
+285
+00:19:19,760 --> 00:19:23,000
+ال complex تاخد من الفترة a و b لكن غير متهيأش في
+
+286
+00:19:23,000 --> 00:19:26,520
+ال complex on a و b corresponding to this norm in
+
+287
+00:19:26,520 --> 00:19:32,080
+each case real or complex L2 is a Hilbert space
+
+288
+00:19:32,080 --> 00:19:35,440
+لأن L2 في a و b إذا ما له و إش ما له Hilbert space
+
+289
+00:19:35,440 --> 00:19:43,050
+ال space L2 ال L2 برضه Hilbert spaceهذا الـ
+
+290
+00:19:43,050 --> 00:19:48,390
+Hilbert space of all functions الـ two big
+
+291
+00:19:48,390 --> 00:19:51,330
+integrable functions هذا الـ Hilbert space مقابل
+
+292
+00:19:51,330 --> 00:19:55,330
+له الـ two الهو of .. اللي بنسميه sequence space
+
+293
+00:19:55,330 --> 00:19:58,310
+Hilbert sequence space أو اللي بيسموه classical
+
+294
+00:19:58,310 --> 00:20:01,850
+Hilbert space يعني اللي أصلا هو .. يعني سمي الجثة
+
+295
+00:20:01,850 --> 00:20:06,740
+كلها على علب هو يعنيThis space is a Hilbert space
+
+296
+00:20:06,740 --> 00:20:10,000
+with inner product اللي هو زي بي قبل بشوية inner
+
+297
+00:20:10,000 --> 00:20:13,260
+product بين X Y بيصير X I I في القمة I conjugate
+
+298
+00:20:13,260 --> 00:20:16,440
+بس I من عند واحد مش لأن في حالة الأران إلى ما
+
+299
+00:20:16,440 --> 00:20:20,940
+لنهاية هذا بيعمل inner product و هيحقق الشروط كلها
+
+300
+00:20:21,220 --> 00:20:25,640
+Norm هو نورم التبع للـ L2 زمان إيش هو نورم الـ X؟
+
+301
+00:20:25,640 --> 00:20:28,360
+اللي هو هذا X و X بيصير هذا تربيع و هذا أص نص اللي
+
+302
+00:20:28,360 --> 00:20:32,000
+هو نورم اللي في الـ L2 الأصلي فبكون عند ال inner
+
+303
+00:20:32,000 --> 00:20:34,760
+product هذا هو اللي ولد ال .. ال .. ال norm اللي
+
+304
+00:20:34,760 --> 00:20:38,940
+احنا عارفينه اللي أثبتنا عنه أن الـ L2 is a
+
+305
+00:20:38,940 --> 00:20:44,500
+complete normed space ماشي الحالة و بيكون اللي هو
+
+306
+00:20:44,500 --> 00:20:48,220
+هذا inner product space السؤال الآن أنت حكيت عن
+
+307
+00:20:48,220 --> 00:20:54,540
+الـ L2طب الـ LB و الـ B لا تساوي اتنين هل هذا
+
+308
+00:20:54,540 --> 00:20:58,420
+inner product space هذا أحد الأمثلة اللي عندنا
+
+309
+00:20:58,420 --> 00:21:04,260
+بيكون normed space لكن مش البرت space أو مش inner
+
+310
+00:21:04,260 --> 00:21:08,900
+أو مش مش لا يمكن اللي هو ان نولده من inner product
+
+311
+00:21:08,900 --> 00:21:17,030
+ده مشوفأطلع فوق This space with B لـ 99 و 2 is not
+
+312
+00:21:17,030 --> 00:21:21,790
+an inner product space hence أكيد is not a Hilbert
+
+313
+00:21:21,790 --> 00:21:25,290
+space مين اللي بدو يثبت لنا اللي قبل شوية ال
+
+314
+00:21:25,290 --> 00:21:29,150
+program equalityالان البراجرام equality بيقول لي
+
+315
+00:21:29,150 --> 00:21:32,630
+if x is a non-product space then it satisfies
+
+316
+00:21:32,630 --> 00:21:35,910
+البراجرام equality الان بدنا نثبت ان هذه غير
+
+317
+00:21:35,910 --> 00:21:39,690
+متساوية جيبلي مثال هيوغو جايبلك مثال حلو هيك وسريع
+
+318
+00:21:39,690 --> 00:21:43,150
+consider x بتساوي واحد واحد وصفر كلين التاني y
+
+319
+00:21:43,150 --> 00:21:47,120
+بيساوي واحد وناقص واحد والباقي صفاربقولك اجمعلي
+
+320
+00:21:47,120 --> 00:21:49,960
+هذا مع هذا هذا مع هذا بيصير اتنين و هدولة بيصير
+
+321
+00:21:49,960 --> 00:21:53,420
+سفر و الباقي سفار اترحل من بعض واحد نفس واحد سفر و
+
+322
+00:21:53,420 --> 00:21:56,080
+هد بيصير واحد نفس واحد بيصير اتنين ماشي و الباقي
+
+323
+00:21:56,080 --> 00:21:59,480
+سفار الان بيصير عبارة عن normal x زاد y عبارة عن
+
+324
+00:21:59,480 --> 00:22:02,620
+اتنين و سفر و سفر و سفر لكل تربيع normal زاد
+
+325
+00:22:02,620 --> 00:22:06,480
+التاني سفر و اتنين و سفر و سفر لكل تربيعنورم هذا
+
+326
+00:22:06,480 --> 00:22:09,780
+اللي هو عبارة عن جديش و انا وين قاعد في الال بيه
+
+327
+00:22:09,780 --> 00:22:13,800
+اللي هو summation تربيع و بعدين باخده اللي هو اللي
+
+328
+00:22:13,800 --> 00:22:18,060
+هو بدون قصر بيقول القصر اللي عندي واحد على بيه لكن
+
+329
+00:22:18,060 --> 00:22:23,020
+احنا مااخده ليهاش نورم تربيعبصير عندى هذا 2 فى 2
+
+330
+00:22:23,020 --> 00:22:27,180
+بقى 4 بطلع 4 و هذا التانى 2 فى 2 هيطلع برضه ايه اش
+
+331
+00:22:27,180 --> 00:22:30,620
+اربعة اربعة اربعة تمانية تعرفوا كيف احنا بنحسب
+
+332
+00:22:30,620 --> 00:22:36,820
+النور summation xi i أُس بي الكل أسمن واحد على
+
+333
+00:22:36,820 --> 00:22:40,740
+اتنين طيب
+
+334
+00:22:40,740 --> 00:22:44,300
+but
+
+335
+00:22:44,300 --> 00:22:50,100
+اتنينفي Normal X تربيع زاد Normal Y تربيع بساوي ال
+
+336
+00:22:50,100 --> 00:22:52,980
+Normal X اللي هو عبارة عن واحد واحد والباقي صفر
+
+337
+00:22:52,980 --> 00:22:58,140
+والتاني واحد ناقص واحد والباقي صفر ماشي الحال طيب
+
+338
+00:22:58,140 --> 00:23:04,100
+شوفوا الآن الأولاني اللي هو عبارة عن ال .. اللي
+
+339
+00:23:04,100 --> 00:23:10,120
+عندي Y ساوي اتنين فيه هذا قيمته اللي هو عبارة عن
+
+340
+00:23:10,120 --> 00:23:16,560
+ال summationاللي هو واحد انتوا ايش ال .. ال .. ال
+
+341
+00:23:16,560 --> 00:23:21,720
+..
+
+342
+00:23:21,720 --> 00:23:27,880
+عشان عندي X بساوي ساية واحد ساية اتنين إلى ما يعني
+
+343
+00:23:27,880 --> 00:23:34,000
+انها هي normal X بساوية summation ساية I أس بيه
+
+344
+00:23:34,000 --> 00:23:38,360
+كله واحد على مين على بيه صح ولا لأ طيب الانوية
+
+345
+00:23:38,360 --> 00:23:46,080
+ساويةالان عندى ال X عندى انا واحد واحد واحد واحد
+
+346
+00:23:46,080 --> 00:23:51,180
+والباقي مين اصفر بنحسبلها ال norm ل واحد واحد
+
+347
+00:23:51,180 --> 00:23:57,720
+والباقي اصفر و يساوي ال summation الاولانى هدقس بي
+
+348
+00:23:57,720 --> 00:24:04,660
+واحد مظبوط زائد التانى1 لأن 1 أُس بيه هو واحد،
+
+349
+00:24:04,660 --> 00:24:08,380
+مظبوط؟ الآن زائد الباقي أسفار، هذا يكون أسمين
+
+350
+00:24:08,380 --> 00:24:15,080
+ويسوء 2 أسمين 1 على بيه، ماشي؟ هذا norm ال X mean،
+
+351
+00:24:15,080 --> 00:24:21,500
+norm ال X تربية، بيصير لأن 2 في 1 و 1 و 1 اللي هي
+
+352
+00:24:21,500 --> 00:24:25,840
+2 في .. هاد 2 برا، هاد برا برا خالص، بحسب بيه، 2
+
+353
+00:24:25,840 --> 00:24:29,620
+في X تربية زي Y تربيةالأن هذه اللي جوا اتنين
+
+354
+00:24:29,620 --> 00:24:32,000
+اصواحى دالا بيه لكل تربية و تاني اتنين اصواحى دالا
+
+355
+00:24:32,000 --> 00:24:35,340
+بيه لكل تربية هدولة مجموحين بساوي اللي هو عبارة عن
+
+356
+00:24:35,340 --> 00:24:39,340
+هدولة تمتين اه دلوقتي طبعا بيصير اتنين على بي
+
+357
+00:24:39,340 --> 00:24:42,440
+اتنين على بي تمتين وهي في اتنين بيصير اربعة في
+
+358
+00:24:42,440 --> 00:24:45,780
+اتنين اقصى اتنين على بي هذه مش ممكن تصير تمانية
+
+359
+00:24:45,780 --> 00:24:49,140
+إلا في حالة الـB أش بتساوي اتنين يعني في حالة
+
+360
+00:24:49,140 --> 00:24:52,640
+الـL2 و الـB لاتساوي اتنين إذا هذه أكيد مالها
+
+361
+00:24:52,640 --> 00:24:56,330
+بتسويش تمانيةوها دي طبعا x زائد y اللي هي عبارة عن
+
+362
+00:24:56,330 --> 00:25:00,310
+اتنين وشفر وشفر بس اتنين أس بي أس واحد علميه بيصير
+
+363
+00:25:00,310 --> 00:25:04,690
+اتنين و تربيه بيصير أربع فاهمين؟ فعلا إذا صارت
+
+364
+00:25:04,690 --> 00:25:07,850
+البراجرام law is not satisfied إذا القلبي is not a
+
+365
+00:25:07,850 --> 00:25:13,440
+Hilbert space اللي بعته اللي بعتهمثال آخر اللي هو
+
+366
+00:25:13,440 --> 00:25:17,840
+الـ space of all continuous functions space C of A
+
+367
+00:25:17,840 --> 00:25:22,620
+وB this space is not an inner product space hence
+
+368
+00:25:22,620 --> 00:25:25,460
+is not Hilbert space طبعا ال continuous functions
+
+369
+00:25:25,460 --> 00:25:29,080
+هذه الأولاني
+
+370
+00:25:29,080 --> 00:25:34,190
+ال norm اللي عليها ال integrationالان هذا ال norm
+
+371
+00:25:34,190 --> 00:25:37,910
+تبعه مين؟ اللي هو ال maximum اللي ال norm عليه
+
+372
+00:25:37,910 --> 00:25:43,630
+maximum مش هيعمل inner product خد الآن خد لك two
+
+373
+00:25:43,630 --> 00:25:48,550
+functions مش هيحققن ال parallelogram له X of T
+
+374
+00:25:48,550 --> 00:25:51,950
+بيساوي واحد و Y of T اللي هو ثابتة و Y of T linear
+
+375
+00:25:51,950 --> 00:25:55,210
+اللي هي عبارة عن T على B minus A ناقص A على B
+
+376
+00:25:55,210 --> 00:25:59,260
+minus A اللي هي عبارة عن دالة اللي هي أيش خطيةشوف
+
+377
+00:25:59,260 --> 00:26:02,320
+الآن on the closed interval mean J اللي هي J
+
+378
+00:26:02,320 --> 00:26:05,500
+بتساوي إيهاش A وB وده بدي تشتغل على الـ 01 بينما
+
+379
+00:26:06,500 --> 00:26:09,180
+كانت تجيب مثال على النساء بس احنا بدنا C و V و A و
+
+380
+00:26:09,180 --> 00:26:15,220
+B in general خد الآن هذه الدالة خطية متصلة وهذه
+
+381
+00:26:15,220 --> 00:26:18,260
+الدالة ثابتة متصلة اذا انا اكيد ال X و ال Y مالهم
+
+382
+00:26:18,260 --> 00:26:22,300
+دوال موجودات في ال C و V و A و B ونورم الأولى نورم
+
+383
+00:26:22,300 --> 00:26:25,480
+الأولى ال maximum للواحد واحد نورم الثانية ال
+
+384
+00:26:25,480 --> 00:26:29,380
+maximum لل T minus A و B minus A لما تتراوح بين ال
+
+385
+00:26:29,380 --> 00:26:34,740
+A و بين مين ال Bماشي هذا الـ T تزايد للدالة هذا
+
+386
+00:26:34,740 --> 00:26:39,900
+تزايدية لأن T على B minus A موجبة وهذه كانت ثابت
+
+387
+00:26:39,900 --> 00:26:44,680
+زائد ثابت اه ماشي الحال فالان اعلى قيمة لها عند
+
+388
+00:26:44,680 --> 00:26:48,900
+مين عند اللي هي T بتساوي B واقع القيمة عند الأولى
+
+389
+00:26:48,900 --> 00:26:54,360
+ليه لها تزايدية فإذا القيمة القصوى لها عند B يعني
+
+390
+00:26:54,360 --> 00:26:58,290
+B minus A على B minus A ويسويهاش واحدالـ X زائد Y
+
+391
+00:26:58,290 --> 00:27:02,250
+بيساوي ال maximum للـ X اللي هي واحد والـ Y هيها
+
+392
+00:27:02,250 --> 00:27:06,350
+يجمعوها لبعض هذه طبعا ثابتة وهذه ال maximum اللي
+
+393
+00:27:06,350 --> 00:27:09,470
+هي جديش واحد يعني كلها على بعض هذه بتكون ال
+
+394
+00:27:09,470 --> 00:27:12,790
+maximum اللي هي عندك بيساوي بي ويساوي جديش اتنين
+
+395
+00:27:13,410 --> 00:27:18,490
+الان X-Y هي واحد ناقص هذه بيصير الآن هذه اللي هي
+
+396
+00:27:18,490 --> 00:27:21,110
+ال maximum اللي عند مين عند ال A مش عند ال B ده
+
+397
+00:27:21,110 --> 00:27:24,690
+لاتنقصيها لأنها صارت بنضربها بناقص فالان هذه بيصير
+
+398
+00:27:24,690 --> 00:27:29,130
+عندي ال maximum عند T بتساوي ال maximum بيصير عند
+
+399
+00:27:29,130 --> 00:27:33,510
+T بتساوي A اللي هي A-A على B-A يعني بتساوي ايه؟
+
+400
+00:27:33,510 --> 00:27:38,560
+واحد فاهمينطيب إذا صار عندى حسبنا اللى هو النرمات
+
+401
+00:27:38,560 --> 00:27:42,040
+كلها لو جيت ضربت 2 في normal X تربيع زاد normal Y
+
+402
+00:27:42,040 --> 00:27:45,600
+تربيع هذا واحد و هذا واحد اللى هو واحد و واحد
+
+403
+00:27:45,600 --> 00:27:48,640
+اتنين في اتنين بطلع اربعة لكن هذا تربيع زاد هذا
+
+404
+00:27:48,640 --> 00:27:52,320
+تربيع هي الأولان اتنين ربعه بطلع اربعة و هذا
+
+405
+00:27:52,320 --> 00:27:55,420
+التاني واحد ربعه بطلع خمسة الأربعة مش الخمسة اكيد
+
+406
+00:27:55,420 --> 00:27:59,740
+إذا مش متحققة إذا ال space اللى عندى is not an
+
+407
+00:27:59,740 --> 00:28:00,080
+inner
+
+408
+00:28:07,850 --> 00:28:15,270
+Remark الأخيرة حسبت رمارك واحد for any x و y in a
+
+409
+00:28:15,270 --> 00:28:20,470
+real inner product space الحكي في واحد عالمين على
+
+410
+00:28:20,470 --> 00:28:23,850
+real inner product space ان ال inner product بين x
+
+411
+00:28:23,850 --> 00:28:27,270
+و y بساوة ربع في normal x زاد y لكل تربيع ناقص x
+
+412
+00:28:27,270 --> 00:28:31,550
+minus y لكل تربيعللفرقان XY in the complex inner
+
+413
+00:28:31,550 --> 00:28:36,710
+product space الآن الـ real تبعه هذا الـ HD هذا
+
+414
+00:28:36,710 --> 00:28:40,170
+المكان inner product بسوء هذا اللي فوق و ال
+
+415
+00:28:40,170 --> 00:28:44,070
+imaginary عبارة عن ربع ال X زائد IY و ال X minus
+
+416
+00:28:44,070 --> 00:28:48,990
+main IY الكتر بيعمل شغل حسابات بحت يعني بتيجي
+
+417
+00:28:48,990 --> 00:28:54,610
+بتاخد تحسب هذا تحسب هذاهيطلع عندك اللي هو المقدار
+
+418
+00:28:54,610 --> 00:28:59,810
+اللي هو بيطلع عندك بساوء أربع الريال بايت لل X وY
+
+419
+00:28:59,810 --> 00:29:03,010
+هذا في حالة الكمبيوتر في حالة الريال بيطلع هذا
+
+420
+00:29:03,010 --> 00:29:09,290
+أحسبلكم واحدة والتانية زيها عشان برضه ليطمئنوا
+
+421
+00:29:09,290 --> 00:29:19,930
+قلوبكم أنا بقلبي مطمئن عليها طيب شوفوا صلى على
+
+422
+00:29:19,930 --> 00:29:24,590
+النبي عليه الصلاة والسلامعندي الـ inner product
+
+423
+00:29:24,590 --> 00:29:34,750
+اللي هي norm ال X زائد Y الكل تربيع ناقص norm ال X
+
+424
+00:29:34,750 --> 00:29:38,650
+minus Y الكل تربيع، صح؟ بساوي ال inner product لل
+
+425
+00:29:38,650 --> 00:29:44,470
+X زائد Y و X زائد Y ناقص ال X minus Y و X minus Y
+
+426
+00:29:44,470 --> 00:29:49,630
+معايا يا جماعة، اه؟ و يساوي الفك هذه الأولى بساوي
+
+427
+00:29:49,630 --> 00:30:00,830
+X و Xزائد x و y زائد y و x زائد y و y أي واحدة
+
+428
+00:30:00,830 --> 00:30:06,050
+تنتيج تلاتة أيه الرابعة اللي بعيدها ناقص x و x
+
+429
+00:30:06,050 --> 00:30:14,150
+ناقص يبصير زائد x و y لأن x و minus y ناقص ناقص
+
+430
+00:30:14,150 --> 00:30:24,640
+اللي هي ناقص y و y تلت ناقصزائد Y أو X طيب هدولة
+
+431
+00:30:24,640 --> 00:30:31,480
+مع بعض لأ هدولة مع بعض و هدولة مع بعض ضال بساوي
+
+432
+00:30:31,480 --> 00:30:43,980
+اتنين في X و Y زائد اتنين Y و X صح؟ و يساوي و
+
+433
+00:30:43,980 --> 00:30:54,590
+يساوي اتنين في X و Yزاد XY conjugate هذا الآن
+
+434
+00:30:54,590 --> 00:30:57,590
+العدد زاد ال conjugate له بطلع اللي هو اتنين
+
+435
+00:30:57,590 --> 00:31:05,340
+الريالأي العدد a زاد ib بنضيف له a minus ib لو
+
+436
+00:31:05,340 --> 00:31:10,600
+ضفناها مع بعض إيش بطلع اتنين الريال فبصير عندى هذا
+
+437
+00:31:10,600 --> 00:31:16,540
+بسوء اتنين الريال part لل x و y اللي هو في اتنين
+
+438
+00:31:16,540 --> 00:31:22,060
+بصير معله اربعة ريال part فبصير عندى اللي هو هذا
+
+439
+00:31:22,960 --> 00:31:29,680
+هذا ناقص هذا في ربع بطلع الريال برضه لو كان ريال
+
+440
+00:31:29,680 --> 00:31:35,440
+لو كان ريال بكون أصلا اللي هو هذا صفار فبكون ال X
+
+441
+00:31:35,440 --> 00:31:39,540
+و ال Y هو نفسه ال Y و ال X فبصير الأولى يشملها
+
+442
+00:31:39,540 --> 00:31:43,760
+automatic الأخيرة similarly احسبها دي هتطلعولها
+
+443
+00:31:43,760 --> 00:31:47,600
+أربعة في ال imaginary برضه مبارك الله فيكم و إلى
+
+444
+00:31:47,600 --> 00:31:48,380
+لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/4GZHS19Cyqk_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/4GZHS19Cyqk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..41bd42c57fe81831665c2ccbc92aa47ef8a5e4c2
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/4GZHS19Cyqk_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2286, "start": 5.04, "end": 22.86, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى أهله وصحبه أجمعين المحاضرة رقم 17 مساق تحليل اقتراني أو تحليل دالي طلاب وطالبات الجامعة الإسلامية ماجستير رياضيات", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 5551, 3224, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 3282, 47524, 995, 4587, 6055, 5016, 20292, 1211, 1975, 38149, 2288, 7649, 1829, 34051, 6055, 5016, 20292, 1211, 11778, 6027, 1829, 23032, 15040, 3555, 4032, 9566, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 3714, 26108, 14851, 13546, 12602, 1829, 46958, 1829, 9307], "avg_logprob": -0.07755160495775555, "compression_ratio": 1.9238578680203047, "no_speech_prob": 1.52587890625e-05, "words": [{"start": 5.04, "end": 5.42, "word": "بسم", "probability": 0.86474609375}, {"start": 5.42, "end": 5.6, "word": " الله", "probability": 0.9580078125}, {"start": 5.6, "end": 5.98, "word": " الرحمن", "probability": 0.9734700520833334}, {"start": 5.98, "end": 6.36, "word": " الرحيم", "probability": 0.9952799479166666}, {"start": 6.36, "end": 6.72, "word": " الحمد", "probability": 0.8875325520833334}, {"start": 6.72, "end": 7.04, "word": " لله", "probability": 0.92431640625}, {"start": 7.04, "end": 7.26, "word": " رب", "probability": 0.967529296875}, {"start": 7.26, "end": 7.76, "word": " العالمين", "probability": 0.9923502604166666}, {"start": 7.76, "end": 8.18, "word": " والصلاة", "probability": 0.8773193359375}, {"start": 8.18, "end": 8.6, "word": " والسلام", "probability": 0.9617513020833334}, {"start": 8.6, "end": 8.8, "word": " على", "probability": 0.484375}, 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topology و بيسير عندنا اللي هي او بيعمل metric space و ثم بيعملنا topology", "tokens": [2304, 33599, 1829, 2423, 7649, 257, 19914, 4290, 1901, 307, 257, 3566, 7284, 1674, 1901, 2423, 19914, 4290, 1901, 31439, 5551, 8592, 42213, 3224, 3566, 7284, 1674, 4032, 4117, 33456, 3224, 9154, 6055, 33753, 4724, 9566, 1863, 4724, 39648, 24793, 16472, 2423, 7284, 1674, 4724, 1829, 25957, 1211, 1192, 1793, 31439, 8978, 2423, 14407, 4587, 3615, 2423, 7284, 1674, 4724, 1829, 25957, 1211, 2026, 3714, 3555, 33599, 25720, 4032, 2423, 2026, 4724, 1829, 25957, 1211, 13672, 1829, 31439, 13672, 1829, 39896, 1192, 1793, 4032, 4724, 1829, 3794, 13546, 43242, 8315, 13672, 1829, 39896, 1975, 2407, 4724, 1829, 25957, 1211, 20678, 1901, 4032, 38637, 2304, 4724, 1829, 25957, 1211, 8315, 1192, 1793], "avg_logprob": -0.21163504956556217, "compression_ratio": 2.018181818181818, "no_speech_prob": 2.1278858184814453e-05, "words": [{"start": 122.19999999999999, "end": 122.88, "word": "ماشي", "probability": 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فعلا إذا صارت البراجرام law is not satisfied إذا القلبي is not a Hilbert space اللي بعته اللي بعته", "tokens": [2407, 11296, 11778, 1829, 23032, 3555, 3615, 995, 2031, 30767, 16373, 3215, 288, 13672, 1829, 39896, 6225, 3555, 9640, 3660, 18871, 1975, 2655, 1863, 9957, 4032, 8592, 5172, 2288, 4032, 8592, 5172, 2288, 4724, 3794, 1975, 2655, 1863, 9957, 5551, 3794, 4724, 1829, 5551, 3794, 36764, 24401, 11203, 2304, 1829, 3224, 4724, 1829, 9381, 13546, 1975, 2655, 1863, 9957, 4032, 6055, 2288, 21292, 3224, 4724, 1829, 9381, 13546, 5551, 25513, 3615, 6156, 995, 16095, 9957, 22807, 6156, 3615, 15040, 11933, 15730, 20328, 9640, 2655, 2423, 26890, 26108, 2288, 10943, 2101, 307, 406, 11239, 11933, 15730, 25062, 1211, 21292, 307, 406, 257, 19914, 4290, 1901, 13672, 1829, 4724, 34268, 3224, 13672, 1829, 4724, 34268, 3224], "avg_logprob": -0.3198369477106177, "compression_ratio": 1.7129186602870814, "no_speech_prob": 8.344650268554688e-06, "words": [{"start": 1494.35, "end": 1494.67, "word": "وها", 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space hence is not Hilbert space طبعا ال continuous functions هذه الأولاني ال norm اللي عليها ال integration", "tokens": [2304, 12984, 6027, 19753, 34740, 13672, 1829, 31439, 2423, 39184, 1901, 295, 439, 10957, 6828, 1901, 383, 295, 316, 4032, 33, 341, 1901, 307, 406, 364, 7284, 1674, 1901, 16678, 307, 406, 19914, 4290, 1901, 23032, 3555, 3615, 995, 2423, 10957, 6828, 29538, 16247, 12610, 7649, 1829, 2423, 2026, 13672, 1829, 25894, 11296, 2423, 10980], "avg_logprob": -0.3476562404206821, "compression_ratio": 1.535294117647059, "no_speech_prob": 1.8477439880371094e-06, "words": [{"start": 1511.36, "end": 1511.82, "word": "مثال", "probability": 0.8253580729166666}, {"start": 1511.82, "end": 1512.34, "word": " آخر", "probability": 0.765380859375}, {"start": 1512.34, "end": 1513.3, "word": " اللي", "probability": 0.53369140625}, {"start": 1513.3, "end": 1513.44, "word": " هو", "probability": 0.98583984375}, {"start": 1513.44, "end": 1513.6, "word": " الـ", "probability": 0.55224609375}, 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1839.46, "word": " Y", "probability": 0.919921875}, {"start": 1839.46, "end": 1839.6, "word": " و", "probability": 0.92578125}, {"start": 1839.6, "end": 1839.88, "word": " X", "probability": 0.95751953125}, {"start": 1839.88, "end": 1841.46, "word": " صح؟", "probability": 0.7724609375}, {"start": 1841.46, "end": 1841.78, "word": " و", "probability": 0.53125}, {"start": 1841.78, "end": 1842.18, "word": " يساوي", "probability": 0.931640625}, {"start": 1842.18, "end": 1843.98, "word": " و", "probability": 0.87060546875}, {"start": 1843.98, "end": 1844.3, "word": " يساوي", "probability": 0.970458984375}, {"start": 1844.3, "end": 1844.82, "word": " اتنين", "probability": 0.9871826171875}, {"start": 1844.82, "end": 1845.44, "word": " في", "probability": 0.9892578125}, {"start": 1845.44, "end": 1846.54, "word": " X", "probability": 0.9658203125}, {"start": 1846.54, "end": 1846.7, "word": " و", "probability": 0.99072265625}, {"start": 1846.7, "end": 1847.04, "word": " Y", "probability": 0.84912109375}], "temperature": 1.0}, {"id": 81, "seek": 185801, "start": 1848.01, "end": 1858.01, "text": "زاد XY conjugate هذا الآن العدد زاد ال conjugate له بطلع اللي هو اتنين الريال", "tokens": [11622, 18513, 48826, 45064, 23758, 6024, 48506, 18863, 3215, 3215, 30767, 18513, 2423, 45064, 46740, 4724, 9566, 1211, 3615, 13672, 1829, 31439, 1975, 2655, 1863, 9957, 2423, 16572, 6027], "avg_logprob": -0.4046875109275182, "compression_ratio": 1.2765957446808511, "no_speech_prob": 0.0005950927734375, "words": [{"start": 1848.01, "end": 1848.55, "word": "زاد", "probability": 0.4613037109375}, {"start": 1848.55, "end": 1849.25, "word": " XY", "probability": 0.48046875}, {"start": 1849.25, "end": 1851.37, "word": " conjugate", "probability": 0.9306640625}, {"start": 1851.37, "end": 1852.79, "word": " هذا", "probability": 0.1907958984375}, {"start": 1852.79, "end": 1854.59, "word": " الآن", "probability": 0.802490234375}, {"start": 1854.59, "end": 1855.39, "word": " العدد", "probability": 0.91748046875}, {"start": 1855.39, "end": 1855.63, "word": " زاد", "probability": 0.84716796875}, {"start": 1855.63, "end": 1855.71, "word": " ال", "probability": 0.6806640625}, {"start": 1855.71, "end": 1856.01, "word": " conjugate", "probability": 0.9033203125}, {"start": 1856.01, "end": 1856.47, "word": " له", "probability": 0.319580078125}, {"start": 1856.47, "end": 1857.13, "word": " بطلع", "probability": 0.7425537109375}, {"start": 1857.13, "end": 1857.25, "word": " اللي", "probability": 0.572998046875}, {"start": 1857.25, "end": 1857.35, "word": " هو", "probability": 0.95947265625}, {"start": 1857.35, "end": 1857.59, "word": " اتنين", "probability": 0.9171142578125}, {"start": 1857.59, "end": 1858.01, "word": " الريال", "probability": 0.7771809895833334}], "temperature": 1.0}, {"id": 82, "seek": 188206, "start": 1859.96, "end": 1882.06, "text": "أي العدد a زاد ib بنضيف له a minus ib لو ضفناها مع بعض إيش بطلع اتنين الريال فبصير عندى هذا بسوء اتنين الريال part لل x و y اللي هو في اتنين بصير معله اربعة ريال part فبصير عندى اللي هو هذا", "tokens": [10721, 1829, 18863, 3215, 3215, 257, 30767, 18513, 39073, 44945, 11242, 33911, 46740, 257, 3175, 39073, 45164, 48812, 5172, 8315, 11296, 20449, 45030, 11242, 11933, 1829, 8592, 4724, 9566, 1211, 3615, 1975, 2655, 1863, 9957, 2423, 16572, 6027, 6156, 3555, 9381, 13546, 43242, 7578, 23758, 4724, 3794, 2407, 38207, 1975, 2655, 1863, 9957, 2423, 16572, 6027, 644, 24976, 2031, 4032, 288, 13672, 1829, 31439, 8978, 1975, 2655, 1863, 9957, 4724, 9381, 13546, 20449, 43761, 1975, 25513, 27884, 12602, 1829, 6027, 644, 6156, 3555, 9381, 13546, 43242, 7578, 13672, 1829, 31439, 23758], "avg_logprob": -0.24881115134643472, "compression_ratio": 1.8103448275862069, "no_speech_prob": 0.00034737586975097656, "words": [{"start": 1859.96, "end": 1860.76, "word": "أي", "probability": 0.5208740234375}, {"start": 1860.76, "end": 1861.56, "word": " العدد", "probability": 0.9357096354166666}, {"start": 1861.56, "end": 1861.88, "word": " a", 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0.6983235677083334}, {"start": 1866.24, "end": 1866.7, "word": " بطلع", "probability": 0.7406005859375}, {"start": 1866.7, "end": 1867.66, "word": " اتنين", "probability": 0.8662109375}, {"start": 1867.66, "end": 1868.08, "word": " الريال", "probability": 0.9171549479166666}, {"start": 1868.08, "end": 1869.54, "word": " فبصير", "probability": 0.8895263671875}, {"start": 1869.54, "end": 1869.94, "word": " عندى", "probability": 0.6038818359375}, {"start": 1869.94, "end": 1870.6, "word": " هذا", "probability": 0.82666015625}, {"start": 1870.6, "end": 1871.84, "word": " بسوء", "probability": 0.58160400390625}, {"start": 1871.84, "end": 1872.3, "word": " اتنين", "probability": 0.9276123046875}, {"start": 1872.3, "end": 1872.8, "word": " الريال", "probability": 0.9619140625}, {"start": 1872.8, "end": 1873.4, "word": " part", "probability": 0.685546875}, {"start": 1873.4, "end": 1874.04, "word": " لل", "probability": 0.51025390625}, {"start": 1874.04, "end": 1874.34, "word": " x", 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1886.28, "word": " بطلع", "probability": 0.75543212890625}, {"start": 1886.28, "end": 1886.56, "word": " الريال", "probability": 0.8912760416666666}, {"start": 1886.56, "end": 1887.0, "word": " برضه", "probability": 0.927734375}, {"start": 1887.0, "end": 1887.78, "word": " لو", "probability": 0.83642578125}, {"start": 1887.78, "end": 1888.68, "word": " كان", "probability": 0.99169921875}, {"start": 1888.68, "end": 1889.68, "word": " ريال", "probability": 0.9200846354166666}, {"start": 1889.68, "end": 1890.76, "word": " لو", "probability": 0.572265625}, {"start": 1890.76, "end": 1891.14, "word": " كان", "probability": 0.98388671875}, {"start": 1891.14, "end": 1891.6, "word": " ريال", "probability": 0.9547526041666666}, {"start": 1891.6, "end": 1892.28, "word": " بكون", "probability": 0.859130859375}, {"start": 1892.28, "end": 1892.76, "word": " أصلا", "probability": 0.8668619791666666}, {"start": 1892.76, "end": 1893.0, "word": " اللي", "probability": 0.938232421875}, {"start": 1893.0, "end": 1893.22, "word": " هو", "probability": 0.96533203125}, {"start": 1893.22, "end": 1893.46, "word": " هذا", "probability": 0.921875}, {"start": 1893.46, "end": 1894.0, "word": " صفار", "probability": 0.7320149739583334}, {"start": 1894.0, "end": 1894.98, "word": " فبكون", "probability": 0.9392903645833334}, {"start": 1894.98, "end": 1895.16, "word": " ال", "probability": 0.93896484375}, {"start": 1895.16, "end": 1895.44, "word": " X", "probability": 0.796875}, {"start": 1895.44, "end": 1895.66, "word": " و", "probability": 0.7880859375}, {"start": 1895.66, "end": 1895.76, "word": " ال", "probability": 0.475341796875}, {"start": 1895.76, "end": 1896.14, "word": " Y", "probability": 0.9794921875}, {"start": 1896.14, "end": 1896.42, "word": " هو", "probability": 0.978515625}, {"start": 1896.42, "end": 1896.8, "word": " نفسه", "probability": 0.822265625}, {"start": 1896.8, "end": 1896.86, "word": " ال", "probability": 0.607421875}, {"start": 1896.86, "end": 1896.98, "word": " Y", "probability": 0.97265625}, {"start": 1896.98, "end": 1897.1, "word": " و", "probability": 0.96044921875}, {"start": 1897.1, "end": 1897.16, "word": " ال", "probability": 0.75048828125}, {"start": 1897.16, "end": 1897.46, "word": " X", "probability": 0.9921875}, {"start": 1897.46, "end": 1898.54, "word": " فبصير", "probability": 0.9429931640625}, {"start": 1898.54, "end": 1898.98, "word": " الأولى", "probability": 0.83642578125}, {"start": 1898.98, "end": 1899.54, "word": " يشملها", "probability": 0.9248046875}, {"start": 1899.54, "end": 1900.06, "word": " automatic", "probability": 0.67919921875}, {"start": 1900.06, "end": 1901.18, "word": " الأخيرة", "probability": 0.92431640625}, {"start": 1901.18, "end": 1901.86, "word": " similarly", "probability": 0.378173828125}, {"start": 1901.86, "end": 1902.42, "word": " احسبها", "probability": 0.816162109375}, {"start": 1902.42, "end": 1902.88, "word": " دي", "probability": 0.6676025390625}, {"start": 1902.88, "end": 1903.76, "word": " هتطلعولها", "probability": 0.8719482421875}, {"start": 1903.76, "end": 1904.36, "word": " أربعة", "probability": 0.9051106770833334}, {"start": 1904.36, "end": 1904.52, "word": " في", "probability": 0.91650390625}, {"start": 1904.52, "end": 1904.6, "word": " ال", "probability": 0.94873046875}, {"start": 1904.6, "end": 1904.96, "word": " imaginary", "probability": 0.6015625}, {"start": 1904.96, "end": 1906.16, "word": " برضه", "probability": 0.923828125}, {"start": 1906.16, "end": 1906.88, "word": " مبارك", "probability": 0.82489013671875}, {"start": 1906.88, "end": 1906.98, "word": " الله", "probability": 0.97607421875}, {"start": 1906.98, "end": 1907.36, "word": " فيكم", "probability": 0.9755859375}, {"start": 1907.36, "end": 1907.48, "word": " و", "probability": 0.9375}, {"start": 1907.48, "end": 1907.6, "word": " إلى", "probability": 0.71923828125}, {"start": 1907.6, "end": 1907.96, "word": " لقاء", "probability": 0.93017578125}, {"start": 1907.96, "end": 1908.38, "word": " آخر", "probability": 0.813232421875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1908.93575, "duration_after_vad": 1878.0037499999955}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/9LHmh6ZbiLE_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/9LHmh6ZbiLE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a86fcf2bebbc1a253c82fb33e5fddc62bf4c07b5
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/9LHmh6ZbiLE_postprocess.srt
@@ -0,0 +1,1484 @@
+1
+00:00:05,110 --> 00:00:07,690
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,690 --> 00:00:10,410
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,410 --> 00:00:16,970
+آله وصحبه أجمعين هذه المحاضرة الفامنة مساق تحليل
+
+4
+00:00:16,970 --> 00:00:19,910
+دالي أو تحليل اقتراني لطلاب وطالبات الجامعة
+
+5
+00:00:19,910 --> 00:00:24,700
+الإسلامية ماجستير رياضيةهنا المرة الماضية اللى هو
+
+6
+00:00:24,700 --> 00:00:28,780
+في المحاضرة السابعة اللى هو chapter واحد والان
+
+7
+00:00:28,780 --> 00:00:31,460
+بدنا ندخل ل chapter اتنين اللى هو normal spaces
+
+8
+00:00:31,460 --> 00:00:35,480
+and banach spaces حكينا في الأول عن metric spaces
+
+9
+00:00:35,480 --> 00:00:39,450
+والان بنحكي عن اللى هو ال banach spacesأحنا قلنا
+
+10
+00:00:39,450 --> 00:00:42,650
+فيه topological spaces وفيه في داخله اللي هو ال
+
+11
+00:00:42,650 --> 00:00:45,610
+metric spaces يعني كل metric spaces او topological
+
+12
+00:00:45,610 --> 00:00:49,490
+spaces او لكن العكس ليس صحيح ممكن نلاقي
+
+13
+00:00:49,490 --> 00:00:52,490
+topological spaces مش metric spaces الان ديين على
+
+14
+00:00:52,490 --> 00:00:57,720
+اللي هو احنا اللي هو بعد ما أخدناالـ Topological
+
+15
+00:00:57,720 --> 00:01:03,020
+Spaces اللي هو عندنا الـ Metric Spaces في داخله
+
+16
+00:01:03,020 --> 00:01:06,340
+وفيه في داخله اللي الآن هناخد مين الـ Normed
+
+17
+00:01:06,340 --> 00:01:09,860
+Spaces والشبطن الثالث هناخد في داخله اللي هو الـ
+
+18
+00:01:09,860 --> 00:01:15,220
+Hilbert Spaces يعني كل هيكة اللي هو عندك كل
+
+19
+00:01:15,220 --> 00:01:19,400
+Hilbert Norm وكل Normed Metric وكل Metric
+
+20
+00:01:19,400 --> 00:01:23,860
+Topological لكن الرجوع في أمثلة بتقول لأ ليس شرطة
+
+21
+00:01:24,290 --> 00:01:28,130
+طيب إذا هذه هي الصورة العامة و في داخل ال ال space
+
+22
+00:01:28,130 --> 00:01:31,410
+ال ال space اللي احنا بنشتغل عليه ال R و R تربيع و
+
+23
+00:01:31,410 --> 00:01:35,050
+R تقعيب اللي هو ال Herbert spaces و من ثم هتكون
+
+24
+00:01:35,050 --> 00:01:39,790
+اللي هو كل اللي فوق متحققة فيه اللي هو ال space
+
+25
+00:01:39,790 --> 00:01:42,210
+اللي احنا بنشتغل فيه في ال calculus و في ال
+
+26
+00:01:43,370 --> 00:01:46,850
+المعادلة التفاضلية في الاحتبانات و الاخرين طيب
+
+27
+00:01:46,850 --> 00:01:51,250
+صلّعنا بلس والسلام نيجي نشوف معنات الاتنين واحد
+
+28
+00:01:51,250 --> 00:01:55,110
+اللي هو مقدمة عن vector spaces طبعا هذه background
+
+29
+00:01:55,110 --> 00:01:57,330
+موجودة من الأصل عند الواحد من ال baccalaureate
+
+30
+00:01:57,330 --> 00:02:02,730
+ماعرفش ال vector space الآن northern space بنخ
+
+31
+00:02:02,730 --> 00:02:07,960
+space إذا بتتذكروا ال metric space بنى على ست6
+
+32
+00:02:07,960 --> 00:02:12,160
+عليها إيهاش metric دي لأ لأ احنا بدنا ندخل الآن
+
+33
+00:02:12,160 --> 00:02:16,300
+لعمليات الجبرية يعني ال X نفسها مش مجرد اللي هو
+
+34
+00:02:16,300 --> 00:02:19,740
+نقول والله هذا عبارة عن عن 6 ونحط عليها metric لأ
+
+35
+00:02:19,740 --> 00:02:25,730
+بديكون ال X نفسها فيه هي vector spaceبحط مبني على
+
+36
+00:02:25,730 --> 00:02:29,750
+vector space و بعرف عليه اللي هو حاجة اسمها norm
+
+37
+00:02:29,750 --> 00:02:33,510
+norm في الواقع التالت هو تعميم لل absolute value
+
+38
+00:02:33,510 --> 00:02:39,110
+اللي عندنا أو ال absolute value حالة خاصة منه
+
+39
+00:02:39,110 --> 00:02:43,910
+definition a normed space X is a vector space with
+
+40
+00:02:43,910 --> 00:02:49,250
+a norm defined on it ال normed space هو عبارة عن
+
+41
+00:02:49,250 --> 00:02:52,830
+vector space Xلما نعرف عليه اللي هو ده اللي
+
+42
+00:02:52,830 --> 00:02:57,810
+بنسميها non نشوف ايه الشروطة الان بمخ space هو
+
+43
+00:02:57,810 --> 00:03:02,980
+complete non-spaceالـ Complete in the metric
+
+44
+00:03:02,980 --> 00:03:05,980
+defined by the norm يعني الـ Completeness لأن أحنا
+
+45
+00:03:05,980 --> 00:03:09,420
+أخدنا الـ Completeness with respect to metric بعد
+
+46
+00:03:09,420 --> 00:03:12,300
+شوية هنشوف أنه اللي هو الـ Completeness تبع الـ
+
+47
+00:03:12,300 --> 00:03:15,900
+normed space with the metric اللي بنسميه induced
+
+48
+00:03:15,900 --> 00:03:19,700
+by the norm يعني اللي اتولد منه من ال norm اللي
+
+49
+00:03:19,700 --> 00:03:23,590
+عندنا طيب هل جيه تفهموا إيش اللي بقوله؟لأن a norm
+
+50
+00:03:23,590 --> 00:03:28,770
+on a real or complex vector space X is a real
+
+51
+00:03:28,770 --> 00:03:33,110
+valued function on X with whose value at an X is
+
+52
+00:03:33,110 --> 00:03:35,790
+denoted by norm X which has the following
+
+53
+00:03:35,790 --> 00:03:39,950
+properties يعني الآن تتعرفي النورم النورم ما هو
+
+54
+00:03:39,950 --> 00:03:45,250
+اللي عبارة عن دالة من X لعند اللي هو R positive
+
+55
+00:03:45,250 --> 00:03:52,710
+اتحادمين الـ0 تحقق ما يليهإنه F of X هي رمزنا برمز
+
+56
+00:03:52,710 --> 00:03:57,930
+Normal X إذا دمتنا اللي بنحكي عنها هي Normal X
+
+57
+00:03:57,930 --> 00:04:01,830
+تحقق الشروط التالية الشرط الأول إنها تكون أكبر أو
+
+58
+00:04:01,830 --> 00:04:06,370
+يساوي 0 طبيعيالشرط الثاني انها تساوي صفر if and
+
+59
+00:04:06,370 --> 00:04:11,250
+only if x ايش منها بتساوي صفر الشرط الثالث ال norm
+
+60
+00:04:11,250 --> 00:04:14,030
+من ال alpha في x بساوي ال absolute value من ال
+
+61
+00:04:14,030 --> 00:04:17,230
+alpha في ال norm من ال x او المدلس من ال alpha في
+
+62
+00:04:17,230 --> 00:04:20,190
+norm من ال x حسب ال alpha ال scale هذا ال scale من
+
+63
+00:04:20,190 --> 00:04:22,950
+ال alpha اللي هو انا بحكي عن vector space vector
+
+64
+00:04:22,950 --> 00:04:26,470
+space اذا في الارضية اللي هو ال R او ال C ال R او
+
+65
+00:04:26,470 --> 00:04:30,580
+ال C اللي بشتغل فيه بسالخاصية الرابعة هي
+
+66
+00:04:30,580 --> 00:04:33,760
+Triangling Quality Normal X زي Y أصغر من Normal X
+
+67
+00:04:33,760 --> 00:04:39,220
+زي Normal Y لكل X و Y Vectors و Alpha Scalar إذا
+
+68
+00:04:39,220 --> 00:04:44,320
+اتحققت الشروط الأربع هذه بنسميه norm مع هذا ال
+
+69
+00:04:44,320 --> 00:04:48,300
+vector space بنسميه norm of this space
+
+70
+00:04:52,340 --> 00:04:57,460
+بعض الملاحظات المهمة a norm on X defines a metric
+
+71
+00:04:57,460 --> 00:05:01,520
+D on X في الواقع انا بقدر اجيب من ال norm metric
+
+72
+00:05:01,520 --> 00:05:07,300
+كيف بعرفه؟ باجي بقول المسافة بين X و Y بده عنصر
+
+73
+00:05:07,300 --> 00:05:12,360
+بسوء norm X ناقص من Y لو جيت على الشروط الأربعة
+
+74
+00:05:12,360 --> 00:05:15,800
+تبعات ال metric هتلاقيها automatic اشمالها متحققة
+
+75
+00:05:15,800 --> 00:05:18,840
+ايش هالشروط ال metric اول شي دي X و Y أكبر او سوى
+
+76
+00:05:18,840 --> 00:05:24,060
+0وهذا أكبر بشروط النورم الشرط الثاني Normal X
+
+77
+00:05:24,060 --> 00:05:31,300
+minus Y بساوي 0 if and only if يعني DX وY بساوي 0
+
+78
+00:05:31,300 --> 00:05:35,160
+if and only if Normal X minus Y بساوي 0 if and
+
+79
+00:05:35,160 --> 00:05:38,940
+only if حسب اللي هي الخاصية الأولى في ال norm اللي
+
+80
+00:05:38,940 --> 00:05:42,720
+هو X ناطس Y بساوي 0 اللي هو if and only if X إيش
+
+81
+00:05:42,720 --> 00:05:47,590
+بتساوي إذا الشرط التاني للمتريك متحققالشرط اللي هو
+
+82
+00:05:47,590 --> 00:05:52,790
+الثالث ال distance بين ال X و ال Y بيساوي نورم ال
+
+83
+00:05:52,790 --> 00:05:58,530
+X minus Y ماشي اللي هو نفسه بيساوي نورم المين ال Y
+
+84
+00:05:58,530 --> 00:06:03,070
+minus إيش minus X اللي هو بيساوي ال distance بين
+
+85
+00:06:03,070 --> 00:06:07,990
+ال X و ال Y آسف ال Y و ال X ال symmetry إذا الشرط
+
+86
+00:06:07,990 --> 00:06:11,030
+الرابعاللي هو الـ Triangling Quality برضه
+
+87
+00:06:11,030 --> 00:06:14,950
+Automatic بتطلع اللي هي إيش الشرط الرابع؟ ان نورم
+
+88
+00:06:14,950 --> 00:06:21,490
+ال X دي X و Y اللي هو بساوة نورم ال X minus Y بال
+
+89
+00:06:21,490 --> 00:06:25,910
+Triangling Quality تبعت ال norm أصغر وسوء، نورم ال
+
+90
+00:06:25,910 --> 00:06:32,410
+X minus Z زاد نورم ال Z minus Y اللي هي بساوة دي X
+
+91
+00:06:32,410 --> 00:06:37,660
+و Zزا دي زد OI إذا ال triangle inequality برضه
+
+92
+00:06:37,660 --> 00:06:41,920
+متحققة لأن هذا فعلا metric إذا اللي هو أنا بقدر
+
+93
+00:06:41,920 --> 00:06:46,260
+أجيب من ال norm أو أولد من ال norm metric و هذا ال
+
+94
+00:06:46,260 --> 00:06:52,500
+normed space بتسميه the metric space induced by
+
+95
+00:06:52,500 --> 00:06:58,260
+the norm اللي مذكورة طيب هذه الملاحظة الأولىand
+
+96
+00:06:58,260 --> 00:07:00,760
+called the metric induced by the norm. Hence,
+
+97
+00:07:00,960 --> 00:07:04,640
+among the spaces and benefit spaces ايش هتكون؟
+
+98
+00:07:04,640 --> 00:07:09,100
+Metric spaces لكن العكس مش صحيح جدًا و هنجيب بعد
+
+99
+00:07:09,100 --> 00:07:14,070
+شوية مثالييجي الآن لـ .. اللي هي الـ .. الـ
+
+100
+00:07:14,070 --> 00:07:17,710
+equality اللي أمامنا for all x y limited x لـ
+
+101
+00:07:17,710 --> 00:07:20,430
+absolute value لـ normal x ناقص normal y أصغر شويه
+
+102
+00:07:20,430 --> 00:07:23,910
+لـ normal الـ x minus y وهنا سؤال بندوبه عادة في
+
+103
+00:07:23,910 --> 00:07:26,490
+الـ calculus طلاب الـ calculus بنشيل .. بنشيل
+
+104
+00:07:26,490 --> 00:07:29,170
+العصيتين اللي هي عصيتين ونحط عصة عصها لـ absolute
+
+105
+00:07:29,170 --> 00:07:34,510
+value والبرهانة نفس الأسلوب بالظبط زي ما بنبرهن في
+
+106
+00:07:34,510 --> 00:07:40,140
+الـ calculus بنقول احنا normal xبالـ Triangle
+
+107
+00:07:40,140 --> 00:07:45,160
+Inquality أصغر أشهر نورم الـ X ناقص Y زائد نورمين
+
+108
+00:07:45,160 --> 00:07:48,820
+الـ Y بالـ Triangle Inquality اللي قبل بشوية إذا
+
+109
+00:07:48,820 --> 00:07:53,860
+صار عندي نورم الـ X ناقص نورم الـ Y أصغر أشهر نورم
+
+110
+00:07:53,860 --> 00:07:58,660
+الـ X ناقص Y، مظبوط؟ لأن Similarly بدل مبدأ بـ X
+
+111
+00:07:58,660 --> 00:08:03,420
+بتبدأ بـ Y نورم الـ Y أصغر أشهر نورم الـ X minus Y
+
+112
+00:08:03,420 --> 00:08:09,380
+فاهمين؟زائد norm ال X Triangling equality ضفت ال X
+
+113
+00:08:09,380 --> 00:08:14,720
+و طرحت ال X هذي بيصير norm ال Y ناقص norm ال X
+
+114
+00:08:14,720 --> 00:08:21,440
+أصغر يساوي norm ال X minus Y هذي و هذي ضلبت هذي
+
+115
+00:08:21,440 --> 00:08:27,380
+بسالب بيصير عندي اضم هذي بسالب بيصير ناقص او عندي
+
+116
+00:08:27,380 --> 00:08:32,910
+norm ال Xنقص Normal Y أكبر أفشاوي ناقص Normal X
+
+117
+00:08:32,910 --> 00:08:40,690
+minus Y هذه مع هذه بتعطيك Normal X ناقص Normal Y
+
+118
+00:08:40,690 --> 00:08:45,970
+أصغر أفشاوي Normal X ناقص Y وأكبر أفشاوي Normal X
+
+119
+00:08:45,970 --> 00:08:50,030
+minus Y بالثانب وهذه بتعطيني ال absolute value
+
+120
+00:08:50,030 --> 00:08:55,990
+أصغر أفشاوي Normal X minus Normal Y كلام سهلفنجي
+
+121
+00:08:55,990 --> 00:08:59,330
+اللي هو الملاحظة التانية the norm is continuous
+
+122
+00:08:59,330 --> 00:09:03,730
+يعني ال norm نفسه is a continuous function بمعنى
+
+123
+00:09:03,730 --> 00:09:08,170
+آخر اللي هو لما ال X ترسل ل norm ال X اللي هي
+
+124
+00:09:08,170 --> 00:09:13,730
+بنسميها continuous mapping من ال X لعند مين لعند
+
+125
+00:09:13,730 --> 00:09:17,490
+ال R شوفوا كيف نثبت إنها continuous mapping أو
+
+126
+00:09:17,490 --> 00:09:22,050
+continuous function شوفوا
+
+127
+00:09:23,350 --> 00:09:28,530
+الدالة اللي عنده اللي هي مين نسميها F من اللي هو
+
+128
+00:09:28,530 --> 00:09:33,330
+ال X لعند مين طبعا ال X و ال metric تبعها ال
+
+129
+00:09:33,330 --> 00:09:37,170
+induced by the norm لعند ال R positive اتحاد مين
+
+130
+00:09:37,170 --> 00:09:42,050
+ال zero ممكن نثبت انها اللي هو continuous انا جانب
+
+131
+00:09:42,050 --> 00:09:45,830
+ايش احنا بنقول كيف نثبت رايحة وين هي دي فعلا في ال
+
+132
+00:09:45,830 --> 00:09:48,210
+topology تبعنا تبع ال video ال topology يعني ال
+
+133
+00:09:48,210 --> 00:09:54,710
+netF of X لما X تروح ل X0 هذي طبعا X تروح ل X0
+
+134
+00:09:54,710 --> 00:10:00,590
+اللي هو نقوين في ال metric تبعد ل more بتساوي F of
+
+135
+00:10:00,590 --> 00:10:06,190
+X0 يعني for every Y أكبر من 0 there exists Delta
+
+136
+00:10:06,190 --> 00:10:10,360
+بقول أنا بساوي Y such thatلما X تروح للـ X0، إيش
+
+137
+00:10:10,360 --> 00:10:14,380
+معناته؟ إنه نورم الـ X minus X0 يكون أصغر من
+
+138
+00:10:14,380 --> 00:10:19,800
+إبسلون أو من دلتا، يعطيك نورم، اللي هو دي بيصير F
+
+139
+00:10:19,800 --> 00:10:23,860
+of X نقصة في Y، اللي هي نورما من Absolute value،
+
+140
+00:10:23,860 --> 00:10:28,470
+اللي هو Absolute value للـ F of Xناقص f of x0
+
+141
+00:10:28,470 --> 00:10:33,070
+بيتواصلها تكون أصغر من مين؟ من أبسلوت هذه مين هي
+
+142
+00:10:33,070 --> 00:10:39,450
+بساوية absolute value؟ f of x هي نورم الـx ناقص
+
+143
+00:10:39,450 --> 00:10:45,590
+نورم الـx0 هذه الآن من الملاحظة اللي جابلها أصغر
+
+144
+00:10:45,590 --> 00:10:52,090
+أو يساويnorm الـ X ناقص X0 ومن هنا أصغر من دلتا
+
+145
+00:10:52,090 --> 00:10:56,550
+اللي أنا مختار دلتا إيه بتساوي اهو المفروض إذا
+
+146
+00:10:56,550 --> 00:11:01,770
+صارت ال norm إيه شماله is a continuous function
+
+147
+00:11:01,770 --> 00:11:06,030
+طيب، اللي بعد ال
+
+148
+00:11:06,030 --> 00:11:10,270
+median examples اللي هم ناخدهم في العالمين على
+
+149
+00:11:10,270 --> 00:11:16,350
+metric spaces كلها مثبتة يعني مافيش إيش يثبتهمالآن
+
+150
+00:11:16,350 --> 00:11:19,830
+الـ Euclidean space are N Unitary space CN هدولة
+
+151
+00:11:19,830 --> 00:11:22,570
+تبعتنا اللي قبل شوية كنا نعملهم إيه إيش؟ Metric
+
+152
+00:11:22,570 --> 00:11:27,450
+Spaces These are Banach Spaces كل نسبة ناهم
+
+153
+00:11:27,450 --> 00:11:31,450
+completed Complete Metric Spaces with respect to
+
+154
+00:11:31,450 --> 00:11:36,930
+their نوع اللي هي Metrics With norm norm X بساوي
+
+155
+00:11:36,930 --> 00:11:39,750
+ال summation XII كل تربية I من واحد لديه N كل
+
+156
+00:11:39,750 --> 00:11:46,860
+إشماله نصهذا إثباته إنه نورم سهل تثبته نورم بشكل
+
+157
+00:11:46,860 --> 00:11:51,920
+سريع مشابه لما أثبتناها قبل this norm induce the
+
+158
+00:11:51,920 --> 00:11:56,020
+metric هذا النورم إيش معله بولد ال metric التالي
+
+159
+00:11:56,020 --> 00:11:59,720
+دي x y بيساوي نورم ال x minus y و سوصة هذا النورم
+
+160
+00:11:59,720 --> 00:12:03,200
+هيه بيولد metric معين نشوف أشهر ال metric هذا
+
+161
+00:12:03,200 --> 00:12:06,180
+بيساوي ال summation x i i minus gamma i تربيع x i
+
+162
+00:12:06,180 --> 00:12:10,870
+i تبع ال x أو تبع ال y من gamma iطب ما هذا ال
+
+163
+00:12:10,870 --> 00:12:13,810
+metric اللي هتبع زمان ال metric الأولاني إذا صار
+
+164
+00:12:13,810 --> 00:12:16,990
+ال norm هذا بولد نفس ال metric اللي انا أثبتت انه
+
+165
+00:12:16,990 --> 00:12:22,130
+complete metric space إذا صار عندي الآن ال space
+
+166
+00:12:22,130 --> 00:12:26,110
+هذا under this norm اللي وولد نفس ال metric is a
+
+167
+00:12:26,110 --> 00:12:31,690
+complete metric spaceإذا صار بنخ SPS والان إثباته
+
+168
+00:12:31,690 --> 00:12:35,690
+ال norm أكبر أوي يساوي سفر والان اللي هو بيساوي
+
+169
+00:12:35,690 --> 00:12:38,150
+سفر if and only if X بيساوي سفر كله على طول من هنا
+
+170
+00:12:38,150 --> 00:12:43,130
+وبعدين اللي هي ال scalar norm ال alpha X بيساوي ال
+
+171
+00:12:43,130 --> 00:12:48,830
+summationبنعملكم إياها هذه مادلة بس جديدة بقى
+
+172
+00:12:48,830 --> 00:12:53,590
+الباق اللي ال triangles هي Normal Alpha X X بتساوي
+
+173
+00:12:53,590 --> 00:12:59,370
+X I واحد لعندك X I N الان ال Alpha X بتساوي اللي
+
+174
+00:12:59,370 --> 00:13:03,430
+هي Alpha X I واحد لعند ال Alpha X I N هذه بتساوي
+
+175
+00:13:03,430 --> 00:13:09,550
+معايا اه So summation Alpha اللي هي X I I تربيع
+
+176
+00:13:09,550 --> 00:13:16,560
+الكل أص نص I من واحد لعند ال Nماشي الحال
+
+177
+00:13:21,850 --> 00:13:26,170
+طيب هو يساوي هذا ال alpha بيطلع من جوا بيطلع اللي
+
+178
+00:13:26,170 --> 00:13:28,830
+هو alpha تربيه بيطلع برا ال alpha تربيه و نص بيطلع
+
+179
+00:13:28,830 --> 00:13:30,830
+من ال alpha then بيطلع ال absolute value of alpha
+
+180
+00:13:30,830 --> 00:13:35,630
+في ال summation xi i تربيه الكل أص نص من عند واحد
+
+181
+00:13:35,630 --> 00:13:39,210
+لعند ان و هذا عبارة عنه يساوي alpha absolute value
+
+182
+00:13:39,210 --> 00:13:42,530
+of alpha for normal x اذا اللي هي هذه برضه متحققة
+
+183
+00:13:42,530 --> 00:13:46,360
+و و و الاخرىالـ Triangling Collision هي نفس اللي
+
+184
+00:13:46,360 --> 00:13:50,480
+عملناها في الـ Matrix العادي طيب اطلع لفوق الان
+
+185
+00:13:50,480 --> 00:13:55,640
+عند ال space التاني هو ال LB space طبعا هو هذا ال
+
+186
+00:13:55,640 --> 00:14:02,120
+RN نفسه vector space ال RN vector space ال LB برضه
+
+187
+00:14:02,120 --> 00:14:05,670
+vector spaceالـ Vector Space بيحقق شروط الـ Vector
+
+188
+00:14:05,670 --> 00:14:11,070
+Space كلها و الجمع اللي بين عناصره هو جمع بين
+
+189
+00:14:11,070 --> 00:14:15,630
+Sequences عادية Alpha I و Gamma I بيصير Alpha I
+
+190
+00:14:15,630 --> 00:14:18,690
+زائد Gamma I و مجموحين واحد الأخرى عملية الجمع
+
+191
+00:14:18,690 --> 00:14:20,910
+الحادة مع الـ Scalar Multiplication اللي عادي اللي
+
+192
+00:14:20,910 --> 00:14:24,230
+هو Born Twice فاهمين اللي بحكيه؟يعني أنا بقول
+
+193
+00:14:24,230 --> 00:14:29,110
+Alpha في X كيف نضربها Alpha في الأولى؟ زي ما عملت
+
+194
+00:14:29,110 --> 00:14:33,270
+قبل شوية ال point twice اللي هو multiplication هذا
+
+195
+00:14:33,270 --> 00:14:36,970
+بعمله vector space بالقلبي القلبي vector space لو
+
+196
+00:14:36,970 --> 00:14:40,990
+عرفت عليه ال norm التالي هيطلع non despase و ال
+
+197
+00:14:40,990 --> 00:14:43,450
+metric اللي بيطلعه ال norm هو ال metric تبعنا اللي
+
+198
+00:14:43,450 --> 00:14:46,450
+استخدمناه و أثبتنا فيه complete قبل بشوية فبكون
+
+199
+00:14:46,450 --> 00:14:50,550
+عندي أشمله عبارة عن complete non despase إذا حيطلع
+
+200
+00:14:50,550 --> 00:14:55,810
+عندي بنخ spaceإذاً هذا المجلد هو مجلد بنخ مع نورم
+
+201
+00:14:55,810 --> 00:15:00,330
+مخصصة بي نورم ال X بيساوي ثميتي من XI بي الكل اس
+
+202
+00:15:00,330 --> 00:15:05,550
+واحد على بي هيا لان لما نحتاج طول من الميطرك هذا
+
+203
+00:15:05,550 --> 00:15:10,530
+النورم يدفع الميطرك DXY بيساوي نورم ال X minus Y
+
+204
+00:15:11,520 --> 00:15:16,860
+وإي ساوي هذا هو نفس ال metric الأصلي إذا عندي ال
+
+205
+00:15:16,860 --> 00:15:20,000
+metric هذا عملني ال b space وهذا ال metric اللي
+
+206
+00:15:20,000 --> 00:15:23,800
+جيناه المتولد من ال norm اللي عندي إذا ال norm
+
+207
+00:15:23,800 --> 00:15:28,260
+اللي عندي complete اللي هو بيعمل complete اللي هو
+
+208
+00:15:28,260 --> 00:15:30,940
+normed space يعني بيعمل بنخ space
+
+209
+00:15:33,850 --> 00:15:39,110
+نفس القصة الـ space من هو هذا الـ infinity الـ
+
+210
+00:15:39,110 --> 00:15:42,070
+space الـ infinity برضه عناصر و bounded sequences
+
+211
+00:15:42,070 --> 00:15:45,530
+و هو هيعمل vector space ليش هيعمل vector space
+
+212
+00:15:45,530 --> 00:15:48,250
+اللي هو under ال addition اللي هو ال pointwise
+
+213
+00:15:48,250 --> 00:15:49,990
+addition تبع ال sequence و ال scalar
+
+214
+00:15:49,990 --> 00:15:53,430
+multiplication برضه pointwise إذن هيطلع عند هذا ال
+
+215
+00:15:53,430 --> 00:15:56,590
+infinity vector space بشروط اللي بدأنا بنعرفها في
+
+216
+00:15:56,590 --> 00:16:01,670
+الجبر الخطي الآن هذا بدأ عرف عليه metric ال metric
+
+217
+00:16:01,670 --> 00:16:05,150
+اللي بدأ عرفهas if norm ال norm يعرفه norm
+
+218
+00:16:05,150 --> 00:16:09,470
+supernormal xii تبع ال x ال super normal هى واضح
+
+219
+00:16:09,470 --> 00:16:13,050
+ان هذا ال norm هيطلع ليه metric dxy بساعة norm x
+
+220
+00:16:13,050 --> 00:16:16,050
+minus y اللى هو عبارة عن ال super norm الأولانى
+
+221
+00:16:16,050 --> 00:16:18,530
+يعنى نفس ال metric اللى اشتغلنا عليه و أثبتنا ان
+
+222
+00:16:18,530 --> 00:16:22,770
+ال infinity is .. is ايش ماله complete واضح ها إذا
+
+223
+00:16:22,770 --> 00:16:27,250
+صار عند ال ال infinity is ابنخ space يعني complete
+
+224
+00:16:27,250 --> 00:16:32,890
+normed spaceأي شؤال و لا مسرع ما السهل الكلام
+
+225
+00:16:32,890 --> 00:16:38,090
+ماعلكم لا بيض ولا شفطة طيب صلى الله عليه الصلاة
+
+226
+00:16:38,090 --> 00:16:44,850
+والسلام ال space ال space اللي عند c of a و b اللي
+
+227
+00:16:44,850 --> 00:16:48,950
+هو the continuous functions اللي هو عالميا على
+
+228
+00:16:48,950 --> 00:16:54,370
+الفترة a و b اللي قبل بشوية الان الحمال norm يولد
+
+229
+00:16:54,370 --> 00:16:58,970
+نفس اللي هو اللاجنين اللي هو ال metric اللي تبقى
+
+230
+00:16:58,970 --> 00:17:03,480
+ال maximumماذا يعني هذا؟ this space is أبناءك
+
+231
+00:17:03,480 --> 00:17:06,680
+space و ال norm defined by ال norm من هو ال
+
+232
+00:17:06,680 --> 00:17:10,240
+maximum نورم ال X بيساوي ال maximum ل X of T، T
+
+233
+00:17:10,240 --> 00:17:13,900
+Elemental J هذا هيعملني norm of this space كامل،
+
+234
+00:17:13,900 --> 00:17:16,620
+تدربوا في البيت انتوا، تخشوه و تطلعوا بعض لجوهتك،
+
+235
+00:17:16,620 --> 00:17:23,000
+هذا كيف تطلعهذا البرمجة يدعم البرمجة DXY بيساوي
+
+236
+00:17:23,000 --> 00:17:24,820
+البرمجة DXY بيساوي البرمجة DXY بيساوي البرمجة DXY
+
+237
+00:17:24,820 --> 00:17:34,580
+بيساوي البرمجة DXY بيساوي
+
+238
+00:17:34,580 --> 00:17:41,320
+البرمجةالان اللي حكينا عنه قبل بشوية incomplete
+
+239
+00:17:41,320 --> 00:17:44,780
+metric space بالرغم ان هو the space of continuous
+
+240
+00:17:44,780 --> 00:17:49,500
+functions لكن under this metric يعني على المعيار
+
+241
+00:17:49,500 --> 00:17:52,460
+هذا تبع ال metric شوفوا مع اختلاف المعيامات الدنيا
+
+242
+00:17:52,460 --> 00:17:57,600
+هيك أصلاإخن في المعيار بيصير كل الأمور بتختلف فلإن
+
+243
+00:17:57,600 --> 00:18:01,480
+انت خلفت المعيار اللي عليه بدك تجيس أو تبني أو كده
+
+244
+00:18:01,480 --> 00:18:04,360
+أو تعمل limit أو تعمل continuity تبعتك و تعمل ال
+
+245
+00:18:04,360 --> 00:18:07,380
+.. هو كيف اعمل limits احنا و continuous functions
+
+246
+00:18:07,380 --> 00:18:09,740
+و differentiability و كده كل اللي لازم يكون فيه
+
+247
+00:18:09,740 --> 00:18:12,600
+اللي هو عايش topology لإن ال topology هذا أخلفته
+
+248
+00:18:12,600 --> 00:18:14,800
+من إيش لا إيش خلاص بيختلف بيصير ال space اختلف
+
+249
+00:18:15,300 --> 00:18:19,820
+اختلفت .. اختلفت بيصير .. بيصير حتى هو انه .. انه
+
+250
+00:18:19,820 --> 00:18:23,600
+متحقق خاصية الاكتمال او مايتحققش لأنه .. و هذا
+
+251
+00:18:23,600 --> 00:18:28,040
+خاصية الاكتمال تعتمد على ايهاش؟ على خاصية تبوليجية
+
+252
+00:18:28,040 --> 00:18:31,600
+اللي هي على الـmetric نفسه لإنه تعتمد على
+
+253
+00:18:31,600 --> 00:18:34,380
+الـconvergence وانه الـCauchy sequence تكون
+
+254
+00:18:34,380 --> 00:18:37,530
+convergenceوالـ Cauchy Sequence أو الـ Convergence
+
+255
+00:18:37,530 --> 00:18:41,090
+أصلا هي ما يمكن أن نتحدث عنها بدون Metric إذا
+
+256
+00:18:41,090 --> 00:18:44,370
+الأساسي فيها أن هو وجود Metric أو وجود Tomology أو
+
+257
+00:18:44,370 --> 00:18:47,990
+وجود أن هو Norm عشان هي ما اختلف ال Norm أو ما
+
+258
+00:18:47,990 --> 00:18:51,870
+اختلف ال Tomology بصير المقالات مختلفة صار ال
+
+259
+00:18:51,870 --> 00:18:55,370
+continuous function قبل بشوية مش complete وكل
+
+260
+00:18:55,370 --> 00:18:58,310
+continuous function complete طب هنا ماشي لأن هنا
+
+261
+00:18:58,310 --> 00:19:01,150
+norm هنا اختلف عن ال norm هنا واضح الدنيا كيف
+
+262
+00:19:01,150 --> 00:19:07,270
+ناشيها؟ طيبالأمور القليلة هذه مهمة الـ space X of
+
+263
+00:19:07,270 --> 00:19:11,010
+R continuous real valued functions on J with norm
+
+264
+00:19:11,010 --> 00:19:14,310
+defined by norm X بسواق ال integration 0 1 X of T
+
+265
+00:19:14,310 --> 00:19:17,810
+DT إذا أنا أخدت النوم من هنا ال integration is an
+
+266
+00:19:17,810 --> 00:19:23,160
+incomplete metric space لإن هذاالنورم بيولد لي
+
+267
+00:19:23,160 --> 00:19:28,220
+نورم DXY بيسوي نورم X-Y اللي هو الـ metric اللي
+
+268
+00:19:28,220 --> 00:19:31,280
+جابه قبل بشوية أثبتناه إنه مش complete إذا صار
+
+269
+00:19:31,280 --> 00:19:36,220
+عندي هذا is a non-bamach space أو is a non-despace
+
+270
+00:19:36,220 --> 00:19:40,670
+which is not completeأنا non يعني بانخ space
+
+271
+00:19:40,670 --> 00:19:44,270
+خلّيني نقول ان non هنا بس بأنفي فيها ال
+
+272
+00:19:44,270 --> 00:19:47,390
+completeness مابديش أقول non بانخ لإنه وسيلكون
+
+273
+00:19:47,390 --> 00:19:51,370
+نفيها قد يكون من هنا جاية أو من هنا لأ لأ اللي
+
+274
+00:19:51,370 --> 00:19:56,810
+بقصد فيها ان هو التعبير الأدق incomplete non space
+
+275
+00:19:56,810 --> 00:20:03,640
+طيب صلّع لنا بالأساس دي اللي ورسمتها قبل شويةالـ
+
+276
+00:20:03,640 --> 00:20:08,640
+topological space جواته اللي هو metric جواته
+
+277
+00:20:08,640 --> 00:20:14,290
+normed الان ال normedالـ Non-metric الـ Metric مش
+
+278
+00:20:14,290 --> 00:20:17,110
+شرط يكون Non-Dohaي مثال بدي أجيبلكم الـ Metric
+
+279
+00:20:17,110 --> 00:20:23,870
+اللي أخدناه في المحاضرات السابقة مش هيكون مولّج من
+
+280
+00:20:23,870 --> 00:20:29,290
+أي نوم في عندي الآن لمّة هي اللي بتشرّعلي الإثبات
+
+281
+00:20:29,290 --> 00:20:34,630
+هذا اللي هي Translation Invariance بتقولّي a
+
+282
+00:20:34,630 --> 00:20:36,150
+metric space D
+
+283
+00:20:39,590 --> 00:20:44,910
+induced by a norm around space X satisfies the
+
+284
+00:20:44,910 --> 00:20:48,590
+following يعني بيقول ليه لو كان عندكم metric space
+
+285
+00:20:48,590 --> 00:20:54,410
+مولد من norm لازم يحقق ما يليه ماحققش معناته
+
+286
+00:20:54,410 --> 00:21:00,650
+metricك مش مولد من norm ماشي الان a metric space D
+
+287
+00:21:00,650 --> 00:21:08,750
+مولد من normلازم يحقق واحد اتنين الخاصية الاولى ان
+
+288
+00:21:08,750 --> 00:21:12,530
+دي اكس زايد ايه ودي ايه زايد ايه بيساوي دي اكس
+
+289
+00:21:12,530 --> 00:21:19,290
+ومين او ايه هذه الخاصية بس متحققة لو كان ال metric
+
+290
+00:21:19,290 --> 00:21:22,410
+مولد
+
+291
+00:21:22,410 --> 00:21:28,070
+منهم اكيد هتتحققالان لو كان ال metric مولد من ال
+
+292
+00:21:28,070 --> 00:21:32,070
+norm برضه هيكون D α X α Y بسبب شجوط value Alpha في
+
+293
+00:21:32,070 --> 00:21:36,230
+D XY لكل XY اللي انت نفسي والألفة أشمالها scalar
+
+294
+00:21:36,230 --> 00:21:40,670
+ماشي الحالة لأن بمعنى لو هذه الخاصية غير متحققة
+
+295
+00:21:40,670 --> 00:21:43,890
+معناته ال metric تبعك مش مولد من ال norm لأنه لو
+
+296
+00:21:43,890 --> 00:21:46,930
+مولد من ال norm لازم ياش تحققها نفس الاشي التانية
+
+297
+00:21:46,930 --> 00:21:52,950
+عشان تعرفوا فيدتها اللي اثبتها سهل كتيردى x زي دي
+
+298
+00:21:52,950 --> 00:21:57,710
+و y زي دي ايش بيساوي لان ال norm لهذه ناقص هذه x
+
+299
+00:21:57,710 --> 00:22:00,190
+زي دي a ناقص y زي دي a ويساوي ال norm من ال x
+
+300
+00:22:00,190 --> 00:22:05,610
+minus y ويساوي اللى المسافة بين مين x و y اذا نزيح
+
+301
+00:22:05,610 --> 00:22:10,500
+شويةالجهتين، المقطين، X وY، وناخد المسافر بينهم،
+
+302
+00:22:10,500 --> 00:22:14,340
+مش هتفرج، هدف وين؟ هدف وين؟ انتوا، زي ما بيقول،
+
+303
+00:22:14,340 --> 00:22:17,560
+our mind restricted to R، احنا هيك اصلا مركبة،
+
+304
+00:22:17,560 --> 00:22:20,500
+لكن، الان هذا الكلام بيحكي عن وين، فعلا، بس ال
+
+305
+00:22:20,500 --> 00:22:24,720
+North Space، يعني هذا الكلام ليس شرط من انه يتحقق
+
+306
+00:22:24,720 --> 00:22:28,620
+وين، في ال metric space in general، او في ال .. في
+
+307
+00:22:28,620 --> 00:22:32,580
+ال .. في ال .. ال topological spaces، لو ترجمنا
+
+308
+00:22:32,580 --> 00:22:34,580
+هذا الكلام بواسط North and South Spaces، اللي هو
+
+309
+00:22:34,580 --> 00:22:37,630
+Matrix،لأن مافيش متركز فيه، مش شرط يكون فيه متركز
+
+310
+00:22:37,630 --> 00:22:43,990
+في الـ Topology فاهمين ما أقول هو؟ طيب، D Alpha X
+
+311
+00:22:43,990 --> 00:22:48,150
+و Alpha Y بيساوي المعاملة الـ Alpha X ناقص Alpha Y
+
+312
+00:22:48,150 --> 00:22:50,390
+وبيساوي الـ Absolute Value Alpha نوع X وبيساوي
+
+313
+00:22:50,390 --> 00:22:54,690
+Absolute Value Alpha في D X و Y هذا بس متحقق أو
+
+314
+00:22:54,690 --> 00:22:57,670
+مديش أقول بس، مديش أقول بس هذا لو كان الـ Metric
+
+315
+00:22:57,670 --> 00:23:01,800
+induced by the norm هيتحققفعلا لأنه ليش بقول
+
+316
+00:23:01,800 --> 00:23:04,880
+ماتقولش بس لأنه أصلا ممكن ألاجي اللي هو مش metric
+
+317
+00:23:04,880 --> 00:23:10,780
+spaces لكن بتحقق هذه مش non-spaces لكن بتحقق هذه
+
+318
+00:23:12,250 --> 00:23:17,930
+واطلع لفوق space S الـ S مين هو إذا بتذكروا الـ
+
+319
+00:23:17,930 --> 00:23:25,750
+space of all sequences بغض النظر بغض
+
+320
+00:23:25,750 --> 00:23:29,050
+النظر عن إيش ال sequence بيقولي bounded
+
+321
+00:23:29,050 --> 00:23:33,490
+convergence لأ لأ أنا بأخد اللي هو space of مين of
+
+322
+00:23:33,490 --> 00:23:42,680
+sequences طيب نشوف هذا ال space هذا خدناهالآن دعنا
+
+323
+00:23:42,680 --> 00:23:46,860
+نكون الـ vector space من كل التجارب مع مترة بيكس
+
+324
+00:23:46,860 --> 00:23:52,040
+واي بسوء كده vector space of all continuous
+
+325
+00:23:52,040 --> 00:23:56,440
+sequences سيعمل limiters إذا كان الأل الافينية
+
+326
+00:23:56,440 --> 00:24:00,200
+يعمل متر كسباس فهو يعمل متر كسباس والأل الفينية
+
+327
+00:24:00,200 --> 00:24:03,540
+يعمل متر كسباس فهو يعمل متر كسباس أسف vector space
+
+328
+00:24:03,540 --> 00:24:06,900
+ال .. ال .. ال .. الاشي لل .. العليات اللي هي ال
+
+329
+00:24:06,900 --> 00:24:09,200
+pointwise addition وال pointwise scalar
+
+330
+00:24:09,200 --> 00:24:14,860
+multiplicationسيكوانسيز عادية اذا S عبارة عن
+
+331
+00:24:14,860 --> 00:24:18,800
+vector space of all sequences بس هذا احنا عرفنا
+
+332
+00:24:18,800 --> 00:24:22,300
+عليه metric قبل هيك و بعيدا عن vector space عرفنا
+
+333
+00:24:22,300 --> 00:24:24,500
+metric ان المسافة بين X و Y بيساوي ال summation X
+
+334
+00:24:24,500 --> 00:24:28,240
+I I نقص جمع I على اتنين ساي اذا بتذكروا في واحد
+
+335
+00:24:28,240 --> 00:24:31,080
+زياد X I I كده و قلنا ايه ما حطينا هذا عشان نضمن
+
+336
+00:24:31,080 --> 00:24:35,360
+ان ال series Z دي دايما شمالها convergesماشي لأن
+
+337
+00:24:35,360 --> 00:24:38,020
+هذا المقدار اللي فوق هيكون اصغر او شاوي واحد اه
+
+338
+00:24:38,020 --> 00:24:40,900
+فبصير هذا المقدار دايما اصغر او شاوي نص معناته
+
+339
+00:24:40,900 --> 00:24:45,420
+مضمون اللي هو يعني بكون converged لإنه ال geometry
+
+340
+00:24:45,420 --> 00:24:47,520
+accessories واحد على اتنين are converged و ال
+
+341
+00:24:47,520 --> 00:24:51,590
+comparison test الاخر انتوا عارفين طيبفرانكس بيسوي
+
+342
+00:24:51,590 --> 00:24:57,150
+xii and y بيسوي gamma yns show that this metric
+
+343
+00:24:57,150 --> 00:25:01,670
+can't be obtained from a norm اثبت ان هذا ايش ماله
+
+344
+00:25:01,670 --> 00:25:07,110
+مش ممكن يحصل عليه من ال norm اللي هو اثبت واحدة من
+
+345
+00:25:07,110 --> 00:25:10,230
+الخاصية التامة بتتحقق مش كل سنة انت سالمين بيكون
+
+346
+00:25:10,230 --> 00:25:14,190
+مش induced by the normالآن let alpha be scalar
+
+347
+00:25:14,190 --> 00:25:17,290
+such that الـ absolute value أفعى شمالها ابعد مثلا
+
+348
+00:25:17,290 --> 00:25:20,170
+لألفات اللي بتساوي واحد عشان الألفات اللي بتساوي
+
+349
+00:25:20,170 --> 00:25:24,150
+واحد الـ absolute value بيحققن بيحققن بيحققن أنا
+
+350
+00:25:24,150 --> 00:25:30,510
+بدي أجيب إشي ما بيحققش معانا معانا؟إن أنا أقول بيه
+
+351
+00:25:30,510 --> 00:25:35,150
+Alpha X و Alpha Min Y بيساوي ال summation ال Alpha
+
+352
+00:25:35,150 --> 00:25:38,430
+X من ال Alpha Xi I وال Alpha I Alpha Gamma I
+
+353
+00:25:38,430 --> 00:25:41,830
+كسيكونس فبيصير absolute value Alpha Xi minus Alpha
+
+354
+00:25:41,830 --> 00:25:45,790
+Gamma I على 2Xi على 1 زي Alpha Xi I زي Alpha Min
+
+355
+00:25:45,790 --> 00:25:51,010
+Gamma I مثهوم هي ال sequence Alpha X وهي ال
+
+356
+00:25:51,010 --> 00:25:55,560
+sequence Alpha Yالان هذا بيساوي خد هذا absolute
+
+357
+00:25:55,560 --> 00:26:00,180
+value برا وهذه اتنين I وهذه طلحها برا واضح واضح
+
+358
+00:26:00,180 --> 00:26:04,460
+واضح انه بقدرش اللي هو اقول ان هذا بيساوي من
+
+359
+00:26:04,460 --> 00:26:07,280
+absolute value لألفة في هذه يعني انا بقدرش ان اجي
+
+360
+00:26:07,280 --> 00:26:10,660
+اقول والله خد هذا absolute value لألفة وطير هذا
+
+361
+00:26:10,660 --> 00:26:15,080
+وطير هذا هذا الأولاني ايش ما الببطل يساوي هذا واضح
+
+362
+00:26:15,080 --> 00:26:18,680
+فاهمي اللي بحكي اه؟ ويساوي اللي هو
+
+363
+00:26:39,460 --> 00:26:45,810
+بمعنى أخر بمعنى أخرالان من الممال اللي قبل بشوية
+
+364
+00:26:45,810 --> 00:26:50,310
+مستحيل يكون ال metric هذا induced by main by the
+
+365
+00:26:50,310 --> 00:26:55,010
+norm والملاحظة الأخيرة the above example shows
+
+366
+00:26:55,010 --> 00:27:01,890
+that the metric in space need not be normed spaces
+
+367
+00:27:01,890 --> 00:27:11,600
+اه قلها ان لأ عندي بيصير اللي هوماشي اللي هو عند
+
+368
+00:27:11,600 --> 00:27:15,600
+ال topological بحتوى على ال metric و ال metric
+
+369
+00:27:15,600 --> 00:27:19,920
+بحتوى على ال norm و ال norm بحتوى على ال Hilbert و
+
+370
+00:27:19,920 --> 00:27:23,300
+ال Hilbert بحتوى على ال R و ال U ليس شرطا و الله
+
+371
+00:27:23,300 --> 00:27:24,200
+يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/BsKCqLUcy6s.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/BsKCqLUcy6s.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4146468703df00cc073d555440d06d9b49126d3f
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/BsKCqLUcy6s.srt
@@ -0,0 +1,3367 @@
+1
+00:00:05,200 --> 00:00:07,980
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,980 --> 00:00:10,940
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,940 --> 00:00:15,500
+أهله وصحبه أجمعين هذه هي المحاضرة الأولى في مساق 
+
+4
+00:00:15,500 --> 00:00:19,700
+تحليل دالي أو تحليل اقتراني Functional analysis
+
+5
+00:00:19,700 --> 00:00:26,160
+رقم المادة Maths 6324 وهي من المواد الاختيارية 
+
+6
+00:00:26,160 --> 00:00:30,220
+لطلاب وطالبات ماجستير رياضيات في الجامعة الإسلامية 
+
+7
+00:00:30,810 --> 00:00:35,430
+كذلك أيضًا اللي هو نستطيع أن نعطي هذه المادة في 
+
+8
+00:00:35,430 --> 00:00:38,490
+وجود طلاب الـ Baccalaureate ونطلب منهم من المادة 
+
+9
+00:00:38,490 --> 00:00:44,230
+ما هو مناسب لهم الآن راح نتحدث في البداية عن اللي 
+
+10
+00:00:44,230 --> 00:00:48,170
+هو وصف المساق وصف المساق أول شيء اللي هو ال
+
+11
+00:00:48,170 --> 00:00:51,350
+textbook اللي هو Introductory Functional Analysis
+
+12
+00:00:51,350 --> 00:00:55,270
+with Applications لإيروين كريزينج وهذا طبعًا من 
+
+13
+00:00:55,270 --> 00:01:03,280
+الكتب السهلة وفي نفس الوقت الكتب اللي يعني المادة 
+
+14
+00:01:03,280 --> 00:01:06,560
+العلمية فيها تؤدي الغرض بل أنه المادة العلمية 
+
+15
+00:01:06,560 --> 00:01:12,980
+خلينا نقول في الـ course الأولي في التحليل الإلكتروني 
+
+16
+00:01:12,980 --> 00:01:18,970
+لأ هو مناسب ومناسب جداً الآن الموضوعات اللي احنا 
+
+17
+00:01:18,970 --> 00:01:22,390
+هنغطيها المتوقع أن هنغطيها في هذا المساق اللي هي 
+
+18
+00:01:22,390 --> 00:01:26,570
+عبارة عن اللي هي أربع شباتر بالإضافة لجزء من 
+
+19
+00:01:26,570 --> 00:01:30,410
+chapter 7 الشابتر الأول والشابتر الثاني والشابتر 
+
+20
+00:01:30,410 --> 00:01:34,300
+الثالث والشابتر الرابع وجزء من الشابتر السابع طبعًا
+
+21
+00:01:34,300 --> 00:01:36,680
+طلاب الـ Baccalaureate حيكون في عندي أو طلبات الـ 
+
+22
+00:01:36,680 --> 00:01:39,400
+Baccalaureate حيكون في عندي اللي هو chapter 1
+
+23
+00:01:39,400 --> 00:01:42,100
+chapter 2 و chapter 3 معظمه مطلوب منه إن شاء الله 
+
+24
+00:01:42,100 --> 00:01:45,040
+في حينه في كل .. في كل شغلة احنا بدنا إياها بس 
+
+25
+00:01:45,040 --> 00:01:49,180
+للماجستير بنقولهم عنها و chapter 4 يعني جزء منه أو 
+
+26
+00:01:49,180 --> 00:01:52,020
+خلينا نقول شغلات أساسية منه بنعطيها للـ 
+
+27
+00:01:52,020 --> 00:01:54,420
+Baccalaureate والباقي بيكون ل اللي هو طلاب 
+
+28
+00:01:54,420 --> 00:01:58,480
+الماجستير واللي هو جزء أو chapter 7 برضه شغلات 
+
+29
+00:01:58,480 --> 00:02:00,860
+بسيطة لطلاب الـ Baccalaureate والباقي اللي هو 
+
+30
+00:02:00,860 --> 00:02:05,240
+لطلاب الماجستير خليني نشوف مع بعض اللي هو الـ ..
+
+31
+00:02:05,240 --> 00:02:08,380
+إيش الـ course outline بالظبط الجزء الأول اللي هو 
+
+32
+00:02:08,380 --> 00:02:11,660
+هنحكي عن اللي هو في الأسبوعين الأولانيات تقريباً 
+
+33
+00:02:11,660 --> 00:02:15,500
+اللي هو هنحكي عن اللي هو الـ metric spaces اللي هو 
+
+34
+00:02:15,500 --> 00:02:18,100
+chapter واحد هذا هو الـ metric spaces والـ 
+
+35
+00:02:18,100 --> 00:02:21,200
+topological conceptual metric spaces وبعدين هنحكي 
+
+36
+00:02:21,200 --> 00:02:23,320
+عن completeness والـ completion of metric spaces
+
+37
+00:02:23,320 --> 00:02:26,260
+طبعًا كل هذه الكلام .. الكلام هنيجي له بالتفصيل أنا 
+
+38
+00:02:26,260 --> 00:02:29,850
+بقى مروح عليه مرور سريع الآن بنكون خلصنا chapter
+
+39
+00:02:29,850 --> 00:02:34,330
+اللي هو واحد وبنبدأ في chapter اثنين حيكون عن الـ 
+
+40
+00:02:34,330 --> 00:02:38,170
+normed spaces والـ Banach spaces هنعرف شو معناه normed 
+
+41
+00:02:38,170 --> 00:02:40,430
+space وشو معناه Banach space وبعدين هنحكي عن الـ 
+
+42
+00:02:40,430 --> 00:02:42,990
+compactness اللي هي خاصية طوبولوجية طبعًا هنجيها إن 
+
+43
+00:02:42,990 --> 00:02:47,490
+شاء الله وبعدين هنحكي عن اللي هو قطع عريض منيح والـ 
+
+44
+00:02:47,490 --> 00:02:50,640
+لي هو applications هائلة اللي هو linear .. linear
+
+45
+00:02:50,640 --> 00:02:53,340
+and bounded linear operators on and functionals
+
+46
+00:02:53,340 --> 00:02:57,400
+وحنحكي عن اللي هو الـ dual spaces ومن ثم حيكون 
+
+47
+00:02:57,400 --> 00:03:01,500
+عندنا اللي هو الـ first exam الآن الجزء الثاني على 
+
+48
+00:03:01,500 --> 00:03:04,620
+طول بنبدأ اللي هو نكون خلصنا الشابتر الأول وتقريباً 
+
+49
+00:03:04,620 --> 00:03:07,700
+اللي هو الشابتر الثاني بنيجي بشابتر ثلاثة اللي هو الـ 
+
+50
+00:03:07,700 --> 00:03:11,300
+Hilbert spaces هنحكي عن الـ Hilbert spaces هنحكي عن 
+
+51
+00:03:11,300 --> 00:03:13,460
+الـ orthogonal complement والـ direct sum والـ 
+
+52
+00:03:13,460 --> 00:03:16,540
+orthonormal والـ total orthonormal sets and
+
+53
+00:03:16,540 --> 00:03:20,210
+sequences بعدين هنحكي عن اللي هو representation of 
+
+54
+00:03:20,210 --> 00:03:23,450
+functional on Hilbert spaces شيء مرتب وشيء منيح و
+
+55
+00:03:23,450 --> 00:03:28,330
+شيء حلو إن شاء الله هنحكي عنه في حينه بعدين هنحكي 
+
+56
+00:03:28,330 --> 00:03:31,490
+عن اللي هو أنواع بعض الـ operators الـ operators
+
+57
+00:03:31,490 --> 00:03:35,930
+طبعًا عالم واسع وأنواع عالم كبير وعليه دراسات في 
+
+58
+00:03:35,930 --> 00:03:39,110
+كل المجلات في الـ functional equations في الـ 
+
+59
+00:03:39,110 --> 00:03:41,570
+functional analysis في الـ applications في الـ 
+
+60
+00:03:41,570 --> 00:03:45,740
+mechanics في كثير من الـ .. اللي هو .. اللي له 
+
+61
+00:03:45,740 --> 00:03:49,460
+تطبيقات في الفيزياء وفي الـ .. وفي الهندسة إلى آخره 
+
+62
+00:03:49,460 --> 00:03:51,920
+وفي الرياضيات بصورة عامة طبعًا هي الـ Functional
+
+63
+00:03:51,920 --> 00:03:55,380
+Analysis نفسها فيه لها تطبيقات عالية وتطباق .. 
+
+64
+00:03:55,380 --> 00:03:58,060
+وتطبيقات هائلة طبعًا وعلاقتها بالـ Topology
+
+65
+00:03:58,060 --> 00:04:02,440
+وعلاقتها بالجبر يعني زي .. خليني أقول اللي بيعرف 
+
+66
+00:04:02,440 --> 00:04:04,800
+Functional Analysis بيعرف جبر بيعرف .. بيعرف تحليل 
+
+67
+00:04:04,800 --> 00:04:08,020
+بيعرف Topology بيعرف جبر خطي إلى آخره لأن الجبر 
+
+68
+00:04:08,020 --> 00:04:11,150
+الخطي أصلاً من الحياة دي المادة ما تخافوش منها المادة
+
+69
+00:04:11,150 --> 00:04:14,170
+المادة بنعطيها بشكل بسيط وبشكل حلو وبشكل جميل 
+
+70
+00:04:14,170 --> 00:04:19,720
+وماحدش اللي بيتابع مش هيلاقي إن شاء الله مشاكل قلنا 
+
+71
+00:04:19,720 --> 00:04:24,000
+أنواع الـ operators الهيلبرت أت جوينت أوبراتر سلفة 
+
+72
+00:04:24,000 --> 00:04:47,620
+جوينت أوبراتر 
+
+73
+00:04:48,090 --> 00:04:52,210
+كانت الـ exam سريع لأنه بنعرض احنا يعني الـ .. 
+
+74
+00:04:52,210 --> 00:04:56,910
+قاعدين اللي هو الـ course outline الجزء الثاني ..
+
+75
+00:04:56,910 --> 00:05:00,310
+الجزء الثالث من المادة اللي هو الـ .. الـ .. الـ ..
+
+76
+00:05:00,310 --> 00:05:02,210
+أو الـ .. الـ .. بعد الامتحان الثاني اللي هو الـ 
+
+77
+00:05:02,210 --> 00:05:05,450
+Adjoint Operator and Reflexive Spaces هنحكي شو 
+
+78
+00:05:05,450 --> 00:05:08,690
+معناه .. شو معناه Adjoint Operator ومن ثم هنحكي 
+
+79
+00:05:08,690 --> 00:05:12,110
+عن حاجة حلوة وجميلة اسمها الـ Reflexive Spaces و
+
+80
+00:05:12,110 --> 00:05:15,870
+بعدين هنحكي عن الـ category theorem من نظرية المهمة 
+
+81
+00:05:16,100 --> 00:05:20,200
+ومن ثم على اللي هي النظرية الأساسية الأخرى بعد 
+
+82
+00:05:20,200 --> 00:05:23,380
+الـ HN اللي هي الـ Non Form Boundedness Theorem بقى 
+
+83
+00:05:23,380 --> 00:05:26,340
+دي هيك هنحكي عن اللي هو الـ Convergence، شو معناه 
+
+84
+00:05:26,340 --> 00:05:29,040
+Strong وشو معناه Weak Convergence هنحكي عن 
+
+85
+00:05:29,040 --> 00:05:32,280
+الـ Strongest أو Weakest Convergence إلى آخره، إن 
+
+86
+00:05:32,280 --> 00:05:36,140
+شاء الله في الحين وبنكون موجود، أنا يعني وجد نظر 
+
+87
+00:05:36,140 --> 00:05:39,690
+أنه مواضيع ممتعة يعني Convergence of Sequences of 
+
+88
+00:05:39,690 --> 00:05:42,570
+Operators and Functionals ماهي معنية Convergence 
+
+89
+00:05:42,570 --> 00:05:45,730
+of Sequences من Operators أو Convergence of 
+
+90
+00:05:45,730 --> 00:05:49,230
+Sequences من Functionals سنرى ماهي معناه إن شاء 
+
+91
+00:05:49,230 --> 00:05:53,870
+الله ثم سنحكي عن نظرية الأساسية الـ Open Mapping 
+
+92
+00:05:53,870 --> 00:05:57,770
+Theorem ثم سنحكي عن Closed Linear Operators ثم 
+
+93
+00:05:57,770 --> 00:06:01,990
+نختم بالنظرية الرابعة الأساسية Closed Graph
+
+94
+00:06:01,990 --> 00:06:06,050
+Theorem ثم سأكون عندي الـ Third Exam اللي معيشه إن 
+
+95
+00:06:06,050 --> 00:06:10,110
+شاء الله ومن ثم هنبدأ اللي هو في Chapter 7 اللي هو 
+
+96
+00:06:10,110 --> 00:06:13,570
+Spectral اللي هو Theory of Linear Operators on 
+
+97
+00:06:13,570 --> 00:06:16,210
+Known Displaces طبعًا عالم الـ Spectral Theory هذا
+
+98
+00:06:16,210 --> 00:06:20,730
+عالم مهم جدًا وعالم تطبيقات هائلة خصوصًا في الفيزياء 
+
+99
+00:06:20,730 --> 00:06:26,590
+وفي الهندسة إلى آخره وبعدين هنحكي عن اللي هو يعني 
+
+100
+00:06:26,590 --> 00:06:29,750
+طبعًا introductions هدولة لإن بس هنعطيكوا فكرة عنهم 
+
+101
+00:06:30,030 --> 00:06:33,450
+لأن هذا على مواسع يعني ونحكي عن اللي هو البنخ 
+
+102
+00:06:33,450 --> 00:06:37,750
+Algebra اللي هو جبر بنخ وجبر بنخ طبعًا لحاله عالم 
+
+103
+00:06:37,750 --> 00:06:41,670
+يعني اللي هو الناس كثير بتشغل فيه، بتتخصص فيه، و
+
+104
+00:06:41,670 --> 00:06:46,590
+applications تبعته عديدة بنجي بنكون وصلنا لمين لل
+
+105
+00:06:46,590 --> 00:06:50,030
+final exam في كل اللي هو المسار في بعض الـ 
+
+106
+00:06:50,030 --> 00:06:53,890
+references اللي هو عندنا الكتاب المشهور تبع Conway
+
+107
+00:06:53,890 --> 00:06:59,530
+أو مادوكس Conway في عمقه في كده لكن كتاب يعني 
+
+108
+00:06:59,530 --> 00:07:04,850
+كمُرجع مهم مادوكس سهل ولذيذ وسريع لكن بليان برضه 
+
+109
+00:07:05,840 --> 00:07:09,260
+وإن كان بتناول جزء يعني من الـ .. اللي .. اللي في
+
+110
+00:07:09,260 --> 00:07:12,860
+.. اللي في .. اللي في .. اللي في .. اللي هو في Conway أو اللي 
+
+111
+00:07:12,860 --> 00:07:16,460
+هو في Kresing. نيجي بعدين لـ .. في كمان مرجع اسمه 
+
+112
+00:07:16,460 --> 00:07:18,240
+Linear Operator Theory in Engineering and Science
+
+113
+00:07:18,240 --> 00:07:21,400
+ده في الـ Linear Operator .. كثير كثير كثير كثير 
+
+114
+00:07:21,400 --> 00:07:27,780
+للمهتم الكتاب يعني عرضه شيق وعرضه سهل وعرضه كده 
+
+115
+00:07:27,780 --> 00:07:30,760
+ومليان معلومات حول الـ operators وحتى في 
+
+116
+00:07:30,760 --> 00:07:33,710
+applications. introduction to functional analysis
+
+117
+00:07:33,710 --> 00:07:38,350
+تبع تيلر هذا من الكتب القديمة القيمة برضه في الـ 
+
+118
+00:07:38,350 --> 00:07:41,250
+functional analysis للي حابب يطلع عليها نيجي 
+
+119
+00:07:41,250 --> 00:07:43,850
+لموضوع الـ grading الموضوع الأخير اللي هو the final
+
+120
+00:07:43,850 --> 00:07:47,110
+grade will be based on the best six of seven 
+
+121
+00:07:47,110 --> 00:07:50,230
+homeworks يعني أحطيكوا homeworks هتاخدوا هتعطوني 
+
+122
+00:07:50,230 --> 00:07:55,150
+اللي هو تسلموني الـ homeworks كلها وأنا بختار أحسن 
+
+123
+00:07:55,150 --> 00:07:59,010
+ستة من سبعة أو أكثر من ستة من ثمانية اللي بدكم إياها و
+
+124
+00:07:59,010 --> 00:08:02,910
+بعدين هذا يكون عليه 10% الامتحانات اللي حكينا عنها 
+
+125
+00:08:02,910 --> 00:08:06,610
+الـ first و second و third هاخد أحسن اثنين من ثلاثة 
+
+126
+00:08:06,610 --> 00:08:10,210
+وعليها الـ 40% أحسن اثنين والـ final بكون 50% و
+
+127
+00:08:10,210 --> 00:08:14,670
+بكون هيك اللي هو بكون اكتمل اللي هو المية من المية 
+
+128
+00:08:14,670 --> 00:08:17,830
+وإن شاء الله بكون التوفيق لكم جميعًا يا رب 
+
+129
+00:08:17,830 --> 00:08:21,660
+العالمين الآن هذا هو الـ course outline خلينا نبدأ 
+
+130
+00:08:21,660 --> 00:08:26,700
+الآن في الشابتر الأول والـ section الأول الشابتر 
+
+131
+00:08:26,700 --> 00:08:31,620
+الأول هو عبارة عن metric spaces أو الفرغات المترية 
+
+132
+00:08:31,620 --> 00:08:36,160
+أو بمعنى آخر احنا قاعدين بدنا نُعمم المسافة اللي 
+
+133
+00:08:36,160 --> 00:08:39,220
+احنا بنعرفها في اللي هو الـ R وفي الـ R تربيع وفي 
+
+134
+00:08:39,220 --> 00:08:44,680
+القدر بدنا نُعممها ونخرجها على صورة اللي هو أن 
+
+135
+00:08:44,680 --> 00:08:48,950
+تكون in general نشوف إيش اللي بحكيه الشابتر الأول هو 
+
+136
+00:08:48,950 --> 00:08:52,190
+metric spaces الفرغات المترية الـ section الأول هو 
+
+137
+00:08:52,190 --> 00:08:55,550
+حيحكي عن الـ metric spaces الفرغات المترية هندخل 
+
+138
+00:08:55,550 --> 00:09:00,870
+للتعريف وبعض الأمثلة السهلة واللي هي فش فيها إن 
+
+139
+00:09:00,870 --> 00:09:05,190
+شاء الله يعني اللي هو صعوبة وهنشوف كيف نتناول كل 
+
+140
+00:09:05,190 --> 00:09:11,290
+مثال من الأمثلة اللي عندنا الآن تعريف الـ metric
+
+141
+00:09:11,290 --> 00:09:16,610
+a metric space is a pair X وD يعني أنا بحكي 
+
+142
+00:09:16,610 --> 00:09:22,810
+عن الـ metric space هو عبارة عن X معها D دالة إيش 
+
+143
+00:09:22,810 --> 00:09:27,990
+هذه الدالة اللي بتخليني اللي هي مع الـ X تخليني
+
+144
+00:09:27,990 --> 00:09:32,230
+metric space هذه الدالة بتسميها metric هي عبارة عن
+
+145
+00:09:32,230 --> 00:09:36,990
+دالة اللي هي دالة المسافة تعميم لدالة المسافة اللي
+
+146
+00:09:36,990 --> 00:09:41,650
+احنا بنعرفها زمان في سواء في R أو في R تربيعي الآن
+
+147
+00:09:41,650 --> 00:09:47,190
+من X across X لعند هو في الواقع لعند بالظبط بالظبط
+
+148
+00:09:47,190 --> 00:09:51,710
+لعند R positive اتحاد الـ Zero بس لو قلنا R في
+
+149
+00:09:51,710 --> 00:09:54,590
+وجود الشروط اللي بحكيها بكفي الكلام ويكون الكلام
+
+150
+00:09:54,590 --> 00:10:00,270
+اللي هو كمكتمل خليني أشوف الان هي عبارة عن دي 
+
+151
+00:10:00,270 --> 00:10:05,410
+عبارة عن دالة من X across X الى الـ real value of
+
+152
+00:10:05,410 --> 00:10:08,790
+function الى R بالظبط هتكون عند R وزي اتحاد الـ
+
+153
+00:10:08,790 --> 00:10:13,570
+Zero تحقق الشروط التالية أول شرط أن المسافة بين أي
+
+154
+00:10:13,570 --> 00:10:17,750
+نقطتين لازم تكون أكبر أو يساوي صفر هذه الـ X و Y من
+
+155
+00:10:17,750 --> 00:10:21,010
+أين جيات الـ X من الـ X و Y من الـ Y لأن X cross Y
+
+156
+00:10:21,010 --> 00:10:25,940
+أشمالها عبارة عن ordered pair عناصرها إذا الـD X Y
+
+157
+00:10:25,940 --> 00:10:29,200
+أكبر أو يساوي صفر أو المسافة بين X وY أشمال أكبر
+
+158
+00:10:29,200 --> 00:10:31,700
+أو يساوي صفر هذا طبيعي ما احنا عارفين أن مسافتنا
+
+159
+00:10:31,700 --> 00:10:34,920
+المسافة اللي بنحكي عنها اللي هو دايما عمرنا في R وR
+
+160
+00:10:34,920 --> 00:10:38,340
+تربيع هي عبارة عن مسافة يعني أكبر أو يساوي صفر
+
+161
+00:10:38,340 --> 00:10:42,380
+فاحنا عمال قاعدين بنستقي تعريفنا و بنعمم اللي هو
+
+162
+00:10:42,380 --> 00:10:49,290
+اللي بنحكي في الـ metric العادي اتنين المسافة بين X 
+
+163
+00:10:49,290 --> 00:10:54,810
+و Y بتساوي 0 إذا و فقط إذا X بتساوي 100 بتساوي Y
+
+164
+00:10:54,810 --> 00:10:59,290
+يعني المسافة بين النقطة و نفسها 0 ولو كانت 
+
+165
+00:10:59,290 --> 00:11:02,690
+المسافة بين نقطة و أخرى 0 بكون هي النقطة نفسها
+
+166
+00:11:02,690 --> 00:11:07,290
+يعني لن نجد اللي هو نقطتين المسافة بينهم بتساوي 0
+
+167
+00:11:07,290 --> 00:11:10,490
+و لنا مش متساويتين لن نجد هذا اللي هو الشرط الثاني
+
+168
+00:11:10,950 --> 00:11:16,130
+الشرط الثالث أنه دائما المسافة بين X و Y هي نفسها 
+
+169
+00:11:16,130 --> 00:11:19,830
+المسافة بين Y و X طبعا المسافة بين X و Y هي نفسها 
+
+170
+00:11:19,830 --> 00:11:23,330
+المسافة بين Y و X اللي بنسميها في العلاقات اللي هي
+
+171
+00:11:23,330 --> 00:11:28,770
+الـ Symmetric الشرط الثالث أو الرابع اللي هي
+
+172
+00:11:28,770 --> 00:11:32,810
+Triangle Inequality اللي هي جاية من اللي هو من
+
+173
+00:11:32,810 --> 00:11:37,710
+المتباينة المثلثة اللي احنا بنعرفها اللي هو DXY
+
+174
+00:11:38,510 --> 00:11:45,350
+أصغر أو تساوي D X و Z زائد D Z و Y جاي من من 
+
+175
+00:11:45,350 --> 00:11:50,410
+من الهى اللى انتوا بتعرفوها اللى هى لو كان عندى 
+
+176
+00:11:50,410 --> 00:11:54,610
+نقطة هي نقطة و هي نقطة فى الفراغ أو فى الـ plane
+
+177
+00:11:54,610 --> 00:11:58,510
+المسافة بين هذه و هذه بين D X و Y أكيد أصغر أو
+
+178
+00:11:58,510 --> 00:12:02,750
+تساوي المسافة بين هذه و هذه زائد هذه و هذه أي نقطة 
+
+179
+00:12:02,750 --> 00:12:06,350
+أخرى هيعندي X وY لو كانت أي نقطة أخرى Z هيكون
+
+180
+00:12:06,350 --> 00:12:09,590
+مسافة بين X وY أكيد أقل أو يساوي المسافة بين هذه
+
+181
+00:12:09,590 --> 00:12:13,390
+وهذه زائد هذه وهذه هذي الـ Triangle اللي قلتيه
+
+182
+00:12:13,390 --> 00:12:16,330
+طبعا في المثلث أكيد strict لأكبر هذي بحكي عن وين
+
+183
+00:12:16,330 --> 00:12:21,250
+فعلا ما ترى اللي هو الـ R الأرض تربيع الآن قد يكون
+
+184
+00:12:21,250 --> 00:12:24,530
+اللي هو المسافة بالظبط فيها مساواتها يعني هذه strict
+
+185
+00:12:24,530 --> 00:12:28,310
+الأكبر دول لكن قد يكونوا سواها لو كانت X هنا أو Z
+
+186
+00:12:28,310 --> 00:12:32,070
+هنا و Y هنا فبكون المسافة بين X و Y بالظبط تساوي 
+
+187
+00:12:32,070 --> 00:12:35,530
+المسافة بين X و Z زائد المسافة بين Z و Y وعشان هيك
+
+188
+00:12:35,530 --> 00:12:39,670
+تبين الـ triangle equality أصغر أو يساوي إذا تحققت
+
+189
+00:12:39,670 --> 00:12:44,990
+الأربع شروط الأمام هذولة automatically automatically بقول 
+
+190
+00:12:44,990 --> 00:12:49,780
+على الـ ومن ثم مكانة الـ D metric ما على طول بيصير
+
+191
+00:12:49,780 --> 00:12:54,200
+الـ X والـ D أشمالها metric space بتكون عبارة عن
+
+192
+00:12:54,200 --> 00:12:59,900
+مين؟ عن metric space هذه اللي هي اللي هو تعريف
+
+193
+00:12:59,900 --> 00:13:04,200
+اللي هو الـ metric لأن نيجي لبعض الخواص اللي بنقدر 
+
+194
+00:13:04,200 --> 00:13:07,280
+نستقيها أو تعريف الـ metric space بعض الخواص اللي
+
+195
+00:13:07,280 --> 00:13:11,420
+بنقدر نستقيها من اللي هو التعريف اللي أمامنا
+
+196
+00:13:13,310 --> 00:13:18,550
+الخاصية الأولى بقول لي لو كان عندي N element in N
+
+197
+00:13:18,550 --> 00:13:24,550
+ودي ناخدنا أي X واحد و X اتنين و X N element اللي 
+
+198
+00:13:24,550 --> 00:13:28,530
+هي NX اللي بنحكي عليها اللي بنقول عليها متر هيكون
+
+199
+00:13:28,530 --> 00:13:33,070
+المسافة بين distance يعني الـ N عبارة عن بدل اللي
+
+200
+00:13:33,070 --> 00:13:35,490
+هو المسافة بين نقطتين ظهر بس هو المسافة بين
+
+201
+00:13:35,490 --> 00:13:36,350
+نقطتين ونقطتين ونقطتين ونقطتين ونقطتين و
+
+202
+00:13:36,350 --> 00:13:38,370
+نقطتين ونقطتين ونقطتين ونقطتين ونقطتين و
+
+203
+00:13:38,370 --> 00:13:41,910
+نقطتين 
+
+204
+00:13:43,110 --> 00:13:48,810
+و Xn ظهر إيش هو المسافة بين X1 و X2 زائد المسافة
+
+205
+00:13:48,810 --> 00:13:56,210
+بين X2 و X3 زائد المسافة بين Xn-1 و Xn يعني هذه 
+
+206
+00:13:56,210 --> 00:14:00,850
+تعميم للحالة الأولى هذه بدنا نبرهنها أو برهانها
+
+207
+00:14:00,850 --> 00:14:04,030
+سهل by induction انتم حالكم بتقدروا تبرهنوها لكن 
+
+208
+00:14:04,030 --> 00:14:07,450
+خلينا على السريع اعطيكم outline لبرهانها خليها دي
+
+209
+00:14:07,450 --> 00:14:12,110
+نسميها إيه إيش star عارفين كده بنبرهن by induction
+
+210
+00:14:12,110 --> 00:14:16,860
+أول حاجة أول شيء عشان بنها دي لكل n element صحيحة
+
+211
+00:14:16,860 --> 00:14:21,980
+بتقول for n بتساوي واحدة trivial فالان for n
+
+212
+00:14:21,980 --> 00:14:24,560
+بتساوي اتنين for n بتساوي اتنين
+
+213
+00:14:29,300 --> 00:14:35,100
+اللي هي أصغر حتى اتنين برضه trivial لو أنا بالساعة
+
+214
+00:14:35,100 --> 00:14:40,020
+تلاتة X1 و X3 أصغر الساعة المسافة بين X1 و X2 زائد 
+
+215
+00:14:40,020 --> 00:14:44,700
+المسافة بين X2 و X3 الـ Trivial الـ Trivial برضه
+
+216
+00:14:44,700 --> 00:14:47,620
+هذا من وين جاوب من الـ triangle inequality مباشرة
+
+217
+00:14:47,620 --> 00:14:52,370
+من سرعة لأنه كلام سهل أو outline هذا اتنين بنقول 
+
+218
+00:14:52,370 --> 00:14:59,930
+suppose that star is true for n بتساوي k ده نفترض 
+
+219
+00:14:59,930 --> 00:15:03,590
+أنه هذه الجملة صحيحة لأن بتساوي k وبدأت بتها صحيحة
+
+220
+00:15:03,590 --> 00:15:08,150
+لمين ل k زائد واحد يعني بالمعنى الآخر فقضيت هذا صحيح
+
+221
+00:15:08,150 --> 00:15:15,460
+ل k معناته صارت DX1 لعين DXK DX1 لعين DXK أصغر أو
+
+222
+00:15:15,460 --> 00:15:20,080
+يساوي لما أصل لعند XK-1 و XK هذي صحيحة من 
+
+223
+00:15:20,080 --> 00:15:24,080
+الhypothesis induction اللي هم بيدثبتها لمين لـ K
+
+224
+00:15:24,080 --> 00:15:29,660
+زائد واحد سهلة نيجي نثبتها لـ K زائد واحد دي X1 و
+
+225
+00:15:29,660 --> 00:15:36,020
+XK زائد واحد ما لها أصغر أو يساوي دي X واحد و XK
+
+226
+00:15:36,020 --> 00:15:41,140
+زائد دي XK و XK زائد واحد هذي منين؟ من الـ 
+
+227
+00:15:41,140 --> 00:15:45,740
+Triangle equality العادية طبقتها على مين؟ على اللي
+
+228
+00:15:45,740 --> 00:15:48,720
+هو المسافة بين النقطة هذه و النقطة هذه أصغر أو
+
+229
+00:15:48,720 --> 00:15:51,220
+ساوي المسافة بين هذه النقطة و أي نقطة بديها مين
+
+230
+00:15:51,220 --> 00:15:54,260
+هي اللي أخدتها أنا XK زائد المسافة بين النقطة 
+
+231
+00:15:54,260 --> 00:15:56,760
+اللي أخدتها و بين هذه هذه اللي هي by the triangle 
+
+232
+00:15:56,760 --> 00:16:03,490
+equality اللي هي موجودة الـ M4 طيب هذا نفسه هذه
+
+233
+00:16:03,490 --> 00:16:08,390
+أصغر أو ساوي من هنا من الـ hypothesis induction
+
+234
+00:16:08,390 --> 00:16:11,810
+اللي مفترضها يعني by star بتكون هذه أصغر أو ساوي
+
+235
+00:16:11,810 --> 00:16:24,510
+dx1 و x2 زائد dx2 و x3 لما أصل لعين زائد dxk و x-1
+
+236
+00:16:24,510 --> 00:16:31,510
+لعين xk و زائد هذه من الأصل dxk و X K زائد واحد
+
+237
+00:16:31,510 --> 00:16:37,110
+معناته صارت اللي هي هذه اللي فوق صحيحة لمين ل K
+
+238
+00:16:37,110 --> 00:16:40,450
+زائد واحد و معناته أنه أثبتنا هذا صحيحة by
+
+239
+00:16:40,450 --> 00:16:44,670
+induction لكل N element هنا إذا هيك بيكون احنا
+
+240
+00:16:44,670 --> 00:16:49,470
+أثبتنا اللي هو اللي هي الـ note الأولى و كانت صحيحة
+
+241
+00:16:49,470 --> 00:16:49,750
+دائما
+
+242
+00:16:52,970 --> 00:16:56,510
+طيب يا جماعة اتصلوا عندنا عليه الصلاة والسلام نيجي 
+
+243
+00:16:56,510 --> 00:16:59,990
+اللي هو ناخد الملاحظة الثانية إيش الملاحظة الثانية
+
+244
+00:16:59,990 --> 00:17:06,330
+بتقول بدنا نحرف الآن حاجة اسمها إيش sub space sub
+
+245
+00:17:06,330 --> 00:17:11,090
+space من اسمه sub space اذا اكيد اكيد اللي بدي 
+
+246
+00:17:11,090 --> 00:17:14,670
+اشتغل عليها جزء من الـ space الأصلي عشان تكون sub
+
+247
+00:17:14,670 --> 00:17:18,150
+space منه وsub space منه كاملة بدي اتحقق خياصه
+
+248
+00:17:18,150 --> 00:17:20,770
+يعني الصغير هذا بيكون إيش ايه للكبير يعني بحقق
+
+249
+00:17:20,770 --> 00:17:31,960
+خياصه كاملة فبنقول ان الـ y و d تلدى sub space of x
+
+250
+00:17:31,960 --> 00:17:35,000
+و d إيش الـ x و الـ d طبعا x و d في مفترضين و metric 
+
+251
+00:17:35,000 --> 00:17:38,820
+space إيش معناه هذا يكون sub metric space من هذا 
+
+252
+00:17:38,820 --> 00:17:45,080
+شرطين الشرط الأول ان الـ y جزء من x ها كيف الـ y جزء
+
+253
+00:17:45,080 --> 00:17:50,160
+من من من x اي واحد اتنين اتنين ان الـ d تلد هذا
+
+254
+00:17:50,160 --> 00:17:53,100
+اللي بترك اللي على الـ d اللي على الـ y طبعا الـ d
+
+255
+00:17:53,100 --> 00:17:56,380
+تلد هذا بشتغل من وين من y cross y و برمي في r
+
+256
+00:17:56,380 --> 00:18:02,160
+positive اتحاد الـ zero هذا D تلدى لازم يكون هو نفسه
+
+257
+00:18:02,160 --> 00:18:06,160
+الـD بس شغل وين طبعا الـD بيشغل على مين الـD
+
+258
+00:18:06,160 --> 00:18:10,440
+بيشغل على X across X لعند R positive اتحاد الـ0
+
+259
+00:18:10,440 --> 00:18:14,860
+الـD برضه أصلا لما هي الـY cross Y جزئية من X
+
+260
+00:18:14,860 --> 00:18:18,960
+cross X فالآن عشان نسميها The subspace لازم تكون D
+
+261
+00:18:18,960 --> 00:18:23,600
+تلدى اللي بتشغل على الـY هي نفسها D لما اشتغلت على 
+
+262
+00:18:23,600 --> 00:18:27,770
+الـY across Y يعني بمعنى آخر D تلد ده هي the 
+
+263
+00:18:27,770 --> 00:18:32,850
+restricted function D on Y cross Y يعني نفسها D بس
+
+264
+00:18:32,850 --> 00:18:37,470
+على مين على Y cross Y في هذه الحالة بنسمي الـ Y وD
+
+265
+00:18:37,470 --> 00:18:41,490
+تل ده عبارة عن subspace من مين يا جماعة من اللي
+
+266
+00:18:41,490 --> 00:18:47,140
+هو الـ X وD طيب نيجي الآن هذا اللي هو تعريف الـ
+
+267
+00:18:47,140 --> 00:18:52,280
+subspace اللي حكينا عنه نيجي الآن نحكي عن بعض 
+
+268
+00:18:52,280 --> 00:18:59,940
+الأمثلة عن اللي هو الـ metric spaces نيجي للأمثلة
+
+269
+00:18:59,940 --> 00:19:04,040
+أكيد هنبدأ بمثالنا اللي احنا بنقول عليه سهل و اللي
+
+270
+00:19:04,040 --> 00:19:09,300
+بنعرفه من زمان اللي هو أي مثال اللي هو المثال انه
+
+271
+00:19:09,300 --> 00:19:14,100
+ناخد الـ real line الـ real line R ر  line line الـ
+
+272
+00:19:14,100 --> 00:19:18,860
+real line هايه هبدنا نعرف المسافة بين X و بين وين
+
+273
+00:19:18,860 --> 00:19:22,400
+و بين Y هنعرف المسافة اللي بتعرفوها انتم اللي هو
+
+274
+00:19:22,400 --> 00:19:28,700
+DX و Y بدي أعرفها على الـ R يعني هتكون D تبعته من
+
+275
+00:19:28,700 --> 00:19:33,140
+R cross R هترمي وين اكيد هنرميها في R positive
+
+276
+00:19:33,140 --> 00:19:35,700
+تحت Zero عشان يكون metric بالشروط اللي احنا 
+
+277
+00:19:35,700 --> 00:19:40,780
+عارفينها طيب، D X Y كده بدي أعرفها عبارة عن اللي هو
+
+278
+00:19:40,780 --> 00:19:43,560
+y minus x وحيانا ما كنتش عارف مين البعد ومين 
+
+279
+00:19:43,560 --> 00:19:46,280
+الإيجابي لو ما كنتش عارف كان المجهولات على طول
+
+280
+00:19:46,280 --> 00:19:50,000
+بكتب absolute value لـ y minus x وهذا يعني المسافة
+
+281
+00:19:50,000 --> 00:19:53,060
+بين x و y هل هذه بتحقق شروط أ أو بتحقق شروط
+
+282
+00:19:53,060 --> 00:19:56,960
+الأربعة ما أنتم شايفين هذه أول شرط أكبر أو يساوي
+
+283
+00:19:56,960 --> 00:20:00,080
+صفر تريفياً y minus x أكبر أو يساوي صفر هاي واحد
+
+284
+00:20:00,080 --> 00:20:05,060
+اثنين أكيد dy dx y اللي هو absolute value اللي هو
+
+285
+00:20:05,060 --> 00:20:10,080
+y minus x بساوي x minus y اللي هو عبارة عن مين dy
+
+286
+00:20:10,080 --> 00:20:15,380
+ومين dx  وx إذا المسافة بين y وx هي نفس المسافة بين
+
+287
+00:20:15,380 --> 00:20:24,880
+مين x وy الشرط الثالث اللي هو لو dxy بتساوي صفر
+
+288
+00:20:25,650 --> 00:20:29,790
+بدأ أثبت لكم if and only if اللي هو مين اللي هو x
+
+289
+00:20:29,790 --> 00:20:32,490
+بيساوي y شرط الثالث يا جماعة هاي الشرط الثالث ده
+
+290
+00:20:32,490 --> 00:20:35,690
+أنتم أنصحوه هاي الشرط الثالث بدأ أثبت الشرط
+
+291
+00:20:35,690 --> 00:20:39,990
+الثالث هذا بقول dx y بيساوي صفر if and only if
+
+292
+00:20:39,990 --> 00:20:43,650
+إيش تعرف dx y بيساوي صفر dx y اللي هو absolute
+
+293
+00:20:43,650 --> 00:20:48,250
+value لو y minus x بتساوي صفر if and only if هذه
+
+294
+00:20:48,250 --> 00:20:51,770
+الأرقام عادية بتعرفوها أن y إيش بتساوي x هذا الشرط
+
+295
+00:20:51,770 --> 00:20:56,250
+الثالث محقق نجي للشرط الرابع الشرط الرابع أنتم
+
+296
+00:20:56,250 --> 00:21:00,150
+عارفين هو هذا ما هي مَخاصة absolute value عند D لو
+
+297
+00:21:00,150 --> 00:21:06,430
+أخذنا أي x و y و z  دالّات وين هو البدايات؟ في ℝ dx
+
+298
+00:21:06,430 --> 00:21:12,600
+و y بساوي ال absolute value of x minus y بساوي ال
+
+299
+00:21:12,600 --> 00:21:16,520
+absolute value of x minus y هذه absolute value
+
+300
+00:21:16,520 --> 00:21:20,940
+عادية اللي بنعرفها أكيد أكيد أكيد أصغر أو يساوي ال
+
+301
+00:21:20,940 --> 00:21:23,940
+absolute value of x minus z زي ال absolute value
+
+302
+00:21:23,940 --> 00:21:29,650
+of z minus y طب هذه من هي اللي تعرفتها عبارة عن dx
+
+303
+00:21:29,650 --> 00:21:35,910
+و z و هذه من هي dz y إذا dx y أصغر يساوي dx و z
+
+304
+00:21:35,910 --> 00:21:40,630
+dz y إذا تحققت شروط الأربعة إذا في المثال الأول
+
+305
+00:21:40,630 --> 00:21:44,750
+الـ dx y بسبب absolute value x minus y على الـ ℝ
+
+306
+00:21:44,750 --> 00:21:50,850
+أشمله حقق شروط المتر كلها إذا صارت الـ ℝ  محاذة الـ
+
+307
+00:21:50,850 --> 00:21:55,650
+metric اللي هو عبارة عن metric space مع هذه الدالة
+
+308
+00:21:55,650 --> 00:21:58,810
+عبارة عن metric space وهذا بنسميه الـ Euclidean
+
+309
+00:21:58,810 --> 00:22:03,110
+metric space الـ ℝ أو اللي هو اللي مستقبلاً نجيه
+
+310
+00:22:03,110 --> 00:22:06,950
+بولدنا ال topology اللي احنا بنعرفه اللي هو بنسميه
+
+311
+00:22:06,950 --> 00:22:12,370
+usual topology هذا مستقبله هذا المثال الأول سهل
+
+312
+00:22:12,370 --> 00:22:16,010
+البسيط المثال الثاني برضه سهل إيش المثال الثاني
+
+313
+00:22:16,010 --> 00:22:22,190
+المثال الثاني اللي هو بده يعرف الآن metric على مين
+
+314
+00:22:22,190 --> 00:22:26,450
+على الـ ℝ تربيع نشوف إيش الـ metric اللي اللي
+
+315
+00:22:26,450 --> 00:22:30,150
+بنعرفه على الـ ℝ تربيع شوفوا يا جماعة صلوا على
+
+316
+00:22:30,150 --> 00:22:33,710
+النبي عليه الصلاة والسلام الآن عندي الـ ℝ بتاعة الـ
+
+317
+00:22:33,710 --> 00:22:40,100
+helix أشمالها هي عبارة عن الـ ℝ تربيع هذه الـ ℝ اللي
+
+318
+00:22:40,100 --> 00:22:45,240
+هي الـ ℝ تربيع الآن عصرها إيه أشمالها Ordered pair
+
+319
+00:22:45,240 --> 00:22:53,720
+بتعرف دي دي من ℝ تربيع across ℝ تربيع وبدأ ارميها
+
+320
+00:22:53,720 --> 00:22:56,340
+في المكان اللي احنا بنرميها اللي هو ℝ بزوجة اتحاد
+
+321
+00:22:56,340 --> 00:23:00,820
+الـ zero الآن بدأ أعرفها كالتالي العناصر اللي في
+
+322
+00:23:00,820 --> 00:23:04,660
+الـ ℝ تربيع لو أخذت أي x و y في الـ ℝ تربيع الـ x
+
+323
+00:23:04,660 --> 00:23:07,340
+نفسه هيكون زوج مرتب ما بتعرفين وإذا الـ x إيش
+
+324
+00:23:07,340 --> 00:23:13,210
+هيساوي x1 و x2 مثلاً و y إيش هيساوي بساوي
+
+325
+00:23:13,210 --> 00:23:16,530
+γ1 و γ2 خلّيني أستخدم الحروف اللاتينية
+
+326
+00:23:16,530 --> 00:23:21,690
+عشان أخلفها عن الـ x و الـ y عشان يكون اللغة مميزة
+
+327
+00:23:21,690 --> 00:23:27,610
+هيك أو اللي هو نتوافق مع لغة الكتاب كمان حي بده
+
+328
+00:23:27,610 --> 00:23:35,400
+يعرف المسافة بين x و y بساوي ال absolute value ال
+
+329
+00:23:35,400 --> 00:23:39,720
+absolute value x1 ناقص γ1 زائد ال
+
+330
+00:23:39,720 --> 00:23:43,940
+absolute value x2 ناقص γ2 هذا
+
+331
+00:23:43,940 --> 00:23:47,140
+بتدعي أنه metric هو بتدعي أنه metric خلينا نشوف
+
+332
+00:23:47,140 --> 00:23:53,840
+شروطه هل متحقق ولا لأ نيجي بناخد الآن خد أي فرعاني
+
+333
+00:23:56,060 --> 00:24:02,500
+يعني x و y و z element in ℝ تربيع شكل هنا x1
+
+334
+00:24:02,500 --> 00:24:06,360
+بيساوي مثلاً x1 و x2 و y بيساوي
+
+335
+00:24:06,360 --> 00:24:11,160
+γ1 و γ2 و z بتساوي α1 مثلاً
+
+336
+00:24:11,160 --> 00:24:15,180
+و α2 خلينا نشوف اللي هو الشروط الأربعة طبعاً
+
+337
+00:24:15,180 --> 00:24:18,020
+أول تلت شروط عادة أن جماعة سهلة و أنا سهلة طبعاً
+
+338
+00:24:18,020 --> 00:24:21,580
+بس خلينا نمروا سريع عليها و أنتم بت .. بت .. بت
+
+339
+00:24:21,580 --> 00:24:29,730
+.. بتعيدوا شغل كتابة الشرط الأول عندي dxy dxy هايه
+
+340
+00:24:29,730 --> 00:24:33,370
+أكيد إيش ماله أكبر أو يساوي صفر واضح لإن هذه أعداد
+
+341
+00:24:33,370 --> 00:24:35,250
+أكبر أو يساوي صفر وهذه أعداد أكبر أو يساوي صفر لإن
+
+342
+00:24:35,250 --> 00:24:39,930
+absolute value اثنين الشرط التالي اللي هو هذا
+
+343
+00:24:39,930 --> 00:24:45,730
+بيساوي صفر dxy هي ساوي صفر إذا و فقط إذا اللي هو
+
+344
+00:24:45,730 --> 00:24:48,810
+هذا بساوي صفر يعني بمعنى آخر absolute value x y
+
+345
+00:24:48,810 --> 00:24:52,970
+واحد ناقص γ1 زائد الثاني بسفر هذا أكبر
+
+346
+00:24:52,970 --> 00:24:55,210
+ساوي صفر وهذا أكبر ساوي صفر إذا التانين مع بعض
+
+347
+00:24:55,210 --> 00:24:58,390
+صفر أكيد هذا هيكون صفر وهذا هيكون صفر مش ممكن
+
+348
+00:24:58,390 --> 00:25:01,770
+يواحد يكون سالب الثاني لأ التانين كل واحد إيش ماله
+
+349
+00:25:01,770 --> 00:25:06,070
+كل واحد تساوي صفر إذا هذا ناقص هذا بساوي اللي هو x
+
+350
+00:25:06,070 --> 00:25:09,810
+y2 ناقص γ2 بساوي إيه الصفر لإن هذا
+
+351
+00:25:09,810 --> 00:25:15,080
+بيساوي صفر بس إذا و فقط إذا هذا صفر وهذا صفر وهذا
+
+352
+00:25:15,080 --> 00:25:18,940
+الكلام واضح إيش معناه هذا الكلام هذا معناه إنك
+
+353
+00:25:18,940 --> 00:25:22,280
+x1 إيش هتساوي γ1 إيش هذا معناه
+
+354
+00:25:22,280 --> 00:25:26,120
+x2 بيساوي γ2 وهذا شو معناه إنك
+
+355
+00:25:26,120 --> 00:25:30,240
+x1 و x2 هي نفس γ1 و γ
+
+356
+00:25:30,240 --> 00:25:35,040
+2 وهذا معناه أن x إيش هي y إذا المسافة بين x
+
+357
+00:25:35,040 --> 00:25:37,740
+و y بيساوي صفر إذا و فقط إذا اللي هو الـ x بالها
+
+358
+00:25:37,740 --> 00:25:44,050
+بتساوي y الخاصية الثالثة الطبيعية السهلة والسريعة
+
+359
+00:25:44,050 --> 00:25:49,870
+المسافة بين x و y هي المسافة بين y و x γ1
+
+360
+00:25:49,870 --> 00:26:00,070
+ناقص x1 إذا dxy بساوي dyx أو x كلام trivial
+
+361
+00:26:00,070 --> 00:26:04,370
+و سهل طيب نجي يا جماعة لأ الخاصية الرابعة الخاصية
+
+362
+00:26:04,370 --> 00:26:09,290
+الرابعة إيش الخاصية الرابعة أنه dx و y dx
+
+363
+00:26:09,290 --> 00:26:13,490
+و y اللي هو ظهر بساوي dx و z dz و y
+
+364
+00:26:13,490 --> 00:26:18,850
+ظهر عليها الآن أكيد x1 ناقص γ1 انتبه
+
+365
+00:26:18,850 --> 00:26:26,370
+بس هالشغل ظهر أو ساوي x1 ناقص α1 زائد
+
+366
+00:26:26,370 --> 00:26:30,530
+α1 ناقص γ1 أكيد بالتالي ال quality
+
+367
+00:26:30,530 --> 00:26:33,550
+بتبعد زمان أنت بتلافش absolute value لأن هدول أشمال
+
+368
+00:26:33,550 --> 00:26:39,000
+نقابلها نجيب شوف شيء اللي بساوي هذا الآن x2 ناقص
+
+369
+00:26:39,000 --> 00:26:44,680
+γ2 برضه أصغر يساوي x2 ناقص α2 زائد
+
+370
+00:26:44,680 --> 00:26:49,920
+α2 ناقص γ2 برضه طبقت ال .. ال .. ال ..
+
+371
+00:26:49,920 --> 00:26:52,820
+اللي هو مين اللي هو ال triangle inequality تبعت ال
+
+372
+00:26:52,820 --> 00:26:55,820
+absolute value تبعت من تبعت ال calculus زمان الأهم
+
+373
+00:26:55,820 --> 00:26:59,990
+هو هدولة التنتين إجمح هذه زائد هذه أصغر أو يساوي
+
+374
+00:26:59,990 --> 00:27:04,430
+هذه زائد هذه تمشوا في k4 بعد أذنكم بس بدي أمسح
+
+375
+00:27:04,430 --> 00:27:10,870
+حدّه بيصير عندي اللي هو التالي بيصير .. أكتب فيه
+
+376
+00:27:10,870 --> 00:27:15,070
+لون ثاني عشان نميزه عنه بيصير عندي يا جماعة اللي
+
+377
+00:27:15,070 --> 00:27:20,910
+هو x1 ناقص γ1 زائد x2 ناقص γ
+
+378
+00:27:20,910 --> 00:27:27,350
+2 أصغر أو يساوي أصغر أو يساوي هذه x1 ناقص
+
+379
+00:27:27,350 --> 00:27:32,190
+α1 هذه زائد هذه ماشي يا جماعة x1
+
+380
+00:27:32,190 --> 00:27:36,930
+ناقص α2 
+
+381
+00:27:36,930 --> 00:27:42,950
+ناقص α2 زائد الجزء هذا زائد هذا زائد هذا
+
+382
+00:27:42,950 --> 00:27:49,580
+اللي هو α1 ناقص γ1 زائد α2 ناقص γ
+
+383
+00:27:49,580 --> 00:27:54,380
+2 اتطلعوا عليهم هذول واضحة الصورة تتصور بعضكم جال
+
+384
+00:27:54,380 --> 00:27:59,940
+خلصناها هذه هي مين في الواقع هي المسافة بين x و y
+
+385
+00:28:00,870 --> 00:28:04,410
+أصغر أو ساوي هذه في الواقع هذه المسافة بين مين هذه
+
+386
+00:28:04,410 --> 00:28:13,490
+تبعات x وهذه تبعات z اللي هي α1 ناقص x
+
+387
+00:28:13,490 --> 00:28:16,730
+1 ناقص α1 زي α1 ناقص γ1
+
+388
+00:28:16,730 --> 00:28:21,370
+خليني أخد دليل تبعات z اللي هي α1 مع x
+
+389
+00:28:21,370 --> 00:28:27,630
+1 مع α1 و x2 مع α2 هذه
+
+390
+00:28:27,630 --> 00:28:29,910
+2 آسف هذه 2 x2 و α2 هي
+
+391
+00:28:29,910 --> 00:28:34,130
+2 2 مع بعض هذه α2 x1 نقص
+
+392
+00:28:34,130 --> 00:28:37,990
+γ1 اصغر sorry x1 نقص α1 زائد
+
+393
+00:28:37,990 --> 00:28:40,590
+α1 نقص γ1 وهذه x2 نقص α
+
+394
+00:28:40,590 --> 00:28:42,350
+2 ناخدنا هذول 2 2 مع بعض و جمعها في
+
+395
+00:28:42,350 --> 00:28:46,390
+الأول ليه x1 نقص α1 وهذه زائد x
+
+396
+00:28:46,390 --> 00:28:51,130
+2 نقص α2 آسف α2 والتانية α
+
+397
+00:28:51,130 --> 00:28:54,750
+1 ناقص γ1 وهيها والتانية α2 ناقص
+
+398
+00:28:54,750 --> 00:28:58,170
+γ2 هذه الكلامية في الميزة هذه مين هي هي
+
+399
+00:28:58,170 --> 00:29:04,170
+تبعات x وهي تبعات z هي هنا هي هنا هي هنا هي x وهي
+
+400
+00:29:04,170 --> 00:29:08,970
+y و z اللي فرضناها قبل بشوية كتبناها و اشيلناها z
+
+401
+00:29:08,970 --> 00:29:12,790
+بساوي اللي هو γ1 و γ2 صار عندي
+
+402
+00:29:12,790 --> 00:29:19,420
+الآن هذول التنتين هم المثلين dx و z زائد هذول اللي
+
+403
+00:29:19,420 --> 00:29:23,080
+بيمثل من مين هي تبعات α1 تبعات z و هذول
+
+404
+00:29:23,080 --> 00:29:27,760
+تبعات من y الأولى زائد dz و y و بيكون ال
+
+405
+00:29:27,760 --> 00:29:30,980
+triangle inequality أشمالها تحققت و بيكون هذا
+
+406
+00:29:30,980 --> 00:29:38,660
+أثبتنا أن هذا عبارة عن metric space يعني
+
+407
+00:29:38,660 --> 00:29:43,020
+الـ d هذا metric space مع الـ ℝ تربيع بعضكم أكيد
+
+408
+00:29:43,020 --> 00:29:46,000
+سأل قال طب احنا مافيه metric احنا الزمان اللي
+
+409
+00:29:46,000 --> 00:29:49,160
+اتعلمناه و احنا صغار اللي هو أو احنا في ال .. في
+
+410
+00:29:49,160 --> 00:29:53,280
+ال .. في ال .. حتى في الاعدادية أو اللي هو في اللي
+
+411
+00:29:53,280 --> 00:29:56,800
+هي الـ calculus احنا بنعرف المسافة بين نقطتين في
+
+412
+00:29:56,800 --> 00:30:04,280
+الفرق لما يكون عندي النقطة x و y اللي هو في الفرق
+
+413
+00:30:04,280 --> 00:30:06,540
+العادي في ال .. في ال .. في ال .. في ال .. في ال
+
+414
+00:30:06,540 --> 00:30:09,320
+plane العادي اللي احنا أخذنا هندسته لما نزجنا
+
+415
+00:30:09,320 --> 00:30:11,920
+الهندسة الإقليدية x بالساعة و كده و y بالساعة و
+
+416
+00:30:11,920 --> 00:30:16,460
+كده أخذنا المسافة بين x و y اللي هو عبارة عن الجذر
+
+417
+00:30:16,460 --> 00:30:22,610
+التربيعي لـ x1 ناقص γ1 الكل تربيع زائد
+
+418
+00:30:22,610 --> 00:30:27,110
+x2 ناقص γ2 الكل إيش تربيع اه هذا
+
+419
+00:30:27,110 --> 00:30:30,210
+نفسه metric برضه هذا هيحقق شروطه الـ metric و
+
+420
+00:30:30,210 --> 00:30:34,790
+بنسميه برضه أشماله الـ Euclidean metric لإن بعد 
+
+421
+00:30:34,790 --> 00:30:39,370
+فترة هتولوجي بقول أنت بقولها المعلومة هتولوجي بقول
+
+422
+00:30:39,370 --> 00:30:44,670
+في الـ final dimensional space Finite vector space
+
+423
+00:30:44,670 --> 00:30:46,870
+هذا لاحقًا إن شاء الله في الـ finite dimensional
+
+424
+00:30:46,870 --> 00:30:48,970
+space يعني الأرض تربيع finite dimension, dimension
+
+425
+00:30:48,970 --> 00:30:52,970
+له اثنين في الأرض تكعيب في الأرض أرخمس مليون  أر
+
+426
+00:30:52,970 --> 00:30:55,770
+إن هذول finite dimensional space هنلاقي الـ finite
+
+427
+00:30:55,770 --> 00:31:00,390
+dimensional space لو عرفنا كان متر كثير يعرفنا 
+
+428
+00:31:00,390 --> 00:31:04,990
+مليون متر كعلى الـ جد ما بدك عرف Matrix إذا عرفت 
+
+429
+00:31:04,990 --> 00:31:09,430
+Matrix صار عندك Matrix 2، 3، 4، 5 مليون واحد على
+
+430
+00:31:09,430 --> 00:31:13,890
+Final Dimensional Space كلهم هيولدون نفس الـ
+
+431
+00:31:13,890 --> 00:31:16,610
+Topology يعني هيطلع عندنا نفس الـ Topology عشان هي
+
+432
+00:31:17,240 --> 00:31:21,200
+إحنا في الـ R في الـ R في الـ R أو في الـ R تربيع
+
+433
+00:31:21,200 --> 00:31:25,000
+أفضل تكييف هذا الـ Matrix هذا و الـ Matrix هذا 
+
+434
+00:31:25,000 --> 00:31:30,340
+الاثنين R هنجيبهم equivalent يعني هناخد شو معناه
+
+435
+00:31:30,340 --> 00:31:34,420
+equivalent هنجيبهم نفس الـ .. الـ .. الـ Matrix  وهما 
+
+436
+00:31:34,420 --> 00:31:38,680
+اللي بيولد الـ usual topology اللي إحنا بنعرفه الـ
+
+437
+00:31:38,680 --> 00:31:41,480
+usual topology اللي إحنا عايشين فيه في الـ calculus
+
+438
+00:31:41,480 --> 00:31:45,620
+وفي المعادلة التفاضلية وفي التحليل الحقيقي واحد و
+
+439
+00:31:45,620 --> 00:31:48,220
+و و الآخر تحليل حقيقي اثنين هذا اللي هو الـ
+
+440
+00:31:48,220 --> 00:31:52,300
+Euclidean اللي هي الـ usual topologyالـ Limit
+
+441
+00:31:52,300 --> 00:31:54,620
+سبعتنا و الـ Continuity بتبعاتها كلها على أساسها دي
+
+442
+00:31:54,620 --> 00:31:56,740
+مش هأقول لكم في هالشغلها دي إن شاء الله بتيجي لها
+
+443
+00:31:56,740 --> 00:32:02,700
+لاحقًا في حينها بنوضحها أما ملخص الحديث هي عند
+
+444
+00:32:02,700 --> 00:32:06,220
+metric هذا أسمتنا إنه metric وهي الـ metric تبع مين
+
+445
+00:32:06,220 --> 00:32:09,900
+اللي بنعرفه إحنا و هذا الـ metric اللي بنعرفه سهلة
+
+446
+00:32:09,900 --> 00:32:12,800
+وأمه أصلاً الـ team England quality إحنا عارفينها 
+
+447
+00:32:12,800 --> 00:32:18,260
+هي نقطة هي نقطتين هذه مثلاً إحداثية Xi واحد و Gamma
+
+448
+00:32:18,260 --> 00:32:24,290
+واحد و هذه اللي هيأسكساي واحد وكساي اثنين وهذه
+
+449
+00:32:24,290 --> 00:32:30,210
+جامعة واحد و جامعة اثنين هيها المسافة بين هذول
+
+450
+00:32:30,210 --> 00:32:34,910
+الاثنين هيها هي عبارة عن أصغر سواء المسافة بين هذه
+
+451
+00:32:34,910 --> 00:32:40,490
+لو كانت أخذت أي زد ثاني هاي زد الآن قبل ما ناخذ الـ
+
+452
+00:32:40,490 --> 00:32:43,230
+triangle inequality هذه إحنا لو جينا حسبناها
+
+453
+00:32:43,230 --> 00:32:48,170
+المسافة حساب المسافة سهلةاللي هي بالسير هذه اللي
+
+454
+00:32:48,170 --> 00:32:55,010
+هو طولها عبارة عن جاء اللي هي xi2 جامعة واحد جامعة
+
+455
+00:32:55,010 --> 00:32:58,870
+واحد ناقص xi واحد على الاكسات هذه وهذه عبارة عن
+
+456
+00:32:58,870 --> 00:33:01,750
+طولها جامعة اثنين ناقص xi اثنين فبكون الجدر
+
+457
+00:33:01,750 --> 00:33:06,180
+التربيعي هذا اللي هي المسافة اللي هو عبارة عن
+
+458
+00:33:06,180 --> 00:33:08,780
+قانون في The Girth في The Girth هذا التربيع بيساوي
+
+459
+00:33:08,780 --> 00:33:11,640
+هذا التربيع زائد هذا التربيع إذا المسافة بينهم اللي
+
+460
+00:33:11,640 --> 00:33:14,940
+هي المسافة بين هذه وهذه طوله عبارة عن جدر التربيع
+
+461
+00:33:14,940 --> 00:33:18,600
+اللي هذه تربيع زائد هذه تربيع فبكون هذا اللي هو الـ
+
+462
+00:33:18,600 --> 00:33:22,060
+Euclidean metric اللي إحنا بنعرفه في الأصل وكل
+
+463
+00:33:22,060 --> 00:33:26,550
+الشروط اللي هي اللي عندنا مطبقة على الأرض الكعيب
+
+464
+00:33:26,550 --> 00:33:29,730
+بقدر أعمل شيء متشابه يعني على الأرض الكعيب بقدر
+
+465
+00:33:29,730 --> 00:33:33,570
+أقول والله أنا بتاخد الـ X في الأرض الكعيب معناته
+
+466
+00:33:33,570 --> 00:33:37,030
+ايش صارت هذه بدل ما هي اثنين تان صارنمي ثلاثة X I
+
+467
+00:33:37,030 --> 00:33:40,660
+ثلاثة ماشي و هذه جامعة اثنين و هذه بيصير جامعة ثلاثة 
+
+468
+00:33:40,660 --> 00:33:46,120
+فبيصير المسافة هذه زائد هذه زائد اللي بتعرفونه xi 
+
+469
+00:33:46,120 --> 00:33:51,700
+اللي هي ثلاثة ناقص جامعة ثلاثة لكل تربيع هذا برضه 
+
+470
+00:33:51,700 --> 00:33:56,700
+اللي هو metric space بيعمل هذا D بيعمل من R تكعيب
+
+471
+00:33:56,700 --> 00:34:02,230
+metric space أو R تكعيب مع مين مع الـ D واحد قال لي
+
+472
+00:34:02,230 --> 00:34:05,850
+طب حتى in general يا ربّي نبدأ نعمل آه صحيح يعني
+
+473
+00:34:05,850 --> 00:34:11,050
+الآن لو كانت RN RN اللي هي عناصرها n couples يعني
+
+474
+00:34:11,050 --> 00:34:15,310
+عناصرها xi واحد xi اثنين عند xi n مع من مع الـ
+
+475
+00:34:15,310 --> 00:34:18,790
+metric هذا برضه هتعمل metric space الـ metric في 
+
+476
+00:34:18,790 --> 00:34:23,230
+هذه الحالة هتكون dxy الـ x ايش هتكون xi واحد xi
+
+477
+00:34:23,230 --> 00:34:26,630
+اثنين xi ثلاثة عند xi n والـ Y جامعة واحد جامعة 
+
+478
+00:34:26,630 --> 00:34:29,550
+اثنين جامعة ثلاثة عين جامعة n فبكون المسافة بينه
+
+479
+00:34:29,550 --> 00:34:34,530
+عبارة عن الجادر التربيعي لـ XI واحد ناقص جامعة واحد
+
+480
+00:34:34,530 --> 00:34:39,210
+لكل تربيع زائد لما أصل لآخر واحدة XI n ناقص جامعة
+
+481
+00:34:39,210 --> 00:34:42,790
+n لكل تربيع حد هيعمل metric وحده بسميه اللي هو
+
+482
+00:34:42,790 --> 00:34:49,300
+برضه Euclidean metric اللي هو Dimension of N نفس
+
+483
+00:34:49,300 --> 00:34:53,680
+الأسلوب بقدر أعرف عالمين على الـ Complex plane
+
+484
+00:34:53,680 --> 00:34:59,220
+اللي و CN يعني بمعنى آخر بده يصير الـ X عناصره
+
+485
+00:34:59,220 --> 00:35:03,380
+عبارة عن XI واحد و XI اثنين و XI N عناصره الـ X
+
+486
+00:35:03,380 --> 00:35:09,100
+بتساوي XI واحد و XI اثنين لعند XI N وكل واحد كل
+
+487
+00:35:09,100 --> 00:35:12,550
+واحد دولة Complex numbers في الـC ففي هذه الحالة
+
+488
+00:35:12,550 --> 00:35:17,390
+بأعرف الـ metric بتعديل بسيط اللي هو dxy بيساوي 
+
+489
+00:35:17,390 --> 00:35:21,610
+الجدر التربيعي له بكتمش اللي هو هذه تربيعه لأنه
+
+490
+00:35:21,610 --> 00:35:25,350
+بيبقى وقم اشماله بيبقى اللي هو عبارة عن complex
+
+491
+00:35:25,350 --> 00:35:28,330
+number لما أخده الجدر في الآخر بيطلع complex
+
+492
+00:35:28,330 --> 00:35:31,530
+number يعني بيطلعش عدد العدد لازم يكون مسافة كم
+
+493
+00:35:31,530 --> 00:35:34,430
+ولا سافة سفر فباخد اللي هنا اشماله هنا absolute
+
+494
+00:35:34,430 --> 00:35:39,250
+values فبيصير هذا الـ metric هذا الـ metric لما أخد
+
+495
+00:35:39,250 --> 00:35:41,730
+absolute value عن الـ magnitude يعني عبارة عن عدد
+
+496
+00:35:41,730 --> 00:35:45,130
+صار هذا تربيع زي هذا تربيع زي هذا الآخر تربيع 
+
+497
+00:35:45,130 --> 00:35:49,830
+فبكون هذا dxy اللي هو عبارة عن metric على مين على
+
+498
+00:35:49,830 --> 00:35:56,230
+cn وبيحقق كل الشروط هذا اللي هو اللي هي أمثلة على
+
+499
+00:35:56,230 --> 00:36:00,890
+اللي هي على الـ R و R تربيع و R تكعيب و RN و C و C
+
+500
+00:36:00,890 --> 00:36:08,830
+و C تربيع و C أُس N الآن نيجي إلى اللي هو مثالنا
+
+501
+00:36:08,830 --> 00:36:13,330
+المهم اللي هو حاجة اسمها sequence space sequence
+
+502
+00:36:13,330 --> 00:36:18,770
+space جماعة من اسمه هو عبارة عن فراغ عناصر أو
+
+503
+00:36:18,770 --> 00:36:26,830
+مجموعة على سرها اللي هي sequences متتابعات لكن 
+
+504
+00:36:26,830 --> 00:36:30,910
+هذه المتتابعات بديها تكون bounded شو اللي بتقوله
+
+505
+00:36:30,910 --> 00:36:31,690
+خليني نشوف
+
+506
+00:36:34,860 --> 00:36:41,660
+المهم اللي هو حاجة اسمها الـ infinity ايش الـ الـ
+
+507
+00:36:41,660 --> 00:36:47,020
+infinity يا جماعة الـ الـ infinity هي كالتالي
+
+508
+00:36:47,020 --> 00:36:53,220
+إنّ يعرفها حاجة اسمها sequence space طيب نشوف ايش الـ
+
+509
+00:36:53,220 --> 00:36:58,080
+sequence space هذا المصدر بالرمز مين الـ infinity
+
+510
+00:36:58,080 --> 00:37:02,290
+هاي الـ الـ infinity الـ sequence space عناصره يعني
+
+511
+00:37:02,290 --> 00:37:05,590
+الـ L infinity هو عبارة عن كل الـ sequences X
+
+512
+00:37:05,590 --> 00:37:09,730
+بتساوي قصاي I قصاي I sequence يعني قصاي 1، قصاي 2،
+
+513
+00:37:09,730 --> 00:37:12,010
+قصاي 3، قصاي 4، لمالا نهاية من زمان بتعرفوا اللي هي
+
+514
+00:37:12,010 --> 00:37:18,330
+ايش sequences I من عند 1 لمالا نهاية such that تكون
+
+515
+00:37:18,330 --> 00:37:20,110
+الـ sequence اللي قال الـ infinity مش كل الـ
+
+516
+00:37:20,110 --> 00:37:23,890
+sequences اللي في الدنيا بدي إياها بدي إياها تكون XI I
+
+517
+00:37:23,890 --> 00:37:28,550
+is bounded يعني bounded sequence شو معناه bounded
+
+518
+00:37:28,550 --> 00:37:33,740
+sequence؟ يعني في النهاية XI I اللي هو there exists
+
+519
+00:37:33,740 --> 00:37:38,280
+C element in R such that Xi I أصغر أو يساوي هذا
+
+520
+00:37:38,280 --> 00:37:44,380
+الـ C لكل I بتساوي واحد واثنين أمنة يعني في
+
+521
+00:37:44,380 --> 00:37:48,160
+النهاية العناصر تبعات الـ sequences لن تتجاوز حد
+
+522
+00:37:48,160 --> 00:37:52,520
+معين طبعًا هذه الـ C لمن؟ للـ sequence هذه الـ
+
+523
+00:37:52,520 --> 00:37:56,440
+sequence هذه لو سميناها X بتساوي XI I منقول عنها
+
+524
+00:37:56,440 --> 00:38:00,180
+bounded إذا كان فيه لها C عشان هيك بنقوله CX نرمز
+
+525
+00:38:00,180 --> 00:38:03,360
+الـ X لإنه C هذه لمن؟ لـ X لو كان فيه sequence
+
+526
+00:38:03,360 --> 00:38:08,040
+ثانية بتكون لها X C ثانية فاهمين؟ اللي أنا أصغر شو
+
+527
+00:38:08,040 --> 00:38:14,460
+مين CX يعني لو كان في عندي Y بسمّيه Gamma I وموجودة
+
+528
+00:38:14,460 --> 00:38:17,460
+في الـ Infinity، هتكون bounded هتكون bounded، ايش
+
+529
+00:38:17,460 --> 00:38:20,780
+معناه bounded؟ إنه there exists C ت .. الـ C ايش
+
+530
+00:38:20,780 --> 00:38:24,920
+معناها؟ إنها للـ Y، عشان هيك بيسمّيها Cy ثابت طبعًا
+
+531
+00:38:24,920 --> 00:38:28,520
+such that اللي هو Gamma I أصغر أو يساوي الـ C اللي
+
+532
+00:38:28,520 --> 00:38:32,810
+لاجيناه هذه الـ sequence ده Y لكل مين I مثلًا
+
+533
+00:38:32,810 --> 00:38:37,110
+أعطيكم مثال يعني عشان تشوفوا مين ممكن نقعد هنا لو
+
+534
+00:38:37,110 --> 00:38:41,410
+جينا أخذنا الـ sequence واحد ونصف وثلت وربع اللي
+
+535
+00:38:41,410 --> 00:38:44,390
+هي الـ sequence واحد على n بمعنى آخر واضح إن الـ
+
+536
+00:38:44,390 --> 00:38:49,640
+sequence هذه أشماله is bounded الـ Terms تبعتها لا 
+
+537
+00:38:49,640 --> 00:38:52,840
+يمكن أن تتجاوز الواحد يعني الـ bound لها ايش واحد
+
+538
+00:38:52,840 --> 00:38:56,320
+يعني هنا في هذه الحالة جامع I لو سمّيناها جامع I هذه
+
+539
+00:38:56,320 --> 00:39:00,320
+أصغر أو يساوي مين واحد لكل I فهذه الـ sequence أكيد 
+
+540
+00:39:00,320 --> 00:39:05,360
+موجودة وين في الـ infinity بينما لو اجيت للـ
+
+541
+00:39:05,360 --> 00:39:11,580
+sequence التالية اللي هو 1 و 2 و 3 و 4 أو un in
+
+542
+00:39:11,580 --> 00:39:14,260
+general هذه الـ sequence غير موجودة في الـ L
+
+543
+00:39:14,260 --> 00:39:16,900
+infinity لأنها is not bounded لأنها عمالها بتروح
+
+544
+00:39:16,900 --> 00:39:20,300
+إلى مالا نهاية قاعدة ففيش عدد أكبر من كل عناصر
+
+545
+00:39:20,300 --> 00:39:22,780
+الـ sequence إذا نضحت شو معناه اللي هي الـ
+
+546
+00:39:22,780 --> 00:39:26,380
+infinity الست هذه إن عناصرها عبارة عن bounded
+
+547
+00:39:26,380 --> 00:39:30,660
+sequences طيب ليش أنت بتأمل هيك يعني أنت بتبني الـ
+
+548
+00:39:30,660 --> 00:39:33,400
+L infinity عشان بعد شوية أنا بدي أعرف لكم metric
+
+549
+00:39:34,280 --> 00:39:37,940
+الـ Metric اللي بتعرف الكيمياء عشان يكون موجود لازم 
+
+550
+00:39:37,940 --> 00:39:41,180
+تكون الـ sequences bounded لازم مدان bounded يعني
+
+551
+00:39:41,180 --> 00:39:45,040
+أنت شكلك بتحكي عن supremum و infimum اه بتعرف الـ
+
+552
+00:39:45,040 --> 00:39:47,940
+metric عن طريق الـ supremum و الـ infimum أو بالضبط
+
+553
+00:39:47,940 --> 00:39:53,360
+عن طريق الـ supremum عشان اللي هو أضمن الـ supremum
+
+554
+00:39:53,360 --> 00:39:56,340
+موجود لازم تكون اللي هي اللي هي اللي بتاخده لها الـ
+
+555
+00:39:56,340 --> 00:40:01,170
+supremum تكون bounded عشان هيك الآن نرتب أمورنا
+
+556
+00:40:01,170 --> 00:40:05,230
+ونقول
+
+557
+00:40:05,230 --> 00:40:10,770
+التالي هذه مبررات اللي حكيتها اللي بدها تخليني
+
+558
+00:40:10,770 --> 00:40:12,530
+أعرف metric D
+
+559
+00:40:17,040 --> 00:40:20,280
+ايش الـ metric اللي بدي أعرفه عليه اللي هو لو أخذت 
+
+560
+00:40:20,280 --> 00:40:25,300
+الآن I X بيساوي X I I sequence و Y بيساوي Gamma I 
+
+561
+00:40:25,300 --> 00:40:27,820
+sequence وين موجودة التنتين في الـ l infinity
+
+562
+00:40:27,820 --> 00:40:33,240
+يعني bounded بدي أعرف اللي هو الـ metric بين X و Y
+
+563
+00:40:33,240 --> 00:40:36,460
+للـ sequences هدول اللي في الـ l infinity بيساوي
+
+564
+00:40:36,460 --> 00:40:42,220
+supremum لـ X I I ناقص Gamma I over I
+
+565
+00:40:42,400 --> 00:40:47,360
+السوبر مومنت يوجد آه لإن XI I bounded و Gamma I
+
+566
+00:40:47,360 --> 00:40:51,080
+bounded إذا هذا بعده bounded ليش؟ لإن بيصير XI I
+
+567
+00:40:51,080 --> 00:40:56,080
+ناقص Gamma I أصغر أو يساوي XI I هذه الأعداد
+
+568
+00:40:56,080 --> 00:41:00,050
+دا جماعة زائد Gamma I وهذه الـ bounded sequence
+
+569
+00:41:00,050 --> 00:41:04,890
+بالـ CX تبعتها وهذه الـ bounded بالـ CY تبعتها إذا
+
+570
+00:41:04,890 --> 00:41:08,830
+في النهاية كل الـ terms هذولة bounded by اللي هو
+
+571
+00:41:08,830 --> 00:41:12,590
+العدد اللي هو مجموع هذولة التنتين يعني صارت هذه
+
+572
+00:41:12,590 --> 00:41:15,950
+bounded مادام bounded إذا مضمون من الـ supermoment
+
+573
+00:41:15,950 --> 00:41:21,590
+أشماله موجود الآن إذا هذا هو الـ defined فعلا الآن
+
+574
+00:41:21,590 --> 00:41:26,170
+الشرط الأول إنه الـ metric الآن هذا أكبر أو يساوي 0 إذا
+
+575
+00:41:26,170 --> 00:41:31,870
+الـ supremum أشماله أكبر أو يساوي 0 إذا الـ Dxy أكبر
+
+576
+00:41:31,870 --> 00:41:37,410
+أو يساوي 0 اتنين Dxy بساوي 0 .. قاعد ببرهن إن أنا
+
+577
+00:41:37,410 --> 00:41:42,850
+الـ metric .. الـ metric هذا Dxy بساوي 0 if and only if الـ
+
+578
+00:41:42,850 --> 00:41:46,050
+supremum .. هي .. هي .. هي .. هي .. supremum لـ Xi
+
+579
+00:41:46,050 --> 00:41:51,230
+I ناقص Gamma I over I بساوي 0 إذا الـ supremum اللي
+
+580
+00:41:51,230 --> 00:41:55,990
+هنا صفر قطعاً قطعاً قطعاً كله صفر لإن لو ال
+
+581
+00:41:55,990 --> 00:41:59,030
+supremum .. لو .. لو واحدة فيه مش صفر معناته الـ
+
+582
+00:41:59,030 --> 00:42:01,470
+supremum مش صفر هيكون هذا اللي .. اللي .. اللي هو
+
+583
+00:42:01,470 --> 00:42:07,610
+مش صفر إذا if and only if xi i ناقص gamma i بتساوي
+
+584
+00:42:07,610 --> 00:42:13,100
+صفر لكل i ماشي معناته هذا ايش معناته إن هذا صفر
+
+585
+00:42:13,100 --> 00:42:18,080
+معناته xi I بساوي Gamma I لكل I معناته ايش معناته xi
+
+586
+00:42:18,080 --> 00:42:21,980
+I بساوي Gamma I يعني كل عناصر اللي هو الـ sequence xi
+
+587
+00:42:21,980 --> 00:42:23,900
+واحد بساوي Gamma واحد بساوي Gamma اتنين بساوي 
+
+588
+00:42:23,900 --> 00:42:26,700
+Gamma اتنين يعني الـ sequences بتساوي بعض يعني if and
+
+589
+00:42:26,700 --> 00:42:32,020
+only if x بتساوي y وهذا الشرط الثالث تحقق نيجي
+
+590
+00:42:32,020 --> 00:42:36,940
+للشرط الرابع الشرط الثالث ده من سهل هنا دي x و
+
+591
+00:42:36,940 --> 00:42:40,610
+y اللي هو عبارة عن الـ supremum Xi I ناقص Gamma I
+
+592
+00:42:40,610 --> 00:42:43,550
+طب ما هي Xi I ناقص Gamma I absolute value و هي
+
+593
+00:42:43,550 --> 00:42:46,770
+نفسها absolute value Gamma I ناقص Xi I و من ثم الـ
+
+594
+00:42:46,770 --> 00:42:51,210
+supremum بتاعها صح و من ثم بيساوي Dxy بساوي Dyx
+
+595
+00:42:51,210 --> 00:42:56,390
+إذن هذا متحقق automatic نيجي الآن لشرط رابع و شرط
+
+596
+00:42:56,390 --> 00:42:59,970
+رابع انتبهولي عليه مش صعب بس يعني إن شاء الله
+
+597
+00:42:59,970 --> 00:43:01,410
+بوضحه لكم معاه تماما و أنتم فاهمون
+
+598
+00:43:04,170 --> 00:43:07,770
+اللي هو يا جماعة الـ Triangle Inequality الـ
+
+599
+00:43:07,770 --> 00:43:12,470
+Triangle Inequality نشوف
+
+600
+00:43:12,470 --> 00:43:16,810
+معلش
+
+601
+00:43:16,810 --> 00:43:21,270
+مساحة الـ Metric هي مكتوبة أنا ما بهمّش طيب الآن
+
+602
+00:43:21,270 --> 00:43:24,030
+بتاخد عشان تثبت الـ Triangle Inequality أنتم 
+
+603
+00:43:24,030 --> 00:43:29,810
+المفروض تحفظوها بتاخد أي X sequence بيساوي Xi I
+
+604
+00:43:29,810 --> 00:43:34,950
+و sequence Y بيساوي Gamma I و sequence Z بيساوي
+
+605
+00:43:34,950 --> 00:43:43,070
+Alpha I الآن يا جماعة انتبهولي لشغلها لأن لكل I في
+
+606
+00:43:43,070 --> 00:43:47,990
+الدنيا لو جيت أخدت XI I ناقص Gamma I ماشي الحال
+
+607
+00:43:47,990 --> 00:43:52,230
+هدولة تبعات مين X و Y أكيد أصغرها يساوي بال
+
+608
+00:43:52,230 --> 00:43:58,390
+triangle inequality هذا الكلام for any fixed I
+
+609
+00:43:58,390 --> 00:44:03,400
+ماشي I arbitrary لكن fixed بحكي عن واحدة بعينة لكن
+
+610
+00:44:03,400 --> 00:44:08,200
+arbitrary شيلته arbitrary منه أصغر أو يساوي Xi I
+
+611
+00:44:08,200 --> 00:44:11,940
+ناقص Alpha I بدخل هذه الحر أنا triangle inequality
+
+612
+00:44:11,940 --> 00:44:18,360
+زي Alpha I ناقص Gamma I بدخل ما يخدمني طيب الآن
+
+613
+00:44:18,360 --> 00:44:21,460
+هذا
+
+614
+00:44:21,460 --> 00:44:26,200
+الكلام صحيح لكل I في الدنيا إذا أكيد أكيد أكيد هذه
+
+615
+00:44:27,380 --> 00:44:31,280
+أصغر أو يساوي supremum اكس اي انا ناقصها معايا
+
+616
+00:44:31,280 --> 00:44:36,160
+ناقص الفايا over I ليش؟ لأن الـ supremum أكبر أو يساوي
+
+617
+00:44:36,160 --> 00:44:38,880
+أكيد اللي هو واحدة اللي ماخذ عليها الـ supremum
+
+618
+00:44:38,880 --> 00:44:44,790
+ماشي أو هذه برضه أصغر أو يساوي الـ supremum تبعها
+
+619
+00:44:44,790 --> 00:44:48,890
+supremum Alpha I ناقص Gamma I إذا صار عندي Over I
+
+620
+00:44:48,890 --> 00:44:52,910
+إذا صار عندي هذا أكبر أو يساوي هذا و هذا أكبر أو
+
+621
+00:44:52,910 --> 00:44:55,610
+يساوي هذا مجموعهم إن أكبر أو يساوي هذا الكلام سهل
+
+622
+00:44:55,610 --> 00:45:01,750
+هذه مين هي يا جماعة هذه اللي هي بالظبط D X و Z هذه
+
+623
+00:45:01,750 --> 00:45:07,040
+تبعات الـ X هيهم و هذه تبعات مين الـ Z زائد هذي مين
+
+624
+00:45:07,040 --> 00:45:12,100
+يا جماعة دي هذي الـ Alpha I تبع الـ Z دي Z و الـ Gamma
+
+625
+00:45:12,100 --> 00:45:17,020
+I تبع مين الـ Y دي Z أو Y إذا صار عندي لكل fixed
+
+626
+00:45:17,020 --> 00:45:22,060
+I هذا المقدار أصغر أو يساوي هذا المقدار طبعا هذا
+
+627
+00:45:22,060 --> 00:45:26,920
+المقدار عباره عن عدد عدد عدد عدد إذا صار عندك xi I
+
+628
+00:45:26,920 --> 00:45:34,400
+ناقص Gamma I لكل I في الدنيا أظهر أو يساوي ال D X و
+
+629
+00:45:34,400 --> 00:45:39,660
+Z زائد ال D Z و Y و زي ما قلت لكم هذا عدد صار هذا
+
+630
+00:45:39,660 --> 00:45:45,900
+عبارة عن upper bound للمجموعة المتكونة من xi واحد
+
+631
+00:45:45,900 --> 00:45:50,400
+ناقص Gamma واحد و xi اتنين ناقص Gamma اتنين إلى مالا
+
+632
+00:45:50,400 --> 00:45:54,150
+نهاية إذا صار هذا upper bound لها بالستما دام هو
+
+633
+00:45:54,150 --> 00:45:59,590
+lower bound إذا هو أكبر أو يساوي الـ least lower
+
+634
+00:45:59,590 --> 00:46:04,790
+bound لهم يا بمعنى آخر صار هذا أكبر أو يساوي الـ
+
+635
+00:46:04,790 --> 00:46:08,130
+supremum لهم لأن الـ supremum هو الـ least lower
+
+636
+00:46:08,130 --> 00:46:13,990
+bound إذا هذا اللي هو أصلا ايش اسمه اللي سميناه
+
+637
+00:46:13,990 --> 00:46:15,750
+عبارة عن DX
+
+638
+00:46:18,090 --> 00:46:21,910
+و مين؟ OY إذا صار عندي DX وY أصغر أو يساوي DX وZ زي
+
+639
+00:46:21,910 --> 00:46:27,270
+الـ DZ OY إذا هي كما نكون أثبتنا هذا برضه عبارة عن
+
+640
+00:46:27,270 --> 00:46:31,950
+ايش عبارة عن metric إذا صار عندي اللي هو اللي
+
+641
+00:46:31,950 --> 00:46:35,970
+أمامنا يا جماعة اللي هو الـ l infinity مع هذا الـ
+
+642
+00:46:35,970 --> 00:46:40,550
+metric دي على هذا الأساس التعريف عبارة عن metric
+
+643
+00:46:40,550 --> 00:46:45,870
+space اللي هو الـ L infinity تبعنا وهذا من الأمثلة
+
+644
+00:46:45,870 --> 00:46:52,730
+المهمة والملازمة معنا على طول الفصل طيب برضه space
+
+645
+00:46:52,730 --> 00:46:58,330
+آخر مهم اللي هو الـ space تبعنا تبع زمان عناصر اللي
+
+646
+00:46:58,330 --> 00:47:03,130
+هو the space of continuous functions on a closed
+
+647
+00:47:03,130 --> 00:47:09,890
+bounded interval نشوف ايش بقوله هذا طبعا معلوماته
+
+648
+00:47:09,890 --> 00:47:14,140
+من الـ calculus بتيجي أنا دايمًا بحكيها في القصة دي
+
+649
+00:47:14,140 --> 00:47:17,940
+اللي هي المعلومات حول اللي هو الدوال المتصلة على
+
+650
+00:47:17,940 --> 00:47:21,880
+closed bounded interval ايش اللي بقوله اللي بقوله
+
+651
+00:47:21,880 --> 00:47:26,710
+صلى الله عليه وسلم بدي أخد اللي هو المجموعة اسمها C A
+
+652
+00:47:26,710 --> 00:47:30,810
+و B برمز لها هذه C اللي هي continuous و الـ A و B هي
+
+653
+00:47:30,810 --> 00:47:32,670
+الـ closed bounded interval اللي عليها بدعرف
+
+654
+00:47:32,670 --> 00:47:37,270
+الدالة هي عبارة عن كل الدوال X ده سميها X الدالة
+
+655
+00:47:37,270 --> 00:47:42,190
+اللي ماخدة من A و B و بتودّي في R يعني real valued
+
+656
+00:47:42,190 --> 00:47:47,140
+function the set of all real valued functions on a
+
+657
+00:47:47,140 --> 00:47:51,420
+closed bounded interval which are continuous such
+
+658
+00:47:51,420 --> 00:47:57,880
+that X is continuous إذا هذا الفراغ هو عبارة عن
+
+659
+00:47:57,880 --> 00:48:03,080
+الفراغ المتكون من جميع الدوال المتصلة الحقيقية
+
+660
+00:48:03,080 --> 00:48:08,960
+طبعا على الفترة A O B الآن مدامة X متصلة على
+
+661
+00:48:08,960 --> 00:48:13,520
+الفترة A O B كنا نحكي إعلان في الـ calculus ونقول إذا
+
+662
+00:48:13,520 --> 00:48:20,280
+كانت الدالة مستمرة في فترة مغلقة فهي تصل إلى
+
+663
+00:48:20,280 --> 00:48:24,300
+قيمة أعلى وقيمة أعلى في هذه القيمة وهذا
+
+664
+00:48:24,300 --> 00:48:28,940
+الكلام بيحكي .. بيحكي .. بيحكي لكم يعني تشريع لكيف نوجد
+
+665
+00:48:28,940 --> 00:48:31,640
+الـ absolute وضمان وجود الـ absolute maximum
+
+666
+00:48:31,640 --> 00:48:34,920
+و absolute minimum على الدالة المتصلة على فترة
+
+667
+00:48:34,920 --> 00:48:40,220
+مغلقة حتى في الثانوية فهذه معلومة سابقة إذا ما دامت
+
+668
+00:48:40,220 --> 00:48:42,920
+الدالة متصلة على closed bounded interval إذا الـ
+
+669
+00:48:42,920 --> 00:48:46,240
+maximum و الـ minimum لها ايه أشماله مضمون إنه موجود
+
+670
+00:48:46,240 --> 00:48:50,000
+طب ليش بتحكي هيك عشان بدي أعرف الآن الـ metric على
+
+671
+00:48:50,000 --> 00:48:52,720
+أساس على هذا الأساس يعني بدي أعرف الـ metric
+
+672
+00:48:52,720 --> 00:48:56,340
+بواسطة الـ maximum قبل بشوية الـ l infinity حكينا عنه
+
+673
+00:48:56,340 --> 00:49:01,300
+الـ supremum هنا على غراره و البرهان نفس البرهان
+
+674
+00:49:01,300 --> 00:49:04,660
+اللي هو على غرار البرهان الأولاني هنا هناك كان الـ
+
+675
+00:49:04,660 --> 00:49:07,980
+sequences وهنا للدوال هنا كان الـ bounded sequences
+
+676
+00:49:07,980 --> 00:49:11,060
+وهنا أشماله للدوال المتصلة على closed bounded
+
+677
+00:49:11,060 --> 00:49:16,000
+interval سألنا بالـ Function specific of A و B دعوا
+
+678
+00:49:16,000 --> 00:49:17,580
+C و A و B يكونوا مجموعة من جميع الدوال
+
+679
+00:49:17,580 --> 00:49:21,360
+الواقعية التي مستمرة في الـ closed bounded
+
+680
+00:49:21,360 --> 00:49:24,800
+interval إذا لكل X و Y في C و A و B أريد أن أعرف
+
+681
+00:49:24,800 --> 00:49:31,340
+الـ D X Y الـ D X Y للإكسات و الوايات الموجودة في
+
+682
+00:49:31,340 --> 00:49:35,910
+C و B يعني الدوال المتصلة X و Y هي عبارة عن الـ
+
+683
+00:49:35,910 --> 00:49:40,870
+maximum لـ X of T X of T الـ T المتغير اللي في الـ
+
+684
+00:49:40,870 --> 00:49:44,910
+A و الـ B ناقص الـ Y of T و الـ T طبعا اللي موجودة
+
+685
+00:49:44,910 --> 00:49:48,550
+على الفترة A و B يعني اللي هو بدي المسافة بين X و
+
+686
+00:49:48,550 --> 00:49:52,290
+Y هي عبارة عن الـ maximum اللي هو بين .. اللي هو
+
+687
+00:49:52,290 --> 00:49:56,670
+البعد بين كل point و الثانية عند X و T ناقص Y و T
+
+688
+00:49:56,670 --> 00:50:00,170
+لإن هل الـ maximum موجودة؟ آه طبعًا، ليش؟ لأن X
+
+689
+00:50:00,170 --> 00:50:03,610
+متصلة و Y متصلة، إذا حصل طرح متصل إذا حصل طرح
+
+690
+00:50:03,610 --> 00:50:06,970
+متصل، إذا صار من التنتين متصلات أو هذه كلها على
+
+691
+00:50:06,970 --> 00:50:09,590
+بعض is a continuous function on a closed bounded
+
+692
+00:50:09,590 --> 00:50:12,510
+interval إذا لازم يكون لها maximum و minimum ..
+
+693
+00:50:12,510 --> 00:50:16,050
+إذا الـ maximum و الـ minimum مضمونات وجودهم في
+
+694
+00:50:16,050 --> 00:50:20,830
+الفترة a و b إذا عندي اللي هو التعريف و الـ defined
+
+695
+00:50:20,830 --> 00:50:25,570
+ما فيش مشاكل في التعريف البرهان .. البرهان سهل إنه
+
+696
+00:50:25,570 --> 00:50:29,230
+metric واحد هذا absolute value إذا أكبر أو يساوي صفر
+
+697
+00:50:29,230 --> 00:50:31,450
+إذا الـ maximum ما هي أشماله أكبر أو يساوي صفر إذا
+
+698
+00:50:31,450 --> 00:50:35,370
+دي اكس واي automatic أكبر أو يساوي صفر شاطر أول
+
+699
+00:50:35,370 --> 00:50:40,050
+متحقق سريع لإن هذا نفس البرهان اللي قبله اتنين لو
+
+700
+00:50:40,050 --> 00:50:46,030
+الآن دي اكس واي بساوي صفر فاندول اف الماكسيموم بيساوي
+
+701
+00:50:46,030 --> 00:50:49,410
+صفر الماكسيمم بيساوي صفر لأن كل واحدة من هذول صفر
+
+702
+00:50:49,410 --> 00:50:51,870
+لأنها absolute value لأن كل واحدة من هذول صفر
+
+703
+00:50:51,870 --> 00:50:51,990
+لأنها absolute value لأن كل واحدة من هذول صفر
+
+704
+00:50:51,990 --> 00:50:52,490
+لأنها absolute value لأن كل واحدة من هذول صفر
+
+705
+00:50:52,490 --> 00:50:53,090
+لأنها absolute value لأنها absolute value لأنها
+
+706
+00:50:53,090 --> 00:50:54,310
+absolute value لأنها absolute value لأنها absolute
+
+707
+00:50:54,310 --> 00:50:54,670
+value لأنها absolute value لأنها absolute value
+
+708
+00:50:54,670 --> 00:50:56,150
+لأنها absolute value لأنها absolute value لأنها
+
+709
+00:50:56,150 --> 00:50:56,310
+absolute value لأنها absolute value لأنها absolute
+
+710
+00:50:56,310 --> 00:50:56,350
+value لأنها absolute value لأنها absolute value
+
+711
+00:50:56,350 --> 00:50:58,310
+لأنها absolute value لأنها absolute value لأنها
+
+712
+00:50:58,310 --> 00:51:03,240
+absolute value لـ ناقص y of t بتساوي صفر لكل t في 
+
+713
+00:51:03,240 --> 00:51:09,260
+الفترة a و b وهذا معناته أن x of t هي نفسها y of t
+
+714
+00:51:09,260 --> 00:51:12,540
+الـ delta نفس الـ .. نفس الشيء لكل t في domain هنا
+
+715
+00:51:12,540 --> 00:51:17,560
+يعني بمعنى آخر اللي هو delta n x بتساوي y وهو
+
+716
+00:51:17,560 --> 00:51:21,520
+المطلوب الشرط الثالث الشرط السهل هذا اللي بنقول
+
+717
+00:51:21,520 --> 00:51:27,970
+عنه dxy بتساوي dy و x لأن Dxy هو الماكسيمم x of t
+
+718
+00:51:27,970 --> 00:51:30,650
+ناقص y of t absolute value الـ absolute value x of t
+
+719
+00:51:30,650 --> 00:51:33,270
+و y of t هو نفس الـ absolute value y of t ناقص x of
+
+720
+00:51:33,270 --> 00:51:36,830
+t إذا الماكسيمم عاملة تلتين زي بعض إذا Dxy بتساوي
+
+721
+00:51:36,830 --> 00:51:40,610
+Dy و X نجي للشرط الثالث الأخير و الشرط الثالث
+
+722
+00:51:40,610 --> 00:51:45,890
+الأخير برضه زي مين؟ زي الشرط الثالث اللي في المثال
+
+723
+00:51:45,890 --> 00:51:56,620
+اللي دوبنا أخذنا any T any T limiting a و bx of 
+
+724
+00:51:56,620 --> 00:52:01,060
+t ناقص y of t أخذ دالة ثالثة arbitrarily present في
+
+725
+00:52:01,060 --> 00:52:04,320
+الـ continuous أكيد absolute value إنهم أصغر أو
+
+726
+00:52:04,320 --> 00:52:12,560
+ساوي absolute value of x of t ناقص z of t زائد زائد
+
+727
+00:52:12,560 --> 00:52:19,160
+اللي هو absolute value of z of t-Y of T هذا الكلام
+
+728
+00:52:19,160 --> 00:52:21,960
+لكل T لأن هذا الكلام Absolute Value Triangle
+
+729
+00:52:21,960 --> 00:52:24,640
+Inequality تبعت زمان لأن هذا أعداد X of T قيمت
+
+730
+00:52:24,640 --> 00:52:28,560
+عددها وY of T قيمت عددها وZ of T قيمت عددها إذا
+
+731
+00:52:28,560 --> 00:52:32,260
+هذه Triangle Inequality أشمالها صحيحة دائماً وزي ما
+
+732
+00:52:32,260 --> 00:52:37,580
+عملنا قبل شوية أصغر أو ساوي هذه اللي هي نفسها أصغر
+
+733
+00:52:37,580 --> 00:52:45,320
+أو ساوي الـ maximum تبعتها X of T-Z of Tوهذه أصغر
+
+734
+00:52:45,320 --> 00:52:50,920
+في شوية maximum تبعتها Z of T ماقص Y of T وهذه
+
+735
+00:52:50,920 --> 00:52:58,960
+عبارة عن DXYDX و Z آسف وهذه ثانية DZY وهذه صار عدد
+
+736
+00:52:58,960 --> 00:53:03,760
+أكبر أو ساوي هذول لكل T هذه أكبر أو ساوي X of T نقص Y
+
+737
+00:53:03,760 --> 00:53:06,800
+of T لكل T هنا إذن أكيد أكبر أو ساوي مين؟ الـ maximum
+
+738
+00:53:06,800 --> 00:53:09,560
+لأن الـ maximum واحدة منهن لأن احنا بنقول الـ tens
+
+739
+00:53:09,560 --> 00:53:14,360
+is maximum وين فيها؟ إذن واحدة منهن إذن DX وZY أكبر
+
+740
+00:53:14,360 --> 00:53:19,200
+أو ساوي الـ maximum هذه اللي هو عبارة عن DXY وهو
+
+741
+00:53:19,200 --> 00:53:22,130
+المطلوب إذن صار اللي هو هنا الـD برضه إيش ماله؟
+
+742
+00:53:22,130 --> 00:53:27,730
+عبارة عن metric space ماشي يا بنات صلوا علينا بهم 
+
+743
+00:53:27,730 --> 00:53:34,510
+عليه الصلاة والسلام الآن المثال الأخير اللي هو 
+
+744
+00:53:34,510 --> 00:53:39,050
+حاجة اسمها بنسميه discrete metric space discrete
+
+745
+00:53:39,050 --> 00:53:44,570
+metric space discrete metric space هو اللي بيولد الـ
+
+746
+00:53:44,570 --> 00:53:48,830
+discrete topology إن شاء الله بنجيه في حينه الـ
+
+747
+00:53:48,830 --> 00:53:54,910
+discrete metric space بناخد 6x أي 6x و بنعرف عليها 
+
+748
+00:53:54,910 --> 00:53:58,870
+D إيش الـ D اللي بدي أعرفها؟ اللي بدي أسميه metric
+
+749
+00:53:58,870 --> 00:54:02,090
+الآن هذا الـ D هسميه metric آسف هسميه اللي هو
+
+750
+00:54:02,090 --> 00:54:06,670
+discrete الـ D هعرفها لأي نقطتين في الـ X المسافة 
+
+751
+00:54:06,670 --> 00:54:12,260
+بينهم هسميهم يا صفر يا واحد هذا هي المتريك اللي 
+
+752
+00:54:12,260 --> 00:54:13,940
+أريد أن أعرفه أنا أو هذا الدالة اللي أريد أن
+
+753
+00:54:13,940 --> 00:54:19,400
+أعرفها Dxy بتساوي صفر إذا كانت X بتساوي Y و بتساوي
+
+754
+00:54:19,400 --> 00:54:23,580
+واحد إذا كانت X أشمالها لا تساوي Y هاي كل قصتنا إذا
+
+755
+00:54:23,580 --> 00:54:28,420
+المتريك اللي بندعي أنه متريك إنه قيمتين يا صفر في 
+
+756
+00:54:28,420 --> 00:54:32,440
+حالة المساواة يا واحد في حالة عدم المساواة إذا X
+
+757
+00:54:32,440 --> 00:54:38,260
+و D هيعملني metric space اثبت اثبات سهل أول حاجة 
+
+758
+00:54:39,780 --> 00:54:45,100
+واضح أن Dxy أكبر أو ساوي صفر Dxy أكبر أو ساوي صفر
+
+759
+00:54:45,100 --> 00:54:47,340
+لأن قيمته يا صفر يا واحد إذا ما أكبر أو ساوي صفر
+
+760
+00:54:47,340 --> 00:54:52,140
+اثنين الـ Dxy
+
+761
+00:54:52,140 --> 00:55:01,870
+بتساوي صفر إذا و فقط إذا الـ X متساوي و متعريفلأن 
+
+762
+00:55:01,870 --> 00:55:05,150
+لو كانت X Y بيساوي 0 أكيد X بتساوي Y ولو كانت X 
+
+763
+00:55:05,150 --> 00:55:09,650
+بيساوي Y أكيد X بتساوي 0، بتساوي 0، بتساوي 0، 
+
+764
+00:55:09,650 --> 00:55:09,690
+بتساوي 0، بتساوي 0، بتساوي 0، بتساوي 0، بتساوي 0،
+
+765
+00:55:09,690 --> 00:55:10,650
+بتساوي 0، بتساوي 0، بتساوي 0، بتساوي 0، بتساوي 0،
+
+766
+00:55:10,650 --> 00:55:11,570
+بتساوي 0، بتساوي 0، بتساوي 0، بتساوي 0، بتساوي 0،
+
+767
+00:55:11,570 --> 00:55:19,670
+بتساوي 0، بتساوي 0، بتساوي 0، بتساوي 0، بتساوي 0،
+
+768
+00:55:19,670 --> 00:55:28,100
+بتساوي 0، بتساوي 0، بتساوي 0، بتساوي اللي هو إننا نثبت 
+
+769
+00:55:28,100 --> 00:55:30,300
+الـ Triangle Inequality انتبه على الـ Triangle
+
+770
+00:55:30,300 --> 00:55:33,220
+Inequality الـ Triangle Inequality مش غلبتها كتير
+
+771
+00:55:33,220 --> 00:55:36,300
+بسيطة يعني إن شاء الله ده بيكتمك و نخلصناها عندي
+
+772
+00:55:36,300 --> 00:55:41,660
+بتاخد الآن أي X و أي Y و أي Z وين موجودات في الـ X
+
+773
+00:55:41,660 --> 00:55:50,340
+هذول اللي هين حالتين الحالة الأولى X بتساوي Y
+
+774
+00:55:50,340 --> 00:55:58,260
+الحالة الثانية X لا تساوي y في غيرها بالنسبالي الـ X
+
+775
+00:55:58,260 --> 00:56:02,760
+و الـ Y لأ احتمالات الـ X و الـ Y لبعض هذه بتساوي هذه 
+
+776
+00:56:02,760 --> 00:56:09,260
+أو هذه بتساوي هذه لو X بتساوي Y فبتصير الـ D X و Y 
+
+777
+00:56:09,260 --> 00:56:14,500
+بتساوي صفر لأن أي إن كانت الـ Z بتساويهم ولا 
+
+778
+00:56:14,500 --> 00:56:18,260
+بتساويهم مش فارقة كتير ليش؟ لأنه هتكون هذه أكيد
+
+779
+00:56:18,260 --> 00:56:25,280
+أصغر أو ساوي D X و Z زائد D Z و Y لأن هذولا قيمهم
+
+780
+00:56:25,280 --> 00:56:30,260
+يا صفر يا واحد إذا مستحيل هذه تكون أكبر منهم لأنه 
+
+781
+00:56:30,260 --> 00:56:33,800
+مجموح أنه يكون يا صفر يا واحد يا اثنين حسب
+
+782
+00:56:33,800 --> 00:56:38,500
+العلاقات اللي موجودة هنا ماشي الحال طيب إذا صار 
+
+783
+00:56:38,500 --> 00:56:42,480
+عندي الآن الحالة الأولى متحققة ده الحالة الثانية X
+
+784
+00:56:42,480 --> 00:56:46,680
+لا تساوي Y X لا تساوي Y في عندي في حالة .. لأن بدأت 
+
+785
+00:56:46,680 --> 00:56:50,920
+أجيب I Z بتدافع ثاني DX وY أزرع ثاني DX وZ زي دي Z
+
+786
+00:56:50,920 --> 00:56:54,960
+وY في هذه الحالة عندي ثلاث حالات في داخل الحالة هذه 
+
+787
+00:56:54,960 --> 00:57:01,340
+يما التنتين هذول باختلف عن الـ Z يعني لا الـ X
+
+788
+00:57:01,340 --> 00:57:07,420
+بتساوي Y و طبعاً هي المفروض لا الـ X بتساوي Z ولا الـ 
+
+789
+00:57:07,420 --> 00:57:11,200
+Y بتساوي Z يعني ولا واحدة منهم الثلاث مختلفات 
+
+790
+00:57:11,200 --> 00:57:16,160
+الحالة الأولى الحالة الثانية إن هذول مختلفات صح بس 
+
+791
+00:57:16,160 --> 00:57:19,740
+الـ Z بتساوي واحدة منهم إذا الحالة الأولى إن
+
+792
+00:57:19,740 --> 00:57:22,940
+المختلفات و الـ Z مختلفة عنها التلتين الحالة 
+
+793
+00:57:22,940 --> 00:57:27,580
+الثانية إن الـ Z بتساوي واحدة منهم إذا الحالتين، يا 
+
+794
+00:57:27,580 --> 00:57:31,140
+الـ z بتساويش ولا واحدة منهن، يا واحدة منهن، الآن
+
+795
+00:57:31,140 --> 00:57:34,980
+ولا واحدة منهن أيها، الحالة الثانية إنها بتساوي 
+
+796
+00:57:34,980 --> 00:57:40,480
+واحدة منهم، يعني z بتساوي x و z لا تساوي y أو z 
+
+797
+00:57:40,480 --> 00:57:46,320
+بتساوي y و z لا تساوي x، يعني الحالة الثانية هذه، 
+
+798
+00:57:46,320 --> 00:57:51,750
+اللي هو بتساوي واحدة من هذول، مستحيل تسوي إن تتمثل 
+
+799
+00:57:51,750 --> 00:57:54,730
+مع بعض لأن هنا تحت عدوان إيه شمال و X ذات شوية إذا 
+
+800
+00:57:54,730 --> 00:57:57,950
+هذه الثلاث حالات اللي عندي في الحالة اللي عندي هذه 
+
+801
+00:57:57,950 --> 00:58:00,450
+الحالة الثانية جزء إيه؟ الجزء الأول جزء الثاني
+
+802
+00:58:00,450 --> 00:58:05,930
+الحالة الأولى اللي هو Dxy أكيد برضه أصغر يساوي Dx 
+
+803
+00:58:05,930 --> 00:58:14,970
+و z زائد Dz وY ليه؟ لأن Dx وz واحد DX و Z DX و Y
+
+804
+00:58:14,970 --> 00:58:18,610
+واحد مختلفات DX و Z DX و Y واحد مختلفات DX و Z DX 
+
+805
+00:58:18,610 --> 00:58:21,050
+و Y واحد مختلفات DX و Z DX و Y واحد مختلفات DX و Z
+
+806
+00:58:21,050 --> 00:58:22,170
+DX و Y واحد مختلفات DX و Z DX و Y واحد مختلفات DX
+
+807
+00:58:22,170 --> 00:58:24,010
+و Z DX و Z DX و Y واحد مختلفات DX و Z DX و Z DX و 
+
+808
+00:58:24,010 --> 00:58:24,430
+Y واحد مختلفات DX و Z DX و Z DX و Z DX و Z DX و Z
+
+809
+00:58:24,430 --> 00:58:27,410
+DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z
+
+810
+00:58:27,410 --> 00:58:28,290
+DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z
+
+811
+00:58:28,290 --> 00:58:30,530
+DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z
+
+812
+00:58:30,530 --> 00:58:30,610
+DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z
+
+813
+00:58:30,610 --> 00:58:34,780
+DX الآن الحالة الثانية z بتساوي x أول حاجة هذول
+
+814
+00:58:34,780 --> 00:58:38,940
+المختلفة إذا واحد أولاً واحدة z بتساوي x إذا ندي
+
+815
+00:58:38,940 --> 00:58:42,680
+صفر z تتساوي y واحد إذا بتظل الحالة المساواة
+
+816
+00:58:42,680 --> 00:58:45,380
+متحققة إذا متحققة الـ triangle inequality الـ
+
+817
+00:58:45,380 --> 00:58:49,920
+triangle inequality أصغر أو يساوي الحالة الثالثة 
+
+818
+00:58:49,920 --> 00:58:55,640
+بيصير اللي هو الحالة الثالثة عندي هذه قول واحدة
+
+819
+00:58:55,640 --> 00:59:03,540
+واحدة لأن XZ يتساوي Y XZ يتساوي Y وهو صفر زي ده 
+
+820
+00:59:03,540 --> 00:59:08,180
+تساوي x واحد إذا واحد بساوي اللي هو الحالة اللي هي 
+
+821
+00:59:08,180 --> 00:59:11,880
+الواحد إذا في الحالة هذه برضه دائماً دي x و y أصغر
+
+822
+00:59:11,880 --> 00:59:14,980
+يساوي دي x و z زائد دي z و y من كل الحالات الثانية
+
+823
+00:59:14,980 --> 00:59:17,000
+الحالة الأولى و الحالة الثانية و الـ sub cases اللي
+
+824
+00:59:17,000 --> 00:59:21,060
+من الثلاث دجينا دائماً دي x و y أصغر يساوي دي x و
+
+825
+00:59:21,060 --> 00:59:24,920
+z زائد دي z و y و بهذا بيكون عندي هذا عبارة عن 
+
+826
+00:59:24,920 --> 00:59:30,340
+metric space هذا بيسميه discrete metric space و 
+
+827
+00:59:30,340 --> 00:59:35,340
+بيكون عندكم الآن homework السؤال الأول، هذه السؤال
+
+828
+00:59:35,340 --> 00:59:41,140
+الأول، السؤال الأول، و السؤال الثاني، هو أسئلة
+
+829
+00:59:41,140 --> 00:59:44,720
+الكتاب. الآن هتلاقوا في الـ Homework، اللي هو
+
+830
+00:59:44,720 --> 00:59:49,100
+Homework، و هنا Homework Star، اللي بدكم تسلموني إياها 
+
+831
+00:59:49,100 --> 00:59:52,240
+Homework Star، يعني بتكون تسلموني أربعة أو خمسة أو 
+
+832
+00:59:52,240 --> 00:59:55,120
+ثمانية أو عشرة من الكتاب، و الواحد و الاثنين الـ 
+
+833
+00:59:55,120 --> 00:59:58,180
+Above هذول، هذول اللي بتكون تسلموني إياها من ضمن الـ 
+
+834
+00:59:58,180 --> 01:00:01,150
+Homeworks اللي اتفقنا عليهم، الآن هذول أنت في
+
+835
+01:00:01,150 --> 01:00:05,450
+البيت بدك تحلهم اللي هو بفضل إنك تطلع عليهم و
+
+836
+01:00:05,450 --> 01:00:08,050
+تحلهم بس تكشف السبب إنك يعني لا سبب بتعرفوش تحلوها
+
+837
+01:00:08,050 --> 01:00:12,650
+أنا حل كل الأسئلة بنقدر نعطيكم اللي هو إذا ما
+
+838
+01:00:12,650 --> 01:00:16,630
+أسفناش الوجود في داخل المحاضرة بنعطيكم الحلول و 
+
+839
+01:00:16,630 --> 01:00:21,230
+بتحلوها و بتشوفوها و الشيء اللي بدكم إياه مش فاهمينه
+
+840
+01:00:21,230 --> 01:00:26,350
+بنشوف ساعات مكتبية أو في داخل هنا بنجاوبكم و هيك
+
+841
+01:00:26,350 --> 01:00:29,680
+بتكون نهينا المحاضرة و السلام عليكم ورحمة الله و 
+
+842
+01:00:29,680 --> 01:00:30,040
+بركاته
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/BsKCqLUcy6s_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/BsKCqLUcy6s_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..db9412f3c289d1fdebce757ef8ab64c91c1c0f5c
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/BsKCqLUcy6s_postprocess.srt
@@ -0,0 +1,3368 @@
+1
+00:00:05,200 --> 00:00:07,980
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,980 --> 00:00:10,940
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,940 --> 00:00:15,500
+أهله وصحبه أجمعين هذه هي المحاضرة الأولى في مساق
+
+4
+00:00:15,500 --> 00:00:19,700
+تحليل دالي أو تحليل اقتراني functional analysis
+
+5
+00:00:19,700 --> 00:00:26,160
+رقم المادة Maths 6324 وهي من المواد الاختيارية
+
+6
+00:00:26,160 --> 00:00:30,220
+لطلاب وطالبات ماجستير رياضيات في الجامعة الإسلامية
+
+7
+00:00:30,810 --> 00:00:35,430
+كذلك أيضًا اللي هو نستطيع أن نعطي هذه المادة في
+
+8
+00:00:35,430 --> 00:00:38,490
+وجود طلاب الـ Baccalaureate ونطلب منهم من المادة
+
+9
+00:00:38,490 --> 00:00:44,230
+ما هو مناسب لهم الآن راح نتحدث في البداية عن اللي
+
+10
+00:00:44,230 --> 00:00:48,170
+هو وصف المساق وصف المساق أول إشي اللي هو ال
+
+11
+00:00:48,170 --> 00:00:51,350
+textbook اللي هو Introductory Functional Analysis
+
+12
+00:00:51,350 --> 00:00:55,270
+with Applications لإيروين كريزينج وهذا طبعًا من
+
+13
+00:00:55,270 --> 00:01:03,280
+الكتب السهلة وفي نفس الوقت الكتب اللييعني المادة
+
+14
+00:01:03,280 --> 00:01:06,560
+العلمية فيها تؤدي الغرض بل انه المادة العلمية
+
+15
+00:01:06,560 --> 00:01:12,980
+خلينا نقول في ال course أولي في التحليل الإلكتروني
+
+16
+00:01:12,980 --> 00:01:18,970
+لأ هو مناسب ومناسب جداالان الموضوعات اللي احنا
+
+17
+00:01:18,970 --> 00:01:22,390
+هنغطيها المتوقع انه هنغطيها في هذا المساق اللي هي
+
+18
+00:01:22,390 --> 00:01:26,570
+عبارة عن اللي هي اربع شباتر بالاضافة لدزق من
+
+19
+00:01:26,570 --> 00:01:30,410
+chapter 7 الشابتر الأول والشابتر التاني والشابتر
+
+20
+00:01:30,410 --> 00:01:34,300
+التالت والشابتر الرابع ودزق من الشابتر السابعطبعا
+
+21
+00:01:34,300 --> 00:01:36,680
+طلاب الـ Baccalaureate حيكون في عندي أو طلبات الـ
+
+22
+00:01:36,680 --> 00:01:39,400
+Baccalaureate حيكون في عندي اللي هو chapter 1
+
+23
+00:01:39,400 --> 00:01:42,100
+chapter 2 و chapter 3 معظمه مطلوب منه ان شاء الله
+
+24
+00:01:42,100 --> 00:01:45,040
+في حينه في كل .. في كل شغلة احنا بدنا يها بس
+
+25
+00:01:45,040 --> 00:01:49,180
+للماجستير بنقولهم عنها و chapter 4 يعني جزء منه او
+
+26
+00:01:49,180 --> 00:01:52,020
+خلينا نقول شغلات أساسية منه بنعطيها للـ
+
+27
+00:01:52,020 --> 00:01:54,420
+Baccalaureate و الباقى بيكون لاللي هو طلاب
+
+28
+00:01:54,420 --> 00:01:58,480
+الماجستير و اللي هو جزء أو chapter 7 برضه شغلات
+
+29
+00:01:58,480 --> 00:02:00,860
+بسيطة لطلاب الـ Baccalaureate و الباقي اللي هو
+
+30
+00:02:00,860 --> 00:02:05,240
+لطلاب الماجستيرخلّيني نشوف مع بعض اللي هو ال ..
+
+31
+00:02:05,240 --> 00:02:08,380
+إيش ال course outline بالظبط الجزء الأول اللي هو
+
+32
+00:02:08,380 --> 00:02:11,660
+هنحكي عن اللي هو في الأسبوعين الأولانيات تقريبا
+
+33
+00:02:11,660 --> 00:02:15,500
+اللي هو هنحكي عن اللي هو ال metric spaces اللي هو
+
+34
+00:02:15,500 --> 00:02:18,100
+chapter واحد هذا هو ال metric spaces و ال
+
+35
+00:02:18,100 --> 00:02:21,200
+topological conceptual metric spaces و بعدين هنحكي
+
+36
+00:02:21,200 --> 00:02:23,320
+عن completeness و ال completion of metric spaces
+
+37
+00:02:23,320 --> 00:02:26,260
+طبعا كل هذه الكلام .. الكلام هنيجي له بالتفصيل أنا
+
+38
+00:02:26,260 --> 00:02:29,850
+بقى مروح عليه مرور سريع الآنبنكون خلصنا chapter
+
+39
+00:02:29,850 --> 00:02:34,330
+اللي هو واحد و بنبدأ في chapter اتنين حيكون عن ال
+
+40
+00:02:34,330 --> 00:02:38,170
+normed spaces و البنخ spaces هنعرف شو معناه normed
+
+41
+00:02:38,170 --> 00:02:40,430
+space و شو معناه بنخ space و بعدين هنحكي عن ال
+
+42
+00:02:40,430 --> 00:02:42,990
+compactness اللي هي خاصية طبوليجية طبعا هنجيها ان
+
+43
+00:02:42,990 --> 00:02:47,490
+شاء الله و بعدين هنحكي عن اللي هو قطع عريض منيح و
+
+44
+00:02:47,490 --> 00:02:50,640
+اللي هو applications هائلةاللي هو linear .. linear
+
+45
+00:02:50,640 --> 00:02:53,340
+and bounded linear operators on and functionals
+
+46
+00:02:53,340 --> 00:02:57,400
+وحنحكي عن اللي هو ال dual spaces ومن ثم حيكون
+
+47
+00:02:57,400 --> 00:03:01,500
+عندنا اللي هو ال first exam الان الجزء الثاني على
+
+48
+00:03:01,500 --> 00:03:04,620
+طول بنبدأ اللي هو نكون خلصنا الشبتر الأول وتقريبا
+
+49
+00:03:04,620 --> 00:03:07,700
+اللي هو الشبتر التاني بنيجي بشبتر تلاتة اللي هو ال
+
+50
+00:03:07,700 --> 00:03:11,300
+Hilbert spaces هنحكي عن ال Hilbert spaces هنحكي عن
+
+51
+00:03:11,300 --> 00:03:13,460
+ال orthogonal complement و direct sum و ال
+
+52
+00:03:13,460 --> 00:03:16,540
+orthonormal و ال total orthonormal sets and
+
+53
+00:03:16,540 --> 00:03:20,210
+sequencesبعدين هنحكي عن اللي هو representation of
+
+54
+00:03:20,210 --> 00:03:23,450
+functional on Hilbert spaces إشي مرتب و إشي منيح و
+
+55
+00:03:23,450 --> 00:03:28,330
+إشي حلو ان شاء الله هنحكي عنه في حينه بعدين هنحكي
+
+56
+00:03:28,330 --> 00:03:31,490
+عن اللي هو أنواع بعض ال operators ال operators
+
+57
+00:03:31,490 --> 00:03:35,930
+طبعا عالم واسع و أنواع عالم كبير و عليه دراسات في
+
+58
+00:03:35,930 --> 00:03:39,110
+كل المجلات في ال functional equations في ال
+
+59
+00:03:39,110 --> 00:03:41,570
+functional analysis في ال applications في ال
+
+60
+00:03:41,570 --> 00:03:45,740
+mechanicsفي كتير من الـ .. اللي هو .. اللي له
+
+61
+00:03:45,740 --> 00:03:49,460
+تطبيقات في الفيزيا وفي ال .. وفي الهندسة إلى أخرى
+
+62
+00:03:49,460 --> 00:03:51,920
+وفي الرياضيات بصورة عامة طبعاً هي الـ Functional
+
+63
+00:03:51,920 --> 00:03:55,380
+Analysis نفسها فيه لها تطبيقات عالية وتطباق ..
+
+64
+00:03:55,380 --> 00:03:58,060
+وتطبيقات هائلة طبعاً وعلاقتها بالـ Topology
+
+65
+00:03:58,060 --> 00:04:02,440
+وعلاقتها بالجبر يعني زي .. خليني أقول اللي بيعرف
+
+66
+00:04:02,440 --> 00:04:04,800
+Functional Analysis بيعرف جبر بيعرف .. بيعرف تحليل
+
+67
+00:04:04,800 --> 00:04:08,020
+بيعرف Topology بيعرف جبر خطي إلى آخره لأن الجبر
+
+68
+00:04:08,020 --> 00:04:11,150
+خطي أصلا من الحياة دي المادةما تخافوش منها المادة
+
+69
+00:04:11,150 --> 00:04:14,170
+المادة بنعطيها بشكل بسيط وبشكل حلو وبشكل جميل
+
+70
+00:04:14,170 --> 00:04:19,720
+وماحدش اللي بتابع مش هيلاقي ان شاء الله مشاكلقلنا
+
+71
+00:04:19,720 --> 00:04:24,000
+أنواع الoperators الهيلبرت ات جوينت أوبراتر سلفة
+
+72
+00:04:24,000 --> 00:04:47,620
+جوينت أوبراتر
+
+73
+00:04:48,090 --> 00:04:52,210
+كانت الـ exam سريع لأنه بنعرض احنا يعني ال ..
+
+74
+00:04:52,210 --> 00:04:56,910
+قاعدين اللي هو ال course outline الجزء الثاني ..
+
+75
+00:04:56,910 --> 00:05:00,310
+الجزء الثالث من المادة اللي هو ال .. ال .. ال ..
+
+76
+00:05:00,310 --> 00:05:02,210
+او ال .. ال .. بعد الامتحان التاني اللي هو الـ
+
+77
+00:05:02,210 --> 00:05:05,450
+Adjoint Operator and Reflexive Spaces هنحكي شو
+
+78
+00:05:05,450 --> 00:05:08,690
+معناه .. شو معناه Adjoint Operator ومن فمها هنحكي
+
+79
+00:05:08,690 --> 00:05:12,110
+عن حاجة حلوة و جميلة اسمها الـ Reflexive Spaces و
+
+80
+00:05:12,110 --> 00:05:15,870
+بعدين هنحكي عن ال category theorem من نظرية المهمة
+
+81
+00:05:16,100 --> 00:05:20,200
+ومن ثم على اللي هي النظرية الأساسية الأخرى بعد
+
+82
+00:05:20,200 --> 00:05:23,380
+الـHN اللي هي الـNon Form Boundedness Theorem بقى
+
+83
+00:05:23,380 --> 00:05:26,340
+دي هيك هنحكي عن اللي هو الـConvergence، شو معناته
+
+84
+00:05:26,340 --> 00:05:29,040
+Strong وش معناته Weaken Convergence وحنحكي عن
+
+85
+00:05:29,040 --> 00:05:32,280
+الـStrongest أو Weakest Convergence إلى آخره، إن
+
+86
+00:05:32,280 --> 00:05:36,140
+شاء الله في الحين وبنكون موجود، أنا يعني وجد نظر
+
+87
+00:05:36,140 --> 00:05:39,690
+أنه مواضيع ممتعة يعنيConvergence of Sequences of
+
+88
+00:05:39,690 --> 00:05:42,570
+Operators and Functionals ماهي معنية Convergence
+
+89
+00:05:42,570 --> 00:05:45,730
+of Sequences من Operators أو Convergence of
+
+90
+00:05:45,730 --> 00:05:49,230
+Sequences من Functionals سنرى ماهي معناته إن شاء
+
+91
+00:05:49,230 --> 00:05:53,870
+الله ثم سنحكي عن نظرية الأساسية الـ Open Mapping
+
+92
+00:05:53,870 --> 00:05:57,770
+Theorem ثم سنحكي عن Closed Linear Operators ثم
+
+93
+00:05:57,770 --> 00:06:01,990
+نختم بالنظرية الرابعة الأساسية Closed Graph
+
+94
+00:06:01,990 --> 00:06:06,050
+Theorem ثم سأكون عندي الـ Third Exam اللي معيشه إن
+
+95
+00:06:06,050 --> 00:06:10,110
+شاء اللهومن ثم هنبدأ اللي هو في Chapter 7 اللي هو
+
+96
+00:06:10,110 --> 00:06:13,570
+Spectral اللي هو Theory of Linear Operators on
+
+97
+00:06:13,570 --> 00:06:16,210
+Known Displaces طبعا عالم الـ Spectral Theory هذا
+
+98
+00:06:16,210 --> 00:06:20,730
+عالم مهم جدا وعالم تطبيقات هائلة خصوصا في الفيزيا
+
+99
+00:06:20,730 --> 00:06:26,590
+وفي الهندسة إلى آخره وبعدين هنحكي عن اللي هو يعني
+
+100
+00:06:26,590 --> 00:06:29,750
+طبعا introductions هدولة لإن بس هنعطيكوا فكرة عنهم
+
+101
+00:06:30,030 --> 00:06:33,450
+لأن هذا على مواسع يعني ونحكي عن اللي هو البنخ
+
+102
+00:06:33,450 --> 00:06:37,750
+Algebra اللي هو جبربنخ وجبربنخ طبعاً لحاله عالم
+
+103
+00:06:37,750 --> 00:06:41,670
+يعني اللي هو الناس كتير بتشغل فيه، بتتخصص فيه، و
+
+104
+00:06:41,670 --> 00:06:46,590
+applications تبعته عديدةبنجي بنكون وصلنا لمين لل
+
+105
+00:06:46,590 --> 00:06:50,030
+final exam في كل اللي هو المسار في بعض ال
+
+106
+00:06:50,030 --> 00:06:53,890
+references اللي هو عندنا الكتاب المشهور تبع Conway
+
+107
+00:06:53,890 --> 00:06:59,530
+أو مادوكس Conway في عمقه في كده لكن كتاب يعني
+
+108
+00:06:59,530 --> 00:07:04,850
+كمرجع مهم مادوكس سهل و لذيذ وسريع لكن بليان برضه
+
+109
+00:07:05,840 --> 00:07:09,260
+وإن كان بتناول جزء يعني من الـ .. اللي .. اللي في
+
+110
+00:07:09,260 --> 00:07:12,860
+.. اللي في .. اللي في .. اللي هو في Conway أو اللي
+
+111
+00:07:12,860 --> 00:07:16,460
+هو في Kresing. نيجي بعدين ل .. في كمان مرجع اسمه
+
+112
+00:07:16,460 --> 00:07:18,240
+Linear Operator Theory in Engineering and Science
+
+113
+00:07:18,240 --> 00:07:21,400
+ده في الـ Linear Operator .. كتير كتير كتير كتير
+
+114
+00:07:21,400 --> 00:07:27,780
+للمهتم الكتاب يعني عرضه شيق وعرضه سهل وعرضه كده
+
+115
+00:07:27,780 --> 00:07:30,760
+ومليان معلومات حول ال operators وحتى في
+
+116
+00:07:30,760 --> 00:07:33,710
+applications.introduction to functional analysis
+
+117
+00:07:33,710 --> 00:07:38,350
+تبع تيلر هذا من الكتب القديمة القيمة برضه في ال
+
+118
+00:07:38,350 --> 00:07:41,250
+functional analysis للي حابب يطلع عليها نيجي
+
+119
+00:07:41,250 --> 00:07:43,850
+لموضوع ال grading الموضوع الأخير اللي هو the final
+
+120
+00:07:43,850 --> 00:07:47,110
+grade will be bound on the best six of seven
+
+121
+00:07:47,110 --> 00:07:50,230
+homeworks يعني احطيكوا homeworks هتاخدوا هتعطوني
+
+122
+00:07:50,230 --> 00:07:55,150
+اللي هو تسلموني ال homeworks كلها وأنا بختار أحسن
+
+123
+00:07:55,150 --> 00:07:59,010
+ستة من سبعة أو أكتر من ستة من تمانية اللي بدكميهاو
+
+124
+00:07:59,010 --> 00:08:02,910
+بعدين هذا يكون عليه 10% الامتحانات اللي حكينا عنها
+
+125
+00:08:02,910 --> 00:08:06,610
+ال first و second و third هاخد احسن اتنين من تلاتة
+
+126
+00:08:06,610 --> 00:08:10,210
+و عليها ال 40% احسن اتنين و ال final بكون 50% و
+
+127
+00:08:10,210 --> 00:08:14,670
+بكون هيك اللي هو بكون اكتمل اللي هو المية من المية
+
+128
+00:08:14,670 --> 00:08:17,830
+و ان شاء الله بكون التوفيق لكم جميعا يا رب
+
+129
+00:08:17,830 --> 00:08:21,660
+العالمينالان هذا هو ال course outline خلينا نبدأ
+
+130
+00:08:21,660 --> 00:08:26,700
+الان في الشبتر الأول وال section الأول الشبتر
+
+131
+00:08:26,700 --> 00:08:31,620
+الأول هو عبارة عن metric spaces او الفرغات المترية
+
+132
+00:08:31,620 --> 00:08:36,160
+او بمعنى اخر احنا جاعدين بدنا نعمم المسافة اللي
+
+133
+00:08:36,160 --> 00:08:39,220
+احنا بنعرفها في اللي هو ال R وفي ال R تربيع وفي
+
+134
+00:08:39,220 --> 00:08:44,680
+القدر بدنا نعممها ونخرجها على صورة اللي هو انه
+
+135
+00:08:44,680 --> 00:08:48,950
+تكون in general نشوف ايش اللي بحكيهالشبط الأول هو
+
+136
+00:08:48,950 --> 00:08:52,190
+metric spaces الفرغات المترية ال section الأول هو
+
+137
+00:08:52,190 --> 00:08:55,550
+هيحكي عن ال metric spaces الفرغات المترية هندخل
+
+138
+00:08:55,550 --> 00:09:00,870
+للتعريف و بعض الأمثلة السهلة و اللي هي فش فيها ان
+
+139
+00:09:00,870 --> 00:09:05,190
+شاء الله يعني اللي هو صعوبة و هنشوف كيف نتناول كل
+
+140
+00:09:05,190 --> 00:09:11,290
+مثال من الأمثلة اللي عندنالأن تعريف الـ metric
+
+141
+00:09:11,290 --> 00:09:16,610
+space a metric space is a pair X وD يعني أنا بحكي
+
+142
+00:09:16,610 --> 00:09:22,810
+عن ال metric space هو عبارة عن 6X معها D دالة إيش
+
+143
+00:09:22,810 --> 00:09:27,990
+هذه الدالة اللي بتخليني اللي هي مع ال X تخليني
+
+144
+00:09:27,990 --> 00:09:32,230
+metric space هذه الدالة بتسميها metric هي عبارة عن
+
+145
+00:09:32,230 --> 00:09:36,990
+دالةاللي هي دالة المسافة تعميم لدالة المسافة اللي
+
+146
+00:09:36,990 --> 00:09:41,650
+احنا بنعرفها زمان في سواء في R أو في R تربيعي الآن
+
+147
+00:09:41,650 --> 00:09:47,190
+من X across X لعند هو في الواقع لعند بالظبط بالظبط
+
+148
+00:09:47,190 --> 00:09:51,710
+لعند R positive اتحاد الـ Zero بس لو قلنا R في
+
+149
+00:09:51,710 --> 00:09:54,590
+وجود الشروط اللي بحكيها بكفي الكلام ويكون الكلام
+
+150
+00:09:54,590 --> 00:10:00,270
+اللي هو كمكتمل خليني أشوف الان هي عبارة عن دي
+
+151
+00:10:00,270 --> 00:10:05,410
+عبارة عن دالة من X across Xالى الـ real value of
+
+152
+00:10:05,410 --> 00:10:08,790
+function الى R بالظبط هتكون عند R وزي الاتحاد الـ
+
+153
+00:10:08,790 --> 00:10:13,570
+Zero تحقق الشروط التالية أول شرط أن المسافة بين أي
+
+154
+00:10:13,570 --> 00:10:17,750
+نقطين لازم تكون أكبر أو ساوى سفر هذه ال X و Y من
+
+155
+00:10:17,750 --> 00:10:21,010
+أين جيات ال X من ال X و Y من ال Y لأن X cross Y
+
+156
+00:10:21,010 --> 00:10:25,940
+أشمالهاعبارة عن order بيارة عناصرها إذا الـD X Y
+
+157
+00:10:25,940 --> 00:10:29,200
+أكبر أو يساوي سفر أو المسافة بين X وY أشمال أكبر
+
+158
+00:10:29,200 --> 00:10:31,700
+أو يساوي سفر هذا طبيعي ما احنا عارفين أن مسافتنا
+
+159
+00:10:31,700 --> 00:10:34,920
+المسافة اللي بنحكي عنها اللي هو ديمة عمرنا في R وR
+
+160
+00:10:34,920 --> 00:10:38,340
+تربيه هي عبارة عن مسافة يعني أكبر أو يساوي سفر
+
+161
+00:10:38,340 --> 00:10:42,380
+فاحنا عمال جاعدين بنستقي تعريفنا و بنعمم اللي هو
+
+162
+00:10:42,380 --> 00:10:49,290
+اللي بنحكي في ال metric العادي اتنينالمسافة بين X
+
+163
+00:10:49,290 --> 00:10:54,810
+و Y بساوي 0 إذا و فقط إذا X بتساوي 100 بساوي Y
+
+164
+00:10:54,810 --> 00:10:59,290
+يعني المسافة بين النقطة و نفسها 0 و لو كانت
+
+165
+00:10:59,290 --> 00:11:02,690
+المسافة بين نقطة و أخرها 0 بكون هي النقطة نفسها
+
+166
+00:11:02,690 --> 00:11:07,290
+يعني لن نجد اللي هو نقطتين المسافة بينهم بتساوي 0
+
+167
+00:11:07,290 --> 00:11:10,490
+و لنا مش متساويتين لن نجد هذا اللي هو الشرط الثاني
+
+168
+00:11:10,950 --> 00:11:16,130
+الشرط الثالث أنه دائما المسافة بين X و Y هي نفسها
+
+169
+00:11:16,130 --> 00:11:19,830
+المسافة بين Y و X طبعا المسافة بين X و Y هي نفسها
+
+170
+00:11:19,830 --> 00:11:23,330
+المسافة بين Y و X اللي بنسميها في العلاقات اللي هي
+
+171
+00:11:23,330 --> 00:11:28,770
+الـ Symmetric الشرط الثالث أو الرابع اللي هي
+
+172
+00:11:28,770 --> 00:11:32,810
+Triangle Inquality اللي هي جاية من اللي هو من
+
+173
+00:11:32,810 --> 00:11:37,710
+المتباينة المثلثة اللي احنا بنعرفها اللي هو DXY
+
+174
+00:11:38,510 --> 00:11:45,350
+أصغر أو تساوي D X و Z زائد D Z و 100 و Y جاي من من
+
+175
+00:11:45,350 --> 00:11:50,410
+من الهى اللى انتوا بتعرفوها اللى هى لو كان عندى
+
+176
+00:11:50,410 --> 00:11:54,610
+نقطة هي نقطة و هي نقطة فى الفراغ أو فى ال plane
+
+177
+00:11:54,610 --> 00:11:58,510
+المسافة بين هذه و هذه بين D X و Y أكيد أصغر أو
+
+178
+00:11:58,510 --> 00:12:02,750
+تساوي المسافة بين هذه و هذه زائد هذه و هذهأي نقطة
+
+179
+00:12:02,750 --> 00:12:06,350
+أخرى هيعندي X وY لو كانت أي نقطة أخرى Z هيكون
+
+180
+00:12:06,350 --> 00:12:09,590
+مسافة بين X وY أكيد أقل أو يساوي المسافة بين هذه
+
+181
+00:12:09,590 --> 00:12:13,390
+وهذه زائد هذه وهذه هذي ال Triangle اللي قُلتيه
+
+182
+00:12:13,390 --> 00:12:16,330
+طبعا في المثلة أكيد strict لأكبر هذي بحكي عن وين
+
+183
+00:12:16,330 --> 00:12:21,250
+فعلا ما ترى اللي هو ال Rالأرض تربيع الآن قد يكون
+
+184
+00:12:21,250 --> 00:12:24,530
+اللي هو المسافة بالظبط فيها مسواها يعني هذه strict
+
+185
+00:12:24,530 --> 00:12:28,310
+الأكبر دول لكن قد يكونوا سواها لو كانت X هان او Z
+
+186
+00:12:28,310 --> 00:12:32,070
+هان و Y هان فبكون المسافة بين X و Y بالظبط حساوي
+
+187
+00:12:32,070 --> 00:12:35,530
+المسافة بين X و Z زائد المسافة بين Z و Y وعشان هيك
+
+188
+00:12:35,530 --> 00:12:39,670
+تبين ال triangle equality أصغر أو يساوي إذا تحققت
+
+189
+00:12:39,670 --> 00:12:44,990
+الأربع شروط الأمام هذولة automatic automatic بقول
+
+190
+00:12:44,990 --> 00:12:49,780
+على الومن ثم مكانة الـ D metric ما على طول بيصير
+
+191
+00:12:49,780 --> 00:12:54,200
+الـ X والـ D أشمالها metric space بتكون عبارة عن
+
+192
+00:12:54,200 --> 00:12:59,900
+مين؟ عن metric space هذه اللي هي اللي هو تعريف
+
+193
+00:12:59,900 --> 00:13:04,200
+اللي هو ال metric لأن نيجي لبعض الخواص اللي بنقدر
+
+194
+00:13:04,200 --> 00:13:07,280
+نستقيها أو تعريف ال metric space بعض الخواص اللي
+
+195
+00:13:07,280 --> 00:13:11,420
+بنقدر نستقيها من اللي هو التعريف اللي أمامنا
+
+196
+00:13:13,310 --> 00:13:18,550
+الخاصية الأولى بقول لي لو كان عندى N element in N
+
+197
+00:13:18,550 --> 00:13:24,550
+ودي ناخدنا أي X واحد و X اتنين و X N element اللي
+
+198
+00:13:24,550 --> 00:13:28,530
+هي NX اللي بنحكي عليها اللي بنقول عليها متر هيكون
+
+199
+00:13:28,530 --> 00:13:33,070
+المسافة بين distance يعني الـ N عبارة عن بدل اللي
+
+200
+00:13:33,070 --> 00:13:35,490
+هو المسافة بين نجوطين أظهر بس هو المسافة بين
+
+201
+00:13:35,490 --> 00:13:36,350
+نجوطين و نجوطين و نجوطين و نجوطين و نجوطين و
+
+202
+00:13:36,350 --> 00:13:38,370
+نجوطين و نجوطين و نجوطين و نجوطين و نجوطين و
+
+203
+00:13:38,370 --> 00:13:41,910
+نجوطين
+
+204
+00:13:43,110 --> 00:13:48,810
+و Xn أظهر ايش هو المسافة بين X1 و X2 زائد المسافة
+
+205
+00:13:48,810 --> 00:13:56,210
+بين X2 و X3 زائد المسافة بين Xn-1 و Xn يعني هذه
+
+206
+00:13:56,210 --> 00:14:00,850
+تعميل للحالة الأولى هذه بدنا نبرهنها أو برهانها
+
+207
+00:14:00,850 --> 00:14:04,030
+سهل by induction انتوا حالكم بتقدروا تبرهنوها لكن
+
+208
+00:14:04,030 --> 00:14:07,450
+خلينا على السريع اعطيكم outline لبرهانها خليها دي
+
+209
+00:14:07,450 --> 00:14:12,110
+نسميها إيه إيش star عارفين كده بنبرهن by induction
+
+210
+00:14:12,110 --> 00:14:16,860
+أول حاجةأول اشي عشان بنها دي لكل n element صحيحة
+
+211
+00:14:16,860 --> 00:14:21,980
+بتقول for n بتساوي واحدة trivial فالان for n
+
+212
+00:14:21,980 --> 00:14:24,560
+بتساوي اتنين for n بتساوي اتنين
+
+213
+00:14:29,300 --> 00:14:35,100
+اللي هي أصغر حتى التين برضه trivial لو أنا بالساعة
+
+214
+00:14:35,100 --> 00:14:40,020
+تلاتة X1 و X3 أصغر الساعة المسافة بين X1 و X2 زائد
+
+215
+00:14:40,020 --> 00:14:44,700
+المسافة بين X2 و X3 الـ Trivial الـ Trivial برضه
+
+216
+00:14:44,700 --> 00:14:47,620
+هذا من وين جاوب من ال triangle inequality مباشرة
+
+217
+00:14:47,620 --> 00:14:52,370
+من سرعة لأنه كلام سهل أو outline هذا التينبنقول
+
+218
+00:14:52,370 --> 00:14:59,930
+suppose that star is true for n بتساوي k ده نفترض
+
+219
+00:14:59,930 --> 00:15:03,590
+أنه هذه الجملة صحيحة لأن بتساوي k وبدتبتها صحيحة
+
+220
+00:15:03,590 --> 00:15:08,150
+لمين ل k زائد واحد يعني بالمعنى أخر فقضيت هذا صحيح
+
+221
+00:15:08,150 --> 00:15:15,460
+ل k معناته صارت DX1 لعين DXK DX1 لعين DXKأصغر أو
+
+222
+00:15:15,460 --> 00:15:20,080
+يساوي لما أصل لعند XK-1 و XK هذي صحيحة من
+
+223
+00:15:20,080 --> 00:15:24,080
+الhypothesis induction اللي هم بيدثبتها لمين لـ K
+
+224
+00:15:24,080 --> 00:15:29,660
+زائد واحد سهلة نيجي نثبتها لـ K زائد واحد دي X1 و
+
+225
+00:15:29,660 --> 00:15:36,020
+XK زائد واحدما لها أصغر أو يساوي دي X واحد و XK
+
+226
+00:15:36,020 --> 00:15:41,140
+زائد دي XK و XK زائد واحد هذي منين؟ من الـ
+
+227
+00:15:41,140 --> 00:15:45,740
+Triangle equality العادية طبقتها على مين؟ على اللي
+
+228
+00:15:45,740 --> 00:15:48,720
+هو المسافة بين النقطة هذه و النقطة هذه أصغر أو
+
+229
+00:15:48,720 --> 00:15:51,220
+ساوي المسافة بين هذه النقطة و أي نقطة بديها؟ مين
+
+230
+00:15:51,220 --> 00:15:54,260
+هي اللي أخدتها أنا؟ XK زائد المسافة بين النقطة
+
+231
+00:15:54,260 --> 00:15:56,760
+اللي أخدتها و بين هذه هذه اللي هي by the triangle
+
+232
+00:15:56,760 --> 00:16:03,490
+equality اللي هي موجودة الـ M4طيب هذا نفسه هذه
+
+233
+00:16:03,490 --> 00:16:08,390
+أصغر أو ساوي من هنا من ال hypothesis induction
+
+234
+00:16:08,390 --> 00:16:11,810
+اللي مفترضها يعني by star بتكون هذه أصغر أو ساوي
+
+235
+00:16:11,810 --> 00:16:24,510
+dx1 و x2 زائد dx2 و x3 لما أصل لعين زائد dxk و x-1
+
+236
+00:16:24,510 --> 00:16:31,510
+لعين xk و زائد هذه من الأصل dxkو X K زائد واحد
+
+237
+00:16:31,510 --> 00:16:37,110
+معناته صارت اللي هي هذه اللي فوق صحيحة لمين ل K
+
+238
+00:16:37,110 --> 00:16:40,450
+زائد واحد و معناته أنه أثبتنا هذا صحيحة by
+
+239
+00:16:40,450 --> 00:16:44,670
+induction لكل N element هنا إذا هيك بيكون احنا
+
+240
+00:16:44,670 --> 00:16:49,470
+أثبتنا اللي هو اللي هي ال note الأولى و كانت صحيحة
+
+241
+00:16:49,470 --> 00:16:49,750
+دائما
+
+242
+00:16:52,970 --> 00:16:56,510
+طيب يا جماعة اتصلوا عندنا عليه الصلاة والسلام نيجي
+
+243
+00:16:56,510 --> 00:16:59,990
+اللي هو ناخد الملاحظة التانية ايش الملاحظة التانية
+
+244
+00:16:59,990 --> 00:17:06,330
+بتقول بدنا نحرف الآن حاجة اسمها أيش sub space sub
+
+245
+00:17:06,330 --> 00:17:11,090
+space من اسمه sub space اذا اكيد اكيد اللي بدي
+
+246
+00:17:11,090 --> 00:17:14,670
+اشتغل عليها جزء من ال space الأصلي عشان تكون sub
+
+247
+00:17:14,670 --> 00:17:18,150
+space منه وsub space منه كامله بدي اتحقق خياصه
+
+248
+00:17:18,150 --> 00:17:20,770
+يعني الصغير هذا بيكون أيش ايه للكبير يعني بحقق
+
+249
+00:17:20,770 --> 00:17:31,960
+خياصه كاملهفبنقول ان الـ y و d تلدة sub spaceof x
+
+250
+00:17:31,960 --> 00:17:35,000
+و d ايش ال x و ال d طبعا x و d في مفترضين و metric
+
+251
+00:17:35,000 --> 00:17:38,820
+space ايش معناه هذا يكون sub metric space من هذا
+
+252
+00:17:38,820 --> 00:17:45,080
+شرطين الشرط الاول ان ال y جزء من x ها كيف ال y جزء
+
+253
+00:17:45,080 --> 00:17:50,160
+من من من x اي واحد اتنين اتنين ان ال d تلد هذا
+
+254
+00:17:50,160 --> 00:17:53,100
+اللي بترك اللي على ال d اللي على ال y طبعا ال d
+
+255
+00:17:53,100 --> 00:17:56,380
+تلد هذا بشتغل من وين من y cross y و برمي في r
+
+256
+00:17:56,380 --> 00:18:02,160
+positive اتحاد ال zeroهذا D تلدى لازم يكون هو نفسه
+
+257
+00:18:02,160 --> 00:18:06,160
+الـD بس شغل وين؟ طبعا الـD بيشغل على مين؟ الـD
+
+258
+00:18:06,160 --> 00:18:10,440
+بيشغل على X across X لعند R positive اتحاد الـ0
+
+259
+00:18:10,440 --> 00:18:14,860
+الـD برضه أصلا لما هي الـY cross Y جزئية من X
+
+260
+00:18:14,860 --> 00:18:18,960
+cross X فالآن عشان نسميها The subspace لازم تكون D
+
+261
+00:18:18,960 --> 00:18:23,600
+تلدى اللي بتشغل على الـY هي نفسها D لما اشتغلت على
+
+262
+00:18:23,600 --> 00:18:27,770
+الـY across Yيعني بمعنى أخر D تل ده هي the
+
+263
+00:18:27,770 --> 00:18:32,850
+restricted function D on Y cross Y يعني نفسها D بس
+
+264
+00:18:32,850 --> 00:18:37,470
+على مين؟ على Y cross Y في هذه الحالة بنسمي ال Y وD
+
+265
+00:18:37,470 --> 00:18:41,490
+تل ده عبارة عن subspace من مين يا جماعة؟ من اللي
+
+266
+00:18:41,490 --> 00:18:47,140
+هو ال X وDطيب نيجي الآن هذا اللي هو تعريف ال
+
+267
+00:18:47,140 --> 00:18:52,280
+subspace اللي حكينا عنه نيجي الآن نحكي عن بعض
+
+268
+00:18:52,280 --> 00:18:59,940
+الأمثلة عن اللي هوالـ metric spaces نيجي للأمثلة
+
+269
+00:18:59,940 --> 00:19:04,040
+أكيد هنبدأ ببثالنا اللي احنا بنقول عليه سهل و اللي
+
+270
+00:19:04,040 --> 00:19:09,300
+بنعرفه من زمان اللي هو اي مثال اللي هو البثال انه
+
+271
+00:19:09,300 --> 00:19:14,100
+ناخد ال real line ال real line I ر ر line line ال
+
+272
+00:19:14,100 --> 00:19:18,860
+real line هايه هبدنا نعرف المسافة بين X و بين وين
+
+273
+00:19:18,860 --> 00:19:22,400
+و بين Y هنعرف المسافة اللي بتعرفوها انتوا اللي هو
+
+274
+00:19:22,400 --> 00:19:28,700
+DX و Y بدي أعرفها على الـ R يعني هتكون D تبعته من
+
+275
+00:19:28,700 --> 00:19:33,140
+R cross R هترمي وين؟ أكيد هنرميها في R positive
+
+276
+00:19:33,140 --> 00:19:35,700
+تحت Zero عشان يكون metric بالشروط اللي احنا
+
+277
+00:19:35,700 --> 00:19:40,780
+عارفينها طيب، D X Y كده بدي أعرفها عبارة عناللي هو
+
+278
+00:19:40,780 --> 00:19:43,560
+y minus x وحيانا ماكنتش عارف مين البعد ومين
+
+279
+00:19:43,560 --> 00:19:46,280
+الإيجابيل لو ماكنتش عارف كان المجهولات على طول
+
+280
+00:19:46,280 --> 00:19:50,000
+بكتب absolute value ل y minus x وهذا تعني المسافر
+
+281
+00:19:50,000 --> 00:19:53,060
+بين x و y هل هذه بتحقق شروط ا او بتحقق شروط
+
+282
+00:19:53,060 --> 00:19:56,960
+الأربعة ما أنتوا شايفين هذه أول شرطأكبر أو يساوي
+
+283
+00:19:56,960 --> 00:20:00,080
+سفر اتريفياً y minus x أكبر أو يساوي سفر هاي واحد
+
+284
+00:20:00,080 --> 00:20:05,060
+اتنين اكيد dy dx y اللي هو absolute value اللي هو
+
+285
+00:20:05,060 --> 00:20:10,080
+y minus x بساول x minus y اللي هو عبارة عن مين dy
+
+286
+00:20:10,080 --> 00:20:15,380
+ومين وx إذا المسافة بين y وx هي نفس المسافة بين
+
+287
+00:20:15,380 --> 00:20:24,880
+مين x وy الشرط الثالث اللي هو لو كdxy بتساوي سفر
+
+288
+00:20:25,650 --> 00:20:29,790
+بدأ اثبت لكم if and only if اللي هو مين اللي هو x
+
+289
+00:20:29,790 --> 00:20:32,490
+بيساوي y شرط الثالث يا جماعة هاي الشرط الثالث ده
+
+290
+00:20:32,490 --> 00:20:35,690
+انتوا انسطوه هاي الشرط الثالث بدأ اثبت الشرط
+
+291
+00:20:35,690 --> 00:20:39,990
+الثالث هذا بقول دي x y بيساوي سفر if and only if
+
+292
+00:20:39,990 --> 00:20:43,650
+ايش تعرف دي x y بيساوي سفر دي x y اللي هو absolute
+
+293
+00:20:43,650 --> 00:20:48,250
+value لو y minus x بتساوي سفر if and only if هده
+
+294
+00:20:48,250 --> 00:20:51,770
+الأرقام عادية بتعرفوها ان y ايش بتساوي x هذا الشرط
+
+295
+00:20:51,770 --> 00:20:56,250
+الثالث محقق نجي للشرط الرابعالشرف الرابع انتوا
+
+296
+00:20:56,250 --> 00:21:00,150
+عارفين هو هذا ما هي مخاصة absolute value عند D لو
+
+297
+00:21:00,150 --> 00:21:06,430
+أخدنا أي x و y و z دلان وين هو البدايات؟ في R دي x
+
+298
+00:21:06,430 --> 00:21:12,600
+و yبساوة ال absolute value of x minus y بساوة ال
+
+299
+00:21:12,600 --> 00:21:16,520
+absolute value of x minus y هذه absolute value
+
+300
+00:21:16,520 --> 00:21:20,940
+عادية اللي بنعرفها أكيد أكيد أكيد أصغر أو ساوي ال
+
+301
+00:21:20,940 --> 00:21:23,940
+absolute value of x minus z زي ال absolute value
+
+302
+00:21:23,940 --> 00:21:29,650
+of z minus yطب هذه من هي اللي تعرفتها عبارة عن D X
+
+303
+00:21:29,650 --> 00:21:35,910
+و Z و هذه من هي D Z Y إذا D X Y أصغر يساوي D X و Z
+
+304
+00:21:35,910 --> 00:21:40,630
+D Z Y إذا انتحقت شروط الأربعة إذا في المثال الأول
+
+305
+00:21:40,630 --> 00:21:44,750
+الـ D X Y بسبب absolute value X minus Y على الـ A
+
+306
+00:21:44,750 --> 00:21:50,850
+أشمله حقق شروط المتر كلها إذا صارت الـ R محاذةالـ
+
+307
+00:21:50,850 --> 00:21:55,650
+metric اللي هو عبارة عن metric space مع هذه الدالة
+
+308
+00:21:55,650 --> 00:21:58,810
+عبارة عن metric space وهذا بنسميه الـ Euclidean
+
+309
+00:21:58,810 --> 00:22:03,110
+metric space الـ R أو اللي هو اللي مستقبلا نجيه
+
+310
+00:22:03,110 --> 00:22:06,950
+بولدنا ال topology اللي احنا بنعرفه اللي هو بنسميه
+
+311
+00:22:06,950 --> 00:22:12,370
+usual topology هذا مستقبلاهذا المثال الأول سهل
+
+312
+00:22:12,370 --> 00:22:16,010
+البسيط المثال التاني برضه سهل ايش المثال التاني
+
+313
+00:22:16,010 --> 00:22:22,190
+المثال التاني اللي هو بده يعرف الآن metric على مين
+
+314
+00:22:22,190 --> 00:22:26,450
+على ال R تربيهة نشوف ايش ال metric اللي اللي
+
+315
+00:22:26,450 --> 00:22:30,150
+بنعرفه على ال R تربيهة شوفوا يا جماعة صلوا على
+
+316
+00:22:30,150 --> 00:22:33,710
+النبي عليه الصلاة والسلام الان عندي ال 6 بتاعة ال
+
+317
+00:22:33,710 --> 00:22:40,100
+helix أشمالهاهي عبارة عن الـ R تربية هذه الست اللي
+
+318
+00:22:40,100 --> 00:22:45,240
+هي الـ R تربية الأن عصرها إيه اشمالها Ordered pair
+
+319
+00:22:45,240 --> 00:22:53,720
+بتعرف دي ديمن R تربيع across R تربيع وبدأ ارميها
+
+320
+00:22:53,720 --> 00:22:56,340
+في المكان اللي احنا بنرميها اللي هو R بزوجة اتحاد
+
+321
+00:22:56,340 --> 00:23:00,820
+الـ Zero الآن بدأ اعرفها كالتالي العناصر اللي في
+
+322
+00:23:00,820 --> 00:23:04,660
+الـ R تربيع لو أخدت أي X و Y في الـ R تربيع الـ X
+
+323
+00:23:04,660 --> 00:23:07,340
+نفسه هيكون زوج مرتب ما بتعرفين وإذا الـ X إيش
+
+324
+00:23:07,340 --> 00:23:13,210
+هيساوي XI واحد وXI اتنين مثلاو Y أيش هيساوي بساوي
+
+325
+00:23:13,210 --> 00:23:16,530
+Gamma 1 و Gamma 2 خلّيني أستخدم العروف اللاتينية
+
+326
+00:23:16,530 --> 00:23:21,690
+عشان أخلفها عن ال X و ال Y عشان يكون اللغة مميزة
+
+327
+00:23:21,690 --> 00:23:27,610
+هيك أو اللي هو نتوافق مع لغة الكتاب كمان حيش بده
+
+328
+00:23:27,610 --> 00:23:35,400
+يعرف المسافة بين X و Yبساوي ال absolute value ال
+
+329
+00:23:35,400 --> 00:23:39,720
+absolute value اكساي واحد ناقص جامعة واحد زاد ال
+
+330
+00:23:39,720 --> 00:23:43,940
+absolute value اكساي اتنين ناقص جامعة اتنين هذا
+
+331
+00:23:43,940 --> 00:23:47,140
+بتدعي انه metric هو بتدعي انه metric خلينا نشوف
+
+332
+00:23:47,140 --> 00:23:53,840
+شروطه هل متحقق ولا لأ نيجي بناخد الآن خد اي فرعاني
+
+333
+00:23:56,060 --> 00:24:02,500
+يعني x و y و z element in R تربيع شكل هنا 1x
+
+334
+00:24:02,500 --> 00:24:06,360
+بيساوي مثلا إكساي واحد و إكساي اتنين و y بيساوي
+
+335
+00:24:06,360 --> 00:24:11,160
+جامعة واحد و جامعة اتنين و z بتساوي ألفة واحد مثلا
+
+336
+00:24:11,160 --> 00:24:15,180
+و ألف اتنين خلينا نشوف اللي هو الشروط الأربعة طبعا
+
+337
+00:24:15,180 --> 00:24:18,020
+أول تلت شروط عادة انها جماعة سهلة و أنا سهلة طبعا
+
+338
+00:24:18,020 --> 00:24:21,580
+بس خلينا نمروا سريع عليها و انتوا بت .. بت .. بت
+
+339
+00:24:21,580 --> 00:24:29,730
+.. بتعيدوا شغل كتابة الشرط الأولعندي DXY DXY هايه
+
+340
+00:24:29,730 --> 00:24:33,370
+أكيد ايش ماله أكبر أو ساوي سفر واضح لإن هذه أعداد
+
+341
+00:24:33,370 --> 00:24:35,250
+أكبر أو ساوي سفر وهذه أعداد أكبر أو ساوي سفر لإن
+
+342
+00:24:35,250 --> 00:24:39,930
+absolute value اتنين الشرط التالي اللي هو هذا
+
+343
+00:24:39,930 --> 00:24:45,730
+بيساوي سفر DXYهي ساوي سفر إذا و فقط إذا اللي هو
+
+344
+00:24:45,730 --> 00:24:48,810
+هذا بساوي سفر يعني بمعنى أخر absolute value x y
+
+345
+00:24:48,810 --> 00:24:52,970
+واحد ناقص جامعة واحد زائد التاني بسفر هذا أكبر
+
+346
+00:24:52,970 --> 00:24:55,210
+ساوية سفر وهذا أكبر ساوية سفر إذا التانين مع بعض
+
+347
+00:24:55,210 --> 00:24:58,390
+سفر أكيد هذا هيكون سفر وهذا هيكون سفر مش ممكن
+
+348
+00:24:58,390 --> 00:25:01,770
+يواحد يكون سالب التاني لأ التانين كل واحد إيش ماله
+
+349
+00:25:01,770 --> 00:25:06,070
+كل واحد تساوي سفر إذا هذا ناقص هذا بساوي اللي هو x
+
+350
+00:25:06,070 --> 00:25:09,810
+y اتنين ناقص جامعة اتنين بساوي إيه السفر لإن هذا
+
+351
+00:25:09,810 --> 00:25:15,080
+بساوي سفر بسإذا و فقط إذا هذا سفر وهذا سفر وهذا
+
+352
+00:25:15,080 --> 00:25:18,940
+الكلام واضح إيش معناته هذا الكلام هذا معناته إنك
+
+353
+00:25:18,940 --> 00:25:22,280
+ساية واحد إيش هتساوي جامعة واحد إيش هذا معناته
+
+354
+00:25:22,280 --> 00:25:26,120
+كساية اتنين بيساوي جامعة اتنين وهذا شو معناته إنك
+
+355
+00:25:26,120 --> 00:25:30,240
+ساية واحد وكساية اتنين هي نفس جامعة واحد و جامعة
+
+356
+00:25:30,240 --> 00:25:35,040
+اتنين وهذا معناته إن X إيش هي Y إذا المسافة بين X
+
+357
+00:25:35,040 --> 00:25:37,740
+و Y بيساوي سفر إذا و فقط إذا اللي هو ال X بالها
+
+358
+00:25:37,740 --> 00:25:44,050
+بتساوي Yالخاصية التالتة الطبيعية السهلة وسريعة
+
+359
+00:25:44,050 --> 00:25:49,870
+المسافة بين X و Y هي المسافة بين Y و X جامعة واحدة
+
+360
+00:25:49,870 --> 00:26:00,070
+نقص XI واحدة اذا دي DXYبساوة dy او x كلام trivial
+
+361
+00:26:00,070 --> 00:26:04,370
+و سهل طيب ميجي يا جماعة لأ الخاصية الرابعة الخاصية
+
+362
+00:26:04,370 --> 00:26:09,290
+الرابعة ايش الخاصية الرابعة انه دي اكس و اي دي اكس
+
+363
+00:26:09,290 --> 00:26:13,490
+و اي اللي هو اظهر بساوية دي اكس و زي دي زد و اي
+
+364
+00:26:13,490 --> 00:26:18,850
+اظهر عليها الان اكيد xi واحد ناقص جامعة واحد انتبه
+
+365
+00:26:18,850 --> 00:26:26,370
+بس هالشغلأظهر أو ساويت XI واحد ناقص Alpha واحد زاد
+
+366
+00:26:26,370 --> 00:26:30,530
+Alpha واحد ناقص Gamma واحد أكيد بالتالي ال quality
+
+367
+00:26:30,530 --> 00:26:33,550
+بتبعد زمان انت بتلافش weight value لأن هدول أشمال
+
+368
+00:26:33,550 --> 00:26:39,000
+نقابهلجيب شوف أشي اللي بسويه هاد الأن إكساي 2 ناقص
+
+369
+00:26:39,000 --> 00:26:44,680
+Gamma 2 برضه أصغر يساوي إكساي 2 ناقص Alpha 2 زائد
+
+370
+00:26:44,680 --> 00:26:49,920
+Alpha 2 ناقص Gamma 2 برضه طبقت ال .. ال .. ال ..
+
+371
+00:26:49,920 --> 00:26:52,820
+اللي هو مين اللي هو ال triangle inequality تبعت ال
+
+372
+00:26:52,820 --> 00:26:55,820
+absolute value تبعت من تبعت ال calculus زمان الأهم
+
+373
+00:26:55,820 --> 00:26:59,990
+هو هدولة التنتين إجمح هذه زائد هذهأصغر أو يساوي
+
+374
+00:26:59,990 --> 00:27:04,430
+هذه زائد هذه تمشيوا في K4 بعد أذنكم بس بدي أمسح
+
+375
+00:27:04,430 --> 00:27:10,870
+حده بيصير عندي اللي هو التالي بيصير .. أكتب فيه
+
+376
+00:27:10,870 --> 00:27:15,070
+لون تاني عشان نميزه عنه بيصير عندي يا جماعة اللي
+
+377
+00:27:15,070 --> 00:27:20,910
+هو XI واحد ناقص Gamma واحد زائد XI تنين ناقص Gamma
+
+378
+00:27:20,910 --> 00:27:27,350
+تنين أصغر أو يساوي أصغر أو يساوي هذه XI واحد ناقص
+
+379
+00:27:27,350 --> 00:27:32,190
+Alpha واحدهذه زائد هذه ماشي يا جماعة اكساي واحد
+
+380
+00:27:32,190 --> 00:27:36,930
+ناقص ألف اتنين
+
+381
+00:27:36,930 --> 00:27:42,950
+ناقص ألف اتنين زائد الجزء هذا زائد هذا زائد هذا
+
+382
+00:27:42,950 --> 00:27:49,580
+اللي هو الف واحدنقص Gamma 1 زائد Alpha 2 نقص Gamma
+
+383
+00:27:49,580 --> 00:27:54,380
+2 اتطلعوا عليهم هذول واضحة الصورة تتصور بعضكم جال
+
+384
+00:27:54,380 --> 00:27:59,940
+خلصناها هذه هي مين في الواقع هي المسافة بين X وY
+
+385
+00:28:00,870 --> 00:28:04,410
+أصغر أو ساوي هذه في الواقع هذه المسافة بين مين هذه
+
+386
+00:28:04,410 --> 00:28:13,490
+تبعات X وهذه تبعات Z اللي هي Alpha واحد ناقص XI
+
+387
+00:28:13,490 --> 00:28:16,730
+واحد ناقص Alpha واحد زي Alpha واحد ناقص Gamma واحد
+
+388
+00:28:16,730 --> 00:28:21,370
+خليني أخد دليل تبعات Z اللي هي Alpha واحد مع XI
+
+389
+00:28:21,370 --> 00:28:27,630
+واحد مع Alpha واحد و XI اتنينمع Alpha اتنين هذه
+
+390
+00:28:27,630 --> 00:28:29,910
+اتنين آسف هذه اتنين Xi اتنين و Alpha اتنين هي
+
+391
+00:28:29,910 --> 00:28:34,130
+اتنين اتنين مع بعض هذه Alpha اتنين Xi واحد نقص
+
+392
+00:28:34,130 --> 00:28:37,990
+Gamma واحد اصغر sorry Xi واحد نقص Alpha واحد زائد
+
+393
+00:28:37,990 --> 00:28:40,590
+Alpha واحد نقص Gamma واحد وهذه Xi اتنين نقص Alpha
+
+394
+00:28:40,590 --> 00:28:42,350
+اتنين ناخدنا هذول اتنين اتنين مع بعض و جمعها في
+
+395
+00:28:42,350 --> 00:28:46,390
+الأول ليه Xi واحد نقص Alpha واحد وهذه زائد Xi
+
+396
+00:28:46,390 --> 00:28:51,130
+اتنين نقص Alpha اتنين آسفألف اتنين والتانية ألف
+
+397
+00:28:51,130 --> 00:28:54,750
+واحد ناجس جامعة واحد وهيها والتانية ألف اتنين ناجس
+
+398
+00:28:54,750 --> 00:28:58,170
+جامعة اتنين هذه الكلامية في الميزة هذه مين هي هي
+
+399
+00:28:58,170 --> 00:29:04,170
+تبعات X وهي تبعات Z هي هنا هي هنا هي هنا هي X وهي
+
+400
+00:29:04,170 --> 00:29:08,970
+Y و Z اللي فرضناها قبل بشوية كتبناها و اشيلناها Z
+
+401
+00:29:08,970 --> 00:29:12,790
+بساوي اللي هو جامعة واحد وجامعة اتنين صار عندي
+
+402
+00:29:12,790 --> 00:29:19,420
+الآن هذول التنتين هم المثلين DX وZزائد هذول اللي
+
+403
+00:29:19,420 --> 00:29:23,080
+بيمثل من مين هي تبعات Alpha واحد تبعات Z و هذول
+
+404
+00:29:23,080 --> 00:29:27,760
+تبعات من Y الأولى زائد دي Z و Y و بيكون ال
+
+405
+00:29:27,760 --> 00:29:30,980
+triangle inequality أشمالها تحققت و بيكون هذا
+
+406
+00:29:30,980 --> 00:29:38,660
+أثبتنا أن هذا عبارة عن metric space يعني
+
+407
+00:29:38,660 --> 00:29:43,020
+ال D هذاmetric space مع الارض التربية بعضكم أكيد
+
+408
+00:29:43,020 --> 00:29:46,000
+سأل قال طب احنا مافيه metric احنا الزمان اللي
+
+409
+00:29:46,000 --> 00:29:49,160
+اتعلمناه و احنا اصغار اللي هو او احنا في ال .. في
+
+410
+00:29:49,160 --> 00:29:53,280
+ال .. في ال .. حتى في الاعدادية او اللي هو في اللي
+
+411
+00:29:53,280 --> 00:29:56,800
+هي ال calculus احنا بنعرف المسافة بين نقطتين في
+
+412
+00:29:56,800 --> 00:30:04,280
+الفرق لما يكون عندى النقطة x و yاللي هو في الفرق
+
+413
+00:30:04,280 --> 00:30:06,540
+العادي في ال .. في ال .. في ال .. في ال .. في ال
+
+414
+00:30:06,540 --> 00:30:09,320
+plane العادي اللي احنا اخدنا هندسته لما نزجنا
+
+415
+00:30:09,320 --> 00:30:11,920
+الهندسة الإقليدية X بالساعة و كده و Y بالساعة و
+
+416
+00:30:11,920 --> 00:30:16,460
+كده أخدنا المسافة بين X و Y اللي هو عبارة عن الجدر
+
+417
+00:30:16,460 --> 00:30:22,610
+التربيعي ل X I واحد ناقص Gamma واحدالكل تربيع زائد
+
+418
+00:30:22,610 --> 00:30:27,110
+اكسايه تنين ناجس جامعة تنين الكل اياش تربيع اه هذا
+
+419
+00:30:27,110 --> 00:30:30,210
+نفسه metric برضه هذا هيحقق شروطه ال metric و
+
+420
+00:30:30,210 --> 00:30:34,790
+بنسميه برضه اشماله ال Euclidean metric لإن بعد
+
+421
+00:30:34,790 --> 00:30:39,370
+فترة هتلجوني بقول انت بقولها المعلومة هتلجوني بقول
+
+422
+00:30:39,370 --> 00:30:44,670
+في ال final dimensional spaceFinite vector space
+
+423
+00:30:44,670 --> 00:30:46,870
+هذا لاحق ان شاء الله في الـ finite dimensional
+
+424
+00:30:46,870 --> 00:30:48,970
+space يعني الارض تربيع finite dimension, dimension
+
+425
+00:30:48,970 --> 00:30:52,970
+له اتنين في الارض تكعيب في الارض ارخمس ار مليون ار
+
+426
+00:30:52,970 --> 00:30:55,770
+ان هذوله finite dimensional space هنلاقي ال finite
+
+427
+00:30:55,770 --> 00:31:00,390
+dimensional space لو عرفنا كان متر كثير يعرفنا
+
+428
+00:31:00,390 --> 00:31:04,990
+مليون متركعلى الـ جد ما بدك عرف Matrix إذا عرفت
+
+429
+00:31:04,990 --> 00:31:09,430
+Matrix صار عندك Matrix 2، 3، 4، 5 مليون واحد على
+
+430
+00:31:09,430 --> 00:31:13,890
+Final Dimensional Space كلهم هيولدن نفس الـ
+
+431
+00:31:13,890 --> 00:31:16,610
+Topology يعني هيطلع عندنا نفس الـ Topology عشان هي
+
+432
+00:31:17,240 --> 00:31:21,200
+أحنا في الـ R في الـ R في الـ R أو في الـ R تربيه
+
+433
+00:31:21,200 --> 00:31:25,000
+أفضل تكييب هذا الـ Matrix هذا و الـ Matrix هذا
+
+434
+00:31:25,000 --> 00:31:30,340
+التنين R هنجيهم equivalent يعني هناخدشو معناه
+
+435
+00:31:30,340 --> 00:31:34,420
+equivalent هنجيهم نفس ال .. ال .. ال Matrixوهما
+
+436
+00:31:34,420 --> 00:31:38,680
+اللي بيولد الـ usual topology اللي احنا بنعرفه ال
+
+437
+00:31:38,680 --> 00:31:41,480
+usual topology اللي احنا عايشين فيه في ال calculus
+
+438
+00:31:41,480 --> 00:31:45,620
+وفي المعادلة التفاضلية وفي التحليل الحقيقي واحد و
+
+439
+00:31:45,620 --> 00:31:48,220
+و و الاخر تحليل حقيقي اتنين هذا اللي هو ال
+
+440
+00:31:48,220 --> 00:31:52,300
+Euclidean اللي هي ال usual topologyالـ Limit
+
+441
+00:31:52,300 --> 00:31:54,620
+سبعتنا و الـ Continuity بتبعات كلها على أساسها دي
+
+442
+00:31:54,620 --> 00:31:56,740
+مش هأقولكن في هالشغلها دي ان شاء الله بتيجيها
+
+443
+00:31:56,740 --> 00:32:02,700
+لاحقا في حينها بنوضحها أما ملخص الحديث هي عند
+
+444
+00:32:02,700 --> 00:32:06,220
+metric هذا أسمتنا انه metric وهي ال metric تبع مين
+
+445
+00:32:06,220 --> 00:32:09,900
+اللي بنعرفه احنا و هذا ال metric اللي بنعرفه سهلة
+
+446
+00:32:09,900 --> 00:32:12,800
+و أمه أصلا ال team England quality احنا عارفينها
+
+447
+00:32:12,800 --> 00:32:18,260
+هي نقطة هي نقطين هدي مثلا احدثية Xi واحد و Gamma
+
+448
+00:32:18,260 --> 00:32:24,290
+واحد وهدي اللي هياسكساي واحد وكساي اتنين وهذه
+
+449
+00:32:24,290 --> 00:32:30,210
+جامعة واحد و جامعة اتنين هيها المسافة بين هذول
+
+450
+00:32:30,210 --> 00:32:34,910
+التنتين هيها هي عبارة عن اصغر سواء المسافة بين هذه
+
+451
+00:32:34,910 --> 00:32:40,490
+لو كانت اخدت اي زد تاني هاي زد الان قبل ما ناخد ال
+
+452
+00:32:40,490 --> 00:32:43,230
+training inequality هذه احنا لو جينا حسبناها
+
+453
+00:32:43,230 --> 00:32:48,170
+المسافة حساب المسافة سهلةاللي هي بالسير هذه اللي
+
+454
+00:32:48,170 --> 00:32:55,010
+هو طولها عبارة عن جاء اللي هي xi2 جامعة واحد جامعة
+
+455
+00:32:55,010 --> 00:32:58,870
+واحد ناقص xi واحد على الاكسات هذه وهذه عبارة عن
+
+456
+00:32:58,870 --> 00:33:01,750
+طولها جامعة اتنين ناقص xi اتنين فبكون الجدر
+
+457
+00:33:01,750 --> 00:33:06,180
+التربيعيلهذا اللي هي المسافة اللي هو عبارة عن
+
+458
+00:33:06,180 --> 00:33:08,780
+قانون في The Girth في The Girth هذا التربيع بيساوي
+
+459
+00:33:08,780 --> 00:33:11,640
+هذا التربيع زاد هذا التربيع إذا المسافة بينهم اللي
+
+460
+00:33:11,640 --> 00:33:14,940
+هي المسافة بين هذه وهذه طوله عبارة عن جدر التربيع
+
+461
+00:33:14,940 --> 00:33:18,600
+اللي هذه تربيع زاد هذه تربيع فبكون هذا اللي هو ال
+
+462
+00:33:18,600 --> 00:33:22,060
+Euclidean metric اللي إحنا بنعرفه في الأصل وكل
+
+463
+00:33:22,060 --> 00:33:26,550
+الشروط اللي هي اللي عندنا مطبقةعلى الأرض الكعيب
+
+464
+00:33:26,550 --> 00:33:29,730
+بقدر اعمل اشي متشابه يعني على الأرض الكعيب بقدر
+
+465
+00:33:29,730 --> 00:33:33,570
+اقول والله انا بتاخد الهو X في الأرض الكعيب معناته
+
+466
+00:33:33,570 --> 00:33:37,030
+ايش صارت هذه بدل مهنتين تان صارنمي تلاتة اكساي
+
+467
+00:33:37,030 --> 00:33:40,660
+تلاتةماشي وهد جامعة اتنين وهد بيصير جامعة تلاتة
+
+468
+00:33:40,660 --> 00:33:46,120
+فبيصير المسافة هد زاد هد زاد اللي بتعرفونته xi
+
+469
+00:33:46,120 --> 00:33:51,700
+اللي هي تلاتة ناقص جامعة تلاتة لكل تربية هذا برضه
+
+470
+00:33:51,700 --> 00:33:56,700
+اللي هو metric space بيعمل هد D بيعمل من R تكعيب
+
+471
+00:33:56,700 --> 00:34:02,230
+metric space او R تكعيب مع مين مع ال Dواحد قال لي
+
+472
+00:34:02,230 --> 00:34:05,850
+طب حتى in general يا ربي نبدأ نعمل آه صحيح يعني
+
+473
+00:34:05,850 --> 00:34:11,050
+الان لو كانت RN RN اللي هي عناصرها n couples يعني
+
+474
+00:34:11,050 --> 00:34:15,310
+عناصرها xi واحد xi اتنين عند xi ان مع من مع ال
+
+475
+00:34:15,310 --> 00:34:18,790
+metric هذا برضه هتعمل metric space ال metric في
+
+476
+00:34:18,790 --> 00:34:23,230
+هذا الحالة هتكون dxy ال x ايش هتكون xi واحد xi
+
+477
+00:34:23,230 --> 00:34:26,630
+اتنين xi تلاته عند xi انوالـ Y جامعة واحد جامعة
+
+478
+00:34:26,630 --> 00:34:29,550
+اتنين جامعة تلاتة عين جامعة ان فبكون المسافة بينه
+
+479
+00:34:29,550 --> 00:34:34,530
+عبارة عن الجادر التربيعي ل XI واحد ناقص جامعة واحد
+
+480
+00:34:34,530 --> 00:34:39,210
+لكل تربيع زائد لما أصل لآخر واحدة XI ان ناقص جامعة
+
+481
+00:34:39,210 --> 00:34:42,790
+ان لكل تربيع حد هيعمل metric وحده بسميه اللي هو
+
+482
+00:34:42,790 --> 00:34:49,300
+برضه Euclidean metric اللي هو Dimension of Nنفس
+
+483
+00:34:49,300 --> 00:34:53,680
+الأسلوب بقدر أعرف عالمين على الـ Complex plane
+
+484
+00:34:53,680 --> 00:34:59,220
+اللي و CN يعني بمعنى آخر بده يصير ال X عناصره
+
+485
+00:34:59,220 --> 00:35:03,380
+عبارة عن XI واحد و XI اتنين و XI N عناصره ال X
+
+486
+00:35:03,380 --> 00:35:09,100
+بتساوي XI واحد و XI اتنين لعند XI N وكل واحد كل
+
+487
+00:35:09,100 --> 00:35:12,550
+واحد دولة Complex numbers في الـCففي هذه الحالة
+
+488
+00:35:12,550 --> 00:35:17,390
+بأعرف الـ metric بتعديل بسيط اللي هو dxy بساوي
+
+489
+00:35:17,390 --> 00:35:21,610
+الجدر التربيعي له بكتمش اللي هو هذه تربيعه لأنه
+
+490
+00:35:21,610 --> 00:35:25,350
+بيبقى وقم ا شماله بيبقى اللي هو عبارة عن complex
+
+491
+00:35:25,350 --> 00:35:28,330
+number لما أخده الجدر في الآخر بيطلع complex
+
+492
+00:35:28,330 --> 00:35:31,530
+number يعني بيطلعش عدد العدد لازم يكون مسافة كم
+
+493
+00:35:31,530 --> 00:35:34,430
+ولا سافة سفر فباخد اللي هنا ا شمال هنا absolute
+
+494
+00:35:34,430 --> 00:35:39,250
+valuesفبصير هذا الـ metric هذا الـ metric لما أخد
+
+495
+00:35:39,250 --> 00:35:41,730
+absolute value عن ال magnitude يعني عبارة عن عدد
+
+496
+00:35:41,730 --> 00:35:45,130
+صار هذا تربيع زي هذا تربيع زي هذا الأخر تربيع
+
+497
+00:35:45,130 --> 00:35:49,830
+فبكون هذا dxy اللي هو عبارة عن metric على مين على
+
+498
+00:35:49,830 --> 00:35:56,230
+cn و بحقق كل الشروط هذا اللي هو اللي هي أمثلة على
+
+499
+00:35:56,230 --> 00:36:00,890
+اللي هي على ال R و R تربيع و R تكعيب و RN و C و C
+
+500
+00:36:00,890 --> 00:36:08,830
+و C تربيع و C أُس Nالآن نيجي إلى اللي هو مثالنا
+
+501
+00:36:08,830 --> 00:36:13,330
+المهم اللي هو حاجة اسمها sequence space sequence
+
+502
+00:36:13,330 --> 00:36:18,770
+space جماعة من اسمه هو عبارة عن فراغ عناصر أو
+
+503
+00:36:18,770 --> 00:36:26,830
+مجموعة على سرها اللي هي sequences متتابعات لكن
+
+504
+00:36:26,830 --> 00:36:30,910
+هذه المتتابعات بديها تكون bounded شو اللي بتقوله
+
+505
+00:36:30,910 --> 00:36:31,690
+خليني نشوف
+
+506
+00:36:34,860 --> 00:36:41,660
+المهم اللي هو حاجة اسمها ال infinity ايش ال ال
+
+507
+00:36:41,660 --> 00:36:47,020
+infinity يا جماعة ال ال infinity هي كالتالي
+
+508
+00:36:47,020 --> 00:36:53,220
+انعرفها حاجة اسمها sequence space طيب نشوف ايش ال
+
+509
+00:36:53,220 --> 00:36:58,080
+sequence space هذا المصدر بالرمز مين ال infinity
+
+510
+00:36:58,080 --> 00:37:02,290
+هاي ال ال infinity ال sequence spaceعناصره يعني
+
+511
+00:37:02,290 --> 00:37:05,590
+الـ L infinity هو عبارة عن كل الـ sequences X
+
+512
+00:37:05,590 --> 00:37:09,730
+بتساوي قصاي I قصاي I sequence يعني قصاي 1، قصاي 2،
+
+513
+00:37:09,730 --> 00:37:12,010
+قصاي 3، قصاي 4، لملا نهاية من زمان بتعرفوا اللي هي
+
+514
+00:37:12,010 --> 00:37:18,330
+إيش sequences I من عند 1 لملا نهايةsuch that تكون
+
+515
+00:37:18,330 --> 00:37:20,110
+الـ sequence اللي قال الـ infinity مش كل الـ
+
+516
+00:37:20,110 --> 00:37:23,890
+sequences اللي في الدنيا بدياها بدياها تكون XI I
+
+517
+00:37:23,890 --> 00:37:28,550
+is bounded يعني bounded sequence شو معناه bounded
+
+518
+00:37:28,550 --> 00:37:33,740
+sequence؟ يعني في النهاية XI Iاللي هو there exists
+
+519
+00:37:33,740 --> 00:37:38,280
+C element in R such that Xi I أصغر أو يساوي هذا
+
+520
+00:37:38,280 --> 00:37:44,380
+الـ C لكل I بتساوي واحد واتنين أمنة يعني في
+
+521
+00:37:44,380 --> 00:37:48,160
+النهاية العناصر تبعات الـ sequences لن تتجاوز حد
+
+522
+00:37:48,160 --> 00:37:52,520
+معينطبعا هذه الـ C لمن؟ للـ sequence هذه الـ
+
+523
+00:37:52,520 --> 00:37:56,440
+sequence هذه لو سمناها X بتساوي XI I منقول عنها
+
+524
+00:37:56,440 --> 00:38:00,180
+bounded إذا كان فيه إلها C عشان هيك بنقوله CX نرمز
+
+525
+00:38:00,180 --> 00:38:03,360
+الـ X لإنه C هدي لمن؟ لـ X لو كان فيه sequence
+
+526
+00:38:03,360 --> 00:38:08,040
+ثانية بتكون لها X C تانية فاهمين؟اللي أنا أصغر شوه
+
+527
+00:38:08,040 --> 00:38:14,460
+مين CX يعني لو كان في عندي Y بسووه Gamma I وموجودة
+
+528
+00:38:14,460 --> 00:38:17,460
+في الـ Infinity، هتكون bounded هتكون bounded، إيش
+
+529
+00:38:17,460 --> 00:38:20,780
+معناه bounded؟ إنه there exists C ت .. الـ C إيش
+
+530
+00:38:20,780 --> 00:38:24,920
+معناها؟ إنها للـ Y، عشان هيك بيسميها Cy ثابت طبعا
+
+531
+00:38:24,920 --> 00:38:28,520
+such that اللي هو Gamma I أصغر أو سوى الـ C اللي
+
+532
+00:38:28,520 --> 00:38:32,810
+لاجيناه هذه الـ sequence ده Y لكل مين Iمثلًا
+
+533
+00:38:32,810 --> 00:38:37,110
+أعطيكم مثال يعني عشان تشوفوا مين ممكن نقعد هان لو
+
+534
+00:38:37,110 --> 00:38:41,410
+جينا أخذنا ال sequence واحد و نص و تلت و ربع اللي
+
+535
+00:38:41,410 --> 00:38:44,390
+هي ال sequence واحد على أن بمعنى آخر واضح إن ال
+
+536
+00:38:44,390 --> 00:38:49,640
+sequence هذه أشمالها is boundedالـ Terms تبعتها لا
+
+537
+00:38:49,640 --> 00:38:52,840
+يمكن أن تتجاوز الواحد يعني الـ bound لها إيش واحد
+
+538
+00:38:52,840 --> 00:38:56,320
+يعني هنا في هذه الحالة جامع I لو سمناها جامع I هذه
+
+539
+00:38:56,320 --> 00:39:00,320
+أصغر أو شاومين واحد لكل I فهذه ال sequence أكيد
+
+540
+00:39:00,320 --> 00:39:05,360
+موجودة وين في ال infinity بينما لو أجيته لل
+
+541
+00:39:05,360 --> 00:39:11,580
+sequence التالية اللي هو 1 و 2 و 3 و 4أو un in
+
+542
+00:39:11,580 --> 00:39:14,260
+general هذه الـ sequence غير موجودة في الـ L
+
+543
+00:39:14,260 --> 00:39:16,900
+infinity لأنها is not bounded لأنها عمالها بتروح
+
+544
+00:39:16,900 --> 00:39:20,300
+إلى مقل النهائية قاعدة ففيش عدد أكبر من كل عناصر
+
+545
+00:39:20,300 --> 00:39:22,780
+الـ sequence إذا نضحت شو معناته اللي هي ال
+
+546
+00:39:22,780 --> 00:39:26,380
+infinity الست هذه أن عناصرها عبارة عن bounded
+
+547
+00:39:26,380 --> 00:39:30,660
+sequences طيب ليش انت بتأمل هيك يعني انت بتبني ال
+
+548
+00:39:30,660 --> 00:39:33,400
+L infinity عشان بعد شوية أنا بدي أعرّفلكم metric
+
+549
+00:39:34,280 --> 00:39:37,940
+الـ Metric اللي بتعرف الكمياء عشان يكون موجود لازم
+
+550
+00:39:37,940 --> 00:39:41,180
+تكون ال sequences bounded لازم مدان bounded يعني
+
+551
+00:39:41,180 --> 00:39:45,040
+انت شكلك بتحكي عن supremum و infimum اه بتعرف ال
+
+552
+00:39:45,040 --> 00:39:47,940
+metric عن طريق ال supremum و ال infimum او بالظبط
+
+553
+00:39:47,940 --> 00:39:53,360
+عن طريق ال supremum عشان اللي هو أضمن ال supremum
+
+554
+00:39:53,360 --> 00:39:56,340
+موجود لازم تكون اللي هي اللي هي اللي بتاخده لها ال
+
+555
+00:39:56,340 --> 00:40:01,170
+supremum تكون bounded عشان هيكالان نرتب امورنا
+
+556
+00:40:01,170 --> 00:40:05,230
+ونقول
+
+557
+00:40:05,230 --> 00:40:10,770
+التالي هذه مبررات اللي حكيتها اللي بدها تخليني
+
+558
+00:40:10,770 --> 00:40:12,530
+اعرف metric D
+
+559
+00:40:17,040 --> 00:40:20,280
+ايش الـ metric اللي بدى أعرفه عليه اللي هو لو أخدت
+
+560
+00:40:20,280 --> 00:40:25,300
+الآن I X بيساوي X I I sequence و Y بيساوي Gamma I
+
+561
+00:40:25,300 --> 00:40:27,820
+sequence وين موجودة التنتين في القلة الانفينيتي
+
+562
+00:40:27,820 --> 00:40:33,240
+يعني bounded بدى أعرف اللي هو ال metric بين X و Y
+
+563
+00:40:33,240 --> 00:40:36,460
+لل sequences هدول اللي في القلة الانفينيتي بيساوي
+
+564
+00:40:36,460 --> 00:40:42,220
+super amount ل X I I ناقص Gamma I over mean over I
+
+565
+00:40:42,400 --> 00:40:47,360
+سيبرون المضمون يوجد آه لإن XI I bounded و Gamma I
+
+566
+00:40:47,360 --> 00:40:51,080
+bounded إذا هذا أبعاد bounded ليش؟ لإن بيصير XI I
+
+567
+00:40:51,080 --> 00:40:56,080
+ناقص Gamma I أصغر أوي ساوي XI I أعداد هذه الأعداد
+
+568
+00:40:56,080 --> 00:41:00,050
+دا جماعة زائد Gamma Iوهذه الـ bounded sequence
+
+569
+00:41:00,050 --> 00:41:04,890
+بالـ CX تبعتها وهذه الـ bounded بالـ CY تبعتها إذا
+
+570
+00:41:04,890 --> 00:41:08,830
+في النهاية كل ال terms هذولة bounded by اللي هو
+
+571
+00:41:08,830 --> 00:41:12,590
+العدد اللي هو المجموح هذولة التنتين يعني صارت هذه
+
+572
+00:41:12,590 --> 00:41:15,950
+bounded مادام bounded إذا مضمون من الـ supermoment
+
+573
+00:41:15,950 --> 00:41:21,590
+أشماله موجود الآن إذا هذا هو الـ defined فعلا الآن
+
+574
+00:41:21,590 --> 00:41:26,170
+الشرط الأول إنه metricالان هذا أكبر أساوي 0 إذا
+
+575
+00:41:26,170 --> 00:41:31,870
+الـ Supremum يشماله أكبر أساوي 0 إذا الـ Dxy أكبر
+
+576
+00:41:31,870 --> 00:41:37,410
+أساوي 0 اتنين Dxy بساوي 0 .. قاعد ببره أن أنا
+
+577
+00:41:37,410 --> 00:41:42,850
+انمترك .. انمترك هذا Dxy بساوي 0 if and only if ال
+
+578
+00:41:42,850 --> 00:41:46,050
+Supremum .. هي .. هي .. هي .. هي .. Supremum لـ Xi
+
+579
+00:41:46,050 --> 00:41:51,230
+I ناجس Gamma I over I بساوي 0إذا الـ supremum اللي
+
+580
+00:41:51,230 --> 00:41:55,990
+هين سفر قطعاً قطعاً قطعاً كلهين سفاري لإن لو ال
+
+581
+00:41:55,990 --> 00:41:59,030
+supremum .. لو .. لو واحدة فيه مش سفر معناته ال
+
+582
+00:41:59,030 --> 00:42:01,470
+supremum مش سفر هيكون هذا اللي .. اللي .. اللي هو
+
+583
+00:42:01,470 --> 00:42:07,610
+مش سفر إذا if and only if xi i ناجس gamma i بتساوي
+
+584
+00:42:07,610 --> 00:42:13,100
+سفر لكل iماشي معناته هذا ايش معناته ان هذا سفر
+
+585
+00:42:13,100 --> 00:42:18,080
+معناته xi I بسوء جامع I لكل I معناته ايش معناته xi
+
+586
+00:42:18,080 --> 00:42:21,980
+I بسوء جامع I يعني كل عناصر اللي هو ال sequence xi
+
+587
+00:42:21,980 --> 00:42:23,900
+واحد بسوء جامع واحد بسوء جامع اتنين بسوء جامع
+
+588
+00:42:23,900 --> 00:42:26,700
+اتنين يعني ال sequences بتسوء اتنين يعني if and
+
+589
+00:42:26,700 --> 00:42:32,020
+only if x بتسوء y وهذا الشرط الثالث تحقق نيجي
+
+590
+00:42:32,020 --> 00:42:36,940
+للشرط من الثالث الشرط الثالث ده من سهل هنا دي x و
+
+591
+00:42:36,940 --> 00:42:40,610
+yاللي هو عبارة عن الـ supermoment Xi I نقص Gamma I
+
+592
+00:42:40,610 --> 00:42:43,550
+طب ما هي Xi I نقص Gamma I absolute value و هي
+
+593
+00:42:43,550 --> 00:42:46,770
+نفسها absolute value Gamma I نقص Xi I و من ثم ال
+
+594
+00:42:46,770 --> 00:42:51,210
+supermoment بحثة صح و من ثم بيساوي Dxy بساوي Dy Ox
+
+595
+00:42:51,210 --> 00:42:56,390
+إذن هذا متحقق automatic نيجي الآن لشرط ثالث و شرط
+
+596
+00:42:56,390 --> 00:42:59,970
+ثالث انتبهولي عليه مش صعب بس يعني ان شاء الله
+
+597
+00:42:59,970 --> 00:43:01,410
+بوضحكوا معاه تماما و انتوا فاهمون
+
+598
+00:43:04,170 --> 00:43:07,770
+اللي هو يا جماعة الـ Triangle Inqualite الـ
+
+599
+00:43:07,770 --> 00:43:12,470
+Triangle Inqualite نشوف
+
+600
+00:43:12,470 --> 00:43:16,810
+معلش
+
+601
+00:43:16,810 --> 00:43:21,270
+مساحة الـ Metric هي مكتوبة أنا مابهمش طيب الآن
+
+602
+00:43:21,270 --> 00:43:24,030
+بتاخد عشان اثبت ال Triangle Inqualite انتوا
+
+603
+00:43:24,030 --> 00:43:29,810
+المفروض احفظوها بتاخد أي Xسيكوانس بيساوي Xi I
+
+604
+00:43:29,810 --> 00:43:34,950
+وسيكوانس Y بيساوي Gamma I وسيكوانس Delta Z بيساوي
+
+605
+00:43:34,950 --> 00:43:43,070
+Alpha Iالان يا جماعة انتبهولي لشغلها لأن لكل I في
+
+606
+00:43:43,070 --> 00:43:47,990
+الدنيا لو جيت أخدت XI I ناقص Gamma I ماشي الحال
+
+607
+00:43:47,990 --> 00:43:52,230
+هدولة تبعات مين X و Y أكيد أصغرها يساوي بال
+
+608
+00:43:52,230 --> 00:43:58,390
+triangle inequality هذا الكلام for any fixed I
+
+609
+00:43:58,390 --> 00:44:03,400
+ماشيI arbitrary لكن fixed بحكي عن واحدة بعيّنة لكن
+
+610
+00:44:03,400 --> 00:44:08,200
+arbitrary شيلته arbitrary منه أصغر أو ساوي Xi I
+
+611
+00:44:08,200 --> 00:44:11,940
+ناقص Alpha I بدخل هذه الحر أنا triangling quality
+
+612
+00:44:11,940 --> 00:44:18,360
+زي Alpha I ناقص Gamma I بدخل ما يخدمني طيب الآن
+
+613
+00:44:18,360 --> 00:44:21,460
+هذا
+
+614
+00:44:21,460 --> 00:44:26,200
+الكلام صحيح لكل I في الدنيا إذا أكيد أكيد أكيد هذه
+
+615
+00:44:27,380 --> 00:44:31,280
+أصغر أو يساوي سبريمانها اكس اي انا ناجسها معايا
+
+616
+00:44:31,280 --> 00:44:36,160
+ناجس الفايا over I ليش؟ لأن السبريمان أكبر أوي
+
+617
+00:44:36,160 --> 00:44:38,880
+ساوي أكيد اللي هو واحدة اللي ماخود عليها السبريمان
+
+618
+00:44:38,880 --> 00:44:44,790
+ماشي أو هذهبرضه أصغر أو يساوي الـ Supremum تبعها
+
+619
+00:44:44,790 --> 00:44:48,890
+Supremum Alpha I ناجز Gamma I إذا صار عندي Over I
+
+620
+00:44:48,890 --> 00:44:52,910
+إذا صار عندي هذا أكبر أو يساوي هذا و هذا أكبر أو
+
+621
+00:44:52,910 --> 00:44:55,610
+يساوي هذا مجموح أن أكبر أو يساوي هذا الكلام سهل
+
+622
+00:44:55,610 --> 00:45:01,750
+هذه مين هي يا جماعة هذه اللي هي بالظبط D X و Z هذه
+
+623
+00:45:01,750 --> 00:45:07,040
+تبعات ال X هيهم و هذه تبعات مين ال Zزائد هذي مين
+
+624
+00:45:07,040 --> 00:45:12,100
+يا جماعة دي هذي ال alpha I تبع ال Z دي Z وال gamma
+
+625
+00:45:12,100 --> 00:45:17,020
+I تبع ات مين ال Y دي Z أو Y إذا صار عندي لكل fixed
+
+626
+00:45:17,020 --> 00:45:22,060
+I هذا المقدار أصغر أو يساوي هذا المقدار طبعا هذا
+
+627
+00:45:22,060 --> 00:45:26,920
+المقدار عدن عن عددعدد عدد عدد إذا صار عندك xi I
+
+628
+00:45:26,920 --> 00:45:34,400
+ناجس جامع I لكل I في الدنيا أظهر أو يساوي ال D X و
+
+629
+00:45:34,400 --> 00:45:39,660
+Z زائد ال D Z و Y و زي ما قلت لكم هذا عدد صار هذا
+
+630
+00:45:39,660 --> 00:45:45,900
+عبارة عن upper bound للمجموعة المتكونة من xi واحد
+
+631
+00:45:45,900 --> 00:45:50,400
+ناجس جامع واحد و xi اتنين ناجس جامع اتنين إلى مالا
+
+632
+00:45:50,400 --> 00:45:54,150
+نهاية إذا صار هذا upper bound لها بالستما دام هو
+
+633
+00:45:54,150 --> 00:45:59,590
+other bound إذا هو أكبر أو يساوي ال least other
+
+634
+00:45:59,590 --> 00:46:04,790
+bound لهم يا بمعنى أخر صار هذا أكبر أو يساوي ال
+
+635
+00:46:04,790 --> 00:46:08,130
+supremum لهم لأن ال supremum هو ال least other
+
+636
+00:46:08,130 --> 00:46:13,990
+bound إذا هذا اللي هو أصلا إيش اسمه اللي سمناه
+
+637
+00:46:13,990 --> 00:46:15,750
+عبارة عن DX
+
+638
+00:46:18,090 --> 00:46:21,910
+ومين؟ OY إذا صار عندي DX وY أصغر سوى DX وZ زي
+
+639
+00:46:21,910 --> 00:46:27,270
+الـDZ OY إذا هي كما نكون أثبتنا هذا برضه عبارة عن
+
+640
+00:46:27,270 --> 00:46:31,950
+إيش عبارة عن metric إذا صار عندي اللي هو اللي
+
+641
+00:46:31,950 --> 00:46:35,970
+أمامنا يا جماعة اللي هو ال ال infinity مع هذا ال
+
+642
+00:46:35,970 --> 00:46:40,550
+metric دي على هذا الأساس التعريف عبارة عن metric
+
+643
+00:46:40,550 --> 00:46:45,870
+spaceاللي هو الـ L infinity تبعنا وهذا من الأمثلة
+
+644
+00:46:45,870 --> 00:46:52,730
+المهمة والملازمة معنا على طول الفصل طيب برضه space
+
+645
+00:46:52,730 --> 00:46:58,330
+آخر مهم اللي هو space تبعنا تبع زمان عناصره اللي
+
+646
+00:46:58,330 --> 00:47:03,130
+هو the space of continuous functions on a closed
+
+647
+00:47:03,130 --> 00:47:09,890
+bounded interval نشوف إيش بقوله هذا طبعا معلوماته
+
+648
+00:47:09,890 --> 00:47:14,140
+من ال calculusبتيجي انا دايما بحكيها في القصة دي
+
+649
+00:47:14,140 --> 00:47:17,940
+اللي هي المعلومات حول اللي هو الدول المتصلة على
+
+650
+00:47:17,940 --> 00:47:21,880
+closed bounded interval ايش اللي بقوله اللي بقوله
+
+651
+00:47:21,880 --> 00:47:26,710
+صلى الله عليه وسلمبدي أخد اللي هو مجموع اسمها C A
+
+652
+00:47:26,710 --> 00:47:30,810
+وB بدرمزلها هذه C اللي هي continuous والـ A وB هي
+
+653
+00:47:30,810 --> 00:47:32,670
+الـ closed bounded interval اللي عليها بدعرف
+
+654
+00:47:32,670 --> 00:47:37,270
+الدالة هي عبارة عن كل الدوال X ده سبيها X الدالة
+
+655
+00:47:37,270 --> 00:47:42,190
+اللي ماخدة من A وB وبتود في R يعني real valued
+
+656
+00:47:42,190 --> 00:47:47,140
+functionthe set of all real valued functions on a
+
+657
+00:47:47,140 --> 00:47:51,420
+closed bounded interval which are continuous such
+
+658
+00:47:51,420 --> 00:47:57,880
+that X is continuous إذا هذا الفراغ هو عبارة عن
+
+659
+00:47:57,880 --> 00:48:03,080
+الفراغ المتكون من جميع الديال المتصلة الحقيقية
+
+660
+00:48:03,080 --> 00:48:08,960
+طبعا على الفترة A O B الآن مدامة X متصلة على
+
+661
+00:48:08,960 --> 00:48:13,520
+الفترة A O B كنا نحكي إعلان في الcalculus ونقولإذا
+
+662
+00:48:13,520 --> 00:48:20,280
+كانت المشكلة مستمرة في مقارنة مغلقة فهي تصل إلى
+
+663
+00:48:20,280 --> 00:48:24,300
+مقارنة أعلى ومقارنة أعلى في هذه المقارنة وهذا
+
+664
+00:48:24,300 --> 00:48:28,940
+الكلام بيحكي .. بيحكي .. بيحكيكميا تشريع لكيف نود
+
+665
+00:48:28,940 --> 00:48:31,640
+الabsolute وضمان وجود ال absolute maximum
+
+666
+00:48:31,640 --> 00:48:34,920
+وabsolute minimum على الدالة المتصلة على مقارنة
+
+667
+00:48:34,920 --> 00:48:40,220
+مغلقة حتى في الثانويةفهذه معلومة سابقة إذا ما دامت
+
+668
+00:48:40,220 --> 00:48:42,920
+الدالة متصلة على closed bounded interval إذا ال
+
+669
+00:48:42,920 --> 00:48:46,240
+maximum و ال minimum لها إيه شماله مضمون إنه موجود
+
+670
+00:48:46,240 --> 00:48:50,000
+طب ليش بتحكي هيك عشان بدي أعرف الآن ال metric على
+
+671
+00:48:50,000 --> 00:48:52,720
+أساسي على هذا الأساس يعني بدي أعرف ال metric
+
+672
+00:48:52,720 --> 00:48:56,340
+بواسطة ال maximum قبل بشوية ال infinity حكينا عنه
+
+673
+00:48:56,340 --> 00:49:01,300
+ال supremumهنا على غراره و البرهان نفس البرهان
+
+674
+00:49:01,300 --> 00:49:04,660
+اللي هو على غرار البرهان الأولاني هنا هناك كان ال
+
+675
+00:49:04,660 --> 00:49:07,980
+sequences وهنا للدول هنا كان ال bounded sequences
+
+676
+00:49:07,980 --> 00:49:11,060
+وهنا إشماله للدول المتصلة على closed bounded
+
+677
+00:49:11,060 --> 00:49:16,000
+intervalسألنا بالـ Function specific of A و B دعوا
+
+678
+00:49:16,000 --> 00:49:17,580
+C و A و B يكونوا مجموعة من جميع الاصطناعات
+
+679
+00:49:17,580 --> 00:49:21,360
+الواقعية التي مستمرة في الـ closed bounded
+
+680
+00:49:21,360 --> 00:49:24,800
+interval إذا لكل X و Y في C و A و B أريد أن أعرف
+
+681
+00:49:24,800 --> 00:49:31,340
+الـ D X Y الـ D X Y للإكسات و الوايات الموجودة في
+
+682
+00:49:31,340 --> 00:49:35,910
+C و B يعني الدوال المتصلة X و Y هي عبارة عنالـ
+
+683
+00:49:35,910 --> 00:49:40,870
+Maximum لأ X of T X of T الـ T المتغير اللي في الـ
+
+684
+00:49:40,870 --> 00:49:44,910
+A و الـ B ناقص الـ Y of T و الـ T طبعا اللي موجودة
+
+685
+00:49:44,910 --> 00:49:48,550
+على الفترة A و B يعني اللي هو بدّي المسافة بين X و
+
+686
+00:49:48,550 --> 00:49:52,290
+Y هي عبارة عن الـ Maximumاللي هو بين .. اللي هو
+
+687
+00:49:52,290 --> 00:49:56,670
+البعد بين كل point و التانية عند X و T نقص Y و T
+
+688
+00:49:56,670 --> 00:50:00,170
+لأن هل ال maximum موجودة؟ أه طبعاً، ليش؟ لأن X
+
+689
+00:50:00,170 --> 00:50:03,610
+متصل و Y متصل، إذا حصل طرح المتصل إذا حصل طرح
+
+690
+00:50:03,610 --> 00:50:06,970
+المتصل، إذا صار من التمتين متصلات أو هذه كلها على
+
+691
+00:50:06,970 --> 00:50:09,590
+بعض is a continuous function on a closed bounded
+
+692
+00:50:09,590 --> 00:50:12,510
+interval إذا لازم يكون لها maximum و minimum ..
+
+693
+00:50:12,510 --> 00:50:16,050
+إذا ال maximum و ال minimum مضموناتوجودهم في
+
+694
+00:50:16,050 --> 00:50:20,830
+الفترة a و b إذا عندي اللي هو التعريف و ال defined
+
+695
+00:50:20,830 --> 00:50:25,570
+مافيش مشاكل في التعريف البرهان .. البرهان سهل إنه
+
+696
+00:50:25,570 --> 00:50:29,230
+مترك واحد هذا absolute value إذا أكبر أو ساوية سفر
+
+697
+00:50:29,230 --> 00:50:31,450
+إذا ال maximum ما هي شماله أكبر أو ساوية سفر إذا
+
+698
+00:50:31,450 --> 00:50:35,370
+دي اكس واي automatic أكبر أو ساوية سفر شاطر أول
+
+699
+00:50:35,370 --> 00:50:40,050
+متحقق سريع لإنه هذا نفس البرهان اللي قبله اتنين لو
+
+700
+00:50:40,050 --> 00:50:46,030
+الان دي اكس واي بساوية سفرفاندول F الماكسمن بيساوي
+
+701
+00:50:46,030 --> 00:50:49,410
+صفر الماكسمن بيساوي صفر لأن كل واحدة من هدولة صفر
+
+702
+00:50:49,410 --> 00:50:51,870
+لأنها absolute value لأن كل واحدة من هدولة صفر
+
+703
+00:50:51,870 --> 00:50:51,990
+لأنها absolute value لأن كل واحدة من هدولة صفر
+
+704
+00:50:51,990 --> 00:50:52,490
+لأنها absolute value لأن كل واحدة من هدولة صفر
+
+705
+00:50:52,490 --> 00:50:53,090
+لإنها absolute value لإنها absolute value لإنها
+
+706
+00:50:53,090 --> 00:50:54,310
+absolute value لإنها absolute value لإنها absolute
+
+707
+00:50:54,310 --> 00:50:54,670
+value لإنها absolute value لإنها absolute value
+
+708
+00:50:54,670 --> 00:50:56,150
+لإنها absolute value لإنها absolute value لإنها
+
+709
+00:50:56,150 --> 00:50:56,310
+absolute value لإنها absolute value لإنها absolute
+
+710
+00:50:56,310 --> 00:50:56,350
+value لإنها absolute value لإنها absolute value
+
+711
+00:50:56,350 --> 00:50:58,310
+لإنها absolute value لإنها absolute value لإنها
+
+712
+00:50:58,310 --> 00:51:03,240
+absolute value لناقص y of t بتساوي سفر لكل t في
+
+713
+00:51:03,240 --> 00:51:09,260
+الفترة a وb وهذا معناته أن x of t هي نفسها y of t
+
+714
+00:51:09,260 --> 00:51:12,540
+الـ delta نفس ال .. نفس الاشي لكل t في domain هن
+
+715
+00:51:12,540 --> 00:51:17,560
+يعني بمعنى أخر اللي هو delta n x بتساوي y وهو
+
+716
+00:51:17,560 --> 00:51:21,520
+المطلوب الشرط الثالث الشرط السهل هذا اللي بنقول
+
+717
+00:51:21,520 --> 00:51:27,970
+عنه dxy بساوي dy وx لإنهDxy هو الماكسيمة x of t
+
+718
+00:51:27,970 --> 00:51:30,650
+نقص y of t absolute value ال absolute value x of t
+
+719
+00:51:30,650 --> 00:51:33,270
+و y of t هو نفس ال absolute value y of t نقص x of
+
+720
+00:51:33,270 --> 00:51:36,830
+t إذا الماكسيمة عاملة تلتين زي بعض إذا Dxy بيساوي
+
+721
+00:51:36,830 --> 00:51:40,610
+Dy و X نجي للشرط الثالث الأخير و الشرط الثالث
+
+722
+00:51:40,610 --> 00:51:45,890
+الأخير برضه زي مين زي الشرط الثالث اللي في المثال
+
+723
+00:51:45,890 --> 00:51:56,620
+اللي دبلو الان خدوا any T any T limiting a و bx of
+
+724
+00:51:56,620 --> 00:52:01,060
+t نقص y of t أخد دالة تالتة arbitrarily present في
+
+725
+00:52:01,060 --> 00:52:04,320
+ال continuous أكيد absolute value انهم أصغر أو
+
+726
+00:52:04,320 --> 00:52:12,560
+ساول absolute value of x of t نقص z of t زائد زائد
+
+727
+00:52:12,560 --> 00:52:19,160
+اللي هو absolute value of z of t-Y of T هذا الكلام
+
+728
+00:52:19,160 --> 00:52:21,960
+لكل T لأن هذا الكلام Absolute Value Triangle
+
+729
+00:52:21,960 --> 00:52:24,640
+Inquality تبعت زمان لأن هذا أعداد X of T قيمت
+
+730
+00:52:24,640 --> 00:52:28,560
+عددها وY of T قيمت عددها وZ of T قيمت عددها إذا
+
+731
+00:52:28,560 --> 00:52:32,260
+هذه Triangle Inquality أشمالها صحيحة دائما وزي ما
+
+732
+00:52:32,260 --> 00:52:37,580
+عملنا قبل شوية أصغر أو ساوي هذه اللي هي نفسها أصغر
+
+733
+00:52:37,580 --> 00:52:45,320
+أو ساوي ال maximum تبعتها X of T-Z of Tوهذه أصغر
+
+734
+00:52:45,320 --> 00:52:50,920
+في شوية maximum تبعدها Z of T ماقص Y of T وهذه
+
+735
+00:52:50,920 --> 00:52:58,960
+عبارة عن DXYDX و Z أسف وهذه تانية DZY وهذه صار عدد
+
+736
+00:52:58,960 --> 00:53:03,760
+أكبر أساوي هذوله لكل T هذه أكبر أساوي X of T نقص Y
+
+737
+00:53:03,760 --> 00:53:06,800
+of T لكل T هنا إذن أكيد أكبر أساوي مين ال maximum
+
+738
+00:53:06,800 --> 00:53:09,560
+لإن ال maximum واحدة منهن لإن احنا بنقول ال tens
+
+739
+00:53:09,560 --> 00:53:14,360
+is maximum وين فيها إذن واحدة منهن إذن DX وZY أكبر
+
+740
+00:53:14,360 --> 00:53:19,200
+أو ساوي ال maximum هذه اللي هو عبارة عن DXY وهو
+
+741
+00:53:19,200 --> 00:53:22,130
+المطلوبإذاً صار اللي هو هنا الـD برضه إيش ماله
+
+742
+00:53:22,130 --> 00:53:27,730
+عبارة عن metric space ماشي يا بنات صلوا عنا بيهم
+
+743
+00:53:27,730 --> 00:53:34,510
+عليه الصلاة والسلام الآن المثال الأخير اللي هو
+
+744
+00:53:34,510 --> 00:53:39,050
+حاجة اسمها بنسميه discrete metric space discrete
+
+745
+00:53:39,050 --> 00:53:44,570
+metric space discrete metric space هو اللي بولد ال
+
+746
+00:53:44,570 --> 00:53:48,830
+discrete topologyإن شاء الله بنجيه في حينه ال
+
+747
+00:53:48,830 --> 00:53:54,910
+discrete metric space بناخد 6x أي 6x و بعرف عليها
+
+748
+00:53:54,910 --> 00:53:58,870
+D إيش ال D اللي بدي أعرفها اللي بدي أسميه metric
+
+749
+00:53:58,870 --> 00:54:02,090
+الآن هذا ال D هسميه metric آسف هسميه اللي هو
+
+750
+00:54:02,090 --> 00:54:06,670
+discrete ال D هعرفها لأي نقطين في ال X المسافة
+
+751
+00:54:06,670 --> 00:54:12,260
+بينهم هسميهم يا صفر يا واحدهذا هي المتريك اللي
+
+752
+00:54:12,260 --> 00:54:13,940
+اريد ان اعرفه انا او هذا الديالة اللي اريد ان
+
+753
+00:54:13,940 --> 00:54:19,400
+اعرفها Dxy بتساوي سفر إذا كانت X بتساوي Y و بتساوي
+
+754
+00:54:19,400 --> 00:54:23,580
+واحد إذا كانت X أشمالها لاتساوي Y هاي كل قصتنا إذا
+
+755
+00:54:23,580 --> 00:54:28,420
+المتريك اللي بندعي انه متريك إنه قمتين يا سفر في
+
+756
+00:54:28,420 --> 00:54:32,440
+حالة المساوية يا واحد في حالة عدم المساوية إذا X
+
+757
+00:54:32,440 --> 00:54:38,260
+وD هيعملني metric space اثبت اثبات سهل أول حاجة
+
+758
+00:54:39,780 --> 00:54:45,100
+واضح ان Dxy أكبر و ساوي سفر Dxy أكبر و ساوي سفر
+
+759
+00:54:45,100 --> 00:54:47,340
+لأن قيمته يا سفر يا واحد إذا ما أكبر و ساوي سفر
+
+760
+00:54:47,340 --> 00:54:52,140
+اتنين ال Dxy
+
+761
+00:54:52,140 --> 00:55:01,870
+بساوي سفر إذا و فقط إذا ال X متساوي و متتعريفلأن
+
+762
+00:55:01,870 --> 00:55:05,150
+لو كانت X Y بيساوي 0 أكيد X بيساوي Y ولو كانت X
+
+763
+00:55:05,150 --> 00:55:09,650
+بيساوي Y أكيد X بيساوي 0، بيساوي 0، بيساوي 0،
+
+764
+00:55:09,650 --> 00:55:09,690
+بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0،
+
+765
+00:55:09,690 --> 00:55:10,650
+بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0،
+
+766
+00:55:10,650 --> 00:55:11,570
+بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0،
+
+767
+00:55:11,570 --> 00:55:19,670
+بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0،
+
+768
+00:55:19,670 --> 00:55:28,100
+بيساوي 0، بيساوي 0، بيساوي 0، بيساللي هو إننا نثبت
+
+769
+00:55:28,100 --> 00:55:30,300
+الـ Triangle Inquality انتبه على ال Triangle
+
+770
+00:55:30,300 --> 00:55:33,220
+Inquality ال Triangle Inquality مش غلبتها كتير
+
+771
+00:55:33,220 --> 00:55:36,300
+بسيطة يعني ان شاء الله ده بيكتمك و نخلصناها عيندي
+
+772
+00:55:36,300 --> 00:55:41,660
+بتاخد الآن أي X و أي Y و أي Z وين موجودات في ال X
+
+773
+00:55:41,660 --> 00:55:50,340
+هدولة اللي هين حالتين الحالة الأولى X بتساوي Y
+
+774
+00:55:50,340 --> 00:55:58,260
+الحالة التانية Xلا تساوي y في غيرها بالنسبالي ال X
+
+775
+00:55:58,260 --> 00:56:02,760
+و ال Y لأ احتمالات ال X و ال Y لبعض هذه بتساوي هذه
+
+776
+00:56:02,760 --> 00:56:09,260
+او هذه بتساوي هذه لو X بتساوي Y فبتصير ال D X و Y
+
+777
+00:56:09,260 --> 00:56:14,500
+بتساوي صفر لأن اي ان كانت ال Z بتساويهم ولا
+
+778
+00:56:14,500 --> 00:56:18,260
+بتساويهم مش فارقة كتير ليش لأنه هتكون هذه اكيد
+
+779
+00:56:18,260 --> 00:56:25,280
+اصغر او ساوي D X و Zزائد D Z و Y لأن هذولا قيمهم
+
+780
+00:56:25,280 --> 00:56:30,260
+يا سفر يا واحد إذا مستحيل هذه تكون أكبر منهم لأنه
+
+781
+00:56:30,260 --> 00:56:33,800
+مجموح أنه يكون يا سفر يا واحد يا اتنين حسب
+
+782
+00:56:33,800 --> 00:56:38,500
+العلاقات اللي موجودة هنا ماشي الحال طيب إذا صار
+
+783
+00:56:38,500 --> 00:56:42,480
+عندي الآن الحالة الأولى متحققة ده الحالة التانية X
+
+784
+00:56:42,480 --> 00:56:46,680
+لات سوى Y X لات سوى Y في عندي في حالة .. لان بدأت
+
+785
+00:56:46,680 --> 00:56:50,920
+أجيب I Zبتدافع تاني DX وY أزرع تاني DX وZ زي دي Z
+
+786
+00:56:50,920 --> 00:56:54,960
+وY في هذه الحالة عندي تلت حالات في داخل الحالة هذه
+
+787
+00:56:54,960 --> 00:57:01,340
+يما التنتين هدولة باختلف عن الـ Z يعني لا ال X
+
+788
+00:57:01,340 --> 00:57:07,420
+بتساوي Yو طبعا هي المفروض لا ال X بتساوي Z ولا ال
+
+789
+00:57:07,420 --> 00:57:11,200
+Y بتساوي Z يعني ولا واحدة منهم التلاتة مختلفات
+
+790
+00:57:11,200 --> 00:57:16,160
+الحالة الأولى الحالة التانية ان هدول مختلفات صح بس
+
+791
+00:57:16,160 --> 00:57:19,740
+ال Z بتساوي واحدة منهم إذا الحالة الأولى ان
+
+792
+00:57:19,740 --> 00:57:22,940
+المختلفات و ال Z مختلفة عنها التلتين الحالة
+
+793
+00:57:22,940 --> 00:57:27,580
+التانية ان ال Z بتساوي واحدة منهمإذا الحالتين، يا
+
+794
+00:57:27,580 --> 00:57:31,140
+الـ z بتسويش ولا واحدة منهن، يا واحدة منهن، الان
+
+795
+00:57:31,140 --> 00:57:34,980
+ولا واحدة منهن أيها، الحالة التانية إنها بتساوي
+
+796
+00:57:34,980 --> 00:57:40,480
+واحدة منهم، يعني z بتساوي x و z لا تساوي y أو z
+
+797
+00:57:40,480 --> 00:57:46,320
+بتساوي y و z لا تساوي x، يعني الحالة التانية هذه،
+
+798
+00:57:46,320 --> 00:57:51,750
+اللي هو بتساوي واحدة من هدول،مستحيل تسوي أن تتمثل
+
+799
+00:57:51,750 --> 00:57:54,730
+مع بعض لأن هنا تحت عدوان إيه شمال و X ذات شويه إذا
+
+800
+00:57:54,730 --> 00:57:57,950
+هذه التلت حالات اللي عندى في الحالة اللي عندى هذه
+
+801
+00:57:57,950 --> 00:58:00,450
+الحالة التانية جزء إيه الجزء الأول جزء الثاني
+
+802
+00:58:00,450 --> 00:58:05,930
+الحالة الأولى اللي هو Dxy أكيد برضه أصغر يسوي Dx
+
+803
+00:58:05,930 --> 00:58:14,970
+وz زائد Dz وY ليه؟ لأن Dx وz واحدDX و Z DX و Y
+
+804
+00:58:14,970 --> 00:58:18,610
+واحد مختلفات DX و Z DX و Y واحد مختلفات DX و Z DX
+
+805
+00:58:18,610 --> 00:58:21,050
+و Y واحد مختلفات DX و Z DX و Y واحد مختلفات DX و Z
+
+806
+00:58:21,050 --> 00:58:22,170
+DX و Y واحد مختلفات DX و Z DX و Y واحد مختلفات DX
+
+807
+00:58:22,170 --> 00:58:24,010
+و Z DX و Z DX و Y واحد مختلفات DX و Z DX و Z DX و
+
+808
+00:58:24,010 --> 00:58:24,430
+Y واحد مختلفات DX و Z DX و Z DX و Z DX و Z DX و Z
+
+809
+00:58:24,430 --> 00:58:27,410
+DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z
+
+810
+00:58:27,410 --> 00:58:28,290
+DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z
+
+811
+00:58:28,290 --> 00:58:30,530
+DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z
+
+812
+00:58:30,530 --> 00:58:30,610
+DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z
+
+813
+00:58:30,610 --> 00:58:34,780
+DXالآن الحالة التانية z بتساوي x اول حاجة هدول
+
+814
+00:58:34,780 --> 00:58:38,940
+المختلفة اذا واحد اولا واحدة z بتساوي x اذا ندي
+
+815
+00:58:38,940 --> 00:58:42,680
+سفر z تتساوي y واحد اذا بتظل الحالة المساوية
+
+816
+00:58:42,680 --> 00:58:45,380
+متحققة اذا متحققة ال triangle inequality ال
+
+817
+00:58:45,380 --> 00:58:49,920
+triangle inequality اصغر او يساوي الحالة التالتة
+
+818
+00:58:49,920 --> 00:58:55,640
+بيصير اللي هو الحالة التالتة عنديهذه قولة واحدة
+
+819
+00:58:55,640 --> 00:59:03,540
+واحدة لأن XZ يتساوي Y XZ يتساوي Y وهو سفرزي ده
+
+820
+00:59:03,540 --> 00:59:08,180
+تساوي x واحد إذا واحد بساوي اللي هو الحالة اللي هي
+
+821
+00:59:08,180 --> 00:59:11,880
+الواحد إذا في الحالة هذه برضه دائما دي x و y أصغر
+
+822
+00:59:11,880 --> 00:59:14,980
+يساوي دي x و z زائد دي z و y من كل الحالات التانية
+
+823
+00:59:14,980 --> 00:59:17,000
+الحالة الأولى و الحالة التانية و ال sub cases اللي
+
+824
+00:59:17,000 --> 00:59:21,060
+من التلاتة دجينا دائما دي x و y أصغر يساوي دي x و
+
+825
+00:59:21,060 --> 00:59:24,920
+z زائد دي z و y و بهذا بيكون عندي هذا عبارة عن
+
+826
+00:59:24,920 --> 00:59:30,340
+metric space هذا بيسميه discrete metric space و
+
+827
+00:59:30,340 --> 00:59:35,340
+بيكون عندكم الآن homeworkالسؤال الأول، هذه السؤال
+
+828
+00:59:35,340 --> 00:59:41,140
+الأول، السؤال الأول، والسؤال التاني، هو أسئلة
+
+829
+00:59:41,140 --> 00:59:44,720
+الكتاب. الآن هتلاقوا في الـ Homework، اللي هو
+
+830
+00:59:44,720 --> 00:59:49,100
+Homework، وهنا Homework Star، اللي بدكم تسلمونيها
+
+831
+00:59:49,100 --> 00:59:52,240
+Homework Star، يعني بتكون تسلموني أربعة أو خمسة أو
+
+832
+00:59:52,240 --> 00:59:55,120
+تمانية أو عشرة من الكتاب، والواحد والتانين الـ
+
+833
+00:59:55,120 --> 00:59:58,180
+Above هذولة، هذول اللي بتكون تسلمونيها من ضمن الـ
+
+834
+00:59:58,180 --> 01:00:01,150
+Homeworks اللي اتفقنا عليهم،الان هدولة انت في
+
+835
+01:00:01,150 --> 01:00:05,450
+البيت بدك تحلهم اللي هو بفضل انك تطلع عليهم و
+
+836
+01:00:05,450 --> 01:00:08,050
+تحلهم بس تكشف السبب اني يعني لا سبب بتعرفوش تحلوها
+
+837
+01:00:08,050 --> 01:00:12,650
+انا حل كل الأسئلة بنقدر نعطيكم اللي هو اذا ما
+
+838
+01:00:12,650 --> 01:00:16,630
+أسافناش الوجد في داخل المحاضرة بعطيكم الحلول و
+
+839
+01:00:16,630 --> 01:00:21,230
+بتحلوها و بتشوفوها و الاشي اللي بدكميا مش فاهمينه
+
+840
+01:00:21,230 --> 01:00:26,350
+بنشوف ساعات مكتبية او في داخل هنا بنجاوبكم و هيك
+
+841
+01:00:26,350 --> 01:00:29,680
+بتكون نهينا المحاضرةو السلام عليكم و رحمة الله و
+
+842
+01:00:29,680 --> 01:00:30,040
+بركاته
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/BsKCqLUcy6s_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/BsKCqLUcy6s_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..8d11d68b81f508f3eb3dcedc2b3aa8e54a905fbb
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/BsKCqLUcy6s_raw.json
@@ -0,0 +1 @@
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"end": 816.67, "word": " و", "probability": 0.84033203125}, {"start": 816.67, "end": 816.67, "word": " نجوطين", "probability": 0.97734375}, {"start": 816.67, "end": 816.73, "word": " و", "probability": 0.8779296875}, {"start": 816.73, "end": 816.73, "word": " نجوطين", "probability": 0.98349609375}, {"start": 816.73, "end": 816.73, "word": " و", "probability": 0.90673828125}, {"start": 816.73, "end": 816.73, "word": " نجوطين", "probability": 0.9890625}, {"start": 816.73, "end": 817.57, "word": " و", "probability": 0.91845703125}, {"start": 817.57, "end": 818.09, "word": " نجوطين", "probability": 0.9921875}, {"start": 818.09, "end": 818.37, "word": " و", "probability": 0.93505859375}, {"start": 818.37, "end": 821.91, "word": " نجوطين", "probability": 0.99443359375}], "temperature": 1.0}, {"id": 35, "seek": 85287, "start": 823.11, "end": 852.87, "text": "و Xn أظهر ايش هو المسافة بين X1 و X2 زائد المسافة بين X2 و X3 زائد المسافة بين Xn-1 و Xn يعني هذه تعميل للحالة الأولى هذه بدنا نبرهنها أو برهانها سهل by induction انتوا حالكم بتقدروا تبرهنوها لكن خلينا على السريع اعطيكم outline لبرهانها خليها دي نسميها إيه إيش star عارفين كده بنبرهن by induction أول حاجة", "tokens": [2407, 1783, 77, 5551, 19913, 3224, 2288, 1975, 1829, 8592, 31439, 9673, 3794, 31845, 3660, 49374, 1783, 16, 4032, 1783, 17, 30767, 16373, 3215, 9673, 3794, 31845, 3660, 49374, 1783, 17, 4032, 1783, 18, 30767, 16373, 3215, 9673, 3794, 31845, 3660, 49374, 1783, 77, 12, 16, 4032, 1783, 77, 37495, 22653, 29538, 37279, 2304, 26895, 24976, 5016, 6027, 3660, 16247, 12610, 7578, 29538, 47525, 8315, 8717, 26890, 3224, 1863, 11296, 34051, 4724, 2288, 3224, 7649, 11296, 8608, 3224, 1211, 538, 33371, 16472, 2655, 14407, 11331, 6027, 24793, 39894, 28543, 2288, 14407, 6055, 26890, 3224, 1863, 2407, 11296, 44381, 16490, 20292, 8315, 15844, 21136, 16572, 3615, 1975, 3615, 9566, 1829, 24793, 16387, 5296, 26890, 3224, 7649, 11296, 16490, 20292, 11296, 11778, 1829, 8717, 38251, 1829, 11296, 11933, 1829, 3224, 11933, 1829, 8592, 3543, 6225, 9640, 5172, 9957, 9122, 3215, 3224, 44945, 26890, 3224, 1863, 538, 33371, 5551, 12610, 11331, 26108, 3660], "avg_logprob": -0.24130795373032424, "compression_ratio": 1.8909774436090225, "no_speech_prob": 0.94677734375, "words": [{"start": 823.11, "end": 823.55, "word": "و", "probability": 0.294677734375}, {"start": 823.55, "end": 824.05, "word": " Xn", "probability": 0.6787109375}, {"start": 824.05, "end": 824.45, "word": " أظهر", "probability": 0.7777099609375}, {"start": 824.45, "end": 824.59, "word": " ايش", "probability": 0.5373942057291666}, {"start": 824.59, "end": 824.69, "word": " هو", "probability": 0.89599609375}, {"start": 824.69, "end": 825.13, "word": " المسافة", "probability": 0.9815673828125}, {"start": 825.13, "end": 825.35, "word": " بين", "probability": 0.923828125}, {"start": 825.35, "end": 825.99, "word": " X1", "probability": 0.745361328125}, {"start": 825.99, "end": 826.67, "word": " و", "probability": 0.9365234375}, {"start": 826.67, "end": 827.25, "word": " X2", "probability": 0.95703125}, {"start": 827.25, "end": 827.93, "word": " زائد", "probability": 0.6333821614583334}, {"start": 827.93, "end": 828.81, "word": " المسافة", "probability": 0.992431640625}, {"start": 828.81, "end": 829.07, "word": " بين", "probability": 0.95166015625}, {"start": 829.07, "end": 829.77, "word": " X2", "probability": 0.98828125}, {"start": 829.77, "end": 830.13, "word": " و", "probability": 0.982421875}, {"start": 830.13, "end": 830.79, "word": " X3", "probability": 0.942626953125}, {"start": 830.79, "end": 831.73, "word": " زائد", "probability": 0.9560546875}, {"start": 831.73, "end": 832.65, "word": " المسافة", "probability": 0.973388671875}, {"start": 832.65, "end": 832.99, "word": " بين", "probability": 0.92724609375}, {"start": 832.99, "end": 833.57, "word": " Xn", "probability": 0.90771484375}, {"start": 833.57, "end": 834.47, "word": "-1", "probability": 0.69189453125}, {"start": 834.47, "end": 834.95, "word": " و", "probability": 0.958984375}, {"start": 834.95, "end": 835.53, "word": " Xn", "probability": 0.906494140625}, {"start": 835.53, "end": 835.95, "word": " يعني", "probability": 0.872802734375}, {"start": 835.95, "end": 836.21, "word": " هذه", "probability": 0.66552734375}, {"start": 836.21, "end": 836.67, "word": " تعميل", "probability": 0.6837565104166666}, {"start": 836.67, "end": 837.81, "word": " للحالة", "probability": 0.72686767578125}, {"start": 837.81, "end": 838.29, "word": " الأولى", "probability": 0.9656575520833334}, {"start": 838.29, "end": 839.05, "word": " هذه", "probability": 0.736328125}, {"start": 839.05, "end": 839.49, "word": " بدنا", "probability": 0.909423828125}, {"start": 839.49, "end": 840.11, "word": " نبرهنها", "probability": 0.982421875}, {"start": 840.11, "end": 840.29, "word": " أو", "probability": 0.62890625}, {"start": 840.29, "end": 840.85, "word": " برهانها", "probability": 0.8943359375}, {"start": 840.85, "end": 841.23, "word": " سهل", "probability": 0.9591471354166666}, {"start": 841.23, "end": 841.57, "word": " by", "probability": 0.7529296875}, {"start": 841.57, "end": 841.99, "word": " induction", "probability": 0.98095703125}, {"start": 841.99, "end": 842.39, "word": " انتوا", "probability": 0.7279459635416666}, {"start": 842.39, "end": 842.65, "word": " حالكم", "probability": 0.3968505859375}, {"start": 842.65, "end": 842.95, "word": " بتقدروا", "probability": 0.9244384765625}, {"start": 842.95, "end": 843.51, "word": " تبرهنوها", "probability": 0.8750406901041666}, {"start": 843.51, "end": 844.03, "word": " لكن", "probability": 0.921875}, {"start": 844.03, "end": 844.51, "word": " خلينا", "probability": 0.7669270833333334}, {"start": 844.51, "end": 845.01, "word": " على", "probability": 0.880859375}, {"start": 845.01, "end": 845.43, "word": " السريع", "probability": 0.96044921875}, {"start": 845.43, "end": 845.79, "word": " اعطيكم", "probability": 0.8296875}, {"start": 845.79, "end": 846.29, "word": " outline", "probability": 0.56298828125}, {"start": 846.29, "end": 847.03, "word": " لبرهانها", "probability": 0.91875}, {"start": 847.03, "end": 847.35, "word": " خليها", "probability": 0.6798502604166666}, {"start": 847.35, "end": 847.45, "word": " دي", "probability": 0.6165771484375}, {"start": 847.45, "end": 847.77, "word": " نسميها", "probability": 0.8673095703125}, {"start": 847.77, "end": 847.95, "word": " إيه", "probability": 0.62841796875}, {"start": 847.95, "end": 848.11, "word": " إيش", "probability": 0.752197265625}, {"start": 848.11, "end": 848.95, "word": " star", "probability": 0.2154541015625}, {"start": 848.95, "end": 849.55, "word": " عارفين", "probability": 0.8021240234375}, {"start": 849.55, "end": 849.93, "word": " كده", "probability": 0.667724609375}, {"start": 849.93, "end": 851.63, "word": " بنبرهن", "probability": 0.82525634765625}, {"start": 851.63, "end": 851.77, "word": " by", "probability": 0.89892578125}, {"start": 851.77, "end": 852.11, "word": " induction", "probability": 0.96826171875}, {"start": 852.11, "end": 852.41, "word": " أول", "probability": 0.767578125}, {"start": 852.41, "end": 852.87, "word": " حاجة", "probability": 0.99560546875}], "temperature": 1.0}, {"id": 36, "seek": 86456, "start": 853.2, "end": 864.56, "text": "أول اشي عشان بنها دي لكل n element صحيحة بتقول for n بتساوي واحدة trivial فالان for n بتساوي اتنين for n بتساوي اتنين", "tokens": [10721, 12610, 1975, 8592, 1829, 6225, 8592, 7649, 44945, 11296, 11778, 1829, 5296, 28820, 297, 4478, 20328, 5016, 1829, 5016, 3660, 39894, 39648, 337, 297, 39894, 3794, 995, 45865, 36764, 24401, 3660, 26703, 6156, 6027, 7649, 337, 297, 39894, 3794, 995, 45865, 1975, 2655, 1863, 9957, 337, 297, 39894, 3794, 995, 45865, 1975, 2655, 1863, 9957], "avg_logprob": -0.4155701712558144, "compression_ratio": 1.5206611570247934, "no_speech_prob": 2.1636486053466797e-05, "words": [{"start": 853.2, "end": 853.98, "word": "أول", "probability": 0.84619140625}, {"start": 853.98, "end": 854.34, "word": " اشي", "probability": 0.63507080078125}, {"start": 854.34, "end": 854.7, "word": " عشان", "probability": 0.8256022135416666}, {"start": 854.7, "end": 855.02, "word": " بنها", "probability": 0.4647216796875}, {"start": 855.02, "end": 855.18, "word": " دي", "probability": 0.797119140625}, {"start": 855.18, "end": 855.46, "word": " لكل", "probability": 0.967041015625}, {"start": 855.46, "end": 855.72, "word": " n", "probability": 0.2841796875}, {"start": 855.72, "end": 856.0, "word": " element", "probability": 0.626953125}, {"start": 856.0, "end": 856.86, "word": " صحيحة", "probability": 0.820947265625}, {"start": 856.86, "end": 857.8, "word": " بتقول", "probability": 0.922607421875}, {"start": 857.8, "end": 858.02, "word": " for", "probability": 0.58984375}, {"start": 858.02, "end": 858.14, "word": " n", "probability": 0.89794921875}, {"start": 858.14, "end": 858.48, "word": " بتساوي", "probability": 0.73388671875}, {"start": 858.48, "end": 858.72, "word": " واحدة", "probability": 0.5201619466145834}, {"start": 858.72, "end": 859.06, "word": " trivial", "probability": 0.7001953125}, {"start": 859.06, "end": 861.58, "word": " فالان", "probability": 0.541748046875}, {"start": 861.58, "end": 861.82, "word": " for", "probability": 0.9375}, {"start": 861.82, "end": 861.98, "word": " n", "probability": 0.966796875}, {"start": 861.98, "end": 862.4, "word": " بتساوي", "probability": 0.968994140625}, {"start": 862.4, "end": 862.86, "word": " اتنين", "probability": 0.80615234375}, {"start": 862.86, "end": 863.38, "word": " for", "probability": 0.247802734375}, {"start": 863.38, "end": 863.58, "word": " n", "probability": 0.9150390625}, {"start": 863.58, "end": 864.0, "word": " بتساوي", "probability": 0.97021484375}, {"start": 864.0, "end": 864.56, "word": " اتنين", "probability": 0.984130859375}], "temperature": 1.0}, {"id": 37, "seek": 89122, "start": 869.3, "end": 891.22, "text": "اللي هي أصغر حتى التين برضه trivial لو أنا بالساعة تلاتة X1 و X3 أصغر الساعة المسافة بين X1 و X2 زائد المسافة بين X2 و X3 الـ Trivial الـ Trivial برضه هذا من وين جاوب من ال triangle inequality مباشرة من سرعة لأنه كلام سهل أو outline هذا التين", "tokens": [6027, 20292, 39896, 5551, 9381, 17082, 2288, 11331, 49975, 16712, 9957, 4724, 43042, 3224, 26703, 45164, 41850, 20666, 3794, 995, 27884, 6055, 1211, 9307, 3660, 1783, 16, 4032, 1783, 18, 5551, 9381, 17082, 2288, 21136, 995, 27884, 9673, 3794, 31845, 3660, 49374, 1783, 16, 4032, 1783, 17, 30767, 16373, 3215, 9673, 3794, 31845, 3660, 49374, 1783, 17, 4032, 1783, 18, 2423, 39184, 10931, 22640, 2423, 39184, 10931, 22640, 4724, 43042, 3224, 23758, 9154, 4032, 9957, 10874, 995, 37746, 9154, 2423, 13369, 16970, 3714, 3555, 33599, 25720, 9154, 8608, 2288, 27884, 5296, 33456, 3224, 28242, 10943, 8608, 3224, 1211, 34051, 16387, 23758, 16712, 9957], "avg_logprob": -0.3124999853853996, "compression_ratio": 1.7699530516431925, "no_speech_prob": 0.00024366378784179688, "words": [{"start": 869.3, "end": 869.68, "word": "اللي", "probability": 0.361328125}, {"start": 869.68, "end": 870.06, "word": " هي", "probability": 0.92431640625}, {"start": 870.06, "end": 871.56, "word": " أصغر", "probability": 0.94921875}, {"start": 871.56, "end": 872.9, "word": " حتى", "probability": 0.8076171875}, {"start": 872.9, "end": 873.18, "word": " التين", "probability": 0.5565185546875}, {"start": 873.18, "end": 873.46, "word": " برضه", "probability": 0.9503580729166666}, {"start": 873.46, "end": 874.42, "word": " trivial", "probability": 0.48046875}, {"start": 874.42, "end": 874.68, "word": " لو", "probability": 0.70361328125}, {"start": 874.68, "end": 874.84, "word": " أنا", "probability": 0.1199951171875}, {"start": 874.84, "end": 875.1, "word": " بالساعة", "probability": 0.50531005859375}, {"start": 875.1, "end": 875.46, "word": " تلاتة", "probability": 0.88671875}, {"start": 875.46, "end": 875.86, "word": " X1", "probability": 0.5908203125}, {"start": 875.86, "end": 875.94, "word": " و", "probability": 0.83740234375}, {"start": 875.94, "end": 876.5, "word": " X3", "probability": 0.87158203125}, {"start": 876.5, "end": 877.12, "word": " أصغر", "probability": 0.973388671875}, {"start": 877.12, "end": 877.26, "word": " الساعة", "probability": 0.7963053385416666}, {"start": 877.26, "end": 877.62, "word": " المسافة", "probability": 0.9805908203125}, {"start": 877.62, "end": 877.78, "word": " بين", "probability": 0.94482421875}, {"start": 877.78, "end": 878.38, "word": " X1", "probability": 0.978515625}, {"start": 878.38, "end": 878.76, "word": " و", "probability": 0.96630859375}, {"start": 878.76, "end": 879.32, "word": " X2", "probability": 0.947998046875}, {"start": 879.32, "end": 880.02, "word": " زائد", "probability": 0.8663736979166666}, {"start": 880.02, "end": 880.5, "word": " المسافة", "probability": 0.9854736328125}, {"start": 880.5, "end": 880.72, "word": " بين", "probability": 0.9453125}, {"start": 880.72, "end": 881.36, "word": " X2", "probability": 0.990234375}, {"start": 881.36, "end": 881.92, "word": " و", "probability": 0.98974609375}, {"start": 881.92, "end": 883.12, "word": " X3", "probability": 0.95947265625}, {"start": 883.12, "end": 883.36, "word": " الـ", "probability": 0.4005126953125}, {"start": 883.36, "end": 883.7, "word": " Trivial", "probability": 0.6708984375}, {"start": 883.7, "end": 883.82, "word": " الـ", "probability": 0.58154296875}, {"start": 883.82, "end": 884.1, "word": " Trivial", "probability": 0.927978515625}, {"start": 884.1, "end": 884.7, "word": " برضه", "probability": 0.8995768229166666}, {"start": 884.7, "end": 885.02, "word": " هذا", "probability": 0.58544921875}, {"start": 885.02, "end": 885.14, "word": " من", "probability": 0.91943359375}, {"start": 885.14, "end": 885.3, "word": " وين", "probability": 0.35546875}, {"start": 885.3, "end": 885.7, "word": " جاوب", "probability": 0.6834309895833334}, {"start": 885.7, "end": 886.16, "word": " من", "probability": 0.81982421875}, {"start": 886.16, "end": 886.28, "word": " ال", "probability": 0.92138671875}, {"start": 886.28, "end": 886.58, "word": " triangle", "probability": 0.29638671875}, {"start": 886.58, "end": 887.04, "word": " inequality", "probability": 0.93896484375}, {"start": 887.04, "end": 887.62, "word": " مباشرة", "probability": 0.990966796875}, {"start": 887.62, "end": 887.76, "word": " من", "probability": 0.546875}, {"start": 887.76, "end": 888.0, "word": " سرعة", "probability": 0.4899088541666667}, {"start": 888.0, "end": 888.26, "word": " لأنه", "probability": 0.5974934895833334}, {"start": 888.26, "end": 888.58, "word": " كلام", "probability": 0.853759765625}, {"start": 888.58, "end": 888.94, "word": " سهل", "probability": 0.9970703125}, {"start": 888.94, "end": 889.48, "word": " أو", "probability": 0.8896484375}, {"start": 889.48, "end": 889.9, "word": " outline", "probability": 0.646484375}, {"start": 889.9, "end": 890.2, "word": " هذا", "probability": 0.9287109375}, {"start": 890.2, "end": 891.22, "word": " التين", "probability": 0.5703125}], "temperature": 1.0}, {"id": 38, "seek": 91363, "start": 891.89, "end": 913.63, "text": "بنقول suppose that star is true for n بتساوي k ده نفترض أنه هذه الجملة صحيحة لأن بتساوي k وبدتبتها صحيحة لمين ل k زائد واحد يعني بالمعنى أخر فقضيت هذا صحيح ل k معناته صارت DX1 لعين DXK DX1 لعين DXK", "tokens": [3555, 1863, 39648, 7297, 300, 3543, 307, 2074, 337, 297, 39894, 3794, 995, 45865, 350, 11778, 3224, 8717, 5172, 2655, 43042, 14739, 3224, 29538, 25724, 2304, 37977, 20328, 5016, 1829, 5016, 3660, 5296, 10721, 1863, 39894, 3794, 995, 45865, 350, 4032, 44510, 2655, 3555, 2655, 11296, 20328, 5016, 1829, 5016, 3660, 32767, 9957, 5296, 350, 30767, 16373, 3215, 36764, 24401, 37495, 22653, 20666, 2304, 3615, 1863, 7578, 5551, 34740, 6156, 4587, 11242, 36081, 23758, 20328, 5016, 1829, 5016, 5296, 350, 20449, 8315, 47395, 20328, 9640, 2655, 48817, 16, 5296, 3615, 9957, 48817, 42, 48817, 16, 5296, 3615, 9957, 48817, 42], "avg_logprob": -0.2359220297029703, "compression_ratio": 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نفترض", "probability": 0.83160400390625}, {"start": 899.93, "end": 900.21, "word": " أنه", "probability": 0.4940185546875}, {"start": 900.21, "end": 900.43, "word": " هذه", "probability": 0.580078125}, {"start": 900.43, "end": 900.91, "word": " الجملة", "probability": 0.966796875}, {"start": 900.91, "end": 901.65, "word": " صحيحة", "probability": 0.9806640625}, {"start": 901.65, "end": 902.07, "word": " لأن", "probability": 0.71044921875}, {"start": 902.07, "end": 902.45, "word": " بتساوي", "probability": 0.9478759765625}, {"start": 902.45, "end": 902.57, "word": " k", "probability": 0.73828125}, {"start": 902.57, "end": 903.17, "word": " وبدتبتها", "probability": 0.7626139322916666}, {"start": 903.17, "end": 903.59, "word": " صحيحة", "probability": 0.9947265625}, {"start": 903.59, "end": 904.15, "word": " لمين", "probability": 0.85693359375}, {"start": 904.15, "end": 904.67, "word": " ل", "probability": 0.84375}, {"start": 904.67, "end": 905.09, "word": " k", "probability": 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"end": 910.29, "word": " DX1", "probability": 0.5186767578125}, {"start": 910.29, "end": 910.61, "word": " لعين", "probability": 0.6537272135416666}, {"start": 910.61, "end": 911.37, "word": " DXK", "probability": 0.912841796875}, {"start": 911.37, "end": 912.71, "word": " DX1", "probability": 0.91943359375}, {"start": 912.71, "end": 912.95, "word": " لعين", "probability": 0.9567057291666666}, {"start": 912.95, "end": 913.63, "word": " DXK", "probability": 0.985595703125}], "temperature": 1.0}, {"id": 39, "seek": 93094, "start": 914.76, "end": 930.94, "text": "أصغر أو يساوي لما أصل لعند XK-1 و XK هذي صحيحة من الhypothesis induction اللي هم بيدثبتها لمين لـ K زائد واحد سهلة نيجي نثبتها لـ K زائد واحد دي X1 و XK زائد واحد", "tokens": [10721, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 5296, 15042, 5551, 36520, 5296, 3615, 41260, 1783, 42, 12, 16, 4032, 1783, 42, 8032, 8848, 1829, 20328, 5016, 1829, 5016, 3660, 9154, 2423, 3495, 79, 4624, 271, 33371, 13672, 1829, 8032, 2304, 4724, 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أكيد سأل قال طب احنا مافيه metric احنا الزمان اللي اتعلمناه و احنا اصغار اللي هو او احنا في ال .. في ال .. في ال .. حتى في الاعدادية او اللي هو في اللي هي ال calculus احنا بنعرف المسافة بين نقطتين في الفرق لما يكون عندى النقطة x و y", "tokens": [5537, 1341, 1901, 20449, 2423, 9640, 11242, 16712, 25513, 10632, 45030, 11242, 24793, 5551, 4117, 25708, 8608, 10721, 1211, 50239, 23032, 3555, 1975, 5016, 8315, 19446, 41185, 3224, 20678, 1975, 5016, 8315, 6024, 110, 2304, 7649, 13672, 1829, 1975, 2655, 3615, 19528, 8315, 3224, 4032, 1975, 5016, 8315, 1975, 9381, 17082, 9640, 13672, 1829, 31439, 1975, 2407, 1975, 5016, 8315, 8978, 2423, 4386, 8978, 2423, 4386, 8978, 2423, 4386, 11331, 49975, 8978, 42963, 22488, 18513, 10632, 1975, 2407, 13672, 1829, 31439, 8978, 13672, 1829, 39896, 2423, 33400, 1975, 5016, 8315, 44945, 3615, 28480, 9673, 3794, 31845, 3660, 49374, 8717, 47432, 2655, 9957, 8978, 27188, 2288, 4587, 5296, 15042, 7251, 30544, 43242, 7578, 28239, 47432, 3660, 2031, 4032, 288], 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219169, "start": 2164.61, "end": 2191.69, "text": "الآن نيجي إلى اللي هو مثالنا المهم اللي هو حاجة اسمها sequence space sequence space جماعة من اسمه هو عبارة عن فراغ عناصر أو مجموعة على سرها اللي هي sequences متتابعات لكن هذه المتتابعات بديها تكون bounded شو اللي بتقوله خليني نشوف", "tokens": [6027, 148, 48506, 8717, 1829, 7435, 1829, 30731, 13672, 1829, 31439, 50113, 6027, 8315, 9673, 16095, 13672, 1829, 31439, 11331, 26108, 3660, 24525, 2304, 11296, 8310, 1901, 8310, 1901, 10874, 15042, 27884, 9154, 24525, 2304, 3224, 31439, 6225, 3555, 9640, 3660, 18871, 6156, 2288, 5718, 118, 18871, 33546, 2288, 34051, 3714, 7435, 2304, 2407, 27884, 15844, 8608, 2288, 11296, 13672, 1829, 39896, 22978, 44650, 2655, 16758, 3615, 9307, 44381, 29538, 9673, 2655, 2655, 16758, 3615, 9307, 4724, 16254, 11296, 6055, 30544, 37498, 13412, 2407, 13672, 1829, 39894, 39648, 3224, 16490, 1211, 9957, 1829, 8717, 8592, 38688], "avg_logprob": -0.14618234536082475, "compression_ratio": 1.821256038647343, 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إيش", "probability": 0.8341471354166666}, {"start": 2232.19, "end": 2232.93, "word": " sequences", "probability": 0.3779296875}, {"start": 2232.93, "end": 2233.55, "word": " I", "probability": 0.9267578125}, {"start": 2233.55, "end": 2233.69, "word": " من", "probability": 0.97412109375}, {"start": 2233.69, "end": 2233.93, "word": " عند", "probability": 0.978515625}, {"start": 2233.93, "end": 2234.39, "word": " 1", "probability": 0.884765625}, {"start": 2234.39, "end": 2235.39, "word": " لملا", "probability": 0.741943359375}, {"start": 2235.39, "end": 2235.69, "word": " نهاية", "probability": 0.9104817708333334}], "temperature": 1.0}, {"id": 99, "seek": 225167, "start": 2235.83, "end": 2251.67, "text": "such that تكون الـ sequence اللي قال الـ infinity مش كل الـ sequences اللي في الدنيا بدياها بدياها تكون XI I is bounded يعني bounded sequence شو معناه bounded sequence؟ يعني في النهاية XI I", "tokens": [39974, 300, 6055, 30544, 2423, 39184, 8310, 13672, 1829, 50239, 2423, 39184, 13202, 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{"start": 2239.33, "end": 2239.45, "word": " الـ", "probability": 0.673095703125}, {"start": 2239.45, "end": 2239.65, "word": " infinity", "probability": 0.400146484375}, {"start": 2239.65, "end": 2239.81, "word": " مش", "probability": 0.66064453125}, {"start": 2239.81, "end": 2239.99, "word": " كل", "probability": 0.923828125}, {"start": 2239.99, "end": 2240.11, "word": " الـ", "probability": 0.72705078125}, {"start": 2240.11, "end": 2240.41, "word": " sequences", "probability": 0.95751953125}, {"start": 2240.41, "end": 2240.65, "word": " اللي", "probability": 0.989990234375}, {"start": 2240.65, "end": 2240.73, "word": " في", "probability": 0.88916015625}, {"start": 2240.73, "end": 2240.97, "word": " الدنيا", "probability": 0.9876302083333334}, {"start": 2240.97, "end": 2241.43, "word": " بدياها", "probability": 0.74591064453125}, {"start": 2241.43, "end": 2242.45, "word": " بدياها", "probability": 0.8773193359375}, {"start": 2242.45, "end": 2242.87, "word": " تكون", "probability": 0.992919921875}, {"start": 2242.87, "end": 2243.47, "word": " XI", "probability": 0.43408203125}, {"start": 2243.47, "end": 2243.89, "word": " I", "probability": 0.318603515625}, {"start": 2243.89, "end": 2244.35, "word": " is", "probability": 0.8720703125}, {"start": 2244.35, "end": 2245.67, "word": " bounded", "probability": 0.95263671875}, {"start": 2245.67, "end": 2246.75, "word": " يعني", "probability": 0.90185546875}, {"start": 2246.75, "end": 2247.13, "word": " bounded", "probability": 0.87060546875}, {"start": 2247.13, "end": 2247.71, "word": " sequence", "probability": 0.9814453125}, {"start": 2247.71, "end": 2247.97, "word": " شو", "probability": 0.812744140625}, {"start": 2247.97, "end": 2248.21, "word": " معناه", "probability": 0.7972005208333334}, {"start": 2248.21, "end": 2248.55, "word": " bounded", "probability": 0.84716796875}, {"start": 2248.55, "end": 2249.73, "word": " sequence؟", "probability": 0.7193603515625}, {"start": 2249.73, "end": 2249.97, "word": " يعني", "probability": 0.905517578125}, {"start": 2249.97, "end": 2250.09, "word": " في", "probability": 0.94091796875}, {"start": 2250.09, "end": 2250.61, "word": " النهاية", "probability": 0.962890625}, {"start": 2250.61, "end": 2251.29, "word": " XI", "probability": 0.90283203125}, {"start": 2251.29, "end": 2251.67, "word": " I", "probability": 0.947265625}], "temperature": 1.0}, {"id": 100, "seek": 226864, "start": 2252.68, "end": 2268.64, "text": "اللي هو there exists C element in R such that Xi I أصغر أو يساوي هذا الـ C لكل I بتساوي واحد واتنين أمنة يعني في النهاية العناصر تبعات الـ sequences لن تتجاوز حد معين", "tokens": [6027, 20292, 31439, 456, 8198, 383, 4478, 294, 497, 1270, 300, 15712, 286, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 23758, 2423, 39184, 383, 5296, 28820, 286, 39894, 3794, 995, 45865, 36764, 24401, 4032, 9307, 1863, 9957, 5551, 27842, 3660, 37495, 22653, 8978, 28239, 11296, 10632, 18863, 1863, 33546, 2288, 6055, 3555, 3615, 9307, 2423, 39184, 22978, 5296, 1863, 6055, 2655, 7435, 995, 2407, 11622, 11331, 3215, 20449, 9957], "avg_logprob": -0.2136501798199283, "compression_ratio": 1.3956043956043955, "no_speech_prob": 3.8564205169677734e-05, "words": [{"start": 2252.68, "end": 2252.96, "word": "اللي", "probability": 0.740478515625}, {"start": 2252.96, "end": 2253.08, "word": " هو", "probability": 0.86376953125}, {"start": 2253.08, "end": 2253.28, "word": " there", "probability": 0.5068359375}, {"start": 2253.28, "end": 2253.74, "word": " exists", "probability": 0.7109375}, {"start": 2253.74, "end": 2254.16, "word": " C", "probability": 0.391357421875}, {"start": 2254.16, "end": 2254.6, "word": " element", "probability": 0.78515625}, {"start": 2254.6, "end": 2254.92, "word": " in", "probability": 0.9609375}, {"start": 2254.92, "end": 2255.24, "word": " R", "probability": 0.98388671875}, {"start": 2255.24, "end": 2255.96, "word": " such", "probability": 0.76708984375}, {"start": 2255.96, "end": 2256.28, "word": " that", "probability": 0.9453125}, {"start": 2256.28, "end": 2256.56, "word": " Xi", "probability": 0.28125}, {"start": 2256.56, "end": 2256.92, "word": " I", "probability": 0.6826171875}, {"start": 2256.92, "end": 2257.5, "word": " أصغر", "probability": 0.951416015625}, {"start": 2257.5, "end": 2257.64, "word": " أو", "probability": 0.9560546875}, {"start": 2257.64, "end": 2258.02, "word": " يساوي", "probability": 0.9527587890625}, {"start": 2258.02, "end": 2258.28, "word": " هذا", "probability": 0.45654296875}, {"start": 2258.28, "end": 2258.46, "word": " الـ", "probability": 0.75}, {"start": 2258.46, "end": 2258.68, "word": " C", "probability": 0.428466796875}, {"start": 2258.68, "end": 2259.94, "word": " لكل", "probability": 0.943359375}, {"start": 2259.94, "end": 2261.06, "word": " I", "probability": 0.90234375}, {"start": 2261.06, "end": 2262.44, "word": " بتساوي", "probability": 0.8123779296875}, {"start": 2262.44, "end": 2262.78, "word": " واحد", "probability": 0.694091796875}, {"start": 2262.78, "end": 2263.2, "word": " واتنين", "probability": 0.8828125}, {"start": 2263.2, "end": 2263.64, "word": " أمنة", "probability": 0.591796875}, {"start": 2263.64, "end": 2263.98, "word": " يعني", "probability": 0.83447265625}, {"start": 2263.98, "end": 2264.38, "word": " في", "probability": 0.74267578125}, {"start": 2264.38, "end": 2264.92, "word": " النهاية", "probability": 0.9537760416666666}, {"start": 2264.92, "end": 2265.96, "word": " العناصر", "probability": 0.868408203125}, {"start": 2265.96, "end": 2266.32, "word": " تبعات", "probability": 0.72515869140625}, {"start": 2266.32, "end": 2266.44, "word": " الـ", "probability": 0.824462890625}, {"start": 2266.44, "end": 2266.8, "word": " sequences", "probability": 0.5712890625}, {"start": 2266.8, "end": 2267.24, "word": " لن", "probability": 0.97998046875}, {"start": 2267.24, "end": 2267.86, "word": " تتجاوز", "probability": 0.995849609375}, {"start": 2267.86, "end": 2268.16, "word": " حد", "probability": 0.986572265625}, {"start": 2268.16, "end": 2268.64, "word": " معين", "probability": 0.978759765625}], "temperature": 1.0}, {"id": 101, "seek": 228678, "start": 2269.32, "end": 2286.78, "text": "طبعا هذه الـ C لمن؟ للـ sequence هذه الـ sequence هذه لو سمناها X بتساوي XI I منقول عنها bounded إذا كان فيه إلها C عشان هيك بنقوله CX نرمز الـ X لإنه C هدي لمن؟ لـ X لو كان فيه sequence ثانية بتكون لها X C تانية فاهمين؟", "tokens": [9566, 3555, 3615, 995, 29538, 2423, 39184, 383, 5296, 27842, 22807, 24976, 39184, 8310, 29538, 2423, 39184, 8310, 29538, 45164, 8608, 2304, 8315, 11296, 1783, 39894, 3794, 995, 45865, 1783, 40, 286, 9154, 39648, 18871, 11296, 37498, 11933, 15730, 25961, 8978, 3224, 11933, 1211, 11296, 383, 6225, 8592, 7649, 39896, 4117, 44945, 39648, 3224, 383, 55, 8717, 2288, 2304, 11622, 2423, 39184, 1783, 5296, 28814, 1863, 3224, 383, 8032, 16254, 5296, 27842, 22807, 5296, 39184, 1783, 45164, 25961, 8978, 3224, 8310, 38637, 7649, 10632, 39894, 30544, 5296, 11296, 1783, 383, 6055, 7649, 10632, 6156, 995, 16095, 9957, 22807], "avg_logprob": -0.39299242123208866, "compression_ratio": 1.766497461928934, "no_speech_prob": 0.00046253204345703125, "words": [{"start": 2269.32, "end": 2269.96, "word": "طبعا", "probability": 0.82550048828125}, {"start": 2269.96, "end": 2270.18, "word": " هذه", "probability": 0.484375}, {"start": 2270.18, "end": 2270.38, "word": " الـ", "probability": 0.6923828125}, {"start": 2270.38, "end": 2270.52, "word": " C", "probability": 0.455322265625}, {"start": 2270.52, "end": 2271.08, "word": " لمن؟", "probability": 0.5489095052083334}, {"start": 2271.08, "end": 2271.32, "word": " للـ", "probability": 0.4276123046875}, {"start": 2271.32, "end": 2271.66, "word": " sequence", "probability": 0.7958984375}, {"start": 2271.66, "end": 2272.02, "word": " هذه", "probability": 0.75048828125}, {"start": 2272.02, "end": 2272.52, "word": " الـ", "probability": 0.6640625}, {"start": 2272.52, "end": 2272.78, "word": " sequence", "probability": 0.93408203125}, {"start": 2272.78, 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2281.08, "word": " هدي", "probability": 0.3499755859375}, {"start": 2281.08, "end": 2281.72, "word": " لمن؟", "probability": 0.8274739583333334}, {"start": 2281.72, "end": 2282.4, "word": " لـ", "probability": 0.3763427734375}, {"start": 2282.4, "end": 2282.56, "word": " X", "probability": 0.80029296875}, {"start": 2282.56, "end": 2282.74, "word": " لو", "probability": 0.84814453125}, {"start": 2282.74, "end": 2282.88, "word": " كان", "probability": 0.99169921875}, {"start": 2282.88, "end": 2283.04, "word": " فيه", "probability": 0.833740234375}, {"start": 2283.04, "end": 2283.36, "word": " sequence", "probability": 0.89404296875}, {"start": 2283.36, "end": 2283.72, "word": " ثانية", "probability": 0.8986002604166666}, {"start": 2283.72, "end": 2284.46, "word": " بتكون", "probability": 0.936767578125}, {"start": 2284.46, "end": 2284.72, "word": " لها", "probability": 0.6966552734375}, {"start": 2284.72, "end": 2284.92, "word": " X", "probability": 0.81640625}, {"start": 2284.92, "end": 2285.52, "word": " C", "probability": 0.424560546875}, {"start": 2285.52, "end": 2286.0, "word": " تانية", "probability": 0.92236328125}, {"start": 2286.0, "end": 2286.78, "word": " فاهمين؟", "probability": 0.92109375}], "temperature": 1.0}, {"id": 102, "seek": 231190, "start": 2287.12, "end": 2311.9, "text": "اللي أنا أصغر شوه مين CX يعني لو كان في عندي Y بسووه Gamma I وموجودة في الـ Infinity، هتكون bounded هتكون bounded، إيش معناه bounded؟ إنه there exists C ت .. الـ C إيش معناها؟ إنها للـ Y، عشان هيك بيسميها Cy ثابت طبعا such that اللي هو Gamma I أصغر أو سوى الـ C اللي لاجيناه هذه الـ sequence ده Y لكل مين I", "tokens": [6027, 20292, 41850, 5551, 9381, 17082, 2288, 13412, 2407, 3224, 3714, 9957, 383, 55, 37495, 22653, 45164, 25961, 8978, 18871, 16254, 398, 4724, 3794, 2407, 2407, 3224, 24723, 1696, 286, 4032, 2304, 29245, 23328, 3660, 8978, 2423, 39184, 34762, 12399, 8032, 2655, 30544, 37498, 8032, 2655, 30544, 37498, 12399, 11933, 1829, 8592, 20449, 8315, 3224, 37498, 22807, 36145, 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هيك", "probability": 0.302001953125}, {"start": 2303.44, "end": 2303.72, "word": " بيسميها", "probability": 0.742529296875}, {"start": 2303.72, "end": 2304.0, "word": " Cy", "probability": 0.5947265625}, {"start": 2304.0, "end": 2304.62, "word": " ثابت", "probability": 0.9114583333333334}, {"start": 2304.62, "end": 2304.92, "word": " طبعا", "probability": 0.98388671875}, {"start": 2304.92, "end": 2305.52, "word": " such", "probability": 0.33642578125}, {"start": 2305.52, "end": 2305.9, "word": " that", "probability": 0.9560546875}, {"start": 2305.9, "end": 2306.06, "word": " اللي", "probability": 0.923095703125}, {"start": 2306.06, "end": 2306.2, "word": " هو", "probability": 0.984375}, {"start": 2306.2, "end": 2306.58, "word": " Gamma", "probability": 0.9150390625}, {"start": 2306.58, "end": 2306.98, "word": " I", "probability": 0.9892578125}, {"start": 2306.98, "end": 2307.72, "word": " أصغر", "probability": 0.994140625}, {"start": 2307.72, "end": 2307.84, "word": " أو", "probability": 0.9580078125}, {"start": 2307.84, "end": 2308.06, "word": " سوى", "probability": 0.6061197916666666}, {"start": 2308.06, "end": 2308.2, "word": " الـ", "probability": 0.822998046875}, {"start": 2308.2, "end": 2308.36, "word": " C", "probability": 0.7314453125}, {"start": 2308.36, "end": 2308.52, "word": " اللي", "probability": 0.984375}, {"start": 2308.52, "end": 2308.88, "word": " لاجيناه", "probability": 0.702197265625}, {"start": 2308.88, "end": 2309.08, "word": " هذه", "probability": 0.430908203125}, {"start": 2309.08, "end": 2309.28, "word": " الـ", "probability": 0.610107421875}, {"start": 2309.28, "end": 2309.62, "word": " sequence", "probability": 0.7275390625}, {"start": 2309.62, "end": 2309.88, "word": " ده", "probability": 0.47705078125}, {"start": 2309.88, "end": 2310.14, "word": " Y", "probability": 0.90087890625}, {"start": 2310.14, "end": 2311.1, "word": " لكل", "probability": 0.86279296875}, {"start": 2311.1, "end": 2311.62, "word": " مين", "probability": 0.99072265625}, {"start": 2311.62, "end": 2311.9, "word": " I", "probability": 0.9765625}], "temperature": 1.0}, {"id": 103, "seek": 232653, "start": 2312.29, "end": 2326.53, "text": "مثلًا أعطيكم مثال يعني عشان تشوفوا مين ممكن نقعد هان لو جينا أخذنا ال sequence واحد و نص و تلت و ربع اللي هي ال sequence واحد على أن بمعنى آخر واضح إن ال sequence هذه أشمالها is bounded", "tokens": [2304, 12984, 1211, 14111, 995, 5551, 3615, 9566, 1829, 24793, 50113, 6027, 37495, 22653, 6225, 8592, 7649, 6055, 8592, 38688, 14407, 3714, 9957, 3714, 43020, 8717, 4587, 22488, 8032, 7649, 45164, 10874, 1829, 8315, 5551, 9778, 8848, 8315, 2423, 8310, 36764, 24401, 4032, 8717, 9381, 4032, 6055, 1211, 2655, 4032, 12602, 3555, 3615, 13672, 1829, 39896, 2423, 8310, 36764, 24401, 15844, 14739, 4724, 2304, 3615, 1863, 7578, 19753, 34740, 4032, 46958, 5016, 36145, 2423, 8310, 29538, 5551, 8592, 2304, 6027, 11296, 307, 37498], "avg_logprob": -0.1975446366483257, "compression_ratio": 1.633879781420765, "no_speech_prob": 0.0006985664367675781, "words": [{"start": 2312.29, "end": 2312.81, "word": "مثلًا", "probability": 0.774951171875}, {"start": 2312.81, "end": 2313.21, "word": " أعطيكم", "probability": 0.7671630859375}, {"start": 2313.21, "end": 2313.61, "word": " مثال", "probability": 0.8525390625}, {"start": 2313.61, "end": 2313.81, "word": " يعني", "probability": 0.680419921875}, {"start": 2313.81, "end": 2314.01, "word": " عشان", "probability": 0.92822265625}, {"start": 2314.01, "end": 2314.51, "word": " تشوفوا", "probability": 0.990234375}, {"start": 2314.51, "end": 2315.27, "word": " مين", "probability": 0.883544921875}, {"start": 2315.27, "end": 2315.69, "word": " ممكن", "probability": 0.964111328125}, {"start": 2315.69, "end": 2316.03, "word": " نقعد", "probability": 0.8961588541666666}, {"start": 2316.03, "end": 2316.37, "word": " هان", "probability": 0.701904296875}, {"start": 2316.37, "end": 2317.11, "word": " لو", "probability": 0.394287109375}, {"start": 2317.11, "end": 2317.39, "word": " جينا", "probability": 0.9112955729166666}, {"start": 2317.39, "end": 2317.83, "word": " أخذنا", "probability": 0.826171875}, {"start": 2317.83, "end": 2317.95, "word": " ال", "probability": 0.95458984375}, {"start": 2317.95, "end": 2318.27, "word": " sequence", "probability": 0.60009765625}, {"start": 2318.27, "end": 2318.79, "word": " واحد", "probability": 0.963623046875}, {"start": 2318.79, "end": 2319.11, "word": " و", "probability": 0.98876953125}, {"start": 2319.11, "end": 2319.43, "word": " نص", "probability": 0.773681640625}, {"start": 2319.43, "end": 2319.91, "word": " و", "probability": 0.89208984375}, {"start": 2319.91, "end": 2320.35, "word": " تلت", "probability": 0.96728515625}, {"start": 2320.35, "end": 2320.73, "word": " و", "probability": 0.99462890625}, {"start": 2320.73, "end": 2321.11, "word": " ربع", "probability": 0.8336588541666666}, {"start": 2321.11, "end": 2321.41, "word": " اللي", "probability": 0.942626953125}, {"start": 2321.41, "end": 2321.51, "word": " هي", "probability": 0.90380859375}, {"start": 2321.51, "end": 2321.59, "word": " ال", "probability": 0.87939453125}, {"start": 2321.59, "end": 2321.87, "word": " sequence", "probability": 0.974609375}, {"start": 2321.87, "end": 2322.23, "word": " واحد", "probability": 0.98291015625}, {"start": 2322.23, "end": 2322.39, "word": " على", "probability": 0.6787109375}, {"start": 2322.39, "end": 2322.57, "word": " أن", "probability": 0.41162109375}, {"start": 2322.57, "end": 2322.97, "word": " بمعنى", "probability": 0.92392578125}, {"start": 2322.97, "end": 2323.27, "word": " آخر", "probability": 0.7333984375}, {"start": 2323.27, "end": 2324.13, "word": " واضح", "probability": 0.9737955729166666}, {"start": 2324.13, "end": 2324.27, "word": " إن", "probability": 0.4365234375}, {"start": 2324.27, "end": 2324.39, "word": " ال", "probability": 0.97900390625}, {"start": 2324.39, "end": 2324.81, "word": " sequence", "probability": 0.98388671875}, {"start": 2324.81, "end": 2325.15, "word": " هذه", "probability": 0.67626953125}, {"start": 2325.15, "end": 2325.83, "word": " أشمالها", "probability": 0.85693359375}, {"start": 2325.83, "end": 2326.11, "word": " is", "probability": 0.90966796875}, {"start": 2326.11, "end": 2326.53, "word": " bounded", "probability": 0.90380859375}], "temperature": 1.0}, {"id": 104, "seek": 235019, "start": 2327.48, "end": 2350.2, "text": "الـ Terms تبعتها لا يمكن أن تتجاوز الواحد يعني الـ bound لها إيش واحد يعني هنا في هذه الحالة جامع I لو سمناها جامع I هذه أصغر أو شاومين واحد لكل I فهذه ال sequence أكيد موجودة وين في ال infinity بينما لو أجيته لل sequence التالية اللي هو 1 و 2 و 3 و 4", "tokens": [6027, 39184, 19835, 82, 6055, 3555, 34268, 11296, 20193, 7251, 43020, 14739, 6055, 2655, 7435, 995, 2407, 11622, 2423, 14407, 24401, 37495, 22653, 2423, 39184, 5472, 5296, 11296, 11933, 1829, 8592, 36764, 24401, 37495, 22653, 34105, 8978, 29538, 21542, 6027, 3660, 10874, 10943, 3615, 286, 45164, 8608, 2304, 8315, 11296, 10874, 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2330.12, "end": 2330.68, "word": " تتجاوز", "probability": 0.9305013020833334}, {"start": 2330.68, "end": 2331.1, "word": " الواحد", "probability": 0.9479166666666666}, {"start": 2331.1, "end": 2331.6, "word": " يعني", "probability": 0.76025390625}, {"start": 2331.6, "end": 2331.82, "word": " الـ", "probability": 0.701904296875}, {"start": 2331.82, "end": 2332.04, "word": " bound", "probability": 0.32666015625}, {"start": 2332.04, "end": 2332.36, "word": " لها", "probability": 0.6925048828125}, {"start": 2332.36, "end": 2332.6, "word": " إيش", "probability": 0.69677734375}, {"start": 2332.6, "end": 2332.84, "word": " واحد", "probability": 0.961181640625}, {"start": 2332.84, "end": 2333.0, "word": " يعني", "probability": 0.61181640625}, {"start": 2333.0, "end": 2333.2, "word": " هنا", "probability": 0.65966796875}, {"start": 2333.2, "end": 2333.36, "word": " في", "probability": 0.5908203125}, {"start": 2333.36, "end": 2333.68, "word": " هذه", "probability": 0.367431640625}, {"start": 2333.68, "end": 2334.08, "word": " الحالة", "probability": 0.9856770833333334}, {"start": 2334.08, "end": 2334.7, "word": " جامع", "probability": 0.7713216145833334}, {"start": 2334.7, "end": 2334.98, "word": " I", "probability": 0.654296875}, {"start": 2334.98, "end": 2335.18, "word": " لو", "probability": 0.6181640625}, {"start": 2335.18, "end": 2335.52, "word": " سمناها", "probability": 0.784423828125}, {"start": 2335.52, "end": 2335.84, "word": " جامع", "probability": 0.9235026041666666}, {"start": 2335.84, "end": 2336.02, "word": " I", "probability": 0.986328125}, {"start": 2336.02, "end": 2336.32, "word": " هذه", "probability": 0.88427734375}, {"start": 2336.32, "end": 2337.02, "word": " أصغر", "probability": 0.9677734375}, {"start": 2337.02, "end": 2337.14, "word": " أو", "probability": 0.9580078125}, {"start": 2337.14, "end": 2337.56, "word": " شاومين", "probability": 0.6953125}, {"start": 2337.56, "end": 2337.94, "word": " واحد", "probability": 0.952392578125}, {"start": 2337.94, "end": 2338.32, "word": " لكل", "probability": 0.98193359375}, {"start": 2338.32, "end": 2338.66, "word": " I", "probability": 0.984375}, {"start": 2338.66, "end": 2339.34, "word": " فهذه", "probability": 0.9140625}, {"start": 2339.34, "end": 2339.48, "word": " ال", "probability": 0.94482421875}, {"start": 2339.48, "end": 2339.9, "word": " sequence", "probability": 0.63525390625}, {"start": 2339.9, "end": 2340.32, "word": " أكيد", "probability": 0.91943359375}, {"start": 2340.32, "end": 2340.78, "word": " موجودة", "probability": 0.982177734375}, {"start": 2340.78, "end": 2341.04, "word": " وين", "probability": 0.752197265625}, {"start": 2341.04, "end": 2341.48, "word": " في", "probability": 0.82470703125}, {"start": 2341.48, "end": 2341.8, "word": " ال", "probability": 0.9794921875}, {"start": 2341.8, "end": 2342.32, "word": " infinity", "probability": 0.32568359375}, {"start": 2342.32, "end": 2343.1, "word": " بينما", "probability": 0.9296875}, {"start": 2343.1, "end": 2344.66, "word": " لو", "probability": 0.65478515625}, {"start": 2344.66, "end": 2345.16, "word": " أجيته", "probability": 0.7135009765625}, {"start": 2345.16, "end": 2345.36, "word": " لل", "probability": 0.82275390625}, {"start": 2345.36, "end": 2346.02, "word": " sequence", "probability": 0.89013671875}, {"start": 2346.02, "end": 2347.1, "word": " التالية", "probability": 0.9918619791666666}, {"start": 2347.1, "end": 2347.66, "word": " اللي", "probability": 0.937255859375}, {"start": 2347.66, "end": 2347.88, "word": " هو", "probability": 0.9892578125}, {"start": 2347.88, "end": 2348.3, "word": " 1", "probability": 0.456298828125}, {"start": 2348.3, "end": 2348.5, "word": " و", "probability": 0.92578125}, {"start": 2348.5, "end": 2348.94, "word": " 2", "probability": 0.525390625}, {"start": 2348.94, "end": 2349.18, "word": " و", "probability": 0.98974609375}, {"start": 2349.18, "end": 2349.6, "word": " 3", "probability": 0.74560546875}, {"start": 2349.6, "end": 2349.8, "word": " و", 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3616.63, "word": " و", "probability": 0.546875}, {"start": 3616.63, "end": 3617.33, "word": " بتحلوها", "probability": 0.87861328125}, {"start": 3617.33, "end": 3617.41, "word": " و", "probability": 0.841796875}, {"start": 3617.41, "end": 3618.21, "word": " بتشوفوها", "probability": 0.96484375}, {"start": 3618.21, "end": 3618.77, "word": " و", "probability": 0.892578125}, {"start": 3618.77, "end": 3619.17, "word": " الاشي", "probability": 0.78662109375}, {"start": 3619.17, "end": 3619.67, "word": " اللي", "probability": 0.982421875}, {"start": 3619.67, "end": 3620.45, "word": " بدكميا", "probability": 0.8036295572916666}, {"start": 3620.45, "end": 3620.65, "word": " مش", "probability": 0.939453125}, {"start": 3620.65, "end": 3621.23, "word": " فاهمينه", "probability": 0.9837890625}, {"start": 3621.23, "end": 3622.31, "word": " بنشوف", "probability": 0.726318359375}, {"start": 3622.31, "end": 3622.65, "word": " ساعات", "probability": 0.8111979166666666}, {"start": 3622.65, "end": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/BsKCqLUcy6s_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/BsKCqLUcy6s_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ba5443ace1d3cab78a7c1686a7c7fb86e7301769
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/BsKCqLUcy6s_raw.srt
@@ -0,0 +1,3376 @@
+1
+00:00:05,200 --> 00:00:07,980
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,980 --> 00:00:10,940
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,940 --> 00:00:15,500
+أهله وصحبه أجمعين هذه هي المحاضرة الأولى في مساق
+
+4
+00:00:15,500 --> 00:00:19,700
+تحليل دالي أو تحليل اقتراني functional analysis
+
+5
+00:00:19,700 --> 00:00:26,160
+رقم المادة Maths 6324 وهي من المواد الاختيارية
+
+6
+00:00:26,160 --> 00:00:30,220
+لطلاب وطالبات ماجستير رياضيات في الجامعة الإسلامية
+
+7
+00:00:30,810 --> 00:00:35,430
+كذلك أيضًا اللي هو نستطيع أن نعطي هذه المادة في
+
+8
+00:00:35,430 --> 00:00:38,490
+وجود طلاب الـ Baccalaureate ونطلب منهم من المادة
+
+9
+00:00:38,490 --> 00:00:44,230
+ما هو مناسب لهم الآن راح نتحدث في البداية عن اللي
+
+10
+00:00:44,230 --> 00:00:48,170
+هو وصف المساق وصف المساق أول إشي اللي هو ال
+
+11
+00:00:48,170 --> 00:00:51,350
+textbook اللي هو Introductory Functional Analysis
+
+12
+00:00:51,350 --> 00:00:55,270
+with Applications لإيروين كريزينج وهذا طبعًا من
+
+13
+00:00:55,270 --> 00:01:03,280
+الكتب السهلة وفي نفس الوقت الكتب اللييعني المادة
+
+14
+00:01:03,280 --> 00:01:06,560
+العلمية فيها تؤدي الغرض بل انه المادة العلمية
+
+15
+00:01:06,560 --> 00:01:12,980
+خلينا نقول في ال course أولي في التحليل الإلكتروني
+
+16
+00:01:12,980 --> 00:01:18,970
+لأ هو مناسب ومناسب جداالان الموضوعات اللي احنا
+
+17
+00:01:18,970 --> 00:01:22,390
+هنغطيها المتوقع انه هنغطيها في هذا المساق اللي هي
+
+18
+00:01:22,390 --> 00:01:26,570
+عبارة عن اللي هي اربع شباتر بالاضافة لدزق من
+
+19
+00:01:26,570 --> 00:01:30,410
+chapter 7 الشابتر الأول والشابتر التاني والشابتر
+
+20
+00:01:30,410 --> 00:01:34,300
+التالت والشابتر الرابع ودزق من الشابتر السابعطبعا
+
+21
+00:01:34,300 --> 00:01:36,680
+طلاب الـ Baccalaureate حيكون في عندي أو طلبات الـ
+
+22
+00:01:36,680 --> 00:01:39,400
+Baccalaureate حيكون في عندي اللي هو chapter 1
+
+23
+00:01:39,400 --> 00:01:42,100
+chapter 2 و chapter 3 معظمه مطلوب منه ان شاء الله
+
+24
+00:01:42,100 --> 00:01:45,040
+في حينه في كل .. في كل شغلة احنا بدنا يها بس
+
+25
+00:01:45,040 --> 00:01:49,180
+للماجستير بنقولهم عنها و chapter 4 يعني جزء منه او
+
+26
+00:01:49,180 --> 00:01:52,020
+خلينا نقول شغلات أساسية منه بنعطيها للـ
+
+27
+00:01:52,020 --> 00:01:54,420
+Baccalaureate و الباقى بيكون لاللي هو طلاب
+
+28
+00:01:54,420 --> 00:01:58,480
+الماجستير و اللي هو جزء أو chapter 7 برضه شغلات
+
+29
+00:01:58,480 --> 00:02:00,860
+بسيطة لطلاب الـ Baccalaureate و الباقي اللي هو
+
+30
+00:02:00,860 --> 00:02:05,240
+لطلاب الماجستيرخلّيني نشوف مع بعض اللي هو ال ..
+
+31
+00:02:05,240 --> 00:02:08,380
+إيش ال course outline بالظبط الجزء الأول اللي هو
+
+32
+00:02:08,380 --> 00:02:11,660
+هنحكي عن اللي هو في الأسبوعين الأولانيات تقريبا
+
+33
+00:02:11,660 --> 00:02:15,500
+اللي هو هنحكي عن اللي هو ال metric spaces اللي هو
+
+34
+00:02:15,500 --> 00:02:18,100
+chapter واحد هذا هو ال metric spaces و ال
+
+35
+00:02:18,100 --> 00:02:21,200
+topological conceptual metric spaces و بعدين هنحكي
+
+36
+00:02:21,200 --> 00:02:23,320
+عن completeness و ال completion of metric spaces
+
+37
+00:02:23,320 --> 00:02:26,260
+طبعا كل هذه الكلام .. الكلام هنيجي له بالتفصيل أنا
+
+38
+00:02:26,260 --> 00:02:29,850
+بقى مروح عليه مرور سريع الآنبنكون خلصنا chapter
+
+39
+00:02:29,850 --> 00:02:34,330
+اللي هو واحد و بنبدأ في chapter اتنين حيكون عن ال
+
+40
+00:02:34,330 --> 00:02:38,170
+normed spaces و البنخ spaces هنعرف شو معناه normed
+
+41
+00:02:38,170 --> 00:02:40,430
+space و شو معناه بنخ space و بعدين هنحكي عن ال
+
+42
+00:02:40,430 --> 00:02:42,990
+compactness اللي هي خاصية طبوليجية طبعا هنجيها ان
+
+43
+00:02:42,990 --> 00:02:47,490
+شاء الله و بعدين هنحكي عن اللي هو قطع عريض منيح و
+
+44
+00:02:47,490 --> 00:02:50,640
+اللي هو applications هائلةاللي هو linear .. linear
+
+45
+00:02:50,640 --> 00:02:53,340
+and bounded linear operators on and functionals
+
+46
+00:02:53,340 --> 00:02:57,400
+وحنحكي عن اللي هو ال dual spaces ومن ثم حيكون
+
+47
+00:02:57,400 --> 00:03:01,500
+عندنا اللي هو ال first exam الان الجزء الثاني على
+
+48
+00:03:01,500 --> 00:03:04,620
+طول بنبدأ اللي هو نكون خلصنا الشبتر الأول وتقريبا
+
+49
+00:03:04,620 --> 00:03:07,700
+اللي هو الشبتر التاني بنيجي بشبتر تلاتة اللي هو ال
+
+50
+00:03:07,700 --> 00:03:11,300
+Hilbert spaces هنحكي عن ال Hilbert spaces هنحكي عن
+
+51
+00:03:11,300 --> 00:03:13,460
+ال orthogonal complement و direct sum و ال
+
+52
+00:03:13,460 --> 00:03:16,540
+orthonormal و ال total orthonormal sets and
+
+53
+00:03:16,540 --> 00:03:20,210
+sequencesبعدين هنحكي عن اللي هو representation of
+
+54
+00:03:20,210 --> 00:03:23,450
+functional on Hilbert spaces إشي مرتب و إشي منيح و
+
+55
+00:03:23,450 --> 00:03:28,330
+إشي حلو ان شاء الله هنحكي عنه في حينه بعدين هنحكي
+
+56
+00:03:28,330 --> 00:03:31,490
+عن اللي هو أنواع بعض ال operators ال operators
+
+57
+00:03:31,490 --> 00:03:35,930
+طبعا عالم واسع و أنواع عالم كبير و عليه دراسات في
+
+58
+00:03:35,930 --> 00:03:39,110
+كل المجلات في ال functional equations في ال
+
+59
+00:03:39,110 --> 00:03:41,570
+functional analysis في ال applications في ال
+
+60
+00:03:41,570 --> 00:03:45,740
+mechanicsفي كتير من الـ .. اللي هو .. اللي له
+
+61
+00:03:45,740 --> 00:03:49,460
+تطبيقات في الفيزيا وفي ال .. وفي الهندسة إلى أخرى
+
+62
+00:03:49,460 --> 00:03:51,920
+وفي الرياضيات بصورة عامة طبعاً هي الـ Functional
+
+63
+00:03:51,920 --> 00:03:55,380
+Analysis نفسها فيه لها تطبيقات عالية وتطباق ..
+
+64
+00:03:55,380 --> 00:03:58,060
+وتطبيقات هائلة طبعاً وعلاقتها بالـ Topology
+
+65
+00:03:58,060 --> 00:04:02,440
+وعلاقتها بالجبر يعني زي .. خليني أقول اللي بيعرف
+
+66
+00:04:02,440 --> 00:04:04,800
+Functional Analysis بيعرف جبر بيعرف .. بيعرف تحليل
+
+67
+00:04:04,800 --> 00:04:08,020
+بيعرف Topology بيعرف جبر خطي إلى آخره لأن الجبر
+
+68
+00:04:08,020 --> 00:04:11,150
+خطي أصلا من الحياة دي المادةما تخافوش منها المادة
+
+69
+00:04:11,150 --> 00:04:14,170
+المادة بنعطيها بشكل بسيط وبشكل حلو وبشكل جميل
+
+70
+00:04:14,170 --> 00:04:19,720
+وماحدش اللي بتابع مش هيلاقي ان شاء الله مشاكلقلنا
+
+71
+00:04:19,720 --> 00:04:24,000
+أنواع الoperators الهيلبرت ات جوينت أوبراتر سلفة
+
+72
+00:04:24,000 --> 00:04:47,620
+جوينت أوبراتر
+
+73
+00:04:48,090 --> 00:04:52,210
+كانت الـ exam سريع لأنه بنعرض احنا يعني ال ..
+
+74
+00:04:52,210 --> 00:04:56,910
+قاعدين اللي هو ال course outline الجزء الثاني ..
+
+75
+00:04:56,910 --> 00:05:00,310
+الجزء الثالث من المادة اللي هو ال .. ال .. ال ..
+
+76
+00:05:00,310 --> 00:05:02,210
+او ال .. ال .. بعد الامتحان التاني اللي هو الـ
+
+77
+00:05:02,210 --> 00:05:05,450
+Adjoint Operator and Reflexive Spaces هنحكي شو
+
+78
+00:05:05,450 --> 00:05:08,690
+معناه .. شو معناه Adjoint Operator ومن فمها هنحكي
+
+79
+00:05:08,690 --> 00:05:12,110
+عن حاجة حلوة و جميلة اسمها الـ Reflexive Spaces و
+
+80
+00:05:12,110 --> 00:05:15,870
+بعدين هنحكي عن ال category theorem من نظرية المهمة
+
+81
+00:05:16,100 --> 00:05:20,200
+ومن ثم على اللي هي النظرية الأساسية الأخرى بعد
+
+82
+00:05:20,200 --> 00:05:23,380
+الـHN اللي هي الـNon Form Boundedness Theorem بقى
+
+83
+00:05:23,380 --> 00:05:26,340
+دي هيك هنحكي عن اللي هو الـConvergence، شو معناته
+
+84
+00:05:26,340 --> 00:05:29,040
+Strong وش معناته Weaken Convergence وحنحكي عن
+
+85
+00:05:29,040 --> 00:05:32,280
+الـStrongest أو Weakest Convergence إلى آخره، إن
+
+86
+00:05:32,280 --> 00:05:36,140
+شاء الله في الحين وبنكون موجود، أنا يعني وجد نظر
+
+87
+00:05:36,140 --> 00:05:39,690
+أنه مواضيع ممتعة يعنيConvergence of Sequences of
+
+88
+00:05:39,690 --> 00:05:42,570
+Operators and Functionals ماهي معنية Convergence
+
+89
+00:05:42,570 --> 00:05:45,730
+of Sequences من Operators أو Convergence of
+
+90
+00:05:45,730 --> 00:05:49,230
+Sequences من Functionals سنرى ماهي معناته إن شاء
+
+91
+00:05:49,230 --> 00:05:53,870
+الله ثم سنحكي عن نظرية الأساسية الـ Open Mapping
+
+92
+00:05:53,870 --> 00:05:57,770
+Theorem ثم سنحكي عن Closed Linear Operators ثم
+
+93
+00:05:57,770 --> 00:06:01,990
+نختم بالنظرية الرابعة الأساسية Closed Graph
+
+94
+00:06:01,990 --> 00:06:06,050
+Theorem ثم سأكون عندي الـ Third Exam اللي معيشه إن
+
+95
+00:06:06,050 --> 00:06:10,110
+شاء اللهومن ثم هنبدأ اللي هو في Chapter 7 اللي هو
+
+96
+00:06:10,110 --> 00:06:13,570
+Spectral اللي هو Theory of Linear Operators on
+
+97
+00:06:13,570 --> 00:06:16,210
+Known Displaces طبعا عالم الـ Spectral Theory هذا
+
+98
+00:06:16,210 --> 00:06:20,730
+عالم مهم جدا وعالم تطبيقات هائلة خصوصا في الفيزيا
+
+99
+00:06:20,730 --> 00:06:26,590
+وفي الهندسة إلى آخره وبعدين هنحكي عن اللي هو يعني
+
+100
+00:06:26,590 --> 00:06:29,750
+طبعا introductions هدولة لإن بس هنعطيكوا فكرة عنهم
+
+101
+00:06:30,030 --> 00:06:33,450
+لأن هذا على مواسع يعني ونحكي عن اللي هو البنخ
+
+102
+00:06:33,450 --> 00:06:37,750
+Algebra اللي هو جبربنخ وجبربنخ طبعاً لحاله عالم
+
+103
+00:06:37,750 --> 00:06:41,670
+يعني اللي هو الناس كتير بتشغل فيه، بتتخصص فيه، و
+
+104
+00:06:41,670 --> 00:06:46,590
+applications تبعته عديدةبنجي بنكون وصلنا لمين لل
+
+105
+00:06:46,590 --> 00:06:50,030
+final exam في كل اللي هو المسار في بعض ال
+
+106
+00:06:50,030 --> 00:06:53,890
+references اللي هو عندنا الكتاب المشهور تبع Conway
+
+107
+00:06:53,890 --> 00:06:59,530
+أو مادوكس Conway في عمقه في كده لكن كتاب يعني
+
+108
+00:06:59,530 --> 00:07:04,850
+كمرجع مهم مادوكس سهل و لذيذ وسريع لكن بليان برضه
+
+109
+00:07:05,840 --> 00:07:09,260
+وإن كان بتناول جزء يعني من الـ .. اللي .. اللي في
+
+110
+00:07:09,260 --> 00:07:12,860
+.. اللي في .. اللي في .. اللي هو في Conway أو اللي
+
+111
+00:07:12,860 --> 00:07:16,460
+هو في Kresing. نيجي بعدين ل .. في كمان مرجع اسمه
+
+112
+00:07:16,460 --> 00:07:18,240
+Linear Operator Theory in Engineering and Science
+
+113
+00:07:18,240 --> 00:07:21,400
+ده في الـ Linear Operator .. كتير كتير كتير كتير
+
+114
+00:07:21,400 --> 00:07:27,780
+للمهتم الكتاب يعني عرضه شيق وعرضه سهل وعرضه كده
+
+115
+00:07:27,780 --> 00:07:30,760
+ومليان معلومات حول ال operators وحتى في
+
+116
+00:07:30,760 --> 00:07:33,710
+applications.introduction to functional analysis
+
+117
+00:07:33,710 --> 00:07:38,350
+تبع تيلر هذا من الكتب القديمة القيمة برضه في ال
+
+118
+00:07:38,350 --> 00:07:41,250
+functional analysis للي حابب يطلع عليها نيجي
+
+119
+00:07:41,250 --> 00:07:43,850
+لموضوع ال grading الموضوع الأخير اللي هو the final
+
+120
+00:07:43,850 --> 00:07:47,110
+grade will be bound on the best six of seven
+
+121
+00:07:47,110 --> 00:07:50,230
+homeworks يعني احطيكوا homeworks هتاخدوا هتعطوني
+
+122
+00:07:50,230 --> 00:07:55,150
+اللي هو تسلموني ال homeworks كلها وأنا بختار أحسن
+
+123
+00:07:55,150 --> 00:07:59,010
+ستة من سبعة أو أكتر من ستة من تمانية اللي بدكميهاو
+
+124
+00:07:59,010 --> 00:08:02,910
+بعدين هذا يكون عليه 10% الامتحانات اللي حكينا عنها
+
+125
+00:08:02,910 --> 00:08:06,610
+ال first و second و third هاخد احسن اتنين من تلاتة
+
+126
+00:08:06,610 --> 00:08:10,210
+و عليها ال 40% احسن اتنين و ال final بكون 50% و
+
+127
+00:08:10,210 --> 00:08:14,670
+بكون هيك اللي هو بكون اكتمل اللي هو المية من المية
+
+128
+00:08:14,670 --> 00:08:17,830
+و ان شاء الله بكون التوفيق لكم جميعا يا رب
+
+129
+00:08:17,830 --> 00:08:21,660
+العالمينالان هذا هو ال course outline خلينا نبدأ
+
+130
+00:08:21,660 --> 00:08:26,700
+الان في الشبتر الأول وال section الأول الشبتر
+
+131
+00:08:26,700 --> 00:08:31,620
+الأول هو عبارة عن metric spaces او الفرغات المترية
+
+132
+00:08:31,620 --> 00:08:36,160
+او بمعنى اخر احنا جاعدين بدنا نعمم المسافة اللي
+
+133
+00:08:36,160 --> 00:08:39,220
+احنا بنعرفها في اللي هو ال R وفي ال R تربيع وفي
+
+134
+00:08:39,220 --> 00:08:44,680
+القدر بدنا نعممها ونخرجها على صورة اللي هو انه
+
+135
+00:08:44,680 --> 00:08:48,950
+تكون in general نشوف ايش اللي بحكيهالشبط الأول هو
+
+136
+00:08:48,950 --> 00:08:52,190
+metric spaces الفرغات المترية ال section الأول هو
+
+137
+00:08:52,190 --> 00:08:55,550
+هيحكي عن ال metric spaces الفرغات المترية هندخل
+
+138
+00:08:55,550 --> 00:09:00,870
+للتعريف و بعض الأمثلة السهلة و اللي هي فش فيها ان
+
+139
+00:09:00,870 --> 00:09:05,190
+شاء الله يعني اللي هو صعوبة و هنشوف كيف نتناول كل
+
+140
+00:09:05,190 --> 00:09:11,290
+مثال من الأمثلة اللي عندنالأن تعريف الـ metric
+
+141
+00:09:11,290 --> 00:09:16,610
+space a metric space is a pair X وD يعني أنا بحكي
+
+142
+00:09:16,610 --> 00:09:22,810
+عن ال metric space هو عبارة عن 6X معها D دالة إيش
+
+143
+00:09:22,810 --> 00:09:27,990
+هذه الدالة اللي بتخليني اللي هي مع ال X تخليني
+
+144
+00:09:27,990 --> 00:09:32,230
+metric space هذه الدالة بتسميها metric هي عبارة عن
+
+145
+00:09:32,230 --> 00:09:36,990
+دالةاللي هي دالة المسافة تعميم لدالة المسافة اللي
+
+146
+00:09:36,990 --> 00:09:41,650
+احنا بنعرفها زمان في سواء في R أو في R تربيعي الآن
+
+147
+00:09:41,650 --> 00:09:47,190
+من X across X لعند هو في الواقع لعند بالظبط بالظبط
+
+148
+00:09:47,190 --> 00:09:51,710
+لعند R positive اتحاد الـ Zero بس لو قلنا R في
+
+149
+00:09:51,710 --> 00:09:54,590
+وجود الشروط اللي بحكيها بكفي الكلام ويكون الكلام
+
+150
+00:09:54,590 --> 00:10:00,270
+اللي هو كمكتمل خليني أشوف الان هي عبارة عن دي
+
+151
+00:10:00,270 --> 00:10:05,410
+عبارة عن دالة من X across Xالى الـ real value of
+
+152
+00:10:05,410 --> 00:10:08,790
+function الى R بالظبط هتكون عند R وزي الاتحاد الـ
+
+153
+00:10:08,790 --> 00:10:13,570
+Zero تحقق الشروط التالية أول شرط أن المسافة بين أي
+
+154
+00:10:13,570 --> 00:10:17,750
+نقطين لازم تكون أكبر أو ساوى سفر هذه ال X و Y من
+
+155
+00:10:17,750 --> 00:10:21,010
+أين جيات ال X من ال X و Y من ال Y لأن X cross Y
+
+156
+00:10:21,010 --> 00:10:25,940
+أشمالهاعبارة عن order بيارة عناصرها إذا الـD X Y
+
+157
+00:10:25,940 --> 00:10:29,200
+أكبر أو يساوي سفر أو المسافة بين X وY أشمال أكبر
+
+158
+00:10:29,200 --> 00:10:31,700
+أو يساوي سفر هذا طبيعي ما احنا عارفين أن مسافتنا
+
+159
+00:10:31,700 --> 00:10:34,920
+المسافة اللي بنحكي عنها اللي هو ديمة عمرنا في R وR
+
+160
+00:10:34,920 --> 00:10:38,340
+تربيه هي عبارة عن مسافة يعني أكبر أو يساوي سفر
+
+161
+00:10:38,340 --> 00:10:42,380
+فاحنا عمال جاعدين بنستقي تعريفنا و بنعمم اللي هو
+
+162
+00:10:42,380 --> 00:10:49,290
+اللي بنحكي في ال metric العادي اتنينالمسافة بين X
+
+163
+00:10:49,290 --> 00:10:54,810
+و Y بساوي 0 إذا و فقط إذا X بتساوي 100 بساوي Y
+
+164
+00:10:54,810 --> 00:10:59,290
+يعني المسافة بين النقطة و نفسها 0 و لو كانت
+
+165
+00:10:59,290 --> 00:11:02,690
+المسافة بين نقطة و أخرها 0 بكون هي النقطة نفسها
+
+166
+00:11:02,690 --> 00:11:07,290
+يعني لن نجد اللي هو نقطتين المسافة بينهم بتساوي 0
+
+167
+00:11:07,290 --> 00:11:10,490
+و لنا مش متساويتين لن نجد هذا اللي هو الشرط الثاني
+
+168
+00:11:10,950 --> 00:11:16,130
+الشرط الثالث أنه دائما المسافة بين X و Y هي نفسها
+
+169
+00:11:16,130 --> 00:11:19,830
+المسافة بين Y و X طبعا المسافة بين X و Y هي نفسها
+
+170
+00:11:19,830 --> 00:11:23,330
+المسافة بين Y و X اللي بنسميها في العلاقات اللي هي
+
+171
+00:11:23,330 --> 00:11:28,770
+الـ Symmetric الشرط الثالث أو الرابع اللي هي
+
+172
+00:11:28,770 --> 00:11:32,810
+Triangle Inquality اللي هي جاية من اللي هو من
+
+173
+00:11:32,810 --> 00:11:37,710
+المتباينة المثلثة اللي احنا بنعرفها اللي هو DXY
+
+174
+00:11:38,510 --> 00:11:45,350
+أصغر أو تساوي D X و Z زائد D Z و 100 و Y جاي من من
+
+175
+00:11:45,350 --> 00:11:50,410
+من الهى اللى انتوا بتعرفوها اللى هى لو كان عندى
+
+176
+00:11:50,410 --> 00:11:54,610
+نقطة هي نقطة و هي نقطة فى الفراغ أو فى ال plane
+
+177
+00:11:54,610 --> 00:11:58,510
+المسافة بين هذه و هذه بين D X و Y أكيد أصغر أو
+
+178
+00:11:58,510 --> 00:12:02,750
+تساوي المسافة بين هذه و هذه زائد هذه و هذهأي نقطة
+
+179
+00:12:02,750 --> 00:12:06,350
+أخرى هيعندي X وY لو كانت أي نقطة أخرى Z هيكون
+
+180
+00:12:06,350 --> 00:12:09,590
+مسافة بين X وY أكيد أقل أو يساوي المسافة بين هذه
+
+181
+00:12:09,590 --> 00:12:13,390
+وهذه زائد هذه وهذه هذي ال Triangle اللي قُلتيه
+
+182
+00:12:13,390 --> 00:12:16,330
+طبعا في المثلة أكيد strict لأكبر هذي بحكي عن وين
+
+183
+00:12:16,330 --> 00:12:21,250
+فعلا ما ترى اللي هو ال Rالأرض تربيع الآن قد يكون
+
+184
+00:12:21,250 --> 00:12:24,530
+اللي هو المسافة بالظبط فيها مسواها يعني هذه strict
+
+185
+00:12:24,530 --> 00:12:28,310
+الأكبر دول لكن قد يكونوا سواها لو كانت X هان او Z
+
+186
+00:12:28,310 --> 00:12:32,070
+هان و Y هان فبكون المسافة بين X و Y بالظبط حساوي
+
+187
+00:12:32,070 --> 00:12:35,530
+المسافة بين X و Z زائد المسافة بين Z و Y وعشان هيك
+
+188
+00:12:35,530 --> 00:12:39,670
+تبين ال triangle equality أصغر أو يساوي إذا تحققت
+
+189
+00:12:39,670 --> 00:12:44,990
+الأربع شروط الأمام هذولة automatic automatic بقول
+
+190
+00:12:44,990 --> 00:12:49,780
+على الومن ثم مكانة الـ D metric ما على طول بيصير
+
+191
+00:12:49,780 --> 00:12:54,200
+الـ X والـ D أشمالها metric space بتكون عبارة عن
+
+192
+00:12:54,200 --> 00:12:59,900
+مين؟ عن metric space هذه اللي هي اللي هو تعريف
+
+193
+00:12:59,900 --> 00:13:04,200
+اللي هو ال metric لأن نيجي لبعض الخواص اللي بنقدر
+
+194
+00:13:04,200 --> 00:13:07,280
+نستقيها أو تعريف ال metric space بعض الخواص اللي
+
+195
+00:13:07,280 --> 00:13:11,420
+بنقدر نستقيها من اللي هو التعريف اللي أمامنا
+
+196
+00:13:13,310 --> 00:13:18,550
+الخاصية الأولى بقول لي لو كان عندى N element in N
+
+197
+00:13:18,550 --> 00:13:24,550
+ودي ناخدنا أي X واحد و X اتنين و X N element اللي
+
+198
+00:13:24,550 --> 00:13:28,530
+هي NX اللي بنحكي عليها اللي بنقول عليها متر هيكون
+
+199
+00:13:28,530 --> 00:13:33,070
+المسافة بين distance يعني الـ N عبارة عن بدل اللي
+
+200
+00:13:33,070 --> 00:13:35,490
+هو المسافة بين نجوطين أظهر بس هو المسافة بين
+
+201
+00:13:35,490 --> 00:13:36,350
+نجوطين و نجوطين و نجوطين و نجوطين و نجوطين و
+
+202
+00:13:36,350 --> 00:13:38,370
+نجوطين و نجوطين و نجوطين و نجوطين و نجوطين و
+
+203
+00:13:38,370 --> 00:13:41,910
+نجوطين
+
+204
+00:13:43,110 --> 00:13:48,810
+و Xn أظهر ايش هو المسافة بين X1 و X2 زائد المسافة
+
+205
+00:13:48,810 --> 00:13:56,210
+بين X2 و X3 زائد المسافة بين Xn-1 و Xn يعني هذه
+
+206
+00:13:56,210 --> 00:14:00,850
+تعميل للحالة الأولى هذه بدنا نبرهنها أو برهانها
+
+207
+00:14:00,850 --> 00:14:04,030
+سهل by induction انتوا حالكم بتقدروا تبرهنوها لكن
+
+208
+00:14:04,030 --> 00:14:07,450
+خلينا على السريع اعطيكم outline لبرهانها خليها دي
+
+209
+00:14:07,450 --> 00:14:12,110
+نسميها إيه إيش star عارفين كده بنبرهن by induction
+
+210
+00:14:12,110 --> 00:14:16,860
+أول حاجةأول اشي عشان بنها دي لكل n element صحيحة
+
+211
+00:14:16,860 --> 00:14:21,980
+بتقول for n بتساوي واحدة trivial فالان for n
+
+212
+00:14:21,980 --> 00:14:24,560
+بتساوي اتنين for n بتساوي اتنين
+
+213
+00:14:29,300 --> 00:14:35,100
+اللي هي أصغر حتى التين برضه trivial لو أنا بالساعة
+
+214
+00:14:35,100 --> 00:14:40,020
+تلاتة X1 و X3 أصغر الساعة المسافة بين X1 و X2 زائد
+
+215
+00:14:40,020 --> 00:14:44,700
+المسافة بين X2 و X3 الـ Trivial الـ Trivial برضه
+
+216
+00:14:44,700 --> 00:14:47,620
+هذا من وين جاوب من ال triangle inequality مباشرة
+
+217
+00:14:47,620 --> 00:14:52,370
+من سرعة لأنه كلام سهل أو outline هذا التينبنقول
+
+218
+00:14:52,370 --> 00:14:59,930
+suppose that star is true for n بتساوي k ده نفترض
+
+219
+00:14:59,930 --> 00:15:03,590
+أنه هذه الجملة صحيحة لأن بتساوي k وبدتبتها صحيحة
+
+220
+00:15:03,590 --> 00:15:08,150
+لمين ل k زائد واحد يعني بالمعنى أخر فقضيت هذا صحيح
+
+221
+00:15:08,150 --> 00:15:15,460
+ل k معناته صارت DX1 لعين DXK DX1 لعين DXKأصغر أو
+
+222
+00:15:15,460 --> 00:15:20,080
+يساوي لما أصل لعند XK-1 و XK هذي صحيحة من
+
+223
+00:15:20,080 --> 00:15:24,080
+الhypothesis induction اللي هم بيدثبتها لمين لـ K
+
+224
+00:15:24,080 --> 00:15:29,660
+زائد واحد سهلة نيجي نثبتها لـ K زائد واحد دي X1 و
+
+225
+00:15:29,660 --> 00:15:36,020
+XK زائد واحدما لها أصغر أو يساوي دي X واحد و XK
+
+226
+00:15:36,020 --> 00:15:41,140
+زائد دي XK و XK زائد واحد هذي منين؟ من الـ
+
+227
+00:15:41,140 --> 00:15:45,740
+Triangle equality العادية طبقتها على مين؟ على اللي
+
+228
+00:15:45,740 --> 00:15:48,720
+هو المسافة بين النقطة هذه و النقطة هذه أصغر أو
+
+229
+00:15:48,720 --> 00:15:51,220
+ساوي المسافة بين هذه النقطة و أي نقطة بديها؟ مين
+
+230
+00:15:51,220 --> 00:15:54,260
+هي اللي أخدتها أنا؟ XK زائد المسافة بين النقطة
+
+231
+00:15:54,260 --> 00:15:56,760
+اللي أخدتها و بين هذه هذه اللي هي by the triangle
+
+232
+00:15:56,760 --> 00:16:03,490
+equality اللي هي موجودة الـ M4طيب هذا نفسه هذه
+
+233
+00:16:03,490 --> 00:16:08,390
+أصغر أو ساوي من هنا من ال hypothesis induction
+
+234
+00:16:08,390 --> 00:16:11,810
+اللي مفترضها يعني by star بتكون هذه أصغر أو ساوي
+
+235
+00:16:11,810 --> 00:16:24,510
+dx1 و x2 زائد dx2 و x3 لما أصل لعين زائد dxk و x-1
+
+236
+00:16:24,510 --> 00:16:31,510
+لعين xk و زائد هذه من الأصل dxkو X K زائد واحد
+
+237
+00:16:31,510 --> 00:16:37,110
+معناته صارت اللي هي هذه اللي فوق صحيحة لمين ل K
+
+238
+00:16:37,110 --> 00:16:40,450
+زائد واحد و معناته أنه أثبتنا هذا صحيحة by
+
+239
+00:16:40,450 --> 00:16:44,670
+induction لكل N element هنا إذا هيك بيكون احنا
+
+240
+00:16:44,670 --> 00:16:49,470
+أثبتنا اللي هو اللي هي ال note الأولى و كانت صحيحة
+
+241
+00:16:49,470 --> 00:16:49,750
+دائما
+
+242
+00:16:52,970 --> 00:16:56,510
+طيب يا جماعة اتصلوا عندنا عليه الصلاة والسلام نيجي
+
+243
+00:16:56,510 --> 00:16:59,990
+اللي هو ناخد الملاحظة التانية ايش الملاحظة التانية
+
+244
+00:16:59,990 --> 00:17:06,330
+بتقول بدنا نحرف الآن حاجة اسمها أيش sub space sub
+
+245
+00:17:06,330 --> 00:17:11,090
+space من اسمه sub space اذا اكيد اكيد اللي بدي
+
+246
+00:17:11,090 --> 00:17:14,670
+اشتغل عليها جزء من ال space الأصلي عشان تكون sub
+
+247
+00:17:14,670 --> 00:17:18,150
+space منه وsub space منه كامله بدي اتحقق خياصه
+
+248
+00:17:18,150 --> 00:17:20,770
+يعني الصغير هذا بيكون أيش ايه للكبير يعني بحقق
+
+249
+00:17:20,770 --> 00:17:31,960
+خياصه كاملهفبنقول ان الـ y و d تلدة sub spaceof x
+
+250
+00:17:31,960 --> 00:17:35,000
+و d ايش ال x و ال d طبعا x و d في مفترضين و metric
+
+251
+00:17:35,000 --> 00:17:38,820
+space ايش معناه هذا يكون sub metric space من هذا
+
+252
+00:17:38,820 --> 00:17:45,080
+شرطين الشرط الاول ان ال y جزء من x ها كيف ال y جزء
+
+253
+00:17:45,080 --> 00:17:50,160
+من من من x اي واحد اتنين اتنين ان ال d تلد هذا
+
+254
+00:17:50,160 --> 00:17:53,100
+اللي بترك اللي على ال d اللي على ال y طبعا ال d
+
+255
+00:17:53,100 --> 00:17:56,380
+تلد هذا بشتغل من وين من y cross y و برمي في r
+
+256
+00:17:56,380 --> 00:18:02,160
+positive اتحاد ال zeroهذا D تلدى لازم يكون هو نفسه
+
+257
+00:18:02,160 --> 00:18:06,160
+الـD بس شغل وين؟ طبعا الـD بيشغل على مين؟ الـD
+
+258
+00:18:06,160 --> 00:18:10,440
+بيشغل على X across X لعند R positive اتحاد الـ0
+
+259
+00:18:10,440 --> 00:18:14,860
+الـD برضه أصلا لما هي الـY cross Y جزئية من X
+
+260
+00:18:14,860 --> 00:18:18,960
+cross X فالآن عشان نسميها The subspace لازم تكون D
+
+261
+00:18:18,960 --> 00:18:23,600
+تلدى اللي بتشغل على الـY هي نفسها D لما اشتغلت على
+
+262
+00:18:23,600 --> 00:18:27,770
+الـY across Yيعني بمعنى أخر D تل ده هي the
+
+263
+00:18:27,770 --> 00:18:32,850
+restricted function D on Y cross Y يعني نفسها D بس
+
+264
+00:18:32,850 --> 00:18:37,470
+على مين؟ على Y cross Y في هذه الحالة بنسمي ال Y وD
+
+265
+00:18:37,470 --> 00:18:41,490
+تل ده عبارة عن subspace من مين يا جماعة؟ من اللي
+
+266
+00:18:41,490 --> 00:18:47,140
+هو ال X وDطيب نيجي الآن هذا اللي هو تعريف ال
+
+267
+00:18:47,140 --> 00:18:52,280
+subspace اللي حكينا عنه نيجي الآن نحكي عن بعض
+
+268
+00:18:52,280 --> 00:18:59,940
+الأمثلة عن اللي هوالـ metric spaces نيجي للأمثلة
+
+269
+00:18:59,940 --> 00:19:04,040
+أكيد هنبدأ ببثالنا اللي احنا بنقول عليه سهل و اللي
+
+270
+00:19:04,040 --> 00:19:09,300
+بنعرفه من زمان اللي هو اي مثال اللي هو البثال انه
+
+271
+00:19:09,300 --> 00:19:14,100
+ناخد ال real line ال real line I ر ر line line ال
+
+272
+00:19:14,100 --> 00:19:18,860
+real line هايه هبدنا نعرف المسافة بين X و بين وين
+
+273
+00:19:18,860 --> 00:19:22,400
+و بين Y هنعرف المسافة اللي بتعرفوها انتوا اللي هو
+
+274
+00:19:22,400 --> 00:19:28,700
+DX و Y بدي أعرفها على الـ R يعني هتكون D تبعته من
+
+275
+00:19:28,700 --> 00:19:33,140
+R cross R هترمي وين؟ أكيد هنرميها في R positive
+
+276
+00:19:33,140 --> 00:19:35,700
+تحت Zero عشان يكون metric بالشروط اللي احنا
+
+277
+00:19:35,700 --> 00:19:40,780
+عارفينها طيب، D X Y كده بدي أعرفها عبارة عناللي هو
+
+278
+00:19:40,780 --> 00:19:43,560
+y minus x وحيانا ماكنتش عارف مين البعد ومين
+
+279
+00:19:43,560 --> 00:19:46,280
+الإيجابيل لو ماكنتش عارف كان المجهولات على طول
+
+280
+00:19:46,280 --> 00:19:50,000
+بكتب absolute value ل y minus x وهذا تعني المسافر
+
+281
+00:19:50,000 --> 00:19:53,060
+بين x و y هل هذه بتحقق شروط ا او بتحقق شروط
+
+282
+00:19:53,060 --> 00:19:56,960
+الأربعة ما أنتوا شايفين هذه أول شرطأكبر أو يساوي
+
+283
+00:19:56,960 --> 00:20:00,080
+سفر اتريفياً y minus x أكبر أو يساوي سفر هاي واحد
+
+284
+00:20:00,080 --> 00:20:05,060
+اتنين اكيد dy dx y اللي هو absolute value اللي هو
+
+285
+00:20:05,060 --> 00:20:10,080
+y minus x بساول x minus y اللي هو عبارة عن مين dy
+
+286
+00:20:10,080 --> 00:20:15,380
+ومين وx إذا المسافة بين y وx هي نفس المسافة بين
+
+287
+00:20:15,380 --> 00:20:24,880
+مين x وy الشرط الثالث اللي هو لو كdxy بتساوي سفر
+
+288
+00:20:25,650 --> 00:20:29,790
+بدأ اثبت لكم if and only if اللي هو مين اللي هو x
+
+289
+00:20:29,790 --> 00:20:32,490
+بيساوي y شرط الثالث يا جماعة هاي الشرط الثالث ده
+
+290
+00:20:32,490 --> 00:20:35,690
+انتوا انسطوه هاي الشرط الثالث بدأ اثبت الشرط
+
+291
+00:20:35,690 --> 00:20:39,990
+الثالث هذا بقول دي x y بيساوي سفر if and only if
+
+292
+00:20:39,990 --> 00:20:43,650
+ايش تعرف دي x y بيساوي سفر دي x y اللي هو absolute
+
+293
+00:20:43,650 --> 00:20:48,250
+value لو y minus x بتساوي سفر if and only if هده
+
+294
+00:20:48,250 --> 00:20:51,770
+الأرقام عادية بتعرفوها ان y ايش بتساوي x هذا الشرط
+
+295
+00:20:51,770 --> 00:20:56,250
+الثالث محقق نجي للشرط الرابعالشرف الرابع انتوا
+
+296
+00:20:56,250 --> 00:21:00,150
+عارفين هو هذا ما هي مخاصة absolute value عند D لو
+
+297
+00:21:00,150 --> 00:21:06,430
+أخدنا أي x و y و z دلان وين هو البدايات؟ في R دي x
+
+298
+00:21:06,430 --> 00:21:12,600
+و yبساوة ال absolute value of x minus y بساوة ال
+
+299
+00:21:12,600 --> 00:21:16,520
+absolute value of x minus y هذه absolute value
+
+300
+00:21:16,520 --> 00:21:20,940
+عادية اللي بنعرفها أكيد أكيد أكيد أصغر أو ساوي ال
+
+301
+00:21:20,940 --> 00:21:23,940
+absolute value of x minus z زي ال absolute value
+
+302
+00:21:23,940 --> 00:21:29,650
+of z minus yطب هذه من هي اللي تعرفتها عبارة عن D X
+
+303
+00:21:29,650 --> 00:21:35,910
+و Z و هذه من هي D Z Y إذا D X Y أصغر يساوي D X و Z
+
+304
+00:21:35,910 --> 00:21:40,630
+D Z Y إذا انتحقت شروط الأربعة إذا في المثال الأول
+
+305
+00:21:40,630 --> 00:21:44,750
+الـ D X Y بسبب absolute value X minus Y على الـ A
+
+306
+00:21:44,750 --> 00:21:50,850
+أشمله حقق شروط المتر كلها إذا صارت الـ R محاذةالـ
+
+307
+00:21:50,850 --> 00:21:55,650
+metric اللي هو عبارة عن metric space مع هذه الدالة
+
+308
+00:21:55,650 --> 00:21:58,810
+عبارة عن metric space وهذا بنسميه الـ Euclidean
+
+309
+00:21:58,810 --> 00:22:03,110
+metric space الـ R أو اللي هو اللي مستقبلا نجيه
+
+310
+00:22:03,110 --> 00:22:06,950
+بولدنا ال topology اللي احنا بنعرفه اللي هو بنسميه
+
+311
+00:22:06,950 --> 00:22:12,370
+usual topology هذا مستقبلاهذا المثال الأول سهل
+
+312
+00:22:12,370 --> 00:22:16,010
+البسيط المثال التاني برضه سهل ايش المثال التاني
+
+313
+00:22:16,010 --> 00:22:22,190
+المثال التاني اللي هو بده يعرف الآن metric على مين
+
+314
+00:22:22,190 --> 00:22:26,450
+على ال R تربيهة نشوف ايش ال metric اللي اللي
+
+315
+00:22:26,450 --> 00:22:30,150
+بنعرفه على ال R تربيهة شوفوا يا جماعة صلوا على
+
+316
+00:22:30,150 --> 00:22:33,710
+النبي عليه الصلاة والسلام الان عندي ال 6 بتاعة ال
+
+317
+00:22:33,710 --> 00:22:40,100
+helix أشمالهاهي عبارة عن الـ R تربية هذه الست اللي
+
+318
+00:22:40,100 --> 00:22:45,240
+هي الـ R تربية الأن عصرها إيه اشمالها Ordered pair
+
+319
+00:22:45,240 --> 00:22:53,720
+بتعرف دي ديمن R تربيع across R تربيع وبدأ ارميها
+
+320
+00:22:53,720 --> 00:22:56,340
+في المكان اللي احنا بنرميها اللي هو R بزوجة اتحاد
+
+321
+00:22:56,340 --> 00:23:00,820
+الـ Zero الآن بدأ اعرفها كالتالي العناصر اللي في
+
+322
+00:23:00,820 --> 00:23:04,660
+الـ R تربيع لو أخدت أي X و Y في الـ R تربيع الـ X
+
+323
+00:23:04,660 --> 00:23:07,340
+نفسه هيكون زوج مرتب ما بتعرفين وإذا الـ X إيش
+
+324
+00:23:07,340 --> 00:23:13,210
+هيساوي XI واحد وXI اتنين مثلاو Y أيش هيساوي بساوي
+
+325
+00:23:13,210 --> 00:23:16,530
+Gamma 1 و Gamma 2 خلّيني أستخدم العروف اللاتينية
+
+326
+00:23:16,530 --> 00:23:21,690
+عشان أخلفها عن ال X و ال Y عشان يكون اللغة مميزة
+
+327
+00:23:21,690 --> 00:23:27,610
+هيك أو اللي هو نتوافق مع لغة الكتاب كمان حيش بده
+
+328
+00:23:27,610 --> 00:23:35,400
+يعرف المسافة بين X و Yبساوي ال absolute value ال
+
+329
+00:23:35,400 --> 00:23:39,720
+absolute value اكساي واحد ناقص جامعة واحد زاد ال
+
+330
+00:23:39,720 --> 00:23:43,940
+absolute value اكساي اتنين ناقص جامعة اتنين هذا
+
+331
+00:23:43,940 --> 00:23:47,140
+بتدعي انه metric هو بتدعي انه metric خلينا نشوف
+
+332
+00:23:47,140 --> 00:23:53,840
+شروطه هل متحقق ولا لأ نيجي بناخد الآن خد اي فرعاني
+
+333
+00:23:56,060 --> 00:24:02,500
+يعني x و y و z element in R تربيع شكل هنا 1x
+
+334
+00:24:02,500 --> 00:24:06,360
+بيساوي مثلا إكساي واحد و إكساي اتنين و y بيساوي
+
+335
+00:24:06,360 --> 00:24:11,160
+جامعة واحد و جامعة اتنين و z بتساوي ألفة واحد مثلا
+
+336
+00:24:11,160 --> 00:24:15,180
+و ألف اتنين خلينا نشوف اللي هو الشروط الأربعة طبعا
+
+337
+00:24:15,180 --> 00:24:18,020
+أول تلت شروط عادة انها جماعة سهلة و أنا سهلة طبعا
+
+338
+00:24:18,020 --> 00:24:21,580
+بس خلينا نمروا سريع عليها و انتوا بت .. بت .. بت
+
+339
+00:24:21,580 --> 00:24:29,730
+.. بتعيدوا شغل كتابة الشرط الأولعندي DXY DXY هايه
+
+340
+00:24:29,730 --> 00:24:33,370
+أكيد ايش ماله أكبر أو ساوي سفر واضح لإن هذه أعداد
+
+341
+00:24:33,370 --> 00:24:35,250
+أكبر أو ساوي سفر وهذه أعداد أكبر أو ساوي سفر لإن
+
+342
+00:24:35,250 --> 00:24:39,930
+absolute value اتنين الشرط التالي اللي هو هذا
+
+343
+00:24:39,930 --> 00:24:45,730
+بيساوي سفر DXYهي ساوي سفر إذا و فقط إذا اللي هو
+
+344
+00:24:45,730 --> 00:24:48,810
+هذا بساوي سفر يعني بمعنى أخر absolute value x y
+
+345
+00:24:48,810 --> 00:24:52,970
+واحد ناقص جامعة واحد زائد التاني بسفر هذا أكبر
+
+346
+00:24:52,970 --> 00:24:55,210
+ساوية سفر وهذا أكبر ساوية سفر إذا التانين مع بعض
+
+347
+00:24:55,210 --> 00:24:58,390
+سفر أكيد هذا هيكون سفر وهذا هيكون سفر مش ممكن
+
+348
+00:24:58,390 --> 00:25:01,770
+يواحد يكون سالب التاني لأ التانين كل واحد إيش ماله
+
+349
+00:25:01,770 --> 00:25:06,070
+كل واحد تساوي سفر إذا هذا ناقص هذا بساوي اللي هو x
+
+350
+00:25:06,070 --> 00:25:09,810
+y اتنين ناقص جامعة اتنين بساوي إيه السفر لإن هذا
+
+351
+00:25:09,810 --> 00:25:15,080
+بساوي سفر بسإذا و فقط إذا هذا سفر وهذا سفر وهذا
+
+352
+00:25:15,080 --> 00:25:18,940
+الكلام واضح إيش معناته هذا الكلام هذا معناته إنك
+
+353
+00:25:18,940 --> 00:25:22,280
+ساية واحد إيش هتساوي جامعة واحد إيش هذا معناته
+
+354
+00:25:22,280 --> 00:25:26,120
+كساية اتنين بيساوي جامعة اتنين وهذا شو معناته إنك
+
+355
+00:25:26,120 --> 00:25:30,240
+ساية واحد وكساية اتنين هي نفس جامعة واحد و جامعة
+
+356
+00:25:30,240 --> 00:25:35,040
+اتنين وهذا معناته إن X إيش هي Y إذا المسافة بين X
+
+357
+00:25:35,040 --> 00:25:37,740
+و Y بيساوي سفر إذا و فقط إذا اللي هو ال X بالها
+
+358
+00:25:37,740 --> 00:25:44,050
+بتساوي Yالخاصية التالتة الطبيعية السهلة وسريعة
+
+359
+00:25:44,050 --> 00:25:49,870
+المسافة بين X و Y هي المسافة بين Y و X جامعة واحدة
+
+360
+00:25:49,870 --> 00:26:00,070
+نقص XI واحدة اذا دي DXYبساوة dy او x كلام trivial
+
+361
+00:26:00,070 --> 00:26:04,370
+و سهل طيب ميجي يا جماعة لأ الخاصية الرابعة الخاصية
+
+362
+00:26:04,370 --> 00:26:09,290
+الرابعة ايش الخاصية الرابعة انه دي اكس و اي دي اكس
+
+363
+00:26:09,290 --> 00:26:13,490
+و اي اللي هو اظهر بساوية دي اكس و زي دي زد و اي
+
+364
+00:26:13,490 --> 00:26:18,850
+اظهر عليها الان اكيد xi واحد ناقص جامعة واحد انتبه
+
+365
+00:26:18,850 --> 00:26:26,370
+بس هالشغلأظهر أو ساويت XI واحد ناقص Alpha واحد زاد
+
+366
+00:26:26,370 --> 00:26:30,530
+Alpha واحد ناقص Gamma واحد أكيد بالتالي ال quality
+
+367
+00:26:30,530 --> 00:26:33,550
+بتبعد زمان انت بتلافش weight value لأن هدول أشمال
+
+368
+00:26:33,550 --> 00:26:39,000
+نقابهلجيب شوف أشي اللي بسويه هاد الأن إكساي 2 ناقص
+
+369
+00:26:39,000 --> 00:26:44,680
+Gamma 2 برضه أصغر يساوي إكساي 2 ناقص Alpha 2 زائد
+
+370
+00:26:44,680 --> 00:26:49,920
+Alpha 2 ناقص Gamma 2 برضه طبقت ال .. ال .. ال ..
+
+371
+00:26:49,920 --> 00:26:52,820
+اللي هو مين اللي هو ال triangle inequality تبعت ال
+
+372
+00:26:52,820 --> 00:26:55,820
+absolute value تبعت من تبعت ال calculus زمان الأهم
+
+373
+00:26:55,820 --> 00:26:59,990
+هو هدولة التنتين إجمح هذه زائد هذهأصغر أو يساوي
+
+374
+00:26:59,990 --> 00:27:04,430
+هذه زائد هذه تمشيوا في K4 بعد أذنكم بس بدي أمسح
+
+375
+00:27:04,430 --> 00:27:10,870
+حده بيصير عندي اللي هو التالي بيصير .. أكتب فيه
+
+376
+00:27:10,870 --> 00:27:15,070
+لون تاني عشان نميزه عنه بيصير عندي يا جماعة اللي
+
+377
+00:27:15,070 --> 00:27:20,910
+هو XI واحد ناقص Gamma واحد زائد XI تنين ناقص Gamma
+
+378
+00:27:20,910 --> 00:27:27,350
+تنين أصغر أو يساوي أصغر أو يساوي هذه XI واحد ناقص
+
+379
+00:27:27,350 --> 00:27:32,190
+Alpha واحدهذه زائد هذه ماشي يا جماعة اكساي واحد
+
+380
+00:27:32,190 --> 00:27:36,930
+ناقص ألف اتنين
+
+381
+00:27:36,930 --> 00:27:42,950
+ناقص ألف اتنين زائد الجزء هذا زائد هذا زائد هذا
+
+382
+00:27:42,950 --> 00:27:49,580
+اللي هو الف واحدنقص Gamma 1 زائد Alpha 2 نقص Gamma
+
+383
+00:27:49,580 --> 00:27:54,380
+2 اتطلعوا عليهم هذول واضحة الصورة تتصور بعضكم جال
+
+384
+00:27:54,380 --> 00:27:59,940
+خلصناها هذه هي مين في الواقع هي المسافة بين X وY
+
+385
+00:28:00,870 --> 00:28:04,410
+أصغر أو ساوي هذه في الواقع هذه المسافة بين مين هذه
+
+386
+00:28:04,410 --> 00:28:13,490
+تبعات X وهذه تبعات Z اللي هي Alpha واحد ناقص XI
+
+387
+00:28:13,490 --> 00:28:16,730
+واحد ناقص Alpha واحد زي Alpha واحد ناقص Gamma واحد
+
+388
+00:28:16,730 --> 00:28:21,370
+خليني أخد دليل تبعات Z اللي هي Alpha واحد مع XI
+
+389
+00:28:21,370 --> 00:28:27,630
+واحد مع Alpha واحد و XI اتنينمع Alpha اتنين هذه
+
+390
+00:28:27,630 --> 00:28:29,910
+اتنين آسف هذه اتنين Xi اتنين و Alpha اتنين هي
+
+391
+00:28:29,910 --> 00:28:34,130
+اتنين اتنين مع بعض هذه Alpha اتنين Xi واحد نقص
+
+392
+00:28:34,130 --> 00:28:37,990
+Gamma واحد اصغر sorry Xi واحد نقص Alpha واحد زائد
+
+393
+00:28:37,990 --> 00:28:40,590
+Alpha واحد نقص Gamma واحد وهذه Xi اتنين نقص Alpha
+
+394
+00:28:40,590 --> 00:28:42,350
+اتنين ناخدنا هذول اتنين اتنين مع بعض و جمعها في
+
+395
+00:28:42,350 --> 00:28:46,390
+الأول ليه Xi واحد نقص Alpha واحد وهذه زائد Xi
+
+396
+00:28:46,390 --> 00:28:51,130
+اتنين نقص Alpha اتنين آسفألف اتنين والتانية ألف
+
+397
+00:28:51,130 --> 00:28:54,750
+واحد ناجس جامعة واحد وهيها والتانية ألف اتنين ناجس
+
+398
+00:28:54,750 --> 00:28:58,170
+جامعة اتنين هذه الكلامية في الميزة هذه مين هي هي
+
+399
+00:28:58,170 --> 00:29:04,170
+تبعات X وهي تبعات Z هي هنا هي هنا هي هنا هي X وهي
+
+400
+00:29:04,170 --> 00:29:08,970
+Y و Z اللي فرضناها قبل بشوية كتبناها و اشيلناها Z
+
+401
+00:29:08,970 --> 00:29:12,790
+بساوي اللي هو جامعة واحد وجامعة اتنين صار عندي
+
+402
+00:29:12,790 --> 00:29:19,420
+الآن هذول التنتين هم المثلين DX وZزائد هذول اللي
+
+403
+00:29:19,420 --> 00:29:23,080
+بيمثل من مين هي تبعات Alpha واحد تبعات Z و هذول
+
+404
+00:29:23,080 --> 00:29:27,760
+تبعات من Y الأولى زائد دي Z و Y و بيكون ال
+
+405
+00:29:27,760 --> 00:29:30,980
+triangle inequality أشمالها تحققت و بيكون هذا
+
+406
+00:29:30,980 --> 00:29:38,660
+أثبتنا أن هذا عبارة عن metric space يعني
+
+407
+00:29:38,660 --> 00:29:43,020
+ال D هذاmetric space مع الارض التربية بعضكم أكيد
+
+408
+00:29:43,020 --> 00:29:46,000
+سأل قال طب احنا مافيه metric احنا الزمان اللي
+
+409
+00:29:46,000 --> 00:29:49,160
+اتعلمناه و احنا اصغار اللي هو او احنا في ال .. في
+
+410
+00:29:49,160 --> 00:29:53,280
+ال .. في ال .. حتى في الاعدادية او اللي هو في اللي
+
+411
+00:29:53,280 --> 00:29:56,800
+هي ال calculus احنا بنعرف المسافة بين نقطتين في
+
+412
+00:29:56,800 --> 00:30:04,280
+الفرق لما يكون عندى النقطة x و yاللي هو في الفرق
+
+413
+00:30:04,280 --> 00:30:06,540
+العادي في ال .. في ال .. في ال .. في ال .. في ال
+
+414
+00:30:06,540 --> 00:30:09,320
+plane العادي اللي احنا اخدنا هندسته لما نزجنا
+
+415
+00:30:09,320 --> 00:30:11,920
+الهندسة الإقليدية X بالساعة و كده و Y بالساعة و
+
+416
+00:30:11,920 --> 00:30:16,460
+كده أخدنا المسافة بين X و Y اللي هو عبارة عن الجدر
+
+417
+00:30:16,460 --> 00:30:22,610
+التربيعي ل X I واحد ناقص Gamma واحدالكل تربيع زائد
+
+418
+00:30:22,610 --> 00:30:27,110
+اكسايه تنين ناجس جامعة تنين الكل اياش تربيع اه هذا
+
+419
+00:30:27,110 --> 00:30:30,210
+نفسه metric برضه هذا هيحقق شروطه ال metric و
+
+420
+00:30:30,210 --> 00:30:34,790
+بنسميه برضه اشماله ال Euclidean metric لإن بعد
+
+421
+00:30:34,790 --> 00:30:39,370
+فترة هتلجوني بقول انت بقولها المعلومة هتلجوني بقول
+
+422
+00:30:39,370 --> 00:30:44,670
+في ال final dimensional spaceFinite vector space
+
+423
+00:30:44,670 --> 00:30:46,870
+هذا لاحق ان شاء الله في الـ finite dimensional
+
+424
+00:30:46,870 --> 00:30:48,970
+space يعني الارض تربيع finite dimension, dimension
+
+425
+00:30:48,970 --> 00:30:52,970
+له اتنين في الارض تكعيب في الارض ارخمس ار مليون ار
+
+426
+00:30:52,970 --> 00:30:55,770
+ان هذوله finite dimensional space هنلاقي ال finite
+
+427
+00:30:55,770 --> 00:31:00,390
+dimensional space لو عرفنا كان متر كثير يعرفنا
+
+428
+00:31:00,390 --> 00:31:04,990
+مليون متركعلى الـ جد ما بدك عرف Matrix إذا عرفت
+
+429
+00:31:04,990 --> 00:31:09,430
+Matrix صار عندك Matrix 2، 3، 4، 5 مليون واحد على
+
+430
+00:31:09,430 --> 00:31:13,890
+Final Dimensional Space كلهم هيولدن نفس الـ
+
+431
+00:31:13,890 --> 00:31:16,610
+Topology يعني هيطلع عندنا نفس الـ Topology عشان هي
+
+432
+00:31:17,240 --> 00:31:21,200
+أحنا في الـ R في الـ R في الـ R أو في الـ R تربيه
+
+433
+00:31:21,200 --> 00:31:25,000
+أفضل تكييب هذا الـ Matrix هذا و الـ Matrix هذا
+
+434
+00:31:25,000 --> 00:31:30,340
+التنين R هنجيهم equivalent يعني هناخدشو معناه
+
+435
+00:31:30,340 --> 00:31:34,420
+equivalent هنجيهم نفس ال .. ال .. ال Matrixوهما
+
+436
+00:31:34,420 --> 00:31:38,680
+اللي بيولد الـ usual topology اللي احنا بنعرفه ال
+
+437
+00:31:38,680 --> 00:31:41,480
+usual topology اللي احنا عايشين فيه في ال calculus
+
+438
+00:31:41,480 --> 00:31:45,620
+وفي المعادلة التفاضلية وفي التحليل الحقيقي واحد و
+
+439
+00:31:45,620 --> 00:31:48,220
+و و الاخر تحليل حقيقي اتنين هذا اللي هو ال
+
+440
+00:31:48,220 --> 00:31:52,300
+Euclidean اللي هي ال usual topologyالـ Limit
+
+441
+00:31:52,300 --> 00:31:54,620
+سبعتنا و الـ Continuity بتبعات كلها على أساسها دي
+
+442
+00:31:54,620 --> 00:31:56,740
+مش هأقولكن في هالشغلها دي ان شاء الله بتيجيها
+
+443
+00:31:56,740 --> 00:32:02,700
+لاحقا في حينها بنوضحها أما ملخص الحديث هي عند
+
+444
+00:32:02,700 --> 00:32:06,220
+metric هذا أسمتنا انه metric وهي ال metric تبع مين
+
+445
+00:32:06,220 --> 00:32:09,900
+اللي بنعرفه احنا و هذا ال metric اللي بنعرفه سهلة
+
+446
+00:32:09,900 --> 00:32:12,800
+و أمه أصلا ال team England quality احنا عارفينها
+
+447
+00:32:12,800 --> 00:32:18,260
+هي نقطة هي نقطين هدي مثلا احدثية Xi واحد و Gamma
+
+448
+00:32:18,260 --> 00:32:24,290
+واحد وهدي اللي هياسكساي واحد وكساي اتنين وهذه
+
+449
+00:32:24,290 --> 00:32:30,210
+جامعة واحد و جامعة اتنين هيها المسافة بين هذول
+
+450
+00:32:30,210 --> 00:32:34,910
+التنتين هيها هي عبارة عن اصغر سواء المسافة بين هذه
+
+451
+00:32:34,910 --> 00:32:40,490
+لو كانت اخدت اي زد تاني هاي زد الان قبل ما ناخد ال
+
+452
+00:32:40,490 --> 00:32:43,230
+training inequality هذه احنا لو جينا حسبناها
+
+453
+00:32:43,230 --> 00:32:48,170
+المسافة حساب المسافة سهلةاللي هي بالسير هذه اللي
+
+454
+00:32:48,170 --> 00:32:55,010
+هو طولها عبارة عن جاء اللي هي xi2 جامعة واحد جامعة
+
+455
+00:32:55,010 --> 00:32:58,870
+واحد ناقص xi واحد على الاكسات هذه وهذه عبارة عن
+
+456
+00:32:58,870 --> 00:33:01,750
+طولها جامعة اتنين ناقص xi اتنين فبكون الجدر
+
+457
+00:33:01,750 --> 00:33:06,180
+التربيعيلهذا اللي هي المسافة اللي هو عبارة عن
+
+458
+00:33:06,180 --> 00:33:08,780
+قانون في The Girth في The Girth هذا التربيع بيساوي
+
+459
+00:33:08,780 --> 00:33:11,640
+هذا التربيع زاد هذا التربيع إذا المسافة بينهم اللي
+
+460
+00:33:11,640 --> 00:33:14,940
+هي المسافة بين هذه وهذه طوله عبارة عن جدر التربيع
+
+461
+00:33:14,940 --> 00:33:18,600
+اللي هذه تربيع زاد هذه تربيع فبكون هذا اللي هو ال
+
+462
+00:33:18,600 --> 00:33:22,060
+Euclidean metric اللي إحنا بنعرفه في الأصل وكل
+
+463
+00:33:22,060 --> 00:33:26,550
+الشروط اللي هي اللي عندنا مطبقةعلى الأرض الكعيب
+
+464
+00:33:26,550 --> 00:33:29,730
+بقدر اعمل اشي متشابه يعني على الأرض الكعيب بقدر
+
+465
+00:33:29,730 --> 00:33:33,570
+اقول والله انا بتاخد الهو X في الأرض الكعيب معناته
+
+466
+00:33:33,570 --> 00:33:37,030
+ايش صارت هذه بدل مهنتين تان صارنمي تلاتة اكساي
+
+467
+00:33:37,030 --> 00:33:40,660
+تلاتةماشي وهد جامعة اتنين وهد بيصير جامعة تلاتة
+
+468
+00:33:40,660 --> 00:33:46,120
+فبيصير المسافة هد زاد هد زاد اللي بتعرفونته xi
+
+469
+00:33:46,120 --> 00:33:51,700
+اللي هي تلاتة ناقص جامعة تلاتة لكل تربية هذا برضه
+
+470
+00:33:51,700 --> 00:33:56,700
+اللي هو metric space بيعمل هد D بيعمل من R تكعيب
+
+471
+00:33:56,700 --> 00:34:02,230
+metric space او R تكعيب مع مين مع ال Dواحد قال لي
+
+472
+00:34:02,230 --> 00:34:05,850
+طب حتى in general يا ربي نبدأ نعمل آه صحيح يعني
+
+473
+00:34:05,850 --> 00:34:11,050
+الان لو كانت RN RN اللي هي عناصرها n couples يعني
+
+474
+00:34:11,050 --> 00:34:15,310
+عناصرها xi واحد xi اتنين عند xi ان مع من مع ال
+
+475
+00:34:15,310 --> 00:34:18,790
+metric هذا برضه هتعمل metric space ال metric في
+
+476
+00:34:18,790 --> 00:34:23,230
+هذا الحالة هتكون dxy ال x ايش هتكون xi واحد xi
+
+477
+00:34:23,230 --> 00:34:26,630
+اتنين xi تلاته عند xi انوالـ Y جامعة واحد جامعة
+
+478
+00:34:26,630 --> 00:34:29,550
+اتنين جامعة تلاتة عين جامعة ان فبكون المسافة بينه
+
+479
+00:34:29,550 --> 00:34:34,530
+عبارة عن الجادر التربيعي ل XI واحد ناقص جامعة واحد
+
+480
+00:34:34,530 --> 00:34:39,210
+لكل تربيع زائد لما أصل لآخر واحدة XI ان ناقص جامعة
+
+481
+00:34:39,210 --> 00:34:42,790
+ان لكل تربيع حد هيعمل metric وحده بسميه اللي هو
+
+482
+00:34:42,790 --> 00:34:49,300
+برضه Euclidean metric اللي هو Dimension of Nنفس
+
+483
+00:34:49,300 --> 00:34:53,680
+الأسلوب بقدر أعرف عالمين على الـ Complex plane
+
+484
+00:34:53,680 --> 00:34:59,220
+اللي و CN يعني بمعنى آخر بده يصير ال X عناصره
+
+485
+00:34:59,220 --> 00:35:03,380
+عبارة عن XI واحد و XI اتنين و XI N عناصره ال X
+
+486
+00:35:03,380 --> 00:35:09,100
+بتساوي XI واحد و XI اتنين لعند XI N وكل واحد كل
+
+487
+00:35:09,100 --> 00:35:12,550
+واحد دولة Complex numbers في الـCففي هذه الحالة
+
+488
+00:35:12,550 --> 00:35:17,390
+بأعرف الـ metric بتعديل بسيط اللي هو dxy بساوي
+
+489
+00:35:17,390 --> 00:35:21,610
+الجدر التربيعي له بكتمش اللي هو هذه تربيعه لأنه
+
+490
+00:35:21,610 --> 00:35:25,350
+بيبقى وقم ا شماله بيبقى اللي هو عبارة عن complex
+
+491
+00:35:25,350 --> 00:35:28,330
+number لما أخده الجدر في الآخر بيطلع complex
+
+492
+00:35:28,330 --> 00:35:31,530
+number يعني بيطلعش عدد العدد لازم يكون مسافة كم
+
+493
+00:35:31,530 --> 00:35:34,430
+ولا سافة سفر فباخد اللي هنا ا شمال هنا absolute
+
+494
+00:35:34,430 --> 00:35:39,250
+valuesفبصير هذا الـ metric هذا الـ metric لما أخد
+
+495
+00:35:39,250 --> 00:35:41,730
+absolute value عن ال magnitude يعني عبارة عن عدد
+
+496
+00:35:41,730 --> 00:35:45,130
+صار هذا تربيع زي هذا تربيع زي هذا الأخر تربيع
+
+497
+00:35:45,130 --> 00:35:49,830
+فبكون هذا dxy اللي هو عبارة عن metric على مين على
+
+498
+00:35:49,830 --> 00:35:56,230
+cn و بحقق كل الشروط هذا اللي هو اللي هي أمثلة على
+
+499
+00:35:56,230 --> 00:36:00,890
+اللي هي على ال R و R تربيع و R تكعيب و RN و C و C
+
+500
+00:36:00,890 --> 00:36:08,830
+و C تربيع و C أُس Nالآن نيجي إلى اللي هو مثالنا
+
+501
+00:36:08,830 --> 00:36:13,330
+المهم اللي هو حاجة اسمها sequence space sequence
+
+502
+00:36:13,330 --> 00:36:18,770
+space جماعة من اسمه هو عبارة عن فراغ عناصر أو
+
+503
+00:36:18,770 --> 00:36:26,830
+مجموعة على سرها اللي هي sequences متتابعات لكن
+
+504
+00:36:26,830 --> 00:36:30,910
+هذه المتتابعات بديها تكون bounded شو اللي بتقوله
+
+505
+00:36:30,910 --> 00:36:31,690
+خليني نشوف
+
+506
+00:36:34,860 --> 00:36:41,660
+المهم اللي هو حاجة اسمها ال infinity ايش ال ال
+
+507
+00:36:41,660 --> 00:36:47,020
+infinity يا جماعة ال ال infinity هي كالتالي
+
+508
+00:36:47,020 --> 00:36:53,220
+انعرفها حاجة اسمها sequence space طيب نشوف ايش ال
+
+509
+00:36:53,220 --> 00:36:58,080
+sequence space هذا المصدر بالرمز مين ال infinity
+
+510
+00:36:58,080 --> 00:37:02,290
+هاي ال ال infinity ال sequence spaceعناصره يعني
+
+511
+00:37:02,290 --> 00:37:05,590
+الـ L infinity هو عبارة عن كل الـ sequences X
+
+512
+00:37:05,590 --> 00:37:09,730
+بتساوي قصاي I قصاي I sequence يعني قصاي 1، قصاي 2،
+
+513
+00:37:09,730 --> 00:37:12,010
+قصاي 3، قصاي 4، لملا نهاية من زمان بتعرفوا اللي هي
+
+514
+00:37:12,010 --> 00:37:18,330
+إيش sequences I من عند 1 لملا نهايةsuch that تكون
+
+515
+00:37:18,330 --> 00:37:20,110
+الـ sequence اللي قال الـ infinity مش كل الـ
+
+516
+00:37:20,110 --> 00:37:23,890
+sequences اللي في الدنيا بدياها بدياها تكون XI I
+
+517
+00:37:23,890 --> 00:37:28,550
+is bounded يعني bounded sequence شو معناه bounded
+
+518
+00:37:28,550 --> 00:37:33,740
+sequence؟ يعني في النهاية XI Iاللي هو there exists
+
+519
+00:37:33,740 --> 00:37:38,280
+C element in R such that Xi I أصغر أو يساوي هذا
+
+520
+00:37:38,280 --> 00:37:44,380
+الـ C لكل I بتساوي واحد واتنين أمنة يعني في
+
+521
+00:37:44,380 --> 00:37:48,160
+النهاية العناصر تبعات الـ sequences لن تتجاوز حد
+
+522
+00:37:48,160 --> 00:37:52,520
+معينطبعا هذه الـ C لمن؟ للـ sequence هذه الـ
+
+523
+00:37:52,520 --> 00:37:56,440
+sequence هذه لو سمناها X بتساوي XI I منقول عنها
+
+524
+00:37:56,440 --> 00:38:00,180
+bounded إذا كان فيه إلها C عشان هيك بنقوله CX نرمز
+
+525
+00:38:00,180 --> 00:38:03,360
+الـ X لإنه C هدي لمن؟ لـ X لو كان فيه sequence
+
+526
+00:38:03,360 --> 00:38:08,040
+ثانية بتكون لها X C تانية فاهمين؟اللي أنا أصغر شوه
+
+527
+00:38:08,040 --> 00:38:14,460
+مين CX يعني لو كان في عندي Y بسووه Gamma I وموجودة
+
+528
+00:38:14,460 --> 00:38:17,460
+في الـ Infinity، هتكون bounded هتكون bounded، إيش
+
+529
+00:38:17,460 --> 00:38:20,780
+معناه bounded؟ إنه there exists C ت .. الـ C إيش
+
+530
+00:38:20,780 --> 00:38:24,920
+معناها؟ إنها للـ Y، عشان هيك بيسميها Cy ثابت طبعا
+
+531
+00:38:24,920 --> 00:38:28,520
+such that اللي هو Gamma I أصغر أو سوى الـ C اللي
+
+532
+00:38:28,520 --> 00:38:32,810
+لاجيناه هذه الـ sequence ده Y لكل مين Iمثلًا
+
+533
+00:38:32,810 --> 00:38:37,110
+أعطيكم مثال يعني عشان تشوفوا مين ممكن نقعد هان لو
+
+534
+00:38:37,110 --> 00:38:41,410
+جينا أخذنا ال sequence واحد و نص و تلت و ربع اللي
+
+535
+00:38:41,410 --> 00:38:44,390
+هي ال sequence واحد على أن بمعنى آخر واضح إن ال
+
+536
+00:38:44,390 --> 00:38:49,640
+sequence هذه أشمالها is boundedالـ Terms تبعتها لا
+
+537
+00:38:49,640 --> 00:38:52,840
+يمكن أن تتجاوز الواحد يعني الـ bound لها إيش واحد
+
+538
+00:38:52,840 --> 00:38:56,320
+يعني هنا في هذه الحالة جامع I لو سمناها جامع I هذه
+
+539
+00:38:56,320 --> 00:39:00,320
+أصغر أو شاومين واحد لكل I فهذه ال sequence أكيد
+
+540
+00:39:00,320 --> 00:39:05,360
+موجودة وين في ال infinity بينما لو أجيته لل
+
+541
+00:39:05,360 --> 00:39:11,580
+sequence التالية اللي هو 1 و 2 و 3 و 4أو un in
+
+542
+00:39:11,580 --> 00:39:14,260
+general هذه الـ sequence غير موجودة في الـ L
+
+543
+00:39:14,260 --> 00:39:16,900
+infinity لأنها is not bounded لأنها عمالها بتروح
+
+544
+00:39:16,900 --> 00:39:20,300
+إلى مقل النهائية قاعدة ففيش عدد أكبر من كل عناصر
+
+545
+00:39:20,300 --> 00:39:22,780
+الـ sequence إذا نضحت شو معناته اللي هي ال
+
+546
+00:39:22,780 --> 00:39:26,380
+infinity الست هذه أن عناصرها عبارة عن bounded
+
+547
+00:39:26,380 --> 00:39:30,660
+sequences طيب ليش انت بتأمل هيك يعني انت بتبني ال
+
+548
+00:39:30,660 --> 00:39:33,400
+L infinity عشان بعد شوية أنا بدي أعرّفلكم metric
+
+549
+00:39:34,280 --> 00:39:37,940
+الـ Metric اللي بتعرف الكمياء عشان يكون موجود لازم
+
+550
+00:39:37,940 --> 00:39:41,180
+تكون ال sequences bounded لازم مدان bounded يعني
+
+551
+00:39:41,180 --> 00:39:45,040
+انت شكلك بتحكي عن supremum و infimum اه بتعرف ال
+
+552
+00:39:45,040 --> 00:39:47,940
+metric عن طريق ال supremum و ال infimum او بالظبط
+
+553
+00:39:47,940 --> 00:39:53,360
+عن طريق ال supremum عشان اللي هو أضمن ال supremum
+
+554
+00:39:53,360 --> 00:39:56,340
+موجود لازم تكون اللي هي اللي هي اللي بتاخده لها ال
+
+555
+00:39:56,340 --> 00:40:01,170
+supremum تكون bounded عشان هيكالان نرتب امورنا
+
+556
+00:40:01,170 --> 00:40:05,230
+ونقول
+
+557
+00:40:05,230 --> 00:40:10,770
+التالي هذه مبررات اللي حكيتها اللي بدها تخليني
+
+558
+00:40:10,770 --> 00:40:12,530
+اعرف metric D
+
+559
+00:40:17,040 --> 00:40:20,280
+ايش الـ metric اللي بدى أعرفه عليه اللي هو لو أخدت
+
+560
+00:40:20,280 --> 00:40:25,300
+الآن I X بيساوي X I I sequence و Y بيساوي Gamma I
+
+561
+00:40:25,300 --> 00:40:27,820
+sequence وين موجودة التنتين في القلة الانفينيتي
+
+562
+00:40:27,820 --> 00:40:33,240
+يعني bounded بدى أعرف اللي هو ال metric بين X و Y
+
+563
+00:40:33,240 --> 00:40:36,460
+لل sequences هدول اللي في القلة الانفينيتي بيساوي
+
+564
+00:40:36,460 --> 00:40:42,220
+super amount ل X I I ناقص Gamma I over mean over I
+
+565
+00:40:42,400 --> 00:40:47,360
+سيبرون المضمون يوجد آه لإن XI I bounded و Gamma I
+
+566
+00:40:47,360 --> 00:40:51,080
+bounded إذا هذا أبعاد bounded ليش؟ لإن بيصير XI I
+
+567
+00:40:51,080 --> 00:40:56,080
+ناقص Gamma I أصغر أوي ساوي XI I أعداد هذه الأعداد
+
+568
+00:40:56,080 --> 00:41:00,050
+دا جماعة زائد Gamma Iوهذه الـ bounded sequence
+
+569
+00:41:00,050 --> 00:41:04,890
+بالـ CX تبعتها وهذه الـ bounded بالـ CY تبعتها إذا
+
+570
+00:41:04,890 --> 00:41:08,830
+في النهاية كل ال terms هذولة bounded by اللي هو
+
+571
+00:41:08,830 --> 00:41:12,590
+العدد اللي هو المجموح هذولة التنتين يعني صارت هذه
+
+572
+00:41:12,590 --> 00:41:15,950
+bounded مادام bounded إذا مضمون من الـ supermoment
+
+573
+00:41:15,950 --> 00:41:21,590
+أشماله موجود الآن إذا هذا هو الـ defined فعلا الآن
+
+574
+00:41:21,590 --> 00:41:26,170
+الشرط الأول إنه metricالان هذا أكبر أساوي 0 إذا
+
+575
+00:41:26,170 --> 00:41:31,870
+الـ Supremum يشماله أكبر أساوي 0 إذا الـ Dxy أكبر
+
+576
+00:41:31,870 --> 00:41:37,410
+أساوي 0 اتنين Dxy بساوي 0 .. قاعد ببره أن أنا
+
+577
+00:41:37,410 --> 00:41:42,850
+انمترك .. انمترك هذا Dxy بساوي 0 if and only if ال
+
+578
+00:41:42,850 --> 00:41:46,050
+Supremum .. هي .. هي .. هي .. هي .. Supremum لـ Xi
+
+579
+00:41:46,050 --> 00:41:51,230
+I ناجس Gamma I over I بساوي 0إذا الـ supremum اللي
+
+580
+00:41:51,230 --> 00:41:55,990
+هين سفر قطعاً قطعاً قطعاً كلهين سفاري لإن لو ال
+
+581
+00:41:55,990 --> 00:41:59,030
+supremum .. لو .. لو واحدة فيه مش سفر معناته ال
+
+582
+00:41:59,030 --> 00:42:01,470
+supremum مش سفر هيكون هذا اللي .. اللي .. اللي هو
+
+583
+00:42:01,470 --> 00:42:07,610
+مش سفر إذا if and only if xi i ناجس gamma i بتساوي
+
+584
+00:42:07,610 --> 00:42:13,100
+سفر لكل iماشي معناته هذا ايش معناته ان هذا سفر
+
+585
+00:42:13,100 --> 00:42:18,080
+معناته xi I بسوء جامع I لكل I معناته ايش معناته xi
+
+586
+00:42:18,080 --> 00:42:21,980
+I بسوء جامع I يعني كل عناصر اللي هو ال sequence xi
+
+587
+00:42:21,980 --> 00:42:23,900
+واحد بسوء جامع واحد بسوء جامع اتنين بسوء جامع
+
+588
+00:42:23,900 --> 00:42:26,700
+اتنين يعني ال sequences بتسوء اتنين يعني if and
+
+589
+00:42:26,700 --> 00:42:32,020
+only if x بتسوء y وهذا الشرط الثالث تحقق نيجي
+
+590
+00:42:32,020 --> 00:42:36,940
+للشرط من الثالث الشرط الثالث ده من سهل هنا دي x و
+
+591
+00:42:36,940 --> 00:42:40,610
+yاللي هو عبارة عن الـ supermoment Xi I نقص Gamma I
+
+592
+00:42:40,610 --> 00:42:43,550
+طب ما هي Xi I نقص Gamma I absolute value و هي
+
+593
+00:42:43,550 --> 00:42:46,770
+نفسها absolute value Gamma I نقص Xi I و من ثم ال
+
+594
+00:42:46,770 --> 00:42:51,210
+supermoment بحثة صح و من ثم بيساوي Dxy بساوي Dy Ox
+
+595
+00:42:51,210 --> 00:42:56,390
+إذن هذا متحقق automatic نيجي الآن لشرط ثالث و شرط
+
+596
+00:42:56,390 --> 00:42:59,970
+ثالث انتبهولي عليه مش صعب بس يعني ان شاء الله
+
+597
+00:42:59,970 --> 00:43:01,410
+بوضحكوا معاه تماما و انتوا فاهمون
+
+598
+00:43:04,170 --> 00:43:07,770
+اللي هو يا جماعة الـ Triangle Inqualite الـ
+
+599
+00:43:07,770 --> 00:43:12,470
+Triangle Inqualite نشوف
+
+600
+00:43:12,470 --> 00:43:16,810
+معلش
+
+601
+00:43:16,810 --> 00:43:21,270
+مساحة الـ Metric هي مكتوبة أنا مابهمش طيب الآن
+
+602
+00:43:21,270 --> 00:43:24,030
+بتاخد عشان اثبت ال Triangle Inqualite انتوا
+
+603
+00:43:24,030 --> 00:43:29,810
+المفروض احفظوها بتاخد أي Xسيكوانس بيساوي Xi I
+
+604
+00:43:29,810 --> 00:43:34,950
+وسيكوانس Y بيساوي Gamma I وسيكوانس Delta Z بيساوي
+
+605
+00:43:34,950 --> 00:43:43,070
+Alpha Iالان يا جماعة انتبهولي لشغلها لأن لكل I في
+
+606
+00:43:43,070 --> 00:43:47,990
+الدنيا لو جيت أخدت XI I ناقص Gamma I ماشي الحال
+
+607
+00:43:47,990 --> 00:43:52,230
+هدولة تبعات مين X و Y أكيد أصغرها يساوي بال
+
+608
+00:43:52,230 --> 00:43:58,390
+triangle inequality هذا الكلام for any fixed I
+
+609
+00:43:58,390 --> 00:44:03,400
+ماشيI arbitrary لكن fixed بحكي عن واحدة بعيّنة لكن
+
+610
+00:44:03,400 --> 00:44:08,200
+arbitrary شيلته arbitrary منه أصغر أو ساوي Xi I
+
+611
+00:44:08,200 --> 00:44:11,940
+ناقص Alpha I بدخل هذه الحر أنا triangling quality
+
+612
+00:44:11,940 --> 00:44:18,360
+زي Alpha I ناقص Gamma I بدخل ما يخدمني طيب الآن
+
+613
+00:44:18,360 --> 00:44:21,460
+هذا
+
+614
+00:44:21,460 --> 00:44:26,200
+الكلام صحيح لكل I في الدنيا إذا أكيد أكيد أكيد هذه
+
+615
+00:44:27,380 --> 00:44:31,280
+أصغر أو يساوي سبريمانها اكس اي انا ناجسها معايا
+
+616
+00:44:31,280 --> 00:44:36,160
+ناجس الفايا over I ليش؟ لأن السبريمان أكبر أوي
+
+617
+00:44:36,160 --> 00:44:38,880
+ساوي أكيد اللي هو واحدة اللي ماخود عليها السبريمان
+
+618
+00:44:38,880 --> 00:44:44,790
+ماشي أو هذهبرضه أصغر أو يساوي الـ Supremum تبعها
+
+619
+00:44:44,790 --> 00:44:48,890
+Supremum Alpha I ناجز Gamma I إذا صار عندي Over I
+
+620
+00:44:48,890 --> 00:44:52,910
+إذا صار عندي هذا أكبر أو يساوي هذا و هذا أكبر أو
+
+621
+00:44:52,910 --> 00:44:55,610
+يساوي هذا مجموح أن أكبر أو يساوي هذا الكلام سهل
+
+622
+00:44:55,610 --> 00:45:01,750
+هذه مين هي يا جماعة هذه اللي هي بالظبط D X و Z هذه
+
+623
+00:45:01,750 --> 00:45:07,040
+تبعات ال X هيهم و هذه تبعات مين ال Zزائد هذي مين
+
+624
+00:45:07,040 --> 00:45:12,100
+يا جماعة دي هذي ال alpha I تبع ال Z دي Z وال gamma
+
+625
+00:45:12,100 --> 00:45:17,020
+I تبع ات مين ال Y دي Z أو Y إذا صار عندي لكل fixed
+
+626
+00:45:17,020 --> 00:45:22,060
+I هذا المقدار أصغر أو يساوي هذا المقدار طبعا هذا
+
+627
+00:45:22,060 --> 00:45:26,920
+المقدار عدن عن عددعدد عدد عدد إذا صار عندك xi I
+
+628
+00:45:26,920 --> 00:45:34,400
+ناجس جامع I لكل I في الدنيا أظهر أو يساوي ال D X و
+
+629
+00:45:34,400 --> 00:45:39,660
+Z زائد ال D Z و Y و زي ما قلت لكم هذا عدد صار هذا
+
+630
+00:45:39,660 --> 00:45:45,900
+عبارة عن upper bound للمجموعة المتكونة من xi واحد
+
+631
+00:45:45,900 --> 00:45:50,400
+ناجس جامع واحد و xi اتنين ناجس جامع اتنين إلى مالا
+
+632
+00:45:50,400 --> 00:45:54,150
+نهاية إذا صار هذا upper bound لها بالستما دام هو
+
+633
+00:45:54,150 --> 00:45:59,590
+other bound إذا هو أكبر أو يساوي ال least other
+
+634
+00:45:59,590 --> 00:46:04,790
+bound لهم يا بمعنى أخر صار هذا أكبر أو يساوي ال
+
+635
+00:46:04,790 --> 00:46:08,130
+supremum لهم لأن ال supremum هو ال least other
+
+636
+00:46:08,130 --> 00:46:13,990
+bound إذا هذا اللي هو أصلا إيش اسمه اللي سمناه
+
+637
+00:46:13,990 --> 00:46:15,750
+عبارة عن DX
+
+638
+00:46:18,090 --> 00:46:21,910
+ومين؟ OY إذا صار عندي DX وY أصغر سوى DX وZ زي
+
+639
+00:46:21,910 --> 00:46:27,270
+الـDZ OY إذا هي كما نكون أثبتنا هذا برضه عبارة عن
+
+640
+00:46:27,270 --> 00:46:31,950
+إيش عبارة عن metric إذا صار عندي اللي هو اللي
+
+641
+00:46:31,950 --> 00:46:35,970
+أمامنا يا جماعة اللي هو ال ال infinity مع هذا ال
+
+642
+00:46:35,970 --> 00:46:40,550
+metric دي على هذا الأساس التعريف عبارة عن metric
+
+643
+00:46:40,550 --> 00:46:45,870
+spaceاللي هو الـ L infinity تبعنا وهذا من الأمثلة
+
+644
+00:46:45,870 --> 00:46:52,730
+المهمة والملازمة معنا على طول الفصل طيب برضه space
+
+645
+00:46:52,730 --> 00:46:58,330
+آخر مهم اللي هو space تبعنا تبع زمان عناصره اللي
+
+646
+00:46:58,330 --> 00:47:03,130
+هو the space of continuous functions on a closed
+
+647
+00:47:03,130 --> 00:47:09,890
+bounded interval نشوف إيش بقوله هذا طبعا معلوماته
+
+648
+00:47:09,890 --> 00:47:14,140
+من ال calculusبتيجي انا دايما بحكيها في القصة دي
+
+649
+00:47:14,140 --> 00:47:17,940
+اللي هي المعلومات حول اللي هو الدول المتصلة على
+
+650
+00:47:17,940 --> 00:47:21,880
+closed bounded interval ايش اللي بقوله اللي بقوله
+
+651
+00:47:21,880 --> 00:47:26,710
+صلى الله عليه وسلمبدي أخد اللي هو مجموع اسمها C A
+
+652
+00:47:26,710 --> 00:47:30,810
+وB بدرمزلها هذه C اللي هي continuous والـ A وB هي
+
+653
+00:47:30,810 --> 00:47:32,670
+الـ closed bounded interval اللي عليها بدعرف
+
+654
+00:47:32,670 --> 00:47:37,270
+الدالة هي عبارة عن كل الدوال X ده سبيها X الدالة
+
+655
+00:47:37,270 --> 00:47:42,190
+اللي ماخدة من A وB وبتود في R يعني real valued
+
+656
+00:47:42,190 --> 00:47:47,140
+functionthe set of all real valued functions on a
+
+657
+00:47:47,140 --> 00:47:51,420
+closed bounded interval which are continuous such
+
+658
+00:47:51,420 --> 00:47:57,880
+that X is continuous إذا هذا الفراغ هو عبارة عن
+
+659
+00:47:57,880 --> 00:48:03,080
+الفراغ المتكون من جميع الديال المتصلة الحقيقية
+
+660
+00:48:03,080 --> 00:48:08,960
+طبعا على الفترة A O B الآن مدامة X متصلة على
+
+661
+00:48:08,960 --> 00:48:13,520
+الفترة A O B كنا نحكي إعلان في الcalculus ونقولإذا
+
+662
+00:48:13,520 --> 00:48:20,280
+كانت المشكلة مستمرة في مقارنة مغلقة فهي تصل إلى
+
+663
+00:48:20,280 --> 00:48:24,300
+مقارنة أعلى ومقارنة أعلى في هذه المقارنة وهذا
+
+664
+00:48:24,300 --> 00:48:28,940
+الكلام بيحكي .. بيحكي .. بيحكيكميا تشريع لكيف نود
+
+665
+00:48:28,940 --> 00:48:31,640
+الabsolute وضمان وجود ال absolute maximum
+
+666
+00:48:31,640 --> 00:48:34,920
+وabsolute minimum على الدالة المتصلة على مقارنة
+
+667
+00:48:34,920 --> 00:48:40,220
+مغلقة حتى في الثانويةفهذه معلومة سابقة إذا ما دامت
+
+668
+00:48:40,220 --> 00:48:42,920
+الدالة متصلة على closed bounded interval إذا ال
+
+669
+00:48:42,920 --> 00:48:46,240
+maximum و ال minimum لها إيه شماله مضمون إنه موجود
+
+670
+00:48:46,240 --> 00:48:50,000
+طب ليش بتحكي هيك عشان بدي أعرف الآن ال metric على
+
+671
+00:48:50,000 --> 00:48:52,720
+أساسي على هذا الأساس يعني بدي أعرف ال metric
+
+672
+00:48:52,720 --> 00:48:56,340
+بواسطة ال maximum قبل بشوية ال infinity حكينا عنه
+
+673
+00:48:56,340 --> 00:49:01,300
+ال supremumهنا على غراره و البرهان نفس البرهان
+
+674
+00:49:01,300 --> 00:49:04,660
+اللي هو على غرار البرهان الأولاني هنا هناك كان ال
+
+675
+00:49:04,660 --> 00:49:07,980
+sequences وهنا للدول هنا كان ال bounded sequences
+
+676
+00:49:07,980 --> 00:49:11,060
+وهنا إشماله للدول المتصلة على closed bounded
+
+677
+00:49:11,060 --> 00:49:16,000
+intervalسألنا بالـ Function specific of A و B دعوا
+
+678
+00:49:16,000 --> 00:49:17,580
+C و A و B يكونوا مجموعة من جميع الاصطناعات
+
+679
+00:49:17,580 --> 00:49:21,360
+الواقعية التي مستمرة في الـ closed bounded
+
+680
+00:49:21,360 --> 00:49:24,800
+interval إذا لكل X و Y في C و A و B أريد أن أعرف
+
+681
+00:49:24,800 --> 00:49:31,340
+الـ D X Y الـ D X Y للإكسات و الوايات الموجودة في
+
+682
+00:49:31,340 --> 00:49:35,910
+C و B يعني الدوال المتصلة X و Y هي عبارة عنالـ
+
+683
+00:49:35,910 --> 00:49:40,870
+Maximum لأ X of T X of T الـ T المتغير اللي في الـ
+
+684
+00:49:40,870 --> 00:49:44,910
+A و الـ B ناقص الـ Y of T و الـ T طبعا اللي موجودة
+
+685
+00:49:44,910 --> 00:49:48,550
+على الفترة A و B يعني اللي هو بدّي المسافة بين X و
+
+686
+00:49:48,550 --> 00:49:52,290
+Y هي عبارة عن الـ Maximumاللي هو بين .. اللي هو
+
+687
+00:49:52,290 --> 00:49:56,670
+البعد بين كل point و التانية عند X و T نقص Y و T
+
+688
+00:49:56,670 --> 00:50:00,170
+لأن هل ال maximum موجودة؟ أه طبعاً، ليش؟ لأن X
+
+689
+00:50:00,170 --> 00:50:03,610
+متصل و Y متصل، إذا حصل طرح المتصل إذا حصل طرح
+
+690
+00:50:03,610 --> 00:50:06,970
+المتصل، إذا صار من التمتين متصلات أو هذه كلها على
+
+691
+00:50:06,970 --> 00:50:09,590
+بعض is a continuous function on a closed bounded
+
+692
+00:50:09,590 --> 00:50:12,510
+interval إذا لازم يكون لها maximum و minimum ..
+
+693
+00:50:12,510 --> 00:50:16,050
+إذا ال maximum و ال minimum مضموناتوجودهم في
+
+694
+00:50:16,050 --> 00:50:20,830
+الفترة a و b إذا عندي اللي هو التعريف و ال defined
+
+695
+00:50:20,830 --> 00:50:25,570
+مافيش مشاكل في التعريف البرهان .. البرهان سهل إنه
+
+696
+00:50:25,570 --> 00:50:29,230
+مترك واحد هذا absolute value إذا أكبر أو ساوية سفر
+
+697
+00:50:29,230 --> 00:50:31,450
+إذا ال maximum ما هي شماله أكبر أو ساوية سفر إذا
+
+698
+00:50:31,450 --> 00:50:35,370
+دي اكس واي automatic أكبر أو ساوية سفر شاطر أول
+
+699
+00:50:35,370 --> 00:50:40,050
+متحقق سريع لإنه هذا نفس البرهان اللي قبله اتنين لو
+
+700
+00:50:40,050 --> 00:50:46,030
+الان دي اكس واي بساوية سفرفاندول F الماكسمن بيساوي
+
+701
+00:50:46,030 --> 00:50:49,410
+صفر الماكسمن بيساوي صفر لأن كل واحدة من هدولة صفر
+
+702
+00:50:49,410 --> 00:50:51,870
+لأنها absolute value لأن كل واحدة من هدولة صفر
+
+703
+00:50:51,870 --> 00:50:51,870
+لأنها absolute value لأن كل واحدة من هدولة صفر
+
+704
+00:50:51,870 --> 00:50:51,990
+لأنها absolute value لأن كل واحدة من هدولة صفر
+
+705
+00:50:51,990 --> 00:50:52,490
+لأنها absolute value لأن كل واحدة من هدولة صفر
+
+706
+00:50:52,490 --> 00:50:53,090
+لإنها absolute value لإنها absolute value لإنها
+
+707
+00:50:53,090 --> 00:50:54,310
+absolute value لإنها absolute value لإنها absolute
+
+708
+00:50:54,310 --> 00:50:54,670
+value لإنها absolute value لإنها absolute value
+
+709
+00:50:54,670 --> 00:50:56,150
+لإنها absolute value لإنها absolute value لإنها
+
+710
+00:50:56,150 --> 00:50:56,310
+absolute value لإنها absolute value لإنها absolute
+
+711
+00:50:56,310 --> 00:50:56,350
+value لإنها absolute value لإنها absolute value
+
+712
+00:50:56,350 --> 00:50:58,310
+لإنها absolute value لإنها absolute value لإنها
+
+713
+00:50:58,310 --> 00:51:03,240
+absolute value لناقص y of t بتساوي سفر لكل t في
+
+714
+00:51:03,240 --> 00:51:09,260
+الفترة a وb وهذا معناته أن x of t هي نفسها y of t
+
+715
+00:51:09,260 --> 00:51:12,540
+الـ delta نفس ال .. نفس الاشي لكل t في domain هن
+
+716
+00:51:12,540 --> 00:51:17,560
+يعني بمعنى أخر اللي هو delta n x بتساوي y وهو
+
+717
+00:51:17,560 --> 00:51:21,520
+المطلوب الشرط الثالث الشرط السهل هذا اللي بنقول
+
+718
+00:51:21,520 --> 00:51:27,970
+عنه dxy بساوي dy وx لإنهDxy هو الماكسيمة x of t
+
+719
+00:51:27,970 --> 00:51:30,650
+نقص y of t absolute value ال absolute value x of t
+
+720
+00:51:30,650 --> 00:51:33,270
+و y of t هو نفس ال absolute value y of t نقص x of
+
+721
+00:51:33,270 --> 00:51:36,830
+t إذا الماكسيمة عاملة تلتين زي بعض إذا Dxy بيساوي
+
+722
+00:51:36,830 --> 00:51:40,610
+Dy و X نجي للشرط الثالث الأخير و الشرط الثالث
+
+723
+00:51:40,610 --> 00:51:45,890
+الأخير برضه زي مين زي الشرط الثالث اللي في المثال
+
+724
+00:51:45,890 --> 00:51:56,620
+اللي دبلو الان خدوا any T any T limiting a و bx of
+
+725
+00:51:56,620 --> 00:52:01,060
+t نقص y of t أخد دالة تالتة arbitrarily present في
+
+726
+00:52:01,060 --> 00:52:04,320
+ال continuous أكيد absolute value انهم أصغر أو
+
+727
+00:52:04,320 --> 00:52:12,560
+ساول absolute value of x of t نقص z of t زائد زائد
+
+728
+00:52:12,560 --> 00:52:19,160
+اللي هو absolute value of z of t-Y of T هذا الكلام
+
+729
+00:52:19,160 --> 00:52:21,960
+لكل T لأن هذا الكلام Absolute Value Triangle
+
+730
+00:52:21,960 --> 00:52:24,640
+Inquality تبعت زمان لأن هذا أعداد X of T قيمت
+
+731
+00:52:24,640 --> 00:52:28,560
+عددها وY of T قيمت عددها وZ of T قيمت عددها إذا
+
+732
+00:52:28,560 --> 00:52:32,260
+هذه Triangle Inquality أشمالها صحيحة دائما وزي ما
+
+733
+00:52:32,260 --> 00:52:37,580
+عملنا قبل شوية أصغر أو ساوي هذه اللي هي نفسها أصغر
+
+734
+00:52:37,580 --> 00:52:45,320
+أو ساوي ال maximum تبعتها X of T-Z of Tوهذه أصغر
+
+735
+00:52:45,320 --> 00:52:50,920
+في شوية maximum تبعدها Z of T ماقص Y of T وهذه
+
+736
+00:52:50,920 --> 00:52:58,960
+عبارة عن DXYDX و Z أسف وهذه تانية DZY وهذه صار عدد
+
+737
+00:52:58,960 --> 00:53:03,760
+أكبر أساوي هذوله لكل T هذه أكبر أساوي X of T نقص Y
+
+738
+00:53:03,760 --> 00:53:06,800
+of T لكل T هنا إذن أكيد أكبر أساوي مين ال maximum
+
+739
+00:53:06,800 --> 00:53:09,560
+لإن ال maximum واحدة منهن لإن احنا بنقول ال tens
+
+740
+00:53:09,560 --> 00:53:14,360
+is maximum وين فيها إذن واحدة منهن إذن DX وZY أكبر
+
+741
+00:53:14,360 --> 00:53:19,200
+أو ساوي ال maximum هذه اللي هو عبارة عن DXY وهو
+
+742
+00:53:19,200 --> 00:53:22,130
+المطلوبإذاً صار اللي هو هنا الـD برضه إيش ماله
+
+743
+00:53:22,130 --> 00:53:27,730
+عبارة عن metric space ماشي يا بنات صلوا عنا بيهم
+
+744
+00:53:27,730 --> 00:53:34,510
+عليه الصلاة والسلام الآن المثال الأخير اللي هو
+
+745
+00:53:34,510 --> 00:53:39,050
+حاجة اسمها بنسميه discrete metric space discrete
+
+746
+00:53:39,050 --> 00:53:44,570
+metric space discrete metric space هو اللي بولد ال
+
+747
+00:53:44,570 --> 00:53:48,830
+discrete topologyإن شاء الله بنجيه في حينه ال
+
+748
+00:53:48,830 --> 00:53:54,910
+discrete metric space بناخد 6x أي 6x و بعرف عليها
+
+749
+00:53:54,910 --> 00:53:58,870
+D إيش ال D اللي بدي أعرفها اللي بدي أسميه metric
+
+750
+00:53:58,870 --> 00:54:02,090
+الآن هذا ال D هسميه metric آسف هسميه اللي هو
+
+751
+00:54:02,090 --> 00:54:06,670
+discrete ال D هعرفها لأي نقطين في ال X المسافة
+
+752
+00:54:06,670 --> 00:54:12,260
+بينهم هسميهم يا صفر يا واحدهذا هي المتريك اللي
+
+753
+00:54:12,260 --> 00:54:13,940
+اريد ان اعرفه انا او هذا الديالة اللي اريد ان
+
+754
+00:54:13,940 --> 00:54:19,400
+اعرفها Dxy بتساوي سفر إذا كانت X بتساوي Y و بتساوي
+
+755
+00:54:19,400 --> 00:54:23,580
+واحد إذا كانت X أشمالها لاتساوي Y هاي كل قصتنا إذا
+
+756
+00:54:23,580 --> 00:54:28,420
+المتريك اللي بندعي انه متريك إنه قمتين يا سفر في
+
+757
+00:54:28,420 --> 00:54:32,440
+حالة المساوية يا واحد في حالة عدم المساوية إذا X
+
+758
+00:54:32,440 --> 00:54:38,260
+وD هيعملني metric space اثبت اثبات سهل أول حاجة
+
+759
+00:54:39,780 --> 00:54:45,100
+واضح ان Dxy أكبر و ساوي سفر Dxy أكبر و ساوي سفر
+
+760
+00:54:45,100 --> 00:54:47,340
+لأن قيمته يا سفر يا واحد إذا ما أكبر و ساوي سفر
+
+761
+00:54:47,340 --> 00:54:52,140
+اتنين ال Dxy
+
+762
+00:54:52,140 --> 00:55:01,870
+بساوي سفر إذا و فقط إذا ال X متساوي و متتعريفلأن
+
+763
+00:55:01,870 --> 00:55:05,150
+لو كانت X Y بيساوي 0 أكيد X بيساوي Y ولو كانت X
+
+764
+00:55:05,150 --> 00:55:09,650
+بيساوي Y أكيد X بيساوي 0، بيساوي 0، بيساوي 0،
+
+765
+00:55:09,650 --> 00:55:09,690
+بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0،
+
+766
+00:55:09,690 --> 00:55:10,650
+بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0،
+
+767
+00:55:10,650 --> 00:55:11,570
+بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0،
+
+768
+00:55:11,570 --> 00:55:19,670
+بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0، بيساوي 0،
+
+769
+00:55:19,670 --> 00:55:28,100
+بيساوي 0، بيساوي 0، بيساوي 0، بيساللي هو إننا نثبت
+
+770
+00:55:28,100 --> 00:55:30,300
+الـ Triangle Inquality انتبه على ال Triangle
+
+771
+00:55:30,300 --> 00:55:33,220
+Inquality ال Triangle Inquality مش غلبتها كتير
+
+772
+00:55:33,220 --> 00:55:36,300
+بسيطة يعني ان شاء الله ده بيكتمك و نخلصناها عيندي
+
+773
+00:55:36,300 --> 00:55:41,660
+بتاخد الآن أي X و أي Y و أي Z وين موجودات في ال X
+
+774
+00:55:41,660 --> 00:55:50,340
+هدولة اللي هين حالتين الحالة الأولى X بتساوي Y
+
+775
+00:55:50,340 --> 00:55:58,260
+الحالة التانية Xلا تساوي y في غيرها بالنسبالي ال X
+
+776
+00:55:58,260 --> 00:56:02,760
+و ال Y لأ احتمالات ال X و ال Y لبعض هذه بتساوي هذه
+
+777
+00:56:02,760 --> 00:56:09,260
+او هذه بتساوي هذه لو X بتساوي Y فبتصير ال D X و Y
+
+778
+00:56:09,260 --> 00:56:14,500
+بتساوي صفر لأن اي ان كانت ال Z بتساويهم ولا
+
+779
+00:56:14,500 --> 00:56:18,260
+بتساويهم مش فارقة كتير ليش لأنه هتكون هذه اكيد
+
+780
+00:56:18,260 --> 00:56:25,280
+اصغر او ساوي D X و Zزائد D Z و Y لأن هذولا قيمهم
+
+781
+00:56:25,280 --> 00:56:30,260
+يا سفر يا واحد إذا مستحيل هذه تكون أكبر منهم لأنه
+
+782
+00:56:30,260 --> 00:56:33,800
+مجموح أنه يكون يا سفر يا واحد يا اتنين حسب
+
+783
+00:56:33,800 --> 00:56:38,500
+العلاقات اللي موجودة هنا ماشي الحال طيب إذا صار
+
+784
+00:56:38,500 --> 00:56:42,480
+عندي الآن الحالة الأولى متحققة ده الحالة التانية X
+
+785
+00:56:42,480 --> 00:56:46,680
+لات سوى Y X لات سوى Y في عندي في حالة .. لان بدأت
+
+786
+00:56:46,680 --> 00:56:50,920
+أجيب I Zبتدافع تاني DX وY أزرع تاني DX وZ زي دي Z
+
+787
+00:56:50,920 --> 00:56:54,960
+وY في هذه الحالة عندي تلت حالات في داخل الحالة هذه
+
+788
+00:56:54,960 --> 00:57:01,340
+يما التنتين هدولة باختلف عن الـ Z يعني لا ال X
+
+789
+00:57:01,340 --> 00:57:07,420
+بتساوي Yو طبعا هي المفروض لا ال X بتساوي Z ولا ال
+
+790
+00:57:07,420 --> 00:57:11,200
+Y بتساوي Z يعني ولا واحدة منهم التلاتة مختلفات
+
+791
+00:57:11,200 --> 00:57:16,160
+الحالة الأولى الحالة التانية ان هدول مختلفات صح بس
+
+792
+00:57:16,160 --> 00:57:19,740
+ال Z بتساوي واحدة منهم إذا الحالة الأولى ان
+
+793
+00:57:19,740 --> 00:57:22,940
+المختلفات و ال Z مختلفة عنها التلتين الحالة
+
+794
+00:57:22,940 --> 00:57:27,580
+التانية ان ال Z بتساوي واحدة منهمإذا الحالتين، يا
+
+795
+00:57:27,580 --> 00:57:31,140
+الـ z بتسويش ولا واحدة منهن، يا واحدة منهن، الان
+
+796
+00:57:31,140 --> 00:57:34,980
+ولا واحدة منهن أيها، الحالة التانية إنها بتساوي
+
+797
+00:57:34,980 --> 00:57:40,480
+واحدة منهم، يعني z بتساوي x و z لا تساوي y أو z
+
+798
+00:57:40,480 --> 00:57:46,320
+بتساوي y و z لا تساوي x، يعني الحالة التانية هذه،
+
+799
+00:57:46,320 --> 00:57:51,750
+اللي هو بتساوي واحدة من هدول،مستحيل تسوي أن تتمثل
+
+800
+00:57:51,750 --> 00:57:54,730
+مع بعض لأن هنا تحت عدوان إيه شمال و X ذات شويه إذا
+
+801
+00:57:54,730 --> 00:57:57,950
+هذه التلت حالات اللي عندى في الحالة اللي عندى هذه
+
+802
+00:57:57,950 --> 00:58:00,450
+الحالة التانية جزء إيه الجزء الأول جزء الثاني
+
+803
+00:58:00,450 --> 00:58:05,930
+الحالة الأولى اللي هو Dxy أكيد برضه أصغر يسوي Dx
+
+804
+00:58:05,930 --> 00:58:14,970
+وz زائد Dz وY ليه؟ لأن Dx وz واحدDX و Z DX و Y
+
+805
+00:58:14,970 --> 00:58:18,610
+واحد مختلفات DX و Z DX و Y واحد مختلفات DX و Z DX
+
+806
+00:58:18,610 --> 00:58:21,050
+و Y واحد مختلفات DX و Z DX و Y واحد مختلفات DX و Z
+
+807
+00:58:21,050 --> 00:58:22,170
+DX و Y واحد مختلفات DX و Z DX و Y واحد مختلفات DX
+
+808
+00:58:22,170 --> 00:58:24,010
+و Z DX و Z DX و Y واحد مختلفات DX و Z DX و Z DX و
+
+809
+00:58:24,010 --> 00:58:24,430
+Y واحد مختلفات DX و Z DX و Z DX و Z DX و Z DX و Z
+
+810
+00:58:24,430 --> 00:58:27,410
+DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z
+
+811
+00:58:27,410 --> 00:58:28,290
+DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z
+
+812
+00:58:28,290 --> 00:58:30,530
+DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z
+
+813
+00:58:30,530 --> 00:58:30,610
+DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z
+
+814
+00:58:30,610 --> 00:58:30,610
+DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z DX و Z
+
+815
+00:58:30,610 --> 00:58:34,780
+DXالآن الحالة التانية z بتساوي x اول حاجة هدول
+
+816
+00:58:34,780 --> 00:58:38,940
+المختلفة اذا واحد اولا واحدة z بتساوي x اذا ندي
+
+817
+00:58:38,940 --> 00:58:42,680
+سفر z تتساوي y واحد اذا بتظل الحالة المساوية
+
+818
+00:58:42,680 --> 00:58:45,380
+متحققة اذا متحققة ال triangle inequality ال
+
+819
+00:58:45,380 --> 00:58:49,920
+triangle inequality اصغر او يساوي الحالة التالتة
+
+820
+00:58:49,920 --> 00:58:55,640
+بيصير اللي هو الحالة التالتة عنديهذه قولة واحدة
+
+821
+00:58:55,640 --> 00:59:03,540
+واحدة لأن XZ يتساوي Y XZ يتساوي Y وهو سفرزي ده
+
+822
+00:59:03,540 --> 00:59:08,180
+تساوي x واحد إذا واحد بساوي اللي هو الحالة اللي هي
+
+823
+00:59:08,180 --> 00:59:11,880
+الواحد إذا في الحالة هذه برضه دائما دي x و y أصغر
+
+824
+00:59:11,880 --> 00:59:14,980
+يساوي دي x و z زائد دي z و y من كل الحالات التانية
+
+825
+00:59:14,980 --> 00:59:17,000
+الحالة الأولى و الحالة التانية و ال sub cases اللي
+
+826
+00:59:17,000 --> 00:59:21,060
+من التلاتة دجينا دائما دي x و y أصغر يساوي دي x و
+
+827
+00:59:21,060 --> 00:59:24,920
+z زائد دي z و y و بهذا بيكون عندي هذا عبارة عن
+
+828
+00:59:24,920 --> 00:59:30,340
+metric space هذا بيسميه discrete metric space و
+
+829
+00:59:30,340 --> 00:59:35,340
+بيكون عندكم الآن homeworkالسؤال الأول، هذه السؤال
+
+830
+00:59:35,340 --> 00:59:41,140
+الأول، السؤال الأول، والسؤال التاني، هو أسئلة
+
+831
+00:59:41,140 --> 00:59:44,720
+الكتاب. الآن هتلاقوا في الـ Homework، اللي هو
+
+832
+00:59:44,720 --> 00:59:49,100
+Homework، وهنا Homework Star، اللي بدكم تسلمونيها
+
+833
+00:59:49,100 --> 00:59:52,240
+Homework Star، يعني بتكون تسلموني أربعة أو خمسة أو
+
+834
+00:59:52,240 --> 00:59:55,120
+تمانية أو عشرة من الكتاب، والواحد والتانين الـ
+
+835
+00:59:55,120 --> 00:59:58,180
+Above هذولة، هذول اللي بتكون تسلمونيها من ضمن الـ
+
+836
+00:59:58,180 --> 01:00:01,150
+Homeworks اللي اتفقنا عليهم،الان هدولة انت في
+
+837
+01:00:01,150 --> 01:00:05,450
+البيت بدك تحلهم اللي هو بفضل انك تطلع عليهم و
+
+838
+01:00:05,450 --> 01:00:08,050
+تحلهم بس تكشف السبب اني يعني لا سبب بتعرفوش تحلوها
+
+839
+01:00:08,050 --> 01:00:12,650
+انا حل كل الأسئلة بنقدر نعطيكم اللي هو اذا ما
+
+840
+01:00:12,650 --> 01:00:16,630
+أسافناش الوجد في داخل المحاضرة بعطيكم الحلول و
+
+841
+01:00:16,630 --> 01:00:21,230
+بتحلوها و بتشوفوها و الاشي اللي بدكميا مش فاهمينه
+
+842
+01:00:21,230 --> 01:00:26,350
+بنشوف ساعات مكتبية او في داخل هنا بنجاوبكم و هيك
+
+843
+01:00:26,350 --> 01:00:29,680
+بتكون نهينا المحاضرةو السلام عليكم و رحمة الله و
+
+844
+01:00:29,680 --> 01:00:30,040
+بركاته
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/CRLpGXH9NAM.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/CRLpGXH9NAM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..899e2168c5279f214a5579a9c9c0ceb3db738ca0
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/CRLpGXH9NAM.srt
@@ -0,0 +1,3011 @@
+1
+00:00:05,060 --> 00:00:07,820
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,820 --> 00:00:10,740
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,740 --> 00:00:16,160
+آله وصحبه أجمعين هذه المحاضرة رقم 22 مساب تحليل
+
+4
+00:00:16,160 --> 00:00:18,960
+اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:18,960 --> 00:00:22,440
+الإسلامية مجلسية الرياضيات اليوم وصلنا لعند أو
+
+6
+00:00:22,440 --> 00:00:26,530
+اليوم هنحكي في هذه المحاضرة على ثلاثة ستة اللي هي 
+
+7
+00:00:26,530 --> 00:00:30,470
+تحت عنوان Total Orthonormal Sets and Sequences
+
+8
+00:00:30,470 --> 00:00:34,130
+إحنا حكينا عن الـ Orthonormal Sets و Orthonormal
+
+9
+00:00:34,130 --> 00:00:38,070
+Sequences الآن الفكرة في الـ Total Orthonormal
+
+10
+00:00:38,070 --> 00:00:42,950
+Sets and Sequences إحنا
+
+11
+00:00:42,950 --> 00:00:49,330
+بدنا نبحث عن set إنّها من خلالها نجيب الـ space كله
+
+12
+00:00:49,880 --> 00:00:55,760
+كل space يعني ما كأنه مشابه لعمل اللي هي roughly
+
+13
+00:00:55,760 --> 00:00:59,600
+هذا الكلام مشابه لعمل الـ bases في حالة اللي هو في
+
+14
+00:00:59,600 --> 00:01:02,480
+الـ finite dimensional case في حالة الـ finite
+
+15
+00:01:02,480 --> 00:01:05,140
+dimensional case اللي بتجيب الـ space اللي هو اللي
+
+16
+00:01:05,140 --> 00:01:08,060
+أنتوا عارفين الـ bases إنّه على طول اللي هو linearly
+
+17
+00:01:08,060 --> 00:01:12,120
+independent linearly independent معناته
+
+18
+00:01:12,120 --> 00:01:16,500
+يعني إنّ هي بمعنى آخر إنّه اقتصادي إنّي أنا ما بحطّش أش
+
+19
+00:01:16,500 --> 00:01:21,480
+زيادة بقدر أجيبه منهم الجزء الثاني إنّه بعمل span و
+
+20
+00:01:21,480 --> 00:01:25,820
+بعمل كل space الآن في حالة الـ infinite dimensional
+
+21
+00:01:25,820 --> 00:01:29,600
+في الـ separable الأمور كمان أبسط شوية في حالة الـ
+
+22
+00:01:29,600 --> 00:01:34,740
+non separable spaces بصير الأمور حتى شغل فيها شوية
+
+23
+00:01:34,740 --> 00:01:39,720
+أعقد إحنا هنشتغل بما ي .. خلّانا نقول بما يناسبنا 
+
+24
+00:01:39,720 --> 00:01:44,460
+في الـ course هذا يعني اللي هيعمل ال .. العمل هذا
+
+25
+00:01:44,460 --> 00:01:48,480
+اللي هو إنّه من خلاله إنّه هنحاول نجيب الـ space أو
+
+26
+00:01:48,480 --> 00:01:51,600
+اللي حصل عن الـ space رفلي هذا الكلام اللي هو حاجة
+
+27
+00:01:51,600 --> 00:01:57,100
+اسمها total orthonormal set المرة الفاترة حكينا عن
+
+28
+00:01:57,100 --> 00:01:59,640
+الـ orthonormal set اليوم ده نحكي عن الـ total اللي
+
+29
+00:01:59,640 --> 00:02:03,800
+هي هتعمل هذا العمل خلينا نيجي نطلع على اللي هو شو
+
+30
+00:02:03,800 --> 00:02:06,760
+معناته الـ definition أو شو الـ definition لـ الـ
+
+31
+00:02:06,760 --> 00:02:09,280
+total set أو الـ issue وبعدين نيجي للي هو الـ 
+
+32
+00:02:09,280 --> 00:02:12,950
+orthonormal اللي إحنا عارفينه الـ Total set أو الـ
+
+33
+00:02:12,950 --> 00:02:16,610
+Fundamental set هي عبارة عن a norm of this base X
+
+34
+00:02:16,610 --> 00:02:19,170
+في أي norm of this base in general إحنا بس شغلنا
+
+35
+00:02:19,170 --> 00:02:22,810
+هيكون في الـ Hilbert is a subset M عبارة عن مجموعة ZM
+
+36
+00:02:22,810 --> 00:02:27,370
+of X whose span is dense in X يعني بس المطلوب منها
+
+37
+00:02:27,370 --> 00:02:31,450
+إنّ سبانها .. سبان .. بقول على room total .. إذا 
+
+38
+00:02:31,450 --> 00:02:37,080
+كان span للـ closure بيساوي مين؟ كل space X فهذه
+
+39
+00:02:37,080 --> 00:02:41,880
+الحالة بنسمي اللي هي الـ set أم إيه شمالها is total
+
+40
+00:02:44,210 --> 00:02:48,210
+الآن a total orthonormal set هي بتكون total في نفس
+
+41
+00:02:48,210 --> 00:02:51,370
+الوجه إيه شمالها orthonormal يعني الجهتين والـ
+
+42
+00:02:51,370 --> 00:02:55,590
+orthonormal أنتوا عارفين شو معناه orthonormal الـ 
+
+43
+00:02:55,590 --> 00:02:59,630
+inner product بين كلتين تان مختلفتين صفر وبين
+
+44
+00:02:59,630 --> 00:03:04,270
+الواحدة ونفسها عبارة عن واحد اطلع لفوق الآن بعض
+
+45
+00:03:04,270 --> 00:03:10,150
+الملاحظات عندي الملاحظتين اللي عندي أمورهم خلينا
+
+46
+00:03:10,150 --> 00:03:14,090
+نقول مقدور عليها وفي إشي يعني trivial في حالة الـ
+
+47
+00:03:14,090 --> 00:03:17,610
+finite dimensional والتانية اللي هي في حالة الـ non
+
+48
+00:03:17,610 --> 00:03:20,910
+separable هذا خارج نطاق شغلنا فإحنا الملاحظات
+
+49
+00:03:20,910 --> 00:03:24,550
+التانية اللي هنحكيهم بشكل أساسي يعني اللي هو برهان
+
+50
+00:03:24,550 --> 00:03:27,230
+هنا الجزء الأول الـ trivial اللي هو بما يتعلق بالـ
+
+51
+00:03:27,230 --> 00:03:30,730
+finite dimensional والتاني بده شوية شغل بتعلق
+
+52
+00:03:30,730 --> 00:03:33,710
+بنظرية اللي خدناها اللي هناخدهم إيش هنا الملاحظات
+
+53
+00:03:33,710 --> 00:03:38,990
+التانية؟ In every Hilbert space H لأنّ أنا أنا
+
+54
+00:03:38,990 --> 00:03:42,250
+قاعد بده أروح باتجاه إنّه هو هذا الـ total orthonormal 
+
+55
+00:03:42,250 --> 00:03:47,680
+set هي اللي هتجيب لي الـ space فعليها هسمي الـ
+
+56
+00:03:47,680 --> 00:03:51,220
+dimension زي ما بنسمي الـ dimension على الـ bases
+
+57
+00:03:51,220 --> 00:03:55,180
+في الحالة اللي هي الـ finite dimensional هنحن بنسمي
+
+58
+00:03:55,180 --> 00:03:57,700
+الـ bases اللي هو الـ dimension اللي هنا على حسب
+
+59
+00:03:57,700 --> 00:04:00,660
+اللي هو الـ total orthonormal set اللي عندك انتبهش
+
+60
+00:04:00,660 --> 00:04:03,800
+بقول in every Hilbert space H لـ H سواء صفر there
+
+61
+00:04:03,800 --> 00:04:07,680
+exists a total orthonormal set يعني مضمون إنّه أيّ
+
+62
+00:04:07,680 --> 00:04:10,500
+Hilbert space H سواء الـ finite dimension في حالة الـ 
+
+63
+00:04:10,500 --> 00:04:14,180
+finite اللي هو الـ bases ما قيّاش بتثبيت إنّه يكون اللي
+
+64
+00:04:14,180 --> 00:04:17,940
+هي الـ norm لكل واحدة بيساوي واحد الـ .. الـ .. الـ ..
+
+65
+00:04:17,940 --> 00:04:20,680
+الحالة الـ inseparable حالة الـ non inseparable
+
+66
+00:04:20,680 --> 00:04:23,680
+انسوها مش .. مش مدّيعنة الحالة الـ inseparable اللي
+
+67
+00:04:23,680 --> 00:04:28,700
+هو فيه hint عليها في .. في الكتاب أيّ Hilbert space
+
+68
+00:04:28,700 --> 00:04:35,220
+H مضمون له total orthonormal set هاي واحد اثنين كلّ
+
+69
+00:04:35,220 --> 00:04:38,160
+الـ total orthonormal set في الـ Hilbert space H
+
+70
+00:04:38,160 --> 00:04:40,760
+لايه تساوي صفر أيّ Hilbert space الـ total
+
+71
+00:04:40,760 --> 00:04:43,240
+orthonormal set لهم كلهم have the same
+
+72
+00:04:43,240 --> 00:04:46,960
+cardinality يعني اللي هو زي في حالة الـ bases اللي 
+
+73
+00:04:46,960 --> 00:04:50,820
+هي نفس العدد هي the same cardinality لخوف إنّها
+
+74
+00:04:50,820 --> 00:04:55,680
+تكون إيه شمالها infinite number of elements الآن
+
+75
+00:04:55,680 --> 00:04:59,100
+بناء عليه مدام كلهن لهم نفس الـ cardinality هذه الـ 
+
+76
+00:04:59,100 --> 00:05:01,200
+cardinality اللي لهم هي اللي بنسميها الـ dimension
+
+77
+00:05:01,200 --> 00:05:05,400
+لهلـ Hilbert space اللي بنحكي عنه where the 
+
+78
+00:05:05,400 --> 00:05:08,220
+cardinality of the total orthonormal sit in a
+
+79
+00:05:08,220 --> 00:05:12,140
+Hilbert space إيه شمالها أو صفر الآن هذا اللي هي الأولى
+
+80
+00:05:12,140 --> 00:05:16,130
+اللي هي اللي بدّها الـ hint للبرهانة Where the
+
+81
+00:05:16,130 --> 00:05:18,670
+cardinality of the total orthonormal set in
+
+82
+00:05:18,670 --> 00:05:23,570
+Hilbert 3H0900 is called the Hilbert dimension or
+
+83
+00:05:23,570 --> 00:05:25,990
+orthogonal dimension of H
+
+84
+00:05:36,100 --> 00:05:38,960
+ملاقى باسيس ما يكونش هيك الأمر في الـ Final
+
+85
+00:05:38,960 --> 00:05:42,080
+Dimension لك إذا H بتساوي صفر الـ Hilbert
+
+86
+00:05:42,080 --> 00:05:47,240
+Dimension اللي نعرفه هو الـ Zero اللي هو الـ
+
+87
+00:05:47,240 --> 00:05:53,060
+Dimension له بروف left to the reader اللي فيه هند
+
+88
+00:05:53,060 --> 00:05:57,080
+في الكتاب الجزء
+
+89
+00:05:57,080 --> 00:06:00,520
+اللي هو الـ separable اللي المطلوب نيجي للنظرية 
+
+90
+00:06:00,520 --> 00:06:06,320
+اللي عندنا اطلع لفوق شوية أيوة هنا وقفت بقول لي let
+
+91
+00:06:06,320 --> 00:06:09,820
+m be a subset of an inner product space X ماشي
+
+92
+00:06:09,820 --> 00:06:14,950
+الحالة عندي M subset من مين؟ من inner product مش الـ
+
+93
+00:06:14,950 --> 00:06:18,870
+part space inner product بلزم يشترط بها then الشرط
+
+94
+00:06:18,870 --> 00:06:25,030
+الأول if M is total in X then X element in X and X
+
+95
+00:06:25,030 --> 00:06:28,350
+عمودية على X implies X إيش بتساوي؟ بتساوي صفر هذا
+
+96
+00:06:28,350 --> 00:06:31,310
+كله على بعض شو معناه إنّه لما تكون X في X و X
+
+97
+00:06:31,310 --> 00:06:34,770
+عمودية على M لازم يعطيني إنّ X بتساوي صفر يعني
+
+98
+00:06:34,770 --> 00:06:38,830
+وكأني بدّي أقول اللي هي بدل هذه كلّها إنّ M
+
+99
+00:06:38,830 --> 00:06:43,370
+orthogonal بتساوي 0 بس إنّ كلّ X عمودي على M هيطلع إيش
+
+100
+00:06:43,370 --> 00:06:48,010
+بس؟ هو الصفر يعني و كأني بقول إنّ M Orthogonal هو
+
+101
+00:06:48,010 --> 00:06:51,970
+صفر يعني لو كانت M Total in X then M Orthogonal
+
+102
+00:06:51,970 --> 00:06:56,830
+بتساوي صفر الآن الجزء الثاني إذا كانت X Complete
+
+103
+00:06:56,830 --> 00:07:01,190
+يعني Hilbert Space بمعنى آخر و if the condition
+
+104
+00:07:01,190 --> 00:07:06,270
+اللي هو M Orthogonal بتساوي صفر is satisfied then
+
+105
+00:07:06,270 --> 00:07:12,880
+M إيش هتطلع؟ Total Set in X ماشي الحالة البرهان بقى 
+
+106
+00:07:12,880 --> 00:07:18,240
+فيه أخدنا المرة الفاتة نظرية في حالة الـ H H اللي
+
+107
+00:07:18,240 --> 00:07:22,700
+هي Hilbert space وكأنه بكون عندي M orthogonal و M
+
+108
+00:07:22,700 --> 00:07:27,000
+subset منها أخدناها بتصير M orthogonal بتساوي صفر
+
+109
+00:07:27,000 --> 00:07:35,060
+if and only if M أو لسبان لـ M is dense in mean in
+
+110
+00:07:35,060 --> 00:07:41,450
+H أخدناها المرة الماضية هدف عن استخدامها الكلام
+
+111
+00:07:41,450 --> 00:07:47,410
+هذا عبارة عن إعادة صياغة لهذه النظرية تقريبا اللي
+
+112
+00:07:47,410 --> 00:07:52,770
+هو بلغة الـ total لأنّ الـ total عرفناها إيش ماله، الـ
+
+113
+00:07:52,770 --> 00:07:55,870
+span لـ omicron بتساوي إيش، الـ space، الـ space
+
+114
+00:07:55,870 --> 00:08:01,710
+كله نجي الآن البرهان لت H بي the completion of X
+
+115
+00:08:01,710 --> 00:08:04,250
+لأنّه عشان .. ليش أخدت completion للـ X؟ لأنّه أنا 
+
+116
+00:08:04,250 --> 00:08:08,110
+بدأ أستخدم نيل النظرية هذه اللي هي بتعتمد على إيش
+
+117
+00:08:08,110 --> 00:08:12,350
+إنّه تكون H عبارة عن الـ part space وإحنا ضمنين إنّه
+
+118
+00:08:12,350 --> 00:08:17,770
+product إيه له completion، الـ completion بتكون X
+
+119
+00:08:17,770 --> 00:08:21,780
+then C ما إحنا عارفين لما نركبنا اللي هو عملنا الـ
+
+120
+00:08:21,780 --> 00:08:25,160
+completion بتكون الـ X dense فيه then X can be
+
+121
+00:08:25,160 --> 00:08:29,580
+regarded ممكن تعتبر as a subspace of H which is
+
+122
+00:08:29,580 --> 00:08:34,960
+dense in مين؟ in H طيب however M نفسها is total in
+
+123
+00:08:34,960 --> 00:08:38,800
+X مازال total in X إذا الـ closure إلها with
+
+124
+00:08:38,800 --> 00:08:43,480
+respect to X هي .. السباق .. آسف .. السباق لـ M الـ
+
+125
+00:08:43,480 --> 00:08:46,760
+closure إلها with respect to X هي سواء مين؟ الـ X
+
+126
+00:08:46,760 --> 00:08:50,770
+dense فيها والـ X نفسها أصلاً dense في الـ H فبكون
+
+127
+00:08:50,770 --> 00:08:54,410
+السبان لـ M closure with respect to H هيطلع برضه
+
+128
+00:08:54,410 --> 00:08:58,970
+مين؟ H فبتكون it is dense in مين؟ in H إذا صار هذا
+
+129
+00:08:58,970 --> 00:09:03,090
+متحقق إذا أكيد الـ M Orthogonal إيش هتساوي؟ هتساوي 
+
+130
+00:09:03,090 --> 00:09:06,610
+صفر إذا M Orthogonal هذا من لمّا إيش اللي حكيت
+
+131
+00:09:06,610 --> 00:09:11,890
+عنها ديك اسمها ليه لمّا ثلاثة ثلاثة سبعة اللي
+
+132
+00:09:11,890 --> 00:09:17,620
+بعدها مباشرة خلي بس نزلت شوية عشان نشوف النص اللي
+
+133
+00:09:17,620 --> 00:09:21,620
+بعدها إذا كانت X Complete يعني X is Hilbert space
+
+134
+00:09:21,620 --> 00:09:27,080
+و M Orthogonal بتساوي 0 من هذه مباشرة مباشرة هيكون
+
+135
+00:09:27,080 --> 00:09:32,120
+اللي هو الـ M Orthogonal إيش بتساوي؟ و هذه Span
+
+136
+00:09:32,120 --> 00:09:36,120
+Closure بتساوي H متكافئتين إذا على طول بنستخدمها
+
+137
+00:09:36,120 --> 00:09:40,980
+لهذه بصير عندي الآن H Complete و M Orthogonal Zero
+
+138
+00:09:40,980 --> 00:09:45,490
+إذا عليه طلعت على طول لسبان Closure إيش بيساوي؟ بيساوي
+
+139
+00:09:45,490 --> 00:09:49,430
+الـ H لسبان Closure بيساوي H شو معناته؟ M is total
+
+140
+00:09:49,430 --> 00:09:57,670
+واضحة طيب اللي قلته يا جماعة إنّه بما إنّه X 
+
+141
+00:09:57,670 --> 00:10:03,160
+M Orthogonal بتساوي صفر إذا كانت completeو بواسطتها
+
+142
+00:10:03,160 --> 00:10:08,120
+النظرية أنه مادامت M Orthogonal Zero بتطلع لـ Span
+
+143
+00:10:08,120 --> 00:10:11,180
+لـ M closure إيش بيساوي؟ إتش يعني Span لـ M between
+
+144
+00:10:11,180 --> 00:10:18,090
+Mين إتش يعني M is total هي عرفنا بـ totalالنظرية 
+
+145
+00:10:18,090 --> 00:10:25,550
+تلاتة ستة تلاتة تلاتة
+
+146
+00:10:25,550 --> 00:10:32,840
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتةالـ
+
+147
+00:10:32,840 --> 00:10:37,260
+orthonormal set M in a Hilbert space H is total in 
+
+148
+00:10:37,260 --> 00:10:41,740
+H if and only if الـ equality بتصير يعني الـ bar θ
+
+149
+00:10:41,740 --> 00:10:44,000
+summation بدل ما كانت بيصير ده تكون أي شمالها
+
+150
+00:10:44,000 --> 00:10:48,420
+بيكون بيصير الـ summation للـ X والـ E K تربيع K over 
+
+151
+00:10:48,420 --> 00:10:52,380
+K بيساوي من Normal X تربيع for all X المتناجح إذا 
+
+152
+00:10:52,380 --> 00:10:58,910
+بتتذكروا المرة الماضية قلنا بس على جهة هنا هذه اللي
+
+153
+00:10:58,910 --> 00:11:01,510
+هو الـ terms اللي جوا الـ for real series هذول
+
+154
+00:11:01,510 --> 00:11:05,750
+coefficients هذولة كلهين is far ما عدا countable
+
+155
+00:11:05,750 --> 00:11:08,990
+number منهم قلنا الـ countable number هو اللي بتكون
+
+156
+00:11:08,990 --> 00:11:12,030
+اللي هي ممكن تكون non-zero element لكن كل الباقي
+
+157
+00:11:12,030 --> 00:11:15,910
+إيش ماله يعني مش فارقة معايا في الآخر هذه over k
+
+158
+00:11:15,910 --> 00:11:20,260
+لو كانت uncountable اللي هي العدادبظل اللي هي
+
+159
+00:11:20,260 --> 00:11:24,780
+الشيء اللي فيه قيمة عددية غير الـ Zero بيكون فعلا
+
+160
+00:11:24,780 --> 00:11:29,580
+هو إيش ماله countable طيب هذا على جهة بس الآن بدنا
+
+161
+00:11:29,580 --> 00:11:32,480
+نأخذ الاتجاه الأول وبعدين الاتجاه الثاني أول
+
+162
+00:11:32,480 --> 00:11:36,500
+اتجاه بيقول لي بدنا .. الآن عندي .. بدنا نثبت أنه 
+
+163
+00:11:36,500 --> 00:11:37,700
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+164
+00:11:37,700 --> 00:11:37,920
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+165
+00:11:37,920 --> 00:11:38,120
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+166
+00:11:38,120 --> 00:11:39,440
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+167
+00:11:39,440 --> 00:11:39,520
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+168
+00:11:39,520 --> 00:11:41,580
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+169
+00:11:41,580 --> 00:11:42,100
+.. ا .. 
+
+170
+00:11:45,630 --> 00:11:50,550
+if and only if اللي هو normal X تربيع بساوية الـ 
+
+171
+00:11:50,550 --> 00:11:53,770
+summation لأ اللي هي الـ Fourier coefficients دولة
+
+172
+00:11:53,770 --> 00:12:00,170
+A over K اللي أنا بدي أفترض الآن اللي هو بدي أثبت
+
+173
+00:12:00,170 --> 00:12:05,710
+الآن عشان أثبت اللي هو الاتجاه هذا يعني بدي أبدأ
+
+174
+00:12:05,710 --> 00:12:09,390
+بهذا وأصل لهذا، ماشي؟ يعني بدي أقول suppose هذا
+
+175
+00:12:09,390 --> 00:12:13,410
+متحقق وأصل لهذا عشان أثبتها هذه بدي أثبتها by
+
+176
+00:12:13,410 --> 00:12:16,510
+contraposition يعني بدي أفترض أن الـM is not total
+
+177
+00:12:16,510 --> 00:12:20,870
+وأصل لهذه معناته أن هذه بيصير تؤدي لهذه إذا الآن
+
+178
+00:12:20,870 --> 00:12:27,430
+if suppose that M is not total ماشي؟ مدام مش total
+
+179
+00:12:28,800 --> 00:12:33,960
+إذا الـ M .. اللي احنا قلنا لو كانت M total M
+
+180
+00:12:33,960 --> 00:12:37,080
+total اللي هو معناته اللي .. اللي هو بتكون M
+
+181
+00:12:37,080 --> 00:12:41,340
+أرثوجونال الشمالها، ها Zero ماشي، مدامت M .. و هذه F
+
+182
+00:12:41,340 --> 00:12:45,260
+and F، اشتغلنا قد ايه تاني إذا كانت M is not
+
+183
+00:12:45,260 --> 00:12:47,540
+total، اللي من الـ theorem اللي قبل بشوية، تلاتة،
+
+184
+00:12:47,540 --> 00:12:52,920
+ستة اتنين، B، هيكون عندي أكيد في اللي هو الـ M
+
+185
+00:12:52,920 --> 00:12:57,950
+أرثوجونال المش Zeroإذا بمعنى آخر بلاقي X إيش معناه M
+
+186
+00:12:57,950 --> 00:13:01,050
+Orthogonal مش Zero يعني في X في الـ M Orthogonal
+
+187
+00:13:01,050 --> 00:13:06,270
+مقله عمودي على الـ M وبيساوي صفر إذا there is X
+
+188
+00:13:06,270 --> 00:13:10,030
+element لأتش وX لاته يساوي صفر and X Orthogonal
+
+189
+00:13:10,030 --> 00:13:15,510
+لمين؟ للـ M هذا امسكوا فيه then صار عند X و EK
+
+190
+00:13:15,510 --> 00:13:22,740
+بيساوي صفر لكل EK element من M هو نفسه مش سفرطيب
+
+191
+00:13:22,740 --> 00:13:28,140
+إذا hence الـ summation لـ X و EK تربيع over K كله
+
+192
+00:13:28,140 --> 00:13:32,160
+نفسه هيساوي صفر ومش هيساوي من norm X تربيعه إن X
+
+193
+00:13:32,160 --> 00:13:36,380
+نفسه مش zero إذا صار عندي الـ contraposition تحققت
+
+194
+00:13:36,380 --> 00:13:39,540
+إنه لو كانت هذه مش total هتأدي هذا وهذا معناه أن
+
+195
+00:13:39,540 --> 00:13:43,960
+هذا يؤدي هذا therefore if الـ summation بيساوي كذا
+
+196
+00:13:43,960 --> 00:13:48,840
+for all اللي هي X المتناش then M اسمها is total in 
+
+197
+00:13:48,840 --> 00:13:57,340
+H وconversely الآن بدأ أفترض أنه M is total وأصل
+
+198
+00:13:57,340 --> 00:14:02,720
+للمساواة دي اللي الـ Parseval مالها متحققة لاحظوا
+
+199
+00:14:02,720 --> 00:14:08,400
+ما هي اللي الآن suppose that M is total in H وخد X
+
+200
+00:14:08,400 --> 00:14:12,600
+be any element in M in H في arbitrary لكن fixed
+
+201
+00:14:12,600 --> 00:14:16,060
+عشان أثبت لكم أنه نور متربية بساوي الـ summation
+
+202
+00:14:16,060 --> 00:14:21,540
+اللي عندها طيب صلى الله عليه الصلاة والسلام الآن
+
+203
+00:14:21,540 --> 00:14:25,540
+الـ Range of all its non-zero Fourier coefficients
+
+204
+00:14:25,540 --> 00:14:30,220
+in a sequence X و E1 و X و E2 و إلى آخرها وبقدر
+
+205
+00:14:30,220 --> 00:14:33,400
+أعمل هيك حتى لو كانت uncountable ليش؟ لأن قبل شوية
+
+206
+00:14:33,400 --> 00:14:38,440
+قلت لكم اللي هي الـ non-zero منها اللي هي حاجة تكون
+
+207
+00:14:38,440 --> 00:14:42,420
+countable هم اللي بيعملوا هنا arrangement إذا الآن
+
+208
+00:14:42,420 --> 00:14:46,480
+هدول اللي اختارتهم من هنا اللي هم مش صفر فبيصير
+
+209
+00:14:46,480 --> 00:14:50,120
+عندي X و E واحد و X و E اتنين إلى ماله نهاية اللي
+
+210
+00:14:50,120 --> 00:14:55,830
+هي عملت .. حطيتهم في sequenceوإذا كان في نايت
+
+211
+00:14:55,830 --> 00:14:59,210
+خلاص من كتب الـ X و X و Y أحد و X و Y اتنين و X و Y
+
+212
+00:14:59,210 --> 00:15:04,710
+انتصار إذا ر مكتوب في حركة محددة إذا كان هناك عدد
+
+213
+00:15:04,710 --> 00:15:05,610
+منهم فقط في نايت
+
+214
+00:15:09,690 --> 00:15:14,930
+واضح طيب الآن define y by الآن هاي الألداء اللي
+
+215
+00:15:14,930 --> 00:15:20,290
+بتوصلني للي بديها الآن خليني أن أعرف y بواسطة y
+
+216
+00:15:20,290 --> 00:15:23,250
+بالسواء والـ summation x و ek ek كامن عند واحد إلى
+
+217
+00:15:23,250 --> 00:15:28,030
+مين إلى ماله نهاية طيب شو سميلي هذه واحدة لأن بعد
+
+218
+00:15:28,030 --> 00:15:34,350
+شوية أرجع لها أنا بعرف أن أم شمالها is orthonormal
+
+219
+00:15:34,350 --> 00:15:39,540
+set مدام orthonormal set then for every ej
+
+220
+00:15:39,540 --> 00:15:45,280
+occurring in one اللي هي الـ ej اللي في واحد اللي هي
+
+221
+00:15:45,280 --> 00:15:49,120
+واحد لما أخذنا الـ summation هذا over k فيه جزئين
+
+222
+00:15:49,120 --> 00:15:53,240
+جزء منه اللي هو عملت له arranging اللي هو xe واحد
+
+223
+00:15:53,240 --> 00:15:57,120
+إلى آخرهم وهذول اللي هي non-zero elements والجزء
+
+224
+00:15:57,120 --> 00:16:02,020
+الثاني منهم خلّينا نسميه v والـ v هذا إيش ماله صفر
+
+225
+00:16:02,020 --> 00:16:06,470
+ماشي الحال طيب اوبتيجي الآن عملنا arrangement
+
+226
+00:16:06,470 --> 00:16:11,230
+since M is orthonormal then for every EJ occurring
+
+227
+00:16:11,230 --> 00:16:15,790
+in one اللي عملنا لها arrangement we have X minus
+
+228
+00:16:15,790 --> 00:16:19,770
+Y و EJ الـ X الـ arbitrator الـ botfix اللي أخذناها في
+
+229
+00:16:19,770 --> 00:16:24,990
+الأول هي عليها الشغل طيب بتساوي X و EJ ناقص Y مين
+
+230
+00:16:24,990 --> 00:16:30,200
+و EJ ويساوي X و EJ زي ما هي ناقص هذه ناقص الـ
+
+231
+00:16:30,200 --> 00:16:35,740
+summation X و EK في EK و EJ الآن عندنا كل هين
+
+232
+00:16:35,740 --> 00:16:40,460
+هيتسفر مع ده EJ إيش مع EJ لأن هو orthonormal إذا
+
+233
+00:16:40,460 --> 00:16:44,940
+صار عند هذا X EJ وهذا X EJ إذا إيش هيساوي؟ هيساوي
+
+234
+00:16:44,940 --> 00:16:50,060
+صفر إذا أثبت لكم الآن X minus Y و EJ بساوي صفر لكل
+
+235
+00:16:50,060 --> 00:16:54,940
+واحدة من العائلة الأولى هذه نيجي الآن نأخذ لأن for
+
+236
+00:16:54,940 --> 00:16:59,100
+all V elements in M not occurring in one يعني اللي
+
+237
+00:16:59,100 --> 00:17:01,140
+ما حصلت .. اللي ما أخذناهنش منها .. احنا قلنا
+
+238
+00:17:01,140 --> 00:17:04,680
+جزأناها جزئين الجزء اللي بيسفرن هو الجزء الصفر
+
+239
+00:17:04,680 --> 00:17:08,080
+اللي بيسفرنش هو الجزء الصفر هذا أخذنا الـ V الـ
+
+240
+00:17:08,080 --> 00:17:12,180
+element in M اللي بيعمل لي صفر we have .. اللي هي
+
+241
+00:17:12,180 --> 00:17:16,520
+طبعا الـ V هذه مش هذا الـ V اللي هو اللي بيعمله صفر
+
+242
+00:17:16,520 --> 00:17:20,360
+اللي هي .. اللي هو X و V اللي هو أيّاش يساوي صفر
+
+243
+00:17:20,360 --> 00:17:27,640
+فاهمين عليها أه؟ عشان تكون الأمور واضحة إذا we have
+
+244
+00:17:27,640 --> 00:17:32,320
+x و v بيساوي صفر so that احسب لي برضه الـ x minus y
+
+245
+00:17:32,320 --> 00:17:37,440
+و v ايش حيسوي؟ x و v ناقص اللي هو الـ 
+
+246
+00:17:37,440 --> 00:17:41,260
+summation اللي هو y عبارة عن x و ek و ek و v
+
+247
+00:17:41,260 --> 00:17:46,780
+و v برضه نفس الجثة الـ v ولا واحدة من هدول أصلا أه إذا
+
+248
+00:17:46,780 --> 00:17:49,020
+.. إذا صار عند الـ inner product بينه إيش ماله
+
+249
+00:17:49,020 --> 00:17:54,580
+بيساوي صفر وهذا أصلا عند X و EK و EK في V هيطلع
+
+250
+00:17:54,580 --> 00:17:59,420
+القيمة كل مرة صفر إذا صار عند X minus Y و V بساوي
+
+251
+00:17:59,420 --> 00:18:05,400
+صفر يعني بمعنى آخر X minus Y وكل العناصر اللي في M
+
+252
+00:18:05,400 --> 00:18:08,860
+سواء العصورة هذه أو العصورة هذه صار الـ inner
+
+253
+00:18:08,860 --> 00:18:12,200
+product بينهم صفر يعني X minus Y إيش صارت؟ عمودية
+
+254
+00:18:12,200 --> 00:18:17,720
+على الـ M ما دام X minus Y عمودية على الـ M والـ M
+
+255
+00:18:17,720 --> 00:18:21,360
+however M is totally matched then by لمّة ثلاثة
+
+256
+00:18:21,360 --> 00:18:25,120
+سبعة اتنين هيطلع عند .. كان عند الـ M ارتجونالاش
+
+257
+00:18:25,120 --> 00:18:28,760
+بساوي صفر دي ما هي مهمة وقالش أتمنى في الأول إذا
+
+258
+00:18:28,760 --> 00:18:31,720
+صار عند الـ X minus Y اللي موجود هنا هيساوي صفر
+
+259
+00:18:31,720 --> 00:18:36,740
+معناته صارت الـ X بتساوي من .. بتساوي Y لأن هذا
+
+260
+00:18:36,740 --> 00:18:40,460
+هتوصلنا للي بديها خد وحسب norm الـ X صار بيعيش
+
+261
+00:18:40,460 --> 00:18:43,550
+بساوي الـ inner product بين الـ X والـ X اللي هو Y و
+
+262
+00:18:43,550 --> 00:18:47,590
+Y صارت ميهم؟ يساوي إيه؟ دلها؟ الآن Y إيش بتساوي؟ الـ
+
+263
+00:18:47,590 --> 00:18:51,070
+inner product لأ فاهمين الـ summation هذا والـ 
+
+264
+00:18:51,070 --> 00:18:53,950
+summation نفسه هذا الآن بنطلع الـ two summations
+
+265
+00:18:53,950 --> 00:18:57,350
+بره صارت هذه معهودة عندنا القول هذا اللي من بعيد
+
+266
+00:18:57,350 --> 00:19:01,490
+هيطلع conjugate وهذا هيكون عادي وهيظل EK و مين و
+
+267
+00:19:01,490 --> 00:19:07,330
+EM كل اللي عندي هنا هيتصفر summation مع ده عند الـ 
+
+268
+00:19:07,330 --> 00:19:10,990
+K بتساوي مين؟ بتساوي M يعني هيصير الـ summation بس
+
+269
+00:19:10,990 --> 00:19:15,810
+على مين؟ على واحدة منهم اللي نسميها K وهذا واحد
+
+270
+00:19:15,810 --> 00:19:18,930
+ولقينا الـ product بين التنتين اللي زي بعض الواحدة
+
+271
+00:19:18,930 --> 00:19:22,110
+والـ conjugate إلها بيصير المربع فبيصير
+
+272
+00:19:22,110 --> 00:19:27,090
+عنده Normal X المربع بساوي هذه وهو المطلوب طيب
+
+273
+00:19:27,090 --> 00:19:35,710
+نيجي نشوف نظرية 364 إيش النظرية بتقول؟ نقول نظرية
+
+274
+00:19:35,710 --> 00:19:40,780
+let H be a Hilbert space then الجزئين الجزئ الأول
+
+275
+00:19:40,780 --> 00:19:44,220
+اللي هو if H is separable هذا بتساعدنا أصلا في
+
+276
+00:19:44,220 --> 00:19:48,000
+برهان واحدة من اللي فوق if H is separable إذا كانت
+
+277
+00:19:48,000 --> 00:19:51,880
+H separable then every orthonormal sitting H
+
+278
+00:19:51,880 --> 00:19:56,700
+شمالها يعني كلهين countable بمثلين اللي هي الـ 
+
+279
+00:19:56,700 --> 00:20:01,350
+total الـ Total Orthonormal بما فيه هنا إذا صار كل
+
+280
+00:20:01,350 --> 00:20:05,970
+اللي هي الـ Total Orthonormal ستة حسب النظرية هذه
+
+281
+00:20:05,970 --> 00:20:09,530
+في حالة السيبرانجل كلهن أشملن countable number
+
+282
+00:20:09,530 --> 00:20:13,090
+يعني ال cardinality اللي بيساوي ألف null يعني ال
+
+283
+00:20:13,090 --> 00:20:15,510
+dimension اللي بدنا نسميه بيصير أشمل ألف percent
+
+284
+00:20:15,510 --> 00:20:19,940
+اللي فوق هنا ماشي في حالة السيبرانجل إذا H تحتوي
+
+285
+00:20:19,940 --> 00:20:24,520
+على سيكوان أورثو نورمال يكون تماماً لـ H، فهو
+
+286
+00:20:24,520 --> 00:20:25,600
+أيضاً Separable
+
+287
+00:20:30,890 --> 00:20:35,530
+هذا بيعطينا إنه هذا الـ Total Orthonormal هي سر
+
+288
+00:20:35,530 --> 00:20:38,630
+إنه يكون separable ولا مش separable إذا كان إحنا
+
+289
+00:20:38,630 --> 00:20:42,390
+اللي جينا أتش بتحتوي على واحدة من الـOrthonormal
+
+290
+00:20:42,390 --> 00:20:45,570
+Sequences وتكون Total، يعني الـCardinality اللي
+
+291
+00:20:45,570 --> 00:20:50,250
+هالف Null وهي Total، هيطلع الأتش separable، ماشي
+
+292
+00:20:50,250 --> 00:20:52,930
+الحال، إذا اللي هو في حالة الـseparable يعني
+
+293
+00:20:52,930 --> 00:20:56,810
+الأمور تمام تمام ومافيش إشكالية، وحتكون اللي هي
+
+294
+00:20:57,510 --> 00:21:01,610
+اللي هي الـ cardinality بتساوي اللي هو ألف Null
+
+295
+00:21:01,610 --> 00:21:08,570
+فنجي برهن الأولى نتأتش بـ separable الآن أنتم 
+
+296
+00:21:08,570 --> 00:21:10,810
+بيقولوا البرهن البرهن اللذيذ وفيه فكرة يعني
+
+297
+00:21:24,720 --> 00:21:28,580
+الآن انزل بس عشان نقولكم ايش اللي بدنا نثبته شوية
+
+298
+00:21:28,580 --> 00:21:32,760
+بقى الآن إذا كانت بدنا نثبت نفرض انه H separable و
+
+299
+00:21:32,760 --> 00:21:37,220
+منها نصل انه ناخد أي orthonormal set in H و نثبت
+
+300
+00:21:37,220 --> 00:21:41,480
+انها accountable يعني بتاخد الآن M أي orthonormal
+
+301
+00:21:41,480 --> 00:21:49,520
+set in H و اثبتلكم انه و لما يكون H separable
+
+302
+00:21:49,520 --> 00:21:55,250
+اثبتلكم من هذا مع بعض انه M اللي هو إيه شمالها
+
+303
+00:21:55,250 --> 00:22:02,590
+countable نشوف كده شوفوا اللي بدي أسوي بدي أخد
+
+304
+00:22:02,590 --> 00:22:07,390
+أخد H بـ separable space شو معناه separable؟ ركزوا
+
+305
+00:22:07,390 --> 00:22:12,810
+في اللي بحكي إنه اللاجي اللاجي اللي هو countable
+
+306
+00:22:12,810 --> 00:22:17,450
+dense من مين؟ من اللي هي الـH أنا بدي أخدوا لكم
+
+307
+00:22:17,450 --> 00:22:28,560
+الآن I B dense set in mean in H ايه dense set in H؟
+
+308
+00:22:28,560 --> 00:22:34,360
+وبدى الآن افرضلكم ان H نفسها شمالها م
+
+309
+00:22:34,360 --> 00:22:44,270
+uncountable واصل لك إن هذا هيقدى إن هذولا ولا واحدة
+
+310
+00:22:44,270 --> 00:22:47,230
+منهم هتكون countable يعني كلهم uncountable
+
+311
+00:22:47,230 --> 00:22:51,830
+للمؤهلات إنهم يدوء يكونوا يقوموا بدور إنه هنا
+
+312
+00:22:51,830 --> 00:22:55,130
+dense subset in H كلهم يكونوا uncountable وهذا
+
+313
+00:22:55,130 --> 00:22:59,210
+معناته بطل H separable إذن هي كما يكون التناقض إذن
+
+314
+00:22:59,210 --> 00:23:03,250
+هي هي السرتيجية الحل نيجي الآن نقول لت H بيه
+
+315
+00:23:03,250 --> 00:23:08,690
+separable and suppose that او let B be any dense
+
+316
+00:23:08,690 --> 00:23:14,550
+set in H و suppose that M any orthonormal H set
+
+317
+00:23:14,550 --> 00:23:19,350
+ماشي الحال بعد شوية بثبتلكم انه لو كانت M الهي is
+
+318
+00:23:19,350 --> 00:23:23,430
+uncountable هيكون H اللي هو contradiction ومنه على
+
+319
+00:23:23,430 --> 00:23:26,670
+طول ال sentence uncountable since M is orthonormal
+
+320
+00:23:26,670 --> 00:23:31,610
+set شوفوا هذه الخاصية الحلوة فيها أم orthonormal
+
+321
+00:23:31,610 --> 00:23:36,170
+إذا لأي x و y في الـ M و المسافة بين x لا تساوي y
+
+322
+00:23:36,170 --> 00:23:41,490
+احسبولي احسبولي المسافة أو ال x لا تساوي y احسبولي
+
+323
+00:23:41,490 --> 00:23:45,730
+المسافة بين x minus y تربيع ايش بتساوي نحسبها
+
+324
+00:23:45,730 --> 00:23:48,610
+عبارة عن linear product بين x ناقص y و x ناقص y
+
+325
+00:23:48,610 --> 00:23:52,170
+وهذا عبارة عن اللي كلهم بيروحوا معاها ده بيظل x و
+
+326
+00:23:52,170 --> 00:23:55,710
+x و 100 و y و y لإن x و y و y و x كلهم إيش أسفار
+
+327
+00:23:55,710 --> 00:24:00,380
+لأنه orthonormal هذه نورمها واحد وهذه نورمها واحد
+
+328
+00:24:00,380 --> 00:24:02,860
+لأن هذه نورم تربيع واحد لها وهذه تربيع واحد لها
+
+329
+00:24:02,860 --> 00:24:06,380
+إذا إيش هيطلع عند المسافة بين أي نقطتين إذا في ال
+
+330
+00:24:06,380 --> 00:24:12,100
+M في داخل ال M المسافة بين كل نقطتين إيش بتساوي هذا
+
+331
+00:24:12,100 --> 00:24:15,600
+بس يعني تجرب اللي هدا بساوي اللي هو مين عبارة عن
+
+332
+00:24:15,600 --> 00:24:18,700
+جذر التنين صح المسافة بين التنتين هدولة بين
+
+333
+00:24:18,700 --> 00:24:24,490
+النقطتين جذر التنين إذا بقدر .. بقدر أعمل حوالين
+
+334
+00:24:24,490 --> 00:24:28,590
+هذه neighborhood هذه ال X و هذه ال Y وهذا بعمل
+
+335
+00:24:28,590 --> 00:24:31,430
+حوالين neighborhood بحيث أنه يكون ال neighborhood
+
+336
+00:24:31,430 --> 00:24:36,810
+دين التقطح مش بساوي فيه ماشي بقدر .. خده مثلا ..
+
+337
+00:24:36,810 --> 00:24:39,970
+خده اللي هو ال .. ال .. ال .. ال .. ال radius تبع
+
+338
+00:24:39,970 --> 00:24:42,830
+هذا اللي هو عبارة عن جذر التنين على تلاتة عشان
+
+339
+00:24:42,830 --> 00:24:46,630
+أضمن كمان يبعدن عن بعض و هذا جذر التنين على اثنين على
+
+340
+00:24:46,630 --> 00:24:53,430
+تلاتة الأنصار الآن كل نقطتين في داخل الـ M أنا بقدر
+
+341
+00:24:53,430 --> 00:24:57,750
+أبعدهن عن بعض بحيث أن هذا برضه النقطة اللي بعد هو
+
+342
+00:24:57,750 --> 00:25:00,850
+ده اللي بعد هو اللي بعد كلهين disjoint ماشي الحال
+
+343
+00:25:00,850 --> 00:25:04,810
+طيب هنا الخطورة أصلا شوفوا الآن هو ال superiority
+
+344
+00:25:04,810 --> 00:25:09,130
+شو معناته انه انه هذي اللي بتكون dense بتجيب ال
+
+345
+00:25:09,130 --> 00:25:12,250
+dense بتجيب كل space يعني ال double does لازم إيش
+
+346
+00:25:12,250 --> 00:25:16,770
+تكون item ثاني تكون فيه تقاطع بين احتياط
+
+347
+00:25:20,340 --> 00:25:24,420
+Hence spherical neighbourhoods NX of X and NY of Y
+
+348
+00:25:24,420 --> 00:25:28,420
+of radii جذر التنين على تلاتة are disjoint Y قلت Y
+
+349
+00:25:28,420 --> 00:25:33,880
+لأن B is dense in H لكن بيه dense in H إحنا بنقول
+
+350
+00:25:33,880 --> 00:25:38,780
+مادام بيه dense in H إذا أي X في ال M بقدر الاقي
+
+351
+00:25:38,780 --> 00:25:43,020
+neighbourhood  NX اللي هو بيكون .. بيكون أي
+
+352
+00:25:43,020 --> 00:25:46,900
+neighborhood NX تقاطع ال B إيش ما له لا يساوي فاي
+
+353
+00:25:46,900 --> 00:25:50,500
+لأن اللي هي مالها B dense ماشي الآن، dense يعني
+
+354
+00:25:50,500 --> 00:25:54,420
+مهما زغرت ال neighborhood بدك تبعد عن B بتقدرش لإن
+
+355
+00:25:54,420 --> 00:25:57,400
+B هي ال .. ال .. ال .. الكلوة دي اللي لها بيساوي
+
+356
+00:25:57,400 --> 00:26:02,600
+كل space إذن لكل then for NX element of M NX
+
+357
+00:26:02,600 --> 00:26:07,320
+تقاطع ال B لا يساوي إيش فاي إذا كل واحدة من هذولة
+
+358
+00:26:07,320 --> 00:26:10,740
+من هذولة الآن اكس و الآن واي و الآن زد و الآن كل
+
+359
+00:26:10,740 --> 00:26:16,360
+هنا دولة كل واحدة بكون NX تقاطع البي لا يساوي فاي
+
+360
+00:26:16,360 --> 00:26:20,500
+يعني بمعنى آخر في element هنا مصبوط ال element
+
+361
+00:26:20,500 --> 00:26:25,440
+الأول a في ال NX الثاني في ال NY فيه element
+
+362
+00:26:25,440 --> 00:26:29,420
+ومش هيكون ال A ليش مش هيكون ال A؟ لأن MX مع ال
+
+363
+00:26:29,420 --> 00:26:33,520
+NY أشمعنى ال Phi إذا هذه برضه فيها مين B وهذه
+
+364
+00:26:33,520 --> 00:26:38,200
+فيها C وهذه فيها D وهذه كذا لو كانت .. لو كانت ال
+
+365
+00:26:38,200 --> 00:26:43,380
+M uncountable معناته أنه صار عندي uncountable
+
+366
+00:26:43,380 --> 00:26:48,260
+points هدولة موجودات كل من في مين في ال B إذا صارت
+
+367
+00:26:48,260 --> 00:26:51,200
+B شمالها uncountable وهذا contradiction لأنه
+
+368
+00:26:51,200 --> 00:26:55,600
+كانت B arbitral dense set إذا اللي قلته اللي
+
+369
+00:26:55,600 --> 00:27:00,280
+قلته اللي هناك قلته And since B is densely notched
+
+370
+00:27:00,280 --> 00:27:04,420
+in for any X element in M, NX تقاطع ال B ليساوي
+
+371
+00:27:04,420 --> 00:27:09,160
+Phi Hence there is A element in NX تقاطع ال B و B
+
+372
+00:27:09,160 --> 00:27:14,400
+في NY تقاطع ال B و ال B لا تساوي A لأن ال NX
+
+373
+00:27:14,400 --> 00:27:17,460
+نفسها و ال NY تقاطعهم بساوي Phi في الشأنص المشتركة
+
+374
+00:27:17,460 --> 00:27:21,860
+بينهم لأن لو فرضنا إن M is uncountable، then we
+
+375
+00:27:21,860 --> 00:27:26,940
+have uncountably many pairwise disjoint spherical
+
+376
+00:27:26,940 --> 00:27:31,900
+neighborhoods، فإن هدول النقسات So that B would
+
+377
+00:27:31,900 --> 00:27:35,060
+contains uncountable number of points، يعني B
+
+378
+00:27:35,060 --> 00:27:38,060
+would be uncountable since B was arbitrary dense
+
+379
+00:27:38,060 --> 00:27:41,800
+set، this makes that H would not contain a
+
+380
+00:27:41,800 --> 00:27:45,920
+countable dense set which contradicts the fact that
+
+381
+00:27:45,920 --> 00:27:49,200
+which is separable therefore أنا لازم تكون إيه شمالها
+
+382
+00:27:49,200 --> 00:27:54,800
+مالها اللي هي countable واضح؟ ماشي الحال نيجي نشوف
+
+383
+00:27:54,800 --> 00:28:00,520
+اللي بعدها بيكون طوله روحكم برضه شوية نيجي لين؟
+
+384
+00:28:00,520 --> 00:28:05,120
+ارجع لنا للنص عشان نذكركم بإيش اللي بدنا نثبته الآن
+
+385
+00:28:05,120 --> 00:28:08,920
+النظرية بتقول إذا كانت H بتحتوي على orthonormal
+
+386
+00:28:08,920 --> 00:28:12,840
+sequence اه orthonormal sequence which is total
+
+387
+00:28:12,840 --> 00:28:17,320
+يعني بتحتوي على total orthonormal sequence لازم
+
+388
+00:28:17,320 --> 00:28:19,420
+ال H تكون separable
+
+389
+00:28:21,650 --> 00:28:24,870
+Total orthonormal sequence معناته countable الست
+
+390
+00:28:24,870 --> 00:28:29,010
+هي ماشي لأن orthonormal sequence بنقصد فيها اللي
+
+391
+00:28:29,010 --> 00:28:33,070
+هو a1, a2, a3 أو x1, x2, x3 لما لا نهاية يعني
+
+392
+00:28:33,070 --> 00:28:37,790
+بمعنى آخر اللي هو countable set طيب اطلع للبرهاد
+
+393
+00:28:37,790 --> 00:28:43,240
+لنشوف بدنا نثبت أن H is separable طيب بدنا نجيلنا
+
+394
+00:28:43,240 --> 00:28:47,340
+بمعنى آخر بدنا نعملنا construction هو بده يعملنا
+
+395
+00:28:47,340 --> 00:28:54,100
+construction بده يعملنا construction ل اللي هي set
+
+396
+00:28:54,100 --> 00:28:58,420
+تكون dense in H من ال orthonormal sequence اللي
+
+397
+00:28:58,420 --> 00:29:04,100
+عندها let em be a total orthonormal sequence in
+
+398
+00:29:04,100 --> 00:29:08,470
+mean in H قالي لها هي بين إيدينا عند خد A إيش
+
+399
+00:29:08,470 --> 00:29:13,370
+بتساوي؟ بتساوي عبارة عن كل ال formations Gamma K N
+
+400
+00:29:13,370 --> 00:29:19,250
+E K K من واحد لعندها ال E K هذولة اللي من هذه ماشي
+
+401
+00:29:19,250 --> 00:29:25,750
+الحال الآن ال ال coefficients هذولة بتدخلهم طبعا
+
+402
+00:29:25,750 --> 00:29:28,430
+أنا بحكي بس يشتغل في real أو complex خلينا ال
+
+403
+00:29:28,430 --> 00:29:30,810
+complex in general وفي حالة ال real بتسافروا ال
+
+404
+00:29:30,810 --> 00:29:34,850
+imaginary part الآن Gamma K N هذا ال coefficients
+
+405
+00:29:34,850 --> 00:29:38,970
+اللي Gamma K N بتساوي اللي هو عبارة عن A K N زي I
+
+406
+00:29:38,970 --> 00:29:42,990
+B K N ماشي الحال هذولة اللي هو ال real
+
+407
+00:29:42,990 --> 00:29:45,650
+coefficients و ال imaginary coefficients بتاخدهم
+
+408
+00:29:45,650 --> 00:29:51,290
+من مين؟ من ال Q عشان أضمن انه تطلع اللي هو الصمم
+
+409
+00:29:51,290 --> 00:29:54,970
+هذه ال Q is countable لأنه بيصير عندي هذا اللي هو
+
+410
+00:29:54,970 --> 00:29:58,770
+وكأنه اللي هي هدولة جايات هدولة نفسهم جايات من Q
+
+411
+00:29:58,770 --> 00:30:01,590
+cross Q ماشي الحالة او ايزا ما اللي هو ال
+
+412
+00:30:01,590 --> 00:30:04,310
+cardinality اللي هنا هيكون اللي هو عبارة عن الف
+
+413
+00:30:04,310 --> 00:30:07,270
+Null countable لأن countable cross countable is
+
+414
+00:30:07,270 --> 00:30:10,930
+countable و ال finite union ال finite اللي هو
+
+415
+00:30:10,930 --> 00:30:15,910
+summation هذا وكأني باخد ال union ل finite number
+
+416
+00:30:15,910 --> 00:30:20,770
+ال finite ال union ل countable sets برضه هيطلع إيش
+
+417
+00:30:20,770 --> 00:30:25,370
+ما له countable إذا بكل الأحوال A is countable طيب
+
+418
+00:30:25,370 --> 00:30:30,810
+كيف شكلوا ال summation هذا يعني مثلا لو اخذناها
+
+419
+00:30:30,810 --> 00:30:34,030
+واحد بيصير الصمي اللي هو عبارة عن العنصر هذا Gamma
+
+420
+00:30:34,030 --> 00:30:39,960
+K واحد EK ممكن أنصر ثاني يقولك أنا بدي أبقيها من 
+
+421
+00:30:39,960 --> 00:30:43,360
+واحد لعند مين لعند عشرة اللي هو ال submission a,k
+
+422
+00:30:43,360 --> 00:30:48,760
+,n,e,k عدد من واحد لعشرة لعشرين للتلاتين لكل ال
+
+423
+00:30:48,760 --> 00:30:50,880
+finite اللي في الدنيا جات ما بدك اللي هي الآن
+
+424
+00:30:50,880 --> 00:30:54,560
+تاخدها واحد اثنين ثلاثة إذا شكل العناصر هذا أنا
+
+425
+00:30:54,560 --> 00:30:58,020
+عارف كيف شكله اللي هي ال coefficients هدول من مين
+
+426
+00:30:58,020 --> 00:31:01,920
+من ال complex numbers لكن ال coefficients تبعات
+
+427
+00:31:01,920 --> 00:31:04,740
+اللي هي ال real part و ال imaginary part عبارة عن
+
+428
+00:31:04,740 --> 00:31:09,080
+أعداد نسبية rational numbers طيب عشان نضمن اللي هو
+
+429
+00:31:09,080 --> 00:31:13,360
+تكون countable الآن BKM بتساوي صفر لما ال H تكون
+
+430
+00:31:13,360 --> 00:31:16,940
+أيش ما لها real Hilbert space هنا خلينا نشتغل عن
+
+431
+00:31:16,940 --> 00:31:20,760
+ال general و بيكون ده كحالة خاصة منه زي ما قلت A
+
+432
+00:31:20,760 --> 00:31:24,900
+is countable هو قولناها هو ايش الآن we show that
+
+433
+00:31:24,900 --> 00:31:28,380
+هذه المؤهلة إننا اثبتناها إنها dense in H إذا
+
+434
+00:31:28,380 --> 00:31:30,980
+اثبتناها dense in H بيكون خلصناها بتكون H أيش ما 
+
+435
+00:31:30,980 --> 00:31:35,900
+لها inseparable اطلع تشوف كإعلان كيف بدي اثبت إنه
+
+436
+00:31:35,900 --> 00:31:40,240
+dense؟ بدي أخد الـ NX and fixed element in H ماشي الحال هو ألاجيه لك إن NX تقاطع اللي هو الـ
+
+437
+00:31:40,240 --> 00:31:45,380
+set هذه لا يساوي 5 بقول خلصها بس ماتناهيش إنها 
+
+438
+00:31:45,380 --> 00:31:49,020
+dense عشان اثبت إنها dense إنه لو أخدنا أي element
+
+439
+00:31:49,020 --> 00:31:52,320
+هنا بقدر ألاجي اللي هو بيكون عندي أي neighborhood
+
+440
+00:31:52,320 --> 00:31:55,700
+حوالينها ذاك و بطلع هذاك اللي بتشوفه إن شاء الله
+
+441
+00:31:55,700 --> 00:31:57,920
+حوالينها ذاك و بطلع هذاك اللي بتشوفه إن شاء الله
+
+442
+00:31:57,920 --> 00:32:03,320
+let X be and fixed element in H الآن since
+
+443
+00:32:03,320 --> 00:32:07,660
+EM is a total or from a total set in H إذا 
+
+444
+00:32:07,660 --> 00:32:11,640
+الإسبانيك لو جعل ال EM إيش حيساوي؟ من التعريف طيب
+
+445
+00:32:11,640 --> 00:32:15,720
+إذا for every إبسلون أكبر من صفر مهما كانت إبسلون
+
+446
+00:32:15,720 --> 00:32:19,020
+صغيرة هذه اللي بتعبر عن ال arbitrary
+
+447
+00:32:19,020 --> 00:32:24,340
+neighborhood الآن there is w element ل span em such
+
+448
+00:32:24,340 --> 00:32:28,700
+that المسافة بين x نقص w أصغر من أي أصغر من أي
+
+449
+00:32:28,700 --> 00:32:31,980
+epsilon في الدنيا أنا بتسميه y على 2 للحسابات ماشي
+
+450
+00:32:31,980 --> 00:32:37,340
+الحال إذا الآن لإن span لل em dense in H إذا لأي x
+
+451
+00:32:37,340 --> 00:32:41,260
+في ال H بقدر ألاقي اللي هو element في اللي جوا هذا
+
+452
+00:32:41,260 --> 00:32:46,240
+بحيث المسافة بين x و w أصغر من أي epsilon في
+
+453
+00:32:46,240 --> 00:32:50,710
+الدنياماشي الحال أو تعبير اللي هو إن نكس و Y على
+
+454
+00:32:50,710 --> 00:32:54,750
+اثنين اللي هو تقاطع اللي هو ال H اللي نسباننا
+
+455
+00:32:54,750 --> 00:32:59,110
+اليوم ليه ال W هذه ماشي إن شاء الله نجمعين معايا
+
+456
+00:32:59,110 --> 00:33:01,230
+طيب الآن
+
+457
+00:33:03,350 --> 00:33:11,450
+Hence وين موجودة؟ و موجودة في الـ YN و ما هي وين
+
+458
+00:33:11,450 --> 00:33:14,350
+موجودة في الإسماعيل للـ EM؟ مادام هي في الإسماعيل
+
+459
+00:33:14,350 --> 00:33:17,710
+للـ EM يعني و عبارة عن اللي هو الـ Finite Linear
+
+460
+00:33:17,710 --> 00:33:21,120
+combination من مين؟ من عناصر من الـ EM نفترض إنه
+
+461
+00:33:21,120 --> 00:33:25,060
+finite combination من E1 وE2 وE3 وE4 لعندي يعني مش
+
+462
+00:33:25,060 --> 00:33:28,560
+عاجبكم EI واحد EI اثنين لعندي EIN على الأساس ما
+
+463
+00:33:28,560 --> 00:33:31,560
+تقولوش أول أول تلاتة من هدول أو أول خمسة من هدول
+
+464
+00:33:31,560 --> 00:33:35,560
+مش مشكلة فاهمين إنهم تكون finite اللي هو summation
+
+465
+00:33:35,560 --> 00:33:39,680
+أو finite combination من مين من عناصر اللي هي
+
+466
+00:33:39,680 --> 00:33:44,960
+موجودة في مين في الإيام طيب أسميتها هذه الـ span
+
+467
+00:33:44,960 --> 00:33:48,580
+للـ E1 و E2 اللي عندي لأن إيش سميتها وي أنت ماشي
+
+468
+00:33:48,580 --> 00:33:52,980
+الحال إذا صارت الـ W هذه اللي لجيتها للمسافة بينها
+
+469
+00:33:52,980 --> 00:33:56,560
+وبين ال X اللي بتحكي عليها أصغر من X أسلوب على 2
+
+470
+00:33:56,560 --> 00:34:00,870
+سميتها W في ال span اللي عندي for someoneby لمّة
+
+471
+00:34:00,870 --> 00:34:04,670
+قبل بشوية تلاتة و تلاتة اثنين there is y element
+
+472
+00:34:04,670 --> 00:34:07,050
+اللي هي أخدناها قبل هيك there is y element in yn
+
+473
+00:34:07,050 --> 00:34:11,510
+such that x minus y element عمودي عالميين على ال
+
+474
+00:34:11,510 --> 00:34:15,050
+yn إيش هتستنى عشان ماتطلعوش عنها إيش اللمّة هذه
+
+475
+00:34:15,050 --> 00:34:19,890
+احنا المرة اللي فاتت لما نأجينا خدنا x في ال space
+
+476
+00:34:20,550 --> 00:34:25,050
+X في الـ Space جينا و رسمتلكم عدة رسمات إذا
+
+477
+00:34:25,050 --> 00:34:29,870
+بتتذكروا اللي هو هاي الرسم هادي و قولنا إن هذا الـ
+
+478
+00:34:29,870 --> 00:34:33,430
+Space H أو هذا الـ Space H و هاي الـ X هنا و هاي
+
+479
+00:34:33,430 --> 00:34:38,370
+الـ X هنا ماشي الحال قولنا إنه عرفنا إن الـ Delta
+
+480
+00:34:38,370 --> 00:34:44,530
+هي عبارة عن المسافة بين النقطة X و بين الـ Space
+
+481
+00:34:44,530 --> 00:34:49,420
+الـ M هذه سميناها M هذه بين الـ X و مين و M في
+
+482
+00:34:49,420 --> 00:34:54,280
+نظرية قلنا إذا كانت M subspace بنضمن اللي نجيلكم
+
+483
+00:34:54,280 --> 00:34:58,760
+واحدة وحيدة إن there exist unique Y such that
+
+484
+00:34:58,760 --> 00:35:04,680
+normal X minus Y هو اللي بيمثل مين ال Delta وفي
+
+485
+00:35:04,680 --> 00:35:10,280
+النظرية اللي بعدها اللي هي 3 3 2 قلنا إنه لو كانت
+
+486
+00:35:10,280 --> 00:35:15,460
+هذه complete هيكون عندي ال Y الوحيدة هذه اللي هي
+
+487
+00:35:15,460 --> 00:35:19,240
+هتنزل هذه العمود هذي بيصير X هي عندي ال X وهي ال Y
+
+488
+00:35:19,240 --> 00:35:24,060
+اللي وجناها هذه المسافة هتنزل عمودي على مين؟ على
+
+489
+00:35:24,060 --> 00:35:29,520
+هذا، هيكون ال X minus Y Orthogonal على مين؟ على
+
+490
+00:35:29,520 --> 00:35:34,430
+العين، ماشي الحال، إذن الآن بهذه النظرية بهذه
+
+491
+00:35:34,430 --> 00:35:37,870
+النظرية بقدر هذا هذا هذا ال subspace اللي عندي
+
+492
+00:35:37,870 --> 00:35:41,750
+اللي عليه بده اطبق فبصير عندي الآن بقدر ألاقي y في
+
+493
+00:35:41,750 --> 00:35:45,750
+داخله وكأنه هذا ال subspace يا جماعة اه هذا ال
+
+494
+00:35:45,750 --> 00:35:50,590
+subspace بقدر ألاقي في داخله y بحيث إنه norm x
+
+495
+00:35:50,590 --> 00:35:54,530
+minus y هو اللي يمثل delta ويكون x minus y نفسه
+
+496
+00:35:54,530 --> 00:36:00,830
+عمود عالمين على ال M طيب إذا الآن there exists y
+
+497
+00:36:00,830 --> 00:36:04,990
+element in y-end such that x minus y عمودي على ال
+
+498
+00:36:04,990 --> 00:36:08,450
+y-end ما هو احنا في الطبيعي بنقول اقرب واحد على
+
+499
+00:36:08,450 --> 00:36:12,610
+الست اللي هو القمود عليه اه اه طيب الآن صار عندي
+
+500
+00:36:12,610 --> 00:36:15,650
+ايه هدف الهندسة الطبيعية اللي في ال space اللي
+
+501
+00:36:15,650 --> 00:36:18,110
+منيح اللي .. اللي .. اللي .. اللي منيحة و مش فيه
+
+502
+00:36:18,110 --> 00:36:23,300
+مشاكل اللي هو بيقول complete subspace There is y
+
+503
+00:36:23,300 --> 00:36:26,040
+element in yn such that x minus y عمودي عالمين على
+
+504
+00:36:26,040 --> 00:36:30,380
+yn و ال norm ل ال x minus y هو ال infimum هو ال
+
+505
+00:36:30,380 --> 00:36:34,020
+delta مدام هو ال delta إذا حيكون أصغر أو يساوي ال
+
+506
+00:36:34,020 --> 00:36:37,760
+norm ل ال x ناقص أي element في الدنيا ثاني في ال
+
+507
+00:36:37,760 --> 00:36:39,660
+.. في ال .. في ال .. في ال .. في ال .. في ال M
+
+508
+00:36:39,660 --> 00:36:44,020
+اللي عندي اللي بشغل عليها أو ال H من ضمن اليومين
+
+509
+00:36:44,020 --> 00:36:49,260
+ال W لجناها إذا صار عند نورنا الـ X-Y أصغر من مين؟
+
+510
+00:36:49,260 --> 00:36:53,560
+من Y على 2 لأن X-W من فوق يشملها أصغر من Y على 2
+
+511
+00:36:54,350 --> 00:37:01,170
+الآن by a و b in theorem 3-4 y can be written as
+
+512
+00:37:01,170 --> 00:37:06,150
+اللي هي أخدناها قبل هيك إنه y اللي عندها دي بنقدر
+
+513
+00:37:06,150 --> 00:37:08,810
+نكتبها على صورة summation ال for real coefficient
+
+514
+00:37:08,810 --> 00:37:12,090
+بتاعتها summation x و ek , ek كامل عند واحد لمين
+
+515
+00:37:12,090 --> 00:37:17,030
+لعند n اللي هي موجودة في مين y في الاسم علي طيب
+
+516
+00:37:17,780 --> 00:37:22,400
+الآن إذا احسبولي اطلع لفوق احسبلي الآن normal X
+
+517
+00:37:22,400 --> 00:37:27,000
+نقص ال summation هذا اللي هو ال Y حسبنا أصغر من
+
+518
+00:37:27,000 --> 00:37:31,300
+مين من نفسنا على اثنين الآن ال Q نفسها الآن هل جيه
+
+519
+00:37:31,300 --> 00:37:33,980
+تبدأ تيجي اللي هو استخدام اللي هو التركيب الأصلي
+
+520
+00:37:33,980 --> 00:37:39,700
+لل A since Q is dense in R then for any X و E K
+
+521
+00:37:39,700 --> 00:37:43,900
+هذا اللي هو عبارة عن complex number هذا في ال .. في
+
+522
+00:37:43,900 --> 00:37:48,120
+ال complex number ماشي الحال أي x .. ال .. ال ..
+
+523
+00:37:48,120 --> 00:37:50,060
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+524
+00:37:50,060 --> 00:37:50,220
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+525
+00:37:50,220 --> 00:37:50,300
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+526
+00:37:50,300 --> 00:37:50,740
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+527
+00:37:50,740 --> 00:37:51,420
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+528
+00:37:51,420 --> 00:37:51,840
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+529
+00:37:51,840 --> 00:37:52,420
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+530
+00:37:52,420 --> 00:37:52,960
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+531
+00:37:52,960 --> 00:37:54,600
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+532
+00:37:54,600 --> 00:37:54,660
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+533
+00:37:54,660 --> 00:37:54,920
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+534
+00:37:54,920 --> 00:37:57,140
+..ال ..ال ..ال ..ال ..ال ..ال ..ال ..ال
+
+535
+00:38:02,140 --> 00:38:06,680
+ننتقل من R كيو دينس في R إذا كيو كروس كيو دينس في
+
+536
+00:38:06,680 --> 00:38:09,620
+مين في C اللي هو اللي حكينا عنه لأنه كامتر
+
+537
+00:38:09,620 --> 00:38:13,400
+بالتقرير سنس كيو سنس في R هي المفتاح then for any
+
+538
+00:38:13,400 --> 00:38:18,700
+X و EK there is Gamma KN AKN زائد IBKN such that
+
+539
+00:38:18,700 --> 00:38:24,000
+AKN و BKN element لكيو such that اللي هو المسافة
+
+540
+00:38:24,000 --> 00:38:28,050
+بين اللي هو ال summation لل X و EK لحالة هذه
+
+541
+00:38:28,050 --> 00:38:31,570
+المسافة بين الـ X و الـ E K و العدد اللي هنا أصغر
+
+542
+00:38:31,570 --> 00:38:36,030
+ما يكون لأن مجموع هذا برضه ما هو Complex هيطلع أو
+
+543
+00:38:36,030 --> 00:38:39,170
+هيطلع اللي هو .. خلّيني .. نقدر نطبق عليه اللي
+
+544
+00:38:39,170 --> 00:38:42,950
+بنطبقه على هذا لأن أنا بتدث .. بتدث بتتثار ال ..
+
+545
+00:38:42,950 --> 00:38:47,250
+ال summation لل X و ال E K over ال K اللي بحكي
+
+546
+00:38:47,250 --> 00:38:52,980
+عنها من 1 لـ N في الآخر هذا الآن ال summation في
+
+547
+00:38:52,980 --> 00:38:57,440
+الآخر اللي هو بقدر اتعامل معاه بدل ما هي ال X E K
+
+548
+00:38:57,440 --> 00:39:04,320
+لحالها عندي بما إنه Q dense in R وطبيعي اللي هو أنا
+
+549
+00:39:04,320 --> 00:39:07,080
+أخدت ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+550
+00:39:07,080 --> 00:39:07,220
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+551
+00:39:07,220 --> 00:39:07,360
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+552
+00:39:07,360 --> 00:39:07,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+553
+00:39:07,440 --> 00:39:08,680
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+554
+00:39:08,680 --> 00:39:09,120
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+555
+00:39:09,120 --> 00:39:09,480
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+556
+00:39:09,480 --> 00:39:09,560
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+557
+00:39:09,560 --> 00:39:11,420
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+558
+00:39:11,420 --> 00:39:19,220
+ال .. ال .. ال .. ال ..
+
+559
+00:39:19,220 --> 00:39:19,560
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+560
+00:39:19,560 --> 00:39:22,680
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. 
+
+561
+00:39:22,680 --> 00:39:25,880
+ال
+
+562
+00:39:27,860 --> 00:39:30,780
+ما دامت اللي هي Q dense إذا بقدر أجلاج ال
+
+563
+00:39:30,780 --> 00:39:37,540
+coefficients من اللي هي ال .. ال Q العصورة AKN
+
+564
+00:39:37,540 --> 00:39:44,360
+زائد IBKN اللي سنتها Gamma KN بحيث أنه المسافة بين
+
+565
+00:39:44,360 --> 00:39:50,360
+هذه و بين اللي هي ال elements اللي عندي Gamma KEK
+
+566
+00:39:50,360 --> 00:39:55,240
+يكون إيش ماله أصغر ما يمكن و ليكن أصغر من مين من
+
+567
+00:39:55,240 --> 00:40:01,300
+إبسيلون على اثنين إذا الآن من
+
+568
+00:40:01,300 --> 00:40:07,530
+كل اللي فات بقدر أخص ما يلي إنه لجهة الـ V اللي هي
+
+569
+00:40:07,530 --> 00:40:11,170
+عبارة عن X و EK في EK الـ summation اللي لها V
+
+570
+00:40:11,170 --> 00:40:16,690
+بيساوي ال summation لـ Gamma KN و EK SF Element NA
+
+571
+00:40:16,690 --> 00:40:23,890
+بحيث أن المسافة بين X و V X و V اللي هو بيساوي X
+
+572
+00:40:23,890 --> 00:40:27,810
+خلوها زي ما هي ناقص اللي هي ال summation هذا أصغر
+
+573
+00:40:27,810 --> 00:40:31,590
+أو يساوي بدأت
+
+574
+00:40:31,590 --> 00:40:36,030
+بـ X arbitrary ولجئت اللي هو element v element a
+
+575
+00:40:36,030 --> 00:40:41,770
+بحيث المسافة بين x minus v يساوي .. انشوف x ناقص
+
+576
+00:40:41,770 --> 00:40:45,750
+هذا عوضت بال triangling quality بدي أضيف term
+
+577
+00:40:45,750 --> 00:40:49,450
+واطح term أصغر أو ساوي x ناقص اللي هو المفتاح هذا
+
+578
+00:40:49,450 --> 00:40:58,190
+اللي حصلته هنا x ek و ek زائد اللي هو نفسه هذا ناقص
+
+579
+00:40:58,190 --> 00:41:02,970
+ال V اللي هي ال submission هذا أثبتناها سابقا أصغر
+
+580
+00:41:02,970 --> 00:41:06,030
+من إبسيلون على اثنين وهذا أثبتناها سابقا أصغر من
+
+581
+00:41:06,030 --> 00:41:09,070
+إبسيلون على اثنين من الجهتين صار عند ال X minus V
+
+582
+00:41:09,070 --> 00:41:13,230
+أصغر من مين من إبسيلون إيش اللي عملته أخدت X
+
+583
+00:41:13,230 --> 00:41:18,780
+arbitrary ولجيت اللي هو V في الـA بحيث أنه المسافة
+
+584
+00:41:18,780 --> 00:41:23,260
+بين الـX والـV اللي لجيتها أقل ما يمكن يعني بمعنى
+
+585
+00:41:23,260 --> 00:41:29,020
+آخر أنه for every اللي هو ball أو every
+
+586
+00:41:29,020 --> 00:41:34,030
+neighborhood بيكس وإبسيلون تقاطع اللي إيه إيه إيه
+
+587
+00:41:34,030 --> 00:41:35,490
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+588
+00:41:35,490 --> 00:41:39,370
+إيه
+
+589
+00:41:39,370 --> 00:41:48,170
+إيه
+
+590
+00:41:48,690 --> 00:41:53,350
+الآن ال V هذه موجودة هنا أثبتت هيها من خلال هذه و
+
+591
+00:41:53,350 --> 00:41:56,570
+في نفس الوجهة ال V و الموجودة في ال A يعني ال ball
+
+592
+00:41:56,570 --> 00:42:01,490
+تقاطع ال A ليس هو Phi و هذا يعني أن ال A صارت
+
+593
+00:42:01,490 --> 00:42:05,170
+dense في mean في ال space الأصل اللي أخدت X فيه
+
+594
+00:42:05,170 --> 00:42:09,670
+arbitrary ومعناته صارت اللي هي H is separable يلا
+
+595
+00:42:09,670 --> 00:42:15,000
+اللي بعده اللي بعده يا بابا النظرية الأخيرة في هذا
+
+596
+00:42:15,000 --> 00:42:18,460
+الـ section Theorem two Hilbert spaces H and H
+
+597
+00:42:18,460 --> 00:42:22,700
+tilde both real or both complex are isomorphic if
+
+598
+00:42:22,700 --> 00:42:25,100
+and only if they have the same Hilbert dimension
+
+599
+00:42:25,100 --> 00:42:32,480
+يعني وكأنه بيقولنا من تحت بطن أنه يا جماعة كل ال
+
+600
+00:42:32,480 --> 00:42:35,940
+Hilbert spaces اللي ال dimension إليهم زي بعض
+
+601
+00:42:35,940 --> 00:42:39,260
+هدولة isomorphic يعني واحدة كلها تجدوش و تقولي
+
+602
+00:42:39,260 --> 00:42:45,350
+إنها واحدة كلها واحدة ماشي بناء عليه أحنا اللي بدنا
+
+603
+00:42:45,350 --> 00:42:52,170
+نثبته إنه ناخد أي two Hilbert spaces قدش قدش تل ده
+
+604
+00:42:52,170 --> 00:42:57,070
+أو أو إذا أثبتنا إنه isomorphic معناته أي شماله
+
+605
+00:42:57,070 --> 00:43:00,430
+اللي هو الهن the same Hilbert dimension إذا الهن
+
+606
+00:43:00,430 --> 00:43:02,750
+the same Hilbert dimension معناته أي شمالهن
+
+607
+00:43:02,750 --> 00:43:07,800
+isomorphic الآن نجي للاتجاه الأول suppose that أو
+
+608
+00:43:07,800 --> 00:43:10,660
+isomorphism بين هنا عارفين إيش معناه isomorphism
+
+609
+00:43:10,660 --> 00:43:14,260
+بينهم بنحكيها الآن الآن suppose that H is
+
+610
+00:43:14,260 --> 00:43:17,080
+isomorphic with H تلده ما بديش أدخل في التفاصيل
+
+611
+00:43:17,080 --> 00:43:20,360
+تفاصيل الحسابات حتكون لكم suppose that H is
+
+612
+00:43:20,360 --> 00:43:24,110
+isomorphic لمن لH تلده يعني في isomorphism بين
+
+613
+00:43:24,110 --> 00:43:28,390
+التنتين then there is a bijective linear mapping T
+
+614
+00:43:28,390 --> 00:43:33,350
+من H لH تل ده that satisfies T X و T Y بيساوي X و
+
+615
+00:43:33,350 --> 00:43:37,830
+Y يعني اللي هي preserve the inner product زي ما
+
+616
+00:43:37,830 --> 00:43:40,150
+قلنا شو معناته ال geomorphic preserve inner
+
+617
+00:43:40,150 --> 00:43:43,690
+product preserve اللي هو العمليات اللي هو preserve
+
+618
+00:43:43,690 --> 00:43:46,550
+cardinality اللي هي one to one أو أنتو هي التلات
+
+619
+00:43:46,550 --> 00:43:54,920
+شغلات الآن صار عندي اطلع لفوق اللي فوق الآن ال ال
+
+620
+00:43:54,920 --> 00:43:58,540
+orthonormal hence orthonormal elements in H have
+
+621
+00:43:58,540 --> 00:44:02,120
+orthonormal images under mean under T أكيد لإنه
+
+622
+00:44:02,120 --> 00:44:05,380
+اللي بيحصل ال ال inner product بين X و X بيساوي X
+
+623
+00:44:05,380 --> 00:44:08,500
+و Y بيساوي T X و T Y لو كان ال inner product بين
+
+624
+00:44:08,500 --> 00:44:11,200
+هدولة صفر هيكون بين صفر لو كان واحد بيكون واحد إذا
+
+625
+00:44:11,200 --> 00:44:15,040
+أكيد اللي بيكون اللي هو ال orthonormal هنا image
+
+626
+00:44:15,040 --> 00:44:19,870
+ها هيكون إيش شماله orthonormal طيب الآن however T
+
+627
+00:44:19,870 --> 00:44:23,850
+is bijective إذا T تنقل every total orthonormal
+
+628
+00:44:23,850 --> 00:44:28,650
+set in إيش onto a total orthonormal set in مين in
+
+629
+00:44:28,650 --> 00:44:34,090
+H تلده ماشي و تفصيله لكم لإنه بيصير ال span هنا ال
+
+630
+00:44:34,090 --> 00:44:40,610
+span لل M الأولى ال closure بيساوي ال H الآن T لل
+
+631
+00:44:40,610 --> 00:44:43,750
+span لل M ال closure للثاني هتصير إيش ما لها ال H
+
+632
+00:44:43,750 --> 00:44:48,460
+تلده طيب، therefore H and H tilde have the same إيش
+
+633
+00:44:48,460 --> 00:44:52,100
+مالهم هلبرت دايمينشين لإنه صارت اللي هي نفس
+
+634
+00:44:52,100 --> 00:44:56,920
+العدد، طيب، الآن conversely suppose that، في تفصيل
+
+635
+00:44:56,920 --> 00:45:00,080
+الكلام، بس تفصيله مش صعب، suppose that, conversely
+
+636
+00:45:00,080 --> 00:45:02,700
+suppose that H and H tilde have the same hell bar
+
+637
+00:45:02,700 --> 00:45:06,280
+dimension، برضه بتلاقي isomorphism بينهم اللي هو
+
+638
+00:45:06,280 --> 00:45:08,620
+one to one و one to one و كده و كده، تفاصيله برضه
+
+639
+00:45:08,620 --> 00:45:15,770
+اللي هو صارت معهودة يعني، الآن في حالة H تساوي 0 و H
+
+640
+00:45:15,770 --> 00:45:19,290
+تلدة تساوي 0 هي تريفيال لأنه ما دام التنتين الهن في
+
+641
+00:45:19,290 --> 00:45:21,830
+نفس القرص اللي لديه واحد صفر تان هيتلاعياش صفر
+
+642
+00:45:21,830 --> 00:45:24,810
+معناته ال function بينهن سهل إنك ترتاب ال function
+
+643
+00:45:24,810 --> 00:45:28,690
+بينهن تكون one to one و one to كل شيء الآن إذا let
+
+644
+00:45:28,690 --> 00:45:33,110
+H لا تساوي مين لا تساوي صفر automatic ال H تلدة
+
+645
+00:45:33,110 --> 00:45:36,050
+حتكون إيش ما لها برضه مش صفر لأن إحنا قلنا إن
+
+646
+00:45:36,050 --> 00:45:40,630
+الـCMDL برضه مينشين and any total orthonormal set M
+
+647
+00:45:40,630 --> 00:45:44,350
+in H و M tilde in H اله in the same cardinality هه
+
+648
+00:45:44,350 --> 00:45:47,070
+إيش معناته إنه in the same dimension إن ال total
+
+649
+00:45:47,070 --> 00:45:50,410
+orthonormal set هنا ال cardinality لها هي نفس ال
+
+650
+00:45:50,410 --> 00:45:56,970
+cardinality في من؟ في الثانية معايا طيب الآن so we
+
+651
+00:45:56,970 --> 00:46:00,250
+can index them by the same index set يعني إحنا
+
+652
+00:46:00,250 --> 00:46:03,330
+بنقدر نرمز لهم بنفس ال index set لو هذولة كان
+
+653
+00:46:03,330 --> 00:46:05,890
+countable هذولة countable لو هذولة uncountable
+
+654
+00:46:05,890 --> 00:46:09,090
+uncountable لو عددهم ألف note ألف note لو عددهم
+
+655
+00:46:09,090 --> 00:46:13,050
+اللي هو زي عدد ال power of R عددهم زي عدد ال power
+
+656
+00:46:13,050 --> 00:46:15,610
+of R لو عددهم زي ال R بيكون عددهم زي ال R عارفين
+
+657
+00:46:15,610 --> 00:46:19,310
+إيش عدد ال R؟ cardinal of ال R هو C اللي هو ال
+
+658
+00:46:19,310 --> 00:46:23,750
+power of R بيصير 2 to the C و هكذا عارفين ما هذا
+
+659
+00:46:23,750 --> 00:46:28,400
+الكلام؟ إذا نسينا تذكروا it so we can index them by
+
+660
+00:46:28,400 --> 00:46:32,860
+the same index set اللي هي K and write M بتساوي EK
+
+661
+00:46:32,860 --> 00:46:38,960
+and M تلده بتساوي EK شماله تلده لإن هم نفس ال ..
+
+662
+00:46:38,960 --> 00:46:42,200
+ال .. ال .. البرده دايما شده now define بقولك اللي
+
+663
+00:46:42,200 --> 00:46:45,660
+هنعرف اللي هو T من H للH تلده بناء على ال teamتين
+
+664
+00:46:45,660 --> 00:46:51,270
+هذوله بدنا نعرف TX X من وين جاية من H بتساوي اللي
+
+665
+00:46:51,270 --> 00:46:56,190
+هو الـ X إيش أصلا هي summation X و EK في EK ماشي
+
+666
+00:46:56,190 --> 00:46:59,890
+هذا جلطنات زي ما أقولنا عبّر عنها على طول زي هي
+
+667
+00:46:59,890 --> 00:47:05,290
+لأن TX بده عبّر عن X و EK في مين في EK إيش ما لها
+
+668
+00:47:05,290 --> 00:47:09,190
+تلدة تبعت اللي هي ال M تلدة this is well defined
+
+669
+00:47:09,190 --> 00:47:13,350
+because لكل X element in H we have ال X بتساوي ال
+
+670
+00:47:13,350 --> 00:47:17,370
+summation هذا زي ما قلنا الآن عندي by Bezel's
+
+671
+00:47:17,370 --> 00:47:20,970
+Inquality ال summation هذا هيكون يشمل و converge
+
+672
+00:47:20,970 --> 00:47:24,270
+ماشي الحال إذا أكيد اللي هداك له قيمة then by
+
+673
+00:47:24,270 --> 00:47:27,810
+theorem تلتة خمسة اثنين ال X و ال EK و EK تلتة
+
+674
+00:47:27,810 --> 00:47:31,990
+over K ما دام هداك converge هيكون converge so that
+
+675
+00:47:31,990 --> 00:47:35,530
+ال TX و الموجودة في ال H تلتة يعني well defined
+
+676
+00:47:35,530 --> 00:47:41,550
+اللي الها قيمة الآن let X بتساوي كده و Y بتساوي كده
+
+677
+00:47:41,550 --> 00:47:44,870
+بيثبتوا إنه Linear وهذه شغل الحسابات اللي هي
+
+678
+00:47:44,870 --> 00:47:51,730
+الحسابات سهلة أخدت X اللي هي بشكل هذا و Y بشكل هذا
+
+679
+00:47:51,730 --> 00:47:56,990
+عارفين هذا الكلام سنة بي any element سيناتش والألف
+
+680
+00:47:56,990 --> 00:48:00,580
+عن ال scalar وحسب لي T Alpha X زائد Y حسب اللي ..
+
+681
+00:48:00,580 --> 00:48:02,900
+اللي .. اللي حكينا عنه قبل شوية بيصير الـ
+
+682
+00:48:02,900 --> 00:48:07,040
+summation اللي هو Alpha X زائد Y E K مع مين؟ مع E
+
+683
+00:48:07,040 --> 00:48:12,200
+K تلدة هيت القانون Y ساوي Alpha الآن بطالة الأن دي
+
+684
+00:48:12,200 --> 00:48:17,370
+اللي جوا هذه اللي هي بيصير X وE K وE K تلدة بقى الـ
+
+685
+00:48:17,370 --> 00:48:22,350
+inner product بفصلهم عادي و ال YK و ال A شماله و
+
+686
+00:48:22,350 --> 00:48:26,370
+EK تلده هذه إيه اللي هي عبارة عن TX و هذه شماله
+
+687
+00:48:26,370 --> 00:48:30,230
+TY فبصينا عند Alpha TX زي TY hence T is linear
+
+688
+00:48:30,230 --> 00:48:36,250
+اطلع على السوق الآن since EK تلده
+
+689
+00:48:36,250 --> 00:48:41,990
+is orthonormal then اللي هو احسب ليه ال TX و TX
+
+690
+00:48:42,830 --> 00:48:46,090
+بنسخد منها Orthonormal الـ TX والـ TX الـ TX إيش
+
+691
+00:48:46,090 --> 00:48:50,390
+عرفناها summation X و EK و EK تلدة كله هتلاقو
+
+692
+00:48:50,390 --> 00:48:54,710
+شغلات سهلة و بتنحسن و ال X و EK و EK تلدة over K
+
+693
+00:48:54,710 --> 00:48:58,030
+طلعوهم برة ال summation زي ما بنعمل دايما اللي
+
+694
+00:48:58,030 --> 00:49:00,990
+بعيد اللي هو بتلعب conjugate و الجريب بتلعب عادي
+
+695
+00:49:00,990 --> 00:49:05,110
+ماشي اللي عملناها عشرين مرة هذه بيساوي X و EK و X
+
+696
+00:49:05,110 --> 00:49:10,640
+و EM تلدة و EK و EK تلدة كل هيتسفر هيبقى البث مين
+
+697
+00:49:10,640 --> 00:49:13,880
+اللي هو summation واحدة عند K بيساوي M وهيكون اللي
+
+698
+00:49:13,880 --> 00:49:16,580
+هو هذا بيساوي واحد والتنتين هذا هو ال conjugate
+
+699
+00:49:16,580 --> 00:49:20,000
+تبعة اللي هو بيطلع هذا المضولة السربيع وهذا إيش
+
+700
+00:49:20,000 --> 00:49:25,440
+بيساوي normal X سربيع اتوح منها لسه إذا صار عندي 
+
+701
+00:49:25,440 --> 00:49:29,700
+الآن اللي إيش اللي سوّيته أنا اللي أثبته أنا بدي
+
+702
+00:49:29,700 --> 00:49:34,570
+أثبت إيش بدي أثبت إنه preserve inner product إيش 
+
+703
+00:49:34,570 --> 00:49:40,650
+يعني .. يعني X T X و T Y بساوي X و Y أنا إيش اللي
+
+704
+00:49:40,650 --> 00:49:44,350
+أثبتته قبل .. الآن اللي أثبته في الحسابات اللي
+
+705
+00:49:44,350 --> 00:49:53,450
+قبل بشويّة أثبتت إنه اللي هو الـ X و الـ X بساوي T X
+
+706
+00:49:53,450 --> 00:49:59,830
+و T X بدأ نتقل من هذه للـ general عشان نقول preserve
+
+707
+00:49:59,830 --> 00:50:04,790
+inner product طيب عشان تكون اللي هو خلّصنا الجزء
+
+708
+00:50:04,790 --> 00:50:08,050
+اللي .. اللي .. اللي خلّينا نقول الأهم الآن for any
+
+709
+00:50:08,050 --> 00:50:12,030
+x و y element .. x و y element in H بدأ نشتغل على
+
+710
+00:50:12,030 --> 00:50:16,190
+الريال و الـ .. و الـ complex بنفس الأسلوب كان اللي
+
+711
+00:50:16,190 --> 00:50:21,050
+هي .. اللي هي حالتين إذا بتذكروا لما أثبتناهم 
+
+712
+00:50:21,450 --> 00:50:27,210
+الأولى كانت T X و T Y بتساوي ربع في T X
+
+713
+00:50:27,210 --> 00:50:30,290
+ناقص T Y لكل تربيع ناقص T X و T Y لكل إيش
+
+714
+00:50:30,290 --> 00:50:36,850
+ما له تربيع ماشي الحال الآن و Y ساوي ربع في T X
+
+715
+00:50:36,850 --> 00:50:40,010
+زي T Y هي عبارة عن T X زي دوّي لكل إيش ما له
+
+716
+00:50:40,010 --> 00:50:45,050
+تربيع ماشي و الثانية T ويكس واي لكل إيش ما له تربيع
+
+717
+00:50:45,050 --> 00:50:50,540
+أنا اللي قبل بشويّة أثبتها في حالة اللي هي هذه أه
+
+718
+00:50:50,540 --> 00:50:54,000
+بساوي اللي هو X زي دوّي تربيع اللي اتّبعته مش اتّبعت
+
+719
+00:50:54,000 --> 00:50:57,980
+إن أنا X و X بتساوي T X و T X إيه إن كانت X, X minus
+
+720
+00:50:57,980 --> 00:51:02,580
+y, X زي دوّي اللي كانت بيصير عندي الآن هذه كلّها
+
+721
+00:51:02,580 --> 00:51:06,360
+حوّلتها لـ X زي دوّي تربيع و الـ .. هذه آسف و هذه
+
+722
+00:51:06,360 --> 00:51:11,080
+حوّلتها لـ X minus Y لكل تربيع لأن احسبوا هذه مع هذه
+
+723
+00:51:11,080 --> 00:51:14,760
+اللي هي إيش بتساوي بتساوي الـ inner product بين X و
+
+724
+00:51:14,760 --> 00:51:18,670
+Y similarly for the complex case بتعملوها أنتم نفس
+
+725
+00:51:18,670 --> 00:51:23,510
+الحسبة في .. في .. في برضه equality زيّها بالظبط
+
+726
+00:51:23,510 --> 00:51:27,890
+طيب hence T preserves the main, the inner product
+
+727
+00:51:27,890 --> 00:51:32,790
+لأنه أثبتنا أن T X Y إيشو بتساوي X أو Y طيب
+
+728
+00:51:32,790 --> 00:51:35,770
+similarly for the complex hence T preserves the
+
+729
+00:51:35,770 --> 00:51:39,630
+inner product which implies T is ما لها one to one
+
+730
+00:51:39,630 --> 00:51:42,860
+بدنا نثبت أخر حاجة اللي هي إيش ما لها onto ماشي،
+
+731
+00:51:42,860 --> 00:51:46,320
+أنتم كيف بناخد؟ بناخد أيّ X تِلدة الموجودة في الـ H
+
+732
+00:51:46,320 --> 00:51:52,160
+تِلدة وبدنا نجيلها أصل، ماشي؟ شوفوا، خدوا أيّ X تِلدة
+
+733
+00:51:52,160 --> 00:51:55,380
+بتساوي summation Alpha K E K تِلدة over K element
+
+734
+00:51:55,380 --> 00:51:59,420
+in mean الـ H تِلدة، هذه الصورة عناصرها طيب، by
+
+735
+00:51:59,420 --> 00:52:02,280
+Besselin quality الـ summation للـ Alpha K تربيع
+
+736
+00:52:02,280 --> 00:52:08,810
+over K converts الآن الـ summation للـ α K E K is
+
+737
+00:52:08,810 --> 00:52:12,910
+finite sum of a series which converts to X element
+
+738
+00:52:12,910 --> 00:52:16,130
+in H by theorem تلاتة خمس اتنين مادام الـ summation
+
+739
+00:52:16,130 --> 00:52:21,810
+هذه إيش ملها معايا؟ طيب
+
+740
+00:52:21,810 --> 00:52:28,180
+الآن صحيح عند الـ summation هذا is finite اللي هو
+
+741
+00:52:28,180 --> 00:52:32,480
+قيمته finite بغض النظر اللي هو عبارة عن finite sum
+
+742
+00:52:32,480 --> 00:52:37,280
+من الواحد اللي عند أن أو series converts اللي هو
+
+743
+00:52:37,280 --> 00:52:41,520
+twitch من theorem طلعت خمس اتنين and الفا كيه هدول
+
+744
+00:52:41,520 --> 00:52:44,880
+الفا كيه عبارة عن فرير coefficients بتطلع اللي هي
+
+745
+00:52:44,880 --> 00:52:49,360
+الـ X و الـ E K الآن نفس النظرية فبتصير الآن الـ X
+
+746
+00:52:49,360 --> 00:52:53,900
+تِلدة هذه هتساوي الـ Alpha K هي عبارة عن X و E K أيّ K
+
+747
+00:52:53,900 --> 00:52:58,880
+تِلدة اللي هي في الواقع إيش هتكون الـ T X إذا لجيت
+
+748
+00:52:58,880 --> 00:53:04,910
+أنا الآن بدأت بـ X تِلدة arbitrary و لجيت X موجودة في
+
+749
+00:53:04,910 --> 00:53:09,150
+الـ H بحيث أن T X بتساوي X تِلدة معناته صارت T is
+
+750
+00:53:09,150 --> 00:53:13,330
+onto و أثبتت إنها Linear و أثبتت بـ Reserve the
+
+751
+00:53:13,330 --> 00:53:17,270
+norm و أثبتت onto one to one صارت اللي هي T is an
+
+752
+00:53:17,270 --> 00:53:20,910
+isomorphism بين H and H تِلدة و إلى لقاء آخر السلام
+
+753
+00:53:20,910 --> 00:53:21,670
+عليكم و رحمة الله
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/CRLpGXH9NAM_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/CRLpGXH9NAM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a95204c742d3636267c08d03168cbe65a4de26d8
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/CRLpGXH9NAM_raw.srt
@@ -0,0 +1,3016 @@
+1
+00:00:05,060 --> 00:00:07,820
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,820 --> 00:00:10,740
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,740 --> 00:00:16,160
+آله وصحبه أجمعين هذه المحاضرة رقم 22 مساب تحليل
+
+4
+00:00:16,160 --> 00:00:18,960
+اقتراني او تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:18,960 --> 00:00:22,440
+الإسلامية مجلسية الرياضيات اليوم وصلنا لعند او
+
+6
+00:00:22,440 --> 00:00:26,530
+اليوم هنحكي في هذه المحاضرة على تلاتة ستةاللي هي
+
+7
+00:00:26,530 --> 00:00:30,470
+تحت عنوان Total Orthonormal Sets and Sequences
+
+8
+00:00:30,470 --> 00:00:34,130
+احنا حكينا عن الـ Orthonormal Sets و Orthonormal
+
+9
+00:00:34,130 --> 00:00:38,070
+Sequences الآن الفكرة في الـ Total Orthonormal
+
+10
+00:00:38,070 --> 00:00:42,950
+Sets and Sequences احنا
+
+11
+00:00:42,950 --> 00:00:49,330
+بدنا نبحث عن set انها من خلالها نجيب ال space كله
+
+12
+00:00:49,880 --> 00:00:55,760
+كل space يعني ما كأنه مشابه لعمل اللي هي roughly
+
+13
+00:00:55,760 --> 00:00:59,600
+هذا الكلام مشابه لعمل ال bases في حالة اللي هو في
+
+14
+00:00:59,600 --> 00:01:02,480
+ال finite dimensional case في حالة ال finite
+
+15
+00:01:02,480 --> 00:01:05,140
+dimensional case اللي بتجيب ال space اللي هو اللي
+
+16
+00:01:05,140 --> 00:01:08,060
+انتوا عارفين ال bases انه على طول اللي هو linearly
+
+17
+00:01:08,060 --> 00:01:12,120
+independent independentlinearly independent معناته
+
+18
+00:01:12,120 --> 00:01:16,500
+يعني ان هي بمعنى اخر انه اقتصادي انه انا مابحطش اش
+
+19
+00:01:16,500 --> 00:01:21,480
+زيادة بقدر اجيبه منهم الجزء الثاني انه بعمل span و
+
+20
+00:01:21,480 --> 00:01:25,820
+بعمل كل space الان في حالة ال infinite dimensional
+
+21
+00:01:25,820 --> 00:01:29,600
+في ال separable الأمور كمان أبسط شوية في حالة ال
+
+22
+00:01:29,600 --> 00:01:34,740
+non separable spacesبصير الأمور حتى شغل فيها شوية
+
+23
+00:01:34,740 --> 00:01:39,720
+أعقد احنا هنشتغل بما ي .. خلانا نقول بما يناسبنا
+
+24
+00:01:39,720 --> 00:01:44,460
+في ال course هذا يعني اللي هيعمل ال .. العمل هذا
+
+25
+00:01:44,460 --> 00:01:48,480
+اللي هو انه من خلاله انه هحنحاول نجيب ال space او
+
+26
+00:01:48,480 --> 00:01:51,600
+اللي حصل عن ال space رفلي هذا الكلام اللي هو حاجة
+
+27
+00:01:51,600 --> 00:01:57,100
+اسمها total orthonormal setالمرة الفاترة حكينا عن
+
+28
+00:01:57,100 --> 00:01:59,640
+ال orthonormal set اليوم ده نحكي عن ال total اللي
+
+29
+00:01:59,640 --> 00:02:03,800
+هي هتعمل هذا العمل خلينا نيجي نطلع على اللي هو شو
+
+30
+00:02:03,800 --> 00:02:06,760
+معناته ال definition أو شو ال definition ل ال
+
+31
+00:02:06,760 --> 00:02:09,280
+total set أو ال issue و بعدين نيجي ل اللي هو ال
+
+32
+00:02:09,280 --> 00:02:12,950
+orthonormal اللي احنا عارفينهالـ Total set أو الـ
+
+33
+00:02:12,950 --> 00:02:16,610
+Fundamental set هي عبارة ان a norm of this base X
+
+34
+00:02:16,610 --> 00:02:19,170
+في أي نوم of this base in general احنا بس شغلنا
+
+35
+00:02:19,170 --> 00:02:22,810
+هيكون في الهيلبرغ is a subset M عبارة عن مجموعة ZM
+
+36
+00:02:22,810 --> 00:02:27,370
+of X whose span is dense in X يعني بس المطلوب منها
+
+37
+00:02:27,370 --> 00:02:31,450
+ان سبانها .. سبان .. بقول على room total .. اذا
+
+38
+00:02:31,450 --> 00:02:37,080
+كان سبانللأم closure بيساوي مين كل space X فهذه
+
+39
+00:02:37,080 --> 00:02:41,880
+الحالة بنسمي اللي هي الست أم إيه شمالها is total
+
+40
+00:02:44,210 --> 00:02:48,210
+الان a total orthonormal set هي بتكون total في نفس
+
+41
+00:02:48,210 --> 00:02:51,370
+الوجه ايه اشمالها orthonormal يعني الجهتين وال
+
+42
+00:02:51,370 --> 00:02:55,590
+orthonormal انتوا عارفين شو معناه orthonormal ال
+
+43
+00:02:55,590 --> 00:02:59,630
+inner product بين كلتين تان مختلفتين سفر وبين
+
+44
+00:02:59,630 --> 00:03:04,270
+الواحدة ونفسها عبارة عن واحد اطلع لفوق الان بعض
+
+45
+00:03:04,270 --> 00:03:10,150
+الملاحظات عندي الملاحظتين اللي عندي أمورهمخلّينا
+
+46
+00:03:10,150 --> 00:03:14,090
+نقول مقدور عليها وفي إشي يعني trivial في حالة ال
+
+47
+00:03:14,090 --> 00:03:17,610
+finite dimensional والتانية اللي هي في حالة ال non
+
+48
+00:03:17,610 --> 00:03:20,910
+separable هذا خارج نطاق شغلنا فإحنا الملاحظات
+
+49
+00:03:20,910 --> 00:03:24,550
+تانية اللي هنحكيهن بشكل أساسي يعني اللي هو برهان
+
+50
+00:03:24,550 --> 00:03:27,230
+هنا الجزء الأول ال trivial اللي هو بما يتعلق بال
+
+51
+00:03:27,230 --> 00:03:30,730
+finite dimensional والتاني بده شوية شغل بتعلق
+
+52
+00:03:30,730 --> 00:03:33,710
+بنظرية اللي خدناها اللي هناخدهن إيش هنا الملاحظات
+
+53
+00:03:33,710 --> 00:03:38,990
+تانية؟In every Hilbert space hatch لأن انا انا
+
+54
+00:03:38,990 --> 00:03:42,250
+قاعد بده اروح باتجاه ان هو هذا ال total earth is
+
+55
+00:03:42,250 --> 00:03:47,680
+normal setهي اللي هتجيبلي ال space فعليها هسمي ال
+
+56
+00:03:47,680 --> 00:03:51,220
+dimension زي ما بنسمي ال dimension على ال ال bases
+
+57
+00:03:51,220 --> 00:03:55,180
+في الحالة اللي هي ال finite dimensional هنحن بنسمي
+
+58
+00:03:55,180 --> 00:03:57,700
+ال bases اللي هو ال dimension اللي هنا على حسب
+
+59
+00:03:57,700 --> 00:04:00,660
+اللي هو ال total orthonormal set اللي عندك انتبهش
+
+60
+00:04:00,660 --> 00:04:03,800
+بقول in every Hilbert space H ل H سوا سفر there
+
+61
+00:04:03,800 --> 00:04:07,680
+exists a total orthonormal set يعني مضمون انه اي
+
+62
+00:04:07,680 --> 00:04:10,500
+Hilbert space H سوا ال finite dimension في حالة ال
+
+63
+00:04:10,500 --> 00:04:14,180
+finite اللي هو ال basesماقياش بتثبيت أنه يكون اللي
+
+64
+00:04:14,180 --> 00:04:17,940
+هي ال norm لكل واحدة بساوي واحد ال .. ال .. ال ..
+
+65
+00:04:17,940 --> 00:04:20,680
+الحالة ال inseparable حالة ال non inseparable
+
+66
+00:04:20,680 --> 00:04:23,680
+انسوها مش .. مش مديعنة الحالة ال inseparable اللي
+
+67
+00:04:23,680 --> 00:04:28,700
+هو فيه hint عليها في .. في الكتابأي Hilbert space
+
+68
+00:04:28,700 --> 00:04:35,220
+H مضمون له total orthonormal set هاي واحد اتنين كل
+
+69
+00:04:35,220 --> 00:04:38,160
+ال total orthonormal set في ال Hilbert space H
+
+70
+00:04:38,160 --> 00:04:40,760
+لايه تساوي سفر اي Hilbert space ال total
+
+71
+00:04:40,760 --> 00:04:43,240
+orthonormal set لهم كلهين have the same
+
+72
+00:04:43,240 --> 00:04:46,960
+cardinality يعني اللي هو زي في حالة ال bases اللي
+
+73
+00:04:46,960 --> 00:04:50,820
+هي نفس العدد هي the same cardinality لخوف انها
+
+74
+00:04:50,820 --> 00:04:55,680
+تكون ايه اش ما لها infinite number of elementsالان
+
+75
+00:04:55,680 --> 00:04:59,100
+بناء عليه مدام كله نلهم نفس ال cardinality هذه ال
+
+76
+00:04:59,100 --> 00:05:01,200
+cardinality اللي لهم هي اللي بنسميها ال diamonds
+
+77
+00:05:01,200 --> 00:05:05,400
+شلمين لل Hilbert space اللي بنحكي عنه where the
+
+78
+00:05:05,400 --> 00:05:08,220
+cardinality of the total orthonormal sit in a
+
+79
+00:05:08,220 --> 00:05:12,140
+Hilbert space أشلس أو شفر الآن هذا اللي هي الأولى
+
+80
+00:05:12,140 --> 00:05:16,130
+اللي هي اللي بدها ال hint للبرهانةWhere the
+
+81
+00:05:16,130 --> 00:05:18,670
+cardinality of the total orthonormal set in
+
+82
+00:05:18,670 --> 00:05:23,570
+Hilbert 3H0900 is called the Hilbert dimension or
+
+83
+00:05:23,570 --> 00:05:25,990
+orthogonal dimension of H
+
+84
+00:05:36,100 --> 00:05:38,960
+ملاقى باسيس مايكونش هيك الأمر في الـ Final
+
+85
+00:05:38,960 --> 00:05:42,080
+Dimension لك اذا H بتساوي سفر الـ Hilbert
+
+86
+00:05:42,080 --> 00:05:47,240
+Dimension اللي نعرفه هو الـ Zero اللي هو الـ
+
+87
+00:05:47,240 --> 00:05:53,060
+Dimension له بروف left to the reader اللي فيه هند
+
+88
+00:05:53,060 --> 00:05:57,080
+في الكتاب الجزء
+
+89
+00:05:57,080 --> 00:06:00,520
+اللي هو الـ separable اللي المطلوب نيجي للنظرية
+
+90
+00:06:00,520 --> 00:06:06,320
+اللي عندناأطلع لفوق شوية ايوة هنا وقفت بقول لي let
+
+91
+00:06:06,320 --> 00:06:09,820
+m be a subset of an inner product space X ماشي
+
+92
+00:06:09,820 --> 00:06:14,950
+الحالعندي M subset من مين؟ من inner product مش ال
+
+93
+00:06:14,950 --> 00:06:18,870
+part space inner product بلزم يشتر بها then الشرط
+
+94
+00:06:18,870 --> 00:06:25,030
+الأول if M is total in X then X element in X and X
+
+95
+00:06:25,030 --> 00:06:28,350
+عموديه على X implies X ايش بتساوي؟ بتساوي سفر هذا
+
+96
+00:06:28,350 --> 00:06:31,310
+كله على بعض شو معناه انه لما تكون X في X و X
+
+97
+00:06:31,310 --> 00:06:34,770
+عموديه على M لازم يعطيني ان X بتساوي سفر يعني
+
+98
+00:06:34,770 --> 00:06:38,830
+وكأني بدي اقول اللي هي بدل هذه كلها ان M
+
+99
+00:06:38,830 --> 00:06:43,370
+orthogonal بساوي 0 بسإن كل X عمودي على M هيطلع إيش
+
+100
+00:06:43,370 --> 00:06:48,010
+بس؟ هو السفر يعني و كأني بقول إن M Orthogonal هو
+
+101
+00:06:48,010 --> 00:06:51,970
+Zero يعني لو كانت M Total in X then M Orthogonal
+
+102
+00:06:51,970 --> 00:06:56,830
+بساوة Zero الآن الجزء الثاني إذا كانت X Complete
+
+103
+00:06:56,830 --> 00:07:01,190
+يعني Hilbert Space بمعنى آخر و if the condition
+
+104
+00:07:01,190 --> 00:07:06,270
+اللي هو M Orthogonal بساوة Zero is satisfied then
+
+105
+00:07:06,270 --> 00:07:12,880
+M إيش هتطلع Total Set in X ماشي الحالةالبرهان بقى
+
+106
+00:07:12,880 --> 00:07:18,240
+فيه أخدنا المرة الفاتة نظرية في حالة الـ H H اللي
+
+107
+00:07:18,240 --> 00:07:22,700
+هي Hilbert space وكأس بكون عندي M orthogonal و M
+
+108
+00:07:22,700 --> 00:07:27,000
+subset منها أخدناها بتيصير M orthogonal بساوة Zero
+
+109
+00:07:27,000 --> 00:07:35,060
+if and only if M أو لسبان لـ M is dense in mean in
+
+110
+00:07:35,060 --> 00:07:41,450
+H أخدناها المرة الماضية أهدف عن استخدامهاالكلام
+
+111
+00:07:41,450 --> 00:07:47,410
+هذا عبارة عن إعادة صياغة لهذه النظرية تقريبا اللي
+
+112
+00:07:47,410 --> 00:07:52,770
+هو بلغة ال total لأن ال total عرفناها إيش ماله، ال
+
+113
+00:07:52,770 --> 00:07:55,870
+span ل ال omicron بساوي إيش، ال space، ال space
+
+114
+00:07:55,870 --> 00:08:01,710
+كلهنجي الآن البرهن لت H بي the completion of X
+
+115
+00:08:01,710 --> 00:08:04,250
+لإنه عشان .. ليش أخدتش completion لل X؟ لإنه أنا
+
+116
+00:08:04,250 --> 00:08:08,110
+بدأ أستخدم نيل النظرية هذه اللي هي بتعتمد على إياش
+
+117
+00:08:08,110 --> 00:08:12,350
+إنه تكون H عبارة عن ال part space وإحنا ضمنين إنه
+
+118
+00:08:12,350 --> 00:08:17,770
+product إيه له completion، ال completion بتكون X
+
+119
+00:08:17,770 --> 00:08:21,780
+then Cماحنا عارفين لما نركبنا اللي هو عملنا ال
+
+120
+00:08:21,780 --> 00:08:25,160
+completion بتكون ال X dense فيه then X can be
+
+121
+00:08:25,160 --> 00:08:29,580
+regarded ممكن تعتبر as a subspace of H which is
+
+122
+00:08:29,580 --> 00:08:34,960
+dense in مين in H طيب however M نفسها is total in
+
+123
+00:08:34,960 --> 00:08:38,800
+X مازال total in X إذا ال closure إلها with
+
+124
+00:08:38,800 --> 00:08:43,480
+respect to X هي .. السباق .. أسف .. السباق لل M ال
+
+125
+00:08:43,480 --> 00:08:46,760
+closure إلها with respect to X هي سوى مين ال X
+
+126
+00:08:46,760 --> 00:08:50,770
+dense فيهاوالـ X نفسها أصلاً زنس في الـ H فبكون
+
+127
+00:08:50,770 --> 00:08:54,410
+نسبان للـ M closure with respect to H هيطلع برضه
+
+128
+00:08:54,410 --> 00:08:58,970
+مين H فبتكون it is zens in مين in H إذا صار هذا
+
+129
+00:08:58,970 --> 00:09:03,090
+متحقق إذا أكيد ال M Orthogonal إيش هتساوي؟ هتساوي
+
+130
+00:09:03,090 --> 00:09:06,610
+سفر إذا M Orthogonal هذا من لمّا إيش اللي بحكيت
+
+131
+00:09:06,610 --> 00:09:11,890
+عنها ديك اسمها ليه لمّا تلاتة تلاتة سبعة اللي
+
+132
+00:09:11,890 --> 00:09:17,620
+بعدها مباشرةخلّي بس نزلت شوية عشان نشوف النص اللي
+
+133
+00:09:17,620 --> 00:09:21,620
+بعدها إذا كانت X Complete يعني X is Hilbert space
+
+134
+00:09:21,620 --> 00:09:27,080
+و M Orthogonal بساوي 0 من هذه مباشرة مباشرة هيكون
+
+135
+00:09:27,080 --> 00:09:32,120
+اللي هو ال M Orthogonal إيش بتساوي؟ و هذي Span
+
+136
+00:09:32,120 --> 00:09:36,120
+Closure بتساوي H متكافئتين إذا على طول بنستخدمها
+
+137
+00:09:36,120 --> 00:09:40,980
+لهذه بصير عندي الآن H Complete و M Orthogonal Zero
+
+138
+00:09:40,980 --> 00:09:45,490
+إذا عليه طلعتعلى طول لسبان كلوجر ايش بيساوي بيساوي
+
+139
+00:09:45,490 --> 00:09:49,430
+ال H لسبان كلوجر بيساوي H شو معناته M is total
+
+140
+00:09:49,430 --> 00:09:57,670
+واضحة طيب اللي قلته يا جماعة انه بما انه X
+
+141
+00:09:57,670 --> 00:10:03,160
+completeو M Orthogonal بتساوي سفر إذا بواسط تهاد
+
+142
+00:10:03,160 --> 00:10:08,120
+النظرية أنه مادامة M Orthogonal Zero بتطلع ل Span
+
+143
+00:10:08,120 --> 00:10:11,180
+ل M closure إيش بيساوي إتش يعني Span ل M between
+
+144
+00:10:11,180 --> 00:10:18,090
+Mين إتش يعني M is total هي عرفنا ب totalالنظرية
+
+145
+00:10:18,090 --> 00:10:25,550
+تلاتة ستة تلاتة تلاتة
+
+146
+00:10:25,550 --> 00:10:32,840
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتةالـ
+
+147
+00:10:32,840 --> 00:10:37,260
+orthonormal set M in a Hilbert space H is total in
+
+148
+00:10:37,260 --> 00:10:41,740
+H if and only if الbar θ ال equality بتصير يعني ال
+
+149
+00:10:41,740 --> 00:10:44,000
+summation بدل ما كانت بيصير ده تكون اي شمالها
+
+150
+00:10:44,000 --> 00:10:48,420
+بيكون بيصير ال summation لل X وال E K تربيع K over
+
+151
+00:10:48,420 --> 00:10:52,380
+K بيسووا من Normal X تربيع for all X المتناجح إذا
+
+152
+00:10:52,380 --> 00:10:58,910
+بتتذكروا المرة الماضيةقلنا بس على جهة هنا هذه اللي
+
+153
+00:10:58,910 --> 00:11:01,510
+هو ال terms اللي جوا ال for real series هذول
+
+154
+00:11:01,510 --> 00:11:05,750
+coefficients هذولة كلهين is far ماعدا countable
+
+155
+00:11:05,750 --> 00:11:08,990
+number منهم قلنا ال countable number هو اللي بتكون
+
+156
+00:11:08,990 --> 00:11:12,030
+اللي هي ممكن تكون non-zero element لكن كل الباقي
+
+157
+00:11:12,030 --> 00:11:15,910
+إيش ماله يعني مش فارقة معايا في الآخر هذه over k
+
+158
+00:11:15,910 --> 00:11:20,260
+لو كانت uncountable اللي هي العدادبظل اللي هي
+
+159
+00:11:20,260 --> 00:11:24,780
+الاشي اللي فيهه قيمة عددية غير الـ Zero بيكون فعلا
+
+160
+00:11:24,780 --> 00:11:29,580
+هو أيش ماله countable طيب هذا على جهة بس الان بدنا
+
+161
+00:11:29,580 --> 00:11:32,480
+ناخد الاتجاه الأول و بعدين الاتجاه الثاني أول
+
+162
+00:11:32,480 --> 00:11:36,500
+اتجاه بيقوللي بدنا .. الآن عندي .. بدنا نثبت انه ا
+
+163
+00:11:36,500 --> 00:11:37,700
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+164
+00:11:37,700 --> 00:11:37,920
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+165
+00:11:37,920 --> 00:11:38,120
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+166
+00:11:38,120 --> 00:11:39,440
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+167
+00:11:39,440 --> 00:11:39,520
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+168
+00:11:39,520 --> 00:11:41,580
+.. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا .. ا
+
+169
+00:11:41,580 --> 00:11:42,100
+.. ا ..
+
+170
+00:11:45,630 --> 00:11:50,550
+if and only if اللي هو normal X تربيع بساوية الـ
+
+171
+00:11:50,550 --> 00:11:53,770
+summation لأ اللي هي الـ Fourier coefficients دولة
+
+172
+00:11:53,770 --> 00:12:00,170
+A over K اللي أنا بدي أفترض الآن اللي هو بدي أثبت
+
+173
+00:12:00,170 --> 00:12:05,710
+الآن عشان أثبت اللي هو الاتجاه هذايعني بدي أبدأ
+
+174
+00:12:05,710 --> 00:12:09,390
+بهذا و أصل لهذا، ماشي؟ يعني بدي أقول suppose هذا
+
+175
+00:12:09,390 --> 00:12:13,410
+متحقق و أصل لهذا عشان أثبتها هذه بدي أثبتها by
+
+176
+00:12:13,410 --> 00:12:16,510
+contraposition يعني بدي أفترض أن الـM is not total
+
+177
+00:12:16,510 --> 00:12:20,870
+و أصل لهذه معناته أن هذه بيصير تؤدي لهذه إذا الآن
+
+178
+00:12:20,870 --> 00:12:27,430
+if suppose that M is not total ماشي؟ مدام مش total
+
+179
+00:12:28,800 --> 00:12:33,960
+إذا الـ M .. اللي احنا قلنا لو كانت M total M
+
+180
+00:12:33,960 --> 00:12:37,080
+total اللي هو معناته اللي .. اللي هو بتكون M
+
+181
+00:12:37,080 --> 00:12:41,340
+أرثجون الأشمال،ها Zero ماشي، مدامت M .. و هذه F
+
+182
+00:12:41,340 --> 00:12:45,260
+and F، أشتغلنا قدّيها تاني إذا كانت M is not
+
+183
+00:12:45,260 --> 00:12:47,540
+total، اللي من ال theorem اللي قبل بشوية، تلاتة،
+
+184
+00:12:47,540 --> 00:12:52,920
+ستة اتنين، B، هيكون عندي أكيد في اللي هو الـ M
+
+185
+00:12:52,920 --> 00:12:57,950
+أرثجون المش Zeroإذا بمعنى أخر بلاقي X إيش معناه M
+
+186
+00:12:57,950 --> 00:13:01,050
+Orthogonal مش Zero يعني في X في ال M Orthogonal
+
+187
+00:13:01,050 --> 00:13:06,270
+مقله عمودي على ال M و بيسويش سفر إذا there is X
+
+188
+00:13:06,270 --> 00:13:10,030
+element لأتش و X لاته ساوى سفر and X Orthogonal
+
+189
+00:13:10,030 --> 00:13:15,510
+لمين؟ لل M هذا امسكوا فيه then صار عند X و EK
+
+190
+00:13:15,510 --> 00:13:22,740
+بيساوى سفر لكل EK element من M هو نفسه مش سفرطيب
+
+191
+00:13:22,740 --> 00:13:28,140
+إذا hence ال summation ل X و EK تربيع over K كله
+
+192
+00:13:28,140 --> 00:13:32,160
+نفسه هيساوي سفر و مش هيساوي من norm X تربيعه إن X
+
+193
+00:13:32,160 --> 00:13:36,380
+نفسه مش zero إذا صار عندي ال contraposition تحققت
+
+194
+00:13:36,380 --> 00:13:39,540
+إنه لو كانت هذه مش total هتأدي هذا وهذا معناه أن
+
+195
+00:13:39,540 --> 00:13:43,960
+هذا يؤدي هذا therefore if ال summation بيساوي كذا
+
+196
+00:13:43,960 --> 00:13:48,840
+for all اللي هي X المتناش then M اسمها is total in
+
+197
+00:13:48,840 --> 00:13:57,340
+H و converselyالان بدأ افترض انه M is total واصل
+
+198
+00:13:57,340 --> 00:14:02,720
+للمساواة دي اللي ال بارسيفال مالها متحققة لاحظوا
+
+199
+00:14:02,720 --> 00:14:08,400
+ما هي اللي الان suppose that M is total in H وخد X
+
+200
+00:14:08,400 --> 00:14:12,600
+be any element in M in H في arbitrary لكن fixed
+
+201
+00:14:12,600 --> 00:14:16,060
+عشان اثبت لكم انه نور متربية بساوي ال summation
+
+202
+00:14:16,060 --> 00:14:21,540
+اللي عندها طيب صلى الله عليه الصلاة والسلامالان
+
+203
+00:14:21,540 --> 00:14:25,540
+الـ Range of all its non-zero Fourier coefficients
+
+204
+00:14:25,540 --> 00:14:30,220
+in a sequence X و E1 و X و E2 و الى اخرها و بقدر
+
+205
+00:14:30,220 --> 00:14:33,400
+اعمل هيك حتى لو كانت uncountable ليش؟ لان قبل شوية
+
+206
+00:14:33,400 --> 00:14:38,440
+قلتلكم اللي هي الـ non-zero منهااللي هي حاجة تكون
+
+207
+00:14:38,440 --> 00:14:42,420
+countable هم اللي بيعملوا هنا arrangement إذا الأن
+
+208
+00:14:42,420 --> 00:14:46,480
+هدول اللي اختارتهم من هنا اللي هم مش سفر فبصير
+
+209
+00:14:46,480 --> 00:14:50,120
+عندي X و E واحد و X و E اتنين إلى مالة نهاية اللي
+
+210
+00:14:50,120 --> 00:14:55,830
+هي أعملت .. أحطيتهم في sequenceوإذا كان في نايت
+
+211
+00:14:55,830 --> 00:14:59,210
+خلاص من كتب ال X و X و Y أحد و X و Y اتنين و X و Y
+
+212
+00:14:59,210 --> 00:15:04,710
+انتصار اذا ر مكتوب في حركة محددة إذا كان هناك عدد
+
+213
+00:15:04,710 --> 00:15:05,610
+منهم فقط في نايت
+
+214
+00:15:09,690 --> 00:15:14,930
+واضح طيب الان define y by الان هاي الألداء اللي
+
+215
+00:15:14,930 --> 00:15:20,290
+بتوصلني للي بديها الان خليني أن أعرف y بواسطة y
+
+216
+00:15:20,290 --> 00:15:23,250
+بالسواء و ال summation x و ek ek كامن عند واحد إلى
+
+217
+00:15:23,250 --> 00:15:28,030
+مين إلى مال نهاية طيب شو سميلي هذه واحدة لأن بعد
+
+218
+00:15:28,030 --> 00:15:34,350
+شوية أرجعلها أنا بعرف أن أم اشمالها is orthonormal
+
+219
+00:15:34,350 --> 00:15:39,540
+set مدام orthonormal setthen for every ej
+
+220
+00:15:39,540 --> 00:15:45,280
+occurring in one اللي هي الاج اللي في واحد اللي هي
+
+221
+00:15:45,280 --> 00:15:49,120
+واحد لما أخدنا ال summation هذا over k فيه جزئين
+
+222
+00:15:49,120 --> 00:15:53,240
+جزء منه اللي هو عملتله arranging اللي هو xe واحد
+
+223
+00:15:53,240 --> 00:15:57,120
+إلى آخرهم وهدولة اللي هي non-zero elements والجزء
+
+224
+00:15:57,120 --> 00:16:02,020
+الثاني منهم خلّينا نسميه v و ال v هذا ايش مالوسفار
+
+225
+00:16:02,020 --> 00:16:06,470
+ماشي الحال طيب اوبتيجي الآن عملنا arrangement
+
+226
+00:16:06,470 --> 00:16:11,230
+since M is orthonormal then for every EJ occurring
+
+227
+00:16:11,230 --> 00:16:15,790
+in one اللي عملنا لها arrangement we have X minus
+
+228
+00:16:15,790 --> 00:16:19,770
+Y و EJ ال X ال arbitrator ال botfix اللي خدناها في
+
+229
+00:16:19,770 --> 00:16:24,990
+الأول هي عليها الشغل طيب بتساوي X و EJ ناقص Y مين
+
+230
+00:16:24,990 --> 00:16:30,200
+و EJو يساوي X و EJ زي ما هي ناقص هذه ناقص ال
+
+231
+00:16:30,200 --> 00:16:35,740
+summation X و EK في EK و EJ الان عندنا كل هين
+
+232
+00:16:35,740 --> 00:16:40,460
+هيتسفر مع ده EJ ايش مع EJ لإن هو orthonormal إذا
+
+233
+00:16:40,460 --> 00:16:44,940
+صار عند هذا X EJ و هذا X EJ إذا إيش هيساوي؟ هيساوي
+
+234
+00:16:44,940 --> 00:16:50,060
+سفر إذا أثبت لكم الآن X minus Y و EJ بساوي سفر لكل
+
+235
+00:16:50,060 --> 00:16:54,940
+واحدة من العائلة الأولى هذه نيجي الآن ناخدلأن for
+
+236
+00:16:54,940 --> 00:16:59,100
+all V elements in M not occurring in one يعني اللي
+
+237
+00:16:59,100 --> 00:17:01,140
+ما حصلت .. اللي ما أخدناهنش منها .. نحنا قلنا
+
+238
+00:17:01,140 --> 00:17:04,680
+جزأناها جزءين الجزء اللي بيسفرن هو الجزء السفر
+
+239
+00:17:04,680 --> 00:17:08,080
+اللي بيسفرنش هو الجزء السفر هذا أخدنا ال V ال
+
+240
+00:17:08,080 --> 00:17:12,180
+element in M اللي بيعملني سفر we have .. اللي هي
+
+241
+00:17:12,180 --> 00:17:16,520
+طبعا ال V هذي مش هذا ال V اللي هو اللي بيعمله سفر
+
+242
+00:17:16,520 --> 00:17:20,360
+اللي هي .. اللي هو X و V اللي هو أياش مستوى سفر
+
+243
+00:17:20,360 --> 00:17:27,640
+فاهمين عليها أه؟عشان تكون الأمور واضحة اذا we have
+
+244
+00:17:27,640 --> 00:17:32,320
+x و v بيساوي سفر so that احسبني برضه ال x minus y
+
+245
+00:17:32,320 --> 00:17:37,440
+و mean و ال v ايش حيسوي x و v ناقص اللي هو ال
+
+246
+00:17:37,440 --> 00:17:41,260
+summation اللي هو y عبارة عن x و ek و ek و mean و
+
+247
+00:17:41,260 --> 00:17:46,780
+v برضه نفس الجثة ال v ولا واحدة من هدول أصلاأه إذا
+
+248
+00:17:46,780 --> 00:17:49,020
+.. إذا صار عند ال inner product بينه إيش ماله
+
+249
+00:17:49,020 --> 00:17:54,580
+بساوي سفر وهذا أصلا عند X و EK و EK في V هيطلع
+
+250
+00:17:54,580 --> 00:17:59,420
+القيمة كل مرة سفر إذا صار عند X minus Y و V بساوي
+
+251
+00:17:59,420 --> 00:18:05,400
+سفر يعني بمعنى آخر X minus Y وكل العناصر اللي في M
+
+252
+00:18:05,400 --> 00:18:08,860
+سواء العصورة هذه أو العصورة هذه صار ال inner
+
+253
+00:18:08,860 --> 00:18:12,200
+product بينهم سفر يعني X minus Y إيش صارت عمودية
+
+254
+00:18:12,200 --> 00:18:17,720
+على ال Mما دام X minus Y عمودية على الـ M و الـ M
+
+255
+00:18:17,720 --> 00:18:21,360
+however M is totally matched then by لمّة ثلاثة
+
+256
+00:18:21,360 --> 00:18:25,120
+سبعة اتنين هيطلع عند .. كان عند الـ M ارتجونالاش
+
+257
+00:18:25,120 --> 00:18:28,760
+بساوة سفر دي ما هي مهمة و قالش اتمنى في الأول إذا
+
+258
+00:18:28,760 --> 00:18:31,720
+صار عند ال X minus Y اللي موجود هان هيساوة سفر
+
+259
+00:18:31,720 --> 00:18:36,740
+معناته صارت ال X بتساوة من .. بتساوة Y لأن هذا
+
+260
+00:18:36,740 --> 00:18:40,460
+هتوصلنا للي بديها خد و حسن norm ال X سار بيعيش
+
+261
+00:18:40,460 --> 00:18:43,550
+بساوة ال inner product بين ال X و ال Xاللي هو Y و
+
+262
+00:18:43,550 --> 00:18:47,590
+Y صارت ميهم؟ ساوى إيه دلها؟ الان Y إيش بتساوي ال
+
+263
+00:18:47,590 --> 00:18:51,070
+inner product لأ فاهمين ال summation هذا و ال
+
+264
+00:18:51,070 --> 00:18:53,950
+summation نفسه هذا الان بنطلع ال two summations
+
+265
+00:18:53,950 --> 00:18:57,350
+برا صارت هذه معهودة عندنا القول هذا اللي من بعيد
+
+266
+00:18:57,350 --> 00:19:01,490
+هيطلع conjugate و هذا هيكون عادي و هيظل EK و مين و
+
+267
+00:19:01,490 --> 00:19:07,330
+EM كل اللي عندي هنا هيتصفر summation مع ده عند ال
+
+268
+00:19:07,330 --> 00:19:10,990
+K بتساوي مين بتساوي M يعني هيصير ال summation بس
+
+269
+00:19:10,990 --> 00:19:15,810
+على مينعلى واحدة منهم اللي نسميها K وهذا واحد
+
+270
+00:19:15,810 --> 00:19:18,930
+ولقينا ال product بين التنتين اللي زي بعض الواحدة
+
+271
+00:19:18,930 --> 00:19:22,110
+و ال conjugate إلها بيصير المضلة السربيع فبصير
+
+272
+00:19:22,110 --> 00:19:27,090
+عنده Normal X السربيع بساوية هذه و هو المطلوب طيب
+
+273
+00:19:27,090 --> 00:19:35,710
+نيجي نشوف نظرية 364 ايش النظرية بتقول نقول نظرية
+
+274
+00:19:35,710 --> 00:19:40,780
+let H be a Hilbert space thenالجزئين الجزئ الأول
+
+275
+00:19:40,780 --> 00:19:44,220
+اللي هو if H is separable هذا بتساعدنا أصلا في
+
+276
+00:19:44,220 --> 00:19:48,000
+برهان واحدة من اللي فوق if H is separable إذا كانت
+
+277
+00:19:48,000 --> 00:19:51,880
+H separable then every orthonormal sitting H
+
+278
+00:19:51,880 --> 00:19:56,700
+إشمالها يعني كلهين countable بمثلين اللي هي ال
+
+279
+00:19:56,700 --> 00:20:01,350
+totalالـ Total Orthonormal بما فين هنا إذا صار كل
+
+280
+00:20:01,350 --> 00:20:05,970
+اللي هي الـ Total Orthonormal ستة حسب النظرية هذه
+
+281
+00:20:05,970 --> 00:20:09,530
+في حالة السيبرانجل كلهن أشملن countable number
+
+282
+00:20:09,530 --> 00:20:13,090
+يعني ال cardinality اللي بيساوي ألف note يعني ال
+
+283
+00:20:13,090 --> 00:20:15,510
+dimension اللي بدنا نسميه بيصير أشمل ألف percent
+
+284
+00:20:15,510 --> 00:20:19,940
+اللي فوق هنا ماشي في حالة السيبرانجلإذا H تحتوي
+
+285
+00:20:19,940 --> 00:20:24,520
+على سيكوان أورثو نورمال يكون تماماً لـ H، فهو
+
+286
+00:20:24,520 --> 00:20:25,600
+أيضاً Separable
+
+287
+00:20:30,890 --> 00:20:35,530
+هذا بيعطينا إنه هذا الـ Total Orthonormal هي سر
+
+288
+00:20:35,530 --> 00:20:38,630
+إنه يكون separable ولا مش separable إذا كان إحنا
+
+289
+00:20:38,630 --> 00:20:42,390
+اللي جينا أتش بتحتوي على واحدة من الـOrthonormal
+
+290
+00:20:42,390 --> 00:20:45,570
+Sequences وتكون Total، يعني الـCardinality اللي
+
+291
+00:20:45,570 --> 00:20:50,250
+هالف Note وهي Total، هيطلع الأتش separable، ماشي
+
+292
+00:20:50,250 --> 00:20:52,930
+الحال، إذا اللي هو في حالة الـseparable يعني
+
+293
+00:20:52,930 --> 00:20:56,810
+الأمور تمام تمام ومافيش إشكالية، وحتكون اللي هي
+
+294
+00:20:57,510 --> 00:21:01,610
+اللي هي الـ cardinality بتساوي اللي هو ألف نوت
+
+295
+00:21:01,610 --> 00:21:08,570
+فنجي برهن الأولى نتأتش بـ separable الان انتوا
+
+296
+00:21:08,570 --> 00:21:10,810
+بيقولوا البرهن البرهن اللذيذ وفيه فكرة يعني
+
+297
+00:21:24,720 --> 00:21:28,580
+الان انزل بس عشان نقولكم ايش اللي بدنا نثبته شوية
+
+298
+00:21:28,580 --> 00:21:32,760
+بقى الان اذا كانت بدنا نثبت نفرض انه H separable و
+
+299
+00:21:32,760 --> 00:21:37,220
+منها نصل انه ناخد اي orthonormal set in H و نثبت
+
+300
+00:21:37,220 --> 00:21:41,480
+انها accountable يعني بتاخد الان M اي orthonormal
+
+301
+00:21:41,480 --> 00:21:49,520
+set in H و اثبتلكم انه و لما يكون H separable
+
+302
+00:21:49,520 --> 00:21:55,250
+اثبتلكم من هذا مع بعض انه Mاللي هو إيه شمالها
+
+303
+00:21:55,250 --> 00:22:02,590
+countable تنشوف كده شوفوا اللي بدي أسوي بدي أخد
+
+304
+00:22:02,590 --> 00:22:07,390
+أخد H بـ separable space شو معناه separable؟ ركزوا
+
+305
+00:22:07,390 --> 00:22:12,810
+في اللي بحكي إنه اللاجي اللاجي اللي هو countable
+
+306
+00:22:12,810 --> 00:22:17,450
+dense من مين؟ من اللي هي الـH أنا بدي أخدوا لكم
+
+307
+00:22:17,450 --> 00:22:28,560
+الآن I Bdense set in mean in H ايه dense set in H؟
+
+308
+00:22:28,560 --> 00:22:34,360
+وبدى الآن افرضلكم ان Hم نفسها اشمالها م
+
+309
+00:22:34,360 --> 00:22:44,270
+uncountable واصل لك ان هذا هيقدىإن هذولا ولا واحدة
+
+310
+00:22:44,270 --> 00:22:47,230
+منهم هتكون countable يعني كلهم uncountable
+
+311
+00:22:47,230 --> 00:22:51,830
+للمؤهلات إنهم يدوء يكونوا يقوموا بدور إنه هنا
+
+312
+00:22:51,830 --> 00:22:55,130
+dense subset in H كلهم يكونوا uncountable وهذا
+
+313
+00:22:55,130 --> 00:22:59,210
+معناته بطل H separable إذن هي كما يكون التناقض إذن
+
+314
+00:22:59,210 --> 00:23:03,250
+هي هي السرتيجية الحل نيجي الآن نقول لت H بيه
+
+315
+00:23:03,250 --> 00:23:08,690
+separableand suppose that او let B be any dense
+
+316
+00:23:08,690 --> 00:23:14,550
+set in H وsuppose that M any orthonormal H set
+
+317
+00:23:14,550 --> 00:23:19,350
+ماشي الحال بعد شوية بثبتلكم انه لو كانت M الهي is
+
+318
+00:23:19,350 --> 00:23:23,430
+uncountable هيكون H اللي هو contradiction ومنه على
+
+319
+00:23:23,430 --> 00:23:26,670
+طول ال sentence uncountable since M is orthonormal
+
+320
+00:23:26,670 --> 00:23:31,610
+set شوفوا هذه الخاصية الحلوة فيهاأم orthonormal
+
+321
+00:23:31,610 --> 00:23:36,170
+إذا لأي x و y في الام و المسافة بين x لا تسوى y
+
+322
+00:23:36,170 --> 00:23:41,490
+احسبولي احسبولي المسافة او ال x لا تسوى y احسبولي
+
+323
+00:23:41,490 --> 00:23:45,730
+المسافة بين x minus y تربيع ايش بتساوي نحسبها
+
+324
+00:23:45,730 --> 00:23:48,610
+عبارة عن linear product بين x ناقص y و x ناقص y
+
+325
+00:23:48,610 --> 00:23:52,170
+وهذا عبارة عن اللي كلهم بيروحوا معاها ده بيظل x و
+
+326
+00:23:52,170 --> 00:23:55,710
+x و 100 و y و y لإن x و y و y و x كلهم إياش أسفار
+
+327
+00:23:55,710 --> 00:24:00,380
+لإنه orthonormalهذه نورمها واحد وهذه نورمها واحد
+
+328
+00:24:00,380 --> 00:24:02,860
+لأن هذه نورم تربيع واحد لها وهذه تربيع واحد لها
+
+329
+00:24:02,860 --> 00:24:06,380
+إذا إيش هيطلع عند المسافة بين أي نقطتين إذا في ال
+
+330
+00:24:06,380 --> 00:24:12,100
+M في داخل ال M المسافة بين كل نقطتين إيش بساوي هذا
+
+331
+00:24:12,100 --> 00:24:15,600
+بس يعني تجرب اللي هدا بساوي اللي هو مين عبارة عن
+
+332
+00:24:15,600 --> 00:24:18,700
+جدر التنين صح المسافة بين التنتين هدولة بين
+
+333
+00:24:18,700 --> 00:24:24,490
+النقطتين جدر التنينإذا بقدر .. بقدر أعمل حوالين
+
+334
+00:24:24,490 --> 00:24:28,590
+هذه neighborhood هذه ال X و هذه ال Y وهذا بعمل
+
+335
+00:24:28,590 --> 00:24:31,430
+حوالين neighborhood بحيث أنه يكون ال neighborhood
+
+336
+00:24:31,430 --> 00:24:36,810
+دين التقطح مش بساوي فيه ماشي بقدر .. خده مثلا ..
+
+337
+00:24:36,810 --> 00:24:39,970
+خده اللي هو ال .. ال .. ال .. ال .. ال radius تبع
+
+338
+00:24:39,970 --> 00:24:42,830
+هذا اللي هو عبارة عن جدر التنين على تلاتة عشان
+
+339
+00:24:42,830 --> 00:24:46,630
+أضمن كمان يبعدن عن بعض و هذا جدر التنين عالمين على
+
+340
+00:24:46,630 --> 00:24:53,430
+تلاتةالأنصار الآن كل نقطتين في داخل الـ M أنا بقدر
+
+341
+00:24:53,430 --> 00:24:57,750
+أبعدهن عن بعض بحيث أن هذا برضه النقطة اللي بعد هو
+
+342
+00:24:57,750 --> 00:25:00,850
+ده اللي بعد هو اللي بعد كلهين disjoint ماشي الحال
+
+343
+00:25:00,850 --> 00:25:04,810
+طيب هنا الخطورة أصلا شوفوا الآن هو ال superiority
+
+344
+00:25:04,810 --> 00:25:09,130
+شو معناته انه انه هذي اللي بتكون dense بتجيب ال
+
+345
+00:25:09,130 --> 00:25:12,250
+dense بتجيب كل space يعني ال double does لازم ايش
+
+346
+00:25:12,250 --> 00:25:16,770
+تكون item تاني تكون فيه تقاطع بين احتياط
+
+347
+00:25:20,340 --> 00:25:24,420
+Hence spherical neighbourhoods NX of X and NY of Y
+
+348
+00:25:24,420 --> 00:25:28,420
+of radii جدر التنين على تلاتة are disjoint Y قلت Y
+
+349
+00:25:28,420 --> 00:25:33,880
+لأن B is dense in H لكن بيه dense in H احنا بنقول
+
+350
+00:25:33,880 --> 00:25:38,780
+مادام بيه dense in H اذا أي X في ال M بقدر الاقي
+
+351
+00:25:38,780 --> 00:25:43,020
+neighbourhoodن X اللي هو بيكون .. بيكون أي
+
+352
+00:25:43,020 --> 00:25:46,900
+neighborhood ن X تقاطع ال B إيش ما له لا يساوي فاي
+
+353
+00:25:46,900 --> 00:25:50,500
+لإن اللي هي مالها B dense ماشي الآن، dense يعني
+
+354
+00:25:50,500 --> 00:25:54,420
+مهما زغرت ال neighborhood بدك تبعد عن B بتقدرش لإن
+
+355
+00:25:54,420 --> 00:25:57,400
+B هي ال .. ال .. ال .. الكلوة دي اللي لها بيساوي
+
+356
+00:25:57,400 --> 00:26:02,600
+كل space إذن لكل then for N X element of M ن X
+
+357
+00:26:02,600 --> 00:26:07,320
+تقاطع ال B لا يساوي إيش فايإذا كل واحدة من هذولة
+
+358
+00:26:07,320 --> 00:26:10,740
+من هذولة الان اكس و الان واي و الان زد و الان كل
+
+359
+00:26:10,740 --> 00:26:16,360
+هنا دولة كل واحدة بكون ان اكس تقاطع البي لايساو في
+
+360
+00:26:16,360 --> 00:26:20,500
+يعني بمعنى أخر في element هنا مصبوط ال element
+
+361
+00:26:20,500 --> 00:26:25,440
+الأول a في الان اكسالتاني في الـ NY فيه element
+
+362
+00:26:25,440 --> 00:26:29,420
+ومش هيكون الـ A ليش مش هيكون الـ A؟ لأن MX مع الـ
+
+363
+00:26:29,420 --> 00:26:33,520
+NY أشمعنى الـ Phi إذا هذه برضه فيها مين B وهذه
+
+364
+00:26:33,520 --> 00:26:38,200
+فيها C وهذه فيها D وهذه كذا لو كانت .. لو كانت الـ
+
+365
+00:26:38,200 --> 00:26:43,380
+N uncountable معناته أنه صار عندي uncountable
+
+366
+00:26:43,380 --> 00:26:48,260
+points هدولة موجودات كل من في مين في الـ Bإذا صارت
+
+367
+00:26:48,260 --> 00:26:51,200
+بيه إشمالها uncountable وهذا contradiction لأنه
+
+368
+00:26:51,200 --> 00:26:55,600
+كانت بيه arbitral dense set إذا اللي قلته اللي
+
+369
+00:26:55,600 --> 00:27:00,280
+قلته اللي هناك قلتهAnd since B is densely notched
+
+370
+00:27:00,280 --> 00:27:04,420
+in for any X element in M, NX تقاطع الـ B ليسوى
+
+371
+00:27:04,420 --> 00:27:09,160
+Phi Hence there is A element in NX تقاطع الـ B و B
+
+372
+00:27:09,160 --> 00:27:14,400
+في NAY تقاطع الـ B و الـ B لا تسوى A لأن الـ NX
+
+373
+00:27:14,400 --> 00:27:17,460
+نفسها و الـ NY تقاطعهم بسوى Phi في الشأنص المشتركة
+
+374
+00:27:17,460 --> 00:27:21,860
+بينهملأن لو فرضنا إن M is uncountable، then we
+
+375
+00:27:21,860 --> 00:27:26,940
+have uncountably many pairwise disjoint spherical
+
+376
+00:27:26,940 --> 00:27:31,900
+neighborhoods، فإن هدول النقسات So that B would
+
+377
+00:27:31,900 --> 00:27:35,060
+contains uncountable number of points، يعني B
+
+378
+00:27:35,060 --> 00:27:38,060
+would be uncountable since B was arbitrary dense
+
+379
+00:27:38,060 --> 00:27:41,800
+set، this makes that H would not contain a
+
+380
+00:27:41,800 --> 00:27:45,920
+countable dense setwhich contradicts the fact that
+
+381
+00:27:45,920 --> 00:27:49,200
+which is separable therefore انا لازم تكون ايه اش
+
+382
+00:27:49,200 --> 00:27:54,800
+مالها اللي هي countable واضح؟ ماشي الحال نيجي نشوف
+
+383
+00:27:54,800 --> 00:28:00,520
+اللي بعدها بيكون طوله روحكم برضه شوية نيجي لين؟
+
+384
+00:28:00,520 --> 00:28:05,120
+ارجعلنا للنص عشان نذكركم بإيش اللي بدنا نثبتهالان
+
+385
+00:28:05,120 --> 00:28:08,920
+النظرية بتقول إذا كانت H بتحتوي على orthonormal
+
+386
+00:28:08,920 --> 00:28:12,840
+sequence اه orthonormal sequence which is total
+
+387
+00:28:12,840 --> 00:28:17,320
+يعني بتحتوي على total orthonormal sequence لازم
+
+388
+00:28:17,320 --> 00:28:19,420
+الـHش تكون separable
+
+389
+00:28:21,650 --> 00:28:24,870
+Total orthonormal sequence معناته countable الست
+
+390
+00:28:24,870 --> 00:28:29,010
+هي ماشي لأن orthonormal sequence بنقصد فيها اللي
+
+391
+00:28:29,010 --> 00:28:33,070
+هو a1, a2, a3 أو x1, x2, x3 لما لا نهاية يعني
+
+392
+00:28:33,070 --> 00:28:37,790
+بمعنى آخر اللي هو countable set طيب اطلع للبرهاد
+
+393
+00:28:37,790 --> 00:28:43,240
+لنشوف بدنا نثبت أن H is separableطيب بدنا نجيلنا
+
+394
+00:28:43,240 --> 00:28:47,340
+بمعنى واخر بدنا نعملنا construction هو بده يعملنا
+
+395
+00:28:47,340 --> 00:28:54,100
+construction بده يعملنا construction لاللي هي set
+
+396
+00:28:54,100 --> 00:28:58,420
+تكون dense in H من ال orthonormal sequence اللي
+
+397
+00:28:58,420 --> 00:29:04,100
+عندها let em be a total orthonormal sequence in
+
+398
+00:29:04,100 --> 00:29:08,470
+mean in H قالي لها هي بين إيديناعند خد A إيش
+
+399
+00:29:08,470 --> 00:29:13,370
+بتساوي؟ بساوي عبارة عن كل ال formations Gamma K N
+
+400
+00:29:13,370 --> 00:29:19,250
+E K K من واحد لعندها ال E K هذولة اللي من هذه ماشي
+
+401
+00:29:19,250 --> 00:29:25,750
+الحال الآن ال ال coefficients هذولة بتدخلهم طبعا
+
+402
+00:29:25,750 --> 00:29:28,430
+أنا بحكي بس يشتغل في real أو complex خلينا ال
+
+403
+00:29:28,430 --> 00:29:30,810
+complex in general وفي حالة ال real بتسافروا ال
+
+404
+00:29:30,810 --> 00:29:34,850
+imaginary partالان Gamma K N هذا ال coefficients
+
+405
+00:29:34,850 --> 00:29:38,970
+اللي Gamma K N بتساوي اللي هو عبارة عن A K N زي I
+
+406
+00:29:38,970 --> 00:29:42,990
+B K N ماشي الحال هذولة اللي هو ال real
+
+407
+00:29:42,990 --> 00:29:45,650
+coefficients و ال imaginary coefficients بتاخدهم
+
+408
+00:29:45,650 --> 00:29:51,290
+من مين؟ من ال Q عشان أضمن انه تطلع اللي هو الصمم
+
+409
+00:29:51,290 --> 00:29:54,970
+هذه ال 6 is countableلأنه بيصير عندي هذا اللي هو
+
+410
+00:29:54,970 --> 00:29:58,770
+وكأنه اللي هي هدولة جايات هدولة نفسي جايات من Q
+
+411
+00:29:58,770 --> 00:30:01,590
+cross Q ماشي الحالة او ايزا ما اللي هو ال
+
+412
+00:30:01,590 --> 00:30:04,310
+cardinality اللي هنا هيكون اللي هو عبارة عن الف
+
+413
+00:30:04,310 --> 00:30:07,270
+note countable لأن countable cross countable is
+
+414
+00:30:07,270 --> 00:30:10,930
+countableوالـ finite union الـ finite اللي هو
+
+415
+00:30:10,930 --> 00:30:15,910
+summation هذا وكأني باخد ال union ل finite number
+
+416
+00:30:15,910 --> 00:30:20,770
+ال finite ال union ل countable sets برضه هيطلع إيش
+
+417
+00:30:20,770 --> 00:30:25,370
+ماله countable إذا بكل الأحوال A is countable طيب
+
+418
+00:30:25,370 --> 00:30:30,810
+كيف شكلوا ال summation هذا يعني مثلا لو ناخدناها
+
+419
+00:30:30,810 --> 00:30:34,030
+واحد بيصير الصمي اللي هو عبارة عن العنصر هذا Gamma
+
+420
+00:30:34,030 --> 00:30:39,960
+K واحد EKممكن أنصر تاني يقولك أنا بدي أبقيها من
+
+421
+00:30:39,960 --> 00:30:43,360
+واحد لعند مين لعند عشرة اللي هو ال submission a,k
+
+422
+00:30:43,360 --> 00:30:48,760
+,n,e,k عده من واحد لعشرة لعشرين للا تلاتي لكل ال
+
+423
+00:30:48,760 --> 00:30:50,880
+finite اللي في الدنيا جات ما بدك اللي هي الأن
+
+424
+00:30:50,880 --> 00:30:54,560
+تاخدها واحد اتنين تلاتة إذا شكل العناصر هذا أنا
+
+425
+00:30:54,560 --> 00:30:58,020
+عارف كيف شكله اللي هي ال coefficients هدولة من مين
+
+426
+00:30:58,020 --> 00:31:01,920
+من ال complex numbers لكن ال coefficients تبعات
+
+427
+00:31:01,920 --> 00:31:04,740
+اللي هي ال real part و ال imaginary part عبارة عن
+
+428
+00:31:04,740 --> 00:31:09,080
+أعداد نسبية rational numbersطيب عشان نضمن اللي هو
+
+429
+00:31:09,080 --> 00:31:13,360
+تكون countable الان BKM بتساوي سفر لما ال H تكون
+
+430
+00:31:13,360 --> 00:31:16,940
+أيش ما لها real Hilbert space هنا خلينا نشتغل عن
+
+431
+00:31:16,940 --> 00:31:20,760
+ال general و بيكون ده كحالة خاصة منه زي ما قولت A
+
+432
+00:31:20,760 --> 00:31:24,900
+is countable هو قولناها هو ايش الان we show that
+
+433
+00:31:24,900 --> 00:31:28,380
+هذه المؤهلة اننا اثبتناها انها dense in H اذا
+
+434
+00:31:28,380 --> 00:31:30,980
+اثبتناها dense in H بيكون خلصناها بتكون H أيش ما
+
+435
+00:31:30,980 --> 00:31:35,900
+لها inseparable اطلع تشوف كإعلانكيف بدي اثبت انه
+
+436
+00:31:35,900 --> 00:31:40,240
+dense؟ بدي اخد الـ NX and fixed element in mean in
+
+437
+00:31:40,240 --> 00:31:45,380
+H ماشي الحال هو ألاجيه لك ان NX تقاطع اللي هو الـ
+
+438
+00:31:45,380 --> 00:31:49,020
+set هذه لا يساوي 5 بقول خلصها بس ماتناهيش انها
+
+439
+00:31:49,020 --> 00:31:52,320
+dense عشان اثبت انها dense انه لو أخدنا أي element
+
+440
+00:31:52,320 --> 00:31:55,700
+هنا بقدر ألاجي اللي هو بيكون عندى أي neighborhood
+
+441
+00:31:55,700 --> 00:31:57,920
+حوالينها ذاك و بطلع هذاك اللي بتشوفه ان شاء الله
+
+442
+00:31:57,920 --> 00:32:03,320
+let X be and fixed element in mean in Hالآن since
+
+443
+00:32:03,320 --> 00:32:07,660
+EM is a total or from a total set in H إذا
+
+444
+00:32:07,660 --> 00:32:11,640
+الإسبانيك لو جعل ال EM إيش حيساوي؟ من التعريف طيب
+
+445
+00:32:11,640 --> 00:32:15,720
+إذا for every إبسلون أكبر من سفر مهما كانت إبسلون
+
+446
+00:32:15,720 --> 00:32:19,020
+صغيرة هذه اللي بتبتعبر عن ال arbitrary
+
+447
+00:32:19,020 --> 00:32:24,340
+neighborhoodالان there is w element ل span em such
+
+448
+00:32:24,340 --> 00:32:28,700
+that المسافة بين x نقص w أصغر من أي أسغر من أي
+
+449
+00:32:28,700 --> 00:32:31,980
+epsilon في الدنيا أنا بتسميه y على 2 للحسابات ماشي
+
+450
+00:32:31,980 --> 00:32:37,340
+الحال إذا الأن لإن span لل em dense in H إذا لأي x
+
+451
+00:32:37,340 --> 00:32:41,260
+في ال H بقدر ألاقي اللي هو element في اللي جوا هذا
+
+452
+00:32:41,260 --> 00:32:46,240
+بحيث المسافة بين x و w أصغر من أي epsilon في
+
+453
+00:32:46,240 --> 00:32:50,710
+الدنياماشي الحال أو تعبير اللي هو ان نكس و Y على
+
+454
+00:32:50,710 --> 00:32:54,750
+اتنين اللي هو تقاطع اللي هو ال H اللي نسباننا
+
+455
+00:32:54,750 --> 00:32:59,110
+اليوم ليه ال W هذه ماشي ان شاء الله نجمعين معايا
+
+456
+00:32:59,110 --> 00:33:01,230
+طيب الان
+
+457
+00:33:03,350 --> 00:33:11,450
+Hence وين موجودة؟ و موجودة في الـ YN و ما هي وين
+
+458
+00:33:11,450 --> 00:33:14,350
+موجودة في الإسماعيل للـ EM؟ مادام هي في الإسماعيل
+
+459
+00:33:14,350 --> 00:33:17,710
+للـ EM يعني و عبارة عن اللي هو الـ Finite Linear
+
+460
+00:33:17,710 --> 00:33:21,120
+combination من مين؟ من عناصر من الـ EMنفترض إنه
+
+461
+00:33:21,120 --> 00:33:25,060
+finite combination من E1 وE2 وE3 وE4 لعندي يعني مش
+
+462
+00:33:25,060 --> 00:33:28,560
+عاجبكم EI واحد EI اتنين لعندي EIN على الأساس ما
+
+463
+00:33:28,560 --> 00:33:31,560
+تقولوش أول أول تلاتة من هدول أو أول خمسة من هدول
+
+464
+00:33:31,560 --> 00:33:35,560
+مش مشكلة فاهمين إنهم تكون finite اللي هو summation
+
+465
+00:33:35,560 --> 00:33:39,680
+أو finite combination من مين من عناصر اللي هي
+
+466
+00:33:39,680 --> 00:33:44,960
+موجودة في مين في الإيام طيبأسميتها هذه الـ span
+
+467
+00:33:44,960 --> 00:33:48,580
+للـ E1 و E2 اللي عندي لأن إيش سميتها وي أنت ماشي
+
+468
+00:33:48,580 --> 00:33:52,980
+الحال إذا صارت الـ W هذه اللي لجيتها للمسافة بينها
+
+469
+00:33:52,980 --> 00:33:56,560
+وبين ال X اللي بتحكي عليها أصغر من X أسلوب على 2
+
+470
+00:33:56,560 --> 00:34:00,870
+سميتها W في ال span اللي عندي for someoneby لمّة
+
+471
+00:34:00,870 --> 00:34:04,670
+قبل بشوية تلاتة و تلاتة اتنين there is y element
+
+472
+00:34:04,670 --> 00:34:07,050
+اللي هي أخدناها قبل هيك there is y element in yn
+
+473
+00:34:07,050 --> 00:34:11,510
+such that x minus y element عمودي عالميين على ال
+
+474
+00:34:11,510 --> 00:34:15,050
+yn ايش هتستنى عشان ماتطلعوش عنها ايش اللمّة هذه
+
+475
+00:34:15,050 --> 00:34:19,890
+احنا المرة اللي فاتت لما نأجينا خدنا x في ال space
+
+476
+00:34:20,550 --> 00:34:25,050
+X في الـ Space جينا و رسمتلكم عدة رسمات إذا
+
+477
+00:34:25,050 --> 00:34:29,870
+بتتذكروا اللي هو هاي الرسم هادي و قولنا إن هذا الـ
+
+478
+00:34:29,870 --> 00:34:33,430
+Space H أو هذا الـ Space H و هاي الـ X هنا و هاي
+
+479
+00:34:33,430 --> 00:34:38,370
+الـ X هنا ماشي الحال قولنا أنه عرفنا إن الـ Delta
+
+480
+00:34:38,370 --> 00:34:44,530
+هي عبارة عن المسافة بين النقطة X و بين الـ Space
+
+481
+00:34:44,530 --> 00:34:49,420
+الـ M هذه سميناها M هذه بين الـ X و مين و Mفي
+
+482
+00:34:49,420 --> 00:34:54,280
+نظرية قلنا إذا كانت M subspace بنضمن اللي نجيلكم
+
+483
+00:34:54,280 --> 00:34:58,760
+واحدة وحيدة ان there exist unique Y such that
+
+484
+00:34:58,760 --> 00:35:04,680
+normal X minus Y هو اللي بيمثل مين ال Deltaوفي
+
+485
+00:35:04,680 --> 00:35:10,280
+النظرية اللي بعدها اللي هي 3 3 2 قلنا إنه لو كانت
+
+486
+00:35:10,280 --> 00:35:15,460
+هذه complete هيكون عندي ال Y الوحيدة هذه اللي هي
+
+487
+00:35:15,460 --> 00:35:19,240
+هتنزل هذه العمود هذي بيصير X هي عندي ال X وهي ال Y
+
+488
+00:35:19,240 --> 00:35:24,060
+اللي وجناها هذه المسافة هتنزل عمودي على مين؟ على
+
+489
+00:35:24,060 --> 00:35:29,520
+هذا، هيكون ال X minus Y Orthogonal على مين؟ على
+
+490
+00:35:29,520 --> 00:35:34,430
+العين، ماشي الحال، إذن الآن بهذه النظريةبهذه
+
+491
+00:35:34,430 --> 00:35:37,870
+النظرية بقدر هذا هذا هذا ال subspace اللي عندي
+
+492
+00:35:37,870 --> 00:35:41,750
+اللي عليه بده اطبق فبصير عندي الآن بقدر الاقي y في
+
+493
+00:35:41,750 --> 00:35:45,750
+داخله وكأنه هذا ال subspace يا جماعة اه هذا ال
+
+494
+00:35:45,750 --> 00:35:50,590
+subspace بقدر الاقي في داخله y بحيث انه norm x
+
+495
+00:35:50,590 --> 00:35:54,530
+minus y هو اللي يمثل delta ويكون x minus y نفسه
+
+496
+00:35:54,530 --> 00:36:00,830
+عمود عالمين على ال M طيب اذاالان there exists y
+
+497
+00:36:00,830 --> 00:36:04,990
+element in y-end such that x minus y عمودي على ال
+
+498
+00:36:04,990 --> 00:36:08,450
+y-end ما هو احنا في الطبيعي بنقول اقرب واحد على
+
+499
+00:36:08,450 --> 00:36:12,610
+الست اللي هو القمود عليه اه اه طيب الان صار عندي
+
+500
+00:36:12,610 --> 00:36:15,650
+ايه هدف الهندسة الطبيعية اللي في ال space اللي
+
+501
+00:36:15,650 --> 00:36:18,110
+منيح اللي .. اللي .. اللي .. اللي منيحه و مش فيه
+
+502
+00:36:18,110 --> 00:36:23,300
+مشاكل اللي هو بيقول complete subspaceThere is y
+
+503
+00:36:23,300 --> 00:36:26,040
+element in yn such that x minus y عمودي عالمين على
+
+504
+00:36:26,040 --> 00:36:30,380
+yn و ال norm ل ال x minus y هو ال infimum هو ال
+
+505
+00:36:30,380 --> 00:36:34,020
+delta مدام هو ال delta إذا حيكون أصغر أو يساوي ال
+
+506
+00:36:34,020 --> 00:36:37,760
+norm ل ال x ناقص أي element في الدنيا تاني في ال
+
+507
+00:36:37,760 --> 00:36:39,660
+.. في ال .. في ال .. في ال .. في ال .. في ال M
+
+508
+00:36:39,660 --> 00:36:44,020
+اللي عندى اللي بشغل عليها أو ال H من ضمن اليومين
+
+509
+00:36:44,020 --> 00:36:49,260
+ال W لجناهاإذا صار عند نورنا الـ X-Y أصغر من مين؟
+
+510
+00:36:49,260 --> 00:36:53,560
+من Y على 2 لأن X-W من فوق يشملها أصغر من Y على 2
+
+511
+00:36:54,350 --> 00:37:01,170
+الان by a و b in theorem 3-4 y can be written as
+
+512
+00:37:01,170 --> 00:37:06,150
+اللي هي أخدناها قبل هيك انه y اللي عندها دي بنقدر
+
+513
+00:37:06,150 --> 00:37:08,810
+نكتبها على صورة summation ال for real coefficient
+
+514
+00:37:08,810 --> 00:37:12,090
+بتاعتها summation x و ek , ek كامل عند واحد لمين
+
+515
+00:37:12,090 --> 00:37:17,030
+لعند n اللي هي موجودة في مين y في الاسم علي طيب
+
+516
+00:37:17,780 --> 00:37:22,400
+الان اذا احسبولي اطلع لفوق احسبلي الان normal X
+
+517
+00:37:22,400 --> 00:37:27,000
+نقص ال summation هذا اللي هو ال Y حسبنا اصغر من
+
+518
+00:37:27,000 --> 00:37:31,300
+مين من نفسنا على اتنين الان ال Q نفسها الان هل جيه
+
+519
+00:37:31,300 --> 00:37:33,980
+تبدأ تيجي اللي هو استخدام اللي هو التركيب الأصلي
+
+520
+00:37:33,980 --> 00:37:39,700
+لل A since Q is dense in R then for any X و E K
+
+521
+00:37:39,700 --> 00:37:43,900
+هذا اللي هو عبارة عن complex numberهذا في ال .. في
+
+522
+00:37:43,900 --> 00:37:48,120
+ال complex number ماشي الحال أي x .. ال .. ال ..
+
+523
+00:37:48,120 --> 00:37:50,060
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+524
+00:37:50,060 --> 00:37:50,220
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+525
+00:37:50,220 --> 00:37:50,300
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+526
+00:37:50,300 --> 00:37:50,740
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+527
+00:37:50,740 --> 00:37:51,420
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+528
+00:37:51,420 --> 00:37:51,840
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+529
+00:37:51,840 --> 00:37:52,420
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+530
+00:37:52,420 --> 00:37:52,960
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+531
+00:37:52,960 --> 00:37:54,600
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+532
+00:37:54,600 --> 00:37:54,660
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+533
+00:37:54,660 --> 00:37:54,920
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+534
+00:37:54,920 --> 00:37:57,140
+..ال ..ال ..ال ..ال ..ال ..ال ..ال ..ال
+
+535
+00:38:02,140 --> 00:38:06,680
+ننتقل من R كيو دينس في R إذا كيو كروس كيو دينس في
+
+536
+00:38:06,680 --> 00:38:09,620
+مين في C اللي هو اللي حكينا عنه لأنه كامتر
+
+537
+00:38:09,620 --> 00:38:13,400
+بالتقرير سنس كيو سنس في R هي المفتاح then for any
+
+538
+00:38:13,400 --> 00:38:18,700
+X و EK there is Gamma KN AKN زاد IBKN such that
+
+539
+00:38:18,700 --> 00:38:24,000
+AKN و BKN element لكيو such that اللي هو المسافة
+
+540
+00:38:24,000 --> 00:38:28,050
+بين اللي هو ال summation لل X و EKلحالة هذه
+
+541
+00:38:28,050 --> 00:38:31,570
+المسافة بين الـ X و الـ E K و العدد اللي هنا أصغر
+
+542
+00:38:31,570 --> 00:38:36,030
+ما يكون لأن مجموحا هذا برضه ما هو Complex هيطلع أو
+
+543
+00:38:36,030 --> 00:38:39,170
+هيطلع اللي هو .. خلّيني .. نقدر نطبق عليه اللي
+
+544
+00:38:39,170 --> 00:38:42,950
+بنطبقه على هذا لأن أنا بتدث .. بتدث بتتثار ال ..
+
+545
+00:38:42,950 --> 00:38:47,250
+ال summation لل X و ال E K over ال K اللي بحكي
+
+546
+00:38:47,250 --> 00:38:52,980
+عنها من 1 لـ N في الآخر هذا الآن ال summationفي
+
+547
+00:38:52,980 --> 00:38:57,440
+الآخر اللي هو بقدر اتعامل معاه بدل ما هي ال X E K
+
+548
+00:38:57,440 --> 00:39:04,320
+لحالها عندى بما انه Q dense in Rوطبيعي اللي هو أنا
+
+549
+00:39:04,320 --> 00:39:07,080
+أخدت ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+550
+00:39:07,080 --> 00:39:07,080
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+551
+00:39:07,080 --> 00:39:07,220
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+552
+00:39:07,220 --> 00:39:07,360
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+553
+00:39:07,360 --> 00:39:07,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+554
+00:39:07,440 --> 00:39:08,680
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+555
+00:39:08,680 --> 00:39:09,120
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+556
+00:39:09,120 --> 00:39:09,480
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+557
+00:39:09,480 --> 00:39:09,560
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+558
+00:39:09,560 --> 00:39:11,420
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+559
+00:39:11,420 --> 00:39:19,220
+ال .. ال .. ال .. ال ..
+
+560
+00:39:19,220 --> 00:39:19,560
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+561
+00:39:19,560 --> 00:39:22,680
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+562
+00:39:22,680 --> 00:39:25,880
+ال
+
+563
+00:39:27,860 --> 00:39:30,780
+ما دامت اللي هي Q dense إذا بقدر أجلاج ال
+
+564
+00:39:30,780 --> 00:39:37,540
+coefficients من اللي هي ال .. ال Q العصورة AKN
+
+565
+00:39:37,540 --> 00:39:44,360
+زائد IBKN اللي سنتها Gamma KN بحيث أنه المسافة بين
+
+566
+00:39:44,360 --> 00:39:50,360
+هذه و بين اللي هي ال elements اللي عندي Gamma KEK
+
+567
+00:39:50,360 --> 00:39:55,240
+يكون ايش ماله اصغر ما يمكن و ليكن اصغر من مين من
+
+568
+00:39:55,240 --> 00:40:01,300
+ابسلون على اتنين اذا الان من
+
+569
+00:40:01,300 --> 00:40:07,530
+كل اللي فات بقدر الخص ما يليإنه لجهة الـ V اللي هي
+
+570
+00:40:07,530 --> 00:40:11,170
+عبارة عن X و EK في EK الـ summation اللي لها V
+
+571
+00:40:11,170 --> 00:40:16,690
+بيساوي ال summation لـ Gamma KN و EK SF Element NA
+
+572
+00:40:16,690 --> 00:40:23,890
+بحيث أن المسافة بين X و V X و V اللي هو بيساوي X
+
+573
+00:40:23,890 --> 00:40:27,810
+خلوها زي ما هي ناقص اللي هي ال summation هذا أصغر
+
+574
+00:40:27,810 --> 00:40:31,590
+أو يساوي بدأت
+
+575
+00:40:31,590 --> 00:40:36,030
+بـ X arbitraryولاجئت اللي هو element v element a
+
+576
+00:40:36,030 --> 00:40:41,770
+بحيث المسافة بين x minus v يساوي .. انشوف x ناقص
+
+577
+00:40:41,770 --> 00:40:45,750
+هذا العوضت بال triangling quality بدي اضيف term
+
+578
+00:40:45,750 --> 00:40:49,450
+واطح term اصغر او ساوي x ناقص اللي هو المفتاح هذا
+
+579
+00:40:49,450 --> 00:40:58,190
+اللي حصلته هنا x ek و ekزائد اللي هو نفسه هذا ناقص
+
+580
+00:40:58,190 --> 00:41:02,970
+ال V اللي هي ال submission هذا أثبتناها سابقا أصغر
+
+581
+00:41:02,970 --> 00:41:06,030
+من يبسلون على اتنين وهذا أثبتناها سابقا أصغر من
+
+582
+00:41:06,030 --> 00:41:09,070
+يبسلون على اتنين من الجهتين صار عند ال X minus V
+
+583
+00:41:09,070 --> 00:41:13,230
+أصغر من مين من يبسلون أيش اللي عملته أخدت X
+
+584
+00:41:13,230 --> 00:41:18,780
+arbitraryو لجيت اللي هو V في الـA بحيث انه المسافة
+
+585
+00:41:18,780 --> 00:41:23,260
+بين الـX والـV اللي لجيتها أقل ما يمكن يعني بمعنى
+
+586
+00:41:23,260 --> 00:41:29,020
+آخر انه for every اللي هو ball أو every
+
+587
+00:41:29,020 --> 00:41:34,030
+neighborhood بيكس وإبسلونتقاطع اللي إيه إيه إيه
+
+588
+00:41:34,030 --> 00:41:35,490
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+589
+00:41:35,490 --> 00:41:39,370
+إيه
+
+590
+00:41:39,370 --> 00:41:48,170
+إيه
+
+591
+00:41:48,690 --> 00:41:53,350
+الان ال V هذه موجودة هان أثبتت هيها من خلال هذه و
+
+592
+00:41:53,350 --> 00:41:56,570
+في نفس الوجهة ال V و الموجودة في ال A يعني ال ball
+
+593
+00:41:56,570 --> 00:42:01,490
+تقاطع ال A ليس هو Phi و هذا يعني أن ال A صارت
+
+594
+00:42:01,490 --> 00:42:05,170
+dense في mean في ال space الأصل اللي أخدت X فيه
+
+595
+00:42:05,170 --> 00:42:09,670
+arbitrary و معناته صارت اللي هي H is separable يلا
+
+596
+00:42:09,670 --> 00:42:15,000
+اللي بعده اللي بعده يا باباالنظرية الأخيرة في هذا
+
+597
+00:42:15,000 --> 00:42:18,460
+الـ section Theorem two Hilbert spaces H and H
+
+598
+00:42:18,460 --> 00:42:22,700
+tilde both real or both complex are isomorphic if
+
+599
+00:42:22,700 --> 00:42:25,100
+and only if they have the same Hilbert dimension
+
+600
+00:42:25,100 --> 00:42:32,480
+يعني و كأنه بيقولنا من تحت بطن أنه يا جماعة كل ال
+
+601
+00:42:32,480 --> 00:42:35,940
+Hilbert spaces اللي ال dimension إليهم زي بعض
+
+602
+00:42:35,940 --> 00:42:39,260
+هدولة isomorphic يعني واحدة كلها تجدوش و تقولي
+
+603
+00:42:39,260 --> 00:42:45,350
+انها واحدة كلها واحدة ماشي بناء عليهأحنا اللي بدنا
+
+604
+00:42:45,350 --> 00:42:52,170
+نثبته انه ناخد اي two Hilbert spaces قدش قدش تل ده
+
+605
+00:42:52,170 --> 00:42:57,070
+او او اذا أثبتنا انه isomorphic معناته اي شمالها
+
+606
+00:42:57,070 --> 00:43:00,430
+اللي هو الهن the same Hilbert dimension اذا الهن
+
+607
+00:43:00,430 --> 00:43:02,750
+the same Hilbert dimension معناته اي شمالهن
+
+608
+00:43:02,750 --> 00:43:07,800
+isomorphicالان نجي للاتجاه الاول suppose that او
+
+609
+00:43:07,800 --> 00:43:10,660
+isomorphism بين هنا عارفين واش معناه isomorphism
+
+610
+00:43:10,660 --> 00:43:14,260
+بينهم بنحكيها الان الان suppose that H is
+
+611
+00:43:14,260 --> 00:43:17,080
+isomorphic with H تلده مابديش ادخل في التفاصيل
+
+612
+00:43:17,080 --> 00:43:20,360
+تفاصيل الحسابات هتكون لكم suppose that H is
+
+613
+00:43:20,360 --> 00:43:24,110
+isomorphic لمن لH تلدهيعني في isomorphism بين
+
+614
+00:43:24,110 --> 00:43:28,390
+التنتين then there is a bijective linear mapping T
+
+615
+00:43:28,390 --> 00:43:33,350
+من H لH تل ده that satisfies T X و T Y بيساوي X و
+
+616
+00:43:33,350 --> 00:43:37,830
+Y يعني اللي هي preserve the inner product زي ما
+
+617
+00:43:37,830 --> 00:43:40,150
+قلنا شو معناته ال geomorphic preserve inner
+
+618
+00:43:40,150 --> 00:43:43,690
+product preserve اللي هو العمليات اللي هو preserve
+
+619
+00:43:43,690 --> 00:43:46,550
+cardinality اللي هي one to one او انتوا هي التلات
+
+620
+00:43:46,550 --> 00:43:54,920
+شغلاتالأن صار عندى اطلع لفوق اللى فوق الان ال ال
+
+621
+00:43:54,920 --> 00:43:58,540
+orthonormal hence orthonormal elements in H have
+
+622
+00:43:58,540 --> 00:44:02,120
+orthonormal images under mean under T أكيد لإنه
+
+623
+00:44:02,120 --> 00:44:05,380
+اللى بيحصل ال ال inner product بين X و X بيساوي X
+
+624
+00:44:05,380 --> 00:44:08,500
+و Y بيساوي T X و T Y لو كان ال inner product بين
+
+625
+00:44:08,500 --> 00:44:11,200
+هدولة سفر هكون بين سفر لو كان واحد بيكون واحد اذا
+
+626
+00:44:11,200 --> 00:44:15,040
+أكيد اللى بيكون اللى هو ال orthonormal هان image
+
+627
+00:44:15,040 --> 00:44:19,870
+ها هيكون إيه شماله orthonormal طيبالآن however T
+
+628
+00:44:19,870 --> 00:44:23,850
+is bijective إذا T تنقل every total orthonormal
+
+629
+00:44:23,850 --> 00:44:28,650
+set in إيش onto a total orthonormal set in مين in
+
+630
+00:44:28,650 --> 00:44:34,090
+H تلده ماشي و تفصيله لكم لإنه بيصير ال span هنا ال
+
+631
+00:44:34,090 --> 00:44:40,610
+span لل M الأولى ال closure بيساوي ال H الان T لل
+
+632
+00:44:40,610 --> 00:44:43,750
+span لل M ال closure للثاني هتصير إيش ما لها ال H
+
+633
+00:44:43,750 --> 00:44:48,460
+تلدهطيب، therefore H and H tilde have the same إيش
+
+634
+00:44:48,460 --> 00:44:52,100
+مالين هل بار دايمينشين لإنه صارت اللي هي نفس
+
+635
+00:44:52,100 --> 00:44:56,920
+العدد، طيب، الان conversely suppose that، في تفصيل
+
+636
+00:44:56,920 --> 00:45:00,080
+الكلام، بس تفصيله مش صعب، suppose that, conversely
+
+637
+00:45:00,080 --> 00:45:02,700
+suppose that H and H tilde have the same hell bar
+
+638
+00:45:02,700 --> 00:45:06,280
+dimension، برضه بتلاقي isomorphism بينهم اللي هو
+
+639
+00:45:06,280 --> 00:45:08,620
+one to one و one to one و كده و كده، تفاصيله برضه
+
+640
+00:45:08,620 --> 00:45:15,770
+اللي هو صارت معهودة يعني،الان في حالة H تسوى 0 و H
+
+641
+00:45:15,770 --> 00:45:19,290
+تلدة تسوى 0 هي تريفيال لأنه مادام تنتين الهن في
+
+642
+00:45:19,290 --> 00:45:21,830
+نفس القرص اللي لديه واحد سفر تان هيتلاعياش سفر
+
+643
+00:45:21,830 --> 00:45:24,810
+معناته ال function بينهن سهل انك ترتاب ال function
+
+644
+00:45:24,810 --> 00:45:28,690
+بينهن تكون one to one و one to كل شيء الان اذا let
+
+645
+00:45:28,690 --> 00:45:33,110
+H لا تسوى مين لا تسوى سفر automatic ال H تلدة
+
+646
+00:45:33,110 --> 00:45:36,050
+هتكون اي شمالها برضه مش سفر لأن احنا قلنا ان
+
+647
+00:45:36,050 --> 00:45:40,630
+الـCMDL برضه مينشينand any total orthonormal set M
+
+648
+00:45:40,630 --> 00:45:44,350
+in H و M tilde in H اله in the same cardinality هه
+
+649
+00:45:44,350 --> 00:45:47,070
+ايش معناته انه in the same dimension ان ال total
+
+650
+00:45:47,070 --> 00:45:50,410
+orthonormal set هنا ال cardinality لها هي نفس ال
+
+651
+00:45:50,410 --> 00:45:56,970
+cardinality في من؟ في التانية معاياطيب الان so we
+
+652
+00:45:56,970 --> 00:46:00,250
+can index them by the same index set يعني احنا
+
+653
+00:46:00,250 --> 00:46:03,330
+بنقدر نرمزلهم بنفس ال index set لو هذولة كان
+
+654
+00:46:03,330 --> 00:46:05,890
+countable هذولة countable لو هذولة uncountable
+
+655
+00:46:05,890 --> 00:46:09,090
+uncountable لو عددهم ألف note ألف note لو عددهم
+
+656
+00:46:09,090 --> 00:46:13,050
+اللي هو زي عدد ال power of R عددهم زي عدد ال power
+
+657
+00:46:13,050 --> 00:46:15,610
+of R لو عددهم زي ال R بيكون عددهم زي ال R عارفين
+
+658
+00:46:15,610 --> 00:46:19,310
+ايش عدد ال R؟ cardinal of ال R هو C اللي هو ال
+
+659
+00:46:19,310 --> 00:46:23,750
+power of R بيصير 2 to the C و هكذا عارفين ما هذا
+
+660
+00:46:23,750 --> 00:46:28,400
+الكلام؟إذا نسينا تذكروا it so we can index them by
+
+661
+00:46:28,400 --> 00:46:32,860
+the same index set اللي هي K and write M بتساوي EK
+
+662
+00:46:32,860 --> 00:46:38,960
+and M تلده بتساوي EK شمالها تلده لإن هم نفس ال ..
+
+663
+00:46:38,960 --> 00:46:42,200
+ال .. ال .. البرده دايما شده now define بقولك اللي
+
+664
+00:46:42,200 --> 00:46:45,660
+هنعرف اللي هو T من H للH تلده بناء على ال teamتين
+
+665
+00:46:45,660 --> 00:46:51,270
+هذوله بدنا نعرفTX X من وين جاية من H بتساوي اللي
+
+666
+00:46:51,270 --> 00:46:56,190
+هو الـ X إيش أصلا هي summation X و EK في EK ماشي
+
+667
+00:46:56,190 --> 00:46:59,890
+هذا جلطنات زي ما أقولنا عبّر عنها على طول زي هي
+
+668
+00:46:59,890 --> 00:47:05,290
+لأن TX بده عبّر عن X و EK في مين في EK إيش مالها
+
+669
+00:47:05,290 --> 00:47:09,190
+تلدة تبعت اللي هي ال M تلدة this is well defined
+
+670
+00:47:09,190 --> 00:47:13,350
+because لكل X element in H we have ال X بتساوي ال
+
+671
+00:47:13,350 --> 00:47:17,370
+summation هذا زي ما قلناالان عندي by Bezel's
+
+672
+00:47:17,370 --> 00:47:20,970
+Inquality ال summation هذا هيكون يشمل و converge
+
+673
+00:47:20,970 --> 00:47:24,270
+ماشي الحال اذا اكيد اللي هداك له قيمة then by
+
+674
+00:47:24,270 --> 00:47:27,810
+theorem تلتة خمسة اتنين ال X و ال EK و EK تلتة
+
+675
+00:47:27,810 --> 00:47:31,990
+over K مدام هداك converge هيكون converge so that
+
+676
+00:47:31,990 --> 00:47:35,530
+ال TX و الموجودة في ال H تلتة يعني well defined
+
+677
+00:47:35,530 --> 00:47:41,550
+اللي الها قيمة الانلت X بتساوي كده و Y بتساوي كده
+
+678
+00:47:41,550 --> 00:47:44,870
+بيدثبتوا انه Linear وهذه شغل الحسابات اللي هي
+
+679
+00:47:44,870 --> 00:47:51,730
+الحسابات سهلة أخدت X اللي هي بشكل هذا و Y بشكل هذا
+
+680
+00:47:51,730 --> 00:47:56,990
+عارفين هذا الكلام سنة بي any element سيناتش والألف
+
+681
+00:47:56,990 --> 00:48:00,580
+عن ال scalar وحسبلي T Alpha X زائد Yحسب اللي ..
+
+682
+00:48:00,580 --> 00:48:02,900
+اللي .. اللي حكينا عنه قبل شوية بيصير الـ
+
+683
+00:48:02,900 --> 00:48:07,040
+summation اللي هو Alpha X زائد Y E K مع مين؟ مع E
+
+684
+00:48:07,040 --> 00:48:12,200
+K تلدة هيت القانون Y ساوي Alpha الآن بطالة الأن دي
+
+685
+00:48:12,200 --> 00:48:17,370
+اللي جوا هذه اللي هي بيصير X وE K وE K تلدةبقى الـ
+
+686
+00:48:17,370 --> 00:48:22,350
+inner product بفصلهم عادي و ال YK و ال A أشماله و
+
+687
+00:48:22,350 --> 00:48:26,370
+EK تلده هذه إيه اللي هي عبارة عن TX و هذه أشمالها
+
+688
+00:48:26,370 --> 00:48:30,230
+TY فبصينا عند Alpha TX زي TY hence T is linear
+
+689
+00:48:30,230 --> 00:48:36,250
+اطلع على السوق الآن since EK تلده
+
+690
+00:48:36,250 --> 00:48:41,990
+is orthonormal then اللي هو احسب ليه ال TX و TX
+
+691
+00:48:42,830 --> 00:48:46,090
+بنسخد منها Orthonormal الـ TX والـ TX الـ TX إيش
+
+692
+00:48:46,090 --> 00:48:50,390
+أعرفناها summation X و EK و EK تلدة كله هتلاقو
+
+693
+00:48:50,390 --> 00:48:54,710
+شغلات سهلة و بتنحسن و ال X و EK و EK تلدة over K
+
+694
+00:48:54,710 --> 00:48:58,030
+طلعوهم برا ال summation زي ما بنعمل دايما اللي
+
+695
+00:48:58,030 --> 00:49:00,990
+بعيد اللي هو بتلعب conjugate و الجريب بتلعب عادي
+
+696
+00:49:00,990 --> 00:49:05,110
+ماشي اللي عملناها عشرين مرة هذه بيساوي X و EK و X
+
+697
+00:49:05,110 --> 00:49:10,640
+و EM تلدة و EK و EK تلدةكل هيتسفر هيبقى البث مين
+
+698
+00:49:10,640 --> 00:49:13,880
+اللي هو summation واحدة عند K بيساوي M وهيكون اللي
+
+699
+00:49:13,880 --> 00:49:16,580
+هو هذا بيساوي واحد والتنتين هذا هو ال conjugate
+
+700
+00:49:16,580 --> 00:49:20,000
+تبعه اللي هو بيطلع هذا المضولة السربيع وهذا ايش
+
+701
+00:49:20,000 --> 00:49:25,440
+بيساوي normal X سربيع اتوح منها لسه اذا صار عندى
+
+702
+00:49:25,440 --> 00:49:29,700
+الان اللي ايش اللي سويته انا اللي اثبته انا بدي
+
+703
+00:49:29,700 --> 00:49:34,570
+اثبت ايش بدي اثبت انه preserve inner productإيش
+
+704
+00:49:34,570 --> 00:49:40,650
+يعني .. يعني X TX و TY بساوة X و Y أنا إيش اللي
+
+705
+00:49:40,650 --> 00:49:44,350
+أثبتته قبل .. الآن اللي أثبتته في الحسابات اللي
+
+706
+00:49:44,350 --> 00:49:53,450
+قبل بشوية أثبتت أنه اللي هو ال X و ال Xبساوة Tx
+
+707
+00:49:53,450 --> 00:49:59,830
+وTx بدأ نتقل من هذه لل general عشان نقول preserve
+
+708
+00:49:59,830 --> 00:50:04,790
+inner product طيب عشان تكون اللي هو خلصنا الجزء
+
+709
+00:50:04,790 --> 00:50:08,050
+اللي .. اللي .. اللي خلنا نقول الأهم الان for any
+
+710
+00:50:08,050 --> 00:50:12,030
+x و h element .. x و y element in H بدأ نشتغل على
+
+711
+00:50:12,030 --> 00:50:16,190
+الريال و ال .. و ال complex بنفس الأسلوب كان اللي
+
+712
+00:50:16,190 --> 00:50:21,050
+هي .. اللي هي حالتين إذا بتذكروا لما أثبتناهم
+
+713
+00:50:21,450 --> 00:50:27,210
+الأولى كانت تي إكس وتي واي بتساوي ربع في تي إكس
+
+714
+00:50:27,210 --> 00:50:30,290
+ناقص تي واي لكل تربيع ناقص تي إكس وتي واي لكل إش
+
+715
+00:50:30,290 --> 00:50:36,850
+ماله تربيع ماشي الحال الان وي ساوي ربع في تي إكس
+
+716
+00:50:36,850 --> 00:50:40,010
+زي تي واي هي عبارة عن تي إكس زي إدوى لكل إش ماله
+
+717
+00:50:40,010 --> 00:50:45,050
+تربيع ماشي والتانية تي ويكس واي لكل إش ماله تربيع
+
+718
+00:50:45,050 --> 00:50:50,540
+أنا اللي قبل بشوية أثبتها في حالة اللي هي هذهأه
+
+719
+00:50:50,540 --> 00:50:54,000
+بساوي اللي هو x زي دوي تربيع اللي اتبعته مش اتبعت
+
+720
+00:50:54,000 --> 00:50:57,980
+ان انا x وx بتساوي Tx وTx ايه ان كانت x, x minus
+
+721
+00:50:57,980 --> 00:51:02,580
+y, x زي دوي اللي كانت بيصير عندي الآن هذه كلها
+
+722
+00:51:02,580 --> 00:51:06,360
+حولتها ل x زي دوي تربيع و الت .. هذه اسف و هذه
+
+723
+00:51:06,360 --> 00:51:11,080
+حولتها ل x minus y لكل تربيع لأن احسبوا هذه مع هذه
+
+724
+00:51:11,080 --> 00:51:14,760
+اللي هي اش بتساوي بتساوي ال inner product بين x و
+
+725
+00:51:14,760 --> 00:51:18,670
+y similarly for the complex case بتعملوها انتوانفس
+
+726
+00:51:18,670 --> 00:51:23,510
+الحسبة في .. في .. في برضه equality زيها بالظبط
+
+727
+00:51:23,510 --> 00:51:27,890
+طيب hence T preserves the main, the inner product
+
+728
+00:51:27,890 --> 00:51:32,790
+لأنه أثبتنا أن T X Y ياشو بتساوي X أو Y طيب
+
+729
+00:51:32,790 --> 00:51:35,770
+similarly for the complex hence T preserves the
+
+730
+00:51:35,770 --> 00:51:39,630
+inner product which implies T is ما لها one to one
+
+731
+00:51:39,630 --> 00:51:42,860
+بدنا نثبت أخر حاجة اللي هي إيش ما لها انتواماشي،
+
+732
+00:51:42,860 --> 00:51:46,320
+أنتوا كيف بناخد؟ بناخد أي X تلدة الموجودة في الـH
+
+733
+00:51:46,320 --> 00:51:52,160
+تلدة وبدنا نجيلها أصل، ماشي؟ شوفوا، خدوا أي X تلدة
+
+734
+00:51:52,160 --> 00:51:55,380
+بتساوي summation Alpha K E K تلدة over K element
+
+735
+00:51:55,380 --> 00:51:59,420
+in mean الـH تلدة، هذه الصورة أناصرها طيب، by
+
+736
+00:51:59,420 --> 00:52:02,280
+Besselin quality ال summation للـAlpha K تربيع
+
+737
+00:52:02,280 --> 00:52:08,810
+over K convertsالأن الـ summation للـ α K E K is
+
+738
+00:52:08,810 --> 00:52:12,910
+finite sum of a series which converts to X element
+
+739
+00:52:12,910 --> 00:52:16,130
+in H by theorem تلاتة خمس اتنين مادام ال summation
+
+740
+00:52:16,130 --> 00:52:21,810
+هذه اشملها معايا؟ طيب
+
+741
+00:52:21,810 --> 00:52:28,180
+الآن صحيح عند ال summation هذا is finiteاللي هو
+
+742
+00:52:28,180 --> 00:52:32,480
+قيمته finite بغض النظر اللي هو عبارة عن finite sum
+
+743
+00:52:32,480 --> 00:52:37,280
+من الواحد اللي عند أن أو series convertsاللي هو
+
+744
+00:52:37,280 --> 00:52:41,520
+twitch من theorem طلعت خمس اتنين and الفا كيه هدول
+
+745
+00:52:41,520 --> 00:52:44,880
+الفا كيه عبارة عن فرير coefficients بتطلع اللي هي
+
+746
+00:52:44,880 --> 00:52:49,360
+ال X و ال E K الآن نفس النظرية فبتصير الآن ال X
+
+747
+00:52:49,360 --> 00:52:53,900
+تلد هذه هتساوي ال Alpha K هي عبارة عن X و E K اي K
+
+748
+00:52:53,900 --> 00:52:58,880
+تلدة اللي هي في الواقع ايش هتكون ال TX اذا لجيت
+
+749
+00:52:58,880 --> 00:53:04,910
+انا الآن بدأت ب X تلد arbitrary و لجيت Xموجودة في
+
+750
+00:53:04,910 --> 00:53:09,150
+الـ H بحيث أن TX بتساوي X تلدى معناته صارت T is
+
+751
+00:53:09,150 --> 00:53:13,330
+onto و أثبتت إنها Linear و أثبتت بـ Reserve the
+
+752
+00:53:13,330 --> 00:53:17,270
+norm و أثبتت onto one to one صارت اللي هي T is an
+
+753
+00:53:17,270 --> 00:53:20,910
+isomorphism بين H and H تلدى و إلى لقاء آخر السلام
+
+754
+00:53:20,910 --> 00:53:21,670
+عليكم و رحمة الله
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/ClvCjQJddZs.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/ClvCjQJddZs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..35c2c727e70d66b3ad9d4418555f15e91934e9a0
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/ClvCjQJddZs.srt
@@ -0,0 +1,839 @@
+1
+00:00:05,350 --> 00:00:07,910
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,910 --> 00:00:10,770
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,770 --> 00:00:15,390
+أهله وصحابه الأجمعين هذه هي المحاضرة رقم 26 مساق 
+
+4
+00:00:15,390 --> 00:00:20,290
+تحليل اقتراني أو تحليل دالي طلاب وطالبات الجامعة 
+
+5
+00:00:20,290 --> 00:00:23,710
+الإسلامية كلية رياضيات هنبدأ اليوم إن شاء الله 
+
+6
+00:00:23,710 --> 00:00:28,370
+في اللي هو chapter 4 بعد ما خلصنا chapter 3 اللي 
+
+7
+00:00:28,370 --> 00:00:31,810
+هو chapter 4 خليني أقول في مرة المادة اللي هو 
+
+8
+00:00:31,810 --> 00:00:35,850
+Fundamental Theorems of  normed and Banach 
+
+9
+00:00:35,850 --> 00:00:39,490
+spaces اللي هي النظريات الأربعة أو الثلاث 
+
+10
+00:00:39,490 --> 00:00:43,530
+الرئيسية في المساق أو في الـfunctional analysis بصورة 
+
+11
+00:00:43,530 --> 00:00:50,650
+عامة بما يتعلق بالـnormed أو الـBanach spaces عشان 
+
+12
+00:00:50,650 --> 00:00:55,870
+نصل لهذه النظريات الأساسية هنحكي أول شيء عن حاجة 
+
+13
+00:00:55,870 --> 00:00:58,970
+اسمها Zorn's Lemma هذا المفروض يعني هذا section 
+
+14
+00:00:58,970 --> 00:01:02,930
+سريع يعني خلينا نقول هو background لشغل إحنا 
+
+15
+00:01:02,930 --> 00:01:06,130
+بنشتغله في الـset theory لكن بعض الناس ممكن يكون 
+
+16
+00:01:06,130 --> 00:01:11,070
+مُرّ  عليهُم فعشان هيك نشرحه على السريع نيجي لـZorn's 
+
+17
+00:01:11,070 --> 00:01:16,310
+Lemma عشان نعرف إيش هي Zorn's Lemma بالضبط اللي هو 
+
+18
+00:01:16,310 --> 00:01:18,670
+نعرف اللي هو بعض التعريفات 
+
+19
+00:01:21,080 --> 00:01:23,800
+اللي هو إيش معنى partially ordered set  
+
+20
+00:01:23,800 --> 00:01:26,680
+partially ordered set is a set  مجرد set عليها 
+
+21
+00:01:27,950 --> 00:01:31,970
+عليها partial order relation الآن إحنا في 
+
+22
+00:01:31,970 --> 00:01:37,210
+عندي 6M  وفي عندي عليها اللي هي relation اللي هي 
+
+23
+00:01:37,210 --> 00:01:40,990
+تسمى بالأصغر أو يساوي اللي في الأعداد اللي هي M 
+
+24
+00:01:40,990 --> 00:01:44,150
+اللي هي 6  وهذه partial order relation إيش الـ
+
+25
+00:01:44,150 --> 00:01:47,710
+partial order relation تحقق؟ تحقق ثلاث شروط الشرط الأول 
+
+26
+00:01:47,710 --> 00:01:52,490
+أنها تكون اللي هو A أصغر أو يساوي A for all A  
+
+27
+00:01:52,490 --> 00:01:56,410
+A اللي هم بنسميها إيش مالها؟ اللي هو reflexive الآن 
+
+28
+00:01:56,860 --> 00:02:00,500
+بـ فـ A أصغر أو يساوي B  و B أصغر أو يساوي A بتعطيني A 
+
+29
+00:02:00,500 --> 00:02:03,520
+بـيساوي B اللي بنسميها antisymmetric الـsymmetric 
+
+30
+00:02:03,520 --> 00:02:07,760
+طبعًا إحنا اللي هي الخاصية في الـequivalence 
+
+31
+00:02:07,760 --> 00:02:11,240
+relation اللي بتختلف عن الـequivalence relation بس 
+
+32
+00:02:11,240 --> 00:02:14,930
+اللي هي منين؟ الـantisymmetric الخاصية الثّانية F A أصغر 
+
+33
+00:02:14,930 --> 00:02:18,310
+أو يساوي B and B أصغر أو يساوي C بيعطينا A أصغر أو يساوي C لخاصية 
+
+34
+00:02:18,310 --> 00:02:21,930
+التعدي أو Transitive الثلاث خواص دول مع بعض بيعملوا 
+
+35
+00:02:21,930 --> 00:02:25,850
+أنه يصبح partial order relation ولو استبدلنا 
+
+36
+00:02:25,850 --> 00:02:28,670
+الـantisymmetric بالـsymmetric بتصير equivalence 
+
+37
+00:02:28,670 --> 00:02:33,770
+relation مش موضوعنا الآن إحنا هذه اللي هي partial 
+
+38
+00:02:33,770 --> 00:02:37,830
+order relation أول مثال إحنا بنعطيه بنعطيه على الـ 
+
+39
+00:02:37,830 --> 00:02:40,990
+partial order relation اللي هو كنا نعطيه اللي هي 
+
+40
+00:02:40,990 --> 00:02:44,730
+اللي هي لو أخذنا set X  وأخذنا subset من الـpower set
+
+41
+00:02:44,730 --> 00:02:48,170
+of X  وأخذنا عليها اللي هي مين؟ اللي هي الـinclusion 
+
+42
+00:02:48,170 --> 00:02:51,250
+الـset inclusion هذه بتعمل partial order relation 
+
+43
+00:02:51,250 --> 00:02:54,470
+ماشي الحال؟ مش موضوعنا بس هذا في الـ في الـ 
+
+44
+00:02:54,470 --> 00:02:58,480
+يعني بنعطيه مثال في اللي هي الـset theory الآن نيجي 
+
+45
+00:02:58,480 --> 00:03:02,540
+لتعريف نعرف حاجة اسمها upper bound اللي هي an 
+
+46
+00:03:02,540 --> 00:03:05,800
+upper bound of a subset W of a partially ordered 
+
+47
+00:03:05,800 --> 00:03:09,080
+set M يعني لو كانت عندي partially ordered set هي 
+
+48
+00:03:09,080 --> 00:03:11,820
+partially ordered set هي partially ordered set هي 
+
+49
+00:03:11,820 --> 00:03:15,700
+اللي هي اللي هي الـset اللي عندي وكانت مش بشكل هذا 
+
+50
+00:03:15,700 --> 00:03:19,740
+أو أي إن كانت هذه W  هذه M  الـset M لو جينا أخذنا 
+
+51
+00:03:19,740 --> 00:03:26,100
+جزء منها اللي هي هذا W وجزء منها من هذه الست هذه 
+
+52
+00:03:26,100 --> 00:03:29,540
+عنصر عنصرين ثلاثة أربعة هذه الـpartial ordered relation
+
+53
+00:03:29,540 --> 00:03:33,580
+يعني هذا أصغر شوي من هذا فهذا أصغر شوي من هذاك partial 
+
+54
+00:03:33,580 --> 00:03:37,600
+order وهذا أصغر شوي من هذا وهذا أصغر شوي من هذا لو 
+
+55
+00:03:37,600 --> 00:03:41,380
+أخذنا الـ W جزء من الـ M بدنا نعرف حاجة إيش اسمها an 
+
+56
+00:03:41,380 --> 00:03:44,840
+upper bound an upper bound of a subset W of a 
+
+57
+00:03:44,840 --> 00:03:49,940
+partially ordered set M is U element من M إذا الـ
+
+58
+00:03:49,940 --> 00:03:54,380
+upper bound عبارة عن مين؟ عن عنصر وين بيكون؟ في الـ
+
+59
+00:03:54,380 --> 00:03:58,080
+M يعني مش شرط يكون بس في الـ W ممكن يكون وين؟ برا الـ 
+
+60
+00:03:58,080 --> 00:04:02,810
+W المهم وين؟ من الـ M such that بيحقق إن X أصغر 
+
+61
+00:04:02,810 --> 00:04:07,530
+شوي من U لكل X الموجودة في W بيكون أكبر شوي من كل 
+
+62
+00:04:07,530 --> 00:04:11,810
+عناصر مين؟ الـ W اللي هو such that U أصغر شوي من X 
+
+63
+00:04:11,810 --> 00:04:14,950
+أصغر شوي for all X element in M هذا اللي بنسميه 
+
+64
+00:04:14,950 --> 00:04:19,210
+إيش ماله؟ عبارة عن اللي هو element اللي هو إيش ماله؟ 
+
+65
+00:04:19,210 --> 00:04:23,350
+اللي هو Upper Bound يعني الآن لو أجينا أخذنا اللي 
+
+66
+00:04:23,350 --> 00:04:27,190
+هو بالشكل هذا وأخذنا بالشكل هذا هذا أكيد إيش 
+
+67
+00:04:27,190 --> 00:04:31,110
+ماله؟ عبارة عن Upper Bound لمين؟ اللي هي الـCW 
+
+68
+00:04:31,110 --> 00:04:36,130
+لأنه أكبر شوي من كل عناصرها، معايا؟ طيب، الآن بدنا 
+
+69
+00:04:36,130 --> 00:04:40,000
+نحلل رفحاجة اسمها Maximal Element of M a maximal 
+
+70
+00:04:40,000 --> 00:04:43,260
+element of M is M element of M إذا الـmaximal من 
+
+71
+00:04:43,260 --> 00:04:47,240
+وين بيكون؟ من نفس الـset نفسها لو بدي أجيب الـmaximum 
+
+72
+00:04:47,240 --> 00:04:51,160
+للـ W في الـ W الـmaximal للـ M الـmaximal من وين؟ في 
+
+73
+00:04:51,160 --> 00:04:56,120
+الـ M بحيث ما لو such that if M أصغر أو يساوي X then M 
+
+74
+00:04:56,120 --> 00:05:01,080
+بتساوي X يعني ماحد بيكون أنا maximal إذا ماكانش حد 
+
+75
+00:05:01,080 --> 00:05:06,030
+له علاقة فيه أكبر مني شرط إن يكون له علاقة فيه 
+
+76
+00:05:06,030 --> 00:05:09,710
+أما أصغر أو يساوي X بيكون M إيش بيبقى؟ بتساوي X يعني كل 
+
+77
+00:05:09,710 --> 00:05:13,650
+اللي له علاقة فيه ماحدش يكون أكبر منه يعني هذا لو 
+
+78
+00:05:13,650 --> 00:05:17,150
+جينا للست هذه اللي جوا هذا بيكون maximal ماشي 
+
+79
+00:05:17,150 --> 00:05:21,270
+الحال وهذا هيكون maximal اه لإنه مافيش واحد له 
+
+80
+00:05:21,270 --> 00:05:23,890
+على .. انسى اللي فوق بحكي عن .. عن هذه الـmaximal 
+
+81
+00:05:23,890 --> 00:05:27,030
+.. ال .. ال .. هذا maximal وهذا maximal لكن الـ 
+
+82
+00:05:27,030 --> 00:05:30,690
+upper bound بيكون إيش ماله؟ أكبر من كل العناصر 
+
+83
+00:05:30,690 --> 00:05:36,870
+ماشي؟ طيب الـ N a subset C of M is called a chain 
+
+84
+00:05:36,870 --> 00:05:40,210
+بنقول اللي هو C مجموعة جزئية من M بنسميها chain 
+
+85
+00:05:40,210 --> 00:05:44,810
+or a totally ordered set إذا كان لكل A و B في الـ
+
+86
+00:05:44,810 --> 00:05:47,650
+C  الـ A أصغر شوي من B أو الـ B أصغر شوي من A  الـ A 
+
+87
+00:05:47,650 --> 00:05:51,790
+يعني الـchain هي عناصر لازم يكون كلها نقلها علاقة 
+
+88
+00:05:51,790 --> 00:05:55,550
+في بعض هذه مش chain هذه على بعض مش chain لأن هذا 
+
+89
+00:05:55,550 --> 00:05:59,500
+العنصر مالهوش علاقة في هذا لكن هذه chain وهذا الـ
+
+90
+00:05:59,500 --> 00:06:02,900
+Chain وهذول اللي حالهم الـChain وهذول اللي حالهم 
+
+91
+00:06:02,900 --> 00:06:06,000
+الـChain وهذول اللي حالهم الـChain واضح؟ إذا 
+
+92
+00:06:06,000 --> 00:06:09,020
+مافهمش إيش معنى الـChain طيب، الآن نيجي لـZorn's
+
+93
+00:06:09,020 --> 00:06:11,940
+Lemma هو مش موضوعنا بس عشان تفهموا علينا إيش بنقول 
+
+94
+00:06:11,940 --> 00:06:14,740
+Zorn's Lemma، أطلع لـZorn's Lemma عشان Zorn's Lemma
+
+95
+00:06:14,740 --> 00:06:20,040
+أبدأ استخدمها في برهان النظرية الـ4.114 عندنا 
+
+96
+00:06:20,040 --> 00:06:24,740
+إحنا، إذا بتذكروا الـWell Ordering Principle و
+
+97
+00:06:24,740 --> 00:06:31,420
+الـHausdorff Principle و الـZorn's Lemma هذه كلها 
+
+98
+00:06:31,420 --> 00:06:37,440
+أكسيومات الاختيار الأربعة اللي هي أكسيومات في الواقع 
+
+99
+00:06:37,440 --> 00:06:42,780
+واحدة فيها أكسيوم والثانية بتتبرهن منها أو بتتبرهن 
+
+100
+00:06:42,780 --> 00:06:45,640
+أنها بتكافئها يعني هذول الأربعة الـHouse of
+
+101
+00:06:45,640 --> 00:06:51,320
+Principles و الـZorn's Lemma و الـAxiom of Choice
+
+102
+00:06:51,320 --> 00:06:55,660
+والأربعة 
+
+103
+00:06:55,660 --> 00:07:02,260
+هذول كلهم متكافئات لكن لازم نفترض واحدة منها Axiom 
+
+104
+00:07:02,700 --> 00:07:07,040
+ومن ثم الباقية بيتبرهنوا منها طيب Zorn's Lemma let M 
+
+105
+00:07:07,040 --> 00:07:09,780
+اللي بتديه اللي بتديه اللي بتديه اللي بتديه
+
+106
+00:07:09,780 --> 00:07:10,120
+اللي بتديه اللي بتديه اللي بتديه اللي بتديه
+
+107
+00:07:10,120 --> 00:07:10,420
+اللي بتديه اللي بتديه اللي بتديه اللي بتديه
+
+108
+00:07:10,420 --> 00:07:11,080
+اللي بتديه اللي بتديه اللي بتديه اللي بتديه
+
+109
+00:07:11,080 --> 00:07:11,460
+اللي بتديه اللي بتديه اللي بتديه اللي بتديه
+
+110
+00:07:11,460 --> 00:07:11,800
+اللي بتديه اللي بتديه اللي بتديه اللي بتديه
+
+111
+00:07:11,800 --> 00:07:13,360
+اللي بتديه اللي بتديه اللي بتديه اللي بتديه
+
+112
+00:07:13,360 --> 00:07:32,660
+اللي بتديه اللي بتديه اللي بتديه اللي 
+
+113
+00:07:32,660 --> 00:07:37,650
+بتعيه اللي أنا بقول اللي لو كانت M اللي عبارة عن 
+
+114
+00:07:37,650 --> 00:07:41,650
+partial order set طبعًا من M to T وكانت 
+
+115
+00:07:41,650 --> 00:07:45,510
+بخاصية إن كل chain منها subset من M لها upper 
+
+116
+00:07:45,510 --> 00:07:50,630
+bound لازم تكون M إيش مالها؟ at least one maximal 
+
+117
+00:07:50,630 --> 00:07:54,070
+element هذه الـZorn's اللي بدي أستخدمها في برهان 
+
+118
+00:07:54,070 --> 00:08:01,220
+نظريتي اللي هي الـexistence اللي وعدناكم فيه للـ
+
+119
+00:08:01,220 --> 00:08:08,040
+total orthonormal set الآن الإعلان هو كالتالي in 
+
+120
+00:08:08,040 --> 00:08:15,460
+every Hilbert space H لا تساوي صفر there exists a 
+
+121
+00:08:15,460 --> 00:08:22,080
+total orthonormal set بغض النظر عن الـHilbert 
+
+122
+00:08:22,080 --> 00:08:28,100
+space اللي هو finite dimensional أو اللي هو 
+
+123
+00:08:28,100 --> 00:08:32,840
+separable أو non-separable في اللي هو واحدة بتلعب 
+
+124
+00:08:32,840 --> 00:08:37,560
+دور اللي هو roughly roughly دور الـbases في 
+
+125
+00:08:37,560 --> 00:08:39,920
+اللي هو الـfinite dimensional اللي هي إيش اسمها 
+
+126
+00:08:39,920 --> 00:08:45,320
+total orthonormal set وهذه دائمًا إيش مالها؟ موجودة 
+
+127
+00:08:45,320 --> 00:08:49,980
+هذه بدنا نثبتها اعتمادًا على الأكسيوم اللي 
+
+128
+00:08:49,980 --> 00:08:54,950
+هي Zorn's Lemma شوفوا كيف بدنا نبرهن البرهان البرهان 
+
+129
+00:08:54,950 --> 00:09:02,080
+سهل وبسيط مش يعني مش صعب بنشوف كيف الآن let M be
+
+130
+00:09:02,080 --> 00:09:05,860
+the set of all orthonormal subsets of H إجينا الآن 
+
+131
+00:09:05,860 --> 00:09:10,420
+بدنا نجيب عائلة الـorthonormal subsets ونسميها 
+
+132
+00:09:10,420 --> 00:09:17,100
+إيش؟ M  كل الـorthonormal subsets of H بنسميها M طيب 
+
+133
+00:09:17,100 --> 00:09:21,400
+هل هال موجودة؟ يعني في عناصر فيها اللي هي هذه 
+
+134
+00:09:21,400 --> 00:09:27,250
+العائلة هل العائلة هذه فيها عناصر؟ اه فيها عناصر ما 
+
+135
+00:09:27,250 --> 00:09:31,430
+إحنا فرضنا إن الـH إيش مالها؟ لا تساوي صفر مدام الـH 
+
+136
+00:09:31,430 --> 00:09:36,090
+لا تساوي صفر إذا بقدر ألاقي فيها Zero element سميه 
+
+137
+00:09:36,090 --> 00:09:39,530
+من X إذا there is X element في الـH شاشه X ده ماله 
+
+138
+00:09:39,530 --> 00:09:44,140
+لا تساوي صفر إذا خذوا الـX على الـnorm X هذه 
+
+139
+00:09:44,140 --> 00:09:48,640
+orthonormal set لإني الـnorm اللي هو إيش بيساوي 
+
+140
+00:09:48,640 --> 00:09:52,960
+normها بيساوي واحد ماشي الحال؟ إذا هذه بتمثل 
+
+141
+00:09:52,960 --> 00:09:57,880
+orthonormal subset من مين من H إذا أكيد الـ M إيش
+
+142
+00:09:57,880 --> 00:10:02,260
+مالها لاتساوي Phi إذا هي أول حاجة M لاتساوي Phi
+
+143
+00:10:03,280 --> 00:10:07,600
+الآن لو جينا أخذنا هذه عائلة من المجموعات الـ
+
+144
+00:10:07,600 --> 00:10:11,120
+subset مع العائلة من المجموعات بتعمل partial order
+
+145
+00:10:11,120 --> 00:10:14,440
+relation لأن الـ subset مالها إيش مالها اللي هي الـ
+
+146
+00:10:14,440 --> 00:10:19,000
+subset نفسها إيه الـ subset من إيه؟ لأي a subset
+
+147
+00:10:19,000 --> 00:10:25,500
+منهم اثنين لو a subset من b لـ a و b في الـ m و b 
+
+148
+00:10:25,500 --> 00:10:29,340
+subset من a لـ b و a في الـ m أكيد هيعطينا الـ a
+
+149
+00:10:29,340 --> 00:10:33,720
+بتساوي من الـ b هذا بنعرفه من خلاص المجموعات اللي
+
+150
+00:10:33,720 --> 00:10:38,640
+قال الخصية الثالثة لو a subset من b و B subset من C
+
+151
+00:10:38,640 --> 00:10:43,680
+و A و B و C في الـ M هيعطينا الـ A subset من C إذا 
+
+152
+00:10:43,680 --> 00:10:48,280
+أكيد هذه إيش بتعمل ليه partial order relation إذا
+
+153
+00:10:48,280 --> 00:10:53,380
+صارت عندها دي the collection of all ortho normal
+
+154
+00:10:53,380 --> 00:10:59,220
+subsets of H with the set inclusion is a partially 
+
+155
+00:10:59,220 --> 00:11:03,200
+order relation  جاعت بحقق في خواص الـ zones لما أو
+
+156
+00:11:03,200 --> 00:11:04,280
+معتادة من الـ zones لما
+
+157
+00:11:07,620 --> 00:11:12,440
+طيب .. let الـ N .. اطلع لفوق .. اطلع .. let C ..
+
+158
+00:11:12,440 --> 00:11:15,220
+حلوة الـ .. الـ inclusion هذا إنه على طول الـ chain
+
+159
+00:11:15,220 --> 00:11:18,360
+اللي .. اللي هو الـ .. الـ .. الـ .. الـ .. الـ upper
+
+160
+00:11:18,360 --> 00:11:22,740
+bound بتجيبه على طول .. let C الـ N subset من M بـ N
+
+161
+00:11:22,740 --> 00:11:27,420
+chain خد أي chain في الـ M .. ماشي الحال .. الـ N ..
+
+162
+00:11:27,420 --> 00:11:32,290
+then خد الـ X بتساوي الـ Union للـ A حيث A element
+
+163
+00:11:32,290 --> 00:11:37,430
+in C يعني جمع هالـ .. هالـ Chains وخدوله للاتحاد
+
+164
+00:11:37,430 --> 00:11:42,270
+ماشي؟ لو الـ C الأولى فيها A1 وA2 وA3 وC تانية فيها
+
+165
+00:11:42,270 --> 00:11:46,250
+A5 وA6 خد اتحاد بين كلهين اللي في الـ Chains
+
+166
+00:11:46,250 --> 00:11:52,010
+وسميهمين X صار هذا أكيد Upper Bound of C ليش Upper
+
+167
+00:11:52,010 --> 00:11:57,650
+Bound of C؟ Upper Bound لمن؟ لـ Chain ليش؟ لأن الـ
+
+168
+00:11:57,650 --> 00:12:02,430
+union لهم بحتوي كل واحد فيهم إذا صار Upper Bound
+
+169
+00:12:02,430 --> 00:12:05,470
+طيب إذا صار عندي الآن
+
+170
+00:12:07,940 --> 00:12:13,080
+each chain under the set inclusion لهاد الـ M لهاد
+
+171
+00:12:13,080 --> 00:12:15,700
+الـ M لهاد الـ M لهاد الـ M لهاد الـ M لهاد الـ M
+
+172
+00:12:15,700 --> 00:12:16,720
+لهاد الـ M لهاد الـ M لهاد الـ M لهاد الـ M لهاد
+
+173
+00:12:16,720 --> 00:12:17,500
+الـ M لهاد الـ M لهاد الـ M لهاد الـ M لهاد الـ M
+
+174
+00:12:17,500 --> 00:12:17,700
+لهاد الـ M لهاد الـ M لهاد الـ M لهاد الـ M لهاد
+
+175
+00:12:17,700 --> 00:12:19,440
+الـ M لهاد الـ M لهاد الـ M لهاد الـ M لهاد الـ M
+
+176
+00:12:19,440 --> 00:12:21,340
+الـ M لهاd the M لهاd the M لهاd the M لهاd the M
+
+177
+00:12:21,340 --> 00:12:34,600
+لهاd the M لهاd the M لهاd the M لهاd the M لهاd
+
+178
+00:12:34,630 --> 00:12:39,750
+الـ total orthonormal set لأن هذا موجود و وين
+
+179
+00:12:39,750 --> 00:12:43,230
+موجود في الـ M إذا الـ orthonormal أنا بقولك هيكون
+
+180
+00:12:43,230 --> 00:12:48,490
+total الـ F هيكون إيه شماله؟ total ماشي إذا نضل
+
+181
+00:12:48,490 --> 00:12:52,690
+عليه أثبت لكم إنه total طيب الآن suppose that F is
+
+182
+00:12:52,690 --> 00:12:58,190
+not total in H لكن في theorem 3.6.2 إذا بتتذكروا
+
+183
+00:12:58,190 --> 00:13:05,280
+لما قلنا M أو خلينا نقول F is total هيعطيني على طول
+
+184
+00:13:05,280 --> 00:13:10,280
+الـ F Orthogonal إيش بيساوي بيساوي Zero الـ F
+
+185
+00:13:10,280 --> 00:13:14,260
+أرثجونال إيش بيساوي؟ بيساوي 0 هدف 362 إذا من
+
+186
+00:13:14,260 --> 00:13:19,080
+theorem 362 لو جينا قولنا نفترض أن F is not total
+
+187
+00:13:19,080 --> 00:13:23,880
+إذا من theorem 362 هيكون الـ F أرثجونال إشماله لا
+
+188
+00:13:23,880 --> 00:13:29,300
+يساوي 0 إشماله لا يساوي 0 يعني في عنصر في مش صفر
+
+189
+00:13:29,300 --> 00:13:33,320
+يعني there exists z element in F أرثجونال و الـ z
+
+190
+00:13:33,320 --> 00:13:39,740
+إشماله بيساوي 0 لا يساوي 0 الآن ساعرفلي F1 بتساوي F
+
+191
+00:13:39,740 --> 00:13:45,060
+اتحاد العنصر هذا بس على normal ماشي صار هذا اللي
+
+192
+00:13:45,060 --> 00:13:49,140
+هو إيش معله normal واحد إذا صارت F اتحاد العنصر
+
+193
+00:13:49,140 --> 00:13:52,720
+هذا والعنصر هذا الـ Z مع كل واحد اللي هو product
+
+194
+00:13:52,720 --> 00:13:56,840
+صفر يعني Orthogonal على كل مين معاهن إذا صارت كل
+
+195
+00:13:56,840 --> 00:14:01,630
+الـ F1 عبارة عن orthonormal set بصبوط الآن هذه F
+
+196
+00:14:01,630 --> 00:14:05,410
+orthonormal ماشي اللي هو الـ product من أي عنصرين
+
+197
+00:14:05,410 --> 00:14:09,250
+فيها صفرو هذا الـ Z عمودي على الـ F إذا الـ inner
+
+198
+00:14:09,250 --> 00:14:12,490
+product بينه وبين أي عنصر هنا برضه مش بيساوي صفر إذا
+
+199
+00:14:12,490 --> 00:14:16,530
+صار F اتحاد و هذا مش موجود هنا دلوا بالكم صار F
+
+200
+00:14:16,530 --> 00:14:23,370
+اتحاد هذا عبارة عن Orthonormal set ماشي الحال و
+
+201
+00:14:23,370 --> 00:14:27,450
+أكبر من مين؟ بتحتوي على مين على الـ F إذا بطل الـ
+
+202
+00:14:27,450 --> 00:14:30,880
+F maximal element which is a contradiction الآن
+
+203
+00:14:30,880 --> 00:14:34,440
+which is orthonormal and F is a proper subset of
+
+204
+00:14:34,440 --> 00:14:39,160
+F1 which is a contradiction of the maximality of F
+
+205
+00:14:39,160 --> 00:14:43,720
+therefore الفرضية اللي فرضناها ان F is not total
+
+206
+00:14:43,720 --> 00:14:47,520
+مش صحيحة therefore the orthonormal set اللي هي الـ
+
+207
+00:14:47,520 --> 00:14:51,120
+F اللي كانت اللي هي maximum لازم تكون إيش مالها
+
+208
+00:14:51,120 --> 00:14:55,960
+total in H وبهيك إن احنا أثبتنا ان any Hilbert
+
+209
+00:14:55,960 --> 00:15:01,690
+space H لا تساوي صفر has الـ Total Orthonormal Set
+
+210
+00:15:01,690 --> 00:15:03,610
+وإلى لقاء آخر 
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/ClvCjQJddZs_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/ClvCjQJddZs_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..a03a793fff92fd07cb0c5e5eabd7b83f33b6fe65
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/ClvCjQJddZs_raw.json
@@ -0,0 +1 @@
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"text": "ومن ثم الباقية بيبرهنوا منها طيب zones لما let m اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بتديها اللي بت", "tokens": [20498, 1863, 38637, 2304, 29739, 995, 4587, 10632, 4724, 1829, 26890, 3224, 1863, 14407, 9154, 11296, 23032, 1829, 3555, 710, 266, 279, 5296, 15042, 718, 275, 13672, 1829, 39894, 16254, 11296, 13672, 1829, 39894, 16254, 11296, 13672, 1829, 39894, 16254, 11296, 13672, 1829, 39894, 16254, 11296, 13672, 1829, 39894, 16254, 11296, 13672, 1829, 39894, 16254, 11296, 13672, 1829, 39894, 16254, 11296, 13672, 1829, 39894, 16254, 11296, 13672, 1829, 39894, 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اللي هو separable أو non-separable في اللي هو واحدة تلعب دور اللي هو roughly .. roughly دور ال bases في المين ال finite dimensional اللي هي إيش اسمها total orthonormal 6 وهذه دائما إيه شمالها موجودة هذه بدنا نثبتها اعتمادا عالميا على الأكسيوم اللي هي zone slim", "tokens": [10721, 2407, 13672, 1829, 31439, 3128, 712, 34051, 2107, 12, 405, 42012, 8978, 13672, 1829, 31439, 36764, 24401, 3660, 6055, 1211, 3615, 3555, 11778, 13063, 13672, 1829, 31439, 9810, 4386, 9810, 11778, 13063, 2423, 17949, 8978, 9673, 9957, 2423, 19362, 18795, 13672, 1829, 39896, 11933, 1829, 8592, 24525, 2304, 11296, 3217, 420, 11943, 24440, 1386, 37037, 24192, 11778, 16373, 15042, 11933, 1829, 3224, 13412, 2304, 6027, 11296, 3714, 29245, 23328, 3660, 29538, 47525, 8315, 8717, 12984, 3555, 2655, 11296, 1975, 34268, 15042, 28259, 6225, 45340, 25528, 15844, 16247, 4117, 3794, 1829, 20498, 13672, 1829, 39896, 6668, 25357], "avg_logprob": -0.229432397807131, "compression_ratio": 1.7356828193832599, "no_speech_prob": 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{"start": 512.84, "end": 513.5, "word": " دور", "probability": 0.9853515625}, {"start": 513.5, "end": 514.26, "word": " اللي", "probability": 0.94482421875}, {"start": 514.26, "end": 514.74, "word": " هو", "probability": 0.99072265625}, {"start": 514.74, "end": 515.38, "word": " roughly", "probability": 0.53369140625}, {"start": 515.38, "end": 515.5, "word": " ..", "probability": 0.29541015625}, {"start": 515.5, "end": 515.84, "word": " roughly", "probability": 0.56591796875}, {"start": 515.84, "end": 516.28, "word": " دور", "probability": 0.92724609375}, {"start": 516.28, "end": 516.46, "word": " ال", "probability": 0.98828125}, {"start": 516.46, "end": 516.94, "word": " bases", "probability": 0.61474609375}, {"start": 516.94, "end": 517.56, "word": " في", "probability": 0.927734375}, {"start": 517.56, "end": 518.02, "word": " المين", "probability": 0.634033203125}, {"start": 518.02, "end": 518.12, "word": " ال", "probability": 0.78857421875}, {"start": 518.12, "end": 518.34, "word": 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"probability": 0.953125}, {"start": 524.3, "end": 525.32, "word": " موجودة", "probability": 0.9915771484375}, {"start": 525.32, "end": 525.72, "word": " هذه", "probability": 0.7607421875}, {"start": 525.72, "end": 525.94, "word": " بدنا", "probability": 0.802490234375}, {"start": 525.94, "end": 526.52, "word": " نثبتها", "probability": 0.9904296875}, {"start": 526.52, "end": 527.74, "word": " اعتمادا", "probability": 0.82470703125}, {"start": 527.74, "end": 528.58, "word": " عالميا", "probability": 0.754150390625}, {"start": 528.58, "end": 528.94, "word": " على", "probability": 0.87744140625}, {"start": 528.94, "end": 529.76, "word": " الأكسيوم", "probability": 0.8093505859375}, {"start": 529.76, "end": 529.98, "word": " اللي", "probability": 0.9765625}, {"start": 529.98, "end": 530.16, "word": " هي", "probability": 0.93359375}, {"start": 530.16, "end": 530.86, "word": " zone", "probability": 0.80419921875}, {"start": 530.86, "end": 531.38, "word": " slim", "probability": 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{"start": 534.95, "end": 535.33, "word": " سهل", "probability": 0.9938151041666666}, {"start": 535.33, "end": 535.91, "word": " وبسيط", "probability": 0.9217529296875}, {"start": 535.91, "end": 536.59, "word": " مش", "probability": 0.8671875}, {"start": 536.59, "end": 537.23, "word": " يعني", "probability": 0.91796875}, {"start": 537.23, "end": 537.97, "word": " مش", "probability": 0.92333984375}, {"start": 537.97, "end": 538.35, "word": " صعب", "probability": 0.84130859375}], "temperature": 1.0}, {"id": 25, "seek": 56296, "start": 539.34, "end": 562.96, "text": "بنشوف كيف الان let M be the set of all orthonormal subsets of H إجينا الآن بدنا نجيب عائلة ال orthonormal subsets و نسميها إيش M كل ال orthonormal subsets of H نسميها M طب هل هال موجودة؟ يعني في عناصر فيها اللي هي هذه العائلة", "tokens": [3555, 1863, 8592, 38688, 9122, 33911, 2423, 7649, 718, 376, 312, 264, 992, 295, 439, 420, 11943, 24440, 2090, 1385, 295, 389, 11933, 7435, 1829, 8315, 6024, 48506, 47525, 8315, 8717, 7435, 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bound بتجيبه على طول .. let C ال N subset من M ب N chain خد أي chain في ال M .. ماشي الحال .. ال N .. then خد ال X بتساوي", "tokens": [9566, 1829, 3555, 4386, 718, 2423, 39184, 426, 4386, 1975, 9566, 1211, 3615, 5296, 5172, 30543, 4386, 1975, 9566, 1211, 3615, 4386, 718, 383, 4386, 11331, 1211, 2407, 3660, 2423, 4386, 2423, 15874, 23758, 16472, 3224, 15844, 23032, 12610, 2423, 5021, 13672, 1829, 4386, 13672, 1829, 31439, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 6597, 5472, 39894, 7435, 1829, 3555, 3224, 15844, 23032, 12610, 4386, 718, 383, 2423, 426, 25993, 9154, 376, 4724, 426, 5021, 16490, 3215, 36632, 5021, 8978, 2423, 376, 4386, 3714, 33599, 1829, 21542, 6027, 4386, 2423, 426, 4386, 550, 16490, 3215, 2423, 1783, 39894, 3794, 995, 45865], "avg_logprob": -0.2190504867870074, "compression_ratio": 1.8115942028985508, "no_speech_prob": 1.2099742889404297e-05, "words": [{"start": 667.62, "end": 668.18, "word": "طيب", "probability": 0.9710286458333334}, {"start": 668.18, 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{"start": 842.65, "end": 843.67, "word": " ماشي", "probability": 0.7950846354166666}, {"start": 843.67, "end": 844.17, "word": " اللي", "probability": 0.91015625}, {"start": 844.17, "end": 844.33, "word": " هو", "probability": 0.52783203125}, {"start": 844.33, "end": 844.41, "word": " ال", "probability": 0.5458984375}, {"start": 844.41, "end": 844.69, "word": " product", "probability": 0.92529296875}, {"start": 844.69, "end": 844.87, "word": " من", "probability": 0.84130859375}, {"start": 844.87, "end": 844.99, "word": " أي", "probability": 0.6162109375}, {"start": 844.99, "end": 845.41, "word": " عنصرين", "probability": 0.9530029296875}, {"start": 845.41, "end": 845.61, "word": " فيها", "probability": 0.963623046875}, {"start": 845.61, "end": 845.97, "word": " سفر", "probability": 0.7396647135416666}], "temperature": 1.0}, {"id": 40, "seek": 86971, "start": 846.55, "end": 869.71, "text": "وهذا الـ Z عمودي على الـ F إذا الـ inner product بينه بين أي عنصر هنا برضه مش بساوي سفر إذا صار F إتحاد و هذا مش موجود هان دلوا بالكم صار F إتحاد هذا عبارة عن Orthonormal set ماشي الحال و أكبر من مين؟ بتحتوى على مين على الـ F إذا بطل الـ F maximal element which is a contradiction", "tokens": [2407, 3224, 15730, 2423, 39184, 1176, 6225, 2304, 2407, 16254, 15844, 2423, 39184, 479, 11933, 15730, 2423, 39184, 7284, 1674, 49374, 3224, 49374, 36632, 18871, 9381, 2288, 34105, 4724, 43042, 3224, 37893, 4724, 3794, 995, 45865, 8608, 5172, 2288, 11933, 15730, 20328, 9640, 479, 11933, 2655, 5016, 18513, 4032, 23758, 37893, 3714, 29245, 23328, 8032, 7649, 11778, 1211, 14407, 20666, 24793, 20328, 9640, 479, 11933, 2655, 5016, 18513, 23758, 6225, 3555, 9640, 3660, 18871, 27554, 266, 24440, 992, 3714, 33599, 1829, 21542, 6027, 4032, 5551, 4117, 26890, 9154, 3714, 9957, 22807, 39894, 33753, 2407, 7578, 15844, 3714, 9957, 15844, 2423, 39184, 479, 11933, 15730, 4724, 9566, 1211, 2423, 39184, 479, 49336, 4478, 597, 307, 257, 34937], "avg_logprob": -0.2409188080037761, "compression_ratio": 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858.97, "word": " عن", "probability": 0.9873046875}, {"start": 858.97, "end": 860.65, "word": " Orthonormal", "probability": 0.630859375}, {"start": 860.65, "end": 861.41, "word": " set", "probability": 0.5771484375}, {"start": 861.41, "end": 862.25, "word": " ماشي", "probability": 0.8992513020833334}, {"start": 862.25, "end": 862.69, "word": " الحال", "probability": 0.974609375}, {"start": 862.69, "end": 863.37, "word": " و", "probability": 0.4375}, {"start": 863.37, "end": 863.81, "word": " أكبر", "probability": 0.9708658854166666}, {"start": 863.81, "end": 864.09, "word": " من", "probability": 0.98095703125}, {"start": 864.09, "end": 864.95, "word": " مين؟", "probability": 0.8123372395833334}, {"start": 864.95, "end": 865.61, "word": " بتحتوى", "probability": 0.8087158203125}, {"start": 865.61, "end": 865.77, "word": " على", "probability": 0.7734375}, {"start": 865.77, "end": 866.07, "word": " مين", "probability": 0.989013671875}, {"start": 866.07, "end": 866.25, "word": " على", "probability": 0.441650390625}, {"start": 866.25, "end": 866.41, "word": " الـ", "probability": 0.799560546875}, {"start": 866.41, "end": 866.57, "word": " F", "probability": 0.8740234375}, {"start": 866.57, "end": 866.79, "word": " إذا", "probability": 0.7392578125}, {"start": 866.79, "end": 867.27, "word": " بطل", "probability": 0.8626302083333334}, {"start": 867.27, "end": 867.45, "word": " الـ", "probability": 0.8994140625}, {"start": 867.45, "end": 867.57, "word": " F", "probability": 0.9306640625}, {"start": 867.57, "end": 867.95, "word": " maximal", "probability": 0.32421875}, {"start": 867.95, "end": 868.65, "word": " element", "probability": 0.9658203125}, {"start": 868.65, "end": 869.07, "word": " which", "probability": 0.8369140625}, {"start": 869.07, "end": 869.23, "word": " is", "probability": 0.96875}, {"start": 869.23, "end": 869.35, "word": " a", "probability": 0.65380859375}, {"start": 869.35, "end": 869.71, "word": " contradiction", "probability": 0.94091796875}], "temperature": 1.0}, {"id": 41, "seek": 89862, "start": 870.36, "end": 898.62, "text": "الان which is orthonormal and F is a proper subset of F1 which is a contradiction of the maximality of F therefore الفرضية اللي فرضناها ان F is not total مش صحيحة therefore the orthonormal set اللي هي ال F اللي كانت اللي هي maximum لازم تكون ايش ما لها total in H وبهيك ان احنا اثبتنا ان any Hilbert space H لا تساوي سفر has", "tokens": [6027, 7649, 597, 307, 420, 11943, 24440, 293, 479, 307, 257, 2296, 25993, 295, 479, 16, 597, 307, 257, 34937, 295, 264, 5138, 1860, 295, 479, 4412, 27188, 43042, 10632, 13672, 1829, 6156, 43042, 8315, 11296, 16472, 479, 307, 406, 3217, 37893, 20328, 5016, 1829, 5016, 3660, 4412, 264, 420, 11943, 24440, 992, 13672, 1829, 39896, 2423, 479, 13672, 1829, 25961, 2655, 13672, 1829, 39896, 6674, 5296, 31377, 2304, 6055, 30544, 1975, 1829, 8592, 19446, 5296, 11296, 3217, 294, 389, 4032, 3555, 3224, 1829, 4117, 16472, 1975, 5016, 8315, 1975, 12984, 3555, 2655, 8315, 16472, 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895.96, "word": " Hilbert", "probability": 0.89794921875}, {"start": 895.96, "end": 896.52, "word": " space", "probability": 0.8974609375}, {"start": 896.52, "end": 896.8, "word": " H", "probability": 0.91943359375}, {"start": 896.8, "end": 896.98, "word": " لا", "probability": 0.775390625}, {"start": 896.98, "end": 897.32, "word": " تساوي", "probability": 0.7137451171875}, {"start": 897.32, "end": 897.7, "word": " سفر", "probability": 0.8513997395833334}, {"start": 897.7, "end": 898.62, "word": " has", "probability": 0.71337890625}], "temperature": 1.0}, {"id": 42, "seek": 90361, "start": 899.03, "end": 903.61, "text": "الـ Total Orthonormal Set وإلى لقاء آخر", "tokens": [6027, 39184, 23170, 27554, 266, 24440, 8928, 4032, 28814, 23942, 5296, 4587, 16606, 19753, 34740], "avg_logprob": -0.17224120907485485, "compression_ratio": 0.8983050847457628, "no_speech_prob": 0.0, "words": [{"start": 899.03, "end": 899.47, "word": "الـ", "probability": 0.850341796875}, {"start": 899.47, "end": 899.79, "word": " Total", "probability": 0.76025390625}, {"start": 899.79, "end": 901.23, "word": " Orthonormal", "probability": 0.75732421875}, {"start": 901.23, "end": 901.69, "word": " Set", "probability": 0.87841796875}, {"start": 901.69, "end": 902.33, "word": " وإلى", "probability": 0.7526041666666666}, {"start": 902.33, "end": 903.07, "word": " لقاء", "probability": 0.9697265625}, {"start": 903.07, "end": 903.61, "word": " آخر", "probability": 0.93896484375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 903.906375, "duration_after_vad": 888.2175000000005}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Dna28R7jBBs.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Dna28R7jBBs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c943146e92f2b1cf4d06e607914fa6fddd96d1ba
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Dna28R7jBBs.srt
@@ -0,0 +1,3390 @@
+1
+00:00:05,620 --> 00:00:08,620
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,620 --> 00:00:11,440
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:11,440 --> 00:00:15,240
+آله وصحبه أجمعين هذه هي المحاضرة السادسة مساق
+
+4
+00:00:15,240 --> 00:00:19,140
+تحليل اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:19,140 --> 00:00:27,110
+الإسلامية قسم رياضيات ماجستير رياضيات حكينا احنا عند
+
+6
+00:00:27,110 --> 00:00:31,530
+واحد أربعة وصلنا ونهينا واحد أربعة وقلنا خلينا
+
+7
+00:00:31,530 --> 00:00:33,930
+اللي هو المرة الجاية اللي نحكي عن واحد خمسة اللي
+
+8
+00:00:33,930 --> 00:00:39,390
+هو examples أمثلة على completeness proofs على
+
+9
+00:00:39,390 --> 00:00:43,870
+براهين اللي هي ناخد هناخد أمثلة لـ spaces تكون
+
+10
+00:00:43,870 --> 00:00:48,030
+complete و spaces تكون ايش منها non complete طبعا
+
+11
+00:00:48,030 --> 00:00:53,330
+هذا الموضوع من الموضوعات الهامة في اللي هو المادة
+
+12
+00:00:53,330 --> 00:00:59,470
+فخلينا نركز منيح على اللي هو اللي بنحكيه اليوم أول
+
+13
+00:00:59,470 --> 00:01:04,870
+مثال طبعا احنا عرفنا على اللي هو الـ space ℝ<sup>n</sup> والـ
+
+14
+00:01:04,870 --> 00:01:09,730
+ℂ<sup>n</sup> وقلنا الـ ℝ<sup>n</sup> ايش عناصره الـ ℝ<sup>n</sup> هو عبارة عن
+
+15
+00:01:09,730 --> 00:01:14,490
+عناصر x<sub>1</sub> وx<sub>2</sub> لعند x<sub>n</sub> and untables كل
+
+16
+00:01:14,490 --> 00:01:18,770
+واحد منهم موجود وين x<sub>i</sub> element in ℝ for every i
+
+17
+00:01:18,770 --> 00:01:22,130
+للي عندنا هذه اللي هي عناصر مين اللي هي الـ ℝ<sup>n</sup>
+
+18
+00:01:22,130 --> 00:01:26,090
+طبعا تعميم للـ ℝ لـ ℝ تربيع و لـ ℝ تكعيب اللي هو ℝ<sup>n</sup> in
+
+19
+00:01:26,090 --> 00:01:28,410
+general اللي الـ n بتاخد واحد اثنين ثلاثة أربعة
+
+20
+00:01:28,410 --> 00:01:33,330
+اللي بدناها الآن بدنا نعرف عليه اللي هو metric هذا
+
+21
+00:01:33,330 --> 00:01:36,130
+اللي هو الـ Euclidean metric عرفنا عليه هذا
+
+22
+00:01:36,130 --> 00:01:39,850
+متذكرين اللي هو و الـ ℂ<sup>n</sup> برضه نفس الشيء بيصير
+
+23
+00:01:39,850 --> 00:01:44,130
+doubles من الـ ℂ نسميه اللي هو Euclidean space ℝ<sup>n</sup>
+
+24
+00:01:44,130 --> 00:01:47,510
+and Unitary space اللي هو الـ ℂ<sup>n</sup> الثانية  أشملها
+
+25
+00:01:47,510 --> 00:01:51,530
+are complete spaces هنبرهن على الـ ℝ<sup>n</sup> والثانية 
+
+26
+00:01:51,530 --> 00:01:56,480
+بالضبط زي اللي هو نفس البرهان الآن ايش استراتيجية 
+
+27
+00:01:56,480 --> 00:02:00,400
+البرهان اللي هناخدها عشان أثبت أنه complete بدي
+
+28
+00:02:00,400 --> 00:02:04,600
+آخذ أي Cauchy sequence وأثبت الـ .. أي Cauchy sequence
+
+29
+00:02:04,600 --> 00:02:07,380
+في الـ ℝ<sup>n</sup> وأثبت الـ .. وأثبت الهيناي شمالها
+
+30
+00:02:07,380 --> 00:02:11,940
+converge في وين في الـ ℝ<sup>n</sup> مش الحال فالآن بدي آخذ
+
+31
+00:02:11,940 --> 00:02:19,240
+أي sequence x<sub>m</sub> تكون Cauchy وموجودة في الـ ℝ<sup>n</sup> مدام x
+
+32
+00:02:19,240 --> 00:02:23,340
+يعني بمعنى آخر x<sub>1</sub> وx<sub>2</sub> وx<sub>3</sub> وx<sub>4</sub> وx<sub>5</sub> إلى ما 
+
+33
+00:02:23,340 --> 00:02:27,580
+لنهاية عبارة عن عناصر من وين ماخدها أنا من الـ ℝ<sup>n</sup>
+
+34
+00:02:27,580 --> 00:02:31,580
+والـ x<sub>n</sub> هذه أشملها Cauchy sequence خلينا نتطلع على
+
+35
+00:02:31,580 --> 00:02:38,530
+عناصرها x<sub>1</sub> مثلا هي عبارة عن x<sub>i</sub> 11 ماشي هذه الواحد
+
+36
+00:02:38,530 --> 00:02:42,370
+اللي هي مين لـ .. اللي هو الـ Inter اللي هان x<sub>i</sub>
+
+37
+00:02:42,370 --> 00:02:47,910
+اثنين واحد x<sub>i</sub> ثلاثة واحد مجرد رموز المقول هنا
+
+38
+00:02:47,910 --> 00:02:50,990
+دول real numbers اللي عنده أصل لآخر واحد لانه كيف
+
+39
+00:02:50,990 --> 00:02:54,490
+شكل العناصر اللي في الـ ℝ<sup>n</sup> عبارة عن إن عنده أصل
+
+40
+00:02:54,490 --> 00:02:59,370
+لآخر واحد x<sub>i</sub> n هذه ايش؟ واحد هي اللي هو العنصر
+
+41
+00:02:59,370 --> 00:03:03,590
+الأول في الـ sequence x<sub>1</sub> x<sub>2</sub> بنفس الأسلوب بساوي
+
+42
+00:03:03,590 --> 00:03:16,100
+x<sub>i</sub> اثنين x<sub>1</sub> x<sub>2</sub> x<sub>3</sub> x<sub>4</sub> x<sub>5</sub> x<sub>6</sub> x<sub>7</sub> x<sub>8</sub> x<sub>9</sub>
+
+43
+00:03:16,100 --> 00:03:16,820
+x<sub>10</sub> x<sub>11</sub> x<sub>12</sub> x<sub>12</sub> x<sub>13</sub> x<sub>14</sub> x<sub>15</sub> x<sub>16</sub> x<sub>16</sub> x<sub>17</sub>
+
+44
+00:03:16,820 --> 00:03:18,280
+x<sub>18</sub> x<sub>19</sub> x<sub>20</sub> x<sub>20</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub>
+
+45
+00:03:18,280 --> 00:03:19,000
+x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub>
+
+46
+00:03:19,000 --> 00:03:20,260
+x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub>
+
+47
+00:03:20,260 --> 00:03:20,740
+x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub>
+
+48
+00:03:20,740 --> 00:03:21,120
+x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub>
+
+49
+00:03:21,120 --> 00:03:27,820
+x<sub>21</sub> x<sub>21</sub> x<sub>21</sub> x<sub>21</sub>
+
+50
+00:03:27,820 --> 00:03:31,840
+x<sub>21</sub>
+
+51
+00:03:31,840 --> 00:03:37,790
+x<sub>i</sub> x<sub>i</sub> اثنين m لعند x<sub>i</sub> m ايش 
+
+52
+00:03:37,790 --> 00:03:42,130
+m اذا هذه هي الـ sequence اللي عندي اللي ماخدها
+
+53
+00:03:42,130 --> 00:03:48,230
+Cauchy sequence في وين أنا في الـ ℝ<sup>n</sup> غرضي أن أوصلكم
+
+54
+00:03:48,230 --> 00:03:56,400
+أن في x موجودة في الـ ℝ<sup>n</sup> بحيث أن x<sub>m</sub> بتروح للـ x 
+
+55
+00:03:56,400 --> 00:04:06,100
+under the metric اللي عندنا في الـ ℝ<sup>n</sup> خليني 
+
+56
+00:04:06,100 --> 00:04:09,420
+انحقق اللي بدناها
+
+57
+00:04:19,570 --> 00:04:26,360
+بما أن x<sub>m</sub> Cauchy عرفين شو معناه Cauchy بما أن x<sub>m</sub> Cauchy
+
+58
+00:04:26,360 --> 00:04:31,840
+sequence إذا لكل ε أكبر من 0 بقدر ألاقي k بحيث الـ
+
+59
+00:04:31,840 --> 00:04:39,040
+مسافة بين x<sub>m</sub> وx<sub>r</sub> أشملها أصغر من ε لكل m وr
+
+60
+00:04:39,040 --> 00:04:44,340
+أشملها أكبر من k هذا تعريف مين الـ Cauchy sequence طيب 
+
+61
+00:04:44,340 --> 00:04:51,250
+المسافة بين x<sub>m</sub> وx<sub>r</sub> احنا عارفين ايش هي الـ x<sub>r</sub> ايش 
+
+62
+00:04:51,250 --> 00:05:00,870
+هي؟ بتساوي x<sub>1r</sub> x<sub>2r</sub> لعند ما أصل x<sub>nr</sub> هذه
+
+63
+00:05:00,870 --> 00:05:04,590
+اللي هي المسافة بين عنصرين موجودات في الـ ℝ<sup>n</sup> عن ايش
+
+64
+00:05:04,590 --> 00:05:11,570
+هي عبارة عن اللي هو x<sub>i</sub> هذا ناقص هذا تربيع مظبوط 
+
+65
+00:05:11,570 --> 00:05:15,510
+زائد هذا ناقص التربيع والأخير لما أصل لهم كلهم
+
+66
+00:05:15,510 --> 00:05:19,770
+بجموعهم وكل وش بياخذه أصله نص هذا الـ metric اجتلعنا
+
+67
+00:05:19,770 --> 00:05:26,770
+الآن بما أنه الـ x<sub>m</sub> Cauchy إذا المسافة اللي هي هذه 
+
+68
+00:05:26,770 --> 00:05:33,360
+أصغر من مين من ε لاحظوا التالي، الآن أنا بدي أحول
+
+69
+00:05:33,360 --> 00:05:38,140
+استراتيجية حلي بدي أحول الحديث إلى من اللي هي
+
+70
+00:05:38,140 --> 00:05:43,020
+Cauchy sequences في الـ ℝ<sup>n</sup> إلى Cauchy sequences في الـ ℝ
+
+71
+00:05:43,020 --> 00:05:47,220
+وأنا بعرف سابقا أن الـ ℝ أشملها is complete ركزوا 
+
+72
+00:05:47,220 --> 00:05:50,600
+كيف بدي أعملها، الآن بما أن المجموع هذا كله أصغر 
+
+73
+00:05:50,600 --> 00:05:55,740
+من ε إذا أكيد اللي هو كل واحدة منهم، كل 
+
+74
+00:05:55,740 --> 00:05:59,810
+واحدة من هذه تربيع أصغر من المجموع مش أنت رايحها هذه 
+
+75
+00:05:59,810 --> 00:06:04,310
+مجموخة كلها وهذه واحدة منها لكل i i واحد اثنين 
+
+76
+00:06:04,310 --> 00:06:08,370
+ثلاثة ان يعني لكل واحدة من هدول وكأن أنا بتاخد
+
+77
+00:06:08,370 --> 00:06:13,700
+الـ sequence هذه مع بعض والـ sequence هذه مع بعض و
+
+78
+00:06:13,700 --> 00:06:17,580
+الـ sequence الثانية مع بعض الأخره وكل واحدة منهم 
+
+79
+00:06:17,580 --> 00:06:22,620
+هي x<sub>i</sub> i m نقص x<sub>i</sub> r r كل تربيع i بتساوي واحد أو
+
+80
+00:06:22,620 --> 00:06:27,140
+اثنين أو ثلاثة أو n كله صح انهم أصغر أو صحوا
+
+81
+00:06:27,140 --> 00:06:32,800
+المجموع اللي هو أصغر منين من ε تربيع من هذه بصير كل
+
+82
+00:06:32,800 --> 00:06:36,880
+واحدة أصغر من نين من ε إذا صار هذه اللي عند 
+
+83
+00:06:36,880 --> 00:06:41,000
+الـ absolute value لها أصغر من ε هذه لكل
+
+84
+00:06:41,000 --> 00:06:49,480
+sequence اللي هي x<sub>i</sub> i واقة x<sub>i</sub> i واحد x<sub>i</sub> i اثنين x<sub>i</sub>
+
+85
+00:06:49,480 --> 00:06:55,240
+i m الأخره هذه الـ sequence الآن ايش أثبتت أنا إلها
+
+86
+00:06:55,240 --> 00:07:04,000
+إن x<sub>i</sub> i m ناقص x<sub>i</sub> i r عندي أصغر من مين من ε
+
+87
+00:07:04,000 --> 00:07:09,160
+لكن هذه sequence of numbers إذا صارت Cauchy sequence 
+
+88
+00:07:09,160 --> 00:07:13,320
+in real numbers إذا أكيد أي شمالها converge إذا
+
+89
+00:07:13,320 --> 00:07:18,180
+hence for any fixed i i من واحد لعين دلان the
+
+90
+00:07:18,180 --> 00:07:22,920
+sequence x<sub>i</sub> i واحد x<sub>i</sub> i اثنين إلى ما لنهاية هيها 
+
+91
+00:07:22,920 --> 00:07:26,460
+x<sub>i</sub> i واحد x<sub>i</sub> i اثنين x<sub>i</sub> i تلاتة إلى ما لنهاية
+
+92
+00:07:27,690 --> 00:07:31,990
+converges لما صارت ايش ما لها Cauchy sequence of 
+
+93
+00:07:31,990 --> 00:07:34,730
+real numbers then it converges خليني أقول
+
+94
+00:07:34,730 --> 00:07:41,190
+converges ده مين لـ x<sub>i</sub> i إذا صار عندي الآن كل
+
+95
+00:07:41,190 --> 00:07:45,950
+البرهين لها نفس الروح فركزوا كويس عشان نرتاح في
+
+96
+00:07:45,950 --> 00:07:51,700
+اللي بعدها صارت عندي الآن الـ sequence x<sub>ii</sub> m
+
+97
+00:07:51,700 --> 00:07:54,960
+converged domain قلنا يعني خليت هذا الـ sequence
+
+98
+00:07:54,960 --> 00:07:58,920
+شايفين هذا x<sub>ii</sub> قلنا هذا as m goes to infinity .. 
+
+99
+00:07:58,920 --> 00:08:01,880
+as i goes to infinity .. as m goes to infinity هذه
+
+100
+00:08:01,880 --> 00:08:06,440
+بدت تروح لمين؟ للـ x<sub>ii</sub> سميت x<sub>ii</sub> يعني وكأني أخدت
+
+101
+00:08:06,440 --> 00:08:10,280
+هذه الـ sequence أثبت انها Cauchy وراحت لـ x<sub>i</sub> واحد
+
+102
+00:08:10,280 --> 00:08:14,820
+هذه Cauchy وراحت لـ x<sub>i</sub> اثنين هذه Cauchy وراحت لـ x<sub>i</sub> 
+
+103
+00:08:14,820 --> 00:08:18,980
+ايه الأخيرة Cauchy وراحت لـ x<sub>i</sub> n اذا صار عند
+
+104
+00:08:18,980 --> 00:08:24,180
+الآن x بيتساوي x<sub>1</sub> x<sub>2</sub> x<sub>n</sub> كل هى نوع
+
+105
+00:08:24,180 --> 00:08:30,780
+موجودات في الـ ℝ<sup>n</sup> الآن بتثبتلكم أثبتتلكم ان الـ x
+
+106
+00:08:30,780 --> 00:08:36,620
+بتساوي x<sub>1</sub> وx<sub>2</sub> لعند x<sub>n</sub> وموجودة في
+
+107
+00:08:36,620 --> 00:08:41,280
+الـ ℝ<sup>n</sup> وكل واحدة من هدولة converge لواحدة من الـ
+
+108
+00:08:41,280 --> 00:08:48,180
+interest هدى بتثبتلكم ان x<sub>m</sub> convergence لهدى الـ x 
+
+109
+00:08:48,660 --> 00:08:53,820
+يعني ايش؟ يعني المسافة بين x<sub>m</sub> وx تكون أصغر من
+
+110
+00:08:53,820 --> 00:08:59,140
+الـ ε تحت الشروط اللي حكيتناها طيب الآن by one
+
+111
+00:08:59,140 --> 00:09:04,320
+اللي حكينا عنها في الأول هي شايفين هذه by one الآن
+
+112
+00:09:04,320 --> 00:09:10,480
+as n as m أو r اللي بتديها وديها لنا لنهاية بتروح
+
+113
+00:09:10,480 --> 00:09:14,360
+حسب اللي حكيته as r goes to infinity لـ x<sub>ir</sub> وين
+
+114
+00:09:14,360 --> 00:09:19,910
+هتروح؟ لـ x<sub>ir</sub> هي يا جماعة اللي أثبتته قبل بشوية اللي
+
+115
+00:09:19,910 --> 00:09:23,730
+هو هذه بتروح لـ x<sub>1</sub> هذه لـ x<sub>2</sub> x<sub>ii</sub> in
+
+116
+00:09:23,730 --> 00:09:27,990
+general بتروح لمين لـ x<sub>ii</sub> اذا as m goes to infinity
+
+117
+00:09:27,990 --> 00:09:34,210
+بيسير عندي من واحد هي من واحد الآن as m أو r goes 
+
+118
+00:09:34,210 --> 00:09:37,570
+to infinity we have المسافة بين x<sub>m</sub> وx هي عبارة عن
+
+119
+00:09:37,570 --> 00:09:41,810
+x<sub>ii</sub> m x<sub>ii</sub> تربيع أصغر يساوي مين ε هذا صحيح لكل
+
+120
+00:09:41,810 --> 00:09:46,550
+مين لكل m أكبر من k وهذا في حد ذاته ايش يعني بيعني 
+
+121
+00:09:46,550 --> 00:09:51,530
+ان x<sub>m</sub> is converged لـ x واتلتت انها في الـ ℝ<sup>n</sup> فصارت
+
+122
+00:09:51,530 --> 00:09:54,590
+اللي هي الـ ℝ<sup>n</sup> أشملها is complete
+
+123
+00:09:57,610 --> 00:10:03,290
+هي عندنا واحد اللي أخدته وديت r إلى مالها نهاية هذه 
+
+124
+00:10:03,290 --> 00:10:09,450
+as r goes to infinity راحت x<sub>ir</sub> إلى x<sub>i</sub> فصار
+
+125
+00:10:09,450 --> 00:10:13,350
+اللي هو المقدار اللي تحت x<sub>i</sub> كل تربيع أصلي نص 
+
+126
+00:10:13,350 --> 00:10:19,170
+أصلي من ε وهذه المسافة زي ما قلنا بين x وx الآن لو
+
+127
+00:10:19,170 --> 00:10:24,250
+بدنا نفسه بالـ ℂ<sup>n</sup> كل الكلام اللي حد هنا بنفسه بس
+
+128
+00:10:24,250 --> 00:10:27,870
+بنقول بدل الإكسايات هدول ما فنهانا في الـ ℝ<sup>n</sup> بدين
+
+129
+00:10:27,870 --> 00:10:32,530
+نكون في الـ ℂ<sup>n</sup> وبس بيكون هو نفس البرهان
+
+130
+00:10:37,110 --> 00:10:41,390
+فاهم صلوا علينا باللي ما ركز معايا هنا هنعيد تقريبا
+
+131
+00:10:41,390 --> 00:10:46,110
+كلام مشابه في إثبات الـ completeness لمن؟ لـ l 
+
+132
+00:10:46,110 --> 00:10:48,310
+infinity وl completeness اللي بعد ما هي اختلافات 
+
+133
+00:10:48,310 --> 00:10:52,050
+بسيطة تناسب الـ space اللي موجود عندنا الآن 
+
+134
+00:10:52,050 --> 00:10:55,290
+completeness of l infinity l infinity عارفين أنتو
+
+135
+00:10:55,290 --> 00:10:59,190
+هو the space of bounded sequences اللي هي the
+
+136
+00:10:59,190 --> 00:11:02,290
+space l infinity is complete كله under the metric
+
+137
+00:11:02,290 --> 00:11:09,490
+اللي احنا خدناه الآن عندنا عناصر برضه نفس الـ
+
+138
+00:11:09,490 --> 00:11:13,710
+استراتيجية ايش بتاخد بتاخد x<sub>m</sub> أي Cauchy sequence في الـ
+
+139
+00:11:13,710 --> 00:11:18,010
+l infinity ولاجه x في الـ l infinity بحيث ان x<sub>m</sub>
+
+140
+00:11:18,010 --> 00:11:22,350
+Converges لها بقول خلصت أثبتت أنه Complete معناته
+
+141
+00:11:22,350 --> 00:11:31,230
+إنه بدايته إنه بتاخد أي XM كوشي سيكوانس لت X M
+
+142
+00:11:31,230 --> 00:11:33,890
+كوشي سيكوانس ينقل لإنفينيتي هتلاقيه
+
+143
+00:11:33,890 --> 00:11:38,870
+استراتيجية البرهام في الأمثلة الثلاثة الأولى زي
+
+144
+00:11:38,870 --> 00:11:42,010
+بعض وان X M بتساوي X1 واحد  M X2 اثنين  M
+
+145
+00:11:42,010 --> 00:11:45,400
+إلى ما لا نهاية لأن شكل العنصر في الـ L-Infinity
+
+146
+00:11:45,400 --> 00:11:54,520
+Sequence لما نقول X1 بساوي XI 1 1 XI 2 1 XI 3 1 ده
+
+147
+00:11:54,520 --> 00:11:58,060
+جافش لعند الـ Un بتضلها إشنانها لأنها دي مش
+
+148
+00:11:58,060 --> 00:12:00,520
+Uncountable اللي هي عناصرها الـ L-Infinity عناصرها
+
+149
+00:12:00,520 --> 00:12:06,290
+عبارة عن Sequencesو X2 نفس الشيء بيساوي XI واحد
+
+150
+00:12:06,290 --> 00:12:11,790
+اثنين XI 2 2 إلى ما لا نهاية ونفس الشيء X M
+
+151
+00:12:11,790 --> 00:12:17,590
+in general بيساوي XI واحد M XI اثنين M إلى ما لا
+
+152
+00:12:17,590 --> 00:12:22,530
+نهاية وعندك XR برضه نفس الشيء وبيضلوا إلى ما لا 
+
+153
+00:12:22,530 --> 00:12:28,110
+نهاية XI واحد R XI اثنين R إلى ما لا نهاية واضح إذا
+
+154
+00:12:28,110 --> 00:12:31,310
+هذه اللي هي الـ Cauchy Sequence اللي بدي أخدها بدي
+
+155
+00:12:31,310 --> 00:12:34,130
+أقول let Xm be any Cauchy Sequence in L infinity
+
+156
+00:12:34,130 --> 00:12:37,930
+where Xm بتساوي كده ذنب من تعريف الـ Cauchy 
+
+157
+00:12:37,930 --> 00:12:41,470
+sequence إيش بيكون for every Y أكبر من 0 there
+
+158
+00:12:41,470 --> 00:12:44,930
+exists K element in N such that المسافة بين X M
+
+159
+00:12:44,930 --> 00:12:49,330
+و XR أصغر من Y لكل N و M أشمالها أكبر من K هذا
+
+160
+00:12:49,330 --> 00:12:53,510
+التعريف العام للـ Cauchy sequence طيب المسافة في
+
+161
+00:12:53,510 --> 00:12:56,950
+هذا ال space اللي هي ال L infinity بين X M و XR اللي
+
+162
+00:12:56,950 --> 00:13:01,210
+هو عبارة عن ال supremum للأبعاد XI واحد مقص XI
+
+163
+00:13:01,210 --> 00:13:04,470
+واحد N  XI اثنين M  ناقص XI اثنين N
+
+164
+00:13:04,700 --> 00:13:10,200
+الأخيرة كله بيصير عندي الـ Supremum لإكساي IM ناقص
+
+165
+00:13:10,200 --> 00:13:15,200
+إكساي IN over I يعني إكساي واحد M، إكساي واحد N
+
+166
+00:13:15,200 --> 00:13:19,980
+التانية إكساي اثنين M، إكساي اثنين N الـ 
+
+167
+00:13:19,980 --> 00:13:24,140
+Supremum اللي هو عبارة عن المسافة بينين؟ بين X M و
+
+168
+00:13:24,140 --> 00:13:30,780
+X N وهذا أخدناه سابقا لأن مدام الـ Supremum أصغر من
+
+169
+00:13:30,780 --> 00:13:34,640
+إبسلون إذاً كل واحدة منهم أصغر من إبسلون إذاً أكيد
+
+170
+00:13:34,640 --> 00:13:38,840
+صار عندي كل واحدة من هدولة لأي Fixed I وين موجودة
+
+171
+00:13:38,840 --> 00:13:43,140
+هنا الـ I هذه اللي هي أشمالها ليها واحد اللي هنا
+
+172
+00:13:43,140 --> 00:13:46,420
+واثنين اللي هنا وكأن زي ما أعملت قبل بشوية باخد
+
+173
+00:13:46,420 --> 00:13:49,640
+Sequences Sequences هذه الـ Sequence صارت عبارة عن
+
+174
+00:13:49,640 --> 00:13:57,670
+إيش؟ اللي هي تحقق إن KSI IM نقص KSI IN أصغر من مين؟
+
+175
+00:13:57,670 --> 00:14:02,150
+من إبسلون يعني صارت هي نفس أشمالها كوشي sequence
+
+176
+00:14:03,530 --> 00:14:07,010
+هذه الـ sequence صارت إيش مالها؟ كوشي sequence of
+
+177
+00:14:07,010 --> 00:14:10,310
+إيش؟ of real numbers لأن هذولا ال interest إيش
+
+178
+00:14:10,310 --> 00:14:14,970
+مالهم؟ عبارة عن مين؟ عن أعداد حقيقية أو complex
+
+179
+00:14:14,970 --> 00:14:19,410
+سواء في C أو في R إحنا بنعرف C وR إيش مالهم
+
+180
+00:14:19,410 --> 00:14:23,650
+complete إذاً مداميك إذاً أكيد بتروح لمين؟ لـ limit
+
+181
+00:14:23,650 --> 00:14:27,390
+سموها XI واحد وهذه ل limit سموها مين؟ XI اثنين
+
+182
+00:14:27,390 --> 00:14:34,970
+وهذه ل limit سموها XI مين؟ I فصار عند الـ M ثم لكل
+
+183
+00:14:34,970 --> 00:14:40,870
+M أكبر من K ولأي I مخصصة من هؤلاء هذا المقدار
+
+184
+00:14:40,870 --> 00:14:47,530
+أصغر من Y وهذا يعني لأي I مخصصة سيكون سيكوينس XI I
+
+185
+00:14:47,530 --> 00:14:51,230
+واحد XI I اثنين إلى ما لا نهاية is a Cauchy 
+
+186
+00:14:51,230 --> 00:14:57,050
+sequence of numbers سواء حقيقية أو كمبليكسية في كل
+
+187
+00:14:57,050 --> 00:15:02,520
+حالة بعد ذلك تتعامل بالخطوات التي تتعامل بالخطوات
+
+188
+00:15:02,520 --> 00:15:03,040
+التي تتعامل بالخطوات التي تتعامل بالخطوات التي
+
+189
+00:15:03,040 --> 00:15:04,660
+تتعامل بالخطوات التي تتعامل بالخطوات التي تتعامل
+
+190
+00:15:04,660 --> 00:15:08,480
+بالخطوات التي تتعامل بالخطوات التي تتعامل بالخطوات
+
+191
+00:15:08,480 --> 00:15:09,980
+اللي تتعامل بالخطوات اللي تتعامل بالخطوات اللي
+
+192
+00:15:09,980 --> 00:15:12,180
+اللي تتعامل بالخطوات اللي تتعامل بالخطوات اللي
+
+193
+00:15:12,180 --> 00:15:21,120
+تتعامل بالخطوات
+
+194
+00:15:21,120 --> 00:15:25,150
+اللي اللي أنا متوقع أن الـ sequence إيه تروح لها
+
+195
+00:15:25,150 --> 00:15:29,870
+أنا غرضي أن أناجي X N بتروح ل some X والـ X هذه
+
+196
+00:15:29,870 --> 00:15:33,670
+تكون في الـ L infinity الـ L من الـ X ركبتها أنا 
+
+197
+00:15:33,670 --> 00:15:37,050
+بس بدي اتأكد أنها في الـ L infinity إيش الـ X عندي
+
+198
+00:15:37,050 --> 00:15:40,390
+الـ X بالساوية XI 1 XI 2 إلى ما لا نهاية معناه
+
+199
+00:15:40,390 --> 00:15:43,290
+نهاية أول حاجة أريد أن أثبت لكم أن هدف الـ L
+
+200
+00:15:43,290 --> 00:15:46,490
+infinity هو واحد بالاستعانة باللي حكيته قبل شوية
+
+201
+00:15:46,490 --> 00:15:51,110
+اثنين أثبت لكم إن الـ X فعلا بدأ تروح لمين؟ للـ X وهذا
+
+202
+00:15:51,110 --> 00:15:55,070
+الكلام مشابه بالظبط للي حكيته قبل شوية عشان هي
+
+203
+00:15:55,070 --> 00:15:59,270
+كالأول أسرعت مهمش لأن using these infinity limits
+
+204
+00:16:00,100 --> 00:16:03,040
+اللي هي XI واحد و XI اثنين و XI تلاتة اللي رقبتهم
+
+205
+00:16:03,040 --> 00:16:07,620
+We define XI واحد و XI اثنين إلى ما لا نهاية We show
+
+206
+00:16:07,620 --> 00:16:11,840
+that X وين موجودة في الـL infinity وهنثبت أن X M
+
+207
+00:16:11,840 --> 00:16:15,340
+بتروح لمين؟ للـ X as M goes to infinity لأن
+
+208
+00:16:15,340 --> 00:16:20,320
+الاتنين اللي جابل بشوية as M goes to infinity we
+
+209
+00:16:20,320 --> 00:16:25,380
+see that اثنين هيها as N goes to infinity ومن مين
+
+210
+00:16:25,380 --> 00:16:30,760
+بدي أودي الآن بدي أودي الآن تروح إلى ما لا نهاية لما
+
+211
+00:16:30,760 --> 00:16:34,960
+الآن تروح لما لا نهاية بيصير عنده أو خلينا نودي إن
+
+212
+00:16:34,960 --> 00:16:39,880
+هي إن تروح لما لا نهاية أي واحد منهم بنفع ناشط ودنيل
+
+213
+00:16:39,880 --> 00:16:43,040
+الآن إن بتروح لما لا نهاية على افتراض أن إن أكبر من
+
+214
+00:16:43,040 --> 00:16:47,730
+مين من إن فبنودي إن إلى ما لا نهاية يابنات وشباب
+
+215
+00:16:47,730 --> 00:16:52,950
+المثبتك صي M نقص صي N أصغر من إبسلون هذا لكل ال N 
+
+216
+00:16:52,950 --> 00:16:58,150
+و ال M أكبر من K لو فرضت أنا ال N أكبر من M مش
+
+217
+00:16:58,150 --> 00:17:01,930
+هتجيبكم بثبتوا لهم أكبر من M لو فرضنا أن ال N أكبر
+
+218
+00:17:01,930 --> 00:17:06,390
+من M هذه as N goes to infinity هيصير اللي هو هذا
+
+219
+00:17:06,390 --> 00:17:11,140
+limitه أنا أثبتته إنه بيساوي مين؟ XII فبيصير هذا 
+
+220
+00:17:11,140 --> 00:17:16,340
+المقدار XII M ناقص XII أصغر من مين؟ من إبسلون فصار
+
+221
+00:17:16,340 --> 00:17:21,600
+XII M أصغر أو يساوي إيش؟ إبسلون وهذا صار عندي لكل
+
+222
+00:17:21,600 --> 00:17:26,100
+M أكبر من K XII M ناقص XII أصغر من إبسلون وهذا
+
+223
+00:17:26,100 --> 00:17:32,600
+يعني إيش؟ هذا يعني إنه صار عندي كل واحدة منهمهتصير
+
+224
+00:17:32,600 --> 00:17:38,680
+بعد شوية اللي هي X نفسها في الـ L Infinity والـ X 
+
+225
+00:17:38,680 --> 00:17:44,170
+هم بتروح للـ X نشوف هذا الكلام نكمل احفظونها دي
+
+226
+00:17:44,170 --> 00:17:48,370
+لإني بديها حتى سأتي الزمن بعد شوية Xm قلنا هيها
+
+227
+00:17:48,370 --> 00:17:52,590
+ماشي الحال واتفجين وين لها في L infinity مدام في L
+
+228
+00:17:52,590 --> 00:17:56,010
+infinity is a bounded sequence يعني بمعنى آخر اللي
+
+229
+00:17:56,010 --> 00:18:02,150
+هي Xim لها أصغر من some number إذاً then there is
+
+230
+00:18:02,150 --> 00:18:07,050
+KM such that Xim أصغر من some number سمناه KM على 
+
+231
+00:18:07,050 --> 00:18:10,610
+أساس أنه للواحد
+
+232
+00:18:11,220 --> 00:18:15,120
+الـ K الواحد للإثنين الـ K اثنين للثلاثة الـ K
+
+233
+00:18:15,120 --> 00:18:20,220
+ثلاثة أيها كذا ال XI M أصغر أو شوية منين KM for
+
+234
+00:18:20,220 --> 00:18:25,540
+all منين or all or all I وين رايحنا؟ رايح أثبت لكم 
+
+235
+00:18:25,540 --> 00:18:31,220
+إن ال X هذي is bounded رايح
+
+236
+00:18:31,220 --> 00:18:34,560
+أثبت لكم إن ال X is bounded إيش يعني؟ ده أثبت لكم
+
+237
+00:18:34,560 --> 00:18:40,810
+إن ال XI I هذي أصغر أو شوية some number هذه اللي
+
+238
+00:18:40,810 --> 00:18:46,190
+بدأت أدوى، معناه بيصار في الأقل Infinity لأن
+
+239
+00:18:46,190 --> 00:18:50,470
+XI I triangle inequality أصغر شوية XI I ناقص XI M
+
+240
+00:18:50,470 --> 00:18:56,130
+دخلت اللي بيحت خدمني، زاد XI IM هذي من اللي فوق
+
+241
+00:18:56,130 --> 00:19:01,760
+اللي أثبتناها أصغر من Epsilon وهذه اللي هو الـ L
+
+242
+00:19:01,760 --> 00:19:05,200
+infinity أصغر من KM هذا صار رقم صار عندي هذا
+
+243
+00:19:05,200 --> 00:19:08,560
+المقدار أصغر أو يساوي XI إذاً صارت الـ sequence
+
+244
+00:19:08,560 --> 00:19:12,560
+bounded إذاً صارت الـ U الموجودة الـ X صارت موجودة في
+
+245
+00:19:12,560 --> 00:19:17,920
+الـ L infinity الآن من ثلاثة هذه اللي فوق مدام كل
+
+246
+00:19:17,920 --> 00:19:21,760
+واحدة منهم هذولة لأي I أصغر أو يساوي يابسيلون إذا
+
+247
+00:19:21,760 --> 00:19:24,920
+السبريمام منهم برضه كون أصغر أو يساوي يابسيلون إذا
+
+248
+00:19:24,920 --> 00:19:28,620
+صار السبريمام لهدي over I أصغر أو يساوي يابسيلون
+
+249
+00:19:29,380 --> 00:19:34,140
+وهذا الكلام صحيح لكل مين؟ لكل M أكبر من K وهذه في
+
+250
+00:19:34,140 --> 00:19:38,440
+الواقع هي عبارة عن مسافة بين X M و X N و X M خاصة X
+
+251
+00:19:38,440 --> 00:19:41,120
+في الأقل Infinity و X M في الأقل Infinity زي
+
+252
+00:19:41,120 --> 00:19:44,220
+المشروع أن أخد اللي هي المسافة بينهم حسب الأقل
+
+253
+00:19:44,220 --> 00:19:47,870
+Infinity فصار عندها الـ distance أصغر أو أسوأ أو أسوأ
+
+254
+00:19:47,870 --> 00:19:52,410
+أبسلون لكل M أكبر من K وهذا يعني أنه limit الـ
+
+255
+00:19:52,410 --> 00:19:56,090
+X M بسوء X معناته بدأنا بـ X M Cauchy sequence
+
+256
+00:19:56,090 --> 00:19:59,410
+وانتهينا بـ X M Converged في الـ X بالقلة
+
+257
+00:19:59,410 --> 00:20:02,610
+الأنفينيتي وهذا يعني أن القلة الانفينيتي is إيش؟
+
+258
+00:20:02,610 --> 00:20:06,810
+is a complete space طيب يلّا الآن ال complete نسنا
+
+259
+00:20:06,810 --> 00:20:14,650
+من؟ نصي إحنا لحد الآن اللي عملناه في المثالين نأخذ 
+
+260
+00:20:14,650 --> 00:20:18,530
+الـ Cauchy Sequence ونصل إلي أشمالها Converse
+
+261
+00:20:18,530 --> 00:20:26,570
+وتقريبا طريقة الأصول متشابهة في الجهتين الآن بدنا
+
+262
+00:20:26,570 --> 00:20:30,770
+نروح لفكرة أخرى بدنا نأخذ الـ completeness للـ 
+
+263
+00:20:30,770 --> 00:20:34,990
+space مافيش داعي نأخذ أي كوش سيكوينس في ال space وبعدين
+
+264
+00:20:34,990 --> 00:20:38,130
+أثبتها وأديها وين اللي هي ال convinced في
+
+265
+00:20:38,130 --> 00:20:42,530
+شيء خلّيني أقول أبسط أو أنسب لهذا المثال لإن هو
+
+266
+00:20:42,530 --> 00:20:46,970
+يغلبني في الأول أنا أخدت فيه هذه وبعدين وديتها ل
+
+267
+00:20:46,970 --> 00:20:53,020
+X ده space C consists of all convergent sequences
+
+268
+00:20:53,020 --> 00:20:56,300
+of complex numbers أو real مش مشكلة with the
+
+269
+00:20:56,300 --> 00:20:59,280
+metric induced from the space L infinity is
+
+270
+00:20:59,280 --> 00:21:05,140
+complete إيش اللي بقوله بقول إحنا بنعرف أن any 
+
+271
+00:21:05,140 --> 00:21:11,610
+convergent sequence is bounded إذاً الـ space of 
+
+272
+00:21:11,610 --> 00:21:16,610
+all convergent sequences is a subspace أو is a
+
+273
+00:21:16,610 --> 00:21:19,050
+subset خلّيني أقول subspace لسه ما حكيناش عن ال
+
+274
+00:21:19,050 --> 00:21:22,910
+vector space is a subset من مين؟ من الـ L infinity ال
+
+275
+00:21:22,910 --> 00:21:26,030
+L infinity كل ال bounded sequences الـ C هي ال
+
+276
+00:21:26,030 --> 00:21:29,250
+convergent sequences وكل convergence اللي هي
+
+277
+00:21:29,250 --> 00:21:33,830
+bounded إذاً C جزء من مين؟ من الـ L infinity وكأنه
+
+278
+00:21:33,830 --> 00:21:38,550
+الآن أذكركم في اللي حكيناه المرة الماضية وكيف بدي
+
+279
+00:21:38,550 --> 00:21:44,890
+أستخدمه عندي أنا الـ الـ L infinity الـ L infinity علي
+
+280
+00:21:44,890 --> 00:21:49,520
+مترك اللي هو الـ D تبع الـ supremum الآن بدي أخذ الـ 
+
+281
+00:21:49,520 --> 00:21:55,560
+C واخد نفس الـ D صار جزء منه صار .. صار sub metric
+
+282
+00:21:55,560 --> 00:21:59,700
+space منه آه sub metric space منه من الـ D لأن كل
+
+283
+00:21:59,700 --> 00:22:02,460
+عنصر هنا موجود هنا و ال metric اللي هنا هو نفس
+
+284
+00:22:02,460 --> 00:22:06,340
+اللي هنا بدي أثبت لكم أنه الآن هذا برضه إيش
+
+285
+00:22:06,340 --> 00:22:11,300
+complete ماشي الحال طبعًا هذا أثبتنا complete طيب
+
+286
+00:22:11,300 --> 00:22:14,780
+إحنا المرة الفاتت قلنا إن ال .. نعم
+
+287
+00:22:17,650 --> 00:22:23,730
+أخدنا من المرة الماضية قلنا إنه لو كان في عندي 
+
+288
+00:22:23,730 --> 00:22:27,630
+space closed subspace من complete space إيش هيكون
+
+289
+00:22:27,630 --> 00:22:31,970
+is complete إذا يكفي عشان أثبت إنه هذا إنه
+
+290
+00:22:31,970 --> 00:22:36,230
+complete إن أثبته إنه closed space طب كيف بدي أثبت
+
+291
+00:22:36,230 --> 00:22:41,270
+إنه closed space؟ بدي آخد X في الـC closure و أثبت
+
+292
+00:22:41,270 --> 00:22:45,940
+لك إن X موجودة في الـC يعني صار الـC closure بيساوي
+
+293
+00:22:45,940 --> 00:22:49,820
+الـC، معناته صار الـC is إيش؟ closed، إذا هي
+
+294
+00:22:49,820 --> 00:22:54,280
+استراتيجية البرهان اللي بدي أعملها، واضح؟ طيب، إذا
+
+295
+00:22:54,280 --> 00:22:57,900
+الآن بدي أقول لكم عشان تثبتوا الـcompleteness of C،
+
+296
+00:22:57,900 --> 00:23:01,380
+let X بيساوي إكساي I، اللي هي هذه الـsequence،
+
+297
+00:23:01,380 --> 00:23:03,660
+إكساي 1، إكساي 2، إكساي 3، إكساي 4، إلى ما لا نهاية
+
+298
+00:23:03,660 --> 00:23:09,120
+element in C closure و أثبت لكم أن هذه ستكون
+
+299
+00:23:09,120 --> 00:23:13,720
+في الـ C طيب، ما معنى الـ X في الـ C-closure؟ أن
+
+300
+00:23:13,720 --> 00:23:18,760
+هناك C .. أخذناها المرة الماضية أن X element in C
+
+301
+00:23:18,760 --> 00:23:25,800
+-closure هذا معناته أن هناك سيكوينس XMNC in C such
+
+302
+00:23:25,800 --> 00:23:30,620
+that الـ XN بتروح لمين؟ للـ C هذا معناه أن الـ X
+
+303
+00:23:30,620 --> 00:23:35,720
+أشوان موجودة في اللي هو الـ C closure اللي ناسي
+
+304
+00:23:35,720 --> 00:23:36,300
+يتذكر
+
+305
+00:23:39,080 --> 00:23:44,680
+أنه X in between C closure إيش معناته؟ إنه بنلاقي
+
+306
+00:23:44,680 --> 00:23:49,200
+sequence XM أو XN اللي بدكم إياها في الـC بحيث أن
+
+307
+00:23:49,200 --> 00:23:55,800
+XM بتروح لمين؟ لأسفة لمين؟ للـX فبتكون اللي هي X
+
+308
+00:23:55,800 --> 00:24:02,700
+و اللي موجودة في الـC closure طيب الآن أخذت ال ..
+
+309
+00:24:02,700 --> 00:24:07,230
+ال .. ال .. لو أثبتت هذا إن هاد الـ X في الـ C
+
+310
+00:24:07,230 --> 00:24:10,950
+closure وصلت في الـ C بكون خلصت. انفجرت؟ يلا 
+
+311
+00:24:10,950 --> 00:24:16,930
+خلّينا نروح نشوف الآن أخذت X في الـ C closure إذا
+
+312
+00:24:16,930 --> 00:24:20,110
+حسب تعريف X في الـ C closure you get sequence XM
+
+313
+00:24:20,110 --> 00:24:24,910
+in C بحيث أن XM بتروح لمين؟ لل X where؟ إيش هي الـ
+
+314
+00:24:24,910 --> 00:24:28,670
+XM؟ زي ما عملنا قبل شوية X واحد يعني X واحد واحد
+
+315
+00:24:28,670 --> 00:24:32,190
+واحد X اتنين واحد الأخرى XM in general X واحد أم X
+
+316
+00:24:32,190 --> 00:24:35,190
+اتنين أم إلى ما لا نهاية هذه الـ sequence of elements
+
+317
+00:24:35,190 --> 00:24:40,930
+هو الموجودة في الـ C نفسها ماشي الحال؟ طيب، مدام
+
+318
+00:24:40,930 --> 00:24:43,930
+في الـ C، إذا كل واحدة converges لأن مدينة الـ C
+
+319
+00:24:43,930 --> 00:24:46,850
+عبارة عن الـ space أو الـ set of all convergent
+
+320
+00:24:46,850 --> 00:24:50,690
+sequences إذا hence for every ي أكبر من صفر there
+
+321
+00:24:50,690 --> 00:24:53,670
+exists k elements and such that تعريف إيش؟ إنها
+
+322
+00:24:53,670 --> 00:24:59,890
+الـ sequence converges إيش هو للتعريف؟ أن الـ
+
+323
+00:24:59,890 --> 00:25:04,320
+distance بين Xم أو Xاللي هو أصغر من ي على تلاتة
+
+324
+00:25:04,320 --> 00:25:08,540
+أصغر من أي قيمة من ضمنها ي على تلاتة اللي هتخدمني
+
+325
+00:25:08,540 --> 00:25:11,580
+في الحسابات زي ما بنقول دائمًا for all M أكبر من
+
+326
+00:25:11,580 --> 00:25:17,460
+مين؟ مين أو سوى K هذا معنى إنه XM مالها؟ converge ال
+
+327
+00:25:17,460 --> 00:25:23,770
+mean لل X اللي فوق ما هو الـ metric اللي موجود هنا
+
+328
+00:25:23,770 --> 00:25:28,330
+ال metric أن ال distance بين xm و x بتساوي ال
+
+329
+00:25:28,330 --> 00:25:33,370
+supremum من xi m نقص xi i over mu over I هاي اللي
+
+330
+00:25:33,370 --> 00:25:39,600
+هي ال sequence اللي هي ال XM وهي ال X اللي عندي
+
+331
+00:25:39,600 --> 00:25:43,840
+اللي سمنها XI واحد XI اتنين XI تلاتة اللي هي هذه
+
+332
+00:25:43,840 --> 00:25:48,200
+فالفرق بينهم واخدوا ال supermom له فقبل ال
+
+333
+00:25:48,200 --> 00:25:51,100
+interest اللي عاجبها البعض اللي هو بيساوي اللي هو
+
+334
+00:25:51,100 --> 00:25:56,960
+دي XM و X أصغر من Y ع التلاتة إذا الآن هذه من XM
+
+335
+00:25:56,960 --> 00:26:04,340
+بتروح لل X من جهة أخرى ما إحنا عاملين بنقول الآن
+
+336
+00:26:04,340 --> 00:26:10,040
+عندي الـ XI .. XII موجودة في الـ C Closure طيب
+
+337
+00:26:10,040 --> 00:26:12,880
+انتجوا لها .. لها المعلومة خذوا المعلومة الأولى
+
+338
+00:26:14,420 --> 00:26:19,640
+عندي الآن for all m أكبر أو يساوي k and any fixed i
+
+339
+00:26:19,640 --> 00:26:24,840
+هيكون عندي x i i m ناقص x i i أصغر من مين؟ من 
+
+340
+00:26:24,840 --> 00:26:27,840
+epsilon ع تلاتة وعملت هذا قبل بشوية مدام السوبرمان
+
+341
+00:26:27,840 --> 00:26:31,760
+نفسه أصغر من epsilon ع تلاتة إذا كل ال interest
+
+342
+00:26:31,760 --> 00:26:36,380
+اللي جوا برضه اصغر من epsilon ع تلاتة طيب الآن بدي
+
+343
+00:26:36,380 --> 00:26:39,560
+آخذ أحكي عن شيء محدد عشان بدي أحطه بين إيديا و
+
+344
+00:26:39,560 --> 00:26:44,580
+أشتغل عليه عشان هي أخذت .. طبعًا هذا صحيح لمن؟ لكل M
+
+345
+00:26:44,580 --> 00:26:49,980
+أكبر يساوي إيش؟ K لكل M أكبر يساوي K بدي آخذ اللي هو
+
+346
+00:26:49,980 --> 00:26:54,500
+الـ K عند M أيش بتساوي K؟ بتبقى ده أشمالها صحيحة
+
+347
+00:26:54,500 --> 00:27:00,000
+إذا XI I K نقص XI I أصغر من مين؟ من إبسلن ع تلاتة
+
+348
+00:27:00,000 --> 00:27:04,980
+إذا أخدت مين أنا؟ ال M بتساوي K عشان بعمل حساباتي
+
+349
+00:27:04,980 --> 00:27:11,470
+على شيء بين إيدي ملموس يعني عن واحدة محددة طيب الآن
+
+350
+00:27:11,470 --> 00:27:15,890
+كما قلنا قبل بشوية كل مننا دولة ال sequence من نوع
+
+351
+00:27:15,890 --> 00:27:20,610
+جاية من ال C يعني X واحد من ال C يعني convergence
+
+352
+00:27:20,610 --> 00:27:24,530
+sequence of real numbers أو of complex X اتنين في
+
+353
+00:27:24,530 --> 00:27:28,830
+ال C X ثلاثة في ال C X M in general في ال C X K في
+
+354
+00:27:28,830 --> 00:27:32,170
+ال C إذا ال sequence هذه كل عناصرها موجودة في ال
+
+355
+00:27:32,170 --> 00:27:37,870
+C مدام XK في ال C إذا نفس ال XK converge ال XK مين
+
+356
+00:27:37,870 --> 00:27:46,180
+هيعبارة عن x1k, x2k, x3k, x4k, x5k إلى ما لا نهاية
+
+357
+00:27:46,180 --> 00:27:52,100
+هذا الـ sequence أجمع لـ converge الآن its terms
+
+358
+00:27:52,100 --> 00:27:55,440
+xik form a convergent sequence such that الـ
+
+359
+00:27:55,440 --> 00:28:00,340
+sequence is Cauchy أكيد عن مين بحكي يا جماعة؟ بحكي
+
+360
+00:28:00,340 --> 00:28:07,360
+عن الـ sequence x1k, x2k, x3k
+
+361
+00:28:13,050 --> 00:28:19,370
+من الـ real numbers مظبوط الـ N اللي هي مزام في
+
+362
+00:28:19,370 --> 00:28:23,350
+الـ C في الـ C حسب تعريف الـ C وهو converse إذا
+
+363
+00:28:23,350 --> 00:28:25,370
+ركيب كوشي من تعريف الكوشي
+
+364
+00:28:38,700 --> 00:28:42,880
+طيب، الآن بدي ألمها المعلومات كلها اللي عندي و
+
+365
+00:28:42,880 --> 00:28:49,260
+أحصل على اللي بدياه الآن، إيش أنا بدياه؟ بدي أثبت
+
+366
+00:28:49,260 --> 00:28:56,080
+لكم إن XII هذه، اللي هي X هذه، و إن موجودة في
+
+367
+00:28:56,080 --> 00:28:59,180
+الـC، يعني أثبت لكم إنها Converges، رايح بهذا
+
+368
+00:28:59,180 --> 00:29:04,380
+الاتجاه، بكون خلصته شوفوا الآن، حسبولي الآن، لكل I
+
+369
+00:29:04,380 --> 00:29:08,760
+و J أكبر من مين؟ من أنت، إذا هذا بنطبق عليه بكون
+
+370
+00:29:08,760 --> 00:29:14,020
+بيساوي أصغر ويساوي XII-XIIK اللي حسبتها قبل بشوية
+
+371
+00:29:14,020 --> 00:29:20,780
+زائد XIIK XIJK زائد XIJK-XIAJ عملت ال training
+
+372
+00:29:20,780 --> 00:29:26,160
+quality ع مرتين مرة دخلت XIIK و مرة دخلت XIJK
+
+373
+00:29:26,160 --> 00:29:33,000
+بالسلب والإيجاب اللي هو أصغر الأولى xi i ناقص xi ik
+
+374
+00:29:33,000 --> 00:29:38,200
+اللي هو هي أصغر من مين؟ إبسلن ع تلاتة و xi ik ناقص
+
+375
+00:29:38,200 --> 00:29:42,700
+xi jk هي أصغر من مين برضه؟ إبسلن ع تلاتة و xi jk
+
+376
+00:29:42,700 --> 00:29:48,680
+ناقص xi j نفسها برضه أصغر من مين؟ من إبسلن ع تلاتة
+
+377
+00:29:48,680 --> 00:29:55,880
+برضه اللي هو عملناها قبل هيك ماشي الحال هذه
+
+378
+00:29:55,880 --> 00:30:00,970
+ما هي صحيحة لكل I مظبوط هذه صحيحة لكل I اللي هي هذه
+
+379
+00:30:00,970 --> 00:30:05,830
+لكل صحيحة لكل I إذا سواء I أو J صحيحة لها هي ال I
+
+380
+00:30:05,830 --> 00:30:09,390
+هنا وهي ال J هنا فاهمين؟ فبصير هذا أصغر من هذا
+
+381
+00:30:09,390 --> 00:30:11,090
+أصغر من هذا أصغر من هذا أصغر من هذا أصغر من هذا
+
+382
+00:30:11,090 --> 00:30:11,710
+أصغر من هذا أصغر من هذا أصغر من هذا أصغر من هذا
+
+383
+00:30:11,710 --> 00:30:11,810
+أصغر من هذا أصغر من هذا أصغر من هذا أصغر من هذا
+
+384
+00:30:11,810 --> 00:30:11,910
+أصغر من هذا أصغر من هذا أصغر من هذا أصغر من هذا
+
+385
+00:30:11,910 --> 00:30:12,070
+أصغر من هذا أصغر من هذا أصغر من هذا أصغر من هذا
+
+386
+00:30:12,070 --> 00:30:13,030
+أصغر من هذا أصغر من هذا أصغر من هذا أصغر من هذا
+
+387
+00:30:13,030 --> 00:30:19,310
+أصغر من هذا أصغر
+
+388
+00:30:19,310 --> 00:30:25,290
+من هذا أصغر of numbers و ال number سواء real أو
+
+389
+00:30:25,290 --> 00:30:30,010
+complex هتكون complete مدام complete إذا صارت
+
+390
+00:30:30,010 --> 00:30:33,990
+اللي هي ال sequence هذا يشملها convergence مدام
+
+391
+00:30:33,990 --> 00:30:39,870
+convergence إذا صارت عند ال x اللي هي مساوي XII
+
+392
+00:30:39,870 --> 00:30:45,590
+هذه صارت موجودة في الـC نفسها لإنه صارت converge
+
+393
+00:30:45,590 --> 00:30:48,530
+ومعناته أنه صار الـC بتساوي C closure زي ما بدأنا
+
+394
+00:30:48,530 --> 00:30:53,430
+في الأول معناته صارت اللي هو الـC اللي هي عبارة عن
+
+395
+00:30:53,430 --> 00:30:57,110
+complete metric space لإنه هي صارت closed subspace
+
+396
+00:30:57,110 --> 00:31:02,230
+of a complete metric space which is complete أي
+
+397
+00:31:02,230 --> 00:31:04,350
+سؤال طيب
+
+398
+00:31:07,100 --> 00:31:11,980
+الآن بدنا نيجي ل ال completeness of LB جاعدين إحنا
+
+399
+00:31:11,980 --> 00:31:15,580
+بنجرد كل ال spaces اللي هتعيش معنا طول الفصل اللي
+
+400
+00:31:15,580 --> 00:31:20,360
+هو ال RN و ال CN و ال L∞ و ال LB و ال C و بعد شوية
+
+401
+00:31:20,360 --> 00:31:24,700
+ال continuous functions كل
+
+402
+00:31:24,700 --> 00:31:27,780
+هذه هنميز مين ال complete و مين اللي هو مش
+
+403
+00:31:27,780 --> 00:31:32,400
+complete و كل واحدة completeness تبعها حسب تريكها
+
+404
+00:31:38,690 --> 00:31:45,450
+هلاجة spaces إذا غيرنا المترقب بيتبطل complete أو
+
+405
+00:31:45,450 --> 00:31:50,730
+غيرنا المترقب بتصير complete حسب الأصل والتغيير
+
+406
+00:31:50,730 --> 00:31:55,310
+طيب شوفوا صلى الله عليه الصلاة والسلام الآن الال
+
+407
+00:31:55,310 --> 00:31:59,050
+بيه برضه من ال spaces الملازمة لنا برضه spaces of
+
+408
+00:31:59,050 --> 00:32:02,740
+sequences لكن إحنا بقول الـ spaces و ال sequences
+
+409
+00:32:02,740 --> 00:32:07,660
+ده شرطه أنه إنهم تكون ال summation لل XI I بي is
+
+410
+00:32:07,660 --> 00:32:10,380
+finite ماشي الحال يعني ال sequence هتكون converse
+
+411
+00:32:10,380 --> 00:32:13,680
+السيريز هتكون converse هاي شرط إنهم تكون ال X ..
+
+412
+00:32:13,680 --> 00:32:16,140
+اللي .. اللي هي ال sequence .. اللي هي X وا .. X
+
+413
+00:32:16,140 --> 00:32:18,580
+واحد .. XI واحد .. XI اتنين .. XI تلت .. XI اربعة
+
+414
+00:32:18,580 --> 00:32:21,640
+إلى ما لا نهاية تكون وين في القلبي طيب
+
+415
+00:32:25,310 --> 00:32:33,650
+أي رقم بين واحد وبين ما لا نهاية بكل مكان الـ B
+
+416
+00:32:33,650 --> 00:32:40,230
+تبعه أشمالها is a complete metric space نفس القصة،
+
+417
+00:32:40,230 --> 00:32:44,470
+هأسرع شوية لأن الكلام مكرر Let XM be any Cauchy
+
+418
+00:32:44,470 --> 00:32:48,970
+Sequence الموجودة في الـ LB بالدرجة لـ X حيث أن XM
+
+419
+00:32:48,970 --> 00:32:51,210
+هي الـ Conversion لها و الـ X تكون في الـ LB، هي
+
+420
+00:32:51,210 --> 00:32:56,530
+القصة كلها، الآن Where XM، صرنا عارفين، XI و XII M
+
+421
+00:32:56,530 --> 00:33:01,350
+إلى ما لا نهاية، الآن من تعريف اللي هو الـ Sequence
+
+422
+00:33:01,350 --> 00:33:06,910
+في الـ l<sup>p</sup> ومن تعريف أن الـ x<sub>m</sub> كون كوشي إذا لكل ε
+
+423
+00:33:06,910 --> 00:33:10,870
+أكبر من 0 بيوجد K بحيث أن لكل n و m أكبر من K
+
+424
+00:33:10,870 --> 00:33:15,310
+بيكون المسافة بين x<sub>m</sub> و x<sub>n</sub> أَشملها أصغر من ε المسافة
+
+425
+00:33:15,310 --> 00:33:19,710
+في حالة الـ l<sup>p</sup> مين هي summation x<sub>i</sub><sup>p</sup> ناقص x<sub>i</sub><sup>p</sup>
+
+426
+00:33:19,710 --> 00:33:25,090
+اللي هو أصغر من كل ε نص ε أصغر من مين؟ من ε هذه خلوها 
+
+427
+00:33:25,090 --> 00:33:31,930
+اسمها أربعة. الآن من اللي فوق هذه برضه بنفس الأسلوب
+
+428
+00:33:31,930 --> 00:33:35,650
+مدام الـ summation كله أصغر من ε إذا أكيد كل
+
+429
+00:33:35,650 --> 00:33:39,130
+واحد من جوا الـ summation برضه هيكون أَشملها اللي هو
+
+430
+00:33:39,130 --> 00:33:42,650
+أصغر من ε هذه بيصير كلها .. شو سيبكوا من هذي
+
+431
+00:33:42,650 --> 00:33:45,390
+.. هذي بدون الواحد على p بيصير هذا الـ summation
+
+432
+00:33:45,390 --> 00:33:49,710
+أصغر من ε<sup>p</sup> ما تجي؟ إذا كل واحدة منهم ε<sup>p</sup> أصغر
+
+433
+00:33:49,710 --> 00:33:53,150
+من ε<sup>p</sup> يعني كل واحدة أصغر من مين؟ من ε
+
+434
+00:33:53,150 --> 00:33:58,000
+زي ما عملنا في التربيعة. إذا صار عنده هذا إيش بثبت
+
+435
+00:33:58,000 --> 00:34:02,940
+This shows that for any fixed i هذه أصغر من ε يعني
+
+436
+00:34:02,940 --> 00:34:06,600
+صارت عبارة عن Cauchy sequence نفس الشيء اللي هي الـ
+
+437
+00:34:06,600 --> 00:34:09,700
+sequence اللي هنا والـ sequence اللي هنا الطولية
+
+438
+00:34:09,700 --> 00:34:12,640
+هذه اللي عملها في الأول كلهم Cauchy sequences و
+
+439
+00:34:12,640 --> 00:34:15,780
+Cauchy sequences of mean of numbers نفس اللي يعني
+
+440
+00:34:15,780 --> 00:34:19,650
+أن كله حكيته. الآن مدام كوشي سيكوانسيز of number
+
+441
+00:34:19,650 --> 00:34:23,150
+سواء real أو complex وبعرف الـ R والـ C complete
+
+442
+00:34:23,150 --> 00:34:26,410
+بعيد نفس الكلام إذا أكيد هذه الـ sequence الشمالها
+
+443
+00:34:26,410 --> 00:34:30,750
+converge خلينا نسمي أن هذا الـ x<sub>i</sub><sup>p</sup> اللي هي الـ
+
+444
+00:34:30,750 --> 00:34:35,210
+converge هذي converge لمن؟ للـ x<sub>i</sub> فانصرت عندي أنا 
+
+445
+00:34:35,210 --> 00:34:40,900
+x بتساوي x<sub>1</sub>، x<sub>2</sub> إلى ما لا نهاية. غلط زي قبل 
+
+446
+00:34:40,900 --> 00:34:44,440
+شوية أهدى الـ x<sub>m</sub> على مين؟ على الـ x وأثبت لك الـ x هو
+
+447
+00:34:44,440 --> 00:34:47,980
+الموجودة في القلبي كله بالاستعانة بالموجود وبنفس
+
+448
+00:34:47,980 --> 00:34:48,580
+الأسلوب
+
+449
+00:34:52,210 --> 00:34:55,950
+الآن using these infinitely limits we define الـ x
+
+450
+00:34:55,950 --> 00:34:59,290
+اللي قلنا عنها x<sub>1</sub>، x<sub>2</sub> كده وبدنا نثبت
+
+451
+00:34:59,290 --> 00:35:03,230
+أملنا إنه نثبت أن الـ x وموجودة في القلبي ونثبت
+
+452
+00:35:03,230 --> 00:35:06,750
+أن x<sub>m</sub> بتروح للـ x as m goes to infinity ماشي الحال
+
+453
+00:35:06,750 --> 00:35:11,370
+من أربعة فوق we have that هاي أربعة أربعة أربعة
+
+454
+00:35:11,870 --> 00:35:15,890
+أربعة هذه أربعة شايفينها هي اللي عندي بيطلع عندي الـ
+
+455
+00:35:15,890 --> 00:35:19,990
+summation لهذا أصغر من ε ونص ε ماشي الحال الآن
+
+456
+00:35:19,990 --> 00:35:24,430
+ودّنا نروح لمين؟ إلى ما لا نهاية بتصير لما n تروح
+
+457
+00:35:24,430 --> 00:35:27,710
+لما لا نهاية على افتراض أن n أكبر من p بتصير هذي
+
+458
+00:35:27,710 --> 00:35:30,890
+تروح لما لا نهاية لما n تروح لما لا نهاية تروح لمين؟
+
+459
+00:35:30,890 --> 00:35:35,570
+للنهاية للـ x<sub>i</sub> فبيصير عندي الـ summation الـ
+
+460
+00:35:35,570 --> 00:35:41,270
+summation للـ x<sub>i</sub> ناقص x<sub>i</sub> اللي راحت إليه ε<sup>p</sup> أَزرع
+
+461
+00:35:41,270 --> 00:35:44,630
+أَسَأوَمِينَ ε<sup>نص p</sup> طبعاً أخذت أنا لعند مين؟ عشان حدّش 
+
+462
+00:35:44,630 --> 00:35:48,130
+يقول أنت بدأت تدخل limit علامة. بدأ أخذ اللي هو i
+
+463
+00:35:48,130 --> 00:35:51,330
+من واحد لعند مين؟ لعند l أخدت l arbitrarily مش كله
+
+464
+00:35:51,330 --> 00:35:55,370
+الـ summation اللي أخدته أخدته لعند أي l فاهمين عليا؟
+
+465
+00:35:55,370 --> 00:35:58,250
+عشان إنه ما يصيرش limit علامة ويصير فيه عندي
+
+466
+00:35:58,250 --> 00:36:03,750
+إيش إشكالية. فالآن as n يعني هدول مجموعات لبعض هذا زائد
+
+467
+00:36:03,750 --> 00:36:06,750
+هذا زائد هذا خمس مرات، عشر مرات مجموعات ألا من
+
+468
+00:36:06,750 --> 00:36:09,610
+المرات إلى إذا بقدر أدخل الـ limit وأزاى على 
+
+469
+00:36:09,610 --> 00:36:13,030
+الجمال احنا عارفين ما زالت موجودة إذا صار عندي الـ
+
+470
+00:36:13,030 --> 00:36:17,290
+limit هذه as n goes to infinity راح تقلّ x<sub>i</sub><sup>p</sup>
+
+471
+00:36:17,290 --> 00:36:22,110
+من واحد لمين؟ للـ l لأن بعد ما خلصت شروع عامة الأمر
+
+472
+00:36:22,110 --> 00:36:26,970
+وصلت لهذا الحد كانت الـ l هي arbitrary إذا بقدر أور
+
+473
+00:36:26,970 --> 00:36:30,870
+بـ l وين ما بدي لأن هذا الكلام صحيح لمن؟ لأي l في
+
+474
+00:36:30,870 --> 00:36:34,350
+الدنيا لأن الـ l أخدت fixed لكن arbitrarily إذا صار 
+
+475
+00:36:34,350 --> 00:36:37,850
+عندي as l goes to infinity برجع هذا i من واحد إلى
+
+476
+00:36:37,850 --> 00:36:46,190
+المقدار هذا أصغر من ε<sup>p</sup> أصغر من ε<sup>p</sup> و منه الـ 
+
+477
+00:36:46,190 --> 00:36:51,570
+summation أزرع سواء من ε أي سؤال؟ طيب هذه
+
+478
+00:36:51,570 --> 00:36:57,490
+اليمين خمسة. الآن x و y موجودة في الـ l<sup>p</sup> إذا الـ
+
+479
+00:36:57,490 --> 00:37:02,610
+summation هذا is found out من تعريف الـ l<sup>p</sup> الآن بدي
+
+480
+00:37:02,610 --> 00:37:06,870
+أثبت لكم إن هذه في الـ l<sup>p</sup> بدي أستخدم الـ course key
+
+481
+00:37:06,870 --> 00:37:13,650
+inequality اللي هي بيصير عندي على اللي هي x<sub>ii</sub> و x<sub>im</sub>
+
+482
+00:37:16,160 --> 00:37:18,740
+هي عند باقي من الـ course key inequality الـ summation
+
+483
+00:37:18,740 --> 00:37:23,600
+هذا x<sub>i</sub> i<sup>p</sup> الكل<sup>p</sup> أصغر يساوي واحد على p أصغر يساوي x<sub>i</sub>
+
+484
+00:37:23,600 --> 00:37:29,900
+i m ناقص x<sub>i</sub> j<sup>p</sup> اللي اضفتها مين هي؟ x<sub>i</sub> i m مطرحتها
+
+485
+00:37:29,900 --> 00:37:34,220
+<sup>p</sup> أصغر يساوي واحد على p زائد الـ summation x<sub>i</sub> j m <sup>p</sup>
+
+486
+00:37:34,220 --> 00:37:37,200
+أصغر يساوي واحد على p هذه اللي هي مين؟ مين هي الـ main
+
+487
+00:37:37,200 --> 00:37:41,040
+course key inequality اللي نسيها يراجعها. الآن صارت هذه
+
+488
+00:37:41,040 --> 00:37:46,120
+عندي أصلاً عندي finite من فوق أثبتناها وهذه finite
+
+489
+00:37:46,120 --> 00:37:49,320
+من فوق أثبتناها إذًا هذا المقدار كله إيش حيصير؟
+
+490
+00:37:49,320 --> 00:37:53,400
+حيصير finite شوفتوا إنها من فوق finite هذه finite
+
+491
+00:37:53,400 --> 00:37:58,240
+هيها واللي فوق هذه برضه إيش مالها؟ finite إذًا صارت
+
+492
+00:37:58,240 --> 00:38:01,800
+النتين finite وهذا بعني مدام هذه صارت الـ summation
+
+493
+00:38:01,800 --> 00:38:07,100
+finite إذًا x بالساوية اللي هي هذه x<sub>i</sub> element in
+
+494
+00:38:07,100 --> 00:38:12,650
+l<sup>p</sup>. الآن بنفس الأسلوب مدام صارت في الـ l<sup>p</sup> إذا
+
+495
+00:38:12,650 --> 00:38:17,830
+بيصير الآن عندي من خمسة من خمسة اللي هي الـ 
+
+496
+00:38:17,830 --> 00:38:23,230
+distance هذه في الواقع إيش بتمثل؟ المسافة بين x<sub>m</sub> و
+
+497
+00:38:23,230 --> 00:38:28,590
+x معايا اه هذه اللي هي الجوا بس حسّ واحد عربية يعني 
+
+498
+00:38:28,590 --> 00:38:34,030
+هذه أَشملها المسافة بين x<sub>m</sub> و x أصغر يساوي ε لكل
+
+499
+00:38:34,030 --> 00:38:38,510
+أكبر من K إذا صارت عندي x<sub>m</sub> بتروح للـ x والـ x في
+
+500
+00:38:38,510 --> 00:38:43,690
+القلبي اللي هي صارت القلبي أَشملها is complete
+
+501
+00:38:43,690 --> 00:38:46,870
+نيجي الآن عندي the space of continuous functions
+
+502
+00:38:46,870 --> 00:38:52,940
+the space of continuous functions بدأ أثبت لكم إن
+
+503
+00:38:52,940 --> 00:38:58,280
+هذا الـ space is complete under the maximum metric
+
+504
+00:38:58,280 --> 00:39:02,260
+اللي هو الـ metric اللي عرفنا عليه هو اللي بيساوي
+
+505
+00:39:02,260 --> 00:39:07,460
+الـ maximum للـ x(t) ناقص اللي هو y(t)، t over
+
+506
+00:39:07,460 --> 00:39:19,560
+الـ interval اللي عندنا اللي هي c(a و b) is the
+
+507
+00:39:19,560 --> 00:39:25,780
+space of all continuous functions على closed
+
+508
+00:39:25,780 --> 00:39:29,940
+bounded interval a و b. مذا تبقلكم أن هذا الـ space 
+
+509
+00:39:29,940 --> 00:39:33,100
+is complete under our metric اللي هو الـ maximum
+
+510
+00:39:33,100 --> 00:39:36,020
+نفس الأسئلة، إيش بتسوي؟ هتلاقوا نفس الأسئلة
+
+511
+00:39:36,020 --> 00:39:42,210
+بالظبط. Let x<sub>m</sub> be any Cauchy sequence in c(a و b) إذًا
+
+512
+00:39:42,210 --> 00:39:44,250
+for every ε أكبر من صفر there exists K element 
+
+513
+00:39:44,250 --> 00:39:47,690
+such that for all m أكبر من K نحن لدينا المسافة
+
+514
+00:39:47,690 --> 00:39:52,070
+بين x<sub>m</sub> و x<sub>n</sub> أصغر من ε. المسافة بين x<sub>m</sub> و x<sub>n</sub>
+
+515
+00:39:52,070 --> 00:39:56,150
+دوال هذولة اللي هي عبارة عن x<sub>m</sub>(t) ناقص x<sub>n</sub>(t)
+
+516
+00:39:56,150 --> 00:39:58,970
+الـ t الموجودة في الـ j اللي هي الـ interval اللي
+
+517
+00:39:58,970 --> 00:40:02,870
+عليها اللي هي معرفة هذه الدوال ماشي الحال. هذه اللي
+
+518
+00:40:02,870 --> 00:40:09,070
+هي المسافة بين أي x<sub>m</sub> و x<sub>n</sub> الـ x<sub>m</sub> والـ x<sub>n</sub> ويمال هنا
+
+519
+00:40:09,070 --> 00:40:13,010
+يا جماعة الـ x<sub>m</sub> والـ x<sub>n</sub> موجودات في الـ c(a و b) يعني 
+
+520
+00:40:13,010 --> 00:40:17,210
+عبارة عن continuous functions إذن الـ supremum أو الـ
+
+521
+00:40:17,210 --> 00:40:20,030
+maximum للـ x<sub>m</sub>(t) ناقص x<sub>n</sub>(t) ومضمون إنها موجودة
+
+522
+00:40:20,030 --> 00:40:23,250
+لإنها على closed bounded interval t element in j
+
+523
+00:40:23,250 --> 00:40:28,130
+أصغر من ε هذا تعريف الكوشي مباشرة إذن بدل ما
+
+524
+00:40:28,130 --> 00:40:31,510
+نتعامل مع الـ n اللي قبل بشوية أو الـ i أو الـ j
+
+525
+00:40:31,510 --> 00:40:37,660
+بنتعامل مع الـ t فبيصير عندي لأن مدام الـ maximum أصغر
+
+526
+00:40:37,660 --> 00:40:41,880
+من ε لكل n و m أكبر من K إذا لكل n و m أكبر
+
+527
+00:40:41,880 --> 00:40:45,300
+من K هيكون هذا المقدار اللي جوا أصغر من ε
+
+528
+00:40:45,300 --> 00:40:48,940
+لكل مين؟ لكل t المخود عليه كل إياش الـ maximum مدام
+
+529
+00:40:48,940 --> 00:40:52,580
+الـ maximum أصغر من ε إذا قيمة الدالة هذه مع
+
+530
+00:40:52,580 --> 00:40:56,780
+قصدها عند أي نقطة في الـ interval أصغر من ε هذا
+
+531
+00:40:56,780 --> 00:41:00,960
+ينصاري عندي for all  انه أما اكبر من كهان ده نفقز d
+
+532
+00:41:00,960 --> 00:41:04,700
+انه متين جوهر ان جهر ان جهر هيكون x<sub>m</sub>(t<sub>0</sub>) ناقص
+
+533
+00:41:04,700 --> 00:41:09,500
+x<sub>n</sub>(t<sub>0</sub>) أصغر من مين؟ من ε هذا إيش معناه؟
+
+534
+00:41:09,500 --> 00:41:16,200
+معناه الـ sequence هذه x<sub>1</sub>(t<sub>0</sub>)، x<sub>2</sub>(t<sub>0</sub>)، x<sub>3</sub>
+
+535
+00:41:16,200 --> 00:41:20,760
+(t<sub>0</sub>)، x<sub>4</sub>(t<sub>0</sub>) عبارة عن كوشي sequence ومرمية
+
+536
+00:41:20,760 --> 00:41:25,060
+وين خنتها؟ في R لأن هذا عبارة عن continuous function
+
+537
+00:41:25,060 --> 00:41:27,880
+قيمتها وهي real valued function أو complex مش 
+
+538
+00:41:27,880 --> 00:41:31,880
+مش مشكلة خلينا أقول علي الـ real بيكون x<sub>1</sub>(t<sub>0</sub>) real
+
+539
+00:41:31,880 --> 00:41:34,880
+وهذا real وهذا real إذا صارت sequence of real
+
+540
+00:41:34,880 --> 00:41:39,360
+numbers وكوشي إذا converge نفترض إنها converge
+
+541
+00:41:39,360 --> 00:41:44,900
+خلينا أقول نفترض إن x<sub>m</sub>(t<sub>0</sub>) إيش بتروح للـ x(t<sub>0</sub>)
+
+542
+00:41:44,900 --> 00:41:49,680
+وهذا الكلام أخذناه لـ arbitrary t<sub>0</sub> لكل t<sub>0</sub> يعني
+
+543
+00:41:49,680 --> 00:41:57,710
+بمعنى آخر صارت الآن x<sub>m</sub>(t) بتروح لـ x(t) و
+
+544
+00:41:57,710 --> 00:42:00,650
+الآن أنا أخدت الـ t وarbitrary لها إذا بتروح كل
+
+545
+00:42:00,650 --> 00:42:04,350
+حدثين وقت بتروح لها إيش؟ x<sub>m</sub>(t) بتروح لقيمة x(t)
+
+546
+00:42:04,350 --> 00:42:08,870
+x<sub>m</sub>(t) برضه بتروح لـ x(t) برضه ده كل الـ t اللي
+
+547
+00:42:08,870 --> 00:42:14,860
+موجود أمامي في الـ j وكأني أنا هذه عملت لي دالة. ده لو
+
+548
+00:42:14,860 --> 00:42:20,920
+يعني على اللي هي من اللي هو a وb لعند مين؟ لعند R
+
+549
+00:42:20,920 --> 00:42:25,120
+لأن هذا الـ t صحيح على كل element هنا إذا أنا عمال
+
+550
+00:42:25,120 --> 00:42:29,980
+بعمل construction للـ limit x اللي هتكون وين موجودة
+
+551
+00:42:29,980 --> 00:42:35,460
+في الـ c(a و b) زي الأول مشابه للأول. هذا يظهر أن 
+
+552
+00:42:35,460 --> 00:42:38,140
+هناك سيكوانس كثيرة وكثيرة وكثيرة وكثيرة وكثيرة
+
+553
+00:42:38,140 --> 00:42:38,360
+وكثيرة وكثيرة وكثيرة وكثيرة وكثيرة وكثيرة و
+
+554
+00:42:38,360 --> 00:42:38,840
+كثيرة وكثيرة وكثيرة وكثيرة وكثيرة وكثيرة و
+
+555
+00:42:38,840 --> 00:42:39,860
+كثيرة وكثيرة وكثيرة وكثيرة وكثيرة وكثيرة و
+
+556
+00:42:39,860 --> 00:42:42,060
+كثيرة وكثيرة وكثيرة وكثيرة وكثيرة وكثيرة و
+
+557
+00:42:42,060 --> 00:42:46,400
+كثيرة وكثيرة وكثيرة وكثيرة وكثيرة وكثيرة و
+
+558
+00:42:46,400 --> 00:42:46,900
+كثيرة وكثيرة وكثيرة وكثيرة وكثيرة وكثيرة و
+
+559
+00:42:46,900 --> 00:42:47,320
+كثيرة وكثيرة وكثيرة وكثيرة وكثيرة وكثيرة و
+
+560
+00:42:47,320 --> 00:42:53,220
+كثيرة وكثيرة وكثيرة وكثيرة وكثيرة وكل ودينا
+
+561
+00:42:53,220 --> 00:42:56,960
+على افتراض أن M أكبر من M لما M تروح لنا للنهاية
+
+562
+00:42:56,960 --> 00:43:00,680
+بيصير عندي هذا المقدار اللي هو الـ maximum الـ XM of
+
+563
+00:43:00,680 --> 00:43:05,760
+T لما M تروح لنا للنهاية هيروح لمن؟ لـ X of T فكدا
+
+564
+00:43:05,760 --> 00:43:11,180
+نثبتنا لـ X of T صار عندي XM of T بتروح لـ X of T 
+
+565
+00:43:11,180 --> 00:43:14,700
+الـ maximum اللي هين أزروا سوى مين؟ Y من هذه لأن as
+
+566
+00:43:14,700 --> 00:43:19,690
+M goes to infinity XM of T بتروح للـ X of T الآن ما
+
+567
+00:43:19,690 --> 00:43:23,190
+ده ايش معناته؟ هذا هو عبارة عن المسافة بين xm ومين
+
+568
+00:43:23,190 --> 00:43:28,890
+و الـ x صارت اللي هي عندي الـ n اللي وصلناله for
+
+569
+00:43:28,890 --> 00:43:32,370
+every epsilon أكبر من صفر and any t element من كده
+
+570
+00:43:32,370 --> 00:43:37,390
+xm of t نقص x of t أصغر أو يساوي epsilon هنا من
+
+571
+00:43:37,390 --> 00:43:40,690
+هذه، مداها أصغر وإبسلون كلها that means xm ايش ما
+
+572
+00:43:40,690 --> 00:43:45,650
+لها converges uniformly من x انتبهوا عند ال
+
+573
+00:43:45,650 --> 00:43:52,070
+maximum أصغر أو يساوي epsilon بغض النظر عن اللي هي
+
+574
+00:43:52,070 --> 00:43:57,510
+الـ T الـ maximum أصغر من Y إذا أكيد اللي جوا فيهم
+
+575
+00:43:57,510 --> 00:44:01,070
+بغض النظر عن مين هي T يعني مش لكل T بلاقي Y
+
+576
+00:44:01,070 --> 00:44:07,210
+المحددة لأ عند XM of T ناقص X of T أصغر أو يساوي Y
+
+577
+00:44:07,210 --> 00:44:11,970
+من هذه لكل T في الدنيا إذا الـY للنجاة هذه لا
+
+578
+00:44:11,970 --> 00:44:16,430
+تعتمد على الـT إذا معناته أن ال convergence لـ XM of
+
+579
+00:44:16,430 --> 00:44:20,370
+T هيروح لـ X of T يشمله uniform convergence إذا
+
+580
+00:44:20,370 --> 00:44:23,230
+نسينا أن هو uniform convergence احنا كنا نقول for
+
+581
+00:44:23,230 --> 00:44:27,290
+every epsilon أكبر من صفر and for every T there
+
+582
+00:44:27,290 --> 00:44:31,170
+exists Delta أو there exists K حسب اللي هو اللي
+
+583
+00:44:31,170 --> 00:44:36,710
+بنها الآن اللي بيكون متبد على الـ T عالميا على الـ A
+
+584
+00:44:36,710 --> 00:44:39,990
+أعلادك بيكون continuity عادي لكن الـ continuity ال
+
+585
+00:44:39,990 --> 00:44:43,110
+uniform ليه؟ بنقول for every ي أكبر من صفرها على
+
+586
+00:44:43,110 --> 00:44:47,530
+طول there exists ي such that و بتتحقق هذه لكل T
+
+587
+00:44:47,530 --> 00:44:51,170
+يعني لا تعتمد عالميا على الـ T فبكون ال convergence
+
+588
+00:44:51,170 --> 00:44:54,890
+ايش اسمه؟ uniform convergence إذا صارت عندي
+
+589
+00:44:54,890 --> 00:44:57,790
+sequence of continuous functions وهذا مهم طبعا
+
+590
+00:44:57,790 --> 00:45:00,950
+أخذته في تحليل واحد تحليل اثنين آسف عندي صار
+
+591
+00:45:00,950 --> 00:45:06,090
+sequence XM of continuous functions converts لـ
+
+592
+00:45:06,090 --> 00:45:10,090
+Function X وهذه كلها الـ Continuous والـ
+
+593
+00:45:10,090 --> 00:45:13,590
+Convergence uniformly إذا غصب عنها ستظهر الـ X
+
+594
+00:45:13,590 --> 00:45:18,130
+ايش مالها Continuous كمان مرة اللي بقوله اللي
+
+595
+00:45:18,130 --> 00:45:22,150
+استخدمت قبل شوية لو كانت عند XM Sequence of
+
+596
+00:45:22,150 --> 00:45:27,480
+Continuous Functions وكانت converge uniformly to
+
+597
+00:45:27,480 --> 00:45:33,020
+some x function x هتطلع الـ x نفسها برضه continuous
+
+598
+00:45:33,020 --> 00:45:36,760
+function لكن لو كانت ال convergence مش uniformly
+
+599
+00:45:36,760 --> 00:45:40,080
+ليس شرط أن تطلع continuous وهذا الكلام أخذناه في
+
+600
+00:45:40,080 --> 00:45:42,940
+تحليل اثنين وفيه أمثلة تبع الـ bachelor's طيب يا
+
+601
+00:45:42,940 --> 00:45:48,020
+جماعة منخّص الحديث اللي حكيته الآن أنا إنه من ال
+
+602
+00:45:48,020 --> 00:45:51,200
+maximum أزرع يساوي إبسلون طلعت ال absolute value
+
+603
+00:45:51,200 --> 00:45:55,400
+هذا أزرع يساوي إبسلون لكل T بغض النظر عن الـ T يعني
+
+604
+00:45:55,400 --> 00:46:00,780
+بمعنى آخر XM of T بتروح لـ X of T بغض النظر عن ال
+
+605
+00:46:00,780 --> 00:46:04,600
+T بنلاقي إبسلون تصلح لكل الـ T اللي موجودة عندنا
+
+606
+00:46:04,600 --> 00:46:09,820
+وهذا يعني XM of T أو XM بتروح لـ X uniformly و XM
+
+607
+00:46:09,820 --> 00:46:13,370
+continuous إذا الـ x ايش هتطلع continuous إذا صار
+
+608
+00:46:13,370 --> 00:46:20,010
+عندي الآن ال distance هذا عنالى يعني أن الـ xm
+
+609
+00:46:20,010 --> 00:46:25,030
+بتروح لـ x والكلام اللي تحت عطاني x element اللي
+
+610
+00:46:25,030 --> 00:46:29,970
+هو c of a و b إذا صارت الـ xm الـ sequence converge
+
+611
+00:46:29,970 --> 00:46:35,490
+to some x in c of a و b وهذا يعني أن الـ xm اللي هي
+
+612
+00:46:35,490 --> 00:46:39,230
+الـ c of a و b is a complete metric space
+
+613
+00:46:42,560 --> 00:46:47,740
+الآن في البرهان اللي .. اللي ضغطناه قبل بشوية في
+
+614
+00:46:47,740 --> 00:46:51,940
+داخله في الواقع أثبتنا أن ال convergence اللي في
+
+615
+00:46:51,940 --> 00:46:55,700
+الـ C of A بي involve convergence ده بعمل بقول يعني
+
+616
+00:46:55,700 --> 00:46:59,380
+بقول لي الآن Theorem of Uniform Convergence
+
+617
+00:46:59,380 --> 00:47:03,520
+Convergence XM بتروح لـ X in the space C of A و B
+
+618
+00:47:03,520 --> 00:47:07,580
+Under the metric اللي حكينا عنه is a Uniform
+
+619
+00:47:07,580 --> 00:47:12,680
+Convergence That is XM converges uniformly on A و
+
+620
+00:47:12,680 --> 00:47:18,420
+B to mean 2X الأهمية حطيناها لحالها الآن أمثلة من
+
+621
+00:47:18,420 --> 00:47:21,820
+مجموعات متركز بيس هل كل المجموعات يجب أن تكون
+
+622
+00:47:21,820 --> 00:47:25,860
+مكملة؟ بالتأكيد لا، إذا قمتم بإزالة مجموعة منها
+
+623
+00:47:25,860 --> 00:47:30,320
+فإن نقطة واحدة لا تبقى مكملة لأن بلاغ سيكوينس تذهب
+
+624
+00:47:30,320 --> 00:47:34,120
+إلى النقطة التي نتحدث عنها أو هي ليست موجودة يعني
+
+625
+00:47:34,120 --> 00:47:38,890
+كوشي ليس convergence طيب صلوا الله عليه الصلاة
+
+626
+00:47:38,890 --> 00:47:43,390
+والسلام الآن أول مثال عندنا المثال المشهور أن
+
+627
+00:47:43,390 --> 00:47:46,990
+examples of incomplete metric spaces اللي هو space
+
+628
+00:47:46,990 --> 00:47:51,690
+Q اللي هو Q the set of all rational numbers the
+
+629
+00:47:51,690 --> 00:47:55,530
+set of all rational numbers with the usual metric
+
+630
+00:47:56,040 --> 00:48:00,800
+الـ Metrical هو DXY بسوء ايه أبسط قيمة X-Y عندنا
+
+631
+00:48:00,800 --> 00:48:04,680
+احنا ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+632
+00:48:04,680 --> 00:48:04,840
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+633
+00:48:04,840 --> 00:48:04,960
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+634
+00:48:04,960 --> 00:48:05,380
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+635
+00:48:05,380 --> 00:48:05,620
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+636
+00:48:05,620 --> 00:48:06,000
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+637
+00:48:06,000 --> 00:48:06,360
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+638
+00:48:06,360 --> 00:48:07,520
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+639
+00:48:07,520 --> 00:48:07,940
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+640
+00:48:07,940 --> 00:48:08,160
+.. ال .. ال .. ال .. ال .. ال
+
+641
+00:48:14,460 --> 00:48:18,620
+جذر الاثنين مثلا جذر الاثنين أو أي rational number
+
+642
+00:48:18,620 --> 00:48:24,280
+بقول لك لكل n الممتاز أن بقدر ألاقي rn الممتاز q بحيث
+
+643
+00:48:24,280 --> 00:48:28,780
+أن rn بين x وبين x زائد 2 واحدة الآن لأن between
+
+644
+00:48:28,780 --> 00:48:30,480
+any two real numbers there exists a rational
+
+645
+00:48:30,480 --> 00:48:33,100
+number يعني الآن مثلا خذوا جذر الاثنين على سبيل
+
+646
+00:48:33,100 --> 00:48:38,560
+المثال الآن عندي جذر الاثنين أكيد بقدر ألاقي r واحد
+
+647
+00:48:38,560 --> 00:48:43,540
+أصغر منه أصغر من جذر الاثنين زائد ايش واحد أكيد هؤلاء
+
+648
+00:48:43,540 --> 00:48:47,900
+ريالين number أكيد في بينها relational number لأن
+
+649
+00:48:47,900 --> 00:48:53,500
+R اثنين أكبر من جذر الاثنين وأصغر من جذر الاثنين
+
+650
+00:48:53,500 --> 00:48:54,140
+زائد نص
+
+651
+00:48:59,350 --> 00:49:05,290
+الآن جذر الاثنين زائد واحد على n in general أكبر من
+
+652
+00:49:05,290 --> 00:49:09,410
+جذر الاثنين إذا ماقدر ألاقي بينهم مين Rn يعني قدرت
+
+653
+00:49:09,410 --> 00:49:13,350
+ألاقي sequence of rational numbers لو أخذنا ال
+
+654
+00:49:13,350 --> 00:49:15,790
+limit لهذه as n goes to infinity هتظهر هذه جذر
+
+655
+00:49:15,790 --> 00:49:19,510
+الاثنين وهتصبح as n goes to infinity بيصير جذر
+
+656
+00:49:19,510 --> 00:49:22,730
+الاثنين بيصير هذه ال limit اللي موجودة وال limit لل
+
+657
+00:49:22,730 --> 00:49:27,470
+Rn ايش بيساوي جذر الاثنين إذا يعني بمعنى آخر إذا
+
+658
+00:49:27,470 --> 00:49:32,390
+جيت sequence of rational numbers converts the mean
+
+659
+00:49:32,390 --> 00:49:36,510
+لـ irrational number يعني بمعنى آخر لجأت sequence
+
+660
+00:49:36,510 --> 00:49:40,970
+of rational numbers which is Cauchy but not
+
+661
+00:49:40,970 --> 00:49:45,630
+converts ليش not converts يعني هي لما بتروح بتروح
+
+662
+00:49:45,630 --> 00:49:48,670
+under the norm اللي عندنا بتروح لعنصر مش موجود
+
+663
+00:49:48,670 --> 00:49:54,070
+فيها فإذا صارت عندي أيش مالها a queue is not complete
+
+664
+00:49:54,070 --> 00:50:00,950
+طيب يا جماعة اللي بعده صلوا على النبي عليه الصلاة
+
+665
+00:50:00,950 --> 00:50:06,030
+والسلام الآن space of all polynomials الـ polynomials
+
+666
+00:50:06,030 --> 00:50:09,830
+أنتم تذكرون كيف كنا نجيب الـ exponential function
+
+667
+00:50:09,830 --> 00:50:12,970
+لما
+
+668
+00:50:12,970 --> 00:50:18,840
+لها exponential series فيها series ماشي الحال let x
+
+669
+00:50:18,840 --> 00:50:23,520
+be the set of all polynomials over the real
+
+670
+00:50:23,520 --> 00:50:28,940
+interval d of a,b and define a metric d on x by d
+
+671
+00:50:28,940 --> 00:50:32,100
+of x بساوية من الـ maximum الـ polynomials اللي
+
+672
+00:50:32,100 --> 00:50:35,200
+موجودة في continuous functions صح ولا لا فانا أخدت
+
+673
+00:50:35,200 --> 00:50:38,900
+بس هالعائلة من الـ continuous functions اللي يمين
+
+674
+00:50:38,900 --> 00:50:43,100
+اللي هي الـ polynomials بقول لك هذه العائلة هتعمل لي
+
+675
+00:50:43,100 --> 00:50:46,360
+ايش مالها الـ Incomplete metric space is not
+
+676
+00:50:46,360 --> 00:50:49,360
+complete ماهي اللي بدنا اياها بدنا تجيبونا كوشي
+
+677
+00:50:49,360 --> 00:50:56,180
+sequence من الـ polynomials تروح وين إلى element مش
+
+678
+00:50:56,180 --> 00:50:59,580
+في الـ polynomials under the metric DXY بيسوي
+
+679
+00:50:59,580 --> 00:51:02,940
+ماكسيمال هذا وهذا بيكون معاكم ايش ماله exercise
+
+680
+00:51:02,940 --> 00:51:10,480
+من المطلبات نجي الآن نحكي عن space آخر الـ space
+
+681
+00:51:10,480 --> 00:51:15,070
+هذا ايش انا بدي اسوي عشان اقول الرسمة بس الـ space
+
+682
+00:51:15,070 --> 00:51:26,410
+انا بدي أجي اللي هو اعمل اللي هو اجيب لكم الـ space
+
+683
+00:51:26,410 --> 00:51:31,530
+of continuous functions بس بتغير الـ metric بتغير
+
+684
+00:51:31,530 --> 00:51:35,630
+الـ metric من metric اللي هو الـ maximum إلى الـ
+
+685
+00:51:35,630 --> 00:51:40,320
+integration سأقول لكم أن في هذه الحالة بيبطل الـ
+
+686
+00:51:40,320 --> 00:51:44,940
+metric ايش معناه Complete metric space ماشي الحال
+
+687
+00:51:44,940 --> 00:51:50,880
+طيب خلينا أنه نشوف ايش اللي هي الدالة اللي عندنا
+
+688
+00:51:50,880 --> 00:51:57,210
+الدالة اللي عندنا الدوال اللي عندنا انا اسف او ال
+
+689
+00:51:57,210 --> 00:52:00,730
+sequence اللي عندنا sequence of دوال ماهي لأن انا
+
+690
+00:52:00,730 --> 00:52:04,470
+بحكي عن مين عن space of continuous functions يعني
+
+691
+00:52:04,470 --> 00:52:09,090
+انصرها دوال صلوا على النبي عليه الصلاة والسلام ال
+
+692
+00:52:09,090 --> 00:52:11,930
+space of continuous functions let X be the set of
+
+693
+00:52:11,930 --> 00:52:15,170
+all continuous functions real valid functions على
+
+694
+00:52:15,170 --> 00:52:18,950
+مين على الفترة 0 و1 and define a metric D on X by
+
+695
+00:52:20,230 --> 00:52:22,610
+عرف الـ metric كتر يعني بديش ال maximum ال
+
+696
+00:52:22,610 --> 00:52:25,050
+maximum يعمل ليه complete؟ بدي اعرف دي x و y
+
+697
+00:52:25,050 --> 00:52:26,870
+بسهولة integration من صفر إلى واحد سنين value of x
+
+698
+00:52:26,870 --> 00:52:30,330
+of t minus y of t dt then x و d is not complete
+
+699
+00:52:30,330 --> 00:52:33,790
+metric space طبعا هذا ال D بيعمل metric لأن هذا ال
+
+700
+00:52:33,790 --> 00:52:38,610
+metric مش complete طيب بنشوف كيف let x m بيه أقاشي 
+
+701
+00:52:38,610 --> 00:52:43,220
+هي a sequence of continuous functions of 0 و 1 هذه
+
+702
+00:52:43,220 --> 00:52:48,680
+الـ XM بدي أقول لكم إن هذه الـ sequence اللي هو كوشي
+
+703
+00:52:48,680 --> 00:52:53,340
+sequence لكن مستحيل .. مستحيل تكون أيش شمالها؟
+
+704
+00:52:53,340 --> 00:52:57,560
+تكون convergence، ماشي؟ هتكون convergence لـ
+
+705
+00:52:57,560 --> 00:53:01,680
+sequence مش continuous في الواقع .. في الواقع
+
+706
+00:53:01,680 --> 00:53:05,780
+السبب هتلاقوه إن ال convergence في هذه الحالة مش
+
+707
+00:53:05,780 --> 00:53:11,970
+uniform convergence مش uniform فهيودي لدالة مش شرط
+708
+00:53:11,970 --> 00:53:14,810
+أنها تكون continuous تكون خلاص نعم ماشي
+
+709
+00:53:18,480 --> 00:53:22,160
+عرفونا اللي هي xM of T بتساوي 0 إذا كانت T في
+
+710
+00:53:22,160 --> 00:53:26,320
+الفترة 0.5 و بتساوي M في T نقص نص إذا كانت T
+
+711
+00:53:26,320 --> 00:53:29,760
+بين نص و نص زائد واحدة على M بس بدون ال M من
+
+712
+00:53:29,760 --> 00:53:36,360
+اثنين و طالع عشان يكون التعريف مكتمل و بتساوي 1 إذا
+
+713
+00:53:36,360 --> 00:53:39,480
+كانت T في الفترة المتبقية و كأن إيجيت أنا فترة ال
+
+714
+00:53:39,480 --> 00:53:43,200
+domain اللي هي 01 فهي فترة ال domain 01 هي 01
+
+715
+00:53:43,200 --> 00:53:47,770
+لعندي 1 قسمتُها إلى 3 أجزاءالجزء الأول من صفر لعند
+
+716
+00:53:47,770 --> 00:53:53,530
+نص و قلتله أثبت والتاني اللي هو عبارة عن مين عن
+
+717
+00:53:53,530 --> 00:54:01,250
+اللي هو نص زائد واحد على M في الفترة هذه فأعرفت  دلًّا
+
+718
+00:54:01,250 --> 00:54:05,830
+صفر ماشي الحال في الفترة التانية عبارة عن M في T ماكس 
+
+719
+00:54:05,830 --> 00:54:10,370
+نصف في الآخر اللي هو عبارة عن خط دلّا خطية خط خط
+
+720
+00:54:10,370 --> 00:54:14,490
+فالخط بيجي خط بالشكل هذا ومن عند واقع ان هذه
+
+721
+00:54:14,490 --> 00:54:19,490
+المنطقة نص واحدة  بتصير إيش بيساوي واحد أيه اه
+
+722
+00:54:19,490 --> 00:54:23,730
+فهذه الرسمة in general ماشي الحال هذه رسمتها in
+
+723
+00:54:23,730 --> 00:54:30,080
+general الآن أنا بدي أثبت لكم أن هذه كوشي sequence
+
+724
+00:54:30,080 --> 00:54:33,920
+انتبهوا كيف واضحة الرسمة واضح اللي بحكيه طيب سلم 
+
+725
+00:54:33,920 --> 00:54:36,800
+النبع عليه الصلاة والسلام لأن لكل إبسلون أكبر من 0
+
+726
+00:54:37,920 --> 00:54:42,640
+بقدر ألاقي natural number كأكبر من سوية واحدة أكثر من
+
+727
+00:54:42,640 --> 00:54:44,700
+أكثر من أكثر من أكثر من أكثر من أكثر من أكثر من
+
+728
+00:54:44,700 --> 00:54:44,720
+أكثر من أكثر من أكثر من أكثر من أكثر من أكثر من
+
+729
+00:54:44,720 --> 00:54:48,680
+أكثر من أكثر من أكثر من أكثر من أكثر من أكثر من
+
+730
+00:54:48,680 --> 00:54:56,920
+أكثر من أكثر من أكثر من أكثر من أكثر من أكثر من
+
+731
+00:54:56,920 --> 00:54:57,720
+أكثر من أكثر من أكثر من أكثر من أكثر من أكثر من
+
+732
+00:54:57,720 --> 00:55:00,060
+أكثر من أكثر من أكثر من أكثر من 
+
+733
+00:55:05,150 --> 00:55:09,190
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+734
+00:55:09,190 --> 00:55:09,430
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+735
+00:55:09,430 --> 00:55:11,830
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+736
+00:55:11,830 --> 00:55:12,930
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+737
+00:55:12,930 --> 00:55:13,050
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+738
+00:55:13,050 --> 00:55:18,340
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر منلو
+
+739
+00:55:18,340 --> 00:55:23,660
+أخذنا الـ 1 على N أصغر من 1 على M فبصير عنده اللي
+
+740
+00:55:23,660 --> 00:55:28,620
+هو عنده اللي هي هذا نص زائد 1 على N بعده بصير نص
+
+741
+00:55:28,620 --> 00:55:33,720
+زائد 1 على M لأن 1 على M أكبر منه صح ولا لأ فبصير
+
+742
+00:55:33,720 --> 00:55:39,340
+دالته هذا الدالة تبعته بتمشي زي هيك وبعدين بتطلع
+
+743
+00:55:39,340 --> 00:55:41,880
+زي هيك عند الـ 1 على M بتجف
+
+744
+00:55:50,110 --> 00:55:55,190
+من وش تعرف الدالة؟ لحظة هذه الأولى لتبعت الواحد
+
+745
+00:55:55,190 --> 00:56:01,250
+على N اللى هو بتساوي اللى هو صفر لهنا وبعدين
+
+746
+00:56:01,250 --> 00:56:05,650
+بعدها بتظلها بتساوي الخط هذا للفترة من عند نصنا
+
+747
+00:56:05,650 --> 00:56:09,670
+عند نص زائد واحد على N اه فيها هنا الآن اللي
+
+748
+00:56:09,670 --> 00:56:13,490
+بعدها طبعا بتكمل بالواحد اللي بعدها بتنزل من نصنا
+
+749
+00:56:13,490 --> 00:56:18,270
+من نص واحد على N هنا ماشي الحال واضح اللي بحكيه؟
+
+750
+00:56:18,270 --> 00:56:25,330
+فالآن عشان بدي أحسب لكم XM of T ناقص XN of T الفرق
+
+751
+00:56:25,330 --> 00:56:30,210
+بين مين؟ بين التنين هأجيكم تشوفوا إيش اللي بحكيه
+
+752
+00:56:30,210 --> 00:56:32,090
+طيب شوفوا صلى الله عليه وصلى الله عليه الصلاة
+
+753
+00:56:32,090 --> 00:56:32,350
+والسلام
+
+754
+00:56:42,770 --> 00:56:51,070
+النسافة بين Xm و Xn هي إيش بتساوي ال
+
+755
+00:56:51,070 --> 00:56:57,720
+integrationالانتجريشن من 0 ل 1 هذا كله إيش معله DT
+
+756
+00:56:57,720 --> 00:57:02,800
+صح ولا لأ الفرق بين الدالتين الفرق بين الدالتين يعني
+
+757
+00:57:02,800 --> 00:57:07,380
+المساحة المساحة الفرق بين المساحتين مساحة الدالة
+
+758
+00:57:07,380 --> 00:57:12,360
+الأولى هذه 0 شوفوا منها مساحة الدالة هذه و المساحة
+
+759
+00:57:12,360 --> 00:57:15,580
+اللي هي هذه المنطقة اللي تحت هذه الدالة الأولى
+
+760
+00:57:16,320 --> 00:57:20,160
+الدالة التانية من هنا و من هنا لما تطرح المساحتين
+
+761
+00:57:20,160 --> 00:57:24,820
+من بعض مين اللي بقى الباس المثلج هذا ماشي الحال
+
+762
+00:57:24,820 --> 00:57:30,420
+المثلث هذا قدش طوله من هنا لهنا هذه عبارة عن واحد
+
+763
+00:57:30,420 --> 00:57:35,540
+على N زائد واحد على N و واحد على N بيطلع واحد على N
+
+764
+00:57:35,540 --> 00:57:39,860
+ناقص واحد على N الـ fact بين هذي المنطقة واحد على N
+
+765
+00:57:39,860 --> 00:57:44,540
+ناقص واحد على N هذه القاعدة وضربه في الارتفاع إيش
+
+766
+00:57:44,540 --> 00:57:48,240
+بيساوى واحد فبيصير هذا ال integration بيساوي نص
+
+767
+00:57:48,240 --> 00:57:53,240
+القاعدة في واحد على N ناقص واحد على N هذا قيمة ال
+
+768
+00:57:53,240 --> 00:57:57,230
+integration اللي هو الـ integration إذا بيصير عندي ال
+
+769
+00:57:57,230 --> 00:58:03,370
+distance بين X و M و XM عبارة عن نص في واحد على M
+
+770
+00:58:03,370 --> 00:58:07,870
+ناقص مين؟ واحد على M هذا حسب ال triangle inequality
+
+771
+00:58:07,870 --> 00:58:15,290
+أصغر منه أو يساوي نص في واحد على M زائد واحد على مين؟
+
+772
+00:58:15,290 --> 00:58:19,230
+على M أكيد أكيد صح ولا لأ؟ طب الواحد على M أصغر من
+
+773
+00:58:19,230 --> 00:58:22,210
+واحد على K والواحد على M أصغر من واحد على K و
+
+774
+00:58:22,210 --> 00:58:29,340
+الواحد على K أصغر من Epsilonفهذه أصغر من Y وهذه
+
+775
+00:58:29,340 --> 00:58:34,600
+أصغر من Y إذا أصبح Y وY 2.5 يصبح Y واحد فبيصير هذا
+
+776
+00:58:34,600 --> 00:58:38,420
+شقبه هذا وكتبه هذا يصبح ال distance بين Xm وXn
+
+777
+00:58:38,420 --> 00:58:48,210
+أصغر من Y يعني بمعنى آخر أثبتنا الآن إن المسافة بين
+
+778
+00:58:48,210 --> 00:58:52,630
+X و M و XM أصغر من أي إبسيلون إذا صارت عندي XM كوشي
+
+779
+00:58:52,630 --> 00:58:57,970
+سيكوانس إذا صارت كل اللي حكيته هنا الآن hence XM
+
+780
+00:58:57,970 --> 00:59:03,050
+is a Cauchy sequence عندي الآن بقول لكم أي X في
+
+781
+00:59:03,050 --> 00:59:09,570
+الدنيا أي X في الدنيا في الـ X مش هتكون في الـ X مش
+
+782
+00:59:09,570 --> 00:59:13,410
+فيش إمكانية إنها تكون عبارة عن continuous function
+
+783
+00:59:13,410 --> 00:59:21,490
+يعني مش هتكون موجودة في ال space اللي عندي لو
+
+784
+00:59:21,490 --> 00:59:26,670
+قدينا قولنا يا جماعة نعمل حسبة عشان نثبت إن هذا ال
+
+785
+00:59:26,670 --> 00:59:30,370
+X اللي في الـ X مش مستحيل تكون اللي هي أيش شمالها
+
+786
+00:59:30,370 --> 00:59:33,590
+limit ل .. ل .. ل .. ل .. ل .. ل اللي عندنا طيب
+
+787
+00:59:35,210 --> 00:59:41,730
+خذوا أي X موجودة في الـ X تبعنا وعسبها الحسبة
+
+788
+00:59:41,730 --> 00:59:46,610
+المسافة بين X أم و X بتساوي ال integration من صفر
+
+789
+00:59:46,610 --> 00:59:49,630
+لعند واحد هذه X وين في spaceنا في spaceنا اللي
+
+790
+00:59:49,630 --> 00:59:54,410
+بتقول لكم أنه مستحيل أن X أم تروح لها لو بدها تروح لها
+
+791
+00:59:54,410 --> 00:59:57,210
+نقول أنه جبناها تروح لها نقول فيه لأ بضالة العقوبة
+
+792
+00:59:57,480 --> 01:00:00,780
+شوفوا الآن المسافة بين Xم و X إيش بتساوي حسب
+
+793
+01:00:00,780 --> 01:00:03,660
+التعريف ال integration من صفر لواحد Xm of T نقص X
+
+794
+01:00:03,660 --> 01:00:09,320
+of T ب T ماشي Xm of T معروفة صفر في الأول في الفترة
+
+795
+01:00:09,320 --> 01:00:14,870
+من صفر لمين لنص بربال هذه جاعدة لحالها ماشي زائد ال
+
+796
+01:00:14,870 --> 01:00:18,510
+integration من نص لنص زائد واحد على M XM of T ناقص
+
+797
+01:00:18,510 --> 01:00:24,370
+مين؟ X of T ماشي الحال XM of T إلها قيمتها اللي هي
+
+798
+01:00:24,370 --> 01:00:30,030
+القيمة هذه الميلة وفي المنطقة الأخيرة من نص زائد
+
+799
+01:00:30,030 --> 01:00:32,830
+واحد على M عند الواحد بتكون قيمتها إيش بتساوي؟
+
+800
+01:00:32,830 --> 01:00:39,590
+واحد ناقص X of T دي تي طيب الآن since the integrals
+
+801
+01:00:39,590 --> 01:00:42,990
+on the right are non-negative كل من هدول أشمالهم
+
+802
+01:00:42,990 --> 01:00:48,810
+non-negative مظبوط ولا لأ؟ إذا لما نأخذ هدولة non
+
+803
+01:00:48,810 --> 01:00:51,830
+-negative مظبوط هدولة non-negative هدولة نفسهم non
+
+804
+01:00:51,830 --> 01:00:54,350
+-negative اللي جوا فبتطلع ليه قيمة ال integration
+
+805
+01:00:54,350 --> 01:00:59,070
+أشمالها عبارة عن أكبر أو يساوي صفر إذا لو أنا بدأ
+
+806
+01:00:59,070 --> 01:01:06,230
+أقول أن Xm مستحيل تذهب إلى X في الـ space اللي
+
+807
+01:01:06,230 --> 01:01:11,270
+عندي، لو بدأ أقول، أفترض أن Xm تذهب إلى X، يعني
+
+808
+01:01:11,270 --> 01:01:14,430
+المسافة بين هذه وهذه تذهب إلى صفر As M goes to
+
+809
+01:01:14,430 --> 01:01:19,680
+infinity، ماشي، إذاً بدنا نقول suppose that إن
+
+810
+01:01:19,680 --> 01:01:23,640
+distance بين X أما و X تروح لمين للصفر as M goes
+
+811
+01:01:23,640 --> 01:01:28,220
+to infinity لما أم تروح إلى مالانهاية طبعاً هذا
+
+812
+01:01:28,220 --> 01:01:30,500
+بيصير ال integration كله أم تروح لمن بيصير من نص
+
+813
+01:01:30,500 --> 01:01:33,760
+لنص بيطلع صفر إذاً هذا هيروح للصفر وهذا يروح لمين
+
+814
+01:01:33,760 --> 01:01:37,960
+للصفر هذا ما هو مش مانتومد على M فبيصير ال
+
+815
+01:01:37,960 --> 01:01:41,940
+integration X of T من صفر لنص عشان ساقية صفر وهذا
+
+816
+01:01:41,940 --> 01:01:45,320
+بيصير ال integration اللي بيساوي بيروح لصفر as M
+
+817
+01:01:45,320 --> 01:01:49,480
+goes to مين To infinity مظبوط وهذا راح يرميه لما
+
+818
+01:01:49,480 --> 01:01:53,640
+الصفر روح ما فيش هيطلع علينا اشي واضح اللي بحكيه طيب
+
+819
+01:01:53,640 --> 01:01:59,370
+اطلع لفوق بيصير عندي ال integrationلـ Integration
+
+820
+01:01:59,370 --> 01:02:06,610
+من 0 لعند نص XM of T DT هي صفر والتاني as M goes
+
+821
+01:02:06,610 --> 01:02:10,370
+to infinity هذي بتروح لنص، مظبوط؟ as M goes to
+
+822
+01:02:10,370 --> 01:02:12,990
+infinity بيصير لو حاجة لها صفر بيصير من نص لعند
+
+823
+01:02:12,990 --> 01:02:17,610
+واحد أش بساوي صفر بيصير هذا بساوي صفر وهذا بساوي
+
+824
+01:02:17,610 --> 01:02:21,490
+صفر طيب ما احنا بنقول X of T continuous لأن هو
+
+825
+01:02:21,490 --> 01:02:23,810
+موجودة في ال space سبعنا ال space of continuous
+
+826
+01:02:23,810 --> 01:02:29,630
+functions إذا هيطلع عندي الآن مدام هذا المقدار صفر
+
+827
+01:02:29,630 --> 01:02:34,530
+وهذه الدالة متصلة إذا غصب عنها هيطلع ال X of T ال
+
+828
+01:02:34,530 --> 01:02:39,170
+integration على دالة متصلة بيساوي صفر معناته الدالة
+
+829
+01:02:39,170 --> 01:02:42,550
+إن هو جوا هي في الصفر من أين جاء ذلك؟ وهو
+
+830
+01:02:42,550 --> 01:02:45,370
+أكبر أو يساوي صفر ما انخلطتش تقولوا الله صار من تحت
+
+831
+01:02:45,370 --> 01:02:48,970
+و من فوق لأ هي فوق وأكبر أو يساوي صفر و طلعت عند ال
+
+832
+01:02:48,970 --> 01:02:51,330
+integration أنها بيساوي صفر فأنا هي قد الصفر ومش
+
+833
+01:02:51,330 --> 01:02:55,210
+غيرها فبيصير x of t أشفت يساوي صفر واللي جوا برضه
+
+834
+01:02:55,210 --> 01:02:59,300
+إيش هيساوي؟ برضه هيساوي صفر لأن نفس الشيء هذا أكبر
+
+835
+01:02:59,300 --> 01:03:03,700
+شو صفر وعلى فترة والمساحة على فترة وهي على أكبر
+
+836
+01:03:03,700 --> 01:03:07,380
+شو صفر فمستحيل اللي يكون اللي جواي شماله عبارة عن
+
+837
+01:03:07,380 --> 01:03:10,520
+صفر لأن دالنا متصلة وأكبر شو صفر إذا صار عندي
+
+838
+01:03:10,520 --> 01:03:14,500
+هذا صفر معناه تصار x of t بتساوي واحد صارت عندي x
+
+839
+01:03:14,500 --> 01:03:18,360
+of t بتساوي صفر على فترة من صفر لمين لنص و x of t
+
+840
+01:03:18,360 --> 01:03:21,820
+بتساوي واحد على فترة من نص لعند مين لعند واحد صار 
+
+841
+01:03:21,820 --> 01:03:26,730
+في عندي هذه الدالة مش متصلة، بتبقى ماشية سفيراً 
+
+842
+01:03:26,730 --> 01:03:29,810
+وبعدين بتنط لعند مين؟ لعند الواحد، لعند الـ 1 بتنط،
+
+843
+01:03:29,810 --> 01:03:35,190
+فبتكون هذه is not continuous، إذا لو فرضنا أن
+
+844
+01:03:35,190 --> 01:03:39,610
+المسافة بين Xm و X بتروح للصفر، يعني لو فرضنا Xm
+
+845
+01:03:39,610 --> 01:03:42,490
+بتروح للـ X، الـ X مش هتكون continuous function،
+
+846
+01:03:42,490 --> 01:03:48,070
+هتكون برة الـ X، وبناء عليه no limit in X
+
+847
+01:03:53,790 --> 01:04:02,290
+وهذا يثبت أن الـ space is not complete وبارك الله 
+
+848
+01:04:02,290 --> 01:04:03,790
+فيكم الله يعطيكم العافية 
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Dna28R7jBBs_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Dna28R7jBBs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..54f37154a772026cbc39c72b9bb9a6dc5684f833
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Dna28R7jBBs_postprocess.srt
@@ -0,0 +1,3392 @@
+1
+00:00:05,620 --> 00:00:08,620
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,620 --> 00:00:11,440
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:11,440 --> 00:00:15,240
+آله وصحبه أجمعين هذه هي المحاضرة السادسة مساق
+
+4
+00:00:15,240 --> 00:00:19,140
+تحليل اقتراني أو تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:19,140 --> 00:00:27,110
+الإسلامية قسم رياضيات مجستير رياضيةحكينا احنا عند
+
+6
+00:00:27,110 --> 00:00:31,530
+واحد اربعة وصلنا ونهينا واحد اربعة وقلنا خلينا
+
+7
+00:00:31,530 --> 00:00:33,930
+اللي هو المرة الجاية اللي نحكي عن واحد خمسة اللي
+
+8
+00:00:33,930 --> 00:00:39,390
+هو examples أمثلة على completeness proofsعلى
+
+9
+00:00:39,390 --> 00:00:43,870
+براهين اللي هي ناخد هناخد أمثلة ل spaces تكون
+
+10
+00:00:43,870 --> 00:00:48,030
+complete و spaces تكون ايش منها non complete طبعا
+
+11
+00:00:48,030 --> 00:00:53,330
+هذا الموضوع من الموضوعات الهامة في اللي هو المادة
+
+12
+00:00:53,330 --> 00:00:59,470
+فخلينا نركز منيح على اللي هو اللي بنحكيه اليوم أول
+
+13
+00:00:59,470 --> 00:01:04,870
+مثالطبعا احنا عرفنا على اللي هو الـ space Rn و الـ
+
+14
+00:01:04,870 --> 00:01:09,730
+Cn و قلنا الـ Rn ايش عناصره الـ Rn هو عبارة عن
+
+15
+00:01:09,730 --> 00:01:14,490
+عناصر XI واحد و XI اتنين لعند XI and untables كل
+
+16
+00:01:14,490 --> 00:01:18,770
+واحد منهم موجود وين XI element in R for every I
+
+17
+00:01:18,770 --> 00:01:22,130
+للي عندنا هذه اللي هي عناصر مين اللي هي الـ Rn
+
+18
+00:01:22,130 --> 00:01:26,090
+طبعا تعميم للـ R لر تربيع و لر تكعيب اللي هو Rn in
+
+19
+00:01:26,090 --> 00:01:28,410
+general اللي الـ N بتاخد واحد اتنين تلاتة اربعة
+
+20
+00:01:28,410 --> 00:01:33,330
+اللي بدناهاالان بدنا نعرف عليه اللي هو metric هذا
+
+21
+00:01:33,330 --> 00:01:36,130
+اللي هو الـ Euclidean metric عرفنا عليه هذا
+
+22
+00:01:36,130 --> 00:01:39,850
+متذكرين اللي هو و الـCN برضه نفس الاشي بيصير
+
+23
+00:01:39,850 --> 00:01:44,130
+doubles من الـC نسميه اللي هو Euclidean space RN
+
+24
+00:01:44,130 --> 00:01:47,510
+and Unitary space اللي هو الـCN التانية أشمالين
+
+25
+00:01:47,510 --> 00:01:51,530
+are complete spaces هنبرهن على الـ RN والتانية
+
+26
+00:01:51,530 --> 00:01:56,480
+بالظبط زي اللي هو نفس البرهانالان ايش استراتيجية
+
+27
+00:01:56,480 --> 00:02:00,400
+البرهان اللي هناخدها عشان اثبت انه complete بدي
+
+28
+00:02:00,400 --> 00:02:04,600
+اخد اي كوشي sequence و اثبت ال .. اي كوشي sequence
+
+29
+00:02:04,600 --> 00:02:07,380
+في الارقن و اثبت ال .. و اثبت الهيناي شمالها
+
+30
+00:02:07,380 --> 00:02:11,940
+converge في وين في الارقن مش الحال فالان بدي اخد
+
+31
+00:02:11,940 --> 00:02:19,240
+اي sequence xmتكون كوشي ون موجودة في الـ RN مدام X
+
+32
+00:02:19,240 --> 00:02:23,340
+يعني بمعنى آخر X1 و X2 و X3 و X4 و X5 إلى ما
+
+33
+00:02:23,340 --> 00:02:27,580
+لنهاية عبارة عن عناصر من وين ماخدها أنا من الـ RN
+
+34
+00:02:27,580 --> 00:02:31,580
+والـ XN هذه أشمالها كوشي sequence خلّينا نتطلع على
+
+35
+00:02:31,580 --> 00:02:38,530
+عناصرها X1 مثلا هي عبارة عن Xi 11ماشي هذه الواحد
+
+36
+00:02:38,530 --> 00:02:42,370
+اللي هي مين ل .. اللي هو الـ Inter اللي هان إكساي
+
+37
+00:02:42,370 --> 00:02:47,910
+اتنين واحد إكساي تلاتة واحد مجرد رموز المقول هنا
+
+38
+00:02:47,910 --> 00:02:50,990
+دول real numbers اللي عنده أصل لآخر واحد لانه كيف
+
+39
+00:02:50,990 --> 00:02:54,490
+شكل العناصر اللي في الـ RN عبارة عن إن عنده أصل
+
+40
+00:02:54,490 --> 00:02:59,370
+لآخر واحد إكساي N هذه إيش؟ واحد هي اللي هو العنصر
+
+41
+00:02:59,370 --> 00:03:03,590
+الأول في ال sequence X1 X2 بنفس الاسلوب بساوي
+
+42
+00:03:03,590 --> 00:03:16,100
+إكساي اتنينXI1 XI2 XI3 XI4 XI5 XI6 XI7 XI8 XI9
+
+43
+00:03:16,100 --> 00:03:16,820
+XI10 XI11 XI12 XI12 XI13 XI14 XI15 XI16 XI16 XI17
+
+44
+00:03:16,820 --> 00:03:18,280
+XI18 XI19 XI20 XI20 XI21 XI21 XI21 XI21 XI21 XI21
+
+45
+00:03:18,280 --> 00:03:19,000
+XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21
+
+46
+00:03:19,000 --> 00:03:20,260
+XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21
+
+47
+00:03:20,260 --> 00:03:20,740
+XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21
+
+48
+00:03:20,740 --> 00:03:21,120
+XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21 XI21
+
+49
+00:03:21,120 --> 00:03:27,820
+XI21 XI21 XI21 XI21
+
+50
+00:03:27,820 --> 00:03:31,840
+XI21
+
+51
+00:03:31,840 --> 00:03:37,790
+XIكساي اتنين ام لعند مقاصة اللي عندك كساي ام ايش
+
+52
+00:03:37,790 --> 00:03:42,130
+ام اذا هذه هي ال sequence اللي عندي اللي ماخدها
+
+53
+00:03:42,130 --> 00:03:48,230
+كوشي sequence في وين انا في الار ان غرضي ان اوصلكم
+
+54
+00:03:48,230 --> 00:03:56,400
+ان في اكسو موجودة في الارعن بحيث ان Xm بتروح لل X
+
+55
+00:03:56,400 --> 00:04:06,100
+under the مترك اللي عندنا في الارعن خلّيني
+
+56
+00:04:06,100 --> 00:04:09,420
+انحقق اللي بدناها
+
+57
+00:04:19,570 --> 00:04:26,360
+بما أن Xm كوشي عرفين شو معناه كوشيبما أن XM كوشي
+
+58
+00:04:26,360 --> 00:04:31,840
+سيكوانس إذا لكل Y أكبر من 0 بقدر ألاقي K بحيث ال
+
+59
+00:04:31,840 --> 00:04:39,040
+مسافة بين XM و XR أشمالها أصغر من Y لكل M و R
+
+60
+00:04:39,040 --> 00:04:44,340
+أشمالها أكبر من K هذا تعريف مين الكوشي سيكوانس طيب
+
+61
+00:04:44,340 --> 00:04:51,250
+المسافة بين XM و XR احنا عارفين إيش هيوالـ XR إيش
+
+62
+00:04:51,250 --> 00:05:00,870
+هي؟ بتساوي XI 1R XI 2R لعند ما أصل XI أنهينR هذه
+
+63
+00:05:00,870 --> 00:05:04,590
+اللي هي المسافة بين عنصرين موجودات في الـ R عن إيش
+
+64
+00:05:04,590 --> 00:05:11,570
+هي عبارة عن اللي هو XI هذا ناقص هذا تربية مظلوط
+
+65
+00:05:11,570 --> 00:05:15,510
+زائد هذا ناقص التربية و الأخير لما أصل لهم كلهم
+
+66
+00:05:15,510 --> 00:05:19,770
+بجمحهم و كل وش بياخدوه أص نص هذا ال متر اجتلعنا
+
+67
+00:05:19,770 --> 00:05:26,770
+الآن بما أنه ال X مكوشي إذا المسافة اللي هي هذه
+
+68
+00:05:26,770 --> 00:05:33,360
+أصغر من مين من Yلاحظوا التالي، الآن أنا بدي أحول
+
+69
+00:05:33,360 --> 00:05:38,140
+استراتيجية حلّي بدي أحول الحديث إلى من اللي هي
+
+70
+00:05:38,140 --> 00:05:43,020
+قوشي sequences في الـRN إلى قوشي sequences في الـR
+
+71
+00:05:43,020 --> 00:05:47,220
+وانا بعرف سابقا أن الـR يشمالها is complete ركزوا
+
+72
+00:05:47,220 --> 00:05:50,600
+كيف بدي أعملها، الان بما أن المجموح هذا كله أصغر
+
+73
+00:05:50,600 --> 00:05:55,740
+من Epsilon إذا أكيد اللي هو كل واحدة منهم، كل
+
+74
+00:05:55,740 --> 00:05:59,810
+واحدة من هذه تربية أصغر من الصممش انت راحهاهذه
+
+75
+00:05:59,810 --> 00:06:04,310
+مجموحة كلها وهذه واحدة منها لكل I I واحد اتنين
+
+76
+00:06:04,310 --> 00:06:08,370
+تلاتة انهي يعني لكل واحدة من هذول وكأن انا بتاخد
+
+77
+00:06:08,370 --> 00:06:13,700
+ال sequence هذه مع بعضوالـ sequence هذه مع بعض و
+
+78
+00:06:13,700 --> 00:06:17,580
+الـ sequence التانية مع بعض الاخره و كل واحدة منهم
+
+79
+00:06:17,580 --> 00:06:22,620
+هي xi i m نقص xi r ار كل تربيع ا بتساوي واحد او
+
+80
+00:06:22,620 --> 00:06:27,140
+اتنين او تلاتة او ان كله صح انهم اصغر او صحوا
+
+81
+00:06:27,140 --> 00:06:32,800
+المجموع اللي هو اصغر منين من y تربيع من هذهبصير كل
+
+82
+00:06:32,800 --> 00:06:36,880
+واحدة أصغر من نين من ويبسولون إذا صار هذه اللي عند
+
+83
+00:06:36,880 --> 00:06:41,000
+ال absolute value لها أصغر من ويبسولون هذه لكل
+
+84
+00:06:41,000 --> 00:06:49,480
+sequence اللي هي xi i واقة xi i واحد xi i اتنين xi
+
+85
+00:06:49,480 --> 00:06:55,240
+i m الاخره هذه ال sequence الآن إيش أثبتت أنا إلها
+
+86
+00:06:55,240 --> 00:07:04,000
+إن xi i m ناقص xi i rعندي أصغر من مين من أبسلون
+
+87
+00:07:04,000 --> 00:07:09,160
+لكن هذه sequence of numbers إذا صارت كوشي sequence
+
+88
+00:07:09,160 --> 00:07:13,320
+in real numbers إذا أكيد اي شمالها converge إذا
+
+89
+00:07:13,320 --> 00:07:18,180
+hence for any fixed I I من واحد لعين دلان the
+
+90
+00:07:18,180 --> 00:07:22,920
+sequence xi I واحد xi I اتنين إلى ما لنهاية هيها
+
+91
+00:07:22,920 --> 00:07:26,460
+xi I واحد xi I اتنين xi I تلتة إلى ما لنهاية
+
+92
+00:07:27,690 --> 00:07:31,990
+converges لما صارت ايش ما لها كوشي sequence of
+
+93
+00:07:31,990 --> 00:07:34,730
+real numbers then it converges خلّيني أقول
+
+94
+00:07:34,730 --> 00:07:41,190
+converges ده مين لـXi I إذا صار عندي الآن كل
+
+95
+00:07:41,190 --> 00:07:45,950
+البرهين لها نفس الروح فركزوا كويس عشان نرتاح في
+
+96
+00:07:45,950 --> 00:07:51,700
+اللي بعدهاصارت عندي الآن الـ sequence XII M
+
+97
+00:07:51,700 --> 00:07:54,960
+converged domain قلنا يعني خلّيت هذا الـ sequence
+
+98
+00:07:54,960 --> 00:07:58,920
+شايفين هذا XII قلنا هذا as M goes to infinity ..
+
+99
+00:07:58,920 --> 00:08:01,880
+as I goes to infinity .. as M goes to infinity هذه
+
+100
+00:08:01,880 --> 00:08:06,440
+بدت تروح لمين؟ للـ XII سميت XII يعني وكأني أخدت
+
+101
+00:08:06,440 --> 00:08:10,280
+هذه الـ sequenceأثبت انها كوشي و راحت لك صي واحد
+
+102
+00:08:10,280 --> 00:08:14,820
+هذه كوشي و راحت لك صي اتنين هذه كوشي و راحت لك صي
+
+103
+00:08:14,820 --> 00:08:18,980
+ايه الأخيرة كوشي و راحت لك صي اتنين اذا صار عند
+
+104
+00:08:18,980 --> 00:08:24,180
+الانX بيتساوي XY واحد XI اتنين XI N كل هى نوع
+
+105
+00:08:24,180 --> 00:08:30,780
+موجودات في الار أن الان بتثبتلكم أثبتتلكم ان ال X
+
+106
+00:08:30,780 --> 00:08:36,620
+بتساوي XI واحد و XI اتنين لعند XI N و موجودة في
+
+107
+00:08:36,620 --> 00:08:41,280
+الار أن وكل واحدة من هدولة converge لواحدة من ال
+
+108
+00:08:41,280 --> 00:08:48,180
+interest هدى بتثبتلكم ان XM convergence لهدى ال X
+
+109
+00:08:48,660 --> 00:08:53,820
+يعني إيش؟ يعني المسافة بين Xm و X تكون أصغر من
+
+110
+00:08:53,820 --> 00:08:59,140
+الإمسلون تحت الشروط اللي حكيتناها طيب الآن by one
+
+111
+00:08:59,140 --> 00:09:04,320
+اللي حكينا عنها في الأول هي شايفين هذه by one الآن
+
+112
+00:09:04,320 --> 00:09:10,480
+as N as M أو R اللي بتديها وديها لنا لنهاية بتروح
+
+113
+00:09:10,480 --> 00:09:14,360
+حسب اللي حكيته as R goes to infinity ل Xir وين
+
+114
+00:09:14,360 --> 00:09:19,910
+هتروح؟ ل Xirهي يا جماعة اللي أثبتته قبل بشوية اللي
+
+115
+00:09:19,910 --> 00:09:23,730
+هو هذه بتروح ل XI واحد هذه ل XI اتنين XII in
+
+116
+00:09:23,730 --> 00:09:27,990
+general بتروح لمين ل XII اذا as M goes to infinity
+
+117
+00:09:27,990 --> 00:09:34,210
+بيسير عندي من واحد هي من واحد الان as M أو R goes
+
+118
+00:09:34,210 --> 00:09:37,570
+to infinity we have المسافة بين X M و Xهي عبارة عن
+
+119
+00:09:37,570 --> 00:09:41,810
+XII M XII تربيع أصغر يساوي مين إبسلون هذا صحيح لكل
+
+120
+00:09:41,810 --> 00:09:46,550
+مين لكل M أكبر من K وهذا في حد ذاته ايش يعني بيعني
+
+121
+00:09:46,550 --> 00:09:51,530
+ان XM is converged ل X واتلتت انها في الارأن فصارت
+
+122
+00:09:51,530 --> 00:09:54,590
+اللي هي الارأن اشمالها is complete
+
+123
+00:09:57,610 --> 00:10:03,290
+هي عندنا واحد اللي أخدته وديت R إلى مالة نهاية هذه
+
+124
+00:10:03,290 --> 00:10:09,450
+as R goes to infinity راحت XI IR إلى XI I فصار
+
+125
+00:10:09,450 --> 00:10:13,350
+اللي هو المقدار اللي تحت XI I كل تربية أصلي نص
+
+126
+00:10:13,350 --> 00:10:19,170
+أصلي من Y وهذه المسافة زي ما قلنا بين X و Xالان لو
+
+127
+00:10:19,170 --> 00:10:24,250
+بدنا نفسه بالـCN كل الكلام اللي حد هنا بنفسه بس
+
+128
+00:10:24,250 --> 00:10:27,870
+بنقول بدل الإكسايات هدول ما فنهانا في الارواح بدين
+
+129
+00:10:27,870 --> 00:10:32,530
+نكون في الـC وبس بيكون هو نفس البرهر
+
+130
+00:10:37,110 --> 00:10:41,390
+فاهم صلوا عنا باللي ما ركزش معايا هنا هنعيد تقريبا
+
+131
+00:10:41,390 --> 00:10:46,110
+كلام مشابه في إثبات الـ completeness لمن؟ لـ L
+
+132
+00:10:46,110 --> 00:10:48,310
+infinity و L completeness اللي بعد ما هي اختلافات
+
+133
+00:10:48,310 --> 00:10:52,050
+بسيطة تناسب ال space اللي موجود عندنا الان
+
+134
+00:10:52,050 --> 00:10:55,290
+completeness of L infinity L infinity عارفين انتوا
+
+135
+00:10:55,290 --> 00:10:59,190
+هو the space of bounded sequences اللي هي the
+
+136
+00:10:59,190 --> 00:11:02,290
+space L infinity is complete كله under the metric
+
+137
+00:11:02,290 --> 00:11:09,490
+اللي احنا خدناه الآن عنديعماصر برضه نفس ال
+
+138
+00:11:09,490 --> 00:11:13,710
+استراتيجية ايش بتاخد بتاخد XM أي كوش سيكوينس في ال
+
+139
+00:11:13,710 --> 00:11:18,010
+L Infinity ولاجه X في ال L Infinity بحيث ان XM
+
+140
+00:11:18,010 --> 00:11:22,350
+Converges لها بقول خلصت اثبتت انه Complete معناته
+
+141
+00:11:22,350 --> 00:11:31,230
+انه بدايته انه بتاخد اي XMكوشي سيكوانس لت اكس ام
+
+142
+00:11:31,230 --> 00:11:33,890
+بياني كوشي سيكوانس ينقل لإنفينيتي هتلاقيه
+
+143
+00:11:33,890 --> 00:11:38,870
+استراتيجية البرهام في الأمثلة الثلاثة الأولى زي
+
+144
+00:11:38,870 --> 00:11:42,010
+بعض وان اكس ام بتساوي اكسهاي واحد ام اكسهاي اتنين
+
+145
+00:11:42,010 --> 00:11:45,400
+ام إلى ما لنهايةلأن شكل العنصر في الـ L-Infinity
+
+146
+00:11:45,400 --> 00:11:54,520
+Sequence لما نقول X1 بساوي XI 1 1 XI 2 1 XI 3 1 ده
+
+147
+00:11:54,520 --> 00:11:58,060
+جافش لعند الـ Un بتضلها إشنانها لأنها دي مش
+
+148
+00:11:58,060 --> 00:12:00,520
+Untables اللي هي عناصرها الـ L-Infinity عناصرها
+
+149
+00:12:00,520 --> 00:12:06,290
+عبارة عن Sequencesو X2 نفس الاشي بيساوي XI واحد
+
+150
+00:12:06,290 --> 00:12:11,790
+اتنين XI اتنين اتنين إلى مال نهاية و نفس الاشي XM
+
+151
+00:12:11,790 --> 00:12:17,590
+in general بيساوي XI واحد M XI اتنين M إلى مال
+
+152
+00:12:17,590 --> 00:12:22,530
+نهاية و عندك XR برضه نفس الاشي و بيضلوا إلى مال
+
+153
+00:12:22,530 --> 00:12:28,110
+نهاية XI واحد R XI اتنين R إلى مال نهايةواضح إذا
+
+154
+00:12:28,110 --> 00:12:31,310
+هذه اللي هي الـ Cauchy Sequence اللي بدي أخدها بدي
+
+155
+00:12:31,310 --> 00:12:34,130
+أقول let Xm be any Cauchy Sequence in N infinity
+
+156
+00:12:34,130 --> 00:12:37,930
+where Xm بتساوي كدهذنب من تعريف الـ Cauchy
+
+157
+00:12:37,930 --> 00:12:41,470
+sequence إيش بيكون for every Y أكبر من 0 there
+
+158
+00:12:41,470 --> 00:12:44,930
+exists K element in N such that المسافة بين X و M
+
+159
+00:12:44,930 --> 00:12:49,330
+و XR أصغر من Y لكل N و M إيه شمالها أكبر من K هذا
+
+160
+00:12:49,330 --> 00:12:53,510
+التعريف العام للـ Cauchy sequence طيب المسافة في
+
+161
+00:12:53,510 --> 00:12:56,950
+هذا ال space اللي هي ال infinity بين XM و XR اللي
+
+162
+00:12:56,950 --> 00:13:01,210
+هو عبارة عن ال supremum للأبعاد XI واحد مقص XI
+
+163
+00:13:01,210 --> 00:13:04,470
+واحد اللهان XI اتنين اللهان مقص XI اتنين اللهان
+
+164
+00:13:04,700 --> 00:13:10,200
+الآخره كله بيصير عندي الـ Supremum لإكساي IM ناقص
+
+165
+00:13:10,200 --> 00:13:15,200
+إكساي IN over I يعني إكساي واحد M، إكساي واحد N
+
+166
+00:13:15,200 --> 00:13:19,980
+التانية إكساي اتنين M، إكساي تلاء اتنين N الـ
+
+167
+00:13:19,980 --> 00:13:24,140
+Supremum اللي هو عبارة عن المسافة بينين؟ بين XM و
+
+168
+00:13:24,140 --> 00:13:30,780
+XN وهذا أخدناه سابقالأن مدام الـ Supremum أصغر من
+
+169
+00:13:30,780 --> 00:13:34,640
+إبسلون إذاً كل واحدة منهم أصغر من إبسلون إذاً أكيد
+
+170
+00:13:34,640 --> 00:13:38,840
+صار عندي كل واحدة من هدولة لأي Fixed I وين موجودة
+
+171
+00:13:38,840 --> 00:13:43,140
+هنا الـ I هذه اللي هي أشمالها ليها واحد اللي هنا
+
+172
+00:13:43,140 --> 00:13:46,420
+واتنين اللي هنا وكأن زي ما أعملت قبل بشوية باخد
+
+173
+00:13:46,420 --> 00:13:49,640
+Sequences Sequences هذه الـ Sequence صارت عبارة عن
+
+174
+00:13:49,640 --> 00:13:57,670
+إيش؟ اللي هي تحققإن KSI IM نقص KSI IN أصغر من مين؟
+
+175
+00:13:57,670 --> 00:14:02,150
+من إبسلون يعني صارت هي نفس أشمالها كوشي sequence
+
+176
+00:14:03,530 --> 00:14:07,010
+هذه الـ sequence صارت إيش مالها؟ كوشي sequence of
+
+177
+00:14:07,010 --> 00:14:10,310
+إيش؟ of real numbers لأن هذولا ال interest إيش
+
+178
+00:14:10,310 --> 00:14:14,970
+مالهم؟ عبارة عن مين؟ عن أعداد حقيقية أو complex
+
+179
+00:14:14,970 --> 00:14:19,410
+سواء في C أو في R إحنا بنعرف C وR إيش مالهم
+
+180
+00:14:19,410 --> 00:14:23,650
+complete إذا مدانيك إذا أكيد بتروح لمين؟ لـ limit
+
+181
+00:14:23,650 --> 00:14:27,390
+سموها XI واحد وهذه ل limit سموها مين؟ XI اتنين
+
+182
+00:14:27,390 --> 00:14:34,970
+وهذه ل limit سموها XI مين؟ I فصار عند الـ Mثم لكل
+
+183
+00:14:34,970 --> 00:14:40,870
+M أكبر من K و لأي I مخصصة من هؤلاء هذا المقدار
+
+184
+00:14:40,870 --> 00:14:47,530
+أصغر من Y وهذا يعني لأي I مخصصة سيكون سيكوينس XI I
+
+185
+00:14:47,530 --> 00:14:51,230
+واحد XI I اتنين إلى ما لا نهاية is a Cauchy
+
+186
+00:14:51,230 --> 00:14:57,050
+sequence of numbers سواء حقيقية أو كمبليكسية في كل
+
+187
+00:14:57,050 --> 00:15:02,520
+حالةبعد ذلك تتعامل بالخطوط التي تتعامل بالخطوط
+
+188
+00:15:02,520 --> 00:15:03,040
+التي تتعامل بالخطوط التي تتعامل بالخطوط التي
+
+189
+00:15:03,040 --> 00:15:04,660
+تتعامل بالخطوط التي تتعامل بالخطوط التي تتعامل
+
+190
+00:15:04,660 --> 00:15:08,480
+بالخطوط التي تتعامل بالخطوط التي تتعامل بالخطوط
+
+191
+00:15:08,480 --> 00:15:09,980
+اللي تتعامل بالخطوط اللي تتعامل بالخطوط اللي
+
+192
+00:15:09,980 --> 00:15:12,180
+اللي تتعامل بالخطوط اللي تتعامل بالخطوط اللي
+
+193
+00:15:12,180 --> 00:15:21,120
+تتعامل بالخطوط
+
+194
+00:15:21,120 --> 00:15:25,150
+اللياللي انا متوقع ان الـ sequence ايه تروح لها
+
+195
+00:15:25,150 --> 00:15:29,870
+انا غرض ان اناجي xn بتروح ل some x و الـ x هذه
+
+196
+00:15:29,870 --> 00:15:33,670
+تكون في الـ L infinity الـ L من الـ x ركبتها انا
+
+197
+00:15:33,670 --> 00:15:37,050
+بس بدي اتأكد انها في الـ L infinity ايش الـ x عندى
+
+198
+00:15:37,050 --> 00:15:40,390
+الـ x بالساوية صاري واحد صاري اتنين إلى معناه
+
+199
+00:15:40,390 --> 00:15:43,290
+نهايةأول حاجة أريد أن أثبت لكم أن هادف الـL
+
+200
+00:15:43,290 --> 00:15:46,490
+infinity هو واحد بالاستعانة باللي حكيته قبل شوية
+
+201
+00:15:46,490 --> 00:15:51,110
+اتنين أثبت لكم إن الـX فعلا بدأ تروح لمين؟ للـX و
+
+202
+00:15:51,110 --> 00:15:55,070
+هذا الكلام مشابه بالظبط للي حكيته قبل شوية عشان هي
+
+203
+00:15:55,070 --> 00:15:59,270
+كالأول أسرعت مهمش لأن using these infinity limits
+
+204
+00:16:00,100 --> 00:16:03,040
+اللي هي XI واحد و XI اتنين و XI تلاتة اللي رقبتهم
+
+205
+00:16:03,040 --> 00:16:07,620
+We define XI واحد و XI اتنين إلى مالانهية We show
+
+206
+00:16:07,620 --> 00:16:11,840
+that X وين موجودة في الـL infinity و هنثبت أن XM
+
+207
+00:16:11,840 --> 00:16:15,340
+بتروح لمين؟ للـ X as M goes to infinity لأن
+
+208
+00:16:15,340 --> 00:16:20,320
+الاتنين اللي جابل بشوية as M goes to infinitywe
+
+209
+00:16:20,320 --> 00:16:25,380
+see that اتنين هيها as n goes so infinity ومن مين
+
+210
+00:16:25,380 --> 00:16:30,760
+بدى يودى الان بدى يودى الان تروح إلى ما لنهاية لما
+
+211
+00:16:30,760 --> 00:16:34,960
+الان تروح لما لنهاية بيصير عنده او خلينا نودى ان
+
+212
+00:16:34,960 --> 00:16:39,880
+هي ان تروح لما نهاية اي واحد منهم بنفع ناشط ودنيل
+
+213
+00:16:39,880 --> 00:16:43,040
+الان ان بتروح لما نهاية على افتراض ان ان اكبر من
+
+214
+00:16:43,040 --> 00:16:47,730
+مين من ان فبنودى الان إلى ما لنهايةيابنات و شباب
+
+215
+00:16:47,730 --> 00:16:52,950
+المثبتتك صي M نقص صي N أصغر من إبسلون هذا لكل ال N
+
+216
+00:16:52,950 --> 00:16:58,150
+و ال M أكبر من K لو فرضت أنا ال N أكبر من M مش
+
+217
+00:16:58,150 --> 00:17:01,930
+هتجيبكم بثبتوا لهم أكبر من M لو فرضنا أن ال N أكبر
+
+218
+00:17:01,930 --> 00:17:06,390
+من M هذه as N plus infinity هيصير اللي هو هذا
+
+219
+00:17:06,390 --> 00:17:11,140
+limitه أنا أثبتتهانه بيساوي مين؟ XII فبصير هذا
+
+220
+00:17:11,140 --> 00:17:16,340
+المقدار XII M ناقص XII أصغر من مين؟ من إبسلون فصار
+
+221
+00:17:16,340 --> 00:17:21,600
+XII M أصغر أو يساوي إيش؟ إبسلون وهذا صار عندى لكل
+
+222
+00:17:21,600 --> 00:17:26,100
+M أكبر من K XII M ناقص XII أصغر من إبسلون وهذا
+
+223
+00:17:26,100 --> 00:17:32,600
+يعني إيش؟ هذا يعني انه صار عندى كل واحدة منهمهتصير
+
+224
+00:17:32,600 --> 00:17:38,680
+بعد شوية اللي هي X نفسها في الـ L Infinity والـ X
+
+225
+00:17:38,680 --> 00:17:44,170
+هم بتروح للـ X، انشوف هذا الكلام، انكملأحفظونها دي
+
+226
+00:17:44,170 --> 00:17:48,370
+لإني بديها حتى سأتي الزمن بعد شوية Xm قلنا هيها
+
+227
+00:17:48,370 --> 00:17:52,590
+ماشي الحال واتفجين وين لها في L infinity مدان في L
+
+228
+00:17:52,590 --> 00:17:56,010
+infinity is a bounded sequence يعني بمعنى أخر اللي
+
+229
+00:17:56,010 --> 00:18:02,150
+هي Xim لها أصغر من some number اذا then there is
+
+230
+00:18:02,150 --> 00:18:07,050
+km such that Xim أصغر من some number سمناه km على
+
+231
+00:18:07,050 --> 00:18:10,610
+اساس أنه للواحد
+
+232
+00:18:11,220 --> 00:18:15,120
+الـ K الواحد للإتنين الـ K إتنين للتلاتة الـ K
+
+233
+00:18:15,120 --> 00:18:20,220
+تلاتة أيها كذا ال X I M أصغر أو شويه منين K M for
+
+234
+00:18:20,220 --> 00:18:25,540
+all منين or all or all I وين رايحنا؟ رايح أثبت لكم
+
+235
+00:18:25,540 --> 00:18:31,220
+إن ال X هذي is bounded رايح
+
+236
+00:18:31,220 --> 00:18:34,560
+أثبت لكم إن ال X is bounded إيش يعني؟ ده أثبت لكم
+
+237
+00:18:34,560 --> 00:18:40,810
+إن ال X I I هذي أصغر أو شويه some numberهذه اللي
+
+238
+00:18:40,810 --> 00:18:46,190
+بدأت أدوى، معناه بيصار في الأقل infinity لأن
+
+239
+00:18:46,190 --> 00:18:50,470
+XI I triangle inequality أصغر شوي XI I ناقص XI M
+
+240
+00:18:50,470 --> 00:18:56,130
+دخلت اللي بيحت خدمني، زاد XI IM هذي من اللي فوق
+
+241
+00:18:56,130 --> 00:19:01,760
+اللي أثبتناها أصغر من Epsilonوهذه اللي هو الـ L
+
+242
+00:19:01,760 --> 00:19:05,200
+infinity أصغر من KM هذا صار رقم صار عندي هذا
+
+243
+00:19:05,200 --> 00:19:08,560
+المقدار أصغر أو ساوية XI إذا صارت الـ sequence
+
+244
+00:19:08,560 --> 00:19:12,560
+bounded إذا صارت U الموجودة الـ X صارت موجودة في
+
+245
+00:19:12,560 --> 00:19:17,920
+الـ L infinityالأن من ثلاثة هذه اللي فوق مدام كل
+
+246
+00:19:17,920 --> 00:19:21,760
+واحدة منهم هذولة لأي I أصغر أو ساوي يابسيلون إذا
+
+247
+00:19:21,760 --> 00:19:24,920
+السبريمام منهم برضه كون أصغر أو ساوي يابسيلون إذا
+
+248
+00:19:24,920 --> 00:19:28,620
+صار السبريمام لهدي over I أصغر أو ساوي يابسيلون
+
+249
+00:19:29,380 --> 00:19:34,140
+وهذا الكلام صحيح لكل مين لكل M أكبر من K وهذه في
+
+250
+00:19:34,140 --> 00:19:38,440
+الواقع هي عبارة عن مسافة بين XM و Min و XM خاصة X
+
+251
+00:19:38,440 --> 00:19:41,120
+في الأقل Infinity و XM في الأقل Infinity زي
+
+252
+00:19:41,120 --> 00:19:44,220
+المشروع أن أخد اللي هي المسافة بينهم حسب الأقل
+
+253
+00:19:44,220 --> 00:19:47,870
+Infinityفصار عندها الـ distance أزار أسوأ أو أسوأ
+
+254
+00:19:47,870 --> 00:19:52,410
+أبسلون لكل أكم أكبر من K وهذا يعني أنه limit الـ
+
+255
+00:19:52,410 --> 00:19:56,090
+XM بسوء X معناته بدأنا بـ XM Cauchy sequence
+
+256
+00:19:56,090 --> 00:19:59,410
+وانتهينا بـ XM Converged في الـ X بالقلة
+
+257
+00:19:59,410 --> 00:20:02,610
+الانفينيتي وهذا يعني أن القلة الانفينيتي is إيش؟
+
+258
+00:20:02,610 --> 00:20:06,810
+is a complete space طيب يلّا الان ال complete نسنا
+
+259
+00:20:06,810 --> 00:20:14,650
+من؟ نصي احنا لحد الآن اللي عملناه في المثالينناخد
+
+260
+00:20:14,650 --> 00:20:18,530
+الـ Cauchy Sequence ونصل إلي إشمالها Converse
+
+261
+00:20:18,530 --> 00:20:26,570
+وتقريبا طريقة الأصول متشابهة في الجهتين الآن بدنا
+
+262
+00:20:26,570 --> 00:20:30,770
+نروح لفكرة أخرىبدنا ناخد الـ completeness للـ
+
+263
+00:20:30,770 --> 00:20:34,990
+scene مافيش داعي ناخد أي كوش سيكوينس في ال scene و
+
+264
+00:20:34,990 --> 00:20:38,130
+بعدين أثبتها و أديها وين اللي هي ال convinced في
+
+265
+00:20:38,130 --> 00:20:42,530
+شيء خلّيني أقول أبسط أو أنسب لهذا المثال لإن هو
+
+266
+00:20:42,530 --> 00:20:46,970
+يغلبني في الأول أنا واخدت فيه هذه و بعدين وديتها ل
+
+267
+00:20:46,970 --> 00:20:53,020
+X ده spaceC Consists Of All Convergent Sequences
+
+268
+00:20:53,020 --> 00:20:56,300
+Of Complex Numbers أو ريال مش مشكلة With The
+
+269
+00:20:56,300 --> 00:20:59,280
+Metric Induced From The Space الانفينيتي is
+
+270
+00:20:59,280 --> 00:21:05,140
+complete ايش اللي بقوله بقول احنا بنعرف ان any
+
+271
+00:21:05,140 --> 00:21:11,610
+convergent sequence is boundedإذاً الـ space of
+
+272
+00:21:11,610 --> 00:21:16,610
+all convergent sequences is a subspace أو is a
+
+273
+00:21:16,610 --> 00:21:19,050
+subset .. خلّيني أقول subspace لسه ما حكيناش عن ال
+
+274
+00:21:19,050 --> 00:21:22,910
+vector space is a subset من مين؟ من ال infinity ال
+
+275
+00:21:22,910 --> 00:21:26,030
+infinity كل ال bounded sequences ال C هي ال
+
+276
+00:21:26,030 --> 00:21:29,250
+convergent sequences وكل convergence اللي هي
+
+277
+00:21:29,250 --> 00:21:33,830
+bounded إذاً C جزء من مين؟ من ال infinity وكأنه
+
+278
+00:21:33,830 --> 00:21:38,550
+الآنأذكركم في اللي حكيناها المرة الماضية وكيف بدي
+
+279
+00:21:38,550 --> 00:21:44,890
+أستخدمه عندي أنا ال ال infinity ال ال infinity علي
+
+280
+00:21:44,890 --> 00:21:49,520
+مترك اللي هو ال D تبع ال supremumالان بدي اخد الـ
+
+281
+00:21:49,520 --> 00:21:55,560
+C واخد نفس الـ D صار جزء منه صار .. صار sub metric
+
+282
+00:21:55,560 --> 00:21:59,700
+space منه اه sub metric space منه من الـ D لأن كل
+
+283
+00:21:59,700 --> 00:22:02,460
+أنصر هنا موجود هنا و ال metric اللي هنا هو نفس
+
+284
+00:22:02,460 --> 00:22:06,340
+اللي هنا بدي اثبتلكم انه الآن هذا برضه ايش
+
+285
+00:22:06,340 --> 00:22:11,300
+complete ماشي الحالة طبعا هذا أثبتنا complete طيب
+
+286
+00:22:11,300 --> 00:22:14,780
+احنا المرة الفاتة قلنا ان ال .. نعم
+
+287
+00:22:17,650 --> 00:22:23,730
+اخدنا من المرة الماضية قلنا إنه لو كان في عندي
+
+288
+00:22:23,730 --> 00:22:27,630
+space closed subspace من complete space إيش هيكون
+
+289
+00:22:27,630 --> 00:22:31,970
+is complete إذا يكفي عشان أثبت إنه هذا إنه
+
+290
+00:22:31,970 --> 00:22:36,230
+complete إن أثبته إنه closed space طب كيف بدأ أثبت
+
+291
+00:22:36,230 --> 00:22:41,270
+إنه closed space؟ بدي أخد X في الـC closure و أثبت
+
+292
+00:22:41,270 --> 00:22:45,940
+لك إن X موجودة في الـCيعني صار الـC closure بيساوي
+
+293
+00:22:45,940 --> 00:22:49,820
+الـC، معناته صار الـC is إيش؟ closed، إذا هي
+
+294
+00:22:49,820 --> 00:22:54,280
+استراتيجية البرهان اللي بدي أعملها، واضح؟ طيب، إذا
+
+295
+00:22:54,280 --> 00:22:57,900
+الآن بدي أقولكم عشان أثبتوا الـcompleteness of C،
+
+296
+00:22:57,900 --> 00:23:01,380
+let X بيساوي إكساي I، اللي هي هذه الـsequence،
+
+297
+00:23:01,380 --> 00:23:03,660
+إكساي 1، إكساي 2، إكساي 3، إكساي 4، إلى مهلا
+
+298
+00:23:03,660 --> 00:23:09,120
+نهاية، element in C closureو أثبت لكم أن هذه ستكون
+
+299
+00:23:09,120 --> 00:23:13,720
+في الـ C طيب، ما معنى الـ X في الـ C-closure؟ ان
+
+300
+00:23:13,720 --> 00:23:18,760
+هناك C .. خدناها المرة الماضية ان X element in C
+
+301
+00:23:18,760 --> 00:23:25,800
+-closure هذا معناته ان هناك سيكوينس XMNC in C such
+
+302
+00:23:25,800 --> 00:23:30,620
+that الـ XN بتروح لمين للـ C هذا معناه ان الـ X
+
+303
+00:23:30,620 --> 00:23:35,720
+أشوان موجودة في اللي هو الـ C closure اللي ناسي
+
+304
+00:23:35,720 --> 00:23:36,300
+يتذكر
+
+305
+00:23:39,080 --> 00:23:44,680
+إنه X in between C closure إيش معناته إنه بنلاقي
+
+306
+00:23:44,680 --> 00:23:49,200
+sequence XM أو XN اللي بدكم إياها في الـC بحيث إن
+
+307
+00:23:49,200 --> 00:23:55,800
+XM بتروح لمين لأسفة لمين للـX فبتكون اللي هي X
+
+308
+00:23:55,800 --> 00:24:02,700
+واللي موجودة في الـC closure طيب الآن أخدت ال ..
+
+309
+00:24:02,700 --> 00:24:07,230
+ال .. ال .. لو أثبتت هذاإن هاد الـ X في الـ C
+
+310
+00:24:07,230 --> 00:24:10,950
+closure وصلت في الـ C بكون خلصت اتفجنا؟ يلّا
+
+311
+00:24:10,950 --> 00:24:16,930
+خلّينا نروح نشوف الآن أخدت X في الـ C closure إذا
+
+312
+00:24:16,930 --> 00:24:20,110
+حسب تعريف X في الـ C closure you get sequence XM
+
+313
+00:24:20,110 --> 00:24:24,910
+in C بحيث أن XM بتروح لمين؟ لل X where؟ إيش هي الـ
+
+314
+00:24:24,910 --> 00:24:28,670
+XM؟ زي ما عملنا قبل شوية X واحد يعني X واحد واحد
+
+315
+00:24:28,670 --> 00:24:32,190
+واحد X اتنين واحد الاخري XM in general X واحد أم X
+
+316
+00:24:32,190 --> 00:24:35,190
+اتنين أم إلى مدى نهايةهذه الـ sequence of elements
+
+317
+00:24:35,190 --> 00:24:40,930
+هو الموجودة في الـ C نفسها ماشي الحال؟ طيب، مدان
+
+318
+00:24:40,930 --> 00:24:43,930
+في الـ C، إذا كل واحدة converges لأن مدينة الـ C
+
+319
+00:24:43,930 --> 00:24:46,850
+عبارة عن الـ space أو الـ set of all convergent
+
+320
+00:24:46,850 --> 00:24:50,690
+sequences إذا hence for every ي أكبر من سفر there
+
+321
+00:24:50,690 --> 00:24:53,670
+exists k elements and such that تعريف أيش؟ إنها
+
+322
+00:24:53,670 --> 00:24:59,890
+الـ sequence converges إيش هو للتعريف أن الـ
+
+323
+00:24:59,890 --> 00:25:04,320
+distance بين Xم أو Xاللي هو أصغر من ي على تلاتة
+
+324
+00:25:04,320 --> 00:25:08,540
+أصغر من أي قيمة من ضمنها ي على تلاتة اللي هتخدمني
+
+325
+00:25:08,540 --> 00:25:11,580
+في الحسابات زي ما بنقول دايما for all M أكبر من
+
+326
+00:25:11,580 --> 00:25:17,460
+مين مين or سوى K هذا معنى إنه XM مالها converge ال
+
+327
+00:25:17,460 --> 00:25:23,770
+mean لل X اللي فوقما هو الـ metric اللي موجود هنا
+
+328
+00:25:23,770 --> 00:25:28,330
+ال metric ان ال distance بين xm و x بتساوي ال
+
+329
+00:25:28,330 --> 00:25:33,370
+supremum من xi m نقص xi i over mu over I هاي اللي
+
+330
+00:25:33,370 --> 00:25:39,600
+هي ال sequenceاللي هي ال XM وهي ال X اللي عندي
+
+331
+00:25:39,600 --> 00:25:43,840
+اللي سمنها XI واحد XI اتنين XI تلاتة اللي هي هذه
+
+332
+00:25:43,840 --> 00:25:48,200
+فالفرق بينهم واخدوا ال supermom له فقبل ال
+
+333
+00:25:48,200 --> 00:25:51,100
+interest اللي عاجبها البعض اللي هو بساوي اللي هو
+
+334
+00:25:51,100 --> 00:25:56,960
+دي XM و X أصغر من Y ع التلاتة إذا الآن هذه من XM
+
+335
+00:25:56,960 --> 00:26:04,340
+بتروح لل Xمن جهة الأخرى ما احنا عامال بنقول الان
+
+336
+00:26:04,340 --> 00:26:10,040
+عندى الـ XI .. XII موجودة في الـ C Clotar طيب
+
+337
+00:26:10,040 --> 00:26:12,880
+انتجوا لها .. لها المعلومة خذوا المعلومة الأولى
+
+338
+00:26:14,420 --> 00:26:19,640
+عندي الأن for all m أكبر أو ساوء k and any fixed i
+
+339
+00:26:19,640 --> 00:26:24,840
+هيكون عندي x i i m ناقص x i i أصغر من مين من
+
+340
+00:26:24,840 --> 00:26:27,840
+epsilon ع تلاتة وعملت هذا قبل بشوية مدام السوبرمان
+
+341
+00:26:27,840 --> 00:26:31,760
+نفسه أصغر من epsilon ع تلاتة إذا كل ال interest
+
+342
+00:26:31,760 --> 00:26:36,380
+اللي جوا برضه اصغر من epsilon ع تلاتة طيب الان بدي
+
+343
+00:26:36,380 --> 00:26:39,560
+أخد أحكي عن إشي محدد عشان بدي أحطه بين إيديا و
+
+344
+00:26:39,560 --> 00:26:44,580
+أشتغل عليهعشان هي أخدت .. طبعا هذا صحيح لمن؟ لكل M
+
+345
+00:26:44,580 --> 00:26:49,980
+أكبر سوى إيش؟ K لكل M أكبر سوى K بدي أخد اللي هو
+
+346
+00:26:49,980 --> 00:26:54,500
+الـ K عند M أيش بتساوي K؟ بتبقى ده أشمالها صحيحة
+
+347
+00:26:54,500 --> 00:27:00,000
+إذا XI I K نقص XI I أصغر من مين؟ من إبسن ع تلاتة
+
+348
+00:27:00,000 --> 00:27:04,980
+إذا أخدت مين أنا ال M بتساوي K عشان بتعمل حساباتي
+
+349
+00:27:04,980 --> 00:27:11,470
+على إشي بين إيدي ملموس يعني عن واحدة محددة طيبالان
+
+350
+00:27:11,470 --> 00:27:15,890
+كما قلنا قبل بشوية كل مننا دولة ال sequence من نوع
+
+351
+00:27:15,890 --> 00:27:20,610
+جاية من ال C يعني X واحد من ال C يعني convergence
+
+352
+00:27:20,610 --> 00:27:24,530
+sequence of real numbers او of complex X اتنين في
+
+353
+00:27:24,530 --> 00:27:28,830
+ال C X ثلاثة في ال C X M in general في ال C X K في
+
+354
+00:27:28,830 --> 00:27:32,170
+ال C إذا ال sequence هذه كل العناصرها موجودة في ال
+
+355
+00:27:32,170 --> 00:27:37,870
+C مدام XK في ال C إذا نفس ال XK converge ال XK مين
+
+356
+00:27:37,870 --> 00:27:46,180
+هيعبارة عن x1k, x2k, x3k, x4k, x5k إلى مالا نهاية
+
+357
+00:27:46,180 --> 00:27:52,100
+هذا الـ sequence أجمع لـ converge الان its terms
+
+358
+00:27:52,100 --> 00:27:55,440
+xik form a convergent sequence such that الـ
+
+359
+00:27:55,440 --> 00:28:00,340
+sequence is Cauchy أكيد عن مين بحكي يا جماعة؟ بحكي
+
+360
+00:28:00,340 --> 00:28:07,360
+عن الـ sequence x1k, x2k, x3k
+
+361
+00:28:13,050 --> 00:28:19,370
+من الـ real numbers مظبوط الـ N اللي هي مزام في
+
+362
+00:28:19,370 --> 00:28:23,350
+الـ C في الـ C حسب تعريف الـ C وهو converse إذا
+
+363
+00:28:23,350 --> 00:28:25,370
+ركيب كوشي من تعريف الكوشي
+
+364
+00:28:38,700 --> 00:28:42,880
+طيب، الآن بدي ألمها المعلومات كلها اللي عندي و
+
+365
+00:28:42,880 --> 00:28:49,260
+أحصل على اللي بدياه الآن، إيش أنا بديه؟ بدي أثبت
+
+366
+00:28:49,260 --> 00:28:56,080
+لكم إن XII هذه، اللي هي X هذه، و إن موجودة في
+
+367
+00:28:56,080 --> 00:28:59,180
+الـC، يعني أثبت لكم إنها Converges، رايح بهذا
+
+368
+00:28:59,180 --> 00:29:04,380
+الاتجاه، بكون خلصته شوفوا الآن، حسبولي الآن، لكل I
+
+369
+00:29:04,380 --> 00:29:08,760
+و J أكبر من مين؟ من أنت، إذا هذا بنطبق عليهبكون
+
+370
+00:29:08,760 --> 00:29:14,020
+بيساوي أصغر ويساوي XII-XIIK اللي حسبتها قبل و شوية
+
+371
+00:29:14,020 --> 00:29:20,780
+زاد XIIK XIJK زاد XIJK-XIAJ عملت ال training
+
+372
+00:29:20,780 --> 00:29:26,160
+quality ع مرتين مرة دخلت XIIK و مرة دخلت XIJK
+
+373
+00:29:26,160 --> 00:29:33,000
+بالسلب والإيجاب اللي هو أصغرالأولى xi i ناقص xi ik
+
+374
+00:29:33,000 --> 00:29:38,200
+اللي هو هي أصغر من مين إبسلن ع تلاتة و xi ik ناقص
+
+375
+00:29:38,200 --> 00:29:42,700
+xi jk هي أصغر من مين برضه إبسلن ع تلاتة و xi jk
+
+376
+00:29:42,700 --> 00:29:48,680
+ناقص xi j نفسها برضه أصغر من مين من إبسلن ع تلاتة
+
+377
+00:29:48,680 --> 00:29:55,880
+برضه اللي هو عملناها قبل هيك ماشي الحال هذه
+
+378
+00:29:55,880 --> 00:30:00,970
+ما هي صحيحة لكل I مظبوطهذه صحيحة لكل I اللي هي هذه
+
+379
+00:30:00,970 --> 00:30:05,830
+لكل صحيحة لكل I إذا سواء I أو J صحيحة لها هي ال I
+
+380
+00:30:05,830 --> 00:30:09,390
+هنا وهي ال J هنا فاهمين؟ فبصير هذا أصغر من هذا
+
+381
+00:30:09,390 --> 00:30:11,090
+أصغر من هذا اصغر من هذا اصغر من هذا اصغر من هذا
+
+382
+00:30:11,090 --> 00:30:11,710
+اصغر من هذا اصغر من هذا اصغر من هذا اصغر من هذا
+
+383
+00:30:11,710 --> 00:30:11,810
+اصغر من هذا اصغر من هذا اصغر من هذا اصغر من هذا
+
+384
+00:30:11,810 --> 00:30:11,910
+اصغر من هذا اصغر من هذا اصغر من هذا اصغر من هذا
+
+385
+00:30:11,910 --> 00:30:12,070
+اصغر من هذا اصغر من هذا اصغر من هذا اصغر من هذا
+
+386
+00:30:12,070 --> 00:30:13,030
+اصغر من هذا اصغر من هذا اصغر من هذا اصغر من هذا
+
+387
+00:30:13,030 --> 00:30:19,310
+اصغر من هذا اصغر
+
+388
+00:30:19,310 --> 00:30:25,290
+من هذا اصغرof numbers و ال number سواء real او
+
+389
+00:30:25,290 --> 00:30:30,010
+complex هتكون complete مادام complete اذا صارت
+
+390
+00:30:30,010 --> 00:30:33,990
+اللي هي ال sequence هذا يشملها convergence مادام
+
+391
+00:30:33,990 --> 00:30:39,870
+convergence اذا صارت عند ال xاللي هي مِساوي XII
+
+392
+00:30:39,870 --> 00:30:45,590
+هذه صارت موجودة في الـC نفسها لإنه صارت converge
+
+393
+00:30:45,590 --> 00:30:48,530
+ومعناته انه صار الـC بتساوي C closure زي ما بدأنا
+
+394
+00:30:48,530 --> 00:30:53,430
+في الأول معناته صارت اللي هو الـC اللي هي عبارة عن
+
+395
+00:30:53,430 --> 00:30:57,110
+complete metric space لإن هي صارت closed subspace
+
+396
+00:30:57,110 --> 00:31:02,230
+of a complete metric space which is complete أي
+
+397
+00:31:02,230 --> 00:31:04,350
+سؤال طيب
+
+398
+00:31:07,100 --> 00:31:11,980
+الان بدنا نيجي ل ال completeness of LB جاعدين احنا
+
+399
+00:31:11,980 --> 00:31:15,580
+بنجرد كل ال spaces اللي هتعيش معنا طول الفصل اللي
+
+400
+00:31:15,580 --> 00:31:20,360
+هو ال RN و ال CN و ال L∞ و ال LB و ال C و بعد شوية
+
+401
+00:31:20,360 --> 00:31:24,700
+ال continuous functions كل
+
+402
+00:31:24,700 --> 00:31:27,780
+هذه هنميز مين ال complete و مين اللي هو مش
+
+403
+00:31:27,780 --> 00:31:32,400
+complete و كل واحدة completeness تبعها حسب تريكها
+
+404
+00:31:38,690 --> 00:31:45,450
+هلاجة spaces إذا غيرنا المترقب بيتبطل complete أو
+
+405
+00:31:45,450 --> 00:31:50,730
+غيرنا المترقب بتصير complete حسب الأصل والتغيير
+
+406
+00:31:50,730 --> 00:31:55,310
+طيب شوفوا صلى الله عليه الصلاة والسلام الان الال
+
+407
+00:31:55,310 --> 00:31:59,050
+بيه برضه من ال spaces الملازمة لنا برضه spaces of
+
+408
+00:31:59,050 --> 00:32:02,740
+sequencesلكن احنا بقول الـ spaces و ال sequences
+
+409
+00:32:02,740 --> 00:32:07,660
+ده شرطه انه انها تكون ال summation لل XI I بي is
+
+410
+00:32:07,660 --> 00:32:10,380
+finite ماشي الحال يعني ال sequence هتكون converse
+
+411
+00:32:10,380 --> 00:32:13,680
+السيريز هتكون converse هاي شرط انها تكون ال X ..
+
+412
+00:32:13,680 --> 00:32:16,140
+اللي .. اللي هي ال sequence .. اللي هي X وا .. X
+
+413
+00:32:16,140 --> 00:32:18,580
+واحد .. XI واحد .. XI اتنين .. XI تلت .. XI اربعة
+
+414
+00:32:18,580 --> 00:32:21,640
+إلى ما لان هي تكون وين في القلبي طيب
+
+415
+00:32:25,310 --> 00:32:33,650
+أي رقم بين واحد وبين مين ماله نهاية بكل مكان الـ B
+
+416
+00:32:33,650 --> 00:32:40,230
+تبعه أشمالها is a complete metric spaceنفس القصة،
+
+417
+00:32:40,230 --> 00:32:44,470
+هأسرع شوية لأن الكلام مكرر Let XM be any Cauchy
+
+418
+00:32:44,470 --> 00:32:48,970
+Sequence الموجودة في الـ LB بالدرجة لـ X حيث أن XM
+
+419
+00:32:48,970 --> 00:32:51,210
+هي الـ Conversion لها والـ X تكون في الـ LB، هي
+
+420
+00:32:51,210 --> 00:32:56,530
+القصة كلها، الآن Where XM، صرنا عارفين، XI و XII M
+
+421
+00:32:56,530 --> 00:33:01,350
+إلى مالا نهاية، الآن من تعريف اللي هو الـ Sequence
+
+422
+00:33:01,350 --> 00:33:06,910
+في الـ LBومن تعريف ان الـ XM كون أكوشي إذا لكل Y
+
+423
+00:33:06,910 --> 00:33:10,870
+أكبر من 0 بيلاجي K بحيث ان لكل N و M أكبر من K
+
+424
+00:33:10,870 --> 00:33:15,310
+بيكون المسافة بين XM و XN أشملها أصغر من Y المسافة
+
+425
+00:33:15,310 --> 00:33:19,710
+في حالة الـ L بي مين هي summation XI IM نقص XI IM
+
+426
+00:33:19,710 --> 00:33:25,090
+اللي هو أص بي وكل أص نص أصغر من مين من Y هذه خلوها
+
+427
+00:33:25,090 --> 00:33:31,930
+اسمها أربعةالان من اللي فوق هذه برضه بنفس الأسلوب
+
+428
+00:33:31,930 --> 00:33:35,650
+مدام ال summation كله أصغر من epsilon إذا أكيد كل
+
+429
+00:33:35,650 --> 00:33:39,130
+واحد من جوا ال summation برضه هيكون أشمله اللي هو
+
+430
+00:33:39,130 --> 00:33:42,650
+أصغر من epsilon هذي بيصير كلها .. شو سيبكوا من هذي
+
+431
+00:33:42,650 --> 00:33:45,390
+.. هذي بدون الواحد على B بيصير هذا ال summation
+
+432
+00:33:45,390 --> 00:33:49,710
+أصغر من أُس B ماتجه؟ إذا كل واحدة منهم أُس B أصغر
+
+433
+00:33:49,710 --> 00:33:53,150
+من هذي أُس B يعني كل واحدة أصغر من مين؟ من epsilon
+
+434
+00:33:53,150 --> 00:33:58,000
+زي ما عملنا في التربيةإذا صار عنده هذا ايش بثبت
+
+435
+00:33:58,000 --> 00:34:02,940
+this shows that for any fixed I هذه أصغر من Y يعني
+
+436
+00:34:02,940 --> 00:34:06,600
+صارت عبارة عن Cauchy sequence نفس الاشي اللي هي ال
+
+437
+00:34:06,600 --> 00:34:09,700
+sequence اللي هنا و ال sequence اللي هنا الطولية
+
+438
+00:34:09,700 --> 00:34:12,640
+هذه اللي عملها في الأول كلهم Cauchy sequences و
+
+439
+00:34:12,640 --> 00:34:15,780
+Cauchy sequences of mean of numbers نفس اللي يعني
+
+440
+00:34:15,780 --> 00:34:19,650
+ان كله حكيتهالان مادام كوشي سيكوانسيز of number
+
+441
+00:34:19,650 --> 00:34:23,150
+سواء real او complex و بعرف ال R والC complete
+
+442
+00:34:23,150 --> 00:34:26,410
+بعيد نفس الكلام اذا اكيد هذه ال sequence الشمالها
+
+443
+00:34:26,410 --> 00:34:30,750
+converge خلّينا نسمي ان هذا ال XI IM اللي هي ال
+
+444
+00:34:30,750 --> 00:34:35,210
+converge هذي converge لمن؟ لل XII فانصرت عندى انا
+
+445
+00:34:35,210 --> 00:34:40,900
+Xبتساوي XI واحد XI اتنين إلى مال انهيار غلط زي قبل
+
+446
+00:34:40,900 --> 00:34:44,440
+شوية اهد ال XM على مين؟ على ال X واثبت لك ال X هو
+
+447
+00:34:44,440 --> 00:34:47,980
+الموجودة في القلبي كله بالاستعانة بالموجود وبنفس
+
+448
+00:34:47,980 --> 00:34:48,580
+الأسلوب
+
+449
+00:34:52,210 --> 00:34:55,950
+الان using these infinitely limits we define ال X
+
+450
+00:34:55,950 --> 00:34:59,290
+اللي قلنا عنها X واحد X اتنين كده و بدنا نثبت
+
+451
+00:34:59,290 --> 00:35:03,230
+أملنا انه نثبت ان ال X و موجودة في القلبي و نثبت
+
+452
+00:35:03,230 --> 00:35:06,750
+ان XM بتروح لل X as M goes to infinity ماشي الحال
+
+453
+00:35:06,750 --> 00:35:11,370
+من أربعة فوق we have that هاي أربعة أربعة أربعة
+
+454
+00:35:11,870 --> 00:35:15,890
+أربعة هذه أربعة شايفينها هي اللي عندى بطلع عندى ال
+
+455
+00:35:15,890 --> 00:35:19,990
+summation لهذا أصغر من ياس و نص بي ماشي الحال الان
+
+456
+00:35:19,990 --> 00:35:24,430
+ود ان تروح لمين إلى مالة نهاية بتسير لما ان تروح
+
+457
+00:35:24,430 --> 00:35:27,710
+لمالة نهاية على افتراض ان ان أكبر من بي بيسير هذي
+
+458
+00:35:27,710 --> 00:35:30,890
+تروح لمالة نهاية لما ان تروح لمناهد تروح لمين
+
+459
+00:35:30,890 --> 00:35:35,570
+للنهاية لل XII فبيصير عندى ال summation ال
+
+460
+00:35:35,570 --> 00:35:41,270
+summation لل XIIماقص XII اللي راحت إله أُس بي أزرع
+
+461
+00:35:41,270 --> 00:35:44,630
+أساومين أُس نص بي طبعا أخدت أنا لعند مين عشان حدش
+
+462
+00:35:44,630 --> 00:35:48,130
+يقول أنت بدأت تدخل limit علامة بدأ أخد اللي هو I
+
+463
+00:35:48,130 --> 00:35:51,330
+من واحد لعند مين لعند L أخدت L arbitrarily مش كله
+
+464
+00:35:51,330 --> 00:35:55,370
+الصممش اللي أخدته أخدته لعند أي L فاهمين عليا؟
+
+465
+00:35:55,370 --> 00:35:58,250
+عساس إنه مايصيرش limit علامة و يصير فيه عندي
+
+466
+00:35:58,250 --> 00:36:03,750
+إيشكاليةفالان as n يعني هدول مجموعات لبعض هذا زائد
+
+467
+00:36:03,750 --> 00:36:06,750
+هذا زائد هذا خمس مرات عشر مرات مجموعات ألا من
+
+468
+00:36:06,750 --> 00:36:09,610
+المرات إلى إذا بقدر أدخل ال limit و أزاى على
+
+469
+00:36:09,610 --> 00:36:13,030
+الجمال احنا عارفين ما زالت موجودة إذا صار عندي ال
+
+470
+00:36:13,030 --> 00:36:17,290
+limit هذه as n goes to infinity راح تقل إكس آي I I
+
+471
+00:36:17,290 --> 00:36:22,110
+من واحد لمين للأل لأن بعد ما خلصت شروع عامة الأمر
+
+472
+00:36:22,110 --> 00:36:26,970
+وصلت لهذا الحد كانت المهيأ arbitraryأذا بقدر أور
+
+473
+00:36:26,970 --> 00:36:30,870
+بL وين ما بدي لأن هذا الكلام صحيح لمن؟ لأي L في
+
+474
+00:36:30,870 --> 00:36:34,350
+الدنيا لأن ال L أخدت fixed لكن arbitrarily إذا صار
+
+475
+00:36:34,350 --> 00:36:37,850
+عندي as L goes to infinity برجع هذا I من واحد إلى
+
+476
+00:36:37,850 --> 00:36:46,190
+المقدار هذا أصغر من Y الأسمن أس Band منه ال
+
+477
+00:36:46,190 --> 00:36:51,570
+summation أزرع سواء من epsilon أي سؤال طيب هذه
+
+478
+00:36:51,570 --> 00:36:57,490
+اليمين خمسة الان x and y موجودة في ال LB إذا ال
+
+479
+00:36:57,490 --> 00:37:02,610
+summation هذا is found out من تعرف ال LB الآن بدي
+
+480
+00:37:02,610 --> 00:37:06,870
+أثبت لكم إن هذه في ال LB بدي أستخدم ال course key
+
+481
+00:37:06,870 --> 00:37:13,650
+inequalityاللي هي بيصير عندي على اللي هي xii وxim
+
+482
+00:37:16,160 --> 00:37:18,740
+هي عند باقي من ال course keen quality ال summation
+
+483
+00:37:18,740 --> 00:37:23,600
+هذا xi i اص بي الكل اص واحد على بي اصغر اي ساوي xi
+
+484
+00:37:23,600 --> 00:37:29,900
+i m ماقص xi j بي اللي اضفتها مين هي xi i m مطرحتها
+
+485
+00:37:29,900 --> 00:37:34,220
+اص بي اص واحد على بي زاد ال summation xi j m اص بي
+
+486
+00:37:34,220 --> 00:37:37,200
+اص واحد على بي هذه اللي هي مينها مين هي ال main
+
+487
+00:37:37,200 --> 00:37:41,040
+course keen quality اللي نسيها يرجحهاالآن صارت هذه
+
+488
+00:37:41,040 --> 00:37:46,120
+عندي أصلاً عندي finite من فوق أثبتناها وهذه finite
+
+489
+00:37:46,120 --> 00:37:49,320
+من فوق أثبتناها إذاً هذا المقدار كله إيش حيصير
+
+490
+00:37:49,320 --> 00:37:53,400
+حيصير finite شوفتوا أنها من فوق finite هذه finite
+
+491
+00:37:53,400 --> 00:37:58,240
+هيها واللي فوق هذه برضه إيش مالها finite إذاً صارت
+
+492
+00:37:58,240 --> 00:38:01,800
+تنتين finite وهذا بعني مدام هذه صارت ال summation
+
+493
+00:38:01,800 --> 00:38:07,100
+finite إذاً x بالساوية اللي هي هذه xi I element in
+
+494
+00:38:07,100 --> 00:38:12,650
+LBالان بمثل الأسلوب مدينة صارت في الال بي إذا
+
+495
+00:38:12,650 --> 00:38:17,830
+بيصير الان عندي من خمسة من خمسة اللي هي ال
+
+496
+00:38:17,830 --> 00:38:23,230
+distance هذه في الواقع إيش بتمثل المسافة بين XM و
+
+497
+00:38:23,230 --> 00:38:28,590
+Xمعايا اه هذه اللي هي الجوا بس حس واحد عربية يعني
+
+498
+00:38:28,590 --> 00:38:34,030
+هذه اشمالها المسافة بين XM و X أصغر يساوي Y لكل
+
+499
+00:38:34,030 --> 00:38:38,510
+أكبر من K إذا صارت عندي XM بتروح لل X وال X في
+
+500
+00:38:38,510 --> 00:38:43,690
+القلبي اللي هي صارت القلبي اشمالها is complete
+
+501
+00:38:43,690 --> 00:38:46,870
+نيجي الآن عندي the space of continuous functions
+
+502
+00:38:46,870 --> 00:38:52,940
+the space of continuous functions بدأ أثبت لكمإن
+
+503
+00:38:52,940 --> 00:38:58,280
+هذا الـ space is complete under the maximum metric
+
+504
+00:38:58,280 --> 00:39:02,260
+اللي هو الـ metric اللي عرفنا عليه هو اللي بيساوي
+
+505
+00:39:02,260 --> 00:39:07,460
+ال maximum لل X of T ناقص اللي هو Y of T, T over
+
+506
+00:39:07,460 --> 00:39:19,560
+ال interval اللي عندنا اللي أما C of A وBis the
+
+507
+00:39:19,560 --> 00:39:25,780
+space of all continuous functions على closed
+
+508
+00:39:25,780 --> 00:39:29,940
+bounded interval a و b مذا تبقلكم أن هذا ال space
+
+509
+00:39:29,940 --> 00:39:33,100
+is complete under our metric اللي هو ال maximum
+
+510
+00:39:33,100 --> 00:39:36,020
+نفس الأسئلة، إيش بتسوي؟ هتلاقيوا نفس الأسئلة
+
+511
+00:39:36,020 --> 00:39:42,210
+بالظبطلت XM be any Cauchy sequence in C or B إذاً
+
+512
+00:39:42,210 --> 00:39:44,250
+for every Y أكبر من سفر there exists K element
+
+513
+00:39:44,250 --> 00:39:47,690
+such that for all M أكبر من K نحن لدينا المسافة
+
+514
+00:39:47,690 --> 00:39:52,070
+بين XM و XM أصغر من إبسلون المسافة بين XM و XM
+
+515
+00:39:52,070 --> 00:39:56,150
+دوال هذولة اللي هي عبارة عن XM of T نقص XM of T
+
+516
+00:39:56,150 --> 00:39:58,970
+الـT الموجودة في الـJ اللي هي الـinterval اللي
+
+517
+00:39:58,970 --> 00:40:02,870
+عليها اللي هي معرفة هذه الدوال ماشي الحال هذه اللي
+
+518
+00:40:02,870 --> 00:40:09,070
+هي المسافة بين أي XMو Xn الـ Xm والـ Xn ويمال هنا
+
+519
+00:40:09,070 --> 00:40:13,010
+يا جماعة الـ Xm والـ Xn موجودات في الـ C A وB يعني
+
+520
+00:40:13,010 --> 00:40:17,210
+عبارة عن continuous functions إذن السبريموم أو ال
+
+521
+00:40:17,210 --> 00:40:20,030
+maximum للـ Xm of T نقص Xn of T ومضمون إنها موجودة
+
+522
+00:40:20,030 --> 00:40:23,250
+لإنها على close bounded interval T element in J
+
+523
+00:40:23,250 --> 00:40:28,130
+أصغر من Y هذا تعريف الكوشي مباشرة إذن بدل ما
+
+524
+00:40:28,130 --> 00:40:31,510
+نتعامل مع الـN اللي قبل بشوية أو الـI أو الـJ
+
+525
+00:40:31,510 --> 00:40:37,660
+بنتعامل مع الـTفبصير عندى لان مدام ال maximum أصغر
+
+526
+00:40:37,660 --> 00:40:41,880
+من epsilon لكل N و M أكبر من K إذا لكل N و M أكبر
+
+527
+00:40:41,880 --> 00:40:45,300
+من K هيكون هذا المقدار اللى جوا أصغر من epsilon
+
+528
+00:40:45,300 --> 00:40:48,940
+لكل مين لكل T المخود عليه كل إياش ال maximum مدام
+
+529
+00:40:48,940 --> 00:40:52,580
+ال maximum أصغر من epsilon إذا قيمة الدولة هذه مع
+
+530
+00:40:52,580 --> 00:40:56,780
+قصدها عند أي نقطة في الinterval أصغر من epsilonهذا
+
+531
+00:40:56,780 --> 00:41:00,960
+نصارى عندى four or انه اما اكبر من كهان ده نفقز D
+
+532
+00:41:00,960 --> 00:41:04,700
+انه متين جوهر ان جهر ان جهر هيكون XM of T not نقص
+
+533
+00:41:04,700 --> 00:41:09,500
+XM of T not اصغر من مين من ابسلون هذا ايش معناته؟
+
+534
+00:41:09,500 --> 00:41:16,200
+معناته ال sequence هذه X1 of T not X2 of T not X3
+
+535
+00:41:16,200 --> 00:41:20,760
+of T not X4 of T not عبارة عن كوشي sequence ومرمية
+
+536
+00:41:20,760 --> 00:41:25,060
+وين خنتها في R لأن هذا عبارة عنcontinuous function
+
+537
+00:41:25,060 --> 00:41:27,880
+قيمتها الو هي real valued function او complex مش
+
+538
+00:41:27,880 --> 00:41:31,880
+مشكلة خلّيني أقول علي الـ real بيكون x1 of t0 real
+
+539
+00:41:31,880 --> 00:41:34,880
+و هذا real و هذا real إذا صارت sequence of real
+
+540
+00:41:34,880 --> 00:41:39,360
+numbers و قوشي إذا converge نفترض إنها converge
+
+541
+00:41:39,360 --> 00:41:44,900
+خلّيني أقول نفترض إن xm of t0 إيش بتروح لل x of t0
+
+542
+00:41:44,900 --> 00:41:49,680
+و هذا الكلام أخدناه ل arbitrary t0 لكل t0 يعني
+
+543
+00:41:49,680 --> 00:41:57,710
+بمعنى آخر صارت الآن xmxm of t بتروح ل x of t و
+
+544
+00:41:57,710 --> 00:42:00,650
+الان انا اخدت ال t و ات اربط لها اذا بتروح كل
+
+545
+00:42:00,650 --> 00:42:04,350
+حدثين وقت بتروح لها ايش xm of t بتروح لقيمة x of t
+
+546
+00:42:04,350 --> 00:42:08,870
+xm of t براين بتروح ل x of t براين ده كل ال t اللي
+
+547
+00:42:08,870 --> 00:42:14,860
+موجود امامي في ال j وكأني انا هذه عملتلي دالةده لو
+
+548
+00:42:14,860 --> 00:42:20,920
+يعني على اللي هي من اللي هو A وB لعند مين لعند R
+
+549
+00:42:20,920 --> 00:42:25,120
+لأن هذا الـT صحيح على كل element هنا إذا أنا عمال
+
+550
+00:42:25,120 --> 00:42:29,980
+بعمل construction للـLimit X اللي هتكون وين موجودة
+
+551
+00:42:29,980 --> 00:42:35,460
+في الـC of A وB زي الأول مشابه للأولهذا يظهر أن
+
+552
+00:42:35,460 --> 00:42:38,140
+هناك سيكوانس كثيرة و كثيرة و كثيرة و كثيرة و كثيرة
+
+553
+00:42:38,140 --> 00:42:38,360
+و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+554
+00:42:38,360 --> 00:42:38,840
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+555
+00:42:38,840 --> 00:42:39,860
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+556
+00:42:39,860 --> 00:42:42,060
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+557
+00:42:42,060 --> 00:42:46,400
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+558
+00:42:46,400 --> 00:42:46,900
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+559
+00:42:46,900 --> 00:42:47,320
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و
+
+560
+00:42:47,320 --> 00:42:53,220
+كثيرة و كثيرة و كثيرة و كثيرة و كثيرة و كلو ودينا
+
+561
+00:42:53,220 --> 00:42:56,960
+على افتراض انه M أكبر من M لما M تروح لنا لنهاية
+
+562
+00:42:56,960 --> 00:43:00,680
+بيصير عندي هذا المقدار اللي هو ال maximum ال XM of
+
+563
+00:43:00,680 --> 00:43:05,760
+T لما M تروح لنا لنهاية هيروح لمن؟ ل X of T فكدا
+
+564
+00:43:05,760 --> 00:43:11,180
+نثبتنا ل X of T صار عندي XM of T بتروح لنقص X of T
+
+565
+00:43:11,180 --> 00:43:14,700
+ال maximum اللي هين أزروا سوى مين؟ Y من هذه لأن as
+
+566
+00:43:14,700 --> 00:43:19,690
+M goes to infinity XM of T بتروح لل X of Tالآن ما
+
+567
+00:43:19,690 --> 00:43:23,190
+ده ايش معناته؟ هذا هو عبارة عن المسافة بين xm ومين
+
+568
+00:43:23,190 --> 00:43:28,890
+و الـ x صارت اللي هي عندي الـ n اللي وصلناله for
+
+569
+00:43:28,890 --> 00:43:32,370
+every epsilon أكبر من سفر and any t element من كده
+
+570
+00:43:32,370 --> 00:43:37,390
+xm of t نقص x of t أصغر أو يساوي epsilon هانا من
+
+571
+00:43:37,390 --> 00:43:40,690
+هذه، مدنها أصغر وإبسلون كلها that means xm ايش ما
+
+572
+00:43:40,690 --> 00:43:45,650
+لها converges uniformly من x انتبهوا عند ال
+
+573
+00:43:45,650 --> 00:43:52,070
+maximum أصغر أو يساوي epsilonبغض النظر عن اللي هي
+
+574
+00:43:52,070 --> 00:43:57,510
+الـ T ال maximum أصغر من Y إذا أكيد اللي جوا فيهم
+
+575
+00:43:57,510 --> 00:44:01,070
+بغض النظر عن مين هي T يعني مش لكل T بلاجي Y
+
+576
+00:44:01,070 --> 00:44:07,210
+المحددة لأ عند XM of T ناقص X of T أصغر أو ساوي Y
+
+577
+00:44:07,210 --> 00:44:11,970
+من هذه لكل T في الدنيا إذا الـY للنجاة هذه لا
+
+578
+00:44:11,970 --> 00:44:16,430
+تعتمد على الـTإذا معناته ان ال convergence ل XM of
+
+579
+00:44:16,430 --> 00:44:20,370
+T هيروح ل X of T يشماله uniform convergence إذا
+
+580
+00:44:20,370 --> 00:44:23,230
+نسينا ان هو uniform convergence احنا كنا نقول for
+
+581
+00:44:23,230 --> 00:44:27,290
+every epsilon أكبر من سفر and for every T there
+
+582
+00:44:27,290 --> 00:44:31,170
+exists Delta أو there exists K حسب اللي هو اللي
+
+583
+00:44:31,170 --> 00:44:36,710
+بنها الان اللي بيكون متبد على ال T عالمياعلى الـ A
+
+584
+00:44:36,710 --> 00:44:39,990
+أعلادك بيكون continuity عادي لكن ال continuity ال
+
+585
+00:44:39,990 --> 00:44:43,110
+uniform ليه؟ بنقول for every ي أكبر من صفرها على
+
+586
+00:44:43,110 --> 00:44:47,530
+طول there exists ي such that و بتتحقق هذه لكل T
+
+587
+00:44:47,530 --> 00:44:51,170
+يعني لا تعتمد عالميا على ال T فبكون ال convergence
+
+588
+00:44:51,170 --> 00:44:54,890
+إيش اسمه؟ uniform convergence إذا صارت عندي
+
+589
+00:44:54,890 --> 00:44:57,790
+sequence of continuous functions و هذا مهم طبعا
+
+590
+00:44:57,790 --> 00:45:00,950
+أخدته في تحليل واحد تحليل اتنين أسف عندي صار
+
+591
+00:45:00,950 --> 00:45:06,090
+sequence XM of continuous functionsConverts لـ
+
+592
+00:45:06,090 --> 00:45:10,090
+Function X وهذه كلها الـ Continuous والـ
+
+593
+00:45:10,090 --> 00:45:13,590
+Convergence uniformly إذا غصب عنها ستظهر الـ X
+
+594
+00:45:13,590 --> 00:45:18,130
+أشمالها Continuous كمان مرة اللي بقوله اللي
+
+595
+00:45:18,130 --> 00:45:22,150
+استخدمت قبل شوية لو كانت عند XM Sequence of
+
+596
+00:45:22,150 --> 00:45:27,480
+Continuous Functionsوكانت converge uniformly to
+
+597
+00:45:27,480 --> 00:45:33,020
+some x function x هتطلع ال x نفسها برضه continuous
+
+598
+00:45:33,020 --> 00:45:36,760
+function لكن لو كانت ال convergence مش uniformly
+
+599
+00:45:36,760 --> 00:45:40,080
+ليس شرط انها تطلع continuous وهذا الكلام أخدناه في
+
+600
+00:45:40,080 --> 00:45:42,940
+تحليل اتنين وفيه أمثلة تبع ال bachelor's طيب يا
+
+601
+00:45:42,940 --> 00:45:48,020
+جماعةمُنَخَص الحديث اللي حكيته الآن أنا إنه من ال
+
+602
+00:45:48,020 --> 00:45:51,200
+maximum أزرع يساوي إبسلون طلعت ال absolute value
+
+603
+00:45:51,200 --> 00:45:55,400
+هذا أزرع يساوي إبسلون لكل T بغض النظر عن ال T يعني
+
+604
+00:45:55,400 --> 00:46:00,780
+بمعنى أخر XM of T بتروح لل X of T بغض النظر عن ال
+
+605
+00:46:00,780 --> 00:46:04,600
+T بنلاقي إبسلون تصلح لكل ال T اللي موجودة عندنا
+
+606
+00:46:04,600 --> 00:46:09,820
+وهذا يعني XM of T أو XM بتروح لل X uniformly و XM
+
+607
+00:46:09,820 --> 00:46:13,370
+continuous إذا الإكس إيش هتطلع continuousإذا صار
+
+608
+00:46:13,370 --> 00:46:20,010
+عندى الان ال distance هذا عنالى يعني ان ال xm
+
+609
+00:46:20,010 --> 00:46:25,030
+بتروح لل x و الكلام اللى تحت اعطانى x element اللى
+
+610
+00:46:25,030 --> 00:46:29,970
+هو c of a و b إذا صارت ال xm ال sequence converge
+
+611
+00:46:29,970 --> 00:46:35,490
+to some x in c of a و b وهذا يعني ان ال xm اللى هي
+
+612
+00:46:35,490 --> 00:46:39,230
+ال c of a و b is a complete metric space
+
+613
+00:46:42,560 --> 00:46:47,740
+الان في البرهان اللى .. اللى بضغطناه قبل بشوية فى
+
+614
+00:46:47,740 --> 00:46:51,940
+داخله فى الواقع أثبتنا ان ال convergence اللى فى
+
+615
+00:46:51,940 --> 00:46:55,700
+الـC of A بيinvolve convergence ده بعمل بقول يعنى
+
+616
+00:46:55,700 --> 00:46:59,380
+بقوللى الآنTheorem of Uniform Convergence
+
+617
+00:46:59,380 --> 00:47:03,520
+Convergence XM بتروح للـ X in the space C of A و B
+
+618
+00:47:03,520 --> 00:47:07,580
+Under the metric اللي حكينا عنه is a Uniform
+
+619
+00:47:07,580 --> 00:47:12,680
+Convergence That is XM converges uniformly on A و
+
+620
+00:47:12,680 --> 00:47:18,420
+B to mean 2X الأهمية حطناها لحالهاالان مثالات من
+
+621
+00:47:18,420 --> 00:47:21,820
+مجموعات متركز بيس هل كل المجموعات يجب أن تكون
+
+622
+00:47:21,820 --> 00:47:25,860
+مكملة؟ بالتأكيد لا، اذا قمتم بإزالة مجموعة منها
+
+623
+00:47:25,860 --> 00:47:30,320
+فإن نقطة واحدة لا تبقى مكملة لأن بلاغ سيكوينس تذهب
+
+624
+00:47:30,320 --> 00:47:34,120
+إلى النقطة التي نتحدث عنها أو هي ليست موجودة يعني
+
+625
+00:47:34,120 --> 00:47:38,890
+كوشي ليس convergenceطيب صلى الله عليه الصلاة
+
+626
+00:47:38,890 --> 00:47:43,390
+والسلام الان اول مثال عندنا المثال المشهور انه
+
+627
+00:47:43,390 --> 00:47:46,990
+examples of incomplete metric spaces اللي هو space
+
+628
+00:47:46,990 --> 00:47:51,690
+Q اللي هو Q the set of all rational numbers the
+
+629
+00:47:51,690 --> 00:47:55,530
+set of all rational numbers with the usual metric
+
+630
+00:47:56,040 --> 00:48:00,800
+الـ Metrical هو DXY بسوء إيه أبسط قيمة X-Y عندنا
+
+631
+00:48:00,800 --> 00:48:04,680
+احنا ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+632
+00:48:04,680 --> 00:48:04,840
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+633
+00:48:04,840 --> 00:48:04,960
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+634
+00:48:04,960 --> 00:48:05,380
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+635
+00:48:05,380 --> 00:48:05,620
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+636
+00:48:05,620 --> 00:48:06,000
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+637
+00:48:06,000 --> 00:48:06,360
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+638
+00:48:06,360 --> 00:48:07,520
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+639
+00:48:07,520 --> 00:48:07,940
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+640
+00:48:07,940 --> 00:48:08,160
+.. ال .. ال .. ال .. ال .. ال
+
+641
+00:48:14,460 --> 00:48:18,620
+جدر التنين مثلا جدر التنين او اي rational number
+
+642
+00:48:18,620 --> 00:48:24,280
+بقولك لكل n اليمتن ان بقدر الاقي rn اليمتن q بحيث
+
+643
+00:48:24,280 --> 00:48:28,780
+ان rn بين x و بين x زائد 2 واحدة الان لأن between
+
+644
+00:48:28,780 --> 00:48:30,480
+any two real numbers there exists a rational
+
+645
+00:48:30,480 --> 00:48:33,100
+number يعني الان مثلا خدوا جدر التنين على سبيل
+
+646
+00:48:33,100 --> 00:48:38,560
+المثال الان عندي جدر التنين اكيد بقدر الاقي r واحد
+
+647
+00:48:38,560 --> 00:48:43,540
+اصغر منه اصغر من جدر التنين زائداش واحد اكيدهؤلاء
+
+648
+00:48:43,540 --> 00:48:47,900
+ريالين number أكيد في بينها relational number لأن
+
+649
+00:48:47,900 --> 00:48:53,500
+R رتنين أكبر من جدر التنين و أصغر من جدر التنين
+
+650
+00:48:53,500 --> 00:48:54,140
+زائد نص
+
+651
+00:48:59,350 --> 00:49:05,290
+الأن جدر التنين زائد واحد على n in general أكبر من
+
+652
+00:49:05,290 --> 00:49:09,410
+جدر التنين إذا ماقدر ألاقي بينهم مين Rn يعني قدرت
+
+653
+00:49:09,410 --> 00:49:13,350
+ألاقي sequence of rational numbers لو أخدنا ال
+
+654
+00:49:13,350 --> 00:49:15,790
+limit لهذه as n goes to infinity هتظهر هذه جدر
+
+655
+00:49:15,790 --> 00:49:19,510
+التنين و هتصبح as n goes to infinity بيصير جدر
+
+656
+00:49:19,510 --> 00:49:22,730
+التنين بيصير هذه ال limit اللي موجودة وال limit لل
+
+657
+00:49:22,730 --> 00:49:27,470
+Rn إيش بيساوي جدر التنين إذا يعني بمعنى آخر إذا
+
+658
+00:49:27,470 --> 00:49:32,390
+جيت sequenceof rational numbers converts the mean
+
+659
+00:49:32,390 --> 00:49:36,510
+ل irrational number يعني بمعنى أخر لجأت sequence
+
+660
+00:49:36,510 --> 00:49:40,970
+of rational numbers which is Cauchy but not
+
+661
+00:49:40,970 --> 00:49:45,630
+converts ليش not converts يعني هي لما بتروح بتروح
+
+662
+00:49:45,630 --> 00:49:48,670
+under the norm اللي عندنا بتروح لعنصر مش موجود
+
+663
+00:49:48,670 --> 00:49:54,070
+فيها فإذا صارت عندي أشملها a queue is not complete
+
+664
+00:49:54,070 --> 00:50:00,950
+طيب يا جماعة اللي بعدهصلوا على النبي عليه الصلاة
+
+665
+00:50:00,950 --> 00:50:06,030
+والسلام الان space of all polynomials البرونوميالز
+
+666
+00:50:06,030 --> 00:50:09,830
+انتم تذكرين كيف كنا نجيب ال exponential function
+
+667
+00:50:09,830 --> 00:50:12,970
+لما
+
+668
+00:50:12,970 --> 00:50:18,840
+لها exponential سيريز فيها سيريزماشي الحال let x
+
+669
+00:50:18,840 --> 00:50:23,520
+be the set of all polynomials over the real
+
+670
+00:50:23,520 --> 00:50:28,940
+interval d of a,b and define a metric d on x by d
+
+671
+00:50:28,940 --> 00:50:32,100
+of x بساوية من ال maximum ال polynomials اللي
+
+672
+00:50:32,100 --> 00:50:35,200
+موجودة في continuous functions صح ولا لأ فانا أخدت
+
+673
+00:50:35,200 --> 00:50:38,900
+بس هالعائلة من ال continuous functions اللي يمين
+
+674
+00:50:38,900 --> 00:50:43,100
+اللي هي ال polynomials بقولك هذه العائلة هتعمل لي
+
+675
+00:50:43,100 --> 00:50:46,360
+إيش مالهالـ Incomplete metric space is not
+
+676
+00:50:46,360 --> 00:50:49,360
+complete ماهي اللي بدنا ياه بدنا تجيبونا كوشي
+
+677
+00:50:49,360 --> 00:50:56,180
+sequence من ال polynomials تروح وين إلى element مش
+
+678
+00:50:56,180 --> 00:50:59,580
+في ال polynomials under the metric DXY بيسوي
+
+679
+00:50:59,580 --> 00:51:02,940
+ماكسيمال هذا و هذا بيكون معاكم إيه اشماله exercise
+
+680
+00:51:02,940 --> 00:51:10,480
+من المطلبات نجي الآن نحكي عن space آخر ال space
+
+681
+00:51:10,480 --> 00:51:15,070
+هذا إيش أنا بدي أسويعشان أقول الرسمة بس ال space
+
+682
+00:51:15,070 --> 00:51:26,410
+أنا بدي أجي اللي هو أعمل اللي هو أجيبلكم ال space
+
+683
+00:51:26,410 --> 00:51:31,530
+of continuous functions بس بتغير ال metric بتغير
+
+684
+00:51:31,530 --> 00:51:35,630
+ال metric من metric اللي هو ال maximum إلى ال
+
+685
+00:51:35,630 --> 00:51:40,320
+integrationسأقول لكم إن في هذه الحالة بيبطل الـ
+
+686
+00:51:40,320 --> 00:51:44,940
+metric ايش معناه Complete metric space ماشي الحال
+
+687
+00:51:44,940 --> 00:51:50,880
+طيب خلّينا أنه نشوف إيش اللي هي الدالة اللي عندنا
+
+688
+00:51:50,880 --> 00:51:57,210
+الدالة اللي عندناالدوال اللي عندنا انا اسف او ال
+
+689
+00:51:57,210 --> 00:52:00,730
+sequence اللي عندنا sequence of دوال ماهي لان انا
+
+690
+00:52:00,730 --> 00:52:04,470
+بحكي عن مين عن space of continuous functions يعني
+
+691
+00:52:04,470 --> 00:52:09,090
+أنصرها دوال صلوا على النبي عليه الصلاة والسلام ال
+
+692
+00:52:09,090 --> 00:52:11,930
+space of continuous functions let X be the set of
+
+693
+00:52:11,930 --> 00:52:15,170
+all continuous functions real valid functions على
+
+694
+00:52:15,170 --> 00:52:18,950
+مين على الفترة 0 و1 and define a metric D on X by
+
+695
+00:52:20,230 --> 00:52:22,610
+عرفه الـ metric كتر يعني بديش ال maximum ال
+
+696
+00:52:22,610 --> 00:52:25,050
+maximum يعمل ليه complete؟ بدي أعرف دي x و y
+
+697
+00:52:25,050 --> 00:52:26,870
+بسهولة integration من صفر إلى واحد سنين value of x
+
+698
+00:52:26,870 --> 00:52:30,330
+of t minus y of t dt then x و d is not complete
+
+699
+00:52:30,330 --> 00:52:33,790
+metric space طبعا هذا ال D بيعمل metric لأن هذا ال
+
+700
+00:52:33,790 --> 00:52:38,610
+metric مش complete طيب بنشوف كيف let x m بيه أقاشي
+
+701
+00:52:38,610 --> 00:52:43,220
+بيه a sequence of continuous functions of 0 و 1هذه
+
+702
+00:52:43,220 --> 00:52:48,680
+الـ XM بدي أقولكم إن هذه الـ sequence اللي هو كوشي
+
+703
+00:52:48,680 --> 00:52:53,340
+sequence لكن مستحيل .. مستحيل تكون إيه شمالها؟
+
+704
+00:52:53,340 --> 00:52:57,560
+تكون convergence، ماشي؟ هتكون convergence لـ
+
+705
+00:52:57,560 --> 00:53:01,680
+sequence مش continuous في الواقع .. في الواقع
+
+706
+00:53:01,680 --> 00:53:05,780
+السبب هتلاقوه إن ال convergence في هذه الحالة مش
+
+707
+00:53:05,780 --> 00:53:11,970
+uniform convergenceمش uniform فهيودي لدالة مش شرط
+
+708
+00:53:11,970 --> 00:53:14,810
+انها تكون continuous تكون خلاص نعم ماشي
+
+709
+00:53:18,480 --> 00:53:22,160
+عرفونا اللي هي xM of T بتساوي 0 إذا كانت T في
+
+710
+00:53:22,160 --> 00:53:26,320
+الفترة 0.5 و بتساوي M في T نقص نص إذا كانت T
+
+711
+00:53:26,320 --> 00:53:29,760
+element نص و نص زائد واحدة لM بس بدون ال M من
+
+712
+00:53:29,760 --> 00:53:36,360
+اتنين و طالع عشان يكون التعريف مكتمل و بساوي 1 إذا
+
+713
+00:53:36,360 --> 00:53:39,480
+كانت T في الفترة المتبقية و كإن إيجيت أنا فترة ال
+
+714
+00:53:39,480 --> 00:53:43,200
+domain اللي هي 01 فهي فترة ال domain 01 هي 01
+
+715
+00:53:43,200 --> 00:53:47,770
+لعندي 1 دزأتها إلى 3 أجزاءالجزء الأول من سفر لعند
+
+716
+00:53:47,770 --> 00:53:53,530
+نص و قلتله أثبت والتاني اللي هو عبارة عن مين عن
+
+717
+00:53:53,530 --> 00:54:01,250
+اللي هو نص زائد واحد علمفي الفترة هذه فأعرفت دلّا
+
+718
+00:54:01,250 --> 00:54:05,830
+صفر ماشي الحال في الفترة التانية عبارة عن MFT ماكس
+
+719
+00:54:05,830 --> 00:54:10,370
+نصف في الآخر اللي هو عبارة عن خط دلّا خطية خط خط
+
+720
+00:54:10,370 --> 00:54:14,490
+فالخط بيجي خط بالشكل هذا ومن عند واقع ان هذه
+
+721
+00:54:14,490 --> 00:54:19,490
+المنطقة نص واحدة انت بيصير ايش بيساوي واحد ايه اه
+
+722
+00:54:19,490 --> 00:54:23,730
+فهذه الرسمة in general ماشي الحال هذه رسمتها in
+
+723
+00:54:23,730 --> 00:54:30,080
+general الآنأنا بدي أثبتلكم أن هذه كوجي sequence
+
+724
+00:54:30,080 --> 00:54:33,920
+انتبهوا كيف واضح الرسمة واضح اللي بحكيه طيب سلّع
+
+725
+00:54:33,920 --> 00:54:36,800
+النبع عليه الصلاة والسلام لأن لكل إبسلون أكبر من 0
+
+726
+00:54:37,920 --> 00:54:42,640
+بقدر ألاقي natural number كأكبر سوية واحدة أكتر من
+
+727
+00:54:42,640 --> 00:54:44,700
+أكتر من أكتر من أكتر من أكتر من أكتر من أكتر من
+
+728
+00:54:44,700 --> 00:54:44,720
+أكتر من أكتر من أكتر من أكتر من أكتر من أكتر من
+
+729
+00:54:44,720 --> 00:54:48,680
+أكتر من أكتر من أكتر من أكتر من أكتر من أكتر من
+
+730
+00:54:48,680 --> 00:54:56,920
+أكتر من أكتر من أكتر من أكتر من أكتر من أكتر من
+
+731
+00:54:56,920 --> 00:54:57,720
+أكتر من أكتر من أكتر من أكتر من أكتر من أكتر من
+
+732
+00:54:57,720 --> 00:55:00,060
+أكتر من أكتر من أكتر من أكتر من أ
+
+733
+00:55:05,150 --> 00:55:09,190
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+734
+00:55:09,190 --> 00:55:09,430
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+735
+00:55:09,430 --> 00:55:11,830
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+736
+00:55:11,830 --> 00:55:12,930
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+737
+00:55:12,930 --> 00:55:13,050
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر من M
+
+738
+00:55:13,050 --> 00:55:18,340
+أكبر من M أكبر من M أكبر من M أكبر من M أكبر منلو
+
+739
+00:55:18,340 --> 00:55:23,660
+أخدنا الـ 1 على N أصغر من 1 على M فبصير عنده اللي
+
+740
+00:55:23,660 --> 00:55:28,620
+هو عنده اللي هي هذا نص زائد 1 على N بعده بصير نص
+
+741
+00:55:28,620 --> 00:55:33,720
+زائد 1 على M لأن 1 على M أكبر منه صح ولا لأ فبصير
+
+742
+00:55:33,720 --> 00:55:39,340
+دالته هذا الدالة تبعته بتمشي زي هيك وبعدين بتطلع
+
+743
+00:55:39,340 --> 00:55:41,880
+زي هيك عند الـ 1 على M بتجف
+
+744
+00:55:50,110 --> 00:55:55,190
+من وش تعرف الدالة؟ لحظة هذه الأولى لتبعت الواحد
+
+745
+00:55:55,190 --> 00:56:01,250
+على ان اللى هو بتساوي اللى هو سفر لهنا وبعدين
+
+746
+00:56:01,250 --> 00:56:05,650
+بعدها بتظلها بتساوي الخط هذا للفترة من عند نصنا
+
+747
+00:56:05,650 --> 00:56:09,670
+عند نص زائد واحد على ان اه فيها هنا الان اللى
+
+748
+00:56:09,670 --> 00:56:13,490
+بعدها طبعا بتكمن بالواحد اللى بعدها بتسيل من نصنا
+
+749
+00:56:13,490 --> 00:56:18,270
+من نص واحد على ان هناماشي الحال واضح اللي بحكيه؟
+
+750
+00:56:18,270 --> 00:56:25,330
+فالان عشان بدي أحسبلكم XM of T ناقص XN of T الفرق
+
+751
+00:56:25,330 --> 00:56:30,210
+بين مين؟ بين التنين هلجيكم تشوفوا إيش اللي بحكيه
+
+752
+00:56:30,210 --> 00:56:32,090
+طيب شوفوا صلى الله عليه وصلى الله عليه الصلاة
+
+753
+00:56:32,090 --> 00:56:32,350
+والسلام
+
+754
+00:56:42,770 --> 00:56:51,070
+النسافة بين Xm و Xn هي ايش بتساوي ال
+
+755
+00:56:51,070 --> 00:56:57,720
+integrationالانتجريشن من 0 ل 1 هذا كله ايش معله DT
+
+756
+00:56:57,720 --> 00:57:02,800
+صح ولا لأ الفرق بين الدلتين الفرق بين الدلتين يعني
+
+757
+00:57:02,800 --> 00:57:07,380
+المساحة المساحة الفرق بين المساحتين مساحة الدلة
+
+758
+00:57:07,380 --> 00:57:12,360
+الأولى هذه 0 شوفوا منها مساحة الدلة هذه و المساحة
+
+759
+00:57:12,360 --> 00:57:15,580
+اللي هي هذه المنطقة اللي تحت هذه الدلة الأولى
+
+760
+00:57:16,320 --> 00:57:20,160
+الدالة التانية من هان و من هان لما تطرح المساحتين
+
+761
+00:57:20,160 --> 00:57:24,820
+من بعض مين اللي بقى الباس المثلج هذاماشي الحال
+
+762
+00:57:24,820 --> 00:57:30,420
+المثلث هذا قدش طوله من هان لهان هذه عبارة عن واحد
+
+763
+00:57:30,420 --> 00:57:35,540
+نص زاد واحدة لان و نص واحدة لان بيطلع واحدة لان
+
+764
+00:57:35,540 --> 00:57:39,860
+ناقص واحدة لان ال fact بين هذي المنطقة واحدة لان
+
+765
+00:57:39,860 --> 00:57:44,540
+ناقص واحدة لان هذه القاعدة وضربه في الارتفاع ايش
+
+766
+00:57:44,540 --> 00:57:48,240
+بيساوي واحد فبيصير هذا ال integration بساوي نص
+
+767
+00:57:48,240 --> 00:57:53,240
+القاعدة فواحدة لان ناقص واحدة لان هذا قيمة ال
+
+768
+00:57:53,240 --> 00:57:57,230
+rhetoricاللي هو الـ integration إذا بيصير عندى ال
+
+769
+00:57:57,230 --> 00:58:03,370
+distance بين X و M و XM عبارة عن نص في واحدة ل M
+
+770
+00:58:03,370 --> 00:58:07,870
+واقص مين؟ واحدة ل M هذا حسب ال triangle inequality
+
+771
+00:58:07,870 --> 00:58:15,290
+أصغر منه أو ساوى نص في واحدة ل M زائد واحدة ل مين؟
+
+772
+00:58:15,290 --> 00:58:19,230
+على M أكيد أكيد صح ولا لأ؟ طب الواحدة ل M أصغر من
+
+773
+00:58:19,230 --> 00:58:22,210
+واحدة ل K و الواحدة ل M أصغر من واحدة ل K و
+
+774
+00:58:22,210 --> 00:58:29,340
+الواحدة ل K أصغر من Epsilonفهذه أصغر من Y وهذه
+
+775
+00:58:29,340 --> 00:58:34,600
+أصغر من Y إذا أصبح Y وY 2.5 يصبح Y واحدة فبصير هذا
+
+776
+00:58:34,600 --> 00:58:38,420
+شقبه هذا وكتبه هذا يصبح ال distance بين Xm وXn
+
+777
+00:58:38,420 --> 00:58:48,210
+أصغر من Y يعني بمعنى آخر أثبتنا الآنإن المسافة بين
+
+778
+00:58:48,210 --> 00:58:52,630
+X و M و XM أصغر من أي إيزون إذا صارت عندي XM كوشي
+
+779
+00:58:52,630 --> 00:58:57,970
+سيكوانس إذا صارت كل اللي حكيته هنا الان hence XM
+
+780
+00:58:57,970 --> 00:59:03,050
+is a Cauchy sequence عندي الآن بقولكم أي X في
+
+781
+00:59:03,050 --> 00:59:09,570
+الدنيا أي X في الدنيا في ال X مش هتكونفي ال X مش
+
+782
+00:59:09,570 --> 00:59:13,410
+فيش إمكانية إنها تكون عبارة عن continuous function
+
+783
+00:59:13,410 --> 00:59:21,490
+يعني مش هتكون موجودة في ال space اللي عندي لو
+
+784
+00:59:21,490 --> 00:59:26,670
+قدينا قولنا يا جماعة نعمل حسبة عشان نثبت إن هذا ال
+
+785
+00:59:26,670 --> 00:59:30,370
+X اللي في ال X مش مستحيل تكون اللي هي أية شمالها
+
+786
+00:59:30,370 --> 00:59:33,590
+limit ل .. ل .. ل .. ل .. ل .. ل اللي عندنا طيب
+
+787
+00:59:35,210 --> 00:59:41,730
+خُدوا أي X موجودة في الـ X تبعنا وعسبها الحسبة
+
+788
+00:59:41,730 --> 00:59:46,610
+المسافة بين X أم و X بتساوى ال integration من سفر
+
+789
+00:59:46,610 --> 00:59:49,630
+لعند واحد هذه X وين في spaceنا في spaceنا اللي
+
+790
+00:59:49,630 --> 00:59:54,410
+بتقولكم أنه مستحيل أن X أم تروحلها لو بدها تروحلها
+
+791
+00:59:54,410 --> 00:59:57,210
+نقول أنه جبناها تروحلها نقول فيه لأ بضالة العقوبة
+
+792
+00:59:57,480 --> 01:00:00,780
+شوفوا الان المسافة بين Xم و X ايش بتساوي حسب
+
+793
+01:00:00,780 --> 01:00:03,660
+التعريف ال integration من صفر لواحد Xm of T نقص X
+
+794
+01:00:03,660 --> 01:00:09,320
+of T بT ماشي Xm of T معروفة صفر في الأول في الفترة
+
+795
+01:00:09,320 --> 01:00:14,870
+من صفر نمين لنص بربال هذه جاعدة لحالها ماشيزائد ال
+
+796
+01:00:14,870 --> 01:00:18,510
+integration من نص لنص زائد واحد علامة XM of T ناقص
+
+797
+01:00:18,510 --> 01:00:24,370
+مين؟ X of T ماشي الحال XM of T إلها قيمتها اللي هي
+
+798
+01:00:24,370 --> 01:00:30,030
+القيمة هذه الميلة وفي المنطقة الأخيرة من نص زائد
+
+799
+01:00:30,030 --> 01:00:32,830
+واحد علامة عند الواحد بتكون قريتها إيش بتساوي؟
+
+800
+01:00:32,830 --> 01:00:39,590
+واحد ناقص X of T ديتي طيبالان since the integrals
+
+801
+01:00:39,590 --> 01:00:42,990
+on the right are non-negative كل من هدول أشمالهم
+
+802
+01:00:42,990 --> 01:00:48,810
+non-negative مظبوط ولا لأ؟ إذا لما نلها هدولة non
+
+803
+01:00:48,810 --> 01:00:51,830
+-negative مظبوط هدولة non-negative هدولة نفسهم non
+
+804
+01:00:51,830 --> 01:00:54,350
+-negative اللي جوا فبتطلع ليه قيمة ال integration
+
+805
+01:00:54,350 --> 01:00:59,070
+أشماله عبارة عن أكبر أو ساهم سفرإذا لو أنا بدأ
+
+806
+01:00:59,070 --> 01:01:06,230
+أقول أن Xm مستحيل تذهب إلى X في الـ space اللي
+
+807
+01:01:06,230 --> 01:01:11,270
+عندي، لو بدأ أقول، أفترض أن Xm تذهب إلى X، يعني
+
+808
+01:01:11,270 --> 01:01:14,430
+المسافة بين هذه وهذه تذهب إلى سفر As M goes to
+
+809
+01:01:14,430 --> 01:01:19,680
+infinity،ماشي، إذاً بدنا نقول suppose that إن
+
+810
+01:01:19,680 --> 01:01:23,640
+distance بين X أما و X تروح لمين للصفر as M goes
+
+811
+01:01:23,640 --> 01:01:28,220
+to infinity لما أم تروح إلى مالة نهاية طبعاً هذا
+
+812
+01:01:28,220 --> 01:01:30,500
+بيصير ال integration كله أم تروح لمن بيصير من نص
+
+813
+01:01:30,500 --> 01:01:33,760
+لنص بيطلع صفر إذاً هذا هيروح للصفر وهذا يروح لمين
+
+814
+01:01:33,760 --> 01:01:37,960
+للصفرهذا ما هو مش مانتومد على M فبصير ال
+
+815
+01:01:37,960 --> 01:01:41,940
+integration X of T من صفر لنص عشان ساقية صفر وهذا
+
+816
+01:01:41,940 --> 01:01:45,320
+بيصير ال integration اللي بيساوي بروح لصفر as M
+
+817
+01:01:45,320 --> 01:01:49,480
+goes to مين To infinity مظبوط وهذا راح يرميه لما
+
+818
+01:01:49,480 --> 01:01:53,640
+الصفر روح مافيش حيطلع علنا اشي واضح اللي بحكيه طيب
+
+819
+01:01:53,640 --> 01:01:59,370
+اطلع لفوق بيصير عندي ال integrationلـ Integration
+
+820
+01:01:59,370 --> 01:02:06,610
+من 0 لعند نص XM of T DT هي سفر والتاني as M goes
+
+821
+01:02:06,610 --> 01:02:10,370
+to infinity هذي بتروح لنص، مظبوط؟ as M goes to
+
+822
+01:02:10,370 --> 01:02:12,990
+infinity بيصير لو حاجة لها سفر، بيصير من نص لعند
+
+823
+01:02:12,990 --> 01:02:17,610
+واحد أش بساوي سفر، بيصير هذا بساوي سفر وهذا بساوي
+
+824
+01:02:17,610 --> 01:02:21,490
+سفرطيب ما احنا بنقول X of T continuous لان هو
+
+825
+01:02:21,490 --> 01:02:23,810
+موجودة في ال space سبعنا ال space of continuous
+
+826
+01:02:23,810 --> 01:02:29,630
+functions اذا هيطلع عندي الآن مدام هذا المقدار سفر
+
+827
+01:02:29,630 --> 01:02:34,530
+وهذه الدالة متصلة اذا غصب عنها هيطلع ال X of T ال
+
+828
+01:02:34,530 --> 01:02:39,170
+integration على دالة متصلة بساوي سفر معناته الدالة
+
+829
+01:02:39,170 --> 01:02:42,550
+ان هو جوا هي في السفرمن أين جاء الله ذاك؟ و هو
+
+830
+01:02:42,550 --> 01:02:45,370
+أكبر و ساوء صفر ما انخلطتش تقولوا الله صار من تحت
+
+831
+01:02:45,370 --> 01:02:48,970
+و من فوق لأ هي فوق و أكبر و ساوء صفر و طلعت عند ال
+
+832
+01:02:48,970 --> 01:02:51,330
+integration انها بساوء صفر فانا هي قد الصفر و مش
+
+833
+01:02:51,330 --> 01:02:55,210
+غيرها فبصير x of t أشفت ساوء صفر و اللي جوا برضه
+
+834
+01:02:55,210 --> 01:02:59,300
+أيش هيساوي؟ برضه هيساوي صفرلأن نفس الاشي هذا أكبر
+
+835
+01:02:59,300 --> 01:03:03,700
+شو سفر و على فترة و المساحة على فترة و هي على أكبر
+
+836
+01:03:03,700 --> 01:03:07,380
+شو سفر فمستحيل اللي يكون اللي جواي شماله عبارة عن
+
+837
+01:03:07,380 --> 01:03:10,520
+سفر لأنه دالنا متصلة و أكبر شو سفر إذا صار عندي
+
+838
+01:03:10,520 --> 01:03:14,500
+هذا سفر معناه تصار x of t بتسوى واحد صارت عندي x
+
+839
+01:03:14,500 --> 01:03:18,360
+of t بتسوى سفر على فترة من سفر لمين لنص و x of t
+
+840
+01:03:18,360 --> 01:03:21,820
+بتسوى واحد على فترة من نص لعند مين لعند واحد صار
+
+841
+01:03:21,820 --> 01:03:26,730
+في عندي jumpهذه الدالة مش متصلة، بتبقى ماشية سفير
+
+842
+01:03:26,730 --> 01:03:29,810
+وبعدين بتنط لعند مين؟ لعند الواحد، لعند المش بتنط،
+
+843
+01:03:29,810 --> 01:03:35,190
+فبتكون هذه is not continuous، إذا لو فرضنا إن
+
+844
+01:03:35,190 --> 01:03:39,610
+المسافة بين Xm و X بتروح للسفر، يعني لو فرضنا Xm
+
+845
+01:03:39,610 --> 01:03:42,490
+بتروح لل X، ال X مش هتكون continuous function،
+
+846
+01:03:42,490 --> 01:03:48,070
+هتكون براة ال X، وبناء عليه no limit in X
+
+847
+01:03:53,790 --> 01:04:02,290
+وهذا يثبت أن الـ space is not complete وبرك الله
+
+848
+01:04:02,290 --> 01:04:03,790
+فيكم الله يعطيكم العافية
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Dna28R7jBBs_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Dna28R7jBBs_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..30ffc0b2356120a16304a91704dffb490794be7b
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Dna28R7jBBs_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2162, "start": 5.62, "end": 21.62, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى آله وصحبه أجمعين هذه هي المحاضرة السادسة مساق تحليل اقتراني أو تحليل دالي طلاب طالبات الجامعة الإسلامية قسم رياضيات مجستير رياضية", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 19753, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 29538, 39896, 9673, 5016, 46958, 25720, 21136, 18513, 3794, 3660, 47524, 995, 4587, 6055, 5016, 20292, 1211, 1975, 38149, 2288, 7649, 1829, 34051, 6055, 5016, 20292, 1211, 11778, 6027, 1829, 23032, 15040, 3555, 23032, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 12174, 38251, 12602, 1829, 46958, 1829, 9307, 3714, 7435, 14851, 13546, 12602, 1829, 46958, 10632], "avg_logprob": -0.1056385901959046, "compression_ratio": 2.0398009950248754, "no_speech_prob": 6.35981559753418e-05, "words": [{"start": 5.62, "end": 5.98, "word": "بسم", "probability": 0.817626953125}, {"start": 5.98, "end": 6.14, "word": " الله", "probability": 0.96044921875}, {"start": 6.14, "end": 6.5, "word": " الرحمن", "probability": 0.96875}, {"start": 6.5, "end": 7.08, "word": " الرحيم", "probability": 0.9938151041666666}, {"start": 7.08, "end": 7.72, "word": " الحمد", "probability": 0.8699544270833334}, {"start": 7.72, "end": 7.96, "word": " لله", "probability": 0.933349609375}, {"start": 7.96, "end": 8.1, "word": " رب", "probability": 0.9267578125}, {"start": 8.1, "end": 8.62, "word": " العالمين", "probability": 0.9957682291666666}, {"start": 8.62, "end": 9.04, "word": " والصلاة", "probability": 0.869140625}, {"start": 9.04, "end": 9.46, "word": " والسلام", "probability": 0.9632161458333334}, {"start": 9.46, "end": 9.7, "word": " على", "probability": 0.33837890625}, {"start": 9.7, "end": 9.96, "word": " سيد", "probability": 0.9658203125}, {"start": 9.96, "end": 10.5, "word": " المرسلين", "probability": 0.95830078125}, {"start": 10.5, "end": 10.86, "word": " سيدنا", "probability": 0.9558919270833334}, {"start": 10.86, "end": 11.24, "word": " محمد", "probability": 0.9850260416666666}, {"start": 11.24, "end": 11.44, "word": " وعلى", "probability": 0.9215494791666666}, {"start": 11.44, "end": 11.74, "word": " آله", "probability": 0.837646484375}, {"start": 11.74, "end": 12.24, "word": " وصحبه", "probability": 0.81533203125}, {"start": 12.24, "end": 12.74, "word": " أجمعين", "probability": 0.8310546875}, {"start": 12.74, "end": 13.52, "word": " هذه", "probability": 0.90673828125}, {"start": 13.52, "end": 13.7, "word": " هي", "probability": 0.53662109375}, {"start": 13.7, "end": 14.18, "word": " المحاضرة", "probability": 0.9903564453125}, {"start": 14.18, "end": 14.76, "word": " السادسة", "probability": 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{"start": 20.5, "end": 21.06, "word": " مجستير", "probability": 0.7196044921875}, {"start": 21.06, "end": 21.62, "word": " رياضية", "probability": 0.9556884765625}], "temperature": 1.0}, {"id": 2, "seek": 3886, "start": 22.67, "end": 38.87, "text": "حكينا احنا عند واحد اربعة وصلنا ونهينا واحد اربعة وقلنا خلينا اللي هو المرة الجاية اللي نحكي عن واحد خمسة اللي هو examples أمثلة على completeness proofs", "tokens": [5016, 4117, 1829, 8315, 1975, 5016, 8315, 43242, 36764, 24401, 1975, 25513, 27884, 4032, 36520, 8315, 4032, 1863, 3224, 1829, 8315, 36764, 24401, 1975, 25513, 27884, 4032, 4587, 1211, 8315, 16490, 1211, 9957, 995, 13672, 1829, 31439, 9673, 25720, 25724, 995, 10632, 13672, 1829, 8717, 5016, 4117, 1829, 18871, 36764, 24401, 16490, 2304, 3794, 3660, 13672, 1829, 31439, 5110, 5551, 2304, 12984, 37977, 15844, 1557, 15264, 8177, 82], "avg_logprob": -0.18840580055679101, "compression_ratio": 1.691275167785235, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 22.67, "end": 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اربعة", "probability": 0.7853190104166666}, {"start": 88.41, "end": 88.57, "word": " اللي", "probability": 0.941162109375}, {"start": 88.57, "end": 89.03, "word": " بدناها", "probability": 0.8175455729166666}], "temperature": 1.0}, {"id": 5, "seek": 11415, "start": 90.43, "end": 114.15, "text": "الان بدنا نعرف عليه اللي هو metric هذا اللي هو الـ Euclidean metric عرفنا عليه هذا متذكرين اللي هو و الـCN برضه نفس الاشي بيصير doubles من الـC نسميه اللي هو Euclidean space RN and Unitary space اللي هو الـCN التانية أشمالين are complete spaces هنبرهن على الـ RN والتانية بالظبط زي اللي هو نفس البرهان", "tokens": [6027, 7649, 47525, 8315, 8717, 3615, 28480, 47356, 13672, 1829, 31439, 20678, 23758, 13672, 1829, 31439, 2423, 39184, 462, 1311, 31264, 282, 20678, 6225, 28480, 8315, 47356, 23758, 44650, 8848, 37983, 9957, 13672, 1829, 31439, 4032, 2423, 39184, 34, 45, 4724, 43042, 3224, 8717, 36178, 2423, 33599, 1829, 4724, 1829, 9381, 13546, 31634, 9154, 2423, 39184, 34, 8717, 38251, 1829, 3224, 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"word": " metric", "probability": 0.430419921875}, {"start": 92.99, "end": 93.33, "word": " هذا", "probability": 0.5400390625}, {"start": 93.33, "end": 93.49, "word": " اللي", "probability": 0.941650390625}, {"start": 93.49, "end": 93.61, "word": " هو", "probability": 0.92333984375}, {"start": 93.61, "end": 93.77, "word": " الـ", "probability": 0.3057861328125}, {"start": 93.77, "end": 94.11, "word": " Euclidean", "probability": 0.79541015625}, {"start": 94.11, "end": 94.37, "word": " metric", "probability": 0.71826171875}, {"start": 94.37, "end": 94.85, "word": " عرفنا", "probability": 0.841796875}, {"start": 94.85, "end": 95.19, "word": " عليه", "probability": 0.98681640625}, {"start": 95.19, "end": 96.13, "word": " هذا", "probability": 0.1417236328125}, {"start": 96.13, "end": 96.91, "word": " متذكرين", "probability": 0.8060302734375}, {"start": 96.91, "end": 97.25, "word": " اللي", "probability": 0.868896484375}, {"start": 97.25, "end": 97.51, "word": " هو", "probability": 0.99169921875}, {"start": 97.51, "end": 97.85, "word": " و", "probability": 0.496826171875}, {"start": 97.85, "end": 98.13, "word": " الـCN", "probability": 0.410247802734375}, {"start": 98.13, "end": 98.39, "word": " برضه", "probability": 0.9248046875}, {"start": 98.39, "end": 98.67, "word": " نفس", "probability": 0.993896484375}, {"start": 98.67, "end": 99.15, "word": " الاشي", "probability": 0.7599283854166666}, {"start": 99.15, "end": 99.85, "word": " بيصير", "probability": 0.8408203125}, {"start": 99.85, "end": 100.25, "word": " doubles", "probability": 0.478759765625}, {"start": 100.25, "end": 100.53, "word": " من", "probability": 0.990234375}, {"start": 100.53, "end": 100.91, "word": " الـC", "probability": 0.8605143229166666}, {"start": 100.91, "end": 102.85, "word": " نسميه", "probability": 0.892578125}, {"start": 102.85, "end": 102.93, "word": " اللي", "probability": 0.826416015625}, {"start": 102.93, "end": 103.05, "word": " هو", "probability": 0.9755859375}, {"start": 103.05, "end": 103.55, "word": " Euclidean", "probability": 0.904052734375}, {"start": 103.55, "end": 103.85, "word": " space", "probability": 0.82763671875}, {"start": 103.85, "end": 104.13, "word": " RN", "probability": 0.689453125}, {"start": 104.13, "end": 104.43, "word": " and", "probability": 0.69580078125}, {"start": 104.43, "end": 104.87, "word": " Unitary", "probability": 0.805419921875}, {"start": 104.87, "end": 105.27, "word": " space", "probability": 0.90283203125}, {"start": 105.27, "end": 105.43, "word": " اللي", "probability": 0.888427734375}, {"start": 105.43, "end": 105.57, "word": " هو", "probability": 0.9736328125}, {"start": 105.57, "end": 106.05, "word": " الـCN", "probability": 0.793701171875}, {"start": 106.05, "end": 106.85, "word": " التانية", "probability": 0.7236328125}, {"start": 106.85, "end": 107.51, "word": " أشمالين", "probability": 0.661572265625}, {"start": 107.51, "end": 107.73, "word": " are", "probability": 0.52294921875}, {"start": 107.73, "end": 108.25, "word": " complete", "probability": 0.89013671875}, {"start": 108.25, "end": 108.85, "word": " spaces", "probability": 0.8603515625}, {"start": 108.85, "end": 110.33, "word": " هنبرهن", "probability": 0.87109375}, {"start": 110.33, "end": 110.55, "word": " على", "probability": 0.876953125}, {"start": 110.55, "end": 110.73, "word": " الـ", "probability": 0.890380859375}, {"start": 110.73, "end": 110.99, "word": " RN", "probability": 0.72412109375}, {"start": 110.99, "end": 111.53, "word": " والتانية", "probability": 0.775390625}, {"start": 111.53, "end": 112.09, "word": " بالظبط", "probability": 0.9713134765625}, {"start": 112.09, "end": 112.47, "word": " زي", "probability": 0.953125}, {"start": 112.47, "end": 112.67, "word": " اللي", "probability": 0.970947265625}, {"start": 112.67, "end": 113.05, "word": " هو", "probability": 0.9892578125}, {"start": 113.05, "end": 113.49, "word": " نفس", "probability": 0.7371826171875}, {"start": 113.49, "end": 114.15, "word": " البرهان", "probability": 0.754150390625}], "temperature": 1.0}, {"id": 6, "seek": 13441, "start": 114.66, "end": 134.42, "text": "الان ايش استراتيجية البرهان اللي هناخدها عشان اثبت انه complete بدي اخد اي كوشي sequence و اثبت ال .. اي كوشي sequence في الارقن و اثبت ال .. و اثبت الهيناي شمالها converge في وين في الارقن مش الحال فالان بدي اخد اي sequence xm", "tokens": [6027, 7649, 1975, 1829, 8592, 44713, 2288, 9307, 1829, 7435, 10632, 2423, 26890, 3224, 7649, 13672, 1829, 8032, 1863, 47283, 3215, 11296, 6225, 8592, 7649, 1975, 12984, 3555, 2655, 16472, 3224, 3566, 4724, 16254, 1975, 9778, 3215, 1975, 1829, 9122, 2407, 8592, 1829, 8310, 4032, 1975, 12984, 3555, 2655, 2423, 4386, 1975, 1829, 9122, 2407, 8592, 1829, 8310, 8978, 2423, 9640, 4587, 1863, 4032, 1975, 12984, 3555, 2655, 2423, 4386, 4032, 1975, 12984, 3555, 2655, 2423, 3224, 1829, 8315, 1829, 13412, 2304, 6027, 11296, 41881, 8978, 4032, 9957, 8978, 2423, 9640, 4587, 1863, 37893, 21542, 6027, 6156, 6027, 7649, 4724, 16254, 1975, 9778, 3215, 1975, 1829, 8310, 2031, 76], "avg_logprob": -0.2928977223959836, "compression_ratio": 1.989071038251366, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 114.66, "end": 115.04, "word": "الان", "probability": 0.687744140625}, {"start": 115.04, "end": 115.84, "word": " ايش", "probability": 0.7023111979166666}, {"start": 115.84, "end": 116.48, "word": " استراتيجية", "probability": 0.8628743489583334}, {"start": 116.48, "end": 116.86, "word": " البرهان", "probability": 0.635986328125}, {"start": 116.86, "end": 116.96, "word": " اللي", "probability": 0.853759765625}, {"start": 116.96, "end": 117.56, "word": " هناخدها", "probability": 0.826171875}, {"start": 117.56, "end": 118.44, "word": " عشان", "probability": 0.8837890625}, {"start": 118.44, "end": 118.8, "word": " اثبت", "probability": 0.9052734375}, {"start": 118.8, "end": 119.04, "word": " انه", "probability": 0.917236328125}, {"start": 119.04, "end": 119.5, "word": " complete", "probability": 0.68603515625}, {"start": 119.5, "end": 120.4, "word": " بدي", "probability": 0.4432373046875}, {"start": 120.4, "end": 120.88, "word": " اخد", "probability": 0.861328125}, {"start": 120.88, "end": 121.36, "word": " اي", "probability": 0.6949462890625}, {"start": 121.36, "end": 121.66, "word": " كوشي", "probability": 0.69171142578125}, {"start": 121.66, "end": 122.26, "word": " sequence", "probability": 0.828125}, {"start": 122.26, "end": 122.84, "word": " و", "probability": 0.448486328125}, {"start": 122.84, "end": 123.12, "word": " اثبت", "probability": 0.8929443359375}, {"start": 123.12, "end": 123.24, "word": " ال", "probability": 0.348876953125}, {"start": 123.24, "end": 123.34, "word": " ..", "probability": 0.367919921875}, {"start": 123.34, "end": 124.0, "word": " اي", "probability": 0.927978515625}, {"start": 124.0, "end": 124.24, "word": " كوشي", "probability": 0.976806640625}, {"start": 124.24, "end": 124.6, "word": " sequence", "probability": 0.984375}, {"start": 124.6, "end": 124.74, "word": " في", "probability": 0.8896484375}, {"start": 124.74, "end": 125.14, "word": " الارقن", "probability": 0.64678955078125}, {"start": 125.14, "end": 125.58, "word": " و", "probability": 0.943359375}, {"start": 125.58, "end": 125.82, "word": " اثبت", "probability": 0.9332275390625}, {"start": 125.82, "end": 125.96, "word": " ال", "probability": 0.51318359375}, {"start": 125.96, "end": 126.02, "word": " ..", "probability": 0.64208984375}, {"start": 126.02, "end": 126.22, "word": " و", "probability": 0.69677734375}, {"start": 126.22, "end": 126.46, "word": " اثبت", "probability": 0.93798828125}, {"start": 126.46, "end": 126.92, "word": " الهيناي", "probability": 0.53427734375}, {"start": 126.92, "end": 127.38, "word": " شمالها", "probability": 0.83282470703125}, {"start": 127.38, "end": 128.06, "word": " converge", "probability": 0.33740234375}, {"start": 128.06, "end": 128.6, "word": " في", "probability": 0.85107421875}, {"start": 128.6, "end": 129.0, "word": " وين", "probability": 0.8251953125}, {"start": 129.0, "end": 129.2, "word": " في", "probability": 0.86279296875}, {"start": 129.2, "end": 129.74, "word": " الارقن", "probability": 0.980712890625}, {"start": 129.74, "end": 130.26, "word": " مش", "probability": 0.12744140625}, {"start": 130.26, "end": 130.62, "word": " الحال", "probability": 0.875244140625}, {"start": 130.62, "end": 131.34, "word": " فالان", "probability": 0.87744140625}, {"start": 131.34, "end": 131.58, "word": " بدي", "probability": 0.94873046875}, {"start": 131.58, "end": 131.94, "word": " اخد", "probability": 0.94482421875}, {"start": 131.94, "end": 132.4, "word": " اي", "probability": 0.915771484375}, {"start": 132.4, "end": 133.74, "word": " sequence", "probability": 0.9873046875}, {"start": 133.74, "end": 134.42, "word": " xm", "probability": 0.591552734375}], "temperature": 1.0}, {"id": 7, "seek": 15562, "start": 135.22, "end": 155.62, "text": "تكون كوشي ون موجودة في الـ RN مدام X يعني بمعنى آخر X1 و X2 و X3 و X4 و X5 إلى ما لنهاية عبارة عن عناصر من وين ماخدها أنا من الـ RN والـ XN هذه أشمالها كوشي sequence خلّينا نتطلع على عناصرها X1 مثلا هي عبارة عن Xi 11", "tokens": [2655, 30544, 9122, 2407, 8592, 1829, 4032, 1863, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 45702, 3714, 3215, 10943, 1783, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 19753, 34740, 1783, 16, 4032, 1783, 17, 4032, 1783, 18, 4032, 1783, 19, 4032, 1783, 20, 30731, 19446, 5296, 1863, 11296, 10632, 6225, 3555, 9640, 3660, 18871, 18871, 33546, 2288, 9154, 4032, 9957, 3714, 47283, 3215, 11296, 41850, 9154, 2423, 39184, 45702, 16070, 39184, 1783, 45, 29538, 5551, 8592, 2304, 6027, 11296, 9122, 2407, 8592, 1829, 8310, 16490, 1211, 11703, 9957, 995, 8717, 2655, 9566, 1211, 3615, 15844, 18871, 33546, 2288, 11296, 1783, 16, 50113, 15040, 39896, 6225, 3555, 9640, 3660, 18871, 15712, 2975], "avg_logprob": -0.23660714950944697, "compression_ratio": 1.6401869158878504, "no_speech_prob": 2.6345252990722656e-05, "words": [{"start": 135.22, "end": 135.74, "word": 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{"start": 140.68, "end": 140.8, "word": " و", "probability": 0.9072265625}, {"start": 140.8, "end": 141.26, "word": " X2", "probability": 0.83935546875}, {"start": 141.26, "end": 141.4, "word": " و", "probability": 0.9833984375}, {"start": 141.4, "end": 141.86, "word": " X3", "probability": 0.95458984375}, {"start": 141.86, "end": 142.0, "word": " و", "probability": 0.974609375}, {"start": 142.0, "end": 142.42, "word": " X4", "probability": 0.95654296875}, {"start": 142.42, "end": 142.54, "word": " و", "probability": 0.98046875}, {"start": 142.54, "end": 142.96, "word": " X5", "probability": 0.961669921875}, {"start": 142.96, "end": 143.2, "word": " إلى", "probability": 0.734375}, {"start": 143.2, "end": 143.34, "word": " ما", "probability": 0.1573486328125}, {"start": 143.34, "end": 143.94, "word": " لنهاية", "probability": 0.8153076171875}, {"start": 143.94, "end": 144.7, "word": " عبارة", "probability": 0.9937744140625}, {"start": 144.7, "end": 144.92, "word": " عن", "probability": 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149.68, "word": " كوشي", "probability": 0.9393310546875}, {"start": 149.68, "end": 150.22, "word": " sequence", "probability": 0.81298828125}, {"start": 150.22, "end": 150.98, "word": " خلّينا", "probability": 0.82841796875}, {"start": 150.98, "end": 151.44, "word": " نتطلع", "probability": 0.8734375}, {"start": 151.44, "end": 151.58, "word": " على", "probability": 0.908203125}, {"start": 151.58, "end": 152.22, "word": " عناصرها", "probability": 0.9720458984375}, {"start": 152.22, "end": 153.04, "word": " X1", "probability": 0.8330078125}, {"start": 153.04, "end": 153.58, "word": " مثلا", "probability": 0.9638671875}, {"start": 153.58, "end": 154.14, "word": " هي", "probability": 0.80517578125}, {"start": 154.14, "end": 154.54, "word": " عبارة", "probability": 0.99755859375}, {"start": 154.54, "end": 154.7, "word": " عن", "probability": 0.9794921875}, {"start": 154.7, "end": 155.02, "word": " Xi", "probability": 0.43798828125}, {"start": 155.02, "end": 155.62, "word": " 11", 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328.89, "word": " Y", "probability": 0.360595703125}], "temperature": 1.0}, {"id": 16, "seek": 35820, "start": 329.68, "end": 358.2, "text": "لاحظوا التالي، الآن أنا بدي أحول استراتيجية حلّي بدي أحول الحديث إلى من اللي هي قوشي sequences في الـRN إلى قوشي sequences في الـR وانا بعرف سابقا أن الـR يشمالها is complete ركزوا كيف بدي أعملها، الان بما أن المجموح هذا كله أصغر من Epsilon إذا أكيد اللي هو كل واحدة منهم، كل واحدة من هذه تربية أصغر من الصممش انت راحها", "tokens": [15040, 5016, 19913, 14407, 16712, 6027, 1829, 12399, 6024, 48506, 41850, 4724, 16254, 5551, 5016, 12610, 44713, 2288, 9307, 1829, 7435, 10632, 11331, 1211, 11703, 1829, 4724, 16254, 5551, 5016, 12610, 21542, 16254, 12984, 30731, 9154, 13672, 1829, 39896, 12174, 2407, 8592, 1829, 22978, 8978, 2423, 39184, 49, 45, 30731, 12174, 2407, 8592, 1829, 22978, 8978, 2423, 39184, 49, 4032, 7649, 995, 45030, 28480, 8608, 16758, 4587, 995, 14739, 2423, 39184, 49, 7251, 8592, 2304, 6027, 11296, 307, 3566, 12602, 4117, 11622, 14407, 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350.3, "end": 350.6, "word": " أصغر", "probability": 0.992919921875}, {"start": 350.6, "end": 350.74, "word": " من", "probability": 0.99365234375}, {"start": 350.74, "end": 351.28, "word": " Epsilon", "probability": 0.463165283203125}, {"start": 351.28, "end": 352.56, "word": " إذا", "probability": 0.7041015625}, {"start": 352.56, "end": 353.22, "word": " أكيد", "probability": 0.9456380208333334}, {"start": 353.22, "end": 353.44, "word": " اللي", "probability": 0.938232421875}, {"start": 353.44, "end": 353.68, "word": " هو", "probability": 0.98681640625}, {"start": 353.68, "end": 354.0, "word": " كل", "probability": 0.9775390625}, {"start": 354.0, "end": 354.46, "word": " واحدة", "probability": 0.9625651041666666}, {"start": 354.46, "end": 355.58, "word": " منهم،", "probability": 0.7731119791666666}, {"start": 355.58, "end": 355.74, "word": " كل", "probability": 0.923828125}, {"start": 355.74, "end": 356.04, "word": " واحدة", "probability": 0.9930013020833334}, {"start": 356.04, "end": 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0.94580078125}, {"start": 412.96, "end": 413.44, "word": " sequence", "probability": 0.97509765625}, {"start": 413.44, "end": 413.9, "word": " الآن", "probability": 0.57916259765625}, {"start": 413.9, "end": 414.16, "word": " إيش", "probability": 0.7926432291666666}, {"start": 414.16, "end": 414.64, "word": " أثبتت", "probability": 0.95498046875}, {"start": 414.64, "end": 414.82, "word": " أنا", "probability": 0.78173828125}, {"start": 414.82, "end": 415.24, "word": " إلها", "probability": 0.6796875}, {"start": 415.24, "end": 415.92, "word": " إن", "probability": 0.4140625}, {"start": 415.92, "end": 416.26, "word": " xi", "probability": 0.89208984375}, {"start": 416.26, "end": 416.98, "word": " i", "probability": 0.6630859375}, {"start": 416.98, "end": 417.42, "word": " m", "probability": 0.87255859375}, {"start": 417.42, "end": 417.8, "word": " ناقص", "probability": 0.7542724609375}, {"start": 417.8, "end": 418.12, "word": " xi", "probability": 0.9580078125}, {"start": 418.12, "end": 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دلان", "probability": 0.7744140625}, {"start": 437.62, "end": 438.18, "word": " the", "probability": 0.48681640625}, {"start": 438.18, "end": 438.9, "word": " sequence", "probability": 0.97314453125}, {"start": 438.9, "end": 439.22, "word": " xi", "probability": 0.399169921875}, {"start": 439.22, "end": 439.6, "word": " I", "probability": 0.5244140625}, {"start": 439.6, "end": 439.94, "word": " واحد", "probability": 0.6846923828125}, {"start": 439.94, "end": 440.16, "word": " xi", "probability": 0.56591796875}, {"start": 440.16, "end": 440.5, "word": " I", "probability": 0.98046875}, {"start": 440.5, "end": 441.02, "word": " اتنين", "probability": 0.93017578125}, {"start": 441.02, "end": 441.56, "word": " إلى", "probability": 0.92431640625}, {"start": 441.56, "end": 441.84, "word": " ما", "probability": 0.5224609375}, {"start": 441.84, "end": 442.42, "word": " لنهاية", "probability": 0.8719482421875}, {"start": 442.42, "end": 442.92, "word": " هيها", "probability": 0.746826171875}, {"start": 442.92, "end": 443.54, "word": " xi", "probability": 0.9111328125}, {"start": 443.54, "end": 443.84, "word": " I", "probability": 0.986328125}, {"start": 443.84, "end": 444.1, "word": " واحد", "probability": 0.90673828125}, {"start": 444.1, "end": 444.28, "word": " xi", "probability": 0.87939453125}, {"start": 444.28, "end": 444.56, "word": " I", "probability": 0.99462890625}, {"start": 444.56, "end": 444.84, "word": " اتنين", "probability": 0.9635009765625}, {"start": 444.84, "end": 445.04, "word": " xi", "probability": 0.68408203125}, {"start": 445.04, "end": 445.26, "word": " I", "probability": 0.9951171875}, {"start": 445.26, "end": 445.7, "word": " تلتة", "probability": 0.7774658203125}, {"start": 445.7, "end": 445.88, "word": " إلى", "probability": 0.96142578125}, {"start": 445.88, "end": 446.06, "word": " ما", "probability": 0.94482421875}, {"start": 446.06, "end": 446.46, "word": " لنهاية", "probability": 0.908447265625}], "temperature": 1.0}, {"id": 21, "seek": 46649, "start": 447.69, "end": 466.49, "text": "converges لما صارت ايش ما لها كوشي sequence of real numbers then it converges خلّيني أقول converges ده مين لـXi I إذا صار عندي الآن كل البرهين لها نفس الروح فركزوا كويس عشان نرتاح في اللي بعدها", "tokens": [1671, 331, 2880, 5296, 15042, 20328, 9640, 2655, 1975, 1829, 8592, 19446, 5296, 11296, 9122, 2407, 8592, 1829, 8310, 295, 957, 3547, 550, 309, 9652, 2880, 16490, 1211, 11703, 9957, 1829, 5551, 39648, 416, 331, 2880, 11778, 3224, 3714, 9957, 5296, 39184, 41577, 286, 11933, 15730, 20328, 9640, 43242, 1829, 6024, 48506, 28242, 2423, 26890, 3224, 9957, 5296, 11296, 8717, 36178, 2423, 32887, 5016, 6156, 31747, 11622, 14407, 9122, 45865, 3794, 6225, 8592, 7649, 8717, 43500, 39319, 8978, 13672, 1829, 39182, 11296], "avg_logprob": -0.38403613165200473, "compression_ratio": 1.4723618090452262, "no_speech_prob": 1.3589859008789062e-05, "words": [{"start": 447.69, "end": 448.53, "word": "converges", "probability": 0.5587158203125}, {"start": 448.53, "end": 448.93, "word": " لما", "probability": 0.525634765625}, {"start": 448.93, "end": 449.31, "word": " صارت", "probability": 0.7760416666666666}, {"start": 449.31, "end": 449.49, "word": " ايش", "probability": 0.5431315104166666}, {"start": 449.49, "end": 449.63, "word": " ما", "probability": 0.43505859375}, {"start": 449.63, "end": 450.05, "word": " لها", "probability": 0.734130859375}, {"start": 450.05, "end": 450.85, "word": " كوشي", "probability": 0.79742431640625}, {"start": 450.85, "end": 451.75, "word": " sequence", "probability": 0.7333984375}, {"start": 451.75, "end": 451.99, "word": " of", "probability": 0.91357421875}, {"start": 451.99, "end": 452.25, "word": " real", "probability": 0.93896484375}, {"start": 452.25, "end": 452.73, "word": " numbers", "probability": 0.71923828125}, {"start": 452.73, "end": 453.03, "word": " then", "probability": 0.56787109375}, {"start": 453.03, "end": 453.23, "word": " it", "probability": 0.93359375}, {"start": 453.23, "end": 453.89, "word": " converges", "probability": 0.7138671875}, {"start": 453.89, "end": 454.49, "word": " خلّيني", "probability": 0.8388671875}, {"start": 454.49, "end": 454.73, "word": " أقول", "probability": 0.705322265625}, {"start": 454.73, "end": 455.15, "word": " converges", "probability": 0.6023356119791666}, {"start": 455.15, "end": 455.33, "word": " ده", "probability": 0.62451171875}, {"start": 455.33, "end": 455.73, "word": " مين", "probability": 0.7186279296875}, {"start": 455.73, "end": 456.77, "word": " لـXi", "probability": 0.3375244140625}, {"start": 456.77, "end": 457.49, "word": " I", "probability": 0.59326171875}, {"start": 457.49, "end": 458.05, "word": " إذا", "probability": 0.73193359375}, {"start": 458.05, "end": 458.45, "word": " صار", "probability": 0.95849609375}, {"start": 458.45, "end": 458.91, "word": " عندي", "probability": 0.634765625}, {"start": 458.91, "end": 459.49, "word": " الآن", "probability": 0.718017578125}, {"start": 459.49, "end": 461.19, "word": " كل", "probability": 0.10247802734375}, {"start": 461.19, "end": 461.85, "word": " البرهين", "probability": 0.7275390625}, {"start": 461.85, "end": 463.39, "word": " لها", "probability": 0.59747314453125}, {"start": 463.39, "end": 463.63, "word": " نفس", "probability": 0.991455078125}, {"start": 463.63, "end": 464.09, "word": " الروح", "probability": 0.9290364583333334}, {"start": 464.09, "end": 464.95, "word": " فركزوا", "probability": 0.8970947265625}, {"start": 464.95, "end": 465.21, "word": " كويس", "probability": 0.9446614583333334}, {"start": 465.21, "end": 465.49, "word": " عشان", "probability": 0.9181315104166666}, {"start": 465.49, "end": 465.83, "word": " نرتاح", "probability": 0.9070638020833334}, {"start": 465.83, "end": 465.95, "word": " في", "probability": 0.857421875}, {"start": 465.95, "end": 466.05, "word": " اللي", "probability": 0.965087890625}, {"start": 466.05, "end": 466.49, "word": " بعدها", "probability": 0.73828125}], "temperature": 1.0}, {"id": 22, "seek": 48738, "start": 467.74, "end": 487.38, "text": "صارت عندي الآن الـ sequence XII M converged domain قلنا يعني خلّيت هذا الـ sequence شايفين هذا XII قلنا هذا as M goes to infinity .. as I goes to infinity .. as M goes to infinity هذه بدت تروح لمين؟ للـ XII سميت XII يعني وكأني أخدت هذه الـ sequence", "tokens": [9381, 9640, 2655, 18871, 16254, 6024, 48506, 2423, 39184, 8310, 1783, 40, 40, 376, 9652, 3004, 9274, 12174, 1211, 8315, 37495, 22653, 16490, 1211, 11703, 36081, 23758, 2423, 39184, 8310, 13412, 995, 33911, 9957, 23758, 1783, 40, 40, 12174, 1211, 8315, 23758, 382, 376, 1709, 281, 13202, 4386, 382, 286, 1709, 281, 13202, 4386, 382, 376, 1709, 281, 13202, 29538, 47525, 2655, 6055, 32887, 5016, 32767, 9957, 22807, 24976, 39184, 1783, 40, 40, 8608, 2304, 36081, 1783, 40, 40, 37495, 22653, 4032, 4117, 33456, 1829, 5551, 9778, 3215, 2655, 29538, 2423, 39184, 8310], "avg_logprob": -0.3563829926734275, "compression_ratio": 1.6782178217821782, "no_speech_prob": 3.516674041748047e-06, 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completeness لمن؟ لـ L infinity و L completeness اللي بعد ما هي اختلافات بسيطة تناسب ال space اللي موجود عندنا الان completeness of L infinity L infinity عارفين انتوا هو the space of bounded sequences اللي هي the space L infinity is complete كله under the metric اللي احنا خدناه الآن عندي", "tokens": [5172, 995, 16095, 20328, 1211, 14407, 6225, 8315, 20666, 20292, 19446, 12602, 4117, 11622, 8592, 20449, 995, 25528, 34105, 8032, 1863, 3615, 25708, 6055, 4587, 16572, 3555, 995, 28242, 10943, 37893, 16758, 3224, 8978, 11933, 12984, 3555, 9307, 2423, 39184, 1557, 15264, 5296, 27842, 22807, 5296, 39184, 441, 13202, 4032, 441, 1557, 15264, 13672, 1829, 39182, 19446, 39896, 1975, 46456, 15040, 5172, 9307, 4724, 3794, 1829, 9566, 3660, 6055, 8315, 35457, 2423, 1901, 13672, 1829, 3714, 29245, 23328, 43242, 8315, 2423, 7649, 1557, 15264, 295, 441, 13202, 441, 13202, 6225, 9640, 5172, 9957, 16472, 2655, 14407, 31439, 264, 1901, 295, 37498, 22978, 13672, 1829, 39896, 264, 1901, 441, 13202, 307, 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700.91, "word": " اكسهاي", "probability": 0.725732421875}, {"start": 700.91, "end": 701.19, "word": " واحد", "probability": 0.962646484375}, {"start": 701.19, "end": 701.41, "word": " ام", "probability": 0.96923828125}, {"start": 701.41, "end": 701.79, "word": " اكسهاي", "probability": 0.89912109375}, {"start": 701.79, "end": 702.01, "word": " اتنين", "probability": 0.9688720703125}, {"start": 702.01, "end": 702.23, "word": " ام", "probability": 0.954345703125}, {"start": 702.23, "end": 702.43, "word": " إلى", "probability": 0.6142578125}, {"start": 702.43, "end": 702.57, "word": " ما", "probability": 0.68994140625}, {"start": 702.57, "end": 703.01, "word": " لنهاية", "probability": 0.617431640625}], "temperature": 1.0}, {"id": 33, "seek": 72206, "start": 703.38, "end": 722.06, "text": "لأن شكل العنصر في الـ L-Infinity Sequence لما نقول X1 بساوي XI 1 1 XI 2 1 XI 3 1 ده جافش لعند الـ Un بتضلها إشنانها لأنها دي مش Untables اللي هي عناصرها الـ L-Infinity عناصرها عبارة عن Sequences", "tokens": [1211, 33456, 13412, 28820, 18863, 1863, 9381, 2288, 8978, 2423, 39184, 441, 12, 4575, 5194, 507, 46859, 655, 5296, 15042, 8717, 39648, 1783, 16, 4724, 3794, 995, 45865, 1783, 40, 502, 502, 1783, 40, 568, 502, 1783, 40, 805, 502, 11778, 3224, 10874, 31845, 8592, 5296, 3615, 41260, 2423, 39184, 1156, 39894, 11242, 1211, 11296, 11933, 8592, 1863, 7649, 11296, 5296, 33456, 11296, 11778, 1829, 37893, 8256, 2965, 13672, 1829, 39896, 18871, 33546, 2288, 11296, 2423, 39184, 441, 12, 4575, 5194, 507, 18871, 33546, 2288, 11296, 6225, 3555, 9640, 3660, 18871, 46859, 2667], "avg_logprob": -0.2790891096947041, "compression_ratio": 1.5157894736842106, "no_speech_prob": 4.76837158203125e-06, "words": [{"start": 703.38, "end": 703.8, "word": "لأن", "probability": 0.790283203125}, {"start": 703.8, "end": 704.24, "word": " شكل", "probability": 0.953369140625}, {"start": 704.24, "end": 704.74, "word": " العنصر", "probability": 0.9627685546875}, {"start": 704.74, "end": 704.86, "word": " في", "probability": 0.658203125}, {"start": 704.86, "end": 704.96, "word": " الـ", "probability": 0.85205078125}, {"start": 704.96, "end": 705.06, "word": " L", "probability": 0.4765625}, {"start": 705.06, "end": 705.4, "word": "-Infinity", "probability": 0.605743408203125}, {"start": 705.4, "end": 706.06, "word": " Sequence", "probability": 0.6673583984375}, {"start": 706.06, "end": 706.68, "word": " لما", "probability": 0.77587890625}, {"start": 706.68, "end": 706.94, "word": " نقول", "probability": 0.9853515625}, {"start": 706.94, "end": 707.96, "word": " X1", "probability": 0.5279541015625}, {"start": 707.96, "end": 708.68, "word": " بساوي", "probability": 0.6578369140625}, {"start": 708.68, "end": 709.5, "word": " XI", "probability": 0.6065673828125}, {"start": 709.5, "end": 709.96, "word": " 1", "probability": 0.1536865234375}, {"start": 709.96, "end": 710.38, "word": " 1", "probability": 0.311767578125}, {"start": 710.38, "end": 711.52, "word": " XI", "probability": 0.808837890625}, {"start": 711.52, "end": 711.86, "word": " 2", "probability": 0.955078125}, {"start": 711.86, "end": 712.42, "word": " 1", "probability": 0.99267578125}, {"start": 712.42, "end": 713.26, "word": " XI", "probability": 0.975341796875}, {"start": 713.26, "end": 713.62, "word": " 3", "probability": 0.95654296875}, {"start": 713.62, "end": 714.12, "word": " 1", "probability": 0.99658203125}, {"start": 714.12, "end": 714.52, "word": " ده", "probability": 0.4532470703125}, {"start": 714.52, "end": 714.88, "word": " جافش", "probability": 0.7449544270833334}, {"start": 714.88, "end": 715.22, "word": " لعند", "probability": 0.7718098958333334}, {"start": 715.22, "end": 715.42, "word": " الـ", "probability": 0.854248046875}, {"start": 715.42, "end": 715.58, "word": " Un", "probability": 0.270751953125}, {"start": 715.58, "end": 716.18, "word": " بتضلها", "probability": 0.6439208984375}, {"start": 716.18, "end": 716.9, "word": " إشنانها", "probability": 0.815478515625}, {"start": 716.9, "end": 717.84, "word": " لأنها", "probability": 0.6533203125}, {"start": 717.84, "end": 717.94, "word": " دي", "probability": 0.75439453125}, {"start": 717.94, "end": 718.06, "word": " مش", "probability": 0.99560546875}, {"start": 718.06, "end": 718.56, "word": " Untables", "probability": 0.815185546875}, {"start": 718.56, "end": 718.8, "word": " اللي", "probability": 0.967041015625}, {"start": 718.8, "end": 718.94, "word": " هي", "probability": 0.89404296875}, {"start": 718.94, "end": 719.38, "word": " عناصرها", "probability": 0.8345947265625}, {"start": 719.38, "end": 719.5, "word": " الـ", "probability": 0.828369140625}, {"start": 719.5, "end": 719.6, "word": " L", "probability": 0.90576171875}, {"start": 719.6, "end": 720.0, "word": "-Infinity", "probability": 0.9427490234375}, {"start": 720.0, "end": 720.52, "word": " عناصرها", "probability": 0.9034423828125}, {"start": 720.52, "end": 720.92, "word": " عبارة", "probability": 0.988525390625}, {"start": 720.92, "end": 721.18, "word": " عن", "probability": 0.9970703125}, {"start": 721.18, "end": 722.06, "word": " Sequences", "probability": 0.9189453125}], "temperature": 1.0}, {"id": 34, "seek": 74689, "start": 722.89, "end": 746.89, "text": "و X2 نفس الاشي بيساوي XI واحد اتنين XI اتنين اتنين إلى مال نهاية و نفس الاشي XM in general بيساوي XI واحد M XI اتنين M إلى مال نهاية و عندك XR برضه نفس الاشي و بيضلوا إلى مال نهاية XI واحد R XI اتنين R إلى مال نهاية", "tokens": [2407, 1783, 17, 8717, 36178, 2423, 33599, 1829, 4724, 1829, 3794, 995, 45865, 1783, 40, 36764, 24401, 1975, 2655, 1863, 9957, 1783, 40, 1975, 2655, 1863, 9957, 1975, 2655, 1863, 9957, 30731, 3714, 6027, 8717, 11296, 10632, 4032, 8717, 36178, 2423, 33599, 1829, 1783, 44, 294, 2674, 4724, 1829, 3794, 995, 45865, 1783, 40, 36764, 24401, 376, 1783, 40, 1975, 2655, 1863, 9957, 376, 30731, 3714, 6027, 8717, 11296, 10632, 4032, 43242, 4117, 1783, 49, 4724, 43042, 3224, 8717, 36178, 2423, 33599, 1829, 4032, 4724, 1829, 11242, 1211, 14407, 30731, 3714, 6027, 8717, 11296, 10632, 1783, 40, 36764, 24401, 497, 1783, 40, 1975, 2655, 1863, 9957, 497, 30731, 3714, 6027, 8717, 11296, 10632], "avg_logprob": -0.11225328738229316, "compression_ratio": 2.3026315789473686, "no_speech_prob": 2.562999725341797e-06, "words": [{"start": 722.89, "end": 723.19, "word": "و", "probability": 0.77001953125}, {"start": 723.19, "end": 723.73, "word": " X2", "probability": 0.72314453125}, {"start": 723.73, "end": 724.13, "word": " نفس", "probability": 0.970703125}, {"start": 724.13, "end": 724.69, "word": " الاشي", "probability": 0.7871907552083334}, {"start": 724.69, "end": 725.37, "word": " بيساوي", "probability": 0.79306640625}, {"start": 725.37, "end": 725.77, "word": " XI", "probability": 0.62841796875}, {"start": 725.77, "end": 726.29, "word": " واحد", "probability": 0.5821533203125}, {"start": 726.29, "end": 726.79, "word": " اتنين", "probability": 0.955322265625}, {"start": 726.79, "end": 727.73, "word": " XI", "probability": 0.79296875}, {"start": 727.73, "end": 728.17, "word": " اتنين", "probability": 0.8961181640625}, {"start": 728.17, "end": 728.71, "word": " اتنين", "probability": 0.9886474609375}, {"start": 728.71, "end": 729.29, "word": " إلى", "probability": 0.55712890625}, {"start": 729.29, "end": 729.55, "word": " مال", "probability": 0.802734375}, {"start": 729.55, "end": 730.01, "word": " نهاية", "probability": 0.8455403645833334}, {"start": 730.01, "end": 730.47, "word": " و", "probability": 0.9404296875}, {"start": 730.47, "end": 730.73, "word": " نفس", "probability": 0.932373046875}, {"start": 730.73, "end": 731.13, "word": " الاشي", "probability": 0.94970703125}, {"start": 731.13, "end": 731.79, "word": " XM", "probability": 0.940185546875}, {"start": 731.79, "end": 732.11, "word": " in", "probability": 0.95068359375}, {"start": 732.11, "end": 732.65, "word": " general", "probability": 0.90185546875}, {"start": 732.65, "end": 733.05, "word": " بيساوي", "probability": 0.9837890625}, {"start": 733.05, "end": 733.41, "word": " XI", "probability": 0.977294921875}, {"start": 733.41, "end": 733.87, "word": " واحد", "probability": 0.990966796875}, {"start": 733.87, "end": 734.45, "word": " M", "probability": 0.82080078125}, {"start": 734.45, "end": 735.53, "word": " XI", "probability": 0.96875}, {"start": 735.53, "end": 735.99, "word": " اتنين", "probability": 0.9825439453125}, {"start": 735.99, "end": 736.41, "word": " M", "probability": 0.99560546875}, {"start": 736.41, "end": 737.33, "word": " إلى", "probability": 0.93994140625}, {"start": 737.33, "end": 737.59, "word": " مال", "probability": 0.846923828125}, {"start": 737.59, "end": 738.11, "word": " نهاية", "probability": 0.9620768229166666}, {"start": 738.11, "end": 738.77, "word": " و", "probability": 0.98291015625}, {"start": 738.77, "end": 739.17, "word": " عندك", "probability": 0.938232421875}, {"start": 739.17, "end": 739.97, "word": " XR", "probability": 0.9814453125}, {"start": 739.97, "end": 740.31, "word": " برضه", "probability": 0.95361328125}, {"start": 740.31, "end": 740.57, "word": " نفس", "probability": 0.996337890625}, {"start": 740.57, "end": 741.53, "word": " الاشي", "probability": 0.9622395833333334}, {"start": 741.53, "end": 741.87, "word": " و", "probability": 0.8427734375}, {"start": 741.87, "end": 742.21, "word": " بيضلوا", "probability": 0.84921875}, {"start": 742.21, "end": 742.35, "word": " إلى", "probability": 0.98583984375}, {"start": 742.35, "end": 742.53, "word": " مال", "probability": 0.814208984375}, {"start": 742.53, "end": 742.87, "word": " نهاية", "probability": 0.9358723958333334}, {"start": 742.87, "end": 743.23, "word": " XI", "probability": 0.979736328125}, {"start": 743.23, "end": 743.57, "word": " واحد", "probability": 0.96923828125}, {"start": 743.57, "end": 744.07, "word": " R", "probability": 0.98681640625}, {"start": 744.07, "end": 744.85, "word": " XI", "probability": 0.98046875}, {"start": 744.85, "end": 745.21, "word": " اتنين", "probability": 0.9864501953125}, {"start": 745.21, "end": 745.67, "word": " R", "probability": 0.99462890625}, {"start": 745.67, "end": 746.29, "word": " إلى", "probability": 0.96337890625}, {"start": 746.29, "end": 746.53, "word": " مال", "probability": 0.84912109375}, {"start": 746.53, "end": 746.89, "word": " نهاية", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 35, "seek": 75541, "start": 747.29, "end": 755.41, "text": "واضح إذا هذه اللي هي الـ Cauchy Sequence اللي بدي أخدها بدي أقول let Xm be any Cauchy Sequence in N infinity where Xm بتساوي كده", "tokens": [2407, 46958, 5016, 11933, 15730, 29538, 13672, 1829, 39896, 2423, 39184, 7544, 625, 88, 46859, 655, 13672, 1829, 4724, 16254, 5551, 9778, 3215, 11296, 4724, 16254, 5551, 39648, 718, 1783, 76, 312, 604, 7544, 625, 88, 46859, 655, 294, 426, 13202, 689, 1783, 76, 39894, 3794, 995, 45865, 9122, 3215, 3224], "avg_logprob": -0.3094952049163672, "compression_ratio": 1.286764705882353, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 747.29, "end": 747.81, "word": "واضح", "probability": 0.87646484375}, {"start": 747.81, "end": 748.11, "word": " إذا", "probability": 0.441070556640625}, {"start": 748.11, "end": 748.49, "word": " هذه", "probability": 0.7763671875}, {"start": 748.49, "end": 748.65, "word": " اللي", "probability": 0.816650390625}, {"start": 748.65, "end": 749.01, "word": " هي", "probability": 0.9541015625}, {"start": 749.01, "end": 749.29, "word": " الـ", "probability": 0.801513671875}, {"start": 749.29, "end": 749.55, "word": " Cauchy", "probability": 0.9287109375}, {"start": 749.55, "end": 749.97, "word": " Sequence", "probability": 0.669677734375}, {"start": 749.97, "end": 750.13, "word": " اللي", "probability": 0.964111328125}, {"start": 750.13, "end": 750.25, "word": " بدي", "probability": 0.3802490234375}, {"start": 750.25, "end": 750.61, "word": " أخدها", "probability": 0.92041015625}, {"start": 750.61, "end": 751.31, "word": " بدي", "probability": 0.719970703125}, {"start": 751.31, "end": 751.63, "word": " أقول", "probability": 0.956787109375}, {"start": 751.63, "end": 751.85, "word": " let", "probability": 0.45849609375}, {"start": 751.85, "end": 752.33, "word": " Xm", "probability": 0.4886474609375}, {"start": 752.33, "end": 752.47, "word": " be", "probability": 0.326416015625}, {"start": 752.47, "end": 752.69, "word": " any", "probability": 0.919921875}, {"start": 752.69, "end": 753.07, "word": " Cauchy", "probability": 0.9646809895833334}, {"start": 753.07, "end": 753.49, "word": " Sequence", "probability": 0.975341796875}, {"start": 753.49, "end": 753.65, "word": " in", "probability": 0.794921875}, {"start": 753.65, "end": 753.79, "word": " N", "probability": 0.424560546875}, {"start": 753.79, "end": 754.13, "word": " infinity", "probability": 0.457275390625}, {"start": 754.13, "end": 754.41, "word": " where", "probability": 0.634765625}, {"start": 754.41, "end": 754.77, "word": " Xm", "probability": 0.975830078125}, {"start": 754.77, "end": 755.09, "word": " بتساوي", "probability": 0.795654296875}, {"start": 755.09, "end": 755.41, "word": " كده", "probability": 0.8590494791666666}], "temperature": 1.0}, {"id": 36, "seek": 78447, "start": 756.59, "end": 784.47, "text": "ذنب من تعريف الـ Cauchy sequence إيش بيكون for every Y أكبر من 0 there exists K element in N such that المسافة بين X و M و XR أصغر من Y لكل N و M إيه شمالها أكبر من K هذا التعريف العام للـ Cauchy sequence طيب المسافة في هذا ال space اللي هي ال infinity بين XM و XR اللي هو عبارة عن ال supremum للأبعاد XI واحد مقص XI واحد اللهان XI اتنين اللهان مقص XI اتنين اللهان", "tokens": [8848, 1863, 3555, 9154, 37279, 16572, 5172, 2423, 39184, 7544, 625, 88, 8310, 11933, 1829, 8592, 4724, 1829, 30544, 337, 633, 398, 5551, 4117, 26890, 9154, 1958, 456, 8198, 591, 4478, 294, 426, 1270, 300, 9673, 3794, 31845, 3660, 49374, 1783, 4032, 376, 4032, 1783, 49, 5551, 9381, 17082, 2288, 9154, 398, 5296, 28820, 426, 4032, 376, 11933, 1829, 3224, 13412, 2304, 6027, 11296, 5551, 4117, 26890, 9154, 591, 23758, 16712, 3615, 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97904, "start": 960.1, "end": 979.04, "text": "اللي هي XI واحد و XI اتنين و XI تلاتة اللي رقبتهم We define XI واحد و XI اتنين إلى مالانهية We show that X وين موجودة في الـL infinity و هنثبت أن XM بتروح لمين؟ للـ X as M goes to infinity لأن الاتنين اللي جابل بشوية as M goes to infinity", "tokens": [6027, 20292, 39896, 1783, 40, 36764, 24401, 4032, 1783, 40, 1975, 2655, 1863, 9957, 4032, 1783, 40, 6055, 1211, 9307, 3660, 13672, 1829, 12602, 4587, 3555, 2655, 16095, 492, 6964, 1783, 40, 36764, 24401, 4032, 1783, 40, 1975, 2655, 1863, 9957, 30731, 3714, 6027, 7649, 3224, 10632, 492, 855, 300, 1783, 4032, 9957, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 43, 13202, 4032, 8032, 1863, 12984, 3555, 2655, 14739, 1783, 44, 39894, 32887, 5016, 32767, 9957, 22807, 24976, 39184, 1783, 382, 376, 1709, 281, 13202, 5296, 33456, 2423, 9307, 1863, 9957, 13672, 1829, 10874, 16758, 1211, 4724, 8592, 2407, 10632, 382, 376, 1709, 281, 13202], "avg_logprob": -0.3183962221977846, "compression_ratio": 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رقبتهم", "probability": 0.755517578125}, {"start": 963.04, "end": 963.6, "word": " We", "probability": 0.144287109375}, {"start": 963.6, "end": 964.16, "word": " define", "probability": 0.92578125}, {"start": 964.16, "end": 964.5, "word": " XI", "probability": 0.95458984375}, {"start": 964.5, "end": 964.82, "word": " واحد", "probability": 0.978271484375}, {"start": 964.82, "end": 965.22, "word": " و", "probability": 0.97265625}, {"start": 965.22, "end": 965.52, "word": " XI", "probability": 0.952880859375}, {"start": 965.52, "end": 965.88, "word": " اتنين", "probability": 0.9605712890625}, {"start": 965.88, "end": 966.08, "word": " إلى", "probability": 0.85400390625}, {"start": 966.08, "end": 966.76, "word": " مالانهية", "probability": 0.6328125}, {"start": 966.76, "end": 967.36, "word": " We", "probability": 0.64990234375}, {"start": 967.36, "end": 967.62, "word": " show", "probability": 0.94677734375}, {"start": 967.62, "end": 967.9, "word": " that", "probability": 0.9248046875}, {"start": 967.9, "end": 968.14, "word": " X", "probability": 0.9619140625}, {"start": 968.14, "end": 968.36, "word": " وين", "probability": 0.5577392578125}, {"start": 968.36, "end": 969.22, "word": " موجودة", "probability": 0.9827880859375}, {"start": 969.22, "end": 969.62, "word": " في", "probability": 0.83935546875}, {"start": 969.62, "end": 969.86, "word": " الـL", "probability": 0.4659016927083333}, {"start": 969.86, "end": 970.28, "word": " infinity", "probability": 0.468994140625}, {"start": 970.28, "end": 970.78, "word": " و", "probability": 0.90771484375}, {"start": 970.78, "end": 971.3, "word": " هنثبت", "probability": 0.93525390625}, {"start": 971.3, "end": 971.4, "word": " أن", "probability": 0.474853515625}, {"start": 971.4, "end": 971.84, "word": " XM", "probability": 0.49688720703125}, {"start": 971.84, "end": 972.16, "word": " بتروح", "probability": 0.9578450520833334}, {"start": 972.16, "end": 973.04, "word": " لمين؟", "probability": 0.604248046875}, {"start": 973.04, "end": 973.34, "word": " للـ", "probability": 0.590576171875}, {"start": 973.34, "end": 973.52, "word": " X", "probability": 0.50048828125}, {"start": 973.52, "end": 973.74, "word": " as", "probability": 0.798828125}, {"start": 973.74, "end": 973.92, "word": " M", "probability": 0.591796875}, {"start": 973.92, "end": 974.08, "word": " goes", "probability": 0.08056640625}, {"start": 974.08, "end": 974.18, "word": " to", "probability": 0.96044921875}, {"start": 974.18, "end": 974.52, "word": " infinity", "probability": 0.79052734375}, {"start": 974.52, "end": 975.34, "word": " لأن", "probability": 0.905517578125}, {"start": 975.34, "end": 975.84, "word": " الاتنين", "probability": 0.83697509765625}, {"start": 975.84, "end": 976.02, "word": " اللي", "probability": 0.982666015625}, {"start": 976.02, "end": 976.3, "word": " جابل", "probability": 0.8033854166666666}, {"start": 976.3, "end": 976.92, "word": " بشوية", "probability": 0.9298095703125}, {"start": 976.92, "end": 978.02, "word": " as", "probability": 0.61376953125}, {"start": 978.02, "end": 978.24, "word": " M", "probability": 0.88525390625}, {"start": 978.24, "end": 978.48, "word": " goes", "probability": 0.95361328125}, {"start": 978.48, "end": 978.6, "word": " to", "probability": 0.97265625}, {"start": 978.6, "end": 979.04, "word": " infinity", "probability": 0.88330078125}], "temperature": 1.0}, {"id": 46, "seek": 100560, "start": 979.96, "end": 1005.6, "text": "we see that اتنين هيها as n goes so infinity ومن مين بدى يودى الان بدى يودى الان تروح إلى ما لنهاية لما الان تروح لما لنهاية بيصير عنده او خلينا نودى ان هي ان تروح لما نهاية اي واحد منهم بنفع ناشط ودنيل الان ان بتروح لما نهاية على افتراض ان ان اكبر من مين من ان فبنودى الان إلى ما لنهاية", "tokens": [826, 536, 300, 1975, 2655, 1863, 9957, 39896, 11296, 382, 297, 1709, 370, 13202, 4032, 27842, 3714, 9957, 47525, 7578, 7251, 23328, 7578, 2423, 7649, 47525, 7578, 7251, 23328, 7578, 2423, 7649, 6055, 32887, 5016, 30731, 19446, 5296, 1863, 11296, 10632, 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987.28, "end": 987.74, "word": " يودى", "probability": 0.9352213541666666}, {"start": 987.74, "end": 988.14, "word": " الان", "probability": 0.63916015625}, {"start": 988.14, "end": 988.54, "word": " تروح", "probability": 0.9143880208333334}, {"start": 988.54, "end": 988.68, "word": " إلى", "probability": 0.427490234375}, {"start": 988.68, "end": 988.86, "word": " ما", "probability": 0.580078125}, {"start": 988.86, "end": 989.42, "word": " لنهاية", "probability": 0.7825927734375}, {"start": 989.42, "end": 990.76, "word": " لما", "probability": 0.86572265625}, {"start": 990.76, "end": 990.98, "word": " الان", "probability": 0.753173828125}, {"start": 990.98, "end": 991.28, "word": " تروح", "probability": 0.98046875}, {"start": 991.28, "end": 991.5, "word": " لما", "probability": 0.8310546875}, {"start": 991.5, "end": 991.92, "word": " لنهاية", "probability": 0.91796875}, {"start": 991.92, "end": 992.28, "word": " بيصير", "probability": 0.8070068359375}, {"start": 992.28, "end": 992.72, "word": " عنده", "probability": 0.900390625}, {"start": 992.72, "end": 993.58, "word": " او", "probability": 0.818603515625}, {"start": 993.58, "end": 994.5, "word": " خلينا", "probability": 0.7510579427083334}, {"start": 994.5, "end": 994.88, "word": " نودى", "probability": 0.7469889322916666}, {"start": 994.88, "end": 994.96, "word": " ان", "probability": 0.650390625}, {"start": 994.96, "end": 995.08, "word": " هي", "probability": 0.7412109375}, {"start": 995.08, "end": 995.36, "word": " ان", "probability": 0.40771484375}, {"start": 995.36, "end": 995.62, "word": " تروح", "probability": 0.9856770833333334}, {"start": 995.62, "end": 995.82, "word": " لما", "probability": 0.8876953125}, {"start": 995.82, "end": 995.98, "word": " نهاية", "probability": 0.8123372395833334}, {"start": 995.98, "end": 996.16, "word": " اي", "probability": 0.757568359375}, {"start": 996.16, "end": 996.32, "word": " واحد", "probability": 0.990966796875}, {"start": 996.32, "end": 996.54, "word": " منهم", "probability": 0.802978515625}, {"start": 996.54, "end": 998.0, "word": " بنفع", "probability": 0.8811848958333334}, {"start": 998.0, "end": 998.66, "word": " ناشط", "probability": 0.63671875}, {"start": 998.66, "end": 999.88, "word": " ودنيل", "probability": 0.53076171875}, {"start": 999.88, "end": 1000.28, "word": " الان", "probability": 0.85888671875}, {"start": 1000.28, "end": 1000.8, "word": " ان", "probability": 0.457275390625}, {"start": 1000.8, "end": 1001.12, "word": " بتروح", "probability": 0.9524739583333334}, {"start": 1001.12, "end": 1001.32, "word": " لما", "probability": 0.915771484375}, {"start": 1001.32, "end": 1001.6, "word": " نهاية", "probability": 0.65771484375}, {"start": 1001.6, "end": 1001.76, "word": " على", "probability": 0.89111328125}, {"start": 1001.76, "end": 1002.1, "word": " افتراض", "probability": 0.93720703125}, {"start": 1002.1, "end": 1002.26, "word": " ان", "probability": 0.86865234375}, {"start": 1002.26, "end": 1002.5, "word": " ان", "probability": 0.57568359375}, {"start": 1002.5, "end": 1002.86, "word": " اكبر", "probability": 0.9373372395833334}, {"start": 1002.86, "end": 1003.04, "word": " من", "probability": 0.97998046875}, {"start": 1003.04, "end": 1003.32, "word": " مين", "probability": 0.8291015625}, {"start": 1003.32, "end": 1003.54, "word": " من", "probability": 0.953125}, {"start": 1003.54, "end": 1003.78, "word": " ان", "probability": 0.73876953125}, {"start": 1003.78, "end": 1004.68, "word": " فبنودى", "probability": 0.80849609375}, {"start": 1004.68, "end": 1004.82, "word": " الان", "probability": 0.7340087890625}, {"start": 1004.82, "end": 1005.0, "word": " إلى", "probability": 0.487060546875}, {"start": 1005.0, "end": 1005.14, "word": " ما", "probability": 0.837890625}, {"start": 1005.14, "end": 1005.6, "word": " لنهاية", "probability": 0.9381103515625}], "temperature": 1.0}, {"id": 47, "seek": 102853, "start": 1006.39, "end": 1028.53, "text": "يابنات و شباب المثبتتك صي M نقص صي N أصغر من إبسلون هذا لكل ال N و ال M أكبر من K لو فرضت أنا ال N أكبر من M مش هتجيبكم بثبتوا لهم أكبر من M لو فرضنا أن ال N أكبر من M هذه as N plus infinity هيصير اللي هو هذا limitه أنا أثبتته", "tokens": [1829, 16758, 8315, 2655, 4032, 13412, 3555, 16758, 9673, 12984, 3555, 2655, 2655, 4117, 20328, 1829, 376, 8717, 4587, 9381, 20328, 1829, 426, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536, 23758, 5296, 28820, 2423, 426, 4032, 2423, 376, 5551, 4117, 26890, 9154, 591, 45164, 6156, 43042, 2655, 41850, 2423, 426, 5551, 4117, 26890, 9154, 376, 37893, 8032, 2655, 7435, 1829, 3555, 24793, 4724, 12984, 3555, 2655, 14407, 5296, 16095, 5551, 4117, 26890, 9154, 376, 45164, 6156, 43042, 8315, 14739, 2423, 426, 5551, 4117, 26890, 9154, 376, 29538, 382, 426, 1804, 13202, 39896, 9381, 13546, 13672, 1829, 31439, 23758, 4948, 3224, 41850, 5551, 12984, 3555, 2655, 47395], "avg_logprob": -0.34943182224577124, "compression_ratio": 1.7681159420289856, "no_speech_prob": 1.4185905456542969e-05, "words": 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1245.21, "end": 1246.19, "word": " وديتها", "probability": 0.97314453125}, {"start": 1246.19, "end": 1246.97, "word": " ل", "probability": 0.7490234375}, {"start": 1246.97, "end": 1247.39, "word": " X", "probability": 0.5869140625}, {"start": 1247.39, "end": 1247.69, "word": " ده", "probability": 0.597900390625}, {"start": 1247.69, "end": 1248.13, "word": " space", "probability": 0.6044921875}], "temperature": 1.0}, {"id": 59, "seek": 126806, "start": 1248.9, "end": 1268.06, "text": "C Consists Of All Convergent Sequences Of Complex Numbers أو ريال مش مشكلة With The Metric Induced From The Space الانفينيتي is complete ايش اللي بقوله بقول احنا بنعرف ان any convergent sequence is bounded", "tokens": [34, 6923, 1751, 2720, 1057, 2656, 331, 6930, 46859, 2667, 2720, 41184, 22592, 1616, 34051, 12602, 1829, 6027, 37893, 37893, 28820, 3660, 2022, 440, 6377, 1341, 2333, 41209, 3358, 440, 8705, 2423, 7649, 5172, 9957, 1829, 31371, 307, 3566, 1975, 1829, 8592, 13672, 1829, 4724, 39648, 3224, 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"probability": 0.987060546875}, {"start": 1380.56, "end": 1380.68, "word": " هي", "probability": 0.93359375}, {"start": 1380.68, "end": 1380.8, "word": " هذه", "probability": 0.36376953125}, {"start": 1380.8, "end": 1381.38, "word": " الـsequence،", "probability": 0.79580078125}, {"start": 1381.38, "end": 1381.6, "word": " إكساي", "probability": 0.902587890625}, {"start": 1381.6, "end": 1381.88, "word": " 1،", "probability": 0.806640625}, {"start": 1381.88, "end": 1382.04, "word": " إكساي", "probability": 0.9208984375}, {"start": 1382.04, "end": 1382.38, "word": " 2،", "probability": 0.985595703125}, {"start": 1382.38, "end": 1382.56, "word": " إكساي", "probability": 0.92041015625}, {"start": 1382.56, "end": 1382.88, "word": " 3،", "probability": 0.987548828125}, {"start": 1382.88, "end": 1383.04, "word": " إكساي", "probability": 0.9215087890625}, {"start": 1383.04, "end": 1383.36, "word": " 4،", "probability": 0.968505859375}, {"start": 1383.36, "end": 1383.46, "word": " إلى", 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1443.02, "end": 1443.24, "word": " ال", "probability": 0.87646484375}, {"start": 1443.24, "end": 1443.8, "word": " ..", "probability": 0.97314453125}, {"start": 1443.8, "end": 1444.14, "word": " لو", "probability": 0.966796875}, {"start": 1444.14, "end": 1444.72, "word": " أثبتت", "probability": 0.99443359375}, {"start": 1444.72, "end": 1445.04, "word": " هذا", "probability": 0.9609375}], "temperature": 1.0}, {"id": 68, "seek": 147357, "start": 1445.95, "end": 1473.57, "text": "إن هاد الـ X في الـ C closure وصلت في الـ C بكون خلصت اتفجنا؟ يلّا خلّينا نروح نشوف الآن أخدت X في الـ C closure إذا حسب تعريف X في الـ C closure you get sequence XM in C بحيث أن XM بتروح لمين؟ لل X where؟ إيش هي الـ XM؟ زي ما عملنا قبل شوية X واحد يعني X واحد واحد واحد X اتنين واحد الاخري XM in general X واحد أم X اتنين أم إلى مدى نهاية", "tokens": [28814, 1863, 8032, 18513, 2423, 39184, 1783, 8978, 2423, 39184, 383, 24653, 4032, 36520, 2655, 8978, 2423, 39184, 383, 4724, 30544, 16490, 1211, 9381, 2655, 1975, 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للتعريف أن الـ distance بين Xم أو X", "tokens": [3224, 24192, 2423, 39184, 8310, 295, 4959, 31439, 9673, 29245, 23328, 3660, 8978, 2423, 39184, 383, 8717, 36178, 11296, 3714, 33599, 1829, 21542, 6027, 22807, 23032, 1829, 3555, 12399, 3714, 3215, 7649, 8978, 2423, 39184, 383, 12399, 11933, 15730, 28242, 36764, 24401, 3660, 9652, 2880, 5296, 33456, 3714, 3215, 9957, 3660, 2423, 39184, 383, 6225, 3555, 9640, 3660, 18871, 2423, 39184, 1901, 34051, 2423, 39184, 992, 295, 439, 9652, 6930, 22978, 11933, 15730, 16678, 337, 633, 7251, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 456, 8198, 350, 4959, 293, 1270, 300, 37279, 16572, 5172, 36632, 8592, 22807, 36145, 11296, 2423, 39184, 8310, 9652, 2880, 11933, 1829, 8592, 31439, 24976, 2655, 3615, 16572, 5172, 14739, 2423, 39184, 4560, 49374, 1783, 2304, 34051, 1783], "avg_logprob": -0.3419715582839842, "compression_ratio": 1.75, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 1473.81, "end": 1474.21, "word": "هذه", "probability": 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جوا أصغر من epsilon لكل مين لكل T المخود عليه كل إياش ال maximum مدام ال maximum أصغر من epsilon إذا قيمة الدولة هذه مع قصدها عند أي نقطة في الinterval أصغر من epsilon", "tokens": [5172, 3555, 9381, 13546, 43242, 7578, 5296, 7649, 3714, 3215, 10943, 2423, 6674, 5551, 9381, 17082, 2288, 9154, 17889, 5296, 28820, 426, 4032, 376, 5551, 4117, 26890, 9154, 591, 11933, 15730, 5296, 28820, 426, 4032, 376, 5551, 4117, 26890, 9154, 591, 39896, 30544, 23758, 9673, 28543, 9640, 13672, 7578, 10874, 14407, 5551, 9381, 17082, 2288, 9154, 17889, 5296, 28820, 3714, 9957, 5296, 28820, 314, 9673, 9778, 23328, 47356, 28242, 11933, 1829, 33599, 2423, 6674, 3714, 3215, 10943, 2423, 6674, 5551, 9381, 17082, 2288, 9154, 17889, 11933, 15730, 12174, 32640, 3660, 32748, 12610, 3660, 29538, 20449, 12174, 9381, 3215, 11296, 43242, 36632, 8717, 47432, 3660, 8978, 2423, 5106, 3337, 5551, 9381, 17082, 2288, 9154, 17889], "avg_logprob": -0.23206521842790687, "compression_ratio": 2.0325581395348835, "no_speech_prob": 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"word": " b", "probability": 0.92724609375}, {"start": 2796.63, "end": 2796.95, "word": " is", "probability": 0.94140625}, {"start": 2796.95, "end": 2797.13, "word": " a", "probability": 0.94482421875}, {"start": 2797.13, "end": 2797.73, "word": " complete", "probability": 0.82177734375}, {"start": 2797.73, "end": 2798.67, "word": " metric", "probability": 0.95947265625}, {"start": 2798.67, "end": 2799.23, "word": " space", "probability": 0.912109375}], "temperature": 1.0}, {"id": 125, "seek": 281664, "start": 2802.56, "end": 2816.64, "text": "الان في البرهان اللى .. اللى بضغطناه قبل بشوية فى داخله فى الواقع أثبتنا ان ال convergence اللى فى الـC of A بيinvolve convergence ده بعمل بقول يعنى بقوللى الآن", "tokens": [6027, 7649, 8978, 2423, 26890, 3224, 7649, 13672, 7578, 4386, 13672, 7578, 4724, 11242, 17082, 9566, 8315, 3224, 12174, 36150, 4724, 8592, 2407, 10632, 6156, 7578, 11778, 47283, 43761, 6156, 7578, 2423, 14407, 4587, 3615, 5551, 12984, 3555, 2655, 8315, 16472, 2423, 32181, 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in the space C of A و B Under the metric اللي حكينا عنه is a Uniform Convergence That is XM converges uniformly on A و B to mean 2X الأهمية حطناها لحالها", "tokens": [2278, 37956, 295, 1156, 8629, 2656, 331, 15260, 2656, 331, 15260, 1783, 44, 39894, 32887, 5016, 24976, 39184, 1783, 294, 264, 1901, 383, 295, 316, 4032, 363, 6974, 264, 20678, 13672, 1829, 11331, 4117, 1829, 8315, 18871, 3224, 307, 257, 1156, 8629, 2656, 331, 15260, 663, 307, 1783, 44, 9652, 2880, 48806, 322, 316, 4032, 363, 281, 914, 568, 55, 16247, 16095, 10632, 11331, 9566, 8315, 11296, 5296, 5016, 6027, 11296], "avg_logprob": -0.3726128356324302, "compression_ratio": 1.3922651933701657, "no_speech_prob": 2.8014183044433594e-06, "words": [{"start": 2817.68, "end": 2818.24, "word": "Theorem", "probability": 0.54364013671875}, {"start": 2818.24, "end": 2818.38, "word": " of", "probability": 0.368408203125}, {"start": 2818.38, "end": 2818.72, "word": " Uniform", "probability": 0.785400390625}, {"start": 2818.72, "end": 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2829.22, "word": " That", "probability": 0.7060546875}, {"start": 2829.22, "end": 2829.56, "word": " is", "probability": 0.88916015625}, {"start": 2829.56, "end": 2830.04, "word": " XM", "probability": 0.86474609375}, {"start": 2830.04, "end": 2830.56, "word": " converges", "probability": 0.6220703125}, {"start": 2830.56, "end": 2831.08, "word": " uniformly", "probability": 0.9697265625}, {"start": 2831.08, "end": 2831.4, "word": " on", "probability": 0.6884765625}, {"start": 2831.4, "end": 2831.8, "word": " A", "probability": 0.43896484375}, {"start": 2831.8, "end": 2832.68, "word": " و", "probability": 0.9375}, {"start": 2832.68, "end": 2832.96, "word": " B", "probability": 0.830078125}, {"start": 2832.96, "end": 2833.26, "word": " to", "probability": 0.712890625}, {"start": 2833.26, "end": 2833.58, "word": " mean", "probability": 0.8837890625}, {"start": 2833.58, "end": 2834.22, "word": " 2X", "probability": 0.675048828125}, {"start": 2834.22, "end": 2835.08, "word": " الأهمية", 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موجود", "probability": 0.98828125}, {"start": 2988.67, "end": 2989.17, "word": " فيها", "probability": 0.985107421875}, {"start": 2989.17, "end": 2990.11, "word": " فإذا", "probability": 0.8976236979166666}, {"start": 2990.11, "end": 2990.49, "word": " صارت", "probability": 0.8961588541666666}, {"start": 2990.49, "end": 2990.75, "word": " عندي", "probability": 0.77392578125}, {"start": 2990.75, "end": 2991.37, "word": " أشملها", "probability": 0.71026611328125}, {"start": 2991.37, "end": 2991.83, "word": " a", "probability": 0.27392578125}, {"start": 2991.83, "end": 2992.09, "word": " queue", "probability": 0.6162109375}, {"start": 2992.09, "end": 2992.37, "word": " is", "probability": 0.9541015625}, {"start": 2992.37, "end": 2992.71, "word": " not", "probability": 0.9638671875}, {"start": 2992.71, "end": 2994.07, "word": " complete", "probability": 0.86083984375}, {"start": 2994.07, "end": 2994.95, "word": " طيب", "probability": 0.92138671875}, {"start": 2994.95, "end": 2995.09, "word": " يا", "probability": 0.9541015625}, {"start": 2995.09, "end": 2995.47, "word": " جماعة", "probability": 0.984375}, {"start": 2995.47, "end": 2996.59, "word": " اللي", "probability": 0.943603515625}, {"start": 2996.59, "end": 2996.97, "word": " بعده", "probability": 0.916015625}], "temperature": 1.0}, {"id": 134, "seek": 301599, "start": 2999.39, "end": 3015.99, "text": "صلوا على النبي عليه الصلاة والسلام الان space of all polynomials البرونوميالز انتم تذكرين كيف كنا نجيب ال exponential function لما لها exponential سيريز فيها سيريز", "tokens": [9381, 1211, 14407, 15844, 28239, 21292, 47356, 31767, 15040, 3660, 16070, 3794, 37440, 2423, 7649, 1901, 295, 439, 22560, 12356, 2423, 26890, 11536, 20498, 1829, 6027, 11622, 16472, 39237, 6055, 8848, 37983, 9957, 9122, 33911, 9122, 8315, 8717, 7435, 1829, 3555, 2423, 21510, 2445, 5296, 15042, 5296, 11296, 21510, 8608, 13546, 1829, 11622, 8978, 11296, 8608, 13546, 1829, 11622], "avg_logprob": -0.3125000074505806, "compression_ratio": 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{"start": 3003.79, "end": 3006.03, "word": " البرونوميالز", "probability": 0.7530691964285714}, {"start": 3006.03, "end": 3006.89, "word": " انتم", "probability": 0.552001953125}, {"start": 3006.89, "end": 3007.39, "word": " تذكرين", "probability": 0.717041015625}, {"start": 3007.39, "end": 3007.57, "word": " كيف", "probability": 0.978271484375}, {"start": 3007.57, "end": 3007.85, "word": " كنا", "probability": 0.816650390625}, {"start": 3007.85, "end": 3008.79, "word": " نجيب", "probability": 0.8582763671875}, {"start": 3008.79, "end": 3008.87, "word": " ال", "probability": 0.8955078125}, {"start": 3008.87, "end": 3009.21, "word": " exponential", "probability": 0.80859375}, {"start": 3009.21, "end": 3009.83, "word": " function", "probability": 0.95361328125}, {"start": 3009.83, "end": 3012.97, "word": " لما", "probability": 0.6376953125}, {"start": 3012.97, "end": 3013.15, "word": " لها", "probability": 0.90576171875}, {"start": 3013.15, "end": 3013.69, "word": " exponential", "probability": 0.8720703125}, {"start": 3013.69, "end": 3014.27, "word": " سيريز", "probability": 0.761688232421875}, {"start": 3014.27, "end": 3015.25, "word": " فيها", "probability": 0.4354248046875}, {"start": 3015.25, "end": 3015.99, "word": " سيريز", "probability": 0.9556884765625}], "temperature": 1.0}, {"id": 135, "seek": 304384, "start": 3016.98, "end": 3043.84, "text": "ماشي الحال let x be the set of all polynomials over the real interval d of a,b and define a metric d on x by d of x بساوية من ال maximum ال polynomials اللي موجودة في continuous functions صح ولا لأ فانا أخدت بس هالعائلة من ال continuous functions اللي يمين اللي هي ال polynomials بقولك هذه العائلة هتعمل لي إيش ماله", "tokens": [2304, 33599, 1829, 21542, 6027, 718, 2031, 312, 264, 992, 295, 439, 22560, 12356, 670, 264, 957, 15035, 274, 295, 257, 11, 65, 293, 6964, 257, 20678, 274, 322, 2031, 538, 274, 295, 2031, 4724, 3794, 995, 2407, 10632, 9154, 2423, 6674, 2423, 22560, 12356, 13672, 1829, 3714, 29245, 23328, 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and", "probability": 0.80908203125}, {"start": 3026.22, "end": 3026.66, "word": " define", "probability": 0.96044921875}, {"start": 3026.66, "end": 3026.86, "word": " a", "probability": 0.95849609375}, {"start": 3026.86, "end": 3027.18, "word": " metric", "probability": 0.95166015625}, {"start": 3027.18, "end": 3027.56, "word": " d", "probability": 0.705078125}, {"start": 3027.56, "end": 3027.74, "word": " on", "probability": 0.263427734375}, {"start": 3027.74, "end": 3028.54, "word": " x", "probability": 0.82470703125}, {"start": 3028.54, "end": 3028.76, "word": " by", "probability": 0.8759765625}, {"start": 3028.76, "end": 3028.94, "word": " d", "probability": 0.86669921875}, {"start": 3028.94, "end": 3029.06, "word": " of", "probability": 0.9130859375}, {"start": 3029.06, "end": 3029.2, "word": " x", "probability": 0.99365234375}, {"start": 3029.2, "end": 3029.54, "word": " بساوية", "probability": 0.60458984375}, {"start": 3029.54, "end": 3029.66, "word": " من", "probability": 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"probability": 0.86767578125}, {"start": 3034.36, "end": 3034.92, "word": " فانا", "probability": 0.7130533854166666}, {"start": 3034.92, "end": 3035.2, "word": " أخدت", "probability": 0.8929443359375}, {"start": 3035.2, "end": 3035.46, "word": " بس", "probability": 0.792724609375}, {"start": 3035.46, "end": 3036.62, "word": " هالعائلة", "probability": 0.80185546875}, {"start": 3036.62, "end": 3037.14, "word": " من", "probability": 0.9609375}, {"start": 3037.14, "end": 3037.26, "word": " ال", "probability": 0.55908203125}, {"start": 3037.26, "end": 3037.58, "word": " continuous", "probability": 0.92236328125}, {"start": 3037.58, "end": 3038.1, "word": " functions", "probability": 0.86572265625}, {"start": 3038.1, "end": 3038.34, "word": " اللي", "probability": 0.95654296875}, {"start": 3038.34, "end": 3038.9, "word": " يمين", "probability": 0.4713541666666667}, {"start": 3038.9, "end": 3039.54, "word": " اللي", "probability": 0.961669921875}, {"start": 3039.54, "end": 3039.74, "word": " هي", "probability": 0.88916015625}, {"start": 3039.74, "end": 3039.84, "word": " ال", "probability": 0.73388671875}, {"start": 3039.84, "end": 3040.6, "word": " polynomials", "probability": 0.9072265625}, {"start": 3040.6, "end": 3041.54, "word": " بقولك", "probability": 0.9264322916666666}, {"start": 3041.54, "end": 3041.82, "word": " هذه", "probability": 0.84228515625}, {"start": 3041.82, "end": 3042.34, "word": " العائلة", "probability": 0.9969075520833334}, {"start": 3042.34, "end": 3042.92, "word": " هتعمل", "probability": 0.8704833984375}, {"start": 3042.92, "end": 3043.1, "word": " لي", "probability": 0.4306640625}, {"start": 3043.1, "end": 3043.36, "word": " إيش", "probability": 0.6773274739583334}, {"start": 3043.36, "end": 3043.84, "word": " ماله", "probability": 0.8271484375}], "temperature": 1.0}, {"id": 136, "seek": 307190, "start": 3044.38, "end": 3071.9, "text": "الـ Incomplete metric space is not complete ماهي اللي بدنا ياه بدنا تجيبونا كوشي sequence من ال polynomials تروح وين إلى element مش في ال polynomials under the metric DXY بيسوي ماكسيمال هذا و هذا بيكون معاكم إيه اشماله exercise من المطلبات نجي الآن نحكي عن space آخر ال space هذا إيش أنا بدي أسوي", "tokens": [6027, 39184, 682, 1112, 17220, 20678, 1901, 307, 406, 3566, 19446, 3224, 1829, 13672, 1829, 47525, 8315, 35186, 3224, 47525, 8315, 6055, 7435, 1829, 3555, 2407, 8315, 9122, 2407, 8592, 1829, 8310, 9154, 2423, 6754, 77, 9220, 1124, 6055, 32887, 5016, 4032, 9957, 30731, 4478, 37893, 8978, 2423, 6754, 77, 9220, 1124, 833, 264, 20678, 48817, 56, 4724, 1829, 3794, 45865, 3714, 995, 4117, 3794, 1829, 2304, 6027, 23758, 4032, 23758, 4724, 1829, 30544, 20449, 995, 24793, 11933, 1829, 3224, 1975, 8592, 2304, 6027, 3224, 5380, 9154, 9673, 9566, 46152, 9307, 8717, 7435, 1829, 6024, 48506, 8717, 5016, 4117, 1829, 18871, 1901, 19753, 34740, 2423, 1901, 23758, 11933, 1829, 8592, 41850, 4724, 16254, 5551, 3794, 45865], "avg_logprob": -0.4695512800135164, "compression_ratio": 1.6551724137931034, 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0.41943359375}, {"start": 3060.7, "end": 3060.92, "word": " بيكون", "probability": 0.8230794270833334}, {"start": 3060.92, "end": 3061.3, "word": " معاكم", "probability": 0.9679361979166666}, {"start": 3061.3, "end": 3061.46, "word": " إيه", "probability": 0.702880859375}, {"start": 3061.46, "end": 3061.92, "word": " اشماله", "probability": 0.703271484375}, {"start": 3061.92, "end": 3062.94, "word": " exercise", "probability": 0.40966796875}, {"start": 3062.94, "end": 3063.3, "word": " من", "probability": 0.93310546875}, {"start": 3063.3, "end": 3064.6, "word": " المطلبات", "probability": 0.8944091796875}, {"start": 3064.6, "end": 3065.18, "word": " نجي", "probability": 0.6534016927083334}, {"start": 3065.18, "end": 3065.52, "word": " الآن", "probability": 0.7115478515625}, {"start": 3065.52, "end": 3068.16, "word": " نحكي", "probability": 0.9891357421875}, {"start": 3068.16, "end": 3068.52, "word": " عن", "probability": 0.9833984375}, {"start": 3068.52, "end": 3069.08, "word": " space", "probability": 0.8203125}, {"start": 3069.08, "end": 3069.64, "word": " آخر", "probability": 0.812255859375}, {"start": 3069.64, "end": 3070.1, "word": " ال", "probability": 0.9169921875}, {"start": 3070.1, "end": 3070.48, "word": " space", "probability": 0.85986328125}, {"start": 3070.48, "end": 3070.76, "word": " هذا", "probability": 0.66162109375}, {"start": 3070.76, "end": 3071.02, "word": " إيش", "probability": 0.7586263020833334}, {"start": 3071.02, "end": 3071.18, "word": " أنا", "probability": 0.7568359375}, {"start": 3071.18, "end": 3071.44, "word": " بدي", "probability": 0.593994140625}, {"start": 3071.44, "end": 3071.9, "word": " أسوي", "probability": 0.8888346354166666}], "temperature": 1.0}, {"id": 137, "seek": 309609, "start": 3073.05, "end": 3096.09, "text": "عشان أقول الرسمة بس ال space أنا بدي أجي اللي هو أعمل اللي هو أجيبلكم ال space of continuous functions بس بتغير ال metric بتغير ال metric من metric اللي هو ال maximum إلى ال integration", "tokens": [3615, 8592, 7649, 5551, 39648, 34892, 38251, 3660, 4724, 3794, 2423, 1901, 41850, 4724, 16254, 5551, 7435, 1829, 13672, 1829, 31439, 5551, 25957, 1211, 13672, 1829, 31439, 5551, 7435, 1829, 3555, 23275, 2304, 2423, 1901, 295, 10957, 6828, 4724, 3794, 39894, 17082, 13546, 2423, 20678, 39894, 17082, 13546, 2423, 20678, 9154, 20678, 13672, 1829, 31439, 2423, 6674, 30731, 2423, 10980], "avg_logprob": -0.17328380561265788, "compression_ratio": 1.6441717791411044, "no_speech_prob": 7.152557373046875e-06, "words": [{"start": 3073.05, "end": 3073.41, "word": "عشان", "probability": 0.8849283854166666}, {"start": 3073.41, "end": 3073.65, "word": " أقول", "probability": 0.5927734375}, {"start": 3073.65, "end": 3074.07, "word": " الرسمة", "probability": 0.93359375}, {"start": 3074.07, "end": 3074.27, "word": " بس", "probability": 0.7298583984375}, {"start": 3074.27, "end": 3074.59, "word": " ال", "probability": 0.85595703125}, {"start": 3074.59, "end": 3075.07, "word": " space", "probability": 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0.94482421875}, {"start": 3086.59, "end": 3087.03, "word": " continuous", "probability": 0.8818359375}, {"start": 3087.03, "end": 3087.85, "word": " functions", "probability": 0.85595703125}, {"start": 3087.85, "end": 3089.17, "word": " بس", "probability": 0.973876953125}, {"start": 3089.17, "end": 3089.57, "word": " بتغير", "probability": 0.7613118489583334}, {"start": 3089.57, "end": 3089.71, "word": " ال", "probability": 0.93603515625}, {"start": 3089.71, "end": 3090.13, "word": " metric", "probability": 0.8505859375}, {"start": 3090.13, "end": 3091.53, "word": " بتغير", "probability": 0.8709309895833334}, {"start": 3091.53, "end": 3091.67, "word": " ال", "probability": 0.93310546875}, {"start": 3091.67, "end": 3092.03, "word": " metric", "probability": 0.96044921875}, {"start": 3092.03, "end": 3092.37, "word": " من", "probability": 0.9296875}, {"start": 3092.37, "end": 3093.87, "word": " metric", "probability": 0.4326171875}, {"start": 3093.87, "end": 3094.53, "word": " اللي", "probability": 0.984619140625}, {"start": 3094.53, "end": 3094.67, "word": " هو", "probability": 0.9833984375}, {"start": 3094.67, "end": 3094.77, "word": " ال", "probability": 0.83056640625}, {"start": 3094.77, "end": 3095.23, "word": " maximum", "probability": 0.9697265625}, {"start": 3095.23, "end": 3095.49, "word": " إلى", "probability": 0.8251953125}, {"start": 3095.49, "end": 3095.63, "word": " ال", "probability": 0.9794921875}, {"start": 3095.63, "end": 3096.09, "word": " integration", "probability": 0.97265625}], "temperature": 1.0}, {"id": 138, "seek": 311326, "start": 3097.22, "end": 3113.26, "text": "سأقول لكم إن في هذه الحالة بيبطل الـ metric ايش معناه Complete metric space ماشي الحال طيب خلّينا أنه نشوف إيش اللي هي الدالة اللي عندنا الدالة اللي عندنا", "tokens": [3794, 10721, 39648, 5296, 24793, 36145, 8978, 29538, 21542, 6027, 3660, 4724, 1829, 3555, 9566, 1211, 2423, 39184, 20678, 1975, 1829, 8592, 20449, 8315, 3224, 34687, 20678, 1901, 3714, 33599, 1829, 21542, 6027, 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"probability": 0.8995768229166666}, {"start": 3108.96, "end": 3109.22, "word": " إيش", "probability": 0.7486165364583334}, {"start": 3109.22, "end": 3109.36, "word": " اللي", "probability": 0.805419921875}, {"start": 3109.36, "end": 3109.6, "word": " هي", "probability": 0.86767578125}, {"start": 3109.6, "end": 3110.04, "word": " الدالة", "probability": 0.9654947916666666}, {"start": 3110.04, "end": 3110.18, "word": " اللي", "probability": 0.964599609375}, {"start": 3110.18, "end": 3110.88, "word": " عندنا", "probability": 0.91650390625}, {"start": 3110.88, "end": 3112.52, "word": " الدالة", "probability": 0.9851888020833334}, {"start": 3112.52, "end": 3112.8, "word": " اللي", "probability": 0.9921875}, {"start": 3112.8, "end": 3113.26, "word": " عندنا", "probability": 0.9794921875}], "temperature": 1.0}, {"id": 139, "seek": 313895, "start": 3113.93, "end": 3138.95, "text": "الدوال اللي عندنا انا اسف او ال sequence اللي عندنا sequence of دوال ماهي لان انا بحكي عن مين عن space of continuous functions يعني أنصرها دوال صلوا على النبي عليه الصلاة والسلام ال space of continuous functions let X be the set of all continuous functions real valid functions على مين على الفترة 0 و1 and define a metric D on X by", "tokens": [6027, 3215, 2407, 6027, 13672, 1829, 43242, 8315, 1975, 8315, 24525, 5172, 1975, 2407, 2423, 8310, 13672, 1829, 43242, 8315, 8310, 295, 11778, 2407, 6027, 19446, 3224, 1829, 5296, 7649, 1975, 8315, 4724, 5016, 4117, 1829, 18871, 3714, 9957, 18871, 1901, 295, 10957, 6828, 37495, 22653, 14739, 9381, 2288, 11296, 11778, 2407, 6027, 20328, 1211, 14407, 15844, 28239, 21292, 47356, 31767, 15040, 3660, 16070, 3794, 37440, 2423, 1901, 295, 10957, 6828, 718, 1783, 312, 264, 992, 295, 439, 10957, 6828, 957, 7363, 6828, 15844, 3714, 9957, 15844, 27188, 2655, 25720, 1958, 4032, 16, 293, 6964, 257, 20678, 413, 322, 1783, 538], "avg_logprob": -0.27818627275672614, "compression_ratio": 1.8713692946058091, "no_speech_prob": 2.6226043701171875e-06, "words": [{"start": 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أن", "probability": 0.56103515625}, {"start": 3668.71, "end": 3669.63, "word": " Xm", "probability": 0.936279296875}, {"start": 3669.63, "end": 3669.97, "word": " تذهب", "probability": 0.94140625}, {"start": 3669.97, "end": 3670.11, "word": " إلى", "probability": 0.9443359375}, {"start": 3670.11, "end": 3670.99, "word": " X،", "probability": 0.8798828125}, {"start": 3670.99, "end": 3671.27, "word": " يعني", "probability": 0.9375}, {"start": 3671.27, "end": 3671.73, "word": " المسافة", "probability": 0.9039306640625}, {"start": 3671.73, "end": 3671.87, "word": " بين", "probability": 0.95263671875}, {"start": 3671.87, "end": 3672.09, "word": " هذه", "probability": 0.453857421875}, {"start": 3672.09, "end": 3672.43, "word": " وهذه", "probability": 0.83642578125}, {"start": 3672.43, "end": 3672.81, "word": " تذهب", "probability": 0.9069010416666666}, {"start": 3672.81, "end": 3673.03, "word": " إلى", "probability": 0.97998046875}, {"start": 3673.03, "end": 3673.33, "word": " سفر", 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M goes to مين To infinity مظبوط وهذا راح يرميه لما الصفر روح مافيش حيطلع علنا اشي واضح اللي بحكيه طيب اطلع لفوق بيصير عندي ال integration", "tokens": [3224, 15730, 19446, 31439, 37893, 3714, 7649, 2655, 20498, 3215, 15844, 376, 6156, 3555, 9381, 13546, 2423, 10980, 1783, 295, 314, 9154, 20328, 5172, 2288, 5296, 1863, 9381, 6225, 8592, 7649, 8608, 995, 4587, 10632, 20328, 5172, 2288, 37037, 15730, 4724, 1829, 9381, 13546, 2423, 10980, 13672, 1829, 4724, 1829, 3794, 995, 45865, 4724, 32887, 5016, 5296, 9381, 5172, 2288, 382, 376, 1709, 281, 3714, 9957, 1407, 13202, 3714, 19913, 3555, 2407, 9566, 37037, 15730, 12602, 39319, 7251, 2288, 2304, 1829, 3224, 5296, 15042, 31767, 5172, 2288, 12602, 2407, 5016, 19446, 41185, 8592, 11331, 1829, 9566, 1211, 3615, 11203, 8315, 1975, 8592, 1829, 4032, 46958, 5016, 13672, 1829, 4724, 5016, 4117, 1829, 3224, 23032, 1829, 3555, 1975, 9566, 1211, 3615, 5296, 5172, 30543, 4724, 1829, 9381, 13546, 18871, 16254, 2423, 10980], "avg_logprob": 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function،", "probability": 0.9267578125}, {"start": 3822.49, "end": 3822.85, "word": " هتكون", "probability": 0.96240234375}, {"start": 3822.85, "end": 3823.23, "word": " براة", "probability": 0.7787272135416666}, {"start": 3823.23, "end": 3823.33, "word": " ال", "probability": 0.78955078125}, {"start": 3823.33, "end": 3824.01, "word": " X،", "probability": 0.83544921875}, {"start": 3824.01, "end": 3824.39, "word": " وبناء", "probability": 0.8089192708333334}, {"start": 3824.39, "end": 3824.81, "word": " عليه", "probability": 0.970703125}, {"start": 3824.81, "end": 3825.63, "word": " no", "probability": 0.33837890625}, {"start": 3825.63, "end": 3826.39, "word": " limit", "probability": 0.97314453125}, {"start": 3826.39, "end": 3827.19, "word": " in", "probability": 0.7998046875}, {"start": 3827.19, "end": 3828.07, "word": " X", "probability": 0.9931640625}], "temperature": 1.0}, {"id": 172, "seek": 384379, "start": 3833.79, "end": 3843.79, "text": "وهذا يثبت أن الـ space is not complete وبرك الله فيكم الله يعطيكم العافية", "tokens": [2407, 3224, 15730, 7251, 12984, 3555, 2655, 14739, 2423, 39184, 1901, 307, 406, 3566, 4032, 26890, 4117, 21984, 8978, 24793, 21984, 37495, 9566, 1829, 24793, 18863, 31845, 10632], "avg_logprob": -0.3440194006623893, "compression_ratio": 1.1979166666666667, "no_speech_prob": 1.8715858459472656e-05, "words": [{"start": 3833.79, "end": 3834.89, "word": "وهذا", "probability": 0.444580078125}, {"start": 3834.89, "end": 3835.89, "word": " يثبت", "probability": 0.97216796875}, {"start": 3835.89, "end": 3836.51, "word": " أن", "probability": 0.591796875}, {"start": 3836.51, "end": 3837.21, "word": " الـ", "probability": 0.66650390625}, {"start": 3837.21, "end": 3837.49, "word": " space", "probability": 0.6220703125}, {"start": 3837.49, "end": 3838.15, "word": " is", "probability": 0.470947265625}, {"start": 3838.15, "end": 3838.63, "word": " not", "probability": 0.9267578125}, {"start": 3838.63, "end": 3840.13, "word": " complete", "probability": 0.84912109375}, {"start": 3840.13, "end": 3842.15, "word": " وبرك", "probability": 0.81494140625}, {"start": 3842.15, "end": 3842.29, "word": " الله", "probability": 0.859375}, {"start": 3842.29, "end": 3842.75, "word": " فيكم", "probability": 0.97265625}, {"start": 3842.75, "end": 3843.07, "word": " الله", "probability": 0.394775390625}, {"start": 3843.07, "end": 3843.37, "word": " يعطيكم", "probability": 0.7633056640625}, {"start": 3843.37, "end": 3843.79, "word": " العافية", "probability": 0.8839518229166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3844.528, "duration_after_vad": 3750.9649999999847}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/EaC1QqfjIDE.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/EaC1QqfjIDE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4fab5593bcc74b5abb4e16016ecd7b3cb958080c
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/EaC1QqfjIDE.srt
@@ -0,0 +1,2841 @@
+1
+00:00:05,210 --> 00:00:07,970
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,970 --> 00:00:10,890
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,890 --> 00:00:15,610
+آله وصحبه أجمعين هذه هي المحاضرة رقم 11 مساق تحليل 
+
+4
+00:00:15,610 --> 00:00:18,710
+الاقتران أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:18,710 --> 00:00:23,810
+الإسلامية قسم رياضيات ماجستيريا اليوم إن شاء الله
+
+6
+00:00:23,810 --> 00:00:30,370
+هنكمل اللي هو في المادة هناخد Section 2 و 5 
+
+7
+00:00:30,370 --> 00:00:33,690
+اللي هو Compactness and Finite Dimension هنحكي عن
+
+8
+00:00:34,570 --> 00:00:39,210
+شو مفهوم الـ Compact Set و .. و خلّيني أقوله علاقة 
+
+9
+00:00:39,210 --> 00:00:42,410
+الـ Finiteness في حالة اللي هو الـ .. الـ Compact في
+
+10
+00:00:42,410 --> 00:00:48,390
+حالة الـ Finiteness كـ Dimension منيح إنه أنا أحكي 
+
+11
+00:00:48,390 --> 00:00:54,130
+عن الأمور الكلية في موضوع الـ Compactness احنا 
+
+12
+00:00:54,130 --> 00:00:57,910
+جسمنا الدنيا تبعتنا اللي هو قلنا في عندي 
+
+13
+00:00:57,910 --> 00:01:02,000
+Topological Space اللي هو  Autobiographical Space in
+
+14
+00:01:02,000 --> 00:01:05,980
+General في داخله اللي هو Autobiographical Spaces
+
+15
+00:01:05,980 --> 00:01:10,740
+في داخله اللي هو Metric Spaces في داخله اللي هو
+
+16
+00:01:10,740 --> 00:01:15,980
+Normed Spaces في داخله اللي هو Hilbert Spaces فيه
+
+17
+00:01:15,980 --> 00:01:19,500
+في داخله الـ Spaces تبعاتنا الحلوات هذي R و R<sup>2</sup> و مش
+
+18
+00:01:19,500 --> 00:01:25,660
+عارف ايش الأخر و C الأخر الآن احنا بندرس الـ
+
+19
+00:01:25,660 --> 00:01:28,380
+Compactness حتى كنا ندرسها في الـ Real Analysis
+
+20
+00:01:28,380 --> 00:01:33,230
+و ممكن أدرسه في الـ Calculus كمان أو ممكن اللي هو 
+
+21
+00:01:33,230 --> 00:01:38,470
+أدرسه اللي هو في Normed Spaces أو Metric Spaces و
+
+22
+00:01:38,470 --> 00:01:41,690
+بندرسه في الـ Topological Spaces في الـ Topological
+
+23
+00:01:41,690 --> 00:01:46,610
+Spaces إيش بنعرفه؟ بنقول أن الـ .. الـ .. الـ .. الـ
+
+24
+00:01:46,610 --> 00:01:46,930
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+25
+00:01:46,930 --> 00:01:47,050
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+26
+00:01:47,050 --> 00:01:47,130
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+27
+00:01:47,130 --> 00:01:47,270
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+28
+00:01:47,270 --> 00:01:47,510
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+29
+00:01:47,510 --> 00:01:49,070
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+30
+00:01:49,070 --> 00:01:49,110
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+31
+00:01:49,110 --> 00:01:52,710
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. 
+
+32
+00:01:52,710 --> 00:01:54,670
+الـ .. الـ 
+
+33
+00:01:58,490 --> 00:02:06,110
+لما نحكي في الـ Metric Spaces، سنبدأ بشيء آخر، وهو 
+
+34
+00:02:06,110 --> 00:02:10,650
+أن كل .. لأنه صار فيه Sets .. صار فيه Sequences ..
+
+35
+00:02:10,650 --> 00:02:13,290
+كل Sequence .. هذا في الـ Metric Spaces .. كل
+
+36
+00:02:13,290 --> 00:02:16,410
+Sequence لديها Sub-Sequence Convergent .. الـ Set
+
+37
+00:02:16,410 --> 00:02:23,970
+اللي يتحقق هذه، نسميها Compact Set في الـ R وفي الـ
+
+38
+00:02:23,970 --> 00:02:27,370
+R<sup>N</sup> أو حتى في الـ Finite Dimensional Vector Spaces
+
+39
+00:02:27,370 --> 00:02:31,390
+أو الـ Normed Spaces بنعرف الـ Compact على أساس
+
+40
+00:02:31,390 --> 00:02:33,810
+أنه الـ Set اللي بتكون Closed و Bounded على طول 
+
+41
+00:02:33,810 --> 00:02:39,790
+أشمالها Compact طب هو بنفع أه بنفع هنا ليش؟ لأنه 
+
+42
+00:02:39,790 --> 00:02:44,640
+أنا في الـ Topological Spaces in General Every Open
+
+43
+00:02:44,640 --> 00:02:48,420
+Cover has a Finite Sub Cover لا يكافئ أنه .. اللي
+
+44
+00:02:48,420 --> 00:02:51,560
+هو أنه Every Sequence has a Convergent Subsequence
+
+45
+00:02:51,560 --> 00:02:54,840
+عشان هيك بنعرف في الـ Topological Spaces بـ Every
+
+46
+00:02:54,840 --> 00:02:57,740
+Open Cover has a Finite Cover اللي هو تعريف الـ
+
+47
+00:02:57,740 --> 00:03:02,520
+Compactness الأصلي إذا كنت تكتب تعطيهم الكلام اللي
+
+48
+00:03:02,520 --> 00:03:05,920
+حكيته اللي هو Every اللي هو Set has a Convergent
+
+49
+00:03:05,920 --> 00:03:09,860
+.. Every Sequence has a Convergent Subsequence لكن
+
+50
+00:03:09,860 --> 00:03:12,740
+العكس مش صحيح هذا في Topological Spaces in General
+
+51
+00:03:12,740 --> 00:03:17,260
+لأن لما نيجي ندخل في الـ Metric Space لأ بصير صحيح 
+
+52
+00:03:17,260 --> 00:03:20,640
+في الـ Metric Space هنلاقي أن Every Open Cover has
+
+53
+00:03:20,640 --> 00:03:25,770
+a Finite Sub Cover يكافئ إنه نقول إن Every Sequence
+
+54
+00:03:25,770 --> 00:03:30,590
+has a Convergent Subsequence و بناء عليه بنتجرأ للي
+
+55
+00:03:30,590 --> 00:03:33,450
+بديش أعرفله أنا بدي أسهل عليه بديش أنا بديش أتكلم 
+
+56
+00:03:33,450 --> 00:03:36,970
+في أمور الـ General بعد دي أعرفله في الـ Metric
+
+57
+00:03:36,970 --> 00:03:42,050
+Space إن الـ Comeback يعني Every Open .. Every اللي
+
+58
+00:03:42,050 --> 00:03:46,330
+هي Sequence has a Convergent Subsequence طب الآن
+
+59
+00:03:46,330 --> 00:03:50,410
+هذا الكلام طب لو أجينا دخلنا طبعا في الـ Normed
+
+60
+00:03:50,410 --> 00:03:52,590
+Spaces و في الـ Metric Spaces التانية اللي بنشتغل 
+
+61
+00:03:52,590 --> 00:03:55,630
+فيها بنفس الأسلوب في موضوع الـ Compactics لكن لما 
+
+62
+00:03:55,630 --> 00:04:00,070
+أدخل للـ R و R<sup>n</sup> و لما أدرسهم في التحليل أو في الـ
+
+63
+00:04:00,070 --> 00:04:02,750
+Complex على طول بقوله أنا مغمض بس اللي هو الـ
+
+64
+00:04:02,750 --> 00:04:06,030
+Compacts تتعني إنها Closed و Bounded ماجبلوش
+
+65
+00:04:06,030 --> 00:04:08,130
+Series of Sequences ماجبلوش Series of Sequences
+
+66
+00:04:08,130 --> 00:04:12,230
+ليش لأنه أنا عارف أنه في داخل الـ Finite
+
+67
+00:04:12,230 --> 00:04:16,420
+Dimensional Spaces هنلاقي الـ Closed و الـ Bounded 
+
+68
+00:04:16,420 --> 00:04:20,180
+تكافئ الـ Compactness يعني تكافئ أن كل Sequence هذا 
+
+69
+00:04:20,180 --> 00:04:25,480
+Convergent Subsequence يعني في داخل الـ R و الـ R
+
+70
+00:04:25,480 --> 00:04:28,580
+تربيع و كل الـ Finite Dimensional Spaces ما يلي 
+
+71
+00:04:28,580 --> 00:04:32,320
+متكافئ Every Open Cover has a Finite Sub Cover «كل 
+
+72
+00:04:32,320 --> 00:04:35,500
+مفتاح مفتاح» «كل مفتاح مفتاح» «كل سيقونس مفتاح
+
+73
+00:04:35,500 --> 00:04:36,720
+مفتاح مفتاح» «كل سيقونس مفتاح مفتاح مفتاح مفتاح»
+
+74
+00:04:36,720 --> 00:04:49,220
+«كل سيقونس
+
+75
+00:04:49,220 --> 00:04:50,780
+مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح 
+
+76
+00:04:50,780 --> 00:04:52,160
+مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح
+
+77
+00:04:52,160 --> 00:04:59,320
+مفتاح مفتاح مفتاح م
+
+78
+00:05:01,430 --> 00:05:03,830
+العنوان الـ Compactness and Finite Dimension
+
+79
+00:05:11,270 --> 00:05:13,750
+مافي تعليقات كتير عن الـ Compactness بس مش وقته
+
+80
+00:05:13,750 --> 00:05:16,670
+يعني لو في Topology احنا بنصح لكن هالجت احنا خلينا
+
+81
+00:05:16,670 --> 00:05:20,990
+حالنا في الـ Functional Definition A Metric Space X 
+
+82
+00:05:20,990 --> 00:05:24,390
+is Said to be Compact ده بيعرف وين في الـ Metric
+
+83
+00:05:24,390 --> 00:05:28,010
+Space Compact if Every Sequence in X has a
+
+84
+00:05:28,010 --> 00:05:31,810
+Convergent Subsequence ماشي هذا بيعني فيه Compactة
+
+85
+00:05:31,810 --> 00:05:35,910
+الآن لأن A Subset M of X is Said to be Compact if 
+
+86
+00:05:35,910 --> 00:05:41,710
+اتعاملنا مع الـ M As a Compact Subspace من الـ X 
+
+87
+00:05:41,710 --> 00:05:45,670
+يعني بمعنى آخر بنتعامل بالـ Metric اللي هو الـ
+
+88
+00:05:45,670 --> 00:05:48,490
+Metric الأصل اللي هنا اللي هو بمعنى is Said to be 
+
+89
+00:05:48,490 --> 00:05:52,690
+Compact if M نفسها is a Compact Considered as a 
+
+90
+00:05:52,690 --> 00:05:55,890
+Subspace of X يعني بمعنى آخر That is Every 
+
+91
+00:05:55,890 --> 00:05:58,710
+Sequence in M has a Convergent Subsequence whose
+
+92
+00:05:58,710 --> 00:06:02,910
+Limit Belongs to M في ضوء الـ Metric المعرف الأصلي 
+
+93
+00:06:02,910 --> 00:06:07,690
+في مين؟ في الـ X. طيب، إننا نيجي لأول لمّة، اطلع
+
+94
+00:06:07,690 --> 00:06:12,690
+لللمّة اللي فوق، اللمّة بتقول لي لمّة 2 5 2، A
+
+95
+00:06:12,690 --> 00:06:16,570
+Compact Subset M of a Metric Space is Closed و
+
+96
+00:06:16,570 --> 00:06:20,430
+Bounded، على طول خاصية سهلة دي، إذا كانت Compact،
+
+97
+00:06:20,430 --> 00:06:23,950
+على طول بتكون أشمالها Closed و Bounded، ده نشوف 
+
+98
+00:06:23,950 --> 00:06:30,330
+الآن، Let X be أي Element in M Closure، بدي الأن
+
+99
+00:06:30,330 --> 00:06:35,230
+أثبت لك أنه M Closed يعني أخد X في الـ M Closure 
+
+100
+00:06:35,230 --> 00:06:37,830
+لأثبت لك أن X دي لازم تكون في مين في الـ M نفسها
+
+101
+00:06:37,830 --> 00:06:41,790
+ماشي الحال طيب مدام X في الـ M Closure then There
+
+102
+00:06:41,790 --> 00:06:45,510
+is a Sequence Xn of Elements in M Such That Xn
+
+103
+00:06:45,510 --> 00:06:49,940
+بتروح لمين للـ X هذا صارت محفوظة يعني مفهوم هذا إذن 
+
+104
+00:06:49,940 --> 00:06:55,040
+However M is Compact ما زم F is Compact إذن Every
+
+105
+00:06:55,040 --> 00:06:59,240
+Sequence has a Convergent Subsequence إذن Then X
+
+106
+00:06:59,240 --> 00:07:02,660
+Element in M لأنه فيه لها Subsequence سموها X and 
+
+107
+00:07:02,660 --> 00:07:05,260
+K بتروح للـ X طب ما هي الـ Subsequence و الـ Sequence
+
+108
+00:07:05,260 --> 00:07:09,600
+الأصلية بروح لنفس الـ X معايا؟ إذن غصب عنها هتطلع
+
+109
+00:07:09,600 --> 00:07:13,720
+الـ X موجودة في الـ M معناته Then اللي هي M is
+
+110
+00:07:13,720 --> 00:07:18,670
+Closed طيب بدنا نثبت الأن إيه أشمالها is Bounded
+
+111
+00:07:18,670 --> 00:07:22,670
+بدنا نفترض العكس Suppose That M is Not Bounded
+
+112
+00:07:22,670 --> 00:07:25,930
+مدام Bounded طب احنا إذا بتتذكر شو معناه Bounded
+
+113
+00:07:25,930 --> 00:07:31,450
+أنه الـ Diameter الـ Diameter الـ Diameter لـ ماعرفش 
+
+114
+00:07:31,450 --> 00:07:35,550
+كيف أقولنا عنه الـ Diameter لـ اللي هو الـ M بيساوي الـ 
+
+115
+00:07:35,550 --> 00:07:42,230
+Supremum لـ D(X,Y) لكل الـ X و Y الموجودة في الـ M هذا
+
+116
+00:07:42,230 --> 00:07:44,710
+الـ Diameter من الـ M بنقول عنها Bounded وكان 
+
+117
+00:07:44,710 --> 00:07:48,410
+الـ Diameter نفسه ماهو؟ is Finite يعني الـ Supremum
+
+118
+00:07:48,410 --> 00:07:53,530
+ماهو؟ is Finite يعني الآن لو أي Sequence هنا في 
+
+119
+00:07:53,530 --> 00:07:56,790
+الـ M لازم المسافة بين الـ Sequence هذه و بين أي
+
+120
+00:07:56,790 --> 00:07:59,910
+Element هنا يكون إيش مالوفاينات، ماينفعش اللي هو
+
+121
+00:07:59,910 --> 00:08:05,850
+يكبر، يروح لما لا نهاية، لأن لو بدأ افترض، لو بدأ
+
+122
+00:08:05,850 --> 00:08:10,110
+أفترض الآن أن M is Not Bounded، Suppose That M is 
+
+123
+00:08:10,110 --> 00:08:12,750
+Not Bounded، معناته الـ Supremum هذا بيروح لمين؟
+
+124
+00:08:12,750 --> 00:08:17,680
+لما لا نهاية، معناته أكيد أكيد أكيد أكيد لازم ألاقي 
+
+125
+00:08:17,680 --> 00:08:22,360
+Unbounded Sequence YN بحيث أن المسافة بين YN و B
+
+126
+00:08:22,360 --> 00:08:26,260
+تكون إيه أشمالها أكبر من N لأن لو ما جيتش معناته
+
+127
+00:08:26,260 --> 00:08:29,000
+أنه حيصير إيش كل المسافات الصغيرة معناته سارة اللي
+
+128
+00:08:29,000 --> 00:08:31,160
+هو إيه إيه إيش الـ Supremum موجود معناته Supremum
+
+129
+00:08:31,160 --> 00:08:36,040
+Finite و أنا بقول نفترض إنه Unbounded يعني الـ Supremum ما 
+
+130
+00:08:36,040 --> 00:08:39,720
+عمله بيروح إلى ما لا نهاية معايا إذا لازم نلاقي
+
+131
+00:08:39,720 --> 00:08:44,000
+Subsequence أو Unbounded Sequence YN بحيث المسافة 
+
+132
+00:08:44,000 --> 00:08:49,160
+بين YN و B أكبر من اللي هو N Where B is Any
+
+133
+00:08:49,160 --> 00:08:54,100
+Fixed Element زي ما قلنا هنس YN أشمالها has Not a 
+
+134
+00:08:54,100 --> 00:08:57,240
+Bounded Subsequence ما دام الـ .. الـ .. الـ Distance 
+
+135
+00:08:57,240 --> 00:09:00,600
+بين الـ YN و الـ B أكبر من N معناته لو أخدت أي 
+
+136
+00:09:00,600 --> 00:09:04,780
+Subsequence تانية يعني منها .. أسف مش تانية لو
+
+137
+00:09:04,780 --> 00:09:08,280
+أخدت أي Subsequence منها YNK هكون الـ Distance بين
+
+138
+00:09:08,280 --> 00:09:13,040
+YNK و B أكبر من الـ NK هذه و هكذا فبتصير فش ولا 
+
+139
+00:09:13,040 --> 00:09:17,840
+Subsequence Bounded لأن كل .. كل .. كل .. كل ال ..
+
+140
+00:09:17,840 --> 00:09:21,880
+كل البعد بين YN و الـ B دايما إيه أشمالها أكبر من N 
+
+78
+00:05:01,430 --> 00:05:03,830
+العنوان: الـ Compactness and Finite Dimension
+
+79
+00:05:11,270 --> 00:05:13,750
+ما في تعليقات كتير عن الـ Compactness بس مش وقته
+
+80
+00:05:13,750 --> 00:05:16,670
+يعني لو في Topology احنا بنصح لكن هالجت احنا خلينا
+
+81
+00:05:16,670 --> 00:05:20,990
+حالنا في الـ Functional Definition: A Metric Space X
+
+82
+00:05:20,990 --> 00:05:24,390
+is Said to be Compact. ده بيعرف وين في الـ Metric
+
+83
+00:05:24,390 --> 00:05:28,010
+Space Compact if Every Sequence in X has a 
+
+84
+00:05:28,010 --> 00:05:31,810
+Convergent Subsequence. ماشي هذا بيعني فيه Compactة
+
+85
+00:05:31,810 --> 00:05:35,910
+الآن لأن A Subset M of X is Said to be Compact if 
+
+86
+00:05:35,910 --> 00:05:41,710
+اتعاملنا مع الـ M As a Compact Subspace من الـ X
+
+87
+00:05:41,710 --> 00:05:45,670
+يعني بمعنى آخر بنتعامل بالـ Metric اللي هو الـ
+
+88
+00:05:45,670 --> 00:05:48,490
+Metric الأصل اللي هنا اللي هو بمعنى is Said to be
+
+89
+00:05:48,490 --> 00:05:52,690
+Compact if M نفسها is a Compact Considered as a
+
+90
+00:05:52,690 --> 00:05:55,890
+Subspace of X. يعني بمعنى آخر That is Every
+
+91
+00:05:55,890 --> 00:05:58,710
+Sequence in M has a Convergent Subsequence whose
+
+92
+00:05:58,710 --> 00:06:02,910
+Limit Belongs to M. في ضوء الـ Metric المعرف الأصلي
+
+93
+00:06:02,910 --> 00:06:07,690
+في مين؟ في الـ X. طيب، إننا نيجي لأول لمّة، اطلع
+
+94
+00:06:07,690 --> 00:06:12,690
+لللمّة اللي فوق، اللمّة بتقول لي لمّة 2 5 2، A
+
+95
+00:06:12,690 --> 00:06:16,570
+Compact Subset M of a Metric Space is Closed و
+
+96
+00:06:16,570 --> 00:06:20,430
+Bounded، على طول خاصية سهلة دي، إذا كانت Compact،
+
+97
+00:06:20,430 --> 00:06:23,950
+على طول بتكون أشمالها Closed و Bounded، ده نشوف
+
+98
+00:06:23,950 --> 00:06:30,330
+الآن، Let X be أي Element in M Closure، بدي الآن 
+
+99
+00:06:30,330 --> 00:06:35,230
+أثبت لك أنه M Closed يعني أخد X في الـ M Closure
+
+100
+00:06:35,230 --> 00:06:37,830
+لأثبت لك أن X دي لازم تكون في مين في الـ M نفسها
+
+101
+00:06:37,830 --> 00:06:41,790
+ماشي الحال طيب مدام X في الـ M Closure then There
+
+102
+00:06:41,790 --> 00:06:45,510
+is a Sequence Xn of Elements in M Such That Xn
+
+103
+00:06:45,510 --> 00:06:49,940
+بتروح لمين للـ X هذا صارت محفوظة يعني مفهوم هذا إذن 
+
+104
+00:06:49,940 --> 00:06:55,040
+However M is Compact. ما زم F is Compact. إذن Every
+
+105
+00:06:55,040 --> 00:06:59,240
+Sequence has a Convergent Subsequence. إذن Then X
+
+106
+00:06:59,240 --> 00:07:02,660
+Element in M لأنه فيه لها Subsequence سموها X and
+
+107
+00:07:02,660 --> 00:07:05,260
+K بتروح للـ X. طب ما هي الـ Subsequence و الـ Sequence
+
+108
+00:07:05,260 --> 00:07:09,600
+الأصلية بروح لنفس الـ X معايا؟ إذن غصب عنها هتطلع
+
+109
+00:07:09,600 --> 00:07:13,720
+الـ X موجودة في الـ M معناته Then اللي هي M is
+
+110
+00:07:13,720 --> 00:07:18,670
+Closed. طيب بدنا نثبت الأن إيه أشمالها is Bounded.
+
+111
+00:07:18,670 --> 00:07:22,670
+بدنا نفترض العكس Suppose That M is Not Bounded.
+
+112
+00:07:22,670 --> 00:07:25,930
+مدام Bounded. طب احنا إذا بتتذكر شو معناه Bounded.
+
+113
+
+141
+00:09:21,880 --> 00:09:27,650
+إذا Why N has not bounded subsequence؟ بدأ مالهاش
+
+142
+00:09:27,650 --> 00:09:31,190
+bounded subsequence إذا أكيد مش converge إذا مافيش
+
+143
+00:09:31,190 --> 00:09:34,770
+ولا subsequence converge وهذا ينقض مين أن the M is
+
+144
+00:09:34,770 --> 00:09:40,650
+compact إذا الـ N لازم تكون عنده اللي هي الفرضية
+
+145
+00:09:40,650 --> 00:09:45,090
+مش مظبوطة لازم تكون the M is bounded therefore the M is
+
+146
+00:09:45,090 --> 00:09:52,580
+bounded الآن زي ما وعدتكم اطلع لفوق اطلع لفوق اطلع
+
+147
+00:09:52,580 --> 00:09:55,320
+لفوق أخذنا وورينا هنا الآن the converse of لما
+
+148
+00:09:55,320 --> 00:09:59,460
+اللي فوق need not be true in general زي ما وعدناكم
+
+149
+00:09:59,460 --> 00:10:03,760
+احنا في ال .. في ال .. في ال .. في ال .. في ال
+
+150
+00:10:03,760 --> 00:10:07,100
+normed space أو الـ metric space in general ال
+
+151
+00:10:07,100 --> 00:10:10,880
+closed والـ bounded ليس شرطا أنه يكافئ أن every
+
+152
+00:10:10,880 --> 00:10:13,940
+sequence is a convergent subsequence إذا الآن بدي
+
+153
+00:10:13,940 --> 00:10:19,330
+أجيب لك اللي هو مثلًا أقول لك اللي هو في عنده
+
+154
+00:10:19,330 --> 00:10:25,170
+sequence اللي هو تكون bounded و closed أو في عنده
+
+155
+00:10:25,170 --> 00:10:29,230
+الـ .. اللي هو set bounded و closed لكن مافيش فيها
+
+156
+00:10:29,990 --> 00:10:34,450
+اللي هو الـ sequence اللي عنده فيه sequence مش
+
+157
+00:10:34,450 --> 00:10:37,650
+هلاقي إليها ولا convergence subsequence يعني مش
+
+158
+00:10:37,650 --> 00:10:43,090
+compact بمعنى آخر الآن بدأ أجيب مثال على a closed
+
+159
+00:10:43,090 --> 00:10:48,180
+bounded set which is not compact باختصار ماشي هذا
+
+160
+00:10:48,180 --> 00:10:52,940
+أكيد من وين بده يجيبه من اللي هو أكيد يعني حسب
+
+161
+00:10:52,940 --> 00:10:55,360
+كلام الأولاني مش هجيبه من الـ final dimensional
+
+162
+00:10:55,360 --> 00:10:58,880
+space هجيبه من infinite dimensional space لأنه في
+
+163
+00:10:58,880 --> 00:11:01,080
+الـ final dimensional زي ما قعدناكم هيطلع نقش
+
+164
+00:11:01,080 --> 00:11:05,800
+مهلين زي بعض طيب a proof consider the sequence en
+
+165
+00:11:05,800 --> 00:11:10,020
+in the L2 the L2 the space of all sequences هذا
+
+166
+00:11:10,020 --> 00:11:13,700
+infinite dimensional space where en لأنه جيبنا الـ
+
+167
+00:11:13,700 --> 00:11:16,260
+standard bases اللي عارفينه E1 E2 E3 المرة الماضية
+
+168
+00:11:16,260 --> 00:11:17,840
+E1 E2 E3 ..
+
+169
+00:11:20,970 --> 00:11:24,530
+Where en بيساوي لـ kronecker delta and j اللي هي
+
+170
+00:11:24,530 --> 00:11:29,090
+عارفينها أي واحد واحد والباقي أسفار اتنين واحد
+
+171
+00:11:29,090 --> 00:11:32,710
+صفر والباقي أسفار تلاتة صفر صفر واحد والباقي
+
+172
+00:11:32,710 --> 00:11:37,720
+أسفار وهكذا الآن this sequence is bounded ليش
+
+173
+00:11:37,720 --> 00:11:41,620
+bounded؟ لأنه norm كل واحدة اللي هو عبارة عن واحد
+
+174
+00:11:41,620 --> 00:11:45,100
+لإن الـ en عبارة عن صفر، صفر، صفر، وفي الـ nth term
+
+175
+00:11:45,100 --> 00:11:48,540
+واحد، والباقي صفر، صفر، normها بصممش ينقلهم كلها
+
+176
+00:11:48,540 --> 00:11:51,400
+نصها ويبقوا المية واحد، إذا الـ norm هم إيه إيش
+
+177
+00:11:51,400 --> 00:11:57,120
+واحد، إذا اخترت أن أنا اللي هي عناصر الـ L2 هذولة،
+
+178
+00:11:57,120 --> 00:12:00,820
+أراء ليها دي، اخترتهم أنه في بينهم بعض، يعني مش
+
+179
+00:12:00,820 --> 00:12:03,360
+اللي ملزج أدم هو الـ compact هو أرس، في حاجة اسم
+
+180
+00:12:03,360 --> 00:12:09,420
+أرس، فأنا اخترت بالعمدن زي هيك، to show that the M is
+
+181
+00:12:09,420 --> 00:12:13,940
+closed we show that the M has no accumulation point
+
+182
+00:12:13,940 --> 00:12:21,680
+إذا الآن إيش بده يعملنا الـ M اختارها اللي هي عبارة
+
+183
+00:12:21,680 --> 00:12:28,270
+عن مين اللي هو الـ sequence EN ماشي أريد أن أثبت أن
+
+184
+00:12:28,270 --> 00:12:34,930
+الـ M هذه مغلقة وبعضية بعضية أثبتناها لأن norm
+
+185
+00:12:34,930 --> 00:12:38,850
+عنصرها مش بساوي بساوية حد يان كل عنصر نورمه اللي
+
+186
+00:12:38,850 --> 00:12:43,530
+هو finite الـ M يجب أن أثبت أنها مغلقة عارفين كيف
+
+187
+00:12:43,530 --> 00:12:48,080
+تثبت أنها مغلقة؟ أريد أن أثبت أنها the M Closed بحيث
+
+188
+00:12:48,080 --> 00:12:52,520
+أثبت لك أنه ليس فيها أي مقاومة يعني ليس فيها
+
+189
+00:12:52,520 --> 00:12:56,080
+مقاومة مقاومة الـ M بمعنى آخر بيصير الـ closure هو
+
+190
+00:12:56,080 --> 00:13:01,720
+الـ M لأن the M الـ Prime بتساوي Phi واحنا بنعرف أن the M
+
+191
+00:13:01,720 --> 00:13:08,500
+closure بتساوي the M اتحاد the M Prime لو هذه Phi معناته the M
+
+192
+00:13:08,500 --> 00:13:11,960
+closure بتساوي the M معناته Closed إذن هأثبت لكم إن هناك
+
+193
+00:13:11,960 --> 00:13:16,260
+لا مقاومة إذا أثبتت إن هناك لا مقاومة إذا أخدت الـ
+
+194
+00:13:16,260 --> 00:13:22,120
+M هي عبارة عن E1 E2 E3 إلى مدى نهاية وهذه جزء من
+
+195
+00:13:22,120 --> 00:13:27,820
+مين؟ من الـ L2 بدي أبحث فيه أمرين بدي أثبت لكم إن
+
+196
+00:13:27,820 --> 00:13:31,660
+أول إشي ولا واحدة من هدولة ممكن تكون مقاومة السبب
+
+197
+00:13:31,660 --> 00:13:35,400
+بسيط أن البعد بينها جذر التنين لما تاخدوا البعد
+
+198
+00:13:35,400 --> 00:13:39,170
+بين التنين حتى جوا جذر التنين بعد شوية يعني عشان
+
+199
+00:13:39,170 --> 00:13:44,790
+تكون accumulation point دنيا كلها ملزقة فيها إن
+
+200
+00:13:44,790 --> 00:13:47,950
+شاء الله فاهمين عليها الآن الـ .. الـ .. الـ .. الـ ..
+
+201
+00:13:47,950 --> 00:13:48,810
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+202
+00:13:48,810 --> 00:13:48,830
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+203
+00:13:48,830 --> 00:13:48,950
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+204
+00:13:48,950 --> 00:13:48,990
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+205
+00:13:48,990 --> 00:13:49,190
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+206
+00:13:49,190 --> 00:13:49,610
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+207
+00:13:49,610 --> 00:13:49,630
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+208
+00:13:49,630 --> 00:13:51,730
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+209
+00:13:51,730 --> 00:13:52,290
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. ال
+
+210
+00:13:52,290 --> 00:13:59,250
+الـ .. الـ .. الـ .. الـ .. الـ ..
+
+211
+00:13:59,250 --> 00:14:00,290
+الـ .. الـ ..
+
+212
+00:14:07,930 --> 00:14:13,450
+وأولا نظرح أن أي نقطة في the M يكون نقطة اكمل ممكن
+
+213
+00:14:13,450 --> 00:14:23,350
+أن يكون أي نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+214
+00:14:23,350 --> 00:14:30,470
+نقطة نقطة نقطة نقطة يعني بين الـ N عناصر الـ M مين
+
+215
+00:14:30,470 --> 00:14:34,870
+هي؟ E1 E2 E3 الأخرى بيدثبتلكم إن المسافة بين the E N
+
+216
+00:14:34,870 --> 00:14:38,550
+وأي عنصر ثاني اللي هو بتوجة للاتنين خدوا المسافة
+
+217
+00:14:38,550 --> 00:14:43,330
+بين the E N والـ E M حيث الـ E M أي عنصر موجود في الـ M بيختلف
+
+218
+00:14:43,330 --> 00:14:48,300
+عن الـ E N هي ساوي الـ norm هذا إيه اشمله 000 هذا في
+
+219
+00:14:48,300 --> 00:14:52,640
+الـ nth term وهذا في الـ nth term مثلًا أو العكس ماشي فبكون
+
+220
+00:14:52,640 --> 00:14:57,680
+حاصل طرحه هيه ماشي الحال أو ممكن واحد يكون ناقص
+
+221
+00:14:57,680 --> 00:15:01,360
+واحد مش هتفرج كتير الـ norm هنا بيساوي summation للـ
+
+222
+00:15:01,360 --> 00:15:05,560
+absolute value هنا قص نص لأن أنا بحكي عن الـ two
+
+223
+00:15:06,270 --> 00:15:09,710
+فاهمين عليها إذا هذا بيساوي مين بيطلع عند جذر
+
+224
+00:15:09,710 --> 00:15:13,850
+التنين إذا صار عند المسافة بين the EN والـ EN بيساوي جذر
+
+225
+00:15:13,850 --> 00:15:19,610
+التنين إذا .. إذا لجيت أنا لو جيت للـ ball the EN واحد
+
+226
+00:15:19,610 --> 00:15:23,170
+ونص القطر واحد مش عادي بكم the EN ونص شيله من الـ EN
+
+227
+00:15:23,170 --> 00:15:26,930
+طاقاته لأ مش هيساوي fine إذا مش limit point عشان
+
+228
+00:15:26,930 --> 00:15:32,170
+limit point إيش بيكون أنه لأي neighborhood the BEN أي
+
+229
+00:15:32,170 --> 00:15:37,110
+اللي هو ball the EN بأي نص خطر شيله منها العنصر هذا
+
+230
+00:15:37,110 --> 00:15:40,790
+تقطعها مع الـ M لازم إيش لله؟ لا يساوي five لجيتلكم
+
+231
+00:15:40,790 --> 00:15:46,550
+اللي هو نص خطر واحد ونص وربع كل بعمل إنه the BEN هو
+
+232
+00:15:46,550 --> 00:15:50,490
+واحد أو نص أو ربع شيله منه the EN تقطع له مش بيساوي
+
+233
+00:15:50,490 --> 00:15:55,150
+five سببه إن المسافات بين العناصر جذر التنين إذن
+
+234
+00:15:55,150 --> 00:15:58,860
+المسافات بين العناصر اللي هنالو بدي أكون في عنصر
+
+235
+00:15:58,860 --> 00:16:05,300
+من the M اشمله لازم تاخد هذا اتنين أو تلاتة أو أربعة
+
+236
+00:16:05,300 --> 00:16:10,560
+أو خمسة فاهمين؟ طيب صار عندي الآن hence any point
+
+237
+00:16:10,560 --> 00:16:15,080
+in the M can't be an accumulation point second اللي ضال
+
+238
+00:16:15,080 --> 00:16:18,360
+we show that any point in the M complement يعني برة
+
+239
+00:16:18,360 --> 00:16:21,160
+الـ M في الـ L2 بس مش في الـ M complement can't be
+
+240
+00:16:21,160 --> 00:16:26,000
+an accumulation point ماشي في سؤال اللي هو 13
+
+241
+00:16:26,000 --> 00:16:29,520
+Problem 6 كان بيقولنا إذا كانت النقطة accumulation
+
+242
+00:16:29,520 --> 00:16:35,740
+point بدي يكون أي neighborhood حوالين النقطة تقاطع
+
+243
+00:16:35,740 --> 00:16:39,250
+مع الـ M هيكون infinite number of dots مش هيكون
+
+244
+00:16:39,250 --> 00:16:41,970
+نقطة في infinite number of points هذا اللي هو سؤال
+
+245
+00:16:41,970 --> 00:16:45,930
+ستة في problem 138 مش صعب عمومًا طيب شوفوا صلوا على
+
+246
+00:16:45,930 --> 00:16:49,470
+النبي عز وجل أنا بدي أستعينه الآن بدي آخذ أي
+
+247
+00:16:49,470 --> 00:16:52,790
+نقطة في الـ M complement وأثبت لكم أنه لا يمكن أن تكون
+
+248
+00:16:52,790 --> 00:16:56,770
+accumulation point أو limit point للـ M شوف
+
+249
+00:16:56,770 --> 00:17:00,490
+كيف let X be any fixed point in the M complement خدوا
+
+250
+00:17:00,490 --> 00:17:05,350
+الآن الـ ball الـ نص قطرها اللي هو نص ومركزها الـ X
+
+251
+00:17:05,350 --> 00:17:11,340
+هذه شيلوا منها الـ X تقاطع الـ M مستحيل تحتوي على
+
+252
+00:17:11,340 --> 00:17:14,280
+الأكثر على الأكثر حيكون نقطة واحدة من الـ M على
+
+253
+00:17:14,280 --> 00:17:17,980
+الأكثر نقطة واحدة إيش من الـ M ليش؟ لأن لو كان في
+
+254
+00:17:17,980 --> 00:17:22,220
+نقطتين من الـ M ومصففرة .. وهي كانت جواة بهذا الـ
+
+255
+00:17:22,220 --> 00:17:25,220
+ball كيف بيبقى تكون جواة الـ ball والمسافة بين كل
+
+256
+00:17:25,220 --> 00:17:27,700
+نقطتين في الـ .. في الـ .. في الـ M إيش ماله؟ جذر
+
+257
+00:17:27,700 --> 00:17:29,920
+التنين معايا؟
+
+258
+00:17:31,370 --> 00:17:34,030
+المسافات بين النقاط اللي جوا موجودة هنا إيش هيكون
+
+259
+00:17:34,030 --> 00:17:38,590
+نص؟ لو بدوا يكون تنتين من الأم هنا طب هم المسافات
+
+260
+00:17:38,590 --> 00:17:41,210
+اللي بين التنتين اللي في الأم مش أثبتنا أنها جذر
+
+261
+00:17:41,210 --> 00:17:44,270
+التنين يعني مش هيكون التنتين جوا يعني إيه ده
+
+262
+00:17:44,270 --> 00:17:47,390
+بيلاجينا .. بيلاجينا واحدة جريبة من هذه اللي هو
+
+263
+00:17:47,390 --> 00:17:50,450
+ابن أُص لكن لو بنجول فيه كمان واحدة بيصير بينها وبين
+
+264
+00:17:50,450 --> 00:17:54,750
+كمان أختها أجال من النص وهذا مش سهل إذن هنا
+
+265
+00:17:54,750 --> 00:18:01,430
+has at most one element why قلته؟ ماشي وهذا مستحيل
+
+266
+00:18:01,430 --> 00:18:05,810
+لأن X is not an accumulation point لأنه في الـ
+
+267
+00:18:05,810 --> 00:18:08,310
+problem واحدة ستة اللي هي واحدة تلاتة بنقول إنه لو
+
+268
+00:18:08,310 --> 00:18:10,970
+كانت accumulation point لازم يكون في عند infinite
+
+269
+00:18:10,970 --> 00:18:12,990
+number of points مشتركة
+
+270
+00:18:15,030 --> 00:18:18,330
+أي point في الـ M can't be an accumulation point
+
+271
+00:18:18,330 --> 00:18:21,850
+therefore the M has no accumulation point hence the M
+
+272
+00:18:21,850 --> 00:18:24,650
+بتساوي the M closure زي ما أقولها ومن ثم the M is closed
+
+273
+00:18:24,650 --> 00:18:29,070
+إذا صار عندي the M closed و open إذا صار عندي اللي هي
+
+274
+00:18:29,070 --> 00:18:34,050
+إيش مالها اللي هي متحققة لأن بدنا نقول إنها إيش
+
+275
+00:18:34,050 --> 00:18:39,670
+مالها خليني بدنا نقول إيش إنها مش compact ماشي
+
+276
+00:18:39,670 --> 00:18:44,710
+moreover the M has no convergence subsequence ليش؟
+
+277
+00:18:44,710 --> 00:18:48,490
+Because the M has no accumulation point لو بدها تكون
+
+278
+00:18:48,490 --> 00:18:53,530
+في عندي subsequence في الـ M Xn subsequence في الـ
+
+279
+00:18:53,530 --> 00:18:58,550
+M والـ Xn has a convergence subsequence to some X في
+
+280
+00:18:58,550 --> 00:19:03,730
+الـ M بيصير اللي هو أنه عندي تكدس من الـ .. من ..
+
+281
+00:19:03,730 --> 00:19:07,330
+من .. من .. من المقاطع اللي موجودة في الـ M المسافة
+
+282
+00:19:07,330 --> 00:19:09,710
+بينها و بينها بقى أصغر من الـ Y في الدنيا طبعاً
+
+283
+00:19:09,710 --> 00:19:14,160
+جدر التنين المسافة بينهم بعيد عن بعض فاهمين اللي
+
+284
+00:19:14,160 --> 00:19:20,080
+بحكيه؟ أي سؤال؟ إذا الـ M is not compact الـ M is not 
+
+285
+00:19:20,080 --> 00:19:23,500
+compact ليش؟ لأنه لو أخدنا أي sequence في الـ M
+
+286
+00:19:23,500 --> 00:19:26,020
+مستحيل مستحيل مستحيل مستحيل مستحيل مستحيل مستحيل
+
+287
+00:19:26,020 --> 00:19:26,320
+مستحيل مستحيل مستحيل مستحيل مستحيل يستحيل يستحيل
+
+288
+00:19:26,320 --> 00:19:26,380
+يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل
+
+289
+00:19:26,380 --> 00:19:26,500
+يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل
+
+290
+00:19:26,500 --> 00:19:26,620
+يستحيل
+
+291
+00:19:37,700 --> 00:19:40,780
+Xn بتروح للـ X عشان تكون converged إلى الـ X بيكون 
+
+292
+00:19:40,780 --> 00:19:44,600
+أي ball حوالين الـ X بحتوي عدد لا نهائي من النقاط
+
+293
+00:19:44,600 --> 00:19:47,660
+مع عدد finite number مش هيك معناه الـ limit limit
+
+294
+00:19:47,660 --> 00:19:52,400
+Xn بتروح بتساوي X معناه تقرير every Y أكبر من 0
+
+295
+00:19:52,400 --> 00:19:57,360
+there exist K element in N such that الـ ball للـ X 
+
+296
+00:19:57,360 --> 00:20:03,700
+هذه و الـ Y اللي هو تحتوي
+
+297
+00:20:03,700 --> 00:20:10,500
+أو XnXn element الـ ball for every n أكبر شوء إيش 
+
+298
+00:20:10,500 --> 00:20:16,040
+فيه وهذا مستحيل لأنه إذا كانت جوا هنا بيصير البعد
+
+299
+00:20:16,040 --> 00:20:19,840
+بين عناصر الـ M إيه شمالهم اللي هو أقل من إبسلون
+
+300
+00:20:19,840 --> 00:20:22,800
+طب إبسلون هذا كل إبسلون طب أنا جدر التنين عن جدر 
+
+301
+00:20:22,800 --> 00:20:26,100
+التنين و بس أقل من جدر التنين ببطّل فيه إيش إيه
+
+302
+00:20:27,060 --> 00:20:31,500
+الآن الـ
+
+303
+00:20:31,500 --> 00:20:34,200
+M ليس كمبكت
+
+304
+00:20:37,090 --> 00:20:40,350
+المثال تبعنا جبناه على infinite dimensional space
+
+305
+00:20:40,350 --> 00:20:44,410
+زي ما وعدناكم بدنا نقول للإعلان التالي in a finite
+
+306
+00:20:44,410 --> 00:20:49,010
+dimensional normed space X any subset M of X is 
+
+307
+00:20:49,010 --> 00:20:51,670
+compact if and only if M is closed and M is
+
+308
+00:20:51,670 --> 00:20:54,630
+bounded إذا في الـ finite dimensional space الدنيا
+
+309
+00:20:54,630 --> 00:20:58,970
+حلوة و تمامة تمام والـ closed و الـ compact يكافئ
+
+310
+00:20:58,970 --> 00:21:03,920
+closed و bounded شوفوا كيف بعد مجموعة 2.5.2 مقاومة
+
+311
+00:21:03,920 --> 00:21:07,200
+تشير إلى مقاومة مقاومة ومقاومة هذا موجود في كل 
+
+312
+00:21:07,200 --> 00:21:10,780
+الأساسيات حتى في الأساسيات التبولوجية الـ M يجب
+
+313
+00:21:10,780 --> 00:21:14,360
+أن نثبت الـ Converse مقاومة مقاومة مقاومة تشير إلى
+
+314
+00:21:14,360 --> 00:21:18,300
+مقاومة مقاومة ومقاومة يجب أن أثبت لكم أن M يجب أن
+
+315
+00:21:18,300 --> 00:21:22,070
+تكون مقاومة في هذه الحالة أكيد مدام بحكي عن finite
+
+316
+00:21:22,070 --> 00:21:24,990
+dimension أنا هستخدم اللي هو الـ finite dimension
+
+317
+00:21:24,990 --> 00:21:27,730
+له هو أكيد فيدي يكون صح في .. مش صح في الـ infinite
+
+318
+00:21:27,730 --> 00:21:31,990
+و أنا صح أكيد هستخدم خاصية أنه بما أنه dimension
+
+319
+00:21:31,990 --> 00:21:35,750
+الـ X finite بساوي N و الـ E واحد و الـ E اتنين bases 
+
+320
+00:21:35,750 --> 00:21:40,530
+له أخد ايه الـ bases له؟ إذا عندي consider any
+
+321
+00:21:40,530 --> 00:21:44,410
+sequence XM بده لجيلها إيش ما لها subsequence
+
+322
+00:21:44,410 --> 00:21:47,650
+converged في ال .. في الـ M عاية؟ مش هي معناته
+
+323
+00:21:47,650 --> 00:21:51,890
+compactness؟ الآن أنا أخدنا أي sequence xm في الـ M 
+
+324
+00:21:51,890 --> 00:21:57,250
+الآن الـ xm موجودة في الـ M والـ M جزء من الـ X والـ X
+
+325
+00:21:57,250 --> 00:22:00,450
+finite dimensional إذا أكيد بقدر أكتب عناصر الـ XM
+
+326
+00:22:00,450 --> 00:22:03,250
+على صورة Linear Combination من الـ E1 وE2 لإدريان 
+
+327
+00:22:04,770 --> 00:22:09,570
+هيكون عندي xm ممكن كتبتها على صورة scalar في E1 
+
+328
+00:22:09,570 --> 00:22:15,550
+scalar في E2 لعندي scalar في مين في E1 X1 E1 XI 1
+
+329
+00:22:15,550 --> 00:22:21,090
+E1 XI 2 E1 XI N 1 in general XM بيساوي XI 1 M E1
+
+330
+00:22:21,090 --> 00:22:30,110
+XI 2 M E2 لعندي XI N M E N since M is bounded إذا
+
+331
+00:22:30,110 --> 00:22:34,950
+الـ sequence اللي جوه bounded مظبوط؟ إذا since M is 
+
+332
+00:22:34,950 --> 00:22:39,750
+bounded so XM is bounded إيش معناه bounded؟
+
+333
+00:22:39,750 --> 00:22:42,970
+معناتها there exists K بحيث أن norm لـ XM أصغر أو
+
+334
+00:22:42,970 --> 00:22:49,230
+شويه مين K for all مين M من لمّة اتنين اربعة واحد
+
+335
+00:22:49,230 --> 00:22:52,090
+المليح هذا اللي استخدمنا .. اللي أثبتناها في الأول
+
+336
+00:22:52,090 --> 00:22:56,010
+there exists C أكبر من صفر such that K أكبر أو 
+
+337
+00:22:56,010 --> 00:23:02,790
+شويه اللي هو الـ norm هذا اللي هوهيها من هنا الـ K
+
+338
+00:23:02,790 --> 00:23:06,970
+أكبر سواء norm XM والـ XM هيها هيها الـ XM اللي هي
+
+339
+00:23:06,970 --> 00:23:10,910
+هذه أه بس كتر ده في الـ summation إذا الـ normal X
+
+340
+00:23:10,910 --> 00:23:16,950
+الـ K أكبر سواء norm XM اللي هو هذا و هذا من اللمّة
+
+341
+00:23:16,950 --> 00:23:21,730
+اللي قبل بشوية باللاجة C بحيث أنه هي أكبر سواء C
+
+342
+00:23:21,730 --> 00:23:28,640
+في mean في الـ summation طيب اللي هنطلع لفوق Hence,
+
+343
+00:23:28,820 --> 00:23:35,780
+for any fixed I من 1 إلى N in the sequence Xim is
+
+344
+00:23:35,780 --> 00:23:41,440
+a bounded sequence of numbers أكيد الـ Xim bounded
+
+345
+00:23:41,440 --> 00:23:45,250
+sequence ليه؟ لأنه صار الـ summation هذا أكبر أو
+
+346
+00:23:45,250 --> 00:23:50,210
+أصغر أو ساوي هذا على C كل واحدة من اندولا Cy M 
+
+347
+00:23:50,210 --> 00:23:53,670
+هتكون أصغر أو تساوي K على C يعني صارت الـ sequence
+
+348
+00:23:53,670 --> 00:23:56,530
+هذي bounded sequence إذا صارت عندي bounded 
+
+349
+00:23:56,530 --> 00:24:00,710
+sequence of مين؟ of numbers باشر و دوين على الـ R 
+
+350
+00:24:00,710 --> 00:24:05,430
+أو على الـ C اللي ضامن انه انه في مدام اللي هو 
+
+351
+00:24:05,430 --> 00:24:09,010
+sequence of numbers و بولزانو بتقول every sequence
+
+352
+00:24:09,010 --> 00:24:12,210
+bounded sequence هذا convergence subsequence إذا 
+
+353
+00:24:12,210 --> 00:24:17,030
+لازم it has a convergent subsequence say that it 
+
+354
+00:24:17,030 --> 00:24:20,530
+converges to mean to Xi I إذا الـ subsequence من
+
+355
+00:24:20,530 --> 00:24:25,770
+هذه converges to mean لـ Xi I بالظبط بديش أقول عيد
+
+356
+00:24:25,770 --> 00:24:28,530
+اللي قلناه قبل و شوية then as in the proof of لمّة
+
+357
+00:24:28,530 --> 00:24:34,180
+2 4 5 we show that XM A شمالها has بنركّب منهن
+
+358
+00:24:34,180 --> 00:24:36,440
+هدولة مش هدولة جيناها الـ bounded بنركّب منهن
+
+359
+00:24:36,440 --> 00:24:42,800
+subsequence ZM اللي هنا الـ scalars سبعتها من الـ 
+
+360
+00:24:42,800 --> 00:24:45,940
+XM اللي قبل شوية قلتها اللي كنا بسميينها هنا YM و
+
+361
+00:24:45,940 --> 00:24:50,860
+YM1 و YM2 و الاخرى which converts to mean to اللي
+
+362
+00:24:50,860 --> 00:24:55,560
+هو الـ Z اليمين الـ Z اللي هي XI 1 في E1 اللي 
+
+363
+00:24:55,560 --> 00:25:01,200
+عملتين قبل شوية لأنه صارت limit XI IM هي XI I ماشي
+
+364
+00:25:01,200 --> 00:25:07,440
+فالـ XM اللي قبل بشوية limit هيصير XII EI الـ Z 
+
+365
+00:25:07,440 --> 00:25:11,120
+بساوي اللي هو Z M converged to Z however M is 
+
+366
+00:25:11,120 --> 00:25:16,980
+closed إذا هذي هتكون الموجودة في M therefore M is
+
+367
+00:25:16,980 --> 00:25:23,520
+compact وهو المطلوب نيجي الآن نظرية محترمة ومهمة
+
+368
+00:25:23,520 --> 00:25:29,290
+برضه من النظريات اللي اللي .. يعني اللي هسا عملتها
+
+369
+00:25:29,290 --> 00:25:34,470
+عندنا واسعة اطلع لفوق اخليها على رأس اللي هناك
+
+370
+00:25:34,470 --> 00:25:39,650
+ريزيز لمّة اه ريزيز لمّة ايش بتقول ريزيز لمّة 
+
+371
+00:25:39,650 --> 00:25:46,670
+خليني أوضحها بالرسم نيح عشان
+
+372
+00:25:46,670 --> 00:25:51,410
+نصها أنا بالنسبة لي مهم برضه برهان مش صعب سهل إن
+
+373
+00:25:51,410 --> 00:25:51,670
+شاء الله
+
+374
+00:26:06,170 --> 00:26:10,270
+عندي الآن let y and z be subspaces of a normed
+
+375
+00:26:10,270 --> 00:26:15,130
+space x هي في عندي normed space مين؟ x برا هذا
+
+376
+00:26:15,130 --> 00:26:19,070
+normed space الأصلي x اللي تبعنا اللي هو اللي كلنا 
+
+377
+00:26:19,070 --> 00:26:24,870
+subspaces منهو Y و Z subspaces من X و Y closed and
+
+378
+00:26:24,870 --> 00:26:30,810
+proper subset من من من Z يعني هي Y جوا Y و proper
+
+379
+00:26:30,810 --> 00:26:35,790
+subset منين من Z يعني في element هنا مش موجود وين 
+
+380
+00:26:35,790 --> 00:26:41,270
+مش موجود في Y و Y و Z نفسهم subspaces من من من X
+
+381
+00:26:41,270 --> 00:26:50,380
+الآن بقولي إذا لأي θ لأي θ Element in Zero و واحد 
+
+382
+00:26:50,380 --> 00:26:56,220
+بقدر ألاقي Element in Min in Z there exist Z
+
+383
+00:26:56,220 --> 00:27:03,620
+Element in Z ومش هيك كمان و Normal بساوي واحد و
+
+384
+00:27:03,620 --> 00:27:10,120
+بعضه و بعض ال .. يعني بعض الـ Z هذا عن الـ Y بعض ال
+
+385
+00:27:10,120 --> 00:27:18,460
+Z عن الـ Y أكبر أو تساوي Min فترةعنا .. تنسوش هذا 
+
+386
+00:27:18,460 --> 00:27:23,780
+أن Y بروبر سبسيط .. بروبر سبسيط من مين؟ من Z مزامه
+
+387
+00:27:23,780 --> 00:27:27,100
+بروبر سبسيط يعني الكلام منطقي أنه بلاقي لكل Z في
+
+388
+00:27:27,100 --> 00:27:31,960
+الـ Y في الـ Z لكل .. آسف لكل θ التي تزيد واحد بقدر 
+
+389
+00:27:31,960 --> 00:27:35,920
+لاقي Z في الـ Y بحيث أن المسافة بين الـ Z و الـ Y 
+
+390
+00:27:35,920 --> 00:27:41,450
+أكبر أو يساوي الـ θ تبعتك لكل Y وين موجودة في الـ Y 
+
+391
+00:27:41,450 --> 00:27:45,450
+Capital يعني بمعنى آخر وكإني بقول Roughly أن لكل 
+
+392
+00:27:45,450 --> 00:27:49,170
+θة من Zero لواحد نص ربع طولت حتى لو زغرتها حتى لو
+
+393
+00:27:49,170 --> 00:27:54,250
+كبرتها اللي هو بيكون بقدر ألاقي Z في Z نورمها
+
+394
+00:27:54,250 --> 00:27:58,270
+بيساوي واحد بحيث أن الـ norm للـ Z minus Y يكون إيه
+
+395
+00:27:58,270 --> 00:28:03,450
+أشمله أكبر أو يساوي θة يعني بعضها عن الـ Y أكبر أو
+
+396
+00:28:03,450 --> 00:28:09,900
+يساوي θة و الـ θة نفسها أكبر من مين؟ من صفر آه يعني 
+
+397
+00:28:09,900 --> 00:28:13,580
+في مسافة لإن هو بروبرت يعني لو مشوا بروبرت بيصيب
+
+398
+00:28:13,580 --> 00:28:16,600
+الموضوع لأ بختلف طيب نشوف إيش البرهان
+
+399
+00:28:21,360 --> 00:28:24,900
+let v be any element in z minus y يعني أخدت
+
+400
+00:28:24,900 --> 00:28:29,840
+element من وين من هنا بين اللي هو الـ z في الـ z و
+
+401
+00:28:29,840 --> 00:28:33,000
+مش من وين مش في الـ y وهذا اللي بدي يوصلني للي
+
+402
+00:28:33,000 --> 00:28:37,260
+بديها الآن let v be any element in z minus y and
+
+403
+00:28:37,260 --> 00:28:40,920
+let a بيساوي الـ infimum للنورم للـ v minus y y
+
+404
+00:28:40,920 --> 00:28:45,300
+element in y يعني بتاخد الـ a شمالها هي عبارة عن 
+
+405
+00:28:45,300 --> 00:28:51,990
+المسافة مسافة بين الـ v اللي أخدته من هنا بين ال ..
+
+406
+00:28:51,990 --> 00:28:57,930
+و بين مين الـ Y الـ infimum للـ norms الـ V minus Y و
+
+407
+00:28:57,930 --> 00:29:02,770
+Y limit on Y هو اللي بتسميه إيش بتسميه الـ A الآن
+
+408
+00:29:02,770 --> 00:29:07,750
+بقولي since Y is closed then A إيش مالها A أكبر
+
+409
+00:29:07,750 --> 00:29:09,170
+من مين من صفر
+
+410
+00:29:12,520 --> 00:29:17,360
+بما أنه Y closed إذا الـ A هد إيش ما لها أكبر من 
+
+411
+00:29:17,360 --> 00:29:24,440
+صفر إيش علاقتها؟ عنده ما أعطيك الـ A الـ A سوى الـ 
+
+412
+00:29:24,440 --> 00:29:31,180
+infimum لـ unknown V minus Y حيث Y element in Y
+
+413
+00:29:32,280 --> 00:29:37,000
+يعني باخد الأبعاد بعض الـ V عن الـ Y و باخد الـ 
+
+414
+00:29:37,000 --> 00:29:39,860
+infimum لكل الـ ال white اللي في الـ Y و باخد الـ 
+
+415
+00:29:39,860 --> 00:29:43,000
+infimum اللي هم ده سميمن الـ A هذا بقول الـ A 
+
+416
+00:29:43,000 --> 00:29:49,960
+شماله أكيد شماله أكبر من صفر وقلت سبب عشان Y 
+
+417
+00:29:49,960 --> 00:29:58,800
+closed Y is closed الآن الآن لو الـ infimum هذا بده 
+
+418
+00:29:58,800 --> 00:30:05,080
+يساوي صفر الآنفمان بيساوي صفر معناته صار عندي من 
+
+419
+00:30:05,080 --> 00:30:11,020
+تعريف الانفمان بقدر ألاقي sequence من الـ Y YN اللي
+
+420
+00:30:11,020 --> 00:30:16,700
+هو بحيث أن normal V minus الـ YN يقول إلى مين الـ A 
+
+421
+00:30:16,700 --> 00:30:22,140
+هذه اللي أصبحت إيش تسمينها سفر معناته صار عندي ..
+
+422
+00:30:22,140 --> 00:30:25,860
+هد شو معناته؟ هد معناته أنه صار الـ yn converged
+
+423
+00:30:25,860 --> 00:30:33,460
+من للـV يعني لجيت sequence yn من اللي هي الـY
+
+424
+00:30:33,460 --> 00:30:38,900
+converged من للـV طب my Y closed، إذا الـV وين
+
+425
+00:30:38,900 --> 00:30:43,400
+هتكون؟ في الـY Contradiction لأن الـ V من أين أخدها
+
+426
+00:30:43,400 --> 00:30:48,880
+أنا؟ من Z minus Y إذا أكيد ما دامت الـ Y closed و
+
+427
+00:30:48,880 --> 00:30:52,220
+الـ A هي الـ infimum هتكون الـ A أشمالها أكبر من
+
+428
+00:30:52,220 --> 00:31:00,000
+سفر و الـ Y هي اللي وضحتها اطلع لفوق now .. now ..
+
+429
+00:31:00,000 --> 00:31:03,100
+take any θ element in 0 و 1 بتحصر على اللي بديها
+
+430
+00:31:03,100 --> 00:31:07,720
+then by definition of infimum there exists y
+
+431
+00:31:07,720 --> 00:31:11,880
+nought element in Y such that الـ V minus Y not
+
+432
+00:31:11,880 --> 00:31:14,960
+اللي هو أكبر يساوي A لإنه الـ A infimum لهم كلهم
+
+433
+00:31:14,960 --> 00:31:19,580
+اللي هو greatest lower bound lower bound في
+
+434
+00:31:19,580 --> 00:31:24,640
+النهاية إذاً الـ A أصغر يساويها دي طيب الآن ال θ
+
+435
+00:31:24,640 --> 00:31:29,160
+بين ال 0 و ال 1 مظبوط ولا لأ مزام ال θ بين ال 0 و
+
+436
+00:31:29,160 --> 00:31:33,720
+ال 1 إذاً ال A على θ أيش مالها هتصير أيش مالها
+
+437
+00:31:33,720 --> 00:31:39,240
+أصغر من الـ A، مظبوط ولا لا؟ آسف أكبر من الـ A، 
+
+438
+00:31:39,240 --> 00:31:43,080
+مظبوط؟ يعني مدام صارت أكبر من A، إذا بطلت lower
+
+439
+00:31:43,080 --> 00:31:46,860
+bound لأن الـ A إيش مالها؟ the greatest lower
+
+440
+00:31:46,860 --> 00:31:51,500
+bound أي إيش أكبر منها، ببطل lower bound مدام بطلت
+
+441
+00:31:51,500 --> 00:31:55,180
+هذه lower bound لأنها أكبر من الـ A إذا أكيد،
+
+442
+00:31:55,180 --> 00:31:59,560
+أكيد، أكيد، بلاكي عنصر في ال 6 هنا و اليكن Y not
+
+443
+00:31:59,560 --> 00:32:04,220
+بكون هذا أيه شماله؟ هو اللي أفسد عليها انها تكون
+
+444
+00:32:04,220 --> 00:32:11,940
+lower bound يعني هيكون أصغر أو يسويها واضح؟
+
+445
+00:32:11,940 --> 00:32:18,380
+أنه الآن a على θ أكبر من الـ A والـ A greatest
+
+446
+00:32:18,380 --> 00:32:23,420
+lower bound يعني الـ A على ثيتا بتبطل lower bound
+
+447
+00:32:23,420 --> 00:32:28,320
+مدام بطلت lower bound لهذه المجموعة إذا أكيد في
+
+448
+00:32:28,320 --> 00:32:32,700
+عنصر في المجموعة خلّها تبطل يعني بمعنى آخر تخلّها
+
+449
+00:32:32,700 --> 00:32:35,160
+تبطل lower bound تخلّها تبطل إنها أصغر من الكل
+
+450
+00:32:35,160 --> 00:32:39,400
+خلّه إن V minus Y not يكون أصغر أو يساوي من A على
+
+451
+00:32:39,400 --> 00:32:43,890
+ثيتا اللي بطل lower bound نتعرف على طول طيب خلوه
+
+452
+00:32:43,890 --> 00:32:47,830
+هادي إذا هادي اللي هي صحيحة مائة بالمائة و لجينا
+
+453
+00:32:47,830 --> 00:32:52,970
+why not بحقق هادي الآن أنا غلط مين؟ أنا أنا أنا
+
+454
+00:32:52,970 --> 00:33:00,450
+أنا أنا أنا
+
+455
+00:33:00,450 --> 00:33:01,010
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+456
+00:33:01,010 --> 00:33:01,090
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+457
+00:33:01,090 --> 00:33:01,730
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+458
+00:33:01,730 --> 00:33:02,330
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+459
+00:33:02,330 --> 00:33:02,490
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+460
+00:33:02,490 --> 00:33:03,450
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+461
+00:33:03,450 --> 00:33:03,990
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+462
+00:33:03,990 --> 00:33:15,710
+أنا أنا أنا أنا
+
+463
+00:33:15,710 --> 00:33:21,130
+أنا اللي هي مقلوبة دي C في V minus Y not أخدني ال V
+
+464
+00:33:21,130 --> 00:33:26,270
+minus Y not على نورمها يعني Z بتساوي V minus Y not
+
+465
+00:33:26,270 --> 00:33:31,930
+على نورمها ونورمها مش سفر أه لإن هد مش سفر و هد
+
+466
+00:33:31,930 --> 00:33:37,370
+أكبر يسوي هد إن هد اسمه مهدنا قبل إنه قلنا لإيه مش
+
+467
+00:33:37,370 --> 00:33:41,110
+سفر إذا صار هد مش سفر لإنه أكبر منها أسويها إذا
+
+468
+00:33:41,110 --> 00:33:44,750
+صار عندي الآن فيه إمكانية أقسم على نورمها خد الآن
+
+469
+00:33:44,750 --> 00:33:49,620
+Z بتساوي هذا المقدر الآن ال C طبعا هي واحد على نورم
+
+470
+00:33:49,620 --> 00:33:54,500
+هذا الآن أنا بقولك ال Z نورم ال Z إيش هيساوي واحد
+
+471
+00:33:54,500 --> 00:33:59,500
+و هيحقق اللي بديها نورم ال Z بيساوي واحد واضح لأن
+
+472
+00:33:59,500 --> 00:34:05,160
+let Y be any fixed element in Y وحسب الآن نورم ال
+
+473
+00:34:05,160 --> 00:34:11,160
+Z minus Y إيش بيساوي بيساوي Z طلع لي اللي هي عوض ليها
+
+474
+00:34:11,160 --> 00:34:14,280
+زي ده إيش بالساوية C فيها ده اللي هو C في V minus
+
+475
+00:34:14,280 --> 00:34:20,780
+Y not ناقص من ال Y طلع لي لو سمحت C برا و بيصير هد
+
+476
+00:34:20,780 --> 00:34:25,260
+V minus Y not و هد بيصير إيش مالها Y على C اللي هو
+
+477
+00:34:25,260 --> 00:34:30,920
+C inverse في مين في Y Y ساوي C في ال norm لل V
+
+478
+00:34:30,920 --> 00:34:35,180
+minus Y واحد إيش ال Y واحد؟ Y واحد أخدت السالب برا
+
+479
+00:34:35,180 --> 00:34:40,240
+صارت هد Y not زاد C inverse في Y أه إذا ال Y واحد
+
+480
+00:34:40,240 --> 00:34:46,280
+هي هذه الآن هذه why not من ال Y و ال Y من ال Y إذا
+
+481
+00:34:46,280 --> 00:34:49,400
+المجموح من ال Y واحد هتكون برضه من وين من ال Y
+
+482
+00:34:49,400 --> 00:34:56,000
+which belongs to Y إذا ملخص الحديث إنه صار V minus
+
+483
+00:34:56,000 --> 00:35:04,060
+Y واحد عندي اللي هو في C بيساوي اللي هو المقدار هذا
+
+484
+00:35:06,150 --> 00:35:13,050
+الآن عندي V-Y1 هيكون أكبر أو يساوي مين أو يساوي
+
+485
+00:35:13,050 --> 00:35:25,810
+أيه V-Y1 V-Y1 أكبر أو يساوي أيه طيب
+
+486
+00:35:25,810 --> 00:35:27,390
+حلينا عشان نوضح لكم
+
+487
+00:35:38,040 --> 00:35:41,100
+طيب يا جماعة لأ نزلي عشان نشوف ال .. ال .. ال ..
+
+488
+00:35:41,100 --> 00:35:47,120
+عندي أثبتنا أنه عند Normal Z minus Y Z minus Y
+
+489
+00:35:47,120 --> 00:35:53,260
+اللي هو بيساوي C في Normal V minus Y واحد الآن عندي
+
+490
+00:35:53,260 --> 00:35:56,720
+ال y واحد بيساوي نوت زي c inverse one which belongs
+
+491
+00:35:56,720 --> 00:36:01,740
+to me into y إذا صارت مدام y واحد في ال y إذا أكيد
+
+492
+00:36:01,740 --> 00:36:05,680
+أكيد أكيد ال v minus y واحد أكبر يسوى من أيه لأن
+
+493
+00:36:05,680 --> 00:36:11,080
+الامين هي الامسفة من الهن كلهن واضح طيب الآن بدنا
+
+494
+00:36:11,080 --> 00:36:16,060
+نستخدم one to get to get الآن أنا بدي أستخدم هذه
+
+495
+00:36:16,060 --> 00:36:20,600
+احسب لي يعني حسابات بدي أحسب لك أيه يعني Z-Y بالساوي
+
+496
+00:36:20,600 --> 00:36:25,420
+هيها Z-Y بالساوي C في المقدار هذا C في المقدار هذا
+
+497
+00:36:25,420 --> 00:36:29,380
+والمقدار هذا قولنا عنه أشماله أكبر يساوي أيه إذا
+
+498
+00:36:29,380 --> 00:36:32,220
+أكبر يساوي مين C في A
+
+499
+00:36:35,900 --> 00:36:38,920
+الآن عندي ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+500
+00:36:38,920 --> 00:36:39,180
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+501
+00:36:39,180 --> 00:36:39,240
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+502
+00:36:39,240 --> 00:36:39,320
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+503
+00:36:39,320 --> 00:36:40,780
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+504
+00:36:40,780 --> 00:36:41,520
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+505
+00:36:41,520 --> 00:36:43,180
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+506
+00:36:43,180 --> 00:36:43,900
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+507
+00:36:43,900 --> 00:36:49,220
+ال .. ال .. ال .. ال ..
+
+508
+00:36:49,220 --> 00:36:52,440
+ال .. ال .. ال ..
+
+509
+00:36:52,440 --> 00:36:55,700
+ال .. ال .. ال ..
+
+510
+00:36:57,590 --> 00:37:01,430
+الآن هذه ليها مقلوبها C بيصير C أكبر أو يساوي θ
+
+511
+00:37:01,430 --> 00:37:01,770
+على A
+
+512
+00:37:06,030 --> 00:37:10,510
+أضربه في a بيصير c أكبر من θ على a في a ال a بتروح
+
+513
+00:37:10,510 --> 00:37:13,590
+مع ال a ويبقى مين يعني ال c z minus y أكبر من
+
+514
+00:37:13,590 --> 00:37:18,390
+مين θ أخدت الآن اللي هو أي θ في ال zero و ال واحد
+
+515
+00:37:18,390 --> 00:37:23,950
+أيه من هنا أخدت ال theta أي element من zero و واحد
+
+516
+00:37:23,950 --> 00:37:30,210
+لجيت ال z هيها نورمها بيساوي واحد و البعد بين z و
+
+517
+00:37:30,210 --> 00:37:34,550
+minus y أكبر و يساوي θ وهو المطلوب طيب
+
+518
+00:37:37,750 --> 00:37:47,810
+ملاحظة الآن في عندي اطلع لفوق in
+
+519
+00:37:47,810 --> 00:37:53,210
+a finite dimensional space the closed unit ball is
+
+520
+00:37:53,210 --> 00:37:57,900
+compact في الـ finite dimensional space الـ closed
+
+521
+00:37:57,900 --> 00:38:01,160
+ball is compact أكيد لأن الـ closed ball a closed
+
+522
+00:38:01,160 --> 00:38:06,040
+set abounded و finite dimensional إذا إيش مالها؟
+
+523
+00:38:06,040 --> 00:38:09,880
+compact لكن هذه الخاصية لن تتحقق في ال infinite
+
+524
+00:38:09,880 --> 00:38:13,960
+dimensional space في ال finite dimensional space
+
+525
+00:38:13,960 --> 00:38:18,730
+أي closed unit ball is compact لكن الموضوع بختلف في
+
+526
+00:38:18,730 --> 00:38:23,350
+ال infinite شوف الآن theorem if unknown space X
+
+527
+00:38:23,350 --> 00:38:27,890
+has the property that the closed unit ball M is
+
+528
+00:38:27,890 --> 00:38:32,650
+compact then X is finite dimensional لاحظ؟ كلام
+
+529
+00:38:32,650 --> 00:38:36,370
+خطير الآن إذا كان في ال norm of the space X عندك
+
+530
+00:38:36,370 --> 00:38:40,530
+بتحقق الخاصية في ال .. في ال .. جيت .. أخدت لك norm
+
+531
+00:38:40,530 --> 00:38:44,630
+of the space اسمه X لجيت فيه خاصية أنه أي نوع ..
+
+532
+00:38:44,630 --> 00:38:48,010
+أي unit ball .. closed unit ball هذه لجيتها
+
+533
+00:38:48,010 --> 00:38:51,530
+compact على طول و أنت مغمض قول عنه إيش هذا finite
+
+534
+00:38:51,530 --> 00:38:55,410
+dimensional space إيش معناته؟ يعني لو كان infinite
+
+535
+00:38:55,410 --> 00:38:58,290
+dimensional مش هتكون اللي هي ال closed unit ball
+
+536
+00:38:58,290 --> 00:39:06,270
+إيش مالها compact طيب Suppose that M is compact but
+
+537
+00:39:06,270 --> 00:39:11,490
+dimension X بساوة Infinity و بدنا نصل إيه؟ لـ
+
+538
+00:39:11,490 --> 00:39:15,470
+Contradiction يعني مستحيل أنه يجتمع أن M is
+
+539
+00:39:15,470 --> 00:39:18,910
+compact و dimension X ملومة لنهاية إذا كانت الـ M
+
+540
+00:39:18,910 --> 00:39:22,010
+close و M compact لازم تكون final dimensional و لو
+
+541
+00:39:22,010 --> 00:39:24,350
+كانت dimension X بساوة Infinity، الـ M مش compact
+
+542
+00:39:24,350 --> 00:39:29,480
+واضح؟ طيب تختار أنا X واحد .. شوف كيف الآن بده يركب
+
+543
+00:39:29,480 --> 00:39:33,280
+لك تختار أنا X واحد الأمن X with norm X واحد إيش
+
+544
+00:39:33,280 --> 00:39:39,080
+بيساوى واحد بقدر الآن هو دائما في الاختصار الانفنت
+
+545
+00:39:39,080 --> 00:39:43,900
+لأن في عناصر .. عنصره اسمه X جسمه على نرمه بطلع
+
+546
+00:39:43,900 --> 00:39:48,620
+نرمه أشماله واحد و بطلع الدوة إذا إذا اختار أنا X
+
+547
+00:39:48,620 --> 00:39:52,000
+واحد أنا من X with norm ال X واحد بيساوى واحد this
+
+548
+00:39:52,000 --> 00:39:55,620
+X واحد generate a one dimensional space X واحد of
+
+549
+00:39:55,620 --> 00:40:02,680
+X يعني الآن بدي اخذ X بيساوي من X واحد هذا ال X
+
+550
+00:40:02,680 --> 00:40:08,600
+واحد هذا اللي هو اللي هو في طبعا الإسباني له
+
+551
+00:40:08,600 --> 00:40:13,380
+الإسباني له كل يعني ال scholars فيه هذا ال .. ال ..
+
+552
+00:40:13,380 --> 00:40:16,780
+ال .. ال space اللي هو دايما مش اللي هو مش بساوى
+
+553
+00:40:16,780 --> 00:40:23,140
+بيساوى واحد ب .. ب .. ب .. خليني أقول ببساطة أخدت
+
+554
+00:40:23,140 --> 00:40:26,000
+مدام دايما مش ال X بساوى infinity إذا في عناصر مش
+
+555
+00:40:26,000 --> 00:40:31,300
+سفر أخدت واحد من هنا X واحد و .. و .. و .. و من ال
+
+556
+00:40:31,300 --> 00:40:35,180
+X و Normal بيساوى واحد الآن كيف Normal بيساوى واحد
+
+557
+00:40:35,180 --> 00:40:38,190
+خد أي واحد و جسمه Normal و بطلع واحد واخد اللي هو
+
+558
+00:40:38,190 --> 00:40:41,390
+إيه النتج بيطلع لها x1 element in x وضمه مو بيساوى
+
+559
+00:40:41,390 --> 00:40:44,830
+واحد this x1 generates a one dimensional subspace
+
+560
+00:40:44,830 --> 00:40:49,970
+سميه مين؟ x1 of x which is closed وبروبر subspace
+
+561
+00:40:49,970 --> 00:40:53,250
+من مين؟ أكيد لأنه ذاك الـ dimension هو infinity
+
+562
+00:40:53,250 --> 00:40:56,790
+وهذا الـ dimension له اللي الـ x1 إيش ماله؟ بيساوي
+
+563
+00:40:56,790 --> 00:41:01,020
+واحد since الـ dimension لكسه مش بيساوي infinity لأن
+
+564
+00:41:01,020 --> 00:41:04,120
+by Riesz لمّا .. اطلع لفوق .. by Riesz لمّا مدام
+
+565
+00:41:04,120 --> 00:41:07,760
+هذا proper subspace close to proper subspace إذن
+
+566
+00:41:07,760 --> 00:41:11,760
+الـ Riesz لمّا تتحقق by Riesz لمّا there is x2
+
+567
+00:41:11,760 --> 00:41:15,480
+element in X و الـ norm لـ x2 بيساوي 1 و المسافة
+
+568
+00:41:15,480 --> 00:41:19,760
+بين x2 ناقص x1 أكبر يساوي مين أي θ  بيداخد مين
+
+569
+00:41:19,760 --> 00:41:25,440
+أنا النص بعد .. بعد ازمكم طيب الان و الـ X1 و X2
+
+570
+00:41:25,440 --> 00:41:30,260
+نفسي إيش مالهم بقدر أعمل منهم إيش ماله normed
+
+571
+00:41:30,260 --> 00:41:35,740
+space X2 اه و هيكون subspace من مين؟ من الـ X و الـ
+
+572
+00:41:35,740 --> 00:41:39,160
+dimension له إيش؟ بيساوي 2 يعني هيصير بروبر
+
+573
+00:41:39,160 --> 00:41:44,240
+subspace من مين؟ من X يعني هيكون X2 عبارة عن الـ span
+
+574
+00:41:44,240 --> 00:41:49,400
+للـ X1 و X2 الـ X1 الأولى و الـ X2 اللي جيتها من خلال
+
+575
+00:41:49,400 --> 00:41:55,110
+الـ Riesz طيب الان by Riesz لمّا برضه there
+
+576
+00:41:55,110 --> 00:41:59,570
+exist x3 من X لأنه proper subspace with normal x3
+
+577
+00:41:59,570 --> 00:42:05,390
+بيساوى واحد and for all x element in X2 اللي هو الـ norm 
+
+578
+00:42:05,390 --> 00:42:09,910
+الـ X3 عن الـ X أكبر أو يساوي مين برضه الـ θ اللي
+
+579
+00:42:09,910 --> 00:42:13,810
+بتاخدهاش بالساوية نص يعني طبقت الـ Riesz لمّا كمان
+
+580
+00:42:13,810 --> 00:42:18,710
+مرة بس عالميا على الـ X2 لجيت X3 بحيث بعد الـ X3
+
+581
+00:42:18,710 --> 00:42:23,210
+عن كل عناصرها أكبر أو يساوي مين نص من ضمنها لأن
+
+582
+00:42:23,210 --> 00:42:29,790
+الـ span لها X2 الـ span للـ X1 و X2 إذا x3-x1 أكبر شوهو نص
+
+583
+00:42:29,790 --> 00:42:35,210
+و x3-x2 أكبر شوهو إياه نص إذا صار عندي x3-x1 أكبر
+
+584
+00:42:35,210 --> 00:42:39,750
+شوهو نص و x3-x2 أكبر شوهو إياه نص أنا proceeding
+
+585
+00:42:39,750 --> 00:42:43,950
+by induction we obtain a sequence xn of elements
+
+586
+00:42:43,950 --> 00:42:49,430
+xn في الـ M من الـ M كلهم اللي هي مين الـ M هي الـ
+
+587
+00:42:49,430 --> 00:42:53,950
+span للـ X1 X2 الأخرى such that norm الـ xn ناقص الـ
+
+588
+00:42:53,950 --> 00:42:58,110
+xn أي شماله أكبر أو يساوي نصف البعد بينهم أي شماله
+
+589
+00:42:58,110 --> 00:43:01,990
+أكبر أو يساوي نصف، إذن هذه البعد هناك for all m
+
+590
+00:43:01,990 --> 00:43:06,990
+لا تساوي n، hence xn يستحيل يكون لها convergence
+
+591
+00:43:06,990 --> 00:43:12,050
+subsequence لأن الأبعاد بين كل العناصر ثابتة اللي
+
+592
+00:43:12,050 --> 00:43:16,210
+هي أكبر أو يساوي إيش نص يعني بعيدة عن بعض مستحيل
+
+593
+00:43:16,210 --> 00:43:19,870
+بعد شوية تقولولي والله أجيت العنصرين اللي المسافة
+
+594
+00:43:19,870 --> 00:43:23,550
+بينهم أصغر من نص أو أصغر من أي ε في الدنيا لأ لأ مدام
+
+595
+00:43:23,550 --> 00:43:27,170
+مافيش إذا X and can't have a convergence
+
+596
+00:43:27,170 --> 00:43:31,360
+subsequence this contradicts the compactness of M
+
+597
+00:43:31,360 --> 00:43:34,560
+لأنه لجهة Sequence ما فيش إلا إيش مالها Convergent
+
+598
+00:43:34,560 --> 00:43:38,000
+subsequence Therefore the dimension of X لازم يكون
+
+599
+00:43:38,000 --> 00:43:47,080
+إيش ماله is finite اللي بعده Theorem let X and Y be
+
+600
+00:43:47,080 --> 00:43:52,000
+metric spaces and خذ T من X لعند Y بيكون a
+
+601
+00:43:52,000 --> 00:43:57,550
+continuous mapping الان T T عبارة عن continuous
+
+602
+00:43:57,550 --> 00:44:02,410
+mapping من X لعين مين لعين واحد continuous mapping
+
+603
+00:44:02,410 --> 00:44:08,190
+الآن then the image of a compact subset of T of M
+
+604
+00:44:08,190 --> 00:44:13,030
+under T is compact يعني الـ image للكمبكت إيش مالها
+
+605
+00:44:13,030 --> 00:44:21,390
+is compact اه الآن شوف عشان أثبت لك في الـ .. بحكي
+
+606
+00:44:21,390 --> 00:44:26,130
+وين أنا في .. اللي هو من metric space X to metric
+
+607
+00:44:26,130 --> 00:44:31,750
+space Y و الـ T is continuous إذا كانت الـ M
+
+608
+00:44:31,750 --> 00:44:34,730
+compact، ده تكون إيش مالها compact؟ يعني ترسل الـ
+
+609
+00:44:34,730 --> 00:44:40,930
+compact إلى compact الان نشوف كيف let yn yn بيقن
+
+610
+00:44:40,930 --> 00:44:46,290
+الـ sequence in T of M T of M صورة الان
+
+611
+00:44:46,290 --> 00:44:50,330
+بدّي أجيلك subsequence من هذه conversion في T of M
+
+612
+00:44:50,990 --> 00:44:56,470
+بما إنه اللي هو الـ yn sequence في الـ T of M إذن
+
+613
+00:44:56,470 --> 00:45:01,290
+هي عبارة عن صور لعناصر وين في الـ M إذا then for
+
+614
+00:45:01,290 --> 00:45:05,910
+any n there exists xn element in M such that yn
+
+615
+00:45:05,910 --> 00:45:11,770
+بيساوي Txn الـ y1 صورة عنصر هنا اسمه Tx1 الـ
+
+616
+00:45:11,770 --> 00:45:15,390
+y2 صورة عنصر هنا اسمه Tx2 وين كدا الـ yn بيساوي
+
+617
+00:45:15,390 --> 00:45:20,090
+Txn صارت الان الـ xn عبارة عن sequence وين موجودة
+
+618
+00:45:20,090 --> 00:45:26,050
+في الـ M لكن M is compact و الـ xn موجودة اللي هو في
+
+619
+00:45:26,050 --> 00:45:31,260
+الـ M إذا لازم تحتوي على subsequence منها اللي هي
+
+620
+00:45:31,260 --> 00:45:38,560
+which converges in M إذا صارت الـ xnk subsequence
+
+621
+00:45:38,560 --> 00:45:44,240
+بتروح لمين للـ x في وين؟ في الـ M وبما أنه T is
+
+622
+00:45:44,240 --> 00:45:49,900
+continuous إذا نقوم تقمتك Txnك اللي هو بتروح لمين؟
+
+623
+00:45:49,900 --> 00:45:55,340
+للـ Tx وين هتكون الـ Tx؟ في الـ T of M إذا صار في
+
+624
+00:45:55,340 --> 00:46:01,340
+عندي subsequence هذه Txnك من مين؟ من الـ yn لأن الـ
+
+625
+00:46:01,340 --> 00:46:06,960
+yn إيش هي؟ الـ yn هي عبارة عن الـ Txn لجيت
+
+626
+00:46:06,960 --> 00:46:11,340
+subsequence من هذولة اللي هي subsequence من الـ n
+
+627
+00:46:11,340 --> 00:46:15,440
+راحت للـ Tx و الموجودة في الـ T of M صار الان any
+
+628
+00:46:15,440 --> 00:46:18,520
+sequence yn في الـ T of M اللي هي subsequence
+
+629
+00:46:18,520 --> 00:46:21,740
+converge برضه في المين في الـ T of M إذا صارت الـ
+
+630
+00:46:21,740 --> 00:46:26,320
+T of M is compact اللي بعدها الكورولر اللي بعدها
+
+631
+00:46:26,320 --> 0:46:32,350
+اطلع لفوق معنى continuous mapping T of a compact
+
+632
+00:46:32,350 --> 00:46:36,530
+subset M of a metric space X onto R assumes a
+
+633
+00:46:36,530 --> 00:46:40,330
+maximum and a minimum at some point of M هذا إعلان
+
+634
+00:46:40,330 --> 00:46:43,090
+كنا نعلنه للطلاب في الـ Calculus إنه إذا كانت الـ
+
+635
+00:46:43,090 --> 00:46:46,350
+function continuous على closed bounded interval
+
+636
+00:46:46,350 --> 00:46:49,070
+then it attains its maximum and its minimum
+
+637
+00:46:49,070 --> 00:46:54,450
+هجيتها in general لو كانت T من vectors من .. من
+
+638
+00:46:54,450 --> 00:47:02,540
+.. من metric space لعند R أهه ترسل اللي هي أو كانت
+
+639
+00:47:02,540 --> 00:47:06,280
+اللي هي a mapping T of a compact subset M of a
+
+640
+00:47:06,280 --> 00:47:09,720
+metric space يعني ايه ده 800 من compact subset
+
+641
+00:47:09,720 --> 00:47:15,640
+يعني T is a continuous on a closed bounded اللي هي
+
+642
+00:47:15,640 --> 00:47:20,460
+a compact set اسمها في الـ Metric Space The
+
+643
+00:47:20,460 --> 00:47:25,120
+continuous of a continuous function on a compact
+
+644
+00:47:25,120 --> 00:47:29,240
+set must attain its maximum and minimum هم يعني
+
+645
+00:47:29,240 --> 00:47:32,460
+هيكون الان فيه maximum و فيه minimum و هي موجود في
+
+646
+00:47:32,460 --> 00:47:38,570
+الار موضوع سهل اطلع لفوق اطلع آخر إشي هدا By
+
+647
+00:47:38,570 --> 00:47:42,830
+theorem 2.56 اللي قبل شوية هتطلع الـ T of M subset من
+
+648
+00:47:42,830 --> 00:47:47,230
+R و compact ماشي مدام compact إذا نقول close و إيه
+
+649
+00:47:47,230 --> 00:47:50,550
+إيش؟ bounded ما هو الـ compact set إيش معناه؟
+
+650
+00:47:50,550 --> 00:47:55,810
+closed و bounded طيب الان مدام closed و bounded
+
+651
+00:47:55,810 --> 00:48:02,190
+إذا صار عندي الـ infimum للـ T of M موجود وين؟ في
+
+652
+00:48:02,190 --> 00:48:09,940
+الـ T of M closed bounded then الانفمام موجود و
+
+653
+00:48:09,940 --> 00:48:13,400
+closed الانفمام وين حيكون؟ في جواهات الـ set الماخدين
+
+654
+00:48:13,400 --> 00:48:17,500
+لها الانفمام و الـ supremum برضه وين حيكون؟ نفس
+
+655
+00:48:17,500 --> 00:48:20,540
+الأشياء حيكون الـ supremum موجود مدام bounded و هو
+
+656
+00:48:20,540 --> 00:48:25,840
+حيكون مدام closed وين موجود؟ في الـ T of M إذاً then
+
+657
+00:48:25,840 --> 00:48:29,600
+the inverse image of two points consists of points
+
+658
+00:48:29,600 --> 00:48:34,600
+of T of M الـ infimum لهدي و الـ supremum في الـ T
+
+659
+00:48:34,600 --> 00:48:37,920
+of M يعني إيش معناة الـ infimum .. خلّيني أخد
+
+660
+00:48:37,920 --> 00:48:42,340
+واحدة و تانية زيها الـ infimum للـ T of M إيش
+
+661
+00:48:42,340 --> 00:48:46,800
+معناته موجود في الـ T of M؟ يعني هذا عبارة على
+
+662
+00:48:46,800 --> 00:48:52,820
+صورة عنصر اسمه Tx موجود في الـ T of M إذاً هذا الـ
+
+663
+00:48:52,820 --> 00:48:58,570
+x وين موجود؟ في الـ M اللي عندي معايا؟ إذا صار عندي
+
+664
+00:48:58,570 --> 00:49:04,910
+الـ T of x هو الـ infimum يعني بمعنى آخر صار الـ T
+
+665
+00:49:04,910 --> 00:49:11,650
+of x عند النقطة هذه اللي هنا is the minimum point
+
+666
+00:49:11,650 --> 00:49:15,870
+يعني صار الان الـ T attains its minimum عند نقطة
+
+667
+00:49:15,870 --> 00:49:21,170
+وين موجودة في الـ M Similarly اللي هو الـ supremum
+
+668
+00:49:21,170 --> 00:49:27,220
+موجود للـ T of M موجود في الـ T of M إذا صار في
+
+669
+00:49:27,220 --> 00:49:32,220
+عنده نقطة اللي هي اسمها T و T مثلاً x0
+
+670
+00:49:32,220 --> 00:49:37,300
+هي اللي بتساوي الـ supremum هذه الـ T هي الـ maximum
+
+671
+00:49:37,300 --> 00:49:40,380
+عند الـ x0 الـ maximum إذا برضه الـ x0
+
+672
+00:49:40,380 --> 00:49:44,500
+موجودة في الـ M و الـ T maximum عندها يعني الـ T
+
+673
+00:49:44,500 --> 00:49:49,060
+attains its maximum and its minimum on points in
+
+674
+00:49:49,060 --> 00:49:55,320
+M وهو المطلوب وهيك ممكن فلسنا اللي هو هذا
+
+675
+00:49:55,320 --> 00:49:58,380
+الـ section وإلى لقاء آخر السلام عليكم ورحمة الله
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/EaC1QqfjIDE_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/EaC1QqfjIDE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..9175b65277e02c159538baa2ef4228918d3d403e
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/EaC1QqfjIDE_raw.json
@@ -0,0 +1 @@
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{"start": 401.79, "end": 401.97, "word": " is", "probability": 0.95556640625}, {"start": 401.97, "end": 402.11, "word": " a", "probability": 0.8876953125}, {"start": 402.11, "end": 402.47, "word": " sequence", "probability": 0.96875}, {"start": 402.47, "end": 402.85, "word": " Xn", "probability": 0.5806884765625}, {"start": 402.85, "end": 403.03, "word": " of", "probability": 0.95703125}, {"start": 403.03, "end": 403.57, "word": " elements", "probability": 0.8896484375}, {"start": 403.57, "end": 404.19, "word": " in", "probability": 0.9365234375}, {"start": 404.19, "end": 404.51, "word": " M", "probability": 0.99560546875}, {"start": 404.51, "end": 404.93, "word": " such", "probability": 0.92236328125}, {"start": 404.93, "end": 405.19, "word": " that", "probability": 0.94482421875}, {"start": 405.19, "end": 405.51, "word": " Xn", "probability": 0.882568359375}, {"start": 405.51, "end": 405.79, "word": " بتروح", "probability": 0.9519856770833334}, {"start": 405.79, "end": 406.23, "word": " لمين", "probability": 0.8935546875}, {"start": 406.23, "end": 406.59, "word": " لل", "probability": 0.6875}, {"start": 406.59, "end": 406.77, "word": " X", "probability": 0.497314453125}, {"start": 406.77, "end": 406.97, "word": " هذا", "probability": 0.65771484375}, {"start": 406.97, "end": 407.41, "word": " مصارت", "probability": 0.7276611328125}, {"start": 407.41, "end": 407.83, "word": " محفوظة", "probability": 0.9138997395833334}, {"start": 407.83, "end": 407.95, "word": " يعني", "probability": 0.912109375}, {"start": 407.95, "end": 408.27, "word": " مفهوم", "probability": 0.89208984375}, {"start": 408.27, "end": 408.99, "word": " هذا", "probability": 0.837890625}], "temperature": 1.0}, {"id": 19, "seek": 43540, "start": 409.6, "end": 435.4, "text": "إذن however M is compact ما زم F is compact إذن every sequence has a convergent subsequence إذن then X element in M لأنه فيه لها subsequence سموها X and K بتروح لل X طب ما هي ال subsequence والsequence الأصلية بروح لنفس ال X معايا؟ إذن غصب عنها هتطلع ال X موجودة في ال M معناته then اللي هي M is enclosed طيب", "tokens": [28814, 8848, 1863, 4461, 376, 307, 14679, 19446, 30767, 2304, 479, 307, 14679, 11933, 8848, 1863, 633, 8310, 575, 257, 9652, 6930, 13924, 655, 11933, 8848, 1863, 550, 1783, 4478, 294, 376, 5296, 33456, 3224, 8978, 3224, 5296, 11296, 13924, 655, 8608, 2304, 2407, 11296, 1783, 293, 591, 39894, 32887, 5016, 24976, 1783, 23032, 3555, 19446, 39896, 2423, 13924, 655, 16070, 11834, 655, 16247, 9381, 20292, 3660, 4724, 32887, 5016, 5296, 1863, 36178, 2423, 1783, 20449, 995, 25528, 22807, 11933, 8848, 1863, 32771, 9381, 3555, 18871, 11296, 8032, 2655, 9566, 1211, 3615, 2423, 1783, 3714, 29245, 23328, 3660, 8978, 2423, 376, 20449, 8315, 47395, 550, 13672, 1829, 39896, 376, 307, 42089, 23032, 1829, 3555], "avg_logprob": -0.2653532530950463, "compression_ratio": 1.6431372549019607, "no_speech_prob": 3.355741500854492e-05, "words": [{"start": 409.6, "end": 409.94, "word": "إذن", "probability": 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{"start": 424.28, "end": 424.76, "word": " subsequence", "probability": 0.9853515625}, {"start": 424.76, "end": 425.26, "word": " والsequence", "probability": 0.6371256510416666}, {"start": 425.26, "end": 425.58, "word": " الأصلية", "probability": 0.6893310546875}, {"start": 425.58, "end": 425.72, "word": " بروح", "probability": 0.72998046875}, {"start": 425.72, "end": 425.96, "word": " لنفس", "probability": 0.7378743489583334}, {"start": 425.96, "end": 426.1, "word": " ال", "probability": 0.7978515625}, {"start": 426.1, "end": 426.44, "word": " X", "probability": 0.96875}, {"start": 426.44, "end": 427.62, "word": " معايا؟", "probability": 0.840087890625}, {"start": 427.62, "end": 427.96, "word": " إذن", "probability": 0.8614908854166666}, {"start": 427.96, "end": 428.28, "word": " غصب", "probability": 0.9775390625}, {"start": 428.28, "end": 428.92, "word": " عنها", "probability": 0.6053466796875}, {"start": 428.92, "end": 429.6, "word": " هتطلع", "probability": 0.879541015625}, {"start": 429.6, "end": 429.7, "word": " ال", "probability": 0.85888671875}, {"start": 429.7, "end": 429.86, "word": " X", "probability": 0.95556640625}, {"start": 429.86, "end": 430.44, "word": " موجودة", "probability": 0.8411865234375}, {"start": 430.44, "end": 430.54, "word": " في", "probability": 0.9716796875}, {"start": 430.54, "end": 430.66, "word": " ال", "probability": 0.572265625}, {"start": 430.66, "end": 430.86, "word": " M", "probability": 0.92724609375}, {"start": 430.86, "end": 431.82, "word": " معناته", "probability": 0.9781901041666666}, {"start": 431.82, "end": 432.12, "word": " then", "probability": 0.74853515625}, {"start": 432.12, "end": 432.5, "word": " اللي", "probability": 0.690185546875}, {"start": 432.5, "end": 432.8, "word": " هي", "probability": 0.7958984375}, {"start": 432.8, "end": 433.22, "word": " M", "probability": 0.9580078125}, {"start": 433.22, "end": 433.72, "word": " is", "probability": 0.96728515625}, {"start": 433.72, "end": 434.38, "word": " enclosed", "probability": 0.625}, {"start": 434.38, "end": 435.4, "word": " طيب", "probability": 0.8863932291666666}], "temperature": 1.0}, {"id": 20, "seek": 45619, "start": 436.27, "end": 456.19, "text": "بدنا نثبت الأن إيه شمالها is bounded بدنا نفترض العكس suppose that M is not bounded مدام bounded طب إحنا إذا بتتذكر شو معناه bounded أنه ال diameter ال diameter ال diameter ل ماعرفش كيف أقولنا عنه ال diameter ل اللي هو ال M بساوي ال supremum", "tokens": [3555, 3215, 8315, 8717, 12984, 3555, 2655, 16247, 1863, 11933, 1829, 3224, 13412, 2304, 6027, 11296, 307, 37498, 47525, 8315, 8717, 5172, 2655, 43042, 18863, 4117, 3794, 7297, 300, 376, 307, 406, 37498, 3714, 3215, 10943, 37498, 23032, 3555, 11933, 5016, 8315, 11933, 15730, 39894, 2655, 8848, 37983, 13412, 2407, 20449, 8315, 3224, 37498, 14739, 3224, 2423, 14196, 2423, 14196, 2423, 14196, 5296, 19446, 3615, 28480, 8592, 9122, 33911, 5551, 39648, 8315, 18871, 3224, 2423, 14196, 5296, 13672, 1829, 31439, 2423, 376, 4724, 3794, 995, 45865, 2423, 23710, 449], "avg_logprob": -0.2887152642011642, "compression_ratio": 1.697560975609756, "no_speech_prob": 1.6689300537109375e-06, "words": [{"start": 436.27, "end": 436.57, "word": "بدنا", "probability": 0.3756103515625}, {"start": 436.57, "end": 436.89, "word": " نثبت", "probability": 0.9892578125}, {"start": 436.89, "end": 437.09, "word": " الأن", "probability": 0.7115478515625}, {"start": 437.09, "end": 437.27, "word": " إيه", "probability": 0.6725260416666666}, {"start": 437.27, "end": 437.69, "word": " شمالها", "probability": 0.84063720703125}, {"start": 437.69, "end": 438.33, "word": " is", "probability": 0.54931640625}, {"start": 438.33, "end": 438.67, "word": " bounded", "probability": 0.88916015625}, {"start": 438.67, "end": 439.23, "word": " بدنا", "probability": 0.684326171875}, {"start": 439.23, "end": 439.61, "word": " نفترض", "probability": 0.9918212890625}, {"start": 439.61, "end": 440.25, "word": " العكس", "probability": 0.97998046875}, {"start": 440.25, "end": 440.89, "word": " suppose", "probability": 0.52978515625}, {"start": 440.89, "end": 441.51, "word": " that", "probability": 0.84521484375}, {"start": 441.51, "end": 441.75, "word": " M", "probability": 0.61669921875}, {"start": 441.75, "end": 441.95, "word": " is", "probability": 0.93994140625}, {"start": 441.95, "end": 442.19, "word": " not", "probability": 0.95654296875}, {"start": 442.19, "end": 442.67, "word": " bounded", "probability": 0.90478515625}, {"start": 442.67, "end": 443.53, "word": " مدام", "probability": 0.533935546875}, {"start": 443.53, "end": 443.85, "word": " bounded", "probability": 0.7578125}, {"start": 443.85, "end": 444.03, "word": " طب", "probability": 0.90087890625}, {"start": 444.03, "end": 444.21, "word": " إحنا", "probability": 0.75244140625}, {"start": 444.21, "end": 444.63, "word": " إذا", "probability": 0.947265625}, {"start": 444.63, "end": 445.09, "word": " بتتذكر", "probability": 0.84918212890625}, {"start": 445.09, "end": 445.29, "word": " 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0.98388671875}, {"start": 451.63, "end": 452.57, "word": " أقولنا", "probability": 0.5980021158854166}, {"start": 452.57, "end": 452.77, "word": " عنه", "probability": 0.94775390625}, {"start": 452.77, "end": 452.83, "word": " ال", "probability": 0.97509765625}, {"start": 452.83, "end": 453.17, "word": " diameter", "probability": 0.89892578125}, {"start": 453.17, "end": 453.45, "word": " ل", "probability": 0.9658203125}, {"start": 453.45, "end": 453.99, "word": " اللي", "probability": 0.65673828125}, {"start": 453.99, "end": 454.15, "word": " هو", "probability": 0.98779296875}, {"start": 454.15, "end": 454.25, "word": " ال", "probability": 0.72705078125}, {"start": 454.25, "end": 454.55, "word": " M", "probability": 0.9423828125}, {"start": 454.55, "end": 455.37, "word": " بساوي", "probability": 0.8173828125}, {"start": 455.37, "end": 455.55, "word": " ال", "probability": 0.364501953125}, {"start": 455.55, "end": 456.19, "word": " supremum", "probability": 0.76416015625}], "temperature": 1.0}, {"id": 21, "seek": 47389, "start": 457.65, "end": 473.89, "text": "لـDXY لكل الـX وY الموجودة في الـM هذا الـDiameter من الـM بنقول عنها bounded وكان الـDiameter نفسه ماهو؟ is finite يعني الـSupermom ماهو؟ is finite يعني الآن لو أي sequence هنا في الـM", "tokens": [1211, 39184, 35, 55, 56, 5296, 28820, 2423, 39184, 55, 4032, 56, 9673, 29245, 23328, 3660, 8978, 2423, 39184, 44, 23758, 2423, 39184, 35, 2918, 2398, 9154, 2423, 39184, 44, 4724, 1863, 39648, 18871, 11296, 37498, 4032, 41361, 2423, 39184, 35, 2918, 2398, 8717, 36178, 3224, 19446, 3224, 2407, 22807, 307, 19362, 37495, 22653, 2423, 39184, 30152, 42544, 19446, 3224, 2407, 22807, 307, 19362, 37495, 22653, 6024, 48506, 45164, 36632, 8310, 34105, 8978, 2423, 39184, 44], "avg_logprob": -0.386160726671095, "compression_ratio": 1.5714285714285714, "no_speech_prob": 4.4286251068115234e-05, "words": [{"start": 457.65000000000003, "end": 458.53000000000003, "word": "لـDXY", "probability": 0.50703125}, {"start": 458.53000000000003, "end": 459.41, "word": " لكل", "probability": 0.833740234375}, {"start": 459.41, "end": 459.81, "word": " الـX", "probability": 0.56640625}, {"start": 459.81, "end": 460.37, "word": " وY", "probability": 0.705810546875}, {"start": 460.37, "end": 461.37, "word": " الموجودة", "probability": 0.7318115234375}, {"start": 461.37, "end": 461.79, "word": " في", "probability": 0.8740234375}, {"start": 461.79, "end": 462.03, "word": " الـM", "probability": 0.85693359375}, {"start": 462.03, "end": 462.23, "word": " هذا", "probability": 0.278564453125}, {"start": 462.23, "end": 462.67, "word": " الـDiameter", "probability": 0.77451171875}, {"start": 462.67, "end": 462.83, "word": " من", "probability": 0.12548828125}, {"start": 462.83, "end": 462.99, "word": " الـM", "probability": 0.8444010416666666}, {"start": 462.99, "end": 463.69, "word": " بنقول", "probability": 0.5707194010416666}, {"start": 463.69, "end": 463.99, "word": " عنها", "probability": 0.8955078125}, {"start": 463.99, "end": 464.37, "word": " bounded", "probability": 0.5712890625}, {"start": 464.37, "end": 464.71, "word": " وكان", "probability": 0.6083984375}, {"start": 464.71, "end": 465.29, "word": " الـDiameter", "probability": 0.833203125}, {"start": 465.29, "end": 465.59, "word": " نفسه", "probability": 0.9612630208333334}, {"start": 465.59, "end": 466.73, "word": " ماهو؟", "probability": 0.4188232421875}, {"start": 466.73, "end": 467.21, "word": " is", "probability": 0.1578369140625}, {"start": 467.21, "end": 467.61, "word": " finite", "probability": 0.978515625}, {"start": 467.61, "end": 467.85, "word": " يعني", "probability": 0.798095703125}, {"start": 467.85, "end": 468.41, "word": " الـSupermom", "probability": 0.580810546875}, {"start": 468.41, "end": 469.17, "word": " ماهو؟", "probability": 0.9486083984375}, {"start": 469.17, "end": 469.65, "word": " is", "probability": 0.82177734375}, {"start": 469.65, "end": 470.23, "word": " finite", "probability": 0.978515625}, {"start": 470.23, "end": 471.01, "word": " يعني", "probability": 0.9462890625}, {"start": 471.01, "end": 471.57, "word": " الآن", "probability": 0.783935546875}, {"start": 471.57, "end": 472.23, "word": " لو", "probability": 0.701171875}, {"start": 472.23, "end": 472.49, "word": " أي", "probability": 0.70654296875}, {"start": 472.49, "end": 473.07, "word": " sequence", "probability": 0.57861328125}, {"start": 473.07, "end": 473.37, "word": " هنا", "probability": 0.95556640625}, {"start": 473.37, "end": 473.53, "word": " في", "probability": 0.98193359375}, {"start": 473.53, "end": 473.89, "word": " الـM", "probability": 0.9739583333333334}], "temperature": 1.0}, {"id": 22, "seek": 49377, "start": 474.51, "end": 493.77, "text": "لازم المسافة بين الـ sequence هذه وبين أي element هنا يكون إيش مالوفاينات، ماينفعش اللي هو يكبر، يروح لما لا نهاية، لأن لو بدأ أفترض، لو بدأ أفترض الآن أن M is not bounded، suppose that M is not bounded، معناته ال supermom هذا بيروح لمين؟ لما لا نهاية،", "tokens": [1211, 31377, 2304, 9673, 3794, 31845, 3660, 49374, 2423, 39184, 8310, 29538, 46599, 9957, 36632, 4478, 34105, 7251, 30544, 11933, 1829, 8592, 3714, 6027, 38688, 995, 9957, 9307, 12399, 19446, 9957, 5172, 3615, 8592, 13672, 1829, 31439, 7251, 4117, 26890, 12399, 7251, 32887, 5016, 5296, 15042, 20193, 8717, 11296, 10632, 12399, 5296, 33456, 45164, 47525, 10721, 5551, 5172, 2655, 43042, 12399, 45164, 47525, 10721, 5551, 5172, 2655, 43042, 6024, 48506, 14739, 376, 307, 406, 37498, 12399, 7297, 300, 376, 307, 406, 37498, 12399, 20449, 8315, 47395, 2423, 1687, 42544, 23758, 4724, 13546, 2407, 5016, 32767, 9957, 22807, 5296, 15042, 20193, 8717, 11296, 10632, 12399], "avg_logprob": -0.34255951699756443, "compression_ratio": 1.7292576419213974, "no_speech_prob": 2.5033950805664062e-06, "words": [{"start": 474.51, "end": 474.93, "word": "لازم", "probability": 0.7920735677083334}, {"start": 474.93, "end": 475.47, "word": " المسافة", "probability": 0.9681396484375}, {"start": 475.47, "end": 475.67, "word": " بين", "probability": 0.95751953125}, {"start": 475.67, "end": 475.83, "word": " الـ", "probability": 0.802001953125}, {"start": 475.83, "end": 476.15, "word": " sequence", "probability": 0.55322265625}, {"start": 476.15, "end": 476.35, "word": " هذه", "probability": 0.333740234375}, {"start": 476.35, "end": 476.61, "word": " وبين", "probability": 0.765869140625}, {"start": 476.61, "end": 476.79, "word": " أي", "probability": 0.8515625}, {"start": 476.79, "end": 477.13, "word": " element", "probability": 0.93310546875}, {"start": 477.13, "end": 477.57, "word": " هنا", "probability": 0.90380859375}, {"start": 477.57, "end": 478.29, "word": " يكون", "probability": 0.780029296875}, {"start": 478.29, "end": 478.49, "word": " إيش", "probability": 0.5538736979166666}, {"start": 478.49, "end": 479.21, "word": " مالوفاينات،", "probability": 0.4705287388392857}, {"start": 479.21, "end": 479.63, "word": " ماينفعش", "probability": 0.875439453125}, {"start": 479.63, "end": 479.75, "word": " اللي", "probability": 0.77001953125}, {"start": 479.75, "end": 479.91, "word": " هو", "probability": 0.9765625}, {"start": 479.91, "end": 481.37, "word": " يكبر،", "probability": 0.69097900390625}, {"start": 481.37, "end": 481.77, "word": " يروح", "probability": 0.7373046875}, {"start": 481.77, "end": 481.97, "word": " لما", "probability": 0.5787353515625}, {"start": 481.97, "end": 482.07, "word": " لا", "probability": 0.5966796875}, {"start": 482.07, "end": 482.97, "word": " نهاية،", "probability": 0.780029296875}, {"start": 482.97, "end": 483.21, "word": " لأن", "probability": 0.438232421875}, {"start": 483.21, "end": 483.39, "word": " لو", "probability": 0.9775390625}, {"start": 483.39, "end": 483.79, "word": " بدأ", "probability": 0.67041015625}, {"start": 483.79, "end": 485.27, "word": " أفترض،", "probability": 0.7607421875}, {"start": 485.27, "end": 485.53, "word": " لو", "probability": 0.703125}, {"start": 485.53, "end": 485.85, "word": " بدأ", "probability": 0.902587890625}, {"start": 485.85, "end": 486.35, "word": " أفترض", "probability": 0.9732666015625}, {"start": 486.35, "end": 486.85, "word": " الآن", "probability": 0.5985107421875}, {"start": 486.85, "end": 487.33, "word": " أن", "probability": 0.485107421875}, {"start": 487.33, "end": 487.75, "word": " M", "probability": 0.349365234375}, {"start": 487.75, "end": 488.09, "word": " is", "probability": 0.92822265625}, {"start": 488.09, "end": 488.43, "word": " not", "probability": 0.96044921875}, {"start": 488.43, "end": 489.25, "word": " bounded،", "probability": 0.6826171875}, {"start": 489.25, "end": 489.53, "word": " suppose", "probability": 0.71337890625}, {"start": 489.53, "end": 489.81, "word": " that", "probability": 0.91162109375}, {"start": 489.81, "end": 489.97, "word": " M", "probability": 0.94384765625}, {"start": 489.97, "end": 490.11, "word": " is", "probability": 0.962890625}, {"start": 490.11, "end": 490.29, "word": " not", "probability": 0.96240234375}, {"start": 490.29, "end": 491.09, "word": " bounded،", "probability": 0.9150390625}, {"start": 491.09, "end": 491.47, "word": " معناته", "probability": 0.921875}, {"start": 491.47, "end": 491.59, "word": " ال", "probability": 0.58837890625}, {"start": 491.59, "end": 491.93, "word": " supermom", "probability": 0.54052734375}, {"start": 491.93, "end": 492.13, "word": " هذا", "probability": 0.48583984375}, {"start": 492.13, "end": 492.39, "word": " بيروح", "probability": 0.93505859375}, {"start": 492.39, "end": 492.75, "word": " لمين؟", "probability": 0.76025390625}, {"start": 492.75, "end": 492.97, "word": " لما", "probability": 0.75390625}, {"start": 492.97, "end": 493.07, "word": " لا", "probability": 0.962890625}, {"start": 493.07, "end": 493.77, "word": " نهاية،", "probability": 0.906982421875}], "temperature": 1.0}, {"id": 23, "seek": 51358, "start": 493.96, "end": 513.58, "text": "معناته أكيد أكيد أكيد أكيد لازم ألاقي unbounded sequence YN بحيث أن المسافة بين YN و B تكون إيه شمالها أكبر من N لأنه لو مالجيتش معناته أنه حيصير إيش كل المسافات الصغيرة معناته سارة اللي هو إيه إيه إيش ال superman موجود معناته superman finite وانا بقول نفترض", "tokens": [2304, 3615, 8315, 47395, 5551, 4117, 25708, 5551, 4117, 25708, 5551, 4117, 25708, 5551, 4117, 25708, 5296, 31377, 2304, 5551, 15040, 38436, 517, 18767, 292, 8310, 398, 45, 4724, 5016, 1829, 12984, 14739, 9673, 3794, 31845, 3660, 49374, 398, 45, 4032, 363, 6055, 30544, 11933, 1829, 3224, 13412, 2304, 6027, 11296, 5551, 4117, 26890, 9154, 426, 5296, 33456, 3224, 45164, 3714, 6027, 7435, 36081, 8592, 20449, 8315, 47395, 14739, 3224, 11331, 1829, 9381, 13546, 11933, 1829, 8592, 28242, 9673, 3794, 31845, 9307, 31767, 17082, 48923, 20449, 8315, 47395, 8608, 9640, 3660, 13672, 1829, 31439, 11933, 1829, 3224, 11933, 1829, 3224, 11933, 1829, 8592, 2423, 1687, 1601, 3714, 29245, 23328, 20449, 8315, 47395, 1687, 1601, 19362, 4032, 7649, 995, 4724, 39648, 8717, 5172, 2655, 43042], "avg_logprob": -0.2448750066757202, "compression_ratio": 1.8076923076923077, "no_speech_prob": 1.6689300537109375e-06, "words": [{"start": 493.96, "end": 494.44, "word": "معناته", "probability": 0.9212646484375}, {"start": 494.44, "end": 494.9, "word": " أكيد", "probability": 0.8474934895833334}, {"start": 494.9, "end": 495.4, "word": " أكيد", "probability": 0.8566080729166666}, {"start": 495.4, "end": 495.82, "word": " أكيد", "probability": 0.9697265625}, {"start": 495.82, "end": 496.28, "word": " أكيد", "probability": 0.9640299479166666}, {"start": 496.28, "end": 497.14, "word": " لازم", "probability": 0.9685872395833334}, {"start": 497.14, "end": 497.68, "word": " ألاقي", "probability": 0.8004557291666666}, {"start": 497.68, "end": 498.74, "word": " unbounded", "probability": 0.760009765625}, {"start": 498.74, "end": 499.22, "word": " sequence", "probability": 0.94580078125}, {"start": 499.22, "end": 499.78, "word": " YN", "probability": 0.2789306640625}, {"start": 499.78, "end": 500.78, "word": " بحيث", "probability": 0.7994384765625}, {"start": 500.78, "end": 500.92, "word": " أن", "probability": 0.65478515625}, {"start": 500.92, "end": 501.46, "word": " المسافة", "probability": 0.9334716796875}, {"start": 501.46, "end": 501.64, "word": " بين", "probability": 0.89306640625}, {"start": 501.64, "end": 502.08, "word": " YN", "probability": 0.95263671875}, {"start": 502.08, "end": 502.2, "word": " و", "probability": 0.92529296875}, {"start": 502.2, "end": 502.36, "word": " B", "probability": 0.4921875}, {"start": 502.36, "end": 502.68, "word": " تكون", "probability": 0.875}, {"start": 502.68, "end": 502.9, "word": " إيه", "probability": 0.8133138020833334}, {"start": 502.9, "end": 503.36, "word": " شمالها", "probability": 0.82159423828125}, {"start": 503.36, "end": 504.02, "word": " أكبر", "probability": 0.9143880208333334}, {"start": 504.02, "end": 504.2, "word": " من", "probability": 0.9833984375}, {"start": 504.2, "end": 504.42, "word": " N", "probability": 0.88427734375}, {"start": 504.42, "end": 505.4, "word": " لأنه", "probability": 0.79345703125}, {"start": 505.4, "end": 505.46, "word": " لو", "probability": 0.3291015625}, {"start": 505.46, "end": 505.9, "word": " مالجيتش", "probability": 0.805126953125}, {"start": 505.9, "end": 506.26, "word": " معناته", "probability": 0.9449869791666666}, {"start": 506.26, "end": 506.42, "word": " أنه", "probability": 0.796630859375}, {"start": 506.42, "end": 506.76, "word": " حيصير", "probability": 0.7991943359375}, {"start": 506.76, "end": 506.94, "word": " إيش", "probability": 0.6336263020833334}, {"start": 506.94, "end": 507.14, "word": " كل", "probability": 0.93408203125}, {"start": 507.14, "end": 507.66, "word": " المسافات", "probability": 0.9849853515625}, {"start": 507.66, "end": 507.94, "word": " الصغيرة", "probability": 0.9560546875}, {"start": 507.94, "end": 508.22, "word": " معناته", "probability": 0.8880208333333334}, {"start": 508.22, "end": 508.48, "word": " سارة", "probability": 0.498046875}, {"start": 508.48, "end": 509.0, "word": " اللي", "probability": 0.91357421875}, {"start": 509.0, "end": 509.16, "word": " هو", "probability": 0.98388671875}, {"start": 509.16, "end": 509.34, "word": " إيه", "probability": 0.7705078125}, {"start": 509.34, "end": 509.42, "word": " إيه", "probability": 0.6417643229166666}, {"start": 509.42, "end": 509.54, "word": " إيش", "probability": 0.6526692708333334}, {"start": 509.54, "end": 509.8, "word": " ال", "probability": 0.587890625}, {"start": 509.8, "end": 510.16, "word": " superman", "probability": 0.347442626953125}, {"start": 510.16, "end": 510.5, "word": " موجود", "probability": 0.9850260416666666}, {"start": 510.5, "end": 510.78, "word": " معناته", "probability": 0.8885091145833334}, {"start": 510.78, "end": 511.16, "word": " superman", "probability": 0.841552734375}, {"start": 511.16, "end": 511.5, "word": " finite", "probability": 0.984375}, {"start": 511.5, "end": 511.96, "word": " وانا", "probability": 0.6605631510416666}, {"start": 511.96, "end": 512.36, "word": " بقول", "probability": 0.991455078125}, {"start": 512.36, "end": 513.58, "word": " نفترض", "probability": 0.9825439453125}], "temperature": 1.0}, {"id": 24, "seek": 53512, "start": 513.96, "end": 535.12, "text": "إنه Unbounded يعني السبري ما معمله بيروح إلى ما لا نهاية معايا إذا لازم نلاقي subsequence أو unbounded sequence yn بحيث المسافة بين yn و b أكبر من اللي هو الان where b is any fixed element زي ما قلنا هنس yn إشمالها has not a bounded subsequence", "tokens": [28814, 1863, 3224, 1156, 18767, 292, 37495, 22653, 21136, 3555, 16572, 19446, 20449, 42213, 3224, 4724, 13546, 2407, 5016, 30731, 19446, 20193, 8717, 11296, 10632, 20449, 995, 25528, 11933, 15730, 5296, 31377, 2304, 8717, 15040, 38436, 13924, 655, 34051, 517, 18767, 292, 8310, 17861, 4724, 5016, 1829, 12984, 9673, 3794, 31845, 3660, 49374, 17861, 4032, 272, 5551, 4117, 26890, 9154, 13672, 1829, 31439, 2423, 7649, 689, 272, 307, 604, 6806, 4478, 30767, 1829, 19446, 12174, 1211, 8315, 8032, 1863, 3794, 17861, 11933, 8592, 2304, 6027, 11296, 575, 406, 257, 37498, 13924, 655], "avg_logprob": -0.289146509221805, "compression_ratio": 1.6009174311926606, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 513.96, "end": 514.46, "word": "إنه", "probability": 0.63409423828125}, {"start": 514.46, "end": 515.22, "word": " Unbounded", "probability": 0.7520345052083334}, {"start": 515.22, "end": 515.48, "word": " يعني", "probability": 0.882568359375}, {"start": 515.48, "end": 515.9, "word": " السبري", "probability": 0.6029459635416666}, {"start": 515.9, "end": 516.04, "word": " ما", "probability": 0.28369140625}, {"start": 516.04, "end": 516.5, "word": " معمله", "probability": 0.7259114583333334}, {"start": 516.5, "end": 516.76, "word": " بيروح", "probability": 0.7786865234375}, {"start": 516.76, "end": 516.92, "word": " إلى", "probability": 0.87890625}, {"start": 516.92, "end": 517.08, "word": " ما", "probability": 0.9296875}, {"start": 517.08, "end": 517.18, "word": " لا", "probability": 0.452392578125}, {"start": 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five سببه إن المسافات بين العناصر جدر التنين إذن المسافات بين العناصر اللي هنا", "tokens": [33, 2195, 36632, 13672, 1829, 31439, 2594, 15244, 4724, 10721, 1829, 8717, 9381, 16490, 9566, 2288, 13412, 26895, 3224, 9154, 11296, 18863, 1863, 9381, 2288, 23758, 6055, 47432, 5016, 11296, 20449, 2423, 376, 5296, 31377, 2304, 11933, 1829, 8592, 5296, 43761, 22807, 20193, 7251, 3794, 995, 45865, 1732, 5296, 7435, 2655, 23275, 2304, 13672, 1829, 31439, 8717, 9381, 16490, 9566, 2288, 36764, 24401, 4032, 8717, 9381, 4032, 12602, 3555, 3615, 28242, 4724, 25957, 1211, 36145, 3224, 363, 2195, 31439, 36764, 24401, 34051, 8717, 9381, 34051, 12602, 3555, 3615, 13412, 26895, 3224, 9154, 3224, 15244, 6055, 47432, 3615, 46740, 37893, 4724, 1829, 3794, 995, 45865, 1732, 8608, 3555, 3555, 3224, 36145, 9673, 3794, 31845, 9307, 49374, 18863, 1863, 33546, 2288, 10874, 3215, 2288, 16712, 1863, 9957, 11933, 8848, 1863, 9673, 3794, 31845, 9307, 49374, 18863, 1863, 33546, 2288, 13672, 1829, 34105], "avg_logprob": 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0.9859619140625}, {"start": 955.61, "end": 955.77, "word": " بين", "probability": 0.95849609375}, {"start": 955.77, "end": 956.35, "word": " العناصر", "probability": 0.9755859375}, {"start": 956.35, "end": 956.53, "word": " اللي", "probability": 0.9736328125}, {"start": 956.53, "end": 956.83, "word": " هنا", "probability": 0.931640625}], "temperature": 1.0}, {"id": 44, "seek": 97258, "start": 957.72, "end": 972.58, "text": "لو بدي اكون في عنصر من M اشمله لازم تاخد هذا اتنين او تلاتة او اربعة او خمسة فاهمين؟ طيب صار عندي الان hence any point in M can't be an accumulation point", "tokens": [1211, 2407, 4724, 16254, 1975, 30544, 8978, 18871, 9381, 2288, 9154, 376, 1975, 8592, 42213, 3224, 5296, 31377, 2304, 6055, 47283, 3215, 23758, 1975, 2655, 1863, 9957, 1975, 2407, 6055, 1211, 9307, 3660, 1975, 2407, 1975, 25513, 27884, 1975, 2407, 16490, 2304, 3794, 3660, 6156, 995, 16095, 9957, 22807, 23032, 1829, 3555, 20328, 9640, 18871, 16254, 2423, 7649, 16678, 604, 935, 294, 376, 393, 380, 312, 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هذا", "probability": 0.426513671875}, {"start": 963.36, "end": 964.38, "word": " اتنين", "probability": 0.79736328125}, {"start": 964.38, "end": 964.5, "word": " او", "probability": 0.947265625}, {"start": 964.5, "end": 964.92, "word": " تلاتة", "probability": 0.9207763671875}, {"start": 964.92, "end": 965.02, "word": " او", "probability": 0.962646484375}, {"start": 965.02, "end": 965.3, "word": " اربعة", "probability": 0.83154296875}, {"start": 965.3, "end": 965.42, "word": " او", "probability": 0.9521484375}, {"start": 965.42, "end": 965.94, "word": " خمسة", "probability": 0.9735107421875}, {"start": 965.94, "end": 967.22, "word": " فاهمين؟", "probability": 0.8138671875}, {"start": 967.22, "end": 967.54, "word": " طيب", "probability": 0.8854166666666666}, {"start": 967.54, "end": 968.06, "word": " صار", "probability": 0.862060546875}, {"start": 968.06, "end": 968.38, "word": " عندي", "probability": 0.762939453125}, {"start": 968.38, "end": 968.76, "word": " الان", "probability": 0.6710205078125}, {"start": 968.76, "end": 969.52, "word": " hence", "probability": 0.5498046875}, {"start": 969.52, "end": 970.16, "word": " any", "probability": 0.73046875}, {"start": 970.16, "end": 970.56, "word": " point", "probability": 0.9921875}, {"start": 970.56, "end": 970.74, "word": " in", "probability": 0.91796875}, {"start": 970.74, "end": 971.0, "word": " M", "probability": 0.9697265625}, {"start": 971.0, "end": 971.42, "word": " can't", "probability": 0.890380859375}, {"start": 971.42, "end": 971.58, "word": " be", "probability": 0.9677734375}, {"start": 971.58, "end": 971.72, "word": " an", "probability": 0.7626953125}, {"start": 971.72, "end": 972.08, "word": " accumulation", "probability": 0.990234375}, {"start": 972.08, "end": 972.58, "word": " point", "probability": 0.98388671875}], "temperature": 1.0}, {"id": 45, "seek": 99788, "start": 973.4, "end": 997.88, "text": "second اللي ضال we show that any point in M complement يعني براة الـ M في الـ L2 بس مش في الـ M complement can't be an accumulation point ماشي في سؤال اللي هو 13 Problem 6 كان بيقولنا إذا كانت النقطة accumulation point بدي يكون أي neighborhood حوالين النقطة تقاطع مع الـ M هيكون infinite number of dots", "tokens": [27375, 13672, 1829, 48812, 6027, 321, 855, 300, 604, 935, 294, 376, 17103, 37495, 22653, 4724, 23557, 3660, 2423, 39184, 376, 8978, 2423, 39184, 441, 17, 4724, 3794, 37893, 8978, 2423, 39184, 376, 17103, 393, 380, 312, 364, 35647, 935, 3714, 33599, 1829, 8978, 8608, 33604, 6027, 13672, 1829, 31439, 3705, 11676, 1386, 25961, 4724, 1829, 39648, 8315, 11933, 15730, 25961, 2655, 28239, 47432, 3660, 35647, 935, 4724, 16254, 7251, 30544, 36632, 7630, 11331, 2407, 6027, 9957, 28239, 47432, 3660, 6055, 4587, 41193, 3615, 20449, 2423, 39184, 376, 39896, 30544, 13785, 1230, 295, 15026], "avg_logprob": -0.21513157173206932, "compression_ratio": 1.579150579150579, "no_speech_prob": 2.86102294921875e-06, "words": [{"start": 973.4000000000001, "end": 974.08, "word": "second", "probability": 0.10638427734375}, {"start": 974.08, "end": 974.76, "word": " اللي", "probability": 0.895263671875}, {"start": 974.76, "end": 975.08, "word": " ضال", "probability": 0.7049560546875}, {"start": 975.08, "end": 975.54, "word": " we", "probability": 0.301513671875}, {"start": 975.54, "end": 975.8, "word": " show", "probability": 0.92138671875}, {"start": 975.8, "end": 976.1, "word": " that", "probability": 0.94384765625}, {"start": 976.1, "end": 976.34, "word": " any", "probability": 0.83154296875}, {"start": 976.34, "end": 976.74, "word": " point", "probability": 0.98779296875}, {"start": 976.74, "end": 977.02, "word": " in", "probability": 0.94775390625}, {"start": 977.02, "end": 977.18, "word": " M", "probability": 0.77490234375}, {"start": 977.18, "end": 977.66, "word": " complement", "probability": 0.671875}, {"start": 977.66, "end": 978.0, "word": " يعني", "probability": 0.864013671875}, {"start": 978.0, "end": 978.36, "word": " براة", "probability": 0.77294921875}, {"start": 978.36, "end": 978.52, "word": " الـ", "probability": 0.768310546875}, {"start": 978.52, "end": 978.6, "word": " M", "probability": 0.55615234375}, {"start": 978.6, "end": 978.72, "word": " في", "probability": 0.57568359375}, {"start": 978.72, "end": 978.84, "word": " الـ", "probability": 0.74658203125}, {"start": 978.84, "end": 979.0, "word": " L2", "probability": 0.798828125}, {"start": 979.0, "end": 979.18, "word": " بس", "probability": 0.968505859375}, {"start": 979.18, "end": 979.28, "word": " مش", "probability": 0.98291015625}, {"start": 979.28, "end": 979.38, "word": " في", "probability": 0.8291015625}, {"start": 979.38, "end": 979.48, "word": " الـ", "probability": 0.92041015625}, {"start": 979.48, "end": 979.56, "word": " M", "probability": 0.8955078125}, {"start": 979.56, "end": 980.08, "word": " complement", "probability": 0.853515625}, {"start": 980.08, "end": 980.92, "word": " can't", "probability": 0.82373046875}, {"start": 980.92, "end": 981.16, "word": " be", "probability": 0.9697265625}, {"start": 981.16, "end": 981.4, "word": " an", "probability": 0.61279296875}, {"start": 981.4, "end": 981.74, "word": " accumulation", "probability": 0.9873046875}, {"start": 981.74, "end": 982.36, "word": " point", "probability": 0.9853515625}, {"start": 982.36, "end": 983.1, "word": " ماشي", "probability": 0.769287109375}, {"start": 983.1, "end": 983.86, "word": " في", "probability": 0.404541015625}, {"start": 983.86, "end": 984.8, "word": " سؤال", "probability": 0.9915364583333334}, {"start": 984.8, "end": 985.44, "word": " اللي", "probability": 0.927978515625}, {"start": 985.44, "end": 985.6, "word": " هو", "probability": 0.98876953125}, {"start": 985.6, "end": 986.0, "word": " 13", "probability": 0.7490234375}, {"start": 986.0, "end": 986.54, "word": " Problem", "probability": 0.31591796875}, {"start": 986.54, "end": 987.06, "word": " 6", "probability": 0.94775390625}, {"start": 987.06, "end": 987.86, "word": " كان", "probability": 0.9619140625}, {"start": 987.86, "end": 988.32, "word": " بيقولنا", "probability": 0.973876953125}, {"start": 988.32, "end": 988.52, "word": " إذا", "probability": 0.903076171875}, {"start": 988.52, "end": 988.84, "word": " كانت", "probability": 0.98388671875}, {"start": 988.84, "end": 989.14, "word": " النقطة", "probability": 0.9597981770833334}, {"start": 989.14, "end": 989.52, "word": " accumulation", "probability": 0.98828125}, {"start": 989.52, "end": 990.22, "word": " point", "probability": 0.9873046875}, {"start": 990.22, "end": 990.98, "word": " بدي", "probability": 0.70703125}, {"start": 990.98, "end": 991.26, "word": " يكون", "probability": 0.75390625}, {"start": 991.26, "end": 991.62, "word": " أي", "probability": 0.7255859375}, {"start": 991.62, "end": 992.32, "word": " neighborhood", "probability": 0.625}, {"start": 992.32, "end": 993.94, "word": " حوالين", "probability": 0.928466796875}, {"start": 993.94, "end": 995.0, "word": " النقطة", "probability": 0.9913736979166666}, {"start": 995.0, "end": 995.74, "word": " تقاطع", "probability": 0.78302001953125}, {"start": 995.74, "end": 995.86, "word": " مع", "probability": 0.89208984375}, {"start": 995.86, "end": 996.12, "word": " الـ", "probability": 0.894775390625}, {"start": 996.12, "end": 996.24, "word": " M", "probability": 0.84912109375}, {"start": 996.24, "end": 996.66, "word": " هيكون", "probability": 0.876953125}, {"start": 996.66, "end": 997.02, "word": " infinite", "probability": 0.87841796875}, {"start": 997.02, "end": 997.38, "word": " number", "probability": 0.98779296875}, {"start": 997.38, "end": 997.58, "word": " of", "probability": 0.98681640625}, {"start": 997.58, "end": 997.88, "word": " dots", "probability": 0.4267578125}], "temperature": 1.0}, {"id": 46, "seek": 102565, "start": 998.71, "end": 1025.65, "text": "مش هيكون نقطة في infinite number of points هذا اللي هو سؤال ستة في problem 138 مش صعب عموما طيب شوفوا صلى الله على النبي عز وجل انا بدي استعينيه الان بدي اخد اي نقطة في ال M complement و اثبتلكم انه لا يمكن انها تكون accumulation point او limit point لل M شوف كيف let X be any fixed point in M complement خدوا الان ال ball ال نص خطرها اللي هو نص و مركزها ال X هذه", "tokens": [2304, 8592, 39896, 30544, 8717, 47432, 3660, 8978, 13785, 1230, 295, 2793, 23758, 13672, 1829, 31439, 8608, 33604, 6027, 8608, 2655, 3660, 8978, 1154, 3705, 23, 37893, 20328, 3615, 3555, 6225, 2304, 2407, 15042, 23032, 1829, 3555, 13412, 38688, 14407, 20328, 23942, 21984, 15844, 28239, 21292, 6225, 11622, 49610, 1211, 1975, 8315, 4724, 16254, 44713, 3615, 9957, 1829, 3224, 2423, 7649, 4724, 16254, 1975, 9778, 3215, 1975, 1829, 8717, 47432, 3660, 8978, 2423, 376, 17103, 4032, 1975, 12984, 3555, 2655, 23275, 2304, 16472, 3224, 20193, 7251, 43020, 16472, 11296, 6055, 30544, 35647, 935, 1975, 2407, 4948, 935, 24976, 376, 13412, 38688, 9122, 33911, 718, 1783, 312, 604, 6806, 935, 294, 376, 17103, 16490, 3215, 14407, 2423, 7649, 2423, 2594, 2423, 8717, 9381, 16490, 9566, 2288, 11296, 13672, 1829, 31439, 8717, 9381, 4032, 3714, 31747, 11622, 11296, 2423, 1783, 29538], "avg_logprob": -0.2749999861632075, "compression_ratio": 1.7419354838709677, "no_speech_prob": 1.3709068298339844e-05, "words": [{"start": 998.71, "end": 998.97, "word": "مش", "probability": 0.77734375}, {"start": 998.97, "end": 999.25, "word": " هيكون", "probability": 0.877685546875}, {"start": 999.25, "end": 999.55, "word": " نقطة", "probability": 0.9674479166666666}, {"start": 999.55, "end": 999.61, "word": " في", "probability": 0.8427734375}, {"start": 999.61, "end": 999.89, "word": " infinite", "probability": 0.30712890625}, {"start": 999.89, "end": 1000.23, "word": " number", "probability": 0.97314453125}, {"start": 1000.23, "end": 1000.37, "word": " of", "probability": 0.96435546875}, {"start": 1000.37, "end": 1000.61, "word": " points", "probability": 0.83984375}, {"start": 1000.61, "end": 1001.41, "word": " هذا", "probability": 0.81298828125}, {"start": 1001.41, "end": 1001.53, "word": " اللي", "probability": 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{"start": 1005.77, "end": 1005.93, "word": " الله", "probability": 0.375}, {"start": 1005.93, "end": 1006.01, "word": " على", "probability": 0.51025390625}, {"start": 1006.01, "end": 1006.23, "word": " النبي", "probability": 0.9580078125}, {"start": 1006.23, "end": 1006.43, "word": " عز", "probability": 0.23712158203125}, {"start": 1006.43, "end": 1006.49, "word": " وجل", "probability": 0.60302734375}, {"start": 1006.49, "end": 1006.67, "word": " انا", "probability": 0.49517822265625}, {"start": 1006.67, "end": 1006.79, "word": " بدي", "probability": 0.43768310546875}, {"start": 1006.79, "end": 1007.33, "word": " استعينيه", "probability": 0.692236328125}, {"start": 1007.33, "end": 1008.53, "word": " الان", "probability": 0.6187744140625}, {"start": 1008.53, "end": 1008.83, "word": " بدي", "probability": 0.85302734375}, {"start": 1008.83, "end": 1009.21, "word": " اخد", "probability": 0.9093424479166666}, {"start": 1009.21, "end": 1009.47, "word": " اي", "probability": 0.9208984375}, 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"probability": 0.69287109375}, {"start": 1085.81, "end": 1086.19, "word": " problem", "probability": 0.7763671875}, {"start": 1086.19, "end": 1086.61, "word": " واحدة", "probability": 0.53106689453125}, {"start": 1086.61, "end": 1086.91, "word": " ستة", "probability": 0.9514973958333334}, {"start": 1086.91, "end": 1086.97, "word": " اللي", "probability": 0.7353515625}, {"start": 1086.97, "end": 1087.05, "word": " هي", "probability": 0.8330078125}, {"start": 1087.05, "end": 1087.29, "word": " واحدة", "probability": 0.888671875}, {"start": 1087.29, "end": 1087.53, "word": " تلاتة", "probability": 0.8837890625}, {"start": 1087.53, "end": 1087.95, "word": " بنقول", "probability": 0.8466796875}, {"start": 1087.95, "end": 1088.21, "word": " إنه", "probability": 0.476806640625}, {"start": 1088.21, "end": 1088.31, "word": " لو", "probability": 0.97119140625}, {"start": 1088.31, "end": 1088.63, "word": " كانت", "probability": 0.974609375}, {"start": 1088.63, "end": 1088.99, "word": " 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{"start": 1373.25, "end": 1373.53, "word": " C", "probability": 0.8974609375}, {"start": 1373.53, "end": 1373.83, "word": " أكبر", "probability": 0.9602864583333334}, {"start": 1373.83, "end": 1374.01, "word": " من", "probability": 0.98828125}, {"start": 1374.01, "end": 1374.23, "word": " صفر", "probability": 0.6981608072916666}, {"start": 1374.23, "end": 1374.47, "word": " such", "probability": 0.767578125}, {"start": 1374.47, "end": 1374.81, "word": " that", "probability": 0.9404296875}, {"start": 1374.81, "end": 1375.45, "word": " K", "probability": 0.89013671875}, {"start": 1375.45, "end": 1375.87, "word": " أكبر", "probability": 0.9645182291666666}, {"start": 1375.87, "end": 1376.01, "word": " أو", "probability": 0.91552734375}, {"start": 1376.01, "end": 1376.49, "word": " شويه", "probability": 0.9215494791666666}, {"start": 1376.49, "end": 1376.79, "word": " اللي", "probability": 0.960693359375}, {"start": 1376.79, "end": 1377.03, "word": " هو", "probability": 0.99462890625}, {"start": 1377.03, "end": 1377.33, "word": " ال", "probability": 0.85986328125}, {"start": 1377.33, "end": 1377.99, "word": " norm", "probability": 0.837890625}, {"start": 1377.99, "end": 1379.15, "word": " هذا", "probability": 0.8916015625}, {"start": 1379.15, "end": 1380.09, "word": " اللي", "probability": 0.97119140625}, {"start": 1380.09, "end": 1380.39, "word": " هو", "probability": 0.99462890625}], "temperature": 1.0}, {"id": 62, "seek": 140601, "start": 1381.79, "end": 1406.01, "text": "هيها من هنا ال K أكبر سواء norm XM وال XM هيها هيها ال XM اللي هي هذه أه بس كتر ده في ال summation إذا ال normal X ال K أكبر سواء norm XM اللي هو هذا و هذا من اللمّة اللي قبل بشوية باللاجة C بحيث أنه هي أكبر سواء C في mean في ال summation طيب اللي هنطلع لفوق", "tokens": [3224, 1829, 11296, 9154, 34105, 2423, 591, 5551, 4117, 26890, 8608, 2407, 16606, 2026, 1783, 44, 16070, 1783, 44, 39896, 11296, 39896, 11296, 2423, 1783, 44, 13672, 1829, 39896, 29538, 5551, 3224, 4724, 3794, 9122, 2655, 2288, 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"probability": 0.78857421875}, {"start": 1386.97, "end": 1387.29, "word": " هذه", "probability": 0.6640625}, {"start": 1387.29, "end": 1388.31, "word": " أه", "probability": 0.6251220703125}, {"start": 1388.31, "end": 1388.45, "word": " بس", "probability": 0.92578125}, {"start": 1388.45, "end": 1388.63, "word": " كتر", "probability": 0.57373046875}, {"start": 1388.63, "end": 1388.73, "word": " ده", "probability": 0.6865234375}, {"start": 1388.73, "end": 1388.85, "word": " في", "probability": 0.90771484375}, {"start": 1388.85, "end": 1388.89, "word": " ال", "probability": 0.72900390625}, {"start": 1388.89, "end": 1389.31, "word": " summation", "probability": 0.853515625}, {"start": 1389.31, "end": 1389.99, "word": " إذا", "probability": 0.907470703125}, {"start": 1389.99, "end": 1390.13, "word": " ال", "probability": 0.434326171875}, {"start": 1390.13, "end": 1390.39, "word": " normal", "probability": 0.45458984375}, {"start": 1390.39, "end": 1390.91, "word": " X", "probability": 0.974609375}, {"start": 1390.91, "end": 1391.83, "word": " ال", "probability": 0.71728515625}, {"start": 1391.83, "end": 1392.17, "word": " K", "probability": 0.9814453125}, {"start": 1392.17, "end": 1392.87, "word": " أكبر", "probability": 0.9812825520833334}, {"start": 1392.87, "end": 1393.05, "word": " سواء", "probability": 0.9768880208333334}, {"start": 1393.05, "end": 1393.27, "word": " norm", "probability": 0.496337890625}, {"start": 1393.27, "end": 1393.79, "word": " XM", "probability": 0.908447265625}, {"start": 1393.79, "end": 1394.21, "word": " اللي", "probability": 0.98583984375}, {"start": 1394.21, "end": 1394.47, "word": " هو", "probability": 0.9931640625}, {"start": 1394.47, "end": 1394.95, "word": " هذا", "probability": 0.95849609375}, {"start": 1394.95, "end": 1395.79, "word": " و", "probability": 0.490234375}, {"start": 1395.79, "end": 1396.09, "word": " هذا", "probability": 0.82373046875}, {"start": 1396.09, "end": 1396.33, "word": " من", "probability": 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"probability": 0.90869140625}, {"start": 1401.73, "end": 1401.95, "word": " في", "probability": 0.9541015625}, {"start": 1401.95, "end": 1402.23, "word": " mean", "probability": 0.31591796875}, {"start": 1402.23, "end": 1402.79, "word": " في", "probability": 0.96533203125}, {"start": 1402.79, "end": 1402.93, "word": " ال", "probability": 0.93310546875}, {"start": 1402.93, "end": 1403.39, "word": " summation", "probability": 0.93212890625}, {"start": 1403.39, "end": 1404.39, "word": " طيب", "probability": 0.9645182291666666}, {"start": 1404.39, "end": 1405.21, "word": " اللي", "probability": 0.88671875}, {"start": 1405.21, "end": 1405.57, "word": " هنطلع", "probability": 0.782666015625}, {"start": 1405.57, "end": 1406.01, "word": " لفوق", "probability": 0.7412109375}], "temperature": 1.0}, {"id": 63, "seek": 142366, "start": 1408.18, "end": 1423.66, "text": "Hence, for any fixed I من 1 إلى N in the sequence Xim is a bounded sequence of numbers أكيد الـ Xim bounded sequence ليه؟ لأنه صار الـ summation هذا", "tokens": [39, 655, 11, 337, 604, 6806, 286, 9154, 502, 30731, 426, 294, 264, 8310, 1783, 332, 307, 257, 37498, 8310, 295, 3547, 5551, 4117, 25708, 2423, 39184, 1783, 332, 37498, 8310, 32239, 3224, 22807, 5296, 33456, 3224, 20328, 9640, 2423, 39184, 28811, 23758], "avg_logprob": -0.4772727218541232, "compression_ratio": 1.2377622377622377, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 1408.18, "end": 1408.64, "word": "Hence,", "probability": 0.405853271484375}, {"start": 1408.82, "end": 1408.94, "word": " for", "probability": 0.9228515625}, {"start": 1408.94, "end": 1409.28, "word": " any", "probability": 0.91796875}, {"start": 1409.28, "end": 1409.68, "word": " fixed", "probability": 0.8564453125}, {"start": 1409.68, "end": 1410.08, "word": " I", "probability": 0.470458984375}, {"start": 1410.08, "end": 1412.0, "word": " من", "probability": 0.34716796875}, {"start": 1412.0, "end": 1412.26, "word": " 1", "probability": 0.5634765625}, {"start": 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أو ساوي هذا على C كل واحدة من اندولا Cy M هتكون أصغر أو تساوي K على C يعني صارت ال sequence هذي bounded sequence اذا صارت عندي bounded sequence of مين؟ of numbers باشر و دوين على ال R أو على ال C اللي ضامن انه انه في مدام اللي هو sequence of numbers و بولزانو بتقول every sequence bounded sequence هذا convergence subsequence", "tokens": [10721, 4117, 26890, 34051, 5551, 9381, 17082, 2288, 34051, 8608, 995, 45865, 23758, 15844, 383, 28242, 36764, 24401, 3660, 9154, 16472, 3215, 12610, 995, 10295, 376, 8032, 2655, 30544, 5551, 9381, 17082, 2288, 34051, 6055, 3794, 995, 45865, 591, 15844, 383, 37495, 22653, 20328, 9640, 2655, 2423, 8310, 8032, 8848, 1829, 37498, 8310, 1975, 15730, 20328, 9640, 2655, 18871, 16254, 37498, 8310, 295, 3714, 9957, 22807, 295, 3547, 4724, 33599, 2288, 4032, 11778, 2407, 9957, 15844, 2423, 497, 34051, 15844, 2423, 383, 13672, 1829, 48812, 10943, 1863, 16472, 3224, 16472, 3224, 8978, 3714, 3215, 10943, 13672, 1829, 31439, 8310, 295, 3547, 4032, 4724, 12610, 11622, 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0.95703125}, {"start": 1441.23, "end": 1441.49, "word": " C", "probability": 0.9453125}, {"start": 1441.49, "end": 1442.19, "word": " اللي", "probability": 0.96240234375}, {"start": 1442.19, "end": 1442.79, "word": " ضامن", "probability": 0.900390625}, {"start": 1442.79, "end": 1443.23, "word": " انه", "probability": 0.836669921875}, {"start": 1443.23, "end": 1443.69, "word": " انه", "probability": 0.712890625}, {"start": 1443.69, "end": 1444.03, "word": " في", "probability": 0.9306640625}, {"start": 1444.03, "end": 1445.11, "word": " مدام", "probability": 0.8287760416666666}, {"start": 1445.11, "end": 1445.25, "word": " اللي", "probability": 0.853515625}, {"start": 1445.25, "end": 1445.43, "word": " هو", "probability": 0.98095703125}, {"start": 1445.43, "end": 1445.91, "word": " sequence", "probability": 0.96875}, {"start": 1445.91, "end": 1446.15, "word": " of", "probability": 0.98046875}, {"start": 1446.15, "end": 1446.71, "word": " numbers", "probability": 0.9150390625}, {"start": 1446.71, "end": 1447.17, "word": " و", "probability": 0.72607421875}, {"start": 1447.17, "end": 1447.67, "word": " بولزانو", "probability": 0.790625}, {"start": 1447.67, "end": 1448.09, "word": " بتقول", "probability": 0.96142578125}, {"start": 1448.09, "end": 1448.47, "word": " every", "probability": 0.74267578125}, {"start": 1448.47, "end": 1449.01, "word": " sequence", "probability": 0.82763671875}, {"start": 1449.01, "end": 1449.39, "word": " bounded", "probability": 0.60791015625}, {"start": 1449.39, "end": 1449.91, "word": " sequence", "probability": 0.9755859375}, {"start": 1449.91, "end": 1450.13, "word": " هذا", "probability": 0.63525390625}, {"start": 1450.13, "end": 1450.67, "word": " convergence", "probability": 0.671875}, {"start": 1450.67, "end": 1451.45, "word": " subsequence", "probability": 0.980224609375}], "temperature": 1.0}, {"id": 65, "seek": 147259, "start": 1451.85, "end": 1472.59, "text": "إذا لازم it has a convergent subsequence say that it converges to mean to Xi I إذا ال subsequence من هذه converges to mean لXi I بالظبط بديش أقول عيد اللي قلناه قبل و شوية then as in the proof of لبمة 2 4 5 we show that XM A شمالها has", "tokens": [28814, 15730, 5296, 31377, 2304, 309, 575, 257, 9652, 6930, 13924, 655, 584, 300, 309, 9652, 2880, 281, 914, 281, 15712, 286, 11933, 15730, 2423, 13924, 655, 9154, 29538, 9652, 2880, 281, 914, 5296, 41577, 286, 20666, 19913, 3555, 9566, 4724, 16254, 8592, 5551, 39648, 6225, 25708, 13672, 1829, 12174, 1211, 8315, 3224, 12174, 36150, 4032, 13412, 2407, 10632, 550, 382, 294, 264, 8177, 295, 5296, 3555, 46007, 568, 1017, 1025, 321, 855, 300, 1783, 44, 316, 13412, 2304, 6027, 11296, 575], "avg_logprob": -0.3224774038935282, "compression_ratio": 1.4210526315789473, "no_speech_prob": 1.9669532775878906e-06, "words": [{"start": 1451.85, "end": 1452.21, "word": "إذا", "probability": 0.510009765625}, {"start": 1452.21, "end": 1453.53, "word": " لازم", "probability": 0.8883463541666666}, {"start": 1453.53, "end": 1453.85, 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"probability": 0.63818359375}, {"start": 2851.44, "end": 2851.48, "word": " هي", "probability": 0.1461181640625}, {"start": 2851.48, "end": 2852.0, "word": " موجود", "probability": 0.9358723958333334}, {"start": 2852.0, "end": 2852.46, "word": " في", "probability": 0.89892578125}, {"start": 2852.46, "end": 2852.8, "word": " الار", "probability": 0.67626953125}, {"start": 2852.8, "end": 2853.48, "word": " موضوع", "probability": 0.87548828125}, {"start": 2853.48, "end": 2853.92, "word": " سهل", "probability": 0.9970703125}, {"start": 2853.92, "end": 2854.24, "word": " اطلع", "probability": 0.9410400390625}, {"start": 2854.24, "end": 2855.28, "word": " لفوق", "probability": 0.7357584635416666}, {"start": 2855.28, "end": 2856.24, "word": " اطلع", "probability": 0.9725341796875}], "temperature": 1.0}, {"id": 126, "seek": 288439, "start": 2857.05, "end": 2884.39, "text": "أخر إشي هدى By theorem 2.56 اللي قبل شوية هتطلع الـ T M subset من R و Combact ماشي مادام Combact إذا ن close و إيه إيش؟ Abounded ما هو ال Combact الست إيش معناه؟ Closed و Abounded طيب الآن مادام Closed و Abounded إذا صار عندي الـ infimum للـ T of M موجود وين؟ في الـ T of M Closed", "tokens": [10721, 34740, 11933, 8592, 1829, 8032, 3215, 7578, 3146, 20904, 568, 13, 18317, 13672, 1829, 12174, 36150, 13412, 2407, 10632, 8032, 2655, 9566, 1211, 3615, 2423, 39184, 314, 376, 25993, 9154, 497, 4032, 25939, 578, 3714, 33599, 1829, 3714, 18513, 10943, 25939, 578, 11933, 15730, 8717, 1998, 4032, 11933, 1829, 3224, 11933, 1829, 8592, 22807, 2847, 37706, 19446, 31439, 2423, 25939, 578, 2423, 14851, 11933, 1829, 8592, 20449, 8315, 3224, 22807, 2033, 1744, 4032, 2847, 37706, 23032, 1829, 3555, 6024, 48506, 3714, 18513, 10943, 2033, 1744, 4032, 2847, 37706, 11933, 15730, 20328, 9640, 18871, 16254, 2423, 39184, 1536, 332, 449, 24976, 39184, 314, 295, 376, 3714, 29245, 23328, 4032, 9957, 22807, 8978, 2423, 39184, 314, 295, 376, 2033, 1744], "avg_logprob": -0.4223958266278108, "compression_ratio": 1.58, "no_speech_prob": 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موجود في الـ T of M؟ يعني هذا عبارة على صورة عنصر اسمه TX موجود في الـ T of M إذاً هذا الـ X وين موجود؟", "tokens": [28814, 15730, 14111, 550, 264, 17340, 3256, 295, 732, 2793, 14689, 295, 2793, 295, 914, 295, 376, 2423, 39184, 1536, 332, 449, 46740, 16254, 4032, 9673, 5016, 1829, 30544, 8978, 2423, 39184, 314, 295, 376, 37495, 22653, 11933, 1829, 8592, 20449, 8315, 3660, 2423, 39184, 1536, 332, 449, 4386, 16490, 1211, 11703, 9957, 1829, 5551, 9778, 3215, 36764, 24401, 3660, 4032, 6055, 7649, 10632, 30767, 1829, 11296, 2423, 39184, 1536, 332, 449, 24976, 39184, 314, 295, 376, 11933, 1829, 8592, 20449, 8315, 47395, 3714, 29245, 23328, 8978, 2423, 39184, 314, 295, 376, 22807, 37495, 22653, 23758, 6225, 3555, 9640, 3660, 15844, 20328, 13063, 3660, 18871, 9381, 2288, 24525, 2304, 3224, 314, 55, 3714, 29245, 23328, 8978, 2423, 39184, 314, 295, 376, 11933, 15730, 14111, 23758, 2423, 39184, 1783, 4032, 9957, 3714, 29245, 23328, 22807], "avg_logprob": -0.22743055158191258, "compression_ratio": 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"probability": 0.087646484375}, {"start": 2990.08, "end": 2990.42, "word": " ام", "probability": 0.764892578125}, {"start": 2990.42, "end": 2991.2, "word": " وهو", "probability": 0.7061767578125}, {"start": 2991.2, "end": 2991.94, "word": " المطلوب", "probability": 0.980224609375}, {"start": 2991.94, "end": 2992.58, "word": " وهيك", "probability": 0.465087890625}, {"start": 2992.58, "end": 2992.78, "word": " ممكن", "probability": 0.84033203125}, {"start": 2992.78, "end": 2993.54, "word": " فلسنا", "probability": 0.7352294921875}, {"start": 2993.54, "end": 2994.24, "word": " اللي", "probability": 0.692138671875}, {"start": 2994.24, "end": 2994.52, "word": " هو", "probability": 0.94384765625}, {"start": 2994.52, "end": 2995.32, "word": " هذا", "probability": 0.83251953125}, {"start": 2995.32, "end": 2995.44, "word": " ال", "probability": 0.83447265625}, {"start": 2995.44, "end": 2995.82, "word": " section", "probability": 0.8671875}, {"start": 2995.82, "end": 2996.36, "word": " وإلى", "probability": 0.6354166666666666}, {"start": 2996.36, "end": 2996.74, "word": " لقاء", "probability": 0.7900390625}, {"start": 2996.74, "end": 2997.04, "word": " آخر", "probability": 0.903076171875}, {"start": 2997.04, "end": 2997.46, "word": " السلام", "probability": 0.90478515625}, {"start": 2997.46, "end": 2997.9, "word": " عليكم", "probability": 0.915283203125}, {"start": 2997.9, "end": 2998.24, "word": " ورحمة", "probability": 0.93701171875}, {"start": 2998.24, "end": 2998.38, "word": " الله", "probability": 0.962890625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2998.6715, "duration_after_vad": 2925.739374999992}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/EaC1QqfjIDE_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/EaC1QqfjIDE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bb9f3cfca5e056d45440906fc2940bc666172d4a
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/EaC1QqfjIDE_raw.srt
@@ -0,0 +1,2748 @@
+1
+00:00:05,210 --> 00:00:07,970
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,970 --> 00:00:10,890
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,890 --> 00:00:15,610
+آله وصحبه أجمعين هذه هي المحاضرة رقم 11 مساق تحليل
+
+4
+00:00:15,610 --> 00:00:18,710
+اقتراني او تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:18,710 --> 00:00:23,810
+الإسلامية قسم رياضيات ماجستيريا اليوم ان شاء الله
+
+6
+00:00:23,810 --> 00:00:30,370
+هنكمل اللي هو في المادة هناخد section اتنين وخمسة
+
+7
+00:00:30,370 --> 00:00:33,690
+اللي هو compactness and finite dimension هنحكي عن
+
+8
+00:00:34,570 --> 00:00:39,210
+شو مفهوم الـ compact set و .. و خلّيني أقوله علاقة
+
+9
+00:00:39,210 --> 00:00:42,410
+الـ Finiteness في حالة اللي هو ال .. ال compact في
+
+10
+00:00:42,410 --> 00:00:48,390
+حالة ال Finiteness ك dimension منيح إنه أنا أحكي
+
+11
+00:00:48,390 --> 00:00:54,130
+عن الأمور الكلية في موضوع ال compactness احنا
+
+12
+00:00:54,130 --> 00:00:57,910
+جسمنا الدنيا تبعتنا اللي هو قلنا في عندي
+
+13
+00:00:57,910 --> 00:01:02,000
+topological spaceاللي هو autobiographical space in
+
+14
+00:01:02,000 --> 00:01:05,980
+general في داخله اللي هو autobiographical spaces
+
+15
+00:01:05,980 --> 00:01:10,740
+في داخله اللي هو metric spaces في داخله اللي هو
+
+16
+00:01:10,740 --> 00:01:15,980
+normed spaces في داخله اللي هو Hilbert spacesفيه
+
+17
+00:01:15,980 --> 00:01:19,500
+في داخله الـ spaces تبعاتنا الحلوات هذي R وRR ومش
+
+18
+00:01:19,500 --> 00:01:25,660
+عارف ايش الاخره وC الاخره الآن احنا بندرس ال
+
+19
+00:01:25,660 --> 00:01:28,380
+compactness حتى كنا ندرسها في ال real analysis
+
+20
+00:01:28,380 --> 00:01:33,230
+وممكن ادرسه في ال calculus كمانأو ممكن اللي هو
+
+21
+00:01:33,230 --> 00:01:38,470
+أدرسه اللي هو في normed spaces أو metric spaces و
+
+22
+00:01:38,470 --> 00:01:41,690
+بندرسه في ال topological spaces في ال topological
+
+23
+00:01:41,690 --> 00:01:46,610
+spaces إيش بنعرفه؟ بنقول أن ال .. ال .. ال .. ال
+
+24
+00:01:46,610 --> 00:01:46,930
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+25
+00:01:46,930 --> 00:01:47,050
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+26
+00:01:47,050 --> 00:01:47,050
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+27
+00:01:47,050 --> 00:01:47,130
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+28
+00:01:47,130 --> 00:01:47,270
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+29
+00:01:47,270 --> 00:01:47,510
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+30
+00:01:47,510 --> 00:01:49,070
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+31
+00:01:49,070 --> 00:01:49,070
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+32
+00:01:49,070 --> 00:01:49,110
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+33
+00:01:49,110 --> 00:01:52,710
+ال .. ال .. ال .. ال .. ال .. ال ..
+
+34
+00:01:52,710 --> 00:01:54,670
+ال .. ال
+
+35
+00:01:58,490 --> 00:02:06,110
+لما نحكي في الـ Metric Spaces، سنبدأ بشيء آخر، وهو
+
+36
+00:02:06,110 --> 00:02:10,650
+أن كل .. لأنه صار فيه Sets .. صار فيه Sequences ..
+
+37
+00:02:10,650 --> 00:02:13,290
+كل Sequence .. هذا في الـ Metric Spaces .. كل
+
+38
+00:02:13,290 --> 00:02:16,410
+Sequence لديها Sub-Sequence Convergent .. الـ Set
+
+39
+00:02:16,410 --> 00:02:23,970
+اللي يتحقق هذه، نسميها كمباكد Setفي الـ R وفي الـ
+
+40
+00:02:23,970 --> 00:02:27,370
+RN أو حتى في الـ Finite Dimensional Vector Spaces
+
+41
+00:02:27,370 --> 00:02:31,390
+أو الـ Enormed Spaces بنعرف الـ compact على أساس
+
+42
+00:02:31,390 --> 00:02:33,810
+أنه ال city اللي بتكون closed و bounded على طول
+
+43
+00:02:33,810 --> 00:02:39,790
+أشمالها compact طب هو بنفع أه بنفع هنا ليش؟ لأنه
+
+44
+00:02:39,790 --> 00:02:44,640
+أنافي الـ topological spaces in general every open
+
+45
+00:02:44,640 --> 00:02:48,420
+cover has a finite sub cover لا يكافئ أنه .. اللي
+
+46
+00:02:48,420 --> 00:02:51,560
+هو أنه every sequence has a convergent subsequence
+
+47
+00:02:51,560 --> 00:02:54,840
+عشان هيك بنعرف في ال topological spaces ب every
+
+48
+00:02:54,840 --> 00:02:57,740
+open cover has a finite cover اللي هو تعريف ال
+
+49
+00:02:57,740 --> 00:03:02,520
+compactness الأصليإذا كنت تكتب تعطيهم الكلام اللي
+
+50
+00:03:02,520 --> 00:03:05,920
+حكيته اللي هو every اللي هو set has a convergent
+
+51
+00:03:05,920 --> 00:03:09,860
+.. every sequence has a convergent subsequence لكن
+
+52
+00:03:09,860 --> 00:03:12,740
+العكس مش صحيح هذا في topological spaces in general
+
+53
+00:03:12,740 --> 00:03:17,260
+لأن لما نيجي ندخل في ال metric space لأ بصير صحيح
+
+54
+00:03:17,260 --> 00:03:20,640
+في ال metric space هنلاقي أن every open cover has
+
+55
+00:03:20,640 --> 00:03:25,770
+a finite sub cover يكافئإنه نقول إن every sequence
+
+56
+00:03:25,770 --> 00:03:30,590
+has a convergent subsequence وبناء عليه بنتجرأ للي
+
+57
+00:03:30,590 --> 00:03:33,450
+بديش أعرفله أنا بدي أسهل عليه بديش أنا بديش أتكلم
+
+58
+00:03:33,450 --> 00:03:36,970
+في أمور الطب الجنرال بعد دي أعرفله في ال metric
+
+59
+00:03:36,970 --> 00:03:42,050
+space إن ال comeback يعني every open .. every اللي
+
+60
+00:03:42,050 --> 00:03:46,330
+هي sequence has a convergent subsequenceطب الآن
+
+61
+00:03:46,330 --> 00:03:50,410
+هذا الكلام طب لو أجينا دخلنا طبعا في ال normed
+
+62
+00:03:50,410 --> 00:03:52,590
+spaces و في ال metric spaces التانية اللي بنشتغل
+
+63
+00:03:52,590 --> 00:03:55,630
+فيها بنفس الأسلوب في موضوع ال compactics لكن لما
+
+64
+00:03:55,630 --> 00:04:00,070
+أدخل لل R و Rn و لما أدرسهم في التحليل أو في ال
+
+65
+00:04:00,070 --> 00:04:02,750
+complex على طول بقوله أنا مغمض بس اللي هو ال
+
+66
+00:04:02,750 --> 00:04:06,030
+compacts تتعني إنها closed و bounded ماجبلوش
+
+67
+00:04:06,030 --> 00:04:08,130
+series of sequences ماجبلوش series of sequences
+
+68
+00:04:08,130 --> 00:04:12,230
+ليش لأنه أنا عارف أنه في داخل ال finite
+
+69
+00:04:12,230 --> 00:04:16,420
+dimensional spacesهنلاقي الـ Closed و الـ Bounded
+
+70
+00:04:16,420 --> 00:04:20,180
+تكافئ الـ Compactness يعني تكافئ أن كل سيكوينس هذا
+
+71
+00:04:20,180 --> 00:04:25,480
+Convergent إيش سبسيكوينس يعني في داخل الـR و الـR
+
+72
+00:04:25,480 --> 00:04:28,580
+تربيع و كل الـFinite Dimensional Spaces ما يلي
+
+73
+00:04:28,580 --> 00:04:32,320
+متكافئEvery open cover has a finite sub cover «كل
+
+74
+00:04:32,320 --> 00:04:35,500
+مفتاح مفتاح» «كل مفتاح مفتاح» «كل سيقونس مفتاح
+
+75
+00:04:35,500 --> 00:04:36,720
+مفتاح مفتاح» «كل سيقونس مفتاح مفتاح مفتاح مفتاح»
+
+76
+00:04:36,720 --> 00:04:49,220
+«كل سيقونس
+
+77
+00:04:49,220 --> 00:04:50,780
+مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح
+
+78
+00:04:50,780 --> 00:04:52,160
+مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح
+
+79
+00:04:52,160 --> 00:04:52,160
+مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح
+
+80
+00:04:52,160 --> 00:04:52,160
+مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح مفتاح
+
+81
+00:04:52,160 --> 00:04:59,320
+مفتاح مفتاح مفتاح م
+
+82
+00:05:01,430 --> 00:05:03,830
+العنوان الـ compactness and finite dimension
+
+83
+00:05:11,270 --> 00:05:13,750
+مافي تعليقات كتير عن الـ compactness بس مش وقته
+
+84
+00:05:13,750 --> 00:05:16,670
+يعني لو في topology احنا بنصح لكن هالجت احنا خلينا
+
+85
+00:05:16,670 --> 00:05:20,990
+حالنا في ال functional definition a metric space X
+
+86
+00:05:20,990 --> 00:05:24,390
+is said to be compact ده بيعرف وين في ال metric
+
+87
+00:05:24,390 --> 00:05:28,010
+space compact if every sequence in X has a
+
+88
+00:05:28,010 --> 00:05:31,810
+convergent subsequence ماشي هذا بيعني فيه compactة
+
+89
+00:05:31,810 --> 00:05:35,910
+الآنلأن a subset M of X is said to be compact if
+
+90
+00:05:35,910 --> 00:05:41,710
+اتعاملنا مع الـ M as a compact subspace من الـ X
+
+91
+00:05:41,710 --> 00:05:45,670
+يعني بمعنى أخر بنتعامل بالـ Metric اللي هو الـ
+
+92
+00:05:45,670 --> 00:05:48,490
+Metric الأصل اللي هنا اللي هو بمعنى is said to be
+
+93
+00:05:48,490 --> 00:05:52,690
+compact if M نفسها is a compact considered as a
+
+94
+00:05:52,690 --> 00:05:55,890
+subspace of X يعني بمعنى أخر that is every
+
+95
+00:05:55,890 --> 00:05:58,710
+sequence in M has a convergent subsequence whose
+
+96
+00:05:58,710 --> 00:06:02,910
+limit belongs to Mفي ضوء الـ Metric المعرف الأصلي
+
+97
+00:06:02,910 --> 00:06:07,690
+في مين؟ في الـ X. طيب، اننا نيجي لأول لمّة، اطلع
+
+98
+00:06:07,690 --> 00:06:12,690
+لللمّة اللي فوق، اللمّة بتقول لي لمّة 2 5 2، a
+
+99
+00:06:12,690 --> 00:06:16,570
+compact subset M of a metric space is closed و
+
+100
+00:06:16,570 --> 00:06:20,430
+bounded، على طول خاصية سهلة دي، إذا كانت compact،
+
+101
+00:06:20,430 --> 00:06:23,950
+على طول بتكون أشمالها closed و bounded، ده نشوف
+
+102
+00:06:23,950 --> 00:06:30,330
+الآن، let X be أي element in M closure،بدي الأن
+
+103
+00:06:30,330 --> 00:06:35,230
+أثبت لك أنه M Closed يعني أخد X في الـ M Closure
+
+104
+00:06:35,230 --> 00:06:37,830
+لأثبت لك أن X دي لازم تكون في مين في الـ M نفسها
+
+105
+00:06:37,830 --> 00:06:41,790
+ماشي الحال طيب مدام X في الـ M Closure then there
+
+106
+00:06:41,790 --> 00:06:45,510
+is a sequence Xn of elements in M such that Xn
+
+107
+00:06:45,510 --> 00:06:49,940
+بتروح لمين لل X هذا مصارت محفوظة يعني مفهوم هذاإذن
+
+108
+00:06:49,940 --> 00:06:55,040
+however M is compact ما زم F is compact إذن every
+
+109
+00:06:55,040 --> 00:06:59,240
+sequence has a convergent subsequence إذن then X
+
+110
+00:06:59,240 --> 00:07:02,660
+element in M لأنه فيه لها subsequence سموها X and
+
+111
+00:07:02,660 --> 00:07:05,260
+K بتروح لل X طب ما هي ال subsequence والsequence
+
+112
+00:07:05,260 --> 00:07:09,600
+الأصلية بروح لنفس ال X معايا؟ إذن غصب عنها هتطلع
+
+113
+00:07:09,600 --> 00:07:13,720
+ال X موجودة في ال M معناته then اللي هي M is
+
+114
+00:07:13,720 --> 00:07:18,670
+enclosed طيببدنا نثبت الأن إيه شمالها is bounded
+
+115
+00:07:18,670 --> 00:07:22,670
+بدنا نفترض العكس suppose that M is not bounded
+
+116
+00:07:22,670 --> 00:07:25,930
+مدام bounded طب إحنا إذا بتتذكر شو معناه bounded
+
+117
+00:07:25,930 --> 00:07:31,450
+أنه ال diameter ال diameter ال diameter ل ماعرفش
+
+118
+00:07:31,450 --> 00:07:35,550
+كيف أقولنا عنه ال diameter ل اللي هو ال M بساوي ال
+
+119
+00:07:35,550 --> 00:07:42,230
+supremumلـDXY لكل الـX وY الموجودة في الـM هذا
+
+120
+00:07:42,230 --> 00:07:44,710
+الـDiameter من الـM بنقول عنها bounded وكان
+
+121
+00:07:44,710 --> 00:07:48,410
+الـDiameter نفسه ماهو؟ is finite يعني الـSupermom
+
+122
+00:07:48,410 --> 00:07:53,530
+ماهو؟ is finite يعني الآن لو أي sequence هنا في
+
+123
+00:07:53,530 --> 00:07:56,790
+الـMلازم المسافة بين الـ sequence هذه وبين أي
+
+124
+00:07:56,790 --> 00:07:59,910
+element هنا يكون إيش مالوفاينات، ماينفعش اللي هو
+
+125
+00:07:59,910 --> 00:08:05,850
+يكبر، يروح لما لا نهاية، لأن لو بدأ أفترض، لو بدأ
+
+126
+00:08:05,850 --> 00:08:10,110
+أفترض الآن أن M is not bounded، suppose that M is
+
+127
+00:08:10,110 --> 00:08:12,750
+not bounded، معناته ال supermom هذا بيروح لمين؟
+
+128
+00:08:12,750 --> 00:08:17,680
+لما لا نهاية،معناته أكيد أكيد أكيد أكيد لازم ألاقي
+
+129
+00:08:17,680 --> 00:08:22,360
+unbounded sequence YN بحيث أن المسافة بين YN و B
+
+130
+00:08:22,360 --> 00:08:26,260
+تكون إيه شمالها أكبر من N لأنه لو مالجيتش معناته
+
+131
+00:08:26,260 --> 00:08:29,000
+أنه حيصير إيش كل المسافات الصغيرة معناته سارة اللي
+
+132
+00:08:29,000 --> 00:08:31,160
+هو إيه إيه إيش ال superman موجود معناته superman
+
+133
+00:08:31,160 --> 00:08:36,040
+finite وانا بقول نفترضإنه Unbounded يعني السبري ما
+
+134
+00:08:36,040 --> 00:08:39,720
+معمله بيروح إلى ما لا نهاية معايا إذا لازم نلاقي
+
+135
+00:08:39,720 --> 00:08:44,000
+subsequence أو unbounded sequence yn بحيث المسافة
+
+136
+00:08:44,000 --> 00:08:49,160
+بين yn و b أكبر من اللي هو الان where b is any
+
+137
+00:08:49,160 --> 00:08:54,100
+fixed element زي ما قلنا هنس yn إشمالها has not a
+
+138
+00:08:54,100 --> 00:08:57,240
+bounded subsequenceما دام ال .. ال .. ال distance
+
+139
+00:08:57,240 --> 00:09:00,600
+بين ال YN و ال B أكبر من N معناته لو أخدت أي
+
+140
+00:09:00,600 --> 00:09:04,780
+subsequence تانية يعني منها .. أسف مش تانية لو
+
+141
+00:09:04,780 --> 00:09:08,280
+أخدت أي subsequence منها YNK هكون ال distance بين
+
+142
+00:09:08,280 --> 00:09:13,040
+YNK و B أكبر من ال NK هذه و هكذا فبتصير فش ولا
+
+143
+00:09:13,040 --> 00:09:17,840
+subsequence bounded لأن كل .. كل .. كل .. كل ال ..
+
+144
+00:09:17,840 --> 00:09:21,880
+كل البعد بين YN و ال B دايما إيه شماله أكبر من N
+
+145
+00:09:21,880 --> 00:09:27,650
+إذاWhy N has not bounded subsequence؟ بدأ مالهاش
+
+146
+00:09:27,650 --> 00:09:31,190
+bounded subsequence إذا أكيد مش converge إذا مافيش
+
+147
+00:09:31,190 --> 00:09:34,770
+ولا subsequence converge وهذا ينقض مين أن M is
+
+148
+00:09:34,770 --> 00:09:40,650
+compact إذا الـ N لازم تكون عنده اللي هي الفرضية
+
+149
+00:09:40,650 --> 00:09:45,090
+مش مظبوطة لازم تكون M is bounded therefore M is
+
+150
+00:09:45,090 --> 00:09:52,580
+boundedالآن زي ما وعدتكم اطلع لفوق اطلع لفوق اطلع
+
+151
+00:09:52,580 --> 00:09:55,320
+لفوق اخدنا نورجينا هنا الان the converse of لما
+
+152
+00:09:55,320 --> 00:09:59,460
+اللي فوق need not be true in general زي ما وعدناكم
+
+153
+00:09:59,460 --> 00:10:03,760
+احنا في ال .. في ال .. في ال .. في ال .. في ال
+
+154
+00:10:03,760 --> 00:10:07,100
+normed space او ال metric space in general ال
+
+155
+00:10:07,100 --> 00:10:10,880
+closed و ال bounded ليس شرطا انه يكافئ ان every
+
+156
+00:10:10,880 --> 00:10:13,940
+sequence is a convergent subsequence اذا الان بدي
+
+157
+00:10:13,940 --> 00:10:19,330
+اجيبلكاللي هو مثلًا اقول لي اللي هو في عنده
+
+158
+00:10:19,330 --> 00:10:25,170
+sequence اللي هو تكون bounded و closed او في عنده
+
+159
+00:10:25,170 --> 00:10:29,230
+ال .. اللي هو set bounded و closed لكن مافيش فيها
+
+160
+00:10:29,990 --> 00:10:34,450
+اللي هو الـ sequence اللي عنده فيه sequence مش
+
+161
+00:10:34,450 --> 00:10:37,650
+هلاقي إليها ولا convergence subsequence يعني مش
+
+162
+00:10:37,650 --> 00:10:43,090
+compact بمعنى أخر الآن بدأ أجيب مثال على a closed
+
+163
+00:10:43,090 --> 00:10:48,180
+bounded set which is not compactباختصار ماشي هذا
+
+164
+00:10:48,180 --> 00:10:52,940
+اكيد من وين بده يجيبه من اللي هو اكيد يعني حسب
+
+165
+00:10:52,940 --> 00:10:55,360
+كلام الأولاني مش هجيبه من ال final dimensional
+
+166
+00:10:55,360 --> 00:10:58,880
+space هجيبه من infinite dimensional space لأنه في
+
+167
+00:10:58,880 --> 00:11:01,080
+ال final dimensional زي ما قعدناكوا هيطلع نقش
+
+168
+00:11:01,080 --> 00:11:05,800
+مهلين زي بعضطيب a proof consider the sequence en
+
+169
+00:11:05,800 --> 00:11:10,020
+in main ال L2 ال L2 the space of all sequences هذا
+
+170
+00:11:10,020 --> 00:11:13,700
+infinite dimensional space where en لأنه جيبنا ال
+
+171
+00:11:13,700 --> 00:11:16,260
+shoulder bases اللي عارفينه E1 E2 E3 المرة الماضية
+
+172
+00:11:16,260 --> 00:11:17,840
+E1 E2 E3 ..
+
+173
+00:11:20,970 --> 00:11:24,530
+Where en بيساوي ل chronicle delta and j اللي هي
+
+174
+00:11:24,530 --> 00:11:29,090
+عارفينها اي واحد واحد و الباقي أسفار اتنين واحد
+
+175
+00:11:29,090 --> 00:11:32,710
+سفر و الباقي أسفار اتلاتة سفر سفر واحد و الباقي
+
+176
+00:11:32,710 --> 00:11:37,720
+أسفار و هكذا الان this sequence is boundedليش
+
+177
+00:11:37,720 --> 00:11:41,620
+bounded؟ لأنه norm كل واحدة اللي هو عبارة عن واحد
+
+178
+00:11:41,620 --> 00:11:45,100
+لإن الـen عبارة عن سفر، سفر، سفر، وفي ال-nth term
+
+179
+00:11:45,100 --> 00:11:48,540
+واحد، والباقي سفر، سفر، نورمها بصممش ينقلهم كلها
+
+180
+00:11:48,540 --> 00:11:51,400
+نصفها ويبقوا الميه الواحد، إذا الـnorm هم إيه إيش
+
+181
+00:11:51,400 --> 00:11:57,120
+واحد، إذا اخترت أن أنا اللي هي عناصر الـL2 هذولة،
+
+182
+00:11:57,120 --> 00:12:00,820
+أراء ليها دي، اخترتهم أنه في بينهم بعض، يعني مش
+
+183
+00:12:00,820 --> 00:12:03,360
+اللي ملزج أدم هو الـcompact هو أرس، في حاجة اسم
+
+184
+00:12:03,360 --> 00:12:09,420
+أرس، فانا اخترت بالعمدن زي هيك، to show thatM is
+
+185
+00:12:09,420 --> 00:12:13,940
+closed we show that M has no accumulation point
+
+186
+00:12:13,940 --> 00:12:21,680
+إذا الأن إيش بده يعملنا ال M اختارها اللي هي عبارة
+
+187
+00:12:21,680 --> 00:12:28,270
+عن مين اللي هو ال sequence EN ماشيأريد أن أثبت أن
+
+188
+00:12:28,270 --> 00:12:34,930
+الـ M هذه مغلقة وبعضية بعضية أثبتناها لأن نورم
+
+189
+00:12:34,930 --> 00:12:38,850
+عنصرها مش بساوي بساوية حد يان كل عنصر نورمه اللي
+
+190
+00:12:38,850 --> 00:12:43,530
+هو finite الـ M يجب أن أثبت أنها مغلقة عارفين كيف
+
+191
+00:12:43,530 --> 00:12:48,080
+تثبت أنها مغلقة؟أريد أن أثبت أنها M Closed بحيث
+
+192
+00:12:48,080 --> 00:12:52,520
+أثبت لك أنه ليس فيها أي مقاومة يعني ليس فيها
+
+193
+00:12:52,520 --> 00:12:56,080
+مقاومة مقاومة الـ M بمعنى آخر بيصير الـ closure هو
+
+194
+00:12:56,080 --> 00:13:01,720
+الـ M لأن M الـ Prime بتسوء Phi واحنا بنعرف أن M
+
+195
+00:13:01,720 --> 00:13:08,500
+closure بتسوء M إتحاد M Prime لو هذه Phi معناته M
+
+196
+00:13:08,500 --> 00:13:11,960
+closure بتسوء M معناته Closedإذن هأثبت لكم إن هناك
+
+197
+00:13:11,960 --> 00:13:16,260
+لا مقاومة إذا أثبتت إن هناك لا مقاومة إذا أخدت الـ
+
+198
+00:13:16,260 --> 00:13:22,120
+M هي إعبارة عن E1 E2 E3 إلى مدى نهاية وهذه جزء من
+
+199
+00:13:22,120 --> 00:13:27,820
+مين؟ من الأقل 2 بدي أبحث فيه أمرين بدي أثبت لكم إن
+
+200
+00:13:27,820 --> 00:13:31,660
+أول إشي ولا واحدة من هدولة ممكن تكون مقاومة السبب
+
+201
+00:13:31,660 --> 00:13:35,400
+بسيط أن البعد بينها جدر التنين لما تاخدوا البعد
+
+202
+00:13:35,400 --> 00:13:39,170
+بين التنين حتى جوا جدر التنين بعد شويةيعني عشان
+
+203
+00:13:39,170 --> 00:13:44,790
+تكون accumulation point دنيا كلها ملزقة فيها ان
+
+204
+00:13:44,790 --> 00:13:47,950
+شاء الله فاهمين عليها الان ال .. ال .. ال .. ال ..
+
+205
+00:13:47,950 --> 00:13:48,810
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+206
+00:13:48,810 --> 00:13:48,830
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+207
+00:13:48,830 --> 00:13:48,950
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+208
+00:13:48,950 --> 00:13:48,990
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+209
+00:13:48,990 --> 00:13:49,190
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+210
+00:13:49,190 --> 00:13:49,610
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+211
+00:13:49,610 --> 00:13:49,610
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+212
+00:13:49,610 --> 00:13:49,630
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+213
+00:13:49,630 --> 00:13:51,730
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+214
+00:13:51,730 --> 00:13:52,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+215
+00:13:52,290 --> 00:13:59,250
+ال .. ال .. ال .. ال .. ال ..
+
+216
+00:13:59,250 --> 00:14:00,290
+ال .. ال ..
+
+217
+00:14:07,930 --> 00:14:13,450
+و اولا نظرح ان اي مقام في M يكون مقام اكمال ممكن
+
+218
+00:14:13,450 --> 00:14:23,350
+ان يكون اي مقام مقام مقام مقام مقام مقام مقام مقام
+
+219
+00:14:23,350 --> 00:14:30,470
+مقام مقام مقام مقاميعني بين الـ N عناصر الـ M مين
+
+220
+00:14:30,470 --> 00:14:34,870
+هي؟ E1 E2 E3 الاخرى بيدثبتلكم إن المسافة بين E N
+
+221
+00:14:34,870 --> 00:14:38,550
+وأي عنصر تاني اللي هو بثوجة للاتنين خدوا المسافة
+
+222
+00:14:38,550 --> 00:14:43,330
+بين E N وE M حيث E M أي عنصر موجود في الـ M بيختلف
+
+223
+00:14:43,330 --> 00:14:48,300
+عن الـ E Nهي ساوي النورم هذا ايه اشمله 000 هذا في
+
+224
+00:14:48,300 --> 00:14:52,640
+الانث تير وهذا في الانتر مثلا او العكس ماشي فبكون
+
+225
+00:14:52,640 --> 00:14:57,680
+حاصل ترحيل هيه ماشي الحال او ممكن واحد يكون ناقص
+
+226
+00:14:57,680 --> 00:15:01,360
+واحد مش هتفرج كتير نورم هنا بساوي summation لل
+
+227
+00:15:01,360 --> 00:15:05,560
+absolute value هنا قص نص لان أنا بحكي عن ال two
+
+228
+00:15:06,270 --> 00:15:09,710
+فاهمين عليها إذا هذا بيساوي مين بيطلع عند جذر
+
+229
+00:15:09,710 --> 00:15:13,850
+التنين إذا صار عند المسافة بين EN و EN بيساوي جذر
+
+230
+00:15:13,850 --> 00:15:19,610
+التنين إذا .. إذا لجيت أنا لو جيت لل ball EN واحد
+
+231
+00:15:19,610 --> 00:15:23,170
+و نص القطر واحد مش عادي بكم EN و نص شيله من ال EN
+
+232
+00:15:23,170 --> 00:15:26,930
+طاقاته لأ مش هيساوي fine إذا مش limit point عشان
+
+233
+00:15:26,930 --> 00:15:32,170
+limit point أيش بيكون أنه لأي neighborhoodBEN أي
+
+234
+00:15:32,170 --> 00:15:37,110
+اللي هو ball EN بأي نص خطر شيله منها العنصر هذا
+
+235
+00:15:37,110 --> 00:15:40,790
+تقطحها مع ال M لازم إيش لله؟ لا يساوي five لجتلكم
+
+236
+00:15:40,790 --> 00:15:46,550
+اللي هو نص خطر واحد و نص و ربع كل بعمل إنه BEN هو
+
+237
+00:15:46,550 --> 00:15:50,490
+واحد أو نص أو ربع شيله منه EN تقطع له مش بيساوي
+
+238
+00:15:50,490 --> 00:15:55,150
+five سببه إن المسافات بين العناصر جدر التنين إذن
+
+239
+00:15:55,150 --> 00:15:58,860
+المسافات بين العناصر اللي هنالو بدي اكون في عنصر
+
+240
+00:15:58,860 --> 00:16:05,300
+من M اشمله لازم تاخد هذا اتنين او تلاتة او اربعة
+
+241
+00:16:05,300 --> 00:16:10,560
+او خمسة فاهمين؟ طيب صار عندي الان hence any point
+
+242
+00:16:10,560 --> 00:16:15,080
+in M can't be an accumulation pointsecond اللي ضال
+
+243
+00:16:15,080 --> 00:16:18,360
+we show that any point in M complement يعني براة
+
+244
+00:16:18,360 --> 00:16:21,160
+الـ M في الـ L2 بس مش في الـ M complement can't be
+
+245
+00:16:21,160 --> 00:16:26,000
+an accumulation point ماشي في سؤال اللي هو 13
+
+246
+00:16:26,000 --> 00:16:29,520
+Problem 6 كان بيقولنا إذا كانت النقطة accumulation
+
+247
+00:16:29,520 --> 00:16:35,740
+point بدي يكون أي neighborhood حوالين النقطة تقاطع
+
+248
+00:16:35,740 --> 00:16:39,250
+مع الـ M هيكون infinite number of dotsمش هيكون
+
+249
+00:16:39,250 --> 00:16:41,970
+نقطة في infinite number of points هذا اللي هو سؤال
+
+250
+00:16:41,970 --> 00:16:45,930
+ستة في problem 138 مش صعب عموما طيب شوفوا صلى الله
+
+251
+00:16:45,930 --> 00:16:49,470
+على النبي عز وجل انا بدي استعينيه الان بدي اخد اي
+
+252
+00:16:49,470 --> 00:16:52,790
+نقطة في ال M complement و اثبتلكم انه لا يمكن انها
+
+253
+00:16:52,790 --> 00:16:56,770
+تكون accumulation point او limit point لل M شوف
+
+254
+00:16:56,770 --> 00:17:00,490
+كيف let X be any fixed point in M complement خدوا
+
+255
+00:17:00,490 --> 00:17:05,350
+الان ال ball ال نص خطرها اللي هو نص و مركزها ال X
+
+256
+00:17:05,350 --> 00:17:11,340
+هذهشيلوا منها الـ X تقاطع الـ M مستحيل تحتوي على
+
+257
+00:17:11,340 --> 00:17:14,280
+الأكثر على الأكثر حيكون نقطة واحدة من الـ M على
+
+258
+00:17:14,280 --> 00:17:17,980
+الأكثر نقطة واحدة أيش من الـ M ليش؟ لأن لو كان في
+
+259
+00:17:17,980 --> 00:17:22,220
+نقطتين من الـ M ومصفره .. وهي كانت جواة بهذا ال
+
+260
+00:17:22,220 --> 00:17:25,220
+ball كيف بيبقى تكون جواة ال ball والمسافة بين كل
+
+261
+00:17:25,220 --> 00:17:27,700
+نقطتين في ال .. في ال .. في ال M إيش ماله؟ جدر
+
+262
+00:17:27,700 --> 00:17:29,920
+التنين معايا؟
+
+263
+00:17:31,370 --> 00:17:34,030
+المسافات بين النقاط اللي جوا موجودة هنا إيش هيكون
+
+264
+00:17:34,030 --> 00:17:38,590
+نص؟ لو بدوا يكون تنتين من الأم هنا طب هم المسافات
+
+265
+00:17:38,590 --> 00:17:41,210
+اللي بين التنتين اللي في الأم مش أثبتنا أنها نجدر
+
+266
+00:17:41,210 --> 00:17:44,270
+التنين يعني مش هيكون التنتين جوا يعني إيه ده
+
+267
+00:17:44,270 --> 00:17:47,390
+بيلاجينا .. بيلاجينا واحدة جريبة من هذه اللي هو
+
+268
+00:17:47,390 --> 00:17:50,450
+ابن أُص لكن لو بنجول فيه كمان واحدة بيصير بينها و
+
+269
+00:17:50,450 --> 00:17:54,750
+بين كمان أختها أجال من النص و هذا مش سهل إذن هنا
+
+270
+00:17:54,750 --> 00:18:01,430
+has at most one element why قلته؟ماشي و هذا مستحيل
+
+271
+00:18:01,430 --> 00:18:05,810
+لأن X is not an accumulation point لأنه في ال
+
+272
+00:18:05,810 --> 00:18:08,310
+problem واحدة ستة اللي هي واحدة تلاتة بنقول إنه لو
+
+273
+00:18:08,310 --> 00:18:10,970
+كانت accumulation point لازم يكون في عند infinite
+
+274
+00:18:10,970 --> 00:18:12,990
+number of points مشتركة
+
+275
+00:18:15,030 --> 00:18:18,330
+أي point في الـ mk can't be an accumulation point
+
+276
+00:18:18,330 --> 00:18:21,850
+therefore m has no accumulation point hence m
+
+277
+00:18:21,850 --> 00:18:24,650
+بيسوي m closure زي ما أقولها ومن ثم m is closed
+
+278
+00:18:24,650 --> 00:18:29,070
+إذا صار عندي m closed و open إذا صار عندي اللي هي
+
+279
+00:18:29,070 --> 00:18:34,050
+إيش مالها اللي هي متحققة لأن بدنا نقول إنها إيش
+
+280
+00:18:34,050 --> 00:18:39,670
+مالها خليني بدنا نقول إيش إنها مش compact ماشي
+
+281
+00:18:39,670 --> 00:18:44,710
+moreover m has no convergence subsequenceليش؟
+
+282
+00:18:44,710 --> 00:18:48,490
+Because M has no accumulation point لو بدها تكون
+
+283
+00:18:48,490 --> 00:18:53,530
+في عندي subsequence في الـ M Xn subsequence في الـ
+
+284
+00:18:53,530 --> 00:18:58,550
+M و Xn has a convergence subsequence to some X في
+
+285
+00:18:58,550 --> 00:19:03,730
+الـ M بيصير اللي هو أنه عندي تكدس من ال .. من ..
+
+286
+00:19:03,730 --> 00:19:07,330
+من .. من .. من المقاط اللي موجودة في الـ M المسافة
+
+287
+00:19:07,330 --> 00:19:09,710
+بينها و بينها بقى أصغر من الـ Y في الدنيا طبعاً
+
+288
+00:19:09,710 --> 00:19:14,160
+جدر التنين المسافة بينهم بعاد عن بعضفاهمين اللي
+
+289
+00:19:14,160 --> 00:19:20,080
+بحكيه؟ أي سؤال؟ اذا ال M is not compact M is not
+
+290
+00:19:20,080 --> 00:19:23,500
+compact ليش؟ لأنه لو أخدنا أي sequence في ال M
+
+291
+00:19:23,500 --> 00:19:26,020
+يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل
+
+292
+00:19:26,020 --> 00:19:26,020
+يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل
+
+293
+00:19:26,020 --> 00:19:26,020
+يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل يستحيل
+
+294
+00:19:26,020 --> 00:19:26,320
+يستحيل يستحيل يستحيل يستحيل يستحيل يستحل يستحل
+
+295
+00:19:26,320 --> 00:19:26,380
+يستحل يستحل يستحل يستحل يستحل يستحل يستحل يستحل
+
+296
+00:19:26,380 --> 00:19:26,500
+يستحل يستحل يستحل يستحل يستحل يستحل يستحل يستحل
+
+297
+00:19:26,500 --> 00:19:26,620
+يستحل
+
+298
+00:19:37,700 --> 00:19:40,780
+Xn بتروح للـ X عشان تكون converged إلى الـ X بيكون
+
+299
+00:19:40,780 --> 00:19:44,600
+أي ball حوالين الـ X بحتوي عدد لا نهائي من النخاق
+
+300
+00:19:44,600 --> 00:19:47,660
+مع عدد finite number مش هيك معناه ال limit limit
+
+301
+00:19:47,660 --> 00:19:52,400
+Xn بتروح بتساوي X معناه تقرر every Y أكبر من 0
+
+302
+00:19:52,400 --> 00:19:57,360
+there exist K element in N such that ال ball لل X
+
+303
+00:19:57,360 --> 00:20:03,700
+هذه و ال Y اللي هو تحتوي
+
+304
+00:20:03,700 --> 00:20:10,500
+أو XnXn element الـ ball for every n أكبر شوء إيش
+
+305
+00:20:10,500 --> 00:20:16,040
+فيه وهذا مستحيل لأنه إذا كانت جوا هنا بيصير البقط
+
+306
+00:20:16,040 --> 00:20:19,840
+بين عناصر الـ M إيه شمالهم اللي هو أقل من إبسلون
+
+307
+00:20:19,840 --> 00:20:22,800
+طب إبسلون هذا كل إبسلون طب أنا جدر التنين عن جدر
+
+308
+00:20:22,800 --> 00:20:26,100
+التنين و بس أقل من جدر التنين ببطلر فيه إيش إيه
+
+309
+00:20:27,060 --> 00:20:31,500
+الأن الـ
+
+310
+00:20:31,500 --> 00:20:34,200
+M ليس كمبكت
+
+311
+00:20:37,090 --> 00:20:40,350
+المثال تبعنا جيبناه على infinite dimensional space
+
+312
+00:20:40,350 --> 00:20:44,410
+زي ما وعدناكم بدنا نقول للإعلان التالي in a finite
+
+313
+00:20:44,410 --> 00:20:49,010
+dimensional normed space X any subset M of X is
+
+314
+00:20:49,010 --> 00:20:51,670
+compact if and only if M is closed and A is
+
+315
+00:20:51,670 --> 00:20:54,630
+bounded إذا في ال finite dimensional space الدنيا
+
+316
+00:20:54,630 --> 00:20:58,970
+حلوة و تمامة تمام والclosed و ال compact يكافئ
+
+317
+00:20:58,970 --> 00:21:03,920
+closed و bounded شوفوا كيفبعد مجموعة 2.5.2 مقاومة
+
+318
+00:21:03,920 --> 00:21:07,200
+تشير إلى مقاومة مقاومة ومقاومة هذا موجود في كل
+
+319
+00:21:07,200 --> 00:21:10,780
+الاسباسيات حتى في الاسباسيات التبوليجية الـ M يجب
+
+320
+00:21:10,780 --> 00:21:14,360
+أن نثبت الـ Converse مقاومة مقاومة مقاومة تشير إلى
+
+321
+00:21:14,360 --> 00:21:18,300
+مقاومة مقاومة ومقاومة يجب أن أثبتكم أن M يجب أن
+
+322
+00:21:18,300 --> 00:21:22,070
+تكون مقاومة في هذه الحالةأكيد مدام بحكي عن finite
+
+323
+00:21:22,070 --> 00:21:24,990
+dimension انا هستخدم اللي هو الـ finite dimension
+
+324
+00:21:24,990 --> 00:21:27,730
+له هو أكيد فيدي يكون صح في .. مش صح في ال infinite
+
+325
+00:21:27,730 --> 00:21:31,990
+و أنا صح أكيد هستخدم خاصية انه بما انه dimension
+
+326
+00:21:31,990 --> 00:21:35,750
+ال X finite بساوي N و ال E واحد و ال E اتنين bases
+
+327
+00:21:35,750 --> 00:21:40,530
+له أخد ايه ال bases له؟ اذا عندي consider any
+
+328
+00:21:40,530 --> 00:21:44,410
+sequence XM بده لجيلها إيش ما لها subsequence
+
+329
+00:21:44,410 --> 00:21:47,650
+converged في ال .. في ال M عاية؟ مش هي معناته
+
+330
+00:21:47,650 --> 00:21:51,890
+compactness؟الان انا اخدنا اي sequence xm في ال M
+
+331
+00:21:51,890 --> 00:21:57,250
+الان ال xm موجودة في ال M وال M جزء من ال X وال X
+
+332
+00:21:57,250 --> 00:22:00,450
+finite dimensional اذا اكيد بقدر اكتب عناصر ال XM
+
+333
+00:22:00,450 --> 00:22:03,250
+على صورة Linear Comparison من ال E1 وE2 لإدريان
+
+334
+00:22:04,770 --> 00:22:09,570
+هيكون عندي xm ممكن كتبتها على صورة scalar في E1
+
+335
+00:22:09,570 --> 00:22:15,550
+scalar في E2 لعندي scalar في مين في E1 X1 E1 XI 1
+
+336
+00:22:15,550 --> 00:22:21,090
+E1 XI 2 E1 XI N 1 in general XM بيساوي XI 1 M E1
+
+337
+00:22:21,090 --> 00:22:30,110
+XI 2 M E2 لعندي XI N M E N since M is bounded إذا
+
+338
+00:22:30,110 --> 00:22:34,950
+ال sequence اللي جوه boundedمظبوط؟ إذا since M is
+
+339
+00:22:34,950 --> 00:22:39,750
+bounded so XM is bounded إيش معناه bounded؟
+
+340
+00:22:39,750 --> 00:22:42,970
+معناتها there exists K بحيث انه norm لـ XM أصغر أو
+
+341
+00:22:42,970 --> 00:22:49,230
+شويه مين K for all مين M من لمّة اتنين اربعة واحد
+
+342
+00:22:49,230 --> 00:22:52,090
+المليح هذا اللي استخدمنا .. اللي أثبتناها في الأول
+
+343
+00:22:52,090 --> 00:22:56,010
+there exists C أكبر من صفر such that K أكبر أو
+
+344
+00:22:56,010 --> 00:23:02,790
+شويه اللي هو ال norm هذا اللي هوهيها من هنا ال K
+
+345
+00:23:02,790 --> 00:23:06,970
+أكبر سواء norm XM وال XM هيها هيها ال XM اللي هي
+
+346
+00:23:06,970 --> 00:23:10,910
+هذه أه بس كتر ده في ال summation إذا ال normal X
+
+347
+00:23:10,910 --> 00:23:16,950
+ال K أكبر سواء norm XM اللي هو هذا و هذا من اللمّة
+
+348
+00:23:16,950 --> 00:23:21,730
+اللي قبل بشوية باللاجة C بحيث أنه هي أكبر سواء C
+
+349
+00:23:21,730 --> 00:23:28,640
+في mean في ال summation طيب اللي هنطلع لفوقHence,
+
+350
+00:23:28,820 --> 00:23:35,780
+for any fixed I من 1 إلى N in the sequence Xim is
+
+351
+00:23:35,780 --> 00:23:41,440
+a bounded sequence of numbers أكيد الـ Xim bounded
+
+352
+00:23:41,440 --> 00:23:45,250
+sequence ليه؟ لأنه صار الـ summation هذاأكبر أو
+
+353
+00:23:45,250 --> 00:23:50,210
+أصغر أو ساوي هذا على C كل واحدة من اندولا Cy M
+
+354
+00:23:50,210 --> 00:23:53,670
+هتكون أصغر أو تساوي K على C يعني صارت ال sequence
+
+355
+00:23:53,670 --> 00:23:56,530
+هذي bounded sequence اذا صارت عندي bounded
+
+356
+00:23:56,530 --> 00:24:00,710
+sequence of مين؟ of numbers باشر و دوين على ال R
+
+357
+00:24:00,710 --> 00:24:05,430
+أو على ال C اللي ضامن انه انه في مدام اللي هو
+
+358
+00:24:05,430 --> 00:24:09,010
+sequence of numbers و بولزانو بتقول every sequence
+
+359
+00:24:09,010 --> 00:24:12,210
+bounded sequence هذا convergence subsequenceإذا
+
+360
+00:24:12,210 --> 00:24:17,030
+لازم it has a convergent subsequence say that it
+
+361
+00:24:17,030 --> 00:24:20,530
+converges to mean to Xi I إذا ال subsequence من
+
+362
+00:24:20,530 --> 00:24:25,770
+هذه converges to mean لXi I بالظبط بديش أقول عيد
+
+363
+00:24:25,770 --> 00:24:28,530
+اللي قلناه قبل و شوية then as in the proof of لبمة
+
+364
+00:24:28,530 --> 00:24:34,180
+2 4 5 we show that XM A شمالها hasبنركّب منهن
+
+365
+00:24:34,180 --> 00:24:36,440
+هدولة مش هدولة جيناها الـ bounded بنركّب منهن
+
+366
+00:24:36,440 --> 00:24:42,800
+subsequence ZM اللي هنا الـ scalars سبعتها من الـ
+
+367
+00:24:42,800 --> 00:24:45,940
+XM اللي قبل شوية قلتها اللي كنا بسميينها هنا YM و
+
+368
+00:24:45,940 --> 00:24:50,860
+YM1 و YM2 و الاخرى which converts to mean to اللي
+
+369
+00:24:50,860 --> 00:24:55,560
+هو الـ Z اليمين الـ Z اللي هي XI 1 في E1 اللي
+
+370
+00:24:55,560 --> 00:25:01,200
+عملتين قبل شوية لأنه صارت limit XI IM هي XI Iماشي
+
+371
+00:25:01,200 --> 00:25:07,440
+فال XM اللي قبل بشوية limit هيصير XII EI ال Z
+
+372
+00:25:07,440 --> 00:25:11,120
+بساوي اللي هو Z M converged to Z however M is
+
+373
+00:25:11,120 --> 00:25:16,980
+closed إذا هذي هتكون الموجودة في M therefore M is
+
+374
+00:25:16,980 --> 00:25:23,520
+compact وهو المطلوب نيجي الآن نظرية محترمة ومهمة
+
+375
+00:25:23,520 --> 00:25:29,290
+برضه من النظريات اللياللي .. يعني اللي هسا عملتها
+
+376
+00:25:29,290 --> 00:25:34,470
+عندنا واسعة اطلع لفوق اخليها على رأس اللي هناك
+
+377
+00:25:34,470 --> 00:25:39,650
+ريزيز لمّة اه ريزيز لمّة ايش بتقول ريزيز لمّة
+
+378
+00:25:39,650 --> 00:25:46,670
+خليني اوضحها بالرسم نيح عشان
+
+379
+00:25:46,670 --> 00:25:51,410
+نصها انا بالنسبة لي مهم برضه برهان مش صعب سهل ان
+
+380
+00:25:51,410 --> 00:25:51,670
+شاء الله
+
+381
+00:26:06,170 --> 00:26:10,270
+عندى الان let y and z be subspaces of a normed
+
+382
+00:26:10,270 --> 00:26:15,130
+space x هى فى عندى normed space مين؟ x برا هذا
+
+383
+00:26:15,130 --> 00:26:19,070
+normed space الأصلي x اللى تبعنا اللى هو اللى كلنا
+
+384
+00:26:19,070 --> 00:26:24,870
+subspaces منهو Y و Z subspaces من X و Y closed and
+
+385
+00:26:24,870 --> 00:26:30,810
+proper subset من من من Z يعني هي Y جوا Y و proper
+
+386
+00:26:30,810 --> 00:26:35,790
+subset منين من Z يعني في element هنا مش موجود وين
+
+387
+00:26:35,790 --> 00:26:41,270
+مش موجود في Y و Y و Z نفسهم subspaces من من من X
+
+388
+00:26:41,270 --> 00:26:50,380
+الآن بقولي إذا لأي θ لأي θElement in Zero و واحد
+
+389
+00:26:50,380 --> 00:26:56,220
+بقدر ألاقي Element in Min in Z there exist Z
+
+390
+00:26:56,220 --> 00:27:03,620
+Element in Z ومش هيك كمان و Normal بساوي واحد و
+
+391
+00:27:03,620 --> 00:27:10,120
+بعضه و بعض ال .. يعني بعض ال Z هذا عن ال Y بعض ال
+
+392
+00:27:10,120 --> 00:27:18,460
+Z عن ال Y أكبر أو تساوي Min فترةعنا .. تنسوش هذا
+
+393
+00:27:18,460 --> 00:27:23,780
+أن Y بروبر سبسيط .. بروبر سبسيط من مين؟ من Z مزامه
+
+394
+00:27:23,780 --> 00:27:27,100
+بروبر سبسيط يعني الكلام منطقي أنه بلاقي لكل Z في
+
+395
+00:27:27,100 --> 00:27:31,960
+ال Y في ال Z لكل .. آسف لكل θ التي تزيد واحد بقدر
+
+396
+00:27:31,960 --> 00:27:35,920
+لاقي Z في ال Y بحيث أن المسافة بين ال Z و ال Y
+
+397
+00:27:35,920 --> 00:27:41,450
+أكبر أو يساوي ال θ تبعتكلكل Y وين موجودة في الـ Y
+
+398
+00:27:41,450 --> 00:27:45,450
+Capital يعني بمعنى أخر و كإني بقول Roughly أن لكل
+
+399
+00:27:45,450 --> 00:27:49,170
+θة من Zero لواحد نص ربع طولت حتى لو زغرتها حتى لو
+
+400
+00:27:49,170 --> 00:27:54,250
+كبرتها اللي هو بيكون بقدر ألاقي Z في Z نورمها
+
+401
+00:27:54,250 --> 00:27:58,270
+بيساوي واحد بحيث أن ال norm لل Z minus Y يكون إيه
+
+402
+00:27:58,270 --> 00:28:03,450
+اشمله أكبر أو يساوي θة يعني بعضها عن ال Y أكبر أو
+
+403
+00:28:03,450 --> 00:28:09,900
+يساوي θة و الثتة نفسها أكبر من مين؟ من سفرأه يعني
+
+404
+00:28:09,900 --> 00:28:13,580
+في مسافة لإن هو بروبرت يعني لو مشوا بروبرت بيصيب
+
+405
+00:28:13,580 --> 00:28:16,600
+الموضوع لأ بختلف طيب نشوف إيش البرهان
+
+406
+00:28:21,360 --> 00:28:24,900
+let v be any element in z minus y يعني أخدت
+
+407
+00:28:24,900 --> 00:28:29,840
+element من وين من هنا بين اللي هو ال z في ال z و
+
+408
+00:28:29,840 --> 00:28:33,000
+مش من وين مش في ال y وهذا اللي بدي يوصلني للي
+
+409
+00:28:33,000 --> 00:28:37,260
+بديها الان let v be any element in z minus y and
+
+410
+00:28:37,260 --> 00:28:40,920
+let a بيساوي ال infimum للنورم لل v minus y y
+
+411
+00:28:40,920 --> 00:28:45,300
+element in y يعني بتاخد ال a أشمالها هي عبارة عن
+
+412
+00:28:45,300 --> 00:28:51,990
+المسافة مسافة بين ال v اللي أخدته من هنابين ال ..
+
+413
+00:28:51,990 --> 00:28:57,930
+و بين مين ال Y ال infimum لل norms ال V minus Y و
+
+414
+00:28:57,930 --> 00:29:02,770
+Y limit on Y هو اللي بتسميه ايش بتسميه ال A الان
+
+415
+00:29:02,770 --> 00:29:07,750
+بقوللي since Y is closed then A ايش مالها A أكبر
+
+416
+00:29:07,750 --> 00:29:09,170
+من مين من سفر
+
+417
+00:29:12,520 --> 00:29:17,360
+بما انه Y closed إذا الـ A هد إيش ما لها أكبر من
+
+418
+00:29:17,360 --> 00:29:24,440
+سفر إيش علاقتها؟ عنده ماعطيك الـ A الـ A سوى الـ
+
+419
+00:29:24,440 --> 00:29:31,180
+infimum لـ unknown V minus Y حيث Y element in Y
+
+420
+00:29:32,280 --> 00:29:37,000
+يعني باخد الأبعاد بعض ال V عن ال Y و باخد ال
+
+421
+00:29:37,000 --> 00:29:39,860
+infimum لكل ال ال white اللي في ال Y و باخد ال
+
+422
+00:29:39,860 --> 00:29:43,000
+infimum اللي هم ده سميمين ال A هذا بقول ال A
+
+423
+00:29:43,000 --> 00:29:49,960
+أشماله أكيد أشماله أكبر من سفر و جلت سبب عشان Y
+
+424
+00:29:49,960 --> 00:29:58,800
+closed Y is closed الان الان لو ال infimum هذا بده
+
+425
+00:29:58,800 --> 00:30:05,080
+يساوي سفرالانفمان بيسوي سفر معناته صار عندي من
+
+426
+00:30:05,080 --> 00:30:11,020
+تعريف الانفمان بقدر ألاقي sequence من ال Y YN اللي
+
+427
+00:30:11,020 --> 00:30:16,700
+هو بحيث ان normal V minus ال YN يقول إلى مين ال A
+
+428
+00:30:16,700 --> 00:30:22,140
+هذه اللي أصبحت إيش تسمينها سفرمعناته صار عندى ..
+
+429
+00:30:22,140 --> 00:30:25,860
+هد شو معناته؟ هد معناته انه صار الـ yn converged
+
+430
+00:30:25,860 --> 00:30:33,460
+من للـV يعني لجيت sequence yn من اللي هي الـY
+
+431
+00:30:33,460 --> 00:30:38,900
+converged من للـV طب my Y closed، إذا الـV وين
+
+432
+00:30:38,900 --> 00:30:43,400
+هتكون؟ في الـY Contradictionلأن الـ V من أين أخدها
+
+433
+00:30:43,400 --> 00:30:48,880
+أنا؟ من Z minus Y إذا أكيد ما دامت الـ Y closed و
+
+434
+00:30:48,880 --> 00:30:52,220
+الـ A هي الـ infimum هتكون الـ A أشمالها أكبر من
+
+435
+00:30:52,220 --> 00:31:00,000
+سفر و الـ Y هي اللي وضحتها اطلع لفوق now .. now ..
+
+436
+00:31:00,000 --> 00:31:03,100
+take any θ element in 0 و 1 بتحصر على اللي بديها
+
+437
+00:31:03,100 --> 00:31:07,720
+then by definition of infimum there exists y
+
+438
+00:31:07,720 --> 00:31:11,880
+naught element in Y such thatالـ V minus Y note
+
+439
+00:31:11,880 --> 00:31:14,960
+اللي هو أكبر يساوي A لإنه الـ A infimum لهم كلهم
+
+440
+00:31:14,960 --> 00:31:19,580
+اللي هو greatest lower bound lower bound في
+
+441
+00:31:19,580 --> 00:31:24,640
+النهاية إذاً الـ A أصغر يساويها دي طيب الآن ال θ
+
+442
+00:31:24,640 --> 00:31:29,160
+بين ال 0 و ال 1 مظبوط ولا لأ مزام ال θ بين ال 0 و
+
+443
+00:31:29,160 --> 00:31:33,720
+ال 1 إذاً ال A على θ أيش مالها هتصير أيش مالها
+
+444
+00:31:33,720 --> 00:31:39,240
+أصغرمن الـ A، مظبوط ولا لا؟ آسف أكبر من الـ A،
+
+445
+00:31:39,240 --> 00:31:43,080
+مظبوط؟ يعني مدان صارت أكبر من A، إذا بطلت lower
+
+446
+00:31:43,080 --> 00:31:46,860
+bound لأن الـ A إيش مالها؟ the greatest lower
+
+447
+00:31:46,860 --> 00:31:51,500
+bound أي إيش أكبر منها، ببطل lower bound مدان بطلت
+
+448
+00:31:51,500 --> 00:31:55,180
+هذه lower bound لأنها أكبر من الـ A إذا أكيد،
+
+449
+00:31:55,180 --> 00:31:59,560
+أكيد، أكيد، بلاكي عنصر في ال 6 هنا و اليكن Y note
+
+450
+00:31:59,560 --> 00:32:04,220
+بكون هذاأيه شماله؟ هو اللي أفسد عليها انها تكون
+
+451
+00:32:04,220 --> 00:32:11,940
+lower bound يعني هيكون أصغر أو يسويها واضح؟
+
+452
+00:32:11,940 --> 00:32:18,380
+انه الآن a على θأكبر من الـ A والـ A greatest
+
+453
+00:32:18,380 --> 00:32:23,420
+lower bound يعني الـ A على ثيتا بتبطل lower bound
+
+454
+00:32:23,420 --> 00:32:28,320
+مدام بطلت lower bound لهذه المجموعة إذا أكيد في
+
+455
+00:32:28,320 --> 00:32:32,700
+عنصر في المجموعة خلّها تبطل يعني بمعنى آخر تخلّها
+
+456
+00:32:32,700 --> 00:32:35,160
+تبطل lower bound تخلّها تبطل إنها أصغر من الكل
+
+457
+00:32:35,160 --> 00:32:39,400
+خلّه إن V minus Y not يكون أصغر أو يساوي من A على
+
+458
+00:32:39,400 --> 00:32:43,890
+ثيتا اللي بطل lower bound نتعرف على طولطيب خلوه
+
+459
+00:32:43,890 --> 00:32:47,830
+هادي إذا هادي اللي هي صحيحة مائة بالمائة و لجينا
+
+460
+00:32:47,830 --> 00:32:52,970
+why note بحقق هاديالان انا غلط مين؟ انا انا انا
+
+461
+00:32:52,970 --> 00:33:00,450
+انا انا انا
+
+462
+00:33:00,450 --> 00:33:01,010
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+463
+00:33:01,010 --> 00:33:01,090
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+464
+00:33:01,090 --> 00:33:01,730
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+465
+00:33:01,730 --> 00:33:02,330
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+466
+00:33:02,330 --> 00:33:02,330
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+467
+00:33:02,330 --> 00:33:02,490
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+468
+00:33:02,490 --> 00:33:03,450
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+469
+00:33:03,450 --> 00:33:03,990
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+470
+00:33:03,990 --> 00:33:15,710
+انا انا انا انا
+
+471
+00:33:15,710 --> 00:33:21,130
+انااللي هي مقلوبة دي C في V minus Y not أخدني ال V
+
+472
+00:33:21,130 --> 00:33:26,270
+minus Y not على نورمها يعني Z بتساوي V minus Y not
+
+473
+00:33:26,270 --> 00:33:31,930
+على نورمها ونورمها مش سفر أه لإن هد مش سفر و هد
+
+474
+00:33:31,930 --> 00:33:37,370
+أكبر يسوي هد ان هد اسمه مهدنا قبل إنه قلنا لإيه مش
+
+475
+00:33:37,370 --> 00:33:41,110
+سفر إذا صار هد مش سفر لإنه أكبر منها أسويها إذا
+
+476
+00:33:41,110 --> 00:33:44,750
+صار عندي الآن فيه إمكانية أقسم على نورمها خد الآن
+
+477
+00:33:44,750 --> 00:33:49,620
+Z بتساوي هذا المقدرالان ال C طبعا هي واحد على نورم
+
+478
+00:33:49,620 --> 00:33:54,500
+هذا الان انا بقولك ال Z نورم ال Z ايش هيساوي واحد
+
+479
+00:33:54,500 --> 00:33:59,500
+و هيحقق اللي بديها نورم ال Z بيساوي واحد واضح لان
+
+480
+00:33:59,500 --> 00:34:05,160
+let Y be any fixed element in Y وحسب للان نورم ال
+
+481
+00:34:05,160 --> 00:34:11,160
+Z minus Y ايش بيساوي بساوي Zطلعلي اللي هي عوضليها
+
+482
+00:34:11,160 --> 00:34:14,280
+زي ده إيش بالساوية C فيها ده اللي هو C في V minus
+
+483
+00:34:14,280 --> 00:34:20,780
+Y not ناقص من ال Y طلعلي لو سمحت C برا و بيصير هد
+
+484
+00:34:20,780 --> 00:34:25,260
+V minus Y not و هد بيصير إيش مالها Y على C اللي هو
+
+485
+00:34:25,260 --> 00:34:30,920
+C inverse في مين في Y Y ساوي C في ال norm لل V
+
+486
+00:34:30,920 --> 00:34:35,180
+minus Y واحد إيش ال Y واحد؟ Y واحد أخدت السالب برا
+
+487
+00:34:35,180 --> 00:34:40,240
+صارت هد Y not زاد C inverse في Yأه إذا ال Y واحد
+
+488
+00:34:40,240 --> 00:34:46,280
+هي هذه الآن هذه why not من ال Y و ال Y من ال Y إذا
+
+489
+00:34:46,280 --> 00:34:49,400
+المجموح من ال Y واحد هتكون برضه من وين من ال Y
+
+490
+00:34:49,400 --> 00:34:56,000
+which belongs to Y إذا ملخص الحديث إنه صار V minus
+
+491
+00:34:56,000 --> 00:35:04,060
+Y واحد عندي اللي هو في C بساوي اللي هو المقدار هذا
+
+492
+00:35:06,150 --> 00:35:13,050
+الان عندى V-Y1 هيكون اكبر او يساوي مين او يساوي
+
+493
+00:35:13,050 --> 00:35:25,810
+ايه V-Y1 V-Y1 اكبر او يساوي ايه طيب
+
+494
+00:35:25,810 --> 00:35:27,390
+حلينا عشان نوضح لكم
+
+495
+00:35:38,040 --> 00:35:41,100
+طيب يا جماعة لأ نزلي عشان نشوف ال .. ال .. ال ..
+
+496
+00:35:41,100 --> 00:35:47,120
+عندي أثبتنا أنه عند Normal Z minus Y Z minus Y
+
+497
+00:35:47,120 --> 00:35:53,260
+اللي هو بساوي C في Normal V minus Y واحدالان عندي
+
+498
+00:35:53,260 --> 00:35:56,720
+ال y واحد بيسوي نوت زي c inverse one which belongs
+
+499
+00:35:56,720 --> 00:36:01,740
+to me into y اذا صارت مدام y واحد في ال y اذا اكيد
+
+500
+00:36:01,740 --> 00:36:05,680
+اكيد اكيد ال v minus y واحد اكبر يسوى من ايه لان
+
+501
+00:36:05,680 --> 00:36:11,080
+الامين هي الامسفة من الهن كلهن واضح طيب الان بدنا
+
+502
+00:36:11,080 --> 00:36:16,060
+نستخدم one to get to get الانأنا بدي أستخدم هذه
+
+503
+00:36:16,060 --> 00:36:20,600
+احسبلي يعني حسابات بدي أحسبلك ايه يعني Z-Y بالساوي
+
+504
+00:36:20,600 --> 00:36:25,420
+هيها Z-Y بالساوي C في المقدار هذا C في المقدار هذا
+
+505
+00:36:25,420 --> 00:36:29,380
+والمقدار هذا قولنا عنه اشماله أكبر يساوي ايه اذا
+
+506
+00:36:29,380 --> 00:36:32,220
+اكبر يساوي مين C في A
+
+507
+00:36:35,900 --> 00:36:38,920
+الان عندى ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+508
+00:36:38,920 --> 00:36:39,180
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+509
+00:36:39,180 --> 00:36:39,240
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+510
+00:36:39,240 --> 00:36:39,320
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+511
+00:36:39,320 --> 00:36:40,780
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+512
+00:36:40,780 --> 00:36:41,520
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+513
+00:36:41,520 --> 00:36:43,180
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+514
+00:36:43,180 --> 00:36:43,900
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+515
+00:36:43,900 --> 00:36:49,220
+ال .. ال .. ال .. ال ..
+
+516
+00:36:49,220 --> 00:36:49,220
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+517
+00:36:49,220 --> 00:36:49,220
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+518
+00:36:49,220 --> 00:36:49,220
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+519
+00:36:49,220 --> 00:36:49,220
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+520
+00:36:49,220 --> 00:36:52,440
+ال .. ال .. ال ..
+
+521
+00:36:52,440 --> 00:36:55,700
+ال .. ال .. ال ..
+
+522
+00:36:57,590 --> 00:37:01,430
+الان هذه ليها مقلوبها C بيصير C أكبر أو ثواء ثتا
+
+523
+00:37:01,430 --> 00:37:01,770
+على A
+
+524
+00:37:06,030 --> 00:37:10,510
+أضربه في a بيصير c أكبر من θ على a في a ال a بتروح
+
+525
+00:37:10,510 --> 00:37:13,590
+مع ال a ويبقى المين يعني ال c z minus y أكبر من
+
+526
+00:37:13,590 --> 00:37:18,390
+مين θ أخدت الآن اللي هو أي θ في ال zero و ال واحد
+
+527
+00:37:18,390 --> 00:37:23,950
+أيه من هنا أخدت ال theta أي element من zero و واحد
+
+528
+00:37:23,950 --> 00:37:30,210
+لجيت ال z هيها نورمها بيساوي واحد و البعد بين z و
+
+529
+00:37:30,210 --> 00:37:34,550
+minus y أكبر و يساوي θ وهو المطلوب طيب
+
+530
+00:37:37,750 --> 00:37:47,810
+ملاحظة الان في عندي اطلع لفوق in
+
+531
+00:37:47,810 --> 00:37:53,210
+a finite dimensional space the closed unit ball is
+
+532
+00:37:53,210 --> 00:37:57,900
+compactفي الـ finite dimensional space الـ closed
+
+533
+00:37:57,900 --> 00:38:01,160
+ball is compact أكيد لأن الـ closed ball a closed
+
+534
+00:38:01,160 --> 00:38:06,040
+set abounded و finite dimensional إذا إيش مالها؟
+
+535
+00:38:06,040 --> 00:38:09,880
+compact لكن هذه الخاصية لن تتحقق في ال infinite
+
+536
+00:38:09,880 --> 00:38:13,960
+dimensional space في ال finite dimensional space
+
+537
+00:38:13,960 --> 00:38:18,730
+أي closed unit ball is compactلكن الموضوع بختلف في
+
+538
+00:38:18,730 --> 00:38:23,350
+ال infinite شوف الآن theorem if unknown space X
+
+539
+00:38:23,350 --> 00:38:27,890
+has the property that the closed unit ball M is
+
+540
+00:38:27,890 --> 00:38:32,650
+compact then X is finite dimensionalلاحظ؟ كلام
+
+541
+00:38:32,650 --> 00:38:36,370
+خطير الان إذا كان في ال norm of the space X عندك
+
+542
+00:38:36,370 --> 00:38:40,530
+بتحقق الخاصية في ال .. في ال .. جيت .. أخدتلك norm
+
+543
+00:38:40,530 --> 00:38:44,630
+of the space اسمه X لجيت فيه خاصية انه اي نوع ..
+
+544
+00:38:44,630 --> 00:38:48,010
+اي unit ball .. closed unit ball هذه لجيتها
+
+545
+00:38:48,010 --> 00:38:51,530
+compact على طول و انت مغمض قول عنه ايش هذا finite
+
+546
+00:38:51,530 --> 00:38:55,410
+dimensional space ايش معناته؟ يعني لو كان infinite
+
+547
+00:38:55,410 --> 00:38:58,290
+dimensional مش هتكون اللي هي ال closed unit ball
+
+548
+00:38:58,290 --> 00:39:06,270
+ايش مالها compact طيبSuppose that M is compact but
+
+549
+00:39:06,270 --> 00:39:11,490
+dimension X بساوة Infinity و بدنا نصل إيه؟ لـ
+
+550
+00:39:11,490 --> 00:39:15,470
+Contradiction يعني مستحيل أنه يجتمع أن M is
+
+551
+00:39:15,470 --> 00:39:18,910
+compact و dimension X ملومة لنهاية إذا كانت الـ M
+
+552
+00:39:18,910 --> 00:39:22,010
+close و M compact لازم تكون final dimensional و لو
+
+553
+00:39:22,010 --> 00:39:24,350
+كانت dimension X بساوة Infinity، الـ M مش compact
+
+554
+00:39:24,350 --> 00:39:29,480
+واضح؟ طيبتختار انا X واحد .. شوف كيف الان بده يركب
+
+555
+00:39:29,480 --> 00:39:33,280
+لك تختار انا X واحد الامن X with norm X واحد ايش
+
+556
+00:39:33,280 --> 00:39:39,080
+بساوي واحد بقدر الان هو دائما في الاختصار الانفنت
+
+557
+00:39:39,080 --> 00:39:43,900
+لان في عناصر .. عنصره اسمه Xجسمه على نرمه بطلع
+
+558
+00:39:43,900 --> 00:39:48,620
+نرمه يشماله واحد و بطلع الدوة اذا اذا اختار انا X
+
+559
+00:39:48,620 --> 00:39:52,000
+واحد انا من X with norm ال X واحد بيساوي واحد this
+
+560
+00:39:52,000 --> 00:39:55,620
+X واحد generate a one dimensional space X واحد of
+
+561
+00:39:55,620 --> 00:40:02,680
+X يعني الآن بدي اخد X بيساوي من X واحد هذا ال X
+
+562
+00:40:02,680 --> 00:40:08,600
+واحد هذا اللي هو اللي هو في طبعا الاسباني له
+
+563
+00:40:08,600 --> 00:40:13,380
+الاسباني له كل يعني ال scholars فيههذا ال .. ال ..
+
+564
+00:40:13,380 --> 00:40:16,780
+ال .. ال space اللي هو دايما مش اللي هو مش بساوي
+
+565
+00:40:16,780 --> 00:40:23,140
+بساوي واحد ب .. ب .. ب .. خليني أقول ببساطة أخدت
+
+566
+00:40:23,140 --> 00:40:26,000
+مدام دايما مش ال X بساوي infinity إذا في عناصر مش
+
+567
+00:40:26,000 --> 00:40:31,300
+سفر أخدت واحد من هنا X واحد و .. و .. و .. و من ال
+
+568
+00:40:31,300 --> 00:40:35,180
+X و Normal بساوي واحد الآن كيف Normal بساوي واحد
+
+569
+00:40:35,180 --> 00:40:38,190
+خد أي واحد و جسمه Normal و بطلع واحدوخد اللي هو
+
+570
+00:40:38,190 --> 00:40:41,390
+إيه النتج بيطلع لها x1 element in x وضمه مو بساوي
+
+571
+00:40:41,390 --> 00:40:44,830
+واحد this x1 generates a one dimensional subspace
+
+572
+00:40:44,830 --> 00:40:49,970
+سميه مين؟ x1 of x which is closed وبروبر subspace
+
+573
+00:40:49,970 --> 00:40:53,250
+من مين؟ أكيد لأنه ذاك ال dimension هو infinity
+
+574
+00:40:53,250 --> 00:40:56,790
+وهذا ال dimension له اللي ال x1 إيش ماله؟ بساوي
+
+575
+00:40:56,790 --> 00:41:01,020
+واحد since ال dimension لكسه مش بساوي infinityلأن
+
+576
+00:41:01,020 --> 00:41:04,120
+by raises لمّا .. اطلع لفوق .. by raises لمّا مدام
+
+577
+00:41:04,120 --> 00:41:07,760
+هذا proper subspace close to proper subspace إذن
+
+578
+00:41:07,760 --> 00:41:11,760
+ال raises لمّا تتحقق by raises لمّا there is x2
+
+579
+00:41:11,760 --> 00:41:15,480
+element in x و ال norm لـ x2 بيساوي 1 و المسافة
+
+580
+00:41:15,480 --> 00:41:19,760
+بين x2 نقص x1 أكبر يساوي مين أي θيتا بيداخد مين
+
+581
+00:41:19,760 --> 00:41:25,440
+أنا النص بعد .. بعد ازمكم طيبالان و ال X1 و X2
+
+582
+00:41:25,440 --> 00:41:30,260
+نفسي ايش مالهم بقدر اعمل منهم ايش ماله normed
+
+583
+00:41:30,260 --> 00:41:35,740
+space X2 اه و هيكون subspace من مين؟ من ال X و ال
+
+584
+00:41:35,740 --> 00:41:39,160
+dimension له ايش؟ بساوة 2 يعني هيصير بروبر
+
+585
+00:41:39,160 --> 00:41:44,240
+subspace من مين؟ من X يعني هيكون X2 عبارة عن لسبان
+
+586
+00:41:44,240 --> 00:41:49,400
+لل X1 و X2 ال X1 الأولى و ال X2 اللى جيتها من خلال
+
+587
+00:41:49,400 --> 00:41:55,110
+ال raises لمّا طيبالان by raises لما برضه there
+
+588
+00:41:55,110 --> 00:41:59,570
+exist x3 من x لانه proper subspace with normal x3
+
+589
+00:41:59,570 --> 00:42:05,390
+بسوء واحد and for all x element in x2اللي هو norm
+
+590
+00:42:05,390 --> 00:42:09,910
+الـ X3 عن الـ X أكبر أو ساومين برضه الـ θة اللي
+
+591
+00:42:09,910 --> 00:42:13,810
+بتاخدهاش بالساوية نص يعني طبقت ال raises لمّة كمان
+
+592
+00:42:13,810 --> 00:42:18,710
+مرة بس عالميا على الـ X2 لجيت X3 بحيث بعد الـ X3
+
+593
+00:42:18,710 --> 00:42:23,210
+عن كل عناصرها أكبر أو ساومين نص من ضمنها لإن
+
+594
+00:42:23,210 --> 00:42:29,790
+إسبانها X2 إسبان للـ X1 و X2إذا x3-x1 أكبر شوهو نص
+
+595
+00:42:29,790 --> 00:42:35,210
+و x3-x2 أكبر شوهو إياش نص إذا صار عندي x3-x1 أكبر
+
+596
+00:42:35,210 --> 00:42:39,750
+شوهو نص و x3-x2 أكبر شوهو إياش نص أنا proceeding
+
+597
+00:42:39,750 --> 00:42:43,950
+by induction we obtain a sequence xn of elements
+
+598
+00:42:43,950 --> 00:42:49,430
+xn في ال Mمن الـ M كلهم اللي هي مين الـ M هي الـ
+
+599
+00:42:49,430 --> 00:42:53,950
+span للـ X1 X2 الاخرى such that norm ال XM نقص ال
+
+600
+00:42:53,950 --> 00:42:58,110
+XN أي شماله أكبر أو يسوى نصف البعد بينهم أي شماله
+
+601
+00:42:58,110 --> 00:43:01,990
+أكبر أو يسوى نصف، إذن هذه البعد هناك for all M
+
+602
+00:43:01,990 --> 00:43:06,990
+لاتوا سوى N، hence XN يستحيل يكون لها convergence
+
+603
+00:43:06,990 --> 00:43:12,050
+subsequenceلأن الأبعاد بين كل العناصر ثابتة اللي
+
+604
+00:43:12,050 --> 00:43:16,210
+هي أكبر أو يساوي إيش نص يعني بعيدة عن بعض مستحيل
+
+605
+00:43:16,210 --> 00:43:19,870
+بعد شوية تقولولي والله أجيت العنصرين اللي المسافة
+
+606
+00:43:19,870 --> 00:43:23,550
+بينهم أصغر من نص أو أصغر من ي في الدنيا لأ لأ مدان
+
+607
+00:43:23,550 --> 00:43:27,170
+مافيش إذا X and can't have a convergence
+
+608
+00:43:27,170 --> 00:43:31,360
+subsequence this contradictsThe compactness of M
+
+609
+00:43:31,360 --> 00:43:34,560
+لإنه لجهة Sequence مافيش إلا إشمالها Convergent
+
+610
+00:43:34,560 --> 00:43:38,000
+subsequence Therefore the dimension of X لازم يكون
+
+611
+00:43:38,000 --> 00:43:47,080
+إشماله is finite اللي بعده Theorem let X and Y be
+
+612
+00:43:47,080 --> 00:43:52,000
+metric spaces and خد T من X لعند Y بيكون a
+
+613
+00:43:52,000 --> 00:43:57,550
+continuous mappingالان T T عبارة عن continuous
+
+614
+00:43:57,550 --> 00:44:02,410
+mapping من X لعين مين لعين واحد continuous mapping
+
+615
+00:44:02,410 --> 00:44:08,190
+الآن then the image of a compact subset of T of M
+
+616
+00:44:08,190 --> 00:44:13,030
+under T is compact يعني ال image للكمبكت 6 اشمالها
+
+617
+00:44:13,030 --> 00:44:21,390
+is compact اه الآن شوفعشان أثبت لك في الـ .. بحكي
+
+618
+00:44:21,390 --> 00:44:26,130
+وين أنا في .. اللي هو من metric space X to metric
+
+619
+00:44:26,130 --> 00:44:31,750
+space Y و الـ T is continuous إذا كانت الـ M
+
+620
+00:44:31,750 --> 00:44:34,730
+compact، ده تكون إيش مالها compact؟ يعني ترسل الـ
+
+621
+00:44:34,730 --> 00:44:40,930
+compact إلى compactالآن نشوف كيف let yn yn بيقن
+
+622
+00:44:40,930 --> 00:44:46,290
+الـ sequence in mean in T of M T of M صورة الآن
+
+623
+00:44:46,290 --> 00:44:50,330
+بدّي أجيلك subsequence من هذه conversion في T of M
+
+624
+00:44:50,990 --> 00:44:56,470
+بما إنه اللي هو الـ Yn sequence في الـ T of M إذن
+
+625
+00:44:56,470 --> 00:45:01,290
+هي عبارة عن صور لعناصر وين في الـ M إذا then for
+
+626
+00:45:01,290 --> 00:45:05,910
+any n there exists Xn element in N such that Yn
+
+627
+00:45:05,910 --> 00:45:11,770
+بيساوي بيين TXn الـ Y1 صورة وانصر هنا اسمه TX1 الـ
+
+628
+00:45:11,770 --> 00:45:15,390
+Y2 صورة وانصر هنا اسمه TX2 وين كدا الـ Yn بيساوي
+
+629
+00:45:15,390 --> 00:45:20,090
+TXn صارت الآن الـ Xn عبارة عن sequence وين موجودة
+
+630
+00:45:20,090 --> 00:45:26,050
+في الـ Mلكن M is compact والـ XM موجودة اللي هو في
+
+631
+00:45:26,050 --> 00:45:31,260
+الـ M إذا لازم تحتوي على subsequence منهااللي هي
+
+632
+00:45:31,260 --> 00:45:38,560
+which converges in M إذا صارت ال XNK sub sequence
+
+633
+00:45:38,560 --> 00:45:44,240
+بتروح لمين لل X في وين؟ في ال M وبما أنه T is
+
+634
+00:45:44,240 --> 00:45:49,900
+continuous إذا نقوم تقمتك TXNK اللي هو بتروح لمين؟
+
+635
+00:45:49,900 --> 00:45:55,340
+لل TX وين هتكون ال TX؟ في ال T وفي M إذا صار في
+
+636
+00:45:55,340 --> 00:46:01,340
+عندي sub sequence هذه TXNK من مين؟ من ال YNلأن الـ
+
+637
+00:46:01,340 --> 00:46:06,960
+Yn إيش هي؟ الـ Yn هي عبارة عن الـ TXN لجيت
+
+638
+00:46:06,960 --> 00:46:11,340
+subsequence من هذولة اللي هي subsequence من الـ N
+
+639
+00:46:11,340 --> 00:46:15,440
+راحت للـ TX و الموجودة في الـ T of M صار الآن any
+
+640
+00:46:15,440 --> 00:46:18,520
+sequence Yn في الـ T of M اللي هي subsequence
+
+641
+00:46:18,520 --> 00:46:21,740
+converge برضه في المين في الـ T of M إذا صارت الـ
+
+642
+00:46:21,740 --> 00:46:26,320
+T of M is compact اللي بعدها الكورولر اللي بعدها
+
+643
+00:46:26,320 --> 00:46:32,350
+اطلع لفوقمعنى continuous mapping T of a compact
+
+644
+00:46:32,350 --> 00:46:36,530
+subset M of a metric space X onto R assumes a
+
+645
+00:46:36,530 --> 00:46:40,330
+maximum and a minimum at some point of M هذا إعلان
+
+646
+00:46:40,330 --> 00:46:43,090
+كنا نعلنه للطلاب في الـ Calculus إنه إذا كانت الـ
+
+647
+00:46:43,090 --> 00:46:46,350
+function continuous على closed bounded interval
+
+648
+00:46:46,350 --> 00:46:49,070
+then it attains its maximum and its minimum
+
+649
+00:46:49,070 --> 00:46:54,450
+هلجيتها in general لو كانت T من vectors من .. من
+
+650
+00:46:54,450 --> 00:47:02,540
+.. من metric space لعند R أههترسل اللي هي أو كانت
+
+651
+00:47:02,540 --> 00:47:06,280
+اللي هي a mapping T of a compact subset M of a
+
+652
+00:47:06,280 --> 00:47:09,720
+metric space يعني ايه ده 800 من compact subset
+
+653
+00:47:09,720 --> 00:47:15,640
+يعني T is a continuous on a closed bounded اللي هي
+
+654
+00:47:15,640 --> 00:47:20,460
+6A compact set اسمها في الـ Metric Space The
+
+655
+00:47:20,460 --> 00:47:25,120
+continuous of a continuous function on a compact
+
+656
+00:47:25,120 --> 00:47:29,240
+set must attain its maximum and minimum هم يعني
+
+657
+00:47:29,240 --> 00:47:32,460
+هيكون الآن فيه maximum و فيه minimum و هي موجود في
+
+658
+00:47:32,460 --> 00:47:38,570
+الار موضوع سهل اطلع لفوق اطلعأخر إشي هدى By
+
+659
+00:47:38,570 --> 00:47:42,830
+theorem 2.56 اللي قبل شوية هتطلع الـ T M subset من
+
+660
+00:47:42,830 --> 00:47:47,230
+R و Combact ماشي مادام Combact إذا ن close و إيه
+
+661
+00:47:47,230 --> 00:47:50,550
+إيش؟ Abounded ما هو ال Combact الست إيش معناه؟
+
+662
+00:47:50,550 --> 00:47:55,810
+Closed و Abounded طيب الآن مادام Closed و Abounded
+
+663
+00:47:55,810 --> 00:48:02,190
+إذا صار عندي الـ infimum للـ T of M موجود وين؟ في
+
+664
+00:48:02,190 --> 00:48:09,940
+الـ T of M Closedbounded than الانفمام موجود و
+
+665
+00:48:09,940 --> 00:48:13,400
+closed الانفمام وين حيكون؟ في جواهات الست الماخدين
+
+666
+00:48:13,400 --> 00:48:17,500
+لها الانفمام و ال superman برضه وين حيكون؟ نفس
+
+667
+00:48:17,500 --> 00:48:20,540
+الأشياء حيكون ال superman موجود مذان bounded و هو
+
+668
+00:48:20,540 --> 00:48:25,840
+حيكون مذان closed وين موجود؟ في ال T of Mإذاً then
+
+669
+00:48:25,840 --> 00:48:29,600
+the inverse image of two points consists of points
+
+670
+00:48:29,600 --> 00:48:34,600
+of mean of M الـ infimum لهدي و المحيكون في الـ T
+
+671
+00:48:34,600 --> 00:48:37,920
+of M يعني إيش معناة الـ infimum .. خلّيني أخد
+
+672
+00:48:37,920 --> 00:48:42,340
+واحدة و تانية زيها الـ infimum للـ T of M إيش
+
+673
+00:48:42,340 --> 00:48:46,800
+معناته موجود في الـ T of M؟ يعني هذا عبارة على
+
+674
+00:48:46,800 --> 00:48:52,820
+صورة عنصر اسمه TX موجود في الـ T of M إذاً هذا الـ
+
+675
+00:48:52,820 --> 00:48:58,570
+X وين موجود؟في الـ M اللي عندي معايا؟ إذا صار عندي
+
+676
+00:48:58,570 --> 00:49:04,910
+الـ T of X هو الـ infimum يعني بمعنى آخر صار الـ T
+
+677
+00:49:04,910 --> 00:49:11,650
+of X عند النقطة هذه اللي هنا is the minimum point
+
+678
+00:49:11,650 --> 00:49:15,870
+يعني صار الآن الـ T attains its minimum عند نقطة
+
+679
+00:49:15,870 --> 00:49:21,170
+وين موجودة في الـ M Similarly اللي هو ال supremum
+
+680
+00:49:21,170 --> 00:49:27,220
+موجود للـ T of Mموجود في الـ T of M إذا صار في
+
+681
+00:49:27,220 --> 00:49:32,220
+عنده نقطة اللي هي اسمها T و T مثلا X برا X naught
+
+682
+00:49:32,220 --> 00:49:37,300
+هي اللي بتساوي ال supremum هذه الـ T هي ال maximum
+
+683
+00:49:37,300 --> 00:49:40,380
+عند ال X naught ال maximum إذا برضه ال X naught
+
+684
+00:49:40,380 --> 00:49:44,500
+موجودة في ال M و ال T maximum عندها يعني ال T
+
+685
+00:49:44,500 --> 00:49:49,060
+attains its maximum and its minimum on points in
+
+686
+00:49:49,060 --> 00:49:55,320
+meanان ام وهو المطلوب وهيك ممكن فلسنا اللي هو هذا
+
+687
+00:49:55,320 --> 00:49:58,380
+ال section وإلى لقاء آخر السلام عليكم ورحمة الله
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Iph5MyF7UCE_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Iph5MyF7UCE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c1629dc1d5b1c1f6cae7830981ff60f7e456254c
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Iph5MyF7UCE_postprocess.srt
@@ -0,0 +1,2564 @@
+1
+00:00:05,090 --> 00:00:07,870
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,870 --> 00:00:10,890
+والصلاة والسلام على سيدنا محمد وعلى أهله وصحبه
+
+3
+00:00:10,890 --> 00:00:15,730
+أجمعين هذه هي المحاضرة الرابعة مساق تحليل اقتراني
+
+4
+00:00:15,730 --> 00:00:21,930
+او تحليل دالي لطلب وطالبات الجامعة الإسلامية لطلبة
+
+5
+00:00:21,930 --> 00:00:27,220
+الماجستيران شاء الله هنكمل اللي بدناه المحاضرة
+
+6
+00:00:27,220 --> 00:00:30,940
+الرقم تلاتة المرة الماضية كنا حاكين عن ال open
+
+7
+00:00:30,940 --> 00:00:35,980
+sets وعلى اللي هو ال neighborhood وعلى اللي هو ال
+
+8
+00:00:35,980 --> 00:00:39,140
+closed sets فالان بدنا نكمل اليوم اللي حكيناه اللي
+
+9
+00:00:39,140 --> 00:00:43,420
+بدناه المرة الماضية وحكينا عن الاتصال أيضا ووصلنا
+
+10
+00:00:43,420 --> 00:00:48,720
+لعند التعريف اللي هو 113 الان بدنا نعرف حاجة اسمها
+
+11
+00:00:48,720 --> 00:00:51,840
+ال closure وقبل هنعرف حاجة اسمها ال accumulation
+
+12
+00:00:51,840 --> 00:00:56,740
+pointأو الـ Limit Points أو اللي هي الـ Cluster
+
+13
+00:00:56,740 --> 00:01:01,020
+Points كلها نفس المفهوم اللي هي نقطة الإلتصاق أو
+
+14
+00:01:01,020 --> 00:01:04,980
+نقطة التجميع A subset M of a metric space X is
+
+15
+00:01:04,980 --> 00:01:10,540
+said to be dense in X بنقول أنه اللي هو الـ M هذه
+
+16
+00:01:10,540 --> 00:01:13,500
+اللي هي subset من X إنها تتمتع بخاصية الكثافة
+
+17
+00:01:13,500 --> 00:01:17,800
+dense in X if اللي هو الـ M closure أيش بيساوي؟
+
+18
+00:01:17,800 --> 00:01:22,470
+بيساوي Xالأن X is said to be separable if it has a
+
+19
+00:01:22,470 --> 00:01:26,810
+countable subset which is dense in main M X إذا في
+
+20
+00:01:26,810 --> 00:01:32,890
+عندى مفهومين المفهوم الأول أنه بنقول M densefix
+
+21
+00:01:32,890 --> 00:01:37,990
+معناته الام مقلوجر لها بساوي مين بساوي كل x هذا ما
+
+22
+00:01:37,990 --> 00:01:42,010
+هو معناته اللي هو اللي هي dense اللي أنا بقول عن
+
+23
+00:01:42,010 --> 00:01:46,870
+ال space x نفسه انه separable إذا كدرنا نلاقي
+
+24
+00:01:46,870 --> 00:01:51,210
+subset منه countable اللي هو و تكون هذه countable
+
+25
+00:01:51,210 --> 00:01:54,130
+اللي مقلوجر لها إيش بساوي بساوي ال x فهذا الحالة
+
+26
+00:01:54,130 --> 00:01:58,250
+بنسمي اللي هو ال space هذا إيش ماله is a separable
+
+27
+00:01:58,250 --> 00:02:03,880
+إيشاللي هو is inseparable الـ space لأن شو معناه M
+
+28
+00:02:03,880 --> 00:02:07,060
+closure إيش أمعنى M closure اللي بدو يزوّبنا عليه
+
+29
+00:02:07,060 --> 00:02:11,340
+اللي هو التعريف اللي جابله اللي هو تلاتة تسعة واحد
+
+30
+00:02:11,340 --> 00:02:14,540
+تلاتة تسعة لت M لإنه ماحكينا عن الشيء برضه المرة
+
+31
+00:02:14,540 --> 00:02:19,380
+الماضية لت M بيقصب situometric space X منقول X0
+
+32
+00:02:19,380 --> 00:02:23,020
+المتين X is called an accumulation point اللي هي
+
+33
+00:02:23,020 --> 00:02:28,200
+نقطة تجميع أو cluster point أو limit pointof M إذا
+
+34
+00:02:28,200 --> 00:02:32,500
+كان every neighborhood M of X0 of X0 اللي هو لو
+
+35
+00:02:32,500 --> 00:02:36,220
+شيلته من ال X0 تقاطع ال M أيش ماله؟ اللي هو يساوي
+
+36
+00:02:36,220 --> 00:02:43,990
+Phi إذا اللي بنقوله بالظبط هنا لو أجيناأخدنا X0 في
+
+37
+00:02:43,990 --> 00:02:49,050
+الـ X بنقول عن هذه الـ X0 إنها accumulation point
+
+38
+00:02:49,050 --> 00:02:54,590
+أو نقطة تجميع للـ X وكانت هذه الـ X مثلا وهي X0
+
+39
+00:02:54,590 --> 00:02:57,790
+فيها بنقول إنها X0 is accumulation point أو limit
+
+40
+00:02:57,790 --> 00:03:01,010
+point أو cluster point إذا كان إيدينا أخدنا أي
+
+41
+00:03:01,010 --> 00:03:05,410
+جوار حواليها أو بنوب عنه بأي open ball حواليها
+
+42
+00:03:05,410 --> 00:03:10,830
+اللي هو تكون هذه ال open ball تحتوي من إيه؟ من X
+
+43
+00:03:10,830 --> 00:03:15,080
+يعني ال open ball هذهمع الـ X Note لأي نصف خطر Y
+
+44
+00:03:15,080 --> 00:03:20,980
+شيلوا منه الـ X Note تقاطع الـ M إيش ماله؟ لا
+
+45
+00:03:20,980 --> 00:03:24,420
+يساوي إيش؟ لا يساوي Phi الـ M أي إن كانت اللي هي
+
+46
+00:03:24,420 --> 00:03:29,700
+الـ M اللي هي ثابتة من Xإذا الـ X node هي عبارة عن
+
+47
+00:03:29,700 --> 00:03:35,540
+accumulation point للـ M إذا بنقدر اللي هو أي أي
+
+48
+00:03:35,540 --> 00:03:39,140
+neighborhood أو أي اللي هو open ball حوالين الـ X
+
+49
+00:03:39,140 --> 00:03:45,680
+node فقاطع الـ M على الأقل بيكون المقطة مين اللي
+
+50
+00:03:45,680 --> 00:03:48,940
+هو X node كمان مقطة يعني بمعنى أخر لو شيلت ال X
+
+51
+00:03:48,940 --> 00:03:53,180
+node تقاطع ال M أشمله لا يساوي 5 هذا معناته اللي
+
+52
+00:03:53,180 --> 00:03:58,170
+هواللي هي انه x not عبارة عن accumulation point
+
+53
+00:03:58,170 --> 00:04:05,550
+لمن لاللي هي ال set M الان ال closure لل M هو
+
+54
+00:04:05,550 --> 00:04:10,570
+عبارة عن is the set consisting of M مع مين ماهي ال
+
+55
+00:04:10,570 --> 00:04:13,990
+accumulation points إلها إذا ال M من الآن وطالع
+
+56
+00:04:13,990 --> 00:04:19,050
+بدنا نعرفها M closure بتساوي M اتحاد مجموعة ال
+
+57
+00:04:19,050 --> 00:04:22,150
+limit points او ال accumulation points اللي عادة
+
+58
+00:04:22,150 --> 00:04:28,520
+الناس برمزولها بMإبراهيم إذا الست المتكونة من M مع
+
+59
+00:04:28,520 --> 00:04:30,700
+ال limit points لها هي اللي بنسميها إيش معناه يا
+
+60
+00:04:30,700 --> 00:04:38,340
+جماعة؟ بنسميها اللي هي ال closure للـ Mملاحظة لإن
+
+61
+00:04:38,340 --> 00:04:42,040
+احنا نستخدمها P of X0 و R الـ closure هذه إلها
+
+62
+00:04:42,040 --> 00:04:46,580
+عارفينها P of X0 و R need not equal to P of X0 و
+
+63
+00:04:46,580 --> 00:04:51,460
+مين و R الآن P تلدة of X0 و R يعني اللي بيقول اللي
+
+64
+00:04:51,460 --> 00:04:57,240
+بيقوله اللي بيقوله إنه قد
+
+65
+00:04:57,240 --> 00:05:02,100
+يتمدى إلى الذهب للبعض إنه لو أجينا أخدنا ال P تلدة
+
+66
+00:05:03,480 --> 00:05:08,960
+of X0 OR الـ B تلد هي إيش هذه الـ closed ball
+
+67
+00:05:08,960 --> 00:05:14,960
+مظبوط قد يتبادل لديهم ويقول لك إن هي نفسهاالبول
+
+68
+00:05:14,960 --> 00:05:18,340
+للـ X note وR ال open ball بس ناخده ماهي إيش ال
+
+69
+00:05:18,340 --> 00:05:22,520
+closure هذا الكلام ممكن يظبط في الـR في الـR وفي
+
+70
+00:05:22,520 --> 00:05:26,080
+الـR تربيع وفي الـR كده لكن in general need not to
+
+71
+00:05:26,080 --> 00:05:29,200
+be true in general يعني هذا الكلام في صورة عامة
+
+72
+00:05:29,200 --> 00:05:34,160
+إيش ماله ليس صحيحا وماخدلك مثال ماخدلك مثال أكيد
+
+73
+00:05:34,160 --> 00:05:36,580
+اللي هو المثال المشهور اللي هو بظله حياته اللي هو
+
+74
+00:05:36,580 --> 00:05:38,840
+discrete metric SBS
+
+75
+00:05:44,530 --> 00:05:50,090
+لو انت اجيت اخدت اللي هو X عبارة عن ال discrete
+
+76
+00:05:50,090 --> 00:05:57,890
+metric space ماشي الحال لو اجيت اخدت ال ball اللي
+
+77
+00:05:57,890 --> 00:06:05,810
+ب X نوت و R ب X نوت و R هذه ال ball اللي لان هي
+
+78
+00:06:05,810 --> 00:06:11,070
+عبارة عن كل ال R ايش بتاخدها انتوا متذكرين ايش ال
+
+79
+00:06:11,070 --> 00:06:15,000
+metric اللي عليها يا واحد يا ايشبتاخد الحرفة اللي
+
+80
+00:06:15,000 --> 00:06:20,000
+هو مين بتاخد اللي هو إيش بتساوي واحد ال ball هذه
+
+81
+00:06:20,000 --> 00:06:23,300
+اللي عبارة عن فيه عارفين إيش تعرف هي عبارة عن كل
+
+82
+00:06:23,300 --> 00:06:27,920
+ال Xات اللي في ال X حيث المسافة بين X note و X
+
+83
+00:06:27,920 --> 00:06:32,280
+بتكون أصغر من مين من واحد و المصفات عارفين احنا يا
+
+84
+00:06:32,280 --> 00:06:34,900
+واحد يا سفر بدنا أصغر من واحد دلوقتي بس بيظل عندنا
+
+85
+00:06:34,900 --> 00:06:39,600
+مين السفر يعني مين بيظل هذه بس فيهاالمقطة X0 لأن
+
+86
+00:06:39,600 --> 00:06:41,900
+لا يوجد أحد يبدأ بالـ X0 نفسه لغاية السفر اللي هي
+
+87
+00:06:41,900 --> 00:06:47,420
+X0 نفسها إذاً هذا اللي هو الـ ball للـ X0 بواحد
+
+88
+00:06:47,420 --> 00:06:52,800
+إيش بساوي اللي هو المقطة Singleton X0 الآن الـ
+
+89
+00:06:52,800 --> 00:06:59,500
+closure له اللي هو عبارة عن الـ closure لهذه هيطلع
+
+90
+00:06:59,500 --> 00:07:05,730
+نفس المقطة X0 لأنه في الـ discrete metric spaceكل
+
+91
+00:07:05,730 --> 00:07:12,510
+set موجودة closed و open وبرهانها
+
+92
+00:07:12,510 --> 00:07:16,150
+سهل حتى المرة الماضية احنا حكينا على انه كيف
+
+93
+00:07:16,150 --> 00:07:21,270
+نبرهنها بتبقى معاكم هذه الهمورك مش صعبة سهل يعني
+
+94
+00:07:21,630 --> 00:07:26,530
+فبيبقى عنده الـ closure لكلوة الست إيش بيطلع الست
+
+95
+00:07:26,530 --> 00:07:30,550
+نفسها إذا اللي هو في هذه الحالة بتطلع البون اللي
+
+96
+00:07:30,550 --> 00:07:34,570
+أمامي اللي هي ال closure إليها إيش بيطلع ال
+
+97
+00:07:34,570 --> 00:07:40,610
+singleton it's notبينما .. بينما .. لو جيت أخدت
+
+98
+00:07:40,610 --> 00:07:46,390
+انت الآن الـ B تلدة الـ B تلدة لل X نقطه A واحد
+
+99
+00:07:46,390 --> 00:07:50,870
+ايش تعريف عرفناه المرة الماضية؟ هي عبارة عن كل
+
+100
+00:07:50,870 --> 00:07:58,730
+النقاط X في الـ Xحيث المسافة بين X و X not أصغر أو
+
+101
+00:07:58,730 --> 00:08:02,730
+يساوي واحد أصغر أو يساوي واحد معناته أشمالنا جدنا
+
+102
+00:08:02,730 --> 00:08:07,970
+كل الست لأن المسافة تانية ياسفر يمين يواحد فبتطلع
+
+103
+00:08:07,970 --> 00:08:12,980
+عند كل الست مين Xفلو احنا من البداية أخدنا الـ X
+
+104
+00:08:12,980 --> 00:08:17,960
+بتحتوي على أكثر من عنصر فبصير قطعاً قطعاً قطعاً
+
+105
+00:08:17,960 --> 00:08:21,140
+اللي هي الـ P X not واحد اللي هي هذه بتطلع ال
+
+106
+00:08:21,140 --> 00:08:25,720
+singleton لا تساومين ال X اللي فيها عنصرين فبتكون
+
+107
+00:08:25,720 --> 00:08:31,900
+عندي هذا مثال على اللي هو metric space بيكون عندي
+
+108
+00:08:31,900 --> 00:08:37,420
+ال closed ball need not to equal to the closure of
+
+109
+00:08:37,420 --> 00:08:46,370
+the open ball واضح؟5 then
+
+110
+00:08:47,340 --> 00:08:51,060
+إذا عرفنا إيش معنات accumulation point أو limit
+
+111
+00:08:51,060 --> 00:08:55,960
+point أو cluster point منه عرفنا ال closure منه
+
+112
+00:08:55,960 --> 00:09:01,020
+عرفنا اللي هو ال dense شو معناته dense اللي هو
+
+113
+00:09:01,020 --> 00:09:04,500
+عرفنا منه اللي هو شو معناته separable و separable
+
+114
+00:09:04,500 --> 00:09:07,940
+قولنا انه countable dense subset تكون موجودة في ال
+
+115
+00:09:07,940 --> 00:09:12,520
+space فبكون عندي ال space ال separable ناخد أمثلة
+
+116
+00:09:12,520 --> 00:09:19,330
+الآن المثال الأولبس في ملاحظة هنا عندنا قبل المثال
+
+117
+00:09:19,330 --> 00:09:24,010
+الأول بيقول لي M is dense if and only if every
+
+118
+00:09:24,010 --> 00:09:31,330
+ball in X will contains points of mean of M ده نجف
+
+119
+00:09:31,330 --> 00:09:41,090
+عند هذا الملاحظة شوية الان
+
+120
+00:09:41,090 --> 00:09:48,080
+M is dense أيش معناتها؟اللي هو معناته تكافئ أن الـ
+
+121
+00:09:48,080 --> 00:09:53,440
+M closure إيش بيساوي بيساوي X هذا بيقول لي if and
+
+122
+00:09:53,440 --> 00:09:58,640
+only if if and only if أي open ball أي open ball
+
+123
+00:09:58,640 --> 00:10:07,340
+بيكس وإبسلون اللي هي تقاطع الـ M لا يساوي إيش لا
+
+124
+00:10:07,340 --> 00:10:09,220
+يساوي Phi ماشي الحال
+
+125
+00:10:13,710 --> 00:10:20,530
+لو كانت الـ M closure بيساوي X في عندي بالنسبة
+
+126
+00:10:20,530 --> 00:10:25,570
+لهذه حالتين الحال الأولى أعطيكم وانت على الكلام مش
+
+127
+00:10:25,570 --> 00:10:32,770
+صعب الحال الأولى ان X not في الـ M و X not ايش
+
+128
+00:10:32,770 --> 00:10:35,830
+مالها برّت لها بهذه الحالتين اللي ممكن تحدث لها لل
+
+129
+00:10:35,830 --> 00:10:42,800
+X ماشي الحال الان لو X not في الـ Mقطعاً هيكون BND
+
+130
+00:10:42,800 --> 00:10:46,760
+بي X وY فقطع ال M إيه إيه إيه إيه إيه إيه إيه إيه
+
+131
+00:10:46,760 --> 00:10:48,080
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+132
+00:10:48,080 --> 00:10:48,200
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+133
+00:10:48,200 --> 00:10:55,340
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+134
+00:10:55,340 --> 00:10:55,720
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+135
+00:10:55,720 --> 00:11:08,940
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+136
+00:11:08,940 --> 00:11:13,620
+إأي neighborhood و أي ball حوالين الـ X و الـ Y و
+
+137
+00:11:13,620 --> 00:11:19,500
+الـ X note اللي أخدتها و الـ Y تقاطع الـ M برضه مش
+
+138
+00:11:19,500 --> 00:11:23,720
+هيسوي فعي لأنه من التعريف اللي قلناه قبل شوية اللي
+
+139
+00:11:23,720 --> 00:11:25,640
+هو شيلوا منه ال X note
+
+140
+00:11:29,190 --> 00:11:32,870
+وقطعوها معاها بيظل لا يساوي فيه طب هي الاصلة من
+
+141
+00:11:32,870 --> 00:11:35,370
+الـ X نوت مش بروحة الام مش في الأمن مش هي اللي في
+
+142
+00:11:35,370 --> 00:11:39,290
+الطيارات دا فبيظل أش ماله في عندي أش فقطحها لا
+
+143
+00:11:39,290 --> 00:11:43,010
+يساوي من أمنه إيش تعريفنا بيقول إيش تعريف اللي هو
+
+144
+00:11:43,010 --> 00:11:47,590
+limit point هي فوق يا جماعة مالكم فوق إن ال
+
+145
+00:11:47,590 --> 00:11:50,310
+neighbor هتشيله ال X نوت وقطعوه مع الام إيش ماله
+
+146
+00:11:50,310 --> 00:11:56,940
+يساوي فيه مدام إحنا الآنمدام اكس نوت مش في الام
+
+147
+00:11:56,940 --> 00:12:00,420
+اذا زي ما قولنا اكس نوت موجودة في الام برايل
+
+148
+00:12:00,420 --> 00:12:03,460
+المدام limit point مدام limit point اذا اي
+
+149
+00:12:03,460 --> 00:12:08,360
+neighborhood او اي وابن بول هذي شيل منها ال اكس
+
+150
+00:12:08,360 --> 00:12:12,380
+نوت وخطعها مع الام اشمالها مش هيساوي فارقة حسب
+
+151
+00:12:12,380 --> 00:12:16,660
+التعريف طب ما هي هذي مش فارقة معها لان اصلا ان
+
+152
+00:12:16,660 --> 00:12:23,160
+عندي الاملأن في نقطة في الـ M غير مين الـ X note
+
+153
+00:12:23,160 --> 00:12:27,740
+والـ M مش في الـ X note إذا أكيد تقطحين لما تشيل
+
+154
+00:12:27,740 --> 00:12:31,960
+هذه تقطحين برضه أشماله مش هيساوي Phi لأن في نقطة
+
+155
+00:12:31,960 --> 00:12:34,860
+غير مين الـ X note اللي هي في التقطع
+
+156
+00:12:37,370 --> 00:12:41,750
+إذاً الآن لو الـ M closure بساوء الـ X معناته هذا
+
+157
+00:12:41,750 --> 00:12:47,010
+إيش معنو؟ لا يساوي اللي هو فال في الجهتين لأي X في
+
+158
+00:12:47,010 --> 00:12:51,010
+الـ X non و ال conversely بنفس الأسلوب تاخد ال X
+
+159
+00:12:51,010 --> 00:12:55,620
+جوا ال M و X برا ال Mأه اللي هو بيكون عنده اللي هو
+
+160
+00:12:55,620 --> 00:12:58,480
+ال .. ال .. ال .. ال X في هذا الحالة يا في اللي بت
+
+161
+00:12:58,480 --> 00:13:02,120
+point يا في مين يا في ال M يعني في النهاية تاخدوا
+
+162
+00:13:02,120 --> 00:13:04,900
+أي X هتكون يا براها يا جوا اللي براها هتكون اللي
+
+163
+00:13:04,900 --> 00:13:08,480
+بت point و اللي .. و اللي جواها ال M هتكون اللي هي
+
+164
+00:13:08,480 --> 00:13:11,100
+في ال M إذا اللي هو ال M ال closure حسه و ال X
+
+165
+00:13:11,100 --> 00:13:18,100
+تابعوا تفاصيلة بتكتبوها انتوا طيب
+
+166
+00:13:18,100 --> 00:13:20,380
+ليه جدا اللي بعدها
+
+167
+00:13:36,540 --> 00:13:40,460
+المثال الأول هو هذا يعني باعتبار معلومة ان انت
+
+168
+00:13:40,460 --> 00:13:46,340
+بتعرفوهالأنه ذكرتها قبل ما أبدأ أسجل خلّيني أقولكم
+
+169
+00:13:46,340 --> 00:13:51,480
+إياها الآن عندي اللي هو the real line R إيش ماله
+
+170
+00:13:51,480 --> 00:13:56,400
+is اللي هو separable ليش separable لإن أنا ده عارف
+
+171
+00:13:56,400 --> 00:14:01,600
+من زمان يعني من تحليل واحد إنه ال Q count بال 6
+
+172
+00:14:01,600 --> 00:14:08,060
+وهي dense in من R الكلوجر لها إيش بساوي بساوي اللي
+
+173
+00:14:08,060 --> 00:14:13,530
+هو من Rو طبعا هذا الكلام اثبتناه يعني و مثبت في
+
+174
+00:14:13,530 --> 00:14:16,910
+تحليل واحد تبع ال bachelor's فمافيش داعي لنا نقعد
+
+175
+00:14:16,910 --> 00:14:20,330
+نحكي فيه كمان مرة اللي هذاك اللي بيضل معاكم اللي
+
+176
+00:14:20,330 --> 00:14:25,210
+هو exercise ال Q closure ايش بيساوي بيساوي R و Q
+
+177
+00:14:25,210 --> 00:14:29,310
+is countable اذا صار عند ال R عبارة عن اللي هي
+
+178
+00:14:29,310 --> 00:14:34,570
+separable space اللي زي يمينالـ C اللي هو the
+
+179
+00:14:34,570 --> 00:14:39,070
+complex plane C اللي هو برضه اسمه الـ inseparable
+
+180
+00:14:39,070 --> 00:14:43,250
+الان inseparable انتوا عارفين الـ C هي عبارة عن كل
+
+181
+00:14:43,250 --> 00:14:47,710
+الأعداد على صورة X ذات IY حيث اللي هو I انتوا
+
+182
+00:14:47,710 --> 00:14:49,910
+عارفين جدر نقص واحد والـ X وY عبارة عن real
+
+183
+00:14:49,910 --> 00:14:56,670
+numbers فالان اللي مؤهلة انها تكون اللي هي dense
+
+184
+00:14:57,530 --> 00:15:02,810
+Accountable اللي هي الست مين M اللي هناخده M اللي
+
+185
+00:15:02,810 --> 00:15:06,530
+هي مستقام المين من ال rational هي عبارة عن كل
+
+186
+00:15:06,530 --> 00:15:15,450
+الأعداد اللي هي المركبة على صورة R1 زاد IR2 حيث R1
+
+187
+00:15:15,450 --> 00:15:20,550
+وR2 element المين NQأول حاجة وهذه countable
+
+188
+00:15:20,550 --> 00:15:24,710
+countable set ليش countable؟ لأنه الأم لو جيته ك
+
+189
+00:15:24,710 --> 00:15:29,150
+set theory هتلاقوها equivalent للـ Q1 across مين
+
+190
+00:15:29,150 --> 00:15:33,070
+الـ Q2 تقدر تعملوا one to one onto function بينهم
+
+191
+00:15:33,070 --> 00:15:36,650
+اللي هو تاخدوا اللي هو أي element هنا لهنا و
+
+192
+00:15:36,650 --> 00:15:41,110
+تفهمتوا أنها إيش مالها one to one أو onto إذن هذه
+
+193
+00:15:41,110 --> 00:15:46,830
+إيش مالها is a countable setالان الـ closure لها
+
+194
+00:15:46,830 --> 00:15:53,230
+الـ closure لها انت لو جيته طبعا استخدمنا انه الـ
+
+195
+00:15:53,230 --> 00:15:58,550
+Q نفسها is dense الـ Q نفسها is dense في الـ R
+
+196
+00:15:58,550 --> 00:16:03,870
+فالان اي element في الـ R بقدر الاقي اشمله element
+
+197
+00:16:03,870 --> 00:16:08,970
+هنا اللي هو في حواليه يعني بمعنى اخر لو جيت اخدته
+
+198
+00:16:08,970 --> 00:16:15,870
+اي الآن Zفي الـ R أي Z في الـ R احنا بنعرف مسبقا
+
+199
+00:16:15,870 --> 00:16:20,230
+الـ Z إيش ماله هيكون على صورة X زائد IY بحكي بلغة
+
+200
+00:16:20,230 --> 00:16:26,970
+الـ Sequences هو نفس الاشي بقدر ألاقي Sequence RN
+
+201
+00:16:26,970 --> 00:16:32,130
+زائد R'NI
+
+202
+00:16:33,360 --> 00:16:38,520
+اللي هو converge لـ X زائد مين IY من وين تبتعد عن
+
+203
+00:16:38,520 --> 00:16:43,220
+خاصية الكثافة تبعت مين تبعت Q لإيش؟ لأن X في ال ..
+
+204
+00:16:43,220 --> 00:16:46,360
+في ال .. X ماله عبارة عن real number إذا بقدر
+
+205
+00:16:46,360 --> 00:16:49,360
+أجيله sequence من ال real number .. من ال rational
+
+206
+00:16:49,360 --> 00:16:52,640
+numbers converge ال X هذه معلومة أخدتها في ال real
+
+207
+00:16:52,640 --> 00:16:57,840
+ونفس الاشي هذا ما هو اللي هو عبارة عناللي هو real
+
+208
+00:16:57,840 --> 00:17:02,420
+number إذا بقدر ألاقي برضه R prime I أو N زي ما
+
+209
+00:17:02,420 --> 00:17:07,220
+نسميها بتروح من مين للأن لأن متنتقل مع بعض
+
+210
+00:17:07,220 --> 00:17:12,900
+باستخدام ال continuity تبعت الجامعة و بيصير عندي R
+
+211
+00:17:12,900 --> 00:17:19,760
+N زاد R N prime converge في I converge ده ال X زاد
+
+212
+00:17:19,760 --> 00:17:25,460
+I Y اللي هو مين اللي هي Zإذا صار عندي لكل element
+
+213
+00:17:25,460 --> 00:17:30,340
+في الـ C بقدر ألاقي sequence converge لهذا وهذا
+
+214
+00:17:30,340 --> 00:17:35,180
+يعني إنه صارت إيش مالها dense في مين في الـ C
+
+215
+00:17:35,180 --> 00:17:39,260
+طبعاً هذا الكلام الفدوى اللي .. اللي .. اللي احنا
+
+216
+00:17:39,260 --> 00:17:44,100
+.. احنا طبعاً عرفنا الـ Depth على أساس اللي هو الـ
+
+217
+00:17:44,100 --> 00:17:46,660
+Neighborhoods ما هو الـ Neighborhoods ما هو أصلا
+
+218
+00:17:46,660 --> 00:17:51,040
+لما نقول هذه converge لهذهبصير limit لها موجودة،
+
+219
+00:17:51,040 --> 00:17:55,300
+يعني هلاقي حوالين أي نقطة .. حوالين النقطة هذه بأي
+
+220
+00:17:55,300 --> 00:18:01,060
+نفس الخطور لازم ألاقي نقاط موجودة منها دي لإنه عند
+
+221
+00:18:01,060 --> 00:18:05,960
+ال limit .. لإن مش واضح حالي، ال limit للـ Rn زائد
+
+222
+00:18:05,960 --> 00:18:13,760
+I Rn برايم بتسوء X زائد I Y إذا لكل يبسلون أكبر من
+
+223
+00:18:13,760 --> 00:18:15,560
+سفر there exist
+
+224
+00:18:20,270 --> 00:18:26,110
+There exists a element in N such that اللي هو
+
+225
+00:18:26,110 --> 00:18:36,150
+البسافة بين RN زيدي RN' ناقص X زيدي IYأصغر من مين
+
+226
+00:18:36,150 --> 00:18:40,570
+من إبسلون وهذه أصلا ترجنها لمين لـ neighborhood
+
+227
+00:18:40,570 --> 00:18:48,590
+بيكس وزاد اي وإبسلون ان هذه في عندك لكل أكبر شومين
+
+228
+00:18:48,590 --> 00:18:54,010
+K يعني من عند K وK زاد واحد وK زاد اتنين كلهم
+
+229
+00:18:54,010 --> 00:18:57,250
+المسافة بينهم أصغر من إبسلون يعني كلهم موجود وينه
+
+230
+00:18:57,250 --> 00:19:01,390
+في هذا ال neighborhood يعني شيلوا منه X زاد IY
+
+231
+00:19:02,130 --> 00:19:05,590
+بيظلوا تقاطعوا مع ال .. مع اللي أخدناها مين هي ال
+
+232
+00:19:05,590 --> 00:19:09,510
+set M هذه اللي هي ال sequence منها لا يساوي إياش
+
+233
+00:19:09,510 --> 00:19:14,650
+فإذا أكيد أكيد أكيد اللي هي هتكون و موجودة اللي هو
+
+234
+00:19:14,650 --> 00:19:20,090
+كل ال X هذا أخدنا Z arbitrarily ملخص الحديث أخدنا
+
+235
+00:19:20,090 --> 00:19:26,810
+Z arbitrarily و موجودة في ال Cلجينا انه اي open
+
+236
+00:19:26,810 --> 00:19:34,670
+ball اللي هو حوالين ال X Z I Y هنلاقي فيها
+
+237
+00:19:34,670 --> 00:19:39,190
+elements من ال .. بالظبط من هم ال elements اللي هو
+
+238
+00:19:39,190 --> 00:19:44,350
+ال elements اللي .. اللي .. اللي .. اللي هي هذاK
+
+239
+00:19:44,350 --> 00:19:48,270
+وK زائد واحد وK زائد اتنين كل ال sequence هذه كلها
+
+240
+00:19:48,270 --> 00:19:52,010
+اللي دي في وين في هذه المنطقة فاهمين ايش بحكيه
+
+241
+00:19:52,010 --> 00:19:55,690
+فبصير عندي هذا نقص هذا لا يساوي في معناته رجعنا
+
+242
+00:19:55,690 --> 00:20:00,090
+للملاحظة اللي قبل بشوية اللي حكيتها ان M is dense
+
+243
+00:20:00,090 --> 00:20:11,570
+in X if and only if اللي هو every ball تحتوي نقاط
+
+244
+00:20:11,570 --> 00:20:15,900
+من Mأو تقطحها مع ام يشماله لا يساوي فاي وهذا فعلا
+
+245
+00:20:15,900 --> 00:20:22,700
+أثبتته اخدت اي Z limited in C لجأت انه اي open
+
+246
+00:20:22,700 --> 00:20:27,300
+ball حوالين الـ Z هذه هي X Z I Y شيل منها النقطة
+
+247
+00:20:27,300 --> 00:20:31,180
+هيكون تقطحها مع ام لا يساوي فاي وطبيعي زي ما قلنا
+
+248
+00:20:31,180 --> 00:20:34,940
+قبل في حالتين ام هذه جوا ام او برا ام بيطلع اللي
+
+249
+00:20:34,940 --> 00:20:39,580
+هو تقطع اللي هو لا يساوي فاي دائما وبيكون هيك احنا
+
+250
+00:20:39,580 --> 00:20:45,620
+أثبتنا ان ال closureللأمبساوسية هذا exercise معاكم
+
+251
+00:20:45,620 --> 00:20:49,000
+اديروا بالكم هذا exercise عشان هيك انا ماكتبتوش
+
+252
+00:20:49,000 --> 00:20:51,960
+الكلام بترتبوه و بتكتبوه قبرهان
+
+253
+00:20:56,240 --> 00:21:00,120
+هذا المفروض كلها معلومات سابقة لكن خلّينا نيجي
+
+254
+00:21:00,120 --> 00:21:04,000
+الآن للإشي الجديد اللي هو كيف نرتبه و نحكي فيه
+
+255
+00:21:04,000 --> 00:21:10,220
+بالتفصيل نبدأ في ال metric space الان a discrete
+
+256
+00:21:10,220 --> 00:21:14,620
+metric space is
+
+257
+00:21:14,620 --> 00:21:20,920
+separable if and only if x أشمالها is countable
+
+258
+00:21:22,920 --> 00:21:26,900
+عندى الان هو مبرهن برهانه اللى .. البرهان اللى
+
+259
+00:21:26,900 --> 00:21:33,100
+موجود هنا فيه انه .. خلّيني أقول برهانين البرهان
+
+260
+00:21:33,100 --> 00:21:41,340
+هذا اعتمد على انه ال M is closed if and only if ال
+
+261
+00:21:41,340 --> 00:21:46,380
+M closure بتسوى ال X او
+
+262
+00:21:46,380 --> 00:21:49,520
+في حالة ال M is closed بتكون ال M closure بتسوى X
+
+263
+00:21:50,710 --> 00:21:56,090
+أنا الي خاطر أبرهن من نقطة السفر خليني أشوف كيف
+
+264
+00:21:56,090 --> 00:22:00,390
+ايش اللي بقوله a discrete metric space X is
+
+265
+00:22:00,390 --> 00:22:05,150
+separable if and only if X أشمالها is countable
+
+266
+00:22:05,150 --> 00:22:09,330
+يعني و كأنه بيقوللي انه discrete metric space
+
+267
+00:22:10,690 --> 00:22:13,970
+Superable if and only if لما الـ X نفسها شمالها
+
+268
+00:22:13,970 --> 00:22:17,330
+تكون countable لسبب بسيط كل هذا لأنه بس خلّيني على
+
+269
+00:22:17,330 --> 00:22:20,090
+جهة هذا الكلام لأنه هذا بده تفصيل احنا أصلا في الـ
+
+270
+00:22:20,090 --> 00:22:22,730
+Discrete Metric Space اللي .. اللي عندنا اللي
+
+271
+00:22:22,730 --> 00:22:25,770
+عندنا اللي هو ال .. ال sets اللي موجودة كلها
+
+272
+00:22:25,770 --> 00:22:29,560
+closed و كلها openيعني لأن هو عبارة عن ال .. ال ..
+
+273
+00:22:29,560 --> 00:22:31,300
+ال .. ال .. بيعمل discrete topology و discrete
+
+274
+00:22:31,300 --> 00:22:33,100
+topology هذا اللي بيعرف topology و discrete
+
+275
+00:22:33,100 --> 00:22:37,940
+topology كل ال sets اللي موجودة فيها closed و open
+
+276
+00:22:37,940 --> 00:22:43,440
+لأنه كلشي بيحتوي ماشي الحال طيب الآن بناء عليه
+
+277
+00:22:43,440 --> 00:22:47,660
+فبكون عندي لو بدها considerable معناته في
+
+278
+00:22:47,660 --> 00:22:52,050
+countable setالـ Closure لها إيش بيساوي؟ بيساوي
+
+279
+00:22:52,050 --> 00:22:55,230
+الـ X طيب هنا كلهم Closed يعني أي واحدة proper
+
+280
+00:22:55,230 --> 00:22:58,850
+subset الـ Closure لها نفسها يعني مش هتصل لمين لـ
+
+281
+00:22:58,850 --> 00:23:03,490
+X مافيش حد هيصل لـ X إلى مين الـ X نفسها ماشي
+
+282
+00:23:03,490 --> 00:23:06,290
+الحال خلّيني أقول هذا الكلام على جهة خلّيني أجيل
+
+283
+00:23:06,290 --> 00:23:09,250
+البرهان اللي عند هذا و برجعلكم كمان البرهان تاني
+
+284
+00:23:10,430 --> 00:23:13,730
+Suppose that X is separable ما زم X is separable
+
+285
+00:23:13,730 --> 00:23:18,590
+إذا أكيد في countable subset M of X بحيث أن ال M
+
+286
+00:23:18,590 --> 00:23:23,190
+closure إيش بتساوي؟ بتساوي X ماشي الحال لكن
+
+287
+00:23:23,190 --> 00:23:26,530
+however any subset of a discrete metric space is
+
+288
+00:23:26,530 --> 00:23:33,870
+closedمعنى T-Close؟ معناته أن الـ M موجهة لها
+
+289
+00:23:33,870 --> 00:23:36,430
+بساوي نفسها
+
+290
+00:23:40,350 --> 00:23:44,890
+إذا صارت عندي ال X نفسها is countable هيا مش هيك
+
+291
+00:23:44,890 --> 00:23:48,150
+بنقول مش احنا فرضنا separable إذا there is M
+
+292
+00:23:48,150 --> 00:23:51,670
+countable إذا في النهاية وصلنا ل M بساوة X معناته
+
+293
+00:23:51,670 --> 00:23:54,490
+صارت ال X نفسها إشمالها countable conversely
+
+294
+00:23:54,490 --> 00:24:00,210
+suppose that X إشمالها is countable then أكيد ال X
+
+295
+00:24:00,210 --> 00:24:03,310
+كلوجيا اللي هي إيش بيساوي إذا X إشمالها is
+
+296
+00:24:03,310 --> 00:24:08,710
+countable التجارة التانية سهلةطيب خلّينا في .. في
+
+297
+00:24:08,710 --> 00:24:13,710
+شغل انا حابب ا .. افصلها لأنه مش اتفصلتش هنا انه
+
+298
+00:24:13,710 --> 00:24:19,830
+يعني ان انا لو قولنا بدنا نعمل remark هنا ونقول
+
+299
+00:24:19,830 --> 00:24:32,410
+the only .. the only .. the onlyاللي هي dense
+
+300
+00:24:32,410 --> 00:24:40,950
+subset of X is X itself وهذا اللي اعتمدنا عليها
+
+301
+00:24:40,950 --> 00:24:44,830
+اصلا هنا the only dense subset of X أشمالها is X
+
+302
+00:24:44,830 --> 00:24:49,170
+itself يعني الآن أي proper subset منها مستحيل تكون
+
+303
+00:24:49,170 --> 00:24:50,650
+dense approved
+
+304
+00:24:52,690 --> 00:24:56,550
+منقول هدف وين في الـ discrete metric space بدي
+
+305
+00:24:56,550 --> 00:25:00,590
+أقول suppose that
+
+306
+00:25:00,590 --> 00:25:12,850
+M is a proper subset of X and M closure بساوة إيه
+
+307
+00:25:12,850 --> 00:25:17,450
+إيش؟ بساوة X مش الحالة دي نسي انا بدي أسألك
+
+308
+00:25:17,450 --> 00:25:17,970
+contradiction
+
+309
+00:25:20,810 --> 00:25:25,050
+الان مدام أن مقروبر subset من X اذا اكيد اكيد اكيد
+
+310
+00:25:25,050 --> 00:25:32,470
+في X element او X note element in X but X note is
+
+311
+00:25:32,470 --> 00:25:38,970
+not element المين in M ماشي مش في ال M بتثبتلك ان
+
+312
+00:25:38,970 --> 00:25:42,550
+ال X note هدو مش هتكون في ال limit point ا افامش
+
+313
+00:25:42,550 --> 00:25:45,350
+في ال limit point، معناته إيش ماله؟ مستحيل ال M
+
+314
+00:25:45,350 --> 00:25:48,450
+closure إيش مالها؟ تساول X، اللي هو ال M Closure،
+
+315
+00:25:48,450 --> 00:25:51,170
+هي عبارة عن M إتحاد M إبراهيم، مدام M مش في ال ..
+
+316
+00:25:51,170 --> 00:25:53,290
+X not مش في ال M موجودة، أثبت لك إن M مش في ال M
+
+317
+00:25:53,290 --> 00:25:55,970
+إبراهيم، بدون خلاص، في Contradiction ده مافيش ..
+
+318
+00:25:55,970 --> 00:26:00,250
+اللي ممكن يكون بس dense subset of X في إن هو X
+
+319
+00:26:00,250 --> 00:26:07,130
+itself، طيبالان عندى x not limit in x but x not is
+
+320
+00:26:07,130 --> 00:26:12,250
+not a limit in x نعم خدوا ال distance بين x not او
+
+321
+00:26:12,250 --> 00:26:15,730
+x أو خلّيني ناخد ال ball ليش ال distance ناخد ال
+
+322
+00:26:15,730 --> 00:26:19,550
+ball خدوا ال ball ال ball أكيد عرفته إيش بده أعمل
+
+323
+00:26:19,550 --> 00:26:23,700
+ال ball x notمش أحنا بنقول عشان تكون في ال M prime
+
+324
+00:26:23,700 --> 00:26:29,260
+لازم يكون أي ball حواليها بأي نصف خطر لازم يقاطع
+
+325
+00:26:29,260 --> 00:26:32,280
+ال M في نقطة غير ال X0؟ هيك معناه ال limit points
+
+326
+00:26:32,280 --> 00:26:36,820
+أنا بدي أعطيك اللي هو P of X0 و نص مثلا أو طول أو
+
+327
+00:26:36,820 --> 00:26:44,100
+ربع شيلوا منه ال X0 تقاطع ال M إيش حالة جيه بساوي؟
+
+328
+00:26:44,590 --> 00:26:48,630
+فاي لإيش لإن المقاطع اللي بتبعد عن اكس نوت اصغر
+
+329
+00:26:48,630 --> 00:26:53,170
+منه اللي هو أدل من مُص بس الـ X note لإن المسافتين
+
+330
+00:26:53,170 --> 00:26:58,270
+عندنا يا سفر يا واحد إذا كانت المسافة أصغر من واحد
+
+331
+00:26:58,270 --> 00:27:01,770
+معناته سفر إذا صارت اليادي بس بتحتوي على من ال
+
+332
+00:27:01,770 --> 00:27:04,770
+single to ال X note لما تشيلوا X note منه تقعطوا
+
+333
+00:27:04,770 --> 00:27:08,970
+اللي هم إيش حيساويفهي اذا اكيد اكيد ال X نوت اللي
+
+334
+00:27:08,970 --> 00:27:13,750
+مش في ال M مش limit point كمان ماشي والسبب اللي
+
+335
+00:27:13,750 --> 00:27:17,350
+قلناه قبل شهر ان M في الواقع هي closed ما زم M
+
+336
+00:27:17,350 --> 00:27:21,450
+closed اذا ال M prime ال M closure اللي هي نفسها M
+
+337
+00:27:21,450 --> 00:27:27,350
+طيب الان اثبتنا ان the only thing subset of X mean
+
+338
+00:27:27,350 --> 00:27:31,530
+is X itself خليني اعتبد على هدف البرهان طبعا هو
+
+339
+00:27:31,530 --> 00:27:36,910
+البرهان اللي هنا بشكل اوضح الان بدأ اقولطبعا من
+
+340
+00:27:36,910 --> 00:27:40,450
+اتجاه ال time لو كانت x countable اللي هو
+
+341
+00:27:40,450 --> 00:27:44,130
+separable سهلة لان نفترض انها separable نقول
+
+342
+00:27:44,130 --> 00:27:52,150
+suppose suppose that x is separable مادام
+
+343
+00:27:52,150 --> 00:27:56,050
+separable then there exist M such that M closure
+
+344
+00:27:56,050 --> 00:28:02,970
+ايش بيساوي بيساوي xلما الملاحظة اللي فوق XM must
+
+345
+00:28:02,970 --> 00:28:08,930
+be X ليه؟ because the only subset .. دي ال subset
+
+346
+00:28:08,930 --> 00:28:12,750
+of Xاشم هتكون اللي هي ال X نفسها إذا صارت ال M
+
+347
+00:28:12,750 --> 00:28:16,930
+بساوي ال X و ال M is countable إذا ال X is
+
+348
+00:28:16,930 --> 00:28:20,890
+countable بس اللي هي توضيح ل .. اللي هي الثغرة
+
+349
+00:28:20,890 --> 00:28:23,990
+اللي هي .. أو اللي مش موجودة هناطيب اللي بعدها
+
+350
+00:28:23,990 --> 00:28:29,290
+نيجي لان اثبتنا انه discrete metric space بكون
+
+351
+00:28:29,290 --> 00:28:33,970
+separable if and only if X is countable نيجي لان
+
+352
+00:28:33,970 --> 00:28:39,030
+لحاجة اسمها ال LB spaces ركزوا ال LB spaces احنا
+
+353
+00:28:39,030 --> 00:28:44,690
+حكيناها حكيناها دبل هيكبدنا نثبت لكم ان الـ LB
+
+354
+00:28:44,690 --> 00:28:49,650
+spaces الـ B بين الواحد وبين ال infinity is
+
+355
+00:28:49,650 --> 00:28:54,750
+separable تقريبا اللي هو مستقى من اللي قبل بشوية
+
+356
+00:28:54,750 --> 00:29:01,070
+حكينا عنه في الحالة ال complex الآن بدي أجيب 6Mو
+
+357
+00:29:01,070 --> 00:29:03,390
+تكون condensed في مين؟ في الـ LB، انت عارفين ايش
+
+358
+00:29:03,390 --> 00:29:07,590
+الـ LB؟ هي عبارة عن Space of Sequences الصممش لـ
+
+359
+00:29:07,590 --> 00:29:12,090
+Sequence Xi I أُس B أُس 1 على B is finite، ماشي
+
+360
+00:29:12,090 --> 00:29:17,960
+الحال، طيب، صلوا عنا بقالهخدوا الان ال 6M اللي هي
+
+361
+00:29:17,960 --> 00:29:22,420
+عبارة عن عنصرها R1,R2,R3 اللي عند RN والباقي إيش
+
+362
+00:29:22,420 --> 00:29:28,360
+ماله؟ أسفر هذا أكيد وين ما نوجودة في القلبي والـRI
+
+363
+00:29:28,360 --> 00:29:31,380
+كله إيه شماله؟ الـRational Numbers والـN إيه
+
+364
+00:29:31,380 --> 00:29:36,040
+شماله؟ Element N يعني بمعنى أخر هذه ال6 فيها اللي
+
+365
+00:29:36,040 --> 00:29:41,750
+هي كل الـR1والباقي أسفار كل ال R واحد والR اتنين
+
+366
+00:29:41,750 --> 00:29:44,850
+والباقي أسفار كل ال R واحد والR اتنين والR تلاتة
+
+367
+00:29:44,850 --> 00:29:48,330
+والباقي أسفار كل ال finite number of elements
+
+368
+00:29:48,330 --> 00:29:54,970
+والباقي أسفار لأي N كانت فواضح أن هذه اللي هي ال 6
+
+369
+00:29:54,970 --> 00:29:57,850
+بالشكل هذا is equipotent
+
+370
+00:30:01,460 --> 00:30:09,260
+Countable number of كروس كروس كروس
+
+371
+00:30:14,800 --> 00:30:18,200
+اللي هى لو كل واحدة countable اذا اكيد هيكون ان اي
+
+372
+00:30:18,200 --> 00:30:22,900
+شمالها is equipotent للكيو معناته اخر اي شمالهن is
+
+373
+00:30:22,900 --> 00:30:27,120
+countable اذا ال set M عبارة عن countable set
+
+374
+00:30:27,120 --> 00:30:30,660
+الدور الآن بدنا نثبت ان الكيو والنكولوجر ايش
+
+375
+00:30:30,660 --> 00:30:34,420
+بتساوي .. آسف ال M نكولوجر بتساوي اللى هى ال LB
+
+376
+00:30:34,420 --> 00:30:40,300
+بتثبتلكم
+
+377
+00:30:40,300 --> 00:30:47,710
+الآنالأم اللي عندي هذه أم closure لها بساوي القلبي
+
+378
+00:30:47,710 --> 00:30:54,370
+نشوف
+
+379
+00:30:54,370 --> 00:31:00,630
+طبعا هذه subset من هذه طبيعي لأنه من أين بدي أجيب
+
+380
+00:31:00,630 --> 00:31:03,650
+ال limits الآن بدي أخد أي element هنا و بدي أثبت
+
+381
+00:31:03,650 --> 00:31:06,250
+لكم يا ال element هذا يا حكومي limit point يا
+
+382
+00:31:06,250 --> 00:31:12,010
+حكومي فلان مظبوط ولا لا طب خليني نشوفيعني بمعنى
+
+383
+00:31:12,010 --> 00:31:16,750
+اخر اللي قولنا قبل شوية انه ممكن نروح باتجاه انه
+
+384
+00:31:16,750 --> 00:31:19,830
+اي element في القلبي اللي لاجي اللي هو ball حواليه
+
+385
+00:31:19,830 --> 00:31:22,270
+اللي لاجي اي ball حواليه .. اي ball حواليه اسف ..
+
+386
+00:31:22,270 --> 00:31:25,190
+اي ball حواليه تقاطع ال .. ال .. ال .. ال .. ال ..
+
+387
+00:31:25,190 --> 00:31:25,350
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+388
+00:31:25,350 --> 00:31:25,410
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+389
+00:31:25,410 --> 00:31:25,730
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+390
+00:31:25,730 --> 00:31:25,770
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+391
+00:31:25,770 --> 00:31:26,350
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+392
+00:31:26,350 --> 00:31:27,050
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+393
+00:31:27,050 --> 00:31:27,190
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+394
+00:31:27,190 --> 00:31:36,030
+..
+
+395
+00:31:36,030 --> 00:31:40,270
+ال .. ال ..الأن we show that any closure element
+
+396
+00:31:40,270 --> 00:31:44,670
+بتساوي مين؟ قلبي عشان نثبت هيك قولنا ناخد أي X وين
+
+397
+00:31:44,670 --> 00:31:48,430
+موجودة في القلبي ال X كيف شكلها عبارة عن sequence
+
+398
+00:31:48,430 --> 00:31:51,730
+ماحنا عارفين اللي هو شكل العناصر اللي موجودة في
+
+399
+00:31:51,730 --> 00:31:55,750
+القلبي عبارة عن sequences يعني بمعنى آخر عند ال X
+
+400
+00:31:55,750 --> 00:32:02,750
+ال X اللي في القلبياللي هي عبارة عن sequence xi I
+
+401
+00:32:02,750 --> 00:32:05,570
+I من واحد إلى ما لا نهاية وبكون عشان تكون في
+
+402
+00:32:05,570 --> 00:32:09,590
+القلبي summation xi I أس بي I من واحد إلى ما لا
+
+403
+00:32:09,590 --> 00:32:14,210
+نهاية is finite أو converge متفقين عليها هذا من
+
+404
+00:32:14,210 --> 00:32:21,230
+قبل احنا نيجي الآن يا جماعة خدولي أي ي أكبر من مين
+
+405
+00:32:21,230 --> 00:32:26,770
+من سفراللي أنا بقوللي then there is n بسواة n
+
+406
+00:32:26,770 --> 00:32:31,830
+وإبسالون n element in n such that الصماشن x j of b
+
+407
+00:32:31,830 --> 00:32:35,110
+j من عند n زاد واحد إلى infinity أصغر من مين من
+
+408
+00:32:35,110 --> 00:32:38,890
+إبسالون بي على اتنين هذا يسي معناته هيها من هان
+
+409
+00:32:38,890 --> 00:32:44,650
+هدي هدي هدي من هان لعنزل هان إيش معناته أنا مش
+
+410
+00:32:44,650 --> 00:32:53,540
+عمال بقول إنه الصماشن هذا is finiteبالظبط لا يعني
+
+411
+00:32:53,540 --> 00:33:00,500
+بمعنى اخر ان ال limit للصممش XI I قص بي I من واحد
+
+412
+00:33:00,500 --> 00:33:05,360
+لعند K مثلا او لعند M زي ما بدناه as M goes to
+
+413
+00:33:05,360 --> 00:33:11,350
+infinity بساوي ايشعدد اللي هو بيساوي هذا اللي
+
+414
+00:33:11,350 --> 00:33:16,090
+نسميها ده مثلا عدد اسمه مين اسمه العدد ماشي بيساوي
+
+415
+00:33:16,090 --> 00:33:20,530
+L أو بيساوي summation Xi I أس بي I من عند واحد إلى
+
+416
+00:33:20,530 --> 00:33:24,430
+ملارها تعرف اللي متشهو معناته وصيرنا نحكي عن أرقام
+
+417
+00:33:24,430 --> 00:33:27,610
+لأن هذا رقم وهذا رقم ماشي الحال اللي بنحكي في R
+
+418
+00:33:27,610 --> 00:33:32,310
+ثانوية أو في Z أو في C لأن for every أكبر أكبر من
+
+419
+00:33:32,310 --> 00:33:38,670
+0There exist N أو K element in N such that for
+
+420
+00:33:38,670 --> 00:33:44,640
+every N أكبر شو Kهذا اللي هو ال term اللي هو مثلا
+
+421
+00:33:44,640 --> 00:33:48,360
+نسميه SM أو اللي بدنا ياه و SM اللي بدنا ياه اللي
+
+422
+00:33:48,360 --> 00:33:53,320
+هو هذا ال term هذا ال term اللي هو ال summation xi
+
+423
+00:33:53,320 --> 00:33:59,780
+I أس بي I من عند واحد لعند اللي هو أخدتها أنا اللي
+
+424
+00:33:59,780 --> 00:34:06,100
+هي N ناقص ال summation xi I أس بي I من واحد إلى
+
+425
+00:34:06,100 --> 00:34:10,840
+مانا نهاية أصغر من أي أبسلون في الدنياأنا بتاخد
+
+426
+00:34:10,840 --> 00:34:14,740
+الـY أنا حر اسمها Y-B على 2 على 2 عشان الحسابات
+
+427
+00:34:14,740 --> 00:34:20,420
+عندى أصغر من Y-B على 2 هذا من اللي هو أصلا هذا
+
+428
+00:34:20,420 --> 00:34:23,520
+عبارة هذا الكلام صحيح لكل N أكبر شوكة وهي اللي
+
+429
+00:34:23,520 --> 00:34:30,090
+أخدتها وخلصتها أخدت 4N واحدةfor every n بخلّيني
+
+430
+00:34:30,090 --> 00:34:35,310
+أسميها أكبر سوء n عشان أبدأ في اللي بديها بيصير
+
+431
+00:34:35,310 --> 00:34:38,910
+عند ال n هذا ناقص هذا ايش بيكون عبارة عن ال
+
+432
+00:34:38,910 --> 00:34:43,530
+summation اللي هو xi من عند n خلصنا ال n هذولا
+
+433
+00:34:43,530 --> 00:34:47,630
+شيلناهم ضال عند من مين n زائد واحد إلى ما لنهاية
+
+434
+00:34:47,630 --> 00:34:53,050
+xi I أس بي أصغر من و أس بي على مينعلى اتنين واضحت
+
+435
+00:34:53,050 --> 00:34:57,230
+هذه اذا صار عند الان for every y أكبر من 0 there
+
+436
+00:34:57,230 --> 00:35:01,230
+exists an unlimited n such that اللي هو xij أسبي j
+
+437
+00:35:01,230 --> 00:35:07,300
+من n زي 1 من نهاية أصغر من y بي على اتنينأي سؤال
+
+438
+00:35:07,300 --> 00:35:11,800
+من جهة أخرى من جهة أخرى أنا بعرف أنه ال rational
+
+439
+00:35:11,800 --> 00:35:16,980
+numbers اللي أنا أصلا باني قصد عليها اللي هي لأن
+
+440
+00:35:16,980 --> 00:35:20,660
+since the rational numbers are dense in R بدلاً من
+
+441
+00:35:20,660 --> 00:35:26,040
+أنها دنسة في R إذا أقنع بقدر أزغر المسافةاللي هو
+
+442
+00:35:26,040 --> 00:35:31,020
+بين اللي هو الـ XII و أي rational number بقى او او
+
+443
+00:35:31,020 --> 00:35:32,940
+او او او او او او او او او او او او او او او او او
+
+444
+00:35:32,940 --> 00:35:33,020
+او او او او او او او او او او او او او او او او او
+
+445
+00:35:33,020 --> 00:35:33,640
+او او او او او او او او او او او او او او او او او
+
+446
+00:35:33,640 --> 00:35:33,680
+او او او او او او او او او او او او او او او او او
+
+447
+00:35:33,680 --> 00:35:39,800
+او او او او او او او او او او او او او او او او
+
+448
+00:35:40,420 --> 00:35:44,560
+بقدر أجيب rational number is very closed له لأن
+
+449
+00:35:44,560 --> 00:35:48,420
+احنا بنعرف أنه dense يعني بنلاقي انه sequence من
+
+450
+00:35:48,420 --> 00:35:51,980
+ال rationales كلها رايحة لكساي I إذا بلاقي ر I
+
+451
+00:35:51,980 --> 00:35:56,940
+بحيث أنه المسافة بينهم أصغر ما يكون ماشي الحال هذا
+
+452
+00:35:56,940 --> 00:36:01,260
+بعمله لكساي 1 و لكساي 2 و لكساي 3 و لكساي 4 و لهم
+
+453
+00:36:01,260 --> 00:36:07,280
+كلهم بعملهم واضح؟ إذا بقدر ألاقي الآن اللي هو
+
+454
+00:36:08,570 --> 00:36:12,470
+بخاصية الكثافة للـ Q في R بقدر ألاقي rational
+
+455
+00:36:12,470 --> 00:36:19,950
+numbers ر I لـ close to mean to xi Isuch that اللي
+
+456
+00:36:19,950 --> 00:36:27,850
+هو إنها بتحقق إنه xij ناقص RJ أس بي من جيه من واحد
+
+457
+00:36:27,850 --> 00:36:31,670
+إلى ماله نهاية أصغر من مين من أي عدد في الدنيا
+
+458
+00:36:31,670 --> 00:36:35,890
+بديه بزغره جد ما بدي بيصير عندي أصغر برضه من مين
+
+459
+00:36:35,890 --> 00:36:39,170
+من يبسلون بيه على مين على اتنين إذا صار في عندي
+
+460
+00:36:39,170 --> 00:36:46,770
+أمرين هاي الأمر الأولوهي الأمر الثاني الان هذولة
+
+461
+00:36:46,770 --> 00:36:52,230
+هيوصلني للي بديها لحظة انا ايش لجيت انا بدأت في ال
+
+462
+00:36:52,230 --> 00:37:00,010
+X هيها هيها ال X والان بدأت اركب من خاصية الكثافة
+
+463
+00:37:00,010 --> 00:37:08,570
+ل ال Q بدأت الاقي اللي هو sequence من ال RJ ال RJ
+
+464
+00:37:08,570 --> 00:37:13,500
+الان هذه J من 1 إلى ملا نهايةإيش مالها المسافة
+
+465
+00:37:13,500 --> 00:37:18,800
+أصغر من ي من ي بي على اتنين هذه اللي هتمثل لين؟ Y
+
+466
+00:37:18,800 --> 00:37:24,520
+إذا hence we can find Y element in M satisfying
+
+467
+00:37:24,520 --> 00:37:32,260
+the following المسافة
+
+468
+00:37:32,260 --> 00:37:37,000
+بين
+
+469
+00:37:37,000 --> 00:37:43,660
+X و Y هتكون بتساوياللي هو طبعا اسمه عشان مانديش
+
+470
+00:37:43,660 --> 00:37:47,860
+اعملاش واحد على بيه بتساوي ال summation هذا زي اد
+
+471
+00:37:47,860 --> 00:37:55,140
+مين ال summation اللي عندها معايا هذا
+
+472
+00:37:55,140 --> 00:37:59,180
+ال summation طبعا هذا خليه لعند هنا بيقل عندي اللي
+
+473
+00:37:59,180 --> 00:38:06,160
+هو جاي من عند واحد لعند n هذي لعند n بكفينا لعند n
+
+474
+00:38:07,490 --> 00:38:12,850
+عارفين ليه؟ عشان ادنى بتكون هنا لإن هنا أشمالها R1
+
+475
+00:38:12,850 --> 00:38:17,510
+وR2 وR3 والباقي أشمالهم أسفار ماشي الحال فبصير
+
+476
+00:38:17,510 --> 00:38:22,770
+عندي الآن طبعا بسهل عليه أكتر لإن الباقي كله
+
+477
+00:38:22,770 --> 00:38:26,640
+أشماله خلاص بقت خلاص منه إيش بده فيهطيب فبصير عندى
+
+478
+00:38:26,640 --> 00:38:29,360
+اللى هو المسافة بين هذه و هذه عبارة عن هذه زائد
+
+479
+00:38:29,360 --> 00:38:34,160
+هذه عارفين ليش لأن الباقى هان اشماله أسفار يعني ال
+
+480
+00:38:34,160 --> 00:38:38,300
+summation جسمته جسمين المسافة بين X و Y اللى هى Y
+
+481
+00:38:38,300 --> 00:38:46,710
+عندك R1وR2 وR3 لعند RN والباقي إيش ماله أصفر
+
+482
+00:38:46,710 --> 00:38:50,830
+فالمسافة هذه هتروح اللي هي الـRI هتبقى اللي هي
+
+483
+00:38:50,830 --> 00:38:54,430
+أشبه سجادة اللي هي الـXY جاي لحالها واللي هي أصلا
+
+484
+00:38:54,430 --> 00:38:58,110
+أنا مهتلها من الأصل جا جيتها وخلصنا فبصير هذا
+
+485
+00:38:58,110 --> 00:39:02,990
+المسافة التنين بتساوي هذا زائد هذا وهذا أصغر من
+
+486
+00:39:02,990 --> 00:39:06,230
+مين من يبسلون أس بي على اتنين ويبسلون أس بي على
+
+487
+00:39:06,230 --> 00:39:08,810
+اتنين اتنين أصغر من مين من يبسلون
+
+488
+00:39:16,460 --> 00:39:26,590
+ماذا فعلت؟ انا اخدت اي element x في القلبانتبهوا
+
+489
+00:39:26,590 --> 00:39:30,790
+عشان نعرف الـ X الكلي أي X في القلبي و لـ gate Y
+
+490
+00:39:30,790 --> 00:39:36,970
+في الـ M بحيث ان المسافة بين X و Y أصغر من مين من
+
+491
+00:39:36,970 --> 00:39:43,310
+إبسلون لأي إبسلون مين في الدنيا بمعنى آخر لأي ball
+
+492
+00:39:43,310 --> 00:39:52,770
+حوالين ال X أه و بنصف خطر أي نصف خطر تقاطع ال Mالـ
+
+493
+00:39:52,770 --> 00:39:58,170
+YP لا يساوي فاي وهذا ايش معناته؟ معناته صارت اللي
+
+494
+00:39:58,170 --> 00:40:04,810
+هي الـ LB closure .. آسف الـ LB بيساوي الـ M إيش؟
+
+495
+00:40:04,810 --> 00:40:05,310
+Closure
+
+496
+00:40:10,220 --> 00:40:16,460
+هذه اللى عندى لقيت اللى هو الـ M closure بساوى
+
+497
+00:40:16,460 --> 00:40:24,000
+القلبي بدأت في ال X في القلبي وانتهيت ان ال X كانت
+
+498
+00:40:24,000 --> 00:40:28,000
+موجودة في ال M closureوالـ LB صارت جزئية من الـ M
+
+499
+00:40:28,000 --> 00:40:30,500
+closure وزي ما قلنا في الأول الـ M closure دايما
+
+500
+00:40:30,500 --> 00:40:33,840
+جزئية من الـ LB إذا صارت التنتين متساوياتين إذا
+
+501
+00:40:33,840 --> 00:40:38,720
+صرت ملاقي countable subset اللي هي M of LB which
+
+502
+00:40:38,720 --> 00:40:41,940
+is dense in LB إذا صار الـ LB is a separable space
+
+503
+00:40:41,940 --> 00:40:46,820
+نجي الأن ناخد مثال على non-separable space ومثال
+
+504
+00:40:46,820 --> 00:40:53,380
+مهم برضه مثال مهم برضه
+
+505
+00:40:53,380 --> 00:40:57,620
+هتلاقوني اعتمادت على ملاحظةبرجو في كتاب التحليل
+
+506
+00:40:57,620 --> 00:41:03,120
+اللي أتخذناها في ال baccalaureate كتاب بارتل عن
+
+507
+00:41:03,120 --> 00:41:06,640
+اللي
+
+508
+00:41:06,640 --> 00:41:15,400
+هو ال binary representation للعدد وكف ياندي one to
+
+509
+00:41:15,400 --> 00:41:21,220
+one onto function بينهم خليني أشوفها ملاحظة قبل ما
+
+510
+00:41:21,220 --> 00:41:28,370
+نبدأ بالمثالبقول لي for any y element in 0,1 يعني
+
+511
+00:41:28,370 --> 00:41:33,530
+i,y اللي هي بين السفر و بين الواحد there is اللي
+
+512
+00:41:33,530 --> 00:41:38,670
+هو a sequence xii such that xii element in 0,1 for
+
+513
+00:41:38,670 --> 00:41:46,510
+all iلأي Y المتن Zero و واحد بلاقي Sequence Xi I
+
+514
+00:41:46,510 --> 00:41:51,510
+عناصرها يا سفر يا واحد هذه سفر واحد بتذكرنا في
+
+515
+00:41:51,510 --> 00:41:55,210
+اللي هي عناصر اللي هو ال ال ال ال ال binary
+
+516
+00:41:55,210 --> 00:41:59,870
+operation ال binary operation يا Zero يا واحدكلنا
+
+517
+00:41:59,870 --> 00:42:04,350
+أخدنا نظرية أعداد for all i and y ايش بيساوي كصاي
+
+518
+00:42:04,350 --> 00:42:06,710
+واحد على اتنين كصاي اتنين على اتنين ترجل كصاي تلتة
+
+519
+00:42:06,710 --> 00:42:08,210
+تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة
+
+520
+00:42:08,210 --> 00:42:08,530
+تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة
+
+521
+00:42:08,530 --> 00:42:11,310
+تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة
+
+522
+00:42:11,310 --> 00:42:18,410
+تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة تلتة
+
+523
+00:42:18,410 --> 00:42:28,630
+تلتة تل
+
+524
+00:42:28,800 --> 00:42:32,280
+اللي هو بقدر أجيله اللي هو الـBinary
+
+525
+00:42:32,280 --> 00:42:38,960
+Representation اللي هو للـY بساوي اللي هو XI I على
+
+526
+00:42:38,960 --> 00:42:44,140
+Y أتنين زاد XI I على 2 تربيع زاد او هي واحد آسف
+
+527
+00:42:44,140 --> 00:42:50,170
+اتنين إلى اخرى إلى مانا نهايةالان و ال .. و ال ..
+
+528
+00:42:50,170 --> 00:42:55,930
+و ال .. و الويات المختلفة هتلاقيهم بمثل ايش أعداد
+
+529
+00:42:55,930 --> 00:43:01,970
+مختلفة منها يعني هذه التمثيل اللي هو بنظام ال
+
+530
+00:43:01,970 --> 00:43:07,450
+decimal يكافئ تماما one to one correspondence مع
+
+531
+00:43:07,450 --> 00:43:10,350
+التمثيل بإيش بال binary operation خليني أنا أخد
+
+532
+00:43:10,350 --> 00:43:14,530
+على فترة سنة واحد اللي بتلزمنيماشي؟ اذا for any y
+
+533
+00:43:14,530 --> 00:43:17,010
+element in 0,1 there is a sequence xi,i such that
+
+534
+00:43:17,010 --> 00:43:21,590
+xi,i of 0,1 for all i and y بتساوي كده is a binary
+
+535
+00:43:21,590 --> 00:43:24,290
+representation of y moreover اللي قلت قبل شوية
+
+536
+00:43:24,290 --> 00:43:29,050
+different y's element in كده have different binary
+
+537
+00:43:29,050 --> 00:43:32,350
+representations اذا انا مرتاح فاش اشي بتكرر هدولة
+
+538
+00:43:32,350 --> 00:43:35,150
+هنا نفسهم بس هدول اسمهم decimal و هدول اسمهم ايش
+
+539
+00:43:35,150 --> 00:43:39,200
+معلوم binary representationاللي حابب يطلع حيثي
+
+540
+00:43:39,200 --> 00:43:43,320
+introduction to a real analysis لبارتيل وشيربرت
+
+541
+00:43:43,320 --> 00:43:49,330
+اللي بندرسه في ال baccalaureateاللي هي الـ space
+
+542
+00:43:49,330 --> 00:43:53,890
+اللي أمامي the space L infinity is not separable
+
+543
+00:43:53,890 --> 00:43:58,310
+is not separable يعني بدنا نقول مش هنقدر نلاقي
+
+544
+00:43:58,310 --> 00:44:03,110
+countable dense set في الـ L infinity لو بدك تيجي
+
+545
+00:44:03,110 --> 00:44:06,830
+تقول والله بدي أفترض let M be any dense subset of
+
+546
+00:44:06,830 --> 00:44:09,770
+L بيه اللي متاعها L infinity مش هتطلع إيش مالها
+
+547
+00:44:09,770 --> 00:44:15,560
+countable بس باختصار هي الحكيمة الآن عياز سريعlet
+
+548
+00:44:15,560 --> 00:44:19,800
+n be anything subset of main of n infinity طيب ال
+
+549
+00:44:19,800 --> 00:44:23,740
+infinity لأنه بيقولك خد s رعبان عن x i i اللي
+
+550
+00:44:23,740 --> 00:44:27,640
+بتنقل ال infinity و ال x i i اللي بتنزيره main و
+
+551
+00:44:27,640 --> 00:44:30,960
+واحد هذولة يعني ال sequence اللي موجودة في ال
+
+552
+00:44:30,960 --> 00:44:33,400
+infinity على صراية واحد وصفر واحد وصفر واحد وأكيد
+
+553
+00:44:33,400 --> 00:44:36,160
+في ال infinity لأن كيف تكون في ال infinity ال
+
+554
+00:44:36,160 --> 00:44:41,040
+sequence اللي هو تكون bounded sequence يعني ال x i
+
+555
+00:44:41,040 --> 00:44:43,660
+ايات هذولة حطيناها ان جوا absolute value هيكون
+
+556
+00:44:43,660 --> 00:44:47,030
+أصغر من some عددودول هي صفرها واحد إذا أكيد إيش
+
+557
+00:44:47,030 --> 00:44:51,070
+مالها is bounded إذا عندك xi I وين موجودة في الأقل
+
+558
+00:44:51,070 --> 00:44:55,050
+infinity أكيد اللي هي ال xi I المتكونة من اللي هو
+
+559
+00:44:55,050 --> 00:44:59,790
+01 يعني مثلا 10000011100
+
+560
+00:44:59,790 --> 00:45:04,590
+كل هدول ال elements وين موجودات في الأقل infinity
+
+561
+00:45:06,870 --> 00:45:13,550
+شوفوا لها since 01 is uncountable أكيد ما احنا
+
+562
+00:45:13,550 --> 00:45:17,350
+عارفين هدم علوة سابقة and for each y element in 01
+
+563
+00:45:17,350 --> 00:45:21,610
+بنقدر نلاقي their correspondence xi i element in S
+
+564
+00:45:21,610 --> 00:45:27,110
+هدم هي من اللي حكينا عنهم قبل شوية and different
+
+565
+00:45:27,110 --> 00:45:31,690
+y's in 01 have different sequences in S إذا هتطلع
+
+566
+00:45:31,690 --> 00:45:39,120
+ال S هذه اللي هي is uncountable set ماشي؟لأنه عندى
+
+567
+00:45:39,120 --> 00:45:44,280
+اللي هي هذه اللي هي أي element في الـ zero والواحد
+
+568
+00:45:44,280 --> 00:45:48,780
+بقدر أجيله representation هنالأن الـ 01 01 01 01
+
+569
+00:45:48,780 --> 00:45:51,380
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+570
+00:45:51,380 --> 00:45:52,240
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+571
+00:45:52,240 --> 00:45:57,320
+01 01 01 01 01 01 01 01 01 01 01
+
+572
+00:45:57,320 --> 00:45:58,080
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+573
+00:45:58,080 --> 00:45:58,100
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+574
+00:45:58,100 --> 00:45:58,140
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+575
+00:45:58,140 --> 00:45:59,240
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+576
+00:45:59,240 --> 00:46:00,400
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+577
+00:46:00,400 --> 00:46:00,460
+01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01
+
+578
+00:46:00,460 --> 00:46:04,940
+01 01 01 01 01 01 01 01 01 01 01 01 01
+
+579
+00:46:04,940 --> 00:46:15,680
+01 01
+
+580
+00:46:15,680 --> 00:46:20,760
+01 01 01Hence, S is uncountable إلى أن خدوا أي X
+
+581
+00:46:20,760 --> 00:46:25,940
+وY وإن موجودة XII وYI وإن موجودات وGamma I في الـ
+
+582
+00:46:25,940 --> 00:46:32,700
+S أي تنتج وخدوه المختلفات مدام هم مختلفات إذا في
+
+583
+00:46:32,700 --> 00:46:35,720
+واحد من ال interest اللي بينهم مختلف عن التاني على
+
+584
+00:46:35,720 --> 00:46:39,820
+الأقل في واحد يمكن في أكتر من واحدوالـ interest
+
+585
+00:46:39,820 --> 00:46:44,280
+اللي فيه مثلا لو قلنا هذا اللي رقمه خمسة بختلف عن
+
+586
+00:46:44,280 --> 00:46:49,140
+اللي رقمه خمسة يعني فبصير حاصل طرحل لأبسولوت
+
+587
+00:46:49,140 --> 00:46:53,900
+الواحد لأن ولا .. فش عنها ال X هي Zero و واحد فدي
+
+588
+00:46:53,900 --> 00:46:56,920
+كان Zero و واحد فأكيد واحد بينهم بختلف عن التاني
+
+589
+00:46:56,920 --> 00:46:59,720
+إذا المسافة بيننا إيش بساوي واحد إذا انصارة ال
+
+590
+00:46:59,720 --> 00:47:02,920
+distance بين ال X و ال Y في حالة الاختلاف إيش
+
+591
+00:47:02,920 --> 00:47:07,720
+بساوي بساوي اللي هو إيه شمالها بساوي واحديعني
+
+592
+00:47:07,720 --> 00:47:14,200
+بمعنى آخر الـ ball لل X و تلت لل X و تلت تقاطع ال
+
+593
+00:47:14,200 --> 00:47:22,040
+ball لل Y و تلت أكيد هيسوف Y ليش؟ لأنه الآن ال
+
+594
+00:47:22,040 --> 00:47:30,200
+ball لل X و Y لل X و تلتتقاطع الـ ball للـ Y تلت
+
+595
+00:47:30,200 --> 00:47:35,200
+أو نصف اللي بيدك إياه اللي هو بساوي فاي لو بدنا
+
+596
+00:47:35,200 --> 00:47:40,700
+نقول خلّينا نفترض إنه Z فيها إنه Z هنا Z هنا
+
+597
+00:47:40,700 --> 00:47:48,240
+معناته Z في الـ B X و تلت andزد element بي و أيه
+
+598
+00:47:48,240 --> 00:47:52,740
+تلت صح ولا لأ نقول أيه تساوي فيه إذا مساعدت
+
+599
+00:47:52,740 --> 00:47:59,150
+المسافة بين ال X و ال Z بساوي أيه معله تلتإذا مدام
+
+600
+00:47:59,150 --> 00:48:03,690
+بتساوى تلت وانا بعرف المسافات بين أي عنصرين هتكون
+
+601
+00:48:03,690 --> 00:48:06,850
+يا صفر يا مين حسب اللي هم .. انتوا عارفين ايش ال
+
+602
+00:48:06,850 --> 00:48:11,130
+metric هنا اللي هو عبارة عن supremum لل XII ناقص
+
+603
+00:48:11,130 --> 00:48:16,150
+القمر هذوله .. هذوله المسافات بينهم اللي هو يا صفر
+
+604
+00:48:16,150 --> 00:48:20,890
+يا واحد لو بده يكون واحد الان لو بده يكون واحد مش
+
+605
+00:48:20,890 --> 00:48:25,750
+هيكون .. مش .. مش .. مش هيظبط فالان هذه بساللي هو
+
+606
+00:48:25,750 --> 00:48:28,850
+دي زد ودي إكس بيساوي تولك معناته إن زد إيش هتساوي
+
+607
+00:48:28,850 --> 00:48:34,970
+الإكس بس في هذه الحالة الآن التاني لو زد هنا إيش
+
+608
+00:48:34,970 --> 00:48:40,060
+هيعطيني هذا إن زد إيش بتساويمن الجهتين عشان تكون
+
+609
+00:48:40,060 --> 00:48:43,460
+هدي فيه هدي و فيه هدي لازم نزل ال X عشان بتساوي و
+
+610
+00:48:43,460 --> 00:48:47,320
+أنا باعدى بال X و ال Y أشمالهم نختلفت إذا قطعا
+
+611
+00:48:47,320 --> 00:48:51,800
+قطعا يا جماعة البول هدي تقاطع البول هدي لشوفاني
+
+612
+00:48:51,800 --> 00:48:58,740
+أصلا بي X و تلت فش فيها لغير X و ال BY تلت فش فيها
+
+613
+00:48:58,740 --> 00:49:04,020
+لغير ال Y و ال X مابتساوي شوية لازم تقاطع طيب ماشي
+
+614
+00:49:04,020 --> 00:49:12,480
+الحاجة إذا صار عندىلاحظوا أن أي XY مختلفة هيكون
+
+615
+00:49:12,480 --> 00:49:18,000
+اللي هو بلاج بول حوالينها دي و بول حوالينها دي
+
+616
+00:49:18,000 --> 00:49:22,540
+أشمالهم disjoint نكمل القصة، شوف إيش اللي بدهوا
+
+617
+00:49:22,540 --> 00:49:25,720
+إياه يا عزيزي hence we have uncountable number of
+
+618
+00:49:25,720 --> 00:49:33,870
+balls that are not intersectمستحيل يتقاطعي اذا
+
+619
+00:49:33,870 --> 00:49:37,590
+الان how though m is dense in l infinity لكن احنا
+
+620
+00:49:37,590 --> 00:49:40,950
+بنقول قاعدين ان m ايش ما لها dense in l infinity
+
+621
+00:49:40,950 --> 00:49:45,410
+اذا each of the above balls اللي حكينا عنها must
+
+622
+00:49:45,410 --> 00:49:49,410
+contain an element of مين فعلا عشان تكون ان هي
+
+623
+00:49:49,410 --> 00:49:52,790
+dense بظبط مش احنا بنقول m is dense ايش معنات m
+
+624
+00:49:52,790 --> 00:49:58,030
+بيبقى معناه عندنا m is dense in اللي هو مين قلبي
+
+625
+00:49:58,890 --> 00:50:08,290
+إذا أي بول حوالين أي نقطة
+
+626
+00:50:08,290 --> 00:50:17,550
+X وأنا أخدت مثلا تلت تقاطه الأم أشماله ليسوا فايل
+
+627
+00:50:17,550 --> 00:50:21,830
+وهذه العدد الأشمال هي الـ uncountable درنا إذا صار
+
+628
+00:50:21,830 --> 00:50:25,110
+في الام إيش فيه عندي uncountable number of points
+
+629
+00:50:25,920 --> 00:50:32,060
+إذا بدأت بم dense ووصلت
+
+630
+00:50:32,060 --> 00:50:34,560
+مدامة م dense إذا تحتوي on countable number of
+
+631
+00:50:34,560 --> 00:50:37,600
+elements إذا هذا بيقول لي إنه there is no
+
+632
+00:50:37,600 --> 00:50:42,540
+countable dense subset من ال L infinity ومعناته إن
+
+633
+00:50:42,540 --> 00:50:46,430
+ال V is not separableإذن، لذلك، لدينا عدد غير
+
+634
+00:50:46,430 --> 00:50:50,950
+مقارنة من حجمين لا يتعامل مع بعضهم، ولكن M هو نسبة
+
+635
+00:50:50,950 --> 00:50:55,090
+لـInfinity، وكما قلت، فكل حجم من الأعلى يجب أن
+
+636
+00:50:55,090 --> 00:51:00,170
+يحتوي على حجم M، لذلك M نفسية شمالها لديها عدد غير
+
+637
+00:51:00,170 --> 00:51:03,770
+مقارنة من حجمين، ومنذ أن M كانت عبارة عن نفسها،
+
+638
+00:51:03,770 --> 00:51:08,560
+فInfinity ليستالـ separable و بيكون .. هيك احنا
+
+639
+00:51:08,560 --> 00:51:12,120
+خلصنا المحاضرة الرابعة و عندنا ال homework اللي هي
+
+640
+00:51:12,120 --> 00:51:15,800
+star اللي هي ستة واربعتاش و ان شاء الله إلى لقاء
+
+641
+00:51:15,800 --> 00:51:17,640
+آخر السلام عليكم و رحمة الله و بركاته
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/J7SCFPaCRLU_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/J7SCFPaCRLU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0c176c316e4be56fcb9452033dc0497bf29e9103
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/J7SCFPaCRLU_raw.srt
@@ -0,0 +1,2396 @@
+1
+00:00:05,690 --> 00:00:08,790
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,790 --> 00:00:11,910
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:11,910 --> 00:00:17,250
+آله وصحبه أجمعين هذه المحاضرة التاسعة مساق تحليل
+
+4
+00:00:17,250 --> 00:00:20,150
+دالي أو تحليل اقتراني لطلاب طالبات الجامعة
+
+5
+00:00:20,150 --> 00:00:24,470
+الإسلامية ماجستير رياضيات اليوم ان شاء الله هنكمل
+
+6
+00:00:24,470 --> 00:00:27,830
+اللي هو في ال section نبدأ في ال section اللي هو
+
+7
+00:00:27,830 --> 00:00:32,070
+اتنين تلاتة اللي هو further properties of normed
+
+8
+00:00:32,070 --> 00:00:37,220
+spaces اللي هيخلّيني أحكي عن خواص أخرى اللي هو للـ
+
+9
+00:00:37,220 --> 00:00:41,720
+Normed Space الأن نبدأ اللي هو بالتعريف التالي
+
+10
+00:00:41,720 --> 00:00:47,300
+التعريف اللي هو كميالي بيقول لي a subspace Y of a
+
+11
+00:00:47,300 --> 00:00:51,000
+normed space X is a subset of X considered as a
+
+12
+00:00:51,000 --> 00:00:54,440
+vector space with a norm in Y obtained by
+
+13
+00:00:54,440 --> 00:00:58,960
+restricting the norm in X to mean to Yعندي اللي هو
+
+14
+00:00:58,960 --> 00:01:03,240
+الـ X-normed space لأن لو كانت عندي Y مجموعة جزئية
+
+15
+00:01:03,240 --> 00:01:07,720
+من X وY اللي هو ال .. ال .. ال norm اللي عليها هو
+
+16
+00:01:07,720 --> 00:01:09,860
+ال norm اللي .. اللي .. اللي .. اللي هي ال norm
+
+17
+00:01:09,860 --> 00:01:14,680
+الأصلي تبع X وكانت Y نفسها subspace as a vector
+
+18
+00:01:14,680 --> 00:01:18,160
+space من X فبكون عندي في هذه الحياة بنسمي Y
+
+19
+00:01:18,160 --> 00:01:24,880
+أشمالها as a normed subspace من مين؟ من اللي هو X
+
+20
+00:01:25,500 --> 00:01:30,340
+هذا تعريف اللي هو normed subspace نطلع في نظرية
+
+21
+00:01:30,340 --> 00:01:35,220
+أخدناها احنا في اللي هو 148 نظرية كانت بتقول ان هو
+
+22
+00:01:35,220 --> 00:01:38,560
+subspace M of a complete metric space في ال metric
+
+23
+00:01:38,560 --> 00:01:42,720
+space X is itself complete if and only if the
+
+24
+00:01:42,720 --> 00:01:47,500
+situation is closed in Mالان ما احنا عارفين ان كل
+
+25
+00:01:47,500 --> 00:01:51,300
+normed space عبارة عن metric space اذا اللي بنطبق
+
+26
+00:01:51,300 --> 00:01:54,200
+على ال metric space اكيد بنطبق على مين؟ على ال
+
+27
+00:01:54,200 --> 00:01:58,180
+normed space يعني بمعنى اخر، الان النظرية تلت
+
+28
+00:01:58,180 --> 00:02:01,380
+اتنين تلت اتنين automatic هتيجيني من مين؟ من
+
+29
+00:02:01,380 --> 00:02:05,060
+النظرية احد اربعة تمانية، ايش بتقول هذه النظرية؟
+
+30
+00:02:05,060 --> 00:02:09,140
+ان ا sub space Y of بنخ space X، طبعا بنخ space
+
+31
+00:02:09,140 --> 00:02:12,080
+معناته complete normed space، يعني complete metric
+
+32
+00:02:12,080 --> 00:02:17,880
+spaceاللي هي a subspace Y of بنخ space X is
+
+33
+00:02:17,880 --> 00:02:22,180
+complete اللي هي هذه اللي هي Y complete if and
+
+34
+00:02:22,180 --> 00:02:26,860
+only if إيش ما لها Y is closed اللي هي subspace من
+
+35
+00:02:26,860 --> 00:02:30,980
+من من الـ X إذا هذه النظرية ما هي إلا حالة خاصة من
+
+36
+00:02:30,980 --> 00:02:34,020
+النظرية الفجوة النظرية الفجوة على metric space in
+
+37
+00:02:34,020 --> 00:02:37,680
+general هذه عالمين على اللي هو واحد من ال metric
+
+38
+00:02:37,680 --> 00:02:41,480
+spaces اللي هو ال metric space المولد أو ال
+
+39
+00:02:41,480 --> 00:02:46,040
+induced by the normماشي الحال إذا هذه automatic من
+
+40
+00:02:46,040 --> 00:02:50,520
+1 4 8 يعني نيجي الآن ليه بعض الملاحظات اللي بدنا
+
+41
+00:02:50,520 --> 00:02:55,120
+نحكي فيها عشان تلزمنا اللي هو لاحقا الان a
+
+42
+00:02:55,120 --> 00:02:58,540
+sequence xn in a norm of this base x is convergent
+
+43
+00:02:58,540 --> 00:03:02,940
+if there is x a limit in x such that limit norm ال
+
+44
+00:03:02,940 --> 00:03:07,280
+xn ناقص x بسوء 0 as n goes to infinity مش جديد هذا
+
+45
+00:03:07,280 --> 00:03:10,820
+يا جماعة احنا لما نعرفنا ال sequence انها converge
+
+46
+00:03:10,820 --> 00:03:16,170
+xn converge ده ال xفي metric space X وD ايش قلنا
+
+47
+00:03:16,170 --> 00:03:22,370
+انه اللي هو limit لل distance بين X و N و X as N
+
+48
+00:03:22,370 --> 00:03:26,150
+minus infinity ايش يساوي؟ ساوي سفر طيب ما هو ال
+
+49
+00:03:26,150 --> 00:03:30,890
+norm اللي عندنا احنا هنا هو عبارة عن metric يعني
+
+50
+00:03:30,890 --> 00:03:34,590
+الآن لو بدنا نطبق هذا الكلام على ال metric اللي
+
+51
+00:03:34,590 --> 00:03:38,590
+عندنا اللي هو norm ما هو هذا ايش بيمثل؟ بيمثل
+
+52
+00:03:38,590 --> 00:03:43,400
+عبارة عن norm ال X N ناقص X اللي هو limit لهas n
+
+53
+00:03:43,400 --> 00:03:46,980
+goes to infinity بساوة سفر إذا التعريف هذا مش
+
+54
+00:03:46,980 --> 00:03:51,280
+تعريف جديد ما هو إلا عبارة عن تطبيق لتعريف سابق
+
+55
+00:03:51,280 --> 00:03:53,520
+أخدناه في الـ metric space شو معناته الـ xn
+
+56
+00:03:53,520 --> 00:03:58,560
+converge ل some x اللي هو بيكون limit لاللي هو ال
+
+57
+00:03:58,560 --> 00:04:02,400
+norm اللي هو ال distance بين xn و x as n goes to
+
+58
+00:04:02,400 --> 00:04:06,360
+infinity بساوة سفر بس كتبناه بلغة ال norm على أساس
+
+59
+00:04:06,360 --> 00:04:10,300
+إنه هنقدرنا نشتغل عليه الآن بناء على هذا التعريف
+
+60
+00:04:12,030 --> 00:04:16,970
+أحنا خلّيني نقول عرفنا اللي هو شو معناه xn
+
+61
+00:04:16,970 --> 00:04:20,510
+-convergent طيب إذا في إشي تاني دايما بنحكي و
+
+62
+00:04:20,510 --> 00:04:24,210
+بنتهدأك اللي هو لأ إشي تاني بنحكي فيه اللي هو شو
+
+63
+00:04:24,210 --> 00:04:26,330
+معناته للـsequence كوشي يعني بنحكي عن
+
+64
+00:04:26,330 --> 00:04:29,030
+الـconvergent و بنحكي عن مين ال convergence و
+
+65
+00:04:29,030 --> 00:04:32,910
+بنحكي عن الكوشي sequence لأن a sequence xn in
+
+66
+00:04:32,910 --> 00:04:37,120
+around this base x is a كوشي sequenceif for every
+
+67
+00:04:37,120 --> 00:04:40,060
+y أكبر من 0 there exists k element in n such that
+
+68
+00:04:40,060 --> 00:04:44,160
+normal xn ناقص xn أصغر من 100 من y كل n وأكبر من
+
+69
+00:04:44,160 --> 00:04:48,440
+100 برضه مش جديد احنا كنا نقول xn is Cauchy في ال
+
+70
+00:04:48,440 --> 00:04:51,840
+metric إذا كانت اللي هو for every xn أكبر من 0
+
+71
+00:04:51,840 --> 00:04:55,480
+there exists k element in n such that normal x أي
+
+72
+00:04:55,480 --> 00:04:59,500
+اللي هو ال distance في ال xn و ال xيكون أصغر من Y
+
+73
+00:04:59,500 --> 00:05:04,460
+لكل N أكبر من مين من K أو أكبر أو سوء K لأن ال
+
+74
+00:05:04,460 --> 00:05:07,700
+norm ال metric اللي عندنا اليوم بيشتغل عليه هو
+
+75
+00:05:07,700 --> 00:05:12,700
+عبارة عن ال norm XN ناقص XN لأن هذا ال metric اللي
+
+76
+00:05:12,700 --> 00:05:16,100
+عندنا اليوم هو ال induced by the norm إذن برضه مش
+
+77
+00:05:16,100 --> 00:05:19,940
+تعريف جديد ولكن تطبيق على ال metric اللي مولد من
+
+78
+00:05:19,940 --> 00:05:24,290
+ال norm طيبنجي للتعريف اللي بعده بناء عليه طبعا
+
+79
+00:05:24,290 --> 00:05:27,150
+احنا لان احنا في norm of the space يا جماعة مادام
+
+80
+00:05:27,150 --> 00:05:31,050
+في norm of the space اذا هو عبارة عن vector space
+
+81
+00:05:31,050 --> 00:05:33,450
+يعني عملية الجمع وعملية ال scale and
+
+82
+00:05:33,450 --> 00:05:37,590
+multiplication كلها مشرعة عشان هيك الان احنا اكثر
+
+83
+00:05:37,590 --> 00:05:41,570
+حرية قبل كنا ناخد لما ناخد ناخد metric space هيكون
+
+84
+00:05:41,570 --> 00:05:45,890
+عنده X وD X مجرد 6 فمقدرش احكي عن مجموع عناصر
+
+85
+00:05:45,890 --> 00:05:48,770
+بينها او scale and multiplication لالا لالا لالا
+
+86
+00:05:48,770 --> 00:05:53,520
+الان صار عندنا اللي هوعبارة عن norm وهذا عبارة عن
+
+87
+00:05:53,520 --> 00:05:58,000
+norm فهذا عبارة عن vector space مشرّع إلى الحديث
+
+88
+00:05:58,000 --> 00:06:02,160
+عن الجمع وعن الـ scalar multiplication بناء عليه
+
+89
+00:06:02,160 --> 00:06:06,820
+بنفع أقول الآن على مجموع عناصر يعني بنفع أروح
+
+90
+00:06:06,820 --> 00:06:11,800
+باتجاه اللي هو series نشوف كيف let xn be a
+
+91
+00:06:11,800 --> 00:06:17,370
+sequence in a normed space Xand let S1 be a
+
+92
+00:06:17,370 --> 00:06:22,030
+sequence of partial sums يعني S1 بيساوي X1 S2
+
+93
+00:06:22,030 --> 00:06:28,030
+بيساوي X1 زي X2 S3 بيساوي X1 زي X2 زي X3 S1 in
+
+94
+00:06:28,030 --> 00:06:32,370
+general X1 زي X2 زي XN صارت هذه الـ S1 عبارة عن
+
+95
+00:06:32,370 --> 00:06:36,070
+sequence of partial sums زي اللي أخدناها في
+
+96
+00:06:36,070 --> 00:06:39,230
+الكالكولاست العادى بس كنا احنا اللي عارية نشتغل
+
+97
+00:06:44,560 --> 00:06:48,900
+إذا كان الـ S مرتبط بـ S فإن الـ Infinite Series
+
+98
+00:06:48,900 --> 00:06:53,860
+Summation XI قد يكون مرتبط بـ S وS يسمى بالنسبة
+
+99
+00:06:53,860 --> 00:06:57,520
+للعدة من السلسلين وقال S بالسلمانية XI يعني اللي
+
+100
+00:06:57,520 --> 00:07:07,300
+بيقوله لو عندي أن أعرف شو معنات السلسلين مرتبطالان
+
+101
+00:07:07,300 --> 00:07:11,340
+عند الـ sequence of partial sums S N اللي هي الـ S
+
+102
+00:07:11,340 --> 00:07:16,180
+N بتساوي X 1 زائد X N هذا كله اللي موجود في الـ
+
+103
+00:07:16,180 --> 00:07:22,580
+normed space طيب بنقول ان S N بتروح ل Sيعني
+
+104
+00:07:22,580 --> 00:07:26,320
+converts to some element اسمه S و بنكتبه summation
+
+105
+00:07:26,320 --> 00:07:30,940
+XI I من عند واحد لما انه تروح لما نهاية as N goes
+
+106
+00:07:30,940 --> 00:07:34,060
+to infinity يعني بيصير summation بدل لـ Sn هذا
+
+107
+00:07:34,060 --> 00:07:38,640
+عبارة عن summation XI I من عند واحد لعند N لأن as
+
+108
+00:07:38,640 --> 00:07:40,720
+N goes to infinity بيصير ال summation هذا I من
+
+109
+00:07:40,720 --> 00:07:45,580
+واحد إلى ما لنهاية بنسميه أش بساوي بساوي S و بنقول
+
+110
+00:07:45,580 --> 00:07:48,960
+عنه ال sequenceالـ series في هذه الحالة converts
+
+111
+00:07:48,960 --> 00:07:54,120
+to sum اللي هو element S هذا اللي هو sum of the
+
+112
+00:07:54,120 --> 00:08:00,600
+series طيب إذا كان ال norm لـ X1 زاد norm لـ X2
+
+113
+00:08:00,600 --> 00:08:05,180
+زاد norm لـ X3 إلى ما لا نهاية بدل ما أجمع ال X1 و
+
+114
+00:08:05,180 --> 00:08:08,940
+X2 و X3 بأجمع مين ال normات اللي هين و أسارتي اللي
+
+115
+00:08:08,940 --> 00:08:12,380
+هى جمع عداد حقيقية موجبة إذا كان مجموح إن هدولة
+
+116
+00:08:12,380 --> 00:08:17,900
+existبنقول summation xi is absolutely convergent
+
+117
+00:08:17,900 --> 00:08:21,280
+زي ما كنا بالظبط نقول في الريال إن ال absolute
+
+118
+00:08:21,280 --> 00:08:24,620
+value x1 absolute value x2 زائد إلى آخر يكون
+
+119
+00:08:24,620 --> 00:08:27,480
+convergent بنقول ال series الأصلية تبعت اللي هي
+
+120
+00:08:27,480 --> 00:08:31,240
+الريال absolutely convergent وهنا إحنا اللي هو
+
+121
+00:08:31,240 --> 00:08:34,540
+بنفس الطريقة بستعميم أكبر بدء من ناخد على ال R
+
+122
+00:08:34,540 --> 00:08:38,980
+نفسها بناخد على أي norm this base ففي هذا الحالة
+
+123
+00:08:38,980 --> 00:08:41,660
+بنسميها اللي هي absolutely convergent زي ما قلنا
+
+124
+00:08:42,280 --> 00:08:46,100
+ناخد الـ definition الآن الـ definition بدنا نعرف
+
+125
+00:08:46,100 --> 00:08:50,000
+حاجة if a normed space X contains a sequence E N
+
+126
+00:08:50,000 --> 00:08:53,640
+ركزه، إيش ال sequence هذه؟ with the probability
+
+127
+00:08:53,640 --> 00:08:57,360
+that for every X element in X there exists a
+
+128
+00:08:57,360 --> 00:09:01,000
+unique sequence of scalars Alpha N such that اللي
+
+129
+00:09:01,000 --> 00:09:05,420
+هو X limit X ناقصة للألف واحد E1 ألف اتنين E2 نزلت
+
+130
+00:09:05,420 --> 00:09:10,620
+ألف ن E N as N goes to infinity بساوي سفرثم aₙ
+
+131
+00:09:10,620 --> 00:09:15,360
+بيكون نسميها ايش ما لها a Schauder basis for X the
+
+132
+00:09:15,360 --> 00:09:19,740
+series summation XI ألف I EI I من واحد لإنفينيتي
+
+133
+00:09:19,740 --> 00:09:23,180
+is called the expansion of X with respect to mean
+
+134
+00:09:23,180 --> 00:09:28,060
+to aₙ إذا الآن في عنا حاجة اسمها إيش هي Schauder
+
+135
+00:09:28,060 --> 00:09:33,340
+basis إيش Schauder basis كمان مرة؟ هي كتالة إذا
+
+136
+00:09:33,340 --> 00:09:40,800
+أخدنا عندي X element in X arbitraryarbitrary و
+
+137
+00:09:40,800 --> 00:09:51,780
+لجينا sequence αن of scalars ماشي الحال بحيث انه
+
+138
+00:09:51,780 --> 00:09:58,690
+اللي هي يكون عنده limit للنور من ال X ناقصالفا
+
+139
+00:09:58,690 --> 00:10:04,550
+واحد في اي واحد ايش اي واحد هتجهب ونقولك زائد الفا
+
+140
+00:10:04,550 --> 00:10:09,810
+اتنين اي اتنين زائد الفا ان اي ان as n goes to
+
+141
+00:10:09,810 --> 00:10:15,550
+infinity لجناه بيساوي سفر معناته بنقول عن ال
+
+142
+00:10:15,550 --> 00:10:22,260
+sequence هذه اللي هي اي واحد اي اتنين اي تلاتةE4
+
+143
+00:10:22,260 --> 00:10:27,000
+إلى مالة نهاية اللي بنسميها EN بنقول عنها is a
+
+144
+00:10:27,000 --> 00:10:33,770
+shoulder bases forming for ال space اللي عند Xو في
+
+145
+00:10:33,770 --> 00:10:37,650
+هذه الحالة as n goes to infinity بيصير و كأنه
+
+146
+00:10:37,650 --> 00:10:42,650
+بنقول ال norm لل X ناقص ال summation لل alpha I EI
+
+147
+00:10:42,650 --> 00:10:46,390
+I من عند واحد لعند n لما تروح إلى مالة نهاية و
+
+148
+00:10:46,390 --> 00:10:49,250
+كأنه بيصير اللي هو مدام ال limit هذا بيساوي سفر و
+
+149
+00:10:49,250 --> 00:10:54,270
+كأنه بنقول X بتساوي ال summation alpha I EI I من
+
+150
+00:10:54,270 --> 00:10:59,390
+واحد إلى مالة نهاية يعني بمعنى آخربنقول E N is a
+
+151
+00:10:59,390 --> 00:11:05,030
+Schauder basis لـ X إذا كان كل X في الـ X بنقدر
+
+152
+00:11:05,030 --> 00:11:10,410
+نلاقي sequence of scalars Alpha N بحيث إنه الـ X
+
+153
+00:11:10,410 --> 00:11:14,790
+هاد انكتبت على صورة Infinite Series Alpha I E I I
+
+154
+00:11:14,790 --> 00:11:20,930
+من واحد عند مين لعند اللي هو Infinity أي سؤال؟
+
+155
+00:11:24,480 --> 00:11:27,380
+طيب طبعا هذه الـ sequensation اللي جيها unique
+
+156
+00:11:27,380 --> 00:11:32,460
+sequence تنسوش انه صورة وحيدة على اساس ان كل واحد
+
+157
+00:11:32,460 --> 00:11:40,720
+يطلعله بصيغة مختلفة طبعا لكل X في unique sequence
+
+158
+00:11:40,720 --> 00:11:43,240
+of scalars alpha n such that X بالصيغة ال
+
+159
+00:11:43,240 --> 00:11:46,300
+summation هذا مفادلة حول ما نسميه E n as a show of
+
+160
+00:11:46,300 --> 00:11:50,430
+numbers طيب ناخد مثالمثال على الـ show their bases
+
+161
+00:11:50,430 --> 00:11:55,730
+الان example en is a show their bases for البي
+
+162
+00:11:55,730 --> 00:12:00,270
+نشوف ايش en البي عارفينه انتوا واحنا حكينا عنه
+
+163
+00:12:00,270 --> 00:12:02,930
+بالتفصيل
+
+164
+00:12:03,580 --> 00:12:08,980
+E1 هو عبارة عن واحد و الباقي صفار E2 صفر و التاني
+
+165
+00:12:08,980 --> 00:12:13,660
+واحد و الباقي صفار E3 صفر صفر واحد و الباقي صفار
+
+166
+00:12:13,660 --> 00:12:18,240
+EN in general صفر صفر صفر EN ناقص واحد من العناصر
+
+167
+00:12:18,240 --> 00:12:22,620
+صفار و بعدين الرقم ال entry N بتكون واحد و الباقي
+
+168
+00:12:22,620 --> 00:12:27,330
+ايش مالهأصفر هذه الان اللي هي sequence of elements
+
+169
+00:12:27,330 --> 00:12:30,730
+أكيد وين موجودة؟ موجودة في القلبي لإن ال summation
+
+170
+00:12:30,730 --> 00:12:35,790
+إلها عبارة عن واحد بس ف finite ده موجود وين في
+
+171
+00:12:35,790 --> 00:12:40,730
+القلبي مافي أي مشكلة بدنا نثبت إن هذه بتعمل
+
+172
+00:12:40,730 --> 00:12:44,090
+shoulder bases إيش بدنا ناخد؟ بدنا ناخد أي X
+
+173
+00:12:44,090 --> 00:12:49,070
+arbitrary element ونلاقي ال sequence ناخد X أي
+
+174
+00:12:49,070 --> 00:12:55,360
+element في القلبيأيوة يا جماعة بدنا ناخد X أي
+
+175
+00:12:55,360 --> 00:13:00,220
+element في الـ LB ونلاقي ال sequence of scalars αN
+
+176
+00:13:00,220 --> 00:13:04,620
+مثلا أو اللي نسميها بعد شوية بحيث انه اللي هو
+
+177
+00:13:04,620 --> 00:13:07,100
+sequence وحيدة انه X نقدر نكتبها على سورة
+
+178
+00:13:07,100 --> 00:13:12,760
+summation αN في EN N من واحد إلى وين إلى مالة
+
+179
+00:13:12,760 --> 00:13:19,160
+نهاية ده نشوف كده خلّا مع بعضالأن let X be any
+
+180
+00:13:19,160 --> 00:13:23,880
+fixed element in B طبعاً كيف شكله الـ X في القلبي
+
+181
+00:13:23,880 --> 00:13:28,020
+Sequences يعني XI واحد، XI اتنين، XI تلت، XI
+
+182
+00:13:28,020 --> 00:13:30,920
+أربعة، إلى ما لنهاية، إذن X any fixed element in
+
+183
+00:13:30,920 --> 00:13:34,940
+قلبي إذن مدامه في القلبي، إذن أكيد الـ summation
+
+184
+00:13:34,940 --> 00:13:39,180
+الـ XI I، I من واحدة and infinity الـ B إيش ماله؟
+
+185
+00:13:39,180 --> 00:13:43,380
+is finite، convergent، عشان اللي هو شروط وجوده في
+
+186
+00:13:43,380 --> 00:13:47,640
+القلبيمدام هيك إذا then there is a sequence Xi I
+
+187
+00:13:47,640 --> 00:13:50,820
+of scalars such that أنا بتدعي الآتي أنه بقدر
+
+188
+00:13:50,820 --> 00:13:54,560
+ألاقي sequence of scalars Xi I من وين جبتها اللي
+
+189
+00:13:54,560 --> 00:13:57,960
+هي عناصر ال sequence اللي هاني يعني أخدت X1 و X2 و
+
+190
+00:13:57,960 --> 00:14:02,440
+X3 و X4 هي اللي هي من ال sequence of scalars اللي
+
+191
+00:14:02,440 --> 00:14:08,060
+أنا بديها such that ال X ناقص بقعد بطبق في التعريف
+
+192
+00:14:08,060 --> 00:14:13,060
+Xi 1 E 1 زي Xi 2 E 2 زي Xi N E N نحسبها مع بعض
+
+193
+00:14:13,570 --> 00:14:18,270
+ونشوف كيف نوصل إن ال limit لهذه بيساوي سفر نكون
+
+194
+00:14:18,270 --> 00:14:21,750
+خلصت، نكون أثبتت إنه فيه وموجود، وبعدين نثبت إنه
+
+195
+00:14:21,750 --> 00:14:27,530
+إيش وحيد، طيب، بساوي، الآن X نفسها عبارة عن مين؟
+
+196
+00:14:27,530 --> 00:14:31,850
+عن E1, E2, EN, EN, Z1, EN, Z2، Sequence إلى ما لا
+
+197
+00:14:31,850 --> 00:14:38,350
+نهاية، طيب هيها ال CLX، طيب، ناقص، الآن Alpha 1 E1
+
+198
+00:14:39,220 --> 00:14:45,140
+اللي عبارة عن Alpha 1 E 1 زائد Alpha 2 E 2 زائد
+
+199
+00:14:45,140 --> 00:14:51,200
+Alpha N E N ماعملتش فيها ولا شي لسه ماهي الحال و
+
+200
+00:14:51,200 --> 00:14:58,580
+يساوي الآن خلينا نحسبها هذه نحسب هذه الآن نحسب هذه
+
+201
+00:14:58,580 --> 00:15:07,640
+نحسب Alpha 1 E 1 لعند Alpha N E N لعند هذه نشوف
+
+202
+00:15:07,640 --> 00:15:13,850
+إيش هيالفا واحد اي واحد زائد الفا اتنين اي اتنين
+
+203
+00:15:13,850 --> 00:15:20,970
+زائد الفا ان اي ان ويساوي الفا اكساي واحد في اكساي
+
+204
+00:15:20,970 --> 00:15:21,210
+ان
+
+205
+00:15:25,070 --> 00:15:30,130
+في E1 E1 يعني عبارة عن واحد صفر صفر إلى مانا نهاية
+
+206
+00:15:30,130 --> 00:15:37,750
+زائد ال XI2 في Zero واحد Zero Zero زائد لما أصل
+
+207
+00:15:37,750 --> 00:15:44,870
+للأخيرة اللي هي XIN في Zero Zero لما أصل لل term N
+
+208
+00:15:44,870 --> 00:15:51,390
+اللي هو واحد والباقي أشمله أصفر ويسافر نيجي نحسب
+
+209
+00:15:51,390 --> 00:15:58,020
+ان XI واحدو هدولة صفراء إسفار إكساي اتنين والباقي
+
+210
+00:15:58,020 --> 00:16:02,280
+إسفار لما أصل عند مين إكساي أن واللي بعدهم كلهم
+
+211
+00:16:02,280 --> 00:16:08,700
+إيش يا جماعة إسفار طيب الأنصار هذا عبارة عنهذا ..
+
+212
+00:16:08,700 --> 00:16:14,640
+هذا اللي مهشر عليه اللي هو x1 و x2 و x3 و xn و
+
+213
+00:16:14,640 --> 00:16:19,800
+الباقي 0 لما أطرح حد ناقص هذا هيروح من الأولانيات
+
+214
+00:16:19,800 --> 00:16:24,420
+هيطلع 0 .. 0 .. 0 .. 0 و يضل المين اللي هي ال
+
+215
+00:16:24,420 --> 00:16:27,460
+interest دولة لأنهم لما نطرح منهم الأسفار بيضل هنا
+
+216
+00:16:27,460 --> 00:16:32,070
+xn زي 1 و xn زي 2 إلى ما لنهايةواضح حاصل طرح
+
+217
+00:16:32,070 --> 00:16:36,750
+الجهتين هذا الان مجموعه ايش بيساوي بيساوي مجموعه
+
+218
+00:16:36,750 --> 00:16:41,150
+اللي هو ال normه normه انا وين بشتغل في ال ال B و
+
+219
+00:16:41,150 --> 00:16:44,490
+ال B norm ايش معله ال summation لل absolute values
+
+220
+00:16:44,490 --> 00:16:48,890
+ده دول ال interest أس بي الكلس واحد على بي هي xi I
+
+221
+00:16:48,890 --> 00:16:52,930
+أس بي الكلس واحد على بي I الأولميات من واحد لأم
+
+222
+00:16:52,930 --> 00:16:56,470
+نصفار اذا بيبدأ ال summation هنا زاد واحد أمين
+
+223
+00:16:56,470 --> 00:17:01,090
+لماله نهيئةas n goes to infinity هذا ال summation
+
+224
+00:17:01,090 --> 00:17:04,890
+بتلاشى as n goes to infinity هيروح لوين لعين سفر
+
+225
+00:17:04,890 --> 00:17:07,410
+لما قلت روح لما قلت هذا ال summation هيتلاشى ويروح
+
+226
+00:17:07,410 --> 00:17:11,970
+ل zero as n goes to infinity اذا ان انا اللي اجيت
+
+227
+00:17:11,970 --> 00:17:23,130
+سويته ان انا اللي سويته اثبتتلك انه limitNormal X
+
+228
+00:17:23,130 --> 00:17:29,790
+ناقص summation XII EI I من عند واحد لعند N as N
+
+229
+00:17:29,790 --> 00:17:34,730
+goes to infinity ايش بيساوي؟ بيساوي 0 دل أثبت انه
+
+230
+00:17:34,730 --> 00:17:38,570
+وحيدة اللي هي ال sequence of scalars وحيدة يعني ال
+
+231
+00:17:38,570 --> 00:17:42,850
+sequence of scalars اللي جيت XII هذه اللي هي نفس
+
+232
+00:17:42,850 --> 00:17:46,670
+تركيبة مين ال X اللي جوا اللي أخدتها منها اللي هي
+
+233
+00:17:46,670 --> 00:17:52,940
+هتكون ايه اشمالها as unique اطلع لفوقNow assume
+
+234
+00:17:52,940 --> 00:17:56,980
+that there is a sequence تانية αI of scalars such
+
+235
+00:17:56,980 --> 00:18:03,740
+that X- α1 E1 زائد α2 E2 زائد αN EN بتروح لـ 0 أزن
+
+236
+00:18:03,740 --> 00:18:08,080
+جثمين تنفيذ لان افترض انها اشمالها في واحدة تانية
+
+237
+00:18:08,080 --> 00:18:11,700
+بتحقق نفس الشروط الأولى و بعدين اثبتلك انه هتطلع
+
+238
+00:18:11,700 --> 00:18:16,520
+حد ال sequence αI هي نفسها مين لـ Xi I فبتكون خلاص
+
+239
+00:18:16,520 --> 00:18:19,830
+is uniqueإلى and then ال absolute value لل
+
+240
+00:18:19,830 --> 00:18:22,990
+summation هذا هو عبارة عن إيش عبارة عن ال
+
+241
+00:18:22,990 --> 00:18:27,470
+summation xi i ناقص alpha i ei i من عند واحد لعند
+
+242
+00:18:27,470 --> 00:18:33,890
+مين لعند n هذه حسبتها normal x نحسبلكم إياها هان
+
+243
+00:18:41,120 --> 00:18:54,240
+ممكن تحسبوها لحالكم لكن خلّين نحسب الهدف
+
+244
+00:18:54,240 --> 00:18:57,520
+اللي فرضناه و نحسب هذه الهدف عشان نوصلها لما نريده
+
+245
+00:18:59,970 --> 00:19:03,390
+الـ Xi I ناقص Alpha I في EI I من عند واحد لعندان
+
+246
+00:19:03,390 --> 00:19:08,370
+بدنا نفردها ال EI هدولة scalars وال EI ال E1 عبارة
+
+247
+00:19:08,370 --> 00:19:12,010
+عن واحد زيرو زيرو زيرو و لا اخرى بيصير هدى عبارة
+
+248
+00:19:12,010 --> 00:19:23,020
+عن XiI أبدا بالأولى I أبدا
+
+249
+00:19:23,020 --> 00:19:25,480
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+250
+00:19:25,480 --> 00:19:26,260
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+251
+00:19:26,260 --> 00:19:26,300
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+252
+00:19:26,300 --> 00:19:26,420
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+253
+00:19:26,420 --> 00:19:26,420
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+254
+00:19:26,420 --> 00:19:26,440
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+255
+00:19:26,440 --> 00:19:26,440
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+256
+00:19:26,440 --> 00:19:26,560
+بالأولى I أبدا بالأولى I أبدا بالأولى I أبدا
+
+257
+00:19:26,560 --> 00:19:35,040
+بالأولى I أبدا بالأولى I أبدا بالأولىX ناقص اللي
+
+258
+00:19:35,040 --> 00:19:40,680
+هو الأولى اللي هي هذه زائد
+
+259
+00:19:40,680 --> 00:19:45,100
+اللي هو X norm التاني X ناقص مين التاني يعني ضفت X
+
+260
+00:19:45,100 --> 00:19:48,520
+و طرحت مين X و استخدمت ال triangle inequalityطب
+
+261
+00:19:48,520 --> 00:19:53,380
+الآن هذه ما هي من الحالة الأولى ما هي X كتبت على
+
+262
+00:19:53,380 --> 00:19:58,800
+صورة الـ Submission هذا يعني بمعنى أخر هذا ال
+
+263
+00:19:58,800 --> 00:20:01,620
+limit له بساوة سفر وهذا ال limit بساوة سفر اللي
+
+264
+00:20:01,620 --> 00:20:05,520
+فرضته هان إذا صار ال limit لهذا كله أشمله بساوة
+
+265
+00:20:05,520 --> 00:20:11,650
+سفر إذا as n goes to infinity بصير هذا المقدارI من
+
+266
+00:20:11,650 --> 00:20:15,550
+عند واحد إلى ما لا نهاية بساوي سفر اطلع لفوق then
+
+267
+00:20:15,550 --> 00:20:19,090
+as n goes to infinity هذا المقدار بيروح للسفر
+
+268
+00:20:19,090 --> 00:20:22,170
+معناته ايش معناته هذا لما قالنا تروح إلى ما لا
+
+269
+00:20:22,170 --> 00:20:26,970
+نهاية يعني I من واحد إلى ما لا نهاية XII EI ناقص
+
+270
+00:20:26,970 --> 00:20:31,810
+الف I EI ايش بساوي بساوي اللي هو سفر هذا ايش هو في
+
+271
+00:20:31,810 --> 00:20:39,310
+الواقعاللي هو xi i ناقص alpha i as a sequence كيف؟
+
+272
+00:20:39,310 --> 00:20:45,790
+لأن هذا ال summation عبارة عن xi i ناقص ei ناقص
+
+273
+00:20:45,790 --> 00:20:51,580
+alpha iفي I ال summation I من واحد إلى مانع نهائية
+
+274
+00:20:51,580 --> 00:20:56,620
+خلّينا نفردها بساوى الآن الأولى عبارة عن XI واحد
+
+275
+00:20:56,620 --> 00:21:01,140
+ناقص Alpha واحد في E واحد هتطلع و الباقي أسفار
+
+276
+00:21:01,140 --> 00:21:07,520
+ماشي زائد التانية السفر XI اتنين ناقص Alpha اتنين
+
+277
+00:21:07,520 --> 00:21:13,230
+و الباقي ايش أسفارالان اللى عند ما اصل عند اخر
+
+278
+00:21:13,230 --> 00:21:18,270
+واحدة Zero Zero Zero عند N من العناصر بيصير Xi N
+
+279
+00:21:18,270 --> 00:21:24,450
+ناقص E N ناقص Alpha N و الباقى أسفار مافي الحال و
+
+280
+00:21:24,450 --> 00:21:27,170
+بيضلوا إلى ما لا نهاية هذا في الواقع ايش هيكون
+
+281
+00:21:27,170 --> 00:21:31,410
+عبارة عن ال .. هي عبارة عن سارة ايش مالها اللى هى
+
+282
+00:21:31,410 --> 00:21:36,390
+مجموحة مع بعض هي عبارة عن norm اللى هو Xi 1 ناقص
+
+283
+00:21:36,390 --> 00:21:44,620
+Alpha 1 Xi 2نقص ألف اتنين مجمحين مجمحين و XI تلاتة
+
+284
+00:21:44,620 --> 00:21:50,780
+نقص ألف تلاتة و XI N نقص ألف N وهذا بيضلوا إلى مين
+
+285
+00:21:50,780 --> 00:21:53,980
+إلى مالة نهاية إذا في الواقع هذه اللي جوايا شمالها
+
+286
+00:21:53,980 --> 00:21:59,280
+هي ال sequence هذه XI I نقص ألف I لأن هذه صارت
+
+287
+00:21:59,280 --> 00:22:03,460
+بتساوي سفرمعناته مدام النور بيساوي سفر إذا اللي
+
+288
+00:22:03,460 --> 00:22:06,640
+جوا بيساوي سفر معناته أن ال sequence هذه بتساوي ال
+
+289
+00:22:06,640 --> 00:22:09,860
+sequence هذه ومعناته اللي هو ال E أنصار إيش ماله
+
+290
+00:22:09,860 --> 00:22:14,660
+is a shoulder basis لإنه حقق الشرطين إن لكل X في
+
+291
+00:22:14,660 --> 00:22:18,750
+القلبي there exists a unique اللي هي ميناللي هي
+
+292
+00:22:18,750 --> 00:22:22,110
+sequence of scalars such that الـ X can be written
+
+293
+00:22:22,110 --> 00:22:28,150
+as a summation of Alpha N في اللي هي E N أو Xi N
+
+294
+00:22:28,150 --> 00:22:31,950
+في E N من N من 1 إلى ما لنهاية إذا صارت الـ E N is
+
+295
+00:22:31,950 --> 00:22:38,250
+a Schauder basis نيجي الآن لاللي هو النظرية
+
+296
+00:22:38,250 --> 00:22:42,650
+التالية اللي هي completion of a normed space
+
+297
+00:22:48,170 --> 00:22:53,190
+في الواقع هي هذه امتداد للنظرية اللي أخدناها في
+
+298
+00:22:53,190 --> 00:22:59,050
+اللي هي section 16 هي عندي اللي هو theorem اللي هو
+
+299
+00:22:59,050 --> 00:23:05,910
+162 أخدنا اللي هو النظرية كانت انه for any metric
+
+300
+00:23:05,910 --> 00:23:10,250
+space X وD بنقدر اللاجئ completion metric space X
+
+301
+00:23:10,250 --> 00:23:16,650
+hat وD hatwhich has a subspace W as isometric with
+
+302
+00:23:16,650 --> 00:23:21,470
+X and is dense in X hat وقلنا هذا اللي هو X hat is
+
+303
+00:23:21,470 --> 00:23:26,330
+unique up to isomorphism هذه شرحناها بشكل كامل
+
+304
+00:23:26,330 --> 00:23:31,990
+المحاضرة اللي هو السابعة عشان هيك أنا بفضل ان انت
+
+305
+00:23:31,990 --> 00:23:35,330
+مجرد ما بدك تسمح هذه المحاضرة لليوم انك تروح
+
+306
+00:23:35,330 --> 00:23:39,820
+للمحاضرة السابعةوتحضرها ومن ثم اتكمل على الكلام
+
+307
+00:23:39,820 --> 00:23:41,860
+اللي بدأ احكيه لأنه انا بدأ اكمل على البروحان اللي
+
+308
+00:23:41,860 --> 00:23:46,840
+هنا هذا البروحان كان اللي هو عبارة عن عن اللي هي
+
+309
+00:23:46,840 --> 00:23:51,240
+للنظرية اللي هي on metric space ان any metric
+
+310
+00:23:51,240 --> 00:23:55,240
+space can be completed الآن بدأ اقول ان any normed
+
+311
+00:23:55,240 --> 00:23:58,220
+space can be completed ترجعلي على ال .. على
+
+312
+00:23:58,220 --> 00:24:03,660
+النظرية تبعتنا اليوم خلينا نشوف اللي هو الكلام
+
+313
+00:24:03,660 --> 00:24:09,980
+اللي بدنا نحكيهالآن اللي هو بيقوللي theorem اللي
+
+314
+00:24:09,980 --> 00:24:15,340
+هو اتنين تلاتة ستة completion يعني لو أخدنا x بي a
+
+315
+00:24:15,340 --> 00:24:22,220
+normed space then there is a بنخ space x hatand is
+
+316
+00:24:22,220 --> 00:24:26,400
+isometry A from X to a subspace and to a subspace
+
+317
+00:24:26,400 --> 00:24:31,300
+W of X hat which is dense in X hat the space X hat
+
+318
+00:24:31,300 --> 00:24:35,100
+is unique except for isometries أنا في الواقع هذه
+
+319
+00:24:35,100 --> 00:24:40,000
+النظرية مبرهنها لإيش؟ مبرهنها في حال أن X metric
+
+320
+00:24:40,000 --> 00:24:45,500
+space يعني الآن كل ما يتعلق بوجود الـ X hat موجود
+
+321
+00:24:45,500 --> 00:24:50,350
+من الأصل بس موجود as a metric spaceأنا الآن إيش
+
+322
+00:24:50,350 --> 00:24:56,850
+دوري بدي أسويه بدي أخلي اللي هو اللي هو ال X هذا
+
+323
+00:24:56,850 --> 00:25:01,010
+ال X هذا بدي أركبها الآن as a normed space إذا
+
+324
+00:25:01,010 --> 00:25:05,750
+انضل علي أني أشوف ال X hat أن أعملها vector space
+
+325
+00:25:05,750 --> 00:25:09,010
+يعني معناته بدي أعرف scalar multiplication و بدي
+
+326
+00:25:09,010 --> 00:25:12,210
+أعرف اللي هو vector addition بالاستعانة بال X
+
+327
+00:25:12,210 --> 00:25:17,400
+الأصليةوالان اللى هى الشغله الثانيه ال isometric
+
+328
+00:25:17,400 --> 00:25:23,820
+اللى كان بين ال W و ال X اللى هى W و ال X كان جابل
+
+329
+00:25:23,820 --> 00:25:27,340
+اللى هو بس one to one one to function و preserves
+
+330
+00:25:27,340 --> 00:25:30,790
+the distance اللى هى preserves the normالان بده
+
+331
+00:25:30,790 --> 00:25:35,130
+شرط ثالث انه بده يحافظ على اللي هو الانصار اللي هي
+
+332
+00:25:35,130 --> 00:25:38,810
+ال isometric بين vector space و vector space اذا
+
+333
+00:25:38,810 --> 00:25:41,850
+بده ينقل عملية الجمع و عملية ال scalar
+
+334
+00:25:41,850 --> 00:25:45,610
+multiplication عشان يسميه isometry يعني بمعنى اخر
+
+335
+00:25:45,610 --> 00:25:52,750
+الان ال isometry T بين X لعين Wأول شيء Preserve
+
+336
+00:25:52,750 --> 00:25:55,150
+the norm أو Preserve the distance اللي قلناه المرة
+
+337
+00:25:55,150 --> 00:25:59,410
+الفاتة و one to one و one to two وهذا مثبت من قبل
+
+338
+00:25:59,410 --> 00:26:04,710
+الشيء الثاني يجب أن نثبت أن T تحافظ على Alpha X
+
+339
+00:26:06,420 --> 00:26:11,200
+زائد Y بتساوي اللي هو إيه شمالها اللي هو Alpha في
+
+340
+00:26:11,200 --> 00:26:16,840
+TX زائد TY يعني بتحافظ على العملية الجامعة ب
+
+341
+00:26:16,840 --> 00:26:20,760
+preserve the operation يعني بمفهوم اللي هو الجبر
+
+342
+00:26:20,760 --> 00:26:24,780
+الخط Linear اللي هو تكون T Linear و تحافظ على ال
+
+343
+00:26:24,780 --> 00:26:27,760
+scalar multiplication إذا هي اللي بدنا نسويه بس
+
+344
+00:26:27,760 --> 00:26:30,640
+احنا بدنا نكمل على اللي هو السابق خلينا نشوف مع
+
+345
+00:26:30,640 --> 00:26:36,000
+بعضطيب الآن by theorem 162 there is a complete
+
+346
+00:26:36,000 --> 00:26:39,600
+metric space X hat ال metric هنا اللي هو induced
+
+347
+00:26:39,600 --> 00:26:47,340
+by the norm there is a metric space X hat المقصود
+
+348
+00:26:47,340 --> 00:26:51,520
+أنه ال metric اللي بدو ييجي هنا اللي هو اعتمد على
+
+349
+00:26:51,520 --> 00:26:54,700
+ال metric اللي في ال X اللي هو اللي induced by the
+
+350
+00:26:54,700 --> 00:27:00,410
+normand an isometry a من x لعن و اللي سمناها في
+
+351
+00:27:00,410 --> 00:27:04,390
+حين و أيه اشمالها a of x و كنا عارفين كيف أرسلناها
+
+352
+00:27:04,390 --> 00:27:08,430
+راجعوا المحاضرة where a where w is dense in mean
+
+353
+00:27:08,430 --> 00:27:14,450
+in x hat and x hat أثبتناها as a is unique except
+
+354
+00:27:14,450 --> 00:27:19,380
+for isometriesطيب، الآن هذا الكلام كله من المحاضرة
+
+355
+00:27:19,380 --> 00:27:22,460
+السابقة وفصلنا تفصيل واخدنا محاضرة كاملة بيجي
+
+356
+00:27:22,460 --> 00:27:26,300
+حوالي ساعة و نص أو أكتر على البرهان النظرية الآن
+
+357
+00:27:26,300 --> 00:27:30,100
+بدنا نكمل بما يتعلق بال normed space بدأ أبدأ
+
+358
+00:27:30,100 --> 00:27:34,040
+أعرفلك اللي هو عملية جمع وعملية scalar
+
+359
+00:27:34,040 --> 00:27:36,920
+multiplication على مين على ال X hat عشان هذا أقولك
+
+360
+00:27:36,920 --> 00:27:41,620
+إن X hat هتمثل لي vector من S base طيب كيف بدأ
+
+361
+00:27:41,620 --> 00:27:49,290
+أعملها؟ عنديlet x hat و y hat element in x hat إذا
+
+362
+00:27:49,290 --> 00:27:52,310
+بتذكروا إحنا الـ x hat كانت عبارة عن equivalency
+
+363
+00:27:52,310 --> 00:27:55,390
+class اللي هي ال equivalency class كانت اللي هي في
+
+364
+00:27:55,390 --> 00:27:57,810
+داخلها أو اللي عامل اللي هي مين هي Cauchy
+
+365
+00:27:57,810 --> 00:28:00,470
+sequences وكلنا الـ Cauchy sequences اللي هي
+
+366
+00:28:00,470 --> 00:28:03,450
+العلاقة في بعض كان في نفس مين ال equivalency class
+
+367
+00:28:03,450 --> 00:28:07,530
+هذا كله شرحناه المرة الماضية الآن بتاخد أي x أنف
+
+368
+00:28:07,530 --> 00:28:10,230
+موجودة في الـ x hat sequence إنه equivalency class
+
+369
+00:28:10,750 --> 00:28:16,310
+الان وي ان وين موجودة في الـ y hat ماشي الان بدي
+
+370
+00:28:16,310 --> 00:28:21,530
+اعرف الان اللي هو احصل على اللي هي z hat مستوى x
+
+371
+00:28:21,530 --> 00:28:27,100
+hat زايد y hat كيف بدي احصلها ركزوا معاياالآن عندي
+
+372
+00:28:27,100 --> 00:28:30,560
+لو جيت لحظة تشوف الـ Cauchy Sequences الـ Zن تين
+
+373
+00:28:30,560 --> 00:28:35,420
+هدولة لو جمعتها لبعض وسمتها Zn إيش بيكون هدولة الـ
+
+374
+00:28:35,420 --> 00:28:39,760
+Zn الجديدة؟ بتكون الـ Zn عبارة عن Cauchy اللي هو
+
+375
+00:28:39,760 --> 00:28:43,460
+إيش Sequence ليش؟ لأن Xn Cauchy و Yn Cauchy
+
+376
+00:28:43,460 --> 00:28:46,020
+مجموعته Cauchy Sequences إيش هيطلع؟ Cauchy
+
+377
+00:28:46,020 --> 00:28:50,500
+Sequence إذا الآن Zn Cauchy Sequenceالان بما انه
+
+378
+00:28:50,500 --> 00:28:54,780
+زي ما بقولك XN and YN are Cauchy Sequences دين ZN
+
+379
+00:28:54,780 --> 00:28:59,640
+is a Cauchy Sequence الان define Z hat بتساوي X
+
+380
+00:28:59,640 --> 00:29:04,680
+hat زائد Y hat كيف؟ مين هي ال Z hat؟ هذه ال Z hat
+
+381
+00:29:04,680 --> 00:29:08,600
+اللي هي بدها تتحقق equivalency class اللي بدها
+
+382
+00:29:08,600 --> 00:29:12,740
+تتحدد هويتها بواسطة من ال ZN يعني ال Cauchy
+
+383
+00:29:12,740 --> 00:29:16,680
+Sequence اللي طلعت من المجموح هذه زائد هذهالـ
+
+384
+00:29:16,680 --> 00:29:21,240
+equivalence class تبعي تاخدها وسميها إيش مالها Z
+
+385
+00:29:21,240 --> 00:29:25,020
+hat إذا عملية الجمع صارت واضحة في ال X hat في ال X
+
+386
+00:29:25,020 --> 00:29:28,080
+hat عملية الجمع كده باجي باجمع باخد X hat
+
+387
+00:29:28,080 --> 00:29:32,470
+arbitrary هات و Y hat arbitrary هاتإنما بقول X hat
+
+388
+00:29:32,470 --> 00:29:36,970
+زائد Y hat إيش بيساوي Z hat طب مين Z hat هذه؟ هذه
+
+389
+00:29:36,970 --> 00:29:43,110
+Z hat L اللي هي بتساوي Zn اللي هي ال equivalence
+
+390
+00:29:43,110 --> 00:29:47,330
+class لها طب مين Zn هذه؟ Zn هي اللي ناتجة من
+
+391
+00:29:47,330 --> 00:29:52,370
+sequence من هنا زائد sequence من هنا إذن صارت الآن
+
+392
+00:29:52,370 --> 00:29:56,590
+اللي هي عملية الجمع تمدت على جمالية الجمع الأصلية
+
+393
+00:29:56,590 --> 00:29:59,430
+اللي بين اللي هي ال sequences L في ال space الأصل
+
+394
+00:29:59,430 --> 00:30:04,050
+هو ال Xهذا عملية الجمع الان طب هذه العملية ال well
+
+395
+00:30:04,050 --> 00:30:08,750
+defined يعني بمعنى آخر لو أنا أخدت xn و yn و جه
+
+396
+00:30:08,750 --> 00:30:12,990
+واحد تاني قال أنا بدي أخد wn موجودة في ال x hat و
+
+397
+00:30:12,990 --> 00:30:16,330
+kn موجودة في ال y hat و جيت جماعة تاني و طلع ليها
+
+398
+00:30:16,330 --> 00:30:20,690
+sequence هل هذه ال sequence هيكون ال equivalency
+
+399
+00:30:20,690 --> 00:30:25,070
+class لها نفس هذه أنا بقولك أه و عشان هيك بدي أكون
+
+400
+00:30:25,070 --> 00:30:28,010
+well defined وشوف كيف بدنا نثبت أنها well defined
+
+401
+00:30:28,010 --> 00:30:34,590
+اطلع لفوقطيب this definition is independent of the
+
+402
+00:30:34,590 --> 00:30:38,950
+choice of the Cauchy sequences in X hat and Y hat
+
+403
+00:30:38,950 --> 00:30:44,390
+ماشي نشوف كده in fact لو انت اخترت عشان الجامع
+
+404
+00:30:44,390 --> 00:30:48,930
+اللي قولنا عنه قبل شوية XN واخترت WN معناته
+
+405
+00:30:48,930 --> 00:30:51,870
+التنتين في نفس ال equivalence class معناته related
+
+406
+00:30:51,870 --> 00:30:55,180
+حسب ال relation اللي عرفناها المرة الماضيةو جيت
+
+407
+00:30:55,180 --> 00:31:00,420
+انت اخترت في ال Y hat YN و انا اخترت VN او WN او
+
+408
+00:31:00,420 --> 00:31:03,680
+اللي هي VN اللي هي طبعا مادامن في نفس ال
+
+409
+00:31:03,680 --> 00:31:06,760
+equivalency class اذا التنتين اشمالين related حسب
+
+410
+00:31:06,760 --> 00:31:11,200
+الخاصية او حسب العلاقة اللي عرفناها المرة الماضية
+
+411
+00:31:11,200 --> 00:31:15,140
+طيب طب هذولة متى بيكون ال XN لما تكون XN related
+
+412
+00:31:15,140 --> 00:31:18,880
+to WN ايش قلنا بيكون XN عرفنا ال relation المرة
+
+413
+00:31:18,880 --> 00:31:24,860
+الماضية related to WNفي حال كانت ال limit لل
+
+414
+00:31:24,860 --> 00:31:29,560
+distance بين ال Xn و ال Wn إيش هتساوي؟ هتساوي سفر
+
+415
+00:31:29,560 --> 00:31:32,420
+طب ما هي ال distance الآن إحنا بنحكي عن اللي هو
+
+416
+00:31:32,420 --> 00:31:36,880
+norm ال metric هذا اللي الآن induced by the norm
+
+417
+00:31:36,880 --> 00:31:41,200
+يعني بمعنى آخر norm ال Xn نقص Wn إيش هيساوي؟
+
+418
+00:31:41,200 --> 00:31:47,060
+limitه هيساوي سفر إذا لما Xnrelated to wn معناته
+
+419
+00:31:47,060 --> 00:31:54,280
+اصبح limit xn نقص wn بساوي سفر و limit yn نقص vn
+
+420
+00:31:54,280 --> 00:32:00,620
+بساوي سفر شوف الآناللي بدأ أصل إليه أنا بدأ أصل إن
+
+421
+00:32:00,620 --> 00:32:04,600
+جوابي و جوابكم نفس الاشي اللي هو عند Normal XN
+
+422
+00:32:04,600 --> 00:32:08,440
+زائد YN ناقص WN زائد VN هذا بالـ Triangling
+
+423
+00:32:08,440 --> 00:32:14,260
+Quality أصغر يساوي Normal XN ناقص WN زائد YN ناقص
+
+424
+00:32:14,260 --> 00:32:18,840
+من VNلأن بما أنه اللي هو التمتين هذوله في نفس ال
+
+425
+00:32:18,840 --> 00:32:21,560
+equivalency class زي ما قلنا إذا هذه as n goes to
+
+426
+00:32:21,560 --> 00:32:24,100
+infinity بتروح للصفر وهذه as n goes to infinity
+
+427
+00:32:24,100 --> 00:32:28,440
+بتروح للصفر بمعنى آخر هذه ال limit اللي هتروح لمين
+
+428
+00:32:28,440 --> 00:32:33,480
+للصفر يعني بمعنى آخر ال sequence ال Xn زي Yn اللي
+
+429
+00:32:33,480 --> 00:32:38,170
+اعتمدت عليه جوابهاللي هو و ال sequence هذه related
+
+430
+00:32:38,170 --> 00:32:41,950
+يعني بمعنى آخر التنتين في نفس ال equivalency class
+
+431
+00:32:41,950 --> 00:32:46,110
+يعني بمعنى آخر ال Z hat تبعته هي نفس ال Z hat
+
+432
+00:32:46,110 --> 00:32:49,910
+تبعتك لإن هدولة هيكون التنتين في نفس ال
+
+433
+00:32:49,910 --> 00:32:54,370
+equivalency class فبكون في هذه الحالة إنه فعلا ال
+
+434
+00:32:54,370 --> 00:32:58,470
+Z hat بيساوي X hat زي Y hat is well defined اطلع
+
+435
+00:32:58,470 --> 00:33:04,720
+لفوق شويةإذا نخلصنا من عملية الجمع اللي مبنية على
+
+436
+00:33:04,720 --> 00:33:10,900
+اللي عندنا Similarly بالنسبة لمين we define the
+
+437
+00:33:10,900 --> 00:33:16,500
+product Alpha X hat اللي هيكون element من X hat of
+
+438
+00:33:16,500 --> 00:33:20,340
+a scalar Alpha and X hat to be the equivalence
+
+439
+00:33:20,340 --> 00:33:23,800
+class for which Alpha X hat is representative إيش
+
+440
+00:33:23,800 --> 00:33:29,240
+يعني؟ يعني بنفس الطريقةعشان اعرف اللي هو شو معناته
+
+441
+00:33:29,240 --> 00:33:36,560
+اخد x hat element in x hat واخد alpha scalar بده
+
+442
+00:33:36,560 --> 00:33:40,940
+اعرف الآن عملية ال scalar multiplication في داخل
+
+443
+00:33:40,940 --> 00:33:45,530
+ال x hatوين رايح أنا عشان أثبت لكم إنه هذا X hat
+
+444
+00:33:45,530 --> 00:33:49,350
+هيطلع في vector space عرفنا الجامع والأن بنعرف مين
+
+445
+00:33:49,350 --> 00:33:54,450
+ال scalar multiplication الآن Alpha في ال X hat
+
+446
+00:33:54,450 --> 00:33:59,270
+بدي أعرفها عبارة عن اللي هي ال .. ال .. ال .. ال
+
+447
+00:33:59,270 --> 00:34:02,850
+.. طبعا مدامة ال X hat في ال X hat إذا أكيد في
+
+448
+00:34:02,850 --> 00:34:07,450
+sequence XN موجودة في ال X hatهذا اللي هي البنت
+
+449
+00:34:07,450 --> 00:34:09,290
+عليها ال equivalence class الـ Cauchy sequence
+
+450
+00:34:09,290 --> 00:34:14,070
+الان Alpha في Xn برضه هتطلع Cauchy sequence بدام
+
+451
+00:34:14,070 --> 00:34:18,090
+Xn الان ال Cauchy sequence هذه ال equivalence
+
+452
+00:34:18,090 --> 00:34:22,790
+class هي اللي بتسميها Alpha في مين؟ في X hatيعني
+
+453
+00:34:22,790 --> 00:34:26,910
+بمعنى أخر Alpha في X hat بدي أعرفها على أساس Alpha
+
+454
+00:34:26,910 --> 00:34:31,630
+في X لكل hat يعني هذه إيش بترمز؟ بترمز The set of
+
+455
+00:34:31,630 --> 00:34:36,150
+all equivalency classes اللي هي Alpha XN حيث XN is
+
+456
+00:34:36,150 --> 00:34:40,410
+a Cauchy sequence in X hat Similarly زي اللي قبل
+
+457
+00:34:40,410 --> 00:34:46,840
+بالظبط الآن هذه تحت هذا ال productSimilarly as in
+
+458
+00:34:46,840 --> 00:34:50,640
+the definition above nationalيد الطريقة المباشرة
+
+459
+00:34:50,640 --> 00:34:54,020
+of addition one can see that the definition of a
+
+460
+00:34:54,020 --> 00:34:57,240
+product is independent of the choice of
+
+461
+00:34:57,240 --> 00:35:02,760
+representative of etc يعني بمعنى أخر انت أخدتفي
+
+462
+00:35:02,760 --> 00:35:07,220
+الـ X hat XN كوشي سيكوانس وواحد تاني أخد YN في
+
+463
+00:35:07,220 --> 00:35:11,240
+الكوشي سيكوانس X hat هيطلع عند الألفة في ال XN
+
+464
+00:35:11,240 --> 00:35:14,180
+والألفة في ال YN ال equivalency classes انهم زي
+
+465
+00:35:14,180 --> 00:35:18,220
+بعض يعني بمعنى جوابي وجوابك زي بعض عشان هيك اللي
+
+466
+00:35:18,220 --> 00:35:22,400
+هو ال scalar multiplication برضه ايه شمالها is
+
+467
+00:35:22,400 --> 00:35:27,930
+well definedالان بالاستعانة
+
+468
+00:35:27,930 --> 00:35:37,110
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+469
+00:35:37,110 --> 00:35:39,430
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+470
+00:35:39,430 --> 00:35:40,370
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+471
+00:35:40,370 --> 00:35:40,630
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+472
+00:35:40,630 --> 00:35:40,650
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+473
+00:35:40,650 --> 00:35:40,710
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+474
+00:35:40,710 --> 00:35:41,370
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+475
+00:35:41,370 --> 00:35:42,230
+بالاستعانة بالاستعانة بالاستعانة بالاستعانة
+
+476
+00:35:42,230 --> 00:35:46,070
+بالاستعانة بالاستعانة بالاستعانة بالاستعانةانت
+
+477
+00:35:46,070 --> 00:35:50,830
+الآن لو جيت على حسب التعريف و جيت على كل خواص الـ
+
+478
+00:35:50,830 --> 00:35:54,490
+vector space هتلاقيها متحققة على العملية وهذه
+
+479
+00:35:54,490 --> 00:35:58,390
+بتظلها حسابات عندكم بتعملوها لحالكم اتحققوا العشر
+
+480
+00:35:58,390 --> 00:36:02,890
+شروط تبعات ال vector space يعني بمعنى اخر انا الآن
+
+481
+00:36:02,890 --> 00:36:07,330
+اثبتت ان X hat اشمالها is a vector space و الـ
+
+482
+00:36:07,330 --> 00:36:12,520
+zero elementللـ X hat is the equivalence class
+
+483
+00:36:12,520 --> 00:36:15,360
+contains all Cauchy sequences which converge to 0
+
+484
+00:36:15,360 --> 00:36:19,900
+منطقي، ليش؟ الآن الـ zero element هان الـ zero
+
+485
+00:36:19,900 --> 00:36:24,040
+element هان، بدي أسميه الـ zero hat مين الـ zero
+
+486
+00:36:24,040 --> 00:36:27,700
+hat؟ اللي هو اللي في ال equivalence class له Zero
+
+487
+00:36:27,700 --> 00:36:31,640
+Zero، Zero، Zero، هد Cauchy sequence ولا لأ؟ أكيد
+
+488
+00:36:31,640 --> 00:36:34,900
+Cauchy sequence اللي هن كل ال .. ال .. ال .. ال ..
+
+489
+00:36:34,900 --> 00:36:39,210
+Cauchy sequences اللي converge لـ Zeroconverge to
+
+490
+00:36:39,210 --> 00:36:43,230
+zero هيكون in hand فهادي اللي هي الـ zero hat
+
+491
+00:36:43,230 --> 00:36:47,990
+عبارة عن the set of all كوشي sequences that
+
+492
+00:36:47,990 --> 00:36:52,430
+converge to zero ماشي زي هذه فبكون هذا هو مين هو
+
+493
+00:36:52,430 --> 00:36:58,030
+الـ zero element اللي هو اللي لدك إذا صار عندي
+
+494
+00:36:58,030 --> 00:37:03,490
+land in X hat under these operations is a vector
+
+495
+00:37:03,490 --> 00:37:06,730
+space how؟ إلكم
+
+496
+00:37:09,170 --> 00:37:16,810
+الأن نيجي نشوف اللي هو زي ما وعدناكم بدنا اللي هو
+
+497
+00:37:16,810 --> 00:37:22,970
+نثبت انه اللي هو زي ما قلنا ال isometry في هذه
+
+498
+00:37:22,970 --> 00:37:27,630
+الحالة اللي هي التلت حالات اللي هي one to one و
+
+499
+00:37:27,630 --> 00:37:30,570
+one to two و preserve the distance اللي هي
+
+500
+00:37:30,570 --> 00:37:33,970
+preserve the norm اللي قلته سابقاً و الأخيرة اللي
+
+501
+00:37:33,970 --> 00:37:39,490
+هو linear بتثبت انه T اللي هو طبعا احنا بسميه AA
+
+502
+00:37:39,490 --> 00:37:43,430
+في Alpha X زائد Y بيسوا A Alpha في A X زائد مين A
+
+503
+00:37:43,430 --> 00:37:47,650
+في Y يعني بمعنى آخر برضه ب preserve the mean the
+
+504
+00:37:47,650 --> 00:37:56,890
+distances the operations طيب by using الان X هاد
+
+505
+00:37:56,890 --> 00:37:59,890
+under these operations قولنا vector space لان let
+
+506
+00:37:59,890 --> 00:38:06,020
+Alpha be an scalar and X وY any elements in Xثم
+
+507
+00:38:06,020 --> 00:38:10,900
+يوجد سيكوينس x1 و y1 في الـ x مثلًا مادان x و y في
+
+508
+00:38:10,900 --> 00:38:15,420
+الـ x إذا بقدر ألاقي x unconverged لل x و y
+
+509
+00:38:15,420 --> 00:38:21,220
+unconverged لمن؟ لل y ماشي الحال الان عندى ..
+
+510
+00:38:21,220 --> 00:38:26,980
+بتقولي كيف نلاقي؟وهو اللي فيه أسهل منها اخد مين؟
+
+511
+00:38:26,980 --> 00:38:30,660
+اخد الـ sequence X و X و X و X و X Converged للـ X
+
+512
+00:38:30,660 --> 00:38:33,780
+ولا لا؟ أكيد Converged للـ X وعصرها دولة من وين؟
+
+513
+00:38:33,780 --> 00:38:37,000
+من الـ X لأننا بدأت الـ X من وين؟ من الـ X ونفس
+
+514
+00:38:37,000 --> 00:38:40,540
+الشيء للـ Y إذا أكيد أكيد أكيد هلاقي اللي هو
+
+515
+00:38:40,540 --> 00:38:44,680
+Sequences X unconverged لل X و Y unconverged لل Y
+
+516
+00:38:44,680 --> 00:38:49,040
+وقلنا على سبيل المثال الـ sequence اللي فيها X X X
+
+517
+00:38:49,040 --> 00:38:56,050
+X هي متقدرة للعربالان let XN element in X hat و YN
+
+518
+00:38:56,050 --> 00:39:00,270
+element in Y hat اللي هي الـ X hat اللي هي
+
+519
+00:39:00,270 --> 00:39:06,460
+equivalence classesاللي related to x and الـ y hat
+
+520
+00:39:06,460 --> 00:39:09,560
+هي عبارة عن كل الـ sequences related للـ yn by
+
+521
+00:39:09,560 --> 00:39:12,180
+using the definition of scalar product and vector
+
+522
+00:39:12,180 --> 00:39:15,260
+addition اللي حكينا عنه قبل شوية in excel we have
+
+523
+00:39:15,260 --> 00:39:20,280
+نحسب الآن احسبلي الآن alpha في ax زائد a من ay
+
+524
+00:39:20,280 --> 00:39:27,200
+الان عندي بساوي ال a من وين جاية يا جماعة ال a
+
+525
+00:39:27,200 --> 00:39:32,220
+اللي هي هذهجاية من X لعند مين؟ W و الـ W إذا
+
+526
+00:39:32,220 --> 00:39:35,520
+بتتذكروا عملناها construction كانت سبسيط من مين؟
+
+527
+00:39:35,520 --> 00:39:40,500
+من X hat يعني عاصرها اللي هنا عبارة عن equivalency
+
+528
+00:39:40,500 --> 00:39:43,140
+classes اللي هنا يعني الصور هذه equivalency
+
+529
+00:39:43,140 --> 00:39:47,600
+classes إذا Alpha في AX اللي عبارة عن Alpha في X
+
+530
+00:39:47,600 --> 00:39:52,200
+hat ال X hat .. ال X hat ده .. ال A .. ال AX وين
+
+531
+00:39:52,200 --> 00:39:56,610
+هي تروح؟لـ Element في داخل الـ Main الـ W و الـ W
+
+532
+00:39:56,610 --> 00:39:59,730
+لما كنا أخدنا الـ Element أخدناها الـ Main كل ال
+
+533
+00:39:59,730 --> 00:40:03,850
+equivalency classes X و X و X و X و X ده بتتذكروا
+
+534
+00:40:03,850 --> 00:40:10,350
+يعني بمعنى أخر اللي هي ال A X هي نفسها مين ال X
+
+535
+00:40:10,350 --> 00:40:18,020
+hat هي عرفناها زائد A of Y مين هي ال Y hatجابل
+
+536
+00:40:18,020 --> 00:40:20,700
+بشوية من عملية الجامعة .. العملية الجامعة قلنا
+
+537
+00:40:20,700 --> 00:40:24,940
+alpha في x hat زائد y hat كله بيساوين alpha في x
+
+538
+00:40:24,940 --> 00:40:31,680
+زائد y كل ماله .. كل hat عرفنا عملية الجامعة جابل
+
+539
+00:40:31,680 --> 00:40:35,400
+بشوية ويساوي الآن هذا عبارة عن mean هذا اللي جوا
+
+540
+00:40:35,400 --> 00:40:38,600
+هو عبارة من تعريف ال function a هو عبارة عن a
+
+541
+00:40:38,600 --> 00:40:43,400
+alpha x زائد mean زائد yإذاً واضح إن الـ A is
+
+542
+00:40:43,400 --> 00:40:47,540
+linear يعني الـ A is an isometry that preserves
+
+543
+00:40:47,540 --> 00:40:50,620
+the algebraic operations isometry من المرة الفاتتة
+
+544
+00:40:50,620 --> 00:40:54,540
+وpreserves the algebraic operations إذاً صارت اللي
+
+545
+00:40:54,540 --> 00:41:01,780
+هي ال Wوالـ X زي بعض بس هدولة اللي هي اسم و هدولة
+
+546
+00:41:01,780 --> 00:41:04,480
+اللي هي اسم أخر لكن في one to one non to function
+
+547
+00:41:04,480 --> 00:41:08,220
+وفي اللي هو preserve the distance وفي preserve the
+
+548
+00:41:08,220 --> 00:41:13,980
+operations فكتو vector spaces اتن تين نفس الشيء
+
+549
+00:41:13,980 --> 00:41:19,300
+ولكن بالاسماء متغيرة اسم هناك هات وهنا اسم هنا أو
+
+550
+00:41:19,300 --> 00:41:22,140
+اسم هناك equivalence classes وهنا اسم هنا elements
+
+551
+00:41:22,140 --> 00:41:29,190
+اللي هي جزء من ال .. اللي هي اللي من ال Xطيب بدنا
+
+552
+00:41:29,190 --> 00:41:32,910
+أخر إشي ماحنا .. عن إيش احنا خلصنا احنا الآن هذه
+
+553
+00:41:32,910 --> 00:41:36,930
+vector space و خلصنا ال isometry ضال اللي هو ال X
+
+554
+00:41:36,930 --> 00:41:40,350
+hat بعد ما فبتناها vector space بده عرف عليها norm
+
+555
+00:41:40,350 --> 00:41:45,030
+بده عرف عليها norm شوف كده عرف عليها norm الآن أول
+
+556
+00:41:45,030 --> 00:41:52,050
+إشي احنا عارفين ال W جزء من مين؟ من ال X hat طيب
+
+557
+00:41:53,750 --> 00:41:57,650
+من المرة الماضية بقى ايضا عندي لان خلينا ناخد بس
+
+558
+00:41:57,650 --> 00:42:02,550
+هالشغل قبل for y hat بتساوي ay ال ay ايش بنسميها
+
+559
+00:42:02,550 --> 00:42:07,410
+احنا؟ y hat y hat مين هي؟ هي عبارة عن ال
+
+560
+00:42:07,410 --> 00:42:11,430
+equivalency classإذا بتتذكروا لما ركّبناها الـ Y
+
+561
+00:42:11,430 --> 00:42:17,230
+hat عبارة عن ال equivalency class ل S Y و Y و Y و
+
+562
+00:42:17,230 --> 00:42:21,150
+Y اللي converge ل من؟ ل الـ Zero ل الـ Yات اللي من
+
+563
+00:42:21,150 --> 00:42:25,430
+من؟ اللي من X ماشي هذا حكيناه المرة الماضية فالآن
+
+564
+00:42:25,430 --> 00:42:30,470
+Y hat بيساوي A Y we have بدنا نعرف النورم 1 هالمين
+
+565
+00:42:30,470 --> 00:42:37,330
+على Wكيف بده اعرفه Normal y hat على w بساوي Normal
+
+566
+00:42:37,330 --> 00:42:45,110
+mean ال y Normal y الان لاحظ لما انعرفت هناعند هذا
+
+567
+00:42:45,110 --> 00:42:51,350
+طبعا و هذا نورم كامل فعلى طول هذا هيحقق كل مين كل
+
+568
+00:42:51,350 --> 00:42:55,750
+خواص النورم الآن هذا معناته preserved distances
+
+569
+00:42:55,750 --> 00:42:59,710
+لأنه بيصير ال distance بين اللي هو اللي هي اللي
+
+570
+00:42:59,710 --> 00:43:04,630
+احنا عارفين ال distance preserved by من W ل X فهذه
+
+571
+00:43:04,630 --> 00:43:07,930
+اللي هي بتمثل ال distance بين Y هات و Zero هات
+
+572
+00:43:07,930 --> 00:43:12,760
+وهذه ال distance بين Y و Zeroو preserves في الأصل
+
+573
+00:43:12,760 --> 00:43:16,340
+لما أثبتناها المرة الماضية إذا ال norm بيساوي ال
+
+574
+00:43:16,340 --> 00:43:20,400
+norm مافيش فيها مشكلة الان the corresponding
+
+575
+00:43:20,400 --> 00:43:24,580
+metric on w is the restriction of d hat to w اللي
+
+576
+00:43:24,580 --> 00:43:27,300
+هو ال d hat لما عرفناها عرفته زي ما قلت قبل بشوية
+
+577
+00:43:27,300 --> 00:43:31,600
+المرة الماضية ال d hat اللي هي كان اللي هو عبارة
+
+578
+00:43:31,600 --> 00:43:37,200
+عن اللي أخدناها اللي هي ال preserve d hat of اللي
+
+579
+00:43:37,200 --> 00:43:42,730
+هي ayوأي element تاني أو العناصر اللي هنا بساوي ال
+
+580
+00:43:42,730 --> 00:43:46,850
+D بين العناصر اللي موجودة صورهم أو أصولهم اللي
+
+581
+00:43:46,850 --> 00:43:50,870
+موجودة في ال X إذاً هذا عندي صار عندي ال D هات
+
+582
+00:43:50,870 --> 00:43:59,230
+متلائم مع اللي اللي هو عرفناه اليومالآن بنقدر الآن
+
+583
+00:43:59,230 --> 00:44:03,750
+.. هذا الكلام كان عرفه عالمياً على اللي هو الـ W
+
+584
+00:44:03,750 --> 00:44:08,030
+بنعمله extension الآن بالاستعانة باللي احنا اللي
+
+585
+00:44:08,030 --> 00:44:13,850
+هي عملناها هذا اللي هو الجديد هذا هو عبارة عن لمن
+
+586
+00:44:13,850 --> 00:44:19,400
+متناسق مع الـ D hatعرّف للـ X عباق العناصر اللي
+
+587
+00:44:19,400 --> 00:44:22,680
+موجودة في الـ .. في الـ .. في الـ X hat ككل مش في
+
+588
+00:44:22,680 --> 00:44:25,960
+الـ W في الـ X hat عرّفه كالتالي الـ X hat 2
+
+589
+00:44:25,960 --> 00:44:30,300
+بيساوي ال distance hat بين 0 و 10 والـ X hat for
+
+590
+00:44:30,300 --> 00:44:34,840
+all X elements in X hatنورم الـ X2 هذا هتلاقي إيش
+
+591
+00:44:34,840 --> 00:44:37,500
+ما له نورم و هيحقق الشروط اللي إحنا بنعرفها
+
+592
+00:44:37,500 --> 00:44:41,720
+Therefore صار عندي X hat اللي هو صار عندي normed
+
+593
+00:44:41,720 --> 00:44:45,420
+space و vector space و من ثم normed space و كان
+
+594
+00:44:45,420 --> 00:44:50,950
+عندي ال isometry بين اللي هوالـ W والـ X بكل شروطه
+
+595
+00:44:50,950 --> 00:44:54,350
+اللي هي السابقة بالاضافة لـ Linearity تبعت اليوم
+
+596
+00:44:54,350 --> 00:44:58,450
+بكون حصلنا على الـ X hat is the third اللي هو
+
+597
+00:44:58,450 --> 00:45:03,730
+Space بكون هي كقولنا أو وصلنا انه every complete
+
+598
+00:45:03,730 --> 00:45:08,030
+.. every normed space can be completed وإلى لقاء
+
+599
+00:45:08,030 --> 00:45:09,490
+آخر السلام عليكم ورحمة الله
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/KVXWicAzB2A.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/KVXWicAzB2A.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ffad317603c2fbaed0bbaec92968e478e1730ba6
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/KVXWicAzB2A.srt
@@ -0,0 +1,3555 @@
+1
+00:00:05,210 --> 00:00:07,970
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,970 --> 00:00:11,030
+والصلاة والسلام على سيد المرسلين سيدنا محمد عليه
+
+3
+00:00:11,030 --> 00:00:15,530
+والصحابة أجمعين هذه هي المحاضرة رقم 13 مساق 
+
+4
+00:00:15,530 --> 00:00:19,670
+تحليل اقتراني أو تحليل دالي لطلاب وطالبات الجامعة
+
+5
+00:00:19,670 --> 00:00:25,240
+الإسلامية ماجستير رياضية وصلنا لعند الـ 2.7
+
+6
+00:00:25,240 --> 00:00:28,340
+اللي هو تحت عنوان bounded and continuous linear
+
+7
+00:00:28,340 --> 00:00:33,660
+operators لنتعرف على مفهوم اليوم مفهوم مهم وكمان
+
+8
+00:00:33,660 --> 00:00:38,660
+اللي هو بعض خواصه أو بعض النظريات اللي هتكون
+
+9
+00:00:38,660 --> 00:00:42,420
+ملازمة على طول الفصل اللي هي بما يتعلق شو معنى 
+
+10
+00:00:42,420 --> 00:00:46,770
+bounded linear operatorsالـ Bounded Linear
+
+11
+00:00:46,770 --> 00:00:50,110
+Operator احنا عرفناه المرة الماضية وعرفناه كمان في 
+
+12
+00:00:50,110 --> 00:00:53,190
+الجبر الخطي وبنعرفه بالأصل اللي هنعرفه شو معناه 
+
+13
+00:00:53,190 --> 00:00:56,230
+Bounded Linear Operator؟ وإيش معنى الـ 
+
+14
+00:00:56,230 --> 00:00:58,430
+Continuity؟ طبعًا احنا الـ Continuity بنعرفها شو
+
+15
+00:00:58,430 --> 00:01:01,670
+معناها الـ Continuity؟ بنعرفها بدنا نربط شو علاقة
+
+16
+00:01:01,670 --> 00:01:04,830
+الـ Continuous Linear Operator بالـ Bounded Linear
+
+17
+00:01:04,830 --> 00:01:07,610
+Operator وخلينا نشوف هذا الكلام بنجاوب عليه من 
+
+18
+00:01:07,610 --> 00:01:12,070
+خلال اللي هو حديثنا اليوم إن شاء الله الـ
+
+19
+00:01:12,070 --> 00:01:15,330
+Definition الأول لو كان عندي X و Y normed spaces
+
+20
+00:01:15,330 --> 00:01:21,150
+الاثنين على نفس الـ field الاثنين يا ريال يا اثنين أشمل
+
+21
+00:01:21,150 --> 00:01:25,290
+وكمبلكس والمرة الفاتتة قلنا ليش لأن let domain T
+
+22
+00:01:25,290 --> 00:01:29,010
+من domain of T لعند Y بيقى linear operator والـ
+
+23
+00:01:29,010 --> 00:01:33,390
+domain of T ده جزء من من اللي هو normed space X
+
+24
+00:01:33,390 --> 00:01:38,080
+طبعًا X عليها normها و Y عليها normها The operator T
+
+25
+00:01:38,080 --> 00:01:41,480
+is said to be bounded منقول عنه bounded linear
+
+26
+00:01:41,480 --> 00:01:45,660
+operator هذا عرفنا على مين؟ على linear operator
+
+27
+00:01:45,660 --> 00:01:50,920
+منقول عنه bounded if there is a number c such that
+
+28
+00:01:50,920 --> 00:01:56,200
+for all x element in domain of T norm TX أصغر
+
+29
+00:01:56,200 --> 00:02:03,380
+أو يساوي في مين؟ C في norm LX إذن الآن منقول عن T من
+
+30
+00:02:03,380 --> 00:02:08,560
+domain of T جزء من X طبعًا لعند Y إنه bounded إنه 
+
+31
+00:02:08,560 --> 00:02:13,900
+يتحقق TX normal طبعًا هذا normal موجود في Y أصغر أو
+
+32
+00:02:13,900 --> 00:02:18,560
+يساوي C في norm ال X الـ X طبعًا هو الموجود في domain 
+
+33
+00:02:18,560 --> 00:02:22,780
+of T أو الـ norm الموجود على اللي هي الـ X اللي كان
+
+34
+00:02:22,780 --> 00:02:26,320
+هذا الكلام يكون صحيح لكل x و m موجودة في الـ domain
+
+35
+00:02:26,320 --> 00:02:29,340
+of D إذا كان هذا صحيح معناته أنه على طول بنقول عن
+
+36
+00:02:29,340 --> 00:02:34,700
+الـ T إيش مالها is a bounded linear operator طبعًا
+
+37
+00:02:34,700 --> 00:02:37,800
+هذا الـ bounded linear operator بهذا التعريف والاسم
+
+38
+00:02:37,800 --> 00:02:41,760
+نفسه is standard كل الناس بتستخدمه وفي نفس الوقت
+
+39
+00:02:41,760 --> 00:02:46,170
+برضه الـ bounded functionالـ bounded as a function
+
+40
+00:02:46,170 --> 00:02:51,050
+برضه standard إذا كانت T بعتبرها as a function من
+
+41
+00:02:51,050 --> 00:02:54,930
+domain of T أو من اللي هي لعند X بقول a bounded
+
+42
+00:02:54,930 --> 00:02:58,590
+function أو لعند Y بنقول a bounded function مقصود
+
+43
+00:02:58,590 --> 00:03:01,810
+فيها في كل الـ functions سواء كان اللي هو عند A
+
+44
+00:03:01,810 --> 00:03:05,070
+اللي هي هذا known space أو vector space أو أو
+
+45
+00:03:05,070 --> 00:03:08,030
+الأخرين المهم يكون فيه topology بنقول عنه bounded
+
+46
+00:03:08,030 --> 00:03:13,470
+إذا كان T Xabsolute value أو norm أو اللي هو أصغر
+
+47
+00:03:13,470 --> 00:03:18,570
+أو يساوي اللي هو c for every x element in main in
+
+48
+00:03:18,570 --> 00:03:23,310
+domain of D هذا معناه bounded as a function احنا
+
+49
+00:03:23,310 --> 00:03:27,830
+الآن بنا .. وهذا standardالناس بتستخدمه وهذا ال
+
+50
+00:03:27,830 --> 00:03:31,290
+standard الناس بتستخدمه الآن احنا ال focusing
+
+51
+00:03:31,290 --> 00:03:35,850
+هنعمله على مين؟ على الـ bounded linear operator هذا 
+
+52
+00:03:35,850 --> 00:03:39,810
+معناته إيش ماله is a bounded linear operator هذي
+
+53
+00:03:39,810 --> 00:03:42,690
+is a bounded as a function عشان ما يشيرش confusion
+
+54
+00:03:42,690 --> 00:03:49,190
+عند الناس أو اللي هو أي التباس طيب نجي الآن نشوف 
+
+55
+00:03:49,190 --> 00:03:52,710
+إيش الملاحظة اللي .. الملاحظات اللي بحكيها Notes
+
+56
+00:03:52,710 --> 00:03:56,590
+الملاحظة الأولى The smallest c such that the above
+
+57
+00:03:56,590 --> 00:04:00,750
+inequality holds for all and zero excellent in
+
+58
+00:04:00,750 --> 00:04:05,590
+domain of T is defined as norm of T إيش بيقول؟
+
+59
+00:04:05,590 --> 00:04:09,990
+بيقول أنت مش بتقول bounded إذا لقينا c بحيث norm
+
+60
+00:04:09,990 --> 00:04:14,740
+of T X أصغر أو يساوي مين؟ C في مين؟ في norm of X الآن 
+
+61
+00:04:14,740 --> 00:04:19,340
+أصغر واحدة في الـ Cs هذول أصغر واحدة في الـ Cs اللي
+
+62
+00:04:19,340 --> 00:04:24,560
+هو بنسميه إيش؟ norm الـ T طب مين أصغر واحدة 
+
+63
+00:04:24,560 --> 00:04:29,900
+في الـ Cs هذه؟ الآن معناته إن norm الـ TX على norm
+
+64
+00:04:29,900 --> 00:04:33,240
+الـ X provided that الـ norm لا يساوي صفر أصغر أو
+
+65
+00:04:33,240 --> 00:04:37,140
+يساوي C بدي أصغر واحدة في الـ Cs هذه هذول الـ Cs
+
+66
+00:04:37,140 --> 00:04:40,800
+كلهم upper bound لهذه الـ set أصغر واحدة فين؟ إيش
+
+67
+00:04:40,800 --> 00:04:44,260
+هتكون؟ The least upper bound، اللي هو مين؟ بمعنى
+
+68
+00:04:44,260 --> 00:04:51,500
+آخر الـ Supremum لـ Normal T X على Normal X Such
+
+69
+00:04:51,500 --> 00:04:56,940
+that X element in domain of T ناقص مين؟ الصفر هذا
+
+70
+00:04:56,940 --> 00:05:00,420
+اللي هو الـ Supremum اللي هيطلع عن مين هو؟ عبارة
+
+71
+00:05:00,420 --> 00:05:08,270
+عن مين؟ Normal T الآن إذا كان domain الـ T بيساوي 0
+
+72
+00:05:08,270 --> 00:05:11,850
+يعني ما فيش فيه إلا الـ 0 domain الـ T الـ 0 إذا
+
+73
+00:05:11,850 --> 00:05:15,170
+أي function بتعملها عليها تنجل الـ 0 لمين؟ للـ 0
+
+74
+00:05:15,170 --> 00:05:19,610
+عشان تكون linear إذا هيكون بنعرف في هذه الحالة
+
+75
+00:05:19,610 --> 00:05:23,610
+norm الـ T إيش بيساوي؟ بيساوي 0 أما أي linear
+
+76
+00:05:23,610 --> 00:05:28,470
+operator domainه لا يساوي 0 على طول norm الـ T 
+
+77
+00:05:28,470 --> 00:05:33,250
+تبعته اللي هي الـ operator الـ norm لمين؟ لـ Operator 
+
+78
+00:05:33,250 --> 00:05:38,510
+اللي هو بيساوي هذا الكلام هذا اللي عندي norm الـ T
+
+79
+00:05:38,510 --> 00:05:43,210
+أنا مسميه norm الـ T هو في الواقع هيحقق شروط
+
+80
+00:05:43,210 --> 00:05:47,850
+الـ norm كلها عشان هيك اسمه بنسميه norm فهو فعلًا
+
+81
+00:05:47,850 --> 00:05:52,830
+هيعمل norm norm على مين؟ يعني الآن احنا وكأني قاعد
+
+82
+00:05:52,830 --> 00:05:56,590
+أنا ما احنا كنا نعمل norm norm احنا على مين؟ احنا 
+
+83
+00:05:56,590 --> 00:06:02,760
+بناخد X as a vector space و نعمل عليه مين؟ norm طب
+
+84
+00:06:02,760 --> 00:06:06,040
+هذا الـ norm على مين؟ أنا وكأني بقول the
+
+85
+00:06:06,040 --> 00:06:12,540
+collection of all bounded linear operators بعرف
+
+86
+00:06:12,540 --> 00:06:15,960
+عليه الـ norm المهم الآن طبعًا هذا جاين الكلام الآن 
+
+87
+00:06:15,960 --> 00:06:20,120
+هذا norm الـ T بعرف وأش بيساوي؟ بيساوي المقدار هذا طيب
+
+88
+00:06:20,120 --> 00:06:23,220
+from
+
+89
+00:06:23,220 --> 00:06:27,800
+the definition above من التعريف above norm الـ T X
+
+90
+00:06:30,910 --> 00:06:34,830
+احنا بنقول أصغر أو يساوي C في مين؟ في normal X
+
+91
+00:06:34,830 --> 00:06:40,950
+norm الـ T واحدة منهم مش الـ T the smallest one
+
+92
+00:06:40,950 --> 00:06:47,590
+هيكون عندي norm الـ T X أصغر أو يساوي norm الـ T في
+
+93
+00:06:47,590 --> 00:06:53,850
+مين؟ في norm الـ X ومن هنا كمان اللي هو norm الـ T في
+
+94
+00:06:53,850 --> 00:06:58,190
+X على norm الـ X هيكون اللي هو طبيعي أصغر أو يساوي 
+
+95
+00:06:58,190 --> 00:07:01,930
+مين؟ norm الـ T فأدور بالطرفين فبطلع norm الـ T X
+
+96
+00:07:01,930 --> 00:07:05,070
+أصغر أو يساوي C اللي هو norm الـ T في norm الـ X أي
+
+97
+00:07:05,070 --> 00:07:10,990
+سؤال؟ طيب الآن نيجي لل lemma الأولى اطلع لفوق 
+
+98
+00:07:10,990 --> 00:07:19,790
+بالله lemma الأولى إيش بتقول الـ lemma؟ لما بتقول
+
+99
+00:07:19,790 --> 00:07:24,450
+مرّة ثانية إنّه
+
+100
+00:07:24,450 --> 00:07:29,750
+let T من domain of T لعند الـ Y اللي قلت قبل
+
+101
+00:07:29,750 --> 00:07:36,940
+شوية be bounded linear operator ثم norm الـ T 
+
+102
+00:07:36,940 --> 00:07:40,660
+بيساوي supremum لـ T X X element in domain و T
+
+103
+00:07:40,660 --> 00:07:45,500
+وأخدت مين الآن؟ على normك لـ X بس إيش اللي بيساوي؟
+
+104
+00:07:45,500 --> 00:07:52,360
+واحد، بتدعي .. بتدعي إن هذا هيعمل لي norm و T
+
+105
+00:07:52,360 --> 00:07:56,720
+هيكون satisfied من واحد لعند أربعة يعني وكأنه بيقول 
+
+106
+00:07:56,720 --> 00:08:04,310
+لي في هذه النظرية إن norm الـ T بيساوي supremum لـ
+
+107
+00:08:04,310 --> 00:08:10,930
+Tx as a norm such that norm الـ X بتساوي واحد والـ X
+
+108
+00:08:10,930 --> 00:08:19,810
+في domain الـ T يكافئ الـ supremum لـ norm الـ Tx على
+
+109
+00:08:19,810 --> 00:08:28,830
+norm الـ X such that X element in domain of TX
+
+110
+00:08:28,830 --> 00:08:33,130
+element in domain of T وإثباته مش صعب لأن نثبت إنه
+
+111
+00:08:33,130 --> 00:08:36,610
+norm بده يحقق الأربع شروط والأربع شروط يعني اللي
+
+112
+00:08:36,610 --> 00:08:39,850
+هي سهلة يعني ما فيش فيها إشكالية الآن إنّه هذا
+
+113
+00:08:39,850 --> 00:08:47,030
+بيساوي هذا برضه اللي هو عنده لو أخدنا أي X في في
+
+114
+00:08:47,030 --> 00:08:51,610
+domain T هنلاقي اللي هو الـ X على normها موجود في 
+
+115
+00:08:51,610 --> 00:08:55,480
+domain T فلو سميتها y بيصير normal y هنا بيساوي 
+
+116
+00:08:55,480 --> 00:08:58,280
+واحد وعليه بتشتغلوا فبتقولوا هذا اللي هو أصغر
+
+117
+00:08:58,280 --> 00:09:00,980
+أو يساوي هذا وهذا أصغر أو يساوي هذا وبطلع اللي هي
+
+118
+00:09:00,980 --> 00:09:04,060
+المساواة المهم exercise عشان هي كانت سهلة بقول لكم
+
+119
+00:09:04,060 --> 00:09:11,770
+طيب بالنهاية هو الـ Example الـ Examples لن تثبت أنّ 
+
+120
+00:09:11,770 --> 00:09:17,250
+كلها مرتبطة لأن ما سيثبت من قدام الـ Boundedness
+
+121
+00:09:17,250 --> 00:09:20,410
+سيغنون عن هؤلاء الذين يشعرون أنّ هؤلاء سهلات
+
+122
+00:09:20,410 --> 00:09:25,050
+بالنسبة له وسيكونون على طول بالثبتين الآن Zero
+
+123
+00:09:25,050 --> 00:09:29,940
+Operator واحد من أمثلة اللي هو الـ Bounded Linear
+
+124
+00:09:29,940 --> 00:09:33,580
+Operator إيش الـ Zero Operator؟ الـ Zero Operator
+
+125
+00:09:33,580 --> 00:09:37,480
+زي Zero من X لعند Y on a normed space X is a
+
+126
+00:09:37,480 --> 00:09:41,320
+Bounded Linear Operator وإيش اللي هو الـ Zero
+
+127
+00:09:41,320 --> 00:09:44,620
+Operator؟ بياخد كل Element لـ X للصفر اللي هو هذا
+
+128
+00:09:44,620 --> 00:09:49,560
+norm وإيش هيطلع؟ عبارة عن صفر bounded أو linear الـ
+
+129
+00:09:49,560 --> 00:09:52,640
+linear اللي احنا حكينا المرة الفاتتة عن بعض الأمثلة
+
+130
+00:09:52,640 --> 00:09:56,680
+وهو إثباته إنّه linear سهل وإثباته bounded برضه
+
+131
+00:09:56,680 --> 00:10:02,450
+ما فيش فيه إشكالية اللي بعده خليني أشوف المثال اللي
+
+132
+00:10:02,450 --> 00:10:07,070
+بعده let x اللي بنسميه differentiation operator
+
+133
+00:10:07,070 --> 00:10:10,230
+differentiation operator خليني أبرهنّه وأوريكم
+
+134
+00:10:10,230 --> 00:10:15,090
+أمور البرهان سهلة إن شاء الله البرهان بقصد اللي
+
+135
+00:10:15,090 --> 00:10:19,710
+هو برهان اللي هي أنّ الـ operator اللي بنعرضه إنّه
+
+136
+00:10:19,710 --> 00:10:22,330
+bounded هناخدكم عدة أمثلة الآن ونبرهنها 
+
+137
+00:10:23,470 --> 00:10:27,310
+differentiation operator اللي هو let x be a norm
+
+138
+00:10:27,310 --> 00:10:30,670
+of the space of all polynomials أخدنا مين؟ اللي هو 
+
+139
+00:10:30,670 --> 00:10:35,530
+space of all polynomials on الفترة 0 و 1 والـ norm 
+
+140
+00:10:35,530 --> 00:10:38,490
+الـ X إيش بناخده؟ اللي هو الـ maximum اللي أخذناه 
+
+141
+00:10:38,490 --> 00:10:41,330
+قبل هيك هذا عملنا norm of the space عمليا اللي هو
+
+142
+00:10:41,330 --> 00:10:44,530
+اللي بيساوي طبعا هذه أخدت أنا مين؟ هي norm of the
+
+143
+00:10:44,530 --> 00:10:48,050
+space of all polynomials إذا بتذكر و أثبتنا أن هذا
+
+144
+00:10:48,050 --> 00:10:52,030
+مش complete الآن with the norm ال X بيساوي ال maximum
+
+145
+00:10:52,030 --> 00:10:54,750
+ال absolute value X of T, T element in J, the
+
+146
+00:10:54,750 --> 00:10:58,150
+differential operator T من X لعندي X، ده عارف
+
+147
+00:10:58,150 --> 00:11:02,190
+operator بياخد من X ل X، ايش بيسوي؟ بيجي اللي هو
+
+148
+00:11:02,190 --> 00:11:07,510
+بياخد أي element هنا إلى تفاضله، يعني بياخد أي T X
+
+149
+00:11:07,510 --> 00:11:10,790
+of T, ال X of T هذه يشملها polynomial، ايش بيساوي؟
+
+150
+00:11:10,790 --> 00:11:16,050
+صورتها X prime of T، is an unbounded linear operator
+
+151
+00:11:16,050 --> 00:11:19,650
+مثلًا على مين؟ على unbounded linear operator، نحن
+
+152
+00:11:19,650 --> 00:11:22,750
+ناخده لكم برضه على bounded linear operator، شوفوا
+
+153
+00:11:22,750 --> 00:11:25,850
+الآن كيف نثبت أنه unbounded linear operator؟ ال
+
+154
+00:11:25,850 --> 00:11:31,630
+linearity سهلة لو أثبتوها لحالكم بتنفع عشان
+
+155
+00:11:31,630 --> 00:11:37,150
+أورجيكم أن أنا فعلاً لما أقولكم سهلة هي سهلة، خدوا
+
+156
+00:11:37,150 --> 00:11:40,330
+الآن for all x, y element in X and all scalars
+
+157
+00:11:40,330 --> 00:11:44,200
+alpha، بدأ أثبتلكم أنها linear، ايش اللي هي T of α X 
+
+158
+00:11:44,200 --> 00:11:48,480
+زي Y، بدأت بتبت سواء α T X زي الـ T Y، هذا مناط
+
+159
+00:11:48,480 --> 00:11:53,260
+اللينيه، شوفوا الآن T of α X زي Y، شو معناته هذه؟
+
+160
+00:11:53,260 --> 00:11:58,300
+بترسل إلى α X زي Y prime of مين؟ لأن هذه عبارة عن
+
+161
+00:11:58,300 --> 00:12:00,820
+polynomial، لو هذه polynomial، لو Alpha مضروبة فيها
+
+162
+00:12:00,820 --> 00:12:05,480
+الاخره عبارة عن ال .. ال .. ال .. ال operator تبعي
+
+163
+00:12:05,480 --> 00:12:09,960
+وظيفته أن يفاضل هيك هو اللي هو صار عندي Alpha زياد
+
+164
+00:12:09,960 --> 00:12:14,320
+X وPrime T، وأنا بعرف ان الـ Linearity .. ال .. ال
+
+165
+00:12:14,320 --> 00:12:17,760
+.. التفاضل Linear، اللي هي بمعنى آخر بيصير Alpha في
+
+166
+00:12:17,760 --> 00:12:22,020
+X Prime of T زياد Y Prime of V of T، الأولى هي
+
+167
+00:12:22,020 --> 00:12:25,440
+عبارة عن Alpha T X والتاني عبارة عن T Y، معناته T
+
+168
+00:12:25,440 --> 00:12:28,380
+is Linear، إذا الموضوع سهل وما بدناش نظلنا .. اللي
+
+169
+00:12:28,380 --> 00:12:31,620
+هو .. نحكي فيه سرنا اللي هو تجاوزنا هذه المرحلة
+
+170
+00:12:31,620 --> 00:12:38,750
+احنا نيجي الآن هنثبت أن اللي هو unbounded، بدأ أثبت
+
+171
+00:12:38,750 --> 00:12:42,150
+لكم unbounded، بدأ أجيلكم sequence، احنا لازم نلاقي
+
+172
+00:12:42,150 --> 00:12:47,730
+ايش؟ عشان نثبت bounded، أن نثبت أن norm TX أصغر أو 
+
+173
+00:12:47,730 --> 00:12:52,850
+يساوي C في norm X، لكل X موجودة في domain T، بدأ
+
+174
+00:12:52,850 --> 00:12:57,170
+أجيلكم sequence أو جزء من هال Xات اللي هنا يستحيل
+
+175
+00:12:57,170 --> 00:13:01,490
+ينطبق عليها، مستحيل يجيلها C تنفع لهم كلهم، أو نلاقي
+
+176
+00:13:01,490 --> 00:13:06,250
+C اللي هو بتنفع أو نجيه لـ C مهما كانت كبيرة، تشوفوا
+
+177
+00:13:06,250 --> 00:13:12,710
+كيف؟ الأمر بسيط، let XN of T، ايش بتساوي؟ T أوسان
+
+178
+00:13:12,710 --> 00:13:17,290
+polynomial، مظهورة لا لا، polynomial البسيطة كمان، where
+
+179
+00:13:17,290 --> 00:13:21,350
+n element in N، ثم دور بالـ Xn، إيش هيساوي حسب اللي
+
+180
+00:13:21,350 --> 00:13:25,150
+احنا عارفينه اللي هو maximum لل Xn of T من ال Xn 
+
+181
+00:13:25,150 --> 00:13:29,070
+of T اللي هي T أس N، يعني بدي maximum لل T أس N لل
+
+182
+00:13:29,070 --> 00:13:32,790
+T اللي هو الموجودة في الـ J، والـ J إيش هي؟ ماخدينها
+
+183
+00:13:32,790 --> 00:13:38,330
+01، إذا ال maximum لل T أس N لكل T هنا، ال maximum
+
+184
+00:13:38,330 --> 00:13:46,730
+بيساوي واحد، إذا ال norm لكل ال Xn بيساوي واحد، إذا
+
+185
+00:13:46,730 --> 00:13:51,350
+ال norm هذه لكل ال Xn لجته بيساوي واحد
+
+186
+00:13:54,070 --> 00:13:59,450
+الآن شوفوا T XN، T XN ايش هو؟ normal بيساوي
+
+187
+00:13:59,450 --> 00:14:03,290
+ال maximum لأ، لأنه برضه في وين برمي؟ وين من
+
+188
+00:14:03,290 --> 00:14:08,430
+polynomial ل polynomial لنفس ال space اللي هو صورة
+
+189
+00:14:08,430 --> 00:14:10,850
+T XN اللي هي n في T XN نقص واحد، مش 
+
+190
+00:14:10,850 --> 00:14:16,320
+دقتها، الآن norm، ال maximum له هذا المقدار اللي هو
+
+191
+00:14:16,320 --> 00:14:21,500
+عندك ال T المقصة نقص واحد في T limited J، واحد اللي
+
+192
+00:14:21,500 --> 00:14:25,240
+هو maximum لها، وفي عندك N، إيش بدي يطلع؟ بسوءًا، إذا
+
+193
+00:14:25,240 --> 00:14:31,660
+طلع عندي norm T XN بسوءًا، معناته إن norm T XN
+
+194
+00:14:31,660 --> 00:14:36,260
+على XN ايش بيساوي؟ بسوءًا، لا يمكن بأي حال من
+
+195
+00:14:36,260 --> 00:14:42,380
+الأحوال أن اللي جيلنا C بحيث أن يكون norm الـ T X
+
+196
+00:14:42,380 --> 00:14:47,740
+N على Normal XN يكون أصغر أو يساوي C، لكل أنوية
+
+197
+00:14:47,740 --> 00:14:54,200
+موجودة في الـ N أو لكل XN موجودة في الـ Space، مين؟
+
+198
+00:14:54,200 --> 00:14:59,160
+مش ممكن، لأن الـ N إيش هنا عندي؟ هذا طلع ايش بتساوي؟
+
+199
+00:14:59,160 --> 00:15:03,860
+بيساوة N، فش C تكون أكبر من الـ N زي اللي في الدنيا
+
+200
+00:15:03,860 --> 00:15:07,360
+لأ، لإن احنا بنعرف أصلا The set of all natural
+
+201
+00:15:07,360 --> 00:15:13,670
+numbers is unbounded، هذا اللي هو بناء عليه لا يمكن
+
+202
+00:15:13,670 --> 00:15:17,790
+إيجاد such C، إذا therefore T is not bounded، إذا
+
+203
+00:15:17,790 --> 00:15:24,350
+هذا مثال على Unbounded Linear Operator، اطلع لفوق
+
+204
+00:15:24,350 --> 00:15:29,450
+الآن Integral Operator، لناخد T برضه من ال
+
+205
+00:15:29,450 --> 00:15:31,990
+continuous functions لل continuous functions كلها
+
+206
+00:15:33,970 --> 00:15:38,070
+be defined by T X of T بيساوية ال integration من
+
+207
+00:15:38,070 --> 00:15:42,910
+صفر لعين لواحد K of T وTau X of Tau D من D Tau
+
+208
+00:15:42,910 --> 00:15:45,970
+where K اللي هي هذه is a continuous, is a given
+
+209
+00:15:45,970 --> 00:15:47,870
+continuous function، يعني اللي كنا نسميه kernel
+
+210
+00:15:47,870 --> 00:15:51,590
+زمان في المعادلة التكاملية أو المعادلة التفاضلية
+
+211
+00:15:51,590 --> 00:15:58,000
+هذا الآن عندي اللي هي دالة متصلة، اللي هي دالة متصلة
+
+212
+00:15:58,000 --> 00:16:03,080
+معينة K، الآن صورة X of T هي عبارة عن ال
+
+213
+00:16:03,080 --> 00:16:06,380
+integration من صفر إلى واحد للدالة اللي أنا أخدتها
+
+214
+00:16:06,380 --> 00:16:11,060
+اللي نسميها kernel، مضروبة في مين؟ في ال X اللي هي
+
+215
+00:16:11,060 --> 00:16:15,560
+اللي بدأت أكملها of Tau، دي مين؟ Tau، يعني هي دي
+
+216
+00:16:15,560 --> 00:16:18,320
+function of two variables، وأنا ما عطيكم أن دي
+
+217
+00:16:18,320 --> 00:16:22,950
+continuous function، ماشي الحال، continuous على اللي
+
+218
+00:16:22,950 --> 00:16:25,550
+هي طبعا هذه واضح أن هي function of two variables
+
+219
+00:16:25,550 --> 00:16:29,810
+continuous على الـG cross G، معايا عشان اضمن أن
+
+220
+00:16:29,810 --> 00:16:32,450
+هذه متصلة، وهذه متصلة، إذا الـTin-Tin متصلات
+
+221
+00:16:32,450 --> 00:16:35,350
+بالنسبة لتاو اللي بده كامل إليها، معناته التكامل
+
+222
+00:16:35,350 --> 00:16:40,530
+المضمون أن ايش ماله؟ موجود، طيب إذا صارت هذه T X of
+
+223
+00:16:40,530 --> 00:16:46,250
+T بسوء كده، اللي هو فعلا شيء اللي هو معرف تعريفا
+
+224
+00:16:46,250 --> 00:16:51,540
+تماما، which is called the kernel on D of T، مش مشكلة
+
+225
+00:16:51,540 --> 00:16:55,500
+هذه، then T is a bounded linear operator، ليها مثال
+
+226
+00:16:55,500 --> 00:16:59,940
+عالعمين a bounded linear operator، اطلع على فوق، اطلع
+
+227
+00:16:59,940 --> 00:17:04,940
+على فوق، الآن نيجي نشوف، طبعا احنا ال C01 اتفاجنا ال
+
+228
+00:17:04,940 --> 00:17:10,400
+C01 عبارة عن ال space، ال norms space، ال continuous
+
+229
+00:17:10,400 --> 00:17:13,480
+functions، مين ال normal اللي عليه؟ ال maximum، ماشي
+
+230
+00:17:13,480 --> 00:17:16,180
+ال normal اللي عليه ال maximum، وهذا ال space
+
+231
+00:17:16,180 --> 00:17:22,500
+complete، بالمناسبة، اه، طيب، for all x, y elements in C0
+
+232
+00:17:22,500 --> 00:17:22,980
+,1
+
+233
+00:17:50,230 --> 00:17:53,270
+الـ Scale of Multiplication و الـ Additivity اللي
+
+234
+00:17:53,270 --> 00:17:56,490
+هو الـ Integration بتوزع عليها و يساوي هذه اللي هي
+
+235
+00:17:56,490 --> 00:18:02,410
+TX و التانية TY، إذا صارت اللي هو T is Linear، الآن
+
+236
+00:18:02,410 --> 00:18:05,830
+بتثبتلكم أن اللي هو ال .. ال .. ال .. ال operator
+
+237
+00:18:05,830 --> 00:18:11,990
+اللي عندنا اللي هو TX، TX بيساوي ال Integration من
+
+238
+00:18:11,990 --> 00:18:19,070
+صفر اللي عندي واحد K T و Tau X of TauD τاو، انها
+
+239
+00:18:19,070 --> 00:18:24,470
+ايش معناها؟ is bounded، يعني بمعنى آخر norm ال TX
+
+240
+00:18:24,470 --> 00:18:30,350
+على norm ال X أصغر يساوي some C، نشوف ايش هي ال C
+
+241
+00:18:30,350 --> 00:18:35,110
+اللي بحكي عنها، صلى على النبي عليه الصلاة والسلام
+
+242
+00:18:35,110 --> 00:18:41,160
+نيجي الأن أول شيء عندي اللي هو الـ Kernel الـ
+
+243
+00:18:41,160 --> 00:18:47,000
+Kernel اللي هو الـ K of K، الـ K هذه is continuous
+
+244
+00:18:47,000 --> 00:18:50,720
+على closed bounded square G، اللي اتفاجنا أنّه
+
+245
+00:18:50,720 --> 00:18:54,120
+معرفين على G cross G و G اللي هو عبارة عن اللي هي
+
+246
+00:18:54,120 --> 00:18:57,320
+closed interval، و G cross G بيصير bounded closed
+
+247
+00:18:57,320 --> 00:19:02,350
+اللي هي ايش؟ square، إذن بمعنى آخر continuous على
+
+248
+00:19:02,350 --> 00:19:07,470
+closed bounded region، إذن أكيد هتكون اللي هي ال K
+
+249
+00:19:07,470 --> 00:19:12,390
+نفسها bounded، نظرية دي اللي بدكم، then K is bounded
+
+250
+00:19:12,390 --> 00:19:16,310
+ماشي الحال، as a function that is there is C أكبر
+
+251
+00:19:16,310 --> 00:19:19,530
+من صفر such that ال absolute value لل K of T وTau
+
+252
+00:19:19,530 --> 00:19:23,190
+أصغر أو يساوي مين؟ أصغر أو يساوي C على كل المنطقة
+
+253
+00:19:23,190 --> 00:19:26,610
+المعرفة عليها لإنها continuous على closed bounded
+
+254
+00:19:26,610 --> 00:19:32,680
+region، furthermore، ال absolute value لل X of T اللي
+
+255
+00:19:32,680 --> 00:19:35,980
+هي أكيد واحدة منهن أصغر أو يساوي ال maximum عليهم
+
+256
+00:19:35,980 --> 00:19:40,300
+كلهن عالميا عند ال T معينة، X of T عند T معينة أصغر
+
+257
+00:19:40,300 --> 00:19:43,440
+أو يساوي ال maximum، يعني بمعنى آخر ال X of T أكيد
+
+258
+00:19:43,440 --> 00:19:49,950
+أصغر أو يساوي من normها، يعني الآن X of TX of T هذه
+
+259
+00:19:49,950 --> 00:19:53,530
+أصغر أو يساوي Normal X، لأن Normal X هو ال maximum
+
+260
+00:19:53,530 --> 00:19:59,410
+لكل هذولة، معناه أن Normal X أكبر يساوي X of T لكل
+
+261
+00:19:59,410 --> 00:20:04,950
+T في الفترة 0 و 1 اللي بشتغل عليها، إذا خذوا
+
+262
+00:20:04,950 --> 00:20:08,690
+المعلومتين، المعلومة باتجاه ال kernel، والمعلومة
+
+263
+00:20:08,690 --> 00:20:13,900
+باتجاه X of T، هننسى الآن ال .. الـ norm لـ T of
+
+264
+00:20:13,900 --> 00:20:17,300
+X ايش بيساوي؟ الـ TX ما هي برمي وين؟ برضه في ال
+
+265
+00:20:17,300 --> 00:20:20,580
+continuous، إذن هيطلع عبارة عن .. طبعا هذه function
+
+266
+00:20:20,580 --> 00:20:25,680
+of V، هتطلع of T، تاوة هتطلع اللي هي عدد .. هت ..
+
+267
+00:20:25,680 --> 00:20:28,640
+هتروح .. إذن هتبقى لها function في مين بس؟ في T
+
+268
+00:20:28,640 --> 00:20:33,300
+إذن الآن norm الـ TX أو الـ TX بيساوي، هذا norm هو
+
+269
+00:20:33,300 --> 00:20:37,640
+ال maximum للقيمة هذه على الـ T اللي وين ما لها
+
+270
+00:20:37,640 --> 00:20:41,930
+الـ Ts اللي موجودة في الـ J، اللي هي أكيد أصغر أو
+
+271
+00:20:41,930 --> 00:20:45,550
+يساوي، بما أن هذا absolute value أصغر أو يساوي ال
+
+272
+00:20:45,550 --> 00:20:49,010
+integration لل absolute value صح؟ أصغر أو يساوي ال
+
+273
+00:20:49,010 --> 00:20:51,130
+integration، ال absolute value في ال absolute value
+
+274
+00:20:51,130 --> 00:20:56,150
+الآن هذه من فوق أثبتت أنها أشمالها أصغر أو يساوي C
+
+275
+00:20:56,150 --> 00:21:00,710
+وهذه أصغر أو يساوي 100، اللي هو اللي هو النور،
+
+276
+00:21:00,710 --> 00:21:05,570
+مظبوط؟ معايا، هايها ال X و T أصغر أو أصغر منين؟ ال
+
+277
+00:21:05,570 --> 00:21:09,830
+norm، إذا بشيل هذه بحط مكانها ال C، وهذه بشيلها بحط
+
+278
+00:21:09,830 --> 00:21:13,910
+مكانها اللي هو ال norm، فبصير ال integration اللي
+
+279
+00:21:13,910 --> 00:21:17,310
+هو هذا أصغر أو أصغر منين؟ ال integration C في Norm
+
+280
+00:21:17,310 --> 00:21:21,430
+ال X، بطلع برا برضه لأنه عدد، من Zero ل واحد دي Tau 
+
+281
+00:21:21,430 --> 00:21:25,050
+ومن Zero لواحد دي Tau إيش قيمته واحد إلا إذا بصير
+
+282
+00:21:25,050 --> 00:21:30,090
+C في Norm ال X يعني بمعنى آخر أثبتت الآن أن Norm
+
+283
+00:21:30,090 --> 00:21:37,080
+ال TX أصغر أو يساوي C في Norm ال X لكل X وين
+
+284
+00:21:37,080 --> 00:21:41,400
+موجودة في Domain T وهذا يعني أن T is bounded أي
+
+285
+00:21:41,400 --> 00:21:49,180
+سؤال المفروض أن الكلام بدأ يحلو يعني نيجي الآن
+
+286
+00:21:49,180 --> 00:21:59,620
+نشوف اللي هو نعرف Function من Rn لعند Rm بالاستعانة
+
+287
+00:21:59,620 --> 00:22:03,180
+.. وهذا مثال موجود في الجبر الخطي بالاستعانة ..
+
+288
+00:22:03,180 --> 00:22:07,000
+بالاستعانة بالـ matrix اللي بيحول ال element من
+
+289
+00:22:07,000 --> 00:22:11,720
+هنا إلى element وين في الـ Rm النورم اللي على
+
+290
+00:22:11,720 --> 00:22:15,520
+الـ قرار نعرفينه اللي هو الجذر التربيعي x1 تربيع زائد
+
+291
+00:22:15,520 --> 00:22:20,920
+x2 تربيع زائد xn تربيع لأن عناصرها إيش هذه؟ x1, x2,
+
+292
+00:22:21,020 --> 00:22:26,840
+x3 و xn هذه عناصرها x1, x2, x3 و xm إذا Normها هذا
+
+293
+00:22:26,840 --> 00:22:31,580
+هو الجذر التربيعي لـ x1 تربيع زائد x2 تربيع زائد xn
+
+294
+00:22:31,580 --> 00:22:34,970
+تربيع وهذه كانت Normها مشابه اللي هم بيقولي لو
+
+295
+00:22:34,970 --> 00:22:38,110
+أخذنا Matrix هذا الـ Matrix الـ Real Matrix اللي
+
+296
+00:22:38,110 --> 00:22:42,390
+هو أداة تعريف الـ .. الـ .. الـ .. الـ Function اللي
+
+297
+00:22:42,390 --> 00:22:45,490
+عندي أو ال Operator اللي عندي أخدت A بتساوي Alpha
+
+298
+00:22:45,490 --> 00:22:50,990
+J K بـ M by N Matrix M by N عشان يناسب مين اللي هو
+
+299
+00:22:50,990 --> 00:22:55,270
+في حالة الضرب اللي هو ال Rn و ال Rm و ينجلي من Rn
+
+300
+00:22:55,270 --> 00:23:02,660
+لمين لعند Rm Defined by TX ايش بساوي FX الـ X من وين
+
+301
+00:23:02,660 --> 00:23:06,940
+عبارة عن Element اللي هو XI واحد و XI اثنين و XI N
+
+302
+00:23:06,940 --> 00:23:11,600
+ماشي الحل الآن بقولك إذا T is a bounded linear
+
+303
+00:23:11,600 --> 00:23:14,640
+operator إذا الـ Linear و A شماله bounded خلينا
+
+304
+00:23:14,640 --> 00:23:21,290
+نشوف لكل x و y Element in Rn and all scalars α T of
+
+305
+00:23:21,290 --> 00:23:25,430
+α x زائد y إيش بيساوي؟ بيساوي هذا ولا طبعا هذا
+
+306
+00:23:25,430 --> 00:23:28,790
+اللي هو عبارة عن Element في Rn وهذا Element في Rn
+
+307
+00:23:28,790 --> 00:23:32,290
+هذا ال A matrix اشمله M by N matrix خلينا نجوّه
+
+308
+00:23:32,290 --> 00:23:39,990
+عشان ال A عبارة عن ألف واحد واحد لما نقصل M by N
+
+309
+00:23:39,990 --> 00:23:45,550
+أكم عمود N من الأعمدة لعند Alpha 1 N مظبوط و بمشي
+
+310
+00:23:45,550 --> 00:23:52,490
+من هنا Alpha M 1 لعند Alpha M N هاي ال matrix اللي
+
+311
+00:23:52,490 --> 00:23:58,530
+عندي مش الحال الآن هذا ال matrix بدي أضربه في اللي
+
+312
+00:23:58,530 --> 00:24:06,110
+هو مين عندي T من R N لعند RM بسمحولي بس أكتب على
+
+313
+00:24:06,110 --> 00:24:08,970
+صورة أعمدة اللي هي ال RN اللي هي اللي في ال RN
+
+314
+00:24:08,970 --> 00:24:14,810
+اللي هو عبارة عن Xi 1 لعند Xi N بدها ترمي وين؟ في
+
+315
+00:24:14,810 --> 00:24:21,910
+جامعة 1 لمين؟ لجامعة M ماشي؟ شوفوا الآن T
+
+316
+00:24:25,140 --> 00:24:31,940
+T of هذه الـ X التي هي XI واحد لعند XI N ما هي
+
+317
+00:24:31,940 --> 00:24:37,400
+ساوي الماتريكس هذا مضروب في XI واحد لعند XI N
+
+318
+00:24:37,400 --> 00:24:43,810
+معايا عملية الضرب هذا هيجيب ال element كله وبعدين
+
+319
+00:24:43,810 --> 00:24:46,210
+هذا هيجيب ال element لما أصل للأخر بيجيب ال
+
+320
+00:24:46,210 --> 00:24:49,930
+element أما كم element هنجيب M من ال elements هذا
+
+321
+00:24:49,930 --> 00:24:53,710
+هيجيب واحد هذا اثنين العديش لما أصل عند ال M إذا
+
+322
+00:24:53,710 --> 00:25:01,230
+هيطلع عندي عبارة عن جامعة واحد عند جامعة إذا فعلاً
+
+323
+00:25:01,230 --> 00:25:04,710
+هذا اللي هو بيعمل ليه Linear operator من A بيعمل
+
+324
+00:25:04,710 --> 00:25:08,390
+ليه Operator من RN لعند RM Linear اه Linear ليش
+
+325
+00:25:08,390 --> 00:25:11,930
+Linear لأن لو أخدت T of Alpha X زائد Y تنسوش أن
+
+326
+00:25:11,930 --> 00:25:16,130
+هذا Matrix وهذا Matrix كلهم Matrix الآن إيش هيساوي
+
+327
+00:25:16,130 --> 00:25:21,410
+حسب القانون A matrix في هدولة Alpha scalar ماشي
+
+328
+00:25:21,410 --> 00:25:24,570
+الحال في ضرب ال matrices ال alpha ال scalar بتطلع
+
+329
+00:25:24,570 --> 00:25:27,190
+برا عن المشترك بتظهر اللي هو A في X و بقى دي A في
+
+330
+00:25:27,190 --> 00:25:32,030
+Y اللي هو عبارة عن AX اللي هو ال TX وال AY ال TY
+
+331
+00:25:32,030 --> 00:25:36,580
+إذا صارت عبارة عن Linear operator طيب لأن .. الـ ..
+
+332
+00:25:36,580 --> 00:25:41,060
+ضال عليا أستخدم مين الآن؟ أثبت مين؟ أثبت أنه is
+
+333
+00:25:41,060 --> 00:25:44,920
+bounded بدي أستخدم في .. في أثبات ال boundedness
+
+334
+00:25:44,920 --> 00:25:48,320
+الكوشي شوارتز Inequality مذاكرين الكوشي شوارتز Inequality ال
+
+335
+00:25:48,320 --> 00:25:53,340
+summation xi i gamma i أصغر أو يساوي ال summation
+
+336
+00:25:53,340 --> 00:25:59,520
+xi i تربيع الكل أس نص في ال summation gamma i
+
+337
+00:25:59,520 --> 00:26:03,850
+تربيع الكل أس نص ليه استخدمها؟ خلينا نشوف
+
+338
+00:26:03,850 --> 00:26:06,670
+إيش اللي .. إيش .. إيش اللي بدي أعمله الموضوع
+
+339
+00:26:06,670 --> 00:26:10,990
+حسابات الآن وحسابات سهلة إن شاء الله خدوا الآن زي
+
+340
+00:26:10,990 --> 00:26:14,650
+ما قلنا خدوا أي X موجودة في ال Domain الـR of T هي
+
+341
+00:26:14,650 --> 00:26:19,450
+Column Matrix أخدته Xi واحد and Xi N وحسبوه لنورم
+
+342
+00:26:19,450 --> 00:26:22,390
+الـ TX اللي هو تربيع عشان اللي هو تسهيل عملية
+
+343
+00:26:22,390 --> 00:26:26,870
+الحسابات أخدت التربيع بساوي Norm الـ X الكل تربيع
+
+344
+00:26:26,870 --> 00:26:32,270
+لأن الـ TX مش بساوي A في X الكل تربيع الآن AX هي ال
+
+345
+00:26:32,270 --> 00:26:36,310
+A وهي ال X نضربهم نضرب اللي هو السطر الأول في
+
+346
+00:26:36,310 --> 00:26:40,430
+العمود الأول بيطلع Summation للضرب هذا اه اللي هو
+
+347
+00:26:40,430 --> 00:26:44,570
+بيطلع الـ .. اطلع لفوق شوية لفوق شوية اه بس خلي بس
+
+348
+00:26:44,570 --> 00:26:48,570
+يظهر هنا بيطلع ال Summation الأول Summation اللي هو
+
+349
+00:26:48,570 --> 00:26:52,170
+السطر الأول في العمود الأول في العمود نفسه هاي ال
+
+350
+00:26:52,170 --> 00:26:55,870
+entry الأول الآن ال Summation هذا العمود الثاني في
+
+351
+00:26:55,870 --> 00:26:59,210
+السطر الثاني في العمود اللي عندي هاي و بيطلع لما
+
+352
+00:26:59,210 --> 00:27:03,950
+أصل لأخر واحد اللي هو بيجيب هذا طيب هذول الآن
+
+353
+00:27:03,950 --> 00:27:08,230
+عبارة عن Gamma 1 و Gamma 2 و Gamma 3 و Gamma M إيش
+
+354
+00:27:08,230 --> 00:27:11,870
+Form هنا بشغل في الأرقام الآن اللي هو تربيع هذا و
+
+355
+00:27:11,870 --> 00:27:15,470
+تربيع هذا و تربيع هذا و كل إنترحت مين الجذر و بجمعها
+
+356
+00:27:15,470 --> 00:27:19,920
+صح بجمعها و أخذ إنترحت الجذر معايا كيف؟ بصير الآن
+
+357
+00:27:19,920 --> 00:27:24,000
+عبارة عن Summation مجموع هذا اللي هو لكل واحد
+
+358
+00:27:24,000 --> 00:27:30,200
+تربيع آسف اه هنا اللي هي هذا تربيع اه و هذا تربيع
+
+359
+00:27:30,200 --> 00:27:33,700
+و هذا تربيع و هذا تربيع و بعدين ماله بجمعها و الكل
+
+360
+00:27:33,700 --> 00:27:38,140
+تحت الجذر من مناخ التربيع فاهمين اه؟ اللي هو هذا
+
+361
+00:27:38,140 --> 00:27:41,800
+أصغر أو يساوي بالـ Schwarz Inequality بدي أطبقها
+
+362
+00:27:41,800 --> 00:27:44,620
+على اللي جوا على هذه ال Schwarz Inequality هذه
+
+363
+00:27:44,620 --> 00:27:49,700
+تربيع أس نص تربيع أس نص وهذه تربيع أس نص والباقي
+
+364
+00:27:49,700 --> 00:27:54,580
+فوق أيضا إيش ماله تربيع معايا واضح هذا أصغر أو
+
+365
+00:27:54,580 --> 00:27:58,420
+يساوي الآن لو جينا شوفنا هذه هذه بتمثل مين يا جماعة
+
+366
+00:27:58,420 --> 00:28:02,970
+اللي جوا Norm X صح ولا لأ وهي فيه تربيع بتطلع
+
+367
+00:28:02,970 --> 00:28:06,770
+Norm X ماله تربيع بيظل ال Summation لل Summation
+
+368
+00:28:06,770 --> 00:28:10,450
+لأن هذا ثابت بيصير بيطلع برا فبيصير Norm X تربيع
+
+369
+00:28:10,450 --> 00:28:14,530
+في ال Summation اللي عند Double Summation هذا في
+
+370
+00:28:14,530 --> 00:28:18,850
+النهاية عدد لأن هذا من هو هذا جاي من ال matrix
+
+371
+00:28:18,850 --> 00:28:22,150
+اللي أنا استخدمته في تعريف الدالة يعني إيش محدد
+
+372
+00:28:22,150 --> 00:28:26,110
+يعني هيكون عبارة عن إيش قيمة عددية إذا صار عندي
+
+373
+00:28:26,110 --> 00:28:31,670
+Norm TX تربيع أصغر أو يساوي Norm X تربيع في مين؟
+
+374
+00:28:31,670 --> 00:28:36,850
+في some constant C يلا
+
+375
+00:28:36,850 --> 00:28:40,470
+اللي بعده اطلع لفوق اطلع لفوق فبيصير عندي Norm T
+
+376
+00:28:40,470 --> 00:28:43,370
+X تربيع أصغر أو يساوي اللي هو C تربيع في Norm X
+
+377
+00:28:43,370 --> 00:28:45,710
+حيث و C تربيع بيساوي ال Summation اللي قلنا عنه
+
+378
+00:28:45,710 --> 00:28:51,070
+إذن و هذا يعني T is bounded إذن عبارة عن bounded
+
+379
+00:28:51,070 --> 00:28:54,850
+Linear operator اللي أثبتناه نأتي إلى نظرية
+
+380
+00:28:57,850 --> 00:29:03,610
+لو أنتم لاحظتوا بس قبل أحكيها النظرية Theorem if
+
+381
+00:29:03,610 --> 00:29:06,850
+and only if this base X is finite dimensional then
+
+382
+00:29:06,850 --> 00:29:10,970
+every Linear operator on X شماله is bounded كلام
+
+383
+00:29:10,970 --> 00:29:17,270
+خطير إنه أي Linear Operator في الدنيا على finite
+
+384
+00:29:17,270 --> 00:29:20,970
+dimensional space هيطلع bounded linear اييه
+
+385
+00:29:20,970 --> 00:29:24,930
+Operator يعني اللي جاب البشوية هدول تبع الـ RN و RK
+
+386
+00:29:24,930 --> 00:29:28,110
+خلاص ما هو bounded linear operator على .. linear
+
+387
+00:29:28,110 --> 00:29:31,230
+operator على اللي هو finite dimensional space لأن
+
+388
+00:29:31,230 --> 00:29:34,230
+automatic هيكون إيش ماله؟ bounded linear operator
+
+389
+00:29:35,250 --> 00:29:39,590
+بدنا نبرهنها لأن لو أتيت و لاحظتوا يمكن برهنها بيجي
+
+390
+00:29:39,590 --> 00:29:42,770
+ثلاث نظريات جايب لها دي أو نظريتين على الـ finite
+
+391
+00:29:42,770 --> 00:29:47,670
+dimensional وفيهم كلهم يمكن نروح لبرهان واحدة
+
+392
+00:29:47,670 --> 00:29:52,430
+كلهم استخدمنا فرضنا ال bases واستخدمنا اللمة
+
+393
+00:29:52,430 --> 00:29:56,230
+اللي احنا تبعت اللي هي Summation أكبر أو يساوي
+
+394
+00:29:56,230 --> 00:30:00,250
+اللي هو C في اللي هو اللي هي كتلة ال scalars،
+
+395
+00:30:00,250 --> 00:30:06,640
+مظبوط؟ عشان انه يعني لتتكارب البرهان طيب، الآن
+
+396
+00:30:06,640 --> 00:30:09,360
+خلينا نفترض أن الـ dimension للـ space اللي عندي
+
+397
+00:30:09,360 --> 00:30:14,240
+X إيش بيساوي N ونفترض ال basis تبعته E1 و E2 و EN بيه
+
+398
+00:30:14,240 --> 00:30:18,200
+a basis for X then every X Element in X has a
+
+399
+00:30:18,200 --> 00:30:20,500
+unique representation عارفينه هذا الكلام من الجبر
+
+400
+00:30:20,500 --> 00:30:25,940
+الخطي اللي هي بغسط أي X في الـ X عشان هيك basis بنكد
+
+401
+00:30:25,940 --> 00:30:29,040
+و أسوء as a linear combination من العناصر هدول
+
+402
+00:30:29,040 --> 00:30:34,340
+ووحيد و اللي بيبطل basis ألفا واحد E واحد زي ألفا
+
+403
+00:30:34,340 --> 00:30:37,400
+اثنين E اثنين زي ألفا ان E ان هاد ال X
+
+404
+00:30:37,400 --> 00:30:41,120
+where ألفا واحد و ألفا اثنين are mean scalar by
+
+405
+00:30:41,120 --> 00:30:44,160
+Linearity of T لأنه مفترض إيش ماله Linear و بدك
+
+406
+00:30:44,160 --> 00:30:48,940
+تثبت أنه إيش Bounded شوفوا كيف Norm ال TX إيش
+
+407
+00:30:48,940 --> 00:30:55,100
+هيساوي اللي هو ال Summation لل Alpha I TEI أكيد
+
+408
+00:30:55,770 --> 00:31:01,630
+TX إيش بيساوي .. TX إيش بيساوي اللي هو T لهذا إذا
+
+409
+00:31:01,630 --> 00:31:04,690
+Alpha واحد T واحد زائد Alpha اثنين T اثنين زائد
+
+410
+00:31:04,690 --> 00:31:08,690
+Alpha N T N اللي هو هذا بحطه جوا تمين Norm الآن
+
+411
+00:31:08,690 --> 00:31:13,960
+أنا شغلي وين الآن هذا Norm إذا أصغر أو يساوي
+
+412
+00:31:13,960 --> 00:31:17,760
+اللي هو الـ .. الـ .. الـ .. الـ .. الـ .. الـ Triangle
+
+413
+00:31:17,760 --> 00:31:21,380
+Inequality اللي هو Norm الـ .. الـ .. الـ .. الأول
+
+414
+00:31:21,380 --> 00:31:24,820
+زائد الثاني زائد الثالث زائد مية Norm هنا أصغر أو يساوي
+
+415
+00:31:24,820 --> 00:31:26,700
+Norm الأول زائد Norm الثاني و زائد Norm الآخر
+
+416
+00:31:26,700 --> 00:31:30,440
+هذا اللي استخدمته إذا ال Norm للمجموع أصغر أو يساوي
+
+417
+00:31:30,440 --> 00:31:34,590
+مجموع لل Norm الآن الـ α I اللي هي Scalar فبتدخل و
+
+418
+00:31:34,590 --> 00:31:37,750
+بتخرج من برا النورم بإيش ما لها بـ Absolute value
+
+419
+00:31:37,750 --> 00:31:41,630
+فاهمين اللي بحكيه؟ Summation في Normين اللي بيظل
+
+420
+00:31:41,630 --> 00:31:46,720
+Normين الـ TEI إذا الـ TI كم واحدة هنا معروف أن
+
+421
+00:31:46,720 --> 00:31:50,380
+طبعا الـ E1 و E2 و EN بحكي عن شيء محدد اللي 
+
+422
+00:31:50,380 --> 00:31:53,660
+وعددهن N من العناصر إذا أكيد فيه أكبر واحدة فيهم
+
+423
+00:31:53,660 --> 00:31:57,540
+أكيد لأن هذول أعداد موجبة أكبر أو يساوي صفر خذوا ال
+
+424
+00:31:57,540 --> 00:32:02,580
+maximum  لهن هذول فبصير هذا المقدار أصغر أو يساوي
+
+425
+00:32:02,580 --> 00:32:05,740
+ال maximum لهن في ال main في ال summation اللي
+
+426
+00:32:05,740 --> 00:32:10,560
+عندي اطلعي لفوق الآن من لمّة اتنين أربعة واحد اللي
+
+427
+00:32:10,560 --> 00:32:14,430
+وعدتكم فيها بدي أخلص من هذول بدي أخلص من هذه
+
+428
+00:32:14,430 --> 00:32:19,060
+انزلي نبدأ نخلص منها الـ scalars اللي موجودة و تبدأ
+
+429
+00:32:19,060 --> 00:32:26,100
+تبدأ تبدأ تبدأ تبدأ تبدأ
+
+430
+00:32:26,100 --> 00:32:28,600
+تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ
+
+431
+00:32:28,600 --> 00:32:31,920
+تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ
+
+432
+00:32:31,920 --> 00:32:31,940
+تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ تبدأ
+
+433
+00:32:31,940 --> 00:32:44,340
+تبدأ تبدأ
+
+434
+00:32:44,340 --> 00:32:50,360
+تمام هذه اللي ما الآن بتربط هذه مع الأولى صار هذا
+
+435
+00:32:50,360 --> 00:32:55,140
+ال summation أصغر أو يساوي normal x على ال c انزل
+
+436
+00:32:55,140 --> 00:32:59,060
+لتحت .. انزل لتحت بدي اللي هو اخذ .. اخذ خلص من
+
+437
+00:32:59,060 --> 00:33:02,760
+هذه بيصير أصغر أو يساوي هذا في normal x على مين؟
+
+438
+00:33:02,760 --> 00:33:07,000
+على ال c اطلع لفوق قدر من واحد و اللي عندي هذه
+
+439
+00:33:07,000 --> 00:33:11,020
+بقدر أقول normal T x أصغر أو يساوي واحد على c في ال
+
+440
+00:33:11,020 --> 00:33:17,040
+maximum هذا في normal x هذا كله على بعض ثابت لأن
+
+441
+00:33:17,040 --> 00:33:20,880
+هذا عبارة عن قيمة عددية و 1 على C قيمة عددية إذا
+
+442
+00:33:20,880 --> 00:33:24,680
+نورم الـ TX أصغر أو يساوي some number M في نورم الـ X
+
+443
+00:33:24,680 --> 00:33:28,520
+إذا صار عنده و الـ M طبعا هذه المشمولة هي هذه M
+
+444
+00:33:28,520 --> 00:33:32,800
+مشمولة تغير هذا M كم تهلل الفعل بساوي 1 على C في
+
+445
+00:33:32,800 --> 00:33:39,060
+ال maximum للنورم hence T أشمالها is bounded يلا
+
+446
+00:33:39,060 --> 00:33:43,440
+لبعده نيجي
+
+447
+00:33:43,440 --> 00:33:44,180
+نشوف
+
+448
+00:33:49,850 --> 00:33:57,170
+Theorem 279 إعلان كبير إعلان بقول لكم باختصار لما
+
+449
+00:33:57,170 --> 00:33:59,690
+يكون عندنا linear operator لما يكون عندنا linear
+
+450
+00:33:59,690 --> 00:34:04,190
+operator هتلاقوا مفهوم ال boundedness هو نفس مفهوم
+
+451
+00:34:04,190 --> 00:34:08,250
+ال continuity هو نفس مفهوم ال continuity عند نقطة
+
+452
+00:34:08,250 --> 00:34:12,390
+يعني لو كان عندك linear operator و كانت continuous
+
+453
+00:34:12,390 --> 00:34:16,250
+عند نقطة توكل على الله continuous على كل مين على
+
+454
+00:34:16,250 --> 00:34:19,770
+كل ال domain و هيكون bounded و لو كان bounded
+
+455
+00:34:19,770 --> 00:34:21,850
+هيكون continuous عند كل ال domain و هيكون
+
+456
+00:34:21,850 --> 00:34:25,090
+continuous عند مين عند كل نقطة كلام خوى .. خوى جدا
+
+457
+00:34:25,950 --> 00:34:29,230
+ومريح let T من domain of T لعند Y بيقالينا
+
+458
+00:34:29,230 --> 00:34:32,310
+operator where domain of T subset من X and X and Y
+
+459
+00:34:32,310 --> 00:34:36,450
+are normed spaces then T is continuous if and only
+
+460
+00:34:36,450 --> 00:34:40,530
+if T is bounded هاي واحدة اتنين إذا كانت T
+
+461
+00:34:40,530 --> 00:34:45,030
+continuous عند بس نقطة هتلاقيها نقلها continuous
+
+462
+00:34:45,030 --> 00:34:51,730
+على كل ال domain يلا نشوف بدنا نبرهن ال theorem
+
+463
+00:34:51,730 --> 00:34:57,310
+ناخد اتجاه الأول اتجاه الثاني و بعدين ناخد B طيب
+
+464
+00:34:57,310 --> 00:35:07,370
+سّلّع على النبي عليه الصلاة والسلام شوفوا
+
+465
+00:35:07,370 --> 00:35:13,610
+خلّينا نشوف اللي بحكيها الآن بس بدنا نشيل هالسفر
+
+466
+00:35:13,610 --> 00:35:16,430
+من عندنا عشان لو بدنا نجسم على سفر كده نجسم على T
+
+467
+00:35:16,430 --> 00:35:20,750
+مايكون مرتاحين نفش نجسم على سفر الـ 4T بيساوي سفر
+
+468
+00:35:20,750 --> 00:35:23,110
+ال .. ال .. ال .. ال .. ال .. ال linear operator
+
+469
+00:35:23,110 --> 00:35:25,850
+اللي هو ال zero linear operator هذا linear و
+
+470
+00:35:25,850 --> 00:35:28,530
+bounded و كل الدنيا حلوة فيه و كنتوا حلوة فيه for T
+
+471
+00:35:28,530 --> 00:35:33,130
+بيساوى 0 the statement is trivial لأن لت لا تساوي
+
+472
+00:35:33,130 --> 00:35:38,370
+0 نفترض أنه مش هو ال zero operator ماشي الآن مدام
+
+473
+00:35:38,370 --> 00:35:41,470
+مش هو ال zero operator إذا أكيد ال norm لت أشمالها
+
+474
+00:35:41,470 --> 00:35:45,910
+مش سفر ماشي الحال طيب لان اصلا من تعريف ال norm ال
+
+475
+00:35:45,910 --> 00:35:48,190
+norm ت بيساوى سفر if and only if ت اللي جوه بيساوي
+
+476
+00:35:48,190 --> 00:35:53,250
+سفر طيب إذا ال norm ت لا يساوي سفر لان نفترض ت is
+
+477
+00:35:53,250 --> 00:35:58,270
+bounded ونثبت إنه T Continuous T is bounded عارفين
+
+478
+00:35:58,270 --> 00:36:00,910
+شو معناته؟ bounded norm للـ T X أزرار شوية اللي هو
+
+479
+00:36:00,910 --> 00:36:04,730
+C في norm ال X ده كل ال X أتر الآن و بدنا ناخد X
+
+480
+00:36:04,730 --> 00:36:08,330
+note arbitrary X note بس بدنا نحكي عن واحدة محددة
+
+481
+00:36:08,330 --> 00:36:11,410
+يعني باجي باخد هكوم هالعناصر اللي في ال domain of
+
+482
+00:36:11,410 --> 00:36:15,660
+T باخد من X note arbitrary و ببدأ أحكي عنها إذا
+
+483
+00:36:15,660 --> 00:36:17,960
+اللي بنطبق عليه hard book علي غيرها يعني مش مانهي
+
+484
+00:36:17,960 --> 00:36:24,100
+أنا باخدها عشوائي let X not be any fixed point in
+
+485
+00:36:24,100 --> 00:36:30,640
+domain of T الآن احنا مفترضين انها bounded أو بدنا
+
+486
+00:36:30,640 --> 00:36:33,440
+نثبت انها continuous ايش كيف نثبت انه continuous؟
+
+487
+00:36:33,440 --> 00:36:37,700
+نثبت انه continuous انه اللي هو لكل y أكبر من 0
+
+488
+00:36:37,700 --> 00:36:41,700
+بدي لاجي delta أكبر من 0 such that لما ال X minus
+
+489
+00:36:41,700 --> 00:36:46,460
+X not يكون أصغر من Delta يعطيني ال TX نقص ال TX
+
+490
+00:36:46,460 --> 00:36:50,940
+not ايش ماله أصغر من Y هي اللي بدي اشتغل عليها ماشي
+
+491
+00:36:50,940 --> 00:36:55,820
+بدي أصلّه بدي أصلّه بالاستعانة بالاستعانة باللي هي
+
+492
+00:36:55,820 --> 00:37:04,120
+اللي عندي طيب خذوا الآن suppose that T is bounded
+
+493
+00:37:04,120 --> 00:37:07,580
+and let X not be any fixed point on D of T و let Y
+
+494
+00:37:07,580 --> 00:37:12,560
+أكبر من 0 be arbitrary given Y لأن بما أنه T is
+
+495
+00:37:12,560 --> 00:37:18,950
+linear إذا بقدر ألاقي Delta بتساوي E على norm of T
+
+496
+00:37:18,950 --> 00:37:22,470
+أكبر من 0 such that إذا أنا جاءت بحضر للي بدّيها،
+
+497
+00:37:22,470 --> 00:37:26,850
+بدّي ألاقي مين؟ Delta أنا بقول للمستقبل اللي
+
+498
+00:37:26,850 --> 00:37:31,110
+بدّيها، أنا بتدعي إنها Delta إيش هتساوي E على norm
+
+499
+00:37:31,110 --> 00:37:34,670
+of T، norm of T بين إيديا و الـ E انت عطيتني إيها
+
+500
+00:37:34,670 --> 00:37:37,170
+إذا صارت عندي الـ Delta بتساوي E على norm of T
+
+501
+00:37:37,170 --> 00:37:41,170
+أكبر من مين من 0 such that if X element in domain
+
+502
+00:37:41,170 --> 00:37:47,320
+of T عند x-x0 أصغر من دلتا بدّى أثبت لك أن هذا يكون
+
+503
+00:37:47,320 --> 00:37:51,820
+أصغر من مين من إبسلون شوفوا الآن then norm of T x
+
+504
+00:37:51,820 --> 00:37:58,040
+نقص T x0 ايش بيساوي norm of T في x minus x0 Linear
+
+505
+00:37:58,040 --> 00:38:02,200
+Linear أصغر أو سوى نورم الـ T في نورم من X minus X
+
+506
+00:38:02,200 --> 00:38:05,780
+naught هذا من وين جبته؟ من الـ boundedness للـ T
+
+507
+00:38:05,780 --> 00:38:08,820
+مش عارف معناته الـ bounded؟ طيب أصغر أو سوى نورم
+
+508
+00:38:08,820 --> 00:38:12,460
+الـ T في نورم هذا الآن نورم الـ X minus X naught
+
+509
+00:38:12,460 --> 00:38:16,300
+أنا إيش ماخده؟ أصغر من Delta اللي هي إيش بتسوى Y
+
+510
+00:38:16,300 --> 00:38:20,460
+على مين؟ على نورم الـ T اللي هي أصغر من نورم الـ T
+
+511
+00:38:20,460 --> 00:38:23,500
+في Delta حاصل ضربه Delta Epsilon على نورم الـT
+
+512
+00:38:23,500 --> 00:38:26,440
+بتطلع يشمله Epsilon و هذا Therefore T is
+
+513
+00:38:26,440 --> 00:38:30,020
+continuous at X0 لكن X0 was arbitrarily زي ما قلنا
+
+514
+00:38:30,020 --> 00:38:36,440
+Then T is continuous on all domain of T سهل يلا
+
+515
+00:38:36,440 --> 00:38:42,660
+لبعده الآن بدنا نفترض مين أنها continuous و نصل
+
+516
+00:38:42,660 --> 00:38:48,860
+لمين للboundedness بدا أثبتلكم بدا أستخدم هذا هذا
+
+517
+00:38:48,860 --> 00:38:55,140
+معناه اتنين ال continuity بستخدمه بطريقة ما على إن
+
+518
+00:38:55,140 --> 00:39:00,200
+أثبت الـ norm للـ T Y أصغر أو ساوي C في الـ norm
+
+519
+00:39:00,200 --> 00:39:06,540
+للـ Y لكل Y element in domain of T هذا إذا أثبتت
+
+520
+00:39:06,540 --> 00:39:09,420
+لكم there exists C أكبر من 0 such that هذا إذا
+
+521
+00:39:09,420 --> 00:39:11,640
+أثبتت هذا معناه أنك أثبتت انه bounded كيف بده
+
+522
+00:39:11,640 --> 00:39:15,940
+أثبته بالاستعانة باللي فوق ماشي إذا الأن بده أقول
+
+523
+00:39:18,650 --> 00:39:21,090
+Conversely suppose that أو assume that T is
+
+524
+00:39:21,090 --> 00:39:23,910
+continuous at an arbitrary point x0 element in
+
+525
+00:39:23,910 --> 00:39:27,090
+domain of T مدام continuous ده بنطبق تعريف ال
+
+526
+00:39:27,090 --> 00:39:30,310
+continuity بمعنى then for every أكبر من أكبر من
+
+527
+00:39:30,310 --> 00:39:30,910
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+528
+00:39:30,910 --> 00:39:30,990
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+529
+00:39:30,990 --> 00:39:31,150
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+530
+00:39:31,150 --> 00:39:31,430
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+531
+00:39:31,430 --> 00:39:32,470
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+532
+00:39:32,470 --> 00:39:33,450
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر من
+
+533
+00:39:33,450 --> 00:39:44,390
+أكبر من أكبر من أكبر من أكبر من أكبر من أكبر
+
+534
+00:39:44,390 --> 00:39:47,630
+من أكبر
+
+535
+00:39:47,670 --> 00:39:50,590
+عشان هيك احنا لو استثنينا الصفر مش فارقة معناه قبل
+
+536
+00:39:50,590 --> 00:39:54,430
+شوية اصلا استثنناها من norm وماحكيناش لأن ال
+
+537
+00:39:54,430 --> 00:39:59,070
+inequality دُغر بتشتغل في حالة الصفر الآن عشان
+
+538
+00:39:59,070 --> 00:40:03,450
+أثبت هذه بدي اخد الآن اي واحد دويل موجودة في ال
+
+539
+00:40:03,450 --> 00:40:07,770
+domain of T واشيل الصفر منها، ماشي؟ إذا الآن let Y
+
+540
+00:40:07,770 --> 00:40:11,370
+لا تساوي صفر بي أنقل من تمين in domain of T بدي
+
+541
+00:40:11,370 --> 00:40:15,190
+أثبتلكم ان norm لتي Y عن norm لY أصغر من sum C
+
+542
+00:40:16,230 --> 00:40:21,230
+شوفوا صلوا على النبي عليه الصلاة والسلام and set
+
+543
+00:40:21,230 --> 00:40:26,170
+خذ الآن X بتساوي X not هذول اللي فوق اللي فوق اللي
+
+544
+00:40:26,170 --> 00:40:29,830
+فوق اللي قبل وشوية بدي أقولكم هتتحققن انا بدي
+
+545
+00:40:29,830 --> 00:40:35,890
+أقولكم هذول هيحققن الفوق وخذ X بتساوي X not زائد
+
+546
+00:40:35,890 --> 00:40:41,390
+delta y على 2 normal y ماشي then خذ الآن norm ال x
+
+547
+00:40:41,390 --> 00:40:46,550
+minus x not ايش هيساوي delta في y على 2 normal y
+
+548
+00:40:46,550 --> 00:40:51,030
+norm صح اللي هو ايش ماله norm هذي هيروح مع norm
+
+549
+00:40:51,030 --> 00:40:54,090
+هذي بيصير ايش ماله أصغر من delta اللي هو delta على
+
+550
+00:40:54,090 --> 00:40:59,120
+2 أصغر من delta إذا أدملتلكم الآن هذا أصغر من دلتا
+
+551
+00:40:59,120 --> 00:41:03,120
+مدام أصغر من دلتا إذا يتحقق عليه الشرط هذا لأن
+
+552
+00:41:03,120 --> 00:41:06,580
+احنا مفترضين ال T is continuous إذا أكيد by two
+
+553
+00:41:06,580 --> 00:41:11,400
+هيكون عنده نورم ال T X ناقص T X ناقص أصغر من مين؟
+
+554
+00:41:11,400 --> 00:41:15,500
+من إبسلون since T is continuous ابدأ في حسابات هذه
+
+555
+00:41:15,500 --> 00:41:21,920
+هتوصلي للبدية ويساوي TX-TX0 بيساوي T of X minus TX0
+
+556
+00:41:21,920 --> 00:41:25,720
+عوضلي على ال X minus X0 اللي هي اش بيساوي منها ال
+
+557
+00:41:25,720 --> 00:41:29,680
+X نقص X0 اللي هي Delta Y على 2 في ال normal Y T is
+
+558
+00:41:29,680 --> 00:41:32,680
+linear إذا بتطلع الدلتا بتطلع حد و بتطلع حد براها
+
+559
+00:41:32,680 --> 00:41:37,620
+بيصير عند دلتاعلى 2 في نورم الـY طالعين من برا
+
+560
+00:41:37,620 --> 00:41:42,400
+الـT ومن برا الـNorm هن حرات لإن هن إيه شمال هن 
+
+561
+00:41:42,400 --> 00:41:46,140
+Scalars هدول باعتبار اللي هو بيظل مين اللي جوا
+
+562
+00:41:46,140 --> 00:41:51,200
+الـNorm  نورم الـT of مين؟ of Y نورم الـT of Y صار
+
+563
+00:41:51,200 --> 00:41:56,820
+عندي الآن هذا المقدار هيه هيه أصغر من Epsilon يعني
+
+564
+00:41:56,820 --> 00:42:01,840
+بمعنى آخر نورم الـTY أصغر من هذا في هذا على هذا في
+
+565
+00:42:01,840 --> 00:42:08,390
+Epsilon صار عندي نورم الـTy أصغر من 2 في إبسلون على
+
+566
+00:42:08,390 --> 00:42:11,690
+دلتا في النورم لمين؟ للـY هذا كله سموّه مين؟ الـC
+
+567
+00:42:11,690 --> 00:42:15,630
+فبيصير نورم الـTy أصغر شوي من نورم الـY والـY was 
+
+568
+00:42:15,630 --> 00:42:20,110
+arbitrary بـ element in domain of T وبسوي صفر
+
+569
+00:42:20,110 --> 00:42:25,910
+إذا صار عندي T إيش ما لها؟ is bounded طيب اللي بعد
+
+570
+00:42:25,910 --> 00:42:33,630
+ولنفترض أن الـ T مستمر في موقع واحد نفترض أن الـ
+
+571
+00:42:33,630 --> 00:42:35,210
+T مستمر في موقع واحد
+
+572
+00:42:39,460 --> 00:42:43,260
+أنا كله هنا .. هنا في البرهان لما .. أطلع .. لما
+
+573
+00:42:43,260 --> 00:42:47,740
+جيت براهينك هنا أنا استغلت اللي هو ال continuity لل
+
+574
+00:42:47,740 --> 00:42:52,620
+.. لل .. لل T وين؟ عند نقطة وأثبتت أنه شمالها T 
+
+575
+00:42:52,620 --> 00:42:56,940
+is bounded إذا from this proof أطلع إلى فوق from
+
+576
+00:42:56,940 --> 00:43:03,000
+this proof from this proof الآن from this proof
+
+577
+00:43:03,000 --> 00:43:06,080
+assume that T is continuous at single point إذا
+
+578
+00:43:06,080 --> 00:43:09,680
+from this proof then by the second part of the
+
+579
+00:43:09,680 --> 00:43:14,140
+proof above of A T is bounded واحنا أثبتنا أنه
+
+580
+00:43:14,140 --> 00:43:17,320
+لما تكون T is bounded إيش مالها؟ continuous إذا T 
+
+581
+00:43:17,320 --> 00:43:19,600
+is continuous فعلاً لما تكون continuous عند one
+
+582
+00:43:19,600 --> 00:43:23,640
+single point في بعض الناس طبعاً بتثبتها بيكون الكتب
+
+583
+00:43:23,640 --> 00:43:27,260
+عارضة كيف عارضة هادي بدون اللي هي ال .. ال .. ال
+
+584
+00:43:27,260 --> 00:43:29,480
+.. ال .. ال boundedness اللي في الطريق يعني ممكن
+
+585
+00:43:29,480 --> 00:43:33,080
+تكون عارضة إنه إذا كانت T Linear أثبت لما تكون T
+
+586
+00:43:33,080 --> 00:43:36,720
+continuous تكون على طول شمالها as اللي هي
+
+587
+00:43:36,720 --> 00:43:39,820
+continuous عند single point and continuous عند
+
+588
+00:43:39,820 --> 00:43:43,520
+every point طبعاً بيكون جابلها مثبت اللي هو T is
+
+589
+00:43:43,520 --> 00:43:46,600
+bounded لما تكون continuous is bounded وبشتغل هنا
+
+590
+00:43:46,600 --> 00:43:47,140
+مباشرة
+
+591
+00:43:50,190 --> 00:43:52,630
+أو بعيد البرهان اللي حكيناها قبل شوي عشان يثبتها،
+
+592
+00:43:52,630 --> 00:43:56,230
+فاهمين؟ بعيد البرهان لو كانت اللي هو في الشعار
+
+593
+00:43:56,230 --> 00:44:02,390
+الدلال الأولي طيب، اللي بعد؟ Note ولا Corollary لسه
+
+594
+00:44:02,390 --> 00:44:06,270
+Corollary لت T من domain of T لعند Y بيبقى bounded
+
+595
+00:44:06,270 --> 00:44:09,230
+linear operator where domain of T جزء من مين؟ من X
+
+596
+00:44:09,230 --> 00:44:13,570
+and X وY are normed spaces then ايه؟ لما X قالت
+
+597
+00:44:13,570 --> 00:44:17,150
+تروح .. يعني بمعنى آخر T bounded linear operator T
+
+598
+00:44:17,150 --> 00:44:20,330
+bounded linear operator بقول إذا ما يليه التحقق؟
+
+599
+00:44:20,330 --> 00:44:24,970
+إيش هو؟ إن لما X قالت تروح لل X حيث xn والـ x في
+
+600
+00:44:24,970 --> 00:44:28,610
+domain الـ T بيعطيني automatic T x بتروح لـ .. T xn
+
+601
+00:44:28,610 --> 00:44:32,590
+بتروح لمين؟ لـ Tx هذا ما هو تعريف الـ continuity صح
+
+602
+00:44:32,590 --> 00:44:35,650
+ولا لأ؟ تعريف ال continuity إذن بما أنه bounded إذن
+
+603
+00:44:35,650 --> 00:44:38,210
+من النظرية اللي جابل بشوي is a continuous مدام
+
+604
+00:44:38,210 --> 00:44:42,430
+continuous إذن بيطلع إن لما xn تروح لل X لل X لل X
+
+605
+00:44:42,430 --> 00:44:45,030
+في domain ال T وال Xn في domain ال T أكيد ال T xn
+
+606
+00:44:45,030 --> 00:44:48,580
+بتروح لـ T x by ده continuity الجزء الثاني دلالة ال
+
+607
+00:44:48,580 --> 00:44:52,480
+space N of T إيش ماله؟ is closed خلينا نثبت ال N
+
+608
+00:44:52,480 --> 00:44:57,080
+of T is closed كيف نثبت أنها closed؟ بتاخدوا X في 
+
+609
+00:44:57,080 --> 00:45:02,010
+ال N of T إيش ماله؟ closure وبثبتوا إن X مين موجودة
+
+610
+00:45:02,010 --> 00:45:07,730
+في الـN of T ماشي؟ طيب إيش معنى X في الـN of T 
+
+611
+00:45:07,730 --> 00:45:13,670
+closure؟ إنه there exists Xn in N of T such that
+
+612
+00:45:13,670 --> 00:45:21,010
+Xn converge the mean للـX صح ولا لأ؟ بط T X N
+
+613
+00:45:21,010 --> 00:45:26,310
+بتساوي صفر لكل N صح ولا لأ؟ لأن من وين جايات هدول؟
+
+614
+00:45:26,310 --> 00:45:29,790
+من ال .. من ال .. من ال .. ال non-less base مظبوط
+
+615
+00:45:29,790 --> 00:45:33,790
+أو اللي هو ال .. ال .. ال .. ال .. ال N of T ماشي
+
+616
+00:45:33,790 --> 00:45:41,250
+فمين؟ إذا طيب لكن أنا عمالي بقول إن ال N .. T X N
+
+617
+00:45:41,250 --> 00:45:45,310
+بتروح للصفر إذا أكيد T X N نفسها converge لمين؟
+
+618
+00:45:45,310 --> 00:45:52,280
+للصفر معايا و بال continuity الأصلية ال continuity
+
+619
+00:45:52,280 --> 00:45:55,740
+الأصلية مش continuous about it then continuous إذا
+
+620
+00:45:55,740 --> 00:46:01,200
+هيعطيني TXN وتروح لمين؟ لل TX إن XN و X1 موجودة في
+
+621
+00:46:01,200 --> 00:46:06,010
+domain of T تبعيأه مدام T X N بتروح لـ T X و T X N
+
+622
+00:46:06,010 --> 00:46:09,850
+لجأت تروح لل صفر والوحيدة اللي هي هتكون ال limit
+
+623
+00:46:09,850 --> 00:46:14,710
+إذا T X إيش بتساوي؟ إذا T X بتساوي صفر وما معنى T
+
+624
+00:46:14,710 --> 00:46:18,370
+X بتساوي صفر يعني X element في ال N of T يعني بدأت
+
+625
+00:46:18,370 --> 00:46:20,830
+في ال X N of T closure وصبت ال X في ال N of T
+
+626
+00:46:20,830 --> 00:46:24,210
+معناه أصلاً ال N of T closure جزئية من ال N of T و
+
+627
+00:46:24,210 --> 00:46:26,210
+بعرف ال N of T جزئية من ال N of T closure يعني ال
+
+628
+00:46:26,210 --> 00:46:28,970
+N of T closure بيساوي ال N of T معناه أن ال N of T
+
+629
+00:46:28,970 --> 00:46:34,870
+is a closed set اللي بعده Note for any bounded
+
+630
+00:46:34,870 --> 00:46:38,710
+linear operators أو operator for any bounded
+
+631
+00:46:38,710 --> 00:46:42,520
+linear operator مش operators لأ، بدو أكثر .. آه
+
+632
+00:46:42,520 --> 00:46:46,140
+بدو أكثر آسف For any bounded linear operators T
+
+633
+00:46:46,140 --> 00:46:49,560
+من X عند Y و S من عند Y لعند Z شكل بدو يعملين
+
+634
+00:46:49,560 --> 00:46:54,820
+composition أه؟ Where X .. Y و Z are normed spaces,
+
+635
+00:46:55,020 --> 00:46:59,920
+we have نورم الـ T S أصغر أو يساوي نورم الـ T في نورم
+
+636
+00:46:59,920 --> 00:47:04,320
+الـ S and نورم الـ T N أصغر أو يساوي نورم الـ T أُس N
+
+637
+00:47:04,320 --> 00:47:09,540
+أُس N هذه induction من هذه وهذه تعملوا تعريف اللي
+
+638
+00:47:09,540 --> 00:47:12,860
+هو norm of Ts إيش norm of Ts بيساوي؟ اللي هو
+
+639
+00:47:12,860 --> 00:47:16,520
+Supremum لكده وشتغلوا عليها هتلاقوها أسهل شوي هذه
+
+640
+00:47:16,520 --> 00:47:21,140
+اللي هو بيبقى ال exercise بسيط معاكم بسهولة
+
+641
+00:47:21,140 --> 00:47:29,100
+ما تقلقوش طيب theorem 2711 مفردات المادة كتير عشان
+
+642
+00:47:29,100 --> 00:47:35,090
+هي صعبة الواحد هيبره كل حاجة طيب theorem برضه هذه
+
+643
+00:47:35,090 --> 00:47:38,410
+خليني أقول  سيئة المركزية في ال section اللي
+
+644
+00:47:38,410 --> 00:47:41,390
+بتقول لي let T من domain of T لعند Y بيه a bounded
+
+645
+00:47:41,390 --> 00:47:45,790
+linear operator اه bounded linear operator D of T
+
+646
+00:47:45,790 --> 00:47:50,710
+ماله جزء من normed space اسمه X والـ Y إيش ماله
+
+647
+00:47:50,710 --> 00:47:56,310
+جالنه Banach space اه complete normed space بيقول لي
+
+648
+00:47:56,310 --> 00:48:00,350
+مدام T جاية من اللي هو domain of T في normed space
+
+649
+00:48:00,350 --> 00:48:05,870
+لعند Banach space لعند Banach space then T has an
+
+650
+00:48:05,870 --> 00:48:11,470
+extension بقدر أعملك extension للـ T ومش بس بقدر
+
+651
+00:48:11,470 --> 00:48:14,350
+أعمل extension ال extension هيكون من مين؟ من
+
+652
+00:48:14,350 --> 00:48:20,970
+domain of T ماله closure لعند ال Y وهيكون T تيلدة
+
+653
+00:48:20,970 --> 00:48:25,970
+هيكون برضه bounded linear operator و norm هو norm
+
+654
+00:48:25,970 --> 00:48:34,370
+الأصلي norm هو هيكون norm ال T الأصلية يلا خلينا
+
+655
+00:48:34,370 --> 00:48:45,910
+نشوف البرهان لأن البرهان منيح وفيه فكرة يا
+
+656
+00:48:45,910 --> 00:48:53,350
+رب .. طيب .. نشوف إيش بقول الآن لت X element من ال
+
+657
+00:48:53,350 --> 00:48:56,310
+domain of T مقفل مادة N في ال domain of T مقفل
+
+658
+00:48:56,310 --> 00:48:56,610
+مادة N في ال domain of T مقفل مادة N في ال domain
+
+659
+00:48:56,610 --> 00:48:57,030
+of T مقفل مادة N في ال domain of T مقفل مادة N في
+
+660
+00:48:57,030 --> 00:48:58,330
+ال domain of T مقفل مادة N في ال domain of T مقفل
+
+661
+00:48:58,330 --> 00:49:01,090
+مادة N في ال domain of T مقفل مادة N في ال domain
+
+662
+00:49:01,090 --> 00:49:11,320
+of T مقفل مادة N في ال domain of T معروف By using
+
+663
+00:49:11,320 --> 00:49:14,680
+the linearity and boundedness of T we have ناخذ
+
+664
+00:49:14,680 --> 00:49:20,620
+مين اللي هو إيش اللي هو هذه نستخدم إن الـ T is
+
+665
+00:49:20,620 --> 00:49:24,360
+linear و bounded تشوفوا كده احسبولي إنه أنا أنا
+
+666
+00:49:24,360 --> 00:49:25,600
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+667
+00:49:25,600 --> 00:49:31,530
+أنا أنا أنا أنا أنا T XM ناقص T XM بيساوي T XM ناقص
+
+668
+00:49:31,530 --> 00:49:41,390
+T XM بيساوي T XM ناقص T XM ناقص T XM بيساوي T XM
+
+669
+00:49:41,390 --> 00:49:42,770
+ناقص T XM ناقص T XM بيساوي T XM ناقص T XM ناقص T XM
+
+670
+00:49:42,770 --> 00:49:43,310
+ناقص T XM ناقص T XM ناقص T XM ناقص T XM ناقص T XM
+
+671
+00:49:43,310 --> 00:49:46,250
+ناقص T XM ناقص T XM ناقص T XM ناقص T XM ناقص T XM
+
+672
+00:49:46,250 --> 00:49:47,810
+ناقص T XM ناقص T XM ناقص T XM ناقص T XM ناقص T XM
+
+673
+00:49:47,810 --> 00:49:48,590
+ناقص T XM ناقص T XM ناقص T XM ناقص T XM ناقص إذا
+
+674
+00:49:48,590 --> 00:49:52,490
+أنا أخذت الـ XN معاها اللي هو الـ Conversion of
+
+675
+00:49:52,490 --> 00:49:58,050
+the mean للـ X إذا مدام كوشي إذا هذه اللي هي هيكون
+
+676
+00:49:58,050 --> 00:50:01,770
+عنده أصغر من أي إبسلون في الدنيا من ضبلهم الإبسل
+
+677
+00:50:01,770 --> 00:50:05,610
+على نورميل T يعني بمعنى آخر هذا provided that
+
+678
+00:50:05,610 --> 00:50:08,760
+نورميل T لبش صفر هذا معناته صار إيش ماله؟ أصغر من
+
+679
+00:50:08,760 --> 00:50:12,860
+إبسلون إذا صار برضه إيش ماله؟ كوشي إذا صارت ال TXN
+
+680
+00:50:12,860 --> 00:50:17,000
+كوشي الآن لازم ال إيش ال TXN كوشي في مين؟ في ال Y
+
+681
+00:50:17,000 --> 00:50:22,400
+وال Y complete إذا هذا إيش هتكون؟ converge إذا
+
+682
+00:50:22,400 --> 00:50:27,180
+الآن TXN كوشي sequence because XN is but Y is
+
+683
+00:50:27,180 --> 00:50:31,920
+complete then TXN converge say that T X N converts
+
+684
+00:50:31,920 --> 00:50:37,240
+the mean Y element in Y وشوفوا هل اللي عملناه اللي
+
+685
+00:50:37,240 --> 00:50:41,580
+سوناه عشان هو أساس البرهان الآن أساس تركيبة الـ T
+
+686
+00:50:41,580 --> 00:50:49,280
+Extension الـ T تيلدة أخدت الآن X N راحت لمين؟ لل X
+
+687
+00:50:49,280 --> 00:50:53,480
+ال X من وين هذه؟ هذه هي أصلاً اللي أشغل غرضي إن
+
+688
+00:50:53,480 --> 00:50:58,900
+أعمل T تيلدة من domain of T closure لعند مين؟ لعند
+
+689
+00:50:58,900 --> 00:51:05,140
+ال Y الآن extension معناته أنا مفكر شو معنى
+
+690
+00:51:05,140 --> 00:51:10,520
+extension أصلاً إن ال T تيلدة هتساوي T لكل X في ال
+
+691
+00:51:10,520 --> 00:51:15,890
+domain الأصلي والآن اللي بيظل بتعرفه مين اللي بيظل
+
+692
+00:51:15,890 --> 00:51:18,430
+اللي في الـ .. اللي في الـ closure اللي برا ماشي
+
+693
+00:51:18,430 --> 00:51:23,230
+الحال اللي مش موجود فيها دي وبدو يكون حسابي إنه
+
+694
+00:51:23,230 --> 00:51:25,850
+اللي أنا عرفته اللي هو اللي .. اللي .. اللي في ال
+
+695
+00:51:25,850 --> 00:51:28,470
+domain T وال closure لو التقت واحدة في ال domain
+
+696
+00:51:28,470 --> 00:51:32,190
+T وال closure موجودة في نفسها يعني أحيان ممكن
+
+697
+00:51:32,190 --> 00:51:34,750
+يكون Domain if they close أصلاً فيكون هي نفس الأشياء
+
+698
+00:51:34,750 --> 00:51:38,750
+فلازم يكون اللي هي الصورة under T و under T تيلدة
+
+699
+00:51:38,750 --> 00:51:42,640
+للعناصر اللي موجودة في الأصل زي بعض والجديد بدي
+
+700
+00:51:42,640 --> 00:51:46,720
+أعرفه بطريقة معينة فالآن أنا بدأت في الـ X وإيه 
+
+701
+00:51:46,720 --> 00:51:53,480
+الموجودة في الـ domain of T closure إيش عملت؟ اللي 
+
+702
+00:51:53,480 --> 00:51:56,840
+جاية TXN بتروح لمين؟ للـ X؟ وفدولة موجودة وين؟ في
+
+703
+00:51:56,840 --> 00:51:59,080
+الـ domain of T يعني في الأصل الموجودة ومعرفة عند
+
+704
+00:51:59,080 --> 00:52:07,460
+T ماشي الآن لما مشيت أثبتتلكم أن TXN صورة هدولة
+
+705
+00:52:07,460 --> 00:52:15,710
+راحت لمين؟ لـ Y وين موجودة؟ في الـ Y كابتنال
+
+706
+00:52:19,690 --> 00:52:26,230
+اللي من خلاله بدأ أقول عرفلي T تلدة للـ X اللي
+
+707
+00:52:26,230 --> 00:52:30,370
+بدأتها عشان أشتغل على هذه بساوة مين؟ لـ Y اللي وجيتها
+
+708
+00:52:30,370 --> 00:52:35,090
+هنا إذا Y هذه مين؟ لما عرفت T تلدة X بساوة Y هي Y
+
+709
+00:52:35,090 --> 00:52:41,010
+اللي نتجت من لما XN راحت للـ X وطلعت T XN راحت
+
+710
+00:52:41,010 --> 00:52:45,630
+لإيشي هو الإيشي هذا اللي بدي أسميه T مين؟ T X واضح
+
+711
+00:52:45,630 --> 00:52:55,800
+هذا T تلدة للـ X طيب إذا الآن define T tilde by T
+
+712
+00:52:55,800 --> 00:52:58,940
+tilde X بسوء Y we show that T tilde is well
+
+713
+00:52:58,940 --> 00:53:04,220
+defined الآن T tilde بتنثبت أنها إيش مالها؟ well
+
+714
+00:53:04,220 --> 00:53:09,240
+defined الآن well defined هو خايف إيش؟ خايف إنه
+
+715
+00:53:09,240 --> 00:53:15,600
+إنتوا لما أخدنا X في الـ domain T closure أنا بقول
+
+716
+00:53:15,600 --> 00:53:20,900
+لجيت في عندي XN راحة لـ X ولجيتها وحطيتها روحتوا
+
+717
+00:53:20,900 --> 00:53:24,040
+انتوا وجبتوا واحدة تانية في عندك ممكن infinite
+
+718
+00:53:24,040 --> 00:53:26,880
+number of sequences يروح إلى مين؟ لنفس الـ limit و
+
+719
+00:53:26,880 --> 00:53:31,960
+هدولة من .. زي ما بتعرفوا مثلا لو نحكي في ذاك نص و
+
+720
+00:53:31,960 --> 00:53:35,240
+تلت وربع إلى أخر هدولة كلهم بروح إلى مين؟ للسفر
+
+721
+00:53:35,240 --> 00:53:40,760
+صح؟ فلجيتها نص وربع وثمن الاخر بروح برضه لمين؟ لصفر
+
+722
+00:53:40,760 --> 00:53:45,380
+واحد على اتنين أُس ثلاثة أُس ثلاثان واحد على اتنين
+
+723
+00:53:45,380 --> 00:53:49,480
+أُس أربعان كلهم بروح لصفر فبخافوا كل واحد أخده
+
+724
+00:53:49,480 --> 00:53:52,240
+sequence بتختلف عن التانية حتى لو كلنا أخدنا
+
+725
+00:53:52,240 --> 00:53:55,440
+sequences باختلفنا عن التانية هنلاجيه ال .. ال ..
+
+726
+00:53:55,440 --> 00:54:02,600
+ال .. ال .. لن يؤثر على اللي هو تعريفنا لخوف إن X
+
+727
+00:54:02,600 --> 00:54:06,780
+أنه تروح للـ X أنا ديبتها وانتوا عندكم Z أن تروح
+
+728
+00:54:06,780 --> 00:54:10,580
+لمين؟ للـ X بقولك بالرغم إن هيك ما تجلجوش هيكون
+
+729
+00:54:10,580 --> 00:54:14,800
+التعريف نفس التعريف شوفوا كيف .. شوفوا كيف الان
+
+730
+00:54:14,800 --> 00:54:20,640
+suppose that xn هدأت تعريفك أو تعريفك xn بتروح
+
+731
+00:54:20,640 --> 00:54:26,620
+لمين؟ للـ x وانا جبت zn راحت لمين؟ للـ x وبدأت سلسل
+
+732
+00:54:26,620 --> 00:54:31,340
+اذا الان انا 
+
+733
+00:54:31,340 --> 00:54:36,440
+سلسلت وجبت تي xn راحت لمين؟ لـ y وانت جبت تي zn
+
+734
+00:54:36,440 --> 00:54:39,860
+وراحت لمين؟ لـ y شرطة هتكون y شرطة و y أشمالين نفس
+
+735
+00:54:39,860 --> 00:54:45,550
+الاشي الدليل then الان خدوا VM VM هتروح للـ X مين ال
+
+736
+00:54:45,550 --> 00:54:49,670
+VM هو عبارة عن X واحد Z واحد X اتنين Z اتنين X
+
+737
+00:54:49,670 --> 00:54:52,990
+تلاتة Z تلاتة واضح ان هذه الطيارة وين؟ ناحية الـ X
+
+738
+00:54:52,990 --> 00:54:56,090
+ماشي الحال إذا هذه راحت للـ X طب ما كل ال
+
+739
+00:54:56,090 --> 00:55:01,550
+subsequence اللي انت صار عندي TVM برضه converts
+
+740
+00:55:02,960 --> 00:55:07,560
+بنفس الأشياء VM مش راحت للـ X حسب اللي حكيناه قبل
+
+741
+00:55:07,560 --> 00:55:12,120
+شوية هلاقي الـ TVM مين؟ هتروح لصورة معينة اللي هي
+
+742
+00:55:12,120 --> 00:55:16,520
+TVM converts ده الـ Y اللي بيقول عنها الآن الـ TVM
+
+743
+00:55:16,520 --> 00:55:21,060
+ماهيها and the two subsequences TX and TZ and
+
+744
+00:55:21,060 --> 00:55:25,680
+هدولة subsequences من مين؟ من TVM و هذه راحت ل
+
+745
+00:55:25,680 --> 00:55:30,000
+limit و هدولة converts حسب الحديث الأولاني إذا كله
+
+746
+00:55:30,000 --> 00:55:33,350
+اللي هيروح لمين؟ لنفس الـ Limit إن ده معناته إنه
+
+747
+00:55:33,350 --> 00:55:37,610
+TXN و TZN إيش مابتكم؟ خدوا Sequences بتروح للـ X
+
+748
+00:55:37,610 --> 00:55:43,330
+هنصل في النهاية TXN تبعتي و TZN تبعتكم و TWN تبعت
+
+749
+00:55:43,330 --> 00:55:47,290
+أي واحد اللي هي في الأصل كانت كله نراحل للـ X هيكون
+
+750
+00:55:47,290 --> 00:55:51,470
+نقله نفس الـ T نفس الـ Y اللي بتطلع Limit للـ TXN
+
+751
+00:55:51,470 --> 00:55:55,170
+أو TZN أو TWN إذا .. إذا صار عندنا تعريف Now
+
+752
+00:55:55,170 --> 00:55:59,650
+Defined إذاً hence T تلدة is well-defined in domain
+
+753
+00:55:59,650 --> 00:56:03,570
+of T a closure اللي عم نضل ليش ما نثبت؟ بدنا نثبت
+
+754
+00:56:03,570 --> 00:56:10,550
+أنه اللي هو الـ linearity وبدنا نثبت اللي هي الـ
+
+755
+00:56:10,550 --> 00:56:13,370
+boundedness ونثبت في النهاية نورم هذا بسوء نورم
+
+756
+00:56:13,370 --> 00:56:14,410
+هذا شوفوا الآن
+
+757
+00:56:18,840 --> 00:56:24,320
+Hence T tilde is well defined لان let X and X
+
+758
+00:56:24,320 --> 00:56:31,140
+prime be any elements in domain of T closure عشان
+
+759
+00:56:31,140 --> 00:56:34,640
+أثبت الـ linearity والألفة بيه any scalar then
+
+760
+00:56:34,640 --> 00:56:37,480
+there are sequences مدام X في domain of T إذا
+
+761
+00:56:37,480 --> 00:56:45,840
+بلاجي sequence XN للـ X و XN' للـ X' حيث معايا XN
+
+762
+00:56:45,840 --> 00:56:51,380
+بتروح للـ X و XN' بتروح لمين؟ للـ X' as above بالظبط
+
+763
+00:56:51,380 --> 00:56:55,340
+القالية التعريف اللي عارفينها هيكون ال TXN بيروح
+
+764
+00:56:55,340 --> 00:57:01,780
+لمين؟ ل some Y في الـ Y و TXN' هيروح لمين؟ لـ Y' هذا
+
+765
+00:57:01,780 --> 00:57:07,050
+قالية التعريف إذاً هيكون T تلدة للـ X اللي هي الـ Y
+
+766
+00:57:07,050 --> 00:57:13,610
+اللي روحت للـ X و T تلدة X برايم إيش هتكون؟ الـ Y
+
+767
+00:57:13,610 --> 00:57:20,190
+برايم هذه الآن since T is a linear then T of Alpha
+
+768
+00:57:20,190 --> 00:57:25,400
+X N زائد X N برايم إيش هتساوي؟ الـ T العصرية الـ T
+
+769
+00:57:25,400 --> 00:57:28,180
+العصرية اللي أنا بشتغلها دي بساوة Alpha T X N زي
+
+770
+00:57:28,180 --> 00:57:32,320
+Alpha T X N Prime هدول حيروح لمين؟ Alpha T X N زي T
+
+771
+00:57:32,320 --> 00:57:36,400
+X N Prime الـ T X N هتروح لمين؟ للـ Y و T X N Prime
+
+772
+00:57:36,400 --> 00:57:39,820
+هتروح لمين؟ للـ Y Prime إذا هذا كله راح لمين؟ للـ
+
+773
+00:57:39,820 --> 00:57:45,200
+Alpha I زي Y Prime يعني بمعنى آخر لما Alpha X N زي
+
+774
+00:57:45,200 --> 00:57:50,620
+X M Prime راحت للـ Alpha X زي X Prime الـ T تبعته
+
+775
+00:57:50,620 --> 00:57:55,630
+راحت لهذه إذن هذه هي عبارة عن الـ T تلدة للي قلتن
+
+776
+00:57:55,630 --> 00:58:00,550
+حسب التعريف بمعنى but alpha xn زائد xn prime هذه
+
+777
+00:58:00,550 --> 00:58:04,110
+مش هي بتقدر تتعريف بتروح لل alpha x زايد x prime
+
+778
+00:58:04,110 --> 00:58:08,850
+then by the definition of T تلدة T of هذه اللي
+
+779
+00:58:08,850 --> 00:58:14,080
+راحاتي لها هذه بتساوي سور اللي هو اللي راح اتيلها
+
+780
+00:58:14,080 --> 00:58:18,180
+صورة هادى مين؟ اللي هي صورة هادى؟ راحت لمين؟ للـ α
+
+781
+00:58:18,180 --> 00:58:23,460
+y زائد y' إذن هادى بيصير T of α T تلدة of α x زائد
+
+782
+00:58:23,460 --> 00:58:27,420
+x' بيساوي α y زائد y' اللي هي α y اللي هي مين؟ هي
+
+783
+00:58:27,420 --> 00:58:33,040
+α T تلدة x والـ y' اللي هي T تلدة x' إذن فعلا طلعت
+
+784
+00:58:33,040 --> 00:58:37,600
+عندي T تلدة إيش مالها؟ is linear لذا مفتاح الحل هو
+
+785
+00:58:37,600 --> 00:58:42,720
+هذا هذا مفتاح الشغل كله إنه كيف أنا عرفت المفروض
+
+786
+00:58:42,720 --> 00:58:47,890
+فاهمين مش فاهمين عدوها هتلاقي الكلام واضح أنا بشر
+
+787
+00:58:47,890 --> 00:58:57,390
+أصلا ما يكون الكلام مش واضح وبعيده بعيده
+
+788
+00:58:57,390 --> 00:59:02,770
+بطريقة تصير أوضح لكن بعتقد إنه واضح الان
+
+789
+00:59:03,950 --> 00:59:08,150
+أثبتنا ان T is linear الان نثبت لكم ان T تلد اصلا
+
+790
+00:59:08,150 --> 00:59:12,310
+extension إيش معناه extension؟ ان هي بتساوي الأصل
+
+791
+00:59:12,310 --> 00:59:16,920
+في الأصلي يعني T تلدة على الـ domain of T هي نفس T و
+
+792
+00:59:16,920 --> 00:59:19,480
+لا بتبطئ الـ extension عشواء معايا ده لتانية اصلا
+
+793
+00:59:19,480 --> 00:59:22,760
+أما مادام extension مفهومها أنها بدها تبقى على
+
+794
+00:59:22,760 --> 00:59:26,900
+الأصل زي ما هو وتزيد على زيادة بطريقة تلائم اللي
+
+795
+00:59:26,900 --> 00:59:30,320
+موجود أو تحقق هدف إذا كان بديه هدفانة الهدفانة أن
+
+796
+00:59:30,320 --> 00:59:33,540
+تكون T تلدة normal بيساوي normal T كل هذا حجبناه
+
+797
+00:59:33,540 --> 00:59:38,960
+مرة واحدة الان but T تلدة للـ X أشهر بتساوي T X for
+
+798
+00:59:38,960 --> 00:59:44,620
+all X in every domain من جلك because الـ X عندى X
+
+799
+00:59:44,620 --> 00:59:48,440
+هي بتروح للـ X يعني الـ sequence X X X X بتروح
+
+800
+00:59:48,440 --> 00:59:52,100
+لمين؟ للـ X هاي الـ sequence اللي عندي ماشي بتروح
+
+801
+00:59:52,100 --> 01:00:00,280
+لمين؟ للـ X و الـ TX الـ TX هتروح لمين؟ للـ TX ليش
+
+802
+01:00:00,280 --> 01:00:04,660
+لأن الـ X هادي من وين دي؟ يعني من الـ domain of T و
+
+803
+01:00:04,660 --> 01:00:09,420
+الـ domain of TT continuous عنده اه إذا أكيد هيكون
+
+804
+01:00:09,420 --> 01:00:13,930
+مش bounded ما دام باوندد يا جماعة هال gate فيه عندي
+
+805
+01:00:13,930 --> 01:00:18,310
+sequence of elements كله انثباتات X بيروح لمين؟ للـ
+
+806
+01:00:18,310 --> 01:00:25,760
+X و الـ X وين موجودة؟ في domain الـ T و domain الـ T،
+
+807
+01:00:25,760 --> 01:00:29,340
+T is continuous عنده مدام .. يعني بدل ما أقول Xn
+
+808
+01:00:29,340 --> 01:00:33,980
+بتروح للـ Xn للـ X الـ Xn هذه أشمع للـ X واحد X الـ
+
+809
+01:00:33,980 --> 01:00:37,420
+X اتنين X الـ X ثلاثة X والـ X أربعة X والـ X خمسة
+
+810
+01:00:37,420 --> 01:00:41,940
+X يعني sequence of كل مين؟ X X X هدورها بيروح لمين؟
+
+811
+01:00:41,940 --> 01:00:47,080
+للـ X ماشي الحال الآن أكيد مزامة الـ X موجودة في
+
+812
+01:00:47,080 --> 01:00:54,990
+domain of T هيكون TXn بيروح لمين؟ للـ TX هذه اللي
+
+813
+01:00:54,990 --> 01:01:00,150
+أنا بعرف الـ T تلدة بساوي هذا اللي طلع عندي اللي
+
+814
+01:01:00,150 --> 01:01:06,670
+كنت أسميها Y اللي هي T تلدة للـ X هيساومين؟ TX الـ N
+
+815
+01:01:06,670 --> 01:01:09,930
+TXN هي في الواقع Xات كلها يعني اه فعشانك بقول X
+
+816
+01:01:09,930 --> 01:01:14,310
+بتروح للـ X إذا TX بتروح ل TX ومن ثم T تلدة اللي
+
+817
+01:01:14,310 --> 01:01:21,760
+بعرفها للـ X هي TXN لما تروح لرقم هو اسمه TX هذا
+
+818
+01:01:21,760 --> 01:01:26,800
+بصوتين إذا أكيد أكيد أكيد so T تلده is a linear
+
+819
+01:01:26,800 --> 01:01:32,300
+extension of T وطلع فوق خلّينا ننهي القمر ان نثبت
+
+820
+01:01:32,300 --> 01:01:38,500
+انها bounded ومن ثم نثبت اللي هو norm T هو نفسه
+
+821
+01:01:38,500 --> 01:01:44,440
+norm T تلده وركزوا في ما نتحدث به طيب صلى على
+
+822
+01:01:44,440 --> 01:01:48,880
+النبعخدوا الآن IX في domain الـ T closure خلاص صار
+
+823
+01:01:48,880 --> 01:01:54,070
+domain هو هذا الـ T تلد There is a sequence xn of
+
+824
+01:01:54,070 --> 01:01:57,830
+elements in D of T such that xn بتروح لمين؟ للإكس
+
+825
+01:01:57,830 --> 01:02:02,650
+هذا اللي هو مفتاح الحلو ومفتاح التعريف xn بتروح
+
+826
+01:02:02,650 --> 01:02:06,670
+للإكس وزي ما عملنا فوق هيطلع T xn بتروح لمين؟ للواي
+
+827
+01:02:06,670 --> 01:02:14,310
+و هتكون T تلدة للإكس هو مين؟ الواي and T تلدة للإكس
+
+828
+01:02:14,310 --> 01:02:19,630
+هتكون يش من هي بتساوي Y الان شوف كيف بدي اصل ل T
+
+829
+01:02:19,630 --> 01:02:25,190
+تلده is bounded يعني بدي اثبتلكم ان T تلده T تلده
+
+830
+01:02:25,190 --> 01:02:35,290
+is bounded بمعنى بمعنى
+
+831
+01:02:35,290 --> 01:02:41,950
+بدي اثبت norm T تلده X أصغر لو سوى C في norm X
+
+832
+01:02:45,110 --> 01:02:48,570
+هو في الواقع حثبتلكم أن T تلدة للـ X أصغر أشهر هو C
+
+833
+01:02:48,570 --> 01:02:55,690
+اللي هي نورم الـ T في نورم الـ X طيب تشوف صلوا على
+
+834
+01:02:55,690 --> 01:03:01,290
+النبي عليه الصلاة والسلام احسبولي نورم الـ T X أكيد
+
+835
+01:03:01,290 --> 01:03:04,890
+هيكون تـis bounded أصغر يساوي نورم الـT في نورم
+
+836
+01:03:04,890 --> 01:03:11,090
+الـMain الـXN for all mean N الـNorm الـT
+
+837
+01:03:11,090 --> 01:03:13,490
+continuous ليش معناه continuous؟ بدخل الـlimit جوا
+
+838
+01:03:13,490 --> 01:03:17,190
+وبطلع برا زي ما بده ماشي هنا معناته أن هو نورم
+
+839
+01:03:17,190 --> 01:03:20,850
+الـT continuous letting N بتروح لـinfinity and
+
+840
+01:03:20,850 --> 01:03:25,650
+using the continuity of the norm to get الان خدوا 
+
+841
+01:03:25,650 --> 01:03:30,910
+الآن norm  للـ X من جهة أخرى ايش هيساوي؟ norm
+
+842
+01:03:30,910 --> 01:03:34,470
+الـ Y مش عارفين ماحنا قولنا الـ T للـ X مين هي؟
+
+843
+01:03:34,470 --> 01:03:38,090
+بيساوي .. خدوا norm هذه بيساوي norm هذه ماشي؟  للـ Y
+
+844
+01:03:38,090 --> 01:03:45,010
+ساوي الآن norm  للـ Y اللي هو عبارة عن limit لـ norm
+
+845
+01:03:45,010 --> 01:03:50,390
+T X N مظبوط؟ الـ T X N بيروح لمين؟ الـ T X N بتروح
+
+846
+01:03:50,390 --> 01:03:54,710
+لمين؟ للـ Y إذا الـ limit هذا بيروح لمين؟ لـ Normal Y
+
+847
+01:03:54,710 --> 01:04:04,650
+الـ Y بيساوي T X N صح؟ Normal Y بيساوي norm هذا صح
+
+848
+01:04:04,650 --> 01:04:10,370
+إذا خدوا الـ limit للجهتين بيطلع Normal Y limit 
+
+849
+01:04:10,370 --> 01:04:13,550
+بيساوي
+
+850
+01:04:13,550 --> 01:04:21,800
+limit norm T X N لأن الـ limit بتنزل من جوا الـ norm
+
+851
+01:04:21,800 --> 01:04:28,260
+لأن أنا بعرف الـ Y بيساوي limit الـ T xn صح ولا لأ؟ norm
+
+852
+01:04:28,260 --> 01:04:32,600
+هذه بيساوي norm هذه طلعيني الـ limit برة لأنها
+
+853
+01:04:32,600 --> 01:04:34,860
+continuous بيصير norm الـ y بيساوي limit norm الـ T 
+
+854
+01:04:34,860 --> 01:04:39,820
+xn إذا طلع عندي norm الـ y automatically بيساوي limit 
+
+855
+01:04:39,820 --> 01:04:43,340
+norm الـ T xn نيجي الآن norm الـ T xn أصلا بيساوي
+
+856
+01:04:43,340 --> 01:04:46,170
+norm الـ T في norm الـ x صح؟ إذاً limit هذا أصغر أو يساوي
+
+857
+01:04:46,170 --> 01:04:49,130
+و limit هذه إذاً صار عندي limit هذا أصغر أو يساوي و
+
+858
+01:04:49,130 --> 01:04:52,050
+limit هذه في هذه طب ما هي constant بالنسبة للـ
+
+859
+01:04:52,050 --> 01:04:55,650
+limit اللي بتطلع برة بيصير limit norm الـ xn limit 
+
+860
+01:04:55,650 --> 01:04:59,570
+norm الـ xn مع أن ما أقول الـ xn بتروح للـ x والـ
+
+861
+01:04:59,570 --> 01:05:03,410
+norm continuous إذاً limit norm الـ xn هو عبارة عن 
+
+862
+01:05:03,410 --> 01:05:08,290
+norm الـ x إذاً صار عندي norm الـ T في norm الـ x
+
+863
+01:05:08,290 --> 01:05:15,660
+اللي حصلته norm الـ T للـ x انتبهوا أصغر أو يساوي
+
+864
+01:05:15,660 --> 01:05:20,520
+norm الـT في norm الـX norm الـT هو الـC إذا صارت
+
+865
+01:05:20,520 --> 01:05:25,340
+الـT للـ  is bounded ومش هيك ونورم الـT للـ أصغر
+
+866
+01:05:25,340 --> 01:05:30,700
+يساوي مين؟ norm الـT ليش؟ لأنه أنا أثبتت norm الـ T
+
+867
+01:05:30,700 --> 01:05:35,000
+للـ X أصغر أو يساوي norm الـ T في norm الـ X يعني
+
+868
+01:05:35,000 --> 01:05:37,300
+على norm الـ X للـ X لا تشويه شويه تلد أصغر أو يساوي
+
+869
+01:05:37,300 --> 01:05:39,980
+هذه لكل X في domain الـ T  معدى الـ Zero خدوا الـ
+
+870
+01:05:39,980 --> 01:05:45,240
+Supremum بيصير أصغر أو يساوي هذا معناه أنه هذا الـ 
+
+871
+01:05:45,240 --> 01:05:49,220
+Supremum ايش بيساوي norm الـ T للـ  صارت norm الـ
+
+872
+01:05:49,220 --> 01:05:53,980
+T للـ أصغر أو يساوي norm الـ T العكس سهل العكس سهل
+
+873
+01:05:53,980 --> 01:05:58,920
+وشريعة however norm of T للـ عارفين هو ايش بيساوي
+
+874
+01:05:58,920 --> 01:06:03,360
+احنا supremum لـ norm of T للـ X  X في domain T
+
+875
+01:06:03,360 --> 01:06:06,600
+تبعها closure such that norm of X بيساوي واحد سهل
+
+876
+01:06:06,600 --> 01:06:08,300
+اللي لنا نشتغل على norm of X بيساوي واحد من زمنا
+
+877
+01:06:08,300 --> 01:06:13,650
+التكافئة في قادة الان هذه الست هذه الست أكبر من الـ
+
+878
+01:06:13,650 --> 01:06:17,570
+6 اللي X فيه مالها في domain الـ T وحنا بنعرف في
+
+879
+01:06:17,570 --> 01:06:21,710
+domain الـ T norm الـ T X هو نفسه norm الـ T للـ X 
+
+880
+01:06:21,710 --> 01:06:24,710
+لأنه على domain الـ T الـ T للـ و الـ T زي بعض مش
+
+881
+01:06:24,710 --> 01:06:29,810
+exception إذا هذه المجموعة جزئية من هذه اه، إذا 
+
+882
+01:06:29,810 --> 01:06:32,790
+أكيد الـ Supremum على الكبير أكبر أو يساوي الـ
+
+883
+01:06:32,790 --> 01:06:36,090
+Supremum على الأصغر هذا الـ Supremum هو عبارة عن
+
+884
+01:06:36,090 --> 01:06:40,230
+Norm of T يعني بمعنى آخر أثبتنا Norm of T للـ
+
+885
+01:06:40,230 --> 01:06:45,290
+أكبر أو يساوي Norm من الـ T ومن الأصل Norm of T 
+
+886
+01:06:45,290 --> 01:06:47,750
+للـ أصغر يساوي Norm of T  همالة أصلا الصعوبة في
+
+887
+01:06:47,750 --> 01:06:50,370
+الحل، هذا كسيلة بيطلع Norm of T للـ هو بيساوي
+
+888
+01:06:50,370 --> 01:06:55,350
+Norm of T وهكذا بالإنهاء اللي هو الـ Section هذا
+
+889
+01:06:55,350 --> 01:06:56,670
+وإلى لقاء آخر
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/OMe_05RbxKs.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/OMe_05RbxKs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..05d0fdf56a946ab69a58066040ba71ad783b005f
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/OMe_05RbxKs.srt
@@ -0,0 +1,1051 @@
+1
+00:00:05,110 --> 00:00:07,730
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,730 --> 00:00:10,530
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,530 --> 00:00:18,050
+آله وصحبه أجمعين  المحاضرة هي محاضرة رقم 14 مساق 
+
+4
+00:00:18,050 --> 00:00:21,210
+تحليل اقتراني أو تحليل دالي  طلاب وطالبات الجامعة 
+
+5
+00:00:21,210 --> 00:00:26,430
+الإسلامية ماجستيريا رياضية وصلنا لعند 2.8
+
+6
+00:00:26,430 --> 00:00:32,590
+اللي هو تحت عنوان linear functionals  حكينا المرة 
+
+7
+00:00:32,590 --> 00:00:36,730
+الماضية عن الـ bounded linear operators الآن ده
+
+8
+00:00:36,730 --> 00:00:39,370
+نحكي عن حالة خاصة من الـ bounded linear operators
+
+9
+00:00:39,370 --> 00:00:42,290
+اللي هي حاجة اسمها linear functionals هي عبارة عن 
+
+10
+00:00:42,290 --> 00:00:45,570
+bounded linear operators بس بترمي في الـ field في الـ
+
+11
+00:00:45,570 --> 00:00:51,130
+field أو في الـ scalars  نشوف كده definition a linear
+
+12
+00:00:51,130 --> 00:00:56,930
+functional is a linear operator عادي with domain
+
+13
+00:00:56,930 --> 00:01:02,030
+in a vector space and range when in the scalar
+
+14
+00:01:02,030 --> 00:01:05,210
+field of the vector space هذا كـ linear operator من 
+
+15
+00:01:05,210 --> 00:01:07,970
+دون ما نحكي عن الـ bounded اللي هو اللي عندما نحكي 
+
+16
+00:01:07,970 --> 00:01:10,850
+عن الـ boundedness على طول بنحط vector spaces أو
+
+17
+00:01:10,850 --> 00:01:14,650
+بنحط norms أو بنحط topologies definition a bounded
+
+18
+00:01:14,650 --> 00:01:17,690
+linear functional الآن بدنا نحكي عن bounded linear
+
+19
+00:01:17,690 --> 00:01:21,510
+functional is a bounded linear operator with
+
+20
+00:01:21,510 --> 00:01:27,570
+domain in a normed space عادي and range وين بس in
+
+21
+00:01:27,570 --> 00:01:32,030
+the scalar field لـ normed space اللي إيش اللي في الـ
+
+22
+00:01:32,030 --> 00:01:35,730
+domain ماشي الحالة إذا يعني من normed space إلى الـ
+
+23
+00:01:35,730 --> 00:01:39,690
+scalar field تبعه هذا اللي بنسميه bounded linear 
+
+24
+00:01:39,690 --> 00:01:43,610
+functional يعني أعطينا اسم خاص في النهاية اللي هو 
+
+25
+00:01:43,610 --> 00:01:46,830
+الـ scalar ما هو عليه norm في حالة الـ R الـ
+
+26
+00:01:46,830 --> 00:01:49,930
+absolute value وفي حالة الـ C ما هو الـ modulus اللي هو 
+
+27
+00:01:49,930 --> 00:01:54,690
+يعني اللي احنا بنتعامل معاه دائما نيجي لأول نظرية 
+
+28
+00:01:54,690 --> 00:01:59,310
+النظرية الأولى a linear functional يعني كل linear
+
+29
+00:01:59,310 --> 00:02:02,730
+functional is a linear operator وكل bounded linear
+
+30
+00:02:02,730 --> 00:02:06,070
+functional is a bounded linear operator يعني اللي 
+
+31
+00:02:06,070 --> 00:02:08,710
+انطبق على الـ bounded linear operators هنطبق عالميا
+
+32
+00:02:08,710 --> 00:02:11,090
+على الـ bounded linear functionals
+
+33
+00:02:13,450 --> 00:02:16,670
+النظرية 283 بتقول الـ a linear functional F with
+
+34
+00:02:16,670 --> 00:02:20,150
+domain T in a normed space is continuous if and
+
+35
+00:02:20,150 --> 00:02:24,090
+only if it is bounded، ذات الحق إنها قبل شوية، هي
+
+36
+00:02:24,090 --> 00:02:26,830
+نفس النظرية بس اللي هي بنأكدها على حالة الـ linear
+
+37
+00:02:26,830 --> 00:02:30,600
+functional الآن examples بناخد أمثلة على اللي هو 
+
+38
+00:02:30,600 --> 00:02:33,040
+bounded linear functionals أو على الـ linear
+
+39
+00:02:33,040 --> 00:02:36,680
+functionals أو بدنا ناخد على اللي هو functionals
+
+40
+00:02:36,680 --> 00:02:40,520
+ما تكونش إيش اللي هو linear أحيانا الآن the norm
+
+41
+00:02:40,520 --> 00:02:44,460
+الـ norm اللي إحنا بنعرفه برمي من الـ X لعند مين 
+
+42
+00:02:44,460 --> 00:02:47,340
+لعند الـ R بياخد أي norm في أي element من الـ X 
+
+43
+00:02:47,340 --> 00:02:50,760
+وبياخد له الـ norm بطلع إيش ما له R positive اتحاد 
+
+44
+00:02:50,760 --> 00:02:56,580
+الـ zero on a normed space X is a functional صح لكن
+
+45
+00:02:56,580 --> 00:03:00,960
+إيش ماله إنه X which is not linear مش linear لأنه 
+
+46
+00:03:00,960 --> 00:03:07,720
+بنعرف احنا اللي هو norm norm norm الـ αX + 
+
+47
+00:03:07,720 --> 00:03:12,380
+β أو Y + Y ليس شرطا هذا أصغر أو يساوي 
+
+48
+00:03:12,380 --> 00:03:16,020
+absolute value للـ X في norm الـ X + norm الـ Y
+
+49
+00:03:16,340 --> 00:03:23,120
+ولكن المساواة ليس شرطا أن تحدث عشان هيك إشماله is
+
+50
+00:03:23,120 --> 00:03:27,880
+not linear طيب الآن نجي لـ Dot product الـ dot
+
+51
+00:03:27,880 --> 00:03:31,380
+product العادي اللي احنا بنعرفه let A بتساوي a 1 a 2 a 3 لعند
+
+52
+00:03:31,380 --> 00:03:34,740
+B I fix element in R تكعيب define F من R تكعيب لعند R by F of X إيش 
+
+53
+00:03:39,940 --> 00:03:44,340
+بتساوي؟ X ضد الـ A، ماشي الحال؟ الـ dot product
+
+54
+00:03:44,340 --> 00:03:47,220
+العادي اللي هو بياخد الـ vector في الـ R تكعيب و
+
+55
+00:03:47,220 --> 00:03:49,880
+بضربه في الـ vector لكن بطلع قيمة الـ dot product
+
+56
+00:03:49,880 --> 00:03:54,060
+إشماله scalar اللي هو بطلع في الـ R فهذا مثال على 
+
+57
+00:03:54,060 --> 00:03:58,820
+linear functional which is bounded then F is a
+
+58
+00:03:58,820 --> 00:04:03,640
+bounded linear functional ومش هيك كمان norm F
+
+59
+00:04:03,640 --> 00:04:09,430
+هيساوي مين؟ norm A خلينا نشوف الآن اللي هي نبرهن
+
+60
+00:04:09,430 --> 00:04:15,550
+البرهان for all x y element in x and all scalars α 
+
+61
+00:04:15,550 --> 00:04:21,330
+احسب للآن F of αx + y إيش حسب القانون؟ طبعا 
+
+62
+00:04:21,330 --> 00:04:27,170
+الـ A عبارة عن جبنا A متجه معين وهو أداة التعريف 
+
+63
+00:04:27,770 --> 00:04:31,990
+بضرب الـ X فيه ماشي بيصير αX + Y Dot من 
+
+64
+00:04:31,990 --> 00:04:34,870
+الـ A وعارفين أننا الـ dot و ال product بيتوزع من 
+
+65
+00:04:34,870 --> 00:04:39,090
+الخلق و للـ C بيساوي α في X Dot A + Y في
+
+66
+00:04:39,090 --> 00:04:44,050
+منه Dot A هذه بيصير αF of X + F of Y وهذا 
+
+67
+00:04:44,050 --> 00:04:47,470
+يعني أن F إشماله is a linear functional لإنها 
+
+68
+00:04:47,470 --> 00:04:52,290
+بترمي في الـ R زي ما قلنا الأقل بدأ تبتلكم إنها إيه 
+
+69
+00:04:52,290 --> 00:04:55,490
+شمالها إنها bounded انتبهوا لهذه بس بدأ في شغل 
+
+70
+00:04:55,490 --> 00:04:58,830
+بنصلحها هن Hence, F is linear زي ما قولنا وفرقاني
+
+71
+00:04:58,830 --> 00:05:00,990
+X بتساوي x 1 x 2 x 3
+
+72
+00:05:00,990 --> 00:05:05,110
+عناصر مين اللي هرتكعين حسبون الـ absolute value للـ 
+
+73
+00:05:05,110 --> 00:05:07,990
+F of X الـ absolute value للـ F of X F of X إيش
+
+74
+00:05:07,990 --> 00:05:13,270
+بتساوي X ضد مين انتبهوا هن بس عشان في هنا بس شغلة 
+
+75
+00:05:13,270 --> 00:05:17,190
+بنعملها الـ absolute value للـ F of X بيساوي الـ
+
+76
+00:05:17,190 --> 00:05:21,810
+absolute value للـ X ضد مين الـ A؟ معاها؟ لو فرضنا 
+
+77
+00:05:21,810 --> 00:05:28,930
+الـ A هي عبارة عن α1 α2 α3 معاها؟ و 
+
+78
+00:05:28,930 --> 00:05:34,470
+X زي ما فرضناها عبارة عن x1 x2 x3 dot
+
+79
+00:05:34,470 --> 00:05:38,350
+product بيساوي اللي هو الـ dot product لا mean الـ
+
+80
+00:05:38,350 --> 00:05:44,070
+absolute value لا الـ Dot α1x1 α1x1
+
+81
+00:05:44,070 --> 00:05:50,090
+1 + α2x2 + α3x3 يعني بمعنى
+
+82
+00:05:50,090 --> 00:05:52,650
+آخر هو عبارة عن بلغة الـ summation اللي عملها 
+
+83
+00:05:52,650 --> 00:05:55,870
+عبارة عن الـ absolute value للـ summation αi 
+
+84
+00:05:55,870 --> 00:06:01,230
+xi I معايا يا جماعة i من واحد لمين لثلاثة انتبهوا
+
+85
+00:06:01,230 --> 00:06:04,870
+الآن هذا أصغر أو يساوي عشان تصلحوا اللي مكتوب هنا
+
+86
+00:06:04,870 --> 00:06:07,510
+أصغر أو يساوي الـ summation للـ absolute value α
+
+87
+00:06:07,510 --> 00:06:12,580
+i في الـ absolute value of xi I i من عند واحد لمين 
+
+88
+00:06:12,580 --> 00:06:18,220
+لثلاثة وهذه بالكوشي شوارتز inequality أصغر أو يساوي 
+
+89
+00:06:18,220 --> 00:06:24,360
+الـ summation للـ αi تربيع أص نص في الـ
+
+90
+00:06:24,360 --> 00:06:30,800
+summation للـ xi تربيع أص إيش أص نص، مظبوط؟ 
+
+91
+00:06:30,800 --> 00:06:37,090
+معايا؟ هذه مين هي؟ norm من الـ A لأن وين وين قاعد أنا
+
+92
+00:06:37,090 --> 00:06:41,910
+في الـ R تكعيب وهذا norm مين؟ norm من الـ X إذا صار 
+
+93
+00:06:41,910 --> 00:06:45,910
+عندي الآن absolute value لـ F of X أصغر أو يساوي هذا 
+
+94
+00:06:45,910 --> 00:06:50,870
+المقدار بمعنى صار عندي الـ absolute value لـ F of X 
+
+95
+00:06:51,540 --> 00:06:56,740
+أصغر أو يساوي C في norm الـ X الـ C إيش بيساوي 
+
+96
+00:06:56,740 --> 00:07:02,140
+norm الـ A معايا؟ الآن لاحظوا .. لاحظوا .. خليني
+
+97
+00:07:02,140 --> 00:07:06,680
+أكملكم هنا لاحظوا الـ absolute value of F of X على 
+
+98
+00:07:06,680 --> 00:07:14,120
+norm الـ X اللي هو أصغر أو يساوي normين الـ A لأ 
+
+99
+00:07:14,120 --> 00:07:18,460
+أداة التعريف الآن الآن هذه صارت upper bound لهذا 
+
+100
+00:07:18,460 --> 00:07:21,840
+هذا X لـ كوشي شوارتز طبعا خدوا الـ supremum عليها بيصير 
+
+101
+00:07:21,840 --> 00:07:25,840
+اللي هو الـ supremum هو عبارة عن norm F أصغر أو 
+
+102
+00:07:25,840 --> 00:07:31,040
+شو مين norm A واضح؟ إذا طلع عندي الآن norm F
+
+103
+00:07:31,040 --> 00:07:34,400
+أصغر أو شو مين norm A بدي أجيب اللي هو العكس 
+
+104
+00:07:34,400 --> 00:07:37,880
+norm A أصغر أو شو مين norm F هذا الأسلوب اللي 
+
+105
+00:07:37,880 --> 00:07:43,390
+بدي أجيبه الآن هو أسلوب اختيار نقطة نقطة مناسبة تجيب 
+
+106
+00:07:43,390 --> 00:07:46,750
+ليها هتلاقوها في هذا المثال وفي المثال اللي بعده
+
+107
+00:07:46,750 --> 00:07:49,210
+وإلى آخره نفس الأسلوب انتبهوا الآن عندي 
+
+108
+00:07:52,110 --> 00:07:54,950
+صارت عندي norm الـ F أصغر تساوي norm الـ A however
+
+109
+00:07:54,950 --> 00:07:58,590
+norm الـ F بتساوي زي ما قلنا الـ supremum of absolute
+
+110
+00:07:58,590 --> 00:08:01,430
+value of F of X على norm الـ X X element in X و X 
+
+111
+00:08:01,430 --> 00:08:06,470
+تساوي صفر الآن اللي بدي أجيب أنا اللي هو الـ
+
+112
+00:08:06,470 --> 00:08:09,190
+absolute value of F of X أنا بعرفها عبارة عن X dot
+
+113
+00:08:09,190 --> 00:08:15,760
+mean الـ A ماشي هذه هذه absolute value of x dot a و 
+
+114
+00:08:15,760 --> 00:08:18,940
+norm x هي norm x بدي اختار اللي هو أنا قيمة 
+
+115
+00:08:18,940 --> 00:08:23,080
+معينة عشان اللي هي احصل بس الـ a لو أخدت الـ 
+
+116
+00:08:23,080 --> 00:08:27,780
+absolute value هذا أكيد الـ supremum أكبر أو يساوي 
+
+117
+00:08:27,780 --> 00:08:32,490
+عند أي قيمة من القيمممضمنها عند مين؟ عند الـ A إذا
+
+118
+00:08:32,490 --> 00:08:35,090
+أكبر أو يساوي absolute value of F of A على norm
+
+119
+00:08:35,090 --> 00:08:37,750
+الـ A absolute value of F of A إيش هو؟ نعرفه
+
+120
+00:08:37,750 --> 00:08:41,170
+مسبقًا A Dot A A Dot A هو عبارة عن norm الـ A 
+
+121
+00:08:41,170 --> 00:08:45,190
+تربيع absolute value له على norm الـ A بطلع norm 
+
+122
+00:08:45,190 --> 00:08:49,050
+الـ A إذا حصلت norm الـ F أكبر أو يساوي norm الـ A 
+
+123
+00:08:49,050 --> 00:08:54,870
+باختياري للنقطة المعينة اللي هي الـ A عسى أحصل عن 
+
+124
+00:08:54,870 --> 00:08:58,130
+equality هذه وصار عندي norm الـ F من التلتين بيساوي 
+
+125
+00:08:58,130 --> 00:09:05,560
+norm الـ A اللي بعده يلا خلصنا الدوت بروداكت
+
+126
+00:09:05,560 --> 00:09:12,240
+definite integral الآن اللي جاب في السؤال اللي جابه
+
+127
+00:09:12,240 --> 00:09:16,980
+كنا نرمي .. حطينا kernel جوه الـ integration عشان
+
+128
+00:09:16,980 --> 00:09:20,080
+يطلع function في T ضال function of two variables
+
+129
+00:09:20,080 --> 00:09:23,800
+واحدة بنكملها والثانية بتبقى حرة هي اللي بتخليني 
+
+130
+00:09:23,800 --> 00:09:26,680
+.. بضل اللي ناتج continuous function برمي في الـ 
+
+131
+00:09:26,680 --> 00:09:28,700
+continuous فصار من norm of this space لـ norm of
+
+132
+00:09:28,700 --> 00:09:33,100
+this space هنا الآن لأ بدي أحسب A بدي أحسب اللي أخد
+
+133
+00:09:33,100 --> 00:09:36,400
+الـ J من A إلى الـ B و الـ F من C من A و B إلى R 
+
+134
+00:09:36,400 --> 00:09:40,080
+دي defined by what؟ by F of X هي اللي هنا في الـ 
+
+135
+00:09:40,080 --> 00:09:42,300
+continuous functions بيساوي الـ integration الـ 
+
+136
+00:09:42,300 --> 00:09:45,120
+integration من A إلى B للـ X of T DT يعني ما ضلش إيش
+
+137
+00:09:45,120 --> 00:09:48,760
+هتضل الرقم الرقم اللي هيطلع من هنا اللي هو الـ
+
+138
+00:09:48,760 --> 00:09:53,290
+field اللي هو الـ vector space اللي عندي then F is a
+
+139
+00:09:53,290 --> 00:09:56,890
+bounded linear functional with norm الـ F هيطلع 
+
+141
+00:09:56,890 --> 00:10:02,930
+لمين طول الفترة المذكورة ماشي شوفوا هل مثل المحلق
+
+142
+00:10:03,570 --> 00:10:06,090
+الآن F is a linear functional ما فيش دا أنا أعيد حالي
+
+143
+00:10:06,090 --> 00:10:08,390
+F is linear ما عملناها قبل شوي ال integration is
+
+144
+00:10:08,390 --> 00:10:13,110
+linear فـ why إلكم عملناها اللي الآن بدأ أثبت main
+
+145
+00:10:13,110 --> 00:10:15,770
+اللي هو ال boundedness و أثبت norm الـ F بساوي
+
+146
+00:10:15,770 --> 00:10:18,890
+normal B minus A اللي هو norm الـ F أصغر بساوي B
+
+147
+00:10:18,890 --> 00:10:21,630
+minus A بنثبتها و بعدين بنختار نقطة معينة و بنثبت
+
+148
+00:10:21,630 --> 00:10:28,080
+كده و هتلاقوا الأساليب متشابهة نشوف كيف for any x
+
+149
+00:10:28,080 --> 00:10:31,420
+element in C[0,1] يعني continuous function على فترة
+
+150
+00:10:31,420 --> 00:10:35,080
+0,1 we have حسبول ال absolute value لـ f of x الـ
+
+151
+00:10:35,080 --> 00:10:37,820
+absolute value لـ f of x لأنه ما كتبش norm لأن f of
+
+152
+00:10:37,820 --> 00:10:40,420
+x بترمي في الـ R فإيش الـ norm هو عبارة عن absolute
+
+153
+00:10:40,420 --> 00:10:43,900
+value absolute value لـ f of x بيساوي الـ absolute
+
+154
+00:10:43,900 --> 00:10:47,640
+value لل integration من a و b هذا أصغر أو يساوي من
+
+155
+00:10:47,640 --> 00:10:50,160
+صحيحة ال integration ال integration لل absolute
+
+156
+00:10:50,160 --> 00:10:54,110
+value صح؟ واللي جوا اللي هو X of T أكيد أصغر أو
+
+157
+00:10:54,110 --> 00:10:58,030
+يساوي ال maximum على كل الـ T، ماشي؟ إذا أصغر أو
+
+158
+00:10:58,030 --> 00:11:00,850
+يساوي B minus A في ال maximum لـ X of T T element
+
+159
+00:11:00,850 --> 00:11:06,180
+in J مفهوم، أه؟ إذا صار عندي الآن B minus A مضروب
+
+160
+00:11:06,180 --> 00:11:09,680
+في مين؟ هذا عبارة عن الـ Norm Normal X صار عنده
+
+161
+00:11:09,680 --> 00:11:12,340
+Absolute Value of X أصغر أو يساوي B minus A في
+
+162
+00:11:12,340 --> 00:11:16,380
+Normal X بمعنى آخر صارت F bounded ومش هيك و
+
+163
+00:11:16,380 --> 00:11:20,440
+Absolute Value of X على Normal X أصغر أو يساوي B
+
+164
+00:11:20,440 --> 00:11:23,840
+minus A صارت الـ B minus A يتبع عن Upper Bound لـ
+
+165
+00:11:23,840 --> 00:11:27,260
+Absolute Value of X على Normal X إذا صار Supremum
+
+166
+00:11:27,260 --> 00:11:29,720
+اللي هو الـ Upper Bound أصغر أو يساوي B minus A اللي
+
+167
+00:11:29,720 --> 00:11:32,440
+هي Upper Bound يعني norm of f آخر شو بيه minus a
+
+168
+00:11:32,440 --> 00:11:35,700
+قلته هذا قبلين عيده
+
+169
+00:11:39,850 --> 00:11:43,870
+Conversely أكبر أو يساوي اختيار نقطة تخدمني ماشي
+
+170
+00:11:43,870 --> 00:11:46,990
+الحال النقطة اللي بتجيبلي هذه واحد واضح أن أنا
+
+171
+00:11:46,990 --> 00:11:49,970
+بتاخدها إيه إيش مالها واحد عشان أعمل أنت اللي هو
+
+172
+00:11:49,970 --> 00:11:53,070
+تكامل يطلع عقلي دي بي مانس واحد و تنحل أموري ده
+
+173
+00:11:53,070 --> 00:11:55,670
+نشوف كيف إيش اللي بقوله Now choose X not
+
+174
+00:11:55,670 --> 00:12:00,070
+independent of C,A,B وخد X not of T إيش بتساوي ال
+
+175
+00:12:00,070 --> 00:12:02,670
+constant function واحد وده متصل أما احنا عارفين
+
+176
+00:12:03,230 --> 00:12:07,490
+الآن norm الـ F أكبر أو يساوي اللي هو ال absolute
+
+177
+00:12:07,490 --> 00:12:10,730
+value علي هذه عند نقطة معينة النقطة المعينة أخد
+
+178
+00:12:10,730 --> 00:12:14,010
+تميين اللي هي واحد الآن absolute value لـ F of X
+
+179
+00:12:14,010 --> 00:12:18,550
+بساوي اللي هي بساوي هذه نورمها واحد لأن قيمتها
+
+180
+00:12:18,550 --> 00:12:22,270
+واحد النورم على الفترة من A من A لـ B minus B هيطلع
+
+181
+00:12:22,270 --> 00:12:27,550
+إيش بساوي integration فاهمين أه؟ طيب، الآن بيصير
+
+182
+00:12:27,550 --> 00:12:30,690
+عندي الـ Absolute Value of .. لأ الـ X0 هذه عبارة
+
+183
+00:12:30,690 --> 00:12:34,170
+عن نقطة في الـ Continuous Function قيمتها ..
+
+184
+00:12:34,170 --> 00:12:37,610
+نورمها هو الـ Maximum لقيمة الدالة، ما هي ثابتة،
+
+185
+00:12:37,610 --> 00:12:39,790
+الـ Maximum اللي هو واحد، ما عنديش فراش اللقاء في
+
+186
+00:12:39,790 --> 00:12:42,970
+الـ Integration فبيصير عندي Norm الـ F أكبر أو شو
+
+187
+00:12:42,970 --> 00:12:45,870
+هذا القيمة، والـ H دي واحد، بيصير بس اللي فوقه F
+
+188
+00:12:45,870 --> 00:12:48,370
+of X0 ما عرف الـ F of X0 هي عبارة عن الـ
+
+189
+00:12:48,370 --> 00:12:52,670
+Integration من LBDTabsolute value لها اللي هو هذه
+
+190
+00:12:52,670 --> 00:12:56,690
+اللي عبارة عن نفسها لأن دي موجب أصلا بي ماينوس ايه
+
+191
+00:12:56,690 --> 00:13:00,590
+إذا صار عندي norm of بيساوي أكبره بيساوي أصلا
+
+192
+00:13:00,590 --> 00:13:14,210
+بيساوي إذا في مساواة اللي بعدها نيجي الآن ناخد
+
+193
+00:13:14,210 --> 00:13:20,110
+اللي هي F من continuous function لـ R بس هنسويها
+
+194
+00:13:20,110 --> 00:13:26,790
+بتساوي قيمة الدالة اللي بدرسلها عند نقطة معينة يعني
+
+195
+00:13:26,790 --> 00:13:30,510
+الآن في عندي F باسم C و A و B اللي هو continuous
+
+196
+00:13:30,510 --> 00:13:33,950
+function let F من C و A و B اللي عند الـ R بي
+
+197
+00:13:33,950 --> 00:13:39,990
+defined by إيش عرفتها؟ F of X بتساوي X عن T note
+
+198
+00:13:39,990 --> 00:13:43,010
+أنا ما أخد T note أدى التعريف T note معينة خمسة ستة
+
+199
+00:13:43,010 --> 00:13:46,930
+سبعة نص ربع في الفترة من A و B بحسب قيمة الدالة
+
+200
+00:13:46,930 --> 00:13:51,190
+عند هذا الـ T note وبتكون هي صورة مين الـ X under F
+
+201
+00:13:51,190 --> 00:13:55,290
+فبتكون F of X بيساوي X of مين of T not صارت عبارة
+
+202
+00:13:55,290 --> 00:13:59,750
+عن هذه لأن الـ X من وين جاية من A و B continuous
+
+203
+00:13:59,750 --> 00:14:02,950
+function من A و B بترمي في الـ R فقيمتها إيش مالها
+
+204
+00:14:02,950 --> 00:14:06,930
+عبارة عن عدد حقيقي فـ X عند أي نقطة اللي هو بيساوي
+
+205
+00:14:06,930 --> 00:14:10,970
+اللي هو عدد حقيقي إذا صارت F of X ترمي وين في الـ R
+
+206
+00:14:10,970 --> 00:14:14,570
+طيب F of X بيساوي X of T not where T not is
+
+207
+00:14:14,570 --> 00:14:20,580
+a fixed point in J اللي هي A و B then F is a bounded
+
+208
+00:14:20,580 --> 00:14:24,160
+linear functional و Norm الـ F إيش بيساوي؟ بيساوي
+
+209
+00:14:24,160 --> 00:14:27,620
+واحد، هيكون ال bounded linear functional و نورمه
+
+210
+00:14:27,620 --> 00:14:32,460
+هيساوي مين؟ بس الواحد يشوفه كده، بسهل الأمر F is a
+
+211
+00:14:32,460 --> 00:14:35,400
+linear functional اللي هي سهلة لإنه أصلا هي عبارة
+
+212
+00:14:35,400 --> 00:14:39,760
+عن F of Alpha X زائد Beta Y أو زائد Y بيساوي إيش
+
+213
+00:14:39,760 --> 00:14:43,840
+قيمتها Alpha X زائد Y عند الـ T Note ويساوي Alpha
+
+214
+00:14:43,840 --> 00:14:47,600
+of X عند الـ T Note زائد Y عند الـ T Note وبيصير
+
+215
+00:14:47,600 --> 00:14:51,180
+Alpha في F زائد اللي هي FY إذا اللي لينيارات، إذا
+
+216
+00:14:51,180 --> 00:14:54,640
+الموضوع اللي لينيارات سهل طيب إذا Y تبعت اللي
+
+217
+00:14:54,640 --> 00:14:59,100
+لينيارات سهلة و هيني حكيتها نيجي نحكي عن ال
+
+218
+00:14:59,100 --> 00:15:04,010
+boundedness for any x element in C[0,1] خدلي ال
+
+219
+00:15:04,010 --> 00:15:07,910
+absolute value لمين؟ لـ F of X ال absolute value لـ
+
+220
+00:15:07,910 --> 00:15:10,630
+F of X أحسبه عبارة عن بساوي ال absolute value
+
+221
+00:15:10,630 --> 00:15:16,890
+لقيمتها إيش قيمتها؟ X of T0 X of T0 أكيد أكيد أكيد
+
+222
+00:15:16,890 --> 00:15:21,760
+قيمة ده اللي عند واحدة من هنا T0 إن إذا أكيد أصغر
+
+223
+00:15:21,760 --> 00:15:25,620
+أو يساوي ال maximum على كل الفترة عن T نقطة و T
+
+224
+00:15:25,620 --> 00:15:30,400
+واحد و كل الـ T الموجودة في الجيب اللي هو بمثل مين
+
+225
+00:15:30,400 --> 00:15:33,140
+Normal X إذا صارت عبارة عن ال absolute value of F
+
+226
+00:15:33,140 --> 00:15:37,400
+of X أصغر أو يساوي Normal X و منه ال absolute value
+
+227
+00:15:37,400 --> 00:15:41,220
+of F of X على Normal X لو X لا تساوي صفر أو Normal
+
+228
+00:15:41,220 --> 00:15:44,860
+لا تساوي صفر أصغر أو يساوي واحد ال supremum صار
+
+229
+00:15:44,860 --> 00:15:48,880
+أصغر اللي هو أو يساوي واحد معايا إذا صار عندي
+
+230
+00:15:48,880 --> 00:15:53,780
+Normal F أصغر أو يساوي واحد كده الفكرة مكررة الآن
+
+231
+00:15:53,780 --> 00:15:58,080
+طب الآن بدنا نجيب اللي هو الأكبر يساوي و نختاره عند
+
+232
+00:15:58,080 --> 00:16:02,340
+نقطة معينة Now choose X note في C, V و B with X
+
+233
+00:16:02,340 --> 00:16:06,520
+note إيش بتساوي واحد هيك الحدث بقول أصلا عشان أحصل
+
+234
+00:16:06,520 --> 00:16:10,950
+على الواحد ال absolute value لـ F of X أكبر أو يساوي
+
+235
+00:16:10,950 --> 00:16:14,470
+F عند قيمة معينة absolute value على Norm القيمة
+
+236
+00:16:14,470 --> 00:16:17,530
+اللي أخدتها القيمة اللي أخدتها ما أنا أخدها واحد
+
+237
+00:16:17,530 --> 00:16:21,870
+فنورمها بتساوي واحد و اللي فوق أصلا قيمتها absolute
+
+238
+00:16:21,870 --> 00:16:26,330
+F of X هي عبارة عن قيمة X of T naught و في الأصل ما
+
+239
+00:16:26,330 --> 00:16:30,030
+هي أصلا معرفهاش بتساوي واحد إذا صار عندي Norm لـ F
+
+240
+00:16:30,030 --> 00:16:30,930
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+241
+00:16:30,930 --> 00:16:31,730
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+242
+00:16:31,730 --> 00:16:34,730
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+243
+00:16:34,730 --> 00:16:36,290
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+244
+00:16:36,290 --> 00:16:41,850
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+245
+00:16:41,850 --> 00:16:44,650
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+246
+00:16:44,650 --> 00:16:46,650
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+247
+00:16:46,650 --> 00:16:52,830
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+248
+00:16:52,830 --> 00:16:57,960
+أكبر be a fixed point in L2 من L2 اللي هو summation
+
+249
+00:16:57,960 --> 00:17:02,660
+كذا Norm هال summation المدرستربيع الكل أص نص بدل
+
+250
+00:17:02,660 --> 00:17:05,340
+من I من عند واحد لخمسة أو I من واحد لاتنين I لعند
+
+251
+00:17:05,340 --> 00:17:09,020
+واحد لما لا نهاية يعني مش هيختلف بروحانه عن مين عن
+
+252
+00:17:09,020 --> 00:17:13,160
+الشغلات اللي أثبتناها بالنسبة لـ R تكعيب و R تربيع
+
+253
+00:17:13,160 --> 00:17:18,260
+و R ما الآخرين let αI be الـ بعض الشغلات بسيطة let αI
+
+254
+00:17:18,260 --> 00:17:21,660
+be a fixed point in التربيع and F من التربيع اللي
+
+255
+00:17:21,660 --> 00:17:27,030
+عنده R تربيع be defined by F of X إيش بتساوي صميم
+
+256
+00:17:27,030 --> 00:17:31,190
+XI I Alpha I I من واحد لعند مين لعند infinity for
+
+257
+00:17:31,190 --> 00:17:34,130
+all X elementين قالوا بالظبط بالظبط بالظبط زي
+
+258
+00:17:34,130 --> 00:17:38,610
+المثال اللي قبله شوية F of X بيساوي X Dot A الـ X
+
+259
+00:17:38,610 --> 00:17:42,010
+ضد الـ إيش؟ إيش كانت؟ XI واحد Gamma واحد زيدي XI
+
+260
+00:17:42,010 --> 00:17:44,790
+اتنين Gamma اتنين زيدي XI تلاتة Gamma تلاتة الآن
+
+261
+00:17:44,790 --> 00:17:47,970
+إيش ماله هذا؟ من واحد إلى وين إلى الأعلى نهاية إذا
+
+262
+00:17:47,970 --> 00:17:52,130
+الـ linearity و ال boundedness بالظبط زيها then F
+
+263
+00:17:52,130 --> 00:17:56,330
+is a bounded linear functional عشان هيك لفت to the
+
+264
+00:17:56,330 --> 00:17:59,430
+reader مبارك الله فيكم و إلى لقاء آخر
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/OMe_05RbxKs_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/OMe_05RbxKs_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d8ea8fd634e34b32f7f1bdb9e040d19c4ce8e08f
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/OMe_05RbxKs_raw.srt
@@ -0,0 +1,1060 @@
+1
+00:00:05,110 --> 00:00:07,730
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,730 --> 00:00:10,530
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,530 --> 00:00:18,050
+آله وصحبه أجمعين المحاضرة هي محاضرة رقم 14 مساق
+
+4
+00:00:18,050 --> 00:00:21,210
+تحليل اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:21,210 --> 00:00:26,430
+الإسلامية ماجستيريا رياضيةوصلنا لعند اتنين تمانية
+
+6
+00:00:26,430 --> 00:00:32,590
+اللي هو تحت عنوان linear functionals حكينا المرة
+
+7
+00:00:32,590 --> 00:00:36,730
+الماضية عن ال bounded linear operators الآن ده
+
+8
+00:00:36,730 --> 00:00:39,370
+نحكي عن حالة خاصة من ال bounded linear operators
+
+9
+00:00:39,370 --> 00:00:42,290
+اللي هي حاجة اسمها linear functionals هي عبارة عن
+
+10
+00:00:42,290 --> 00:00:45,570
+bounded linear operators بس بترمي في field في ال
+
+11
+00:00:45,570 --> 00:00:51,130
+field او في scalars انشوف كدهdefinition a linear
+
+12
+00:00:51,130 --> 00:00:56,930
+functional is a linear operator عادى with domain
+
+13
+00:00:56,930 --> 00:01:02,030
+in a vector space and range when in the scalar
+
+14
+00:01:02,030 --> 00:01:05,210
+field of the vector space هذا ك linear operator من
+
+15
+00:01:05,210 --> 00:01:07,970
+دون ما نحكي عن ال bounded اللي هو اللي عندما نحكي
+
+16
+00:01:07,970 --> 00:01:10,850
+عن ال boundedness على طول بنحط vector spaces أو
+
+17
+00:01:10,850 --> 00:01:14,650
+بنحط norms أو بنحط topologiesdefinition a bounded
+
+18
+00:01:14,650 --> 00:01:17,690
+linear functional الان بدنا نحكي عن bounded linear
+
+19
+00:01:17,690 --> 00:01:21,510
+functional is a bounded linear operator with
+
+20
+00:01:21,510 --> 00:01:27,570
+domain in a normed space عادي and range وين بس in
+
+21
+00:01:27,570 --> 00:01:32,030
+the scalar field لnormed space اللي إيش اللي في ال
+
+22
+00:01:32,030 --> 00:01:35,730
+domain ماشي الحالة إذا يعني من normed space إلى ال
+
+23
+00:01:35,730 --> 00:01:39,690
+scalar field تبعه هذا اللي بنسميه bounded linear
+
+24
+00:01:39,690 --> 00:01:43,610
+functional يعني أعطينا اسم خاصفي النهاية اللي هو
+
+25
+00:01:43,610 --> 00:01:46,830
+الـ scalar ما هو عليه نور في حالة الـ R الـ
+
+26
+00:01:46,830 --> 00:01:49,930
+absolute value وفي حالة الـ C ما هو المدلس اللي هو
+
+27
+00:01:49,930 --> 00:01:54,690
+يعني اللي احنا بنتعامل معاه دائما نيجي لأول نظرية
+
+28
+00:01:54,690 --> 00:01:59,310
+النظرية الأولى a linear functional يعني كل linear
+
+29
+00:01:59,310 --> 00:02:02,730
+functional is a linear operator وكل bounded linear
+
+30
+00:02:02,730 --> 00:02:06,070
+functional is a bounded linear operator يعني اللي
+
+31
+00:02:06,070 --> 00:02:08,710
+انطبق على ال bounded linear operators هنطبق عالميا
+
+32
+00:02:08,710 --> 00:02:11,090
+على ال bounded linear functionals
+
+33
+00:02:13,450 --> 00:02:16,670
+النظرية 283 بتقول الـ a linear functional F with
+
+34
+00:02:16,670 --> 00:02:20,150
+domain T in a normed space is continuous if and
+
+35
+00:02:20,150 --> 00:02:24,090
+only if it is H-bound، ذات الحق إنها قبل شوية، هي
+
+36
+00:02:24,090 --> 00:02:26,830
+نفس النظرية بس اللي هي بنأكدها على حالة الـ linear
+
+37
+00:02:26,830 --> 00:02:30,600
+functionalالان examples بناخد أمثلة على اللي هو
+
+38
+00:02:30,600 --> 00:02:33,040
+bounded linear functionals أو على ال linear
+
+39
+00:02:33,040 --> 00:02:36,680
+functionals أو بدنا ناخد على اللي هو functionals
+
+40
+00:02:36,680 --> 00:02:40,520
+ما تكونش إيش اللي هو linear أحيانا الان the norm
+
+41
+00:02:40,520 --> 00:02:44,460
+ال norm اللي إحنا بنعرفه برمى من ال X لعند مين
+
+42
+00:02:44,460 --> 00:02:47,340
+لعند ال R بياخد أي norm في أي element من ال X
+
+43
+00:02:47,340 --> 00:02:50,760
+وبياخدله ال norm بطلع أيش ما له R positive اتحاد
+
+44
+00:02:50,760 --> 00:02:56,580
+ال zeroon a normed space X is a functional صح لكن
+
+45
+00:02:56,580 --> 00:03:00,960
+ايش ماله انه X which is not linear مش linear لأنه
+
+46
+00:03:00,960 --> 00:03:07,720
+بنعرف احنا اللي هو norm norm norm الـ Alpha X زائد
+
+47
+00:03:07,720 --> 00:03:12,380
+Beta أو Y زائد Y ليس شرطا هذا أصغر أو ساوي
+
+48
+00:03:12,380 --> 00:03:16,020
+absolute value لل X في norm ال X زائد norm ال Y
+
+49
+00:03:16,340 --> 00:03:23,120
+ولكن المساواة ليس شرطا أن تحدث عشان هيك اشماله is
+
+50
+00:03:23,120 --> 00:03:27,880
+not linear طيب الان نجي لـ Dot product ال dot
+
+51
+00:03:27,880 --> 00:03:31,380
+product العادل اللي احنا بنعرفه let A بتساوي الف
+
+52
+00:03:31,380 --> 00:03:34,740
+واحد الف اتنين الف تلاتة لعند B I fix element in R
+
+53
+00:03:34,740 --> 00:03:39,940
+تكعيب define F من R تكعيب لعند R byF of X ايش
+
+54
+00:03:39,940 --> 00:03:44,340
+بتساوي؟ X ضد الـA، ماشي الحال؟ الـ dot product
+
+55
+00:03:44,340 --> 00:03:47,220
+العادى اللي هو بياخد ال vector في الـR تكييب و
+
+56
+00:03:47,220 --> 00:03:49,880
+بضربه في ال vector لكن بطلع قيمة ال dot product
+
+57
+00:03:49,880 --> 00:03:54,060
+يشمله scalar اللي هو بطلع في الـR فهذا مثال على
+
+58
+00:03:54,060 --> 00:03:58,820
+linear functional which is bounded then F is a
+
+59
+00:03:58,820 --> 00:04:03,640
+bounded linear functional ومش هيك كمان normal F
+
+60
+00:04:03,640 --> 00:04:09,430
+هيساوي مين؟ normal Aخلّينا نشوف الآن اللي هي نبرهن
+
+61
+00:04:09,430 --> 00:04:15,550
+البرهان for all x y element in x and all scalars α
+
+62
+00:04:15,550 --> 00:04:21,330
+احسب للآن f of α x زائد y ايش حسب القانون؟ طبعا
+
+63
+00:04:21,330 --> 00:04:27,170
+الـ A عبارة عن جيبنا A متجه معين وهو أداة التعريف
+
+64
+00:04:27,770 --> 00:04:31,990
+بضرب الـ X فيه ماشي بيصير Alpha X زائد Y Dot من
+
+65
+00:04:31,990 --> 00:04:34,870
+الـ A وعارفين أننا الـ dot و ال product بيتوزع من
+
+66
+00:04:34,870 --> 00:04:39,090
+الخلق و للـ C بيساوي Alpha في X Dot A زائد Y في
+
+67
+00:04:39,090 --> 00:04:44,050
+منه Dot A هذه بيصير Alpha F of X زائد F of Y وهذا
+
+68
+00:04:44,050 --> 00:04:47,470
+يعني أن F أشماله is a linear functional لإنها
+
+69
+00:04:47,470 --> 00:04:52,290
+بترمي في الـ R زي ما قلناالأقل بدأ تبتلكم إنها إيه
+
+70
+00:04:52,290 --> 00:04:55,490
+شمالها إنها bounded انتبهوا لهذه بس بدأ في شغل
+
+71
+00:04:55,490 --> 00:04:58,830
+بنصلحها هن Hence, F is linear زي ما قولنا وفرقاني
+
+72
+00:04:58,830 --> 00:05:00,990
+X بتساوي كساية واحد وكساية اتنين وكساية تلاتة
+
+73
+00:05:00,990 --> 00:05:05,110
+عناصر مين اللي هرتكعين حسبون ال absolute value لل
+
+74
+00:05:05,110 --> 00:05:07,990
+F of X ال absolute value لل F of X F of X إيش
+
+75
+00:05:07,990 --> 00:05:13,270
+بتساوي X ضد مين انتبهوا هن بس عشان في هنا بس شغلة
+
+76
+00:05:13,270 --> 00:05:17,190
+بنعملها ال absolute value لل F of X بساوي ال
+
+77
+00:05:17,190 --> 00:05:21,810
+absolute value لل X ضد مين ال إيه؟معاها؟ لو فرضنا
+
+78
+00:05:21,810 --> 00:05:28,930
+الـ A هي عبارة عن Alpha 1 Alpha 2 Alpha 3 معاها؟ و
+
+79
+00:05:28,930 --> 00:05:34,470
+X زي ما فرضناها عبارة عن XI 1 XI 2 XI 3 dot
+
+80
+00:05:34,470 --> 00:05:38,350
+product بساوة اللي هو ال dot product لا mean ال
+
+81
+00:05:38,350 --> 00:05:44,070
+absolute value لاالـ Dot Alpha 1 X I 1 Alpha 1 X I
+
+82
+00:05:44,070 --> 00:05:50,090
+1 زاد Alpha 2 X I 2 زاد Alpha 3 X I 2 3 يعني بمعنى
+
+83
+00:05:50,090 --> 00:05:52,650
+آخر هو عبارة عن بلغة الـ summation اللي عملها
+
+84
+00:05:52,650 --> 00:05:55,870
+عبارة عن الـ absolute value للـ summation Alpha I
+
+85
+00:05:55,870 --> 00:06:01,230
+X I I معايا يا جماعة I من واحد لمين لتلتة انتبهوا
+
+86
+00:06:01,230 --> 00:06:04,870
+الآن هذا أصغر أو يساوي عشان تصلحوا اللي مكتوب هنا
+
+87
+00:06:04,870 --> 00:06:07,510
+أصغر أو يساوي ال summation لل absolute value Alpha
+
+88
+00:06:07,510 --> 00:06:12,580
+Iفي الـ absolute value of xi I I من عند واحد لمين
+
+89
+00:06:12,580 --> 00:06:18,220
+لتلاتة وهذه بالكوششوارز in quality أصغر أو يساوي
+
+90
+00:06:18,220 --> 00:06:24,360
+ال summation لل alpha I تربيع أص نص في ال
+
+91
+00:06:24,360 --> 00:06:30,800
+summation لل xi I تربيع أص إياش أص نص، مظبوط؟
+
+92
+00:06:30,800 --> 00:06:37,090
+معايا؟ هذه مين هي؟ نور من الـAلأن وين وين قاعد انا
+
+93
+00:06:37,090 --> 00:06:41,910
+في الـ R تكعيب وهذا نور مين؟ نور من الـ X إذا صار
+
+94
+00:06:41,910 --> 00:06:45,910
+عندي الآن absolute value ل F of X أصغر أو ساوي هذا
+
+95
+00:06:45,910 --> 00:06:50,870
+المقدار بمعنى صار عندي ال absolute value ل F of X
+
+96
+00:06:51,540 --> 00:06:56,740
+أصغر أو يساوي C في نورم الـ X الـ C إيش بيساوي
+
+97
+00:06:56,740 --> 00:07:02,140
+نورم الـ A معايا؟ الآن لاحظوا .. لاحظوا .. خليني
+
+98
+00:07:02,140 --> 00:07:06,680
+أكملكم هنا لاحظوا الـ absolute value of F of X على
+
+99
+00:07:06,680 --> 00:07:14,120
+نورم الـ X اللي هو أصغر أو يساوي نورمين الـ Aلأ
+
+100
+00:07:14,120 --> 00:07:18,460
+الأدات التعريف الان الان هذه صارت upper bound لهذا
+
+101
+00:07:18,460 --> 00:07:21,840
+هذا X لاتشهر شفر طبعا خدوا ال supremum عليها بيصير
+
+102
+00:07:21,840 --> 00:07:25,840
+اللي هو ال supremum هو عبارة عن normal F أصغر أو
+
+103
+00:07:25,840 --> 00:07:31,040
+شو مين normal A واضح؟ إذا طلع عندي الان normal F
+
+104
+00:07:31,040 --> 00:07:34,400
+أصغر أو شو مين normal A بدي أجيب اللي هو العكس
+
+105
+00:07:34,400 --> 00:07:37,880
+normal A أصغر أو شو مين normal F هذا الأسلوب اللي
+
+106
+00:07:37,880 --> 00:07:43,390
+بدي أجيبه الآن هو سلوب اختيار نقطةنقطة مناسبة تجيب
+
+107
+00:07:43,390 --> 00:07:46,750
+ليها هتلاقوها في هذا المثال وفي المثال اللي بعده
+
+108
+00:07:46,750 --> 00:07:49,210
+وإلى آخره نفس الأسلوب انتبهوا الآن عندي
+
+109
+00:07:52,110 --> 00:07:54,950
+صارت عندي نورم ال F أصغر تساوي نورم ال A however
+
+110
+00:07:54,950 --> 00:07:58,590
+نورم ال F بتساوي زي ما قلنا ال suprem of absolute
+
+111
+00:07:58,590 --> 00:08:01,430
+value of F of X على نورم ال X X element in X و X
+
+112
+00:08:01,430 --> 00:08:06,470
+تساوي سفر الآن اللي بدي أجيب أنا اللي هو ال
+
+113
+00:08:06,470 --> 00:08:09,190
+absolute value of F of X أنا بعرفها عبارة عن X dot
+
+114
+00:08:09,190 --> 00:08:15,760
+mean ال A ماشيهذه هذه absolute value of x dot a و
+
+115
+00:08:15,760 --> 00:08:18,940
+normal x هي normal x بدي اختار اللي هو انا قيمة
+
+116
+00:08:18,940 --> 00:08:23,080
+معينة عشان اللي هي احصل بس ال a لو اخدت ال
+
+117
+00:08:23,080 --> 00:08:27,780
+absolute value هذا اكيد ال supremum اكبر او يساوي
+
+118
+00:08:27,780 --> 00:08:32,490
+عند اي قيمة من القيمممضمنها عند مين؟ عند الـ A إذا
+
+119
+00:08:32,490 --> 00:08:35,090
+أكبر أوي يسوى absolute value of F of A على norm
+
+120
+00:08:35,090 --> 00:08:37,750
+الـ A absolute value of F of A إيش هو؟ نعرفه
+
+121
+00:08:37,750 --> 00:08:41,170
+مسبقًا A Dot A A Dot A هو عبارة عن norm الـ A
+
+122
+00:08:41,170 --> 00:08:45,190
+تربية absolute value له على norm الـ A بطلع norm
+
+123
+00:08:45,190 --> 00:08:49,050
+الـ A إذا حصلت norm الـ F أكبر أوي يسوى norm الـ A
+
+124
+00:08:49,050 --> 00:08:54,870
+باختياري للنقطة المعينة اللي هي الـ A عسى أحصل عن
+
+125
+00:08:54,870 --> 00:08:58,130
+quality هذه وصار عند norm الـ F من التلتين بسوى
+
+126
+00:08:58,130 --> 00:09:05,560
+norm الـ Aاللي بعده يالاخلصنا الدبطة البردكتية
+
+127
+00:09:05,560 --> 00:09:12,240
+ديفينيت انتيجرال الان اللي جاب في السؤال اللي جابه
+
+128
+00:09:12,240 --> 00:09:16,980
+كنا نرمي .. حطينا kernel جوه ال integration عشان
+
+129
+00:09:16,980 --> 00:09:20,080
+يطلع function في T ضال function of two variables
+
+130
+00:09:20,080 --> 00:09:23,800
+واحدة بنكملها والتانية بتبقى حرة هي اللي بتخليني
+
+131
+00:09:23,800 --> 00:09:26,680
+.. بضل اللي ناتج continuous function برمي في ال
+
+132
+00:09:26,680 --> 00:09:28,700
+continuous فصار من norm of this space ل norm of
+
+133
+00:09:28,700 --> 00:09:33,100
+this space هنا الآن لأ بدي أحسب Aبدي أحسب اللي أخد
+
+134
+00:09:33,100 --> 00:09:36,400
+الـ J من A إلى الـ B و الـ F من C من A و B إلى R
+
+135
+00:09:36,400 --> 00:09:40,080
+دي defined by what؟ by F of X هي اللي هنا في الـ
+
+136
+00:09:40,080 --> 00:09:42,300
+continuous functions بيساوي ال integration ال
+
+137
+00:09:42,300 --> 00:09:45,120
+integration من A إلى B لل X of T DT يعني ماضلش إيش
+
+138
+00:09:45,120 --> 00:09:48,760
+هتضل الرقم الرقم اللي هيطلع من هنا اللي هو ال
+
+139
+00:09:48,760 --> 00:09:53,290
+field اللي هو ال vector space اللي عنديthen F is a
+
+140
+00:09:53,290 --> 00:09:56,890
+bounded linear functional with norm ال F هيطلع
+
+141
+00:09:56,890 --> 00:10:02,930
+لمين طول الفترة المذكورة ماشي شوفوا هل مثل المحلق
+
+142
+00:10:03,570 --> 00:10:06,090
+الأن F is linear functional مافيش دا أنا أعيد حالي
+
+143
+00:10:06,090 --> 00:10:08,390
+F is linear ماعملناها قبل شويه ال integration is
+
+144
+00:10:08,390 --> 00:10:13,110
+linear ف why إلكم أعملناها اللي الآن بدأ أثبت main
+
+145
+00:10:13,110 --> 00:10:15,770
+اللي هو ال boundedness و أثبت norm ال F بساوي
+
+146
+00:10:15,770 --> 00:10:18,890
+normal B minus A اللي هو norm ال F أصغر بساوي B
+
+147
+00:10:18,890 --> 00:10:21,630
+minus A بنثبتها و بعدين بنختار نقطة معينة و بنثبت
+
+148
+00:10:21,630 --> 00:10:28,080
+كده و هتلاقوا الأساليب متشابهة نشوف كيفfor any x
+
+149
+00:10:28,080 --> 00:10:31,420
+element in c0,1 يعني continuous function على فترة
+
+150
+00:10:31,420 --> 00:10:35,080
+0,1 we have حسبول ال absolute value ل f of x ال
+
+151
+00:10:35,080 --> 00:10:37,820
+absolute value ل f of x لأنه ماكتبش norm لأن f of
+
+152
+00:10:37,820 --> 00:10:40,420
+x بترمي في ال R فإيش ال norm هو عبارة عن absolute
+
+153
+00:10:40,420 --> 00:10:43,900
+value absolute value ل f of x بيساوي ال absolute
+
+154
+00:10:43,900 --> 00:10:47,640
+value لل integration من a و b هذا أصغر أو يساوي من
+
+155
+00:10:47,640 --> 00:10:50,160
+صحيحة ال integration ال integration لل absolute
+
+156
+00:10:50,160 --> 00:10:54,110
+value صح؟واللي جوا اللي هو X of T أكيد أصغر أو
+
+157
+00:10:54,110 --> 00:10:58,030
+يساوي ال maximum على كل ال T، ماشي؟ إذا أصغر أو
+
+158
+00:10:58,030 --> 00:11:00,850
+يساوي B minus A في ال maximum ل X of T T element
+
+159
+00:11:00,850 --> 00:11:06,180
+in Jمفهوم، أه؟ إذا صار عندى الآن B minus A مضروب
+
+160
+00:11:06,180 --> 00:11:09,680
+في مين؟ هذا عبارة عن الـ Norm Normal X صار عنده
+
+161
+00:11:09,680 --> 00:11:12,340
+Absolute Value of X أصغر أو سوى B minus A في
+
+162
+00:11:12,340 --> 00:11:16,380
+Normal X بمعنى أخر صارت F bounded ومش هيك و
+
+163
+00:11:16,380 --> 00:11:20,440
+Absolute Value of X على Normal X أصغر أو سوى B
+
+164
+00:11:20,440 --> 00:11:23,840
+minus A صارت الـ B minus A يتبع عن Upper Bound لـ
+
+165
+00:11:23,840 --> 00:11:27,260
+Absolute Value of X على Normal X إذا صار Supremum
+
+166
+00:11:27,260 --> 00:11:29,720
+اللي هو الـ Upper Bound أصغر أو سوى B minus A اللي
+
+167
+00:11:29,720 --> 00:11:32,440
+هي Upper Boundيعني norm of f أخر شو بيه minus a
+
+168
+00:11:32,440 --> 00:11:35,700
+قلته هذا قبلين عيده
+
+169
+00:11:39,850 --> 00:11:43,870
+Conversely أكبر اوي ساوي اختيار نقطة تخدمني ماشي
+
+170
+00:11:43,870 --> 00:11:46,990
+الحال النقطة اللي بتجيبلي هذه واحد واضح ان انا
+
+171
+00:11:46,990 --> 00:11:49,970
+بتاخدها ايه اش مالها واحد عشان اعمل انت اللي هو
+
+172
+00:11:49,970 --> 00:11:53,070
+تكامل يطلع عقل دي بي مانس واحد و تنحل أموري ده
+
+173
+00:11:53,070 --> 00:11:55,670
+نشوف كيف ايش اللي بقوله Now choose X not
+
+174
+00:11:55,670 --> 00:12:00,070
+independent of C,A,B وخد X not of T ايش بتساوي ال
+
+175
+00:12:00,070 --> 00:12:02,670
+constant function واحد وده متصل اما احنا عارفين
+
+176
+00:12:03,230 --> 00:12:07,490
+الان norm ال F أكبر أو يساوي اللي هو ال absolute
+
+177
+00:12:07,490 --> 00:12:10,730
+value علي هذه عند نقطة معينة النقطة المعينة أخد
+
+178
+00:12:10,730 --> 00:12:14,010
+تميين اللي هي واحد الان absolute value ل F of X
+
+179
+00:12:14,010 --> 00:12:18,550
+بساوي اللي هي بساوي هذه نورمها واحد لأن قيمتها
+
+180
+00:12:18,550 --> 00:12:22,270
+واحد النورم على الفترة من A من A ل B minus B هيطلع
+
+181
+00:12:22,270 --> 00:12:27,550
+ايش بساوي integration فاهمين أه؟طيب، الآن بيصير
+
+182
+00:12:27,550 --> 00:12:30,690
+عندي الـ Absolute Value of .. لأ الـ X0 هذه عبارة
+
+183
+00:12:30,690 --> 00:12:34,170
+عن نقطة في الـ Continuous Function قيمتها ..
+
+184
+00:12:34,170 --> 00:12:37,610
+نورمها هو الـ Maximum لقيمة الدالة، ما هي ثابتة،
+
+185
+00:12:37,610 --> 00:12:39,790
+الـ Maximum اللي هو واحد، ماعنديش فراش اللقاء في
+
+186
+00:12:39,790 --> 00:12:42,970
+الـ Integration فبيصير عندي نورم الـ F أكبر أو شوه
+
+187
+00:12:42,970 --> 00:12:45,870
+هذا القيمة، والـ H دي واحد، بيصير بس اللي فوقه F
+
+188
+00:12:45,870 --> 00:12:48,370
+of X0 ماعرف الـ F of X0 هي عبارة عن الـ
+
+189
+00:12:48,370 --> 00:12:52,670
+Integration من LBDTabsolute value لها اللي هو هذه
+
+190
+00:12:52,670 --> 00:12:56,690
+اللي عبارة عن نفسها لان دي موجب اصلا بي ماينوس ايه
+
+191
+00:12:56,690 --> 00:13:00,590
+اذا صار عندي norm of بيساوي اكبره بيساوي اصلا
+
+192
+00:13:00,590 --> 00:13:14,210
+بيساوي اذا في مساوية اللي بعدها نيجي الان ناخد
+
+193
+00:13:14,210 --> 00:13:20,110
+اللي هيF من continuous function لR بس هنسويها
+
+194
+00:13:20,110 --> 00:13:26,790
+بتساوي قيمة الدالة اللي بدرسلها عند نقطة معينةيعني
+
+195
+00:13:26,790 --> 00:13:30,510
+الآن في عندي F باسم C و A و B اللي هو continuous
+
+196
+00:13:30,510 --> 00:13:33,950
+function let F من C و A و B اللي عند الار بي
+
+197
+00:13:33,950 --> 00:13:39,990
+defined by إيش عرفتها؟ F of X بتساوي X عن T note
+
+198
+00:13:39,990 --> 00:13:43,010
+أنا ماخد T note أدى التعريف T note معينة خمسة ستة
+
+199
+00:13:43,010 --> 00:13:46,930
+سبعة نص ربع في الفترة من A و B بحسب قيمة الدالة
+
+200
+00:13:46,930 --> 00:13:51,190
+عند هذا ال T noteوبتكون هي صورة مين ال X under F
+
+201
+00:13:51,190 --> 00:13:55,290
+فبتكون F of X بيساوي X of مين of T not صارت عبارة
+
+202
+00:13:55,290 --> 00:13:59,750
+عن هذه لأن ال X من وين جاية من A و B continuous
+
+203
+00:13:59,750 --> 00:14:02,950
+function من A و B بترمي في ال R فقيمتها أشمالها
+
+204
+00:14:02,950 --> 00:14:06,930
+عبارة عن عدد حقيقي ف X عند أي نقطة اللي هو بيساوي
+
+205
+00:14:06,930 --> 00:14:10,970
+اللي هو عدد حقيقي إذا صارت F of X ترمي وين في ال R
+
+206
+00:14:10,970 --> 00:14:14,570
+طيب F of X بيساوي X of T not where T not is
+
+207
+00:14:14,570 --> 00:14:20,580
+affixedpoint in J اللي هي A وB then F is a bounded
+
+208
+00:14:20,580 --> 00:14:24,160
+linear functional ونورم ال F أيش بيساوي؟ بيساوي
+
+209
+00:14:24,160 --> 00:14:27,620
+واحد، هيكون ال bounded linear functional ونورمه
+
+210
+00:14:27,620 --> 00:14:32,460
+هيساوي مين؟ بس الواحد يشوفه كده، بسهل الامرF is a
+
+211
+00:14:32,460 --> 00:14:35,400
+linear functional اللي هي سهلة لإنه اصلا هي عبارة
+
+212
+00:14:35,400 --> 00:14:39,760
+عن F of Alpha X زائد Beta Y أو زائد Y بيساوي أيش
+
+213
+00:14:39,760 --> 00:14:43,840
+قيمتها Alpha X زائد Y عند الـT Note ويساوي Alpha
+
+214
+00:14:43,840 --> 00:14:47,600
+of X عند الـT Note زائد Y عند الـT Note وبيصير
+
+215
+00:14:47,600 --> 00:14:51,180
+Alpha في F زائد اللي هي FY إذا اللي لينيارات، إذا
+
+216
+00:14:51,180 --> 00:14:54,640
+الموضوع اللي لينيارات سهل طيب إذا Y تبعت اللي
+
+217
+00:14:54,640 --> 00:14:59,100
+لينيارات سهلة وهيني حكيتها نيجي نحكي عن ال
+
+218
+00:14:59,100 --> 00:15:04,010
+boundednessfor any x element in C01 خدلي ال
+
+219
+00:15:04,010 --> 00:15:07,910
+absolute value لمن؟ لل F of X ال absolute value ل
+
+220
+00:15:07,910 --> 00:15:10,630
+F of X احسبه عبارة عن بساوي ال absolute value
+
+221
+00:15:10,630 --> 00:15:16,890
+لقيمتها ايش قيمتها؟ X of T0 X of T0 اكيد اكيد اكيد
+
+222
+00:15:16,890 --> 00:15:21,760
+قيمة ده اللي عند واحدة من هنا T0إن إذا أكيد أصغر
+
+223
+00:15:21,760 --> 00:15:25,620
+أو يساوي ال maximum على كل الفترة عن T نقطة و T
+
+224
+00:15:25,620 --> 00:15:30,400
+واحد و كل ال T الموجودة في الجيب اللي هو بمثل مين
+
+225
+00:15:30,400 --> 00:15:33,140
+Normal X إذا صارت عبارة عن ال absolute value of F
+
+226
+00:15:33,140 --> 00:15:37,400
+of X أصغر أو يساوي Normal X ومنه ال absolute value
+
+227
+00:15:37,400 --> 00:15:41,220
+of F of X على Normal X لو X لا تساوي سفر أو Normal
+
+228
+00:15:41,220 --> 00:15:44,860
+لا تساوي سفر أصغر أو يساوي واحد ال supremum صار
+
+229
+00:15:44,860 --> 00:15:48,880
+أصغر اللي هو أو يساوي واحدمعايا إذا صار عندي
+
+230
+00:15:48,880 --> 00:15:53,780
+Normal F أصغر أو يساوي واحد كده الفكرة مكررة الآن
+
+231
+00:15:53,780 --> 00:15:58,080
+طب الآن بدنا نجيب اللي هو الأكبر يساوي ونختاره عند
+
+232
+00:15:58,080 --> 00:16:02,340
+نقطة معينة Now choose X note في C, V وB with X
+
+233
+00:16:02,340 --> 00:16:06,520
+note أش بتساوي واحد هيك الحدث بقول أصلا عشان أحصل
+
+234
+00:16:06,520 --> 00:16:10,950
+على الواحد ال absolute value ل F of Xأكبر أو يساوي
+
+235
+00:16:10,950 --> 00:16:14,470
+F عند قيمة معينة absolute value على نورم القيمة
+
+236
+00:16:14,470 --> 00:16:17,530
+اللي أخدتها القيمة اللي أخدتها مانا أخدها واحد
+
+237
+00:16:17,530 --> 00:16:21,870
+فنورمها بتساوي واحد واللي فوق أصلا قيمتها absolute
+
+238
+00:16:21,870 --> 00:16:26,330
+F of X هي عبارة عن قيمة X of T naught وفي الأصل ما
+
+239
+00:16:26,330 --> 00:16:30,030
+هي أصلا معرفهاش بتساوي واحدإذا صار عنده norm لـ F
+
+240
+00:16:30,030 --> 00:16:30,930
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+241
+00:16:30,930 --> 00:16:31,730
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+242
+00:16:31,730 --> 00:16:34,730
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+243
+00:16:34,730 --> 00:16:36,290
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+244
+00:16:36,290 --> 00:16:41,850
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+245
+00:16:41,850 --> 00:16:44,650
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+246
+00:16:44,650 --> 00:16:44,650
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+247
+00:16:44,650 --> 00:16:46,650
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+248
+00:16:46,650 --> 00:16:52,830
+أكبر أو أكبر أو أكبر أو أكبر أو أكبر أو
+
+249
+00:16:52,830 --> 00:16:57,960
+أكbe a fixed point in L2 من L2 اللي هو summation
+
+250
+00:16:57,960 --> 00:17:02,660
+كذا norm هال summation المدرستربيع الكل أص نص بدل
+
+251
+00:17:02,660 --> 00:17:05,340
+من I من عند واحد لخمسة أو I من واحد لاتنين I لعند
+
+252
+00:17:05,340 --> 00:17:09,020
+واحد لما لا نهاية يعني مش هيختلف بروحانه عن مين عن
+
+253
+00:17:09,020 --> 00:17:13,160
+الشغلات اللي أثبتناها بالنسبة لـR تكعيب وR تربيع
+
+254
+00:17:13,160 --> 00:17:18,260
+وRم الاخرين let αI be الا بعض الشغلات بسيطة let αI
+
+255
+00:17:18,260 --> 00:17:21,660
+be a fixed point in التربيع and F من التربيع اللي
+
+256
+00:17:21,660 --> 00:17:27,030
+عنده R تربيع be defined byF of X أيش بتساوي صميم
+
+257
+00:17:27,030 --> 00:17:31,190
+XI I Alpha I I من واحد لعند مين لعند infinity for
+
+258
+00:17:31,190 --> 00:17:34,130
+all X elementين قالتوا بالظبط بالظبط بالظبط زي
+
+259
+00:17:34,130 --> 00:17:38,610
+المثال اللي قبله شوية F of X بيساوي X Dot Aالـ X
+
+260
+00:17:38,610 --> 00:17:42,010
+ضد الـ إيش؟ إيش كانت؟ XI واحد Gamma واحد زيدي XI
+
+261
+00:17:42,010 --> 00:17:44,790
+اتنين Gamma اتنين زيدي XI تلاتة Gamma تلاتة الآن
+
+262
+00:17:44,790 --> 00:17:47,970
+إيش ماله هذا؟ من واحد إلى وين إلى الأعلى نهاية إذا
+
+263
+00:17:47,970 --> 00:17:52,130
+الـ linearity و ال boundedness بالظبط زيها then F
+
+264
+00:17:52,130 --> 00:17:56,330
+is bounded linear functional عشان هيك لفت to the
+
+265
+00:17:56,330 --> 00:17:59,430
+reader مبارك الله فيكم و إلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RRPYe2WUwuA.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RRPYe2WUwuA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0b63ce9c0cc5e498fea33d3c81c19fada44e52a8
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RRPYe2WUwuA.srt
@@ -0,0 +1,1479 @@
+1
+00:00:05,110 --> 00:00:07,690
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,690 --> 00:00:10,690
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,690 --> 00:00:18,990
+آله وصحبه أجمعين المحاضرة رقم عشرين مساق تحليل 
+
+4
+00:00:18,990 --> 00:00:22,630
+اقتراني طلاب وطالبات الجامعة الإسلامية ماجستير
+
+5
+00:00:22,630 --> 00:00:28,210
+رياضيات وصلنا لـ section ثلاثة أربعة اللي هو تحت
+
+6
+00:00:28,210 --> 00:00:34,050
+عنوان orthonormal sets and sequences عرفنا المرة 
+
+7
+00:00:34,050 --> 00:00:38,230
+الماضية شو معنى orthogonal sets أو اللي هو تكون
+
+8
+00:00:38,230 --> 00:00:42,430
+شو معنى element orthogonal على اللي هو مجموعة أو
+
+9
+00:00:42,430 --> 00:00:45,730
+مجموعة على مجموعة كيف يكونوا orthogonal متعامدتين
+
+10
+00:00:45,730 --> 00:00:49,830
+اليوم بنحكي عن مفهوم إيش معنى الـ set نفسها تكون
+
+11
+00:00:49,830 --> 00:00:53,030
+orthogonal أو الـ set نفسها تكون orthonormal
+
+12
+00:00:53,030 --> 00:00:57,650
+باختصار الـ set بتكون orthogonal إذا كان اللي هو كل 
+
+13
+00:00:57,650 --> 00:01:01,710
+عناصرها pairwise are orthogonal و Orthonormal بتكون 
+
+14
+00:01:01,710 --> 00:01:05,250
+اللي هو pairwise Orthogonal بالإضافة إلى أن norm كل 
+
+15
+00:01:05,250 --> 00:01:07,650
+واحد بيساوي واحد فبنسميه Orthonormal set هاي 
+
+16
+00:01:07,650 --> 00:01:11,790
+باختصار اللي هو المعنى لـ Orthogonal
+
+17
+00:01:11,790 --> 00:01:15,830
+و الـ Orthonormal كـ sets الآن نيجي لـ definition اللي
+
+18
+00:01:15,830 --> 00:01:18,450
+قلتُه قبل شوية أن Orthogonal set M in an inner
+
+19
+00:01:18,450 --> 00:01:22,590
+product space X الـ cell is a subset M of X whose
+
+20
+00:01:22,590 --> 00:01:25,610
+elements are pairwise Orthogonal يعني كل اثنتين مع 
+
+21
+00:01:25,610 --> 00:01:30,450
+بعض إشهميا متعمدين An orthonormal subset of M of X
+
+22
+00:01:30,450 --> 00:01:32,970
+is an orthogonal set
+
+23
+00:01:35,660 --> 00:01:39,700
+وفي نفس الوقت whose elements have norm one يعني كل 
+
+24
+00:01:39,700 --> 00:01:42,480
+واحد من الـ elements إشهمال normه بيساوي واحد أو
+
+25
+00:01:42,480 --> 00:01:46,240
+بمعنى آخر ملخص الحديث لـ orthonormal منقول أن الـ
+
+26
+00:01:46,240 --> 00:01:49,340
+orthonormal إذا كان لكل x و y element عند الـ inner
+
+27
+00:01:49,340 --> 00:01:52,940
+product بين الـ x و الـ y يا بيساوي صفر يا واحد صفر
+
+28
+00:01:52,940 --> 00:01:55,980
+إذا كانت x لا تساوي y واحد إذا كانت x إشهمالها
+
+29
+00:01:55,980 --> 00:02:01,500
+بتساوي y ماشي الحال بتساوي طلّع لفوق الآن بعض 
+
+30
+00:02:01,500 --> 00:02:05,820
+الملاحظات على هذا الكلام if an orthogonal or 
+
+31
+00:02:05,820 --> 00:02:10,300
+orthonormal system is countable إذا كانت countable
+
+32
+00:02:10,300 --> 00:02:14,660
+بنقدر نعملها يعني إشهمالها كـ sequence اللي هو we can
+
+33
+00:02:14,660 --> 00:02:17,920
+arrange it in a sequence countable يعني اللي هو
+
+34
+00:02:17,920 --> 00:02:21,400
+بيكون كلها الـ هي one to one on to مع الـ natural 
+
+35
+00:02:21,400 --> 00:02:26,120
+number اللي هي arrange it in a sequence Xn and call
+
+36
+00:02:26,120 --> 00:02:30,420
+it an orthogonal or an orthonormal sequence حسب
+
+37
+00:02:30,420 --> 00:02:34,320
+إيش هي في الأصل ماشي الحال اللي هنا a family X
+
+38
+00:02:34,320 --> 00:02:36,860
+Alpha Alpha element in I is called an orthogonal
+
+39
+00:02:36,860 --> 00:02:40,680
+إذا كانت X Alpha orthogonal to X Beta for all
+
+40
+00:02:40,680 --> 00:02:43,980
+Alpha و Beta element in main in I and Alpha less
+
+41
+00:02:43,980 --> 00:02:46,240
+than أو Beta يعني بتكون هذه يعني لو كانت
+
+42
+00:02:46,240 --> 00:02:49,930
+uncountable اللي هي عدد العناصر X Alpha عدد هنا 
+
+43
+00:02:49,930 --> 00:02:52,530
+uncountable الـ 6 ونقدر نكتبها على صورة اللي هو
+
+44
+00:02:52,530 --> 00:02:55,150
+family X α حيث و Alpha element in I مش sequence ده
+
+45
+00:02:55,150 --> 00:02:58,450
+اللي هي family of elements the family is
+
+46
+00:02:58,450 --> 00:03:02,630
+orthonormal if it is orthogonal and X α have norm
+
+47
+00:03:02,630 --> 00:03:05,890
+إيش بيساوي واحد so that for all Alpha و Beta
+
+48
+00:03:05,890 --> 00:03:08,090
+element in I الـ inner product بين X و Alpha و Beta
+
+49
+00:03:08,090 --> 00:03:11,010
+بيساوي يا صفر يا واحد حتى سبق الألفة اللي بتساوي Beta
+
+50
+00:03:11,010 --> 00:03:13,970
+أو الألفة بتساوي Beta نفس الكلام اللي فوق طلع 
+
+51
+00:03:13,970 --> 00:03:18,540
+لفوق الـ remark الأولى اللي هو تعميم لـ Pythagoras
+
+52
+00:03:18,540 --> 00:03:24,180
+نظرية Pythagoras اللي هو المربع المنشأ على الوتر 
+
+53
+00:03:24,180 --> 00:03:26,680
+بيساوي مجموع المربعين المنشأين على الضلعين الآخرين
+
+54
+00:03:26,680 --> 00:03:30,140
+الآن for unorthogonal elements اللي بيكونوا 
+
+55
+00:03:30,140 --> 00:03:33,960
+متعامدين الـ X و الـ Y متعامدين نحن لدينا norm X زي 
+
+56
+00:03:33,960 --> 00:03:38,260
+Y الكل تربيع بيساوي norm X تربيع زي norm Y تربيع 
+
+57
+00:03:38,260 --> 00:03:42,240
+الآن و هذا أثبتوه سهل norm X زي Y مدام orthogonal 
+
+58
+00:03:44,130 --> 00:03:46,610
+بيصير norm الـ x زائد y لكل تربيع بيساوي الـ inner
+
+59
+00:03:46,610 --> 00:03:51,270
+product بين x زائد y و x زائد y و يساوي بنفكها x و
+
+60
+00:03:51,270 --> 00:03:58,130
+x زائد x و y زائد y و x زائد y و y الآن مدام
+
+61
+00:03:58,130 --> 00:04:01,270
+ارتجينا أن هذول صفر و هذول صفر إذن بيساوي اللي هو 
+
+62
+00:04:01,270 --> 00:04:06,190
+norm الـ x تربيع زائد normal y تربيع وهذا ما هو 
+
+63
+00:04:06,190 --> 00:04:09,110
+إلا يساوي هذا زائد هذا اللي هي المربع المنشأ على
+
+64
+00:04:09,110 --> 00:04:10,550
+الوتر بيساوي مجموع المربعين المنشأين على
+
+65
+00:04:10,550 --> 00:04:12,890
+الضلعين الآخرين اللي هي تعميم لها هذا الكلام في
+
+66
+00:04:12,890 --> 00:04:17,430
+أي inner product space in general لو كانت عندي
+
+67
+00:04:17,430 --> 00:04:23,760
+اللي هو X1 زي X2 و X2 و Xn عبارة عن orthogonal set
+
+68
+00:04:23,760 --> 00:04:26,980
+يعني كل اثنين عموديا على بعض هيطلع عندي الـ inner
+
+69
+00:04:26,980 --> 00:04:30,360
+product بينهم بيساوي اللي هو norm الواحد الأول 
+
+70
+00:04:30,360 --> 00:04:33,260
+تربيع زي norm الأول .. آسف norm التربيع بيساوي
+
+71
+00:04:33,260 --> 00:04:35,780
+norm واحد تربيع زي norm التاني تربيع زي norm الآن
+
+72
+00:04:35,780 --> 00:04:40,160
+تربيع ونفس الشيء اللي هو عن طريق اللي هي اللي 
+
+73
+00:04:40,160 --> 00:04:46,200
+حكيناه قبل شوية بتقدر تعمله بكل سهولة يعني norm الـ
+
+74
+00:04:46,200 --> 00:04:49,340
+X1
+
+75
+00:04:49,340 --> 00:04:54,900
+بالنسبة بالـ induction برضه norm X1 زائد X2 زائد Xn 
+
+76
+00:04:54,900 --> 00:05:01,600
+لكل تربيع بيساوي اللي هو inner product بين 
+
+77
+00:05:01,600 --> 00:05:07,340
+summation XI I من عند 1 لعند N و summation ل XI XJ
+
+78
+00:05:07,340 --> 00:05:13,380
+J من عند 1 لعند N صح ولا لأ؟ بظبط هو يساوي اللي هو 
+
+79
+00:05:13,380 --> 00:05:17,800
+اللي هو بوزع اللي هو أول واحد مع هذول يعني X1 محدد و 
+
+80
+00:05:17,800 --> 00:05:23,580
+X2 محدد و X3 محدد و بجمعها فبيصير summation XI و 
+
+81
+00:05:23,580 --> 00:05:28,580
+summation XJ جي من عند واحد لعند N صح I من عند
+
+82
+00:05:28,580 --> 00:05:33,750
+واحد لعند N ويساوي الـ N زي ما .. هالـ gate خلص من
+
+83
+00:05:33,750 --> 00:05:38,390
+هذا الـ N للـ fixed I X I و الأولى و X Y و الثانية 
+
+84
+00:05:38,390 --> 00:05:41,410
+و X Y و الثالثة إذن A برضه summation إذن بيصير 
+
+85
+00:05:41,410 --> 00:05:45,110
+الـ summation الأولاني الأصلي I بيساوي واحد لعند N و 
+
+86
+00:05:45,110 --> 00:05:49,590
+الـ summation الثاني اللي هو بيصير X I و X I و مين 
+
+87
+00:05:49,590 --> 00:05:55,360
+و X J معاها هنا J من عند واحد برضه و لا عند مين لا 
+
+88
+00:05:55,360 --> 00:06:02,020
+عند N الآن كل هين هيتصفروا ما دام لـ I إيش بتساوي J
+
+89
+00:06:02,020 --> 00:06:07,360
+فبيصير كل صفار بيظل بس اللي هو الـ summation للـ XI
+
+90
+00:06:07,360 --> 00:06:11,540
+و XI يعني الاتنين إيش لما I تساوي J و I من عند
+
+91
+00:06:11,540 --> 00:06:15,000
+واحد لعند N لا إنه هذا بيساوي الـ summation لـ
+
+92
+00:06:15,000 --> 00:06:20,970
+norm XI تربيع I من عند واحد لعند N اللي هو الـ X
+
+93
+00:06:20,970 --> 00:06:26,590
+واحد تربيع زائد آخر واحد norm من الـ X N الكل 
+
+94
+00:06:26,590 --> 00:06:32,290
+تربيع بيصير هذا واضح؟ خلاص ما بتحتاجش الـ induction
+
+95
+00:06:32,290 --> 00:06:39,170
+إذا لكن بنفع بالـ induction طيب إيجاد حلم أن
+
+96
+00:06:39,170 --> 00:06:43,010
+orthonormal set is linearly independent مهمة ده 
+
+97
+00:06:43,010 --> 00:06:47,130
+الكلام تبقوا معايا an orthonormal set is linearly
+
+98
+00:06:47,130 --> 00:06:54,000
+independent يعني خذ الآن اللي هو I ألف واحد X واحد 
+
+99
+00:06:54,000 --> 00:07:00,200
+زائد ألف N X N بيساوي صفر وقصل منه أنه ألف واحد
+
+100
+00:07:00,200 --> 00:07:04,180
+بيساوي ألف اثنين بيساوي ألف N إيش بيساوي صفر الآن
+
+101
+00:07:04,180 --> 00:07:15,090
+بقول الآن خذ اللي هو M orthonormal set وبدأ أثبت لك
+
+102
+00:07:15,090 --> 00:07:19,050
+أن الـ M اللي هو إيش مالها is linearly independent
+
+103
+00:07:19,050 --> 00:07:25,590
+كيف بأثبت linearly independent بأخذ أي X1 و X2 
+
+104
+00:07:25,590 --> 00:07:29,970
+عند Xn element مين element نهر، arbitrary finite و
+
+105
+00:07:29,970 --> 00:07:37,230
+بأخذ Alpha 1 X1 زائد Alpha N Xn و بسوي بإيش؟
+
+106
+00:07:37,230 --> 00:07:41,070
+بالصفر، ماشي الحال؟ لأن حسبوا لي الآن الـ inner
+
+107
+00:07:41,070 --> 00:07:49,210
+product بين اللي هو for N في XI ألف واحد X واحد 
+
+108
+00:07:49,210 --> 00:07:58,250
+زائد Alpha N XN وخده مع XN وحسبوا أن الـ product
+
+109
+00:07:58,250 --> 00:08:03,230
+بينهم برضه هيسوي إيش؟ هيسوي صفر الآن هذا كله 
+
+110
+00:08:03,230 --> 00:08:08,870
+هيتصفر كله هيتصفر مظبوط هذه مع هذه صفرها هذه مع
+
+111
+00:08:08,870 --> 00:08:12,730
+هذه صفرها هذه XN لآخر واحدة بس بفهمكم تاخدوا
+
+112
+00:08:12,730 --> 00:08:15,470
+الأولى بنفهمها وبعدين تقولوا الباقي اللي يعرفوا I
+
+113
+00:08:15,470 --> 00:08:19,470
+fixed till بنفهمها يعني for unfixed I فبيصير عندي 
+
+114
+00:08:19,470 --> 00:08:28,350
+بيصير Alpha واحد و X واحد و X واحد والباقي كله إيش
+
+115
+00:08:28,350 --> 00:08:36,550
+أصفار بيصير هذا إيش بيساوي Alpha واحد في X واحد و X
+
+116
+00:08:36,550 --> 00:08:42,270
+واحد هذا طبعا اللي هو بيصير عندي ألف و واحد إيش
+
+117
+00:08:42,270 --> 00:08:46,470
+بيساوي؟ بيساوي صفر لإنه normal إيش بتساوي واحد؟
+
+118
+00:08:46,470 --> 00:08:52,470
+normal ألف واحد صفر similarly for لبعض نطلع عن كل 
+
+119
+00:08:52,470 --> 00:08:57,250
+صفر بتاعة ترتيب البرهان لإنه لفّة ضريدة خذ for any 
+
+120
+00:08:57,250 --> 00:09:03,110
+fixed i و اشتغل عليها أحسنها طلع من فوق examples
+
+121
+00:09:03,110 --> 00:09:08,900
+Euclidean space are un في القرآن The standard basis
+
+122
+00:09:08,900 --> 00:09:13,040
+of RN forms an orthonormal set الـ standard basis
+
+123
+00:09:13,040 --> 00:09:15,940
+عارفين احنا الـ inner product على الـ RN الـ inner
+
+124
+00:09:15,940 --> 00:09:19,200
+product عارفينه احنا لو جينا أخذنا من الـ R تكعيب
+
+125
+00:09:19,200 --> 00:09:28,640
+مين الـ standard basis له 1 0 0 0 1 0 0 0 1 لو أخذت أي
+
+126
+00:09:28,640 --> 00:09:31,880
+inner product بين التليهيل اللي هو مختلفين صفر و 
+
+127
+00:09:31,880 --> 00:09:34,860
+inner product بين العنصر نفسه إيش بيساوي بيساوي
+
+128
+00:09:34,860 --> 00:09:37,020
+واحد بناء على اللي هو inner product تبعنا في 
+
+129
+00:09:37,020 --> 00:09:40,540
+الارتقال في الـ R N الـ فبيطلع عندي عبارة عن
+
+130
+00:09:40,540 --> 00:09:46,330
+orthonormal set واضح اه مثال آخر نفس الشيء ما هو
+
+131
+00:09:46,330 --> 00:09:49,330
+احنا عرفنا الـ inner product بين هنا دولة الـ E N 
+
+132
+00:09:49,330 --> 00:09:52,190
+اللي هو بيساوي الـ summation لا الـ inner product في
+
+133
+00:09:52,190 --> 00:09:55,410
+الـ L تربيع بيساوي الـ summation للـ alpha I في الـ
+
+134
+00:09:55,410 --> 00:09:59,530
+beta I conjugate الكل اللي هو أصله نص ماشي هي ليها
+
+135
+00:09:59,530 --> 00:10:03,990
+product الآن اعمل لو جيت على the shoulder bases
+
+136
+00:10:03,990 --> 00:10:07,330
+بالذات اللي هو the shoulder bases EN of التربيع
+
+137
+00:10:07,330 --> 00:10:11,270
+هيطلع لي forms and orthonormal sequence in التربيع
+
+138
+00:10:11,270 --> 00:10:14,050
+بالضبط زي اللي عملته هنا ماشي الحال اللي بعده 
+
+139
+00:10:16,250 --> 00:10:19,870
+continuous functions احنا let x be the inner
+
+140
+00:10:19,870 --> 00:10:22,530
+product space of all continuous real valued
+
+141
+00:10:22,530 --> 00:10:26,950
+functions  الـ inner product اللي عرفناها مش  0 و2π 
+
+142
+00:10:26,950 --> 00:10:29,350
+هو طبعا الـ norm مش الـ maximum، الـ maximum ما طلعش
+
+143
+00:10:29,350 --> 00:10:32,470
+الـ inner product اللي عند x و y 
+
+144
+00:10:32,470 --> 00:10:36,550
+بسهولة integration x of t y of t dt من 0 ل 2π لو
+
+145
+00:10:36,550 --> 00:10:40,600
+كانت real لو كان complex بتحطوله conjugate ماشي
+
+146
+00:10:40,600 --> 00:10:45,900
+الحال الآن هي الـ inner product، بقول لك الآن مثال
+
+147
+00:10:45,900 --> 00:10:49,760
+يعني بيعطيك مثال على orthogonal sets cosine الـ N T
+
+148
+00:10:49,760 --> 00:10:53,020
+يعني cosine الـ T cosine الـ 2T cosine الـ 3T cosine
+
+149
+00:10:53,020 --> 00:10:58,300
+الـ 4T cosine الـ 5T  و cosine الـ ... الأخره واللي هي 
+
+150
+00:10:58,300 --> 00:11:04,060
+zero اللي هو الـ N element in N cosine الـ N T مثال
+
+151
+00:11:04,060 --> 00:11:07,780
+ثاني sine الـ T sine الـ 2T ... الأخره و cosine الـ zero
+
+152
+00:11:08,310 --> 00:11:14,630
+بعملين orthogonal sequences
+
+153
+00:11:14,630 --> 00:11:22,090
+بس استثنى اللي هو الـ zero من هنا بتطلع لك اللي هي 
+
+154
+00:11:22,090 --> 00:11:27,390
+واحد على جذر 2π cos T على جذر الـ π هذا 
+
+155
+00:11:27,390 --> 00:11:32,130
+هتطلع لك orthonormal set، جسمها  Anormة هو في الواقع
+
+156
+00:11:32,130 --> 00:11:37,410
+عشان تطلع واحد وهنا sin الانتي على جذر الـ by اللي 
+
+157
+00:11:37,410 --> 00:11:41,550
+هو برضه هتطلع إيش معها orthonormal sequence وهذه
+
+158
+00:11:41,550 --> 00:11:44,250
+orthonormal sequence أثبت ليها إن هدول مش صعبة كل
+
+159
+00:11:44,250 --> 00:11:47,350
+الحسابات من وين؟ من هذه integration تبع اللي هو sin
+
+160
+00:11:47,350 --> 00:11:52,190
+و cos أطلع لكم الآن هدول مثلا أمثلة على
+
+161
+00:11:52,190 --> 00:11:56,170
+orthonormal sequences الآن اطلع لفوق في حاجة اسمها 
+
+162
+00:11:56,170 --> 00:11:59,130
+Bessels Inequality اللي هو الـ Bessels Inequality 
+
+163
+00:11:59,130 --> 00:12:04,730
+اللي هي التالي لو كانت Eₙ بيه orthonormal sequence
+
+164
+00:12:04,730 --> 00:12:07,970
+Eₙ orthonormal sequence ما حدش جايب واحد وزير وزير
+
+165
+00:12:07,970 --> 00:12:12,870
+وزير لأ، هد بس رمز هنا الـ Eₙ مش معناه واحد وزفر
+
+166
+00:12:12,870 --> 00:12:17,590
+وزفر لأ، هـ delete  Eₙ be an orthonormal sequence in
+
+167
+00:12:17,590 --> 00:12:21,610
+an inner product space، then for every x element in
+
+168
+00:12:21,610 --> 00:12:24,810
+X الـ summation للـ absolute value هذا التربيع من
+
+169
+00:12:24,810 --> 00:12:30,410
+واحدة لـ infinity أصحى يا شوميين normal X تربيع يعني و
+
+170
+00:12:30,410 --> 00:12:34,790
+كأنه بيقول لي هنا إنه هذه الـ series دائماً converges
+
+171
+00:12:34,790 --> 00:12:39,730
+الـ series لما تحسب اللي هو الـ inner product بين الـ
+
+172
+00:12:39,730 --> 00:12:45,890
+X و الـ orthonormal sequence هذه هيطلع دائماً اللي
+
+173
+00:12:45,890 --> 00:12:50,250
+هو الـ series هذه المحسوبة تكون دائماً convergent 
+
+174
+00:12:50,250 --> 00:12:55,630
+series لاحظوا الـ orthonormal set قلنا عليها
+
+175
+00:12:55,630 --> 00:12:58,130
+linearly independent
+
+176
+00:13:00,360 --> 00:13:05,480
+إذا الشكل اللي في المستقبل هتعمل لنا إشي نحي ولاحظنا
+
+177
+00:13:05,480 --> 00:13:12,140
+إن الـ basis الـ standard basis في الـ ℝⁿ و الشودر
+
+178
+00:13:12,140 --> 00:13:17,640
+basis في الـ L² كل هين عبارة عن إيه؟ الشمال هين are 
+
+179
+00:13:17,640 --> 00:13:23,780
+orthonormal sets طب الشودر basis في الـ L³ الـ B لتس
+
+180
+00:13:23,780 --> 00:13:25,760
+و 2 تتوقع يكون orthonormal set 
+
+181
+00:13:35,600 --> 00:13:39,580
+الـ orthonormal بيعتمد علي إيش؟ أو الـ orthogonal
+
+182
+00:13:39,580 --> 00:13:43,540
+بيعتمد علي إيش؟ عرفناه وين؟ عرفناه في الـ inner
+
+183
+00:13:43,540 --> 00:13:47,980
+product على أساس الـ inner product طب هو الـ B مش
+
+184
+00:13:47,980 --> 00:13:51,860
+الـ L³ B لسه و 2 مش inner product بناءً على هذا 
+
+185
+00:13:51,860 --> 00:13:56,000
+التعريف طبعاً مظبوطش، لكن فيه دراسات في تعريف اللي
+
+186
+00:13:56,000 --> 00:13:58,880
+هو فيه برخوف orthogonality ومش عارف إيش حتى عن
+
+187
+00:13:58,880 --> 00:14:03,380
+norm dismiss بس طبعاً يعني بشكل آخر يعني في مجالنا
+
+188
+00:14:03,380 --> 00:14:08,360
+احنا ما بنحكيش الآن عن اللي هو أي orthogonality هنا
+
+189
+00:14:08,360 --> 00:14:11,880
+دي اجتهادات في الـ orthogonality بأكثر من نوع من الـ
+
+190
+00:14:11,880 --> 00:14:16,800
+orthogonality وفيها دراسات حديثة كلها طيبلأن يجي له
+
+191
+00:14:16,800 --> 00:14:19,680
+لبس الـ Bessel's Inequality let Eₙ be an orthonormal
+
+192
+00:14:19,680 --> 00:14:23,040
+sequence in an inner product space X then for
+
+193
+00:14:23,040 --> 00:14:25,860
+every X limit in X هذي السيريز converts اطلع لفوق
+
+194
+00:14:25,860 --> 00:14:30,960
+من برهن لأن consider the finite subset E₁ E₂ عند
+
+195
+00:14:30,960 --> 00:14:33,520
+Eₙ أن arbitrarily... arbitrarily يعني بس أنا ما بديش
+
+196
+00:14:33,520 --> 00:14:38,390
+أطلع على الـ finite وبعدين بمدها زي ما بدي طيب هذه
+
+197
+00:14:38,390 --> 00:14:40,950
+subset من مين؟ من الـ E عن الـ Orthonormal set 
+
+198
+00:14:40,950 --> 00:14:46,230
+احسب لي الآن، احسب لي norm الـ X ناقص الـ summation
+
+199
+00:14:46,230 --> 00:14:51,090
+اللي عندي هذا تربيع ماشي الحال اللي هو استقيته من
+
+200
+00:14:51,090 --> 00:14:54,910
+هنا اه اه ده استقي إشي من هنا عشان أصل الـ equality
+
+201
+00:14:54,910 --> 00:15:01,180
+هذه بعد شوية Y ساوى X نقص الـ summation و X نقص الـ
+
+202
+00:15:01,180 --> 00:15:04,560
+summation زي ما عملنا قبل بشوية هذي بيصير X مع الـ
+
+203
+00:15:04,560 --> 00:15:08,380
+X وبعدين X مع الـ summation و summation مع X و
+
+204
+00:15:08,380 --> 00:15:11,440
+summation مع summation Y ساوى هاي الـ X مع الـ X
+
+205
+00:15:11,440 --> 00:15:14,780
+بيطلع X تربيع والـ X مع الـ summation هيه وهذي الـ
+
+206
+00:15:14,780 --> 00:15:17,460
+summation مع الـ X وهذي الـ summation مع الـ
+
+207
+00:15:17,460 --> 00:15:21,240
+summation Y ساوى اللي يعني الأول يعني زي ما هو
+
+208
+00:15:21,240 --> 00:15:26,220
+بنزل التاني بيصير... برضه بيتوزح حد الـ X مع هدول
+
+209
+00:15:26,220 --> 00:15:29,240
+بيطلع الـ summation ماله برا فبيصير الـ summation برا
+
+210
+00:15:29,240 --> 00:15:32,420
+لكن بتاخد هذه إيش مالها؟ بـ conjugate برا فلأنها
+
+211
+00:15:32,420 --> 00:15:36,180
+بعيدة بتاخد هذه الـ conjugate معها ناجهاد وبيظل
+
+212
+00:15:36,180 --> 00:15:39,580
+اللي جوا منين؟ X و Eₖ فبيصير هذه مع هذه هي الـ
+
+213
+00:15:39,580 --> 00:15:43,860
+conjugate اللي بعدها الثانية ناقص هذا جريم فبيطلع
+
+214
+00:15:43,860 --> 00:15:49,260
+برا عادي وبتصير Eᵢ و مين؟ و X هذه بتطلع برا والـ
+
+215
+00:15:49,260 --> 00:15:52,520
+summation هي بيصير هذه Eᵢ و X زاد هدول الـ
+
+216
+00:15:52,520 --> 00:15:55,700
+summation الـ two summations بيطلع عن برا الأول
+
+217
+00:15:55,700 --> 00:15:59,060
+بيطلع عادي والتاني بيطلع الـ conjugate لبعيد بيصير
+
+218
+00:15:59,060 --> 00:16:02,440
+الـ summation summation الأول عادي هيه والتاني
+
+219
+00:16:02,440 --> 00:16:05,980
+بيضل عايش بالـ conjugate وبيضل مين في... عندي Eᵢ و
+
+220
+00:16:05,980 --> 00:16:10,980
+مين؟ و Eₖ Eᵢ و Eₖᵢ من عند واحد لعند n و okay من 
+
+221
+00:16:10,980 --> 00:16:15,540
+عند واحد لعند n اطلع لفوق بيصير عند الـ n ويساوي
+
+222
+00:16:15,540 --> 00:16:24,110
+هذا بنزل زي ما هو عندي والتاني اللي هو هذا هو هذا
+
+223
+00:16:24,110 --> 00:16:29,370
+لأنه هذا لما أشيل أخليه X و Eᵢ بيصير X و Eᵢ أشمال الـ
+
+224
+00:16:29,370 --> 00:16:31,990
+conjugate فهذا conjugate وهذا conjugate والمجموع
+
+225
+00:16:31,990 --> 00:16:34,210
+من واحد لعندي N وهذا conjugate وهذا عادي و
+
+226
+00:16:34,210 --> 00:16:36,810
+المجموع من واحد لعندي N يعني واحد conjugate واحد 
+
+227
+00:16:36,810 --> 00:16:39,310
+عادي في التنين ومن واحد لعندي N إذا المجموع
+
+228
+00:16:39,310 --> 00:16:43,070
+للتنين 2 يعني التنين نفس الشيء فبيصير ناقص
+
+229
+00:16:43,070 --> 00:16:47,400
+2 في الـ summation هذا هذا وهذا زي بعض زائد الـ
+
+230
+00:16:47,400 --> 00:16:50,880
+summation اللي بعده هذا اللي عندي الـ summation هذا
+
+231
+00:16:50,880 --> 00:16:57,640
+كله هيتصفر مع ده لما تكون Eᵢ Eᵢ إيش بتساوي K لأن 
+
+232
+00:16:57,640 --> 00:17:03,570
+Eᵢ و Eᵢ مش orthonormal هيصير Eᵢ و Eₖ اللي هو عبارة
+
+233
+00:17:03,570 --> 00:17:07,230
+عن صفر إذا كانت i لا تساوي k و 1 في حالة المساواة
+
+234
+00:17:07,230 --> 00:17:13,050
+إذا هذا هيصير summation واحد بس وهيصير بس اللي هو
+
+235
+00:17:13,050 --> 00:17:18,870
+summation عندي بيظل X و Eᵢ و X و Eᵢ conjugate معناته
+
+236
+00:17:18,870 --> 00:17:23,490
+هذا تربيع وهذا هيصير 1 فبيصير عبارة عن معايا
+
+237
+00:17:23,490 --> 00:17:28,550
+نفسي هو normal X تربيع هيه وهذا 2X وهذا زائد هذا
+
+238
+00:17:28,550 --> 00:17:33,160
+في هذا وهذيك صار 1 الـ Eᵢ و E كام؟ فاهمين عليها
+
+239
+00:17:33,160 --> 00:17:37,040
+لأن هذا زي ما هو بنزل والآن هذا ناقص 2 وهذا
+
+240
+00:17:37,040 --> 00:17:42,760
+1 بيصير ناقص 1 منهم مظبوط norm تربيع لأن ما
+
+241
+00:17:42,760 --> 00:17:47,440
+بتضرب هذا في هذا بيصير modulus تربيع صار هذا
+
+242
+00:17:47,440 --> 00:17:52,220
+المقدار ها يوم أوصلنا بدأنا من 0 وأصغر أو
+
+243
+00:17:52,220 --> 00:17:55,300
+يساوي لما أوصلنا هذا صار هذا المقدار أكبر أو يساوي
+
+244
+00:17:55,300 --> 00:17:58,400
+0 معناته إنه صار هذا على الجهة الثانية أصغر أو
+
+245
+00:17:58,400 --> 00:18:04,190
+يساوي هذا صارت هذه اللي هي this is inequality لأن
+
+246
+00:18:04,190 --> 00:18:07,610
+هذا في الـ finite ل... ل... ل... ل... ل... ل... ل
+
+247
+00:18:07,610 --> 00:18:07,750
+... ل... ل... ل... ل... ل... ل... ل
+
+248
+00:18:07,750 --> 00:18:08,290
+... ل... ل... ل... ل... ل... ل... ل
+
+249
+00:18:08,290 --> 00:18:09,450
+... ل... ل... ل... ل... ل... ل
+
+250
+00:18:09,450 --> 00:18:09,610
+... ل... ل... ل... ل... ل... ل
+
+251
+00:18:09,610 --> 00:18:10,710
+... ل... ل... ل... ل... ل... ل
+
+252
+00:18:10,710 --> 00:18:10,750
+... ل... ل... ل... ل... ل... ل
+
+253
+00:18:10,750 --> 00:18:11,390
+... ل... ل... ل... ل... ل... ل
+
+254
+00:18:11,390 --> 00:18:11,730
+... ل... ل... ل... ل... ل... ل
+
+255
+00:18:11,730 --> 00:18:11,790
+... ل... ل... ل... ل... ل... ل
+
+256
+00:18:11,790 --> 00:18:19,590
+... ل... ل... ل... ل... ل...
+
+257
+00:18:19,590 --> 00:18:20,190
+ل... ل... 
+
+258
+00:18:28,520 --> 00:18:32,840
+الآن نجي للـ inner product X و Eₖ اللي قبله شوية
+
+259
+00:18:32,840 --> 00:18:38,620
+above هذا بيسميه the Fourier coefficients of X
+
+260
+00:18:38,620 --> 00:18:40,280
+لأنه بيطلع في الـ Fourier series عندنا 
+
+261
+00:18:43,650 --> 00:18:48,330
+الشيء الأساسي X, Y, K أعلى هؤلاء هم معاملات تسمى
+
+262
+00:18:48,330 --> 00:18:52,470
+كالخصوصية الواقعية لـ X بالنسبة للتطبيق التطبيقي 
+
+263
+00:18:52,470 --> 00:18:59,690
+الـ E, K هذا فيه معناه التطبيقي ليس مجال نحكي فيه
+
+264
+00:18:59,690 --> 00:19:03,890
+إذا كانت المعاملة لـ X فينية، فكل تطبيق التطبيق
+
+265
+00:19:03,890 --> 00:19:08,790
+التطبيقي يجب أن يكون فيني because it's linearly
+
+266
+00:19:08,790 --> 00:19:11,670
+independent أكيد إذا كانت الـ dimension للـ space
+
+267
+00:19:11,670 --> 00:19:15,190
+نفسه اللي بس تشتغل فيه finite مش معقول تكون subset
+
+268
+00:19:15,190 --> 00:19:20,110
+منه infinite ليش؟ مش معقول تكون subset منه اللي هو
+
+269
+00:19:20,110 --> 00:19:22,870
+infinite اللي هي من الـ orthonormal لأن الـ
+
+270
+00:19:22,870 --> 00:19:27,290
+orthonormal إيه شمالها linearly independent مدام
+
+271
+00:19:27,290 --> 00:19:31,610
+linearly independent إذا ثقفها عدت على أصل الـ
+
+272
+00:19:31,610 --> 00:19:34,150
+bases اللي هو الـ dimension لأنه لو زادت بتبطل
+
+273
+00:19:34,150 --> 00:19:38,370
+linearly independent فاهمين؟ إذا الآن أكيد مدام 
+
+274
+00:19:38,370 --> 00:19:41,130
+الـ dimensional X finite هتكون الـ orthonormal sets
+
+275
+00:19:41,130 --> 00:19:46,110
+اللي فيها are finite sets الآن بدنا نيجي لـ Gram
+
+276
+00:19:46,110 --> 00:19:49,570
+Schmidt process for orthonormalizing a linearly
+
+277
+00:19:49,570 --> 00:19:53,330
+independent sequence Xⱼ يعني هنا product space X
+
+278
+00:19:53,330 --> 00:19:57,690
+يعني إيش بقول له؟ بقول له كيف بدي أكون اللي هو
+
+279
+00:19:57,690 --> 00:20:02,490
+orthonormal set Orthonormal Set أو Orthonormal
+
+280
+00:20:02,490 --> 00:20:07,650
+Sequence من اللي هو Set تكون Linear لـ Independent
+
+281
+00:20:07,650 --> 00:20:11,250
+هذه الـ process اللي هو حد اسمه Gram-Schmidt
+
+282
+00:20:11,250 --> 00:20:16,350
+Process خلينا نشوف الخطوات .. الخطوات سهلة و .. و
+
+283
+00:20:16,350 --> 00:20:20,210
+.. و الكل بيفهمها يعني شغلات سهلة إن شاء الله The
+
+284
+00:20:20,210 --> 00:20:25,710
+first element لأن X1 .. X2 .. X3 .. X4 .. إلا ما 
+
+285
+00:20:25,710 --> 00:20:31,990
+ننهيها بدي أخد منهم اللي هو الـ 100 اللي هو .. ال .. ال
+
+286
+00:20:31,990 --> 00:20:35,410
+.. ال .. من هنا أولد الـ E1 و الـ E2 و الـ E3 و
+
+287
+00:20:35,410 --> 00:20:39,750
+الـ E4 شوف كيف بدي أجيبهم أول خطوة اللي هو طبيعي
+
+288
+00:20:39,750 --> 00:20:44,010
+اللي بدي أخد first element of EK is E1 بسميه هذا
+
+289
+00:20:44,010 --> 00:20:49,470
+الـ EK الـ orthonormal المبتغى اللي بدي أعملها
+
+290
+00:20:49,470 --> 00:20:53,570
+يعني لأن E1 بساوي X1 على norm X1 هذول اللي بين
+
+291
+00:20:53,570 --> 00:20:55,910
+يديها الـ X1 و X2 و X3 اللي مالها يعني they are
+
+292
+00:20:55,910 --> 00:20:59,030
+independent set إذا المدان لينيال independent
+
+293
+00:20:59,030 --> 00:21:03,850
+sequence ده لو لو واحد فيه صفر لو في واحد صفر
+
+294
+00:21:03,850 --> 00:21:07,010
+بتبطل لينيال independent إذا الـ X1 على norm الـ X1
+
+295
+00:21:07,010 --> 00:21:11,290
+مشروع هذا هيصير نورمه الجديد إيش بساوي بساوي واحد
+
+296
+00:21:11,290 --> 00:21:18,230
+طيب الآن الـ second step بتاخد اللي هو عشان أصل لل
+
+297
+00:21:18,230 --> 00:21:22,730
+E2 بتاخد أوليش حاجة اسمها V2 ومنها أصل للـ E1 V2
+
+298
+00:21:22,730 --> 00:21:26,070
+بعد شوية حاجة قسمها على نورم وحصل على الـ E2 إذا 
+
+299
+00:21:26,070 --> 00:21:33,940
+الآن حصلت على الـ E1 عبارة عن X1 على norm الـ X1 وهذا
+
+300
+00:21:33,940 --> 00:21:41,040
+أكيد norm E1 بساوي اللي هو واحد طيب بدي اجيب E2
+
+301
+00:21:41,040 --> 00:21:46,920
+قبل عشان اجيب E2 E2 و اقولها اجيب حاجة اسمها V2 و
+
+302
+00:21:46,920 --> 00:21:52,040
+اقسمها عالميا على norm V2 طب V2 ايش هو V2 بتاخد
+
+303
+00:21:52,040 --> 00:21:59,330
+اللي هو X2 V2 بتاخدها بتساوي الـ X2 و أطرح منها ال
+
+304
+00:21:59,330 --> 00:22:05,170
+X2 و الـ E1 اللي لجيتها في الأول مضروبة في ايش هم؟ في
+
+305
+00:22:05,170 --> 00:22:10,530
+الـ E1 عشان أضرب عصفرين بحجر أثبتلك أن هذول الـ V2
+
+306
+00:22:10,530 --> 00:22:14,990
+منها هتكون اللي هو الـ inner product مع الـ E1 اللي
+
+307
+00:22:14,990 --> 00:22:17,990
+فوق 0 يعني هأثبتلك أنه Orthogonal وبعدين أقسمها
+
+308
+00:22:17,990 --> 00:22:23,010
+بيصير Orthonormal ماشي طيب احسب ليها الآن و أقول لك
+
+309
+00:22:23,010 --> 00:22:26,690
+let V2 بيساوي and since ZXJ is linearly
+
+310
+00:22:26,690 --> 00:22:31,550
+independent then V2 لك بيساوي 0 أكيد V2 لك بيساوي
+
+311
+00:22:31,550 --> 00:22:36,690
+0 عارفين ليش لك بيساوي 0 عارف ليش اللي لاتساوي صفر؟
+
+312
+00:22:36,690 --> 00:22:40,890
+لأنه لو بتساوي صفر معناته كده اكتب X2 بتساوي E1 في
+
+313
+00:22:40,890 --> 00:22:46,690
+هذا المقدار و E1 X1 على كده إذا صارت X2 مكتوبة X2
+
+314
+00:22:46,690 --> 00:22:49,470
+على صورة linear combination من X1 وهذا
+
+315
+00:22:49,470 --> 00:22:52,210
+contradiction لل linearly independent بين X1 و X2
+
+316
+00:22:52,900 --> 00:22:56,360
+الآن لو فرضنا .. خلّيني أكون واضح بشكل آخر فرضنا
+
+317
+00:22:56,360 --> 00:23:04,540
+إن هذه بتساوي صفر بيصير X2 بتساوي X2 و E1 في E1 Y
+
+318
+00:23:04,540 --> 00:23:10,280
+ساوي X2 و E1 هذا scalar صارت في E1 مين هو الـ E1؟
+
+319
+00:23:10,280 --> 00:23:16,960
+اللي هو X1 ع norm X1 صارت عندي هذا scalar مضروب
+
+320
+00:23:16,960 --> 00:23:20,700
+في X1 يعني X2 صارت scalar في X1 يعني صارت X2 عبارة
+
+321
+00:23:20,700 --> 00:23:23,940
+Linear Completion من X1 وهذا Contradiction
+
+322
+00:23:23,940 --> 00:23:28,320
+Linearly Independent إذا V2 أكيد لا تساوي صفر
+
+323
+00:23:28,320 --> 00:23:35,020
+احسبلي الآن الـ inner product بين V2 و E1 سهلة V2
+
+324
+00:23:35,020 --> 00:23:40,300
+هيها X2 ناقص هذا الوضع و E1 بساوي اللي هو بتتوزع
+
+325
+00:23:40,300 --> 00:23:47,580
+X2 مع مين مع E1 ناقص x2 و e1 في e1 و e1 ماشي هذه
+
+326
+00:23:47,580 --> 00:23:52,760
+بيساوي واحد وهذه الان x2 و e1 ناقص x2 و e1 ايش
+
+327
+00:23:52,760 --> 00:23:58,020
+هيساوي؟ هيساوي صفر باضح اه؟ اذا صارت عندى اللي هو
+
+328
+00:23:58,020 --> 00:24:03,240
+اللي هو V2 صارت عبارة عن ما لها اللي هو الـ inner
+
+329
+00:24:03,240 --> 00:24:06,460
+product بينها وبين E1 اللي هو بيساوي صفر يعني
+
+330
+00:24:06,460 --> 00:24:09,540
+orthogonal على الـ E1 خد الآن E2 بيساوي V2 على
+
+331
+00:24:09,540 --> 00:24:13,960
+norm V2 صارت norm E2 بيساوي واحد وفي نفس الوقت
+
+332
+00:24:13,960 --> 00:24:20,300
+صارت ايه شمالها اللي هو orthogonal على الـ E1 الآن
+
+333
+00:24:20,300 --> 00:24:23,880
+بدنا نعمل نفس الجزء الصلميين بدنا نجيب V3 V3 بنفس
+
+334
+00:24:23,880 --> 00:24:28,640
+الأسلوب كيف بجيب V3 V3 بتساوي بشغل ألمين الآن ع X3
+
+335
+00:24:28,640 --> 00:24:34,770
+X3 بشغل فيها مع E1 و E2 عشان اضمن عملين ال
+
+336
+00:24:34,770 --> 00:24:37,830
+combination وحيث اضمن انها Orthogonal الـ E1 و
+
+337
+00:24:37,830 --> 00:24:40,970
+Orthogonal على مين؟ على الـ E2 اللي ياشف ياخدها
+
+338
+00:24:40,970 --> 00:24:47,510
+بساوي X3 ناقص X3 و E1 في E1 ناقص كمان X3 و E2 مع مين؟
+
+339
+00:24:47,510 --> 00:24:50,430
+مع E2 يعني لو كان عندي الآن بعدها الخطوة اللي
+
+340
+00:24:50,430 --> 00:24:56,830
+بعدها لو بدي اجيب V4 هساوى X4 ناقص X4 و E1 في E1
+
+341
+00:24:56,830 --> 00:25:05,340
+ناقص X4 و E2 في E2 ناقص X4 و E3 في E3 in general VN
+
+342
+00:25:05,340 --> 00:25:10,840
+هتكون عبارة عن XN ناقص مجموع هذولة من واحد لعند
+
+343
+00:25:10,840 --> 00:25:14,560
+اللي هي N ناقص واحد يعني بتصير XN ناقص summation
+
+344
+00:25:14,560 --> 00:25:16,640
+XN EK EK
+
+345
+00:25:19,420 --> 00:25:23,500
+إذا Vن التكوير اتركبت مجسمها نورمها بكون حصلت على
+
+346
+00:25:23,500 --> 00:25:27,180
+الـ En فبكون حصلت على الـ Orthonormal اللي هو 
+
+347
+00:25:27,180 --> 00:25:31,020
+Sequence نيجي لان لتفصيل لت V3 زي ما قلنا ناخدها
+
+348
+00:25:31,020 --> 00:25:35,800
+دي ماشي الحال الان V3 as above V33 ساوى 0 لإن لو
+
+349
+00:25:35,800 --> 00:25:40,750
+ساوى 0 هتصير X3 عبارة عن لينان combination ب X1 و ب
+
+350
+00:25:40,750 --> 00:25:45,090
+X2 وبصير اللي هي بتناقض ال linearly independent
+
+351
+00:25:45,090 --> 00:25:51,750
+ماشي إذا صارت عندي V3 مش لا مش صفر أكيد دائما و V3
+
+352
+00:25:51,750 --> 00:25:55,750
+عمود على الـ E1 ليش احسب الـ inner product بين V3 و
+
+353
+00:25:55,750 --> 00:26:03,890
+E1 هتصير اللي هو E1 و X3 و E1 و E1 و X3 و E1 و هدي
+
+354
+00:26:03,890 --> 00:26:07,450
+و هدي هيطلع في الآخر اللي هو إيش بيساوي بيساوي صفر
+
+355
+00:26:07,450 --> 00:26:13,700
+نحسبلكم إياها والان نفس الشيء V3 هتكون عمودي على E2
+
+356
+00:26:13,700 --> 00:26:17,340
+خد هذه inner product بينها وبين E2 هتلاقي برضه ايش
+
+357
+00:26:17,340 --> 00:26:22,080
+بيساوي بيساوي 0 بناء عليه لو أخدت E3 بيساوي V3 على
+
+358
+00:26:22,080 --> 00:26:27,880
+norm الـ V3 بيصير الان E3 عبارة عن نورمها واحد و
+
+359
+00:26:27,880 --> 00:26:32,020
+Orthogonal على الـ E2 و Orthogonal على الـ E1 إذا
+
+360
+00:26:32,020 --> 00:26:34,800
+إنصار أن الثلاث اللي حتى الآن بيرويس اي شمالين
+
+361
+00:26:34,800 --> 00:26:40,720
+Orthogonal in general let VN بيساوي Xn ناقص الصماش
+
+362
+00:26:40,720 --> 00:26:46,320
+Xn Ek Ek K من عند واحد بدل له ما هو لاتنين اللي هو
+
+363
+00:26:46,320 --> 00:26:51,780
+n ناقص واحد بيطلع n ناقص واحد هذا هيكون الـ Vn اللي
+
+364
+00:26:51,780 --> 00:26:54,120
+هو لا يساوي صفر للسبب نفسه لأنه بيحصل ال
+
+365
+00:26:54,120 --> 00:26:57,580
+combination من اللي جاب الهن وهي linearly
+
+366
+00:26:57,580 --> 00:27:01,380
+independent ده مظبوطش and Vn عمودي عالمين على E1
+
+367
+00:27:01,380 --> 00:27:05,440
+و E2 و E3 و En وهذا بتقدر تحسبه اللي هو زي ما حسبنا
+
+368
+00:27:05,440 --> 00:27:08,810
+اللي فوقو بتاخد الـ E N بيساوي V N ع نورمال V N
+
+369
+00:27:08,810 --> 00:27:13,210
+فبتصير عندك Therefore E K is an orthonormal
+
+370
+00:27:13,210 --> 00:27:17,130
+sequence و بارك الله فيكم و إلى لقاء آخر
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RRPYe2WUwuA_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RRPYe2WUwuA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fcbda8c259287e5f38e698b9022aa7dd2dfe71bc
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RRPYe2WUwuA_postprocess.srt
@@ -0,0 +1,1480 @@
+1
+00:00:05,110 --> 00:00:07,690
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,690 --> 00:00:10,690
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,690 --> 00:00:18,990
+آله وصحبه أجمعين المحاضرة رقم عشرين مساق تحليل
+
+4
+00:00:18,990 --> 00:00:22,630
+اقتراني طلاب طالبات الجامعة الإسلامية ماجستير
+
+5
+00:00:22,630 --> 00:00:28,210
+رياضيات وصلنا ل section تلاتة أربعة اللي هو تحت
+
+6
+00:00:28,210 --> 00:00:34,050
+عنوان orthonormal sets and sequencesعرفنا المرة
+
+7
+00:00:34,050 --> 00:00:38,230
+الماضية شو معناة orthogonal sets أو اللي هو تكون
+
+8
+00:00:38,230 --> 00:00:42,430
+شو معناة element orthogonal على اللي هو مجموعة أو
+
+9
+00:00:42,430 --> 00:00:45,730
+مجموعة على مجموعة كيف يكونوا orthogonal متعامدتين
+
+10
+00:00:45,730 --> 00:00:49,830
+اليوم بنحكي عن مفهوم إيش معناة ال set نفسها تكون
+
+11
+00:00:49,830 --> 00:00:53,030
+orthogonal أو ال set نفسها تكون orthonormal
+
+12
+00:00:53,030 --> 00:00:57,650
+باختصار ال set بتكون orthogonal إذا كان اللي هو كل
+
+13
+00:00:57,650 --> 00:01:01,710
+عناصرها pairwise are orthogonalو Orthonormal بتكون
+
+14
+00:01:01,710 --> 00:01:05,250
+اللي هو pairwise Orthogonal بالإضافة إنه norm كل
+
+15
+00:01:05,250 --> 00:01:07,650
+واحد بيساوي واحد فبنسميه Orthonormal set هاي
+
+16
+00:01:07,650 --> 00:01:11,790
+باختصار اللي هو المعنى لل Orthogonal
+
+17
+00:01:11,790 --> 00:01:15,830
+والOrthonormal ك sets الآن نيجي لل definition اللي
+
+18
+00:01:15,830 --> 00:01:18,450
+قلته قبل شوية أن Orthogonal set M in an inner
+
+19
+00:01:18,450 --> 00:01:22,590
+product space X الcell is a subset M of X whose
+
+20
+00:01:22,590 --> 00:01:25,610
+elements are pairwise Orthogonal يعني كل تنتين مع
+
+21
+00:01:25,610 --> 00:01:30,450
+بعض إشماليا متعمدينAn orthonormal subset of M of X
+
+22
+00:01:30,450 --> 00:01:32,970
+is an orthogonal set
+
+23
+00:01:35,660 --> 00:01:39,700
+وفي نفس الوقت whose elements have norm one يعني كل
+
+24
+00:01:39,700 --> 00:01:42,480
+واحد من ال elements أشماله normه بسوء واحد أو
+
+25
+00:01:42,480 --> 00:01:46,240
+بمعنى أخر ملخص الحديث لل orthonormal منقول أن ال
+
+26
+00:01:46,240 --> 00:01:49,340
+orthonormal إذا كان لكل x و y element عند ال inner
+
+27
+00:01:49,340 --> 00:01:52,940
+product بين ال x و ال y يا بساوي سفر يا واحد سفر
+
+28
+00:01:52,940 --> 00:01:55,980
+إذا كانت x لا تساوي y واحد إذا كانت x أشمالها
+
+29
+00:01:55,980 --> 00:02:01,500
+بتسويش y ماشي الحالة بتساوياتلع لفوق الآن بعض
+
+30
+00:02:01,500 --> 00:02:05,820
+الملاحظات على هذا الكلام if an orthogonal or
+
+31
+00:02:05,820 --> 00:02:10,300
+orthonormal system is countable إذا كانت countable
+
+32
+00:02:10,300 --> 00:02:14,660
+بنقدر نعملها يعني أشملها ك sequence اللي هو we can
+
+33
+00:02:14,660 --> 00:02:17,920
+arrange it in a sequence countable يعني اللي هو
+
+34
+00:02:17,920 --> 00:02:21,400
+بيكون كلها ال هي one to one on to مع ال natural
+
+35
+00:02:21,400 --> 00:02:26,120
+numberاللي هي arrange it in a sequence Xn and call
+
+36
+00:02:26,120 --> 00:02:30,420
+it an orthogonal or an orthonormal sequence حسب
+
+37
+00:02:30,420 --> 00:02:34,320
+إيش هي في الاصل ماشي الحال اللي هان a family X
+
+38
+00:02:34,320 --> 00:02:36,860
+Alpha Alpha element in I is called an orthogonal
+
+39
+00:02:36,860 --> 00:02:40,680
+إذا كانت X Alpha orthogonal to X Beta for all
+
+40
+00:02:40,680 --> 00:02:43,980
+Alpha و Beta element in main in I and Alpha less
+
+41
+00:02:43,980 --> 00:02:46,240
+than أو Beta يعني بتكون هذه يعني لو كانت
+
+42
+00:02:46,240 --> 00:02:49,930
+uncountable اللي هي العدد العناصر X Alphaعداد هنا
+
+43
+00:02:49,930 --> 00:02:52,530
+uncountable الـ 6 ونقدر نكتبها على صورة اللي هو
+
+44
+00:02:52,530 --> 00:02:55,150
+family X α حيث و Alpha element in I مش sequence ده
+
+45
+00:02:55,150 --> 00:02:58,450
+اللي هي family of elements the family is
+
+46
+00:02:58,450 --> 00:03:02,630
+orthonormal if it is orthogonal and X α have norm
+
+47
+00:03:02,630 --> 00:03:05,890
+إيش بيساوي واحد so that for all Alpha و Beta
+
+48
+00:03:05,890 --> 00:03:08,090
+element in I ال inner product بين X و Alpha و Beta
+
+49
+00:03:08,090 --> 00:03:11,010
+بيساوي ياسفر يواحد حتى سبق الألفة اللي بتساوي Beta
+
+50
+00:03:11,010 --> 00:03:13,970
+أو الألفة بتساوي Beta نفس كالحديث اللي فوق اطلع
+
+51
+00:03:13,970 --> 00:03:18,540
+لفوقالرمارك الأولى اللى هو تعنيم لـ Pythagoras
+
+52
+00:03:18,540 --> 00:03:24,180
+نظرية Pythagoras اللى هو المربع المنشئ على الواطر
+
+53
+00:03:24,180 --> 00:03:26,680
+بيساوي جميع المربعين المنشئين على الضلعين الآخرين
+
+54
+00:03:26,680 --> 00:03:30,140
+الان for unorthogonal elements اللى بيكونوا
+
+55
+00:03:30,140 --> 00:03:33,960
+متعامدين ال X و ال Y متعامدين نحن لدينا norm X زي
+
+56
+00:03:33,960 --> 00:03:38,260
+Y كل تربيع بيساوي norm X تربيع زي norm Y تربيع
+
+57
+00:03:38,260 --> 00:03:42,240
+الان و هذا أثبتوا سهل norm X زي Y مدام orthogonal
+
+58
+00:03:44,130 --> 00:03:46,610
+بيصير نورم الـ x زائد y لكل تربيع بيساوي ال inner
+
+59
+00:03:46,610 --> 00:03:51,270
+product بين x زائد y و x زائد y و يساوي بنفكها x و
+
+60
+00:03:51,270 --> 00:03:58,130
+x زائد x و y زائد y و x زائد y و y الان مدام
+
+61
+00:03:58,130 --> 00:04:01,270
+ارتجون ان هذوله سفر و هذوله سفر يدن بيساوي اللي هو
+
+62
+00:04:01,270 --> 00:04:06,190
+نورم ال xتربيع زاده normal y تربيع وهذا ما هو
+
+63
+00:04:06,190 --> 00:04:09,110
+بساوية هذا زاد هذا اللي هي المربع المنشئة على
+
+64
+00:04:09,110 --> 00:04:10,550
+الواطر بساوية المجموع المربعين المشئين على
+
+65
+00:04:10,550 --> 00:04:12,890
+الضلاعين الأخرين اللي هي تعميم لها هذا الكلام في
+
+66
+00:04:12,890 --> 00:04:17,430
+أي inner product space in general لو كانت عنده
+
+67
+00:04:17,430 --> 00:04:23,760
+اللي هوX1 زي X2 و X2 و Xn عبارة عن orthogonal set
+
+68
+00:04:23,760 --> 00:04:26,980
+يعني كل اتنين عموديا على بعض هيطلع عند ال inner
+
+69
+00:04:26,980 --> 00:04:30,360
+product بينهم بيساوي اللي هو نورم الواحد الأول
+
+70
+00:04:30,360 --> 00:04:33,260
+تربيع زي نورم الأول .. أسف نورم التربيع بيساوي
+
+71
+00:04:33,260 --> 00:04:35,780
+نورم واحد تربيع زي نورم التاني تربيع زي نورم الان
+
+72
+00:04:35,780 --> 00:04:40,160
+تربيع و نفس الشيء اللي هو عن طريق اللي هي اللي
+
+73
+00:04:40,160 --> 00:04:46,200
+حاقنا قبل و شوية بتقدر تعمله بكل سهولةيعني نورم ال
+
+74
+00:04:46,200 --> 00:04:49,340
+X1
+
+75
+00:04:49,340 --> 00:04:54,900
+بالنفع بال induction برضه نورم X1 زاد X2 زاد Xn
+
+76
+00:04:54,900 --> 00:05:01,600
+لكل ترجيع بساوي اللي هو inner product بين
+
+77
+00:05:01,600 --> 00:05:07,340
+summation XI I من عند 1 لعند N و summation ل XI XJ
+
+78
+00:05:07,340 --> 00:05:13,380
+J من عند 1 لعند N صح ولا لأ؟بظبط هو يساوي اللي هو
+
+79
+00:05:13,380 --> 00:05:17,800
+اللي بوزع اللي هو أول واحد مع هدوله يعني X1 محدد و
+
+80
+00:05:17,800 --> 00:05:23,580
+X2 محدد و X3 محدد و بجمعها فبصير summation XI و
+
+81
+00:05:23,580 --> 00:05:28,580
+summation XJ جي من عند واحد لعند تاني صح I من عند
+
+82
+00:05:28,580 --> 00:05:33,750
+واحدعند N ويساوي الـ N زي ما .. هالـ gate خلص من
+
+83
+00:05:33,750 --> 00:05:38,390
+هذا الـ N للـ fixed I X I و الأولى و X Y و التاني
+
+84
+00:05:38,390 --> 00:05:41,410
+و X Y و التالتة إذاً A برضه summation إذاً بيصير
+
+85
+00:05:41,410 --> 00:05:45,110
+ال summation الأولاني الأصلي I بيساوي واحد عند N و
+
+86
+00:05:45,110 --> 00:05:49,590
+ال summation التاني اللي هو بيصير X I و X I و مين
+
+87
+00:05:49,590 --> 00:05:55,360
+و X J معاياهنا J من عند واحد برضه و لا عند مين لا
+
+88
+00:05:55,360 --> 00:06:02,020
+عند N الان كل هين هيتصفرن مادة ل I ايش بتساوي J
+
+89
+00:06:02,020 --> 00:06:07,360
+فبيصير كل صفار بيظل بس اللي هو ال summation لل XI
+
+90
+00:06:07,360 --> 00:06:11,540
+و XI يعني الاتنين ايش لما I تساوي J و I من عند
+
+91
+00:06:11,540 --> 00:06:15,000
+واحد لا عند مين لا انه هذا بيساوي ال summation ل
+
+92
+00:06:15,000 --> 00:06:20,970
+norm XI تربيع I من عند واحد لا عند N اللي هوالـ X
+
+93
+00:06:20,970 --> 00:06:26,590
+واحد تربيع زائد آخر واحد نور من الـ X and الكل
+
+94
+00:06:26,590 --> 00:06:32,290
+تربيع وصير هذا واضح؟ خلاص مابتحتاجش ال induction
+
+95
+00:06:32,290 --> 00:06:39,170
+إذا لكن بنفع بال induction طيب إجبال حلم ان
+
+96
+00:06:39,170 --> 00:06:43,010
+orthonormal set is linearly independent مهمة ده
+
+97
+00:06:43,010 --> 00:06:47,130
+الكلام تبقوا معايا an orthonormal set is linearly
+
+98
+00:06:47,130 --> 00:06:54,000
+independent يعني خد الآناللي هو I ألف واحد X واحد
+
+99
+00:06:54,000 --> 00:07:00,200
+زايد ألف ان X ان بيساوي سفر وقصل منه أنه ألف واحد
+
+100
+00:07:00,200 --> 00:07:04,180
+بيساوي ألف اتنين بيساوي ألف ان إيش بيساوي سفر الآن
+
+101
+00:07:04,180 --> 00:07:15,090
+بقول الآن خد اللي هو M orthonormal setوبدأ أثبت لك
+
+102
+00:07:15,090 --> 00:07:19,050
+أن الـ M اللي هو إيش مالها is linearly independent
+
+103
+00:07:19,050 --> 00:07:25,590
+6 كيف بأثبت linearly independent بأخد أي X1 و X2
+
+104
+00:07:25,590 --> 00:07:29,970
+عند Xn element مين element نهر، arbitrary finite و
+
+105
+00:07:29,970 --> 00:07:37,230
+باخد Alpha 1 X1 زائد Alpha N Xn و بسوي بإيش؟
+
+106
+00:07:37,230 --> 00:07:41,070
+بالصفر، ماشي الحال؟ لأن حسبولي الآن ال inner
+
+107
+00:07:41,070 --> 00:07:49,210
+product بيناللي هو for N في XI ألف واحد X واحد
+
+108
+00:07:49,210 --> 00:07:58,250
+زائد Alpha N XN وخده مع XN وحسبوا ان ال product
+
+109
+00:07:58,250 --> 00:08:03,230
+بينهم برضه هيسوي أيش؟ هيسوي سفر الآن هذا كله
+
+110
+00:08:03,230 --> 00:08:08,870
+هيتصفر كله هيتصفر مظبوط هذه مع هذه سفرها هذه مع
+
+111
+00:08:08,870 --> 00:08:12,730
+هذه سفرها هذه XN لخط الأخيرة بسمفهدكم تاخدوا
+
+112
+00:08:12,730 --> 00:08:15,470
+الأولى بنفهد و بعدين تقولوا الباقي الذين يعرفوا I
+
+113
+00:08:15,470 --> 00:08:19,470
+fixed till بنفهد يعني for unfixed I فبصير عندى
+
+114
+00:08:19,470 --> 00:08:28,350
+بصير Alpha واحد و X واحد و X واحد و الباقي كله إيش
+
+115
+00:08:28,350 --> 00:08:36,550
+أسفل بصير هذا إيش بيساوي Alpha واحد في X واحد و X
+
+116
+00:08:36,550 --> 00:08:42,270
+واحدهذا طبعا اللي هو بصير عندي ألف و واحد ايش
+
+117
+00:08:42,270 --> 00:08:46,470
+بساوي؟ بساوي صفر لإنه normal ايش بتساوي واحد؟
+
+118
+00:08:46,470 --> 00:08:52,470
+normal ألف واحد صفر similarly for لبعض نطلع عن كل
+
+119
+00:08:52,470 --> 00:08:57,250
+صفر بتاعة ترتب البرهان لإنه لفته ضريدة خد for any
+
+120
+00:08:57,250 --> 00:09:03,110
+fixed i و اشتغل عليها احسنها اطلع من فوق examples
+
+121
+00:09:03,110 --> 00:09:08,900
+Euclidean space are unفي القرآن The standard basis
+
+122
+00:09:08,900 --> 00:09:13,040
+of RN forms an orthonormal set ال standard basis
+
+123
+00:09:13,040 --> 00:09:15,940
+عارفين احنا ال inner product على ال RN ال inner
+
+124
+00:09:15,940 --> 00:09:19,200
+product عارفينه احنا لو جينا اخدنا من ال R تكعيب
+
+125
+00:09:19,200 --> 00:09:28,640
+مين ال standard basis له 1000 1 0 0 0 1 لو أخدت أي
+
+126
+00:09:28,640 --> 00:09:31,880
+inner product بين التليهيل اللي هو مختلفين سفر و
+
+127
+00:09:31,880 --> 00:09:34,860
+inner product بين العنصر نفسه إيش بيساوي بيساوي
+
+128
+00:09:34,860 --> 00:09:37,020
+واحد بناء على اللي هو inner product تبعنا في
+
+129
+00:09:37,020 --> 00:09:40,540
+الارتقال في الار أنجينال فبطلع عنده عبارة عن
+
+130
+00:09:40,540 --> 00:09:46,330
+orthonormal setماضح اه مثال اخر نفس الاشي ما هو
+
+131
+00:09:46,330 --> 00:09:49,330
+احنا عرفنا ال inner product بين هنا دولة ال E n
+
+132
+00:09:49,330 --> 00:09:52,190
+اللي هو بساوة ال summation لا ال inner product في
+
+133
+00:09:52,190 --> 00:09:55,410
+ال L تربيع بساوة ال summation لل alpha I في ال
+
+134
+00:09:55,410 --> 00:09:59,530
+beta I conjugate الكل اللي هو أص نص ماشي هي ليها
+
+135
+00:09:59,530 --> 00:10:03,990
+productالان اعمل لو جيت على the shoulder bases
+
+136
+00:10:03,990 --> 00:10:07,330
+بالذات اللي هو the shoulder bases EN of التربيع
+
+137
+00:10:07,330 --> 00:10:11,270
+هيطلع لي forms and orthonormal sequence in التربيع
+
+138
+00:10:11,270 --> 00:10:14,050
+بالظبط زي اللي عملته هنا ماشي الحال اللي بعده
+
+139
+00:10:16,250 --> 00:10:19,870
+continuous functions احنا let x be the inner
+
+140
+00:10:19,870 --> 00:10:22,530
+product space of all continuous real valued
+
+141
+00:10:22,530 --> 00:10:26,950
+functions 0 و2π ال inner product اللي عرفناها مش
+
+142
+00:10:26,950 --> 00:10:29,350
+هو طبعا ال norm مش ال maximum الم maximum ماطلعش
+
+143
+00:10:29,350 --> 00:10:32,470
+inner product ال inner product اللي عند x و y
+
+144
+00:10:32,470 --> 00:10:36,550
+بسهولة integration x of t y of t dt من 0 ل2π لو
+
+145
+00:10:36,550 --> 00:10:40,600
+كانت real لو كان complex بتحطوله conjugateماشي
+
+146
+00:10:40,600 --> 00:10:45,900
+الحال الان هي ال inner product بقولك الان مثال
+
+147
+00:10:45,900 --> 00:10:49,760
+يعني بيعطيك مثال على orthogonal sets cosine ال N T
+
+148
+00:10:49,760 --> 00:10:53,020
+يعني cosine ال T cosine ال 2T cosine ال 3T cosine
+
+149
+00:10:53,020 --> 00:10:58,300
+ال 4T cosine ال 5T الاخره و اللي هي و cosine ال
+
+150
+00:10:58,300 --> 00:11:04,060
+zero اللي هو ال N element in N cosine ال N T مثال
+
+151
+00:11:04,060 --> 00:11:07,780
+تاني sine ال T sine ال 2T الاخره و cosine ال zero
+
+152
+00:11:08,310 --> 00:11:14,630
+بعملين orthogonal sequences
+
+153
+00:11:14,630 --> 00:11:22,090
+بس إستثنى اللي هو الـ zero من هنا بتطلعلك اللي هي
+
+154
+00:11:22,090 --> 00:11:27,390
+واحد على جدر اتنين باي cos T على جدر الـ باي هذا
+
+155
+00:11:27,390 --> 00:11:32,130
+هتطلعلك orthonormal setجسمها Anormة هو في الواقع
+
+156
+00:11:32,130 --> 00:11:37,410
+عشان تطلع واحد وهنا sin الانتي على جدر ال by اللي
+
+157
+00:11:37,410 --> 00:11:41,550
+هو برضه هتطلع إيش معلها orthonormal sequence و هذه
+
+158
+00:11:41,550 --> 00:11:44,250
+orthonormal sequence اثبت ليها ان هدولة مش صعبة كل
+
+159
+00:11:44,250 --> 00:11:47,350
+الحسابات من وين من هذه integration تبع اللي هو sin
+
+160
+00:11:47,350 --> 00:11:52,190
+و cos اطلع لكمالان هدولة مثلا امثلة على
+
+161
+00:11:52,190 --> 00:11:56,170
+orthonormal sequences الان اطلع لفوق في حاجة اسمها
+
+162
+00:11:56,170 --> 00:11:59,130
+Bessels Inquality اللي هو الـBessels Inquality
+
+163
+00:11:59,130 --> 00:12:04,730
+اللي هي التالي لو كانت EN بيه orthonormal sequence
+
+164
+00:12:04,730 --> 00:12:07,970
+EN orthonormal sequence ماحدش جالب واحد وزير وزير
+
+165
+00:12:07,970 --> 00:12:12,870
+وزير لأ هد بس رمز هنا ال EN مش معناته واحد وزفر
+
+166
+00:12:12,870 --> 00:12:17,590
+وزفر لأ ه delete EN be an orthonormal sequence in
+
+167
+00:12:17,590 --> 00:12:21,610
+an inner product spacethen for every x element in
+
+168
+00:12:21,610 --> 00:12:24,810
+X الـ summation للـ absolute value هذا التربيع من
+
+169
+00:12:24,810 --> 00:12:30,410
+واحدة infinity أصحى شوميين normal X تربيعيعني و
+
+170
+00:12:30,410 --> 00:12:34,790
+كأنه بيقوللي هنا أنه هذه ال series دايما converges
+
+171
+00:12:34,790 --> 00:12:39,730
+ال series لما تحسب اللي هو ال inner product بين ال
+
+172
+00:12:39,730 --> 00:12:45,890
+X و ال orthonormal sequence هذه هيطلع دايما اللي
+
+173
+00:12:45,890 --> 00:12:50,250
+هو ال series هذه المحسوبة تكون أشملها convergent
+
+174
+00:12:50,250 --> 00:12:55,630
+series راحظوا ال orthonormal set قلنا عليها
+
+175
+00:12:55,630 --> 00:12:58,130
+linearly independent
+
+176
+00:13:00,360 --> 00:13:05,480
+إذا الشكل اللي في المستقبل هتعملنا إشي نحي ولاحظنا
+
+177
+00:13:05,480 --> 00:13:12,140
+إن ال basis ال standard basis في ال RN و الشودر
+
+178
+00:13:12,140 --> 00:13:17,640
+basis في ال L2 كل هين عبارة عن إيه الشمال هين are
+
+179
+00:13:17,640 --> 00:13:23,780
+orthonormal sets طب الشودر basis في ال LB ال B لتس
+
+180
+00:13:23,780 --> 00:13:25,760
+و اتنين تتوقع يكون orthonormal set
+
+181
+00:13:35,600 --> 00:13:39,580
+ال orthonormal بيعتمد علي إيش؟ أو ال orthogonal
+
+182
+00:13:39,580 --> 00:13:43,540
+بيعتمد علي إيش؟ عرفناه وين؟ عرفناه في ال inner
+
+183
+00:13:43,540 --> 00:13:47,980
+product على أساس ال inner product طب هو ال ال B مش
+
+184
+00:13:47,980 --> 00:13:51,860
+ال LBB لسه و اتنين مش inner productبناءً على هذا
+
+185
+00:13:51,860 --> 00:13:56,000
+التعريف طبعًا مظبوطش لكن فيه دراسات في تعريف اللي
+
+186
+00:13:56,000 --> 00:13:58,880
+هو فيه برخوف orthogonality ومش عارف أيش حتى عن
+
+187
+00:13:58,880 --> 00:14:03,380
+norm dismiss بس طبعًا يعني بشكل آخر يعني في مجالنا
+
+188
+00:14:03,380 --> 00:14:08,360
+احنا مابنحكيش الآن عن اللي هو أي orthogonality هنا
+
+189
+00:14:08,360 --> 00:14:11,880
+دي اجتهادات في ال orthogonality بأكتر من نوع من ال
+
+190
+00:14:11,880 --> 00:14:16,800
+orthogonality وفيها دراسات حديثة كلها طيبلأن يجيل
+
+191
+00:14:16,800 --> 00:14:19,680
+لبس الـ Zinquality let Eₙ be an orthonormal
+
+192
+00:14:19,680 --> 00:14:23,040
+sequence in an inner product space X then for
+
+193
+00:14:23,040 --> 00:14:25,860
+every X limit in X هذي السيريز converts اطلع لفوق
+
+194
+00:14:25,860 --> 00:14:30,960
+من برهن لأن consider the finite subset E₁ E₂ عند
+
+195
+00:14:30,960 --> 00:14:33,520
+Eₙ أن arbitrarily .. arbitrarily يعني بس أنا مابدش
+
+196
+00:14:33,520 --> 00:14:38,390
+أطلع على ال finite و بعدين بمدها زي ما بدنيطيب هذه
+
+197
+00:14:38,390 --> 00:14:40,950
+subset من مين؟ من الـ E عن الـ Orthonormal set
+
+198
+00:14:40,950 --> 00:14:46,230
+احسبلي الآن احسبلي norm ال X ناقص ال summation
+
+199
+00:14:46,230 --> 00:14:51,090
+اللي عندي هذا تربيع ماشي الحال اللي هو استقيته من
+
+200
+00:14:51,090 --> 00:14:54,910
+هنا اه اه ده استقي اشي من هنا عشان اصل ال equality
+
+201
+00:14:54,910 --> 00:15:01,180
+هذه بعد شويةY ساوى X نقص ال summation و X نقص ال
+
+202
+00:15:01,180 --> 00:15:04,560
+summation زي ما عملنا قبل بشوية هذي بيصير X مع ال
+
+203
+00:15:04,560 --> 00:15:08,380
+X و بعدين X مع ال summation و summation مع X و
+
+204
+00:15:08,380 --> 00:15:11,440
+summation مع summation Y ساوى هاي ال X مع ال X
+
+205
+00:15:11,440 --> 00:15:14,780
+بيطلع X ربيع و ال X مع ال summation هيه و هذي ال
+
+206
+00:15:14,780 --> 00:15:17,460
+summation مع ال X و هذي ال summation مع ال
+
+207
+00:15:17,460 --> 00:15:21,240
+summation Y ساوى اللي يعني الأول يعني زي ما هو
+
+208
+00:15:21,240 --> 00:15:26,220
+بنزلالتاني بيصير .. برضه بيتوزح حد ال X مع هدولة
+
+209
+00:15:26,220 --> 00:15:29,240
+بيطلع ال summation ماله برا فبصير ال summation برا
+
+210
+00:15:29,240 --> 00:15:32,420
+لكن بتاخد هذه ايش مالها ب conjugate برا فلأنها
+
+211
+00:15:32,420 --> 00:15:36,180
+بعيدة بتاخد هذه ال conjugate معاها ناجهاد و بيظل
+
+212
+00:15:36,180 --> 00:15:39,580
+اللي جوا منين X و EK فبصير هذه مع هذه هي ال
+
+213
+00:15:39,580 --> 00:15:43,860
+conjugate اللي بعدهاالتانية ناقصة هذا جريم فبطلع
+
+214
+00:15:43,860 --> 00:15:49,260
+برا عادي و بتصير EI و مين و X هذه بتطلع برا و ال
+
+215
+00:15:49,260 --> 00:15:52,520
+summation هي بيصير هذه EI و X زاد هدولة ال
+
+216
+00:15:52,520 --> 00:15:55,700
+summation ال two summations بيطلع عن برا الأول
+
+217
+00:15:55,700 --> 00:15:59,060
+بيطلع عادي و التاني بيطلع ال conjugate لبعيد بيصير
+
+218
+00:15:59,060 --> 00:16:02,440
+ال summation summation الأول عادي هيه و التاني
+
+219
+00:16:02,440 --> 00:16:05,980
+بيضل عايش بال conjugate و بيضل مين في .. عندي EI و
+
+220
+00:16:05,980 --> 00:16:10,980
+مين و EK EI و EKI من عند واحد لعند ان و okay من
+
+221
+00:16:10,980 --> 00:16:15,540
+عند واحد لعند ان اطلع لفوق بيصير عند الان و يساوي
+
+222
+00:16:15,540 --> 00:16:24,110
+هذا بنزل زي ما هو عندى و التانياللي هو هذا هو هذا
+
+223
+00:16:24,110 --> 00:16:29,370
+لأنه هذا لما أشي أخليه X وEI بيصير X وEI أشمال ال
+
+224
+00:16:29,370 --> 00:16:31,990
+conjugate فهذا conjugate و هذا conjugate و المجموع
+
+225
+00:16:31,990 --> 00:16:34,210
+من واحد لعندي N و هذا conjugate و هذا عادي و
+
+226
+00:16:34,210 --> 00:16:36,810
+المجموع من واحد لعندي N يعني واحد conjugate واحد
+
+227
+00:16:36,810 --> 00:16:39,310
+عادي في التنين و من واحد لعندي N إذا المجموح
+
+228
+00:16:39,310 --> 00:16:43,070
+للتنين اتنين يعني التنين نفس الاشي فبصير ناقص
+
+229
+00:16:43,070 --> 00:16:47,400
+اتنين في ال summation هذا هذا و هذا زي بعضزائد ال
+
+230
+00:16:47,400 --> 00:16:50,880
+summation اللي بعده هذا اللي عندي ال summation هذا
+
+231
+00:16:50,880 --> 00:16:57,640
+كله هيتصفر مع ده لما تكون EI EI ايش بتساوي K لإن
+
+232
+00:16:57,640 --> 00:17:03,570
+EI وEI مش orthonormalهيصير EI و EK اللي هو عبارة
+
+233
+00:17:03,570 --> 00:17:07,230
+عن سفر إذا كانت I لات شو K و واحد في حالة المساواة
+
+234
+00:17:07,230 --> 00:17:13,050
+إذا هذا هيصير summation واحد بس وهيصير بس اللي هو
+
+235
+00:17:13,050 --> 00:17:18,870
+summation عندى بيظل X وEI و X وEI conjugate معناته
+
+236
+00:17:18,870 --> 00:17:23,490
+هذا تربيع و هذا هيصير واحد فبيصير عبارة عن معايا
+
+237
+00:17:23,490 --> 00:17:28,550
+نفسي هو normal X تربيحيه و هذا 2X و هذا زائد هذا
+
+238
+00:17:28,550 --> 00:17:33,160
+في هذاو هذيك صار واحد ال EI و E كام فاهمين عليها
+
+239
+00:17:33,160 --> 00:17:37,040
+لأن هذا زي ما هو بنزل و الأن هذا ناقص اتنين و هذا
+
+240
+00:17:37,040 --> 00:17:42,760
+واحد بيصير ناقص واحد منهم مظبوط نورم تربية لإن ما
+
+241
+00:17:42,760 --> 00:17:47,440
+بتضرب هذا في هذا بيصير موضولاس تربية صار هذا
+
+242
+00:17:47,440 --> 00:17:52,220
+المقدار ها يوم أوصلنا بدأنا من Zero و أصغر أو
+
+243
+00:17:52,220 --> 00:17:55,300
+يساوي لما أوصلنا هذا صار هذا المقدار أكبر أو ساوي
+
+244
+00:17:55,300 --> 00:17:58,400
+Zero معناته أنه صار هذا على الجهة الثانية أصغر أو
+
+245
+00:17:58,400 --> 00:18:04,190
+ساوي هذاصارت هذه اللي هي this is inequality لأن
+
+246
+00:18:04,190 --> 00:18:07,610
+هذا في ال finite ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+247
+00:18:07,610 --> 00:18:07,750
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+248
+00:18:07,750 --> 00:18:08,290
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+249
+00:18:08,290 --> 00:18:09,450
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+250
+00:18:09,450 --> 00:18:09,610
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+251
+00:18:09,610 --> 00:18:10,710
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+252
+00:18:10,710 --> 00:18:10,750
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+253
+00:18:10,750 --> 00:18:11,390
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+254
+00:18:11,390 --> 00:18:11,730
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+255
+00:18:11,730 --> 00:18:11,790
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+256
+00:18:11,790 --> 00:18:19,590
+.. ل .. ل .. ل .. ل .. ل ..
+
+257
+00:18:19,590 --> 00:18:20,190
+ل .. ل ..
+
+258
+00:18:28,520 --> 00:18:32,840
+الأن نجي لل inner product X وEK اللي قبله شوية
+
+259
+00:18:32,840 --> 00:18:38,620
+above هذا بيسميه the Fourier coefficients of X
+
+260
+00:18:38,620 --> 00:18:40,280
+لإنه بيطلع في ال Fourier series عنا
+
+261
+00:18:43,650 --> 00:18:48,330
+الشيء الأساسي X,Y,K أعلى هؤلاء هما معاملات تسمى
+
+262
+00:18:48,330 --> 00:18:52,470
+كالخصوصية الواقعية لـ X بالنسبة للتطبيق التطبيقي
+
+263
+00:18:52,470 --> 00:18:59,690
+الـ E,K هذا فيه معناه التطبيقي ليس مجال نحكي فيه
+
+264
+00:18:59,690 --> 00:19:03,890
+إذا كانت المعاملة لـ X فينية، فكل تطبيق التطبيق
+
+265
+00:19:03,890 --> 00:19:08,790
+التطبيقي يجب أن يكون فينيbecause it's linearly
+
+266
+00:19:08,790 --> 00:19:11,670
+independent أكيد إذا كانت ال dimension لل space
+
+267
+00:19:11,670 --> 00:19:15,190
+نفسه اللي بس تشتغل فيه finite مش معقول تكون subset
+
+268
+00:19:15,190 --> 00:19:20,110
+منه infinite ليش مش معقول تكون subset منه اللي هو
+
+269
+00:19:20,110 --> 00:19:22,870
+infinite اللي هي من ال orthonormal لأن ال
+
+270
+00:19:22,870 --> 00:19:27,290
+orthonormal إيه شمالها linearly independent مدام
+
+271
+00:19:27,290 --> 00:19:31,610
+linearly independent إذا ثقفها عدت على أصل ال
+
+272
+00:19:31,610 --> 00:19:34,150
+bases اللي هو ال dimension لأنه لو زادت بتبطل
+
+273
+00:19:34,150 --> 00:19:38,370
+linearly independent فاهمينإذا الأن أكيد مدام
+
+274
+00:19:38,370 --> 00:19:41,130
+الـdimensional X finite هتكون الـorthonormal sets
+
+275
+00:19:41,130 --> 00:19:46,110
+اللي فيها are finite sets الآن بدنا نيجي لجرام
+
+276
+00:19:46,110 --> 00:19:49,570
+شمدة process for orthonormalizing a linearly
+
+277
+00:19:49,570 --> 00:19:53,330
+independent sequence XJ يعني هنا product space X
+
+278
+00:19:53,330 --> 00:19:57,690
+يعني إيش بقوليه بقولي كيف بدي أكون اللي هو
+
+279
+00:19:57,690 --> 00:20:02,490
+orthonormal setOrthonormal Set أو Orthonormal
+
+280
+00:20:02,490 --> 00:20:07,650
+Sequence من اللي هو Set تكون Linear ل Independent
+
+281
+00:20:07,650 --> 00:20:11,250
+هذه ال process اللي هو حد اسمه Gram-Schmidt
+
+282
+00:20:11,250 --> 00:20:16,350
+Process خلينا نشوف الخطوات .. الخطوات سهلة و .. و
+
+283
+00:20:16,350 --> 00:20:20,210
+.. و الكل بيفهمها يعني شغلات سهلة ان شاء الله The
+
+284
+00:20:20,210 --> 00:20:25,710
+first element لان X1 .. X2 .. X3 .. X4 .. إلا ما
+
+285
+00:20:25,710 --> 00:20:31,990
+ننهيها بدي أخد منهم اللي هو 100اللي هو .. ال .. ال
+
+286
+00:20:31,990 --> 00:20:35,410
+.. ال .. من هنا أولد الـ E1 و الـ E2 و الـ E3 و
+
+287
+00:20:35,410 --> 00:20:39,750
+الـ E4 شوف كيف بدي أجيبهم أول خطوة اللي هو طبيعي
+
+288
+00:20:39,750 --> 00:20:44,010
+اللي بدي أخد first element of EK is E1 بسميه هذا
+
+289
+00:20:44,010 --> 00:20:49,470
+الـ EK الـ orthonormal المبتغى اللي بدي أعملها
+
+290
+00:20:49,470 --> 00:20:53,570
+يعني لأن E1 بساوي X1 على normal X1 هذول اللي بين
+
+291
+00:20:53,570 --> 00:20:55,910
+يديها الـ X1 و X2 و X3 اللي مالها يعني they are
+
+292
+00:20:55,910 --> 00:20:59,030
+independent setإذا المدان لينيال independent
+
+293
+00:20:59,030 --> 00:21:03,850
+sequence ده لو لو واحد فيه سفر لو في واحد سفر
+
+294
+00:21:03,850 --> 00:21:07,010
+بتبطي لينيال independentإذا الـ X1 على نورم الـ X1
+
+295
+00:21:07,010 --> 00:21:11,290
+مشروع هذا هيصير نورمه الجديد إيش بساوي بساوي واحد
+
+296
+00:21:11,290 --> 00:21:18,230
+طيب الآن ال second step بتاخد اللي هو عشان أصل لل
+
+297
+00:21:18,230 --> 00:21:22,730
+E2 بتاخد أوليش حاجة اسمها V2 ومنها أصل لل E1 V2
+
+298
+00:21:22,730 --> 00:21:26,070
+بعد شوية حاجة قسمها على نورم وحصل على ال E2 إذا
+
+299
+00:21:26,070 --> 00:21:33,940
+الآن حصلت على ال E1 عبارة عن X1 على نورم ال X1وهذا
+
+300
+00:21:33,940 --> 00:21:41,040
+اكيد normal E1 بساوى اللي هو واحد طيب بدي اجيب E2
+
+301
+00:21:41,040 --> 00:21:46,920
+قبل عشان اجيب E2 E2 و اقولها اجيب حاجة اسمها V2 و
+
+302
+00:21:46,920 --> 00:21:52,040
+اقسمها عالميا على normal V2 طب V2 ايش هو V2 بتاخد
+
+303
+00:21:52,040 --> 00:21:59,330
+اللي هو X2 V2بتاخدها بتساوي ال X2 و أطرح منها ال
+
+304
+00:21:59,330 --> 00:22:05,170
+X2 و ال E1 اللي لجيتها في الأول مضروبة في ميهم؟ في
+
+305
+00:22:05,170 --> 00:22:10,530
+ال E1 عشان أضرب عصفرين بحجر أثبتلك أن هذول ال V2
+
+306
+00:22:10,530 --> 00:22:14,990
+منها هتكون اللي هو ال inner product مع ال E1 اللي
+
+307
+00:22:14,990 --> 00:22:17,990
+فوق 0 يعني هأثبتلك أنه Orthogonal و بعدين أقسمها
+
+308
+00:22:17,990 --> 00:22:23,010
+بيصير Orthonormal ماشي طيبأحسب ليها الآن و أقول لك
+
+309
+00:22:23,010 --> 00:22:26,690
+let V2 بيساوي and since ZXJ is linearly
+
+310
+00:22:26,690 --> 00:22:31,550
+independent then V2 لك بيساوي 0 أكيد V2 لك بيساوي
+
+311
+00:22:31,550 --> 00:22:36,690
+0 عارفين ليش لك بيساوي 0عارف ليش اللي لاتساوي سفر؟
+
+312
+00:22:36,690 --> 00:22:40,890
+لأنه لو بتساوي سفر معناته كده اكتب X2 بتساوي E1 في
+
+313
+00:22:40,890 --> 00:22:46,690
+هذا المقدار وE1 X1 على كده إذا صارت X2 مكتوبة X2
+
+314
+00:22:46,690 --> 00:22:49,470
+على صورة linear combination من X1 وهذا
+
+315
+00:22:49,470 --> 00:22:52,210
+contradiction لل linearly independent بين X1 وX2
+
+316
+00:22:52,900 --> 00:22:56,360
+الأن لو فرضنا .. خلّيني أكون واضح بشكل آخر فرضنا
+
+317
+00:22:56,360 --> 00:23:04,540
+إن هذه بتساوي سفر بيصير X2 بتساوي X2 و E1 في E1 Y
+
+318
+00:23:04,540 --> 00:23:10,280
+ساوي X2 و E1 هذا scalar صارت في E1 مين هو ال E1؟
+
+319
+00:23:10,280 --> 00:23:16,960
+اللي هو X1 ع normal X1صارت عندي هذا scalar مضروب
+
+320
+00:23:16,960 --> 00:23:20,700
+في X1 يعني X2 صارت scalar في X1 يعني صارت X2 عبارة
+
+321
+00:23:20,700 --> 00:23:23,940
+Linear Completion من X1 وهذا Contradiction
+
+322
+00:23:23,940 --> 00:23:28,320
+Linearly Independent إذا V2 أكيد لات ساوي سفر
+
+323
+00:23:28,320 --> 00:23:35,020
+احسبلي الآن ال inner product بين V2 و E1 سهلة V2
+
+324
+00:23:35,020 --> 00:23:40,300
+هيها X2 ناقص هذا الوضع و E1 بساوي اللي هو بتتوزع
+
+325
+00:23:40,300 --> 00:23:47,580
+X2 مع مين مع E1ناقص x2 و e1 في e1 و e1 ماشي هذه
+
+326
+00:23:47,580 --> 00:23:52,760
+بيساوي واحد وهذه الان x2 و e1 ناقص x2 و e1 ايش
+
+327
+00:23:52,760 --> 00:23:58,020
+هيساوي؟ هيساوي سفرباضح اه؟ اذا صارت عندى اللى هو
+
+328
+00:23:58,020 --> 00:24:03,240
+اللى هو V2 صارت عبارة عن ما لها اللى هو ال inner
+
+329
+00:24:03,240 --> 00:24:06,460
+product بينها وبين E1 اللى هو بيساوى صفر يعني
+
+330
+00:24:06,460 --> 00:24:09,540
+orthogonal على ال E1 خد الان E2 بيساوى V2 على
+
+331
+00:24:09,540 --> 00:24:13,960
+normal V2 صارت normal E2 بيساوى واحد وفي نفس الوجد
+
+332
+00:24:13,960 --> 00:24:20,300
+صارت ايه شمالها اللى هو orthogonal على ال E1الان
+
+333
+00:24:20,300 --> 00:24:23,880
+بدنا نعمل نفس الجزء الصلميين بدنا نجيب V3 V3 بنفس
+
+334
+00:24:23,880 --> 00:24:28,640
+الأسلوب كيف بجيب V3 V3 بتساوي بشغل ألمين الآن ع X3
+
+335
+00:24:28,640 --> 00:24:34,770
+X3 بشغل فيها مع E1 و E2عشان اضمن عملين ال
+
+336
+00:24:34,770 --> 00:24:37,830
+combination وحيث اضمن انها Orthogonal ال E1 و
+
+337
+00:24:37,830 --> 00:24:40,970
+Orthogonal على مين؟ على ال E2 اللي ياشف ياخدها
+
+338
+00:24:40,970 --> 00:24:47,510
+بسوى X3 ناقص X3 وE1 في E1 ناقص كمان X3 وE2 مع مين؟
+
+339
+00:24:47,510 --> 00:24:50,430
+مع E2 يعني لو كان عندي الآن بعدها الخطوة اللي
+
+340
+00:24:50,430 --> 00:24:56,830
+بعدها لو بدي اجيب V4 هسوى X4 ناقص X4 وE1 في E1
+
+341
+00:24:56,830 --> 00:25:05,340
+ناقص X4 وE2 في E2 ناقص X4 وE3 في E3in general VN
+
+342
+00:25:05,340 --> 00:25:10,840
+هتكون عبارة عن XN ناقص مجموح هذولة من واحد لعند
+
+343
+00:25:10,840 --> 00:25:14,560
+اللي هي N ناقص واحد يعني بتصير XN ناقص summation
+
+344
+00:25:14,560 --> 00:25:16,640
+XN EK EK
+
+345
+00:25:19,420 --> 00:25:23,500
+إذا Vن التكوير اتركبت مجسمها نورمها بكون حصلت على
+
+346
+00:25:23,500 --> 00:25:27,180
+الـ En فبكون حصلت على الـ Orthonormal اللي هو
+
+347
+00:25:27,180 --> 00:25:31,020
+Sequence نيجي لان لتفصيل لت V3 زي ما قلنا ناخدها
+
+348
+00:25:31,020 --> 00:25:35,800
+دي ماشي الحال الان V3 as above V33 سوى 0 لإن لو
+
+349
+00:25:35,800 --> 00:25:40,750
+سوى 0 هتصير X3 عبارة عن لينان combination ب X1و ب
+
+350
+00:25:40,750 --> 00:25:45,090
+X2 وبصير اللي هي بتناقض ال linearly independent
+
+351
+00:25:45,090 --> 00:25:51,750
+ماشي إذا صارت عندي V3 مش لا مش سفر أكيد دائما و V3
+
+352
+00:25:51,750 --> 00:25:55,750
+عمود على ال E1 ليش احسب ال inner product بين V3 و
+
+353
+00:25:55,750 --> 00:26:03,890
+E1 هتصير اللي هو E1 و X3 و E1 و E1 و X3 و E1 و هدي
+
+354
+00:26:03,890 --> 00:26:07,450
+و هدي هيطلع في الآخر اللي هو إيش بيساوي بيساوي سفر
+
+355
+00:26:07,450 --> 00:26:13,700
+نحسبلكم إياهاوالان نفس الاشي V3 هتكون عمودي على E2
+
+356
+00:26:13,700 --> 00:26:17,340
+خد هذه inner product بينها وبين E2 هتلاقي برضه ايش
+
+357
+00:26:17,340 --> 00:26:22,080
+بيساوي بيساوي 0 بناء عليه لو أخدت E3 بيساوي V3 على
+
+358
+00:26:22,080 --> 00:26:27,880
+نورم ال V3 بيصير الان E3 عبارة عن نورمها واحد و
+
+359
+00:26:27,880 --> 00:26:32,020
+Orthogonal على ال E2 و Orthogonal على ال E1 اذا
+
+360
+00:26:32,020 --> 00:26:34,800
+انصار ان التلاتة اللي حتى الان بيرويس اي شمالين
+
+361
+00:26:34,800 --> 00:26:40,720
+Orthogonal in general let VNبساوي Xn ناقص الصماش
+
+362
+00:26:40,720 --> 00:26:46,320
+Xn Ek Ek K من عند واحد بدل له ما هو لاتنين اللي هو
+
+363
+00:26:46,320 --> 00:26:51,780
+n ناقص واحد بيطلع n ناقص واحد هذا هيكون ال Vn اللي
+
+364
+00:26:51,780 --> 00:26:54,120
+هو لا يساوي سفر للسبب نفسه لأنه بيحصل ال
+
+365
+00:26:54,120 --> 00:26:57,580
+combination من اللي جاب الهن وهي linearly
+
+366
+00:26:57,580 --> 00:27:01,380
+independent ده مظبوطش and Vn عمودي عالمين على E1
+
+367
+00:27:01,380 --> 00:27:05,440
+وE2 وE3 وEn وهذا بتقدر تحسبه اللي هو زي ما حسبنا
+
+368
+00:27:05,440 --> 00:27:08,810
+اللي فوقو بتاخد ال E N بيسوي V N ع نورمال V N
+
+369
+00:27:08,810 --> 00:27:13,210
+فبتصير عندك Therefore E K is an orthonormal
+
+370
+00:27:13,210 --> 00:27:17,130
+sequence و بارك الله فيكم و إلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RRPYe2WUwuA_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RRPYe2WUwuA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..7f8703863ca90a4584f4c22589b86fe3ebf69f2f
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RRPYe2WUwuA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3145, "start": 5.11, "end": 31.45, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى آله وصحبه أجمعين المحاضرة رقم عشرين مساق تحليل اقتراني طلاب طالبات الجامعة الإسلامية ماجستير رياضيات وصلنا ل section تلاتة أربعة اللي هو تحت عنوان orthonormal sets and sequences", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 19753, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 6225, 46309, 9957, 47524, 995, 4587, 6055, 5016, 20292, 1211, 1975, 38149, 2288, 7649, 1829, 23032, 15040, 3555, 23032, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 3714, 26108, 14851, 13546, 12602, 1829, 46958, 1829, 9307, 4032, 36520, 8315, 5296, 3541, 6055, 1211, 9307, 3660, 5551, 25513, 27884, 13672, 1829, 31439, 6055, 33753, 18871, 2407, 7649, 420, 11943, 24440, 6352, 293, 22978], "avg_logprob": -0.07018946686128932, "compression_ratio": 1.81640625, "no_speech_prob": 1.7881393432617188e-06, "words": [{"start": 5.11, "end": 5.41, "word": "بسم", "probability": 0.87158203125}, {"start": 5.41, "end": 5.59, "word": " الله", "probability": 0.95703125}, {"start": 5.59, "end": 5.95, "word": " الرحمن", "probability": 0.9612630208333334}, {"start": 5.95, "end": 6.35, "word": " الرحيم", "probability": 0.9957682291666666}, {"start": 6.35, "end": 6.69, "word": " الحمد", "probability": 0.90234375}, {"start": 6.69, "end": 6.99, "word": " لله", "probability": 0.9521484375}, {"start": 6.99, "end": 7.19, "word": " رب", "probability": 0.940185546875}, {"start": 7.19, "end": 7.69, "word": " العالمين", "probability": 0.99267578125}, {"start": 7.69, "end": 8.13, "word": " والصلاة", "probability": 0.898681640625}, {"start": 8.13, "end": 8.57, "word": " والسلام", "probability": 0.9661458333333334}, {"start": 8.57, "end": 8.81, "word": " على", "probability": 0.56787109375}, {"start": 8.81, "end": 9.17, "word": " سيد", "probability": 0.965576171875}, {"start": 9.17, "end": 9.71, "word": " المرسلين", "probability": 0.9802734375}, {"start": 9.71, "end": 10.11, "word": " سيدنا", "probability": 0.94482421875}, {"start": 10.11, "end": 10.47, "word": " محمد", "probability": 0.9833984375}, {"start": 10.47, "end": 10.69, "word": " وعلى", "probability": 0.90673828125}, {"start": 10.69, "end": 10.95, "word": " آله", "probability": 0.959716796875}, {"start": 10.95, "end": 11.45, "word": " وصحبه", "probability": 0.94951171875}, {"start": 11.45, "end": 12.05, "word": " أجمعين", "probability": 0.9697265625}, {"start": 12.05, "end": 14.73, "word": " المحاضرة", "probability": 0.98681640625}, {"start": 14.73, "end": 15.25, "word": " رقم", "probability": 0.97607421875}, {"start": 15.25, "end": 16.05, "word": " عشرين", "probability": 0.9622395833333334}, {"start": 16.05, "end": 17.19, "word": " مساق", "probability": 0.9072265625}, {"start": 17.19, "end": 18.99, "word": " تحليل", "probability": 0.9827880859375}, {"start": 18.99, "end": 19.87, "word": " اقتراني", "probability": 0.944921875}, {"start": 19.87, "end": 20.47, "word": " طلاب", "probability": 0.8362630208333334}, {"start": 20.47, "end": 21.03, "word": " طالبات", "probability": 0.9915771484375}, {"start": 21.03, "end": 21.41, "word": " الجامعة", "probability": 0.9873046875}, {"start": 21.41, "end": 22.07, "word": " الإسلامية", "probability": 0.972412109375}, {"start": 22.07, "end": 22.63, "word": " ماجستير", "probability": 0.93408203125}, {"start": 22.63, "end": 23.33, "word": " رياضيات", "probability": 0.9765625}, {"start": 23.33, "end": 24.93, "word": " وصلنا", "probability": 0.8141276041666666}, {"start": 24.93, "end": 25.07, "word": " ل", "probability": 0.9052734375}, {"start": 25.07, "end": 25.35, "word": " section", "probability": 0.67724609375}, {"start": 25.35, "end": 26.69, "word": " تلاتة", "probability": 0.9371337890625}, {"start": 26.69, "end": 27.17, "word": " أربعة", "probability": 0.8846028645833334}, {"start": 27.17, "end": 27.75, "word": " اللي", "probability": 0.90087890625}, {"start": 27.75, "end": 27.95, "word": " هو", "probability": 0.9150390625}, {"start": 27.95, "end": 28.21, "word": " تحت", "probability": 0.99609375}, {"start": 28.21, "end": 28.69, "word": " عنوان", "probability": 0.9816080729166666}, {"start": 28.69, "end": 29.75, "word": " orthonormal", "probability": 0.7521158854166666}, {"start": 29.75, "end": 30.35, "word": " sets", "probability": 0.94140625}, {"start": 30.35, "end": 30.77, "word": " and", "probability": 0.9521484375}, {"start": 30.77, "end": 31.45, "word": " sequences", "probability": 0.95458984375}], "temperature": 1.0}, {"id": 2, "seek": 5943, "start": 32.91, "end": 59.43, "text": "عرفنا المرة الماضية شو معناة orthogonal sets أو اللي هو تكون شو معناة element orthogonal على اللي هو مجموعة أو مجموعة على مجموعة كيف يكونوا orthogonal متعامدتين اليوم بنحكي عن مفهوم إيش معناة ال set نفسها تكون orthogonal أو ال set نفسها تكون orthonormal باختصار ال set بتكون orthogonal إذا كان اللي هو كل عناصرها pairwise are orthogonal", "tokens": [3615, 28480, 8315, 9673, 25720, 9673, 46958, 10632, 13412, 2407, 20449, 8315, 3660, 41488, 6352, 34051, 13672, 1829, 31439, 6055, 30544, 13412, 2407, 20449, 8315, 3660, 4478, 41488, 15844, 13672, 1829, 31439, 3714, 7435, 2304, 2407, 27884, 34051, 3714, 7435, 2304, 2407, 27884, 15844, 3714, 7435, 2304, 2407, 27884, 9122, 33911, 7251, 30544, 14407, 41488, 44650, 3615, 10943, 3215, 2655, 9957, 45595, 20498, 44945, 5016, 4117, 1829, 18871, 3714, 5172, 3224, 20498, 11933, 1829, 8592, 20449, 8315, 3660, 2423, 992, 8717, 36178, 11296, 6055, 30544, 41488, 34051, 2423, 992, 8717, 36178, 11296, 6055, 30544, 420, 11943, 24440, 4724, 47283, 2655, 9381, 9640, 2423, 992, 39894, 30544, 41488, 11933, 15730, 25961, 13672, 1829, 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49.13, "end": 49.57, "word": " نفسها", "probability": 0.984375}, {"start": 49.57, "end": 49.83, "word": " تكون", "probability": 0.990966796875}, {"start": 49.83, "end": 50.33, "word": " orthogonal", "probability": 0.85009765625}, {"start": 50.33, "end": 51.19, "word": " أو", "probability": 0.94189453125}, {"start": 51.19, "end": 51.35, "word": " ال", "probability": 0.93603515625}, {"start": 51.35, "end": 51.55, "word": " set", "probability": 0.9775390625}, {"start": 51.55, "end": 51.99, "word": " نفسها", "probability": 0.9744466145833334}, {"start": 51.99, "end": 52.39, "word": " تكون", "probability": 0.98583984375}, {"start": 52.39, "end": 53.03, "word": " orthonormal", "probability": 0.8971354166666666}, {"start": 53.03, "end": 53.87, "word": " باختصار", "probability": 0.966796875}, {"start": 53.87, "end": 54.51, "word": " ال", "probability": 0.97119140625}, {"start": 54.51, "end": 54.75, "word": " set", "probability": 0.986328125}, {"start": 54.75, "end": 55.11, "word": " بتكون", "probability": 0.9697265625}, {"start": 55.11, "end": 55.73, "word": " orthogonal", "probability": 0.9375}, {"start": 55.73, "end": 56.27, "word": " إذا", "probability": 0.975341796875}, {"start": 56.27, "end": 56.65, "word": " كان", "probability": 0.9892578125}, {"start": 56.65, "end": 57.23, "word": " اللي", "probability": 0.894287109375}, {"start": 57.23, "end": 57.39, "word": " هو", "probability": 0.94921875}, {"start": 57.39, "end": 57.65, "word": " كل", "probability": 0.96875}, {"start": 57.65, "end": 58.27, "word": " عناصرها", "probability": 0.9427490234375}, {"start": 58.27, "end": 58.83, "word": " pairwise", "probability": 0.864501953125}, {"start": 58.83, "end": 59.01, "word": " are", "probability": 0.84912109375}, {"start": 59.01, "end": 59.43, "word": " orthogonal", "probability": 0.9169921875}], "temperature": 1.0}, {"id": 3, "seek": 8691, "start": 60.11, "end": 86.91, "text": "و Orthonormal بتكون اللي هو pairwise Orthogonal بالإضافة إنه norm كل واحد بيساوي واحد فبنسميه Orthonormal set هاي باختصار اللي هو المعنى لل Orthogonal والOrthonormal ك sets الآن نيجي لل definition اللي قلته قبل شوية أن Orthogonal set M in an inner product space X الcell is a subset M of X whose elements are pairwise Orthogonal يعني كل تنتين مع بعض إشماليا متعمدين", "tokens": [2407, 1610, 11943, 24440, 39894, 30544, 13672, 1829, 31439, 6119, 3711, 27554, 664, 21523, 20666, 28814, 11242, 31845, 3660, 36145, 3224, 2026, 28242, 36764, 24401, 4724, 1829, 3794, 995, 45865, 36764, 24401, 6156, 3555, 1863, 38251, 1829, 3224, 1610, 11943, 24440, 992, 8032, 47302, 4724, 47283, 2655, 9381, 9640, 13672, 1829, 31439, 9673, 3615, 1863, 7578, 24976, 27554, 664, 21523, 16070, 21520, 11943, 24440, 9122, 6352, 6024, 48506, 8717, 1829, 7435, 1829, 24976, 7123, 13672, 1829, 12174, 1211, 47395, 12174, 36150, 13412, 2407, 10632, 14739, 27554, 664, 21523, 992, 376, 294, 364, 7284, 1674, 1901, 1783, 2423, 4164, 307, 257, 25993, 376, 295, 1783, 6104, 4959, 366, 6119, 3711, 27554, 664, 21523, 37495, 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"probability": 0.7177734375}, {"start": 80.43, "end": 80.63, "word": " a", "probability": 0.9580078125}, {"start": 80.63, "end": 81.03, "word": " subset", "probability": 0.95556640625}, {"start": 81.03, "end": 81.41, "word": " M", "probability": 0.9609375}, {"start": 81.41, "end": 81.65, "word": " of", "probability": 0.951171875}, {"start": 81.65, "end": 81.99, "word": " X", "probability": 0.99609375}, {"start": 81.99, "end": 82.59, "word": " whose", "probability": 0.60595703125}, {"start": 82.59, "end": 83.09, "word": " elements", "probability": 0.88818359375}, {"start": 83.09, "end": 83.41, "word": " are", "probability": 0.955078125}, {"start": 83.41, "end": 84.23, "word": " pairwise", "probability": 0.9228515625}, {"start": 84.23, "end": 84.73, "word": " Orthogonal", "probability": 0.9412434895833334}, {"start": 84.73, "end": 84.97, "word": " يعني", "probability": 0.947998046875}, {"start": 84.97, "end": 85.15, "word": " كل", "probability": 0.86474609375}, {"start": 85.15, "end": 85.47, "word": " تنتين", "probability": 0.7823893229166666}, {"start": 85.47, "end": 85.61, "word": " مع", "probability": 0.990234375}, {"start": 85.61, "end": 85.89, "word": " بعض", "probability": 0.990234375}, {"start": 85.89, "end": 86.29, "word": " إشماليا", "probability": 0.6998046875}, {"start": 86.29, "end": 86.91, "word": " متعمدين", "probability": 0.8980712890625}], "temperature": 1.0}, {"id": 4, "seek": 9297, "start": 87.27, "end": 92.97, "text": "An orthonormal subset of M of X is an orthogonal set", "tokens": [7828, 420, 11943, 24440, 25993, 295, 376, 295, 1783, 307, 364, 41488, 992], "avg_logprob": -0.3158482015132904, "compression_ratio": 1.04, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 87.27, "end": 87.57, "word": "An", "probability": 0.12744140625}, {"start": 87.57, "end": 88.47, "word": " orthonormal", "probability": 0.8297526041666666}, {"start": 88.47, "end": 89.15, "word": " subset", "probability": 0.94873046875}, {"start": 89.15, "end": 89.57, 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"probability": 0.5390625}, {"start": 1337.41, "end": 1337.63, "word": " بعدين", "probability": 0.881591796875}, {"start": 1337.63, "end": 1337.99, "word": " أقسمها", "probability": 0.8709716796875}, {"start": 1337.99, "end": 1338.21, "word": " بيصير", "probability": 0.8948974609375}, {"start": 1338.21, "end": 1338.83, "word": " Orthonormal", "probability": 0.7433268229166666}, {"start": 1338.83, "end": 1339.65, "word": " ماشي", "probability": 0.88037109375}, {"start": 1339.65, "end": 1339.99, "word": " طيب", "probability": 0.8655598958333334}], "temperature": 1.0}, {"id": 58, "seek": 135387, "start": 1341.39, "end": 1353.87, "text": "أحسب ليها الآن و أقول لك let V2 بيساوي and since ZXJ is linearly independent then V2 لك بيساوي 0 أكيد V2 لك بيساوي 0 عارفين ليش لك بيساوي 0", "tokens": [10721, 5016, 35457, 32239, 11296, 6024, 48506, 4032, 5551, 39648, 5296, 4117, 718, 691, 17, 4724, 1829, 3794, 995, 45865, 293, 1670, 1176, 55, 41, 307, 43586, 6695, 550, 691, 17, 5296, 4117, 4724, 1829, 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"probability": 0.9892578125}, {"start": 1624.52, "end": 1625.0, "word": " زي", "probability": 0.98095703125}, {"start": 1625.0, "end": 1625.08, "word": " ما", "probability": 0.9814453125}, {"start": 1625.08, "end": 1625.44, "word": " حسبنا", "probability": 0.9845377604166666}, {"start": 1625.44, "end": 1625.58, "word": " اللي", "probability": 0.9560546875}, {"start": 1625.58, "end": 1625.84, "word": " فوق", "probability": 0.91455078125}], "temperature": 1.0}, {"id": 71, "seek": 163713, "start": 1626.17, "end": 1637.13, "text": "و بتاخد ال E N بيسوي V N ع نورمال V N فبتصير عندك Therefore E K is an orthonormal sequence و بارك الله فيكم و إلى لقاء آخر", "tokens": [2407, 39894, 47283, 3215, 2423, 462, 426, 4724, 1829, 3794, 45865, 691, 426, 6225, 8717, 13063, 2304, 6027, 691, 426, 6156, 3555, 2655, 9381, 13546, 43242, 4117, 7504, 462, 591, 307, 364, 420, 11943, 24440, 8310, 4032, 4724, 9640, 4117, 21984, 8978, 24793, 4032, 30731, 5296, 4587, 16606, 19753, 34740], "avg_logprob": 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0.96533203125}, {"start": 1628.61, "end": 1628.81, "word": " N", "probability": 0.84326171875}, {"start": 1628.81, "end": 1629.41, "word": " فبتصير", "probability": 0.85693359375}, {"start": 1629.41, "end": 1629.77, "word": " عندك", "probability": 0.994384765625}, {"start": 1629.77, "end": 1630.31, "word": " Therefore", "probability": 0.45263671875}, {"start": 1630.31, "end": 1630.75, "word": " E", "probability": 0.72607421875}, {"start": 1630.75, "end": 1630.99, "word": " K", "probability": 0.87451171875}, {"start": 1630.99, "end": 1631.25, "word": " is", "probability": 0.85546875}, {"start": 1631.25, "end": 1631.57, "word": " an", "probability": 0.81103515625}, {"start": 1631.57, "end": 1633.21, "word": " orthonormal", "probability": 0.80078125}, {"start": 1633.21, "end": 1634.17, "word": " sequence", "probability": 0.97119140625}, {"start": 1634.17, "end": 1635.01, "word": " و", "probability": 0.64501953125}, {"start": 1635.01, "end": 1635.63, "word": " بارك", "probability": 0.8590494791666666}, {"start": 1635.63, "end": 1635.73, "word": " الله", "probability": 0.94287109375}, {"start": 1635.73, "end": 1636.09, "word": " فيكم", "probability": 0.957763671875}, {"start": 1636.09, "end": 1636.23, "word": " و", "probability": 0.93359375}, {"start": 1636.23, "end": 1636.39, "word": " إلى", "probability": 0.83984375}, {"start": 1636.39, "end": 1636.77, "word": " لقاء", "probability": 0.7457682291666666}, {"start": 1636.77, "end": 1637.13, "word": " آخر", "probability": 0.84912109375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1637.239, "duration_after_vad": 1601.9412499999992}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RRPYe2WUwuA_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RRPYe2WUwuA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fcbda8c259287e5f38e698b9022aa7dd2dfe71bc
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RRPYe2WUwuA_raw.srt
@@ -0,0 +1,1480 @@
+1
+00:00:05,110 --> 00:00:07,690
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,690 --> 00:00:10,690
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,690 --> 00:00:18,990
+آله وصحبه أجمعين المحاضرة رقم عشرين مساق تحليل
+
+4
+00:00:18,990 --> 00:00:22,630
+اقتراني طلاب طالبات الجامعة الإسلامية ماجستير
+
+5
+00:00:22,630 --> 00:00:28,210
+رياضيات وصلنا ل section تلاتة أربعة اللي هو تحت
+
+6
+00:00:28,210 --> 00:00:34,050
+عنوان orthonormal sets and sequencesعرفنا المرة
+
+7
+00:00:34,050 --> 00:00:38,230
+الماضية شو معناة orthogonal sets أو اللي هو تكون
+
+8
+00:00:38,230 --> 00:00:42,430
+شو معناة element orthogonal على اللي هو مجموعة أو
+
+9
+00:00:42,430 --> 00:00:45,730
+مجموعة على مجموعة كيف يكونوا orthogonal متعامدتين
+
+10
+00:00:45,730 --> 00:00:49,830
+اليوم بنحكي عن مفهوم إيش معناة ال set نفسها تكون
+
+11
+00:00:49,830 --> 00:00:53,030
+orthogonal أو ال set نفسها تكون orthonormal
+
+12
+00:00:53,030 --> 00:00:57,650
+باختصار ال set بتكون orthogonal إذا كان اللي هو كل
+
+13
+00:00:57,650 --> 00:01:01,710
+عناصرها pairwise are orthogonalو Orthonormal بتكون
+
+14
+00:01:01,710 --> 00:01:05,250
+اللي هو pairwise Orthogonal بالإضافة إنه norm كل
+
+15
+00:01:05,250 --> 00:01:07,650
+واحد بيساوي واحد فبنسميه Orthonormal set هاي
+
+16
+00:01:07,650 --> 00:01:11,790
+باختصار اللي هو المعنى لل Orthogonal
+
+17
+00:01:11,790 --> 00:01:15,830
+والOrthonormal ك sets الآن نيجي لل definition اللي
+
+18
+00:01:15,830 --> 00:01:18,450
+قلته قبل شوية أن Orthogonal set M in an inner
+
+19
+00:01:18,450 --> 00:01:22,590
+product space X الcell is a subset M of X whose
+
+20
+00:01:22,590 --> 00:01:25,610
+elements are pairwise Orthogonal يعني كل تنتين مع
+
+21
+00:01:25,610 --> 00:01:30,450
+بعض إشماليا متعمدينAn orthonormal subset of M of X
+
+22
+00:01:30,450 --> 00:01:32,970
+is an orthogonal set
+
+23
+00:01:35,660 --> 00:01:39,700
+وفي نفس الوقت whose elements have norm one يعني كل
+
+24
+00:01:39,700 --> 00:01:42,480
+واحد من ال elements أشماله normه بسوء واحد أو
+
+25
+00:01:42,480 --> 00:01:46,240
+بمعنى أخر ملخص الحديث لل orthonormal منقول أن ال
+
+26
+00:01:46,240 --> 00:01:49,340
+orthonormal إذا كان لكل x و y element عند ال inner
+
+27
+00:01:49,340 --> 00:01:52,940
+product بين ال x و ال y يا بساوي سفر يا واحد سفر
+
+28
+00:01:52,940 --> 00:01:55,980
+إذا كانت x لا تساوي y واحد إذا كانت x أشمالها
+
+29
+00:01:55,980 --> 00:02:01,500
+بتسويش y ماشي الحالة بتساوياتلع لفوق الآن بعض
+
+30
+00:02:01,500 --> 00:02:05,820
+الملاحظات على هذا الكلام if an orthogonal or
+
+31
+00:02:05,820 --> 00:02:10,300
+orthonormal system is countable إذا كانت countable
+
+32
+00:02:10,300 --> 00:02:14,660
+بنقدر نعملها يعني أشملها ك sequence اللي هو we can
+
+33
+00:02:14,660 --> 00:02:17,920
+arrange it in a sequence countable يعني اللي هو
+
+34
+00:02:17,920 --> 00:02:21,400
+بيكون كلها ال هي one to one on to مع ال natural
+
+35
+00:02:21,400 --> 00:02:26,120
+numberاللي هي arrange it in a sequence Xn and call
+
+36
+00:02:26,120 --> 00:02:30,420
+it an orthogonal or an orthonormal sequence حسب
+
+37
+00:02:30,420 --> 00:02:34,320
+إيش هي في الاصل ماشي الحال اللي هان a family X
+
+38
+00:02:34,320 --> 00:02:36,860
+Alpha Alpha element in I is called an orthogonal
+
+39
+00:02:36,860 --> 00:02:40,680
+إذا كانت X Alpha orthogonal to X Beta for all
+
+40
+00:02:40,680 --> 00:02:43,980
+Alpha و Beta element in main in I and Alpha less
+
+41
+00:02:43,980 --> 00:02:46,240
+than أو Beta يعني بتكون هذه يعني لو كانت
+
+42
+00:02:46,240 --> 00:02:49,930
+uncountable اللي هي العدد العناصر X Alphaعداد هنا
+
+43
+00:02:49,930 --> 00:02:52,530
+uncountable الـ 6 ونقدر نكتبها على صورة اللي هو
+
+44
+00:02:52,530 --> 00:02:55,150
+family X α حيث و Alpha element in I مش sequence ده
+
+45
+00:02:55,150 --> 00:02:58,450
+اللي هي family of elements the family is
+
+46
+00:02:58,450 --> 00:03:02,630
+orthonormal if it is orthogonal and X α have norm
+
+47
+00:03:02,630 --> 00:03:05,890
+إيش بيساوي واحد so that for all Alpha و Beta
+
+48
+00:03:05,890 --> 00:03:08,090
+element in I ال inner product بين X و Alpha و Beta
+
+49
+00:03:08,090 --> 00:03:11,010
+بيساوي ياسفر يواحد حتى سبق الألفة اللي بتساوي Beta
+
+50
+00:03:11,010 --> 00:03:13,970
+أو الألفة بتساوي Beta نفس كالحديث اللي فوق اطلع
+
+51
+00:03:13,970 --> 00:03:18,540
+لفوقالرمارك الأولى اللى هو تعنيم لـ Pythagoras
+
+52
+00:03:18,540 --> 00:03:24,180
+نظرية Pythagoras اللى هو المربع المنشئ على الواطر
+
+53
+00:03:24,180 --> 00:03:26,680
+بيساوي جميع المربعين المنشئين على الضلعين الآخرين
+
+54
+00:03:26,680 --> 00:03:30,140
+الان for unorthogonal elements اللى بيكونوا
+
+55
+00:03:30,140 --> 00:03:33,960
+متعامدين ال X و ال Y متعامدين نحن لدينا norm X زي
+
+56
+00:03:33,960 --> 00:03:38,260
+Y كل تربيع بيساوي norm X تربيع زي norm Y تربيع
+
+57
+00:03:38,260 --> 00:03:42,240
+الان و هذا أثبتوا سهل norm X زي Y مدام orthogonal
+
+58
+00:03:44,130 --> 00:03:46,610
+بيصير نورم الـ x زائد y لكل تربيع بيساوي ال inner
+
+59
+00:03:46,610 --> 00:03:51,270
+product بين x زائد y و x زائد y و يساوي بنفكها x و
+
+60
+00:03:51,270 --> 00:03:58,130
+x زائد x و y زائد y و x زائد y و y الان مدام
+
+61
+00:03:58,130 --> 00:04:01,270
+ارتجون ان هذوله سفر و هذوله سفر يدن بيساوي اللي هو
+
+62
+00:04:01,270 --> 00:04:06,190
+نورم ال xتربيع زاده normal y تربيع وهذا ما هو
+
+63
+00:04:06,190 --> 00:04:09,110
+بساوية هذا زاد هذا اللي هي المربع المنشئة على
+
+64
+00:04:09,110 --> 00:04:10,550
+الواطر بساوية المجموع المربعين المشئين على
+
+65
+00:04:10,550 --> 00:04:12,890
+الضلاعين الأخرين اللي هي تعميم لها هذا الكلام في
+
+66
+00:04:12,890 --> 00:04:17,430
+أي inner product space in general لو كانت عنده
+
+67
+00:04:17,430 --> 00:04:23,760
+اللي هوX1 زي X2 و X2 و Xn عبارة عن orthogonal set
+
+68
+00:04:23,760 --> 00:04:26,980
+يعني كل اتنين عموديا على بعض هيطلع عند ال inner
+
+69
+00:04:26,980 --> 00:04:30,360
+product بينهم بيساوي اللي هو نورم الواحد الأول
+
+70
+00:04:30,360 --> 00:04:33,260
+تربيع زي نورم الأول .. أسف نورم التربيع بيساوي
+
+71
+00:04:33,260 --> 00:04:35,780
+نورم واحد تربيع زي نورم التاني تربيع زي نورم الان
+
+72
+00:04:35,780 --> 00:04:40,160
+تربيع و نفس الشيء اللي هو عن طريق اللي هي اللي
+
+73
+00:04:40,160 --> 00:04:46,200
+حاقنا قبل و شوية بتقدر تعمله بكل سهولةيعني نورم ال
+
+74
+00:04:46,200 --> 00:04:49,340
+X1
+
+75
+00:04:49,340 --> 00:04:54,900
+بالنفع بال induction برضه نورم X1 زاد X2 زاد Xn
+
+76
+00:04:54,900 --> 00:05:01,600
+لكل ترجيع بساوي اللي هو inner product بين
+
+77
+00:05:01,600 --> 00:05:07,340
+summation XI I من عند 1 لعند N و summation ل XI XJ
+
+78
+00:05:07,340 --> 00:05:13,380
+J من عند 1 لعند N صح ولا لأ؟بظبط هو يساوي اللي هو
+
+79
+00:05:13,380 --> 00:05:17,800
+اللي بوزع اللي هو أول واحد مع هدوله يعني X1 محدد و
+
+80
+00:05:17,800 --> 00:05:23,580
+X2 محدد و X3 محدد و بجمعها فبصير summation XI و
+
+81
+00:05:23,580 --> 00:05:28,580
+summation XJ جي من عند واحد لعند تاني صح I من عند
+
+82
+00:05:28,580 --> 00:05:33,750
+واحدعند N ويساوي الـ N زي ما .. هالـ gate خلص من
+
+83
+00:05:33,750 --> 00:05:38,390
+هذا الـ N للـ fixed I X I و الأولى و X Y و التاني
+
+84
+00:05:38,390 --> 00:05:41,410
+و X Y و التالتة إذاً A برضه summation إذاً بيصير
+
+85
+00:05:41,410 --> 00:05:45,110
+ال summation الأولاني الأصلي I بيساوي واحد عند N و
+
+86
+00:05:45,110 --> 00:05:49,590
+ال summation التاني اللي هو بيصير X I و X I و مين
+
+87
+00:05:49,590 --> 00:05:55,360
+و X J معاياهنا J من عند واحد برضه و لا عند مين لا
+
+88
+00:05:55,360 --> 00:06:02,020
+عند N الان كل هين هيتصفرن مادة ل I ايش بتساوي J
+
+89
+00:06:02,020 --> 00:06:07,360
+فبيصير كل صفار بيظل بس اللي هو ال summation لل XI
+
+90
+00:06:07,360 --> 00:06:11,540
+و XI يعني الاتنين ايش لما I تساوي J و I من عند
+
+91
+00:06:11,540 --> 00:06:15,000
+واحد لا عند مين لا انه هذا بيساوي ال summation ل
+
+92
+00:06:15,000 --> 00:06:20,970
+norm XI تربيع I من عند واحد لا عند N اللي هوالـ X
+
+93
+00:06:20,970 --> 00:06:26,590
+واحد تربيع زائد آخر واحد نور من الـ X and الكل
+
+94
+00:06:26,590 --> 00:06:32,290
+تربيع وصير هذا واضح؟ خلاص مابتحتاجش ال induction
+
+95
+00:06:32,290 --> 00:06:39,170
+إذا لكن بنفع بال induction طيب إجبال حلم ان
+
+96
+00:06:39,170 --> 00:06:43,010
+orthonormal set is linearly independent مهمة ده
+
+97
+00:06:43,010 --> 00:06:47,130
+الكلام تبقوا معايا an orthonormal set is linearly
+
+98
+00:06:47,130 --> 00:06:54,000
+independent يعني خد الآناللي هو I ألف واحد X واحد
+
+99
+00:06:54,000 --> 00:07:00,200
+زايد ألف ان X ان بيساوي سفر وقصل منه أنه ألف واحد
+
+100
+00:07:00,200 --> 00:07:04,180
+بيساوي ألف اتنين بيساوي ألف ان إيش بيساوي سفر الآن
+
+101
+00:07:04,180 --> 00:07:15,090
+بقول الآن خد اللي هو M orthonormal setوبدأ أثبت لك
+
+102
+00:07:15,090 --> 00:07:19,050
+أن الـ M اللي هو إيش مالها is linearly independent
+
+103
+00:07:19,050 --> 00:07:25,590
+6 كيف بأثبت linearly independent بأخد أي X1 و X2
+
+104
+00:07:25,590 --> 00:07:29,970
+عند Xn element مين element نهر، arbitrary finite و
+
+105
+00:07:29,970 --> 00:07:37,230
+باخد Alpha 1 X1 زائد Alpha N Xn و بسوي بإيش؟
+
+106
+00:07:37,230 --> 00:07:41,070
+بالصفر، ماشي الحال؟ لأن حسبولي الآن ال inner
+
+107
+00:07:41,070 --> 00:07:49,210
+product بيناللي هو for N في XI ألف واحد X واحد
+
+108
+00:07:49,210 --> 00:07:58,250
+زائد Alpha N XN وخده مع XN وحسبوا ان ال product
+
+109
+00:07:58,250 --> 00:08:03,230
+بينهم برضه هيسوي أيش؟ هيسوي سفر الآن هذا كله
+
+110
+00:08:03,230 --> 00:08:08,870
+هيتصفر كله هيتصفر مظبوط هذه مع هذه سفرها هذه مع
+
+111
+00:08:08,870 --> 00:08:12,730
+هذه سفرها هذه XN لخط الأخيرة بسمفهدكم تاخدوا
+
+112
+00:08:12,730 --> 00:08:15,470
+الأولى بنفهد و بعدين تقولوا الباقي الذين يعرفوا I
+
+113
+00:08:15,470 --> 00:08:19,470
+fixed till بنفهد يعني for unfixed I فبصير عندى
+
+114
+00:08:19,470 --> 00:08:28,350
+بصير Alpha واحد و X واحد و X واحد و الباقي كله إيش
+
+115
+00:08:28,350 --> 00:08:36,550
+أسفل بصير هذا إيش بيساوي Alpha واحد في X واحد و X
+
+116
+00:08:36,550 --> 00:08:42,270
+واحدهذا طبعا اللي هو بصير عندي ألف و واحد ايش
+
+117
+00:08:42,270 --> 00:08:46,470
+بساوي؟ بساوي صفر لإنه normal ايش بتساوي واحد؟
+
+118
+00:08:46,470 --> 00:08:52,470
+normal ألف واحد صفر similarly for لبعض نطلع عن كل
+
+119
+00:08:52,470 --> 00:08:57,250
+صفر بتاعة ترتب البرهان لإنه لفته ضريدة خد for any
+
+120
+00:08:57,250 --> 00:09:03,110
+fixed i و اشتغل عليها احسنها اطلع من فوق examples
+
+121
+00:09:03,110 --> 00:09:08,900
+Euclidean space are unفي القرآن The standard basis
+
+122
+00:09:08,900 --> 00:09:13,040
+of RN forms an orthonormal set ال standard basis
+
+123
+00:09:13,040 --> 00:09:15,940
+عارفين احنا ال inner product على ال RN ال inner
+
+124
+00:09:15,940 --> 00:09:19,200
+product عارفينه احنا لو جينا اخدنا من ال R تكعيب
+
+125
+00:09:19,200 --> 00:09:28,640
+مين ال standard basis له 1000 1 0 0 0 1 لو أخدت أي
+
+126
+00:09:28,640 --> 00:09:31,880
+inner product بين التليهيل اللي هو مختلفين سفر و
+
+127
+00:09:31,880 --> 00:09:34,860
+inner product بين العنصر نفسه إيش بيساوي بيساوي
+
+128
+00:09:34,860 --> 00:09:37,020
+واحد بناء على اللي هو inner product تبعنا في
+
+129
+00:09:37,020 --> 00:09:40,540
+الارتقال في الار أنجينال فبطلع عنده عبارة عن
+
+130
+00:09:40,540 --> 00:09:46,330
+orthonormal setماضح اه مثال اخر نفس الاشي ما هو
+
+131
+00:09:46,330 --> 00:09:49,330
+احنا عرفنا ال inner product بين هنا دولة ال E n
+
+132
+00:09:49,330 --> 00:09:52,190
+اللي هو بساوة ال summation لا ال inner product في
+
+133
+00:09:52,190 --> 00:09:55,410
+ال L تربيع بساوة ال summation لل alpha I في ال
+
+134
+00:09:55,410 --> 00:09:59,530
+beta I conjugate الكل اللي هو أص نص ماشي هي ليها
+
+135
+00:09:59,530 --> 00:10:03,990
+productالان اعمل لو جيت على the shoulder bases
+
+136
+00:10:03,990 --> 00:10:07,330
+بالذات اللي هو the shoulder bases EN of التربيع
+
+137
+00:10:07,330 --> 00:10:11,270
+هيطلع لي forms and orthonormal sequence in التربيع
+
+138
+00:10:11,270 --> 00:10:14,050
+بالظبط زي اللي عملته هنا ماشي الحال اللي بعده
+
+139
+00:10:16,250 --> 00:10:19,870
+continuous functions احنا let x be the inner
+
+140
+00:10:19,870 --> 00:10:22,530
+product space of all continuous real valued
+
+141
+00:10:22,530 --> 00:10:26,950
+functions 0 و2π ال inner product اللي عرفناها مش
+
+142
+00:10:26,950 --> 00:10:29,350
+هو طبعا ال norm مش ال maximum الم maximum ماطلعش
+
+143
+00:10:29,350 --> 00:10:32,470
+inner product ال inner product اللي عند x و y
+
+144
+00:10:32,470 --> 00:10:36,550
+بسهولة integration x of t y of t dt من 0 ل2π لو
+
+145
+00:10:36,550 --> 00:10:40,600
+كانت real لو كان complex بتحطوله conjugateماشي
+
+146
+00:10:40,600 --> 00:10:45,900
+الحال الان هي ال inner product بقولك الان مثال
+
+147
+00:10:45,900 --> 00:10:49,760
+يعني بيعطيك مثال على orthogonal sets cosine ال N T
+
+148
+00:10:49,760 --> 00:10:53,020
+يعني cosine ال T cosine ال 2T cosine ال 3T cosine
+
+149
+00:10:53,020 --> 00:10:58,300
+ال 4T cosine ال 5T الاخره و اللي هي و cosine ال
+
+150
+00:10:58,300 --> 00:11:04,060
+zero اللي هو ال N element in N cosine ال N T مثال
+
+151
+00:11:04,060 --> 00:11:07,780
+تاني sine ال T sine ال 2T الاخره و cosine ال zero
+
+152
+00:11:08,310 --> 00:11:14,630
+بعملين orthogonal sequences
+
+153
+00:11:14,630 --> 00:11:22,090
+بس إستثنى اللي هو الـ zero من هنا بتطلعلك اللي هي
+
+154
+00:11:22,090 --> 00:11:27,390
+واحد على جدر اتنين باي cos T على جدر الـ باي هذا
+
+155
+00:11:27,390 --> 00:11:32,130
+هتطلعلك orthonormal setجسمها Anormة هو في الواقع
+
+156
+00:11:32,130 --> 00:11:37,410
+عشان تطلع واحد وهنا sin الانتي على جدر ال by اللي
+
+157
+00:11:37,410 --> 00:11:41,550
+هو برضه هتطلع إيش معلها orthonormal sequence و هذه
+
+158
+00:11:41,550 --> 00:11:44,250
+orthonormal sequence اثبت ليها ان هدولة مش صعبة كل
+
+159
+00:11:44,250 --> 00:11:47,350
+الحسابات من وين من هذه integration تبع اللي هو sin
+
+160
+00:11:47,350 --> 00:11:52,190
+و cos اطلع لكمالان هدولة مثلا امثلة على
+
+161
+00:11:52,190 --> 00:11:56,170
+orthonormal sequences الان اطلع لفوق في حاجة اسمها
+
+162
+00:11:56,170 --> 00:11:59,130
+Bessels Inquality اللي هو الـBessels Inquality
+
+163
+00:11:59,130 --> 00:12:04,730
+اللي هي التالي لو كانت EN بيه orthonormal sequence
+
+164
+00:12:04,730 --> 00:12:07,970
+EN orthonormal sequence ماحدش جالب واحد وزير وزير
+
+165
+00:12:07,970 --> 00:12:12,870
+وزير لأ هد بس رمز هنا ال EN مش معناته واحد وزفر
+
+166
+00:12:12,870 --> 00:12:17,590
+وزفر لأ ه delete EN be an orthonormal sequence in
+
+167
+00:12:17,590 --> 00:12:21,610
+an inner product spacethen for every x element in
+
+168
+00:12:21,610 --> 00:12:24,810
+X الـ summation للـ absolute value هذا التربيع من
+
+169
+00:12:24,810 --> 00:12:30,410
+واحدة infinity أصحى شوميين normal X تربيعيعني و
+
+170
+00:12:30,410 --> 00:12:34,790
+كأنه بيقوللي هنا أنه هذه ال series دايما converges
+
+171
+00:12:34,790 --> 00:12:39,730
+ال series لما تحسب اللي هو ال inner product بين ال
+
+172
+00:12:39,730 --> 00:12:45,890
+X و ال orthonormal sequence هذه هيطلع دايما اللي
+
+173
+00:12:45,890 --> 00:12:50,250
+هو ال series هذه المحسوبة تكون أشملها convergent
+
+174
+00:12:50,250 --> 00:12:55,630
+series راحظوا ال orthonormal set قلنا عليها
+
+175
+00:12:55,630 --> 00:12:58,130
+linearly independent
+
+176
+00:13:00,360 --> 00:13:05,480
+إذا الشكل اللي في المستقبل هتعملنا إشي نحي ولاحظنا
+
+177
+00:13:05,480 --> 00:13:12,140
+إن ال basis ال standard basis في ال RN و الشودر
+
+178
+00:13:12,140 --> 00:13:17,640
+basis في ال L2 كل هين عبارة عن إيه الشمال هين are
+
+179
+00:13:17,640 --> 00:13:23,780
+orthonormal sets طب الشودر basis في ال LB ال B لتس
+
+180
+00:13:23,780 --> 00:13:25,760
+و اتنين تتوقع يكون orthonormal set
+
+181
+00:13:35,600 --> 00:13:39,580
+ال orthonormal بيعتمد علي إيش؟ أو ال orthogonal
+
+182
+00:13:39,580 --> 00:13:43,540
+بيعتمد علي إيش؟ عرفناه وين؟ عرفناه في ال inner
+
+183
+00:13:43,540 --> 00:13:47,980
+product على أساس ال inner product طب هو ال ال B مش
+
+184
+00:13:47,980 --> 00:13:51,860
+ال LBB لسه و اتنين مش inner productبناءً على هذا
+
+185
+00:13:51,860 --> 00:13:56,000
+التعريف طبعًا مظبوطش لكن فيه دراسات في تعريف اللي
+
+186
+00:13:56,000 --> 00:13:58,880
+هو فيه برخوف orthogonality ومش عارف أيش حتى عن
+
+187
+00:13:58,880 --> 00:14:03,380
+norm dismiss بس طبعًا يعني بشكل آخر يعني في مجالنا
+
+188
+00:14:03,380 --> 00:14:08,360
+احنا مابنحكيش الآن عن اللي هو أي orthogonality هنا
+
+189
+00:14:08,360 --> 00:14:11,880
+دي اجتهادات في ال orthogonality بأكتر من نوع من ال
+
+190
+00:14:11,880 --> 00:14:16,800
+orthogonality وفيها دراسات حديثة كلها طيبلأن يجيل
+
+191
+00:14:16,800 --> 00:14:19,680
+لبس الـ Zinquality let Eₙ be an orthonormal
+
+192
+00:14:19,680 --> 00:14:23,040
+sequence in an inner product space X then for
+
+193
+00:14:23,040 --> 00:14:25,860
+every X limit in X هذي السيريز converts اطلع لفوق
+
+194
+00:14:25,860 --> 00:14:30,960
+من برهن لأن consider the finite subset E₁ E₂ عند
+
+195
+00:14:30,960 --> 00:14:33,520
+Eₙ أن arbitrarily .. arbitrarily يعني بس أنا مابدش
+
+196
+00:14:33,520 --> 00:14:38,390
+أطلع على ال finite و بعدين بمدها زي ما بدنيطيب هذه
+
+197
+00:14:38,390 --> 00:14:40,950
+subset من مين؟ من الـ E عن الـ Orthonormal set
+
+198
+00:14:40,950 --> 00:14:46,230
+احسبلي الآن احسبلي norm ال X ناقص ال summation
+
+199
+00:14:46,230 --> 00:14:51,090
+اللي عندي هذا تربيع ماشي الحال اللي هو استقيته من
+
+200
+00:14:51,090 --> 00:14:54,910
+هنا اه اه ده استقي اشي من هنا عشان اصل ال equality
+
+201
+00:14:54,910 --> 00:15:01,180
+هذه بعد شويةY ساوى X نقص ال summation و X نقص ال
+
+202
+00:15:01,180 --> 00:15:04,560
+summation زي ما عملنا قبل بشوية هذي بيصير X مع ال
+
+203
+00:15:04,560 --> 00:15:08,380
+X و بعدين X مع ال summation و summation مع X و
+
+204
+00:15:08,380 --> 00:15:11,440
+summation مع summation Y ساوى هاي ال X مع ال X
+
+205
+00:15:11,440 --> 00:15:14,780
+بيطلع X ربيع و ال X مع ال summation هيه و هذي ال
+
+206
+00:15:14,780 --> 00:15:17,460
+summation مع ال X و هذي ال summation مع ال
+
+207
+00:15:17,460 --> 00:15:21,240
+summation Y ساوى اللي يعني الأول يعني زي ما هو
+
+208
+00:15:21,240 --> 00:15:26,220
+بنزلالتاني بيصير .. برضه بيتوزح حد ال X مع هدولة
+
+209
+00:15:26,220 --> 00:15:29,240
+بيطلع ال summation ماله برا فبصير ال summation برا
+
+210
+00:15:29,240 --> 00:15:32,420
+لكن بتاخد هذه ايش مالها ب conjugate برا فلأنها
+
+211
+00:15:32,420 --> 00:15:36,180
+بعيدة بتاخد هذه ال conjugate معاها ناجهاد و بيظل
+
+212
+00:15:36,180 --> 00:15:39,580
+اللي جوا منين X و EK فبصير هذه مع هذه هي ال
+
+213
+00:15:39,580 --> 00:15:43,860
+conjugate اللي بعدهاالتانية ناقصة هذا جريم فبطلع
+
+214
+00:15:43,860 --> 00:15:49,260
+برا عادي و بتصير EI و مين و X هذه بتطلع برا و ال
+
+215
+00:15:49,260 --> 00:15:52,520
+summation هي بيصير هذه EI و X زاد هدولة ال
+
+216
+00:15:52,520 --> 00:15:55,700
+summation ال two summations بيطلع عن برا الأول
+
+217
+00:15:55,700 --> 00:15:59,060
+بيطلع عادي و التاني بيطلع ال conjugate لبعيد بيصير
+
+218
+00:15:59,060 --> 00:16:02,440
+ال summation summation الأول عادي هيه و التاني
+
+219
+00:16:02,440 --> 00:16:05,980
+بيضل عايش بال conjugate و بيضل مين في .. عندي EI و
+
+220
+00:16:05,980 --> 00:16:10,980
+مين و EK EI و EKI من عند واحد لعند ان و okay من
+
+221
+00:16:10,980 --> 00:16:15,540
+عند واحد لعند ان اطلع لفوق بيصير عند الان و يساوي
+
+222
+00:16:15,540 --> 00:16:24,110
+هذا بنزل زي ما هو عندى و التانياللي هو هذا هو هذا
+
+223
+00:16:24,110 --> 00:16:29,370
+لأنه هذا لما أشي أخليه X وEI بيصير X وEI أشمال ال
+
+224
+00:16:29,370 --> 00:16:31,990
+conjugate فهذا conjugate و هذا conjugate و المجموع
+
+225
+00:16:31,990 --> 00:16:34,210
+من واحد لعندي N و هذا conjugate و هذا عادي و
+
+226
+00:16:34,210 --> 00:16:36,810
+المجموع من واحد لعندي N يعني واحد conjugate واحد
+
+227
+00:16:36,810 --> 00:16:39,310
+عادي في التنين و من واحد لعندي N إذا المجموح
+
+228
+00:16:39,310 --> 00:16:43,070
+للتنين اتنين يعني التنين نفس الاشي فبصير ناقص
+
+229
+00:16:43,070 --> 00:16:47,400
+اتنين في ال summation هذا هذا و هذا زي بعضزائد ال
+
+230
+00:16:47,400 --> 00:16:50,880
+summation اللي بعده هذا اللي عندي ال summation هذا
+
+231
+00:16:50,880 --> 00:16:57,640
+كله هيتصفر مع ده لما تكون EI EI ايش بتساوي K لإن
+
+232
+00:16:57,640 --> 00:17:03,570
+EI وEI مش orthonormalهيصير EI و EK اللي هو عبارة
+
+233
+00:17:03,570 --> 00:17:07,230
+عن سفر إذا كانت I لات شو K و واحد في حالة المساواة
+
+234
+00:17:07,230 --> 00:17:13,050
+إذا هذا هيصير summation واحد بس وهيصير بس اللي هو
+
+235
+00:17:13,050 --> 00:17:18,870
+summation عندى بيظل X وEI و X وEI conjugate معناته
+
+236
+00:17:18,870 --> 00:17:23,490
+هذا تربيع و هذا هيصير واحد فبيصير عبارة عن معايا
+
+237
+00:17:23,490 --> 00:17:28,550
+نفسي هو normal X تربيحيه و هذا 2X و هذا زائد هذا
+
+238
+00:17:28,550 --> 00:17:33,160
+في هذاو هذيك صار واحد ال EI و E كام فاهمين عليها
+
+239
+00:17:33,160 --> 00:17:37,040
+لأن هذا زي ما هو بنزل و الأن هذا ناقص اتنين و هذا
+
+240
+00:17:37,040 --> 00:17:42,760
+واحد بيصير ناقص واحد منهم مظبوط نورم تربية لإن ما
+
+241
+00:17:42,760 --> 00:17:47,440
+بتضرب هذا في هذا بيصير موضولاس تربية صار هذا
+
+242
+00:17:47,440 --> 00:17:52,220
+المقدار ها يوم أوصلنا بدأنا من Zero و أصغر أو
+
+243
+00:17:52,220 --> 00:17:55,300
+يساوي لما أوصلنا هذا صار هذا المقدار أكبر أو ساوي
+
+244
+00:17:55,300 --> 00:17:58,400
+Zero معناته أنه صار هذا على الجهة الثانية أصغر أو
+
+245
+00:17:58,400 --> 00:18:04,190
+ساوي هذاصارت هذه اللي هي this is inequality لأن
+
+246
+00:18:04,190 --> 00:18:07,610
+هذا في ال finite ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+247
+00:18:07,610 --> 00:18:07,750
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+248
+00:18:07,750 --> 00:18:08,290
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+249
+00:18:08,290 --> 00:18:09,450
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+250
+00:18:09,450 --> 00:18:09,610
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+251
+00:18:09,610 --> 00:18:10,710
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+252
+00:18:10,710 --> 00:18:10,750
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+253
+00:18:10,750 --> 00:18:11,390
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+254
+00:18:11,390 --> 00:18:11,730
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+255
+00:18:11,730 --> 00:18:11,790
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+256
+00:18:11,790 --> 00:18:19,590
+.. ل .. ل .. ل .. ل .. ل ..
+
+257
+00:18:19,590 --> 00:18:20,190
+ل .. ل ..
+
+258
+00:18:28,520 --> 00:18:32,840
+الأن نجي لل inner product X وEK اللي قبله شوية
+
+259
+00:18:32,840 --> 00:18:38,620
+above هذا بيسميه the Fourier coefficients of X
+
+260
+00:18:38,620 --> 00:18:40,280
+لإنه بيطلع في ال Fourier series عنا
+
+261
+00:18:43,650 --> 00:18:48,330
+الشيء الأساسي X,Y,K أعلى هؤلاء هما معاملات تسمى
+
+262
+00:18:48,330 --> 00:18:52,470
+كالخصوصية الواقعية لـ X بالنسبة للتطبيق التطبيقي
+
+263
+00:18:52,470 --> 00:18:59,690
+الـ E,K هذا فيه معناه التطبيقي ليس مجال نحكي فيه
+
+264
+00:18:59,690 --> 00:19:03,890
+إذا كانت المعاملة لـ X فينية، فكل تطبيق التطبيق
+
+265
+00:19:03,890 --> 00:19:08,790
+التطبيقي يجب أن يكون فينيbecause it's linearly
+
+266
+00:19:08,790 --> 00:19:11,670
+independent أكيد إذا كانت ال dimension لل space
+
+267
+00:19:11,670 --> 00:19:15,190
+نفسه اللي بس تشتغل فيه finite مش معقول تكون subset
+
+268
+00:19:15,190 --> 00:19:20,110
+منه infinite ليش مش معقول تكون subset منه اللي هو
+
+269
+00:19:20,110 --> 00:19:22,870
+infinite اللي هي من ال orthonormal لأن ال
+
+270
+00:19:22,870 --> 00:19:27,290
+orthonormal إيه شمالها linearly independent مدام
+
+271
+00:19:27,290 --> 00:19:31,610
+linearly independent إذا ثقفها عدت على أصل ال
+
+272
+00:19:31,610 --> 00:19:34,150
+bases اللي هو ال dimension لأنه لو زادت بتبطل
+
+273
+00:19:34,150 --> 00:19:38,370
+linearly independent فاهمينإذا الأن أكيد مدام
+
+274
+00:19:38,370 --> 00:19:41,130
+الـdimensional X finite هتكون الـorthonormal sets
+
+275
+00:19:41,130 --> 00:19:46,110
+اللي فيها are finite sets الآن بدنا نيجي لجرام
+
+276
+00:19:46,110 --> 00:19:49,570
+شمدة process for orthonormalizing a linearly
+
+277
+00:19:49,570 --> 00:19:53,330
+independent sequence XJ يعني هنا product space X
+
+278
+00:19:53,330 --> 00:19:57,690
+يعني إيش بقوليه بقولي كيف بدي أكون اللي هو
+
+279
+00:19:57,690 --> 00:20:02,490
+orthonormal setOrthonormal Set أو Orthonormal
+
+280
+00:20:02,490 --> 00:20:07,650
+Sequence من اللي هو Set تكون Linear ل Independent
+
+281
+00:20:07,650 --> 00:20:11,250
+هذه ال process اللي هو حد اسمه Gram-Schmidt
+
+282
+00:20:11,250 --> 00:20:16,350
+Process خلينا نشوف الخطوات .. الخطوات سهلة و .. و
+
+283
+00:20:16,350 --> 00:20:20,210
+.. و الكل بيفهمها يعني شغلات سهلة ان شاء الله The
+
+284
+00:20:20,210 --> 00:20:25,710
+first element لان X1 .. X2 .. X3 .. X4 .. إلا ما
+
+285
+00:20:25,710 --> 00:20:31,990
+ننهيها بدي أخد منهم اللي هو 100اللي هو .. ال .. ال
+
+286
+00:20:31,990 --> 00:20:35,410
+.. ال .. من هنا أولد الـ E1 و الـ E2 و الـ E3 و
+
+287
+00:20:35,410 --> 00:20:39,750
+الـ E4 شوف كيف بدي أجيبهم أول خطوة اللي هو طبيعي
+
+288
+00:20:39,750 --> 00:20:44,010
+اللي بدي أخد first element of EK is E1 بسميه هذا
+
+289
+00:20:44,010 --> 00:20:49,470
+الـ EK الـ orthonormal المبتغى اللي بدي أعملها
+
+290
+00:20:49,470 --> 00:20:53,570
+يعني لأن E1 بساوي X1 على normal X1 هذول اللي بين
+
+291
+00:20:53,570 --> 00:20:55,910
+يديها الـ X1 و X2 و X3 اللي مالها يعني they are
+
+292
+00:20:55,910 --> 00:20:59,030
+independent setإذا المدان لينيال independent
+
+293
+00:20:59,030 --> 00:21:03,850
+sequence ده لو لو واحد فيه سفر لو في واحد سفر
+
+294
+00:21:03,850 --> 00:21:07,010
+بتبطي لينيال independentإذا الـ X1 على نورم الـ X1
+
+295
+00:21:07,010 --> 00:21:11,290
+مشروع هذا هيصير نورمه الجديد إيش بساوي بساوي واحد
+
+296
+00:21:11,290 --> 00:21:18,230
+طيب الآن ال second step بتاخد اللي هو عشان أصل لل
+
+297
+00:21:18,230 --> 00:21:22,730
+E2 بتاخد أوليش حاجة اسمها V2 ومنها أصل لل E1 V2
+
+298
+00:21:22,730 --> 00:21:26,070
+بعد شوية حاجة قسمها على نورم وحصل على ال E2 إذا
+
+299
+00:21:26,070 --> 00:21:33,940
+الآن حصلت على ال E1 عبارة عن X1 على نورم ال X1وهذا
+
+300
+00:21:33,940 --> 00:21:41,040
+اكيد normal E1 بساوى اللي هو واحد طيب بدي اجيب E2
+
+301
+00:21:41,040 --> 00:21:46,920
+قبل عشان اجيب E2 E2 و اقولها اجيب حاجة اسمها V2 و
+
+302
+00:21:46,920 --> 00:21:52,040
+اقسمها عالميا على normal V2 طب V2 ايش هو V2 بتاخد
+
+303
+00:21:52,040 --> 00:21:59,330
+اللي هو X2 V2بتاخدها بتساوي ال X2 و أطرح منها ال
+
+304
+00:21:59,330 --> 00:22:05,170
+X2 و ال E1 اللي لجيتها في الأول مضروبة في ميهم؟ في
+
+305
+00:22:05,170 --> 00:22:10,530
+ال E1 عشان أضرب عصفرين بحجر أثبتلك أن هذول ال V2
+
+306
+00:22:10,530 --> 00:22:14,990
+منها هتكون اللي هو ال inner product مع ال E1 اللي
+
+307
+00:22:14,990 --> 00:22:17,990
+فوق 0 يعني هأثبتلك أنه Orthogonal و بعدين أقسمها
+
+308
+00:22:17,990 --> 00:22:23,010
+بيصير Orthonormal ماشي طيبأحسب ليها الآن و أقول لك
+
+309
+00:22:23,010 --> 00:22:26,690
+let V2 بيساوي and since ZXJ is linearly
+
+310
+00:22:26,690 --> 00:22:31,550
+independent then V2 لك بيساوي 0 أكيد V2 لك بيساوي
+
+311
+00:22:31,550 --> 00:22:36,690
+0 عارفين ليش لك بيساوي 0عارف ليش اللي لاتساوي سفر؟
+
+312
+00:22:36,690 --> 00:22:40,890
+لأنه لو بتساوي سفر معناته كده اكتب X2 بتساوي E1 في
+
+313
+00:22:40,890 --> 00:22:46,690
+هذا المقدار وE1 X1 على كده إذا صارت X2 مكتوبة X2
+
+314
+00:22:46,690 --> 00:22:49,470
+على صورة linear combination من X1 وهذا
+
+315
+00:22:49,470 --> 00:22:52,210
+contradiction لل linearly independent بين X1 وX2
+
+316
+00:22:52,900 --> 00:22:56,360
+الأن لو فرضنا .. خلّيني أكون واضح بشكل آخر فرضنا
+
+317
+00:22:56,360 --> 00:23:04,540
+إن هذه بتساوي سفر بيصير X2 بتساوي X2 و E1 في E1 Y
+
+318
+00:23:04,540 --> 00:23:10,280
+ساوي X2 و E1 هذا scalar صارت في E1 مين هو ال E1؟
+
+319
+00:23:10,280 --> 00:23:16,960
+اللي هو X1 ع normal X1صارت عندي هذا scalar مضروب
+
+320
+00:23:16,960 --> 00:23:20,700
+في X1 يعني X2 صارت scalar في X1 يعني صارت X2 عبارة
+
+321
+00:23:20,700 --> 00:23:23,940
+Linear Completion من X1 وهذا Contradiction
+
+322
+00:23:23,940 --> 00:23:28,320
+Linearly Independent إذا V2 أكيد لات ساوي سفر
+
+323
+00:23:28,320 --> 00:23:35,020
+احسبلي الآن ال inner product بين V2 و E1 سهلة V2
+
+324
+00:23:35,020 --> 00:23:40,300
+هيها X2 ناقص هذا الوضع و E1 بساوي اللي هو بتتوزع
+
+325
+00:23:40,300 --> 00:23:47,580
+X2 مع مين مع E1ناقص x2 و e1 في e1 و e1 ماشي هذه
+
+326
+00:23:47,580 --> 00:23:52,760
+بيساوي واحد وهذه الان x2 و e1 ناقص x2 و e1 ايش
+
+327
+00:23:52,760 --> 00:23:58,020
+هيساوي؟ هيساوي سفرباضح اه؟ اذا صارت عندى اللى هو
+
+328
+00:23:58,020 --> 00:24:03,240
+اللى هو V2 صارت عبارة عن ما لها اللى هو ال inner
+
+329
+00:24:03,240 --> 00:24:06,460
+product بينها وبين E1 اللى هو بيساوى صفر يعني
+
+330
+00:24:06,460 --> 00:24:09,540
+orthogonal على ال E1 خد الان E2 بيساوى V2 على
+
+331
+00:24:09,540 --> 00:24:13,960
+normal V2 صارت normal E2 بيساوى واحد وفي نفس الوجد
+
+332
+00:24:13,960 --> 00:24:20,300
+صارت ايه شمالها اللى هو orthogonal على ال E1الان
+
+333
+00:24:20,300 --> 00:24:23,880
+بدنا نعمل نفس الجزء الصلميين بدنا نجيب V3 V3 بنفس
+
+334
+00:24:23,880 --> 00:24:28,640
+الأسلوب كيف بجيب V3 V3 بتساوي بشغل ألمين الآن ع X3
+
+335
+00:24:28,640 --> 00:24:34,770
+X3 بشغل فيها مع E1 و E2عشان اضمن عملين ال
+
+336
+00:24:34,770 --> 00:24:37,830
+combination وحيث اضمن انها Orthogonal ال E1 و
+
+337
+00:24:37,830 --> 00:24:40,970
+Orthogonal على مين؟ على ال E2 اللي ياشف ياخدها
+
+338
+00:24:40,970 --> 00:24:47,510
+بسوى X3 ناقص X3 وE1 في E1 ناقص كمان X3 وE2 مع مين؟
+
+339
+00:24:47,510 --> 00:24:50,430
+مع E2 يعني لو كان عندي الآن بعدها الخطوة اللي
+
+340
+00:24:50,430 --> 00:24:56,830
+بعدها لو بدي اجيب V4 هسوى X4 ناقص X4 وE1 في E1
+
+341
+00:24:56,830 --> 00:25:05,340
+ناقص X4 وE2 في E2 ناقص X4 وE3 في E3in general VN
+
+342
+00:25:05,340 --> 00:25:10,840
+هتكون عبارة عن XN ناقص مجموح هذولة من واحد لعند
+
+343
+00:25:10,840 --> 00:25:14,560
+اللي هي N ناقص واحد يعني بتصير XN ناقص summation
+
+344
+00:25:14,560 --> 00:25:16,640
+XN EK EK
+
+345
+00:25:19,420 --> 00:25:23,500
+إذا Vن التكوير اتركبت مجسمها نورمها بكون حصلت على
+
+346
+00:25:23,500 --> 00:25:27,180
+الـ En فبكون حصلت على الـ Orthonormal اللي هو
+
+347
+00:25:27,180 --> 00:25:31,020
+Sequence نيجي لان لتفصيل لت V3 زي ما قلنا ناخدها
+
+348
+00:25:31,020 --> 00:25:35,800
+دي ماشي الحال الان V3 as above V33 سوى 0 لإن لو
+
+349
+00:25:35,800 --> 00:25:40,750
+سوى 0 هتصير X3 عبارة عن لينان combination ب X1و ب
+
+350
+00:25:40,750 --> 00:25:45,090
+X2 وبصير اللي هي بتناقض ال linearly independent
+
+351
+00:25:45,090 --> 00:25:51,750
+ماشي إذا صارت عندي V3 مش لا مش سفر أكيد دائما و V3
+
+352
+00:25:51,750 --> 00:25:55,750
+عمود على ال E1 ليش احسب ال inner product بين V3 و
+
+353
+00:25:55,750 --> 00:26:03,890
+E1 هتصير اللي هو E1 و X3 و E1 و E1 و X3 و E1 و هدي
+
+354
+00:26:03,890 --> 00:26:07,450
+و هدي هيطلع في الآخر اللي هو إيش بيساوي بيساوي سفر
+
+355
+00:26:07,450 --> 00:26:13,700
+نحسبلكم إياهاوالان نفس الاشي V3 هتكون عمودي على E2
+
+356
+00:26:13,700 --> 00:26:17,340
+خد هذه inner product بينها وبين E2 هتلاقي برضه ايش
+
+357
+00:26:17,340 --> 00:26:22,080
+بيساوي بيساوي 0 بناء عليه لو أخدت E3 بيساوي V3 على
+
+358
+00:26:22,080 --> 00:26:27,880
+نورم ال V3 بيصير الان E3 عبارة عن نورمها واحد و
+
+359
+00:26:27,880 --> 00:26:32,020
+Orthogonal على ال E2 و Orthogonal على ال E1 اذا
+
+360
+00:26:32,020 --> 00:26:34,800
+انصار ان التلاتة اللي حتى الان بيرويس اي شمالين
+
+361
+00:26:34,800 --> 00:26:40,720
+Orthogonal in general let VNبساوي Xn ناقص الصماش
+
+362
+00:26:40,720 --> 00:26:46,320
+Xn Ek Ek K من عند واحد بدل له ما هو لاتنين اللي هو
+
+363
+00:26:46,320 --> 00:26:51,780
+n ناقص واحد بيطلع n ناقص واحد هذا هيكون ال Vn اللي
+
+364
+00:26:51,780 --> 00:26:54,120
+هو لا يساوي سفر للسبب نفسه لأنه بيحصل ال
+
+365
+00:26:54,120 --> 00:26:57,580
+combination من اللي جاب الهن وهي linearly
+
+366
+00:26:57,580 --> 00:27:01,380
+independent ده مظبوطش and Vn عمودي عالمين على E1
+
+367
+00:27:01,380 --> 00:27:05,440
+وE2 وE3 وEn وهذا بتقدر تحسبه اللي هو زي ما حسبنا
+
+368
+00:27:05,440 --> 00:27:08,810
+اللي فوقو بتاخد ال E N بيسوي V N ع نورمال V N
+
+369
+00:27:08,810 --> 00:27:13,210
+فبتصير عندك Therefore E K is an orthonormal
+
+370
+00:27:13,210 --> 00:27:17,130
+sequence و بارك الله فيكم و إلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RstVGUoRP6o_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RstVGUoRP6o_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3838f96b288863812e5c73b1fd42829400eebb32
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RstVGUoRP6o_postprocess.srt
@@ -0,0 +1,2760 @@
+1
+00:00:05,360 --> 00:00:08,000
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,000 --> 00:00:11,400
+والصلاة والسلام علي سيد المرسلين هذه المحاضرة
+
+3
+00:00:11,400 --> 00:00:18,880
+الثانية في مساق تحليل اقتراني او تحليل دالي لطلب
+
+4
+00:00:18,880 --> 00:00:26,620
+طلبات الماجستير الجامعة الإسلامية بغزا حكينا المرة
+
+5
+00:00:26,620 --> 00:00:30,580
+الماضية بدأنا في المحاضرة الأولى حكينا عن ال
+
+6
+00:00:30,580 --> 00:00:34,930
+metric spaceاليوم إن شاء الله هنحكي عن اللي هو
+
+7
+00:00:34,930 --> 00:00:39,550
+examples on metric space وهو 1،2 تحت عنوان further
+
+8
+00:00:39,550 --> 00:00:43,890
+examples on metric space خليني بس عشان نذكركم باشي
+
+9
+00:00:43,890 --> 00:00:46,990
+اللي حكيناه المرة الماضية عشان تكون الأمور يعني
+
+10
+00:00:46,990 --> 00:00:51,770
+مترابطة وفي عندنا اللي هو تواصل بالحديث اللي المرة
+
+11
+00:00:51,770 --> 00:00:55,500
+الماضيةالمرة الماضية مروش سريعة اللي حكيته المرة
+
+12
+00:00:55,500 --> 00:00:58,940
+الماضية قولت انا شو تعريف ال metric space ايش ال
+
+13
+00:00:58,940 --> 00:01:03,500
+metric space بنعرفه بنيجي بناخد 6x و بعدين بنعرف
+
+14
+00:01:03,500 --> 00:01:08,060
+عليه دالة D هذه ال D اللي هي دالة على مين مش على
+
+15
+00:01:08,060 --> 00:01:12,200
+ال X نفسها ال D هذه عبارة دالة على X cross X يعني
+
+16
+00:01:12,200 --> 00:01:18,180
+D هتاخد من X cross X و ترمي بالظبط في R positive
+
+17
+00:01:18,180 --> 00:01:23,260
+اتحاد ال zeroبنقول عن هذه D عبارة عن دالة مسافة أو
+
+18
+00:01:23,260 --> 00:01:27,700
+metric إذا حققت الشروط التالية الشرط الأول أنها
+
+19
+00:01:27,700 --> 00:01:31,380
+تكون non-negative طبيعي المسافة حتى في R أكيد non
+
+20
+00:01:31,380 --> 00:01:35,520
+-negative أصلا مستقامها اتنين DX وY بتساوي سفر إذا
+
+21
+00:01:35,520 --> 00:01:39,660
+فقط إذا X ياش بتساوي Y يعني النقطتين اللي بيكون
+
+22
+00:01:39,660 --> 00:01:44,720
+مسافتهم عن بعض بتساوي سفر هي بس النقطة ياش نفسها
+
+23
+00:01:45,210 --> 00:01:48,470
+الشغل الثالث هو أن المسافة بين X و Y هي نفس
+
+24
+00:01:48,470 --> 00:01:51,490
+المسافة بين Y و X يعني اللي هو الـ Dissimetry
+
+25
+00:01:51,490 --> 00:01:55,290
+الشغل الثالث هو أن هي الـ Triangling Equality D X
+
+26
+00:01:55,290 --> 00:01:59,950
+و Y أصغر يساوي D X و Z زي ادمين D Z و Y فصلنا
+
+27
+00:01:59,950 --> 00:02:04,930
+المرة الماضية عن هذا اللي هو التعريف الآن أخدنا
+
+28
+00:02:04,930 --> 00:02:11,170
+برضه اللي هو أمثلة على هذا اللي هو أخدنا أمثلة على
+
+29
+00:02:11,170 --> 00:02:14,590
+الـ Matrixاللي هو ع ال R ايش ال mythical ع ال R
+
+30
+00:02:14,590 --> 00:02:17,990
+اللي هو absolute value of X minus Y على R تربيع
+
+31
+00:02:17,990 --> 00:02:22,830
+هيه الان و بعدين وقفنا عند حاجة اسمها سمينا ال ال
+
+32
+00:02:22,830 --> 00:02:26,170
+infinity هذه من ال spaces المهمة عندنا ال ال
+
+33
+00:02:26,170 --> 00:02:29,270
+infinity شو ال ال infinity اذكركم فيه اللي حكينا
+
+34
+00:02:29,270 --> 00:02:33,700
+المرة الماضية هي عضارة عن عناصر و sequencesيعني
+
+35
+00:02:33,700 --> 00:02:38,040
+الـ L infinity اللي هو عبارة عن space of sequences
+
+36
+00:02:38,040 --> 00:02:41,680
+طب أي sequences يكون ال sequence bounded يعني the
+
+37
+00:02:41,680 --> 00:02:46,760
+set of all xii مثلا اللي هي sequence of numbers
+
+38
+00:02:46,760 --> 00:02:51,750
+سواء complex number او real number ابحثإنه اللي هو
+
+39
+00:02:51,750 --> 00:02:56,550
+الـ XiI تكون أصغر أو يساوي مين يساوي sub constant
+
+40
+00:02:56,550 --> 00:03:00,510
+C ماشي ال .. ال .. ال .. ال boundary sequences
+
+41
+00:03:00,510 --> 00:03:03,390
+حطيناها في مين في القلة الانفينيتي وبناء عليه
+
+42
+00:03:03,390 --> 00:03:08,570
+عرفنا ال metric عليها عرفنا الدالة كانت الدالة Dxy
+
+43
+00:03:08,570 --> 00:03:14,250
+بتساوي ال supremum لل absolute value XiI نقص Gamma
+
+44
+00:03:14,250 --> 00:03:22,120
+I I over Iمن هي هذه الـ Xi I؟ X بتساوي Xi I وY
+
+45
+00:03:22,120 --> 00:03:25,060
+بتساوي Gamma I هذا كله كان حكيناه المرة الماضية
+
+46
+00:03:25,060 --> 00:03:30,840
+وقلنا هذه هتعملنا metric عالميين ال infinity يعني
+
+47
+00:03:30,840 --> 00:03:33,760
+هتحقق الشروط الأربعة وبالمناسبة زي ما قلنا المرة
+
+48
+00:03:33,760 --> 00:03:38,420
+الماضيةإن شروط الـ metric الأولى هي التلاتة
+
+49
+00:03:38,420 --> 00:03:42,260
+automatic سهلات والكل بعرف إجابة بظل الشرط الأخير
+
+50
+00:03:42,260 --> 00:03:46,080
+هو اللي شوية بده شغل عموما أمثلة المرة الماضية زي
+
+51
+00:03:46,080 --> 00:03:51,720
+ما قلنا كانت أمثلة سهلة ومباشرةوعرفنا برضه اللي هو
+
+52
+00:03:51,720 --> 00:03:54,960
+الـ function space اللي هو الـ space of all
+
+53
+00:03:54,960 --> 00:03:59,640
+continuous functions على closed bounded interval
+
+54
+00:03:59,640 --> 00:04:03,160
+وعرفنا ال metric برضه بنفس الأسلوب المسافة بين أي
+
+55
+00:04:03,160 --> 00:04:08,260
+نقطين دالتين هدولة Vxy موجودة في CAB بسوء ال
+
+56
+00:04:08,260 --> 00:04:13,390
+maximumلأ اللي حصل طرح الدالتين على مين على الفترة
+
+57
+00:04:13,390 --> 00:04:17,390
+اللي بنحكي فيها هذا برضه عمل ليه metric وشوفنا كيف
+
+58
+00:04:17,390 --> 00:04:22,490
+عمل metric وبررنا انه عمل metric وبصير الـC of A
+
+59
+00:04:22,490 --> 00:04:28,300
+وB مع هذه الـD المعرفة بتصير metric spaceبتحقق
+
+60
+00:04:28,300 --> 00:04:31,140
+الشروطة هذا ما حكيناه المرة الماضية و اللي ناسي
+
+61
+00:04:31,140 --> 00:04:34,620
+اشي ممكن يرجع للمحاضرة ما هي مسجلة و جينا على
+
+62
+00:04:34,620 --> 00:04:38,960
+metric آخر سمناها discrete metric space اللي هو
+
+63
+00:04:38,960 --> 00:04:44,960
+الـD X و Y عرفناها بتساوي سفر إذا كانت ال X هي Y و
+
+64
+00:04:44,960 --> 00:04:48,400
+بيساوي واحد إذا كانت ال X تساوي Y و أبرهنا برضه إن
+
+65
+00:04:48,400 --> 00:04:52,100
+هذا بيعمل metric فسمناها ال X و D is a metric a
+
+66
+00:04:52,100 --> 00:04:56,460
+discrete metric spaceالان يا جماعة أخدنا exercises
+
+67
+00:04:56,460 --> 00:05:01,700
+و قلنا هدولة exercises بتحلوهن و قلنا اللي هو عندي
+
+68
+00:05:01,700 --> 00:05:06,100
+أنا بكتبلكم homeworks اللي هي من الكتاب هدولة
+
+69
+00:05:06,100 --> 00:05:09,540
+الأسئلة أرقام الأسئلة و في homework أسطار من
+
+70
+00:05:09,540 --> 00:05:12,200
+الكتاب هذول ال homework أسطار هم اللي بتكون
+
+71
+00:05:12,200 --> 00:05:16,440
+السلمونيةبتكون السلموني يعني أربعة وخمسة و تمانية
+
+72
+00:05:16,440 --> 00:05:19,980
+و عشرة و واحد و اتنين هدولة اللي هان هذا بتكون ال
+
+73
+00:05:19,980 --> 00:05:23,120
+homework الأول و زي ما حكينا المرة الماضية في خطة
+
+74
+00:05:23,120 --> 00:05:28,420
+المساق انه بدنا نحاول نعطيكم امتحانين و نعطيكوا
+
+75
+00:05:28,420 --> 00:05:31,700
+اللي هو ال هو homework و ممكن نعطيكوا تلت امتحانات
+
+76
+00:05:31,700 --> 00:05:35,820
+و نحصل بلكم أحسن اتنين و عليهم اربعين فمية
+
+77
+00:05:35,820 --> 00:05:38,400
+لامتحانين و عشرة فمية ع ال homework و الخمسين فمية
+
+78
+00:05:38,400 --> 00:05:41,360
+بتكون عالمين ع ال final و موضوع الهدك ان شاء الله
+
+79
+00:05:41,360 --> 00:05:45,870
+بنتفج عليهنيجي لان موضوعنا اليوم نبدأ في محاضرتنا
+
+80
+00:05:45,870 --> 00:05:49,830
+اليوم ان شاء الله بفصل تفصيل اللي بدنا نحكيه لان
+
+81
+00:05:49,830 --> 00:05:55,050
+further examples of metric S bases اللي هو يعني في
+
+82
+00:05:55,050 --> 00:05:59,410
+عندي أمثلة أخرى غير الأمثلة اللي حكيناها المرة
+
+83
+00:05:59,410 --> 00:06:05,920
+الماضية أول مثال بدي أحكي عنهاللي هو مثال آخر على
+
+84
+00:06:05,920 --> 00:06:11,020
+الـ Sequences Base هتلاقونا احنا بنركز على اللي هو
+
+85
+00:06:11,020 --> 00:06:15,840
+الفراغات اللي عناصرها Sequences اللي جابل بشوية
+
+86
+00:06:15,840 --> 00:06:18,520
+الـ L Infinity كانت اللي هي Sequences تبعت L
+
+87
+00:06:18,520 --> 00:06:21,990
+Infinity اللي هي الـ Bounded Sequencesالآن بتاخد
+
+88
+00:06:21,990 --> 00:06:28,470
+الـ S small هذه بـ The space of all sequences طبعا
+
+89
+00:06:28,470 --> 00:06:31,930
+اللي باخده Complex numbers هو الـ Real numbers
+
+90
+00:06:31,930 --> 00:06:35,990
+خلّيني أحكي عن الـ Complex إذا S هذه small هي
+
+91
+00:06:35,990 --> 00:06:42,490
+عبارة عن The set of all sequences of numbersالـ
+
+92
+00:06:42,490 --> 00:06:47,970
+Sequence اللي فيها لو أخدنا X وY في الـ S الـ X
+
+93
+00:06:47,970 --> 00:06:51,390
+هتكون Sequence يعني لو جينا رمزنا لها الـ X بتساوي
+
+94
+00:06:51,390 --> 00:06:55,750
+قصاي I يعني X بتساوي قصاي 1، قصاي 2، قصاي 3، قصاي
+
+95
+00:06:55,750 --> 00:06:59,610
+4، إلى مدى النهاية ونفس الاشي Y لو سمناها مثلا
+
+96
+00:06:59,610 --> 00:07:02,610
+بتساوي Gamma I أو اللي بدكم إياه يعني Gamma 1،
+
+97
+00:07:02,610 --> 00:07:06,580
+Gamma 2، Gamma 3، إلى مدى النهايةالان بدّى اعرف
+
+98
+00:07:06,580 --> 00:07:10,740
+هذا تنسوش ان هدولة any sequences converges مش
+
+99
+00:07:10,740 --> 00:07:14,860
+converges bounded مش bounded اي اشي عشان هيك بدّى
+
+100
+00:07:14,860 --> 00:07:19,980
+اختار metric لان اختار صيغة ل metric انها تكون
+
+101
+00:07:19,980 --> 00:07:24,560
+معجولة و بتلم كل ال sequences هذه تكون صحيحة لكل
+
+102
+00:07:24,560 --> 00:07:28,200
+ال sequences اللي بتنطرع علينا شوفوا اللي باخدها
+
+103
+00:07:28,200 --> 00:07:32,960
+بقولك خدوا DXY عرفة كالتالي DXY بساوة ال summation
+
+104
+00:07:33,800 --> 00:07:45,460
+للـ Xi I ناقص Gamma I على 1 زاد Xi I ناقص Gamma I
+
+105
+00:07:45,460 --> 00:07:51,220
+ماقالش هيكوا بس لإنه لو حتى زي هيكوا بس ال series
+
+106
+00:07:51,220 --> 00:07:55,420
+هذه اللي هي Gamma I من عند 1 لعند infinity حدش
+
+107
+00:07:55,420 --> 00:07:59,300
+بدمنلكوا انها تكون convergeيعني حدش بضمنكم يكون
+
+108
+00:07:59,300 --> 00:08:04,120
+هذا إيش مالو عبارة عن عدد وDxy ده اللي هو metric
+
+109
+00:08:04,120 --> 00:08:08,580
+يعني metric في الآخر بتطلع لإيش عدد الآن ضربوا
+
+110
+00:08:08,580 --> 00:08:14,960
+عشان هيك في واحد على اتنين I في هذا الحلق ضمنكم ان
+
+111
+00:08:14,960 --> 00:08:19,640
+ال series converge ليشلأنه بالـ Comparison Test لو
+
+112
+00:08:19,640 --> 00:08:23,860
+دي نطلعنا أو الحجز الصميشي من 1 على 2I هذه الـC
+
+113
+00:08:23,860 --> 00:08:27,420
+السيريز بنعرف إنها Converse، بظبط؟ أساسها نص اللي
+
+114
+00:08:27,420 --> 00:08:30,020
+هو Geometric Series أساسها نص أتوفتك اللي هو
+
+115
+00:08:30,020 --> 00:08:34,360
+Converse، لاحظوا إن هذا المقدار اللي هو الـNth
+
+116
+00:08:34,360 --> 00:08:39,880
+term هذا اللي جوا اللي مضروف 1 على 2I الـXi I ناقص
+
+117
+00:08:39,880 --> 00:08:47,400
+Γامع I على 1 زاد Xi I ناقص غامع Iهذا الأن أكيد
+
+118
+00:08:47,400 --> 00:08:53,120
+أكيد أكيد أظهر أو يساوي واحد على اتنين أس إيش أس I
+
+119
+00:08:53,120 --> 00:08:57,440
+مظبوط ولا لأ لما نضربه هدف مينوحدة لاتنين لأن هذا
+
+120
+00:08:57,440 --> 00:09:01,280
+المقدار أصغر أو يساوي واحد لأن اللي تحت أكبر من
+
+121
+00:09:01,280 --> 00:09:06,160
+مين؟ من اللي فوق فاهمين؟ إذا ما دامت هذه ال series
+
+122
+00:09:06,160 --> 00:09:09,300
+ال length term تبعها أكبر أو يساوي هذا و ال series
+
+123
+00:09:09,300 --> 00:09:12,860
+هذي converge إذا اكتوماتيك هذي converge إذا الأول
+
+124
+00:09:12,860 --> 00:09:17,360
+حاجة اللي هو شغله اللي هو لحتى الآن بالنسبة للي
+
+125
+00:09:17,360 --> 00:09:22,270
+عرفوا في الطريق الصحيحالان بيقوللي define اللي هو
+
+126
+00:09:22,270 --> 00:09:25,610
+هذا for انا x بالساوية كده وانا ضايع بالساوية كده
+
+127
+00:09:25,610 --> 00:09:31,270
+in S show that S وD ايش مالها is a metric space
+
+128
+00:09:31,270 --> 00:09:37,270
+الان الشروط الشروط الأولى التلاتة الأولى سهلة بتمر
+
+129
+00:09:37,270 --> 00:09:43,300
+عليها على السريعالشرط الأول ان هذا المقدار
+
+130
+00:09:43,300 --> 00:09:47,100
+absolute value او مدرس اذا اكبر ساوة سفر وهذا اكبر
+
+131
+00:09:47,100 --> 00:09:49,820
+ساوة سفر وهذا اكبر ساوة سفر اذا اكيد هذا اكبر ساوة
+
+132
+00:09:49,820 --> 00:09:52,860
+سفر اذا السلسلة الشمالية هتكون اكبر او ساوة سفر
+
+133
+00:09:52,860 --> 00:09:57,420
+اذا الشرط الأول متحقق اذا هذا اكبر او ساوة سفر
+
+134
+00:09:57,420 --> 00:10:02,800
+الشرط الأول تحقق نزل الشرط التاني الشرط الثاني هذا
+
+135
+00:10:02,800 --> 00:10:07,200
+بساوة سفرإذا و فقط إذا هذا المقدار بيساوي صفر إذا
+
+136
+00:10:07,200 --> 00:10:10,920
+و فقط إذا اللي هو دوله هذا non negative و هذا non
+
+137
+00:10:10,920 --> 00:10:15,240
+negative لازم هذا بيكون صفر إذا و فقط إذا اللي هو
+
+138
+00:10:15,240 --> 00:10:18,840
+كل اللي في هذا أجمع اللي هو ساوي صفر و هذا لا
+
+139
+00:10:18,840 --> 00:10:23,920
+يساوي صفر لما بيساوي صفر ال F الدول ال F اللي هو
+
+140
+00:10:23,920 --> 00:10:29,040
+Xi I Magus Gamma I بيساوي صفر مثل عساله سهل هذاF
+
+141
+00:10:29,040 --> 00:10:33,100
+and only F XI I يشملها بساوي Gamma I و هذا الكلام
+
+142
+00:10:33,100 --> 00:10:37,300
+لكل مين I إيش معناه XI I بساوي Gamma I لكله I
+
+143
+00:10:37,300 --> 00:10:42,340
+معناته S X بساوي R وايضا هذا الشرط مرضو إيش معانو
+
+144
+00:10:42,340 --> 00:10:46,290
+شرط سهل وسريعالشرط الأخير اللي هو الـ symmetry
+
+145
+00:10:46,290 --> 00:10:50,550
+اللي هو المسافة بين X و Y هي هذه بين Y و X بيصير
+
+146
+00:10:50,550 --> 00:10:53,370
+جمع على نقص إقصائي ما هي absolute value او modulus
+
+147
+00:10:53,370 --> 00:10:57,550
+ده متساويته، واضح؟ إذا الشرط الثاني كما .. ثالث
+
+148
+00:10:57,550 --> 00:11:02,210
+متحقق، ضال عندنا الشرط الثالث الشرط الثالث، بس
+
+149
+00:11:02,210 --> 00:11:07,770
+عشان نحققه اسمحولي بس ناخد دالة مساعدة auxiliary
+
+150
+00:11:07,770 --> 00:11:12,980
+function وبدنا نشوف هذه الدالة، الدالة هنستقيهامن
+
+151
+00:11:12,980 --> 00:11:17,800
+اللي عندى هذه الان هذه وهذه نفس الاشي فبدي اخد
+
+152
+00:11:17,800 --> 00:11:22,940
+دالة اسميها F of T طبعا هذه بتيجي مع الخبرة سوى T
+
+153
+00:11:22,940 --> 00:11:29,520
+على واحد زائد T هذه الدالة الان لو أخدتلها ال
+
+154
+00:11:29,520 --> 00:11:33,020
+derivative هتطلع ال derivative إليها واحد على واحد
+
+155
+00:11:33,020 --> 00:11:37,760
+زائد T لكل إيه شمالها تربيع ماشي الحال إذا واضح أن
+
+156
+00:11:37,760 --> 00:11:43,190
+ال F prime of Tأكبر أو يساوي إيه إيش؟ سفر حتى
+
+157
+00:11:43,190 --> 00:11:46,210
+strictly أكبر من سفر إذا ال function .. ال ..
+
+158
+00:11:46,210 --> 00:11:50,710
+الدالة إيش ما لها increasing function واضح إذا
+
+159
+00:11:50,710 --> 00:11:55,010
+الدالة increasing إذا الآن بدي أخزن المعلومة عندي
+
+160
+00:11:55,010 --> 00:12:01,350
+f of t is increasing طيب شوفوا إيش بدي أستفيد من
+
+161
+00:12:01,350 --> 00:12:10,120
+هذه أنا الآن بدي أثبت اللي هوDX وY أظهر يسموه DX
+
+162
+00:12:10,120 --> 00:12:16,040
+وZ زائد DZ وY هي ترينجلين كواليتيه شوفوا كيفه خدوا
+
+163
+00:12:16,040 --> 00:12:23,500
+الان X سموها Xi I وY سموها Gamma I وخد Z أي شيء
+
+164
+00:12:23,500 --> 00:12:26,780
+يسميه .. اللي هي أي سيكوينسيز في الاس وسميها Beta
+
+165
+00:12:26,780 --> 00:12:33,800
+I ماشي؟ لاحظوا التالي الآن لو أجينا أخدنا الXi I
+
+166
+00:12:33,800 --> 00:12:40,470
+ناقص Gamma Iطبعا أنا بدور حوالين الـ mean حوالين
+
+167
+00:12:40,470 --> 00:12:44,230
+المسافة بين X و Y هنا بدور حواليها إذا بدي أربطها
+
+168
+00:12:44,230 --> 00:12:48,950
+بين المسافة بين X و Z و Y و Z إذا أصغر أو يساوي X
+
+169
+00:12:48,950 --> 00:12:53,430
+I I أكيد هدخل الـ mean اللي هي طبعة الـ Z زائد
+
+170
+00:12:53,430 --> 00:12:57,370
+Beta I ناجس Gamma I هذه بالـ Triangling Quality
+
+171
+00:12:57,370 --> 00:13:00,610
+العادية اللي بنعرفها اللي هي Triangling Quality of
+
+172
+00:13:00,610 --> 00:13:04,470
+Numbers معايا؟ طيب صليوا على النبي عليه الصلاة
+
+173
+00:13:04,470 --> 00:13:11,940
+والسلامالـ L عندى اللى هو هذه أصغر أو ساوى هذه و
+
+174
+00:13:11,940 --> 00:13:14,220
+ال function اللى عندى increasing مظبوط ولا لا اطلع
+
+175
+00:13:14,220 --> 00:13:19,140
+لفوق شوية خلّيني نكون مع اللى مكتوب صارت عندى هذه
+
+176
+00:13:19,140 --> 00:13:23,360
+أصغر أو ساوى هذه و ال function increasing اذا F
+
+177
+00:13:23,360 --> 00:13:29,140
+لهذه أصغر أو ساوى F لهذه اذا F لهذه أصغر أو ساوى F
+
+178
+00:13:29,140 --> 00:13:33,600
+لهذه because the function is increasing ايش F لهذه
+
+179
+00:13:33,600 --> 00:13:41,170
+هي XIنقص Gamma I هذا ال T لان على واحد زي KSI I
+
+180
+00:13:41,170 --> 00:13:47,130
+نقص Gamma I أصغر أوي ساوي F هذه كلها اللي هي KSI I
+
+181
+00:13:47,130 --> 00:13:53,570
+هذه كلها ال T صارت نقص Beta I زي Beta I نقص Gamma
+
+182
+00:13:53,570 --> 00:14:00,310
+I طبعا كله مدلس على واحد زي KSI I نقص Beta I زي
+
+183
+00:14:00,310 --> 00:14:08,160
+Beta I نقص مين Gamma Iبدينا نجرب على اللي هي
+
+184
+00:14:08,160 --> 00:14:12,260
+المسافة بين x و y هاي المسافة بين x و y احنا
+
+185
+00:14:12,260 --> 00:14:17,580
+معرفينها اللي فوق اه؟ معرفين هي اه؟ بدينا نجرب بس
+
+186
+00:14:17,580 --> 00:14:21,740
+هنا لسه بعادى شوية فخلينا نفصل هذه لحال و هذه لحال
+
+187
+00:14:21,740 --> 00:14:26,940
+عشان نفصل تبعات ال z لحال و ال x و ال y و ال z
+
+188
+00:14:26,940 --> 00:14:29,580
+لحال اذا هذه بتساوي بالظبط
+
+189
+00:14:32,230 --> 00:14:39,390
+نقص Beta I على 1 زائد Xi I نقص Beta I زائد Beta I
+
+190
+00:14:39,390 --> 00:14:46,240
+نقص Gamma I صح اللي بعمله زائد التانية Beta Iناجس
+
+191
+00:14:46,240 --> 00:14:51,640
+Gamma I على واحد زائد Psi I ناجس Beta I بنجلهم
+
+192
+00:14:51,640 --> 00:14:56,740
+نفسي زائد Beta I ناجس Gamma I بس اللي عملته فصلتن
+
+193
+00:14:56,740 --> 00:15:03,200
+عن بعض ماشي الحال الان هذه نفسها هيها أصغر أو
+
+194
+00:15:03,200 --> 00:15:11,640
+يساوي صح اه يعني بتزغر المقام فتكبر هذا و هذا نفس
+
+195
+00:15:11,640 --> 00:15:18,680
+الاشي ماشيواضح اللي عملته الان ايش بده اسوي عشان
+
+196
+00:15:18,680 --> 00:15:22,180
+اصل اللي في ذاك مضياجي اضرب في هذا واحد على اتنين
+
+197
+00:15:22,180 --> 00:15:25,280
+I وهذا في واحد على اتنين I عارفين ليش
+
+198
+00:15:34,970 --> 00:15:40,470
+هذا أصغر شوء Alpha I نقص Beta I و Beta I نقص Gamma
+
+199
+00:15:40,470 --> 00:15:48,030
+I هي ليش اللي دلت اللي مسحناها Beta I نقص Gamma I
+
+200
+00:15:48,030 --> 00:15:51,810
+ماشي الحال واضحة الفكرة أه هذا في واحد على اتنين I
+
+201
+00:15:51,810 --> 00:15:57,530
+هانيو صار هذا أصغر شوء هذا الان باخد ال summation
+
+202
+00:15:57,530 --> 00:16:01,460
+مالهإلى ما لنهاية وضامن إن ال summation كله بتوزع
+
+203
+00:16:01,460 --> 00:16:06,780
+ليش لإن ال series هنا converts و ال series هنا
+
+204
+00:16:06,780 --> 00:16:10,420
+converts واضح إذا صار ال summation على هذه I من
+
+205
+00:16:10,420 --> 00:16:13,880
+واحد إلى ما لنهاية أصغر أو سوى ال summation على
+
+206
+00:16:13,880 --> 00:16:16,880
+هذه I من واحد إلى ما لنهاية زاد ال summation على
+
+207
+00:16:16,880 --> 00:16:20,340
+الأخيرة I من واحد إلى ما لنهاية هذه مين هي يا
+
+208
+00:16:20,340 --> 00:16:26,140
+جماعة هذه عبارة عن Dxy
+
+209
+00:16:27,220 --> 00:16:35,420
+و هد مين هي بين ال X و ال Z دي X و Z ذات هد بين
+
+210
+00:16:35,420 --> 00:16:43,840
+مين؟ بين Y و Z ذات دي Z و Y أو Y و مين؟ و Z مظبوط
+
+211
+00:16:43,840 --> 00:16:51,100
+هيك؟ و بيكون أثبتنا إنه عبارة عن اللي هو metric أي
+
+212
+00:16:51,100 --> 00:17:00,240
+سؤال؟ طيبإذا صار عندي الـ S مع هذا الـ metric is a
+
+213
+00:17:00,240 --> 00:17:05,080
+metric space بتعمل إيه أشماله؟ metric space نيجي
+
+214
+00:17:05,080 --> 00:17:09,720
+الآن ناخد space شبيه بالـ space اللي حكينا عنه قبل
+
+215
+00:17:09,720 --> 00:17:12,800
+شوية اللي هو الـ L infinity هداك كان في حالة الـ
+
+216
+00:17:12,800 --> 00:17:15,420
+sequences الـ L infinity bounded sequences هلا في
+
+217
+00:17:15,420 --> 00:17:18,860
+حالة الدول يعني بتاخد اللي هو the space of all
+
+218
+00:17:18,860 --> 00:17:22,660
+bounded functions على اللي هي الـ 6
+
+219
+00:17:26,720 --> 00:17:31,740
+طيب يا جماعة شوفوا بدأ
+
+220
+00:17:31,740 --> 00:17:38,880
+أحكي الآن عن space آخر اللي هو space of functions
+
+221
+00:17:38,880 --> 00:17:42,160
+المرة الماضية حكينا عن space of continuous
+
+222
+00:17:42,160 --> 00:17:46,540
+functions فسمي continuous functions على closed
+
+223
+00:17:46,540 --> 00:17:49,580
+bounded interval وعرفنا ال metric في حينه ال
+
+224
+00:17:49,580 --> 00:17:54,800
+maximumتجرأنا وعرفنا ال maximum لإنه احنا عارفين
+
+225
+00:17:54,800 --> 00:17:57,240
+ال continuous function على closed bounded interval
+
+226
+00:17:57,240 --> 00:18:00,500
+أكيد attain its maximum و minimum في ال interval
+
+227
+00:18:00,500 --> 00:18:05,580
+عشان ذلك عرفنا ال maximum بس اليوم انابتاخد ال
+
+228
+00:18:05,580 --> 00:18:09,600
+space of bounded functions يعني عناصر ال space
+
+229
+00:18:09,600 --> 00:18:13,100
+اللي عندي هي عبارة عن دوال محدودة bounded
+
+230
+00:18:13,100 --> 00:18:18,300
+functions ال bounded function ليس شرطا أنه ألاقي
+
+231
+00:18:18,300 --> 00:18:20,900
+ال maximum و ال minimum له وين ال absolute maximum
+
+232
+00:18:20,900 --> 00:18:26,120
+و ال absolute minimum وين على اللي هي للست اللي
+
+233
+00:18:26,120 --> 00:18:31,160
+عندي عشان هيكبتعرفهاش بيساوي الـ supermom الـ
+
+234
+00:18:31,160 --> 00:18:35,060
+supermom مضمون انه موجود لأنها bounded عشان ايه
+
+235
+00:18:35,060 --> 00:18:38,080
+بتقول الان let B of A be the set of all bounded
+
+236
+00:18:38,080 --> 00:18:43,060
+functions defined on a set A define ال metric الان
+
+237
+00:18:43,060 --> 00:18:48,120
+المسافة بين اللي هو أي دالتين في ال B of A بتساوي
+
+238
+00:18:48,120 --> 00:18:51,740
+ال supermom لل X of T نقص Y of T over اللي هو T
+
+239
+00:18:51,740 --> 00:18:56,570
+over Aهذا الآن بعرف الـ metric بالظبط .. بالظبط
+
+240
+00:18:56,570 --> 00:19:01,570
+البرهان مشابه بل typical للبرهان تبع الـ L
+
+241
+00:19:01,570 --> 00:19:04,830
+infinity وحاكناها المرة الماضية وشرحناها بالتفصيل
+
+242
+00:19:04,830 --> 00:19:11,050
+اللي نسيه برجعله مافي مشكلة خالص طيب نيجي الآن ل
+
+243
+00:19:11,050 --> 00:19:19,050
+.. اللي هو بدي الآن امهد للوصول
+
+244
+00:19:20,070 --> 00:19:26,830
+الـ Space الـ الأول
+
+245
+00:19:26,830 --> 00:19:33,010
+الـ Infinity الـ Space of Sequences بس هذه Bounded
+
+246
+00:19:33,010 --> 00:19:38,550
+Sequences وحكينا عن Space تاني S اللي هو Space of
+
+247
+00:19:38,550 --> 00:19:43,310
+Sequences in General هذا عرفناه Metric يناسبه وهذا
+
+248
+00:19:43,310 --> 00:19:48,450
+عرفناه Metric يناسبه بعدين أجيناطبعاً هذا كل
+
+249
+00:19:48,450 --> 00:19:52,510
+الكلام فيه إله مستقبل وفيه تبعات في المستقبل إله
+
+250
+00:19:52,510 --> 00:19:57,270
+الآن و جينا عرفنا اللي هو space of sequences و
+
+251
+00:19:57,270 --> 00:20:03,550
+جينا عرفنا اللي هو space آخر اللي هو .. اللي هو C
+
+252
+00:20:03,550 --> 00:20:07,610
+of A و B space of continuous functions على closed
+
+253
+00:20:07,610 --> 00:20:11,750
+bounded intervalودينا بـ metric تبعه ودينا عرفنا
+
+254
+00:20:11,750 --> 00:20:17,610
+قبل بشوية space B of A space of bounded functions
+
+255
+00:20:17,610 --> 00:20:22,830
+على الـ A وعرفنا ال metric تبعهالان واضح تودهنا
+
+256
+00:20:22,830 --> 00:20:28,330
+أننا حديثنا في معظم الأنفلة اللي عندنا على main
+
+257
+00:20:28,330 --> 00:20:31,950
+على space of functions وعلى space of main of
+
+258
+00:20:31,950 --> 00:20:37,510
+sequences وهذا له همية كبيرة في نفس ال functional
+
+259
+00:20:37,510 --> 00:20:42,370
+analysis وحتى تطبيقاتها في الأمور الحياتية الآن
+
+260
+00:20:42,370 --> 00:20:48,530
+بدي أعرف أدخل ل space جديد اسمه ال B spacesالـ B
+
+261
+00:20:48,530 --> 00:20:53,290
+Spaces و B عندي هذه بديها أكبر أو يساوي إيش؟ واحد
+
+262
+00:20:53,290 --> 00:20:58,510
+طيب ال ال ال B Spaces إيش ال ال B هدا؟ هو عبارة عن
+
+263
+00:20:58,510 --> 00:21:02,310
+Space of Sequences طيب إيش .. إيش شروط اللي على ال
+
+264
+00:21:02,310 --> 00:21:05,630
+.. ال .. ال Sequences هدا عشان تكون جوة ال ال B؟
+
+265
+00:21:05,630 --> 00:21:12,680
+بقول إنك Psi I هذه ال Sequence في ال ال Bإذا بتحقق
+
+266
+00:21:12,680 --> 00:21:19,460
+مالي أن الـ summation للـ Xi I أُس بي I من واحد
+
+267
+00:21:19,460 --> 00:21:24,840
+إلى ملا نهاية تكون converge كل الـ sequences اللي
+
+268
+00:21:24,840 --> 00:21:29,920
+في الدنيا اللي Xi I لها بتكون في القلبي إذا تحقق
+
+269
+00:21:29,920 --> 00:21:37,260
+Xi I أُس بي summation is finite هذا بنسميه الـ B
+
+270
+00:21:37,260 --> 00:21:44,430
+spaceبدّي الآن أروح باتجاه تعريف metric عليه بدي
+
+271
+00:21:44,430 --> 00:21:48,310
+أعرف metric على ال space هذا لو قلت هي X بتساوي
+
+272
+00:21:48,310 --> 00:21:54,860
+Psi I و Y بتساوي Gamma I element in LBالمتريك اللي
+
+273
+00:21:54,860 --> 00:22:00,060
+بتعرفه هتلاقوني عرفته بعد شوية DXY بساوي summation
+
+274
+00:22:00,060 --> 00:22:07,840
+لل XI I ناقص Gamma I أس بيه عشان أضبن أنه موجود
+
+275
+00:22:07,840 --> 00:22:12,440
+هال هذا finite و هذا إلها Gamma I finite بس هذا
+
+276
+00:22:12,440 --> 00:22:18,740
+لسه بده شغل و الكل أس واحد عدبيهذا بعد شوية
+
+277
+00:22:18,740 --> 00:22:24,120
+هتلاقونا وصلنا انه هذا هيعمل ليه metric على الـB
+
+278
+00:22:24,120 --> 00:22:28,180
+على القلبي يعني هيصير القلبي مع هذا ال metric
+
+279
+00:22:28,180 --> 00:22:33,480
+المعرف اسمه الـB metric space وهذا من الفراغات
+
+280
+00:22:33,480 --> 00:22:38,890
+المهمة جدااللي هو وفيه اللي هو مقابل حنشوف اللي هو
+
+281
+00:22:38,890 --> 00:22:44,150
+مقابل في ال space of functions برضه اسمه ال B بس
+
+282
+00:22:44,150 --> 00:22:48,890
+بيسميه ال B function وفي حينه انا بقى بنحكيلكم عنه
+
+283
+00:22:48,890 --> 00:22:55,750
+بالتفصيل ممكن الآن عشان نوصل لهذا انه metric انا
+
+284
+00:22:55,750 --> 00:23:02,160
+بلزمني تلت شغلاتبالزمن أول إشي الآن اللي هو
+
+285
+00:23:02,160 --> 00:23:08,780
+متباينة أبرهن متباينة مساعدة المتباينة مساعدة هذه
+
+286
+00:23:08,780 --> 00:23:14,080
+بدي استخدمها في إثبات حاجة اسمها holder inequality
+
+287
+00:23:15,240 --> 00:23:19,840
+الـ Holder Inquality هذه بتستخدمها لإثبات حاجة
+
+288
+00:23:19,840 --> 00:23:24,620
+اسمها Minkowski Inquality اللي هي هتكون سبب في
+
+289
+00:23:24,620 --> 00:23:28,420
+إثبات الـ Triangle Inquality هذه لهذا وبهيك بيكون
+
+290
+00:23:28,420 --> 00:23:33,320
+اجتملت الصورة وخلصناها وعملنا اللي بدناها بخصوص
+
+291
+00:23:33,320 --> 00:23:39,560
+اللي هو مين ال metric space اللي أمامنا طيب شوفوا
+
+292
+00:23:41,150 --> 00:23:45,990
+الدلة المساعدة المتبينة المساعدة هذه المتبينة
+
+293
+00:23:45,990 --> 00:23:51,050
+المساعدة بعد شوية طبعا هتعرفوا ليش هذه أخدناها
+
+294
+00:23:51,050 --> 00:23:53,730
+عشان نستفدمها في أيش كمان
+
+295
+00:23:59,230 --> 00:24:04,430
+في احنا بنعرف في المدارس كنتوا تقولوا المرافق
+
+296
+00:24:04,430 --> 00:24:09,170
+العدد و المرافق هو في سبب للمرافقة المرافقة انه
+
+297
+00:24:09,170 --> 00:24:12,730
+يعملوا فرق بين مربعين او المرافقة اللي هو في حالة
+
+298
+00:24:12,730 --> 00:24:16,750
+ال .. ال .. ال .. العدد و الكنج تبعه الاخرين الان
+
+299
+00:24:16,750 --> 00:24:21,940
+هنا مرافقة برضه بنقول ان بي و كي مرافقات لبعضهمتحت
+
+300
+00:24:21,940 --> 00:24:28,180
+العلاقة 1 على b زائد 1 على q ايش بيساوي هذا اللي
+
+301
+00:24:28,180 --> 00:24:32,500
+بنسميه بي و q conjugate لبعض with respect to this
+
+302
+00:24:32,500 --> 00:24:36,220
+relation ماشي الحال اذا الان احنا في عالمنا هذا
+
+303
+00:24:36,220 --> 00:24:38,880
+لما نقول بي و q بنقصد واحد على بي زائد واحد على
+
+304
+00:24:38,880 --> 00:24:44,000
+كيو بيساوي واحد و بي و كيو اشمالهن اكبر او يساوي
+
+305
+00:24:44,000 --> 00:24:48,960
+واحد طيب نيجي نشوف اللي هو ال auxiliary inequality
+
+306
+00:24:52,520 --> 00:24:56,480
+اللي هنجلب بس لو سمحت أنا سيبني من الواحد أنا
+
+307
+00:24:56,480 --> 00:25:00,980
+بتاخد ب أش مالها strictly أكبر من أش من واحد
+
+308
+00:25:00,980 --> 00:25:03,900
+بتناشي اللي هو حالة اللي هي مين ب بتساوي واحد
+
+309
+00:25:03,900 --> 00:25:08,980
+لإنها هيعملني مشكلة في العلاقة هذه فخليني ما بعدش
+
+310
+00:25:08,980 --> 00:25:11,740
+واحد يلاقوني بشتغل على ال ب أكبر سوا واحد لكن عشان
+
+311
+00:25:11,740 --> 00:25:14,600
+العلاقة هذه ال conjugation بتاخد ال ب أش مالها
+
+312
+00:25:14,600 --> 00:25:20,300
+strictly أكبر من واحد طيب بقوللي هتلاقي دايما لأي
+
+313
+00:25:20,300 --> 00:25:27,180
+Alpha و Betaالفة و بيتا non negative numbers دائما
+
+314
+00:25:27,180 --> 00:25:31,400
+دائما هتلاقي الالفة في بيتا طبعا ال non negative
+
+315
+00:25:31,400 --> 00:25:34,960
+numbers أنا مبسوط فيها بس سرية لإن هو مابنفعش اقول
+
+316
+00:25:34,960 --> 00:25:37,760
+complex لإنه مافيش order في ال complex ماانتوا
+
+317
+00:25:37,760 --> 00:25:41,940
+عارفين إذا الفة في بيتا هتكون أصغر أو ساوي Alpha
+
+318
+00:25:41,940 --> 00:25:47,040
+to the B على B زي بيتا to the Q على مين على Q إذا
+
+319
+00:25:47,040 --> 00:25:52,900
+بدي أثبت الآن الفة في بيتا أصغر أو ساويالف تدا بي
+
+320
+00:25:52,900 --> 00:26:01,180
+على بي زايد بيتا تدا كيو على مين على كيو القلب بدي
+
+321
+00:26:01,180 --> 00:26:07,120
+أستقي من هذه اللي هو اللي هو دالة أُسية بتعرفوا
+
+322
+00:26:07,120 --> 00:26:10,780
+أنتوا الدالة الأُسية اللي هي لو أجينا أخدنا هذه T
+
+323
+00:26:10,780 --> 00:26:16,280
+و هذه U و أخدنا U بتساوي T أُس بي minus واحد مثلا
+
+324
+00:26:16,280 --> 00:26:18,960
+على سبيل المثال هذه الدالة لازم تعرفوا إيش أخدت
+
+325
+00:26:18,960 --> 00:26:20,800
+هذه الدالة
+
+326
+00:26:22,300 --> 00:26:28,120
+هي اللي هو عندي الدالة هذه و كانت هذه عندي Alpha و
+
+327
+00:26:28,120 --> 00:26:34,720
+كانت هذه عندي مثلا مين Beta الآن Alpha في Beta هي
+
+328
+00:26:34,720 --> 00:26:41,900
+Alpha في Beta مظبوط؟
+
+329
+00:26:41,900 --> 00:26:51,870
+هذه عبارة عن مساحة المستطيل هذا مظبوط؟ طيب الآنلو
+
+330
+00:26:51,870 --> 00:26:57,090
+جيت على المساحة تحت المنحنى هذا المساحة تحت
+
+331
+00:26:57,090 --> 00:27:02,410
+المنحنى هذا هيها هيها ماشي هذه المساحة تحت المنحنى
+
+332
+00:27:02,410 --> 00:27:10,510
+هذا هيها صحيح ولا لأ؟ هذه إيش بتمثل؟ بتمثل ال
+
+333
+00:27:10,510 --> 00:27:17,890
+integration التي-1 dt من أين إلى أين؟ من صفر إلى
+
+334
+00:27:17,890 --> 00:27:23,210
+ألفة صح أم لا؟ طيب من صفر إلى ألفة لو جينا تطلعنا
+
+335
+00:27:23,210 --> 00:27:29,290
+من جهة أخرى من جهة أخرى
+
+336
+00:27:29,290 --> 00:27:34,610
+لأ اللي هو المساحة تحت المنحنة هذا هيها اللي
+
+337
+00:27:34,610 --> 00:27:39,710
+بالأخضر هذه المساحة تحت المنحنة هذا هيها هيها هي
+
+338
+00:27:39,710 --> 00:27:46,200
+دول الأخضرهذه المساحة اللي هي بدا تصير اللي هو T
+
+339
+00:27:46,200 --> 00:27:50,520
+أُس U أُس 1 على B-1 صح بيصير ال integration بتبعها
+
+340
+00:27:50,520 --> 00:27:55,540
+زائد ال integration فاني كيف لإنه بتتغير هذا بيصير
+
+341
+00:27:55,540 --> 00:27:58,060
+اللي هو ال independent variable و هذا ال dependent
+
+342
+00:27:58,060 --> 00:28:06,900
+variable بيصير T ال U أُس B أُس 1 على B-1 اللي هو
+
+343
+00:28:06,900 --> 00:28:13,010
+من وين لوين بيصير من 0 ل 100 ل Betaطبعا الرسم هذه
+
+344
+00:28:13,010 --> 00:28:18,270
+الان واضح .. واضح ان المساحة هذه زاد المساحة هذه
+
+345
+00:28:18,270 --> 00:28:23,070
+.. هذه .. هي .. هي اللي بالأحمر هنا أكيد أكبر أو
+
+346
+00:28:23,070 --> 00:28:28,200
+يساوي الألف في مينفي بيتها، لأن هذه زيادة، هذه
+
+347
+00:28:28,200 --> 00:28:32,920
+الجزء زيادة عن اللي هي مساحة المرب، المساطيل،
+
+348
+00:28:32,920 --> 00:28:38,280
+مظبوط؟ الآن قد تكون الشغل مختلفة شوية، قد يكون
+
+349
+00:28:38,280 --> 00:28:43,000
+اللي هو بدل هيك، بدل بالشكل هذا، تكون الرسمة،
+
+350
+00:28:43,000 --> 00:28:50,200
+ماعليش أغير إشي بسيط، الرسمة تكون هاي Alpha Hanهي
+
+351
+00:28:50,200 --> 00:28:53,700
+Alpha وهي Beta فبتكون ليه مساحة الـ Alpha في Beta
+
+352
+00:28:53,700 --> 00:29:00,040
+و بيصير المساحة تحت المنحنة هذه زاد هذه فبتكون هذه
+
+353
+00:29:00,040 --> 00:29:03,520
+الزيادة يعني تكون زيادة هنا أو تكون زيادة من هنا
+
+354
+00:29:03,520 --> 00:29:06,900
+فاهميه ليش اللي بقوله فبالآن أي إن كانتوا لو
+
+355
+00:29:06,900 --> 00:29:09,380
+التقين ال Alpha من الرتم مع بعض بيصير اللي هو إيه
+
+356
+00:29:09,380 --> 00:29:13,780
+في ماله مسواهمعايا فالان صار ال integration هذا ال
+
+357
+00:29:13,780 --> 00:29:16,900
+alpha في beta أصغر شويه ال integration هذا زاد ال
+
+358
+00:29:16,900 --> 00:29:20,060
+integration هذا بدنا نحسب ال integration هذا ال
+
+359
+00:29:20,060 --> 00:29:23,760
+integration هذا إيش بده يكون قيمته؟ كلكم أكيد بعرف
+
+360
+00:29:23,760 --> 00:29:31,060
+اللي هو عبارة عن Tu س بي على بي من سفر لعند alpha
+
+361
+00:29:31,060 --> 00:29:38,180
+زاد الآن هذا يقص ال Du هذا يقص واحد على بي ماينس
+
+362
+00:29:38,180 --> 00:29:44,310
+واحدلو جينا على جهة واحد على بي زائد واحد على كيو
+
+363
+00:29:44,310 --> 00:29:48,370
+ايش بيساوي؟ بيساوي واحد يعني وحدنا المقامات فبصير
+
+364
+00:29:48,370 --> 00:29:53,190
+بي في كيو وانا بي زائد كيو بيساوي واحد يعني عند بي
+
+365
+00:29:53,190 --> 00:29:57,190
+زائد كيو بيساوي بي في كيو خليه في الذاكرة لو جيتوا
+
+366
+00:29:57,190 --> 00:30:00,930
+حسبتوا بي ماينس واحد في كيو ماينس واحد بيساوي
+
+367
+00:30:00,930 --> 00:30:09,600
+اضربوهم في بعض بصير بي في كيو ناقص بي ناقص كيوزائد
+
+368
+00:30:09,600 --> 00:30:14,760
+واحد، صح؟ هذول مع بعض، هذول مع بعض، لو نقول إن أنا
+
+369
+00:30:14,760 --> 00:30:18,500
+بصير إني أشتفر، زائد واحد دلوقتي إيش بيساوي؟ إذا
+
+370
+00:30:18,500 --> 00:30:21,920
+يعني الآن P minus واحد في Q minus واحد إيش بيساوي؟
+
+371
+00:30:21,920 --> 00:30:27,680
+يعني واحد على P minus واحد هي مين؟ Q ناقص واحد،
+
+372
+00:30:27,680 --> 00:30:34,990
+ماشي؟ فبصير زائد، فهذه Q ناقص واحد، وصلتماشي الحال
+
+373
+00:30:34,990 --> 00:30:38,730
+فالان بيصير Q U أُس Q ماينس واحد اللي هي عبارة عن
+
+374
+00:30:38,730 --> 00:30:46,930
+U أُس Q على Q من صفر لمين لـ Beta ويساوي هذا بتصير
+
+375
+00:30:46,930 --> 00:30:54,550
+T يعني بتصير Alpha أُس B على B زائد Beta أُس Q على
+
+376
+00:30:54,550 --> 00:30:58,930
+Q هذا أكبر يساوي مين Alpha في Beta فبتكون ال
+
+377
+00:30:58,930 --> 00:31:04,700
+auxiliary اللي هو inequality تم ضمنهاماشي اذا
+
+378
+00:31:04,700 --> 00:31:09,800
+خلّينا الان نحطها عنا عشان تستخدمها انا برهنتها ان
+
+379
+00:31:09,800 --> 00:31:13,900
+هي مش اصلا هي يعني مش هي مجال اهتمامي لكن انا
+
+380
+00:31:13,900 --> 00:31:17,320
+برهنتها عشان تستخدمها بعد شوية في شغلة مجال
+
+381
+00:31:17,320 --> 00:31:23,930
+اهتمامي Alpha في Beta أزرع يساويقولوا معايا Alpha
+
+382
+00:31:23,930 --> 00:31:30,070
+أس بي على بي زائد Beta SQ على Q هذا خلّيها في
+
+383
+00:31:30,070 --> 00:31:32,830
+الذاكرة هذا ال auxiliary inequality اللي أمامي
+
+384
+00:31:32,830 --> 00:31:37,810
+الآن بدي أجي لاللي هي الهدف الثاني اللي هيوصلني
+
+385
+00:31:37,810 --> 00:31:42,450
+لهدفي اللي هو حاجة اسمها اللي هي holder inequality
+
+386
+00:31:42,450 --> 00:31:46,960
+بس جيبلي me holder inequalityالـ .. كتبته أنا هذا
+
+387
+00:31:46,960 --> 00:31:51,000
+الـ L P كتبته قول قولته قبل شوية will denote the
+
+388
+00:31:51,000 --> 00:31:54,360
+set of all sequences of number xi I number xi I
+
+389
+00:31:54,360 --> 00:31:57,520
+such that ال summation هذا is finite where P
+
+390
+00:31:57,520 --> 00:32:02,520
+أشمالها أكبر أو يساوي واحد الآن
+
+391
+00:32:03,750 --> 00:32:09,330
+الـ Holder Inquality خلّيني أركزوا معايا لأن
+
+392
+00:32:09,330 --> 00:32:14,130
+الرموز هي اللي بت .. شوية بت .. فيها عفاشة لكن ان
+
+393
+00:32:14,130 --> 00:32:20,390
+شاء الله بنفهمها مابديش أكتب كتير هلأ لإنه حنطول
+
+394
+00:32:20,390 --> 00:32:26,370
+خلّيني نشرع على اللي موجود شوف
+
+395
+00:32:26,370 --> 00:32:31,060
+إيش بتقول الـHolder Inquality بتقول إيه لنا؟لو
+
+396
+00:32:31,060 --> 00:32:33,720
+كانت الـ P و الـ Q زي قبل شوية يعني واحد على P زاد
+
+397
+00:32:33,720 --> 00:32:38,220
+واحد على Q بسوء واحد وكان عند XI I و I الموجودة في
+
+398
+00:32:38,220 --> 00:32:42,540
+القلب P و الجامعة I و I الموجودة في القلب Q إذا ما
+
+399
+00:32:42,540 --> 00:32:46,660
+يلي يتحقق إيش هو ما يلي؟ summation of absolute
+
+400
+00:32:46,660 --> 00:32:52,420
+value XI I في جامعة I أصغر أو ساوية XI K أُس P كله
+
+401
+00:32:52,420 --> 00:32:56,770
+واحد على Pفي الـ Summation Gamma M .. اللي بتكون
+
+402
+00:32:56,770 --> 00:33:01,250
+بيسموها K أس Q أس واحد مين على Q هذه اللي بيسميها
+
+403
+00:33:01,250 --> 00:33:03,590
+Whole Dark Inquality يعني الـ Summation ..
+
+404
+00:33:03,590 --> 00:33:14,690
+Summation لـ Xi I Gamma I أزرع أو ساوي Summation
+
+405
+00:33:14,690 --> 00:33:22,230
+Xi I أس B أس واحد على B في الـ Summation Gamma I
+
+406
+00:33:22,910 --> 00:33:29,190
+قصة Q بس واحد على مين الـ Q لحظة لو هذه .. لو هذه
+
+407
+00:33:29,190 --> 00:33:35,890
+XII في الـ LB بضمن إنه هذي Converse هيك تعريفها و
+
+408
+00:33:35,890 --> 00:33:40,070
+Gamma M هذي مدام انت في الـ LQ هذي برضه تكون إيه
+
+409
+00:33:40,070 --> 00:33:43,430
+شمالها Converse إذا الدنيا ده مقام نيحة هيك بيصير
+
+410
+00:33:43,430 --> 00:33:46,130
+هذا Converse أكبر شوة هذي ده أكيد أشماله هذا
+
+411
+00:33:46,130 --> 00:33:53,430
+Converse واضح؟ طيبالان بدو بس شغلة هيكا بدو
+
+412
+00:33:53,430 --> 00:34:00,910
+يستخدمها كجسر بدو يسمي اللي هو طبعا بس بشايلكم
+
+413
+00:34:00,910 --> 00:34:06,030
+شغلة عشان بدو يكسم على الصماش فبدو يشيها سفر فجالك
+
+414
+00:34:06,030 --> 00:34:10,390
+حالة ان XII والجامعة I سفارت انتين هذه سفر او هذه
+
+415
+00:34:10,390 --> 00:34:15,770
+سفر هذا trivial caseلو لو كانت كsequences يعني Xi
+
+416
+00:34:15,770 --> 00:34:21,790
+I 00000 أو Gamma I 000 هيكون اللي هو حاصل الضرب
+
+417
+00:34:21,790 --> 00:34:25,170
+هذا سفر ومن ثم هذا هيكون أكبر أو شهر هذا و تموتك
+
+418
+00:34:25,170 --> 00:34:30,110
+بل بساومي تلان سفر الآن شيلنا هذه الحالة سرنا
+
+419
+00:34:30,110 --> 00:34:35,830
+أخدنا الآن أن Xi I و Gamma I تتمتئن among zero
+
+420
+00:34:35,830 --> 00:34:39,670
+sequences يعني في على الأقل term في كل واحدة مش
+
+421
+00:34:39,670 --> 00:34:47,190
+سفر ماشي طيبسمونك psi I تلده هذا الجسر اللي بدأ
+
+422
+00:34:47,190 --> 00:34:52,450
+عبره من خلاله بساويك psi I على القيمة هذه ماشي ايش
+
+423
+00:34:52,450 --> 00:34:58,930
+القيمة هذه اللي هو هذا ال summation اه اه واضح
+
+424
+00:34:58,930 --> 00:35:04,130
+واخدت الجامعة I بساوي الجامعة I تلده بساوي جامعة I
+
+425
+00:35:04,130 --> 00:35:11,660
+على ال summation هذا ماشيواضح؟ الان لو اجينا ضربنا
+
+426
+00:35:11,660 --> 00:35:17,940
+Xi I في Gamma I ماشي الحال حسب ال auxiliary
+
+427
+00:35:17,940 --> 00:35:23,480
+inequality هيها هيها هيها يعني بتاخد ال Alpha إيش
+
+428
+00:35:23,480 --> 00:35:30,040
+بتساوي Xi I تلده و ال Beta إيش بتساوي Gamma I تلده
+
+429
+00:35:30,040 --> 00:35:34,600
+هتساوي هذه أس بي على بي و هذه أس بي Q على مين؟ على
+
+430
+00:35:34,600 --> 00:35:41,390
+Q إذا صارت بالأماميالان لما أخدته هيك خد ال
+
+431
+00:35:41,390 --> 00:35:46,650
+summation اللي هو للجهتين من I1 I شماله إلى مالة
+
+432
+00:35:46,650 --> 00:35:50,150
+نهاية معايا؟ خد ال summation هنا و ال summation
+
+433
+00:35:50,150 --> 00:35:54,570
+هنا أخدنا ال summation و هي ال summation و هي ال
+
+434
+00:35:54,570 --> 00:36:00,270
+main ال summation ماشي الحالطبعا هذا هتلاقوه مضمون
+
+435
+00:36:00,270 --> 00:36:03,870
+ال summation اللي هو finite تبعا لإن هذا الأصل
+
+436
+00:36:03,870 --> 00:36:07,190
+finite و اللي تحت ما هو عبارة عن ياشعن عدد بتاخد
+
+437
+00:36:07,190 --> 00:36:12,630
+أعمل مشترك طيب .. الآن ما يساوي .. الآن نشوف هذا
+
+438
+00:36:12,630 --> 00:36:16,610
+إيش بده يطلع عنها اللي هو xi i في ال summation هنا
+
+439
+00:36:16,610 --> 00:36:23,330
+خدوا هذا و أس بي أس بيبعدين خدوله ال summation
+
+440
+00:36:23,330 --> 00:36:28,610
+مكان هذا معايا الان هذا بيصير رقم الواحدة والتانية
+
+441
+00:36:28,610 --> 00:36:35,810
+زيها الان xi i تلده بيساوي xi i على اللي هو خليني
+
+442
+00:36:35,810 --> 00:36:40,350
+أسمي هذا مثلا scene أو خليني أكتب ليه ليش
+
+443
+00:36:40,350 --> 00:36:47,690
+summation xi iأُس بي وكل أس واحد عالميا على بي
+
+444
+00:36:47,690 --> 00:36:51,670
+معايا إلا أن رفعولي يا أس بي هذا خدولي مدرس يرفعوا
+
+445
+00:36:51,670 --> 00:36:55,870
+أس بي خمدولي مدرس يرفعوا أس بي بتروح هذا ال بي صح
+
+446
+00:36:55,870 --> 00:37:01,050
+هذا رقم هذا رقم بين دايا خدولي ال summation I من
+
+447
+00:37:01,050 --> 00:37:04,530
+عند واحد إلى ما لنهاية خدولي ال summation I من عند
+
+448
+00:37:04,530 --> 00:37:07,750
+واحد إلى ما لنهاية عام مشترك بطلع لأنه عدا فبصير
+
+449
+00:37:07,750 --> 00:37:12,450
+هذا اللي فوق هو اللي تحت إذا مش هيساويوحد صح ولا
+
+450
+00:37:12,450 --> 00:37:17,550
+لأ فبصير عندى هذا المقدار واحد وهذا زيه بالظبط
+
+451
+00:37:17,550 --> 00:37:21,550
+واحد فبصير عبارة عن واحد عربي زي ادمين واحد عربي
+
+452
+00:37:21,550 --> 00:37:22,190
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+453
+00:37:22,190 --> 00:37:22,550
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+454
+00:37:22,550 --> 00:37:23,810
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+455
+00:37:23,810 --> 00:37:27,870
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+456
+00:37:27,870 --> 00:37:28,910
+واحد عربي واحد عربي واحد عربي واحد عربي واحد عربي
+
+457
+00:37:28,910 --> 00:37:29,880
+واحد عربي واحد عربي واحد عربي واحد عربيالـ
+
+458
+00:37:29,880 --> 00:37:37,700
+Summation للـ Xi I Gamma I تلدة I من واحد إلى ما
+
+459
+00:37:37,700 --> 00:37:43,300
+لنهاية أصغر أو يساوي واحد على B زائد واحد على Q
+
+460
+00:37:43,300 --> 00:37:47,200
+اللي هو إيش بتساوي أكتبها واحد وخلاص مافيش داعي أن
+
+461
+00:37:47,200 --> 00:37:55,200
+أتكرر ماشي الحالة الآن بدي أعوض الآن هذه قيمتها Xi
+
+462
+00:37:55,200 --> 00:38:03,750
+I في Gamma Iاللي هي صارت عندي اللي هو automatic
+
+463
+00:38:03,750 --> 00:38:10,750
+منها لما عوض مكانها هذه و هذه، مظبوط؟ بيصير هذه في
+
+464
+00:38:10,750 --> 00:38:16,830
+هذه و هدول تحت بعض، ماشي الحال معايا؟ طيب خلينا
+
+465
+00:38:16,830 --> 00:38:24,150
+نشوف ال summation ل XI I تلدة في جامعة I تلدة I من
+
+466
+00:38:24,150 --> 00:38:30,400
+واحد إلى وين إلى ما إلى النهايةإيش بتساوي اللي هو
+
+467
+00:38:30,400 --> 00:38:37,400
+ال summation معايا أيه هذولة هذولة طلع عليها xi i
+
+468
+00:38:37,400 --> 00:38:44,640
+gamma i مظبوط على اللي هو مين هذولة عاوز مش شركة
+
+469
+00:38:44,640 --> 00:38:53,380
+بتطلع التانية اه اللي هو ال summation لل xi iSB S1
+
+470
+00:38:53,380 --> 00:38:58,540
+على B في الـ summation Gamma I SQ S1 على Q صح ولا
+
+471
+00:38:58,540 --> 00:39:03,880
+لا؟ ماشي، هذا كله إيش ماله؟ قلنا عنه أصغر أو يساوي
+
+472
+00:39:03,880 --> 00:39:10,540
+واحد خلاص، أدر بهذا في هذا، بطلع ال summation Xi I
+
+473
+00:39:10,540 --> 00:39:17,840
+Gamma I أصغر أو يساوي هذا المقدر و هو المخلوق،
+
+474
+00:39:17,840 --> 00:39:24,490
+واضح؟ إيش يا روحي؟بعيد زي ذلك هل جيت احنا هذا
+
+475
+00:39:24,490 --> 00:39:28,570
+عوضنا طاولة طلح هذا صار هذا ما هو احنا ما نقوله من
+
+476
+00:39:28,570 --> 00:39:31,230
+فوق ان هذا اصغر اصغر و واحد اذا صار هذا المقدر
+
+477
+00:39:31,230 --> 00:39:34,530
+اصغر اصغر واحد اضربه طرفين في وساطين بطلع اللي هو
+
+478
+00:39:34,530 --> 00:39:40,110
+ال inequality اللي بدنا اياها يلا اللي بعده نيجي
+
+479
+00:39:40,110 --> 00:39:47,450
+الان اللي هو بس ملاحظةلو كانت بي بتساوي كيو بساوي
+
+480
+00:39:47,450 --> 00:39:53,770
+اتنين بتطلع عندى XII I من واحد ده ماله نهاية باعود
+
+481
+00:39:53,770 --> 00:39:59,270
+بس عن اتنين اصغره ساوي XIK اص نص جامعان اص اتنين
+
+482
+00:39:59,270 --> 00:40:02,970
+اص مين اص نص هذا ال space محترم هذا ال space
+
+483
+00:40:02,970 --> 00:40:07,790
+هنفردله كلام كتير اللي هو بنسميه ال space العناصره
+
+484
+00:40:07,790 --> 00:40:11,950
+اللي هو في ال L2 اسمه ال L2 هذا اسمه Hilbert
+
+485
+00:40:11,950 --> 00:40:15,910
+Sequence Spaceهذا هنحكي عنه بالتفصيل جدا ان شاء
+
+486
+00:40:15,910 --> 00:40:22,470
+الله الان هو في الواقع تعميم .. تعميم هذا .. تعميم
+
+487
+00:40:22,470 --> 00:40:27,790
+للمترك تبعنا تبع زمان لما كنا ناخد ال .. لو أخدنا
+
+488
+00:40:27,790 --> 00:40:34,490
+في ال .. في ال R2 X بالساوي XI واحدو Psi 2 و Y
+
+489
+00:40:34,490 --> 00:40:38,470
+بتساوي Gamma 1 و Gamma 2 إيش كنا ناخد ال metric في
+
+490
+00:40:38,470 --> 00:40:45,330
+الزمان الجدر التربيعي يعني نقص نص Psi 1 ناقص Gamma
+
+491
+00:40:45,330 --> 00:40:50,230
+1 تربيع زاد Psi 2 ناقص Gamma 2 كل إيش ماله تربيع
+
+492
+00:40:50,740 --> 00:40:54,580
+فهذا في الواقع تعميم إلى مانا لنهاية مش عدد اللي
+
+493
+00:40:54,580 --> 00:40:58,780
+هي تنتين لمانا و أيضا تعميم هذا على الار تربيع
+
+494
+00:40:58,780 --> 00:41:01,680
+بنسميه metric عالمين على الار تربيع وهذا مثلا على
+
+495
+00:41:01,680 --> 00:41:04,800
+ال metric على الار تربيع على الار and in general
+
+496
+00:41:06,700 --> 00:41:12,940
+الـ Rn بيكون الـ Dxy بساوة الـ summation للـ Xi I
+
+497
+00:41:12,940 --> 00:41:18,840
+ناقص Gamma I لكل تربيع I من عند 1 لعند N لكل
+
+498
+00:41:18,840 --> 00:41:31,240
+أسمانه أس نص فالـ Rn و كأنه special case لـ L2 بس
+
+499
+00:41:31,240 --> 00:41:36,050
+العماصر من عند N زايد 1 و طالع كل مسفرواضح يعني
+
+500
+00:41:36,050 --> 00:41:39,170
+بتقدر نعملها ك sequence تصير اكساية واحد اكساية
+
+501
+00:41:39,170 --> 00:41:41,790
+اثنين عندك ساعة و بعدين سفر سفر سفر ناشي الحال
+
+502
+00:41:41,790 --> 00:41:46,250
+اطلع اللي بعده يعني لو أثبتنا ان ال LB metric
+
+503
+00:41:46,250 --> 00:41:50,190
+space بيكون أثبتنا ال RN تبعنا تبع زمان و ال R
+
+504
+00:41:50,190 --> 00:41:53,990
+تربيع كله من هذه ال metric spaces يلّا اللي بعده
+
+505
+00:41:53,990 --> 00:42:00,250
+طيب مينكوسكي inequality ناشي الحال ال
+
+506
+00:42:00,250 --> 00:42:06,010
+auxiliary هذهالآن استخدمناها في إثبات مين اللي هو
+
+507
+00:42:06,010 --> 00:42:09,310
+الـHolder in Quality اللي هو Absolute Value أو
+
+508
+00:42:09,310 --> 00:42:14,310
+Modulus XII Gamma I أصغر أو ساوي Summation XII أُس
+
+509
+00:42:14,310 --> 00:42:19,870
+B أُس واحد على B في الـSummation للـGamma I أُس Q
+
+510
+00:42:19,870 --> 00:42:24,890
+أُس واحد على Q هذه الآن هتلزمنا في إثبات اللي هو
+
+511
+00:42:24,890 --> 00:42:31,680
+مينالـ Minkowski Inquality اللي هي الأساس في إثبات
+
+512
+00:42:31,680 --> 00:42:35,960
+الـ Triangular Inquality دخل الواحد كمان لأنه
+
+513
+00:42:35,960 --> 00:42:40,020
+بيقولك إذا كانت B أكبر شو واحد وكان Xi I وGamma I
+
+514
+00:42:40,020 --> 00:42:45,080
+وين موجودة؟ في القلبي، إذا ال summation للXi I زاد
+
+515
+00:42:45,080 --> 00:42:49,540
+Gamma I أس B أس واحد على B أصغر شو ال summation Xi
+
+516
+00:42:49,540 --> 00:42:54,080
+K أس B أس واحد على B زاد ال summation Gamma B أس 2
+
+517
+00:42:54,080 --> 00:42:58,440
+أس واحد على Bالأن حالة الـ B بيساوي واحد هي حالتنا
+
+518
+00:42:58,440 --> 00:43:01,440
+تبعت زمان الـ Triangling Quality لإنه بتصير
+
+519
+00:43:01,440 --> 00:43:06,480
+أشمالها Xi I زائد Gamma I و بس أصغر بساعة الصممشن
+
+520
+00:43:06,480 --> 00:43:11,100
+Xi K زائد الصممشن من Gamma N وهذه نين هي من ال
+
+521
+00:43:11,100 --> 00:43:16,560
+Triangling Quality العادية، ماشي؟ طيب إذا الأن
+
+522
+00:43:16,560 --> 00:43:19,800
+بدنا نبدأ نشتغل على الـ B أكبر من واحد اللي
+
+523
+00:43:19,800 --> 00:43:27,900
+نظريتنا هذه هي إلها صحيحة، ماشي؟ليجي الآن تطلعوا
+
+524
+00:43:27,900 --> 00:43:34,900
+لها الفكرة اللي بده يشتغل فيها ويطبق الـholding
+
+525
+00:43:34,900 --> 00:43:41,360
+quality عليها شوفوا هاي هدفه هو، باشي، بعدين بياخد
+
+526
+00:43:41,360 --> 00:43:44,900
+الـsummation، بعدين، من الحاجين اللي هانجلك خدوا B
+
+527
+00:43:44,900 --> 00:43:48,180
+أكبر من واحد وخد A fixed I يعني بنحكي عن I
+
+528
+00:43:48,180 --> 00:43:54,330
+arbitrarily لكن يشمله I محددوشوفوا Xi I زي Gamma I
+
+529
+00:43:54,330 --> 00:44:00,350
+أُس B بتساوي، بتدفرطها جزئين جزء أُس واحد وجزء أُس
+
+530
+00:44:00,350 --> 00:44:04,650
+B minus واحد، ماشي الحال؟ لأن حاصل الدرب هدولة
+
+531
+00:44:04,650 --> 00:44:09,850
+التنتين شكله بياخد واحدة هذه وواحدة هذه ويشتغل على
+
+532
+00:44:09,850 --> 00:44:15,720
+مين؟ على المنكوسكي طيب، الأن أصغر أو يساوي؟XII
+
+533
+00:44:15,720 --> 00:44:19,460
+زائد gamma I في المقدار هذا وهي الجزء الأول وهي
+
+534
+00:44:19,460 --> 00:44:23,240
+الجزء مين الثاني وقال ال code اللي هو ال summation
+
+535
+00:44:23,240 --> 00:44:27,770
+من عند واحد لعند مين لعند اناهتلاقيه حسب ال
+
+536
+00:44:27,770 --> 00:44:29,770
+equality اللي هنا أصغر أو سوى ال summation على
+
+537
+00:44:29,770 --> 00:44:33,890
+الجهتين هسير ال summation لهذا أصغر أو سوى ال
+
+538
+00:44:33,890 --> 00:44:37,410
+summation لهذا زائد ال summation للثاني أصغر أو
+
+539
+00:44:37,410 --> 00:44:41,710
+سوى ال summation xi i في ال summation هذا أقصى b-1
+
+540
+00:44:41,710 --> 00:44:45,390
+زائد ال summation للثاني أقسمين b-1 وسميها دي إيش
+
+541
+00:44:45,390 --> 00:44:49,970
+واحد، خليني أكتب هنا عشان هتروح من عندنا الآن ال
+
+542
+00:44:49,970 --> 00:44:57,060
+summation لل xi i زائد gamma iأُس بي أصغر أو ساوي
+
+543
+00:44:57,060 --> 00:45:01,860
+طبعا أخد I من واحدة من عند أنه لأنه لسه مش ضامن من
+
+544
+00:45:01,860 --> 00:45:04,880
+واحد إلى ما لا نهاية يكون converge ولا لأ عشان هيك
+
+545
+00:45:04,880 --> 00:45:10,120
+في الآخر حتلاقي أخدها لما يصير الأمر ناضج أنه كل
+
+546
+00:45:10,120 --> 00:45:13,580
+اللي معناه converge فبشتغل عليها اللي هي إلى ما لا
+
+547
+00:45:13,580 --> 00:45:22,500
+نهاية أصغر أو ساوي summation xi Iفي xi i زائد
+
+548
+00:45:22,500 --> 00:45:27,500
+gamma i أس بي ماينس واحد هذه الأولانة زائد
+
+549
+00:45:27,500 --> 00:45:35,780
+summation gamma i في xi i زائد gamma i أس بي ماينس
+
+550
+00:45:35,780 --> 00:45:39,920
+واحد مظبوط؟
+
+551
+00:45:39,920 --> 00:45:46,240
+طيب الآن هذه سموها واحد و أطلع لفوق واستخدموا الآن
+
+552
+00:45:46,240 --> 00:45:51,080
+ال holding quality بدي أستخدمها للأولىأولات تانية
+
+553
+00:45:51,080 --> 00:45:55,300
+خلّينا نستخدم الأولى و نعوض و بعدين بنشتغل الأولى
+
+554
+00:45:55,300 --> 00:46:02,320
+هي هذه و كأنها اللي هي هذه و هذه و كأنها مين جامعة
+
+555
+00:46:02,320 --> 00:46:06,760
+فبيصير أصغر أو ساوي على هذه بدي أطبّق الأولى Exile
+
+556
+00:46:06,760 --> 00:46:11,480
+is بيوس واحد على بيه ماشي الحال هديك على أي من
+
+557
+00:46:11,480 --> 00:46:15,660
+واحد المالانهاية و غيره و تقولولي fine I تانية اه
+
+558
+00:46:15,660 --> 00:46:17,820
+ما هي اللي بتطبق على مالانهاية بتطبق عليها تبعد
+
+559
+00:46:17,820 --> 00:46:23,450
+تبرهن كل الناس فار البجياتماشي فبتصير
+
+560
+00:46:23,450 --> 00:46:26,930
+أس بي أس واحد على بي والتانية بتصير هذه أس بي
+
+561
+00:46:26,930 --> 00:46:31,190
+ماينوس واحد الكل أس كيو أس واحد على مين على كيو
+
+562
+00:46:31,190 --> 00:46:35,690
+مظبوط طبقت مين ال holder inequality اللي هي اللي
+
+563
+00:46:35,690 --> 00:46:40,330
+هنا هي هذه أس كيو أس واحد على كيو هي أس كيو أس
+
+564
+00:46:40,330 --> 00:46:43,910
+واحد على كيو على هذه طبقت اللي هي الأولى هذه بتنزل
+
+565
+00:46:43,910 --> 00:46:47,130
+زي ما هي والتانية بيصير بي ماينوس واحد في مين في
+
+566
+00:46:47,130 --> 00:46:51,810
+كيوالان اللي هي ال .. ال .. ال .. ال .. و هذه أس
+
+567
+00:46:51,810 --> 00:46:56,870
+مين؟ أس واحد على Q، أه؟ الان B minus واحد في Q
+
+568
+00:46:56,870 --> 00:47:02,990
+بتساوي اللي هو مين؟ بتساوي اللي هي B، أه؟ في ده ..
+
+569
+00:47:02,990 --> 00:47:07,270
+في ده أنا أعملها؟ كده؟
+
+570
+00:47:07,270 --> 00:47:11,610
+أه، مظبوط؟
+
+571
+00:47:11,610 --> 00:47:17,380
+أعملها ولا خلاص؟كلهم جايات من مين؟ من 1 على B زائد
+
+572
+00:47:17,380 --> 00:47:23,800
+1 على Q بساوي 1 ماشي الحال طيب الأنصار عندي XI K
+
+573
+00:47:23,800 --> 00:47:30,780
+أس B أس 1 على B وهذه أس B أس 1 على مين؟ على Q واضح
+
+574
+00:47:30,780 --> 00:47:35,500
+اللي بحكيه؟ طيب التانية similarly بنفس الأسلوب
+
+575
+00:47:35,500 --> 00:47:41,320
+Gamma I في XI هذا عملناها مين يا جماعة؟ هذه هي
+
+576
+00:47:41,320 --> 00:47:48,930
+أصغر أو يساوي هذههذه التانية بالظبط زيها بس بدل
+
+577
+00:47:48,930 --> 00:47:53,410
+لكساي I بتاخد 100 Gram I ماشي الحال إذا خلّيني
+
+578
+00:47:53,410 --> 00:48:01,430
+أسجلها هادي هان أصغر أو يساوي summation XI K أُس B
+
+579
+00:48:01,430 --> 00:48:11,610
+أُس 1 على B في summation XI M زائد Gram M أُس B
+
+580
+00:48:11,610 --> 00:48:13,290
+أُس 1 على 100
+
+581
+00:48:16,590 --> 00:48:22,830
+واضح اه طيب التانية نفس الاشي بس بدل هذه بده احط
+
+582
+00:48:22,830 --> 00:48:27,510
+هذه ماشي فبصير هذه و هذه زي بعض هذه زي الأولى و
+
+583
+00:48:27,510 --> 00:48:32,810
+هذه زائد زائد summation بدل هذه مين هيكون gamma K
+
+584
+00:48:32,810 --> 00:48:41,320
+أس بي أس واحد على بي في ال summation نفسهنفسه
+
+585
+00:48:41,320 --> 00:48:45,280
+ناخده مين عالم المشترك بيصير هذا ويساوي ال
+
+586
+00:48:45,280 --> 00:48:49,400
+summation اللي عامل المشترك هذا هذا مضروب في مين
+
+587
+00:48:49,400 --> 00:48:53,960
+في ال summation gamma k أس بي زاد ال summation
+
+588
+00:48:53,960 --> 00:49:04,700
+اكسايكل ونفعله هذي gamma k أس واحد على بي أس بي أس
+
+589
+00:49:04,700 --> 00:49:10,150
+مينواحد على كيو صح اطلع على فوق نشوف ده عشان نقول
+
+590
+00:49:10,150 --> 00:49:23,850
+خربطنا مافي حاجة substitute
+
+591
+00:49:23,850 --> 00:49:28,210
+of the two inequalities in main in واحد فبصير اللي
+
+592
+00:49:28,210 --> 00:49:30,250
+هو ان شاء الله مانكون خربطناش في الحسابات
+
+593
+00:49:37,050 --> 00:49:47,950
+أه واحد على Q و لا .. خلّيني أرجع لها هذه
+
+594
+00:49:47,950 --> 00:49:54,610
+واحد على B وهذه اللي هي التانية واحد على B أظن
+
+595
+00:49:54,610 --> 00:49:57,750
+واحد على B خلّيني أرجع لها دقيقة .. دقيقة .. دقيقة
+
+596
+00:49:57,750 --> 00:50:00,170
+.. دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة ..
+
+597
+00:50:00,170 --> 00:50:00,730
+.. دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة ..
+
+598
+00:50:00,730 --> 00:50:00,770
+.. دقيقة .. دقيقة .. دقيقة .. دقيقة .. دقيقة ..
+
+599
+00:50:00,770 --> 00:50:00,850
+دقيقة .. دقيقة
+
+600
+00:50:05,230 --> 00:50:21,290
+بـ-1 في Q أس واحد على Q لأ
+
+601
+00:50:21,290 --> 00:50:28,110
+تبقى تلعاب المشتراك التنتين واحد على Qوحد على بي
+
+602
+00:50:28,110 --> 00:50:34,350
+وحد على بي وحد على بي مظبوط ان هذه الواحد على بي و
+
+603
+00:50:34,350 --> 00:50:44,810
+هذه يشبهلها واحد على بي طيب شوف ال .. تبهوا لوين
+
+604
+00:50:44,810 --> 00:50:52,250
+احنا وصلنا .. خليني أمسح حاجة، ميمش؟ بصير عند ال
+
+605
+00:50:52,250 --> 00:50:55,690
+.. and summation
+
+606
+00:50:56,990 --> 00:51:02,850
+Summation هذا شايفينه هذا هذا هذا أصغر أو يساوي
+
+607
+00:51:02,850 --> 00:51:05,950
+اللي هو هذا ال summation و هذا ال summation زائد
+
+608
+00:51:05,950 --> 00:51:10,850
+هذا و قلنا هنا خد عامل مشترك اللي هو هذا شايفينه
+
+609
+00:51:10,850 --> 00:51:16,450
+هاي هاي هذا عامل مشترك دل هذا و دل هذا فطلعنا هذا
+
+610
+00:51:16,450 --> 00:51:20,630
+العامل المشترك هاي و هان و هذول الجمع هاي هان ماشي
+
+611
+00:51:20,630 --> 00:51:24,950
+الحالة الان لاحظوا على هذا و هذا
+
+612
+00:51:27,950 --> 00:51:32,510
+نفس الاشي بس هذا أس واحد على Q و هذا أس واحد فلما
+
+613
+00:51:32,510 --> 00:51:35,730
+أجسم عليها بيصير اللي هو اللي على الطرف هنا أس
+
+614
+00:51:35,730 --> 00:51:40,920
+واحد ماقص واحد على Qواضحة فبصير عنده الآن ال
+
+615
+00:51:40,920 --> 00:51:44,740
+summation هذا اللي حكيته عن نقص واحد ناقص مين واحد
+
+616
+00:51:44,740 --> 00:51:48,620
+على Q اللي هو أصغر أو أساوي هذا بيظل زي ما هو وهذا
+
+617
+00:51:48,620 --> 00:51:53,660
+بيظل زي ما هو قبل N واحد ناقص واحد على Q هو واحد
+
+618
+00:51:53,660 --> 00:51:59,000
+على P مصدود واحد على P واحد على P فبصير عنده الآن
+
+619
+00:51:59,000 --> 00:52:04,480
+هذاصار عبارة عن واحد على بيه ماعليش ده شو جودني
+
+620
+00:52:04,480 --> 00:52:08,140
+بتبقى كتير واحد على مين على بيه الان صار هذا
+
+621
+00:52:08,140 --> 00:52:10,940
+المقدار واحد على بيه و هذا واحد على بيه و هذا واحد
+
+622
+00:52:10,940 --> 00:52:15,360
+على بيه و ال submissions اتوزع زي اللي انا اصلا
+
+623
+00:52:15,360 --> 00:52:23,340
+بروح بدياها الان انا مرتاحهاخد الأن مالة تروح
+
+624
+00:52:23,340 --> 00:52:27,020
+لمالة نهاية ليش مرتاح لإنه ضامن هذا converge زي
+
+625
+00:52:27,020 --> 00:52:29,860
+إنه هذا في القلبي وضامن هذا converge زي إنه في
+
+626
+00:52:29,860 --> 00:52:35,300
+القلبي فبصير عندي هذا من واحد إلى مالة نهاية بالهو
+
+627
+00:52:35,300 --> 00:52:39,840
+اللي أنا بديه أزرع يساوي هذا أس واحد على بيه زائد
+
+628
+00:52:39,840 --> 00:52:42,420
+هذا أس واحد على بيه وكامن واحد إلى مالة نهاية
+
+629
+00:52:42,420 --> 00:52:47,800
+وبكون حصلت عالميا على المينكوسكي in quad واضح
+
+630
+00:52:49,660 --> 00:52:54,420
+طيب، صلى على النبل أسوأ السنة الآن أصلنا للثمرة
+
+631
+00:52:54,420 --> 00:52:58,160
+اللي بتنيها اللي هو الـ sequence space اللي هو مين
+
+632
+00:52:58,160 --> 00:53:04,100
+الـ LB space قلنا الآن consider the asset LB of
+
+633
+00:53:04,100 --> 00:53:08,160
+all sequences of numbers XI I such that الـ
+
+634
+00:53:08,160 --> 00:53:11,380
+summation هذا يكون أشماله converts أو is finite
+
+635
+00:53:11,380 --> 00:53:15,880
+هذه الـ sequences اللي بالخاصية هذه هي اللي بتعمل
+
+636
+00:53:15,880 --> 00:53:22,660
+للـ LBالـ B تحت الـ D اللي في الأول أنا عرفته اللي
+
+637
+00:53:22,660 --> 00:53:26,760
+هو هيه .. هيه عندي D X Y بساوية summation X I I
+
+638
+00:53:26,760 --> 00:53:31,100
+نقص جمعي أس بيقص واحد على B هيعملني metric على الـ
+
+639
+00:53:31,100 --> 00:53:37,610
+B فبصير الـ B عبارة عن metric spaceالان هى المث
+
+640
+00:53:37,610 --> 00:53:43,010
+هذا اللى بنثبته بحقق الخصية الأول واحد اتنين تلاتة
+
+641
+00:53:43,010 --> 00:53:46,130
+أربعة الخصية الأوله automatic أكبر بساوية صفر هين
+
+642
+00:53:46,130 --> 00:53:50,450
+اللى هو بساوية صفر F وان دول F هذى بتساوي هذى يعني
+
+643
+00:53:50,450 --> 00:53:56,480
+X بتساوي Yباللي هو الـ x و y هي نفسها y و x تبع
+
+644
+00:53:56,480 --> 00:53:59,500
+الهادي الآن الخاصية الأخيرة الاتنين in quality
+
+645
+00:53:59,500 --> 00:54:03,520
+جاهزين لها ليش جاهزين لها من ال min cost ك in
+
+646
+00:54:03,520 --> 00:54:07,960
+quality شوفوا كيف احنا جاهزين منها هتلاقوا الأمر
+
+647
+00:54:07,960 --> 00:54:13,490
+automatic بطلع خدوا اي x بساوي psi iو Y بيساوي
+
+648
+00:54:13,490 --> 00:54:16,830
+Gamma I و Z بيساوي Beta I كل هى اللى موجودات فى
+
+649
+00:54:16,830 --> 00:54:22,070
+القلبى خد المسافة X Y بين X Y اللى احنا عرفنا ال
+
+650
+00:54:22,070 --> 00:54:27,070
+metric على أساسها اللى هو بيساوي هذه قطعا اللى هو
+
+651
+00:54:27,810 --> 00:54:32,270
+اللي جوا بس بدي .. بعد إذن كُن بدي أكتبها بضاطيف
+
+652
+00:54:32,270 --> 00:54:36,750
+Beta I واش ونقص Beta I بصير أصغر أو يساوي
+
+653
+00:54:36,750 --> 00:54:40,350
+وأستخدمين الـ Triangling الـ Quality العادية اللي
+
+654
+00:54:40,350 --> 00:54:44,990
+هو XI I نقص Beta I زي ال Beta I نقص من XI I وخلّي
+
+655
+00:54:44,990 --> 00:54:49,610
+.. يعني اشتغل هذه أصغر أو يساوي هذه وهذه B وهذه B
+
+656
+00:54:49,610 --> 00:54:54,220
+واحدة على B واحدة على B فاهمين؟طيب، الآن هذا بيصير
+
+657
+00:54:54,220 --> 00:54:57,760
+عندى حسب المنكسك inequality اللى قبل بشوية هذا
+
+658
+00:54:57,760 --> 00:55:02,900
+لحاله و هذا لحاله هذا بيصير أس بي سواحد على بي و
+
+659
+00:55:02,900 --> 00:55:07,820
+هذا بيصير أس كيو سواحد على كيو فاهمين؟ هذا اللى هو
+
+660
+00:55:07,820 --> 00:55:14,800
+استخدام المنكسك اللى مسحتها مباشرة يعني هذا بيمثل
+
+661
+00:55:14,800 --> 00:55:18,660
+في المنكسك اللى قبل شوية XII و هذا بيمثل Gamma I
+
+662
+00:55:19,950 --> 00:55:26,370
+فطبقتها فطلعت هذه زائد هذه هذه اللي هي DXY DX و Z
+
+663
+00:55:26,370 --> 00:55:30,810
+هي طبعت ال XY ال Z و هذي DY و Z و هيك بيكون عندنا
+
+664
+00:55:30,810 --> 00:55:35,610
+أثبتنا أن هذا عبارة عن مين عن metric space في حالة
+
+665
+00:55:35,610 --> 00:55:40,030
+ال B بالساوة اتنين قولنا هذا metric محترم بنعتبره
+
+666
+00:55:40,490 --> 00:55:44,430
+اللي هو اسمه الهيلبارد سبايس الهيلبارد سيكوينس
+
+667
+00:55:44,430 --> 00:55:49,350
+سبايس الهيلبارد
+
+668
+00:55:49,350 --> 00:55:50,170
+سيكوينس سبايس الهيلبارد سيكوينس سبايس الهيلبارد
+
+669
+00:55:50,170 --> 00:55:51,050
+سيكوينس سبايس الهيلبارد سيكوينس سبايس الهيلبارد
+
+670
+00:55:51,050 --> 00:55:51,110
+سيكوينس سبايس الهيلبارد سيكوينس سبايس الهيلبارد
+
+671
+00:55:51,110 --> 00:55:53,090
+سيكوينس سبايس الهيلبارد سيكوينس سبايس الهيلبارد
+
+672
+00:55:53,090 --> 00:55:55,810
+سيكوينس سبايس الهيلبارد سيكوينس سبايساللي هو
+
+673
+00:55:55,810 --> 00:55:59,390
+العناصر اللي هي X,Y,I,Y الـ R تكعيب اتبعنا اللي هو
+
+674
+00:55:59,390 --> 00:56:02,410
+الـ Ordered Pair اللي هو هذا الـDXY اللي هو الجذر
+
+675
+00:56:02,410 --> 00:56:06,410
+التربيهي اللي حكيته قبل وشوية حالة خاصة منه والـR
+
+676
+00:56:06,410 --> 00:56:13,170
+تكعيب اللي بنفس الأسلوب بنعرفه حالة خاصة لأرضه
+
+677
+00:56:13,170 --> 00:56:18,130
+منين من الـL2 Space وكل هنا بنكون أثبتناه
+
+678
+00:56:18,130 --> 00:56:22,310
+الـMetric Space مادام أثبتنا مين اللي هو الـB in
+
+679
+00:56:22,310 --> 00:56:25,830
+general is a metric spaceلأنه بنعتبر الباقي اللي
+
+680
+00:56:25,830 --> 00:56:30,930
+هو إيش اللي هي أصفار والـ RN برضه زي ما قلت قبل
+
+681
+00:56:30,930 --> 00:56:35,070
+شوية نفس الأسلوب في حالة الـCN الـCN برضه نفس
+
+682
+00:56:35,070 --> 00:56:38,050
+الاشي بس باخد بدل التربية إيش باخد للمدرس عشان
+
+683
+00:56:38,050 --> 00:56:43,350
+يصير إن أعداد يطلع قيمةلأن عشان يطلع DXY عبارة عن
+
+684
+00:56:43,350 --> 00:56:48,310
+عدد فباخد المدرس فبكون هذا عبارة عن ال CN و بيكون
+
+685
+00:56:48,310 --> 00:56:52,750
+كل الحلات خاصة من اللي حكيته قبل بشوية و بيكون
+
+686
+00:56:52,750 --> 00:56:58,310
+معكم exercise الآن هذا اللي عندى بالاضافة ده
+
+687
+00:56:58,310 --> 00:57:03,150
+تمانية و عشرة هدولكم السيرمونيان و هدولة اللي هو
+
+688
+00:57:03,150 --> 00:57:07,790
+حلون و فيها العمون الحلون الموجودة عندى اللي
+
+689
+00:57:07,790 --> 00:57:12,270
+ماعرفش حاجة بنعطيها ان شاء اللهوبرك الله فيكم و
+
+690
+00:57:12,270 --> 00:57:13,110
+الله يعطيكم العافية
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RstVGUoRP6o_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RstVGUoRP6o_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..cd9dc16fa693dcc529f49b4e49c71f3b229681e3
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/RstVGUoRP6o_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3146, "start": 5.36, "end": 31.46, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام علي سيد المرسلين هذه المحاضرة الثانية في مساق تحليل اقتراني او تحليل دالي لطلب طلبات الماجستير الجامعة الإسلامية بغزا حكينا المرة الماضية بدأنا في المحاضرة الأولى حكينا عن ال metric space", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 25894, 8608, 25708, 9673, 2288, 3794, 1211, 9957, 29538, 9673, 5016, 46958, 25720, 6024, 104, 7649, 10632, 8978, 47524, 995, 4587, 6055, 5016, 20292, 1211, 1975, 38149, 2288, 7649, 1829, 1975, 2407, 6055, 5016, 20292, 1211, 11778, 6027, 1829, 5296, 9566, 46152, 23032, 46152, 9307, 9673, 26108, 14851, 13546, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 4724, 17082, 11622, 995, 11331, 4117, 1829, 8315, 9673, 25720, 9673, 46958, 10632, 47525, 10721, 8315, 8978, 9673, 5016, 46958, 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اللي هو يعني في عندي أمثلة أخرى غير الأمثلة اللي حكيناها المرة الماضية أول مثال بدي أحكي عنه", "tokens": [1863, 1829, 7435, 1829, 5296, 7649, 3714, 2407, 11242, 45367, 8315, 45595, 20498, 8717, 44510, 10721, 8978, 3714, 5016, 46958, 43500, 8315, 45595, 20498, 16472, 13412, 16606, 21984, 4724, 5172, 36520, 6055, 5172, 9381, 26895, 13672, 1829, 47525, 8315, 8717, 5016, 4117, 1829, 3224, 5296, 7649, 3052, 5110, 295, 20678, 318, 17949, 13672, 1829, 31439, 37495, 22653, 8978, 18871, 16254, 5551, 2304, 12984, 37977, 5551, 34740, 7578, 32771, 13546, 16247, 2304, 12984, 37977, 13672, 1829, 11331, 4117, 1829, 8315, 11296, 9673, 25720, 9673, 46958, 10632, 5551, 12610, 50113, 6027, 4724, 16254, 5551, 5016, 4117, 1829, 18871, 3224], "avg_logprob": -0.14644451804307043, "compression_ratio": 1.665137614678899, "no_speech_prob": 1.4185905456542969e-05, "words": [{"start": 343.29, "end": 343.73, "word": "نيجي", "probability": 0.649017333984375}, {"start": 343.73, "end": 343.93, "word": " لان", 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"word": " هو", "probability": 0.8681640625}, {"start": 3423.15, "end": 3424.21, "word": " حلون", "probability": 0.8837890625}, {"start": 3424.21, "end": 3424.33, "word": " و", "probability": 0.958984375}, {"start": 3424.33, "end": 3424.61, "word": " فيها", "probability": 0.650390625}, {"start": 3424.61, "end": 3425.15, "word": " العمون", "probability": 0.5558268229166666}, {"start": 3425.15, "end": 3425.43, "word": " الحلون", "probability": 0.9720052083333334}, {"start": 3425.43, "end": 3426.11, "word": " الموجودة", "probability": 0.9078369140625}, {"start": 3426.11, "end": 3427.39, "word": " عندى", "probability": 0.6812744140625}, {"start": 3427.39, "end": 3427.79, "word": " اللي", "probability": 0.939453125}, {"start": 3427.79, "end": 3428.33, "word": " ماعرفش", "probability": 0.8896484375}, {"start": 3428.33, "end": 3428.79, "word": " حاجة", "probability": 0.7587890625}, {"start": 3428.79, "end": 3429.71, "word": " بنعطيها", "probability": 0.873046875}, {"start": 3429.71, "end": 3429.89, "word": " ان", "probability": 0.73388671875}, {"start": 3429.89, "end": 3430.13, "word": " شاء", "probability": 0.92822265625}, {"start": 3430.13, "end": 3430.15, "word": " الله", "probability": 0.93408203125}], "temperature": 1.0}, {"id": 143, "seek": 343311, "start": 3431.29, "end": 3433.11, "text": "وبرك الله فيكم و الله يعطيكم العافية", "tokens": [2407, 26890, 4117, 21984, 8978, 24793, 4032, 21984, 37495, 9566, 1829, 24793, 18863, 31845, 10632], "avg_logprob": -0.2531738206744194, "compression_ratio": 1.2, "no_speech_prob": 0.0, "words": [{"start": 3431.29, "end": 3431.73, "word": "وبرك", "probability": 0.63818359375}, {"start": 3431.73, "end": 3431.85, "word": " الله", "probability": 0.96630859375}, {"start": 3431.85, "end": 3432.15, "word": " فيكم", "probability": 0.962890625}, {"start": 3432.15, "end": 3432.27, "word": " و", "probability": 0.383544921875}, {"start": 3432.27, "end": 3432.35, "word": " الله", "probability": 0.93505859375}, {"start": 3432.35, "end": 3432.67, "word": " يعطيكم", "probability": 0.8753662109375}, {"start": 3432.67, "end": 3433.11, "word": " العافية", "probability": 0.8292643229166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3433.256, "duration_after_vad": 3340.9468749999855}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/T3dQGYbQlAQ_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/T3dQGYbQlAQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e8bc9e260af7c9fd54e9ca180fd72bb816e1ad43
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/T3dQGYbQlAQ_postprocess.srt
@@ -0,0 +1,2340 @@
+1
+00:00:05,110 --> 00:00:07,970
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,970 --> 00:00:10,930
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,930 --> 00:00:15,650
+آله وصحبه أجمعين هذه المحاضرة رقم 27 مساق تحليل
+
+4
+00:00:15,650 --> 00:00:19,210
+اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:19,210 --> 00:00:24,290
+الإسلامية قسم الرياضيات للطلاب وطالبات الماجستير
+
+6
+00:00:25,410 --> 00:00:29,350
+أوصلنا لعند ال section التاني في chapter أربعة و
+
+7
+00:00:29,350 --> 00:00:32,550
+ال section هذا اللي هو نيجي اللي هو اسمه أربعة
+
+8
+00:00:32,550 --> 00:00:36,670
+اتنين هان بنخ تيرم و هان هنحكي عن إحدى النظريات
+
+9
+00:00:36,670 --> 00:00:43,310
+الأساسية في اللي هو التحليل الدالي جابل ما نبدأ
+
+10
+00:00:43,310 --> 00:00:47,230
+نحكي عن النظرية بدنا اللي هو نحكي عنها لبعض
+
+11
+00:00:47,230 --> 00:00:52,670
+التعريفات اللي هتلزمنا في اللي هي النظرية القادمة
+
+12
+00:00:53,740 --> 00:00:56,320
+التعريف الأول اربعة اتنين واحد definition a
+
+13
+00:00:56,320 --> 00:00:59,060
+sublinear functional sublinear احنا بنعرف ال
+
+14
+00:00:59,060 --> 00:01:01,840
+linear functional اللي عن sublinear functional is
+
+15
+00:01:01,840 --> 00:01:06,760
+a real valued function B on a vector space X لما
+
+16
+00:01:06,760 --> 00:01:11,700
+نحكي عن sublinear بحكي عن ايش بحكي عن اللي هو a
+
+17
+00:01:11,700 --> 00:01:14,540
+real valued function لأنه انا بتحكي عن order أصغر
+
+18
+00:01:14,540 --> 00:01:16,460
+أو يساوي انتوا عارفين في ال complex فيش اصغر أو
+
+19
+00:01:16,460 --> 00:01:19,760
+يساوي فيش order بمعنى اخر في ال complex field اللي
+
+20
+00:01:19,760 --> 00:01:20,440
+احنا بنعرفه
+
+21
+00:01:24,990 --> 00:01:28,150
+بحقق الشروط التالية عشان نكون sub linear الشرط
+
+22
+00:01:28,150 --> 00:01:31,870
+الأول بيكس زائد واي أصغر شهو بيكس زائد بي واي for
+
+23
+00:01:31,870 --> 00:01:35,610
+all x و y element in x وهذا اللي استدعت انه يكون
+
+24
+00:01:35,610 --> 00:01:40,290
+real valued functionبـ Positive Homogeneous بألفة
+
+25
+00:01:40,290 --> 00:01:47,470
+X Positive و Homogeneous بألفة
+
+26
+00:01:47,470 --> 00:01:51,290
+X أو أكبر يساوي سفر الألف بألفة X يساوي ألفة في B
+
+27
+00:01:51,290 --> 00:01:54,570
+of X for all X limited in X and all ألف أكبر أو
+
+28
+00:01:54,570 --> 00:01:58,770
+يساوي سفر إذا اتحقق الشرطين اللي أمامنا هذول بنسمي
+
+29
+00:01:58,770 --> 00:02:02,550
+اللي هو الـ B is a sublinear اللي هي functional
+
+30
+00:02:02,550 --> 00:02:06,210
+لإنها بترمي في ال field اللي عندنا اللي هو فعلا ال
+
+31
+00:02:06,210 --> 00:02:10,000
+fieldالـ R اللي هو الـ Real Value يعني الان نجي
+
+32
+00:02:10,000 --> 00:02:14,940
+لانبنغثيورم الانبنغثيورم هذه اللي هو لان فيه أكثر
+
+33
+00:02:14,940 --> 00:02:18,980
+من Formة هناخده ال Formة اللي بتتعامل اول اشي مع
+
+34
+00:02:18,980 --> 00:02:22,280
+vector space بس بعد شوية بنحكي عن اللي هو ال
+
+35
+00:02:22,280 --> 00:02:24,500
+normed space اللي احنا نسبقله اللي هي النظرية اللي
+
+36
+00:02:24,500 --> 00:02:27,540
+بنحكي عنها النظرية الأساسية فهذه النظرية اللي
+
+37
+00:02:27,540 --> 00:02:31,320
+خلينا نقول اللي هي مقدمة للنظرية اللي بعد هيك اللي
+
+38
+00:02:31,320 --> 00:02:36,350
+هي بتحكي على اللي هو normed space in generalخلّينا
+
+39
+00:02:36,350 --> 00:02:39,770
+نشوف طبعا النظرية هي extension ل linear functional
+
+40
+00:02:39,770 --> 00:02:43,310
+يعني بمعنى أخر بدنا نمد فلاحية ال linear
+
+41
+00:02:43,310 --> 00:02:47,450
+functional بحيث أنه يشتغل على vector space أوسع من
+
+42
+00:02:47,450 --> 00:02:52,820
+اللي هو عليه وبخواص معينة خلّينا نشوفهيقولنا
+
+43
+00:02:52,820 --> 00:02:56,620
+extension of linear functional زي هي اللي بتتحدث
+
+44
+00:02:56,620 --> 00:03:00,140
+عنه ال handbanach theorem let X be a real vector
+
+45
+00:03:00,140 --> 00:03:03,060
+space إذا نحكي عن real vector space بعد شوية هنحكي
+
+46
+00:03:03,060 --> 00:03:07,120
+عن complex and B is a sublinear functional on X
+
+47
+00:03:07,120 --> 00:03:09,480
+طبعا لما نحكي عن complex بنعالج اللي هي قصة اللي
+
+48
+00:03:09,480 --> 00:03:13,240
+هي linear functional بطريقة معينة اللي هي real
+
+49
+00:03:13,240 --> 00:03:16,600
+valued هذه and B is a sublinear functional on X
+
+50
+00:03:17,790 --> 00:03:21,550
+Furthermore، خلّينا نعتبر F Linear Functional،
+
+51
+00:03:21,550 --> 00:03:27,570
+which is defined on جزء من الـ X، on Z، من عصابة
+
+52
+00:03:27,570 --> 00:03:33,810
+Space، اللي هو Z of X، and satisfies F of X أصغر
+
+53
+00:03:33,810 --> 00:03:34,830
+يسوا بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+54
+00:03:34,830 --> 00:03:35,550
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+55
+00:03:35,550 --> 00:03:35,770
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+56
+00:03:35,770 --> 00:03:38,640
+بيه بيه بيه بيه بيهإذن الآن المعطيات اللي عندي ال
+
+57
+00:03:38,640 --> 00:03:41,940
+functional اللي عندي هذه ال linear functional هي
+
+58
+00:03:41,940 --> 00:03:45,200
+عبارة عن linear functional على جزء من ال space X
+
+59
+00:03:45,200 --> 00:03:50,900
+على sub space من ال space X وتحقق شاطر شخصية F of
+
+60
+00:03:50,900 --> 00:03:54,100
+X أصغر سوا بيه F of X الغبط من هذه النظرية أن أنا
+
+61
+00:03:54,100 --> 00:03:59,520
+بتدوسع نفوذ ال F هذهأخليها بدل ما هي على Z أعملها
+
+62
+00:03:59,520 --> 00:04:02,380
+extension تشغل على مين؟ على كل ال X يعني تبقى
+
+63
+00:04:02,380 --> 00:04:06,760
+محافظة على شغل على ال Z بنفس الخواص ومن ثم تنطلق
+
+64
+00:04:06,760 --> 00:04:12,660
+لتكون أوسع على ال X الكبيرة وتحافظ على الخواص
+
+65
+00:04:12,660 --> 00:04:21,010
+الموجودة بمعنى الآناللي بحتيه then f has a linear
+
+66
+00:04:21,010 --> 00:04:25,070
+extension هذا المطلوب f تلده الان from z to b into
+
+67
+00:04:25,070 --> 00:04:28,950
+x يعني هال linear extension خطة z و هيشغل عالميا
+
+68
+00:04:28,950 --> 00:04:34,330
+على كل x f تلده على ال x هتصير satisfying برضه
+
+69
+00:04:34,330 --> 00:04:38,250
+هتحقق نفس الشروط f تلده of x أصغر أو أصغر بيه of x
+
+70
+00:04:38,250 --> 00:04:42,950
+لكل x من الموجودة لكل x element in x هذه هي اللي
+
+71
+00:04:42,950 --> 00:04:52,320
+هي اللي مطلوب انه انا اوسع كانت fموجودة من Z إلى R
+
+72
+00:04:52,320 --> 00:04:59,050
+أو إلى اللي هي و كأو بدأ و عند Zsub space من X بدي
+
+73
+00:04:59,050 --> 00:05:03,210
+أجيب F تلده طبعا لو كان اتدت حقق هواس ان F of X
+
+74
+00:05:03,210 --> 00:05:05,470
+أصغر يساوي بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+75
+00:05:05,470 --> 00:05:07,190
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+76
+00:05:07,190 --> 00:05:07,470
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+77
+00:05:07,470 --> 00:05:07,630
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+78
+00:05:07,630 --> 00:05:13,750
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+79
+00:05:13,750 --> 00:05:25,320
+بيه بيه بتحقق F تلدة of X أصغر يساوي P of X لكل X
+
+80
+00:05:25,320 --> 00:05:30,320
+الأنوار الموجودة مش في Z بس فكل X اللي عندي لأن
+
+81
+00:05:30,320 --> 00:05:34,920
+الفكرة .. الفكرة .. الفكرة من الحل أنه أنا بدي
+
+82
+00:05:34,920 --> 00:05:40,040
+أجيب عائلة و أسميها إيه؟ هذه عائلة من الدوال هي
+
+83
+00:05:40,040 --> 00:05:42,480
+فعلا عائلة .. هحكي عنها عائلة من extension
+
+84
+00:05:42,480 --> 00:05:48,960
+functions لل-Fو قادي اللي هو عرف عليها partial
+
+85
+00:05:48,960 --> 00:05:51,780
+order relation بطريقة معينة هتشوفوها بعد شوية
+
+86
+00:05:51,780 --> 00:05:57,720
+هتعمل هذه non-empty set of .. of .. of .. of .. of
+
+87
+00:05:57,720 --> 00:06:01,780
+ordered أو non-empty ordered set بالنسبة لهذه ال
+
+88
+00:06:01,780 --> 00:06:05,540
+partial order relation و هلاجي ان كل ال chain فيها
+
+89
+00:06:05,540 --> 00:06:11,630
+انها ايش انها upper boundمنها هذه طبعاً بتكون شروط
+
+90
+00:06:11,630 --> 00:06:17,510
+zones لما اتحققت هيكون في عندى في maximal element
+
+91
+00:06:17,510 --> 00:06:21,190
+الآن ال maximal element هذا هو after ده هو اللي
+
+92
+00:06:21,190 --> 00:06:24,970
+حاتبته ال maximal element هو اللي بأد الغرض لهيك
+
+93
+00:06:24,970 --> 00:06:29,730
+هذه الاستراتيجية تبعت برهان النظرية ودعونا ندخل
+
+94
+00:06:29,730 --> 00:06:32,030
+الآن إلى التفاصيل
+
+95
+00:06:34,700 --> 00:06:38,940
+صلوا على النبي عليه الصلاة والسلام نشوف تفاصيل
+
+96
+00:06:38,940 --> 00:06:44,500
+الحديث الان بقول لي let E اللي وعدتكم فيها be the
+
+97
+00:06:44,500 --> 00:06:47,760
+set of all linear extensions عبارة عن كل ال linear
+
+98
+00:06:47,760 --> 00:06:52,160
+extensions بتسميها G لمين؟ لل F اللي احنا بدأنا
+
+99
+00:06:52,160 --> 00:06:55,900
+فيها that satisfy برضه هذه ال extension ليش بديها
+
+100
+00:06:55,900 --> 00:07:00,520
+يحقق G of X أصغر يساوي ب X لكل X وين موجود في
+
+101
+00:07:00,520 --> 00:07:04,790
+domain ال extension تبع G هذاهي الـ Ne عبارة عن
+
+102
+00:07:04,790 --> 00:07:08,930
+هذه العائلة أول إشي بقولك مدام العائلة هي عبارة عن
+
+103
+00:07:08,930 --> 00:07:12,830
+هذا ال F نفسها اللي موجودة اللي معطيني إياها أنا
+
+104
+00:07:12,830 --> 00:07:17,490
+هي نفسها تحقق هذه الشروط هي extension لنفسها على
+
+105
+00:07:17,490 --> 00:07:21,210
+نفس ال domain بس بتصير هو تحقق أن F of X أصغر سوى
+
+106
+00:07:21,210 --> 00:07:25,550
+B of X وفي نفس ال .. لكل X والي موجودة في domainها
+
+107
+00:07:25,550 --> 00:07:30,060
+اللي هو مين كان Zإذا أكيد أكيد أكيد ال F نفسه
+
+108
+00:07:30,060 --> 00:07:36,170
+الموجود في ال E إذا ال E is a non-empty setالشغلة
+
+109
+00:07:36,170 --> 00:07:41,910
+الثانية define on E a partial ordering by بدي اعرف
+
+110
+00:07:41,910 --> 00:07:44,870
+على ال D ايش ماله partial order relation اكيد انا
+
+111
+00:07:44,870 --> 00:07:47,950
+جاعد شغال في ال extension فهكيد هفكر في ال partial
+
+112
+00:07:47,950 --> 00:07:51,690
+order relation بناء على هذا ال extension فبصير
+
+113
+00:07:51,690 --> 00:07:54,350
+عندي الان المعرفه انا define on E a partial order
+
+114
+00:07:54,350 --> 00:07:58,890
+relation by D أصغر أو شومين Hكيف يكون G أصغر و
+
+115
+00:07:58,890 --> 00:08:04,310
+أصغر H؟ if and only if H is an extension of مين of
+
+116
+00:08:04,310 --> 00:08:08,490
+G يعني الآن بقول التنتين العنصرين اللي في E
+
+117
+00:08:08,490 --> 00:08:12,730
+بيكونون اللي انعلاقة في بعض إذا كان A شماله الـG
+
+118
+00:08:12,730 --> 00:08:17,710
+الـH extension لمين؟ للـG واضح؟ هذه هي ال partial
+
+119
+00:08:17,710 --> 00:08:24,160
+order relation طيبالان بدي اجيب .. بدي اخد اي
+
+120
+00:08:24,160 --> 00:08:28,600
+chain C subset من ايه و بدي اثبتلك ان ال chain C
+
+121
+00:08:28,600 --> 00:08:32,500
+هذه زي ما قلت هنا ال chain C .. بدي احقق شروط
+
+122
+00:08:32,500 --> 00:08:35,500
+zones لما ال chain .. ال .. ال chain C اخد
+
+123
+00:08:35,500 --> 00:08:39,380
+arbitrary ال chain C و اقولك لازم يكون فيها upper
+
+124
+00:08:39,380 --> 00:08:42,120
+bound اذا كان فيها upper bound automatic صار كل
+
+125
+00:08:42,120 --> 00:08:44,860
+chain اللي لها upper bound اذا حسب zones لما لازم
+
+126
+00:08:44,860 --> 00:08:49,290
+يكون لها ايش ما لها maximum element طيبالان for
+
+127
+00:08:49,290 --> 00:08:55,730
+any chain C subset من E define G hat بي G hat of X
+
+128
+00:08:55,730 --> 00:09:01,070
+بيساوي G X إذا كان X وين موجود في ال domain G و G
+
+129
+00:09:01,070 --> 00:09:04,870
+وين موجود في ال chain C يعني فرضا فرضا فرضا هي في
+
+130
+00:09:04,870 --> 00:09:12,120
+عند ال chain ال chain هي G واحدG2 G3 G4 إلى آخره
+
+131
+00:09:12,120 --> 00:09:14,720
+عنده هاي الـ Chain اللي موجودة عندي ماشي الحال
+
+132
+00:09:14,720 --> 00:09:18,560
+هدول ال Chain موجودة في الـ E كل واحدة كسنش لتالية
+
+133
+00:09:18,560 --> 00:09:24,760
+معايا اللي هم بده أعرف الـ G hat of X بساوي اللي
+
+134
+00:09:24,760 --> 00:09:29,050
+هو G of Xنفسها يعني الـ g hat of x هتساوي g واحد
+
+135
+00:09:29,050 --> 00:09:33,110
+of x إذا كان ال x في domain مين ال g واحد ويساوي g
+
+136
+00:09:33,110 --> 00:09:36,130
+اتنين of x إذا كان ال x في domain التالية و لا إيه
+
+137
+00:09:36,130 --> 00:09:40,810
+آخرية ونظرا لإنهم اتشينت هتلاقي إن ال g hat of x
+
+138
+00:09:40,810 --> 00:09:44,550
+لو كان عددهم finite هيكون ال g hat of x في الواقع
+
+139
+00:09:44,550 --> 00:09:48,980
+بساوي مين؟ g أربعة of xلأن كل واحد extension
+
+140
+00:09:48,980 --> 00:09:52,660
+للتانية فأي x في domain هذا حيكون في domain اللي
+
+141
+00:09:52,660 --> 00:09:57,640
+هو مين اللي جابتها فالآن g hat of x بيساوي g of x
+
+142
+00:09:57,640 --> 00:10:01,840
+إذا كانت x في domain الـ g ماشي خلوها دي في
+
+143
+00:10:01,840 --> 00:10:05,000
+الداكرةthen جيهة is a linear extension of
+
+144
+00:10:05,000 --> 00:10:08,680
+functional الجيهة تلاقي أنه صار أشمالها ووسعت
+
+145
+00:10:08,680 --> 00:10:13,780
+نفوذها عن من؟ عن اللي هي الـ F لأن هدولة كلها
+
+146
+00:10:13,780 --> 00:10:17,800
+extension للـ F فصارت الجيهة اللي هي معرفة على
+
+147
+00:10:17,800 --> 00:10:21,880
+أكبر domain فين هدولة اللي هو عبارة عن extension
+
+148
+00:10:21,880 --> 00:10:26,420
+صار extension functional، linear functional إذن
+
+149
+00:10:28,730 --> 00:10:33,410
+ذن جيهات is a linear functional and دي domain
+
+150
+00:10:33,410 --> 00:10:37,350
+جيهات بساوي الـun لمين لل domains اللي عندى اذا
+
+151
+00:10:37,350 --> 00:10:41,210
+بدك تتأكد ان هذه الجيهات linear functional يعني
+
+152
+00:10:41,210 --> 00:10:43,910
+عشان linear خد linear ماانتوا عارفين كيف linear
+
+153
+00:10:43,910 --> 00:10:49,890
+لذن تتأكد انها linear let x و y element ال main
+
+154
+00:10:49,890 --> 00:10:56,370
+and domainG hat ماشي الحال في domain الـ G hat ما
+
+155
+00:10:56,370 --> 00:10:58,790
+هي الـ G hat اللي هو domain هيه أشماله بيحتوي كل
+
+156
+00:10:58,790 --> 00:11:02,590
+ال domainات اللي عندي إذا عندي أو Alpha scalar
+
+157
+00:11:02,590 --> 00:11:07,970
+مثلا Alpha scalar بيصير عندي ال X و ال Y اللي هو
+
+158
+00:11:07,970 --> 00:11:11,090
+في domain الـ G hat اللي هو مين بيساوي ال union ل
+
+159
+00:11:11,090 --> 00:11:15,090
+domain الـ G G element المين in the chain ال chain
+
+160
+00:11:15,090 --> 00:11:21,290
+اللي مش عالق عليها بيصير عندي XElement X في ال
+
+161
+00:11:21,290 --> 00:11:24,150
+union و Y في element في ال union يعني هتكون X
+
+162
+00:11:24,150 --> 00:11:28,250
+element اللي هو في واحدة من هدول يعني only element
+
+163
+00:11:28,250 --> 00:11:34,530
+in domain G for some G element in main and C و ال
+
+164
+00:11:34,530 --> 00:11:40,030
+Y هتكون في domain G prime مثلا for some G element
+
+165
+00:11:40,030 --> 00:11:44,630
+in main .. G prime element in main and C واضح اللي
+
+166
+00:11:44,630 --> 00:11:49,660
+بحكيه؟ طيب يعني عند X و Y في domain G hatو domain
+
+167
+00:11:49,660 --> 00:11:52,740
+جي هات هو ال union إذا انصرت ال X و ال Y في ال
+
+168
+00:11:52,740 --> 00:11:57,160
+union بتكون ال X في واحدة من .. في واحدة من هدول و
+
+169
+00:11:57,160 --> 00:11:59,320
+ال Y في واحدة من هدول مش شرط تكونوا في نفس الوحدة
+
+170
+00:11:59,320 --> 00:12:02,940
+فX موجودة في domain الجي مثلا و Y في domain الجي
+
+171
+00:12:02,940 --> 00:12:06,860
+هات و الجي و الجي هات .. جي و الجي أبرايم موجودات
+
+172
+00:12:06,860 --> 00:12:12,570
+في ال C في ال chainالان في واحدة من هدولة تنتمي في
+
+173
+00:12:12,570 --> 00:12:15,890
+ال chain مادام في ال chain اكيد في واحد extension
+
+174
+00:12:15,890 --> 00:12:19,610
+لك تاني حسب التعريف ماشي الحال لأن كل اللي في ال
+
+175
+00:12:19,610 --> 00:12:23,870
+chain هي علاقة في بعض الان لو كانت ال جهات هي ال
+
+176
+00:12:23,870 --> 00:12:28,460
+extension بيصير ال x و ال y في دمية الجهاتمظبوط؟
+
+177
+00:12:28,460 --> 00:12:31,480
+لأنه extension إذا صارت الـ X والـ Y في domain الـ
+
+178
+00:12:31,480 --> 00:12:35,680
+G hat طيب ما هو صارت عندى في هذه الحالة اللى هو
+
+179
+00:12:35,680 --> 00:12:40,120
+الـ G الـ G اللى بدأنا فيها الـ X في domain الـ G
+
+180
+00:12:40,120 --> 00:12:43,400
+عشان إيش؟ بتبتلكم إن الـ G hat إيش معناه linear
+
+181
+00:12:43,400 --> 00:12:50,720
+إذا صارت عندى G hat of X أو Alpha X زائد Y بساوى
+
+182
+00:12:53,030 --> 00:12:58,890
+الان التنتين في domain مين الـ G prime إذا صارت
+
+183
+00:12:58,890 --> 00:13:01,010
+هذه الـ G hat هي نفس الـ G prime لأن الـ G hat
+
+184
+00:13:01,010 --> 00:13:04,150
+extension لها هتساويها في domainها و برا domainها
+
+185
+00:13:04,150 --> 00:13:09,930
+بتشتغل شغل تاني في G prime of Alpha X زائد Y و هي
+
+186
+00:13:09,930 --> 00:13:15,550
+ساوي Alpha G prime of X زائد G prime of Y وهذه
+
+187
+00:13:15,550 --> 00:13:20,390
+بتساوي Alpha G hat of X لأن G prime of X هي نفس
+
+188
+00:13:20,390 --> 00:13:26,720
+الـ G hat of Xdomainها زائد g hat of y وهذا يعني
+
+189
+00:13:26,720 --> 00:13:32,480
+أنه صارت الـ g hat إشمالها is linear إذن .. إذن يا
+
+190
+00:13:32,480 --> 00:13:36,500
+جماعة اللي أثبتناه الآن أن الـ g hat is a linear
+
+191
+00:13:36,500 --> 00:13:39,920
+functional و domain الـ g hat هو ال union لل
+
+192
+00:13:39,920 --> 00:13:43,040
+domains اللي عندنا كله العالمين اللي على الـ C
+
+193
+00:13:43,040 --> 00:13:47,640
+لإنه أنا معرفها الـ g hat عبارة عناللي هي
+
+194
+00:13:47,640 --> 00:13:55,120
+extension .. اه اللي هي ل .. معرفها ان جهات of X
+
+195
+00:13:55,120 --> 00:13:58,480
+بيساوي G of X لكل X في domain الجيه و .. ننزل ..
+
+196
+00:13:58,480 --> 00:14:04,520
+لأ و اللي هي ال .. ال domain ها هيكون اللي هو ال
+
+197
+00:14:04,520 --> 00:14:09,740
+union ل domain الجيه حسب التعريف الموضوع طيبالأن
+
+198
+00:14:09,740 --> 00:14:13,040
+الـ Union للـ Domains برضه بنفس الطريقة اللي أخدت
+
+199
+00:14:13,040 --> 00:14:17,040
+المشابهة لهذه برضه بتقدر تثبتها إن هي شمالها
+
+200
+00:14:17,040 --> 00:14:20,280
+Vector Space ماعش الحال اللي هي شئة الـ Vector
+
+201
+00:14:20,280 --> 00:14:23,920
+Space لو X و Y في Domain الجيهات مع أنها الـ X و
+
+202
+00:14:23,920 --> 00:14:25,820
+الـ Y موجودة في الـ Union مدام في الـ Union زي ما
+
+203
+00:14:25,820 --> 00:14:28,640
+عملت حيكون في واحدة منهم في ال .. إذن في ال
+
+204
+00:14:28,640 --> 00:14:32,300
+extension ل .. الأكبر في التنتين إذن حيكون و بما
+
+205
+00:14:32,300 --> 00:14:35,040
+إن Domain كل واحدة من ال extension Vector Space
+
+206
+00:14:35,040 --> 00:14:39,250
+إذن Automatic بتطلع فياللي هي ال union اتوكل الله
+
+207
+00:14:39,250 --> 00:14:45,090
+اذا vector space ارجع ليش جيت هان عندي ماشي اذا
+
+208
+00:14:45,090 --> 00:14:51,670
+عندي اللي هي اللي اللي اللي اللي صارت الجيهات فيها
+
+209
+00:14:51,670 --> 00:14:55,610
+اللي محقق كل الشروط الجيهات صارت عبارة عن
+
+210
+00:14:55,610 --> 00:15:01,720
+extension extension linear extension نفسهاوصارت
+
+211
+00:15:01,720 --> 00:15:06,400
+كمان الـ G hat أكبر يسوى G لكل مين لكل G وين
+
+212
+00:15:06,400 --> 00:15:10,320
+موجودة في ال chain إذا صارت الـ G hat نفسها عبارة
+
+213
+00:15:10,320 --> 00:15:13,900
+عن إيه؟ عبارة عن upper bound للـ C وكانت الـ C
+
+214
+00:15:13,900 --> 00:15:18,260
+مخدها يعني arbitrary chain إذا صار عند الـ non
+
+215
+00:15:18,260 --> 00:15:22,700
+-empty set الإيه اللي بحكي عنها is a non-empty
+
+216
+00:15:22,700 --> 00:15:28,370
+ordered setوالتي تحتوي على الـ Probability أن كل
+
+217
+00:15:28,370 --> 00:15:31,450
+قطعة تحتوي على قطعة أعلى ثم تحتوي على قطعة أعلى
+
+218
+00:15:31,450 --> 00:15:40,330
+باقية إذا بيزونز لما E لديه قطعة أعلى باقية افتل
+
+219
+00:15:40,330 --> 00:15:46,310
+ده افتل ده هذا اللي بتدعي أنه العنصر المطلوب هو
+
+220
+00:15:46,310 --> 00:15:50,360
+اللي هيكون ال extension اللي أنا طالبه على كل Xand
+
+221
+00:15:50,360 --> 00:15:54,240
+by the definition of E this is a linear extension
+
+222
+00:15:54,240 --> 00:15:57,920
+لأنه واحد من مين من اللي هو ال elements اللي في E
+
+223
+00:15:57,920 --> 00:16:02,360
+مظبوط ولا لأ؟ إذا هو ال E عبارة عن extensions إذا
+
+224
+00:16:02,360 --> 00:16:07,520
+ال F تلدة هيكون معله عبارة عن extension لل F ويحقق
+
+225
+00:16:07,520 --> 00:16:11,900
+حسب اللي هو تعريفه لل E هيحقق إنه F تلدة هو بيكس
+
+226
+00:16:11,900 --> 00:16:16,220
+أصغر سوى بيكس لكل X و M موجودة في domain ال F تلدة
+
+227
+00:16:17,330 --> 00:16:22,010
+الان اللى بدى أثبتلكم اللى ضال عليا انا هلجيت
+
+228
+00:16:22,010 --> 00:16:27,790
+اثبتتلكم ان F تلد عبارة عن extension لل F ويحقق F
+
+229
+00:16:27,790 --> 00:16:31,110
+تلد اصغر بساوية P of X لكل X و M موجودة في ال
+
+230
+00:16:31,110 --> 00:16:34,310
+domain F تلدة لو أثبتتلكم ال domain لل F تلدة
+
+231
+00:16:34,310 --> 00:16:38,660
+بساوية X بكون خلصتإذا نضل عليه إيش أثبت أنه domain
+
+232
+00:16:38,660 --> 00:16:42,780
+F تلده بساوي X لو أثبتتوا معيناته صار أنه F تلده
+
+233
+00:16:42,780 --> 00:16:47,400
+عبارة عن linear extension لل F و ال F تلده of X
+
+234
+00:16:47,400 --> 00:16:51,100
+أصغر بساوي P of X لكل X و إيه الموجودة في ال X وهو
+
+235
+00:16:51,100 --> 00:16:55,880
+المطلوب خلّينا نشوف اللي هو رحلة إثبات اللي هو
+
+236
+00:16:55,880 --> 00:16:59,820
+domain ال F تلده بساوي X بدنا نفترض العكس
+
+237
+00:17:08,320 --> 00:17:16,640
+خلّيني اختار Y1 في الـ X-Main-Domain Fماشي الحال
+
+238
+00:17:16,640 --> 00:17:21,380
+اللي بدأصلكم فيها contradiction انه بدأثبتلكم انه
+
+239
+00:17:21,380 --> 00:17:24,200
+في اشي اكبر من ال F تلد و هي ال maximum صار
+
+240
+00:17:24,200 --> 00:17:27,920
+contradiction شوف كيف يعني choose y واحد في ال X
+
+241
+00:17:27,920 --> 00:17:30,900
+minus main minus domain F تلد احنا بنقول domain F
+
+242
+00:17:30,900 --> 00:17:33,240
+تلد ده بتسويش X طبعا domain F تلد ده في نهاية
+
+243
+00:17:33,240 --> 00:17:38,550
+subset من X إذا في element هنا مش موجود هناY1 بطله
+
+244
+00:17:38,550 --> 00:17:41,630
+اللي موجود في domain الـ F اللي هان بدي أركب
+
+245
+00:17:41,630 --> 00:17:45,270
+subspace هو اللي هيجيب لي ال contradiction let Y1
+
+246
+00:17:45,270 --> 00:17:48,670
+be the subspace spanned by يعني الـ Y1 هو ال
+
+247
+00:17:48,670 --> 00:17:52,730
+subspace اللي spanned by domain الـ F تلد هذا اللي
+
+248
+00:17:52,730 --> 00:17:56,650
+بقول عنه ماسويش X بالإضافة لمين للـ Y1 اللي أخدتها
+
+249
+00:17:56,650 --> 00:18:02,810
+من هنا وموجودة هناالان واضح .. واضح ان الـ Y1 ده
+
+250
+00:18:02,810 --> 00:18:07,050
+مش هتساوي سفر ليش؟ لأن السفر موجود وين؟ في domain
+
+251
+00:18:07,050 --> 00:18:12,250
+F تلدة في الـ space أو vector space طيب .. مذا من
+
+252
+00:18:12,250 --> 00:18:16,250
+الـ zero element في domain F تلدة وانا ماخد الـ Y1
+
+253
+00:18:16,250 --> 00:18:19,430
+من ال X وبرّت ال domain F تلدة أكيد هو الـ Y1 ماله
+
+254
+00:18:19,430 --> 00:18:24,550
+مش السفر طيب .. إذا then Y1 ده تساوي سفر وكل X
+
+255
+00:18:24,550 --> 00:18:35,280
+الآن مدام أخدت الـ Y1الـ Y1 الـ
+
+256
+00:18:35,280 --> 00:18:44,000
+Y1 أخدتها عبارة عن الـ span بين الـ Y1 small و
+
+257
+00:18:44,000 --> 00:18:49,220
+domain الـ F تل ده فحقول لها أخدت ال span يعني أي
+
+258
+00:18:49,220 --> 00:18:52,300
+element هنا هيكون هنا combination بين هذه و بين
+
+259
+00:18:52,300 --> 00:18:58,010
+العناصر اللي هنا ماشي طيبالان اي x element y واحد
+
+260
+00:18:58,010 --> 00:19:02,030
+اللي وكّبته هذا can be written as x بتساوي element
+
+261
+00:19:02,030 --> 00:19:07,550
+من ال domain الاف تل ده زائد alpha between y واحد
+
+262
+00:19:07,550 --> 00:19:10,710
+واحد يقول لبيطا y هو البيطا y برضه وين موجود في ال
+
+263
+00:19:10,710 --> 00:19:15,070
+domain الاف تل ده فاهمين؟ فبتسميه y او بسميه z او
+
+264
+00:19:15,070 --> 00:19:19,690
+بسميه حرنة لإن اي mean اي أي scalar مضروف في هذا
+
+265
+00:19:20,460 --> 00:19:22,240
+عشان تقول الـ Linear combination ليش الـ Linear
+
+266
+00:19:22,240 --> 00:19:26,060
+combination X بالساوية Beta Y زايد Alpha Y واحد طب
+
+267
+00:19:26,060 --> 00:19:29,260
+ما هو الـ Beta Y موجود هان؟ لأن هذا عبارة عن
+
+268
+00:19:29,260 --> 00:19:31,960
+vector space فلو كانت الـ Y جوا ال Beta Y ورده جوا
+
+269
+00:19:31,960 --> 00:19:38,440
+فبتسميه Y أريح ليه طيب إذا أي X الآن موجودة في الـ
+
+270
+00:19:38,440 --> 00:19:42,600
+Y واحد can be written uniquely as Y زايد Alpha Y
+
+271
+00:19:42,600 --> 00:19:45,720
+واحد حيث Y في ال domain والـ Y واحد هي اللي احنا
+
+272
+00:19:45,720 --> 00:19:49,380
+حكينا عنها خلينا نقول إن عشان نثبت إن هذا واحد
+
+273
+00:19:50,060 --> 00:19:54,640
+إثبات بسيط سهل to see this to see أنه أنه واحد
+
+274
+00:19:54,640 --> 00:19:57,840
+suppose that فيه تنتين x بتساوي y زائد alpha y
+
+275
+00:19:57,840 --> 00:20:02,940
+واحد and x بتساوي y تلدة زائد مين beta y واحد يعني
+
+276
+00:20:02,940 --> 00:20:08,340
+عنصرين اللي هنا هذا و هذا يكون اللي هنا x بتساوي
+
+277
+00:20:08,340 --> 00:20:11,620
+كده يعني إنها صورتين بمعنى أخر ونتبت إن الصورتين
+
+278
+00:20:11,620 --> 00:20:15,320
+نفس الشيء يعني هتكون ال y هي ال y تلدة و ال alpha
+
+279
+00:20:15,320 --> 00:20:21,810
+هي مين ال beta شوفواخد الآن اترحم من بعض اترحم من
+
+280
+00:20:21,810 --> 00:20:25,670
+بعض او قول هذه بتساوي وهذه لان هذه بتساوي هذه
+
+281
+00:20:25,670 --> 00:20:29,810
+وانقل اللي هي ال Y تلده مع ال Y وانقل ال Y واحد مع
+
+282
+00:20:29,810 --> 00:20:33,250
+ال Y واحد بيصير عنده Alpha ناقص Beta في Y واحد
+
+283
+00:20:33,250 --> 00:20:37,770
+فاهمين؟ بيساوي Y تلده ناقص مين؟ ناقص Y ماشي الحل
+
+284
+00:20:37,770 --> 00:20:42,730
+هذه الان Y تلده وY واحد موجوديات في domain F تلده
+
+285
+00:20:42,730 --> 00:20:48,610
+صح ولا لا؟والـ Alpha نقص Beta في Y1 معروف الـ Y1
+
+286
+00:20:48,610 --> 00:20:52,790
+اللي موجودة في الـ X minus اللي هي domain F تلدة
+
+287
+00:20:52,790 --> 00:20:56,950
+هذه موجودة في domain الـ F تلدة والـ Y1 برا domain
+
+288
+00:20:56,950 --> 00:21:00,650
+الـ F تلدة إذا مستحيل هذا يساوي هذا إلا في حالة
+
+289
+00:21:00,650 --> 00:21:04,530
+واحدة إن هذا اللي هو يساوي يعني هذا سفر بساوي هياش
+
+290
+00:21:04,530 --> 00:21:11,720
+سفر إذا هذا العنصر في domain الـ F تلدةوهذا العنصر
+
+291
+00:21:11,720 --> 00:21:14,900
+في برّا domain الـ F تلدة لأنه ماخدينه في إئم الـ
+
+292
+00:21:14,900 --> 00:21:18,380
+X ناقص domain الـ F تلدة إذاً هذا يستحيل يكون
+
+293
+00:21:18,380 --> 00:21:22,180
+المساواة إلا إذا كانت Alpha ناقص Beta بتساوي سفر
+
+294
+00:21:22,180 --> 00:21:26,160
+وBot اللي هو Y واحد مش في domain الـ F تلدة وY
+
+295
+00:21:26,160 --> 00:21:30,040
+تلدة ناقص Y مش في domain الـ F إذاً Alpha ناقص
+
+296
+00:21:30,040 --> 00:21:33,320
+Beta بتساوي سفر ومن ثم Alpha بتساوي سفر ومعناته أن
+
+297
+00:21:33,320 --> 00:21:38,780
+Y تلدة هي الـ Y ومعناته أن الصورة صارت هذه وحيدةأه
+
+298
+00:21:38,780 --> 00:21:42,620
+والـ Alpha هي الـ Beta and this proves the
+
+299
+00:21:42,620 --> 00:21:46,860
+uniqueness of اللي هو representation لأن بدنا نعرف
+
+300
+00:21:46,860 --> 00:21:50,500
+اللي هو function اتوصلنا ل اللي هو ال
+
+301
+00:21:50,500 --> 00:21:55,900
+contradiction اللي بدنا يعرف طولوا
+
+302
+00:21:55,900 --> 00:22:01,780
+روحكم، البرهان طويل Define
+
+303
+00:22:01,780 --> 00:22:07,360
+G واحدمن Y1 لعنده Rπي عناصر الـ G1 اتفاقنا على هاي
+
+304
+00:22:07,360 --> 00:22:12,760
+شكلها G1 of Y زي الـ α Y1 بدي اعرفها كتالة بتساوي
+
+305
+00:22:12,760 --> 00:22:16,420
+اللي هو ال Y في domain ال F تلده فبدي أسويها بدي
+
+306
+00:22:16,420 --> 00:22:20,920
+أرسلها ل F تلده في domain of Y و هذه ال α Y1 بدي
+
+307
+00:22:20,920 --> 00:22:25,360
+ارسلها لالف في مين؟ في C في C for some constant
+
+308
+00:22:25,360 --> 00:22:30,080
+ماشي؟ إذا هاي ال G1 ال function اللي عندى where C
+
+309
+00:22:30,080 --> 00:22:34,840
+is any real constantIt is easy to see that G1 is
+
+310
+00:22:34,840 --> 00:22:38,400
+linear G1
+
+311
+00:22:38,400 --> 00:22:42,880
+is a linear functional خد شوف الـ G1 كيف ليناير خد
+
+312
+00:22:42,880 --> 00:22:48,000
+الآن any two elements فيه خلّينا ناخد Z بساوي
+
+313
+00:22:48,000 --> 00:22:56,600
+Alpha Y زائد Alpha Y واحد و Z prime بساوياللي هو
+
+314
+00:22:56,600 --> 00:23:05,440
+Y' زائد Beta Y1 مش هي شكل العناصر اللي في الـ Y1
+
+315
+00:23:05,440 --> 00:23:13,040
+اللي في الـ domain الان بتاخد الالد G1of Z زائد
+
+316
+00:23:13,040 --> 00:23:17,040
+Gamma زيد واحد مش هيك ابقنا نثبت انها Linear Y
+
+317
+00:23:17,040 --> 00:23:23,940
+ساوي الان جي واحد of Z ايش بتساوي Y زائد Alpha Y
+
+318
+00:23:23,940 --> 00:23:33,100
+واحد وهادي Y Prime هيها زائد Gamma في Y واحد زائد
+
+319
+00:23:33,100 --> 00:23:42,830
+Gamma في Beta في Y واحد صح ولا لأ Y ساويالأن جمعوا
+
+320
+00:23:42,830 --> 00:23:49,290
+اللي في domain الـ F تلدة مع بعض وتبعات الـ Y1 مع
+
+321
+00:23:49,290 --> 00:23:55,050
+بعض بيصير G1 of Y زائد Gamma Y1 هدولة كلهين وين
+
+322
+00:23:55,050 --> 00:24:00,610
+مالها في domain الـ F تلدة زائد هادي مع هادي اللي
+
+323
+00:24:00,610 --> 00:24:09,410
+عبارة عن Alpha Y1 زائد Gamma Beta Y1 وخلّي الـ Y1
+
+324
+00:24:09,410 --> 00:24:15,680
+مالهابرة فاهمين؟ حسب القانون اللي هو ايش معرفينه
+
+325
+00:24:15,680 --> 00:24:21,180
+احنا J1 بساوي F تلدة of هذه الكتلة زائد Alpha في C
+
+326
+00:24:21,180 --> 00:24:26,880
+بدل Y واحد Y ساوي هذا عبارة عن مين حسب التعريف
+
+327
+00:24:26,880 --> 00:24:34,410
+اللي هي F تلدة of Y زائد Gamma Y Primeوهذا كله
+
+328
+00:24:34,410 --> 00:24:39,630
+بيصير ايش ماله؟ زائد Alpha زائد Gamma في Beta في
+
+329
+00:24:39,630 --> 00:24:47,970
+مين؟ في C واضح هاه؟ ويساوي طويل
+
+330
+00:24:47,970 --> 00:24:53,900
+لكن سهل الهواء ويساويعندي ال F تلده نفسها Linear
+
+331
+00:24:53,900 --> 00:24:59,820
+مظبوط او لا اذا انا اخليك معناه انا F تلده of Y
+
+332
+00:24:59,820 --> 00:25:05,240
+زائد Gamma ف F تلده of Y Prime هذا الاولى لان F
+
+333
+00:25:05,240 --> 00:25:08,360
+تلده ليهاش معناه Linear وهذه constant بتوزع ال
+
+334
+00:25:08,360 --> 00:25:15,090
+constant زائدألفة في C زائد Gamma في Beta في مين
+
+335
+00:25:15,090 --> 00:25:19,910
+في C معايا خلّيني أجمح هدولة مع بعض هدولة التامتين
+
+336
+00:25:19,910 --> 00:25:28,370
+أيش بيساون تعريفها G1 of Y زائد Alpha Y واحد صح
+
+337
+00:25:28,370 --> 00:25:36,990
+ولا لأ هذي زائد هدولة عبارة عن Gamma في G1 of Y
+
+338
+00:25:36,990 --> 00:25:44,340
+واحد زائد Betaفى مين؟ فى Y1 صح ولا لأ؟ من التعريف
+
+339
+00:25:44,340 --> 00:25:51,580
+المباشرة وهذا معناته انه صارت هذا اللي هي Z وهذا
+
+340
+00:25:51,580 --> 00:26:01,160
+Z' يعني بسوء G1 of Z زائد G القامة G1 of Z' فبدأت
+
+341
+00:26:01,160 --> 00:26:09,490
+بهذه وانتهيت بهذه إذا فعلا G1 إيش مالها؟Is Linear
+
+342
+00:26:09,490 --> 00:26:16,420
+نيجي الآنفالفا بتساوي سفر إذا كانت الفا بتساوي سفر
+
+343
+00:26:16,420 --> 00:26:18,860
+عند الالفة هذه اللي .. اللي .. اللي اشتغلت فيها
+
+344
+00:26:18,860 --> 00:26:22,220
+هذه إذا كانت الفا واحد بتساوي .. الالفة بتساوي سفر
+
+345
+00:26:22,220 --> 00:26:27,780
+بيصير عند جي واحد of Y هيو جي واحد of Y هذا بيصير
+
+346
+00:26:27,780 --> 00:26:33,520
+سفر بيساوي F تلد مين of Y لكل Y موجودة في دمين ال
+
+347
+00:26:33,520 --> 00:26:38,400
+F تلدة وهذا معناته إيش أنه جي واحد is a proper
+
+348
+00:26:38,400 --> 00:26:42,840
+extension of مينو F tilde جي واحد extension لأنها
+
+349
+00:26:42,840 --> 00:26:48,000
+اشتغلت عالميا على ال elements هدولة و ساوت جي واحد
+
+350
+00:26:48,000 --> 00:26:53,020
+ساوت ال F تلد لل Y و فيها نفوذ أخرى ماشي الحال و
+
+351
+00:26:53,020 --> 00:26:56,080
+ليش هو proper لإن في element هذا ما هو احنا قولنا
+
+352
+00:26:56,080 --> 00:26:59,340
+عنه براة ال X هان المشكلة أصلا براة اللي هي ال
+
+353
+00:26:59,340 --> 00:27:04,480
+domain ال F tilde ماشي صارت عندنا جي واحد و Y زايد
+
+354
+00:27:04,480 --> 00:27:09,110
+Alpha Y واحداللي هي اللي بتساوي F tilde Y زائد
+
+355
+00:27:09,110 --> 00:27:14,870
+Alpha C هذا تعبر عن انه G1 extension لمين للـ F
+
+356
+00:27:14,870 --> 00:27:20,950
+tilde لإنه G1 هتساوي الـ F tilde لكل عناصر الـ Y و
+
+357
+00:27:20,950 --> 00:27:26,030
+M في دمية الـ F tildeوفي نفوذ أخر إلها اللي هو Y
+
+358
+00:27:26,030 --> 00:27:29,830
+زي الألف و Y واحد للألف لا تساوي سفر بترسل الأف تل
+
+359
+00:27:29,830 --> 00:27:34,130
+ده of Y زي الألف C يعني اشتغلت على اللي هو الأف تل
+
+360
+00:27:34,130 --> 00:27:37,490
+ده اللي هي domain الأف تل ده وما بعده اللي هو مين
+
+361
+00:27:37,490 --> 00:27:40,750
+ما بعد domain الأف تل ده اللي هو ال Y واحد هذا
+
+362
+00:27:40,750 --> 00:27:46,350
+اللي هو domain أف تل ده اتحاد ميناللي هو مش domain
+
+363
+00:27:46,350 --> 00:27:51,150
+الـ Y1 مين هو عبارة عن لسبان الـ Y1 عبارة عن هدى
+
+364
+00:27:51,150 --> 00:27:54,250
+عبارة عن مين؟ عن لسبان ل domain الـ F تلدى
+
+365
+00:27:54,250 --> 00:27:59,650
+بالاضافة للـ Y1 small ماشي؟ إذا أكيد صارت عندي GY1
+
+366
+00:27:59,650 --> 00:28:04,770
+of بتساوي F تلدى of Y for all ال domain F تلدى أدى
+
+367
+00:28:04,770 --> 00:28:09,030
+للسببين إنه G1 is a proper extension of مين؟ و F
+
+368
+00:28:09,030 --> 00:28:12,850
+تلدى يعني F تلدى X اللي هو G1 extension للـ F تلدى
+
+369
+00:28:13,450 --> 00:28:17,650
+وفي كمان اللي هو أكبر منه أو أوسع منه إذا أعرفنا
+
+370
+00:28:17,650 --> 00:28:21,810
+الأكبر أو يساوي كيف احنا في الـA إيش عرفنا الأكبر
+
+371
+00:28:21,810 --> 00:28:24,690
+أو يساوي؟ إنه G أكبر أو يساوي H ده كانت H
+
+372
+00:28:24,690 --> 00:28:30,130
+exceptional من 100 للـG لإن صارت أندي G واحد أكبر
+
+373
+00:28:30,130 --> 00:28:35,750
+أو يساوي من F تلدة وهنا ال contradiction لإنه إيش
+
+374
+00:28:35,750 --> 00:28:39,730
+ماله؟ اللي هو الـF تلدة .. قبل شوية قولنا maximum
+
+375
+00:28:39,730 --> 00:28:44,920
+elementماشي الحال اذا صار عندى بس في شغل ابنان
+
+376
+00:28:44,920 --> 00:28:49,400
+اثبتها however صار عند بروبر existential لكن انا
+
+377
+00:28:49,400 --> 00:28:52,580
+بدي اتجاوز هذه و بدي افترض ان الـG1 of X أصغر
+
+378
+00:28:52,580 --> 00:28:57,440
+شؤميا ب X لكل X where موجودة في domain G1 هذه الآن
+
+379
+00:28:57,440 --> 00:29:01,750
+بدي اثبتهابس خلّينا و كأننا مثبتينها صارت عندي
+
+380
+00:29:01,750 --> 00:29:06,410
+اللي هو لإنه أنا شغل في الإيدي لبالك شغل بقول إن
+
+381
+00:29:06,410 --> 00:29:11,150
+الـG أصغر يساوي H بيحتمل .. ال .. ال .. ال .. ال
+
+382
+00:29:11,150 --> 00:29:14,850
+.. خلّيني أقول شرطين الشرط الأول إن الـH تكون
+
+383
+00:29:14,850 --> 00:29:19,870
+extension للـG هذه واحدة و الشرط الثاني إنه يحقق
+
+384
+00:29:19,870 --> 00:29:25,350
+إن الـH of X أصغر يساوي P of X لكل X موجودة في
+
+385
+00:29:25,350 --> 00:29:30,230
+domain main الـHالان اللي حققته انا بالنسبة للأفتل
+
+386
+00:29:30,230 --> 00:29:33,750
+ده الـ G1 حققت شغلة انه الـ G1 هو Property
+
+387
+00:29:33,750 --> 00:29:38,450
+Essential له لكن لسه ضال بده حقق انه الـ G1 of X
+
+388
+00:29:38,450 --> 00:29:44,190
+أصغر سواء P of X لكل X و N موجود في Domain الـ G1
+
+389
+00:29:44,530 --> 00:29:50,590
+ماشي الحل فضلنا نحققنا صرنا حصلين على g1 اللي هو
+
+390
+00:29:50,590 --> 00:29:54,430
+extension لـ f تل ده و يحقق هذه يعني الـ g1 صار
+
+391
+00:29:54,430 --> 00:29:58,170
+وين موجود؟ في الـ E و أكبر من مين؟ من الـ f تل ده
+
+392
+00:29:58,170 --> 00:30:04,050
+Contradiction فبصير الآن hence g1 element الـ E
+
+393
+00:30:04,050 --> 00:30:07,190
+which is contradicts the maximality of f تل ده
+
+394
+00:30:07,190 --> 00:30:10,330
+Therefore ال domain لـ f تل ده إيش بساوي؟ بساوي x
+
+395
+00:30:10,330 --> 00:30:17,070
+و هيك بكون نهينا البرهان لوأثبتنا هذه اللي انا بدأ
+
+396
+00:30:17,070 --> 00:30:22,210
+أثبتها دل عليها خلّينا نثبتها وهذه برضه قصة اللي
+
+397
+00:30:22,210 --> 00:30:24,630
+انا اشضل عنديا يا جماعة انا بدأ أثبتلكم الـ G1 و
+
+398
+00:30:24,630 --> 00:30:29,770
+Fx أظهر سوء بيه و Fx لكل X والي موجود في domain
+
+399
+00:30:29,770 --> 00:30:34,610
+الـ G1 دلع فوق يا عزيزي دلع فوق يا عزيزي دلع فوق
+
+400
+00:30:34,610 --> 00:30:38,150
+يا عزيزي دلع فوق يا عزيزي دلع فوق يا عزيزي دلع فوق
+
+401
+00:30:38,150 --> 00:30:38,870
+يا عزيزي دلع فوق يا عزيزي دلع فوق يا عزيزي دلع فوق
+
+402
+00:30:38,870 --> 00:30:41,670
+يا عزيزي دلع فوق يا عزيزي دلع فوق يا عزيزي دلع فوق
+
+403
+00:30:41,670 --> 00:31:00,880
+ياالتالي بكون خلصت نظرية هضل
+
+404
+00:31:00,880 --> 00:31:04,420
+عليّ أنه اتصلوا على النبي و بدأ اثبتلكم عليه
+
+405
+00:31:04,420 --> 00:31:11,230
+الصلاة والسلام انه G1 of X أظهر يساوي P of Xلكل X
+
+406
+00:31:11,230 --> 00:31:16,310
+بتساوي Y زي Alpha Y واحد اللي هنا و هنا موجودات في
+
+407
+00:31:16,310 --> 00:31:19,010
+domain الجي واحد اللي هو كان عبارة عن ال span
+
+408
+00:31:19,010 --> 00:31:23,470
+لاللي هو domain الاف تلده بالاضافة لل Y واحد هاي
+
+409
+00:31:23,470 --> 00:31:27,790
+اللي بتثبته ماشي الحال خلينا ناخد حلوات الآن
+
+410
+00:31:27,790 --> 00:31:33,370
+finally to prove one اللي حكينا عنها let Y و Z
+
+411
+00:31:33,370 --> 00:31:36,590
+element in domain mean الاف تلده ده ماخدينه في
+
+412
+00:31:36,590 --> 00:31:38,730
+domain الاف تلده صبر عليها عشان نصركم للي بتكونوا
+
+413
+00:31:38,730 --> 00:31:47,250
+يعنيfor any y1 element in x f tilde of y ناقص f
+
+414
+00:31:47,250 --> 00:31:55,230
+tilde of z بساوية f .. هذه لأي y1 وين من ضمنها ال
+
+415
+00:31:55,230 --> 00:31:59,050
+y1 اللي فوق لأي واحد في الدنيا في ال x من ضمنها
+
+416
+00:31:59,050 --> 00:32:02,870
+مين ال y1 اللي فوق f tilde of y ناقص f tilde of z
+
+417
+00:32:02,870 --> 00:32:03,510
+ايش بتساوي
+
+418
+00:32:10,210 --> 00:32:13,770
+الآن الـ y و الـ z دول الموجودة في الـ F تلدة والـ
+
+419
+00:32:13,770 --> 00:32:17,850
+F تلدة دول الموجودة في الـ E إذا تحقق الشرط إن
+
+420
+00:32:17,850 --> 00:32:24,550
+أصغر يساوي P of y minus z و P اللي عندي بتساويالذى
+
+421
+00:32:24,550 --> 00:32:28,870
+ضيف رقم او اطرح رقم الذى ضيف بي of y زائد y واحد
+
+422
+00:32:28,870 --> 00:32:33,010
+ناقص y واحد ناقص z اللي مين هذا اللي اطرحته واضفته
+
+423
+00:32:33,010 --> 00:32:36,790
+ماشي الحال هذا الان ماهي ال b عبارة عن linear
+
+424
+00:32:36,790 --> 00:32:40,510
+extension sub linear مدام ال b sub linear ده
+
+425
+00:32:40,510 --> 00:32:46,030
+الأصغر شوي بي y واحد زائد y زائد b للتاني مظبوط
+
+426
+00:32:46,030 --> 00:32:49,990
+اللي هو ناقص y ناقص z استخدمت خاصية main انه
+
+427
+00:32:49,990 --> 00:32:56,650
+extensionthen خلّينا أهل جهة حسابات بدي قاعد أنجل
+
+428
+00:32:56,650 --> 00:33:01,830
+أي عندي هذه وصلت أصغر أو أسوأ هذه ماشي هذه مع هذه
+
+429
+00:33:01,830 --> 00:33:05,030
+هذه مع هذه شوف الآن بدي أنجل هذه أجيبها على الطرف
+
+430
+00:33:05,030 --> 00:33:09,450
+التاني بيصير سالب سالب P minus Y واحد ناقص Z ناقص
+
+431
+00:33:09,450 --> 00:33:13,310
+F tilde of Z و بدي ألجأ أودي F tilde of Y وين على
+
+432
+00:33:13,310 --> 00:33:16,450
+الجهة التانية اللي هي أصغر أو أسوأ P of Y واحد
+
+433
+00:33:16,450 --> 00:33:19,710
+زائد Y اللي ما نجلتاش ناقص F tilde of Z اللي
+
+434
+00:33:19,710 --> 00:33:26,580
+نجلتهاالان هذا الكلام صحيح .. صحيح لأي y و z و لأي
+
+435
+00:33:26,580 --> 00:33:35,420
+mean y واحد صحيح دايما الان صارت عندي الان for any
+
+436
+00:33:35,420 --> 00:33:39,840
+fixed y for any fixed y صار هذا أكبر أو يساوي هذا
+
+437
+00:33:39,840 --> 00:33:45,720
+لكل mean لكل ال z صار هذا upper bound للمجموعة هذه
+
+438
+00:33:46,480 --> 00:33:50,200
+اللي هي the set of all اللي هي .. اللي هي القيم
+
+439
+00:33:50,200 --> 00:33:53,780
+اللي على الصورة هذه لكل Z في الدنيا، ماشي الحال؟
+
+440
+00:33:53,780 --> 00:33:56,900
+صار هذا upper bound لهذا، for any fixed Y واحد،
+
+441
+00:33:56,900 --> 00:34:00,580
+اعمل fixation للـY واحد، و fixation لمين؟ للـY،
+
+442
+00:34:00,580 --> 00:34:04,420
+لكن Y والـY واحد اربترا ليه، صار هذا المقدار أكبر
+
+443
+00:34:04,420 --> 00:34:08,060
+أو يساوي هذا المقدار لكل Z في الدنيا، إذا صار هذا
+
+444
+00:34:08,060 --> 00:34:11,440
+المقدار upper bound لهذه، إذا أكيد أكبر أو يساوي
+
+445
+00:34:11,440 --> 00:34:15,420
+السبريمام إلهم،ماشي الحال إذا صار عبارة هذا أكبر
+
+446
+00:34:15,420 --> 00:34:19,380
+أو يساوي ال supremum لهدولة من المتغير الآن هو
+
+447
+00:34:19,380 --> 00:34:22,540
+الذنب ماشي الحال إذا صار اللي هو اللي سميته ال
+
+448
+00:34:22,540 --> 00:34:27,060
+supremum هذا ال U هذا ال U لأن هذا upper bound و
+
+449
+00:34:27,060 --> 00:34:30,760
+ال supremum ليس upper bound فطبيعي اللي هو عبارة
+
+450
+00:34:30,760 --> 00:34:34,700
+عن ال supremum هيكون أصغر أو ساوي من هذا فاهمين؟
+
+451
+00:34:34,700 --> 00:34:39,720
+إذا صار U أصغر أو ساوي هذا صار الآن ال U نفسهاللي
+
+452
+00:34:39,720 --> 00:34:44,260
+هو Lower Bound Lower Bound صار الـ U أصغر أو يساوي
+
+453
+00:34:44,260 --> 00:34:48,120
+هذا لكل الوايات اللي في الدنيا صار الـ U Lower
+
+454
+00:34:48,120 --> 00:34:52,180
+Bound لهذا إذا مدام Lower Bound إذا الـ U أكيد
+
+455
+00:34:52,180 --> 00:34:56,220
+أصغر أو يساوي من الـ Greatest Lower Bound ماشي؟
+
+456
+00:34:56,220 --> 00:34:58,780
+اللي هو الـ Infamous إذا صار عندي الآن الـ
+
+457
+00:34:58,780 --> 00:35:01,540
+Supremum هذا اللي هو الـ U أصغر أو يساوي الـ
+
+458
+00:35:01,540 --> 00:35:04,980
+Infamous لهذه اللي هو من الـ W صار عندي اللي هو
+
+459
+00:35:04,980 --> 00:35:11,540
+الـ U أصغر أو يساوي إيش الـ Wالان مادام هذا الرقم
+
+460
+00:35:11,540 --> 00:35:16,220
+اصغر شوهو هذا اذا اكيد بقدر الاقي فيه ايش then
+
+461
+00:35:16,220 --> 00:35:20,120
+there is a real number C بينهم such that C أكبر
+
+462
+00:35:20,120 --> 00:35:24,740
+شوهو U و اصغر شوهو مين W قطعا between any two real
+
+463
+00:35:24,740 --> 00:35:28,000
+numbers there exist infinite number of real
+
+464
+00:35:28,000 --> 00:35:28,400
+numbers
+
+465
+00:35:31,730 --> 00:35:34,850
+حتى لو كان واحد اصغر اشتوى التاني بيصير هو اللي
+
+466
+00:35:34,850 --> 00:35:39,510
+المساواة هو الرقم اللي بنحكي عنه و لو كان strictly
+
+467
+00:35:39,510 --> 00:35:48,850
+بتلاقي فترة مش عددها بعايا اه اطلع لفوق الان saw
+
+468
+00:35:48,850 --> 00:35:54,430
+that هيصير عندى لأ بس خليني ازل شوية عشان انا اعرف
+
+469
+00:35:54,430 --> 00:36:01,840
+انها الان عندى اللي هو ناقصناقص بي واحد ناقص كذا
+
+470
+00:36:01,840 --> 00:36:08,680
+هذا ال U ال U هذا اه و هذا مين ال W صار عند ال C
+
+471
+00:36:08,680 --> 00:36:14,900
+أصغر أو يساوي اللي هو ال W اه معايا اه و صارت اللي
+
+472
+00:36:14,900 --> 00:36:20,800
+هو ال U أصغر أو يساوي مين ال C لأن هذا ال U و هذا
+
+473
+00:36:20,800 --> 00:36:26,970
+مين ال Wمعايا؟ طيب إذن الآن صار عندي so that نشتغل
+
+474
+00:36:26,970 --> 00:36:30,630
+على هذه ناقص B minus Y واحد ناقص Z ناقص كذا أصغر
+
+475
+00:36:30,630 --> 00:36:34,450
+أو شواء و C لكل Z و N في domain F تلتة سميه اتنين
+
+476
+00:36:34,450 --> 00:36:38,310
+هذا هنرجعله و ال C أصغر أو شواء هذا المقدار لكل Y
+
+477
+00:36:38,310 --> 00:36:41,370
+و N في domain F تلتة و سميه تلتة اتنين هذا وهذا
+
+478
+00:36:41,370 --> 00:36:45,730
+وهذا هو اللي هستخدمه للوصول اللي بديه طيب اطلع على
+
+479
+00:36:45,730 --> 00:36:49,870
+فوق to prove one to prove one اللي احنا بدنا
+
+480
+00:36:49,870 --> 00:36:56,460
+نثبتهاWe have three steps بدنا ناخد case للألفة هي
+
+481
+00:36:56,460 --> 00:36:59,700
+بدأت بتهون هيها هيها بدأ أخد ألفة مرة اللي هي
+
+482
+00:36:59,700 --> 00:37:05,240
+سالبة مرة موجبة مرة بصفر ماشي الحال بصفر سهلة نيجي
+
+483
+00:37:05,240 --> 00:37:08,540
+الآن الموجبة بدأ استخدم فيها مثلا ال upper bound
+
+484
+00:37:08,540 --> 00:37:14,300
+ال U والأصغر من صفر بدأ استخدم التاني أو العكس
+
+485
+00:37:14,300 --> 00:37:18,620
+واضح ليش جسمت؟ عشان واحدة بنفعلها اللي هي السالب
+
+486
+00:37:18,620 --> 00:37:23,830
+وواحدة بنفعلها الأمين للموجب بس هي كل القصةطيب
+
+487
+00:37:27,020 --> 00:37:28,460
+أول خطوة أول خطوة أول خطوة أول خطوة أول خطوة أول
+
+488
+00:37:28,460 --> 00:37:29,860
+ألف أصغر من مين من سفر أول خطوة أول خطوة أول خطوة
+
+489
+00:37:29,860 --> 00:37:31,420
+أول ألف أصغر من مين من سفر أول خطوة أول خطوة أول
+
+490
+00:37:31,420 --> 00:37:37,900
+خطوة أول خطوة أول ألف أصغر من مين من سفر أول خطوة
+
+491
+00:37:37,900 --> 00:37:40,060
+أول خطوة أول خطوة أول خطوة أول ألف أصغر من مين من
+
+492
+00:37:40,060 --> 00:37:40,760
+سفر أول خطوة أول خطوة أول خطوة أول خطوة أول أصغر
+
+493
+00:37:40,760 --> 00:37:47,600
+من مين من سفر أول خطوة أول خطوة أول خطوة أول أصغر
+
+494
+00:37:47,600 --> 00:37:54,300
+من مين من سفر
+
+495
+00:37:54,430 --> 00:37:59,750
+التفاصيل اللي عندكم في دي حسابات يعني ناقص بي لأن
+
+496
+00:37:59,750 --> 00:38:08,190
+بتدعوا بتدعملكم إيه هش بتسويش شوف هي عندي اللي هي
+
+497
+00:38:08,190 --> 00:38:17,130
+اتنين ناقص بي of y واحد ناقص zناقص F of Z أصغر أو
+
+498
+00:38:17,130 --> 00:38:22,290
+شوه 100 أصغر أو شوه C بقوللي أول حاجة حط Z أيش
+
+499
+00:38:22,290 --> 00:38:28,090
+بيساوي Alpha inverse في Y حط ليه ناقص B ناقص Y وحط
+
+500
+00:38:28,090 --> 00:38:32,150
+مكان ال Z 100 Alpha inverse في Y ليه بيصير ناقص
+
+501
+00:38:32,150 --> 00:38:39,990
+Alpha inverse Y صح ولا لأ ناقص F of Alpha inverse
+
+502
+00:38:39,990 --> 00:38:46,160
+100 Yأصغره يساوي عياش اللي هو عياش C و بعدين
+
+503
+00:38:46,160 --> 00:38:50,980
+بقوللي اضرب اضرب اللي هو الجهتين اللي هو then
+
+504
+00:38:50,980 --> 00:38:55,120
+multiply both sides by ناقص Alpha اضرب الجهتين في
+
+505
+00:38:55,120 --> 00:38:58,940
+ناقص Alpha ال Alpha سالبة ناقص Alpha موجلة إذا انه
+
+506
+00:38:58,940 --> 00:39:02,480
+خلاص كمية موجلة بتبقى لها إشارة هذي بيصير Alpha و
+
+507
+00:39:02,480 --> 00:39:08,200
+هذي بيصير Alpha و هذي بيصير صح سالب Alpha في C
+
+508
+00:39:09,970 --> 00:39:14,350
+معايا؟ هي طلعت عندنا اللي بدوياها الان بدك ال ..
+
+509
+00:39:14,350 --> 00:39:19,050
+ال .. ال .. خد الان انا بدي اثبت انه g1 of x اه؟
+
+510
+00:39:19,050 --> 00:39:22,210
+هي بدي اثبتها اصغر شوة ومين بيه of x خد g1 of x
+
+511
+00:39:22,210 --> 00:39:27,730
+انت صار عندى g1 of x اللي هي g1 of y زي ده alpha
+
+512
+00:39:27,730 --> 00:39:32,750
+y1 واضحة تاني اه؟ اللي هي بتساوي حسب تعريف الـ g1
+
+513
+00:39:32,750 --> 00:39:42,180
+ايش بتساوي؟أف تلدة لل Y زي ألفة في C أف
+
+514
+00:39:42,180 --> 00:39:45,140
+تلدة لل Y زي ألفة في C أف تلدة لل Y زي ألفة في C
+
+515
+00:39:45,140 --> 00:39:46,480
+C أف تلدة لل Y زي ألفة في C أف تلدة لل Y زي ألفة
+
+516
+00:39:46,480 --> 00:39:47,580
+في C أف تلدة لل Y زي ألفة في C أف تلدة لل Y زي
+
+517
+00:39:47,580 --> 00:39:48,840
+ألفة في C أف تلدة لل Y زي ألفة في C أف تلدة لل Y
+
+518
+00:39:48,840 --> 00:39:53,060
+زي ألفة في C أف تلدة لل Y زي ألفة في C أف تلدة لل
+
+519
+00:39:53,060 --> 00:39:58,760
+Y زي ألفة في C أف تلدة لل Y زي ألفة في C أف تلدة
+
+520
+00:39:58,760 --> 00:40:04,650
+لل Y زي ألفة فيهذه صارت Alpha F tilde of Alpha
+
+521
+00:40:04,650 --> 00:40:09,830
+inverse Y أصغر أو يساوي أنجلها على الطرف التاني
+
+522
+00:40:09,830 --> 00:40:15,830
+Alpha في Beta ناقص Y ناقص Alpha inverse Y ناقص صح
+
+523
+00:40:15,830 --> 00:40:22,410
+ولا لأ ناقص مين Alpha في C صحيك هاه هي هذه بس نجلت
+
+524
+00:40:22,410 --> 00:40:28,300
+هذه على الجهة التانية عشان بس اعملها هنادخلها دي
+
+525
+00:40:28,300 --> 00:40:34,460
+جوا لانه بدوش إياها دخلها
+
+526
+00:40:34,460 --> 00:40:41,780
+جوا بتسيرواضح هاه؟ اذا صار عندي جي واحد of X
+
+527
+00:40:41,780 --> 00:40:46,720
+بتساوي Alpha of Y زي Alpha C شيل هذه بتصير أصغر أو
+
+528
+00:40:46,720 --> 00:40:51,200
+ساوي هذا المقدار أصغر أو ساوي ناقص Alpha في ال
+
+529
+00:40:51,200 --> 00:40:56,320
+Beta ناقص Alpha C و ال Alpha C وين ال Alpha C اللي
+
+530
+00:40:56,320 --> 00:41:03,960
+في الأصل ما هي ناقص Alpha C جي واحد of X بتساوي
+
+531
+00:41:03,960 --> 00:41:06,640
+كده ناقص
+
+532
+00:41:09,190 --> 00:41:12,430
+زائد alpha c زائد alpha c مع نقص ال alpha c بروح
+
+533
+00:41:12,430 --> 00:41:17,190
+مع بعض واضح هادي زائد هادي إذا أنت بدك تريح حالك
+
+534
+00:41:17,190 --> 00:41:21,370
+من الأول ان جيه زي ما بدك تريح حالك بصير زائد هادي
+
+535
+00:41:21,370 --> 00:41:25,550
+زي هاديهذه الكاملة أصغر أو ساوي هذا المقدار هيك
+
+536
+00:41:25,550 --> 00:41:30,930
+ممكن أسهلها أصغر أو ساوي ناقص Alpha في Beta وكذا
+
+537
+00:41:30,930 --> 00:41:36,450
+إلى آخرين دخل ناقص Alpha جوا بيصير عبارة عن ناقص
+
+538
+00:41:36,450 --> 00:41:41,860
+Alpha في Alpha inverse بيصير Y لحالهاY وناقص Alpha
+
+539
+00:41:41,860 --> 00:41:46,000
+في هذه ناقص يصبح Alpha Y واحد اللي هي في الواقع
+
+540
+00:41:46,000 --> 00:41:49,300
+هذه مين اسمها X فصارت عندي الان D واحد of X أصغر
+
+541
+00:41:49,300 --> 00:41:50,980
+شويه مين بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+542
+00:41:50,980 --> 00:41:52,500
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+543
+00:41:52,500 --> 00:41:52,920
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+544
+00:41:52,920 --> 00:42:08,100
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بي
+
+545
+00:42:08,130 --> 00:42:11,730
+اللي أصغر من واحد الـ α أكبر من واحد نفس الأشياء
+
+546
+00:42:11,730 --> 00:42:15,470
+بس بتستخدم مين بدل ما تستخدم اللي هي الاتنين
+
+547
+00:42:15,470 --> 00:42:19,430
+بتستخدم تلاتة بدل ما تستخدم الـ U و علاقتها بالـ C
+
+548
+00:42:19,430 --> 00:42:23,770
+بتستخدم الـ W و علاقتها بالـ C يلا اقولنا تجمع الـ
+
+549
+00:42:23,770 --> 00:42:28,690
+W اطلع لفوق خد الـ α الصفر سهلةالـ second step هو
+
+550
+00:42:28,690 --> 00:42:32,550
+الـ α بتساوي صفر ثم X أيش بتساوي؟ فهتصير الـ X
+
+551
+00:42:32,550 --> 00:42:35,670
+بتساوي الـ α Y زايد كده هتصير بتساوي إيش مالها؟ Y
+
+552
+00:42:35,670 --> 00:42:39,390
+وين موجودة؟ في الـ domain الـ F تلدة و G1 of X أيش
+
+553
+00:42:39,390 --> 00:42:42,870
+هيساوي؟ F تلدة of Y حسب التعريف اللي هي أصغر يساوي
+
+554
+00:42:42,870 --> 00:42:46,390
+مين؟ P of Y لأن الـ Y هدم هي الـ F تلدة من تعريفها
+
+555
+00:42:46,390 --> 00:42:48,930
+extension وتحقق خادة لأن الـ F تلدة موجودة في الـ
+
+556
+00:42:48,930 --> 00:42:52,030
+Eاذا انصرت الافتيل ده y أصغر ساوي P of Y اللي هي
+
+557
+00:42:52,030 --> 00:42:55,050
+بيساوي P of X لإنه Alpha سفر Thus one is true إن
+
+558
+00:42:55,050 --> 00:42:59,510
+Alpha بيساوي سفر Third step وإن Alpha أشمالها أكبر
+
+559
+00:42:59,510 --> 00:43:02,490
+من سفر انزل عشان تشوف تلاتة بنفس الوثنوب دي شعيده
+
+560
+00:43:04,030 --> 00:43:07,470
+بنفس الأسلوب اطلع خلّيها بس هذه اطلع لفوق شوية
+
+561
+00:43:07,470 --> 00:43:13,950
+ايوة بقى لأ خلّي ايوة اكملي شوية بس طيب الان when
+
+562
+00:43:13,950 --> 00:43:18,810
+alpha الان اكبر من سفر by تلاتة ماشي الحال but
+
+563
+00:43:18,810 --> 00:43:24,250
+triples y by minus مين ما لها alpha ناقص y ماشي
+
+564
+00:43:24,250 --> 00:43:28,370
+الحال and then multiply both sides by مين by alpha
+
+565
+00:43:28,370 --> 00:43:31,260
+to getأكيد بتحصلوا على هذا المقدار نفس الأسلوب
+
+566
+00:43:31,260 --> 00:43:33,980
+اللي قبل بشوية بالظبط اللي شراحته Alpha C أصغر
+
+567
+00:43:33,980 --> 00:43:37,840
+ساوي هذا المقدار هذا المقدار الآن Alpha بتدخله ال
+
+568
+00:43:37,840 --> 00:43:41,500
+Alpha جوه و بتشتغل و كده بنفس الأسلوب هتطلع عندى
+
+569
+00:43:41,500 --> 00:43:45,620
+هذه لما تدخلها دي بيصير بي و اي زايد Alpha Y واحد
+
+570
+00:43:45,620 --> 00:43:49,140
+اللي هي X بي of X فبيصير هذه بي of X و هذه ال
+
+571
+00:43:49,140 --> 00:43:52,240
+Alpha بتدخلوها جوه بيصير اللي هي F tilde of Y
+
+572
+00:43:52,240 --> 00:43:56,640
+مفهوم اه فبيصير عندي الآن Alpha C أصغر ساوي بي of
+
+573
+00:43:56,640 --> 00:44:00,750
+X زايد هذه اطلع لفوق الآنحصلنا على هذه منها بدنا
+
+574
+00:44:00,750 --> 00:44:03,490
+نحصل جي واحد و فيكس اللي هو اش مساوي بنفس الأسلوب
+
+575
+00:44:03,490 --> 00:44:07,210
+برضه اللي هو F تلد of Y زائد Alpha C Alpha tilde
+
+576
+00:44:07,210 --> 00:44:11,790
+of Y هيها زائد Alpha C أصغر من مين من بي و فيكس
+
+577
+00:44:11,790 --> 00:44:16,120
+لما نجلها هيها هادي هادي نجلها هان بالسيرaf tilde
+
+578
+00:44:16,120 --> 00:44:20,120
+of y زي ده alpha c أصغر من b of x ده حسابات كلها و
+
+579
+00:44:20,120 --> 00:44:23,140
+حسبنا زيها فبصير عند af tilde of y زي ده alpha c
+
+580
+00:44:23,140 --> 00:44:26,860
+أصغر سواء بيه of x إذا كانت برضه صحيحة في حالة مين
+
+581
+00:44:26,860 --> 00:44:29,520
+ال alpha أكبر من سفره ولا أصغر من سفره و بيه أصغر
+
+582
+00:44:29,520 --> 00:44:29,860
+من أصغر من أصغر من أصغر من أصغر من أصغر من أصغر من
+
+583
+00:44:29,860 --> 00:44:32,360
+أصغر من أصغر من أصغر من أصغر من أصغر من أصغر من
+
+584
+00:44:32,360 --> 00:44:35,260
+أصغر من أصغر من أصغر من أصغر من أصغر من أصغر من
+
+585
+00:44:35,260 --> 00:44:41,860
+أصغر من أصغر من أصغر من أصغر من أصغر من أص
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/VEACdbo-6Yo_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/VEACdbo-6Yo_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..e0e2c4fc0e934233b7a9cca642f92bbcf478e385
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/VEACdbo-6Yo_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3308, "start": 5.04, "end": 33.08, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى آله وصحبه أجمعين هذه المحاضرة رقم 24 مساق تحليل اقتراني او تحليل دالي طلاب وطالبات الجامعة الإسلامية ماجستير رياضيات وكل عام وانتم بخير مناسبة عيد الفطر المبارك اليوم ان شاء الله هيكون في عندنا الحديث عن اللي هي تلاتة تسعة اللي هو Hilbert Adjoint Operator", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 19753, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 29538, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 4022, 47524, 995, 4587, 6055, 5016, 20292, 1211, 1975, 38149, 2288, 7649, 1829, 1975, 2407, 6055, 5016, 20292, 1211, 11778, 6027, 1829, 23032, 15040, 3555, 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"end": 230.1, "word": " انا", "probability": 0.748779296875}, {"start": 230.1, "end": 231.96, "word": " انعرف", "probability": 0.8009440104166666}, {"start": 231.96, "end": 232.36, "word": " مالي", "probability": 0.8603515625}, {"start": 232.36, "end": 232.6, "word": " عشان", "probability": 0.9264322916666666}, {"start": 232.6, "end": 232.92, "word": " نبره", "probability": 0.9287109375}, {"start": 232.92, "end": 233.02, "word": " ان", "probability": 0.8984375}, {"start": 233.02, "end": 233.08, "word": " انا", "probability": 0.604248046875}, {"start": 233.08, "end": 233.34, "word": " انعرف", "probability": 0.8904622395833334}, {"start": 233.34, "end": 233.78, "word": " مالي", "probability": 0.96875}, {"start": 233.78, "end": 234.6, "word": " البرهان", "probability": 0.8131103515625}, {"start": 234.6, "end": 235.5, "word": " consider", "probability": 0.796875}, {"start": 235.5, "end": 235.86, "word": " H", "probability": 0.13427734375}, {"start": 235.86, "end": 236.12, "word": " Y", 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" و", "probability": 0.927734375}, {"start": 251.78, "end": 251.96, "word": " X", "probability": 0.8994140625}, {"start": 251.96, "end": 252.14, "word": " من", "probability": 0.98828125}, {"start": 252.14, "end": 252.82, "word": " H1", "probability": 0.99072265625}, {"start": 252.82, "end": 253.82, "word": " بساوي", "probability": 0.826416015625}, {"start": 253.82, "end": 253.94, "word": " ال", "probability": 0.6806640625}, {"start": 253.94, "end": 254.14, "word": " inner", "probability": 0.84130859375}, {"start": 254.14, "end": 254.6, "word": " product", "probability": 0.978515625}, {"start": 254.6, "end": 255.26, "word": " Y", "probability": 0.94189453125}, {"start": 255.26, "end": 255.6, "word": " و", "probability": 0.84130859375}, {"start": 255.6, "end": 256.14, "word": " TX", "probability": 0.817138671875}], "temperature": 1.0}, {"id": 12, "seek": 26994, "start": 256.8, "end": 269.94, "text": "طبعا هذا ال operator عرفته بالشكل هذا ytx معرفات لأن هو عبارة عن inner product اللي هي 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"seek": 53033, "start": 509.45, "end": 530.33, "text": "ليش هذه بدياها؟ بدياها عشان أطبّق نظرية اللي هو أخدناها المرة الماضية، الآن صارت عندي هذه عبارة عن CISC و Linear، الآن ومش هيك ومش was inequality، لو أجيت أخدت ال absolute value لل H و V و X، إيش هتطلع؟ ال absolute value ال inner product", "tokens": [20292, 8592, 29538, 4724, 16254, 995, 11296, 22807, 4724, 16254, 995, 11296, 6225, 8592, 7649, 5551, 9566, 3555, 11703, 4587, 8717, 19913, 2288, 10632, 13672, 1829, 31439, 5551, 9778, 3215, 8315, 11296, 9673, 25720, 9673, 46958, 10632, 12399, 6024, 48506, 20328, 9640, 2655, 18871, 16254, 29538, 6225, 3555, 9640, 3660, 18871, 383, 2343, 34, 4032, 14670, 289, 12399, 6024, 48506, 4032, 2304, 8592, 39896, 4117, 4032, 2304, 8592, 390, 16970, 12399, 45164, 5551, 7435, 36081, 5551, 9778, 3215, 2655, 2423, 8236, 2158, 24976, 389, 4032, 691, 4032, 1783, 12399, 11933, 1829, 8592, 8032, 2655, 9566, 1211, 3615, 22807, 2423, 8236, 2158, 2423, 7284, 1674], "avg_logprob": -0.2808035578046526, 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"end": 579.12, "word": " سفر", "probability": 0.8038736979166666}, {"start": 579.12, "end": 579.48, "word": " بصير", "probability": 0.8079427083333334}, {"start": 579.48, "end": 579.8, "word": " على", "probability": 0.73876953125}, {"start": 579.8, "end": 580.6, "word": " نورم", "probability": 0.96875}, {"start": 580.6, "end": 580.76, "word": " الـ", "probability": 0.699951171875}, {"start": 580.76, "end": 581.14, "word": " X", "probability": 0.96142578125}, {"start": 581.14, "end": 581.76, "word": " في", "probability": 0.9755859375}, {"start": 581.76, "end": 582.1, "word": " نورم", "probability": 0.98388671875}, {"start": 582.1, "end": 582.26, "word": " الـ", "probability": 0.966796875}, {"start": 582.26, "end": 582.68, "word": " Y", "probability": 0.91650390625}, {"start": 582.68, "end": 583.64, "word": " أصغر", "probability": 0.9879150390625}, {"start": 583.64, "end": 583.84, "word": " أوي", "probability": 0.921875}, {"start": 583.84, "end": 584.12, "word": " بساوي", "probability": 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في", "probability": 0.6513671875}, {"start": 599.48, "end": 599.58, "word": " ال", "probability": 0.951171875}, {"start": 599.58, "end": 600.08, "word": " H2", "probability": 0.97314453125}, {"start": 600.08, "end": 601.42, "word": " وهذا", "probability": 0.6932373046875}, {"start": 601.42, "end": 601.98, "word": " نفسه", "probability": 0.978515625}, {"start": 601.98, "end": 602.48, "word": " عبارة", "probability": 0.960205078125}, {"start": 602.48, "end": 602.7, "word": " عن", "probability": 0.962890625}, {"start": 602.7, "end": 603.1, "word": " مين؟", "probability": 0.80810546875}, {"start": 603.1, "end": 603.3, "word": " عن", "probability": 0.86962890625}, {"start": 603.3, "end": 604.38, "word": " نور", "probability": 0.6240234375}, {"start": 604.38, "end": 604.72, "word": " ال", "probability": 0.91796875}, {"start": 604.72, "end": 605.04, "word": " H", "probability": 0.6962890625}], "temperature": 1.0}, {"id": 27, "seek": 62157, "start": 605.59, "end": 621.57, "text": "إذا صارت نورم الـH أصغر أو سوء نورم مين؟ الـT إذا أثبتنا إن H is a ciscolinear form which is bounded ونورمها أصغر أو سوء مين؟ نورم الـT من جهة أخرى", "tokens": [28814, 15730, 20328, 9640, 2655, 8717, 13063, 2304, 2423, 39184, 39, 5551, 9381, 17082, 2288, 34051, 8608, 2407, 38207, 8717, 13063, 2304, 3714, 9957, 22807, 2423, 39184, 51, 11933, 15730, 5551, 12984, 3555, 2655, 8315, 36145, 389, 307, 257, 269, 5606, 401, 533, 289, 1254, 597, 307, 37498, 4032, 1863, 13063, 2304, 11296, 5551, 9381, 17082, 2288, 34051, 8608, 2407, 38207, 3714, 9957, 22807, 8717, 13063, 2304, 2423, 39184, 51, 9154, 10874, 3224, 3660, 5551, 34740, 7578], "avg_logprob": -0.2572115495418891, "compression_ratio": 1.4805194805194806, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 605.59, "end": 605.87, "word": "إذا", "probability": 0.6337890625}, {"start": 605.87, "end": 606.37, "word": " صارت", "probability": 0.7628580729166666}, {"start": 606.37, "end": 606.75, "word": " نورم", "probability": 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0.8837890625}, {"start": 699.01, "end": 699.27, "word": " TX", "probability": 0.99267578125}, {"start": 699.27, "end": 699.41, "word": " على", "probability": 0.76318359375}, {"start": 699.41, "end": 699.69, "word": " norm", "probability": 0.90771484375}, {"start": 699.69, "end": 699.79, "word": " ال", "probability": 0.87744140625}, {"start": 699.79, "end": 699.95, "word": " X", "probability": 0.95849609375}, {"start": 699.95, "end": 700.07, "word": " ال", "probability": 0.87109375}, {"start": 700.07, "end": 700.47, "word": " supermom", "probability": 0.9755859375}, {"start": 700.47, "end": 700.61, "word": " اللي", "probability": 0.91259765625}, {"start": 700.61, "end": 700.69, "word": " هو", "probability": 0.521484375}, {"start": 700.69, "end": 700.79, "word": " مين", "probability": 0.963134765625}, {"start": 700.79, "end": 701.45, "word": " هيطلع", "probability": 0.8973388671875}, {"start": 701.45, "end": 702.47, "word": " norm", "probability": 0.83447265625}, {"start": 702.47, "end": 702.99, "word": " اللي", "probability": 0.98828125}, {"start": 702.99, "end": 703.11, "word": " هو", "probability": 0.99072265625}, {"start": 703.11, "end": 703.49, "word": " مين", "probability": 0.968994140625}, {"start": 703.49, "end": 703.93, "word": " ال", "probability": 0.6015625}, {"start": 703.93, "end": 704.09, "word": " T", "probability": 0.98095703125}], "temperature": 1.0}, {"id": 31, "seek": 72779, "start": 704.65, "end": 727.79, "text": "واضح إذا صار عندى برضه norm of H أكبر أو يساوي norm of T واللي جاب ال norm of H أزرع يساوي norm of T together norm of H إيش بيساوي norm of T إذا الأن .. الأن جهزت للنظرية اللي هي 384 أنه اللي هو لجيت H is bounded sesquilinear form إذا من theorem 384", "tokens": [2407, 46958, 5016, 11933, 15730, 20328, 9640, 43242, 7578, 4724, 43042, 3224, 2026, 295, 389, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 2026, 295, 314, 4032, 6027, 20292, 10874, 16758, 2423, 2026, 295, 389, 5551, 11622, 2288, 3615, 7251, 3794, 995, 45865, 2026, 295, 314, 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"start": 745.4, "end": 757.94, "text": "إذا كانت H عبارة عن bounded ciscolinear form إذا بقدر أكتبها uniquely as an inner product بقدر أحولها عبارة عن H وعندي", "tokens": [28814, 15730, 25961, 2655, 389, 6225, 3555, 9640, 3660, 18871, 37498, 269, 5606, 401, 533, 289, 1254, 11933, 15730, 4724, 28543, 2288, 5551, 4117, 2655, 3555, 11296, 31474, 382, 364, 7284, 1674, 4724, 28543, 2288, 5551, 5016, 12610, 11296, 6225, 3555, 9640, 3660, 18871, 389, 4032, 3615, 1863, 16254], "avg_logprob": -0.26734373569488523, "compression_ratio": 1.2651515151515151, "no_speech_prob": 2.3245811462402344e-06, "words": [{"start": 745.4, "end": 745.62, "word": "إذا", "probability": 0.833740234375}, {"start": 745.62, "end": 746.02, "word": " كانت", "probability": 0.95654296875}, {"start": 746.02, "end": 746.36, "word": " H", "probability": 0.58740234375}, {"start": 746.36, "end": 747.36, "word": " عبارة", "probability": 0.9583740234375}, {"start": 747.36, "end": 747.6, "word": " عن", "probability": 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{"start": 1419.66, "end": 1419.9, "word": " إذا", "probability": 0.93505859375}, {"start": 1419.9, "end": 1420.08, "word": " ال", "probability": 0.54931640625}, {"start": 1420.08, "end": 1420.34, "word": " Q", "probability": 0.4755859375}], "temperature": 1.0}, {"id": 63, "seek": 144464, "start": 1421.36, "end": 1444.64, "text": "اللي هو هذا دايماً هيكون عنده سفر لكن الـQ نفسه أشماله مش سفر هذا الهندسيا، دبريا هيه to see this consider the mapping Q من R تربيع لR تربيع given by الـQ Alpha و Beta بيساوي Beta وناقص Alpha it is clear that for any X element in Alpha و Beta element in R تربيع لو جيتوا أخدتوا الـ inner product", "tokens": [6027, 20292, 31439, 23758, 11778, 47302, 15042, 14111, 39896, 30544, 43242, 3224, 8608, 5172, 2288, 44381, 2423, 39184, 48, 8717, 36178, 3224, 5551, 8592, 2304, 6027, 3224, 37893, 8608, 5172, 2288, 23758, 2423, 3224, 41260, 3794, 25528, 12399, 11778, 3555, 16572, 995, 39896, 3224, 281, 536, 341, 1949, 264, 18350, 1249, 9154, 497, 6055, 2288, 21292, 3615, 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" that", "probability": 0.94384765625}, {"start": 1440.52, "end": 1440.8, "word": " for", "probability": 0.94775390625}, {"start": 1440.8, "end": 1441.08, "word": " any", "probability": 0.90283203125}, {"start": 1441.08, "end": 1441.34, "word": " X", "probability": 0.828125}, {"start": 1441.34, "end": 1441.66, "word": " element", "probability": 0.265380859375}, {"start": 1441.66, "end": 1441.84, "word": " in", "probability": 0.79638671875}, {"start": 1441.84, "end": 1442.0, "word": " Alpha", "probability": 0.8544921875}, {"start": 1442.0, "end": 1442.18, "word": " و", "probability": 0.98095703125}, {"start": 1442.18, "end": 1442.34, "word": " Beta", "probability": 0.54345703125}, {"start": 1442.34, "end": 1442.56, "word": " element", "probability": 0.8837890625}, {"start": 1442.56, "end": 1442.76, "word": " in", "probability": 0.321044921875}, {"start": 1442.76, "end": 1442.88, "word": " R", "probability": 0.97412109375}, {"start": 1442.88, "end": 1443.24, "word": " تربيع", 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inner", "probability": 0.81103515625}, {"start": 1484.44, "end": 1484.72, "word": " product", "probability": 0.966796875}, {"start": 1484.72, "end": 1485.04, "word": " بينهم", "probability": 0.959716796875}, {"start": 1485.04, "end": 1485.3, "word": " سفر", "probability": 0.9793294270833334}, {"start": 1485.3, "end": 1485.64, "word": " معناته", "probability": 0.714111328125}, {"start": 1485.64, "end": 1485.9, "word": " لازم", "probability": 0.9371744791666666}, {"start": 1485.9, "end": 1486.14, "word": " يطلع", "probability": 0.990966796875}, {"start": 1486.14, "end": 1486.28, "word": " Q", "probability": 0.6005859375}, {"start": 1486.28, "end": 1486.56, "word": " سفر", "probability": 0.8359375}, {"start": 1486.56, "end": 1486.86, "word": " رسميا", "probability": 0.3937581380208333}, {"start": 1486.86, "end": 1487.28, "word": " حسب", "probability": 0.7435302734375}, {"start": 1487.28, "end": 1487.94, "word": " النظرية", "probability": 0.7821044921875}, {"start": 1487.94, "end": 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"word": " اللي", "probability": 0.970947265625}, {"start": 1508.62, "end": 1509.24, "word": " عرفنا", "probability": 0.9388020833333334}, {"start": 1509.24, "end": 1509.44, "word": " فيه", "probability": 0.89892578125}, {"start": 1509.44, "end": 1509.54, "word": " الـ", "probability": 0.759033203125}, {"start": 1509.54, "end": 1509.78, "word": " Adjoint", "probability": 0.9248046875}, {"start": 1509.78, "end": 1510.4, "word": " Operator", "probability": 0.87109375}, {"start": 1510.4, "end": 1511.04, "word": " قلنا", "probability": 0.7967122395833334}, {"start": 1511.04, "end": 1511.52, "word": " الـ", "probability": 0.900146484375}, {"start": 1511.52, "end": 1512.06, "word": " Adjoint", "probability": 0.92138671875}, {"start": 1512.06, "end": 1512.86, "word": " T", "probability": 0.568359375}], "temperature": 1.0}, {"id": 67, "seek": 152288, "start": 1514.24, "end": 1522.88, "text": "من H1 لعند H2 و T*) من H2 لعند H1 تحقق ما يلي", "tokens": [27842, 389, 16, 5296, 3615, 41260, 389, 17, 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.. في ال .. أيه بقى؟ عندي اللي هو Alpha T Star بس هو Alpha conjugate في مين؟ في T Star Similarly .. 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/WmXLCzkJRL8.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/WmXLCzkJRL8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d1d401265dbf5033abdb0a4a50a5aa63e7f275bb
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/WmXLCzkJRL8.srt
@@ -0,0 +1,2295 @@
+1
+00:00:05,970 --> 00:00:08,510
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,510 --> 00:00:12,170
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:12,170 --> 00:00:16,670
+آله وصحبه أجمعين هذه المحاضرة رقم ثلاثين نساق
+
+4
+00:00:16,670 --> 00:00:20,810
+تحليل اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:20,810 --> 00:00:24,850
+الإسلامية قسم الرياضيات ماجستير وصلنا لعند اللي هو
+
+6
+00:00:24,850 --> 00:00:28,370
+الـ section السادس في شابتر أربعة اللي هو تحت عنوان
+
+7
+00:00:28,370 --> 00:00:29,710
+reflexive spaces
+
+8
+00:00:32,710 --> 00:00:36,690
+نبدأ في البداية بهذه اللمّة الصغيرة على أساس
+
+9
+00:00:36,690 --> 00:00:41,570
+تأهيلنا لإنه نعرف شو معناه بعد شوية لما بعدين نعرف
+
+10
+00:00:41,570 --> 00:00:48,270
+شو معناه reflexive space اللمّة بتقول التالي: for
+
+11
+00:00:48,270 --> 00:00:53,310
+every fixed X in a normed space X the functional
+
+12
+00:00:53,310 --> 00:00:58,610
+GX defined on X' يعني عندي X عبارة عن normed space
+
+13
+00:01:01,290 --> 00:01:06,730
+وعندي x arbitrary element in X لكن اللي هو بنحكي
+
+14
+00:01:06,730 --> 00:01:10,370
+عن إيش محدد أخدته arbitrary but fixed يعني بدي
+
+15
+00:01:10,370 --> 00:01:13,590
+أسير أحكي عن الـ element العشوائي اللي في الـ X اللي
+
+16
+00:01:13,590 --> 00:01:18,230
+أخدته عشوائي بس بدي أحكي عن element معين بعد ما
+
+17
+00:01:18,230 --> 00:01:21,690
+أخده عشوائي بدي أحكي عنه بدي نعرف الـ functional DX
+
+18
+00:01:23,550 --> 00:01:29,470
+معرفتها defined on X' يعني تاخد من X' و ترمى في الـ
+
+19
+00:01:29,470 --> 00:01:35,010
+scalar field تبعته اللي هو الـ K كيف بدي أعرفها؟
+
+20
+00:01:35,010 --> 00:01:41,130
+DX of العناصر اللي هنا dual functional لإن هذا
+
+21
+00:01:41,130 --> 00:01:45,470
+الـ dual اسم بياسم of F بساوي، إيش بدي أعرفها؟ بدي
+
+22
+00:01:45,470 --> 00:01:49,050
+أعرف قيمة الـ F دي اللي أخدتها من هنا عند مين؟ عند
+
+23
+00:01:49,050 --> 00:01:55,550
+النقطة X الـ Fixed هذه بساوي F of X الآن هذه صارت
+
+24
+00:01:55,550 --> 00:01:59,270
+عندي اللي هي function هو بتدعي الآن اللي ما بتقول
+
+25
+00:01:59,270 --> 00:02:03,890
+هتطلع هذا الـ function is a bounded linear
+
+26
+00:02:03,890 --> 00:02:07,770
+functional يعني بمعنى آخر هتطلع اللي عالميا على ال
+
+27
+00:02:07,770 --> 00:02:11,310
+X' إذا هتكون في الـ dual اسمه إسلاميا للـ X' يعني في
+
+28
+00:02:11,310 --> 00:02:15,370
+الـ second dual و كأنها DX element in X double prime
+
+29
+00:02:15,370 --> 00:02:19,550
+و هيطلع عندي norm الـ DX هو norm الـ X طلع ليها
+
+30
+00:02:19,550 --> 00:02:24,190
+الكتاب الآن بدنا نبرهن هذه اللي هي الـ linearity
+
+31
+00:02:24,190 --> 00:02:29,770
+اللي هي يعني بالطرق العادية يعني لو جينا أخدنا G X
+
+32
+00:02:29,770 --> 00:02:40,700
+of Alpha F مثلا زائد F إبراهيم أو F واحد بندن نشوف
+
+33
+00:02:40,700 --> 00:02:45,580
+إيش قيمتها بقى هتكون قيمتها بالساوي Alpha F زائد F
+
+34
+00:02:45,580 --> 00:02:50,780
+واحد الكل of مين؟ حسب التعريف of X صح ولا لأ ويساوي
+
+35
+00:02:50,780 --> 00:02:57,620
+Alpha F of X زائد F واحد of X وهذه فعلا مين هي
+
+36
+00:02:57,620 --> 00:03:06,750
+عبارة عن Alpha DX of F صحيح؟ زائد مين؟ زائد g of dx
+
+37
+00:03:06,750 --> 00:03:14,210
+of f واحد فعلاً طلعت أشملها easily لان لان المرة
+
+38
+00:03:14,210 --> 00:03:18,790
+الماضية اللي هي الـ chapter اللي في الـ section اللي
+
+39
+00:03:18,790 --> 00:03:25,690
+فات أخدنا الـ norm بدلالة الـ x يعني norm الـ X
+
+40
+00:03:25,690 --> 00:03:29,450
+بدلالة الـ F آسف غير إن أحنا بنوجد النورم بدلالة
+
+41
+00:03:29,450 --> 00:03:35,430
+مين؟ اللي هو الـ X نفسها اللي بقصده يعني نقول norm
+
+42
+00:03:35,430 --> 00:03:41,810
+الـ X أو norm الـ F بساوي الـ supremum هذا اللي
+
+43
+00:03:41,810 --> 00:03:49,190
+بنعرفه F of X على X norm لـ X element in X minus
+
+44
+00:03:49,190 --> 00:03:54,930
+مين؟ Zero هذا التعريف العادي ما في الحال الآن أخدنا
+
+45
+00:03:54,930 --> 00:03:58,870
+احنا المرة الفاتتة الـ corollary انه Normal X بنقدر
+
+46
+00:03:58,870 --> 00:04:05,230
+نقول عنها عبارة عن الـ supremum للـ F of X عالميا على
+
+47
+00:04:05,230 --> 00:04:11,050
+norm الـ F والـ F element in X' ماشي الحال الأخرى
+
+48
+00:04:11,050 --> 00:04:13,890
+هذا خدمة المرة الفاتتة اللي هي النتيجة بس أعملها
+
+49
+00:04:13,890 --> 00:04:18,450
+الآن الآن عشان أثبت لكم إنه GX is bounded وNorm ما
+
+50
+00:04:18,450 --> 00:04:22,850
+بيسوي Norm الـ X الأمر سهل Norm الـ GX حسب تعريف
+
+51
+00:04:22,850 --> 00:04:26,490
+اللي هو النورم العادي هو أبداً الـ supremum لقيمة
+
+52
+00:04:26,490 --> 00:04:28,990
+هذه عند اللي هو الـ arbitrary F اللي هي في
+
+53
+00:04:28,990 --> 00:04:33,240
+domainها domainها مين هو؟ X' الآن بيصير absolute
+
+54
+00:04:33,240 --> 00:04:37,420
+value of g x of f على mean normal f دي اللي هي ال
+
+55
+00:04:37,420 --> 00:04:40,220
+element اللي هو الموجود في الـ x' للفاتي اللي
+
+56
+00:04:40,220 --> 00:04:44,440
+بيساوي النشتفر الآن هذا نفسه بيساوي g x of f إيش
+
+57
+00:04:44,440 --> 00:04:49,500
+هي هايها g x of f بتساوي mean F of X إذا بيساوي الـ
+
+58
+00:04:49,500 --> 00:04:54,480
+absolute value الـ F of X على Norm الـ F F limit
+
+59
+00:04:54,480 --> 00:04:58,260
+X' وهذه من الـ corollary اللي حكيت عنها قبل شوية إيش
+
+60
+00:04:58,260 --> 00:05:02,320
+بتساوي Norm الـ X إذا صار عندي Norm الـ GX بيساوي
+
+61
+00:05:02,320 --> 00:05:09,430
+مين؟ Norm اللي هو LX اطلع لفوق إذا صار عندي اللي هي
+
+62
+00:05:09,430 --> 00:05:13,390
+اللي اللي صارت عندي bounded وصارت عندي اللي هو
+
+63
+00:05:13,390 --> 00:05:17,810
+normها بساوي norm هذا إذا الـ GX هذه اللي عندي صارت
+
+64
+00:05:17,810 --> 00:05:22,050
+bounded linear functional و norm هو norm الـ X هذه
+
+65
+00:05:22,050 --> 00:05:25,990
+بتستختمها بعد شوية أطلع لها على التلخيص إلى أن نجي
+
+66
+00:05:25,990 --> 00:05:30,650
+للملة اللي بعدها الملة اللي بعدها كانت تالي بتقول
+
+67
+00:05:30,650 --> 00:05:35,250
+لي let X be a known space هذا كله عشان أصل اللي هو
+
+68
+00:05:35,250 --> 00:05:38,530
+تعريف الـ reflexive space let X be a known space
+
+69
+00:05:38,530 --> 00:05:41,670
+then the canonical mapping هذا بنسميه canonical
+
+70
+00:05:41,670 --> 00:05:47,090
+mapping C هياخد من مين؟ من X لمين؟ للـ X double prime
+
+71
+00:05:47,090 --> 00:05:52,410
+هذا اللي هيحددلي اللي هو هوية الـ reflexive space
+
+72
+00:05:52,410 --> 00:05:56,290
+من خلاله بدي أعرف الـ reflexive space إيه هذا ال
+
+73
+00:05:56,290 --> 00:05:59,170
+mapping؟ then the canonical mapping C من X لـ X 
+
+74
+00:05:59,170 --> 00:06:03,050
+double prime defined by إيش بده ياخد هذا؟ بده ياخد
+
+75
+00:06:03,050 --> 00:06:08,190
+الـ C of X أي X المتنهانة يرميه لمين؟ لـ G X وين
+
+76
+00:06:08,190 --> 00:06:12,140
+موجودة في الـ X double prime اللي تاية مهتلها اللي
+
+77
+00:06:12,140 --> 00:06:16,840
+هي إيش؟ DX الـ Double Prime تعريفها؟ انه DX of F هي
+
+78
+00:06:16,840 --> 00:06:20,220
+اللي عرفتها قبل شوية بساوي F of X لكل F element in
+
+79
+00:06:20,220 --> 00:06:23,300
+X prime إيش هيعمل لي الـ canonical mapping هذا؟
+
+80
+00:06:23,300 --> 00:06:27,440
+المعرف على هذا الأساس هيعمل لي is an isomorphism
+
+81
+00:06:27,440 --> 00:06:32,140
+from X onto mean R of C يعني هيعمل لي one to one و
+
+82
+00:06:32,140 --> 00:06:37,540
+isometric و linear لكن مش هيقول لي ان هو onto اللي
+
+83
+00:06:37,540 --> 00:06:41,660
+هو بس isomorphism من وين؟ من X onto mean range of
+
+84
+00:06:41,660 --> 00:06:45,700
+C the range of mean of C يعني قال له كلمة بتمتعي
+
+85
+00:06:45,700 --> 00:06:49,840
+بكل شيء مع ده خاصية اللي هو الـ onto ممكن أه و
+
+86
+00:06:49,840 --> 00:06:54,100
+ممكن لأ حسب اللي موجود واضح اللي بحكيه؟ طيب الآن
+
+87
+00:06:54,100 --> 00:06:57,500
+لنثبت هذا الكلام عشان نثبت اللي هو isomorphism
+
+88
+00:06:57,500 --> 00:07:03,060
+بنثبت الـ linearity الـ Linearity كالعادة خدوا أي أف
+
+89
+00:07:03,060 --> 00:07:07,080
+في الـ X براي أنا الآن ال .. الـ mapping تبعي من وين
+
+90
+00:07:07,080 --> 00:07:18,580
+لوين؟ الـ mapping ال
+
+91
+00:07:18,580 --> 00:07:25,700
+mapping C من X لعند X مين؟ double prime الـ C هتاخد
+
+92
+00:07:25,700 --> 00:07:28,760
+الـ X و هترميها في مين؟ في الـ element هنا سميناه
+
+93
+00:07:28,760 --> 00:07:32,660
+مين هو؟ الـ GX الـ GX هذا هيكون اللي هو في الـ X
+
+94
+00:07:32,660 --> 00:07:35,700
+double prime يعني هيكون الـ GX من X prime لعند مين؟
+
+95
+00:07:35,700 --> 00:07:40,060
+لعند K تحت القانون GX of F بيساوي مين؟ F of X لكل F
+
+96
+00:07:40,060 --> 00:07:44,000
+موجودة في الـ X prime طب إذن الآن عشان أثبت Linear
+
+97
+00:07:44,000 --> 00:07:49,640
+بدي أثبت لكم إن C α X زائد Y عند كل نقطة من النقاط
+
+98
+00:07:49,640 --> 00:07:52,280
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+99
+00:07:52,280 --> 00:07:53,200
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+100
+00:07:53,200 --> 00:07:54,060
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+101
+00:07:54,060 --> 00:07:54,300
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+102
+00:07:54,300 --> 00:07:57,660
+F F
+
+103
+00:07:57,660 --> 00:07:57,720
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+104
+00:07:57,720 --> 00:07:57,760
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+105
+00:07:57,760 --> 00:08:04,030
+F F F F F F لأن أخذ arbitrary f element in X' و أخذ ل
+
+106
+00:08:04,030 --> 00:08:07,510
+X و Y وين موجودات؟ في الـ domain اللي بنحكي عنها و
+
+107
+00:08:07,510 --> 00:08:13,130
+الـ α scalar احسب لي C α X زي Y عند مين؟ عند الـ F
+
+108
+00:08:13,130 --> 00:08:17,870
+واضح؟ الـ F arbitrary element in وين؟ in X' بساوي
+
+109
+00:08:17,870 --> 00:08:22,210
+حسب التعريف اللي قبله بشوية بيصير G هذه of هذه،
+
+110
+00:08:22,210 --> 00:08:27,290
+مظبوط؟ G α X زي Y of F وهذه تعريفة إيش؟ F لهذا
+
+111
+00:08:27,880 --> 00:08:32,480
+ويساوي f of α x زائد y ويساوي f is linear ما هي f 
+
+112
+00:08:32,480 --> 00:08:36,700
+element in x' إذا هتتوزع α f of x زائد f of mean
+
+113
+00:08:36,700 --> 00:08:42,000
+of y الآن هذه بدرجة حال أصلها هذه عبارة عن مين هذه
+
+114
+00:08:42,000 --> 00:08:46,080
+الحالها اللي هو g x of f وهذه الـ alpha زي ما هي
+
+115
+00:08:46,080 --> 00:08:51,510
+وهذه إيش أصلها؟ g of y of f الآن هذه اللي هي Alpha
+
+116
+00:08:51,510 --> 00:08:56,490
+DX of F هي عبارة عن هذه كلها عبارة عن مين؟ هي C of
+
+117
+00:08:56,490 --> 00:09:01,370
+X of مين؟ of F زي ما احنا معرفينها CX إيشو بتساوي DX
+
+118
+00:09:01,370 --> 00:09:06,290
+CX of F بيساوي DX of F هي عندك DX of F بيصير عبارة
+
+119
+00:09:06,290 --> 00:09:10,530
+عن C of X of مين؟ of F و الـ alpha معاها ونفس الـ
+
+120
+00:09:10,530 --> 00:09:15,710
+relation DY of F هي عبارة عن C of Y of مين؟ of F
+
+121
+00:09:16,160 --> 00:09:19,700
+الآن هذا الكلام صار صحيح لكل F إذا صارت عند C of
+
+122
+00:09:19,700 --> 00:09:24,220
+Alpha X زائد Y بتساوي Alpha C of X زائد C of Y
+
+123
+00:09:24,220 --> 00:09:31,560
+و هذا يعني ان الـ C is Linear طيب الآن note that
+
+124
+00:09:31,560 --> 00:09:39,120
+بدي أحصلكم الآن على إنها bounded و isometric معاها
+
+125
+00:09:39,120 --> 00:09:45,530
+نشوف كيف خدوا الآن أي F element in main in X' و الـ
+
+126
+00:09:45,530 --> 00:09:49,350
+X و Y are arbitrary points in main in X نفسها
+
+127
+00:09:49,350 --> 00:09:55,350
+ويحسبوا لي GX-Y of F إيش هيساوي حسب التعريف الجبل
+
+128
+00:09:55,350 --> 00:10:02,710
+شوية هي عبارة عن F of X minus Y و الـ F is Linear
+
+129
+00:10:02,710 --> 00:10:05,930
+إذا بيساوي F of X ناقص F of Y طب الـ F of X ما هي
+
+130
+00:10:05,930 --> 00:10:10,290
+عبارة عن GX F of F و الـ F of Y هي عبارة عن GY of F
+
+131
+00:10:10,290 --> 00:10:14,730
+إلى أن بيصير عبارة عن GX ناقص GY of مين؟ of F حصل
+
+132
+00:10:14,730 --> 00:10:20,440
+طرح دالكين إلى أن صار عندي الآن هذا المقدار بساوي
+
+133
+00:10:20,440 --> 00:10:25,900
+هذا المقدار عند كل F إذا أكيد هيصير عندي GX-Y هو
+
+134
+00:10:25,900 --> 00:10:30,480
+نفسه G GX ناقص GY لأن دالتين متساويتين عند كل
+
+135
+00:10:30,480 --> 00:10:32,740
+نقطة من النقطة الـ domain هنا اللي هو الـ F إذا
+
+136
+00:10:32,740 --> 00:10:38,500
+هيكون GX-Y بساوي GX ناقص GY من لمّة 4-6-1
+
+137
+00:10:38,500 --> 00:10:43,530
+اللي قبل بشوية خدوا لي الـ Norm CX ناقص CY ماذا يساوي
+
+138
+00:10:43,530 --> 00:10:49,650
+CX GX ناقص مين؟ GY يساوي Norm GX نقص Y هذه اللي
+
+139
+00:10:49,650 --> 00:10:53,710
+أثبتناها اللي هي هذه من اللي قبل بشوية ماذا يساوي
+
+140
+00:10:53,710 --> 00:10:58,730
+Norm X minus Y إذا صار عندي اللي هو C of X نقص C
+
+141
+00:10:58,730 --> 00:11:02,890
+of Y يساوي Norm X minus Y وهذا معناته أن هذا يعني
+
+142
+00:11:02,890 --> 00:11:04,810
+أن C هي عبارة عن عبارة عن عبارة عن عبارة عن عبارة 
+
+143
+00:11:04,810 --> 00:11:08,070
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+144
+00:11:08,070 --> 00:11:09,350
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+145
+00:11:09,350 --> 00:11:10,410
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+146
+00:11:10,410 --> 00:11:12,790
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+147
+00:11:12,790 --> 00:11:13,430
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+148
+00:11:13,430 --> 00:11:13,950
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+149
+00:11:13,950 --> 00:11:19,460
+عن عبارة عن عبارة عن عبارة عن عبارة عن عهلقال الـ
+
+150
+00:11:19,460 --> 00:11:24,480
+Spaces الـ Spaces اللي بيكون Range of C هو الـ X 
+
+151
+00:11:24,480 --> 00:11:26,880
+double prime يعني الدالة اللي جابله شوية لما تكون
+
+152
+00:11:26,880 --> 00:11:31,020
+on two على طول بنسمي الـ Space هذا X أشماله is
+
+153
+00:11:31,020 --> 00:11:35,020
+reflexive إذا الـ Space X is reflexive إذا لجينا
+
+154
+00:11:35,020 --> 00:11:42,330
+ال canonical mapping اللي هو الـ C الـ C من X لعند
+
+155
+00:11:42,330 --> 00:11:47,570
+X double prime ويكون onto لأن دائما هذا C إيش ماله
+
+156
+00:11:47,570 --> 00:11:52,250
+عبارة عن isomorphism للـ Range of C إذا لجينا اللي
+
+157
+00:11:52,250 --> 00:11:56,910
+هو onto هذا أو بمعنى آخر الـ Range of C بيساوي الـ X 
+
+158
+00:11:56,910 --> 00:12:00,930
+double prime على طول بنقول إن الـ X نفسها إيش ماله 
+
+159
+00:12:00,930 --> 00:12:07,630
+is a reflexive space واضح؟ طيب ونشوف الآن Notes
+
+160
+00:12:08,980 --> 00:12:14,140
+بينما 4 6 2 the non-reflexive space X is isomorphic to a
+
+161
+00:12:14,140 --> 00:12:17,700
+subspace of X double prime X double prime اللي هو
+
+162
+00:12:17,700 --> 00:12:24,020
+the range of C هنس .. هنس بنقول X is embedable
+
+163
+00:12:24,020 --> 00:12:27,740
+in مين؟ in X double prime X is embedable in X
+
+164
+00:12:27,740 --> 00:12:32,180
+double prime لأنه في canonical mapping بين الـ X و
+
+165
+00:12:32,180 --> 00:12:35,120
+بين مين؟ اللي هو X double prime يعني في
+
+166
+00:12:35,120 --> 00:12:39,340
+isomorphism بين الـ X و بين اللي هو subspace منها 
+
+167
+00:12:39,340 --> 00:12:43,720
+فهذه الحاجة بنسميها طبعا إيش؟ X is embedable in X
+
+168
+00:12:43,720 --> 00:12:49,080
+double prime يعني isomorphic لـ subspace من XW' وفي
+
+169
+00:12:49,080 --> 00:12:53,620
+هذه الحالة C يسمى كالونيكال اللي هي أداة الـ
+
+170
+00:12:53,620 --> 00:12:59,200
+embedding من X إلى مين إلى XW' لأن إذا كانت الـ 
+
+171
+00:12:59,200 --> 00:13:05,600
+subspace X عرفية فهي عيزومورفية من مين من XW' لكن
+
+172
+00:13:05,600 --> 00:13:11,400
+لو اقل الليل عنديلو فيه isomorphism بين X وXW' ليس
+
+173
+00:13:11,400 --> 00:13:15,780
+شرطًا هيكون reflexive لأن اللي يعمل isomorphism
+
+174
+00:13:15,780 --> 00:13:18,900
+عشان يكون reflexive اللي بيعمل isomorphism بيه هو
+
+175
+00:13:18,900 --> 00:13:25,720
+الـ canonical map واضح؟ اطلع لفوق طيب
+
+176
+00:13:25,720 --> 00:13:34,240
+theorem if
+
+177
+00:13:34,240 --> 00:13:39,840
+a normed space X is reflexive it is إيش ماله
+
+178
+00:13:39,840 --> 00:13:45,060
+complete يعني الـ space اللي مش complete تدوروش على 
+
+179
+00:13:45,060 --> 00:13:48,720
+إنه reflexive على طول إيش ماله is not reflexive
+
+180
+00:13:48,720 --> 00:13:52,620
+مجرد ما يكون الـ Norm of the space X is reflexive
+
+181
+00:13:52,620 --> 00:13:58,040
+على طول بيكون إيش ماله complete نيجي الآن الأمر
+
+182
+00:13:58,040 --> 00:14:02,220
+سهل since X is reflexive then X is isomorphic to
+
+183
+00:14:02,220 --> 00:14:04,800
+مين؟ to X double prime مين X double prime؟
+
+184
+00:14:04,800 --> 00:14:08,140
+complete مش الـ dual space complete سواء الـX 
+
+185
+00:14:08,140 --> 00:14:11,400
+complete أو لا الـX'' أكيد complete إذا على طول
+
+186
+00:14:11,400 --> 00:14:13,980
+اللي هو الـ isomorphic اللي هو إيش هيكون is
+
+187
+00:14:13,980 --> 00:14:19,720
+complete يعني الآن صار عندي اللي هو any reflexive
+
+188
+00:14:19,720 --> 00:14:23,660
+space is a complete space أو إذا بنخ space طيب
+
+189
+00:14:23,660 --> 00:14:28,120
+theorem every
+
+190
+00:14:28,120 --> 00:14:33,200
+finite dimensional every finite dimensional normed
+
+191
+00:14:33,200 --> 00:14:38,870
+space is reflexive أي finite dimensional normed
+
+192
+00:14:38,870 --> 00:14:43,690
+space is reflexive أخدنا .. اعملنا قبل هيك هذا 
+
+193
+00:14:43,690 --> 00:14:46,390
+اللي هو ال canonical mapping في حالة ال .. في حالة 
+
+194
+00:14:46,390 --> 00:14:51,070
+مين اللي هو ال finite dimensional ليش؟ إذا بتذكروا
+
+195
+00:14:52,180 --> 00:14:55,100
+لما كنا نقول إن الـ dimensional لـ X is finite على
+
+196
+00:14:55,100 --> 00:15:00,420
+طول اللي هو بيصير any linear functional is bounded
+
+197
+00:15:00,420 --> 00:15:04,880
+معناته إنه صار الـ X' و الـ X'' و الـ X*) إيش ماله
+
+198
+00:15:04,880 --> 00:15:07,640
+بيلوزي بعض الـ X*) اللي هو the set of all linear
+
+199
+00:15:07,640 --> 00:15:10,400
+اللي هو functional ما فيش bounded نفسي، احنا 
+
+200
+00:15:10,400 --> 00:15:13,280
+مابنحكيش عنها الآن X' في حالة الـ finite
+
+201
+00:15:13,280 --> 00:15:18,440
+dimensional بتكون هي مين طلعت الـ X*) الآن من الـ
+
+202
+00:15:18,440 --> 00:15:22,500
+Theorem 2.9.3 الـ Dimension للـ X*) لجيناها إيش
+
+203
+00:15:22,500 --> 00:15:27,580
+بتساوي؟ الـ Dimension للـ X إذا صار عندي الآن الـ
+
+204
+00:15:27,580 --> 00:15:29,760
+X double prime .. يعني صارت هذه برضه finite
+
+205
+00:15:29,760 --> 00:15:34,780
+dimensional للـ X والـ X*) إذا الـ X*) Star هتكون
+
+206
+00:15:34,780 --> 00:15:38,160
+برضه مين هي؟ الـ X double prime الـ Second Dual
+
+207
+00:15:38,160 --> 00:15:43,370
+Space الآن however .. however اللي هو C من X لعند X
+
+208
+00:15:43,370 --> 00:15:48,290
+double star إيش كانت أثبتناها is an isomorphism
+
+209
+00:15:48,290 --> 00:15:53,510
+مدام isomorphism هذه و هو ال X double prime مين هو 
+
+210
+00:15:53,510 --> 00:15:56,990
+ال X double star هو نفسه ال X double prime إذا 
+
+211
+00:15:56,990 --> 00:16:01,770
+صارت C من X لعند X double star is an isomorphism
+
+212
+00:16:01,770 --> 00:16:06,640
+hence ال X هتطلع is reflexive إذن الآن كلها الـ
+
+213
+00:16:06,640 --> 00:16:10,780
+finite dimensional spaces طلعت لنا أشمالها are
+
+214
+00:16:10,780 --> 00:16:20,200
+reflexive spaces طيب الآن القلبي
+
+215
+00:16:22,330 --> 00:16:26,930
+Ibrahim طلعت عنها LQ صح؟ اللي هي 1 على P زي 1 على
+
+216
+00:16:26,930 --> 00:16:31,550
+Q بيساوي 1 كمان Ibrahim لها هترجع منين؟ للـ LB إذا
+
+217
+00:16:31,550 --> 00:16:34,750
+ال second هو اللي هو ال LB إذا على طول هتطلع
+
+218
+00:16:34,750 --> 00:16:39,210
+أشمالها أكيد الكلمة بين هذا و بين هذا هي نفسها لو 
+
+219
+00:16:39,210 --> 00:16:43,930
+أنتوا جاهز مدام وانتوا وانتوا وانتوا وانتوا وانتوا
+
+220
+00:16:43,930 --> 00:16:44,150
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+221
+00:16:44,150 --> 00:16:46,330
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+222
+00:16:46,330 --> 00:16:47,150
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+223
+00:16:47,150 --> 00:16:49,700
+وانتوا وانتوا وانتوا وانتوا وانتوا وreflexive
+
+224
+00:16:49,700 --> 00:16:54,560
+space إذن الآن كل ال ال B spaces are reflexive
+
+225
+00:16:54,560 --> 00:16:59,880
+spaces طيب الآن في عندي كمان عنوان كبير theorem 6
+
+226
+00:16:59,880 --> 00:17:07,620
+6 اللي هو every Hilbert space is reflexive any
+
+227
+00:17:07,620 --> 00:17:15,280
+Hilbert space is reflexive اللي بعده .. خسرناش
+
+228
+00:17:15,280 --> 00:17:22,250
+الوران اللي بعده لما أربعة ستة سبعة let Y be a
+
+229
+00:17:22,250 --> 00:17:35,310
+proper closed subspace خلّيني أطلع إليه هذا let
+
+230
+00:17:35,310 --> 00:17:39,770
+Y be a proper closed subspace of a normed space X
+
+231
+00:17:44,190 --> 00:17:48,690
+و Proper Closed Subspace منه يعني بمعنى آخر هذا
+
+232
+00:17:48,690 --> 00:17:53,710
+Closed وفي Elements بين الـ aY و بين مين و بين ال
+
+233
+00:17:53,710 --> 00:17:57,890
+X على الأقل في عندي Element هنا ماشي الحال Let X
+
+234
+00:17:57,890 --> 00:18:00,550
+not element in X minus Y خلّيني أخد X not وين
+
+235
+00:18:00,550 --> 00:18:06,470
+موجودة في ال X minus Y بيه Arbitrary و خلّيني أعرف 
+
+236
+00:18:06,470 --> 00:18:10,400
+ال Delta اللي هو بيساوي الـ infimum المسافة يعني 
+
+237
+00:18:10,400 --> 00:18:15,940
+المسافة بين اللي هي ال X note و مين و ال Y ال
+
+238
+00:18:15,940 --> 00:18:23,140
+infimum لأ اللي هي الـ Norm Y note أو أي Y ناقص X
+
+239
+00:18:23,140 --> 00:18:27,020
+note وهي بيسميها D تلدة زي ما هو بيسميها such that
+
+240
+00:18:27,020 --> 00:18:31,660
+Y تلدة element in Y الانفمان بين هذه و بين
+
+241
+00:18:31,660 --> 00:18:35,000
+الست اللي عندى هو سميها Y الدلتة هي اللي هي في 
+
+242
+00:18:35,000 --> 00:18:38,180
+الواقع اللي هي ال distance the distance from X
+
+243
+00:18:38,180 --> 00:18:43,450
+node to Y بقولني then .. then بضمانكم there exists
+
+244
+00:18:43,450 --> 00:18:48,490
+F تلدى وين موجودة في ال X' بحيث أنه Norm ال F تلدى
+
+245
+00:18:48,490 --> 00:18:53,370
+بيساوي واحد و ال F تلدى ل Y بتساوي صفر لكل Y وين
+
+246
+00:18:53,370 --> 00:18:57,450
+موجودة بلي هي بيكون موجودة في ال Y يعني بلاقي اللي
+
+247
+00:18:57,450 --> 00:19:06,830
+هو F تلدى element in X' و ال F تلدى Norm هابس هو
+
+248
+00:19:06,830 --> 00:19:14,150
+واحد والـ F تلدى of أي element هنا Y بساوي 0 ومش 
+
+249
+00:19:14,150 --> 00:19:21,450
+هيك و ال F لل X note هذه هي اللي هتساوي مين؟ اللي
+
+250
+00:19:21,450 --> 00:19:25,610
+هي المسافة F تلدة لل X note بساوي مين؟ بساوي
+
+251
+00:19:25,610 --> 00:19:28,630
+المسافة يعني لجأت ال F تلدة ده ال functional
+
+252
+00:19:28,630 --> 00:19:31,290
+بتساوي المسافة و في نفس ال issue و ال Norm هو
+
+253
+00:19:31,290 --> 00:19:35,850
+بساوي 1 و F تلدة of Y لكل element هنا بساوي اللي
+
+254
+00:19:35,850 --> 00:19:37,770
+هو 0 خليني نبره مع بعض
+
+255
+00:19:42,940 --> 00:19:47,300
+اللي هن consider the subspace Z عبارة عن كل 
+
+256
+00:19:47,300 --> 00:19:52,040
+الـ linear combinations اللي هي Y زائد Alpha X0 يعني
+
+257
+00:19:52,040 --> 00:19:57,000
+هو كأنه span بين الـ X0 و بين مين الـ Y نفسها such
+
+258
+00:19:57,000 --> 00:20:00,020
+that Alpha is the scalar of X هذا subspace من مين؟ 
+
+259
+00:20:00,020 --> 00:20:05,160
+من X لأن Y جزئية من X و الـ X0 موجودة في الـ X بظل
+
+260
+00:20:05,160 --> 00:20:08,940
+span عبارة عن subspace من الـ X and define the
+
+261
+00:20:08,940 --> 00:20:18,410
+functional F on Z يعني عرف الآن F من Z لعند 
+
+262
+00:20:18,410 --> 00:20:23,610
+اللي هو ال scalar field تبعنا الآن هذه العناصر
+
+263
+00:20:23,610 --> 00:20:27,970
+اللي هنا اللي هي F of Z اللي هو كيف شكل العنصر Z
+
+264
+00:20:27,970 --> 00:20:32,770
+بساوي F of Y زائد ال Alpha X not عملنا زيه المرة
+
+265
+00:20:32,770 --> 00:20:37,350
+اللي فاتت اللي هو بساوي إيه؟  F of هذا بساوي مين ال
+
+266
+00:20:37,350 --> 00:20:44,900
+Alpha هذه في مين في ال Delta الألفة في مين؟ في 
+
+267
+00:20:44,900 --> 00:20:49,700
+الـ Delta نشوف كيف then
+
+268
+00:20:49,700 --> 00:20:52,840
+F is linear F is linear عاملة زيها المرة اللي فاتت
+
+269
+00:20:52,840 --> 00:20:56,180
+F is linear تاخدوا two elements بتكون عاملها
+
+270
+00:20:56,180 --> 00:21:03,680
+بعملها اللي هو F خلينا نقول of Gamma زد واحد زائد 
+
+271
+00:21:03,680 --> 00:21:09,930
+زد اثنين بساوي تبقى معايا خلينا نتبتها linear زد 
+
+272
+00:21:09,930 --> 00:21:12,870
+واحد وزد اثنين arbitrarily elementين وين أخدناهين
+
+273
+00:21:12,870 --> 00:21:18,810
+نزد اللي عندي بدا اثبت إنه F is linear معايا Y
+
+274
+00:21:18,810 --> 00:21:25,170
+ساوي اللي هو F of جامعة زد واحد اللي هي جامعة في Y
+
+275
+00:21:25,170 --> 00:21:31,950
+زائد أو Y واحد دعنا نسميها زائد Alpha واحد X Note
+
+276
+00:21:31,950 --> 00:21:36,690
+ماشي هذا زد واحد سميتها زد واحد اللي هو زد اثنين
+
+277
+00:21:37,600 --> 00:21:42,360
+اللي عبارة عن إيش Y2 مش هيك شكلها هي هنا يا جماعة
+
+278
+00:21:42,360 --> 00:21:51,560
+هي من هنا بأخذ زائد Alpha 2 X Note ويساوي جمعهن مع 
+
+279
+00:21:51,560 --> 00:21:59,840
+بعض يصير F of Gamma Y1 زائد Y2 Gamma Y1 زائد Y2
+
+280
+00:21:59,840 --> 00:22:05,180
+مضروبة في مين زائد مين زائد اللي هو Alpha 1 زائد 
+
+281
+00:22:05,180 --> 00:22:11,070
+Alpha 2 في X Note ويساوي ايش قانونه هذه على طول
+
+282
+00:22:11,070 --> 00:22:16,550
+بتنمي مين معامل x0 في مين في دلتا ويساوي معامل x0
+
+283
+00:22:16,550 --> 00:22:22,590
+اللي هو Alpha 1 آه Gamma هذا مضروبة برضه Gamma
+
+284
+00:22:22,590 --> 00:22:27,870
+Gamma مضروبة في Alpha 1 آه صح Gamma مضروبة في
+
+285
+00:22:27,870 --> 00:22:33,170
+Alpha 1 طيب Gamma Alpha 1 زائد مين Alpha 2 كله
+
+286
+00:22:33,170 --> 00:22:36,410
+مضروب في مين في دلتا واضح آه
+
+287
+00:22:39,850 --> 00:22:46,930
+هي بترمي اللي هو العنصر هذا Alpha اللي هو معامل X
+
+288
+00:22:46,930 --> 00:22:52,750
+Note في Delta هاي معامل X Note في مين؟ في Delta
+
+289
+00:22:52,750 --> 00:22:56,590
+وهذا الـ element فيها كلها بعض فبيصير Y ساوي اللي
+
+290
+00:22:56,590 --> 00:23:03,710
+هو Gamma Alpha 1 Delta زائد Alpha 2 في Delta Y
+
+291
+00:23:03,710 --> 00:23:09,120
+ساوي رجح الأصلها هذه Gamma 1 Gamma فالف واحد
+
+292
+00:23:09,120 --> 00:23:14,340
+Delta اللي هي عبارة عن مين هادي مع بعض هو ال
+
+293
+00:23:14,340 --> 00:23:19,160
+element، مظبوط؟ لو بمعنى آخر، عندي بدي أطلع جابة
+
+294
+00:23:19,160 --> 00:23:27,840
+برا، Gamma، بيصير عندي F of Y واحد زائد ألف واحد
+
+295
+00:23:27,840 --> 00:23:35,800
+في Delta، زائد، الثاني نفس الشيء F of Y2 زي الألف
+
+296
+00:23:35,800 --> 00:23:43,680
+اثنين اللي هو لأ بدون دلتا X0 آسف في X0 إذا صارت
+
+297
+00:23:43,680 --> 00:23:48,980
+اللي هي عبارة عن Linear هاي F اللي هي طبعا هادي و
+
+298
+00:23:48,980 --> 00:23:56,600
+يساوي Gamma F of Z1 زي F of Z2 وراجعوا الحسابات
+
+299
+00:23:56,600 --> 00:24:01,430
+لايكون خربطنا في شيء طيب then F is معناه أزلنا
+
+300
+00:24:01,430 --> 00:24:06,550
+خلصنا من الـ linearity لأن since Y is closed then
+
+301
+00:24:06,550 --> 00:24:11,390
+Delta strictly أكبر من مين من صفر المسافة اللي هو
+
+302
+00:24:11,390 --> 00:24:15,430
+بتصير اللي هي بين هذي و هذي بتساوي صفر وعملناها
+
+303
+00:24:15,430 --> 00:24:18,670
+إذا بتتذكروا هذي عملتها في برهان نظرية في شابتر
+
+304
+00:24:18,670 --> 00:24:24,380
+اللي هو في شابتر 2 إنه ليش Delta أكبر من صفر و
+
+305
+00:24:24,380 --> 00:24:28,940
+أرجعولها لأن then Delta أكبر من صفر and so F لا
+
+306
+00:24:28,940 --> 00:24:33,200
+تساوي ايش لا تساوي Zero مدام Delta أكبر من صفر
+
+307
+00:24:33,200 --> 00:24:37,600
+فالـ F مش الـ Zero function لأن F ايش معرفة F of Z
+
+308
+00:24:37,600 --> 00:24:41,780
+بيساوي Alpha في Delta والـ Delta هذه مش صفر معناته
+
+309
+00:24:41,780 --> 00:24:45,300
+اللي هو صار عندي لما ما تكونش هذه صفر على طول الـ F
+
+310
+00:24:45,300 --> 00:24:48,420
+of Z بتساوي قيمة غير الصفر إذا أكيد مش الـ Zero
+
+311
+00:24:48,420 --> 00:24:52,190
+function وعنا اللي هو الـ elements اللي زيها دي Y زي
+
+312
+00:24:52,190 --> 00:24:57,930
+x0 نفسها هي قيمتها مش صفر مظبوط ولا لأ ايش قيمتها
+
+313
+00:24:57,930 --> 00:25:02,730
+بدأ تطلع تطلع
+
+314
+00:25:02,730 --> 00:25:13,210
+عبارة عن f of y زي x0 ايش بيساوي Delta نفسها مش
+
+315
+00:25:13,210 --> 00:25:16,690
+معامل x0 طيب
+
+316
+00:25:19,770 --> 00:25:23,870
+طيب اتفجنا عليها دي note that for all y element in
+
+317
+00:25:23,870 --> 00:25:28,910
+Y f of y ايش بيساوي بيساوي اللي هي أو أنا أنزل
+
+318
+00:25:28,910 --> 00:25:31,130
+عشان أقولكم مين رايح إذا أذكركم أن ايش بدي أبدل
+
+319
+00:25:31,130 --> 00:25:34,350
+ايه اف تل ده اللي هي Norm ما بيساوي واحد وقابلة
+
+320
+00:25:34,350 --> 00:25:37,470
+صفر واٍيش ما لو اف تل ده وفي x not بيساوي اللي هو
+
+321
+00:25:37,470 --> 00:25:41,350
+دلتا الآن أنا بأشر للـ subspace ومنه
+
+322
+00:25:41,350 --> 00:25:47,600
+هنطلق في اللي اللي بديه طيب ثم اقول لنا ان for all
+
+323
+00:25:47,600 --> 00:25:51,740
+Y into Y, f of y بيساوي اطلع لفوق اللي هو f of y
+
+324
+00:25:51,740 --> 00:25:55,840
+زائد مين زائد صفر في x not صح ولا لأ اللي هو ايش
+
+325
+00:25:55,840 --> 00:26:00,100
+هيظهر بساوي بساوي صفر في Delta اللي هو صفر and f of
+
+326
+00:26:00,100 --> 00:26:03,460
+x not هنا أو ده بتجداش بتساوي بيساوي اللي هو Delta
+
+327
+00:26:03,870 --> 00:26:08,470
+واضح طيب طبعا هي التفسير يتواي بيساوي صفر والف
+
+328
+00:26:08,470 --> 00:26:11,310
+بيساوي واحد في الجهتين تطلع عندها دي بيساوي صفر وهذا
+
+329
+00:26:11,310 --> 00:26:16,230
+بيساوي واحد الآن now we show that F is bounded ده
+
+330
+00:26:16,230 --> 00:26:20,110
+أثبتنا أن F خطية وأثبتنا F مش هي الصفر وأثبتنا
+
+331
+00:26:20,110 --> 00:26:25,770
+قيمة الـ F عند الـ Y أي Y في الـ Y هداك بساوي صفر و F
+
+332
+00:26:25,770 --> 00:26:30,700
+of X not بتساوي Delta كل هدول خلّيني لأنه بلزم أني
+
+333
+00:26:30,700 --> 00:26:34,860
+بعد شوية Now we show that F is bounded if Alpha
+
+334
+00:26:34,860 --> 00:26:38,260
+بتساوي صفر إذا F of Z automatically مش هتساوي
+
+335
+00:26:38,260 --> 00:26:41,140
+هتساوي صفر وهذا طبعا الـ boundedness بيطلع
+
+336
+00:26:41,140 --> 00:26:46,200
+automatic يعني لو Alpha مش صفر بدي أسالكم انه F is
+
+337
+00:26:46,200 --> 00:26:50,940
+bounded أو أوصلكم لـ Boundedness لـ F الآن مدام
+
+338
+00:26:50,940 --> 00:26:53,200
+Alpha مش ساوي مش ساوي ليش ساوي صفر؟ زن شكل اللي بده
+
+339
+00:26:53,200 --> 00:26:57,120
+أجسم على Alpha إذا بيصير عندي لأي Y element in Y
+
+340
+00:26:57,120 --> 00:27:01,340
+ناقص واحدة لـ Alpha وين هيكون برضه في Y ماشي الحال
+
+341
+00:27:01,340 --> 00:27:06,900
+طيب بحسبلي الآن absolute value لـ F of Z بتساوي F
+
+342
+00:27:06,900 --> 00:27:11,820
+of Y زائد ألفة مين X Note حسب اللي هو تعريف هذه
+
+343
+00:27:11,820 --> 00:27:15,120
+هيظهر Alpha في Delta و Absolute Value بيصير
+
+344
+00:27:15,120 --> 00:27:18,300
+Absolute Value في الألفة في مين في الدلتا لأن
+
+345
+00:27:18,300 --> 00:27:23,930
+الدلتا أكبر أو يساوي أكبر Circle من صفر Y ساوي الـ
+
+346
+00:27:23,930 --> 00:27:26,550
+Absolute value لـ Alpha في مين في الـ infimum لهذه
+
+347
+00:27:26,550 --> 00:27:30,890
+الأشياء الـ infimum هي الـ distance الآن الـ
+
+348
+00:27:30,890 --> 00:27:35,910
+infimum هذا سيكون أصغر أو يساوي اللي هي نجمة هي
+
+349
+00:27:35,910 --> 00:27:40,630
+الـ Absolute value لـ Alpha زي ما هي وهذه اللي هي
+
+350
+00:27:40,630 --> 00:27:44,190
+الـ infimum أصغر أو يساوي واحدة منهم من الواحدة
+
+351
+00:27:44,190 --> 00:27:47,590
+منهم ياخد Y tilde عبارة عن ناقص واحد على الألفة في
+
+352
+00:27:47,590 --> 00:27:51,510
+مين في Y ناقص X node واخذتها بالشكل هذا عشان لما
+
+353
+00:27:51,510 --> 00:27:55,550
+أنا أدخل Alpha اللي جوا هيصير عبارة عن Y زائد
+
+354
+00:27:55,550 --> 00:27:59,010
+Alpha X naught، مظبوط؟ اللي هي Y زائد Alpha X
+
+355
+00:27:59,010 --> 00:28:02,350
+naught اللي هي مين؟ الـ Z اللي بدأت فيها، إذا صار
+
+356
+00:28:02,350 --> 00:28:07,110
+الـ absolute value للـ F of Z أصغر أو ساوي مين؟ Norm
+
+357
+00:28:07,110 --> 00:28:10,470
+الـ Z، أجسموا انتهيتوا أو خذوا الـ supremum على Norm
+
+358
+00:28:10,470 --> 00:28:14,890
+الـ Z بساوي واحد، بتطلع اللي هو Norm الـ F أصغر أو
+
+359
+00:28:14,890 --> 00:28:20,850
+ساوي ايش؟ أصغر أو ساوي واحد اللي بعده اطلع لفوق
+
+360
+00:28:20,850 --> 00:28:24,250
+لنثبت أن ها اكبر او يساوي ايش اكبر أو يساوي واحد
+
+361
+00:28:24,250 --> 00:28:30,350
+طيب by the definition of infimum there is exist a
+
+362
+00:28:30,350 --> 00:28:34,230
+sequence y and of elements in NY such that normal
+
+363
+00:28:34,230 --> 00:28:38,970
+y and not six note ايش ماله؟ converge لمن؟ لـ Delta،
+
+364
+00:28:38,970 --> 00:28:44,030
+ماشي الحال؟ الآن الـ infimum بيساوي هذا المقدار،
+
+365
+00:28:44,030 --> 00:28:47,750
+ماشي الحال؟ إذا بقدر ألاقي sequence من الـ elements
+
+366
+00:28:47,750 --> 00:28:51,630
+اللي في Y بحيث norm الـ Y الناقص اللي هو X0 يروح
+
+367
+00:28:51,630 --> 00:28:57,510
+لمين؟ لهذه الـ Delta، وثباته سهل هذا الكلام، طيب
+
+368
+00:29:00,530 --> 00:29:05,310
+صار عندي اللي هو sequence من العناصر اللي موجودة
+
+369
+00:29:05,310 --> 00:29:09,930
+في الـ Y Norm الـ Y ناقص X0 وتروح لمين لـ Delta منها
+
+370
+00:29:09,930 --> 00:29:14,350
+هذه الـ sequence بتاخذها كعلخاصة توصل لشق الثاني
+
+371
+00:29:14,350 --> 00:29:17,610
+اللي واف النورم أكبر أو يساوي واحد خدوا بتقياد
+
+372
+00:29:17,610 --> 00:29:20,510
+النورم للأف أكبر أو يساوي واحد اللي هي أكبر أو
+
+373
+00:29:20,510 --> 00:29:24,250
+يساوي هي supremum أكبر أو يساوي القيمة عند نقطة ما
+
+374
+00:29:24,950 --> 00:29:28,410
+أو عند نقاطنا إذا أكبر أو يساوي F of Y N ناقص X Note
+
+375
+00:29:28,410 --> 00:29:33,290
+اللي لجاتهم على Norm Y N ناقص X Note هذا الكلام لكل
+
+376
+00:29:33,290 --> 00:29:38,990
+اللي هي N element هنا قيمة هذه اللي هي عبارة عن ال
+
+377
+00:29:38,990 --> 00:29:42,970
+absolute value لناقص واحد لناقص Delta الـ absolute
+
+378
+00:29:42,970 --> 00:29:46,930
+value لناقص Delta هو مين؟ الـ Delta على الـ Norm هذا
+
+379
+00:29:46,930 --> 00:29:51,010
+نفسه as n goes to infinity هذا بتروح لـ Delta إذا
+
+380
+00:29:51,010 --> 00:29:55,530
+هذا Norm الـ F أكبر أو يساوي هذي for every n إذا
+
+381
+00:29:55,530 --> 00:29:58,130
+خذوا الـ limit as n goes to infinity فتطلع Delta على
+
+382
+00:29:58,130 --> 00:30:00,570
+Delta اللي هي ساوي واحد يصير Norm الـ F أكبر أو
+
+383
+00:30:00,570 --> 00:30:04,450
+يساوي الواحد وجابل أصغر أو يساوي الواحد إذا صار
+
+384
+00:30:04,450 --> 00:30:08,360
+عند Norm الـ F ايش بيساوي؟ بيساوي واحد هذه الـ F
+
+385
+00:30:08,360 --> 00:30:15,000
+اللي اشتغلت عليها لـ Z subspace من مين؟ من الـ X
+
+386
+00:30:15,000 --> 00:30:20,560
+بقدر اعمل له extension أنا معتمد الآن على مين؟ على
+
+387
+00:30:20,560 --> 00:30:23,920
+اللي هو الـ Hahn-Banach theorem الآن by Hahn-Banach
+
+388
+00:30:23,920 --> 00:30:28,860
+theorem أربعة تلاتة اتنين there exist F مين؟
+
+389
+00:30:31,840 --> 00:30:36,780
+بتوسع نفوذها بدل ما كانت على الـ subspace Z هتوسع
+
+390
+00:30:36,780 --> 00:30:40,320
+نفوذها على الـ X' وبنفس الخواص such that norm of F
+
+391
+00:30:40,320 --> 00:30:45,720
+tilde بساوي واحد و F tilde of Y بساوي صفر و F tilde of
+
+392
+00:30:45,720 --> 00:30:51,040
+X0 بساوي Delta وهيك هتكون حصلت على النتيجة اللي
+
+393
+00:30:51,040 --> 00:30:53,280
+بديها وهو المطلوب
+
+394
+00:31:02,880 --> 00:31:04,340
+يوجد كثير من الـ 4,6,8
+
+395
+00:31:08,580 --> 00:31:11,420
+إذا كان الـ Dual Space X' من نفسه نفسه نفسه نفسه
+
+396
+00:31:11,420 --> 00:31:21,600
+نفسه نفسه نفسه نفسه نفسه نفسه
+
+397
+00:31:21,600 --> 00:31:36,380
+نفسه نفسه نفسه
+
+398
+00:31:36,800 --> 00:31:41,680
+A separable normed space X with a non-separable
+
+399
+00:31:41,680 --> 00:31:46,940
+dual space X' can't be reflexive يعني لو كان عندي
+
+400
+00:31:46,940 --> 00:31:53,240
+separable normed space X وكان الـ X' ايش ماله؟ non
+
+401
+00:31:53,240 --> 00:31:58,640
+-separable الآن لو كانت X' separable، فهي Automatic
+
+402
+00:31:58,640 --> 00:32:02,440
+X separable لكن ممكن يكون الـ X' non-separable
+
+403
+00:32:02,440 --> 00:32:06,560
+وهذه تكون يشمالها separable فالآن فرضينا أن X
+
+404
+00:32:06,560 --> 00:32:12,120
+separable و X' non-separable الآن يقول لي مستحيل
+
+405
+00:32:12,120 --> 00:32:15,560
+تطلع الـ X يشمالها reflexive لازم تطلع يشمالها، X
+
+406
+00:32:15,560 --> 00:32:19,440
+is not reflexive suppose that X' is non-separable
+
+407
+00:32:19,440 --> 00:32:25,130
+زي ما هو حاكيه X separable و X يشمالها و X
+
+408
+00:32:25,130 --> 00:32:28,890
+reflexive تقولوا إن كانت بيه reflexive فبنرسلها
+
+409
+00:32:28,890 --> 00:32:32,790
+contradiction الآن X اللي هي ساعة يشمال في تردنها
+
+410
+00:32:32,790 --> 00:32:38,050
+reflexive مدام X reflexive إذن الـ X double-prime
+
+411
+00:32:38,050 --> 00:32:43,740
+isomorphic مدام XW' isomorphic to X which implies
+
+412
+00:32:43,740 --> 00:32:48,500
+that XW' يشمالها separable then by theorem اللي
+
+413
+00:32:48,500 --> 00:32:53,140
+حكينا عنها فوق اللي هي الأجال درجة منها X' separable
+
+414
+00:32:53,140 --> 00:32:57,040
+بظبط ولا لأ بناء على هذه إنه إذا كانت الـ XW'
+
+415
+00:32:57,300 --> 00:33:02,080
+separable هتكون اللي هي X يشمالها برضه separable
+
+416
+00:33:04,580 --> 00:33:07,720
+فاهمين آه؟ الآن صار عندي which is a contradiction
+
+417
+00:33:07,720 --> 00:33:14,840
+therefore X can't be reflexive الآن بتسمحوا لي
+
+418
+00:33:14,840 --> 00:33:20,800
+عادة ديش أيضا .. دي ده مش فاهمين عليها example ال
+
+419
+00:33:20,800 --> 00:33:27,720
+l1 is not reflexive ال l1 is not reflexive since
+
+420
+00:33:27,720 --> 00:33:33,730
+ال l1 is separable اخذناها but ال l1 prime is
+
+421
+00:33:33,730 --> 00:33:38,670
+بتساوي الـ infinity إيش ما لها is not اللي هي
+
+422
+00:33:38,670 --> 00:33:46,250
+separable then الـ one is not reflexive أخدناها ده
+
+423
+00:33:46,250 --> 00:33:53,590
+الكلام سابقا خليني أرجع بس لهذه الشغلة قبل ما ..
+
+424
+00:33:53,590 --> 00:33:54,410
+بعد إذنكم يعني
+
+425
+00:34:08,250 --> 00:34:12,950
+اللي خاطر أشرحها هذه اللي هي الـ .. الـ Hilbert
+
+426
+00:34:12,950 --> 00:34:16,530
+space أنه every Hilbert space is reflexive أنه هي
+
+427
+00:34:16,530 --> 00:34:21,070
+مهمة يعني فالشغلة بس بسيطة مش كبيرة بس اللي أنتم 
+
+428
+00:34:21,070 --> 00:34:24,810
+اللي بدنا نثبته فخليني أطلع عليه بالـ .. يعني
+
+429
+00:34:24,810 --> 00:34:29,350
+المعلومات اللي فيه بتقدروا يعني خليني أقول متوفرة
+
+430
+00:34:29,350 --> 00:34:32,830
+بين إيديكم خليني أشوفها أيش اللي بدنا نثبت أنه
+
+431
+00:34:32,830 --> 00:34:36,390
+every Hilbert space is reflexive
+
+432
+00:34:40,950 --> 00:34:45,670
+الآن عشان نثبت reflexive بدنا نثبت الـ canonical
+
+433
+00:34:45,670 --> 00:34:50,840
+mapping إيش معله إذا إنتهبدنا نركّب لنا ناخد الـ
+
+434
+00:34:50,840 --> 00:34:53,100
+Arbitrary Element هنا و نركّب لنا Element بحيث إنه
+
+435
+00:34:53,100 --> 00:34:56,840
+يكون اللي هو صورته يعني تكون هي اللي بدأنا فيها
+
+436
+00:34:56,840 --> 00:35:00,520
+الآن every Hilbert space H is reflexive we shall
+
+437
+00:35:00,520 --> 00:35:05,040
+prove surjectivity of the canonical mapping C من H
+
+438
+00:35:05,040 --> 00:35:07,920
+لعند H double prime إن إحنا نعرف إن H .. C من H
+
+439
+00:35:07,920 --> 00:35:11,560
+لعند H double prime قبل بشوية قولنا دائماً اللي هو
+
+440
+00:35:11,560 --> 00:35:13,940
+.. اللي هو فيه أيزومورفيزم من عند الـ range of C
+
+441
+00:35:13,940 --> 00:35:18,490
+عشان نكمل القصة بس نثبت إن هي H onto By showing
+
+442
+00:35:18,490 --> 00:35:21,350
+that for every G element in H double prime داخد G
+
+443
+00:35:21,350 --> 00:35:25,090
+وين موجودة في الـ H double prime و ألاقي Element
+
+444
+00:35:25,090 --> 00:35:28,830
+هنا بحيث إنه CX هو يصير اللي هو الـ G اللي بدأت
+
+445
+00:35:28,830 --> 00:35:32,210
+فيه ماشي الحال ستلاقي اللي هو الأمور المشابهة اللي
+
+446
+00:35:32,210 --> 00:35:36,330
+حكيناها قبل شوية لذّن for every G element in H 
+
+447
+00:35:36,330 --> 00:35:40,170
+double prime we want to find X element in H such
+
+448
+00:35:40,170 --> 00:35:47,950
+that G بتساوي CX الآن خلّينا نحضر للوصول لهذا اللي
+
+449
+00:35:47,950 --> 00:35:51,030
+هي .. و نستعمل بعض الشغلات اللي أخدناها قبل هيك
+
+450
+00:35:51,030 --> 00:35:54,010
+خصوصاً الـ Riesz Representation Theorem اللي هي اللي
+
+451
+00:35:54,010 --> 00:35:58,070
+.. اللي بناخد F بدلالة الـ inner product زي ما
+
+452
+00:35:58,070 --> 00:36:00,110
+عملنا المرة الفاتتة في المحاضرة الفاتتة عملنا زي
+
+453
+00:36:00,110 --> 00:36:03,850
+هيك شوفوا كده as a preparation we define A من H'
+
+454
+00:36:04,090 --> 00:36:07,930
+لعند Hπ عملتها قبل هيك المرة الفاتتة اللي هو بي A F
+
+455
+00:36:07,930 --> 00:36:12,980
+إيش بيساوي Z الـ F من أين جاء من أتش برايم و بيساوي
+
+456
+00:36:12,980 --> 00:36:16,640
+Z مين الـ Z هي إحنا بنقول لكل F Element من أتش 
+
+457
+00:36:16,640 --> 00:36:21,400
+برايم اللي هو there exist a unique Z such that F
+
+458
+00:36:21,400 --> 00:36:24,460
+of X can be written as any product X و Z هذا الـ
+
+459
+00:36:24,460 --> 00:36:29,580
+representation theory اللي بيدا استخدمه إنه أخد أي
+
+460
+00:36:29,580 --> 00:36:32,400
+أف اللي متناقش برايم و بالـ Riesz representation
+
+461
+00:36:32,400 --> 00:36:36,260
+theorem for any أف اللي متناقش برايم there exist a
+
+462
+00:36:36,260 --> 00:36:40,400
+unique z such that f of x بيساوي الـ x و مين و الـ z
+
+463
+00:36:40,400 --> 00:36:43,780
+ماشي الحال إذا إنجدرت اللي أنا عرف أي أف مش متساوي
+
+464
+00:36:43,780 --> 00:36:46,580
+بيساوي الـ z اللي لجيتها اللي بتدللتها عرفت اللي هي
+
+465
+00:36:46,580 --> 00:36:53,050
+الأف as another product الآن عندي طبعاً هذا الكلام
+
+466
+00:36:53,050 --> 00:36:56,870
+كله from تلاتة تمانية واحد we know that a is
+
+467
+00:36:56,870 --> 00:37:00,910
+bijective and isometric الـ a is bijective and
+
+468
+00:37:00,910 --> 00:37:03,850
+isometric عملتها المرة الفاتتة في المحاضرة اللي
+
+469
+00:37:03,850 --> 00:37:07,430
+فاتتها عملتها الآن و a is conjugate linear برضه
+
+470
+00:37:07,430 --> 00:37:10,940
+عملتها المرة الفاتتة A is going to get linear إذا
+
+471
+00:37:10,940 --> 00:37:16,460
+بتتذكروا as we see from 16 section 4-5 اللي المرة
+
+472
+00:37:16,460 --> 00:37:20,240
+الفاةتة عندي أثبتنا لـ A is going to get linear
+
+473
+00:37:20,240 --> 00:37:24,540
+رجعوه رجعوه رجعوه كله حكيته بالتفصيل المرة الفاتتة
+
+474
+00:37:25,700 --> 00:37:32,040
+الآن الـ H برايم هو مجتمع مكتمل إذا من اتنين عشرة
+
+475
+00:37:32,040 --> 00:37:35,940
+أربعة اللي هو and a Hilbert space with inner
+
+476
+00:37:35,940 --> 00:37:39,680
+product space defined by برضه أثبتنا إنه لما يكون
+
+477
+00:37:39,680 --> 00:37:43,780
+الـ H اللي هو inner product space أو Hilbert space
+
+478
+00:37:43,780 --> 00:37:48,340
+الـ H برايم تبعه برضه هيكون ماله Hilbert space و
+
+479
+00:37:48,340 --> 00:37:52,220
+الـ inner product تبعه اللي هو الـ H برايم اللي صار
+
+480
+00:37:52,220 --> 00:37:55,040
+Hilbert space بقدر أخده من الـ inner product تبع
+
+481
+00:37:55,040 --> 00:37:58,580
+مين؟ تبع الـ H واخدناه بالطريقة التالية إن الـ inner
+
+482
+00:37:58,580 --> 00:38:04,860
+product F1 F2 تبع الـ H برايم بيساوي اللي هو AF2
+
+483
+00:38:04,860 --> 00:38:09,730
+اللي هي AF2 و AF1 اللي هو Elementين وين هذا؟ هذا
+
+484
+00:38:09,730 --> 00:38:13,710
+بغض النظر إيش هو هذا بيساوي Element من من من الـ ..
+
+485
+00:38:13,710 --> 00:38:17,370
+هذا مش عليه inner product لأن هذا الـ H برايم
+
+486
+00:38:17,370 --> 00:38:21,480
+هيكون عبارة عن Hilbert space وهيكون الـ product
+
+487
+00:38:21,480 --> 00:38:25,660
+تبعه بقدر أخده من هذا كيف باخده من هذا لو عندي x
+
+488
+00:38:25,660 --> 00:38:30,460
+و y هنا في هذا بيصير عندي الـ F1 و الـ F2 تبعته
+
+489
+00:38:30,460 --> 00:38:33,680
+بيساوي inner product بس مجلوب بين الجهتين اللي هو
+
+490
+00:38:33,680 --> 00:38:38,360
+في هذه الحالة هيكون عندي F1 و F2 بيساوي A F2 هيكون
+
+491
+00:38:38,360 --> 00:38:43,280
+في الـ H و الـ A F1 برضه هيكون وين في الـ H طيب
+
+492
+00:38:48,060 --> 00:38:52,340
+الآن بيقولني لاحظ إحنا قبل شوية قولنا إيه is
+
+493
+00:38:52,340 --> 00:38:56,660
+conjugate linear conjugate linear و الترتيب القدر
+
+494
+00:38:56,660 --> 00:39:02,720
+اللي هو عندك الـ inner product هذا اللي هو عكس اللي
+
+495
+00:39:02,720 --> 00:39:09,420
+هي بدل F2 F1 هنا مين عنده بعرفه بالـ F2 و الـ
+
+496
+00:39:09,420 --> 00:39:12,280
+conjugate linear مع هذا العكس هيطلع اللي هو اللي
+
+497
+00:39:12,280 --> 00:39:16,920
+بديه شوفوا كيف الآن note that the order of F1 و F2
+
+498
+00:39:16,920 --> 00:39:22,280
+on both sides اللي هو هذا عكس التاني الآن هذا
+
+499
+00:39:22,280 --> 00:39:25,140
+هيعمل inner product الـ inner product كلها إيه
+
+500
+00:39:25,140 --> 00:39:27,940
+جمال؟ لأن الخواص اللي بتعملوها و بتلاجوها على طول
+
+501
+00:39:27,940 --> 00:39:31,820
+inner product دي شكل في تفصيلها الآن ما أعطيكم
+
+502
+00:39:31,820 --> 00:39:35,360
+ملاحظة عالمين على الخاصية الثانية اللي بتستخدم
+
+503
+00:39:35,360 --> 00:39:39,360
+فيها الـ conjugate linear يعني بمعنى آخر Alpha F1 و
+
+504
+00:39:39,360 --> 00:39:45,160
+F2 هذه بتحقق اللي هو إيش بتساوي Alpha فـ F1 و مين؟
+
+505
+00:39:45,160 --> 00:39:48,380
+F2 اللي حققه اللي هو الـ conjugate linear مع
+
+506
+00:39:48,380 --> 00:39:54,320
+تعريفه هذا كيف Alpha F1 F2 إيش بتساوي؟ بتساوي A F2
+
+507
+00:39:54,320 --> 00:40:00,290
+هذه لهذه و A لهذه A α 1 أهلاً لكن الـ A conjugate
+
+508
+00:40:00,290 --> 00:40:02,630
+ليه؟ يعني إذا اللي بده يطلع منها بتطلع إيه؟
+
+509
+00:40:02,630 --> 00:40:06,790
+conjugate فبتصير الـ α conjugate في A F 1 و ده A F
+
+510
+00:40:06,790 --> 00:40:09,930
+2 لأن هذه لما تطلع من اللي بعيد اللي هو بتطلع
+
+511
+00:40:09,930 --> 00:40:12,250
+إليها كمان conjugate فبتصير لها conjugate
+
+512
+00:40:12,250 --> 00:40:16,470
+conjugate بتطلع Alpha فبتطلع اللي هي فعلاً محققة من
+
+513
+00:40:16,470 --> 00:40:19,990
+اللي هو الشرط الثاني تبع الـ inner product و الشرط
+
+514
+00:40:19,990 --> 00:40:24,310
+الأول وبجاعة الشروط برضه اللي هي سريعة وسهلة الآن
+
+515
+00:40:24,310 --> 00:40:29,090
+إذا صار فعلاً عندي هذا عمل لي اللي هو inner product
+
+516
+00:40:29,090 --> 00:40:34,750
+على اللي هو الـ H برايم و هيكون complete
+
+517
+00:40:38,270 --> 00:40:42,870
+الآن let g element .. كله عشان .. بدي أركب مين؟
+
+518
+00:40:42,870 --> 00:40:47,230
+بدي أركب .. أخدت اللي هو g arbitrary اللي هي الـ ..
+
+519
+00:40:47,230 --> 00:40:48,750
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+520
+00:40:48,750 --> 00:40:48,790
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+521
+00:40:48,790 --> 00:40:49,070
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+522
+00:40:49,070 --> 00:40:49,090
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+523
+00:40:49,090 --> 00:40:49,430
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+524
+00:40:49,430 --> 00:40:50,130
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+525
+00:40:50,130 --> 00:40:50,410
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+526
+00:40:50,410 --> 00:40:51,230
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+527
+00:40:51,230 --> 00:40:51,810
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+528
+00:40:51,810 --> 00:40:59,970
+الـ .. الـ .. الـ .. الـ .. الـ ..
+
+529
+00:40:59,970 --> 00:41:04,590
+الـ .. الـ ..
+
+530
+00:41:06,450 --> 00:41:10,450
+ما هي برضه الـ G في الـ H double prime يعني بمعنى
+
+531
+00:41:10,450 --> 00:41:16,690
+آخر G element in H prime كل أشماله الـ prime بدأ
+
+532
+00:41:16,690 --> 00:41:19,810
+أطبق الـ Riesz representation theorem عليها اللي هو
+
+533
+00:41:19,810 --> 00:41:22,350
+there exist لكل Element هنا there exist a unique
+
+534
+00:41:22,350 --> 00:41:28,310
+Element جوا بحيث إنه اللي هو G of الـ F أي Element
+
+535
+00:41:28,310 --> 00:41:32,830
+بيساوي اللي هو الـ inner product بين اللي هو A of No
+
+536
+00:41:32,830 --> 00:41:40,810
+اللي هو أسف F و F note اللي هو واحد كمان مرة إيش الـ
+
+537
+00:41:40,810 --> 00:41:44,270
+Riesz Representation بتفهم بتقول هذا اسم اللي
+
+538
+00:41:44,270 --> 00:41:47,810
+بدكم إياه أتش برايم سمّونه اللي بدكم إياه أي inner
+
+539
+00:41:47,810 --> 00:41:54,150
+product X ماشي الآن لكل Element في الـ X برايم بقدر
+
+540
+00:41:54,150 --> 00:42:01,390
+أنادي unique Element اللي هو بحيث إنه G of هذي
+
+541
+00:42:01,390 --> 00:42:09,190
+شغالة وين؟ G من H' شغالة وين من H' لمن؟ لـ K فح؟
+
+542
+00:42:09,190 --> 00:42:15,290
+بتاخد الـ Element G of F و بترميه في شغلة لإن الـ
+
+543
+00:42:15,290 --> 00:42:17,910
+Riesz Representation بتقول لك مدام إن الـ product
+
+544
+00:42:17,910 --> 00:42:22,250
+هو الـ Hilbert space أنا بقدر أجيب لك unique Element
+
+545
+00:42:22,250 --> 00:42:27,590
+فيه اللي هو الـ H' بدلالته بتقدر تكتب هذه as inner
+
+546
+00:42:27,590 --> 00:42:32,050
+product يعني G of F بيصير بساوي inner product بين
+
+547
+00:42:32,050 --> 00:42:36,230
+الـ F هذه الـ arbitrary و الـ F note اللي لديته اللي
+
+548
+00:42:36,230 --> 00:42:39,850
+عملته Z قبل شوية في الثانية فصار عندي الآن G of F
+
+549
+00:42:39,850 --> 00:42:44,030
+اللي هي عبارة عن كان بالـ written as الـ inner
+
+550
+00:42:44,030 --> 00:42:47,110
+product بين F و F note مين للـ inner product تبعنا
+
+551
+00:42:47,110 --> 00:42:50,270
+اللي بنشتغل عليه على مين؟ على اللي هو الـ space اللي
+
+552
+00:42:50,270 --> 00:42:55,530
+عندي هذا قبل بشوية إحنا عرفناه كالتالي بيصير A F
+
+553
+00:42:55,530 --> 00:43:03,870
+Note و مين A F إذا هذا حصلته بالشكل هذا طيب الآن
+
+554
+00:43:03,870 --> 00:43:08,090
+عندي لكن F of X أشبه ساوي X زد اللي قبل بشوية
+
+555
+00:43:08,090 --> 00:43:15,650
+حكيته و Z أشبه ساوي A F و عندي الـ A F Note هيكون
+
+556
+00:43:15,650 --> 00:43:20,670
+اللي هيقيمة F نوت F بيساوي زد الـ F نوت حقوقه
+
+557
+00:43:20,670 --> 00:43:26,070
+يسمّوني إيه إيه إيش X إذا الـ F نوت كإنه هي اللي
+
+558
+00:43:26,070 --> 00:43:30,250
+لجيتها اللي بدها توصلني للـ Element اللي لجيتها اللي
+
+559
+00:43:30,250 --> 00:43:38,160
+C اللي عنده اللي هو C اللي هو من HW' لعند H الآن
+
+560
+00:43:38,160 --> 00:43:42,380
+أنا بتاخد الـ CG اللي بتهيأله دي لها إشي ماشي حال 
+
+561
+00:43:42,380 --> 00:43:46,700
+صورة الآن أنا اللي بيوصل لي اللي لجأته الـ F هذا
+
+562
+00:43:46,700 --> 00:43:52,660
+بيوصل لي للـ X اللي الـ CG إيش يساوي؟ يساوي الـ X طيب
+
+563
+00:43:52,660 --> 00:43:57,640
+الآن الـ F note لجأته الـ A F note طبيعي هيكون إيش
+
+564
+00:43:57,640 --> 00:44:01,990
+بيساوي؟ بيساوي اللي هو الـ X ماشي الحال لإنه element
+
+565
+00:44:01,990 --> 00:44:06,330
+في H لإن هذه الصورة will هتكون موجودة في الـ H إذا 
+
+566
+00:44:06,330 --> 00:44:10,250
+الـ A of note بيساوي X إذا صار عندي we have اللي هو
+
+567
+00:44:10,250 --> 00:44:15,930
+A of note و A of إيش هيساوي اللي هو X مكان هذه و
+
+568
+00:44:15,930 --> 00:44:18,190
+هذه الـ A of اللي جيتها من جبل اللي هي عبارة عن مين
+
+569
+00:44:18,190 --> 00:44:24,150
+عن Z و هذه نفسها إيش بتساوي F of X فعند الآن مع بعض
+
+570
+00:44:24,150 --> 00:44:30,530
+هذه g of f إيش بيساوي f of x g of f صارت بيساوي f
+
+571
+00:44:30,530 --> 00:44:34,110
+of x مدام g of f بيساوي f of x اللي هو هذا معناته
+
+572
+00:44:34,110 --> 00:44:38,730
+إن cx إيش هتساوي؟ هتساوي الـ g وهذا معناته صارت
+
+573
+00:44:38,730 --> 00:44:43,710
+اللي هي c الـ subjective أو أنتم وبهيك وكون خلصنا
+
+574
+00:44:43,710 --> 00:44:45,830
+البرهان وإلى لقاء آخر 
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/WmXLCzkJRL8_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/WmXLCzkJRL8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..73c194152edef7152b0325e38ce0822fd08c2e48
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/WmXLCzkJRL8_postprocess.srt
@@ -0,0 +1,2296 @@
+1
+00:00:05,970 --> 00:00:08,510
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,510 --> 00:00:12,170
+والصلاة والسلامة على سيد المرسلين سيدنا محمد وعلي
+
+3
+00:00:12,170 --> 00:00:16,670
+آله وصحبه أجمعين هذه المحاضرة رقم تلاتين نساق
+
+4
+00:00:16,670 --> 00:00:20,810
+تحليل اقتراني أو تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:20,810 --> 00:00:24,850
+الإسلامية قسم الرياضيات ماجستير وصلنا لعند اللي هو
+
+6
+00:00:24,850 --> 00:00:28,370
+ال section السادس في شبطر أربعة اللي هو تحت عنوان
+
+7
+00:00:28,370 --> 00:00:29,710
+reflexive spaces
+
+8
+00:00:32,710 --> 00:00:36,690
+نبدأ في البداية بها اللمّة الصغيرة على أساس
+
+9
+00:00:36,690 --> 00:00:41,570
+تأهيلنا لإنه نعرف شو معناه بعد شوية لما بعدين نعرف
+
+10
+00:00:41,570 --> 00:00:48,270
+شو معناه reflexive space اللمّة بتقول التالي for
+
+11
+00:00:48,270 --> 00:00:53,310
+every fixed X in a normed space X the functional
+
+12
+00:00:53,310 --> 00:00:58,610
+GX defined on X' يعني عندي X عبارة عن normed space
+
+13
+00:01:01,290 --> 00:01:06,730
+وعندي x arbitrary element in X لكن اللي هو بنحكي
+
+14
+00:01:06,730 --> 00:01:10,370
+عن إيش محدد أخدته arbitrary but fixed يعني بدي
+
+15
+00:01:10,370 --> 00:01:13,590
+أسير أحكي عن ال element العشوائي اللي في ال X اللي
+
+16
+00:01:13,590 --> 00:01:18,230
+أخدته عشوائي بس بدي أحكي عن element معين بعد ما
+
+17
+00:01:18,230 --> 00:01:21,690
+أخده عشوائي بدي أحكي عنه بدي نعرف ال functional DX
+
+18
+00:01:23,550 --> 00:01:29,470
+معرفة defined on X' يعني تاخد من X' و ترمى في الـ
+
+19
+00:01:29,470 --> 00:01:35,010
+scalar field تبعته اللي هو الـ K كيف بدي أعرفها؟
+
+20
+00:01:35,010 --> 00:01:41,130
+DX of العناصر اللي هنا dual functional لإن هذا
+
+21
+00:01:41,130 --> 00:01:45,470
+الdual اسم بياسم of F بساوي، إيش بدي أعرفها؟ بدي
+
+22
+00:01:45,470 --> 00:01:49,050
+أعرف قيمة الـ F دي اللي أخدتها من هنا عند مين عنده
+
+23
+00:01:49,050 --> 00:01:55,550
+النقطة X الـ Fixed هذه بساوي F of Xالان هذه صارت
+
+24
+00:01:55,550 --> 00:01:59,270
+عندي اللي هي function هو بتدعي الآن اللي ما بتقول
+
+25
+00:01:59,270 --> 00:02:03,890
+هتطلع هذا ال function is a bounded linear
+
+26
+00:02:03,890 --> 00:02:07,770
+functional يعني بمعنى آخر هتطلع اللي عالميا على ال
+
+27
+00:02:07,770 --> 00:02:11,310
+X' إذا هتكون في الدول اسمه إسلاميا لل X' يعني في
+
+28
+00:02:11,310 --> 00:02:15,370
+ال second دول و كأنها DX element in X double prime
+
+29
+00:02:15,370 --> 00:02:19,550
+و هيطلع عندي نورم ال DX هو نورمين ال X طلع ليها
+
+30
+00:02:19,550 --> 00:02:24,190
+الكتابالان بدنا نبرهن هذه اللي هي ال linearity
+
+31
+00:02:24,190 --> 00:02:29,770
+اللي هي يعني بالطرق العادية يعني لو جينا أخدنا G X
+
+32
+00:02:29,770 --> 00:02:40,700
+of Alpha Fمثلا زائد F إبراهيم أو F واحد بندن نشوف
+
+33
+00:02:40,700 --> 00:02:45,580
+إيش قيمتها بقى هتكون قيمتها بالساوي Alpha F زائد F
+
+34
+00:02:45,580 --> 00:02:50,780
+واحد الكل of مين حسب التعريف of X صح ولا لأ ويساوي
+
+35
+00:02:50,780 --> 00:02:57,620
+Alpha F of X زائد F واحد of X وهذه فعلا مين هي
+
+36
+00:02:57,620 --> 00:03:06,750
+عبارة عن Alpha DX of Fصحيح؟ زائد مين زائد g of dx
+
+37
+00:03:06,750 --> 00:03:14,210
+of f واحد فعلاً طلعت اشملها easily لان لان المرة
+
+38
+00:03:14,210 --> 00:03:18,790
+الماضية اللي هي ال chapter اللي في ال section اللي
+
+39
+00:03:18,790 --> 00:03:25,690
+فات أخدنا ال norm بدلالة ال xيعني نورم الـ X
+
+40
+00:03:25,690 --> 00:03:29,450
+بدلالة الـ F آسف غير إن أحنا بنوجد النورم بدلالة
+
+41
+00:03:29,450 --> 00:03:35,430
+مين اللي هو ال X نفسها اللي بقصده يعني نقول نورم
+
+42
+00:03:35,430 --> 00:03:41,810
+ال X أو نورم ال F بساوي ال supremum هذا اللي
+
+43
+00:03:41,810 --> 00:03:49,190
+بنعرفه F of X على X نورم ل X element in X minus
+
+44
+00:03:49,190 --> 00:03:54,930
+مين Zero هذا التعريف العادي مافي الحالالان اخدنا
+
+45
+00:03:54,930 --> 00:03:58,870
+احنا المره الفاتحة الكورولارى انه Normal X بنقدر
+
+46
+00:03:58,870 --> 00:04:05,230
+نقول عنها عبارة عن ال supreman لل F of X عالمياعلى
+
+47
+00:04:05,230 --> 00:04:11,050
+norm الـ F والـ F element in X' ماشي الحال الأخرى
+
+48
+00:04:11,050 --> 00:04:13,890
+هذا خدمة المرة الفاتتة اللي هي النتيجة بس أعملها
+
+49
+00:04:13,890 --> 00:04:18,450
+الآن الان عشان أثبت لكم إنه GX is bounded وNorm ما
+
+50
+00:04:18,450 --> 00:04:22,850
+بيسوي نورم الـ X الأمر سهل نورم الـ GX حسب تعريف
+
+51
+00:04:22,850 --> 00:04:26,490
+اللي هو النورم العادي هو أبداً ال supremum لقيمة
+
+52
+00:04:26,490 --> 00:04:28,990
+هذه عند اللي هو الـ arbitrary F اللي هي في
+
+53
+00:04:28,990 --> 00:04:33,240
+domainها domainها مين هو؟ X'الان بيصير absolute
+
+54
+00:04:33,240 --> 00:04:37,420
+value of g x of f على mean normal f دي اللي هي ال
+
+55
+00:04:37,420 --> 00:04:40,220
+element اللي هو الموجود في الـ x' للفاتي اللي
+
+56
+00:04:40,220 --> 00:04:44,440
+بيساوي النشتفر الان هذا نفسه بيساوي g x of f ايش
+
+57
+00:04:44,440 --> 00:04:49,500
+هي هايها g x of f بتساوي meanF of X إذا بيساوي الـ
+
+58
+00:04:49,500 --> 00:04:54,480
+absolute value الـ F of X على نورم الـ F F limit
+
+59
+00:04:54,480 --> 00:04:58,260
+X' وهذه من الكورولر اللي حكيت عنها قبل شوية إيش
+
+60
+00:04:58,260 --> 00:05:02,320
+بتساوي نورم ال X إذا صار عندي نورم ال GX بيساوي
+
+61
+00:05:02,320 --> 00:05:09,430
+مين نورم اللي هو LX اطلع لفوقإذا صار عندي اللي هي
+
+62
+00:05:09,430 --> 00:05:13,390
+اللي اللي صارت عندي bounded وصارت عندي اللي هو
+
+63
+00:05:13,390 --> 00:05:17,810
+normها بسواه norm هذا إذا ال GX هذه اللي عندي صارت
+
+64
+00:05:17,810 --> 00:05:22,050
+bounded linear functional و norm هو norm ال X هذه
+
+65
+00:05:22,050 --> 00:05:25,990
+بتستختمها بعد شوية أطلع لها على التلخيص إلى أن نجي
+
+66
+00:05:25,990 --> 00:05:30,650
+للملة اللي باعدها الملة اللي باعدها كانت تاليبتقول
+
+67
+00:05:30,650 --> 00:05:35,250
+لي let X be a known space هذا كله عشان أصل اللي هو
+
+68
+00:05:35,250 --> 00:05:38,530
+تعريف ال reflexive space let X be a known space
+
+69
+00:05:38,530 --> 00:05:41,670
+then the canonical mapping هذا بنسميه canonical
+
+70
+00:05:41,670 --> 00:05:47,090
+mapping C هياخد من مين من X لمين لل X double prime
+
+71
+00:05:47,090 --> 00:05:52,410
+هذا اللي هيحددلي اللي هو هوية ال reflexive space
+
+72
+00:05:52,410 --> 00:05:56,290
+من خلاله بدي أعرف ال reflexive spaceإيه هذا ال
+
+73
+00:05:56,290 --> 00:05:59,170
+mapping؟ then the canonical mapping C من X ليند X
+
+74
+00:05:59,170 --> 00:06:03,050
+double prime defined by إيش بده ياخد هذا؟ بده ياخد
+
+75
+00:06:03,050 --> 00:06:08,190
+ال C of X أي X المتنهانة يرميه لمين ل G X وين
+
+76
+00:06:08,190 --> 00:06:12,140
+موجودة في ال X double prime اللي تاية مهتلهااللي
+
+77
+00:06:12,140 --> 00:06:16,840
+هي ايش DX الـ Double Prime تعريفها؟ انه DX of F هي
+
+78
+00:06:16,840 --> 00:06:20,220
+اللي عرفتها قبل شوية بساوة F of X لكل F element in
+
+79
+00:06:20,220 --> 00:06:23,300
+X prime ايش هيعمللي ال canonical mapping هذا؟
+
+80
+00:06:23,300 --> 00:06:27,440
+المعرف على هذا الأساس هيعمللي is an isomorphism
+
+81
+00:06:27,440 --> 00:06:32,140
+from X onto mean R of C يعني هيعمللي one to one و
+
+82
+00:06:32,140 --> 00:06:37,540
+isometric و linear لكن مش هيقوللي ان هو ontoاللي
+
+83
+00:06:37,540 --> 00:06:41,660
+هو بس isomorphism من وين؟ من X onto mean range of
+
+84
+00:06:41,660 --> 00:06:45,700
+C the range of mean of C يعني قال له كلمة بتمتعي
+
+85
+00:06:45,700 --> 00:06:49,840
+بكل شيء مع ده خاصية اللي هو الـ onto ممكن أه و
+
+86
+00:06:49,840 --> 00:06:54,100
+ممكن لأ حسب اللي موجود واضح اللي بحكيه؟ طيب الآن
+
+87
+00:06:54,100 --> 00:06:57,500
+لنثبت هذا الكلام عشان نثبت اللي هو isomorphism
+
+88
+00:06:57,500 --> 00:07:03,060
+بنثبت ال linearityالـ Linearity كالعادة خدوا أي أف
+
+89
+00:07:03,060 --> 00:07:07,080
+في ال X براي أنا الآن ال .. ال mapping تبعي من وين
+
+90
+00:07:07,080 --> 00:07:18,580
+لوين ال mapping ال
+
+91
+00:07:18,580 --> 00:07:25,700
+mapping Cمن X لعند X مين double prime الـ C هتاخد
+
+92
+00:07:25,700 --> 00:07:28,760
+الـ X و هترنيها في مين في ال element هنا سميناه
+
+93
+00:07:28,760 --> 00:07:32,660
+مين هو الـ GX الـ GX هذا هيكون اللي هو في الـ X
+
+94
+00:07:32,660 --> 00:07:35,700
+double prime يعني هيكون الـ GX من X prime لعند مين
+
+95
+00:07:35,700 --> 00:07:40,060
+لعند K تحت القانون GX of F بيساوي مين F of X لكل F
+
+96
+00:07:40,060 --> 00:07:44,000
+موجودة في الـ X primeطب إذن الآن عشان أثبت Linear
+
+97
+00:07:44,000 --> 00:07:49,640
+بدي أثبتلكم إن C α X زائد Y عند كل نقطة من النقاط
+
+98
+00:07:49,640 --> 00:07:52,280
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+99
+00:07:52,280 --> 00:07:53,200
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+100
+00:07:53,200 --> 00:07:54,060
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+101
+00:07:54,060 --> 00:07:54,300
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+102
+00:07:54,300 --> 00:07:57,660
+F F
+
+103
+00:07:57,660 --> 00:07:57,720
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+104
+00:07:57,720 --> 00:07:57,760
+F F F F F F F F F F F F F F F F F F F F F F F F F
+
+105
+00:07:57,760 --> 00:08:04,030
+F F F F F Fلان خد arbitrary f element in X' وخد ل
+
+106
+00:08:04,030 --> 00:08:07,510
+X و Y وين موجودات في الـ domain اللي بنحكي عنها و
+
+107
+00:08:07,510 --> 00:08:13,130
+الـ α scalar احسبلي C α X زي Y عند مين؟ عند الـ F
+
+108
+00:08:13,130 --> 00:08:17,870
+واضح؟ الـ F arbitrary element in وين؟ in X' بساوي
+
+109
+00:08:17,870 --> 00:08:22,210
+حسب التعريف اللي قبله بشوية بصير G هذه of هذه،
+
+110
+00:08:22,210 --> 00:08:27,290
+مظبوط؟ G α X زي Y of F وهذه تعريفة إيش؟ F لهذا
+
+111
+00:08:27,880 --> 00:08:32,480
+ويساوي f of α x زائد y ويساوي f is linear ما هي f
+
+112
+00:08:32,480 --> 00:08:36,700
+element in x' إذا هتتوزع α f of x زائد f of mean
+
+113
+00:08:36,700 --> 00:08:42,000
+of y الآن هذه بدرجة حال أصلها هذه عبارة عن مين هذه
+
+114
+00:08:42,000 --> 00:08:46,080
+الحالها اللي هو g x of f وهذه ال alpha زي ما هي
+
+115
+00:08:46,080 --> 00:08:51,510
+وهذه ايش أصلها g of y of fالآن هذه اللي هي Alpha
+
+116
+00:08:51,510 --> 00:08:56,490
+DX of F هي عبارة عن هذه كلها عبارة عن مين هي C of
+
+117
+00:08:56,490 --> 00:09:01,370
+X of مين of F زي ما احنا معرفينها CXاشو بتساوي DX
+
+118
+00:09:01,370 --> 00:09:06,290
+CX of F بيساوي DX of F هي عندك DX of F بيصير عبارة
+
+119
+00:09:06,290 --> 00:09:10,530
+عن C of X of مين of F والألفة معاها ونفس ال
+
+120
+00:09:10,530 --> 00:09:15,710
+relation DY of F هي عبارة عن C of Y of مين of F
+
+121
+00:09:16,160 --> 00:09:19,700
+الان هذا الكلام صار صحيح لكل F إذا صارت عند C of
+
+122
+00:09:19,700 --> 00:09:24,220
+Alpha X زائد Y بتساوي Alpha C of X زائد C of Y
+
+123
+00:09:24,220 --> 00:09:31,560
+وهذا يعني ان الـ C is Linear طيب الان note that
+
+124
+00:09:31,560 --> 00:09:39,120
+بدي أحصلكم الآن على إنها bounded و isometric معاية
+
+125
+00:09:39,120 --> 00:09:45,530
+نشوف كيفخدوا الآن أي F element in main in X' والـ
+
+126
+00:09:45,530 --> 00:09:49,350
+X وY are arbitrary points in main in X نفسها
+
+127
+00:09:49,350 --> 00:09:55,350
+ويحسبولي GX-Y of F إيش هيساوي حسب التعريف الجبل
+
+128
+00:09:55,350 --> 00:10:02,710
+شويةهي عبارة عن F of X minus Y والـ F is Linear
+
+129
+00:10:02,710 --> 00:10:05,930
+إذا بيسوا F of X ناقص F of Y طب الـ F of X ما هي
+
+130
+00:10:05,930 --> 00:10:10,290
+عبارة عن GX F of F والـ F of Y هي عبارة عن GY of F
+
+131
+00:10:10,290 --> 00:10:14,730
+إلى أن بيصير عبارة عن GX ناقص GY of مين of F حصل
+
+132
+00:10:14,730 --> 00:10:20,440
+طرح دالكين إلى أن صار عندي الآن هذا المقداربساوي
+
+133
+00:10:20,440 --> 00:10:25,900
+هذا المقدار عند كل F اذا اكيد هيصير عندى GX-Y هو
+
+134
+00:10:25,900 --> 00:10:30,480
+نفسه G GX ناقص GY لأنه دالتين متساويتين عند كل
+
+135
+00:10:30,480 --> 00:10:32,740
+نقطة من النقطة ال domain هنا اللي هو ال F اذا
+
+136
+00:10:32,740 --> 00:10:38,500
+هيكون GX-Y بساوي GX ناقص GY من لمّة أربعة ستة واحد
+
+137
+00:10:38,500 --> 00:10:43,530
+اللي قبل بشوية خدولي ال norm CX ناقص CYماذا يساوي
+
+138
+00:10:43,530 --> 00:10:49,650
+CX GX نقص مين GY يساوي نورم GX نقص Y هذه اللي
+
+139
+00:10:49,650 --> 00:10:53,710
+أثبتناها اللي هي هذه من اللي قبل بشوية ماذا يساوي
+
+140
+00:10:53,710 --> 00:10:58,730
+نورم X minus Y إذا صار عندي اللي هو C of X نقص C
+
+141
+00:10:58,730 --> 00:11:02,890
+of Y يساوي نورم X minus Yوهذا معناته أن هذا يعني
+
+142
+00:11:02,890 --> 00:11:04,810
+أن C هي عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+143
+00:11:04,810 --> 00:11:08,070
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+144
+00:11:08,070 --> 00:11:09,350
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+145
+00:11:09,350 --> 00:11:10,410
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+146
+00:11:10,410 --> 00:11:12,790
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+147
+00:11:12,790 --> 00:11:13,430
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+148
+00:11:13,430 --> 00:11:13,950
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+149
+00:11:13,950 --> 00:11:19,460
+عن عبارة عن عبارة عن عبارة عن عبارة عن عهلقال الـ
+
+150
+00:11:19,460 --> 00:11:24,480
+Spaces الـ Spaces اللي بيكون Range of C هو الـ X
+
+151
+00:11:24,480 --> 00:11:26,880
+double prime يعني الدلة اللي جابله شوية لما تكون
+
+152
+00:11:26,880 --> 00:11:31,020
+on two على طول بنسمي الـ Space هذا X أشماله is
+
+153
+00:11:31,020 --> 00:11:35,020
+reflexive إذا الـ Space X is reflexive إذا لجينا
+
+154
+00:11:35,020 --> 00:11:42,330
+ال canonical mapping اللي هو الـ C الـ Cمن X لعند
+
+155
+00:11:42,330 --> 00:11:47,570
+X double prime ويكون onto لأن دائما هذا C إيش ماله
+
+156
+00:11:47,570 --> 00:11:52,250
+عبارة عن isomorphism لل range of C إذا لجينا اللي
+
+157
+00:11:52,250 --> 00:11:56,910
+هو onto هذا أو بمعنى آخر ال range of C بيساوي ال X
+
+158
+00:11:56,910 --> 00:12:00,930
+double prime على طول بنقول إن ال X نفسها إيش ماله
+
+159
+00:12:00,930 --> 00:12:07,630
+is a reflexive space واضح؟ طيب ونشوف الآن Notes
+
+160
+00:12:08,980 --> 00:12:14,140
+بينما 4 6 2 the non-space x is isomorphic to a
+
+161
+00:12:14,140 --> 00:12:17,700
+subspace of mean of x w برايف x w برايف اللي هو
+
+162
+00:12:17,700 --> 00:12:24,020
+mean ال range of Cهنس .. هنس بنقول X is embedable
+
+163
+00:12:24,020 --> 00:12:27,740
+in مين؟ in X double prime X is embedable in X
+
+164
+00:12:27,740 --> 00:12:32,180
+double prime لأنه في canonical mapping بين ال X و
+
+165
+00:12:32,180 --> 00:12:35,120
+بين مين؟ اللي هو X double prime يعني في
+
+166
+00:12:35,120 --> 00:12:39,340
+isomorphism بين ال X و بين اللي هو subspace منها
+
+167
+00:12:39,340 --> 00:12:43,720
+فهذه الحاجة بنسميها طبعا إيش؟ X is embedable in X
+
+168
+00:12:43,720 --> 00:12:49,080
+double prime يعني isomorphicلـ subspace من XW' وفي
+
+169
+00:12:49,080 --> 00:12:53,620
+هذه الحالة C يسمى كالونيكال اللي هي أدات الـ
+
+170
+00:12:53,620 --> 00:12:59,200
+embedding من X إلى مين إلى XW' لأن إذا كانت الـ
+
+171
+00:12:59,200 --> 00:13:05,600
+subspace X عرفية فهي عيزومورفية من مين من XW' لكن
+
+172
+00:13:05,600 --> 00:13:11,400
+لو اقل الليل عنديلو فيه isomorphism بين X وXW' ليس
+
+173
+00:13:11,400 --> 00:13:15,780
+شرطًا هيكون reflexive لأن اللي يعمل isomorphism
+
+174
+00:13:15,780 --> 00:13:18,900
+عشان يكون reflexive اللي بيعمل isomorphism بيه هو
+
+175
+00:13:18,900 --> 00:13:25,720
+الـ canonical map واضح؟ اطلع لفوق طيب
+
+176
+00:13:25,720 --> 00:13:34,240
+theorem if
+
+177
+00:13:34,240 --> 00:13:39,840
+unknown spaceX is reflexive it is إيش ما له
+
+178
+00:13:39,840 --> 00:13:45,060
+complete يعني ال space اللي مش complete تدوروش على
+
+179
+00:13:45,060 --> 00:13:48,720
+إنه reflexive على طول إيش ما له is not reflexive
+
+180
+00:13:48,720 --> 00:13:52,620
+مجرد ما يكون ال norm of the space X is reflexive
+
+181
+00:13:52,620 --> 00:13:58,040
+على طول بيكون إيش ما له complete نيجي الآن الأمر
+
+182
+00:13:58,040 --> 00:14:02,220
+سهل since X is reflexive then X is isomorphic to
+
+183
+00:14:02,220 --> 00:14:04,800
+مين؟ to X double prime مين X double prime؟
+
+184
+00:14:04,800 --> 00:14:08,140
+completeمش الـdual space complete سواء الـX
+
+185
+00:14:08,140 --> 00:14:11,400
+complete أو لا الـX'' أكيد complete إذا على طول
+
+186
+00:14:11,400 --> 00:14:13,980
+اللي هو الـisomorphic اللي هو إيش هيكون is
+
+187
+00:14:13,980 --> 00:14:19,720
+complete يعني الآن صار عندي اللي هو any reflexive
+
+188
+00:14:19,720 --> 00:14:23,660
+space is a complete space أو إذا بنخ space طيب
+
+189
+00:14:23,660 --> 00:14:28,120
+theorem every
+
+190
+00:14:28,120 --> 00:14:33,200
+finite dimensional every finite dimensional normed
+
+191
+00:14:33,200 --> 00:14:38,870
+space is reflexiveأي finite dimensional normed
+
+192
+00:14:38,870 --> 00:14:43,690
+space is reflexive اخدنا .. اعملنا قبل هيك هذا
+
+193
+00:14:43,690 --> 00:14:46,390
+اللي هو ال canonical mapping في حالة ال .. في حالة
+
+194
+00:14:46,390 --> 00:14:51,070
+مين اللي هو ال finite dimensional ليش؟ إذا بتذكروا
+
+195
+00:14:52,180 --> 00:14:55,100
+لما كنا نقول ان الـdimensional لـ X is finite على
+
+196
+00:14:55,100 --> 00:15:00,420
+طول اللي هو بيصير any linear functional is bounded
+
+197
+00:15:00,420 --> 00:15:04,880
+معناته انه صار الـ X' و الـ X'' و الـ X*) إيش ما
+
+198
+00:15:04,880 --> 00:15:07,640
+يلوزي بعض الـ X*) اللي هو the set of all linear
+
+199
+00:15:07,640 --> 00:15:10,400
+اللي هو functional مافيش bounded نفسي، احنا
+
+200
+00:15:10,400 --> 00:15:13,280
+مابنحكيش عنها الان X' في حالة الـ finite
+
+201
+00:15:13,280 --> 00:15:18,440
+dimensional بتكون هي مين طلعت الـ X*)الأن من الـ
+
+202
+00:15:18,440 --> 00:15:22,500
+Theorem 2.9.3 الـ Dimension للـ X*) لجيناها إيش
+
+203
+00:15:22,500 --> 00:15:27,580
+بتساوي؟ الـ Dimension للـ X إذا صار عندي الآن الـ
+
+204
+00:15:27,580 --> 00:15:29,760
+X double prime .. يعني صارت هذه برضه finite
+
+205
+00:15:29,760 --> 00:15:34,780
+dimensional للـ X والـ X*) إذا الـ X*) Star هتكون
+
+206
+00:15:34,780 --> 00:15:38,160
+برضه مين هي؟ الـ X double prime الـ Second Dual
+
+207
+00:15:38,160 --> 00:15:43,370
+Spaceالان however .. however اللي هو C من X لعند X
+
+208
+00:15:43,370 --> 00:15:48,290
+double star إيش كانت أثبتناها is an isomorphism
+
+209
+00:15:48,290 --> 00:15:53,510
+مدام isomorphism هذه و هو ال X double prime مين هو
+
+210
+00:15:53,510 --> 00:15:56,990
+ال X double star هو نفسه ال X double prime إذا
+
+211
+00:15:56,990 --> 00:16:01,770
+صارت C من X لعند X double star is an isomorphism
+
+212
+00:16:01,770 --> 00:16:06,640
+hence ال X هتطلعis reflexive إذن الآن كلها الـ
+
+213
+00:16:06,640 --> 00:16:10,780
+finite dimensional spaces طلعت لنا إشمالها are
+
+214
+00:16:10,780 --> 00:16:20,200
+reflexive spaces طيب الآن القلبي
+
+215
+00:16:22,330 --> 00:16:26,930
+Ibrahim طلعت عنها LQ صح؟ اللي هي 1 على P زي 1 على
+
+216
+00:16:26,930 --> 00:16:31,550
+Q بيساوي 1 كمان Ibrahim لها هترجع منين؟ للـ LB إذا
+
+217
+00:16:31,550 --> 00:16:34,750
+ال second هو اللي هو ال LB إذا على طول هتطلع
+
+218
+00:16:34,750 --> 00:16:39,210
+أشماله أكيد الكلمة بين هذا و بين هذا هي نفسها لو
+
+219
+00:16:39,210 --> 00:16:43,930
+أنتوا جاهز مدام وانتوا وانتوا وانتوا وانتوا وانتوا
+
+220
+00:16:43,930 --> 00:16:44,150
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+221
+00:16:44,150 --> 00:16:46,330
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+222
+00:16:46,330 --> 00:16:47,150
+وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا وانتوا
+
+223
+00:16:47,150 --> 00:16:49,700
+وانتوا وانتوا وانتوا وانتوا وانتوا وreflexive
+
+224
+00:16:49,700 --> 00:16:54,560
+space إذن الان كل ال ال B spaces are reflexive
+
+225
+00:16:54,560 --> 00:16:59,880
+spaces طيب الان في عندي كمان عنوان كبير theorem 6
+
+226
+00:16:59,880 --> 00:17:07,620
+6 اللي هو every Hilbert space is reflexive any
+
+227
+00:17:07,620 --> 00:17:15,280
+Hilbert space is reflexive اللي بعده .. خسرناش
+
+228
+00:17:15,280 --> 00:17:22,250
+الوران اللي بعدهلما أربعة ستة سبعة let y be a
+
+229
+00:17:22,250 --> 00:17:35,310
+proper closed subspace خلّيني أطلع إليه هذا let
+
+230
+00:17:35,310 --> 00:17:39,770
+y be a proper closed subspace of a normed space x
+
+231
+00:17:44,190 --> 00:17:48,690
+وProper Closed Subspace منه يعني بمعنى آخر هذا
+
+232
+00:17:48,690 --> 00:17:53,710
+Closed وفي Elements بين الـ aY و بين مين و بين ال
+
+233
+00:17:53,710 --> 00:17:57,890
+X على الأقل في عندي Element هنا ماشي الحال Let X
+
+234
+00:17:57,890 --> 00:18:00,550
+not element in X minus Y خلّيني أخد X not وين
+
+235
+00:18:00,550 --> 00:18:06,470
+موجودة في ال X minus Y بيه Arbitrary و خلّيني أعرف
+
+236
+00:18:06,470 --> 00:18:10,400
+ال Deltaاللي هو بيساوي الـ infimum المسافة يعني
+
+237
+00:18:10,400 --> 00:18:15,940
+المسافة بين اللي هي ال X note و مين و ال Y ال
+
+238
+00:18:15,940 --> 00:18:23,140
+infimum لأ اللي هي ال norm Y note أو أيه Y ناقص X
+
+239
+00:18:23,140 --> 00:18:27,020
+noteوهي بيسميها D تلدة زي ما هو بيسميها such that
+
+240
+00:18:27,020 --> 00:18:31,660
+Y تلدة element in mean in Y الانفمان بين هذه و بين
+
+241
+00:18:31,660 --> 00:18:35,000
+الست اللي عندى هو سميها mean الدلتة هي اللي هي في
+
+242
+00:18:35,000 --> 00:18:38,180
+الواقع اللي هي ال distance the distance from X
+
+243
+00:18:38,180 --> 00:18:43,450
+node to Yبقولني then .. then بضمانكم there exists
+
+244
+00:18:43,450 --> 00:18:48,490
+F تلدى وين موجودة في ال X' بحيث أنه norm ال F تلدى
+
+245
+00:18:48,490 --> 00:18:53,370
+بيساوي واحد و ال F تلدى ل Y بتساوي سفر لكل Y وين
+
+246
+00:18:53,370 --> 00:18:57,450
+موجودة بلي هي بيكون موجودة في ال Y يعني بلاقي اللي
+
+247
+00:18:57,450 --> 00:19:06,830
+هو F تلدى element in X' و ال F تلدى normهابس هو
+
+248
+00:19:06,830 --> 00:19:14,150
+واحد والـ F تلدىof أي element هنا y بساوي 0 ومش
+
+249
+00:19:14,150 --> 00:19:21,450
+هيك و ال F لل X note هذه هي اللي هتساوي مين؟ اللي
+
+250
+00:19:21,450 --> 00:19:25,610
+هي المسافة F تلدة لل X note بساوي مين؟ بساوي
+
+251
+00:19:25,610 --> 00:19:28,630
+المسافة يعني لجأت ال F تلدة ده ال functional
+
+252
+00:19:28,630 --> 00:19:31,290
+بتساوي المسافة و في نفس ال issue و ال norm هو
+
+253
+00:19:31,290 --> 00:19:35,850
+بساوي 1 و F تلدة of Y لكل element هنا بساوي اللي
+
+254
+00:19:35,850 --> 00:19:37,770
+هو 0 خليني نبره مع بعض
+
+255
+00:19:42,940 --> 00:19:47,300
+اللي هن consider the subspace Z عبارة عن كل
+
+256
+00:19:47,300 --> 00:19:52,040
+الـlinear combinations اللي هي Y زاد Alpha X0 يعني
+
+257
+00:19:52,040 --> 00:19:57,000
+هو كأنه span بين الـ X0 و بين مين الـ Y نفسها such
+
+258
+00:19:57,000 --> 00:20:00,020
+that Alpha is the scalar of X هذا subspace من مين؟
+
+259
+00:20:00,020 --> 00:20:05,160
+من X لأن Y جزئية من X و الـ X0 موجودة في الـ X بظل
+
+260
+00:20:05,160 --> 00:20:08,940
+span عبارة عن subspace من الـ X and define the
+
+261
+00:20:08,940 --> 00:20:18,410
+functional Fon z يعني عرف الان f من z لعند
+
+262
+00:20:18,410 --> 00:20:23,610
+اللي هو ال scalar field تبعنا الآن هذه العناصر
+
+263
+00:20:23,610 --> 00:20:27,970
+اللي هنا اللي هي f of z اللي هو كيف شكل العنصر z
+
+264
+00:20:27,970 --> 00:20:32,770
+بساوي f of y زي ال alpha x not عملنا زيه المرة
+
+265
+00:20:32,770 --> 00:20:37,350
+الفاتة اللي هو بساوي ايه اش f of هذا بساوي مين ال
+
+266
+00:20:37,350 --> 00:20:44,900
+alpha هذه في مين في ال deltaالألفة في مين؟ في
+
+267
+00:20:44,900 --> 00:20:49,700
+الـDelta تنشوف كيف then
+
+268
+00:20:49,700 --> 00:20:52,840
+F is linear F is linear عاملة زيها المرة اللي فاتت
+
+269
+00:20:52,840 --> 00:20:56,180
+F is linear تاخدوا two elements بتكون عاملها
+
+270
+00:20:56,180 --> 00:21:03,680
+بعملها اللي هو F خلينا نقول of Gamma زد واحد زائد
+
+271
+00:21:03,680 --> 00:21:09,930
+زد اتنين بساوي تبقى معايا خلينا نتبتها linearزد
+
+272
+00:21:09,930 --> 00:21:12,870
+واحد وزد اتنين arbitrarily elementين وين أخدناهين
+
+273
+00:21:12,870 --> 00:21:18,810
+نزد اللي عندى بدا اثبت انه F is linear معايا Y
+
+274
+00:21:18,810 --> 00:21:25,170
+ساوي اللي هو F of جامعة زد واحد اللي هي جامعة في Y
+
+275
+00:21:25,170 --> 00:21:31,950
+زائد او Y واحد دعنا نسميها زائد Alpha واحد X Note
+
+276
+00:21:31,950 --> 00:21:36,690
+ماشي هذا زد واحد سميتها زد واحد اللي هو زد اتنين
+
+277
+00:21:37,600 --> 00:21:42,360
+اللي عبارة عن إيش Y2 مش هيك شكلها هي هنا يا جماعة
+
+278
+00:21:42,360 --> 00:21:51,560
+هي من هنا باخد زائد Alpha 2 X Note ويساوي جمّحن مع
+
+279
+00:21:51,560 --> 00:21:59,840
+بعض يصير F of Gamma Y1 زائد Y2 Gamma Y1 زائد Y2
+
+280
+00:21:59,840 --> 00:22:05,180
+مضروبة في مين زائد مين زائد اللي هو Alpha 1 زائد
+
+281
+00:22:05,180 --> 00:22:11,070
+Alpha 2 في X Noteو يساوي ايش قانونة هذه على طول
+
+282
+00:22:11,070 --> 00:22:16,550
+بتنمي مين معامل x0 في مين في دلتا و يساوي معامل x0
+
+283
+00:22:16,550 --> 00:22:22,590
+اللي هو Alpha 1 أه Gamma هذا مضروبة برضه Gamma
+
+284
+00:22:22,590 --> 00:22:27,870
+Gamma مضروبة في Alpha 1 أه صح Gamma مضروبة في
+
+285
+00:22:27,870 --> 00:22:33,170
+Alpha 1 طيب Gamma Alpha 1 زائد مين Alpha 2 كله
+
+286
+00:22:33,170 --> 00:22:36,410
+مضروب في مين في دلتا واضح أه
+
+287
+00:22:39,850 --> 00:22:46,930
+هي بترمي اللي هو العنصر هذا Alpha اللي هو معامل X
+
+288
+00:22:46,930 --> 00:22:52,750
+Note في Delta هاي معامل X Note في مين؟ في Delta
+
+289
+00:22:52,750 --> 00:22:56,590
+وهذا ال element فيها كلها بعض فبيصير Y ساوي اللي
+
+290
+00:22:56,590 --> 00:23:03,710
+هو Gamma Alpha 1 Delta زائد Alpha 2 في Delta Y
+
+291
+00:23:03,710 --> 00:23:09,120
+ساوية رجّح الاصلها هذه Gamma 1Gamma فالف واحد
+
+292
+00:23:09,120 --> 00:23:14,340
+Delta اللي هي عبارة عن مين هادي مع بعض هو ال
+
+293
+00:23:14,340 --> 00:23:19,160
+element، مظبوط؟ لو بمعنى أخر، عندي بدي أطلع جابة
+
+294
+00:23:19,160 --> 00:23:27,840
+برا، Gamma، بيصير عندي F of Y واحد زائد الف واحد
+
+295
+00:23:27,840 --> 00:23:35,800
+في Delta، زائد، التاني نفس الاشيF of Y2 زي الألف
+
+296
+00:23:35,800 --> 00:23:43,680
+اتنين اللي هو لأ بدون دلتا X0 أسف في X0 إذا صارت
+
+297
+00:23:43,680 --> 00:23:48,980
+اللي هي عبارة عن Linear هاي F اللي هي طبعا هادي و
+
+298
+00:23:48,980 --> 00:23:56,600
+يسوى Gamma F of Z1 زي F of Z2 و راجعوا الحسابات
+
+299
+00:23:56,600 --> 00:24:01,430
+لايكون خربطنا في إشيطيب then F is معناه إزلينا
+
+300
+00:24:01,430 --> 00:24:06,550
+خلصنا من ال linearity لأن since Y is closed then
+
+301
+00:24:06,550 --> 00:24:11,390
+Delta strictly أكبر من مين من سفر المسافة اللي هو
+
+302
+00:24:11,390 --> 00:24:15,430
+بتسير اللي هي بين هذي و هذي بتساوي سفر وعملناها
+
+303
+00:24:15,430 --> 00:24:18,670
+إذا بتتذكروا هذي عملتها في برهان نظرية في شبطر
+
+304
+00:24:18,670 --> 00:24:24,380
+اللي هو في شبطر 2إنه ليش Delta أكبر من سفر و
+
+305
+00:24:24,380 --> 00:24:28,940
+أرجعولها لأن then Delta أكبر من سفر and so F لا
+
+306
+00:24:28,940 --> 00:24:33,200
+تساوي إياش لاتساوي Zero مدام Delta أكبر من سفر
+
+307
+00:24:33,200 --> 00:24:37,600
+فالـ F مش ال Zero function لأن F إيش معرفة F of Z
+
+308
+00:24:37,600 --> 00:24:41,780
+بيساوي Alpha في Delta و ال Delta هذه مش سفر معناته
+
+309
+00:24:41,780 --> 00:24:45,300
+اللي هو صار عندى لما ما تكونش هذه سفر على طول ال F
+
+310
+00:24:45,300 --> 00:24:48,420
+of Z بتساوي قيمة غير السفر إذا أكيد مش ال Zero
+
+311
+00:24:48,420 --> 00:24:52,190
+functionوعنا اللي هو ال elements اللي زيها دي y زي
+
+312
+00:24:52,190 --> 00:24:57,930
+x0 نفسها هي قيمتها مش سفر مظبوط ولا لأ ايش قيمتها
+
+313
+00:24:57,930 --> 00:25:02,730
+بدأ تطلع تطلع
+
+314
+00:25:02,730 --> 00:25:13,210
+عبارة عن f of y زي x0 ايش بساوي دلتا نفسها مش
+
+315
+00:25:13,210 --> 00:25:16,690
+معامد x0 طيب
+
+316
+00:25:19,770 --> 00:25:23,870
+طيب اتفجنا عليها دي note that for all y element in
+
+317
+00:25:23,870 --> 00:25:28,910
+y f of y ايش بيساوي بيساوي اللي هي او انا انزل
+
+318
+00:25:28,910 --> 00:25:31,130
+عشان اقولكم مين رايح اذا اذكركم ان ايش بدي ابدل
+
+319
+00:25:31,130 --> 00:25:34,350
+ايه اف تل ده اللي هي نور ما بيساوي واحد و قابلة
+
+320
+00:25:34,350 --> 00:25:37,470
+سفر و ايش ما لو اف تل ده و في x not بيساوي اللي هو
+
+321
+00:25:37,470 --> 00:25:41,350
+دلتا الان انا بشر العلق اللي هو subspace ومنه
+
+322
+00:25:41,350 --> 00:25:47,600
+هنطلق في اللي اللي بديه طيبثم اقول لنا ان for all
+
+323
+00:25:47,600 --> 00:25:51,740
+y into y, f of y بيساوي اطلع لفوق اللي هو f of y
+
+324
+00:25:51,740 --> 00:25:55,840
+زائد مين زائد سفر في x not صح ولا لأ اللي هو ايش
+
+325
+00:25:55,840 --> 00:26:00,100
+هيطلع بساوي بساوي سفر في دلتا اللي هو سفر and f of
+
+326
+00:26:00,100 --> 00:26:03,460
+x not هنا او ده بتجداش بتساوي بساوي اللي هو دلتا
+
+327
+00:26:03,870 --> 00:26:08,470
+واضح طيب طبعا هي التفسير يتواي بساوي صفر و الف
+
+328
+00:26:08,470 --> 00:26:11,310
+بساوي واحد في الجهتين تطلع عندها دي بساوي صفر وهذا
+
+329
+00:26:11,310 --> 00:26:16,230
+بساوي واحد الان now we show that F is bounded ده
+
+330
+00:26:16,230 --> 00:26:20,110
+اثبتنا ان F لينيا و اثبتنا F مش هي الصفر و اثبتنا
+
+331
+00:26:20,110 --> 00:26:25,770
+قيمة ال F عند ال Y اي Y في ال Y هداك بساوي صفر و F
+
+332
+00:26:25,770 --> 00:26:30,700
+of X not بتساوي دلتاكل هدولة خلّيني لأنه بلزم اني
+
+333
+00:26:30,700 --> 00:26:34,860
+بعد شوية Now we show that F is bounded if Alpha
+
+334
+00:26:34,860 --> 00:26:38,260
+بتساوي سفر اذا F of Z automatically مش هتساوي
+
+335
+00:26:38,260 --> 00:26:41,140
+هتساوي سفر وهذا طبعا ال boundedness بيطلع
+
+336
+00:26:41,140 --> 00:26:46,200
+automatic يعني لو Alpha مش سفر بدي أسالكم انه F is
+
+337
+00:26:46,200 --> 00:26:50,940
+boundedأو أوصلكم لـ Boundedness لـ F الان مدام
+
+338
+00:26:50,940 --> 00:26:53,200
+Alpha مش ساوي مش ساوي ليش ساوي سيفرزن شكل اللي بده
+
+339
+00:26:53,200 --> 00:26:57,120
+أجسم على Alpha إذا بيصير عندي لأي Y element in Y
+
+340
+00:26:57,120 --> 00:27:01,340
+ناقص واحدة لـ Alpha وين هيكون برضه في Y ماشي الحال
+
+341
+00:27:01,340 --> 00:27:06,900
+طيب بحسبلي الآن absolute value لـ F of Zبتساوي F
+
+342
+00:27:06,900 --> 00:27:11,820
+of Y زائد ألفة مين X Note حسب اللي هو تعريف هذه
+
+343
+00:27:11,820 --> 00:27:15,120
+هيطلع Alpha في Delta و Absolute Value بيصير
+
+344
+00:27:15,120 --> 00:27:18,300
+Absolute Value في الألفة في المين في الدلتة لأن
+
+345
+00:27:18,300 --> 00:27:23,930
+الدلتة أكبر أو يساوي أكبر Circle من سفرY ساوي الـ
+
+346
+00:27:23,930 --> 00:27:26,550
+Absolute value لـ Alpha في مين في الـ infimum لهذه
+
+347
+00:27:26,550 --> 00:27:30,890
+الأشياء الـ infimum هي الـ distance الان الـ
+
+348
+00:27:30,890 --> 00:27:35,910
+infimum هذا سيكون أصغر أو يساوي اللي هي نجامة هي
+
+349
+00:27:35,910 --> 00:27:40,630
+الـ Absolute value لـ Alpha زي ما هي و هذه اللي هي
+
+350
+00:27:40,630 --> 00:27:44,190
+الـ infimum أصغر أو يساوي واحدة منهم من الواحدة
+
+351
+00:27:44,190 --> 00:27:47,590
+منهم ياخد Y تلدة عبارة عن ناقص واحد على الألفة في
+
+352
+00:27:47,590 --> 00:27:51,510
+مين في Y ناقص X nodeواخدتها بالشكل هذا عشان لما
+
+353
+00:27:51,510 --> 00:27:55,550
+أنا أدخل Alpha اللي جوا هيصير عبارة عن Y زائد
+
+354
+00:27:55,550 --> 00:27:59,010
+Alpha X naught، مظبوط؟ اللي هي Y زائد Alpha X
+
+355
+00:27:59,010 --> 00:28:02,350
+naught اللي هي مين؟ الـ Z اللي بدأت فيها، إذا صار
+
+356
+00:28:02,350 --> 00:28:07,110
+ال absolute value لل F of Z أصغر أو ساوي مين؟ نورم
+
+357
+00:28:07,110 --> 00:28:10,470
+الـ Z، اجسموا انتهتين أو خدوا ال suprem على نورم
+
+358
+00:28:10,470 --> 00:28:14,890
+الـ Z بساوي واحد، بتطلع اللي هو نورم ال F أصغر أو
+
+359
+00:28:14,890 --> 00:28:20,850
+ساوي إيش؟ أصغر أو ساوي واحداللي بعده اطلع لفوق
+
+360
+00:28:20,850 --> 00:28:24,250
+لنثبت انها اكبر او يساوي ايش اكبر او يساوي واحد
+
+361
+00:28:24,250 --> 00:28:30,350
+طيب by the definition of infimum there is exist a
+
+362
+00:28:30,350 --> 00:28:34,230
+sequence y and of elements in NY such that normal
+
+363
+00:28:34,230 --> 00:28:38,970
+y and not six note ايش ماله؟converge لمن؟ لـDelta،
+
+364
+00:28:38,970 --> 00:28:44,030
+ماشي الحال؟ الان الـ infimum بيساوي هذا المقدار،
+
+365
+00:28:44,030 --> 00:28:47,750
+ماشي الحال؟ إذا بقدر ألاقي sequence من ال elements
+
+366
+00:28:47,750 --> 00:28:51,630
+اللي في Y بحيث norm الـ Y الناقص اللي هو X0 يروح
+
+367
+00:28:51,630 --> 00:28:57,510
+لمن؟ لهذه الـ Delta، وثباته سهل هذا الكلام، طيب
+
+368
+00:29:00,530 --> 00:29:05,310
+صار عندى اللى هو sequence من العناصر اللى موجودة
+
+369
+00:29:05,310 --> 00:29:09,930
+في الـY نورم الـEI أنقص X0 وتروح لمين لـDelta منها
+
+370
+00:29:09,930 --> 00:29:14,350
+هذه الـsequence بتاخدها كعلخاصة توصلى لشق الثاني
+
+371
+00:29:14,350 --> 00:29:17,610
+اللى و أف النورم أكبر أو يساوي واحد خدوا بتقياد
+
+372
+00:29:17,610 --> 00:29:20,510
+النورم للأف أكبر أو يساوي واحد اللى هي أكبر أو
+
+373
+00:29:20,510 --> 00:29:24,250
+يساوم هي supreme أكبر أو يساوم القيمة عند نقطة ما
+
+374
+00:29:24,950 --> 00:29:28,410
+أو عند نقاطنا إذا أكبر أو ساوي F of Y N نقص X Note
+
+375
+00:29:28,410 --> 00:29:33,290
+اللي لجاتهم ع نورم Y N نقص X Note هذا الكلام لكل
+
+376
+00:29:33,290 --> 00:29:38,990
+اللي هي N element هناقيمة هذه اللي هي عبارة عن ال
+
+377
+00:29:38,990 --> 00:29:42,970
+absolute value لناقص واحد لناقص Delta ال absolute
+
+378
+00:29:42,970 --> 00:29:46,930
+value لناقص Delta هو مين؟ ال Delta على ال norm هذا
+
+379
+00:29:46,930 --> 00:29:51,010
+نفسه as n goes to infinity هذا بتروح ل Delta إذا
+
+380
+00:29:51,010 --> 00:29:55,530
+هذا norm ال F أكبر أو يساوي هذي for every n إذا
+
+381
+00:29:55,530 --> 00:29:58,130
+خدوا ال limit as n goes to infinity فتطلع دلتة ع
+
+382
+00:29:58,130 --> 00:30:00,570
+دلتة اللي هي ساوي واحد يصير نورم ال F أكبر أو
+
+383
+00:30:00,570 --> 00:30:04,450
+يساوي ال واحد و جابل أصغر أو يساوي ال واحد إذا صار
+
+384
+00:30:04,450 --> 00:30:08,360
+عند نورم ال F إيش بيساوي؟ بيساوي واحدهذه الـ F
+
+385
+00:30:08,360 --> 00:30:15,000
+اللي اشتغلت عليها لزد subspace من مين؟ من ال X
+
+386
+00:30:15,000 --> 00:30:20,560
+بقدر اعمل له extension أنا معتمد الآن على مين؟ على
+
+387
+00:30:20,560 --> 00:30:23,920
+اللي هو ال hand-benach theorem الان by hand-benach
+
+388
+00:30:23,920 --> 00:30:28,860
+theorem أربعة تلاتة اتنين there exist F مين؟
+
+389
+00:30:31,840 --> 00:30:36,780
+بتوسع نفوذها بدل ما كانت على الـ subspace Z هتوسع
+
+390
+00:30:36,780 --> 00:30:40,320
+نفوذها على الـ X' وبنفس الخواص such that norm of F
+
+391
+00:30:40,320 --> 00:30:45,720
+تلده بسوء واحد و F تلده of Y بسوء سفر و F تلده of
+
+392
+00:30:45,720 --> 00:30:51,040
+X0 بسوء دلتا وهيك هتكون حصلت على النتيجة اللي
+
+393
+00:30:51,040 --> 00:30:53,280
+بديها وهو المطلوب
+
+394
+00:31:02,880 --> 00:31:04,340
+يوجد كثير من الـ 4,6,8
+
+395
+00:31:08,580 --> 00:31:11,420
+إذا كان الـ Dual Space X' من نفسه نفسه نفسه نفسه
+
+396
+00:31:11,420 --> 00:31:21,600
+نفسه نفسه نفسه نفسه نفسه نفسه
+
+397
+00:31:21,600 --> 00:31:36,380
+نفسه نفسه نفسه
+
+398
+00:31:36,800 --> 00:31:41,680
+A separable normed space X with a non-separable
+
+399
+00:31:41,680 --> 00:31:46,940
+dual space X' can't be reflexive يعني لو كان عندي
+
+400
+00:31:46,940 --> 00:31:53,240
+separable normed space X وكان ال X' إيش ماله؟ non
+
+401
+00:31:53,240 --> 00:31:58,640
+-separableالآن لو كانت X' separable، فهي Automatic
+
+402
+00:31:58,640 --> 00:32:02,440
+X separable لكن ممكن يكون الـ X' non-separable
+
+403
+00:32:02,440 --> 00:32:06,560
+وهذه تكون يشمالها separable فالآن فرضينا أن X
+
+404
+00:32:06,560 --> 00:32:12,120
+separable و X' non-separable الآن يقول لي مستحيل
+
+405
+00:32:12,120 --> 00:32:15,560
+تطلع الـ X يشمالها reflexive لازم تطلع يشمالها، X
+
+406
+00:32:15,560 --> 00:32:19,440
+is not reflexive suppose that X' is non-separable
+
+407
+00:32:19,440 --> 00:32:25,130
+زي ما هو حاكيو X separable و X أشمالها و X
+
+408
+00:32:25,130 --> 00:32:28,890
+reflexive تقولوا إن كانت بيه reflexive فبنرسلها
+
+409
+00:32:28,890 --> 00:32:32,790
+contradiction الآن X اللي هي ساعة أشمال في تردنها
+
+410
+00:32:32,790 --> 00:32:38,050
+reflexive مدام X reflexive إذن الـ X double-brane
+
+411
+00:32:38,050 --> 00:32:43,740
+isomorphicمدام XW' أزو مورفك تاكس which implies
+
+412
+00:32:43,740 --> 00:32:48,500
+that XW' أشمالها separable then by theorem اللي
+
+413
+00:32:48,500 --> 00:32:53,140
+حكينا عنها فوق اللي هي الأجال درجة منها X' أسبرابل
+
+414
+00:32:53,140 --> 00:32:57,040
+بظبط ولا لأ بناء على هذه إنه إذا كانت ال XW'
+
+415
+00:32:57,300 --> 00:33:02,080
+أسبرابل هتكون اللي هي X أشمالها براي أسبرابل
+
+416
+00:33:04,580 --> 00:33:07,720
+فاهمين أه؟ الان صار عندي which is a contradiction
+
+417
+00:33:07,720 --> 00:33:14,840
+therefore x can't be reflexive الان بتسمحوا لي
+
+418
+00:33:14,840 --> 00:33:20,800
+عادة ديش أيضا .. دي ده مش فاهمين عليها example ال
+
+419
+00:33:20,800 --> 00:33:27,720
+one is not reflexive ال one is not reflexive since
+
+420
+00:33:27,720 --> 00:33:33,730
+ال one is separableأخدناها but الـ one prime
+
+421
+00:33:33,730 --> 00:33:38,670
+بتساوي ال infinity إيش ما لها is not اللي هي
+
+422
+00:33:38,670 --> 00:33:46,250
+separable then ال one is not reflexive أخدناها ده
+
+423
+00:33:46,250 --> 00:33:53,590
+الكلام سابقا خليني أرجع بس لهذه الشغلة قبل ما ..
+
+424
+00:33:53,590 --> 00:33:54,410
+بعد إذنكم يعني
+
+425
+00:34:08,250 --> 00:34:12,950
+اللي خاطر أشرحها هذه اللي هي ال .. الـ Hilbert
+
+426
+00:34:12,950 --> 00:34:16,530
+space أنه every Hilbert space is reflexive أنه هي
+
+427
+00:34:16,530 --> 00:34:21,070
+مهمة يعني فالشغلة بس بسيطة مش كبيرة بس اللي أنتوا
+
+428
+00:34:21,070 --> 00:34:24,810
+اللي بدنا نثبته فخليني أطلع عليه بال .. يعني
+
+429
+00:34:24,810 --> 00:34:29,350
+المعلومات اللي فيه بتقدروا يعني خليني أقول متوفرة
+
+430
+00:34:29,350 --> 00:34:32,830
+بين إيديكم خليني أشوفها أيش اللي بدنا نثبت أنه
+
+431
+00:34:32,830 --> 00:34:36,390
+every Hilbert space is reflexive
+
+432
+00:34:40,950 --> 00:34:45,670
+الان عشان نثبت reflexive بدنا نثبت الـ canonical
+
+433
+00:34:45,670 --> 00:34:50,840
+mapping ايش معله اذا انتهبدنا نركّب لنا ناخد الـ
+
+434
+00:34:50,840 --> 00:34:53,100
+Arbitrary Element هنا و نركّب لنا Element بحيث انه
+
+435
+00:34:53,100 --> 00:34:56,840
+يكون اللي هو صورته يعني تكون هي اللي بدأنا فيها
+
+436
+00:34:56,840 --> 00:35:00,520
+الان every Hilbert space H is reflexive we shall
+
+437
+00:35:00,520 --> 00:35:05,040
+prove surjectivity of the canonical mapping C من H
+
+438
+00:35:05,040 --> 00:35:07,920
+لعند H double prime ان احنا نعرف ان H .. C من H
+
+439
+00:35:07,920 --> 00:35:11,560
+لعند H double prime قبل بشوية قولنا دايما اللي هو
+
+440
+00:35:11,560 --> 00:35:13,940
+.. اللي هو فيه أزيومرفيزي من عند ال range of C
+
+441
+00:35:13,940 --> 00:35:18,490
+عشان نكمل القصة بس نثبت ان هي H ontoBy showing
+
+442
+00:35:18,490 --> 00:35:21,350
+that for every G element in H double prime داخد G
+
+443
+00:35:21,350 --> 00:35:25,090
+وين موجودة في الـ H double prime و ألاقي element
+
+444
+00:35:25,090 --> 00:35:28,830
+هنا بحيث انه CX هو يصير اللي هو الـ G اللي بدأت
+
+445
+00:35:28,830 --> 00:35:32,210
+فيه ماشي الحال ستلاقي اللي هو الأمور المشابهة اللي
+
+446
+00:35:32,210 --> 00:35:36,330
+حكيناها قبل شوية لذن for every G element in H
+
+447
+00:35:36,330 --> 00:35:40,170
+double prime we want to find X element in H such
+
+448
+00:35:40,170 --> 00:35:47,950
+that G بتساوي CXالآن خلّينا نحضر للوصول لهذا اللي
+
+449
+00:35:47,950 --> 00:35:51,030
+هي .. و نستعمل بعض الشغلات اللي أخدناها قبل هيك
+
+450
+00:35:51,030 --> 00:35:54,010
+خصوصا الـ ResRepresentation Theorem اللي هي اللي
+
+451
+00:35:54,010 --> 00:35:58,070
+.. اللي بناخد F بدلالة الـ inner product زي ما
+
+452
+00:35:58,070 --> 00:36:00,110
+عملنا المرة الفاتتة في المحاضرة الفاتتة عملنا زي
+
+453
+00:36:00,110 --> 00:36:03,850
+هيك شوفوا كده as a preparation we define A من H'
+
+454
+00:36:04,090 --> 00:36:07,930
+لعند Hπ عملتها قبل هيك المرة الفاتة اللي هو بي A F
+
+455
+00:36:07,930 --> 00:36:12,980
+إيش بيساوي Zالـ F من أين جاء من أتش براين و بساوي
+
+456
+00:36:12,980 --> 00:36:16,640
+Z مين الـ Z هي احنا بنقول لكل F Element من أتش
+
+457
+00:36:16,640 --> 00:36:21,400
+براين اللي هو there exist a unique Z such that F
+
+458
+00:36:21,400 --> 00:36:24,460
+of X can be written as any product X و Z هذا الـ
+
+459
+00:36:24,460 --> 00:36:29,580
+representation theoryاللي بيدا استخدمه أنه أخد أي
+
+460
+00:36:29,580 --> 00:36:32,400
+أف اللي متناقش prime و بال race representation
+
+461
+00:36:32,400 --> 00:36:36,260
+theorem for any أف اللي متناقش prime there exist a
+
+462
+00:36:36,260 --> 00:36:40,400
+unique z such that f of x بيساوي ال x ومين و ال z
+
+463
+00:36:40,400 --> 00:36:43,780
+ماشي الحال إذا انجدرت اللي أنا عرف أي أف مش متساوي
+
+464
+00:36:43,780 --> 00:36:46,580
+بيساوي ال z اللي لجيتها اللي بتدللتها عرفت اللي هي
+
+465
+00:36:46,580 --> 00:36:53,050
+الأف as another productالان عندى طبعا هذا الكلام
+
+466
+00:36:53,050 --> 00:36:56,870
+كله from تلاتة تمانية واحد we know that a is
+
+467
+00:36:56,870 --> 00:37:00,910
+bijective and isometric ال a is bijective and
+
+468
+00:37:00,910 --> 00:37:03,850
+isometric عملتها المرة الفاتتة في المحاضرة اللى
+
+469
+00:37:03,850 --> 00:37:07,430
+فاتتها عملتها الان و a is conjugate linear برضه
+
+470
+00:37:07,430 --> 00:37:10,940
+عملتها المرة الفاتتةA is going to get linear إذا
+
+471
+00:37:10,940 --> 00:37:16,460
+بتتذكروا as we see from 16 section 4-5 اللي المرة
+
+472
+00:37:16,460 --> 00:37:20,240
+الفاتتة عندي الأثبتنا لـA is going to get linear
+
+473
+00:37:20,240 --> 00:37:24,540
+رجعوه رجعوه رجعوه كله حكيته بالتفصيل المرة الفاتتة
+
+474
+00:37:25,700 --> 00:37:32,040
+الأن الـ H براين هو مجتمع مكتمل إذا من اتنين عشرة
+
+475
+00:37:32,040 --> 00:37:35,940
+أربعة اللي هو and a Hilbert space with inner
+
+476
+00:37:35,940 --> 00:37:39,680
+product space defined by برضه أثبتنا أنه لما يكون
+
+477
+00:37:39,680 --> 00:37:43,780
+الـ Hاللي هو inner product space أو Hilbert space
+
+478
+00:37:43,780 --> 00:37:48,340
+الـ H prime تبعه برضه هيكون ماله Hilbert space و
+
+479
+00:37:48,340 --> 00:37:52,220
+ال inner product تبعي اللي هو ال H prime اللي صار
+
+480
+00:37:52,220 --> 00:37:55,040
+Hilbert space بقدر اخده من ال inner product تبع
+
+481
+00:37:55,040 --> 00:37:58,580
+مين؟ تبع ال H واخدناه بالطريقة التالية ان ال inner
+
+482
+00:37:58,580 --> 00:38:04,860
+product F1 F2 تبع ال H prime بساوي اللي هو AF2
+
+483
+00:38:04,860 --> 00:38:09,730
+اللي هي AF2 و AF1 اللي هو elementين وين هذا؟هذا
+
+484
+00:38:09,730 --> 00:38:13,710
+بغض النظر إيش هو هذا بساوي Element من من من ال ..
+
+485
+00:38:13,710 --> 00:38:17,370
+هذا مش عليه inner product لأن هذا الـ H prime
+
+486
+00:38:17,370 --> 00:38:21,480
+هيكون عبارة عن Hilbert spaceوهيكون ال product
+
+487
+00:38:21,480 --> 00:38:25,660
+تبعته بقدر اخده من هذا كيف باخده من هذا لو عندي x
+
+488
+00:38:25,660 --> 00:38:30,460
+و y هنا في هذا بيصير عندي ال F1 و ال F2 تبعته
+
+489
+00:38:30,460 --> 00:38:33,680
+بيساوي inner product بس مجلوب بين الجهتين اللي هو
+
+490
+00:38:33,680 --> 00:38:38,360
+في هذه الحالة هيكون عندي F1 و F2 بيساوي A F2 هيكون
+
+491
+00:38:38,360 --> 00:38:43,280
+في ال H و ال A F1 برضه هيكون وين في ال H طيب
+
+492
+00:38:48,060 --> 00:38:52,340
+الان بيقولني لاحظ احنا قبل شوية قولنا ايه is
+
+493
+00:38:52,340 --> 00:38:56,660
+conjugate linear conjugate linear والترتيب القدر
+
+494
+00:38:56,660 --> 00:39:02,720
+اللي هو عندك ال inner product هذا اللي هو عكس اللي
+
+495
+00:39:02,720 --> 00:39:09,420
+هي بدل F2 F1 هنا مين عنده بعرفه بال F2 و ال
+
+496
+00:39:09,420 --> 00:39:12,280
+conjugate linear مع هذا العكس هيطلع اللي هو اللي
+
+497
+00:39:12,280 --> 00:39:16,920
+بديهشوفوا كيف الان note that the order of F1 و F2
+
+498
+00:39:16,920 --> 00:39:22,280
+on both sides اللي هو هذا عكس التاني الان هذا
+
+499
+00:39:22,280 --> 00:39:25,140
+هيعمل inner product ال inner product كلها إيه
+
+500
+00:39:25,140 --> 00:39:27,940
+جمال؟ لأن الخواص اللي بتعملوها و بتلاجوها على طول
+
+501
+00:39:27,940 --> 00:39:31,820
+inner product دي شكل في تفصيلها الان ماعطيكم
+
+502
+00:39:31,820 --> 00:39:35,360
+ملاحظة عالمين على الخاصية التانية اللي بتستخدم
+
+503
+00:39:35,360 --> 00:39:39,360
+فيها ال conjugate linear يعني بمعنى أخر Alpha F1 و
+
+504
+00:39:39,360 --> 00:39:45,160
+F2هذه بتحقق اللي هو إيش بتساوي Alpha ف F1 و مين؟
+
+505
+00:39:45,160 --> 00:39:48,380
+F2 اللي حققه الليال هو ال conjugate linear مع
+
+506
+00:39:48,380 --> 00:39:54,320
+تعريفه هذا كيف Alpha F1 F2 إيش بتساوي؟ بتساوي A F2
+
+507
+00:39:54,320 --> 00:40:00,290
+هذه لهذه و A لهذهA α 1 أهلاً لكن الـ A conjugate
+
+508
+00:40:00,290 --> 00:40:02,630
+ليه؟ يعني إذا اللي بده يطلع منها بتطلع إيه؟
+
+509
+00:40:02,630 --> 00:40:06,790
+conjugate فبتصير الـ α conjugate في A F 1 وده A F
+
+510
+00:40:06,790 --> 00:40:09,930
+2 لأن هذه لما تطلع من اللي بعيد اللي هو بتطلع
+
+511
+00:40:09,930 --> 00:40:12,250
+إليها كمان conjugate فبتصير لها conjugate
+
+512
+00:40:12,250 --> 00:40:16,470
+conjugate بتطلع Alpha فبتطلع اللي هي فعلا محققة من
+
+513
+00:40:16,470 --> 00:40:19,990
+اللي هو الشرط التاني تبع ال inner product والشرط
+
+514
+00:40:19,990 --> 00:40:24,310
+الأول وبجاعة الشروط برضه اللي هي سريعة وسهلةالان
+
+515
+00:40:24,310 --> 00:40:29,090
+اذا صار فعلا عندى هذا عمللى اللى هو inner product
+
+516
+00:40:29,090 --> 00:40:34,750
+على اللى هو ال H prime و هيكون complete
+
+517
+00:40:38,270 --> 00:40:42,870
+الان let g element .. كله عشان .. بدي أركب مين؟
+
+518
+00:40:42,870 --> 00:40:47,230
+بدي أركب .. أخدت اللي هو g arbitrary اللي هي ال ..
+
+519
+00:40:47,230 --> 00:40:48,750
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+520
+00:40:48,750 --> 00:40:48,790
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+521
+00:40:48,790 --> 00:40:49,070
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+522
+00:40:49,070 --> 00:40:49,090
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+523
+00:40:49,090 --> 00:40:49,430
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+524
+00:40:49,430 --> 00:40:50,130
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+525
+00:40:50,130 --> 00:40:50,410
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+526
+00:40:50,410 --> 00:40:51,230
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+527
+00:40:51,230 --> 00:40:51,810
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+528
+00:40:51,810 --> 00:40:59,970
+ال .. ال .. ال .. ال .. ال ..
+
+529
+00:40:59,970 --> 00:41:04,590
+ال .. ال ..
+
+530
+00:41:06,450 --> 00:41:10,450
+ما هي برضه الـ G في الـ H double prime يعني بمعنى
+
+531
+00:41:10,450 --> 00:41:16,690
+آخر G element in H prime الكل أشماله الـ prime بدا
+
+532
+00:41:16,690 --> 00:41:19,810
+أطبق ال race representation theorem عليها اللي هو
+
+533
+00:41:19,810 --> 00:41:22,350
+there exist لكل element هنا there exist a unique
+
+534
+00:41:22,350 --> 00:41:28,310
+element جوا بحيث انه اللي هو G of ال F أي element
+
+535
+00:41:28,310 --> 00:41:32,830
+بساوي اللي هو ال inner product بين اللي هو A of No
+
+536
+00:41:32,830 --> 00:41:40,810
+اللي هو أسف Fو F note اللي هو واحد كمان مرة ايش ال
+
+537
+00:41:40,810 --> 00:41:44,270
+reservation presentation بتفهم بتقول هذا اسم اللي
+
+538
+00:41:44,270 --> 00:41:47,810
+بدكم إياه اش برايم سمونيه اللي بدكم إياه اي inner
+
+539
+00:41:47,810 --> 00:41:54,150
+product X ماشي الان لكل element في ال X برايم بقدر
+
+540
+00:41:54,150 --> 00:42:01,390
+انادي unique element اللي هو بحيث انه Gof هذي
+
+541
+00:42:01,390 --> 00:42:09,190
+شغالة وين؟ G من H' شغالة وين من H' لمن؟ ل K فح؟
+
+542
+00:42:09,190 --> 00:42:15,290
+بتاخد ال element G of F و بترميه في شغلة لإن ال
+
+543
+00:42:15,290 --> 00:42:17,910
+research presentation بتقول لك مدام أن ال product
+
+544
+00:42:17,910 --> 00:42:22,250
+هو ال birth space أنا بقدر أجيلك unique element
+
+545
+00:42:22,250 --> 00:42:27,590
+فيه اللي هو ال H' بدلالتهبتقدر تكتب هذه as inner
+
+546
+00:42:27,590 --> 00:42:32,050
+product يعني G of F بيصير بساوى inner product بين
+
+547
+00:42:32,050 --> 00:42:36,230
+الـ F هذه ال arbitrary والـ F note اللي لديته اللي
+
+548
+00:42:36,230 --> 00:42:39,850
+عملته Z قبل شوية في الثانية فصار عندى الآن G of F
+
+549
+00:42:39,850 --> 00:42:44,030
+اللي هي عبارة عن كان بالwritten as ال inner
+
+550
+00:42:44,030 --> 00:42:47,110
+product بين F و F note مين لل inner product تبعنا
+
+551
+00:42:47,110 --> 00:42:50,270
+اللي بنشتغل عليه على مين على اللي هو ال space اللي
+
+552
+00:42:50,270 --> 00:42:55,530
+عندىهذا قبل بشوية احنا عرفناه كالتالي بيصير A F
+
+553
+00:42:55,530 --> 00:43:03,870
+Note و مين A F إذا هذا حصلته بالشكل هذا طيب الان
+
+554
+00:43:03,870 --> 00:43:08,090
+عندي لكن F of X أشبه ساوي X زد اللي قبل بشوية
+
+555
+00:43:08,090 --> 00:43:15,650
+حكيته و Z أشبه ساوي A F وعندي ال A F Note هيكون
+
+556
+00:43:15,650 --> 00:43:20,670
+اللي هيقيمةأف نوت أف بساوي زد الأف نوت حقوقه
+
+557
+00:43:20,670 --> 00:43:26,070
+يسموني إيه إيه إيش X إذا الأف نوت كإنه هي اللي
+
+558
+00:43:26,070 --> 00:43:30,250
+لجيتها اللي بدا توصلني لل element اللي لجيته اللي
+
+559
+00:43:30,250 --> 00:43:38,160
+C اللي عنده اللي هو Cاللي هو من HW' لعند H الان
+
+560
+00:43:38,160 --> 00:43:42,380
+انا بتاخد ال CG اللي بتهيأله دي لها إشي ماشي حال
+
+561
+00:43:42,380 --> 00:43:46,700
+صورة الان انا اللي بيوصللي اللي لجأته ال F هذا
+
+562
+00:43:46,700 --> 00:43:52,660
+بيوصللي لل X اللي ال CG إيش يساوي؟ يساوي ال X طيب
+
+563
+00:43:52,660 --> 00:43:57,640
+الان ال F note لجأته ال A F note طبيعي هيكون إيش
+
+564
+00:43:57,640 --> 00:44:01,990
+بيساوي؟ بيساوي اللي هو ال Xماشي الحال لإنه element
+
+565
+00:44:01,990 --> 00:44:06,330
+في H لإن هذه الصورة will هتكون موجودة في الـ H إذا
+
+566
+00:44:06,330 --> 00:44:10,250
+ال A of note بيساوي X إذا صار عندي we have اللي هو
+
+567
+00:44:10,250 --> 00:44:15,930
+A of note و A of إيش هيساوي اللي هو X مكان هذه و
+
+568
+00:44:15,930 --> 00:44:18,190
+هذه ال A of اللي جيتها من جبل اللي هي عبارة عن مين
+
+569
+00:44:18,190 --> 00:44:24,150
+عن Z و هذه نفسها إيش بتساوي F of Xفعند الان مع بعض
+
+570
+00:44:24,150 --> 00:44:30,530
+هذه g of f ايش بيساوي f of x g of f صارت بيساوي f
+
+571
+00:44:30,530 --> 00:44:34,110
+of x مدام g of f بيساوي f of x اللي هو هذا معناته
+
+572
+00:44:34,110 --> 00:44:38,730
+انه cx ايش هتساوي هتساوي ال g وهذا معناته صارت
+
+573
+00:44:38,730 --> 00:44:43,710
+اللي هي c ال subjective او انتوا وبهيك وكون خلصنا
+
+574
+00:44:43,710 --> 00:44:45,830
+البرهان وإلى لقاء ناخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/WmXLCzkJRL8_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/WmXLCzkJRL8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..5f469e826144e976f91181bfdbc2e31c8ba2edcf
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/WmXLCzkJRL8_raw.json
@@ -0,0 +1 @@
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normها بسواه norm هذا إذا ال GX هذه اللي عندي صارت bounded linear functional و norm هو norm ال X هذه بتستختمها بعد شوية أطلع لها على التلخيص إلى أن نجي للملة اللي باعدها الملة اللي باعدها كانت تالي", "tokens": [28814, 15730, 20328, 9640, 18871, 16254, 13672, 1829, 39896, 13672, 1829, 13672, 1829, 20328, 9640, 2655, 18871, 16254, 37498, 4032, 9381, 9640, 2655, 18871, 16254, 13672, 1829, 31439, 2026, 11296, 4724, 3794, 14407, 3224, 2026, 23758, 11933, 15730, 2423, 460, 55, 29538, 13672, 1829, 18871, 16254, 20328, 9640, 2655, 37498, 8213, 11745, 4032, 2026, 31439, 2026, 2423, 1783, 29538, 39894, 14851, 9778, 39237, 11296, 39182, 13412, 2407, 10632, 5551, 9566, 1211, 3615, 5296, 11296, 15844, 16712, 1211, 9778, 1829, 9381, 30731, 14739, 8717, 7435, 1829, 5296, 19528, 37977, 13672, 1829, 4724, 995, 22488, 11296, 9673, 37977, 13672, 1829, 4724, 995, 22488, 11296, 25961, 2655, 6055, 6027, 1829], "avg_logprob": -0.30497686399353874, "compression_ratio": 2.0046728971962615, "no_speech_prob": 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"word": " بعد", "probability": 0.935546875}, {"start": 322.71, "end": 323.09, "word": " شوية", "probability": 0.9256184895833334}, {"start": 323.09, "end": 323.73, "word": " أطلع", "probability": 0.8477783203125}, {"start": 323.73, "end": 323.85, "word": " لها", "probability": 0.4290771484375}, {"start": 323.85, "end": 324.01, "word": " على", "probability": 0.90478515625}, {"start": 324.01, "end": 324.83, "word": " التلخيص", "probability": 0.98642578125}, {"start": 324.83, "end": 325.69, "word": " إلى", "probability": 0.492431640625}, {"start": 325.69, "end": 325.83, "word": " أن", "probability": 0.58544921875}, {"start": 325.83, "end": 325.99, "word": " نجي", "probability": 0.7340494791666666}, {"start": 325.99, "end": 326.39, "word": " للملة", "probability": 0.559814453125}, {"start": 326.39, "end": 326.51, "word": " اللي", "probability": 0.949951171875}, {"start": 326.51, "end": 327.01, "word": " باعدها", "probability": 0.70635986328125}, {"start": 327.01, "end": 327.65, "word": " الملة", "probability": 0.554931640625}, {"start": 327.65, "end": 327.79, "word": " اللي", "probability": 0.980712890625}, {"start": 327.79, "end": 328.09, "word": " باعدها", "probability": 0.8934326171875}, {"start": 328.09, "end": 328.33, "word": " كانت", "probability": 0.953125}, {"start": 328.33, "end": 328.65, "word": " تالي", "probability": 0.9095052083333334}], "temperature": 1.0}, {"id": 15, "seek": 35475, "start": 330.11, "end": 354.75, "text": "بتقول لي let X be a known space هذا كله عشان أصل اللي هو تعريف ال reflexive space let X be a known space then the canonical mapping هذا بنسميه canonical mapping C هياخد من مين من X لمين لل X double prime هذا اللي هيحددلي اللي هو هوية ال reflexive space من خلاله بدي أعرف ال reflexive space", "tokens": [3555, 2655, 39648, 32239, 718, 1783, 312, 257, 2570, 1901, 23758, 28242, 3224, 6225, 8592, 7649, 5551, 36520, 13672, 1829, 31439, 37279, 16572, 5172, 2423, 23802, 488, 1901, 718, 1783, 312, 257, 2570, 1901, 550, 264, 46491, 18350, 23758, 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342.17, "word": " mapping", "probability": 0.958984375}, {"start": 342.17, "end": 342.53, "word": " C", "probability": 0.301025390625}, {"start": 342.53, "end": 343.23, "word": " هياخد", "probability": 0.9064127604166666}, {"start": 343.23, "end": 343.41, "word": " من", "probability": 0.98583984375}, {"start": 343.41, "end": 343.77, "word": " مين", "probability": 0.6739501953125}, {"start": 343.77, "end": 344.27, "word": " من", "probability": 0.54345703125}, {"start": 344.27, "end": 344.59, "word": " X", "probability": 0.9697265625}, {"start": 344.59, "end": 345.17, "word": " لمين", "probability": 0.7174072265625}, {"start": 345.17, "end": 345.99, "word": " لل", "probability": 0.72119140625}, {"start": 345.99, "end": 346.31, "word": " X", "probability": 0.85400390625}, {"start": 346.31, "end": 346.65, "word": " double", "probability": 0.361083984375}, {"start": 346.65, "end": 347.09, "word": " prime", "probability": 0.732421875}, {"start": 347.09, "end": 347.59, "word": " هذا", 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"word": " subspace", "probability": 0.880859375}, {"start": 1540.73, "end": 1541.35, "word": " ومنه", "probability": 0.84912109375}, {"start": 1541.35, "end": 1541.79, "word": " هنطلق", "probability": 0.951171875}, {"start": 1541.79, "end": 1541.93, "word": " في", "probability": 0.828125}, {"start": 1541.93, "end": 1542.05, "word": " اللي", "probability": 0.9189453125}, {"start": 1542.05, "end": 1542.15, "word": " اللي", "probability": 0.76025390625}, {"start": 1542.15, "end": 1542.57, "word": " بديه", "probability": 0.643310546875}, {"start": 1542.57, "end": 1543.35, "word": " طيب", "probability": 0.8994140625}], "temperature": 1.0}, {"id": 66, "seek": 156346, "start": 1545.32, "end": 1563.46, "text": "ثم اقول لنا ان for all y into y, f of y بيساوي اطلع لفوق اللي هو f of y زائد مين زائد سفر في x not صح ولا لأ اللي هو ايش هيطلع بساوي بساوي سفر في دلتا اللي هو سفر and f of x not هنا او ده بتجداش بتساوي بساوي اللي هو دلتا", "tokens": [12984, 2304, 1975, 39648, 5296, 8315, 16472, 337, 439, 288, 294, 1353, 288, 11, 283, 295, 288, 4724, 1829, 3794, 995, 45865, 1975, 9566, 1211, 3615, 5296, 5172, 30543, 13672, 1829, 31439, 283, 295, 288, 30767, 16373, 3215, 3714, 9957, 30767, 16373, 3215, 8608, 5172, 2288, 8978, 2031, 406, 20328, 5016, 49429, 5296, 10721, 13672, 1829, 31439, 1975, 1829, 8592, 39896, 9566, 1211, 3615, 4724, 3794, 995, 45865, 4724, 3794, 995, 45865, 8608, 5172, 2288, 8978, 11778, 1211, 2655, 995, 13672, 1829, 31439, 8608, 5172, 2288, 293, 283, 295, 2031, 406, 34105, 1975, 2407, 11778, 3224, 39894, 7435, 3215, 33599, 39894, 3794, 995, 45865, 4724, 3794, 995, 45865, 13672, 1829, 31439, 11778, 1211, 2655, 995], "avg_logprob": -0.29795259494206, "compression_ratio": 1.881720430107527, "no_speech_prob": 1.1563301086425781e-05, "words": [{"start": 1545.32, "end": 1545.84, "word": "ثم", "probability": 0.53643798828125}, {"start": 1545.84, "end": 1546.36, "word": " اقول", "probability": 0.5511474609375}, {"start": 1546.36, "end": 1546.6, "word": " لنا", "probability": 0.5919189453125}, {"start": 1546.6, "end": 1546.82, "word": " ان", "probability": 0.6640625}, {"start": 1546.82, "end": 1547.28, "word": " for", "probability": 0.55419921875}, {"start": 1547.28, "end": 1547.6, "word": " all", "probability": 0.9208984375}, {"start": 1547.6, "end": 1547.82, "word": " y", "probability": 0.81005859375}, {"start": 1547.82, "end": 1548.12, "word": " into", "probability": 0.172576904296875}, {"start": 1548.12, "end": 1548.46, "word": " y,", "probability": 0.640625}, {"start": 1548.54, "end": 1548.68, "word": " f", "probability": 0.640625}, {"start": 1548.68, "end": 1548.84, "word": " of", "probability": 0.52685546875}, {"start": 1548.84, "end": 1549.0, "word": " y", "probability": 0.9638671875}, {"start": 1549.0, "end": 1549.52, "word": " بيساوي", "probability": 0.684033203125}, {"start": 1549.52, "end": 1549.9, "word": " اطلع", "probability": 0.7952880859375}, {"start": 1549.9, "end": 1550.38, "word": " لفوق", "probability": 0.7980143229166666}, {"start": 1550.38, "end": 1550.82, "word": " اللي", "probability": 0.785888671875}, {"start": 1550.82, "end": 1550.96, "word": " هو", "probability": 0.87109375}, {"start": 1550.96, "end": 1551.16, "word": " f", "probability": 0.7607421875}, {"start": 1551.16, "end": 1551.36, "word": " of", "probability": 0.91162109375}, {"start": 1551.36, "end": 1551.74, "word": " y", "probability": 0.95654296875}, {"start": 1551.74, "end": 1552.26, "word": " زائد", "probability": 0.7394205729166666}, {"start": 1552.26, "end": 1552.74, "word": " مين", "probability": 0.7265625}, {"start": 1552.74, "end": 1553.42, "word": " زائد", "probability": 0.8961588541666666}, {"start": 1553.42, "end": 1553.8, "word": " سفر", "probability": 0.8548177083333334}, {"start": 1553.8, "end": 1553.94, "word": " في", "probability": 0.9150390625}, {"start": 1553.94, "end": 1554.12, "word": " x", "probability": 0.62255859375}, {"start": 1554.12, "end": 1554.38, "word": " not", "probability": 0.2216796875}, {"start": 1554.38, "end": 1554.62, "word": " صح", "probability": 0.965087890625}, {"start": 1554.62, "end": 1554.76, "word": " ولا", "probability": 0.9375}, {"start": 1554.76, "end": 1555.1, "word": " لأ", "probability": 0.840087890625}, {"start": 1555.1, "end": 1555.62, "word": " اللي", "probability": 0.863037109375}, {"start": 1555.62, "end": 1555.72, "word": " هو", "probability": 0.95458984375}, {"start": 1555.72, "end": 1555.84, "word": " ايش", "probability": 0.6116943359375}, {"start": 1555.84, "end": 1556.16, "word": " هيطلع", "probability": 0.893798828125}, {"start": 1556.16, "end": 1556.68, "word": " بساوي", "probability": 0.9090576171875}, {"start": 1556.68, "end": 1557.5, "word": " بساوي", "probability": 0.8909912109375}, {"start": 1557.5, "end": 1557.78, "word": " سفر", "probability": 0.974609375}, {"start": 1557.78, "end": 1557.9, "word": " في", "probability": 0.931640625}, {"start": 1557.9, "end": 1558.14, "word": " دلتا", "probability": 0.8101806640625}, {"start": 1558.14, "end": 1558.24, "word": " اللي", "probability": 0.98388671875}, {"start": 1558.24, "end": 1558.36, "word": " هو", "probability": 0.9794921875}, {"start": 1558.36, "end": 1558.84, "word": " سفر", "probability": 0.9866536458333334}, {"start": 1558.84, "end": 1559.62, "word": " and", "probability": 0.8818359375}, {"start": 1559.62, "end": 1559.92, "word": " f", "probability": 0.888671875}, {"start": 1559.92, "end": 1560.1, "word": " of", "probability": 0.97216796875}, {"start": 1560.1, "end": 1560.24, "word": " x", "probability": 0.98974609375}, {"start": 1560.24, "end": 1560.48, "word": " not", "probability": 0.9443359375}, {"start": 1560.48, "end": 1560.68, "word": " هنا", "probability": 0.2880859375}, {"start": 1560.68, "end": 1560.88, "word": " او", "probability": 0.677734375}, {"start": 1560.88, "end": 1560.98, "word": " ده", "probability": 0.23992919921875}, {"start": 1560.98, "end": 1561.4, "word": " بتجداش", "probability": 0.5870361328125}, {"start": 1561.4, "end": 1561.98, "word": " بتساوي", "probability": 0.9798583984375}, {"start": 1561.98, "end": 1562.7, "word": " بساوي", "probability": 0.93408203125}, {"start": 1562.7, "end": 1562.92, "word": " اللي", "probability": 0.98486328125}, {"start": 1562.92, "end": 1563.06, "word": " هو", "probability": 0.96875}, {"start": 1563.06, "end": 1563.46, "word": " دلتا", "probability": 0.9886474609375}], "temperature": 1.0}, {"id": 67, "seek": 158869, "start": 1563.87, "end": 1588.69, "text": "واضح طيب طبعا هي التفسير يتواي بساوي صفر و الف بساوي واحد في الجهتين تطلع عندها دي بساوي صفر وهذا بساوي واحد الان now we show that F is bounded ده اثبتنا ان F لينيا و اثبتنا F مش هي الصفر و اثبتنا قيمة ال F عند ال Y اي Y في ال Y هداك بساوي صفر و F of X not بتساوي دلتا", "tokens": [2407, 46958, 5016, 23032, 1829, 3555, 23032, 3555, 3615, 995, 39896, 16712, 36178, 13546, 7251, 2655, 14407, 1829, 4724, 3794, 995, 45865, 20328, 5172, 2288, 4032, 27188, 4724, 3794, 995, 45865, 36764, 24401, 8978, 25724, 3224, 2655, 9957, 6055, 9566, 1211, 3615, 43242, 11296, 11778, 1829, 4724, 3794, 995, 45865, 20328, 5172, 2288, 37037, 15730, 4724, 3794, 995, 45865, 36764, 24401, 2423, 7649, 586, 321, 855, 300, 479, 307, 37498, 11778, 3224, 1975, 12984, 3555, 2655, 8315, 16472, 479, 32239, 22653, 995, 4032, 1975, 12984, 3555, 2655, 8315, 479, 37893, 39896, 31767, 5172, 2288, 4032, 1975, 12984, 3555, 2655, 8315, 12174, 32640, 3660, 2423, 479, 43242, 2423, 398, 1975, 1829, 398, 8978, 2423, 398, 8032, 28259, 4117, 4724, 3794, 995, 45865, 20328, 5172, 2288, 4032, 479, 295, 1783, 406, 39894, 3794, 995, 45865, 11778, 1211, 2655, 995], "avg_logprob": -0.2522644895142403, "compression_ratio": 1.9336283185840708, "no_speech_prob": 8.463859558105469e-06, "words": [{"start": 1563.87, "end": 1564.31, "word": "واضح", "probability": 0.9674479166666666}, {"start": 1564.31, "end": 1564.89, "word": " طيب", "probability": 0.7890625}, {"start": 1564.89, "end": 1566.13, "word": " طبعا", "probability": 0.9676513671875}, {"start": 1566.13, "end": 1566.35, "word": " هي", "probability": 0.7578125}, {"start": 1566.35, "end": 1567.03, "word": " التفسير", "probability": 0.955078125}, {"start": 1567.03, "end": 1567.53, "word": " يتواي", "probability": 0.363525390625}, {"start": 1567.53, "end": 1567.83, "word": " بساوي", "probability": 0.7034912109375}, {"start": 1567.83, "end": 1568.15, "word": " صفر", "probability": 0.795654296875}, {"start": 1568.15, "end": 1568.27, "word": " و", "probability": 0.70068359375}, {"start": 1568.27, "end": 1568.47, "word": " الف", "probability": 0.180419921875}, {"start": 1568.47, "end": 1568.89, "word": " بساوي", "probability": 0.850341796875}, {"start": 1568.89, "end": 1569.17, "word": " واحد", "probability": 0.97802734375}, {"start": 1569.17, "end": 1569.31, "word": " في", "probability": 0.85986328125}, {"start": 1569.31, "end": 1569.81, "word": " الجهتين", "probability": 0.9569091796875}, {"start": 1569.81, "end": 1570.15, "word": " تطلع", "probability": 0.83837890625}, {"start": 1570.15, "end": 1570.45, "word": " عندها", "probability": 0.783447265625}, {"start": 1570.45, "end": 1570.61, "word": " دي", "probability": 0.739501953125}, {"start": 1570.61, "end": 1570.83, "word": " بساوي", "probability": 0.9586181640625}, {"start": 1570.83, "end": 1571.13, "word": " صفر", "probability": 0.9656575520833334}, {"start": 1571.13, "end": 1571.31, "word": " وهذا", "probability": 0.5137939453125}, {"start": 1571.31, "end": 1571.83, "word": " بساوي", "probability": 0.9349365234375}, {"start": 1571.83, "end": 1572.57, "word": " واحد", "probability": 0.989501953125}, {"start": 1572.57, "end": 1573.59, "word": " الان", "probability": 0.74365234375}, {"start": 1573.59, "end": 1574.27, "word": " now", "probability": 0.15478515625}, {"start": 1574.27, "end": 1574.47, "word": " we", "probability": 0.85205078125}, {"start": 1574.47, "end": 1574.75, "word": " show", "probability": 0.92919921875}, {"start": 1574.75, "end": 1575.19, "word": " that", "probability": 0.94775390625}, {"start": 1575.19, "end": 1575.49, "word": " F", "probability": 0.437255859375}, {"start": 1575.49, "end": 1575.69, "word": " is", "probability": 0.9384765625}, {"start": 1575.69, "end": 1576.01, "word": " bounded", "probability": 0.9248046875}, {"start": 1576.01, "end": 1576.23, "word": " ده", "probability": 0.4774169921875}, {"start": 1576.23, "end": 1576.87, "word": " اثبتنا", "probability": 0.93857421875}, {"start": 1576.87, "end": 1576.97, "word": " ان", "probability": 0.78955078125}, {"start": 1576.97, "end": 1577.09, "word": " F", "probability": 0.68896484375}, {"start": 1577.09, "end": 1577.61, "word": " لينيا", "probability": 0.5819498697916666}, {"start": 1577.61, "end": 1578.03, "word": " و", "probability": 0.841796875}, {"start": 1578.03, "end": 1578.43, "word": " اثبتنا", "probability": 0.9234375}, {"start": 1578.43, "end": 1578.59, "word": " F", "probability": 0.861328125}, {"start": 1578.59, "end": 1578.81, "word": " مش", "probability": 0.9541015625}, {"start": 1578.81, "end": 1578.99, "word": " هي", "probability": 0.84423828125}, {"start": 1578.99, "end": 1579.43, "word": " الصفر", "probability": 0.90625}, {"start": 1579.43, "end": 1579.75, "word": " و", "probability": 0.88330078125}, {"start": 1579.75, "end": 1580.11, "word": " اثبتنا", "probability": 0.94482421875}, {"start": 1580.11, "end": 1580.55, "word": " قيمة", "probability": 0.9957682291666666}, {"start": 1580.55, "end": 1580.69, "word": " ال", "probability": 0.67822265625}, {"start": 1580.69, "end": 1581.03, "word": " F", "probability": 0.93212890625}, {"start": 1581.03, "end": 1581.85, "word": " عند", "probability": 0.96826171875}, {"start": 1581.85, "end": 1582.09, "word": " ال", "probability": 0.94580078125}, {"start": 1582.09, "end": 1582.37, "word": " Y", "probability": 0.8974609375}, {"start": 1582.37, "end": 1582.69, "word": " اي", "probability": 0.7266845703125}, {"start": 1582.69, "end": 1582.93, "word": " Y", "probability": 0.845703125}, {"start": 1582.93, "end": 1583.05, "word": " في", "probability": 0.9365234375}, {"start": 1583.05, "end": 1583.17, "word": " ال", "probability": 0.9375}, {"start": 1583.17, "end": 1583.37, "word": " Y", "probability": 0.89599609375}, {"start": 1583.37, "end": 1584.15, "word": " هداك", "probability": 0.4930013020833333}, {"start": 1584.15, "end": 1584.59, "word": " بساوي", "probability": 0.8365478515625}, {"start": 1584.59, "end": 1584.97, "word": " صفر", "probability": 0.9573567708333334}, {"start": 1584.97, "end": 1585.45, "word": " و", "probability": 0.95166015625}, {"start": 1585.45, "end": 1585.77, "word": " F", "probability": 0.85107421875}, {"start": 1585.77, "end": 1586.21, "word": " of", "probability": 0.90625}, {"start": 1586.21, "end": 1586.47, "word": " X", "probability": 0.96044921875}, {"start": 1586.47, "end": 1586.77, "word": " not", "probability": 0.287353515625}, {"start": 1586.77, "end": 1587.19, "word": " بتساوي", "probability": 0.908935546875}, {"start": 1587.19, "end": 1588.69, "word": " دلتا", "probability": 0.74542236328125}], "temperature": 1.0}, {"id": 68, "seek": 160656, "start": 1589.1, "end": 1606.56, "text": "كل هدولة خلّيني لأنه بلزم اني بعد شوية Now we show that F is bounded if Alpha بتساوي سفر اذا F of Z automatically مش هتساوي هتساوي سفر وهذا طبعا ال boundedness بيطلع automatic يعني لو Alpha مش سفر بدي أسالكم انه F is bounded", "tokens": [28820, 8032, 3215, 12610, 3660, 16490, 1211, 11703, 9957, 1829, 5296, 33456, 3224, 4724, 1211, 11622, 2304, 16472, 1829, 39182, 13412, 2407, 10632, 823, 321, 855, 300, 479, 307, 37498, 498, 20588, 39894, 3794, 995, 45865, 8608, 5172, 2288, 1975, 15730, 479, 295, 1176, 6772, 37893, 8032, 2655, 3794, 995, 45865, 8032, 2655, 3794, 995, 45865, 8608, 5172, 2288, 37037, 15730, 23032, 3555, 3615, 995, 2423, 37498, 1287, 4724, 1829, 9566, 1211, 3615, 12509, 37495, 22653, 45164, 20588, 37893, 8608, 5172, 2288, 4724, 16254, 5551, 3794, 6027, 24793, 16472, 3224, 479, 307, 37498], "avg_logprob": -0.33743351317466574, "compression_ratio": 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من", "probability": 0.8837890625}, {"start": 1863.4, "end": 1863.54, "word": " الـ", "probability": 0.255615234375}, {"start": 1863.54, "end": 1863.64, "word": " 4", "probability": 0.6826171875}, {"start": 1863.64, "end": 1863.96, "word": ",6", "probability": 0.5107421875}, {"start": 1863.96, "end": 1864.34, "word": ",8", "probability": 0.841064453125}], "temperature": 1.0}, {"id": 81, "seek": 189638, "start": 1868.58, "end": 1896.38, "text": "إذا كان الـ Dual Space X' من نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه نفسه", "tokens": [28814, 15730, 25961, 2423, 39184, 37625, 8705, 1783, 6, 9154, 8717, 36178, 3224, 8717, 36178, 3224, 8717, 36178, 3224, 8717, 36178, 3224, 8717, 36178, 3224, 8717, 36178, 3224, 8717, 36178, 3224, 8717, 36178, 3224, 8717, 36178, 3224, 8717, 36178, 3224, 8717, 36178, 3224, 8717, 36178, 3224, 8717, 36178, 3224], "avg_logprob": -0.5906250250339508, "compression_ratio": 2.689655172413793, "no_speech_prob": 2.5033950805664062e-06, "words": [{"start": 1868.58, "end": 1869.0, "word": "إذا", "probability": 0.691650390625}, {"start": 1869.0, "end": 1869.14, "word": " كان", "probability": 0.460205078125}, {"start": 1869.14, "end": 1869.14, "word": " الـ", "probability": 0.33984375}, {"start": 1869.14, "end": 1869.28, "word": " Dual", "probability": 0.218994140625}, {"start": 1869.28, "end": 1869.7, "word": " Space", "probability": 0.450439453125}, {"start": 1869.7, "end": 1869.88, "word": " X'", "probability": 0.86181640625}, {"start": 1870.26, "end": 1870.42, "word": " من", "probability": 0.40966796875}, {"start": 1870.42, "end": 1871.08, "word": " نفسه", "probability": 0.3418375651041667}, {"start": 1871.08, "end": 1871.38, "word": " نفسه", "probability": 0.547607421875}, {"start": 1871.38, "end": 1871.42, "word": " نفسه", "probability": 0.4784952799479167}, {"start": 1871.42, "end": 1871.42, "word": " نفسه", "probability": 0.6165364583333334}, {"start": 1871.42, "end": 1871.42, "word": " نفسه", "probability": 0.7176513671875}, {"start": 1871.42, "end": 1871.42, "word": " نفسه", "probability": 0.772705078125}, {"start": 1871.42, "end": 1872.04, "word": " نفسه", "probability": 0.8212890625}, {"start": 1872.04, "end": 1874.04, "word": " نفسه", "probability": 0.86865234375}, {"start": 1874.04, "end": 1875.02, "word": " نفسه", "probability": 0.9104817708333334}, {"start": 1875.02, "end": 1881.6, "word": " نفسه", "probability": 0.94287109375}, {"start": 1881.6, "end": 1882.22, "word": " نفسه", "probability": 0.96142578125}, {"start": 1882.22, "end": 1883.38, "word": " نفسه", "probability": 0.9716796875}, {"start": 1883.38, "end": 1896.38, "word": " نفسه", "probability": 0.9767252604166666}], "temperature": 1.0}, {"id": 82, "seek": 191376, "start": 1896.8, "end": 1913.76, "text": "A separable normed space X with a non-separable dual space X' can't be reflexive يعني لو كان عندي separable normed space X وكان ال X' إيش ماله؟ non-separable", "tokens": [32, 3128, 712, 2026, 292, 1901, 1783, 365, 257, 2107, 12, 405, 42012, 11848, 1901, 1783, 6, 393, 380, 312, 23802, 488, 37495, 22653, 45164, 25961, 18871, 16254, 3128, 712, 2026, 292, 1901, 1783, 4032, 41361, 2423, 1783, 6, 11933, 1829, 8592, 3714, 6027, 3224, 22807, 2107, 12, 405, 42012], "avg_logprob": -0.26118258635203045, "compression_ratio": 1.4045801526717556, "no_speech_prob": 1.0728836059570312e-06, "words": [{"start": 1896.8, "end": 1897.1, "word": "A", "probability": 0.0948486328125}, {"start": 1897.1, "end": 1897.78, "word": " separable", "probability": 0.888427734375}, {"start": 1897.78, "end": 1899.0, "word": " normed", "probability": 0.6219482421875}, {"start": 1899.0, "end": 1899.3, "word": " space", "probability": 0.818359375}, {"start": 1899.3, "end": 1899.72, "word": " X", "probability": 0.88427734375}, {"start": 1899.72, "end": 1900.84, "word": " with", "probability": 0.865234375}, {"start": 1900.84, "end": 1901.06, "word": " a", "probability": 0.9091796875}, {"start": 1901.06, "end": 1901.28, "word": " non", "probability": 0.97509765625}, {"start": 1901.28, "end": 1901.68, "word": "-separable", "probability": 0.8919270833333334}, {"start": 1901.68, "end": 1902.04, "word": " dual", "probability": 0.86279296875}, {"start": 1902.04, "end": 1902.56, "word": " space", "probability": 0.900390625}, {"start": 1902.56, "end": 1902.84, "word": " X'", "probability": 0.95849609375}, {"start": 1903.26, "end": 1904.04, "word": " can't", "probability": 0.829833984375}, {"start": 1904.04, "end": 1904.26, "word": " be", "probability": 0.9658203125}, {"start": 1904.26, "end": 1905.2, "word": " reflexive", "probability": 0.9833984375}, {"start": 1905.2, "end": 1906.08, "word": " يعني", "probability": 0.84521484375}, {"start": 1906.08, "end": 1906.26, "word": " لو", "probability": 0.9326171875}, {"start": 1906.26, "end": 1906.52, "word": " كان", "probability": 0.98681640625}, {"start": 1906.52, "end": 1906.94, "word": " عندي", "probability": 0.75341796875}, {"start": 1906.94, "end": 1908.62, "word": " separable", "probability": 0.811279296875}, {"start": 1908.62, "end": 1909.04, "word": " normed", "probability": 0.96728515625}, {"start": 1909.04, "end": 1909.36, "word": " space", "probability": 0.92333984375}, {"start": 1909.36, "end": 1909.82, "word": " X", "probability": 0.9873046875}, {"start": 1909.82, "end": 1910.9, "word": " وكان", "probability": 0.835205078125}, {"start": 1910.9, "end": 1911.06, "word": " ال", "probability": 0.642578125}, {"start": 1911.06, "end": 1911.32, "word": " X'", "probability": 0.5361328125}, {"start": 1911.72, "end": 1911.96, "word": " إيش", "probability": 0.6930338541666666}, {"start": 1911.96, "end": 1912.76, "word": " ماله؟", "probability": 0.7421875}, {"start": 1912.76, "end": 1913.24, "word": " non", "probability": 0.3818359375}, {"start": 1913.24, "end": 1913.76, "word": "-separable", "probability": 0.91357421875}], "temperature": 1.0}, {"id": 83, "seek": 194074, "start": 1915.56, "end": 1940.74, "text": "الآن لو كانت X' separable، فهي Automatic X separable لكن ممكن يكون الـ X' non-separable وهذه تكون يشمالها separable فالآن فرضينا أن X separable و X' non-separable الآن يقول لي مستحيل تطلع الـ X يشمالها reflexive لازم تطلع يشمالها، X is not reflexive suppose that X' is non-separable زي ما هو حاكي", "tokens": [6027, 148, 48506, 45164, 25961, 2655, 1783, 6, 3128, 712, 12399, 6156, 3224, 1829, 6049, 13143, 1783, 3128, 712, 44381, 3714, 43020, 7251, 30544, 2423, 39184, 1783, 6, 2107, 12, 405, 42012, 37037, 24192, 6055, 30544, 7251, 8592, 2304, 6027, 11296, 3128, 712, 6156, 6027, 148, 48506, 6156, 43042, 1829, 8315, 14739, 1783, 3128, 712, 4032, 1783, 6, 2107, 12, 405, 42012, 6024, 48506, 7251, 39648, 32239, 3714, 14851, 5016, 26895, 6055, 9566, 1211, 3615, 2423, 39184, 1783, 7251, 8592, 2304, 6027, 11296, 23802, 488, 5296, 31377, 2304, 6055, 9566, 1211, 3615, 7251, 8592, 2304, 6027, 11296, 12399, 1783, 307, 406, 23802, 488, 7297, 300, 1783, 6, 307, 2107, 12, 405, 42012, 30767, 1829, 19446, 31439, 11331, 995, 4117, 1829], "avg_logprob": -0.34865702479338845, "compression_ratio": 1.7705627705627707, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1915.56, "end": 1916.0, "word": "الآن", "probability": 0.59912109375}, {"start": 1916.0, "end": 1916.42, "word": " لو", "probability": 0.8388671875}, {"start": 1916.42, "end": 1917.0, "word": " كانت", "probability": 0.985107421875}, {"start": 1917.0, "end": 1917.2, "word": " X'", "probability": 0.53125}, {"start": 1917.52, "end": 1918.2, "word": " separable،", "probability": 0.4837239583333333}, {"start": 1918.2, "end": 1918.24, "word": " فهي", "probability": 0.4626871744791667}, {"start": 1918.24, "end": 1918.64, "word": " Automatic", "probability": 0.535797119140625}, {"start": 1918.64, "end": 1918.88, "word": " X", "probability": 0.91015625}, {"start": 1918.88, "end": 1919.46, "word": " separable", "probability": 0.70361328125}, {"start": 1919.46, "end": 1920.32, "word": " لكن", "probability": 0.81787109375}, {"start": 1920.32, "end": 1920.8, "word": " ممكن", "probability": 0.80859375}, {"start": 1920.8, "end": 1921.16, "word": " يكون", "probability": 0.91064453125}, {"start": 1921.16, "end": 1921.32, "word": " الـ", "probability": 0.580078125}, {"start": 1921.32, "end": 1921.52, "word": " X'", "probability": 0.90576171875}, {"start": 1921.8, "end": 1922.06, "word": " non", "probability": 0.37353515625}, {"start": 1922.06, "end": 1922.44, "word": "-separable", "probability": 0.8440755208333334}, {"start": 1922.44, "end": 1922.84, "word": " وهذه", "probability": 0.48046875}, {"start": 1922.84, "end": 1923.04, "word": " تكون", "probability": 0.912841796875}, {"start": 1923.04, "end": 1923.5, "word": " يشمالها", "probability": 0.656494140625}, {"start": 1923.5, "end": 1923.98, "word": " separable", "probability": 0.910400390625}, {"start": 1923.98, "end": 1924.74, "word": " فالآن", "probability": 0.827880859375}, {"start": 1924.74, "end": 1925.74, "word": " فرضينا", "probability": 0.606781005859375}, {"start": 1925.74, "end": 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1932.8, "word": " الـ", "probability": 0.5760498046875}, {"start": 1932.8, "end": 1932.94, "word": " X", "probability": 0.9638671875}, {"start": 1932.94, "end": 1933.52, "word": " يشمالها", "probability": 0.973046875}, {"start": 1933.52, "end": 1934.08, "word": " reflexive", "probability": 0.9462890625}, {"start": 1934.08, "end": 1934.62, "word": " لازم", "probability": 0.91650390625}, {"start": 1934.62, "end": 1934.9, "word": " تطلع", "probability": 0.9794921875}, {"start": 1934.9, "end": 1935.5, "word": " يشمالها،", "probability": 0.8853352864583334}, {"start": 1935.5, "end": 1935.56, "word": " X", "probability": 0.9208984375}, {"start": 1935.56, "end": 1935.74, "word": " is", "probability": 0.90869140625}, {"start": 1935.74, "end": 1935.92, "word": " not", "probability": 0.951171875}, {"start": 1935.92, "end": 1936.5, "word": " reflexive", "probability": 0.98095703125}, {"start": 1936.5, "end": 1937.22, "word": " suppose", "probability": 0.371337890625}, {"start": 1937.22, "end": 1937.82, "word": " that", "probability": 0.9453125}, {"start": 1937.82, "end": 1938.2, "word": " X'", "probability": 0.96728515625}, {"start": 1938.54, "end": 1938.84, "word": " is", "probability": 0.935546875}, {"start": 1938.84, "end": 1939.04, "word": " non", "probability": 0.9609375}, {"start": 1939.04, "end": 1939.44, "word": "-separable", "probability": 0.9236653645833334}, {"start": 1939.44, "end": 1939.72, "word": " زي", "probability": 0.726806640625}, {"start": 1939.72, "end": 1939.78, "word": " ما", "probability": 0.97802734375}, {"start": 1939.78, "end": 1939.96, "word": " هو", "probability": 0.955078125}, {"start": 1939.96, "end": 1940.74, "word": " حاكي", "probability": 0.8543701171875}], "temperature": 1.0}, {"id": 84, "seek": 195881, "start": 1941.69, "end": 1958.81, "text": "و X separable و X أشمالها و X reflexive تقولوا إن كانت بيه reflexive فبنرسلها contradiction الآن X اللي هي ساعة أشمال في تردنها reflexive مدام X reflexive إذن الـ X double-brane isomorphic", 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0.1531982421875}, {"start": 1943.97, "end": 1944.59, "word": " أشمالها", "probability": 0.92841796875}, {"start": 1944.59, "end": 1944.97, "word": " و", "probability": 0.9267578125}, {"start": 1944.97, "end": 1945.13, "word": " X", "probability": 0.68505859375}, {"start": 1945.13, "end": 1945.75, "word": " reflexive", "probability": 0.9521484375}, {"start": 1945.75, "end": 1946.61, "word": " تقولوا", "probability": 0.5113932291666666}, {"start": 1946.61, "end": 1946.73, "word": " إن", "probability": 0.241455078125}, {"start": 1946.73, "end": 1947.01, "word": " كانت", "probability": 0.4605712890625}, {"start": 1947.01, "end": 1947.17, "word": " بيه", "probability": 0.5957234700520834}, {"start": 1947.17, "end": 1948.01, "word": " reflexive", "probability": 0.802734375}, {"start": 1948.01, "end": 1948.89, "word": " فبنرسلها", "probability": 0.5076555524553571}, {"start": 1948.89, "end": 1949.39, "word": " contradiction", "probability": 0.75927734375}, {"start": 1949.39, "end": 1950.45, "word": " الآن", "probability": 0.606689453125}, {"start": 1950.45, "end": 1951.07, "word": " X", "probability": 0.92724609375}, {"start": 1951.07, "end": 1951.37, "word": " اللي", "probability": 0.86328125}, {"start": 1951.37, "end": 1951.51, "word": " هي", "probability": 0.7470703125}, {"start": 1951.51, "end": 1951.79, "word": " ساعة", "probability": 0.646240234375}, {"start": 1951.79, "end": 1952.19, "word": " أشمال", "probability": 0.93408203125}, {"start": 1952.19, "end": 1952.33, "word": " في", "probability": 0.40380859375}, {"start": 1952.33, "end": 1952.79, "word": " تردنها", "probability": 0.65390625}, {"start": 1952.79, "end": 1954.37, "word": " reflexive", "probability": 0.7042236328125}, {"start": 1954.37, "end": 1955.01, "word": " مدام", "probability": 0.6690266927083334}, {"start": 1955.01, "end": 1955.95, "word": " X", "probability": 0.9580078125}, {"start": 1955.95, "end": 1956.63, "word": " reflexive", "probability": 0.96533203125}, {"start": 1956.63, "end": 1956.93, 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canonical mapping C من H لعند H double prime ان احنا نعرف ان H .. 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Y0ewTrfR1Fk_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Y0ewTrfR1Fk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..eecb57eb40985726bcbd19fe97277e2f4e66636a
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Y0ewTrfR1Fk_postprocess.srt
@@ -0,0 +1,1272 @@
+1
+00:00:05,550 --> 00:00:08,150
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,150 --> 00:00:10,970
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,970 --> 00:00:16,750
+آله وصحبه أجمعين هذه هي المحاضرة رقم 15 مساق تحليل
+
+4
+00:00:16,750 --> 00:00:19,630
+اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:19,630 --> 00:00:20,790
+الإسلامية مساق
+
+6
+00:00:23,450 --> 00:00:27,730
+ماجيسير وصلنا اليوم لعند اللي هو ال section التاسع
+
+7
+00:00:27,730 --> 00:00:31,290
+في ال chapter التاني اللي هو اتنين وتسعة تحت عنوان
+
+8
+00:00:31,290 --> 00:00:35,050
+linear operators and functionals يعني linear
+
+9
+00:00:35,050 --> 00:00:38,530
+operators and linear functionals on finite
+
+10
+00:00:38,530 --> 00:00:40,990
+dimensional spaces على ال finite dimensional
+
+11
+00:00:40,990 --> 00:00:43,470
+spaces والدنيا كلها بتكون سهلة على ال finite
+
+12
+00:00:43,470 --> 00:00:47,270
+dimensional spaces وحسينا هذا الكلام في اللي هي
+
+13
+00:00:47,270 --> 00:00:50,900
+succession سابقانيجا والاشي بس نحطها الـ remark
+
+14
+00:00:50,900 --> 00:00:56,820
+عساس بدنا نبدأ الآن نبدأ نبني spaces اليوم هنبني
+
+15
+00:00:56,820 --> 00:01:01,240
+space مقدمة لبناء الـ space اللي هو اللي هنسميه
+
+16
+00:01:01,240 --> 00:01:04,740
+قدام The Dual Space هذا هنسميه The Algebraic Dual
+
+17
+00:01:04,740 --> 00:01:09,460
+Space هذا عائلة عائلة من ال linear functionals
+
+18
+00:01:09,460 --> 00:01:13,280
+بعدها هنحكي عن عائلة من ال bounded linear
+
+19
+00:01:13,280 --> 00:01:16,780
+functionals و هنشوف الآن التفاصيل شوفوا صلى على
+
+20
+00:01:16,780 --> 00:01:21,730
+النبي عليه الصلاة والسلاملت X Star كتابنا هيك اما
+
+21
+00:01:21,730 --> 00:01:24,970
+اخده طبعا في بعض الكتب يعني بتعمل ال X Star ذات
+
+22
+00:01:24,970 --> 00:01:28,310
+Dual Space احنا خلّينا التزم مع كتابنا ال X Star
+
+23
+00:01:28,310 --> 00:01:32,770
+ايش هو Be the set of all linear functionals Linear
+
+24
+00:01:32,770 --> 00:01:38,710
+functionals ماشي Defined on a vector space Xإذن
+
+25
+00:01:38,710 --> 00:01:44,530
+الـ N X Star نتفج من الـ N وطالع X Star يمثل عائلة
+
+26
+00:01:44,530 --> 00:01:48,730
+الـ Linear Functionals على مين؟ على Vector Space
+
+27
+00:01:48,730 --> 00:01:52,210
+أنا مش قاعد بحكي عن مين، عن Topologies ولا بحكي عن
+
+28
+00:01:52,210 --> 00:01:55,310
+Norm يعني أنا بحكي بس عن موجود جرد Vector Space
+
+29
+00:01:55,310 --> 00:01:59,830
+يعني درس جبل خطوة كأننا بنحكيFor any f و g element
+
+30
+00:01:59,830 --> 00:02:04,930
+in x*) بدي أعرف و skill أعرفها بدي أعرف الآن إيش
+
+31
+00:02:04,930 --> 00:02:07,790
+معناة f زي الـ g يعني إيش معناة linear functional
+
+32
+00:02:07,790 --> 00:02:10,950
+زي الlinear functional وإيش معناة الف في الف by
+
+33
+00:02:10,950 --> 00:02:16,030
+باعرف اللي انتوا عارفينهF زائد G of X بيساوي F of
+
+34
+00:02:16,030 --> 00:02:19,970
+X زائد مين G of X هاي معناه الجامع فيه اللي هو في
+
+35
+00:02:19,970 --> 00:02:23,990
+ال elements اللي في ال X*) الآن Alpha في F of X
+
+36
+00:02:23,990 --> 00:02:27,110
+معناته Alpha في F of X يعني pointwise scalar
+
+37
+00:02:27,110 --> 00:02:29,610
+multiplication pointwise addition و ال scalar
+
+38
+00:02:29,610 --> 00:02:32,410
+multiplication اللي أعمامنا for all X element in X
+
+39
+00:02:32,680 --> 00:02:36,720
+then X star نفسه هيعمل لي إيه تحت العملتين هذولة
+
+40
+00:02:36,720 --> 00:02:41,800
+is a vector space called the algebraic dual space
+
+41
+00:02:41,800 --> 00:02:47,200
+of X إذا ال algebraic dual space of X ما هو إلا
+
+42
+00:02:47,200 --> 00:02:50,940
+عبارة عن vector space أو the vector space of all
+
+43
+00:02:50,940 --> 00:02:55,560
+linear functionals in X star يعني بتاخد من X
+
+44
+00:02:55,560 --> 00:02:59,460
+العناصرها بتاخد F من X لعند scalar field تبعته
+
+45
+00:03:00,000 --> 00:03:04,780
+العنوان X Star Star is the base of all linear
+
+46
+00:03:04,780 --> 00:03:09,380
+functionals defined on X Star يعني برد بعرف اللي
+
+47
+00:03:09,380 --> 00:03:13,620
+هو ال functional إيش بتسميها إيش بتسميها G من X
+
+48
+00:03:13,620 --> 00:03:17,840
+Star و برميها وين في ال Rهذه الآن صارت Lena
+
+49
+00:03:17,840 --> 00:03:21,880
+function على هذه هذول العناصر بقى سميه موجودات في
+
+50
+00:03:21,880 --> 00:03:27,920
+الـ X** يعني the second algebraic dual space اللي
+
+51
+00:03:27,920 --> 00:03:33,220
+هو بنسميه second algebraic dual space واضح اطلع
+
+52
+00:03:33,220 --> 00:03:40,220
+لفوق الان نيجي لأ هالنظريةاللي بتلزمنا let X be an
+
+53
+00:03:40,220 --> 00:03:44,240
+undimensional vector space بحكي عن كل جابر خط الآن
+
+54
+00:03:44,240 --> 00:03:50,200
+و عند E بتساوي E1 E2 EN مدام انديمشينال هو مين بيه
+
+55
+00:03:50,200 --> 00:03:56,400
+a basis for Xthen الأن بدي أعرفلكم أو بدي أجيبلكم
+
+56
+00:03:56,400 --> 00:04:00,520
+bases لل X star يعني بدي أجيب من ال X .. من bases
+
+57
+00:04:00,520 --> 00:04:05,840
+ال X bases لمين؟ لل X star شوفوا هالحلوة and then
+
+58
+00:04:05,840 --> 00:04:09,260
+the set of all linear functionals F اللي هي F1,
+
+59
+00:04:09,400 --> 00:04:17,190
+F2, Fn عدد مثل هدولgiven by fk of ej بساوة سفر لما
+
+60
+00:04:17,190 --> 00:04:21,430
+نتجي أشمالها لاتساول k وواحد لما نتجي أشمالها
+
+61
+00:04:21,430 --> 00:04:28,770
+تساول k يعني F1E11 F2E22 لكن F1E البجيات سفر F2
+
+62
+00:04:28,770 --> 00:04:34,940
+للبجيات بدون E2 سفر و هكذاواضح طيب اذا a basis
+
+63
+00:04:34,940 --> 00:04:39,860
+بتدعي انه هذه ال FK هدولة يعمل in basis for X and
+
+64
+00:04:39,860 --> 00:04:43,260
+dimension لل X*) هو نفسه dimension من مين لل X ال
+
+65
+00:04:43,260 --> 00:04:46,760
+basis شغلتين Linear لاندبندن زاد spanning يعمل
+
+66
+00:04:46,760 --> 00:04:50,200
+spanning لكل مين ال space اللي احنا نسبق اليه مين
+
+67
+00:04:50,200 --> 00:04:54,430
+spaceنا اللي هو ال X*) ماشي الحالطيب to show that
+
+68
+00:04:54,430 --> 00:04:57,670
+F is a linearly independent هذي is a linearly
+
+69
+00:04:57,670 --> 00:05:00,610
+independent set عارفين إيه إيش بدنا نسويه goal ال
+
+70
+00:05:00,610 --> 00:05:04,430
+summation لها Beta 1 الف واحد زي Beta 2 F2 زي Beta
+
+71
+00:05:04,430 --> 00:05:07,510
+N بيساوي أفرا بيساوي سفر و نوصل ل Beta 1 Beta 2
+
+72
+00:05:07,510 --> 00:05:12,320
+Beta N كل هنا إيه شمالين أصفر شغل جبر خطرthen الـ
+
+73
+00:05:12,320 --> 00:05:15,740
+summation beta k fk of xk من واحد لعندان ايش
+
+74
+00:05:15,740 --> 00:05:20,720
+بيساوي لكل ال X اللي موجودة element in X in
+
+75
+00:05:20,720 --> 00:05:24,420
+particular in particular مش هذا سوي لكل X in
+
+76
+00:05:24,420 --> 00:05:30,000
+particular for EJاللي هي X بيساوي EJ فبصير عندي
+
+77
+00:05:30,000 --> 00:05:33,740
+السفر هذا بيساوي summation beta K FK of EJ K من
+
+78
+00:05:33,740 --> 00:05:38,020
+واحد لعندنا تنسوش إن هدولة كلها نصفار ما عدا عندك
+
+79
+00:05:38,020 --> 00:05:42,240
+J بتساوي K، صح؟ يعني هيصير عندي بيساوي من Beta J
+
+80
+00:05:42,240 --> 00:05:47,180
+في FJ EJ اللي هي واحد، فصارت الـBJ بيساوي سفر،
+
+81
+00:05:47,180 --> 00:05:50,700
+والـEJ أنا صرتها arbitrarilyزي ما بختار لأي واحد و
+
+82
+00:05:50,700 --> 00:05:53,560
+لأي اتنين و لأي تلاتة لعندي ليه يعني بتطلع ان كلهم
+
+83
+00:05:53,560 --> 00:05:57,620
+الـ Beta إيه شمالهم Beta 1, Beta 2, Beta N صفر إذا
+
+84
+00:05:57,620 --> 00:06:01,840
+صار عندي this implies that Beta J بيساوي 0 for all
+
+85
+00:06:01,840 --> 00:06:05,760
+J معناته therefore F is a linearly independent set
+
+86
+00:06:05,760 --> 00:06:09,620
+اللي هان يجي لان ال span اطلع لفوق جاوبه صحيح let
+
+87
+00:06:09,620 --> 00:06:15,670
+F الآن let F اطلع لفوق كمان letلأ انزل انت اللي ..
+
+88
+00:06:15,670 --> 00:06:19,690
+let F be any fixed element in M in X star بدي أخد
+
+89
+00:06:19,690 --> 00:06:22,770
+أقفل X star و أقولك بقدر أكتب الأفعار زي الـ
+
+90
+00:06:22,770 --> 00:06:26,380
+linear combination إذا انخلصناأه مش هيك اللي معنات
+
+91
+00:06:26,380 --> 00:06:30,000
+ال .. ال .. ال .. little bit bases for any x إذا
+
+92
+00:06:30,000 --> 00:06:33,340
+أنا أخدت f أي element fixed element منين؟ and x
+
+93
+00:06:33,340 --> 00:06:37,060
+star، بدك تبقى أزالينا combination من f1, f2, f3،
+
+94
+00:06:37,060 --> 00:06:41,100
+اللي عندي، الـ fn طيب، for any x بالثماثين، x, i,
+
+95
+00:06:41,140 --> 00:06:43,980
+k، a, k، كامن عند 1، عند n، ليش كتبت هيك؟ لأن
+
+96
+00:06:43,980 --> 00:06:46,440
+هدولة bases و أي element ماقدر أكتبه في الـ .. في
+
+97
+00:06:46,440 --> 00:06:49,240
+الـ x، ماقدر أكتبه على هذه الصورة by using the
+
+98
+00:06:49,240 --> 00:06:53,870
+linearity of f we haveF is linear by اله F of X
+
+99
+00:06:53,870 --> 00:06:58,570
+بيساوي ال summation ل XI K F of EK K من عند واحد
+
+100
+00:06:58,570 --> 00:07:02,530
+لعند مين لعند ان هذا من ال linearity طيب خلي هذه
+
+101
+00:07:02,530 --> 00:07:07,270
+ايش واحد on the other hand for اي fixed J بين واحد
+
+102
+00:07:07,270 --> 00:07:12,940
+وبين ان احسبلي الان F J of X ايش بتساويخلّي هذه في
+
+103
+00:07:12,940 --> 00:07:16,500
+الذاكرة و حسب هذه Fj of summation بدخل لأنه كل
+
+104
+00:07:16,500 --> 00:07:20,220
+أحده Linear بيساوي ال summation ل EK Fj of EK كل
+
+105
+00:07:20,220 --> 00:07:24,280
+هى نصفار معدى عند مين عند اللى هى ياش J بتلتقي مع
+
+106
+00:07:24,280 --> 00:07:28,820
+ال K اللى هى عند مين Xij إذا صارت Fj of X إيش
+
+107
+00:07:28,820 --> 00:07:35,570
+بتساويE E J من هذه ومن هذه خلصنا القصة بيصير F of
+
+108
+00:07:35,570 --> 00:07:40,570
+X بتساوي ال E K بحط مكانها مين F K بساوي ال
+
+109
+00:07:40,570 --> 00:07:46,160
+summation ل F K of X في E في F of E K for all Xهذا
+
+110
+00:07:46,160 --> 00:07:49,500
+الكلام صحيح لكل ال .. لكل ال X في الدنيا إذا صارت
+
+111
+00:07:49,500 --> 00:07:55,760
+ال F إيش بكتبها على صورة FK في F of EK K من واحد
+
+112
+00:07:55,760 --> 00:07:58,300
+لعند مين لإنه function هذه لما كنتوا functions
+
+113
+00:07:58,300 --> 00:08:00,840
+متساويات عند كل النقاط إنها متساويات مين ال
+
+114
+00:08:00,840 --> 00:08:05,220
+functions ال F و ال FK معايا؟إذا صار عندي ال F
+
+115
+00:08:05,220 --> 00:08:08,560
+بتساوي ال summation هذا يعني قدرت أكتب F أزنين هو
+
+116
+00:08:08,560 --> 00:08:12,960
+combination من هذا معناته صار ال F لسبان لل F و
+
+117
+00:08:12,960 --> 00:08:16,280
+لسبان لل F طبيعي جزء من ال X*) إذا صار لسبان لل F
+
+118
+00:08:16,280 --> 00:08:20,080
+إيش بيساوي ال X*) إذا صار عندي hence F is a basis
+
+119
+00:08:20,080 --> 00:08:23,760
+for X*) and ال dimension في الحالتين اللي هو كان
+
+120
+00:08:23,760 --> 00:08:27,520
+اللي هو F1 F2 FN هم ال bases عدد هنا و الأولانية
+
+121
+00:08:27,520 --> 00:08:29,980
+عدد هنا إذا ال dimension لل X بيساوي ال dimension
+
+122
+00:08:29,980 --> 00:08:37,910
+لل X*) وشوف اللي بعدهاطيب لما نشوف اللي لما اللي
+
+123
+00:08:37,910 --> 00:08:45,950
+عندي let
+
+124
+00:08:45,950 --> 00:08:51,790
+C من X عند X Star Star يعني من الـ X نروح نشوف كيف
+
+125
+00:08:51,790 --> 00:08:58,810
+فيه إشي بده يعمل عند الـ X فيه لها Dual Space أو
+
+126
+00:08:58,810 --> 00:09:03,670
+الجبريك Dual Space اسمه X Starالان ال X Star فيه
+
+127
+00:09:03,670 --> 00:09:07,150
+لها Dual Space تاني اللي هو X Star Star صار عندي
+
+128
+00:09:07,150 --> 00:09:12,010
+ال Second Dual Space شكله فيه له لقب الأصل لما
+
+129
+00:09:12,010 --> 00:09:16,010
+نجيب مرتين مرتين زي تبع زمان ال inverse لما نعمله
+
+130
+00:09:16,010 --> 00:09:19,630
+مرتين برجع للأصل يعني مش بالظبط هو فيه له اللي
+
+131
+00:09:19,630 --> 00:09:23,290
+بيعمل هيك بنعطيه خاصية اللي شاطر بيعمل زيك بنعمله
+
+132
+00:09:23,290 --> 00:09:28,330
+خاصيةالان let C من X لعند X ★ ★ هذا اسمه بنسميه
+
+133
+00:09:28,330 --> 00:09:32,250
+canonical mapping on a vector space X defined by
+
+134
+00:09:32,250 --> 00:09:39,790
+CX CX بتاخد ال X لمين ل GX ال GX ماله هذا ال GX
+
+135
+00:09:39,790 --> 00:09:52,450
+احنا ال GX الان C من X لعند X ★ ★الان بياخد الـ C
+
+136
+00:09:52,450 --> 00:09:56,030
+و الـ X بياخدها الـ X من وين بيوديها لـ Element
+
+137
+00:09:56,030 --> 00:10:01,350
+هنا بنسميه GX طب إيش هذا الـ GX؟ هذا الـ GX أكيد
+
+138
+00:10:01,350 --> 00:10:07,250
+function من وين من X Star لعند اللي هو الـ R أو
+
+139
+00:10:07,250 --> 00:10:10,650
+الـ C حسب ال field اللي بتشتغل فيه مش هو هذا عبارة
+
+140
+00:10:10,650 --> 00:10:13,210
+عن Element من X Star Star و هذا إيش هو X Star
+
+141
+00:10:13,210 --> 00:10:16,970
+Star؟ عبارة عن The set of all linear functionals
+
+142
+00:10:16,970 --> 00:10:22,370
+on X Starماشي الحال طب إذا هذا إشماله هذا برضه
+
+143
+00:10:22,370 --> 00:10:28,570
+بيجي بياخد X of F GX of F من هنا و برميها هان كيف
+
+144
+00:10:28,570 --> 00:10:33,690
+بترميها هان ال F إشمالها F عبارة عن دالة من X لعند
+
+145
+00:10:33,690 --> 00:10:38,270
+R مش ال F في ال X السار إذا دالة من X لعند R إذا
+
+146
+00:10:38,270 --> 00:10:43,890
+GX of F بدي أرميها في ال R بدي أقول بتساوي F عند
+
+147
+00:10:43,890 --> 00:10:50,890
+مين عند ال X صارت ال F من X لعند ال Rإذا فعلا هذا
+
+148
+00:10:50,890 --> 00:10:56,390
+بنسميه canonical mappingهو بيه the canonical
+
+149
+00:10:56,390 --> 00:10:59,470
+mapping of vector space X defined by C X بيساوي G
+
+150
+00:10:59,470 --> 00:11:07,150
+X for any fixed X المتين X G X من X أسطار لعند K
+
+151
+00:11:07,150 --> 00:11:10,270
+زي ما قولت K is the real or the complex حسب اللي
+
+152
+00:11:10,270 --> 00:11:13,190
+احنا نشتغل عليها is defined by G X of F بيساوي F
+
+153
+00:11:13,190 --> 00:11:17,010
+of X for any F المتين X أسطار then C اللي عم نثبت
+
+154
+00:11:17,010 --> 00:11:20,190
+إيهاش is a linear operator يعني C هذا ال canonical
+
+155
+00:11:20,190 --> 00:11:23,150
+mapping هيطلع اللي برضه أيه شماله linear operator
+
+156
+00:11:23,150 --> 00:11:27,870
+سهل الدنيا إن شاء اللهأولاً نظرح ذلك جي إكس إليمنت
+
+157
+00:11:27,870 --> 00:11:30,850
+في الـ x** لكي نثبت أن هذا يشمل نفسه جي إكس هذا
+
+158
+00:11:30,850 --> 00:11:34,110
+اللي بتقوله عنه في الـ x** يعني عبارة عن element
+
+159
+00:11:34,110 --> 00:11:36,890
+هذا هو هوين بيقدر ميه بيقدر ميه لازم أرميه هناك
+
+160
+00:11:36,890 --> 00:11:41,070
+الان for any f1 و f2 عشان أثبت أنه هنا بيثبت أن هو
+
+161
+00:11:41,070 --> 00:11:45,700
+نفسه linearأه كيف بدأت بتقوله Linear خد أي two
+
+162
+00:11:45,700 --> 00:11:49,840
+elements Linear عالميا على ال X Star يعني باخد أي
+
+163
+00:11:49,840 --> 00:11:53,640
+two elements يعني هذا ال GX بدأت بتقوله Linear هان
+
+164
+00:11:53,640 --> 00:11:58,860
+أه باخد أي عنصرين من هان و ال scalar و بثبت أنه
+
+165
+00:11:58,860 --> 00:12:05,550
+Linear ده نشوف كيف مع بعض وين وصلنا؟ طيبfor any f1
+
+166
+00:12:05,550 --> 00:12:09,490
+و f2 element in x star and any scalar α we have gx
+
+167
+00:12:09,490 --> 00:12:14,450
+of α f1 زي ده f2 بساوي Alpha حسب التعريف Alpha f1
+
+168
+00:12:14,450 --> 00:12:19,010
+زي ده f2 of mean of x و يساوي Alpha f1 of x من
+
+169
+00:12:19,010 --> 00:12:22,290
+تعريف ال function زي التعريف أنه توزيع ال function
+
+170
+00:12:22,290 --> 00:12:26,970
+العادى و scalar العادى زي ده f2 of x هذه اللي هي
+
+171
+00:12:26,970 --> 00:12:33,370
+f1 of x اللي هي gx of f1 وهذه gx f2 وهي الألفةإذا
+
+172
+00:12:33,370 --> 00:12:38,650
+صار فعلاً الان G هذا بساوي هذا وهذا معناته GX is
+
+173
+00:12:38,650 --> 00:12:44,010
+linear on X star الآن صار عند GX وين موجودة في X
+
+174
+00:12:44,010 --> 00:12:48,390
+star الstar بدي الآن أثبت أنه اللي هو الـ C linear
+
+175
+00:12:48,390 --> 00:12:52,110
+لما أنا على هيك بده أروح هنا for any X element in
+
+176
+00:12:52,110 --> 00:12:56,150
+X there is a unique GX element in X star starsuch
+
+177
+00:12:56,150 --> 00:13:01,010
+that تعريف هذا such that C of X H بيساوي DX
+
+178
+00:13:01,010 --> 00:13:06,650
+because الآن عشان أقولكم أن هذا الكلام فعلا well
+
+179
+00:13:06,650 --> 00:13:10,450
+defined الآن بقول انا ادعاء انه لكل X element in X
+
+180
+00:13:10,450 --> 00:13:14,050
+بلاقي DX element in X من تعريفها الجد حقولكم انه
+
+181
+00:13:14,050 --> 00:13:17,570
+فعلا هذا الكلام هيكون هو ينيك كيف ينيك لأن such
+
+182
+00:13:17,570 --> 00:13:21,410
+that CX بيساوي DX because لو كانت ال CX بيساوي DX
+
+183
+00:13:21,410 --> 00:13:26,120
+وCX بيساوي HXمعناته for some gx وأتش x المتنكستار
+
+184
+00:13:26,120 --> 00:13:33,190
+ستار ستار حيصير ان عندي قنتين الآن بيصير gx of fF
+
+185
+00:13:33,190 --> 00:13:36,170
+بيساوي F of X وما لاقتش X of F بيساوي F of X
+
+186
+00:13:36,170 --> 00:13:39,530
+ومدامة الـ F function يستحيل هدول يكونين إيش
+
+187
+00:13:39,530 --> 00:13:43,810
+مالهين مختلفات لازم يكونين إيش مالهين متساويات
+
+188
+00:13:43,810 --> 00:13:48,470
+which is impossible لأ إذا كانت مختلفات because F
+
+189
+00:13:48,470 --> 00:13:51,870
+is a function إذا لازم غصب عننا يطلع الـ DX هو
+
+190
+00:13:51,870 --> 00:13:55,710
+main نفسه ما لاقتش في X therefore C is well
+
+191
+00:13:55,710 --> 00:13:59,010
+defined لأن في الآخر بنتبه أنها C is Linear إذا
+
+192
+00:13:59,010 --> 00:14:01,530
+أثبتنا أنها و أنه بتودي و باتثبتنا أنها well
+
+193
+00:14:01,530 --> 00:14:05,370
+definedظل نثبت علينا أنها Linear و Linearity سهلة
+
+194
+00:14:05,370 --> 00:14:10,110
+وينالي وي شوه أن C هي Linear لأي X و Y element in
+
+195
+00:14:10,110 --> 00:14:15,910
+X وأي Scalar Alpha وأي F element in X رحلنا لدينا
+
+196
+00:14:15,910 --> 00:14:19,530
+C التعريف على طول هالجيت C of Alpha X زائد Y of F
+
+197
+00:14:19,530 --> 00:14:24,570
+ايش بيساوي اللي هو G Alpha X زائد Y G اللي هي
+
+198
+00:14:24,570 --> 00:14:29,470
+متعلقة بهذه of من؟ of F هذه ايش قيمتها؟ F of هذه
+
+199
+00:14:30,390 --> 00:14:34,130
+لكن تعرفناه و يساوي F of المقدار هذا و F is linear
+
+200
+00:14:34,130 --> 00:14:38,950
+إذا ألف F زائد اللي هي F، مظبوط؟ الآن هذه مين هي؟
+
+201
+00:14:38,950 --> 00:14:43,710
+هي Alpha GX of F و هذه مين هي؟ GY of F الآن هذه
+
+202
+00:14:43,710 --> 00:14:48,950
+إيش هي؟ اللي هي Alpha CX عند ال F، معايا؟ و هذه
+
+203
+00:14:48,950 --> 00:14:52,470
+مين هي؟ CY عند مين؟ عند ال F، صارت عندي هذه
+
+204
+00:14:52,470 --> 00:14:59,050
+المقدار بساوي هذا عند كل F في الدنياعند كل الـ X
+
+205
+00:14:59,050 --> 00:15:01,870
+والـ Y اللي حكيناها إذا صار عند الـ C Alpha X زائد
+
+206
+00:15:01,870 --> 00:15:08,170
+Y بساوة Alpha CX زائد Min Cy فاهمين؟ إذا الـ C is
+
+207
+00:15:08,170 --> 00:15:12,830
+linear اللي بعدها اطلع اللي فوق لأن نيجي لها
+
+208
+00:15:12,830 --> 00:15:18,550
+الملاحظة Note that if R of C بساوة X Star Star
+
+209
+00:15:18,550 --> 00:15:22,270
+اللي قلت كلكم عنها قبل ما شوية يعني لو لجئنا إنه
+
+210
+00:15:22,270 --> 00:15:32,110
+الـ C الـ Cمن X لعند X Star Star بحيث أنه الـ
+
+211
+00:15:32,110 --> 00:15:35,290
+Range للـ C طلع X Star Star يعني بمعنى الاخر سارة
+
+212
+00:15:35,290 --> 00:15:41,050
+تادي onto function بنسمي اللي هو X is said to be
+
+213
+00:15:41,050 --> 00:15:44,430
+algebraically reflexive إذا algebraically
+
+214
+00:15:44,430 --> 00:15:52,020
+reflexive وكأنهبصير عندي اللي هو الـ X والـ X ★ ★
+
+215
+00:15:52,020 --> 00:15:58,680
+R equivalent أو R equivalent أو R isomorphic بكل
+
+216
+00:15:58,680 --> 00:16:02,460
+مفاهيمين الجبرية يعني one to one one to function
+
+217
+00:16:02,460 --> 00:16:08,340
+وكمان اللي هو ال linearity اللي هي أو المحافظة
+
+218
+00:16:08,340 --> 00:16:11,480
+preserve the algebraic operation
+
+219
+00:16:14,210 --> 00:16:23,450
+نأخد .. نأخد الآن اللمّة let
+
+220
+00:16:23,450 --> 00:16:27,570
+X be a finite dimensional vector space
+
+221
+00:16:36,360 --> 00:16:41,080
+إذا كان الجنة F of X not بساوة 0 لكل F في X star
+
+222
+00:16:41,080 --> 00:16:45,700
+لازم ال X not إيش هتتطلع كل الأفات بيودنها ال X
+
+223
+00:16:45,700 --> 00:16:50,750
+not للسفر مش هتكون الا السفر هادي طيب ال proofلت
+
+224
+00:16:50,750 --> 00:16:55,790
+E1, E2, En بيبقى basis for مين؟ for X مدان basis
+
+225
+00:16:55,790 --> 00:16:58,190
+إن X نوت كان بيرتن أزالين ال combination من هنا
+
+226
+00:16:58,190 --> 00:17:02,150
+إذا بيساوي summation XJ AJ J من وحدة لعندها هذا
+
+227
+00:17:02,150 --> 00:17:05,250
+هتكون طبعا وين موجودة في ال X then حسب الكلام اللي
+
+228
+00:17:05,250 --> 00:17:10,430
+بيحكي المعطى سفر هتساوي up of X note هذهطيب الآن f
+
+229
+00:17:10,430 --> 00:17:13,670
+of x not اللي هو بيساوي ال summation بدخل ال f على
+
+230
+00:17:13,670 --> 00:17:16,470
+اللي هو ال summation و linear f إذا بيساوي ال
+
+231
+00:17:16,470 --> 00:17:20,250
+summation xij f of ej for all f element in x star
+
+232
+00:17:20,250 --> 00:17:23,250
+إذا صار الكلام هذا لكل مين؟ لكل الأفات اللي في
+
+233
+00:17:23,250 --> 00:17:27,850
+الدنيا إذا صار عندي ال summation هذا بيساوي سفرfor
+
+234
+00:17:27,850 --> 00:17:33,630
+any choice لمن للـ F of أي جيه مادام هذا بيساوي
+
+235
+00:17:33,630 --> 00:17:37,810
+سفر لكل ال choices لل F of أي جيه مستحيل إلا تكون
+
+236
+00:17:37,810 --> 00:17:40,270
+ال F of أي جيه اللي .. اللي هي ال .. ال .. ال
+
+237
+00:17:40,270 --> 00:17:43,870
+excise هدول اللي أمامي كل واحدة أشمالها بتساوي سفر
+
+238
+00:17:43,870 --> 00:17:49,150
+وهذا يعني ان X not بتساوي سفر وهو المطلوب يلا
+
+239
+00:17:49,150 --> 00:17:54,530
+لبعده theorem
+
+240
+00:17:56,300 --> 00:17:59,240
+A finite dimensional vector space is algebraically
+
+241
+00:17:59,240 --> 00:18:02,100
+reflexive الآن قلنا algebraically reflexive متى
+
+242
+00:18:02,100 --> 00:18:08,460
+بيكون إذا كان عندي اللي هو C من X عند X*) اللي هو
+
+243
+00:18:08,460 --> 00:18:12,830
+is one to function و one to one وهي Linearطيب،
+
+244
+00:18:12,830 --> 00:18:15,930
+تنشوف، يعني التنين isomorphic بمفهوم .. الـ
+
+245
+00:18:15,930 --> 00:18:21,690
+isomorphism بمفهوم اللي هو preserved the linearity
+
+246
+00:18:21,690 --> 00:18:26,330
+أو الـ algebraic operations and اللي هو الـ
+
+247
+00:18:26,330 --> 00:18:31,130
+cardinality أو اللي هو الـ one to one و الانتوا By
+
+248
+00:18:31,130 --> 00:18:36,550
+Limma 2 9 2، C is linear، اتفقنالت CX0 بيساوي سفر
+
+249
+00:18:36,550 --> 00:18:40,050
+عشان انا اثبت اللي هو main اللي هو ال .. ال .. ال
+
+250
+00:18:40,050 --> 00:18:43,510
+.. ال one to one then for all F element in X star
+
+251
+00:18:43,510 --> 00:18:48,830
+هيكون عنده سفر بيساوي CX0 of F مظبوط ولا لا؟ الان
+
+252
+00:18:48,830 --> 00:18:53,710
+Y ساوي من تعريف CX0 of F بيساوي اللي هو GX0 of F
+
+253
+00:18:55,330 --> 00:18:58,170
+هيك التعريف G X knot of F G X knot of F أيش؟
+
+254
+00:18:58,170 --> 00:19:00,970
+بيساوي F of X knot إذا صارت عندي F of X knot
+
+255
+00:19:00,970 --> 00:19:04,510
+بتساوي مين؟ بتساوي سفر لكل الأفات إذا من اللمّة
+
+256
+00:19:04,510 --> 00:19:08,030
+اللي قبل شوية حتى تطلع X knot بيساوي سفر إذا صارت
+
+257
+00:19:08,030 --> 00:19:10,990
+الـ C is one to one لإن C X knot بيساوي سفر أدت X
+
+258
+00:19:10,990 --> 00:19:14,350
+knot بيساوي سفر إذا C is one to one and so C
+
+259
+00:19:14,350 --> 00:19:19,850
+inverse exist ماشي الآن من theorem 2.16 اللي قبل
+
+260
+00:19:19,850 --> 00:19:23,670
+بشوية ال dimension لل R of C بيساوي ال dimension
+
+261
+00:19:23,670 --> 00:19:29,740
+لل Xأه طيب الان صارت two dimensions زي بعض by
+
+262
+00:19:29,740 --> 00:19:37,880
+theorem 291 ركزوا هذه بالساوية دي خلوها في دماغه
+
+263
+00:19:37,880 --> 00:19:42,200
+الان من 9 1 2 9 1 قبل بشوية ال dimension لل X star
+
+264
+00:19:42,200 --> 00:19:44,660
+ال dimension لل X star بيساوي ال dimension لل X
+
+265
+00:19:44,660 --> 00:19:48,260
+أثبتناها وجهها ال dimension X star star هيساوي ال
+
+266
+00:19:48,260 --> 00:19:51,060
+dimension لل X star star إذا صار ان هدول ال
+
+267
+00:19:51,060 --> 00:19:55,010
+dimension اللي هنا شمال هنا زي بعضالان هدولة مح
+
+268
+00:19:55,010 --> 00:19:59,210
+هدول صار عندى dimension للـR of C بيساوي بالظبط ال
+
+269
+00:19:59,210 --> 00:20:02,290
+dimension لمين؟ لل X Star Star لأن هذا بيساوي ال
+
+270
+00:20:02,290 --> 00:20:05,210
+dimension لل X وهذا بيساوي ال dimension لل X إذا
+
+271
+00:20:05,210 --> 00:20:06,990
+أكيد ال dimension لل R of C بيساوي ال dimension
+
+272
+00:20:06,990 --> 00:20:11,570
+لمين؟ لل X Star Star كم هي ال R of C subspace من
+
+273
+00:20:11,570 --> 00:20:15,550
+مين؟ من ال X Star Star و ال dimension زي بعض، إذا
+
+274
+00:20:15,550 --> 00:20:19,870
+هي، ماتكونش هي إذا however R of C is a vector
+
+275
+00:20:19,870 --> 00:20:25,720
+subspace of X Star Starthere by quaternium 2 1 8 R
+
+276
+00:20:25,720 --> 00:20:30,380
+of C بيسوي X السار السار hence C is onto therefore
+
+277
+00:20:30,380 --> 00:20:33,800
+صارت one to one و onto و بتحافظ على اللي هو ال
+
+278
+00:20:33,800 --> 00:20:36,520
+linearity أو العمليات معناته صارت اللي هي
+
+279
+00:20:36,520 --> 00:20:41,500
+algebraically reflexive إذا في حالة ال finite
+
+280
+00:20:41,500 --> 00:20:49,450
+dimensional space ارجع لفي حالة الـ finite
+
+281
+00:20:49,450 --> 00:20:53,590
+dimensional space بكون الـ vector space أشمله
+
+282
+00:20:53,590 --> 00:20:57,870
+algebraically reflexي نيجي لل definition الأخيرة
+
+283
+00:20:57,870 --> 00:21:01,210
+two vector space is said to be isomorphic ال
+
+284
+00:21:01,210 --> 00:21:04,450
+vector space is isomorphic قلته أنا عموما توه في
+
+285
+00:21:04,450 --> 00:21:08,430
+أثناء الحديث إنه if there وصولك هذا حكيناه قبل هذا
+
+286
+00:21:08,430 --> 00:21:13,430
+if there is a bijectiveأو Objection أو Objective
+
+287
+00:21:13,430 --> 00:21:16,690
+Linear Map between the two vector spaces يعني إيش
+
+288
+00:21:16,690 --> 00:21:20,490
+ماله؟ يعني بحق .. هو أصلا إيش؟ هو عبارة عن تركيبة
+
+289
+00:21:20,490 --> 00:21:25,610
+جبرية بالإضافة .. تركيبة جبرية بالإضافة ل .. ل ..
+
+290
+00:21:25,610 --> 00:21:29,310
+لست إحنا كنا نقول الست إن هم ecopotent أو متكافئة
+
+291
+00:21:29,310 --> 00:21:31,690
+تانية ده كانت في one to one onto function يعني بس
+
+292
+00:21:31,690 --> 00:21:34,850
+اللي .. بس ال cardinality اللي هنا زي بعض الان لما
+
+293
+00:21:34,850 --> 00:21:38,750
+صار في عند .. اللي .. اللي هي عمليات جبريةالعمليات
+
+294
+00:21:38,750 --> 00:21:41,050
+الجبرية عشان نقول الـ Tin-Tin equivalent أو الـ
+
+295
+00:21:41,050 --> 00:21:45,290
+Tin-Tin isomorphic بدها تكون كتركيبة جبرية كاملة
+
+296
+00:21:45,290 --> 00:21:49,030
+تكافئت كتركيبة جبرية كاملة إيش التركيبة الجبرية
+
+297
+00:21:49,030 --> 00:21:52,810
+هان اللي هي الـ scalar multiplication و ال vector
+
+298
+00:21:52,810 --> 00:21:57,000
+addition إذا كانت linear بتحفظهاوالـ one to one on
+
+299
+00:21:57,000 --> 00:22:00,100
+two بتحفظ العدد إذا صارت isomorphic بين vector
+
+300
+00:22:00,100 --> 00:22:03,320
+spaces لو بدنا نحط norm ونقول isomorphic أو
+
+301
+00:22:03,320 --> 00:22:06,620
+isomorphism بينهم لازم يحافظ على كل اللي حكيته
+
+302
+00:22:06,620 --> 00:22:10,850
+بالإضافة على ال preserve the normو لو في topology
+
+303
+00:22:10,850 --> 00:22:15,650
+نفس الشيء إذا يعني بيكون هنا نفس هنا بس بتغيرات
+
+304
+00:22:15,650 --> 00:22:19,950
+الأسماء يعني هذه باسم تاني هي بس ال isomorphic بين
+
+305
+00:22:19,950 --> 00:22:23,710
+المعانات و هم زي بعض لكن اللي هي تغيرت الأسماء
+
+306
+00:22:23,710 --> 00:22:25,250
+واحد اسمه X واحد اسمه TX
+
+307
+00:22:43,900 --> 00:22:48,980
+تركيبة الجبرية تركيبة التباليجية تركيبة التباليجية
+
+308
+00:22:48,980 --> 00:22:52,420
+تركيبة التباليجية تركيبة التباليجيةهذا معناته اللي
+
+309
+00:22:52,420 --> 00:22:56,920
+هو الـ isomorphic أو الـ equivalence بين نظامين if
+
+310
+00:22:56,920 --> 00:22:59,780
+the vector space X is isomorphic with a subspace
+
+311
+00:22:59,780 --> 00:23:02,840
+of a vector space Y then we say that X is
+
+312
+00:23:02,840 --> 00:23:08,320
+embedable in Y لما يكون الـ X isomorphic لجزء من
+
+313
+00:23:08,320 --> 00:23:11,420
+الـ Y بنقول على هذا إيش embedable ابنه ابنه ابنه
+
+314
+00:23:11,420 --> 00:23:15,640
+ابنه زيه بالظبط زي اللي جوا بالظبط يعني الآن X هي
+
+315
+00:23:15,640 --> 00:23:28,670
+عندي Y Y Y Y كبير هيك وفي عندياللي هو X إشي تاني
+
+316
+00:23:28,670 --> 00:23:35,910
+وها نتيجة داخله Z لو كان ال X isomorphic مع ال Z
+
+317
+00:23:35,910 --> 00:23:43,070
+هو نفسه بس بسامة ثانية بنقول إن X is embedable in
+
+318
+00:23:43,070 --> 00:23:47,210
+Y وبرك الله فيكم وإلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Y0ewTrfR1Fk_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Y0ewTrfR1Fk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..eecb57eb40985726bcbd19fe97277e2f4e66636a
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/Y0ewTrfR1Fk_raw.srt
@@ -0,0 +1,1272 @@
+1
+00:00:05,550 --> 00:00:08,150
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,150 --> 00:00:10,970
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,970 --> 00:00:16,750
+آله وصحبه أجمعين هذه هي المحاضرة رقم 15 مساق تحليل
+
+4
+00:00:16,750 --> 00:00:19,630
+اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:19,630 --> 00:00:20,790
+الإسلامية مساق
+
+6
+00:00:23,450 --> 00:00:27,730
+ماجيسير وصلنا اليوم لعند اللي هو ال section التاسع
+
+7
+00:00:27,730 --> 00:00:31,290
+في ال chapter التاني اللي هو اتنين وتسعة تحت عنوان
+
+8
+00:00:31,290 --> 00:00:35,050
+linear operators and functionals يعني linear
+
+9
+00:00:35,050 --> 00:00:38,530
+operators and linear functionals on finite
+
+10
+00:00:38,530 --> 00:00:40,990
+dimensional spaces على ال finite dimensional
+
+11
+00:00:40,990 --> 00:00:43,470
+spaces والدنيا كلها بتكون سهلة على ال finite
+
+12
+00:00:43,470 --> 00:00:47,270
+dimensional spaces وحسينا هذا الكلام في اللي هي
+
+13
+00:00:47,270 --> 00:00:50,900
+succession سابقانيجا والاشي بس نحطها الـ remark
+
+14
+00:00:50,900 --> 00:00:56,820
+عساس بدنا نبدأ الآن نبدأ نبني spaces اليوم هنبني
+
+15
+00:00:56,820 --> 00:01:01,240
+space مقدمة لبناء الـ space اللي هو اللي هنسميه
+
+16
+00:01:01,240 --> 00:01:04,740
+قدام The Dual Space هذا هنسميه The Algebraic Dual
+
+17
+00:01:04,740 --> 00:01:09,460
+Space هذا عائلة عائلة من ال linear functionals
+
+18
+00:01:09,460 --> 00:01:13,280
+بعدها هنحكي عن عائلة من ال bounded linear
+
+19
+00:01:13,280 --> 00:01:16,780
+functionals و هنشوف الآن التفاصيل شوفوا صلى على
+
+20
+00:01:16,780 --> 00:01:21,730
+النبي عليه الصلاة والسلاملت X Star كتابنا هيك اما
+
+21
+00:01:21,730 --> 00:01:24,970
+اخده طبعا في بعض الكتب يعني بتعمل ال X Star ذات
+
+22
+00:01:24,970 --> 00:01:28,310
+Dual Space احنا خلّينا التزم مع كتابنا ال X Star
+
+23
+00:01:28,310 --> 00:01:32,770
+ايش هو Be the set of all linear functionals Linear
+
+24
+00:01:32,770 --> 00:01:38,710
+functionals ماشي Defined on a vector space Xإذن
+
+25
+00:01:38,710 --> 00:01:44,530
+الـ N X Star نتفج من الـ N وطالع X Star يمثل عائلة
+
+26
+00:01:44,530 --> 00:01:48,730
+الـ Linear Functionals على مين؟ على Vector Space
+
+27
+00:01:48,730 --> 00:01:52,210
+أنا مش قاعد بحكي عن مين، عن Topologies ولا بحكي عن
+
+28
+00:01:52,210 --> 00:01:55,310
+Norm يعني أنا بحكي بس عن موجود جرد Vector Space
+
+29
+00:01:55,310 --> 00:01:59,830
+يعني درس جبل خطوة كأننا بنحكيFor any f و g element
+
+30
+00:01:59,830 --> 00:02:04,930
+in x*) بدي أعرف و skill أعرفها بدي أعرف الآن إيش
+
+31
+00:02:04,930 --> 00:02:07,790
+معناة f زي الـ g يعني إيش معناة linear functional
+
+32
+00:02:07,790 --> 00:02:10,950
+زي الlinear functional وإيش معناة الف في الف by
+
+33
+00:02:10,950 --> 00:02:16,030
+باعرف اللي انتوا عارفينهF زائد G of X بيساوي F of
+
+34
+00:02:16,030 --> 00:02:19,970
+X زائد مين G of X هاي معناه الجامع فيه اللي هو في
+
+35
+00:02:19,970 --> 00:02:23,990
+ال elements اللي في ال X*) الآن Alpha في F of X
+
+36
+00:02:23,990 --> 00:02:27,110
+معناته Alpha في F of X يعني pointwise scalar
+
+37
+00:02:27,110 --> 00:02:29,610
+multiplication pointwise addition و ال scalar
+
+38
+00:02:29,610 --> 00:02:32,410
+multiplication اللي أعمامنا for all X element in X
+
+39
+00:02:32,680 --> 00:02:36,720
+then X star نفسه هيعمل لي إيه تحت العملتين هذولة
+
+40
+00:02:36,720 --> 00:02:41,800
+is a vector space called the algebraic dual space
+
+41
+00:02:41,800 --> 00:02:47,200
+of X إذا ال algebraic dual space of X ما هو إلا
+
+42
+00:02:47,200 --> 00:02:50,940
+عبارة عن vector space أو the vector space of all
+
+43
+00:02:50,940 --> 00:02:55,560
+linear functionals in X star يعني بتاخد من X
+
+44
+00:02:55,560 --> 00:02:59,460
+العناصرها بتاخد F من X لعند scalar field تبعته
+
+45
+00:03:00,000 --> 00:03:04,780
+العنوان X Star Star is the base of all linear
+
+46
+00:03:04,780 --> 00:03:09,380
+functionals defined on X Star يعني برد بعرف اللي
+
+47
+00:03:09,380 --> 00:03:13,620
+هو ال functional إيش بتسميها إيش بتسميها G من X
+
+48
+00:03:13,620 --> 00:03:17,840
+Star و برميها وين في ال Rهذه الآن صارت Lena
+
+49
+00:03:17,840 --> 00:03:21,880
+function على هذه هذول العناصر بقى سميه موجودات في
+
+50
+00:03:21,880 --> 00:03:27,920
+الـ X** يعني the second algebraic dual space اللي
+
+51
+00:03:27,920 --> 00:03:33,220
+هو بنسميه second algebraic dual space واضح اطلع
+
+52
+00:03:33,220 --> 00:03:40,220
+لفوق الان نيجي لأ هالنظريةاللي بتلزمنا let X be an
+
+53
+00:03:40,220 --> 00:03:44,240
+undimensional vector space بحكي عن كل جابر خط الآن
+
+54
+00:03:44,240 --> 00:03:50,200
+و عند E بتساوي E1 E2 EN مدام انديمشينال هو مين بيه
+
+55
+00:03:50,200 --> 00:03:56,400
+a basis for Xthen الأن بدي أعرفلكم أو بدي أجيبلكم
+
+56
+00:03:56,400 --> 00:04:00,520
+bases لل X star يعني بدي أجيب من ال X .. من bases
+
+57
+00:04:00,520 --> 00:04:05,840
+ال X bases لمين؟ لل X star شوفوا هالحلوة and then
+
+58
+00:04:05,840 --> 00:04:09,260
+the set of all linear functionals F اللي هي F1,
+
+59
+00:04:09,400 --> 00:04:17,190
+F2, Fn عدد مثل هدولgiven by fk of ej بساوة سفر لما
+
+60
+00:04:17,190 --> 00:04:21,430
+نتجي أشمالها لاتساول k وواحد لما نتجي أشمالها
+
+61
+00:04:21,430 --> 00:04:28,770
+تساول k يعني F1E11 F2E22 لكن F1E البجيات سفر F2
+
+62
+00:04:28,770 --> 00:04:34,940
+للبجيات بدون E2 سفر و هكذاواضح طيب اذا a basis
+
+63
+00:04:34,940 --> 00:04:39,860
+بتدعي انه هذه ال FK هدولة يعمل in basis for X and
+
+64
+00:04:39,860 --> 00:04:43,260
+dimension لل X*) هو نفسه dimension من مين لل X ال
+
+65
+00:04:43,260 --> 00:04:46,760
+basis شغلتين Linear لاندبندن زاد spanning يعمل
+
+66
+00:04:46,760 --> 00:04:50,200
+spanning لكل مين ال space اللي احنا نسبق اليه مين
+
+67
+00:04:50,200 --> 00:04:54,430
+spaceنا اللي هو ال X*) ماشي الحالطيب to show that
+
+68
+00:04:54,430 --> 00:04:57,670
+F is a linearly independent هذي is a linearly
+
+69
+00:04:57,670 --> 00:05:00,610
+independent set عارفين إيه إيش بدنا نسويه goal ال
+
+70
+00:05:00,610 --> 00:05:04,430
+summation لها Beta 1 الف واحد زي Beta 2 F2 زي Beta
+
+71
+00:05:04,430 --> 00:05:07,510
+N بيساوي أفرا بيساوي سفر و نوصل ل Beta 1 Beta 2
+
+72
+00:05:07,510 --> 00:05:12,320
+Beta N كل هنا إيه شمالين أصفر شغل جبر خطرthen الـ
+
+73
+00:05:12,320 --> 00:05:15,740
+summation beta k fk of xk من واحد لعندان ايش
+
+74
+00:05:15,740 --> 00:05:20,720
+بيساوي لكل ال X اللي موجودة element in X in
+
+75
+00:05:20,720 --> 00:05:24,420
+particular in particular مش هذا سوي لكل X in
+
+76
+00:05:24,420 --> 00:05:30,000
+particular for EJاللي هي X بيساوي EJ فبصير عندي
+
+77
+00:05:30,000 --> 00:05:33,740
+السفر هذا بيساوي summation beta K FK of EJ K من
+
+78
+00:05:33,740 --> 00:05:38,020
+واحد لعندنا تنسوش إن هدولة كلها نصفار ما عدا عندك
+
+79
+00:05:38,020 --> 00:05:42,240
+J بتساوي K، صح؟ يعني هيصير عندي بيساوي من Beta J
+
+80
+00:05:42,240 --> 00:05:47,180
+في FJ EJ اللي هي واحد، فصارت الـBJ بيساوي سفر،
+
+81
+00:05:47,180 --> 00:05:50,700
+والـEJ أنا صرتها arbitrarilyزي ما بختار لأي واحد و
+
+82
+00:05:50,700 --> 00:05:53,560
+لأي اتنين و لأي تلاتة لعندي ليه يعني بتطلع ان كلهم
+
+83
+00:05:53,560 --> 00:05:57,620
+الـ Beta إيه شمالهم Beta 1, Beta 2, Beta N صفر إذا
+
+84
+00:05:57,620 --> 00:06:01,840
+صار عندي this implies that Beta J بيساوي 0 for all
+
+85
+00:06:01,840 --> 00:06:05,760
+J معناته therefore F is a linearly independent set
+
+86
+00:06:05,760 --> 00:06:09,620
+اللي هان يجي لان ال span اطلع لفوق جاوبه صحيح let
+
+87
+00:06:09,620 --> 00:06:15,670
+F الآن let F اطلع لفوق كمان letلأ انزل انت اللي ..
+
+88
+00:06:15,670 --> 00:06:19,690
+let F be any fixed element in M in X star بدي أخد
+
+89
+00:06:19,690 --> 00:06:22,770
+أقفل X star و أقولك بقدر أكتب الأفعار زي الـ
+
+90
+00:06:22,770 --> 00:06:26,380
+linear combination إذا انخلصناأه مش هيك اللي معنات
+
+91
+00:06:26,380 --> 00:06:30,000
+ال .. ال .. ال .. little bit bases for any x إذا
+
+92
+00:06:30,000 --> 00:06:33,340
+أنا أخدت f أي element fixed element منين؟ and x
+
+93
+00:06:33,340 --> 00:06:37,060
+star، بدك تبقى أزالينا combination من f1, f2, f3،
+
+94
+00:06:37,060 --> 00:06:41,100
+اللي عندي، الـ fn طيب، for any x بالثماثين، x, i,
+
+95
+00:06:41,140 --> 00:06:43,980
+k، a, k، كامن عند 1، عند n، ليش كتبت هيك؟ لأن
+
+96
+00:06:43,980 --> 00:06:46,440
+هدولة bases و أي element ماقدر أكتبه في الـ .. في
+
+97
+00:06:46,440 --> 00:06:49,240
+الـ x، ماقدر أكتبه على هذه الصورة by using the
+
+98
+00:06:49,240 --> 00:06:53,870
+linearity of f we haveF is linear by اله F of X
+
+99
+00:06:53,870 --> 00:06:58,570
+بيساوي ال summation ل XI K F of EK K من عند واحد
+
+100
+00:06:58,570 --> 00:07:02,530
+لعند مين لعند ان هذا من ال linearity طيب خلي هذه
+
+101
+00:07:02,530 --> 00:07:07,270
+ايش واحد on the other hand for اي fixed J بين واحد
+
+102
+00:07:07,270 --> 00:07:12,940
+وبين ان احسبلي الان F J of X ايش بتساويخلّي هذه في
+
+103
+00:07:12,940 --> 00:07:16,500
+الذاكرة و حسب هذه Fj of summation بدخل لأنه كل
+
+104
+00:07:16,500 --> 00:07:20,220
+أحده Linear بيساوي ال summation ل EK Fj of EK كل
+
+105
+00:07:20,220 --> 00:07:24,280
+هى نصفار معدى عند مين عند اللى هى ياش J بتلتقي مع
+
+106
+00:07:24,280 --> 00:07:28,820
+ال K اللى هى عند مين Xij إذا صارت Fj of X إيش
+
+107
+00:07:28,820 --> 00:07:35,570
+بتساويE E J من هذه ومن هذه خلصنا القصة بيصير F of
+
+108
+00:07:35,570 --> 00:07:40,570
+X بتساوي ال E K بحط مكانها مين F K بساوي ال
+
+109
+00:07:40,570 --> 00:07:46,160
+summation ل F K of X في E في F of E K for all Xهذا
+
+110
+00:07:46,160 --> 00:07:49,500
+الكلام صحيح لكل ال .. لكل ال X في الدنيا إذا صارت
+
+111
+00:07:49,500 --> 00:07:55,760
+ال F إيش بكتبها على صورة FK في F of EK K من واحد
+
+112
+00:07:55,760 --> 00:07:58,300
+لعند مين لإنه function هذه لما كنتوا functions
+
+113
+00:07:58,300 --> 00:08:00,840
+متساويات عند كل النقاط إنها متساويات مين ال
+
+114
+00:08:00,840 --> 00:08:05,220
+functions ال F و ال FK معايا؟إذا صار عندي ال F
+
+115
+00:08:05,220 --> 00:08:08,560
+بتساوي ال summation هذا يعني قدرت أكتب F أزنين هو
+
+116
+00:08:08,560 --> 00:08:12,960
+combination من هذا معناته صار ال F لسبان لل F و
+
+117
+00:08:12,960 --> 00:08:16,280
+لسبان لل F طبيعي جزء من ال X*) إذا صار لسبان لل F
+
+118
+00:08:16,280 --> 00:08:20,080
+إيش بيساوي ال X*) إذا صار عندي hence F is a basis
+
+119
+00:08:20,080 --> 00:08:23,760
+for X*) and ال dimension في الحالتين اللي هو كان
+
+120
+00:08:23,760 --> 00:08:27,520
+اللي هو F1 F2 FN هم ال bases عدد هنا و الأولانية
+
+121
+00:08:27,520 --> 00:08:29,980
+عدد هنا إذا ال dimension لل X بيساوي ال dimension
+
+122
+00:08:29,980 --> 00:08:37,910
+لل X*) وشوف اللي بعدهاطيب لما نشوف اللي لما اللي
+
+123
+00:08:37,910 --> 00:08:45,950
+عندي let
+
+124
+00:08:45,950 --> 00:08:51,790
+C من X عند X Star Star يعني من الـ X نروح نشوف كيف
+
+125
+00:08:51,790 --> 00:08:58,810
+فيه إشي بده يعمل عند الـ X فيه لها Dual Space أو
+
+126
+00:08:58,810 --> 00:09:03,670
+الجبريك Dual Space اسمه X Starالان ال X Star فيه
+
+127
+00:09:03,670 --> 00:09:07,150
+لها Dual Space تاني اللي هو X Star Star صار عندي
+
+128
+00:09:07,150 --> 00:09:12,010
+ال Second Dual Space شكله فيه له لقب الأصل لما
+
+129
+00:09:12,010 --> 00:09:16,010
+نجيب مرتين مرتين زي تبع زمان ال inverse لما نعمله
+
+130
+00:09:16,010 --> 00:09:19,630
+مرتين برجع للأصل يعني مش بالظبط هو فيه له اللي
+
+131
+00:09:19,630 --> 00:09:23,290
+بيعمل هيك بنعطيه خاصية اللي شاطر بيعمل زيك بنعمله
+
+132
+00:09:23,290 --> 00:09:28,330
+خاصيةالان let C من X لعند X ★ ★ هذا اسمه بنسميه
+
+133
+00:09:28,330 --> 00:09:32,250
+canonical mapping on a vector space X defined by
+
+134
+00:09:32,250 --> 00:09:39,790
+CX CX بتاخد ال X لمين ل GX ال GX ماله هذا ال GX
+
+135
+00:09:39,790 --> 00:09:52,450
+احنا ال GX الان C من X لعند X ★ ★الان بياخد الـ C
+
+136
+00:09:52,450 --> 00:09:56,030
+و الـ X بياخدها الـ X من وين بيوديها لـ Element
+
+137
+00:09:56,030 --> 00:10:01,350
+هنا بنسميه GX طب إيش هذا الـ GX؟ هذا الـ GX أكيد
+
+138
+00:10:01,350 --> 00:10:07,250
+function من وين من X Star لعند اللي هو الـ R أو
+
+139
+00:10:07,250 --> 00:10:10,650
+الـ C حسب ال field اللي بتشتغل فيه مش هو هذا عبارة
+
+140
+00:10:10,650 --> 00:10:13,210
+عن Element من X Star Star و هذا إيش هو X Star
+
+141
+00:10:13,210 --> 00:10:16,970
+Star؟ عبارة عن The set of all linear functionals
+
+142
+00:10:16,970 --> 00:10:22,370
+on X Starماشي الحال طب إذا هذا إشماله هذا برضه
+
+143
+00:10:22,370 --> 00:10:28,570
+بيجي بياخد X of F GX of F من هنا و برميها هان كيف
+
+144
+00:10:28,570 --> 00:10:33,690
+بترميها هان ال F إشمالها F عبارة عن دالة من X لعند
+
+145
+00:10:33,690 --> 00:10:38,270
+R مش ال F في ال X السار إذا دالة من X لعند R إذا
+
+146
+00:10:38,270 --> 00:10:43,890
+GX of F بدي أرميها في ال R بدي أقول بتساوي F عند
+
+147
+00:10:43,890 --> 00:10:50,890
+مين عند ال X صارت ال F من X لعند ال Rإذا فعلا هذا
+
+148
+00:10:50,890 --> 00:10:56,390
+بنسميه canonical mappingهو بيه the canonical
+
+149
+00:10:56,390 --> 00:10:59,470
+mapping of vector space X defined by C X بيساوي G
+
+150
+00:10:59,470 --> 00:11:07,150
+X for any fixed X المتين X G X من X أسطار لعند K
+
+151
+00:11:07,150 --> 00:11:10,270
+زي ما قولت K is the real or the complex حسب اللي
+
+152
+00:11:10,270 --> 00:11:13,190
+احنا نشتغل عليها is defined by G X of F بيساوي F
+
+153
+00:11:13,190 --> 00:11:17,010
+of X for any F المتين X أسطار then C اللي عم نثبت
+
+154
+00:11:17,010 --> 00:11:20,190
+إيهاش is a linear operator يعني C هذا ال canonical
+
+155
+00:11:20,190 --> 00:11:23,150
+mapping هيطلع اللي برضه أيه شماله linear operator
+
+156
+00:11:23,150 --> 00:11:27,870
+سهل الدنيا إن شاء اللهأولاً نظرح ذلك جي إكس إليمنت
+
+157
+00:11:27,870 --> 00:11:30,850
+في الـ x** لكي نثبت أن هذا يشمل نفسه جي إكس هذا
+
+158
+00:11:30,850 --> 00:11:34,110
+اللي بتقوله عنه في الـ x** يعني عبارة عن element
+
+159
+00:11:34,110 --> 00:11:36,890
+هذا هو هوين بيقدر ميه بيقدر ميه لازم أرميه هناك
+
+160
+00:11:36,890 --> 00:11:41,070
+الان for any f1 و f2 عشان أثبت أنه هنا بيثبت أن هو
+
+161
+00:11:41,070 --> 00:11:45,700
+نفسه linearأه كيف بدأت بتقوله Linear خد أي two
+
+162
+00:11:45,700 --> 00:11:49,840
+elements Linear عالميا على ال X Star يعني باخد أي
+
+163
+00:11:49,840 --> 00:11:53,640
+two elements يعني هذا ال GX بدأت بتقوله Linear هان
+
+164
+00:11:53,640 --> 00:11:58,860
+أه باخد أي عنصرين من هان و ال scalar و بثبت أنه
+
+165
+00:11:58,860 --> 00:12:05,550
+Linear ده نشوف كيف مع بعض وين وصلنا؟ طيبfor any f1
+
+166
+00:12:05,550 --> 00:12:09,490
+و f2 element in x star and any scalar α we have gx
+
+167
+00:12:09,490 --> 00:12:14,450
+of α f1 زي ده f2 بساوي Alpha حسب التعريف Alpha f1
+
+168
+00:12:14,450 --> 00:12:19,010
+زي ده f2 of mean of x و يساوي Alpha f1 of x من
+
+169
+00:12:19,010 --> 00:12:22,290
+تعريف ال function زي التعريف أنه توزيع ال function
+
+170
+00:12:22,290 --> 00:12:26,970
+العادى و scalar العادى زي ده f2 of x هذه اللي هي
+
+171
+00:12:26,970 --> 00:12:33,370
+f1 of x اللي هي gx of f1 وهذه gx f2 وهي الألفةإذا
+
+172
+00:12:33,370 --> 00:12:38,650
+صار فعلاً الان G هذا بساوي هذا وهذا معناته GX is
+
+173
+00:12:38,650 --> 00:12:44,010
+linear on X star الآن صار عند GX وين موجودة في X
+
+174
+00:12:44,010 --> 00:12:48,390
+star الstar بدي الآن أثبت أنه اللي هو الـ C linear
+
+175
+00:12:48,390 --> 00:12:52,110
+لما أنا على هيك بده أروح هنا for any X element in
+
+176
+00:12:52,110 --> 00:12:56,150
+X there is a unique GX element in X star starsuch
+
+177
+00:12:56,150 --> 00:13:01,010
+that تعريف هذا such that C of X H بيساوي DX
+
+178
+00:13:01,010 --> 00:13:06,650
+because الآن عشان أقولكم أن هذا الكلام فعلا well
+
+179
+00:13:06,650 --> 00:13:10,450
+defined الآن بقول انا ادعاء انه لكل X element in X
+
+180
+00:13:10,450 --> 00:13:14,050
+بلاقي DX element in X من تعريفها الجد حقولكم انه
+
+181
+00:13:14,050 --> 00:13:17,570
+فعلا هذا الكلام هيكون هو ينيك كيف ينيك لأن such
+
+182
+00:13:17,570 --> 00:13:21,410
+that CX بيساوي DX because لو كانت ال CX بيساوي DX
+
+183
+00:13:21,410 --> 00:13:26,120
+وCX بيساوي HXمعناته for some gx وأتش x المتنكستار
+
+184
+00:13:26,120 --> 00:13:33,190
+ستار ستار حيصير ان عندي قنتين الآن بيصير gx of fF
+
+185
+00:13:33,190 --> 00:13:36,170
+بيساوي F of X وما لاقتش X of F بيساوي F of X
+
+186
+00:13:36,170 --> 00:13:39,530
+ومدامة الـ F function يستحيل هدول يكونين إيش
+
+187
+00:13:39,530 --> 00:13:43,810
+مالهين مختلفات لازم يكونين إيش مالهين متساويات
+
+188
+00:13:43,810 --> 00:13:48,470
+which is impossible لأ إذا كانت مختلفات because F
+
+189
+00:13:48,470 --> 00:13:51,870
+is a function إذا لازم غصب عننا يطلع الـ DX هو
+
+190
+00:13:51,870 --> 00:13:55,710
+main نفسه ما لاقتش في X therefore C is well
+
+191
+00:13:55,710 --> 00:13:59,010
+defined لأن في الآخر بنتبه أنها C is Linear إذا
+
+192
+00:13:59,010 --> 00:14:01,530
+أثبتنا أنها و أنه بتودي و باتثبتنا أنها well
+
+193
+00:14:01,530 --> 00:14:05,370
+definedظل نثبت علينا أنها Linear و Linearity سهلة
+
+194
+00:14:05,370 --> 00:14:10,110
+وينالي وي شوه أن C هي Linear لأي X و Y element in
+
+195
+00:14:10,110 --> 00:14:15,910
+X وأي Scalar Alpha وأي F element in X رحلنا لدينا
+
+196
+00:14:15,910 --> 00:14:19,530
+C التعريف على طول هالجيت C of Alpha X زائد Y of F
+
+197
+00:14:19,530 --> 00:14:24,570
+ايش بيساوي اللي هو G Alpha X زائد Y G اللي هي
+
+198
+00:14:24,570 --> 00:14:29,470
+متعلقة بهذه of من؟ of F هذه ايش قيمتها؟ F of هذه
+
+199
+00:14:30,390 --> 00:14:34,130
+لكن تعرفناه و يساوي F of المقدار هذا و F is linear
+
+200
+00:14:34,130 --> 00:14:38,950
+إذا ألف F زائد اللي هي F، مظبوط؟ الآن هذه مين هي؟
+
+201
+00:14:38,950 --> 00:14:43,710
+هي Alpha GX of F و هذه مين هي؟ GY of F الآن هذه
+
+202
+00:14:43,710 --> 00:14:48,950
+إيش هي؟ اللي هي Alpha CX عند ال F، معايا؟ و هذه
+
+203
+00:14:48,950 --> 00:14:52,470
+مين هي؟ CY عند مين؟ عند ال F، صارت عندي هذه
+
+204
+00:14:52,470 --> 00:14:59,050
+المقدار بساوي هذا عند كل F في الدنياعند كل الـ X
+
+205
+00:14:59,050 --> 00:15:01,870
+والـ Y اللي حكيناها إذا صار عند الـ C Alpha X زائد
+
+206
+00:15:01,870 --> 00:15:08,170
+Y بساوة Alpha CX زائد Min Cy فاهمين؟ إذا الـ C is
+
+207
+00:15:08,170 --> 00:15:12,830
+linear اللي بعدها اطلع اللي فوق لأن نيجي لها
+
+208
+00:15:12,830 --> 00:15:18,550
+الملاحظة Note that if R of C بساوة X Star Star
+
+209
+00:15:18,550 --> 00:15:22,270
+اللي قلت كلكم عنها قبل ما شوية يعني لو لجئنا إنه
+
+210
+00:15:22,270 --> 00:15:32,110
+الـ C الـ Cمن X لعند X Star Star بحيث أنه الـ
+
+211
+00:15:32,110 --> 00:15:35,290
+Range للـ C طلع X Star Star يعني بمعنى الاخر سارة
+
+212
+00:15:35,290 --> 00:15:41,050
+تادي onto function بنسمي اللي هو X is said to be
+
+213
+00:15:41,050 --> 00:15:44,430
+algebraically reflexive إذا algebraically
+
+214
+00:15:44,430 --> 00:15:52,020
+reflexive وكأنهبصير عندي اللي هو الـ X والـ X ★ ★
+
+215
+00:15:52,020 --> 00:15:58,680
+R equivalent أو R equivalent أو R isomorphic بكل
+
+216
+00:15:58,680 --> 00:16:02,460
+مفاهيمين الجبرية يعني one to one one to function
+
+217
+00:16:02,460 --> 00:16:08,340
+وكمان اللي هو ال linearity اللي هي أو المحافظة
+
+218
+00:16:08,340 --> 00:16:11,480
+preserve the algebraic operation
+
+219
+00:16:14,210 --> 00:16:23,450
+نأخد .. نأخد الآن اللمّة let
+
+220
+00:16:23,450 --> 00:16:27,570
+X be a finite dimensional vector space
+
+221
+00:16:36,360 --> 00:16:41,080
+إذا كان الجنة F of X not بساوة 0 لكل F في X star
+
+222
+00:16:41,080 --> 00:16:45,700
+لازم ال X not إيش هتتطلع كل الأفات بيودنها ال X
+
+223
+00:16:45,700 --> 00:16:50,750
+not للسفر مش هتكون الا السفر هادي طيب ال proofلت
+
+224
+00:16:50,750 --> 00:16:55,790
+E1, E2, En بيبقى basis for مين؟ for X مدان basis
+
+225
+00:16:55,790 --> 00:16:58,190
+إن X نوت كان بيرتن أزالين ال combination من هنا
+
+226
+00:16:58,190 --> 00:17:02,150
+إذا بيساوي summation XJ AJ J من وحدة لعندها هذا
+
+227
+00:17:02,150 --> 00:17:05,250
+هتكون طبعا وين موجودة في ال X then حسب الكلام اللي
+
+228
+00:17:05,250 --> 00:17:10,430
+بيحكي المعطى سفر هتساوي up of X note هذهطيب الآن f
+
+229
+00:17:10,430 --> 00:17:13,670
+of x not اللي هو بيساوي ال summation بدخل ال f على
+
+230
+00:17:13,670 --> 00:17:16,470
+اللي هو ال summation و linear f إذا بيساوي ال
+
+231
+00:17:16,470 --> 00:17:20,250
+summation xij f of ej for all f element in x star
+
+232
+00:17:20,250 --> 00:17:23,250
+إذا صار الكلام هذا لكل مين؟ لكل الأفات اللي في
+
+233
+00:17:23,250 --> 00:17:27,850
+الدنيا إذا صار عندي ال summation هذا بيساوي سفرfor
+
+234
+00:17:27,850 --> 00:17:33,630
+any choice لمن للـ F of أي جيه مادام هذا بيساوي
+
+235
+00:17:33,630 --> 00:17:37,810
+سفر لكل ال choices لل F of أي جيه مستحيل إلا تكون
+
+236
+00:17:37,810 --> 00:17:40,270
+ال F of أي جيه اللي .. اللي هي ال .. ال .. ال
+
+237
+00:17:40,270 --> 00:17:43,870
+excise هدول اللي أمامي كل واحدة أشمالها بتساوي سفر
+
+238
+00:17:43,870 --> 00:17:49,150
+وهذا يعني ان X not بتساوي سفر وهو المطلوب يلا
+
+239
+00:17:49,150 --> 00:17:54,530
+لبعده theorem
+
+240
+00:17:56,300 --> 00:17:59,240
+A finite dimensional vector space is algebraically
+
+241
+00:17:59,240 --> 00:18:02,100
+reflexive الآن قلنا algebraically reflexive متى
+
+242
+00:18:02,100 --> 00:18:08,460
+بيكون إذا كان عندي اللي هو C من X عند X*) اللي هو
+
+243
+00:18:08,460 --> 00:18:12,830
+is one to function و one to one وهي Linearطيب،
+
+244
+00:18:12,830 --> 00:18:15,930
+تنشوف، يعني التنين isomorphic بمفهوم .. الـ
+
+245
+00:18:15,930 --> 00:18:21,690
+isomorphism بمفهوم اللي هو preserved the linearity
+
+246
+00:18:21,690 --> 00:18:26,330
+أو الـ algebraic operations and اللي هو الـ
+
+247
+00:18:26,330 --> 00:18:31,130
+cardinality أو اللي هو الـ one to one و الانتوا By
+
+248
+00:18:31,130 --> 00:18:36,550
+Limma 2 9 2، C is linear، اتفقنالت CX0 بيساوي سفر
+
+249
+00:18:36,550 --> 00:18:40,050
+عشان انا اثبت اللي هو main اللي هو ال .. ال .. ال
+
+250
+00:18:40,050 --> 00:18:43,510
+.. ال one to one then for all F element in X star
+
+251
+00:18:43,510 --> 00:18:48,830
+هيكون عنده سفر بيساوي CX0 of F مظبوط ولا لا؟ الان
+
+252
+00:18:48,830 --> 00:18:53,710
+Y ساوي من تعريف CX0 of F بيساوي اللي هو GX0 of F
+
+253
+00:18:55,330 --> 00:18:58,170
+هيك التعريف G X knot of F G X knot of F أيش؟
+
+254
+00:18:58,170 --> 00:19:00,970
+بيساوي F of X knot إذا صارت عندي F of X knot
+
+255
+00:19:00,970 --> 00:19:04,510
+بتساوي مين؟ بتساوي سفر لكل الأفات إذا من اللمّة
+
+256
+00:19:04,510 --> 00:19:08,030
+اللي قبل شوية حتى تطلع X knot بيساوي سفر إذا صارت
+
+257
+00:19:08,030 --> 00:19:10,990
+الـ C is one to one لإن C X knot بيساوي سفر أدت X
+
+258
+00:19:10,990 --> 00:19:14,350
+knot بيساوي سفر إذا C is one to one and so C
+
+259
+00:19:14,350 --> 00:19:19,850
+inverse exist ماشي الآن من theorem 2.16 اللي قبل
+
+260
+00:19:19,850 --> 00:19:23,670
+بشوية ال dimension لل R of C بيساوي ال dimension
+
+261
+00:19:23,670 --> 00:19:29,740
+لل Xأه طيب الان صارت two dimensions زي بعض by
+
+262
+00:19:29,740 --> 00:19:37,880
+theorem 291 ركزوا هذه بالساوية دي خلوها في دماغه
+
+263
+00:19:37,880 --> 00:19:42,200
+الان من 9 1 2 9 1 قبل بشوية ال dimension لل X star
+
+264
+00:19:42,200 --> 00:19:44,660
+ال dimension لل X star بيساوي ال dimension لل X
+
+265
+00:19:44,660 --> 00:19:48,260
+أثبتناها وجهها ال dimension X star star هيساوي ال
+
+266
+00:19:48,260 --> 00:19:51,060
+dimension لل X star star إذا صار ان هدول ال
+
+267
+00:19:51,060 --> 00:19:55,010
+dimension اللي هنا شمال هنا زي بعضالان هدولة مح
+
+268
+00:19:55,010 --> 00:19:59,210
+هدول صار عندى dimension للـR of C بيساوي بالظبط ال
+
+269
+00:19:59,210 --> 00:20:02,290
+dimension لمين؟ لل X Star Star لأن هذا بيساوي ال
+
+270
+00:20:02,290 --> 00:20:05,210
+dimension لل X وهذا بيساوي ال dimension لل X إذا
+
+271
+00:20:05,210 --> 00:20:06,990
+أكيد ال dimension لل R of C بيساوي ال dimension
+
+272
+00:20:06,990 --> 00:20:11,570
+لمين؟ لل X Star Star كم هي ال R of C subspace من
+
+273
+00:20:11,570 --> 00:20:15,550
+مين؟ من ال X Star Star و ال dimension زي بعض، إذا
+
+274
+00:20:15,550 --> 00:20:19,870
+هي، ماتكونش هي إذا however R of C is a vector
+
+275
+00:20:19,870 --> 00:20:25,720
+subspace of X Star Starthere by quaternium 2 1 8 R
+
+276
+00:20:25,720 --> 00:20:30,380
+of C بيسوي X السار السار hence C is onto therefore
+
+277
+00:20:30,380 --> 00:20:33,800
+صارت one to one و onto و بتحافظ على اللي هو ال
+
+278
+00:20:33,800 --> 00:20:36,520
+linearity أو العمليات معناته صارت اللي هي
+
+279
+00:20:36,520 --> 00:20:41,500
+algebraically reflexive إذا في حالة ال finite
+
+280
+00:20:41,500 --> 00:20:49,450
+dimensional space ارجع لفي حالة الـ finite
+
+281
+00:20:49,450 --> 00:20:53,590
+dimensional space بكون الـ vector space أشمله
+
+282
+00:20:53,590 --> 00:20:57,870
+algebraically reflexي نيجي لل definition الأخيرة
+
+283
+00:20:57,870 --> 00:21:01,210
+two vector space is said to be isomorphic ال
+
+284
+00:21:01,210 --> 00:21:04,450
+vector space is isomorphic قلته أنا عموما توه في
+
+285
+00:21:04,450 --> 00:21:08,430
+أثناء الحديث إنه if there وصولك هذا حكيناه قبل هذا
+
+286
+00:21:08,430 --> 00:21:13,430
+if there is a bijectiveأو Objection أو Objective
+
+287
+00:21:13,430 --> 00:21:16,690
+Linear Map between the two vector spaces يعني إيش
+
+288
+00:21:16,690 --> 00:21:20,490
+ماله؟ يعني بحق .. هو أصلا إيش؟ هو عبارة عن تركيبة
+
+289
+00:21:20,490 --> 00:21:25,610
+جبرية بالإضافة .. تركيبة جبرية بالإضافة ل .. ل ..
+
+290
+00:21:25,610 --> 00:21:29,310
+لست إحنا كنا نقول الست إن هم ecopotent أو متكافئة
+
+291
+00:21:29,310 --> 00:21:31,690
+تانية ده كانت في one to one onto function يعني بس
+
+292
+00:21:31,690 --> 00:21:34,850
+اللي .. بس ال cardinality اللي هنا زي بعض الان لما
+
+293
+00:21:34,850 --> 00:21:38,750
+صار في عند .. اللي .. اللي هي عمليات جبريةالعمليات
+
+294
+00:21:38,750 --> 00:21:41,050
+الجبرية عشان نقول الـ Tin-Tin equivalent أو الـ
+
+295
+00:21:41,050 --> 00:21:45,290
+Tin-Tin isomorphic بدها تكون كتركيبة جبرية كاملة
+
+296
+00:21:45,290 --> 00:21:49,030
+تكافئت كتركيبة جبرية كاملة إيش التركيبة الجبرية
+
+297
+00:21:49,030 --> 00:21:52,810
+هان اللي هي الـ scalar multiplication و ال vector
+
+298
+00:21:52,810 --> 00:21:57,000
+addition إذا كانت linear بتحفظهاوالـ one to one on
+
+299
+00:21:57,000 --> 00:22:00,100
+two بتحفظ العدد إذا صارت isomorphic بين vector
+
+300
+00:22:00,100 --> 00:22:03,320
+spaces لو بدنا نحط norm ونقول isomorphic أو
+
+301
+00:22:03,320 --> 00:22:06,620
+isomorphism بينهم لازم يحافظ على كل اللي حكيته
+
+302
+00:22:06,620 --> 00:22:10,850
+بالإضافة على ال preserve the normو لو في topology
+
+303
+00:22:10,850 --> 00:22:15,650
+نفس الشيء إذا يعني بيكون هنا نفس هنا بس بتغيرات
+
+304
+00:22:15,650 --> 00:22:19,950
+الأسماء يعني هذه باسم تاني هي بس ال isomorphic بين
+
+305
+00:22:19,950 --> 00:22:23,710
+المعانات و هم زي بعض لكن اللي هي تغيرت الأسماء
+
+306
+00:22:23,710 --> 00:22:25,250
+واحد اسمه X واحد اسمه TX
+
+307
+00:22:43,900 --> 00:22:48,980
+تركيبة الجبرية تركيبة التباليجية تركيبة التباليجية
+
+308
+00:22:48,980 --> 00:22:52,420
+تركيبة التباليجية تركيبة التباليجيةهذا معناته اللي
+
+309
+00:22:52,420 --> 00:22:56,920
+هو الـ isomorphic أو الـ equivalence بين نظامين if
+
+310
+00:22:56,920 --> 00:22:59,780
+the vector space X is isomorphic with a subspace
+
+311
+00:22:59,780 --> 00:23:02,840
+of a vector space Y then we say that X is
+
+312
+00:23:02,840 --> 00:23:08,320
+embedable in Y لما يكون الـ X isomorphic لجزء من
+
+313
+00:23:08,320 --> 00:23:11,420
+الـ Y بنقول على هذا إيش embedable ابنه ابنه ابنه
+
+314
+00:23:11,420 --> 00:23:15,640
+ابنه زيه بالظبط زي اللي جوا بالظبط يعني الآن X هي
+
+315
+00:23:15,640 --> 00:23:28,670
+عندي Y Y Y Y كبير هيك وفي عندياللي هو X إشي تاني
+
+316
+00:23:28,670 --> 00:23:35,910
+وها نتيجة داخله Z لو كان ال X isomorphic مع ال Z
+
+317
+00:23:35,910 --> 00:23:43,070
+هو نفسه بس بسامة ثانية بنقول إن X is embedable in
+
+318
+00:23:43,070 --> 00:23:47,210
+Y وبرك الله فيكم وإلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/c4_dQ90VN3U.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/c4_dQ90VN3U.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2ed1e43d3e63f9651119d2e86cc004398dce3211
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/c4_dQ90VN3U.srt
@@ -0,0 +1,2589 @@
+1
+00:00:05,260 --> 00:00:07,600
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,600 --> 00:00:10,240
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,240 --> 00:00:13,700
+آله والصحابة أجمعين هذه المحاضرة رقم ثلاثة وثلاثين
+
+4
+00:00:13,700 --> 00:00:19,300
+مساق تحليل اقترااني أو تحليل دالي  طلاب وطالبات
+
+5
+00:00:19,300 --> 00:00:22,620
+الجامعة الإسلامية ماجستير وصلنا هنا عند أربعة تسعة
+
+6
+00:00:22,620 --> 00:00:25,460
+اللي هو convergence of sequences of operators and
+
+7
+00:00:25,460 --> 00:00:30,050
+functionals اللي هنا المرة الفاتت احنا حكينا طبعًا 
+
+8
+00:00:30,050 --> 00:00:32,910
+احنا حكينا عن اللي هو ال convergence في ال normed
+
+9
+00:00:32,910 --> 00:00:37,230
+space بالنسبة لل sequences في ال normed space قلنا
+
+10
+00:00:37,230 --> 00:00:39,570
+لو كان في عندي sequence في ال normed space xn
+
+11
+00:00:39,570 --> 00:00:44,250
+بتروح للـ x strongly و xn بتروح للـ x اللي هو يعني
+
+12
+00:00:44,250 --> 00:00:47,470
+weakly وعرفنا له شو معناه strongly وشو معناه weakly
+
+13
+00:00:48,150 --> 00:00:52,250
+لاحظوا احنا الـ .. الـ .. الـ .. عادة لما كنا نحكي لما 
+
+14
+00:00:52,250 --> 00:00:55,270
+نشتغل في الـ Real Analysis أو في الـ Complex لما
+
+15
+00:00:55,270 --> 00:00:57,770
+نحكي عن Convergence كنا نحكي عن Convergence واحد
+
+16
+00:00:57,770 --> 00:01:00,790
+اللي هو الـ X بتروح للـ X اللي هو ما نحكيش لا
+
+17
+00:01:00,790 --> 00:01:04,790
+weakly ولا Convergence ولا .. ولا Strongly تبع 
+
+18
+00:01:04,790 --> 00:01:08,570
+للحديث، ركزوا في الكلمتين تبع للحديث إنه احنا في
+
+19
+00:01:08,570 --> 00:01:13,570
+الـ R أو في الـ C الـ dimension للـ R أو للـ C is
+
+20
+00:01:13,570 --> 00:01:16,910
+finite فبما أنه is finite إذا بيكون الـ weak و الـ
+
+21
+00:01:16,910 --> 00:01:22,090
+strong إيش ما له اللي هو are the same الآن أيضًا
+
+22
+00:01:22,090 --> 00:01:25,770
+في لما كنا نحكي في التحليل في التحليل اللي هو
+
+23
+00:01:25,770 --> 00:01:30,190
+الحقيقي كنا لما نيجي نحكي عن sequence of functions
+
+24
+00:01:30,750 --> 00:01:34,850
+كنا نحكي عن نوعين من الـ convergence Fn بتروح للـ
+
+25
+00:01:34,850 --> 00:01:38,290
+F اللي هو بنسكت، شو معناه Fn كنا نسميها
+
+26
+00:01:38,290 --> 00:01:41,710
+pointwise convergence وكنا نحكي عن convergence
+
+27
+00:01:41,710 --> 00:01:46,610
+ثاني اللي هو Fn بتروح uniformly لمين؟ للـ F الآن
+
+28
+00:01:46,610 --> 00:01:51,370
+العالم الجديد هذا مشابه هحكي عن convergence لـ
+
+29
+00:01:51,370 --> 00:01:54,890
+functions هنا هحكي عن convergence لـ operators اللي
+
+30
+00:01:54,890 --> 00:01:59,770
+هي دول برضه في النهاية الآن تبعًا للمنطق اللي 
+
+31
+00:01:59,770 --> 00:02:03,170
+استخدمناه هنا برضه هيكون في عندي بدل اثنين من 
+
+32
+00:02:03,170 --> 00:02:07,030
+انواع الـ convergence هيكون في عندي اللي هو three
+
+33
+00:02:07,030 --> 00:02:12,320
+من الـ convergence طبعًا لأني أنا بحكي عن اللي هو
+
+34
+00:02:12,320 --> 00:02:16,460
+normed spaces in general أما الحديث في الـ real أو
+
+35
+00:02:16,460 --> 00:02:19,920
+كده كل حديث في number أو في finite dimensional
+
+36
+00:02:19,920 --> 00:02:24,940
+space خلينا نشوف كيف بدنا نحكي عن اللي هو الـ
+
+37
+00:02:24,940 --> 00:02:29,280
+sequence of operators إيش الأنواع الـ convergence 
+
+38
+00:02:29,280 --> 00:02:33,160
+بالنسبة إليها اللي هندرسها let x and y be normed
+
+39
+00:02:33,160 --> 00:02:38,140
+space أو spaces a sequence Tn of operators هذه T1
+
+40
+00:02:38,890 --> 00:02:41,990
+bounded linear operator T2 bounded linear operator
+
+41
+00:02:41,990 --> 00:02:45,450
+إلى آخر هي دي sequence من العناصر اللي هي من الـ
+
+42
+00:02:45,450 --> 00:02:48,530
+bounded linear operators اللي في B X Y ده set of
+
+43
+00:02:48,530 --> 00:02:52,430
+all bounded linear operators من X لعندي Y لعندي 
+
+44
+00:02:52,430 --> 00:02:56,270
+إذا عرفنا العالم اللي بنشتغل فيه اللي هو عبارة عن
+
+45
+00:02:56,270 --> 00:03:01,830
+B of X وY وعناصره اللي هي عناصر ال sequence Tn من
+
+46
+00:03:01,830 --> 00:03:06,370
+هذا اللي هو ال space اللي هم بده يبدأ يعرفكم إيش
+
+47
+00:03:06,370 --> 00:03:11,320
+ال convergence واحد uniformly convergent if Tn 
+
+48
+00:03:11,320 --> 00:03:18,780
+converges in the norm of B X Y مجرد
+
+49
+00:03:18,780 --> 00:03:23,340
+اللي هي مين بنحكي في ال norm تبع مين تبع الـ B نفسه
+
+50
+00:03:23,340 --> 00:03:27,040
+اللي هو that is there is T من X لعند Y such that
+
+51
+00:03:27,040 --> 00:03:30,120
+norm Tn نقص T بتروح لـ 0 as N goes from mean to 
+
+52
+00:03:30,120 --> 00:03:34,810
+infinity إذن وكان إنه شبيه بالـ Strongly بس هنا الـ
+
+53
+00:03:34,810 --> 00:03:39,270
+Strongly كان جاعد في الـ X هذا جاعد في مين؟ في الـ
+
+54
+00:03:39,270 --> 00:03:45,570
+Bxy لإن الـ X عناصره Xn بتروح للـ X Strongly
+
+55
+00:03:45,570 --> 00:03:49,450
+معناته Norm Xn نقص الـ X بتروح لـ Zero هنا الآن
+
+56
+00:03:49,450 --> 00:03:55,610
+العناصر هنا دوال Tn بتروح للـ T اللي هو with respect
+
+57
+00:03:55,610 --> 00:03:59,610
+to the space هذا Strongly اسمه لكن عشان نميزه عن
+
+58
+00:03:59,610 --> 00:04:04,670
+strongly اللي بعد شوية هنقول عنه uniformly يعني Tn
+
+59
+00:04:04,670 --> 00:04:13,310
+بتروح للـ T uniformly معنى بإن Norm الـ Tn ناقص T هو
+
+60
+00:04:13,310 --> 00:04:17,450
+اللي بيروح لمين للـ 0 والنورم هذا هو النورم تبع مين
+
+61
+00:04:17,450 --> 00:04:23,730
+تبع الـ B X أو Y في Convergence آخر اللي هو بنقول
+
+62
+00:04:23,730 --> 00:04:27,390
+strongly Convergence شبيه بالـ pointwise
+
+63
+00:04:27,390 --> 00:04:33,410
+Convergence تبع زمان اللي هو إيش بقول اطلع لفوق if
+
+64
+00:04:33,410 --> 00:04:37,870
+Tn X converge strongly in Y for every mean X 
+
+65
+00:04:37,870 --> 00:04:43,270
+element in X إذا الآن بنيجي عندي في عندي sequence
+
+66
+00:04:43,270 --> 00:04:51,510
+Tn في الـ B XY في الـ BX و Y Tn في الـ BX و Y عند
+
+67
+00:04:51,510 --> 00:04:56,590
+Tn في الـ BX و Y وبناخد أي X وين موجودة في الـ X
+
+68
+00:04:56,590 --> 00:05:03,710
+أي X وين موجودة في الـ X بدي أحكي عن اللي هو TnX
+
+69
+00:05:03,710 --> 00:05:08,490
+converged لمين لـ TX هذه الـ sequence صارت of 
+
+70
+00:05:08,490 --> 00:05:12,270
+elements وين موجودة في الـ Y بس بحكي عن X محددة
+
+71
+00:05:12,270 --> 00:05:19,730
+وين موجودة في الـ X بقول TnX بتروح للـ TX strongly
+
+72
+00:05:19,730 --> 00:05:27,710
+إذا كان Norm الـ TnX ناقص TX بيروح للـ 0 as N goes
+
+73
+00:05:27,710 --> 00:05:30,810
+from mean to infinity لحظة أنا شغلي هذا Norm الـ
+
+74
+00:05:30,810 --> 00:05:34,090
+TnX والـ TX وين موجود في الـ Y وكأن العالم اللي
+
+75
+00:05:34,090 --> 00:05:38,210
+بشتغل فيه مين هو اللي هو الـ Y اطلع لفوق
+
+76
+00:05:42,260 --> 00:05:46,360
+وإذا كانت تتعامل بشكل قوي إذا كانت T و X تتعامل
+
+77
+00:05:46,360 --> 00:05:52,480
+بشكل قوي بشكل Y لكل X في أقل X، هذا يعني أن هناك T
+
+78
+00:05:52,480 --> 00:05:56,660
+في أقل X و Y مثل ذلك، Norm T و X يذهب إلى T و X
+
+79
+00:05:56,660 --> 00:06:01,560
+ناقص T و X يذهب إلى Zero كما أن N يذهب إلى أقل لكل
+
+80
+00:06:01,560 --> 00:06:05,880
+X في أقل من من في X هو لو تعمقت في القمر و في 
+
+81
+00:06:05,880 --> 00:06:09,980
+الواقع اللي هو T و X تذهب إلى T و X بشكل قوي في
+
+82
+00:06:09,980 --> 00:06:16,990
+من؟ في Norm تبع الـ Y وهذه Tn بتروح للـ T strongly
+
+83
+00:06:16,990 --> 00:06:22,050
+برضه بس في الـ Norm تبع الـ B هذه بنسميها اللي هي
+
+84
+00:06:22,050 --> 00:06:26,190
+uniform Convergence لأهمية الـ Convergence هذا اللي 
+
+85
+00:06:26,190 --> 00:06:31,330
+هو .. أو لعدم اعتماد Tn-T في الـ Convergence على الـ
+
+86
+00:06:31,330 --> 00:06:36,250
+X المحددة هنا اللي كنا نسميه زمان الـ uniform 
+
+87
+00:06:36,250 --> 00:06:39,150
+Convergence في الـ functions العادية وهذه كنا
+
+88
+00:06:39,150 --> 00:06:43,590
+نسميها pointwise Convergence الآن هذولا النوعين ما 
+
+89
+00:06:43,590 --> 00:06:47,430
+كانوا نوعين قديمات الآن النوع الثالث الجديد اللي 
+
+90
+00:06:47,430 --> 00:06:50,550
+هو الـ weakly Convergent اللي هو الـ weakly
+
+91
+00:06:50,550 --> 00:06:54,630
+Convergent إن الـ TnX Converge اللي هو إيش ما له
+
+92
+00:06:54,630 --> 00:07:03,150
+weakly to some T ماشي الحال الآن TnX شو معناه Tn
+
+93
+00:07:03,150 --> 00:07:07,690
+Tn X
+
+94
+00:07:09,460 --> 00:07:15,880
+Converges weakly to TX نفس اللي قبلنا المرة اللي
+
+95
+00:07:15,880 --> 00:07:19,600
+فاتت يعني مش ليش جديد نفس اللي حكينا عنه في
+
+96
+00:07:19,600 --> 00:07:25,080
+المحاضرة اللي فاتت for every F element اللي هو N 
+
+97
+00:07:25,080 --> 00:07:33,120
+اللي هي الـ Y' عندي يجب أن يكون F of T and X ناقص F 
+
+98
+00:07:33,120 --> 00:07:40,560
+of T X Converge to zero as n goes to infinity الآن 
+
+99
+00:07:40,560 --> 00:07:44,220
+واحدة إنه هذا وهذا هيصير زي بعض في حالة الـ finite
+
+100
+00:07:44,220 --> 00:07:48,640
+dimensional space عشان هيك احنا ما بنحكيش عنه في الـ
+
+101
+00:07:48,640 --> 00:07:50,880
+.. في الـ .. في الـ real العادي ولا في الـ complex
+
+102
+00:07:50,880 --> 00:07:54,640
+العادي بنحكي عن نوعين من الـ Convergence للـ
+
+103
+00:07:54,640 --> 00:07:58,340
+functions أو للـ operators واحد اسمه uniformly واحد
+
+104
+00:07:58,340 --> 00:08:02,780
+اسمه pointwise الآن هذا عندنا هنا هنسميه uniformly
+
+105
+00:08:02,780 --> 00:08:07,440
+uniformly هنسمي الـ pointwise strongly و هنسمي الـ 
+
+106
+00:08:07,440 --> 00:08:11,680
+weakly اللي هو بالتسمية و بالمفهوم اللي حكيناه
+
+107
+00:08:11,680 --> 00:08:16,340
+المرة اللي فاتت في المحاضرة السابقة نيجي الآن واضح 
+
+108
+00:08:16,340 --> 00:08:22,600
+واضح إنه من خلال التعريف اللي حكيناه إنه الـ Tn 
+
+109
+00:08:22,600 --> 00:08:27,660
+إنّه 
+
+110
+00:08:27,660 --> 00:08:31,590
+لما نقول Tn الـ Uniform Convergence، الـ Operator
+
+111
+00:08:31,590 --> 00:08:34,930
+Convergence، يعني قوة قوة قوة قوة قوة قوة قوة قوة
+
+112
+00:08:34,930 --> 00:08:38,110
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+113
+00:08:38,110 --> 00:08:38,570
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+114
+00:08:38,570 --> 00:08:39,550
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+115
+00:08:39,550 --> 00:08:40,650
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+116
+00:08:40,650 --> 00:08:48,150
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+117
+00:08:48,150 --> 00:08:54,050
+قو
+
+118
+00:08:55,430 --> 00:09:00,010
+شو معناه اللي هو اللي هو عندي طبعًا الـ Tn عجبه عن
+
+119
+00:09:00,010 --> 00:09:06,090
+sequence element in B X Y و الـ T برضه element in
+
+120
+00:09:06,090 --> 00:09:15,150
+B X Y اللي هو شو معناه إنه uniformly الـ Norm Tn
+
+121
+00:09:15,150 --> 00:09:22,150
+ناقص T تروح للـ 0 as N goes to infinity لأن let اللي
+
+122
+00:09:22,150 --> 00:09:32,450
+هو Tn X هالجي تاخد for every X element in X let Tn
+
+123
+00:09:32,450 --> 00:09:38,050
+X converge لمين لـ TX strongly إيش معناه معناه
+
+124
+00:09:38,050 --> 00:09:43,130
+Norm الـ Tn X نقص TX اللي هو إيش مهلا بيروح لصفر
+
+125
+00:09:43,130 --> 00:09:47,670
+هذا اللي بدأ يثبت صح؟ الآن بدأ يثبت هذه ما نعش أقول
+
+126
+00:09:47,670 --> 00:09:52,490
+it بدأ يثبت هذه أخذت X شمالها arbitrarily وحسبنا 
+
+127
+00:09:52,490 --> 00:09:58,090
+الآن Norm of Tn X ناقص مين TX هذا بتساوي Norm of
+
+128
+00:09:58,090 --> 00:10:03,870
+Tn ناقص T X وهذه اللي هي أصغر تساوي Norm of Tn
+
+129
+00:10:03,870 --> 00:10:09,170
+ناقص T في Norm X مدام strongly إذا هذا بيروح لـ 0
+
+130
+00:10:09,170 --> 00:10:16,120
+إذا هذا بيروح لـ 0 إذا صارت Tn X هتروح للـ TX 
+
+131
+00:10:16,120 --> 00:10:20,700
+strongly وهو المطلوب الثاني سهل نفس الأسلوب الآن 
+
+132
+00:10:20,700 --> 00:10:27,500
+بتاخد let X element in X و F element in Y' 
+
+133
+00:10:27,780 --> 00:10:30,700
+عشان أثبت الـ weakly
+
+134
+00:10:33,690 --> 00:10:38,870
+وبنفس نفس نفس الأسلوب حتثاني أه الآن احنا
+
+135
+00:10:38,870 --> 00:10:41,950
+أثبتنا في الـ .. في الـ .. في الـ .. في خلينا نقول في
+
+136
+00:10:41,950 --> 00:10:44,110
+الـ normed space العادي الآن ده أثبتها لمين للـ
+
+137
+00:10:44,110 --> 00:10:48,530
+operators برضه هيكون مشابه مشابه خالص الآن Norm
+
+138
+00:10:48,530 --> 00:10:58,610
+Norm حسبولي F of Tn X ناقص F of TX فاهمين أه هذا 
+
+139
+00:10:58,610 --> 00:11:04,290
+أصغر بسبب Norm الـ F في Norm الـ Tn ناقص T في Norm
+
+140
+00:11:04,290 --> 00:11:08,550
+مين؟ الـ X هذا دستور مباشر إنه الـ uniform اللي 
+
+141
+00:11:08,550 --> 00:11:13,650
+بيؤول ل مين؟ لل strongly هذا اللي هو بيبقى بيروح
+
+142
+00:11:13,650 --> 00:11:19,730
+لل zero as n goes to infinity إذاً F of T and X
+
+143
+00:11:19,730 --> 00:11:27,570
+بتروح للـ F of T X هذا أثبت لكم مين الـ uniformly
+
+144
+00:11:27,570 --> 00:11:34,810
+أدى إلى مين إلى الـ weakly يعني T<sub>n</sub>X
+
+145
+00:11:34,810 --> 00:11:39,470
+بتروح لـ TX
+
+146
+00:11:39,470 --> 00:11:42,750
+تقولوا معايا T<sub>n</sub>X بتروح لـ TX weakly
+
+147
+00:11:47,050 --> 00:11:50,310
+أثبتت أن F of T<sub>n</sub>X ناقص F of TX بتروح للـ Zero
+
+148
+00:11:50,310 --> 00:11:54,270
+as N goes to infinity لكل F element in Y' و X
+
+149
+00:11:54,270 --> 00:11:56,890
+element in X' هذا يعني أن T<sub>n</sub>X بتروح للـ TX
+
+150
+00:11:56,890 --> 00:12:00,930
+بشكل weakly هذا أثبته من وين؟ من الـ Uniform
+
+151
+00:12:00,930 --> 00:12:04,390
+يؤدي إلى الـ Weakly مباشرة Strong يؤدي إلى الـ 
+
+152
+00:12:04,390 --> 00:12:09,070
+Weakly ما أثبته قبل بشوية أي سؤال؟ طيب يلا لبعده
+
+153
+00:12:14,430 --> 00:12:17,570
+الأن الـ Converse لا يجب أن يكون عاملًا يعني فيه
+
+154
+00:12:17,570 --> 00:12:22,370
+في عندك اللي هو strong operator convergence لا يجب
+
+155
+00:12:22,370 --> 00:12:26,070
+أن يكون من ال uniform يعني بقدر أجيبلك اللي هو
+
+156
+00:12:26,070 --> 00:12:30,130
+strong convergence لكن ما له مش uniform convergence
+
+157
+00:12:30,130 --> 00:12:36,530
+خد الآن let T<sub>n</sub> be a sequence of operators where T<sub>n</sub>
+
+158
+00:12:36,530 --> 00:12:41,420
+من L<sup>2</sup> لعند ما L<sup>2</sup> is defined by أنتم عارفين طبعا ايش
+
+159
+00:12:41,420 --> 00:12:46,060
+الـ Normal على الـ L<sup>2</sup> وكيف بنحسم وكيف كده المفروض
+
+160
+00:12:46,060 --> 00:12:51,080
+هذا كله يعني معلوم لنا من خلال اللي هي اللي هي
+
+161
+00:12:51,080 --> 00:12:56,800
+معلوماتنا في المادة سابقا نيجي الآن نشوف ايش اللي
+
+162
+00:12:56,800 --> 00:13:02,250
+بدنا نسويه بالظبط بدنا نجيب operator الآن أو
+
+163
+00:13:02,250 --> 00:13:07,430
+sequence of operators إنها الـ T<sub>n</sub>X بتروح للـ
+
+164
+00:13:07,430 --> 00:13:11,330
+TX هذا for every X اللي منتقلته الـ T<sub>n</sub>X بتروح
+
+165
+00:13:11,330 --> 00:13:18,080
+للـ TX strongly طبعا ولكن but  Norm الـ T<sub>n</sub> ناقص الـ
+
+166
+00:13:18,080 --> 00:13:22,740
+T does not converge to 0 يعني الـ T<sub>n</sub> بتروحش لمين؟
+
+167
+00:13:22,740 --> 00:13:26,500
+للـ T uniformly يعني بدنا نثبت أن الـ T<sub>n</sub> does not
+
+168
+00:13:26,500 --> 00:13:32,060
+converge uniformly لمين؟ للـ T لمّا نجيب الـ
+
+169
+00:13:32,060 --> 00:13:35,080
+sequence T نجيب الـ T ايش الـ space اللي اختارنا
+
+170
+00:13:35,080 --> 00:13:40,160
+اللي نشتغل عليه؟ الـ L<sup>2</sup> مين هو ال operator؟ اللي
+
+171
+00:13:40,160 --> 00:13:46,870
+هو ال operator التالي T<sub>n</sub> من الـ L<sup>2</sup> عند الـ L<sup>2</sup> كيف بدي
+
+172
+00:13:46,870 --> 00:13:50,950
+أعرفه ال element اللي في الـ L<sup>2</sup> الـ X بيساوي كـ xi<sub>1</sub>
+
+173
+00:13:50,950 --> 00:13:56,910
+واحد كـ xi<sub>2</sub> كـ xi<sub>3</sub> كـ xi<sub>n</sub> كـ xi<sub>n+1</sub> إلى
+
+174
+00:13:56,910 --> 00:14:01,050
+مال نهاية ماشي هذا عنصر مين الـ L<sup>2</sup> الأن بدي
+
+175
+00:14:01,050 --> 00:14:05,810
+أعرفلكم الـ T<sub>n</sub> ايش الـ T<sub>n</sub> بتسوي بتيجي بتاخد لك الـ X
+
+176
+00:14:05,810 --> 00:14:10,550
+هذا T<sub>n</sub>X بتيجي بت .. بت .. بت .. كل اللي قالها
+
+177
+00:14:10,550 --> 00:14:17,190
+هدولة بتسفرها بترسله هنا مين؟ لـ Zero Zero Zero
+
+178
+00:14:17,190 --> 00:14:22,390
+Zero عن طبعا هذا الـ N لهذه اللي هو xi<sub>n+1</sub>
+
+179
+00:14:22,390 --> 00:14:26,390
+أو xi<sub>n+1</sub> xi<sub>n+2</sub> وبيظل ماشي إلى مال النهاية
+
+180
+00:14:26,390 --> 00:14:35,040
+يعني وكأنه بيقولي T<sub>1</sub>X بيساوي Zero X<sub>2</sub> T<sub>2</sub>X
+
+181
+00:14:35,040 --> 00:14:46,920
+بيساوي 0 0 X<sub>3</sub> وبكمل T<sub>3</sub>X بيساوي 0 0 0 X<sub>4</sub> X<sub>5</sub> وبكمل
+
+182
+00:14:46,920 --> 00:14:50,340
+ماشي الحال إذا نوضح ايش ال sequence of operators
+
+183
+00:14:50,340 --> 00:14:55,470
+اللي عندي معايا هذه اللي هي الـ sequence of
+
+184
+00:14:55,470 --> 00:14:58,590
+operators where x اللي هي زي ما قلنا xi<sub>j</sub> اللي
+
+185
+00:14:58,590 --> 00:15:02,770
+قلته it is easy to see that T<sub>n</sub> is linear for any N
+
+186
+00:15:02,770 --> 00:15:08,090
+Linear فهي سهلة إثباتها خدوا الـ X هيها خدوا Y
+
+187
+00:15:08,090 --> 00:15:13,450
+بيساوي xi<sub>1</sub> xi<sub>2</sub> لما لا نهاية الان T<sub>n</sub>
+
+188
+00:15:13,450 --> 00:15:20,050
+αX زائد Y فمين هو في ده اعملها T<sub>n</sub> بساوية T<sub>n</sub>
+
+189
+00:15:21,090 --> 00:15:26,510
+ايش αX زائد Y؟ اللي هي αxi<sub>1</sub> زائد γ<sub>1</sub>
+
+190
+00:15:26,510 --> 00:15:32,030
+αxi<sub>2</sub> زائد γ<sub>2</sub> وبتظلها ماشية، ماشي؟ ايش
+
+191
+00:15:32,030 --> 00:15:35,530
+بتعمل الـ T<sub>n</sub> هذه؟ بتقول هي سفر، سفر وبيظل الأسفار
+
+192
+00:15:35,530 --> 00:15:41,510
+عند مين؟ αxi<sub>n+1</sub>  αxi<sub>n+1</sub> زائد
+
+193
+00:15:41,510 --> 00:15:45,550
+γ<sub>n+1</sub> وبتكمل، ماشي؟ اللي أنا بفصلها
+
+194
+00:15:45,550 --> 00:15:51,870
+الأجزاء، بسهولة اللي هو α في Zero Zero Zero و
+
+195
+00:15:51,870 --> 00:15:56,370
+xi<sub>n+1</sub> و xi<sub>n+2</sub> وبنكمل
+
+196
+00:15:56,370 --> 00:16:03,510
+زائد Zero Zero Zero γ<sub>n+1</sub> ولما لا
+
+197
+00:16:03,510 --> 00:16:07,670
+نهاية ويساوي هذه α هذه كلها مين هي عبارة عن
+
+198
+00:16:07,670 --> 00:16:13,710
+T<sub>n</sub>X وهذه مين هي T<sub>n</sub>Y إذا T<sub>n</sub> إزلينها وطول ما
+
+199
+00:16:13,710 --> 00:16:18,410
+تكتشف T<sub>n</sub> ايش معناها إزلينها Also for any n since
+
+200
+00:16:18,410 --> 00:16:23,490
+norm of T<sub>n</sub>X بيحسبوا الـ T<sub>n</sub>X مين الـ T<sub>n</sub>X اللي هي
+
+201
+00:16:23,490 --> 00:16:29,710
+هدولة هي هنا الـ T<sub>n</sub>X هيها summation هذا تربيع زائد
+
+202
+00:16:29,710 --> 00:16:31,290
+هذا تربيع زائد هذا تربيع زائد هذا تربيع زائد هذا
+
+203
+00:16:31,290 --> 00:16:32,270
+تربيع زائد هذا تربيع زائد هذا تربيع زائد هذا تربيع
+
+204
+00:16:32,270 --> 00:16:32,630
+زائد هذا تربيع زائد هذا تربيع زائد هذا تربيع زائد
+
+205
+00:16:32,630 --> 00:16:32,790
+هذا تربيع زائد هذا تربيع زائد هذا تربيع زائد هذا
+
+206
+00:16:32,790 --> 00:16:32,810
+تربيع زائد هذا تربيع زائد هذا تربيع زائد هذا تربيع
+
+207
+00:16:32,810 --> 00:16:32,930
+زائد هذا تربيع زائد هذا تربيع زائد هذا تربيع زائد
+
+208
+00:16:32,930 --> 00:16:38,060
+هذا تربيع زائد هذا تربيع صار عندي طبعا الأول هدول
+
+209
+00:16:38,060 --> 00:16:41,800
+الآن أسفار فهيبدأ العد من وين؟ من n زائد 1 إلى
+
+210
+00:16:41,800 --> 00:16:45,720
+مال النهاية أكيد هو هذا أصغر أو يساوي العد من 1
+
+211
+00:16:45,720 --> 00:16:48,060
+إلى مال النهاية هذا العد من 1 إلى مال النهاية هو
+
+212
+00:16:48,060 --> 00:16:52,380
+Norm الـ X إذا صار Norm الـ T<sub>n</sub>X أصغر أو يساوي مين؟
+
+213
+00:16:52,600 --> 00:16:56,800
+Norm الـ X اطلع لفوق الآن خدوا الآن الـ supremum
+
+214
+00:16:56,800 --> 00:17:01,080
+على Norm الـ X بيصير الـ supremum ايه؟ Norm الـ T<sub>n</sub>
+
+215
+00:17:01,080 --> 00:17:06,260
+أكبر أو يساوي 1 اكتبوا معناه، ماشي؟ الآن لو
+
+216
+00:17:06,260 --> 00:17:08,720
+اجينا .. بدي اثبت لك أن Norm الـ T<sub>n</sub> أكبر أو يساوي
+
+217
+00:17:08,720 --> 00:17:12,220
+1 بيصير Norm الـ T<sub>n</sub> ايش بيساوي؟ بيساوي 1 وهذا
+
+218
+00:17:12,220 --> 00:17:14,960
+اللي هيخليني انه .. يعني أستحيل انه .. ان الـ Norm
+
+219
+00:17:14,960 --> 00:17:19,700
+يروح لمين؟ للسفر؟ Norm الـ T<sub>n</sub> ناقص T شوفوا moreover
+
+220
+00:17:19,700 --> 00:17:24,720
+if we choose X<sub>0</sub> بيساوي 0 0 0 يعني هنرسلها
+
+221
+00:17:24,720 --> 00:17:30,320
+نفسها اه فبيصير يعني اخدت هذه هي الـ X<sub>0</sub> عشان انه
+
+222
+00:17:30,320 --> 00:17:33,780
+يصير T<sub>n</sub>X<sub>0</sub> ايش الساوية لإنه هيسفر المهمة
+
+223
+00:17:33,780 --> 00:17:37,890
+بصفرات مراسل فبتطلع T<sub>n</sub>X<sub>0</sub> بيساوي X<sub>0</sub> اللي
+
+224
+00:17:37,890 --> 00:17:41,070
+هنأخذ Norm الـ T<sub>n</sub> اللي هو الـ supremum of ما هين
+
+225
+00:17:41,070 --> 00:17:44,970
+قلنا اكيد أكبر أو يساوي Norm الـ specific value الـ
+
+226
+00:17:44,970 --> 00:17:50,350
+specific function هذه أو specific computation عند
+
+227
+00:17:50,350 --> 00:17:53,550
+X<sub>0</sub> يعني بمعنى آخر عن Norm الـ X<sub>0</sub> هدي زي هدي بيطلع
+
+228
+00:17:53,550 --> 00:17:56,610
+بشكل 1 إذا Norm الـ T<sub>n</sub> أكبر أو يساوي 1 إذا اخذنا
+
+229
+00:17:56,610 --> 00:18:00,040
+من التنتين مع بعض Norm الـ T<sub>n</sub> بيساوي 1 ومنه
+
+230
+00:18:00,040 --> 00:18:04,760
+احسبوله الآن Norm of T<sub>n</sub> ناقص Zero اللي احنا متوقعين
+
+231
+00:18:04,760 --> 00:18:09,020
+يروح عليه point اللي هو strong convergence الـ T<sub>n</sub>
+
+232
+00:18:09,020 --> 00:18:12,960
+ناقص Zero Zero operator بيساوي Norm of T<sub>n</sub> ايش اللي
+
+233
+00:18:12,960 --> 00:18:17,220
+بيساوي؟ بيساوي 1 إذا هذا يستحيل يروح لمين؟
+
+234
+00:18:17,220 --> 00:18:23,270
+للصفر إذا T يعني غير الـ T<sub>1</sub> و T<sub>2</sub> و T<sub>3</sub> ومش هيروح لا
+
+235
+00:18:23,270 --> 00:18:27,830
+إشي مش هيروح للصفر هيضلوا ايش ما لهم 1 إذا which
+
+236
+00:18:27,830 --> 00:18:31,630
+implies that T<sub>n</sub> is not uniformly convergent to
+
+237
+00:18:31,630 --> 00:18:35,350
+the zero operator أنا بدأت أثبت لك الآن but
+
+238
+00:18:35,350 --> 00:18:40,350
+it converges strongly to the zero operator يعني
+
+239
+00:18:40,350 --> 00:18:44,850
+but it is clear that for all x element in L<sup>2</sup> we
+
+240
+00:18:44,850 --> 00:18:50,810
+have خد T<sub>n</sub>X احسب في موقع 4X معادل هي T<sub>n</sub>X as N goes
+
+241
+00:18:50,810 --> 00:18:54,930
+to infinity بسفر بسفر بسفر بسفر بسفر بسفر بسفر
+
+242
+00:18:54,930 --> 00:18:55,530
+بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر
+
+243
+00:18:55,530 --> 00:18:57,330
+بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر
+
+244
+00:18:57,330 --> 00:19:00,810
+بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر
+
+245
+00:19:00,810 --> 00:19:06,370
+بسفر بسفر بسسل Zero operator إذا صار عندي هذا T<sub>n</sub>
+
+246
+00:19:06,370 --> 00:19:09,810
+converges strongly to اللي هو Zero operator إذا صار
+
+247
+00:19:09,810 --> 00:19:13,330
+عندي مثال uniformly convergent ب .. ب .. ب .. ب
+
+248
+00:19:13,330 --> 00:19:16,250
+strongly convergent which is not uniformly
+
+249
+00:19:16,250 --> 00:19:20,970
+convergent الآن بدنا ناخد مثال ثاني اللي هو الـ
+
+250
+00:19:20,970 --> 00:19:23,870
+weak operator convergence need not imply the
+
+251
+00:19:23,870 --> 00:19:30,370
+strong operator ايش convergence الآن مثال .. مثال
+
+252
+00:19:30,370 --> 00:19:31,450
+برضه على دوال
+
+253
+00:19:36,310 --> 00:19:42,310
+الآن برضه عديالة نشوف الآن شغلوش بالكم خلوكم
+
+254
+00:19:42,310 --> 00:19:45,630
+معايا الامتحان ينسوا الامتحان الـ weak operator
+
+255
+00:19:45,630 --> 00:19:48,310
+convergence لا يجب أن يمثل الـ strong operator
+
+256
+00:19:48,310 --> 00:19:52,870
+convergence ناخد الـ sequence اللي بتلبي هذا الغرض
+
+257
+00:19:52,870 --> 00:19:58,590
+شوفوا اللي هي برضه أنا هشتغل على مين على الـ Hilbert
+
+258
+00:19:58,590 --> 00:20:02,470
+space أو الـ L<sup>2</sup> أو الـ Hilbert sequence space
+
+259
+00:20:12,990 --> 00:20:22,930
+خد لي الآن T<sub>n</sub> من الـ L<sup>2</sup> لعند الـ L<sup>2</sup> وخد لي طبعا اللي
+
+260
+00:20:22,930 --> 00:20:28,150
+هي معهودة X بتساوي xi<sub>i</sub>  i من 1 إلى ما لا نهاية
+
+261
+00:20:28,150 --> 00:20:36,570
+خد لي الـ T<sub>n</sub>X بيساوي الآن سفر لي N مرة سفرها لكن لو
+
+262
+00:20:36,570 --> 00:20:40,880
+سمحت خلي لي الباقي زي ما هو يعني اعمل لي shift لـ الـ
+
+263
+00:20:40,880 --> 00:20:45,280
+operator هيك shift للـ X ارميها صفر صفر صفر N
+
+264
+00:20:45,280 --> 00:20:49,480
+من المرات وبعدين ابدأ اقول xi<sub>1</sub> xi<sub>2</sub> إلى ما
+
+265
+00:20:49,480 --> 00:20:53,880
+لنهاية هذا الآن الـ operator برضه اللي هو هتلاقيه
+
+266
+00:20:53,880 --> 00:20:57,720
+bounded linear operator من اللي جابه مثل اللي جابه
+
+267
+00:20:57,720 --> 00:21:00,780
+قبل بشوية حليته ما فيش داعي داعي دو where the
+
+268
+00:21:00,780 --> 00:21:04,540
+number of zeros is N and X بيساوي xi<sub>i</sub> it is easy
+
+269
+00:21:04,540 --> 00:21:08,400
+to see that T<sub>n</sub> is linear and bounded for any n الـ
+
+270
+00:21:08,400 --> 00:21:11,540
+boundedness سهلة الـ linear عملتها الـ boundedness
+
+271
+00:21:11,540 --> 00:21:18,200
+خد T<sub>n</sub>X ايش حيساوي الـ summation of xi<sub>i</sub> تربيع i من
+
+272
+00:21:18,200 --> 00:21:21,460
+1 إلى ما لا نهاية صح ولا لأ؟ لإن هو .. بالحسب إن هو
+
+273
+00:21:21,460 --> 00:21:25,440
+أسفل وبعدين وبعدين وهو عبارة عن مين؟ Norm أص
+
+274
+00:21:25,440 --> 00:21:29,940
+نص هذا Norm الـ X بالظبط ولا لأ؟ إذا أكيد bounded
+
+275
+00:21:29,940 --> 00:21:34,340
+T<sub>n</sub>X هو Norm 1 كمان مش bounded بس و Norm T<sub>n</sub>
+
+276
+00:21:34,340 --> 00:21:42,040
+بيساوى 1 بالظبط طيب اطلع على فوق since L<sup>2</sup> is a
+
+277
+00:21:42,040 --> 00:21:44,900
+Hilbert space then every linear functional F
+
+278
+00:21:44,900 --> 00:21:49,520
+element in L<sup>2</sup> أسهل ليه في الـ L<sup>2</sup> على طول بعمله الـ
+
+279
+00:21:49,520 --> 00:21:52,420
+representation بالـ Riesz representation الـ
+
+280
+00:21:52,420 --> 00:21:55,800
+theorem has Riesz representation F of X بيساوي X و
+
+
+
+281
+00:21:55,800 --> 00:22:00,080
+Z و يساوي كالـ inner product بينهم اللي هو تبعات
+
+282
+00:22:00,080 --> 00:22:03,480
+هدف تبعات هدف بس كواحدة عادية واحدة conjugate X<sub>i</sub>J
+
+283
+00:22:03,480 --> 00:22:07,000
+أو X<sub>i</sub>J Gamma J conjugate J من واحد إلى ما لا نهاية
+
+284
+00:22:07,000 --> 00:22:11,420
+حيث الـ Z هي تبعات Gamma J والـ X هي من X<sub>i</sub>J واضح
+
+285
+00:22:11,420 --> 00:22:15,180
+هذا الـ Z اللي لاجناها for every F element in L<sup>2</sup>
+
+286
+00:22:15,180 --> 00:22:22,040
+there exists Z such that F of X بيساوي X o Z لكن
+
+287
+00:22:22,040 --> 00:22:25,720
+من جهة أخرى أحسب للـ F of T<sup>N</sup> X بدي أثبت ليه
+
+288
+00:22:25,720 --> 00:22:32,400
+convergence لأن أنا بدي أثبتلك أن F of T<sup>N</sup> X بتروح
+
+289
+00:22:32,400 --> 00:22:39,180
+إلى F of something X N نشوف إيش هو الـ something
+
+290
+00:22:39,180 --> 00:22:39,500
+هنا
+
+291
+00:22:44,930 --> 00:22:49,590
+صلى الله على النبي عليه الصلاة والسلام احسب لي F of T<sup>N</sup> 
+
+292
+00:22:49,590 --> 00:22:54,710
+X اللي هي بالساوي حسب اللي هي ال rule اللي عندي T
+
+293
+00:22:54,710 --> 00:22:59,990
+N X و Z و هذه اللي هي بالساوي T<sup>N</sup> X هي اللي هي
+
+294
+00:22:59,990 --> 00:23:08,030
+طيب شوفوا كيف هدول السفر هياخدوا مينهيخدم مين هي
+
+295
+00:23:08,030 --> 00:23:12,610
+الـ Z جامعة واحد جامعة اتنين جامعة N جامعة N زائد
+
+296
+00:23:12,610 --> 00:23:16,650
+واحد الاخره الان ادول الاسفار هيخدم في طريقهم
+
+297
+00:23:16,650 --> 00:23:22,470
+هذوله لما نضرب من فيهم اذا هيبدأ العد ل X<sub>i</sub> واحد هو
+
+298
+00:23:22,470 --> 00:23:28,550
+X<sub>i</sub>N أو جامعة N زائد واحد فطبيعي بساوي هو X<sub>i</sub>J
+
+299
+00:23:28,550 --> 00:23:32,210
+minus N Gamma J J من عند N زائد واحد إلى مين إلى
+
+300
+00:23:32,210 --> 00:23:35,550
+ما لا نهاية و اللي بده يبدأ بهدف J هدف الساقين هي
+
+301
+00:23:35,550 --> 00:23:44,310
+J زائد N و بده يبدأ يشتغل أو J من واحد فاهمين؟ هذا
+
+302
+00:23:44,310 --> 00:23:47,630
+اللي هو نفسه عبارة عن K من واحد إلى ما لا نهاية X
+
+303
+00:23:47,630 --> 00:23:52,520
+I K Gamma N K زائد واحد فاهمين؟كيف اللي هو غيرنا
+
+304
+00:23:52,520 --> 00:23:56,180
+ال index من هاللهان طيب الان by Cauchy Schwarz inequality
+
+305
+00:23:56,180 --> 00:24:01,180
+خد لهذه f of T<sup>N</sup>X اللي هو absolute value
+
+306
+00:24:01,180 --> 00:24:04,040
+لها وهذا ال absolute value وستخدم ال Cauchy
+
+307
+00:24:04,040 --> 00:24:09,060
+Schwarz inequality فبصير absolute value تربيع بساوي
+
+308
+00:24:09,060 --> 00:24:13,480
+هذه تربيع اللي هي أصغر أو اللي هي بساوي هذه norm
+
+309
+00:24:13,480 --> 00:24:17,910
+هذه ماشي اللي هو تربيع أصغر أو .. فاهمين؟مسير أصغر
+
+310
+00:24:17,910 --> 00:24:21,770
+أو يساوي اللي هو summation هذا تربيع اللي جوا فال
+
+311
+00:24:21,770 --> 00:24:25,430
+summation هذا تربيع اللي جوا ال N هذا as N goes to
+
+312
+00:24:25,430 --> 00:24:29,590
+infinity هذا من وين بيبدأ ال K من M من N زائد واحد
+
+313
+00:24:29,590 --> 00:24:33,370
+إلى ما لا نهاية هذا as N goes to infinity بتروح
+
+314
+00:24:33,370 --> 00:24:38,010
+لمين لل zeroفاهمين اللي بحكيه أخدت أنا اشتغلت على
+
+315
+00:24:38,010 --> 00:24:44,150
+هذه أو على اللي هي والأولى من عند واحد فصلت
+
+316
+00:24:44,150 --> 00:24:49,130
+التنتين هذه بديتها اللي هي من عند زائد واحد اللي
+
+317
+00:24:49,130 --> 00:24:53,010
+هي اللي بتبدأ عندها وهذه بتبدأ من واحد وتظل ماشية
+
+318
+00:24:53,620 --> 00:24:57,320
+مفهوم هذا بتروح إلى الـ Zero إذاً هذا كله هيروح
+
+319
+00:24:57,320 --> 00:25:00,700
+للـ Zero إذا صار معناته F of T<sup>N</sup> X لكل تربيع
+
+320
+00:25:00,700 --> 00:25:04,660
+بيروحنا منين للـ Zero اللي هو في الواقع F of Zero
+
+321
+00:25:04,660 --> 00:25:10,280
+Operator منين X يعني اللي أثبتته أنه الـ T<sup>N</sup> الـ T<sup>N</sup>
+
+322
+00:25:10,280 --> 00:25:14,320
+اللي هو weakly Operator converges to the Zero
+
+323
+00:25:14,320 --> 00:25:19,760
+Operator يعني الـ T<sup>N</sup> X بتروح للـ Zero X لكل X
+
+324
+00:25:19,760 --> 00:25:22,440
+element in X ماله
+
+325
+00:25:25,010 --> 00:25:30,290
+بالنسبة لـ T<sup>n</sup> هو كذلك، لكن T<sup>n</sup> ليس عمليًا عمليًا
+
+326
+00:25:30,290 --> 00:25:41,990
+عمليًا عمليًا عمليًا عمليًا عمليًا عمليًا
+
+327
+00:25:42,250 --> 00:25:46,810
+الـ T<sup>N</sup>X ناقص Zero X اللي هو بيروح للـ Zero for
+
+328
+00:25:46,810 --> 00:25:52,330
+every X المنتج من هنا N X لو لجيت X واحدة بس بحيث
+
+329
+00:25:52,330 --> 00:25:57,450
+انه norm الـ T<sup>N</sup>X ناقص Zero X بيروحش للـ Zero
+
+330
+00:25:57,450 --> 00:26:02,170
+معناته الـ T<sup>N</sup>X does not converge this strongly to
+
+331
+00:26:02,170 --> 00:26:07,170
+Zero X هاي X خد X إيش بتساوي واحد صفر صفر صفر
+
+332
+00:26:07,170 --> 00:26:15,690
+وحسبلي الآن T<sup>N</sup>X وT<sup>N</sup>Xهتطلع اللي هي عبارة عن T<sup>M</sup> نقص
+
+333
+00:26:15,690 --> 00:26:19,050
+T<sup>N</sup> of X اللي هو هيطلع إيه أشماله جدر التنين
+
+334
+00:26:19,050 --> 00:26:23,290
+بتعرفوا تحسبوها اللي هي for all M لا تساوي N
+
+335
+00:26:23,290 --> 00:26:26,710
+معناته إنه is not Cauchy sequence مدام is not
+
+336
+00:26:26,710 --> 00:26:30,350
+Cauchy sequence is not converge إذا صار عندي اللي
+
+337
+00:26:30,350 --> 00:26:37,370
+هو norm T<sup>N</sup> X نقص T<sup>N</sup> is not converge strongly ل 0
+
+338
+00:26:40,760 --> 00:26:48,940
+طيب Note الان ال functionals
+
+339
+00:26:49,600 --> 00:26:52,740
+الـ Functionals، لو واحد .. الآن احنا بنحكي عن
+
+340
+00:26:52,740 --> 00:26:56,000
+Operators اللي هي الـ T أن و ان موجودة، انتبهوا
+
+341
+00:26:56,000 --> 00:27:00,660
+للمراحة ده، بين X و بين مين؟ بين Y، من normed
+
+342
+00:27:00,660 --> 00:27:05,680
+space ل normed space طيب لو بدينا بدنا نحكي بـ X و
+
+343
+00:27:05,680 --> 00:27:08,760
+ال scalar field تبعها، يعني بمعنى أخر، بدنا نحكي
+
+344
+00:27:08,760 --> 00:27:13,540
+عن مين؟ عن الـ X' أه يعني الآن ال operators اللي
+
+345
+00:27:13,540 --> 00:27:17,080
+أنا بدأ أخدها من وين من X لعند مين لـ scalar فيه
+
+346
+00:27:17,080 --> 00:27:19,540
+التباحة يعني بدأ أحكي عن ال functionality F
+
+347
+00:27:19,540 --> 00:27:24,560
+element من مين ل X' F<sup>N</sup> element in X' لما أحكي عن
+
+348
+00:27:24,560 --> 00:27:31,780
+ال F<sup>N</sup> element in X' معناته أنا صرت اللي هو اللي
+
+349
+00:27:31,780 --> 00:27:35,940
+.. اللي .. اللي هنا finite dimensional يعني بيصير
+
+350
+00:27:35,940 --> 00:27:41,890
+ال F<sup>N</sup> Xعبارة عن مش فنون انتسبيس عادي صار في
+
+351
+00:27:41,890 --> 00:27:44,970
+finite dimensional فبصير ال strongly و ال weak ليه
+
+352
+00:27:44,970 --> 00:27:50,970
+إيش ماله زي بعض فعشان هيك بحكيش لما احكي عن ال
+
+353
+00:27:50,970 --> 00:27:55,680
+functional بصير احكي بنوعية اخرىالان بيصير عندي
+
+354
+00:27:55,680 --> 00:27:59,580
+نوعين since the real and complex field are finite
+
+355
+00:27:59,580 --> 00:28:04,880
+dimensional then by theorem 48C the weak and
+
+356
+00:28:04,880 --> 00:28:08,660
+strong convergence of any sequence of bounded
+
+357
+00:28:08,660 --> 00:28:15,160
+linear functionals are the same يعني ال weak و ال
+
+358
+00:28:15,160 --> 00:28:19,820
+strong أيش بيصيرن؟ بيصيرن زي بعض الآن definition
+
+359
+00:28:19,820 --> 00:28:24,720
+بناء عليه الان احنا لما بدنا نحكي let F<sup>N</sup> be a
+
+360
+00:28:24,720 --> 00:28:27,220
+sequence of bounded linear functions on and among
+
+361
+00:28:27,220 --> 00:28:31,300
+the space X then في عين دي بدأ احكي عن لان معين من
+
+362
+00:28:31,300 --> 00:28:35,620
+ال operators من ال convergence strong convergence
+
+363
+00:28:35,620 --> 00:28:43,580
+of F<sup>N</sup> الآن اذا بدأ احكي عن نوعيات تخصنين اللي هو
+
+364
+00:28:43,580 --> 00:28:48,330
+ال convergence لل F<sup>N</sup> Strongly convergence of F<sup>N</sup>
+
+365
+00:28:48,330 --> 00:28:52,310
+means that there is F element in X' Such that
+
+366
+00:28:52,310 --> 00:28:55,570
+norm of F<sup>N</sup> minus F بتروح لمين للزيرو as N goes to
+
+367
+00:28:55,570 --> 00:29:00,650
+infinity وكأنه بحكي عن اللي هو مين هنا اللي هو ال
+
+368
+00:29:00,650 --> 00:29:04,090
+uniform convergence هناك مكافئ لمين ال uniform
+
+369
+00:29:04,090 --> 00:29:07,230
+convergence إذا لما الآن بدي أحكي في ال functional
+
+370
+00:29:07,230 --> 00:29:10,870
+ركزوا الآن بدي أحكي في ال functional وكأن زي ما
+
+371
+00:29:10,870 --> 00:29:13,490
+كنت أحكي في الأول في المحاضرة اللي فاتت في ال X في
+
+372
+00:29:13,490 --> 00:29:17,770
+normها وهنا بتحكي في norm منين؟ في norm الـ X' لأن
+
+373
+00:29:17,770 --> 00:29:22,530
+الآن سيرة الـ F<sup>n</sup> وين موجودة؟ في الـ X' فالآن ما
+
+374
+00:29:22,530 --> 00:29:27,770
+بتحكي عن اللي هو strong ل convergence فيها F<sup>n</sup> ناقص
+
+375
+00:29:27,770 --> 00:29:32,250
+F اللي بتروحلها بروح للـ 0 as N goes to infinity
+
+376
+00:29:32,250 --> 00:29:35,210
+هذا اللي في حالة ال operators كنت سميه uniform
+
+377
+00:29:35,210 --> 00:29:39,330
+convergence وهنا بده أسميه إيش ماله؟ strong
+
+378
+00:29:39,330 --> 00:29:43,850
+convergence لمين؟لـ Sequence of Functions عشان ما
+
+379
+00:29:43,850 --> 00:29:47,790
+اتخربتوش في الواقع هذا اللي كنا نسميه Uniform
+
+380
+00:29:47,790 --> 00:29:51,170
+Convergence وحتى أيام الباكاليوروس كنا نسميه
+
+381
+00:29:51,170 --> 00:29:54,990
+Uniform Convergence اللي هي في حالة اللي هي Area
+
+382
+00:29:54,990 --> 00:29:58,130
+اللي هنا نسميه Strong Convergence طيب، اللي هنا في
+
+383
+00:29:58,130 --> 00:30:01,590
+حاجة اسمها Weak Star Convergence الـWeak Star
+
+384
+00:30:01,590 --> 00:30:06,290
+لمين؟ With respect to F طيب الـWeak Convergence
+
+385
+00:30:06,290 --> 00:30:09,730
+كنا ناخد اللي هو For Every F Element ان كنا نقول
+
+386
+00:30:09,730 --> 00:30:16,760
+ان X<sup>N</sup>عشان ما تتربطوش X<sup>N</sup> بتروح لل X weakly ناخد
+
+387
+00:30:16,760 --> 00:30:21,840
+مين؟ ناخد every F element in X' ونقول F of X<sup>N</sup>
+
+388
+00:30:21,840 --> 00:30:25,940
+بتروح لل F of X إيه شماله؟ اذا نقصده في التبسيه
+
+389
+00:30:25,940 --> 00:30:28,830
+sequence of numbersطب إحنا الآن .. طب هي عندنا
+
+390
+00:30:28,830 --> 00:30:33,510
+جاهزة أصلا لما .. عندنا الـ F<sup>N</sup> هي .. هي أصلا
+
+391
+00:30:33,510 --> 00:30:37,330
+functional نفسها فإيش اللي بدي أسوي؟ بدي أسوي ..
+
+392
+00:30:37,330 --> 00:30:41,150
+أسمي حاجة اسم weak star convergence و بكتبها
+
+393
+00:30:41,150 --> 00:30:47,050
+convergence of F<sup>N</sup> means that there is a F  such
+
+394
+00:30:47,050 --> 00:30:51,360
+that الآنبدخلش F عليها على الـ sequence لأ بقول
+
+395
+00:30:51,360 --> 00:30:54,840
+such that F<sup>N</sup> of X بتروح لل F of X as N goes to
+
+396
+00:30:54,840 --> 00:30:58,140
+infinity لكل X هو element in X وهذا معناته F<sup>N</sup>
+
+397
+00:30:58,140 --> 00:31:04,860
+بتروح لل F مين weakly بس
+
+398
+00:31:04,860 --> 00:31:11,400
+طلعونها للفرق بس
+
+399
+00:31:11,400 --> 00:31:18,420
+انتبهوا وصلة لمن؟ هي في عندي Xهذا ما يسمى كـ
+
+400
+00:31:18,420 --> 00:31:23,560
+Normed Space وفي عند X' اللي هو الـ Dual Space
+
+401
+00:31:23,560 --> 00:31:27,800
+اللي لها هذا بتحكي عن weak convergence وهذا weak
+
+402
+00:31:27,800 --> 00:31:32,960
+star convergence و Xاللي هي norm of the space و X'
+
+403
+00:31:33,300 --> 00:31:37,740
+أشماله اللي هو dual space لها طيب، شوفوا، صلى الله
+
+404
+00:31:37,740 --> 00:31:41,140
+عني، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس،
+
+405
+00:31:41,140 --> 00:31:42,640
+بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس،
+
+406
+00:31:42,640 --> 00:31:44,400
+بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس،
+
+407
+00:31:44,400 --> 00:31:52,260
+بلس، بلس، بلس، بلس، بلس، بلس، بلس،
+
+408
+00:31:52,260 --> 00:31:56,320
+بلس،
+
+409
+00:31:57,020 --> 00:32:00,060
+هي هي هي هي هي ال sequence أه ال N ال sequence
+
+410
+00:32:00,060 --> 00:32:04,420
+بينما هنا لما بحكي عن weak star بحكي عن sequence
+
+411
+00:32:04,420 --> 00:32:09,620
+وين موجودة في ال X' مش sequence في ال X فبصير عندي
+
+412
+00:32:09,620 --> 00:32:14,080
+F<sup>N</sup> هي ال sequence وين في ال X' و ال F اللي
+
+413
+00:32:14,080 --> 00:32:18,640
+بتروحلها برضه وين موجودة في ال X' فبقول F<sup>N</sup> بتروح
+
+414
+00:32:18,640 --> 00:32:25,070
+لل F weak star معناته إن الـ N بسير لأن لكل مين ال
+
+415
+00:32:25,070 --> 00:32:30,770
+N بعكسها لكل X في ال X بطلع عند أف<sup>N</sup> of X بتروح لل
+
+416
+00:32:30,770 --> 00:32:35,450
+أف of مين of X يعني الآن ال sequence هذه لمين لل
+
+417
+00:32:35,450 --> 00:32:39,390
+أف<sup>N</sup> اللي في وين في ال X' بينما ال X<sup>N</sup> هذه ال
+
+418
+00:32:39,390 --> 00:32:44,730
+sequence في وين في ال X نفسهاالطول هنا لتحقيق الـ
+
+419
+00:32:44,730 --> 00:32:48,490
+weak star هي الـ F اللي في الـ X' بينما الطول هنا
+
+420
+00:32:48,490 --> 00:32:52,750
+لتحقيق الـ W star اللي يمين الـ Xات اللي في الـ L<sup>2</sup> 
+
+421
+00:32:52,750 --> 00:33:00,810
+في الـ X و الـ Y  let X and Y be
+
+422
+00:33:00,810 --> 00:33:05,330
+normed spaces and T and B a sequence of
+
+423
+00:33:05,330 --> 00:33:12,500
+elements in B(X, Y) إذا Tن تتعامل بشكل عام لـ T،
+
+424
+00:33:12,500 --> 00:33:17,020
+فإن T تتعامل بشكل عام لـ T، فإن T تتعامل بشكل عام 
+
+425
+00:33:17,020 --> 00:33:26,360
+ل T، فإن T تتعامل
+
+426
+00:33:26,360 --> 00:33:34,520
+بشكل
+
+427
+00:33:34,520 --> 00:33:37,490
+عام ل T، فإن لكن كنا نقول أن الـ Pointwise لا
+
+428
+00:33:37,490 --> 00:33:41,730
+يستطيع أن يضمن أن Fn converge للـF اللي هو 
+
+429
+00:33:41,730 --> 00:33:44,970
+زمان، تبع زمان، تبع الـReal أو تبع الـC إذا كانت
+
+430
+00:33:44,970 --> 00:33:48,610
+Fn بتروح للـF pointwise وكانت Fn sequence of
+
+431
+00:33:48,610 --> 00:33:51,210
+continuous functions ليس شرط أن الـF تكون
+
+432
+00:33:51,210 --> 00:33:54,510
+continuous وكنا لما نحكي عن الـintegrable ونحكي عن
+
+433
+00:33:54,510 --> 00:33:56,530
+الـdifferentiability برضه كان لهم conditions كان
+
+434
+00:33:56,530 --> 00:33:59,650
+يمكن الـdifferentiability بتهزج تاني غير اللي هو
+
+435
+00:33:59,650 --> 00:34:06,600
+الـUFO طيب الآن Strongly or weakly convergence of
+
+436
+00:34:06,600 --> 00:34:11,260
+TN to some T إلى كده need not imply أيش معلوه زي
+
+437
+00:34:11,260 --> 00:34:14,240
+اللي قلته قبل شوية إنه الـ weakly و الـ strongly
+
+438
+00:34:14,240 --> 00:34:19,160
+convergence للـ TN غير مؤهل إنه ياخد ال sequence
+
+439
+00:34:19,160 --> 00:34:23,120
+of continuous bounded functions أو continuous
+
+440
+00:34:23,120 --> 00:34:26,980
+linear functions أو bounded linear functions
+
+441
+00:34:26,980 --> 00:34:30,720
+ل bounded linear function إذا الموهّل مين بس اللي
+
+442
+00:34:30,720 --> 00:34:34,620
+بقدر يودّهيه اللي هو بس اللي هو مين ال uniform
+
+443
+00:34:34,620 --> 00:34:42,480
+convergence الآن الواحد البرهان لكم مش صعب نيجي
+
+444
+00:34:42,480 --> 00:34:44,680
+نبرهن مين اتنين يعني بدي اجيب مثال
+
+445
+00:34:48,960 --> 00:34:54,240
+بـ strong أو weak convergence من continuous
+
+446
+00:34:54,240 --> 00:34:57,640
+functions أو bounded linear operators التي مش
+
+447
+00:34:57,640 --> 00:35:03,820
+موجودة في B(X,Y) لأ يمكنها تكون تشوفوا اطلع لفوق to
+
+448
+00:35:03,820 --> 00:35:09,220
+verify two اللي هاد اتنين consider the subspace X
+
+449
+00:35:09,220 --> 00:35:15,030
+ايش بتساوي اطلع لفوق بيساوي x بيساوي xij الامتنان 2
+
+450
+00:35:15,030 --> 00:35:19,090
+such that x has finitely many non-zero elements of L2
+
+451
+00:35:19,090 --> 00:35:23,890
+اشمالها اللي هي ال non zero finite بس و البعدي
+
+452
+00:35:23,890 --> 00:35:30,630
+اشماله أصفر let Tn من x لعند x be defined by Tn x
+
+453
+00:35:30,630 --> 00:35:35,590
+ايش بتساوي اللي هو هدول بس اشماله في عندك finite
+
+454
+00:35:35,590 --> 00:35:41,250
+number of elements مش zero X has finitely many non
+
+455
+00:35:41,250 --> 00:35:44,490
+-zero elements هذا اللي هو ال space اللي عندي هذا
+
+456
+00:35:44,490 --> 00:35:50,150
+ال subspace من مين؟ من ال L2 نفسه طيب يعني تقولي
+
+457
+00:35:50,150 --> 00:35:59,030
+ال element اللي هو اللي في ال L2 نص؟ ربع؟ تسع؟
+
+458
+00:35:59,030 --> 00:36:02,570
+واحد ع ستاش؟ إلى ما لا نهاية؟ هذا مش موجود في ال X
+
+459
+00:36:02,570 --> 00:36:10,080
+هذه لكن موجود في ال L2 لأن الـ summation له finite
+
+460
+00:36:10,080 --> 00:36:13,520
+طيب
+
+461
+00:36:13,520 --> 00:36:17,120
+لكن .. لكن مش كل ال terms كل ال terms بيبقى
+
+462
+00:36:17,120 --> 00:36:19,240
+لانهاية مش zero طيب
+
+463
+00:36:21,410 --> 00:36:28,370
+طيب أخدنا T ان X ايش بتساوي T واحد X بتساوي ال .. ال
+
+464
+00:36:28,370 --> 00:36:29,150
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+465
+00:36:29,150 --> 00:36:29,430
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+466
+00:36:29,430 --> 00:36:29,610
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+467
+00:36:29,610 --> 00:36:30,950
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+468
+00:36:30,950 --> 00:36:32,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+469
+00:36:32,290 --> 00:36:32,530
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+470
+00:36:32,530 --> 00:36:33,010
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+471
+00:36:33,010 --> 00:36:35,890
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+472
+00:36:35,890 --> 00:36:36,170
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+473
+00:36:36,170 --> 00:36:36,190
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+474
+00:36:36,190 --> 00:36:43,370
+ال .. ال .. ال .. ال .. ال .. ال
+
+475
+00:36:44,750 --> 00:36:49,410
+T3 نفس الشيء الـ TN التي تضرب 1×2×3×4 لما تصل لـ N
+
+476
+00:36:49,410 --> 00:36:54,590
+و بعدها تبقى كما هي هذه التي هي TNX و خد TX
+
+477
+00:36:54,590 --> 00:37:02,470
+defined by TX ايش بتساوي GXiJ هذي لاحظ لما N تروح
+
+478
+00:37:02,470 --> 00:37:04,930
+إلى ما على النهاية يضرب و يضرب و يضرب و يضرب و
+
+479
+00:37:04,930 --> 00:37:11,290
+يضرب و يضرب و يضرب مشكلة مكبرة N بزيادة ضرب عند N
+
+480
+00:37:11,290 --> 00:37:13,670
+زيادة واحد بيصير ضربان فما بالكم اللي مروحوا
+
+481
+00:37:13,670 --> 00:37:16,190
+البلد؟ هذا بيصير كل المضروبات وكأنهم هذا roughly
+
+482
+00:37:16,190 --> 00:37:19,270
+الكلام طيب it is left to the reader to show that
+
+483
+00:37:19,270 --> 00:37:23,810
+for each N TN is linear and bounded برضه نفس
+
+484
+00:37:23,810 --> 00:37:26,230
+الأشياء ال linearity و ال boundedness مشابه اللي
+
+485
+00:37:26,230 --> 00:37:30,310
+حكيناه قبل و شوية ال unboundedness سهل ال bounded
+
+486
+00:37:30,310 --> 00:37:34,570
+norm TN هذا بيساوي norm هذا و هذا أصغر أو ساوي
+
+487
+00:37:34,570 --> 00:37:40,500
+اللي هو N فى Normal X على اعتبار ان كله واضربات
+
+488
+00:37:40,500 --> 00:37:49,300
+عندك انا لان انا اكبر واحدة مش فاهمين؟
+
+489
+00:37:49,300 --> 00:37:50,780
+طيب لأ
+
+490
+00:38:03,150 --> 00:38:08,630
+TNX بساوية اللي هو عبارة عن مين اللي هو norm TNX
+
+491
+00:38:08,630 --> 00:38:14,030
+بساوية norm اللي هو XI واحد XI اتنين XI اتنين لعند
+
+492
+00:38:14,030 --> 00:38:19,310
+ان ان XI ان والباب المضروب الاخر هنا هذا أصغر أوي
+
+493
+00:38:19,310 --> 00:38:25,570
+ساوي اللي هو اعتبر ان هذا اللي هو norm هنا اللي هو
+
+494
+00:38:25,570 --> 00:38:27,610
+عبارة عن ال summation لهذا و لهذا و لهذا ال
+
+495
+00:38:27,610 --> 00:38:32,570
+summation أصغر و أصغر ال summation ان في xii I من
+
+496
+00:38:32,570 --> 00:38:39,010
+عند واحد إلى ما لنهاية تربيع الكل أص نص norm تربيع
+
+497
+00:38:39,010 --> 00:38:42,970
+نحسب norm تربيع مش مشكلة كأني سحبت الان هذول لإن
+
+498
+00:38:42,970 --> 00:38:47,750
+هذول بس الان هنا أنا ضربت انفين كله طيب
+
+499
+00:38:50,470 --> 00:38:53,450
+It is left to the reader to show that TN is a bounded linear operator or
+
+500
+00:38:53,450 --> 00:38:57,770
+unbounded Moreover T is linear but is not bounded
+
+501
+00:38:57,770 --> 00:39:01,710
+T هذه هذه T is linear لكن أشمالها is not bounded
+
+502
+00:39:01,710 --> 00:39:06,890
+الآن T X بتساوي J في مين كساية واحد في كساية اتنين
+
+503
+00:39:06,890 --> 00:39:11,510
+في كساية تلاتة is not bounded إنها متعبرة وليس
+
+504
+00:39:11,510 --> 00:39:15,730
+متعبرة ثم T هو إيش معناه element in B(X,Y) وليس element
+
+505
+00:39:15,730 --> 00:39:23,670
+in B(X, Y) of X إذا مش مستحيل أن الـTن تكون مرتبط لمن؟
+
+506
+00:39:23,670 --> 00:39:31,630
+لـT أه الـTن مستحيل تروح لمن؟ لـT أخيراً واضح أن
+
+507
+00:39:31,630 --> 00:39:36,080
+الـTن مرتبط بشكل قوي لمن؟ لـT اللي قلته في الأول،
+
+508
+00:39:36,080 --> 00:39:39,900
+أول ما حكيت، الـTN، شو معناه الـTN؟ شو معناه الـTN
+
+509
+00:39:39,900 --> 00:39:45,260
+strongly تروح convergence to T؟ إنه، اللي هو TN X
+
+510
+00:39:45,260 --> 00:39:51,200
+معقص TX يروح نمين للسفر، TN as N goes to infinity،
+
+511
+00:39:51,200 --> 00:39:56,410
+هذه اللي هي هيهاهو as n goes to infinity بيصير كل
+
+512
+00:39:56,410 --> 00:40:01,750
+هنا إشمع من XI J التي عرفناها
+
+513
+00:40:01,750 --> 00:40:06,250
+TX XI J في J هذا as n goes to infinity بيصير هيلية
+
+514
+00:40:06,250 --> 00:40:11,900
+فهو بيصير هذا النقص هذا تقوله أحلاميين للزيرو لكن
+
+515
+00:40:11,900 --> 00:40:16,260
+الـ Tn اللي هو a sequence where norm of Tn X
+
+516
+00:40:16,260 --> 00:40:19,080
+بتروح لـ 0 as N goes to infinity لجبته لكن قبل
+
+517
+00:40:19,080 --> 00:40:25,340
+بشوية الـ Tn does not converge uniformly does not
+
+518
+00:40:25,340 --> 00:40:29,260
+converge to T  T can't be an element in B(X,Y) فهذا اللي هو
+
+519
+00:40:29,260 --> 00:40:32,360
+بيعطيني اللي هو strongly or weakly conversion of
+
+520
+00:40:32,360 --> 00:40:37,420
+Tn so it need not imply that T is an element in B(X,Y)
+
+521
+00:40:37,420 --> 00:40:47,040
+or Y يعني رغم هيك كان عنديالـ TN عشان ابعدنا طبعا
+
+522
+00:40:47,040 --> 00:40:51,900
+مش هيكون uniformly أكيد مش هيكون uniformly أه مش
+
+523
+00:40:51,900 --> 00:40:56,340
+هيكون uniformly لإن شو معناته uniformly أنك تقدر
+
+524
+00:40:56,340 --> 00:41:00,200
+تحسب ان norm الـ TN ناقص الـ T لكن أنا ماقدرش
+
+525
+00:41:00,200 --> 00:41:03,480
+أحسبه أصلا لإن الـ T أشمالها has not bounded باشي
+
+526
+00:41:03,480 --> 00:41:09,640
+الحال فالأن أثبتنا أن TN X بتروح للـ TX strongly
+
+527
+00:41:11,650 --> 00:41:18,230
+الـ T is not in B(X,Y) أو Y يعني الآن اللي
+
+528
+00:41:18,230 --> 00:41:21,230
+هو الـ strong convergence طبعا مادام الـ strong
+
+529
+00:41:21,230 --> 00:41:25,570
+convergence ده أكيد أشمل weak convergence إذن سواء
+
+530
+00:41:25,570 --> 00:41:28,790
+strong أو weak مش هيقدر يكون مؤهل يودّي الـ T في
+
+531
+00:41:28,790 --> 00:41:32,970
+الـ B(X,Y) نيجي
+
+532
+00:41:32,970 --> 00:41:39,610
+نشوف كده إجتماعيل يلّا
+
+533
+00:41:39,610 --> 00:41:46,850
+ما بنخلصين تفكّر على لما let X be a Banach space وY
+
+534
+00:41:46,850 --> 00:41:49,550
+a Banach space and T and B a sequence of elements
+
+535
+00:41:49,550 --> 00:41:53,910
+in B(X,Y) that converge strongly to a limit T
+
+536
+00:41:53,910 --> 00:41:57,910
+is an element in B(X,Y) then T is an element in B(X,Y)
+
+537
+00:41:57,910 --> 00:42:03,570
+إذا أنا بقولك أنت
+
+538
+00:42:03,570 --> 00:42:07,870
+ممكن تكون في ذكية بسيطة تخلي اللي هو الـ strongly
+
+539
+00:42:07,870 --> 00:42:13,050
+convergentأه يخلّي الـ Limit وإن موجودة في الـ B(X,Y)
+
+540
+00:42:13,050 --> 00:42:17,290
+وY بس اللي مطلوب أن الـ X وY يكونوا إيه الشمالين
+
+541
+00:42:17,290 --> 00:42:24,770
+بنخس Basis ماشي لإنه هيحولك اللي هو هيحصل على ال
+
+542
+00:42:24,770 --> 00:42:28,450
+boundedness المفقود أو اللي هو ال boundedness
+
+543
+00:42:28,450 --> 00:42:35,970
+لميلة T نشوف كيف أو حتى ال sequence نفسها تصير الـ
+
+544
+00:42:35,970 --> 00:42:40,290
+T أن تروح خلّيني أقول Roughly بالـ TN uniformly it
+
+545
+00:42:40,290 --> 00:42:43,190
+is left to the reader to prove that T is linear
+
+546
+00:42:43,190 --> 00:42:48,090
+سيبها لكم الان since TN X بتروح لل TX لكل X
+
+547
+00:42:48,090 --> 00:42:53,130
+element in X by Lemma 1.4.2 A the sequence TN X is
+
+548
+00:42:53,130 --> 00:42:57,070
+bounded اتفاقنا عليه اه عارفين هو هذا TN X بتروح
+
+549
+00:42:57,070 --> 00:43:01,970
+لل TX في ال norm تبع مين؟ تبع ال X تبع ال Y و ال Y
+
+550
+00:43:01,970 --> 00:43:05,430
+إذا بنخس بي اس إذا TN X الشمال هتكون is bounded
+
+551
+00:43:05,430 --> 00:43:11,650
+however X is complete صارت هذه bounded و الـ X is
+
+552
+00:43:11,650 --> 00:43:14,550
+complete إذا بالـ Uniform Boundedness Theorem
+
+553
+00:43:14,550 --> 00:43:19,290
+هتحولك الـ boundedness لهذه لـ boundedness لميه
+
+554
+00:43:19,290 --> 00:43:22,830
+للـ TN هتصير اللي هي نوم الـ TN أصغر شهر و C for
+
+555
+00:43:22,830 --> 00:43:27,650
+all N يعني independent of X بتصير هذا الـ Uniform
+
+556
+00:43:27,650 --> 00:43:33,170
+Boundedness وهذه بتطلب الـ X إيش تكون complete هنا
+
+557
+00:43:33,170 --> 00:43:36,030
+Hence خدوا نورم الـ TN X هيكون أصغر أو ساوى نورم
+
+558
+00:43:36,030 --> 00:43:40,130
+الـ TN في نورم الـ X وهذه أصغر أو ساوى C في نورم
+
+559
+00:43:40,130 --> 00:43:43,770
+الـ X الآن دخلوا ال limit علي الجهد التاني
+
+560
+00:43:43,770 --> 00:43:46,470
+وستستخدموا ال continuity لل TN و ال continuity لل 
+
+561
+00:43:46,470 --> 00:43:50,840
+هذا صار أصغر أو يساوي C في norm X دخلوا ال limit هنا
+
+562
+00:43:50,840 --> 00:43:54,100
+واستخدوا ال continuity لل TN و ال continuity لل norm
+
+563
+00:43:54,100 --> 00:43:59,640
+لل norm بس يوم norm limit ال TN ال X هو TX وهذا
+
+564
+00:43:59,640 --> 00:44:02,760
+limit اللي هو norm TN X أصغر أو يساوي C في norm X
+
+565
+00:44:02,760 --> 00:44:06,840
+hence اللي هي صارت عند T is bounded then T element
+
+566
+00:44:06,840 --> 00:44:14,000
+in B(X,Y) أو B(X) اطلع لفوق بعدها let X و Y يكون
+
+567
+00:44:14,000 --> 00:44:19,140
+باناخ سباسي و TN يكون سيكوانس من الأشياء المينة في
+
+568
+00:44:19,140 --> 00:44:24,320
+B(X) و B(Y) إذا X و Y أشمل باناخ سباسي و TN سيكوانس في B
+
+569
+00:44:24,320 --> 00:44:30,900
+(X,Y) و B(X) ثم TN تتعامل بشكل قوي إذا كانت تتعامل بشكل
+
+570
+00:44:30,900 --> 00:44:33,500
+قوي إذا كانت تتعامل بشكل قوي إذا كانت تتعامل بشكل
+
+571
+00:44:33,500 --> 00:44:38,290
+قوي اللي هو الـ sequence TNX is Cauchy in Y for
+
+572
+00:44:38,290 --> 00:44:42,670
+every X in a total subset M of X ما هي الـ
+
+573
+00:44:42,670 --> 00:44:47,750
+TNX مزام converge إذا Cauchy ما يمشي الحال Cauchy
+
+574
+00:44:47,750 --> 00:44:51,730
+إذا سواء Cauchy كانت الـ X في الـ Y نفسها أو في
+
+575
+00:44:51,730 --> 00:44:54,790
+الـ X نفسها أو في subset منها إذا الـ automatic
+
+576
+00:44:54,790 --> 00:44:58,150
+هذا جزء منها زي ما حكينا في الجبل طيب
+
+577
+00:45:00,170 --> 00:45:04,890
+بالتدريج if TN X بتروح ل TX لكل X element in X
+
+578
+00:45:04,890 --> 00:45:09,590
+يعني strongly هذا إيش معناه strongly then TN X is
+
+579
+00:45:09,590 --> 00:45:14,990
+bounded ماشي الحال أخذناها and so بقى uniform
+
+580
+00:45:14,990 --> 00:45:18,810
+bounded نص فيهم إيش هتطلع norm TN is bounded إذن
+
+581
+00:45:18,810 --> 00:45:22,850
+هذه automatic طلعت في حالة تسأل هي مين فردت اللي هو
+
+582
+00:45:22,850 --> 00:45:26,110
+الـ strongly convergence الآن بيجي from the
+
+583
+00:45:26,110 --> 00:45:29,850
+definition of strongly operator convergence and
+
+584
+00:45:29,850 --> 00:45:33,840
+the fact that every convergence sequence is Cauchy اللي
+
+585
+00:45:33,840 --> 00:45:36,340
+هو ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+586
+00:45:36,340 --> 00:45:36,460
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+587
+00:45:36,460 --> 00:45:36,520
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+588
+00:45:36,520 --> 00:45:36,560
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+589
+00:45:36,560 --> 00:45:36,800
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+590
+00:45:36,800 --> 00:45:37,320
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+591
+00:45:37,320 --> 00:45:37,380
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+592
+00:45:37,380 --> 00:45:42,680
+ال .. ال .. ال .. ال ..
+
+593
+00:45:42,680 --> 00:45:47,360
+ال
+
+594
+00:45:47,360 --> 00:45:48,280
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+595
+00:45:48,280 --> 00:45:48,360
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+596
+00:45:48,360 --> 00:45:56,920
+ال .. ال .. ال .. ال .. ال
+
+597
+00:46:03,400 --> 00:46:06,960
+اطلع لفوق مشابه للي حكينا قبل بشوية suppose that a
+
+598
+00:46:06,960 --> 00:46:09,860
+and b holds then there exists c أكبر من صفر such
+
+599
+00:46:09,860 --> 00:46:12,880
+that norm T أن يش ماله أصغر أو يساوي c من
+
+600
+00:46:12,880 --> 00:46:17,680
+المعطى for all n since m is totally in x فزي ما
+
+601
+00:46:17,680 --> 00:46:21,480
+عملنا قبل بشوية ال span ل ال m أن يش ماله then is في
+
+602
+00:46:21,480 --> 00:46:25,900
+ال x ما دام span لـ M دنس في الـ X إذا لكل X في الـ
+
+603
+00:46:25,900 --> 00:46:29,280
+X بقدر ألاقي sequence من هنا اللي هو Converge إلها
+
+604
+00:46:29,280 --> 00:46:35,000
+أو بقدر أقول لكل X هنا بقدر أخد المسافة بينها وبين
+
+605
+00:46:35,000 --> 00:46:38,620
+اللي هو elements من هنا صغيرة صغيرة صغيرة جدا زي
+
+606
+00:46:38,620 --> 00:46:47,360
+ما بدي فاهمين؟ الآن يا جماعة ال span لـ M دنس في
+
+607
+00:46:47,360 --> 00:46:54,950
+من؟ في الـ X إذا لكل X في الـ X اللي هو بقدر ألاقي
+
+608
+00:46:54,950 --> 00:47:01,130
+element في الـ M يكون very close إليه لأن هي أصلا
+
+609
+00:47:01,130 --> 00:47:04,870
+dense فيه فبكون عندي for every Y أكبر من 0 there
+
+610
+00:47:04,870 --> 00:47:08,190
+exists Y element اسمها للـ M such that normal X
+
+611
+00:47:08,190 --> 00:47:14,880
+minus Y أن يش ماله أصغر من Y على 3C لأن الـ M
+
+612
+00:47:14,880 --> 00:47:22,420
+dense في الـ X، أي X هنا can be .. we can find M Y
+
+613
+00:47:22,420 --> 00:47:26,580
+في الـ span تكون very close له، نفس منطقة الـ
+
+614
+00:47:26,580 --> 00:47:30,560
+sequence، وبرمجانه سهل، ال norm X minus Y أصغر من
+
+615
+00:47:30,560 --> 00:47:33,300
+Y على مين؟ على تلاتة C، يعني زغرت المسافة زي ما
+
+616
+00:47:33,300 --> 00:47:38,320
+بديالان من B اللي هو Tny is Cauchy مدام Cauchy
+
+617
+00:47:38,320 --> 00:47:44,320
+بقدر عليها K بحيث أن Tny نقص Tmy أصغر من أي أبسلون
+
+618
+00:47:44,320 --> 00:47:46,580
+في الدنيا من ضمن هذه الأبسلون على تلاتة اللي بديها
+
+619
+00:47:46,580 --> 00:47:52,620
+الآن therefore لكل M و N أكبر من K اللي جيت هنا
+
+620
+00:47:53,810 --> 00:47:59,530
+بحصل معالي وأنا fixed x we have احسبلي Tnx نقص Tmx
+
+621
+00:47:59,530 --> 00:48:03,690
+اللي هو أصغر أو يساوي ضيفوا الtermين واطرحوهن
+
+622
+00:48:03,690 --> 00:48:07,310
+واستخدموا ال triangle inequality أصغر أو يساوي Tnx
+
+623
+00:48:07,310 --> 00:48:15,320
+نقص Tny زي Tmy نقص Tmx الآن نفس اللي عملته قبل
+
+624
+00:48:15,320 --> 00:48:19,760
+بشوية هذي بيصير أصغر TN of X minus Y إذا أصغر يسوي
+
+625
+00:48:19,760 --> 00:48:25,100
+norm TN في norm X minus Y وهذه التانية أصغر من مين
+
+626
+00:48:25,100 --> 00:48:29,900
+من Y على 3 حكيناها وهذه نفس اللي عملته قبل بشوية
+
+627
+00:48:29,900 --> 00:48:33,900
+في البرهان اللي في المحاضرة اللي فاتت norm TN في
+
+628
+00:48:33,900 --> 00:48:39,510
+norm Y minus X الآن هذا أصغر أو يساوي C وهذا أصغر من
+
+629
+00:48:39,510 --> 00:48:44,990
+Y على 3C وهذه Y على 3 وهذا أصغر من C وهذا
+
+630
+00:48:44,990 --> 00:48:48,610
+أصغر من Y على 3C وكل معلومات أصغر من مين من Y
+
+631
+00:48:48,610 --> 00:48:52,510
+وإذا صار عندي ال TNX نقص TNX أصغر من أي Y في
+
+632
+00:48:52,510 --> 00:48:56,130
+الدنيا ماشي الحال إذا صارت ال TNX عبارة عن إيه
+
+633
+00:48:56,130 --> 00:48:59,550
+كوشي سيكوينس كوشي سيكوينس وفيه complete إذا
+
+634
+00:48:59,550 --> 00:49:03,010
+converges إذا صارت عند T and X converges in B and
+
+635
+00:49:03,010 --> 00:49:07,350
+Y وهذا يعني T and X converges strongly آخر
+
+636
+00:49:07,350 --> 00:49:12,210
+corollary منها اللي هي a sequence of N of bounded
+
+637
+00:49:12,210 --> 00:49:17,810
+linear functionals on a باناخ space X is weak star
+
+638
+00:49:17,810 --> 00:49:22,680
+convergence القاعدة تكون عبارة عن عبارة عالية على X
+
+639
+00:49:22,680 --> 00:49:25,240
+إذا كانت عبارة عنها عبارة عنها عبارة عنها عبارة
+
+640
+00:49:25,240 --> 00:49:25,940
+عنها عبارة عنها عبارة عنها عبارة عنها عبارة عنها
+
+641
+00:49:25,940 --> 00:49:26,640
+عبارة عنها عبارة عنها عبارة عنها عبارة عنها عبارة
+
+642
+00:49:26,640 --> 00:49:26,780
+عنها عبارة عنها عبارة عنها عبارة عنها عبارة عنها
+
+643
+00:49:26,780 --> 00:49:28,460
+عبارة عنها عبارة عنها عبارة عنها عبارة عنها عبارة
+
+644
+00:49:28,460 --> 00:49:29,300
+عنها عبارة عنها عبارة عنها عبارة عنها عبارة عنها
+
+645
+00:49:29,300 --> 00:49:30,640
+عبارة عنها عبارة عنها عبارة عنها عبارة عنها عبارة
+
+646
+00:49:30,640 --> 00:49:34,260
+عنها عبارة عنها عبارة
+
+647
+00:49:34,260 --> 00:49:34,760
+عنها ع
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/c4_dQ90VN3U_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/c4_dQ90VN3U_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5089635b9789489bf252c05d365686cb4aa931d2
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/c4_dQ90VN3U_raw.srt
@@ -0,0 +1,2612 @@
+1
+00:00:05,260 --> 00:00:07,600
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,600 --> 00:00:10,240
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,240 --> 00:00:13,700
+آله والصحابي أجمعين هذه المحاضرة رقم تلاتة وتلاتين
+
+4
+00:00:13,700 --> 00:00:19,300
+مساق تحليل اقتراني أو تحليل دالي طلاب طالبات
+
+5
+00:00:19,300 --> 00:00:22,620
+الجامعة الإسلامية ماجستير وصلنا هنا عند أربعة تسعة
+
+6
+00:00:22,620 --> 00:00:25,460
+اللي هو convergence of sequences of operators and
+
+7
+00:00:25,460 --> 00:00:30,050
+functionalsاللي هان المرة الفاتة احنا حكينا طبعا
+
+8
+00:00:30,050 --> 00:00:32,910
+احنا حكينا عن اللي هو ال convergence في ال normed
+
+9
+00:00:32,910 --> 00:00:37,230
+space بالنسبة لل sequences في ال normed space قلنا
+
+10
+00:00:37,230 --> 00:00:39,570
+لو كان في عند ال sequence في ال normed space xn
+
+11
+00:00:39,570 --> 00:00:44,250
+بتروح لل x strongly و xn بتروح لل x اللي هو mean
+
+12
+00:00:44,250 --> 00:00:47,470
+weekly وعرفله شو معناته strongly وشو معناته weakly
+
+13
+00:00:48,150 --> 00:00:52,250
+لحظوا احنا ال .. ال .. ال .. عادة لما كنا نحكي لما
+
+14
+00:00:52,250 --> 00:00:55,270
+نشتغل في الـ Real Analysis أو في ال Complex لما
+
+15
+00:00:55,270 --> 00:00:57,770
+نحكي عن Convergence كنا نحكي عن Convergence واحد
+
+16
+00:00:57,770 --> 00:01:00,790
+اللي هو الـ X بتروح للـ X اللي هو مانحكيش لا
+
+17
+00:01:00,790 --> 00:01:04,790
+Weekly ولا Convergence ولا .. ولا Strongly تبع
+
+18
+00:01:04,790 --> 00:01:08,570
+للحديث، ركزوا في الكلمتين تبع للحديث إنه احنا في
+
+19
+00:01:08,570 --> 00:01:13,570
+الـ Rأو في الـ C الـ dimension للـ R أو للـ C is
+
+20
+00:01:13,570 --> 00:01:16,910
+finite فبما أنه is finite إذا بيكون ال weak و ال
+
+21
+00:01:16,910 --> 00:01:22,090
+strong إيش ما له اللي هو are the same الآن بأيضا
+
+22
+00:01:22,090 --> 00:01:25,770
+في لما كنا نحكي في التحليل في التحليل اللي هو
+
+23
+00:01:25,770 --> 00:01:30,190
+الحقيقي كنا لما نيجي نحكي عن sequence of functions
+
+24
+00:01:30,750 --> 00:01:34,850
+كنا نحكي عن نوعين من الـ convergence FN بتروح للـ
+
+25
+00:01:34,850 --> 00:01:38,290
+F اللي هو بنسكت، شو معناه F ان كنا نسميها
+
+26
+00:01:38,290 --> 00:01:41,710
+pointwise convergence وكنا نحكي عن convergence
+
+27
+00:01:41,710 --> 00:01:46,610
+تاني اللي هو FN بتروح uniformly لمين؟ للـ Fالآن
+
+28
+00:01:46,610 --> 00:01:51,370
+العالم الجديد هذا مشابه هحكي عن convergence لـ
+
+29
+00:01:51,370 --> 00:01:54,890
+functions هنا هحكي عن convergence ل operators اللي
+
+30
+00:01:54,890 --> 00:01:59,770
+هي دول برضه في النهاية الآن تبعاً للمنطق اللي
+
+31
+00:01:59,770 --> 00:02:03,170
+استشغلناه هنا برضه هيكون في عندى بدل اتنين من
+
+32
+00:02:03,170 --> 00:02:07,030
+انواع ال convergence هيكون في عندى اللي هو three
+
+33
+00:02:07,030 --> 00:02:12,320
+من ال convergenceطبعاً لأني أنا بحكي عن اللي هو
+
+34
+00:02:12,320 --> 00:02:16,460
+normed spaces in general أما الحديث في الـ real أو
+
+35
+00:02:16,460 --> 00:02:19,920
+كده كل حديث في number أو في finite dimensional
+
+36
+00:02:19,920 --> 00:02:24,940
+space خلينا نشوف كيف بدنا نحكي عن اللي هو ال
+
+37
+00:02:24,940 --> 00:02:29,280
+sequence of operators إيش الأنواع ال convergence
+
+38
+00:02:29,280 --> 00:02:33,160
+بالنسبة إليها اللي هندرسها let x and y be normed
+
+39
+00:02:33,160 --> 00:02:38,140
+space أو spaces a sequence TN of operators هذه T1
+
+40
+00:02:38,890 --> 00:02:41,990
+bounded linear operator T2 bounded linear operator
+
+41
+00:02:41,990 --> 00:02:45,450
+إلى آخر هي دي sequence من العناصر اللي هي من ال
+
+42
+00:02:45,450 --> 00:02:48,530
+bounded linear operators اللي في B X Y ده set of
+
+43
+00:02:48,530 --> 00:02:52,430
+all bounded linear operators من X لعندي M لعندي I
+
+44
+00:02:52,430 --> 00:02:56,270
+إذا عرفنا العالم اللي بنشتغل فيه اللي هو عبارة عن
+
+45
+00:02:56,270 --> 00:03:01,830
+B of X وY وعناصره اللي هي عناصر ال sequence TN من
+
+46
+00:03:01,830 --> 00:03:06,370
+هذا اللي هو ال space اللي هم بده يبدأ يعرفكم إيش
+
+47
+00:03:06,370 --> 00:03:11,320
+ال convergence واحدuniformly convergent if TN
+
+48
+00:03:11,320 --> 00:03:18,780
+converges in the norm of B X Y مجرد
+
+49
+00:03:18,780 --> 00:03:23,340
+اللي هي مين بنحكي في ال norm تبع مين تبع ال B نفسه
+
+50
+00:03:23,340 --> 00:03:27,040
+اللي هو that is there is T من X لعند Y such that
+
+51
+00:03:27,040 --> 00:03:30,120
+norm TN نقص T بتروح ل 0 as N goes from mean to
+
+52
+00:03:30,120 --> 00:03:34,810
+infinityإذن وكان إنه شبيه بالـ Strongly بس هنا الـ
+
+53
+00:03:34,810 --> 00:03:39,270
+Strongly كان جاعد في الـ X هذا جاعد في مين؟ في الـ
+
+54
+00:03:39,270 --> 00:03:45,570
+Bxy لإن الـ X عناصره Xn بتروح للـ X Strongly
+
+55
+00:03:45,570 --> 00:03:49,450
+معناته Normal Xn نقص الـ X بتروح لـ Zero هنا الآن
+
+56
+00:03:49,450 --> 00:03:55,610
+العناصر هنا دوالTn بتروح للـT اللي هو with respect
+
+57
+00:03:55,610 --> 00:03:59,610
+to space هذا strongly اسمه لكن عشان نميزه عن
+
+58
+00:03:59,610 --> 00:04:04,670
+strongly اللي بعد شوية هنقول عنه uniformly يعني Tn
+
+59
+00:04:04,670 --> 00:04:13,310
+بتروح للـT uniformly معنى بإن نورم الـTn ناقص T هو
+
+60
+00:04:13,310 --> 00:04:17,450
+اللي بيروح لمين للـ0 والنورم هذا هو النورم تبع مين
+
+61
+00:04:17,450 --> 00:04:23,730
+تبع الـP X أو Yفي convergence آخر اللي هو بنقول
+
+62
+00:04:23,730 --> 00:04:27,390
+strongly convergence شبيه بال pointwise
+
+63
+00:04:27,390 --> 00:04:33,410
+convergence تبع زمان اللي هو إيش بقول اطلع لفوق if
+
+64
+00:04:33,410 --> 00:04:37,870
+TN X converge strongly in Y for every mean X
+
+65
+00:04:37,870 --> 00:04:43,270
+element in X إذا الآن بنيجي عندى في عندى sequence
+
+66
+00:04:43,270 --> 00:04:51,510
+TN في الـP XY في الـ BX و Y TN في الـ BX و Y عند
+
+67
+00:04:51,510 --> 00:04:56,590
+TN في الـ BX و Y و بناخد أي X وين موجودة في الـ X
+
+68
+00:04:56,590 --> 00:05:03,710
+أي X وين موجودة في الـ X بدي أحكي عن اللي هو TNX
+
+69
+00:05:03,710 --> 00:05:08,490
+converged لمين لـ TX هذه الـ sequence صارت of
+
+70
+00:05:08,490 --> 00:05:12,270
+elements وين موجودة في الـ Y بس بحكي عن X محددة
+
+71
+00:05:12,270 --> 00:05:19,730
+وين موجودة في الـ X بقول TNXبتروح للـ TX strongly
+
+72
+00:05:19,730 --> 00:05:27,710
+إذا كان نورم الـ TNX ناقص TX بروح للـ 0 as N goes
+
+73
+00:05:27,710 --> 00:05:30,810
+from mean to infinity لحظة أنا شغلي هذا نورم الـ
+
+74
+00:05:30,810 --> 00:05:34,090
+TNX والـ TX وين موجود في الـ Y وكأن عالم اللي
+
+75
+00:05:34,090 --> 00:05:38,210
+بشتغل فيه مين هو اللي هو الـ Y اطلع لفوق
+
+76
+00:05:42,260 --> 00:05:46,360
+وإذا كانت تتعامل بشكل قوى إذا كانت T و X تتعامل
+
+77
+00:05:46,360 --> 00:05:52,480
+بشكل قوى بشكل Y لكل X في أقل X، هذا يعني أن هناك T
+
+78
+00:05:52,480 --> 00:05:56,660
+في أقل X و Y مثل ذلك، نورم T و X يذهب إلى T و X
+
+79
+00:05:56,660 --> 00:06:01,560
+نقص T و X يذهب إلى Zero كما أن N يذهب إلى أقل لكل
+
+80
+00:06:01,560 --> 00:06:05,880
+X في أقل من من في X هو لو تعمقت في القمر و في
+
+81
+00:06:05,880 --> 00:06:09,980
+الواقع اللي هو T و X تذهب إلى T و X بشكل قوى في
+
+82
+00:06:09,980 --> 00:06:16,990
+من؟في النوم تبع ال Yوهذه Tn بتروح للـ T strongly
+
+83
+00:06:16,990 --> 00:06:22,050
+برضه بس في الـ norm تبع ال B هذه بنسميها اللي هي
+
+84
+00:06:22,050 --> 00:06:26,190
+uniform convergence لأهمية ال convergence هذا اللي
+
+85
+00:06:26,190 --> 00:06:31,330
+هو .. او لعدم اعتماد Tn-T في ال convergence على ال
+
+86
+00:06:31,330 --> 00:06:36,250
+X المحددة هنا اللي كنا نسميه زمان ال uniform
+
+87
+00:06:36,250 --> 00:06:39,150
+convergence في ال functions العادية وهذه كنا
+
+88
+00:06:39,150 --> 00:06:43,590
+نسميها pointwise convergenceالان هذولا النوعين ما
+
+89
+00:06:43,590 --> 00:06:47,430
+كانوا نوعين قديمات الان النوع الثالث الجديد اللي
+
+90
+00:06:47,430 --> 00:06:50,550
+هو الـ weakly convergent اللي هو الـ weakly
+
+91
+00:06:50,550 --> 00:06:54,630
+convergent ان الـ TNX converge اللي هو ايه اش ماله
+
+92
+00:06:54,630 --> 00:07:03,150
+weakly to some T ماشي الحال الان TNX شو معناه TN
+
+93
+00:07:03,150 --> 00:07:07,690
+TN X
+
+94
+00:07:09,460 --> 00:07:15,880
+converges weakly to TX نفس اللي قدلنا المرة اللي
+
+95
+00:07:15,880 --> 00:07:19,600
+فاتت يعني مش ليش جديد نفس اللي حكينا عنه في
+
+96
+00:07:19,600 --> 00:07:25,080
+المحاضرة اللي فاتت for every F element اللي هو N
+
+97
+00:07:25,080 --> 00:07:33,120
+اللي هي الـY' عندي يجب أن يكون F of T and X ناقص F
+
+98
+00:07:33,120 --> 00:07:40,560
+of T Xconverge to zero as n goes to infinity الان
+
+99
+00:07:40,560 --> 00:07:44,220
+واحده انه هذا وهذا هيصير زي بعض في حالة الـ finite
+
+100
+00:07:44,220 --> 00:07:48,640
+dimensional space عشان هيك احنا مابنحكيش عنه في ال
+
+101
+00:07:48,640 --> 00:07:50,880
+.. في ال .. في الـ real العادى ولا في ال complex
+
+102
+00:07:50,880 --> 00:07:54,640
+العادى بنحكي عن نوعين من ال convergence لل
+
+103
+00:07:54,640 --> 00:07:58,340
+functions او لل operators واحد اسمه uniformly واحد
+
+104
+00:07:58,340 --> 00:08:02,780
+اسمه pointwiseالآن هذا عنا هنا هنسميه uniformly
+
+105
+00:08:02,780 --> 00:08:07,440
+uniformly هنسمي ال point wise strongly و هنسمي ال
+
+106
+00:08:07,440 --> 00:08:11,680
+weakly اللي هو بالتسمياء و بالمفهوم اللي حكيناه
+
+107
+00:08:11,680 --> 00:08:16,340
+المرة اللي فاتت في المحاضرة السابقة نيجي الآن واضح
+
+108
+00:08:16,340 --> 00:08:22,600
+واضح أنه من خلال التعريف اللي حكيناها أنه ال TN
+
+109
+00:08:22,600 --> 00:08:27,660
+أنه
+
+110
+00:08:27,660 --> 00:08:31,590
+لما نقول TNالـ Uniform Convergence، الـ Operator
+
+111
+00:08:31,590 --> 00:08:34,930
+Convergence، يعني قوة قوة قوة قوة قوة قوة قوة قوة
+
+112
+00:08:34,930 --> 00:08:38,110
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+113
+00:08:38,110 --> 00:08:38,570
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+114
+00:08:38,570 --> 00:08:39,550
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+115
+00:08:39,550 --> 00:08:40,650
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+116
+00:08:40,650 --> 00:08:48,150
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+117
+00:08:48,150 --> 00:08:54,050
+قو
+
+118
+00:08:55,430 --> 00:09:00,010
+شو معناته اللي هو اللي هو عندي طبعا الـ TN عجبه عن
+
+119
+00:09:00,010 --> 00:09:06,090
+sequence element in B X Y و الـ T برضه element in
+
+120
+00:09:06,090 --> 00:09:15,150
+B X Y اللي هو شو معناته انه uniformly ال norm TN
+
+121
+00:09:15,150 --> 00:09:22,150
+نقص T تروح للـ 0 as N goes to infinity لان letاللي
+
+122
+00:09:22,150 --> 00:09:32,450
+هو TN X هالجي تاخد for every X element in X let TN
+
+123
+00:09:32,450 --> 00:09:38,050
+X converge لمين لـ TX strongly إيش معناته معناته
+
+124
+00:09:38,050 --> 00:09:43,130
+norm الـ TN X نقص TX اللي هو إيش مهلا بروح لصفر
+
+125
+00:09:43,130 --> 00:09:47,670
+هذا اللي بدأ تبته صح؟ الآن بدأ أثبت هذه مانعش أقول
+
+126
+00:09:47,670 --> 00:09:52,490
+it بدأ أثبت هذهأخذت X أشمالها arbitrarily وحسبني
+
+127
+00:09:52,490 --> 00:09:58,090
+الآن norm of TN X ناقص مين TX هذا بتساوي norm of
+
+128
+00:09:58,090 --> 00:10:03,870
+TN ناقص T X وهذه اللي هي أصغر تساوي norm of TN
+
+129
+00:10:03,870 --> 00:10:09,170
+ناقص T في norm X مدام strongly إذا هذا بيروح لـ0
+
+130
+00:10:09,170 --> 00:10:16,120
+إذا هذا بيروح لـ0 إذا صارت TN Xهتروح للـ TX
+
+131
+00:10:16,120 --> 00:10:20,700
+strongly وهو المطلوب التاني سهل نفس الأسلوب الآن
+
+132
+00:10:20,700 --> 00:10:27,500
+بتاخد let X element in X و F element in main in Y'
+
+133
+00:10:27,780 --> 00:10:30,700
+عشان أثبت main ال weekly
+
+134
+00:10:33,690 --> 00:10:38,870
+وبنفسي نفسي نفسي الأسلوب حتتاني أه الآن احنا
+
+135
+00:10:38,870 --> 00:10:41,950
+أثبتنا في ال .. في ال .. في ال .. في خلينا نقول في
+
+136
+00:10:41,950 --> 00:10:44,110
+ال normed space العادى الآن ده أثبتها لمي لل
+
+137
+00:10:44,110 --> 00:10:48,530
+operators برضه هيكون مشابه مشابه خالص الان norm
+
+138
+00:10:48,530 --> 00:10:58,610
+norm الحسبولي F of TN X ناقص F of TX فاهمين أه هذا
+
+139
+00:10:58,610 --> 00:11:04,290
+أصغر بسبب نورم ال F في norm ال TN ناقص Tفي نور
+
+140
+00:11:04,290 --> 00:11:08,550
+مين؟ الـ X هذا دستور مباشر أنه الـ uniform اللي
+
+141
+00:11:08,550 --> 00:11:13,650
+بيقدي ل مين؟ لل strongly هذا اللي هو بيبقى بيروح
+
+142
+00:11:13,650 --> 00:11:19,730
+لل zero as n goes to infinity إذاً F of T and X
+
+143
+00:11:19,730 --> 00:11:27,570
+بتروح لل F of T Xهذا أثبت لكم مين الـ uniformly
+
+144
+00:11:27,570 --> 00:11:34,810
+أدى إلى مين إلى الـ weekly يعني TNX
+
+145
+00:11:34,810 --> 00:11:39,470
+بتروح لTX
+
+146
+00:11:39,470 --> 00:11:42,750
+تقولوا معايا TNX بتروح لTX weekly
+
+147
+00:11:47,050 --> 00:11:50,310
+أثبتت أن F of T and X نقص F of T X بروح للـ Zero
+
+148
+00:11:50,310 --> 00:11:54,270
+As N goes to infinity لكل F element in Y' و X
+
+149
+00:11:54,270 --> 00:11:56,890
+element in X' هذا يعني أن T and X بتروح للـ T X
+
+150
+00:11:56,890 --> 00:12:00,930
+أشمالها Weekly هذا أثبته من وين؟ من الـ Uniform
+
+151
+00:12:00,930 --> 00:12:04,390
+يؤدي إلى الـ Weekly مباشرة Strong يؤدي إلى الـ
+
+152
+00:12:04,390 --> 00:12:09,070
+Weekly ما أثبته قبل بشوية أي سؤال؟ طيب يلّا لبعده
+
+153
+00:12:14,430 --> 00:12:17,570
+الأن الـ Converse لا يجب أن يكون عاملًا يعني فيه
+
+154
+00:12:17,570 --> 00:12:22,370
+في عندك اللي هو strong operator convergence لا يجب
+
+155
+00:12:22,370 --> 00:12:26,070
+أن يكون من ال uniform يعني بقدر أجيبلك اللي هو
+
+156
+00:12:26,070 --> 00:12:30,130
+strong convergence لكن ماله مش uniform convergence
+
+157
+00:12:30,130 --> 00:12:36,530
+خد الآن let TN be a sequence of operators where TN
+
+158
+00:12:36,530 --> 00:12:41,420
+من L2 لعند ما L2 is defined byانت عارفين طبعا ايش
+
+159
+00:12:41,420 --> 00:12:46,060
+الـ Normal على الـ L2 وكيف بنحسم وكيف كده المفروض
+
+160
+00:12:46,060 --> 00:12:51,080
+هذا كله يعني معلوم لنا من خلال اللي هي اللي هي
+
+161
+00:12:51,080 --> 00:12:56,800
+معلوماتنا في المادة سابقا نيجي الآن نشوف ايش اللي
+
+162
+00:12:56,800 --> 00:13:02,250
+بدنا نسويه بالظبطبدنا نجيب operator الآن أو
+
+163
+00:13:02,250 --> 00:13:07,430
+sequence of operators إنها الـ T and X بتروح للـ
+
+164
+00:13:07,430 --> 00:13:11,330
+TX هذا forever X اللي منتقلته الـ T and X بتروح
+
+165
+00:13:11,330 --> 00:13:18,080
+للـ TX strongly طبعا ولكن butنورم الـ TN ناقص الـ
+
+166
+00:13:18,080 --> 00:13:22,740
+T does not converge to 0 يعني الـ TN بتروحش لمن؟
+
+167
+00:13:22,740 --> 00:13:26,500
+للـ T uniformly يعني بدنا نثبت أن الـ TN does not
+
+168
+00:13:26,500 --> 00:13:32,060
+converge uniformly لمن؟ للـ T لمّا نجيب الـ
+
+169
+00:13:32,060 --> 00:13:35,080
+Sequence T نجيب الـ T إيش الـ space اللي اختارنا
+
+170
+00:13:35,080 --> 00:13:40,160
+اللي نشتغل عليه؟ الـ L2 مين هو ال operator؟ اللي
+
+171
+00:13:40,160 --> 00:13:46,870
+هو ال operator التالي TNمن الـ 2 عند الـ 2 كيف بدي
+
+172
+00:13:46,870 --> 00:13:50,950
+أعرفه ال element اللي في ال ال 2 ال X بيساوي كصي
+
+173
+00:13:50,950 --> 00:13:56,910
+واحد كصي اتنين كصي تلاتة كصي N كصي N زائد واحد إلى
+
+174
+00:13:56,910 --> 00:14:01,050
+مال نهاية ماشي هذا عنصر مين ال ال 2 الأن بدي
+
+175
+00:14:01,050 --> 00:14:05,810
+أعرفلكم ال TN إيش ال TN بتسوي بتيجي بتاخد لك ال X
+
+176
+00:14:05,810 --> 00:14:10,550
+هذا TN X بتيجي بت .. بت .. بت .. كل اللي قالها
+
+177
+00:14:10,550 --> 00:14:17,190
+هدولة بتسفرهابترسله هنا مين؟ لـ Zero Zero Zero
+
+178
+00:14:17,190 --> 00:14:22,390
+Zero عن طبعا هذا الـ N لهذه اللي هو Zn زائد واحد
+
+179
+00:14:22,390 --> 00:14:26,390
+او Xn زائد واحد Xn زائد اتنين و بيظل ماشي إلى ماله
+
+180
+00:14:26,390 --> 00:14:35,040
+نهاية يعني و كأنه بيقولي T1 X بساوي Zero X2T2X
+
+181
+00:14:35,040 --> 00:14:46,920
+بيساوي 0 0 X3 و بكمل T3X بيساوي 0 0 0 X4 X5 و بكمل
+
+182
+00:14:46,920 --> 00:14:50,340
+ماشي الحال إذا نوضح إيش ال sequence of operators
+
+183
+00:14:50,340 --> 00:14:55,470
+اللي عندى معاياهذه اللي هي الـ sequence of
+
+184
+00:14:55,470 --> 00:14:58,590
+operators where x اللي هي زي ما قلنا size J اللي
+
+185
+00:14:58,590 --> 00:15:02,770
+قلته it is easy to see that TN is linear for any N
+
+186
+00:15:02,770 --> 00:15:08,090
+Linear فهي سهل اثباتها خدوا الـ N X هيها خدوا Y
+
+187
+00:15:08,090 --> 00:15:13,450
+بساوي جامعة واحد جامعة اتنين لما لا نهاية الان T
+
+188
+00:15:13,450 --> 00:15:20,050
+Alpha X زائد Y فمين هو في ده اعملها TN بساوية TN
+
+189
+00:15:21,090 --> 00:15:26,510
+أيش α X زائد Y؟ اللي هي Alpha Xi 1 زائد Gamma 1
+
+190
+00:15:26,510 --> 00:15:32,030
+Alpha Xi 2 زائد Gamma 2 وبتظلها ماشية، ماشي؟ أيش
+
+191
+00:15:32,030 --> 00:15:35,530
+بتعمل ال Tn هذه؟ بتقول هي سفر، سفر و بيظل الأسافر
+
+192
+00:15:35,530 --> 00:15:41,510
+عند مين؟ Alpha N زائد 1 Alpha Xi N زائد 1 زائد
+
+193
+00:15:41,510 --> 00:15:45,550
+Gamma N زائد 1 و بتكمل، ماشي؟ اللي أنا بفصلها
+
+194
+00:15:45,550 --> 00:15:51,870
+الأجزاء، بسهولاللي هو Alpha في Zero Zero Zero و
+
+195
+00:15:51,870 --> 00:15:56,370
+Exide N زائد واحد و Exide N زائد اتنين و بنكمل
+
+196
+00:15:56,370 --> 00:16:03,510
+زائد Zero Zero Zero Gamma N زائد واحد و لما لا
+
+197
+00:16:03,510 --> 00:16:07,670
+نهاية و يساوي هذه Alpha هذه كلها مين هي عبارة عن
+
+198
+00:16:07,670 --> 00:16:13,710
+TN X و هذه مين هي TN Y إذا TN إزلينا و طول ما
+
+199
+00:16:13,710 --> 00:16:18,410
+تكتشف TN إيش معناها إزليناAlso for any n sense
+
+200
+00:16:18,410 --> 00:16:23,490
+norm of TNX بيحسبوا الـ TNX مين ال TNX اللي هي
+
+201
+00:16:23,490 --> 00:16:29,710
+هذولة هي هنا ال TNX هيها summation هذا تربيع زائد
+
+202
+00:16:29,710 --> 00:16:31,290
+هذا تربيع زائد هذا تربيع زائد هذا تربيع زائد هذا
+
+203
+00:16:31,290 --> 00:16:32,270
+تربيع زائد هذا تربيع زائد هذا تربيع زائد هذا تربيع
+
+204
+00:16:32,270 --> 00:16:32,630
+زائد هذا تربيع زائد هذا تربيع زائد هذا تربيع زائد
+
+205
+00:16:32,630 --> 00:16:32,790
+هذا تربيع زائد هذا تربيع زائد هذا تربيع زائد هذا
+
+206
+00:16:32,790 --> 00:16:32,810
+تربيع زائد هذا تربيع زائد هذا تربيع زائد هذا تربيع
+
+207
+00:16:32,810 --> 00:16:32,930
+زائد هذا تربيع زائد هذا تربيع زائد هذا تربيع زائد
+
+208
+00:16:32,930 --> 00:16:38,060
+هذا تربيع زائد هذا تربيعصار عندي طبعا الأول هدول
+
+209
+00:16:38,060 --> 00:16:41,800
+الأن أسفار فهيبدأ العد من وين؟ من n زاد واحد إلى
+
+210
+00:16:41,800 --> 00:16:45,720
+مال النهاية أكيد هو هذا أصغر أو شاوي العد من واحد
+
+211
+00:16:45,720 --> 00:16:48,060
+إلى مال النهاية هذا العد من واحد إلى مال نهاية هو
+
+212
+00:16:48,060 --> 00:16:52,380
+نورم ال X إذا صار نورم ال TL X أصغر أو شاوي مين؟
+
+213
+00:16:52,600 --> 00:16:56,800
+نورم الـ X اطلع لفوق الان اخدوا الان ال supermom
+
+214
+00:16:56,800 --> 00:17:01,080
+على نورم ال X بيصير ال supermom ايه؟ نورم ال TN
+
+215
+00:17:01,080 --> 00:17:06,260
+أكبر أو يسوى واحد اخلقوا معناه، ماشي؟ الان لو
+
+216
+00:17:06,260 --> 00:17:08,720
+اجينا .. بدي اثبتلك ان نورم ال TN أكبر أو يسوى
+
+217
+00:17:08,720 --> 00:17:12,220
+واحد بيصير نورم ال TN أيش بيسوى؟ بيسوى واحد و هذا
+
+218
+00:17:12,220 --> 00:17:14,960
+اللي هيخليني انه .. يعني أستحين انه .. ان النورم
+
+219
+00:17:14,960 --> 00:17:19,700
+يروح لمين؟ للسفر؟ نورم ال TN نقصتي؟ شوفوا moreover
+
+220
+00:17:19,700 --> 00:17:24,720
+if we choose X0بساوة صفر صفر صفر يعني هنرسلها
+
+221
+00:17:24,720 --> 00:17:30,320
+نفسها اه فبصير يعني اخدت هذه هي ال X note عساس انه
+
+222
+00:17:30,320 --> 00:17:33,780
+يصير TN X note ايش الساوية لإنه هيسفر المهمة
+
+223
+00:17:33,780 --> 00:17:37,890
+بصفرات مراسل فبتطلع TN X note بساوية X noteاللي
+
+224
+00:17:37,890 --> 00:17:41,070
+هنأنصره نورم الـ TN اللي هو الـ suprem of ما هين
+
+225
+00:17:41,070 --> 00:17:44,970
+كلين أكيد أكبر و سوى نورم ال specific value ال
+
+226
+00:17:44,970 --> 00:17:50,350
+specific function هذه أو specific computation عند
+
+227
+00:17:50,350 --> 00:17:53,550
+X0 يعني بمعنى آخر عن نورم الـ X0 هدي زي هدي بيطلع
+
+228
+00:17:53,550 --> 00:17:56,610
+أشمال واحد إذا نورم الـ TN أكبر سوى واحد إذا نصر
+
+229
+00:17:56,610 --> 00:18:00,040
+من التنتين مع بعض نورم الـ TN بيسوى واحدومنه
+
+230
+00:18:00,040 --> 00:18:04,760
+احسبوله الان norm of TN نقص Zero اللي احنا متوقعين
+
+231
+00:18:04,760 --> 00:18:09,020
+يروح عليه point اللي هو strong convergence ال TN
+
+232
+00:18:09,020 --> 00:18:12,960
+نقص Zero Zero operator بيساوي norm of TN ايش اللي
+
+233
+00:18:12,960 --> 00:18:17,220
+بيساوي؟ بيساوي واحد اذا هذا يستحيل يروح لمين؟
+
+234
+00:18:17,220 --> 00:18:23,270
+للصفرأذا T يعني غير الـ T1 و T2 و T3 و مش هيروح لا
+
+235
+00:18:23,270 --> 00:18:27,830
+إشي مش هيروح للصفر هيضلوا إش ما لواحد إذا which
+
+236
+00:18:27,830 --> 00:18:31,630
+implies that Tn is not uniformly convergent to
+
+237
+00:18:31,630 --> 00:18:35,350
+mean to the zero operator أنا بدأ أثبتلك الآن but
+
+238
+00:18:35,350 --> 00:18:40,350
+it converges strongly to the zero operator يعني
+
+239
+00:18:40,350 --> 00:18:44,850
+but it is clear that for all x element in L2 we
+
+240
+00:18:44,850 --> 00:18:50,810
+haveخد TNX احسب في موقع 4X معادل هي TNX as N goes
+
+241
+00:18:50,810 --> 00:18:54,930
+to infinity بسفر بسفر بسفر بسفر بسفر بسفر بسفر
+
+242
+00:18:54,930 --> 00:18:54,930
+بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر
+
+243
+00:18:54,930 --> 00:18:55,530
+بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر
+
+244
+00:18:55,530 --> 00:18:57,330
+بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر
+
+245
+00:18:57,330 --> 00:19:00,810
+بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر بسفر
+
+246
+00:19:00,810 --> 00:19:06,370
+بسفر بسفر بسللـ Zero operator إذا صار عندي هذا TN
+
+247
+00:19:06,370 --> 00:19:09,810
+converts strongly to اللي هو Zero operator إذا صار
+
+248
+00:19:09,810 --> 00:19:13,330
+عندي مثال uniformly convergent ب .. ب .. ب .. ب
+
+249
+00:19:13,330 --> 00:19:16,250
+strongly convergent which is not uniformly
+
+250
+00:19:16,250 --> 00:19:20,970
+convergent الآن بدنا ناخد مثال تاني اللي هو ال
+
+251
+00:19:20,970 --> 00:19:23,870
+weak operator convergence need not imply mean
+
+252
+00:19:23,870 --> 00:19:30,370
+strong operator إيش convergence الآن مثال .. مثال
+
+253
+00:19:30,370 --> 00:19:31,450
+برضه على دوال
+
+254
+00:19:36,310 --> 00:19:42,310
+الآن برضه عديالة نشوف الآن تشغلوش بالكم خلوكم
+
+255
+00:19:42,310 --> 00:19:45,630
+معايا الامتحان ينسوا الامتحان الـ weak operator
+
+256
+00:19:45,630 --> 00:19:48,310
+convergence لا يجب أن يمثل الـ strong operator
+
+257
+00:19:48,310 --> 00:19:52,870
+convergence ناخد الـ sequence اللي بتلبي هذا الغرض
+
+258
+00:19:52,870 --> 00:19:58,590
+شوفوا اللي هي برضه أنا هشتغل ع مين على الـ Hilbert
+
+259
+00:19:58,590 --> 00:20:02,470
+space أو الـ L2 أو الـ Hilbert sequence space
+
+260
+00:20:12,990 --> 00:20:22,930
+خدلي الان TN من الـ 2 لعند الـ L2 و خدلي طبعا اللي
+
+261
+00:20:22,930 --> 00:20:28,150
+هي معهودة X بتساوي XI I I من واحد إلى ملا نهاية
+
+262
+00:20:28,150 --> 00:20:36,570
+خدلي ال TN X بساوي الان سفرلي N مرة سفرها لكن لو
+
+263
+00:20:36,570 --> 00:20:40,880
+سمحت خليلي الباقي زي ما هو يعني اعملي shiftلأ الـ
+
+264
+00:20:40,880 --> 00:20:45,280
+operator هيك shift للـ X ارميها صفار صفار صفار N
+
+265
+00:20:45,280 --> 00:20:49,480
+من المرات و بعدين ابدأ اقول XI 1 XI 2 إلى ما
+
+266
+00:20:49,480 --> 00:20:53,880
+لنهاية هذا الآن ال operator برضه اللي هو هتلاقيه
+
+267
+00:20:53,880 --> 00:20:57,720
+bounded linear operator من اللي جابه مثل اللي جابه
+
+268
+00:20:57,720 --> 00:21:00,780
+قبل بشوية حليته مافيش داعي داعي دو where the
+
+269
+00:21:00,780 --> 00:21:04,540
+number of zeros is N and X بيستوي XI IIt is easy
+
+270
+00:21:04,540 --> 00:21:08,400
+to see that Tn is linear and bounded for any n الـ
+
+271
+00:21:08,400 --> 00:21:11,540
+boundedness سهل الـ linear تعملته الـ boundedness
+
+272
+00:21:11,540 --> 00:21:18,200
+خد Tn X إيش حيساوي ال summation of xi I تربيع I من
+
+273
+00:21:18,200 --> 00:21:21,460
+واحد إلى ملاها، صح ولا لأ؟ لإن هو .. بالحسب إن هو
+
+274
+00:21:21,460 --> 00:21:25,440
+أسفل و بعدين و بعدين و هو عبارة عن مين؟ norm أص
+
+275
+00:21:25,440 --> 00:21:29,940
+نص، هذا norm الـ Xبالظبط ولا لأ؟ إذا أكيد bounded
+
+276
+00:21:29,940 --> 00:21:34,340
+Tn X هو نورم واحد كمان مش bounded بس و نورم Tn
+
+277
+00:21:34,340 --> 00:21:42,040
+بسوء واحد بالظبط طيب اطلع على فوق since L2 is a
+
+278
+00:21:42,040 --> 00:21:44,900
+Hilbert space then every linear functional F
+
+279
+00:21:44,900 --> 00:21:49,520
+element in L2أسهل ليه في الـ L2 على طول بعمله الـ
+
+280
+00:21:49,520 --> 00:21:52,420
+Representation بالـ Ray's Representation الـ
+
+281
+00:21:52,420 --> 00:21:55,800
+theorem has Ray's Representation F of X بيساوي X و
+
+282
+00:21:55,800 --> 00:22:00,080
+Z و يساوي كالـ inner product بينهم اللي هو تبعات
+
+283
+00:22:00,080 --> 00:22:03,480
+هدف تبعات هدف بس كواحدة عادية واحدة conjugate XII
+
+284
+00:22:03,480 --> 00:22:07,000
+أو XIJ Gamma J conjugate J من واحد إلى ما ننهيها
+
+285
+00:22:07,000 --> 00:22:11,420
+حيث الـ Z هي تبعات Gamma J والـ X هي من XIIواضح
+
+286
+00:22:11,420 --> 00:22:15,180
+هذا الـ Z اللي لاجناها for every F element in L2
+
+287
+00:22:15,180 --> 00:22:22,040
+there exists Z such that F of X بيساومين X O Z لكن
+
+288
+00:22:22,040 --> 00:22:25,720
+من جهة أخرى أحسب للـ F of T X N بدي أثبت ليه
+
+289
+00:22:25,720 --> 00:22:32,400
+convergence لأن أنا بدي أثبتلك أن F of T X N بتروح
+
+290
+00:22:32,400 --> 00:22:39,180
+إلى F of something X N نشوف إيش هو الـ something
+
+291
+00:22:39,180 --> 00:22:39,500
+هنا
+
+292
+00:22:44,930 --> 00:22:49,590
+صلى على النبي عليه الصلاة والسلام احسب لي F of T N
+
+293
+00:22:49,590 --> 00:22:54,710
+X اللي هي بالساوي حسب اللي هي ال rule اللي عندى T
+
+294
+00:22:54,710 --> 00:22:59,990
+N X و Z و هذه اللي هي بالساوي T N X H هي اللي هي
+
+295
+00:22:59,990 --> 00:23:08,030
+طيب شوفوا كيف هدول السفر هياخدوا مينهيخدم مين هي
+
+296
+00:23:08,030 --> 00:23:12,610
+الـ Z جامعة واحد جامعة اتنين جامعة N جامعة N زائد
+
+297
+00:23:12,610 --> 00:23:16,650
+واحد الاخره الان ادول الاسفار هيخدم في طريقهم
+
+298
+00:23:16,650 --> 00:23:22,470
+هذوله لما نضرب من فيهم اذا هيبدأ العد ل XI واحد هو
+
+299
+00:23:22,470 --> 00:23:28,550
+XI N او جامعة N زائد واحد فطبيعي بساول هو XIJ
+
+300
+00:23:28,550 --> 00:23:32,210
+minus N Gamma J J من عند N زائد واحد إلى مين إلى
+
+301
+00:23:32,210 --> 00:23:35,550
+ما لا نهاية و اللي بده يبدأ بهدف J هدف الساقين هي
+
+302
+00:23:35,550 --> 00:23:44,310
+J زائد N و بده يبدأ يشتغل أو J من واحد فاهمين؟ هذا
+
+303
+00:23:44,310 --> 00:23:47,630
+اللي هو نفسه عبارة عن K من واحد إلى ما لا نهاية X
+
+304
+00:23:47,630 --> 00:23:52,520
+I K Gamma N K زائد واحد فاهمين؟كيف اللي هو غيرنا
+
+305
+00:23:52,520 --> 00:23:56,180
+ال index من هاللهان طيب الان by Cauchy Schwarzen
+
+306
+00:23:56,180 --> 00:24:01,180
+quality خد لهذه f of TNX اللي هو absolute value
+
+307
+00:24:01,180 --> 00:24:04,040
+لها وهذا ال absolute value وستخدم ال Cauchy
+
+308
+00:24:04,040 --> 00:24:09,060
+Schwarzen quality فبصير absolute value تربيع بساوي
+
+309
+00:24:09,060 --> 00:24:13,480
+هذه تربيع اللي هي أصغر أو اللي هي بساوي هذه نورم
+
+310
+00:24:13,480 --> 00:24:17,910
+هذه ماشي اللي هو تربيع أصغر أو .. فاهمين؟مسير أصغر
+
+311
+00:24:17,910 --> 00:24:21,770
+أو يساوي اللي هو summation هذا تربيع اللي جوا فال
+
+312
+00:24:21,770 --> 00:24:25,430
+summation هذا تربيع اللي جوا ال N هذا as N goes to
+
+313
+00:24:25,430 --> 00:24:29,590
+infinity هذا من وين بيبدأ ال K من M من N زائد واحد
+
+314
+00:24:29,590 --> 00:24:33,370
+إلى مانا النهاية هذا as N goes to infinity بتروح
+
+315
+00:24:33,370 --> 00:24:38,010
+لمين لل zeroفاهمين اللي بحكيه أخدت أنا اشتغلت على
+
+316
+00:24:38,010 --> 00:24:44,150
+هذه أو على اللي هي والأولى من عند واحد فصلت
+
+317
+00:24:44,150 --> 00:24:49,130
+التنتين هذه بديتها اللي هي من عند زائد واحد اللي
+
+318
+00:24:49,130 --> 00:24:53,010
+هي اللي بتبدأ عندها وهذه بتبدأ من واحد وتظل ماشية
+
+319
+00:24:53,620 --> 00:24:57,320
+مفهوم هذا بتروح إلى الـ Zero إذاً هذا كله هيروح
+
+320
+00:24:57,320 --> 00:25:00,700
+للـ Zero إذا صار معناته F of TN X لكل تربيع
+
+321
+00:25:00,700 --> 00:25:04,660
+بيروحنا منين للـ Zero اللي هو في الواقع F of Zero
+
+322
+00:25:04,660 --> 00:25:10,280
+Operator منين X يعني اللي أثبتته أنه الـ TN الـ TN
+
+323
+00:25:10,280 --> 00:25:14,320
+اللي هو Weekly Operator converges to the Zero
+
+324
+00:25:14,320 --> 00:25:19,760
+Operator يعني الـ TN X بتروح للـ Zero X لكل X
+
+325
+00:25:19,760 --> 00:25:22,440
+element in X ماله
+
+326
+00:25:25,010 --> 00:25:30,290
+بالنسبة لـ Tn هو كذلك، لكن Tn ليس عمليًا عمليًا
+
+327
+00:25:30,290 --> 00:25:41,990
+عمليًا عمليًا عمليًا عمليًا عمليًا عمليًا
+
+328
+00:25:42,250 --> 00:25:46,810
+الـ TNX ناقص Zero X اللي هو بيروح للـ Zero for
+
+329
+00:25:46,810 --> 00:25:52,330
+every X المنتج من هنا NX لو لجيت X واحدة بس بحيث
+
+330
+00:25:52,330 --> 00:25:57,450
+انه نورم الـ TNX ناقص Zero X بيروحش للـ Zero
+
+331
+00:25:57,450 --> 00:26:02,170
+معناته الـ TNX does not converge this strongly to
+
+332
+00:26:02,170 --> 00:26:07,170
+Zero X هاي X خد X إيش بتساوي واحد سفر سفر سفر
+
+333
+00:26:07,170 --> 00:26:15,690
+وحسبلي الآن TNX وTNXهتطلع اللي هي عبارة عن T M نقص
+
+334
+00:26:15,690 --> 00:26:19,050
+T N of X اللي هو هيطلع إيه أشماله جدر التنين
+
+335
+00:26:19,050 --> 00:26:23,290
+بتعرفوا تحسبوها اللي هي for all M لا تساوي N
+
+336
+00:26:23,290 --> 00:26:26,710
+معناته إنه is not Cauchy sequence مدام is not
+
+337
+00:26:26,710 --> 00:26:30,350
+Cauchy sequence is not converge إذا صار عندي اللي
+
+338
+00:26:30,350 --> 00:26:37,370
+هو norm T N X نقص T N is not converge strongly ل 0
+
+339
+00:26:40,760 --> 00:26:48,940
+طيب Note الان ال functionals
+
+340
+00:26:49,600 --> 00:26:52,740
+الـ Functionals، لو واحد .. الآن احنا بنحكي عن
+
+341
+00:26:52,740 --> 00:26:56,000
+Operators اللي هي الـ T أن و ان موجودة، انتبهوا
+
+342
+00:26:56,000 --> 00:27:00,660
+للمراحة ده، بين X و بين مين؟ بين Y، من normed
+
+343
+00:27:00,660 --> 00:27:05,680
+space ل normed space طيب لو بدينا بدنا نحكي بـ X و
+
+344
+00:27:05,680 --> 00:27:08,760
+ال scalar field تبعها، يعني بمعنى أخر، بدنا نحكي
+
+345
+00:27:08,760 --> 00:27:13,540
+عن مين؟ عن الـ X'أه يعني الأن ال operators اللي
+
+346
+00:27:13,540 --> 00:27:17,080
+أنا بدأ أخدها من وين من X لعند مين لـ scalar فيه
+
+347
+00:27:17,080 --> 00:27:19,540
+التباحة يعني بدأ أحكي عن ال functionality F
+
+348
+00:27:19,540 --> 00:27:24,560
+element من مين ل X' F N element in X' لما أحكي عن
+
+349
+00:27:24,560 --> 00:27:31,780
+ال F N element in X' معناته أنا صرت اللي هو اللي
+
+350
+00:27:31,780 --> 00:27:35,940
+.. اللي .. اللي هنا finite dimensional يعني بيصير
+
+351
+00:27:35,940 --> 00:27:41,890
+ال F N Xعبارة عن مش فنون انتسبيس عادي صار في
+
+352
+00:27:41,890 --> 00:27:44,970
+finite dimensional فبصير ال strongly و ال weak ليه
+
+353
+00:27:44,970 --> 00:27:50,970
+ايش ماله زي بعض فعشان هيك بحكيش لما احكي عن ال
+
+354
+00:27:50,970 --> 00:27:55,680
+functional بصير احكي بنوعية اخرىالان بيصير عندي
+
+355
+00:27:55,680 --> 00:27:59,580
+نوعين since the real and complex field are finite
+
+356
+00:27:59,580 --> 00:28:04,880
+dimensional then by theorem 48C the weak and
+
+357
+00:28:04,880 --> 00:28:08,660
+strong convergence of any sequence of bounded
+
+358
+00:28:08,660 --> 00:28:15,160
+linear functionals are the same يعني ال weak و ال
+
+359
+00:28:15,160 --> 00:28:19,820
+strong أيش بيصيرن؟ بيصيرن زي بعضالان definition
+
+360
+00:28:19,820 --> 00:28:24,720
+بناء عليه الان احنا لما بدنا نحكي let FN be a
+
+361
+00:28:24,720 --> 00:28:27,220
+sequence of bounded linear functions on and among
+
+362
+00:28:27,220 --> 00:28:31,300
+the space X then في عين دي بدأ احكي عن لان معين من
+
+363
+00:28:31,300 --> 00:28:35,620
+ال operators من ال convergence strong convergence
+
+364
+00:28:35,620 --> 00:28:43,580
+of FN الان اذا بدأ احكي عن نوعيات تخصنين اللي هو
+
+365
+00:28:43,580 --> 00:28:48,330
+ال convergence لل FNStrongly convergence of FN
+
+366
+00:28:48,330 --> 00:28:52,310
+means that there is F element in X prime Such that
+
+367
+00:28:52,310 --> 00:28:55,570
+norm of FN minus F بتروح لمين للزيرو as N goes to
+
+368
+00:28:55,570 --> 00:29:00,650
+infinity وكأنه بحكي عن اللي هو مين هنا اللي هو ال
+
+369
+00:29:00,650 --> 00:29:04,090
+uniform convergence هناك مكافئ لمين ال uniform
+
+370
+00:29:04,090 --> 00:29:07,230
+convergence إذا لما الآن بدي أحكي في ال functional
+
+371
+00:29:07,230 --> 00:29:10,870
+ركزوا الآن بدي أحكي في ال functional وكأن زي ما
+
+372
+00:29:10,870 --> 00:29:13,490
+كنت أحكي في الأول في المحاضرة اللي فاتت في ال X في
+
+373
+00:29:13,490 --> 00:29:17,770
+نورمهاوهنا بتحكي في norm منين؟ في norm الـ X' لأن
+
+374
+00:29:17,770 --> 00:29:22,530
+الآن سيرة الـ Fn وين موجودة؟ في الـ X' فالآن ما
+
+375
+00:29:22,530 --> 00:29:27,770
+بتحكي عن اللي هو strong ل convergence فيها Fn ناقص
+
+376
+00:29:27,770 --> 00:29:32,250
+F اللي بتروحلها بروح للـ 0 as N goes to infinity
+
+377
+00:29:32,250 --> 00:29:35,210
+هذا اللي في حالة ال operators كنت سميه uniform
+
+378
+00:29:35,210 --> 00:29:39,330
+convergence وهنا بده أسميه إيش ماله؟ strong
+
+379
+00:29:39,330 --> 00:29:43,850
+convergence لمين؟لـ Sequence of Functions عشان ما
+
+380
+00:29:43,850 --> 00:29:47,790
+اتخربتوش في الواقع هذا اللي كنا نسميه Uniform
+
+381
+00:29:47,790 --> 00:29:51,170
+Convergence وحتى أيام الباكاليوروس كنا نسميه
+
+382
+00:29:51,170 --> 00:29:54,990
+Uniform Convergence اللي هي في حالة اللي هي Area
+
+383
+00:29:54,990 --> 00:29:58,130
+اللي هنا نسميه Strong Convergence طيب، اللي هنا في
+
+384
+00:29:58,130 --> 00:30:01,590
+حاجة اسمها Weak Star Convergence الـWeak Star
+
+385
+00:30:01,590 --> 00:30:06,290
+لمين؟ With respect to F طيب الـWeak Convergence
+
+386
+00:30:06,290 --> 00:30:09,730
+كنا ناخد اللي هو For Every F Element ان كنا نقول
+
+387
+00:30:09,730 --> 00:30:16,760
+ان XNعشان ما تتربطوش Xn بتروح لل X weekly ناخد
+
+388
+00:30:16,760 --> 00:30:21,840
+مين؟ ناخد every F element in X prime ونقول F of Xn
+
+389
+00:30:21,840 --> 00:30:25,940
+بتروح لل F of X إيه شماله؟ اذا نقصده في التبسيه
+
+390
+00:30:25,940 --> 00:30:28,830
+sequence of numbersطب إحنا الآن .. طب هي عندنا
+
+391
+00:30:28,830 --> 00:30:33,510
+جاهزة أصلا لما .. عندنا الـ Fn هي .. هي أصلا
+
+392
+00:30:33,510 --> 00:30:37,330
+functional نفسها فإيش اللي بدي أسوي؟ بدي أسوي ..
+
+393
+00:30:37,330 --> 00:30:41,150
+أسمي حاجة اسم weak star convergence و بكتبها
+
+394
+00:30:41,150 --> 00:30:47,050
+convergence of Fn means that there is a prime such
+
+395
+00:30:47,050 --> 00:30:51,360
+that الآنبدخلش F عليها على الـ sequence لأ بقول
+
+396
+00:30:51,360 --> 00:30:54,840
+such that F N of X بتروح لل F of X as N goes to
+
+397
+00:30:54,840 --> 00:30:58,140
+infinity لكل X هو element in X وهذا معناته F N
+
+398
+00:30:58,140 --> 00:31:04,860
+بتروح لل F مين weekly بس
+
+399
+00:31:04,860 --> 00:31:11,400
+طلعونها للفرق بس
+
+400
+00:31:11,400 --> 00:31:18,420
+انتبهوا وصلة لمن؟ هي في عندي Xهذا ما يسمى كـ
+
+401
+00:31:18,420 --> 00:31:23,560
+Normed Space وفي عند X' اللي هو الـ Dual Space
+
+402
+00:31:23,560 --> 00:31:27,800
+اللي لها هذا بتحكي عن weak convergence وهذا weak
+
+403
+00:31:27,800 --> 00:31:32,960
+star convergence و Xاللي هي norm of the space و X'
+
+404
+00:31:33,300 --> 00:31:37,740
+أشماله اللي هو dual space لها طيب، شوفوا، صلى الله
+
+405
+00:31:37,740 --> 00:31:41,140
+عني، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس،
+
+406
+00:31:41,140 --> 00:31:42,640
+بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس،
+
+407
+00:31:42,640 --> 00:31:42,640
+بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس،
+
+408
+00:31:42,640 --> 00:31:44,400
+بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس، بلس،
+
+409
+00:31:44,400 --> 00:31:52,260
+بلس، بلس، بلس، بلس، بلس، بلس، بلس،
+
+410
+00:31:52,260 --> 00:31:56,320
+بلس،
+
+411
+00:31:57,020 --> 00:32:00,060
+هي هي هي هي هي ال sequence أه ال N ال sequence
+
+412
+00:32:00,060 --> 00:32:04,420
+بينما هنا لما بحكي عن weak star بحكي عن sequence
+
+413
+00:32:04,420 --> 00:32:09,620
+وين موجودة في ال X' مش sequence في ال X فبصير عندي
+
+414
+00:32:09,620 --> 00:32:14,080
+FN هي ال sequence وين في ال X' و ال F اللي
+
+415
+00:32:14,080 --> 00:32:18,640
+بتروحلها برضه وين موجودة في ال X' فبقول FN بتروح
+
+416
+00:32:18,640 --> 00:32:25,070
+لل F weak star معناتهإن الـ N بسير لأن لكل مين ال
+
+417
+00:32:25,070 --> 00:32:30,770
+N بعكسها لكل X في ال X بطلع عند أف N of X بتروح لل
+
+418
+00:32:30,770 --> 00:32:35,450
+أف of مين of X يعني الآن ال sequence هذه لمين لل
+
+419
+00:32:35,450 --> 00:32:39,390
+أف N اللي في وين في ال X' بينما ال XN هذه ال
+
+420
+00:32:39,390 --> 00:32:44,730
+sequence في وين في ال X نفسهاالطول هنا لتحقيق الـ
+
+421
+00:32:44,730 --> 00:32:48,490
+weak star هي الـ F اللي في الـ X' بينما الطول هنا
+
+422
+00:32:48,490 --> 00:32:52,750
+لتحقيق الـ W star اللي يمين الـ Xات اللي في الـ L
+
+423
+00:32:52,750 --> 00:33:00,810
+في الـ X يلّا نبعدها إلى أن نرمحك let X and Y be
+
+424
+00:33:00,810 --> 00:33:05,330
+normed this basis and T and B a sequence of
+
+425
+00:33:05,330 --> 00:33:12,500
+elements in B X or Yإذا Tن تتعامل بشكل عام لـ T،
+
+426
+00:33:12,500 --> 00:33:17,020
+فإن T تتعامل بشكل عام لـ T، فإن T تتعامل بشكل عام
+
+427
+00:33:17,020 --> 00:33:26,360
+ل T، فإن T تتعامل
+
+428
+00:33:26,360 --> 00:33:34,520
+بشكل
+
+429
+00:33:34,520 --> 00:33:37,490
+عام ل T، فإنلكن كنا نقول أن الـ Pointwise لا
+
+430
+00:33:37,490 --> 00:33:41,730
+يستطيع أن المقدرة عنده Fn converge للـF اللي هو
+
+431
+00:33:41,730 --> 00:33:44,970
+زمان، تبع زمان، تبع الـReal أو تبع الـC إذا كانت
+
+432
+00:33:44,970 --> 00:33:48,610
+Fn بتروح للـF pointwise وكانت Fn sequence of
+
+433
+00:33:48,610 --> 00:33:51,210
+continuous functions ليس شرط أن الـF تكون
+
+434
+00:33:51,210 --> 00:33:54,510
+continuous وكنا لما نحكي عن الـintegrable ونحكي عن
+
+435
+00:33:54,510 --> 00:33:56,530
+الـdifferentiability برضه كان لهم conditions كان
+
+436
+00:33:56,530 --> 00:33:59,650
+يمكن الـdifferentiability بتهزج تاني غير اللي هو
+
+437
+00:33:59,650 --> 00:34:06,600
+الـUFO طيبالآن Strongly or weakly convergence of
+
+438
+00:34:06,600 --> 00:34:11,260
+TN to some T إلى كده need not imply أيش معلوه زي
+
+439
+00:34:11,260 --> 00:34:14,240
+اللي قلته قبل شوية إنه الـ weakly و الـ strongly
+
+440
+00:34:14,240 --> 00:34:19,160
+convergence للـ TN غير مؤهل إنه ياخد ال sequence
+
+441
+00:34:19,160 --> 00:34:23,120
+of continuous bounded functions أو continuous
+
+442
+00:34:23,120 --> 00:34:26,980
+linear functions أو bounded linear functions
+
+443
+00:34:26,980 --> 00:34:30,720
+لbounded linear functionإذا الموهّل مين بس اللي
+
+444
+00:34:30,720 --> 00:34:34,620
+بقدر يودّهيه اللي هو بس اللي هو مين ال uniform
+
+445
+00:34:34,620 --> 00:34:42,480
+convergence الان الواحد البرهان لكم مش صعب نيجي
+
+446
+00:34:42,480 --> 00:34:44,680
+نبرهن مين اتنين يعني بدي اجيب مثال
+
+447
+00:34:48,960 --> 00:34:54,240
+بـ strong أو weak convergence من continuous
+
+448
+00:34:54,240 --> 00:34:57,640
+functions أو bounded linear operators التي مش
+
+449
+00:34:57,640 --> 00:35:03,820
+موجودة في Bxy لأ يمكنها تكون تشوفوا اطلع لفوق to
+
+450
+00:35:03,820 --> 00:35:09,220
+verify two اللي هاد اتنين consider the subspace X
+
+451
+00:35:09,220 --> 00:35:15,030
+ايش بتساوي اطلع لفوقبيساوي x بيساوي xij الامتنان 2
+
+452
+00:35:15,030 --> 00:35:19,090
+such that x has many finitely many zeros of L2
+
+453
+00:35:19,090 --> 00:35:23,890
+اشمالها اللي هي ال non zero finite بس و البعدي
+
+454
+00:35:23,890 --> 00:35:30,630
+اشماله أصفر let Tn من x لعند x be defined by Tn x
+
+455
+00:35:30,630 --> 00:35:35,590
+ايش بتساوي اللي هو هدول بس اشماله في عندك finite
+
+456
+00:35:35,590 --> 00:35:41,250
+number of elements مش zeroX has finitely many non
+
+457
+00:35:41,250 --> 00:35:44,490
+-zero numbers هذا اللي هو ال space اللي عندي هذا
+
+458
+00:35:44,490 --> 00:35:50,150
+ال subspace من مين؟ من ال L2 نفسه طيب يعني تقولي
+
+459
+00:35:50,150 --> 00:35:59,030
+ال element اللي هو اللي في ال L2 نص؟ ربع؟ تسع؟
+
+460
+00:35:59,030 --> 00:36:02,570
+واحد ع ستاش؟ إلى ما لا نهاية؟ هذا مش موجود في ال X
+
+461
+00:36:02,570 --> 00:36:10,080
+هذه لكن موجود في ال L2لأن الـ summation له finite
+
+462
+00:36:10,080 --> 00:36:13,520
+طيب
+
+463
+00:36:13,520 --> 00:36:17,120
+لكن .. لكن مش كل ال terms كل ال terms بيبقى
+
+464
+00:36:17,120 --> 00:36:19,240
+لانهاية مش zero طيب
+
+465
+00:36:21,410 --> 00:36:28,370
+طيب أخدنا T ان Xاش بتساوي T واحد X بتساوي ال .. ال
+
+466
+00:36:28,370 --> 00:36:29,150
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+467
+00:36:29,150 --> 00:36:29,430
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+468
+00:36:29,430 --> 00:36:29,610
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+469
+00:36:29,610 --> 00:36:30,950
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+470
+00:36:30,950 --> 00:36:32,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+471
+00:36:32,290 --> 00:36:32,530
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+472
+00:36:32,530 --> 00:36:33,010
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+473
+00:36:33,010 --> 00:36:35,890
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+474
+00:36:35,890 --> 00:36:36,170
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+475
+00:36:36,170 --> 00:36:36,170
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+476
+00:36:36,170 --> 00:36:36,190
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+477
+00:36:36,190 --> 00:36:43,370
+ال .. ال .. ال .. ال .. ال .. ال
+
+478
+00:36:44,750 --> 00:36:49,410
+T3 نفس الشيء الـ TN التي تضرب 1×2×3×4 لما تصل لـ N
+
+479
+00:36:49,410 --> 00:36:54,590
+و بعدها تبقى كما هي هذه التي هي TNX و خد TX
+
+480
+00:36:54,590 --> 00:37:02,470
+defined by TX ايش بتساوي GXiJ هذي لاحظ لما N تروح
+
+481
+00:37:02,470 --> 00:37:04,930
+إلى ما على النهاية يضرب و يضرب و يضرب و يضرب و
+
+482
+00:37:04,930 --> 00:37:11,290
+يضرب و يضرب و يضربمشكلة مكبرة N بزيادة ضرب عند N
+
+483
+00:37:11,290 --> 00:37:13,670
+زيادة واحد بيصير ضربان فما بالكم اللي مروحوا
+
+484
+00:37:13,670 --> 00:37:16,190
+البلد؟ هذا بيصير كل المضروبات وكأنهم هذا roughly
+
+485
+00:37:16,190 --> 00:37:19,270
+الكلام طيب it is left to the reader to show that
+
+486
+00:37:19,270 --> 00:37:23,810
+for unfixed N TN is linear and bounded برضه نفس
+
+487
+00:37:23,810 --> 00:37:26,230
+الأشياء ال linearity و ال boundedness مشابه اللي
+
+488
+00:37:26,230 --> 00:37:30,310
+حكيناه قبل و شوية ال unboundedness سهل ال bounded
+
+489
+00:37:30,310 --> 00:37:34,570
+norm TN هذا بيساوي norm هذا و هذا أصغر أو ساوي
+
+490
+00:37:34,570 --> 00:37:40,500
+اللي هو Nفى Normal X على اعتبار ان كله واضربات
+
+491
+00:37:40,500 --> 00:37:49,300
+عندك انا لان انا اكبر واحدة مش فاهمين؟
+
+492
+00:37:49,300 --> 00:37:50,780
+طيب لأ
+
+493
+00:38:03,150 --> 00:38:08,630
+TNX بساوية اللي هو عبارة عن مين اللي هو norm TNX
+
+494
+00:38:08,630 --> 00:38:14,030
+بساوية norm اللي هو XI واحد XI اتنين XI اتنين لعند
+
+495
+00:38:14,030 --> 00:38:19,310
+ان ان XI ان والباب المضروب الاخر هنا هذا أصغر أوي
+
+496
+00:38:19,310 --> 00:38:25,570
+ساوياللي هو اعتبر ان هذا اللي هو norm هنا اللي هو
+
+497
+00:38:25,570 --> 00:38:27,610
+عبارة عن ال summation لهذا و لهذا و لهذا ال
+
+498
+00:38:27,610 --> 00:38:32,570
+summation أصغر و أصغر ال summation ان في xii I من
+
+499
+00:38:32,570 --> 00:38:39,010
+عند واحد إلى ما لنهاية تربيع الكل أص نص norm تربيع
+
+500
+00:38:39,010 --> 00:38:42,970
+نحسب norm تربيع مش مشكلة كأني سحبت الان هذول لإن
+
+501
+00:38:42,970 --> 00:38:47,750
+هذول بس الان هنا أنا ضربت انفين كله طيب
+
+502
+00:38:50,470 --> 00:38:53,450
+It is left to infix TN is bound linear or
+
+503
+00:38:53,450 --> 00:38:57,770
+unbounded Moreover T is linear but is not bounded
+
+504
+00:38:57,770 --> 00:39:01,710
+T هذه هذه T is linear لكن أشمالها is not bounded
+
+505
+00:39:01,710 --> 00:39:06,890
+الآن T X بتساوي J في مين كساية واحد في كساية اتنين
+
+506
+00:39:06,890 --> 00:39:11,510
+في كساية تلاتة is not boundedإنها متعبرة وليس
+
+507
+00:39:11,510 --> 00:39:15,730
+متعبرة ثم T هو إيش معناه element in B وليس element
+
+508
+00:39:15,730 --> 00:39:23,670
+in B of X إذا مش مستحيل أن الـTن تكون مرتبط لمن؟
+
+509
+00:39:23,670 --> 00:39:31,630
+لـT أه الـTن مستحيل تروح لمن؟ لـT أخيراً واضح أن
+
+510
+00:39:31,630 --> 00:39:36,080
+الـTن مرتبط بشكل قوي لمن؟ لـTاللي قلته في الأول،
+
+511
+00:39:36,080 --> 00:39:39,900
+أول ما حكيت، الـTN، شو معناه الـTN؟ شو معناه الـTN
+
+512
+00:39:39,900 --> 00:39:45,260
+strongly تروح convergence to T؟ إنه، اللي هو TN X
+
+513
+00:39:45,260 --> 00:39:51,200
+معقص TX يروح نمين للسفر، TN as N goes to infinity،
+
+514
+00:39:51,200 --> 00:39:56,410
+هذه اللي هي هيهاهو as n goes to infinity بيصير كل
+
+515
+00:39:56,410 --> 00:40:01,750
+هنا إشمع من XI J التي عرفناها
+
+516
+00:40:01,750 --> 00:40:06,250
+TX XI J في J هذا as n goes to infinity بيصير هيلية
+
+517
+00:40:06,250 --> 00:40:11,900
+فهو بيصير هذا النقص هذا تقوله أحلاميين للزيرولكن
+
+518
+00:40:11,900 --> 00:40:16,260
+الـ Tn اللي هو a conversion where norm of Tn X
+
+519
+00:40:16,260 --> 00:40:19,080
+بتروح لـ 0 as N goes to infinity لجبته لكن قبل
+
+520
+00:40:19,080 --> 00:40:25,340
+بشوية الـ Tn does not converge uniformly does not
+
+521
+00:40:25,340 --> 00:40:29,260
+converge T can't be element in B of X فهذا اللي هو
+
+522
+00:40:29,260 --> 00:40:32,360
+بيعطيني اللي هو strongly or weakly conversion of
+
+523
+00:40:32,360 --> 00:40:37,420
+Tn so it need not imply that T element in B of X
+
+524
+00:40:37,420 --> 00:40:47,040
+or Y يعني رغم هيك كان عنديالـ TN عشان ابعدنا طبعا
+
+525
+00:40:47,040 --> 00:40:51,900
+مش هيكون uniformly أكيد مش هيكون uniformly أه مش
+
+526
+00:40:51,900 --> 00:40:56,340
+هيكون uniformly لإن شو معناته uniformly أنك تقدر
+
+527
+00:40:56,340 --> 00:41:00,200
+تحسب ان norm الـ TN ناقص الـ T لكن أنا ماقدرش
+
+528
+00:41:00,200 --> 00:41:03,480
+أحسبه أصلا لإن الـ T أشمال has not bounded باشي
+
+529
+00:41:03,480 --> 00:41:09,640
+الحال فالأن أثبتنا أن TN X بتروح للـ TX strongly
+
+530
+00:41:11,650 --> 00:41:18,230
+الـ T is not in between B of X أو Y يعني الآن اللي
+
+531
+00:41:18,230 --> 00:41:21,230
+هو الـ strong convergence طبعا مادام الـ strong
+
+532
+00:41:21,230 --> 00:41:25,570
+convergence ده أكيد أشمل weak convergence إذن سواء
+
+533
+00:41:25,570 --> 00:41:28,790
+strong أو weak مش هيقدر يكون مؤهل يودّي الـ T في
+
+534
+00:41:28,790 --> 00:41:32,970
+الـ B L of X نيجي
+
+535
+00:41:32,970 --> 00:41:39,610
+نشوف كده إجتماعيل يلّا
+
+536
+00:41:39,610 --> 00:41:46,850
+ما بنخلصين تفكّر علىلما let X be أبلغ space وY
+
+537
+00:41:46,850 --> 00:41:49,550
+along the space and T and B a sequence of elements
+
+538
+00:41:49,550 --> 00:41:53,910
+in B X Y that converge strongly to a limit T
+
+539
+00:41:53,910 --> 00:41:57,910
+element in B X Y then T أشملها element in B X Y
+
+540
+00:41:57,910 --> 00:42:03,570
+إذا أنا بقولك انت
+
+541
+00:42:03,570 --> 00:42:07,870
+ممكن تكون في ذكية بسيطة تخلي اللي هو الـ strongly
+
+542
+00:42:07,870 --> 00:42:13,050
+convergentأه يخلّي الـ Limit وإن موجودة في الـ P X
+
+543
+00:42:13,050 --> 00:42:17,290
+وY بس اللي مطلوب أن الـ X وY يكونوا إيه الشمالين
+
+544
+00:42:17,290 --> 00:42:24,770
+بنخس Basis ماشي لإنه هيحولك اللي هو هيحصل على ال
+
+545
+00:42:24,770 --> 00:42:28,450
+boundedness المفقود أو اللي هو ال boundedness
+
+546
+00:42:28,450 --> 00:42:35,970
+لميلة T نشوف كيف أو حتى ال sequence نفسها تصير الـ
+
+547
+00:42:35,970 --> 00:42:40,290
+T أن تروح خلّيني أقول Roughlyبالـ TN uniformly it
+
+548
+00:42:40,290 --> 00:42:43,190
+is left to the reader to prove that T is linear
+
+549
+00:42:43,190 --> 00:42:48,090
+سيبها لكم الان since TN X بتروح لل TX لكل X
+
+550
+00:42:48,090 --> 00:42:53,130
+element in X by لمّة 1 4 2 A the sequence TN X is
+
+551
+00:42:53,130 --> 00:42:57,070
+bounded اتفاقنا عليه اه عارفين هو هذا TN X بتروح
+
+552
+00:42:57,070 --> 00:43:01,970
+لل TX في ال norm تبع مين؟ تبع ال X تبع ال Y و ال Y
+
+553
+00:43:01,970 --> 00:43:05,430
+إذا بنخس بي اس إذا TN X الشمال هتكون is bounded
+
+554
+00:43:05,430 --> 00:43:11,650
+however X is completeصارت هذه bounded و الـ X is
+
+555
+00:43:11,650 --> 00:43:14,550
+complete إذا بالـ Uniform Boundedness Theorem
+
+556
+00:43:14,550 --> 00:43:19,290
+هتحولك الـ boundedness لهذه لـ boundedness لميه
+
+557
+00:43:19,290 --> 00:43:22,830
+للـ TN هتصير اللي هي نوم الـ TN أصغر شهر و C for
+
+558
+00:43:22,830 --> 00:43:27,650
+all N يعني independent of X بتصير هذا الـ Uniform
+
+559
+00:43:27,650 --> 00:43:33,170
+Boundedness وهذه بتطلب الـ X إيش تكون completeهنا
+
+560
+00:43:33,170 --> 00:43:36,030
+Hence خدوا نورم الـ TN X هيكون أصغر أو ساوى نورم
+
+561
+00:43:36,030 --> 00:43:40,130
+الـ TN في نورم الـ X وهذه أصغر أو ساوى C في نورم
+
+562
+00:43:40,130 --> 00:43:43,770
+الـ X الآن دخلوا ال limit علي الجهد التاني
+
+563
+00:43:43,770 --> 00:43:46,470
+وستستخدموا ال continuity لل TN و ال continuity لل
+
+564
+00:43:46,470 --> 00:43:50,840
+normهذا صار أصغر أشهر و C في X دخلوا ال limit هنا
+
+565
+00:43:50,840 --> 00:43:54,100
+واستخدوا ال continuity لل TN و ال continuity نميين
+
+566
+00:43:54,100 --> 00:43:59,640
+لل norm بس يوم norm limit ال TN ال X هو TX وهذا
+
+567
+00:43:59,640 --> 00:44:02,760
+limit اللي هو norm TN X أصغر أشهر و C في norm X
+
+568
+00:44:02,760 --> 00:44:06,840
+hence اللي هي صارت عند T is bounded then T element
+
+569
+00:44:06,840 --> 00:44:14,000
+in B X أو Y اطلع للفوق البعدها let Xدع X و Y يكون
+
+570
+00:44:14,000 --> 00:44:19,140
+بانخسباسي و TN يكون سيكوانس من الأشياء الميانة في
+
+571
+00:44:19,140 --> 00:44:24,320
+B X و Y إذا X و Y أشمل بانخسباسي و TN سيكوانس في B
+
+572
+00:44:24,320 --> 00:44:30,900
+X و Y ثم TN تتعامل بشكل قوى إذا كانت تتعامل بشكل
+
+573
+00:44:30,900 --> 00:44:33,500
+قوى إذا كانت تتعامل بشكل قوى إذا كانت تتعامل بشكل
+
+574
+00:44:33,500 --> 00:44:38,290
+قوىاللي هو الـ sequence TNX is Cauchy in Y for
+
+575
+00:44:38,290 --> 00:44:42,670
+every X in a total subset M of mean of X ما هي الـ
+
+576
+00:44:42,670 --> 00:44:47,750
+TNX مزام converge إذا Cauchy ماياشي الحال Cauchy
+
+577
+00:44:47,750 --> 00:44:51,730
+إذا سواء Cauchy كانت الـ X في الـ Y نفسها أو في
+
+578
+00:44:51,730 --> 00:44:54,790
+الـ X نفسها أو في subset منها إذا الـ automatic
+
+579
+00:44:54,790 --> 00:44:58,150
+هذا جزء منها زي ما حكينا في الجبل طيب
+
+580
+00:45:00,170 --> 00:45:04,890
+بالتدريج if TN X بتروح ل TX لكل X element in X
+
+581
+00:45:04,890 --> 00:45:09,590
+يعني strongly هذا إيش معلوق strongly then TN X is
+
+582
+00:45:09,590 --> 00:45:14,990
+bounded ماشي الحال أخدناها and so بقى uniform
+
+583
+00:45:14,990 --> 00:45:18,810
+bounded نص فيهم إيش هتطلع norm TN is bounded إذن
+
+584
+00:45:18,810 --> 00:45:22,850
+هذه automatic طلعتفي حالة تسأل هي مين فردت اللي هو
+
+585
+00:45:22,850 --> 00:45:26,110
+الـ strongly convergence الان بيه from the
+
+586
+00:45:26,110 --> 00:45:29,850
+definition of strongly operator convergence and
+
+587
+00:45:29,850 --> 00:45:33,840
+the fact every convergence sequence is Cauchyاللي
+
+588
+00:45:33,840 --> 00:45:36,340
+هو ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+589
+00:45:36,340 --> 00:45:36,460
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+590
+00:45:36,460 --> 00:45:36,520
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+591
+00:45:36,520 --> 00:45:36,560
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+592
+00:45:36,560 --> 00:45:36,800
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+593
+00:45:36,800 --> 00:45:37,320
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+594
+00:45:37,320 --> 00:45:37,380
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+595
+00:45:37,380 --> 00:45:42,680
+ال .. ال .. ال .. ال ..
+
+596
+00:45:42,680 --> 00:45:47,360
+ال
+
+597
+00:45:47,360 --> 00:45:48,280
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+598
+00:45:48,280 --> 00:45:48,280
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+599
+00:45:48,280 --> 00:45:48,280
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+600
+00:45:48,280 --> 00:45:48,360
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+601
+00:45:48,360 --> 00:45:48,360
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+602
+00:45:48,360 --> 00:45:56,920
+ال .. ال .. ال .. ال .. ال
+
+603
+00:46:03,400 --> 00:46:06,960
+أطلع لفوق مشابه للي حكينا قبل بشوية suppose that a
+
+604
+00:46:06,960 --> 00:46:09,860
+and b holds then there exists c أكبر من صفر such
+
+605
+00:46:09,860 --> 00:46:12,880
+that more than t أن اش ماله أصغر أو ساوسين من
+
+606
+00:46:12,880 --> 00:46:17,680
+المعطى for all n since m is totally in x فزي ما
+
+607
+00:46:17,680 --> 00:46:21,480
+عملنا قبل بشوية ال span ل ال m اش ماله then is في
+
+608
+00:46:21,480 --> 00:46:25,900
+ال xما دام span لـ M دنس في الـ X إذا لكل X في الـ
+
+609
+00:46:25,900 --> 00:46:29,280
+X بقدر ألاقي sequence من هنا اللي هو Converge إلها
+
+610
+00:46:29,280 --> 00:46:35,000
+أو بقدر أقول لكل X هنا بقدر أخد المسافة بينها وبين
+
+611
+00:46:35,000 --> 00:46:38,620
+اللي هو elements من هنا صغيرة صغيرة صغيرة جدا زي
+
+612
+00:46:38,620 --> 00:46:47,360
+ما بدي فاهمين؟ الآن يا جماعة ال span لـ M دنس في
+
+613
+00:46:47,360 --> 00:46:54,950
+من؟ في الـ X إذا لكل X في الـ Xاللي هو بقدر ألاقي
+
+614
+00:46:54,950 --> 00:47:01,130
+element في الـ M يكون very close إليه لأن هي أصلا
+
+615
+00:47:01,130 --> 00:47:04,870
+dense فيه فبكون عندي for every Y أكبر من 0 there
+
+616
+00:47:04,870 --> 00:47:08,190
+exists Y element اسمها للـ M such that normal X
+
+617
+00:47:08,190 --> 00:47:14,880
+minus Y أشمل أصغر من تلت عالمين على Cلأن الـ M
+
+618
+00:47:14,880 --> 00:47:22,420
+dense في الـ X، أي X هنا can be .. we can find M Y
+
+619
+00:47:22,420 --> 00:47:26,580
+في الـ span تكون very close له، نفس منطقة الـ
+
+620
+00:47:26,580 --> 00:47:30,560
+sequence، وبرمجانه سهل، الـ norm X minus Y أصغر من
+
+621
+00:47:30,560 --> 00:47:33,300
+Y على مين؟ على تلاتة C، يعني زغرت المسافة زي ما
+
+622
+00:47:33,300 --> 00:47:38,320
+بديالان من B اللي هو Tny is Cauchy مدام Cauchy
+
+623
+00:47:38,320 --> 00:47:44,320
+بقدر عليها K بحيث أن Tny نقص Tmy أصغر من أي أبسلون
+
+624
+00:47:44,320 --> 00:47:46,580
+في الدنيا من ضمن هذه الأبسلون على تلاتة اللي بديها
+
+625
+00:47:46,580 --> 00:47:52,620
+الان therefore لكل M و N أكبر من K اللي لجيت هنا
+
+626
+00:47:53,810 --> 00:47:59,530
+بحصل معالي وانا fixed x we have احسبلي Tnx نقص Tmx
+
+627
+00:47:59,530 --> 00:48:03,690
+اللي هو اصغر او شاوي ضيفوا الtermين واطرحوهن
+
+628
+00:48:03,690 --> 00:48:07,310
+واستخدموا ال triangle inequality اصغر او شاوي Tnx
+
+629
+00:48:07,310 --> 00:48:15,320
+نقص Tny زي Tmy نقص Tmxالأن نفس اللي عملته قبل
+
+630
+00:48:15,320 --> 00:48:19,760
+بشوية هذي بيصير أصغر TN of X minus Y إذا أصغر يسوي
+
+631
+00:48:19,760 --> 00:48:25,100
+نورم TN في نورم X minus Y وهذه التانية أصغر من مين
+
+632
+00:48:25,100 --> 00:48:29,900
+من Y على 3 حكيناها وهذه نفس اللي عملته قبل بشوية
+
+633
+00:48:29,900 --> 00:48:33,900
+في البرهان اللي في المحاضرة اللي فاتت نورم TN في
+
+634
+00:48:33,900 --> 00:48:39,510
+نورم Y minus Xالأن هذا أصغر أو ساوى C وهذا أصغر من
+
+635
+00:48:39,510 --> 00:48:44,990
+Y ع تلاتة C وهذه Y ع تلاتة وهذا أصغر من C وهذا
+
+636
+00:48:44,990 --> 00:48:48,610
+أصغر من Y ع تلاتة C وكل معلومات أصغر من مين من Y
+
+637
+00:48:48,610 --> 00:48:52,510
+وإذا صار عندي ال TNX نقص TNX أصغر من أي Y في
+
+638
+00:48:52,510 --> 00:48:56,130
+الدنيا ماشي الحال إذا صارت ال TNX عبارة عن إيه
+
+639
+00:48:56,130 --> 00:48:59,550
+شكوشي sequenceكوشي سيكوينس وفيه complete إذا
+
+640
+00:48:59,550 --> 00:49:03,010
+converges إذا صارت عند T and X converges in B and
+
+641
+00:49:03,010 --> 00:49:07,350
+Y وهذا يعني T and X converges strongly آخر
+
+642
+00:49:07,350 --> 00:49:12,210
+corollary منها اللي هي a sequence of N of bounded
+
+643
+00:49:12,210 --> 00:49:17,810
+linear functionals on a بنخ space X is weak star
+
+644
+00:49:17,810 --> 00:49:22,680
+convergenceالقاعدة تكون عبارة عن عبارة عالية على X
+
+645
+00:49:22,680 --> 00:49:25,240
+إذا كانت عبارة عنها عبارة عنها عبارة عنها عبارة
+
+646
+00:49:25,240 --> 00:49:25,940
+عنها عبارة عنها عبارة عنها عبارة عنها عبارة عنها
+
+647
+00:49:25,940 --> 00:49:26,640
+عبارة عنها عبارة عنها عبارة عنها عبارة عنها عبارة
+
+648
+00:49:26,640 --> 00:49:26,780
+عنها عبارة عنها عبارة عنها عبارة عنها عبارة عنها
+
+649
+00:49:26,780 --> 00:49:28,460
+عبارة عنها عبارة عنها عبارة عنها عبارة عنها عبارة
+
+650
+00:49:28,460 --> 00:49:29,300
+عنها عبارة عنها عبارة عنها عبارة عنها عبارة عنها
+
+651
+00:49:29,300 --> 00:49:30,640
+عبارة عنها عبارة عنها عبارة عنها عبارة عنها عبارة
+
+652
+00:49:30,640 --> 00:49:34,260
+عنها عبارة عنها عبارة
+
+653
+00:49:34,260 --> 00:49:34,760
+عنها ع
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/cy-kIawWPhI.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/cy-kIawWPhI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d6d76ad5e7b582919c44c9995cd87f0cb6c92087
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/cy-kIawWPhI.srt
@@ -0,0 +1,699 @@
+1
+00:00:05,430 --> 00:00:07,810
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,810 --> 00:00:10,490
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,490 --> 00:00:15,370
+آله وصحبه أجمعين هذه المحاضرة رقم واحد وعشرين مساق 
+
+4
+00:00:15,370 --> 00:00:20,010
+تحليل دالي أو تحليل اقتراني طلاب وطالبات الجامعة 
+
+5
+00:00:20,010 --> 00:00:24,770
+الإسلامية ماجستير رياضيات وصلنا لعند section ثلاثة
+
+6
+00:00:24,770 --> 00:00:27,250
+خمسة series related to orthonormal sets and
+
+7
+00:00:27,250 --> 00:00:31,810
+sequences  احنا هناخد الجزئية هذه بس من ال section 
+
+8
+00:00:31,810 --> 00:00:34,130
+هذا المطلوب من ال section بس اللي موجود في التلخيص
+
+9
+00:00:34,130 --> 00:00:38,370
+النظرية اللي عندي اللي هو let A K B an orthonormal
+
+10
+00:00:38,370 --> 00:00:41,350
+sequence in a Hilbert space etched in for 
+
+11
+00:00:41,350 --> 00:00:44,510
+unscalars ألف واحد و ألف اثنين و ألف ثلاثة اللي هو
+
+12
+00:00:44,510 --> 00:00:49,350
+إلى ما لانهاية هذه ال A و B و C صحيحة إذا احنا حكينا
+
+13
+00:00:49,350 --> 00:00:54,630
+عن مين عن orthonormal sequence بقولي summation للـ
+
+14
+00:00:54,630 --> 00:00:58,510
+α K E K كامل عند واحد لما لنهاية هذه بتكون 
+
+15
+00:00:58,510 --> 00:01:00,750
+convergence إذا وفقط إذا مين اللي بتحكم في ال
+
+16
+00:01:00,750 --> 00:01:03,410
+convergence ل ال scalars if and only if ال
+
+17
+00:01:03,410 --> 00:01:06,010
+summation ل ال modulus لل scalars تربيع تكون إيش
+
+18
+00:01:06,010 --> 00:01:08,730
+مالها convergence يعني ال series هذه ال convergence
+
+19
+00:01:08,730 --> 00:01:12,390
+تبعها عشان أفحص test بكفي أن أفحص اللي هو يعني
+
+20
+00:01:12,390 --> 00:01:16,350
+بحول الحديث وكأني من convergence ال convergence في 
+
+21
+00:01:16,350 --> 00:01:19,330
+Hilbert space أو في norm تبع ال Hilbert space إلى 
+
+22
+00:01:19,330 --> 00:01:23,000
+convergence في C أو في R يعني في تبعات الـ Calculus
+
+23
+00:01:23,000 --> 00:01:26,200
+العادى اللي هي الـ Calculus G الآن ال .. ال .. ال
+
+24
+00:01:26,200 --> 00:01:28,940
+.. ال B اللي هو إذا كان الصممش اللي Alpha K, E, K
+
+25
+00:01:28,940 --> 00:01:33,200
+هذا K من واحدة مهلاً هي Converse هتكون الـ Alpha K
+
+26
+00:01:33,200 --> 00:01:35,960
+هذه هي عبارة عن الـ Fourier coefficients اللي 
+
+27
+00:01:35,960 --> 00:01:39,260
+حكيناها قبل شوية اللي هي إيه شمالها X و E, K يعني
+
+28
+00:01:39,260 --> 00:01:43,480
+إذا كانت هذه Converse هتكون حتماً حتماً حتماً الـ
+
+29
+00:01:43,480 --> 00:01:47,400
+Alpha K هي عبارة عن ال inner products بين X و E, K
+
+30
+00:01:47,930 --> 00:01:51,550
+Where X denotes X مين هي ال summation اللي أمامي
+
+31
+00:01:51,550 --> 00:01:56,170
+أو بمعنى 
+
+32
+00:01:56,170 --> 00:02:00,150
+آخر يعني هذا الكلام كله بنقدر نقول ان ال summation 
+
+33
+00:02:00,150 --> 00:02:05,580
+للألف ك إي ك ك من واحد دائماً بيساوي X هتلاقي هيساوي
+
+34
+00:02:05,580 --> 00:02:10,080
+هو نفسه الـ X والـ EK EK K من واحد إلى ما لا نهاية هذا 
+
+35
+00:02:10,080 --> 00:02:13,600
+في حال ال series أشمل هتكون converts يعني لو كانت 
+
+36
+00:02:13,600 --> 00:02:15,900
+اللي هي X مكتوبة على الصورة هذه يعني ال
+
+37
+00:02:15,900 --> 00:02:19,960
+convergence هتكون هذه الـ X أنا بقدر أكتبها على
+
+38
+00:02:19,960 --> 00:02:23,640
+صورة X و EK EK K من واحد إلى ما لا نهاية هذه الصورة
+
+39
+00:02:23,640 --> 00:02:26,120
+اللي هي مفيدة كتير ل .. اللي هي شغلات في ال
+
+40
+00:02:26,120 --> 00:02:30,520
+applications للـ Fourier series اطلع لفوق for any x
+
+41
+00:02:30,520 --> 00:02:34,740
+element in H هيكون ال summation لأن بيقولك أي x في 
+
+42
+00:02:34,740 --> 00:02:37,660
+ال H الآن بناء عليه أي x في ال H بناء عليه ال
+
+43
+00:02:37,660 --> 00:02:43,520
+inequality هيكون ال summation لل x و ال ek و ال ek
+
+44
+00:02:43,520 --> 00:02:48,660
+هذه دائماً إيه شمالها converge لأنه قبل بشوية خدنا
+
+45
+00:02:48,660 --> 00:02:52,660
+المدلس إلها أصغر أو يساوي نورمال x تربيه يعني لأنها 
+
+46
+00:02:52,660 --> 00:02:58,580
+ستصبح converge لل x في ال H طيب نيجي الآن انبرهنلت 
+
+47
+00:02:58,580 --> 00:03:02,540
+أس أن بتساوي Alpha E1 E1 زي Alpha 2 E2 زي Alpha N
+
+48
+00:03:02,540 --> 00:03:08,080
+EN مجرد رموز عشان نصل منها الـ Sigma N هي عبارة عن 
+
+49
+00:03:08,080 --> 00:03:11,900
+Alpha 1 Alpha 2 إلى ما لا نهاية تربيع وكأنه هذه عبارة
+
+50
+00:03:11,900 --> 00:03:14,980
+عن sequence of partial sums للسيريز الأولى وهذه
+
+51
+00:03:14,980 --> 00:03:18,160
+sequence of partial sums لمين للسيريز تبعت مين
+
+52
+00:03:18,160 --> 00:03:22,070
+اللي هي ال .. ال .. ال .. ال scalars لأن بما أنه EK
+
+53
+00:03:22,070 --> 00:03:27,210
+is an orthonormal إذا لكل N أكبر من M أحسب للأس أن
+
+54
+00:03:27,210 --> 00:03:31,510
+ناقص أس M لكل تربيع هذا بيساوي اللي هو أس أن ناقص
+
+55
+00:03:31,510 --> 00:03:34,810
+أس M اللي N أكبر من M ماشي الحال فبتروح لتبعات ال
+
+56
+00:03:34,810 --> 00:03:38,450
+M و بظل اللي هي اللي بعيدها بيصير ألف M زائد واحد
+
+57
+00:03:38,450 --> 00:03:42,670
+في E واحد زائد ألف M زائد اثنين في E اثنين في E
+
+58
+00:03:42,670 --> 00:03:48,660
+واحد ألا واحد مكتوب هنافزائد ألف أم زائد اثنين في
+
+59
+00:03:48,660 --> 00:03:52,260
+أم زائد اثنين ماشي الحال زائد واحد زائد واحد ماشي 
+
+60
+00:03:52,260 --> 00:03:57,020
+زائد اللي هو ألف أن إي أن فاهمين اللي هو حصل طرح
+
+61
+00:03:57,020 --> 00:04:00,640
+اللان مع اللهان ويساوي ال inner product هذا بقي 
+
+62
+00:04:00,640 --> 00:04:04,520
+أشماله بنفسفسه ال norm إلى inner product ال inner
+
+63
+00:04:04,520 --> 00:04:08,140
+product الأول والتاني هذا مع التاني واحنا زي ما
+
+64
+00:04:08,140 --> 00:04:13,360
+احنا عارفين المختلفة هتتصفرن و هيضلين اللي زي بعض
+
+65
+00:04:13,360 --> 00:04:17,400
+فبصير عندي α M زائد واحد تربيع في نورم ال E M زائد
+
+66
+00:04:17,400 --> 00:04:21,140
+واحد لكل تربيع عملناها كتير هذه زائد ألف M زائد
+
+67
+00:04:21,140 --> 00:04:24,260
+اثنين تربيع في E M زائد اثنين لكل تربيع لما أصل
+
+68
+00:04:24,260 --> 00:04:28,140
+لآخر واحدة ألف N تربيع في E N لكل تربيع لإن ال
+
+69
+00:04:28,140 --> 00:04:32,060
+product بين أي اثنين E I و E J مختلفة بيطلع عياش
+
+70
+00:04:32,060 --> 00:04:36,040
+صفر إذا بضلم بس المتشابهات و يساوي النورمات ما هن
+
+71
+00:04:36,040 --> 00:04:42,820
+واحد نورتو نورمال ست إذا هيظل هذا كله هيروح هيظل
+
+72
+00:04:42,820 --> 00:04:46,540
+باسمين المضلس لألف M تربيع زاد ألف M اثنين تربيع
+
+73
+00:04:46,540 --> 00:04:49,460
+زاد ألف M لكل تربيع اللي هو في الواقع مين مين هو
+
+74
+00:04:49,460 --> 00:04:54,980
+سيجما ان ناقص مين سيجما ان إذا صار وكأنه عندي ال
+
+75
+00:04:54,980 --> 00:05:00,220
+norm لالأسئن ناقص أسئن من كل تربيع هو نفس مين
+
+76
+00:05:00,220 --> 00:05:06,300
+سيجما ان ناقص سيجما ان إذن therefore Sn is Cauchy 
+
+77
+00:05:06,300 --> 00:05:11,220
+in H if and only if Σn is Cauchy in C أو in R لأن 
+
+78
+00:05:11,220 --> 00:05:15,620
+الاثنين أشمالهم الفرق بين Sn و Sm هو نفس الفرق بين
+
+79
+00:05:15,620 --> 00:05:19,400
+Σن و Σم إذا لو كانت هذه Cauchy هتكون هذه Cauchy لو
+
+80
+00:05:19,400 --> 00:05:24,910
+كانت هذه Cauchy هتكون أشمالها Cauchy واضحة أفصلها
+
+81
+00:05:24,910 --> 00:05:31,250
+ماشي لحظة اطلع لفوق however both H and R are 
+
+82
+00:05:31,250 --> 00:05:35,010
+complete إذا أسأل converts if and only if سجلنا
+
+83
+00:05:35,010 --> 00:05:40,270
+إيش مالها converts إذا الآن صار عندي الان hence
+
+84
+00:05:40,840 --> 00:05:43,960
+اللي هي Sn هي sequence of partial sums لها دي و
+
+85
+00:05:43,960 --> 00:05:46,620
+Sigma N هي sequence of partial sums لها دي إذا
+
+86
+00:05:46,620 --> 00:05:48,980
+الحاجة صار عند ال summation هذا converge if and
+
+87
+00:05:48,980 --> 00:05:52,080
+only if ال summation هذا ليهاش converge لإنه اللي 
+
+88
+00:05:52,080 --> 00:05:54,980
+هو ال series بتكون converge if and only if اللي هو 
+
+89
+00:05:54,980 --> 00:05:57,900
+ال sequence of partial sums اللي هت converge واضح
+
+90
+00:05:57,900 --> 00:06:04,130
+أه نيجي الأن للجزء الثاني نفترض إن الأسئلة اللي قبل
+
+91
+00:06:04,130 --> 00:06:08,630
+شوية converged a mean ل some x أو بمعنى آخر الـ x 
+
+92
+00:06:08,630 --> 00:06:11,630
+إيش بتساوي الـ summation Alpha K إي K كامل عند
+
+93
+00:06:11,630 --> 00:06:14,910
+واحد عنين لعين انفجر K بدنا نثبت أن الـ Alpha K
+
+94
+00:06:14,910 --> 00:06:18,730
+زائد إي شمالين هي عبارة عن الـ X والـ E K طيب let n
+
+95
+00:06:18,730 --> 00:06:24,850
+be any fixed natural number then for any fixed J
+
+96
+00:06:24,850 --> 00:06:28,650
+بيساوي واحد واثنين إلى آخر K والـ K أصغر أو يساوي
+
+97
+00:06:28,650 --> 00:06:34,920
+100 N إيش عملت ثبتت N أخدت N إشي معين و أخدتلك الـ 
+
+98
+00:06:34,920 --> 00:06:40,280
+N J واحدة من الواحد والاثنين والثلاثة اللي عند ال K
+
+99
+00:06:40,280 --> 00:06:44,540
+و ال K أصغر شو ومين N يعني جيت أخدت من هدول اللي 
+
+100
+00:06:44,540 --> 00:06:48,020
+من الواحد اللي عند ال K اللي هن أصغر شو ومين N وأخدت 
+
+101
+00:06:48,020 --> 00:06:51,860
+واحدة معينة و بحكي عنها طيب الآن we have احسب لي S
+
+102
+00:06:51,860 --> 00:06:56,920
+N و مين و ال E J ال J بجبلها في الطريق لما أصل ل N
+
+103
+00:06:58,590 --> 00:07:01,710
+إذا عندي 1000E1 1000E2 1000E3 1000E4 1000E5 1000E6
+
+104
+00:07:01,710 --> 00:07:02,150
+1000E7 1000E9 1000E8 1000E9 1000E9 1000E9 1000E9
+
+105
+00:07:02,150 --> 00:07:02,310
+1000E9 1000E9 1000E9 1000E9 1000E9 1000E9 1000E9
+
+106
+00:07:02,310 --> 00:07:02,510
+1000E9 1000E9 1000E9 1000E9 1000E9 1000E9 1000E9
+
+107
+00:07:02,510 --> 00:07:02,690
+1000E9 1000E9 1000E9 1000E9 1000E9 1000E9 1000E9
+
+108
+00:07:02,690 --> 00:07:02,750
+1000E9 1000E9 1000E9 1000E9 1000E9 1000E9 1000E9
+
+109
+00:07:02,750 --> 00:07:04,450
+1000E9 1000E9 1000E9 1000E9 1000 اللي هنحي تصفر
+
+110
+00:07:04,450 --> 00:07:08,570
+كلهم معدة واحدة من الإجابة اللي هنا اليمين Alpha
+
+111
+00:07:08,570 --> 00:07:12,770
+J لأن J مهلة بجابلها من العدد من واحد لعند مين
+
+112
+00:07:12,770 --> 00:07:17,270
+لعند N واضح لإن ال J من عند واحد لعند كلا كلا
+
+113
+00:07:17,270 --> 00:07:22,050
+ما بتجلطش N أزرع سبعاً إذا أكيد كلهن هيتصفر من
+
+114
+00:07:22,050 --> 00:07:26,970
+المختلفات معدة عند ال EJ وEJ اللي هيبصير Alpha J
+
+115
+00:07:26,970 --> 00:07:31,650
+EJ ويساوي مين ال Alpha J إذا صارت هذه بيساوي Alpha J
+
+116
+00:07:32,420 --> 00:07:35,640
+يعني by the continuity of the inner product يعني
+
+117
+00:07:35,640 --> 00:07:39,320
+ال limit بدخل و بطلع برا اللي ده we have alpha j
+
+118
+00:07:39,320 --> 00:07:43,780
+بتساوي ال S N و ال E J هذا بروح as N goes to
+
+119
+00:07:43,780 --> 00:07:46,840
+infinity هذا ال sequence of partial sums بيصير إيه
+
+120
+00:07:46,840 --> 00:07:50,360
+أشماله؟ اللي هو ال series نفسها اللي هي مين؟ ال X 
+
+121
+00:07:50,360 --> 00:07:56,050
+ال X أيها as N goes to infinity بيصير هذه ماشي طيب
+
+122
+00:07:56,050 --> 00:07:59,370
+فبصير عندي الآن as n goes to infinity الـ alpha j
+
+123
+00:07:59,370 --> 00:08:04,980
+إيش هتساوي؟ هتساوي x و Ej أو الـ limit اللي هتساوي
+
+124
+00:08:04,980 --> 00:08:09,880
+X و EJ لكن إن أنا we can take K أصغر يساوي N as 
+
+125
+00:08:09,880 --> 00:08:15,100
+large as possible زي ما بدنا نوديها اللي هو إلى أي
+
+126
+00:08:15,100 --> 00:08:19,960
+رقم بدنا إياها إذا وكأنه بقدر أمسح الـ Alpha J كله
+
+127
+00:08:19,960 --> 00:08:22,360
+بتمسحن بتاخد الفا واحد و الاثنين و الثلاثة إلى ما 
+
+128
+00:08:22,360 --> 00:08:27,840
+لانهاية لأن الـ K بقدر أخدها زي ما بدي لاقي إنه أنا
+
+129
+00:08:27,840 --> 00:08:32,520
+وديت ال N إلى وين إلى ما لانهاية إذا صارت عندي الـ α
+
+130
+00:08:32,520 --> 00:08:36,540
+J بتساوي X و EJ لكل J واحد اثنين ثلاثة Therefore
+
+131
+00:08:36,540 --> 00:08:39,540
+هيساوي ال X بتساوي هذا الكلام بشيل هذا و بحط
+
+132
+00:08:39,540 --> 00:08:44,340
+قيمتها اللي حصلتها اللي هي X و EK EK فبكون هي حصلت
+
+133
+00:08:44,340 --> 00:08:48,620
+على X نيجي الآن لآخر واحدة قلناها برهانها الأخيرة 
+
+134
+00:08:48,620 --> 00:08:55,670
+C مش Bلتكس بيه يعني إيه الهدسي لتكس بيه يعني إيه 
+
+135
+00:08:55,670 --> 00:08:58,930
+ال element نتش بسلزين quality ال summation هذا
+
+136
+00:08:58,930 --> 00:08:59,990
+عزيزي عزيزي عزيزي عزيزي عزيزي عزيزي عزيزي عزيزي 
+
+137
+00:08:59,990 --> 00:09:04,690
+عزيزي إذا هذا إيه شماله is bounded above y أكثر بعد
+
+138
+00:09:04,690 --> 00:09:07,210
+أن converged إذا صار عند ال summation هذا
+
+139
+00:09:07,210 --> 00:09:11,890
+converged and so by a summation xe k converged k
+
+140
+00:09:11,890 --> 00:09:17,450
+من واحد لمين لما لا نهاية أعرف لأن هذه ال k هي الألفز 
+
+141
+00:09:17,450 --> 00:09:21,670
+لما تمت converged إذا إيه شمالها اللي جوا converged
+
+142
+00:09:21,670 --> 00:09:27,570
+نيجي للمعرفة الأخيرة NX in a narrow product
+
+143
+00:09:27,570 --> 00:09:32,170
+space X can have at most countably many non-zero
+
+144
+00:09:32,170 --> 00:09:35,970
+Fourier coefficients X وEK with respect to an
+
+145
+00:09:35,970 --> 00:09:45,550
+orthonormal family E, K, K من عند واحد لـ NX لأن
+
+146
+00:09:45,550 --> 00:09:51,320
+أي X في narrow product space أكثر حاجة أكثر حاجة
+
+147
+00:09:51,320 --> 00:09:54,800
+بيكون لها countably many non-zero Fourier 
+
+148
+00:09:54,800 --> 00:09:57,440
+coefficients يعني هتكون اللي مش صفر من الـ Fourier 
+
+149
+00:09:57,440 --> 00:10:01,140
+coefficients اللي هي أشملها أقصى حاجة sequence إلى
+
+150
+00:10:01,140 --> 00:10:06,630
+مال نهاية countable يعني ماشي الحال الـ remark
+
+151
+00:10:06,630 --> 00:10:10,470
+الأخيرة الـ Bessel Inequality holds in the case
+
+152
+00:10:10,470 --> 00:10:14,470
+of E, K, K elements in I as an orthonormal
+
+153
+00:10:14,470 --> 00:10:17,530
+family summation هذه أصغر family number X تربيع
+
+154
+00:10:17,530 --> 00:10:21,070
+اللي بيقولوا احنا اللي جابلناها بشوية ركزوا في الحديد
+
+155
+00:10:21,070 --> 00:10:24,130
+جابلناها بشوية احنا اللي أثبتناها الـ Bessel 
+
+156
+00:10:24,130 --> 00:10:26,790
+Inequality على الـ sequence ده ما تكون sequence of
+
+157
+00:10:26,790 --> 00:10:30,970
+orthonormal set أو
+
+158
+00:10:30,970 --> 00:10:36,540
+sequence الآن لو كانت any ... any family of
+
+159
+00:10:36,540 --> 00:10:41,200
+orthonormal set EKK ∈I برضه الـ Bessel Inequality
+
+160
+00:10:41,200 --> 00:10:45,180
+هتكون صحيحة إثباتها سهل بناء على الملاحظة هذه وعالـ
+
+161
+00:10:45,180 --> 00:10:49,400
+Bessel Inequality الملاحظة بتقول لي إن هذول اللي
+
+162
+00:10:49,400 --> 00:10:54,380
+هي الـ ... الـ ... الـ ... الـ scalars اللي عندك أقصى حد
+
+163
+00:10:54,380 --> 00:10:57,860
+... أقصى حد اللي هين count بالـ number of non-zero
+
+164
+00:10:57,860 --> 00:11:02,110
+elements والباقي هو إيش ما قاله صفر إذا ... إذا
+
+165
+00:11:02,110 --> 00:11:05,930
+بتتحول الجثة وكأنه إلى countable number of
+
+166
+00:11:05,930 --> 00:11:09,230
+elements من هذا اللي بيكون إن هدول الـ scalars مش
+
+167
+00:11:09,230 --> 00:11:12,790
+صفر احنا أثبتناها في الـ ... في الـ ... في الـ ... في 
+
+168
+00:11:12,790 --> 00:11:15,230
+الـ Bessel inequality ... quality نمين لأي sequence
+
+169
+00:11:15,230 --> 00:11:18,610
+بالشروط اللي حكيناها فبيصير عندي هذا أخر سوء نوع من
+
+170
+00:11:18,610 --> 00:11:23,550
+X أربعة بغض النظر عن K element incountable أو
+
+171
+00:11:23,550 --> 00:11:27,830
+uncountable اللي هي index family، ماشي؟ إذا صار
+
+172
+00:11:27,830 --> 00:11:31,870
+عندي اللي هي هذه اللي هي Bessel inequality صحيحة لأي
+
+173
+00:11:31,870 --> 00:11:37,670
+حالة ومنها اللي هو تسمية بس لو كان فيه مساواة
+
+174
+00:11:37,670 --> 00:11:43,400
+بنسميها Parseval relation وإلى لقاء آخر بارك الله
+
+175
+00:11:43,400 --> 00:11:44,580
+فيكم وأعطيكم العافية 
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/cy-kIawWPhI_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/cy-kIawWPhI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..581100d18871fbcdae088e5d5a11fa56e36c1ab6
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/cy-kIawWPhI_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2261, "start": 5.43, "end": 22.61, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى آله وصحبه أجمعين هذه المحاضرة رقم واحد وعشرين مساق تحليل دالي أو تحليل اقتراني طلاب وطالبات الجامعة الإسلامية ماجستير رياضيات", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 19753, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 29538, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 36764, 24401, 4032, 3615, 46309, 9957, 47524, 995, 4587, 6055, 5016, 20292, 1211, 11778, 6027, 1829, 34051, 6055, 5016, 20292, 1211, 1975, 38149, 2288, 7649, 1829, 23032, 15040, 3555, 4032, 9566, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 3714, 26108, 14851, 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المضلس لألف M تربيع زاد ألف M اتنين تربيع زاد ألف M لكل تربيع اللي هو في الواقع مين مين هو سيجما ان ناقص مين سيجما ان إذا صار وكأنه عندي ال norm لالأسئن ناقص أسئن من كل تربيع هو نفس مين سيجما ان ناقص سيجما ان", "tokens": [1863, 13063, 2655, 2407, 8717, 13063, 2304, 6027, 8608, 2655, 11933, 15730, 39896, 19913, 1211, 23758, 28242, 3224, 39896, 32887, 5016, 39896, 19913, 1211, 4724, 32277, 2304, 9957, 9673, 11242, 1211, 3794, 5296, 10721, 46538, 376, 6055, 2288, 21292, 3615, 30767, 18513, 5551, 46538, 376, 1975, 2655, 1863, 9957, 6055, 2288, 21292, 3615, 30767, 18513, 5551, 46538, 376, 5296, 28820, 6055, 2288, 21292, 3615, 13672, 1829, 31439, 8978, 2423, 14407, 4587, 3615, 3714, 9957, 3714, 9957, 31439, 8608, 1829, 7435, 15042, 16472, 8717, 995, 4587, 9381, 3714, 9957, 8608, 1829, 7435, 15042, 16472, 11933, 15730, 20328, 9640, 4032, 4117, 33456, 3224, 18871, 16254, 2423, 2026, 5296, 6027, 10721, 3794, 19986, 1863, 8717, 995, 4587, 9381, 5551, 3794, 19986, 1863, 9154, 28242, 6055, 2288, 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therefore Sn is Cauchy in H if and only if Σn is Cauchy in C أو in R لأن الاتنين أشمالهم الفرق بين Sn و Sm هو نفس الفرق بين Σن و Σم إذا لو كانت هذه Cauchy هتكون هذه Cauchy لو كانت هذه Cauchy هتكون أشمالها Cauchy واضحة", "tokens": [28814, 8848, 1863, 4412, 9264, 307, 7544, 625, 88, 294, 389, 498, 293, 787, 498, 26408, 77, 307, 7544, 625, 88, 294, 383, 34051, 294, 497, 5296, 33456, 2423, 9307, 1863, 9957, 5551, 8592, 2304, 6027, 16095, 27188, 2288, 4587, 49374, 9264, 4032, 3915, 31439, 8717, 36178, 27188, 2288, 4587, 49374, 26408, 1863, 4032, 26408, 2304, 11933, 15730, 45164, 25961, 2655, 29538, 7544, 625, 88, 8032, 2655, 30544, 29538, 7544, 625, 88, 45164, 25961, 2655, 29538, 7544, 625, 88, 8032, 2655, 30544, 5551, 8592, 2304, 6027, 11296, 7544, 625, 88, 4032, 46958, 5016, 3660], "avg_logprob": -0.26496710777282717, "compression_ratio": 1.761111111111111, "no_speech_prob": 4.172325134277344e-06, "words": [{"start": 303.05999999999995, "end": 303.71999999999997, "word": "إذن", 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"temperature": 1.0}, {"id": 14, "seek": 34027, "start": 324.03, "end": 340.27, "text": "أفصلها ماشي لحظة اطلع لفوق however both H and R are complete إذا أسأل converts if and only if سجلنا إيش مالها converts إذا الآن صار عندى الان hence", "tokens": [10721, 5172, 36520, 11296, 3714, 33599, 1829, 5296, 5016, 19913, 3660, 1975, 9566, 1211, 3615, 5296, 5172, 30543, 4461, 1293, 389, 293, 497, 366, 3566, 11933, 15730, 5551, 3794, 10721, 1211, 38874, 498, 293, 787, 498, 8608, 7435, 1211, 8315, 11933, 1829, 8592, 3714, 6027, 11296, 38874, 11933, 15730, 6024, 48506, 20328, 9640, 43242, 7578, 2423, 7649, 16678], "avg_logprob": -0.40492583533464854, "compression_ratio": 1.2857142857142858, "no_speech_prob": 0.00040149688720703125, "words": [{"start": 324.03000000000003, "end": 324.91, "word": "أفصلها", "probability": 0.7490234375}, {"start": 324.91, "end": 325.79, "word": " ماشي", "probability": 0.686767578125}, {"start": 325.79, "end": 325.97, "word": " لحظة", "probability": 0.631561279296875}, 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فبصير عندي هذا أخر سوء نوع من X أربع بغض النظر عن K element incountable أو uncountable اللي هي index family، ماشي؟ إذا صار عندي اللي هي هذه اللي هي best inequality صحيحة لأي حالة ومنها اللي هو تسمية بس لو كان فيه مسواة بنسميها Parsival relation", "tokens": [2407, 39319, 8315, 5551, 12984, 3555, 2655, 8315, 11296, 8978, 2423, 39184, 4386, 8978, 2423, 39184, 4386, 8978, 2423, 39184, 4386, 8978, 2423, 39184, 1151, 16970, 4386, 3125, 8717, 2304, 1829, 1863, 5296, 10721, 1829, 8310, 20666, 8592, 32887, 9566, 13672, 1829, 11331, 4117, 1829, 8315, 11296, 6156, 3555, 9381, 13546, 18871, 16254, 23758, 5551, 34740, 8608, 2407, 38207, 8717, 45367, 9154, 1783, 5551, 25513, 3615, 4724, 17082, 11242, 28239, 19913, 2288, 18871, 591, 4478, 834, 792, 712, 34051, 6219, 792, 712, 13672, 1829, 39896, 8186, 1605, 12399, 3714, 33599, 1829, 22807, 11933, 15730, 20328, 9640, 18871, 16254, 13672, 1829, 39896, 29538, 13672, 1829, 39896, 1151, 16970, 20328, 5016, 1829, 5016, 3660, 5296, 10721, 1829, 11331, 6027, 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0.8150634765625}, {"start": 675.99, "end": 676.09, "word": " اللي", "probability": 0.968994140625}, {"start": 676.09, "end": 676.65, "word": " حكيناها", "probability": 0.87646484375}, {"start": 676.65, "end": 677.33, "word": " فبصير", "probability": 0.81591796875}, {"start": 677.33, "end": 677.63, "word": " عندي", "probability": 0.653076171875}, {"start": 677.63, "end": 677.85, "word": " هذا", "probability": 0.330322265625}, {"start": 677.85, "end": 678.13, "word": " أخر", "probability": 0.4241943359375}, {"start": 678.13, "end": 678.35, "word": " سوء", "probability": 0.4635416666666667}, {"start": 678.35, "end": 678.53, "word": " نوع", "probability": 0.402587890625}, {"start": 678.53, "end": 678.61, "word": " من", "probability": 0.9677734375}, {"start": 678.61, "end": 678.79, "word": " X", "probability": 0.830078125}, {"start": 678.79, "end": 679.15, "word": " أربع", "probability": 0.6476236979166666}, {"start": 679.15, "end": 680.09, "word": " بغض", "probability": 0.9733072916666666}, {"start": 680.09, "end": 680.75, "word": " النظر", "probability": 0.9794921875}, {"start": 680.75, "end": 681.09, "word": " عن", "probability": 0.99169921875}, {"start": 681.09, "end": 681.43, "word": " K", "probability": 0.61767578125}, {"start": 681.43, "end": 682.07, "word": " element", "probability": 0.81298828125}, {"start": 682.07, "end": 683.09, "word": " incountable", "probability": 0.7115071614583334}, {"start": 683.09, "end": 683.55, "word": " أو", "probability": 0.9375}, {"start": 683.55, "end": 684.53, "word": " uncountable", "probability": 0.9637044270833334}, {"start": 684.53, "end": 684.99, "word": " اللي", "probability": 0.97314453125}, {"start": 684.99, "end": 685.25, "word": " هي", "probability": 0.9033203125}, {"start": 685.25, "end": 685.71, "word": " index", "probability": 0.85791015625}, {"start": 685.71, "end": 686.57, "word": " family،", "probability": 0.5960693359375}, {"start": 686.57, "end": 687.31, "word": " ماشي؟", "probability": 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691.87, "end": 692.55, "word": " حالة", "probability": 0.9983723958333334}, {"start": 692.55, "end": 693.83, "word": " ومنها", "probability": 0.9482421875}, {"start": 693.83, "end": 694.75, "word": " اللي", "probability": 0.9931640625}, {"start": 694.75, "end": 695.07, "word": " هو", "probability": 0.98828125}, {"start": 695.07, "end": 695.61, "word": " تسمية", "probability": 0.9889322916666666}, {"start": 695.61, "end": 695.91, "word": " بس", "probability": 0.966552734375}, {"start": 695.91, "end": 696.29, "word": " لو", "probability": 0.5986328125}, {"start": 696.29, "end": 696.53, "word": " كان", "probability": 0.994140625}, {"start": 696.53, "end": 696.75, "word": " فيه", "probability": 0.727294921875}, {"start": 696.75, "end": 697.67, "word": " مسواة", "probability": 0.7760416666666666}, {"start": 697.67, "end": 698.27, "word": " بنسميها", "probability": 0.91748046875}, {"start": 698.27, "end": 698.93, "word": " Parsival", "probability": 0.4815673828125}, {"start": 698.93, "end": 699.91, "word": " relation", "probability": 0.82763671875}], "temperature": 1.0}, {"id": 32, "seek": 70458, "start": 701.48, "end": 704.58, "text": "وإلى لقاء آخر برك الله فيكم و أعطيكم العافية", "tokens": [2407, 28814, 23942, 5296, 4587, 16606, 19753, 34740, 4724, 31747, 21984, 8978, 24793, 4032, 5551, 3615, 9566, 1829, 24793, 18863, 31845, 10632], "avg_logprob": -0.27836277173913043, "compression_ratio": 1.1111111111111112, "no_speech_prob": 0.0, "words": [{"start": 701.48, "end": 702.02, "word": "وإلى", "probability": 0.765380859375}, {"start": 702.02, "end": 702.38, "word": " لقاء", "probability": 0.9265950520833334}, {"start": 702.38, "end": 702.8, "word": " آخر", "probability": 0.76953125}, {"start": 702.8, "end": 703.22, "word": " برك", "probability": 0.56640625}, {"start": 703.22, "end": 703.4, "word": " الله", "probability": 0.93505859375}, {"start": 703.4, "end": 703.72, "word": " فيكم", "probability": 0.857177734375}, {"start": 703.72, "end": 703.94, "word": " و", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/cy-kIawWPhI_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/cy-kIawWPhI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..82258745f40c32efb26efa7f2417e9040ba4082e
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/cy-kIawWPhI_raw.srt
@@ -0,0 +1,716 @@
+1
+00:00:05,430 --> 00:00:07,810
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,810 --> 00:00:10,490
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,490 --> 00:00:15,370
+آله وصحبه أجمعين هذه المحاضرة رقم واحد وعشرين مساق
+
+4
+00:00:15,370 --> 00:00:20,010
+تحليل دالي أو تحليل اقتراني طلاب وطالبات الجامعة
+
+5
+00:00:20,010 --> 00:00:24,770
+الإسلامية ماجستير رياضياتوصلنا لعند section تلاتة
+
+6
+00:00:24,770 --> 00:00:27,250
+خمسة series related to orthonormal sets and
+
+7
+00:00:27,250 --> 00:00:31,810
+sequences احنا هناخد الجزئية هذه بس من ال section
+
+8
+00:00:31,810 --> 00:00:34,130
+هذا المطلوب من ال section بس اللي موجود في التلخيص
+
+9
+00:00:34,130 --> 00:00:38,370
+النظرية اللي عندي اللي هو let A K B an orthonormal
+
+10
+00:00:38,370 --> 00:00:41,350
+sequence in a Hilbert space etched in for
+
+11
+00:00:41,350 --> 00:00:44,510
+unscalars ألف واحد و ألف اتنين و ألف تلاتة اللي هو
+
+12
+00:00:44,510 --> 00:00:49,350
+إلى ملانهاية هذه ال A و B و C صحيحة إذا احنا حكينا
+
+13
+00:00:49,350 --> 00:00:54,630
+عن مين عن orthonormal sequenceبقولي summation للـ
+
+14
+00:00:54,630 --> 00:00:58,510
+α K E K كامل عند واحد لما لنهاية هذه بتكون
+
+15
+00:00:58,510 --> 00:01:00,750
+convergence إذا وفقط إذا مين اللي بتحكم في ال
+
+16
+00:01:00,750 --> 00:01:03,410
+convergence ل ال scalars if and only if ال
+
+17
+00:01:03,410 --> 00:01:06,010
+summation ل ال modulus لل scalars تربيع تكون إيش
+
+18
+00:01:06,010 --> 00:01:08,730
+ما ل convergence يعني ال series هذه ال convergence
+
+19
+00:01:08,730 --> 00:01:12,390
+تبعها عشان أفحص test بكفي أن أفحص اللي هو يعني
+
+20
+00:01:12,390 --> 00:01:16,350
+بحول الحديث وكأني من convergence ال convergence في
+
+21
+00:01:16,350 --> 00:01:19,330
+Hilbert space أو في norm تبع ال Hilbert space إلى
+
+22
+00:01:19,330 --> 00:01:23,000
+convergence في C أو في Rيعني في تبعات الـ Calculus
+
+23
+00:01:23,000 --> 00:01:26,200
+العادى اللي هي الـ Calculus G الان ال .. ال .. ال
+
+24
+00:01:26,200 --> 00:01:28,940
+.. ال B اللي هو إذا كان الصممش اللي Alpha K, E, K
+
+25
+00:01:28,940 --> 00:01:33,200
+هذا K من واحدة مهلاً هي Converse هتكون الـ Alpha K
+
+26
+00:01:33,200 --> 00:01:35,960
+هذه هي عبارة عن الـ Fourier coefficients اللي
+
+27
+00:01:35,960 --> 00:01:39,260
+حكيناها قبل شوية اللي هي إيه شمالها X و E, K يعني
+
+28
+00:01:39,260 --> 00:01:43,480
+إذا كانت هذه Converse هتكون حتماً حتماً حتماً الـ
+
+29
+00:01:43,480 --> 00:01:47,400
+Alpha K هي عبارة عن ال inner products بين X و E, K
+
+30
+00:01:47,930 --> 00:01:51,550
+Where X denotes X مين هي ال summation اللي أمامي
+
+31
+00:01:51,550 --> 00:01:56,170
+أو بمعنى
+
+32
+00:01:56,170 --> 00:02:00,150
+آخر يعني هذا الكلام كله بنقدر نقول ان ال summation
+
+33
+00:02:00,150 --> 00:02:05,580
+للألف ك إي ك ك من واحد دايما بيساوي Xهتلاقي هيساوي
+
+34
+00:02:05,580 --> 00:02:10,080
+هو نفسه الـ X والـ EK EK K من واحد إلى مانعها هذا
+
+35
+00:02:10,080 --> 00:02:13,600
+في حال ال series أشمل هتكون converts يعني لو كانت
+
+36
+00:02:13,600 --> 00:02:15,900
+اللي هي X مكتوبة على الصورة هذه يعني ال
+
+37
+00:02:15,900 --> 00:02:19,960
+convergence هتكون هذه الـ X أنا بقدر أكتبها على
+
+38
+00:02:19,960 --> 00:02:23,640
+صورة X و EK EK K من واحد إلى مانعها هذه الصورة
+
+39
+00:02:23,640 --> 00:02:26,120
+اللي هي مفيدة كتير ل .. اللي هي شغلات في ال
+
+40
+00:02:26,120 --> 00:02:30,520
+applications للـ Fourier series اطلع لفوقfor any x
+
+41
+00:02:30,520 --> 00:02:34,740
+element in H هيكون ال summation لان بيقولك أي x في
+
+42
+00:02:34,740 --> 00:02:37,660
+ال H الآن بناء عليه أي x في ال H بناء عليه ال
+
+43
+00:02:37,660 --> 00:02:43,520
+inequality هيكون ال summation لل x و ال ek و ال ek
+
+44
+00:02:43,520 --> 00:02:48,660
+هذه دايما إيه شمالها converge لأنه قبل بشوية خدنا
+
+45
+00:02:48,660 --> 00:02:52,660
+المدلس إلها أصغر أو يساوي نورمل x تربيه يعني لأنها
+
+46
+00:02:52,660 --> 00:02:58,580
+ستصبح converge لل x في ال H طيب نيجي الآن انبرهنلت
+
+47
+00:02:58,580 --> 00:03:02,540
+أس أن بتساوي Alpha E1 E1 زي Alpha 2 E2 زي Alpha N
+
+48
+00:03:02,540 --> 00:03:08,080
+EN مجرد رموز عشان نصل منها الـ Sigma N هي عبارة عن
+
+49
+00:03:08,080 --> 00:03:11,900
+Alpha 1 Alpha 2 إلى ما لهي تربيع وكأنه هذه عبارة
+
+50
+00:03:11,900 --> 00:03:14,980
+عن sequence of partial sums للسيريز الأولى وهذه
+
+51
+00:03:14,980 --> 00:03:18,160
+sequence of partial sums لمين للسيريز تبعت مين
+
+52
+00:03:18,160 --> 00:03:22,070
+اللي هي ال .. ال .. ال .. ال scalarsلأن بما أنه EK
+
+53
+00:03:22,070 --> 00:03:27,210
+is an orthonormal إذا لكل N أكبر من M أحسب للأس أن
+
+54
+00:03:27,210 --> 00:03:31,510
+ناقص أس M لكل تربية هذا بساوي اللي هو أس أن ناقص
+
+55
+00:03:31,510 --> 00:03:34,810
+أس M اللي N أكبر من M ماشي الحال فبتروح لتبعات ال
+
+56
+00:03:34,810 --> 00:03:38,450
+M و بظل اللي هي اللي بعيدها بيصير ألف M زائد واحد
+
+57
+00:03:38,450 --> 00:03:42,670
+في E واحد زائد ألف M زائد اتنين في E اتنين في E
+
+58
+00:03:42,670 --> 00:03:48,660
+واحد ألا واحد مكتوب هنافزائد ألف أم زائد اتنين في
+
+59
+00:03:48,660 --> 00:03:52,260
+أم زائد اتنين ماشي الحال زائد واحد زائد واحد ماشي
+
+60
+00:03:52,260 --> 00:03:57,020
+زائد اللي هو ألف أن إي أن فاهمين اللي هو حصل طرح
+
+61
+00:03:57,020 --> 00:04:00,640
+اللهان مع اللهان ويساوي ال inner product هذا بقي
+
+62
+00:04:00,640 --> 00:04:04,520
+أشماله بنفسفسه ال norm إلى inner product ال inner
+
+63
+00:04:04,520 --> 00:04:08,140
+product الأول والتاني هذا مع التاني واحنا زي ما
+
+64
+00:04:08,140 --> 00:04:13,360
+احنا عارفينالمختلفات هيتصفرن و هيضلمين اللي زي بعض
+
+65
+00:04:13,360 --> 00:04:17,400
+فبصير عندي α M زائد واحد تربيع في نورم ال E M زائد
+
+66
+00:04:17,400 --> 00:04:21,140
+واحد لكل تربيع عملناها كتير هذه زائد ألف M زائد
+
+67
+00:04:21,140 --> 00:04:24,260
+اتنين تربيع في E M زائد اتنين لكل تربيع لما أصل
+
+68
+00:04:24,260 --> 00:04:28,140
+لآخر واحدة ألف N تربيع في E N لكل تربيع لإن ال
+
+69
+00:04:28,140 --> 00:04:32,060
+product بين اي اتنين E I و E J مختلفة بيطلع عياش
+
+70
+00:04:32,060 --> 00:04:36,040
+سفر إذا بضلم بس المتشابهات و يساوي النورمات ما هن
+
+71
+00:04:36,040 --> 00:04:42,820
+واحدنورتو نورمال ست إذا هيظل هذا كله هيروح هيظل
+
+72
+00:04:42,820 --> 00:04:46,540
+باسمين المضلس لألف M تربيع زاد ألف M اتنين تربيع
+
+73
+00:04:46,540 --> 00:04:49,460
+زاد ألف M لكل تربيع اللي هو في الواقع مين مين هو
+
+74
+00:04:49,460 --> 00:04:54,980
+سيجما ان ناقص مين سيجما ان إذا صار وكأنه عندي ال
+
+75
+00:04:54,980 --> 00:05:00,220
+norm لالأسئن ناقص أسئن من كل تربيع هو نفس مين
+
+76
+00:05:00,220 --> 00:05:06,300
+سيجما ان ناقص سيجما انإذن therefore Sn is Cauchy
+
+77
+00:05:06,300 --> 00:05:11,220
+in H if and only if Σn is Cauchy in C أو in R لأن
+
+78
+00:05:11,220 --> 00:05:15,620
+الاتنين أشمالهم الفرق بين Sn و Sm هو نفس الفرق بين
+
+79
+00:05:15,620 --> 00:05:19,400
+Σن و Σم إذا لو كانت هذه Cauchy هتكون هذه Cauchy لو
+
+80
+00:05:19,400 --> 00:05:24,910
+كانت هذه Cauchy هتكون أشمالها Cauchy واضحةأفصلها
+
+81
+00:05:24,910 --> 00:05:31,250
+ماشي لحظة اطلع لفوق however both H and R are
+
+82
+00:05:31,250 --> 00:05:35,010
+complete إذا أسأل converts if and only if سجلنا
+
+83
+00:05:35,010 --> 00:05:40,270
+إيش مالها converts إذا الآن صار عندى الان hence
+
+84
+00:05:40,840 --> 00:05:43,960
+اللي هي Sn هي sequence of partial sums لها دي و
+
+85
+00:05:43,960 --> 00:05:46,620
+Sigma N هي sequence of partial sums لها دي إذا
+
+86
+00:05:46,620 --> 00:05:48,980
+الحاجة صار عند ال summation هذا converge if and
+
+87
+00:05:48,980 --> 00:05:52,080
+only if ال summation هذا ليهاش converge لإنه اللي
+
+88
+00:05:52,080 --> 00:05:54,980
+هو ال series بتكون converge if and only if اللي هو
+
+89
+00:05:54,980 --> 00:05:57,900
+ال sequence of partial sums اللي هت converge واضح
+
+90
+00:05:57,900 --> 00:06:04,130
+أه نيجي الأن للجزء الثانينفترض إن الأسئلة اللي قبل
+
+91
+00:06:04,130 --> 00:06:08,630
+شوية converged a mean ل some x أو بمعنى آخر الـ x
+
+92
+00:06:08,630 --> 00:06:11,630
+إيش بتساوي الـ summation Alpha K إي K كامل عند
+
+93
+00:06:11,630 --> 00:06:14,910
+واحد عنين لعين انفجر K بدنا نثبت أن الـ Alpha K
+
+94
+00:06:14,910 --> 00:06:18,730
+زاد إي شمالين هي عبارة عن الـ X والـ E K طيب let n
+
+95
+00:06:18,730 --> 00:06:24,850
+be any fixed natural number then for any fixed J
+
+96
+00:06:24,850 --> 00:06:28,650
+بيساوي واحد واتنين إلى آخر K والـ K أصغر أو يساوي
+
+97
+00:06:28,650 --> 00:06:34,920
+100 N إيش عملتثبتت N أخدت N إشي معين و أخدتلك الـ
+
+98
+00:06:34,920 --> 00:06:40,280
+N J واحدة من الواحد والتنين والتلاتة اللي عند ال K
+
+99
+00:06:40,280 --> 00:06:44,540
+و ال K أصغر شو و مين N يعني جيت أخدت من هدول اللي
+
+100
+00:06:44,540 --> 00:06:48,020
+من الواحد اللي عند ال K اللي هن أصغر شو و N وأخدت
+
+101
+00:06:48,020 --> 00:06:51,860
+واحدة معينة و بحكي عنها طيب الآن we have احسب لي S
+
+102
+00:06:51,860 --> 00:06:56,920
+N و مين و ال E J ال J بجبلها في الطريق لما أصل ل N
+
+103
+00:06:58,590 --> 00:07:01,710
+أذا عندي 1000E1 1000E2 1000E3 1000E4 1000E5 1000E6
+
+104
+00:07:01,710 --> 00:07:02,150
+1000E7 1000E9 1000E8 1000E9 1000E9 1000E9 1000E9
+
+105
+00:07:02,150 --> 00:07:02,310
+1000E9 1000E9 1000E9 1000E9 1000E9 1000E9 1000E9
+
+106
+00:07:02,310 --> 00:07:02,510
+1000E9 1000E9 1000E9 1000E9 1000E9 1000E9 1000E9
+
+107
+00:07:02,510 --> 00:07:02,690
+1000E9 1000E9 1000E9 1000E9 1000E9 1000E9 1000E9
+
+108
+00:07:02,690 --> 00:07:02,750
+1000E9 1000E9 1000E9 1000E9 1000E9 1000E9 1000E9
+
+109
+00:07:02,750 --> 00:07:02,750
+1000E9 1000E9 1000E9 1000E9 1000E9 1000E9 1000E9
+
+110
+00:07:02,750 --> 00:07:02,750
+1000E9 1000E9 1000E9 1000E9 1000E9 1000E9 1000E9
+
+111
+00:07:02,750 --> 00:07:02,750
+1000E9 1000E9 1000E9 1000E9 1000E9 1000E9 1000E9
+
+112
+00:07:02,750 --> 00:07:02,750
+1000E9 1000E9 1000E9 1000E9 1000E9 1000E9 1000E9
+
+113
+00:07:02,750 --> 00:07:04,450
+1000E9 1000E9 1000E9 1000E9 1000اللي هنحي تصفر
+
+114
+00:07:04,450 --> 00:07:08,570
+كلهم معدة واحدة من البجابة اللي هنا اليامين Alpha
+
+115
+00:07:08,570 --> 00:07:12,770
+J لأن J مهلة بجابلها من العدد من واحد لعند مين
+
+116
+00:07:12,770 --> 00:07:17,270
+لعند الان واضح لإن ال J من عند واحد لعند كلا كلا
+
+117
+00:07:17,270 --> 00:07:22,050
+مابتجلطش ان أزرع سبعاً إذا أكيد كلهن هيتصفر من
+
+118
+00:07:22,050 --> 00:07:26,970
+المختلفات معدة عند ال EJ وEJ اللي هيبصير Alpha J
+
+119
+00:07:26,970 --> 00:07:31,650
+EJ ويسوء مين ال Alpha J إذا صارت هذه بيسوء Alpha J
+
+120
+00:07:32,420 --> 00:07:35,640
+يعني by the continuity of the inner product يعني
+
+121
+00:07:35,640 --> 00:07:39,320
+ال limit بدخل و بطلع برا اللي ده we have alpha j
+
+122
+00:07:39,320 --> 00:07:43,780
+بتساوي ال S N و ال E J هذا بروح as N goes to
+
+123
+00:07:43,780 --> 00:07:46,840
+infinity هذا ال sequence of partial sums بيصير إيه
+
+124
+00:07:46,840 --> 00:07:50,360
+أشماله؟ اللي هو ال series نفسها اللي هي مين؟ ال X
+
+125
+00:07:50,360 --> 00:07:56,050
+ال X أيها as N goes to infinity بيصير هذهماشي طيب
+
+126
+00:07:56,050 --> 00:07:59,370
+فبصير عندى الآن as n goes to infinity الـ alpha j
+
+127
+00:07:59,370 --> 00:08:04,980
+إيش هتساوي؟ هتساوي x و Ejأو الـ limit اللي هتساوي
+
+128
+00:08:04,980 --> 00:08:09,880
+X و EJ لكن إن أنا we can take K أصغر يساوي N as
+
+129
+00:08:09,880 --> 00:08:15,100
+large as possible زي ما بدنا نوديها اللي هو إلى أي
+
+130
+00:08:15,100 --> 00:08:19,960
+رقم بدنيها إذا و كأنه بقدر أمسح الـ Alpha J كله
+
+131
+00:08:19,960 --> 00:08:22,360
+بتمسحن بتاخد الفا واحد و الفتن و الفترة إلى ما
+
+132
+00:08:22,360 --> 00:08:27,840
+لنهاية لأن الـ K بقدر أخدها زي ما بدي لاقي إنه أنا
+
+133
+00:08:27,840 --> 00:08:32,520
+وديت ال N إلى وين إلى ما لنهايةإذا صارت عندي الـ α
+
+134
+00:08:32,520 --> 00:08:36,540
+J بتساوي X و EJ لكل J واحد اتنين تلاتة Therefore
+
+135
+00:08:36,540 --> 00:08:39,540
+هيساوي ال X بتساوي هذا الكلام بشيل هذا و بحط
+
+136
+00:08:39,540 --> 00:08:44,340
+قيمتها اللي حصلتها اللي هي X و EK EK فبكون هي حصلت
+
+137
+00:08:44,340 --> 00:08:48,620
+على X نيجي الآن لآخر واحدة قلناها برهانها الأخيرة
+
+138
+00:08:48,620 --> 00:08:55,670
+C مش Bلتكس بيه يعني إيه الهدسي لتكس بيه يعني إيه
+
+139
+00:08:55,670 --> 00:08:58,930
+ال element نتش بسلزين quality ال summation هذا
+
+140
+00:08:58,930 --> 00:08:59,990
+عزيزي عزيزي عزيزي عزيزي عزيزي عزيزي عزيزي عزيزي
+
+141
+00:08:59,990 --> 00:09:04,690
+عزيزيإذا هذا إيه شماله is bounded above y أكثر بعد
+
+142
+00:09:04,690 --> 00:09:07,210
+أن converged إذا صار عند ال summation هذا
+
+143
+00:09:07,210 --> 00:09:11,890
+converged and so by a summation xe k converged k
+
+144
+00:09:11,890 --> 00:09:17,450
+من واحد لمين لما لنا أعرف لأن هذه ال k هي الألفز
+
+145
+00:09:17,450 --> 00:09:21,670
+لما تمت converged إذا إيه شماله اللي جوا converged
+
+146
+00:09:21,670 --> 00:09:27,570
+نيجيهي للمعرفة الأخيرة NX in a narrow product
+
+147
+00:09:27,570 --> 00:09:32,170
+space X can have at most accountably many non-zero
+
+148
+00:09:32,170 --> 00:09:35,970
+Fourier coefficients X وEK with respect to an
+
+149
+00:09:35,970 --> 00:09:45,550
+orthonormal family E, K, K من عند واحد NX لأن
+
+150
+00:09:45,550 --> 00:09:51,320
+أي X في narrow product spaceأكتر حاجة أكتر حاجة
+
+151
+00:09:51,320 --> 00:09:54,800
+بيكون لها countably money non zero for real
+
+152
+00:09:54,800 --> 00:09:57,440
+coefficients يعني هتكون اللي مش صفر من ال for real
+
+153
+00:09:57,440 --> 00:10:01,140
+coefficients اللي هي أشملها أقصى حاجة sequence إلى
+
+154
+00:10:01,140 --> 00:10:06,630
+مال نهاية countable يعني ماشي الحالالـ remark
+
+155
+00:10:06,630 --> 00:10:10,470
+الأخيرة الـ Bisexual Inquality holds in the case
+
+156
+00:10:10,470 --> 00:10:14,470
+of E, K, K elements in I as an as an orthonormal
+
+157
+00:10:14,470 --> 00:10:17,530
+family summation هذه أصغر family number X تربية
+
+158
+00:10:17,530 --> 00:10:21,070
+اللي بيقولوا احنا اللي جابل بشوية ركزوا في الحديد
+
+159
+00:10:21,070 --> 00:10:24,130
+جابل بشوية احنا اللي أثبتناها الـ Bisexual
+
+160
+00:10:24,130 --> 00:10:26,790
+Inquality على ال sequence ده ما تكون sequence of
+
+161
+00:10:26,790 --> 00:10:30,970
+orthonormal set او
+
+162
+00:10:30,970 --> 00:10:36,540
+sequence الآن لو كانت any .. any familyof
+
+163
+00:10:36,540 --> 00:10:41,200
+orthonormal set EKK ∈I برضه الـ Bessel Inquality
+
+164
+00:10:41,200 --> 00:10:45,180
+هتكون صحيحة إثباتها سهل بناء على الملاحظة هذه وعال
+
+165
+00:10:45,180 --> 00:10:49,400
+Bessel Inquality الملاحظة بتقول لي ان هذولة اللي
+
+166
+00:10:49,400 --> 00:10:54,380
+هي ال .. ال .. ال .. ال scalars اللي عندك اقصى حد
+
+167
+00:10:54,380 --> 00:10:57,860
+.. اقصى حد اللي هين count بال number of non-zero
+
+168
+00:10:57,860 --> 00:11:02,110
+elements والباقي هو إيش ما قاله سفارإذا .. إذا
+
+169
+00:11:02,110 --> 00:11:05,930
+بتتحول الجثة وكأنه إلى countable number of
+
+170
+00:11:05,930 --> 00:11:09,230
+elements من هذا اللي بيكون إن هدول ال scalars مش
+
+171
+00:11:09,230 --> 00:11:12,790
+سفرواحنا أثبتناها في الـ .. في الـ .. في الـ .. في
+
+172
+00:11:12,790 --> 00:11:15,230
+الـ best inequality .. quality نمين لأي sequence
+
+173
+00:11:15,230 --> 00:11:18,610
+بالشروط اللي حكيناها فبصير عندي هذا أخر سوء نوع من
+
+174
+00:11:18,610 --> 00:11:23,550
+X أربع بغض النظر عن K element incountable أو
+
+175
+00:11:23,550 --> 00:11:27,830
+uncountable اللي هي index family، ماشي؟ إذا صار
+
+176
+00:11:27,830 --> 00:11:31,870
+عندي اللي هي هذه اللي هي best inequality صحيحة لأي
+
+177
+00:11:31,870 --> 00:11:37,670
+حالة ومنها اللي هو تسمية بس لو كان فيه مسواة
+
+178
+00:11:37,670 --> 00:11:43,400
+بنسميها Parsival relationوإلى لقاء آخر برك الله
+
+179
+00:11:43,400 --> 00:11:44,580
+فيكم و أعطيكم العافية
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/dAhzu2_CB2I.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/dAhzu2_CB2I.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1b9eb1b3118fab6ea3d6900918332dc9224e2e44
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/dAhzu2_CB2I.srt
@@ -0,0 +1,723 @@
+1
+00:00:05,470 --> 00:00:08,230
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,230 --> 00:00:11,930
+والصلاة والسلام على سيد المرسلين سيدنا محمد عليه
+
+3
+00:00:11,930 --> 00:00:15,690
+آله وصحبه أجمعين هذه المحاضرة رقم أربعة وثلاثين
+
+4
+00:00:15,690 --> 00:00:20,310
+مساق تحليل دالي أو تحليل اقتراني لطلاب وطالبات 
+
+5
+00:00:20,310 --> 00:00:27,030
+الجامعة الإسلامية ماجستير رياضيات وصلنا لعند أربعة
+
+6
+00:00:27,030 --> 00:00:31,250
+نظريات اللي هي الـ open mapping theorem اللي هي عشر
+
+7
+00:00:31,250 --> 00:00:32,490
+أو إحدى عشرة مش مقلبات
+
+8
+00:00:35,050 --> 00:00:39,410
+النظرية الثالثة من النظريات الأساسية بعد الـ
+
+9
+00:00:39,410 --> 00:00:47,350
+uniform boundedness theorem هو أخذناها المرة
+
+10
+00:00:47,350 --> 00:00:50,310
+الماضية وهذه الثالثة وقبلها أخذنا الـ Banach
+
+11
+00:00:50,310 --> 00:00:54,990
+theorem فبكون هذه الثالثة نظرية أساسية ونظريات اللي
+
+12
+00:00:54,990 --> 00:01:00,090
+اللي بنعتبرها أساسية في مساق اللي هو أو في تحليل
+
+13
+00:01:00,090 --> 00:01:07,130
+في التحليل الدالي. الديفينيشن اللي أخذناها قبل هيك
+
+14
+00:01:07,130 --> 00:01:12,270
+بعتقد اللي هو شو معنى open mapping. let
+
+15
+00:01:12,270 --> 00:01:15,870
+X be and Y be metric spaces then T من domain of T
+
+16
+00:01:15,870 --> 00:01:20,390
+لعند Y with domain of T جزء من الـ metric space X
+
+17
+00:01:20,390 --> 00:01:23,690
+is called an open mapping. هذا اللي هو open mapping
+
+18
+00:01:23,690 --> 00:01:27,830
+ده كان بيرسل الـ open لـ open. باختصار الآن الـ
+
+19
+00:01:27,830 --> 00:01:32,170
+continuous برجع ورجوع بياخد اللي هو the inverse
+
+20
+00:01:32,170 --> 00:01:36,490
+image of open event is open. إذا هاي اللي هو معناه
+
+21
+00:01:36,490 --> 00:01:39,390
+الـ open mapping. نيجي الآن للّمة اللي عندها دي اللي
+
+22
+00:01:39,390 --> 00:01:44,010
+ما بنقرش ورهنها اللي هي بتقول مع أنه قبل ذلك إحنا
+
+23
+00:01:44,010 --> 00:01:49,490
+رهنناها يعني 4.2.2 اللي أما bounded
+
+24
+00:01:49,490 --> 00:01:55,760
+linear operator T from Banach space X on to a
+
+25
+00:01:55,760 --> 00:01:59,880
+Banach space Y has the property that the image T
+
+26
+00:01:59,880 --> 00:02:05,400
+of B of the open unit ball B اللي هو يحتوي على an
+
+27
+00:02:05,400 --> 00:02:11,120
+open ball about zero element in Y. يعني الآن لو كان
+
+28
+00:02:11,120 --> 00:02:19,220
+عندي الـ T عبارة عن bounded linear operator بس من
+
+29
+00:02:19,220 --> 00:02:28,340
+وين لوين؟ من Banach space X لـ Banach space Y. بقول اللي هو
+
+30
+00:02:28,340 --> 00:02:31,580
+bounded linear operator T يعني زي على لغتنا اللي
+
+31
+00:02:31,580 --> 00:02:35,820
+كنا نحكي فيها المرة الماضية T element in B L أو B
+
+32
+00:02:35,820 --> 00:02:41,280
+of X أو Y أو B L of X Y. حالها السابق الـ .. الـ ..
+
+33
+00:02:41,280 --> 00:02:46,260
+الـ .. الـ .. الرمز اللي إحنا بنستخدمه اللي هو the
+
+34
+00:02:46,260 --> 00:02:48,820
+space of all bounded linear operators. لو كان T is
+
+35
+00:02:48,820 --> 00:02:52,220
+a bounded linear operator then it has الخاصية
+
+36
+00:02:52,220 --> 00:03:00,650
+التالية أنه لو أجينا أخذنا أي open unit ball B 0 و 1
+
+37
+00:03:00,650 --> 00:03:13,450
+المركز 0 ونصف القطر 1 من الـ X. هذه ترسلها T of
+
+38
+00:03:13,450 --> 00:03:21,690
+B إلى T of B اللي بتحتوي في داخلها على open
+
+39
+00:03:21,690 --> 00:03:31,120
+ball B prime اللي هو with center 0 وركز R for some
+
+40
+00:03:31,120 --> 00:03:36,880
+R أكبر من 0. إذا اللي هي الـ bounded linear operator
+
+41
+00:03:36,880 --> 00:03:40,360
+from Banach space into Banach space أو into
+
+42
+00:03:40,360 --> 00:03:45,460
+Banach space has the property that it اللي هو
+
+43
+00:03:45,460 --> 00:03:52,700
+أي ball الـ unit ball في الـ X هيكون T of B يحتوي
+
+44
+00:03:52,700 --> 00:03:59,830
+في داخلها open ball يعني open circle. الآن .. الآن
+
+45
+00:03:59,830 --> 00:04:03,850
+.. هذه الخاصية على الـ B نفسها. الآن في النظرية
+
+46
+00:04:03,850 --> 00:04:05,910
+اللي هو ما بين فيه اللي بدأت تنجل الخاصية على
+
+47
+00:04:05,910 --> 00:04:08,850
+كل الـ .. الـ .. الـ .. الـ sets يعني مش بدأت هي تنجل
+
+48
+00:04:08,850 --> 00:04:12,330
+الـ open .. الـ .. تنجل اللي هو الـ .. الـ .. الـ .. الـ
+
+49
+00:04:12,330 --> 00:04:15,870
+.. الـ open unit ball إلى open set. لأ بدأت تنجل أي
+
+50
+00:04:15,870 --> 00:04:19,210
+open set إلى مين؟ إلى open set. يعني صارت اللي هو
+
+51
+00:04:19,210 --> 00:04:23,410
+برهان النظرية سهل اعتمادا على مين؟ على اللي فوق
+
+52
+00:04:23,410 --> 00:04:28,230
+اللي فوق. في بعض الكتب ممكن يبدأ لك من الصفر من هنا
+
+53
+00:04:28,230 --> 00:04:31,490
+ويبدأ يبرهن في داخله الّمة. في الواقع بياخد أولا
+
+54
+00:04:31,490 --> 00:04:34,770
+حالة خاصة وبعدين منها بنتقل إلى الحالة العامة
+
+55
+00:04:34,770 --> 00:04:39,110
+الآن إحنا بدنا اللي هو طبعا ضيق الوقت وعنا يعني
+
+56
+00:04:39,110 --> 00:04:45,620
+خليني أقول صارت الكمية شوية يعني كبيرة يعني. بدنا
+
+57
+00:04:45,620 --> 00:04:49,820
+ناخد اللي هو الـ open mapping theorem اللي نسميها
+
+58
+00:04:49,820 --> 00:04:55,060
+bounded inverse theorem. هو الاسم هذا الـ open
+
+59
+00:04:55,060 --> 00:04:57,660
+mapping theorem لإنه هي بترسل open إلى open. هي
+
+60
+00:04:57,660 --> 00:05:01,840
+واحدة اللي هي الـ bounded operator. الشغل الثاني لو
+
+61
+00:05:01,840 --> 00:05:05,040
+كانت one to one و one to two بيصير اللي هو الـ
+
+62
+00:05:05,040 --> 00:05:09,830
+inverse ماله is a bounded linear operator. لإنه
+
+63
+00:05:09,830 --> 00:05:13,270
+بيصير اللي هو continuous وما كان continuous وlinear
+
+64
+00:05:13,270 --> 00:05:17,030
+لذا راح يصير إسمه اللي هو bounded. لإنه أنتم
+
+65
+00:05:17,030 --> 00:05:19,490
+عارفين أن الـ continuity تكافئ الـ boundedness في
+
+66
+00:05:19,490 --> 00:05:22,890
+حالة من الـ linear operators. اتفجنا عليها هذا زمان.
+
+67
+00:05:23,880 --> 00:05:28,440
+طيب a bounded linear operator from a Banach space X
+
+68
+00:05:28,440 --> 00:05:35,040
+onto a Banach space Y is an open mapping. هذه الإعلان
+
+69
+00:05:35,040 --> 00:05:40,060
+اللي هو الآن any bounded linear operator يعني أنتَ
+
+70
+00:05:40,060 --> 00:05:43,120
+بتعطيني وقت إيش بيكون الـ bounded linear operator
+
+71
+00:05:43,120 --> 00:05:47,420
+أو الـ continuous operator. وقت إيش بيكون open. إذا
+
+72
+00:05:47,420 --> 00:05:54,030
+كان الـ T من Banach space لـ Banach space وكان الـ T عبارة
+
+73
+00:05:54,030 --> 00:06:00,870
+عن bounded linear operator. هذا بيقول لي أكيد هيطلع
+
+74
+00:06:00,870 --> 00:06:06,540
+طبعا on to أكيد حيطلع عندي إيش ماله؟ الـ T is an
+
+75
+00:06:06,540 --> 00:06:10,620
+open mapping أو الـ T is open. هذه النظرية خليني
+
+76
+00:06:10,620 --> 00:06:14,480
+أتبرهن لإنه الجزء الثاني اللي بيظل hence if T is
+
+77
+00:06:14,480 --> 00:06:19,280
+bijective. مثلا تي بيجيكتف صارت إيش مالها؟ one to
+
+78
+00:06:19,280 --> 00:06:22,180
+one و one to two إذا الـ inverse صارت موجودة والـ
+
+79
+00:06:22,180 --> 00:06:26,200
+inverse ما هي من خاصية الـ open. هياخد الـ open و
+
+80
+00:06:26,200 --> 00:06:30,810
+يرجع لمن؟ لـ open ويكون إحنا الـ T inverse طبعا هو
+
+81
+00:06:30,810 --> 00:06:32,890
+الـ T بودّي الـ open لـ open. صارت الـ T inverse هي
+
+82
+00:06:32,890 --> 00:06:35,610
+ترجع الـ open لـ open. إذا صارت الـ T inverse is
+
+83
+00:06:35,610 --> 00:06:38,290
+continuous is then bounded لإنه تكون linear
+
+84
+00:06:38,290 --> 00:06:42,510
+automatic. إذا من الجزء الثاني إذا أثبتنا الأول
+
+85
+00:06:42,510 --> 00:06:47,530
+خلصنا. خليني عشان ما أطولش عليكم لإنه let E عشان
+
+86
+00:06:47,530 --> 00:06:51,590
+أثبتوا أن T is open بتاخد open set هنا وأثبت لك إن
+
+87
+00:06:51,590 --> 00:06:57,260
+هي إسمها open في مين؟ في الـ Y. خليني ناخد الآن هي
+
+88
+00:06:57,260 --> 00:07:05,000
+عندي الآن T من X لعند Y onto function. خذ الآن let
+
+89
+00:07:05,000 --> 00:07:10,360
+A subset من مين؟ من X. ماشي الحال الآن والـ A
+
+90
+00:07:10,360 --> 00:07:13,840
+مأخذها أنا A إسمها open set. بدي أثبت لكم الـ T of
+
+91
+00:07:13,840 --> 00:07:20,000
+A is open. بدي أثبت الـ T of A is open. كيف أثبتها؟
+
+92
+00:07:20,000 --> 00:07:23,860
+بأخذ أي نقطة هنا وبلاقي بقى كل مكان ماله جوا الـ T of
+
+93
+00:07:23,860 --> 00:07:30,820
+T of A. طيب الآن let Y بتساوي T X. طبعا أكيد T X هتكون
+
+94
+00:07:30,820 --> 00:07:36,220
+بأي element منين؟ in T of A عشان ألاجي ball حوالها
+
+95
+00:07:36,220 --> 00:07:39,640
+تكون في داخل الـ team في A. طيب صارت الآن الـ Y
+
+96
+00:07:39,640 --> 00:07:41,780
+بتساوي Y element in T of A.
+
+97
+00:07:45,360 --> 00:07:48,820
+إذا صار معناه Y element in T of A. إذا صار there
+
+98
+00:07:48,820 --> 00:07:53,600
+exist X element in A such that T X هي مين؟ الـ Y.
+
+99
+00:07:53,600 --> 00:07:57,940
+مظبوط ولا لأ؟ هيت معناه يهو Y element in T of A.
+
+100
+00:07:57,940 --> 00:08:03,920
+إذا ما هي A open. since A is open then A contains
+
+101
+00:08:03,920 --> 00:08:08,660
+an open ball with center مين؟ X. إذا صارت مادام A
+
+102
+00:08:08,660 --> 00:08:15,180
+is open إذا عندي فيه ball with center X و Radius R
+
+103
+00:08:15,180 --> 00:08:22,960
+جزئية من الـ Min من الـ A. Hence,
+
+104
+00:08:23,080 --> 00:08:28,260
+A minus X X يحتوي على an open ball with center Min 0
+
+105
+00:08:28,260 --> 00:08:37,780
+بتكون A minus X تحتوي ball with center Min 0 و
+
+106
+00:08:37,780 --> 00:08:43,450
+some radius اللي هو R. طيب كيف هذه؟ خذوا الـ element
+
+107
+00:08:43,450 --> 00:08:47,030
+هنا وبدأ أوصلكم إيه وإيه موجودة اعتمادًا على هذه
+
+108
+00:08:47,030 --> 00:08:51,030
+الـ element هذه. الآن اتفجنا أنه متحقق. هذي بيقول لك
+
+109
+00:08:51,030 --> 00:08:57,830
+أنت أعطيها هذي. خذوا الآن Y element بي Zero R إيش
+
+110
+00:08:57,830 --> 00:09:03,210
+معناه؟ أن المسافة بين هذي وهذي أصغر من R. ماشي
+
+111
+00:09:03,210 --> 00:09:08,530
+الحال الآن عندك المسافة عشان بتثبت أنه .. بتثبت أنه
+
+112
+00:09:08,530 --> 00:09:12,170
+الـ .. الـ .. الـ .. الـ .. الـ element المهانة element
+
+113
+00:09:12,170 --> 00:09:18,630
+هنا. ماشي الحال الآن عندك الـ Y يعني وكـ .. وكأنه
+
+114
+00:09:18,630 --> 00:09:22,670
+بتثبت الـ Y هنا يعني وكأنه بتثبت الـ Y زيادة X اللي
+
+115
+00:09:22,670 --> 00:09:26,950
+هو وين موجودة؟ في هذه. ده نشوف كيف عندي لو جيت أخدت
+
+116
+00:09:26,950 --> 00:09:35,090
+الـ Y زيادة X. Y زيادة X ماقص الـ X صح؟ اللي هي إيش
+
+117
+00:09:35,090 --> 00:09:40,910
+بتساوي؟ الـ Y ما هي الـ Y هنا إذا أنا هتكون أصغر من
+
+118
+00:09:40,910 --> 00:09:46,730
+مين؟ يعني ساعة الـ Y زيادة X وين موجودة؟ في هذه، صح؟
+
+119
+00:09:46,730 --> 00:09:49,430
+مادام ما صارت في هنا إذا الـ Y زيادة X فين؟ في الـ A.
+
+120
+00:09:49,430 --> 00:09:53,430
+إذا صارت الـ Y زيادة X في الـ A. إيش معناه الـ Y زيادة
+
+121
+00:09:53,430 --> 00:09:58,230
+X في الـ A؟ يعني الـ Y element الـ A minus من؟ minus
+
+122
+00:09:58,230 --> 00:10:02,890
+الـ X. يعني بدأت الآن Y في الـ Heavy وانتهيت Y موجودة
+
+123
+00:10:02,890 --> 00:10:06,590
+في الـ A-X. إذا اعتمادا على هذه بما أن الـ A
+
+124
+00:10:06,590 --> 00:10:11,530
+تحتوي على الـ ball X و R أكيد الـ A-X هتحتوي على
+
+125
+00:10:11,530 --> 00:10:16,910
+مين؟ على الـ B, 0, R وهذا يعني أن A-X نفسها is
+
+126
+00:10:16,910 --> 00:10:22,670
+open. خليني هذا خطوة الـ Hence A-X contains an
+
+127
+00:10:22,670 --> 00:10:27,900
+open ball with center 0 اللي هنلق الـ radius of the
+
+128
+00:10:27,900 --> 00:10:31,300
+ball إيش ماله؟ R إحنا مسميه R الـ radius of the
+
+129
+00:10:31,300 --> 00:10:36,140
+ball بساوي R لإنه end K بساوي هذا الـ R then K في A
+
+130
+00:10:36,140 --> 00:10:41,360
+minus X اللي هنهيعني اتفجنا عشان تكون واضحة لكم
+
+131
+00:10:42,210 --> 00:10:47,470
+اتفجنا إن الـ A-X تحتوي على هذه لو الآن أخذنا
+
+132
+00:10:47,470 --> 00:10:52,130
+الواحد على R في هذه هتكون بتحتوي على مين؟ الـ
+
+133
+00:10:52,130 --> 00:10:57,010
+ball zero ومين؟ وواحد وأثبتها سهل كمان يعني
+
+134
+00:10:57,010 --> 00:10:59,910
+زي هذه مجرد إن الواحد ده لكيد تدخل تدخل في الـ
+
+135
+00:10:59,910 --> 00:11:03,910
+norm وتدخل في تعريف الـ A-X. إذا صار عندي يا
+
+136
+00:11:03,910 --> 00:11:11,060
+جماعة الآن زي ما اتفجنا الـ A أخدت الـ K بصيغة 1
+
+137
+00:11:11,060 --> 00:11:14,000
+على 4 ثم اللي هي الـ 1 على R اللي هي الـ K في A
+
+138
+00:11:14,000 --> 00:11:16,960
+minus X زي ما قلنا هنا Contains the open ball mean
+
+139
+00:11:16,960 --> 00:11:22,540
+B 0 1. الآن إيش بتستخدم؟ الّمة Then by lemma 4 و
+
+140
+00:11:22,540 --> 00:11:26,300
+11 2 2 2 بيكون الـ T لهذه الست اللي 
+
+141
+00:11:26,300 --> 00:11:30,580
+هو بيحتوي بيصير الـ T لهذه الست الآن هذه الست اللي
+
+142
+00:11:30,580 --> 00:11:38,730
+هي K اتفقنا الآن أوصلنا إلى إنه الـ K اللي هي الـ 1
+
+143
+00:11:38,730 --> 00:11:42,630
+على R أو الـ K زي ما بيبقى بيحسبوا في A minus X
+
+144
+00:11:42,630 --> 00:11:52,410
+هذه contains an open ball with center 0 ماشي
+
+145
+00:11:52,410 --> 00:12:00,030
+الحال؟ طيب الآن هذه اللي هي الـ K A minus X الـ T
+
+146
+00:12:00,030 --> 00:12:06,020
+لها هي اللي بتحتوي A من اللمّة اللي جوه احتواء الـ
+
+147
+00:12:06,020 --> 00:12:09,360
+open vol هي هتحتوي من مين open vol about مين اللي
+
+148
+00:12:09,360 --> 00:12:15,680
+هو الـ zero هذه نفسها عبارة عن طبعا الـ T Linear
+
+149
+00:12:15,680 --> 00:12:18,780
+الـ K لما يدخل على أي element بتطلع بتعرفوا تثبتوا
+
+150
+00:12:18,780 --> 00:12:25,240
+هذا بتاخدوا ال element هنا تاخدوا ال T of K a
+
+151
+00:12:25,240 --> 00:12:28,740
+small نقص X وبعدين تطلعوه برا أو الآخر تطلع نفس
+
+152
+00:12:28,740 --> 00:12:34,060
+الشيء بسوء K of T of A نقص mean T of X هذي
+
+153
+00:12:34,060 --> 00:12:39,490
+contains a ball about mean zero الآن unthought T of
+
+154
+00:12:39,490 --> 00:12:44,810
+A نقص T X بتحتوي اللي هو برضه open المؤمن يعني
+
+155
+00:12:44,810 --> 00:12:55,650
+الآن K T of A minus X contains اللي هو سمناها
+
+156
+00:12:55,650 --> 00:13:03,130
+عبارة عن K T of A نقص T X، مظبوط؟ هذه كلها على بعض
+
+157
+00:13:03,130 --> 00:13:15,950
+بتحتوي ball زيرو وريدس إبشلون الآن عندي ك مش هتفرق
+
+158
+00:13:15,950 --> 00:13:19,790
+معاها بس هتفرق في ريدس تبع حاجة بيصير T of A minus
+
+159
+00:13:19,790 --> 00:13:26,070
+T of X بتحتوي على ball بيزيرو و بيصير إبشلون في
+
+160
+00:13:26,070 --> 00:13:33,240
+مين في ك نصف القطر بس بتتغير أو على كل الأن هذا
+
+161
+00:13:33,240 --> 00:13:37,320
+بيحتوي هذا إذا نزلنا عاملنا قبل بشوية هيصير T of A
+
+162
+00:13:37,320 --> 00:13:45,580
+يحتوي ball إذا قشنطت دي صراحة TX وY صح؟ اللي هو
+
+163
+00:13:45,580 --> 00:13:50,580
+مين؟ ball Y اللي سميناها من رأس الدور Y و some
+
+164
+00:13:50,580 --> 00:13:56,300
+radius اللي هو R إذا صارت T of A contains a ball
+
+165
+00:13:56,300 --> 00:14:02,590
+about مين؟ اللي هو TX بالساوي Y الآن أخذنا احنا إذا 
+
+166
+00:14:02,590 --> 00:14:07,970
+ايش اللي صار في كل الجثة إنه أخذت a open set واخذت
+
+167
+00:14:07,970 --> 00:14:12,490
+اللي هي arbitrary y عند T of a لجأتي اللي هو T of
+
+168
+00:14:12,490 --> 00:14:17,170
+a بتحتوي open بولة about مين ال Y وهذا معنى ايش
+
+169
+00:14:17,170 --> 00:14:21,770
+إنه but Y was arbitrary then T of a is open
+
+170
+00:14:21,770 --> 00:14:28,490
+therefore T is an open mapping أي سؤال؟ طيب آخر
+
+171
+00:14:28,490 --> 00:14:28,950
+نقطة
+
+172
+00:14:35,020 --> 00:14:41,240
+خلّيني بس نكمل Therefore
+
+173
+00:14:41,240 --> 00:14:45,600
+T is an open mapping ماشي الحال finally if T is
+
+174
+00:14:45,600 --> 00:14:51,420
+bijective then T inverse exist and linear by
+
+175
+00:14:51,420 --> 00:14:56,760
+theorem 2,6,10 طبعا هذا الكلام مفهوم however T is
+
+176
+00:14:56,760 --> 00:15:03,300
+open by open mapping theorem by theorem 1,3,4 إذاً
+
+177
+00:15:03,300 --> 00:15:07,260
+T is إيش مالها؟ continuous كل هذا خدناتنا بهذه
+
+178
+00:15:07,260 --> 00:15:10,820
+الطريقة الآن and so by theorem إتنين سبعة تسعة
+
+179
+00:15:10,820 --> 00:15:13,760
+مدام تكون continuous هذا كل كل اللي قلته في أول
+
+180
+00:15:13,760 --> 00:15:17,900
+محاضرة إذاً is bounded وهيك بيكون الله يعطيك
+
+181
+00:15:17,900 --> 00:15:19,420
+العافية وإلى لقاء آخر
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/dAhzu2_CB2I_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/dAhzu2_CB2I_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..18b0862b6fe66a5cd217b03bc9f4154723ffc458
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/dAhzu2_CB2I_postprocess.srt
@@ -0,0 +1,724 @@
+1
+00:00:05,470 --> 00:00:08,230
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,230 --> 00:00:11,930
+والصلاة والسلام على سيد المرسلين سيدنا محمد على
+
+3
+00:00:11,930 --> 00:00:15,690
+آله وصحبه أجمعين هذه المحاضرة رقم اربع وتلاتين
+
+4
+00:00:15,690 --> 00:00:20,310
+مساق تحليل daily او تحليل اقتراني طلاب وطالبات
+
+5
+00:00:20,310 --> 00:00:27,030
+الجامعة الإسلامية ماجستير رياضية وصلنا لعند اربع
+
+6
+00:00:27,030 --> 00:00:31,250
+اتناش اللي هي ال open mapping theorem اللي هي عشر
+
+7
+00:00:31,250 --> 00:00:32,490
+او واحداش مش مقلبات
+
+8
+00:00:35,050 --> 00:00:39,410
+النظرية الثالثة في من النظريات الأساسية بعد ال
+
+9
+00:00:39,410 --> 00:00:47,350
+uniform boundedness theorem هو أخدناها المرة
+
+10
+00:00:47,350 --> 00:00:50,310
+الماضية وهذه الثالثة وقبلها أخدنا لها البنغ
+
+11
+00:00:50,310 --> 00:00:54,990
+theorem فبكون هذه الثالث نظرية أساسية ونظريات اللي
+
+12
+00:00:54,990 --> 00:01:00,090
+اللي بنعتبرها أساسية في مساق اللي هو أو في تحليل
+
+13
+00:01:00,090 --> 00:01:07,130
+في التحليل الداليالدفينيشن اللي أخدناها قبل هيك
+
+14
+00:01:07,130 --> 00:01:12,270
+بعتقد اللي هو شو معناته open mapping let
+
+15
+00:01:12,270 --> 00:01:15,870
+X be and Y be metric spaces then T من domain of T
+
+16
+00:01:15,870 --> 00:01:20,390
+لعند Y with domain of T جزء من ال metric space X
+
+17
+00:01:20,390 --> 00:01:23,690
+is called an open mapping هذا اللي هو open mapping
+
+18
+00:01:23,690 --> 00:01:27,830
+ده كان بيرسل ال open ل openباختصار الان ال
+
+19
+00:01:27,830 --> 00:01:32,170
+continuous برجع ورجوع بياخد اللي هو the inverse
+
+20
+00:01:32,170 --> 00:01:36,490
+image of open event is open إذا هاي اللي هو معناته
+
+21
+00:01:36,490 --> 00:01:39,390
+ال open mapping نيجي الآن لللمة اللي عندها دي اللي
+
+22
+00:01:39,390 --> 00:01:44,010
+ما بنقش و رهنها اللي هي بتقول مع أنه قبل ذلك احنا
+
+23
+00:01:44,010 --> 00:01:49,490
+رهنناها يعني اربعة اتنين اتنين اللي اما bounded
+
+24
+00:01:49,490 --> 00:01:55,760
+linear operator T from أبنخ space XX on to a
+
+25
+00:01:55,760 --> 00:01:59,880
+banach space Y has the property that the image T
+
+26
+00:01:59,880 --> 00:02:05,400
+of B of the open unit ball B اللي هو contains an
+
+27
+00:02:05,400 --> 00:02:11,120
+open ball about zero element in Y يعني الآن لو كان
+
+28
+00:02:11,120 --> 00:02:19,220
+عندي ال T عبارة عن bounded linear operator بس من
+
+29
+00:02:19,220 --> 00:02:28,340
+وين لوينمن بنخس Base X لبنخس Base Yبقول اللي هو
+
+30
+00:02:28,340 --> 00:02:31,580
+bounded linear operator T يعني زي على لغتنا اللي
+
+31
+00:02:31,580 --> 00:02:35,820
+كنا نحكي فيها المرة الماضية T element in B L أو B
+
+32
+00:02:35,820 --> 00:02:41,280
+of X أو Y أو B L of X Y حالها السابقة ال .. ال ..
+
+33
+00:02:41,280 --> 00:02:46,260
+ال .. ال .. الرمز اللي احنا بنستخدمه اللي هو the
+
+34
+00:02:46,260 --> 00:02:48,820
+space of all bounded linear operators لو كان T is
+
+35
+00:02:48,820 --> 00:02:52,220
+a bounded linear operator then it has البرمجة
+
+36
+00:02:52,220 --> 00:03:00,650
+التالية أنه لو أجينا أخدنا أي أبنUnit ball B 0 و 1
+
+37
+00:03:00,650 --> 00:03:13,450
+المركز 0 و نصف القطر 1 من الـ X هذه ترسلها تي أوف
+
+38
+00:03:13,450 --> 00:03:21,690
+بي إلى تي أوف بي اللي بتحتوي في داخلها على open
+
+39
+00:03:21,690 --> 00:03:31,120
+ball B primeاللي هو with center 0 ووركز R for some
+
+40
+00:03:31,120 --> 00:03:36,880
+R أكبر من 0إذا اللي هي الـ bounded linear operator
+
+41
+00:03:36,880 --> 00:03:40,360
+from أبناء في space into أبناء في space أو into
+
+42
+00:03:40,360 --> 00:03:45,460
+أبناء في space has the property that it اللي هو
+
+43
+00:03:45,460 --> 00:03:52,700
+any ball ال unit ball في ال X هيكون T of B يحتوي
+
+44
+00:03:52,700 --> 00:03:59,830
+في داخلها open ball يعني open circleالان .. الان
+
+45
+00:03:59,830 --> 00:04:03,850
+.. هذه الخاصية على الـ B نفسها الان في النظرية
+
+46
+00:04:03,850 --> 00:04:05,910
+اللي هو بالما بين فيه اللي بدأت تنجل الخاصية على
+
+47
+00:04:05,910 --> 00:04:08,850
+كل ال .. ال .. ال .. ال sets يعني مش بدأت هي تنجل
+
+48
+00:04:08,850 --> 00:04:12,330
+ال open .. ال .. نجلة اللي هو ال .. ال .. ال .. ال
+
+49
+00:04:12,330 --> 00:04:15,870
+.. ال open unit ball إلى open set لأ بدت تنجل أي
+
+50
+00:04:15,870 --> 00:04:19,210
+open set إلى مين إلى open set يعني صارت اللي هو
+
+51
+00:04:19,210 --> 00:04:23,410
+برهان النظرية سهل اعتمادا على مين؟ على اللي ماء
+
+52
+00:04:23,410 --> 00:04:28,230
+اللي فوقفي بعض الكتب ممكن يبدأ لك من الصفر من هنا
+
+53
+00:04:28,230 --> 00:04:31,490
+و يبدأ يبرهن في داخله اللمّة في الواقع بياخد أولا
+
+54
+00:04:31,490 --> 00:04:34,770
+حالة الهادي وبعدين منها بنتقل إلى الحالة العامة
+
+55
+00:04:34,770 --> 00:04:39,110
+الان احنا بدنا اللي هو طبعا ضيق الوقت وعنا يعني
+
+56
+00:04:39,110 --> 00:04:45,620
+خليني أقول صارت الكمية شوية يعني كبيرة يعنيفبدنا
+
+57
+00:04:45,620 --> 00:04:49,820
+ناخد اللي هو ال open mapping theorem اللي نسميها
+
+58
+00:04:49,820 --> 00:04:55,060
+bounded inverse theorem هو الاسم هذا ال open
+
+59
+00:04:55,060 --> 00:04:57,660
+mapping theorem لإنه هي بترسل open إلى open هي
+
+60
+00:04:57,660 --> 00:05:01,840
+واحد اللي هي ال bounded operator الشغل الثاني لو
+
+61
+00:05:01,840 --> 00:05:05,040
+كانت one to one و one to two بيصير اللي هو ال
+
+62
+00:05:05,040 --> 00:05:09,830
+inverseماله is a bounded linear operator لانه
+
+63
+00:05:09,830 --> 00:05:13,270
+بيصير اللي هو continuous وماكن continuous وlinear
+
+64
+00:05:13,270 --> 00:05:17,030
+لذا راح يصير اشماله اللي هو bounded لان انتوا
+
+65
+00:05:17,030 --> 00:05:19,490
+عارفين ان ال continuity تكافئ ال boundedness في
+
+66
+00:05:19,490 --> 00:05:22,890
+حالة من ال linear operators اتفجنا عليها هذا زمان
+
+67
+00:05:23,880 --> 00:05:28,440
+طيب a bounded linear operator from a بنخس base x
+
+68
+00:05:28,440 --> 00:05:35,040
+onto a بنخس base y is an open mapping هذه الإعلان
+
+69
+00:05:35,040 --> 00:05:40,060
+اللي هو الآن any bounded linear operator يعني أنت
+
+70
+00:05:40,060 --> 00:05:43,120
+بتعطيني وقت إيش بيكون ال bounded linear operator
+
+71
+00:05:43,120 --> 00:05:47,420
+أو ال continuous operator وقت إيش بيكون open إذا
+
+72
+00:05:47,420 --> 00:05:54,030
+كان ال T من بنخس base لبنخس baseوكان الـ T عبارة
+
+73
+00:05:54,030 --> 00:06:00,870
+عن bounded linear operator هذا بيقوللي أكيد هيطلع
+
+74
+00:06:00,870 --> 00:06:06,540
+طبعا on toأكيد حيطلع عندي إيش ماله الـ T is an
+
+75
+00:06:06,540 --> 00:06:10,620
+open mapping أو الـ T is open هذه النظرية خلّيني
+
+76
+00:06:10,620 --> 00:06:14,480
+أتبرهن لأن الجزء الثاني اللي بيظل hence if T is
+
+77
+00:06:14,480 --> 00:06:19,280
+bijective مثلا تي بيجيكتف صارت إيش مالها one to
+
+78
+00:06:19,280 --> 00:06:22,180
+one و one to two إذا ال inverse صارت موجودة و ال
+
+79
+00:06:22,180 --> 00:06:26,200
+inverse ما هي من خاصية ال open هياخد ال open و
+
+80
+00:06:26,200 --> 00:06:30,810
+يرجع لمن؟ ل open و يكون احناالـ T inverse طبعاً هو
+
+81
+00:06:30,810 --> 00:06:32,890
+الـ T بودّي الـ open لـ open صارت الـ T inverse هي
+
+82
+00:06:32,890 --> 00:06:35,610
+ترجع الـ open لـ open إذا صارت الـ T inverse is
+
+83
+00:06:35,610 --> 00:06:38,290
+continuous is then bounded لأنها تكون linear
+
+84
+00:06:38,290 --> 00:06:42,510
+automatic إذا من الجزء الثاني إذا أثبتنا الأول
+
+85
+00:06:42,510 --> 00:06:47,530
+خلصنا خلّينا عشان ما أطولش عليكم لأن let E عشان
+
+86
+00:06:47,530 --> 00:06:51,590
+أثبتوا أن T is open بتاخد open ست هنا و أثبتلك إن
+
+87
+00:06:51,590 --> 00:06:57,260
+هي أشمالها open في مين؟ في ال Y خلّينا ناخد الآنهي
+
+88
+00:06:57,260 --> 00:07:05,000
+عندي الان T من X لعند Y onto function خد الان let
+
+89
+00:07:05,000 --> 00:07:10,360
+A subset من مين من X ماشي الحال الان و ال A
+
+90
+00:07:10,360 --> 00:07:13,840
+مااخدها انا A شمالها open set بدي اثبتلكم ال T of
+
+91
+00:07:13,840 --> 00:07:20,000
+A is open بدي اثبت ال T of A is open كيف اثبتها
+
+92
+00:07:20,000 --> 00:07:23,860
+باخد اي نقطة هنا و بلاقي بقى كل مكان ماله جوا ت ال
+
+93
+00:07:23,860 --> 00:07:30,820
+T of A طيبالان لت Y بتساوي TX طبعا اكيد TX هتكون
+
+94
+00:07:30,820 --> 00:07:36,220
+بأي element منين in T of A عشان ألاجي ball حوالها
+
+95
+00:07:36,220 --> 00:07:39,640
+تكون في داخل ال team في A طيب صارت الان ال Y
+
+96
+00:07:39,640 --> 00:07:41,780
+بتساوي Y element in T of A
+
+97
+00:07:45,360 --> 00:07:48,820
+إذاً صار معناه y element in T of A إذاً صار there
+
+98
+00:07:48,820 --> 00:07:53,600
+exist x element in A such that Tx هي مين ال Y
+
+99
+00:07:53,600 --> 00:07:57,940
+مظبوط ولا لأ؟ هيت معناه يهو y element in T of A
+
+100
+00:07:57,940 --> 00:08:03,920
+إذاً ما هي A open since A is open then A contains
+
+101
+00:08:03,920 --> 00:08:08,660
+an open ball with center مين X إذاً صارت مادام A
+
+102
+00:08:08,660 --> 00:08:15,180
+is open إذا عندي فيه ballwith center X و Radius R
+
+103
+00:08:15,180 --> 00:08:22,960
+جزئية من الـ Min من الـ A Hence,
+
+104
+00:08:23,080 --> 00:08:28,260
+A minus XX contains an open ball with center Min 0
+
+105
+00:08:28,260 --> 00:08:37,780
+بتكون A minus X تحتوي ball with center Min 0 و
+
+106
+00:08:37,780 --> 00:08:43,450
+some radius اللي هو R طيب كيف هذه؟خدوا الـ Element
+
+107
+00:08:43,450 --> 00:08:47,030
+هنا وبدأ أوصلكم إيه وإيه موجودها اعتمادًا على هذه
+
+108
+00:08:47,030 --> 00:08:51,030
+الـ Element هذه الان اتفجنا انه متحقق هذي بيقولك
+
+109
+00:08:51,030 --> 00:08:57,830
+انت اعطيها هذي خدوا الان Y element بي Zero R ايش
+
+110
+00:08:57,830 --> 00:09:03,210
+معناته ان المسافة بين هذي و هذي أصغر من R ماشي
+
+111
+00:09:03,210 --> 00:09:08,530
+الحال الان عندك المسافةعشان بتثبت أنه .. بتثبت أنه
+
+112
+00:09:08,530 --> 00:09:12,170
+ال .. ال .. ال .. ال .. ال element المهانة element
+
+113
+00:09:12,170 --> 00:09:18,630
+هنا ماشي الحال الان عندك ال Y يعني و ك .. و كأنه
+
+114
+00:09:18,630 --> 00:09:22,670
+بتثبت ال Y هنا يعني و كأنه بتثبت ال Y زياد X اللي
+
+115
+00:09:22,670 --> 00:09:26,950
+هو وين موجودة في هذه ده نشوف كيف عندى لو جيت أخدت
+
+116
+00:09:26,950 --> 00:09:35,090
+ال Y زياد X Y زياد X ماقص ال X صح؟ اللي هي إيش
+
+117
+00:09:35,090 --> 00:09:40,910
+بتساوي؟الـY ما هي الـY هنا إذا أنا هتكون أصغر من
+
+118
+00:09:40,910 --> 00:09:46,730
+مين يعني ساعة الـY زيادة X وين موجودة؟ في هذه، صح؟
+
+119
+00:09:46,730 --> 00:09:49,430
+مادة ما صارت في هنا إذا الـY زيادة X فين؟ في الـA
+
+120
+00:09:49,430 --> 00:09:53,430
+إذا صارت الـY زيادة X في الـA إيش معناه الـY زيادة
+
+121
+00:09:53,430 --> 00:09:58,230
+X في الـA؟ يعني الـY element الـA minus من؟ minus
+
+122
+00:09:58,230 --> 00:10:02,890
+الـXيعني بدأت الآن Y في الـ Heavy وانتهيت Y موجودة
+
+123
+00:10:02,890 --> 00:10:06,590
+في الـ A-X إذاً اعتمادًا على هذه بما أن الـ A
+
+124
+00:10:06,590 --> 00:10:11,530
+تحتوي على الـ ball X و R أكيد الـ A-X هتحتوي على
+
+125
+00:10:11,530 --> 00:10:16,910
+مين؟ على الـ B, 0, H, R وهذا يعني أن A-X نفسها is
+
+126
+00:10:16,910 --> 00:10:22,670
+open خلّيني هذا خطوة الـ Hence A-X contains an
+
+127
+00:10:22,670 --> 00:10:27,900
+open ball with center 0اللي هنلق ال radius of the
+
+128
+00:10:27,900 --> 00:10:31,300
+ball ايش ماله؟ R، احنا مسميه R ال radius of the
+
+129
+00:10:31,300 --> 00:10:36,140
+ball بساوي R لأن end K بساوي هذا ال R، then K في A
+
+130
+00:10:36,140 --> 00:10:41,360
+minus X، اللي هنهيعنى اتفجنا عشان تكون واضحة لكم
+
+131
+00:10:42,210 --> 00:10:47,470
+إتفجنا إن الـ a-x تحتوي على هذه، لو الآن أخدنا
+
+132
+00:10:47,470 --> 00:10:52,130
+الواحد على R في هذه، هتكون بتحتوي على مين؟ الـ
+
+133
+00:10:52,130 --> 00:10:57,010
+ball، zero و مين و واحد، و أثبتها سهل كمان يعني،
+
+134
+00:10:57,010 --> 00:10:59,910
+زي هذه، مجرد إن الواحد ده لكيد تدخل، تدخل في الـ
+
+135
+00:10:59,910 --> 00:11:03,910
+norm و تدخل في تعريف الـ a-x إذا صار عندي يا
+
+136
+00:11:03,910 --> 00:11:11,060
+جماعة، الآن زي ما اتفجناالـ A أخدت الـ K بصيحة 1
+
+137
+00:11:11,060 --> 00:11:14,000
+على 4 ثم اللي هي الـ 1 على R اللي هي الـ K في A
+
+138
+00:11:14,000 --> 00:11:16,960
+minus X زي ما قلنا هنا Contains the open ball mean
+
+139
+00:11:16,960 --> 00:11:22,540
+B01 الآن إيش بتستخدم؟ اللمّة Then by لمّة أربعة و
+
+140
+00:11:22,540 --> 00:11:26,300
+أتناش اتنين اتنين اتنين بيكون الـ T لهذه الست اللي
+
+141
+00:11:26,300 --> 00:11:30,580
+هو بحتوي بيصير الـ T لهذه الست الآن هذه الست اللي
+
+142
+00:11:30,580 --> 00:11:38,730
+هي K اتفجنا الآن أوصلنا إلى إنه الـ Kاللي هي الـ 1
+
+143
+00:11:38,730 --> 00:11:42,630
+على R أو الـ K زي ما بيبقى بيحسبوا في A minus X
+
+144
+00:11:42,630 --> 00:11:52,410
+هذه contains an open ball with center 0 ماشي
+
+145
+00:11:52,410 --> 00:12:00,030
+الحال؟ طيب الآن هذه اللي هي الـ K A minus X الـ T
+
+146
+00:12:00,030 --> 00:12:06,020
+لها هي اللي بتحتوي Aمن اللمّة اللي جوه احتواط الـ
+
+147
+00:12:06,020 --> 00:12:09,360
+open vol هي هتحتوى من مين open vol about مين اللي
+
+148
+00:12:09,360 --> 00:12:15,680
+هو الـ zero هذه نفسها عبارة عنطبعا الـ T Linear
+
+149
+00:12:15,680 --> 00:12:18,780
+الـ K لما يدخل على أي element بتطلع بتعرفوا تثبتوا
+
+150
+00:12:18,780 --> 00:12:25,240
+هذا بتاخدوا ال element هنا تاخدوا ال T of K a
+
+151
+00:12:25,240 --> 00:12:28,740
+small نقص X و بعدين تطلعوه برا او الاخر تطلع نفس
+
+152
+00:12:28,740 --> 00:12:34,060
+الشيء بسوء K of T of A نقص mean T of X هذي
+
+153
+00:12:34,060 --> 00:12:39,490
+contains a ball about mean zeroالآن unthought T of
+
+154
+00:12:39,490 --> 00:12:44,810
+A نقص T X بتحتوي اللي هو برضه open المؤمن يعني
+
+155
+00:12:44,810 --> 00:12:55,650
+الآن K T of A minus X contains اللي هو سمناها
+
+156
+00:12:55,650 --> 00:13:03,130
+عبارة عن K T of A نقص T X، مظبوط؟ هذه كلها على بعض
+
+157
+00:13:03,130 --> 00:13:15,950
+بتحتوي ballزيرو و ريدس إبشلون الان عندي ك مش هتفرق
+
+158
+00:13:15,950 --> 00:13:19,790
+معاها بس هتفرق في ريدس تبع حاجة بيصير T of A minus
+
+159
+00:13:19,790 --> 00:13:26,070
+T of X بتحتوي على ball بيزيرو و بيصير إبشلون في
+
+160
+00:13:26,070 --> 00:13:33,240
+مين في ك نصف القطر بس بتتغير أو على كلأن هذا
+
+161
+00:13:33,240 --> 00:13:37,320
+بيحتوي هذا إذا نزلنا عاملنا قبل بشوية هيصير T of A
+
+162
+00:13:37,320 --> 00:13:45,580
+يحتوي ball إذا قشنطت دي صراحة TX وY صح؟ اللي هو
+
+163
+00:13:45,580 --> 00:13:50,580
+مين؟ ball Y اللي سميناها من رأس الدور Y و some
+
+164
+00:13:50,580 --> 00:13:56,300
+radius اللي هو R إذا صرت T of A contains a ball
+
+165
+00:13:56,300 --> 00:14:02,590
+about مين؟ اللي هو TX بالساوي Yالان اخدنا احنا اذا
+
+166
+00:14:02,590 --> 00:14:07,970
+ايش اللي صار في كل الجثة انه اخدت a open set واخدت
+
+167
+00:14:07,970 --> 00:14:12,490
+اللي هي arbitrary y عند T of a لجأتي اللي هو T of
+
+168
+00:14:12,490 --> 00:14:17,170
+a بتحتوي open بولة about مين ال Y وهذا معنى ايش
+
+169
+00:14:17,170 --> 00:14:21,770
+انه but Y was arbitrary then T of a is open
+
+170
+00:14:21,770 --> 00:14:28,490
+therefore T is an open mapping اي سؤال؟ طيب اخر
+
+171
+00:14:28,490 --> 00:14:28,950
+نقطة
+
+172
+00:14:35,020 --> 00:14:41,240
+خلّيني بس نكمل Therefore
+
+173
+00:14:41,240 --> 00:14:45,600
+T is an open mapping ماشي الحال finally if T is
+
+174
+00:14:45,600 --> 00:14:51,420
+bijective then T inverse exist and linear by
+
+175
+00:14:51,420 --> 00:14:56,760
+theorem 2,6,10 طبعا هذا الكلام مفهوم however T is
+
+176
+00:14:56,760 --> 00:15:03,300
+open by open mapping theorem by theorem 1,3,4إذاً
+
+177
+00:15:03,300 --> 00:15:07,260
+T is إيش مالها؟ continuous كل هذا خدناتنا بهذه
+
+178
+00:15:07,260 --> 00:15:10,820
+الطريقة الآن and so by theorem إتنين سبعة تسعة
+
+179
+00:15:10,820 --> 00:15:13,760
+مدام تكون continuous هذا كل كل اللي قلته في أول
+
+180
+00:15:13,760 --> 00:15:17,900
+محاضرة إذاً is bounded وهيك بيكون الله يعطيك
+
+181
+00:15:17,900 --> 00:15:19,420
+العافية وإلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/fs3UcYAAOXg.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/fs3UcYAAOXg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6e9570675736a9e80174dac0c259569a8f445566
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/fs3UcYAAOXg.srt
@@ -0,0 +1,1023 @@
+1
+00:00:05,040 --> 00:00:07,660
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,660 --> 00:00:10,380
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,380 --> 00:00:14,660
+آله وصحبه أجمعين هذه المحاضرة رقم 18 مساق تحليل 
+
+4
+00:00:14,660 --> 00:00:17,840
+دالي أو تحليل إقتراني طلاب وطالبات الجامعة 
+
+5
+00:00:17,840 --> 00:00:22,710
+الإسلامية ماجستير رياضية ووصلنا لعند اليوم عند
+
+6
+00:00:22,710 --> 00:00:25,370
+section 3-2 further properties of inner product
+
+7
+00:00:25,370 --> 00:00:29,110
+spaces اللي هي خواص أخرى للـ inner product spaces
+
+8
+00:00:29,110 --> 00:00:34,270
+والمحاضرة ليه قصيرة وسهلة على السريع إن شاء الله
+
+9
+00:00:34,270 --> 00:00:38,230
+اللي هي لمّة الأولى 3-2-1 اللي هم تسميها Schwarz
+
+10
+00:00:38,230 --> 00:00:43,390
+Inequality و Triangle Inequality الآن if X and Y are
+
+11
+00:00:43,390 --> 00:00:46,070
+elements in an inner product space يعني أنا جاعد
+
+12
+00:00:46,070 --> 00:00:49,270
+في الـ inner product space then the following holds ال
+
+13
+00:00:49,270 --> 00:00:51,850
+absolute value أو الـ modulus للـ inner product بين
+
+14
+00:00:51,850 --> 00:00:55,490
+X و Y  أصغر يساوي نورم الأولى في نورم مين الثانية 
+
+15
+00:00:55,490 --> 00:01:01,150
+والجزء الثاني where the equality sign هذه تحدث إذا
+
+16
+00:01:01,150 --> 00:01:05,530
+وفقط إذا كانت الـ X و Y إشمالهم is linearly
+
+17
+00:01:05,530 --> 00:01:08,650
+dependent يعني واحدة linear combination من الثانية 
+
+18
+00:01:08,650 --> 00:01:13,370
+أو واحدة منهم صفر الآن الـ norm لـ X زائد Y أصغر أو 
+
+19
+00:01:13,370 --> 00:01:19,890
+يساوي norm X زائد norm Y هذا برضه بيحدث في حالة الـ
+
+20
+00:01:19,890 --> 00:01:23,850
+inner product الآن where the equality sign هذا 
+
+21
+00:01:23,850 --> 00:01:27,050
+طبعا حدوته ما احنا عارفينه الآن where the equality
+
+22
+00:01:27,050 --> 00:01:31,970
+sign holds if and only if يا Y بتساوي صفر or X
+
+23
+00:01:31,970 --> 00:01:35,990
+إشمالها بتساوي Cy for some C إشمالها أكبر أو يساوي
+
+24
+00:01:35,990 --> 00:01:39,510
+صفر زي اللي فوق بس هنا بيحددلك أكتر أن الـ C
+
+25
+00:01:39,510 --> 00:01:42,170
+الـ linear combination أكبر أو يساوي صفر يعني
+
+26
+00:01:42,170 --> 00:01:45,210
+المُستعمل اللي هي ياش C أكبر أو يساوي صفر نشوف
+
+27
+00:01:45,210 --> 00:01:48,090
+نبرهن على السريع اللي هو اللي .. اللي .. اللي ..
+
+28
+00:01:48,090 --> 00:01:48,590
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+29
+00:01:48,590 --> 00:01:48,710
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+30
+00:01:48,710 --> 00:01:48,910
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+31
+00:01:48,910 --> 00:01:49,250
+اللي .. اللي .. اللي .. اللي .. اللي .. اللي ..
+
+32
+00:01:49,250 --> 00:01:51,180
+اللي .. اللي .. اللي .. اللي .. اللي .. إذا 
+
+33
+00:01:51,180 --> 00:01:54,740
+كانت Y بتساوي صفر هيكون عند الـ inner product بين
+
+34
+00:01:54,740 --> 00:01:57,520
+الـ X والـ Y إيش هي .. أوتوماتيك هيساوي .. هيساوي صفر 
+
+35
+00:01:57,520 --> 00:02:01,020
+أوتوماتيك هذه and the result is trivial والـ result
+
+36
+00:02:01,020 --> 00:02:03,960
+بيصير إيش مالها اللي جاب البشوية على طول اللي هي
+
+37
+00:02:03,960 --> 00:02:07,120
+نزل عليها الـ result هي هذه بتطلع هذه و هذه إيش
+
+38
+00:02:07,120 --> 00:02:10,220
+مالها مساواة والتنتين صفر إذن هذه خلصنا من
+
+39
+00:02:10,220 --> 00:02:12,990
+المساواة تبع الصفر وخلصنا من اللي هي اللي
+
+40
+00:02:12,990 --> 00:02:16,130
+inequality صحتها في حالة الـ Y بتساوي صفر الآن
+
+41
+00:02:16,130 --> 00:02:19,710
+suppose that إن Y إشمالها لا تساوي صفر لأن شكلنا 
+
+42
+00:02:19,710 --> 00:02:23,930
+بدنا نجسم على مين؟ على اللي هو Y أو Normal Y and
+
+43
+00:02:23,930 --> 00:02:28,110
+let F be a scalar we have إيه الآن؟ احسب لي الآن ال
+
+44
+00:02:28,110 --> 00:02:31,370
+inner product للـ X ناقص Alpha Y اللي هو تربيعه 
+
+45
+00:02:31,370 --> 00:02:34,720
+طبعا أكبر أو يساوي صفر لأنه Normal اللي هو بيساوي
+
+46
+00:02:34,720 --> 00:02:38,780
+بنفكها X ناقص Alpha Y و X ناقص Alpha Y ويساوي و
+
+47
+00:02:38,780 --> 00:02:42,640
+الفك زي ما أنتم عارفين X مع الـ X هي X مع الـ X و
+
+48
+00:02:42,640 --> 00:02:46,720
+بعدين اللي هي الـ X مع الـ Alpha Y وطلعها بالمرة
+
+49
+00:02:46,720 --> 00:02:50,380
+بتطلع بالـ conjugate بيصير X و Y وبعدين اللي هي
+
+50
+00:02:50,380 --> 00:02:54,380
+طلع لي اللي هي التانية بتضل اللي هي ناقص Alpha Y مع
+
+51
+00:02:54,380 --> 00:02:57,710
+ناقص Alpha Y اللي هي بتصير الـ Alpha في Alpha
+
+52
+00:02:57,710 --> 00:03:00,810
+conjugate بتصير تربيع برا مع الـ Y والـ Y وبعدين
+
+53
+00:03:00,810 --> 00:03:04,110
+ناقص Alpha Y مع مين؟ مع الـ X وبتطلع ناقص Alpha
+
+54
+00:03:04,110 --> 00:03:07,990
+إلها برا أخذنا من الجهتين الأخرانيات اللي حكيتن 
+
+55
+00:03:07,990 --> 00:03:11,810
+قبل شوية ناقص Alpha برا فبصير عبارة عن ناقص Alpha
+
+56
+00:03:11,810 --> 00:03:14,510
+في Y و X اللي قلتها وبعدين ناقص Alpha في Alpha 
+
+57
+00:03:14,510 --> 00:03:17,390
+conjugate بالسال بيصير زائد Alpha تربيع absolute
+
+58
+00:03:17,390 --> 00:03:22,550
+value في Y و Y  ماشي الآن أنا كتبت هذه على
+
+59
+00:03:22,550 --> 00:03:28,490
+الصورة اللي أمامكم عشان بدي أسفر هذا المقدار وأحصل
+
+60
+00:03:28,490 --> 00:03:32,030
+على إشي يخدمني يوصلني الـ Inequality إيش اللي 
+
+61
+00:03:32,030 --> 00:03:34,730
+أخدتها؟ أخدت الـ Alpha conjugate هذه الـ Alpha
+
+62
+00:03:34,730 --> 00:03:38,950
+conjugate بتساوي الـ Alpha conjugate الـ Alpha
+
+63
+00:03:38,950 --> 00:03:42,490
+conjugate ننزل شوية إشي بسيط عشان تشوف الناس الـ
+
+64
+00:03:42,490 --> 00:03:46,290
+Alpha conjugate بتساوي اللي هي عبارة عن الـ Y والـ
+
+65
+00:03:46,290 --> 00:03:51,850
+X على الـ Y والـ Y ماشي فالآن لما أحط الـ α
+
+66
+00:03:51,850 --> 00:03:55,770
+conjugate هنا هذي بيصير الـ Y والـ X وهذي بتروح مع
+
+67
+00:03:55,770 --> 00:03:59,490
+هذي بيصير اللي هي إيه إيش مالها هذي ناقص نفسها
+
+68
+00:03:59,490 --> 00:04:04,730
+فبتتسفر بيصير عندي we have بعد ما نحط الـ α conjugate 
+
+69
+00:04:04,730 --> 00:04:08,270
+قيمتها هذي اللي فوق هذي صحيحة لا ألفة في
+
+70
+00:04:08,270 --> 00:04:12,210
+الدنيا من ضمن إن الألفة هذي بحطها فوق عشان تختمني 
+
+71
+00:04:12,210 --> 00:04:17,130
+بيصير عندي الـ inner product بين الـ X والـ X الـ
+
+72
+00:04:17,130 --> 00:04:20,330
+inner product بين الـ X والـ X اللي بيظل ناقص اللي
+
+73
+00:04:20,330 --> 00:04:23,970
+ضال هذا في الـ α conjugate اللي هي مين هذا الكلام
+
+74
+00:04:23,970 --> 00:04:28,510
+اللي هي Y و X على Y و Y عوضت مكان الـ α conjugate 
+
+75
+00:04:28,510 --> 00:04:33,090
+قيمتها هذه في الـ X والـ Y هذا بيساوي هذه إيش هي
+
+76
+00:04:33,090 --> 00:04:36,660
+عبارة عن norm X تربيع طبعا كله أكبر يساوي صفروهذا
+
+77
+00:04:36,660 --> 00:04:40,340
+كله بيساوي اللي هو هذا المقدار اللي هو أكبر أو يساوي
+
+78
+00:04:40,340 --> 00:04:43,960
+صفر فلما حطيت هذه مكانها وصفرتها ضل المقدار اللي
+
+79
+00:04:43,960 --> 00:04:47,200
+هو برضه أكبر أو يساوي صفر يعني ضل المقدار هذا اللي 
+
+80
+00:04:47,200 --> 00:04:51,800
+حصلت عليه أكبر أو يساوي صفر بدأ آجة بس طول ويساوي هذه
+
+81
+00:04:51,800 --> 00:04:56,660
+norm الـ X تربيع وهذه عبارة عن Y و X و X و Y هي و
+
+82
+00:04:56,660 --> 00:05:00,280
+الـ conjugate تبعتها فبصير الـ modulus تربيع على ال
+
+83
+00:05:00,280 --> 00:05:04,000
+inner product لها اللي هي بصير norm الـ Y تربيع إذا
+
+84
+00:05:04,000 --> 00:05:09,820
+صار عندي هذا ناقص هذا أكبر أو يساوي صفر انقلي اللي
+
+85
+00:05:09,820 --> 00:05:12,500
+هو هذا المقدار خليه هنا وانقلي المقدار هذا على 
+
+86
+00:05:12,500 --> 00:05:17,060
+الجهة الثانية صار هذا أصغر أو يساوي هذا وهضرب 
+
+87
+00:05:17,060 --> 00:05:19,840
+الجهتين في normal واي تربيع فبصير هذا اللي فوق
+
+88
+00:05:19,840 --> 00:05:22,600
+أصغر أو يساوي normal هذا في normal هذا إلى أنشير 
+
+89
+00:05:22,600 --> 00:05:26,900
+التربيع بصير هذا أصغر من هذا في هذا واضح؟ واضح طيب
+
+90
+00:05:29,370 --> 00:05:34,390
+الآن الـ me جي لمين الآن if x y is linearly
+
+91
+00:05:34,390 --> 00:05:37,610
+dependent في حالة الـ Alpha بتساوي صفر خلصناها الـ Y 
+
+92
+00:05:37,610 --> 00:05:40,930
+بتساوي صفر خلصناها في حالة اللي هي X Y linearly
+
+93
+00:05:40,930 --> 00:05:44,930
+dependent معناته بقدر أكتب الـ X اللي هو على صورة
+
+94
+00:05:44,930 --> 00:05:47,110
+linear combination من Y أو الـ Y على صورة linear
+
+95
+00:05:47,110 --> 00:05:51,570
+combination من X يعني X بتساوي من Alpha في Y ماشي
+
+96
+00:05:51,570 --> 00:05:54,830
+الحال احسب للـ inner product الآن الـ absolute value 
+
+97
+00:05:54,830 --> 00:05:58,110
+للـ X و Y بتثبت لك المستوى الآنفعادة الـ Linear
+
+98
+00:05:58,110 --> 00:06:02,490
+Dependent بدت بتلك مساواة الـ Equality يعني تحدث
+
+99
+00:06:02,490 --> 00:06:06,730
+مساواة بين هذه وهذه احسبها هذه بيصير Alpha Y و Y
+
+100
+00:06:06,730 --> 00:06:10,150
+لأن الـ X حطيتها Alpha Y Y يساوي الـ Alpha برا بتطلع 
+
+101
+00:06:10,150 --> 00:06:14,850
+مدلس وبتظهر norm Y تربيعا هذه بتساوي norm الـ
+
+102
+00:06:14,850 --> 00:06:18,950
+Alpha Y في norm الـ Y الـ norm الـ Alpha Y هو الـ X
+
+103
+00:06:18,950 --> 00:06:24,410
+norm الـ X في norm Y إذا حدثت المساواة Conversely لو 
+
+104
+00:06:24,410 --> 00:06:29,410
+المساواة تحدث هتطلع لنا اللي هي الـ X والـ Y
+
+105
+00:06:29,410 --> 00:06:34,990
+linearly dependent طيب Conversely if equality 
+
+106
+00:06:34,990 --> 00:06:41,390
+holds then by Y by واحد يا إما الـ Y بتساوي صفر أو 
+
+107
+00:06:41,390 --> 00:06:44,750
+الـ X ناقص Alpha Y بتساوي صفر إن الـ .. لو الـ
+
+108
+00:06:44,750 --> 00:06:48,530
+equality .. لو الـ equality حدثت الـ equality بتحدث
+
+109
+00:06:48,530 --> 00:06:53,350
+.. بتحدث .. اطلع لفوق هي من اللي حسبناها هنا 
+
+110
+00:06:53,350 --> 00:06:57,550
+اللي حسبناها هنا الـ equality وين الـ X نقص Alpha Y
+
+111
+00:06:57,550 --> 00:07:02,150
+اطلع فوق هي هنا هنا هنا الـ equality هذه بتحدث هذه
+
+112
+00:07:02,150 --> 00:07:05,290
+الـ equality بتحدث لما هذه إيش عملها هتساوي إيش 
+
+113
+00:07:05,290 --> 00:07:10,790
+تساوي اللي هو صفر الـ equality حدثت عندي اللي هو الـ
+
+114
+00:07:10,790 --> 00:07:15,530
+norm هذا هيصير اللي ساوي بيساوي اللي هو إيش صفر for
+
+115
+00:07:15,530 --> 00:07:21,470
+every Alpha عملناها الآن لما تحدث الـ equality مايش
+
+116
+00:07:21,470 --> 00:07:24,990
+بده تسير لما الـ .. الـ .. الـ quality تحدث ..
+
+117
+00:07:24,990 --> 00:07:28,090
+تحدث هذه بيساوي بيساوي هذه وبناء عليه هذا 
+
+118
+00:07:28,090 --> 00:07:31,370
+المقدار هيسير يساوي اللي هو عبارة عالميا عن الصفر
+
+119
+00:07:31,370 --> 00:07:34,930
+من الحسابات اللي حسبناها هنا في المنطقة هذه ب ..
+
+120
+00:07:34,930 --> 00:07:36,990
+اللي هي وضع إن الـ Alpha conjugate بيساوي هذه
+
+121
+00:07:36,990 --> 00:07:39,930
+تفاصيل .. التفاصيل بتطلعوها لحالكم ما عنا نرجع لها 
+
+122
+00:07:39,930 --> 00:07:45,520
+كمان مرة صار عندي .. الآن الـ Normal X و Y بيساوي 
+
+123
+00:07:45,520 --> 00:07:49,480
+Normal Alpha Y و Y ويساوي Normal L Absolute L
+
+124
+00:07:49,480 --> 00:07:53,960
+Alpha في Normal Y تربيع Normal Alpha في Y 
+
+125
+00:07:53,960 --> 00:07:59,580
+تربيع قلنا هذا لأ هذا قلناه عندي نفترض دلوقت الـ 
+
+126
+00:07:59,580 --> 00:08:06,700
+equality holds من واحد هتكون عندي اللي حلناه كله 
+
+127
+00:08:06,700 --> 00:08:11,760
+الـ Y ناقص Alpha X بدون الـ Y بيساوي صفر في حالة الـ
+
+128
+00:08:11,760 --> 00:08:16,750
+Y بيساوي صفر الـ equality holds يا إما Y بيساوي 0
+
+129
+00:08:16,750 --> 00:08:19,410
+أو الحالة الثانية الحالة الثانية اللي هي ال .. الـ 
+
+130
+00:08:19,410 --> 00:08:23,630
+.. ال .. الـ Y الـ X نقص Alpha Y اللي حسبناها بتصير 
+
+131
+00:08:23,630 --> 00:08:26,670
+اللي هي المساواة بينهم في حالة اللي هي هذه إشمالها
+
+132
+00:08:26,670 --> 00:08:29,470
+بيساوى 0 نتيجة الحسابات اللي حسبناها قبل شوية
+
+133
+00:08:29,470 --> 00:08:32,550
+لأن X minus Alpha Y بيساوى 0 معناته اللي هو الـ X 
+
+134
+00:08:32,550 --> 00:08:36,030
+والـ Y إشمالي Linearly Dependent سواء هذه أو هذه
+
+135
+00:08:36,030 --> 00:08:39,730
+بتتنقل هي الـ X و Y Linearly Dependent وخلاص إيش 
+
+136
+00:08:39,730 --> 00:08:42,050
+بسرعة طيب اللي بعيد هنا
+
+137
+00:08:45,170 --> 00:08:49,310
+انزل تشوفيش اللي بعيدها انزل انزل أيوة اللي بعيدها 
+
+138
+00:08:49,310 --> 00:08:53,450
+اللي بعيدها الوهم الـ X Z و Y أصغر شوية هادم مسرح
+
+139
+00:08:53,450 --> 00:08:57,970
+هادم هي عارفين احنا وعلى طول بتنحسب war ده الـ
+
+140
+00:08:57,970 --> 00:09:01,290
+equality sign بتحدث إذا و فقط إذا يا Y بيساوي
+
+141
+00:09:01,290 --> 00:09:04,430
+سفر يا C بالساوية Y X بالساوية سفر نبدأ هادم ونصل
+
+142
+00:09:04,430 --> 00:09:07,810
+لهادم ونبدأ هادم يالا البعد يالا يالا خليني أشوف
+
+143
+00:09:07,810 --> 00:09:13,570
+احسبت يالا ع السريع By using Schwarz inequality
+
+144
+00:09:13,570 --> 00:09:18,370
+Normal X زائد Y الكل تربيع بساوي X زائد Y و X زائد Y
+
+145
+00:09:18,370 --> 00:09:21,610
+الحسابات ده ده اللي أنتو عارفينها بساوي هذه زائد
+
+146
+00:09:21,610 --> 00:09:25,710
+هذه زائد هذه زائد هذه وهذه أصغر أو يساوي Normal X 
+
+147
+00:09:25,710 --> 00:09:29,290
+زائد Y تربيع زائد absolute value زائد absolute value
+
+148
+00:09:29,290 --> 00:09:32,670
+لإن أنا كده الـ absolute value أكبر أو يساوي هذه و
+
+149
+00:09:32,670 --> 00:09:35,910
+أكبر أو يساوي هذه حد يقول complex مش complex ما هذا
+
+150
+00:09:35,910 --> 00:09:39,510
+أصلاً وهذا هتطلعاش مالهان real التنتين هيطلعين 
+
+151
+00:09:39,510 --> 00:09:45,300
+real آه ماشي فاللي هو المجموع لـ absolute value له
+
+152
+00:09:45,300 --> 00:09:49,000
+أصغر أو يساوي المدرسة هذه زي المدرسة هذه واضح مافيش
+
+153
+00:09:49,000 --> 00:09:54,640
+خوف الآن هذه الآن زائد norm y تربيعي الأولى زي ما
+
+154
+00:09:54,640 --> 00:09:58,340
+هي والثانية من الـ .. الـ .. الـ .. الـ Schwarz in
+
+155
+00:09:58,340 --> 00:10:01,480
+equality أصغر أو يساوي norm هذي في norm لهذه اللي قبل
+
+156
+00:10:01,480 --> 00:10:06,020
+شوية زائد اللي هو هذي نفس الشيء فبيصير واحدة و
+
+157
+00:10:06,020 --> 00:10:10,770
+واحدة بتلغي تنتين الـ absolute value لهذه أصغر
+
+158
+00:10:10,770 --> 00:10:13,390
+يساوي norm هذه في norm هذه وهذه زيها إذا واحدة و
+
+159
+00:10:13,390 --> 00:10:17,110
+واحدة بيصير أنت أنت الاثنين هذه زي normal y تربيع طيب
+
+160
+00:10:17,110 --> 00:10:20,970
+الآن صار عندي هذا عبارة عن مين؟ عبارة عن normal x
+
+161
+00:10:20,970 --> 00:10:25,610
+زي normal y لكل ما له تربيع صار عندي الآن الـ x زي
+
+162
+00:10:25,610 --> 00:10:28,930
+الـ y لكل تربيع أصغر يساوي هذه إذا normal x زي أصغر
+
+163
+00:10:28,930 --> 00:10:33,710
+يساوي normal x زي y هذا أثبتنا مباشرة من مين؟ أثبتنا 
+
+164
+00:10:33,710 --> 00:10:37,350
+مباشرة من الـ inner product اللي هو استخدامنا للـ 
+
+165
+00:10:37,350 --> 00:10:40,310
+inner product طبعًا إحنا بنقدر نقول ما هو الـ inner
+
+166
+00:10:40,310 --> 00:10:44,390
+product is إيش ماله بيولد norm وده بيولد norm و
+
+167
+00:10:44,390 --> 00:10:48,350
+ده automatic إيش ماله كده بس قبل بدك تثبت إنه اللي
+
+168
+00:10:48,350 --> 00:10:55,110
+بيولده لهذا norm حتى تضطر تروح لهذا فاهمين؟ if 
+
+169
+00:10:55,110 --> 00:11:01,090
+equality holds then اللي هو هذا مزام الـ equality
+
+170
+00:11:01,090 --> 00:11:07,600
+hold الـ equality hold بالـ Equality Hold هذا بساوي
+
+171
+00:11:07,600 --> 00:11:11,800
+هذا إذا كل اللي في الطريق متساويات الأول واحدة
+
+172
+00:11:11,800 --> 00:11:13,780
+وآخر واحدة أطلع على فوق جيش الباكستورز زي اللي قبل
+
+173
+00:11:13,780 --> 00:11:17,180
+بشوية اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع 
+
+174
+00:11:17,180 --> 00:11:19,680
+اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع 
+
+175
+00:11:19,680 --> 00:11:19,820
+اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع
+
+176
+00:11:19,820 --> 00:11:24,320
+اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع اطلع 
+
+177
+00:11:24,320 --> 00:11:28,120
+اطلع اطلع 
+
+178
+00:11:30,690 --> 00:11:34,410
+كله بيصير مساوي الـ Equality holds يعني معناته الـ
+
+179
+00:11:34,410 --> 00:11:39,530
+X زائد Y زائد الـ Y و X بيساوي 2 في norm الـ A
+
+180
+00:11:39,530 --> 00:11:44,810
+شماله الـ X زائد Y واضح؟ هذا من اللي هو المساوية
+
+181
+00:11:44,810 --> 00:11:48,010
+اللي في الوسط هذه في تفاصيل بدك تشطب على بعض و
+
+182
+00:11:48,010 --> 00:11:51,930
+تطلع حادة بتساوي هذه واضح؟ بدكم تعملوها بنعملها طيب
+
+183
+00:11:51,930 --> 00:11:55,330
+عندي
+
+184
+00:11:55,330 --> 00:12:02,350
+صار عند الـ X والـ Y زائد الـ Y والـ X هيو ..
+
+185
+00:12:02,350 --> 00:12:06,990
+هيطلع لهذه مازالتكم تفاصيلكم في صنافته هيها مع
+
+186
+00:12:06,990 --> 00:12:13,590
+مين؟ مع اللي هي التانية هذه آه .. آه هذه فبروح أن 
+
+187
+00:12:13,590 --> 00:12:18,950
+هدول مع بعض بضل هذه زائد هذه بساوي اثنين في الـ X
+
+188
+00:12:18,950 --> 00:12:26,390
+زائد Y واضح؟ من هذه مع هذه ها دي بتروح معها دي وها 
+
+189
+00:12:26,390 --> 00:12:33,830
+دي بتروح معها دي وها دي بتروح معها دي وها دي بتروح
+
+190
+00:12:33,830 --> 00:12:36,010
+معها دي وها دي بتروح معها دي وها دي بتروح معها دي
+
+191
+00:12:36,010 --> 00:12:36,290
+و ها دي بتروح معها دي وها دي بتروح معها دي وها دي
+
+192
+00:12:36,290 --> 00:12:36,330
+بتروح معها دي وها دي بتروح معها دي وها دي بتروح
+
+193
+00:12:36,330 --> 00:12:37,770
+معها دي وها دي بتروح معها دي وها دي بتروح معها دي
+
+194
+00:12:37,770 --> 00:12:37,810
+و ها دي بتروح معها دي وها دي بتروح معها دي وها دي
+
+195
+00:12:37,810 --> 00:12:43,230
+بتروح معها دي وها دي بتروح معها دي وها دي بتروح
+
+196
+00:12:43,230 --> 00:12:52,010
+معها دي وها دي بتروح معها دي وها دي بتروح معها دي
+
+197
+00:12:52,010 --> 00:12:56,710
+و ها دي بت إذا هذه هي هذه اثنين مع اثنين فبيصير الـ
+
+198
+00:12:56,710 --> 00:12:59,190
+real part للـ X والـ Y بيصيح Normal X في Normal Y
+
+199
+00:12:59,190 --> 00:13:03,750
+وهذه أكبر أو يساوي اللي هي Normal X في Normal Y
+
+200
+00:13:03,750 --> 00:13:09,390
+أكبر أو يساوي الـ absolute value للـ X والـ Y لتو الـ 
+
+201
+00:13:09,390 --> 00:13:11,950
+absolute value للـ X والـ Y أصغر يساوي Normal هذي في
+
+202
+00:13:11,950 --> 00:13:16,310
+Normal هذي الآن صار عنده اللي هو الـ real part أكبر
+
+203
+00:13:16,310 --> 00:13:20,080
+أو يساوي المدلس وهذا مستحيل اللي يسويه الـ real part
+
+204
+00:13:20,080 --> 00:13:22,920
+أكبر يساوي البوضلاص البوضلاص إيش هو البوضلاص؟
+
+205
+00:13:22,920 --> 00:13:27,300
+البوضلاص عبارة عن الجدر التربيع الـ X تربيع مثلًا A
+
+206
+00:13:27,300 --> 00:13:31,660
+تربيع زائد B تربيع وهذه تلقى الـ A لحالها إذا لازم
+
+207
+00:13:31,660 --> 00:13:37,820
+يكون فيه مساواة لأن دائمًا دائمًا الـ real part أصغر
+
+208
+00:13:37,820 --> 00:13:41,600
+أو يساوي المودلوس هنا أثبتنا الـ real part أكبر
+
+209
+00:13:41,600 --> 00:13:44,540
+يساوي المدلس إذا since the real part can't exceed
+
+210
+00:13:44,540 --> 00:13:47,740
+the modulus then the real part must equal the 
+
+211
+00:13:47,740 --> 00:13:50,920
+modulus يعني التلاتة هذول هيصيرين إيه؟ الشمال هنا
+
+212
+00:13:50,920 --> 00:13:55,600
+متساوية يعني norm الـ Real part للـ X والـ Y هي
+
+213
+00:13:55,600 --> 00:14:00,860
+بساوي هذا بساوي المودلوس اللي عندي وهذا أكبر ويساوي
+
+214
+00:14:00,860 --> 00:14:07,100
+سفر مدام أكبر ويساوي سفر إذا صار عندي هذا أكبر و
+
+215
+00:14:07,100 --> 00:14:10,160
+يساوي سفر وبساوي اللي هو الـ Real part من قبل
+
+216
+00:14:10,160 --> 00:14:13,440
+بشوية قولنا اللي هو تحدث المساواة إذا كانت X و Y
+
+217
+00:14:13,440 --> 00:14:19,120
+أشماله linearly dependent أو اللي هو الـ Y بساوي
+
+218
+00:14:19,120 --> 00:14:23,040
+سفر إذا صار عندي ما دام هذا الـ linearly dependent
+
+219
+00:14:23,040 --> 00:14:27,100
+إذا Y بيساوي صفر أو X بيساوي مين؟ CY بس إحنا إيش
+
+220
+00:14:27,100 --> 00:14:32,120
+بدنا نثبته؟ إنه C أكبر أو يساوي إيش؟ أكبر أو يساوي 
+
+221
+00:14:32,120 --> 00:14:41,060
+صفر بدنا نثبت .. بدنا نثبت إنه C أكبر أو يساوي اللي
+
+222
+00:14:41,060 --> 00:14:50,020
+هو السفر طيب then y a x و y linearly demanded ومن
+
+223
+00:14:50,020 --> 00:14:54,920
+ثم اللي هو صار عندي اللي هو y بتساوي أو x بتساوي c
+
+224
+00:14:54,920 --> 00:14:58,280
+في y بدنا نثبت الـ c أكبر أو يساوي سفر طلع فوق تشوف
+
+225
+00:14:58,280 --> 00:15:04,480
+كيف عندي الـ x والـ y x والـ y قولنا عنها أكبر أو 
+
+226
+00:15:04,480 --> 00:15:09,830
+يساوي سفر ماشي .. إيه .. real part للـ X والـ Y بيساوي
+
+227
+00:15:09,830 --> 00:15:13,510
+المودلوس اللي هي بيساوي الـ absolute value للـ X والـ Y
+
+228
+00:15:13,510 --> 00:15:16,730
+عندي
+
+229
+00:15:16,730 --> 00:15:21,490
+الـ .. الـ .. الـ X قلنا عنها بيساوي C في Y وهد مين؟
+
+230
+00:15:21,490 --> 00:15:26,310
+الـ Y هد بيساوي C في norm للـ Y تربيع إذا صار عندي
+
+231
+00:15:26,310 --> 00:15:30,130
+هد أكبر يساوي سفر إذا الـ C نفسها أكبر أو يساوي سفر
+
+232
+00:15:30,720 --> 00:15:34,900
+الآن لو كانت Y بالساوية 0 أو X بالساوية Cy تعملوها
+
+233
+00:15:34,900 --> 00:15:38,700
+لحالكم إذا it is an easy calculation اللي هو أن
+
+234
+00:15:38,700 --> 00:15:41,680
+نثبت أن X زائد Y بساوي Normal X زائد Normal Y
+
+235
+00:15:41,680 --> 00:15:46,060
+بتعرفوا بتعملوها مافيش داعي لنا نعملها Cy حطها دي
+
+236
+00:15:46,060 --> 00:15:51,330
+Cy طيب لمّا continuity of inner product If N is an 
+
+237
+00:15:51,330 --> 00:15:55,610
+inner product space و XN بتروح لـ X و YN بتروح لـ Y
+
+238
+00:15:55,610 --> 00:16:01,210
+إذا الـ XN و YN بتروح لـ X و M و Y هذه ما هي إلا
+
+239
+00:16:01,210 --> 00:16:05,430
+عملية حسابات بدكم تحسبوا الـ inner product بين XN و
+
+240
+00:16:05,430 --> 00:16:10,090
+YN ناقص الـ X و Y و تضيفوا term وتطرحوا term و
+
+241
+00:16:10,090 --> 00:16:14,630
+تجيبوه بدلالة هذه وهذه هيروح للـ سفر بناء على XN 
+
+242
+00:16:14,630 --> 00:16:17,610
+ناقص XY بيروح للـ سفر و YN ناقص Y بتروح للـ سفر
+
+243
+00:16:18,910 --> 00:16:23,650
+البرهان سهل بتاخدوا XN عشان نثبت XN و YN بتروح لـ X
+
+244
+00:16:23,650 --> 00:16:28,990
+و Y بنيجي بناخد XN و YN ناقص X و Y بتحسبوها
+
+245
+00:16:28,990 --> 00:16:33,950
+بتضيفوا term وبتطرحوا term الـ term اللي بتضفوه XN
+
+246
+00:16:33,950 --> 00:16:40,190
+و Y و Y و XN و Y بالسلب السالب وبتجمعوا اللي زي
+
+247
+00:16:40,190 --> 00:16:46,800
+بعض اللي بتعلق بين XN و X وبين Y و N و Y هذا عبارة
+
+248
+00:16:46,800 --> 00:16:50,380
+عن مين؟ Xn بتروح للـ X معناته norm لـ Xn ناقص X
+
+249
+00:16:50,380 --> 00:16:53,920
+بتروح للـ 0 معناته الـ error product بين Xn ناقص X
+
+250
+00:16:53,920 --> 00:16:58,540
+و Xn ناقص X بيروح للـ 0 هذا بتكتبوه حاصل الطرح
+
+251
+00:16:58,540 --> 00:17:02,280
+بدلالة هذا وبدلالة هذا ومضروب فيه بحيث تجد مضروب
+
+252
+00:17:02,280 --> 00:17:04,940
+مرة في الـ norm هنا ومرة في الـ norm هنا اللي هو
+
+253
+00:17:04,940 --> 00:17:07,540
+بيروح هذا للسفر وهذا للسفر فكل هذا حاصل الطرح
+
+254
+00:17:07,540 --> 00:17:10,700
+بيروح للسفر معناته XN و YN بتروح لـ X و Y بضل
+
+255
+00:17:10,700 --> 00:17:14,300
+التفاصيل لكم لإنها تفاصيل حسابات وإلى لقاء آخر
+
+256
+00:17:14,300 --> 00:17:17,580
+معلش احنا استعجلنا في الـ section هذا
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/gwzFsK74bdc.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/gwzFsK74bdc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3da939ef29d69ec7d292506151b408f470d55233
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/gwzFsK74bdc.srt
@@ -0,0 +1,2765 @@
+1
+00:00:05,080 --> 00:00:08,520
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,520 --> 00:00:11,720
+والصلاة والسلام على سيد المسلمين سيدنا محمد وعلى آله 
+
+3
+00:00:11,720 --> 00:00:16,040
+وصحبه أجمعين، اليوم إن شاء الله المحاضرة الثالثة في
+
+4
+00:00:16,040 --> 00:00:21,120
+مساق تحليل اقتراني لطلاب وطالبات الجامعة الإسلامية
+
+5
+00:00:21,120 --> 00:00:22,280
+مساق الماجستير
+
+6
+00:00:24,670 --> 00:00:29,530
+وصلنا لعند اللي هو الـ section الثالث اللي هو 1.3
+
+7
+00:00:29,530 --> 00:00:33,470
+وفي هذا الـ section طبعا الحديث هيكون حول اللي هو
+
+8
+00:00:33,470 --> 00:00:36,690
+العنوان open sets و closed sets و neighborhoods
+
+9
+00:00:36,690 --> 00:00:40,730
+وفي الواقع يعني هذا اللي هو يعني هيتم الحديث عن
+
+10
+00:00:40,730 --> 00:00:44,390
+مفاهيم طوبولوجية أو topological concepts أو
+
+11
+00:00:44,390 --> 00:00:48,270
+topological properties in the metric اللي هو SBS
+
+12
+00:00:48,610 --> 00:00:52,930
+هنشوف الموضوع، الموضوع إن شاء الله سهل وإن شاء الله 
+
+13
+00:00:52,930 --> 00:00:57,390
+مش صعب، الآن نيجي للتعريف الأول، الـ definition الأول
+
+14
+00:00:57,390 --> 00:01:02,750
+بده يعرف اللي هو لو جيت أخدت X وD متريك سبيس و X 
+
+15
+00:01:02,750 --> 00:01:06,950
+not أي X في الـ .. في الـ space وR positive real 
+
+16
+00:01:06,950 --> 00:01:12,300
+number، Define the sets، الآن بدي أعرف اللي هو B X0
+
+17
+00:01:12,300 --> 00:01:16,680
+وR اللي هي عبارة عن حاجة اسمها open ball بنصف 
+
+18
+00:01:16,680 --> 00:01:22,060
+قطر R واللي هو مركزها X0، طبعا هتلاقوا اللي هو
+
+19
+00:01:22,060 --> 00:01:26,560
+التعريف اللي بحكي فيه تيمنا باللي احنا كنا نعرفه
+
+20
+00:01:26,560 --> 00:01:29,580
+الـ open ball أو الـ closed ball أو الـ sphere اللي في
+
+21
+00:01:29,580 --> 00:01:34,290
+الـ R تربيع، الآن أنا لكن بحكي عن X وD in general هي 
+
+22
+00:01:34,290 --> 00:01:38,670
+X وهي D، X أنا 6 وD متريك عليها فصار متريك space
+
+23
+00:01:38,670 --> 00:01:43,370
+وأخدت X not موجودة في مين؟ في الـ X، الآن بمثلكم 
+
+24
+00:01:43,370 --> 00:01:48,650
+إياها بالرسم تيمنا بالـ R تربيع، لكن هو كيف شكله
+
+25
+00:01:48,650 --> 00:01:51,910
+اللي هو الـ ball في الـ X وD ما أعرفش كيف شكله لأن X 
+
+26
+00:01:51,910 --> 00:01:54,670
+وD مش شرط أن يكون R أو R تربيع أو R تكعيب أو 
+
+27
+00:01:54,670 --> 00:02:00,210
+الآخرين، فالآن عندي اللي هو بقول X not مركز وعندي
+
+28
+00:02:00,210 --> 00:02:04,630
+اللي هو النقاط اللي بتبعد ببعد R، كل هذه النقاط هي
+
+29
+00:02:04,630 --> 00:02:09,710
+اللي بتسميها الـ ball of X not وR، إذا الـ ball of X 
+
+30
+00:02:09,710 --> 00:02:13,450
+not وR هي عبارة عن كل النقاط اللي من الـ space X 
+
+31
+00:02:13,450 --> 00:02:18,970
+التي تبعد وفق الـ metric D عندي بمسافة أقل من 100 
+
+32
+00:02:18,970 --> 00:02:23,990
+من R، هذا بتسميها أيش عبارة عن open ball، اللي قال 
+
+33
+00:02:23,990 --> 00:02:28,750
+closed ball similarly، بس بدي أدخل فيها مين اللي هو
+
+34
+00:02:28,750 --> 00:02:34,010
+المحيط إن صح التعبير، بدي أدخل اللي هي أقول B tilde 
+
+35
+00:02:34,010 --> 00:02:38,130
+of X0 وR هي عبارة عن كل الاكسات اللي في الـD اللي
+
+36
+00:02:38,130 --> 00:02:44,550
+بعدها عن X0 بمسافة تساوي أو أقل، إذا هذه بالإضافة 
+
+37
+00:02:44,550 --> 00:02:49,830
+إيش للي بعدها متساوي عن X0، هذه بدي أسميها closed
+
+38
+00:02:49,830 --> 00:02:56,350
+ball، الآن التعريف الثالث اللي هو عبارة عن احنا
+
+39
+00:02:56,350 --> 00:02:59,130
+عرفنا الآن اللي هو الـ open ball اللي جوا الـ 
+
+40
+00:02:59,130 --> 00:03:02,650
+closed ball اللي هنا اللي على اللي هي المساواة
+
+41
+00:03:02,650 --> 00:03:06,450
+بالإضافة للي جوا سميتها اللي هي closed ball، الآن
+
+42
+00:03:06,450 --> 00:03:12,670
+هذا لحاله، هذا لحاله اللي هي المقاطع الـ X في الـ X
+
+43
+00:03:12,670 --> 00:03:16,650
+اللي بتبعد عن X not بمقدار بالظبط R، هذا بدي
+
+44
+00:03:16,650 --> 00:03:19,230
+أسميها S of X not وR، وبدي أقول هي إيه إيه إيه 
+
+45
+00:03:19,230 --> 00:03:20,690
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+46
+00:03:20,690 --> 00:03:22,150
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+47
+00:03:22,150 --> 00:03:22,790
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+48
+00:03:22,790 --> 00:03:23,810
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+49
+00:03:23,810 --> 00:03:31,710
+إيه إيه إيه إيه إيه إيه إيه إيه 
+
+50
+00:03:31,710 --> 00:03:39,840
+إيه، طيب صلوا على النبي عليه الصلاة والسلام، من 
+
+51
+00:03:39,840 --> 00:03:43,940
+التعريف اللي جوه فوق وأثناء الحديث أكيد كلكم شاف
+
+52
+00:03:43,940 --> 00:03:48,120
+وقال، والله ما هو أصلا لو أنت قلت B tilde و شلت 
+
+53
+00:03:48,120 --> 00:03:52,200
+منها الـ B هيطلع مين؟ الـ S، يعني لو أخدت الـ closed 
+
+54
+00:03:52,200 --> 00:03:56,080
+ball وشلت منها الـ ball اللي جوه، حتى اللي هي الجُشرة 
+
+55
+00:03:56,080 --> 00:03:59,800
+اللي برا، اللي بمعنى آخر هي الـ sphere، عشان هيك اللي
+
+56
+00:03:59,800 --> 00:04:06,210
+في الملاحظة أسفل هنا، from the definition one can
+
+57
+00:04:06,210 --> 00:04:10,810
+easily see that S of X not of R بيساوي الـ B tilde 
+
+58
+00:04:10,810 --> 00:04:16,490
+ناقص الـ B، ماشي الحال، من الآن وطالع على أساس أنه
+
+59
+00:04:16,490 --> 00:04:20,650
+نتفاهم مع بعض، بدي أبطل أظل أقول X وD metric space
+
+60
+00:04:20,650 --> 00:04:24,790
+خلاص، لما أقول X بحاجة بقصد أن X عليها metric اسم
+
+61
+00:04:24,790 --> 00:04:27,790
+مين؟ اسم D، على أساس أنه احنا بنضل عشان نغلب حالنا
+
+62
+00:04:27,790 --> 00:04:33,040
+وهيك توافقنا على أن X نقصد فيها X وD، طيب نيجي
+
+63
+00:04:33,040 --> 00:04:40,040
+الآن للتعريف 1.3.2، التعريف بيقول لي اللي 
+
+64
+00:04:40,040 --> 00:04:46,990
+أنا بده يعرف لي اللي هو حاجة اسمها open set، لما ندخل 
+
+65
+00:04:46,990 --> 00:04:50,650
+لشكل، ندخلين مدخل أنه بتعرف الـ open set، أنا عرفت
+
+66
+00:04:50,650 --> 00:04:53,950
+الآن الـ open ball وعرفت الـ closed ball وعرفت الـ 
+
+67
+00:04:53,950 --> 00:04:58,750
+sphere، بتستعين بالـ open ball أن يعرف الـ open set 
+
+68
+00:04:58,750 --> 00:05:04,210
+وهتلاقي إن في النهاية وصلت إلى شيء متوافق مع اللي
+
+69
+00:05:04,210 --> 00:05:07,190
+احنا بنعرفه في الأصل اللي هو مفهوم الـ open set
+
+70
+00:05:07,190 --> 00:05:10,550
+سواء في التحليل أو حتى في الـ topology in general
+
+71
+00:05:11,120 --> 00:05:16,160
+نأتي الآن نشوف أيش معنى اللي هو الـ 6 تكون Open
+
+72
+00:05:16,160 --> 00:05:24,620
+بنقول أن M هي M جزء من متريك سبيس اسمه X، بقول أن الـ 
+
+73
+00:05:24,620 --> 00:05:33,400
+M هذا أنها open set، M is open، إذا تحقق الشرط
+
+74
+00:05:33,400 --> 00:05:38,880
+التالي، أنه لو أتيت أخدت أي X في الـ M أو X not في
+
+75
+00:05:38,880 --> 00:05:44,060
+الـ M، أخدت أي X not في الـ M لازم ألاقي there 
+
+76
+00:05:44,060 --> 00:05:48,900
+exists ball، نصف مركزها الـ X not هذه اللي بدأت 
+
+77
+00:05:48,900 --> 00:05:54,700
+فيها ونصف قطرها R تكون كلها جوات مين؟ جوات الـ M
+
+78
+00:05:54,700 --> 00:05:57,900
+لو لجيت الخاصية هذه على طول بقول إن الـ M إيه
+
+79
+00:05:57,900 --> 00:06:02,660
+شمالها؟ is an open set، يعني a subset M of a metric 
+
+80
+00:06:02,660 --> 00:06:08,410
+space X is said to be open if it contains a ball about
+
+81
+00:06:08,410 --> 00:06:11,750
+each of its points، يعني كل نقطة من نقاطها بلاقي 
+
+82
+00:06:11,750 --> 00:06:16,450
+ball كلها جواتها، a subset K بنسميه K it has closed 
+
+83
+00:06:16,450 --> 00:06:21,230
+set إذا كانت مكملتها open، هذه تعريف اللي بديها
+
+84
+00:06:21,230 --> 00:06:26,030
+لحظة، هذه ممكن أنت تتخيلها كالتالي، أنه لو أخدنا set 
+
+85
+00:06:26,030 --> 00:06:31,200
+X أي M set بقول عنها أنها open set، إذا جيت أخدت
+
+86
+00:06:31,200 --> 00:06:34,260
+أنا طبعا احنا برسم برسم مكاني، برسم في R تربيع
+
+87
+00:06:34,260 --> 00:06:37,260
+بس هو احنا بنحكي عن أي space، لكن أنا بقرّب لكم 
+
+88
+00:06:37,260 --> 00:06:41,460
+الصورة بالرسم ماشي، لو بنقول عنها دي open set إذا 
+
+89
+00:06:41,460 --> 00:06:45,560
+جيت أخدت أي نقطة X، أي نقطة X وين وجودها؟ في الـ M
+
+90
+00:06:45,560 --> 00:06:50,620
+بدي ألاقي open ball حواليها بنصف قطر R تكون كلها
+
+91
+00:06:50,620 --> 00:06:53,860
+الـ open ball جوات مين؟ جوات الـ M، في هذه الحالة 
+
+92
+00:06:53,860 --> 00:07:00,160
+بنقول M is an open set، واضح يا طيب .. صلوا على 
+
+93
+00:07:00,160 --> 00:07:05,130
+النبي عليه الصلاة والسلام، عندي في تعريف 1.3
+
+94
+00:07:05,130 --> 00:07:09,830
+قبلها خلّيني نشوف أيش الملاحظة اللي بيقولها، it is 
+
+95
+00:07:09,830 --> 00:07:14,470
+easy، بيقول من السهل to see from the definition 
+
+96
+00:07:14,470 --> 00:07:19,070
+above that the open balls is an open set and the 
+
+97
+00:07:19,070 --> 00:07:21,990
+closed ball is a closed set، انتبهوا علينا، خلّيني 
+
+98
+00:07:21,990 --> 00:07:25,910
+نشوف هذه، بيقولوا إنه من السهل إنك تثبت إن أي open 
+
+99
+00:07:25,910 --> 00:07:32,380
+ball open set، بنشوف كلامه صحيح صحيح، لكن بنشوف اللي
+
+100
+00:07:32,380 --> 00:07:38,320
+هو كيف نثبت كلامه، لو جينا أخدنا N اللي هو أخدنا الـ 
+
+101
+00:07:38,320 --> 00:07:44,100
+ball X not و Epsilon، بدنا نشوف هذه كيف هي open 
+
+102
+00:07:44,100 --> 00:07:47,760
+set ماشي الحال، عشان نثبت إنها open 
+
+103
+00:07:51,130 --> 00:07:55,610
+خلّينا نص قطرها R، ليش نسميه Y، نص قطرها R هي جي
+
+104
+00:07:55,610 --> 00:08:01,730
+تاخدت open ball هي نص اللي هو مركزها X not ونص
+
+105
+00:08:01,730 --> 00:08:07,870
+قطرها R، ماشي الحال، بدي أثبت أن هذه عبارة عن مين؟ عن
+
+106
+00:08:07,870 --> 00:08:12,030
+open set، عشان أثبت open إيش بدي أخد؟ بدي أخد أي
+
+107
+00:08:12,030 --> 00:08:18,260
+نقطة في داخلها، أي نقطة X في داخلها، وأناجي open ball
+
+108
+00:08:18,260 --> 00:08:23,380
+حواليها تكون كلها جواها مين؟ جواها الـ set يعني أو هذا
+
+109
+00:08:23,380 --> 00:08:26,800
+الـ set لأ سميتها B X not يعني جواها مين؟ B X not 
+
+110
+00:08:26,800 --> 00:08:34,440
+وR، لاحظوا يعني بدها تجي لي B واحد ball اللي هو 
+
+111
+00:08:34,440 --> 00:08:40,620
+مركزها X ونصف قطرها H اللي أجمل يكون معله جواها الـ 
+
+112
+00:08:40,620 --> 00:08:43,820
+B of X not ومين؟ وR
+
+113
+00:08:46,130 --> 00:08:50,790
+خذ الآن X اعتباطية، كلكم بالعين بيقول لي تدور على
+
+114
+00:08:50,790 --> 00:08:53,950
+نصف القطر اللي بيخلي الـ ball حوالين هذا كله جوا
+
+115
+00:08:53,950 --> 00:08:58,690
+من الـ ball الكبيرة هذه، الآن واحد هيقول لي ابعد عن
+
+116
+00:08:58,690 --> 00:09:03,070
+هنا عن المسافة هذه بالمقدار هذا، نصف القطر هذه
+
+117
+00:09:03,070 --> 00:09:07,290
+بتضمن إنك تلاقيها جوا، يعني خذ نصف القطر هذه، طب 
+
+118
+00:09:07,290 --> 00:09:13,970
+هذه إيش بتساوي؟ هذه بتساوي المسافة كلها هذه الـ Epsilon R
+
+119
+00:09:15,390 --> 00:09:20,190
+هذه كلها منها نقّص شيل منها مين؟ المسافة بين
+
+120
+00:09:20,190 --> 00:09:27,370
+النقطتين ناقص D(x, x not)، هذا لو أخذته نصف قطر بضمن لك
+
+121
+00:09:27,370 --> 00:09:29,670
+الـ ball هذه الكورة كلها جوا الـ ball الكبيرة 
+
+122
+00:09:29,670 --> 00:09:36,110
+يعني الآن وكأنه بقول لك جوابي، خذ أي X not، خذ اللي 
+
+123
+00:09:36,110 --> 00:09:42,270
+هو أي X في داخل اللي هو الـ 6 هذه، وخذ اللي هو الـ
+
+124
+00:09:42,270 --> 00:09:49,510
+ball اللي مركزها X ونصف قطرها عبارة عن R ناقص D(X,
+
+125
+00:09:49,510 --> 00:09:55,610
+X not)، بضمن لك في هذه الحالة نصف القطر هذا إن
+
+126
+00:09:55,610 --> 00:10:00,620
+يخليني هذه الـ ball جوا هذه الـ ball، ماشي الحال، طب 
+
+127
+00:10:00,620 --> 00:10:03,420
+واحد يقول لي طب هو أصلا ممكن تكون هذه X مش قريبة 
+
+128
+00:10:03,420 --> 00:10:06,500
+هان، ممكن تكون X هنا، وأقول له حتى لو كانت قريبة أو
+
+129
+00:10:06,500 --> 00:10:10,360
+ما كانت، بأخدها نفس الشيء هي بتطلع هيك وبتضلها 
+
+130
+00:10:10,360 --> 00:10:15,420
+وين؟ جواك الـ ball وجبريا هذا الكلام صحيح، طب إيش 
+
+131
+00:10:15,420 --> 00:10:18,980
+.. كيف أعرف إنه صحيح؟ خذ بدليل هذه جزئية من مين؟ من
+
+132
+00:10:18,980 --> 00:10:26,860
+هذه، خذ الآن z، أي element in B(X, R) ناقص D(X, 
+
+133
+00:10:26,860 --> 00:10:29,620
+X not)، بتثبت لك، عشان أنت بتاخد الـ subset من هنا
+
+134
+00:10:29,620 --> 00:10:33,500
+بتاخد أي element هنا، ولا بيهمني ولا شيء، الحال، طب الآن
+
+135
+00:10:33,500 --> 00:10:37,140
+z في هذه، إيش معنى z في هذه؟ معنى z كيف بتكون 
+
+136
+00:10:37,140 --> 00:10:40,820
+في الـ ball، إن تكون المسافة بين الـ z والـ x اللي
+
+137
+00:10:40,820 --> 00:10:45,400
+عندي أصغر من مين؟ من نصف القطر، نصف القطر في هذه
+
+138
+00:10:45,400 --> 00:10:52,820
+الحالة R ناقص D(X, X not)، طب ما هو يا جماعة عندي
+
+139
+00:10:52,820 --> 00:11:03,240
+الآن صار عندي دي، لو جيت أخدت دي z وx0، دي z وx0 
+
+140
+00:11:03,240 --> 00:11:08,600
+إيش مالها دي؟ أنا إيش بدي أثبت؟ بدي أثبت إن z هان عشان
+
+
+
+141
+00:11:08,600 --> 00:11:11,700
+اثبت انه z لازم اثبت المسافة بين z و x0 اصغر
+
+142
+00:11:11,700 --> 00:11:16,610
+من مين؟ من R صح ولا لأ؟ عشان أثبت أن الـ z في هذه
+
+143
+00:11:16,610 --> 00:11:21,030
+بتثبت أن المسافة بين z و بين x0 أصغر منها فنشوف خد
+
+144
+00:11:21,030 --> 00:11:26,150
+المسافة بين z و x0 شوفوا نفكر مع بعض هذه
+
+145
+00:11:26,150 --> 00:11:34,070
+اللي هي بتكون أصغر أو تساوي d(z,x) + d(x, x0) صح
+
+146
+00:11:34,070 --> 00:11:38,430
+ولا لأ؟ بتراينجل إينيكواليتي بتراينجل إينيكواليتي لأن
+
+147
+00:11:38,430 --> 00:11:46,240
+d(z,x) و d(x, x0) هذه أصغر من R، عارفين
+
+148
+00:11:46,240 --> 00:11:50,900
+ليه؟ من هنا، من هنا، من هنا، جيب هذه على الجهة
+
+149
+00:11:50,900 --> 00:11:55,640
+هنا، بيصير d(z,x) + d(x, x0) أصغر من مين؟
+
+150
+00:11:55,640 --> 00:11:59,460
+من R، فالآن هذه أصغر من هذه، و هذه نفسها من اللي
+
+151
+00:11:59,460 --> 00:12:02,940
+فوق أصغر من R، إذا صارت d(z, x0) أصغر 
+
+152
+00:12:02,940 --> 00:12:08,140
+من R، إذا Automatically هتكون الـ z موجودة في الـ
+
+153
+00:12:08,140 --> 00:12:15,800
+ball اللي مركزها x0 ونصف قطرها R معناته بدأنا في z
+
+154
+00:12:15,800 --> 00:12:20,100
+هنا وانتهينا في z هنا صارت هذه مجموعة جزئية من هذه
+
+155
+00:12:20,100 --> 00:12:24,840
+يعني بمعنى أنه أخدت أي نقطة x عشوائية في داخل ال
+
+156
+00:12:24,840 --> 00:12:29,320
+ball هذا لقيته بال  نصف القطر اللي حكيته كله جواها
+
+157
+00:12:29,320 --> 00:12:37,460
+هذه وهذا التسبب في النتيجة هذه is an open set اللي 
+
+158
+00:12:37,460 --> 00:12:42,120
+حكيته صحيح البرهان بطريقة اللي هو الإجابة اللي 
+
+159
+00:12:42,120 --> 00:12:49,760
+حكيتها طيب يا جماعة لأن مكملتها بيقول ليه مكملتها
+
+160
+00:12:49,760 --> 00:12:55,000
+مكملت ال closed ball is open ده نشوف كيف بدنا نثبت
+
+161
+00:12:55,000 --> 00:12:59,260
+الآن مكملت ال closed ball is open ده نشوف كيف
+
+162
+00:12:59,260 --> 00:13:04,540
+نثبت مكملت ال closed ball is open هي عندي ال ball
+
+163
+00:13:04,540 --> 00:13:13,770
+تلدة of x0 OR هذي بنثبتها إنها open إنها
+
+164
+00:13:13,770 --> 00:13:20,410
+مكملتها open طيب خلينا نطلع بس على الرسم هيك
+
+165
+00:13:20,410 --> 00:13:24,570
+التقريبي x0 و هذا مين و هذا R أو الاستئناسي
+
+166
+00:13:24,570 --> 00:13:27,030
+الرسم الاستئناسي اللي نتخيل فيه ما هو مش شرط أن
+
+167
+00:13:27,030 --> 00:13:29,890
+نكون شكل الرسم هيك لأننا بس ما نعرفوش احنا كيف
+
+168
+00:13:29,890 --> 00:13:35,120
+شكله طيب x0 وهي نصف القطر R هذه اللي هي .. هذه
+
+169
+00:13:35,120 --> 00:13:39,440
+مع الجشرة الخارجية هي اللي بتمثل B tilde ده وكملت
+
+170
+00:13:39,440 --> 00:13:44,480
+همين؟ اللي برا صح ولا لأ؟ لأن عشان أثبت اللي برا
+
+171
+00:13:44,480 --> 00:13:50,540
+أنه open بتاخد أي نقطة برا واسميها x وألاقي ball
+
+172
+00:13:50,540 --> 00:13:56,190
+كامل وين برا يعني في المنطقة هذه إذا أثبتت هذا
+
+173
+00:13:56,190 --> 00:14:02,310
+الكلام يعني الآن بدي أخد x في مكملة هذه إيش
+
+174
+00:14:02,310 --> 00:14:09,550
+مكملتها هي x - B(x0,R) tilde و بدي ألاقي اللي
+
+175
+00:14:09,550 --> 00:14:17,210
+هو ball بدي ألاقي بقول أنا there exists ball اللي
+
+176
+00:14:17,210 --> 00:14:24,150
+هي ball نصف اللي هي مركزها x هذه ونصف القطر
+
+177
+00:14:24,150 --> 00:14:28,790
+بتاعي أشوفه يكون كلها جزء من مين؟ من اللي برا هذا
+
+178
+00:14:28,790 --> 00:14:34,850
+اللي هو جزء من x - B tilde(x0,R) إذا عملت
+
+179
+00:14:34,850 --> 00:14:38,670
+هيك بكون أثبتت إنه فعلا الست اللي برا هذا إيش ما
+
+180
+00:14:38,670 --> 00:14:44,060
+لها is open سهل شوف لها نصف القطر هذا نصف القطر
+
+181
+00:14:44,060 --> 00:14:48,500
+نهمًا كانت بعيدة بقدر أخد هو نصف القطر لأن هذا اللي
+
+182
+00:14:48,500 --> 00:14:50,880
+بيظل لما لنهاية ما فيش خوف منها خوف من وين المنطقة
+
+183
+00:14:50,880 --> 00:14:55,440
+هذه فأخدت البعد من هالهال هو نصف القطر طب كدهش
+
+184
+00:14:55,440 --> 00:15:04,860
+البعد من هالهال هو عبارة عن R مظبوط هذا هي R طب
+
+185
+00:15:04,860 --> 00:15:10,080
+و هذه المنطقة كيف بدي أحسبها بقول المسافة بين هذه
+
+186
+00:15:10,080 --> 00:15:18,090
+و هذه شيل منها هذه تطلع هذه يعني بمعنى آخر اللي
+
+187
+00:15:18,090 --> 00:15:22,750
+جابل بس بالنار بس هذه الآن بتاخد المسافة عكسها
+
+188
+00:15:22,750 --> 00:15:26,550
+يعني عكس اللي جابل في الإشارة هي عبارة عن هذه
+
+189
+00:15:26,550 --> 00:15:31,890
+المنطقة دي إيش بتساوي المسافة بين x و x0 شيل
+
+190
+00:15:31,890 --> 00:15:35,770
+منها منهم ال R اللي جابل كانت إيش العكس R معكوسها
+
+191
+00:15:37,190 --> 00:15:41,750
+واضحة فالآن هذه ال ball اللي هي بالنصف قطر هذا
+
+192
+00:15:41,750 --> 00:15:45,610
+بضمن لكم انها تكون كلها قاعدة في ال set اللي احنا
+
+193
+00:15:45,610 --> 00:15:49,570
+بيقول عنها x نقص منه x0 و R  tilde وثباتها دي
+
+194
+00:15:49,570 --> 00:15:52,630
+subset سهل بنفس الطريقة اللي جابها قبل شوية خد z
+
+195
+00:15:52,630 --> 00:15:57,630
+هان هتلاقي d(z,x) أصغر من هذه وبستعين بال triangle
+
+196
+00:15:57,630 --> 00:16:01,690
+inequality بأصل إنه اللي هو موجودة وين في المنطقة
+
+197
+00:16:01,690 --> 00:16:07,550
+الثانية طيب يا جماعة إذا اللي أثبتناه هنا إن ال
+
+198
+00:16:07,550 --> 00:16:10,470
+open هي أول open sets اتعرفنا عليها أن ال open
+
+199
+00:16:10,470 --> 00:16:16,370
+balls are open sets و ال complement لل closed
+
+200
+00:16:16,370 --> 00:16:22,830
+balls برضه open sets الآن نيجي للتعريف اللي بعده
+
+201
+00:16:22,830 --> 00:16:33,350
+بدنا نعرف حاجة اسمها الجوار بنصف قطر إبسيلون باختصار
+
+202
+00:16:33,350 --> 00:16:39,150
+بدي أعرف لكم الجوار للنقطة x0 بنصف قطر y هي عبارة
+
+203
+00:16:39,150 --> 00:16:43,550
+عن الـ open ball اللي نصف قطرها اللي هو الـ y
+
+204
+00:16:43,550 --> 00:16:54,640
+مركزها x0 إذا الآن بقول أن B(x0,y) هو عبارة عن
+
+205
+00:16:54,640 --> 00:17:01,680
+neighborhood of x0 with radius y أو بدي أسميه الـ
+
+206
+00:17:01,680 --> 00:17:06,980
+y neighborhood of x0 إذا لو قلنا x metric
+
+207
+00:17:06,980 --> 00:17:14,700
+space an open ball B(x0,y) of radius y إيش بنسميه
+
+208
+00:17:14,700 --> 00:17:20,740
+is called an y neighborhood of x0 element in x إذا
+
+209
+00:17:20,740 --> 00:17:25,620
+الـ neighborhood أو الجوار للـ x0 بنصف قطر y ما هو
+
+210
+00:17:25,620 --> 00:17:33,020
+إلا عبارة عن الـ open ball اللي أمامي طيب بنقول إن
+
+211
+00:17:33,020 --> 00:17:41,300
+أن .. أن of x0 هو عبارة عن جوار بس بنقول جوار و
+
+212
+00:17:41,300 --> 00:17:49,110
+بنسكت جوار للـ x0 بنعني في إن هذا الست  بغض النظر
+
+213
+00:17:49,110 --> 00:17:52,190
+كيف شكلها هيك ولا هيك ولا هيك ولا هيك ما أعرفش احنا
+
+214
+00:17:52,190 --> 00:17:57,950
+كيف شكلها بنقول أن هذا جوار لل x0 إذا قدرت ألاقي
+
+215
+00:17:57,950 --> 00:18:05,770
+اللي هو داخله جوار بنصف قطر y يعني قدرت ألاقي اللي
+
+216
+00:18:05,770 --> 00:18:13,840
+هو B(x0,y) كله جوات مين؟ جوات N إذاً N is a
+
+217
+00:18:13,840 --> 00:18:19,340
+neighbourhood أو جوار لـ x0 if we can find an
+
+218
+00:18:19,340 --> 00:18:25,320
+epsilon neighbourhood inside N واضح؟ إذاً هذا
+
+219
+00:18:25,320 --> 00:18:33,120
+بيحكي بصراحة a neighbourhood of x0 which is
+
+220
+00:18:33,120 --> 00:18:41,320
+denoted by N(x0) is a subset of x which contains
+
+221
+00:18:41,320 --> 00:18:49,020
+إيش ماله الـy neighborhood of x0 طيب نيجي
+
+222
+00:18:49,020 --> 00:19:03,280
+لللي هو definition 134 definition 134 فبدنا
+
+223
+00:19:03,280 --> 00:19:13,670
+نعرف يا جماعة شو معنى x0 نقطة داخلية يعني الآن لو
+
+224
+00:19:13,670 --> 00:19:24,970
+أجيت أخدت لكم اللي هو M أي M أي M هذه M ماشي
+
+225
+00:19:24,970 --> 00:19:30,860
+هذه جزئية من metric space بقول النقطة x0 هذه
+
+226
+00:19:30,860 --> 00:19:36,180
+إنها نقطة داخلية في الـ M يعني x0 عبارة عن
+
+227
+00:19:36,180 --> 00:19:41,180
+interior point يعني element in M أو نرمز لها x
+
+228
+00:19:41,180 --> 00:19:45,700
+0 element in interior of M أي من هذا الرمز أو
+
+229
+00:19:45,700 --> 00:19:50,160
+هذا الرمز بنقصد فيه ما له ال interior point أو the
+
+230
+00:19:50,160 --> 00:19:54,480
+set of interior balls نقول x0 هي عبارة عن element
+
+231
+00:19:54,480 --> 00:19:57,620
+in M interior يعني عبارة عن نقطة داخلية للـ M
+
+232
+00:19:57,620 --> 00:20:03,540
+انتبهوا إذا لجيت جوار بنصف قطر ال epsilon كله
+
+233
+00:20:03,540 --> 00:20:09,720
+الموجود في داخل الـ M ماشي الحال يعني لجيت ball of
+
+234
+00:20:09,720 --> 00:20:15,150
+x0 و epsilon subset من M لأن لحظة لو النقطة هنا على
+
+235
+00:20:15,150 --> 00:20:19,530
+ال .. على ال .. على الحدود بتكون مش داخلية لأن هو
+
+236
+00:20:19,530 --> 00:20:22,330
+هياخد من برا و من جوه و زي ما كنا بنقول في ال
+
+237
+00:20:22,330 --> 00:20:25,490
+calculus وهذا خليني أقول استئناس اللي يبقى إذا لو
+
+238
+00:20:25,490 --> 00:20:30,150
+بدأت أحكي هذا الكلام بالرموز بقول x0 element in
+
+239
+00:20:30,150 --> 00:20:39,130
+M interior إيش تعني أنه there exist اللي هو B(x0,y)
+
+240
+00:20:39,130 --> 00:20:44,870
+و y كل جزء من مين منها إذا اللي بجزده إنه x0
+
+241
+00:20:44,870 --> 00:20:49,230
+interior point إذا كان لجهة ball بنص في قطر y أو
+
+242
+00:20:49,230 --> 00:20:53,810
+neighborhood بنص في قطر y كل جزء من مين منها
+
+243
+00:20:53,810 --> 00:20:57,790
+معايا؟
+
+244
+00:20:57,790 --> 00:21:03,290
+زي
+
+245
+00:21:03,290 --> 00:21:07,500
+ما اتفقنا the set of all interior points of M
+
+246
+00:21:07,500 --> 00:21:12,260
+بنرمزلها بالرمز interior of M or M interior هذه
+
+247
+00:21:12,260 --> 00:21:16,680
+مجموعة كل النقاط الداخلية للـ M طيب نيجي الآن بقول
+
+248
+00:21:16,680 --> 00:21:20,200
+لي it is easy to see that interior of M is an open
+
+249
+00:21:20,200 --> 00:21:25,540
+set يعني بتقدر احنا بنقول انه الآن إعلان وفق
+
+250
+00:21:25,540 --> 00:21:30,180
+الكلام هذا إن ال interior point the set of all
+
+251
+00:21:30,180 --> 00:21:36,680
+interior points interior points of M هذه is an open
+
+252
+00:21:36,680 --> 00:21:43,870
+set عارف؟ is an open set يعني بدك تاخد أي x في
+
+253
+00:21:43,870 --> 00:21:50,750
+الـ interior للـ M x في الـ interior للـ M و تصل
+
+254
+00:21:50,750 --> 00:21:58,910
+.. و تصل .. و تصل من خلالها أنه there exist B(x,r)
+
+255
+00:21:58,910 --> 00:22:05,070
+أو x0 B(x0,r) و some radius r كله جزء من
+
+256
+00:22:05,070 --> 00:22:13,580
+مين من الـ interior لمين للـ M ماشي الحال هذا بتعملوه
+
+257
+00:22:13,580 --> 00:22:17,100
+لحالكم إنه اللي هو تاخدوا x0 في ال interior من
+
+258
+00:22:17,100 --> 00:22:21,220
+ال M و تصلوا إنه بتلاقي ال ball بنفس القطر كذا
+
+259
+00:22:21,220 --> 00:22:23,880
+شوية في ال interior من ال M طبعا أنتم بتعرفوا إن
+
+260
+00:22:23,880 --> 00:22:28,820
+مدام x interior إذا بلاقي ball جزئية من مين؟ من
+
+261
+00:22:28,820 --> 00:22:33,370
+ال M أه كيف الآن تلاقي ال ball جزئية من الان وفي
+
+262
+00:22:33,370 --> 00:22:37,790
+الآخر تلاقي ball منها جزئية من مين من ال interior
+
+263
+00:22:37,790 --> 00:22:42,870
+لل الان هذا بيضل معكم طيب نيجي الآن لل theorem اللي
+
+264
+00:22:42,870 --> 00:22:49,110
+أمامنا ال theorem اللي هو اللي أمامي أنا حكيته
+
+265
+00:22:49,110 --> 00:22:54,090
+الآن عن ال .. ركزوا معي عن ال open sets الآن
+
+266
+00:22:54,090 --> 00:22:56,710
+هدول ال collection of open sets يعني هائلة ال
+
+267
+00:22:56,710 --> 00:23:00,770
+open sets بتحطها مع بعض وبتثبت لكم الآن هي بتحقق
+
+268
+00:23:00,770 --> 00:23:05,710
+ثلاثة شروط الثلاثة شروط هذه اللي بتحققها هي في الواقع
+
+269
+00:23:05,710 --> 00:23:09,690
+الشروط اللي بتخلي ال collection هي topology يعني
+
+270
+00:23:09,690 --> 00:23:13,410
+وكأني الآن بدأت من ال B trick عرفت منه ال open
+
+271
+00:23:13,410 --> 00:23:17,270
+sets ال open sets عملين لـ collection of sets هذه
+
+272
+00:23:17,270 --> 00:23:20,610
+ال collection of sets هي عملت topology يعني هذا
+
+273
+00:23:20,610 --> 00:23:24,090
+ال topology بنسميه the topology induced by ال
+
+274
+00:23:24,090 --> 00:23:28,290
+metric يعني ال topology المولدة من مين من ال metric
+
+275
+00:23:28,290 --> 00:23:33,110
+إذا .. إذا واضح إنه any metric space هيكون أيضا
+
+276
+00:23:33,110 --> 00:23:37,340
+topological space لكن إذا كان topological space ليس
+
+277
+00:23:37,340 --> 00:23:40,880
+شرط أن يكون metric space وهذا الكلام طبعا اللي هو
+
+278
+00:23:40,880 --> 00:23:44,240
+تاخده بالتفصيل في مادة ال topology خليني احنا
+
+279
+00:23:44,240 --> 00:23:49,680
+نشوف النظرية اللي عندي اللي بتوصلني للي بحكيه في
+
+280
+00:23:49,680 --> 00:23:52,540
+الرموز 3.5 بيقول لي let x be a metric space
+
+281
+00:23:53,070 --> 00:24:00,410
+and let G script be the collection of all open
+
+282
+00:24:00,410 --> 00:24:05,390
+subsets of N of X هي عائلة من اللي هي الـ open
+
+283
+00:24:05,390 --> 00:24:09,430
+sets اللي هي زي ما عرفناها then the following
+
+284
+00:24:09,430 --> 00:24:13,310
+properties  hold الشروط التلاتة التالية
+
+285
+00:24:13,310 --> 00:24:17,310
+محققة من الشروط التالية الشرط الأول أنه في element
+
+286
+00:24:17,310 --> 00:24:22,090
+in G script و X element in G script يعني فاي
+
+287
+00:24:22,090 --> 00:24:26,310
+المجموعة الخالية open set والمجموعة ال universal
+
+288
+00:24:26,310 --> 00:24:31,190
+set is an open set اتنين the union of any members
+
+289
+00:24:31,190 --> 00:24:35,130
+of open sets ايش مالها is again open يعني لو أخدت
+
+290
+00:24:35,130 --> 00:24:37,990
+ال union من ال open sets countable و non countable
+
+291
+00:24:37,990 --> 00:24:44,140
+مش مشكلة هيكون عبارة عن open set الشرط الثالث أو
+
+292
+00:24:44,140 --> 00:24:48,420
+الخاصية الثالث أن the finite intersection of open
+
+293
+00:24:48,420 --> 00:24:51,420
+sets is open sets يعني لو كان في عند ا واحد ا
+
+294
+00:24:51,420 --> 00:24:55,680
+اتنين عند ا and open sets هيكون اللي هو union
+
+295
+00:24:55,680 --> 00:25:00,820
+اتقطحن is an open set أما ال infinite اللي هو
+
+296
+00:25:00,820 --> 00:25:05,080
+intersection ليس شرطا ولا مثل على هذه موجودة طيب
+
+297
+00:25:05,750 --> 00:25:08,730
+الآن نجي نبرهم الأولى وبعدين التانية وبعدين
+
+298
+00:25:08,730 --> 00:25:13,590
+التالتة خلنا نبرهم نوضح لكم يا البرهان هان فأول
+
+299
+00:25:13,590 --> 00:25:18,070
+شي بالنسبة ل X انها open set سهل خالص هذه عشان
+
+300
+00:25:18,070 --> 00:25:22,790
+أثبت انها open بقول let XElement of X عشان لا اثبت
+
+301
+00:25:22,790 --> 00:25:26,090
+انها open بتاخد اي X في الـ X ولاقي ball كلها
+
+302
+00:25:26,090 --> 00:25:28,970
+جواها ال X طب هي ال X هي العالم تبعي كل العالم تبع
+
+303
+00:25:28,970 --> 00:25:32,650
+النقاط اللي تبعوني اذا اي ball هنا في هذه الحالة
+
+304
+00:25:32,650 --> 00:25:38,910
+أن لو اخترت الان اي ball B of X وR هتلاقيها جزء
+
+305
+00:25:38,910 --> 00:25:43,570
+من مين؟ من X لانه العالم تبعي اذا الان اكيد X is
+
+306
+00:25:43,570 --> 00:25:52,580
+an open set واضح نيجي الآن نثبت نثبت أن فاي is an
+
+307
+00:25:52,580 --> 00:25:57,020
+open set فاي is an open set أيش معناه open؟ نقول X
+
+308
+00:25:57,020 --> 00:26:04,940
+element في يؤدي إلى there exist ball of X وR جزئية
+
+309
+00:26:04,940 --> 00:26:09,430
+من مين من فاي هذا معناه أنها تكون open إن كل X في
+
+310
+00:26:09,430 --> 00:26:14,170
+الـ Phi لازم يعطينا إنه فيه ball تكون اللي هو وين
+
+311
+00:26:14,170 --> 00:26:16,790
+وجودة في الـ Phi طب ما هي هذه اللي هي الجملة
+
+312
+00:26:16,790 --> 00:26:21,210
+شرطية؟ هذه false واحنا بنعرف الجملة كلها على معاك
+
+313
+00:26:21,210 --> 00:26:26,070
+بتكون true دائما اللي هي false implies تحت عنوان
+
+314
+00:26:26,070 --> 00:26:29,110
+false implies anything is true يعني لو كانت اللي هي
+
+315
+00:26:29,110 --> 00:26:32,530
+هذا الـ False إيش ما يكون هنا كل الجملة بتكون إيش
+
+316
+00:26:32,530 --> 00:26:36,570
+مالها true إذا فعلا يتحقق الشرط أن فاي is an open
+
+317
+00:26:36,570 --> 00:26:40,230
+set واحد بده ينظر لها نظرة تانية أو بده يقول لأ طب
+
+318
+00:26:40,230 --> 00:26:43,310
+أنا يخليني بس أقبل هنا بطريقة تانية بقول يا سيدي
+
+319
+00:26:43,310 --> 00:26:51,180
+suppose that suppose that فاية ليست مفتوحة مازالت
+
+320
+00:26:51,180 --> 00:27:00,840
+ليست مفتوحة إذن أكيد في X في الفاية لكي يكون هناك
+
+321
+00:27:00,840 --> 00:27:03,480
+X في الفاية لكي يكون هناك X في الفاية لكي يكون
+
+322
+00:27:03,480 --> 00:27:05,040
+هناك X في الفاية لكي يكون هناك X في الفاية لكي
+
+323
+00:27:05,040 --> 00:27:05,860
+يكون هناك X في الفاية لكي يكون هناك X في الفاية
+
+324
+00:27:05,860 --> 00:27:09,480
+لكي يكون هناك X في الفاية لكي يكون هناك X في
+
+325
+00:27:09,480 --> 00:27:13,060
+الفاية لكي يكون هناك X في الفاية لكي يكون هناك X
+
+326
+00:27:13,060 --> 00:27:13,660
+X في الفاية لكي يكون هناك X في الفاية لكي يكون
+
+327
+00:27:13,660 --> 00:27:16,000
+هناك X في الفاية لكي يكون هناك X في الفاية لكي
+
+328
+00:27:16,000 --> 00:27:22,580
+يكون هناك X في واضح ؟ إذا أكيد Phi مستحيل اللي هو
+
+329
+00:27:22,580 --> 00:27:27,580
+نفي
+
+330
+00:27:27,580 --> 00:27:33,200
+Phi إنها open إنه نفترض إنها مش open هذا وصلني ل
+
+331
+00:27:33,200 --> 00:27:36,780
+contradiction لكن أنا بفضل اعتمد على هذه عشان ما
+
+332
+00:27:36,780 --> 00:27:45,080
+تجودش في مشكلة إنه اللي هي مش open ممكن تكون ال
+
+333
+00:27:45,080 --> 00:27:48,400
+contradiction أنها تكون .. يعني اللي احنا بنعرف
+
+334
+00:27:48,400 --> 00:27:52,040
+أنه لـ closed set ممكن ناجي ال set اللي هي open و
+
+335
+00:27:52,040 --> 00:27:56,140
+لا هي closed بس برضه لإن مافي حقه اللي حاكيناه
+
+336
+00:27:56,140 --> 00:27:59,880
+مافي صحيح و ممكن الاعتماد عليه في الوصول ل
+
+337
+00:27:59,880 --> 00:28:04,260
+contradiction و من ثم نقول فقهي is an open set طيب
+
+338
+00:28:04,260 --> 00:28:10,880
+ايش اللي بدقوله بعد هيك ان ال union is open طيب هو
+
+339
+00:28:10,880 --> 00:28:17,820
+شوفوا خليني أخد الـ U عبارة عن .. بتمثّل .. هو
+
+340
+00:28:17,820 --> 00:28:22,780
+عبارة عن الـ union للـ O .. O element in B and in
+
+341
+00:28:22,780 --> 00:28:28,860
+J .. Any أو الـ element in Delta subset من الجهة
+
+342
+00:28:28,860 --> 00:28:34,550
+عساس أنك تاخد أي اللي هو .. اللي هو union يعني تاخد
+
+343
+00:28:34,550 --> 00:28:37,310
+أي نيون من أي انكانة دي من من من ل open sets
+
+344
+00:28:37,310 --> 00:28:41,910
+سمينين اليوم لان اثبت ان هذا open set سهل اثبات
+
+345
+00:28:41,910 --> 00:28:49,190
+كيف؟ بدك تقول let X element in U ايش غرضك؟ اتلاقي
+
+346
+00:28:49,190 --> 00:28:55,710
+open ball حوالين ال X كل جواه اتنين اليوم مدان X
+
+347
+00:28:55,710 --> 00:29:02,990
+في اليوم اذا اكيد there exist O element in J such
+
+348
+00:29:02,990 --> 00:29:07,330
+that X element in O صح ولا لأ؟ مدام X في ال union
+
+349
+00:29:07,330 --> 00:29:13,090
+إذا X واحدة منهم ماشي؟ مدام X في ال union لمن؟ لأ،
+
+350
+00:29:13,090 --> 00:29:17,290
+O من ست ساة مدام ال X في ال union إذا X واحدة من
+
+351
+00:29:17,290 --> 00:29:22,350
+هدول إيش سميتها O؟ و ال O من وين جاية؟ من ال J لأن
+
+352
+00:29:22,350 --> 00:29:25,270
+اللي بتيجي منها اللي بتيجي من وين اللي جنبها اللي
+
+353
+00:29:25,270 --> 00:29:28,610
+subset منها إذا صار عندى there exists o element in
+
+354
+00:29:28,610 --> 00:29:33,330
+J such that x element in o but o is open مدام open
+
+355
+00:29:33,330 --> 00:29:41,310
+إذا بناجي بي of x وإبسلون جزئية من مين من ال o لإن
+
+356
+00:29:41,310 --> 00:29:46,030
+o is open طيب ال b هذى x وإبسلون جزئية من ال o و
+
+357
+00:29:46,030 --> 00:29:49,150
+ال o أصلا جزئية من ال u لإن واحدة منهم هذول من
+
+358
+00:29:49,150 --> 00:29:52,490
+هذول إذا أكيد subset من مين من u إذا أخدت x في ال
+
+359
+00:29:52,490 --> 00:29:59,780
+u لجهة open ball كلها جواة الـ U وهذا يعني أن U is
+
+360
+00:29:59,780 --> 00:30:05,880
+open وهي البرهان واضح بضوح الشمس بدكم تمر عليه
+
+361
+00:30:05,880 --> 00:30:10,540
+البرهان المكتوب مافيش مشكلة اللي هو let U be the
+
+362
+00:30:10,540 --> 00:30:15,300
+union of L arbitrary elements of open sets of X in
+
+363
+00:30:15,300 --> 00:30:20,060
+J and let X be any element in U زي ما قلت then X
+
+364
+00:30:20,060 --> 00:30:24,660
+لكن لازم تكون belongs to some at least one of
+
+365
+00:30:24,660 --> 00:30:33,160
+these open sets اللي سميتها O غاض at least
+
+366
+00:30:33,160 --> 00:30:35,100
+one of these open sets اللي سميتها O غاض at
+
+367
+00:30:35,100 --> 00:30:36,660
+least one of these open sets اللي سميتها O غاض
+
+368
+00:30:36,660 --> 00:30:38,600
+at least one of these open sets اللي سميتها O
+
+369
+00:30:38,600 --> 00:30:39,440
+غاض at least one of these open sets اللي
+
+370
+00:30:39,440 --> 00:30:43,620
+سميتها O غاض at least one of these open sets
+
+371
+00:30:43,620 --> 00:30:43,640
+اللي سميتها O غاض at least one of these open
+
+372
+00:30:43,640 --> 00:30:43,720
+sets اللي سميتها O غاض at least one of
+
+373
+00:30:43,720 --> 00:30:48,380
+these open sets اللي سميتها O غاض at least
+
+374
+00:30:48,380 --> 00:30:49,780
+one of these open sets اللي سميتها O غاض at
+
+375
+00:30:49,780 --> 00:30:52,560
+least one of these open sets اللي سميتها O غاض
+
+376
+00:30:52,560 --> 00:30:53,020
+at least one of these open sets اللي سميت
+
+377
+00:31:00,000 --> 00:31:00,440
+شوفوا خلّيني أخد نفس الرموز اللي كاتبها اللي أخدها
+
+378
+00:31:00,440 --> 00:31:06,160
+بالنسبة لنا و أخد رموز مختلفة حبت أقول عشان أثبت
+
+379
+00:31:06,160 --> 00:31:17,780
+أقول لت لت M1 و M2 لعند MN بي open sets any finite
+
+380
+00:31:17,780 --> 00:31:22,770
+number of open sets من ال J script هذه الآن بدي
+
+381
+00:31:22,770 --> 00:31:27,930
+أشوف تقاطحن أثبت انه تقاطحن اللي هو open بقولك let
+
+382
+00:31:27,930 --> 00:31:34,270
+X element ان التقاطع لـM I I من واحد لعند مين عدنا
+
+383
+00:31:34,270 --> 00:31:38,230
+بدي اخد X في التقاطع و اثبتلك ان فيه ball حوالين
+
+384
+00:31:38,230 --> 00:31:42,650
+ال X وجودة في التقاطع و بكون خلصنا طيب let X
+
+385
+00:31:42,650 --> 00:31:49,130
+element في التقاطع اذا عندي X في الـM I لكل I
+
+386
+00:31:49,130 --> 00:31:54,610
+فحولها فيهم كلها فإن كل واحدة فيهم is an open set
+
+387
+00:31:54,610 --> 00:31:59,590
+إذا كل واحدة بلقيلها open بالجواتها إذا for every
+
+388
+00:31:59,590 --> 00:32:08,790
+I there exist B of X وRI كلها جوات منين؟ الـMI صح
+
+389
+00:32:08,790 --> 00:32:14,030
+ولا لأ؟ طيب، هالجهة الصار عندي الآن اللي إن مركز
+
+390
+00:32:14,030 --> 00:32:22,650
+واحد X والنصف قطار ما له R1 وR2 وR3 وR4 وR5 بدي أخد
+
+391
+00:32:22,650 --> 00:32:27,310
+اللي هو نصف .. بدي أخد إيش يكون جواتهم كلهم إذا
+
+392
+00:32:27,310 --> 00:32:30,830
+أخي أكيد هاخد نصف القطر إيش أصغر واحد فيهم عشان
+
+393
+00:32:30,830 --> 00:32:34,250
+أضمن بولو تكون إيش ما لها جوات الكل إذا بدي أقول
+
+394
+00:32:34,250 --> 00:32:41,690
+let .. let R بتساوي ال minimum بين R1 وR2 لعند RN
+
+395
+00:32:41,690 --> 00:32:47,910
+صح ولا لأ؟ مدام أخدت هي ال minimum إذا أكيد هتعطيني
+
+396
+00:32:47,910 --> 00:32:55,270
+الغرض تلبيلي غرضي إذا then there exist ball of X
+
+397
+00:32:55,270 --> 00:33:03,770
+وR واحدة منهم subsequent من ال ball of X وR I لكل
+
+398
+00:33:03,770 --> 00:33:07,730
+I لأن هي مركزين واحد وهي أصغر نصف وطول ده ما هتكون
+
+399
+00:33:07,730 --> 00:33:11,490
+فيهم كلهم مدام هتكون فيهم كلهم إذا موجودة فتقطع
+
+400
+00:33:11,490 --> 00:33:21,370
+حين إذا B of X و R subset من تقاطع ال boils X و R I
+
+401
+00:33:21,370 --> 00:33:29,330
+I من عند 1 لعند N لكن احنا بنعرف ان هذا سبسفت من M
+
+402
+00:33:29,330 --> 00:33:35,150
+I لكل I اذا تقاطح هذول جزء من مين تقاطع ال M I اذا
+
+403
+00:33:35,150 --> 00:33:40,590
+تقاطع هذا نفس جزء تقاطع ال M I I من عند واحد لعند
+
+404
+00:33:40,590 --> 00:33:46,900
+N اذا بدأت في ال X في التقاطع ال X في التقاطع و
+
+405
+00:33:46,900 --> 00:33:51,120
+لاجئت أنه فيه ball حوالين الـ X بنص خطور R جزئية
+
+406
+00:33:51,120 --> 00:33:56,620
+من هذا التقاطع إذا therefore اللي هو التقاطع is an
+
+407
+00:33:56,620 --> 00:34:03,730
+open set إذا فعلا اللي هوعندي .. انا .. the
+
+408
+00:34:03,730 --> 00:34:05,490
+intersection of .. if I not intersection of an
+
+409
+00:34:05,490 --> 00:34:09,090
+open set is an open set وهيه بقولك let Y be an
+
+410
+00:34:09,090 --> 00:34:13,250
+element in the intersection of M1 and MN then each
+
+411
+00:34:13,250 --> 00:34:17,650
+M I contains a ball about Y and the smallest of
+
+412
+00:34:17,650 --> 00:34:21,870
+these balls هي اللي contained in the intersection
+
+413
+00:34:21,870 --> 00:34:26,050
+therefore the intersection is an open set وهذا
+
+414
+00:34:26,050 --> 00:34:35,090
+تفصيل اللي هي البرهان اللي موجودة نجي الآن تعريف
+
+415
+00:34:35,090 --> 00:34:38,110
+بدنا
+
+416
+00:34:38,110 --> 00:34:42,830
+الآن اللي حكيناه قبل شوية بدنا نحطه فى ثمرة بدنا
+
+417
+00:34:42,830 --> 00:34:47,730
+ناخد ثمرته الآن بدنا نعرفلك a topological space X
+
+418
+00:34:47,730 --> 00:34:52,970
+وG script بنسمي X وG script topological space
+
+419
+00:34:55,700 --> 00:35:01,040
+إذا كانت G script هو a collection of subsets of G
+
+420
+00:35:01,040 --> 00:35:08,880
+بتحقق منهم T1 وT2 وT3 يعني الآن بنسمي X وTau أو G 
+
+421
+00:35:08,880 --> 00:35:13,810
+script هذه بنسميهم الـ topological space إذا كانت
+
+422
+00:35:13,810 --> 00:35:18,290
+الـ G script هذه اللي هي عائلة من المجموعات
+
+423
+00:35:18,290 --> 00:35:22,550
+الجزئية من X تحقق تلت شروط، الشرط الأول X و Φ
+
+424
+00:35:22,550 --> 00:35:26,850
+فيها، الشرط الثاني اتحاد أي عناصر فيها فيها، الشرط
+
+425
+00:35:26,850 --> 00:35:29,890
+الثالث تقاطع أي finite تقاطع من اللي فيها فيها
+
+426
+00:35:29,890 --> 00:35:33,250
+ماشي الحال، إذا اتحققت الثلاث شروط بنسميه 
+
+427
+00:35:33,250 --> 00:35:39,100
+topological space، إذا من هذا التعريف ومن النظرية
+
+428
+00:35:39,100 --> 00:35:42,400
+اللي قبل بشوية أثبتناها اللي هي الثلاث خواص لها
+
+429
+00:35:42,400 --> 00:35:47,680
+ده لجينا إن الـ metric space is a topological space
+
+430
+00:35:49,180 --> 00:35:55,220
+إذن واضح from theorem 1.3.5 اللي قبله شوية and 
+
+431
+00:35:55,220 --> 00:35:58,920
+above definition هذا we can say that a metric
+
+432
+00:35:58,920 --> 00:36:02,600
+space is a topological space، وقلنا العكس ليس صحيح
+
+433
+00:36:02,600 --> 00:36:07,440
+وصحيح لكن لجينا مش مجننة اللي هو نيجي الآن التعريف
+
+434
+00:36:07,440 --> 00:36:15,580
+اللي بعده، طيب التعريف الآن يا جماعة بتعرفلكم 
+
+435
+00:36:15,580 --> 00:36:17,960
+اللي هو الـ continuous functions
+
+436
+00:36:20,830 --> 00:36:26,470
+بدأ أشوف أورديك كيف احنا يعني التعريف هو يعني
+
+437
+00:36:26,470 --> 00:36:31,870
+خلّيني نقول مستقى من تعريف الـ continuity اللي احنا
+
+438
+00:36:31,870 --> 00:36:35,230
+بنعرفه في الـ calculus ولكن اللي هو بما يناسب الـ
+
+439
+00:36:35,230 --> 00:36:38,790
+metric space، طبعا احنا يمكن اللي هو في الـ topology
+
+440
+00:36:39,760 --> 00:36:42,520
+لما نحكي عن الـ topological spaces ما نحكيش أنه الـ
+
+441
+00:36:42,520 --> 00:36:46,400
+function من X لعند Y أنها continuous ونقول بواسطة
+
+442
+00:36:46,400 --> 00:36:49,140
+الـ limit أو بواسطة اللي هو الـ metric أو كده لأ لأ
+
+443
+00:36:49,140 --> 00:36:52,820
+لأ لأ ما نعرفش ايش احنا الـ metric هنا احنا ممكن نعرفه 
+
+444
+00:36:52,820 --> 00:36:56,850
+هناك يا اما بواسطة اللي هو الـ neighborhoods أو
+
+445
+00:36:56,850 --> 00:37:00,770
+بواسطة أن نقول أن الـ inverse image of any … of
+
+446
+00:37:00,770 --> 00:37:04,310
+any اللي هو open set is an open كنا نعرفه في
+
+447
+00:37:04,310 --> 00:37:07,130
+الطلاب الجهيك ونبدأ فيه ونبدأ نصل لما نصل لموضوع
+
+448
+00:37:07,130 --> 00:37:10,710
+الـ limit لما نصير نعرف الـ limit عن طريق الجوار طيب
+
+449
+00:37:10,710 --> 00:37:15,550
+الآن احنا دخلت نهام مشابه للدخلة في الـ calculus في
+
+450
+00:37:15,550 --> 00:37:17,270
+الـ metric space لأن الـ metric space شغلها من 
+
+451
+00:37:17,270 --> 00:37:20,890
+الشغلات الجميلة يعني اللي اللي خليني نقول اللي
+
+452
+00:37:20,890 --> 00:37:24,190
+فيها metric فيها مسافة فيه دالة مسافة فيها معناه
+
+453
+00:37:24,190 --> 00:37:28,270
+اقتراب اقتراب طبعا بالمفهوم اللي احنا بنحكي فيه أو
+
+454
+00:37:28,270 --> 00:37:32,730
+خليني نقول الـ … الـ … الـ … الاقتراب بواسطة الـ
+
+455
+00:37:32,730 --> 00:37:37,370
+metric لكن الاقترابك limit في الـ topological
+
+456
+00:37:37,370 --> 00:37:41,090
+space in general كنا بنحكي في معنى الاقتراب عن
+
+457
+00:37:41,090 --> 00:37:43,850
+طريق الـ neighborhoods نذاكر neighborhood جد ما
+
+458
+00:37:43,850 --> 00:37:47,590
+بدنا أو نكبره جد ما بدنا عشان نودّي الـ X للـ X not
+
+459
+00:37:47,590 --> 00:37:50,790
+والآخرين وده موضوع آخر في الـ topology بتاخده
+
+460
+00:37:50,790 --> 00:37:57,150
+خلّيني بس نحكي عن الموضوع نحنا الآن لو عندي T من X
+
+461
+00:37:57,150 --> 00:38:01,570
+لعند Y زمان زمان هتبع زمان يعني من R لـ R يعني إذا 
+
+462
+00:38:01,570 --> 00:38:06,400
+بدكم ترتاحوا خليها من R لعند R كنا نقول إن الـ
+
+463
+00:38:06,400 --> 00:38:09,960
+function هذه T continuous على الـ R إذا كانت 
+
+464
+00:38:09,960 --> 00:38:13,200
+continuous على كل نقطة من النقاطها وكنا نقول إن T
+
+465
+00:38:13,200 --> 00:38:16,540
+continuous على الـ X not يعني T continuous على
+
+466
+00:38:16,540 --> 00:38:21,600
+الـ X not إذا كانت limit T of X لما X تروح للـ X
+
+467
+00:38:21,600 --> 00:38:27,390
+not إيش بتساوي T of X not إذا تحقق هذا الشرط كنا 
+
+468
+00:38:27,390 --> 00:38:31,510
+نقول عن الدالة إشمالها continuous هذا كنا نعبر عنه 
+
+469
+00:38:31,510 --> 00:38:34,630
+بتعبير آخر كنا نقول لو كنا نعبر عنه بالـ epsilon
+
+470
+00:38:34,630 --> 00:38:38,310
+delta definition نعبر عنه ونقول لكل epsilon أكبر
+
+471
+00:38:38,310 --> 00:38:41,050
+من صفر there exists delta أكبر من صفر such that
+
+472
+00:38:41,050 --> 00:38:44,070
+هذا تعبر عن اقتراح بهذه من هذه وهذه تعبر عن اقتراح 
+
+473
+00:38:44,070 --> 00:38:46,630
+بهذه من هذه هي كنا نقول في الـ calculus أو في
+
+474
+00:38:46,630 --> 00:38:50,890
+التحليل الحقيقيلكل y أكبر من 0 there exists دلتا 
+
+475
+00:38:50,890 --> 00:38:55,290
+أكبر من 0 فجدت لما x تقترب من x0 يعني الـ x minus
+
+476
+00:38:55,290 --> 00:39:02,010
+x0 تكون أصغر من دلتا يعطيني الـ Tx ناقص الـ Tx أشماله
+
+477
+00:39:02,010 --> 00:39:06,750
+أصغر من y هذا تعريفنا تبع زمان اللي هو في التحليل
+
+478
+00:39:06,750 --> 00:39:12,950
+أو في الـ calculus لأن
+
+479
+00:39:12,950 --> 00:39:18,590
+تعريف في الـ … في الـ metric نفس الشيء بدأ أقول إن
+
+480
+00:39:18,590 --> 00:39:23,470
+لو كانت X وD وY وD tilde metric spaces يعني هذا 
+
+481
+00:39:23,470 --> 00:39:28,050
+metric space وهذا metric space ثاني بقول إن T من X
+
+482
+00:39:28,050 --> 00:39:32,070
+لعند Y is set to be continuous عند X not لعند X if
+
+483
+00:39:32,070 --> 00:39:42,170
+and only if يعني T من X أو D لعند Y وD tilde بقول
+
+484
+00:39:42,170 --> 00:39:48,710
+إن T continuous عند X not في X إذا اتحقق قمالي لكل
+
+485
+00:39:48,710 --> 00:39:53,670
+Y أكبر من 0 there exist نفسه نفسه لفوق Delta أكبر 
+
+486
+00:39:53,670 --> 00:39:58,650
+من 0 such that الآن هذا في الواقع metric بس تبع
+
+487
+00:39:58,650 --> 00:40:03,130
+metric تبع الار زمان الآن بشيل اللي هو الـ absolute
+
+488
+00:40:03,130 --> 00:40:07,090
+value وبكتب الـ metric in general لما X يعني وكأن
+
+489
+00:40:07,090 --> 00:40:11,510
+لما الـ X تقترب من X not تعبر عنها أن المسافة بين
+
+490
+00:40:11,510 --> 00:40:18,310
+X و X not تكون أصغر من مين؟ من Delta يؤدي إلى
+
+491
+00:40:18,310 --> 00:40:23,210
+المسافة بين اللي هو TX و TX0 اللي هي تحت هذا 
+
+492
+00:40:23,210 --> 00:40:33,390
+البتريك اللي هي دي … دي Delta of TX و TX0 يكون
+
+493
+00:40:33,390 --> 00:40:40,490
+أشماله أصغر من أبسلون إذن هذا هو نفسه هذا التعريف
+
+494
+00:40:40,490 --> 00:40:45,520
+معمّم عليه هذا معمّم على هذا يعني الـ metric اللي 
+
+495
+00:40:45,520 --> 00:40:48,340
+هان صار metric in general والـ metric اللي هان
+
+496
+00:40:48,340 --> 00:40:52,620
+برضه صار metric آخر in general فهذا هو معناته اللي 
+
+497
+00:40:52,620 --> 00:40:55,940
+هو إنها تكون الدالة متصلة وهنا كاتبينه هان إنه
+
+498
+00:40:55,940 --> 00:40:58,940
+متصل عند X node إذا كان لكل ي أكبر من صفر there
+
+499
+00:40:58,940 --> 00:41:03,040
+exist دلتا أكبر من صفر such that D tilde of TX و TX
+
+500
+00:41:03,040 --> 00:41:06,900
+node تكون أصغر من يبسون عندنا اللي هو for all X
+
+501
+00:41:06,900 --> 00:41:12,840
+satisfying أو whenever DX و X node أصغر من دلتا لأن
+
+502
+00:41:12,840 --> 00:41:16,360
+T is said to be continuous ونسكت إذا كانت هي
+
+503
+00:41:16,360 --> 00:41:21,660
+continuous عند كل نقاط الدمين هذا معناته اللي هو
+
+504
+00:41:21,660 --> 00:41:26,680
+الـ continuity الآن بيجينا النظرية التالية اللي هي
+
+505
+00:41:26,680 --> 00:41:31,740
+النظرية اللي أنا قلت قبلها قبل شوية أنه احنا بنعرف
+
+506
+00:41:41,300 --> 00:41:46,280
+اللي أنا أدهل كده احنا هنطلعها نتيجة هنطلعها نظرية
+
+507
+00:41:46,280 --> 00:41:48,300
+من اللي قبل اللي أحكي عنها قبل شوية أشياء اللي 
+
+508
+00:41:48,300 --> 00:41:54,960
+بتقولوا هذا theorem 138 بتقول let x و d and y و d
+
+509
+00:41:54,960 --> 00:42:00,030
+tilde be metric spaces الآن هذا الإعلان كان تالي a
+
+510
+00:42:00,030 --> 00:42:06,190
+metric T من X لعين Y is continuous if and only if
+
+511
+00:42:06,190 --> 00:42:10,450
+الـ inverse image of any open subset of Y أي شماله
+
+512
+00:42:10,450 --> 00:42:16,190
+is an open subset of X هذا الإعلان كما يليه هستخدم
+
+513
+00:42:16,190 --> 00:42:23,550
+هذا طبعا في الإثبات النظرية
+
+514
+00:42:23,550 --> 00:42:34,530
+بتقول أن T من X و D لعند Y و D tilde is continuous
+
+515
+00:42:34,530 --> 00:42:42,750
+if and only if أي open set في هنا الـ inverse M دي
+
+516
+00:42:42,750 --> 00:42:48,490
+لها لازم يكون ايه شماله open set يعني كل S open in 
+
+517
+00:42:48,490 --> 00:42:57,500
+Y هيعطيني أنه اللي هو T inverse of S open in ين in X
+
+518
+00:42:57,500 --> 00:43:03,620
+فهي المظهرية، بدنا نثبتها، بدنا نفترض أوليشي T is 
+
+519
+00:43:03,620 --> 00:43:08,340
+open is continuous أسف، T is continuous وبعدين 
+
+520
+00:43:08,340 --> 00:43:13,960
+نثبت هذه كيف بتثبت هذه؟ بتاخد أي S Open Set في الـ Y
+
+521
+00:43:13,960 --> 00:43:18,600
+وتثبت لك إن الـ T Inverse اللي هي أشمالها Open كيف
+
+522
+00:43:18,600 --> 00:43:21,520
+بتثبت الـ Community T Inverse Open؟ ركزوا عشان نحط
+
+523
+00:43:21,520 --> 00:43:24,240
+الخطوط العامة للبرمجان بتثبتوا إن الـ Community T
+
+524
+00:43:24,240 --> 00:43:29,660
+Inverse of S Us Open احنا خلينا نسميها G عشان
+
+525
+00:43:29,660 --> 00:43:35,260
+أثبت هذه Open في X بدي أناجي لو أخدت أي X في الـ G
+
+526
+00:43:35,260 --> 00:43:46,110
+أناجي there exists BX وصم اللي هو نصف قطر يكون كله 
+
+527
+00:43:46,110 --> 00:43:51,430
+جزء من الـ G إذا عملت هذه معناته صارت الـ T inverse 
+
+528
+00:43:51,430 --> 00:43:56,850
+في أسفل دي أشمالها is open طبعا هستعين بهذه من وين
+
+529
+00:43:56,850 --> 00:43:59,850
+من الـ continuity المعطنية لأن عليها بدأ السند ماشي
+
+530
+00:43:59,850 --> 00:44:03,110
+الحال شوفوا ركزوا معايا الآن كيف بدأ أسأل هذا
+
+531
+00:44:03,110 --> 00:44:09,820
+الكلام كلام إن شاء الله سهل ومافي مشكلة ركزوا في
+
+532
+00:44:09,820 --> 00:44:13,120
+اللي مكتوب هنا، الكتابة هنا منيح ومرتب إلى أن
+
+533
+00:44:13,120 --> 00:44:16,820
+بيقول لي suppose that T is continuous، هذا الاتجاه
+
+534
+00:44:16,820 --> 00:44:23,300
+الأول أو let S be any open set in B in Y، بتثبت لك
+
+535
+00:44:23,300 --> 00:44:29,180
+أن T inverse of S is open من مين؟ مين in X عشان أثبت
+
+536
+00:44:29,180 --> 00:44:34,540
+الـ T inverse للـ S element in X بدي أسهل على حالي
+
+537
+00:44:34,540 --> 00:44:37,540
+بس الرموز بدي أسمه T inverse للـ S ده إيش بدي
+
+538
+00:44:37,540 --> 00:44:43,270
+أسميه G بدي أقول G تسميها T inverse للـ S الآن لو
+
+539
+00:44:43,270 --> 00:44:48,730
+كانت الـ G هذه في فـ automatic الـ G هتكون open في
+
+540
+00:44:48,730 --> 00:44:53,790
+مين؟ في الـ … في الـ X يعني مافيش إيش أثبته الآن لو
+
+541
+00:44:53,790 --> 00:44:57,330
+طبعا عملت هذه لأن بعد شوية بدت طر أخد element في
+
+542
+00:44:57,330 --> 00:45:00,870
+الـ G عشان هي فرضت لحالها إن الـ G بتسوي في لحالها
+
+543
+00:45:00,870 --> 00:45:06,750
+الآن بقول لك let G لتسوي في وخد أي element X not في
+
+544
+00:45:06,750 --> 00:45:12,350
+مين؟ في الـ G أخدت X not في الـ G بدي أتسلسلك في 
+
+545
+00:45:12,350 --> 00:45:16,310
+الخطوات وامشي وامشي لما أسألك أنه في بي X not و
+
+546
+00:45:16,310 --> 00:45:21,990
+some اللي هو نصف قطر كله some من مين؟ من الـ G
+
+547
+00:45:21,990 --> 00:45:27,450
+واضح؟ إذا هذه الطريق اللي رايح لها أنا طيب خليني
+
+548
+00:45:27,450 --> 00:45:32,230
+نشوف كيف بدنا نحقق اللي هو اللي بدنا يعني أخدنا X
+
+549
+00:45:32,230 --> 00:45:38,070
+not أي element وين في الـ G هاي عندي اللي هو الـ X
+
+550
+00:45:39,810 --> 00:45:50,010
+وهي الـ Y وهي اللي هو الـ S وهي T inverse للـ S واخدت 
+
+551
+00:45:50,010 --> 00:45:56,930
+ايش اسمها G ماشي لما أخد X not هان X not في الـ G
+
+552
+00:45:56,930 --> 00:46:01,630
+اللي هو T inverse للـ S إذا أكيد فيها صورة سموها 
+
+553
+00:46:01,630 --> 00:46:09,260
+ايش Y not ماشي إذا let x0 be element in G إذا أكيد
+
+554
+00:46:09,260 --> 00:46:13,020
+there is y لأنه function لازم كل صورة there is y0
+
+555
+00:46:13,020 --> 00:46:20,010
+element in Such that y0  اكتساوي T x0 طيب لكن S is
+
+556
+00:46:20,010 --> 00:46:24,990
+an open set S نفسها ايه؟ شماله open set مدام open
+
+557
+00:46:24,990 --> 00:46:29,630
+set إذا بقدر ألاقي اللي هو open point جوات مين؟
+
+558
+00:46:29,630 --> 00:46:34,450
+جوات الـ S الآن صارت Y not في الـ S تنسوش أنا X 
+
+559
+00:46:34,450 --> 00:46:37,730
+not مين؟ واخدها من رأس الدور ها يعني أخدت X not
+
+560
+00:46:37,730 --> 00:46:42,840
+مين؟ موجودة في الـ G ولقبية الـ G اللي هي موجودة
+
+561
+00:46:42,840 --> 00:46:47,000
+هان أكيد الـ TX Note فيها صورة وسمّيتها من هي Y
+
+562
+00:46:47,000 --> 00:46:52,500
+الـ Y Note منها دي موجودة في الـ S ماشي معايا
+
+563
+00:46:52,500 --> 00:46:56,500
+أه؟ إذن الآن Y Note في الـ S مدام Y Note في الـ S
+
+564
+00:46:56,500 --> 00:47:01,800
+انتبهوا عليها إذا إنه SO بن ستأخذ  open بثبتين
+
+565
+00:47:01,800 --> 00:47:06,140
+بيسمها open y not element less و open  إذن أكيد
+
+566
+00:47:06,140 --> 00:47:11,700
+there exist بي إكس no there exist بي و ي نوت و
+
+567
+00:47:11,700 --> 00:47:17,700
+إبسنون كلها duetين duet less صح أنت عارف ال open
+
+568
+00:47:17,700 --> 00:47:21,520
+طيب
+
+569
+00:47:21,520 --> 00:47:30,250
+طب ما أنا عارف ما أنا عارف أنه X نوت موجود أويان في
+
+570
+00:47:30,250 --> 00:47:33,490
+الـ domain هذا و احنا بنقول ان الـ tree continuous
+
+571
+00:47:33,490 --> 00:47:37,050
+هذا اذا continuous عند الـ X نوت ايه معناه
+
+572
+00:47:37,050 --> 00:47:40,610
+continuous عند الـ X نوت ان اي ابسلون في الدنيا من
+
+573
+00:47:40,610 --> 00:47:45,060
+بين هذه الابسلون for ابسلوناللي جيت أكبر من صفر
+
+574
+00:47:45,060 --> 00:47:49,380
+بقدر ألاقي delta أكبر من صفر such that ال distance
+
+575
+00:47:49,380 --> 00:47:53,780
+بين ال X وال X0 أصغر من دلتا بيعطيني ال distance
+
+576
+00:47:53,780 --> 00:48:00,240
+بين ال TX والTX0 أصغر من مين الأيسرون صح ولا لأ
+
+577
+00:48:00,240 --> 00:48:05,540
+أكيد أكيد هذا منين جبته من اللي هو تعريف ال
+
+578
+00:48:05,540 --> 00:48:11,580
+continuity لأنه بسبب ان Xاللي هو T إذا كنتوا معيصة
+
+579
+00:48:11,580 --> 00:48:15,160
+عندي X Note طبعا هذه X تي X Note إيش سميناها احنا؟
+
+580
+00:48:15,160 --> 00:48:19,200
+Y Note عشان تكون في الصورة صح ولا لأ؟ معايا أه؟
+
+581
+00:48:19,200 --> 00:48:24,220
+طيب لأن أنا أين رايح؟ أنا رايح هذا كله هستعين فيه
+
+582
+00:48:24,220 --> 00:48:29,780
+إن X Note في الـG وأصلكم من خلاله إن أت إلى أخدت
+
+583
+00:48:29,780 --> 00:48:34,860
+أي X لازم ألاقي ball كلها سبست من مين؟ من الـG
+
+584
+00:48:34,860 --> 00:48:41,650
+ماشي الحال إذا اللي عملناه لحد تلانإنه لجينا ..
+
+585
+00:48:41,650 --> 00:48:45,350
+مادام أخدنا وقلنا دي ده تسوى فاى إذا الـ X0 الـ
+
+586
+00:48:45,350 --> 00:48:49,310
+element MG أخدناها إذا لجينا Y0 element S بحيث Y0
+
+587
+00:48:49,310 --> 00:48:53,650
+بساوة T X0 لكن قلنا S Open Set إذا بنلاقي اللي هو
+
+588
+00:48:53,650 --> 00:48:56,810
+ball كل هوا اللي موجودة في الـ S بعدين استخدمنا ال
+
+589
+00:48:56,810 --> 00:49:01,030
+continuity عند ال X0 وقولنا إنه بنلاقي Delta بحيث
+
+590
+00:49:01,030 --> 00:49:05,230
+إن المسافة بين X و X0 أصغر من Delta بيعطي المسافة
+
+591
+00:49:05,230 --> 00:49:10,040
+بين X و .. TX و X0 إيش ماله؟أصغر من Epsilon الآن
+
+592
+00:49:10,040 --> 00:49:15,900
+بيدثبتلك إنه هذه نص القطر اللي بيقدّي الغرض اللي
+
+593
+00:49:15,900 --> 00:49:23,500
+هو عبارة عن Delta لـGeta لـGeta صارت من ده يا
+
+594
+00:49:23,500 --> 00:49:28,520
+Delta، مظبوط؟ إذن الآن بيدثبتلك إنه P X Note
+
+595
+00:49:28,520 --> 00:49:32,540
+وDelta subset من إيش؟ من D، هذا بيدثبتك، لو
+
+596
+00:49:32,540 --> 00:49:35,880
+أثبتتوا يكونوا خلاصين، إن أنا قلت
+
+597
+00:49:37,580 --> 00:49:45,400
+زد element in B X0 ومين أو دلتا ماشي هو ماخدها زد
+
+598
+00:49:45,400 --> 00:49:51,100
+ولا إيش؟ ماخدها X أظن مش مشكلة خلّيني أخدها احنا
+
+599
+00:49:51,100 --> 00:49:58,940
+هيك سميها X هو ايش
+
+600
+00:49:58,940 --> 00:50:04,000
+معنات X في ال B X0 ودلتا؟هذا بيعطيني أنه إذا
+
+601
+00:50:04,000 --> 00:50:08,760
+المسافة بين X و X0 لازم أصغر من أصغر من مين من
+
+602
+00:50:08,760 --> 00:50:14,040
+بلتا okay طيب ما هي المقاط اللي X و X0 أصغر من
+
+603
+00:50:14,040 --> 00:50:17,540
+بلتا حسب ال continuity اللي هنا لازم تعطيني
+
+604
+00:50:17,540 --> 00:50:22,300
+المسافة بين TX و Y0 أشمالها إذا هذا بيعطيني أن ال
+
+605
+00:50:22,300 --> 00:50:29,560
+distance بين TX و Y0 أصغر من مين من إبشرون واضحة
+
+606
+00:50:30,390 --> 00:50:37,090
+إيش معنات هذه؟ هذه معناتها إن الـ TX هذه الـ TX
+
+607
+00:50:37,090 --> 00:50:43,750
+موجودة في مين؟ الـ TX معناته موجودة في الـ ball أه
+
+608
+00:50:43,750 --> 00:50:51,130
+اللي مركزها Y نوت و نصف قطرةها مين؟ إبسلونهذا
+
+609
+00:50:51,130 --> 00:50:54,430
+عملناه .. عملناه إيش ماله قبل هيك أثبتنا أنه
+
+610
+00:50:54,430 --> 00:50:58,510
+subset من مين؟ من S فهذه صارت T X elementين هذه
+
+611
+00:50:58,510 --> 00:51:02,850
+اللي هي subset من S إذا صار عندي ال T X هذه
+
+612
+00:51:02,850 --> 00:51:08,650
+element في ال S إيش معناته؟ إن ال X element in T
+
+613
+00:51:08,650 --> 00:51:15,330
+inverse of S اللي هي مين هي؟ اللي هي ال G اللي
+
+614
+00:51:15,330 --> 00:51:17,690
+نسيته أه
+
+615
+00:51:19,300 --> 00:51:25,520
+عندي S أو G متساوي الـ T inverse لـ S إذا بدأت في
+
+616
+00:51:25,520 --> 00:51:28,940
+الـ X في الـ B X not و Delta ووصلتلكم اللي من الـ
+
+617
+00:51:28,940 --> 00:51:32,260
+X و اللي موجودة في الـ G يعني أثبتلكم البُقى
+
+618
+00:51:32,260 --> 00:51:38,500
+الهادي بزق من الـ G إذا من كله دي اتأخدت أي X not
+
+619
+00:51:38,500 --> 00:51:45,150
+في الـ Gو لجتلكم اللي هو open ball حوالينها جوا
+
+620
+00:51:45,150 --> 00:51:48,810
+الـG إيش معناته هذا الكلام؟ معناته إنه صارت الـG
+
+621
+00:51:48,810 --> 00:51:54,570
+is an open set إذن اللي بدأنا فيه إن S is any open
+
+622
+00:51:54,570 --> 00:51:58,730
+set في الـY لجينا الـT inverse للـS is an open set
+
+623
+00:51:58,730 --> 00:52:02,790
+في الـX وهو المطلوب، الاتجاه التاني الآن
+
+624
+00:52:02,790 --> 00:52:09,890
+conversely
+
+625
+00:52:14,860 --> 00:52:19,240
+Conversely Assume that the inverse image of every
+
+626
+00:52:19,240 --> 00:52:25,480
+open set in Y is an open set in X وبدأ أثبت لك أن
+
+627
+00:52:25,480 --> 00:52:32,140
+الـ T is continuous عند اللي هي H على اللي هي الـ
+
+628
+00:52:32,140 --> 00:52:37,480
+X كلها إذن الآن اللي مفترضه .. اللي أنا بدأ أثبت
+
+629
+00:52:37,480 --> 00:52:46,600
+عكس النظرية إيش عكس النظرية؟بدي افترض انه اللي هو
+
+630
+00:52:46,600 --> 00:52:49,800
+assume that the inverse image of every open set is
+
+631
+00:52:49,800 --> 00:52:54,160
+an open set in Y and X و بدي اثبتلك ان الـ T is
+
+632
+00:52:54,160 --> 00:53:01,140
+continuous عشان اثبت الـ T continuous من X and Y
+
+633
+00:53:01,140 --> 00:53:05,900
+بدي اخدلك اي X نقطة في الـ X و اثبتلك ان الـ T
+
+634
+00:53:05,900 --> 00:53:10,480
+continuous عندهاما هي معناته الـ Continuity عندها؟
+
+635
+00:53:10,480 --> 00:53:14,900
+إن لكل Y أكبر من 0، يجب أن أجد دلتا أكبر من 0 Such
+
+636
+00:53:14,900 --> 00:53:20,340
+that لما تكون الـDX وX0 أصغر من Y، يعطينا الـD بين
+
+637
+00:53:20,340 --> 00:53:26,540
+TX وTX0 أصغر من مين؟ أصغر من مين؟ من Y، صح ولا لأ؟
+
+638
+00:53:26,540 --> 00:53:29,060
+هل مش عارف معناته الـ Continuity؟ إذن، هذه اللي
+
+639
+00:53:29,060 --> 00:53:34,360
+بدأ أثبتهبدايتي الأن أخدت بين إيديا أن الـ inverse
+
+640
+00:53:34,360 --> 00:53:40,480
+image of any open set is open طيب، الآن عشان أثبت
+
+641
+00:53:40,480 --> 00:53:46,040
+هيك، قلتلك let X0 be any fixed point in X and let
+
+642
+00:53:46,040 --> 00:53:50,560
+Y إيه شمالها أكبر من صفر بيه arbitrary أخدت Y أكبر
+
+643
+00:53:50,560 --> 00:53:53,340
+من صفر arbitrary بالدرجة Delta اللي بيتحقق، هذا
+
+644
+00:53:53,340 --> 00:53:57,020
+بكون خلصت، ماشي؟ طيب، صلى الله عليه الصلاة والسلام
+
+645
+00:53:58,750 --> 00:54:05,070
+الآن الـ ball اللي هي T X Note و Epsilon is 1 أو 6
+
+646
+00:54:05,070 --> 00:54:10,040
+أكيد .. أكيدإذن الـ inverse image اللي حسب الخصية
+
+647
+00:54:10,040 --> 00:54:13,720
+اللي مقضيني هيها هتكون open set in main in X إذا
+
+648
+00:54:13,720 --> 00:54:17,160
+ال T inverse لها T inverse ده ال P of T X not Y
+
+649
+00:54:17,160 --> 00:54:21,920
+إيش معناها إذا open set in main in X إيش معنات هذه
+
+650
+00:54:21,920 --> 00:54:28,480
+تكون open set بقدر ألاقي اللي هو open ball اللي هو
+
+651
+00:54:28,480 --> 00:54:33,280
+كلها جوات هذهأكيد ما هي معناه open set إذا .. إذا
+
+652
+00:54:33,280 --> 00:54:36,420
+there is delta اللي هذا نصف القطر له اللي بتكون
+
+653
+00:54:36,420 --> 00:54:40,420
+جوا there is delta أكبر من صفر such that ال ball
+
+654
+00:54:40,420 --> 00:54:47,380
+of X not أو delta أصغر من ال T inverse لل B T X
+
+655
+00:54:47,380 --> 00:54:53,340
+not أو إبسلون كمان مرة أقولكم إياها دي يتبعوا الآن
+
+656
+00:54:53,340 --> 00:54:56,900
+احنا قلنا B T X not أو إبسلون إيش معناها open set
+
+657
+00:54:58,340 --> 00:55:01,660
+من الخاصية في I من الخاصية اللي ماعطينيها أن الـ T
+
+658
+00:55:01,660 --> 00:55:07,540
+inverse لها open صارت هذه open مدام هذه open وعندي
+
+659
+00:55:07,540 --> 00:55:13,220
+ال X note في داخلها ال X note في داخل هذه عارفين
+
+660
+00:55:13,220 --> 00:55:16,720
+ليش ال X note في داخل هذه لأن ال T X note موجودة
+
+661
+00:55:16,720 --> 00:55:19,380
+في هذه اللي جوا وماقدر ال T inverse ده اكيد ال X
+
+662
+00:55:19,380 --> 00:55:24,860
+note جوتها ماشي بما أن X note هانإذا بقدر ألاقي بو
+
+663
+00:55:24,860 --> 00:55:28,440
+.. وهذه open .. وهذه open .. إذا بي of x0 و sum
+
+664
+00:55:28,440 --> 00:55:32,980
+اللي هو .. اللي هو نصف قطر سميته delta كل جزء من
+
+665
+00:55:32,980 --> 00:55:39,580
+مين؟ جزء من الـ T inverse لل بي of T x0 و إبسل
+
+666
+00:55:39,580 --> 00:55:47,300
+واضح؟ بعد؟ إذا اللي حصلته الآن .. اللي حصلته كان
+
+667
+00:55:47,300 --> 00:55:51,640
+التالي إن لكل إبسل أكبر من 0 لجيت مين؟ الدلت هادي
+
+668
+00:55:52,490 --> 00:55:58,250
+بحيث إن هذا subset من هذا ماشي لأن أنا بدي أخد
+
+669
+00:55:58,250 --> 00:56:01,490
+أوصل للي بديها اللي بديها forever ي أكبر من سفر
+
+670
+00:56:01,490 --> 00:56:05,390
+لجد delta أكبر من سفر such that بدي أثبت لكم إن
+
+671
+00:56:05,390 --> 00:56:10,590
+لما تكون المسافة بين x و x0 أصغر من دلتا يعطيني
+
+672
+00:56:10,590 --> 00:56:15,070
+المسافة بين Tx و Tx أصغر من ي و بكون خلصت طيب
+
+673
+00:56:15,070 --> 00:56:18,890
+المسافة بين x و x0 أصغر من دلتا إيش معناته هذا
+
+674
+00:56:18,890 --> 00:56:25,030
+معناته إن ال Xهتكون في الـ pole للـ X0 وDelta صح
+
+675
+00:56:25,030 --> 00:56:29,470
+أو لا؟ هذا معناته هذا طيب، مدام الـ X في الـ pole
+
+676
+00:56:29,470 --> 00:56:33,630
+تبقى X0 وDelta وهذه subset من هذه إذا أكيد، أكيد
+
+677
+00:56:33,630 --> 00:56:41,970
+الـ X element in T inverse of B of T X0 وY، أكيد؟
+
+678
+00:56:41,970 --> 00:56:45,450
+بقى هذه، لأن هذه جزئية من هذه إيش معناة X في الـ T
+
+679
+00:56:45,450 --> 00:56:50,310
+inverse لهذه؟ معناته، هذا هيعطيني إن الـ TX نفسها
+
+680
+00:56:54,690 --> 00:56:57,550
+أكس في الـ T inverse أدكّي ده الـ TX و الموجودة في
+
+681
+00:56:57,550 --> 00:57:01,950
+هذا طيب إيش معناة الـ TX هنا هذا معناته أنه
+
+682
+00:57:01,950 --> 00:57:07,550
+المسافة بين الـ TX هذه و الـ TX naught أصغر من
+
+683
+00:57:07,550 --> 00:57:12,780
+مين؟ من إبسطإذا خدت لكل Y اللي جاءت Delta بحيث أن
+
+684
+00:57:12,780 --> 00:57:14,980
+المسافة هذه أزرق من Delta و أضفت أن المسافة هذه
+
+685
+00:57:14,980 --> 00:57:17,780
+أزرق من Y وهذا يعني أن ال function continuous عند
+
+686
+00:57:17,780 --> 00:57:20,760
+X0 و X0 بطأة was arbitrarily إذا ال T is
+
+687
+00:57:20,760 --> 00:57:24,380
+continuous على ال X في ضوء اللي هي الخاصية اللي
+
+688
+00:57:24,380 --> 00:57:28,040
+حكيناها معطينيها وبهيك ان شاء الله بنصل لعين ال
+
+689
+00:57:28,040 --> 00:57:30,820
+definition واحدة تلاتة ساعة المرة القادمة ان شاء
+
+690
+00:57:30,820 --> 00:57:33,400
+الله بنكمل وبرك الله فيكم والسلام عليكم ورحمة الله
+
+691
+00:57:33,400 --> 00:57:34,020
+وبركاته
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/gwzFsK74bdc_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/gwzFsK74bdc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ff467f70a31b2efa506986c6ff6cd923719b8bd4
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/gwzFsK74bdc_raw.json
@@ -0,0 +1 @@
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الملاحظة اللي بيقولها it is easy بيقول من السهل to see from the definition above that the open balls is an open set and the closed ball is a closed set انتبهوا علينا خلّيني نشوف هذه بيقولوا انه من السهل انك تثبت انه اي open ball open set", "tokens": [3615, 1863, 16254, 8978, 37279, 16572, 5172, 36764, 24401, 3660, 6055, 1211, 9307, 3660, 12174, 36150, 11296, 16490, 1211, 11703, 9957, 1829, 8717, 8592, 38688, 36632, 8592, 9673, 15040, 5016, 19913, 3660, 13672, 1829, 4724, 1829, 39648, 11296, 309, 307, 1858, 4724, 1829, 39648, 9154, 21136, 3224, 1211, 281, 536, 490, 264, 7123, 3673, 300, 264, 1269, 9803, 307, 364, 1269, 992, 293, 264, 5395, 2594, 307, 257, 5395, 992, 16472, 2655, 3555, 3224, 14407, 25894, 8315, 16490, 1211, 11703, 9957, 1829, 8717, 8592, 38688, 29538, 4724, 1829, 39648, 14407, 16472, 3224, 9154, 21136, 3224, 1211, 16472, 4117, 6055, 12984, 3555, 2655, 16472, 3224, 1975, 1829, 1269, 2594, 1269, 992], "avg_logprob": -0.17032657657657657, "compression_ratio": 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0.98388671875}, {"start": 457.48, "end": 458.06, "word": " أخدنا", "probability": 0.9793701171875}, {"start": 458.06, "end": 458.32, "word": " ال", "probability": 0.9345703125}, {"start": 458.32, "end": 458.72, "word": " ball", "probability": 0.343994140625}, {"start": 458.72, "end": 460.24, "word": " X", "probability": 0.6845703125}, {"start": 460.24, "end": 460.7, "word": " note", "probability": 0.19482421875}, {"start": 460.7, "end": 460.92, "word": " و", "probability": 0.95751953125}, {"start": 460.92, "end": 461.38, "word": " Epsilon", "probability": 0.59625244140625}, {"start": 461.38, "end": 462.36, "word": " بدنا", "probability": 0.5743408203125}, {"start": 462.36, "end": 462.64, "word": " نشوف", "probability": 0.9860026041666666}, {"start": 462.64, "end": 463.0, "word": " هذه", "probability": 0.708984375}, {"start": 463.0, "end": 463.38, "word": " كيف", "probability": 0.9404296875}, {"start": 463.38, "end": 463.64, "word": " هي", "probability": 0.93701171875}, {"start": 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"probability": 0.862548828125}, {"start": 472.01, "end": 472.35, "word": " خطرها", "probability": 0.81829833984375}, {"start": 472.35, "end": 472.49, "word": " R", "probability": 0.61962890625}, {"start": 472.49, "end": 472.79, "word": " ليش", "probability": 0.805419921875}, {"start": 472.79, "end": 473.13, "word": " نسميه", "probability": 0.768035888671875}, {"start": 473.13, "end": 473.27, "word": " Y", "probability": 0.349853515625}, {"start": 473.27, "end": 473.63, "word": " ر", "probability": 0.1400146484375}, {"start": 473.63, "end": 474.25, "word": " نص", "probability": 0.701171875}, {"start": 474.25, "end": 474.57, "word": " خطرها", "probability": 0.9844970703125}, {"start": 474.57, "end": 474.83, "word": " R", "probability": 0.93505859375}, {"start": 474.83, "end": 475.35, "word": " هي", "probability": 0.6044921875}, {"start": 475.35, "end": 475.61, "word": " جي", "probability": 0.4422607421875}, {"start": 475.61, "end": 476.25, "word": " تاخدت", "probability": 0.744140625}, {"start": 476.25, "end": 476.73, "word": " open", "probability": 0.57421875}, {"start": 476.73, "end": 477.15, "word": " pool", "probability": 0.25390625}, {"start": 477.15, "end": 477.73, "word": " هي", "probability": 0.5517578125}, {"start": 477.73, "end": 479.43, "word": " نص", "probability": 0.736572265625}, {"start": 479.43, "end": 479.77, "word": " اللي", "probability": 0.747802734375}, {"start": 479.77, "end": 479.89, "word": " هو", "probability": 0.79443359375}, {"start": 479.89, "end": 480.29, "word": " مركزها", "probability": 0.9822998046875}, {"start": 480.29, "end": 480.47, "word": " X", "probability": 0.90087890625}, {"start": 480.47, "end": 480.85, "word": " node", "probability": 0.376708984375}, {"start": 480.85, "end": 481.51, "word": " و", "probability": 0.8681640625}, {"start": 481.51, "end": 481.73, "word": " نص", "probability": 0.861572265625}, {"start": 481.73, "end": 482.17, "word": " خطرها", "probability": 0.9840087890625}, {"start": 482.17, "end": 483.17, "word": " R", "probability": 0.46533203125}, {"start": 483.17, "end": 484.35, "word": " ماشي", "probability": 0.83154296875}, {"start": 484.35, "end": 484.63, "word": " الحال", "probability": 0.90673828125}, {"start": 484.63, "end": 485.51, "word": " بدي", "probability": 0.562255859375}, {"start": 485.51, "end": 485.87, "word": " أثبت", "probability": 0.9290771484375}, {"start": 485.87, "end": 485.99, "word": " أن", "probability": 0.4873046875}, {"start": 485.99, "end": 486.31, "word": " هذه", "probability": 0.58056640625}, {"start": 486.31, "end": 486.69, "word": " عبارة", "probability": 0.992919921875}, {"start": 486.69, "end": 486.89, "word": " عن", "probability": 0.982421875}, {"start": 486.89, "end": 487.27, "word": " مين", "probability": 0.84375}, {"start": 487.27, "end": 487.87, "word": " عن", "probability": 0.82958984375}, {"start": 487.87, "end": 488.43, "word": " open", "probability": 0.80712890625}, {"start": 488.43, "end": 488.83, "word": " set", "probability": 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X minus B tilde of X0 OR إذا عملت هيك بكون أثبتت إنه فعلا الست اللي برا هذا إيش ما لها is open سهل شوف لها نصف الخطورة", "tokens": [6027, 1863, 9381, 5172, 13672, 1829, 39896, 3714, 31747, 11622, 11296, 1783, 29538, 4032, 1863, 9381, 5172, 33962, 9566, 13063, 3660, 39894, 45761, 1829, 5551, 8592, 38688, 3224, 7251, 30544, 28242, 11296, 10874, 11622, 38207, 9154, 3714, 9957, 22807, 9154, 13672, 1829, 4724, 23557, 23758, 13672, 1829, 31439, 10874, 11622, 38207, 9154, 1783, 3175, 363, 45046, 295, 1783, 15, 19654, 11933, 15730, 6225, 42213, 2655, 39896, 4117, 4724, 30544, 5551, 12984, 3555, 2655, 2655, 36145, 3224, 6156, 3615, 15040, 2423, 14851, 13672, 1829, 4724, 23557, 23758, 11933, 1829, 8592, 19446, 5296, 11296, 307, 1269, 8608, 3224, 1211, 13412, 38688, 5296, 11296, 8717, 9381, 5172, 33962, 9566, 13063, 3660], "avg_logprob": -0.2494265989426079, "compression_ratio": 1.7582938388625593, "no_speech_prob": 0.00012540817260742188, "words": [{"start": 859.83, "end": 860.53, "word": 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معايا؟", "probability": 0.8294677734375}, {"start": 1257.79, "end": 1263.29, "word": " زي", "probability": 0.87548828125}, {"start": 1263.29, "end": 1263.37, "word": " ما", "probability": 0.986328125}, {"start": 1263.37, "end": 1263.85, "word": " اتفجنا", "probability": 0.9361328125}], "temperature": 1.0}, {"id": 53, "seek": 127411, "start": 1264.32, "end": 1274.12, "text": "the set of all interior points of M بنرمزلها بالرمز interior of M or M interior هذه مجموعة كل النقاط الداخلية للـ M", "tokens": [3322, 992, 295, 439, 10636, 2793, 295, 376, 4724, 1863, 2288, 2304, 11622, 1211, 11296, 20666, 2288, 2304, 11622, 10636, 295, 376, 420, 376, 10636, 29538, 3714, 7435, 2304, 2407, 27884, 28242, 28239, 4587, 41193, 32748, 47283, 1211, 10632, 24976, 39184, 376], "avg_logprob": -0.26435319351595504, "compression_ratio": 1.2868852459016393, "no_speech_prob": 1.1324882507324219e-06, "words": [{"start": 1264.32, "end": 1264.6, "word": "the", "probability": 0.22216796875}, {"start": 1264.6, 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هذا ان ال interior point the set of all interior point interior point of M هذه is an open set عارف؟ is an open set يعني بدك تاخد أي X", "tokens": [9566, 1829, 3555, 8717, 1829, 7435, 1829, 6024, 48506, 4724, 39648, 32239, 309, 307, 1858, 281, 536, 300, 10636, 295, 376, 307, 364, 1269, 992, 37495, 22653, 39894, 28543, 2288, 1975, 5016, 8315, 44945, 39648, 16472, 3224, 6024, 48506, 1975, 30241, 7649, 4032, 5172, 4587, 2423, 28820, 10943, 23758, 16472, 2423, 10636, 935, 264, 992, 295, 439, 10636, 935, 10636, 935, 295, 376, 29538, 307, 364, 1269, 992, 6225, 9640, 5172, 22807, 307, 364, 1269, 992, 37495, 22653, 47525, 4117, 6055, 47283, 3215, 36632, 1783], "avg_logprob": -0.19967296702224155, "compression_ratio": 1.7208121827411167, "no_speech_prob": 2.7418136596679688e-06, "words": [{"start": 1274.9, "end": 1275.28, "word": "طيب", "probability": 0.70263671875}, {"start": 1275.28, "end": 1275.86, "word": " نيجي", "probability": 0.746826171875}, {"start": 1275.86, "end": 1276.18, "word": " 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{"start": 1430.04, "end": 1430.44, "word": " تلاتة", "probability": 0.83917236328125}, {"start": 1430.44, "end": 1430.76, "word": " خمسة", "probability": 0.98095703125}, {"start": 1430.76, "end": 1430.98, "word": " بيقول", "probability": 0.7554524739583334}, {"start": 1430.98, "end": 1431.08, "word": " لي", "probability": 0.326416015625}, {"start": 1431.08, "end": 1431.28, "word": " let", "probability": 0.7666015625}, {"start": 1431.28, "end": 1431.54, "word": " x", "probability": 0.5810546875}, {"start": 1431.54, "end": 1431.72, "word": " be", "probability": 0.63671875}, {"start": 1431.72, "end": 1431.82, "word": " a", "probability": 0.96142578125}, {"start": 1431.82, "end": 1432.06, "word": " metric", "probability": 0.92919921875}, {"start": 1432.06, "end": 1432.54, "word": " space", "probability": 0.94970703125}], "temperature": 1.0}, {"id": 61, "seek": 145821, "start": 1433.07, "end": 1458.21, "text": "and let G script be the collection of all open subsets of N of X هي عائلة من اللي هي الـ open sets اللي هي زي ما عرفناها then the following properties اشمالها hold الشروط التلاتة التالية محققة من الشروط التالية الشرط الأول أنه في element in G script", "tokens": [474, 718, 460, 5755, 312, 264, 5765, 295, 439, 1269, 2090, 1385, 295, 426, 295, 1783, 39896, 6225, 16373, 37977, 9154, 13672, 1829, 39896, 2423, 39184, 1269, 6352, 13672, 1829, 39896, 30767, 1829, 19446, 6225, 28480, 8315, 11296, 550, 264, 3480, 7221, 1975, 8592, 2304, 6027, 11296, 1797, 25124, 32887, 9566, 16712, 1211, 9307, 3660, 16712, 6027, 10632, 3714, 5016, 4587, 28671, 9154, 25124, 32887, 9566, 16712, 6027, 10632, 25124, 2288, 9566, 16247, 12610, 14739, 3224, 8978, 4478, 294, 460, 5755], "avg_logprob": -0.30506860155884813, "compression_ratio": 1.6093023255813954, "no_speech_prob": 3.159046173095703e-06, "words": [{"start": 1433.07, "end": 1433.51, "word": "and", "probability": 0.0271453857421875}, {"start": 1433.51, "end": 1434.07, "word": " let", "probability": 0.8955078125}, {"start": 1434.07, "end": 1436.21, "word": " G", "probability": 0.4970703125}, {"start": 1436.21, "end": 1436.83, "word": " script", "probability": 0.337158203125}, {"start": 1436.83, "end": 1437.83, "word": " be", "probability": 0.70947265625}, {"start": 1437.83, "end": 1438.21, "word": " the", "probability": 0.837890625}, {"start": 1438.21, "end": 1438.87, "word": " collection", "probability": 0.85546875}, {"start": 1438.87, "end": 1439.25, "word": " of", "probability": 0.95068359375}, {"start": 1439.25, "end": 1439.81, "word": " all", "probability": 0.908203125}, {"start": 1439.81, "end": 1440.41, "word": " open", "probability": 0.89208984375}, {"start": 1440.41, "end": 1441.07, "word": " subsets", "probability": 0.9638671875}, {"start": 1441.07, "end": 1441.35, "word": " of", "probability": 0.953125}, {"start": 1441.35, "end": 1441.53, "word": " N", "probability": 0.17626953125}, {"start": 1441.53, "end": 1442.33, "word": " of", "probability": 0.79296875}, {"start": 1442.33, "end": 1442.57, "word": " X", "probability": 0.9794921875}, {"start": 1442.57, "end": 1442.73, "word": " هي", "probability": 0.1134033203125}, {"start": 1442.73, "end": 1444.07, "word": " عائلة", "probability": 0.9913736979166666}, {"start": 1444.07, "end": 1444.49, "word": " من", "probability": 0.970703125}, {"start": 1444.49, "end": 1444.81, "word": " اللي", "probability": 0.8505859375}, {"start": 1444.81, "end": 1445.05, "word": " هي", "probability": 0.9560546875}, {"start": 1445.05, "end": 1445.19, "word": " الـ", "probability": 0.6044921875}, {"start": 1445.19, "end": 1445.39, "word": " open", "probability": 0.6962890625}, {"start": 1445.39, "end": 1445.79, "word": " sets", "probability": 0.90966796875}, {"start": 1445.79, "end": 1446.75, "word": " اللي", "probability": 0.89404296875}, {"start": 1446.75, "end": 1447.07, "word": " هي", "probability": 0.96337890625}, {"start": 1447.07, "end": 1447.47, "word": " زي", "probability": 0.938232421875}, {"start": 1447.47, "end": 1447.55, "word": " ما", "probability": 0.98095703125}, {"start": 1447.55, "end": 1448.29, "word": " عرفناها", "probability": 0.9600830078125}, {"start": 1448.29, "end": 1448.89, "word": " then", "probability": 0.78466796875}, {"start": 1448.89, "end": 1449.11, "word": " the", "probability": 0.83056640625}, {"start": 1449.11, "end": 1449.43, "word": " following", "probability": 0.8837890625}, {"start": 1449.43, "end": 1449.97, "word": " properties", "probability": 0.239013671875}, {"start": 1449.97, "end": 1450.75, "word": " اشمالها", "probability": 0.665478515625}, {"start": 1450.75, "end": 1451.15, "word": " hold", "probability": 0.89794921875}, {"start": 1451.15, "end": 1452.37, "word": " الشروط", "probability": 0.904296875}, {"start": 1452.37, "end": 1452.89, "word": " التلاتة", "probability": 0.7803955078125}, {"start": 1452.89, "end": 1453.31, "word": " التالية", "probability": 0.9910481770833334}, {"start": 1453.31, "end": 1453.87, "word": " محققة", "probability": 0.85595703125}, {"start": 1453.87, "end": 1454.09, "word": " من", "probability": 0.43310546875}, {"start": 1454.09, "end": 1454.55, "word": " الشروط", "probability": 0.9539388020833334}, {"start": 1454.55, "end": 1455.15, "word": " التالية", "probability": 0.99658203125}, {"start": 1455.15, "end": 1456.03, "word": " الشرط", "probability": 0.9348958333333334}, {"start": 1456.03, "end": 1456.37, "word": " الأول", "probability": 0.942626953125}, {"start": 1456.37, "end": 1456.73, "word": " أنه", "probability": 0.4638671875}, {"start": 1456.73, "end": 1456.97, "word": " في", "probability": 0.2061767578125}, {"start": 1456.97, "end": 1457.31, "word": " element", "probability": 0.70263671875}, {"start": 1457.31, "end": 1457.63, "word": " in", "probability": 0.69921875}, {"start": 1457.63, "end": 1457.79, "word": " G", "probability": 0.9091796875}, {"start": 1457.79, "end": 1458.21, "word": " script", "probability": 0.9306640625}], "temperature": 1.0}, {"id": 62, "seek": 148141, "start": 1459.01, "end": 1481.41, "text": "و X element in G script يعني فاي المجموعة الخالية open set والمجموعة ال universal set is an open set اتنين the union of any members of open sets ايش مالها is again open يعني لو أخدت ال union من ال open sets countable و non countable مش مشكلة هيكون عبارة عن open set", "tokens": [2407, 1783, 4478, 294, 460, 5755, 37495, 22653, 6156, 47302, 9673, 7435, 2304, 2407, 27884, 33962, 6027, 10632, 1269, 992, 16070, 2304, 7435, 2304, 2407, 27884, 2423, 11455, 992, 307, 364, 1269, 992, 1975, 2655, 1863, 9957, 264, 11671, 295, 604, 2679, 295, 1269, 6352, 1975, 1829, 8592, 3714, 6027, 11296, 307, 797, 1269, 37495, 22653, 45164, 5551, 9778, 3215, 2655, 2423, 11671, 9154, 2423, 1269, 6352, 1207, 712, 4032, 2107, 1207, 712, 37893, 37893, 28820, 3660, 39896, 30544, 6225, 3555, 9640, 3660, 18871, 1269, 992], "avg_logprob": -0.22054597906682682, "compression_ratio": 1.6571428571428573, "no_speech_prob": 3.606081008911133e-05, "words": [{"start": 1459.01, "end": 1459.23, "word": "و", "probability": 0.724609375}, {"start": 1459.23, "end": 1459.99, "word": " X", "probability": 0.7041015625}, {"start": 1459.99, "end": 1460.29, "word": " element", "probability": 0.1431884765625}, {"start": 1460.29, "end": 1460.51, "word": " in", "probability": 0.91943359375}, {"start": 1460.51, "end": 1460.65, "word": " G", "probability": 0.71533203125}, {"start": 1460.65, "end": 1460.99, "word": " script", "probability": 0.70458984375}, {"start": 1460.99, "end": 1461.29, "word": " يعني", "probability": 0.82666015625}, {"start": 1461.29, "end": 1462.09, "word": " فاي", "probability": 0.36480712890625}, {"start": 1462.09, "end": 1462.85, "word": " المجموعة", "probability": 0.9068359375}, {"start": 1462.85, "end": 1463.59, "word": " الخالية", "probability": 0.9886067708333334}, {"start": 1463.59, "end": 1463.91, "word": " open", "probability": 0.60888671875}, {"start": 1463.91, "end": 1464.37, "word": " set", "probability": 0.931640625}, {"start": 1464.37, "end": 1465.73, "word": " والمجموعة", "probability": 0.877197265625}, {"start": 1465.73, "end": 1465.89, "word": " ال", "probability": 0.97265625}, {"start": 1465.89, "end": 1466.31, "word": " universal", "probability": 0.81005859375}, {"start": 1466.31, "end": 1466.73, "word": " set", "probability": 0.9375}, {"start": 1466.73, "end": 1466.93, "word": " is", "probability": 0.9296875}, {"start": 1466.93, "end": 1467.07, "word": " an", "probability": 0.70703125}, {"start": 1467.07, "end": 1467.33, "word": " open", "probability": 0.9375}, {"start": 1467.33, "end": 1467.75, "word": " set", "probability": 0.9677734375}, {"start": 1467.75, "end": 1468.91, "word": " اتنين", "probability": 0.8297119140625}, {"start": 1468.91, "end": 1469.71, "word": " the", "probability": 0.4794921875}, {"start": 1469.71, "end": 1470.13, "word": " union", "probability": 0.95947265625}, {"start": 1470.13, "end": 1470.41, "word": " of", "probability": 0.96533203125}, {"start": 1470.41, "end": 1470.69, "word": " any", "probability": 0.88916015625}, {"start": 1470.69, "end": 1471.19, "word": " members", "probability": 0.70654296875}, {"start": 1471.19, "end": 1471.39, "word": " of", "probability": 0.9638671875}, {"start": 1471.39, "end": 1471.73, "word": " open", "probability": 0.8857421875}, {"start": 1471.73, "end": 1472.13, "word": " sets", "probability": 0.88623046875}, {"start": 1472.13, "end": 1472.45, "word": " ايش", "probability": 0.7298177083333334}, {"start": 1472.45, "end": 1472.85, "word": " مالها", "probability": 0.86474609375}, {"start": 1472.85, "end": 1473.07, "word": " is", "probability": 0.89501953125}, {"start": 1473.07, "end": 1473.45, "word": " again", "probability": 0.93408203125}, {"start": 1473.45, "end": 1473.85, "word": " open", "probability": 0.93896484375}, {"start": 1473.85, "end": 1474.21, "word": " يعني", "probability": 0.930419921875}, {"start": 1474.21, "end": 1474.71, "word": " لو", "probability": 0.95751953125}, {"start": 1474.71, "end": 1475.13, "word": " أخدت", "probability": 0.9171142578125}, {"start": 1475.13, "end": 1475.39, "word": " ال", "probability": 0.740234375}, {"start": 1475.39, "end": 1475.81, "word": " union", "probability": 0.962890625}, {"start": 1475.81, "end": 1476.01, "word": " من", "probability": 0.9931640625}, {"start": 1476.01, "end": 1476.13, "word": " ال", "probability": 0.861328125}, {"start": 1476.13, "end": 1476.37, "word": " open", "probability": 0.9267578125}, {"start": 1476.37, "end": 1476.77, "word": " sets", "probability": 0.8740234375}, {"start": 1476.77, "end": 1477.33, "word": " countable", "probability": 0.6689453125}, {"start": 1477.33, "end": 1477.47, "word": " و", "probability": 0.2332763671875}, {"start": 1477.47, "end": 1477.55, "word": " non", "probability": 0.3916015625}, {"start": 1477.55, "end": 1477.99, "word": " countable", "probability": 0.868408203125}, {"start": 1477.99, "end": 1478.11, "word": " مش", "probability": 0.95068359375}, {"start": 1478.11, "end": 1478.53, "word": " مشكلة", "probability": 0.9720052083333334}, {"start": 1478.53, "end": 1479.49, "word": " هيكون", "probability": 0.6978759765625}, {"start": 1479.49, "end": 1480.15, "word": " عبارة", "probability": 0.99609375}, {"start": 1480.15, "end": 1480.55, "word": " عن", "probability": 0.998046875}, {"start": 1480.55, "end": 1481.11, "word": " open", "probability": 0.9384765625}, {"start": 1481.11, "end": 1481.41, "word": " set", "probability": 0.9677734375}], "temperature": 1.0}, {"id": 63, "seek": 150508, "start": 1482.04, "end": 1505.08, "text": "الشرط الثالث أو الخاصية الثالث ان the finite intersection of open sets is open sets يعني لو كان في عند ا واحد ا اتنين عند ا and open sets هيكون اللي هو union اتقطحن is an open set اما ال infinite اللي هو intersection ليس شرطا ولا مثل على هذه موجودة طيب", "tokens": [6027, 8592, 2288, 9566, 6024, 104, 6027, 12984, 34051, 33962, 33546, 10632, 6024, 104, 6027, 12984, 16472, 264, 19362, 15236, 295, 1269, 6352, 307, 1269, 6352, 37495, 22653, 45164, 25961, 8978, 43242, 1975, 36764, 24401, 1975, 1975, 2655, 1863, 9957, 43242, 1975, 293, 1269, 6352, 39896, 30544, 13672, 1829, 31439, 11671, 1975, 2655, 47432, 5016, 1863, 307, 364, 1269, 992, 1975, 15042, 2423, 13785, 13672, 1829, 31439, 15236, 32239, 3794, 13412, 2288, 9566, 995, 49429, 50113, 1211, 15844, 29538, 3714, 29245, 23328, 3660, 23032, 1829, 3555], "avg_logprob": -0.21839080562536745, "compression_ratio": 1.7632850241545894, "no_speech_prob": 6.496906280517578e-06, "words": [{"start": 1482.04, "end": 1482.76, "word": "الشرط", "probability": 0.874755859375}, {"start": 1482.76, "end": 1483.84, "word": " الثالث", "probability": 0.901123046875}, {"start": 1483.84, "end": 1484.14, "word": " أو", "probability": 0.76611328125}, {"start": 1484.14, "end": 1484.68, "word": " الخاصية", "probability": 0.9518229166666666}, {"start": 1484.68, "end": 1485.16, "word": " الثالث", "probability": 0.9669189453125}, {"start": 1485.16, "end": 1485.64, "word": " ان", "probability": 0.285400390625}, {"start": 1485.64, "end": 1485.82, "word": " the", "probability": 0.196533203125}, {"start": 1485.82, "end": 1486.2, "word": " finite", "probability": 0.9873046875}, {"start": 1486.2, "end": 1487.28, "word": " intersection", "probability": 0.896484375}, {"start": 1487.28, "end": 1488.1, "word": " of", "probability": 0.94873046875}, {"start": 1488.1, "end": 1488.42, "word": " open", "probability": 0.8779296875}, {"start": 1488.42, "end": 1488.76, "word": " sets", "probability": 0.935546875}, {"start": 1488.76, "end": 1488.94, "word": " is", "probability": 0.89501953125}, {"start": 1488.94, "end": 1489.18, "word": " open", "probability": 0.86669921875}, {"start": 1489.18, "end": 1489.46, "word": " sets", "probability": 0.8818359375}, {"start": 1489.46, "end": 1489.7, "word": " يعني", "probability": 0.83349609375}, {"start": 1489.7, "end": 1489.84, "word": " لو", "probability": 0.97021484375}, {"start": 1489.84, "end": 1490.0, "word": " كان", "probability": 0.98974609375}, {"start": 1490.0, "end": 1490.12, "word": " في", "probability": 0.8251953125}, {"start": 1490.12, "end": 1490.3, "word": " عند", "probability": 0.541015625}, {"start": 1490.3, "end": 1490.8, "word": " ا", "probability": 0.169677734375}, {"start": 1490.8, "end": 1491.22, "word": " واحد", "probability": 0.7054443359375}, {"start": 1491.22, "end": 1491.42, "word": " ا", "probability": 0.83837890625}, {"start": 1491.42, "end": 1491.76, "word": " اتنين", "probability": 0.77685546875}, {"start": 1491.76, "end": 1492.02, "word": " عند", "probability": 0.70849609375}, {"start": 1492.02, "end": 1492.28, "word": " ا", "probability": 0.640625}, {"start": 1492.28, "end": 1492.44, "word": " and", "probability": 0.3046875}, {"start": 1492.44, "end": 1492.78, "word": " open", "probability": 0.7568359375}, {"start": 1492.78, "end": 1493.26, "word": " sets", "probability": 0.875}, {"start": 1493.26, "end": 1494.14, "word": " هيكون", "probability": 0.799072265625}, {"start": 1494.14, "end": 1494.38, "word": " اللي", "probability": 0.9384765625}, {"start": 1494.38, "end": 1494.88, "word": " هو", "probability": 0.98046875}, {"start": 1494.88, "end": 1495.68, "word": " union", "probability": 0.79833984375}, {"start": 1495.68, "end": 1496.82, "word": " اتقطحن", "probability": 0.80234375}, {"start": 1496.82, "end": 1497.08, "word": " is", "probability": 0.93408203125}, {"start": 1497.08, "end": 1497.48, "word": " an", "probability": 0.908203125}, {"start": 1497.48, "end": 1498.12, "word": " open", "probability": 0.92822265625}, {"start": 1498.12, "end": 1498.6, "word": " set", "probability": 0.9765625}, {"start": 1498.6, "end": 1499.28, "word": " اما", "probability": 0.748291015625}, {"start": 1499.28, "end": 1499.52, "word": " ال", "probability": 0.978515625}, {"start": 1499.52, "end": 1500.02, "word": " infinite", "probability": 0.84814453125}, {"start": 1500.02, "end": 1500.52, "word": " اللي", "probability": 0.9765625}, {"start": 1500.52, "end": 1500.82, "word": " هو", "probability": 0.98876953125}, {"start": 1500.82, "end": 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1578.87, "end": 1579.49, "word": " واحنا", "probability": 0.71240234375}, {"start": 1579.49, "end": 1579.87, "word": " بنعرف", "probability": 0.8733723958333334}, {"start": 1579.87, "end": 1580.33, "word": " الجملة", "probability": 0.92724609375}, {"start": 1580.33, "end": 1580.65, "word": " كلها", "probability": 0.99267578125}, {"start": 1580.65, "end": 1580.85, "word": " على", "probability": 0.8681640625}, {"start": 1580.85, "end": 1581.21, "word": " معاك", "probability": 0.5860188802083334}, {"start": 1581.21, "end": 1581.67, "word": " بتكون", "probability": 0.8154296875}, {"start": 1581.67, "end": 1582.11, "word": " true", "probability": 0.8642578125}, {"start": 1582.11, "end": 1582.81, "word": " دائما", "probability": 0.9440104166666666}, {"start": 1582.81, "end": 1583.69, "word": " اللي", "probability": 0.959716796875}, {"start": 1583.69, "end": 1584.17, "word": " هي", "probability": 0.95068359375}, {"start": 1584.17, "end": 1584.89, "word": " false", "probability": 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{"id": 72, "seek": 171316, "start": 1692.34, "end": 1713.16, "text": "خلّيني أخد الـ U عبارة عن .. بتمثّل .. هو عبارة عن الـ union للـ O .. O element in B and in J .. 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بدي", "probability": 0.7685546875}, {"start": 1895.11, "end": 1895.31, "word": " اخد", "probability": 0.8723958333333334}, {"start": 1895.31, "end": 1895.49, "word": " X", "probability": 0.98486328125}, {"start": 1895.49, "end": 1895.61, "word": " في", "probability": 0.888671875}, {"start": 1895.61, "end": 1896.01, "word": " التقاطع", "probability": 0.9957275390625}, {"start": 1896.01, "end": 1896.13, "word": " و", "probability": 0.734375}, {"start": 1896.13, "end": 1896.47, "word": " اثبتلك", "probability": 0.7792724609375}, {"start": 1896.47, "end": 1896.61, "word": " ان", "probability": 0.84375}, {"start": 1896.61, "end": 1897.05, "word": " فيه", "probability": 0.703857421875}, {"start": 1897.05, "end": 1897.65, "word": " ball", "probability": 0.499755859375}, {"start": 1897.65, "end": 1898.23, "word": " حوالين", "probability": 0.9227294921875}, {"start": 1898.23, "end": 1898.37, "word": " ال", "probability": 0.486572265625}, {"start": 1898.37, "end": 1898.55, "word": " X", "probability": 0.7265625}, {"start": 1898.55, "end": 1899.19, "word": " وجودة", "probability": 0.6888020833333334}, {"start": 1899.19, "end": 1899.35, "word": " في", "probability": 0.9296875}, {"start": 1899.35, "end": 1899.79, "word": " التقاطع", "probability": 0.995849609375}, {"start": 1899.79, "end": 1899.91, "word": " و", "probability": 0.2578125}, {"start": 1899.91, "end": 1900.07, "word": " بكون", "probability": 0.5498046875}, {"start": 1900.07, "end": 1900.65, "word": " خلصنا", "probability": 0.8250732421875}, {"start": 1900.65, "end": 1902.07, "word": " طيب", "probability": 0.93896484375}, {"start": 1902.07, "end": 1902.35, "word": " let", "probability": 0.9033203125}, {"start": 1902.35, "end": 1902.65, "word": " X", "probability": 0.9873046875}, {"start": 1902.65, "end": 1902.99, "word": " element", "probability": 0.95849609375}, {"start": 1902.99, "end": 1903.19, "word": " في", "probability": 0.96923828125}, {"start": 1903.19, "end": 1903.93, "word": " التقاطع", "probability": 0.9971923828125}, {"start": 1903.93, "end": 1904.55, "word": " اذا", "probability": 0.84814453125}, {"start": 1904.55, "end": 1906.35, "word": " عندي", "probability": 0.6865234375}, {"start": 1906.35, "end": 1906.69, "word": " X", "probability": 0.986328125}, {"start": 1906.69, "end": 1906.85, "word": " في", "probability": 0.95849609375}, {"start": 1906.85, "end": 1907.17, "word": " الـM", "probability": 0.6909993489583334}, {"start": 1907.17, "end": 1907.67, "word": " I", "probability": 0.95703125}, {"start": 1907.67, "end": 1908.83, "word": " لكل", "probability": 0.98095703125}, {"start": 1908.83, "end": 1909.13, "word": " I", "probability": 0.94970703125}, {"start": 1909.13, "end": 1910.17, "word": " فحولها", "probability": 0.6700439453125}], "temperature": 1.0}, {"id": 80, "seek": 193493, "start": 1910.91, "end": 1934.93, "text": "فيهم كلها فإن كل واحدة فيهم is an open set إذا كل واحدة بلقيلها open بالجواتها إذا for every I there exist B of X وRI كلها جوات منين؟ الـMI صح ولا لأ؟ طيب، هالجهة الصار عندي الآن اللي إن مركز واحد X", "tokens": [41185, 16095, 28242, 11296, 6156, 28814, 1863, 28242, 36764, 24401, 3660, 8978, 16095, 307, 364, 1269, 992, 11933, 15730, 28242, 36764, 24401, 3660, 4724, 1211, 4587, 26895, 11296, 1269, 20666, 7435, 2407, 9307, 11296, 11933, 15730, 337, 633, 286, 456, 2514, 363, 295, 1783, 4032, 5577, 28242, 11296, 10874, 2407, 9307, 9154, 9957, 22807, 2423, 39184, 13808, 20328, 5016, 49429, 5296, 10721, 22807, 23032, 1829, 3555, 12399, 8032, 6027, 7435, 3224, 3660, 31767, 9640, 18871, 16254, 6024, 48506, 13672, 1829, 36145, 3714, 31747, 11622, 36764, 24401, 1783], "avg_logprob": -0.30681816962632263, "compression_ratio": 1.480952380952381, "no_speech_prob": 4.0531158447265625e-06, "words": [{"start": 1910.91, "end": 1911.23, "word": "فيهم", "probability": 0.48779296875}, {"start": 1911.23, "end": 1912.11, "word": " كلها", "probability": 0.80078125}, {"start": 1912.11, "end": 1912.79, "word": " فإن", "probability": 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0.80615234375}, {"start": 1916.91, "end": 1917.95, "word": " بالجواتها", "probability": 0.736328125}, {"start": 1917.95, "end": 1918.75, "word": " إذا", "probability": 0.761962890625}, {"start": 1918.75, "end": 1919.25, "word": " for", "probability": 0.93505859375}, {"start": 1919.25, "end": 1919.59, "word": " every", "probability": 0.822265625}, {"start": 1919.59, "end": 1920.03, "word": " I", "probability": 0.63818359375}, {"start": 1920.03, "end": 1920.59, "word": " there", "probability": 0.7919921875}, {"start": 1920.59, "end": 1921.29, "word": " exist", "probability": 0.5263671875}, {"start": 1921.29, "end": 1922.23, "word": " B", "probability": 0.478271484375}, {"start": 1922.23, "end": 1923.03, "word": " of", "probability": 0.79443359375}, {"start": 1923.03, "end": 1923.43, "word": " X", "probability": 0.93017578125}, {"start": 1923.43, "end": 1924.09, "word": " وRI", "probability": 0.5321044921875}, {"start": 1924.09, "end": 1925.49, "word": " كلها", "probability": 0.96484375}, {"start": 1925.49, "end": 1926.05, "word": " جوات", "probability": 0.7029622395833334}, {"start": 1926.05, "end": 1927.17, "word": " منين؟", "probability": 0.5457356770833334}, {"start": 1927.17, "end": 1927.77, "word": " الـMI", "probability": 0.6078287760416666}, {"start": 1927.77, "end": 1928.79, "word": " صح", "probability": 0.923828125}, {"start": 1928.79, "end": 1928.99, "word": " ولا", "probability": 0.88330078125}, {"start": 1928.99, "end": 1930.01, "word": " لأ؟", "probability": 0.8727213541666666}, {"start": 1930.01, "end": 1930.31, "word": " طيب،", "probability": 0.8001708984375}, {"start": 1930.31, "end": 1930.65, "word": " هالجهة", "probability": 0.80361328125}, {"start": 1930.65, "end": 1930.93, "word": " الصار", "probability": 0.502197265625}, {"start": 1930.93, "end": 1931.29, "word": " عندي", "probability": 0.72900390625}, {"start": 1931.29, "end": 1931.81, "word": " الآن", "probability": 0.870849609375}, {"start": 1931.81, "end": 1932.67, "word": " اللي", "probability": 0.930908203125}, {"start": 1932.67, "end": 1932.93, "word": " إن", "probability": 0.6435546875}, {"start": 1932.93, "end": 1934.03, "word": " مركز", "probability": 0.8424479166666666}, {"start": 1934.03, "end": 1934.49, "word": " واحد", "probability": 0.68896484375}, {"start": 1934.49, "end": 1934.93, "word": " X", "probability": 0.82568359375}], "temperature": 1.0}, {"id": 81, "seek": 196305, "start": 1936.05, "end": 1963.05, "text": "والنصف قطار ما له R1 وR2 وR3 وR4 وR5 بدي أخد اللي هو نصف .. بدي أخد إيش يكون جواتهم كلهم إذا أخي أكيد هاخد نصف القطر إيش أصغر واحد فيهم عشان أضمن بولو تكون إيش ما لها جوات الكل إذا بدي أقول let .. let R بتساوي ال minimum بين R1 وR2 لعند RN صح ولا لأ؟", "tokens": [2407, 6027, 1863, 9381, 5172, 12174, 9566, 9640, 19446, 46740, 497, 16, 4032, 49, 17, 4032, 49, 18, 4032, 49, 19, 4032, 49, 20, 4724, 16254, 5551, 9778, 3215, 13672, 1829, 31439, 8717, 9381, 5172, 4386, 4724, 16254, 5551, 9778, 3215, 11933, 1829, 8592, 7251, 30544, 10874, 2407, 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{"start": 1937.57, "end": 1938.17, "word": " R1", "probability": 0.724853515625}, {"start": 1938.17, "end": 1938.79, "word": " وR2", "probability": 0.9161783854166666}, {"start": 1938.79, "end": 1939.49, "word": " وR3", "probability": 0.9659830729166666}, {"start": 1939.49, "end": 1940.23, "word": " وR4", "probability": 0.9654947916666666}, {"start": 1940.23, "end": 1941.03, "word": " وR5", "probability": 0.9921875}, {"start": 1941.03, "end": 1942.15, "word": " بدي", "probability": 0.705078125}, {"start": 1942.15, "end": 1942.65, "word": " أخد", "probability": 0.7755533854166666}, {"start": 1942.65, "end": 1942.93, "word": " اللي", "probability": 0.98095703125}, {"start": 1942.93, "end": 1943.21, "word": " هو", "probability": 0.9931640625}, {"start": 1943.21, "end": 1943.79, "word": " نصف", "probability": 0.9361979166666666}, {"start": 1943.79, "end": 1943.83, "word": " ..", "probability": 0.6337890625}, {"start": 1943.83, "end": 1944.07, "word": " بدي", "probability": 0.9404296875}, {"start": 1944.07, "end": 1944.43, "word": " أخد", "probability": 0.9475911458333334}, {"start": 1944.43, "end": 1944.75, "word": " إيش", "probability": 0.6766764322916666}, {"start": 1944.75, "end": 1945.21, "word": " يكون", "probability": 0.98291015625}, {"start": 1945.21, "end": 1945.71, "word": " جواتهم", "probability": 0.75067138671875}, {"start": 1945.71, "end": 1946.19, "word": " كلهم", "probability": 0.835205078125}, {"start": 1946.19, "end": 1947.31, "word": " إذا", "probability": 0.760498046875}, {"start": 1947.31, "end": 1947.61, "word": " أخي", "probability": 0.687255859375}, {"start": 1947.61, "end": 1948.01, "word": " أكيد", "probability": 0.9021809895833334}, {"start": 1948.01, "end": 1948.39, "word": " هاخد", "probability": 0.7622884114583334}, {"start": 1948.39, "end": 1948.59, "word": " نصف", "probability": 0.9853515625}, {"start": 1948.59, "end": 1948.91, "word": " القطر", "probability": 0.9619140625}, {"start": 1948.91, "end": 1949.17, "word": " إيش", "probability": 0.849609375}, {"start": 1949.17, "end": 1949.55, "word": " أصغر", "probability": 0.946044921875}, {"start": 1949.55, "end": 1949.77, "word": " واحد", "probability": 0.9912109375}, {"start": 1949.77, "end": 1950.11, "word": " فيهم", "probability": 0.90478515625}, {"start": 1950.11, "end": 1950.83, "word": " عشان", "probability": 0.9737955729166666}, {"start": 1950.83, "end": 1951.11, "word": " أضمن", "probability": 0.939453125}, {"start": 1951.11, "end": 1951.45, "word": " بولو", "probability": 0.4820963541666667}, {"start": 1951.45, "end": 1951.67, "word": " تكون", "probability": 0.976318359375}, {"start": 1951.67, "end": 1951.85, "word": " إيش", "probability": 0.9777018229166666}, {"start": 1951.85, "end": 1951.99, "word": " ما", "probability": 0.9091796875}, {"start": 1951.99, "end": 1952.15, "word": " لها", "probability": 0.7275390625}, {"start": 1952.15, "end": 1952.55, "word": " جوات", "probability": 0.8103841145833334}, {"start": 1952.55, "end": 1952.91, "word": " الكل", "probability": 0.8564453125}, {"start": 1952.91, "end": 1953.59, "word": " إذا", "probability": 0.915283203125}, {"start": 1953.59, "end": 1953.91, "word": " بدي", "probability": 0.9599609375}, {"start": 1953.91, "end": 1954.25, "word": " أقول", "probability": 0.944091796875}, {"start": 1954.25, "end": 1954.81, "word": " let", "probability": 0.6484375}, {"start": 1954.81, "end": 1955.21, "word": " ..", "probability": 0.55224609375}, {"start": 1955.21, "end": 1956.01, "word": " let", "probability": 0.8740234375}, {"start": 1956.01, "end": 1956.95, "word": " R", "probability": 0.525390625}, {"start": 1956.95, "end": 1957.45, "word": " بتساوي", "probability": 0.8497314453125}, {"start": 1957.45, "end": 1957.59, "word": " ال", "probability": 0.85595703125}, {"start": 1957.59, "end": 1958.11, "word": " minimum", "probability": 0.61669921875}, {"start": 1958.11, "end": 1959.05, "word": " بين", "probability": 0.9072265625}, {"start": 1959.05, "end": 1959.83, "word": " R1", "probability": 0.9208984375}, {"start": 1959.83, "end": 1960.59, "word": " وR2", "probability": 0.98291015625}, {"start": 1960.59, "end": 1961.05, "word": " لعند", "probability": 0.93017578125}, {"start": 1961.05, "end": 1961.69, "word": " RN", "probability": 0.405517578125}, {"start": 1961.69, "end": 1962.45, "word": " صح", "probability": 0.982666015625}, {"start": 1962.45, "end": 1962.61, "word": " ولا", "probability": 0.9521484375}, {"start": 1962.61, "end": 1963.05, "word": " لأ؟", "probability": 0.765625}], "temperature": 1.0}, {"id": 82, "seek": 199181, "start": 1964.77, "end": 1991.81, "text": "مدام أخدت هي ال minimum إذا أكيد هتعطيني الغرض تلبيلي غرضي إذا then there exist ball of X وR واحدة منهم subsequent من ال ball of X وR I لكل I لأن هي مركزين واحد وهي أصغر نصف وطول ده ما هتكون فيهم كلهم مدام هتكون فيهم كلهم إذا موجودة فتقطع حين", "tokens": [2304, 3215, 10943, 5551, 9778, 3215, 2655, 39896, 2423, 7285, 11933, 15730, 5551, 4117, 25708, 8032, 2655, 3615, 9566, 9957, 1829, 6024, 118, 43042, 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2102.5, "word": " بتحقق", "probability": 0.8682861328125}, {"start": 2102.5, "end": 2103.06, "word": " منهم", "probability": 0.3406982421875}, {"start": 2103.06, "end": 2104.24, "word": " T1", "probability": 0.829345703125}, {"start": 2104.24, "end": 2104.86, "word": " وT2", "probability": 0.8162434895833334}, {"start": 2104.86, "end": 2105.5, "word": " وT3", "probability": 0.9765625}, {"start": 2105.5, "end": 2105.84, "word": " يعني", "probability": 0.802001953125}, {"start": 2105.84, "end": 2106.22, "word": " الآن", "probability": 0.7222900390625}, {"start": 2106.22, "end": 2107.44, "word": " بنسمي", "probability": 0.93603515625}, {"start": 2107.44, "end": 2107.84, "word": " X", "probability": 0.90673828125}, {"start": 2107.84, "end": 2108.44, "word": " وTau", "probability": 0.6138509114583334}, {"start": 2108.44, "end": 2108.68, "word": " أو", "probability": 0.76318359375}, {"start": 2108.68, "end": 2108.88, "word": " G", "probability": 0.8359375}, {"start": 2108.88, "end": 2109.34, 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إن", "probability": 0.61279296875}, {"start": 2144.06, "end": 2144.26, "word": " ال", "probability": 0.9140625}, {"start": 2144.26, "end": 2144.68, "word": " metric", "probability": 0.49365234375}, {"start": 2144.68, "end": 2145.54, "word": " space", "probability": 0.9521484375}, {"start": 2145.54, "end": 2146.04, "word": " is", "probability": 0.923828125}, {"start": 2146.04, "end": 2146.24, "word": " a", "probability": 0.64306640625}, {"start": 2146.24, "end": 2146.9, "word": " topological", "probability": 0.938232421875}, {"start": 2146.9, "end": 2147.68, "word": " space", "probability": 0.95263671875}], "temperature": 1.0}, {"id": 91, "seek": 217796, "start": 2149.18, "end": 2177.96, "text": "إذن واضح from theorem 1.3.5 اللي قبله شوية and above definition هذا we can say that a metric space is a topological space وقلنا العكس ليس شطر وصحيح لكن لجيت مش مجننة اللي هو نيجي الآن التعريف اللي بعده طيب التعريف الآن يا جماعة بتتعريفلكم اللي هو ال continuous functions", "tokens": [28814, 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"probability": 0.7705078125}, {"start": 2759.15, "end": 2759.51, "word": " اكيد", "probability": 0.88916015625}, {"start": 2759.51, "end": 2759.77, "word": " فيها", "probability": 0.4998779296875}, {"start": 2759.77, "end": 2760.75, "word": " صورة", "probability": 0.7762044270833334}, {"start": 2760.75, "end": 2761.63, "word": " سموها", "probability": 0.9014892578125}, {"start": 2761.63, "end": 2762.23, "word": " ايش", "probability": 0.87451171875}, {"start": 2762.23, "end": 2762.95, "word": " Y", "probability": 0.85546875}, {"start": 2762.95, "end": 2763.29, "word": " note", "probability": 0.71240234375}], "temperature": 1.0}, {"id": 116, "seek": 277792, "start": 2763.8, "end": 2777.92, "text": "ماشي اذا let x0 be element in G اذا اكيد there is y لانه function لازم كل صورة there is y0 element in Such that y0 اكت ساوي T x0 طيب", "tokens": [2304, 33599, 1829, 1975, 15730, 718, 2031, 15, 312, 4478, 294, 460, 1975, 15730, 1975, 4117, 25708, 456, 307, 288, 5296, 7649, 3224, 2445, 5296, 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3098.5, "end": 3099.96, "word": " في", "probability": 0.96630859375}, {"start": 3099.96, "end": 3100.18, "word": " الـ", "probability": 0.9482421875}, {"start": 3100.18, "end": 3100.44, "word": " G", "probability": 0.9501953125}], "temperature": 1.0}, {"id": 130, "seek": 312989, "start": 3101.37, "end": 3129.89, "text": "و لجتلكم اللي هو open ball حوالينها جوا الـG إيش معناته هذا الكلام؟ معناته إنه صارت الـG is an open set إذن اللي بدأنا فيه إن S is any open set في الـY لجينا الـT inverse للـS is an open set في الـX وهو المطلوب، الاتجاه التاني الآن conversely", "tokens": [2407, 5296, 7435, 2655, 23275, 2304, 13672, 1829, 31439, 1269, 2594, 11331, 2407, 6027, 9957, 11296, 10874, 14407, 2423, 39184, 38, 11933, 1829, 8592, 20449, 8315, 47395, 23758, 2423, 28820, 10943, 22807, 20449, 8315, 47395, 36145, 3224, 20328, 9640, 2655, 2423, 39184, 38, 307, 364, 1269, 992, 11933, 8848, 1863, 13672, 1829, 47525, 10721, 8315, 8978, 3224, 36145, 318, 307, 604, 1269, 992, 8978, 2423, 39184, 56, 5296, 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3439.88, "word": " arbitrarily", "probability": 0.697509765625}, {"start": 3439.88, "end": 3440.36, "word": " إذا", "probability": 0.6219482421875}, {"start": 3440.36, "end": 3440.52, "word": " ال", "probability": 0.7958984375}, {"start": 3440.52, "end": 3440.62, "word": " T", "probability": 0.748046875}, {"start": 3440.62, "end": 3440.76, "word": " is", "probability": 0.84765625}, {"start": 3440.76, "end": 3441.2, "word": " continuous", "probability": 0.9072265625}, {"start": 3441.2, "end": 3442.12, "word": " على", "probability": 0.759765625}, {"start": 3442.12, "end": 3442.26, "word": " ال", "probability": 0.403564453125}, {"start": 3442.26, "end": 3442.5, "word": " X", "probability": 0.9892578125}, {"start": 3442.5, "end": 3442.8, "word": " في", "probability": 0.9140625}, {"start": 3442.8, "end": 3443.22, "word": " ضوء", "probability": 0.9069010416666666}, {"start": 3443.22, "end": 3443.38, "word": " اللي", "probability": 0.927734375}, {"start": 3443.38, "end": 3443.5, "word": " هي", "probability": 0.91943359375}, {"start": 3443.5, "end": 3444.08, "word": " الخاصية", "probability": 0.89892578125}, {"start": 3444.08, "end": 3444.38, "word": " اللي", "probability": 0.968994140625}, {"start": 3444.38, "end": 3444.94, "word": " حكيناها", "probability": 0.9373046875}, {"start": 3444.94, "end": 3445.72, "word": " معطينيها", "probability": 0.65830078125}, {"start": 3445.72, "end": 3446.68, "word": " وبهيك", "probability": 0.74078369140625}, {"start": 3446.68, "end": 3446.92, "word": " ان", "probability": 0.56982421875}, {"start": 3446.92, "end": 3447.12, "word": " شاء", "probability": 0.98193359375}, {"start": 3447.12, "end": 3447.24, "word": " الله", "probability": 0.94873046875}, {"start": 3447.24, "end": 3447.62, "word": " بنصل", "probability": 0.787109375}, {"start": 3447.62, "end": 3447.94, "word": " لعين", "probability": 0.6141764322916666}, {"start": 3447.94, "end": 3448.04, "word": " ال", "probability": 0.91796875}, {"start": 3448.04, "end": 3448.38, "word": " definition", "probability": 0.87255859375}, {"start": 3448.38, "end": 3448.76, "word": " واحدة", "probability": 0.6227213541666666}, {"start": 3448.76, "end": 3449.02, "word": " تلاتة", "probability": 0.8995361328125}, {"start": 3449.02, "end": 3449.36, "word": " ساعة", "probability": 0.84619140625}, {"start": 3449.36, "end": 3450.06, "word": " المرة", "probability": 0.942138671875}, {"start": 3450.06, "end": 3450.52, "word": " القادمة", "probability": 0.9938151041666666}, {"start": 3450.52, "end": 3450.66, "word": " ان", "probability": 0.677734375}, {"start": 3450.66, "end": 3450.82, "word": " شاء", "probability": 0.994873046875}, {"start": 3450.82, "end": 3450.92, "word": " الله", "probability": 0.95751953125}, {"start": 3450.92, "end": 3451.52, "word": " بنكمل", "probability": 0.9453125}, {"start": 3451.52, "end": 3451.94, "word": " وبرك", "probability": 0.7169596354166666}, {"start": 3451.94, "end": 3452.04, "word": " الله", "probability": 0.892578125}, {"start": 3452.04, "end": 3452.32, "word": " فيكم", "probability": 0.967041015625}, {"start": 3452.32, "end": 3452.62, "word": " والسلام", "probability": 0.7705891927083334}, {"start": 3452.62, "end": 3452.98, "word": " عليكم", "probability": 0.921142578125}, {"start": 3452.98, "end": 3453.18, "word": " ورحمة", "probability": 0.867431640625}, {"start": 3453.18, "end": 3453.4, "word": " الله", "probability": 0.9580078125}, {"start": 3453.4, "end": 3454.02, "word": " وبركاته", "probability": 0.9923828125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3454.17725, "duration_after_vad": 3376.4174999999836}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mRYCDgWMxU8.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mRYCDgWMxU8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..54a63b2cdf2e220e9d33cfb00d7c46febefd1bdf
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mRYCDgWMxU8.srt
@@ -0,0 +1,1451 @@
+1
+00:00:05,030 --> 00:00:07,610
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,610 --> 00:00:10,370
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:10,370 --> 00:00:14,910
+آله وصحبه أجمعين هذه المحاضرة رقم خمسة وعشرين مساق
+
+4
+00:00:14,910 --> 00:00:19,230
+تحليل اقتراني أو تحليل دالي طولته بطالبات الجامعة
+
+5
+00:00:19,230 --> 00:00:25,110
+الإسلامية قسم الرياضيات ماجستير الرياضيات الآن إن
+
+6
+00:00:25,110 --> 00:00:28,330
+شاء الله هناخد آخر section في شبطر ثلاثة اللي هو
+
+7
+00:00:28,330 --> 00:00:32,550
+أنواع الـ operators اللي هنحكي عنها اللي هي self
+
+8
+00:00:32,550 --> 00:00:36,010
+-adjoint وunitary وnormal operators المحاضرة
+
+9
+00:00:36,010 --> 00:00:41,210
+الماضية عرفنا شو معنى a joint operator الآن هنحكي
+
+10
+00:00:41,210 --> 00:00:45,630
+عن شو معنى الـ self-adjoint operator شو معنى الـ
+
+11
+00:00:45,630 --> 00:00:49,450
+normal operator شو معنى الـ unitary operator و
+
+12
+00:00:49,450 --> 00:00:53,110
+بالمناسبة في طبعاً احنا هذه الأسماء مرت علينا في
+
+13
+00:00:53,110 --> 00:00:59,090
+الجبر الخطي فكلها مقابل في الجبر الخطي أصلاً الـ
+
+14
+00:00:59,090 --> 00:01:01,890
+matrix في الآخر اللي هو احنا بنقدر نعمل نشتغل و
+
+15
+00:01:01,890 --> 00:01:06,360
+كأنه operator على finite dimensional فاحنا طبعاً
+
+16
+00:01:06,360 --> 00:01:10,080
+هنحكي عن الـ operators بصورة عامة مش هنتطرق لتفاصيل
+
+17
+00:01:10,080 --> 00:01:13,860
+الـ matrices نيجي نشوف اللي هو الـ definition
+
+18
+00:01:13,860 --> 00:01:18,060
+الثلاثة عشر واحد a bounded linear operator T من H
+
+19
+00:01:18,060 --> 00:01:21,820
+لعند H أنه Hilbert space H الـ set to be إذا أنا 
+
+20
+00:01:21,820 --> 00:01:26,080
+تصنيفه في هذا الاتجاه لمين الـ bounded linear
+
+21
+00:01:26,080 --> 00:01:30,020
+operator على مين على Hilbert space بنقول عنه كمان
+
+22
+00:01:30,020 --> 00:01:34,220
+من H لمين لـ H اللي احنا حكينا عنه الـ Adjoint قبل
+
+23
+00:01:34,220 --> 00:01:39,840
+شوية من H1 أو الـ H2 لأن لأ بحكي عن اللي بتدعرفهم 
+
+24
+00:01:39,840 --> 00:01:43,760
+الآن لحالياً من H لـ H اللي هو مين أول شيء self-adjoint
+
+25
+00:01:43,760 --> 00:01:47,600
+أو hermitian إذا كان الـ T ستار تبعه إيش بيساوي 
+
+26
+00:01:47,600 --> 00:01:51,020
+بيساوي الـ T اللي هو الـ adjoint بيساوي نفس الـ T
+
+27
+00:01:51,020 --> 00:01:55,740
+بنسميه إيش ماله hermitian أو self-adjoint operator
+
+28
+00:01:55,740 --> 00:02:00,700
+بنسميه unitary إذا كان الـ T bijective
+
+29
+00:02:02,270 --> 00:02:09,150
+والـ T* إيش بيساوي الـ T inverse والـ
+
+30
+00:02:09,150 --> 00:02:16,330
+T نفسه unitary بيجيكشن أو بيجيكتف ماب بيصير عندي
+
+31
+00:02:16,330 --> 00:02:19,930
+اللي هو شرطين inverse اللي هو الـ T تكون bijective
+
+32
+00:02:19,930 --> 00:02:23,850
+شرط الثاني T* بيساوي T inverse ثلاثة الـ normal
+
+33
+00:02:23,850 --> 00:02:27,410
+operator إذا كان الـ T في الـ T* إيش بيساوي 
+
+34
+00:02:27,410 --> 00:02:30,430
+بيساوي T* في T طبعاً في أنواع الـ operators
+
+35
+00:02:30,430 --> 00:02:33,850
+عديدة يعني غير هذه اللي هي الـ operators بس خلينا 
+
+36
+00:02:33,850 --> 00:02:38,070
+نركز على هذه في هذا الـ course المحدود طيب الآن أول
+
+37
+00:02:38,070 --> 00:02:42,780
+ملاحظة إذا كان الـ T self-adjoint هيكون عند الـ T X
+
+38
+00:02:42,780 --> 00:02:46,160
+والـ Y بيساوي X و T* Y ومزام الـ T* Y
+
+39
+00:02:46,160 --> 00:02:50,220
+بيساوي T إذا بيصير الـ T X و Y بيساوي X و T Y يعني
+
+40
+00:02:50,220 --> 00:02:53,360
+بتنقل الـ T من هنا إلى هنا زي ما بدك في حال مين 
+
+41
+00:02:53,360 --> 00:02:59,310
+أن يكون T self-adjoint لأن لو كان الـ T self
+
+42
+00:02:59,310 --> 00:03:04,850
+-adjoint أو unitary بتكون الـ T normal شوف كيف لو 
+
+43
+00:03:04,850 --> 00:03:09,310
+كان self-adjoint بيصير الـ T في الـ T* هي 
+
+44
+00:03:09,310 --> 00:03:12,810
+عبارة عن الـ T في T إذا كان self-adjoint اللي هي T
+
+45
+00:03:12,810 --> 00:03:15,710
+تربيع اللي هي نفس الـ T* في T اللي هي T في T
+
+46
+00:03:15,710 --> 00:03:19,110
+في T تربيع إذا لما يكون self-adjoint automatic
+
+47
+00:03:19,110 --> 00:03:25,880
+هيكون يشملـه normal لو كان unitary بيكون الـ T* هو
+
+48
+00:03:25,880 --> 00:03:30,060
+T inverse ماشي الحال و تنسوش الـ T bijective إذا
+
+49
+00:03:30,060 --> 00:03:32,340
+الـ T inverse bijective يعني الـ T في الـ T
+
+50
+00:03:32,340 --> 00:03:36,460
+inverse هيساوي الـ identity و الآن الـ T inverse في
+
+51
+00:03:36,460 --> 00:03:39,520
+الـ T برضه هيساوي الـ identity لأنه bijective إذاً
+
+52
+00:03:39,520 --> 00:03:41,940
+هيكون الـ T في الـ T* بيساوي الـ T* في الـ T
+
+53
+00:03:41,940 --> 00:03:46,280
+automatic ما دام إيش اسمه Unitary إذاً إذا كانت
+
+54
+00:03:46,280 --> 00:03:49,460
+Unitary أو self-adjoint automatic هيكون Normal
+
+55
+00:03:49,460 --> 00:03:54,380
+الآن Normal Operators need not to be self-adjoint
+
+56
+00:03:54,380 --> 00:03:58,440
+ولا Unitary يعني ليس شرطاً ليكون self-adjoint ولا 
+
+57
+00:03:58,440 --> 00:04:01,780
+يكون إيش ماله Unitary الآن بدنا مثال على Normal
+
+58
+00:04:01,780 --> 00:04:06,060
+Operator لا يكون self-adjoint ولا يكون Unitary خد
+
+59
+00:04:06,690 --> 00:04:09,830
+خد المثال التالي To see this consider the identity
+
+60
+00:04:09,830 --> 00:04:13,970
+operator I من H لعند مين لعند H الـ identity العادي
+
+61
+00:04:13,970 --> 00:04:18,810
+اه الآن إن هيلبرت اسمه H it is easy to see that الـ
+
+62
+00:04:18,810 --> 00:04:23,650
+T خدوا الـ T لأن بيساوي 2I في مين في I إذا المثال
+
+63
+00:04:23,650 --> 00:04:27,750
+اللي أنا بدأ أقول لكم إنه عبارة عن اللي هو الـ الـ الـ
+
+64
+00:04:27,750 --> 00:04:34,070
+normal لكن مش self-adjoint T بيساوي 2I في مين في I
+
+65
+00:04:34,670 --> 00:04:39,910
+ماشي الحال الآن لو جينا أخذنا الـ T* له الـ T
+
+66
+00:04:39,910 --> 00:04:44,370
+star اللي هو هيساوي اللي هو سالب اثنين I في مين 
+
+67
+00:04:44,370 --> 00:04:48,850
+فالـ identity ماشي الحال هذا اللي هو إيش الـ T*
+
+68
+00:04:48,850 --> 00:04:52,570
+له الكون جيت له طبعاً واثباته سهل هذا لو اللي هو
+
+69
+00:04:52,570 --> 00:05:00,220
+عندك الـ T X و الـ Y بيساوي اللي هو X أو الآن الـ T
+
+70
+00:05:00,220 --> 00:05:05,220
+star خذ 2I الآن على الجهة الثانية لما يحصل كنت
+
+71
+00:05:05,220 --> 00:05:08,820
+جيب C سالب 2I، مظبوط؟ إذن طبيعي بيكون اللي هو T
+
+72
+00:05:08,820 --> 00:05:13,960
+star هو مين الـ T نفسه، بسوء تناقص 2I في I طيب، 
+
+73
+00:05:13,960 --> 00:05:20,660
+الآن الـ T inverse هيسوي 1 على 2I في مين في I،
+
+74
+00:05:20,660 --> 00:05:25,040
+ماشي الحاله واضح إن الـ T بتسويش الـ T inverse
+
+75
+00:05:25,040 --> 00:05:31,960
+والـ T* بتسويش الـ T معايا واضح إن الـ T في T
+
+76
+00:05:31,960 --> 00:05:38,380
+star T في T* بيساوي اللي هو T* في T بيساوي
+
+77
+00:05:38,380 --> 00:05:45,980
+أربعة I بظبط لإن اضربه هذي اثنين I في اثنين I
+
+78
+00:05:45,980 --> 00:05:49,520
+بيطلع اللي هو أربعة الـ identity I تربية ما هي الـ I
+
+79
+00:05:49,520 --> 00:05:52,200
+ما أنتم عارفين إذا اللي عندي الآن
+
+80
+00:05:54,790 --> 00:05:57,610
+هذا مثال على الـ Normal operator need not to be
+
+81
+00:05:57,610 --> 00:06:01,670
+self-adjoint normally تبقى اطلع على فوق هنجي الآن
+
+82
+00:06:01,670 --> 00:06:05,690
+نظريتنا الأولى theorem 13-3 let T من H مع اند H be
+
+83
+00:06:05,690 --> 00:06:09,010
+a bounded linear operator on a Hilbert space H
+
+84
+00:06:09,010 --> 00:06:14,310
+then if T self-adjoint then الـ T X والـ X هيكون إيش 
+
+85
+00:06:14,310 --> 00:06:18,650
+ماله real لكل X في الـ X هذا كلام مهم إذا كانت الـ T
+
+86
+00:06:18,650 --> 00:06:22,070
+عبارة عن self-adjoint هيكون automatic الـ T X والـ X
+
+87
+00:06:22,070 --> 00:06:27,350
+إيش ماله دائماً real ماشي الآن إذا كان H complex
+
+88
+00:06:28,260 --> 00:06:32,280
+إذا كان نفسه H is a complex هذا اللي فوق بغض النظر
+
+89
+00:06:32,280 --> 00:06:35,980
+إيش هي الـ H هيكون الـ TX والـ X إيش ماله real الآن 
+
+90
+00:06:35,980 --> 00:06:40,380
+اللي كانت H complex وكان الـ TX والـ X real automatic
+
+91
+00:06:40,380 --> 00:06:46,520
+هيكون عند الـ T self-adjoint لكن لو كان H مش Complex
+
+92
+00:06:46,520 --> 00:06:51,520
+وكانت الـ TX والـ X ريال ليس شرطاً أنه تكون الـ T
+
+93
+00:06:51,520 --> 00:06:55,620
+سلف الدولة أصلاً ممكن تكون TX والـ X مزام ريال هيكون
+
+94
+00:06:55,620 --> 00:07:01,970
+TX والـ X ريال طبيعي اه فهذا طبعاً ليس شرطاً إنه لو
+
+95
+00:07:01,970 --> 00:07:06,950
+بدنا نسلم بهذا if H is real و T X و X real إذن الـ 
+
+96
+00:07:06,950 --> 00:07:09,830
+T الـ self-adjoint ما هو كل الـ T .. كل اللي في
+
+97
+00:07:09,830 --> 00:07:13,030
+الدنيا الـ T اللي على الـ real هيكون الـ T X و الـ 
+
+98
+00:07:13,030 --> 00:07:15,450
+X real يعني هذا الشرط متحقق أوتوماتيكي يعني كل 
+
+99
+00:07:15,450 --> 00:07:18,670
+اللي هيطلع الـ self-adjoint لأ طبعاً واضح إذن .. 
+
+100
+00:07:18,670 --> 00:07:22,450
+إذن .. إذن النظرية الجزء B هذا وين بيحدث في حالة 
+
+101
+00:07:22,450 --> 00:07:30,160
+main H is complex نيجي لبنهم نيجي الآن الـ suppose
+
+102
+00:07:30,160 --> 00:07:33,420
+ده الـ T self الـ joint لكل X في الـ H احسب
+
+103
+00:07:33,420 --> 00:07:36,620
+ما يليه عشان اثبت إن الـ T X والـ X الريال ده ثبت
+
+104
+00:07:36,620 --> 00:07:39,180
+أن الـ conjugate هيطلع نفسه ماشي إن أنا اخد الـ
+
+105
+00:07:39,180 --> 00:07:44,460
+conjugate لـ T X والـ X بسوء X و T X مظبوط X و T X
+
+106
+00:07:44,460 --> 00:07:50,170
+وT سلف الـ joint هيسوء T X و X بس هيفضّوهم إذا صار 
+
+107
+00:07:50,170 --> 00:07:56,110
+عندي اللي هو TX و X is real الآن الـ B suppose that
+
+108
+00:07:56,110 --> 00:08:00,250
+H is complex هستخدم شكل النظرية تبعت المرة اللي
+
+109
+00:08:00,250 --> 00:08:03,990
+فاتت اللي مال اللي فاتت للمحاضر اللي فاتت suppose
+
+110
+00:08:03,990 --> 00:08:09,430
+that H is complex and TX و X يشملـه is real لكل X
+
+111
+00:08:09,430 --> 00:08:14,090
+element in H هذا الفرضية then شوف كيف يثبت لك إنه
+
+112
+00:08:14,090 --> 00:08:21,180
+اللي هو الـ T بتساوي الـ T* عندي TX و X بيساوي TX
+
+113
+00:08:21,180 --> 00:08:27,100
+و X conjugate صح ولا لأ لإنها real ويساوي الآن الـ
+
+114
+00:08:27,100 --> 00:08:33,160
+TX و الـ X من تعريف الـ joint بيساوي X و T* X صح
+
+115
+00:08:33,160 --> 00:08:38,270
+الـ conjugate اللي هو هيطلع T* X و 100 و X الآن 
+
+116
+00:08:38,270 --> 00:08:45,770
+عند خدق الآن السفر بيساوي T X و X ناقص T* X و X
+
+117
+00:08:45,770 --> 00:08:49,110
+نجلناها ما هو على طول احنا جابلنا كلنا ما دام هذا
+
+118
+00:08:49,110 --> 00:08:51,710
+بيساوي و هذا دائماً أيضاً على طول بيساوي T* بس
+
+119
+00:08:51,710 --> 00:08:57,570
+خلينا الآن نبسطها للاخر الآن صار عند T X و X ناقص
+
+120
+00:08:57,570 --> 00:09:01,600
+T* X و X بتساوي صفر و بيساوي جيبوا الـ inner
+
+121
+00:09:01,600 --> 00:09:07,280
+product مع بعض بيصير T نقص T* X O X بيساوي صفر 
+
+122
+00:09:07,280 --> 00:09:11,320
+وهذا الكلام صحيح لكل X في الدنيا إذن هذا اللي
+
+123
+00:09:11,320 --> 00:09:15,160
+كانوا بيسمونه Q احنا في المرة اللي فاتت فهيطلع Q
+
+124
+00:09:15,160 --> 00:09:18,820
+بتساوي صفر من اللمة ثلاثة تسعة ثلاثة بيه إذا صار
+
+125
+00:09:18,820 --> 00:09:22,340
+عندي Q اللي هو T minus T* بيساوي صفر ومن ثم T
+
+126
+00:09:22,340 --> 00:09:25,200
+بيساوي T* ومن ثم T is self-adjoint إذا أنا 
+
+127
+00:09:25,200 --> 00:09:30,180
+automatic اللي هو T is self-adjoint طبعاً اللي
+
+128
+00:09:30,180 --> 00:09:33,920
+بتطلب التطبيق هذي لإن ما يكون H إيش ماله Complex
+
+129
+00:09:33,920 --> 00:09:39,480
+اطلع لفوق الآن the product of two bounded self
+
+130
+00:09:39,480 --> 00:09:43,900
+-adjoint linear operators S and T إن هيلبرت سبيس H
+
+131
+00:09:43,900 --> 00:09:47,140
+is self-adjoint if and only if S في T بيساوي TS
+
+132
+00:09:47,140 --> 00:09:55,460
+يعني بقول لي الآن لو كان عندي T و S self-adjoint كل 
+
+133
+00:09:55,460 --> 00:10:01,480
+واحد ماشي الحال بقول لي إذا .. إذا اللي هو S في T
+
+134
+00:10:01,480 --> 00:10:11,800
+is self-adjoint if and only if ST إيش بيساوي TS
+
+135
+00:10:11,800 --> 00:10:18,000
+ماشي الحال؟ طيب هذا الأمر بسيط وسهل a proof .. a
+
+136
+00:10:18,000 --> 00:10:24,720
+proof بنبدأ نفوض صباز that
+
+137
+00:10:25,640 --> 00:10:35,740
+S T الـ self-adjoint ماشي الحال؟ لأ دهن، دهن S T
+
+138
+00:10:35,740 --> 00:10:45,280
+بيساوي S T اللي هو S* في T* صح ولا لأ؟ من
+
+139
+00:10:45,280 --> 00:10:51,230
+التعريف، لأن T و S يشمل أنه self-adjoint معايا اه
+
+140
+00:10:51,230 --> 00:10:59,390
+الآن S T لكل Star بيساوي أنا بدأ أثبت هذه الآن اه S 
+
+141
+00:10:59,390 --> 00:11:04,890
+T بساوي T* S معي الآن S* في T* ماهو الآن
+
+142
+00:11:04,890 --> 00:11:12,950
+S T self-adjoint joint اذا هو عبارة عن S T* T S لكل
+
+143
+00:11:12,950 --> 00:11:22,620
+T* ده خليني ابدأ بالعكس عشان T S وهناA T* S
+
+144
+00:11:22,620 --> 00:11:30,240
+T* فبساوي S في T الكل T* بتظبط بحيط بتظبط صحيح
+
+145
+00:11:30,240 --> 00:11:33,620
+دايماً صحيح هو يساوي S في T سلفة ال joint ايش
+
+146
+00:11:33,620 --> 00:11:39,560
+هيساوي عشان بس هذه عشان الأخيرة S في T* سلفة S
+
+147
+00:11:39,560 --> 00:11:43,420
+T لأنه مفترض من سلفة ال joint S T اذا T S ايش
+
+148
+00:11:43,420 --> 00:11:50,210
+بتساوي S T conversely conversely suppose that S T
+
+149
+00:11:50,210 --> 00:11:55,070
+بيساوي TS ماشي الحال الآن بدي اتبعتلكم S T self-adjoint
+
+150
+00:11:55,070 --> 00:12:00,810
+joint الآن S T لكل T* مش هيساوي اللي هو حسب
+
+151
+00:12:00,810 --> 00:12:06,270
+القانون T* S* صح؟ و يساوي T* هو الـ T
+
+152
+00:12:06,270 --> 00:12:09,950
+لأن الـ self-adjoint من رأس الدور و الـ S* S
+
+153
+00:12:09,950 --> 00:12:13,230
+اللي هي الـ self-adjoint من رأس الدور و أنا الآن
+
+154
+00:12:13,230 --> 00:12:18,770
+مفترض S T ايش بيساوي P S اذا T فاس ايش هتساوي S في
+
+155
+00:12:18,770 --> 00:12:23,550
+T اذا صار S في T بيساوي S في T ايش لكل T* اذا S
+
+156
+00:12:23,550 --> 00:12:28,290
+T is self-adjoint هذه اللي هي theorem
+
+157
+00:12:31,340 --> 00:12:37,200
+اللي هو تلاتة عشر خمسة الآن تخليني تخليني على
+
+158
+00:12:37,200 --> 00:12:42,400
+النظرية اللي قبلها theorem تلاتة عشر خمسة let T<sub>n</sub>
+
+159
+00:12:42,400 --> 00:12:45,520
+be a sequence of bounded linear self-adjoint
+
+160
+00:12:45,520 --> 00:12:49,820
+linear operators وT<sub>n</sub> من H لعند H انها ال
+
+161
+00:12:49,820 --> 00:12:56,190
+participate H suppose that T<sub>n</sub> بتروح لـ T S اللي هو
+
+162
+00:12:56,190 --> 00:13:01,910
+that is norm of T<sub>n</sub> بتروح لصفر بتروح لصفر where
+
+163
+00:13:01,910 --> 00:13:05,470
+this norm is the norm on the space B(H,H) عارفينه
+
+164
+00:13:05,470 --> 00:13:08,590
+طبعاً يعني then T is a bounded self-adjoint linear
+
+165
+00:13:08,590 --> 00:13:12,810
+operator يعني و كأنه بيقول اللي خلّي بيقول انه
+
+166
+00:13:12,810 --> 00:13:16,550
+اللي هو sequence of sequence of self-adjoint
+
+167
+00:13:16,550 --> 00:13:22,350
+operators لو converged لـ some T لازم الـ T تكون
+
+168
+00:13:22,350 --> 00:13:24,370
+ايه أشمالها؟ self-adjoint
+
+169
+00:13:27,030 --> 00:13:32,650
+معنى ايش بقول؟ لو كانت عندي اللي بقوله T<sub>n</sub> sequence
+
+170
+00:13:32,650 --> 00:13:37,170
+of self-adjoint linear operators و هدى conveges
+
+171
+00:13:37,170 --> 00:13:42,890
+لصم T لازم الـ T هدى ايش تطلع self-adjoint يعني
+
+172
+00:13:42,890 --> 00:13:47,550
+بمعنى آخر لازم أثبتلك إنه norm T نقص T* اللي
+
+173
+00:13:47,550 --> 00:13:51,930
+هو بيساوي صفر ماشي معناته ال T بتساوي مين؟ T*
+
+174
+00:13:51,930 --> 00:14:00,750
+شوف عليها الآن ال T<sub>n</sub> الـ T<sub>n</sub> الـ T<sub>n</sub> اللي هو self-
+
+175
+00:14:00,750 --> 00:14:07,030
+adjoint مظبوط ولا لأ؟ اذا الـ T<sub>n</sub> converts للـ T و
+
+176
+00:14:07,030 --> 00:14:12,410
+T<sub>n</sub>* converts للـ T ليش؟ لأن كل واحدة من هدول هي
+
+177
+00:14:12,410 --> 00:14:17,110
+هدول ماشي الحال اذا هذه بتعطيني هدولة بيعطيني norm
+
+178
+00:14:17,110 --> 00:14:24,300
+الـ T<sub>n</sub> ناقص الـ T بروح للـ 0 اه و هذا بيعطيني norm
+
+179
+00:14:24,300 --> 00:14:29,460
+الـ T<sub>n</sub>* ناقص الـ T برضه هيروح لين للـ Zero
+
+180
+00:14:29,460 --> 00:14:39,620
+احسبلي الآن norm الـ T ناقص الـ T* اللي
+
+181
+00:14:39,620 --> 00:14:48,420
+هو أصغر أو يساوي أصغر أو يساوي norm الـ T ناقص
+
+182
+00:14:50,680 --> 00:15:06,660
+الـ T<sub>n</sub> زائد norm الـ T<sub>n</sub> ناقص T<sub>n</sub>* مظبوط زائد
+
+183
+00:15:06,660 --> 00:15:15,320
+norm فعله بس على الكتاب بالله فعله الكتاب زائد
+
+184
+00:15:16,400 --> 00:15:26,940
+Norm نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+185
+00:15:26,940 --> 00:15:30,100
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+186
+00:15:30,100 --> 00:15:36,100
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+187
+00:15:36,100 --> 00:15:37,840
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+188
+00:15:37,840 --> 00:15:38,380
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+189
+00:15:38,380 --> 00:15:38,460
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+190
+00:15:38,460 --> 00:15:43,040
+نزل نزل نزل نزل
+
+191
+00:15:43,040 --> 00:15:53,880
+نزل الـ T<sub>n</sub> ناقص T* T* ماشي الحال طيب الآن
+
+192
+00:15:53,880 --> 00:16:02,400
+هذه بتروح لمين؟ للصفر وهذه ايش بتساوي صفر ماشي وهذه
+
+193
+00:16:02,400 --> 00:16:11,030
+بتساوي norm ال T<sub>n</sub> ناقص T الكل T<sub>n</sub> ماشي الحال هذه
+
+194
+00:16:11,030 --> 00:16:15,110
+اللي جوه بتروح لمين؟ برضه للصفر اذا هذا الآن كمان
+
+195
+00:16:15,110 --> 00:16:20,830
+هيروح لمين؟ كله للزيرو اذا صار عندي norm of T نقص T
+
+196
+00:16:20,830 --> 00:16:23,310
+طبعاً هذا دايماً اكبر تساوي مين؟ صفر يعني اخذنا نمية
+
+197
+00:16:23,310 --> 00:16:28,130
+اذا الآن goes to infinity فبطلع T بتساوي T*
+
+198
+00:16:28,130 --> 00:16:34,040
+ومن ثم T ايش مالها؟ الـ self-adjoint طبعاً كل وين هذا ال
+
+199
+00:16:34,040 --> 00:16:38,880
+convergence في ال B(H,H) اللي هي اللي هي the set
+
+200
+00:16:38,880 --> 00:16:43,220
+of all bounded linear operators من H لعند H اذا
+
+201
+00:16:43,220 --> 00:16:49,780
+احنا اللي اثبتنا انه ال T<sub>n</sub> لو كانت sequence of
+
+202
+00:16:49,780 --> 00:16:53,420
+bounded self-adjoint linear operators converge the
+
+203
+00:16:53,420 --> 00:16:57,440
+sum T هيكون limitها برضه ايش مالها؟ اللي هو self
+
+204
+00:16:57,440 --> 00:17:04,760
+-adjoint linear operator اطلع لفوق اطلع لفوق يالا
+
+205
+00:17:04,760 --> 00:17:10,080
+البعد خلاص خليني اشرح منها خلاص خلاص خليني اشرح
+
+206
+00:17:10,080 --> 00:17:14,160
+منها let the operator U من H لعند H و V من H لH be
+
+207
+00:17:14,160 --> 00:17:20,710
+unitary او H is a Hilbert space then الخاصية التالية
+
+208
+00:17:20,710 --> 00:17:25,910
+متحققة كلها يعني محسبتها حتى سريعة U is
+
+209
+00:17:25,910 --> 00:17:30,010
+isometric اخذ معاه ايش؟ هو معناه ايزومتري norm ال U
+
+210
+00:17:30,010 --> 00:17:32,910
+X ايش بيساوي؟ norm ال X لكل X هو اللي موجودة في ال
+
+211
+00:17:32,910 --> 00:17:38,110
+H و norm ال U ال unitary هذا طبعاً احنا اخذنا اللي
+
+212
+00:17:38,110 --> 00:17:42,190
+هو ال U ايش مالها؟ و ال V unitary operators هذه خاص
+
+213
+00:17:42,190 --> 00:17:47,420
+ال unitary operators بيصير Normal U بساوي واحد على
+
+214
+00:17:47,420 --> 00:17:52,640
+اعتبار ان الـH أشمالها مش الـ0 ال part space و ال
+
+215
+00:17:52,640 --> 00:17:58,040
+U inverse اللي هو طبعاً مادام Unitary اللي هو الـU
+
+216
+00:17:58,040 --> 00:18:02,600
+inverse نفسه برضه أشمالها is Unitary وهذه سهلة برضه
+
+217
+00:18:02,600 --> 00:18:06,440
+و ال U في V ايش برضه هيطلع Unitary اذا كانت U
+
+218
+00:18:06,440 --> 00:18:10,380
+Unitary و V Unitary برضه حاصل ضربين Unitary و برضه
+
+219
+00:18:10,380 --> 00:18:14,520
+كلام كله سهل و ال U ايش مالها؟ Normal اثبتناها
+
+220
+00:18:14,520 --> 00:18:17,720
+قلناها المرة الفاترة او في اول محاضرة اطلع لفوق
+
+221
+00:18:17,720 --> 00:18:23,360
+اطلع الان a bounded linear operator T on a Hilbert
+
+222
+00:18:23,360 --> 00:18:26,920
+.. on a complex Hilbert space H is unitary if and
+
+223
+00:18:26,920 --> 00:18:30,790
+only if T ايش مالها؟ is isometric لو كانت Unitary
+
+224
+00:18:30,790 --> 00:18:34,210
+بتعطينا ايزومتريك بتكون اثبتناها في الاول بتظهر الـ
+
+225
+00:18:34,210 --> 00:18:38,450
+Main العكس خلينا نشوف الاولى بدنا نثبت انها الـ
+
+226
+00:18:38,450 --> 00:18:42,570
+Unitary is isometry اخذ norm لـUX لكل تربيع ايش
+
+227
+00:18:42,570 --> 00:18:47,010
+بيساوي اللي هي norm بردكت بين الـUX والـUX ماشي
+
+228
+00:18:47,010 --> 00:18:50,610
+الانوي ساوي X من خلاص ال joint بيصير X و U* في
+
+229
+00:18:50,610 --> 00:18:54,050
+U U* في U ماهي ال U* في ال Unitary بيساوي
+
+230
+00:18:54,050 --> 00:18:56,870
+U Inverse فال U Inverse في ال U و ال U is
+
+231
+00:18:56,870 --> 00:19:00,750
+bijective إذن هيصير ال identity إذن X و ال IX اللي
+
+232
+00:19:00,750 --> 00:19:03,950
+هو norm ال X تربيع إذن ال U X بيساوي norm ال X إذن
+
+233
+00:19:03,950 --> 00:19:06,510
+he preserved the norm او preserve the distance او
+
+234
+00:19:06,510 --> 00:19:11,860
+preserve the inner product ده الايزومتري الآن الجزء
+
+235
+00:19:11,860 --> 00:19:16,860
+الثاني بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+236
+00:19:16,860 --> 00:19:17,520
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+237
+00:19:17,520 --> 00:19:17,540
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+238
+00:19:17,540 --> 00:19:17,800
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+239
+00:19:17,800 --> 00:19:20,900
+بي بي بي
+
+240
+00:19:20,900 --> 00:19:27,140
+بي بي بي بي
+
+241
+00:19:27,140 --> 00:19:27,520
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+242
+00:19:27,520 --> 00:19:30,640
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+243
+00:19:30,640 --> 00:19:36,320
+بي
+
+244
+00:19:36,320 --> 00:19:42,230
+بي ببسوء norm ال X هذا في ال unitary اذا الان norm
+
+245
+00:19:42,230 --> 00:19:48,110
+اللي هو ال U X على norm ال X اللي هو بيساوي واحد ال
+
+246
+00:19:48,110 --> 00:19:53,150
+supremum اللي هو norm ال U هي يساوي واحد اذا طبيعي
+
+247
+00:19:53,150 --> 00:19:59,250
+norm ال unitary بيساوي واحد طيب الان ال .. ال .. ال
+
+248
+00:19:59,250 --> 00:20:03,030
+.. ال U inverse ال U bijective لنثبت ان ال U
+
+249
+00:20:03,030 --> 00:20:07,830
+inverse unitary U unitary اذا bijective و ال U
+
+250
+00:20:07,830 --> 00:20:12,670
+inverse يساوي U* طيب الان U is bijective اذا
+
+251
+00:20:12,670 --> 00:20:17,530
+ال U inverse موجودة و برضه bijective ماشي؟ اذا
+
+252
+00:20:17,530 --> 00:20:20,310
+الان الشرط الاول بالنسبة لل U inverse هتكون
+
+253
+00:20:20,310 --> 00:20:25,000
+unitary تحقق ان هي bijective و لو اخذنا ال U
+
+254
+00:20:25,000 --> 00:20:28,560
+Inverse* هي ساوي ال U Inverse ما هي Unitary
+
+255
+00:20:28,560 --> 00:20:34,060
+ماشي؟ اذا ال U** صارت اليمين بيساوي ال U
+
+256
+00:20:34,060 --> 00:20:37,400
+اللي هي بتساوي U Inverse Inverse اذا صارت ال U
+
+257
+00:20:37,400 --> 00:20:41,860
+Inverse* بيساوي U Inverse Inverse اذا صارت
+
+258
+00:20:41,860 --> 00:20:46,640
+اللي هي ال U Inverse نفسها is Unitary فاضح؟ طيب
+
+259
+00:20:46,640 --> 00:20:52,140
+الان ال U V بتثبت انها Unitary ال U Unitary و ال V
+
+260
+00:20:52,140 --> 00:20:56,100
+Unitary اذا ال U بيجيكتف و ال V بيجيكتف اذا ال
+
+261
+00:20:56,100 --> 00:21:00,340
+composition اللي هنا ال U V بيجيكتف هو مش هيك كمان
+
+262
+00:21:00,340 --> 00:21:04,500
+و لو اخدت ال U V لكل * هيساوي ال U V لكل
+
+263
+00:21:04,500 --> 00:21:08,760
+Inverse ليش؟ لأن هذا الـ U V لكل * من خلاص اللي
+
+264
+00:21:08,760 --> 00:21:12,140
+هي الـ * اللي هي V* U* و الـ V*
+
+265
+00:21:12,140 --> 00:21:15,320
+مادام V Unitary بيساوي الـ V Inverse و الـ U*
+
+266
+00:21:15,320 --> 00:21:18,280
+برضه بيساوي U Inverse لأنها Unitary برضه اللي هي
+
+267
+00:21:18,280 --> 00:21:22,160
+هذه بتساوي ايش؟ U في V لكل ايش؟ Inverse اذا صار U V
+
+268
+00:21:22,160 --> 00:21:25,820
+لكل * بيساوي U V لكل Inverse بمعنى آخر صارت الـ
+
+269
+00:21:25,820 --> 00:21:29,600
+U في V is Unitary طيب الان
+
+270
+00:21:31,660 --> 00:21:35,620
+U inverse بيساوي U* اللي هو و ال U في ال U
+
+271
+00:21:35,620 --> 00:21:38,680
+inverse بيساوي ال U inverse في ال U بيساوي مين؟
+
+272
+00:21:38,680 --> 00:21:45,220
+بيساوي ال ايش؟ ال identity مباشرة طيب الان صار عندي
+
+273
+00:21:45,220 --> 00:21:48,460
+الان اللي هو هذا بالنسبة ليه؟ انزل انزل انزل انزل
+
+274
+00:21:48,460 --> 00:21:52,480
+بالنسبة ليه؟ انزل انزل انزل بالنسبة ليه؟ بالنسبة ليه؟
+
+275
+00:21:52,480 --> 00:21:56,420
+الان U is ايش ماله؟ normal اخببته انا اه اطلع لفوق
+
+276
+00:21:56,420 --> 00:21:57,880
+طيب
+
+277
+00:22:00,640 --> 00:22:03,960
+النجلة اللي هي الجزء الأول اللي قلنا automatic
+
+278
+00:22:03,960 --> 00:22:09,700
+صبوس that is isometric and surjective ماشي and
+
+279
+00:22:09,700 --> 00:22:14,520
+surjective isometry implies injectivity قلناها اذا
+
+280
+00:22:14,520 --> 00:22:18,160
+كانت isometric قبلها ذكرناها كثير اذا كانت اللي .. 
+
+281
+00:22:18,160 --> 00:22:21,700
+اللي هي isometric على طول أشملها indicative عندي T
+
+282
+00:22:21,700 --> 00:22:25,260
+دثويت الكوم الآن أنتم تعرفون أين راح دثويت الكوم
+
+283
+00:22:25,260 --> 00:22:28,900
+اللي هي الـ F and O الـ F أنزل .. أنزل .. أنزل ..
+
+284
+00:22:28,900 --> 00:22:32,160
+أنزل .. أنزل .. أنزل .. أنزل .. أنزل .. أنزل ..
+
+285
+00:22:32,160 --> 00:22:34,420
+أنزل .. أنزل .. أنزل .. أنزل .. أنزل .. أنزل ..
+
+286
+00:22:34,420 --> 00:22:34,580
+أنزل .. أنزل .. أنزل .. أنزل .. أنزل .. أنزل ..
+
+287
+00:22:34,580 --> 00:22:37,460
+أنزل .. أنزل .. أنزل .. أنزل A bounded linear
+
+288
+00:22:37,460 --> 00:22:41,800
+operator T in a complex Hilbert space H is unitary 
+
+289
+00:22:41,800 --> 00:22:45,120
+if and only if T is isometric and surjective
+
+290
+00:22:52,540 --> 00:22:56,400
+و Unitary بالجكتف إذا صارت اللي هو الـ Unitary
+
+291
+00:22:56,400 --> 00:23:00,020
+أوتوماتيكي بتعطي ايزومتريكي بتعطي سيرجكتف الآن بدي 
+
+292
+00:23:00,020 --> 00:23:04,760
+العكس إذا كانت ايزومتري و سيرجكتف يعطيني مين؟
+
+293
+00:23:04,760 --> 00:23:13,020
+Unitary واضح؟ اطلع لفظك نفترض الآن أن T T نفترض أنه
+
+294
+00:23:13,020 --> 00:23:18,000
+الآن T نفترض أنه الآن T is isometric and
+
+295
+00:23:18,000 --> 00:23:22,840
+surjective مدام isometric وقبل هيك قلنا احنا الـ
+
+296
+00:23:22,840 --> 00:23:27,000
+isometric operator هيطلع one to one إذا صار عندي 
+
+297
+00:23:27,000 --> 00:23:29,960
+one to one و surjective يعني bijective إذا دلت
+
+298
+00:23:29,960 --> 00:23:35,160
+خاصية أخيرة أنه نثبت أنه اللي هو الـ T star بساوي T 
+
+299
+00:23:35,160 --> 00:23:40,400
+inverse بكون خلصنا بكون أثبتنا أنه T is unitary
+
+300
+00:23:40,820 --> 00:23:44,500
+واضح؟ طيب، شوفوا الآن اللي ضال اللي بدأت بيقولكوا
+
+301
+00:23:44,500 --> 00:23:48,720
+أنه T Star بيساوي T Inverse من الـ Isometry الآن،
+
+302
+00:23:48,720 --> 00:23:52,440
+تشوفوا الآن T Star في Txa و في X، إيش بيساوي؟
+
+303
+00:23:52,440 --> 00:23:57,360
+انجلها عادية هنا، بيصير Tx و Tx، واضح؟ ما هي عنده
+
+304
+00:23:57,360 --> 00:24:04,500
+اللي هي TX و TX بيساوي X و X لإيزومتري ماشي طيب الـ
+
+305
+00:24:04,500 --> 00:24:08,160
+X و X إذا صار I X و منه X إذا صار هذا الكلام صحيح
+
+306
+00:24:08,160 --> 00:24:12,410
+لكل X في الدنيا إذا الـ I إيش هتساوي T Star في T أو
+
+307
+00:24:12,410 --> 00:24:17,610
+بالتفصيل بنجل هذه هنا و بيصير T star في T ناقص I X
+
+308
+00:24:17,610 --> 00:24:20,770
+بيساوي X لكل X و من اللمة اللي بنستخدمها دائما 
+
+309
+00:24:20,770 --> 00:24:24,970
+هيكون اللي هو هذا بيساوي إيه؟ بيساوي صفر إذا صار
+
+310
+00:24:24,970 --> 00:24:30,850
+عندي T star في T اللي هو بيساوي الـ identity، ماشي؟
+
+311
+00:24:30,850 --> 00:24:34,530
+الآن تعالوا احسبوا T في T star
+
+312
+00:24:38,510 --> 00:24:46,570
+الثانية هي similar لزيها و سهلة تفت
+
+313
+00:24:46,570 --> 00:24:55,180
+تستار تفت تستار تفت تستار الآن بدي أجيب T Star في T 
+
+314
+00:24:55,180 --> 00:24:59,500
+عشان أستخدمها من اللي فوق فبصير T في T Star مع بعض
+
+315
+00:24:59,500 --> 00:25:03,420
+و T في T Inverse هدولة الـ identity فبصير T في الـ
+
+316
+00:25:03,420 --> 00:25:06,680
+identity في T Inverse بصير T في T Inverse و يساوي 
+
+317
+00:25:06,680 --> 00:25:09,220
+الـ identity إذا طلعت برضه T في T Star بيساوي الـ
+
+318
+00:25:09,220 --> 00:25:12,180
+identity إذا من الجهتين T Star في T بيساوي الـ
+
+319
+00:25:12,180 --> 00:25:15,960
+identity و T في T Star بيساوي الـ identity إذا صارت
+
+320
+00:25:15,960 --> 00:25:20,570
+هذه T Star هي الـ inverse إذا صارت P star يبقى 17
+
+321
+00:25:20,570 --> 00:25:24,110
+versus So T is unitary The converse is clear قولنا 
+
+322
+00:25:24,110 --> 00:25:37,590
+إيش معنى الـ Converse ارجعلي على التلخيص طيب
+
+323
+00:25:37,590 --> 00:25:41,110
+الآن
+
+324
+00:25:41,110 --> 00:25:43,710
+المثال أو الـ remark الأخيرة
+
+325
+00:25:46,190 --> 00:25:53,570
+بتقول إيه؟ ايزيومتريك لحالها لتكفل أن تكون إيه
+
+326
+00:25:53,570 --> 00:25:57,250
+شمالها؟ Unitary لازم تحطلها زججة زججة يعني أن هي 
+
+327
+00:25:57,250 --> 00:26:01,940
+surjective الآن الـ Geometric Operators need not be
+
+328
+00:26:01,940 --> 00:26:05,620
+unitary وخد مثال بدي أجيبك مثال أكيد مش subjective
+
+329
+00:26:05,620 --> 00:26:10,080
+بس هاي كل الجزء الآن consider the bounded linear
+
+330
+00:26:10,080 --> 00:26:15,220
+operator T من L2 لعند L2 given by بس بيعملني shift
+
+331
+00:26:15,220 --> 00:26:19,720
+shift operator بيشتد اللي هو الـ XI1 XI2 XI3
+
+332
+00:26:19,720 --> 00:26:23,980
+وبيعمل له shift لقدام شوية و بيحط الـ zero في الـ
+
+333
+00:26:23,980 --> 00:26:28,050
+entry الأول و بعدين بيبقوا ماشي زي ما هو إذا الـ T
+
+334
+00:26:28,050 --> 00:26:30,970
+of XI واحد XI اثنين XI تلعب تلعب إلى ما لا نهاية
+
+335
+00:26:30,970 --> 00:26:35,130
+بيساوي Zero XI واحد وXI اثنين إلى ما لا نهاية لأن 
+
+336
+00:26:35,130 --> 00:26:39,230
+it is easy to see that T is an isometric سهل خالص
+
+337
+00:26:39,230 --> 00:26:43,290
+خدوا الـ TX، إيش هو الـ TX؟ هو لحاله طالع ايزومتري 
+
+338
+00:26:43,290 --> 00:26:49,550
+شوفوا 
+
+339
+00:26:49,550 --> 00:26:51,890
+كيف بيطلع Automatic Isometry
+
+340
+00:26:57,570 --> 00:27:01,790
+صلى على النبي عليه الصلاة والسلام اللهم صل على
+
+341
+00:27:01,790 --> 00:27:08,890
+سيدنا محمد norm الـ T XI 1 XI 2 إلى ما لا نهاية
+
+342
+00:27:08,890 --> 00:27:15,130
+اليد اللي هو جوا من الـ X بساوي اللي هو norm T XI 1
+
+343
+00:27:15,130 --> 00:27:20,600
+بساوي 0 XI 1 XI 2 إلى ما لا نهاية وهذا الـ norm هيش
+
+344
+00:27:20,600 --> 00:27:26,320
+فالـ summation لـ XI I سواء summation لـ XI I تربيع
+
+345
+00:27:26,320 --> 00:27:30,760
+I من واحد إلى ما لا نهاية الكل أص نص لأنه أول واحد
+
+346
+00:27:30,760 --> 00:27:35,940
+صفر فيها اللي هو عبارة عن مين norm من الـ X ماشي 
+
+347
+00:27:35,940 --> 00:27:41,780
+إذا صار اللي هو isometric إذا الآن إذا T is an 
+
+348
+00:27:41,780 --> 00:27:49,070
+isometric But T is not onto مدام مش onto ده متحكوش
+
+349
+00:27:49,070 --> 00:27:55,530
+عن الـ unitary But T is not onto for example خد
+
+350
+00:27:55,530 --> 00:28:01,430
+اللي هو أقصى و آخد و أقول لك آخد الواحد و الصفر و
+
+351
+00:28:01,430 --> 00:28:07,650
+الصفر و الصفر إلى ما لنهاية element نقلته في TX
+
+352
+00:28:07,650 --> 00:28:13,960
+بتساوي هذآ يمكن لإن أي و أي TX تبتدأ تكون صورتها
+
+353
+00:28:13,960 --> 00:28:17,400
+أولها Zero و بعدين نحط اللي بدك إياه و هذا مش Zero
+
+354
+00:28:17,400 --> 00:28:21,160
+إذا مش on to طبعا هو بيقولك T is not on to where 
+
+355
+00:28:21,160 --> 00:28:25,360
+there is XI واحد و XI اثنين و XI واحد ده ساوي صفر 
+
+356
+00:28:25,360 --> 00:28:28,960
+but there is no X element in L2 بحيث أنه TX 
+
+357
+00:28:28,960 --> 00:28:32,860
+بالساوي XI واحد لإن هو بعمل shift و بخلي أول واحد
+
+358
+00:28:32,860 --> 00:28:38,050
+اسمه hence we have an isometric which is not onto
+
+359
+00:28:38,050 --> 00:28:41,690
+so it is not unitary لأن الـ unitary عشان يكون
+
+360
+00:28:41,690 --> 00:28:47,370
+unitary لازم يكون say adjective و هو isometric 
+
+361
+00:28:47,370 --> 00:28:54,530
+أو لو T inverse بسبب T star unitary بتكون
+
+362
+00:28:54,530 --> 00:29:00,670
+اللي هي adjective زي T inverse بسبب T star مبارك 
+
+363
+00:29:00,670 --> 00:29:02,290
+الله فيكم و إلى لقاء آخر 
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mRYCDgWMxU8_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mRYCDgWMxU8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..4cf27fddf610f334deedb1b078ab5c5cd26b4035
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mRYCDgWMxU8_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 1169, "start": 5.03, "end": 11.69, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى آله وصحبه أجمعين", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 19753, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957], "avg_logprob": -0.11049106850155763, "compression_ratio": 1.7719298245614035, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 5.03, "end": 5.39, "word": "بسم", "probability": 0.76513671875}, {"start": 5.39, "end": 5.59, "word": " الله", "probability": 0.9658203125}, {"start": 5.59, "end": 5.95, "word": " الرحمن", "probability": 0.9765625}, {"start": 5.95, "end": 6.37, "word": " الرحيم", "probability": 0.9951171875}, {"start": 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اللي", "probability": 0.880859375}, {"start": 27.57, "end": 28.33, "word": " هو", "probability": 0.95703125}, {"start": 28.33, "end": 29.57, "word": " انواع", "probability": 0.9143880208333334}, {"start": 29.57, "end": 29.89, "word": " ال", "probability": 0.95263671875}, {"start": 29.89, "end": 30.37, "word": " operators", "probability": 0.89013671875}, {"start": 30.37, "end": 30.93, "word": " اللي", "probability": 0.906982421875}, {"start": 30.93, "end": 31.71, "word": " هنحكي", "probability": 0.95185546875}, {"start": 31.71, "end": 31.99, "word": " عنها", "probability": 0.98974609375}, {"start": 31.99, "end": 32.15, "word": " اللي", "probability": 0.935302734375}, {"start": 32.15, "end": 32.33, "word": " هي", "probability": 0.63525390625}, {"start": 32.33, "end": 32.55, "word": " self", "probability": 0.9345703125}, {"start": 32.55, "end": 33.11, "word": "-adjoint", "probability": 0.8444010416666666}, {"start": 33.11, "end": 34.25, "word": " وunitary", "probability": 0.7833658854166666}, {"start": 34.25, "end": 34.91, "word": " وnormal", "probability": 0.782470703125}, {"start": 34.91, "end": 35.41, "word": " operators", "probability": 0.8369140625}, {"start": 35.41, "end": 36.01, "word": " المحاضرة", "probability": 0.9879150390625}, {"start": 36.01, "end": 36.51, "word": " الماضية", "probability": 0.9908854166666666}, {"start": 36.51, "end": 37.29, "word": " عرفنا", "probability": 0.9064127604166666}, {"start": 37.29, "end": 37.47, "word": " شو", "probability": 0.89111328125}, {"start": 37.47, "end": 37.83, "word": " معنات", "probability": 0.8414713541666666}, {"start": 37.83, "end": 38.35, "word": " a", "probability": 0.1947021484375}, {"start": 38.35, "end": 38.67, "word": " joint", "probability": 0.91162109375}, {"start": 38.67, "end": 39.17, "word": " operator", "probability": 0.94677734375}], "temperature": 1.0}, {"id": 3, "seek": 6253, "start": 39.99, "end": 62.53, "text": "الان هنحكي عن شو معناه الـ self-adjoint operator شو معناه الـ normal operator شو معناه الـ unitary operator و بالمناسبة في طبعا احنا هذه الأسماء مرت علينا في الجبر الخطي فكلها مقابل في الجبر الخطي اصلا ال matrix في الآخر اللي هو احنا بنقدر نعمل نشتغل و كأنه", "tokens": [6027, 7649, 8032, 1863, 5016, 4117, 1829, 18871, 13412, 2407, 20449, 8315, 3224, 2423, 39184, 2698, 12, 345, 48613, 12973, 13412, 2407, 20449, 8315, 3224, 2423, 39184, 2710, 12973, 13412, 2407, 20449, 8315, 3224, 2423, 39184, 517, 4109, 12973, 4032, 20666, 2304, 8315, 35457, 3660, 8978, 23032, 3555, 3615, 995, 1975, 5016, 8315, 29538, 16247, 38251, 16606, 3714, 43500, 25894, 8315, 8978, 25724, 26890, 33962, 9566, 1829, 6156, 28820, 11296, 3714, 4587, 16758, 1211, 8978, 25724, 26890, 33962, 9566, 1829, 1975, 9381, 15040, 2423, 8141, 8978, 6024, 95, 34740, 13672, 1829, 31439, 1975, 5016, 8315, 44945, 28543, 2288, 8717, 25957, 1211, 8717, 8592, 2655, 17082, 1211, 4032, 9122, 33456, 3224], "avg_logprob": -0.2347972948808928, "compression_ratio": 1.8475336322869955, "no_speech_prob": 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"start": 354.79, "end": 359.95, "text": "هذا مثال على الـ Normal operator need not to be self-adjoint normally تبقى اطلع على فوق", "tokens": [3224, 15730, 50113, 6027, 15844, 2423, 39184, 21277, 12973, 643, 406, 281, 312, 2698, 12, 345, 48613, 5646, 6055, 3555, 4587, 7578, 1975, 9566, 1211, 3615, 15844, 6156, 30543], "avg_logprob": -0.4091145763794581, "compression_ratio": 1.0458715596330275, "no_speech_prob": 0.0, "words": [{"start": 354.78999999999996, "end": 355.27, "word": "هذا", "probability": 0.8828125}, {"start": 355.27, "end": 355.69, "word": " مثال", "probability": 0.970703125}, {"start": 355.69, "end": 355.87, "word": " على", "probability": 0.75341796875}, {"start": 355.87, "end": 356.11, "word": " الـ", "probability": 0.56317138671875}, {"start": 356.11, "end": 356.33, "word": " Normal", "probability": 0.73974609375}, {"start": 356.33, "end": 356.83, "word": " operator", "probability": 0.51318359375}, {"start": 356.83, "end": 357.11, "word": " need", "probability": 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..", "probability": 0.79150390625}, {"start": 438.67, "end": 439.07, "word": " إذن", "probability": 0.9051106770833334}, {"start": 439.07, "end": 439.17, "word": " ..", "probability": 0.9501953125}, {"start": 439.17, "end": 439.45, "word": " إذن", "probability": 0.9503580729166666}, {"start": 439.45, "end": 440.15, "word": " النظرية", "probability": 0.966796875}, {"start": 440.15, "end": 440.53, "word": " الجزء", "probability": 0.9806315104166666}, {"start": 440.53, "end": 440.71, "word": " B", "probability": 0.62158203125}, {"start": 440.71, "end": 441.01, "word": " هذا", "probability": 0.75927734375}, {"start": 441.01, "end": 441.31, "word": " وين", "probability": 0.945068359375}, {"start": 441.31, "end": 441.85, "word": " بيحدث", "probability": 0.966796875}, {"start": 441.85, "end": 442.01, "word": " في", "probability": 0.939453125}, {"start": 442.01, "end": 442.45, "word": " حالة", "probability": 0.9931640625}, {"start": 442.45, "end": 442.73, "word": " main", "probability": 0.40234375}, {"start": 442.73, "end": 443.17, "word": " H", "probability": 0.9189453125}, {"start": 443.17, "end": 443.77, "word": " is", "probability": 0.82080078125}, {"start": 443.77, "end": 444.23, "word": " complex", "probability": 0.87939453125}, {"start": 444.23, "end": 444.71, "word": " نيجي", "probability": 0.9619140625}, {"start": 444.71, "end": 445.17, "word": " لبنهم", "probability": 0.5067138671875}, {"start": 445.17, "end": 447.33, "word": " نيجي", "probability": 0.9449462890625}, {"start": 447.33, "end": 447.53, "word": " الآن", "probability": 0.791015625}], "temperature": 1.0}, {"id": 21, "seek": 46760, "start": 449.5, "end": 467.6, "text": "الـ subpose ده الـ T السلفة الـ joint تن لكل X في الـ H احسب ما يليه عشان اثبت ان الـ T X وال X الريالد ده تبت أن ال conjugate هيطلع نفسه ماشي ان انا اخد ال conjugate ل T X وال X بسوء X و T X مظبوط X و T X وT سلفة ال joint هيسوء T X و X", "tokens": [6027, 39184, 1422, 43501, 11778, 3224, 2423, 39184, 314, 21136, 46538, 3660, 2423, 39184, 7225, 6055, 1863, 5296, 28820, 1783, 8978, 2423, 39184, 389, 1975, 5016, 35457, 19446, 7251, 20292, 3224, 6225, 8592, 7649, 1975, 12984, 3555, 2655, 16472, 2423, 39184, 314, 1783, 16070, 1783, 2423, 16572, 6027, 3215, 11778, 3224, 6055, 3555, 2655, 14739, 2423, 45064, 39896, 9566, 1211, 3615, 8717, 36178, 3224, 3714, 33599, 1829, 16472, 1975, 8315, 1975, 9778, 3215, 2423, 45064, 5296, 314, 1783, 16070, 1783, 4724, 3794, 2407, 38207, 1783, 4032, 314, 1783, 3714, 19913, 3555, 2407, 9566, 1783, 4032, 314, 1783, 4032, 51, 8608, 46538, 3660, 2423, 7225, 39896, 3794, 2407, 38207, 314, 1783, 4032, 1783], "avg_logprob": -0.34706859673019, "compression_ratio": 1.7889447236180904, "no_speech_prob": 8.881092071533203e-06, "words": [{"start": 449.5, "end": 449.8, "word": "الـ", "probability": 0.419189453125}, {"start": 449.8, "end": 450.16, "word": " subpose", "probability": 0.22186279296875}, {"start": 450.16, "end": 450.38, "word": " ده", "probability": 0.736572265625}, {"start": 450.38, "end": 450.48, "word": " الـ", "probability": 0.559814453125}, {"start": 450.48, "end": 450.6, "word": " T", "probability": 0.70361328125}, {"start": 450.6, "end": 451.02, "word": " السلفة", "probability": 0.6631673177083334}, {"start": 451.02, "end": 451.12, "word": " الـ", "probability": 0.545654296875}, {"start": 451.12, "end": 451.36, "word": " joint", "probability": 0.457275390625}, {"start": 451.36, "end": 451.78, "word": " تن", "probability": 0.51312255859375}, {"start": 451.78, "end": 452.1, "word": " لكل", "probability": 0.960693359375}, {"start": 452.1, "end": 452.3, "word": " X", "probability": 0.896484375}, {"start": 452.3, "end": 452.42, "word": " في", "probability": 0.94091796875}, {"start": 452.42, "end": 452.58, "word": " الـ", "probability": 0.910400390625}, {"start": 452.58, "end": 452.8, "word": " H", "probability": 0.63818359375}, {"start": 452.8, "end": 453.42, "word": " احسب", "probability": 0.7836100260416666}, {"start": 453.42, "end": 453.6, "word": " ما", 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464.1, "end": 464.46, "word": " X", "probability": 0.94873046875}, {"start": 464.46, "end": 464.98, "word": " وT", "probability": 0.68798828125}, {"start": 464.98, "end": 465.42, "word": " سلفة", "probability": 0.9396158854166666}, {"start": 465.42, "end": 465.5, "word": " ال", "probability": 0.7724609375}, {"start": 465.5, "end": 465.9, "word": " joint", "probability": 0.55615234375}, {"start": 465.9, "end": 466.84, "word": " هيسوء", "probability": 0.861083984375}, {"start": 466.84, "end": 467.0, "word": " T", "probability": 0.96533203125}, {"start": 467.0, "end": 467.2, "word": " X", "probability": 0.87548828125}, {"start": 467.2, "end": 467.34, "word": " و", "probability": 0.91943359375}, {"start": 467.34, "end": 467.6, "word": " X", "probability": 0.86083984375}], "temperature": 1.0}, {"id": 22, "seek": 49621, "start": 468.19, "end": 496.21, "text": "بس هيفضّوهم إذا صار عندي اللي هو TX و X is real الآن ال B suppose that H is complex هستخدم شكلي النظرية تبعت المرة اللي فاتت اللي مال اللي فاتت للمحاضر اللي فاتت suppose that H is complex and TX و X أشماله is real لكل X element in H هذا الفرضية then شوف كيف يثبت لك إنه اللي هو ال T بتساوي ال T star", "tokens": [3555, 3794, 8032, 33911, 11242, 11703, 2407, 16095, 11933, 15730, 20328, 9640, 18871, 16254, 13672, 1829, 31439, 314, 55, 4032, 1783, 307, 957, 6024, 48506, 2423, 363, 7297, 300, 389, 307, 3997, 8032, 14851, 9778, 40448, 13412, 28820, 1829, 28239, 19913, 2288, 10632, 6055, 3555, 34268, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 13672, 1829, 3714, 6027, 13672, 1829, 6156, 9307, 2655, 5296, 19528, 5016, 46958, 2288, 13672, 1829, 6156, 9307, 2655, 7297, 300, 389, 307, 3997, 293, 314, 55, 4032, 1783, 5551, 8592, 2304, 6027, 3224, 307, 957, 5296, 28820, 1783, 4478, 294, 389, 23758, 27188, 43042, 10632, 550, 13412, 38688, 9122, 33911, 7251, 12984, 3555, 2655, 5296, 4117, 36145, 3224, 13672, 1829, 31439, 2423, 314, 39894, 3794, 995, 45865, 2423, 314, 3543], "avg_logprob": -0.25487499713897704, "compression_ratio": 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real", "probability": 0.537109375}, {"start": 472.91, "end": 473.93, "word": " الآن", "probability": 0.57257080078125}, {"start": 473.93, "end": 474.29, "word": " ال", "probability": 0.703125}, {"start": 474.29, "end": 474.65, "word": " B", "probability": 0.42529296875}, {"start": 474.65, "end": 475.47, "word": " suppose", "probability": 0.72607421875}, {"start": 475.47, "end": 476.11, "word": " that", "probability": 0.90869140625}, {"start": 476.11, "end": 476.47, "word": " H", "probability": 0.8173828125}, {"start": 476.47, "end": 476.81, "word": " is", "probability": 0.9453125}, {"start": 476.81, "end": 477.29, "word": " complex", "probability": 0.8486328125}, {"start": 477.29, "end": 478.17, "word": " هستخدم", "probability": 0.9195556640625}, {"start": 478.17, "end": 478.85, "word": " شكلي", "probability": 0.6863606770833334}, {"start": 478.85, "end": 479.65, "word": " النظرية", "probability": 0.93994140625}, {"start": 479.65, "end": 479.91, "word": " تبعت", "probability": 0.641357421875}, {"start": 479.91, "end": 480.15, "word": " المرة", "probability": 0.8984375}, {"start": 480.15, "end": 480.25, "word": " اللي", "probability": 0.884765625}, {"start": 480.25, "end": 480.63, "word": " فاتت", "probability": 0.9928385416666666}, {"start": 480.63, "end": 480.87, "word": " اللي", "probability": 0.6146240234375}, {"start": 480.87, "end": 481.13, "word": " مال", "probability": 0.5960693359375}, {"start": 481.13, "end": 481.25, "word": " اللي", "probability": 0.97216796875}, {"start": 481.25, "end": 481.77, "word": " فاتت", "probability": 0.9928385416666666}, {"start": 481.77, "end": 482.59, "word": " للمحاضر", "probability": 0.760205078125}, {"start": 482.59, "end": 482.71, "word": " اللي", "probability": 0.995361328125}, {"start": 482.71, "end": 483.31, "word": " فاتت", "probability": 0.9933268229166666}, {"start": 483.31, "end": 483.99, "word": " suppose", "probability": 0.732421875}, {"start": 483.99, "end": 484.61, "word": " that", "probability": 0.95166015625}, {"start": 484.61, "end": 485.01, "word": " H", "probability": 0.935546875}, {"start": 485.01, "end": 485.23, "word": " is", "probability": 0.9638671875}, {"start": 485.23, "end": 485.67, "word": " complex", "probability": 0.873046875}, {"start": 485.67, "end": 485.99, "word": " and", "probability": 0.9111328125}, {"start": 485.99, "end": 486.41, "word": " TX", "probability": 0.908447265625}, {"start": 486.41, "end": 486.55, "word": " و", "probability": 0.955078125}, {"start": 486.55, "end": 486.71, "word": " X", "probability": 0.7421875}, {"start": 486.71, "end": 487.41, "word": " أشماله", "probability": 0.7487060546875}, {"start": 487.41, "end": 488.01, "word": " is", "probability": 0.94775390625}, {"start": 488.01, "end": 488.39, "word": " real", "probability": 0.94482421875}, {"start": 488.39, "end": 488.95, "word": " لكل", "probability": 0.97265625}, {"start": 488.95, "end": 489.43, "word": " X", "probability": 0.962890625}, {"start": 489.43, "end": 489.91, "word": " element", "probability": 0.9404296875}, {"start": 489.91, "end": 490.13, "word": " in", "probability": 0.93017578125}, {"start": 490.13, "end": 490.29, "word": " H", "probability": 0.986328125}, {"start": 490.29, "end": 490.53, "word": " هذا", "probability": 0.76904296875}, {"start": 490.53, "end": 491.13, "word": " الفرضية", "probability": 0.9441731770833334}, {"start": 491.13, "end": 491.93, "word": " then", "probability": 0.68212890625}, {"start": 491.93, "end": 492.89, "word": " شوف", "probability": 0.954833984375}, {"start": 492.89, "end": 493.07, "word": " كيف", "probability": 0.953857421875}, {"start": 493.07, "end": 493.45, "word": " يثبت", "probability": 0.84765625}, {"start": 493.45, "end": 493.67, "word": " لك", "probability": 0.70703125}, {"start": 493.67, "end": 494.09, "word": " إنه", "probability": 0.562255859375}, {"start": 494.09, "end": 494.33, "word": " اللي", "probability": 0.939697265625}, {"start": 494.33, "end": 494.63, "word": " هو", "probability": 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"end": 539.79, "text": "الان عند خدق الآن السفر بساوي T X و X ناقص T Star X و X نجلناها ما هو على طول احنا جابلنا كلنا مادام هذا بساوي و هذا دايما ايضا على طول بساوي T Star بس خلينا الان نبسطها للاخر الان صار عند T X و X ناقص T Star X و X بتساوي سفر و يساوي", "tokens": [6027, 7649, 43242, 16490, 3215, 4587, 6024, 48506, 21136, 5172, 2288, 4724, 3794, 995, 45865, 314, 1783, 4032, 1783, 8717, 995, 4587, 9381, 314, 5705, 1783, 4032, 1783, 8717, 7435, 1211, 8315, 11296, 19446, 31439, 15844, 23032, 12610, 1975, 5016, 8315, 10874, 16758, 1211, 8315, 28242, 8315, 3714, 18513, 10943, 23758, 4724, 3794, 995, 45865, 4032, 23758, 11778, 47302, 15042, 1975, 1829, 11242, 995, 15844, 23032, 12610, 4724, 3794, 995, 45865, 314, 5705, 4724, 3794, 16490, 1211, 9957, 995, 2423, 7649, 8717, 3555, 3794, 9566, 11296, 24976, 47283, 2288, 2423, 7649, 20328, 9640, 43242, 314, 1783, 4032, 1783, 8717, 995, 4587, 9381, 314, 5705, 1783, 4032, 1783, 39894, 3794, 995, 45865, 8608, 5172, 2288, 4032, 7251, 3794, 995, 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"probability": 0.9684244791666666}, {"start": 730.69, "end": 730.87, "word": " من", "probability": 0.990234375}, {"start": 730.87, "end": 731.07, "word": " رأس", "probability": 0.98974609375}, {"start": 731.07, "end": 731.43, "word": " الدور", "probability": 0.99169921875}, {"start": 731.43, "end": 732.21, "word": " و", "probability": 0.90234375}, {"start": 732.21, "end": 732.55, "word": " أنا", "probability": 0.83154296875}, {"start": 732.55, "end": 733.23, "word": " الآن", "probability": 0.706298828125}, {"start": 733.23, "end": 733.91, "word": " مفترض", "probability": 0.99169921875}, {"start": 733.91, "end": 734.19, "word": " S", "probability": 0.51025390625}, {"start": 734.19, "end": 734.29, "word": " T", "probability": 0.64990234375}, {"start": 734.29, "end": 734.43, "word": " إيش", "probability": 0.7257486979166666}, {"start": 734.43, "end": 734.95, "word": " بيساوي", "probability": 0.825341796875}, {"start": 734.95, "end": 735.61, "word": " P", "probability": 0.270751953125}, {"start": 735.61, "end": 735.91, "word": " S", "probability": 0.97265625}, {"start": 735.91, "end": 736.39, "word": " إذا", "probability": 0.876708984375}, {"start": 736.39, "end": 736.65, "word": " T", "probability": 0.673828125}, {"start": 736.65, "end": 736.93, "word": " فاس", "probability": 0.79833984375}, {"start": 736.93, "end": 737.09, "word": " إيش", "probability": 0.9708658854166666}, {"start": 737.09, "end": 737.67, "word": " هتساوي", "probability": 0.89228515625}, {"start": 737.67, "end": 738.55, "word": " S", "probability": 0.822265625}, {"start": 738.55, "end": 738.77, "word": " في", "probability": 0.204833984375}, {"start": 738.77, "end": 738.91, "word": " T", "probability": 0.97607421875}, {"start": 738.91, "end": 739.41, "word": " إذا", "probability": 0.957763671875}, {"start": 739.41, "end": 739.69, "word": " صار", "probability": 0.82861328125}, {"start": 739.69, "end": 739.87, "word": " S", "probability": 0.9697265625}, {"start": 739.87, "end": 740.05, "word": " في", "probability": 0.94189453125}, {"start": 740.05, "end": 740.17, "word": " T", "probability": 0.98583984375}, {"start": 740.17, "end": 740.49, "word": " بيساوي", "probability": 0.95703125}, {"start": 740.49, "end": 740.73, "word": " S", "probability": 0.98681640625}, {"start": 740.73, "end": 740.97, "word": " في", "probability": 0.97216796875}, {"start": 740.97, "end": 741.17, "word": " T", "probability": 0.98681640625}, {"start": 741.17, "end": 741.43, "word": " إيش", "probability": 0.9033203125}, {"start": 741.43, "end": 741.75, "word": " لكل", "probability": 0.806884765625}, {"start": 741.75, "end": 742.17, "word": " Star", "probability": 0.79931640625}, {"start": 742.17, "end": 742.87, "word": " إذا", "probability": 0.717529296875}, {"start": 742.87, "end": 743.55, "word": " S", "probability": 0.62109375}, {"start": 743.55, "end": 743.89, "word": " T", "probability": 0.97607421875}, {"start": 743.89, "end": 744.75, "word": " is", "probability": 0.56005859375}, {"start": 744.75, "end": 745.35, "word": " self", "probability": 0.86767578125}, {"start": 745.35, "end": 746.67, "word": "-adjoint", "probability": 0.9410807291666666}, {"start": 746.67, "end": 747.49, "word": " هذه", "probability": 0.483642578125}, {"start": 747.49, "end": 747.73, "word": " اللي", "probability": 0.9736328125}, {"start": 747.73, "end": 747.91, "word": " هي", "probability": 0.95458984375}, {"start": 747.91, "end": 748.29, "word": " theorem", "probability": 0.77392578125}], "temperature": 1.0}, {"id": 33, "seek": 77068, "start": 751.34, "end": 770.68, "text": "اللي هو تلاتة عشر خمسة الان تخليني تخليني على النظرية اللي قبلها theorem تلاتة عشر خمسة let TN be a sequence of bounded linear self and joint linear operators وTN من H لعند H انها ال participate H", "tokens": [6027, 20292, 31439, 6055, 1211, 9307, 3660, 6225, 46309, 16490, 2304, 3794, 3660, 2423, 7649, 6055, 9778, 1211, 9957, 1829, 6055, 9778, 1211, 9957, 1829, 15844, 28239, 19913, 2288, 10632, 13672, 1829, 12174, 36150, 11296, 20904, 6055, 1211, 9307, 3660, 6225, 46309, 16490, 2304, 3794, 3660, 718, 314, 45, 312, 257, 8310, 295, 37498, 8213, 2698, 293, 7225, 8213, 19077, 4032, 51, 45, 9154, 389, 5296, 3615, 41260, 389, 16472, 11296, 2423, 8197, 389], "avg_logprob": -0.3275000143051148, "compression_ratio": 1.4972677595628416, "no_speech_prob": 3.4570693969726562e-06, "words": [{"start": 751.34, "end": 751.78, "word": "اللي", "probability": 0.5439453125}, {"start": 751.78, "end": 752.2, "word": " هو", "probability": 0.9541015625}, {"start": 752.2, "end": 753.18, "word": " تلاتة", "probability": 0.78485107421875}, {"start": 753.18, "end": 753.48, "word": " عشر", "probability": 0.83251953125}, {"start": 753.48, "end": 754.74, "word": " خمسة", "probability": 0.93359375}, {"start": 754.74, "end": 755.36, "word": " الان", "probability": 0.576904296875}, {"start": 755.36, "end": 756.38, "word": " تخليني", "probability": 0.727685546875}, {"start": 756.38, "end": 757.04, "word": " تخليني", "probability": 0.7407958984375}, {"start": 757.04, "end": 757.2, "word": " على", "probability": 0.57470703125}, {"start": 757.2, "end": 757.7, "word": " النظرية", "probability": 0.8668212890625}, {"start": 757.7, "end": 757.8, "word": " اللي", "probability": 0.784423828125}, {"start": 757.8, "end": 758.66, "word": " قبلها", "probability": 0.5853678385416666}, {"start": 758.66, "end": 759.36, "word": " theorem", "probability": 0.22119140625}, {"start": 759.36, "end": 759.92, "word": " تلاتة", "probability": 0.876953125}, {"start": 759.92, "end": 760.14, "word": " عشر", "probability": 0.980712890625}, {"start": 760.14, "end": 761.2, "word": " خمسة", "probability": 0.992919921875}, {"start": 761.2, "end": 761.74, "word": " let", "probability": 0.61865234375}, {"start": 761.74, "end": 762.4, "word": " TN", "probability": 0.6690673828125}, {"start": 762.4, "end": 763.38, "word": " be", "probability": 0.74853515625}, {"start": 763.38, "end": 763.58, "word": " a", "probability": 0.94921875}, {"start": 763.58, "end": 763.98, "word": " sequence", "probability": 0.96875}, {"start": 763.98, "end": 764.16, "word": " of", "probability": 0.96875}, {"start": 764.16, "end": 764.42, "word": " bounded", "probability": 0.8017578125}, {"start": 764.42, "end": 764.82, "word": " linear", "probability": 0.51611328125}, {"start": 764.82, "end": 765.08, "word": " self", "probability": 0.362060546875}, {"start": 765.08, "end": 765.28, "word": " and", "probability": 0.82958984375}, {"start": 765.28, "end": 765.52, "word": " joint", "probability": 0.90869140625}, {"start": 765.52, "end": 765.84, "word": " linear", "probability": 0.92578125}, {"start": 765.84, "end": 766.46, "word": " operators", "probability": 0.94970703125}, {"start": 766.46, "end": 767.78, "word": " وTN", "probability": 0.7576497395833334}, {"start": 767.78, "end": 767.96, "word": " من", "probability": 0.98486328125}, {"start": 767.96, "end": 768.18, "word": " H", "probability": 0.9189453125}, {"start": 768.18, "end": 768.48, "word": " لعند", "probability": 0.8365885416666666}, {"start": 768.48, "end": 768.88, "word": " H", "probability": 0.97216796875}, {"start": 768.88, "end": 769.7, "word": " انها", "probability": 0.502197265625}, {"start": 769.7, "end": 769.82, "word": " ال", "probability": 0.9443359375}, {"start": 769.82, "end": 770.12, "word": " participate", "probability": 0.211669921875}, {"start": 770.12, "end": 770.68, "word": " H", "probability": 0.8876953125}], "temperature": 1.0}, {"id": 34, "seek": 79715, "start": 772.27, "end": 797.15, "text": "suppose that TN بتروح لـ T S اللي هو that is norm of TN بتروح لنخستي بتروح لصفر where this norm is the norm on the space BHWH عارفينه طبعا يعني then T is a bounded self-adjoint linear operator يعني و كأنه بيقول اللي خلّي بيقول انه اللي هو sequence of sequence of self-adjoint operators", "tokens": [36622, 541, 300, 314, 45, 39894, 32887, 5016, 5296, 39184, 314, 318, 13672, 1829, 31439, 300, 307, 2026, 295, 314, 45, 39894, 32887, 5016, 5296, 1863, 9778, 14851, 1829, 39894, 32887, 5016, 5296, 9381, 5172, 2288, 689, 341, 2026, 307, 264, 2026, 322, 264, 1901, 40342, 28206, 6225, 9640, 5172, 9957, 3224, 23032, 3555, 3615, 995, 37495, 22653, 550, 314, 307, 257, 37498, 2698, 12, 345, 48613, 8213, 12973, 37495, 22653, 4032, 9122, 33456, 3224, 4724, 1829, 39648, 13672, 1829, 16490, 1211, 11703, 1829, 4724, 1829, 39648, 16472, 3224, 13672, 1829, 31439, 8310, 295, 8310, 295, 2698, 12, 345, 48613, 19077], "avg_logprob": -0.39859069474771913, "compression_ratio": 1.6255506607929515, "no_speech_prob": 1.3113021850585938e-06, "words": [{"start": 772.27, "end": 772.91, "word": "suppose", "probability": 0.546630859375}, {"start": 772.91, "end": 773.09, "word": " that", "probability": 0.30419921875}, {"start": 773.09, "end": 773.41, "word": " TN", "probability": 0.46307373046875}, {"start": 773.41, "end": 773.73, "word": " بتروح", "probability": 0.7198486328125}, {"start": 773.73, "end": 773.93, "word": " لـ", "probability": 0.605224609375}, {"start": 773.93, "end": 774.19, "word": " T", "probability": 0.7021484375}, {"start": 774.19, "end": 774.89, "word": " S", "probability": 0.2301025390625}, {"start": 774.89, "end": 775.81, "word": " اللي", "probability": 0.7022705078125}, {"start": 775.81, "end": 776.19, "word": " هو", "probability": 0.98974609375}, {"start": 776.19, "end": 779.19, "word": " that", "probability": 0.3291015625}, {"start": 779.19, "end": 779.49, "word": " is", "probability": 0.92626953125}, {"start": 779.49, "end": 779.81, "word": " norm", "probability": 0.5849609375}, {"start": 779.81, "end": 779.91, "word": " of", "probability": 0.2490234375}, {"start": 779.91, "end": 780.17, "word": " TN", "probability": 0.5538330078125}, {"start": 780.17, "end": 780.47, "word": " بتروح", "probability": 0.77197265625}, {"start": 780.47, "end": 781.01, "word": " لنخستي", "probability": 0.529833984375}, {"start": 781.01, "end": 781.27, "word": " بتروح", "probability": 0.7872721354166666}, {"start": 781.27, "end": 781.67, "word": " لصفر", "probability": 0.7587890625}, {"start": 781.67, "end": 781.91, "word": " where", "probability": 0.76171875}, {"start": 781.91, "end": 782.15, "word": " this", "probability": 0.9365234375}, {"start": 782.15, "end": 782.51, "word": " norm", "probability": 0.8837890625}, {"start": 782.51, "end": 782.79, "word": " is", "probability": 0.94091796875}, {"start": 782.79, "end": 782.99, "word": " the", "probability": 0.83251953125}, {"start": 782.99, "end": 783.35, "word": " norm", "probability": 0.96826171875}, {"start": 783.35, "end": 783.65, "word": " on", "probability": 0.78515625}, {"start": 783.65, "end": 783.77, "word": " the", "probability": 0.8857421875}, {"start": 783.77, "end": 784.05, "word": " space", "probability": 0.92431640625}, {"start": 784.05, "end": 784.79, "word": " BHWH", "probability": 0.217041015625}, {"start": 784.79, "end": 785.47, "word": " عارفينه", "probability": 0.9107421875}, {"start": 785.47, "end": 785.73, "word": " طبعا", "probability": 0.9862060546875}, {"start": 785.73, "end": 785.91, "word": " يعني", "probability": 0.5313720703125}, {"start": 785.91, "end": 786.59, "word": " then", "probability": 0.64697265625}, {"start": 786.59, "end": 786.95, "word": " T", "probability": 0.95458984375}, {"start": 786.95, "end": 787.17, "word": " is", "probability": 0.9462890625}, {"start": 787.17, "end": 787.31, "word": " a", "probability": 0.310546875}, {"start": 787.31, "end": 787.61, "word": " bounded", "probability": 0.9423828125}, {"start": 787.61, "end": 787.91, "word": " self", "probability": 0.70849609375}, {"start": 787.91, "end": 788.29, "word": "-adjoint", "probability": 0.8341471354166666}, {"start": 788.29, "end": 788.59, "word": " linear", "probability": 0.81982421875}, {"start": 788.59, "end": 788.97, "word": " operator", "probability": 0.873046875}, {"start": 788.97, "end": 789.97, "word": " يعني", "probability": 0.54791259765625}, {"start": 789.97, "end": 790.07, "word": " و", "probability": 0.9013671875}, {"start": 790.07, "end": 790.39, "word": " كأنه", "probability": 0.6824544270833334}, {"start": 790.39, "end": 790.71, "word": " بيقول", "probability": 0.8421223958333334}, {"start": 790.71, "end": 790.89, "word": " اللي", "probability": 0.59613037109375}, {"start": 790.89, "end": 791.41, "word": " خلّي", "probability": 0.74200439453125}, {"start": 791.41, "end": 791.99, "word": " بيقول", "probability": 0.7926432291666666}, {"start": 791.99, "end": 792.81, "word": " انه", "probability": 0.646728515625}, {"start": 792.81, "end": 793.03, "word": " اللي", "probability": 0.958984375}, {"start": 793.03, "end": 793.17, "word": " هو", "probability": 0.9697265625}, {"start": 793.17, "end": 793.79, "word": " sequence", "probability": 0.90673828125}, {"start": 793.79, "end": 794.15, "word": " of", "probability": 0.91943359375}, {"start": 794.15, "end": 795.17, "word": " sequence", "probability": 0.5126953125}, {"start": 795.17, "end": 795.85, "word": " of", "probability": 0.9658203125}, {"start": 795.85, "end": 796.13, "word": " self", "probability": 0.916015625}, {"start": 796.13, "end": 796.55, "word": "-adjoint", "probability": 0.9305013020833334}, {"start": 796.55, "end": 797.15, "word": " operators", "probability": 0.9326171875}], "temperature": 1.0}, {"id": 35, "seek": 80437, "start": 798.47, "end": 804.37, "text": "لو converged لـ some T لازم الـ T تكون إيه أشمالها؟ self-adjoint", "tokens": [1211, 2407, 9652, 3004, 5296, 39184, 512, 314, 5296, 31377, 2304, 2423, 39184, 314, 6055, 30544, 11933, 1829, 3224, 5551, 8592, 2304, 6027, 11296, 22807, 2698, 12, 345, 48613], "avg_logprob": -0.41354167064030967, "compression_ratio": 0.9782608695652174, "no_speech_prob": 0.0, "words": [{"start": 798.47, "end": 798.93, "word": "لو", "probability": 0.91357421875}, {"start": 798.93, "end": 799.83, "word": " converged", "probability": 0.57623291015625}, {"start": 799.83, "end": 800.15, "word": " لـ", "probability": 0.771240234375}, {"start": 800.15, "end": 800.29, "word": " some", "probability": 0.161376953125}, {"start": 800.29, "end": 800.79, "word": " T", "probability": 0.828125}, {"start": 800.79, "end": 801.77, "word": " لازم", "probability": 0.9202473958333334}, {"start": 801.77, "end": 801.97, "word": " الـ", "probability": 0.718017578125}, {"start": 801.97, "end": 802.05, "word": " T", "probability": 0.88037109375}, {"start": 802.05, "end": 802.35, "word": " تكون", "probability": 0.948486328125}, {"start": 802.35, "end": 802.49, "word": " إيه", "probability": 0.7208658854166666}, {"start": 802.49, "end": 803.35, "word": " أشمالها؟", "probability": 0.6249186197916666}, {"start": 803.35, "end": 803.77, "word": " self", "probability": 0.31982421875}, {"start": 803.77, "end": 804.37, "word": "-adjoint", "probability": 0.8024088541666666}], "temperature": 1.0}, {"id": 36, "seek": 83601, "start": 807.03, "end": 836.01, "text": "معنى إيش بقول؟ لو كانت عندى اللى بقوله TN sequence of self-adjoint linear operators و هدى conveges لصم T لازم الـ T هدى إيش 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" ..", "probability": 0.297607421875}, {"start": 1103.48, "end": 1103.58, "word": " on", "probability": 0.19189453125}, {"start": 1103.58, "end": 1103.72, "word": " a", "probability": 0.98095703125}, {"start": 1103.72, "end": 1104.08, "word": " complex", "probability": 0.78662109375}, {"start": 1104.08, "end": 1104.46, "word": " Hilbert", "probability": 0.96337890625}, {"start": 1104.46, "end": 1104.86, "word": " space", "probability": 0.82763671875}, {"start": 1104.86, "end": 1105.26, "word": " H", "probability": 0.94580078125}, {"start": 1105.26, "end": 1106.1, "word": " is", "probability": 0.900390625}, {"start": 1106.1, "end": 1106.52, "word": " unitary", "probability": 0.810302734375}, {"start": 1106.52, "end": 1106.76, "word": " if", "probability": 0.87890625}, {"start": 1106.76, "end": 1106.92, "word": " and", "probability": 0.94873046875}, {"start": 1106.92, "end": 1107.06, "word": " only", "probability": 0.88671875}, {"start": 1107.06, "end": 1107.28, "word": " if", 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"probability": 0.2369384765625}, {"start": 1522.65, "end": 1523.17, "word": " converse", "probability": 0.79150390625}, {"start": 1523.17, "end": 1523.37, "word": " is", "probability": 0.96337890625}, {"start": 1523.37, "end": 1523.69, "word": " clear", "probability": 0.92822265625}, {"start": 1523.69, "end": 1524.11, "word": " قولنا", "probability": 0.6619466145833334}, {"start": 1524.11, "end": 1524.45, "word": " إيش", "probability": 0.77978515625}, {"start": 1524.45, "end": 1525.03, "word": " معناة", "probability": 0.77490234375}, {"start": 1525.03, "end": 1525.33, "word": " الـ", "probability": 0.764404296875}, {"start": 1525.33, "end": 1525.73, "word": " Converse", "probability": 0.59912109375}, {"start": 1525.73, "end": 1526.55, "word": " ارجعلي", "probability": 0.71112060546875}, {"start": 1526.55, "end": 1526.77, "word": " على", "probability": 0.8876953125}, {"start": 1526.77, "end": 1528.23, "word": " التلخيص", "probability": 0.97783203125}, {"start": 1528.23, "end": 1537.59, "word": " طيب", "probability": 0.82861328125}, {"start": 1537.59, "end": 1541.11, "word": " الآن", "probability": 0.628173828125}, {"start": 1541.11, "end": 1542.05, "word": " المثال", "probability": 0.9373372395833334}, {"start": 1542.05, "end": 1542.29, "word": " أو", "probability": 0.87939453125}, {"start": 1542.29, "end": 1542.77, "word": " ال", "probability": 0.68603515625}, {"start": 1542.77, "end": 1543.11, "word": " remark", "probability": 0.3974609375}, {"start": 1543.11, "end": 1543.71, "word": " الأخيرة", "probability": 0.9431966145833334}], "temperature": 1.0}, {"id": 68, "seek": 155797, "start": 1546.19, "end": 1557.97, "text": "بتقول ايه؟ ايزيومتريك لحالها لتكفل انها تكون ايه شمالها؟ Unitary لازم تحطلها زججة زججة يعني ان هي surjective", "tokens": [3555, 2655, 39648, 1975, 1829, 3224, 22807, 1975, 1829, 11622, 1829, 20498, 2655, 16572, 4117, 5296, 5016, 6027, 11296, 5296, 2655, 4117, 5172, 1211, 16472, 11296, 6055, 30544, 1975, 1829, 3224, 13412, 2304, 6027, 11296, 22807, 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بس هاي كل الجزء الان consider the bounded linear operator T من L2 لعند L2 given by بس بيعملني shift shift operator بيشتد اللي هو ال XI1 XI2 XI3 وبيعمله shift لقدام شوية و بيحط ال zero في ال entry الأول و بعدين بيبقوا ماشي زي ما هو", "tokens": [6027, 33456, 2423, 39184, 2876, 29470, 12480, 3391, 643, 406, 312, 517, 4109, 4032, 9778, 3215, 50113, 6027, 4724, 16254, 5551, 7435, 1829, 3555, 4117, 50113, 6027, 5551, 4117, 25708, 37893, 25972, 4724, 3794, 8032, 47302, 28242, 25724, 11622, 38207, 2423, 7649, 1949, 264, 37498, 8213, 12973, 314, 9154, 441, 17, 5296, 3615, 41260, 441, 17, 2212, 538, 4724, 3794, 4724, 1829, 25957, 1211, 22653, 5513, 5513, 12973, 4724, 1829, 8592, 2655, 3215, 13672, 1829, 31439, 2423, 1783, 40, 16, 1783, 40, 17, 1783, 40, 18, 4032, 21292, 25957, 43761, 5513, 5296, 28543, 10943, 13412, 2407, 10632, 4032, 4724, 1829, 5016, 9566, 2423, 4018, 8978, 2423, 8729, 16247, 12610, 4032, 39182, 9957, 4724, 1829, 3555, 4587, 14407, 3714, 33599, 1829, 30767, 1829, 19446, 31439], "avg_logprob": -0.26225000858306885, "compression_ratio": 1.516778523489933, "no_speech_prob": 1.7285346984863281e-06, "words": [{"start": 1558.4, "end": 1558.9, "word": "الأن", "probability": 0.684814453125}, {"start": 1558.9, "end": 1559.5, "word": " الـ", "probability": 0.667236328125}, {"start": 1559.5, "end": 1560.14, "word": " Geometric", "probability": 0.6898193359375}, {"start": 1560.14, "end": 1560.92, "word": " Operators", "probability": 0.814208984375}, {"start": 1560.92, "end": 1561.18, "word": " need", "probability": 0.2366943359375}, {"start": 1561.18, "end": 1561.56, "word": " not", "probability": 0.951171875}, {"start": 1561.56, "end": 1561.94, "word": " be", "probability": 0.86083984375}, {"start": 1561.94, "end": 1562.64, "word": " unitary", "probability": 0.840576171875}, {"start": 1562.64, "end": 1563.3, "word": " وخد", "probability": 0.6886393229166666}, {"start": 1563.3, "end": 1563.72, "word": " مثال", "probability": 0.914794921875}, {"start": 1563.72, "end": 1564.06, "word": " بدي", "probability": 0.50164794921875}, {"start": 1564.06, "end": 1564.44, "word": " أجيبك", "probability": 0.880078125}, {"start": 1564.44, "end": 1564.74, "word": " مثال", "probability": 0.98779296875}, {"start": 1564.74, "end": 1565.0, "word": " أكيد", "probability": 0.95849609375}, {"start": 1565.0, "end": 1565.16, "word": " مش", "probability": 0.98291015625}, {"start": 1565.16, "end": 1565.62, "word": " subjective", "probability": 0.75341796875}, {"start": 1565.62, "end": 1566.2, "word": " بس", "probability": 0.909423828125}, {"start": 1566.2, "end": 1566.64, "word": " هاي", "probability": 0.590087890625}, {"start": 1566.64, "end": 1566.84, "word": " كل", "probability": 0.98828125}, {"start": 1566.84, "end": 1567.26, "word": " الجزء", "probability": 0.6615397135416666}, {"start": 1567.26, "end": 1568.2, "word": " الان", "probability": 0.634765625}, {"start": 1568.2, "end": 1568.9, "word": " consider", "probability": 0.86083984375}, {"start": 1568.9, "end": 1569.22, "word": " the", "probability": 0.88818359375}, {"start": 1569.22, "end": 1569.68, "word": " bounded", "probability": 0.89013671875}, {"start": 1569.68, "end": 1570.08, "word": " linear", "probability": 0.82763671875}, {"start": 1570.08, "end": 1570.6, "word": " operator", "probability": 0.9404296875}, {"start": 1570.6, "end": 1571.04, "word": " T", "probability": 0.89697265625}, {"start": 1571.04, "end": 1571.74, "word": " من", "probability": 0.9443359375}, {"start": 1571.74, "end": 1572.14, "word": " L2", "probability": 0.8955078125}, {"start": 1572.14, "end": 1572.46, "word": " لعند", "probability": 0.7762044270833334}, {"start": 1572.46, "end": 1572.86, "word": " L2", "probability": 0.98291015625}, {"start": 1572.86, "end": 1573.12, "word": " given", "probability": 0.57568359375}, {"start": 1573.12, "end": 1573.62, "word": " by", "probability": 0.97998046875}, {"start": 1573.62, "end": 1574.4, "word": " بس", "probability": 0.88916015625}, {"start": 1574.4, "end": 1574.98, "word": " بيعملني", "probability": 0.773486328125}, {"start": 1574.98, "end": 1575.22, "word": " shift", "probability": 0.8017578125}, {"start": 1575.22, "end": 1575.54, "word": " shift", "probability": 0.18994140625}, {"start": 1575.54, "end": 1575.98, "word": " operator", "probability": 0.908203125}, {"start": 1575.98, "end": 1576.48, "word": " بيشتد", "probability": 0.703076171875}, {"start": 1576.48, "end": 1576.64, "word": " اللي", "probability": 0.94384765625}, {"start": 1576.64, "end": 1576.96, "word": " هو", "probability": 0.94775390625}, {"start": 1576.96, "end": 1577.48, "word": " ال", "probability": 0.775390625}, {"start": 1577.48, "end": 1578.62, "word": " XI1", "probability": 0.4640299479166667}, {"start": 1578.62, "end": 1579.14, "word": " XI2", "probability": 0.7940266927083334}, {"start": 1579.14, "end": 1579.72, "word": " XI3", "probability": 0.9698893229166666}, {"start": 1579.72, "end": 1580.38, "word": " وبيعمله", "probability": 0.6490478515625}, {"start": 1580.38, "end": 1580.74, "word": " shift", "probability": 0.8876953125}, {"start": 1580.74, "end": 1581.86, "word": " لقدام", "probability": 0.9254557291666666}, {"start": 1581.86, "end": 1582.34, "word": " شوية", "probability": 0.8938802083333334}, {"start": 1582.34, "end": 1582.68, "word": " و", "probability": 0.87451171875}, {"start": 1582.68, "end": 1582.94, "word": " بيحط", "probability": 0.9010009765625}, {"start": 1582.94, "end": 1583.06, "word": " ال", "probability": 0.65966796875}, {"start": 1583.06, "end": 1583.36, "word": " zero", "probability": 0.423095703125}, {"start": 1583.36, "end": 1583.58, "word": " في", "probability": 0.7548828125}, {"start": 1583.58, "end": 1583.98, "word": " ال", "probability": 0.98291015625}, {"start": 1583.98, "end": 1584.22, "word": " entry", "probability": 0.84375}, {"start": 1584.22, "end": 1584.54, "word": " الأول", "probability": 0.947265625}, {"start": 1584.54, "end": 1584.7, "word": " و", "probability": 0.8603515625}, {"start": 1584.7, "end": 1585.02, "word": " بعدين", "probability": 0.849365234375}, {"start": 1585.02, "end": 1585.22, "word": " بيبقوا", "probability": 0.73955078125}, {"start": 1585.22, "end": 1585.5, "word": " ماشي", "probability": 0.9217122395833334}, {"start": 1585.5, "end": 1585.7, "word": " زي", "probability": 0.965576171875}, {"start": 1585.7, "end": 1585.78, "word": " ما", "probability": 0.9755859375}, {"start": 1585.78, "end": 1585.98, "word": " هو", "probability": 0.99365234375}], "temperature": 1.0}, {"id": 70, "seek": 161189, "start": 1586.59, "end": 1611.89, "text": "إذا الـ T of XI واحد XI اتنين XI تلعب تلعب إلى ما لا نهاية بيساوي Zero XI واحد وXI اتنين إلى ما لا نهاية لأن it is easy to see that T is an isometric سهل خالص خدوا ال TX، إيش هو ال TX؟ هو لحاله طالع ايزومتري شوفوا كيف بيطلع Automatic Isometry", "tokens": [28814, 15730, 2423, 39184, 314, 295, 1783, 40, 36764, 24401, 1783, 40, 1975, 2655, 1863, 9957, 1783, 40, 6055, 1211, 3615, 3555, 6055, 1211, 3615, 3555, 30731, 19446, 20193, 8717, 11296, 10632, 4724, 1829, 3794, 995, 45865, 17182, 1783, 40, 36764, 24401, 4032, 55, 40, 1975, 2655, 1863, 9957, 30731, 19446, 20193, 8717, 11296, 10632, 5296, 33456, 309, 307, 1858, 281, 536, 300, 314, 307, 364, 307, 29470, 8608, 3224, 1211, 16490, 6027, 9381, 16490, 3215, 14407, 2423, 314, 55, 12399, 11933, 1829, 8592, 31439, 2423, 314, 55, 22807, 31439, 5296, 5016, 6027, 3224, 23032, 6027, 3615, 1975, 1829, 11622, 20498, 2655, 16572, 13412, 38688, 14407, 9122, 33911, 4724, 1829, 9566, 1211, 3615, 6049, 13143, 1119, 34730], "avg_logprob": -0.24894068529040125, "compression_ratio": 1.5947136563876652, "no_speech_prob": 0.0, "words": [{"start": 1586.59, "end": 1586.99, "word": "إذا", "probability": 0.73291015625}, {"start": 1586.99, "end": 1587.65, "word": " الـ", "probability": 0.5802001953125}, {"start": 1587.65, "end": 1588.05, "word": " T", "probability": 0.6103515625}, {"start": 1588.05, "end": 1588.53, "word": " of", "probability": 0.61328125}, {"start": 1588.53, "end": 1588.91, "word": " XI", "probability": 0.59521484375}, {"start": 1588.91, "end": 1589.21, "word": " واحد", "probability": 0.679443359375}, {"start": 1589.21, "end": 1589.57, "word": " XI", "probability": 0.623291015625}, {"start": 1589.57, "end": 1589.79, "word": " اتنين", "probability": 0.8603515625}, {"start": 1589.79, "end": 1590.13, "word": " XI", "probability": 0.8017578125}, {"start": 1590.13, "end": 1590.37, "word": " تلعب", "probability": 0.6019287109375}, {"start": 1590.37, "end": 1590.57, "word": " تلعب", "probability": 0.7974853515625}, {"start": 1590.57, "end": 1590.61, "word": " إلى", "probability": 0.56103515625}, {"start": 1590.61, "end": 1590.69, "word": " ما", "probability": 0.52880859375}, {"start": 1590.69, "end": 1590.77, "word": " لا", "probability": 0.6416015625}, {"start": 1590.77, "end": 1590.97, "word": " نهاية", "probability": 0.8497721354166666}, {"start": 1590.97, "end": 1591.47, "word": " بيساوي", "probability": 0.84287109375}, {"start": 1591.47, "end": 1592.17, "word": " Zero", "probability": 0.69580078125}, {"start": 1592.17, "end": 1592.61, "word": " XI", "probability": 0.883056640625}, {"start": 1592.61, "end": 1592.87, "word": " واحد", "probability": 0.992431640625}, {"start": 1592.87, "end": 1593.19, "word": " وXI", "probability": 0.7600911458333334}, {"start": 1593.19, "end": 1593.49, "word": " اتنين", "probability": 0.9630126953125}, {"start": 1593.49, "end": 1593.69, "word": " إلى", "probability": 0.900390625}, {"start": 1593.69, "end": 1593.83, "word": " ما", "probability": 0.9736328125}, {"start": 1593.83, "end": 1593.93, "word": " لا", "probability": 0.98583984375}, {"start": 1593.93, "end": 1594.37, "word": " نهاية", "probability": 0.9033203125}, {"start": 1594.37, "end": 1595.13, "word": " لأن", "probability": 0.529541015625}, {"start": 1595.13, "end": 1595.39, "word": " it", "probability": 0.73681640625}, {"start": 1595.39, "end": 1595.59, "word": " is", "probability": 0.95068359375}, {"start": 1595.59, "end": 1595.89, "word": " easy", "probability": 0.9609375}, {"start": 1595.89, "end": 1596.05, "word": " to", "probability": 0.98388671875}, {"start": 1596.05, "end": 1596.27, "word": " see", "probability": 0.666015625}, {"start": 1596.27, "end": 1596.51, "word": " that", "probability": 0.91357421875}, {"start": 1596.51, "end": 1596.75, "word": " T", "probability": 0.931640625}, {"start": 1596.75, "end": 1596.95, "word": " is", "probability": 0.96484375}, {"start": 1596.95, "end": 1597.23, "word": " an", "probability": 0.88916015625}, {"start": 1597.23, "end": 1598.07, "word": " isometric", "probability": 0.8916015625}, {"start": 1598.07, "end": 1598.73, "word": " سهل", "probability": 0.8548177083333334}, {"start": 1598.73, "end": 1599.23, "word": " خالص", "probability": 0.994140625}, {"start": 1599.23, "end": 1599.91, "word": " خدوا", "probability": 0.9049479166666666}, {"start": 1599.91, "end": 1600.01, "word": " ال", "probability": 0.8466796875}, {"start": 1600.01, "end": 1600.55, "word": " TX،", "probability": 0.5253092447916666}, {"start": 1600.55, "end": 1600.71, "word": " إيش", "probability": 0.6728515625}, {"start": 1600.71, "end": 1600.83, "word": " هو", "probability": 0.99365234375}, {"start": 1600.83, "end": 1600.95, "word": " ال", "probability": 0.8701171875}, {"start": 1600.95, "end": 1601.37, "word": " TX؟", "probability": 0.8898111979166666}, {"start": 1601.37, "end": 1601.45, "word": " هو", "probability": 0.71240234375}, {"start": 1601.45, "end": 1602.39, "word": " لحاله", "probability": 0.9696044921875}, {"start": 1602.39, "end": 1602.67, "word": " طالع", "probability": 0.9899088541666666}, {"start": 1602.67, "end": 1603.29, "word": " ايزومتري", "probability": 0.7729288736979166}, {"start": 1603.29, "end": 1609.55, "word": " شوفوا", "probability": 0.85595703125}, {"start": 1609.55, "end": 1609.91, "word": " كيف", "probability": 0.975830078125}, {"start": 1609.91, "end": 1610.45, "word": " بيطلع", "probability": 0.830859375}, {"start": 1610.45, "end": 1611.15, "word": " Automatic", "probability": 0.7237548828125}, {"start": 1611.15, "end": 1611.89, "word": " Isometry", "probability": 0.730712890625}], "temperature": 1.0}, {"id": 71, "seek": 163907, "start": 1617.57, "end": 1639.07, "text": "صلى على النبي عليه الصلاة والسلام اللهم صلى على سيدنا محمد norm ال T XI 1 XI 2 إلى ما لا نهاية اليد اللي هو جوا من ال X بساوي اللي هو norm T XI 1 بساوي 0 XI 1 XI 2 إلى ما لا نهاية", "tokens": [9381, 23942, 15844, 28239, 21292, 47356, 31767, 15040, 3660, 16070, 3794, 37440, 13672, 16095, 20328, 23942, 15844, 8608, 25708, 8315, 3714, 35571, 3215, 2026, 2423, 314, 1783, 40, 502, 1783, 40, 568, 30731, 19446, 20193, 8717, 11296, 10632, 2423, 25708, 13672, 1829, 31439, 10874, 14407, 9154, 2423, 1783, 4724, 3794, 995, 45865, 13672, 1829, 31439, 2026, 314, 1783, 40, 502, 4724, 3794, 995, 45865, 1958, 1783, 40, 502, 1783, 40, 568, 30731, 19446, 20193, 8717, 11296, 10632], "avg_logprob": -0.23036859490168402, "compression_ratio": 1.9066666666666667, "no_speech_prob": 8.386373519897461e-05, "words": [{"start": 1617.57, "end": 1618.01, "word": "صلى", "probability": 0.63330078125}, {"start": 1618.01, "end": 1618.19, "word": " على", "probability": 0.8310546875}, {"start": 1618.19, "end": 1618.45, "word": " النبي", "probability": 0.94580078125}, {"start": 1618.45, "end": 1618.73, "word": " عليه", "probability": 0.8564453125}, {"start": 1618.73, "end": 1619.23, "word": " الصلاة", "probability": 0.9861653645833334}, {"start": 1619.23, "end": 1619.83, "word": " والسلام", "probability": 0.95654296875}, {"start": 1619.83, "end": 1621.29, "word": " اللهم", "probability": 0.7265625}, {"start": 1621.29, "end": 1621.61, "word": " صلى", "probability": 0.9580078125}, {"start": 1621.61, "end": 1621.79, "word": " على", "probability": 0.9052734375}, {"start": 1621.79, "end": 1622.17, "word": " سيدنا", "probability": 0.9876302083333334}, {"start": 1622.17, "end": 1622.51, "word": " محمد", "probability": 0.9850260416666666}, {"start": 1622.51, "end": 1622.95, "word": " norm", "probability": 0.377197265625}, {"start": 1622.95, "end": 1624.17, "word": " ال", "probability": 0.25341796875}, {"start": 1624.17, "end": 1625.15, "word": " T", "probability": 0.451171875}, {"start": 1625.15, "end": 1626.13, "word": " XI", "probability": 0.593017578125}, {"start": 1626.13, "end": 1626.69, "word": " 1", "probability": 0.37646484375}, {"start": 1626.69, "end": 1627.37, "word": " XI", "probability": 0.939208984375}, {"start": 1627.37, "end": 1627.89, "word": " 2", "probability": 0.87548828125}, {"start": 1627.89, "end": 1628.17, "word": " إلى", "probability": 0.8369140625}, {"start": 1628.17, "end": 1628.35, "word": " ما", "probability": 0.27392578125}, {"start": 1628.35, "end": 1628.45, "word": " لا", "probability": 0.54443359375}, {"start": 1628.45, "end": 1628.89, "word": " نهاية", "probability": 0.9303385416666666}, {"start": 1628.89, "end": 1629.61, "word": " اليد", "probability": 0.644775390625}, {"start": 1629.61, "end": 1629.79, "word": " اللي", "probability": 0.899169921875}, {"start": 1629.79, "end": 1629.99, "word": " هو", "probability": 0.94189453125}, {"start": 1629.99, "end": 1630.27, "word": " جوا", "probability": 0.84375}, {"start": 1630.27, "end": 1630.41, "word": " من", "probability": 0.943359375}, {"start": 1630.41, "end": 1630.73, "word": " ال", "probability": 0.2724609375}, {"start": 1630.73, "end": 1631.09, "word": " X", "probability": 0.92236328125}, {"start": 1631.09, "end": 1631.97, "word": " بساوي", "probability": 0.7857666015625}, {"start": 1631.97, "end": 1632.75, "word": " اللي", "probability": 0.74462890625}, {"start": 1632.75, "end": 1632.91, "word": " هو", "probability": 0.98828125}, {"start": 1632.91, "end": 1633.55, "word": " norm", "probability": 0.8447265625}, {"start": 1633.55, "end": 1634.37, "word": " T", "probability": 0.88671875}, {"start": 1634.37, "end": 1634.83, "word": " XI", "probability": 0.8427734375}, {"start": 1634.83, "end": 1635.13, "word": " 1", "probability": 0.92919921875}, {"start": 1635.13, "end": 1635.49, "word": " بساوي", "probability": 0.74151611328125}, {"start": 1635.49, "end": 1636.05, "word": " 0", "probability": 0.483154296875}, {"start": 1636.05, "end": 1636.81, "word": " XI", "probability": 0.977294921875}, {"start": 1636.81, "end": 1637.19, "word": " 1", "probability": 0.93701171875}, {"start": 1637.19, "end": 1637.73, "word": " XI", "probability": 0.98828125}, {"start": 1637.73, "end": 1638.09, "word": " 2", "probability": 0.95947265625}, {"start": 1638.09, "end": 1638.35, "word": " إلى", "probability": 0.96337890625}, {"start": 1638.35, "end": 1638.55, "word": " ما", "probability": 0.939453125}, {"start": 1638.55, "end": 1638.63, "word": " لا", "probability": 0.98193359375}, {"start": 1638.63, "end": 1639.07, "word": " نهاية", "probability": 0.951171875}], "temperature": 1.0}, {"id": 72, "seek": 166308, "start": 1639.44, "end": 1663.08, "text": "وهذا الـ norm هيش فالـ summation لـ XI I سوى summation لـ XI I تربيع I من واحد إلى مالة نهاية الكل أص نص لأنه أول واحد سفر فيها اللي هو عبارة عن مين norm من ال X ماشي إذا صار اللي هو isometric إذا الان إذا T is an isometric", "tokens": [2407, 3224, 15730, 2423, 39184, 2026, 39896, 8592, 6156, 6027, 39184, 28811, 5296, 39184, 1783, 40, 286, 8608, 2407, 7578, 28811, 5296, 39184, 1783, 40, 286, 6055, 2288, 21292, 3615, 286, 9154, 36764, 24401, 30731, 3714, 6027, 3660, 8717, 11296, 10632, 2423, 28820, 5551, 9381, 8717, 9381, 5296, 33456, 3224, 5551, 12610, 36764, 24401, 8608, 5172, 2288, 8978, 11296, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 3714, 9957, 2026, 9154, 2423, 1783, 3714, 33599, 1829, 11933, 15730, 20328, 9640, 13672, 1829, 31439, 307, 29470, 11933, 15730, 2423, 7649, 11933, 15730, 314, 307, 364, 307, 29470], "avg_logprob": -0.3872422582095431, "compression_ratio": 1.6865671641791045, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 1639.44, "end": 1639.92, "word": "وهذا", "probability": 0.5533040364583334}, {"start": 1639.92, "end": 1640.06, "word": " الـ", "probability": 0.3682861328125}, {"start": 1640.06, "end": 1640.22, "word": " norm", "probability": 0.391845703125}, {"start": 1640.22, "end": 1640.6, "word": " هيش", "probability": 0.594970703125}, {"start": 1640.6, "end": 1640.88, "word": " فالـ", "probability": 0.2947591145833333}, {"start": 1640.88, "end": 1641.3, "word": " summation", "probability": 0.83251953125}, {"start": 1641.3, "end": 1641.5, "word": " لـ", "probability": 0.293701171875}, {"start": 1641.5, "end": 1641.84, "word": " XI", "probability": 0.3311767578125}, {"start": 1641.84, "end": 1642.12, "word": " I", "probability": 0.576171875}, {"start": 1642.12, "end": 1642.9, "word": " سوى", "probability": 0.5645751953125}, {"start": 1642.9, "end": 1643.8, "word": " summation", "probability": 0.278564453125}, {"start": 1643.8, "end": 1644.66, "word": " لـ", "probability": 0.861328125}, {"start": 1644.66, "end": 1645.06, "word": " XI", "probability": 0.933837890625}, {"start": 1645.06, "end": 1645.52, "word": " I", "probability": 0.94384765625}, {"start": 1645.52, "end": 1646.32, "word": " تربيع", "probability": 0.82958984375}, {"start": 1646.32, "end": 1646.54, "word": " I", "probability": 0.9716796875}, {"start": 1646.54, "end": 1646.76, "word": " من", "probability": 0.9873046875}, {"start": 1646.76, "end": 1647.28, "word": " واحد", "probability": 0.80517578125}, {"start": 1647.28, "end": 1647.5, "word": " إلى", "probability": 0.9072265625}, {"start": 1647.5, "end": 1647.84, "word": " مالة", "probability": 0.5199381510416666}, {"start": 1647.84, "end": 1648.36, "word": " نهاية", "probability": 0.92041015625}, {"start": 1648.36, "end": 1649.08, "word": " الكل", "probability": 0.754150390625}, {"start": 1649.08, "end": 1649.3, "word": " أص", "probability": 0.572265625}, {"start": 1649.3, "end": 1649.6, "word": " نص", "probability": 0.82080078125}, {"start": 1649.6, "end": 1650.02, "word": " لأنه", "probability": 0.6563313802083334}, {"start": 1650.02, "end": 1650.4, "word": " أول", "probability": 0.967529296875}, {"start": 1650.4, "end": 1650.76, "word": " واحد", "probability": 0.99365234375}, {"start": 1650.76, "end": 1651.1, "word": " سفر", "probability": 0.85498046875}, {"start": 1651.1, "end": 1651.54, "word": " فيها", "probability": 0.71875}, {"start": 1651.54, "end": 1652.52, "word": " اللي", "probability": 0.9619140625}, {"start": 1652.52, "end": 1652.64, "word": " هو", "probability": 0.986328125}, {"start": 1652.64, "end": 1652.9, "word": " عبارة", "probability": 0.986328125}, {"start": 1652.9, "end": 1653.1, "word": " عن", "probability": 0.98291015625}, {"start": 1653.1, "end": 1653.4, "word": " مين", "probability": 0.736328125}, {"start": 1653.4, "end": 1654.24, "word": " norm", "probability": 0.341796875}, {"start": 1654.24, "end": 1654.46, "word": " من", "probability": 0.495849609375}, {"start": 1654.46, "end": 1654.54, "word": " ال", "probability": 0.5224609375}, {"start": 1654.54, "end": 1654.9, "word": " X", "probability": 0.82958984375}, {"start": 1654.9, "end": 1655.94, "word": " ماشي", "probability": 0.8336588541666666}, {"start": 1655.94, "end": 1656.22, "word": " إذا", "probability": 0.749755859375}, {"start": 1656.22, "end": 1656.54, "word": " صار", "probability": 0.913818359375}, {"start": 1656.54, "end": 1656.64, "word": " اللي", "probability": 0.765625}, {"start": 1656.64, "end": 1656.88, "word": " هو", "probability": 0.982421875}, {"start": 1656.88, "end": 1658.0, "word": " isometric", "probability": 0.730712890625}, {"start": 1658.0, "end": 1659.12, "word": " إذا", "probability": 0.759033203125}, {"start": 1659.12, "end": 1659.86, "word": " الان", "probability": 0.584228515625}, {"start": 1659.86, "end": 1660.2, "word": " إذا", "probability": 0.754150390625}, {"start": 1660.2, "end": 1660.66, "word": " T", "probability": 0.8740234375}, {"start": 1660.66, "end": 1661.16, "word": " is", "probability": 0.94921875}, {"start": 1661.16, "end": 1661.78, "word": " an", "probability": 0.916015625}, {"start": 1661.78, "end": 1663.08, "word": " isometric", "probability": 0.937744140625}], "temperature": 1.0}, {"id": 73, "seek": 168873, "start": 1664.23, "end": 1688.73, "text": "But T is not onto مدام مش onto ده متحكوش عن ال unitary But T is not onto for example خد اللي هو اقصى و اخد و اقولك خد الواحد و السفر و السفر و السفر إلى ما لنهاية element انقلته في TX بتساوي هذا", "tokens": [7835, 314, 307, 406, 3911, 3714, 3215, 10943, 37893, 3911, 11778, 3224, 44650, 5016, 4117, 2407, 8592, 18871, 2423, 517, 4109, 583, 314, 307, 406, 3911, 337, 1365, 16490, 3215, 13672, 1829, 31439, 1975, 4587, 9381, 7578, 4032, 1975, 9778, 3215, 4032, 1975, 39648, 4117, 16490, 3215, 2423, 14407, 24401, 4032, 21136, 5172, 2288, 4032, 21136, 5172, 2288, 4032, 21136, 5172, 2288, 30731, 19446, 5296, 1863, 11296, 10632, 4478, 16472, 4587, 1211, 47395, 8978, 314, 55, 39894, 3794, 995, 45865, 23758], "avg_logprob": -0.3913871936681794, "compression_ratio": 1.591160220994475, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 1664.23, "end": 1664.57, "word": "But", "probability": 0.1318359375}, {"start": 1664.57, "end": 1665.05, "word": " T", "probability": 0.6513671875}, {"start": 1665.05, "end": 1665.99, "word": " is", "probability": 0.84716796875}, {"start": 1665.99, "end": 1666.35, "word": " not", "probability": 0.93896484375}, {"start": 1666.35, "end": 1666.81, "word": " onto", "probability": 0.488037109375}, {"start": 1666.81, "end": 1667.81, "word": " مدام", "probability": 0.5051066080729166}, {"start": 1667.81, "end": 1668.01, "word": " مش", "probability": 0.322509765625}, {"start": 1668.01, "end": 1668.31, "word": " onto", "probability": 0.54052734375}, {"start": 1668.31, "end": 1668.51, "word": " ده", "probability": 0.59130859375}, {"start": 1668.51, "end": 1669.07, "word": " متحكوش", "probability": 0.841455078125}, {"start": 1669.07, "end": 1669.25, "word": " عن", "probability": 0.99072265625}, {"start": 1669.25, "end": 1669.39, "word": " ال", "probability": 0.87060546875}, {"start": 1669.39, "end": 1669.87, "word": " unitary", "probability": 0.544891357421875}, {"start": 1669.87, "end": 1670.99, "word": " But", "probability": 0.3232421875}, {"start": 1670.99, "end": 1671.43, "word": " T", "probability": 0.91845703125}, {"start": 1671.43, "end": 1671.63, "word": " is", "probability": 0.95556640625}, {"start": 1671.63, "end": 1671.85, "word": " not", "probability": 0.95947265625}, {"start": 1671.85, "end": 1673.31, "word": " onto", "probability": 0.80419921875}, {"start": 1673.31, "end": 1674.05, "word": " for", "probability": 0.51513671875}, {"start": 1674.05, "end": 1674.85, "word": " example", "probability": 0.9658203125}, {"start": 1674.85, "end": 1675.53, "word": " خد", "probability": 0.915771484375}, {"start": 1675.53, "end": 1675.65, "word": " اللي", "probability": 0.700927734375}, {"start": 1675.65, "end": 1676.01, "word": " هو", "probability": 0.98486328125}, {"start": 1676.01, "end": 1676.93, "word": " اقصى", "probability": 0.45819091796875}, {"start": 1676.93, "end": 1677.11, "word": " و", "probability": 0.310302734375}, {"start": 1677.11, "end": 1677.75, "word": " اخد", "probability": 0.506103515625}, {"start": 1677.75, "end": 1677.81, "word": " و", "probability": 0.48681640625}, {"start": 1677.81, "end": 1678.23, "word": " اقولك", "probability": 0.8736979166666666}, {"start": 1678.23, "end": 1678.49, "word": " خد", "probability": 0.81103515625}, {"start": 1678.49, "end": 1679.21, "word": " الواحد", "probability": 0.8992513020833334}, {"start": 1679.21, "end": 1680.73, "word": " و", "probability": 0.48291015625}, {"start": 1680.73, "end": 1681.23, "word": " السفر", "probability": 0.8489583333333334}, {"start": 1681.23, "end": 1681.43, "word": " و", "probability": 0.94970703125}, {"start": 1681.43, "end": 1681.97, "word": " السفر", "probability": 0.9879557291666666}, {"start": 1681.97, "end": 1682.13, "word": " و", "probability": 0.9765625}, {"start": 1682.13, "end": 1682.59, "word": " السفر", "probability": 0.9923502604166666}, {"start": 1682.59, "end": 1682.79, "word": " إلى", "probability": 0.479248046875}, {"start": 1682.79, "end": 1682.95, "word": " ما", "probability": 0.36865234375}, {"start": 1682.95, "end": 1683.49, "word": " لنهاية", "probability": 0.7861328125}, {"start": 1683.49, "end": 1684.23, "word": " element", "probability": 0.771484375}, {"start": 1684.23, "end": 1685.07, "word": " انقلته", "probability": 0.79364013671875}, {"start": 1685.07, "end": 1686.35, "word": " في", "probability": 0.92138671875}, {"start": 1686.35, "end": 1687.65, "word": " TX", "probability": 0.6763916015625}, {"start": 1687.65, "end": 1688.37, "word": " بتساوي", "probability": 0.9171142578125}, {"start": 1688.37, "end": 1688.73, "word": " هذا", "probability": 0.9365234375}], "temperature": 1.0}, {"id": 74, "seek": 171420, "start": 1689.44, "end": 1714.2, "text": "لأ يمكن لإن أي و أي TX تبتدأ تكون صورتها أوليش Zero و بعدين نحط اللي بدك هيها و هذا مش Zero إذا مش on to طبعا هو بقولك T is not on to where there is XI واحد و XI اتنين و XI واحد ده ساوي سفر but there is no X element in L2 بحيث أنه TX بالساوي XI واحد لإن هو بعمل shift و بخلي أول واحد اسمه hence we have", "tokens": [1211, 10721, 7251, 43020, 5296, 28814, 1863, 36632, 4032, 36632, 314, 55, 6055, 3555, 2655, 3215, 10721, 6055, 30544, 20328, 13063, 2655, 11296, 5551, 12610, 1829, 8592, 17182, 4032, 39182, 9957, 8717, 5016, 9566, 13672, 1829, 47525, 4117, 39896, 11296, 4032, 23758, 37893, 17182, 11933, 15730, 37893, 322, 281, 23032, 3555, 3615, 995, 31439, 4724, 39648, 4117, 314, 307, 406, 322, 281, 689, 456, 307, 1783, 40, 36764, 24401, 4032, 1783, 40, 1975, 2655, 1863, 9957, 4032, 1783, 40, 36764, 24401, 11778, 3224, 8608, 995, 45865, 8608, 5172, 2288, 457, 456, 307, 572, 1783, 4478, 294, 441, 17, 4724, 5016, 1829, 12984, 14739, 3224, 314, 55, 20666, 3794, 995, 45865, 1783, 40, 36764, 24401, 5296, 28814, 1863, 31439, 4724, 25957, 1211, 5513, 4032, 4724, 9778, 20292, 5551, 12610, 36764, 24401, 24525, 2304, 3224, 16678, 321, 362], "avg_logprob": -0.3478558272340872, "compression_ratio": 1.654275092936803, "no_speech_prob": 5.424022674560547e-06, "words": [{"start": 1689.44, "end": 1689.84, "word": "لأ", "probability": 0.510009765625}, {"start": 1689.84, "end": 1690.36, "word": " يمكن", "probability": 0.8779296875}, {"start": 1690.36, "end": 1691.16, "word": " لإن", "probability": 0.6261393229166666}, {"start": 1691.16, "end": 1691.5, "word": " أي", "probability": 0.6748046875}, {"start": 1691.5, "end": 1691.68, "word": " و", "probability": 0.37646484375}, {"start": 1691.68, "end": 1691.94, "word": " أي", "probability": 0.91748046875}, {"start": 1691.94, "end": 1692.36, "word": " TX", "probability": 0.660888671875}, {"start": 1692.36, "end": 1692.92, "word": " تبتدأ", "probability": 0.36588134765625}, {"start": 1692.92, "end": 1693.06, "word": " تكون", "probability": 0.4561767578125}, {"start": 1693.06, "end": 1693.96, "word": " صورتها", "probability": 0.871337890625}, {"start": 1693.96, "end": 1694.68, "word": " أوليش", "probability": 0.56280517578125}, {"start": 1694.68, "end": 1695.02, "word": " Zero", "probability": 0.404296875}, {"start": 1695.02, "end": 1695.14, "word": " و", "probability": 0.4091796875}, {"start": 1695.14, "end": 1695.36, "word": " بعدين", "probability": 0.8623046875}, {"start": 1695.36, "end": 1695.66, "word": " نحط", "probability": 0.718994140625}, {"start": 1695.66, "end": 1695.8, "word": " اللي", "probability": 0.947265625}, {"start": 1695.8, "end": 1696.1, "word": " بدك", "probability": 0.6826171875}, {"start": 1696.1, "end": 1696.46, "word": " هيها", "probability": 0.5546875}, {"start": 1696.46, "end": 1696.82, "word": " و", "probability": 0.60791015625}, {"start": 1696.82, "end": 1696.98, "word": " هذا", "probability": 0.85498046875}, {"start": 1696.98, "end": 1697.12, "word": " مش", "probability": 0.947265625}, {"start": 1697.12, "end": 1697.4, "word": " Zero", "probability": 0.91357421875}, {"start": 1697.4, "end": 1697.64, "word": " إذا", "probability": 0.6884765625}, {"start": 1697.64, "end": 1697.86, "word": " مش", "probability": 0.94482421875}, {"start": 1697.86, "end": 1698.1, "word": " on", "probability": 0.333251953125}, {"start": 1698.1, "end": 1698.26, "word": " to", "probability": 0.45849609375}, {"start": 1698.26, "end": 1698.88, "word": " طبعا", "probability": 0.9505615234375}, {"start": 1698.88, "end": 1698.98, "word": " هو", "probability": 0.97412109375}, {"start": 1698.98, "end": 1699.56, "word": " بقولك", "probability": 0.8473307291666666}, {"start": 1699.56, "end": 1700.2, "word": " T", "probability": 0.70654296875}, {"start": 1700.2, "end": 1700.34, "word": " is", "probability": 0.83447265625}, {"start": 1700.34, "end": 1700.54, "word": " not", "probability": 0.96142578125}, {"start": 1700.54, "end": 1700.76, "word": " on", "probability": 0.9150390625}, {"start": 1700.76, "end": 1700.9, "word": " to", "probability": 0.955078125}, {"start": 1700.9, "end": 1701.16, "word": " where", "probability": 0.88623046875}, {"start": 1701.16, "end": 1701.46, "word": " there", "probability": 0.8828125}, {"start": 1701.46, "end": 1701.76, "word": " is", "probability": 0.9609375}, {"start": 1701.76, "end": 1702.1, "word": " XI", "probability": 0.470947265625}, {"start": 1702.1, "end": 1702.3, "word": " واحد", "probability": 0.6707763671875}, {"start": 1702.3, "end": 1702.42, "word": " و", "probability": 0.287841796875}, {"start": 1702.42, "end": 1702.62, "word": " XI", "probability": 0.90966796875}, {"start": 1702.62, "end": 1702.88, "word": " اتنين", "probability": 0.880615234375}, {"start": 1702.88, "end": 1703.22, "word": " و", "probability": 0.552734375}, {"start": 1703.22, "end": 1704.36, "word": " XI", "probability": 0.90087890625}, {"start": 1704.36, "end": 1704.62, "word": " واحد", "probability": 0.988037109375}, {"start": 1704.62, "end": 1704.8, "word": " ده", "probability": 0.822509765625}, {"start": 1704.8, "end": 1704.98, "word": " ساوي", "probability": 0.548095703125}, {"start": 1704.98, "end": 1705.36, "word": " سفر", "probability": 0.8805338541666666}, {"start": 1705.36, "end": 1705.88, "word": " but", "probability": 0.5986328125}, {"start": 1705.88, "end": 1706.18, "word": " there", "probability": 0.90478515625}, {"start": 1706.18, "end": 1706.38, "word": " is", "probability": 0.95703125}, {"start": 1706.38, "end": 1706.58, "word": " no", "probability": 0.943359375}, {"start": 1706.58, "end": 1706.82, "word": " X", "probability": 0.89404296875}, {"start": 1706.82, "end": 1707.08, "word": " element", "probability": 0.23388671875}, {"start": 1707.08, "end": 1707.34, "word": " in", "probability": 0.402587890625}, {"start": 1707.34, "end": 1707.8, "word": " L2", "probability": 0.8759765625}, {"start": 1707.8, "end": 1708.48, "word": " بحيث", "probability": 0.9261474609375}, {"start": 1708.48, "end": 1708.66, "word": " أنه", "probability": 0.4599609375}, {"start": 1708.66, "end": 1708.96, "word": " TX", "probability": 0.935791015625}, {"start": 1708.96, "end": 1709.3, "word": " بالساوي", "probability": 0.70404052734375}, {"start": 1709.3, "end": 1709.6, "word": " XI", "probability": 0.91357421875}, {"start": 1709.6, "end": 1710.08, "word": " واحد", "probability": 0.991943359375}, {"start": 1710.08, "end": 1710.74, "word": " لإن", "probability": 0.9207356770833334}, {"start": 1710.74, "end": 1711.14, "word": " هو", "probability": 0.88427734375}, {"start": 1711.14, "end": 1711.62, "word": " بعمل", "probability": 0.9495442708333334}, {"start": 1711.62, "end": 1711.9, "word": " shift", "probability": 0.83056640625}, {"start": 1711.9, "end": 1712.02, "word": " و", "probability": 0.6376953125}, {"start": 1712.02, "end": 1712.38, "word": " بخلي", "probability": 0.7357584635416666}, {"start": 1712.38, "end": 1712.62, "word": " أول", "probability": 0.87548828125}, {"start": 1712.62, "end": 1712.86, "word": " واحد", "probability": 0.989013671875}, {"start": 1712.86, "end": 1713.26, "word": " اسمه", "probability": 0.93359375}, {"start": 1713.26, "end": 1713.72, "word": " hence", "probability": 0.650390625}, {"start": 1713.72, "end": 1713.94, "word": " we", "probability": 0.9384765625}, {"start": 1713.94, "end": 1714.2, "word": " have", "probability": 0.97021484375}], "temperature": 1.0}, {"id": 75, "seek": 174229, "start": 1714.87, "end": 1742.29, "text": "an isometric which is not onto so it is not unitary لأن ال unitary عشان يكون unitary لازم يكون say adjective و الهو isometric او لو T inverse بسبب T star unitary بتكون اللي هي adjective زي T inverse بسبب T star مبارك الله فيكم و إلى لقاء آخر", "tokens": [282, 307, 29470, 597, 307, 406, 3911, 370, 309, 307, 406, 517, 4109, 5296, 33456, 2423, 517, 4109, 6225, 8592, 7649, 7251, 30544, 517, 4109, 5296, 31377, 2304, 7251, 30544, 584, 44129, 4032, 2423, 3224, 2407, 307, 29470, 1975, 2407, 45164, 314, 17340, 4724, 35457, 3555, 314, 3543, 517, 4109, 39894, 30544, 13672, 1829, 39896, 44129, 30767, 1829, 314, 17340, 4724, 35457, 3555, 314, 3543, 3714, 3555, 9640, 4117, 21984, 8978, 24793, 4032, 30731, 5296, 4587, 16606, 19753, 34740], "avg_logprob": -0.34023436829447745, "compression_ratio": 1.6808510638297873, "no_speech_prob": 4.410743713378906e-06, "words": [{"start": 1714.87, "end": 1715.17, "word": "an", "probability": 0.0386962890625}, {"start": 1715.17, "end": 1715.95, "word": " isometric", "probability": 0.915771484375}, {"start": 1715.95, "end": 1716.49, "word": " which", "probability": 0.8125}, {"start": 1716.49, "end": 1716.79, "word": " is", "probability": 0.9306640625}, {"start": 1716.79, "end": 1717.27, "word": " not", "probability": 0.923828125}, {"start": 1717.27, "end": 1718.05, "word": " onto", "probability": 0.5283203125}, {"start": 1718.05, "end": 1718.67, "word": " so", "probability": 0.27880859375}, {"start": 1718.67, "end": 1718.95, "word": " it", "probability": 0.9404296875}, {"start": 1718.95, "end": 1719.13, "word": " is", "probability": 0.896484375}, {"start": 1719.13, "end": 1719.45, "word": " not", "probability": 0.93408203125}, {"start": 1719.45, "end": 1719.87, "word": " unitary", "probability": 0.88623046875}, {"start": 1719.87, "end": 1720.13, "word": " لأن", "probability": 0.72802734375}, {"start": 1720.13, "end": 1720.27, "word": " ال", "probability": 0.6171875}, {"start": 1720.27, "end": 1720.65, "word": " unitary", "probability": 0.67578125}, {"start": 1720.65, "end": 1721.51, "word": " عشان", "probability": 0.93603515625}, {"start": 1721.51, "end": 1721.69, "word": " يكون", "probability": 0.925048828125}, {"start": 1721.69, "end": 1721.99, "word": " unitary", "probability": 0.8642578125}, {"start": 1721.99, "end": 1722.33, "word": " لازم", "probability": 0.8717447916666666}, {"start": 1722.33, "end": 1722.53, "word": " يكون", "probability": 0.964599609375}, {"start": 1722.53, "end": 1722.77, "word": " say", "probability": 0.1837158203125}, {"start": 1722.77, "end": 1723.35, "word": " adjective", "probability": 0.546875}, {"start": 1723.35, "end": 1723.93, "word": " و", "probability": 0.83984375}, {"start": 1723.93, "end": 1725.65, "word": " الهو", "probability": 0.4978841145833333}, {"start": 1725.65, "end": 1727.37, "word": " isometric", "probability": 0.867919921875}, {"start": 1727.37, "end": 1729.11, "word": " او", "probability": 0.690185546875}, {"start": 1729.11, "end": 1729.41, "word": " لو", "probability": 0.2388916015625}, {"start": 1729.41, "end": 1729.59, "word": " T", "probability": 0.61328125}, {"start": 1729.59, "end": 1729.93, "word": " inverse", "probability": 0.71484375}, {"start": 1729.93, "end": 1730.19, "word": " بسبب", "probability": 0.6920572916666666}, {"start": 1730.19, "end": 1730.35, "word": " T", "probability": 0.82080078125}, {"start": 1730.35, "end": 1730.67, "word": " star", "probability": 0.11944580078125}, {"start": 1730.67, "end": 1731.43, "word": " unitary", "probability": 0.549713134765625}, {"start": 1731.43, "end": 1734.53, "word": " بتكون", "probability": 0.902099609375}, {"start": 1734.53, "end": 1735.23, "word": " اللي", "probability": 0.75634765625}, {"start": 1735.23, "end": 1735.57, "word": " هي", "probability": 0.88916015625}, {"start": 1735.57, "end": 1736.75, "word": " adjective", "probability": 0.491455078125}, {"start": 1736.75, "end": 1737.13, "word": " زي", "probability": 0.638916015625}, {"start": 1737.13, "end": 1737.69, "word": " T", "probability": 0.53759765625}, {"start": 1737.69, "end": 1738.81, "word": " inverse", "probability": 0.8037109375}, {"start": 1738.81, "end": 1739.11, "word": " بسبب", "probability": 0.9697265625}, {"start": 1739.11, "end": 1739.29, "word": " T", "probability": 0.97900390625}, {"start": 1739.29, "end": 1739.57, "word": " star", "probability": 0.67041015625}, {"start": 1739.57, "end": 1740.67, "word": " مبارك", "probability": 0.9383544921875}, {"start": 1740.67, "end": 1740.79, "word": " الله", "probability": 0.9638671875}, {"start": 1740.79, "end": 1741.13, "word": " فيكم", "probability": 0.96240234375}, {"start": 1741.13, "end": 1741.25, "word": " و", "probability": 0.8681640625}, {"start": 1741.25, "end": 1741.41, "word": " إلى", "probability": 0.708984375}, {"start": 1741.41, "end": 1741.83, "word": " لقاء", "probability": 0.9567057291666666}, {"start": 1741.83, "end": 1742.29, "word": " آخر", "probability": 0.7169189453125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1742.72725, "duration_after_vad": 1699.4743749999966}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mRYCDgWMxU8_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mRYCDgWMxU8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9d03312666839de43102da058384df0df2e45cc0
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mRYCDgWMxU8_raw.srt
@@ -0,0 +1,1460 @@
+1
+00:00:05,030 --> 00:00:07,610
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,610 --> 00:00:10,370
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,370 --> 00:00:14,910
+آله وصحبه أجمعينهذه المحاضرة رقم خمسة وعشرين مساق
+
+4
+00:00:14,910 --> 00:00:19,230
+تحليل اقتراني او تحليل دالي طولة بطالبات الجامعة
+
+5
+00:00:19,230 --> 00:00:25,110
+الإسلامية قسم الرياضيات ماجستير الرياضيات الان ان
+
+6
+00:00:25,110 --> 00:00:28,330
+شاء الله هناخد اخر section في شبطر تلاتة اللي هو
+
+7
+00:00:28,330 --> 00:00:32,550
+انواع ال operators اللي هنحكي عنها اللي هي self
+
+8
+00:00:32,550 --> 00:00:36,010
+-adjoint وunitary وnormal operators المحاضرة
+
+9
+00:00:36,010 --> 00:00:41,210
+الماضية عرفنا شو معنات a joint operatorالان هنحكي
+
+10
+00:00:41,210 --> 00:00:45,630
+عن شو معناه الـ self-adjoint operator شو معناه الـ
+
+11
+00:00:45,630 --> 00:00:49,450
+normal operator شو معناه الـ unitary operator و
+
+12
+00:00:49,450 --> 00:00:53,110
+بالمناسبة في طبعا احنا هذه الأسماء مرت علينا في
+
+13
+00:00:53,110 --> 00:00:59,090
+الجبر الخطي فكلها مقابل في الجبر الخطي اصلا ال
+
+14
+00:00:59,090 --> 00:01:01,890
+matrix في الآخر اللي هو احنا بنقدر نعمل نشتغل و
+
+15
+00:01:01,890 --> 00:01:06,360
+كأنهoperator على finite dimensional فاحنا طبعا
+
+16
+00:01:06,360 --> 00:01:10,080
+هنحكي عن ال operators بصورة عامة مش هنتطرق لتفاصيل
+
+17
+00:01:10,080 --> 00:01:13,860
+ال matrices نيجي نشوف اللي هو ال definition
+
+18
+00:01:13,860 --> 00:01:18,060
+التلاتة عشرة واحد a bounded linear operator T من H
+
+19
+00:01:18,060 --> 00:01:21,820
+لعند H انه Hilbert space H ال set to be اذا انا
+
+20
+00:01:21,820 --> 00:01:26,080
+تصنيفي في هذا الاتجاه لمين ال bounded linear
+
+21
+00:01:26,080 --> 00:01:30,020
+operator على مين على Hilbert space بنقول عنه كمان
+
+22
+00:01:30,020 --> 00:01:34,220
+من H لمين لHاللي احنا حاكينا عنه الـ Adjoint قبل
+
+23
+00:01:34,220 --> 00:01:39,840
+شوية من H1 أو الـ H2 لأن لأ بحكي عن اللي بتدعرفهم
+
+24
+00:01:39,840 --> 00:01:43,760
+الآن لحاليا من HLH اللي هو مين اولاشي self-adjoint
+
+25
+00:01:43,760 --> 00:01:47,600
+او hermitian اذا كان الـT ستار تبعه ايش بيساوي
+
+26
+00:01:47,600 --> 00:01:51,020
+بيساوي الـT اللي هو الـadjoint بيساوي نفس الـT
+
+27
+00:01:51,020 --> 00:01:55,740
+بنسميه ايش ماله hermitian او self-adjoint operator
+
+28
+00:01:55,740 --> 00:02:00,700
+بنسميه unitary اذا كان الـT bidictive
+
+29
+00:02:02,270 --> 00:02:09,150
+والـ T*) ايش بيساوي الـ T انفرس والـ
+
+30
+00:02:09,150 --> 00:02:16,330
+T نفسه unitary بيجيكشن او بيجيكتف ماب بيصير عندي
+
+31
+00:02:16,330 --> 00:02:19,930
+اللي هو شرطين انفرسياللي هو الـ T تكون bijective
+
+32
+00:02:19,930 --> 00:02:23,850
+شرط التاني T star بيساوي T inverse تلاتة ال normal
+
+33
+00:02:23,850 --> 00:02:27,410
+operator إذا كان ال T في ال T star إيش بيساوي
+
+34
+00:02:27,410 --> 00:02:30,430
+بيساوي T star في T طبعا في أنواع ال operators
+
+35
+00:02:30,430 --> 00:02:33,850
+عديدة يعني غير هذه اللي هي ال operators بس خلينا
+
+36
+00:02:33,850 --> 00:02:38,070
+نركز على هذه في هذا ال course المحدود طيب الآن أول
+
+37
+00:02:38,070 --> 00:02:42,780
+ملاحظة إذا كان ال T self-adjointهيكون عند الـ T X
+
+38
+00:02:42,780 --> 00:02:46,160
+وال Y بيساوي X و T Star Y ومزام الـ T Star Y
+
+39
+00:02:46,160 --> 00:02:50,220
+بيساوي T إذا بيصير الـ T X و Y بيساوي X و T Y يعني
+
+40
+00:02:50,220 --> 00:02:53,360
+بتنقل الـ T من هنا إلى هنا زي ما بدك في حالك مين
+
+41
+00:02:53,360 --> 00:02:59,310
+أن يكون T self-adjointلأن لو كان الـ T self
+
+42
+00:02:59,310 --> 00:03:04,850
+-adjoint أو unitary بتكون الـ T normal شوف كيف لو
+
+43
+00:03:04,850 --> 00:03:09,310
+كان self-adjoint بيصير الـ T في الـ T star هي
+
+44
+00:03:09,310 --> 00:03:12,810
+عبارة عن الـ T في T إذا كان self-adjoint اللي هي T
+
+45
+00:03:12,810 --> 00:03:15,710
+تربيع اللي هي نفس الـ T star في T اللي هي T في T
+
+46
+00:03:15,710 --> 00:03:19,110
+في T تربيع إذا لما يكون self-adjoint automatic
+
+47
+00:03:19,110 --> 00:03:25,880
+هيكون يشماله normalلو كان unitary بيكون الـ T*) هو
+
+48
+00:03:25,880 --> 00:03:30,060
+T inverse ماشي الحال و تنسوش الـ T bijective إذا
+
+49
+00:03:30,060 --> 00:03:32,340
+الـ T inverse bijective يعني الـ T في الـ T
+
+50
+00:03:32,340 --> 00:03:36,460
+inverse هيساوي ال identity و الآن الـ T inverse في
+
+51
+00:03:36,460 --> 00:03:39,520
+الـ T برضه هيساوي ال identity لأنه bijectiveإذاً
+
+52
+00:03:39,520 --> 00:03:41,940
+هيكون الـ T في الـ T*) بيساوي الـ T*) في الـ T
+
+53
+00:03:41,940 --> 00:03:46,280
+Automatic مادام إيش اسمه Unitary إذاً إذا كانت
+
+54
+00:03:46,280 --> 00:03:49,460
+Unitary أو self-adjoint Automatic هيكون Normal
+
+55
+00:03:49,460 --> 00:03:54,380
+الآن Normal Operators need not to be self-adjoint
+
+56
+00:03:54,380 --> 00:03:58,440
+ولا Unitary يعني ليس شرطاً ليكون self-adjoint ولا
+
+57
+00:03:58,440 --> 00:04:01,780
+يكون إيش ما له Unitary الآن بدنا مثال على Normal
+
+58
+00:04:01,780 --> 00:04:06,060
+Operator لا يكون self-adjoint ولا يكون Unitary خد
+
+59
+00:04:06,690 --> 00:04:09,830
+خد المثال التالي To see this consider the identity
+
+60
+00:04:09,830 --> 00:04:13,970
+operator I من H لعند مين لعند H ال identity العادى
+
+61
+00:04:13,970 --> 00:04:18,810
+اه الان ان هيلبرت اسمه H it is easy to see that ال
+
+62
+00:04:18,810 --> 00:04:23,650
+T خدوا ال T لان بساوة 2I في مين في I اذا المثال
+
+63
+00:04:23,650 --> 00:04:27,750
+اللي انا بدأ اقولكم انه عبارة عن اللي هو ال ال ال
+
+64
+00:04:27,750 --> 00:04:34,070
+normal لكن مش self-adjoint T بساوة 2I في مين في I
+
+65
+00:04:34,670 --> 00:04:39,910
+ماشي الحال الان لو جينا أخدنا ال T star له ال T
+
+66
+00:04:39,910 --> 00:04:44,370
+star اللي هو هيساوي اللي هو سالب اتنين I في مين
+
+67
+00:04:44,370 --> 00:04:48,850
+فال identity ماشي الحال هذا اللي هو إيش ال T star
+
+68
+00:04:48,850 --> 00:04:52,570
+له الكون جيت له طبعا و اثباته سهل هذا لو اللي هو
+
+69
+00:04:52,570 --> 00:05:00,220
+عندك ال T X و ال Y بساوي اللي هو Xأو الآن الـ T
+
+70
+00:05:00,220 --> 00:05:05,220
+star خُذ 2I الآن على الجهة الثانية لما يحصل كنت
+
+71
+00:05:05,220 --> 00:05:08,820
+جيب C سالب 2I، مظبوط؟ إذن طبيعي بيكون اللي هو T
+
+72
+00:05:08,820 --> 00:05:13,960
+star هو مين الـ T نفسه، بسوء تناقص 2I في I طيب،
+
+73
+00:05:13,960 --> 00:05:20,660
+الآن الـ T inverse هيسوي 1 على 2I في مين في I،
+
+74
+00:05:20,660 --> 00:05:25,040
+ماشي الحالة واضح إن الـ T بتسويش الـ T inverse
+
+75
+00:05:25,040 --> 00:05:31,960
+والـ T star بتسويش الـ Tمعايا واضح ان ال T في T
+
+76
+00:05:31,960 --> 00:05:38,380
+star T في T star بساوي اللي هو T star في T بساوي
+
+77
+00:05:38,380 --> 00:05:45,980
+أربعة I بظبط لإن اضربه هذي اتنين I في اتنين I
+
+78
+00:05:45,980 --> 00:05:49,520
+بيطلع اللي هو أربعة ال identity I تربية ما هي ال I
+
+79
+00:05:49,520 --> 00:05:52,200
+ما انتوا عارفين اذا اللي عندي الان
+
+80
+00:05:54,790 --> 00:05:57,610
+هذا مثال على الـ Normal operator need not to be
+
+81
+00:05:57,610 --> 00:06:01,670
+self-adjoint normally تبقى اطلع على فوقهنجي الان
+
+82
+00:06:01,670 --> 00:06:05,690
+نظريتنا الأولى theorem 13-3 let T من H مع اند H be
+
+83
+00:06:05,690 --> 00:06:09,010
+a bounded linear operator on a Hilbert space H
+
+84
+00:06:09,010 --> 00:06:14,310
+then if T self-adjoint then ال T X والX هيكون إيش
+
+85
+00:06:14,310 --> 00:06:18,650
+ماله real لكل X في ال X هذا كلام مهم إذا كانت ال T
+
+86
+00:06:18,650 --> 00:06:22,070
+عبارة عن self-adjoint هيكون automatic ال T X والX
+
+87
+00:06:22,070 --> 00:06:27,350
+إيش ماله دايماً real ماشي الان إذا كان H complex
+
+88
+00:06:28,260 --> 00:06:32,280
+إذا كان نفسه H is a complex هذا اللي فوق بغض النظر
+
+89
+00:06:32,280 --> 00:06:35,980
+إيش هي الـH هيكون الـTX والX إيش ما له real الآن
+
+90
+00:06:35,980 --> 00:06:40,380
+اللي كانت H complex وكان الـTX والX real automatic
+
+91
+00:06:40,380 --> 00:06:46,520
+هيكون عند الـT self-adjointلكن لو كان H مش Complex
+
+92
+00:06:46,520 --> 00:06:51,520
+وكانت الـ TX والـ X ريال ليس شرطاً انه تكون الهو T
+
+93
+00:06:51,520 --> 00:06:55,620
+سلف الدولة اصلا ممكن تكون TX والX مزام ريال هيكون
+
+94
+00:06:55,620 --> 00:07:01,970
+TX والX ريال طبيعي اه فهذا طبعا ليس شرطاإنه لو
+
+95
+00:07:01,970 --> 00:07:06,950
+بدنا نسلم بهذا if H is real و T X و X real إذن الـ
+
+96
+00:07:06,950 --> 00:07:09,830
+T الـ self-adjoint ما هو كل الـ T .. كل اللي في
+
+97
+00:07:09,830 --> 00:07:13,030
+الدنيا الـ T اللي على الـ real هيكون الـ T X و الـ
+
+98
+00:07:13,030 --> 00:07:15,450
+X real يعني هذا الشرط متحقق اوتوماتيكي يعني كل
+
+99
+00:07:15,450 --> 00:07:18,670
+اللي هيطلع الـ self-adjoint لأ طبعا واضح إذن ..
+
+100
+00:07:18,670 --> 00:07:22,450
+إذن .. إذن النظرية الجزء B هذا وين بيحدث في حالة
+
+101
+00:07:22,450 --> 00:07:30,160
+main H is complex نيجي لبنهم نيجي الآنالـ subpose
+
+102
+00:07:30,160 --> 00:07:33,420
+ده الـ T السلفة الـ joint تن لكل X في الـ H احسب
+
+103
+00:07:33,420 --> 00:07:36,620
+ما يليه عشان اثبت ان الـ T X وال X الريالد ده تبت
+
+104
+00:07:36,620 --> 00:07:39,180
+أن ال conjugate هيطلع نفسه ماشي ان انا اخد ال
+
+105
+00:07:39,180 --> 00:07:44,460
+conjugate ل T X وال X بسوء X و T X مظبوط X و T X
+
+106
+00:07:44,460 --> 00:07:50,170
+وT سلفة ال joint هيسوء T X و Xبس هيفضّوهم إذا صار
+
+107
+00:07:50,170 --> 00:07:56,110
+عندي اللي هو TX و X is real الآن ال B suppose that
+
+108
+00:07:56,110 --> 00:08:00,250
+H is complex هستخدم شكلي النظرية تبعت المرة اللي
+
+109
+00:08:00,250 --> 00:08:03,990
+فاتت اللي مال اللي فاتت للمحاضر اللي فاتت suppose
+
+110
+00:08:03,990 --> 00:08:09,430
+that H is complex and TX و X أشماله is real لكل X
+
+111
+00:08:09,430 --> 00:08:14,090
+element in H هذا الفرضية then شوف كيف يثبت لك إنه
+
+112
+00:08:14,090 --> 00:08:21,180
+اللي هو ال T بتساوي ال T starعندي TX و X بيساوي TX
+
+113
+00:08:21,180 --> 00:08:27,100
+و X conjugate صح ولا لأ لإنها real و يساوي الآن ال
+
+114
+00:08:27,100 --> 00:08:33,160
+TX و ال X من تعريف ال joint بيساوي X و T star X صح
+
+115
+00:08:33,160 --> 00:08:38,270
+ال conjugate اللي هو هيطلع T star X و 100 و Xالان
+
+116
+00:08:38,270 --> 00:08:45,770
+عند خدق الآن السفر بساوي T X و X ناقص T Star X و X
+
+117
+00:08:45,770 --> 00:08:49,110
+نجلناها ما هو على طول احنا جابلنا كلنا مادام هذا
+
+118
+00:08:49,110 --> 00:08:51,710
+بساوي و هذا دايما ايضا على طول بساوي T Star بس
+
+119
+00:08:51,710 --> 00:08:57,570
+خلينا الان نبسطها للاخر الان صار عند T X و X ناقص
+
+120
+00:08:57,570 --> 00:09:01,600
+T Star X و X بتساوي سفر و يساويجيبوا الـ inner
+
+121
+00:09:01,600 --> 00:09:07,280
+product مع بعض بيصير T نقص T star X O X بساوة سفر
+
+122
+00:09:07,280 --> 00:09:11,320
+وهذا الكلام صحيح لكل X في الدنيا إذن هذا اللي
+
+123
+00:09:11,320 --> 00:09:15,160
+كانوا بيسمونه Q احنا في المرة اللي فاتت فهيطلع Q
+
+124
+00:09:15,160 --> 00:09:18,820
+بتساوة سفر من اللمّة تلاتة تسعة تلاتة بيه إذا صار
+
+125
+00:09:18,820 --> 00:09:22,340
+عند Q اللي هو T minus T star بساوة سفر ومن ثم T
+
+126
+00:09:22,340 --> 00:09:25,200
+بساوة T star ومن ثم T is self-adjoint إذا انا
+
+127
+00:09:25,200 --> 00:09:30,180
+automatic اللي هو T is self-adjointطبعاً اللي
+
+128
+00:09:30,180 --> 00:09:33,920
+بتطلب التطبيق هذي لإنما ان يكون Hاش ما له Complex
+
+129
+00:09:33,920 --> 00:09:39,480
+اطلع لفوق الان the product of two bounded self
+
+130
+00:09:39,480 --> 00:09:43,900
+-adjoint linear operators S and T ان هيلبرت سبيس H
+
+131
+00:09:43,900 --> 00:09:47,140
+is self-adjoint if and only if S في T بيساوي TS
+
+132
+00:09:47,140 --> 00:09:55,460
+يعني بقوللي الآن لو كان عندي T و S self-adjoint كل
+
+133
+00:09:55,460 --> 00:10:01,480
+واحد ماشي الحالبقول لي إذا .. إذا اللي هو S في T
+
+134
+00:10:01,480 --> 00:10:11,800
+is self-adjoint if and only if ST أش بيساوي TS
+
+135
+00:10:11,800 --> 00:10:18,000
+ماشي الحال؟ طيب هذا الأمر بسيط وسهل a proof .. a
+
+136
+00:10:18,000 --> 00:10:24,720
+proof بنا نفض صباز that
+
+137
+00:10:25,640 --> 00:10:35,740
+S T الـ self-adjoint ماشي الحال؟ لأ دهن، دهن S T
+
+138
+00:10:35,740 --> 00:10:45,280
+بساوي S T اللي هو S Star في T Star صح ولا لأ؟ من
+
+139
+00:10:45,280 --> 00:10:51,230
+التعريف، لأن T و S يشمل أنه self-adjointمعايا اه
+
+140
+00:10:51,230 --> 00:10:59,390
+الان S T لكل Star بساوي انا بدأ اثبت هذه الان اه S
+
+141
+00:10:59,390 --> 00:11:04,890
+T بساوية T S معايا الان S Star في T Star ماهو الان
+
+142
+00:11:04,890 --> 00:11:12,950
+S T silver joint اذا هو عبارة عن S T Star T S لكل
+
+143
+00:11:12,950 --> 00:11:22,620
+Star ده خليني ابدأ بالعكس عشان T S وهناA T Star S
+
+144
+00:11:22,620 --> 00:11:30,240
+Star فبساوي S في T الكل Star بتظبط بحيط بتظبط صحيح
+
+145
+00:11:30,240 --> 00:11:33,620
+دايما صحيح هو يساوي S في T سلفة ال joint ايش
+
+146
+00:11:33,620 --> 00:11:39,560
+هيساوي عشان بس هذه عشان الأخيرة S في T Star سلفة S
+
+147
+00:11:39,560 --> 00:11:43,420
+T لأنه مفترض من سلفة ال joint S T اذا T S ايش
+
+148
+00:11:43,420 --> 00:11:50,210
+بتساوي S T conversely conversely suppose thatأس تي
+
+149
+00:11:50,210 --> 00:11:55,070
+بيساوي TS ماشي الحال الان بدي اتبعتلكم أس تي سيلفا
+
+150
+00:11:55,070 --> 00:12:00,810
+جون الان أس تي لكل ستار مش هيساوياللي هو حسب
+
+151
+00:12:00,810 --> 00:12:06,270
+القانون T Star S Star صح؟ و يساوي T Star هو الـ T
+
+152
+00:12:06,270 --> 00:12:09,950
+لأن الـ self-adjoint من رأس الدور و الـ S Star S
+
+153
+00:12:09,950 --> 00:12:13,230
+اللي هي الـ self-adjoint من رأس الدور و أنا الآن
+
+154
+00:12:13,230 --> 00:12:18,770
+مفترض S T إيش بيساوي P S إذا T فاس إيش هتساوي S في
+
+155
+00:12:18,770 --> 00:12:23,550
+T إذا صار S في T بيساوي S في T إيش لكل Star إذا S
+
+156
+00:12:23,550 --> 00:12:28,290
+T is self-adjoint هذه اللي هي theorem
+
+157
+00:12:31,340 --> 00:12:37,200
+اللي هو تلاتة عشر خمسة الان تخليني تخليني على
+
+158
+00:12:37,200 --> 00:12:42,400
+النظرية اللي قبلها theorem تلاتة عشر خمسة let TN
+
+159
+00:12:42,400 --> 00:12:45,520
+be a sequence of bounded linear self and joint
+
+160
+00:12:45,520 --> 00:12:49,820
+linear operators وTN من H لعند H انها ال
+
+161
+00:12:49,820 --> 00:12:56,190
+participate Hsuppose that TN بتروح لـ T S اللي هو
+
+162
+00:12:56,190 --> 00:13:01,910
+that is norm of TN بتروح لنخستي بتروح لصفر where
+
+163
+00:13:01,910 --> 00:13:05,470
+this norm is the norm on the space BHWH عارفينه
+
+164
+00:13:05,470 --> 00:13:08,590
+طبعا يعني then T is a bounded self-adjoint linear
+
+165
+00:13:08,590 --> 00:13:12,810
+operator يعني و كأنه بيقول اللي خلّي بيقول انه
+
+166
+00:13:12,810 --> 00:13:16,550
+اللي هو sequence of sequence of self-adjoint
+
+167
+00:13:16,550 --> 00:13:22,350
+operatorsلو converged لـ some T لازم الـ T تكون
+
+168
+00:13:22,350 --> 00:13:24,370
+إيه أشمالها؟ self-adjoint
+
+169
+00:13:27,030 --> 00:13:32,650
+معنى إيش بقول؟ لو كانت عندى اللى بقوله TN sequence
+
+170
+00:13:32,650 --> 00:13:37,170
+of self-adjoint linear operators و هدى conveges
+
+171
+00:13:37,170 --> 00:13:42,890
+لصم T لازم الـ T هدى إيش تطلع self-adjoint يعني
+
+172
+00:13:42,890 --> 00:13:47,550
+بمعنى أخر لازم أثبتلك إنه norm T نقص T star اللى
+
+173
+00:13:47,550 --> 00:13:51,930
+هو بساوي سفر ماشي معناته ال T بتساوي مين؟ T star
+
+174
+00:13:51,930 --> 00:14:00,750
+شوف عليها الآن ال TNالـ TN الـ TN اللي هو Silver
+
+175
+00:14:00,750 --> 00:14:07,030
+Joint مظبوط ولا لأ؟ إذا الـ TN converts للـ T و
+
+176
+00:14:07,030 --> 00:14:12,410
+TN*) converts للـ T ليش؟ لأن كل واحدة من هدول هي
+
+177
+00:14:12,410 --> 00:14:17,110
+هدول ماشي الحال إذا هذه بتعطيني هدولة بيعطيني نورم
+
+178
+00:14:17,110 --> 00:14:24,300
+الـ TN ناقص الـ T بروح للـ 0أه و هذا بيعطيني نورم
+
+179
+00:14:24,300 --> 00:14:29,460
+الـ T N Star ناقص الـ T برضه هيروح لين للـ Zero
+
+180
+00:14:29,460 --> 00:14:39,620
+احسبلي الآن نورم الـ T ناقص الـ T Star اللي
+
+181
+00:14:39,620 --> 00:14:48,420
+هو أصغر أو يساوي أصغر أو يساوي نورم الـ T ناقص
+
+182
+00:14:50,680 --> 00:15:06,660
+الـ TN زائد نورم الـ TN ناقص TN*) مظبوط زائد
+
+183
+00:15:06,660 --> 00:15:15,320
+نورم فعله بس على الكتاب بالله فعله الكتاب زائد
+
+184
+00:15:16,400 --> 00:15:26,940
+Norm نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+185
+00:15:26,940 --> 00:15:30,100
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+186
+00:15:30,100 --> 00:15:36,100
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+187
+00:15:36,100 --> 00:15:37,840
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+188
+00:15:37,840 --> 00:15:38,380
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+189
+00:15:38,380 --> 00:15:38,460
+نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل نزل
+
+190
+00:15:38,460 --> 00:15:43,040
+نزل نزل نزل نزل
+
+191
+00:15:43,040 --> 00:15:53,880
+نزلالـ TN ناقص T أسطار أسطار ماشي الحال طيب الآن
+
+192
+00:15:53,880 --> 00:16:02,400
+هذه بتروح لمين للسفر وهذه ايش بتساوي سفر ماشي وهذه
+
+193
+00:16:02,400 --> 00:16:11,030
+بتساوي norm ال TN ناقص T الكل نالهماشي الحال هذه
+
+194
+00:16:11,030 --> 00:16:15,110
+اللي جوه بتروح لمين برضه للصفر اذا هذا الان كمان
+
+195
+00:16:15,110 --> 00:16:20,830
+هيروح لمين كله للزيرو اذا صار عندي norm of T نقص T
+
+196
+00:16:20,830 --> 00:16:23,310
+طبعا هذا دايما اكبر تساوي مين صفر يعني اخدنا نمية
+
+197
+00:16:23,310 --> 00:16:28,130
+اذا الان goes to infinity فبطلع T بتساوي T star
+
+198
+00:16:28,130 --> 00:16:34,040
+ومن ثم Tيشملها الـ self-adjoint طبعا كل وين هذا ال
+
+199
+00:16:34,040 --> 00:16:38,880
+convergence في ال B H وH اللي هي اللي هي the set
+
+200
+00:16:38,880 --> 00:16:43,220
+of all bounded linear operators من H لعند H اذا
+
+201
+00:16:43,220 --> 00:16:49,780
+احنا اللي اثبتنا انه ال TN لو كانت sequence of
+
+202
+00:16:49,780 --> 00:16:53,420
+bounded self-adjoint linear operatorsconverge the
+
+203
+00:16:53,420 --> 00:16:57,440
+sum T هيكون limitها برضه ايش ماله اللي هو self
+
+204
+00:16:57,440 --> 00:17:04,760
+-adjoint linear operator اطلع لفوق اطلع لفوق يالا
+
+205
+00:17:04,760 --> 00:17:10,080
+البعد خلاص خليني اشرح منها خلاص خلاص خليني اشرح
+
+206
+00:17:10,080 --> 00:17:14,160
+منها let the operator U من H لعند H و V من H لH be
+
+207
+00:17:14,160 --> 00:17:20,710
+unitary او H is a Hilbert space thenالخاص التالية
+
+208
+00:17:20,710 --> 00:17:25,910
+متحققة خاص كلها يعني محسبتها حتى سريعة U is
+
+209
+00:17:25,910 --> 00:17:30,010
+isometric اخد معاه ايش هو معناه انزومتري نورم ال U
+
+210
+00:17:30,010 --> 00:17:32,910
+X ايش بيساوي نورم ال X لكل X هو اللي موجودة في ال
+
+211
+00:17:32,910 --> 00:17:38,110
+H و نورم ال U ال unitary هذا طبعا احنا اخدنا اللي
+
+212
+00:17:38,110 --> 00:17:42,190
+هو ال U ايش ماله و ال V unitary operators هذه خاص
+
+213
+00:17:42,190 --> 00:17:47,420
+ال unitary operatorsبيصير Normal U بساوي واحد على
+
+214
+00:17:47,420 --> 00:17:52,640
+اعتبار ان الـH أشمالها مش الـ0 ال part space و ال
+
+215
+00:17:52,640 --> 00:17:58,040
+U inverse اللي هو طبعا مادام Unitary اللي هو الـU
+
+216
+00:17:58,040 --> 00:18:02,600
+inverse نفسه برضه أشماله is Unitaryوهذه سهلة برضه
+
+217
+00:18:02,600 --> 00:18:06,440
+و ال U في V إيش برضه هيطلع Unitary إذا كانت U
+
+218
+00:18:06,440 --> 00:18:10,380
+Unitary و V Unitary برضه حاصر ضربين Unitary و برضه
+
+219
+00:18:10,380 --> 00:18:14,520
+كلام كله سهل و ال U إيش مالها Normal أثبتناها
+
+220
+00:18:14,520 --> 00:18:17,720
+قولناها المرة الفاترة أو في أول محاضرة اطلع لفوق
+
+221
+00:18:17,720 --> 00:18:23,360
+اطلع الان a bounded linear operator T on a Hilbert
+
+222
+00:18:23,360 --> 00:18:26,920
+.. on a complex Hilbert space H is unitary if and
+
+223
+00:18:26,920 --> 00:18:30,790
+only if T إيش مالها is isometricلو كانت Unitary
+
+224
+00:18:30,790 --> 00:18:34,210
+بتعطينا زيومتريك بتكون أثبتناها في الأول بتظهر الـ
+
+225
+00:18:34,210 --> 00:18:38,450
+Main العكس خلّينا نشوف الأولى بدنا نثبت أنها الـ
+
+226
+00:18:38,450 --> 00:18:42,570
+Unitary is isometry خد النورم لـUX لكل تربيع إيش
+
+227
+00:18:42,570 --> 00:18:47,010
+بيساوي اللي هي نورمبردكت بين الـUX والـUXماشي
+
+228
+00:18:47,010 --> 00:18:50,610
+الانوي ساوي X من خلاص ال joint بيصير X و U Star في
+
+229
+00:18:50,610 --> 00:18:54,050
+U U Star في U ماهي ال U Star في ال Unitary بيساوي
+
+230
+00:18:54,050 --> 00:18:56,870
+U Inverse فال U Inverse في ال U و ال U is
+
+231
+00:18:56,870 --> 00:19:00,750
+bijective إذن هيصير ال identity إذن X و ال IX اللي
+
+232
+00:19:00,750 --> 00:19:03,950
+هو نورم ال X تربيه إذن ال U X بيساوي نورم ال X إذن
+
+233
+00:19:03,950 --> 00:19:06,510
+he preserved the norm أو preserve the distance أو
+
+234
+00:19:06,510 --> 00:19:11,860
+preserve the inner product ده العيزومتريالان الجزء
+
+235
+00:19:11,860 --> 00:19:16,860
+الثاني بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+236
+00:19:16,860 --> 00:19:17,520
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+237
+00:19:17,520 --> 00:19:17,540
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+238
+00:19:17,540 --> 00:19:17,800
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+239
+00:19:17,800 --> 00:19:20,900
+بي بي بي
+
+240
+00:19:20,900 --> 00:19:27,140
+بي بي بي بي
+
+241
+00:19:27,140 --> 00:19:27,520
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+242
+00:19:27,520 --> 00:19:30,640
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+243
+00:19:30,640 --> 00:19:36,320
+بي
+
+244
+00:19:36,320 --> 00:19:42,230
+بي ببسوء norm ال X هذا في ال unitary إذا الأن norm
+
+245
+00:19:42,230 --> 00:19:48,110
+اللي هو ال U X على norm ال X اللي هو بسوء واحد ال
+
+246
+00:19:48,110 --> 00:19:53,150
+supremum اللي هو norm ال U هي سوء واحد إذا طبيعي
+
+247
+00:19:53,150 --> 00:19:59,250
+norm ال unitary بسوء واحد طيبالان ال .. ال .. ال
+
+248
+00:19:59,250 --> 00:20:03,030
+.. ال U inverse ال U bijective لنثبت ان ال U
+
+249
+00:20:03,030 --> 00:20:07,830
+inverse unitary U unitary اذا bijective و ال U
+
+250
+00:20:07,830 --> 00:20:12,670
+inverse يساوي U star طيب الان U is bijective اذا
+
+251
+00:20:12,670 --> 00:20:17,530
+ال U inverse موجودة و برضه bijective ماشي؟ اذا
+
+252
+00:20:17,530 --> 00:20:20,310
+الان الشرط الاول بالنسبة لل U inverse هتكون
+
+253
+00:20:20,310 --> 00:20:25,000
+unitary تحقق ان هي bijectiveو لو أخدنا ال U
+
+254
+00:20:25,000 --> 00:20:28,560
+Inverse Star هي ساوي ال U Inverse ما هي Unitary
+
+255
+00:20:28,560 --> 00:20:34,060
+ماشي؟ إذا ال U Star Star صارت اليمين بيساوي ال U
+
+256
+00:20:34,060 --> 00:20:37,400
+اللي هي بتساوي U Inverse Inverse إذا صارت ال U
+
+257
+00:20:37,400 --> 00:20:41,860
+Inverse Star بيساوي U Inverse Inverse إذا صارت
+
+258
+00:20:41,860 --> 00:20:46,640
+اللي هي ال U Inverse نفسها is Unitaryفاضح؟ طيب
+
+259
+00:20:46,640 --> 00:20:52,140
+الان ال U V بتثبت انها Unitary ال U Unitary و ال V
+
+260
+00:20:52,140 --> 00:20:56,100
+Unitary اذا ال U بيجيكتف و ال V بيجيكتف اذا ال
+
+261
+00:20:56,100 --> 00:21:00,340
+composition اللي هنا ال U V بيجيكتف هو مش هيك كمان
+
+262
+00:21:00,340 --> 00:21:04,500
+و لو اخدت ال U V لكل Star هيساوي ال U V لكل
+
+263
+00:21:04,500 --> 00:21:08,760
+Inverse ليش؟لأن هذا الـ U V لكل Star من خلاص اللي
+
+264
+00:21:08,760 --> 00:21:12,140
+هي الـ Star اللي هي V Star U Star و الـ V Star
+
+265
+00:21:12,140 --> 00:21:15,320
+مدام V Unitary بيساوي الـ V Inverse و الـ U Star
+
+266
+00:21:15,320 --> 00:21:18,280
+برضه بيساوي U Inverse لأنها Unitary برضه اللي هي
+
+267
+00:21:18,280 --> 00:21:22,160
+هذه بتساوي إيش U في V لكل إيش Inverse إذا صار U V
+
+268
+00:21:22,160 --> 00:21:25,820
+لكل Star بيساوي U V لكل Inverse بمعنى آخر صارت الـ
+
+269
+00:21:25,820 --> 00:21:29,600
+U في V is Unitary طيب الان
+
+270
+00:21:31,660 --> 00:21:35,620
+U inverse بيساوي U star اللي هو و ال U في ال U
+
+271
+00:21:35,620 --> 00:21:38,680
+inverse بيساوي ال U inverse في ال U بيساوي مين
+
+272
+00:21:38,680 --> 00:21:45,220
+بيساوي ال ايش ال identity مباشرة طيب الان صار عندي
+
+273
+00:21:45,220 --> 00:21:48,460
+الان اللي هو هذا بالنسبة ليه انزل انزل انزل انزل
+
+274
+00:21:48,460 --> 00:21:52,480
+بالنسبة ليه انزل انزل انزل بالنسبة ليه بالنسبة ليه
+
+275
+00:21:52,480 --> 00:21:56,420
+الان U is ايش ماله normal اخببته انا اه اطلع لفوق
+
+276
+00:21:56,420 --> 00:21:57,880
+طيب
+
+277
+00:22:00,640 --> 00:22:03,960
+النجلة اللي هي الجزء الأول اللي قلنا automatic
+
+278
+00:22:03,960 --> 00:22:09,700
+صبوس that is isometric and surjective ماشي and
+
+279
+00:22:09,700 --> 00:22:14,520
+surjective isometry implies injectivityقلناها إذا
+
+280
+00:22:14,520 --> 00:22:18,160
+كانت isometric قبلها ذكرناها كثير إذا كانت اللي ..
+
+281
+00:22:18,160 --> 00:22:21,700
+اللي هي isometric على طول أشملها indicative عندي T
+
+282
+00:22:21,700 --> 00:22:25,260
+دثويت الكوم الان انتوا عارفين وين راح دثويت الكوم
+
+283
+00:22:25,260 --> 00:22:28,900
+اللي هي ال F and O ال F أنزل .. أنزل .. أنزل ..
+
+284
+00:22:28,900 --> 00:22:32,160
+أنزل .. أنزل .. أنزل .. أنزل .. أنزل .. أنزل ..
+
+285
+00:22:32,160 --> 00:22:34,420
+أنزل .. أنزل .. أنزل .. أنزل .. أنزل .. أنزل ..
+
+286
+00:22:34,420 --> 00:22:34,580
+أنزل .. أنزل .. أنزل .. أنزل .. أنزل .. أنزل ..
+
+287
+00:22:34,580 --> 00:22:34,580
+أنزل .. أنزل .. أنزل .. أنزل .. أنزل .. أنزل ..
+
+288
+00:22:34,580 --> 00:22:34,580
+أنزل .. أنزل .. أنزل .. أنزل .. أنزل .. أنزل ..
+
+289
+00:22:34,580 --> 00:22:37,460
+أنزل .. أنزل .. أنزل .. أنزلA bounded linear
+
+290
+00:22:37,460 --> 00:22:41,800
+operator T in a complex Hilbert space H is unitary
+
+291
+00:22:41,800 --> 00:22:45,120
+if and only if T is isometric and surjective
+
+292
+00:22:52,540 --> 00:22:56,400
+و Unitary بالجكتف إذا صارت اللي هو ال Unitary
+
+293
+00:22:56,400 --> 00:23:00,020
+اوتوماتيكي بتعطي ايزومتريكي بتعطي سيرجكتف الآن بدي
+
+294
+00:23:00,020 --> 00:23:04,760
+العكس إذا كانت ايزومتري و سيرجكتف يعطيني مين؟
+
+295
+00:23:04,760 --> 00:23:13,020
+Unitary واضح؟ اطلع لفظك نفترض الآن أن TT نفترض أنه
+
+296
+00:23:13,020 --> 00:23:18,000
+الآن T نفترض أنه الآن T is isometric and
+
+297
+00:23:18,000 --> 00:23:22,840
+surjective مدام isometric وقبل هيك قلنا احنا ال
+
+298
+00:23:22,840 --> 00:23:27,000
+isometric operator هيطلع one to one إذا صار عندي
+
+299
+00:23:27,000 --> 00:23:29,960
+one to one و surjective يعني bijective إذا دلت
+
+300
+00:23:29,960 --> 00:23:35,160
+خاصية أخيرة أنه نثبت أنه اللي هو ال T star بساوي T
+
+301
+00:23:35,160 --> 00:23:40,400
+inverse بكون خلصنا بكون أثبتنا أنه T is unitary
+
+302
+00:23:40,820 --> 00:23:44,500
+واضح؟ طيب، شوفوا الآن اللي ضال اللي بدأت بيقولكوا
+
+303
+00:23:44,500 --> 00:23:48,720
+انه T Star بيساوي T Inverse من الـ Isometry الآن،
+
+304
+00:23:48,720 --> 00:23:52,440
+تشوفوا الآن T Star في Txa و في X، إيش بيساوي؟
+
+305
+00:23:52,440 --> 00:23:57,360
+انجلة عادية هنا، بيصير Tx و Tx، واضح؟ما هي عنده
+
+306
+00:23:57,360 --> 00:24:04,500
+اللي هي TX و TX بيساوي X و X لإيزومتري ماشي طيب ال
+
+307
+00:24:04,500 --> 00:24:08,160
+X و X إذا صار I X و مينه X إذا صار هذا الكلام صحيح
+
+308
+00:24:08,160 --> 00:24:12,410
+لكل X في الدنيا إذا ال I إيش هتساوي T Star في Tأو
+
+309
+00:24:12,410 --> 00:24:17,610
+بالتفصيل بنجل هذه هنا و بيصير T star في T نقص I X
+
+310
+00:24:17,610 --> 00:24:20,770
+بيساوي X لكل X و من اللمّة اللي بنستخدمها دايما
+
+311
+00:24:20,770 --> 00:24:24,970
+هيكون اللي هو هذا بيساوي إيه؟ بيساوي سفر إذا صار
+
+312
+00:24:24,970 --> 00:24:30,850
+عندي T star في T اللي هو بيساوي ال identity، ماشي؟
+
+313
+00:24:30,850 --> 00:24:34,530
+الآن تعالوا أحسبوا T في T star
+
+314
+00:24:38,510 --> 00:24:46,570
+التانية هي similar لزيها و سهلة تفت
+
+315
+00:24:46,570 --> 00:24:55,180
+تستار تفت تستار تفت تستارالان بدي أجيب T Star في T
+
+316
+00:24:55,180 --> 00:24:59,500
+عشان أستخدمها من اللي فوق فبصير T في T Star مع بعض
+
+317
+00:24:59,500 --> 00:25:03,420
+و T في T Inverse هدولة ال identity فبصير T في ال
+
+318
+00:25:03,420 --> 00:25:06,680
+identity في T Inverse بصير T في T Inverse و يسوا
+
+319
+00:25:06,680 --> 00:25:09,220
+ال identity إذا طلعت برضه T في T Star بيسوا ال
+
+320
+00:25:09,220 --> 00:25:12,180
+identity إذا من الجهتين T Star في T بيسوا ال
+
+321
+00:25:12,180 --> 00:25:15,960
+identity و T في T Star بيسوا ال identity إذا صارت
+
+322
+00:25:15,960 --> 00:25:20,570
+هذه T Star هي ال inverseإذا صارت P star يبقى 17
+
+323
+00:25:20,570 --> 00:25:24,110
+versus So T is unitary The converse is clear قولنا
+
+324
+00:25:24,110 --> 00:25:37,590
+إيش معناة الـ Converse ارجعلي على التلخيص طيب
+
+325
+00:25:37,590 --> 00:25:41,110
+الآن
+
+326
+00:25:41,110 --> 00:25:43,710
+المثال أو ال remark الأخيرة
+
+327
+00:25:46,190 --> 00:25:53,570
+بتقول ايه؟ ايزيومتريك لحالها لتكفل انها تكون ايه
+
+328
+00:25:53,570 --> 00:25:57,250
+شمالها؟ Unitary لازم تحطلها زججة زججة يعني ان هي
+
+329
+00:25:57,250 --> 00:26:01,940
+surjectiveالأن الـ Geometric Operators need not be
+
+330
+00:26:01,940 --> 00:26:05,620
+unitary وخد مثال بدي أجيبك مثال أكيد مش subjective
+
+331
+00:26:05,620 --> 00:26:10,080
+بس هاي كل الجزء الان consider the bounded linear
+
+332
+00:26:10,080 --> 00:26:15,220
+operator T من L2 لعند L2 given by بس بيعملني shift
+
+333
+00:26:15,220 --> 00:26:19,720
+shift operator بيشتد اللي هو ال XI1 XI2 XI3
+
+334
+00:26:19,720 --> 00:26:23,980
+وبيعمله shift لقدام شوية و بيحط ال zero في ال
+
+335
+00:26:23,980 --> 00:26:28,050
+entry الأول و بعدين بيبقوا ماشي زي ما هوإذا الـ T
+
+336
+00:26:28,050 --> 00:26:30,970
+of XI واحد XI اتنين XI تلعب تلعب إلى ما لا نهاية
+
+337
+00:26:30,970 --> 00:26:35,130
+بيساوي Zero XI واحد وXI اتنين إلى ما لا نهاية لأن
+
+338
+00:26:35,130 --> 00:26:39,230
+it is easy to see that T is an isometric سهل خالص
+
+339
+00:26:39,230 --> 00:26:43,290
+خدوا ال TX، إيش هو ال TX؟ هو لحاله طالع ايزومتري
+
+340
+00:26:43,290 --> 00:26:49,550
+شوفوا
+
+341
+00:26:49,550 --> 00:26:51,890
+كيف بيطلع Automatic Isometry
+
+342
+00:26:57,570 --> 00:27:01,790
+صلى على النبي عليه الصلاة والسلام اللهم صلى على
+
+343
+00:27:01,790 --> 00:27:08,890
+سيدنا محمد norm ال T XI 1 XI 2 إلى ما لا نهاية
+
+344
+00:27:08,890 --> 00:27:15,130
+اليد اللي هو جوا من ال X بساوي اللي هو norm T XI 1
+
+345
+00:27:15,130 --> 00:27:20,600
+بساوي 0 XI 1 XI 2 إلى ما لا نهايةوهذا الـ norm هيش
+
+346
+00:27:20,600 --> 00:27:26,320
+فالـ summation لـ XI I سوى summation لـ XI I تربيع
+
+347
+00:27:26,320 --> 00:27:30,760
+I من واحد إلى مالة نهاية الكل أص نص لأنه أول واحد
+
+348
+00:27:30,760 --> 00:27:35,940
+سفر فيها اللي هو عبارة عن مين norm من ال X ماشي
+
+349
+00:27:35,940 --> 00:27:41,780
+إذا صار اللي هو isometric إذا الان إذا T is an
+
+350
+00:27:41,780 --> 00:27:49,070
+isometricBut T is not onto مدام مش onto ده متحكوش
+
+351
+00:27:49,070 --> 00:27:55,530
+عن ال unitary But T is not onto for example خد
+
+352
+00:27:55,530 --> 00:28:01,430
+اللي هو اقصى و اخد و اقولك خد الواحد و السفر و
+
+353
+00:28:01,430 --> 00:28:07,650
+السفر و السفر إلى ما لنهاية element انقلته في TX
+
+354
+00:28:07,650 --> 00:28:13,960
+بتساوي هذالأ يمكن لإن أي و أي TX تبتدأ تكون صورتها
+
+355
+00:28:13,960 --> 00:28:17,400
+أوليش Zero و بعدين نحط اللي بدك هيها و هذا مش Zero
+
+356
+00:28:17,400 --> 00:28:21,160
+إذا مش on to طبعا هو بقولك T is not on to where
+
+357
+00:28:21,160 --> 00:28:25,360
+there is XI واحد و XI اتنين و XI واحد ده ساوي سفر
+
+358
+00:28:25,360 --> 00:28:28,960
+but there is no X element in L2 بحيث أنه TX
+
+359
+00:28:28,960 --> 00:28:32,860
+بالساوي XI واحد لإن هو بعمل shift و بخلي أول واحد
+
+360
+00:28:32,860 --> 00:28:38,050
+اسمه hence we havean isometric which is not onto
+
+361
+00:28:38,050 --> 00:28:41,690
+so it is not unitary لأن ال unitary عشان يكون
+
+362
+00:28:41,690 --> 00:28:47,370
+unitary لازم يكون say adjective و الهو isometric
+
+363
+00:28:47,370 --> 00:28:54,530
+او لو T inverse بسبب T star unitary بتكون
+
+364
+00:28:54,530 --> 00:29:00,670
+اللي هي adjective زي T inverse بسبب T star مبارك
+
+365
+00:29:00,670 --> 00:29:02,290
+الله فيكم و إلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mlM0h2WP1Sg_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mlM0h2WP1Sg_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..62706f99872dfce3fc34cfc06b7bec450e51e6b4
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/mlM0h2WP1Sg_raw.srt
@@ -0,0 +1,2352 @@
+1
+00:00:05,300 --> 00:00:09,480
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:09,480 --> 00:00:12,680
+والصلاة والسلام على سيدنا محمد وعلى آله وصحبه
+
+3
+00:00:12,680 --> 00:00:17,360
+أجمعين هذه المحاضرة العاشرة مساق تحليل اقتراني أو
+
+4
+00:00:17,360 --> 00:00:21,380
+تحليل دالي طلاب وطالبات الجامعة الإسلامية قسم
+
+5
+00:00:21,380 --> 00:00:27,480
+رياضيات طلاب وطالبات الماجستيرهنبدأ اليوم ان شاء
+
+6
+00:00:27,480 --> 00:00:31,520
+الله او هناخد اليوم اللي هو اتنين اربعة تحت عنوان
+
+7
+00:00:31,520 --> 00:00:34,540
+اللي هو finite dimensional normed spaces and
+
+8
+00:00:34,540 --> 00:00:38,080
+subspaces يعني اللي هنحكي فيه اللي هو ال spaces
+
+9
+00:00:38,080 --> 00:00:42,840
+اللي هنحكي فيه أو ال normed spaces اللي هنحكي فيه
+
+10
+00:00:42,840 --> 00:00:47,320
+اللي هي finite dimensional اللي هي بيكون ال
+
+11
+00:00:47,320 --> 00:00:51,100
+dimension لها أيش لها finite dimension as a vector
+
+12
+00:00:51,100 --> 00:00:57,760
+spaceنأخد اللمّة ضرورية لإثبات العديد من النظريات
+
+13
+00:00:57,760 --> 00:01:01,580
+في هذا الـ section اللمّة بتقول ما يليه اللي هو
+
+14
+00:01:01,580 --> 00:01:07,260
+let X1, X2, Xn بيقى linearly independent set of
+
+15
+00:01:07,260 --> 00:01:15,620
+vectors in a known space Xثم هناك رقم C أكبر من
+
+16
+00:01:15,620 --> 00:01:20,740
+صفر مثلًا، لأي اختار من الـ Scalars Alpha 1, Alpha
+
+17
+00:01:20,740 --> 00:01:25,920
+2, Alpha N لدينا دائمًا نورم للـ Linear
+
+18
+00:01:25,920 --> 00:01:29,590
+Combinationللألف واحد X واحد ألف اتنين زائد ألف
+
+19
+00:01:29,590 --> 00:01:33,770
+اتنين X اتنين زائد ألف ان X ان هيكون أكبر أو يساوي
+
+20
+00:01:33,770 --> 00:01:39,490
+C في ال summation لل scalars اللي أخدتها أي كان ال
+
+21
+00:01:39,490 --> 00:01:45,130
+scalars اللي أخدتهم بقدر ألاجي Cبحيث انه there
+
+22
+00:01:45,130 --> 00:01:49,490
+exists C بحيث انه لكل choice يعني الـC ده بتنفع
+
+23
+00:01:49,490 --> 00:01:53,450
+لكل choices للألف واحد ألف اتنين لعندي ألف N بحيث
+
+24
+00:01:53,450 --> 00:01:56,590
+انه يكون ال norm للألف واحد X2 للألف اتنين X2
+
+25
+00:01:56,590 --> 00:01:59,810
+لعندي الألف N XN أكبر أو يساوي C في ال summation
+
+26
+00:01:59,810 --> 00:02:05,010
+لمين لل absolute value للألف I هذا الكلام ان شاء
+
+27
+00:02:05,010 --> 00:02:09,750
+الله بنشوف كيف وينفعته في خلال اللي هو النظريات
+
+28
+00:02:09,750 --> 00:02:14,920
+اللي هناخدها قدامخلّينا نبرهن هذا البرهان .. نبرهن
+
+29
+00:02:14,920 --> 00:02:20,180
+هذه النظرية أول شيء أبرهن النظرية أو اللي أبدا
+
+30
+00:02:20,180 --> 00:02:27,200
+أبرهنها اللي هو ل Beta 1 و Beta 2 و Beta 3 اللي ال
+
+31
+00:02:27,200 --> 00:02:31,840
+summation لهم بيساوي 1 وبعد هيك هنتقل in general
+
+32
+00:02:31,840 --> 00:02:36,790
+بيصير سهل الانتقال هتشوفوا كيفالان اولا نشهد ان
+
+33
+00:02:36,790 --> 00:02:40,830
+هناك C أكبر من صفر مثل ذلك لأي اختار من الـ
+
+34
+00:02:40,830 --> 00:02:45,470
+Scalars Beta 1, Beta 2, Beta N والـ Scalars بس
+
+35
+00:02:45,470 --> 00:02:49,210
+بتحط عليهم شرط نصممش ان هنا ايش بيساوي، بيساوي
+
+36
+00:02:49,210 --> 00:02:53,080
+واحد، بعد شوية هذه حاجلتها هتصير سهلةالان نحن
+
+37
+00:02:53,080 --> 00:02:56,200
+لدينا نورم بي واحد اكس واحد بي اتنين اكس اتنين
+
+38
+00:02:56,200 --> 00:02:59,440
+زائد بي انكسا ناكوراساوسي فيه C إذا هذه الآن اللي
+
+39
+00:02:59,440 --> 00:03:04,040
+بدأ أثبتها ماشي الحال خلينا نثبت هذه ومن ثم ببعدها
+
+40
+00:03:04,040 --> 00:03:08,140
+اللي هو نثبت in general اللي طالبه في ال M اطلع
+
+41
+00:03:08,140 --> 00:03:13,100
+على فوق البرهان قايم على انه نفترض العكسونصل مين
+
+42
+00:03:13,100 --> 00:03:16,360
+لـ contradiction الان اللي .. اللي .. اللي .. اللي
+
+43
+00:03:16,360 --> 00:03:21,160
+عندي بيدقول assume that one does not hold ماشي
+
+44
+00:03:21,160 --> 00:03:26,340
+الحال يعني بدي أنفي الجملة الو there exists such
+
+45
+00:03:26,340 --> 00:03:30,900
+that for any choice of beta 1 عند beta n و الاخره
+
+46
+00:03:31,340 --> 00:03:34,960
+إذا نفيها أكيد إيش باله بدل اللي هو there exist
+
+47
+00:03:34,960 --> 00:03:40,560
+بده يصير عنده الان for all then assume that الان
+
+48
+00:03:40,560 --> 00:03:47,070
+one does not hold يعني بده أنفل اللي هو المطلوبو
+
+49
+00:03:47,070 --> 00:03:51,810
+بدي أسأل الـ contradiction مافيه؟ for all M أكبر
+
+50
+00:03:51,810 --> 00:03:55,410
+من 0 بدي أغير بس السياق سميها ايش بقى لأ for all M
+
+51
+00:03:55,410 --> 00:04:00,410
+أكبر من 0 there exist scalars بدل ما هو for all
+
+52
+00:04:00,410 --> 00:04:03,810
+for any choice of scalars بدي أسير ايش ماله there
+
+53
+00:04:03,810 --> 00:04:09,090
+exist scalars Beta واحد خاصة بمين؟ بالـ M هذهبيتا
+
+54
+00:04:09,090 --> 00:04:13,470
+واحد M بيتا اتنين M بيتا N M بتحت نفس الشروط الـ
+
+55
+00:04:13,470 --> 00:04:17,030
+Summation تبحن من واحد عند N مش هو يساوي ايه اش
+
+56
+00:04:17,030 --> 00:04:21,310
+واحد وفي نفس الوقت اشمال وهذا ما تتحقق اشها بدأت
+
+57
+00:04:21,310 --> 00:04:25,470
+بتنفيها ان ال norm هذا بيتا واحد X واحد زي بيتا
+
+58
+00:04:25,470 --> 00:04:29,730
+اتنين X اتنين زي بيتا M X M اصغر او ساو مين واحد
+
+59
+00:04:29,730 --> 00:04:34,620
+على Mماشي الحال يعني اللي مش عاجبه M اكتب for all
+
+60
+00:04:34,620 --> 00:04:38,020
+أحد على M بنفع نفس الاشي for all M أو for one أحد
+
+61
+00:04:38,020 --> 00:04:40,880
+على M يعني ال C's اللي أنا ال C اللي بدي أخدها
+
+62
+00:04:40,880 --> 00:04:44,520
+طبعا صارت for all بدل اللي هي ال C اللي بدي أسميها
+
+63
+00:04:44,520 --> 00:04:49,080
+أشمالها واحد على M لغرض أنا بديها ماشي الحال لأن
+
+64
+00:04:49,080 --> 00:04:54,220
+for all is choice طيب الآن صار عندي اللي هو اللي
+
+65
+00:04:54,220 --> 00:05:01,100
+هي هذا اللي هو متحققهذا فرضته انا الان طيب يا
+
+66
+00:05:01,100 --> 00:05:04,680
+جماعة الان
+
+67
+00:05:04,680 --> 00:05:11,020
+بمعنى اخر ل M بتساوي واحد انتبهوا for all M قولنا
+
+68
+00:05:11,020 --> 00:05:15,780
+اذا ل M بتساوي واحد for واحد there exist معايا
+
+69
+00:05:15,780 --> 00:05:23,280
+sequence اسمها اللي هي بي واحد واحد بيتا واحد واحد
+
+70
+00:05:23,280 --> 00:05:32,490
+بيتا اتنين واحدبيتا ان واحد عددين ان صح ومجموع ال
+
+71
+00:05:32,490 --> 00:05:38,330
+absolute values له دول ايش بيساوي واحد for n طبعا
+
+72
+00:05:38,330 --> 00:05:45,230
+ايش بتحقق ال norm ل beta واحد x واحد زائد beta n
+
+73
+00:05:45,230 --> 00:05:51,030
+واحد xn ايش ماله اصغر من واحد على واحد اللي هو
+
+74
+00:05:51,030 --> 00:05:57,560
+واحد اللي بعدها forاللي هو n بتساوي 2 there exist
+
+75
+00:05:57,560 --> 00:06:07,500
+beta 1 2 و beta 2 2 فاهمين عليها لعند beta n 2ماله
+
+76
+00:06:07,500 --> 00:06:10,640
+هذا sequence of scalars الـ summation اللي بيساوي
+
+77
+00:06:10,640 --> 00:06:16,720
+واحد absolute value لهن و norm هن beta 1 2 x 1
+
+78
+00:06:16,720 --> 00:06:27,560
+زائد beta 1 2 2 x 2 زائد beta n 2 x n برضه أصغر من
+
+79
+00:06:27,560 --> 00:06:34,640
+minimum واحد على اتنين in general for MThere
+
+80
+00:06:34,640 --> 00:06:44,340
+exists Beta 1M و Beta 2M لعند Beta nM such that
+
+81
+00:06:44,340 --> 00:06:51,940
+Norمجموح بساوية Absolute Value 1 و Beta 1M في X1
+
+82
+00:06:51,940 --> 00:07:01,280
+زائد Beta nM Xn أصغر من 1 على N ماشي الحالة هذا
+
+83
+00:07:01,280 --> 00:07:10,180
+الكلام for any Mصحيح طيب شوفوا عليا الان then بناء
+
+84
+00:07:10,180 --> 00:07:12,820
+على الكلام هذا there exist a sequence YM of
+
+85
+00:07:12,820 --> 00:07:18,400
+vectors اللي هو YM بتساوي Beta 1 M X 1 زائد Beta 2
+
+86
+00:07:18,400 --> 00:07:25,020
+M X 2 زائد Beta M X M ماشي الحال اللي هي هذه ال
+
+87
+00:07:25,020 --> 00:07:33,710
+sequence Y1هي الأولى Y1 Beta 1 1 Beta 2 1 الى عند
+
+88
+00:07:33,710 --> 00:07:38,890
+Beta هي عنصر الان الأولاني ال Y2 العنصر الثاني ال
+
+89
+00:07:38,890 --> 00:07:41,510
+Y تلقى نفس الاشي إلى ما ندلنا دهانا دي صارت
+
+90
+00:07:41,510 --> 00:07:45,710
+sequence شك كيف شكل عناصرها عناصرها هذوله ال
+
+91
+00:07:45,710 --> 00:07:50,620
+linear combinationمن اللي أنا حكيت عنه هنا بحيث ان
+
+92
+00:07:50,620 --> 00:07:56,500
+الـ summation L الـ absolute value لكل اللي
+
+93
+00:07:56,500 --> 00:08:02,260
+بتتكون منها لكل YM مجبوح ان يش بيساوي واحد ومش هيك
+
+94
+00:08:02,260 --> 00:08:08,700
+ولو اجيت اخدت norm ال YM هي norm ال YM هذا هو من
+
+95
+00:08:08,700 --> 00:08:14,420
+هي هي في الواقع هذا من نورم ال YM هيساوي ال norm
+
+96
+00:08:14,420 --> 00:08:21,470
+لهذهas M goes to infinity هذا الـ norm يشير إلى
+
+97
+00:08:21,470 --> 00:08:29,870
+أين نروح إلى Zero بمعنى آخر صارت عندي اللي هو الـ
+
+98
+00:08:29,870 --> 00:08:34,490
+sequence YM من الـ vectors هذه الـ norm تبعها goes
+
+99
+00:08:34,490 --> 00:08:38,930
+to zero as M goes to mean to infinity خلوا هذه في
+
+100
+00:08:38,930 --> 00:08:43,850
+الذاكرة إذا انت حصلت على sequenceYM هي شكل الـ
+
+101
+00:08:43,850 --> 00:08:48,970
+sequence نورمها بروح لمن؟ للصفر بدا أصلكم في الآخر
+
+102
+00:08:48,970 --> 00:08:54,810
+ل contradiction شوفوا كيف الان نتفجين احنا ان ال
+
+103
+00:08:54,810 --> 00:08:59,290
+summation لكل مجموعة من هدولة ال absolute values
+
+104
+00:08:59,290 --> 00:09:02,650
+لهم كل مجموعة ال summation انهي مش بساوي بساوي
+
+105
+00:09:02,650 --> 00:09:09,190
+واحد بمعنى بمعنى ان كل واحدة منهم BIM أصغر بساوي
+
+106
+00:09:09,190 --> 00:09:14,350
+واحد لكل Iمعايا كلهم دايما ال norm أشماله أصغر من
+
+107
+00:09:14,350 --> 00:09:17,470
+واحد ده كل I ولا كل مين واحد يعني بي واحد واحد
+
+108
+00:09:17,470 --> 00:09:21,430
+أصغر شوي واحد بي واحد اتنين اصغر .. و هكذا ماشي
+
+109
+00:09:21,430 --> 00:09:25,230
+الحال .. هذا إيه اللي معناه hence الآن for any
+
+110
+00:09:25,230 --> 00:09:36,330
+fixed I اختارولي BIM اللي هي بي اي واحدبي اتنين بي
+
+111
+00:09:36,330 --> 00:09:41,450
+اي تلاتة بي اي اربعة بي اي خمسة يعني بدي اجل بي اي
+
+112
+00:09:41,450 --> 00:09:52,680
+هنا بي اي واحد بي اي اتنينbim in general هذه عبارة
+
+113
+00:09:52,680 --> 00:09:57,660
+عن sequence of numbers مظبوط ولا لأ؟ كل واحدة منهم
+
+114
+00:09:57,660 --> 00:10:00,200
+هدولة sequence of numbers و هذه sequence of
+
+115
+00:10:00,200 --> 00:10:04,640
+numbers و هذه sequence of numbers عدد من هدولة
+
+116
+00:10:04,640 --> 00:10:07,640
+واحدة اتنين اتنين تلاتة اربع ان من اللي من ال
+
+117
+00:10:07,640 --> 00:10:12,890
+sequences كل واحدة فيهم is a bounded sequenceلماذا
+
+118
+00:10:12,890 --> 00:10:17,010
+اسمها Sequence؟ لأن اي انكالة الواحدة فيهم اصغر او
+
+119
+00:10:17,010 --> 00:10:18,550
+يساوي ايش واحد
+
+120
+00:10:21,120 --> 00:10:26,080
+بشرد من الـ space اللي عندي إلى الـ space في R أو
+
+121
+00:10:26,080 --> 00:10:30,420
+في C أخدتها sequence of main of numbers بي اي واحد
+
+122
+00:10:30,420 --> 00:10:34,820
+بي اي اتنين is a bounded sequence then بي واحد
+
+123
+00:10:34,820 --> 00:10:39,520
+اللي هي M و بي اتنين M كل هى نفس الشيء sequence of
+
+124
+00:10:39,520 --> 00:10:43,040
+ايش؟ of numbers و bounded فبنيجي نشوف العالمين على
+
+125
+00:10:43,040 --> 00:10:48,280
+بي واحد of Mالأن بي واحد of M has مادام sequence
+
+126
+00:10:48,280 --> 00:10:51,580
+of numbers وهي bounded احنا بنعرف في الريال ان any
+
+127
+00:10:51,580 --> 00:10:53,860
+bounded sequence has a convergence of a
+
+128
+00:10:53,860 --> 00:11:00,140
+subsequence بلزانو اه مذاكرين؟ اذا يا جماعة صار
+
+129
+00:11:00,140 --> 00:11:09,900
+عند بي واحد M اللي هيبعد ذلك لديها سبسيكوانس
+
+130
+00:11:09,900 --> 00:11:14,920
+بي واحد ام ايش واحد هذه سبسيكوانس من مين؟ من
+
+131
+00:11:14,920 --> 00:11:20,320
+السيكوانس هذه يعني من السيكوانس بي واحد of ام اللي
+
+132
+00:11:20,320 --> 00:11:25,960
+هي هذه فيها سبسيكوانس منها بي ام واحد
+
+133
+00:11:28,760 --> 00:11:33,280
+طيب الان مدان converts اذا نقول نسميها conversion
+
+134
+00:11:33,280 --> 00:11:38,100
+from mean to beta واحد يعني الان فرضنا ان ال beta
+
+135
+00:11:38,100 --> 00:11:40,300
+واحد
+
+136
+00:11:41,560 --> 00:11:53,620
+بواحد of m بواحد
+
+137
+00:11:53,620 --> 00:12:10,920
+of m
+
+138
+00:12:12,230 --> 00:12:16,310
+الان ما هي ال .. ال .. ال .. ال .. ال .. الـ YMs
+
+139
+00:12:16,310 --> 00:12:20,030
+هدولة ما هي سيكونس بتتكون من اللي بيكونها هي
+
+140
+00:12:20,030 --> 00:12:23,590
+linear combinations بين X1 و X2 و XN أدات ال
+
+141
+00:12:23,590 --> 00:12:26,250
+linear combinations اللي هي ال scalar هدول ال
+
+142
+00:12:26,250 --> 00:12:30,010
+scalars هدول اللي هي في الأصل من مين جاية من ال بي
+
+143
+00:12:30,010 --> 00:12:34,670
+و .. من بي I of M in general ماشي الحالة إذا الآن
+
+144
+00:12:34,670 --> 00:12:40,710
+thenعندي Y1M
+
+145
+00:12:40,710 --> 00:12:45,090
+بدي أسميها هي الـ subsequence اللي الـ scale
+
+146
+00:12:45,090 --> 00:12:51,690
+الذبعاتها من وين جايت من B و Beta 1 OM لت Y1M بي
+
+147
+00:12:51,690 --> 00:12:55,930
+the corresponding sequence which is a subsequence
+
+148
+00:12:55,930 --> 00:13:04,160
+of mean of YMWhere Y1M بالظبط ايش بتساوي Beta 1 M1
+
+149
+00:13:04,160 --> 00:13:09,580
+X1 زائد Beta 2 M X2 يعني بس أخدت من الأولى مين من
+
+150
+00:13:09,580 --> 00:13:13,980
+ال Beta 1 و M هذه و الباقى أخدت من مين من الأصلية
+
+151
+00:13:13,980 --> 00:13:21,380
+تبعت ال YM Beta 2 M X2 زائد Beta N M X2 XN هذي
+
+152
+00:13:21,380 --> 00:13:23,500
+اللي هي Y1M
+
+153
+00:13:25,220 --> 00:13:29,820
+هذه الآن الـ subsequence برضه اللي عملته على الـ
+
+154
+00:13:29,820 --> 00:13:35,180
+Beta 1 of M بدي اعمله على مين؟ Beta 2 of M وهذه
+
+155
+00:13:35,180 --> 00:13:38,640
+اتفاجنة عبارة عن sequence of برضه أيش؟ of numbers
+
+156
+00:13:38,640 --> 00:13:41,380
+which is bounded إذن لها برضه أيش؟ subsequence
+
+157
+00:13:41,730 --> 00:13:46,090
+بالتالي، بما أن B2 و M هي سيكوانات مرتبطة، فهي
+
+158
+00:13:46,090 --> 00:13:52,410
+تحتوي على سبسيكوانت مرتبطة تسميها Beta 2 M 2 هذا
+
+159
+00:13:52,410 --> 00:13:54,490
+أيضًا مرتبط إلى B2
+
+160
+00:13:58,090 --> 00:14:04,830
+بتكون B2 of M و 2 converges فرقنا ل مين ل B2 لأنها
+
+161
+00:14:04,830 --> 00:14:11,070
+sub sequence من bounded sequence يعني بمعنى أخر
+
+162
+00:14:11,070 --> 00:14:13,930
+فما ده في عندي bounded sequence إذا بقدر ألاقي
+
+163
+00:14:13,930 --> 00:14:16,810
+convergent subsequence سميتها اللي قلتها قبل شوية
+
+164
+00:14:16,810 --> 00:14:22,030
+it has a convergent subsequence منها B2 M that
+
+165
+00:14:22,030 --> 00:14:29,090
+converges to مين to B2 اطلع لفوقالآن Y2M نفس الجثة
+
+166
+00:14:29,090 --> 00:14:33,810
+بدي أخدها الـ Corresponding Sequence المكوّنة من
+
+167
+00:14:33,810 --> 00:14:36,990
+Y1 .. اللي هي Y1 .. اللي مكوّنة .. اللي هتكون
+
+168
+00:14:36,990 --> 00:14:41,910
+جزئية من من Y1 و في M ليش؟ لأن Y2 و في M على سرها
+
+169
+00:14:41,910 --> 00:14:49,010
+متكونة B1M1 زي اللي هي تمامته الـY1و M و B2 و M2
+
+170
+00:14:49,010 --> 00:14:53,790
+جزء من هذيك اللي هي X2 زاد هذي بتخليهم زي ما هما
+
+171
+00:14:53,790 --> 00:14:57,330
+الأصليات إذا بس اتغيرت هذي إذا صارت هذي Y2 of M
+
+172
+00:14:57,330 --> 00:15:02,930
+subsequence من مين؟ من Y1 of M بدي لأنا كموحدة إن
+
+173
+00:15:02,930 --> 00:15:07,210
+هذول أن من العناصر بدي أشتغل على البجيات بنفس
+
+174
+00:15:07,210 --> 00:15:13,640
+الأسلوب we after any stepsWe get YNM as a
+
+175
+00:15:13,640 --> 00:15:19,540
+subsequence of YN With YNM أيش بتساوي؟ Beta 1 M1
+
+176
+00:15:19,540 --> 00:15:27,400
+Beta 2 M2 و Beta N يعني MNXN هذي و طبعا كل اللي
+
+177
+00:15:27,400 --> 00:15:31,980
+بنشتغل فيه اللي هو ال absolute values اللي ما له
+
+178
+00:15:31,980 --> 00:15:35,580
+مجموعة بساوي واحد من ضمنه هذول اللي اشتغلت عليه
+
+179
+00:15:35,580 --> 00:15:41,180
+هنا إذا مجموعة دولة بساوي واحدإذا صار عندى Beta 1
+
+180
+00:15:41,180 --> 00:15:47,280
+M1 و Beta 1 و Beta 2 M2 بتروح ل Beta 2 و Beta N MN
+
+181
+00:15:47,280 --> 00:15:52,600
+بتروح ل Beta N هذا كله as mean as M الـ goals
+
+182
+00:15:52,600 --> 00:15:57,680
+المعلنة هي لأن M هي اللى بتعمل ال sequence طيب
+
+183
+00:15:57,680 --> 00:16:08,110
+also برضه واحد بيساوي limitLimit اللي هو Beta 1 M1
+
+184
+00:16:08,110 --> 00:16:14,690
+زي Beta 2 M2 زي Beta N MN مجموح انش هيساويالان
+
+185
+00:16:14,690 --> 00:16:21,070
+مجموحين هذولة اللي هو بساوي واحد و limit كل واحدة
+
+186
+00:16:21,070 --> 00:16:26,250
+بتساوي الأولى Beta 1 والتانية Beta 2 والتالتة Beta
+
+187
+00:16:26,250 --> 00:16:32,270
+N إذا limit المجموع بساوي مجموحين هذولة لقيمة ال
+
+188
+00:16:32,270 --> 00:16:35,550
+limits بنوزع ال limit يعني بمعنى أخر بوزع ال limit
+
+189
+00:16:35,550 --> 00:16:39,320
+على مجموع عدد عشر عشرين تلاتين N من ال limitsبكون
+
+190
+00:16:39,320 --> 00:16:42,140
+limit الأول زي limit التاني زي limit التالت بساوة
+
+191
+00:16:42,140 --> 00:16:45,420
+summation beta I وهذا المجموع زي ما قلنا أيش بساوة
+
+192
+00:16:45,420 --> 00:16:51,320
+واحد إذا المجموع هذا النهايات نفسها بساوة واحد إذا
+
+193
+00:16:51,320 --> 00:16:56,220
+حصلت على إن مجموع النهايات بساوة واحد إذا الآن
+
+194
+00:16:56,220 --> 00:17:03,220
+مدان مجموع هذولة، انتبهوا الآن مجموع هذولة بساوة
+
+195
+00:17:03,220 --> 00:17:09,560
+واحد إذا فيه على الأقل، على الأقل واحدة مش سفرهكذا
+
+196
+00:17:09,560 --> 00:17:11,900
+أصبح مجموح من بساوي واحد absolute values هذه
+
+197
+00:17:11,900 --> 00:17:15,280
+absolute values مجموح من إيش بساوي بساوي واحد يعني
+
+198
+00:17:15,280 --> 00:17:18,260
+قيم موجة بأكبر بساوي سفر مجموح من واحد إذا على
+
+199
+00:17:18,260 --> 00:17:21,620
+الأقل أكيد في واحدة يشمالها لا تساوي سفر إذا then
+
+200
+00:17:21,620 --> 00:17:26,200
+there is at least beta I لا تساوي إيش سفر لكن ال X
+
+201
+00:17:26,200 --> 00:17:30,660
+واحد وال X اتنين وال X unlinearly independent then
+
+202
+00:17:30,660 --> 00:17:36,480
+أكيد ال Y لا تساوي سفر ال Y مين هي ال Y ال Y هي
+
+203
+00:17:36,480 --> 00:17:46,520
+عبارة ال Yعبارة عن X1 Beta 1 زي X2 Beta 2 زي XN
+
+204
+00:17:46,520 --> 00:17:55,090
+Beta N هذا أكيد لا تساوي سفرليش لا تساوي سفر؟ لأن
+
+205
+00:17:55,090 --> 00:18:00,910
+لو كانت سفر لو كانت سفر طبعا في عندي واحدة منهم XI
+
+206
+00:18:00,910 --> 00:18:05,570
+Beta I زائد إلى أخير لإن عندك Xn هذه ال Beta I
+
+207
+00:18:05,570 --> 00:18:10,370
+تبعتها مش سفر لو بدنا نقول هذه بتساوي سفر معناته
+
+208
+00:18:10,370 --> 00:18:16,120
+صارت ال XIبكتبها على صورة X1 Beta 1 على Beta I
+
+209
+00:18:16,120 --> 00:18:22,880
+زائد Xn Beta N على اليمين Beta I يعني قدرت أكتب X
+
+210
+00:18:22,880 --> 00:18:26,260
+أزالين ال combination من هذا وهذا أشماله
+
+211
+00:18:26,260 --> 00:18:30,580
+contradiction لأن X1 و X2 و Xn are linearly
+
+212
+00:18:30,580 --> 00:18:36,220
+independent إذن ال linearly independent هو اللي
+
+213
+00:18:36,220 --> 00:18:43,300
+ضمنلي أن ال Y هذه أشمالها لاتساوى 0لكن في الأصل،
+
+214
+00:18:43,300 --> 00:18:47,760
+since the norm is continuous، إذا الـ Normal Y and
+
+215
+00:18:47,760 --> 00:18:53,440
+M بيروح لـ Normal Yمدام ال .. لأنه limit ال Yn و M
+
+216
+00:18:53,440 --> 00:18:57,540
+إيش بيساوي؟ بيساوي ال Y إذا norm ال Yn و M هيروح
+
+217
+00:18:57,540 --> 00:19:04,080
+لمين؟ ل norm ال Y but Yn و M اللي ركّبناها .. نرجع
+
+218
+00:19:04,080 --> 00:19:08,700
+لقصتنا الأولى is a subsequence من مين؟ من Yn
+
+219
+00:19:08,700 --> 00:19:14,340
+الأصلية Yn الأصلية إيش مالها؟ normها راح لمين؟ لل
+
+220
+00:19:14,340 --> 00:19:18,040
+0 .. أو للتركيبة .. أنزل .. أنزل .. أنزل ..هنزل
+
+221
+00:19:18,040 --> 00:19:22,260
+هايو عندنا في واحة اتنين اثبتنا ان normal YM ايش
+
+222
+00:19:22,260 --> 00:19:27,420
+مروح للسفر لازم goes to infinity اذا الان الان
+
+223
+00:19:28,880 --> 00:19:32,980
+أثبتنا أن الـ sub-sequence هذه راحت لـ Normal Y و
+
+224
+00:19:32,980 --> 00:19:37,660
+الـ M اللي هي الـ Y and M sub-sequence من YM و
+
+225
+00:19:37,660 --> 00:19:40,520
+Normal YM ما أثبتناه في الأول بيروح لـ Zero إذا
+
+226
+00:19:40,520 --> 00:19:43,400
+الـ Norm هذي إيش بيروح لمين؟ لـ Zero و احنا قلنا
+
+227
+00:19:43,400 --> 00:19:46,860
+هنا الـ Y إيش ما لها؟ لأ تساوي سفر فصار في عندي
+
+228
+00:19:46,860 --> 00:19:51,280
+Contradiction إذا الفرضية الأصلية مش صحيحة Hence
+
+229
+00:19:51,280 --> 00:19:57,600
+اللي هو Therefore واحد is proved بمعنى آخر أنه لكل
+
+230
+00:19:57,600 --> 00:20:02,900
+اللي هيPfffThere exists C such that لكل choice ل
+
+231
+00:20:02,900 --> 00:20:06,300
+Beta 1 و Beta 2 المجموحين بيساوي واحد norm اللي هو
+
+232
+00:20:06,300 --> 00:20:12,500
+أكبر أو يساوي C الان الان انزل شوية خليني أرجع
+
+233
+00:20:12,500 --> 00:20:16,620
+اللي بس الان from this and three we have a
+
+234
+00:20:16,620 --> 00:20:21,200
+contradiction therefore one is approved now if ال
+
+235
+00:20:21,200 --> 00:20:24,600
+absolute اللي أثبتناه كله في حالة اللي هو
+
+236
+00:20:24,600 --> 00:20:28,020
+summation لل Beta I's بيساوي واحد اللي انا بتاخده
+
+237
+00:20:28,020 --> 00:20:31,960
+arbitrarilyالأن اذا الـ F ألف واحد أفضل قيمة ألف
+
+238
+00:20:31,960 --> 00:20:35,620
+واحد زاد أفضل قيمة ألف اتنين زاد أفضل قيمة ألف ألف
+
+239
+00:20:35,620 --> 00:20:41,540
+ن افترض انه ايش ماله بساوء سفر اذا الف اي سفر لكله
+
+240
+00:20:41,540 --> 00:20:47,040
+مش الحال اذا ال norm للألف واحد X واحد زاد ألف ن
+
+241
+00:20:47,040 --> 00:20:53,180
+Xn اللي هو أكبر أو ساوء C في ال summation hold ايش
+
+242
+00:20:53,180 --> 00:20:55,380
+اللي بده اعمله يا جماعة انا اللي بده اتبطه الان
+
+243
+00:20:55,380 --> 00:20:57,080
+انتبهوا
+
+244
+00:20:58,550 --> 00:21:04,790
+اللي بيدثبتلكم إياه الآن الـ arbitrary scalars
+
+245
+00:21:04,790 --> 00:21:10,610
+يعني there exists C أكبر من 0 such that for any
+
+246
+00:21:10,610 --> 00:21:15,010
+choice of Alpha 1, Alpha 2 لعند Alpha N with
+
+247
+00:21:15,010 --> 00:21:21,930
+summation اللي هو such that norm اللي هي الـ Alpha
+
+248
+00:21:21,930 --> 00:21:28,940
+1 X 1 زي Alpha N X Nاللي هو أكبر أو يساوي C ال
+
+249
+00:21:28,940 --> 00:21:32,520
+summation absolute value of I I من عند واحد لمنين
+
+250
+00:21:32,520 --> 00:21:37,060
+لعندك for any choice لأن بتاخد حالتين الحالة
+
+251
+00:21:37,060 --> 00:21:42,660
+الأولى أن يكون ال summation هذا ال summation Alpha
+
+252
+00:21:42,660 --> 00:21:48,620
+I بساوي سفر إذا سفر معناته automatically كل واحدة
+
+253
+00:21:48,620 --> 00:21:51,540
+فيه سفر معناته اللي هو كل ال C's اللي في الدنيا
+
+254
+00:21:51,540 --> 00:21:55,700
+بتظبطيعني هذا الـ Trivial Case لما نفترض إن الـ
+
+255
+00:21:55,700 --> 00:21:59,020
+summation للأبسوليوت V للألف I أشمالها لا يساوي
+
+256
+00:21:59,020 --> 00:22:04,780
+سفر عشان بتقسم عليها بالعالم طيب طيب finally if S
+
+257
+00:22:04,780 --> 00:22:08,300
+بتساوي ال summation للألف I أشمالها لا تساوي إيش
+
+258
+00:22:08,300 --> 00:22:12,610
+سفرخدوا الـ N أحنا أثبتناها لـ Beta I الـ
+
+259
+00:22:12,610 --> 00:22:15,570
+summation اللي بيساوي واحد خدوا Beta 1 بيساوي
+
+260
+00:22:15,570 --> 00:22:20,090
+Alpha 1 على S Beta 2 Alpha 2 على S Beta N Alpha N
+
+261
+00:22:20,090 --> 00:22:23,730
+على S in general لكل I Beta I بيساوي Alpha I على S
+
+262
+00:22:23,730 --> 00:22:28,210
+لـ I بيساوي واحد لعند الـ N حسبولي الآن لـ Beta Z
+
+263
+00:22:28,210 --> 00:22:31,330
+للـ N ال summation لـ Beta I I من عند واحد لـ N
+
+264
+00:22:31,330 --> 00:22:35,750
+بيساوي ال summationباخد الـ 1 على أسماله عامل
+
+265
+00:22:35,750 --> 00:22:39,050
+مشترك في الـ summation هذا هو هذا فاش بيساوي
+
+266
+00:22:39,050 --> 00:22:42,810
+بيساوي واحد إذا أنا أثبته للي ال beta بيساوي واحد
+
+267
+00:22:42,810 --> 00:22:48,290
+إذا النظرية صحيحة لهذه اه طيب by substituting beta
+
+268
+00:22:48,290 --> 00:22:53,110
+I بيساوي Alpha I على S الواحد اللي أثبتناها we get
+
+269
+00:22:53,110 --> 00:22:58,170
+norm Alpha 1 على S Fix 1 زاد Alpha 2 على S Fix 2
+
+270
+00:22:58,170 --> 00:23:03,400
+زاد Alpha N عكس N أكبر بيساوي مين؟ Cالان هناخد الـ
+
+271
+00:23:03,400 --> 00:23:07,360
+C مالها برا عام المشترك اللي هي 1 على ال S فالـ S
+
+272
+00:23:07,360 --> 00:23:10,760
+1 على ال S ناخدها عام المشترك و بعدين نضربها في
+
+273
+00:23:10,760 --> 00:23:14,100
+الطرفين بنكون حصلنا Alpha 1 X 1 Alpha 2 X 2 زاد
+
+274
+00:23:14,100 --> 00:23:18,340
+Alpha X N أكبر من مين من C فS اللي هي C بتساوي ال
+
+275
+00:23:18,340 --> 00:23:26,530
+summation this completes the proof أي سؤالطيب نجي
+
+276
+00:23:26,530 --> 00:23:31,770
+لان نظريتنا هذه لما يعني عبارة عن أداء لاللي هو
+
+277
+00:23:31,770 --> 00:23:39,170
+للوصول لإثبات النظريات اللاحقة نجي
+
+278
+00:23:39,170 --> 00:23:42,770
+لان صار النظرية بداخل بيتها لجهة النظرية المهمة
+
+279
+00:23:42,770 --> 00:23:47,630
+هذه المهمة المنيحة و الحلوة هذه صار برهانها سهل
+
+280
+00:23:47,630 --> 00:23:51,010
+الآن أو بسيط بالاستعانة بال .. بال .. بال ..
+
+281
+00:23:51,420 --> 00:23:55,100
+باللمّة اللي قبله شوية يعني قد يكون بعض الكتب اللي
+
+282
+00:23:55,100 --> 00:23:59,000
+هي بتثبتها بتثبتش اللمّة فبتروح تثبتها مباشرة و
+
+283
+00:23:59,000 --> 00:24:02,560
+بتبدأ تشتغل شغل طبعا أكثر تعقيدا الان بعد ما
+
+284
+00:24:02,560 --> 00:24:07,080
+أثبتنا اللمّة بيسير شغلها أكتر سهولة نيجي نشوف أيش
+
+285
+00:24:07,080 --> 00:24:11,900
+اللي بيقوله إعلان هذا theorem every finite
+
+286
+00:24:11,900 --> 00:24:15,420
+dimensional subspace y of a normed space x أشماله
+
+287
+00:24:15,420 --> 00:24:20,460
+is complete أي في ال finite dimensional spaceلو
+
+288
+00:24:20,460 --> 00:24:25,920
+أخدنا أو في اللي هو تكون الـ subspace نفسه finite
+
+289
+00:24:25,920 --> 00:24:29,440
+dimensional من space على طول هذا ال subspace بيكون
+
+290
+00:24:29,440 --> 00:24:34,140
+complete يعني الآن أنا finite dimensional space is
+
+291
+00:24:34,140 --> 00:24:38,020
+complete هذا الحالة الخاصة بتصير لأن الحالة العامة
+
+292
+00:24:38,020 --> 00:24:43,600
+أن أنا finite dimensional subspace of a normed
+
+293
+00:24:43,600 --> 00:24:49,090
+space must be completeعشان هيك كل اللي بنشتغل فيه
+
+294
+00:24:49,090 --> 00:24:54,410
+R وR تربيع وR تكعيب وR أنه وC وC1 وC2 كلهم finite
+
+295
+00:24:54,410 --> 00:24:58,390
+dimensional spaces هدولة كلهم complete metric
+
+296
+00:24:58,390 --> 00:25:04,930
+spaces أو complete normed spaces معين؟ طيبIn
+
+297
+00:25:04,930 --> 00:25:08,050
+particular, every finite dimensional normed space
+
+298
+00:25:08,050 --> 00:25:14,030
+كله is complete بدنا نثبت الآن خدوا الآن لثبات سهل
+
+299
+00:25:14,030 --> 00:25:18,070
+let Y be .. عشان نثبت complete ناخد any Cauchy
+
+300
+00:25:18,070 --> 00:25:22,110
+sequence و نثبت انها converged وبس هي كل جثتنا بما
+
+301
+00:25:22,110 --> 00:25:26,170
+يلقم السؤال طبعا let Y be any Cauchy sequence in Y
+
+302
+00:25:27,070 --> 00:25:30,790
+Suppose that الـ dimension للـ Y إيش بيساوي N هذا
+
+303
+00:25:30,790 --> 00:25:35,070
+الـ Y sub space من a normed space اسمه إيه إيش X
+
+304
+00:25:35,070 --> 00:25:38,530
+ال sub space Y هو اللي ال dimension إيه بيساوي N
+
+305
+00:25:38,530 --> 00:25:42,290
+طيب مدام ال dimension إيه بيساوي N إذا إنه bases
+
+306
+00:25:42,290 --> 00:25:45,830
+ال bases تبع جبل الخطة تبع جبل الخطة زمان اللي أن
+
+307
+00:25:45,830 --> 00:25:49,370
+ال bases إيه نفترض إنه اسمه E1 وE2 وEN بيه any
+
+308
+00:25:49,370 --> 00:25:54,640
+basis forming for Y لأنه finite dimensionalمدام
+
+309
+00:25:54,640 --> 00:25:58,980
+اللي هو الـ E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12
+
+310
+00:25:58,980 --> 00:26:04,780
+E13 E14 E14 E15 E16 E17 E18 E19 E21 E21 E21 E21
+
+311
+00:26:04,780 --> 00:26:06,260
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+312
+00:26:06,260 --> 00:26:06,500
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+313
+00:26:06,500 --> 00:26:06,500
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+314
+00:26:06,500 --> 00:26:07,140
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+315
+00:26:07,140 --> 00:26:07,980
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+316
+00:26:07,980 --> 00:26:07,980
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21
+
+317
+00:26:07,980 --> 00:26:15,030
+E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21 E21of
+
+318
+00:26:15,030 --> 00:26:18,710
+the form YM بسوء ألف واحد M هذي scalar رمز ال
+
+319
+00:26:18,710 --> 00:26:22,850
+scalar حطيت ال M هنا عشان يشملها بنقول عنها لمين
+
+320
+00:26:22,850 --> 00:26:27,010
+لل YM لو Y واحد هنحط لها واحد عشان تكون لمين لل Y
+
+321
+00:26:27,010 --> 00:26:32,130
+واحد وهكذا لأن YM بتسوء ألف واحد M E واحد زاد ألف
+
+322
+00:26:32,130 --> 00:26:36,790
+اتنين M E اتنين زاد ألف N E M E N اللي هي YM
+
+323
+00:26:36,790 --> 00:26:39,250
+مكتوبة على هذه الصورة لإنه ال E واحد وال E اتنين
+
+324
+00:26:39,250 --> 00:26:43,910
+وال E N are a basis طيب
+
+325
+00:26:44,930 --> 00:26:49,830
+Since YM is Cauchy Sequence إذا لكل Y أكبر من 0
+
+326
+00:26:49,830 --> 00:26:52,930
+there exists K limiting and such that البعد بين أي
+
+327
+00:26:52,930 --> 00:26:59,010
+نخطين YM نقص YR أصغر من Y لكل R و M أكبر من مين من
+
+328
+00:26:59,010 --> 00:27:03,370
+ال K اللي لجيناها طيب الآن بدي أستخدم اللمة اللي
+
+329
+00:27:03,370 --> 00:27:07,130
+قابلت بشويها لجيت و بدي أستخدمها دي لإن from this
+
+330
+00:27:07,130 --> 00:27:11,450
+and by لمة اتنين اربعة واحد بنقدر نلاقي ال C أكبر
+
+331
+00:27:11,450 --> 00:27:16,990
+من 0 معايا؟هذا الـ C أكبر من 0 لمين؟ الـ norm اللي
+
+332
+00:27:16,990 --> 00:27:19,870
+هو الـ vector أكبر يساوي C في الصممشي للـ scalar
+
+333
+00:27:19,870 --> 00:27:23,390
+استبعاته، صح؟ هذا اللي قبل شوية اللي ما هو أتعبنا
+
+334
+00:27:23,390 --> 00:27:26,770
+حالنا كلنا أتعب there exists C أكبر من 0 such that
+
+335
+00:27:26,770 --> 00:27:31,270
+YM ناقص YR زي من إبسنون، هي الإبسنون أكبر من YM
+
+336
+00:27:31,270 --> 00:27:36,010
+ناقص YR من إنها قوشي، هي واحد، الآن YM ناقص YR إيش
+
+337
+00:27:36,010 --> 00:27:41,420
+هي؟ الـ YM هي صورتهاوالـ Yr هي صورتها بس بمشينا
+
+338
+00:27:41,420 --> 00:27:45,640
+الـ M بحط مين؟ R بصير الصممشن لهادي نقصها دي بصير
+
+339
+00:27:45,640 --> 00:27:46,460
+الصممشن لهادي نقصها دي بصير الصممشن لهادي نقصها دي
+
+340
+00:27:46,460 --> 00:27:48,680
+بصير الصممشن لهادي نقصها دي بصير الصممشن لهادي
+
+341
+00:27:48,680 --> 00:27:49,200
+نقصها دي نقصها نقصها نقصها نقصها نقصها نقصها نقصها
+
+342
+00:27:49,200 --> 00:27:51,960
+نقصها نقصها نقصها نقصها نقصها نقصها نقصها نقصها
+
+343
+00:27:51,960 --> 00:27:52,760
+نقصها نقصها نقصها نقصها نقصها نقصها نقصها نقصها
+
+344
+00:27:52,760 --> 00:28:02,190
+نقصها نقصها نقصها نقصها نقصهاأه فاهمين هذا خطها
+
+345
+00:28:02,190 --> 00:28:05,630
+هيك فاهمين ليش اللي بحكيه لأن I من عند واحد لعند
+
+346
+00:28:05,630 --> 00:28:10,870
+مين لعند أنا هذا الان لل vector اللي هنا هذا اللي
+
+347
+00:28:10,870 --> 00:28:14,970
+هو اللي هو بدي استخدم اللي لمّا اللي قبل شوية أكبر
+
+348
+00:28:14,970 --> 00:28:19,550
+أو ساوي C في الصممش لأبسل يوت values لمين لل
+
+349
+00:28:19,550 --> 00:28:24,410
+scalars هذه اللي عندي هذه صار هذا المقدار هاي و
+
+350
+00:28:24,410 --> 00:28:29,880
+هذا أصغر أو يساوي مين أبسلونthis implies that for
+
+351
+00:28:29,880 --> 00:28:32,860
+any fixed I لكل واحدة من هدول مدام ال summation
+
+352
+00:28:32,860 --> 00:28:36,720
+هذا هذا ال summation مضروب في C أصغر من يابسولون
+
+353
+00:28:36,720 --> 00:28:41,620
+إذا كل واحدة منهم absolute value لها هذول أصغر
+
+354
+00:28:41,620 --> 00:28:45,040
+يعني ال summation هذا مضروب في C يعني ال summation
+
+355
+00:28:45,040 --> 00:28:48,460
+هذا لحاله أصغر من يابسولون ع C إذا كل واحدة من
+
+356
+00:28:48,460 --> 00:28:51,360
+اللي جوا أصغر من يابسولون على مين على C
+
+357
+00:28:54,290 --> 00:28:58,890
+then for any fixed I من الـ I هولا واحد و اتنين و
+
+358
+00:28:58,890 --> 00:29:03,630
+ان ال sequence Alpha I M عبارة عن Alpha I واحد
+
+359
+00:29:03,630 --> 00:29:07,370
+Alpha I اتنين Alpha I تلاتة هتكون يشمالها is a
+
+360
+00:29:07,370 --> 00:29:10,190
+Cauchy sequence لإن لجينا كل أبساط أكبر من سفر
+
+361
+00:29:10,190 --> 00:29:17,000
+لجينا Kبحيث أن الـ absolute value لهذه أصغر من Y
+
+362
+00:29:17,000 --> 00:29:22,400
+على C for every M وR أكبر من الـ K يعني بمعنى أخر
+
+363
+00:29:22,400 --> 00:29:25,560
+صارت الـ sequence هذه اللي هي هي ال sequence
+
+364
+00:29:25,560 --> 00:29:29,700
+تبعتها هذه اللي هي ال entry تبعت ال sequenceمش هده
+
+365
+00:29:29,700 --> 00:29:33,620
+هدى بس بنحكي عن واحدة من الـ sequences الان مش
+
+366
+00:29:33,620 --> 00:29:37,600
+عندنا للواحد و للتنين و للتلتة اللي عند الان هدولة
+
+367
+00:29:37,600 --> 00:29:41,580
+sequences هدى لل I in general هدى sequence هدى
+
+368
+00:29:41,580 --> 00:29:44,600
+طلعت كوشي sequence من هن مادام كوشي sequence و هي
+
+369
+00:29:44,600 --> 00:29:48,490
+كوشي sequence و فيهاشof numbers و لا .. ولا .. ولا
+
+370
+00:29:48,490 --> 00:29:50,970
+real numbers أو ال complex numbers complete إذا
+
+371
+00:29:50,970 --> 00:29:54,310
+أكيد في إلها إيه أشمالها اللي هي hence it
+
+372
+00:29:54,310 --> 00:29:59,430
+converges say to alpha I لأنه any Cauchy sequence
+
+373
+00:29:59,430 --> 00:30:03,780
+of real .. of numbers must convergemust converge
+
+374
+00:30:03,780 --> 00:30:10,680
+لأن use these unlimits ألف واحد M بتروح لألف واحد
+
+375
+00:30:10,680 --> 00:30:17,360
+ألف اتنين M لألف اتنين ألف N M بتروح للألف N إذا
+
+376
+00:30:17,360 --> 00:30:20,380
+صارت كل واحدة فيه لها limit لأن use these
+
+377
+00:30:20,380 --> 00:30:24,320
+unlimited to define من هذولة بدي أعرف مين اللي هو
+
+378
+00:30:24,320 --> 00:30:28,020
+Y Y بتساوي ألف واحد E واحد ألف اتنين E اتنين زي
+
+379
+00:30:28,020 --> 00:30:32,120
+ألف N E N اللي هي combination بينهمهذا الـ Y أكيد
+
+380
+00:30:32,120 --> 00:30:37,540
+في الـ space اللي عندي لأن الـ bases إله و هذولا
+
+381
+00:30:37,540 --> 00:30:41,200
+صارت إتنين ال combinations of bases إلا إن استخدمت
+
+382
+00:30:41,200 --> 00:30:44,420
+هذولا ال limits اللي لقيتهم قبل بشوية إذا صارت
+
+383
+00:30:44,420 --> 00:30:49,320
+عندي Y element ومش هيك كمان وخدوا الـ Y أم ناقصوا
+
+384
+00:30:49,320 --> 00:30:55,290
+الـ Yنورم الـ YM ناقص نورم الـ Y بساوي النورم لـ
+
+385
+00:30:55,290 --> 00:30:59,070
+summation هذين هي ال combination من مين Alpha I M
+
+386
+00:30:59,070 --> 00:31:02,870
+مع الـEI وهذه هي ال combination من مين من Alpha I
+
+387
+00:31:02,870 --> 00:31:06,490
+في الـEI نورم هذه ناقص هذه ناقص هذه ناقص هذه ناقص
+
+388
+00:31:06,490 --> 00:31:06,490
+هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه
+
+389
+00:31:06,490 --> 00:31:06,710
+ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص
+
+390
+00:31:06,710 --> 00:31:07,270
+هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه
+
+391
+00:31:07,270 --> 00:31:08,550
+ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص
+
+392
+00:31:08,550 --> 00:31:09,490
+هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه ناقص هذه
+
+393
+00:31:09,490 --> 00:31:14,070
+ناقص هذه
+
+394
+00:31:14,100 --> 00:31:19,360
+الان صار عندى summation لهذا في هذا however لكل
+
+395
+00:31:19,360 --> 00:31:23,280
+واحدة من هدول Alpha I M بتروح لمين لل Alpha I as M
+
+396
+00:31:23,280 --> 00:31:26,160
+goes to infinity اذا هذا المقدار as M goes to
+
+397
+00:31:26,160 --> 00:31:31,120
+infinity هو ان بدوح لصفر لأن هذه هتروح لهذه as M
+
+398
+00:31:31,120 --> 00:31:33,880
+goes to infinity اذا هذا هيروح لصفر بمعنى اخر
+
+399
+00:31:33,880 --> 00:31:38,920
+Normal Y M ناقص ال Y هيروح لصفربمعنى أخر صارت الـ
+
+400
+00:31:38,920 --> 00:31:42,680
+Y M converges لمن؟ لـ Y إذن الآن بدأت Y M ماكوش
+
+401
+00:31:42,680 --> 00:31:46,900
+sequence و أثبتت أن الـ Y M converges لـ Y في ال
+
+402
+00:31:46,900 --> 00:31:53,780
+space نفس Y، therefore Y is complete اللي بعده
+
+403
+00:31:53,780 --> 00:32:00,220
+المادة مفيدة للي بدوا علم منيح مفيدة مفيدة و بتدير
+
+404
+00:32:00,220 --> 00:32:04,860
+بقاكم و أي مكان لو الواحد يعني القدر اللي يكمل
+
+405
+00:32:04,860 --> 00:32:06,960
+كمان و كمان هتلاجوها
+
+406
+00:32:09,310 --> 00:32:13,450
+يستعانى بهوى المكان انه spaces لازم تكون في هال
+
+407
+00:32:13,450 --> 00:32:17,970
+spaces عشان تشتغل اي شغل تشتغل في الاحتمالات تشتغل
+
+408
+00:32:17,970 --> 00:32:23,010
+في الاحصة تشتغل في يعني انا بتذكر في الاحتمالات
+
+409
+00:32:23,010 --> 00:32:27,610
+أخدنا course كامل بنشتغل فيه في ال LB spaces ال LB
+
+410
+00:32:27,610 --> 00:32:30,370
+طبعا اللي هي مش ال sequences ال functions اللي هي
+
+411
+00:32:30,370 --> 00:32:33,650
+ال .. اللي بيجي integrable functions طب على معناته
+
+412
+00:32:33,650 --> 00:32:36,550
+انك بدك تسير بتعرف اللي هو اللي هو كل الكلام اللي
+
+413
+00:32:36,550 --> 00:32:43,020
+بنحكيه هذا بيكون مفيد إلىكوهكذا طيب theorem every
+
+414
+00:32:43,020 --> 00:32:45,880
+finite dimensional subspace Y of a normed space X
+
+415
+00:32:45,880 --> 00:32:51,080
+إيش ماله is closed طب هو complete و ال complete
+
+416
+00:32:51,080 --> 00:32:55,500
+أكيد إيش ماله closed بتعرفوا تثبتوها أن ال
+
+417
+00:32:55,500 --> 00:33:01,900
+complete space is closed يعني لو كانك X complete
+
+418
+00:33:03,330 --> 00:33:07,890
+بيعطينا انه X اللي هو خلينا نقول Y sub space Y sub
+
+419
+00:33:07,890 --> 00:33:12,210
+space من X و Y complete اكيد ال Y اشمالها closed
+
+420
+00:33:12,210 --> 00:33:14,710
+ماحكتش عن ال space اللي كله ال X ماهو ال space
+
+421
+00:33:14,710 --> 00:33:21,090
+دايما اللي هو closed و open فاهمين؟ طيب
+
+422
+00:33:22,590 --> 00:33:26,810
+إذاً أي finite dimensional subspace Y of X is
+
+423
+00:33:26,810 --> 00:33:34,090
+closed لأنه مدام Y subspace من X و finite
+
+424
+00:33:34,090 --> 00:33:37,970
+dimensional من X إذاً Y complete مدام complete على
+
+425
+00:33:37,970 --> 00:33:42,270
+طول إشماله closed بتقفل تثبتوها إن ال close ده قال
+
+426
+00:33:42,270 --> 00:33:47,330
+لو كانت عندي Y complete هتكون closed خد X في ال Y
+
+427
+00:33:47,330 --> 00:33:53,650
+closure إذاً there exist XNin Y such that Xn
+
+428
+00:33:53,650 --> 00:33:58,490
+converts الـ mean للـ X ماشي الحال طيب الآن صارت
+
+429
+00:33:58,490 --> 00:34:02,850
+عندي ال Xn مدينة converts لل X إذا صارت Xn كوشي
+
+430
+00:34:02,850 --> 00:34:05,990
+سيكوينس في مين؟ في ال Y مدينة كوشي سيكوينس في ال Y
+
+431
+00:34:05,990 --> 00:34:08,710
+و ال Y complete إذا converts يعني ال X هذا هتكون
+
+432
+00:34:08,710 --> 00:34:12,550
+وين؟ في ال Y مدينة X صارت في ال Y إذا صارت ال X في
+
+433
+00:34:12,550 --> 00:34:15,370
+ال Y closure تؤدي ال X في ال Y معناته ال Y closure
+
+434
+00:34:15,370 --> 00:34:19,100
+جزئية من ال Y و ال Y جزئية من ال Y closureمعناته
+
+435
+00:34:19,100 --> 00:34:21,880
+صحيح الـ Y بيساوي Y closure معناته الـ Y أشبه لها
+
+436
+00:34:21,880 --> 00:34:31,200
+S closed طيب .. اللي بعده؟ ان قال بجلد الملاحظة
+
+437
+00:34:31,200 --> 00:34:35,560
+التالية Infinite dimensional subspaceneed not be
+
+438
+00:34:35,560 --> 00:34:38,340
+closed يعني لو كان في عند infinite dimensional
+
+439
+00:34:38,340 --> 00:34:43,040
+subspace مش شرط closed احنا بنقول عن اللي هو طبعا
+
+440
+00:34:43,040 --> 00:34:46,220
+و اكيد مش شرط ماله complete اكيد مش شرط complete
+
+441
+00:34:46,220 --> 00:34:52,220
+ال infinite dimensional subspace اللي هو need not
+
+442
+00:34:52,220 --> 00:34:57,060
+be closed ماحدش قاله closed to see this consider
+
+443
+00:34:57,060 --> 00:35:04,710
+the space C C01 الكل continuous functionsخُد الـ
+
+444
+00:35:04,710 --> 00:35:10,110
+subspace منها مين؟ Y بتساوي لسبب X0 X1 X2 X3 X4 X5
+
+445
+00:35:10,110 --> 00:35:11,170
+X6 X7 X8 X9 X10 X11 X12 X13 X12 X13 X13 X13 X13
+
+446
+00:35:11,170 --> 00:35:11,610
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+447
+00:35:11,610 --> 00:35:11,830
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+448
+00:35:11,830 --> 00:35:11,830
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+449
+00:35:11,830 --> 00:35:11,830
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+450
+00:35:11,830 --> 00:35:11,850
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+451
+00:35:11,850 --> 00:35:14,370
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+452
+00:35:14,370 --> 00:35:14,390
+X13 X13 X13 X13 X13 X13 X13 X13 X13 X13 X13
+
+453
+00:35:22,100 --> 00:35:28,880
+بس .. اه؟ الان .. الان بدنا نجيبلكم مثال على
+
+454
+00:35:28,880 --> 00:35:32,800
+infinite dimensional subspace ليست closed مش شرط
+
+455
+00:35:32,800 --> 00:35:37,180
+يكون closed الان المثال اللي كان فيه سؤال معاكم في
+
+456
+00:35:37,180 --> 00:35:44,720
+ال .. في ال .. في ال home work هذا .. هذا بيجاوب
+
+457
+00:35:44,720 --> 00:35:49,640
+عليه الان خد ال space mean C of 0 و 1 continuous
+
+458
+00:35:49,640 --> 00:35:55,140
+functionsانظر من الـ Normal هو الـ Maximum الآن
+
+459
+00:35:55,140 --> 00:35:59,480
+الـ Sub-spacement هو ما يساوي الـ span لـ X0 X1 X2
+
+460
+00:35:59,480 --> 00:36:03,240
+إلى ما لا نهاية ماشي الحالة طب مين هدول X0 X0
+
+461
+00:36:03,240 --> 00:36:08,000
+بساوي اللي هو واحد X1 اللي هو بساوي T X2 بساوي T
+
+462
+00:36:08,000 --> 00:36:12,300
+تربيع X3 بساوي T تكعيب وكأنه قاعد بقولي ال span
+
+463
+00:36:12,300 --> 00:36:16,370
+اللي من الـ Polynomialsيعني و كأنه بيقول هذا why
+
+464
+00:36:16,370 --> 00:36:19,150
+is a subspace اللي هو the space they span by this
+
+465
+00:36:19,150 --> 00:36:25,370
+.. this اللي هي terms اللي هو بعملي اللي هو ال
+
+466
+00:36:25,370 --> 00:36:29,350
+polynomials هذا the space of all polynomials هان
+
+467
+00:36:29,350 --> 00:36:36,130
+is notClosed لأن بلاجة الـ sequence بتروح براته من
+
+468
+00:36:36,130 --> 00:36:40,430
+ضمن الـ mean اللي هو الـ exponential و هكذا و كتير
+
+469
+00:36:40,430 --> 00:36:43,490
+فيه شغلات المهم then why is not closed و why
+
+470
+00:36:43,490 --> 00:36:48,590
+هينجلته و why لكم كمان بتفصلوا أنتوا إذا في عندي
+
+471
+00:36:48,590 --> 00:36:51,370
+infinite dimensional spaces need not to be closed
+
+472
+00:36:51,370 --> 00:36:56,070
+طيب نجي الآن في حد اسمها equivalent norms
+
+473
+00:36:58,340 --> 00:37:02,900
+الـ equivalent norms بنقول عن الـ two norms a norm
+
+474
+00:37:02,900 --> 00:37:06,980
+on a vector space X is said to be equivalent to a
+
+475
+00:37:06,980 --> 00:37:11,900
+norm تاني نسميه norm not on X if there are
+
+476
+00:37:11,900 --> 00:37:16,520
+positive numbers A and B such that for all X
+
+477
+00:37:16,520 --> 00:37:20,560
+element in X لكل X في الـ X هنلاقي اللي هو norm ال
+
+478
+00:37:20,560 --> 00:37:24,440
+X محصور بين norm ال X not في constant و بين norm
+
+479
+00:37:24,440 --> 00:37:29,930
+ال X not برضه في constant آخرإذا لجينا العلاقة هذه
+
+480
+00:37:29,930 --> 00:37:34,030
+موجودة على طول بنقول .. لكل X بنقول إن الـNormal
+
+481
+00:37:34,030 --> 00:37:38,210
+هذولة الـNorm هذا و الـNorm هذا are equivalent
+
+482
+00:37:38,210 --> 00:37:43,630
+بنسميهم إيش مالهين؟ equivalent norms يعني جديتها
+
+483
+00:37:43,630 --> 00:37:46,470
+اللي هو constant في هذه و constant في هذه يحصر
+
+484
+00:37:46,470 --> 00:37:48,670
+اللي هو الـNorm الأصلي الـNorm اللي بنحكي عنه
+
+485
+00:37:48,670 --> 00:37:52,590
+بينهم معناته إنه صارت اللي هي .. اللي هي بس اللي
+
+486
+00:37:52,590 --> 00:37:56,430
+هي .. الفرق بينهم constant معناته هيكون are
+
+487
+00:37:56,430 --> 00:38:00,720
+equivalent normsله مابعده هذا التعريف اللي مابعده
+
+488
+00:38:00,720 --> 00:38:05,240
+أول واحد هذه equivalent norms on X defines the
+
+489
+00:38:05,240 --> 00:38:09,240
+same topology for X يعني الآن ال topology اللي
+
+490
+00:38:09,240 --> 00:38:12,380
+هيتولد من هذا ال norm و من هذا ال norm are
+
+491
+00:38:12,380 --> 00:38:18,440
+equivalent are equivalent topologies then the
+
+492
+00:38:18,440 --> 00:38:24,560
+proof is left to the reader الموضوع سهل ابتخدوا
+
+493
+00:38:24,560 --> 00:38:29,180
+الآن ال topology المولد من هنامن هذه و ال topology
+
+494
+00:38:29,180 --> 00:38:33,920
+المولد من هذه بتقولوا خلّونا ناخد اللي هو a بين 6
+
+495
+00:38:33,920 --> 00:38:37,700
+مولدة من ال topology هذا و بتثبتوها a بين 6
+
+496
+00:38:37,700 --> 00:38:41,320
+بالنسبالي مين اللي هي ال topology التانية و العكس
+
+497
+00:38:41,320 --> 00:38:44,520
+صحيح اتلاقيها اللي هو سهلة يعني الموضوع بس اللعب
+
+498
+00:38:44,520 --> 00:38:51,920
+في مين في ال constant اللي موجودة عندناأي سؤال أو
+
+499
+00:38:51,920 --> 00:38:56,940
+تاخد .. انت بدك تحكي عن ال open balls و منها تصل
+
+500
+00:38:56,940 --> 00:39:01,280
+طيب اتنين اربعة خمسة theorem تشوفها ال theorem
+
+501
+00:39:01,280 --> 00:39:09,220
+الحلوة و الجميلة و المفيدة خالص و بتريحنا كثير in
+
+502
+00:39:09,220 --> 00:39:13,860
+a finite dimensional vector space any norm is
+
+503
+00:39:13,860 --> 00:39:21,080
+equivalent to any norm تاني يعني انت لو جيتوبديت
+
+504
+00:39:21,080 --> 00:39:24,800
+اتفكر في انك تعمل بحكي عن ال norm مش عن ال metric
+
+505
+00:39:24,800 --> 00:39:31,860
+لو بتيجي تتفكر تعمل جد ما بدك norms على اللي هو ال
+
+506
+00:39:31,860 --> 00:39:35,840
+R اعمل norm على ال R بأي شكل أو على ال R تربيع أو
+
+507
+00:39:35,840 --> 00:39:39,980
+R تكعيب أو R unارو اللي بدك يعمل norms إذا عملت
+
+508
+00:39:39,980 --> 00:39:44,280
+norms اللي هي كل ال norms اللي بتعملها R
+
+509
+00:39:44,280 --> 00:39:48,920
+equivalent بولد بس one topologyاللي هو اللي بنسميه
+
+510
+00:39:48,920 --> 00:39:53,860
+احنا U Dual Topology اللي هي على الـ R أو R تربيع
+
+511
+00:39:53,860 --> 00:39:57,140
+أو R تكعيب تقول في الـ R تربيع بتدخل مربعات أو
+
+512
+00:39:57,140 --> 00:40:00,560
+بتدخل دوائر أو بتدخل الـ neighbourhood أو بتدخل
+
+513
+00:40:00,560 --> 00:40:05,700
+اللي هي اللي بدكيا في الآخر لما نولد نورم لما نولد
+
+514
+00:40:05,700 --> 00:40:09,660
+نورم كل هدولة أو ولدت من نورم على طول R equivalent
+
+515
+00:40:10,590 --> 00:40:13,610
+لكن انت بتقدر تعمل على الأرض اللي هو metric تاني
+
+516
+00:40:13,610 --> 00:40:17,230
+الـ discrete metric مش مولد من norm أصلا ماشي
+
+517
+00:40:17,230 --> 00:40:20,210
+الحال لكن ال .. ال .. ال .. ال .. ال .. ال
+
+518
+00:40:20,210 --> 00:40:23,870
+metricات المولدة من ال norms أو ال .. أو ال
+
+519
+00:40:23,870 --> 00:40:27,070
+topologies .. ال topologies المولدة من ال norm على
+
+520
+00:40:27,070 --> 00:40:30,530
+ال finite dimensional spaces كلهم are equivalent
+
+521
+00:40:30,530 --> 00:40:37,090
+هذا كلام خطير أو كلام كتير مهملدت الان dimension
+
+522
+00:40:37,090 --> 00:40:39,930
+للـ X أش بساوي بسوان نفترض ان احنا بنشتغل في
+
+523
+00:40:39,930 --> 00:40:43,390
+finite dimensional نفترض ان ال dimension لل X أش
+
+524
+00:40:43,390 --> 00:40:47,630
+بساوي بسوان وخد E واحد E اتنين E ان مادام finite
+
+525
+00:40:47,630 --> 00:40:50,890
+dimension لازم بقدر أجواء and bases بيصير E واحد E
+
+526
+00:40:50,890 --> 00:40:54,750
+اتنين E ان بياني bases for mean for X وبنيضيق كمان
+
+527
+00:40:54,750 --> 00:40:55,790
+ومحصورات
+
+528
+00:40:58,070 --> 00:41:01,390
+then ماقدر أحكي عن finite bases جزيه أما كل ال
+
+529
+00:41:01,390 --> 00:41:04,670
+vector space فيه له bases ما هو ال and then every
+
+530
+00:41:04,670 --> 00:41:06,930
+طب ما أنا مش هامش أودر bases أو الاخر هذا الموضوع
+
+531
+00:41:06,930 --> 00:41:11,030
+همل bases الاخرين then every x element in X has a
+
+532
+00:41:11,030 --> 00:41:14,630
+unique representation X بالساوية ألف واحد E واحد
+
+533
+00:41:14,630 --> 00:41:17,030
+زي ألف اتنين E اتنين زي ألف and E and خلاص حطته
+
+534
+00:41:17,030 --> 00:41:19,750
+بني دايم لإن صار فيه عنده اللي هو ال bases وصار
+
+535
+00:41:19,750 --> 00:41:21,650
+فيه عند ال scalars وال X موجودة كده لينا
+
+536
+00:41:21,650 --> 00:41:24,670
+compilation من بينهم a unique representation مظهوط
+
+537
+00:41:24,670 --> 00:41:28,430
+ولا مشاك في ال vector space؟طيب و الف واحد الف
+
+538
+00:41:28,430 --> 00:41:31,570
+اتنين الف ان are scalars بيلمّوا اتنين اربع واحد
+
+539
+00:41:31,570 --> 00:41:34,450
+اللي غلبتنا هذه في الأول there is a positive
+
+540
+00:41:34,450 --> 00:41:37,990
+constant C such that normal X هذا اللي هو اللي هي
+
+541
+00:41:37,990 --> 00:41:40,550
+ال compilation منهم أكبر أو يساوي C في ال
+
+542
+00:41:40,550 --> 00:41:44,090
+summation لأ اللي هو ال scalars سبعته ال absolute
+
+543
+00:41:44,090 --> 00:41:47,830
+value of scalars سبعته مظبوط؟طيب on the other hand
+
+544
+00:41:47,830 --> 00:41:50,430
+خلّيها في الذاكرة اللي بنستخدمها بعد شوية on the
+
+545
+00:41:50,430 --> 00:41:54,390
+other hand normal X not أصغر أو ساوى ال summation
+
+546
+00:41:54,390 --> 00:41:59,950
+لل alpha I E I notهذا .. الآن أنا فا .. ال .. ال
+
+547
+00:41:59,950 --> 00:42:00,650
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+548
+00:42:00,650 --> 00:42:01,870
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+549
+00:42:01,870 --> 00:42:03,450
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+550
+00:42:03,450 --> 00:42:03,610
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+551
+00:42:03,610 --> 00:42:04,310
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+552
+00:42:04,310 --> 00:42:04,590
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+553
+00:42:04,590 --> 00:42:07,530
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+554
+00:42:07,530 --> 00:42:08,290
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+555
+00:42:08,290 --> 00:42:08,390
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+556
+00:42:08,390 --> 00:42:10,130
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+557
+00:42:10,130 --> 00:42:13,110
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+558
+00:42:13,110 --> 00:42:13,390
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+559
+00:42:13,390 --> 00:42:16,830
+.. ال .. ال ..
+
+560
+00:42:16,830 --> 00:42:23,070
+ال .. الاللي هو أصغر أو يساوي الـSummation Alpha I
+
+561
+00:42:23,070 --> 00:42:26,530
+نورم الـEI Note Triangling Quality اللي هي نورم
+
+562
+00:42:26,530 --> 00:42:29,870
+الأول زائد نورم التاني زائد نورم التالت زائد نورم
+
+563
+00:42:29,870 --> 00:42:33,730
+الـN الأخير هذا الـTriangling Quality أصغر أو
+
+564
+00:42:33,730 --> 00:42:40,650
+يساوي هذا الـN كيف نورم للـAlpha I كمين هي بتدخل
+
+565
+00:42:40,650 --> 00:42:44,740
+أكبر واحد في هدولوفي maximum الهن ليه عشان الواحدة
+
+566
+00:42:44,740 --> 00:42:47,640
+اتن تان تلاتة ان من الاعداد فى الهن maximum ايش
+
+567
+00:42:47,640 --> 00:42:51,540
+تمته بساوة K اذا اصغر او ساوة K فى ال summation
+
+568
+00:42:51,540 --> 00:42:56,900
+اللى عندى الان بدى هي عندى حصلت Normal X Note اصغر
+
+569
+00:42:56,900 --> 00:43:00,760
+او ساوة K فى هذا المقدار وهذا اثبتوا انه اكبر او
+
+570
+00:43:00,760 --> 00:43:06,960
+ساوة بده ادمجن مع بعض الان together بيصير
+
+571
+00:43:06,960 --> 00:43:08,360
+انه اطلع لفوق بقى شوية
+
+572
+00:43:13,180 --> 00:43:19,020
+Together Normal X Note أصغر أو ساوي K في summation
+
+573
+00:43:19,020 --> 00:43:25,220
+للـ FI هذه وهذه اللي عندي summation أصغر أو ساوي
+
+574
+00:43:25,220 --> 00:43:29,420
+Normal X على C صح؟ هذه بيصير أصغر أو ساوي K على C
+
+575
+00:43:29,420 --> 00:43:32,840
+في Normal X صارت هذه Normal X Note أصغر أو ساوي
+
+576
+00:43:32,840 --> 00:43:38,320
+some number في الـ X إذا صارت اللي هيHence اللي هو
+
+577
+00:43:38,320 --> 00:43:42,120
+A في نورم ال X نوت أصغر يساوي نورم ال X جيبت هذا
+
+578
+00:43:42,120 --> 00:43:45,320
+على الجهد أنا عشان يلاقم اللي بدي يعني هي C على K
+
+579
+00:43:45,320 --> 00:43:50,140
+بتصير A بتساوي C على K لأن similarly بنفس الطريقة
+
+580
+00:43:50,140 --> 00:43:54,220
+بدل ما استخدم لل X لنورم النوت لنورم بستخدم نورم
+
+581
+00:43:54,220 --> 00:43:56,780
+النوت وبدل نورم النوت بستخدم نورم في الحالتين
+
+582
+00:43:56,780 --> 00:44:00,040
+فبطلع عندى similarly نورم ال X أصغر يساوي B في
+
+583
+00:44:00,040 --> 00:44:04,000
+نورم ال X نوتتنتهي المحاضرة مع بعض يظهر نورم X بين
+
+584
+00:44:04,000 --> 00:44:08,060
+نورم X نوت ونورم X نوت واحدة بسكيلر والثانية
+
+585
+00:44:08,060 --> 00:44:12,180
+بسكيلر آخر معناته هذا وهذا الهن إيه اشمالهن are
+
+586
+00:44:12,180 --> 00:44:15,580
+equivalent norms إذن في الـ finite dimensional
+
+587
+00:44:15,580 --> 00:44:20,720
+spaces كل ال norms are equivalent وبرك الله فيكم
+
+588
+00:44:20,720 --> 00:44:22,400
+تنتهي المحاضرة العاشرة
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/oa3DVUxeS2g_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/oa3DVUxeS2g_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..cb0cc0c35d7cb7fe31e94c31e047a1fbe530933d
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/oa3DVUxeS2g_postprocess.srt
@@ -0,0 +1,1156 @@
+1
+00:00:05,740 --> 00:00:08,400
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,400 --> 00:00:11,260
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:11,260 --> 00:00:16,300
+آله وصحبه أجمعين هذه المحاضرة رقم 28 مساق تحليل
+
+4
+00:00:16,300 --> 00:00:19,560
+اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:19,560 --> 00:00:24,820
+الإسلامية قسم الرياضيات للماجستيرأوصلنا لعند اللي
+
+6
+00:00:24,820 --> 00:00:28,900
+هو ال section الثالث في شبط أربعة اللي هي اربعة
+
+7
+00:00:28,900 --> 00:00:31,220
+تلاتة اللي هو ال hand-built theorem for complex
+
+8
+00:00:31,220 --> 00:00:34,500
+normed space المرة الفاترة أخدنا ال real vector
+
+9
+00:00:34,500 --> 00:00:38,800
+space وبرهنناه والبرهن كان طويل شويةعند normed
+
+10
+00:00:38,800 --> 00:00:41,660
+spaces وهذه اللي بتهمني أن ال normed spaces فعلا
+
+11
+00:00:41,660 --> 00:00:44,440
+هي اللي .. اللي أنا .. لأنه أنا شغلي functional
+
+12
+00:00:44,440 --> 00:00:48,140
+analysis بشكل أساسي عند لازم يكون فيه topology و
+
+13
+00:00:48,140 --> 00:00:51,160
+ال topology اللي هو induced by the norm فالآن هاخد
+
+14
+00:00:51,160 --> 00:00:54,760
+.. الآن بنختير المقصود فيها أحدى النظريات الأساسية
+
+15
+00:00:55,080 --> 00:00:59,360
+الاربع أو الخمسة اللي موجودة في ال .. ال .. ال ..
+
+16
+00:00:59,360 --> 00:01:02,580
+ال .. الـ Function Analysis هي الـ Hahnbenach
+
+17
+00:01:02,580 --> 00:01:06,120
+theorem for main .. for non spaces طبعا احنا
+
+18
+00:01:06,120 --> 00:01:08,440
+عرفناش اللي Hahnbenach theorem بدها الـ Hahnbenach
+
+19
+00:01:08,440 --> 00:01:11,080
+theorem هي عبارة عن extension يعني بدها توسيع نفوذ
+
+20
+00:01:11,080 --> 00:01:14,940
+يعني هاي الهدف طبعا الهدف الكبير هذالأن حققنا
+
+21
+00:01:14,940 --> 00:01:17,480
+الهدف هذا في حالة الـ real vector space والآن
+
+22
+00:01:17,480 --> 00:01:21,200
+هنحقق في حالة ال complex vector space ومش هنبره
+
+23
+00:01:21,200 --> 00:01:25,400
+نوع على السريع هنذكر نظرية واللي هنحكي فيه هو
+
+24
+00:01:25,400 --> 00:01:29,620
+توسيع النفوذ هذا في حالة ال normed spaces نيجي
+
+25
+00:01:29,620 --> 00:01:32,780
+نشوف الهانبنغ فيورم في حالة اللي هي ال complex
+
+26
+00:01:32,780 --> 00:01:39,540
+vector spaces وهي generalization للي فاتت let X be
+
+27
+00:01:39,540 --> 00:01:44,070
+a real or complex لأن real ولا complexVector space
+
+28
+00:01:44,070 --> 00:01:47,410
+and B is a sub additive real valued function on X
+
+29
+00:01:47,410 --> 00:01:50,630
+الـ
+
+30
+00:01:50,630 --> 00:01:55,110
+B صارت مالها sub additive نفسها لكن دلت ليش مالها
+
+31
+00:01:55,110 --> 00:01:59,410
+real vector اللي هي real valued function عشان بدها
+
+32
+00:01:59,410 --> 00:02:02,790
+يصير فيها مقارنة فيها أصغر و أصغر و إذا بتلزم اللي
+
+33
+00:02:02,790 --> 00:02:07,900
+هو تكون ريالand for any scalar α عرف P α X إيش
+
+34
+00:02:07,900 --> 00:02:11,560
+بيثاور لـ absolute value لـ P of X يعني الـ
+
+35
+00:02:11,560 --> 00:02:16,500
+positive homogeneity حيصير عندى لسه بدلنا بمين أنه
+
+36
+00:02:16,500 --> 00:02:19,600
+يشتغل على كل ألفة ال scalar بما فيه السالب و المدب
+
+37
+00:02:19,600 --> 00:02:23,220
+بس الان إيش هيطلع P α X هيثور لـ absolute value
+
+38
+00:02:23,220 --> 00:02:26,740
+لألفة في مين؟ في P of X الآن هاي الشروط طبعات اللى
+
+39
+00:02:26,740 --> 00:02:30,720
+هي النظريةFurthermore، لت F، اللي هي اللي بدنا
+
+40
+00:02:30,720 --> 00:02:34,340
+نعملها extension، لت F بيه a linear functional،
+
+41
+00:02:34,340 --> 00:02:36,900
+linear functional، complex ولا real، مش مشكلة،
+
+42
+00:02:36,900 --> 00:02:39,940
+which is defined on mean ونقصها بspace Z of mean
+
+43
+00:02:39,940 --> 00:02:44,340
+of X، and satisfies، الآن مابنقدرش نقول F of X
+
+44
+00:02:44,340 --> 00:02:47,840
+أصغر أو أشاوي، لأ، لأنه F of X complex ممكن تكون
+
+45
+00:02:48,040 --> 00:02:52,300
+فعشان هيك أخدنا المدرس له يكون مدرس ال F of X أصغر
+
+46
+00:02:52,300 --> 00:02:53,520
+يساوي بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+47
+00:02:53,520 --> 00:02:54,320
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+48
+00:02:54,320 --> 00:02:54,500
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+49
+00:02:54,500 --> 00:02:55,020
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+50
+00:02:55,020 --> 00:02:57,360
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+51
+00:02:57,360 --> 00:03:08,500
+بيه بيه بيه بيه
+
+52
+00:03:08,500 --> 00:03:14,420
+بيما دام فيه لجهود معينة هي عملته في حياتها الجهود
+
+53
+00:03:14,420 --> 00:03:17,740
+هذا اللي هو ان هي هتكون أصغر سواء بي وف اكس لكل
+
+54
+00:03:17,740 --> 00:03:22,060
+اكس اللي بتنزد الان و ال .. و ال .. و ال .. و ال
+
+55
+00:03:22,060 --> 00:03:26,240
+بيها دي اللي اللي قولنا عنها اللي عنديالآن فمن
+
+56
+00:03:26,240 --> 00:03:30,780
+عطاء رب نقلها إن هي قدرت تعمل extension هيك الدنيا
+
+57
+00:03:30,780 --> 00:03:35,300
+حتى في الحياة الطبيعية مدام أنت جدمت جهود إذا فيه
+
+58
+00:03:35,300 --> 00:03:39,200
+إمكانية إنك تعملك extension تعملك زيادة نفوذ إذا
+
+59
+00:03:39,200 --> 00:03:44,850
+thenthere is أو F has a linear extension of تلدة
+
+60
+00:03:44,850 --> 00:03:49,310
+from z to مين to x وسعت نفوذة من z على مين على كل
+
+61
+00:03:49,310 --> 00:03:52,890
+x وحافظت على حقوقها الأولى اللي هي أصغر سواء بي و
+
+62
+00:03:52,890 --> 00:03:56,250
+في x ومدت هذه الحقوق على كل مين أو كل هذا الجود
+
+63
+00:03:56,250 --> 00:03:59,830
+مدته على مين على كل x اللي عندنا اللي هو
+
+64
+00:03:59,830 --> 00:04:02,370
+satisfying absolute value of تلدة و في x أصغر سواء
+
+65
+00:04:02,370 --> 00:04:06,530
+بي و في x لكل x where موجودة في x البرهام بناشية
+
+66
+00:04:07,250 --> 00:04:09,550
+فحالة الريال اللي أثبتناها وطولنا خلّينا نيجي
+
+67
+00:04:09,550 --> 00:04:15,890
+لحالة ال normed space وهو الشغل برهانها طبعا
+
+68
+00:04:15,890 --> 00:04:19,010
+اعتمادا عن البرهين اللي حكيناها هيكون سهل لكن لو
+
+69
+00:04:19,010 --> 00:04:23,930
+بدك تبرهنه من الصفر هيصير برهانه عايش طويلإذن قصر
+
+70
+00:04:23,930 --> 00:04:28,370
+البرهان هنا لأنه أحنا أسسنا في البرهان الأولاني
+
+71
+00:04:28,370 --> 00:04:30,970
+الان هان بنخ theorem اللي هي normed space اللي هي
+
+72
+00:04:30,970 --> 00:04:34,190
+النظرية اللي بتحكي عنها الان بتقولي برضه نفس
+
+73
+00:04:34,190 --> 00:04:37,090
+الفحوة اللي حكيته لان بس ال extension هيصير mean
+
+74
+00:04:37,090 --> 00:04:41,950
+على normed space بدل اللي هي vector spacelet F be
+
+75
+00:04:41,950 --> 00:04:44,990
+a bounded linear functional على طول ما زي ما بنحكي
+
+76
+00:04:44,990 --> 00:04:48,050
+عن linear functional في حالة ال vector space إذا
+
+77
+00:04:48,050 --> 00:04:50,890
+إذا بنحكي عن non-dismissed بنحكي عن مين؟ عن
+
+78
+00:04:50,890 --> 00:04:55,350
+bounded linear functional ماشي الحال و اللي هي
+
+79
+00:04:55,350 --> 00:04:59,350
+برضه على غرار الأول ال linear functional فيه ال
+
+80
+00:04:59,350 --> 00:05:02,490
+extension ال bounded linear functional برضه هيكون
+
+81
+00:05:02,490 --> 00:05:07,020
+اللي هي إيه أشماله؟ extension بنفس المنطقالأن دع F
+
+82
+00:05:07,020 --> 00:05:08,620
+يكون مجموعة عامة عامة عامة عامة عامة عامة عامة
+
+83
+00:05:08,620 --> 00:05:09,340
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+84
+00:05:09,340 --> 00:05:13,980
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+85
+00:05:13,980 --> 00:05:18,440
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+86
+00:05:18,440 --> 00:05:18,820
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+87
+00:05:18,820 --> 00:05:24,860
+عامة عامة عامة عامand has the same norm شوف الآن
+
+88
+00:05:24,860 --> 00:05:29,500
+الزيادة أنه norm هو norm الأصلي بتحافظ على كل
+
+89
+00:05:29,500 --> 00:05:33,420
+حقوقها الأولى مش بتقول لأ زرعت و حصدت إش أكبر ال
+
+90
+00:05:33,420 --> 00:05:37,100
+norm ال F تلد X إيش بيساوي norm ال F على ال Z
+
+91
+00:05:37,100 --> 00:05:41,640
+where norm ال F تلد X إيش بنفسد فيه هو ال supremum
+
+92
+00:05:41,640 --> 00:05:44,880
+لل F تلد أو ب X لل Xات اللي في ال X و norm هين
+
+93
+00:05:44,880 --> 00:05:48,100
+بيساوي واحد بينما التانية اللي هي على ال Z اللي هي
+
+94
+00:05:48,100 --> 00:05:52,310
+ال supremum لل absolute value لل F of Xللـ X ∈ Z
+
+95
+00:05:52,310 --> 00:05:55,690
+أن المراتقين أشمالهم بيساوي واحد ماشي الحاجة إذا
+
+96
+00:05:55,690 --> 00:05:59,510
+هذه Z على ال .. على Z ال .. ال .. السوبرمان وهذه
+
+97
+00:05:59,510 --> 00:06:04,410
+على X السوبرمان هو Normal of Z بيساوي سفر في حالة
+
+98
+00:06:04,410 --> 00:06:08,470
+مين ال trivial case أن Z أيش بيساوي اللي هو مين ال
+
+99
+00:06:08,470 --> 00:06:13,050
+zero طيب نيجي الآن نبرهن اطلع البرهن سهل اطلع لفوق
+
+100
+00:06:13,050 --> 00:06:20,290
+Fزت بتساوي Zero اللي هو Zero Zero Zero Zero Space
+
+101
+00:06:20,290 --> 00:06:23,970
+يعني then أف بتساوي سفر وال extension اللي هيكون
+
+102
+00:06:23,970 --> 00:06:26,830
+مين أف تلداش بتساوي سفر خلّيني أقول ال trivial
+
+103
+00:06:26,830 --> 00:06:30,950
+case قيمتها
+
+104
+00:06:30,950 --> 00:06:36,250
+مش كثيرة إلا للحالات اللي ممكن يعني بدك .. يعني
+
+105
+00:06:36,250 --> 00:06:40,180
+مانكونش مستثنين ال Zero إنما بتنفع على كل شيءفعشان
+
+106
+00:06:40,180 --> 00:06:44,380
+ايه؟ خصصنا عليها ليه زد لا تساو سفر الآن؟ ناخد
+
+107
+00:06:44,380 --> 00:06:49,240
+حالة مين زد لا تساو سفر؟ then for any x element in
+
+108
+00:06:49,240 --> 00:06:54,100
+z we have فليه f bounded in a functional إذن ال
+
+109
+00:06:54,100 --> 00:06:57,200
+absolute value of f of x أزرع سوى، norm ال F norm
+
+110
+00:06:57,200 --> 00:07:00,700
+ال F على مين؟ هي F dismal زي شغالة مين على z norm
+
+111
+00:07:00,700 --> 00:07:04,300
+ال F z في norm مين ال x؟ لكل ال x وين موجودات في z
+
+112
+00:07:04,300 --> 00:07:10,170
+الان أعرف هاي ال bridge اللي بدياللي هو طبيعة ..
+
+113
+00:07:10,170 --> 00:07:13,150
+اللي هو الـ norm أنه هيعمل لي sublinear functional
+
+114
+00:07:13,150 --> 00:07:16,330
+يعني هيعمل .. هيعمل اللي .. اللي .. اللي كانت
+
+115
+00:07:16,330 --> 00:07:19,350
+المطلوب في معطيات النظريات السابقة هيعملها الـ
+
+116
+00:07:19,350 --> 00:07:22,010
+norm فهيكون automatic تطلع النظرية في extension
+
+117
+00:07:22,010 --> 00:07:27,230
+طيب define P من X ل عند R by P of X أش بساوي ..
+
+118
+00:07:27,230 --> 00:07:32,850
+بساوي normal FZ في normal Xهي اللي بدي أعرفه حر
+
+119
+00:07:32,850 --> 00:07:36,870
+أنا بدي أعرف الـP of X هي عبارة عن مين؟ عن نورم
+
+120
+00:07:36,870 --> 00:07:40,390
+الـFz اللي أنا عرفته خلاص نورم الـFz صار معروف
+
+121
+00:07:40,390 --> 00:07:44,290
+لأنه bounded لأن نورم هذا معروف في نورم مين الـX
+
+122
+00:07:44,290 --> 00:07:46,730
+هذه اللي .. اللي .. اللي هداك إذا .. إذا هذا هو
+
+123
+00:07:46,730 --> 00:07:49,970
+كأنه مقدر ثابت بضربه في مين؟ في نورم الـX اللي هي
+
+124
+00:07:49,970 --> 00:07:54,870
+هذه تتغير بتغير مين؟ X إذا هذا الـP of X أكيد
+
+125
+00:07:54,870 --> 00:07:58,950
+هيحقق ضمن الـabsolute value للـF of X اللي هو إيه
+
+126
+00:07:58,950 --> 00:08:03,660
+اش ماله؟اللي هو عبارة عن أصغر المقدار هذا صح؟ هي
+
+127
+00:08:03,660 --> 00:08:07,600
+اتلت فاض و هذا المقدار هو اللي أقرفته P of X إذا
+
+128
+00:08:07,600 --> 00:08:11,480
+صار ال absolute value of X أصغر أو يساوي P of X
+
+129
+00:08:11,480 --> 00:08:15,040
+لكل X element in Z إذا هاي أول شرط اتحقق من شروط
+
+130
+00:08:15,040 --> 00:08:18,300
+مين النظرية اللي حكينا عنها المرة الماضية تبعت ال
+
+131
+00:08:18,300 --> 00:08:20,660
+handballing theorem أو اللي حكينا عنها قبل شوية
+
+132
+00:08:20,660 --> 00:08:29,600
+واضح ها؟ طيبFurthermore, for any x, y element in X
+
+133
+00:08:29,600 --> 00:08:34,140
+and any scalar α element in R, we have شغلتين أول
+
+134
+00:08:34,140 --> 00:08:40,100
+شيء احسب ليه B of X زائد Y ايش بيساوي؟ بيساوي norm
+
+135
+00:08:40,880 --> 00:08:45,720
+الـ Absolute Value F of Z F over Z فنور Main الـ X
+
+136
+00:08:45,720 --> 00:08:51,760
+زائد Y حسب التعريف اللي أعرفته وهذا أصغر أو سوى
+
+137
+00:08:51,760 --> 00:08:57,280
+بالـ Triangling Quality هدي في هدي زائد هدي بفكها
+
+138
+00:08:57,280 --> 00:09:01,660
+هدي في هدي هي P of X وهدي في هدي اللي هي Main P of
+
+139
+00:09:01,660 --> 00:09:07,470
+Yإذا صارت عندى بيكزائد Y أصغر أو سوى بيكزائد مين
+
+140
+00:09:07,470 --> 00:09:14,110
+البي الان P of Alpha X بساوى حسب التعريف اللى عندى
+
+141
+00:09:14,110 --> 00:09:18,430
+عبارة عن حسب التعريف اللى هان عبارة عن norm اللى
+
+142
+00:09:18,430 --> 00:09:25,110
+هى ال FZفي مين؟ في norm الـ α X بطلع الألفة برا
+
+143
+00:09:25,110 --> 00:09:29,750
+بصير absolute value في هذه في هذه اللي هي مين P of
+
+144
+00:09:29,750 --> 00:09:33,970
+X إذا برضه اللي هو الشرط الثاني ماله اتحقق إذا
+
+145
+00:09:33,970 --> 00:09:37,930
+hence by theorem أربعة تلاتة .. لأ مش linear hence
+
+146
+00:09:37,930 --> 00:09:43,380
+by theorem أربعة تلاتة واحدأه نعم there exist a
+
+147
+00:09:43,380 --> 00:09:46,380
+linear extension من اللي قبل بشوية اللي حكيناها في
+
+148
+00:09:46,380 --> 00:09:50,840
+حالة ال vector space إذا صار عندي الآن الشروط
+
+149
+00:09:50,840 --> 00:09:54,740
+النظرية أربعة تلاتة واحد اللي قبل بشوية كلها تحققت
+
+150
+00:09:54,740 --> 00:09:58,700
+إذا في عندي ال linear extension اسمه f تلدان x
+
+151
+00:09:58,700 --> 00:10:02,720
+which is an extension of f and satisfies كمان ال
+
+152
+00:10:02,720 --> 00:10:07,260
+absolute value لفتل دو فيكس أصغر شو مين بيو فيكس
+
+153
+00:10:07,650 --> 00:10:10,910
+ماشي الحال لكن ال P of X بيساوي ال norm هذا في هذا
+
+154
+00:10:10,910 --> 00:10:16,490
+الان هذا الكلام لكل mean X limit X إذا هذا إذا
+
+155
+00:10:16,490 --> 00:10:21,870
+حصلنا على extension ويحقق هذا أصغر يساوي هذا طيب
+
+156
+00:10:21,870 --> 00:10:27,060
+من هذولة مع بعض التنتين هيها هيها هيهاالـ Code
+
+157
+00:10:27,060 --> 00:10:29,560
+اللي هو الـ Supremum على النورمات اللي بيساوي سفر
+
+158
+00:10:29,560 --> 00:10:32,400
+الـ Supremum اللي هدى على النورمات اللي بيساوي سفر
+
+159
+00:10:32,400 --> 00:10:36,580
+هو عبارة عن نورم العندي طبعا احنا بنحكي عن ال Xات
+
+160
+00:10:36,580 --> 00:10:40,400
+اللي وين موجودات في X فبصير نورم ال F تلد على ال X
+
+161
+00:10:40,400 --> 00:10:45,480
+أصغر أو ساوي مين نورم ال FZ هاي واحدةلكن من جهة
+
+162
+00:10:45,480 --> 00:10:52,180
+أخرى Normal of Z اللي هو supremum على ال Xات اللي
+
+163
+00:10:52,180 --> 00:10:55,620
+في الـ Z بينما هذا supremum اللي هو نفسه طبعا
+
+164
+00:10:55,620 --> 00:10:59,460
+after ده Z لأن هذا extension بينما هذا supremum
+
+165
+00:10:59,460 --> 00:11:03,550
+على مين؟على العناصر اللي في الـ X والـ X بتحتوى
+
+166
+00:11:03,550 --> 00:11:07,850
+الـ Z إذا سوبرمام على مجموعة أقل من مجموعة تانية
+
+167
+00:11:07,850 --> 00:11:10,690
+فأكيد السوبرمام هن أصغر يساوي مين؟ السوبرمام هن
+
+168
+00:11:10,690 --> 00:11:15,690
+فهذا أصغر يساوي هذا فبنكون حصلنا على الـ Normal FZ
+
+169
+00:11:15,690 --> 00:11:22,490
+مرة أصغر يساوي ومرة أكبر يساوي من التنتين في إيه
+
+170
+00:11:22,490 --> 00:11:25,870
+شماله؟ فيه يساوي إذا أثبتنا الـ Extension و أثبتنا
+
+171
+00:11:25,870 --> 00:11:32,310
+اللي هي الشروط المطلوبةأو خلّيني أقول ما حققته
+
+172
+00:11:32,310 --> 00:11:37,030
+اللي هي النظرية نجلة
+
+173
+00:11:37,030 --> 00:11:42,570
+theorem 433 bounded linear functional انتبهوا إيش
+
+174
+00:11:42,570 --> 00:11:48,650
+هذا اللي بتقول let X be a normed space ركزوا في
+
+175
+00:11:48,650 --> 00:11:54,540
+النصعند X0 لاتساوي 0 بيه any element in X أي
+
+176
+00:11:54,540 --> 00:11:56,980
+element in X أخدناها على البيت الرأي وسميناها X0
+
+177
+00:11:56,980 --> 00:12:01,540
+ماشي الحالة أو X normed space بيقولك then there
+
+178
+00:12:01,540 --> 00:12:06,060
+exists a bounded linear functional F tilde و X
+
+179
+00:12:06,060 --> 00:12:11,700
+such that نورمه بيساوي واحد وال F tilde و X0 إيش
+
+180
+00:12:11,700 --> 00:12:18,030
+حيسوي نورمين ال X0يعني اللي بيحكيلكيا بيقولك انه
+
+181
+00:12:18,030 --> 00:12:22,330
+انت خد اي X note في normed space بقدر ألاجيلك
+
+182
+00:12:22,330 --> 00:12:26,410
+bounded linear functional يحدد بمين بواسطة النقطة
+
+183
+00:12:26,410 --> 00:12:29,590
+هذه اللي أخدتها انت arbitrarily بتفكز بقدر ألاجي
+
+184
+00:12:29,590 --> 00:12:32,330
+bounded linear functional F tilde و X و يقوه normه
+
+185
+00:12:32,330 --> 00:12:36,550
+بساوء واحد و ال F tilde of X note هذه اللي أخدتها
+
+186
+00:12:36,550 --> 00:12:40,930
+هو ايش هيطلع عنده عبارة عن norm ال X note خلينا
+
+187
+00:12:40,930 --> 00:12:48,200
+نشوف مع بعضConsider the subspace Z المكوّن من مين؟
+
+188
+00:12:48,200 --> 00:12:54,400
+Alpha X0 هي الـ Span لـ X0 يعني الـ X0 هي النقطة
+
+189
+00:12:54,400 --> 00:12:57,320
+الأربترية اللي أخدناها Alpha is the scalar Define
+
+190
+00:12:57,320 --> 00:13:04,350
+F من Z لعند مين؟ لعند scalar field KF of ZX F of X
+
+191
+00:13:04,350 --> 00:13:11,190
+بيساوي F of Alpha X0 و يساوي Alpha في مين في
+
+192
+00:13:11,190 --> 00:13:17,650
+Normal X0 هذا اللي هو واضح انه Alpha X0 where K is
+
+193
+00:13:17,650 --> 00:13:21,570
+scalar field real or complex it is easy to see
+
+194
+00:13:21,570 --> 00:13:25,840
+that F is linearفها دي إيه عشان إذنها بتعرفوا
+
+195
+00:13:25,840 --> 00:13:34,760
+تثبتوها F of Beta X زائد Y بتساوي كده نفهمها خلاص
+
+196
+00:13:34,760 --> 00:13:38,180
+هي بتعرفوا تثبتوها لأ من التعريف هذا هيه التعريف
+
+197
+00:13:38,180 --> 00:13:42,500
+هيه بتعرفوا تثبتوها على طولمباشرة الان و also f is
+
+198
+00:13:42,500 --> 00:13:45,800
+bounded و ال boundedness برضه سهل ال boundedness
+
+199
+00:13:45,800 --> 00:13:50,280
+بيقولك خد ايش معله absolute value of f of x ايش
+
+200
+00:13:50,280 --> 00:13:52,720
+هيساوي؟ بيساوي ال absolute value هذه بيساوي ال
+
+201
+00:13:52,720 --> 00:13:55,900
+absolute value هذه اللي هو هيطلع alpha mean في x0
+
+202
+00:13:55,900 --> 00:14:00,420
+اللي هو بيساوي mean اللي هو normal x لأن ال x ايش
+
+203
+00:14:00,420 --> 00:14:05,220
+بتساوي؟ alpha x0 هيك شكل العناصر جوامعايا صار عندى
+
+204
+00:14:05,220 --> 00:14:08,780
+لأن absolute value of f of x ايش بيساوي normal x
+
+205
+00:14:08,780 --> 00:14:12,940
+لكل x و موجودة بيساوي x يعني بمعنى اخر صار عندى
+
+206
+00:14:12,940 --> 00:14:19,260
+اللي هو ال f is linear و ال f is bounded ماشي و لو
+
+207
+00:14:19,260 --> 00:14:22,480
+اتطلعت على قِبتها absolute value of f of x بيساوي
+
+208
+00:14:22,480 --> 00:14:29,380
+normal x absolute value ل ال f of x بيساوي normal
+
+209
+00:14:29,380 --> 00:14:36,930
+x اذا ال supremumعلى ال norm ال X أو X ده تساوي
+
+210
+00:14:36,930 --> 00:14:43,270
+شفر هيساوي ايه؟ واحد وهذا عبارة عن norm ال F over
+
+211
+00:14:43,270 --> 00:14:43,730
+X
+
+212
+00:14:47,220 --> 00:14:50,300
+النظرية اللي قبل بشوية اتحققت
+
+213
+00:15:15,050 --> 00:15:19,210
+الـ X في الـ Z كيف شكل الـ X ألفة في X نور فح؟
+
+214
+00:15:19,210 --> 00:15:23,850
+ألفة scalar أنه scalar لأن طب F of X0 نفسها بساوي
+
+215
+00:15:23,850 --> 00:15:29,650
+اللي هو يعني و كأني بقول F of واحد في X0 حسب
+
+216
+00:15:29,650 --> 00:15:32,850
+القانون اللي هو إيش بيساوي واحد في نورم ال X0
+
+217
+00:15:32,850 --> 00:15:38,810
+فاهمين؟ بيساوي واحد في نورم ال X0 بيساوي نورم ال
+
+218
+00:15:38,810 --> 00:15:45,720
+X0 يعني الف بيساوي واحدأه فبصير عندى f of x0 بساوة
+
+219
+00:15:45,720 --> 00:15:49,280
+.. f .. f tilde of x0 بساوة f of x0 بساوة مين؟
+
+220
+00:15:49,280 --> 00:15:57,680
+نورم ال x0 أي سؤال؟ اللي بعده؟ Corollary لأن for
+
+221
+00:15:57,680 --> 00:16:02,740
+any x in a normed space X we have لأن احنا كنا
+
+222
+00:16:02,740 --> 00:16:12,190
+نجيب نقول نورم ال F بساوة supremumللـ f of x
+
+223
+00:16:12,190 --> 00:16:17,990
+absolute value على نورم الـ x الـ x element in x
+
+224
+00:16:17,990 --> 00:16:22,930
+minus mean الـ zero يعني كنا نجيب ال norm بدلالة
+
+225
+00:16:22,930 --> 00:16:25,310
+mean الـ f و الـ f سبرهما من الـ f على نورم الـ x
+
+226
+00:16:25,310 --> 00:16:31,370
+الآن بده يجيبلك اللي هو نورم الـ x الآن مش نورم
+
+227
+00:16:31,370 --> 00:16:36,770
+الـ f بنضغط بدلالة mean الـ f و الـ f ماشي؟ إذا
+
+228
+00:16:36,770 --> 00:16:42,680
+بقوللي henceنستطيع أن نجد لأي X في عضلة X نستطيع
+
+229
+00:16:42,680 --> 00:16:46,840
+أن نجد X عضلة X بساوية سبريمام للقيم الأبسط F of X
+
+230
+00:16:46,840 --> 00:16:53,300
+عالمي لـN عن عضلة F فالـN المتغير بدل ما هو X في X
+
+231
+00:16:53,300 --> 00:16:57,360
+minus Zero هو عبارة عن الـlinear functionals F
+
+232
+00:16:57,360 --> 00:16:59,480
+element in X برايم من X برايم من X برايم من X
+
+233
+00:16:59,480 --> 00:17:01,700
+برايم من X برايم من X برايم من X برايم من X برايم
+
+234
+00:17:01,700 --> 00:17:01,800
+من X برايم من X برايم من X برايم من X برايم من X
+
+235
+00:17:01,800 --> 00:17:01,960
+برايم من X برايم من X برايم من X برايم من X برايم
+
+236
+00:17:01,960 --> 00:17:06,020
+برايم من X برايم من X برايم من X برايم من X برايم
+
+237
+00:17:06,020 --> 00:17:09,360
+من X بأف لا تساوي سفر يعني السبريهم هم عالمين على
+
+238
+00:17:09,360 --> 00:17:14,640
+كل الأفات اللي في الـ X' هنس .. من نتيجة مباشرة
+
+239
+00:17:14,640 --> 00:17:18,060
+هنس if X0 is a .. is such that F of X0 بساوي سفر
+
+240
+00:17:18,060 --> 00:17:22,600
+for all أف اللي متين X' then X' أشبه لها بساوي سفر
+
+241
+00:17:23,840 --> 00:17:27,720
+الان راكزوا الكلام سهل الان عندي من theorem أربعة
+
+242
+00:17:27,720 --> 00:17:30,980
+تلاتة في extension of تل دا element of X prime
+
+243
+00:17:30,980 --> 00:17:35,020
+such that normal of تل دا ايش بيساوي واحد وال F تل
+
+244
+00:17:35,020 --> 00:17:39,800
+دا of X ايش بيساوي normal X من اللي قبل بشوية
+
+245
+00:17:39,800 --> 00:17:43,820
+theorem أربعة تلاتة تلاتة اللي أثبتناها where الان
+
+246
+00:17:43,820 --> 00:17:49,100
+إذا لجيناExtension F تلدة في الـ X' بحيث نورمه
+
+247
+00:17:49,100 --> 00:17:53,120
+بساوء واحد والـ F تلدة و X له بساوء جداش نورم الـ
+
+248
+00:17:53,120 --> 00:17:56,380
+X اللي كنا بسميه X ناضلة قبل شوية Where X is
+
+249
+00:17:56,380 --> 00:17:59,420
+around zero element in mean in X So that the
+
+250
+00:17:59,420 --> 00:18:02,880
+supremum لل absolute value F of X على نورم الـ F
+
+251
+00:18:03,560 --> 00:18:06,360
+اللي هي f element in x prime و f أكبر يساوي 0 هذا
+
+252
+00:18:06,360 --> 00:18:09,960
+ال supremum على الكل ماشي الحال أكيد أكبر أو يساوي
+
+253
+00:18:09,960 --> 00:18:12,800
+واحدة منهم من ضمنهم الواحدة المن هناك اللي اللي
+
+254
+00:18:12,800 --> 00:18:17,320
+أجريها إذا أكبر أو يساوي فاهمين أكبر أو يساوي اللي
+
+255
+00:18:17,320 --> 00:18:23,510
+هو الآن ال supremum يا جماعة أنا جيت f تل دهفى الـ
+
+256
+00:18:23,510 --> 00:18:29,250
+X' و لجهة F تلدة of X بيساوي الـ X نفسها و نورم
+
+257
+00:18:29,250 --> 00:18:35,510
+الـ F تلدة بيساوي إيش؟ واحد خدوا الآن ال supremum
+
+258
+00:18:35,510 --> 00:18:40,690
+ال supremum ل absolute value of X على نورم ال F
+
+259
+00:18:40,690 --> 00:18:48,710
+حيث F ويه موجودة فى ال X'والـ F لا تساوي منين؟ الـ
+
+260
+00:18:48,710 --> 00:18:51,930
+Zero هذه اطلع لفوق أكبر أو يساوي أكيد أي واحدة من
+
+261
+00:18:51,930 --> 00:18:55,530
+هنا أكبر أو يساوي أي واحدة من هنا مين أي واحدة من
+
+262
+00:18:55,530 --> 00:19:04,250
+هنا اللي جايك فوق اللي هي F تلدة of X على norm الـ
+
+263
+00:19:04,250 --> 00:19:09,130
+F تلدة اللي هو بيساوي F تلدة of X إيش بتساوي؟ X
+
+264
+00:19:09,130 --> 00:19:16,350
+صح؟ على اللي هو إيه إيش بتساوي هذه؟مايساوة نورم ال
+
+265
+00:19:16,350 --> 00:19:19,690
+X إذا صار عند ال suprem هذا اللي بقول أكبر أو
+
+266
+00:19:19,690 --> 00:19:24,970
+ساوية مين نورم ال X واضح أه؟ بالذات بتلك الأن أصغر
+
+267
+00:19:24,970 --> 00:19:27,430
+أو ساوية معناته حدثت المشاوخ خلصت الكورة ده
+
+268
+00:19:27,430 --> 00:19:30,890
+however ال absolute value of F of X أصغر أو ساوية
+
+269
+00:19:30,890 --> 00:19:34,670
+نورم ال F و نورم مين؟ ال X ماشي الحل لأن F is
+
+270
+00:19:34,670 --> 00:19:38,150
+bounded in our functional then ال suprem على F
+
+271
+00:19:38,150 --> 00:19:42,250
+تلدى على نورم ال F هيكون أصغر أو ساوية مين نورم ال
+
+272
+00:19:42,250 --> 00:19:46,470
+Xصح؟ إذا من الـ 2 مع بعض الـ Superman بساوي Normal
+
+273
+00:19:46,470 --> 00:19:50,070
+X و هو المطلوب الجزء الثاني من نظرية من الكورولالي
+
+274
+00:19:50,070 --> 00:19:54,210
+و يقولك if X0 is such that F of X0 بساوي 0 لكل ..
+
+275
+00:19:54,210 --> 00:19:58,210
+لو لجأت F of X0 بساوي 0 لكل الـ F اللي هي element
+
+276
+00:19:58,210 --> 00:20:01,370
+in X برايم يعني أي bound linear functional اتلاقي
+
+277
+00:20:01,370 --> 00:20:04,350
+قيمتها عند الـ X0 بساوي 0 أكيد الـ X0 هي السفر
+
+278
+00:20:06,700 --> 00:20:10,180
+معايا F لجينا .. أخدنا أي bounded linear
+
+279
+00:20:10,180 --> 00:20:13,460
+functional F حسبناها عند ال X0 لجيناها سفر أخدنا
+
+280
+00:20:13,460 --> 00:20:16,100
+التاني لجيناها سفر أخدنا التالت لجيناها سفر يعني
+
+281
+00:20:16,100 --> 00:20:18,360
+أي bounded linear functional لو جيت حسبتها عند ال
+
+282
+00:20:18,360 --> 00:20:21,820
+X0 هتلاقي سفر هتلاقي ال X0 هي السفر هذا الكلام سهل
+
+283
+00:20:21,820 --> 00:20:25,560
+الآن اللي هو نورم ال X0 بساوي السبرمان هذا قبل مش
+
+284
+00:20:25,560 --> 00:20:32,550
+اي حد اللي .. اللي فضلناها الآن دي F of X0معاه؟
+
+285
+00:20:32,550 --> 00:20:36,450
+لأن هذا الكلام .. بقول إنه هذا سفر دايما، هيه، هذا
+
+286
+00:20:36,450 --> 00:20:39,430
+سفر دايما، إذن صار السبرمان عالمي مع Zero إذا نرم
+
+287
+00:20:39,430 --> 00:20:43,610
+الـ X0 إيش حساوية سفر، إذا X0 إيش حساوية سفر، ما
+
+288
+00:20:43,610 --> 00:20:48,470
+هو المطلوب، اللي بعد الله يعطيكوا العافية وإلى
+
+289
+00:20:48,470 --> 00:20:49,790
+لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/oa3DVUxeS2g_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/oa3DVUxeS2g_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c13d4fd83e882ec8e5a776c2620754c94bc376ec
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/oa3DVUxeS2g_raw.srt
@@ -0,0 +1,1168 @@
+1
+00:00:05,740 --> 00:00:08,400
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,400 --> 00:00:11,260
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:11,260 --> 00:00:16,300
+آله وصحبه أجمعين هذه المحاضرة رقم 28 مساق تحليل
+
+4
+00:00:16,300 --> 00:00:19,560
+اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:19,560 --> 00:00:24,820
+الإسلامية قسم الرياضيات للماجستيرأوصلنا لعند اللي
+
+6
+00:00:24,820 --> 00:00:28,900
+هو ال section الثالث في شبط أربعة اللي هي اربعة
+
+7
+00:00:28,900 --> 00:00:31,220
+تلاتة اللي هو ال hand-built theorem for complex
+
+8
+00:00:31,220 --> 00:00:34,500
+normed space المرة الفاترة أخدنا ال real vector
+
+9
+00:00:34,500 --> 00:00:38,800
+space وبرهنناه والبرهن كان طويل شويةعند normed
+
+10
+00:00:38,800 --> 00:00:41,660
+spaces وهذه اللي بتهمني أن ال normed spaces فعلا
+
+11
+00:00:41,660 --> 00:00:44,440
+هي اللي .. اللي أنا .. لأنه أنا شغلي functional
+
+12
+00:00:44,440 --> 00:00:48,140
+analysis بشكل أساسي عند لازم يكون فيه topology و
+
+13
+00:00:48,140 --> 00:00:51,160
+ال topology اللي هو induced by the norm فالآن هاخد
+
+14
+00:00:51,160 --> 00:00:54,760
+.. الآن بنختير المقصود فيها أحدى النظريات الأساسية
+
+15
+00:00:55,080 --> 00:00:59,360
+الاربع أو الخمسة اللي موجودة في ال .. ال .. ال ..
+
+16
+00:00:59,360 --> 00:01:02,580
+ال .. الـ Function Analysis هي الـ Hahnbenach
+
+17
+00:01:02,580 --> 00:01:06,120
+theorem for main .. for non spaces طبعا احنا
+
+18
+00:01:06,120 --> 00:01:08,440
+عرفناش اللي Hahnbenach theorem بدها الـ Hahnbenach
+
+19
+00:01:08,440 --> 00:01:11,080
+theorem هي عبارة عن extension يعني بدها توسيع نفوذ
+
+20
+00:01:11,080 --> 00:01:14,940
+يعني هاي الهدف طبعا الهدف الكبير هذالأن حققنا
+
+21
+00:01:14,940 --> 00:01:17,480
+الهدف هذا في حالة الـ real vector space والآن
+
+22
+00:01:17,480 --> 00:01:21,200
+هنحقق في حالة ال complex vector space ومش هنبره
+
+23
+00:01:21,200 --> 00:01:25,400
+نوع على السريع هنذكر نظرية واللي هنحكي فيه هو
+
+24
+00:01:25,400 --> 00:01:29,620
+توسيع النفوذ هذا في حالة ال normed spaces نيجي
+
+25
+00:01:29,620 --> 00:01:32,780
+نشوف الهانبنغ فيورم في حالة اللي هي ال complex
+
+26
+00:01:32,780 --> 00:01:39,540
+vector spaces وهي generalization للي فاتت let X be
+
+27
+00:01:39,540 --> 00:01:44,070
+a real or complex لأن real ولا complexVector space
+
+28
+00:01:44,070 --> 00:01:47,410
+and B is a sub additive real valued function on X
+
+29
+00:01:47,410 --> 00:01:50,630
+الـ
+
+30
+00:01:50,630 --> 00:01:55,110
+B صارت مالها sub additive نفسها لكن دلت ليش مالها
+
+31
+00:01:55,110 --> 00:01:59,410
+real vector اللي هي real valued function عشان بدها
+
+32
+00:01:59,410 --> 00:02:02,790
+يصير فيها مقارنة فيها أصغر و أصغر و إذا بتلزم اللي
+
+33
+00:02:02,790 --> 00:02:07,900
+هو تكون ريالand for any scalar α عرف P α X إيش
+
+34
+00:02:07,900 --> 00:02:11,560
+بيثاور لـ absolute value لـ P of X يعني الـ
+
+35
+00:02:11,560 --> 00:02:16,500
+positive homogeneity حيصير عندى لسه بدلنا بمين أنه
+
+36
+00:02:16,500 --> 00:02:19,600
+يشتغل على كل ألفة ال scalar بما فيه السالب و المدب
+
+37
+00:02:19,600 --> 00:02:23,220
+بس الان إيش هيطلع P α X هيثور لـ absolute value
+
+38
+00:02:23,220 --> 00:02:26,740
+لألفة في مين؟ في P of X الآن هاي الشروط طبعات اللى
+
+39
+00:02:26,740 --> 00:02:30,720
+هي النظريةFurthermore، لت F، اللي هي اللي بدنا
+
+40
+00:02:30,720 --> 00:02:34,340
+نعملها extension، لت F بيه a linear functional،
+
+41
+00:02:34,340 --> 00:02:36,900
+linear functional، complex ولا real، مش مشكلة،
+
+42
+00:02:36,900 --> 00:02:39,940
+which is defined on mean ونقصها بspace Z of mean
+
+43
+00:02:39,940 --> 00:02:44,340
+of X، and satisfies، الآن مابنقدرش نقول F of X
+
+44
+00:02:44,340 --> 00:02:47,840
+أصغر أو أشاوي، لأ، لأنه F of X complex ممكن تكون
+
+45
+00:02:48,040 --> 00:02:52,300
+فعشان هيك أخدنا المدرس له يكون مدرس ال F of X أصغر
+
+46
+00:02:52,300 --> 00:02:53,520
+يساوي بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+47
+00:02:53,520 --> 00:02:54,320
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+48
+00:02:54,320 --> 00:02:54,500
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+49
+00:02:54,500 --> 00:02:55,020
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+50
+00:02:55,020 --> 00:02:57,360
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+51
+00:02:57,360 --> 00:03:08,500
+بيه بيه بيه بيه
+
+52
+00:03:08,500 --> 00:03:14,420
+بيما دام فيه لجهود معينة هي عملته في حياتها الجهود
+
+53
+00:03:14,420 --> 00:03:17,740
+هذا اللي هو ان هي هتكون أصغر سواء بي وف اكس لكل
+
+54
+00:03:17,740 --> 00:03:22,060
+اكس اللي بتنزد الان و ال .. و ال .. و ال .. و ال
+
+55
+00:03:22,060 --> 00:03:26,240
+بيها دي اللي اللي قولنا عنها اللي عنديالآن فمن
+
+56
+00:03:26,240 --> 00:03:30,780
+عطاء رب نقلها إن هي قدرت تعمل extension هيك الدنيا
+
+57
+00:03:30,780 --> 00:03:35,300
+حتى في الحياة الطبيعية مدام أنت جدمت جهود إذا فيه
+
+58
+00:03:35,300 --> 00:03:39,200
+إمكانية إنك تعملك extension تعملك زيادة نفوذ إذا
+
+59
+00:03:39,200 --> 00:03:44,850
+thenthere is أو F has a linear extension of تلدة
+
+60
+00:03:44,850 --> 00:03:49,310
+from z to مين to x وسعت نفوذة من z على مين على كل
+
+61
+00:03:49,310 --> 00:03:52,890
+x وحافظت على حقوقها الأولى اللي هي أصغر سواء بي و
+
+62
+00:03:52,890 --> 00:03:56,250
+في x ومدت هذه الحقوق على كل مين أو كل هذا الجود
+
+63
+00:03:56,250 --> 00:03:59,830
+مدته على مين على كل x اللي عندنا اللي هو
+
+64
+00:03:59,830 --> 00:04:02,370
+satisfying absolute value of تلدة و في x أصغر سواء
+
+65
+00:04:02,370 --> 00:04:06,530
+بي و في x لكل x where موجودة في x البرهام بناشية
+
+66
+00:04:07,250 --> 00:04:09,550
+فحالة الريال اللي أثبتناها وطولنا خلّينا نيجي
+
+67
+00:04:09,550 --> 00:04:15,890
+لحالة ال normed space وهو الشغل برهانها طبعا
+
+68
+00:04:15,890 --> 00:04:19,010
+اعتمادا عن البرهين اللي حكيناها هيكون سهل لكن لو
+
+69
+00:04:19,010 --> 00:04:23,930
+بدك تبرهنه من الصفر هيصير برهانه عايش طويلإذن قصر
+
+70
+00:04:23,930 --> 00:04:28,370
+البرهان هنا لأنه أحنا أسسنا في البرهان الأولاني
+
+71
+00:04:28,370 --> 00:04:30,970
+الان هان بنخ theorem اللي هي normed space اللي هي
+
+72
+00:04:30,970 --> 00:04:34,190
+النظرية اللي بتحكي عنها الان بتقولي برضه نفس
+
+73
+00:04:34,190 --> 00:04:37,090
+الفحوة اللي حكيته لان بس ال extension هيصير mean
+
+74
+00:04:37,090 --> 00:04:41,950
+على normed space بدل اللي هي vector spacelet F be
+
+75
+00:04:41,950 --> 00:04:44,990
+a bounded linear functional على طول ما زي ما بنحكي
+
+76
+00:04:44,990 --> 00:04:48,050
+عن linear functional في حالة ال vector space إذا
+
+77
+00:04:48,050 --> 00:04:50,890
+إذا بنحكي عن non-dismissed بنحكي عن مين؟ عن
+
+78
+00:04:50,890 --> 00:04:55,350
+bounded linear functional ماشي الحال و اللي هي
+
+79
+00:04:55,350 --> 00:04:59,350
+برضه على غرار الأول ال linear functional فيه ال
+
+80
+00:04:59,350 --> 00:05:02,490
+extension ال bounded linear functional برضه هيكون
+
+81
+00:05:02,490 --> 00:05:07,020
+اللي هي إيه أشماله؟ extension بنفس المنطقالأن دع F
+
+82
+00:05:07,020 --> 00:05:08,620
+يكون مجموعة عامة عامة عامة عامة عامة عامة عامة
+
+83
+00:05:08,620 --> 00:05:09,340
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+84
+00:05:09,340 --> 00:05:13,980
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+85
+00:05:13,980 --> 00:05:18,440
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+86
+00:05:18,440 --> 00:05:18,820
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+87
+00:05:18,820 --> 00:05:18,820
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+88
+00:05:18,820 --> 00:05:18,820
+عامة عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+89
+00:05:18,820 --> 00:05:24,860
+عامة عامة عامة عامand has the same norm شوف الآن
+
+90
+00:05:24,860 --> 00:05:29,500
+الزيادة أنه norm هو norm الأصلي بتحافظ على كل
+
+91
+00:05:29,500 --> 00:05:33,420
+حقوقها الأولى مش بتقول لأ زرعت و حصدت إش أكبر ال
+
+92
+00:05:33,420 --> 00:05:37,100
+norm ال F تلد X إيش بيساوي norm ال F على ال Z
+
+93
+00:05:37,100 --> 00:05:41,640
+where norm ال F تلد X إيش بنفسد فيه هو ال supremum
+
+94
+00:05:41,640 --> 00:05:44,880
+لل F تلد أو ب X لل Xات اللي في ال X و norm هين
+
+95
+00:05:44,880 --> 00:05:48,100
+بيساوي واحد بينما التانية اللي هي على ال Z اللي هي
+
+96
+00:05:48,100 --> 00:05:52,310
+ال supremum لل absolute value لل F of Xللـ X ∈ Z
+
+97
+00:05:52,310 --> 00:05:55,690
+أن المراتقين أشمالهم بيساوي واحد ماشي الحاجة إذا
+
+98
+00:05:55,690 --> 00:05:59,510
+هذه Z على ال .. على Z ال .. ال .. السوبرمان وهذه
+
+99
+00:05:59,510 --> 00:06:04,410
+على X السوبرمان هو Normal of Z بيساوي سفر في حالة
+
+100
+00:06:04,410 --> 00:06:08,470
+مين ال trivial case أن Z أيش بيساوي اللي هو مين ال
+
+101
+00:06:08,470 --> 00:06:13,050
+zero طيب نيجي الآن نبرهن اطلع البرهن سهل اطلع لفوق
+
+102
+00:06:13,050 --> 00:06:20,290
+Fزت بتساوي Zero اللي هو Zero Zero Zero Zero Space
+
+103
+00:06:20,290 --> 00:06:23,970
+يعني then أف بتساوي سفر وال extension اللي هيكون
+
+104
+00:06:23,970 --> 00:06:26,830
+مين أف تلداش بتساوي سفر خلّيني أقول ال trivial
+
+105
+00:06:26,830 --> 00:06:30,950
+case قيمتها
+
+106
+00:06:30,950 --> 00:06:36,250
+مش كثيرة إلا للحالات اللي ممكن يعني بدك .. يعني
+
+107
+00:06:36,250 --> 00:06:40,180
+مانكونش مستثنين ال Zero إنما بتنفع على كل شيءفعشان
+
+108
+00:06:40,180 --> 00:06:44,380
+ايه؟ خصصنا عليها ليه زد لا تساو سفر الآن؟ ناخد
+
+109
+00:06:44,380 --> 00:06:49,240
+حالة مين زد لا تساو سفر؟ then for any x element in
+
+110
+00:06:49,240 --> 00:06:54,100
+z we have فليه f bounded in a functional إذن ال
+
+111
+00:06:54,100 --> 00:06:57,200
+absolute value of f of x أزرع سوى، norm ال F norm
+
+112
+00:06:57,200 --> 00:07:00,700
+ال F على مين؟ هي F dismal زي شغالة مين على z norm
+
+113
+00:07:00,700 --> 00:07:04,300
+ال F z في norm مين ال x؟ لكل ال x وين موجودات في z
+
+114
+00:07:04,300 --> 00:07:10,170
+الان أعرف هاي ال bridge اللي بدياللي هو طبيعة ..
+
+115
+00:07:10,170 --> 00:07:13,150
+اللي هو الـ norm أنه هيعمل لي sublinear functional
+
+116
+00:07:13,150 --> 00:07:16,330
+يعني هيعمل .. هيعمل اللي .. اللي .. اللي كانت
+
+117
+00:07:16,330 --> 00:07:19,350
+المطلوب في معطيات النظريات السابقة هيعملها الـ
+
+118
+00:07:19,350 --> 00:07:22,010
+norm فهيكون automatic تطلع النظرية في extension
+
+119
+00:07:22,010 --> 00:07:27,230
+طيب define P من X ل عند R by P of X أش بساوي ..
+
+120
+00:07:27,230 --> 00:07:32,850
+بساوي normal FZ في normal Xهي اللي بدي أعرفه حر
+
+121
+00:07:32,850 --> 00:07:36,870
+أنا بدي أعرف الـP of X هي عبارة عن مين؟ عن نورم
+
+122
+00:07:36,870 --> 00:07:40,390
+الـFz اللي أنا عرفته خلاص نورم الـFz صار معروف
+
+123
+00:07:40,390 --> 00:07:44,290
+لأنه bounded لأن نورم هذا معروف في نورم مين الـX
+
+124
+00:07:44,290 --> 00:07:46,730
+هذه اللي .. اللي .. اللي هداك إذا .. إذا هذا هو
+
+125
+00:07:46,730 --> 00:07:49,970
+كأنه مقدر ثابت بضربه في مين؟ في نورم الـX اللي هي
+
+126
+00:07:49,970 --> 00:07:54,870
+هذه تتغير بتغير مين؟ X إذا هذا الـP of X أكيد
+
+127
+00:07:54,870 --> 00:07:58,950
+هيحقق ضمن الـabsolute value للـF of X اللي هو إيه
+
+128
+00:07:58,950 --> 00:08:03,660
+اش ماله؟اللي هو عبارة عن أصغر المقدار هذا صح؟ هي
+
+129
+00:08:03,660 --> 00:08:07,600
+اتلت فاض و هذا المقدار هو اللي أقرفته P of X إذا
+
+130
+00:08:07,600 --> 00:08:11,480
+صار ال absolute value of X أصغر أو يساوي P of X
+
+131
+00:08:11,480 --> 00:08:15,040
+لكل X element in Z إذا هاي أول شرط اتحقق من شروط
+
+132
+00:08:15,040 --> 00:08:18,300
+مين النظرية اللي حكينا عنها المرة الماضية تبعت ال
+
+133
+00:08:18,300 --> 00:08:20,660
+handballing theorem أو اللي حكينا عنها قبل شوية
+
+134
+00:08:20,660 --> 00:08:29,600
+واضح ها؟ طيبFurthermore, for any x, y element in X
+
+135
+00:08:29,600 --> 00:08:34,140
+and any scalar α element in R, we have شغلتين أول
+
+136
+00:08:34,140 --> 00:08:40,100
+شيء احسب ليه B of X زائد Y ايش بيساوي؟ بيساوي norm
+
+137
+00:08:40,880 --> 00:08:45,720
+الـ Absolute Value F of Z F over Z فنور Main الـ X
+
+138
+00:08:45,720 --> 00:08:51,760
+زائد Y حسب التعريف اللي أعرفته وهذا أصغر أو سوى
+
+139
+00:08:51,760 --> 00:08:57,280
+بالـ Triangling Quality هدي في هدي زائد هدي بفكها
+
+140
+00:08:57,280 --> 00:09:01,660
+هدي في هدي هي P of X وهدي في هدي اللي هي Main P of
+
+141
+00:09:01,660 --> 00:09:07,470
+Yإذا صارت عندى بيكزائد Y أصغر أو سوى بيكزائد مين
+
+142
+00:09:07,470 --> 00:09:14,110
+البي الان P of Alpha X بساوى حسب التعريف اللى عندى
+
+143
+00:09:14,110 --> 00:09:18,430
+عبارة عن حسب التعريف اللى هان عبارة عن norm اللى
+
+144
+00:09:18,430 --> 00:09:25,110
+هى ال FZفي مين؟ في norm الـ α X بطلع الألفة برا
+
+145
+00:09:25,110 --> 00:09:29,750
+بصير absolute value في هذه في هذه اللي هي مين P of
+
+146
+00:09:29,750 --> 00:09:33,970
+X إذا برضه اللي هو الشرط الثاني ماله اتحقق إذا
+
+147
+00:09:33,970 --> 00:09:37,930
+hence by theorem أربعة تلاتة .. لأ مش linear hence
+
+148
+00:09:37,930 --> 00:09:43,380
+by theorem أربعة تلاتة واحدأه نعم there exist a
+
+149
+00:09:43,380 --> 00:09:46,380
+linear extension من اللي قبل بشوية اللي حكيناها في
+
+150
+00:09:46,380 --> 00:09:50,840
+حالة ال vector space إذا صار عندي الآن الشروط
+
+151
+00:09:50,840 --> 00:09:54,740
+النظرية أربعة تلاتة واحد اللي قبل بشوية كلها تحققت
+
+152
+00:09:54,740 --> 00:09:58,700
+إذا في عندي ال linear extension اسمه f تلدان x
+
+153
+00:09:58,700 --> 00:10:02,720
+which is an extension of f and satisfies كمان ال
+
+154
+00:10:02,720 --> 00:10:07,260
+absolute value لفتل دو فيكس أصغر شو مين بيو فيكس
+
+155
+00:10:07,650 --> 00:10:10,910
+ماشي الحال لكن ال P of X بيساوي ال norm هذا في هذا
+
+156
+00:10:10,910 --> 00:10:16,490
+الان هذا الكلام لكل mean X limit X إذا هذا إذا
+
+157
+00:10:16,490 --> 00:10:21,870
+حصلنا على extension ويحقق هذا أصغر يساوي هذا طيب
+
+158
+00:10:21,870 --> 00:10:27,060
+من هذولة مع بعض التنتين هيها هيها هيهاالـ Code
+
+159
+00:10:27,060 --> 00:10:29,560
+اللي هو الـ Supremum على النورمات اللي بيساوي سفر
+
+160
+00:10:29,560 --> 00:10:32,400
+الـ Supremum اللي هدى على النورمات اللي بيساوي سفر
+
+161
+00:10:32,400 --> 00:10:36,580
+هو عبارة عن نورم العندي طبعا احنا بنحكي عن ال Xات
+
+162
+00:10:36,580 --> 00:10:40,400
+اللي وين موجودات في X فبصير نورم ال F تلد على ال X
+
+163
+00:10:40,400 --> 00:10:45,480
+أصغر أو ساوي مين نورم ال FZ هاي واحدةلكن من جهة
+
+164
+00:10:45,480 --> 00:10:52,180
+أخرى Normal of Z اللي هو supremum على ال Xات اللي
+
+165
+00:10:52,180 --> 00:10:55,620
+في الـ Z بينما هذا supremum اللي هو نفسه طبعا
+
+166
+00:10:55,620 --> 00:10:59,460
+after ده Z لأن هذا extension بينما هذا supremum
+
+167
+00:10:59,460 --> 00:11:03,550
+على مين؟على العناصر اللي في الـ X والـ X بتحتوى
+
+168
+00:11:03,550 --> 00:11:07,850
+الـ Z إذا سوبرمام على مجموعة أقل من مجموعة تانية
+
+169
+00:11:07,850 --> 00:11:10,690
+فأكيد السوبرمام هن أصغر يساوي مين؟ السوبرمام هن
+
+170
+00:11:10,690 --> 00:11:15,690
+فهذا أصغر يساوي هذا فبنكون حصلنا على الـ Normal FZ
+
+171
+00:11:15,690 --> 00:11:22,490
+مرة أصغر يساوي ومرة أكبر يساوي من التنتين في إيه
+
+172
+00:11:22,490 --> 00:11:25,870
+شماله؟ فيه يساوي إذا أثبتنا الـ Extension و أثبتنا
+
+173
+00:11:25,870 --> 00:11:32,310
+اللي هي الشروط المطلوبةأو خلّيني أقول ما حققته
+
+174
+00:11:32,310 --> 00:11:37,030
+اللي هي النظرية نجلة
+
+175
+00:11:37,030 --> 00:11:42,570
+theorem 433 bounded linear functional انتبهوا إيش
+
+176
+00:11:42,570 --> 00:11:48,650
+هذا اللي بتقول let X be a normed space ركزوا في
+
+177
+00:11:48,650 --> 00:11:54,540
+النصعند X0 لاتساوي 0 بيه any element in X أي
+
+178
+00:11:54,540 --> 00:11:56,980
+element in X أخدناها على البيت الرأي وسميناها X0
+
+179
+00:11:56,980 --> 00:12:01,540
+ماشي الحالة أو X normed space بيقولك then there
+
+180
+00:12:01,540 --> 00:12:06,060
+exists a bounded linear functional F tilde و X
+
+181
+00:12:06,060 --> 00:12:11,700
+such that نورمه بيساوي واحد وال F tilde و X0 إيش
+
+182
+00:12:11,700 --> 00:12:18,030
+حيسوي نورمين ال X0يعني اللي بيحكيلكيا بيقولك انه
+
+183
+00:12:18,030 --> 00:12:22,330
+انت خد اي X note في normed space بقدر ألاجيلك
+
+184
+00:12:22,330 --> 00:12:26,410
+bounded linear functional يحدد بمين بواسطة النقطة
+
+185
+00:12:26,410 --> 00:12:29,590
+هذه اللي أخدتها انت arbitrarily بتفكز بقدر ألاجي
+
+186
+00:12:29,590 --> 00:12:32,330
+bounded linear functional F tilde و X و يقوه normه
+
+187
+00:12:32,330 --> 00:12:36,550
+بساوء واحد و ال F tilde of X note هذه اللي أخدتها
+
+188
+00:12:36,550 --> 00:12:40,930
+هو ايش هيطلع عنده عبارة عن norm ال X note خلينا
+
+189
+00:12:40,930 --> 00:12:48,200
+نشوف مع بعضConsider the subspace Z المكوّن من مين؟
+
+190
+00:12:48,200 --> 00:12:54,400
+Alpha X0 هي الـ Span لـ X0 يعني الـ X0 هي النقطة
+
+191
+00:12:54,400 --> 00:12:57,320
+الأربترية اللي أخدناها Alpha is the scalar Define
+
+192
+00:12:57,320 --> 00:13:04,350
+F من Z لعند مين؟ لعند scalar field KF of ZX F of X
+
+193
+00:13:04,350 --> 00:13:11,190
+بيساوي F of Alpha X0 و يساوي Alpha في مين في
+
+194
+00:13:11,190 --> 00:13:17,650
+Normal X0 هذا اللي هو واضح انه Alpha X0 where K is
+
+195
+00:13:17,650 --> 00:13:21,570
+scalar field real or complex it is easy to see
+
+196
+00:13:21,570 --> 00:13:25,840
+that F is linearفها دي إيه عشان إذنها بتعرفوا
+
+197
+00:13:25,840 --> 00:13:34,760
+تثبتوها F of Beta X زائد Y بتساوي كده نفهمها خلاص
+
+198
+00:13:34,760 --> 00:13:38,180
+هي بتعرفوا تثبتوها لأ من التعريف هذا هيه التعريف
+
+199
+00:13:38,180 --> 00:13:42,500
+هيه بتعرفوا تثبتوها على طولمباشرة الان و also f is
+
+200
+00:13:42,500 --> 00:13:45,800
+bounded و ال boundedness برضه سهل ال boundedness
+
+201
+00:13:45,800 --> 00:13:50,280
+بيقولك خد ايش معله absolute value of f of x ايش
+
+202
+00:13:50,280 --> 00:13:52,720
+هيساوي؟ بيساوي ال absolute value هذه بيساوي ال
+
+203
+00:13:52,720 --> 00:13:55,900
+absolute value هذه اللي هو هيطلع alpha mean في x0
+
+204
+00:13:55,900 --> 00:14:00,420
+اللي هو بيساوي mean اللي هو normal x لأن ال x ايش
+
+205
+00:14:00,420 --> 00:14:05,220
+بتساوي؟ alpha x0 هيك شكل العناصر جوامعايا صار عندى
+
+206
+00:14:05,220 --> 00:14:08,780
+لأن absolute value of f of x ايش بيساوي normal x
+
+207
+00:14:08,780 --> 00:14:12,940
+لكل x و موجودة بيساوي x يعني بمعنى اخر صار عندى
+
+208
+00:14:12,940 --> 00:14:19,260
+اللي هو ال f is linear و ال f is bounded ماشي و لو
+
+209
+00:14:19,260 --> 00:14:22,480
+اتطلعت على قِبتها absolute value of f of x بيساوي
+
+210
+00:14:22,480 --> 00:14:29,380
+normal x absolute value ل ال f of x بيساوي normal
+
+211
+00:14:29,380 --> 00:14:36,930
+x اذا ال supremumعلى ال norm ال X أو X ده تساوي
+
+212
+00:14:36,930 --> 00:14:43,270
+شفر هيساوي ايه؟ واحد وهذا عبارة عن norm ال F over
+
+213
+00:14:43,270 --> 00:14:43,730
+X
+
+214
+00:14:47,220 --> 00:14:50,300
+النظرية اللي قبل بشوية اتحققت
+
+215
+00:15:15,050 --> 00:15:19,210
+الـ X في الـ Z كيف شكل الـ X ألفة في X نور فح؟
+
+216
+00:15:19,210 --> 00:15:23,850
+ألفة scalar أنه scalar لأن طب F of X0 نفسها بساوي
+
+217
+00:15:23,850 --> 00:15:29,650
+اللي هو يعني و كأني بقول F of واحد في X0 حسب
+
+218
+00:15:29,650 --> 00:15:32,850
+القانون اللي هو إيش بيساوي واحد في نورم ال X0
+
+219
+00:15:32,850 --> 00:15:38,810
+فاهمين؟ بيساوي واحد في نورم ال X0 بيساوي نورم ال
+
+220
+00:15:38,810 --> 00:15:45,720
+X0 يعني الف بيساوي واحدأه فبصير عندى f of x0 بساوة
+
+221
+00:15:45,720 --> 00:15:49,280
+.. f .. f tilde of x0 بساوة f of x0 بساوة مين؟
+
+222
+00:15:49,280 --> 00:15:57,680
+نورم ال x0 أي سؤال؟ اللي بعده؟ Corollary لأن for
+
+223
+00:15:57,680 --> 00:16:02,740
+any x in a normed space X we have لأن احنا كنا
+
+224
+00:16:02,740 --> 00:16:12,190
+نجيب نقول نورم ال F بساوة supremumللـ f of x
+
+225
+00:16:12,190 --> 00:16:17,990
+absolute value على نورم الـ x الـ x element in x
+
+226
+00:16:17,990 --> 00:16:22,930
+minus mean الـ zero يعني كنا نجيب ال norm بدلالة
+
+227
+00:16:22,930 --> 00:16:25,310
+mean الـ f و الـ f سبرهما من الـ f على نورم الـ x
+
+228
+00:16:25,310 --> 00:16:31,370
+الآن بده يجيبلك اللي هو نورم الـ x الآن مش نورم
+
+229
+00:16:31,370 --> 00:16:36,770
+الـ f بنضغط بدلالة mean الـ f و الـ f ماشي؟ إذا
+
+230
+00:16:36,770 --> 00:16:42,680
+بقوللي henceنستطيع أن نجد لأي X في عضلة X نستطيع
+
+231
+00:16:42,680 --> 00:16:46,840
+أن نجد X عضلة X بساوية سبريمام للقيم الأبسط F of X
+
+232
+00:16:46,840 --> 00:16:53,300
+عالمي لـN عن عضلة F فالـN المتغير بدل ما هو X في X
+
+233
+00:16:53,300 --> 00:16:57,360
+minus Zero هو عبارة عن الـlinear functionals F
+
+234
+00:16:57,360 --> 00:16:59,480
+element in X برايم من X برايم من X برايم من X
+
+235
+00:16:59,480 --> 00:17:01,700
+برايم من X برايم من X برايم من X برايم من X برايم
+
+236
+00:17:01,700 --> 00:17:01,800
+من X برايم من X برايم من X برايم من X برايم من X
+
+237
+00:17:01,800 --> 00:17:01,960
+برايم من X برايم من X برايم من X برايم من X برايم
+
+238
+00:17:01,960 --> 00:17:01,960
+من X برايم من X برايم من X برايم من X برايم من X
+
+239
+00:17:01,960 --> 00:17:06,020
+برايم من X برايم من X برايم من X برايم من X برايم
+
+240
+00:17:06,020 --> 00:17:09,360
+من X بأف لا تساوي سفر يعني السبريهم هم عالمين على
+
+241
+00:17:09,360 --> 00:17:14,640
+كل الأفات اللي في الـ X' هنس .. من نتيجة مباشرة
+
+242
+00:17:14,640 --> 00:17:18,060
+هنس if X0 is a .. is such that F of X0 بساوي سفر
+
+243
+00:17:18,060 --> 00:17:22,600
+for all أف اللي متين X' then X' أشبه لها بساوي سفر
+
+244
+00:17:23,840 --> 00:17:27,720
+الان راكزوا الكلام سهل الان عندي من theorem أربعة
+
+245
+00:17:27,720 --> 00:17:30,980
+تلاتة في extension of تل دا element of X prime
+
+246
+00:17:30,980 --> 00:17:35,020
+such that normal of تل دا ايش بيساوي واحد وال F تل
+
+247
+00:17:35,020 --> 00:17:39,800
+دا of X ايش بيساوي normal X من اللي قبل بشوية
+
+248
+00:17:39,800 --> 00:17:43,820
+theorem أربعة تلاتة تلاتة اللي أثبتناها where الان
+
+249
+00:17:43,820 --> 00:17:49,100
+إذا لجيناExtension F تلدة في الـ X' بحيث نورمه
+
+250
+00:17:49,100 --> 00:17:53,120
+بساوء واحد والـ F تلدة و X له بساوء جداش نورم الـ
+
+251
+00:17:53,120 --> 00:17:56,380
+X اللي كنا بسميه X ناضلة قبل شوية Where X is
+
+252
+00:17:56,380 --> 00:17:59,420
+around zero element in mean in X So that the
+
+253
+00:17:59,420 --> 00:18:02,880
+supremum لل absolute value F of X على نورم الـ F
+
+254
+00:18:03,560 --> 00:18:06,360
+اللي هي f element in x prime و f أكبر يساوي 0 هذا
+
+255
+00:18:06,360 --> 00:18:09,960
+ال supremum على الكل ماشي الحال أكيد أكبر أو يساوي
+
+256
+00:18:09,960 --> 00:18:12,800
+واحدة منهم من ضمنهم الواحدة المن هناك اللي اللي
+
+257
+00:18:12,800 --> 00:18:17,320
+أجريها إذا أكبر أو يساوي فاهمين أكبر أو يساوي اللي
+
+258
+00:18:17,320 --> 00:18:23,510
+هو الآن ال supremum يا جماعة أنا جيت f تل دهفى الـ
+
+259
+00:18:23,510 --> 00:18:29,250
+X' و لجهة F تلدة of X بيساوي الـ X نفسها و نورم
+
+260
+00:18:29,250 --> 00:18:35,510
+الـ F تلدة بيساوي إيش؟ واحد خدوا الآن ال supremum
+
+261
+00:18:35,510 --> 00:18:40,690
+ال supremum ل absolute value of X على نورم ال F
+
+262
+00:18:40,690 --> 00:18:48,710
+حيث F ويه موجودة فى ال X'والـ F لا تساوي منين؟ الـ
+
+263
+00:18:48,710 --> 00:18:51,930
+Zero هذه اطلع لفوق أكبر أو يساوي أكيد أي واحدة من
+
+264
+00:18:51,930 --> 00:18:55,530
+هنا أكبر أو يساوي أي واحدة من هنا مين أي واحدة من
+
+265
+00:18:55,530 --> 00:19:04,250
+هنا اللي جايك فوق اللي هي F تلدة of X على norm الـ
+
+266
+00:19:04,250 --> 00:19:09,130
+F تلدة اللي هو بيساوي F تلدة of X إيش بتساوي؟ X
+
+267
+00:19:09,130 --> 00:19:16,350
+صح؟ على اللي هو إيه إيش بتساوي هذه؟مايساوة نورم ال
+
+268
+00:19:16,350 --> 00:19:19,690
+X إذا صار عند ال suprem هذا اللي بقول أكبر أو
+
+269
+00:19:19,690 --> 00:19:24,970
+ساوية مين نورم ال X واضح أه؟ بالذات بتلك الأن أصغر
+
+270
+00:19:24,970 --> 00:19:27,430
+أو ساوية معناته حدثت المشاوخ خلصت الكورة ده
+
+271
+00:19:27,430 --> 00:19:30,890
+however ال absolute value of F of X أصغر أو ساوية
+
+272
+00:19:30,890 --> 00:19:34,670
+نورم ال F و نورم مين؟ ال X ماشي الحل لأن F is
+
+273
+00:19:34,670 --> 00:19:38,150
+bounded in our functional then ال suprem على F
+
+274
+00:19:38,150 --> 00:19:42,250
+تلدى على نورم ال F هيكون أصغر أو ساوية مين نورم ال
+
+275
+00:19:42,250 --> 00:19:46,470
+Xصح؟ إذا من الـ 2 مع بعض الـ Superman بساوي Normal
+
+276
+00:19:46,470 --> 00:19:50,070
+X و هو المطلوب الجزء الثاني من نظرية من الكورولالي
+
+277
+00:19:50,070 --> 00:19:54,210
+و يقولك if X0 is such that F of X0 بساوي 0 لكل ..
+
+278
+00:19:54,210 --> 00:19:58,210
+لو لجأت F of X0 بساوي 0 لكل الـ F اللي هي element
+
+279
+00:19:58,210 --> 00:20:01,370
+in X برايم يعني أي bound linear functional اتلاقي
+
+280
+00:20:01,370 --> 00:20:04,350
+قيمتها عند الـ X0 بساوي 0 أكيد الـ X0 هي السفر
+
+281
+00:20:06,700 --> 00:20:10,180
+معايا F لجينا .. أخدنا أي bounded linear
+
+282
+00:20:10,180 --> 00:20:13,460
+functional F حسبناها عند ال X0 لجيناها سفر أخدنا
+
+283
+00:20:13,460 --> 00:20:16,100
+التاني لجيناها سفر أخدنا التالت لجيناها سفر يعني
+
+284
+00:20:16,100 --> 00:20:18,360
+أي bounded linear functional لو جيت حسبتها عند ال
+
+285
+00:20:18,360 --> 00:20:21,820
+X0 هتلاقي سفر هتلاقي ال X0 هي السفر هذا الكلام سهل
+
+286
+00:20:21,820 --> 00:20:25,560
+الآن اللي هو نورم ال X0 بساوي السبرمان هذا قبل مش
+
+287
+00:20:25,560 --> 00:20:32,550
+اي حد اللي .. اللي فضلناها الآن دي F of X0معاه؟
+
+288
+00:20:32,550 --> 00:20:36,450
+لأن هذا الكلام .. بقول إنه هذا سفر دايما، هيه، هذا
+
+289
+00:20:36,450 --> 00:20:39,430
+سفر دايما، إذن صار السبرمان عالمي مع Zero إذا نرم
+
+290
+00:20:39,430 --> 00:20:43,610
+الـ X0 إيش حساوية سفر، إذا X0 إيش حساوية سفر، ما
+
+291
+00:20:43,610 --> 00:20:48,470
+هو المطلوب، اللي بعد الله يعطيكوا العافية وإلى
+
+292
+00:20:48,470 --> 00:20:49,790
+لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/v06nynwDfxc_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/v06nynwDfxc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..baefbf563e7fee27ddc9192fbc1582f3059fb7ab
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/v06nynwDfxc_postprocess.srt
@@ -0,0 +1,1956 @@
+1
+00:00:04,930 --> 00:00:07,570
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,570 --> 00:00:10,950
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,950 --> 00:00:17,170
+أهله وصحبه أجمعين هذه هي محاضرة رقم 29 مساق تحليل
+
+4
+00:00:17,170 --> 00:00:20,290
+اقتراني أو تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:20,290 --> 00:00:25,210
+الإسلامية قسم الرجاليات ماجستيروصلنا لعند اللي هو
+
+6
+00:00:25,210 --> 00:00:29,890
+ال section الخامس اللي هو بعد ما حكينا عن اللي هو
+
+7
+00:00:29,890 --> 00:00:35,190
+ال hand Banach theorem اللي هي ال extension لل
+
+8
+00:00:35,190 --> 00:00:39,070
+linear functional في حالة ال vector spaces سواء
+
+9
+00:00:39,070 --> 00:00:43,260
+real أو nonأو ال extension في حالة اللي هي Named
+
+10
+00:00:43,260 --> 00:00:47,840
+Spaces اليوم بدنا نحكي عن اللي هو ال Adjoint
+
+11
+00:00:47,840 --> 00:00:51,940
+Operators نيجي
+
+12
+00:00:51,940 --> 00:00:58,680
+نشوف شو معناته ال Adjoint Operator قبل هيك حكينا
+
+13
+00:00:58,680 --> 00:01:02,100
+عن حاجة اسمها ال Hilbert Adjoint إذا بتذكرواالان
+
+14
+00:01:02,100 --> 00:01:06,120
+ده نحكي عن الـ Adjoint Operator نشوف شو نقصد بالـ
+
+15
+00:01:06,120 --> 00:01:10,700
+Adjoint Operator أربعة، خمسة تحت هذا العنوان، الـ
+
+16
+00:01:10,700 --> 00:01:14,800
+Definition Let T من X لعند Y be bounded linear
+
+17
+00:01:14,800 --> 00:01:18,900
+operators and X and Y are normed spaces لأن أنا
+
+18
+00:01:18,900 --> 00:01:22,140
+بحكي عن normed spaces in general مش Hilbert spaces
+
+19
+00:01:22,140 --> 00:01:25,380
+ولا inner product spaces زي ما كنا نحكي في حالة
+
+20
+00:01:25,380 --> 00:01:28,900
+اللي هي الـ Hilbert AdjointThen the adjoint
+
+21
+00:01:28,900 --> 00:01:34,900
+operator T cross من وين لوين من Y' لعند ال X' إذا
+
+22
+00:01:34,900 --> 00:01:41,590
+الآن عندي T من X لعند Yاللي هو bounded linear
+
+23
+00:01:41,590 --> 00:01:46,350
+operator من normed space إلى normed space الآن الـ
+
+24
+00:01:46,350 --> 00:01:52,330
+Hilbert Adjoint T× من وين بيجي بياخد؟ بياخد من الـ
+
+25
+00:01:52,330 --> 00:01:56,110
+dual space لهذه من Y' اللي هو the space of all
+
+26
+00:01:56,110 --> 00:01:59,990
+bounded linear functionals إلى اللي هو ال dual
+
+27
+00:01:59,990 --> 00:02:04,010
+space لهذه اللي هو X' ال space of all bounded
+
+28
+00:02:04,010 --> 00:02:09,810
+linear functionals عالمين على ال Xكيف بدنا نعرفه
+
+29
+00:02:09,810 --> 00:02:17,130
+is defined by T across لجيه طبعا الجيه من وين جاها
+
+30
+00:02:17,130 --> 00:02:23,710
+من Y برايم ماشي الحال بدها ترسلها T cross لمين ل
+
+31
+00:02:23,710 --> 00:02:30,650
+element وين في ال X برايم ماشي الحالفى الـ Y' ده
+
+32
+00:02:30,650 --> 00:02:35,550
+ترسلها الأمين للـ F الـ X' طب لحد تلان كنه .. كنه
+
+33
+00:02:35,550 --> 00:02:38,890
+بالشكل هذا الـ function اللى عندى مش واضحة الآن
+
+34
+00:02:38,890 --> 00:02:46,030
+إيش اللى بوضحها بوضحها التالي إنه T cross G of any
+
+35
+00:02:46,030 --> 00:02:50,390
+X element طبعا T cross G وين هيرسل؟ هيحيرسل لهدي
+
+36
+00:02:50,390 --> 00:02:55,890
+فبصير T cross G of X إيش بساوي؟ بساوي F of Xلأن F
+
+37
+00:02:55,890 --> 00:02:59,490
+of X الـ F من وين جاية من الـ X' إذا الـ F وين
+
+38
+00:02:59,490 --> 00:03:04,250
+شغالة لما .. مدام F في الـ X' معناته الـ F شغالة
+
+39
+00:03:04,250 --> 00:03:07,970
+من الـ X ده الـ scalar field تبعها إذا إيش بده
+
+40
+00:03:07,970 --> 00:03:12,570
+تكون domainها عنصرها X إذا الـ X هذه أو هذه من وين
+
+41
+00:03:12,570 --> 00:03:17,290
+جاية من اللي هو الـ X نفسهاطب برضه الأمور لسه مش
+
+42
+00:03:17,290 --> 00:03:22,210
+واضحة T x G of X بيساوي F of X إيش كونه هذه اللي
+
+43
+00:03:22,210 --> 00:03:27,070
+بتساوي F of X اللي هترميها اللي هيوضحها اللي هو T
+
+44
+00:03:27,070 --> 00:03:33,550
+x G of X بنقصد فيها T x G of X اللي بنقصده بالساوي
+
+45
+00:03:33,550 --> 00:03:42,340
+فيها عبارة عن G of T of X اللي هي عبارة عنof T of
+
+46
+00:03:42,340 --> 00:03:47,900
+X الان هل هو هذا معقول الكلام؟ اه معقول لأن ال T
+
+47
+00:03:47,900 --> 00:03:52,840
+من وين من X ل X فبصير ال T X ترمي تاخد من X و
+
+48
+00:03:52,840 --> 00:03:56,820
+ترميها وين في Y فلما رمتها في Y ال G ما هي من وين
+
+49
+00:03:56,820 --> 00:04:01,900
+جاية من Y' هتلقوفها ال G اللي هي ترميها من Y ل ال
+
+50
+00:04:01,900 --> 00:04:07,500
+scalar field فالان عندي صارت اللي هي ال Tمن X لعند
+
+51
+00:04:07,500 --> 00:04:11,360
+Y رمت الـ T X في الـ Y إجت الـ G أخدت ال limit
+
+52
+00:04:11,360 --> 00:04:14,740
+اللي في الـ Y لأن الـ G موجودة في الـ Y' ورمته في
+
+53
+00:04:14,740 --> 00:04:20,260
+الـ scalar field إذن الآن ملخص الحديث احنا الـ T
+
+54
+00:04:20,260 --> 00:04:22,980
+من X لعند Y boundary لدينا operator الـ Adjoint
+
+55
+00:04:22,980 --> 00:04:28,250
+operator من Y' لعند X'قانونه أنه بياخد الـ G في
+
+56
+00:04:28,250 --> 00:04:32,010
+الـ Y' و بيرميه للـ F في الـ X' طيب كيف هذا
+
+57
+00:04:32,010 --> 00:04:35,210
+التفاصيل و كيف التفاصيل اللي عملها اللي هو أن يكون
+
+58
+00:04:35,210 --> 00:04:38,930
+الـ T cross G of X بيساوي F of X طيب إيش معناته
+
+59
+00:04:38,930 --> 00:04:43,350
+هذا؟ معناته هذا أن الـ T cross G of X بيساوي G of
+
+60
+00:04:43,350 --> 00:04:48,640
+T of X وهيك بيكون كتمة التعريفالآن اللي هو طبعا زي
+
+61
+00:04:48,640 --> 00:04:52,240
+ما قلت X' وY' هما الـ Dual Spaces of X وY ريسبك
+
+62
+00:04:52,240 --> 00:04:55,260
+تبلاد X في الـ X والـ F في الـ X' وG وM وD في الـ
+
+63
+00:04:55,260 --> 00:04:59,380
+Y' اطلع لفوق الآن هذا تعريفنا طب هل له معنى
+
+64
+00:04:59,380 --> 00:05:04,420
+التعريف؟ إيش اللي هو كده؟ الـ Theorem هذه بتكملنا
+
+65
+00:05:04,420 --> 00:05:09,760
+الصورة بتقولنا Theorem 4.5.2 The Adjoint Operator
+
+66
+00:05:09,760 --> 00:05:13,920
+of T الـ Adjoint Operator هذا T X of T in the
+
+67
+00:05:13,920 --> 00:05:21,380
+above definition1 is a linear 2 bounded 3 نورمه هو
+
+68
+00:05:21,380 --> 00:05:25,480
+نورم من الـ T الأصلية ماشي الحال إزاي بتذكرنا في
+
+69
+00:05:25,480 --> 00:05:27,780
+الـ Hilbert adjoint الـ Hilbert adjoint إذا بتذكر
+
+70
+00:05:27,780 --> 00:05:32,180
+و كنا نسميه اللي هو T star هذا اللي سمناه الـ
+
+71
+00:05:32,180 --> 00:05:35,340
+Hilbert adjoint operator عموما خلينا نشوف اللي هي
+
+72
+00:05:35,340 --> 00:05:41,020
+كيف نثبت أن الـ T is linear و الـ bounded و نورمها
+
+73
+00:05:41,020 --> 00:05:46,050
+بسوء نورم الأصلي أمر سهل إن شاء الله خد شوفfor any
+
+74
+00:05:46,050 --> 00:05:50,490
+x element in X و أي g1 و g2 اللي موجودة في الـ Y'
+
+75
+00:05:50,850 --> 00:05:55,910
+بدنا نثبت لكم الآن إنها عبارة عن Linear إيش معنات
+
+76
+00:05:55,910 --> 00:06:02,690
+Linear؟ يعني T x α g1 زي g2 بساوي اللي هو α T x g1
+
+77
+00:06:02,690 --> 00:06:06,630
+زي T x main g2، ماشي الحال، هذه محسوبة عن نقطة،
+
+78
+00:06:06,630 --> 00:06:10,060
+سيبك منها، ده عشان أدات الإثباتعشان اثبت دالتين
+
+79
+00:06:10,060 --> 00:06:12,480
+متساويتين لازم اثبتهم متساويتين عند كل نقطة من
+
+80
+00:06:12,480 --> 00:06:17,360
+نقطة دمانهم الان انا .. الان هجيت T cross Alpha G1
+
+81
+00:06:17,360 --> 00:06:23,360
+زي G2 عشان تكون لنا لازم تساوي Alpha T cross G1 زي
+
+82
+00:06:23,360 --> 00:06:28,010
+T cross G2 مش الحال طيب شوفوا الآناحسب اللي هذي
+
+83
+00:06:28,010 --> 00:06:31,310
+عند من عند اي X و اللي موجودة في الـ X حسب التعريف
+
+84
+00:06:31,310 --> 00:06:34,970
+اللي قلنا عنه قبل شوية هو عبارة عن Alpha G1 زائد
+
+85
+00:06:34,970 --> 00:06:41,670
+G2 of T of X، مظبوط؟ الـ N of T of X، ويساوي الـ N
+
+86
+00:06:41,670 --> 00:06:44,850
+بتتوزح حادي، بيصير Alpha دالة مضربات في دالة عادية
+
+87
+00:06:44,850 --> 00:06:50,730
+اللي هي Alpha G1 T of X زائد G2 مالها of T of X،
+
+88
+00:06:50,730 --> 00:06:55,700
+لأ توزيع دالة، لأ توزيع compositionطيب و يساوي
+
+89
+00:06:55,700 --> 00:07:01,800
+الآن Alpha G1 T X بدرجة حال أصلها اللي هي عبارة عن
+
+90
+00:07:01,800 --> 00:07:06,220
+Alpha T cross G1 of X لأن T cross G1 of X هي عبارة
+
+91
+00:07:06,220 --> 00:07:11,500
+عن G1 T of X و نفس الشيء التاني T cross G2 of X
+
+92
+00:07:11,500 --> 00:07:15,380
+صار هذا المقدار بيساوي هذا المقدار عند كل X إذا
+
+93
+00:07:15,380 --> 00:07:19,850
+الدالة هذه بتساوي الدالتين المجموعات هذهHence اللي
+
+94
+00:07:19,850 --> 00:07:23,290
+هي هذه بتساوي هذه معناته صارت الـ D cross is
+
+95
+00:07:23,290 --> 00:07:29,160
+linear هاي واحد اتنانالآن بدنا ناخد اللي هو نسبة
+
+96
+00:07:29,160 --> 00:07:32,000
+الـ boundedness للـ T cross since G element و Y
+
+97
+00:07:32,000 --> 00:07:36,800
+واحد and T are bounded، التنتين bounded، اللي هو
+
+98
+00:07:36,800 --> 00:07:42,700
+الـ G والـ T bounded، أكيد، اللي هو الـ Y prime
+
+99
+00:07:42,700 --> 00:07:45,300
+الـ dual space، اللي هو الـ space of all bounded
+
+100
+00:07:45,300 --> 00:07:48,340
+linear functionals، والـ T معطينا هيها bounded من
+
+101
+00:07:48,340 --> 00:07:51,880
+أصل، من رأس الدورةthen خد هنا ال absolute value of
+
+102
+00:07:51,880 --> 00:07:55,800
+f of x اللي هو ايش حسب التعريف بساوي g of t of x
+
+103
+00:07:55,800 --> 00:08:00,600
+هيها لسه محتاج تي كروس g of x بساوي f of x اللي هي
+
+104
+00:08:00,600 --> 00:08:05,660
+g of t of x بساوي t cross g of x اللي عنده اللي هي
+
+105
+00:08:05,660 --> 00:08:13,220
+بيصير عنده اللي هو ال f of x بساوي g of t of xG of
+
+106
+00:08:13,220 --> 00:08:18,020
+T of X هذه وهذه هي هذه اللي هي G of T of X يمين
+
+107
+00:08:18,020 --> 00:08:23,300
+للـ F of X واضح؟ طيب إذا صار عندي الآن يا جماعة
+
+108
+00:08:23,300 --> 00:08:26,820
+الـ F of X بيساوي الـ G of T of X G is bounded و T
+
+109
+00:08:26,820 --> 00:08:29,780
+is bounded إذا أصغر بيساوي نورم الـ G في نورم الـ
+
+110
+00:08:29,780 --> 00:08:32,400
+T X و T is bounded أصغر بيساوي نورم الـ G في نورم
+
+111
+00:08:32,400 --> 00:08:35,860
+الـ T في نورمين الـ X الآن اقسم الجهتين على نورم
+
+112
+00:08:35,860 --> 00:08:38,720
+الـ X واخدوا السيبرانام على الإكسات بيصير نورم الـ
+
+113
+00:08:38,720 --> 00:08:43,920
+Fأصغر يسوي نرم الـG في نرمين الـT واضح؟ إيش اللي
+
+114
+00:08:43,920 --> 00:08:47,600
+سوناه؟ عند الـabsolute value of F of X أصغر يسوي
+
+115
+00:08:47,600 --> 00:08:51,560
+هذا الآن خُد عن نرمات الـSupremum على الإكسات اللي
+
+116
+00:08:51,560 --> 00:08:53,880
+نرم من واحد أو اقسم عليها تخُد الـSupremum على
+
+117
+00:08:53,880 --> 00:08:57,900
+الإكسات اللي مش سفر بطلع نرم الـF هذا أصغر يسوي
+
+118
+00:08:57,900 --> 00:09:04,360
+نرم الـG في نرمين الـTby the definition of T x T x
+
+119
+00:09:04,360 --> 00:09:08,640
+G أش بساوة بساوة في هي اللي عملتها صار عندي الآن
+
+120
+00:09:08,640 --> 00:09:12,520
+استبدل اللي هو مكان اللي هو ال F في T x G فبصير
+
+121
+00:09:12,520 --> 00:09:19,780
+عندي الان الان norm ال T x G بدل هذه حط norm ال T
+
+122
+00:09:19,780 --> 00:09:22,700
+x G اللي هو بيساوي norm ال F أصغر بيساوي norm ال G
+
+123
+00:09:22,700 --> 00:09:28,080
+في norm ال T اللي عملتها صار عندي الآن هذه الآن هي
+
+124
+00:09:28,080 --> 00:09:34,920
+شايفينها أهالان الـ T cross حصلت اللي هي عبارة عن
+
+125
+00:09:34,920 --> 00:09:39,590
+boundedهذه بتعني الـ T x إيش صارت؟ bounded لأن الـ
+
+126
+00:09:39,590 --> 00:09:43,850
+T x ده المتغير تبعها أصغر أو ساوي اللي هو some
+
+127
+00:09:43,850 --> 00:09:47,390
+اللي هو ال norm المتغير في norm ال T يعني هذا
+
+128
+00:09:47,390 --> 00:09:52,210
+constant بالنسبالها إذا صارت هذه is a bounded اللي
+
+129
+00:09:52,210 --> 00:09:56,590
+هي function واضح؟ a bounded in a functional طيب،
+
+130
+00:09:56,590 --> 00:10:05,310
+الآن عندي اللي هوأقسم لي على النورمات اللي بيساوي
+
+131
+00:10:05,310 --> 00:10:11,150
+واحد واخد الـ Supremum ايها ايها هاي الـ T x G يا
+
+132
+00:10:11,150 --> 00:10:18,750
+جماعة يا جماعة صار عندكم نورم الـ T x G أصغر يساوي
+
+133
+00:10:18,750 --> 00:10:28,480
+نورم الـ G في نورم الـ Tالأن نورم الـ T× يساوي الـ
+
+134
+00:10:28,480 --> 00:10:36,100
+supremum لنورم الـ T×G such that الـ G element in
+
+135
+00:10:36,100 --> 00:10:42,370
+Y'والـ G norm هاخده واحد أو اقسم عليه واخد على
+
+136
+00:10:42,370 --> 00:10:47,170
+اللي بيسوي النشتفر، مظبوط؟ طيب، هذا من فوق، هذا
+
+137
+00:10:47,170 --> 00:10:51,450
+صار أصغر أو شوية هذا، اقسم على مين؟ خد على norm
+
+138
+00:10:51,450 --> 00:10:56,610
+مين؟ نورمات اللي هي واحد، صح؟النورمات فبصير عند
+
+139
+00:10:56,610 --> 00:11:02,190
+نورم الـ T x G أصغر عشان هو نورم الـ T لكل الـ G
+
+140
+00:11:02,190 --> 00:11:05,730
+اللي نورمهن واحد و أنا أخد ال suprem عليها و هن
+
+141
+00:11:05,730 --> 00:11:09,370
+أصغر عشان هو T إذاً هذا ال suprem هيكون لهذه أصغر
+
+142
+00:11:09,370 --> 00:11:13,810
+عشان هو نورم الـ T إذا صار نورم الـ T x أصغر عشان
+
+143
+00:11:13,810 --> 00:11:16,150
+هو نورم الـ T واضح أه؟ طيب
+
+144
+00:11:24,800 --> 00:11:28,920
+وهنا قلنا this means من قبل اصلا that T x is a
+
+145
+00:11:28,920 --> 00:11:33,620
+bounded linear functional باثيرم 4 3 3 اللي قبل
+
+146
+00:11:33,620 --> 00:11:37,120
+بشوية بدلالة ال X note اللي هو بالجيب ال X note
+
+147
+00:11:37,120 --> 00:11:42,390
+بدلالة اللي هي الأفاتللـ X0 لها تساوي صفر في X
+
+148
+00:11:42,390 --> 00:11:48,910
+هناك مصطلح جي نوت يسميه Y1 لذلك نورم الجي نوت
+
+149
+00:11:48,910 --> 00:11:57,220
+يساوي واحد and G note of T X0 لأن X0 في X صحيحو
+
+150
+00:11:57,220 --> 00:12:03,100
+الـ G NOT شغالة على الـ Y مظبوط لكن الآن الـ TX
+
+151
+00:12:03,100 --> 00:12:06,820
+لما X NOT في الـ X الـ TX صارت في الـ Y فبيصير
+
+152
+00:12:06,820 --> 00:12:13,300
+الآن G NOT هذه حسب النظرية أخد بلاقي G NOT بحيث
+
+153
+00:12:13,300 --> 00:12:16,760
+الـ Normal بيساوي واحد من القرن اللي قبله شوية و G
+
+154
+00:12:16,760 --> 00:12:20,820
+NOT of TX NOT أو من الـ Theorem بيساوي Normal من
+
+155
+00:12:20,820 --> 00:12:26,650
+الـ TX NOTواضح؟ طبقتها الآن على مين؟ على اللي هي
+
+156
+00:12:26,650 --> 00:12:30,150
+.. على الـG note اللي في الـY براهم يعني أنا
+
+157
+00:12:30,150 --> 00:12:34,290
+طبقتها على الـY وأخدت اللي هي X note صح أخدتها في
+
+158
+00:12:34,290 --> 00:12:38,650
+الـX لكن أنا أشتغلت فيه مع مين؟ مع TX ألاجيت مش
+
+159
+00:12:38,650 --> 00:12:43,890
+أخدت الأن X note في الـX أخدت X note في الـX هذا
+
+160
+00:12:43,890 --> 00:12:47,900
+أعطانا الـTX note وين موجودة؟ في الـYإذا حسب
+
+161
+00:12:47,900 --> 00:12:50,880
+النظرية صارت هذه element وين؟ في ال space اللي
+
+162
+00:12:50,880 --> 00:12:54,580
+عندى إذا حسب النظرية اللي قبل شوية there exist g
+
+163
+00:12:54,580 --> 00:12:59,900
+سميها note element in y' such that ماشي الحال اللي
+
+164
+00:12:59,900 --> 00:13:05,100
+هو g note of النقطة اللي أخدتها دي أي إن كان اسمها
+
+165
+00:13:05,100 --> 00:13:09,600
+بترسلها لنفس النقطة لتيمين
+
+166
+00:13:11,260 --> 00:13:16,120
+X0 أو بترسلها لأسف لنورمها لنورم مين الـ TX0 حسب
+
+167
+00:13:16,120 --> 00:13:22,120
+النظرية لأن let F0 بسوء مين الـ T x G0 مين هذا الـ
+
+168
+00:13:22,120 --> 00:13:27,000
+G0 اللي لجيتها قبل بشوية يعني F0 خده بسوء T x G0
+
+169
+00:13:27,000 --> 00:13:32,830
+إذن احسبلي الآننورم الـ TX0 الان انا بتحكي انا
+
+170
+00:13:32,830 --> 00:13:35,250
+اثبتت in general نورم ال T cross أصغر أو شويه نورم
+
+171
+00:13:35,250 --> 00:13:38,970
+ال T بتاخد الان عشان أصل للعكس بتحكي عن specific
+
+172
+00:13:38,970 --> 00:13:42,350
+element عشان يكون ال supremum يكون بدل ما هو أصغر
+
+173
+00:13:42,350 --> 00:13:45,290
+أو شويه يصير أكبر أو شويه اللي هو ال .. ال .. ال
+
+174
+00:13:45,290 --> 00:13:46,310
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+175
+00:13:46,310 --> 00:13:46,710
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+176
+00:13:46,710 --> 00:13:46,730
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+177
+00:13:46,730 --> 00:13:47,450
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+178
+00:13:47,450 --> 00:13:47,630
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+179
+00:13:47,630 --> 00:13:47,930
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+180
+00:13:47,930 --> 00:13:50,810
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+181
+00:13:59,580 --> 00:14:03,200
+فاهمين؟ هو لأنه G not T اللي هو عبارة عن T cross G
+
+182
+00:14:03,200 --> 00:14:07,420
+not وT cross G not هو مين؟ الـ F not مش هذه
+
+183
+00:14:07,420 --> 00:14:11,620
+تعريفة، T cross G not أه، إذا هذي صارت مكانها F
+
+184
+00:14:11,620 --> 00:14:15,760
+not of X و F not اللي هي عبارة عن مين؟ عن boundary
+
+185
+00:14:15,760 --> 00:14:18,780
+linear functional أصغر أشهر نورم الـ F not في
+
+186
+00:14:18,780 --> 00:14:25,520
+نورمين الـ X not طيب، الآن نورم الـ F notهي عبارة
+
+187
+00:14:25,520 --> 00:14:31,520
+عن مين نورم الـ T G T X G Note واضحة لأنه نفسها في
+
+188
+00:14:31,520 --> 00:14:36,200
+نورم مين ال X Note صار عندى الآن اللي هو هذا أصغر
+
+189
+00:14:36,200 --> 00:14:40,280
+و ساوي نورم ال T Note في نورم مين ال G Note في
+
+190
+00:14:40,280 --> 00:14:47,310
+نورم مينالـ X note صار عندى الآن تي X note أصغر أو
+
+191
+00:14:47,310 --> 00:14:52,490
+ساوي اللى هو النورم هذا صار عندى هذا لإن النورم G
+
+192
+00:14:52,490 --> 00:14:55,690
+note أنا أصلا استخدمته نظري عشان أشتغل على واحد
+
+193
+00:14:55,690 --> 00:14:59,770
+محدد اللى هى ايش نورمها بساوي واحد اللى لجيتها
+
+194
+00:14:59,770 --> 00:15:08,280
+وينها وينها وينها صار عندى الآن نورمنورم الـ TX0
+
+195
+00:15:08,280 --> 00:15:15,540
+هيه نورم الـ TX0 لجيته أصغر أوي و ساوي في نورم الـ
+
+196
+00:15:15,540 --> 00:15:19,380
+TX في
+
+197
+00:15:19,380 --> 00:15:25,400
+نورم الـ G0 في نورمين الـ X0 أصلا أنا اشتغلت هيك
+
+198
+00:15:25,400 --> 00:15:28,920
+عشان أنا حصلت أصلا على الـ G0 نورمها إيش بساوي
+
+199
+00:15:28,920 --> 00:15:34,120
+بساوي واحد عن specific معينوضمان وجوده من النظرية
+
+200
+00:15:34,120 --> 00:15:37,280
+اللي حكيناها هذا نورمه بيساوي واحد فبيصير عندك
+
+201
+00:15:37,280 --> 00:15:42,360
+نورم ال T X not أصغر أو يساوي نورم ال T cross في
+
+202
+00:15:42,360 --> 00:15:46,860
+نورم ال X not مظبوط ولا لأ؟ ماشي الحالة وال X not
+
+203
+00:15:46,860 --> 00:15:51,440
+كانت point وين في ال X لات شاو سفر ماشي إذا صار
+
+204
+00:15:51,440 --> 00:15:58,800
+عند ال supremumلنورم الـ T X0 على نورم الـ X0 للـ
+
+205
+00:15:58,800 --> 00:16:03,280
+X0 element in X minus Zero بيضل هذا نورم أصغر أشهر
+
+206
+00:16:03,280 --> 00:16:06,940
+من نقطة T cross فبيصير أصغر أشهر منين؟ الـ T cross
+
+207
+00:16:06,940 --> 00:16:12,160
+وهذا مين هو نورم الـ Tصار عند نورم الـ T أصغر
+
+208
+00:16:12,160 --> 00:16:14,880
+ومشاوير نورم الـ T cross وقبل أن اتبعت نورم الـ T
+
+209
+00:16:14,880 --> 00:16:18,380
+cross أصغر من نورم الـ T إذن بيصار مشاوير واضح حتى
+
+210
+00:16:18,380 --> 00:16:21,800
+فلسفة البراهين في هذا الاتجاه أن نورم أصغر ومشاوير
+
+211
+00:16:21,800 --> 00:16:25,820
+نورم أن أنا باخد الأول إشي الـ norm in general تبع
+
+212
+00:16:25,820 --> 00:16:28,700
+السجن ومن العادي و بعدين باخد ال specific point أو
+
+213
+00:16:28,700 --> 00:16:31,940
+بخاصية معينة و بصل ل ال inequality التانية وصارت
+
+214
+00:16:31,940 --> 00:16:38,020
+هذه تقريبا أسلوب .. اللي هي أسلوب البرهن this ..
+
+215
+00:16:40,330 --> 00:16:45,630
+هذا يعني أن هذا يساوي بشكل واحد بسيرة تنتين تجمع
+
+216
+00:16:45,630 --> 00:16:49,530
+النورم بساوية النورم وفعلا أثبتنا أن الـ T× is a
+
+217
+00:16:49,530 --> 00:16:53,010
+bounded linear functional ونورمها هو نورم الـ T
+
+218
+00:16:53,010 --> 00:16:56,690
+الأصلية نجي الآن لبعض الخواصة الأخرى اللي هي اللي
+
+219
+00:16:56,690 --> 00:17:00,580
+اطلع على فوق اللي هي ال joint operatorsهذه الخواص
+
+220
+00:17:00,580 --> 00:17:04,660
+خواص حسابات بتقول لكم بظل للبرهين F, S و T لإن
+
+221
+00:17:04,660 --> 00:17:08,840
+إكسرسايز كلها F, S و T من X لعند Y و W من Y لعند Z
+
+222
+00:17:08,840 --> 00:17:11,600
+ماشي الحال W من Y لعند Z لإنه شكله بدعم ال
+
+223
+00:17:11,600 --> 00:17:14,760
+composition بين الهن و الهن الهن are bounded
+
+224
+00:17:14,760 --> 00:17:18,720
+linear operators bounded linear operators where X
+
+225
+00:17:18,720 --> 00:17:22,520
+and Y and Z are normed spaces دم ما يليه صحيح أول
+
+226
+00:17:22,520 --> 00:17:26,660
+إشيS زي الـ T كله cross يعني الـ Adjoint للمجموع
+
+227
+00:17:26,660 --> 00:17:30,640
+بساوي مجموع الـ Adjoint يعني يوزع الان برضه Alpha
+
+228
+00:17:30,640 --> 00:17:34,280
+T cross بتوزع Alpha في T cross for all scalar mean
+
+229
+00:17:34,280 --> 00:17:40,190
+Alphaالـ W T كله cross بساوي الـ T cross و W cross
+
+230
+00:17:40,190 --> 00:17:43,570
+زي ال composition زي ال inverse قصدي if T inverse
+
+231
+00:17:43,570 --> 00:17:46,590
+element in B قله Y و X يعني T inverse عبارة عن
+
+232
+00:17:46,590 --> 00:17:50,490
+bounded linear operator من Y لعند X إذا الـ T
+
+233
+00:17:50,490 --> 00:17:54,610
+cross inverse هيكون من وين؟ الـ T cross نفسه من
+
+234
+00:17:54,610 --> 00:17:57,850
+الـ Y prime لX prime الـ T cross inverse هيكون من
+
+235
+00:17:57,850 --> 00:18:03,140
+وين؟ من X prime لمين؟لـ Y' ماعرفكم باهتين الـ T
+
+236
+00:18:03,140 --> 00:18:09,860
+cross عندك من Y' ل X' من التعريف هيه ماعرفش ماسحته
+
+237
+00:18:09,860 --> 00:18:13,280
+ولا الـ T cross من Y' ل X' الـ T cross inverse
+
+238
+00:18:13,280 --> 00:18:18,360
+هيكون من X' ل Y' و الـ T cross inverse بيساوي ال
+
+239
+00:18:18,360 --> 00:18:22,020
+inverse ل T cross ماشي الحال، عساسه اللي هو كمان
+
+240
+00:18:22,020 --> 00:18:26,000
+يسهل علينا أكتر و هذا البرهان لكم اللي بعده نيجينا
+
+241
+00:18:26,000 --> 00:18:27,680
+للنظرية اللي بعده
+
+242
+00:18:32,040 --> 00:18:35,360
+ما أعتقد أخدنا نظرية هذه، شوف يا عدنان، طيب
+
+243
+00:18:35,360 --> 00:18:39,460
+النظرية في أخر نظرية في ال section هذا اللي هي
+
+244
+00:18:39,460 --> 00:18:45,160
+بتربطلك بالـ Hilbert Adjoint و بين ال Adjoint،
+
+245
+00:18:45,160 --> 00:18:48,940
+ماشي الحال، شوفوا، ركزوا معايا، الآن ليه اتقدش
+
+246
+00:18:48,940 --> 00:18:51,920
+واحد، انا اتقدش اتنين بيطول Hilbert Spaces،
+
+247
+00:18:51,920 --> 00:18:54,760
+Hilbert Spaces اللي هو inner product spaces
+
+248
+00:18:54,760 --> 00:18:58,560
+complete، كل واحد فيهماللي هنخلّينا نقول T element
+
+249
+00:18:58,560 --> 00:19:02,420
+in B الـH1 لعند H2 يعني T عبارة عن bounded linear
+
+250
+00:19:02,420 --> 00:19:06,760
+operator من H1 لعند مين لH2 شغال على Hilbert
+
+251
+00:19:06,760 --> 00:19:15,000
+spaces then بقولك then anyway there exists A1 من
+
+252
+00:19:15,000 --> 00:19:22,570
+H1' لH1و A2 من H2' لعنده H2 such that يعني بده
+
+253
+00:19:22,570 --> 00:19:26,710
+يقولك انا بقدر اكتب اللي هو الهيلبرت ال joint
+
+254
+00:19:26,710 --> 00:19:32,150
+operator بدلالة ال joint operator عبر اللي هو
+
+255
+00:19:32,150 --> 00:19:37,250
+bridge او عبر اللي هو جسر من اللي هي الدوال A1 و
+
+256
+00:19:37,250 --> 00:19:43,750
+A2 واحدة من H1' لعنده H1 واحدة من H2' يعني بده
+
+257
+00:19:43,750 --> 00:19:49,200
+يكتب ال T star ال Hilbert adjointبدلالة الـ
+
+258
+00:19:49,200 --> 00:19:54,220
+Adjoint شوف كيف بقول لي then there exist كده و كده
+
+259
+00:19:54,220 --> 00:19:58,080
+such that T star ال Hilbert Adjoint operator بساوي
+
+260
+00:19:58,080 --> 00:20:03,720
+A1 T cross زائد في A2 mean inverse هدولة اللي هي
+
+261
+00:20:03,720 --> 00:20:09,090
+العمليات عمليات composition ماشي where T star andT
+
+262
+00:20:09,090 --> 00:20:12,610
+are Hilbert Adjoint and Adjoint Operators of T
+
+263
+00:20:12,610 --> 00:20:17,970
+respectively And both A1 هذولة اللي هن ال bridge
+
+264
+00:20:17,970 --> 00:20:23,290
+اللي وصلين العلاقة بينهم Where both A1 and A2 are
+
+265
+00:20:23,290 --> 00:20:28,520
+bijectiveisometric and conjugate linear كل واحد
+
+266
+00:20:28,520 --> 00:20:32,640
+فيهم اللي هو عبارة عن isometric و bijective و
+
+267
+00:20:32,640 --> 00:20:38,280
+linear conjugate linear الان نيجي نثبت اول اشي ان
+
+268
+00:20:38,280 --> 00:20:42,580
+T star نقدر نكتبها زي هيك و نثبت ان هذا بالخاصية
+
+269
+00:20:42,580 --> 00:20:46,160
+اللي هو جالها و هذا بالخاصية اللي هو جالها واضح
+
+270
+00:20:46,160 --> 00:20:52,810
+ايش النظرية ده ننطلق يلاللـ T من H1 لـ H2 بيـ be a
+
+271
+00:20:52,810 --> 00:20:55,350
+bounded linear operator و الـ T cross تبعها على
+
+272
+00:20:55,350 --> 00:21:02,450
+طول من وين من H2' إلى H1' بـ it's a joint then T
+
+273
+00:21:02,450 --> 00:21:10,790
+cross G بسوء F where تعريف .. تعريف where GG T of
+
+274
+00:21:10,790 --> 00:21:15,510
+X بسوء من F of X هذا اللي بعرف هوية الـ T cross و
+
+275
+00:21:15,510 --> 00:21:23,330
+الـ F من وين جاية من H'من H إبراهيم واحد اللي برمي
+
+276
+00:21:23,330 --> 00:21:27,430
+عليه و الـ G هاد من وين جايبها من H إتنين إبراهيم
+
+277
+00:21:27,430 --> 00:21:32,530
+هيه بياخد الـ G من H إتنين إبراهيم و برميها في الـ
+
+278
+00:21:32,530 --> 00:21:35,770
+F في الـ H واحد إبراهيم و الـ X طبعاً arbitrary
+
+279
+00:21:35,770 --> 00:21:40,150
+element من و من اللي ماخدينها من H Y then by اطلع
+
+280
+00:21:40,150 --> 00:21:43,310
+الآن by theorem تلاتة تمانية واحد اللي هي بتعملي
+
+281
+00:21:43,310 --> 00:21:50,030
+representation لل element بواسطتين productthen by
+
+282
+00:21:50,030 --> 00:21:52,930
+theorem 3.3.1 there exists a unique X note element
+
+283
+00:21:52,930 --> 00:21:57,510
+in H1 بدي أطبّق على الـH1 وعلى مين؟ على H2 الـH1
+
+284
+00:21:57,510 --> 00:22:00,470
+فيه الهينيروبرودكت والـH2 الهينيروبرودكت كل واحدة
+
+285
+00:22:00,470 --> 00:22:05,790
+خاص بها a unique X note و a unique Y note such
+
+286
+00:22:05,790 --> 00:22:10,070
+that F of X can be .. مدام F bounded linear
+
+287
+00:22:10,070 --> 00:22:14,810
+functional on H1 then it can be written as an
+
+288
+00:22:14,810 --> 00:22:19,140
+inner productاللي هو F of X بيساوي X و 100 X Note
+
+289
+00:22:19,140 --> 00:22:23,440
+يعني هذه الـ X Note اللي بدللتها بقدر أكتب الـ F
+
+290
+00:22:23,440 --> 00:22:25,880
+of X على صورة 100 in our product هذا الـ
+
+291
+00:22:25,880 --> 00:22:30,370
+Representation 381النظام الـ F هو نظام الـ mean
+
+292
+00:22:30,370 --> 00:22:35,670
+الـ X نوت اللي بواسطتها عرفت اللي هي الـ F و الـ G
+
+293
+00:22:35,670 --> 00:22:39,650
+of Y برضه لأ Y نوت اللي متنقش 2 بقدر ألاقي اللي هو
+
+294
+00:22:39,650 --> 00:22:43,970
+الـ Y نوت اللي هي بتعمل ال representation للـ G
+
+295
+00:22:43,970 --> 00:22:48,010
+اللي هي عبارة عن bounded linear functional on mean
+
+296
+00:22:48,010 --> 00:22:52,700
+انقش 2G of Y بيسوي Y وY not هذا طبعا ال
+
+297
+00:22:52,700 --> 00:22:54,840
+representation اللي يمكن نعمله غير في ال inner
+
+298
+00:22:54,840 --> 00:22:58,140
+product لما يكون Hilbert space مش Hilbert space لأ
+
+299
+00:22:58,140 --> 00:23:02,420
+and norm of G هو norm من Y not هذه اللي هي خلنا
+
+300
+00:23:02,420 --> 00:23:06,040
+نقول ال fresh أو الأساس اللي هنبني عليه اللي هو
+
+301
+00:23:06,040 --> 00:23:10,110
+اللي بده أسويه الآنبالتأكيد أن الـ X0 وY0 مستخدمين
+
+302
+00:23:10,110 --> 00:23:14,970
+مختلفين من الـ F وG فبعد ذلك نستطيع أن ندفع
+
+303
+00:23:14,970 --> 00:23:18,770
+المتابعين مثلاً كل واحدة ده اللي هي وحيدة إذا بقدر
+
+304
+00:23:18,770 --> 00:23:22,390
+أعرف من خلال الـ functions A1 من H1 براي من عند
+
+305
+00:23:22,390 --> 00:23:26,970
+مين لان H1 والـ A2 من H2 براي من عند مين لان H1
+
+306
+00:23:26,970 --> 00:23:34,920
+لأن لكل Fلكل F في الـ H1 بقدر أجي لها نقطة X0 هنا
+
+307
+00:23:34,920 --> 00:23:39,840
+بحيث انه اللي هي Normal F و Normal X0 و F of X
+
+308
+00:23:39,840 --> 00:23:44,660
+بساوية هذا إذا مدام هذا الـ U وحيدة إذا أنا بقدر
+
+309
+00:23:44,660 --> 00:23:50,150
+أعرف A1 of F بساوية X0 اللي أجيت لها إلهاهذه اللي
+
+310
+00:23:50,150 --> 00:23:54,810
+.. اللي .. اللي كانت وسيلة التعريف الـ F ك Inner
+
+311
+00:23:54,810 --> 00:23:58,990
+Product اللي هي F of X بساوي X ومين و X not إذاً A
+
+312
+00:23:58,990 --> 00:24:02,250
+F واحد F بساوي X not والـ X not عرفنا إيش هي والـ
+
+313
+00:24:02,250 --> 00:24:04,310
+F اللي هي الـ Arbitral اللي لجيتلها الـ X not
+
+314
+00:24:04,310 --> 00:24:08,290
+وبرضه نفس الشيء اتنين G لها مين Y not إذاً صار
+
+315
+00:24:08,290 --> 00:24:11,510
+الآن تعريف اللي هو الـ A واحد والـ A اتنين مشروع
+
+316
+00:24:12,280 --> 00:24:15,360
+ماشي الحالة لأنه uniquely determined ثم كمان
+
+317
+00:24:15,360 --> 00:24:20,260
+normal a1f بس هو normal x0 و normal x0 من فوق أش
+
+318
+00:24:20,260 --> 00:24:24,040
+بيطلع normal mean ال F إذا واضح إن هذا صار
+
+319
+00:24:24,040 --> 00:24:29,370
+isometricأه لإن A1 Fاش بيساوي normal F شايف كيف
+
+320
+00:24:29,370 --> 00:24:33,530
+تلتة تمانية واحد قوتها خودتني مباشرة اللي هي
+
+321
+00:24:33,530 --> 00:24:39,290
+تعريفها دي و طلعتلي isometry similarly مدام one to
+
+322
+00:24:39,290 --> 00:24:42,770
+isometry ده أكيد يشملها one to one ماشي
+
+323
+00:24:45,620 --> 00:24:59,440
+لت H الأن element in H واحد ثم
+
+324
+00:24:59,440 --> 00:25:01,940
+F من H واحد لعند K defined by
+
+325
+00:25:08,570 --> 00:25:10,970
+مع انتوا عارفين ايش معناته انتوا اللي هو element
+
+326
+00:25:10,970 --> 00:25:13,970
+هنا انا جيله element هنا بحيث a واحد لهذا كويسة
+
+327
+00:25:13,970 --> 00:25:17,210
+وهذا طيب لت اتش element من مين ان اتش واحد اتش
+
+328
+00:25:17,210 --> 00:25:21,630
+element صغير زي ال X ها then F من اتش واحد عند K
+
+329
+00:25:21,630 --> 00:25:26,590
+defined by F of X ايش بده اعرفه X وإيش واتش برضه
+
+330
+00:25:26,590 --> 00:25:30,690
+اللي هو استئناسا باللي هو اللي وجدناه في النظرية
+
+331
+00:25:30,690 --> 00:25:35,830
+فوق for all X element اتش واحدis a bounded linear
+
+332
+00:25:35,830 --> 00:25:39,450
+operator هذا bounded linear operator وسهل اثباتها
+
+333
+00:25:39,450 --> 00:25:43,470
+لأن ال product على طول linear لأنه هو معرفها لاللي
+
+334
+00:25:43,470 --> 00:25:46,130
+هي f of x على الجريبة وعلى الجريبة linear لل
+
+335
+00:25:46,130 --> 00:25:50,290
+product و ال norm و ال norm هيطلع أيش برضه اللي هو
+
+336
+00:25:50,290 --> 00:25:54,020
+عبارة عن bounded طيبإذاً is a bounded linear
+
+337
+00:25:54,020 --> 00:25:57,500
+operator و K is the scalar field طبعا اللي جاي لها
+
+338
+00:25:57,500 --> 00:26:03,140
+then A1 لل F بسوة مين بسوة H لأن أثبتت أنا الآن ال
+
+339
+00:26:03,140 --> 00:26:05,940
+F هذا عبارة عن bounded linear operator يعني لجيت
+
+340
+00:26:05,940 --> 00:26:09,000
+أخدت element 10 لجيت bounded linear operator لما
+
+341
+00:26:09,000 --> 00:26:14,060
+.. بحيث أنه A F واحد يسوة مين H واحد إذا صار عندي
+
+342
+00:26:14,060 --> 00:26:19,640
+اللي هو A1 F يسوة H hence A1 is on 2Similarly for
+
+343
+00:26:19,640 --> 00:26:24,220
+a2 ماشي الحال إذا خلصنا a1 و a2 اللي هين عبارة عن
+
+344
+00:26:24,220 --> 00:26:27,500
+isometric و one to one onto function ذرع ال linear
+
+345
+00:26:27,500 --> 00:26:31,660
+conjugate بادثبت لل a1 و ال a2 similarly to show
+
+346
+00:26:31,660 --> 00:26:35,460
+that a1 is conjugate linear خلينا عارفين شو معنات
+
+347
+00:26:35,460 --> 00:26:37,960
+conjugate linear اللي هالجد بتشوفوها زي ناسينها
+
+348
+00:26:37,960 --> 00:26:42,960
+let f1 و f2 element من مين ال H1 prime حيهاهذه a1
+
+349
+00:26:42,960 --> 00:26:47,520
+سأختار أي element هنا و أثبت لكم أنها conjugate
+
+350
+00:26:47,520 --> 00:26:52,400
+linear لل F1 و F2 element H1 and alpha and scalar
+
+351
+00:26:52,400 --> 00:26:57,220
+اللي بتكون conjugate linear then there exist X1 و
+
+352
+00:26:57,220 --> 00:27:01,400
+X2 element H1 برضه استخدام نظري قبل شوية X1 لمين
+
+353
+00:27:01,400 --> 00:27:07,460
+لل F1 و X2 لمين لل F2 هذه بتعمل ليه؟Inner Product
+
+354
+00:27:07,460 --> 00:27:12,700
+F1 of X بيساوي X و X واحد و F2 of X بيساوي X و X
+
+355
+00:27:12,700 --> 00:27:17,940
+اتنين Such that F1 of X بيساوي X و X واحد and F2
+
+356
+00:27:17,940 --> 00:27:21,520
+of X بيساوي X و X اتنين لكل X و element of H واحد
+
+357
+00:27:21,520 --> 00:27:28,460
+و ال A واحد لل F واحد اللي هي X واحد و ال A اتنين
+
+358
+00:27:28,460 --> 00:27:34,660
+لل F اتنين اللي هي X اتنينهو اللي مسمينها انا then
+
+359
+00:27:34,660 --> 00:27:42,460
+حسبولي هذه Alpha F1 زي F2 of X ايش بيساوي Alpha F1
+
+360
+00:27:42,460 --> 00:27:49,430
+of X زي F2 of X مظبوط عوض فاهمينعود مكانها الآن
+
+361
+00:27:49,430 --> 00:27:54,570
+بيصير عبارة عن إيه ساوي Alpha مكان F1 اللي هي X و
+
+362
+00:27:54,570 --> 00:28:00,630
+X1 و مكان هذه X و X main اتنين دخل ليها جبهة مرخصة
+
+363
+00:28:00,630 --> 00:28:04,810
+اللي هي المرضات بيصير X زيد Alpha conjugate X1 زيد
+
+364
+00:28:04,810 --> 00:28:09,550
+X2 صار الآن يا جماعة ركزوا معايا صار هذا المقدار
+
+365
+00:28:09,550 --> 00:28:11,910
+هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه
+
+366
+00:28:11,910 --> 00:28:11,930
+هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه
+
+367
+00:28:11,930 --> 00:28:12,130
+هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه
+
+368
+00:28:12,130 --> 00:28:13,110
+هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه
+
+369
+00:28:13,110 --> 00:28:14,550
+هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه هيه
+
+370
+00:28:15,090 --> 00:28:19,050
+أحنا الآن كيف عرفنا الـ A1 عشان تشوفوا كيف اللي
+
+371
+00:28:19,050 --> 00:28:25,370
+عرفنا عندي عشان
+
+372
+00:28:25,370 --> 00:28:35,390
+تعرفوا كيف وصلنا عندي F1 of Xبساوة X و X واحد
+
+373
+00:28:35,390 --> 00:28:43,110
+مظبوط F2 of X بساوة X و X اتنين صح ولا لأ طيب الان
+
+374
+00:28:43,110 --> 00:28:49,640
+على طول ال A F واحدالـ A F1 إيش هيساوي اللي لجيتها
+
+375
+00:28:49,640 --> 00:28:54,200
+اللي هي الـ X1 أيه من هنا لما عرفنا هاد A1 F إيش
+
+376
+00:28:54,200 --> 00:28:58,940
+بيساوي X Note اللي لجناها اللي تبعت الـ X1 مش لكل
+
+377
+00:28:58,940 --> 00:29:02,960
+F في X Note بواسطتها بقدر أكتب الـ F as a product
+
+378
+00:29:02,960 --> 00:29:07,780
+من تلاتة تمانية واحد إذا الـ A A1 F بيساوي X Note
+
+379
+00:29:07,780 --> 00:29:15,810
+اللي هي هذا بيصير الـ A F1 بيساوي مين؟ X1والـ A F2
+
+380
+00:29:15,810 --> 00:29:21,830
+بساوي X2 مالكم يا جماعة؟ أنا الآن في الـ 381
+
+381
+00:29:21,830 --> 00:29:25,650
+النظرية اللي قلت عنها كيف بدي أعرف الـ A أنا أصلا؟
+
+382
+00:29:25,650 --> 00:29:31,710
+أجيت أخدت أي نقطة، أي F في الـ H1' اللي جاتله X0
+
+383
+00:29:31,710 --> 00:29:36,510
+في الـ H1 بحيث أن هذا الـ Presentation theorem
+
+384
+00:29:36,510 --> 00:29:40,670
+بحيث أن F of X بتساوي ال inner product بين X و X0
+
+385
+00:29:40,950 --> 00:29:45,690
+وبناء عليه عرفت الـ A1 للـ F هذه اللي في الـ H1
+
+386
+00:29:45,690 --> 00:29:50,290
+برايم بتدرسلها بتساوي الـ X0 ماشي الحال اللي
+
+387
+00:29:50,290 --> 00:29:54,650
+لجيتها هذه الان F1 و Fx كتبتها على صورة X و X1 و
+
+388
+00:29:54,650 --> 00:29:58,510
+F2 بتساوي X و X2 بالظبط زيها رح تكون الـ A F1 إلى
+
+389
+00:29:58,510 --> 00:30:02,810
+هذه هي الـ X1اللي بواسطتها كتبت الـNR برضه الـ
+
+390
+00:30:02,810 --> 00:30:06,670
+Function F و إيه أوافد واحد لإيه F2 برضه إيش
+
+391
+00:30:06,670 --> 00:30:12,110
+بتساوي X2 ماشي الحال اللي أنا وصلتلكم التالي في
+
+392
+00:30:12,110 --> 00:30:19,810
+هذه اللي هنا ووصلتلكم إنه الـ AlphaF1 Alpha F1
+
+393
+00:30:19,810 --> 00:30:27,370
+زائد F2 of X بساوي انتبهوا لك كيف عشان المقارنة
+
+394
+00:30:27,370 --> 00:30:32,170
+بين هذه و هذه بساوي اللي هو ال inner product بساوي
+
+395
+00:30:32,170 --> 00:30:37,070
+ال inner product بين X و Alpha conjugate X1 زائد
+
+396
+00:30:37,070 --> 00:30:45,930
+مين X2 صح ولا لأ هذا اللي وصلتكم إياه الآنحسب اللي
+
+397
+00:30:45,930 --> 00:30:51,390
+هو التعريف اللي فوق هيكون الـ A لهذا الـ A لهذا هو
+
+398
+00:30:51,390 --> 00:30:55,870
+هذه الـ A لهذا هو هذه وهنا الآن كتبت برضه own
+
+399
+00:30:55,870 --> 00:31:00,790
+product F of X بساوي X زائد هذا إذا الـ A للـ
+
+400
+00:31:00,790 --> 00:31:05,610
+Alpha F واحد زائد F اتنين هو عبارة عن Alpha
+
+401
+00:31:05,610 --> 00:31:13,300
+conjugate X واحد زائد مين؟ X اتنين واضح؟ ويساويأيه
+
+402
+00:31:13,300 --> 00:31:18,480
+لهذا A1 آسف الان هذا كله للـ A1 طبعا احنا مش شغله
+
+403
+00:31:18,480 --> 00:31:25,120
+الان اصبر على ال seminar اللي احنا وصلناه ايه
+
+404
+00:31:25,120 --> 00:31:28,960
+بساوي هذا بساوي هذا ماشي الان Alpha كون ديجيتايها
+
+405
+00:31:28,960 --> 00:31:37,680
+زي ما هي و X1 مين هي A1 Alpha 1 A1 Alpha 1 زائد X2
+
+406
+00:31:37,680 --> 00:31:41,620
+مين هي A1 F2
+
+407
+00:31:44,850 --> 00:31:49,890
+صارت عندي هذه a1 ألفة أف واحد زائد أف اتنين بساوية
+
+408
+00:31:49,890 --> 00:31:53,570
+ألفة conjugate a1 أف واحد زائد a1 أف اتنين اذا
+
+409
+00:31:53,570 --> 00:31:57,510
+صارت اللي هي ال function a1 هذي conjugate linear
+
+410
+00:31:57,510 --> 00:32:02,990
+similarly for a2 is conjugate linear الأن اطلع for
+
+411
+00:32:02,990 --> 00:32:07,010
+therefore therefore
+
+412
+00:32:07,010 --> 00:32:12,820
+a1 is conjugate linear similarly for a2ظال عندى
+
+413
+00:32:12,820 --> 00:32:21,380
+اخر اشي اثبت انه ا واحد يعني
+
+414
+00:32:21,380 --> 00:32:25,740
+اشي اللى بده اثبته اخر اشي بكون خلصت يعني ا واحد و
+
+415
+00:32:25,740 --> 00:32:29,460
+ا اتنين اثبتت انه زى ما بدهوا ياه تماما عبارة عن
+
+416
+00:32:29,460 --> 00:32:33,420
+conjugate linear او عبارة عن isometric او عبارة عن
+
+417
+00:32:33,420 --> 00:32:41,590
+bijective كل واحدة فيهم ظال عندى اثبت انه ا واحدتي
+
+418
+00:32:41,590 --> 00:32:49,730
+كروس اتنين انفرس بيسوا من التي ستار حيبدأ فيك تعمل
+
+419
+00:32:49,730 --> 00:33:00,910
+ماشي؟ شوفوا الآن تبقى الان
+
+420
+00:33:00,910 --> 00:33:07,820
+for anyWhy not element in H2؟ كررته مائة مرة There
+
+421
+00:33:07,820 --> 00:33:14,060
+exists جي وين موجودة في الـ A2 و الـ G of أي
+
+422
+00:33:14,060 --> 00:33:18,740
+element Y في الـ H2 بيساوي ال inner product بين
+
+423
+00:33:18,740 --> 00:33:25,120
+الـ Y و بين مين؟ اللي هي الـ Y not اللي لجيتها و
+
+424
+00:33:25,120 --> 00:33:31,070
+هيكون الـ A2 للـ G بيساوي مين؟ الـ Y notزي ما أعمل
+
+425
+00:33:31,070 --> 00:33:38,430
+في الأف واحد في الـ A1 طيب إذا فعلا لأي جي .. لأي
+
+426
+00:33:38,430 --> 00:33:41,930
+why not element H2 بقدر أجي G في الـ H2 بحيث يكون
+
+427
+00:33:41,930 --> 00:33:47,350
+A2G2 بتساومين الـ why not بناء على هذا ال bridge و
+
+428
+00:33:47,350 --> 00:33:50,270
+طبعا أثبتنا إحنا خلصنا A2 و A1 one to one و one to
+
+429
+00:33:50,270 --> 00:33:52,770
+two و كده دي إن ال inverse موجود إذا ال automatic
+
+430
+00:33:52,770 --> 00:34:01,440
+هيكون الـ G بساوي 2 A2 inverse لمن؟ صح؟لأن A2 is
+
+431
+00:34:01,440 --> 00:34:02,620
+one to one to one to one to one to one to one to
+
+432
+00:34:02,620 --> 00:34:02,720
+one to one to one to one to one to one to one to
+
+433
+00:34:02,720 --> 00:34:02,860
+one to one to one to one to one to one to one to
+
+434
+00:34:02,860 --> 00:34:02,920
+one to one to one to one to one to one to one to
+
+435
+00:34:02,920 --> 00:34:03,180
+one to one to one to one to one to one to one to
+
+436
+00:34:03,180 --> 00:34:03,900
+one to one to one to one to one to one to one to
+
+437
+00:34:03,900 --> 00:34:07,420
+one to one
+
+438
+00:34:07,420 --> 00:34:07,780
+to one to one to one to one to one to one to one
+
+439
+00:34:07,780 --> 00:34:07,960
+to one to one to one to one to one to one to one
+
+440
+00:34:07,960 --> 00:34:10,900
+to one to one to one to one to one to one to one
+
+441
+00:34:10,900 --> 00:34:12,160
+to one to one to one to one to one to one to one
+
+442
+00:34:12,160 --> 00:34:13,060
+to one to one to one to one to one to one to one
+
+443
+00:34:13,060 --> 00:34:19,440
+to one to one to oneللـ Y not إذا أثبتها بالساوية
+
+444
+00:34:19,440 --> 00:34:23,700
+T star لكل T star Y not بيقول خلصت عشان أثبت
+
+445
+00:34:23,700 --> 00:34:28,720
+دالتين بيثبت هذه إيش أنا .. بيثبتلكم هي A1 T cross
+
+446
+00:34:28,720 --> 00:34:31,240
+A2 inverse بالساوية T star عشان أثبتها بيثبت إن
+
+447
+00:34:31,240 --> 00:34:35,560
+هذا عند أي نقطة بيثبت هذا عند أي نقطة معايا؟ أنا
+
+448
+00:34:35,560 --> 00:34:42,200
+أخدت Y not arbitrary element in H2 بيثبتلك إنه A1
+
+449
+00:34:42,730 --> 00:34:49,930
+تي كروس a2 inverse of y0 تساوي تي ستار y0 معناته
+
+450
+00:34:49,930 --> 00:34:52,650
+ان سعر الدالة دي بيساوي هذه لأن y0 اربيترا في ال
+
+451
+00:34:52,650 --> 00:34:56,150
+domain طيب
+
+452
+00:34:56,150 --> 00:35:07,890
+خدوا الآن احسبوها ايش بتساوي a1 t crossA2-A2-A2-A2
+
+453
+00:35:07,890 --> 00:35:13,210
+-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2
+
+454
+00:35:13,210 --> 00:35:13,590
+-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2
+
+455
+00:35:13,590 --> 00:35:15,290
+-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2
+
+456
+00:35:15,290 --> 00:35:20,310
+-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2-A2
+
+457
+00:35:20,310 --> 00:35:27,320
+-A2-A2-A2-A2-A2-A2-A2والأن A1 للـ F اللي هي إيش
+
+458
+00:35:27,320 --> 00:35:31,160
+بيساوي X0 لأنه لكل X0 لجينا F وهي هذه اللي .. اللي
+
+459
+00:35:31,160 --> 00:35:34,020
+.. اللي بتعمل representation خلنا نقول بدالتها
+
+460
+00:35:34,020 --> 00:35:38,860
+بتتعرف A1 F Also إذا حصلنا .. تشوف إيش اللي
+
+461
+00:35:38,860 --> 00:35:43,400
+حصلناها حصلنا هذا المقدار إيش بيساوي .. بيساوي X0
+
+462
+00:35:43,400 --> 00:35:49,480
+خلينا X0 مين؟ تبعت الـ F اللي لأي X0 لجيناه مين
+
+463
+00:35:49,480 --> 00:35:52,240
+الـ F بحيث الـ F of X بيساوي ال inner product بين
+
+464
+00:35:52,240 --> 00:35:59,880
+X و X0 طيبAlso من جهة ثانية احسب للـ TX ومين و Y
+
+465
+00:35:59,880 --> 00:36:03,340
+not عشان انا اصطلق اللي بديها الـ TX و Y not ايش
+
+466
+00:36:03,340 --> 00:36:09,040
+بيساوي اللي هو G of T of X عارفين ليش؟ لأن لان
+
+467
+00:36:09,040 --> 00:36:16,400
+عندي Y Y not GT of Y G of Y اي اي اشي Y not بيساوي
+
+468
+00:36:16,400 --> 00:36:20,580
+G of اي اشي صح؟ اذا TX و Y not بيساوي G of TX و
+
+469
+00:36:20,580 --> 00:36:25,190
+يساويالـ GTX اللي هو عبارة عن إيش بساوة بساوة F of
+
+470
+00:36:25,190 --> 00:36:28,190
+X عارفين ليش Y ساوية الـ F of X هو عبارة عن inner
+
+471
+00:36:28,190 --> 00:36:32,090
+product بين الـ X ومين و الـ X note اللي بدللتها Y
+
+472
+00:36:32,090 --> 00:36:37,950
+ساوية إن الآن الـ X هيها زي ما هي X و الـ X note
+
+473
+00:36:37,950 --> 00:36:43,470
+هي هذه فبصير عبارة عن ال inner بصارت عبارة عن الـ
+
+474
+00:36:43,470 --> 00:36:52,910
+TX الـ TX و الـ Y note هيساوة الـ X والـ A1 T
+
+475
+00:36:52,910 --> 00:37:03,030
+cross A2 inverse Y0 هذا الكلام صحيح لإيش؟ لأي X
+
+476
+00:37:03,030 --> 00:37:08,810
+عندي، ماشي الحال؟ الآن however الـ TX والـ Y0 إيش
+
+477
+00:37:08,810 --> 00:37:15,590
+بيساوي؟ اللي هو الـ X والـ T star Y0، مظبوط؟ الـ
+
+478
+00:37:15,590 --> 00:37:21,750
+TX والـ Y0 بساوي اللي هو الـ Xوالـ T star why not
+
+479
+00:37:21,750 --> 00:37:26,230
+من تعريف الـ Adjoint الـ Hilbert Adjoint إذا هذا
+
+480
+00:37:26,230 --> 00:37:34,790
+صار بيساوي هذا دائما لكل مين لكل X في الدنيا لكل X
+
+481
+00:37:34,790 --> 00:37:38,830
+في الدنيا هذا صحيح إذا لازم هذا يساوي هذا كله لريه
+
+482
+00:37:38,830 --> 00:37:44,610
+أخدناها قبل هيك لمّا إذا صار عندي اللي هو T starY0
+
+483
+00:37:44,610 --> 00:37:52,210
+بساول A1 T X A2 Inverse Y0 والـ Y0 كانت أشمالها
+
+484
+00:37:52,210 --> 00:37:56,910
+arbitrary هنا for any لحدية for any ومين وY0
+
+485
+00:37:56,910 --> 00:38:02,590
+element انهيش الـ H2والدلتين هدولة قيمتهم عند أي
+
+486
+00:38:02,590 --> 00:38:07,710
+قيمة في الـ Y0 في الدمين متساوية إذا أكيد الدلتين
+
+487
+00:38:07,710 --> 00:38:19,350
+T starبساوي a1t cross a2 inverse و هو المطلوب و
+
+488
+00:38:19,350 --> 00:38:22,930
+إلى لقاء آخر السلام عليكم و رحمة الله الله يعطيكم
+
+489
+00:38:22,930 --> 00:38:23,290
+العافية
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/vjF46QrstMA.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/vjF46QrstMA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a22439cb469cc04602224dbff4ab43b6d0e2094d
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/vjF46QrstMA.srt
@@ -0,0 +1,3899 @@
+1
+00:00:04,960 --> 00:00:07,640
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:07,640 --> 00:00:11,200
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:11,200 --> 00:00:17,500
+أهله وصحبه أجمعين هذه هي المحاضرة رقم 16 تحليل 
+
+4
+00:00:17,500 --> 00:00:20,980
+اقتراني أو تحليل دالي طلاب وطالبات الجامعة
+
+5
+00:00:20,980 --> 00:00:27,200
+الإسلامية. وصلنا احنا لعند الـ section الأخير في اللي 
+
+6
+00:00:27,200 --> 00:00:32,760
+هو chapter 2 وهو يمكن يعني من أحد ثمرات الـ .. الـ
+
+7
+00:00:32,760 --> 00:00:38,640
+.. الـ chapter و .. و مليء بالمعلومات اللي هو 2
+
+8
+00:00:38,640 --> 00:00:43,380
+عشرة اللي هو تحت عنوان normed spaces of operators
+
+9
+00:00:43,380 --> 00:00:47,940
+أو اللي بنسمي الـ dual space المرة الماضية احنا
+
+10
+00:00:47,940 --> 00:00:52,270
+حكينا عن الـ algebraic dual space اللي هو the space 
+
+11
+00:00:52,270 --> 00:00:58,470
+of all linear functionals. الآن بدنا نحكي عن اللي 
+
+12
+00:00:58,470 --> 00:01:05,490
+هو الـ dual space اللي بنسميه الـ space of all 
+
+13
+00:01:06,190 --> 00:01:09,910
+bounded linear functional هو اللي خليني أقول محل
+
+14
+00:01:09,910 --> 00:01:13,570
+اهتمامنا لأنه احنا بنشتغل على شيء فيه norm فهي
+
+15
+00:01:13,570 --> 00:01:17,030
+عندنا اللي هو بدنا نبدأ نشتغل على هذا الـ space 
+
+16
+00:01:17,030 --> 00:01:21,110
+اللي هنعمل فيه norm وهنشوف وكيف بدنا اللي هو
+
+17
+00:01:21,110 --> 00:01:22,710
+نحصل على هذا الـ space
+
+18
+00:01:26,910 --> 00:01:34,690
+الآن نذكركم بالـ remark التالية. B(X,Y) اللي هو رموز
+
+19
+00:01:34,690 --> 00:01:38,450
+الها بالرمز denotes as of the set of all bounded
+
+20
+00:01:38,450 --> 00:01:45,990
+linear operators لت B(X,Y) أو لـ dual space الـ X 
+
+21
+00:01:45,990 --> 00:01:49,330
+prime اللي هي bounded linear functions. أما احنا الـ
+
+22
+00:01:49,330 --> 00:01:52,630
+B(X,Y) ايش هنرمزلها؟ denote the set of all 
+
+23
+00:01:52,630 --> 00:01:58,110
+bounded linear operators من X لعند مين؟ لعند Y نتفق
+
+24
+00:01:58,110 --> 00:02:02,780
+عليا هذا اللي هو الرمز من normed space لـ normed 
+
+25
+00:02:02,780 --> 00:02:07,620
+space. هذا اللي هو الرمز. برمز اللي حكيناه الآن بدنا 
+
+26
+00:02:07,620 --> 00:02:11,680
+نعرف على اللي هي الدوال اللي موجودة هنا عمليتين
+
+27
+00:02:11,680 --> 00:02:14,980
+عملية الأولى اللي هي عملية اللي هي الـ vector
+
+28
+00:02:14,980 --> 00:02:18,560
+addition أو الـ addition لأي two elements في الـ B(X,Y)
+
+29
+00:02:18,560 --> 00:02:24,230
+بدنا نعرف اللي هو T + S كالتالي إن هو مجموعة في 
+
+30
+00:02:24,230 --> 00:02:27,290
+الدالتين عادي T زي دالة of X بيساوي T of X زي
+
+31
+00:02:27,290 --> 00:02:30,830
+دالة of X لكل X وين معله في الـ domain اللي هي
+
+32
+00:02:30,830 --> 00:02:34,230
+اللي هي الـ X اللي عندي X هنا والـ scalar
+
+33
+00:02:34,230 --> 00:02:39,490
+multiplication αT of X بتعني α في T of X 
+
+34
+00:02:39,490 --> 00:02:42,780
+اللي هي point twice بنفس الشيء for all x element in
+
+35
+00:02:42,780 --> 00:02:48,900
+X. الآن تحت هذه العمليتين هيطلع عندي B(X,Y) is a vector 
+
+36
+00:02:48,900 --> 00:02:52,180
+space. تجربوها هتلاقوها إنها تطلع عندي vector space
+
+37
+00:02:52,180 --> 00:02:56,500
+وأصلًا في أي كتاب جاب الخطة هتلاقوا اللي هو الـ set
+
+38
+00:02:56,500 --> 00:02:58,940
+هذه تحت هذول العمليتين بتطلع إن vector space
+
+39
+00:02:58,940 --> 00:03:06,140
+وسهلات والـ zero vector هو الـ zero function وكل 
+
+40
+00:03:06,140 --> 00:03:10,360
+أمور سهلة إن شاء الله نجي لأن لنظرية 2.10.1
+
+41
+00:03:10,800 --> 00:03:14,420
+اثنين عشرة واحد. صار عندنا vector space بس أنتو 
+
+42
+00:03:14,420 --> 00:03:17,380
+عارفين إن احنا شغلنا هنا احنا يعني بتجيب الـ vector
+
+43
+00:03:17,380 --> 00:03:20,760
+الـ vector space عشان نعمل الـ norm عشان نحصل على
+
+44
+00:03:20,760 --> 00:03:25,020
+normed space. اللي عندنا vector space B(X,Y) اللي
+
+45
+00:03:25,020 --> 00:03:28,240
+حكينا عنه فوق of all bounded linear operators from 
+
+46
+00:03:28,240 --> 00:03:33,280
+a normed space X into a normed space Y ماله؟ is
+
+47
+00:03:33,280 --> 00:03:38,960
+itself a normed space ونرمه مين هو النرم؟ with norm
+
+48
+00:03:38,960 --> 00:03:42,920
+defined by نرمه. نرم الـ T هو عبارة عن الـ Supremum 
+
+49
+00:03:42,920 --> 00:03:46,200
+عرفناه قبل هيك. Supremum لنرم الـ TX على نرم الـ X
+
+50
+00:03:46,200 --> 00:03:49,600
+X element in domain of T وX ده تساوي صفر أو زي ما 
+
+51
+00:03:49,600 --> 00:03:53,020
+قلنا سابقا هو Supremum لنرم TX X element in
+
+52
+00:03:53,020 --> 00:03:57,720
+domain of T ونرمات لنرمات الـ X أشماله تساوي نرمها 
+
+53
+00:03:57,720 --> 00:04:03,050
+تساوي واحدة. هذا الآن عبارة عن هيعملني normed SBS وهذا
+
+54
+00:04:03,050 --> 00:04:06,930
+الـ remark طبعًا من اللي هي النظرية من الـ remark
+
+55
+00:04:06,930 --> 00:04:10,050
+اللي فوق ومن اللي لمّة 2.7.1 اللي
+
+56
+00:04:10,050 --> 00:04:13,690
+جالتلنا إن هذا عبارة عن عشان norm فبطلع كله على
+
+57
+00:04:13,690 --> 00:04:21,020
+بعض أشماله normed SBS. إذا الـ B(X,Y) الآن الـ B(X,Y) the
+
+58
+00:04:21,020 --> 00:04:25,360
+space of all bounded linear operators مع الـ norm 
+
+59
+00:04:25,360 --> 00:04:29,660
+لـ T هذا بيعملني أو الـ norm اللي عرفناها لـ T قبل
+
+60
+00:04:29,660 --> 00:04:35,600
+شوية اللي هو بيعملني norm of this space. نيجي الآن
+
+61
+00:04:35,600 --> 00:04:43,940
+نفحص اللي هو النظرية التالية اللي يبدأ تجيبنا على 
+
+62
+00:04:43,940 --> 00:04:50,140
+سؤال متى احنا بنضمن عندي الـ B(X,Y) يكون عبارة عن بنخ
+
+63
+00:04:50,140 --> 00:04:54,660
+space عبارة عن بنخ space. النظرية بتقول التالي اطلع
+
+64
+00:04:54,660 --> 00:05:00,840
+لفوق بالـ ... أدناه. if Y is a بنخ space يعني بترمي في
+
+65
+00:05:00,840 --> 00:05:06,360
+بنخ space. if Y is a بنخ space then الـ B(X,Y) أشماله
+
+66
+00:05:06,360 --> 00:05:11,020
+is a بنخ space for any normed space من X. إذا اللي 
+
+67
+00:05:11,020 --> 00:05:14,780
+بيهمني أنا إذا كان اللي هو الـ Y norm بنخ space
+
+68
+00:05:14,780 --> 00:05:20,360
+بضمن لكم إن الـ B(X,Y) تكون أشمالها is a بنخ space عشان
+
+69
+00:05:20,360 --> 00:05:24,920
+نثبت بنخ space كالعادة بناخد قوشي sequence في هذا
+
+70
+00:05:24,920 --> 00:05:28,820
+الـ space وبنثبت إنها converges. إذا أثبتنا إنها
+
+71
+00:05:28,820 --> 00:05:32,340
+converges بتكون أشمالها اللي هي صار عندي complete 
+
+72
+00:05:32,340 --> 00:05:35,860
+إذا في البداية أكيد هقول let T<sub>n</sub> be any Cauchy
+
+73
+00:05:35,860 --> 00:05:40,760
+sequence in B(X,Y). فكرة البرهان إنه بدي أغير الحديد
+
+74
+00:05:41,230 --> 00:05:44,670
+من اللي هو الـ Cauchy Sequence (T<sub>n</sub>) في الـ (B(X,Y)) في
+
+75
+00:05:44,670 --> 00:05:50,310
+الـ (B(X,Y)) إلى الحديث إن هنحصل منها Cauchy Sequence 
+
+76
+00:05:50,310 --> 00:05:53,310
+(T<sub>n</sub>X) في الـ Y والـ Y Complete إذن Converged من
+
+77
+00:05:53,310 --> 00:05:56,790
+الأصلية اللي نجيها بعرفناها اللي هو فانكشن معينة
+
+78
+00:05:56,790 --> 00:05:59,450
+تكون هي ايش مالها؟ اللي هي Converged لها، هذه قصتنا في
+
+79
+00:05:59,450 --> 00:06:04,000
+كل البرهن، هذه برهانها، خلينا نجي للتفاصيل زي ما
+
+80
+00:06:04,000 --> 00:06:08,560
+قلنا ناخد T<sub>n</sub> إنه كوشي سيكوينس في الـ B(X,Y). إذا من 
+
+81
+00:06:08,560 --> 00:06:11,260
+تعريف الكوشي سيكوينس لاقي ε أكبر من صفر
+
+82
+00:06:11,260 --> 00:06:15,200
+there exist K element in such that نرم الـ T<sub>n</sub> 
+
+83
+00:06:15,200 --> 00:06:19,960
+ناقص T<sub>m</sub> أصغر من 100 من ε لكل أنه M أكبر من K
+
+84
+00:06:19,960 --> 00:06:26,020
+وهذا تعريف الكوشي سيكوينس. تب إن أنا then for all x
+
+85
+00:06:26,020 --> 00:06:29,800
+element in X خد لأي x element in X مدام الـ norm
+
+86
+00:06:29,800 --> 00:06:34,160
+هذا أصغر من ε بدي أحصل على ما يلي إن لكل n وم
+
+87
+00:06:34,160 --> 00:06:38,740
+أكبر من K اللي هذا صحيح إليها احسب لـ نرم T<sub>n</sub>X
+
+88
+00:06:38,740 --> 00:06:44,000
+ناقص T<sub>m</sub>X بساوي اللي هو T<sub>n</sub> ناقص T<sub>m</sub> of x من تعريف
+
+89
+00:06:44,000 --> 00:06:48,750
+اللي هو main functions أو اللي هي الـ operator بهي
+
+90
+00:06:48,750 --> 00:06:51,630
+هذه طبعًا اللي هي bounded وهذه bounded إذا أنت 
+
+91
+00:06:51,630 --> 00:06:54,910
+تنتهي مع بعض bounded إذا أكيد أصغر أو أسوأ نرم
+
+92
+00:06:54,910 --> 00:06:58,030
+الأولى في نرم التانية نرم T<sub>n</sub> نقص T<sub>m</sub> في نرم مين
+
+93
+00:06:58,030 --> 00:07:02,290
+الـ X ده إن T<sub>n</sub> نقص T<sub>m</sub> is a bounded linear operator
+
+94
+00:07:02,290 --> 00:07:09,080
+طيب الآن هذه من فوق أصغر من مين؟ من ||Y|| في ||X|| الآن ثبت
+
+95
+00:07:09,080 --> 00:07:13,180
+لي X عندك for any fixed X element in X وgiven أني 
+
+96
+00:07:13,180 --> 00:07:18,400
+الـ Y الـ Prime بدي أثبت لك الآن الـ T<sub>n</sub>X ناقص الـ T<sub>n</sub>X
+
+97
+00:07:18,400 --> 00:07:24,040
+أصغر من مين؟ من ||Y|| ده. ناخد الآن for every Y الـ Prime
+
+98
+00:07:24,040 --> 00:07:28,630
+أكبر من 0 طبعًا احنا مثلًا بنحكي عن مين؟ for fixed مين؟
+
+99
+00:07:28,630 --> 00:07:34,730
+for fixed x اه الآن بدي أثبت لك إن الـ نرم لـ T<sub>m</sub>x
+
+100
+00:07:34,730 --> 00:07:39,950
+ناقص T<sub>m</sub>x أصغر من مين؟ من ε براي. إذا أثبتت 
+
+101
+00:07:39,950 --> 00:07:43,470
+صار الـ T<sub>m</sub>x هذه نفسها ايش مالها؟ كوشي sequence 
+
+102
+00:07:43,470 --> 00:07:48,190
+لمين؟ للـ x هذه ماشي الحال. بحكي عن x arbitrary لكن
+
+103
+00:07:48,190 --> 00:07:53,680
+بحكي عن شيء محدد معايا ماشي الحال. طيب أنا لأن عندي 
+
+104
+00:07:53,680 --> 00:08:00,900
+أنا نرم الـ T<sub>n</sub> ناقص الـ T<sub>n</sub> ماله؟ أصغر من ε ماشي
+
+105
+00:08:00,900 --> 00:08:04,580
+الحال أصغر من ε. الآن الـ ε هذا الكلام صحيح
+
+106
+00:08:04,580 --> 00:08:07,940
+لأي ε في الدنيا بقدر أحصل على هذا ماشي الحال
+
+107
+00:08:07,940 --> 00:08:11,680
+الآن الـ ε prime مالها؟ بيبقى إيديا إذا أنا 
+
+108
+00:08:11,680 --> 00:08:15,940
+الـ ε هذه بقدر أزغرها جد ما بدي هذا أصغر من
+
+109
+00:08:15,940 --> 00:08:21,120
+مين؟ عندي أصغر من ε من ε. طلع عندي T<sub>n</sub>X 
+
+110
+00:08:21,120 --> 00:08:28,180
+ناقص T<sub>m</sub>X من هذه طلع عندي نرم T<sub>n</sub>X ناقص T<sub>m</sub>X ماله؟
+
+111
+00:08:28,180 --> 00:08:33,740
+أصغر من مين؟ من ε في نرم الـ X هذا اللي حصلناه 
+
+112
+00:08:33,740 --> 00:08:37,160
+وعليه أصلًا البداية التامة اللي هو 1 الآن زي ما 
+
+113
+00:08:37,160 --> 00:08:40,480
+قلنا ε prime أنت عطيتني أي ε prime بدك 
+
+114
+00:08:40,480 --> 00:08:45,920
+تعجزني مش الحال. الآن أنا هذه صحيحة لأي ε
+
+115
+00:08:45,920 --> 00:08:50,820
+مالها؟ في الدنيا إذا أنا بقدر أزغرها جد ما بدي جد
+
+116
+00:08:50,820 --> 00:08:54,640
+ما بدي. بسرعة نحكي عن نرم الـ X أشماله محدد بحيث إنه 
+
+117
+00:08:54,640 --> 00:08:58,280
+مو إن الـ ε في الـ نرم X بقدر أذاكر هذه 
+
+118
+00:08:58,280 --> 00:09:01,860
+جدًا بدي بحيث إنه يكون أصغر من مين؟ من ε
+
+119
+00:09:01,860 --> 00:09:05,720
+برايم. عطيتني ε prime ماشي الحال. بقول لك اللي 
+
+120
+00:09:05,720 --> 00:09:09,300
+هو الآن اختار الـ ε هذه تكون أضرر أصغر من
+
+121
+00:09:09,300 --> 00:09:12,140
+ε prime من نرم X بقدر لأن هذا صحيح لكل
+
+122
+00:09:12,140 --> 00:09:16,560
+مين؟ لكل ε من هذه الحالة صار عندي الـ T<sub>n</sub> ناقص 
+
+123
+00:09:16,560 --> 00:09:19,940
+الـ T<sub>n</sub>X ناقص T<sub>n</sub>X أصغر من مين؟ ε prime و
+
+124
+00:09:19,940 --> 00:09:24,350
+ε prime أصغر بترى إذا صارت عندي T<sub>n</sub>X ايش 
+
+125
+00:09:24,350 --> 00:09:28,230
+مالها؟ عبارة عن كوشي sequence وهذا الكلام بوضوح
+
+126
+00:09:28,230 --> 00:09:32,110
+هايه عندنا هنا for any fixed x and any given x أو 
+
+127
+00:09:32,110 --> 00:09:35,150
+ε prime. given ε prime we can choose
+
+128
+00:09:35,150 --> 00:09:39,190
+ε بتساوي ε<sub>x</sub> such that ε<sub>x</sub> في 
+
+129
+00:09:39,190 --> 00:09:42,710
+المهم الـ X أصغر من مين؟ من ε<sub>x</sub> ابراهيم. بقدر
+
+130
+00:09:42,710 --> 00:09:47,130
+اختار مين؟ ε اللي هي الـ arbiter الأولى اه اللي 
+
+131
+00:09:47,130 --> 00:09:49,290
+بتساوي مين؟ ε اكت اكت اكت اكت اكت اكت اكت اكت
+
+132
+00:09:49,290 --> 00:09:49,910
+اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت
+
+133
+00:09:49,910 --> 00:09:51,250
+اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت
+
+134
+00:09:51,250 --> 00:09:53,970
+اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت
+
+135
+00:09:53,970 --> 00:09:59,530
+اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت
+
+136
+00:09:59,530 --> 00:10:01,490
+اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت اكت
+
+137
+00:10:01,490 --> 00:10:07,060
+اكت. الآن هذه احنا هذا الكلام صحيح لمين؟ لأي X 
+
+138
+00:10:07,060 --> 00:10:12,800
+سميت اللي هي الـ Y اللي بتناسب الـ X اللي حتى الزمن
+
+139
+00:10:12,800 --> 00:10:17,460
+سميتها Y<sub>x</sub>. ماسمتهاش خلوها Y بس عشان تتعرف إن الـ Y 
+
+140
+00:10:17,460 --> 00:10:22,140
+اللي اخترتها تعتمد على مين؟ على الـ X اللي أنت عشان
+
+141
+00:10:22,140 --> 00:10:27,420
+تضمن أنّه ||Y - X|| هذه في norm الـX يكون أصغر من مين؟ من 
+
+142
+00:10:27,420 --> 00:10:30,300
+epsilon إبراهيم وبقدر أعمل هيك أه بقدر لأنّ فعلا الـ
+
+143
+00:10:30,300 --> 00:10:32,440
+epsilon إيه شمالها arbitrary وبختار زي ما بدي
+
+144
+00:10:32,440 --> 00:10:38,580
+بزغّرها بحيث أنّنا نحصل على اللي هي الـ norm لـ ||T<sub>n</sub>X||
+
+145
+00:10:38,580 --> 00:10:42,500
+ناقص ||T<sub>n</sub>X|| أصغر من epsilon إبراهيم hence T<sub>n</sub>X is a
+
+146
+00:10:42,500 --> 00:10:46,280
+Cauchy sequence in Y إذا حصلنا T<sub>n</sub> X شمال هيكلش
+
+147
+00:10:46,280 --> 00:10:48,820
+الـ sequence للـ Y هذا الـ X أخدناها arbitrarily
+
+148
+00:10:48,820 --> 00:10:54,060
+لكن fixed من هذه بدي أعرف الآن however Y is
+
+149
+00:10:54,060 --> 00:10:58,980
+complete إذا T<sub>n</sub> X هذه صارت converged to converged
+
+150
+00:10:58,980 --> 00:11:03,680
+إذا خلّيني أقول إنّ T<sub>n</sub> X هذه converged من Y ماشي
+
+151
+00:11:03,680 --> 00:11:11,120
+بدي أعرف الآن أنا إيش غرضي بدي ألاقي T<sub>n</sub> وتروح لـT
+
+152
+00:11:11,120 --> 00:11:15,700
+T وتكون الـ T موجودة في الـ B(X,Y) شوفوا كيف بدي
+
+153
+00:11:15,700 --> 00:11:20,060
+أعرفها بدي أعرف الـ T هي عبارة عن الأداة اللي
+
+154
+00:11:20,060 --> 00:11:26,400
+جبتها عند T of X تساوي مين؟ Y اللي هي مين؟ Y limited
+
+155
+00:11:26,400 --> 00:11:32,380
+T and X وكإني بدي أقول define T من X لعند Y by T
+
+156
+00:11:32,380 --> 00:11:36,900
+X حكي عن الـ X الـ Fix اللي أخدتها arbitrarily بثانية
+
+157
+00:11:36,900 --> 00:11:42,260
+من الـ Y اللي هي في الواقع limit من T<sub>n</sub> X وهذه الـ
+
+158
+00:11:42,260 --> 00:11:48,600
+limit موجودة وقلنا تنتقل بثانية YوY موجودة في الـ B
+
+159
+00:11:48,600 --> 00:11:52,740
+كابيتال والـ X من أين جاء؟ من الـ X التي هي كابيتال
+
+160
+00:11:52,740 --> 00:11:57,180
+إذاً الـ T تبعته اللي صارت تشتغل من X لعند مين؟
+
+161
+00:11:57,180 --> 00:12:00,640
+لعند Y بمناسبة لكم أنّ هذا الـ T عبارة عن bounded
+
+162
+00:12:00,640 --> 00:12:05,240
+وlinear بيكون وين ما له قعدت هان معناته صار عنده
+
+163
+00:12:05,240 --> 00:12:07,780
+الـ Cauchy sequence converged to some T element
+
+164
+00:12:07,780 --> 00:12:11,460
+بيكسوا Y صار بيكسوا Y is complete خلّيني أشوف
+
+165
+00:12:15,020 --> 00:12:18,620
+عرفنا الـ T زي ما قلنا لكم الآن لكلّ ... بتثبتلكم أنّها
+
+166
+00:12:18,620 --> 00:12:23,640
+Linear T Linear for any X و Z element in X and any
+
+167
+00:12:23,640 --> 00:12:27,700
+scalar Alpha خدّ للـ T و Alpha X زائد Z كيف عرفته
+
+168
+00:12:27,700 --> 00:12:31,180
+هذا؟ كيف بعرف T(Alpha X زائد Z)؟ هو عبارة عن Limit
+
+169
+00:12:31,180 --> 00:12:36,300
+T<sub>n</sub> اللي بتاخد هذه اللي هي Alpha X زائد Main زائد Z
+
+170
+00:12:36,300 --> 00:12:39,100
+من تعريف اللي قبل بشوية، كنا X أكرا Fixed لكن
+
+171
+00:12:39,100 --> 00:12:43,880
+Arbitrary إذن ويساوي الآن هذه الـ T<sub>n</sub> كلها الـ T<sub>1</sub>
+
+172
+00:12:43,880 --> 00:12:48,320
+وT<sub>2</sub> وT<sub>3</sub> وT<sub>4</sub> هي عبارة عن limits وين؟ في الـ B(X,Y)
+
+173
+00:12:48,320 --> 00:12:52,260
+وكلها شمالين linear و bounded إذن الـ Alpha بتقدر
+
+174
+00:12:52,260 --> 00:13:00,360
+تطلع مباشرة من عند اللي هو عند اللي هي Alpha بتطلع
+
+175
+00:13:00,360 --> 00:13:05,230
+من هنا فاهمين؟ وبتطلع برا مباشرة Alpha في T<sub>n</sub>X زائد
+
+176
+00:13:05,230 --> 00:13:08,590
+limit T<sub>n</sub>Z لأنّ ال limit ما لها بتتوزع زي ما أنتم
+
+177
+00:13:08,590 --> 00:13:13,070
+عارفين وهي ساوي هذه مين؟ هي عبارة عن TX وهذه مين؟ هي
+
+178
+00:13:13,070 --> 00:13:16,730
+TZ إذا صارت اللي هي Alpha TX زائد TZ يعني معناته
+
+179
+00:13:16,730 --> 00:13:21,640
+صارت T إيش ما لها؟ is linear كلام سهل هذا الآن نيجي
+
+180
+00:13:21,640 --> 00:13:27,200
+نثبت الـ boundedness لـ T أنّها T is bounded قبل ما
+
+181
+00:13:27,200 --> 00:13:31,680
+أثبت T is bounded بدي أستعين باللي فوق وأثبتلكم أنّ
+
+182
+00:13:31,680 --> 00:13:35,880
+T<sub>n</sub> ناقص T هي الـ bounded وعند T<sub>n</sub> bounded إذا
+
+183
+00:13:35,880 --> 00:13:40,660
+صارت حاصل طرح اثنين اللي هو T تطلع bounded شوفوا كام الآن
+
+184
+00:13:40,660 --> 00:13:46,960
+||T<sub>n</sub> نقص T<sub>x</sub>|| من وين بده يحصلّه؟ شوفوا الواحد خدّ لها
+
+185
+00:13:46,960 --> 00:13:50,280
+ال limit صار ال limit موجودة إحنا خدنا ال limit as M
+
+186
+00:13:50,280 --> 00:13:53,460
+goes to infinity هذا صحيح على كلّ M ... M ... M و M
+
+187
+00:13:53,460 --> 00:13:56,960
+أكبر من K من ضمنه M لما تكون أكبر من N وأكبر من K
+
+188
+00:13:56,960 --> 00:14:02,100
+وبوّدي الـ M إلى نهاية بيصير عندي الآن هذه limit as
+
+189
+00:14:02,100 --> 00:14:05,460
+M goes to infinity بيصير هذه T of X لأنّ عارفين
+
+190
+00:14:05,460 --> 00:14:08,160
+إحنا ال norm is continuous بتدخل ال limit جوا الـ
+
+191
+00:14:08,160 --> 00:14:12,750
+norm وبتطلع طبيعي وبتدخل لـ ... اللي هي عندي limit
+
+192
+00:14:12,750 --> 00:14:17,350
+T<sub>M</sub>X اللي هي بيصير T of X فاهمين اللي بحكيّه؟ صار عندي
+
+193
+00:14:17,350 --> 00:14:23,530
+لأنّ ||T<sub>n</sub> of X نقص T of X|| اللي هي أصغر من مين؟ من
+
+194
+00:14:23,530 --> 00:14:27,550
+epsilon في ||X|| أعملكوا إياها على اللوح لكي
+
+195
+00:14:27,550 --> 00:14:30,770
+تكونوا مش مستوعبين شيء اللي بقوله اللي بحكيّه أنا
+
+196
+00:14:30,770 --> 00:14:35,950
+حصلت حصلت 
+
+197
+00:14:39,410 --> 00:14:45,610
+||T<sub>n</sub>X لاقص TX|| أصغر أو يساوي Y في ||من؟||
+
+198
+00:14:45,610 --> 00:14:50,050
+للـ X، T<sub>n</sub> اللي أنا بتدخّلي اللي أنا بتروح إلى مين؟
+
+199
+00:14:50,050 --> 00:14:53,050
+إلينا للهيئة as N goes to infinity بيصير هذا الـ
+
+200
+00:14:53,050 --> 00:14:59,380
+limit ن أخذ M أكبر من N وهي أكبر أو يساوي مين؟ كما
+
+201
+00:14:59,380 --> 00:15:03,060
+صحيح لكلّ أمها من ضمنها دولة الآن ودّي M لنهاية
+
+202
+00:15:03,060 --> 00:15:05,820
+ما لهاش علاقة N ضالتها زي ما هي ما لهاش علاقة فيها
+
+203
+00:15:05,820 --> 00:15:09,120
+مين اللي بده يوديها لما لنهاية؟ M إذا بيصير T<sub>n</sub>
+
+204
+00:15:09,120 --> 00:15:13,440
+X ناقص لما ال limit تخش هنا as m goes to
+
+205
+00:15:13,440 --> 00:15:17,360
+infinity بتصير إيش؟ بتساوي T X أنّ أثبتنا limit T<sub> </sub>
+
+206
+00:15:17,360 --> 00:15:21,920
+M X as m goes to infinity بساوي اللي هو T X
+
+207
+00:15:21,920 --> 00:15:26,810
+اللي سميناها قبل شوية إيش اسمها؟ هذا بيصير أصغر أو
+
+208
+00:15:26,810 --> 00:15:28,190
+يساوي أو يساوي أو يساوي أو يساوي أو يساوي أو يساوي
+
+209
+00:15:28,190 --> 00:15:30,750
+أو يساوي أو يساوي أو يساوي أو يساوي أو يساوي أو
+
+210
+00:15:30,750 --> 00:15:31,590
+يساوي أو يساوي أو يساوي أو يساوي أو يساوي أو يساوي
+
+211
+00:15:31,590 --> 00:15:32,650
+أو يساوي أو يساوي أو يساوي أو يساوي أو يساوي أو
+
+212
+00:15:32,650 --> 00:15:35,550
+يساوي أو يساوي أو يساوي أو يساوي أو يساوي أو يساوي
+
+213
+00:15:35,550 --> 00:15:35,990
+أو يساوي أو يساوي أو يساوي أو يساوي أو يساوي أو
+
+214
+00:15:35,990 --> 00:15:43,180
+يساوي أو يساوي أو يساوي بناء عليه ||T<sub>n</sub>-T of X||
+
+215
+00:15:43,180 --> 00:15:47,660
+إيش بتساوي؟ ||T<sub>n</sub> X نقص TX||، حسبتها دي هذه اللي
+
+216
+00:15:47,660 --> 00:15:50,540
+أثبتناها إيش ما لها؟ أصغر من Y في مين؟ في الـ||X||
+
+217
+00:15:50,540 --> 00:15:55,420
+هذا معناته، هذه مع هذه معناته أنّ ||T<sub>n</sub>-T<sub>n</sub>|| بيشمّلها
+
+218
+00:15:55,420 --> 00:16:01,050
+bounded operator إذا صار عندي الآن ||T<sub>n</sub> ناقص T|| is a
+
+219
+00:16:01,050 --> 00:16:05,230
+bounded operator هذا لكلّ مين؟ لكلّ N أكبر من مين؟ من
+
+220
+00:16:05,230 --> 00:16:08,630
+K لكن أنا بعرف أنّ الـ T<sub>n</sub> كل واحدة فيها is bounded
+
+221
+00:16:08,630 --> 00:16:13,490
+إذا الـ T بيساوي T<sub>n</sub> ناقص T<sub>n</sub> ناقص T<sub>n</sub> برضه مش هتكون
+
+222
+00:16:13,490 --> 00:16:17,970
+bounded ومن ثمّ الـ T صارت عبارة عن Linear فوق و
+
+223
+00:16:17,970 --> 00:16:22,730
+bounded then T element in B(X,Y) من اتنين من اتنين
+
+224
+00:16:22,730 --> 00:16:30,590
+اللي إحنا وصلنا إلى هنا اللي هو for all n أكبر من K
+
+225
+00:16:30,590 --> 00:16:35,950
+||T<sub>n</sub> ناقص الـ T|| إيش بيساوي؟ يعني أخذوا
+
+226
+00:16:35,950 --> 00:16:39,250
+الـ Supremum بيساوي الـ Supremum للنورم هذا اللي
+
+227
+00:16:39,250 --> 00:16:41,830
+هو أصغر إيه بيساوي مين؟ الـ Supremum على مين؟ على
+
+228
+00:16:41,830 --> 00:16:44,470
+النورمات اللي بيساوي واحد فلما أخذوا الـ Supremum
+
+229
+00:16:44,470 --> 00:16:49,480
+بين هذه وبين هذه والـ ||X|| بساوي 1 فبيصير
+
+230
+00:16:49,480 --> 00:16:51,960
+الـ Supremum لهذه أصغر أو ساوي اللي هو الـ
+
+231
+00:16:51,960 --> 00:16:56,380
+Epsilon، مظبوط؟ الـ Supremum هو تعريف الـ ||T<sub>n</sub>||
+
+232
+00:16:56,380 --> 00:17:01,840
+اللي هو ||T<sub>n</sub> ناقص T|| صار ||T<sub>n</sub> ناقص T|| بيساوي اللي هو
+
+233
+00:17:01,840 --> 00:17:06,280
+هذا المقدار أصغر أو ساوي Epsilon وهذا معناته أنّ
+
+234
+00:17:06,280 --> 00:17:10,060
+جينا أخذنا أيّ Epsilon في الدنيا لجينا K بحيث لأ كلّ
+
+235
+00:17:10,060 --> 00:17:15,610
+N أكبر من K ||T<sub>n</sub> نقص T|| normalها أصغر من epsilon وهذا
+
+236
+00:17:15,610 --> 00:17:19,650
+تعريف أنّ T<sub>n</sub> converges لـT Therefore صار عندي الـ
+
+237
+00:17:19,650 --> 00:17:22,070
+Cauchy sequence الـ arbitrary اللي أخدتها في B(X,Y)
+
+238
+00:17:22,070 --> 00:17:28,130
+راحت لـT في B(X,Y) ومعناته أنّ صار B(X,Y) is a complete
+
+239
+00:17:28,130 --> 00:17:38,480
+normed space اللي بعده الآن بدنا نرجع نرجع زي الراجعة
+
+240
+00:17:38,480 --> 00:17:41,600
+اللي فعلناها المرة اللي فاتت بدل ما نحكي عن الـ
+
+241
+00:17:41,600 --> 00:17:44,880
+algebraic dual space اللي هو the space of all
+
+242
+00:17:44,880 --> 00:17:50,780
+bounded linear functionals بدنا ناخذ الآن the
+
+243
+00:17:50,780 --> 00:17:54,480
+space of all bounded linear functionials وهذا اللي
+
+244
+00:17:54,480 --> 00:18:00,340
+بنسميه الـ dual space وبدنا نرمز له بعد إذنكم بالرمز
+
+245
+00:18:00,340 --> 00:18:07,350
+X'  الدفينيشن التالي let X be a normed space then
+
+246
+00:18:07,350 --> 00:18:10,610
+the set of all bounded linear functionals on X
+
+247
+00:18:10,610 --> 00:18:16,530
+constitutes a normed space أكيد لأنّه حالة خاصة من
+
+248
+00:18:16,530 --> 00:18:19,330
+اللي فوق اللي عندنا الـ ... الـ ... الـ هذا بيصير الـ
+
+249
+00:18:19,330 --> 00:18:21,630
+... الـ ... الـ ... الـ space of all bounded functional
+
+250
+00:18:21,630 --> 00:18:25,770
+دي عارفين هو ... مين هو؟ هذا الـ space اللي عناصره
+
+251
+00:18:25,770 --> 00:18:31,050
+اللي هو B(X,F) والـ scalar field يعني بمعنى آخر و
+
+252
+00:18:31,050 --> 00:18:33,750
+الـ scalar field سواء الـ R أو الـ C is a complete ...
+
+253
+00:18:33,750 --> 00:18:38,050
+complete normed space إذن أكيد كلّه على بعض شماله
+
+254
+00:18:38,050 --> 00:18:44,500
+هيَطلع normed space وهنرمز له بالرمز X' إذا أنّ X' هو the
+
+255
+00:18:44,500 --> 00:18:47,820
+dual space of X which is the set of all bounded
+
+256
+00:18:47,820 --> 00:18:52,300
+linear functionals on X which is a normed space
+
+257
+00:18:53,840 --> 00:18:56,400
+Constitute a normed space with norm defined by
+
+258
+00:18:56,400 --> 00:18:59,720
+||F|| هو نفسه |||F(X)||| عن ||X||
+
+259
+00:18:59,720 --> 00:19:02,460
+الـ X لما الـ X تساوي صفر هو اللي هو نفسه the
+
+260
+00:19:02,460 --> 00:19:04,580
+supremum of the absolute value of F of X أو المدلس
+
+261
+00:19:04,580 --> 00:19:07,820
+X المدلس من X و||X|| تساوي 1 which is
+
+262
+00:19:07,820 --> 00:19:12,120
+called the dual space of X and is denoted by مين؟
+
+263
+00:19:12,120 --> 00:19:16,280
+X' وهي النظرية the dual space X' of a normed space
+
+264
+00:19:16,280 --> 00:19:20,200
+X إذا normed space هذا من automatic من مين؟ من اللي
+
+265
+00:19:20,200 --> 00:19:24,590
+حكيته اللي هي النظرية اللي جاب بشوية اِطلع لفوق نيجي
+
+266
+00:19:24,590 --> 00:19:32,970
+لأنّ لكيفية إثبات اللي هو كده is a dual space أو
+
+267
+00:19:32,970 --> 00:19:38,970
+كده يعني بدنا نشوف كيف نثبت الـ dual space لأمثلة
+
+268
+00:19:38,970 --> 00:19:44,170
+أول واحد بدنا ناخده مين؟ الـ ℝ<sup>n</sup> بدنا نثبتلكم أنّ الـ
+
+269
+00:19:44,170 --> 00:19:50,990
+dual space of ℝ<sup>n</sup> is ℝ<sup>n</sup> شو معناته؟ عشان ندخل للأمر
+
+270
+00:19:50,990 --> 00:20:00,390
+بدنا نبدأ أثبتلكم ثلاث شغلات أو ثلاث أمثلة اللي هو
+
+271
+00:20:00,390 --> 00:20:14,790
+نقول واحد the dual space of ℝ<sup>n</sup> is ℝ<sup>n</sup> هاي واحد اتنين
+
+272
+00:20:14,790 --> 00:20:23,780
+the dual space of L<sup>1</sup> is L<sup>∞</sup> هذه اتنين تلاتة
+
+273
+00:20:23,780 --> 00:20:31,800
+the dual space of L<sup>p</sup> is L<sup>q</sup> حيث 1/p + 1/
+
+274
+00:20:31,800 --> 00:20:37,270
+q بسوء إيش؟ بسوء 1 العنوان شو معناته؟ اللي هو
+
+275
+00:20:37,270 --> 00:20:42,490
+dual space of ℝ<sup>n</sup> اللي هو عبارة عن ℝ<sup>n</sup> إيش ماله؟
+
+276
+00:20:42,490 --> 00:20:46,330
+البراهي اللي هو the space of all bounded linear
+
+277
+00:20:46,330 --> 00:20:51,010
+functionals from ℝ<sup>n</sup> to the scalar field بتاعها،
+
+278
+00:20:51,010 --> 00:20:56,140
+ماشي الحال الآن بتثبتوا لكم أنّ ℝ<sup>n'</sup> هو مين؟ هو ℝ<sup>n</sup> هو
+
+279
+00:20:56,140 --> 00:21:03,960
+في الواقع بتثبت أنّ في isomorphism F من عند ℝ<sup>n'</sup>
+
+280
+00:21:04,440 --> 00:21:08,980
+لعند مين؟ لعند ℝ<sup>n</sup> إيش الـ isomorphism هذا؟ الـ 
+
+281
+00:21:08,980 --> 00:21:13,560
+isomorphism one-to-one onto function هذي اللي
+
+282
+00:21:13,560 --> 00:21:17,600
+بتحافظ زي ما قلنا عن cardinality هاي واحد اثنين
+
+283
+00:21:17,600 --> 00:21:23,040
+اللي هو preserve the norm يعني F of اللي هو الشيء
+
+284
+00:21:23,040 --> 00:21:27,940
+اللي هنا F أو نسميه C هو T  مش مشكلة T of أي
+
+285
+00:21:27,940 --> 00:21:32,380
+element هنا الـ element اللي هنا دوال T of F مثلا
+
+286
+00:21:32,380 --> 00:21:38,510
+norm بتساوي norm الـ F  ماشي اللي هي الـ Isometry
+
+287
+00:21:38,510 --> 00:21:40,490
+اللي سمناها اللي هي في الواقع على طول بتطلع لنا
+
+288
+00:21:40,490 --> 00:21:45,310
+one-to-one الشغل الثالثة اللي هو preserve the norm
+
+289
+00:21:45,310 --> 00:21:49,510
+و preserve the cardinality والشغل الثالثة اللي هي
+
+290
+00:21:49,510 --> 00:21:52,930
+عالمنا عالمنا اللي متكون من الـ RN براميل العمليات
+
+291
+00:21:52,930 --> 00:21:56,030
+الحسابية اللي عليها يعني preserve of العمليات
+
+292
+00:21:56,030 --> 00:21:58,410
+الحسابية اللي هي عبارة عن مين الـ scalar
+
+293
+00:21:58,410 --> 00:22:01,770
+multiplication و الـ vector addition يعني T of
+
+294
+00:22:01,770 --> 00:22:08,690
+Alpha F زائد G اللي هو بتثبتها L TAlpha of T F زي
+
+295
+00:22:08,690 --> 00:22:14,050
+الـ T mean اللي هو إيش الـ G ماشي معايا يا جماعة
+
+296
+00:22:14,050 --> 00:22:18,450
+هاي الآن فلسفة اللي هي إثبات أنه الـ Dual space of
+
+297
+00:22:18,450 --> 00:22:21,790
+RN اللي هو RN يعني بما هو أصلا شو معناه الـ
+
+298
+00:22:21,790 --> 00:22:25,870
+isomorphism أنه بس هذا هو هذا بس اتغيرت الأسامي 
+
+299
+00:22:25,870 --> 00:22:29,570
+هذا أساميهم العناصر F وهذا اسم هي إيش اللي هو
+
+300
+00:22:29,570 --> 00:22:34,100
+Untables ماشي الحال، إذًا اللي هي بس ما هي إلا غير
+
+301
+00:22:34,100 --> 00:22:39,400
+تغيير أسماء أما هو التركيبة الجبرية والتركيبة ال
+
+302
+00:22:39,400 --> 00:22:41,480
+... ال ... ال ... ال ... ال ... ال ... بالنسبة لعدد
+
+303
+00:22:41,480 --> 00:22:44,780
+العناصر أو الـ cardinality وبالنسبة للتركيبة
+
+304
+00:22:44,780 --> 00:22:49,540
+التوبولوجية هي نفسها تمامًا واضح شو معناه اللي هو
+
+305
+00:22:49,540 --> 00:22:55,080
+الـ isomorphism؟ طيب لو كان عندنا الـ structure مش 
+
+306
+00:22:55,080 --> 00:22:57,300
+اللي هو vector space لو الـ structure اللي هو
+
+307
+00:22:57,300 --> 00:23:00,860
+الجبري كان عندنا group أو ... أو ... أو ring أو كده
+
+308
+00:23:00,860 --> 00:23:04,840
+بيبدأ تنجل اللي هي عملية الـ group إلى العملية اللي
+
+309
+00:23:04,840 --> 00:23:08,020
+عاجبالها و تنجل اللي هو اللي لو كانت ring بيبدأ
+
+310
+00:23:08,020 --> 00:23:12,460
+تنجل لعمليتين لأ، لأ، لأ، عمليتين ولو كانت بنخ
+
+311
+00:23:12,460 --> 00:23:14,920
+الجبريان تنجي الـ vector space مع vector space
+
+312
+00:23:14,920 --> 00:23:18,780
+وبعدين اللي هو عملية الضرب وعملية اللي هو ال ... ال
+
+313
+00:23:18,780 --> 00:23:21,100
+... ال ... ال ... الـ vector addition كلها تنجي لها بنفس
+
+314
+00:23:21,100 --> 00:23:23,860
+الاسم وبعدين ال ... التشاكل اللي خلينا نقول ال
+
+315
+00:23:23,860 --> 00:23:28,300
+isomorphism ما هو اللي ... التركيبتين أو ال ... ال
+
+316
+00:23:28,300 --> 00:23:32,400
+... العالمين هن نفسهم بس اختلفت في الأسماء يلا نيجي
+
+317
+00:23:32,400 --> 00:23:34,920
+اللي موضوعناه الكلام اللي حكيته مهم لإنه على أساس
+
+318
+00:23:35,760 --> 00:23:38,060
+بلخص لك كل الدنيا اللي هي بما يتعلق بالـ
+
+319
+00:23:38,060 --> 00:23:40,780
+isomorphism في الجبر في الـ topology و في غيره و
+
+320
+00:23:40,780 --> 00:23:44,060
+حتى في الـ 6 يوري في كل الأماكن اللي أنت بدك كتبت
+
+321
+00:23:44,060 --> 00:23:46,820
+فيها اللي هو اثنين متكافئين
+
+322
+00:23:49,470 --> 00:23:53,130
+Space RN كما قلنا الـ dual space of RN is RN نعرف
+
+323
+00:23:53,130 --> 00:23:57,970
+إنها إيش دييتها إنه بدنا نجي لها function T من RN
+
+324
+00:23:57,970 --> 00:24:00,550
+الـ prime لعند RN تكون one-to-one و one-to-one onto
+
+325
+00:24:00,550 --> 00:24:03,090
+preserve the norm و preserve اللي هو main
+
+326
+00:24:03,090 --> 00:24:05,730
+operations
+
+327
+00:24:07,520 --> 00:24:12,440
+Since Rn is of finite dimensional قلنا الـ finite
+
+328
+00:24:12,440 --> 00:24:15,900
+dimensional Rn finite dimensional في النظرية 2.78
+
+329
+00:24:15,900 --> 00:24:20,340
+المرة الفاتتة قلنا الـ Rn star هتكون هي الـ Rn
+
+330
+00:24:20,340 --> 00:24:24,340
+prime إيش يعني؟ مش قلنا إنه لو كانت Rn اللي هي
+
+331
+00:24:24,340 --> 00:24:27,620
+finite dimensional أي linear operator عليها إيش
+
+332
+00:24:27,620 --> 00:24:33,350
+هيكون؟ bounded Bounded Any linear operator on a
+
+333
+00:24:33,350 --> 00:24:36,350
+finite dimensional space is bounded خدناها المرة
+
+334
+00:24:36,350 --> 00:24:41,370
+الفاة اللي هو إذا كان عند T من finite dimensional
+
+335
+00:24:41,370 --> 00:24:45,850
+space اللي هو إلى برمئهان إذا كان هذا finite
+
+336
+00:24:45,850 --> 00:24:48,930
+dimensional space كل سنة متسلمين بتكون الـ T إذا
+
+337
+00:24:48,930 --> 00:24:54,190
+linear على طول أشمالها is bounded بما أن عليه ليس
+
+338
+00:24:54,190 --> 00:25:00,030
+هناك فرق في هذه الحالة بين الـ algebraic dual space
+
+339
+00:25:00,450 --> 00:25:04,130
+والـ Dual Space تبعنا، يعني لا فرق بين The space
+
+340
+00:25:04,130 --> 00:25:07,450
+of all bounded linear operators و The space of all
+
+341
+00:25:07,450 --> 00:25:11,430
+linear functional و The space of all linear
+
+342
+00:25:11,430 --> 00:25:14,970
+functional لا فرق بينهما لأن Any linear functional
+
+343
+00:25:14,970 --> 00:25:18,930
+in a finite dimensional space is a bounded linear
+
+344
+00:25:18,930 --> 00:25:23,510
+functional إذا الحديث هنا أو الحديث هنا سيان So
+
+345
+00:25:23,510 --> 00:25:30,270
+that for any f element in Rn star أو Rn prime اللي
+
+346
+00:25:30,270 --> 00:25:34,210
+هو can be represented as f of x بيساوي summation
+
+347
+00:25:34,210 --> 00:25:40,830
+xi i gamma i j من واحد لعند n for any x بتساوي
+
+348
+00:25:40,830 --> 00:25:45,850
+summation xi j ej j من عند واحد لعند n أي ... أي ... أي
+
+349
+00:25:45,850 --> 00:25:48,910
+... أي ... أي function bounded linear ... أو linear
+
+350
+00:25:48,910 --> 00:25:52,030
+function هتكون bounded ومن ثم الـ F of X هتكون
+
+351
+00:25:52,030 --> 00:25:55,590
+الصورة هذه إيش هذا اللي كاتبينه؟ هذا يمكن أنتم
+
+352
+00:25:55,590 --> 00:26:00,250
+مستغربينه والـ Gamma K هذه مين هي؟ F of EK والـ
+
+353
+00:26:00,250 --> 00:26:04,190
+E1 والـ E2 الـ EN is the basis for mean RN هذا
+
+354
+00:26:04,190 --> 00:26:12,410
+الكلام ... الكلام سهل إيش هو؟ احنا لو جينا أخدنالو
+
+355
+00:26:12,410 --> 00:26:17,510
+جينا أخدنا أي element في الارئان طبعًا الـ basis
+
+356
+00:26:17,510 --> 00:26:21,710
+تبعت الارئان عارفينها E1 E2 عند الـ E1 وعارفينها E1
+
+357
+00:26:21,710 --> 00:26:25,250
+اللي هي بارعن واحد والباقي صفار الثانية 01 و
+
+358
+00:26:25,250 --> 00:26:31,230
+الباقي صفار الـ A الأخيرة 00000 وآخر 111 هذه الـ
+
+359
+00:26:31,230 --> 00:26:37,560
+basis تبعها يعني لو أخدنا أي X بتساوي XI واحد و XI
+
+360
+00:26:37,560 --> 00:26:41,720
+اثنين عند XI N هي في الواقع إيش هنعملها؟ بنقدر
+
+361
+00:26:41,720 --> 00:26:47,200
+نقولها بتساوي الصميجين XI I في EI I من عند واحد
+
+362
+00:26:47,200 --> 00:26:51,440
+لعند مين لعندها، مظبوط ولا لأ؟ لأن بيصير XI واحد
+
+363
+00:26:51,440 --> 00:26:55,500
+في هذه بتيجي XI واحد زاد XI اثنين في هذه اللي هي
+
+364
+00:26:55,500 --> 00:26:59,120
+بيصير يجي XI اثنين مجوحا كلهم بيطلع مين اللي هي
+
+365
+00:26:59,120 --> 00:27:04,860
+اللي فوق الآن الـ TX اللي هي ... لو أخدنا F في الـ
+
+366
+00:27:04,860 --> 00:27:09,300
+RN برايم أو الـ RN ستار هذه Linear، مدام Linear،
+
+367
+00:27:09,300 --> 00:27:13,180
+إذا نحن نقول تصير F of X بتساوي الـ F هتدخل على
+
+368
+00:27:13,180 --> 00:27:15,980
+summation، هو Linear، ماشي الحالة بتساوي الـ
+
+369
+00:27:15,980 --> 00:27:20,420
+Summation إكساي I Scalar، بتطلع منها برا، وهذا
+
+370
+00:27:20,420 --> 00:27:25,320
+الـ EI هو الـ Vector فبصير إكساي I في F of EI، I من
+
+371
+00:27:25,320 --> 00:27:30,870
+عند واحد لعند أن Y ساوي summation XII وهذا يسميه
+
+372
+00:27:30,870 --> 00:27:36,570
+كمين أنا Gamma I I من عند واحد لعندنا إذن يا جماعة
+
+373
+00:27:36,570 --> 00:27:42,630
+أي X في داخل الـ RN اللي هو بقدر أكتب الـ F of X
+
+374
+00:27:42,630 --> 00:27:46,850
+على الصورة هذه اللي هي في الواقع F of X بيساوي XII
+
+375
+00:27:46,850 --> 00:27:52,710
+في F of EI أو EJ و EJ سميتها مين أنا الـ EK الـ Gamma
+
+376
+00:27:52,710 --> 00:27:57,230
+K بيساوي F of EK اتفقنا؟ طيب
+
+377
+00:27:59,130 --> 00:28:04,850
+By cautious words and quality بدنا نحصل مالي نشوف
+
+378
+00:28:04,850 --> 00:28:08,410
+إيش اللي يدنيها طبعًا أنا وين رايح رايح بدي اثبت لكم
+
+379
+00:28:08,410 --> 00:28:12,130
+T أنا أجيكم T أنا أجيكم أقول لكم إيش الـ T هذي
+
+380
+00:28:12,130 --> 00:28:19,510
+نعرفها من RN برايم أو star لعين مين أرقن وبديها
+
+381
+00:28:19,510 --> 00:28:26,130
+تنجلي T للـ F نورمها يساوي نورمين الـ F لنشوف كيف
+
+382
+00:28:26,130 --> 00:28:29,330
+نحصل عليها هتلاقوا أسلوب الحل هنا وأسلوب الحل في
+
+383
+00:28:29,330 --> 00:28:33,430
+اللي بعده واللي بعده روحه واحد مع تفاصيل كل واحدة
+
+384
+00:28:33,430 --> 00:28:39,090
+بما يناسبها الآن خدوا الـ absolute value لـ F of X هي
+
+385
+00:28:39,090 --> 00:28:42,250
+الـ absolute value لهدي صح ولا لأ أكيد بالـ triangle
+
+386
+00:28:42,250 --> 00:28:45,550
+inequality أصغر أو يساوي الصممشي لـ absolute values
+
+387
+00:28:45,550 --> 00:28:48,430
+مظبوط اللي هي الـ absolute value الأولى في الـ
+
+388
+00:28:48,430 --> 00:28:51,650
+absolute value الثانية هذه الآن بالـ Schwarz
+
+389
+00:28:51,650 --> 00:28:55,510
+inequality Schwarz inequality أصغر أو يساوي اللي هو
+
+390
+00:28:55,510 --> 00:28:59,390
+الصممشي لهذا تربيع قص نص في الصممشي لهذا تربيع قص
+
+391
+00:28:59,390 --> 00:29:02,230
+إيش احفظوا هذه Schwarz inequality اللي استخدمناها
+
+392
+00:29:02,230 --> 00:29:07,020
+كثير اللي هي هذه في الواقع اللي هي مين هي Norm الـ
+
+393
+00:29:07,020 --> 00:29:11,160
+X الـ XI واحد، XI اثنين، XI N الـ N norm هي إيش
+
+394
+00:29:11,160 --> 00:29:13,940
+مالها؟ جدري التربيع إلى هذا تربيع، زاد هذا تربيع،
+
+395
+00:29:13,940 --> 00:29:17,360
+زاد هذا تربيع، زاد هذا تربيع، زاد هذا تربيع، زاد
+
+396
+00:29:17,360 --> 00:29:17,660
+هذا تربيع، زاد هذا تربيع، زاد هذا تربيع، زاد هذا
+
+397
+00:29:17,660 --> 00:29:18,040
+تربيع، زاد هذا تربيع، زاد هذا تربيع، زاد هذا
+
+398
+00:29:18,040 --> 00:29:21,200
+تربيع، زاد هذا تربيع، زاد هذا تربيع، زاد هذا
+
+399
+00:29:21,200 --> 00:29:24,520
+تربيع، زاد هذا تربيع، زاد هذا تربيع مدلص لو كتبنا مدلص
+
+400
+00:29:24,520 --> 00:29:28,080
+بيه عشان نحمي ظهرنا إنّها تكون إيش مالها لو ... لو
+
+401
+00:29:28,080 --> 00:29:31,520
+... لو real تنفع على الـ real و لو مش real complex
+
+402
+00:29:31,520 --> 00:29:35,380
+عشان تصير إيه لإنه هذا أصغر أو شوي يعني order و
+
+403
+00:29:35,380 --> 00:29:37,960
+الـ order ما فيش في الـ order في الـ complex الـ order
+
+404
+00:29:37,960 --> 00:29:43,600
+بين مين بين المدوسات تبعات الـ complex فاهمين طيب،
+
+405
+00:29:43,600 --> 00:29:48,120
+هذا إيش اسمه؟ Normal X وهذه خلّوها لحالها زي هيك،
+
+406
+00:29:48,120 --> 00:29:54,880
+ماشي لحال إذا الآن لو أخدنا Normal F هو عبارة عن
+
+407
+00:29:54,880 --> 00:29:58,340
+الـ Supremum لـ Absolute Value of X X Element X لم
+
+408
+00:29:58,340 --> 00:30:02,310
+نورمات ليش بساويها واحد ماشي إذا أنا أخدت من هدولة
+
+409
+00:30:02,310 --> 00:30:06,270
+لنرمات اللي X بيساوي واحد صارت absolute value أصغر
+
+410
+00:30:06,270 --> 00:30:09,530
+أو يساوي هذه لحالة ماشي إذا صار الآن الـ supremum
+
+411
+00:30:09,530 --> 00:30:14,870
+إلهم أصغر أو يساوي هذه إذا صار norm الـ F بساوي
+
+412
+00:30:14,870 --> 00:30:18,310
+اللي هو الـ supremum ده ما هو هذا الـ F عبارة عن
+
+413
+00:30:18,310 --> 00:30:21,050
+bounded linear function اللي من وين جاية من R
+
+414
+00:30:21,050 --> 00:30:25,720
+النبرانو Normها معرف عرفناها قبل شوية و خلاص
+
+415
+00:30:25,720 --> 00:30:31,480
+عرفناها سنة الآن نشتغلوا كسلوك Norm الـ F أصغر أو
+
+416
+00:30:31,480 --> 00:30:36,860
+يساوي اللي هو هذا الآن however اطلعي لفوق however
+
+417
+00:30:36,860 --> 00:30:42,360
+الآن Norm الـ F أصلا اللي هو عبارة عن الـ supremum
+
+418
+00:30:42,360 --> 00:30:47,520
+لهم مظبوط الـ supremum لكل هذول إذا أكبر أو يساوي
+
+419
+00:30:47,520 --> 00:30:51,840
+واحدة منهم، مين اختارت بس اللي هي الـ Alpha I أفه
+
+420
+00:30:51,840 --> 00:30:57,460
+في Alpha I على Norm Alpha I معايا اللي هي بتساوي 
+
+421
+00:30:57,460 --> 00:31:01,320
+هذا الـ absolute value أيها عبارة عن summation
+
+422
+00:31:01,320 --> 00:31:05,990
+Alpha I في Alpha I مشكلة تعريف اللي عرفناها قبل
+
+423
+00:31:05,990 --> 00:31:09,890
+شوية اللي هو Alpha A هذي لما كانت X بتساوي Xi 1,
+
+424
+00:31:09,970 --> 00:31:14,170
+Xi 2, Xi N كان الـ F of X هو عبارة عن Xi I فهذه لما
+
+425
+00:31:14,170 --> 00:31:17,690
+الـ X صارت Gamma 1, Gamma 2, Gamma N اللي هي هذه
+
+426
+00:31:17,690 --> 00:31:22,080
+بالظبط صارت عندي F of X بتساوي Gamma اللي مفهومين
+
+427
+00:31:22,080 --> 00:31:27,160
+في حالها صارت منها Gamma تربيع واضح إذا صار عندي
+
+428
+00:31:27,160 --> 00:31:32,700
+اللي هي الـ F لأبسوليو دويله F of Xi F of Gamma I F
+
+429
+00:31:32,700 --> 00:31:36,840
+of Gamma I هذي اللي هي Gamma I هي اللي هي Gamma 
+
+430
+00:31:36,840 --> 00:31:40,740
+الـ an interest Gamma 1 Gamma 2 اللي عند Gamma I
+
+431
+00:31:40,740 --> 00:31:43,900
+إيش بتساوي الـ summation لـ Gamma K تربيع K من واحد
+
+432
+00:31:43,900 --> 00:31:47,080
+لأن ده زي ما وضحت على norm هذي اللي هي تربيع أسمين
+
+433
+00:31:47,080 --> 00:31:50,660
+أص نص هذه أس واحد وهذه أس نص بيصير إيه شماله؟ له أس
+
+434
+00:31:50,660 --> 00:31:55,080
+نص يعني وكأني بقوله norm للأف مرة أكبر أو ساوي
+
+435
+00:31:55,080 --> 00:31:57,340
+وجاب الأف بتنا أف أصغر أو ساوي أو نورم أو أصغر أو
+
+436
+00:31:57,340 --> 00:32:01,260
+ساوي إذا بالظبط الـ norm للأف هو هذا وهذا هو أصلا
+
+437
+00:32:01,260 --> 00:32:04,820
+norm مين؟ norm لـ Gamma K لأن Gamma K اللي هي Gamma 
+
+438
+00:32:04,820 --> 00:32:07,540
+1 Gamma 2 اللي عند Gamma E هي إيش N يعني N
+
+439
+00:32:07,540 --> 00:32:10,660
+interest يعني element في الـ R إذا صارت norm للأف
+
+440
+00:32:10,660 --> 00:32:16,730
+بتساوي النورم هذه لاحظوا أن هذه الـ Gamma 1 Gamma 2
+
+441
+00:32:16,730 --> 00:32:22,610
+Gamma N التي هي Gamma I Gamma 1 Gamma 2 لعند Gamma
+
+442
+00:32:22,610 --> 00:32:26,290
+N هي اللي سمناها .. طبعا جيبنا Gamma 1 احنا سمناها
+
+443
+00:32:26,290 --> 00:32:31,670
+لمين؟ اللي عندنا F of E واحد سمناها Gamma 1 و F of 
+
+444
+00:32:31,670 --> 00:32:37,600
+E 2 Gamma 2 لعند F of E N واضح إن هدولة وين
+
+445
+00:32:37,600 --> 00:32:42,580
+موجودات؟ في الـ RN وانا دلوقتي إيش أعمل؟ أجيب
+
+446
+00:32:42,580 --> 00:32:52,170
+function T من RN' لعند مين RN ولاحظوا إنه هذه اللي
+
+447
+00:32:52,170 --> 00:32:56,490
+معتمدة أمين على الـ F وكأن أنا جاية بفرش عشان
+
+448
+00:32:56,490 --> 00:33:02,630
+أقولكم خدوا الـ T للـ F اللي هي Rm' إيش بتساوي F of
+
+449
+00:33:02,630 --> 00:33:09,230
+E1, F of E2 لعند F of Em اللي هي في الواقع عبارة
+
+450
+00:33:09,230 --> 00:33:12,950
+عن Gamma 1, Gamma 2, Gamma N يعني ويساوي Gamma K
+
+451
+00:33:12,950 --> 00:33:16,760
+اللي هنا K من 1 لعند مين لعند أنتوهذا هو ان كله
+
+452
+00:33:16,760 --> 00:33:21,120
+موجود في الـ RN فالان انا رسيت على الأمر ان الـ 
+
+453
+00:33:21,120 --> 00:33:26,080
+function المناسبة لتعريفها من RN' لعند RN اللي هي
+
+454
+00:33:26,080 --> 00:33:32,010
+عبارة عن مين TF بتساوي اللي هي الـuntables F of EK
+
+455
+00:33:32,010 --> 00:33:36,830
+ويسوي اللي هي Gamma K لاحظوا أنا ضربت كل الصفيف في
+
+456
+00:33:36,830 --> 00:33:41,670
+حجر واحد ان هو من هذا التعريف لاجئت انه norm of TF
+
+457
+00:33:41,670 --> 00:33:45,490
+من اللي حكيته قبل شوية يسوي norm هذه اللي هو إيش
+
+458
+00:33:45,490 --> 00:33:50,350
+بيساوي norm ال F ماشي الحال هي أثبته نورم الـ F
+
+459
+00:33:50,350 --> 00:33:54,010
+بيساوي هذه وانا عرفت T of F بيساوي هذه إذا نورم
+
+460
+00:33:54,010 --> 00:33:58,070
+هذه بيساوي نورم هذه وهذه نورم ما هو مين نورم الـ F
+
+461
+00:33:58,070 --> 00:34:03,870
+من سابقا إذا صارت عندي T it preserve the norm يعني
+
+462
+00:34:03,870 --> 00:34:09,070
+بمعنى أخر الـ T صارت أيضا إيه شماله is one to one
+
+463
+00:34:09,070 --> 00:34:17,660
+T is one to one الآن نثبت أنه اللي هو الـ T Linear
+
+464
+00:34:17,660 --> 00:34:21,380
+إثبات الـ T Linear سهلة خدوا الآن أي F وG وإن
+
+465
+00:34:21,380 --> 00:34:25,420
+موجودة في الـ R N' والـ Alpha Scalar اللي لعين T
+
+466
+00:34:25,420 --> 00:34:29,560
+of Alpha F زائد G إيش بتساوي؟ بساوي الـ Element
+
+467
+00:34:29,560 --> 00:34:34,660
+هذا عند E1 E2 E3 اللي عند E N بساوي Alpha F of G
+
+468
+00:34:34,660 --> 00:34:40,280
+of EK اللي هو الـ Untables اللي هي عند E1 عند E2
+
+469
+00:34:40,280 --> 00:34:48,130
+لعند E N ويساوي الـ اف اف of ek ب .. انترز هدوله ب ..
+
+470
+00:34:48,130 --> 00:34:53,190
+ب .. ب .. افصلها عن بعض زائد g of ek فاهمين اه؟
+
+471
+00:34:53,190 --> 00:34:58,750
+لإنه هذه عبارة عن الف زايد الف اف أعملكم إيه هان؟
+
+472
+00:34:58,750 --> 00:35:03,110
+عساس مايضلش حاجة مش موضحة
+
+473
+00:35:15,800 --> 00:35:23,000
+طيب يا جماعة هل جت T of Alpha F زائد G بساوي اللي
+
+474
+00:35:23,000 --> 00:35:28,660
+هو زي ما قلنا عبارة عن Alpha F زائد G of mean of E
+
+475
+00:35:28,660 --> 00:35:38,090
+K اللي هي عبارة عن Alpha F زائد G of E واحد ألف أف
+
+476
+00:35:38,090 --> 00:35:44,850
+زائد G of E2 لعين ماصة الأخر واحدة ألف أف زائد G
+
+477
+00:35:44,850 --> 00:35:49,390
+of E N هاي ال untables تبعتنا اللي أنا دول بقدر
+
+478
+00:35:49,390 --> 00:35:53,590
+أفصلها لأن بعض هدوي بقدر أفصلها بيصير ألف أف of E1
+
+479
+00:35:53,590 --> 00:35:59,970
+دوالها ده عادي زائد G of E1 وهذه αF of E2 زائد G of
+
+480
+00:35:59,970 --> 00:36:03,870
+E2 لعند ما أصل للأخيرة في الواقع هتصير هذه عبارة
+
+481
+00:36:03,870 --> 00:36:11,950
+عن αF of E1 زائد هذه G of E1 لعند ما أصل لآخر
+
+482
+00:36:11,950 --> 00:36:17,550
+واحدة αF of EN زائد G of EN هذه الآن الـ vector
+
+483
+00:36:17,550 --> 00:36:25,150
+buffers law تصير عند ألفة في F of E1 لعند F of EN
+
+484
+00:36:26,190 --> 00:36:35,490
+الزائد اللي هي G of E1 لعين G of EN هذا كله اللي
+
+485
+00:36:35,490 --> 00:36:42,630
+هو عبارة عن Alpha of اللي هي عبارة عن T أو Alpha
+
+486
+00:36:42,630 --> 00:36:47,280
+of T of FT of F هدولها دي مين جامعة واحد جامعة
+
+487
+00:36:47,280 --> 00:36:54,620
+اتنين زائد فاهمين زائد TJ او G اذا صار عندي اللي
+
+488
+00:36:54,620 --> 00:37:00,280
+هو T is linear طيب اخر رقم اللي انا صار عندي T
+
+489
+00:37:00,280 --> 00:37:04,540
+linear و one to one و preserve the norm اذا دل
+
+490
+00:37:04,540 --> 00:37:08,840
+عندي مين اللي قلتهالـ N لونته سهل أموره هنا لأنه
+
+491
+00:37:08,840 --> 00:37:12,320
+finite dimensional أنا الـ N ال dimension للـ R N
+
+492
+00:37:12,320 --> 00:37:17,660
+إيش بيساوي ال dimension للـ R N star و إيش بيساوي
+
+493
+00:37:17,660 --> 00:37:22,020
+هذا التنين بيساوي N إذا على طول T و T كانت linear
+
+494
+00:37:22,020 --> 00:37:26,520
+و one to one إذا T is onto إيش اللي بقوله هذا عندى
+
+495
+00:37:34,360 --> 00:37:44,000
+عندى T من RN أبرايم أو star لعند مين RN ماشي الان
+
+496
+00:37:44,000 --> 00:37:48,000
+ال T هذي one to one اللي احنا قولنا ماشي الحال هذي
+
+497
+00:37:48,000 --> 00:37:56,240
+RN أبرايم و هذي RN الان كل واحد منهم أحلى واحد كله،
+
+498
+00:37:56,240 --> 00:38:00,180
+الـ N هنا يمكن فيه زيادة، يمكن، يمكن، احنا مش
+
+499
+00:38:00,180 --> 00:38:03,220
+عارفين فيه زيادة، اهو مش هيكون فيه زيادة هذا لو في
+
+500
+00:38:03,220 --> 00:38:08,100
+one to one لحالها، بيكون ال dimension للـ R N
+
+501
+00:38:08,100 --> 00:38:12,740
+prime أظهر أو يساوي ال dimension لمين؟ للـ R N،
+
+502
+00:38:12,740 --> 00:38:17,400
+ماشي الحال، هذا في الوضع الطبيعي الـ N، و هذا هو
+
+503
+00:38:17,400 --> 00:38:22,880
+نفسه عبارة عن ال dimension لمين؟ لل T of R N prime
+
+504
+00:38:24,350 --> 00:38:28,310
+ولا صورته ولا صورته لكن طبعا ال dimension لهذا و
+
+505
+00:38:28,310 --> 00:38:31,590
+ال dimension لهذا أشماله متساوي إذا ال dimension
+
+506
+00:38:31,590 --> 00:38:35,990
+للـ T of RN برايم هو نفس ال dimension للـ RN وهذا
+
+507
+00:38:35,990 --> 00:38:40,830
+جزء .. وهذا جزء بالمئة من هذا هذا جزء منه و ال
+
+508
+00:38:40,830 --> 00:38:45,730
+dimension له هو .. إذا صار عند ال .. ال T RN برايم
+
+509
+00:38:45,730 --> 00:38:51,680
+هو مين نفسه الـ RN إذا صارت عبارة عن أنتهاللي صار
+
+510
+00:38:51,680 --> 00:38:55,380
+اللي هو الـ Range كله RN إذا صارت عبارة عن Onetwo
+
+511
+00:38:55,380 --> 00:39:02,660
+واضحة أه؟ يالله اللي بعيدها The dual space of L1
+
+512
+00:39:02,660 --> 00:39:06,120
+is mean is L infinity وبده أسرع هال gate عساس إن
+
+513
+00:39:06,120 --> 00:39:09,780
+الفكرة تقريبا اللي هي مكررة مع بعض اللي هي إيش
+
+514
+00:39:09,780 --> 00:39:15,500
+الشغلات اللي خاصة بالspace تبع L1 و L infinity احنا
+
+515
+00:39:15,500 --> 00:39:19,620
+عارفين عناصر الألوان الألوان هي العناصر اللي هي
+
+516
+00:39:19,620 --> 00:39:26,340
+sequences اللي هو XI I حيث I من واحد لما لنا طبعا
+
+517
+00:39:26,340 --> 00:39:30,260
+حيث summation XI I I من واحد إلى ما لنا نهاية is
+
+518
+00:39:30,260 --> 00:39:36,440
+finite لأنه عندي الـ B واحد طيب لأن الـ N infinity
+
+519
+00:39:36,440 --> 00:39:42,790
+is bounded الـ supreme مابقاش مهلهأه فاهم معايا أه
+
+520
+00:39:42,790 --> 00:39:47,750
+هذا أس واحد أس واحد على واحد هاي norm هه معايا
+
+521
+00:39:47,750 --> 00:39:51,530
+طبعا زمان أه الآن الـ norm اللي في حالتي دلوقتي الـ
+
+522
+00:39:51,530 --> 00:39:56,830
+infinity norm هذا بساوي الـ supremum لل xi I over I
+
+523
+00:39:56,830 --> 00:39:59,530
+اللي هي the space of all bounded اللي هو أيش
+
+524
+00:39:59,530 --> 00:40:03,130
+sequences طيب إذا هاي الـ spaces عشان نذكركوا فيهم
+
+525
+00:40:05,280 --> 00:40:09,400
+الان عندى احنا أثبتنا انه الـ EK عبارة عن shoulder
+
+526
+00:40:09,400 --> 00:40:11,960
+bases ده مين للأل واحد و .. و .. و .. و .. و .. و
+
+527
+00:40:11,960 --> 00:40:12,060
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+528
+00:40:12,060 --> 00:40:12,280
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+529
+00:40:12,280 --> 00:40:12,740
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+530
+00:40:12,740 --> 00:40:13,440
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+531
+00:40:13,440 --> 00:40:13,580
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+532
+00:40:13,580 --> 00:40:16,640
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+533
+00:40:16,640 --> 00:40:16,660
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+534
+00:40:16,660 --> 00:40:18,100
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+535
+00:40:18,100 --> 00:40:22,680
+.. و .. و .. و .. و .. و .. و .. و ..
+
+536
+00:40:22,680 --> 00:40:26,600
+و .. و
+
+537
+00:40:34,620 --> 00:40:38,980
+then أي X في الـ L1 فيه إلها unique representation
+
+538
+00:40:38,980 --> 00:40:44,940
+الـ X أيش بيساوي؟ summation Xik Ek ماشي الحال مدام
+
+539
+00:40:44,940 --> 00:40:48,600
+إلها الـ unique representation هذه الآن شوفوا كيف
+
+540
+00:40:48,600 --> 00:40:52,240
+بتدركي بإيش مشابه لللي قبل بشوية خدوا أي أفوان
+
+541
+00:40:52,240 --> 00:40:56,240
+موجودة في الـ L1' أنا H بمين رايح؟ لنتبط إن الدول
+
+542
+00:40:56,240 --> 00:41:00,000
+space لL1 هو L infinity يعني بمعنى آخر
+
+543
+00:41:07,320 --> 00:41:14,720
+بالدلاجة T من الـ one prime لعند ال infinity تقول
+
+544
+00:41:14,720 --> 00:41:17,700
+one to one و one to one و الاخر كل القصة بتاخد
+
+545
+00:41:17,700 --> 00:41:23,690
+الان T of F وأقولكم إيش بتساوي أرميها وين؟ في الـ L
+
+546
+00:41:23,690 --> 00:41:26,270
+infinity أشوف element مناسب يوديها في الـ L
+
+547
+00:41:26,270 --> 00:41:31,430
+infinity المعهد ده زمسي الأولاني المفتاح الحالي
+
+548
+00:41:31,430 --> 00:41:38,310
+اللي هو مين؟ اللي هي F of E K خدوا
+
+549
+00:41:38,310 --> 00:41:41,650
+F وين موجودة؟ في الـ L1' اللي هو في الـ dual space
+
+550
+00:41:41,650 --> 00:41:44,470
+يعني bounded linear functional اللي هن consider
+
+551
+00:41:44,470 --> 00:41:49,530
+any F element in L1' فـ Dual space of L1 هذا طيب
+
+552
+00:41:49,530 --> 00:41:54,470
+since F is linear and bounded إذن الـ F of X هتساوي
+
+553
+00:41:54,470 --> 00:41:59,870
+اللي هو الـ summation Xik Ek اللي هي حيصيرها عبارة
+
+554
+00:41:59,870 --> 00:42:03,770
+عن Xik زي ما هي و هذه F of Ek اللي هي Gamma K زي
+
+555
+00:42:03,770 --> 00:42:06,910
+اللي قبل بشوية بالظبط بس الآن اللي بدمني هذا
+
+556
+00:42:06,910 --> 00:42:11,440
+السلوك يظبط أن F is continuous مش bounded linear
+
+557
+00:42:11,440 --> 00:42:14,920
+functional هي continuous وقلنا الـ bounded مع الـ
+
+558
+00:42:14,920 --> 00:42:17,160
+linear أكيد إيش مالها بتعطينا الـ continuity و
+
+559
+00:42:17,160 --> 00:42:23,640
+العكس صحيح طيب بالنسبة للـ boundedness طيب عند x
+
+560
+00:42:23,640 --> 00:42:29,560
+بتساوي summation إيش ماخده xi k ek كامل عند واحد 
+
+561
+00:42:29,560 --> 00:42:34,840
+لما لنهاية خدوا n arbitrary ماشي الحال الآن خدوا f
+
+562
+00:42:36,070 --> 00:42:38,890
+أو ليش خلاص ما بديش أخد الاربطانية ما بديش أخد اللي
+
+563
+00:42:38,890 --> 00:42:44,230
+عندك خده الآن f of x بساوي الآن هذا في الواقع هو
+
+564
+00:42:44,230 --> 00:42:49,290
+إيش limit هذا عبارة عن limit limit as n goes to
+
+565
+00:42:49,290 --> 00:42:55,110
+infinity لصم x i k e k من عند واحد لعند مين لعندك
+
+566
+00:42:55,390 --> 00:43:01,130
+وبما أن الـ F هو continuous فالـ F في الـ limit
+
+567
+00:43:01,130 --> 00:43:05,910
+يساوي limit الـ F فبصير على طول الـ limit تتجاوزها
+
+568
+00:43:05,910 --> 00:43:09,530
+الـ F و تدخل داخلها لأن الـ F أشمالها is
+
+569
+00:43:09,530 --> 00:43:17,430
+continuous بصير x i k F of e k x i k k من عند 1 لعند n
+
+570
+00:43:17,430 --> 00:43:22,050
+as n goes to infinity ويساوي الـ limit as n goes
+
+571
+00:43:22,050 --> 00:43:27,110
+to infinity الـ Summation هذي F is linear مهيبون؟
+
+572
+00:43:27,110 --> 00:43:29,990
+إذا .. إذا بتقدر ال scalar بتطلع برا هذا vector دي
+
+573
+00:43:29,990 --> 00:43:34,610
+ببالكم الـ e k ال scalar بتطلع برا بصير x i k F of
+
+574
+00:43:34,610 --> 00:43:40,170
+e k .. k من عند 1 لعند n هذا الـ n as n goes to
+
+575
+00:43:40,170 --> 00:43:42,770
+infinity هذا اللي هو sequence of partial sums
+
+576
+00:43:42,770 --> 00:43:45,290
+وكأنها و ال series converges إذا ايش بيساوي ال
+
+577
+00:43:45,290 --> 00:43:50,590
+summation x i k F of e k كمن عند واحد لعند n إذا
+
+578
+00:43:50,590 --> 00:43:57,330
+فعلا كلامه صحيح أنه بقدر أقول since F is linear
+
+579
+00:43:57,330 --> 00:43:59,930
+and bounded then F of x بيساوي ال summation x i k
+
+580
+00:43:59,930 --> 00:44:06,200
+γ k كمن عند واحد إلى مين إلى ما لا نهاية وها دي
+
+581
+00:44:06,200 --> 00:44:11,120
+سموها الـ γ k اللي هي main عبارة عن F of e k
+
+582
+00:44:11,120 --> 00:44:14,880
+و ها دي اللي هي تلاتة وها دي are uniquely
+
+583
+00:44:14,880 --> 00:44:19,800
+determined by main by F يعني الجامعة واحد من F of
+
+584
+00:44:19,800 --> 00:44:22,340
+e واحد بالظبط بسوء الجامعة واحد و F of e اتنين
+
+585
+00:44:22,340 --> 00:44:26,360
+بسوء e اتنين وهذا اللي هو ال determination واحد
+
+586
+00:44:26,920 --> 00:44:31,900
+الآن لو أخدنا norm ال e k بتعرف أشهر بتساوي واحد
+
+587
+00:44:31,900 --> 00:44:35,160
+عارفين ليش؟ اللي هو عبارة عن ال summation لكل
+
+588
+00:44:35,160 --> 00:44:38,520
+واحدة من واحد إلى مال نهاية وفي شهر واحدة و الباقى
+
+589
+00:44:38,520 --> 00:44:42,340
+أصفار لذا ال norm كل واحدة أشهر بتساوي واحد وكمان
+
+590
+00:44:42,340 --> 00:44:46,280
+قاعد بحضر لل .. حضر .. ده اللي عملت .. عملت قبل
+
+591
+00:44:46,280 --> 00:44:49,940
+شوية ال absolute value لـ γ k بساوي ال
+
+592
+00:44:49,940 --> 00:44:54,050
+absolute value لمين؟ لل F of e k وهذه أصغر أو يساوى F
+
+593
+00:44:54,050 --> 00:44:57,990
+is linear أو bounded أصغر أو يساوى Normal F في Normal
+
+594
+00:44:57,990 --> 00:45:02,450
+e k وهذه الواحد إذا بيصير أشمالها Normal F يعني
+
+595
+00:45:02,450 --> 00:45:06,310
+حصلت ال absolute value أو المدلس للـ γ k أكبر
+
+596
+00:45:06,310 --> 00:45:11,440
+أصغر أو يساوى Normal F من جهة أخرى Normal F لسه
+
+597
+00:45:11,440 --> 00:45:13,780
+ما خلصناش من جواهر لما خلّنا بعدين من جواهر لأن
+
+598
+00:45:13,780 --> 00:45:17,780
+norm ل F صار أكبر أو يساوى هذه الكلام لكل K إذا أكيد
+
+599
+00:45:17,780 --> 00:45:20,840
+norm ل F أكبر أو يساوى ال supermom لها أكيد لأن هذي
+
+600
+00:45:20,840 --> 00:45:25,000
+صارت أشمالها upper bound لها أه هذي صارت هذه ال
+
+601
+00:45:25,000 --> 00:45:27,860
+sequence ألف واحد ألف اتنين γ واحد γ اتنين γ
+
+602
+00:45:27,860 --> 00:45:30,700
+اتلاته صارت bounded sequence bounded by مين؟ by
+
+603
+00:45:30,700 --> 00:45:33,920
+اللي هو norm ل F إذا صار عند ال supermom أصغر أو
+
+604
+00:45:33,920 --> 00:45:37,060
+يساوى هذه إذا صار عند ال supermom لهذه أصغر أو يساوى
+
+605
+00:45:37,060 --> 00:45:42,480
+هذه لاحظوا أنا مدام صارت هذه bounded sequence إذا
+
+606
+00:45:42,480 --> 00:45:47,920
+صارت وين بدها تقعد ال Infinity فصار منطقي إن أعرف
+
+607
+00:45:47,920 --> 00:45:51,760
+T of F بساو مين F of e k لإنها صارت bounded
+
+608
+00:45:51,760 --> 00:45:54,700
+automatically ماشي إذا هذا أول واحدة أحطوه على الجهة
+
+609
+00:45:56,380 --> 00:45:59,420
+Hence γ k وين موجودة في الـ L Infinity وهي
+
+610
+00:45:59,420 --> 00:46:04,240
+نحطناها في أربعة الآن من تلاتة خدوا ال absolute
+
+611
+00:46:04,240 --> 00:46:08,640
+value ل F of x اللي هي بالساوي ال absolute value
+
+612
+00:46:08,640 --> 00:46:11,740
+لهدي أصغر أو يساوى ال triangle inequality هدي كلمة
+
+613
+00:46:11,740 --> 00:46:15,180
+مقرر وهدي بالشوارز .. ال .. ال .. ال .. ال .. ال
+
+614
+00:46:15,180 --> 00:46:19,440
+.. لأ مش بالشوارز هدي الآن ال .. ال .. هدي في هدي
+
+615
+00:46:19,950 --> 00:46:23,570
+أكيد الـ Supremum لهدولة هكون أكبر من كل واحدة من
+
+616
+00:46:23,570 --> 00:46:27,790
+هدول إذا الـ summation في هذه أكبر أصغر أو يساوى
+
+617
+00:46:27,790 --> 00:46:30,910
+الـ summation هذا زي ما هو و حطيت مكان هدولة الـ
+
+618
+00:46:30,910 --> 00:46:33,670
+Supremum الكبيرة اللي موجود الـ Supremum اتبتت فوق
+
+619
+00:46:33,670 --> 00:46:36,910
+أنه موجود إذا صار عنده اللي هو الـ summation في
+
+620
+00:46:36,910 --> 00:46:40,330
+مين اللي هو في هذا اللي هو بمعنى آخر هذا هو عبارة
+
+621
+00:46:40,330 --> 00:46:44,470
+صار قيمة عددية بفلحها برا الـ summation اللي هو
+
+622
+00:46:44,470 --> 00:46:48,990
+اسمه norm الـ x في مين؟ في الـ supremum آسف هذا
+
+623
+00:46:48,990 --> 00:46:51,770
+اسمه norm الـ x وهذا اسمه الـ supremum بعد شوية
+
+624
+00:46:51,770 --> 00:46:57,450
+هيصير norm الـ γ i لأن نورم الـ L infinity هو الـ
+
+625
+00:46:57,450 --> 00:47:02,930
+Supremum إذا صار عندي نورم الـ F بساوي اللي هو
+
+626
+00:47:02,930 --> 00:47:07,330
+نورم هذه من الجهتين لإن هي عندي اللي هو نورم الـ F
+
+627
+00:47:07,330 --> 00:47:10,770
+وين وين وين وين نورم الـ F نورم الـ Absolute value
+
+628
+00:47:10,770 --> 00:47:15,750
+لـ F أظهر أوي بساوي هذه في هذه لما أخد على اللي هو
+
+629
+00:47:15,750 --> 00:47:18,630
+نورم الـ xات بساوي واحد بيصير نورم الـ F أظهر أوي
+
+630
+00:47:18,630 --> 00:47:22,190
+بساوي مين الـ Supremum مكرر عشان هيك بس لان انا صار
+
+631
+00:47:22,190 --> 00:47:25,170
+عندي هدى على هدى اللي هو ال supermomal هنايه أصغر
+
+632
+00:47:25,170 --> 00:47:28,130
+بشوية هذا العدد الثابت هو يساوي اللي هو مين هذا
+
+633
+00:47:28,130 --> 00:47:32,530
+قولنا عنه normal γ k i الآن هل جئت هدى و اللي
+
+634
+00:47:32,530 --> 00:47:36,930
+خليناها في الذاكرة مع بعض طلع عندي اه هي ال normal
+
+635
+00:47:36,930 --> 00:47:40,990
+F أكبر بشوية هدى norm الـ F أكبر أو يساوى و norm الـ F
+
+636
+00:47:40,990 --> 00:47:44,310
+أكبر أو يساوى إذا هو بيساوي إذا صار عندي وينها norm
+
+637
+00:47:44,310 --> 00:47:46,190
+الـ F بتساوي الـ Supremum اللي هو بيساوي هذا
+
+638
+00:47:46,190 --> 00:47:51,510
+النورم إذا الدنيا صارت الآن عندي بنيحة بقدر أتجرأ
+
+639
+00:47:51,510 --> 00:47:56,470
+و أقول اطلع لفوق و أقول Now define T من L1 to L'
+
+640
+00:47:56,470 --> 00:48:02,180
+حضرت تماما لعند L infinity by T of F بترميها في الـ
+
+641
+00:48:02,180 --> 00:48:05,660
+F of e k اللي هي γ k وصار عندي الآن من اللي
+
+642
+00:48:05,660 --> 00:48:09,420
+قبل شوية norm T F بسوء norm هذي اللي هو norm F إذا
+
+643
+00:48:09,420 --> 00:48:13,200
+معناته أن T preserve the norm ومن ثم صارت إيه
+
+644
+00:48:13,200 --> 00:48:18,480
+الشمالة T is one to one دل عندي اللي هو Lينيار سهل
+
+645
+00:48:18,480 --> 00:48:21,860
+زي اللينيار الأولاني ودل عندي إيش أثبت إنها أنتوا
+
+646
+00:48:21,860 --> 00:48:25,440
+خلوكوا معانا نثبت أنتوا لأن هلجيت اللي أنتوا هو
+
+647
+00:48:25,440 --> 00:48:30,340
+اللي شوية بده ياخد معنا شوية حكم إن شاء الله بطولش
+
+648
+00:48:32,930 --> 00:48:36,630
+زي ما بنثبت On To عادةً بناخد element هنا
+
+649
+00:48:36,630 --> 00:48:41,470
+arbitrary وبنجيله أصل هنا وبنكون خلصنا الان هنا
+
+650
+00:48:41,470 --> 00:48:45,830
+element اللي هو اللي بناخده هنا بدعرف من خلال ال
+
+651
+00:48:45,830 --> 00:48:51,610
+function هنا بتكون بتروح بنقدر نرسلها إليه تشوف
+
+652
+00:48:51,610 --> 00:48:56,870
+كده نفس النهج اللي .. عن النهج اللي حكيناه قبل و
+
+653
+00:48:56,870 --> 00:49:01,150
+شوية ولكن بما يناسب الرجول on the other hand for
+
+654
+00:49:01,150 --> 00:49:05,990
+any b بيساو β k element in L infinity we can find
+
+655
+00:49:05,990 --> 00:49:09,030
+g element in L one prime by the following يجب
+
+656
+00:49:09,030 --> 00:49:13,890
+نلاقي g في ال L one prime بحيث انه Tg سو مين اللي
+
+657
+00:49:13,890 --> 00:49:20,020
+بتتهب فيها هذه شوفوا كيف Define d من ال1 لعند الـk
+
+658
+00:49:20,020 --> 00:49:23,220
+عشان boundedly non-functional ايش اللي بدنا نلاقيه
+
+659
+00:49:23,220 --> 00:49:26,860
+هنا بدنا نلاقي boundedly non-functional تناسب انه
+
+660
+00:49:26,860 --> 00:49:32,220
+الـTd الـTd يطلع هذا الكمبليكس أوريا مش فارقة اللي
+
+661
+00:49:32,220 --> 00:49:36,410
+هو الـkباي، أيش بدي أعرفها؟ أكيد هذه اللي بين
+
+662
+00:49:36,410 --> 00:49:42,330
+إيديا، اللي بين إيديا اللي بين إيديا، اللي بين
+
+663
+00:49:42,330 --> 00:49:45,650
+إيديا
+
+664
+00:49:45,650 --> 00:49:46,550
+اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي
+
+665
+00:49:46,550 --> 00:49:46,650
+إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا
+
+666
+00:49:46,650 --> 00:49:46,690
+اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي
+
+667
+00:49:46,690 --> 00:49:47,550
+بين إيديا اللي بين إيديا اللي بين إيديا اللي بين
+
+668
+00:49:47,550 --> 00:49:49,310
+إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا
+
+669
+00:49:49,310 --> 00:49:57,230
+اللي بين إيديا اللي بين إيديا
+
+670
+00:49:57,230 --> 00:50:01,850
+اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي
+
+671
+00:50:01,850 --> 00:50:05,690
+بين اللي هي ال .. ال .. ال .. ال .. دربت كل entry
+
+672
+00:50:05,690 --> 00:50:09,430
+من تبع الـ x اللي بيدوجدلها صورتها مع مين؟ مع الـ
+
+673
+00:50:09,430 --> 00:50:13,850
+β k اللي أعطانيها بين إيدياها هذا أنا بقول الـ g of
+
+674
+00:50:13,850 --> 00:50:17,990
+x هي التي ستؤدى الغرض تنشوف كيف ده تؤدى الغرض
+
+675
+00:50:18,720 --> 00:50:21,140
+احسبني الآن أول حاجة بدأت بتنهيبها و بدليها
+
+676
+00:50:21,140 --> 00:50:25,300
+functional عشان تكون هنا فأخد ال absolute value لل
+
+677
+00:50:25,300 --> 00:50:29,320
+GeoFix ايش بتساوي ال absolute value لهذه أصغر أو
+
+678
+00:50:29,320 --> 00:50:31,100
+ساوي ال absolute value في ال absolute value صارت
+
+679
+00:50:31,100 --> 00:50:35,370
+محفوظة هذه بال triangle inequality هذه نفسها أظهر
+
+680
+00:50:35,370 --> 00:50:37,990
+يساوي، هذه في الـ Supremum تبعتها، برضه محفوظة
+
+681
+00:50:37,990 --> 00:50:42,190
+الآن هذه اللي عبارة عن مين؟ في الـ L1، إذا Normal
+
+682
+00:50:42,190 --> 00:50:47,270
+x هذا، ماشي، في Supremum لـ β i، هذا is finite،
+
+683
+00:50:47,270 --> 00:50:50,150
+ماشي الحال، Supremum لـ β j، عارفين ليش finite؟ لأن
+
+684
+00:50:50,150 --> 00:50:54,600
+الـ β q الموجودة في الـ Infinity إذا صار عند الـ
+
+685
+00:50:54,600 --> 00:50:57,220
+absolute value of g of x أصغر أو يساوى Norm الـ x في
+
+686
+00:50:57,220 --> 00:51:02,520
+سم عدد إذا صارت bounded g طيب خلصنا بأن الـ g تكون
+
+687
+00:51:02,520 --> 00:51:06,020
+أشمالها bounded اللي الآن بدنا ناخد أنها نثبت أنها
+
+688
+00:51:06,020 --> 00:51:10,580
+Linear اللي Linearity سهلة خد أي x بسوء x i k و أي
+
+689
+00:51:10,580 --> 00:51:14,500
+y بسوء λ i k element in L1 وان scalar α
+
+690
+00:51:14,500 --> 00:51:17,720
+وحسبلي الآن g of α x زائد y بناء على التعريف
+
+691
+00:51:17,720 --> 00:51:21,820
+اللي عرفناه هنا اللي هو بيكون اللي هو الـ Element أو
+
+692
+00:51:21,820 --> 00:51:25,260
+الـ Entry تبع الـ Element مضروب في الـ β k الـ Entry
+
+693
+00:51:25,260 --> 00:51:29,040
+تبعها دولة α x i k تبعها دي و λ i k
+
+694
+00:51:29,040 --> 00:51:31,920
+تبعها دي فتكون هذا كله هو تبعها هذه الـ Entry
+
+695
+00:51:31,920 --> 00:51:37,220
+تبعها، فاهمين؟ في الـ β k، هذا بتوزع، بتوزع،
+
+696
+00:51:37,220 --> 00:51:40,900
+أعداد عادية، Complex Velarial اللي هي بيصير، اللي
+
+697
+00:51:40,900 --> 00:51:46,360
+هي .. هذا طبعا فكتور، γ و هنا برضه اللي هو
+
+698
+00:51:46,360 --> 00:51:51,600
+أعداده بيقومها α i k في هذه زائد هذه في هذه ال
+
+699
+00:51:51,600 --> 00:51:56,800
+α بتطلع برا Scale up لأن بيصير α في ال
+
+700
+00:51:56,800 --> 00:52:00,140
+summation في ال summation هذا ال summation هو ال g
+
+701
+00:52:00,140 --> 00:52:05,080
+تبع من؟ تبع الـ X وهذا الـ G تبع من؟ الـ Y فصار الـ G
+
+702
+00:52:05,080 --> 00:52:10,620
+إشمالها is linear إذا الـ G و N موجودة في الـ L1
+
+703
+00:52:10,620 --> 00:52:16,990
+إبراين However الـ X can be written as .. من الأصل
+
+704
+00:52:16,990 --> 00:52:22,440
+هو مش الـ X في الألوان واللي هذا shoulder bases إذاً
+
+705
+00:52:22,440 --> 00:52:24,820
+الـ X بنقدر نكتبها على صورة summation xik أو ek
+
+706
+00:52:24,820 --> 00:52:28,680
+كامل عند واحد لعند مين؟ لعند infinity إذاً الـ G of
+
+707
+00:52:28,680 --> 00:52:32,040
+X ماذا ما الـ G linear إذا أكيد الـ G all bounded
+
+708
+00:52:32,040 --> 00:52:34,920
+أثبتنا إنها Linear و Bounded خلاص ألقيـت أتجرأنا إن
+
+709
+00:52:34,920 --> 00:52:37,520
+أقول G of X بيساوي G of هذا وأدخل جوه الـ limit و
+
+710
+00:52:37,520 --> 00:52:40,640
+أطلع بره الـ limit وأوزع لإن الـ G إشمالها سعارات
+
+711
+00:52:40,640 --> 00:52:43,940
+Linear إذا صار عند الـ G of X بيساوي summation xik
+
+712
+00:52:43,940 --> 00:52:47,380
+G of ek إذاً الآن TG
+
+713
+00:52:49,430 --> 00:52:54,950
+أو TG احنا كيف عرفنا الـ TG هو عبارة عن أو TF
+
+714
+00:52:54,950 --> 00:52:59,430
+عبارة عن الـ F عند مين؟ اللي هي الـ .. الـ .. الـ ..
+
+715
+00:52:59,430 --> 00:53:03,730
+الـ .. الـ sequence اللي عناصرها مكونات من الـ F عند
+
+716
+00:53:03,730 --> 00:53:08,490
+الـ E1 عند الـ E2 عند الـ E3 عند الـ E4 TG عبارة عن الـ
+
+717
+00:53:08,490 --> 00:53:13,340
+G عند الـ E1 عند الـ E2 عند الـ E3T H H عند الواحد H
+
+718
+00:53:13,340 --> 00:53:17,500
+عند E اتنين H عند E تلاتة واضح كيف عرفنا إذا الـ T
+
+719
+00:53:17,500 --> 00:53:21,740
+G حسب اللي عندي هنا هتكون G of E واحد G of E اتنين
+
+720
+00:53:21,740 --> 00:53:26,680
+اللي هي G of E كتر لكن الـ Representation هذا هذا
+
+721
+00:53:26,680 --> 00:53:30,040
+الـ Representation is unique لأن عندي هذه الـ
+
+722
+00:53:30,040 --> 00:53:33,620
+Representation قبل بشوية حصلت عليه الـ G of X من
+
+723
+00:53:33,620 --> 00:53:36,660
+فوق هي الـ G of X اللي هو بيساوي summation X I K
+
+724
+00:53:36,660 --> 00:53:41,370
+Beta K واللي قبل بشوية بساويه Psi K في G of EK والـ
+
+725
+00:53:41,370 --> 00:53:44,110
+representation واحد إذا لازم تطلع البيئة ولا
+
+726
+00:53:44,110 --> 00:53:48,850
+بيبطّت الـ .. بيصير الـ Beta .. الـ Beta K إيش؟ هي الـ
+
+727
+00:53:48,850 --> 00:53:55,620
+G of EK إذا صار عند الـ .. انزل صار عندي الـ TG
+
+728
+00:53:55,620 --> 00:54:00,300
+بيساويه اللي هو G of AK اللي هي من الـ representation
+
+729
+00:54:00,300 --> 00:54:05,000
+تبع الـ G of X بيساوي Xi K G of AK ويساوي Xi K في
+
+730
+00:54:05,000 --> 00:54:09,220
+Beta K هو عبارة عن الـ G of AK هي الـ Beta K إذا
+
+731
+00:54:09,220 --> 00:54:13,200
+الـ TG بيساوي الـ Beta K اللي بدأت فيه لجيتله G
+
+732
+00:54:13,200 --> 00:54:17,880
+بحيث إنه TG بيساوي هذا إذا صارت الـ T is onto والآن
+
+733
+00:54:17,880 --> 00:54:22,760
+الخطوة الأخيرة T is linear والـ Linearity زي اللي
+
+734
+00:54:22,760 --> 00:54:26,880
+قبل بالظبط على السريع Now for any F و G element in
+
+735
+00:54:26,880 --> 00:54:31,220
+L one prime and any scalar Alpha T of Alpha F زائد
+
+736
+00:54:31,220 --> 00:54:34,320
+G إيش بتساوي زي اللي قبل شوية عملتها في الاران
+
+737
+00:54:34,320 --> 00:54:37,920
+Alpha F زائد G عند مين؟ عند الـ EK اللي أنت ريها ده
+
+738
+00:54:37,920 --> 00:54:41,990
+إلى مالا نهاية طبعا مش زي الأولى الـ finite بنفس
+
+739
+00:54:41,990 --> 00:54:45,030
+الأسلوب بيطلع الـ α F of EK زي الـ G of EK هو
+
+740
+00:54:45,030 --> 00:54:48,270
+بيساوي Alpha F Alpha TF زي الـ TG معناته صار الـ T
+
+741
+00:54:48,270 --> 00:54:52,250
+is linear وفي الأول bounded وفي الأول اللي هو
+
+742
+00:54:52,250 --> 00:54:56,710
+قلنا اللي هو preserve the norm وفي الأول كمان
+
+743
+00:54:56,710 --> 00:54:59,370
+اللي هو one to one onto then صار الـ T is an
+
+744
+00:54:59,370 --> 00:55:02,250
+isomorphism ومعناته أنه صار عند الألوان is the
+
+745
+00:55:02,250 --> 00:55:04,170
+dual space of الـ infinity
+
+746
+00:55:08,240 --> 00:55:18,720
+اللي بعده أخر مثال ربنا بعيننا الآن
+
+747
+00:55:18,720 --> 00:55:24,900
+space LB the dual space of LB is LQ الـ dual space
+
+748
+00:55:24,900 --> 00:55:27,880
+ل LB is LQ where B أكبر من واحد وأصغر من infinity
+
+749
+00:55:27,880 --> 00:55:31,640
+and Q is the conjugate of mean of B إيش الـ
+
+750
+00:55:31,640 --> 00:55:35,020
+conjugation هذا الترافق الترافق على أساس واحد على
+
+751
+00:55:35,020 --> 00:55:39,650
+B زائد واحد على Q بيساوي واحد إذا عشان أثبت أن الـ
+
+752
+00:55:39,650 --> 00:55:43,450
+Dual Space لهذا هو هذا بدي ألاجي function من الـ
+
+753
+00:55:43,450 --> 00:55:48,650
+B' لعند الـ LB one to one أنتوا حاجيها اللي هي
+
+754
+00:55:48,650 --> 00:55:53,530
+بنفس الأسلوب هيختلف بس البرهان خليني أقول بما
+
+755
+00:55:53,530 --> 00:55:57,030
+يتعلق بس بالعناصر لهان و لهان شوية هنا فيه تكيات
+
+756
+00:55:57,030 --> 00:56:02,210
+بسيطة بالإضافة لإن أنتوا بدوا شوية فكرة هيكة شوية
+
+757
+00:56:02,210 --> 00:56:07,850
+لكن منيحة و بتمشي عشان ذلك بدي أسرعبما أن الـEK هي
+
+758
+00:56:07,850 --> 00:56:11,970
+أساسي لـLB، أين EK بيساوي لـChronicle Delta، ثم X
+
+759
+00:56:11,970 --> 00:56:14,550
+المتنقل بيها as a unique representation X بيساوي
+
+760
+00:56:14,550 --> 00:56:18,690
+كـPsi K E K من واحد لعند مين؟ إلى مالا نهائيا، ماشي
+
+761
+00:56:18,690 --> 00:56:22,670
+الحال؟ لأن consider أي F في مين؟ في الـLB إيش
+
+762
+00:56:22,670 --> 00:56:26,650
+مالها؟ A'، خذوا الـF وين مالها؟ الـB'، لأن عشان
+
+763
+00:56:26,650 --> 00:56:32,430
+أعرف الـTF من الـB'، أعظيها لمين؟ للـLQ، ماشي
+
+764
+00:56:32,430 --> 00:56:37,920
+الحال؟ الآن خذوا أي أف في الـ أل بي برايم since f is
+
+765
+00:56:37,920 --> 00:56:41,740
+linear and bounded then f of x بيساوي الـ
+
+766
+00:56:41,740 --> 00:56:44,640
+summation اللي قلت زي ما عملت قبل شوية بالظبط هذه
+
+767
+00:56:44,640 --> 00:56:48,060
+أسمها إيهاش خمسة where the numbers دعوة ما كالي
+
+768
+00:56:48,060 --> 00:56:52,180
+يمين هي f of ek يعني f دخلت على اللي جوا فلعت عندك
+
+769
+00:56:52,180 --> 00:56:54,960
+5k, f of ek, k من واحد لما نهيه لأن f of one دو
+
+770
+00:56:54,960 --> 00:56:57,540
+دولينر دو دخولة على الـ summation اللي ما لنهيه نفس
+
+771
+00:56:57,540 --> 00:57:02,880
+الجثة continuous و linear الاخرين الآن جهزة هذه
+
+772
+00:57:02,880 --> 00:57:06,320
+خمسة F of X بيساوي هذه شوفوا إيش اللي بنسويه عشان
+
+773
+00:57:06,320 --> 00:57:11,220
+من خلاله نقدر نحصل عالي بدنيا let Q خليني أحضر
+
+774
+00:57:11,220 --> 00:57:15,180
+البرمجان وأصبروا عليا شوية اطلع لفوق let Q be the
+
+775
+00:57:15,180 --> 00:57:20,260
+conjugate linear of B and consider X N بتساوي X I
+
+776
+00:57:20,260 --> 00:57:24,900
+K N أه إيش اكسان يعني الـ .. هاد الـ sequence نفسها
+
+777
+00:57:24,900 --> 00:57:30,200
+X1 X2 X3 إلى ما لنهاية الـ sequence هذه الـ Xات اللي
+
+778
+00:57:30,200 --> 00:57:35,360
+فيها X1 و X2 و X3 و X ما لنهاية هذه اللي هي موجودة
+
+779
+00:57:35,360 --> 00:57:38,740
+وين؟ هاخدها موجودة في القلبي أو في الـ الـ Q sequence
+
+780
+00:57:38,740 --> 00:57:43,020
+.. sequence من عناصر يعني عناصرها اللي هي الـ X1
+
+781
+00:57:43,020 --> 00:57:51,530
+عناصره مين؟ هي XI 1 1 XI 2 1 XI 3 1 أه فاهمين XI 4 1
+
+782
+00:57:51,530 --> 00:58:01,370
+إلى ما لنهاية الآن XN نفسها عبارة عن XI 1N XI 2N
+
+783
+00:58:01,370 --> 00:58:05,770
+XI 3N XI 4N كلهم إلى ما لنهاية الآن هذه الـ
+
+784
+00:58:05,770 --> 00:58:09,770
+sequence بتعرفها بطريقة معينة تخدمني بعد شوية إيش
+
+785
+00:58:09,770 --> 00:58:14,610
+الطريقة اللي بتعرفها؟ بتعرفها كالتالي إن XIKN
+
+786
+00:58:14,610 --> 00:58:20,050
+بتساوي هذول هاين صانم بينيداية هذول الـ F of E K
+
+787
+00:58:20,050 --> 00:58:23,590
+بتساوي الـ Epsilon .. بدي أخد إشي معحدد عشان هو
+
+788
+00:58:23,590 --> 00:58:29,250
+اللي هيسخدمني في التعريف الجمال دي شوية بدي أعرف
+
+789
+00:58:29,250 --> 00:58:34,610
+Epsilon K M بيساوي Gamma K أُس Q Gamma K هدي على
+
+790
+00:58:34,610 --> 00:58:39,480
+mean Gamma K إذا كانت K أصغر أوي شوية N والـGamma K
+
+791
+00:58:39,480 --> 00:58:43,840
+إشمالها لها تساوي 0 في حالة الـGamma K بتساوي 0
+
+792
+00:58:43,840 --> 00:58:47,980
+أتوماتيك بدي أعرفها ده إيش بتساوي 0 في حالة اللي
+
+793
+00:58:47,980 --> 00:58:55,300
+هي الـK أكبر من N يعني لو الآن عندي بدي أحكي عن
+
+794
+00:58:55,300 --> 00:58:57,420
+XIK1
+
+795
+00:59:00,460 --> 00:59:04,860
+Xi K طبعا اللي هي واحد انترين من مين؟ من هدول يعني
+
+796
+00:59:04,860 --> 00:59:10,300
+الـ N على سبيل المثال أعطيكم عشان
+
+797
+00:59:10,300 --> 00:59:16,320
+تكون الصورة واضحة لكم وللي بسمعها الـ N انتفجنا X
+
+798
+00:59:16,320 --> 00:59:22,080
+N بتعرفها عبارة عن Xi K N ماشي الحاجة هذه في حد
+
+799
+00:59:22,080 --> 00:59:27,420
+ذاتها الـ sequence الـ X واحد تبعتها بيساوي Xi K
+
+800
+00:59:27,420 --> 00:59:32,870
+واحد اللي هو K طبعا إيش بناخدها؟ واحد اتنين واحد
+
+801
+00:59:32,870 --> 00:59:41,290
+ثمين XI واحد ثلاثة XI واحد اربعة إلى ما لا نهاية X
+
+802
+00:59:41,290 --> 00:59:48,370
+اتنين بيساوي XI واحد اتنين XI اتنين اتنين XI تلاتة
+
+803
+00:59:48,370 --> 00:59:53,790
+اتنين XI اربعة اتنين إلى ما لا نهاية شوفوا الآن
+
+804
+00:59:53,790 --> 01:00:00,240
+حسب التعريف اللي ماخده أنا XIKN بيساوي في حالة الآن
+
+805
+01:00:00,240 --> 01:00:05,120
+خلينا ناخد على الأولى على مين؟ على X1 بدي أشوف XI
+
+806
+01:00:05,120 --> 01:00:13,560
+11 XI 11 عندي الآن 11 يعني هذه 11 وهذه 1 بتجه في
+
+807
+01:00:13,560 --> 01:00:17,560
+النطاق هذا مظبوط؟ الآن في النطاق هذا بيساوي Gamma
+
+808
+01:00:17,560 --> 01:00:22,840
+1 على Gamma 1 يعني بمعنى آخر هذه بتصير عبارة عن الـ
+
+809
+01:00:22,840 --> 01:00:29,440
+absolute value لقمة واحد أُس بي أُس كيو على قمة واحد
+
+810
+01:00:29,440 --> 01:00:32,280
+هذا provided that Xاية اللي هي القمة واحد مش صفر
+
+811
+01:00:32,280 --> 01:00:37,280
+ماشي خلينا نقلط الصفر الآن الباقي كله بيجي من
+
+812
+01:00:37,280 --> 01:00:41,880
+اتنين اللي هي الـ K أكبر من مين؟ من الان إذا كل
+
+813
+01:00:41,880 --> 01:00:45,780
+الناس هيكونين Zero Zero Zero Zero إلى مالا نهاية
+
+814
+01:00:46,110 --> 01:00:52,230
+واضح الآن الثانية بتنطبق عليها اللي هي Gamma 1 Q
+
+815
+01:00:52,230 --> 01:00:56,690
+على Gamma 1 وهذا بيصير عبارة عن Gamma 2 Q على
+
+816
+01:00:56,690 --> 01:01:01,050
+Gamma 2 provided that مش صفر والباقي إشمالهم صفر
+
+817
+01:01:01,050 --> 01:01:07,940
+صفر صفر صفر واضح معايا الـ N الجامعة إكسا XN هتكون
+
+818
+01:01:07,940 --> 01:01:12,660
+الأولى الجامعة واحد أقصى Q على جامعة واحد لما أصل
+
+819
+01:01:12,660 --> 01:01:18,300
+لعند الـ .. لعند الـ .. الـ N تبعتها جامعة N Q على
+
+820
+01:01:18,300 --> 01:01:25,220
+جامعة N والباقي إيش ماله؟ هيتصفر واضح؟ طيب هذه مين
+
+821
+01:01:25,220 --> 01:01:29,880
+هي؟ هذه اللي هي الـ XN الـ sequence اللي عندك هذه
+
+822
+01:01:29,880 --> 01:01:37,300
+سموها 6 إذا من الخمسة احسبوه لأن f of xn هي الـ rule
+
+823
+01:01:37,300 --> 01:01:41,380
+تبع تحسيب الحسابات f of xn إيش بتساوي؟ اللي هو
+
+824
+01:01:41,380 --> 01:01:46,700
+summation xikn تبعتها تبعت الـ xn هيها تبعت الـ xn
+
+825
+01:01:46,700 --> 01:01:51,700
+في مين؟ في قامة k هذه تبعت الـ x وهذه تبعت الـ xn
+
+826
+01:01:51,700 --> 01:01:58,130
+اللي بتحسبلها في قامة k ويساوي الآن الجثة من عند
+
+827
+01:01:58,130 --> 01:02:01,070
+واحد لعند أنا بيكون اللي لها قيمة اللي هي إيش
+
+828
+01:02:01,070 --> 01:02:04,750
+قيمتها؟ الباب سفارج فاهم من هنا اللي شفناها الباجي
+
+829
+01:02:04,750 --> 01:02:10,050
+سفارج إيش قيمتها؟ اللي هي SQ على Gamma K ومضروبة
+
+830
+01:02:10,050 --> 01:02:14,190
+في Gamma K بروحن مع بعض هذا provided مش صفر وفي
+
+831
+01:02:14,190 --> 01:02:17,670
+حالة سفر ماهو الـ automatic المساواة Automatic
+
+832
+01:02:17,670 --> 01:02:23,530
+متساوي إذا ويساوي هذا بالظبط بيساوي لإنه هذا عبارة
+
+833
+01:02:23,530 --> 01:02:26,010
+عن مين؟ absolute value يعني موجب إذا بيساوي absolute
+
+834
+01:02:26,010 --> 01:02:31,320
+value لهأكيد وهذا إذن بيساوي الـ absolute value الـ
+
+835
+01:02:31,320 --> 01:02:35,460
+absolute value لمين؟ هذا طلع اللي جوا هذا F of XN
+
+836
+01:02:35,460 --> 01:02:39,760
+الـ absolute value هو absolute value لمين؟ للـ F of
+
+837
+01:02:39,760 --> 01:02:44,320
+XN هذا أكيد أصغر أو يساوي مين؟ أن F is bounded نورم
+
+838
+01:02:44,320 --> 01:02:50,120
+الـ F ونورم الـ XN ويساوي نورم الـ F هيه ونورم
+
+839
+01:02:50,120 --> 01:02:54,500
+الـ XN للـ XN هذه الآن الـ XN من وين أنا بتاخد؟ بتاخد
+
+840
+01:02:54,500 --> 01:03:01,620
+T من وين؟ عند الـ F موجودة في الـ LB إبراهيم، ماشي؟ 
+
+841
+01:03:01,620 --> 01:03:05,320
+إذا الـ X تبعتها، الـ X تبعتها، اللي هي الـ X أو
+
+842
+01:03:05,320 --> 01:03:07,820
+الـ X1 و الـ X2 و الـ X3 و الـ X4 و الـ X5 و الـ
+
+843
+01:03:07,820 --> 01:03:08,000
+X6 و الـ X7 و الـ X8 و الـ X9 و الـ X10 و الـ X11
+
+844
+01:03:08,000 --> 01:03:10,900
+و الـ X12 و الـ X13 و الـ X14 و الـ X14 و الـ X15
+
+845
+01:03:10,900 --> 01:03:15,300
+و الـ X16 و الـ X20 و الـ X21 و الـ X22 و الـ X22
+
+846
+01:03:15,300 --> 01:03:15,840
+و الـ X22 و الـ X22 و الـ X22 و الـ X22 و الـ X22
+
+847
+01:03:15,840 --> 01:03:23,560
+و الـ X22 و الـ X22 و الـ X22 و الـ X22 و الـ X22
+
+848
+01:03:23,560 --> 01:03:26,190
+و الـ X22 و الـ X22 و الـ X22 و الـ X22 فبيصير
+
+849
+01:03:26,190 --> 01:03:29,610
+norm الـ F هو في ال summation هذا كم آن عند واحد
+
+850
+01:03:29,610 --> 01:03:33,310
+عند N والباقي بتتصفر بحط القيمة تبعي تهدي اللي هي
+
+851
+01:03:33,310 --> 01:03:39,610
+Xi K SQ على مين براما K الكل أس مين أس بين و الكل
+
+852
+01:03:39,610 --> 01:03:46,150
+أس مين أس واحد على بين إذا اللي عملته يا جماعة نورم
+
+853
+01:03:46,150 --> 01:03:50,470
+الـ xn كتبته نورم الـ xn الـ xn وين موجود؟ في الـ
+
+854
+01:03:50,470 --> 01:03:55,050
+Lp اللي هي ال interest بتبعته xikn يعني نورم تبعه
+
+855
+01:03:55,050 --> 01:03:58,310
+ال absolute value الو أس بي الكل أس واحد على بي ال
+
+856
+01:03:58,310 --> 01:04:04,040
+summation هيولأن شيلت هدولة وحط قيمها قيم هدولة
+
+857
+01:04:04,040 --> 01:04:09,900
+اللي هي كلهم بيكون هيها جامعة واحد Q على جامعة
+
+858
+01:04:09,900 --> 01:04:18,020
+واحد لما أصل عند جامعة Q SQ على جامعة N والباقي
+
+859
+01:04:18,020 --> 01:04:23,120
+بتصفر بتصفر بتصفر بتصفر بتصفر إذا الـ Submission هتجف عند
+
+860
+01:04:23,120 --> 01:04:26,760
+الأمن والباقي بتصفر لما نيجي في حد الأمن بشيل هذا
+
+861
+01:04:26,760 --> 01:04:29,680
+قيمته هي هذا على هذا و أس بيه و أس واحد على بيه
+
+862
+01:04:29,680 --> 01:04:35,260
+يلا نحسب الآنهو يساوي norm of هذا الكلام هذا
+
+863
+01:04:35,260 --> 01:04:38,980
+الأنصار عنده عبارة عن اللي هو هذا واحد وهذا اللي
+
+864
+01:04:38,980 --> 01:04:43,400
+هو عبارة عن إيش عن ال Q فبيصير Q ناقص واحد قص مين قص
+
+865
+01:04:43,400 --> 01:04:46,080
+بي لإن هذا ال absolute value اللي دي هتان هيه هذا
+
+866
+01:04:46,080 --> 01:04:48,780
+ال absolute value موجود فهياخد للتحت و اللي فوق
+
+867
+01:04:48,780 --> 01:04:52,580
+absolute value أو مضلص بطلع Q ماينس واحد الكل
+
+868
+01:04:52,580 --> 01:04:56,140
+مضروب في مين في بي و في واحد على بيه هذا المقدر
+
+869
+01:04:56,140 --> 01:05:00,940
+اللي هو عبارة عن مين ال Qالـ Q ليش؟ لأن واحد على B
+
+870
+01:05:00,940 --> 01:05:06,280
+واحد على B زائد واحد على Q بيساوي واحد اضربه كله في
+
+871
+01:05:06,280 --> 01:05:11,080
+الـ BQ فبتطلع Q زائد B بيساوي B في Q إذا الـ Q
+
+872
+01:05:11,080 --> 01:05:17,840
+بيساوي BQ ناقص B، ماشي؟ واضح، أه؟ ماشي الحال لأن
+
+873
+01:05:17,840 --> 01:05:22,570
+هذا QB ناقص Q اللي هي عبارة عن مين؟ عن الـ Q صار
+
+874
+01:05:22,570 --> 01:05:27,450
+عنده هذا المقدار Q وهذا S1 على B إذا صار عنده الآن
+
+875
+01:05:27,450 --> 01:05:32,670
+اللي وصلت إليه عنده ال F of Xn أصغر أو يساوي هذا
+
+876
+01:05:32,670 --> 01:05:41,610
+المقدار إذا ال F of Xn بيساوي ال summation هيه F of
+
+877
+01:05:41,610 --> 01:05:46,150
+Xn بيساوي ال summation هذا معاها و في النهاية وصلنا
+
+878
+01:05:46,150 --> 01:05:50,230
+أصغر أو ساوي هذاهي اللي بدك تبهن بس f of xn و اللي
+
+879
+01:05:50,230 --> 01:05:53,370
+بيساوي هذا و أصغر يبساوي هذا أصغر يبساوي norm of f
+
+880
+01:05:53,370 --> 01:05:59,450
+في هذا المقدر الآن من التنتين مع بعض صار عندي اللي
+
+881
+01:05:59,450 --> 01:06:05,090
+هو ال summation ال summation اللي هو انجلوه على
+
+882
+01:06:05,090 --> 01:06:11,890
+الجهة الثانية انجلوه هنا هذا يعني ده اسمهبصير هذا
+
+883
+01:06:11,890 --> 01:06:15,550
+أسوء Q هنقص واحد و هذا أسوء واحد على بيه بيصير
+
+884
+01:06:15,550 --> 01:06:18,450
+واحد ناقصه بيصير واحد ناقص واحد على بيه أصغر أو
+
+885
+01:06:18,450 --> 01:06:23,430
+ساوي مين نورم ال F إذا صار عندي اللي هو هذا طبعا
+
+886
+01:06:23,430 --> 01:06:27,830
+هو واحد على Q صار هذا أصغر أو ساوي نورم ال F يعني
+
+887
+01:06:27,830 --> 01:06:34,590
+هذا صار finite يعني صار ال element هذا وين موجود
+
+888
+01:06:34,590 --> 01:06:41,840
+في القلة Q وهذا اللي بديه أصلا بدي الآن أخد TT من
+
+889
+01:06:41,840 --> 01:06:52,460
+LB' لعند LQ الـ T الآن of IF بيساوي المقدار اللي
+
+890
+01:06:52,460 --> 01:06:58,240
+حصلت عليه اللي عندي اللي جابله شوية since طبعا
+
+891
+01:06:58,240 --> 01:07:01,700
+الان since and بس بتكمل الجثة أساسا هو تكتمل
+
+892
+01:07:01,700 --> 01:07:05,930
+الصورة Since N is arbitrary, I N بودي N من لما
+
+893
+01:07:05,930 --> 01:07:09,270
+لنهاية، then by letting N تروح لما لنهاية، بيصير
+
+894
+01:07:09,270 --> 01:07:12,390
+هذا المقدار من واحد لما لنهاية أصغر أو ساوى F.
+
+895
+01:07:12,750 --> 01:07:15,990
+Normal F إذا صارت الجامعة كي وين موجودة في ال LQ.
+
+896
+01:07:16,210 --> 01:07:23,620
+Now اللي روحت عليه God, Now اطلع لفوق T Define T من
+
+897
+01:07:23,620 --> 01:07:27,860
+الـ B' لعند الـ LQ by T of F أيش بيساوي الـ F of
+
+898
+01:07:27,860 --> 01:07:32,120
+EK اللي هو جامعة K اتجهزناها وين قاعدة في الـ LQ
+
+899
+01:07:32,120 --> 01:07:38,160
+to show الآن .. الآن بدنا نثبت أنه T is onto مافي
+
+900
+01:07:38,160 --> 01:07:43,020
+الحال أخر شوية هو أثبات اللي هو ب reserve the norm
+
+901
+01:07:43,020 --> 01:07:46,720
+بس عشان نثبته onto و بعدين نرجع لل norm لكن بنفع
+
+902
+01:07:46,720 --> 01:07:47,080
+نثبته
+
+903
+01:07:49,890 --> 01:07:54,410
+طيب صلوا على النبي عليه الصلاة والسلام نشف طريقي
+
+904
+01:07:54,410 --> 01:07:59,710
+هو لأ هو عشان الدنيا رمضان هذا هيتسجل تسجيل فالناس
+
+905
+01:07:59,710 --> 01:08:02,490
+هتسمع أنه احنا كنا نشرح في رمضان عشان يقولك رمضان
+
+906
+01:08:02,490 --> 01:08:06,370
+طيب صلوا على النبي عليه الصلاة والسلام الان هو
+
+907
+01:08:06,370 --> 01:08:09,130
+اليوم هذا اصلا اليوم احنا عارفين ان الدنيا رمضان
+
+908
+01:08:09,130 --> 01:08:11,550
+لكن يمكن اللي بسمعه يسمعه كمان عشر سنين خمس عشر
+
+909
+01:08:11,550 --> 01:08:15,530
+سنة ويقول الله يرحمهم كانوا يشرحوا في رمضان طيب
+
+910
+01:08:15,530 --> 01:08:19,130
+صلوا على النبي عليه الصلاة والسلام الحمد لله جميعا
+
+911
+01:08:19,130 --> 01:08:23,330
+الـ Enhance Gamma K Element لـ LQ ماشي الان Now
+
+912
+01:08:23,330 --> 01:08:28,670
+define T-LB' لعند LQ by T of F ال element هنا
+
+913
+01:08:28,670 --> 01:08:32,330
+بيسوي F of EK سواء Gamma K اللي قعدناها to show
+
+914
+01:08:32,330 --> 01:08:36,770
+that T is onto خط B arbitrary element في مين في LQ
+
+915
+01:08:36,770 --> 01:08:42,130
+هنجح مش .. في شبه من اللي فات عرفلي G-LB لعند L ..
+
+916
+01:08:42,130 --> 01:08:45,190
+لعند K function بدي ألاقي function عشان .. عشان
+
+917
+01:08:45,190 --> 01:08:47,630
+اللي هو A لاجي صورتها تسوي مين اللي بدأت فيه
+
+918
+01:08:48,060 --> 01:08:51,720
+كمبليكس أوريال بي جي of X بيساوي بـ Psi K Gamma K
+
+919
+01:08:51,720 --> 01:08:54,480
+Beta K K من 1 لإنفينتي بالظبط زي اللي أحكي الأول
+
+920
+01:08:54,480 --> 01:08:57,240
+يعني for any X و إيه الموجودة بـPsi K و إيه
+
+921
+01:08:57,240 --> 01:09:00,980
+الموجود الآن في الـL بي then as in the previous
+
+922
+01:09:00,980 --> 01:09:05,340
+example G is linear مش هيختلف ماعرف أقول إنها ده G
+
+923
+01:09:05,340 --> 01:09:09,560
+is linear moreover by holder in quality الآن هقول
+
+924
+01:09:09,560 --> 01:09:13,410
+لأبسليوت وينه للـG of X بيساوي الـ Absolute Value
+
+925
+01:09:13,410 --> 01:09:16,550
+لهذه والـ Absolute Value لهذه اللي هي أصغر أو
+
+926
+01:09:16,550 --> 01:09:21,990
+يساوي هذه بيقص واحد على بيقص واحد على بيقص واحد
+
+927
+01:09:21,990 --> 01:09:22,550
+على بيقص واحد على بيقص واحد على بيقص واحد على بيقص
+
+928
+01:09:22,550 --> 01:09:22,690
+واحد على بيقص واحد على بيقص واحد على بيقص واحد على
+
+929
+01:09:22,690 --> 01:09:22,750
+بيقص واحد على بيقص واحد على بيقص واحد على بيقص
+
+930
+01:09:22,750 --> 01:09:22,770
+واحد على بيقص واحد على بيقص واحد على بيقص واحد على
+
+931
+01:09:22,770 --> 01:09:23,970
+بيقص واحد على بيقص واحد على بيقص واحد على بيقص
+
+932
+01:09:23,970 --> 01:09:26,370
+واحد على بيقص واحد على بيقص واحد على بيقص واحد على
+
+933
+01:09:26,370 --> 01:09:35,810
+بيقص واحد على بيقص واحد على بيقص واحد 
+
+934
+01:09:35,810 --> 01:09:39,750
+على بيقص
+
+935
+01:09:39,990 --> 01:09:44,890
+and so ومنها الـ G of X بيساوي الـ summation صارت
+
+936
+01:09:44,890 --> 01:09:48,610
+bound to be linear إذا بقدر أدخل من الـ G جوا زي
+
+937
+01:09:48,610 --> 01:09:51,170
+ما بدها لإنه صارت ال limit تدخل و تطلع لإنه
+
+938
+01:09:51,170 --> 01:09:53,530
+continuous بيصير عند الـ G of X بيساوي الـ
+
+939
+01:09:53,530 --> 01:09:56,550
+summation X I K و G of E K ونظرا لإن ال
+
+940
+01:09:56,550 --> 01:09:59,570
+representation واحد إذا الـ G of E K هي الـ BK
+
+941
+01:09:59,570 --> 01:10:02,290
+اللي غالط إذا زي الحكية الأولى بالظبط then T G
+
+942
+01:10:02,290 --> 01:10:06,810
+أشها تساوي G of E K من التعريف هذا T G بيساوي G
+
+943
+01:10:06,810 --> 01:10:10,890
+of E K اللي عرفناها في الأصل هنا الـ T بيساوي اللي
+
+944
+01:10:10,890 --> 01:10:15,150
+هو Beta K إذا Therefore T is Onto مصر علينه الكلام
+
+945
+01:10:15,150 --> 01:10:21,070
+بتكرر نفس اللي حكيته قبل شوية الآن صارت T Onto
+
+946
+01:10:21,070 --> 01:10:26,240
+بدنا اللي هو نثبت إنها preserve the North الان اذا
+
+947
+01:10:26,240 --> 01:10:29,600
+اثبتنا بـ Reservoir norm و T on two بيبقى هو ال
+
+948
+01:10:29,600 --> 01:10:32,440
+linear بس هو ال linear سهل الان by holder
+
+949
+01:10:32,440 --> 01:10:36,180
+inequality احسبوني ال absolute value ل F of X ال
+
+950
+01:10:36,180 --> 01:10:38,660
+absolute value ل F of X بيساوي ال absolute value
+
+951
+01:10:38,660 --> 01:10:42,490
+of summation X I K بقى ما كال هي F of E K هذه ماشي
+
+952
+01:10:42,490 --> 01:10:46,310
+اللي هي أصغر أو يساوي اللي هو by holder اللي هو
+
+953
+01:10:46,310 --> 01:10:48,970
+أصغر أو يساوي ال summation ب أصواح ده ل بي ال
+
+954
+01:10:48,970 --> 01:10:52,890
+summation of q أصواح ده ل q هذا مين هو نورم ال X
+
+955
+01:10:52,890 --> 01:10:56,490
+وهذا زي ما هو اللي عندى اللي بعد شوية هصير نورم
+
+956
+01:10:56,490 --> 01:10:59,850
+ينقل Gamma K ماشي إذا صارت ال absolute value of f
+
+957
+01:10:59,850 --> 01:11:03,730
+of X أصغر أو يساوي هذا المقدار ومنه على طور اللي
+
+958
+01:11:03,730 --> 01:11:07,170
+ناخد اللي هو ال supremum النورمات اللي بيساوي واحد
+
+959
+01:11:07,170 --> 01:11:11,470
+بطلع ال absolute value النورم لل F فاهمين أه يعني
+
+960
+01:11:11,470 --> 01:11:14,630
+هذه بنجيبها بالسيرة هذا على هذه أصغر أو يساوي هذا
+
+961
+01:11:14,630 --> 01:11:17,210
+ياخد ال supermom على ال Xات اللي بتساوي انيش بتصفر
+
+962
+01:11:17,210 --> 01:11:20,030
+وإذا بدكم على ال Xات اللي بتساوي واحد نورمهن
+
+963
+01:11:20,030 --> 01:11:22,590
+وبيطلع نفس الاشي نورم ال F أصغر أو يساوي هذا
+
+964
+01:11:22,590 --> 01:11:25,650
+المقدار لأن من سبعة اللي جابت اللي بشوية قولنا
+
+965
+01:11:25,650 --> 01:11:29,510
+حطوها في الذاكرة هذا أصغر أو يساوي نورم وهذا ال
+
+966
+01:11:29,510 --> 01:11:32,850
+norm أصغر أو يساويهن إذا ال team team together صار
+
+967
+01:11:32,850 --> 01:11:38,150
+ال norm بيساوي هذا therefore صار ال norm لل TF ما هو
+
+968
+01:11:38,150 --> 01:11:40,870
+الـ TF ايش بيساوي، ما عارفين واحنا، بيساوي الـ
+
+969
+01:11:40,870 --> 01:11:45,610
+Gamma K أدات التغريف نورم الـ TF بيساوي نورم Gamma
+
+970
+01:11:45,610 --> 01:11:49,920
+K ونورم Gamma K في الواقع هو هذا اللي هو بيساوي هذا
+
+971
+01:11:49,920 --> 01:11:52,540
+و هو أثبتنا بيساوي norm of
+
+972
+01:12:18,310 --> 01:12:22,750
+اف اف اي كي اللي هي الـ Gamma K Element in LQ و
+
+973
+01:12:22,750 --> 01:12:26,370
+Preserve the Normal 1 to 1 و Unto و Linear إذن
+
+974
+01:12:26,370 --> 01:12:30,250
+صارت Isomorphism إذن ده Dual Space of الـ B هو الـ
+
+975
+01:12:30,250 --> 01:12:33,570
+LQ و بارك الله فيكم و إلى لقاء آخر 
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/vjF46QrstMA_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/vjF46QrstMA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..78d9b16dd9848596e743103878a8b0db6db6ad68
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/vjF46QrstMA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2174, "start": 4.96, "end": 21.74, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى أهله وصحبه أجمعين هذه هي المحاضرة رقم 16 تحليل اقتراني او تحليل دالي طلاب طالبات الجامعة الإسلامية", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21542, 2304, 3215, 24976, 3224, 12602, 3555, 18863, 45340, 9957, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 8608, 25708, 9673, 2288, 3794, 1211, 9957, 8608, 25708, 8315, 3714, 35571, 3215, 4032, 3615, 23942, 5551, 3224, 43761, 4032, 9381, 5016, 3555, 3224, 5551, 7435, 2304, 3615, 9957, 29538, 39896, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 3165, 6055, 5016, 20292, 1211, 1975, 38149, 2288, 7649, 1829, 1975, 2407, 6055, 5016, 20292, 1211, 11778, 6027, 1829, 23032, 15040, 3555, 23032, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632], "avg_logprob": -0.10093118852437144, "compression_ratio": 1.9125683060109289, 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0.960693359375}, {"start": 8.98, "end": 9.54, "word": " المرسلين", "probability": 0.95634765625}, {"start": 9.54, "end": 9.94, "word": " سيدنا", "probability": 0.9666341145833334}, {"start": 9.94, "end": 10.44, "word": " محمد", "probability": 0.9899088541666666}, {"start": 10.44, "end": 11.2, "word": " وعلى", "probability": 0.94384765625}, {"start": 11.2, "end": 11.54, "word": " أهله", "probability": 0.8435872395833334}, {"start": 11.54, "end": 12.18, "word": " وصحبه", "probability": 0.9611328125}, {"start": 12.18, "end": 12.82, "word": " أجمعين", "probability": 0.97138671875}, {"start": 12.82, "end": 13.7, "word": " هذه", "probability": 0.89599609375}, {"start": 13.7, "end": 13.88, "word": " هي", "probability": 0.7275390625}, {"start": 13.88, "end": 14.4, "word": " المحاضرة", "probability": 0.977294921875}, {"start": 14.4, "end": 14.74, "word": " رقم", "probability": 0.8590494791666666}, {"start": 14.74, "end": 15.4, "word": " 16", "probability": 0.529296875}, {"start": 15.4, "end": 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Normal E K وهذه الواحد إذا بيصير إشماله Normal F يعني حصلت ال absolute value أو المدلس للجامعة K أكبر أصغر يشاوى Normal F من جهة أخرى Normal F", "tokens": [2407, 3224, 24192, 5551, 9381, 17082, 2288, 7251, 8592, 995, 2407, 7578, 479, 307, 8213, 34051, 37498, 5551, 9381, 17082, 2288, 7251, 8592, 995, 2407, 7578, 21277, 479, 8978, 21277, 462, 591, 37037, 24192, 2423, 14407, 24401, 11933, 15730, 4724, 1829, 9381, 13546, 11933, 8592, 2304, 6027, 3224, 21277, 479, 37495, 22653, 11331, 36520, 2655, 2423, 8236, 2158, 34051, 9673, 3215, 1211, 3794, 24976, 7435, 10943, 27884, 591, 5551, 4117, 26890, 5551, 9381, 17082, 2288, 7251, 8592, 995, 2407, 7578, 21277, 479, 9154, 10874, 3224, 3660, 5551, 34740, 7578, 21277, 479], "avg_logprob": -0.3376358604949454, "compression_ratio": 1.6096256684491979, "no_speech_prob": 1.0967254638671875e-05, "words": [{"start": 2692.83, "end": 2693.21, "word": "وهذه", "probability": 0.5276692708333334}, {"start": 2693.21, "end": 2693.53, "word": " أصغر", 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function", "probability": 0.60107421875}, {"start": 2926.15, "end": 2926.61, "word": " هنا", "probability": 0.9755859375}, {"start": 2926.61, "end": 2927.39, "word": " بتكون", "probability": 0.75439453125}, {"start": 2927.39, "end": 2928.49, "word": " بتروح", "probability": 0.89111328125}, {"start": 2928.49, "end": 2929.95, "word": " بنقدر", "probability": 0.6968180338541666}, {"start": 2929.95, "end": 2930.39, "word": " نرسلها", "probability": 0.95341796875}, {"start": 2930.39, "end": 2931.21, "word": " إليه", "probability": 0.6573893229166666}, {"start": 2931.21, "end": 2931.61, "word": " تشوف", "probability": 0.8232421875}, {"start": 2931.61, "end": 2931.81, "word": " كده", "probability": 0.8509114583333334}], "temperature": 1.0}, {"id": 132, "seek": 295597, "start": 2933.25, "end": 2955.97, "text": "نفس النهج اللي .. عن النهج اللي حكيناه قبل و شوية ولكن بما يناسب الرجول on the other hand for any B بيساو بي ك element in L infinity we can find G element in L one prime by the following بيجب نلاقي G في ال L one prime بحيث انه TG سو مين اللي بتتهب فيها هذه شوفوا كيف", "tokens": [1863, 36178, 28239, 3224, 7435, 13672, 1829, 4386, 18871, 28239, 3224, 7435, 13672, 1829, 11331, 4117, 1829, 8315, 3224, 12174, 36150, 4032, 13412, 2407, 10632, 35525, 19452, 4724, 15042, 7251, 8315, 35457, 34892, 7435, 12610, 322, 264, 661, 1011, 337, 604, 363, 4724, 1829, 3794, 995, 2407, 4724, 1829, 9122, 4478, 294, 441, 13202, 321, 393, 915, 460, 4478, 294, 441, 472, 5835, 538, 264, 3480, 4724, 1829, 7435, 3555, 8717, 15040, 38436, 460, 8978, 2423, 441, 472, 5835, 4724, 5016, 1829, 12984, 16472, 3224, 314, 38, 8608, 2407, 3714, 9957, 13672, 1829, 39894, 47395, 3555, 8978, 11296, 29538, 13412, 38688, 14407, 9122, 33911], "avg_logprob": -0.36101190930321103, "compression_ratio": 1.5555555555555556, "no_speech_prob": 1.4722347259521484e-05, "words": [{"start": 2933.25, "end": 2933.91, "word": "نفس", "probability": 0.749755859375}, {"start": 2933.91, "end": 2934.33, "word": " النهج", 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{"start": 2947.69, "end": 2948.33, "word": " by", "probability": 0.89013671875}, {"start": 2948.33, "end": 2948.53, "word": " the", "probability": 0.90087890625}, {"start": 2948.53, "end": 2948.77, "word": " following", "probability": 0.87109375}, {"start": 2948.77, "end": 2949.03, "word": " بيجب", "probability": 0.368927001953125}, {"start": 2949.03, "end": 2949.27, "word": " نلاقي", "probability": 0.8180338541666666}, {"start": 2949.27, "end": 2949.47, "word": " G", "probability": 0.46728515625}, {"start": 2949.47, "end": 2949.63, "word": " في", "probability": 0.9208984375}, {"start": 2949.63, "end": 2949.71, "word": " ال", "probability": 0.55615234375}, {"start": 2949.71, "end": 2949.87, "word": " L", "probability": 0.56591796875}, {"start": 2949.87, "end": 2950.53, "word": " one", "probability": 0.31640625}, {"start": 2950.53, "end": 2950.87, "word": " prime", "probability": 0.78076171875}, {"start": 2950.87, "end": 2951.19, "word": " بحيث", "probability": 0.968017578125}, {"start": 2951.19, "end": 2951.77, "word": " انه", "probability": 0.60205078125}, {"start": 2951.77, "end": 2952.49, "word": " TG", "probability": 0.72119140625}, {"start": 2952.49, "end": 2953.05, "word": " سو", "probability": 0.585205078125}, {"start": 2953.05, "end": 2953.45, "word": " مين", "probability": 0.822998046875}, {"start": 2953.45, "end": 2953.89, "word": " اللي", "probability": 0.965087890625}, {"start": 2953.89, "end": 2954.31, "word": " بتتهب", "probability": 0.5277506510416666}, {"start": 2954.31, "end": 2954.57, "word": " فيها", "probability": 0.972900390625}, {"start": 2954.57, "end": 2954.89, "word": " هذه", "probability": 0.448486328125}, {"start": 2954.89, "end": 2955.79, "word": " شوفوا", "probability": 0.9327799479166666}, {"start": 2955.79, "end": 2955.97, "word": " كيف", "probability": 0.966064453125}], "temperature": 1.0}, {"id": 133, "seek": 297260, "start": 2957.58, "end": 2972.6, "text": "Define D من ال1 لعند الـK عشان boundedly non-functional ايش اللي بدنا نلاقيه هنا بدنا نلاقي boundedly non-functional تناسب انه الـTD الـTD يطلع هذا الكمبليكس أوريا مش فارقة اللي هو الـK", "tokens": [35, 5666, 533, 413, 9154, 2423, 16, 5296, 3615, 41260, 2423, 39184, 42, 6225, 8592, 7649, 37498, 356, 2107, 12, 22845, 304, 1975, 1829, 8592, 13672, 1829, 47525, 8315, 8717, 15040, 38436, 3224, 34105, 47525, 8315, 8717, 15040, 38436, 37498, 356, 2107, 12, 22845, 304, 6055, 8315, 35457, 16472, 3224, 2423, 39184, 51, 35, 2423, 39184, 51, 35, 7251, 9566, 1211, 3615, 23758, 2423, 24793, 3555, 20292, 4117, 3794, 5551, 13063, 25528, 37893, 6156, 9640, 28671, 13672, 1829, 31439, 2423, 39184, 42], "avg_logprob": -0.4205572253250214, "compression_ratio": 1.5555555555555556, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 2957.58, "end": 2958.38, "word": "Define", "probability": 0.7060139973958334}, {"start": 2958.38, "end": 2958.62, "word": " D", "probability": 0.5732421875}, {"start": 2958.62, "end": 2958.8, "word": " من", "probability": 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"probability": 0.9619140625}, {"start": 2963.44, "end": 2964.06, "word": " بدنا", "probability": 0.771484375}, {"start": 2964.06, "end": 2964.32, "word": " نلاقي", "probability": 0.98828125}, {"start": 2964.32, "end": 2964.94, "word": " boundedly", "probability": 0.77294921875}, {"start": 2964.94, "end": 2965.08, "word": " non", "probability": 0.955078125}, {"start": 2965.08, "end": 2965.68, "word": "-functional", "probability": 0.9373372395833334}, {"start": 2965.68, "end": 2966.3, "word": " تناسب", "probability": 0.9607747395833334}, {"start": 2966.3, "end": 2966.86, "word": " انه", "probability": 0.688232421875}, {"start": 2966.86, "end": 2967.64, "word": " الـTD", "probability": 0.77783203125}, {"start": 2967.64, "end": 2968.74, "word": " الـTD", "probability": 0.70526123046875}, {"start": 2968.74, "end": 2969.38, "word": " يطلع", "probability": 0.9300537109375}, {"start": 2969.38, "end": 2969.64, "word": " هذا", "probability": 0.1593017578125}, {"start": 2969.64, "end": 2971.16, "word": " الكمبليكس", "probability": 0.6593221028645834}, {"start": 2971.16, "end": 2971.42, "word": " أوريا", "probability": 0.4545491536458333}, {"start": 2971.42, "end": 2971.58, "word": " مش", "probability": 0.650390625}, {"start": 2971.58, "end": 2971.98, "word": " فارقة", "probability": 0.9269205729166666}, {"start": 2971.98, "end": 2972.22, "word": " اللي", "probability": 0.94091796875}, {"start": 2972.22, "end": 2972.34, "word": " هو", "probability": 0.99072265625}, {"start": 2972.34, "end": 2972.6, "word": " الـK", "probability": 0.900390625}], "temperature": 1.0}, {"id": 134, "seek": 300185, "start": 2973.59, "end": 3001.85, "text": "باي، أيش بدي أعرفها؟ أكيد هذه اللي بين إيديا، اللي بين إيديا اللي بين إيديا، اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين إيديا اللي بين", "tokens": [3555, 47302, 12399, 36632, 8592, 4724, 16254, 5551, 3615, 28480, 11296, 22807, 5551, 4117, 25708, 29538, 13672, 1829, 49374, 11933, 1829, 16254, 995, 12399, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 11933, 1829, 16254, 995, 12399, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 11933, 1829, 16254, 995, 13672, 1829, 49374, 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Normal F إذا صارت الجامعة كي وين موجودة في ال LQ. 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diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/wdHX26yF5r4_raw.json b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/wdHX26yF5r4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..fb336b5f5be056b90f926e8f2b030767fdad6fc8
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/wdHX26yF5r4_raw.json
@@ -0,0 +1 @@
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248.92, "text": "وكان اللي هو ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال", "tokens": [2407, 41361, 13672, 1829, 31439, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 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" في", "probability": 0.89306640625}, {"start": 1320.58, "end": 1320.88, "word": " دومين", "probability": 0.5442708333333334}, {"start": 1320.88, "end": 1321.14, "word": " الـ", "probability": 0.843017578125}, {"start": 1321.14, "end": 1321.28, "word": " T", "probability": 0.92138671875}, {"start": 1321.28, "end": 1322.22, "word": " والـ", "probability": 0.56304931640625}, {"start": 1322.22, "end": 1322.36, "word": " T", "probability": 0.966796875}, {"start": 1322.36, "end": 1322.54, "word": " X", "probability": 0.943359375}, {"start": 1322.54, "end": 1322.98, "word": " بتساوي", "probability": 0.822509765625}, {"start": 1322.98, "end": 1323.32, "word": " Y", "probability": 0.97509765625}, {"start": 1323.32, "end": 1324.24, "word": " Automatic", "probability": 0.55645751953125}, {"start": 1324.24, "end": 1324.56, "word": " هذا", "probability": 0.64453125}, {"start": 1324.56, "end": 1324.8, "word": " إيش", "probability": 0.8810221354166666}, {"start": 1324.8, "end": 1325.36, "word": " معناته", "probability": 0.9684244791666666}, {"start": 1325.36, "end": 1326.02, "word": " إنه", "probability": 0.6217041015625}, {"start": 1326.02, "end": 1326.4, "word": " هتكون", "probability": 0.890625}, {"start": 1326.4, "end": 1326.56, "word": " الـ", "probability": 0.89306640625}, {"start": 1326.56, "end": 1326.86, "word": " T", "probability": 0.92919921875}, {"start": 1326.86, "end": 1327.5, "word": " is", "probability": 0.67724609375}, {"start": 1327.5, "end": 1328.08, "word": " closed", "probability": 0.78564453125}, {"start": 1328.08, "end": 1329.02, "word": " واضح", "probability": 0.9537760416666666}, {"start": 1329.02, "end": 1329.38, "word": " الفرق", "probability": 0.98388671875}, {"start": 1329.38, "end": 1329.58, "word": " بين", "probability": 0.9873046875}, {"start": 1329.58, "end": 1329.72, "word": " ال", "probability": 0.95947265625}, {"start": 1329.72, "end": 1331.34, "word": " continuity", "probability": 0.7197265625}, {"start": 1331.34, "end": 1333.56, "word": " بتلالة", "probability": 0.90625}, {"start": 1333.56, "end": 1334.06, "word": " اللي", "probability": 0.883544921875}, {"start": 1334.06, "end": 1334.36, "word": " هو", "probability": 0.99267578125}, {"start": 1334.36, "end": 1334.74, "word": " ال", "probability": 0.7822265625}, {"start": 1334.74, "end": 1335.2, "word": " sequences", "probability": 0.62841796875}, {"start": 1335.2, "end": 1335.54, "word": " و", "probability": 0.6005859375}, {"start": 1335.54, "end": 1335.74, "word": " ال", "probability": 0.88818359375}, {"start": 1335.74, "end": 1336.66, "word": " closedness", "probability": 0.690185546875}, {"start": 1336.66, "end": 1337.06, "word": " للـ", "probability": 0.70068359375}, {"start": 1337.06, "end": 1337.16, "word": " T", "probability": 0.900390625}, {"start": 1337.16, "end": 1337.7, "word": " بدلالة", "probability": 0.910888671875}, {"start": 1337.7, "end": 1337.9, "word": " ال", "probability": 0.94970703125}, {"start": 1337.9, "end": 1339.08, "word": " sequences", "probability": 0.49560546875}, {"start": 1339.08, "end": 1339.42, "word": " هاي", "probability": 0.5213623046875}, {"start": 1339.42, "end": 1339.82, "word": " الفرق", "probability": 0.9894205729166666}, {"start": 1339.82, "end": 1340.04, "word": " بين", "probability": 0.9814453125}, {"start": 1340.04, "end": 1340.26, "word": " إنه", "probability": 0.45440673828125}, {"start": 1340.26, "end": 1340.48, "word": " هاي", "probability": 0.69482421875}, {"start": 1340.48, "end": 1340.96, "word": " الأمور", "probability": 0.98486328125}, {"start": 1340.96, "end": 1341.34, "word": " واضحة", "probability": 0.9866943359375}], "temperature": 1.0}, {"id": 59, "seek": 135663, "start": 1345.07, "end": 1356.63, "text": "خلّيني بس نكمل اللي بنحكيه suppose that T is closed", "tokens": [9778, 1211, 11703, 9957, 1829, 4724, 3794, 8717, 24793, 1211, 13672, 1829, 44945, 5016, 4117, 1829, 3224, 7297, 300, 314, 307, 5395], "avg_logprob": -0.24371603001718936, "compression_ratio": 0.9733333333333334, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1345.07, "end": 1345.51, "word": "خلّيني", "probability": 0.85869140625}, {"start": 1345.51, "end": 1345.71, "word": " بس", "probability": 0.8916015625}, {"start": 1345.71, "end": 1346.19, "word": " نكمل", "probability": 0.8077799479166666}, {"start": 1346.19, "end": 1346.43, "word": " اللي", "probability": 0.9482421875}, {"start": 1346.43, "end": 1347.47, "word": " بنحكيه", "probability": 0.93935546875}, {"start": 1347.47, "end": 1350.77, "word": " suppose", "probability": 0.1153564453125}, {"start": 1350.77, "end": 1351.29, "word": " that", "probability": 0.93505859375}, {"start": 1351.29, "end": 1355.09, "word": " T", "probability": 0.822265625}, {"start": 1355.09, "end": 1356.09, "word": " is", "probability": 0.95703125}, {"start": 1356.09, "end": 1356.63, "word": " closed", "probability": 0.919921875}], "temperature": 1.0}, {"id": 60, "seek": 138153, "start": 1360.87, "end": 1381.53, "text": "الـ openness بتحكي علاقة بين T inverse و T إذا بدنا نترجم على T inverse بيصير كلام تاني then T is closed إذا دول اللي ده property صحيحة نيجي الآن إبرهن suppose that T is closed إذا G of T إيش ماله؟ Closed", "tokens": [6027, 39184, 1269, 1287, 39894, 5016, 4117, 1829, 11203, 995, 28671, 49374, 314, 17340, 4032, 314, 11933, 15730, 47525, 8315, 8717, 2655, 47341, 2304, 15844, 314, 17340, 4724, 1829, 9381, 13546, 28242, 10943, 6055, 7649, 1829, 550, 314, 307, 5395, 11933, 15730, 11778, 12610, 13672, 1829, 11778, 3224, 4707, 20328, 5016, 1829, 5016, 3660, 8717, 1829, 7435, 1829, 6024, 48506, 11933, 26890, 3224, 1863, 7297, 300, 314, 307, 5395, 11933, 15730, 460, 295, 314, 11933, 1829, 8592, 3714, 6027, 3224, 22807, 2033, 1744], "avg_logprob": -0.3031993955373764, "compression_ratio": 1.4285714285714286, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1360.87, "end": 1361.59, "word": "الـ", "probability": 0.6351318359375}, {"start": 1361.59, "end": 1362.31, "word": " openness", "probability": 0.6021728515625}, {"start": 1362.31, "end": 1362.67, "word": " بتحكي", "probability": 0.881103515625}, {"start": 1362.67, "end": 1363.15, "word": " علاقة", "probability": 0.8800455729166666}, {"start": 1363.15, "end": 1363.31, "word": " بين", "probability": 0.51171875}, {"start": 1363.31, "end": 1363.49, "word": " T", "probability": 0.6572265625}, {"start": 1363.49, "end": 1363.95, "word": " inverse", "probability": 0.46533203125}, {"start": 1363.95, "end": 1364.47, "word": " و", "probability": 0.88525390625}, {"start": 1364.47, "end": 1366.07, "word": " T", "probability": 0.5859375}, {"start": 1366.07, "end": 1366.79, "word": " إذا", "probability": 0.6690673828125}, {"start": 1366.79, "end": 1367.01, "word": " بدنا", "probability": 0.84228515625}, {"start": 1367.01, "end": 1367.39, "word": " نترجم", "probability": 0.990478515625}, {"start": 1367.39, "end": 1367.49, "word": " على", "probability": 0.35986328125}, {"start": 1367.49, "end": 1367.69, "word": " T", "probability": 0.88525390625}, {"start": 1367.69, "end": 1368.15, "word": " inverse", "probability": 0.9013671875}, {"start": 1368.15, "end": 1368.49, "word": " بيصير", "probability": 0.7720947265625}, {"start": 1368.49, "end": 1368.85, "word": " كلام", "probability": 0.84130859375}, {"start": 1368.85, "end": 1369.31, "word": " تاني", "probability": 0.9021809895833334}, {"start": 1369.31, "end": 1369.77, "word": " then", "probability": 0.2359619140625}, {"start": 1369.77, "end": 1370.11, "word": " T", "probability": 0.91552734375}, {"start": 1370.11, "end": 1370.43, "word": " is", "probability": 0.95947265625}, {"start": 1370.43, "end": 1370.91, "word": " closed", "probability": 0.8857421875}, {"start": 1370.91, "end": 1371.13, "word": " إذا", "probability": 0.712646484375}, {"start": 1371.13, "end": 1371.49, "word": " دول", "probability": 0.72900390625}, {"start": 1371.49, "end": 1371.79, "word": " اللي", "probability": 0.743408203125}, {"start": 1371.79, "end": 1372.13, "word": " ده", "probability": 0.5262451171875}, {"start": 1372.13, "end": 1372.39, "word": " property", "probability": 0.353271484375}, {"start": 1372.39, "end": 1374.67, "word": " صحيحة", "probability": 0.8865234375}, {"start": 1374.67, "end": 1375.47, "word": " نيجي", "probability": 0.8948974609375}, {"start": 1375.47, "end": 1375.81, "word": " الآن", "probability": 0.72314453125}, {"start": 1375.81, "end": 1376.33, "word": " إبرهن", "probability": 0.77239990234375}, {"start": 1376.33, "end": 1376.69, "word": " suppose", "probability": 0.76220703125}, {"start": 1376.69, "end": 1377.13, "word": " that", "probability": 0.8916015625}, {"start": 1377.13, "end": 1377.51, "word": " T", "probability": 0.96337890625}, {"start": 1377.51, "end": 1377.77, "word": " is", "probability": 0.96923828125}, {"start": 1377.77, "end": 1378.29, "word": " closed", "probability": 0.93115234375}, {"start": 1378.29, "end": 1379.33, "word": " إذا", "probability": 0.800048828125}, {"start": 1379.33, "end": 1379.69, "word": " G", "probability": 0.288818359375}, {"start": 1379.69, "end": 1379.91, "word": " of", "probability": 0.68701171875}, {"start": 1379.91, "end": 1380.11, "word": " T", "probability": 0.9833984375}, {"start": 1380.11, "end": 1380.35, "word": " إيش", "probability": 0.8699544270833334}, {"start": 1380.35, "end": 1381.03, "word": " ماله؟", "probability": 0.7679443359375}, {"start": 1381.03, "end": 1381.53, "word": " Closed", "probability": 0.71142578125}], "temperature": 1.0}, {"id": 61, "seek": 140704, "start": 1382.6, "end": 1407.04, "text": "الان بدي اثبت لك اخد هذه و هذه و اصلك لهذه المجموعه ماشي؟ ممكن خلصنا الـ visual اول طيب اذا بدي اخد ماعطينيه عشان استعمله بدي اقول له let xn بتروح للـx هيها و الـxn في domain الـT و خلينا ناخد Txn بتروح لمين؟ للـY من الحديث هذا اكيد الـxn و Txn وين موجود؟", "tokens": [6027, 7649, 4724, 16254, 1975, 12984, 3555, 2655, 5296, 4117, 1975, 9778, 3215, 29538, 4032, 29538, 4032, 1975, 36520, 4117, 46740, 24192, 9673, 7435, 2304, 45367, 3224, 3714, 33599, 1829, 22807, 3714, 43020, 16490, 1211, 9381, 8315, 2423, 39184, 5056, 1975, 12610, 23032, 1829, 3555, 1975, 15730, 4724, 16254, 1975, 9778, 3215, 19446, 3615, 9566, 9957, 1829, 3224, 6225, 8592, 7649, 44713, 25957, 43761, 4724, 16254, 1975, 39648, 46740, 718, 2031, 77, 39894, 32887, 5016, 24976, 39184, 87, 39896, 11296, 4032, 2423, 39184, 87, 77, 8978, 9274, 2423, 39184, 51, 4032, 16490, 20292, 8315, 8717, 47283, 3215, 314, 87, 77, 39894, 32887, 5016, 32767, 9957, 22807, 24976, 39184, 56, 9154, 21542, 16254, 12984, 23758, 1975, 4117, 25708, 2423, 39184, 87, 77, 4032, 314, 87, 77, 4032, 9957, 3714, 29245, 23328, 22807], "avg_logprob": -0.35132575554378104, "compression_ratio": 1.7791666666666666, "no_speech_prob": 8.344650268554688e-07, "words": [{"start": 1382.6, "end": 1382.98, "word": "الان", "probability": 0.6328125}, {"start": 1382.98, "end": 1383.3, "word": " بدي", "probability": 0.411865234375}, {"start": 1383.3, "end": 1383.76, "word": " اثبت", "probability": 0.76666259765625}, {"start": 1383.76, "end": 1384.18, "word": " لك", "probability": 0.78466796875}, {"start": 1384.18, "end": 1385.08, "word": " اخد", "probability": 0.86279296875}, {"start": 1385.08, "end": 1385.58, "word": " هذه", "probability": 0.82470703125}, {"start": 1385.58, "end": 1386.32, "word": " و", "probability": 0.68408203125}, {"start": 1386.32, "end": 1386.84, "word": " هذه", "probability": 0.869140625}, {"start": 1386.84, "end": 1387.46, "word": " و", "probability": 0.98779296875}, {"start": 1387.46, "end": 1387.82, "word": " اصلك", "probability": 0.73291015625}, {"start": 1387.82, "end": 1388.22, "word": " لهذه", "probability": 0.885009765625}, {"start": 1388.22, "end": 1388.38, "word": " المجموعه", "probability": 0.440478515625}, {"start": 1388.38, "end": 1389.28, "word": " ماشي؟", "probability": 0.66851806640625}, {"start": 1389.28, "end": 1389.44, "word": " ممكن", "probability": 0.7001953125}, {"start": 1389.44, "end": 1389.92, "word": " خلصنا", "probability": 0.6552734375}, {"start": 1389.92, "end": 1390.1, "word": " الـ", "probability": 0.5450439453125}, {"start": 1390.1, "end": 1390.32, "word": " visual", "probability": 0.04815673828125}, {"start": 1390.32, "end": 1390.62, "word": " اول", "probability": 0.7666015625}, {"start": 1390.62, "end": 1391.12, "word": " طيب", "probability": 0.8098958333333334}, {"start": 1391.12, "end": 1391.26, "word": " اذا", "probability": 0.763916015625}, {"start": 1391.26, "end": 1391.48, "word": " بدي", "probability": 0.76416015625}, {"start": 1391.48, "end": 1392.52, "word": " اخد", "probability": 0.81005859375}, {"start": 1392.52, "end": 1393.84, "word": " ماعطينيه", "probability": 0.7080485026041666}, {"start": 1393.84, "end": 1394.06, "word": " عشان", "probability": 0.9052734375}, {"start": 1394.06, "end": 1394.6, "word": " استعمله", "probability": 0.9108072916666666}, {"start": 1394.6, "end": 1395.06, "word": " بدي", "probability": 0.85595703125}, {"start": 1395.06, "end": 1395.22, "word": " اقول", "probability": 0.88916015625}, {"start": 1395.22, "end": 1395.34, "word": " له", "probability": 0.369140625}, {"start": 1395.34, "end": 1395.48, "word": " let", "probability": 0.67431640625}, {"start": 1395.48, "end": 1395.8, "word": " xn", "probability": 0.576904296875}, {"start": 1395.8, "end": 1396.1, "word": " بتروح", "probability": 0.9065755208333334}, {"start": 1396.1, "end": 1396.56, "word": " للـx", "probability": 0.5055338541666666}, {"start": 1396.56, "end": 1397.16, "word": " هيها", "probability": 0.6666259765625}, {"start": 1397.16, "end": 1397.56, "word": " و", "probability": 0.71923828125}, {"start": 1397.56, "end": 1397.94, "word": " الـxn", "probability": 0.7421875}, {"start": 1397.94, "end": 1398.06, "word": " في", "probability": 0.91455078125}, {"start": 1398.06, "end": 1398.24, "word": " domain", "probability": 0.603515625}, {"start": 1398.24, "end": 1398.7, "word": " الـT", "probability": 0.6961263020833334}, {"start": 1398.7, "end": 1399.26, "word": " و", "probability": 0.50341796875}, {"start": 1399.26, "end": 1399.62, "word": " خلينا", "probability": 0.6817220052083334}, {"start": 1399.62, "end": 1399.92, "word": " ناخد", "probability": 0.984375}, {"start": 1399.92, "end": 1400.36, "word": " Txn", "probability": 0.552978515625}, {"start": 1400.36, "end": 1400.66, "word": " بتروح", "probability": 0.9700520833333334}, {"start": 1400.66, "end": 1401.26, "word": " لمين؟", "probability": 0.6629231770833334}, {"start": 1401.26, "end": 1401.68, "word": " للـY", "probability": 0.8362630208333334}, {"start": 1401.68, "end": 1402.6, "word": " من", "probability": 0.958984375}, {"start": 1402.6, "end": 1403.18, "word": " الحديث", "probability": 0.9757486979166666}, {"start": 1403.18, "end": 1403.7, "word": " هذا", "probability": 0.9794921875}, {"start": 1403.7, "end": 1404.9, "word": " اكيد", "probability": 0.8854166666666666}, {"start": 1404.9, "end": 1405.44, "word": " الـxn", "probability": 0.833984375}, {"start": 1405.44, "end": 1405.54, "word": " و", "probability": 0.9453125}, {"start": 1405.54, "end": 1406.14, "word": " Txn", "probability": 0.8489583333333334}, {"start": 1406.14, "end": 1406.32, "word": " وين", "probability": 0.6060791015625}, {"start": 1406.32, "end": 1407.04, "word": " موجود؟", "probability": 0.9803466796875}], "temperature": 1.0}, {"id": 62, "seek": 143116, "start": 1407.44, "end": 1431.16, "text": "فى الـ G of D ماشي و ال XN و ال T XN وين بتروح لل X و Y لإن هو مضّيل ال X عن وين و مضّيل إيها ال X عن .. على ال X و مضّيل ال T XN على مين؟ على ال T X إذا عند X و Y هتكون وين موجودة؟ فى ال G of D معايا؟ ليش؟ لإن ال T is closed", "tokens": [5172, 7578, 2423, 39184, 460, 295, 413, 3714, 33599, 1829, 4032, 2423, 1783, 45, 4032, 2423, 314, 1783, 45, 4032, 9957, 39894, 32887, 5016, 24976, 1783, 4032, 398, 5296, 28814, 1863, 31439, 3714, 11242, 11703, 26895, 2423, 1783, 18871, 4032, 9957, 4032, 3714, 11242, 11703, 26895, 11933, 1829, 11296, 2423, 1783, 18871, 4386, 15844, 2423, 1783, 4032, 3714, 11242, 11703, 26895, 2423, 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70, "seek": 160410, "start": 1583.82, "end": 1604.1, "text": "طيب ما هو هذا الـ X إيش ما لها عبارة عن continuous functions مش كل ال continuous functions كان بيه إيش ما لها دفعانشياتي ده إذا أكيد اللي هو بده يكون ال domain of T of روبر subspace من مين؟ من ال X إذا هذا ال proper subspace اللي هو of functions اللي بيديها كمان مش بس ما دفعانشيابل", "tokens": [9566, 1829, 3555, 19446, 31439, 23758, 2423, 39184, 1783, 11933, 1829, 8592, 19446, 5296, 11296, 6225, 3555, 9640, 3660, 18871, 10957, 6828, 37893, 28242, 2423, 10957, 6828, 25961, 4724, 1829, 3224, 11933, 1829, 8592, 19446, 5296, 11296, 11778, 5172, 3615, 7649, 8592, 1829, 9307, 1829, 11778, 3224, 11933, 15730, 5551, 4117, 25708, 13672, 1829, 31439, 47525, 3224, 7251, 30544, 2423, 9274, 295, 314, 295, 12602, 2407, 26890, 2090, 17940, 9154, 3714, 9957, 22807, 9154, 2423, 1783, 11933, 15730, 23758, 2423, 2296, 2090, 17940, 13672, 1829, 31439, 295, 6828, 13672, 1829, 4724, 1829, 16254, 11296, 9122, 2304, 7649, 37893, 4724, 3794, 19446, 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1919.25, "end": 1919.61, "word": " then", "probability": 0.6640625}, {"start": 1919.61, "end": 1919.85, "word": " by", "probability": 0.91015625}, {"start": 1919.85, "end": 1920.19, "word": " theorem", "probability": 0.81494140625}, {"start": 1920.19, "end": 1920.53, "word": " كده", "probability": 0.82080078125}, {"start": 1920.53, "end": 1921.13, "word": " T", "probability": 0.814453125}, {"start": 1921.13, "end": 1921.75, "word": " is", "probability": 0.95458984375}, {"start": 1921.75, "end": 1922.27, "word": " closed", "probability": 0.93359375}], "temperature": 1.0}, {"id": 85, "seek": 193569, "start": 1923.97, "end": 1935.69, "text": "إذن هذا مثال على اللي هو closed linear operator which is not bounded يلّا أطلع على فوق ال dot بتقول", "tokens": [28814, 8848, 1863, 23758, 50113, 6027, 15844, 13672, 1829, 31439, 5395, 8213, 12973, 597, 307, 406, 37498, 7251, 1211, 11703, 995, 5551, 9566, 1211, 3615, 15844, 6156, 30543, 2423, 360, 83, 39894, 39648], "avg_logprob": 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لل X", "tokens": [2407, 10721, 4117, 25708, 8978, 1783, 5296, 33456, 8315, 3714, 47283, 3215, 9957, 3224, 4724, 25513, 2288, 2423, 7649, 4032, 8310, 1783, 77, 4478, 294, 9274, 295, 314, 597, 38874, 5296, 27842, 5296, 27842, 24976, 1783], "avg_logprob": -0.4666385167353862, "compression_ratio": 1.125, "no_speech_prob": 8.821487426757812e-06, "words": [{"start": 2141.95, "end": 2142.95, "word": "وأكيد", "probability": 0.8267822265625}, {"start": 2142.95, "end": 2143.09, "word": " في", "probability": 0.83154296875}, {"start": 2143.09, "end": 2143.37, "word": " X", "probability": 0.54150390625}, {"start": 2143.37, "end": 2144.59, "word": " لأننا", "probability": 0.6134440104166666}, {"start": 2144.59, "end": 2144.99, "word": " ماخدينه", "probability": 0.835791015625}, {"start": 2144.99, "end": 2145.33, "word": " بربر", "probability": 0.5927734375}, {"start": 2145.33, "end": 2146.31, "word": " الان", "probability": 0.530059814453125}, {"start": 2146.31, "end": 2146.55, "word": " و", 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new file mode 100644
index 0000000000000000000000000000000000000000..a67452a19a1d03a5ce3753bb08e73e91031abc06
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@@ -0,0 +1 @@
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0.97265625}, {"start": 555.14, "end": 555.64, "word": " التقاطع", "probability": 0.9945068359375}, {"start": 555.64, "end": 555.94, "word": " إذا", "probability": 0.7294921875}, {"start": 555.94, "end": 556.94, "word": " التقاطع", "probability": 0.969970703125}, {"start": 556.94, "end": 557.36, "word": " هيكون", "probability": 0.8671875}, {"start": 557.36, "end": 557.6, "word": " أي", "probability": 0.7470703125}, {"start": 557.6, "end": 558.2, "word": " تقاطع", "probability": 0.9927978515625}, {"start": 558.2, "end": 558.66, "word": " is", "probability": 0.88623046875}, {"start": 558.66, "end": 559.44, "word": " convex", "probability": 0.9326171875}, {"start": 559.44, "end": 560.0, "word": " pipe", "probability": 0.5009765625}], "temperature": 1.0}, {"id": 26, "seek": 56711, "start": 561.29, "end": 567.11, "text": "نجي الآن لنظريتنا الأولى اللي احنا قبل بشوية بدينا نحكي عنها", "tokens": [1863, 7435, 1829, 6024, 48506, 5296, 1863, 19913, 16572, 2655, 8315, 16247, 12610, 7578, 13672, 1829, 1975, 5016, 8315, 12174, 36150, 4724, 8592, 2407, 10632, 47525, 1829, 8315, 8717, 5016, 4117, 1829, 18871, 11296], "avg_logprob": -0.22533482824053083, "compression_ratio": 1.2941176470588236, "no_speech_prob": 0.0, "words": [{"start": 561.29, "end": 561.71, "word": "نجي", "probability": 0.4732666015625}, {"start": 561.71, "end": 561.97, "word": " الآن", "probability": 0.608154296875}, {"start": 561.97, "end": 562.91, "word": " لنظريتنا", "probability": 0.95751953125}, {"start": 562.91, "end": 563.77, "word": " الأولى", "probability": 0.9713541666666666}, {"start": 563.77, "end": 564.11, "word": " اللي", "probability": 0.75244140625}, {"start": 564.11, "end": 564.61, "word": " احنا", "probability": 0.87060546875}, {"start": 564.61, "end": 565.07, "word": " قبل", "probability": 0.931884765625}, {"start": 565.07, "end": 565.65, "word": " بشوية", "probability": 0.899658203125}, {"start": 565.65, "end": 566.09, "word": " بدينا", "probability": 0.7369791666666666}, {"start": 566.09, "end": 566.71, "word": " نحكي", "probability": 0.993408203125}, {"start": 566.71, "end": 567.11, "word": " عنها", "probability": 0.98876953125}], "temperature": 1.0}, {"id": 27, "seek": 57709, "start": 567.93, "end": 577.09, "text": "لأن النظرية بتقول let X be an inner product space and M be a non-empty non-empty convex set", "tokens": [1211, 33456, 28239, 19913, 2288, 10632, 39894, 39648, 718, 1783, 312, 364, 7284, 1674, 1901, 293, 376, 312, 257, 2107, 12, 4543, 88, 2107, 12, 4543, 88, 42432, 992], "avg_logprob": -0.3255208233992259, "compression_ratio": 1.0392156862745099, "no_speech_prob": 0.419189453125, "words": [{"start": 567.93, "end": 568.35, "word": "لأن", "probability": 0.5081787109375}, {"start": 568.35, "end": 568.77, "word": " النظرية", "probability": 0.862060546875}, {"start": 568.77, "end": 569.23, "word": " بتقول", "probability": 0.90380859375}, {"start": 569.23, "end": 569.55, "word": " let", "probability": 0.239990234375}, {"start": 569.55, "end": 569.83, "word": " X", "probability": 0.6982421875}, {"start": 569.83, "end": 570.05, "word": " be", "probability": 0.84033203125}, {"start": 570.05, "end": 570.35, "word": " an", "probability": 0.69091796875}, {"start": 570.35, "end": 570.67, "word": " inner", "probability": 0.91162109375}, {"start": 570.67, "end": 571.11, "word": " product", "probability": 0.947265625}, {"start": 571.11, "end": 571.89, "word": " space", "probability": 0.93115234375}, {"start": 571.89, "end": 573.09, "word": " and", "probability": 0.7060546875}, {"start": 573.09, "end": 573.41, "word": " M", "probability": 0.84326171875}, {"start": 573.41, "end": 573.69, "word": " be", "probability": 0.9013671875}, {"start": 573.69, "end": 573.89, "word": " a", "probability": 0.890625}, {"start": 573.89, "end": 574.05, "word": " non", "probability": 0.84814453125}, {"start": 574.05, "end": 574.75, "word": "-empty", "probability": 0.8186848958333334}, {"start": 574.75, "end": 575.15, "word": " non", "probability": 0.25341796875}, {"start": 575.15, "end": 575.95, "word": "-empty", "probability": 0.9298502604166666}, {"start": 575.95, "end": 576.59, "word": " convex", "probability": 0.95654296875}, {"start": 576.59, "end": 577.09, "word": " set", "probability": 0.96923828125}], "temperature": 1.0}, {"id": 28, "seek": 61546, "start": 607.08, "end": 615.46, "text": "النظرية بتقول ان لو كان عندك X inner product space و M non-empty", "tokens": [6027, 1863, 19913, 2288, 10632, 39894, 39648, 16472, 45164, 25961, 43242, 4117, 1783, 7284, 1674, 1901, 4032, 376, 2107, 12, 4543, 88], "avg_logprob": -0.5224184575288192, "compression_ratio": 0.946236559139785, "no_speech_prob": 7.748603820800781e-07, "words": [{"start": 607.08, "end": 607.96, "word": "النظرية", "probability": 0.7600830078125}, {"start": 607.96, "end": 608.26, "word": " بتقول", "probability": 0.779541015625}, {"start": 608.26, "end": 609.7, "word": " ان", "probability": 0.560546875}, {"start": 609.7, "end": 610.8, "word": " لو", "probability": 0.67431640625}, {"start": 610.8, "end": 611.04, "word": " كان", "probability": 0.8818359375}, {"start": 611.04, "end": 611.34, "word": " عندك", "probability": 0.72021484375}, {"start": 611.34, "end": 611.5, "word": " X", "probability": 0.2457275390625}, {"start": 611.5, "end": 611.84, "word": " inner", "probability": 0.1502685546875}, {"start": 611.84, "end": 612.26, "word": " product", "probability": 0.88134765625}, {"start": 612.26, "end": 612.72, "word": " space", "probability": 0.818359375}, {"start": 612.72, "end": 613.24, "word": " و", "probability": 0.68408203125}, {"start": 613.24, "end": 613.52, "word": " M", "probability": 0.492919921875}, {"start": 613.52, "end": 614.56, "word": " non", "probability": 0.304443359375}, {"start": 614.56, "end": 615.46, "word": "-empty", "probability": 0.68896484375}], "temperature": 1.0}, {"id": 29, "seek": 63954, "start": 615.87, "end": 639.55, "text": "و Convex و Complete إذا التلات شروط هذه تكون موجودة بضمنك أنه لكل X في ال X بقدر ألاقي Y موجودة في M اللي هي normها ال X minus Y بعيد عن ال X هو اللي اللي بيمثل المسافة بين اللي هو ال M و بين ال L ال M و ال X يعني الآن", "tokens": [2407, 2656, 303, 87, 4032, 34687, 11933, 15730, 16712, 1211, 9307, 13412, 32887, 9566, 29538, 6055, 30544, 3714, 29245, 23328, 3660, 4724, 11242, 27842, 4117, 14739, 3224, 5296, 28820, 1783, 8978, 2423, 1783, 4724, 28543, 2288, 5551, 15040, 38436, 398, 3714, 29245, 23328, 3660, 8978, 376, 13672, 1829, 39896, 2026, 11296, 2423, 1783, 3175, 398, 45030, 25708, 18871, 2423, 1783, 31439, 13672, 1829, 13672, 1829, 4724, 32640, 12984, 1211, 9673, 3794, 31845, 3660, 49374, 13672, 1829, 31439, 2423, 376, 4032, 49374, 2423, 441, 2423, 376, 4032, 2423, 1783, 37495, 22653, 6024, 48506], "avg_logprob": -0.2100134479102268, "compression_ratio": 1.7142857142857142, "no_speech_prob": 8.64267349243164e-06, "words": [{"start": 615.87, "end": 616.11, "word": "و", "probability": 0.7001953125}, {"start": 616.11, "end": 616.79, "word": " Convex", "probability": 0.744384765625}, 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634.35, "word": " بين", "probability": 0.9755859375}, {"start": 634.35, "end": 634.51, "word": " اللي", "probability": 0.972412109375}, {"start": 634.51, "end": 634.83, "word": " هو", "probability": 0.98974609375}, {"start": 634.83, "end": 635.11, "word": " ال", "probability": 0.923828125}, {"start": 635.11, "end": 635.35, "word": " M", "probability": 0.98193359375}, {"start": 635.35, "end": 635.49, "word": " و", "probability": 0.60302734375}, {"start": 635.49, "end": 635.77, "word": " بين", "probability": 0.69970703125}, {"start": 635.77, "end": 636.77, "word": " ال", "probability": 0.7021484375}, {"start": 636.77, "end": 637.09, "word": " L", "probability": 0.33349609375}, {"start": 637.09, "end": 637.39, "word": " ال", "probability": 0.5791015625}, {"start": 637.39, "end": 637.69, "word": " M", "probability": 0.962890625}, {"start": 637.69, "end": 637.81, "word": " و", "probability": 0.9228515625}, {"start": 637.81, "end": 637.91, "word": " ال", "probability": 0.85888671875}, {"start": 637.91, "end": 638.19, "word": " X", "probability": 0.9970703125}, {"start": 638.19, "end": 638.93, "word": " يعني", "probability": 0.932861328125}, {"start": 638.93, "end": 639.55, "word": " الآن", "probability": 0.806396484375}], "temperature": 1.0}, {"id": 30, "seek": 66129, "start": 644.01, "end": 661.29, "text": "الان اضمننا اخدنا الان اللي هو شروط معينة على ال M اللي هي لا تسوى Phi او convex او complete بحيث ان هذا بضمنك انه لو اخدت اي X في ال X", "tokens": [6027, 7649, 1975, 11242, 27842, 8315, 1975, 9778, 3215, 8315, 2423, 7649, 13672, 1829, 31439, 13412, 32887, 9566, 20449, 9957, 3660, 15844, 2423, 376, 13672, 1829, 39896, 20193, 6055, 3794, 2407, 7578, 41435, 1975, 2407, 42432, 1975, 2407, 3566, 4724, 5016, 1829, 12984, 16472, 23758, 4724, 11242, 27842, 4117, 16472, 3224, 45164, 1975, 9778, 3215, 2655, 1975, 1829, 1783, 8978, 2423, 1783], "avg_logprob": -0.23177082860280598, "compression_ratio": 1.46, "no_speech_prob": 2.8014183044433594e-06, "words": [{"start": 644.0099999999999, "end": 644.9699999999999, "word": "الان", "probability": 0.7890625}, {"start": 644.9699999999999, "end": 645.93, "word": " اضمننا", "probability": 0.8603515625}, {"start": 645.93, "end": 647.41, "word": " اخدنا", "probability": 0.8974609375}, {"start": 647.41, "end": 648.09, "word": " الان", "probability": 0.74462890625}, {"start": 648.09, "end": 648.83, "word": " اللي", "probability": 0.64208984375}, {"start": 648.83, "end": 648.99, "word": " هو", "probability": 0.97216796875}, {"start": 648.99, "end": 649.49, "word": " شروط", "probability": 0.9645182291666666}, {"start": 649.49, "end": 650.09, "word": " معينة", "probability": 0.95166015625}, {"start": 650.09, "end": 650.27, "word": " على", "probability": 0.78369140625}, {"start": 650.27, "end": 650.43, "word": " ال", "probability": 0.9072265625}, {"start": 650.43, "end": 650.71, "word": " M", "probability": 0.287353515625}, {"start": 650.71, "end": 651.77, "word": " اللي", "probability": 0.81201171875}, {"start": 651.77, "end": 651.93, "word": " هي", "probability": 0.86572265625}, {"start": 651.93, "end": 652.05, "word": " لا", "probability": 0.365966796875}, {"start": 652.05, "end": 652.53, "word": " تسوى", "probability": 0.830322265625}, {"start": 652.53, "end": 652.97, "word": " Phi", "probability": 0.220703125}, {"start": 652.97, "end": 653.75, "word": " او", "probability": 0.751220703125}, {"start": 653.75, "end": 654.43, "word": " convex", "probability": 0.603515625}, {"start": 654.43, "end": 655.19, "word": " او", "probability": 0.876220703125}, {"start": 655.19, "end": 655.97, "word": " complete", "probability": 0.82080078125}, {"start": 655.97, "end": 657.37, "word": " بحيث", "probability": 0.969482421875}, {"start": 657.37, "end": 657.55, "word": " ان", "probability": 0.87744140625}, {"start": 657.55, "end": 657.89, "word": " هذا", "probability": 0.8310546875}, {"start": 657.89, "end": 658.79, "word": " بضمنك", "probability": 0.7275390625}, {"start": 658.79, "end": 659.29, "word": " انه", "probability": 0.595703125}, {"start": 659.29, "end": 659.41, "word": " لو", "probability": 0.71728515625}, {"start": 659.41, "end": 659.89, "word": " اخدت", "probability": 0.9346923828125}, {"start": 659.89, "end": 660.15, "word": " اي", "probability": 0.928955078125}, {"start": 660.15, "end": 660.49, "word": " X", "probability": 0.79931640625}, {"start": 660.49, "end": 660.73, "word": " في", "probability": 0.931640625}, {"start": 660.73, "end": 660.89, "word": " ال", "probability": 0.87939453125}, {"start": 660.89, "end": 661.29, "word": " X", "probability": 0.92724609375}], "temperature": 1.0}, {"id": 31, "seek": 68293, "start": 662.07, "end": 682.93, "text": "و جيت هي ال M هتلاقي نقطة في داخل ال M وحيدة اللي هي هيتمثل المسافة بينها و بين اللي هي ال X اللي هي X minus Y هي اللي تكون Delta المسافة بين X و بين مين اللي هي ال M نيجي الأن للبرهان", "tokens": [2407, 10874, 36081, 39896, 2423, 376, 8032, 2655, 15040, 38436, 8717, 47432, 3660, 8978, 11778, 47283, 1211, 2423, 376, 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"probability": 0.96337890625}, {"start": 676.43, "end": 677.55, "word": " Delta", "probability": 0.57421875}, {"start": 677.55, "end": 678.61, "word": " المسافة", "probability": 0.9825439453125}, {"start": 678.61, "end": 678.83, "word": " بين", "probability": 0.9892578125}, {"start": 678.83, "end": 679.21, "word": " X", "probability": 0.98876953125}, {"start": 679.21, "end": 679.43, "word": " و", "probability": 0.5791015625}, {"start": 679.43, "end": 679.67, "word": " بين", "probability": 0.90869140625}, {"start": 679.67, "end": 680.19, "word": " مين", "probability": 0.85986328125}, {"start": 680.19, "end": 680.71, "word": " اللي", "probability": 0.992919921875}, {"start": 680.71, "end": 681.05, "word": " هي", "probability": 0.94921875}, {"start": 681.05, "end": 681.47, "word": " ال", "probability": 0.9150390625}, {"start": 681.47, "end": 681.61, "word": " M", "probability": 0.99267578125}, {"start": 681.61, "end": 682.03, "word": " نيجي", "probability": 0.9306640625}, {"start": 682.03, "end": 682.29, "word": " الأن", "probability": 0.759765625}, {"start": 682.29, "end": 682.93, "word": " للبرهان", "probability": 0.9425048828125}], "temperature": 1.0}, {"id": 32, "seek": 69432, "start": 684.14, "end": 694.32, "text": "نقسم البرهان لجزءين جزء أثبت ال existence وجود النقطة وقسم أخر يمثل ال uniqueness أو وحدانية النقطة أو النقطة واحدة", "tokens": [1863, 4587, 38251, 2423, 26890, 3224, 7649, 5296, 7435, 11622, 38207, 9957, 10874, 11622, 38207, 5551, 12984, 3555, 2655, 2423, 9123, 49610, 23328, 28239, 47432, 3660, 4032, 4587, 38251, 5551, 34740, 7251, 2304, 12984, 1211, 2423, 48294, 34051, 4032, 24401, 7649, 10632, 28239, 47432, 3660, 34051, 28239, 47432, 3660, 36764, 24401, 3660], "avg_logprob": -0.27211084905660377, "compression_ratio": 1.4545454545454546, "no_speech_prob": 0.0, "words": [{"start": 684.14, "end": 685.1, "word": "نقسم", "probability": 0.4899088541666667}, {"start": 685.1, "end": 685.6, "word": " البرهان", "probability": 0.78717041015625}, {"start": 685.6, "end": 686.06, "word": " لجزءين", "probability": 0.773291015625}, {"start": 686.06, "end": 686.4, "word": " جزء", "probability": 0.83056640625}, {"start": 686.4, "end": 686.86, "word": " أثبت", "probability": 0.5699462890625}, {"start": 686.86, "end": 686.96, "word": " ال", "probability": 0.7236328125}, {"start": 686.96, "end": 687.52, "word": " existence", "probability": 0.90576171875}, {"start": 687.52, "end": 688.2, "word": " وجود", "probability": 0.83056640625}, {"start": 688.2, "end": 688.96, "word": " النقطة", "probability": 0.96923828125}, {"start": 688.96, "end": 689.78, "word": " وقسم", "probability": 0.8045247395833334}, {"start": 689.78, "end": 690.16, "word": " أخر", "probability": 0.733642578125}, {"start": 690.16, "end": 690.86, "word": " يمثل", "probability": 0.947021484375}, {"start": 690.86, "end": 691.02, "word": " ال", "probability": 0.71923828125}, {"start": 691.02, "end": 691.66, "word": " uniqueness", "probability": 0.7451171875}, {"start": 691.66, "end": 692.1, "word": " أو", "probability": 0.8935546875}, {"start": 692.1, "end": 692.72, "word": " وحدانية", "probability": 0.926025390625}, {"start": 692.72, "end": 693.3, "word": " النقطة", "probability": 0.9783528645833334}, {"start": 693.3, "end": 693.48, "word": " أو", "probability": 0.92919921875}, {"start": 693.48, "end": 693.88, "word": " النقطة", "probability": 0.9736328125}, {"start": 693.88, "end": 694.32, "word": " واحدة", "probability": 0.7772623697916666}], "temperature": 1.0}, {"id": 33, "seek": 71570, "start": 694.94, "end": 715.7, "text": "أطلع لفوق خلّينا نشوف ال existence أول اشي احنا ال delta بساوي ال infimum من norm ال X minus Y حيث Y تل ده Y نقص تل ده حيث Y تل ده element من مين هذا تعريف من اللي هي المسافة بينه نقطة X وبين اللي هي ال set ال infimum هذا طبعا لما نتعريف ال infimum", "tokens": [10721, 9566, 1211, 3615, 5296, 5172, 30543, 16490, 1211, 11703, 9957, 995, 8717, 8592, 38688, 2423, 9123, 5551, 12610, 1975, 8592, 1829, 1975, 5016, 8315, 2423, 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ال", "probability": 0.287841796875}, {"start": 701.04, "end": 701.16, "word": " X", "probability": 0.69921875}, {"start": 701.16, "end": 701.46, "word": " minus", "probability": 0.5712890625}, {"start": 701.46, "end": 701.82, "word": " Y", "probability": 0.98974609375}, {"start": 701.82, "end": 702.64, "word": " حيث", "probability": 0.96533203125}, {"start": 702.64, "end": 702.86, "word": " Y", "probability": 0.88720703125}, {"start": 702.86, "end": 703.1, "word": " تل", "probability": 0.6282958984375}, {"start": 703.1, "end": 703.38, "word": " ده", "probability": 0.78076171875}, {"start": 703.38, "end": 703.64, "word": " Y", "probability": 0.27490234375}, {"start": 703.64, "end": 704.1, "word": " نقص", "probability": 0.8020833333333334}, {"start": 704.1, "end": 704.32, "word": " تل", "probability": 0.82470703125}, {"start": 704.32, "end": 704.52, "word": " ده", "probability": 0.982666015625}, {"start": 704.52, "end": 704.78, "word": " حيث", "probability": 0.9422200520833334}, 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"word": " بينه", "probability": 0.8818359375}, {"start": 709.54, "end": 709.86, "word": " نقطة", "probability": 0.9715169270833334}, {"start": 709.86, "end": 710.16, "word": " X", "probability": 0.966796875}, {"start": 710.16, "end": 710.92, "word": " وبين", "probability": 0.7034912109375}, {"start": 710.92, "end": 711.44, "word": " اللي", "probability": 0.944091796875}, {"start": 711.44, "end": 711.8, "word": " هي", "probability": 0.51318359375}, {"start": 711.8, "end": 712.08, "word": " ال", "probability": 0.849609375}, {"start": 712.08, "end": 712.34, "word": " set", "probability": 0.5146484375}, {"start": 712.34, "end": 712.72, "word": " ال", "probability": 0.369140625}, {"start": 712.72, "end": 713.6, "word": " infimum", "probability": 0.8876953125}, {"start": 713.6, "end": 713.88, "word": " هذا", "probability": 0.8515625}, {"start": 713.88, "end": 714.26, "word": " طبعا", "probability": 0.886474609375}, {"start": 714.26, "end": 714.36, "word": " لما", "probability": 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"temperature": 1.0}, {"id": 63, "seek": 137672, "start": 1361.52, "end": 1376.72, "text": "أه فاهمين طرحت وضفت أطبقها عليهم هدولة على اللي هي الجهتين هدول بساوي اتنين هيطرحن ومجوحن اتنين في اتنين في الأولى y minus x في كل تربيع هدول اللي اطلع", "tokens": [10721, 3224, 6156, 995, 16095, 9957, 23032, 2288, 33753, 4032, 11242, 5172, 2655, 5551, 9566, 3555, 4587, 11296, 25894, 16095, 8032, 3215, 12610, 3660, 15844, 13672, 1829, 39896, 25724, 3224, 2655, 9957, 8032, 3215, 12610, 4724, 3794, 995, 45865, 1975, 2655, 1863, 9957, 39896, 9566, 2288, 5016, 1863, 4032, 2304, 7435, 2407, 5016, 1863, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 8978, 16247, 12610, 7578, 288, 3175, 2031, 8978, 28242, 6055, 2288, 21292, 3615, 8032, 3215, 12610, 13672, 1829, 1975, 9566, 1211, 3615], "avg_logprob": -0.25781251316846804, "compression_ratio": 1.7161290322580645, "no_speech_prob": 1.4901161193847656e-06, "words": [{"start": 1361.52, "end": 1361.8, "word": "أه", "probability": 0.3768310546875}, {"start": 1361.8, "end": 1362.24, "word": " فاهمين", "probability": 0.9481201171875}, {"start": 1362.24, "end": 1362.68, "word": " طرحت", "probability": 0.6500651041666666}, {"start": 1362.68, "end": 1363.3, "word": " وضفت", "probability": 0.840087890625}, {"start": 1363.3, "end": 1364.24, "word": " أطبقها", "probability": 0.7943359375}, {"start": 1364.24, "end": 1364.6, "word": " عليهم", "probability": 0.630859375}, {"start": 1364.6, "end": 1365.12, "word": " هدولة", "probability": 0.71502685546875}, {"start": 1365.12, "end": 1365.48, "word": " على", "probability": 0.705078125}, {"start": 1365.48, "end": 1365.74, "word": " اللي", "probability": 0.76953125}, {"start": 1365.74, "end": 1365.88, "word": " هي", "probability": 0.81494140625}, {"start": 1365.88, "end": 1366.38, "word": " الجهتين", "probability": 0.9432373046875}, {"start": 1366.38, "end": 1366.78, "word": " هدول", "probability": 0.8642578125}, {"start": 1366.78, "end": 1367.7, "word": " بساوي", "probability": 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هذا orthogonal عالميا على ال Y ماشي الحالة نشوف الآن هذا اللي هو نشوف كيف نثبت أنه orthogonal to Y طيب", "tokens": [6027, 20292, 12602, 26108, 3615, 8315, 3224, 23758, 41950, 12610, 49374, 8032, 6027, 8717, 3224, 6027, 23758, 41950, 12610, 9673, 3794, 31845, 3660, 49374, 16095, 39896, 30544, 23758, 41488, 6225, 45340, 25528, 15844, 2423, 398, 3714, 33599, 1829, 21542, 6027, 3660, 8717, 8592, 38688, 6024, 48506, 23758, 13672, 1829, 31439, 8717, 8592, 38688, 9122, 33911, 8717, 12984, 3555, 2655, 14739, 3224, 41488, 281, 398, 23032, 1829, 3555], "avg_logprob": -0.35248162816552553, "compression_ratio": 1.6867469879518073, "no_speech_prob": 0.00014162063598632812, "words": [{"start": 1587.99, "end": 1588.25, "word": "اللي", "probability": 0.34716796875}, {"start": 1588.25, "end": 1588.75, "word": " راجعناه", "probability": 0.62958984375}, {"start": 1588.75, "end": 1588.95, "word": " هذا", "probability": 0.6826171875}, {"start": 1588.95, "end": 1589.27, "word": " الطول", "probability": 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{"id": 77, "seek": 166158, "start": 1637.38, "end": 1661.58, "text": "طيب معايا طيب احنا طبعا شغلنا هان وين يا جماعة في inner product space تنسوش بشتغل وين في inner product space و احنا عرفنا ال orthogonality فيها لان نفترض ان زد بيساوي x minus y is not orthogonal to y مدام مش orthogonal اذا هلاجي y في ال y بحيث ان زد و هذا النقطة اللي اشماله لايساوي سفر", "tokens": [9566, 1829, 3555, 20449, 995, 25528, 23032, 1829, 3555, 1975, 5016, 8315, 23032, 3555, 3615, 995, 13412, 17082, 1211, 8315, 8032, 7649, 4032, 9957, 35186, 10874, 15042, 27884, 8978, 7284, 1674, 1901, 6055, 1863, 3794, 2407, 8592, 4724, 8592, 2655, 17082, 1211, 4032, 9957, 8978, 7284, 1674, 1901, 4032, 1975, 5016, 8315, 6225, 28480, 8315, 2423, 38130, 266, 1860, 8978, 11296, 5296, 7649, 8717, 5172, 2655, 43042, 16472, 30767, 3215, 4724, 1829, 3794, 995, 45865, 2031, 3175, 288, 307, 406, 41488, 281, 288, 3714, 3215, 10943, 37893, 41488, 1975, 15730, 8032, 15040, 7435, 1829, 288, 8978, 2423, 288, 4724, 5016, 1829, 12984, 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للوقت ده الآن هذولة بأهلنا لا إشي أنه أقدر أجزء ال space", "tokens": [2407, 3224, 15730, 8978, 4839, 6206, 4105, 7504, 13672, 1829, 31439, 5296, 31377, 2304, 6055, 30544, 43242, 1829, 13672, 1829, 39896, 1176, 29538, 27554, 664, 21523, 15844, 13672, 1829, 39896, 2423, 1422, 1901, 398, 23032, 1829, 3555, 8717, 1863, 7435, 1829, 24976, 30543, 2655, 11778, 3224, 6024, 48506, 8032, 8848, 12610, 3660, 4724, 10721, 3224, 1211, 8315, 20193, 11933, 8592, 1829, 14739, 3224, 5551, 28543, 2288, 5551, 7435, 11622, 38207, 2423, 1901], "avg_logprob": -0.3088612915718392, "compression_ratio": 1.3697916666666667, "no_speech_prob": 1.8477439880371094e-06, "words": [{"start": 2069.4, "end": 2069.96, "word": "وهذا", "probability": 0.7384440104166666}, {"start": 2069.96, "end": 2070.14, "word": " في", "probability": 0.84814453125}, {"start": 2070.14, "end": 2070.84, "word": " Contradiction", "probability": 0.7259521484375}, {"start": 2070.84, "end": 2071.34, "word": " Therefore", "probability": 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0.962890625}, {"start": 2078.12, "end": 2078.5, "word": " هي", "probability": 0.96337890625}, {"start": 2078.5, "end": 2079.1, "word": " ال", "probability": 0.82861328125}, {"start": 2079.1, "end": 2080.52, "word": " sub", "probability": 0.23779296875}, {"start": 2080.52, "end": 2080.88, "word": " space", "probability": 0.52783203125}, {"start": 2080.88, "end": 2081.22, "word": " Y", "probability": 0.91943359375}, {"start": 2081.22, "end": 2082.7, "word": " طيب", "probability": 0.739501953125}, {"start": 2082.7, "end": 2083.66, "word": " ننجي", "probability": 0.74627685546875}, {"start": 2083.66, "end": 2083.98, "word": " للوقت", "probability": 0.6155598958333334}, {"start": 2083.98, "end": 2084.22, "word": " ده", "probability": 0.5543212890625}, {"start": 2084.22, "end": 2086.68, "word": " الآن", "probability": 0.7103271484375}, {"start": 2086.68, "end": 2088.54, "word": " هذولة", "probability": 0.751953125}, {"start": 2088.54, "end": 2089.34, "word": " بأهلنا", "probability": 0.81240234375}, {"start": 2089.34, "end": 2090.14, "word": " لا", "probability": 0.78662109375}, {"start": 2090.14, "end": 2091.22, "word": " إشي", "probability": 0.8240559895833334}, {"start": 2091.22, "end": 2092.14, "word": " أنه", "probability": 0.699951171875}, {"start": 2092.14, "end": 2092.84, "word": " أقدر", "probability": 0.9798177083333334}, {"start": 2092.84, "end": 2093.88, "word": " أجزء", "probability": 0.9200439453125}, {"start": 2093.88, "end": 2094.06, "word": " ال", "probability": 0.92333984375}, {"start": 2094.06, "end": 2094.44, "word": " space", "probability": 0.888671875}], "temperature": 1.0}, {"id": 96, "seek": 211748, "start": 2096.09, "end": 2117.49, "text": "أي space أو inner product space أجزؤه إلى جزئين الجزء والجزء الorthogonal عليه وبدأ أسميت اسمه الآن ماشي الحالة let a vector space X is said to be the direct sum of two subspaces Y and Z of X", "tokens": [10721, 1829, 1901, 34051, 7284, 1674, 1901, 5551, 7435, 11622, 33604, 3224, 30731, 10874, 11622, 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"text": "نفترض الآن suppose that there are y1 و y2 في ال y و z1 و z2 في ال y و ال x نقدر نكتبها على صورة x y1 زي z1 و ال x نقدر نكتبها على صورة y2 زي z2 و نوصلكم أنه لازم يكونين متساويتين ماشي الوصول سهل then احسبلي الآن", "tokens": [1863, 5172, 2655, 43042, 6024, 48506, 7297, 300, 456, 366, 288, 16, 4032, 288, 17, 8978, 2423, 288, 4032, 710, 16, 4032, 710, 17, 8978, 2423, 288, 4032, 2423, 2031, 8717, 28543, 2288, 8717, 4117, 2655, 3555, 11296, 15844, 20328, 13063, 3660, 2031, 288, 16, 30767, 1829, 710, 16, 4032, 2423, 2031, 8717, 28543, 2288, 8717, 4117, 2655, 3555, 11296, 15844, 20328, 13063, 3660, 288, 17, 30767, 1829, 710, 17, 4032, 8717, 2407, 36520, 24793, 14739, 3224, 5296, 31377, 2304, 7251, 30544, 9957, 44650, 3794, 995, 45865, 2655, 9957, 3714, 33599, 1829, 2423, 2407, 9381, 12610, 8608, 3224, 1211, 550, 1975, 5016, 35457, 20292, 6024, 48506], "avg_logprob": -0.20487734146207293, "compression_ratio": 1.7210526315789474, "no_speech_prob": 1.1444091796875e-05, "words": 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هو", "probability": 0.98828125}, {"start": 3553.07, "end": 3553.41, "word": " ال", "probability": 0.8857421875}, {"start": 3553.41, "end": 3553.79, "word": " V", "probability": 0.98828125}, {"start": 3553.79, "end": 3554.43, "word": " closure", "probability": 0.94091796875}, {"start": 3554.43, "end": 3554.67, "word": " هو", "probability": 0.9716796875}, {"start": 3554.67, "end": 3554.77, "word": " ال", "probability": 0.861328125}, {"start": 3554.77, "end": 3555.03, "word": " H،", "probability": 0.878662109375}, {"start": 3555.03, "end": 3555.13, "word": " لو", "probability": 0.9677734375}, {"start": 3555.13, "end": 3555.51, "word": " أخدنا", "probability": 0.9871826171875}, {"start": 3555.51, "end": 3555.71, "word": " X", "probability": 0.95654296875}, {"start": 3555.71, "end": 3555.85, "word": " في", "probability": 0.9716796875}, {"start": 3555.85, "end": 3555.95, "word": " ال", "probability": 0.9072265625}, {"start": 3555.95, "end": 3556.15, "word": " V", "probability": 0.9921875}, {"start": 3556.15, "end": 3557.21, "word": " closure،", "probability": 0.7080078125}, {"start": 3557.21, "end": 3557.43, "word": " يعني", "probability": 0.980712890625}, {"start": 3557.43, "end": 3557.63, "word": " X", "probability": 0.9931640625}, {"start": 3557.63, "end": 3557.75, "word": " في", "probability": 0.96923828125}, {"start": 3557.75, "end": 3557.85, "word": " ال", "probability": 0.95849609375}, {"start": 3557.85, "end": 3559.15, "word": " H،", "probability": 0.906982421875}, {"start": 3559.15, "end": 3559.51, "word": " ماشي؟", "probability": 0.7679443359375}, {"start": 3559.51, "end": 3559.87, "word": " أخدت", "probability": 0.9561767578125}, {"start": 3559.87, "end": 3560.07, "word": " X", "probability": 0.9921875}, {"start": 3560.07, "end": 3560.45, "word": " arbitrary", "probability": 0.38671875}, {"start": 3560.45, "end": 3560.75, "word": " element", "probability": 0.9248046875}, {"start": 3560.75, "end": 3560.89, "word": " in", "probability": 0.37451171875}, {"start": 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[{"start": 3577.35, "end": 3577.75, "word": "لكن", "probability": 0.831787109375}, {"start": 3577.75, "end": 3578.15, "word": " أنا", "probability": 0.308837890625}, {"start": 3578.15, "end": 3578.75, "word": " الآن", "probability": 0.656982421875}, {"start": 3578.75, "end": 3579.61, "word": " هذي", "probability": 0.4779866536458333}, {"start": 3579.61, "end": 3579.69, "word": " ال", "probability": 0.91552734375}, {"start": 3579.69, "end": 3579.79, "word": " X", "probability": 0.339111328125}, {"start": 3579.79, "end": 3580.09, "word": " طبعا", "probability": 0.9169921875}, {"start": 3580.09, "end": 3580.27, "word": " هي", "probability": 0.81640625}, {"start": 3580.27, "end": 3580.45, "word": " اللي", "probability": 0.92578125}, {"start": 3580.45, "end": 3580.55, "word": " في", "probability": 0.919921875}, {"start": 3580.55, "end": 3580.67, "word": " ال", "probability": 0.9189453125}, {"start": 3580.67, "end": 3581.19, "word": " amygdala", "probability": 0.6121673583984375}, {"start": 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Orthogonal ومن ثم قلتلكم أكيد X هتكون في الـV closure اللي هي في الـH إذا X نفسها بقدر أجيلها Sequence Xn في الـV حيث Xn بتروح لمين؟ للـX لأن since X element الـM closure then for all M element الـM هيكون الـX و الـM إيش بتساوي؟ سفر مدام الـX و الـM بتساوي سفر أكيد هذا بيعطيني الـX و الـV برضه إيش هيساوي سفر؟ لكل V والموجودة في الـV", "tokens": [5172, 995, 16095, 9957, 5551, 3224, 22807, 37495, 22653, 27050, 5551, 9778, 3215, 2655, 11296, 8978, 2423, 39184, 44, 27554, 664, 21523, 4032, 27842, 38637, 2304, 12174, 1211, 2655, 23275, 2304, 5551, 4117, 25708, 1783, 8032, 2655, 30544, 8978, 2423, 39184, 53, 24653, 13672, 1829, 39896, 8978, 2423, 39184, 39, 11933, 15730, 1783, 8717, 36178, 11296, 4724, 28543, 2288, 5551, 7435, 26895, 11296, 46859, 655, 1783, 77, 8978, 2423, 39184, 53, 11331, 1829, 12984, 1783, 77, 39894, 32887, 5016, 32767, 9957, 22807, 24976, 39184, 55, 5296, 33456, 1670, 1783, 4478, 2423, 39184, 44, 24653, 550, 337, 439, 376, 4478, 2423, 39184, 44, 8032, 1829, 30544, 2423, 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3882.6, "word": " تلاتة", "probability": 0.91357421875}, {"start": 3882.6, "end": 3883.06, "word": " أربعة", "probability": 0.9410807291666666}, {"start": 3883.06, "end": 3883.42, "word": " إحنا", "probability": 0.7576497395833334}, {"start": 3883.42, "end": 3883.8, "word": " عارفين", "probability": 0.9862060546875}, {"start": 3883.8, "end": 3883.98, "word": " إن", "probability": 0.52197265625}, {"start": 3883.98, "end": 3884.38, "word": " الـH", "probability": 0.9392903645833334}, {"start": 3884.38, "end": 3884.58, "word": " إيش", "probability": 0.92578125}, {"start": 3884.58, "end": 3885.94, "word": " بتساوي؟", "probability": 0.93701171875}, {"start": 3885.94, "end": 3886.2, "word": " V", "probability": 0.96044921875}, {"start": 3886.2, "end": 3886.68, "word": " closure", "probability": 0.96435546875}, {"start": 3886.68, "end": 3886.9, "word": " ليش", "probability": 0.818115234375}, {"start": 3886.9, "end": 3887.24, "word": " أخدت", "probability": 0.9395751953125}, {"start": 3887.24, 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691, 24653, 37495, 22653, 20328, 9640, 2655, 2423, 691, 8717, 36178, 11296, 18011, 294, 389, 46599, 9640, 4117, 21984, 8978, 24793, 4032, 28814, 23942, 5296, 4587, 16606, 19753, 34740], "avg_logprob": -0.2812499860664467, "compression_ratio": 1.5271739130434783, "no_speech_prob": 2.586841583251953e-05, "words": [{"start": 3889.52, "end": 3890.56, "word": "V", "probability": 0.294921875}, {"start": 3890.56, "end": 3891.04, "word": " closure", "probability": 0.7490234375}, {"start": 3891.04, "end": 3891.5, "word": " زائد", "probability": 0.5626627604166666}, {"start": 3891.5, "end": 3891.8, "word": " V", "probability": 0.80029296875}, {"start": 3891.8, "end": 3892.34, "word": " closure", "probability": 0.95703125}, {"start": 3892.34, "end": 3892.88, "word": " orthogonal", "probability": 0.254638671875}, {"start": 3892.88, "end": 3893.68, "word": " هذه", "probability": 0.337158203125}, {"start": 3893.68, "end": 3894.16, "word": " سفر", "probability": 0.8162434895833334}, {"start": 3894.16, "end": 3894.9, "word": " إذا", "probability": 0.55499267578125}, {"start": 3894.9, "end": 3895.28, "word": " V", "probability": 0.76953125}, {"start": 3895.28, "end": 3895.64, "word": " closure", "probability": 0.94580078125}, {"start": 3895.64, "end": 3896.04, "word": " زائد", "probability": 0.92578125}, {"start": 3896.04, "end": 3896.18, "word": " ال", "probability": 0.6708984375}, {"start": 3896.18, "end": 3896.38, "word": " zero", "probability": 0.2322998046875}, {"start": 3896.38, "end": 3896.8, "word": " element", "probability": 0.9443359375}, {"start": 3896.8, "end": 3897.24, "word": " هتطلع", "probability": 0.846044921875}, {"start": 3897.24, "end": 3897.56, "word": " مين", "probability": 0.703369140625}, {"start": 3897.56, "end": 3897.8, "word": " ال", "probability": 0.59326171875}, {"start": 3897.8, "end": 3898.02, "word": " V", "probability": 0.89892578125}, {"start": 3898.02, "end": 3898.54, "word": " closure", "probability": 0.9462890625}, {"start": 3898.54, "end": 3899.3, "word": " إذا", "probability": 0.8271484375}, {"start": 3899.3, "end": 3899.56, "word": " H", "probability": 0.7197265625}, {"start": 3899.56, "end": 3900.04, "word": " هتطلع", "probability": 0.94345703125}, {"start": 3900.04, "end": 3900.18, "word": " ايش", "probability": 0.6787109375}, {"start": 3900.18, "end": 3900.5, "word": " بتساوي", "probability": 0.756103515625}, {"start": 3900.5, "end": 3900.7, "word": " V", "probability": 0.9521484375}, {"start": 3900.7, "end": 3901.0, "word": " closure", "probability": 0.9619140625}, {"start": 3901.0, "end": 3901.28, "word": " يعني", "probability": 0.827392578125}, {"start": 3901.28, "end": 3901.64, "word": " صارت", "probability": 0.7921549479166666}, {"start": 3901.64, "end": 3901.84, "word": " ال", "probability": 0.6767578125}, {"start": 3901.84, "end": 3902.2, "word": " V", "probability": 0.9677734375}, {"start": 3902.2, "end": 3903.14, "word": " نفسها", "probability": 0.9630533854166666}, {"start": 3903.14, "end": 3903.86, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yeiwPsS60fU_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yeiwPsS60fU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5ff6f4bd48dc8a0b6267a98bba17445e20dc299b
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yeiwPsS60fU_raw.srt
@@ -0,0 +1,3304 @@
+1
+00:00:05,110 --> 00:00:08,030
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,030 --> 00:00:11,930
+الصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:11,930 --> 00:00:17,350
+آله وصحبه أجمعين هذه هي المحاضرة رقم 19 مساق تحليل
+
+4
+00:00:17,350 --> 00:00:20,930
+اقتراني او تحليل دالي طلاب طالبات الجامعة
+
+5
+00:00:20,930 --> 00:00:26,170
+الإسلامية ماجستير الرياضيات وصلنا لعند اللي هو ال
+
+6
+00:00:26,170 --> 00:00:28,350
+section الثالث تلاتة تلاتة اللي هو orthogonal
+
+7
+00:00:28,350 --> 00:00:30,450
+complement and direct sum
+
+8
+00:00:33,360 --> 00:00:37,900
+عشان اللي هو ندخل للموضوع اللي أمامنا بنزمنا بعض
+
+9
+00:00:37,900 --> 00:00:43,040
+التعريفات السريعة نذكركم فيها لو كان عندي اللي هو
+
+10
+00:00:43,040 --> 00:00:48,440
+X metric space عليها metric D ومن ثم لو كان عندي X
+
+11
+00:00:48,440 --> 00:00:52,640
+norm of space عليها norm وكانت M اللي هي مجموعة
+
+12
+00:00:52,640 --> 00:00:56,960
+جزئية من X وعندي هذا X space أي إن كان هذا ال
+
+13
+00:00:56,960 --> 00:01:01,480
+space و ال M هي عبارة عن مجموعة جزئية من ال X
+
+14
+00:01:01,480 --> 00:01:07,850
+الكاملةبدنا نعرف شو معنات اللي هو المسافة بين نقطة
+
+15
+00:01:07,850 --> 00:01:14,590
+X جواة الـ X و بين الـ 6 اللي أمامنا اللي هي الـ M
+
+16
+00:01:14,590 --> 00:01:18,910
+هذه الـ X element in X و المسافة بينها و بين 100 و
+
+17
+00:01:18,910 --> 00:01:22,410
+بين الـ M المسافة هذه بتقول عنها بسميها Delta
+
+18
+00:01:22,410 --> 00:01:30,370
+عبارة عن الـ infimum للمسافة بين X هذه و أي نقطة Y
+
+19
+00:01:30,750 --> 00:01:35,470
+والـ Y موخودة من الـ M أو يمكن أن يكتبها Y تلدة
+
+20
+00:01:35,470 --> 00:01:41,370
+إذا الـ infimum للمسافة بين X و6 هي المسافة Delta
+
+21
+00:01:41,370 --> 00:01:44,930
+عن
+
+22
+00:01:44,930 --> 00:01:50,270
+الـ M هذا الكلام in general ويعني في أي metric
+
+23
+00:01:50,270 --> 00:01:55,980
+spaceأطلع لفوق وده كان بيتعامل مع norm فبيصير
+
+24
+00:01:55,980 --> 00:02:00,260
+عندها ال delta بتساوي ال infimum بدل اللي هو
+
+25
+00:02:00,260 --> 00:02:05,200
+المسافة المسافة بتصير يرمز إليها X minus Y حيث Y
+
+26
+00:02:05,200 --> 00:02:08,340
+element in M وهذه تمثل المسافة بين المبطأ X اللي
+
+27
+00:02:08,340 --> 00:02:12,240
+في ال space X وبينها اللي هي ال M subset من X
+
+28
+00:02:12,870 --> 00:02:19,690
+السؤال المهم اللى .. اللى بنحكى دايما هل احنا
+
+29
+00:02:19,690 --> 00:02:27,460
+بنقدر نلاقي لقطةاللي هي في ال M بحيث انه اللي هو
+
+30
+00:02:27,460 --> 00:02:32,560
+هذا النقطة لو سمناها Y not مثلا هي اللي تمثل ال
+
+31
+00:02:32,560 --> 00:02:37,100
+Delta اللي بتساوي اللي هو ال infimum يعني نورما X
+
+32
+00:02:37,100 --> 00:02:40,760
+minus Y not هو اللي يمثل Delta يعني هل بنقدر نلاقي
+
+33
+00:02:40,760 --> 00:02:44,320
+ال infimum عند نقطة Y not في ال M يعني نورما X
+
+34
+00:02:44,320 --> 00:02:48,300
+minus Y not بساوية Delta اللي هي بساوية مسافة يعني
+
+35
+00:02:48,300 --> 00:02:51,960
+يعني نلاقي النقطة اللي في ال M اللي بتكون هي
+
+36
+00:02:51,960 --> 00:02:52,980
+الأقرب
+
+37
+00:02:57,270 --> 00:02:59,910
+سؤال هذا طبعا مطروح سؤال كبير
+
+38
+00:03:02,610 --> 00:03:06,130
+السؤال من شقين وجود النقطة هل النقطة فينا اللي
+
+39
+00:03:06,130 --> 00:03:10,350
+موجودة ولا النقطة لو كانت موجودة هل ممكن نلاقيها
+
+40
+00:03:10,350 --> 00:03:14,330
+واحدة ولا ممكن نلاقي اللي هو اكثر من هي حنلاقي ان
+
+41
+00:03:14,330 --> 00:03:19,810
+هذا الكلام حتى حتى في ال space السهل اللي هو ال R
+
+42
+00:03:19,810 --> 00:03:24,070
+تربيع العادى ال R تربيع اللي هو في ال Cartesian
+
+43
+00:03:24,070 --> 00:03:30,400
+plane العادى هنلاقي اللي هو الأمر مختلفأو يعني له
+
+44
+00:03:30,400 --> 00:03:35,240
+اختلافات أو له حالات يعني هنلاقي بعض ال 6 فعلا
+
+45
+00:03:35,240 --> 00:03:38,860
+اللي هو بنلاقي نقطة وحيدة بعض ال 6 مابنلاقيش
+
+46
+00:03:38,860 --> 00:03:42,680
+بالمرة من أصله وبعض ال 6 بنلاقي عدد لانهائي من
+
+47
+00:03:42,680 --> 00:03:46,650
+النقط أو اللي هو نقطة مش وحيدةخلينا ناخد أمثلة على
+
+48
+00:03:46,650 --> 00:03:49,210
+السريع اللي هي الأمثلة اللي أنتوا أصلا عارفينها
+
+49
+00:03:49,210 --> 00:03:53,610
+اطلع لفوق شويه عندى اطلع لفوق كمان كمان كمان لو
+
+50
+00:03:53,610 --> 00:03:57,470
+جينا أخدنا كمان كمان لو جينا أخدنا هي اللي هي الست
+
+51
+00:03:57,470 --> 00:04:02,290
+أخدنا الست الأولى اللي هي مين اللي هي الست M هذه
+
+52
+00:04:02,290 --> 00:04:04,950
+وهي النقطة X هذه بحكي عن إيه عشان في أرض تربيع
+
+53
+00:04:04,950 --> 00:04:08,210
+ونفترض أن النقطة هذه اللي هي open يعني ال .. ال ..
+
+54
+00:04:08,210 --> 00:04:11,210
+ال .. الست اللي أخدتها عبارة عن ال open ال
+
+55
+00:04:11,210 --> 00:04:14,510
+interval من النقطة هذه مثلا واحد إلى مال نهاية
+
+56
+00:04:15,870 --> 00:04:20,890
+النقطة هذه الـ set هذه الان ال set هذه هل فعلا
+
+57
+00:04:20,890 --> 00:04:26,050
+بنلاقي نقطة في داخلها تكون هذه اللي هو من X لهنا
+
+58
+00:04:26,050 --> 00:04:30,370
+تمثل هي ال .. ال .. ال delta لو جينا اتطلعنا اللي
+
+59
+00:04:30,370 --> 00:04:34,470
+هو بالنظر العادي المسافة اللي هي اقل المسافة هي من
+
+60
+00:04:34,470 --> 00:04:36,690
+هال لهال عنده نقطة هذه بس هذه النقطة أصلا مش
+
+61
+00:04:36,690 --> 00:04:41,770
+موجودة بناء عليه اللي هو ال infimumبين النقطة هذه
+
+62
+00:04:41,770 --> 00:04:45,570
+وبين اللي هي ال 6 هذه does not exist إذا مش موجودة
+
+63
+00:04:45,570 --> 00:04:49,590
+من أصله اللي هي نقطة في داخل ال M بحيث أن ال Delta
+
+64
+00:04:49,590 --> 00:04:54,910
+تساوي ال normal X minus اللي هو X note هنا أو Y
+
+65
+00:04:54,910 --> 00:04:59,540
+note اللي هيالحالة الثانية لو جينا أخدنا اللي هو
+
+66
+00:04:59,540 --> 00:05:04,380
+الـ 6 اللي أمامي هنا وأخدت النقطة X أعلاها بس
+
+67
+00:05:04,380 --> 00:05:08,960
+أعلاها بحيث أنه أنا لو نزلت عمود اللي هو يكون وين
+
+68
+00:05:08,960 --> 00:05:13,260
+موجود النقطة موجودة فيها واحنا بنعرف أنه أقل اللي
+
+69
+00:05:13,260 --> 00:05:16,800
+هو بعض اللي هو العمود بين طبعا احنا بنحكي فيه في
+
+70
+00:05:16,800 --> 00:05:19,160
+space عادي و في earth تربيع اللي بنشغل فيه عادي
+
+71
+00:05:19,690 --> 00:05:23,330
+فبتكون الـ X أخد العمود بتلاقي هذا النقطة اللي
+
+72
+00:05:23,330 --> 00:05:26,850
+بلتقي فيها العمود هذا مع هذا اللي هو الموجودة في
+
+73
+00:05:26,850 --> 00:05:31,430
+داخل المجموعة M فعشان هي كهذه Y not هي فعلاً Delta
+
+74
+00:05:31,430 --> 00:05:35,890
+هتساوي اللي هو norm الـ X minus Y not حيث الـ X
+
+75
+00:05:35,890 --> 00:05:41,450
+هيها والـ Y not هي مكان الإسقاط من الـ X عالمياً
+
+76
+00:05:41,450 --> 00:05:46,390
+على اللي هو الخط المستقيم أو القطعة المستقيمة اللي
+
+77
+00:05:46,390 --> 00:05:51,080
+هنعمللو جينا أخدنا اللي هو الجزء هذا اللي هو جزء
+
+78
+00:05:51,080 --> 00:05:56,000
+من محيط دائرة وهذا بيمثل مين المركز هاي الست عندى
+
+79
+00:05:56,000 --> 00:06:01,260
+M لو جيت أخدته النقطة ال X هنا ال N كلهم على نفس
+
+80
+00:06:01,260 --> 00:06:05,440
+البعدفبناء على الـ Delta اللي هي ال Infimum هي
+
+81
+00:06:05,440 --> 00:06:08,860
+عبارة عن كل النقاط لأن في عدد لا نهاية من النقاط
+
+82
+00:06:08,860 --> 00:06:14,000
+بتمثل اللي هو ايه شماله اللي هو ال Delta اللي ببحث
+
+83
+00:06:14,000 --> 00:06:17,920
+عنها اللي هي المسافة بين ال X و بين ال 6 اللي عندي
+
+84
+00:06:18,230 --> 00:06:22,550
+إذا بالرغم من سهولة ال space اللي عندنا ومنبسطه
+
+85
+00:06:22,550 --> 00:06:26,090
+اللي احنا بنعرفه إلا إنه لجينا هذه المسألة اللي هو
+
+86
+00:06:26,090 --> 00:06:29,390
+البحث عن ال .. عن وجود النقطة اللي هي y naught
+
+87
+00:06:29,390 --> 00:06:33,270
+اللي بتمثل ال .. اللي هي هي اللي هتكون النقطة التي
+
+88
+00:06:33,270 --> 00:06:38,630
+تبعد أقل ما يمكن عن مين عن ال set اللي هي من
+
+89
+00:06:38,630 --> 00:06:44,030
+النقطة x لل set اللي هي اللي بنبحث عنها طيب ارجعلي
+
+90
+00:06:44,030 --> 00:06:44,930
+للتلخيص الآن
+
+91
+00:06:47,900 --> 00:06:52,120
+نأتي الآن لتلخيصنا نكمل عليه a subset remark اللي
+
+92
+00:06:52,120 --> 00:06:55,500
+هو a subset M of a vector space X set to be convex
+
+93
+00:06:55,500 --> 00:07:00,380
+هي لازم هذا التعريف انها تكون convex if for all x,
+
+94
+00:07:00,500 --> 00:07:05,340
+y element in M ال linear combination بين ال X والY
+
+95
+00:07:05,340 --> 00:07:09,180
+لازم يكون في M بس هنا combination بإيش؟ بال scalar
+
+96
+00:07:09,180 --> 00:07:13,510
+Alphaواللي هي واحد ناقص Alpha يكون Alpha X يعني
+
+97
+00:07:13,510 --> 00:07:18,470
+الخط المقطع المستقيمة بين X و بين Y اللي هي Alpha
+
+98
+00:07:18,470 --> 00:07:21,910
+X زاد واحد ميز Alpha Y وY بتكون موجودة في M إذا
+
+99
+00:07:21,910 --> 00:07:26,090
+اتحققت هذه الخاصية بيكون عندي A شماله ال Set M
+
+100
+00:07:26,090 --> 00:07:31,100
+بتكون Convex بناء عليهأي subspace من X هيكون
+
+101
+00:07:31,100 --> 00:07:34,540
+convex لأن subspace مايعنيش subspace بيكون اللي هو
+
+102
+00:07:34,540 --> 00:07:37,440
+أنه أي linear combination بين أنه خطي لازم يكون في
+
+103
+00:07:37,440 --> 00:07:41,240
+main يعني لو كانت X و Y في ال space لازم في
+
+104
+00:07:41,240 --> 00:07:44,200
+subspace اللي بنحكي عنه عشان يكون subspace لازم
+
+105
+00:07:44,200 --> 00:07:48,500
+يكون Alpha X زائد Beta Y يكون في داخل ال Y لكل X و
+
+106
+00:07:48,500 --> 00:07:53,580
+Y موجودة في ال subspace X عشان هيك نسميه subspace
+
+107
+00:07:54,590 --> 00:07:58,730
+إذا أي subspace من X هيكون أشماله convex ومش هيك و
+
+108
+00:07:58,730 --> 00:08:02,130
+the intersection of convex sets is convex يعني لو
+
+109
+00:08:02,130 --> 00:08:08,130
+كان عندي اللي هو تقاطع اللي هوC و الـ C هدول عبارة
+
+110
+00:08:08,130 --> 00:08:13,130
+عن convex sets C α مثلا نسميها هيكون برضه هذا
+
+111
+00:08:13,130 --> 00:08:18,170
+التقاطع أشماله عبارة عن convex خدوا .. خدوا أي X و
+
+112
+00:08:18,170 --> 00:08:24,850
+Y في داخل التقاطع للـ C α أكيد هيعطينا أنه الآن
+
+113
+00:08:24,850 --> 00:08:29,010
+اللي هو كل ال X و ال Y هدولة موجودة في الـ C α for
+
+114
+00:08:29,010 --> 00:08:33,620
+every α صح ولا لأ؟من تعريف الطفافة و بما أن كل
+
+115
+00:08:33,620 --> 00:08:38,140
+واحدة منهم C Alpha Convex إذا حيكون عندي الآن X أو
+
+116
+00:08:38,140 --> 00:08:40,980
+سأسميها C Beta عشان ما أخلطش بين ال Alpha تبعت الـ
+
+117
+00:08:40,980 --> 00:08:47,460
+C Beta Beta لكل Beta الآن بدأنا عليه مدامة C Beta
+
+118
+00:08:47,460 --> 00:08:52,760
+is Convex حيكون CX في Alphaزائد واحد ناقص Alpha في
+
+119
+00:08:52,760 --> 00:08:57,880
+Y والموجودات في الـC Beta لكل Beta معناته صار عندي
+
+120
+00:08:57,880 --> 00:09:02,320
+أكيد هذا بيعطينا ان X Alpha زائد واحد ماينس Alpha
+
+121
+00:09:02,320 --> 00:09:07,540
+في Y اللي هو موجود في التقاطع لـC Beta وبناء عليه
+
+122
+00:09:07,540 --> 00:09:12,760
+أخدنا هذه arbitrary لAlpha Element 01 وجدنا ان
+
+123
+00:09:12,760 --> 00:09:15,640
+اللي هو الـLinear Combination هذا موجود في التقاطع
+
+124
+00:09:15,640 --> 00:09:21,970
+إذا التقاطع هيكون أي تقاطع is convex pipeنجي الآن
+
+125
+00:09:21,970 --> 00:09:26,710
+لنظريتنا الأولى اللي احنا قبل بشوية بدينا نحكي
+
+126
+00:09:26,710 --> 00:09:31,110
+عنهالأن النظرية بتقول let X be an inner product
+
+127
+00:09:31,110 --> 00:09:37,090
+space and M be a non-empty non-empty convex set
+
+128
+00:10:07,080 --> 00:10:12,720
+النظرية بتقول ان لو كان عندك X inner product space
+
+129
+00:10:12,720 --> 00:10:18,710
+و M non-emptyو Convex و Complete إذا التلات شروط
+
+130
+00:10:18,710 --> 00:10:24,790
+هذه تكون موجودة بضمنك أنه لكل X في ال X بقدر ألاقي
+
+131
+00:10:24,790 --> 00:10:30,870
+Y موجودة في M اللي هي normها ال X minus Y بعيد عن
+
+132
+00:10:30,870 --> 00:10:35,490
+ال X هو اللي اللي بيمثل المسافة بين اللي هو ال M و
+
+133
+00:10:35,490 --> 00:10:39,550
+بين ال L ال M و ال X يعني الآن
+
+134
+00:10:44,010 --> 00:10:50,710
+الان اضمننا اخدنا الان اللي هو شروط معينة على ال M
+
+135
+00:10:50,710 --> 00:10:57,550
+اللي هي لا تسوى Phi او convex او complete بحيث ان
+
+136
+00:10:57,550 --> 00:11:03,390
+هذا بضمنك انه لو اخدت اي X في ال Xو جيت هي ال M
+
+137
+00:11:03,390 --> 00:11:09,350
+هتلاقي نقطة في داخل ال M وحيدة اللي هي هيتمثل
+
+138
+00:11:09,350 --> 00:11:14,550
+المسافة بينها و بين اللي هي ال X اللي هي X minus Y
+
+139
+00:11:14,550 --> 00:11:21,050
+هي اللي تكون Delta المسافة بين X و بين مين اللي هي
+
+140
+00:11:21,050 --> 00:11:26,860
+ال M نيجي الأن للبرهاننقسم البرهان لجزءين جزء أثبت
+
+141
+00:11:26,860 --> 00:11:31,020
+ال existence وجود النقطة وقسم أخر يمثل ال
+
+142
+00:11:31,020 --> 00:11:35,400
+uniqueness أو وحدانية النقطة أو النقطة واحدةأطلع
+
+143
+00:11:35,400 --> 00:11:39,340
+لفوق خلّينا نشوف ال existence أول اشي احنا ال
+
+144
+00:11:39,340 --> 00:11:42,860
+delta بساوي ال infimum من norm ال X minus Y حيث Y
+
+145
+00:11:42,860 --> 00:11:46,420
+تل ده Y نقص تل ده حيث Y تل ده element من مين هذا
+
+146
+00:11:46,420 --> 00:11:51,800
+تعريف من اللي هي المسافة بينه نقطة X وبين اللي هي
+
+147
+00:11:51,800 --> 00:11:57,760
+ال set ال infimum هذا طبعا لما نتعريف ال infimumلو
+
+148
+00:11:57,760 --> 00:12:00,340
+الـ infimum هو عبارة عن مين يا جماعة؟ ال greatest
+
+149
+00:12:00,340 --> 00:12:04,880
+lower bound ماشي الحين ال infimum هو اللي بيمثل لي
+
+150
+00:12:04,880 --> 00:12:09,720
+ال greatest lower bound طيب انتبهوا كيف عندى ال
+
+151
+00:12:09,720 --> 00:12:15,800
+delta بسوء ال infimum ل norm ال X minus Y تلده و Y
+
+152
+00:12:15,800 --> 00:12:21,910
+تلده element in مين؟ in Mالان الـ Greatest Lower
+
+153
+00:12:21,910 --> 00:12:25,770
+Bound اول اشي Lower Bound و اكبر Lower Bound لو
+
+154
+00:12:25,770 --> 00:12:30,110
+ضفنا اشي بسيط لانه جولنا جولنا Delta زائد واحد ال
+
+155
+00:12:30,110 --> 00:12:35,330
+Delta زائد واحد بيبطل Lower Bound اه مادام بيبطل
+
+156
+00:12:35,330 --> 00:12:41,410
+Lower Bound اذا بلاجي اللي هو Y واحد في الان بحيث
+
+157
+00:12:41,410 --> 00:12:44,910
+انه Delta زائد واحد يبطل Lower Bound بيصير اكبر او
+
+158
+00:12:44,910 --> 00:12:51,580
+يسوى Normal X minus Y واحدماشي الحال لو اجيت اخدت
+
+159
+00:12:51,580 --> 00:12:58,820
+دلتا ضفتلها نص مش واحد برضه بلاجيلها اللي هو Y2
+
+160
+00:12:58,820 --> 00:13:04,300
+بحيث انه يكون اللي هو هذا اكبر او يساوي X minus Y2
+
+161
+00:13:04,300 --> 00:13:08,660
+لانه بتبطل معلها معلها بتبطل اللي هو lower bound
+
+162
+00:13:09,210 --> 00:13:14,630
+الأن in general لو ضفت عدل تواحد على n لأي n في
+
+163
+00:13:14,630 --> 00:13:19,130
+الدنيا حاليا دي بناء عليه هدف but lower bound ومن
+
+164
+00:13:19,130 --> 00:13:24,970
+ثم there exists xn في ال M يعني يوجد xn في ال M
+
+165
+00:13:25,580 --> 00:13:30,200
+بحيث ان دلتا زياد واحد على ان اتبطل ال power bomb
+
+166
+00:13:30,200 --> 00:13:35,700
+يعني تكون اكبر او يساوي هذه ال X ناقص YN هذه سموها
+
+167
+00:13:35,700 --> 00:13:40,360
+دلتا واحد هذه سموها دلتا اتنين هذه سموها دلتا ان
+
+168
+00:13:40,360 --> 00:13:46,660
+in general اذا الان لكل ان في الدنيا بقدر الاجي
+
+169
+00:13:46,660 --> 00:13:53,920
+اللي هو sequence من ال YN بحيث ان اللي هو دلتا ان
+
+170
+00:13:54,870 --> 00:14:01,350
+يكون أكبر أو يساوي norm الـ X minus Y N الـ Delta
+
+171
+00:14:01,350 --> 00:14:06,920
+N اللي هي عبارة عن Delta زائد واحد على Nوالـ Delta
+
+172
+00:14:06,920 --> 00:14:10,720
+نفسها عبارة عن lower bound إذن هتكون هذه أكبر أو
+
+173
+00:14:10,720 --> 00:14:14,900
+يساوي الـ Delta صح ولا لأ؟ لأن الـ Delta إيش
+
+174
+00:14:14,900 --> 00:14:18,140
+مالها؟ ال greatest lower bound يعني lower bound،
+
+175
+00:14:18,140 --> 00:14:23,000
+ماشي؟ إذن as n goes to infinity هذه هتروح لـ Delta
+
+176
+00:14:23,000 --> 00:14:28,160
+وهذه هتروح لـ Delta ويكون limit ال normal x minus
+
+177
+00:14:28,160 --> 00:14:31,140
+y n صار محصور بين الـ Delta والـ Delta يعني إيش
+
+178
+00:14:31,140 --> 00:14:38,060
+بساوي؟ بساوي Delta يعني بمعنى آخرلجيت sequence yn
+
+179
+00:14:38,060 --> 00:14:41,680
+بحيث أنه الدل تبسو ال limit normal x minus yn هذه
+
+180
+00:14:41,680 --> 00:14:46,200
+ال sequence شوفوا كيف بدا أقولكم إيش بتطلع بالظبط
+
+181
+00:14:46,200 --> 00:14:51,020
+نشوف نرجع لبرهانناالان ساديك على جنب عشان تفسير
+
+182
+00:14:51,020 --> 00:14:54,900
+بعض الأمور انا الان بقوللي مدام ان ال Delta بيساوي
+
+183
+00:14:54,900 --> 00:14:59,020
+ال infimum لل norm هذا اذا بقدر الاجي sequence yn
+
+184
+00:14:59,020 --> 00:15:03,660
+in M هي اللي لجيتها هناك قبل بشوية such that Delta
+
+185
+00:15:03,660 --> 00:15:08,160
+N بتروح لمين لل Delta و Delta N ايش بتساوي norm ال
+
+186
+00:15:08,160 --> 00:15:13,660
+X minus YN الان هذه ال sequence اللي لجيتها YN بده
+
+187
+00:15:13,660 --> 00:15:17,100
+اثبتلك اول حاجة و ي show that YN is اكوشي sequence
+
+188
+00:15:17,760 --> 00:15:20,660
+ماشي انت بقى خلّيكوا معايا خلّيني أشوف كيف نانيت
+
+189
+00:15:20,660 --> 00:15:24,820
+بتنهي كوشي سيكوانس خلّيني نسمي اللي هو ال V1
+
+190
+00:15:24,820 --> 00:15:30,660
+بيساوي Y1 ناقص X V2 Y2 ناقص X in general VN بدي
+
+191
+00:15:30,660 --> 00:15:35,000
+أسميها YN ناقص 200 ناقص X من وين جبتها هذه ال X
+
+192
+00:15:35,000 --> 00:15:37,560
+اللي بدأنا فيها اللي بدنا نبحث عن المسافة بينها و
+
+193
+00:15:37,560 --> 00:15:41,260
+بين ال 6 و ال YN هي ال sequence اللي ركبتها اللي
+
+194
+00:15:41,260 --> 00:15:46,420
+فوق ماشي الحالإذن الآن خدوا سمولي صارت عند الـ Δن
+
+195
+00:15:46,420 --> 00:15:51,940
+هذه هي عبارة عن norm من الـ Vm ماشي طيب و لو أجيت
+
+196
+00:15:51,940 --> 00:15:57,760
+حسبت norm ال Vm زائد Vm ال Vm هذي اللي هي مين
+
+197
+00:15:57,760 --> 00:16:05,410
+هتكون ال Vm هيها Ym ناقص X زائد Ym ناقص Xها دي
+
+198
+00:16:05,410 --> 00:16:10,350
+بيساوي اللي هو norm الـ yn زاد yn ناقص مين اتنين x
+
+199
+00:16:10,350 --> 00:16:15,250
+ويساوي واضح اه اسحبولي اللي هو اتنين عامل مشترك من
+
+200
+00:16:15,250 --> 00:16:18,730
+هنا بيصير عندى اللي هو انا طبعا مافيش فيه عامل
+
+201
+00:16:18,730 --> 00:16:22,990
+فبصير نص و بطلع برا فبصير اتنين في نص yn ناقص y
+
+202
+00:16:22,990 --> 00:16:27,230
+زاد yn ناقص x احنا بنقول انها convex اصلا ماشي
+
+203
+00:16:27,230 --> 00:16:33,890
+الحال الان ynYN في ال .. في ال .. في الست M من
+
+204
+00:16:33,890 --> 00:16:37,330
+جبتها من وين ال YN ؟ هذي YN وين جبتها ؟ هذي بقى
+
+205
+00:16:37,330 --> 00:16:39,850
+قاعد بقول there exist Y واحد element in M و Y
+
+206
+00:16:39,850 --> 00:16:43,900
+اتنين element in M مشان باخد ال M في وم عليهاواضح
+
+207
+00:16:43,900 --> 00:16:47,860
+هاه؟ إذا الـ sequence yn من الـ M مدامت M convex
+
+208
+00:16:47,860 --> 00:16:52,900
+إذا بضمنلكم أنه مصف yn زاد yn مشيكون في الـ Y
+
+209
+00:16:52,900 --> 00:16:57,120
+نفسها، مظبوط؟ إذا هذه صارت element في ال .. آسف في
+
+210
+00:16:57,120 --> 00:17:01,480
+الـ M هذه صارت element وين في الـ M فالان norm
+
+211
+00:17:01,480 --> 00:17:05,340
+element في الـ M ناقص X أكيد .. أكيد .. أكيد هيكون
+
+212
+00:17:05,340 --> 00:17:09,140
+أكبر أو يسوى من Delta لأن دلتا هي لين ثم من لين،
+
+213
+00:17:09,140 --> 00:17:13,070
+ماشيإذا صارت الاتنين في هذا المقدار أكبر أو يساوي
+
+214
+00:17:13,070 --> 00:17:17,250
+مين؟ اتنين دلتا أو بمعنى أخر هذا المقدار أكبر أو
+
+215
+00:17:17,250 --> 00:17:21,790
+يساوي اتنين دلتا زي ما قلت لكم where نصف YN زي ال
+
+216
+00:17:21,790 --> 00:17:26,590
+YM element in M because M إشمالها is convex خلّي
+
+217
+00:17:26,590 --> 00:17:31,170
+هذه في الذاكرة خلّينا نكمل اللي بدناهاFurthermore
+
+218
+00:17:31,170 --> 00:17:39,130
+لو جيت حسبة YM-YM تراحت من بعض اللي هو YM-X فبسيط
+
+219
+00:17:39,130 --> 00:17:43,270
+تروح ال X مع ال X فبتظهر عندي VN ناقص من VM يعني
+
+220
+00:17:43,270 --> 00:17:47,870
+VN ناقص VM هتطلع هذه ناقص اللي هي تبع ال YM ناقص X
+
+221
+00:17:47,870 --> 00:17:51,350
+فبروح مع بعض فبظهر YM ناقص YM احسب أحسابات سهلة
+
+222
+00:17:52,020 --> 00:17:55,060
+الان بدي استخدم باستخدام Parallelogram Equality
+
+223
+00:17:55,060 --> 00:17:57,540
+نحن لدينا الـ Parallelogram Equality اللي هي في
+
+224
+00:17:57,540 --> 00:18:01,960
+نورم ديسمبرز جائزة مظبوط او متحققة اللي هي عبارة
+
+225
+00:18:01,960 --> 00:18:07,250
+عن تخد الان YN نقص و YM من كل تربيع ايش هيساوي؟هي
+
+226
+00:18:07,250 --> 00:18:12,590
+احنا yn ناقص ym ايش لقينها بتساوي عبارة عن vn ناقص
+
+227
+00:18:12,590 --> 00:18:16,630
+vm فبالصحيح انهم تربيع وإيه ساوي احنا بنعرف ال
+
+228
+00:18:16,630 --> 00:18:20,870
+program equality ايش معناتها الطرح والجمع تربيع
+
+229
+00:18:20,870 --> 00:18:24,130
+بساوي اتنين فطول الضلع الأول زي الضلعة الثانية
+
+230
+00:18:24,130 --> 00:18:28,610
+الأقطار ولا ايش ولا ولا ولا واضع المستطيل فاهمين
+
+231
+00:18:29,230 --> 00:18:33,030
+فبصير عندي النورم هذا بساوي ناقص النورم هذا زائد
+
+232
+00:18:33,030 --> 00:18:35,690
+اللي هو اتنين في هذه النورمين هذه اللي هي
+
+233
+00:18:35,690 --> 00:18:41,490
+البروغرام البرلوغرام اللي هي main equality طيب هذا
+
+234
+00:18:41,490 --> 00:18:44,810
+اصغر او ساوي بدنا نستخدم اللي فوق اثبتنا ان هذا
+
+235
+00:18:44,810 --> 00:18:50,830
+المقدار اكبر او اتنين دلتا هذا اللي هو عبارة عن vn
+
+236
+00:18:50,830 --> 00:18:54,750
+زائد vm اكبر او اتنين دلتا واضح فبصير عندي اصغر او
+
+237
+00:18:54,750 --> 00:19:00,690
+ساويالأن هذا ناقص اللي هي هذه هي شايفينها ناقص
+
+238
+00:19:00,690 --> 00:19:03,730
+اتنين ديلتا تربيع لإنه لما نضرب اللي هو المقدار
+
+239
+00:19:03,730 --> 00:19:07,750
+هذا VN زائد VN بناقص من برا هذه بتصير اشمالها
+
+240
+00:19:07,750 --> 00:19:11,150
+بتنجلب الإشارة فبصير أصغر أو يساوي ناقص اتنين
+
+241
+00:19:11,150 --> 00:19:16,470
+ديلتا لكل تربيع واضح ها طيب زائد ال norm ال VN
+
+242
+00:19:16,470 --> 00:19:20,230
+تربيع اللي هو أصغر أو يساوي ال VN لحق لل norm ال
+
+243
+00:19:20,230 --> 00:19:25,480
+VN اللي هي عبارة عن مين ديلتا N هيهاوها delta M
+
+244
+00:19:25,480 --> 00:19:29,940
+التانية فبصير زيادة 2 delta N تربيع زيادة delta M
+
+245
+00:19:29,940 --> 00:19:34,900
+من تربيع إذا صار عندي المقدار اللي هو Y N نقص وين
+
+246
+00:19:34,900 --> 00:19:39,660
+رايح أنا أنا رايحت بين ال Y نكوشي يعني إيش Y نكوشي
+
+247
+00:19:39,660 --> 00:19:43,420
+يعني for large N و M هيقول هذا المقدار السفرة و
+
+248
+00:19:43,420 --> 00:19:46,920
+هيكون أصغر من Y في الدنيا معايا إذا صار هذا
+
+249
+00:19:46,920 --> 00:19:53,760
+المقدارالان اصغر او يساوي هذه الكمية الان as n و n
+
+250
+00:19:53,760 --> 00:19:58,200
+goes to infinity delta n بتروح لدلتا و delta n
+
+251
+00:19:58,200 --> 00:20:02,100
+بتروح لدلتا اذا هذا هيصير اتنين في اتنين اربعة
+
+252
+00:20:02,100 --> 00:20:06,620
+دلتا تربية و انا اربعة دلتا تربية اذا هذا المقدار
+
+253
+00:20:06,620 --> 00:20:10,920
+as n و n goes to infinity هيصير very very small
+
+254
+00:20:10,920 --> 00:20:14,810
+لدرجة ان احنا مينللسفر وهذا معنى as n goes و M
+
+255
+00:20:14,810 --> 00:20:17,710
+goes وهذا المقدر روح السفر hence for every epsilon
+
+256
+00:20:17,710 --> 00:20:21,430
+أكبر من سفر there is K sufficiently large such
+
+257
+00:20:21,430 --> 00:20:25,430
+that ال Ym نقص Ym هتكون إيه شمالها أصغر من إبسلون
+
+258
+00:20:25,430 --> 00:20:31,070
+for all n و M أكبر من K وهذا أثبت لنا اطلع لفوق ال
+
+259
+00:20:31,070 --> 00:20:35,320
+Ym is a Cauchy sequence in Mالان وي ان كوشي
+
+260
+00:20:35,320 --> 00:20:37,720
+سيكوينس في الام و احنا اصلا اخدنا الام complete
+
+261
+00:20:37,720 --> 00:20:41,500
+عشان نقدر نكمل برهاننا الان مادام ات ام complete
+
+262
+00:20:41,500 --> 00:20:46,060
+وعندي كوشي سيكوينس اذا اكيد اكيد بط ام is complete
+
+263
+00:20:46,060 --> 00:20:51,080
+then وي ان converge says ان وي ان converge لمين ل
+
+264
+00:20:51,080 --> 00:20:57,360
+Y element in Mمدام Y في الـ M إذا أكيد نورم X
+
+265
+00:20:57,360 --> 00:21:01,580
+minus Y لكونها نقطة في الـ M أكبر أو يساوي اللي هو
+
+266
+00:21:01,580 --> 00:21:04,640
+الـ Delta اللي هي عبارة عن ال .. ال .. ال Infimum
+
+267
+00:21:04,640 --> 00:21:07,440
+أو ال .. ال .. greatest lower bound يعني في الأخر
+
+268
+00:21:07,440 --> 00:21:11,280
+lower bound هذه بتكون أصغر أو يساوي نورم X minus Y
+
+269
+00:21:11,870 --> 00:21:15,470
+However من جهة أخرى لو جينا أخدنا Normal X minus Y
+
+270
+00:21:15,470 --> 00:21:19,130
+هتكون أصغر أو يساوي بالـ Triangling Quality X ناقص
+
+271
+00:21:19,130 --> 00:21:23,310
+YN زي YN ناقص Y الأولى عبارة عن Delta N والتانية
+
+272
+00:21:23,310 --> 00:21:27,990
+اللى هي Normal YN ناقص Min ناقص Y لأن من فوق as N
+
+273
+00:21:27,990 --> 00:21:30,650
+goes to infinity احنا اتفاجن أن هذا هتروح لمين
+
+274
+00:21:30,650 --> 00:21:34,950
+للزفر و Delta N هتروح لمين للدلتا يعني بمعنى أخر
+
+275
+00:21:34,950 --> 00:21:40,780
+Normal X minus Y هيصير أصغر أو يساوي Deltaوعندي
+
+276
+00:21:40,780 --> 00:21:44,720
+دائما الـ X minus Y أكبر بساوي Delta إذا صار عندي
+
+277
+00:21:44,720 --> 00:21:48,560
+بالظبط الـ Normal X minus Y بساوي Delta يعني بمعنى
+
+278
+00:21:48,560 --> 00:21:53,160
+أخر لجينا الـ Y اللي البعد الـ X عنها هو اللي
+
+279
+00:21:53,160 --> 00:22:01,280
+بيمثل البعد الـ X عن اللي هي الـ M ككل طيب نثبت
+
+280
+00:22:01,280 --> 00:22:05,310
+إنه اللي هي هذه النقطة واحدةإتبعت إن واحدها سهلة
+
+281
+00:22:05,310 --> 00:22:08,370
+suppose that there are y و y not element in M
+
+282
+00:22:08,370 --> 00:22:14,570
+والتنتين اللي بيكون البعد بينهم و بين Y بينهم و
+
+283
+00:22:14,570 --> 00:22:18,510
+بين X هو بمثل الـ Delta هذه Delta وهذه Delta لنشوف
+
+284
+00:22:18,510 --> 00:22:25,170
+كيف نثبت أن y not هي بتساوي ال Yالنقطة واحدة by
+
+285
+00:22:25,170 --> 00:22:30,070
+parallelogram equality برضه اللي هي عبارة عن
+
+286
+00:22:30,070 --> 00:22:35,330
+اطبقها على ال y و ال y not يعني او على ال y minus
+
+287
+00:22:35,330 --> 00:22:39,530
+y not كل تربيع بساوي y minus x ناقص y minus y not
+
+288
+00:22:39,530 --> 00:22:44,600
+ال x كل تربيعأه فاهمين طرحت وضفت أطبقها عليهم
+
+289
+00:22:44,600 --> 00:22:49,760
+هدولة على اللي هي الجهتين هدول بساوي اتنين هيطرحن
+
+290
+00:22:49,760 --> 00:22:55,160
+ومجوحن اتنين في اتنين في الأولى y minus x في كل
+
+291
+00:22:55,160 --> 00:23:00,670
+تربيع هدول اللي اطلعزاد اتنين في yy not ناقص x لكل
+
+292
+00:23:00,670 --> 00:23:05,630
+تربيع ناقص اللي هو قطر التالي اللي هو عبارة عن
+
+293
+00:23:05,630 --> 00:23:09,270
+اللي هو بدّي الطرح اشماله الموجب لان عارفين اللي
+
+294
+00:23:09,270 --> 00:23:11,250
+هو القطرين
+
+295
+00:23:13,100 --> 00:23:18,260
+والاربعة طلعة المفروض أنكم مذكرين يعني بساوي هذا
+
+296
+00:23:18,260 --> 00:23:24,120
+زائد هذا هو يساوي الأولاني عبارة عن احنا فرضين انه
+
+297
+00:23:24,120 --> 00:23:27,620
+اللي هو ادمثل Delta فبصير اتنين Delta تربيعه وهذه
+
+298
+00:23:27,620 --> 00:23:30,180
+فرضينها بيساوي Delta برضه مش قولنا جدتين why why
+
+299
+00:23:30,180 --> 00:23:34,100
+notوها دي برضه اشملها اتنين دلده تربيع ناقص اللي
+
+300
+00:23:34,100 --> 00:23:38,340
+هو اربعة في نص Y نفس اللي عملت قبل شوية بدي اطلع
+
+301
+00:23:38,340 --> 00:23:43,420
+اللي هو الاتنين عامل مشترك فبطلع الاتنين من برة
+
+302
+00:23:43,420 --> 00:23:50,360
+التربيع اربعة عندي هي المقدار هذا شايفينه Yزائد y
+
+303
+00:23:50,360 --> 00:23:56,300
+not ناقص اتنين x طلعت الاتنين من عندها فصارت هذه y
+
+304
+00:23:56,300 --> 00:24:00,800
+minus زائد y not على اتنين يعني نص فيهم واتنين x
+
+305
+00:24:00,800 --> 00:24:04,040
+طلعت من هاتنين ضالت x لحالها ولمّا طلعته برا
+
+306
+00:24:04,040 --> 00:24:08,120
+التربية طلع باربعة فبصير عنده اربعة فنص y minus y
+
+307
+00:24:08,120 --> 00:24:11,800
+not ناقص x لكل تربية وهذا سمو ليه واحد خلّينا
+
+308
+00:24:11,800 --> 00:24:17,360
+نرجعله بعد شوية إذا اللي حصلته أن هذا normalتربيع
+
+309
+00:24:17,360 --> 00:24:20,780
+بيساوي اللي هو اتنين دلتة تربيع زاد اتنين دلتة
+
+310
+00:24:20,780 --> 00:24:25,680
+تربيع ناقص اللي هو اربع يعني اربع دلتة تربيع ناقص
+
+311
+00:24:29,150 --> 00:24:33,550
+since M is convex إذا أكيد هذه وين موجودة برضه في
+
+312
+00:24:33,550 --> 00:24:38,270
+الـ M وهذا معناته إنه نصف YY زاد Y not ناقص Normal
+
+313
+00:24:38,270 --> 00:24:42,590
+X أكبر يساوي مين؟ Delta، مظبوط ولا لأ؟ إذا ناقصه
+
+314
+00:24:42,590 --> 00:24:46,910
+أصغر يساوي Delta، أسالف Delta، إذن by this اللي هو
+
+315
+00:24:46,910 --> 00:24:52,360
+هذهو واحد بيكون عنده y minus y naught لكل تربيع
+
+316
+00:24:52,360 --> 00:24:56,820
+أصغر أو يساوي ماشي اللي هو اتنين دلتة تربيع زي ما
+
+317
+00:24:56,820 --> 00:24:59,960
+هي و اتنين دلتة تربيع زي ما هي و هذا بيصير أشمالها
+
+318
+00:24:59,960 --> 00:25:03,260
+أصغر أو يساوي ناقص أربع دلتة تربيع اللي هي ناقص
+
+319
+00:25:03,260 --> 00:25:07,400
+أربع دلتة تربيع و مجوح ان ايش بيساوي سفر اذا صار
+
+320
+00:25:07,400 --> 00:25:10,900
+عنده normal y minus y naught بيساوي سفر معناه y
+
+321
+00:25:10,900 --> 00:25:15,060
+بيساوي y naught و هذا بيثبت انه اللي هوالـ Y وحيدة
+
+322
+00:25:15,060 --> 00:25:18,440
+النقطة اللي بنحكي عليها إذا موجودة وحيدة بكون هي
+
+323
+00:25:18,440 --> 00:25:26,020
+خلصنا طيب الآن قبل شوية قبل شوية في سؤالنا المثال
+
+324
+00:25:26,020 --> 00:25:29,120
+اللي هو اللي أخدناه في الـ R تربيع لما أخدنا قطعة
+
+325
+00:25:29,120 --> 00:25:34,000
+مستقيمة و أخدنا فجيها اللي هي النقطة كان مين أقرب
+
+326
+00:25:34,000 --> 00:25:39,540
+بعض إلها العمودي؟العمودي الآن بدنا نروح بهذا
+
+327
+00:25:39,540 --> 00:25:43,680
+الاتجاه نشوف كيف نصل لإشي مشابه لهذا اللي بنحكيه
+
+328
+00:25:43,680 --> 00:25:48,900
+في العادى اللي هي نيجي للنمم اللي عندىبتقولي in
+
+329
+00:25:48,900 --> 00:25:53,700
+theorem تلاتة تلاتة واحد اللي قبله شوية نفترض M be
+
+330
+00:25:53,700 --> 00:25:58,860
+a complete subspace يعني مش اي subset يكون Y نفسه
+
+331
+00:25:58,860 --> 00:26:02,900
+ايه اشمالها او M اللي عندك تكون مش subset بس يعني
+
+332
+00:26:02,900 --> 00:26:06,120
+الـ M بالاضافة لشروط اللي كتبناها ال non-empty
+
+333
+00:26:07,940 --> 00:26:11,560
+وconvex و complete ونضيف لها انها تكون subspace في
+
+334
+00:26:11,560 --> 00:26:18,440
+هذه الحالة بقول لك انه then ال z اللي هي ال x
+
+335
+00:26:18,440 --> 00:26:21,560
+minus y اللي لجيتها انت قبل شوية اللي هي ال z هذه
+
+336
+00:26:21,560 --> 00:26:25,820
+هتكون is orthogonal to mean to y يعني الطول هذا
+
+337
+00:26:25,820 --> 00:26:28,950
+اللي قبل شوية اللي لجيناها هنااللي راجعناه هذا
+
+338
+00:26:28,950 --> 00:26:32,590
+الطول بين هال نهال هذا الطول المسافة بينهم هيكون
+
+339
+00:26:32,590 --> 00:26:39,430
+هذا orthogonal عالميا على ال Y ماشي الحالة نشوف
+
+340
+00:26:39,430 --> 00:26:44,470
+الآن هذا اللي هو نشوف كيف نثبت أنه orthogonal to Y
+
+341
+00:26:44,470 --> 00:26:49,580
+طيبsuppose that .. انه لأ suppose that Z بيساوي X
+
+342
+00:26:49,580 --> 00:26:53,040
+minus Y is not orthogonal to Y مدان مش عمودية على
+
+343
+00:26:53,040 --> 00:26:59,140
+Y اذا اكيد في نقطة بين اللي هو ال Y و بينها اللي
+
+344
+00:26:59,140 --> 00:27:01,740
+هي مش عمودية يعني ال inner product بين هنا شماله
+
+345
+00:27:01,740 --> 00:27:05,080
+مش صفر ماعرفشو معناته احنا ماعرفين شو معناته انه X
+
+346
+00:27:05,080 --> 00:27:09,740
+orthogonal to Y معناته inner product بين X و Y
+
+347
+00:27:09,740 --> 00:27:14,700
+بساوي صفر لكل Y وين موجودة في ال Y ماشي؟
+
+348
+00:27:17,380 --> 00:27:22,000
+طيب معايا طيب احنا طبعا شغلنا هان وين يا جماعة في
+
+349
+00:27:22,000 --> 00:27:25,640
+inner product space تنسوش بشتغل وين في inner
+
+350
+00:27:25,640 --> 00:27:28,860
+product space و احنا عرفنا ال orthogonality فيها
+
+351
+00:27:28,860 --> 00:27:33,240
+لان نفترض ان زد بيساوي x minus y is not orthogonal
+
+352
+00:27:33,240 --> 00:27:36,600
+to y مدام مش orthogonal اذا هلاجي y في ال y بحيث
+
+353
+00:27:36,600 --> 00:27:42,960
+ان زد و هذا النقطة اللي اشماله لايساوي سفرإذن then
+
+354
+00:27:42,960 --> 00:27:47,340
+there is y1 element in y such that z و y1 بيساوى
+
+355
+00:27:47,340 --> 00:27:53,100
+beta لاتساوى مين لاتساوى صفر clearly y1 لاتساوى
+
+356
+00:27:53,100 --> 00:27:56,400
+صفر أكيد لأن لو y1 بيساوى صفر معناته z و y1 بيساوى
+
+357
+00:27:56,400 --> 00:28:02,240
+صفر طيب الان otherwise z و y1 بيساوى صفر وهذا إيش
+
+358
+00:28:02,240 --> 00:28:06,940
+معله مش معجول ناشي و احنا لأنه مفترضين انه اللي هو
+
+359
+00:28:06,940 --> 00:28:11,200
+لايساوى صفر فاهمين طيبالأن furthermore for any
+
+360
+00:28:11,200 --> 00:28:15,360
+scalar α أحسبلي الآن لأي scalar α عشان بتصلكم
+
+361
+00:28:15,360 --> 00:28:18,440
+لتناقض احنا فرضنا العكس و بنصل لتناقض شوفوا كده
+
+362
+00:28:18,440 --> 00:28:21,880
+بتوصلكوا للتناقض خدوا ال Z ناقص Alpha Y واحد وكل
+
+363
+00:28:21,880 --> 00:28:25,300
+إيش ماله تربيع بنفك هذه بتعرفوا تفكوها عبارة عن
+
+364
+00:28:25,300 --> 00:28:28,240
+inner product بين هذه و بين نفسها و بنفك فكرة
+
+365
+00:28:28,240 --> 00:28:34,100
+بتطلع Z و Z ناقص أعملكم إياها ولا .. أو واضحة؟
+
+366
+00:28:34,100 --> 00:28:39,500
+الآن .. الآن .. هذه لأ خليني أعملها أحسنthe norm
+
+367
+00:28:39,500 --> 00:28:44,640
+of z-alpha y1 الكل تربية بساوي ال inner product
+
+368
+00:28:44,640 --> 00:28:52,440
+بين z-alpha y1 او z-alpha y1 مظبوط بفك الآن فكها
+
+369
+00:28:52,440 --> 00:28:57,540
+زي ما انتوا عارفين كيف بنفكها y ساوي z مع z
+
+370
+00:29:00,770 --> 00:29:07,610
+الان ناقص α y1 مع مين؟ مع الـ z اللي هي α y1 و مين
+
+371
+00:29:07,610 --> 00:29:12,890
+و z وهذه هتصير معاها بالنقص صح ولا لا؟ اذا الان
+
+372
+00:29:12,890 --> 00:29:17,750
+فكيت هذولة مع حاجة ديالأن بيدفك الآن هذولة مع مين
+
+373
+00:29:17,750 --> 00:29:21,870
+مع التانية Z مع اللي هي هذه ناقص ال Alpha لما تيجي
+
+374
+00:29:21,870 --> 00:29:24,590
+بتيجي أشمالها ال Alpha conjugate اللي Alpha
+
+375
+00:29:24,590 --> 00:29:30,810
+conjugate Z و Y1 وظل اللي هي هذه مع هذه مظبوط اللي
+
+376
+00:29:30,810 --> 00:29:33,850
+هي ناقص ناقص بيصير أشمالها زاد و Alpha في Alpha
+
+377
+00:29:33,850 --> 00:29:39,970
+conjugate فبصير مدرس لAlpha تربيع في Y1 و Y1 مظبوط
+
+378
+00:29:40,630 --> 00:29:45,270
+طيب إذا صار عندى عبارة عن Z و Z زى ما قولنا ناقص
+
+379
+00:29:45,270 --> 00:29:49,370
+Alpha conjugate في Z و Y1 ناقص الآن بدى أخد بين
+
+380
+00:29:49,370 --> 00:29:54,070
+اللي هي التنتين الأخرى التنتين هدولة بين هذه و هذه
+
+381
+00:29:54,070 --> 00:29:59,450
+بدأ أخد من على المشترك ال Alpha ماشي فبتضل Y1 و Z
+
+382
+00:29:59,450 --> 00:30:05,550
+و جوا أشمالها Alpha conjugate Y1 و Y Y1 واضح؟
+
+383
+00:30:05,550 --> 00:30:15,680
+بديها بعد شويةإذا أنا خدت أنا الآن ال alpha عامل
+
+384
+00:30:15,680 --> 00:30:20,300
+مشترك ضالت عندي هذه زي ما هي و هذه زي ما هي ناقص
+
+385
+00:30:20,300 --> 00:30:25,160
+alpha في هذه ناقص هذه طيب و إيه ساوي هذه نزلليها
+
+386
+00:30:25,160 --> 00:30:30,120
+زي ما هي و الآن alpha conjugate إيش أنا سميت z y1
+
+387
+00:30:30,120 --> 00:30:36,500
+z y1 هيها z y1 اللي هي beta هتطلع هذه y1 و z إيش
+
+388
+00:30:36,500 --> 00:30:42,380
+مالهاConjugate لها Beta Conjugate لأن هذه عبارة عن
+
+389
+00:30:42,380 --> 00:30:45,860
+زبد Y1 Conjugate وهذه كانت Beta اسمها إذا بصير
+
+390
+00:30:45,860 --> 00:30:50,740
+ناقص اللي هو Alpha فيه هذه بصير Beta Conjugate هنا
+
+391
+00:30:50,740 --> 00:30:57,910
+حطيتها ناقص Alpha Conjugate في Y1 ومنين؟ Y1بدي
+
+392
+00:30:57,910 --> 00:31:02,130
+أطير هذا الـ Turn فأخدت أنا Alpha conjugate هذه
+
+393
+00:31:02,130 --> 00:31:06,070
+بساوية يعني أنا بدي أسفره بساوية Beta conjugate
+
+394
+00:31:06,070 --> 00:31:11,070
+على Y1 ومين؟ Y1 أنا ضامن إن ال norm Y1 تربيه مش 0
+
+395
+00:31:11,070 --> 00:31:15,150
+لأن اضمنها إن Y1 ما لها مش 0 لذا بقسم عليه وانا
+
+396
+00:31:15,150 --> 00:31:18,790
+مرتاح لأن لما أخدت Alpha conjugate بساوية Beta
+
+397
+00:31:18,790 --> 00:31:22,030
+conjugate على هذه صار عندي الآن هذا المقدار اللي
+
+398
+00:31:22,030 --> 00:31:26,570
+بساوي هذا المقدارصار عبارة عن هذا زي ما هو بنزل
+
+399
+00:31:26,570 --> 00:31:34,790
+وهذا Alpha conjugate في Beta اللي هو ال Alpha
+
+400
+00:31:34,790 --> 00:31:39,710
+conjugate في Beta عنده بيصير عبارة عن norm ال Beta
+
+401
+00:31:39,710 --> 00:31:43,970
+تربيع على norm ال Y1 تربيع نشوف كيف .. كيف ال ..
+
+402
+00:31:43,970 --> 00:31:45,050
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+403
+00:31:45,050 --> 00:31:45,530
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+404
+00:31:45,530 --> 00:31:49,530
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+405
+00:31:49,530 --> 00:31:49,530
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+406
+00:31:49,530 --> 00:31:49,550
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+407
+00:31:49,550 --> 00:31:49,550
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+408
+00:31:49,550 --> 00:31:49,550
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+409
+00:31:49,550 --> 00:31:49,550
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+410
+00:31:49,550 --> 00:31:49,550
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+411
+00:31:49,550 --> 00:31:52,620
+.. ال .. ال ..الآن عندي اللي هو المقدار هذا لما
+
+412
+00:31:52,620 --> 00:31:55,620
+أخدنا Alpha conjugate عبارة عن Beta على هذا
+
+413
+00:31:55,620 --> 00:31:59,860
+المقدار هذا بيصير سفر صح ولا لأ معايا و Beta
+
+414
+00:31:59,860 --> 00:32:03,520
+conjugate مع Beta على هذه بيصير Beta في Beta
+
+415
+00:32:03,520 --> 00:32:07,000
+conjugate اللي هو هذا تربيع وينه؟ أه وعلى هذا اللي
+
+416
+00:32:07,000 --> 00:32:12,130
+هو Normal Y واحد تربيع واضح؟ ماضحش اللي صار؟عيد
+
+417
+00:32:12,130 --> 00:32:16,350
+طيب إذا صار عندي الان ال norm هذا بيساوي المقدار
+
+418
+00:32:16,350 --> 00:32:22,090
+هذا however norm ال z بيساوي norm ال x minus y و
+
+419
+00:32:22,090 --> 00:32:26,510
+هذا بيساوي مين ال delta و ال beta نفسها لا تساوي
+
+420
+00:32:26,510 --> 00:32:32,230
+سفر لا تساوي سفر إذا صار عندي الآن لما نشيل هذا
+
+421
+00:32:32,230 --> 00:32:37,730
+المقدارهذا المقدار اللي هو هذا المقدار Beta لا
+
+422
+00:32:37,730 --> 00:32:41,490
+تساوي سفر يعني Beta فيه رقم لما يصيرها بيصير هذا
+
+423
+00:32:41,490 --> 00:32:44,350
+المقدار لما نشيله اللي هو بيساوي هذا لما نشيله من
+
+424
+00:32:44,350 --> 00:32:47,710
+هذا المقدار بيصير strictly أصغر من مين من نورم الـ
+
+425
+00:32:47,710 --> 00:32:51,470
+Z تربية يعني نشيلنا منه رقم إذا بيصير أقل strictly
+
+426
+00:32:51,470 --> 00:32:56,350
+منه اللي هو هذا مين هو Delta تربية لأن نورم الـ Z
+
+427
+00:32:56,350 --> 00:32:59,790
+هو عبارة عن Delta لأن نورم الـ Z هو مين X minus Y
+
+428
+00:32:59,790 --> 00:33:04,880
+اللي هي اللي بيساوي Deltaمعايا إذا صار norm هذا
+
+429
+00:33:04,880 --> 00:33:09,880
+أصغر أو أسوأ من Delta تربيه لكن من جهة أخرى Y
+
+430
+00:33:09,880 --> 00:33:15,480
+subspace مظبوط إذا ال Y minus Alpha Y واحد هذه Y
+
+431
+00:33:15,480 --> 00:33:21,410
+نقص Alpha Y واحد في ال Yفي الـ Y لأن Y واحد في الـ
+
+432
+00:33:21,410 --> 00:33:24,370
+Y وY في الـ Y أي linear combination فيه في الـ Y
+
+433
+00:33:24,370 --> 00:33:30,410
+لأنها subspace بناء عليه Z ناقص Alpha Y واحد بساوي
+
+434
+00:33:30,410 --> 00:33:37,950
+بساوي norm الـ Z عبارة عن Xminus اللي هو Y ناقص
+
+435
+00:33:37,950 --> 00:33:42,850
+اطلع لفوق ناقص Alpha Y واحد وحطناها هتكون أشملها
+
+436
+00:33:42,850 --> 00:33:46,870
+أكبر أو ساوى Delta لإنه انزل انزل لإنه زي ما قلنا
+
+437
+00:33:46,870 --> 00:33:50,530
+عليا عليا لإنه هذا يقولنا هذا المقدار Y ناقص Alpha
+
+438
+00:33:50,530 --> 00:33:55,270
+Y واحد هذا المقدار في ال Y X ناقص اللي هو element
+
+439
+00:33:55,270 --> 00:33:58,910
+في ال Y أكبر أو ساوى من ال infimum اللي هو مين هو
+
+440
+00:33:58,910 --> 00:34:02,810
+ال Deltaإذا صار أكبر أو شويه Delta إذا صار في عندي
+
+441
+00:34:02,810 --> 00:34:08,550
+المقدار هذا مرة أكبر أو شويه Delta و مرة strictly
+
+442
+00:34:08,550 --> 00:34:12,550
+أصغر من Delta وهذا Contradiction معايا يا جماعة
+
+443
+00:34:12,550 --> 00:34:17,710
+هذا أكبر أو شويه Delta انزل و هنا اشماله أصغر
+
+444
+00:34:17,710 --> 00:34:22,130
+strictly من Delta حصلنا عليه أصغر strictly من مين؟
+
+445
+00:34:22,130 --> 00:34:25,530
+من Delta إذا مرة أصغر strictly من Delta لأن تربية
+
+446
+00:34:25,530 --> 00:34:28,510
+تربية بروحان مش أصغر strictly من Delta و مرة أكبر
+
+447
+00:34:28,510 --> 00:34:31,540
+أو شويه Deltaوهذا في Contradiction Therefore اللي
+
+448
+00:34:31,540 --> 00:34:37,260
+هو لازم تكون عندي اللي هي Z هذه Orthogonal على
+
+449
+00:34:37,260 --> 00:34:46,680
+اللي هي ال sub space Y طيب ننجي للوقت ده الآن
+
+450
+00:34:46,680 --> 00:34:57,150
+هذولة بأهلنا لا إشي أنه أقدر أجزء ال spaceأي space
+
+451
+00:34:57,150 --> 00:35:01,910
+أو inner product space أجزؤه إلى جزئين الجزء
+
+452
+00:35:01,910 --> 00:35:07,270
+والجزء الorthogonal عليه وبدأ أسميت اسمه الآن ماشي
+
+453
+00:35:07,270 --> 00:35:12,950
+الحالة let a vector space X is said to be the
+
+454
+00:35:12,950 --> 00:35:18,800
+direct sum of two subspaces Y and Z of Xأو written
+
+455
+00:35:18,800 --> 00:35:24,480
+X بتساوي Y زائد Z ماشي ال vector space X is said
+
+456
+00:35:24,480 --> 00:35:29,800
+to be direct sum of two subspaces Y and Z of X إذا
+
+457
+00:35:29,800 --> 00:35:33,660
+و بنكتبه على صورة X بتساوي direct sum Y زائد Z إذا
+
+458
+00:35:33,660 --> 00:35:38,920
+كل element في ال X فيه ال unique representation
+
+459
+00:35:38,920 --> 00:35:44,120
+يعني X بتساوي Y زائد Min زائد Z وهذا وحيد
+
+460
+00:35:55,680 --> 00:36:02,240
+واضح هذا بنسميه اللي هو كتبنا اللي هو ال X على
+
+461
+00:36:02,240 --> 00:36:06,800
+صورة direct sum Y زائد Z مركز عليه هذا الكلام لأن
+
+462
+00:36:06,800 --> 00:36:12,360
+هذا هي لازمنا نحتاج له بالتفصيل طيب الآن ال
+
+463
+00:36:12,360 --> 00:36:18,830
+theorem هذهبتحطلك النقاط على الحروف بالنسبة ل ..
+
+464
+00:36:18,830 --> 00:36:24,010
+اللي هي العلاقة بين اللي هو الـY والـY Orthogonal
+
+465
+00:36:24,010 --> 00:36:29,330
+احنا اذا .. خلّيني أسبق الأمور شوية في الـSpace
+
+466
+00:36:29,330 --> 00:36:36,170
+العادى، هي عندي اللي هو الـX Axis وهي الـY Axis،
+
+467
+00:36:36,170 --> 00:36:42,490
+مظبوط؟ عناصر هذولة Zero أو Xiو Zero أو إكساي واحد
+
+468
+00:36:42,490 --> 00:36:48,010
+و Zero خلّينا نسميها عناصرها نميل هي Zero و إكساي
+
+469
+00:36:48,010 --> 00:36:53,140
+اتنينوأي نقطة في ال space التانية Orthogonal على
+
+470
+00:36:53,140 --> 00:36:57,180
+بعض أي نقطة في ال space اللي هي XI واحد وXI اتنين
+
+471
+00:36:57,180 --> 00:37:03,080
+عبارة عن اللي هو النقاط الأولى زائد النقاط التانية
+
+472
+00:37:03,080 --> 00:37:06,960
+اللي هنا واللي هنا ماشي الحال وكأنه اللي هو ال
+
+473
+00:37:06,960 --> 00:37:11,380
+space X عند R تربيع اقدرنا نكتب على صورة direct
+
+474
+00:37:11,380 --> 00:37:20,190
+sum اللي هو R زائد مينR الـ N والـ R المقصود فيها
+
+475
+00:37:20,190 --> 00:37:23,750
+هنا أو خلّيني نقول مانعش نقول هذا isomorphic ل R
+
+476
+00:37:23,750 --> 00:37:29,950
+مش R خلّيني نقول إن هو ال space R اتحاد Zero
+
+477
+00:37:29,950 --> 00:37:35,730
+خلّيني نقول المزوج المرتبة بين R اتحاد Zero اللي
+
+478
+00:37:35,730 --> 00:37:39,610
+هي عبارة عن كل XI واحد و Zero such that XI واحد
+
+479
+00:37:39,610 --> 00:37:43,590
+element in R والتاني اللي هو الجهة التانيةوهذا ايش
+
+480
+00:37:43,590 --> 00:37:48,970
+معنى هنا orthogonal على بعض نشوف هذا الكلام ليش
+
+481
+00:37:48,970 --> 00:37:52,890
+علاقته باللي بنحكيه طيب projection theorem
+
+482
+00:37:52,890 --> 00:37:57,570
+projection theorem اللي بتقول اللي قلت y بيقال
+
+483
+00:37:57,570 --> 00:38:01,890
+close subspace of a Hilbert space H نفترض ان y أيش
+
+484
+00:38:01,890 --> 00:38:05,650
+معنى close subspace مفهوم ايش معنى close subspace
+
+485
+00:38:05,650 --> 00:38:12,140
+then H بيقول لك نقدر نكتب على صورة y زائد زدحيث
+
+486
+00:38:12,140 --> 00:38:16,720
+الـ Z هي مين الـ Y Orthogonal الـ Y Orthogonal
+
+487
+00:38:16,720 --> 00:38:19,740
+أخدنا إيش معنية الـ Y Orthogonal هي كل العناصر
+
+488
+00:38:19,740 --> 00:38:22,940
+اللي في الـ H اللي بتكون عمودية عالميا على الـ Y
+
+489
+00:38:22,940 --> 00:38:27,640
+يعني أي عنصر في الـ H و أكتبه على صورة اللي هو
+
+490
+00:38:27,640 --> 00:38:33,800
+حاصل جامع اللي هو direct sum من Y و Z حيث Y و Z
+
+491
+00:38:33,800 --> 00:38:38,220
+إيش ما هين متعامدين زي المثال للغاية ماشي الحالة
+
+492
+00:38:38,220 --> 00:38:45,340
+طيبالبرهن البرهن هذا الان اه اكيد هذا مبنع اللي
+
+493
+00:38:45,340 --> 00:38:48,600
+فات والبرهن هيكون جليل بناء على انه مبنع اللي فات
+
+494
+00:38:49,320 --> 00:38:53,980
+الان اللى دخلت على الخط جديد الان since Y is a
+
+495
+00:38:53,980 --> 00:38:57,960
+closed subspace of a Hilbert space H then Y ايش
+
+496
+00:38:57,960 --> 00:39:03,140
+ماله؟ اذا ان هي subspace من مين؟ دخلت انه H نفسها
+
+497
+00:39:03,140 --> 00:39:07,360
+تكون أيش معلها؟ Hilbert space احنا كنا نكون في
+
+498
+00:39:07,360 --> 00:39:11,100
+اللى جابلها انزل انزل عشان نقارن بين الجهتين عندى
+
+499
+00:39:11,100 --> 00:39:17,740
+في اللي هاناللي هي هيها X inner product space ماشي
+
+500
+00:39:17,740 --> 00:39:21,080
+الحال و بناء عليه اللي هو جلنا اللي هو بيكون فيه
+
+501
+00:39:21,080 --> 00:39:23,440
+نقطة واحدة و كده بناء على التلات شروط و من ثم
+
+502
+00:39:23,440 --> 00:39:28,160
+بتكون .. اللي هي النقطة هذه اللي هي اتلع لفوق
+
+503
+00:39:28,160 --> 00:39:32,560
+Orthogonal بناء على انه يكون Y subspace لأن لو
+
+504
+00:39:32,560 --> 00:39:36,600
+ضفنا على كل هالجثة انه ال space الأصلي H is
+
+505
+00:39:36,600 --> 00:39:39,600
+complete يصير أمورنا تمام اتتمام و نقدر نكتبه على
+
+506
+00:39:39,600 --> 00:39:45,040
+الصورة اللي أمامنا اتلع لفوقإذن الآن بما أن Y كله
+
+507
+00:39:45,040 --> 00:39:48,380
+ال subspace من Hilbert space H إذاً Y نفسه is H is
+
+508
+00:39:48,380 --> 00:39:50,700
+complete إذا مافيش داعي أن أفترض أن Y complete
+
+509
+00:39:50,700 --> 00:39:56,260
+بقول close subspace وH نفسه إيش ما لها complete
+
+510
+00:39:56,260 --> 00:40:00,120
+إذا ريح التراثي إذا حصلت على الشرط اللي بديها مدام
+
+511
+00:40:00,120 --> 00:40:04,180
+Y complete وY عندي since Y is convex لإنها اللي هي
+
+512
+00:40:04,180 --> 00:40:07,820
+subspacethen by theorem تلاتة تلاتة واحد اللي ..
+
+513
+00:40:07,820 --> 00:40:11,460
+اللي بدأنا فيها أو التانية and لما تلاتة تلاتة
+
+514
+00:40:11,460 --> 00:40:16,970
+اتنين imply that لكل X element in X في Y وحيدةأه
+
+515
+00:40:16,970 --> 00:40:20,730
+بحيث انه Z بتساوي او في Y في ال Y بحيث انه Z ايش
+
+516
+00:40:20,730 --> 00:40:24,650
+بتساوي X minus Y عمودي على مين على ال Y لقد
+
+517
+00:40:24,650 --> 00:40:28,490
+أثبتناها قبل شوية هذا إذا صارت عند ال X كتبتها على
+
+518
+00:40:28,490 --> 00:40:36,300
+صورة Y زائد مين زائد Z بدنا نثبت انه الآن حيثY
+
+519
+00:40:36,300 --> 00:40:40,420
+element in Y والـ Z وين موجودة في الـ Y Orthogonal
+
+520
+00:40:40,420 --> 00:40:44,880
+اللي هي الرمزنالها بالرمز مين Z Capital معايا؟ هذا
+
+521
+00:40:44,880 --> 00:40:48,380
+كله من وين؟ من النظرية الأولى الآن بدنا نفترض ..
+
+522
+00:40:48,380 --> 00:40:53,100
+بدنا نثبت أن هذه الصورة صورة إيه شمالها وحيدة يعني
+
+523
+00:40:53,100 --> 00:40:57,970
+الـ Y وحيدة والـ Z إيه شمالها؟ وحيدةنفترض الآن
+
+524
+00:40:57,970 --> 00:41:02,670
+suppose that there are y1 و y2 في ال y و z1 و z2
+
+525
+00:41:02,670 --> 00:41:07,330
+في ال y و ال x نقدر نكتبها على صورة x y1 زي z1 و
+
+526
+00:41:07,330 --> 00:41:12,350
+ال x نقدر نكتبها على صورة y2 زي z2 و نوصلكم أنه
+
+527
+00:41:12,350 --> 00:41:19,530
+لازم يكونين متساويتين ماشي الوصول سهل then احسبلي
+
+528
+00:41:19,530 --> 00:41:25,250
+الآنهذه بتساوي هذه خد ال Y على جهة و ال Z على جهة
+
+529
+00:41:25,250 --> 00:41:28,730
+بيصير Y واحد نقص Y اتنين بيساوي Z اتنين نقص Z واحد
+
+530
+00:41:28,730 --> 00:41:32,830
+however Y واحد نقص Y اتنين اللي موجودة في ال Y
+
+531
+00:41:32,830 --> 00:41:36,950
+مظبوط و هذه بتساوي هذه و هذه موجودة في ال Y
+
+532
+00:41:36,950 --> 00:41:41,170
+orthogonal اه إذا هذه صارت عمودية على هذه مظبوط
+
+533
+00:41:41,170 --> 00:41:46,920
+إذا صار عندي و Z اتنين في ال Y و Z واحد thenالـ Y1
+
+534
+00:41:46,920 --> 00:41:50,200
+والـ Y2 مدامت بالساوية هذه وهذه موجودة في الـ Y
+
+535
+00:41:50,200 --> 00:41:54,100
+أورثجونال ومن جهة أخرى هذه في الـ Y أورثجونال إذا
+
+536
+00:41:54,100 --> 00:41:58,960
+صارت هذه في الـ Y وبناء على المساوية اللي بتساويها
+
+537
+00:41:58,960 --> 00:42:00,960
+في الـ Y أورثجونال هتكون في الـ Y أورثجونال هي
+
+538
+00:42:00,960 --> 00:42:05,120
+برضه إذا صارت Y1 ناقص Y2 موجودة في الـ Y حسب هذه
+
+539
+00:42:05,120 --> 00:42:07,620
+وهتكون موجودة في الـ Y أورثجونال حسب هذه إذا
+
+540
+00:42:07,620 --> 00:42:11,800
+موجودة في التقاطع وبناء عليه فهتكون عمودية على
+
+541
+00:42:11,800 --> 00:42:16,180
+حالهاالاشي الوحيد اللي بين Y و Y Orthogonal هو مين
+
+542
+00:42:16,180 --> 00:42:19,920
+الصفر؟ ليش؟ لأن لو فرضنا إنه في عندنا Element اسمه
+
+543
+00:42:19,920 --> 00:42:25,780
+Y1-Y2 Element in Y تقاطع الـY Orthogonal معناته
+
+544
+00:42:25,780 --> 00:42:33,560
+هذا الـElement صار Y1-Y2 وY1-Y2 إيش هيساوي؟ صفر،
+
+545
+00:42:33,560 --> 00:42:36,680
+بناءً عليه هيكون هذا الـElement صفر، يعني إذا
+
+546
+00:42:36,680 --> 00:42:41,780
+دائمًا هذا التقاطع بيساوي مين؟الـ Zero إذا Y1-Y2
+
+547
+00:42:41,780 --> 00:42:50,680
+بيساوي 0 إذا Y1 بيساوي Y2 وبناء عليه بيصير عندي
+
+548
+00:42:50,680 --> 00:42:57,280
+اللي هو العنصر Y1 وحيد ومنه ما دام Y1 بيساوي Y2
+
+549
+00:42:57,280 --> 00:43:01,320
+إذا هذا صار سفر إذا Z2-Z1 بيساوي 0 إذا Z2 بيساوي
+
+550
+00:43:01,320 --> 00:43:06,580
+Z1 إذا صارت عندي اللي هي ال uniqueness تم إثباتها
+
+551
+00:43:07,090 --> 00:43:16,750
+نجي للملاحظة اللي بعدها ايش
+
+552
+00:43:16,750 --> 00:43:22,070
+الملاحظة بتقول from اتنين above
+
+553
+00:43:24,590 --> 00:43:28,650
+we can define a mapping called the orthogonal
+
+554
+00:43:28,650 --> 00:43:35,150
+projection of H onto Y صار عندي لان بقدر اعرف
+
+555
+00:43:35,150 --> 00:43:43,730
+mapping B من H اللي هو إيش بيساوي X أو آسف Y زائد
+
+556
+00:43:43,730 --> 00:43:51,880
+Y orthogonal، مظبوط؟ حاشي، لعند مين؟ لعند Yهذا الـ
+
+557
+00:43:51,880 --> 00:43:57,480
+projection بيجي بسقطلي اللي هو كل العناصر هنا
+
+558
+00:43:57,480 --> 00:44:02,780
+بسقطها العنصر على ال element 10 لنشوف كيف بدنا
+
+559
+00:44:02,780 --> 00:44:10,430
+نعرفه هو في الواقع العموداللي هو بي من أدش اللي
+
+560
+00:44:10,430 --> 00:44:16,790
+عند Y defined by بي X بتساوي Y where Y بتساوي X
+
+561
+00:44:16,790 --> 00:44:20,190
+زائد Z ياشي ال element .. Y element و Y و Z
+
+562
+00:44:20,190 --> 00:44:23,050
+element المين in Z this mass being has the
+
+563
+00:44:23,050 --> 00:44:26,490
+following properties شوفوا أمثلكم على اللي إحنا
+
+564
+00:44:26,490 --> 00:44:32,790
+بنعرفه هي عندي اللي هو ال X axis وهي مين ال Y axis
+
+565
+00:44:32,790 --> 00:44:36,390
+وخلّيني أقول .. يعني خلّيني أقول Roughly اللي هو R
+
+566
+00:44:36,390 --> 00:44:41,890
+تربيعبساوي الـ x-axis زائد مين ضايق صمت مع مين؟ مع
+
+567
+00:44:41,890 --> 00:44:47,370
+الـ y-axis ناشي الحال الان عندي ال projection قدوة
+
+568
+00:44:47,370 --> 00:44:53,310
+اي نقطة اي نقطة اللي هي x واحد و y واحد او زي ما
+
+569
+00:44:53,310 --> 00:44:56,590
+هو يسميها psi واحد وpsi اتنين هذا النقطة لما
+
+570
+00:44:56,590 --> 00:45:02,850
+اعملها projection بده نزلها هان صورتها مين؟X1 ماشي
+
+571
+00:45:02,850 --> 00:45:08,810
+الحال فالان بعملته projection X زي Y هو مسميها
+
+572
+00:45:08,810 --> 00:45:15,130
+طبعا هذه اللي هو اللي في الواقع اسمها Y عنده وهذه
+
+573
+00:45:15,130 --> 00:45:20,370
+ايش اسمها ال Z اللي هي ال Y Orthogonal معايافعملت
+
+574
+00:45:20,370 --> 00:45:24,530
+إسقاط صارت اللي هي صورة أي نقطة تاخد mean ال entry
+
+575
+00:45:24,530 --> 00:45:29,290
+الواحد الأول X واحد وكأنه صار له projection من ال
+
+576
+00:45:29,290 --> 00:45:36,020
+space اللي هو R تربيع لعند ال mean ال X axisأو
+
+577
+00:45:36,020 --> 00:45:39,640
+اللي هو مسميه هناك الـ Y ممكن أعمله حكامي وين؟ على
+
+578
+00:45:39,640 --> 00:45:42,300
+الجهة دي بعد شوية بنشوف اللي هو أعمله projection
+
+579
+00:45:42,300 --> 00:45:45,100
+وين؟ هنا بس الآن خلّينا على ال projection تبعنا
+
+580
+00:45:45,100 --> 00:45:49,580
+أنه عملنا projection من H Y زائد Y Orthogonal
+
+581
+00:45:49,580 --> 00:45:53,720
+عالمين على ال Y بعد شوية هنعمله عالمين على ال Y
+
+582
+00:45:53,720 --> 00:45:58,000
+Orthogonal كيف بدنا نعرفه هذا؟ بدنا نعرفه أن ال BX
+
+583
+00:45:58,000 --> 00:46:07,600
+BX اللي هي ال X إيش هتساويB of Y زائد مين؟ زائد Y
+
+584
+00:46:07,600 --> 00:46:14,860
+اللي هو الجزء الثاني أنا بسميها Z إيش بتساوي ال Y؟
+
+585
+00:46:14,860 --> 00:46:22,440
+واضح؟ أي سؤال؟ طيب الآن هذا ال projection has the
+
+586
+00:46:22,440 --> 00:46:27,310
+following propertiesمش احنا اتفاجنا قبل بشوية انه
+
+587
+00:46:27,310 --> 00:46:30,210
+اي X نقدر نكتبها على صورة Y زي Z من ال direct sum
+
+588
+00:46:30,210 --> 00:46:34,770
+هدف ال Y في ال Y و ال Z في ال Y ارتجونال الان ال
+
+589
+00:46:34,770 --> 00:46:37,690
+projection بده اعرفه من H لعند Y اللي هو بياخد ال
+
+590
+00:46:37,690 --> 00:46:42,070
+X و برميها لوين على ال Y الان P is linear and
+
+591
+00:46:42,070 --> 00:46:44,950
+bounded P is linear and bounded دوة دي سهلة P is
+
+592
+00:46:44,950 --> 00:46:52,490
+linear قلكم دي شجرة تفاصيلالان بي .. this mapping
+
+593
+00:46:52,490 --> 00:46:55,430
+has the following properties منها all bounded all
+
+594
+00:46:55,430 --> 00:46:58,890
+bounded برضه نفس الأشياء normal بي X هتصل to other
+
+595
+00:46:58,890 --> 00:47:04,130
+بساوي something في normal X بي maps H onto Y بياخد
+
+596
+00:47:04,130 --> 00:47:08,290
+H onto وين onto Y و هذا واضح بي و فاتش أشمالها خد
+
+597
+00:47:08,290 --> 00:47:11,670
+I X في هدا صورتها مين اللي هو Y خدوا I Y هنا
+
+598
+00:47:11,670 --> 00:47:15,010
+هتلاقوا element هنا بحيث انه صورته مين اللي هي هنا
+
+599
+00:47:16,380 --> 00:47:20,440
+أخدوا أي ويهان هتلاقوا اللي هو فيه element نهان
+
+600
+00:47:20,440 --> 00:47:25,700
+بحيث انه بي of اللي هي ال H بساوي اللي هو ال Y
+
+601
+00:47:29,260 --> 00:47:34,860
+الـ B of Y برضه إيش هتساوي اللي هي مين ال Y برضه
+
+602
+00:47:34,860 --> 00:47:37,360
+هذا كله بده إثبات يعني بس مش صعب إثباته دير بالكم
+
+603
+00:47:37,360 --> 00:47:42,140
+B of Y Orthogonal إيش هيساوي؟ هيساوي الصفر طبيعي
+
+604
+00:47:42,140 --> 00:47:46,040
+ما هو لإنه أي ال اللي هو element هنا في ال Y
+
+605
+00:47:46,040 --> 00:47:49,780
+Orthogonal اللي هو عبارة عن اللي هي في الآخر صورة
+
+606
+00:47:49,780 --> 00:47:52,780
+مين ال Y وعشان يكون في ال Y Orthogonal بيصير Zero
+
+607
+00:47:52,780 --> 00:47:55,540
+زائد ال element اللي في ال Y Orthogonal برميه على
+
+608
+00:47:55,540 --> 00:47:59,820
+ال Zero فبكون ده منصورة مش أي element هناهيصير أي
+
+609
+00:47:59,820 --> 00:48:03,840
+element Y أي element X في الـ Y Orthogonal هيكون
+
+610
+00:48:03,840 --> 00:48:09,800
+على صورة X بتساوي element اللي هو Zero زائد X والـ
+
+611
+00:48:09,800 --> 00:48:12,100
+X موجودة في الـ Y Orthogonal وهذا موجود في الـ Y
+
+612
+00:48:12,100 --> 00:48:18,500
+فهيكون ال projection له مين هو الـ Zero المهم الـ
+
+613
+00:48:18,500 --> 00:48:22,160
+B تربيه هيساوى مين؟ هيساوى الـ B خد الـ B تربيه في
+
+614
+00:48:22,160 --> 00:48:25,880
+Xو ال X طبعا على صورة هذه هتلاقيه وين هيروح في
+
+615
+00:48:25,880 --> 00:48:30,500
+الآخر لل P of X يعني P تربيع of X هتطلع P of X
+
+616
+00:48:30,500 --> 00:48:35,660
+ولكن سينا برضه يعني بمعنى آخر اللي هو هذا بنسميه
+
+617
+00:48:35,660 --> 00:48:40,100
+idempotent and the restriction of P on Y is the
+
+618
+00:48:40,100 --> 00:48:43,760
+identity operator on Y من هذه هي ال restriction
+
+619
+00:48:43,760 --> 00:48:46,800
+اللي فيه حتى تطلع ال identity operator هتاخد اللي
+
+620
+00:48:46,800 --> 00:48:50,560
+هو ال wire اللي بعد هذا left to the reader
+
+621
+00:48:50,560 --> 00:48:56,460
+homework معاكمالآن بناءً على اللي قبل بشوية اللي
+
+622
+00:48:56,460 --> 00:49:01,760
+هو the orthogonal complement of a closed subspace
+
+623
+00:49:01,760 --> 00:49:05,540
+Y of a Hilbert space H is the null space N of B of
+
+624
+00:49:05,540 --> 00:49:12,300
+the orthogonal projection of B onto Y يعني الآن مش
+
+625
+00:49:12,300 --> 00:49:20,890
+هحله بس يعني بعطيكم ال .. ال null space of Bالـ
+
+626
+00:49:20,890 --> 00:49:25,050
+null space of B أيش هيطلع عندك الـ null space of B
+
+627
+00:49:25,050 --> 00:49:32,190
+الـ null space of B هيطلع اللي هو مين هو the
+
+628
+00:49:32,190 --> 00:49:39,550
+orthogonal complement of Y in Hilbert
+
+629
+00:49:39,550 --> 00:49:42,370
+space is the null space of B يعني الـ N of B
+
+630
+00:49:42,370 --> 00:49:52,280
+هتساوي Y Orthogonal الـ N of B أيش تعريفهاهي عبارة
+
+631
+00:49:52,280 --> 00:49:57,520
+عن كل الإكسات اللي بيساوي Y زائد Z element معروف
+
+632
+00:49:57,520 --> 00:50:02,700
+اللي هي Z في ال Y Orthogonal و ال Y في ال Y such
+
+633
+00:50:02,700 --> 00:50:10,520
+that B of X بيساوي Zero يعني B of X ايش B of X في
+
+634
+00:50:10,520 --> 00:50:14,400
+هذه الحالة B of X اللي هي ال Y يعني ال Y ايش
+
+635
+00:50:14,400 --> 00:50:20,770
+بتساوي0 صح يعني النقاط هيصير X تساوي Z اللي وين
+
+636
+00:50:20,770 --> 00:50:23,050
+موجودة في ال Y ارتجونال يعني وين بتساوي ال Y
+
+637
+00:50:23,050 --> 00:50:26,770
+ارتجونال بس بده ترتيب يلا هاي سواء .. الآن اللي
+
+638
+00:50:26,770 --> 00:50:30,730
+بعده اللي بعده ال remark اللي بعده برضه exercises
+
+639
+00:50:30,730 --> 00:50:35,540
+بسيطة هذهإذا M is a non-empty subset of an inner
+
+640
+00:50:35,540 --> 00:50:39,460
+product space X إذا non-empty subset من subspace X
+
+641
+00:50:39,460 --> 00:50:45,960
+then M orthogonal is a closed vector subspace of
+
+642
+00:50:45,960 --> 00:50:52,160
+mean of X إذا حتى لو كانت M عبارة عن مجرد non
+
+643
+00:50:52,160 --> 00:50:55,460
+-empty subset of inner product space هتطلع ال M
+
+644
+00:50:55,460 --> 00:50:59,600
+orthogonal نفسها يشملها closed subspace يعني
+
+645
+00:50:59,600 --> 00:51:04,120
+subspace و closedماشي Sub-spacement عارفين تاخدوا
+
+646
+00:51:04,120 --> 00:51:09,060
+أي XY في الـ M Orthogonal و بتثبتوا أن Alpha X زي
+
+647
+00:51:09,060 --> 00:51:11,060
+الـ Y في الـ M Orthogonal وهذا بالـ Inner Product
+
+648
+00:51:11,060 --> 00:51:14,780
+على طول بتطلع و اللي هي Closed بتاخدوا Sequence X
+
+649
+00:51:14,780 --> 00:51:18,700
+and في الـ M Orthogonal بتكون Verged زي الـ X و
+
+650
+00:51:18,700 --> 00:51:21,300
+بتثبتوا أن الـ X موجودة في الـ M Orthogonal وهذا
+
+651
+00:51:21,300 --> 00:51:24,480
+هتستخدموا ال .. ال .. ال .. ال .. ال continuity لل
+
+652
+00:51:24,480 --> 00:51:27,640
+Inner Product و هتصلوا لنتيجة بسرعة بتثبتوا أن X
+
+653
+00:51:27,640 --> 00:51:31,890
+في الـ M Orthogonaland M is a subset of M
+
+654
+00:51:31,890 --> 00:51:35,370
+Orthogonal و Orthogonal الـ M نفسها هتكون جزئية من
+
+655
+00:51:35,370 --> 00:51:39,570
+مين؟ من M Orthogonal و Orthogonal واضح و برضه هدسي
+
+656
+00:51:39,570 --> 00:51:44,870
+اللي مش صعب .. طيب اللي هنلم اللي عندنا تلاتة
+
+657
+00:51:44,870 --> 00:51:49,830
+تلاتة ستة اطلع لفوق if Y is a closed subspace of a
+
+658
+00:51:49,830 --> 00:51:53,990
+Hilbert space H then هيطلع عند Y ايش متساوي؟ Y
+
+659
+00:51:53,990 --> 00:51:59,610
+Orthogonal و Orthogonal قبل قلنا ان Mجزئية من M
+
+660
+00:51:59,610 --> 00:52:03,570
+Orthogonal أو M Orthogonal لكن M Orthogonal
+
+661
+00:52:03,570 --> 00:52:10,430
+Orthogonal ليس شرطا أن يكون subset من M إلا خلّيني
+
+662
+00:52:10,430 --> 00:52:13,730
+أقول أو شرط أو أحد الشروط اللي بيخليها تتجرأ أن
+
+663
+00:52:13,730 --> 00:52:18,610
+تكون مسوائلها هو الشرط أنها تكون Y a closed
+
+664
+00:52:18,610 --> 00:52:22,130
+subspace وفي هذه الوقت subspace اتشدن Y بيستوي Y
+
+665
+00:52:22,130 --> 00:52:27,110
+Orthogonalخلّينا نبره انه by remark تلاتة y subset
+
+666
+00:52:27,110 --> 00:52:29,950
+من y Orthogonal Orthogonal وهذه سهلة اثباتها كمان
+
+667
+00:52:29,950 --> 00:52:35,390
+يعني لحالة بتثبتوها بشكل سريع طيب conversely ..
+
+668
+00:52:35,390 --> 00:52:39,510
+conversely let x element in y Orthogonal
+
+669
+00:52:39,510 --> 00:52:43,210
+Orthogonalماشي يعني اننا ناخد X في ال Y أرثجونال
+
+670
+00:52:43,210 --> 00:52:46,430
+أرثجونال تبتنها وين موجودة في ال Y by theorem اللي
+
+671
+00:52:46,430 --> 00:52:49,210
+جاب البشوية تلاتة تلاتة أربعة there exists a
+
+672
+00:52:49,210 --> 00:52:52,810
+unique Y element in Y بحيث ان X بتسوى مين Y زي ال
+
+673
+00:52:52,810 --> 00:52:58,610
+Z Y في ال Y و Z في مين في ال Y أرثجونال معايا لكن
+
+674
+00:52:58,610 --> 00:53:03,030
+ال Y جزئية من ال Y أرثجونال أرثجونال ماشي الحال
+
+675
+00:53:03,030 --> 00:53:07,310
+and Y أرثجونال أرثجونال نفسه اشمله is a vector
+
+676
+00:53:07,310 --> 00:53:10,760
+spaceأحنا اتفاجن الـ Y أرثوجونال اللي حالها في
+
+677
+00:53:10,760 --> 00:53:13,220
+vector space بغض النظر عن الـ Y تكون أه ولا لأ
+
+678
+00:53:13,220 --> 00:53:17,240
+الآن Y أرثوجونال أرثوجونال is a vector space إذا Z
+
+679
+00:53:17,240 --> 00:53:22,420
+بتساوي أي linear combination بين أي تنتين XY في
+
+680
+00:53:22,420 --> 00:53:24,640
+الـ Y أرثوجونال أرثوجونال لازم الـ linear
+
+681
+00:53:24,640 --> 00:53:29,860
+combination ماوجودش وين يكون فيها معايا؟ Y جزئية
+
+682
+00:53:29,860 --> 00:53:33,320
+من مين؟ من Y أرثوجونال أرثوجونال والـ Y موجودة
+
+683
+00:53:33,320 --> 00:53:39,850
+وين؟ في الـ Y معايا؟ معايا أهالان و ال .. و ال ..
+
+684
+00:53:39,850 --> 00:53:42,970
+و عندي .. الان حيصير عندي و ال Y Orthogonal
+
+685
+00:53:42,970 --> 00:53:47,170
+Orthogonal عبارة عن ماله عبارة عن subspace إذا
+
+686
+00:53:47,170 --> 00:53:50,770
+أكيد اللي هو Z بالسواء X minus Y برضه موجودة في ال
+
+687
+00:53:50,770 --> 00:53:55,450
+Y Orthogonal Orthogonal و ال .. و هذا معناته ..
+
+688
+00:53:55,450 --> 00:53:59,410
+إيش معناته Z في ال Y Orthogonal Orthogonal إنها
+
+689
+00:53:59,410 --> 00:54:02,790
+عمودية عالمياً على ال Y Orthogonal ولا ليش تكون في
+
+690
+00:54:02,790 --> 00:54:07,280
+ال Y Orthogonal Orthogonalعندى وصلت إن ال Z عمودية
+
+691
+00:54:07,280 --> 00:54:10,960
+على ال Y أرثجونال و ال Y is a closed subspace of a
+
+692
+00:54:10,960 --> 00:54:13,560
+Hilbert space then it is complete
+
+693
+00:54:35,010 --> 00:54:39,130
+والـ z عمودي على ال y orthogonal إذا صارت ال z
+
+694
+00:54:39,130 --> 00:54:42,830
+عمودي على حالها الواحدة منهم إذا صار ال z عمودي
+
+695
+00:54:42,830 --> 00:54:45,690
+على ال z ومن ثم اللي هو inner product بينهم سفر
+
+696
+00:54:45,690 --> 00:54:49,250
+يعني ال z أيش بتساوي سفر ومن ثم x أيش بتساوي y
+
+697
+00:54:49,250 --> 00:54:54,990
+ومدام x بتساوي y احنا بدأنا بxفي الـ Y Orthogonal
+
+698
+00:54:54,990 --> 00:54:58,950
+Orthogonal وانتهينا بالـ X موجودة في الـ Y إذا
+
+699
+00:54:58,950 --> 00:55:01,730
+صارت الـ Y Orthogonal Orthogonal subset من الـ Y و
+
+700
+00:55:01,730 --> 00:55:04,630
+الـ Y Orthogonal Orthogonal هتساوي Y بناء على هذه
+
+701
+00:55:04,630 --> 00:55:07,270
+subset من هذه و هذه أثباتها زي ما قلنا سهل لو
+
+702
+00:55:07,270 --> 00:55:09,930
+أخدتوا X في الـ Y هيكون ال inner product بين الـ X
+
+703
+00:55:09,930 --> 00:55:13,230
+و أي element في الـ Y Orthogonal بساوي سفر فبصير
+
+704
+00:55:13,230 --> 00:55:18,490
+اللي هو اللي هي منها بتقدر تصل لإنه الـ X نفسها
+
+705
+00:55:18,490 --> 00:55:26,870
+موجودة في الـ Y Orthogonalremark 4 if
+
+706
+00:55:26,870 --> 00:55:30,670
+Y is a closed subspace of a Hilbert space H and Z
+
+707
+00:55:30,670 --> 00:55:35,130
+بيساوي Y Orthogonal then
+
+708
+00:55:35,130 --> 00:55:40,850
+Z Orthogonal بيساوي Y Orthogonal Orthogonal بيساوي
+
+709
+00:55:40,850 --> 00:55:47,720
+Y ومن ثمصار انت بتكتب الـ H على صورة إيشي و عمودي
+
+710
+00:55:47,720 --> 00:55:54,320
+عليه مظبوط اللي هو Z زائد مين Z Orthogonal معايا
+
+711
+00:55:54,320 --> 00:56:00,120
+يا جماعة عندي Z بيساوي Y Orthogonal ماشي و Z
+
+712
+00:56:00,120 --> 00:56:04,410
+Orthogonal بيساوي Y Orthogonal Orthogonalاللي هو
+
+713
+00:56:04,410 --> 00:56:08,290
+أثبتناها مين واي هذا كله في حالة مين Y closed
+
+714
+00:56:08,290 --> 00:56:12,290
+subspace of Hilbert space إذا صارت عند أشكتها اللي
+
+715
+00:56:12,290 --> 00:56:16,230
+كاي بكتبها على صورة Z زائد Y صارت على صورة Z زائد
+
+716
+00:56:16,230 --> 00:56:20,170
+مين Z orthogonal لإن ال Y هي ال orthogonal ال
+
+717
+00:56:20,170 --> 00:56:24,070
+orthogonal هي Z orthogonal ماشي الحال إذا ومنه
+
+718
+00:56:24,070 --> 00:56:27,950
+بقدر على اللي حكيته قبل بشوية بنفس الأسلوب ولكن
+
+719
+00:56:27,950 --> 00:56:32,750
+بطبقها على هذه اللي هو direct sum
+
+720
+00:56:35,660 --> 00:56:40,360
+بكس او بكس او بكس او بكس او بكس او بكس او بكس او
+
+721
+00:56:40,360 --> 00:56:43,960
+بكس او بكس او بكس او بكس او بكس او بكس او بكس او
+
+722
+00:56:43,960 --> 00:56:47,860
+بكس او بكس او بكس او بكس او بكس او بكس او بكس او
+
+723
+00:56:47,860 --> 00:56:48,120
+بكس او بكس او بكس او بكس او بكس او بكس او بكس او
+
+724
+00:56:48,120 --> 00:56:48,160
+بكس او بكس او بكس او بكس او بكس او بكس او بكس او
+
+725
+00:56:48,160 --> 00:56:50,580
+بكس او بكس او بكس او بكس او بكس او بكس او بكس او
+
+726
+00:56:50,580 --> 00:56:56,720
+بكس او بكس
+
+727
+00:56:56,720 --> 00:57:04,030
+او بكس اعال Y Axis بسير Bx بدل ما هو عال Y ايش
+
+728
+00:57:04,030 --> 00:57:07,970
+بساوي؟ بساوي اللي هو Z limit in Z Define a
+
+729
+00:57:07,970 --> 00:57:13,590
+projection اللي هو من H لعند Z وهذا اللي هو بنفس
+
+730
+00:57:13,590 --> 00:57:16,870
+الأسلوب السابق نيجي للنمة الأخيرة
+
+731
+00:57:21,770 --> 00:57:26,690
+for any non-empty subset M of a Hilbert space H،
+
+732
+00:57:26,690 --> 00:57:32,930
+ده نرجعنا لمين؟ لمجرد non-empty subset من الـH،
+
+733
+00:57:32,930 --> 00:57:36,270
+the span of M is dense if and only if الامر تجهنا
+
+734
+00:57:36,270 --> 00:57:44,130
+الـH بساوي، بساوي اللي هو الـ0إذا الـ span لـ M هو
+
+735
+00:57:44,130 --> 00:57:47,450
+عبارة عن الـ set of all linear combinations of
+
+736
+00:57:47,450 --> 00:57:52,710
+element M هيكون dense إذا و فقط إذا الـ M مرتجونة
+
+737
+00:57:52,710 --> 00:58:03,370
+لش بتساوي؟ بتساوي سفر إذا
+
+738
+00:58:03,370 --> 00:58:08,170
+يا جماعة فيكم ما تصلوا على النبي بيصير عند الأقل
+
+739
+00:58:08,170 --> 00:58:15,780
+spanللـ M closure بيساوي الـ H او ايش بيسميه هو H
+
+740
+00:58:15,780 --> 00:58:22,000
+F and all F اللي هو الـ M orthogonal بيساوي مين
+
+741
+00:58:22,000 --> 00:58:27,620
+الـ 0 الـ M هذه مجرد مين subset من الـ H وهذه لا
+
+742
+00:58:27,620 --> 00:58:32,260
+تساوي سبق فاتر والـ H عبارة عن Hilbert S V S ماشي
+
+743
+00:58:32,260 --> 00:58:36,080
+تنثبت ناخد اول شي نفترض هذه و نوصل لهذه و نوصل
+
+744
+00:58:36,080 --> 00:58:41,800
+لهذه ماشي طيبلت X الان element of M Orthogonal
+
+745
+00:58:41,800 --> 00:58:46,220
+ونفترض ان V بيساوي ال span لـ M اللي حكيتها to be
+
+746
+00:58:46,220 --> 00:58:49,840
+dense in mean in H بدي اثبتلكم ان الـ X H لازم
+
+747
+00:58:49,840 --> 00:58:53,360
+تساوي السفر عشان اثبت الـ M Orthogonal بساوي الـ
+
+748
+00:58:53,360 --> 00:58:59,410
+Zero طيب صلى الله عليه الصلاة والسلامthen مادام
+
+749
+00:58:59,410 --> 00:59:02,450
+اللي هو ال V بتسوي ال span M، ال span M اللي هو
+
+750
+00:59:02,450 --> 00:59:06,050
+عبارة عن ال closure .. ال span لل M اللي هو ال
+
+751
+00:59:06,050 --> 00:59:09,490
+closure اللي بيسوي ال H يعني ال closure لل V بيسوي
+
+752
+00:59:09,490 --> 00:59:14,430
+ال H، من هيك بيسميه، إذا أكيد اللي هو ال V closure
+
+753
+00:59:14,430 --> 00:59:17,850
+هو ال H، لو أخدنا X في ال V closure، يعني X في ال
+
+754
+00:59:17,850 --> 00:59:21,130
+H، ماشي؟ أخدت X arbitrary element in H
+
+755
+00:59:23,950 --> 00:59:27,350
+الان X في الـ V يصار في الـ V closure مادام في الـ
+
+756
+00:59:27,350 --> 00:59:30,450
+V closure من تعريف الـ V closure إذا بقدر ألاقي
+
+757
+00:59:30,450 --> 00:59:34,390
+sequence XN of elements in mean in V such that XN
+
+758
+00:59:34,390 --> 00:59:40,450
+بيروح لمين؟ لل Xلكن أنا الآن هذي ال X طبعا هي اللي
+
+759
+00:59:40,450 --> 00:59:43,510
+في ال amygdala أسف أنا ال X هي نفس اللي في ال
+
+760
+00:59:43,510 --> 00:59:46,830
+amygdala ماشي اللي في ال amygdala أكيد و موجودة في
+
+761
+00:59:46,830 --> 00:59:50,790
+ال H الامور تجون أناسي في ال H اللي هي أكيد و
+
+762
+00:59:50,790 --> 00:59:54,760
+موجودة في ال VHفاهمين أه؟ يعني XX أخدتها في الـM
+
+763
+00:59:54,760 --> 00:59:58,180
+Orthogonal ومن ثم قلتلكم أكيد X هتكون في الـV
+
+764
+00:59:58,180 --> 01:00:02,260
+closure اللي هي في الـH إذا X نفسها بقدر أجيلها
+
+765
+01:00:02,260 --> 01:00:06,660
+Sequence Xn في الـV حيث Xn بتروح لمين؟ للـX لأن
+
+766
+01:00:06,660 --> 01:00:09,260
+since X element الـM closure then for all M
+
+767
+01:00:09,260 --> 01:00:12,460
+element الـM هيكون الـX و الـM إيش بتساوي؟ سفر
+
+768
+01:00:12,460 --> 01:00:17,300
+مدام الـX و الـM بتساوي سفر أكيد هذا بيعطيني الـX
+
+769
+01:00:17,300 --> 01:00:21,740
+و الـV برضه إيش هيساوي سفر؟ لكل V والموجودة في
+
+770
+01:00:21,740 --> 01:00:31,760
+الـVأسهل هذه عارفين ليش؟ فإنه عندي ال Vمزامة في
+
+771
+01:00:31,760 --> 01:00:40,580
+الـ V يعني الإسبان للـ N كيف شكلها؟ V بساوي Alpha
+
+772
+01:00:40,580 --> 01:00:48,140
+1 X 1 زائد Alpha N في X من الـ N مش V في الإسبان
+
+773
+01:00:48,140 --> 01:00:52,280
+كيف يكون V في الإسبان؟ عبارة عن Linear Combination
+
+774
+01:00:52,280 --> 01:00:54,780
+من الإنسبان في الـ N finite number of Linear
+
+775
+01:00:54,780 --> 01:01:00,210
+Combinations إذا بيصير عند الـ Nالـ X و الـ V
+
+776
+01:01:00,210 --> 01:01:06,770
+بيساوي لإن أنا قلتلك تبحكي عن الـ X و Alpha 1 X 1
+
+777
+01:01:06,770 --> 01:01:13,570
+زائد Alpha N X N صح ولا لأ؟ و يساوي Alpha 1 في X و
+
+778
+01:01:13,570 --> 01:01:19,830
+X 1 زائد لما أصل الأخر واحدة Alpha N في X و X N و
+
+779
+01:01:19,830 --> 01:01:22,810
+الآن الـ X 1 و الـ X 2 و الـ X N One هى الموجودات
+
+780
+01:01:22,810 --> 01:01:29,690
+كلها من الأمام مظبوط؟الـ V في الـ Span يعني V
+
+781
+01:01:29,690 --> 01:01:32,870
+Linear Combination من عناصر الـ M يعني الـ X1 و X2
+
+782
+01:01:32,870 --> 01:01:36,750
+و XN كلها من وين جوا من الـ M و أنا عمالي بقول X
+
+783
+01:01:36,750 --> 01:01:39,230
+وين موجودة في الـ M Orthogonal فما انها موجودة في
+
+784
+01:01:39,230 --> 01:01:41,790
+الـ M Orthogonal إذا الـ X و أي element في الـ M
+
+785
+01:01:41,790 --> 01:01:51,820
+صفر إذا هذا حيث سوى صفروهذا صحيح صحيح صحيح صحيح
+
+786
+01:01:51,820 --> 01:02:04,680
+صحيح صحيح صحيح صحيح صحيح
+
+787
+01:02:09,190 --> 01:02:12,770
+طيب ما احنا قلنا الـ xn من وين جاية sequence of
+
+788
+01:02:12,770 --> 01:02:16,830
+limits من مين في الـ V إذا ال inner product بين ال
+
+789
+01:02:16,830 --> 01:02:23,070
+X و ال Xn حيث أو Zero لكل N لإن هدولة من وين جاية
+
+790
+01:02:23,070 --> 01:02:26,710
+من مين الان by the continuity of inner product
+
+791
+01:02:26,710 --> 01:02:31,270
+بندخل ال limit على هذه ماشي الحال عند ال X و ال Xn
+
+792
+01:02:31,270 --> 01:02:37,210
+بتروح لمين لل X و ال X من هنا لكن هدولة كلها أسفار
+
+793
+01:02:38,010 --> 01:02:42,150
+إذا ال limit هنا صفر إذا هذه هتكون إيش؟ صفر إذا ال
+
+794
+01:02:42,150 --> 01:02:46,070
+X وال X هتساوي صفر ومنها ال X بتساوي صفر ومن ثم ال
+
+795
+01:02:46,070 --> 01:02:48,710
+X اللي بدأنا فيها في ال M Orthogonal طلعت Zero إذا
+
+796
+01:02:48,710 --> 01:02:52,090
+ال M Orthogonal بتساوي صفر نيجي لآخر نقطة
+
+797
+01:02:52,090 --> 01:02:56,250
+conversely suppose that أن ال M Orthogonal بتساوي
+
+798
+01:02:56,250 --> 01:03:02,390
+Zero element بس ماشي بس فيها Zeroالان ال M subset
+
+799
+01:03:02,390 --> 01:03:07,830
+من ال V closure أكيد لأن ال V حبارة عن من؟ عن
+
+800
+01:03:07,830 --> 01:03:11,730
+الإسبان و ال M subset من .. اللي هي من؟ اللي هو
+
+801
+01:03:11,730 --> 01:03:17,330
+الإسبان إذا الان بما أن M subset من V closure إذا
+
+802
+01:03:17,330 --> 01:03:20,090
+ال V closure orthogonal subset من مين؟ من ال M
+
+803
+01:03:20,090 --> 01:03:23,530
+orthogonal يعني لو كانت عندي على جهة هذه ال A
+
+804
+01:03:23,530 --> 01:03:28,920
+subset من ال Bهيعطينا الـ B Orthogonal subset من
+
+805
+01:03:28,920 --> 01:03:31,500
+مين؟ من ايه ال Orthogonal؟ ال Orthogonal ده سهل
+
+806
+01:03:31,500 --> 01:03:36,920
+خدوا .. عشان .. هذه تؤدي لهذه خدوا X هنا X في ال
+
+807
+01:03:36,920 --> 01:03:41,700
+.. او B خلينا ناخد X في مين في الـ B Orthogonal
+
+808
+01:03:41,700 --> 01:03:47,020
+إيش معناته هذا؟ هذا بيعطينا ال X والـ B بساوة 0
+
+809
+01:03:47,020 --> 01:03:52,140
+لكل بيوة موجودة في الـ Bطيب مدام ال inner product
+
+810
+01:03:52,140 --> 01:03:55,920
+بين X و ال B موجودة بساوي 0 لكل B في ال A إذا أكيد
+
+811
+01:03:55,920 --> 01:04:01,000
+في الجزئية منها بيكون صحيح إذا هذا بيعطينا X و B
+
+812
+01:04:01,000 --> 01:04:07,160
+بساوي 0 لكل B والموجودة في الآية لأنه إذا بنفعلها
+
+813
+01:04:07,160 --> 01:04:10,400
+كل اللي هي أنا أكيد بنفعلها الجزء منهم وهذا إيش
+
+814
+01:04:10,400 --> 01:04:14,820
+معناته؟ هذا معناته إن X element in A Orthogonal
+
+815
+01:04:21,300 --> 01:04:28,580
+بما أنه زي ما قلنام جزئية من الـV closure إذا
+
+816
+01:04:28,580 --> 01:04:31,940
+الـorthogonal لهذه جزئية من الـorthogonal لهذه إذا
+
+817
+01:04:31,940 --> 01:04:34,760
+صارت ال .. اللي هي V closure orthogonal subset من
+
+818
+01:04:34,760 --> 01:04:38,220
+M orthogonal اللي هي إيش بتساوي؟ سفر إذا صارت الـV
+
+819
+01:04:38,220 --> 01:04:41,840
+closure orthogonal بتساوي Zero إذا by theorem
+
+820
+01:04:41,840 --> 01:04:45,940
+تلاتة تلاتة أربعة إحنا عارفين إن الـH إيش بتساوي؟
+
+821
+01:04:45,940 --> 01:04:48,480
+V closure ليش أخدت الـV closure عشان أضمنها
+
+822
+01:04:48,480 --> 01:04:54,160
+closed؟V closure زائد V closure orthogonal هذه سفر
+
+823
+01:04:54,160 --> 01:04:58,020
+إذا V closure زائد ال zero element هتطلع مين ال V
+
+824
+01:04:58,020 --> 01:05:01,640
+closure إذا H هتطلع ايش بتساوي V closure يعني صارت
+
+825
+01:05:01,640 --> 01:05:06,840
+ال V نفسها dense in H وبارك الله فيكم وإلى لقاء
+
+826
+01:05:06,840 --> 01:05:07,300
+آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yv5MMmcmY8k_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yv5MMmcmY8k_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ec717e4add381a041fa543b5732aee7c0db791e9
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/yv5MMmcmY8k_postprocess.srt
@@ -0,0 +1,2040 @@
+1
+00:00:05,230 --> 00:00:08,170
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:08,170 --> 00:00:10,790
+والصلاة والسلام على سيد المرسلين سيدنا محمد وعلى
+
+3
+00:00:10,790 --> 00:00:16,990
+أهله وصحبه أجمعين هذه المحاضرة رقم 31 مساق تحليل
+
+4
+00:00:16,990 --> 00:00:19,630
+اقتراني أو تحليل جالي لطلاب وطالبات الجامعة
+
+5
+00:00:19,630 --> 00:00:24,950
+الإسلامية قسم الرياضيات ال magisteriumالان وصلنا
+
+6
+00:00:24,950 --> 00:00:29,890
+لعند اللي هي اربعة سبعة وهي تحت عنوان category
+
+7
+00:00:29,890 --> 00:00:32,930
+theorem and uniform boundedness theorem وهذه
+
+8
+00:00:32,930 --> 00:00:35,610
+النظرية الأساسية الثانية بعد ال handball theorem
+
+9
+00:00:35,610 --> 00:00:40,090
+اللي هي التحليل
+
+10
+00:00:40,090 --> 00:00:46,700
+الداليعشان نصلها بدنا نبرهن الـ Rare Category
+
+11
+00:00:46,700 --> 00:00:51,580
+Theorem وبدنا نعرف بعض التعريفات اللي هي طبولوجية
+
+12
+00:00:51,580 --> 00:00:57,360
+ومن ثم نصلها اللي هي نظريتنا a subset M of a
+
+13
+00:00:57,360 --> 00:01:01,960
+metric space X is said to be واحدة بلان بنسمي الـ
+
+14
+00:01:01,960 --> 00:01:08,030
+M مجموعة جزية من X انها rareor nowhere dense rare
+
+15
+00:01:08,030 --> 00:01:12,250
+أو nowhere dense if الـ M closure إليها has no
+
+16
+00:01:12,250 --> 00:01:16,490
+interior point يعني بمعنى آخر إنه الـ M closure
+
+17
+00:01:16,490 --> 00:01:23,970
+interior بتساوي 5 فهذه الحملة بنسمي الـ M is rare
+
+18
+00:01:23,970 --> 00:01:32,920
+is rare أو nowhere dense طيب الآن بنسمي اللي هوالـ
+
+19
+00:01:32,920 --> 00:01:41,320
+M is major أو of first category in X if M is the
+
+20
+00:01:41,320 --> 00:01:46,180
+union of countably many sets each of which is rare
+
+21
+00:01:46,180 --> 00:01:57,410
+يعني بنسمي ال هوالان ال subset M is major
+
+22
+00:01:57,410 --> 00:02:02,050
+in X إذا كنا نكتب ال M as a union أو countable
+
+23
+00:02:02,050 --> 00:02:06,910
+union of A I مثلا I من عند واحد لعنده اللي هو
+
+24
+00:02:06,910 --> 00:02:11,510
+معناه نهاية countable unionEach of which كل واحدة
+
+25
+00:02:11,510 --> 00:02:15,310
+من هدولة ايش ما لها is rare يعني ايش ما لها كل
+
+26
+00:02:15,310 --> 00:02:18,670
+واحدة من هدول اللي هو ال closure لها interior
+
+27
+00:02:18,670 --> 00:02:22,910
+بيساوي ايش بيساوفها يعني contains no open balls
+
+28
+00:02:23,490 --> 00:02:29,050
+يعني هذه معناته أن الـ M closure contains no open
+
+29
+00:02:29,050 --> 00:02:31,310
+balls لأن لو اختوت open balls معناته الـ M
+
+30
+00:02:31,310 --> 00:02:35,010
+interior يشملها ال closure اللي ال interior بسويش
+
+31
+00:02:35,010 --> 00:02:39,490
+في عجبه طيب إلى ال non-major or of the second
+
+32
+00:02:39,490 --> 00:02:44,070
+category هذه of first category non-major or of the
+
+33
+00:02:44,070 --> 00:02:49,170
+second category in X إذا كانت مش majorأو مش First
+
+34
+00:02:49,170 --> 00:02:52,870
+Category إذا ال Second Category ما هي إلا نفن مين
+
+35
+00:02:52,870 --> 00:02:57,330
+لل First Category حلو تقلت Free Definitions بس حيث
+
+36
+00:02:57,330 --> 00:03:03,460
+يلزمنك أدوات للوصول للي بدناها اطلع لفوقالعنوان
+
+37
+00:03:03,460 --> 00:03:07,220
+الـ Pair Category Theorem ماش بتقول إذا metric
+
+38
+00:03:07,220 --> 00:03:10,820
+space X لات سوى Y is complete إذا ال metric space
+
+39
+00:03:10,820 --> 00:03:15,340
+is complete إذا كان ال metric space X is complete
+
+40
+00:03:15,340 --> 00:03:22,040
+then it is non-major in itself يعني هيكون ال X ال
+
+41
+00:03:22,040 --> 00:03:28,590
+complete space مش major في itselfهنس اوتوماتيك إذا
+
+42
+00:03:28,590 --> 00:03:32,510
+كانت اللي هو a non major in itself if x لتسوى فيه
+
+43
+00:03:32,510 --> 00:03:36,870
+is complete and x بيسوى لينو لل a k و a k is a
+
+44
+00:03:36,870 --> 00:03:41,070
+closed for all k then at least one a k contains a
+
+45
+00:03:41,070 --> 00:03:44,690
+non implicit subset اللي هو الجزء التاني هذا سهل
+
+46
+00:03:44,690 --> 00:03:49,250
+الآن بنقول الآن إذا كانت ال x لتسوى فيه complete
+
+47
+00:03:52,020 --> 00:03:56,240
+ماشي إذا إيه إيش ما هي اللي هتقول non-major مدام
+
+48
+00:03:56,240 --> 00:04:00,900
+non-major إذا اللي هي can't be written as a
+
+49
+00:04:00,900 --> 00:04:05,300
+countable union of rare sets يعني في على الأقل
+
+50
+00:04:05,300 --> 00:04:09,480
+واحدة من هدولة مش rare إيش يعني؟ يعني لو كان عندي
+
+51
+00:04:09,480 --> 00:04:12,840
+يعني خلّيني أقول لو كان عندي ال union للـAK X
+
+52
+00:04:12,840 --> 00:04:15,720
+بيساوي ال union لـAK K من واحد لإنفينيتي وكل واحدة
+
+53
+00:04:15,720 --> 00:04:20,110
+فيه closedإذا أكيد هذا مش rare واحدة من هنا على
+
+54
+00:04:20,110 --> 00:04:22,710
+الأقل مش rare إيش معناته واحدة من هنا مش rare يعني
+
+55
+00:04:22,710 --> 00:04:27,530
+الـ AK closure إلها interior بسويش في يعني بمعنى
+
+56
+00:04:27,530 --> 00:04:32,210
+ال AK closure interior واحدة من هنا على الأقل لا
+
+57
+00:04:32,210 --> 00:04:38,230
+تسويش في بمعنى إنه AK interior لا يساوي في لإنه
+
+58
+00:04:38,230 --> 00:04:41,670
+closed إحنا بنحكي عنه closed يعني بمعنى أخر إنه ال
+
+59
+00:04:41,670 --> 00:04:50,130
+AK contains open set فيهابس هذا اللي هو الجزء هذا
+
+60
+00:04:50,130 --> 00:04:55,030
+لو برهنا اللي فوق هذا الجزء هذا لو برهنا اللي فوق
+
+61
+00:04:55,030 --> 00:05:00,990
+اذا انطلنا برهين مين اللي فوقالان سببوز that the
+
+62
+00:05:00,990 --> 00:05:04,250
+complete metric space X لاتساوه فيه is not major
+
+63
+00:05:04,250 --> 00:05:08,310
+is major اصل الان طولوا رحكم عليها بنفرض انه ايش
+
+64
+00:05:08,310 --> 00:05:13,270
+معنى العكس ان X لاتساوه فيه is major in itself ايش
+
+65
+00:05:13,270 --> 00:05:19,230
+معنى major then X بتساوه ال union خليني عشان نكتب
+
+66
+00:05:19,230 --> 00:05:24,410
+هنا نرخص ما بنحصل عليه عشان نشوف كيف بنحصل على ال
+
+67
+00:05:24,410 --> 00:05:28,250
+contradiction الان
+
+68
+00:05:29,160 --> 00:05:32,860
+ثم X بيساوي ال union لـMK كام من واحد إلى مناهية
+
+69
+00:05:32,860 --> 00:05:36,740
+with each MK إزاي إيش؟ إيش rare؟ حيكون كل واحدة من
+
+70
+00:05:36,740 --> 00:05:41,960
+هنا إشمالها rare in X إذا بمعنى آخر الان M closure
+
+71
+00:05:41,960 --> 00:05:49,320
+واحد interior إشماله بيساوي 5 الآن واحدة واحدة
+
+72
+00:05:49,320 --> 00:05:53,900
+that means ان M1 closure does not contain a non
+
+73
+00:05:53,900 --> 00:05:59,690
+-empty open sets مافيش فيها non-empty open setsBut
+
+74
+00:05:59,690 --> 00:06:04,630
+X does But X إيش؟ Does إذا X نفسها نحنا open set
+
+75
+00:06:04,630 --> 00:06:09,350
+إذا بتحتوي في داخلها عليا شمالها على open sets for
+
+76
+00:06:09,350 --> 00:06:14,410
+example X itself وممكن غيرها So that أم واحد
+
+77
+00:06:14,410 --> 00:06:19,980
+closure مش هي ال X أكيد أكيدلأن هذي rare وهذه مش
+
+78
+00:06:19,980 --> 00:06:24,580
+rare hence اللي هو ال complement لل M1 closure
+
+79
+00:06:24,580 --> 00:06:29,280
+اللي بيساوي X minus M1 closure فيها نقاط لا تساوي
+
+80
+00:06:29,280 --> 00:06:35,450
+5 في نفس الوقت openماشي هذه closed مكملتها open
+
+81
+00:06:35,450 --> 00:06:39,090
+ماشي الحل إذا هذه open و let's say if I is an
+
+82
+00:06:39,090 --> 00:06:44,830
+empty and open set so we can choose B إيش مالها
+
+83
+00:06:44,830 --> 00:06:49,970
+إذا بنقدر نلاقي بي واحد element ال complement للأم
+
+84
+00:06:49,970 --> 00:06:56,450
+واحد closer ماشي نقدر نقدر نلاقي بي واحد ماشيand
+
+85
+00:06:56,450 --> 00:07:00,490
+an open ball about it و open ball كمان بيقدر نجي
+
+86
+00:07:00,490 --> 00:07:07,190
+about it خلّينا نسمي بي واحد بساوة بي of بي واحد و
+
+87
+00:07:07,190 --> 00:07:11,150
+إبسلون واحد هذه ال open ball اللي وجناها حوالين ال
+
+88
+00:07:11,150 --> 00:07:16,330
+بي واحد و جواها كده دي مظبوط؟ فاهمين عليها؟ اللي
+
+89
+00:07:16,330 --> 00:07:24,470
+هي subset مي ال knot M واحد closure و أنا بقدر
+
+90
+00:07:24,470 --> 00:07:28,170
+أزغيرها زي ما بديو بقدر أخد الـ Y الواحد أشمالها
+
+91
+00:07:28,170 --> 00:07:36,730
+أصغر من مين؟ من النص واضح هاه؟ طيب الان since M2
+
+92
+00:07:36,730 --> 00:07:40,590
+is not wordens ما هي زيها M2 is not wordens، rare
+
+93
+00:07:40,590 --> 00:07:46,110
+يعني إذا أكيد الـ M2 closure does not contain a
+
+94
+00:07:46,110 --> 00:07:50,530
+non-empty open set تطلع على فوق برضه الـ M2
+
+95
+00:07:50,530 --> 00:07:54,870
+closure مابتحتويش open set إذا مش هتحتوي هذه
+
+96
+00:08:01,950 --> 00:08:06,570
+الـ M2 is nowhere dense يعني غير موجود يعني بمعنى
+
+97
+00:08:06,570 --> 00:08:10,930
+اخر M2 closure interior بساوي فاي معناته M2
+
+98
+00:08:10,930 --> 00:08:15,510
+closure does not contain any open any non M2 open
+
+99
+00:08:15,510 --> 00:08:23,010
+setبالتالي P of P واحد و نص Y واحد ليس مجموعة من
+
+100
+00:08:23,010 --> 00:08:25,010
+ميان M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان
+
+101
+00:08:25,010 --> 00:08:26,530
+M2 مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2
+
+102
+00:08:26,530 --> 00:08:30,210
+مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2
+
+103
+00:08:30,210 --> 00:08:32,910
+مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2
+
+104
+00:08:32,910 --> 00:08:33,350
+مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2
+
+105
+00:08:33,350 --> 00:08:35,030
+مجموعة ميان M2 مجموعة ميان M2 مجموعة ميان M2
+
+106
+00:08:35,030 --> 00:08:41,630
+مجموعة ميان M2
+
+107
+00:08:41,630 --> 00:08:45,770
+مجموعةSo we can choose B2 من مين من التقاطع إذا
+
+108
+00:08:45,770 --> 00:08:50,730
+بقدر ألاقي B2 من الموجودة B2 element in M2 closure
+
+109
+00:08:50,730 --> 00:08:57,850
+complement تقاطع اللي هو B of B1 و نص إبسلون واحد
+
+110
+00:08:57,850 --> 00:09:06,610
+طيب and an open ball about it أكيد مدام هدولة open
+
+111
+00:09:07,460 --> 00:09:10,940
+و بي اتنين فيهم إذا بقدر لاجي open ball حوالين هذه
+
+112
+00:09:10,940 --> 00:09:17,620
+جوات هذه إذا سميها بي اتنين بي بي اتنين و ابسلون
+
+113
+00:09:17,620 --> 00:09:20,940
+اتنين subset من مين من M اتنين ال closure ال
+
+114
+00:09:20,940 --> 00:09:24,800
+complement لها تقاطع بي واحد بي بي واحد و نص
+
+115
+00:09:24,800 --> 00:09:28,900
+ابسلون و اختار للأبسلون اتنين أصغر من مين من نص
+
+116
+00:09:28,900 --> 00:09:31,900
+ابسلون واحد طبعا نص ابسلون واحد ربع ابسلون واحد
+
+117
+00:09:31,900 --> 00:09:36,010
+عشان بيداخل حاجة convergence بسالأن by induction
+
+118
+00:09:36,010 --> 00:09:40,430
+بقدر أكملها لأن احنا بنعرف الام واحد و الام اتنين
+
+119
+00:09:40,430 --> 00:09:44,290
+و الام تلاتة كلهن where و كلهن اللي سوناه على الام
+
+120
+00:09:44,290 --> 00:09:47,670
+واحد و الام اتنين بقدر أسويه على الباقية اذا by
+
+121
+00:09:47,670 --> 00:09:54,230
+induction we obtain a sequence of ballsبك بساوة بك
+
+122
+00:09:54,230 --> 00:09:58,410
+إبسلون كه والإبسلون كه أخدتها أول واحد أصغر من
+
+123
+00:09:58,410 --> 00:10:01,550
+إبسلون والتاني أصغر من نصها والتالت أصغر من نصها
+
+124
+00:10:01,550 --> 00:10:04,970
+ورابع اذا أكيد حاجة حصل على إبسلون كه أصغر من مين
+
+125
+00:10:04,970 --> 00:10:10,150
+من اتنين أس minus كه وبحيث انه كل مرة باخد ال بك
+
+126
+00:10:10,150 --> 00:10:15,190
+زاد واحد جزئية من مين من اللي هي اللي جابلها بك نص
+
+127
+00:10:15,190 --> 00:10:20,100
+إبسلون كه وهذه جزئية من مين اللي سميتها بكالأن و
+
+128
+00:10:20,100 --> 00:10:25,520
+Epsilon K أصغر من مين؟ من 2 to the minus K إذا
+
+129
+00:10:25,520 --> 00:10:29,960
+بيصير عنده الآن المسافة بين أي بي ك و بي ك زائد
+
+130
+00:10:29,960 --> 00:10:37,260
+واحد اللي هو بيكون أصغر من اللي هو كل مرة أصغر من
+
+131
+00:10:37,260 --> 00:10:39,700
+اللي هي ال Epsilon تبعته أصغر من ال Epsilon تبعته
+
+132
+00:10:39,700 --> 00:10:44,120
+إذا كل واحدة من هذول أصغر من 2 to the minus Kالان
+
+133
+00:10:44,120 --> 00:10:47,720
+بين bk و bk زد واحد أصغر من two تقريبا minus k ال
+
+134
+00:10:47,720 --> 00:10:50,480
+summation اللي من k من واحد إلى نهاية أصغر شهو مين
+
+135
+00:10:50,480 --> 00:10:53,920
+ال summation من سفر إلى مين إلى مانا نهاية صار
+
+136
+00:10:53,920 --> 00:10:57,560
+عندي أنا sequence من ال bees بي واحد و بي اتنين و
+
+137
+00:10:57,560 --> 00:11:02,600
+بي تلاتة و بي أربعة إلى أخره كل مرة اللي هو بديب
+
+138
+00:11:02,600 --> 00:11:05,480
+أكتر و بيصير كله موجودات في آخر واحدة موجودة فيهم
+
+139
+00:11:05,920 --> 00:11:10,200
+الأنفة بيصير ND اللي هو المسافات بينهم مجموح كل
+
+140
+00:11:10,200 --> 00:11:14,640
+واحدة أصغر من 2 إلى الأولى بين B1 وB2 أصغر من 2
+
+141
+00:11:14,640 --> 00:11:20,460
+إلى minus 1 بين B2 وB3 من 2 إلى minus 2 بين B4 وB5
+
+142
+00:11:20,460 --> 00:11:24,340
+إلى أخره إذا صماش اللي هنا أصغر من الصماش الى 2
+
+143
+00:11:24,340 --> 00:11:27,930
+إلى minus Kالأن هذا convergence إذا قطعا هذا
+
+144
+00:11:27,930 --> 00:11:32,310
+إشماله convergence صار إذا عندي sequence of
+
+145
+00:11:32,310 --> 00:11:36,150
+elements BK كوشي sequence in the complete metric
+
+146
+00:11:36,150 --> 00:11:40,760
+space Xوالـ Cauchy Sequence أكيد هتكون إيه اشمالها
+
+147
+00:11:40,760 --> 00:11:45,820
+So it converts C limit BK إيش بيساوي B element in
+
+148
+00:11:45,820 --> 00:11:50,280
+X يعني الآن الـ Sequence هذه صارت Cauchy Sequence
+
+149
+00:11:50,280 --> 00:11:54,280
+في الـ
+
+150
+00:11:54,280 --> 00:11:58,420
+Complete Space X إذا أكيد هذه هتكون converts BK to
+
+151
+00:11:58,420 --> 00:12:03,220
+some element سميه مين؟ سميه B والـ B هتكون وموجودة
+
+152
+00:12:03,220 --> 00:12:09,280
+في الـ X تشوف الآنإذاً بي وان موجود في ال X الآن
+
+153
+00:12:09,280 --> 00:12:15,540
+اطلع لفوق بدي أوصل لك لإن بي مش في ال X اه ويصير
+
+154
+00:12:15,540 --> 00:12:20,940
+Contradiction شوف كده Also for all M and all M
+
+155
+00:12:20,940 --> 00:12:28,780
+أكبر من M we have ال بي and الأمات الصغيرةالـ Bm
+
+156
+00:12:28,780 --> 00:12:32,360
+كل ما كبرت الـ M أشمالها بتصغر الـ B الـ ball مش
+
+157
+00:12:32,360 --> 00:12:35,900
+أنا كل مرة بزغر ال ball فبتصير الـ Bm subset من ال
+
+158
+00:12:35,900 --> 00:12:40,520
+ball اللي بعدها اللي نقطتها مركزها بيبقى BM و نص
+
+159
+00:12:40,520 --> 00:12:47,380
+قطرها نص في EM إذا صارت المسافة بين BM و B أصغر أو
+
+160
+00:12:47,380 --> 00:12:56,900
+يساويBM و BN و BM و B و المسافة بين BM و BN أصغر
+
+161
+00:12:56,900 --> 00:12:59,620
+من مين من نفس N لأن هذه جزئية من مين من التانية
+
+162
+00:12:59,620 --> 00:13:03,280
+اللي هنا فادي فبصير عنده اللي هو المسافة أصغر من
+
+163
+00:13:03,280 --> 00:13:08,050
+مين من أكيد من الصغيرة من الكبيرةمش الـ N هذه BM
+
+164
+00:13:08,050 --> 00:13:13,390
+BM موجودة هنا و BM أصلا موجودة هنا لذا صارت ال BM
+
+165
+00:13:13,390 --> 00:13:17,330
+و ال BM فاد على الأقل ماشي و المسافة بين أي نقطين
+
+166
+00:13:17,330 --> 00:13:21,210
+فيه أصغر من مين من نص EM لذا صار عندي هذه المسافة
+
+167
+00:13:21,210 --> 00:13:27,890
+أصغر من نص EM و هذه زائد D BN OB لأن هذه صارتأصغر
+
+168
+00:13:27,890 --> 00:13:31,090
+أو يساوي هذا المقدار و أنا ماخد ال M أكبر من M
+
+169
+00:13:31,090 --> 00:13:34,130
+بطير ال M إلى ما لنهايه زي ما بده و ال M بتلغى
+
+170
+00:13:34,130 --> 00:13:38,130
+بيعدى زي ما هي إذا as M goes to infinity اللي هم
+
+171
+00:13:38,130 --> 00:13:44,650
+بيصير عندي المسافة بين ال B M و ال B هذي بتروح
+
+172
+00:13:44,650 --> 00:13:49,190
+للصفرلأن as n goes to infinity بيشهر بجد سير بسير
+
+173
+00:13:49,190 --> 00:13:54,170
+فيه بيه هاد ال bm و ال b بتروح لمين للصفر فاهمين
+
+174
+00:13:54,170 --> 00:13:58,130
+اللي بحكيه؟ الان هاد بتظل عند as n goes to
+
+175
+00:13:58,130 --> 00:14:01,690
+infinity ال distance بين ال bm و ال b أصغر من نص
+
+176
+00:14:01,690 --> 00:14:05,570
+ال EM لأن هاد راح لمين للصفر الان هذا إيش معناته
+
+177
+00:14:05,570 --> 00:14:09,570
+أن المسافة بين ال bm و ال b أصغر من نص ال EM؟
+
+178
+00:14:09,910 --> 00:14:14,790
+معناته أن الـ B موجودة في الـ BM لأن المسافة بين
+
+179
+00:14:14,790 --> 00:14:19,030
+الـ BM و الـ B أصغر من نص EM هذه المركز وهذا نص
+
+180
+00:14:19,030 --> 00:14:22,850
+القطر إذن في الـ Bolt بيتهم إذا صارت الـ B موجودة
+
+181
+00:14:22,850 --> 00:14:28,810
+في الـ BM for all M إذا وعندي الـ BM جزئية من مين؟
+
+182
+00:14:28,810 --> 00:14:32,350
+من الـ complement في التركيبة كنت أخد الـ BM جزئية
+
+183
+00:14:32,350 --> 00:14:38,300
+من مين؟هي rare جزء من هذه then B is not element in
+
+184
+00:14:38,300 --> 00:14:44,640
+main in اللي هو جزئية من وين من مكملتها إذا أكيد
+
+185
+00:14:44,640 --> 00:14:47,420
+مش موجودة في الام أم إذا مش موجودة في الام أم
+
+186
+00:14:47,420 --> 00:14:53,370
+مكلوجرإذا مش موجودة في الـMM إذا صارت عندي الـB مش
+
+187
+00:14:53,370 --> 00:14:57,250
+موجودة فيها طب ما هي مدام مش موجودة فيهن كلهن إذا
+
+188
+00:14:57,250 --> 00:15:00,650
+مش موجودة في ال union و ال union هو ال X إذا صارت
+
+189
+00:15:00,650 --> 00:15:04,930
+ال B مش موجودة في من؟ في ال X و هذا معناته صار في
+
+190
+00:15:04,930 --> 00:15:08,330
+عندي contradiction لأن ال B من ال X إذا نفس ال X
+
+191
+00:15:08,330 --> 00:15:11,810
+هتصير إذا ما الفرضية الأولى اللي فرضناها مش صحيحة
+
+192
+00:15:11,810 --> 00:15:14,270
+إذا ال X must be non major
+
+193
+00:15:19,430 --> 00:15:24,550
+يلا لبعدها الـ Uniform Boundedness Theorem هي
+
+194
+00:15:24,550 --> 00:15:27,850
+النظرية اللي بنحكي عنها الأساسية التانية و ألطف
+
+195
+00:15:27,850 --> 00:15:35,790
+برهانها من الأولى خلّينا نشوف أيش اللي بتقوله اللي
+
+196
+00:15:35,790 --> 00:15:42,370
+بتقوله النظرية انه Uniform Boundedness Theorem
+
+197
+00:15:42,370 --> 00:15:47,670
+نشوف كيف let TN be a sequence of bounded linear
+
+198
+00:15:47,670 --> 00:15:52,530
+operatorsTN هي Sequence of Bounded Linear
+
+199
+00:15:52,530 --> 00:16:01,470
+Operators من بنخ X إلى بنخ Y من بنخ X إلى بنخ Y
+
+200
+00:16:04,690 --> 00:16:10,030
+Such that norm of TN is bounded for every X
+
+201
+00:16:10,030 --> 00:16:10,750
+element in X
+
+202
+00:16:23,660 --> 00:16:29,020
+اللي هي لكل X فيه الـ H ياش اللي هي بتجيلها ثابت
+
+203
+00:16:29,020 --> 00:16:33,660
+يعملها bound ثابت يعملها bound يعني بمعنى أخر TNX1
+
+204
+00:16:33,660 --> 00:16:40,080
+بتجيلها CX1 TNX2 بتجيلها CX2 TNX3 بتجيلها CX3 ماشي
+
+205
+00:16:40,080 --> 00:16:44,020
+الحال هذا اللي هو ياش ماله المُعطَى بيقول لو كانت
+
+206
+00:16:44,020 --> 00:16:48,080
+ال sequence هذه تتمتع بالخاصية هذه بيقول لك الآن
+
+207
+00:16:48,770 --> 00:16:53,750
+بما انه هذه sequence of bounded اللي هي بالشكل هذا
+
+208
+00:16:53,750 --> 00:16:58,650
+وكانت من بنخ space ل Y اللي هو normed space انا
+
+209
+00:16:58,650 --> 00:17:03,230
+بضمنك ..الان قوة النظرية بقولك انا بضمنك ان ال
+
+210
+00:17:03,230 --> 00:17:06,070
+sequence هذا يكون ال boundedness uniform يعني لا
+
+211
+00:17:06,070 --> 00:17:09,190
+يعتمد على مين؟ على ال X عشان هي اسمها uniform
+
+212
+00:17:09,190 --> 00:17:12,280
+boundedness theoremuniform boundedness هذا يعني
+
+213
+00:17:12,280 --> 00:17:15,660
+بمعنى أخر بقدر ألاقي C بتنفع لكل شي يعني نورم ال
+
+214
+00:17:15,660 --> 00:17:20,900
+TN أصغر أو ساوي C لكل اللي هي ال Xات بغض النظر
+
+215
+00:17:20,900 --> 00:17:24,700
+يعني بل بقولك نورم ال TN نفسه أصغر أو ساوي مين؟
+
+216
+00:17:24,700 --> 00:17:29,480
+أصغر أو ساوي C لأنه لما نلاقي نورم ال TN X أصغر أو
+
+217
+00:17:29,480 --> 00:17:32,740
+ساوي C في نورم ال X خلاص على نورم ال X بطلع نورم
+
+218
+00:17:32,740 --> 00:17:38,280
+ال TN أصغر أو ساوي مين؟ some constant Cنأتي الآن
+
+219
+00:17:38,280 --> 00:17:48,640
+لنثبت هذا اللي هو اتنين اكيد
+
+220
+00:17:48,640 --> 00:17:51,720
+بستخدم الكتاب البركاتو كوريو تيريم و لا ليش اصلا
+
+221
+00:17:51,720 --> 00:17:59,880
+نثبتها and x is complete مظبوط؟ اه طيب for every k
+
+222
+00:17:59,880 --> 00:18:04,010
+element لانخلّيني أحضر بس سؤال برهان Let A K
+
+223
+00:18:04,010 --> 00:18:08,450
+subset من X أشهى A K be the set of all X such that
+
+224
+00:18:08,450 --> 00:18:12,750
+T N X أصغر شهو K for all N يعني بمعنى أخر خلّيني
+
+225
+00:18:12,750 --> 00:18:20,650
+أنفسر أكتر أنه لو أخدنا A 1 هي عبارة عن كل الإكسات
+
+226
+00:18:20,650 --> 00:18:29,730
+such that T 1 X أصغر أو آسف T N Xأصغر أو سوى واحد
+
+227
+00:18:29,730 --> 00:18:35,530
+لكل N element in R A2
+
+228
+00:18:35,530 --> 00:18:43,430
+بساوية اللي هو كل ال X such that TNX أصغر أو سوى
+
+229
+00:18:43,430 --> 00:18:50,090
+اتنين لكل N element in R AK in general هي عبارة عن
+
+230
+00:18:50,090 --> 00:18:55,470
+كل ال X such that TNXأصغر أو يساوي اللي هو الـ K
+
+231
+00:18:55,470 --> 00:19:04,910
+for every N element in N ماشي الحل ال
+
+232
+00:19:04,910 --> 00:19:08,790
+TNX اللي أصغر أو يساوي واحد أكيد هيكون إيه شماله
+
+233
+00:19:08,790 --> 00:19:13,270
+أصغر أو يساوي اتنين يعني اللي لو خدنا element 10
+
+234
+00:19:13,270 --> 00:19:19,810
+هلاجيه automatic element 10 صح؟فبصير عندى ال .. ال
+
+235
+00:19:19,810 --> 00:19:21,610
+.. ال .. لو أخدنا .. يعني عندنا بصير تانية الـ X
+
+236
+00:19:21,610 --> 00:19:24,130
+أصغر أصغر شويه واحد معناته أصغر شويه اتنين معناته
+
+237
+00:19:24,130 --> 00:19:28,030
+احد يعني ا واحد جزء من اتنين جزء من اتنين طيب
+
+238
+00:19:28,030 --> 00:19:34,430
+مظبوط الحاجة تقولها طيب شوفوا لان بس عشان أتعرف
+
+239
+00:19:34,430 --> 00:19:38,210
+عليها هنا to show that a k is closed ده انت بتقول
+
+240
+00:19:38,210 --> 00:19:40,590
+انه a k مثلا كل واحدة فيه نقش معناها closed set
+
+241
+00:19:40,590 --> 00:19:47,870
+خدوا X في مين في ال a closure اه a k closurethen
+
+242
+00:19:47,870 --> 00:19:51,890
+there exists a sequence xj بدأ اثبت لكم بلق ال
+
+243
+00:19:51,890 --> 00:19:54,410
+sequence xj في ال a كي ا convert the mean لل x
+
+244
+00:19:54,410 --> 00:19:59,030
+بيكون خلصنا صح؟ then there is a sequence xj of
+
+245
+00:19:59,030 --> 00:20:04,010
+elements لأ اسف لان اثبتت اللي هي ال x في ال a كي
+
+246
+00:20:04,010 --> 00:20:09,310
+اخدت في ال a كلوجة بدأ اثبتها في ال a فبصير مش هوا
+
+247
+00:20:09,310 --> 00:20:14,030
+مشاكلكم ما انتم معايا كي باثبت ان ال a كي is
+
+248
+00:20:14,030 --> 00:20:19,340
+closedالـ AK closure بيساوي الـ A كيف بيداخدها؟
+
+249
+00:20:19,340 --> 00:20:23,320
+بيداخد X في الـ AK closure و أثبتها أن X في 100 في
+
+250
+00:20:23,320 --> 00:20:28,040
+الـ AK لأن العكس صحيح دايما، اه، ماشي بخير، اذا
+
+251
+00:20:28,040 --> 00:20:34,450
+خلينا نشوف الآننشوف الآن خدوا x في الـ a k closure
+
+252
+00:20:34,450 --> 00:20:38,510
+إذا حسب تعريف الـ x في ال a k closure بقدر ألاقي
+
+253
+00:20:38,510 --> 00:20:42,530
+sequence xj of elements in a k such that limit الـ
+
+254
+00:20:42,530 --> 00:20:45,610
+xj أيش بساوي بساوي الـ x هذا تعريف الـ x والي
+
+255
+00:20:45,610 --> 00:20:49,470
+موجودة في ال a closure في ال a k closure then for
+
+256
+00:20:49,470 --> 00:20:56,570
+any fixed n we have norm Tn xj هذا الـ xj هذا الـ
+
+257
+00:20:56,570 --> 00:21:01,670
+xj أصغر أو يساوي مين أصغر يساوي kأه من تعريفها لأن
+
+258
+00:21:01,670 --> 00:21:04,990
+الـ X هو الموجودة في ال .. آسف في الـ XJ هو
+
+259
+00:21:04,990 --> 00:21:11,570
+الموجودة في الـ AK وعلاصر الـ AK إيه شمالها؟ XJ
+
+260
+00:21:11,570 --> 00:21:18,090
+فيها إذا TN XJ أظهر فيها OK ماشي الحال شوف شوية
+
+261
+00:21:18,090 --> 00:21:20,050
+علامة ماعرفش علاقة بال convergence إذا انتبهوا
+
+262
+00:21:20,050 --> 00:21:27,370
+الآن عندي الـ XJ هدولة من وين جاية؟ من الـ AK مدام
+
+263
+00:21:27,370 --> 00:21:33,660
+الـ XJفي الـ AK إذا انتحقق شروطها ايش شروطها ان
+
+264
+00:21:33,660 --> 00:21:39,760
+يكون TN هذي ال XJ أصغر يساوي مين؟ أصغر يساوي K صح؟
+
+265
+00:21:39,760 --> 00:21:44,700
+لكل N هذا الكلام طيب إذا صار عندي TN XJ أصغر يساوي
+
+266
+00:21:44,700 --> 00:21:48,880
+Kلأن by the continuity of TN كل واحدة ما هي
+
+267
+00:21:48,880 --> 00:21:52,720
+bounded linear bounded then continuous and the
+
+268
+00:21:52,720 --> 00:21:55,480
+continuity of norm ويهب يعني ما نقدر ندخل ال limit
+
+269
+00:21:55,480 --> 00:22:00,520
+وين؟ جوا norm و جوا mean ال TN فبصير عنده اللي هو
+
+270
+00:22:00,520 --> 00:22:05,100
+limit دخل جوا ودخل على ال TN ودخل جوا الآن فبصير
+
+271
+00:22:05,100 --> 00:22:09,200
+عنده TN limit XJ و limit XJ ايش بيساوي؟ بيصير X
+
+272
+00:22:09,200 --> 00:22:13,940
+إذا صار عنده norm TN X أصغر أو شوه مين؟ أصغر أو
+
+273
+00:22:13,940 --> 00:22:18,190
+شوه كامما معناته هذا؟ مدام الـ TN X أصغر أو يساوي
+
+274
+00:22:18,190 --> 00:22:23,050
+K هذا أحلها أن تكون دوا الـ A K إذا صار عند ال X
+
+275
+00:22:23,050 --> 00:22:29,030
+في الـ A K معناته صارت A K is closed لأنه
+
+276
+00:22:29,030 --> 00:22:33,430
+حسب الكلام اللي حكيته قبل شوية طيب اللي بعده for
+
+277
+00:22:33,430 --> 00:22:38,690
+every X element in X there exists CX such that
+
+278
+00:22:38,690 --> 00:22:43,830
+norm TN X أصغر أو يساوي CX for all N هذا مقطع مقطع
+
+279
+00:22:43,830 --> 00:22:49,720
+الـ Nهلقن then for each x element in x belongs to
+
+280
+00:22:49,720 --> 00:22:54,420
+some a k لإن احنا مسترضين ان ال X ايش بتساوي احنا
+
+281
+00:22:54,420 --> 00:23:02,200
+ال X انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+282
+00:23:02,200 --> 00:23:02,240
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+283
+00:23:02,240 --> 00:23:02,920
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+284
+00:23:02,920 --> 00:23:05,620
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+285
+00:23:05,620 --> 00:23:09,280
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+286
+00:23:09,280 --> 00:23:09,320
+انزل انزل انزل انزل انزل انزل انزل انزل انزل انزل
+
+287
+00:23:22,360 --> 00:23:26,480
+ماشي الحال احنا ماشي الحال هذا أثبتنا
+
+288
+00:23:29,810 --> 00:23:34,050
+الان I X element in X belongs to مين؟ to some A K
+
+289
+00:23:34,050 --> 00:23:37,270
+من مين؟ من اللي عرفناها لأنه في الأخر هيطلع اللي
+
+290
+00:23:37,270 --> 00:23:41,990
+هو T أن X الها أصغر أو شاوى some number الواحد،
+
+291
+00:23:41,990 --> 00:23:43,890
+التاني، التلاتي، ماكانش من الواحد، من التاني، من
+
+292
+00:23:43,890 --> 00:23:46,790
+البعد، من التلاتي، من البعد وكذا وكأن ال X يعضرها
+
+293
+00:23:46,790 --> 00:23:51,280
+عن union مين؟ ونقدر نكتبها union لل A Kإذا صار
+
+294
+00:23:51,280 --> 00:23:55,180
+عندى الان X بelongs to some A K Hence X can be
+
+295
+00:23:55,180 --> 00:23:58,080
+written as ال union لمن؟ لل A K كمان واحدة عند من؟
+
+296
+00:23:58,080 --> 00:24:02,520
+لما أنت منها نهاية وكل واحدة منهم اشمالها اللى هو
+
+297
+00:24:02,520 --> 00:24:08,660
+عبارة عن اللى هو closed كمان مرة يا جماعة الآن أي
+
+298
+00:24:08,660 --> 00:24:16,790
+X في ال X لو حسبنا لها T عن Xالـ T and X لأن T and
+
+299
+00:24:16,790 --> 00:24:24,370
+X هتكون الـ X يانا يانا يانا يانا يانا يانا يانا
+
+300
+00:24:24,370 --> 00:24:26,430
+يانا يانا يانا يانا يانا يانا يانا يانا يانا يانا
+
+301
+00:24:26,430 --> 00:24:27,550
+يانا يانا يانا يانا يانا يانا يانا يانا يانا يانا
+
+302
+00:24:27,550 --> 00:24:28,130
+يانا يانا يانا يانا يانا يانا يانا يانا يانا يانا
+
+303
+00:24:28,130 --> 00:24:34,810
+يانا يانا يانا يانا يانا يانا يانا يانا يانا يانا
+
+304
+00:24:34,810 --> 00:24:41,790
+يانا
+
+305
+00:24:41,790 --> 00:24:48,280
+يانا يحكيتها قبل بشوية أنه ما دامت اللي هي X
+
+306
+00:24:48,280 --> 00:24:53,260
+complete إذا بالـ K-Pair Category Theorem اللي
+
+307
+00:24:53,260 --> 00:24:58,240
+كتبت في آخر النظرية A Knot Contains An Open Ball
+
+308
+00:24:58,240 --> 00:25:02,220
+في واحدة من هنا على الأقل اللي فرهنتها في أول K
+
+309
+00:25:02,220 --> 00:25:05,280
+-Pair Category Theorem الجزء الثاني منها أنه ما
+
+310
+00:25:05,280 --> 00:25:09,720
+دامت X complete و X مكتوبة على صورة Union لClosed
+
+311
+00:25:09,720 --> 00:25:13,790
+Setإذاً في واحدة من هنا مش rare يعني في واحدة من
+
+312
+00:25:13,790 --> 00:25:17,230
+هنا على الأقل a k note contains open ball سمناها
+
+313
+00:25:17,230 --> 00:25:21,130
+إيش اسمها a k note بعد أذنكم say اللي هي ال open
+
+314
+00:25:21,130 --> 00:25:25,310
+ball هذه بي نوت بسوا بي إكس نوت و R جزئية من مين
+
+315
+00:25:25,310 --> 00:25:28,570
+من a k note اللي هي سمناها كنا a k note و كلها
+
+316
+00:25:28,570 --> 00:25:32,910
+جميعها نوت اللي هي close بتطلع نفسها طيب الان اطلع
+
+317
+00:25:32,910 --> 00:25:37,850
+على فوق now let x be element in x be R literally
+
+318
+00:25:38,750 --> 00:25:44,830
+and non-zero و let z بتساوي x not زائد gamma x
+
+319
+00:25:44,830 --> 00:25:52,590
+اللي هي x not اللي حكينا عنها فوق الآن خد gamma
+
+320
+00:25:52,590 --> 00:25:57,060
+بتساوي R على 2 في جذر ال X لاتساوي 0ماشي الحال
+
+321
+00:25:57,060 --> 00:26:00,160
+يعني الجامعة مابتديش إيها سفر اللي .. اللي إيها
+
+322
+00:26:00,160 --> 00:26:03,000
+سفر اللي هي R على 2 جدر ال X مابتش .. مابتسويش سفر
+
+323
+00:26:03,000 --> 00:26:06,640
+ال .. ال .. ال .. الجامعة أخي سميت هيك جامعة R على
+
+324
+00:26:06,640 --> 00:26:09,420
+2 في جدر ال X هذه طبعاً R اللي هي ال .. ال ..
+
+325
+00:26:09,420 --> 00:26:12,140
+المركز اللي .. اللي .. النصف القطر مش سفر إذن هذا
+
+326
+00:26:12,140 --> 00:26:14,300
+كله مش سفر إذا الجامعة نفسي صارت أيه أشمل أنها مش
+
+327
+00:26:14,300 --> 00:26:17,820
+سفر عشان بتكسب عليها بعد شوية أخدت Z بتسوي X نور
+
+328
+00:26:17,820 --> 00:26:21,100
+زي الجامعة X ليش هذه؟ أجيت بعد شوية بتشوف عسى
+
+329
+00:26:21,100 --> 00:26:25,460
+استخدامي أن توصلي أنه نور الـTN
+
+330
+00:26:26,750 --> 00:26:30,170
+أصغر أو ساوي، ايش بالنسبة للـ Gamma؟ هذي C يعني
+
+331
+00:26:30,170 --> 00:26:38,130
+هذي تنشيوفكم احسبلي الآن خد الـ Z minus X naught
+
+332
+00:26:38,130 --> 00:26:43,090
+طالعها بـ C Gamma Xبصير norm of z نقص x0 بيسوي
+
+333
+00:26:43,090 --> 00:26:47,950
+norm of gamma x norm of gamma x اضرب اللي هو اللي
+
+334
+00:26:47,950 --> 00:26:51,670
+هي norm of x في الجامعة هي هذه norm of x مع norm
+
+335
+00:26:51,670 --> 00:26:55,270
+of x بيبقى همين R على اتنين R على اتنين اصغر من
+
+336
+00:26:55,270 --> 00:26:59,030
+مين من R يعني بمعنى اخر z minus x0 اصغر من R صارت
+
+337
+00:26:59,030 --> 00:27:04,510
+z في ال ballباشي إذا hence z في b note and so z في
+
+338
+00:27:04,510 --> 00:27:09,410
+واحدة من مين من ال a k not اللي هي لظبط هذه لأن b
+
+339
+00:27:09,410 --> 00:27:13,110
+not جزء من مين من ال a k not إذا صارت عند ال z هذه
+
+340
+00:27:13,110 --> 00:27:17,250
+اللي كتبته بالصورة هذه في ال a k not then by the
+
+341
+00:27:17,250 --> 00:27:21,130
+definition of a k not هيكون ال T and z أصغر شهو
+
+342
+00:27:21,130 --> 00:27:26,410
+مين؟ k notهذا الكلام for all and عند ال X note في
+
+343
+00:27:26,410 --> 00:27:31,850
+B note صبست من A K note اذا مادام X note هنا اذا
+
+344
+00:27:31,850 --> 00:27:37,250
+هنا مادام X note هنا اذا بتحقق خاصية انه TN X note
+
+345
+00:27:37,250 --> 00:27:42,100
+أظهر شاومين اللي هي K noteمشاكل مؤهلة تدخل في الـ
+
+346
+00:27:42,100 --> 00:27:45,900
+Knot إذا صانعين دي ال norm ال TN X knot برضه أصغر
+
+347
+00:27:45,900 --> 00:27:50,480
+يساوي مين Knot و هاد ال TN Z برضه أصغر يساوي مين
+
+348
+00:27:50,480 --> 00:27:58,120
+Knot لأن خلّينا نستخدم تلاتة و ال X إيش بتساوي Z
+
+349
+00:27:58,120 --> 00:28:04,690
+minus X knot على Gammathen for all and لأن norm of
+
+350
+00:28:04,690 --> 00:28:08,090
+T and X لأنها ال X كانت arbitrary وال X note هذه
+
+351
+00:28:08,090 --> 00:28:11,290
+اللي لجيتها اللي هي ال bridge اللي ده صار من خلاله
+
+352
+00:28:11,290 --> 00:28:19,290
+بيصير norm of T and X بساوي اللي هونورم الـ TN
+
+353
+00:28:19,290 --> 00:28:23,170
+لهذه بنطلع الواحد على جامعة برا بيصير واحد على
+
+354
+00:28:23,170 --> 00:28:28,430
+جامعة لأنها موجبة في TN of Z minus X0 وهذه
+
+355
+00:28:28,430 --> 00:28:31,490
+بالتريان جالين كواليتي أصغر أو ساوي حضرتله هذا
+
+356
+00:28:31,490 --> 00:28:38,570
+أوجدت TN Z و TN X0 أصغر أو ساوي أنه TN Z زي TN X0
+
+357
+00:28:38,570 --> 00:28:43,470
+هذه أوجدناها قبل بشوية فوق اللي هي أصغر أو يساوي
+
+358
+00:28:43,470 --> 00:28:45,710
+اللي هو 2K0
+
+359
+00:28:48,270 --> 00:28:52,490
+أوجدناها هيها أصغر يساوي كنوت وهذه أصغر يساوي مين؟
+
+360
+00:28:52,490 --> 00:28:57,810
+كنوت بدي أعوض مكانها صارت واحد على جامعة TNZ أصغر
+
+361
+00:28:57,810 --> 00:29:01,750
+من كنوت وهذه أصغر من كنوت التنتين أصغر من مين؟ من
+
+362
+00:29:01,750 --> 00:29:06,390
+اتنين كنوت فبصير عبارة عن اللي هو عوضه عن جامعة
+
+363
+00:29:06,390 --> 00:29:10,950
+بقيمتها اللي هي R على اتنين في ال Normal X بصير
+
+364
+00:29:10,950 --> 00:29:15,490
+اللي هو اتنين Normal X على R لأنها مجلوبها فاهمين؟
+
+365
+00:29:15,940 --> 00:29:19,760
+فى اتنين كينوت اتنين مع اتنين فبصير عبارة عن كينوت
+
+366
+00:29:19,760 --> 00:29:22,520
+اتنين فى اتنين لأ اتنين فى اتنين فى اربع بروحانش
+
+367
+00:29:22,520 --> 00:29:26,100
+مبارك اتنين فى اتنين اربع كينوت عالمين على ال R
+
+368
+00:29:26,100 --> 00:29:35,300
+اللى هى في X يعني بصير عندى TNX TNX
+
+369
+00:29:35,300 --> 00:29:40,900
+أزرع شاوي اللى طلع عندى اتنين فى اتنين أربعة على A
+
+370
+00:29:40,900 --> 00:29:47,050
+أربعةكنوت على R فنور main ال X خدوا الأن ال
+
+371
+00:29:47,050 --> 00:29:51,130
+supremum ايه اسمه على هذه لل Xات اللي مش سفر و
+
+372
+00:29:51,130 --> 00:29:56,510
+خدوا ال supremumبطلع هذا norm الـ TN أصغر أو يساوي
+
+373
+00:29:56,510 --> 00:30:02,710
+4k نوت على R وهذا ثابت إذا بغض النظر عن اللي هو
+
+374
+00:30:02,710 --> 00:30:07,550
+الـ TN بطلع نورم الـ TN إلهم كلهم أصغر أو يساوي 4k
+
+375
+00:30:07,550 --> 00:30:14,250
+نوت وهذا يعني T note TN أصغر يساوي C for all N حيث
+
+376
+00:30:14,250 --> 00:30:19,850
+C عبارة عن مقدار ثابت اطلع لفترة يلّا لبعده الان
+
+377
+00:30:19,850 --> 00:30:25,070
+space of polynomialsتطبيق على اللي هو النظرية اللي
+
+378
+00:30:25,070 --> 00:30:30,230
+قبل بشوية إيش
+
+379
+00:30:30,230 --> 00:30:36,510
+بتقول هذه؟النورم الـ space X of all polynomials
+
+380
+00:30:36,510 --> 00:30:42,910
+ليس كامل تحت النورم التي تسمى بالنورم الـ X بيساوي
+
+381
+00:30:42,910 --> 00:30:47,190
+الماكسيمم Gamma J Alpha J over J where Alpha 0
+
+382
+00:30:47,190 --> 00:30:50,970
+وAlpha 1 وAlpha 2 are the coefficients of X يعني
+
+383
+00:30:50,970 --> 00:30:55,590
+بدنا نشوف كيف نستخدم الإجابة اللي قبل بشوية على
+
+384
+00:30:55,590 --> 00:31:02,730
+أساس أننا نثبت أن X ليس كاملالـ X إيش ماله؟ مش
+
+385
+00:31:02,730 --> 00:31:05,170
+complete مين الـ X هذا هو الـ space of all
+
+386
+00:31:05,170 --> 00:31:09,330
+polynomial under this norm under this norm ممكن
+
+387
+00:31:09,330 --> 00:31:14,310
+حكينا عليه قبل هيك بس بطريقة أخرى كان أظن سؤال
+
+388
+00:31:14,310 --> 00:31:19,990
+معاكم و لا لأ سؤال و لا لأ طيب
+
+389
+00:31:19,990 --> 00:31:24,970
+خلينا الأن نستخدم اللي هو النظرية اللي جابله شوية
+
+390
+00:31:24,970 --> 00:31:27,230
+في إثبات اللي هو
+
+391
+00:31:30,090 --> 00:31:36,090
+النظرية كانت تقول إن لو كان عندك TN من X لعند Y
+
+392
+00:31:36,090 --> 00:31:45,150
+هذه complete وهذه لأ ومش شرط يعني قصدي و norm TN X
+
+393
+00:31:45,150 --> 00:31:52,470
+أصغر يساوي CX هذا مع بعض بيعطيني norm TN أصغر
+
+394
+00:31:52,470 --> 00:31:54,050
+يساوي 100 S
+
+395
+00:31:57,120 --> 00:32:03,120
+بدي اللي هي أجيب اللي هو عنده we construct a
+
+396
+00:32:03,120 --> 00:32:06,880
+sequence of bounded linear functionals on مين on X
+
+397
+00:32:06,880 --> 00:32:10,260
+sequence
+
+398
+00:32:10,260 --> 00:32:16,180
+الـ TN بدي الـ TN يعني هاخدها من ال polynomial TN
+
+399
+00:32:16,180 --> 00:32:20,900
+أو أفعى اللي بسميهامن الـ polynomials أو the space
+
+400
+00:32:20,900 --> 00:32:24,540
+of all polynomials لعند مين الـ K اللي هو Escalar
+
+401
+00:32:24,540 --> 00:32:29,100
+field الآن بدّي اللي هو أعملها أن هذه تتحقق لكن
+
+402
+00:32:29,100 --> 00:32:33,240
+هذه إيش مالها؟ لا تتحقق لأن لو كان هذا complete
+
+403
+00:32:33,240 --> 00:32:37,900
+اتوماتيك هذا هتتحقق بما أنه ما اتحققتش إذن وين
+
+404
+00:32:37,900 --> 00:32:41,740
+هيكون عنده؟ لو P is not complete إذن we construct
+
+405
+00:32:41,740 --> 00:32:44,840
+a sequence of bounded linear functional on X أو
+
+406
+00:32:44,840 --> 00:32:49,840
+functional on Xwhich satisfies one but not two
+
+407
+00:32:49,840 --> 00:32:53,680
+ماشي الحال let X be a non-zero polynomial of
+
+408
+00:32:53,680 --> 00:32:57,680
+degree إيش ما قالها NX يعني ال X بولونوميال درجتها
+
+409
+00:32:57,680 --> 00:33:02,930
+إيش بتساوي NX ماشي الحال يعني بعد ال NX أصفراللي
+
+410
+00:33:02,930 --> 00:33:08,030
+هو الـ coefficients ثم X of T بتساوي Alpha T ..
+
+411
+00:33:08,030 --> 00:33:11,890
+Alpha J .. T is J .. J من صفر لمين .. لعند .. من
+
+412
+00:33:11,890 --> 00:33:15,470
+النهاية كتبتها الصورة هذه و أنا بقول أشمالها ال
+
+413
+00:33:15,470 --> 00:33:19,090
+degree اللي هي نكس إذا هتكون ال Alpha J بتساوي صفر
+
+414
+00:33:19,090 --> 00:33:23,250
+فوق كل الجزر اللي أشمالهن اللي أكبر من نكس هذا دي
+
+415
+00:33:23,250 --> 00:33:27,190
+معناته ال degree اللي هي .. بتساوي نكس الان let's
+
+416
+00:33:27,190 --> 00:33:31,540
+of .. هنشوف كيف بدو .. بدو يعرفإذا الأن لأ خلّيني
+
+417
+00:33:31,540 --> 00:33:37,760
+أنزل شوية لأن let FN be a sequence of functionals
+
+418
+00:33:37,760 --> 00:33:48,120
+that are defined on X by FN of 0 بساوي 0 FN of X
+
+419
+00:33:48,120 --> 00:33:51,400
+بساوي Alpha node زي ده الف واحد زي ده الف اتنين زي
+
+420
+00:33:51,400 --> 00:33:55,780
+ده الف انمين ماقص واحد الآن
+
+421
+00:33:57,390 --> 00:34:01,610
+عندي وكأني باخد اللي هو الـ Coefficient إسلاميين
+
+422
+00:34:01,610 --> 00:34:07,080
+للي عندي هانعندي مثلا X of T بيساوي Alpha Note
+
+423
+00:34:07,080 --> 00:34:10,640
+زايد Alpha واحد T زايد Alpha اتنين T تربية زايد
+
+424
+00:34:10,640 --> 00:34:14,080
+Alpha اتنين T تربية الاخرين ايش بياخد مجموع ال
+
+425
+00:34:14,080 --> 00:34:16,320
+coefficients FN of X ايش بيساوي مجموع ال
+
+426
+00:34:16,320 --> 00:34:20,120
+coefficients سبعتها it is left to the reader to
+
+427
+00:34:20,120 --> 00:34:24,180
+show that for any fixed N FN ايش معناه is linear
+
+428
+00:34:24,180 --> 00:34:28,720
+FN is linear بتكون بثبتها بثبتها يعني اثباتها اللي
+
+429
+00:34:28,720 --> 00:34:29,040
+هو
+
+430
+00:34:31,910 --> 00:34:39,290
+برضه قمر يعني ان شاء الله مابكونش صعب طيب
+
+431
+00:34:39,290 --> 00:34:46,570
+عندي بتاخدوا اللي هو X اللي هو بتسوي Alpha node
+
+432
+00:34:46,570 --> 00:34:52,450
+زائد Alpha واحد X زائد Alpha N ناقص واحد مثلا X أس
+
+433
+00:34:52,450 --> 00:34:57,150
+N ناقص واحد الاخري وش ال Xات هاذ T
+
+434
+00:35:02,090 --> 00:35:07,350
+Y بنفس الأشي بيساوي مثلا Gamma node زي Gamma 1
+
+435
+00:35:07,350 --> 00:35:11,170
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+436
+00:35:11,170 --> 00:35:11,210
+Gamma n minus 1 plus Gamma n minus 1 plus Gamma n
+
+437
+00:35:11,210 --> 00:35:11,750
+minus 1 plus Gamma n minus 1 plus Gamma n minus 1
+
+438
+00:35:11,750 --> 00:35:13,190
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+439
+00:35:13,190 --> 00:35:13,230
+Gamma n minus 1 plus Gamma n minus 1 plus Gamma n
+
+440
+00:35:13,230 --> 00:35:13,310
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+441
+00:35:13,310 --> 00:35:13,450
+minus 1 plus Gamma n minus 1 plus Gamma n minus 1
+
+442
+00:35:13,450 --> 00:35:13,550
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+443
+00:35:13,550 --> 00:35:14,250
+Gamma n minus 1 plus Gamma n minus 1 plus Gamma n
+
+444
+00:35:14,250 --> 00:35:15,210
+minus 1 plus Gamma n minus 1 plus Gamma n minus 1
+
+445
+00:35:15,210 --> 00:35:15,710
+plus Gamma n minus 1 plus Gamma n minus 1 plus
+
+446
+00:35:15,710 --> 00:35:21,510
+Gamma n minus 1 plus Gamma n minus 1 plus Gamma n
+
+447
+00:35:21,510 --> 00:35:24,450
+minus 1 plus Gamma n
+
+448
+00:35:30,230 --> 00:35:31,390
+للتفصيل
+
+449
+00:35:33,880 --> 00:35:37,820
+حالان خلاص فكّينا من أنها Linear لأن نثبت أنها إيه
+
+450
+00:35:37,820 --> 00:35:40,960
+شمالها لإن نصل للboundedness أولا الشيء ال
+
+451
+00:35:40,960 --> 00:35:44,460
+absolute value لـ α J ال coefficients هدولة أكيد
+
+452
+00:35:44,460 --> 00:35:48,080
+أصغر أو أشهر هو ال maximum اللي هو مين هو normal X
+
+453
+00:35:48,080 --> 00:35:52,240
+مش normal X هو ال maximum ال maximum لأ اللي هي ال
+
+454
+00:35:52,240 --> 00:35:55,940
+coefficients اللي عند .. اللي عندي normal X كده
+
+455
+00:35:55,940 --> 00:36:00,300
+عرفنا ال norm احنا then ال absolute value لأفقن of
+
+456
+00:36:00,300 --> 00:36:06,620
+Xماله ال FN of X هيهم FN of X اللي هي عبارة عن ألف
+
+457
+00:36:06,620 --> 00:36:10,080
+نوت و ألف واحد و كل واحدة منهم أصغر من مين من نورم
+
+458
+00:36:10,080 --> 00:36:16,640
+ال X إذا مجموحين أصغر يساوي N في مين في نورم ال F
+
+459
+00:36:16,860 --> 00:36:23,780
+هذا كل fixed N يعني F1 أصغر من ساوي Normal X F2
+
+460
+00:36:23,780 --> 00:36:28,720
+أصغر من N2 Normal X وهكذا إذا F1 وF2 وF3 كله نجمان
+
+461
+00:36:28,720 --> 00:36:32,260
+هم bounded functionals إذا صار عبارة عن sequence
+
+462
+00:36:32,260 --> 00:36:36,380
+of bounded functionals ومش هيك لكل X element in X
+
+463
+00:36:36,380 --> 00:36:39,460
+ده أنا متلزمني هذا بعد شوية خدوا ال absolute value
+
+464
+00:36:39,460 --> 00:36:44,740
+ل FN of Xالأبسلوت زي الـ αن نوف إكس هي هتكون أصغر
+
+465
+00:36:44,740 --> 00:36:47,300
+أو ساوية أن إكس زائد واحد في ال maximum للـ alpha
+
+466
+00:36:47,300 --> 00:36:53,760
+jليش؟ لأنه ال .. ال .. ال .. البعد لهذه أسفار أه
+
+467
+00:36:53,760 --> 00:36:57,980
+وكل واحد اللي هو إيش ماله اللي هو أكيد هدولة إيش
+
+468
+00:36:57,980 --> 00:37:02,020
+قمتهن Alpha 0, Alpha 1, Alpha 2, Alpha 3 إلى ..
+
+469
+00:37:02,020 --> 00:37:05,520
+إلى ما .. إلى ما شاء الله أكيد مش هيبقوا الإتعداد
+
+470
+00:37:05,520 --> 00:37:09,820
+هن لأنك زاد واحد لأنه بعدها بيصير إنه أسفار فبيصير
+
+471
+00:37:09,820 --> 00:37:12,800
+عنده أصغر أو ساوي اللي هو هذه في ال coefficients
+
+472
+00:37:12,800 --> 00:37:15,840
+الأولة .. الأولة .. الأولة كله أصغر من ال maximum
+
+473
+00:37:15,840 --> 00:37:19,320
+فصار مقدموح أن أصغر من مين من هذا في ال .. في هذا
+
+474
+00:37:23,670 --> 00:37:29,470
+عيدوا يدمع أف أن أو في X هيها ألف نوت ألف واحد ألف
+
+475
+00:37:29,470 --> 00:37:33,310
+اتنين ألف أن هال جهة ال absolute value لها أصغر أو
+
+476
+00:37:33,310 --> 00:37:36,130
+شاوري هذه ال absolute value هذه زي ال absolute
+
+477
+00:37:36,130 --> 00:37:39,830
+value هذه زي ال absolute value لهذه الآن هذولة
+
+478
+00:37:39,830 --> 00:37:44,270
+أصغر أو شاوري maximum تبحن كل واحدةعداد هنا دولة
+
+479
+00:37:44,270 --> 00:37:49,750
+لن يتجاوز بغض النظر عن X لن يتجاوز ال main اللي هو
+
+480
+00:37:49,750 --> 00:37:53,490
+ال NX زائد واحد اللي هي درجة ال polynomial زائد
+
+481
+00:37:53,490 --> 00:37:57,330
+واحد لن يتجاوزها فبصير عند ال FNX أصغر أو ساوي
+
+482
+00:37:57,330 --> 00:37:59,690
+اللي هو هذا المقدار في هذا اللي هو بعتمد على ال
+
+483
+00:37:59,690 --> 00:38:03,670
+main على X أصغر أو ساوي CX since X has و بقى
+
+484
+00:38:03,670 --> 00:38:08,090
+polynomial of degree NX that has NX زائد واحد من
+
+485
+00:38:08,090 --> 00:38:12,780
+ال coefficients اطلع إلى فوقإذن therefore ال
+
+486
+00:38:12,780 --> 00:38:15,540
+absolute value of N of X satisfies one اللي في
+
+487
+00:38:15,540 --> 00:38:19,540
+الآخر الآن أنا بتثبتلك أنه لن يحقق مين اللي هو هذه
+
+488
+00:38:19,540 --> 00:38:26,320
+norm لأف N مستحيل يحققلك أنه أصغر أو سوى C بل
+
+489
+00:38:26,320 --> 00:38:32,650
+هأثبتلك أنه unbounded شوفخد الآن finally we show
+
+490
+00:38:32,650 --> 00:38:35,570
+that fn does not satisfy اتنين choose a polynomial
+
+491
+00:38:35,570 --> 00:38:39,030
+x by x of t بالساوية وصميش اللي التي جيه جيه من
+
+492
+00:38:39,030 --> 00:38:41,630
+سفر لعند مين لعند ان هاي ال X تبعتين اللي
+
+493
+00:38:41,630 --> 00:38:46,920
+بتاخدلكيها اللي بتخرب الدنيا then norm ال Xبساوة
+
+494
+00:38:46,920 --> 00:38:50,020
+واحدة انه ال maximum اللي هنا دول العوامل كل واحد
+
+495
+00:38:50,020 --> 00:38:52,800
+واحد واحد ده النورم هنا ايش بساوة بساوة واحدة ده
+
+496
+00:38:52,800 --> 00:38:55,420
+النورم ال X بساوة واحدة ال FN of X في هذه الحالة
+
+497
+00:38:55,420 --> 00:38:59,060
+ايش بساوة اللي هو واحد زاد واحد زاد واحد ده ايش
+
+498
+00:38:59,060 --> 00:39:04,820
+بساوة N من المصير اللي بساوة نهن ويساوة N في مين
+
+499
+00:39:04,820 --> 00:39:10,740
+في نورم ال X وهذا معناته صار عنده ال FN of X بساوة
+
+500
+00:39:10,740 --> 00:39:17,310
+N في نورم ال Xإذا Normal FN هيكون هو الـ supremum
+
+501
+00:39:17,310 --> 00:39:21,750
+هيكون أكبر أو يساوي واحدة منهم اللي هي عبارة عن
+
+502
+00:39:21,750 --> 00:39:24,910
+هذا FN of X اللي هي أكبر يساوي FN of X ع Normal X
+
+503
+00:39:25,520 --> 00:39:29,540
+الـ N في X على نورم الـ X و يسوى N صارت نورم الـ
+
+504
+00:39:29,540 --> 00:39:33,540
+FN أكبر ويسوى ومياشي سوى N إذن مستحيل اللي هي
+
+505
+00:39:33,540 --> 00:39:37,760
+hence the sequence of N is unbounded and so two is
+
+506
+00:39:37,760 --> 00:39:42,220
+not satisfied they are satisfied then أو therefore
+
+507
+00:39:42,220 --> 00:39:46,800
+by uniform boundedness theorem ال X is not
+
+508
+00:39:46,800 --> 00:39:49,980
+complete أو اللي هو the space of all such
+
+509
+00:39:49,980 --> 00:39:53,580
+polynomials under this norm is not complete وإلى
+
+510
+00:39:53,580 --> 00:39:54,440
+لقاء آخر
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/zFznbPjt0NA.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/zFznbPjt0NA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..717287039237341e049f307c9b9c9debf6848017
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/zFznbPjt0NA.srt
@@ -0,0 +1,1323 @@
+1
+00:00:05,260 --> 00:00:08,260
+بسم الله الرحمن الرحيم الحمد لله رب العالمين و
+
+2
+00:00:08,260 --> 00:00:11,100
+الصلاة والسلام على سيد المرسلين سيدنا محمد وعلى 
+
+3
+00:00:11,100 --> 00:00:15,220
+آله وصحبه أجمعين هذه هي المحاضرة رقم 36 وهي 
+
+4
+00:00:15,220 --> 00:00:19,500
+المحاضرة الأخيرة في مساق تحليل اقتران أو تحليل 
+
+5
+00:00:19,500 --> 00:00:25,100
+دالي لطلاب وطالبات الجامعة الإسلامية ماجستير 
+
+6
+00:00:25,100 --> 00:00:30,690
+الرياضيات، الفكرة إننا بدنا نأخذ بس فكرة عن اللي هو 
+
+7
+00:00:30,690 --> 00:00:35,850
+مفهوم الباناخ Algebra لأنه له تطبيقات وله استعمالات 
+
+8
+00:00:35,850 --> 00:00:41,950
+كبيرة لو أحد يعني حاب إنه يشتغل فيه أو خلّيني أقول 
+
+9
+00:00:41,950 --> 00:00:48,110
+ينطلق فيه إلى الأمام يعني بيكون فيه له فكرة في 
+
+10
+00:00:48,110 --> 00:00:48,810
+الموضوع
+
+11
+00:00:51,440 --> 00:00:55,440
+نبدأ في definition يعني هو خليط بين الجبر الحديث 
+
+12
+00:00:55,440 --> 00:01:00,240
+وبين اللي هو أو في أحيانًا نقول ملحُه اللي هو الملح 
+
+13
+00:01:00,240 --> 00:01:03,640
+الأولاني كنا نحكي عن الجبر الخطي هو ملحُ 
+
+14
+00:01:03,640 --> 00:01:07,490
+function، ملحُ آخر خلّيني أقول للباناخ Algebra اللي هو 
+
+15
+00:01:07,490 --> 00:01:09,970
+يعني أو خلّيني أقول إيه علاقة فيه اللي هو الـ Ring 
+
+16
+00:01:09,970 --> 00:01:15,390
+Theory فيه شغل في الـ .. في الـ ideals و .. و كل 
+
+17
+00:01:15,390 --> 00:01:18,930
+أسماء اللي .. اللي بتتعلق بالـ .. بالـ ideals والـ 
+
+18
+00:01:18,930 --> 00:01:21,810
+modules و .. و الآخرة اللي موجودة في الـ rings و
+
+19
+00:01:21,810 --> 00:01:24,770
+موجودة كانت موجودة في الباناخ Algebra بس هنا زيادة 
+
+20
+00:01:24,770 --> 00:01:29,870
+شوية إنه .. إنه بيعطيه شوية يعني الـ .. الـ .. الـ 
+
+21
+00:01:29,870 --> 00:01:34,350
+ring ما هي على عمليتين، هنا الآن في هي قاعدة على 
+
+22
+00:01:34,350 --> 00:01:37,150
+vector space اللي هو scalar multiplication و 
+
+23
+00:01:37,150 --> 00:01:39,990
+vector addition بالإضافة بيصير لأن vector 
+
+24
+00:01:39,990 --> 00:01:42,470
+multiplication اللي هي عملية ضرب زي ما عملية ضرب 
+
+25
+00:01:42,470 --> 00:01:45,250
+اللي وين اللي في الـ ring وزيادة على هيك أنه في 
+
+26
+00:01:45,250 --> 00:01:48,990
+عليه norm الـ norm تبعه، نقع norm of this space، صح 
+
+27
+00:01:48,990 --> 00:01:51,410
+لكن norm of this space وفيه كمان شغل آخر على الـ 
+
+28
+00:01:51,410 --> 00:01:54,270
+norm of this space أنه بده الـ norm تبع الباناخ 
+
+29
+00:01:54,270 --> 00:01:57,170
+الجبرية بده يحقق norm الـ x في y أصغر أو يساوي norm الـ
+
+30
+00:01:57,170 --> 00:02:01,060
+x في norm الـ y، لأنه في الأصل في الـ Normed Space 
+
+31
+00:02:01,060 --> 00:02:03,720
+العادي مش شرط تكون فيه عملية ضرب بس إن صار في 
+
+32
+00:02:03,720 --> 00:02:06,620
+عملية ضرب لأن هناك العالم اللي بنشتغل عليه vector 
+
+33
+00:02:06,620 --> 00:02:08,680
+space ومش فيه هناك غير عملية scalar multiplication 
+
+34
+00:02:08,680 --> 00:02:13,980
+و vector addition فاللي هو مش وارد كان عملية الضرب 
+
+35
+00:02:13,980 --> 00:02:18,660
+و norm للـ X في Y مثلا مش وارد كان زمان، هأنا بدي 
+
+36
+00:02:18,660 --> 00:02:23,730
+يصبح وارد و بدي أن أتعامل معاها كتان، شوفش اللي بقوله، 
+
+37
+00:02:23,730 --> 00:02:26,990
+6.1 Definition of Algebra A لأننا نعرف الجبر 
+
+38
+00:02:26,990 --> 00:02:32,830
+بدون ما نحطّناهم لسه Algebra A over a vector over a 
+
+39
+00:02:32,830 --> 00:02:36,730
+field K is a vector space إذا نرسى الدورة الشمالة 
+
+40
+00:02:36,730 --> 00:02:42,060
+vector space عالميًا على اللي هو scalar field K over
+
+41
+00:02:42,060 --> 00:02:46,320
+k such that for all x y element a a unique product 
+
+42
+00:02:46,320 --> 00:02:49,620
+ده أنا عرفنا من a product اللي هم بتضعف للـ vector 
+
+43
+00:02:49,620 --> 00:02:52,100
+addition والـ scale of multiplication عرفنا 
+
+44
+00:02:52,100 --> 00:02:55,100
+product x و y والموجودة في الـ I في ليه؟ is 
+
+45
+00:02:55,100 --> 00:02:58,140
+defined with the properties mainly اللي هي بتحقق 
+
+46
+00:02:58,140 --> 00:03:02,510
+اللي هي الخواص التالية، إن X في Y في Z بيساوي الـ 
+
+47
+00:03:02,510 --> 00:03:06,770
+associativity تبع تليجيه، ده الآن التوزيع بين عملية 
+
+48
+00:03:06,770 --> 00:03:10,850
+الـ vector addition وبين الدرب X في Y زي Z بيساوي
+
+49
+00:03:10,850 --> 00:03:14,670
+X في Y زي X في Z، برضه بدها تربط بين الـ scalar 
+
+50
+00:03:14,670 --> 00:03:16,850
+multiplication والـ multiplication تبعهم أو الـ
+
+51
+00:03:16,850 --> 00:03:20,360
+product، ألفة في X و Y لـ associativity اللي هو 
+
+52
+00:03:20,360 --> 00:03:24,460
+أشمالها واردة أو خلّيني أقول متحققة، هذا الكلام لكل 
+
+53
+00:03:24,460 --> 00:03:28,460
+X و Y والألفة element N هو الـ K طبعًا اللي هو 
+
+54
+00:03:28,460 --> 00:03:31,020
+التوزيع من اليمين ومن الشمال زي ما أنتم ملاحظين
+
+55
+00:03:31,020 --> 00:03:35,160
+الآن A is called an algebra .. هذه الـ algebra A is 
+
+56
+00:03:35,160 --> 00:03:38,940
+called an algebra with unity .. with unity اللي هو 
+
+57
+00:03:38,940 --> 00:03:42,180
+with identity if there exist any element in A such 
+
+58
+00:03:42,180 --> 00:03:45,150
+ذات اللي بتعرفوه E في X بيساوي X في E بيساوي A
+
+59
+00:03:45,150 --> 00:03:48,230
+إشمال و X لكل X و Y موجودة في الـ A، إذا صارت عبارة 
+
+60
+00:03:48,230 --> 00:03:52,790
+عن اللي هي associative موجودة طبعًا و closed this 
+
+61
+00:03:52,790 --> 00:03:56,570
+موجودة أكيد اللي هو لكل X و Y في عندك اللي هو X و
+
+62
+00:03:56,570 --> 00:03:59,450
+Y اللي بتناقصها تتعامل لـ closed، إذا صارت closed 
+
+63
+00:03:59,450 --> 00:04:03,970
+وصارت associative وصار عند A إشمالها الـ identity 
+
+64
+00:04:03,970 --> 00:04:10,290
+موجودة، A is called اللي هو إشمالها algebra with 
+
+65
+00:04:10,290 --> 00:04:15,840
+unity، اللي هم بنسميها commutative algebra إذا كان a
+
+66
+00:04:15,840 --> 00:04:20,880
+في b إيش بيساوي b في a، for all a و b element من مين
+
+67
+00:04:20,880 --> 00:04:25,060
+in a أسبب algebra of a بنفس اللي .. اللي .. اللي 
+
+68
+00:04:25,060 --> 00:04:29,740
+.. اللي هو الغنطق تبع الـ .. اللي هو الـ subgroup، الـ
+
+69
+00:04:29,740 --> 00:04:32,440
+Sub vector space، الـ Sub ring، كله يجب أن يحافظ 
+
+70
+00:04:32,440 --> 00:04:38,000
+عالميًا على أن يكون أصلاً مثله بس جزء صغير منه لأن 
+
+71
+00:04:38,000 --> 00:04:41,080
+كيف يجب أن يحافظها؟ سبق الجبر وفقاه وعبارة عن is 
+
+72
+00:04:41,080 --> 00:04:43,620
+a vector sub space of V هذه أول واحدة لذلك نخلصها 
+
+73
+00:04:43,620 --> 00:04:46,220
+من قصة الـ scalar multiplication والـ vector 
+
+74
+00:04:46,220 --> 00:04:49,780
+addition، الآن ماذا قال؟ that is closed under the 
+
+75
+00:04:49,780 --> 00:04:52,680
+product، اللي هو إيش؟ عشان يضمن إنه صار الجبر 
+
+76
+00:04:52,680 --> 00:04:56,180
+closed under the product وباقي الأمور ما هي متحققة 
+
+77
+00:04:56,180 --> 00:04:58,320
+في الكبير، ده راح تكون متحققة في الصغير اللي هي الـ 
+
+78
+00:04:58,320 --> 00:05:02,180
+associativity والتوزيع والآخرين، الآن if a has an 
+
+79
+00:05:02,180 --> 00:05:06,280
+identity then the identity إشمالها is unique وهذا 
+
+80
+00:05:06,280 --> 00:05:08,900
+إثباته زي ما بنثبت في الـ ring العادي وفي الـ group 
+
+81
+00:05:08,900 --> 00:05:11,940
+العادي اللي هو إثبات الـ identity الوحيد من اللي هي 
+
+82
+00:05:11,940 --> 00:05:17,500
+الخواص المعتادة، طيب ندى الآن هذا دعنا نقول تحديث 
+
+83
+00:05:17,500 --> 00:05:18,840
+جبري بحت
+
+84
+00:05:21,740 --> 00:05:25,440
+الآن جميلها، The product in and on this algebra A 
+
+85
+00:05:25,440 --> 00:05:28,700
+is a continuous mapping of A cross A onto mean 
+
+86
+00:05:28,700 --> 00:05:32,740
+onto A، عملية الضرب عملية إيهاش، عملية متصلة بين A 
+
+87
+00:05:32,740 --> 00:05:36,200
+cross A لعند مين؟ لعند الـ A واثبتها واثبتها يعني 
+
+88
+00:05:36,200 --> 00:05:39,880
+إيه سهل، هذا الآن طبعًا مش هنقدر نحكي فيه إلا إذا 
+
+89
+00:05:39,880 --> 00:05:43,260
+نحكي عن norm، لأنه فيه اتصال يعني ممكن نحكي عن الـ 
+
+90
+00:05:43,260 --> 00:05:48,220
+topology عشان هيك بيستلزم الحديث على اللي هو الـ 
+
+91
+00:05:48,220 --> 00:05:50,740
+algebra أن يكون non-algebra، طبعًا ماهي الـ non 
+
+92
+00:05:50,740 --> 00:05:54,680
+-algebra؟ الـ non-algebra ببساطة non-algebra A is 
+
+93
+00:05:54,680 --> 00:05:55,780
+a non-disbase
+
+94
+00:05:59,000 --> 00:06:03,280
+which is an algebra، هاتين such that norm الـ X 
+
+95
+00:06:03,280 --> 00:06:06,740
+في Y إيش بده يصير؟ أصغر أو يساوي norm X في norm Y لكل 
+
+96
+00:06:06,740 --> 00:06:10,460
+X وY element in A، هذا اللي هو بيعمل ليه normed 
+
+97
+00:06:10,460 --> 00:06:16,660
+algebra، الآن if A has identity، إذا الـ norm الـ E 
+
+98
+00:06:16,660 --> 00:06:21,380
+حيث أننا سنحسب أننا عارفينه إيش بيساوي واحد واللي 
+
+99
+00:06:21,380 --> 00:06:25,860
+هي بيصير عبارة عن normed algebra with identity لو 
+
+100
+00:06:25,860 --> 00:06:29,200
+كان الـ normed algebra with identity is complete 
+
+101
+00:06:29,200 --> 00:06:32,280
+يعني الـ norm بيعطينا اللي هو of recursive sequence 
+
+102
+00:06:32,280 --> 00:06:37,700
+converge بنسميه باناخ ألجيبرا، إذا the باناخ ألجيبرا A 
+
+103
+00:06:37,700 --> 00:06:40,740
+is a complete normed algebra which is a complete 
+
+104
+00:06:40,910 --> 00:06:44,970
+which which which is complete considered as a 
+
+105
+00:06:44,970 --> 00:06:51,770
+normless space، طيب نقول إن هذا product اللي هي الـ 
+
+106
+00:06:51,770 --> 00:06:55,530
+X في Y عملية الضرب اللي هي في الـ A هي عبارة عن a 
+
+107
+00:06:55,530 --> 00:06:59,290
+continuous mapping من A cross A لعند مين؟ لعندي 
+
+108
+00:06:59,290 --> 00:07:00,370
+يعني F 
+
+109
+00:07:03,260 --> 00:07:09,160
+من A cross A لعند الـ A defined by F of A و B 
+
+110
+00:07:09,160 --> 00:07:15,020
+بتساوي A في B هذه إشمالها is a continuous function 
+
+111
+00:07:15,020 --> 00:07:18,060
+وهو الهدف اللي في الكتاب، سهل لو على طول بتطلعوها و 
+
+112
+00:07:18,060 --> 00:07:22,020
+برا لعند في الترخيص الثاني، أنا بس احنا لضيق الوقت 
+
+113
+00:07:22,020 --> 00:07:27,000
+خليه لكم تطلعوا عليه، نيجي الآن نأخذ أمثلة، اطلع لفوق
+
+114
+00:07:27,000 --> 00:07:32,650
+أمثلة على اللي هو normed algebra، The real line هو 
+
+115
+00:07:32,650 --> 00:07:37,570
+فيلد، الـ real line هو الكمبليكس فيلد يعني كل عملية 
+
+116
+00:07:37,570 --> 00:07:41,330
+فيه موجودة سواء ضرب أو وده كده The real line and 
+
+117
+00:07:41,330 --> 00:07:44,010
+the complex plane C are commutative 
+
+118
+00:07:44,010 --> 00:07:49,890
+كممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممم
+
+119
+00:07:50,250 --> 00:07:54,450
+الآن اللي هو الـ R والـ C are commutative بنخ 
+
+120
+00:07:54,450 --> 00:07:57,870
+الـ algebra، وضع identity A بيساوي واحد، إيش عملية 
+
+121
+00:07:57,870 --> 00:08:03,290
+الـ vector addition الجمع العادي؟ إيش عملية الـ 
+
+122
+00:08:03,290 --> 00:08:05,270
+scalar multiplication الـ field اللي عليه في 
+
+123
+00:08:05,270 --> 00:08:09,690
+عناصره؟ إيش عملية الضرب اللي هي الضرب العادي اللي 
+
+124
+00:08:09,690 --> 00:08:19,540
+عليه؟ بناخد مثال آخر space C of A و B خدناه is الهو
+
+125
+00:08:19,540 --> 00:08:25,360
+the space of all continuous functions is 
+
+126
+00:08:25,360 --> 00:08:28,980
+a commutative بنخ ألجيبرا under the maximum norm 
+
+127
+00:08:28,980 --> 00:08:34,340
+is a commutative بنخ ألجيبرا with identity E بيساوي 
+
+128
+00:08:34,340 --> 00:08:38,940
+مين؟ بيساوي الهو إيش؟ بيساوي واحد اللي هي الـ 
+
+129
+00:08:38,940 --> 00:08:44,220
+constant function، the product x y be defined as 
+
+130
+00:08:44,220 --> 00:08:49,040
+usual x y of t الـ functions هي وكانت بنضرب point 
+
+131
+00:08:49,040 --> 00:08:53,160
+wise يعني بيساوي x of t في مين؟ في y of t for all t 
+
+132
+00:08:53,160 --> 00:08:56,220
+in a و b طبعًا احنا نعرف إن ذكريات ده continuous و
+
+133
+00:08:56,220 --> 00:08:58,640
+إذا كنت نفسك حصلت ضرب إيش هيكون؟ continuous أكيد 
+
+134
+00:08:58,640 --> 00:09:04,320
+لأن and the norm is the maximum norm، الآن هذا كله 
+
+135
+00:09:04,320 --> 00:09:09,540
+بيعمل ليه إيش ماله؟ commutative بنخ ألجيبرا إذا اللي 
+
+136
+00:09:09,540 --> 00:09:13,720
+هي اللي على اللي هي الضرب العادي هيطلع commutative 
+
+137
+00:09:13,720 --> 00:09:17,340
+بنخ ألجيبرا، the subspace of c of A و B consisting 
+
+138
+00:09:17,340 --> 00:09:22,980
+of all polynomials is a commutative normed algebra 
+
+139
+00:09:22,980 --> 00:09:26,020
+أنا بقول لها مش complete هذا الـ polynomial مش 
+
+140
+00:09:26,020 --> 00:09:30,820
+complete with identity، إيه بتساوي واحد، اطلع لفوق 
+
+141
+00:09:30,820 --> 00:09:36,940
+التفاصيل اللي هي الخواص كلها بتتحقق in the space P of X P 
+
+142
+00:09:36,940 --> 00:09:40,980
+of X اللي هو عبارة عن من the space of all bounded
+
+143
+00:09:40,980 --> 00:09:45,580
+linear operators from X to X ماشي لإن ده ما
+
+144
+00:09:45,580 --> 00:09:49,420
+كتبناش من X ل Y ماعرفش منه قصده من X لمنين ل X the
+
+145
+00:09:49,420 --> 00:09:51,860
+Banach space P of X of all bounded linear
+
+146
+00:09:51,860 --> 00:09:59,350
+operators on X نفسه X نفسه إيش ماله  the non
+
+147
+00:09:59,350 --> 00:10:04,250
+-zero Banach space the B of X اللي هي the space of
+
+148
+00:10:04,250 --> 00:10:08,150
+all bounded linear operators is بنخ ألجيبرا with
+
+149
+00:10:08,150 --> 00:10:14,130
+identity I اللي هال multiplication هنا اللي هو
+
+150
+00:10:14,130 --> 00:10:18,770
+عبارة عن composition of operators يعني عملية الضرب
+
+151
+00:10:18,770 --> 00:10:22,790
+اللي بنعرفها على الـPX وPXH مالها عبارة عن الـ
+
+152
+00:10:22,790 --> 00:10:25,350
+composition و الـ composition need not to be
+
+153
+00:10:25,350 --> 00:10:28,390
+commutative زي ما انتوا عارفينها إذاً هذا مثال على
+
+154
+00:10:28,390 --> 00:10:33,750
+P of X is a non commutative Banach algebra unless the
+
+155
+00:10:33,750 --> 00:10:41,690
+dimension of X بساوي بساوي واحد اللي بعده الان
+
+156
+00:10:41,690 --> 00:10:42,770
+definition
+
+157
+00:10:44,850 --> 00:10:48,450
+بنعرف الشو معنات طبعاً ده يعني خلّينا اللي عارفه
+
+158
+00:10:48,450 --> 00:10:53,290
+مش هنستعمله لإنه مش هيكون فيه نوجت لنستعمل الان
+
+159
+00:10:53,290 --> 00:10:58,730
+element x in an algebra A is said to be
+
+160
+00:10:58,730 --> 00:11:01,550
+invertible ترفو هذا invertible إيش معناه
+
+161
+00:11:01,550 --> 00:11:05,430
+invertible if it has an inverse in A اللي واش
+
+162
+00:11:05,430 --> 00:11:08,350
+معناته في X inverse بحيث انه X في X inverse بيساوي
+
+163
+00:11:08,350 --> 00:11:11,150
+X inverse في X أش بيساوي ال identity اللي لإن في
+
+164
+00:11:11,150 --> 00:11:14,070
+هذا الحالة بيسمي ال element X إيش ماله is
+
+165
+00:11:14,070 --> 00:11:17,930
+invertible يعني فيه انه inverse with respect to
+
+166
+00:11:17,930 --> 00:11:21,490
+this operation اللي هي ال product if X element in
+
+167
+00:11:21,490 --> 00:11:26,600
+A is SX element in A is invertible then its
+
+168
+00:11:26,600 --> 00:11:28,160
+inverse is ماهي الوحيد
+
+169
+00:11:34,080 --> 00:11:37,740
+الان نيجي اللي هو نتعرف علي حاجة اسمها الـ
+
+170
+00:11:37,740 --> 00:11:40,820
+Resolvent والاسبكترام وهذا قصص طويلة ال Resolvent
+
+171
+00:11:40,820 --> 00:11:44,480
+والاسبكترام لأنه هم .. يعني ال .. ال .. ال .. ال
+
+172
+00:11:44,480 --> 00:11:47,720
+.. الواحدة اسمها اللي هي ال Sigma الطيف .. الطيف
+
+173
+00:11:47,720 --> 00:11:50,940
+.. الطيف العنصر .. الطيف العنصر يعني احنا بنقول
+
+174
+00:11:50,940 --> 00:11:56,420
+الواحد يعني الخيال تبع ال .. تبع الشخص يعني بيعطي
+
+175
+00:11:56,420 --> 00:12:01,790
+مؤشر على الشخص الأثر تبع الشخص بيعطي .. بيعطي ..
+
+176
+00:12:01,790 --> 00:12:07,630
+خلّيني أقول مؤشر على الشخص الان طيف العنصر أحيانا
+
+177
+00:12:07,630 --> 00:12:10,710
+إحنا ما نعرفش العنصر نفسه لكن طبعا هذا الكلام
+
+178
+00:12:10,710 --> 00:12:13,990
+حقيقة يعني في ال .. في ال .. في ال .. في ال .. في
+
+179
+00:12:13,990 --> 00:12:19,330
+ال .. اللي هو العنصر الجيبرا أو الجيبرا طيف العنصر
+
+180
+00:12:20,760 --> 00:12:24,320
+بيعطيك كثير من خواص العنصر عشان هيك الناس بتهتم
+
+181
+00:12:24,320 --> 00:12:28,520
+بالطيف أو اللي هو ال spectrum وحتى ال resolvent
+
+182
+00:12:28,520 --> 00:12:32,340
+اللي هي ال set إيش اللي بقوله؟ إيش اللي بقوله
+
+183
+00:12:32,340 --> 00:12:35,180
+قاعد؟ let A be a complex Banach algebra with
+
+184
+00:12:35,180 --> 00:12:40,880
+identity then the resolvent set of A is Rho of A
+
+185
+00:12:40,880 --> 00:12:48,790
+إيش Rho of A هذه؟الآن وكأنه بيحول الحديث من عناصر
+
+186
+00:12:48,790 --> 00:12:51,990
+في الـA اللي هي عناصر البنخ الـAlgebra إلى عناصر
+
+187
+00:12:51,990 --> 00:12:55,690
+في الـscalar field والحكي على الـscalar field ألطف
+
+188
+00:12:55,690 --> 00:12:59,110
+بظل ألطف من مين من البنخ الـAlgebra وتعقيدات وكيف
+
+189
+00:12:59,110 --> 00:13:02,310
+عناصر وكيف كذا وكيف كذا ودكتبات وإلى آخرية الـRow
+
+190
+00:13:02,310 --> 00:13:04,990
+of A هي عبارة عن كل اللمضة اللي في element in C
+
+191
+00:13:04,990 --> 00:13:08,910
+such that λمضة E minus A inverse E أشماله exist in
+
+192
+00:13:08,910 --> 00:13:15,150
+A هذه الـset اللي بنسميها الـRow of Aالمكملة لها
+
+193
+00:13:15,150 --> 00:13:18,870
+المكملة لها بنسميها الـ Spectrum اللي هو الطيب الـ
+
+194
+00:13:18,870 --> 00:13:22,210
+Spectrum set of A is Sigma of A بساوة C minus Rho
+
+195
+00:13:22,210 --> 00:13:26,230
+of A Any Lambda element in Sigma of A is called a
+
+196
+00:13:26,230 --> 00:13:29,150
+spectral value بنسميها إيه اشمالها Spectral value
+
+197
+00:13:29,150 --> 00:13:34,410
+of A Not that sigma of a هي عبارة عن لمضة يعني الأن
+
+198
+00:13:34,410 --> 00:13:37,830
+لو بدنا نترجم مش معناه sigma of a يعني خلّيني أقول
+
+199
+00:13:37,830 --> 00:13:41,210
+بالإستدالة بهذه هي عبارة عن اللمضات اللي في الـC
+
+200
+00:13:41,210 --> 00:13:44,570
+اللي هذا يشمل و does not exist and does not exist
+
+201
+00:13:44,570 --> 00:13:48,570
+أنا مكملتها اطلع لفوق بس بكفاية تعرفوه الأن نيجي
+
+202
+00:13:49,180 --> 00:13:54,300
+Further Properties of Banach algebra خلّيني أقول
+
+203
+00:13:54,300 --> 00:13:58,240
+مقتطفات من اللي هي بعض خواص البنخ الـalgebra ناخد
+
+204
+00:13:58,240 --> 00:14:02,040
+فكرة عنها أول نظرية، النظرية هذه المشهورة في اللي
+
+205
+00:14:02,040 --> 00:14:06,520
+هي .. بداية .. اللي هي البنخ الـalgebra Let A be a
+
+206
+00:14:06,520 --> 00:14:10,920
+complex Banach algebra with identity E الآن، عند
+
+207
+00:14:10,920 --> 00:14:14,480
+البنخ الـalgebra with identity E if X element in A
+
+208
+00:14:15,460 --> 00:14:19,320
+إذا كان X في الـ A وNormها أصغر من واحد نورمها
+
+209
+00:14:19,320 --> 00:14:22,340
+أصغر من واحد هذا فيه إشي مشابه إله في ال series
+
+210
+00:14:22,340 --> 00:14:26,460
+أصلا طبعا احنا then E to the minus X is invertible
+
+211
+00:14:26,460 --> 00:14:30,240
+يعني E to the minus X نفسه is invertible وعطيني E
+
+212
+00:14:30,240 --> 00:14:33,180
+to the minus X inverse بساوي بالظبط وعبارة عن ال
+
+213
+00:14:33,180 --> 00:14:37,300
+summation لل X JJ من 0 إلى 100 إلى ملا نهايةيعني
+
+214
+00:14:37,300 --> 00:14:41,160
+الآن لو كان الـ norm للـ X أزرع من واحد بنضمن لكم
+
+215
+00:14:41,160 --> 00:14:43,980
+E to minus X inversely أشماله exist و يسوي و كده
+
+216
+00:14:43,980 --> 00:14:46,540
+ده اللي علاقة في اللي حكيناها قبل شوية على الطيف و
+
+217
+00:14:46,540 --> 00:14:52,500
+مطيف و كده طبعا بصير استخدامات لها الان نيجي
+
+218
+00:14:52,500 --> 00:14:56,000
+نبرهنها نبرهن النظر يعني البرهن السهل يعني مش صعب
+
+219
+00:14:56,000 --> 00:15:00,880
+since A is a Banach algebra and X element in A then
+
+220
+00:15:00,880 --> 00:15:05,610
+for any J element in N we have norm X to the J اللي
+
+221
+00:15:05,610 --> 00:15:09,670
+هو بيساوي بيساوي اللي هو Normal X to the J بيساوي
+
+222
+00:15:09,670 --> 00:15:17,250
+Normal X في X اسم J minus 1 أصغر أوي يساوي Normal
+
+223
+00:15:17,250 --> 00:15:22,090
+X في Normal من التالي دالكم نقصوا من هذا وانزلوا
+
+224
+00:15:22,090 --> 00:15:24,810
+وانزلوا وانزلوا لما تحصلوا أصغر يساوي Normal X to
+
+225
+00:15:24,810 --> 00:15:28,390
+the من to the J إذا صار عندي Normal X to the J
+
+226
+00:15:28,390 --> 00:15:33,750
+أصغر أوي ساوي Normal X الكل to the J الآن
+
+227
+00:15:35,800 --> 00:15:40,040
+عندي ماعطيني norm ال X أشماله أصغر من واحد صح ولا
+
+228
+00:15:40,040 --> 00:15:43,280
+لأ؟ مدام norm ال X أصغر من واحد يعني كل element من
+
+229
+00:15:43,280 --> 00:15:46,960
+هذوله ال norm هو أصغر من واحد إذاً هذه صارت ال
+
+230
+00:15:46,960 --> 00:15:50,800
+series converge ال real numbers هذه إذا صارت هذه
+
+231
+00:15:50,800 --> 00:15:53,460
+ال series converge because norm ال X أصغر من واحد
+
+232
+00:15:54,320 --> 00:15:57,660
+بالتالي بالـ Comparison Twist Normal X to the J
+
+233
+00:15:57,660 --> 00:16:00,960
+هذي أصغر أو ساوى هذي، هذي الـ Series Converged،
+
+234
+00:16:00,960 --> 00:16:03,060
+إذا من ببقى ولا إي شمالها، اللي أصغر منها إي
+
+235
+00:16:03,060 --> 00:16:06,340
+شمالها Converged، إذا صارت عندي Normal X to the J
+
+236
+00:16:06,340 --> 00:16:11,140
+Converged That means إيش هذه اللي هي عبارة عن اللي
+
+237
+00:16:11,140 --> 00:16:15,120
+هو لو أخدنا اللي هو J بصفر نعتبرها إيه شمالها اللي
+
+238
+00:16:15,120 --> 00:16:21,980
+هو قبلها ال normal X to the J هذي converts يعني
+
+239
+00:16:21,980 --> 00:16:26,130
+absolutely convergent إذا this means that either
+
+240
+00:16:26,130 --> 00:16:29,510
+summation of X أشماله converges absolutely يعني
+
+241
+00:16:29,510 --> 00:16:33,230
+اللي جوا صارت هاد converges يعني absolutely
+
+242
+00:16:33,230 --> 00:16:36,950
+convergent مين ال absolutely convergent هاد؟ لأنه
+
+243
+00:16:36,950 --> 00:16:39,770
+بدون absolute value أو بدون نهار مين بتطلع ال
+
+244
+00:16:39,770 --> 00:16:42,530
+summation X to the JJ من صفر إلى مين إلى ما لليها
+
+245
+00:16:42,530 --> 00:16:46,010
+يعني اللي في الواقع هي هاد إذا صارت هاد عبارة عن
+
+246
+00:16:46,010 --> 00:16:50,780
+أشماله converges absolutely واحنا كنا نقول مدام
+
+247
+00:16:50,780 --> 00:16:54,960
+complete however A is complete إذا ال summation
+
+248
+00:16:54,960 --> 00:16:58,140
+إيش ماله أنا absolutely convergent إيزا إيش مالها؟
+
+249
+00:16:58,140 --> 00:17:01,060
+convergent أخدنا هذا الكلام أنا absolutely
+
+250
+00:17:01,060 --> 00:17:04,480
+convergent is convergent في ال complete اللي هو
+
+251
+00:17:04,480 --> 00:17:08,520
+non dismissive إذا صار عندى بما أن A is complete
+
+252
+00:17:08,520 --> 00:17:11,260
+وهذه absolutely convergent إذا هذه إيش مالها؟ is
+
+253
+00:17:11,260 --> 00:17:15,100
+convergent إذا نفترض إن هذه ال summation إيش
+
+254
+00:17:15,100 --> 00:17:16,760
+بساوي؟ بساوي
+
+255
+00:17:22,050 --> 00:17:27,790
+اللي هنطلعه لو جينا ضربنا E⁻X اللي احنا متوقعين
+
+256
+00:17:27,790 --> 00:17:34,140
+انها تكون انفر السبحة هو المجموع لو ضربناها في E في
+
+257
+00:17:34,140 --> 00:17:38,940
+X X أربعة إلى خلال X N هادي في هادي و هادي في هادي
+
+258
+00:17:38,940 --> 00:17:43,720
+نفس الشيء لأنه commutative و يساوي و ضربوهم في بعض
+
+259
+00:17:43,720 --> 00:17:47,180
+و هيت cancelهم كلهم بس هيبقى الأول term و آخر term
+
+260
+00:17:47,180 --> 00:17:51,140
+بيصير E to the minus X N زائد واحد إذا صار عندي
+
+261
+00:17:51,140 --> 00:17:56,340
+هذا المقدار بيساوي هذا المقدار و أدوا N إلى مانا
+
+262
+00:17:56,340 --> 00:18:00,600
+نهاية الـ N إلى مانا نهاية بيصير عندي هذا بيصير
+
+263
+00:18:00,600 --> 00:18:05,460
+summation صح؟ لما نروح للمعنى نهائي بيصير هذا بيصير
+
+264
+00:18:05,460 --> 00:18:12,670
+E⁻X في S هذابساوة S فيه to the X ويساوي من ال E
+
+265
+00:18:12,670 --> 00:18:16,950
+هذا هيروح لمين لل Zero لأن Normal X أشماله أصغر من
+
+266
+00:18:16,950 --> 00:18:20,550
+واحد إذا صار عندي هذا في هذا بساوية هذا في هذا
+
+267
+00:18:20,550 --> 00:18:24,410
+يعني صار عندي هذا هو ال inverse لهذا يعني بمعنى
+
+268
+00:18:24,410 --> 00:18:29,350
+أخر S بتساوي E to the minus X inverse ومن ثم ال S
+
+269
+00:18:29,350 --> 00:18:33,130
+هي عبارة عن هذا المقدار يعني صار هذا المقدار هو E
+
+270
+00:18:33,130 --> 00:18:38,120
+to the minus X inverse وهو المطلوب نأتي الآن في الـ
+
+271
+00:18:38,120 --> 00:18:40,360
+Theorem of Invertible Elements اطلع على فوق، شيء
+
+272
+00:18:40,360 --> 00:18:47,200
+بسيط Let A be a complex Banach algebra with identity E
+
+273
+00:18:48,110 --> 00:18:52,450
+Then D، The set of all invertible elements of A is
+
+274
+00:18:52,450 --> 00:18:56,690
+an open subset of A يعني الآن لو كانت A كمبلكس بنخ
+
+275
+00:18:56,690 --> 00:19:02,750
+الجيبرا بيصير مجموعة .. مجموعة .. كل ال invertible
+
+276
+00:19:02,750 --> 00:19:07,410
+elements لA هتكون open subset من مين؟ من اللي هي
+
+277
+00:19:07,410 --> 00:19:11,920
+مين؟ من الـA الآن بناء على الهنس ده subset M بساوة A
+
+278
+00:19:11,920 --> 00:19:16,040
+-G اللي هي مكملتها هتكون of all non-invertible
+
+279
+00:19:16,040 --> 00:19:20,120
+elements A أشماله is closed إذن the set of all non
+
+280
+00:19:20,120 --> 00:19:24,880
+-invertible elements من الـA closed بينما the set 
+
+281
+00:19:24,880 --> 00:19:27,980
+of all of اللي هو ده خلّيني أقول invertible
+
+282
+00:19:27,980 --> 00:19:31,520
+elements A شمالها is an open set وهذا إيه معناه
+
+283
+00:19:31,520 --> 00:19:35,460
+بما يتعلق بـ Pro وLambda مش مشكلة اطلع لفوق خلاص
+
+284
+00:19:35,460 --> 00:19:36,760
+مانعش البرهان اطلع لفوق
+
+285
+00:19:39,650 --> 00:19:44,930
+أطلع لفوق، أطلع لفوق، لأ خلّينا عند النظرية الـ
+
+286
+00:19:44,930 --> 00:19:49,190
+Spectrum اللي هو اللي سمناه اللي هو الطيف لأن let 
+
+287
+00:19:49,190 --> 00:19:52,970
+A be a complex algebra with identity then for
+
+288
+00:19:52,970 --> 00:19:57,790
+any X element in A هذا إعلان كبير ال Spectrum
+
+289
+00:19:57,790 --> 00:20:02,410
+Sigma of X is compact ال Sigma of X يعني is a
+
+290
+00:20:02,410 --> 00:20:06,860
+bounded closed set الـ sigma of X طبعاً subset من C
+
+291
+00:20:06,860 --> 00:20:10,080
+و الـ compactness بيساوي الـ closed و الـ bounded
+
+292
+00:20:10,080 --> 00:20:13,260
+في الـ C و في الـ R اللي يعني ال spectrum C of X
+
+293
+00:20:13,260 --> 00:20:19,780
+is a compact و ال spectral radius satisfies اللي
+
+294
+00:20:19,780 --> 00:20:22,320
+هو ال spectral radius، انزلوا خلّيني أعرفكم ال
+
+295
+00:20:22,320 --> 00:20:26,600
+spectral radius على السريع ال spectral radius اللي
+
+296
+00:20:26,600 --> 00:20:30,530
+هو بنسميه R sigma of X ال spectral radius للـ X هو
+
+297
+00:20:30,530 --> 00:20:33,530
+عبارة عن R Sigma of X بيساوي الـ Supremum لكل الـ
+
+298
+00:20:33,530 --> 00:20:37,010
+Absolute Value لللمضة اللي موجودة في مين في Sigma
+
+299
+00:20:37,010 --> 00:20:41,990
+of X إذا الـ Spectral Radius إلها اللي هو أو
+
+300
+00:20:41,990 --> 00:20:46,170
+خلّيني أقول نصف قطر الطيف اللي هو عبارة عن R Sigma
+
+301
+00:20:46,170 --> 00:20:49,290
+of X بيساوي الـ Supremum للمضة Lambda Element in
+
+302
+00:20:49,290 --> 00:20:53,590
+Sigma of X اللي الآن بيقولني في النظرية إن الـ
+
+303
+00:20:53,590 --> 00:20:59,760
+Sigma of X is compact ومش هيكوالـ Spectral Radius
+
+304
+00:20:59,760 --> 00:21:04,840
+تراحة لن يتجاوز نورمين Norm of X لأن أصلا هي كلها
+
+305
+00:21:04,840 --> 00:21:08,600
+محصورة في داخل الصندوق لأنها Closed و Bounded ماشي
+
+306
+00:21:08,600 --> 00:21:11,660
+الحال إذا الـ Spectral Radius إلها R Sigma اللي هو
+
+307
+00:21:11,660 --> 00:21:14,920
+الـ Supermum عليها على كل اللي في الـ Sigma اللي
+
+308
+00:21:14,920 --> 00:21:18,000
+هو R Sigma of X أزاهر سواء Normal X برضه البرنامج
+
+309
+00:21:18,000 --> 00:21:24,310
+ده شيء أطلع لفوق نيجي الآن للإعلان المهم الآخر اللي
+
+310
+00:21:24,310 --> 00:21:30,270
+هو الـ Spectrum Sigma of X is a non-empty set هذا
+
+311
+00:21:30,270 --> 00:21:33,690
+إعلان كبير Sigma of X لا تساوي Phi under the
+
+312
+00:21:33,690 --> 00:21:37,450
+assumption of the preceding theorem اللي هو اللي
+
+313
+00:21:37,450 --> 00:21:41,930
+في البنخ الجيبرا Sigma of X لا تساوي Phi و
+
+314
+00:21:41,930 --> 00:21:45,850
+consequently is a non-empty set و consequently بناء عليه
+
+315
+00:21:45,850 --> 00:21:53,130
+اللي هو الآن فيه كمان الخاصية مزام الـ Sigma of X
+
+316
+00:21:54,070 --> 00:21:58,750
+الـ is closed الـ sigma of X is closed الـ sigma
+
+317
+00:21:58,750 --> 00:22:01,090
+of X is closed الـ sigma of X is closed الـ sigma 
+
+318
+00:22:01,090 --> 00:22:01,490
+of X is closed الـ sigma of X is closed الـ sigma
+
+319
+00:22:01,490 --> 00:22:01,510
+of X is closed الـ sigma of X is closed الـ sigma
+
+320
+00:22:01,510 --> 00:22:01,930
+of X is closed الـ sigma of X is closed الـ sigma
+
+321
+00:22:01,930 --> 00:22:01,950
+of X is closed الـ sigma of X is closed الـ sigma
+
+322
+00:22:01,950 --> 00:22:01,990
+of X is closed الـ sigma of X is closed الـ sigma
+
+323
+00:22:01,990 --> 00:22:04,070
+of X is closed الـ sigma of X is closed الـ sigma
+
+324
+00:22:04,070 --> 00:22:10,770
+of X is closed الـ sigma of X is closed الـ sigma
+
+325
+00:22:18,120 --> 00:22:24,660
+هذا closed و bounded الـ Rovix هو المنطلق برا هو
+
+326
+00:22:24,660 --> 00:22:31,680
+اللي هو unbounded و open set فانجسمت
+
+327
+00:22:31,680 --> 00:22:35,400
+اللي هي ال complex plane إلى جزئين جزء اللي هو
+
+328
+00:22:35,400 --> 00:22:38,040
+sigma rovix اللي هي عناصر الطرف اللي هي closed و
+
+329
+00:22:38,040 --> 00:22:41,880
+bounded و اللي هو اللي فوق اللي هي open set و
+
+330
+00:22:41,880 --> 00:22:47,370
+unbounded set وبارك الله فيكم والسلام عليكم ورحمة
+
+331
+00:22:47,370 --> 00:22:48,270
+الله وبركاته
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/zFznbPjt0NA_postprocess.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/zFznbPjt0NA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9bab9c6d928ba2f8940a673c76d7c2c585a699b3
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/zFznbPjt0NA_postprocess.srt
@@ -0,0 +1,1324 @@
+1
+00:00:05,260 --> 00:00:08,260
+بسم الله الرحمن الرحيم الحمد لله رب العالمين و
+
+2
+00:00:08,260 --> 00:00:11,100
+الصلاة والسلام على سيده المرسلين سيدنا محمد وعلى
+
+3
+00:00:11,100 --> 00:00:15,220
+آله وصحبه الجماعين هذه هي المحاضرة رقم 36 وهي
+
+4
+00:00:15,220 --> 00:00:19,500
+المحاضرة الأخيرة في مساق تحليل اقتران او تحليل
+
+5
+00:00:19,500 --> 00:00:25,100
+دالي طلاب طالبات الجامعة الإسلامية ماجستير
+
+6
+00:00:25,100 --> 00:00:30,690
+الرياضياتالفكرة إننا بدنا ناخد بس فكرة عن اللي هو
+
+7
+00:00:30,690 --> 00:00:35,850
+مفهوم البنخ Algebra لإنه له تطبيقات وله استعمالات
+
+8
+00:00:35,850 --> 00:00:41,950
+كبيرة لو حد يعني حاب أنه يشتغل فيه أو خلّيني أقول
+
+9
+00:00:41,950 --> 00:00:48,110
+ينطلق فيه إلى الأمام يعني بيكون فيه له فكرة في
+
+10
+00:00:48,110 --> 00:00:48,810
+الموضوع
+
+11
+00:00:51,440 --> 00:00:55,440
+نبدأ في definition يعني هو خليط بين الجبر الحديث
+
+12
+00:00:55,440 --> 00:01:00,240
+وبين اللي هو أو في أحيانًا نقول ملحه اللي هو الملح
+
+13
+00:01:00,240 --> 00:01:03,640
+الأولاني كنا نحكي عن الجبر الخطي هو ملح ال
+
+14
+00:01:03,640 --> 00:01:07,490
+functionملح أخر خلّيني أقول للبنخ Algebra اللي هو
+
+15
+00:01:07,490 --> 00:01:09,970
+يعني أو خلّيني أقول إيه علاقة فيه اللي هو ال Ring
+
+16
+00:01:09,970 --> 00:01:15,390
+Theory فيه شغل في ال .. في ال ideals و .. و كل
+
+17
+00:01:15,390 --> 00:01:18,930
+أسماء اللي .. اللي بتتعلق بال .. بال ideals و ال
+
+18
+00:01:18,930 --> 00:01:21,810
+modules و .. و الاخره اللي موجودة في ال rings و
+
+19
+00:01:21,810 --> 00:01:24,770
+موجودة كانت موجودة في البنخ Algebra بس هنا زيادة
+
+20
+00:01:24,770 --> 00:01:29,870
+شوية انه .. انه بيعطيه شوية يعني ال .. ال .. ال
+
+21
+00:01:29,870 --> 00:01:34,350
+ring ما هي على عمليتينهنا الآن في هي جاعدة على
+
+22
+00:01:34,350 --> 00:01:37,150
+vector space اللي هو scalar multiplication و
+
+23
+00:01:37,150 --> 00:01:39,990
+vector addition بالاضافة بيصير لان vector
+
+24
+00:01:39,990 --> 00:01:42,470
+multiplication اللي هي عملية ضرب زي ما عملية ضرب
+
+25
+00:01:42,470 --> 00:01:45,250
+اللي وين اللي في ال ring وزيادة على هيك أنه في
+
+26
+00:01:45,250 --> 00:01:48,990
+عليه norm ال norm تبعه نقع norm of this space صح
+
+27
+00:01:48,990 --> 00:01:51,410
+لكن norm of this space وفيه كمان شغل أخر على ال
+
+28
+00:01:51,410 --> 00:01:54,270
+norm of this space أنه بدهو ال norm تبع البنخ
+
+29
+00:01:54,270 --> 00:01:57,170
+الجيبرة بدهو يحقق norm ال x في y أصغر شهره norm ال
+
+30
+00:01:57,170 --> 00:02:01,060
+x في norm ال yلأنه في الاصل في الـ Normed Space
+
+31
+00:02:01,060 --> 00:02:03,720
+العادى مش شرط تكون فيه عملية ضرب بس ان صار في
+
+32
+00:02:03,720 --> 00:02:06,620
+عملية ضرب لأن هناك العالم اللي بنشتغل عليه vector
+
+33
+00:02:06,620 --> 00:02:08,680
+space ومش فيه هناك غير عملية scalar multiplication
+
+34
+00:02:08,680 --> 00:02:13,980
+و vector addition فاللي هو مش وارد كان عملية الضرب
+
+35
+00:02:13,980 --> 00:02:18,660
+و norm لل X في Y مثلا مش وارد كان زمان هأنا بدي
+
+36
+00:02:18,660 --> 00:02:23,730
+أصبح وارد و بدي أن أتعالج معاكتان شوفش اللي بقوله7
+
+37
+00:02:23,730 --> 00:02:26,990
+.6.1 Definition of Algebra A لأننا نعرف الجيبرا
+
+38
+00:02:26,990 --> 00:02:32,830
+بدون ما نحطناهم لسه Algebra A over a vector over a
+
+39
+00:02:32,830 --> 00:02:36,730
+field K is a vector space إذا نرسى الدورة الشمالة
+
+40
+00:02:36,730 --> 00:02:42,060
+vector space عالميا على اللي هو scalar field Kover
+
+41
+00:02:42,060 --> 00:02:46,320
+k such that for all x y element a a unique product
+
+42
+00:02:46,320 --> 00:02:49,620
+ده انا عرفنا من a product اللي هم بتضعف لل vector
+
+43
+00:02:49,620 --> 00:02:52,100
+addition و ال scale of multiplication عرفنا
+
+44
+00:02:52,100 --> 00:02:55,100
+product x و y و الموجودة في ال I في ليه؟ is
+
+45
+00:02:55,100 --> 00:02:58,140
+defined with the properties mainly اللي هي بتحقق
+
+46
+00:02:58,140 --> 00:03:02,510
+اللي هي الخواص التاليةإن X في Y في Z بيساوي الـ
+
+47
+00:03:02,510 --> 00:03:06,770
+associativity تبع تليجيه ده الآن التوزيع بين عملية
+
+48
+00:03:06,770 --> 00:03:10,850
+الـ vector addition وبين الدرب X في Y زي Z بيساوي
+
+49
+00:03:10,850 --> 00:03:14,670
+X في Y زي X في Z برضه بدها تربط بين ال scalar
+
+50
+00:03:14,670 --> 00:03:16,850
+multiplication وال multiplication تبعهم أو ال
+
+51
+00:03:16,850 --> 00:03:20,360
+productألفة في X و Y لـ associativity اللي هو
+
+52
+00:03:20,360 --> 00:03:24,460
+أشمالها واردة أو خلّيني أقول متحققة هذا الكلام لكل
+
+53
+00:03:24,460 --> 00:03:28,460
+X و Y والألفة element N هو الـK طبعا اللي هو
+
+54
+00:03:28,460 --> 00:03:31,020
+التوزيع من اليمين ومن الشمال زي ما انتوا ملاحظين
+
+55
+00:03:31,020 --> 00:03:35,160
+الان A is called an algebra .. هذي ال algebra A is
+
+56
+00:03:35,160 --> 00:03:38,940
+called an algebra with unity .. with unity اللي هو
+
+57
+00:03:38,940 --> 00:03:42,180
+with identity if there exist any element in A such
+
+58
+00:03:42,180 --> 00:03:45,150
+ذات اللي بتعرفوهE في X بيساوي X في E بيساوي A
+
+59
+00:03:45,150 --> 00:03:48,230
+إشمال و X لكل X و Y موجودة في الـ A إذا صارت عبارة
+
+60
+00:03:48,230 --> 00:03:52,790
+عن اللي هي associative موجودة طبعا و closed this
+
+61
+00:03:52,790 --> 00:03:56,570
+موجودة أكيد اللي هو لكل X و Y في عندك اللي هو X و
+
+62
+00:03:56,570 --> 00:03:59,450
+Y اللي بتناقصها تتعامل ل closed إذا صارت closed
+
+63
+00:03:59,450 --> 00:04:03,970
+وصارت associative وصار عند A إشمالها ال identity
+
+64
+00:04:03,970 --> 00:04:10,290
+موجودة A is called اللي هو إشمالها algebra with
+
+65
+00:04:10,290 --> 00:04:15,840
+unityاللي هم بنسميها commutative algebra إذا كان a
+
+66
+00:04:15,840 --> 00:04:20,880
+في b إيش بيساوي بأي for all a و b element من مين
+
+67
+00:04:20,880 --> 00:04:25,060
+in a أسبب algebra of a بنفس اللي .. اللي .. اللي
+
+68
+00:04:25,060 --> 00:04:29,740
+.. اللي هو الغنطق تبع ال .. اللي هو ال subgroupالـ
+
+69
+00:04:29,740 --> 00:04:32,440
+Sub vector space الـ Sub ring كله يجب أن يحافظ
+
+70
+00:04:32,440 --> 00:04:38,000
+عالمياً على أن يكون أصلاً مثله بس جزء صغير منه لأن
+
+71
+00:04:38,000 --> 00:04:41,080
+كيف يجب أن يحافظها؟ سبق الجيبرا وفقاه وعبارة عن is
+
+72
+00:04:41,080 --> 00:04:43,620
+a vector sub space of V هذه أول واحدة لذلك نخلصها
+
+73
+00:04:43,620 --> 00:04:46,220
+من قصة الـ scalar multiplication و ال vector
+
+74
+00:04:46,220 --> 00:04:49,780
+addition الآن ماذا قال؟ that is closed under the
+
+75
+00:04:49,780 --> 00:04:52,680
+productاللي هو إيش؟ عشان يضمن إنه صار الجذبرة
+
+76
+00:04:52,680 --> 00:04:56,180
+closed under the product وباقى الأمور ما هي متحققة
+
+77
+00:04:56,180 --> 00:04:58,320
+في الكبير ده راح تكون متحققة في الصغير اللي هي ال
+
+78
+00:04:58,320 --> 00:05:02,180
+associativity والتوزيع والأخرين الآن if a has an
+
+79
+00:05:02,180 --> 00:05:06,280
+identity then the identity أشماله is unique وهذا
+
+80
+00:05:06,280 --> 00:05:08,900
+أثباته زي ما بنثبت في ال ring العادي وفي ال group
+
+81
+00:05:08,900 --> 00:05:11,940
+العادي اللي هو أثبات ال identity الوحيد من اللي هي
+
+82
+00:05:11,940 --> 00:05:17,500
+الخواص المعتاد طيب ندى الآن هذا دعنا نقول تحديث
+
+83
+00:05:17,500 --> 00:05:18,840
+جبري بحت
+
+84
+00:05:21,740 --> 00:05:25,440
+الآن جاملها The product in and on this algebra A
+
+85
+00:05:25,440 --> 00:05:28,700
+is a continuous mapping of A cross A onto mean
+
+86
+00:05:28,700 --> 00:05:32,740
+onto A عملية الضرب عملية إيهاش عملية متصلة بين A
+
+87
+00:05:32,740 --> 00:05:36,200
+cross A لعند مين لعند الـA واثبتها واثبتها يعني
+
+88
+00:05:36,200 --> 00:05:39,880
+إيه سهل هذا الآن طبعا مش هنقدر نحكي فيه إلا إذا
+
+89
+00:05:39,880 --> 00:05:43,260
+نحكي عن نارلأنه فيه اتصال يعني ممكن نحكي عن الـ
+
+90
+00:05:43,260 --> 00:05:48,220
+topology عشان هيك بيستلزم الحديث على اللي هو الـ
+
+91
+00:05:48,220 --> 00:05:50,740
+algebra أن يكون non-algebra، طبعا ماهي الـ non
+
+92
+00:05:50,740 --> 00:05:54,680
+-algebra؟ الـ non-algebra ببساطة non-algebra A is
+
+93
+00:05:54,680 --> 00:05:55,780
+a non-disbase
+
+94
+00:05:59,000 --> 00:06:03,280
+which is an algebra هاي اتنين such that norm ال X
+
+95
+00:06:03,280 --> 00:06:06,740
+في Y ايش بده يصير اصغر يساوي norm X في norm Y لكل
+
+96
+00:06:06,740 --> 00:06:10,460
+X وY element in A هذا اللي هو بيعمل ليه normed
+
+97
+00:06:10,460 --> 00:06:16,660
+algebra الان if A has identityإذا الـ norm الـ E
+
+98
+00:06:16,660 --> 00:06:21,380
+حيث أننا سنسأل أننا عارفه إيش بيساوي واحد و اللي
+
+99
+00:06:21,380 --> 00:06:25,860
+هي بيصير عبارة عن normed algebra with identity لو
+
+100
+00:06:25,860 --> 00:06:29,200
+كان ال normed algebra with identity is complete
+
+101
+00:06:29,200 --> 00:06:32,280
+يعني ال norm بيعطينا اللي هو of recursive sequence
+
+102
+00:06:32,280 --> 00:06:37,700
+converge بنسميه بنف ألجيبرا إذا the بنف ألجيبرا A
+
+103
+00:06:37,700 --> 00:06:40,740
+is a complete normed algebra which is a complete
+
+104
+00:06:40,910 --> 00:06:44,970
+which which which is complete considered as a
+
+105
+00:06:44,970 --> 00:06:51,770
+normless space طيب نقول إن هذا product اللي هي ال
+
+106
+00:06:51,770 --> 00:06:55,530
+X في Y عملية الضرب اللي هي في ال A هي عبارة عن a
+
+107
+00:06:55,530 --> 00:06:59,290
+continuous mapping من A cross A لعند مين لعندي
+
+108
+00:06:59,290 --> 00:07:00,370
+يعني F
+
+109
+00:07:03,260 --> 00:07:09,160
+من A cross A لعند الـ A defined by F of A و B
+
+110
+00:07:09,160 --> 00:07:15,020
+بتساوي A في B هذه أشمالها is a continuous function
+
+111
+00:07:15,020 --> 00:07:18,060
+وهو الهنط اللي في الكتاب سهل لو على طول بتطلوها و
+
+112
+00:07:18,060 --> 00:07:22,020
+برا لعندي في الترخيص التاني أنا بس احنا لضيق الوقت
+
+113
+00:07:22,020 --> 00:07:27,000
+خليه لكم تطلع عليه نيجي الأن ناخد أمثلة اطلع لفوق
+
+114
+00:07:27,000 --> 00:07:32,650
+أمثلة على اللي هو normed algebraThe real line هو
+
+115
+00:07:32,650 --> 00:07:37,570
+فيلد الـ real line هو الكمبليكس فيلد يعني كل عملية
+
+116
+00:07:37,570 --> 00:07:41,330
+فيه موجودة سواء ضرب أو وده كده The real line and
+
+117
+00:07:41,330 --> 00:07:44,010
+the complex plane C are commutative
+
+118
+00:07:44,010 --> 00:07:49,890
+كمممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممم
+
+119
+00:07:50,250 --> 00:07:54,450
+الان اللي هو الـR والـC are commutative بنخ
+
+120
+00:07:54,450 --> 00:07:57,870
+الـgebra وضع identity A بالساوية واحدة إيش عملية
+
+121
+00:07:57,870 --> 00:08:03,290
+ال vector addition الجمع العادى؟ إيش عملية ال
+
+122
+00:08:03,290 --> 00:08:05,270
+scalar multiplication ال field اللي عليه في
+
+123
+00:08:05,270 --> 00:08:09,690
+عناصره؟ إيش عملية الدرب اللي هي الدرب العادى اللي
+
+124
+00:08:09,690 --> 00:08:19,540
+عليه؟بناخد مثال آخر space C of A وB خدناه is الهو
+
+125
+00:08:19,540 --> 00:08:25,360
+the space of all continuous functions is
+
+126
+00:08:25,360 --> 00:08:28,980
+a commutative بنخ ألجيبرا under the maximum norm
+
+127
+00:08:28,980 --> 00:08:34,340
+is a commutative بنخ ألجيبرا with identity E بساوي
+
+128
+00:08:34,340 --> 00:08:38,940
+مين؟ بساوي الهو إيش؟ بساوي واحد اللي هي ال
+
+129
+00:08:38,940 --> 00:08:44,220
+constant functionthe product x y be defined as
+
+130
+00:08:44,220 --> 00:08:49,040
+usual x y of t ال functions هي وكانت بنضرب point
+
+131
+00:08:49,040 --> 00:08:53,160
+twice يعني بيسوى x of t في مين في y of t for all t
+
+132
+00:08:53,160 --> 00:08:56,220
+in a و b طبعا احنا نعرف ان ذكريات ده continuous و
+
+133
+00:08:56,220 --> 00:08:58,640
+اذا كنت نفسي حصلت ضرب ايش هيكون continuous اكيد
+
+134
+00:08:58,640 --> 00:09:04,320
+لان and the norm is the maximum normالان هذا كله
+
+135
+00:09:04,320 --> 00:09:09,540
+بيعمل ليه ايش ماله كميوتيتف بنخ ألجيبرا اذا اللي
+
+136
+00:09:09,540 --> 00:09:13,720
+هي اللي على اللي هي الضرب العادى هيطلع كميوتيتف
+
+137
+00:09:13,720 --> 00:09:17,340
+بنخ ألجيبرا the subspace of c of a و b consisting
+
+138
+00:09:17,340 --> 00:09:22,980
+of all polynomials is a commutative normed algebra
+
+139
+00:09:22,980 --> 00:09:26,020
+انا بقول لها مش complete هذا ال polynomial مش
+
+140
+00:09:26,020 --> 00:09:30,820
+complete with identity ايه بتساوي واحدأطلع لفوق
+
+141
+00:09:30,820 --> 00:09:36,940
+التفاصيل اللي هي الخواص كلها بتتحقق space P of X P
+
+142
+00:09:36,940 --> 00:09:40,980
+of X اللي هو عبارة عن من the space of all bounded
+
+143
+00:09:40,980 --> 00:09:45,580
+linear operators من X لعند ال X ماشي لإن ده ما
+
+144
+00:09:45,580 --> 00:09:49,420
+كتبناش من X ل Y ماعرفش منه قصود من X لمنين ل X the
+
+145
+00:09:49,420 --> 00:09:51,860
+banach space P of X of all bounded linear
+
+146
+00:09:51,860 --> 00:09:59,350
+operators onبنخ X نفسه X نفسه إيش ماله اله الـ non
+
+147
+00:09:59,350 --> 00:10:04,250
+-zero بنخ space الـ B of X اللي هي the space of
+
+148
+00:10:04,250 --> 00:10:08,150
+all bounded linear operators is بنخ ألجيبرا with
+
+149
+00:10:08,150 --> 00:10:14,130
+identity I اللي هال multiplication هنا اللي هو
+
+150
+00:10:14,130 --> 00:10:18,770
+عبارة عن composition of operatorsيعني عملية الضرب
+
+151
+00:10:18,770 --> 00:10:22,790
+اللي بنعرفها على الـPX وPXH مالها عبارة عن الـ
+
+152
+00:10:22,790 --> 00:10:25,350
+composition و الـ composition need not to be
+
+153
+00:10:25,350 --> 00:10:28,390
+commutative زي ما انتوا عارفينها إذاً هذا مثال على
+
+154
+00:10:28,390 --> 00:10:33,750
+P of X is a non commutative بنخ ألجيبرا unless ال
+
+155
+00:10:33,750 --> 00:10:41,690
+dimension للـXH بساوي بساوي واحد اللي بعده الان
+
+156
+00:10:41,690 --> 00:10:42,770
+definition
+
+157
+00:10:44,850 --> 00:10:48,450
+بنعرف الشو معنات طبعاً ده يعني خلّينا اللي عارفه
+
+158
+00:10:48,450 --> 00:10:53,290
+مش هنستعمله لإنه مش هيكون فيه نوجت لنستعمل الان
+
+159
+00:10:53,290 --> 00:10:58,730
+element x in an algebraالـ A is said to be
+
+160
+00:10:58,730 --> 00:11:01,550
+invertible ترفو هذا invertible إيش معناه
+
+161
+00:11:01,550 --> 00:11:05,430
+invertible if it has an inverse in A اللي واش
+
+162
+00:11:05,430 --> 00:11:08,350
+معناته في X inverse بحيث انه X في X inverse بيساوي
+
+163
+00:11:08,350 --> 00:11:11,150
+X inverse في X أش بيساوي ال identity اللي لإن في
+
+164
+00:11:11,150 --> 00:11:14,070
+هذا الحالة بيسمي ال element X إيش ماله is
+
+165
+00:11:14,070 --> 00:11:17,930
+invertible يعني فيه انه inverse with respect to
+
+166
+00:11:17,930 --> 00:11:21,490
+this operation اللي هي ال product if X element in
+
+167
+00:11:21,490 --> 00:11:26,600
+A is SX element in A is invertible then its
+
+168
+00:11:26,600 --> 00:11:28,160
+inverse is ماهي الوحيد
+
+169
+00:11:34,080 --> 00:11:37,740
+الان نيجي اللي هو نتعرف علي حاجة اسمها الـ
+
+170
+00:11:37,740 --> 00:11:40,820
+Resolvent والاسبكترام وهذا قصص طويلة ال Resolvent
+
+171
+00:11:40,820 --> 00:11:44,480
+والاسبكترام لأنه هم .. يعني ال .. ال .. ال .. ال
+
+172
+00:11:44,480 --> 00:11:47,720
+.. الواحدة اسمها اللي هي ال Sigma الطيف .. الطيف
+
+173
+00:11:47,720 --> 00:11:50,940
+.. الطيف العنصر .. الطيف العنصر يعني احنا بنقول
+
+174
+00:11:50,940 --> 00:11:56,420
+الواحد يعني الخيال تبع ال .. تبع الشخص يعني بيعطي
+
+175
+00:11:56,420 --> 00:12:01,790
+مؤشر على الشخصالأثر تبع الشخص بيعطي .. بيعطي ..
+
+176
+00:12:01,790 --> 00:12:07,630
+خلّيني أقول مؤشر على الشخص الان طيف العنصر أحيانا
+
+177
+00:12:07,630 --> 00:12:10,710
+إحنا ما نعرفش العنصر نفسه لكن طبعا هذا الكلام
+
+178
+00:12:10,710 --> 00:12:13,990
+حقيقة يعني في ال .. في ال .. في ال .. في ال .. في
+
+179
+00:12:13,990 --> 00:12:19,330
+ال .. اللي هو العنصر الجيبرا أو الجيبرا طيف العنصر
+
+180
+00:12:20,760 --> 00:12:24,320
+بيعطيك كثير من خواص العنصر عشان هيك الناس بتهتم
+
+181
+00:12:24,320 --> 00:12:28,520
+بالطيف أو اللي هو ال spectrum وحتى ال resolvent
+
+182
+00:12:28,520 --> 00:12:32,340
+اللي هي ال set إيش اللي بقوله؟ إيش اللي بقوله
+
+183
+00:12:32,340 --> 00:12:35,180
+قاعد؟ let A بيكون complex منخ الجيبرا with
+
+184
+00:12:35,180 --> 00:12:40,880
+identity then the resolvent set of A is row of A
+
+185
+00:12:40,880 --> 00:12:48,790
+إيش row of A هذه؟الآن وكأنه بيحول الحديث من عناصر
+
+186
+00:12:48,790 --> 00:12:51,990
+في الـA اللي هي عناصر البنخ الـAlgebra إلى عناصر
+
+187
+00:12:51,990 --> 00:12:55,690
+في الـscalar field والحكي على الـscalar field ألطف
+
+188
+00:12:55,690 --> 00:12:59,110
+بظل ألطف من مين من البنخ الـAlgebra وتعقيدات وكيف
+
+189
+00:12:59,110 --> 00:13:02,310
+عناصر وكيف كذا وكيف كذا ودكتبات وإلى آخرية الـRow
+
+190
+00:13:02,310 --> 00:13:04,990
+of A هي عبارة عن كل اللمضة اللي في element in C
+
+191
+00:13:04,990 --> 00:13:08,910
+such that λمضة E minus A inverse E أشماله exist in
+
+192
+00:13:08,910 --> 00:13:15,150
+A هذه الـset اللي بنسميها الـRow of Aالمكملة لها
+
+193
+00:13:15,150 --> 00:13:18,870
+المكملة لها بنسميها الـ Spectrum اللي هو الطيب الـ
+
+194
+00:13:18,870 --> 00:13:22,210
+Spectrum set of A is Sigma of A بساوة C minus Rho
+
+195
+00:13:22,210 --> 00:13:26,230
+of A Any Lambda element in Sigma of A is called a
+
+196
+00:13:26,230 --> 00:13:29,150
+spectral value بنسميها إيه اشمالها Spectral value
+
+197
+00:13:29,150 --> 00:13:34,410
+of Anot that sigma of a هي عبارة عن لمضة يعني الأن
+
+198
+00:13:34,410 --> 00:13:37,830
+لو بدنا نترجم مش معناه sigma of a يعني خلّيني أقول
+
+199
+00:13:37,830 --> 00:13:41,210
+بالإستدالة بهذه هي عبارة عن اللمضات اللي في الـC
+
+200
+00:13:41,210 --> 00:13:44,570
+اللي هذا يشمل و does not exist and does not exist
+
+201
+00:13:44,570 --> 00:13:48,570
+أنا مكملتها اطلع لفوق بس بكفاية تعرفوه الأن نيجي
+
+202
+00:13:49,180 --> 00:13:54,300
+Further Properties of بنخ الـgebra خلّيني أقول
+
+203
+00:13:54,300 --> 00:13:58,240
+مقتطفات من اللي هي بعض خواص البنخ الـgebra ناخد
+
+204
+00:13:58,240 --> 00:14:02,040
+فكرة عنها أول نظرية، النظرية هذه المشهورة في اللي
+
+205
+00:14:02,040 --> 00:14:06,520
+هي .. بداية .. اللي هي البنخ الـgebra Let A be a
+
+206
+00:14:06,520 --> 00:14:10,920
+complex بنخ الـgebra with identity E الآن، عند
+
+207
+00:14:10,920 --> 00:14:14,480
+البنخ الـgebra with identity E if X element in A
+
+208
+00:14:15,460 --> 00:14:19,320
+إذا كان X في الـ A وNormها أصغر من واحد نورمها
+
+209
+00:14:19,320 --> 00:14:22,340
+أصغر من واحد هذا فيه إشي مشابه إله في ال series
+
+210
+00:14:22,340 --> 00:14:26,460
+أصلا طبعا احنا then E to the minus X is invertible
+
+211
+00:14:26,460 --> 00:14:30,240
+يعني E to the minus X نفسه is invertible وعطيني E
+
+212
+00:14:30,240 --> 00:14:33,180
+to the minus X inverse بساوي بالظبط وعبارة عن ال
+
+213
+00:14:33,180 --> 00:14:37,300
+summation لل X JJ من 0 إلى 100 إلى ملا نهايةيعني
+
+214
+00:14:37,300 --> 00:14:41,160
+الآن لو كان الـ norm للـ X أزرع من واحد بنضمن لكم
+
+215
+00:14:41,160 --> 00:14:43,980
+E to minus X inversely اشماله exist و يسوي و كده
+
+216
+00:14:43,980 --> 00:14:46,540
+ده اللي علاقة في اللي حكيناها قبل شوية على الطيف و
+
+217
+00:14:46,540 --> 00:14:52,500
+مطيف و كده طبعا بصير استخدامات لها الان نيجي
+
+218
+00:14:52,500 --> 00:14:56,000
+نبرهنها نبرهن النظر يعني البرهن السهل يعني مش صعب
+
+219
+00:14:56,000 --> 00:15:00,880
+since A إذا بنخ الجيبرا and X element in A then
+
+220
+00:15:00,880 --> 00:15:05,610
+for any J element in N we have norm X to the Jاللي
+
+221
+00:15:05,610 --> 00:15:09,670
+هو بيساوي بيساوي اللي هو Normal X to the J بيساوي
+
+222
+00:15:09,670 --> 00:15:17,250
+Normal X في X اسم J minus 1 أصغر أوي يساوي Normal
+
+223
+00:15:17,250 --> 00:15:22,090
+X في Normal من التالي دالكم نقصوا من هذا وانزلوا
+
+224
+00:15:22,090 --> 00:15:24,810
+وانزلوا وانزلوا لما تحصلوا أصغر يساوي Normal X to
+
+225
+00:15:24,810 --> 00:15:28,390
+the من to the J إذا صار عندي Normal X to the J
+
+226
+00:15:28,390 --> 00:15:33,750
+أصغر أوي ساوي Normal X الكل to the J الآن
+
+227
+00:15:35,800 --> 00:15:40,040
+عندي ماعطيني norm ال X أشماله أصغر من واحد صح ولا
+
+228
+00:15:40,040 --> 00:15:43,280
+لأ؟ مدام norm ال X أصغر من واحد يعني كل element من
+
+229
+00:15:43,280 --> 00:15:46,960
+هذوله ال norm هو أصغر من واحد إذاً هذه صارت ال
+
+230
+00:15:46,960 --> 00:15:50,800
+series converge ال real numbers هذه إذا صارت هذه
+
+231
+00:15:50,800 --> 00:15:53,460
+ال series converge because norm ال X أصغر من واحد
+
+232
+00:15:54,320 --> 00:15:57,660
+بالتالي بالـ Comparison Twist Normal X to the J
+
+233
+00:15:57,660 --> 00:16:00,960
+هذي أصغر أو ساوى هذي، هذي الـ Series Converged،
+
+234
+00:16:00,960 --> 00:16:03,060
+إذا من ببقى ولا إي شمالها، اللي أصغر منها إي
+
+235
+00:16:03,060 --> 00:16:06,340
+شمالها Converged، إذا صارت عندي Normal X to the J
+
+236
+00:16:06,340 --> 00:16:11,140
+ConvergedThat means إيش هذه اللي هي عبارة عن اللي
+
+237
+00:16:11,140 --> 00:16:15,120
+هو لو أخدنا اللي هو J بصفر نعتبرها إيه شمالها اللي
+
+238
+00:16:15,120 --> 00:16:21,980
+هو قبلها ال normal X to the J هذي converts يعني
+
+239
+00:16:21,980 --> 00:16:26,130
+absolutely convergentإذا this means that either
+
+240
+00:16:26,130 --> 00:16:29,510
+summation of X أشمالها converges absolutely يعني
+
+241
+00:16:29,510 --> 00:16:33,230
+اللي جوا صارت هاد converges يعني absolutely
+
+242
+00:16:33,230 --> 00:16:36,950
+convergent مين ال absolutely convergent هاد؟ لأنه
+
+243
+00:16:36,950 --> 00:16:39,770
+بدون absolute value أو بدون نهار مين بتطلع ال
+
+244
+00:16:39,770 --> 00:16:42,530
+summation X to the JJ من صفر إلى مين إلى ما لليها
+
+245
+00:16:42,530 --> 00:16:46,010
+يعني اللي في الواقع هي هاد إذا صارت هاد عبارة عن
+
+246
+00:16:46,010 --> 00:16:50,780
+أشمالها converges absolutelyوأحنا كنا نقول مدام
+
+247
+00:16:50,780 --> 00:16:54,960
+complete however a is complete إذا ال summation
+
+248
+00:16:54,960 --> 00:16:58,140
+إيش ماله أنا absolutely convergent إيزا إيش مالها؟
+
+249
+00:16:58,140 --> 00:17:01,060
+convergent أخدنا هذا الكلام أنا absolutely
+
+250
+00:17:01,060 --> 00:17:04,480
+convergent is convergent في ال complete اللي هو
+
+251
+00:17:04,480 --> 00:17:08,520
+non dismissive إذا صار عندى بما أن a is complete
+
+252
+00:17:08,520 --> 00:17:11,260
+وهذه absolutely convergent إذا هذه إيش مالها؟ is
+
+253
+00:17:11,260 --> 00:17:15,100
+convergent إذا نفترض إن هذه ال summation إيش
+
+254
+00:17:15,100 --> 00:17:16,760
+بساوي؟ بسواس
+
+255
+00:17:22,050 --> 00:17:27,790
+اللي هنطلعه لو جينا ضربنا E⁻X اللي احنا متوقعين
+
+256
+00:17:27,790 --> 00:17:34,140
+انها تكون انفر السبحة هو المجموعلو ضربناها في E في
+
+257
+00:17:34,140 --> 00:17:38,940
+X X أربعة إلى خلال X N هادي في هادي و هادي في هادي
+
+258
+00:17:38,940 --> 00:17:43,720
+نفس الشيء لأنه commutative و يساوي و ضربوهم في بعض
+
+259
+00:17:43,720 --> 00:17:47,180
+و هيت cancelهم كلهم بس هيبقى الأول term و آخر term
+
+260
+00:17:47,180 --> 00:17:51,140
+بيصير E to the minus X N زائد واحد إذا صار عندي
+
+261
+00:17:51,140 --> 00:17:56,340
+هذا المقدار بيساوي هذا المقدار و أدوا N إلى مانا
+
+262
+00:17:56,340 --> 00:18:00,600
+نهاية الـ N إلى مانا نهاية بيصير عندي هذا بيصير
+
+263
+00:18:00,600 --> 00:18:05,460
+summation صح؟لما نروح للمعنى نهائي بيصير هذا بيصير
+
+264
+00:18:05,460 --> 00:18:12,670
+a²-x في s هذابساوة S فيه to the X ويساوي من ال E
+
+265
+00:18:12,670 --> 00:18:16,950
+هذا هيروح لمين لل Zero لأن Normal X أشماله أصغر من
+
+266
+00:18:16,950 --> 00:18:20,550
+واحد إذا صار عندي هذا في هذا بساوية هذا في هذا
+
+267
+00:18:20,550 --> 00:18:24,410
+يعني صار عندي هذا هو ال inverse لهذا يعني بمعنى
+
+268
+00:18:24,410 --> 00:18:29,350
+أخر S بتساوي E to the minus X inverse ومن ثم ال S
+
+269
+00:18:29,350 --> 00:18:33,130
+هي عبارة عن هذا المقدار يعني صار هذا المقدار هو E
+
+270
+00:18:33,130 --> 00:18:38,120
+to the minus X inverse وهو المطلوبنأتي الآن في الـ
+
+271
+00:18:38,120 --> 00:18:40,360
+Theorem of Invertible Elements اطلع على فوق، شيء
+
+272
+00:18:40,360 --> 00:18:47,200
+بسيط Let A بيكون بلقس بلخ الجيفرة with identity E
+
+273
+00:18:48,110 --> 00:18:52,450
+Then D، The set of all invertible elements of A is
+
+274
+00:18:52,450 --> 00:18:56,690
+an open subset of A يعني الآن لو كانت A كمبلك سبنخ
+
+275
+00:18:56,690 --> 00:19:02,750
+الجيبرا بيصير مجموعة .. مجموعة .. كل ال invertible
+
+276
+00:19:02,750 --> 00:19:07,410
+elements لA هتكون open subset من مين؟ من اللي هي
+
+277
+00:19:07,410 --> 00:19:11,920
+مين؟ من الـAالان بناء على الهنس ده subset M بسوء A
+
+278
+00:19:11,920 --> 00:19:16,040
+-G اللي هي مكملتها هتكون of all non-invertable
+
+279
+00:19:16,040 --> 00:19:20,120
+elements A شمالها is closed إذن the set of all non
+
+280
+00:19:20,120 --> 00:19:24,880
+-invertable elements من الـA closed بينما the set
+
+281
+00:19:24,880 --> 00:19:27,980
+of all of اللي هو ده خلّيني أقول invertable
+
+282
+00:19:27,980 --> 00:19:31,520
+elements A شمالها is an open set وهذا إيه معناه
+
+283
+00:19:31,520 --> 00:19:35,460
+بما يتعلق Pro وLambda مش مشكلة اطلع لفوق خلاص
+
+284
+00:19:35,460 --> 00:19:36,760
+مانعش البرهان اطلع لفوق
+
+285
+00:19:39,650 --> 00:19:44,930
+أطلع لفوق، أطلع لفوق، لأ خلّينا عند النظرية الـ
+
+286
+00:19:44,930 --> 00:19:49,190
+Spectrum اللي هو اللي سمناه اللي هو الطيف لأن let
+
+287
+00:19:49,190 --> 00:19:52,970
+A بيكون Complex بنخ ألجيبرا with identity then for
+
+288
+00:19:52,970 --> 00:19:57,790
+any X element in A هذا إعلان كبير ال Spectrum
+
+289
+00:19:57,790 --> 00:20:02,410
+Sigma of X is compact ال Sigma of X يعني is a
+
+290
+00:20:02,410 --> 00:20:06,860
+bounded closed setالـ sigma of X طبعاً subset من C
+
+291
+00:20:06,860 --> 00:20:10,080
+و الـ compactness بيساوي الـ closed و الـ bounded
+
+292
+00:20:10,080 --> 00:20:13,260
+في الـ C و في الـ R اللي يعني ال spectrum C of X
+
+293
+00:20:13,260 --> 00:20:19,780
+is a compacted و ال spectral radius satisfies اللي
+
+294
+00:20:19,780 --> 00:20:22,320
+هو ال spectral radius، انزلوا خلّيني أعرفكم ال
+
+295
+00:20:22,320 --> 00:20:26,600
+spectral radius على السريع ال spectral radius اللي
+
+296
+00:20:26,600 --> 00:20:30,530
+هو بنسميه R sigma of X ال spectral radius للـ Xهو
+
+297
+00:20:30,530 --> 00:20:33,530
+عبارة عن R Sigma of X بيساوي الـ Supremum لكل الـ
+
+298
+00:20:33,530 --> 00:20:37,010
+Absolute Value لللمضة اللي موجودة في مين في Sigma
+
+299
+00:20:37,010 --> 00:20:41,990
+of X إذا الـ Spectral Radius إلها اللي هو أو
+
+300
+00:20:41,990 --> 00:20:46,170
+خلّيني أقول نصف قطر الطيف اللي هو عبارة عن R Sigma
+
+301
+00:20:46,170 --> 00:20:49,290
+of X بيساوي الـ Supremum للمضة Lambda Element in
+
+302
+00:20:49,290 --> 00:20:53,590
+Sigma of X اللي الآن بيقولني في النظرية إن الـ
+
+303
+00:20:53,590 --> 00:20:59,760
+Sigma of X is compact ومش هيكوالـ Spectral Radius
+
+304
+00:20:59,760 --> 00:21:04,840
+تراحة لن يتجاوز نورمين Normal X لأن أصلا هي كلها
+
+305
+00:21:04,840 --> 00:21:08,600
+محصورة في داخل الصندوق لأنها Closed و Bounded ماشي
+
+306
+00:21:08,600 --> 00:21:11,660
+الحال إذا الـ Spectral Radius إلها R Sigma اللي هو
+
+307
+00:21:11,660 --> 00:21:14,920
+الـ Supermum عليها على كل اللي في الـ Sigma اللي
+
+308
+00:21:14,920 --> 00:21:18,000
+هو R Sigma of X أزاهر سواء Normal X برضه البرنامج
+
+309
+00:21:18,000 --> 00:21:24,310
+ده شيء أطلع لفوق نيجي الآن للإعلان المهم الآخراللي
+
+310
+00:21:24,310 --> 00:21:30,270
+هو الـ Spectrum Sigma of X is a non-empty set هذا
+
+311
+00:21:30,270 --> 00:21:33,690
+إعلان كبير Sigma of X لا تساوي Phi under the
+
+312
+00:21:33,690 --> 00:21:37,450
+assumption of the preceding theorem اللي هو اللي
+
+313
+00:21:37,450 --> 00:21:41,930
+في البنخ الجيبرا Sigma of X لا تساوي Phi و
+
+314
+00:21:41,930 --> 00:21:45,850
+comebackt is non-empty set و comebackت بناء عليه
+
+315
+00:21:45,850 --> 00:21:53,130
+اللي هو الآن فيه كمان الخاصية مزام الـ Sigma of X
+
+316
+00:21:54,070 --> 00:21:58,750
+الـ is closed الـ sigma of X is closed الـ sigma
+
+317
+00:21:58,750 --> 00:22:01,090
+of X is closed الـ sigma of X is closed الـ sigma
+
+318
+00:22:01,090 --> 00:22:01,490
+of X is closed الـ sigma of X is closed الـ sigma
+
+319
+00:22:01,490 --> 00:22:01,510
+of X is closed الـ sigma of X is closed الـ sigma
+
+320
+00:22:01,510 --> 00:22:01,930
+of X is closed الـ sigma of X is closed الـ sigma
+
+321
+00:22:01,930 --> 00:22:01,950
+of X is closed الـ sigma of X is closed الـ sigma
+
+322
+00:22:01,950 --> 00:22:01,990
+of X is closed الـ sigma of X is closed الـ sigma
+
+323
+00:22:01,990 --> 00:22:04,070
+of X is closed الـ sigma of X is closed الـ sigma
+
+324
+00:22:04,070 --> 00:22:10,770
+of X is closed الـ sigma of X is closed الـ sigma
+
+325
+00:22:18,120 --> 00:22:24,660
+هذا closed و bounded الـ Rovix هو المنطلق برا هو
+
+326
+00:22:24,660 --> 00:22:31,680
+اللي هو unbounded و open set فانجسمت
+
+327
+00:22:31,680 --> 00:22:35,400
+اللي هي ال complex plane إلى جزئين جزء اللي هو
+
+328
+00:22:35,400 --> 00:22:38,040
+sigma rovix اللي هي عناصر الطرف اللي هي closed و
+
+329
+00:22:38,040 --> 00:22:41,880
+bounded و اللي هو اللي فوق اللي هي open set و
+
+330
+00:22:41,880 --> 00:22:47,370
+unbounded setوبارك الله فيكم والسلام عليكم ورحمة
+
+331
+00:22:47,370 --> 00:22:48,270
+الله وبركاته
+
diff --git a/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/zFznbPjt0NA_raw.srt b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/zFznbPjt0NA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6dfcfb6a21efdce1088241ffb0c3dadfb8b4ef6d
--- /dev/null
+++ b/PL9fwy3NUQKwZkPblS_KlzYkzv5WfDGlKa/zFznbPjt0NA_raw.srt
@@ -0,0 +1,1352 @@
+1
+00:00:05,260 --> 00:00:08,260
+بسم الله الرحمن الرحيم الحمد لله رب العالمين و
+
+2
+00:00:08,260 --> 00:00:11,100
+الصلاة والسلام على سيده المرسلين سيدنا محمد وعلى
+
+3
+00:00:11,100 --> 00:00:15,220
+آله وصحبه الجماعين هذه هي المحاضرة رقم 36 وهي
+
+4
+00:00:15,220 --> 00:00:19,500
+المحاضرة الأخيرة في مساق تحليل اقتران او تحليل
+
+5
+00:00:19,500 --> 00:00:25,100
+دالي طلاب طالبات الجامعة الإسلامية ماجستير
+
+6
+00:00:25,100 --> 00:00:30,690
+الرياضياتالفكرة إننا بدنا ناخد بس فكرة عن اللي هو
+
+7
+00:00:30,690 --> 00:00:35,850
+مفهوم البنخ Algebra لإنه له تطبيقات وله استعمالات
+
+8
+00:00:35,850 --> 00:00:41,950
+كبيرة لو حد يعني حاب أنه يشتغل فيه أو خلّيني أقول
+
+9
+00:00:41,950 --> 00:00:48,110
+ينطلق فيه إلى الأمام يعني بيكون فيه له فكرة في
+
+10
+00:00:48,110 --> 00:00:48,810
+الموضوع
+
+11
+00:00:51,440 --> 00:00:55,440
+نبدأ في definition يعني هو خليط بين الجبر الحديث
+
+12
+00:00:55,440 --> 00:01:00,240
+وبين اللي هو أو في أحيانًا نقول ملحه اللي هو الملح
+
+13
+00:01:00,240 --> 00:01:03,640
+الأولاني كنا نحكي عن الجبر الخطي هو ملح ال
+
+14
+00:01:03,640 --> 00:01:07,490
+functionملح أخر خلّيني أقول للبنخ Algebra اللي هو
+
+15
+00:01:07,490 --> 00:01:09,970
+يعني أو خلّيني أقول إيه علاقة فيه اللي هو ال Ring
+
+16
+00:01:09,970 --> 00:01:15,390
+Theory فيه شغل في ال .. في ال ideals و .. و كل
+
+17
+00:01:15,390 --> 00:01:18,930
+أسماء اللي .. اللي بتتعلق بال .. بال ideals و ال
+
+18
+00:01:18,930 --> 00:01:21,810
+modules و .. و الاخره اللي موجودة في ال rings و
+
+19
+00:01:21,810 --> 00:01:24,770
+موجودة كانت موجودة في البنخ Algebra بس هنا زيادة
+
+20
+00:01:24,770 --> 00:01:29,870
+شوية انه .. انه بيعطيه شوية يعني ال .. ال .. ال
+
+21
+00:01:29,870 --> 00:01:34,350
+ring ما هي على عمليتينهنا الآن في هي جاعدة على
+
+22
+00:01:34,350 --> 00:01:37,150
+vector space اللي هو scalar multiplication و
+
+23
+00:01:37,150 --> 00:01:39,990
+vector addition بالاضافة بيصير لان vector
+
+24
+00:01:39,990 --> 00:01:42,470
+multiplication اللي هي عملية ضرب زي ما عملية ضرب
+
+25
+00:01:42,470 --> 00:01:45,250
+اللي وين اللي في ال ring وزيادة على هيك أنه في
+
+26
+00:01:45,250 --> 00:01:48,990
+عليه norm ال norm تبعه نقع norm of this space صح
+
+27
+00:01:48,990 --> 00:01:51,410
+لكن norm of this space وفيه كمان شغل أخر على ال
+
+28
+00:01:51,410 --> 00:01:54,270
+norm of this space أنه بدهو ال norm تبع البنخ
+
+29
+00:01:54,270 --> 00:01:57,170
+الجيبرة بدهو يحقق norm ال x في y أصغر شهره norm ال
+
+30
+00:01:57,170 --> 00:02:01,060
+x في norm ال yلأنه في الاصل في الـ Normed Space
+
+31
+00:02:01,060 --> 00:02:03,720
+العادى مش شرط تكون فيه عملية ضرب بس ان صار في
+
+32
+00:02:03,720 --> 00:02:06,620
+عملية ضرب لأن هناك العالم اللي بنشتغل عليه vector
+
+33
+00:02:06,620 --> 00:02:08,680
+space ومش فيه هناك غير عملية scalar multiplication
+
+34
+00:02:08,680 --> 00:02:13,980
+و vector addition فاللي هو مش وارد كان عملية الضرب
+
+35
+00:02:13,980 --> 00:02:18,660
+و norm لل X في Y مثلا مش وارد كان زمان هأنا بدي
+
+36
+00:02:18,660 --> 00:02:23,730
+أصبح وارد و بدي أن أتعالج معاكتان شوفش اللي بقوله7
+
+37
+00:02:23,730 --> 00:02:26,990
+.6.1 Definition of Algebra A لأننا نعرف الجيبرا
+
+38
+00:02:26,990 --> 00:02:32,830
+بدون ما نحطناهم لسه Algebra A over a vector over a
+
+39
+00:02:32,830 --> 00:02:36,730
+field K is a vector space إذا نرسى الدورة الشمالة
+
+40
+00:02:36,730 --> 00:02:42,060
+vector space عالميا على اللي هو scalar field Kover
+
+41
+00:02:42,060 --> 00:02:46,320
+k such that for all x y element a a unique product
+
+42
+00:02:46,320 --> 00:02:49,620
+ده انا عرفنا من a product اللي هم بتضعف لل vector
+
+43
+00:02:49,620 --> 00:02:52,100
+addition و ال scale of multiplication عرفنا
+
+44
+00:02:52,100 --> 00:02:55,100
+product x و y و الموجودة في ال I في ليه؟ is
+
+45
+00:02:55,100 --> 00:02:58,140
+defined with the properties mainly اللي هي بتحقق
+
+46
+00:02:58,140 --> 00:03:02,510
+اللي هي الخواص التاليةإن X في Y في Z بيساوي الـ
+
+47
+00:03:02,510 --> 00:03:06,770
+associativity تبع تليجيه ده الآن التوزيع بين عملية
+
+48
+00:03:06,770 --> 00:03:10,850
+الـ vector addition وبين الدرب X في Y زي Z بيساوي
+
+49
+00:03:10,850 --> 00:03:14,670
+X في Y زي X في Z برضه بدها تربط بين ال scalar
+
+50
+00:03:14,670 --> 00:03:16,850
+multiplication وال multiplication تبعهم أو ال
+
+51
+00:03:16,850 --> 00:03:20,360
+productألفة في X و Y لـ associativity اللي هو
+
+52
+00:03:20,360 --> 00:03:24,460
+أشمالها واردة أو خلّيني أقول متحققة هذا الكلام لكل
+
+53
+00:03:24,460 --> 00:03:28,460
+X و Y والألفة element N هو الـK طبعا اللي هو
+
+54
+00:03:28,460 --> 00:03:31,020
+التوزيع من اليمين ومن الشمال زي ما انتوا ملاحظين
+
+55
+00:03:31,020 --> 00:03:35,160
+الان A is called an algebra .. هذي ال algebra A is
+
+56
+00:03:35,160 --> 00:03:38,940
+called an algebra with unity .. with unity اللي هو
+
+57
+00:03:38,940 --> 00:03:42,180
+with identity if there exist any element in A such
+
+58
+00:03:42,180 --> 00:03:45,150
+ذات اللي بتعرفوهE في X بيساوي X في E بيساوي A
+
+59
+00:03:45,150 --> 00:03:48,230
+إشمال و X لكل X و Y موجودة في الـ A إذا صارت عبارة
+
+60
+00:03:48,230 --> 00:03:52,790
+عن اللي هي associative موجودة طبعا و closed this
+
+61
+00:03:52,790 --> 00:03:56,570
+موجودة أكيد اللي هو لكل X و Y في عندك اللي هو X و
+
+62
+00:03:56,570 --> 00:03:59,450
+Y اللي بتناقصها تتعامل ل closed إذا صارت closed
+
+63
+00:03:59,450 --> 00:04:03,970
+وصارت associative وصار عند A إشمالها ال identity
+
+64
+00:04:03,970 --> 00:04:10,290
+موجودة A is called اللي هو إشمالها algebra with
+
+65
+00:04:10,290 --> 00:04:15,840
+unityاللي هم بنسميها commutative algebra إذا كان a
+
+66
+00:04:15,840 --> 00:04:20,880
+في b إيش بيساوي بأي for all a و b element من مين
+
+67
+00:04:20,880 --> 00:04:25,060
+in a أسبب algebra of a بنفس اللي .. اللي .. اللي
+
+68
+00:04:25,060 --> 00:04:29,740
+.. اللي هو الغنطق تبع ال .. اللي هو ال subgroupالـ
+
+69
+00:04:29,740 --> 00:04:32,440
+Sub vector space الـ Sub ring كله يجب أن يحافظ
+
+70
+00:04:32,440 --> 00:04:38,000
+عالمياً على أن يكون أصلاً مثله بس جزء صغير منه لأن
+
+71
+00:04:38,000 --> 00:04:41,080
+كيف يجب أن يحافظها؟ سبق الجيبرا وفقاه وعبارة عن is
+
+72
+00:04:41,080 --> 00:04:43,620
+a vector sub space of V هذه أول واحدة لذلك نخلصها
+
+73
+00:04:43,620 --> 00:04:46,220
+من قصة الـ scalar multiplication و ال vector
+
+74
+00:04:46,220 --> 00:04:49,780
+addition الآن ماذا قال؟ that is closed under the
+
+75
+00:04:49,780 --> 00:04:52,680
+productاللي هو إيش؟ عشان يضمن إنه صار الجذبرة
+
+76
+00:04:52,680 --> 00:04:56,180
+closed under the product وباقى الأمور ما هي متحققة
+
+77
+00:04:56,180 --> 00:04:58,320
+في الكبير ده راح تكون متحققة في الصغير اللي هي ال
+
+78
+00:04:58,320 --> 00:05:02,180
+associativity والتوزيع والأخرين الآن if a has an
+
+79
+00:05:02,180 --> 00:05:06,280
+identity then the identity أشماله is unique وهذا
+
+80
+00:05:06,280 --> 00:05:08,900
+أثباته زي ما بنثبت في ال ring العادي وفي ال group
+
+81
+00:05:08,900 --> 00:05:11,940
+العادي اللي هو أثبات ال identity الوحيد من اللي هي
+
+82
+00:05:11,940 --> 00:05:17,500
+الخواص المعتاد طيب ندى الآن هذا دعنا نقول تحديث
+
+83
+00:05:17,500 --> 00:05:18,840
+جبري بحت
+
+84
+00:05:21,740 --> 00:05:25,440
+الآن جاملها The product in and on this algebra A
+
+85
+00:05:25,440 --> 00:05:28,700
+is a continuous mapping of A cross A onto mean
+
+86
+00:05:28,700 --> 00:05:32,740
+onto A عملية الضرب عملية إيهاش عملية متصلة بين A
+
+87
+00:05:32,740 --> 00:05:36,200
+cross A لعند مين لعند الـA واثبتها واثبتها يعني
+
+88
+00:05:36,200 --> 00:05:39,880
+إيه سهل هذا الآن طبعا مش هنقدر نحكي فيه إلا إذا
+
+89
+00:05:39,880 --> 00:05:43,260
+نحكي عن نارلأنه فيه اتصال يعني ممكن نحكي عن الـ
+
+90
+00:05:43,260 --> 00:05:48,220
+topology عشان هيك بيستلزم الحديث على اللي هو الـ
+
+91
+00:05:48,220 --> 00:05:50,740
+algebra أن يكون non-algebra، طبعا ماهي الـ non
+
+92
+00:05:50,740 --> 00:05:54,680
+-algebra؟ الـ non-algebra ببساطة non-algebra A is
+
+93
+00:05:54,680 --> 00:05:55,780
+a non-disbase
+
+94
+00:05:59,000 --> 00:06:03,280
+which is an algebra هاي اتنين such that norm ال X
+
+95
+00:06:03,280 --> 00:06:06,740
+في Y ايش بده يصير اصغر يساوي norm X في norm Y لكل
+
+96
+00:06:06,740 --> 00:06:10,460
+X وY element in A هذا اللي هو بيعمل ليه normed
+
+97
+00:06:10,460 --> 00:06:16,660
+algebra الان if A has identityإذا الـ norm الـ E
+
+98
+00:06:16,660 --> 00:06:21,380
+حيث أننا سنسأل أننا عارفه إيش بيساوي واحد و اللي
+
+99
+00:06:21,380 --> 00:06:25,860
+هي بيصير عبارة عن normed algebra with identity لو
+
+100
+00:06:25,860 --> 00:06:29,200
+كان ال normed algebra with identity is complete
+
+101
+00:06:29,200 --> 00:06:32,280
+يعني ال norm بيعطينا اللي هو of recursive sequence
+
+102
+00:06:32,280 --> 00:06:37,700
+converge بنسميه بنف ألجيبرا إذا the بنف ألجيبرا A
+
+103
+00:06:37,700 --> 00:06:40,740
+is a complete normed algebra which is a complete
+
+104
+00:06:40,910 --> 00:06:44,970
+which which which is complete considered as a
+
+105
+00:06:44,970 --> 00:06:51,770
+normless space طيب نقول إن هذا product اللي هي ال
+
+106
+00:06:51,770 --> 00:06:55,530
+X في Y عملية الضرب اللي هي في ال A هي عبارة عن a
+
+107
+00:06:55,530 --> 00:06:59,290
+continuous mapping من A cross A لعند مين لعندي
+
+108
+00:06:59,290 --> 00:07:00,370
+يعني F
+
+109
+00:07:03,260 --> 00:07:09,160
+من A cross A لعند الـ A defined by F of A و B
+
+110
+00:07:09,160 --> 00:07:15,020
+بتساوي A في B هذه أشمالها is a continuous function
+
+111
+00:07:15,020 --> 00:07:18,060
+وهو الهنط اللي في الكتاب سهل لو على طول بتطلوها و
+
+112
+00:07:18,060 --> 00:07:22,020
+برا لعندي في الترخيص التاني أنا بس احنا لضيق الوقت
+
+113
+00:07:22,020 --> 00:07:27,000
+خليه لكم تطلع عليه نيجي الأن ناخد أمثلة اطلع لفوق
+
+114
+00:07:27,000 --> 00:07:32,650
+أمثلة على اللي هو normed algebraThe real line هو
+
+115
+00:07:32,650 --> 00:07:37,570
+فيلد الـ real line هو الكمبليكس فيلد يعني كل عملية
+
+116
+00:07:37,570 --> 00:07:41,330
+فيه موجودة سواء ضرب أو وده كده The real line and
+
+117
+00:07:41,330 --> 00:07:44,010
+the complex plane C are commutative
+
+118
+00:07:44,010 --> 00:07:49,890
+كمممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممم
+
+119
+00:07:50,250 --> 00:07:54,450
+الان اللي هو الـR والـC are commutative بنخ
+
+120
+00:07:54,450 --> 00:07:57,870
+الـgebra وضع identity A بالساوية واحدة إيش عملية
+
+121
+00:07:57,870 --> 00:08:03,290
+ال vector addition الجمع العادى؟ إيش عملية ال
+
+122
+00:08:03,290 --> 00:08:05,270
+scalar multiplication ال field اللي عليه في
+
+123
+00:08:05,270 --> 00:08:09,690
+عناصره؟ إيش عملية الدرب اللي هي الدرب العادى اللي
+
+124
+00:08:09,690 --> 00:08:19,540
+عليه؟بناخد مثال آخر space C of A وB خدناه is الهو
+
+125
+00:08:19,540 --> 00:08:25,360
+the space of all continuous functions is
+
+126
+00:08:25,360 --> 00:08:28,980
+a commutative بنخ ألجيبرا under the maximum norm
+
+127
+00:08:28,980 --> 00:08:34,340
+is a commutative بنخ ألجيبرا with identity E بساوي
+
+128
+00:08:34,340 --> 00:08:38,940
+مين؟ بساوي الهو إيش؟ بساوي واحد اللي هي ال
+
+129
+00:08:38,940 --> 00:08:44,220
+constant functionthe product x y be defined as
+
+130
+00:08:44,220 --> 00:08:49,040
+usual x y of t ال functions هي وكانت بنضرب point
+
+131
+00:08:49,040 --> 00:08:53,160
+twice يعني بيسوى x of t في مين في y of t for all t
+
+132
+00:08:53,160 --> 00:08:56,220
+in a و b طبعا احنا نعرف ان ذكريات ده continuous و
+
+133
+00:08:56,220 --> 00:08:58,640
+اذا كنت نفسي حصلت ضرب ايش هيكون continuous اكيد
+
+134
+00:08:58,640 --> 00:09:04,320
+لان and the norm is the maximum normالان هذا كله
+
+135
+00:09:04,320 --> 00:09:09,540
+بيعمل ليه ايش ماله كميوتيتف بنخ ألجيبرا اذا اللي
+
+136
+00:09:09,540 --> 00:09:13,720
+هي اللي على اللي هي الضرب العادى هيطلع كميوتيتف
+
+137
+00:09:13,720 --> 00:09:17,340
+بنخ ألجيبرا the subspace of c of a و b consisting
+
+138
+00:09:17,340 --> 00:09:22,980
+of all polynomials is a commutative normed algebra
+
+139
+00:09:22,980 --> 00:09:26,020
+انا بقول لها مش complete هذا ال polynomial مش
+
+140
+00:09:26,020 --> 00:09:30,820
+complete with identity ايه بتساوي واحدأطلع لفوق
+
+141
+00:09:30,820 --> 00:09:36,940
+التفاصيل اللي هي الخواص كلها بتتحقق space P of X P
+
+142
+00:09:36,940 --> 00:09:40,980
+of X اللي هو عبارة عن من the space of all bounded
+
+143
+00:09:40,980 --> 00:09:45,580
+linear operators من X لعند ال X ماشي لإن ده ما
+
+144
+00:09:45,580 --> 00:09:49,420
+كتبناش من X ل Y ماعرفش منه قصود من X لمنين ل X the
+
+145
+00:09:49,420 --> 00:09:51,860
+banach space P of X of all bounded linear
+
+146
+00:09:51,860 --> 00:09:59,350
+operators onبنخ X نفسه X نفسه إيش ماله اله الـ non
+
+147
+00:09:59,350 --> 00:10:04,250
+-zero بنخ space الـ B of X اللي هي the space of
+
+148
+00:10:04,250 --> 00:10:08,150
+all bounded linear operators is بنخ ألجيبرا with
+
+149
+00:10:08,150 --> 00:10:14,130
+identity I اللي هال multiplication هنا اللي هو
+
+150
+00:10:14,130 --> 00:10:18,770
+عبارة عن composition of operatorsيعني عملية الضرب
+
+151
+00:10:18,770 --> 00:10:22,790
+اللي بنعرفها على الـPX وPXH مالها عبارة عن الـ
+
+152
+00:10:22,790 --> 00:10:25,350
+composition و الـ composition need not to be
+
+153
+00:10:25,350 --> 00:10:28,390
+commutative زي ما انتوا عارفينها إذاً هذا مثال على
+
+154
+00:10:28,390 --> 00:10:33,750
+P of X is a non commutative بنخ ألجيبرا unless ال
+
+155
+00:10:33,750 --> 00:10:41,690
+dimension للـXH بساوي بساوي واحد اللي بعده الان
+
+156
+00:10:41,690 --> 00:10:42,770
+definition
+
+157
+00:10:44,850 --> 00:10:48,450
+بنعرف الشو معنات طبعاً ده يعني خلّينا اللي عارفه
+
+158
+00:10:48,450 --> 00:10:53,290
+مش هنستعمله لإنه مش هيكون فيه نوجت لنستعمل الان
+
+159
+00:10:53,290 --> 00:10:58,730
+element x in an algebraالـ A is said to be
+
+160
+00:10:58,730 --> 00:11:01,550
+invertible ترفو هذا invertible إيش معناه
+
+161
+00:11:01,550 --> 00:11:05,430
+invertible if it has an inverse in A اللي واش
+
+162
+00:11:05,430 --> 00:11:08,350
+معناته في X inverse بحيث انه X في X inverse بيساوي
+
+163
+00:11:08,350 --> 00:11:11,150
+X inverse في X أش بيساوي ال identity اللي لإن في
+
+164
+00:11:11,150 --> 00:11:14,070
+هذا الحالة بيسمي ال element X إيش ماله is
+
+165
+00:11:14,070 --> 00:11:17,930
+invertible يعني فيه انه inverse with respect to
+
+166
+00:11:17,930 --> 00:11:21,490
+this operation اللي هي ال product if X element in
+
+167
+00:11:21,490 --> 00:11:26,600
+A is SX element in A is invertible then its
+
+168
+00:11:26,600 --> 00:11:28,160
+inverse is ماهي الوحيد
+
+169
+00:11:34,080 --> 00:11:37,740
+الان نيجي اللي هو نتعرف علي حاجة اسمها الـ
+
+170
+00:11:37,740 --> 00:11:40,820
+Resolvent والاسبكترام وهذا قصص طويلة ال Resolvent
+
+171
+00:11:40,820 --> 00:11:44,480
+والاسبكترام لأنه هم .. يعني ال .. ال .. ال .. ال
+
+172
+00:11:44,480 --> 00:11:47,720
+.. الواحدة اسمها اللي هي ال Sigma الطيف .. الطيف
+
+173
+00:11:47,720 --> 00:11:50,940
+.. الطيف العنصر .. الطيف العنصر يعني احنا بنقول
+
+174
+00:11:50,940 --> 00:11:56,420
+الواحد يعني الخيال تبع ال .. تبع الشخص يعني بيعطي
+
+175
+00:11:56,420 --> 00:12:01,790
+مؤشر على الشخصالأثر تبع الشخص بيعطي .. بيعطي ..
+
+176
+00:12:01,790 --> 00:12:07,630
+خلّيني أقول مؤشر على الشخص الان طيف العنصر أحيانا
+
+177
+00:12:07,630 --> 00:12:10,710
+إحنا ما نعرفش العنصر نفسه لكن طبعا هذا الكلام
+
+178
+00:12:10,710 --> 00:12:13,990
+حقيقة يعني في ال .. في ال .. في ال .. في ال .. في
+
+179
+00:12:13,990 --> 00:12:19,330
+ال .. اللي هو العنصر الجيبرا أو الجيبرا طيف العنصر
+
+180
+00:12:20,760 --> 00:12:24,320
+بيعطيك كثير من خواص العنصر عشان هيك الناس بتهتم
+
+181
+00:12:24,320 --> 00:12:28,520
+بالطيف أو اللي هو ال spectrum وحتى ال resolvent
+
+182
+00:12:28,520 --> 00:12:32,340
+اللي هي ال set إيش اللي بقوله؟ إيش اللي بقوله
+
+183
+00:12:32,340 --> 00:12:35,180
+قاعد؟ let A بيكون complex منخ الجيبرا with
+
+184
+00:12:35,180 --> 00:12:40,880
+identity then the resolvent set of A is row of A
+
+185
+00:12:40,880 --> 00:12:48,790
+إيش row of A هذه؟الآن وكأنه بيحول الحديث من عناصر
+
+186
+00:12:48,790 --> 00:12:51,990
+في الـA اللي هي عناصر البنخ الـAlgebra إلى عناصر
+
+187
+00:12:51,990 --> 00:12:55,690
+في الـscalar field والحكي على الـscalar field ألطف
+
+188
+00:12:55,690 --> 00:12:59,110
+بظل ألطف من مين من البنخ الـAlgebra وتعقيدات وكيف
+
+189
+00:12:59,110 --> 00:13:02,310
+عناصر وكيف كذا وكيف كذا ودكتبات وإلى آخرية الـRow
+
+190
+00:13:02,310 --> 00:13:04,990
+of A هي عبارة عن كل اللمضة اللي في element in C
+
+191
+00:13:04,990 --> 00:13:08,910
+such that λمضة E minus A inverse E أشماله exist in
+
+192
+00:13:08,910 --> 00:13:15,150
+A هذه الـset اللي بنسميها الـRow of Aالمكملة لها
+
+193
+00:13:15,150 --> 00:13:18,870
+المكملة لها بنسميها الـ Spectrum اللي هو الطيب الـ
+
+194
+00:13:18,870 --> 00:13:22,210
+Spectrum set of A is Sigma of A بساوة C minus Rho
+
+195
+00:13:22,210 --> 00:13:26,230
+of A Any Lambda element in Sigma of A is called a
+
+196
+00:13:26,230 --> 00:13:29,150
+spectral value بنسميها إيه اشمالها Spectral value
+
+197
+00:13:29,150 --> 00:13:34,410
+of Anot that sigma of a هي عبارة عن لمضة يعني الأن
+
+198
+00:13:34,410 --> 00:13:37,830
+لو بدنا نترجم مش معناه sigma of a يعني خلّيني أقول
+
+199
+00:13:37,830 --> 00:13:41,210
+بالإستدالة بهذه هي عبارة عن اللمضات اللي في الـC
+
+200
+00:13:41,210 --> 00:13:44,570
+اللي هذا يشمل و does not exist and does not exist
+
+201
+00:13:44,570 --> 00:13:48,570
+أنا مكملتها اطلع لفوق بس بكفاية تعرفوه الأن نيجي
+
+202
+00:13:49,180 --> 00:13:54,300
+Further Properties of بنخ الـgebra خلّيني أقول
+
+203
+00:13:54,300 --> 00:13:58,240
+مقتطفات من اللي هي بعض خواص البنخ الـgebra ناخد
+
+204
+00:13:58,240 --> 00:14:02,040
+فكرة عنها أول نظرية، النظرية هذه المشهورة في اللي
+
+205
+00:14:02,040 --> 00:14:06,520
+هي .. بداية .. اللي هي البنخ الـgebra Let A be a
+
+206
+00:14:06,520 --> 00:14:10,920
+complex بنخ الـgebra with identity E الآن، عند
+
+207
+00:14:10,920 --> 00:14:14,480
+البنخ الـgebra with identity E if X element in A
+
+208
+00:14:15,460 --> 00:14:19,320
+إذا كان X في الـ A وNormها أصغر من واحد نورمها
+
+209
+00:14:19,320 --> 00:14:22,340
+أصغر من واحد هذا فيه إشي مشابه إله في ال series
+
+210
+00:14:22,340 --> 00:14:26,460
+أصلا طبعا احنا then E to the minus X is invertible
+
+211
+00:14:26,460 --> 00:14:30,240
+يعني E to the minus X نفسه is invertible وعطيني E
+
+212
+00:14:30,240 --> 00:14:33,180
+to the minus X inverse بساوي بالظبط وعبارة عن ال
+
+213
+00:14:33,180 --> 00:14:37,300
+summation لل X JJ من 0 إلى 100 إلى ملا نهايةيعني
+
+214
+00:14:37,300 --> 00:14:41,160
+الآن لو كان الـ norm للـ X أزرع من واحد بنضمن لكم
+
+215
+00:14:41,160 --> 00:14:43,980
+E to minus X inversely اشماله exist و يسوي و كده
+
+216
+00:14:43,980 --> 00:14:46,540
+ده اللي علاقة في اللي حكيناها قبل شوية على الطيف و
+
+217
+00:14:46,540 --> 00:14:52,500
+مطيف و كده طبعا بصير استخدامات لها الان نيجي
+
+218
+00:14:52,500 --> 00:14:56,000
+نبرهنها نبرهن النظر يعني البرهن السهل يعني مش صعب
+
+219
+00:14:56,000 --> 00:15:00,880
+since A إذا بنخ الجيبرا and X element in A then
+
+220
+00:15:00,880 --> 00:15:05,610
+for any J element in N we have norm X to the Jاللي
+
+221
+00:15:05,610 --> 00:15:09,670
+هو بيساوي بيساوي اللي هو Normal X to the J بيساوي
+
+222
+00:15:09,670 --> 00:15:17,250
+Normal X في X اسم J minus 1 أصغر أوي يساوي Normal
+
+223
+00:15:17,250 --> 00:15:22,090
+X في Normal من التالي دالكم نقصوا من هذا وانزلوا
+
+224
+00:15:22,090 --> 00:15:24,810
+وانزلوا وانزلوا لما تحصلوا أصغر يساوي Normal X to
+
+225
+00:15:24,810 --> 00:15:28,390
+the من to the J إذا صار عندي Normal X to the J
+
+226
+00:15:28,390 --> 00:15:33,750
+أصغر أوي ساوي Normal X الكل to the J الآن
+
+227
+00:15:35,800 --> 00:15:40,040
+عندي ماعطيني norm ال X أشماله أصغر من واحد صح ولا
+
+228
+00:15:40,040 --> 00:15:43,280
+لأ؟ مدام norm ال X أصغر من واحد يعني كل element من
+
+229
+00:15:43,280 --> 00:15:46,960
+هذوله ال norm هو أصغر من واحد إذاً هذه صارت ال
+
+230
+00:15:46,960 --> 00:15:50,800
+series converge ال real numbers هذه إذا صارت هذه
+
+231
+00:15:50,800 --> 00:15:53,460
+ال series converge because norm ال X أصغر من واحد
+
+232
+00:15:54,320 --> 00:15:57,660
+بالتالي بالـ Comparison Twist Normal X to the J
+
+233
+00:15:57,660 --> 00:16:00,960
+هذي أصغر أو ساوى هذي، هذي الـ Series Converged،
+
+234
+00:16:00,960 --> 00:16:03,060
+إذا من ببقى ولا إي شمالها، اللي أصغر منها إي
+
+235
+00:16:03,060 --> 00:16:06,340
+شمالها Converged، إذا صارت عندي Normal X to the J
+
+236
+00:16:06,340 --> 00:16:11,140
+ConvergedThat means إيش هذه اللي هي عبارة عن اللي
+
+237
+00:16:11,140 --> 00:16:15,120
+هو لو أخدنا اللي هو J بصفر نعتبرها إيه شمالها اللي
+
+238
+00:16:15,120 --> 00:16:21,980
+هو قبلها ال normal X to the J هذي converts يعني
+
+239
+00:16:21,980 --> 00:16:26,130
+absolutely convergentإذا this means that either
+
+240
+00:16:26,130 --> 00:16:29,510
+summation of X أشمالها converges absolutely يعني
+
+241
+00:16:29,510 --> 00:16:33,230
+اللي جوا صارت هاد converges يعني absolutely
+
+242
+00:16:33,230 --> 00:16:36,950
+convergent مين ال absolutely convergent هاد؟ لأنه
+
+243
+00:16:36,950 --> 00:16:39,770
+بدون absolute value أو بدون نهار مين بتطلع ال
+
+244
+00:16:39,770 --> 00:16:42,530
+summation X to the JJ من صفر إلى مين إلى ما لليها
+
+245
+00:16:42,530 --> 00:16:46,010
+يعني اللي في الواقع هي هاد إذا صارت هاد عبارة عن
+
+246
+00:16:46,010 --> 00:16:50,780
+أشمالها converges absolutelyوأحنا كنا نقول مدام
+
+247
+00:16:50,780 --> 00:16:54,960
+complete however a is complete إذا ال summation
+
+248
+00:16:54,960 --> 00:16:58,140
+إيش ماله أنا absolutely convergent إيزا إيش مالها؟
+
+249
+00:16:58,140 --> 00:17:01,060
+convergent أخدنا هذا الكلام أنا absolutely
+
+250
+00:17:01,060 --> 00:17:04,480
+convergent is convergent في ال complete اللي هو
+
+251
+00:17:04,480 --> 00:17:08,520
+non dismissive إذا صار عندى بما أن a is complete
+
+252
+00:17:08,520 --> 00:17:11,260
+وهذه absolutely convergent إذا هذه إيش مالها؟ is
+
+253
+00:17:11,260 --> 00:17:15,100
+convergent إذا نفترض إن هذه ال summation إيش
+
+254
+00:17:15,100 --> 00:17:16,760
+بساوي؟ بسواس
+
+255
+00:17:22,050 --> 00:17:27,790
+اللي هنطلعه لو جينا ضربنا E⁻X اللي احنا متوقعين
+
+256
+00:17:27,790 --> 00:17:34,140
+انها تكون انفر السبحة هو المجموعلو ضربناها في E في
+
+257
+00:17:34,140 --> 00:17:38,940
+X X أربعة إلى خلال X N هادي في هادي و هادي في هادي
+
+258
+00:17:38,940 --> 00:17:43,720
+نفس الشيء لأنه commutative و يساوي و ضربوهم في بعض
+
+259
+00:17:43,720 --> 00:17:47,180
+و هيت cancelهم كلهم بس هيبقى الأول term و آخر term
+
+260
+00:17:47,180 --> 00:17:51,140
+بيصير E to the minus X N زائد واحد إذا صار عندي
+
+261
+00:17:51,140 --> 00:17:56,340
+هذا المقدار بيساوي هذا المقدار و أدوا N إلى مانا
+
+262
+00:17:56,340 --> 00:18:00,600
+نهاية الـ N إلى مانا نهاية بيصير عندي هذا بيصير
+
+263
+00:18:00,600 --> 00:18:05,460
+summation صح؟لما نروح للمعنى نهائي بيصير هذا بيصير
+
+264
+00:18:05,460 --> 00:18:12,670
+a²-x في s هذابساوة S فيه to the X ويساوي من ال E
+
+265
+00:18:12,670 --> 00:18:16,950
+هذا هيروح لمين لل Zero لأن Normal X أشماله أصغر من
+
+266
+00:18:16,950 --> 00:18:20,550
+واحد إذا صار عندي هذا في هذا بساوية هذا في هذا
+
+267
+00:18:20,550 --> 00:18:24,410
+يعني صار عندي هذا هو ال inverse لهذا يعني بمعنى
+
+268
+00:18:24,410 --> 00:18:29,350
+أخر S بتساوي E to the minus X inverse ومن ثم ال S
+
+269
+00:18:29,350 --> 00:18:33,130
+هي عبارة عن هذا المقدار يعني صار هذا المقدار هو E
+
+270
+00:18:33,130 --> 00:18:38,120
+to the minus X inverse وهو المطلوبنأتي الآن في الـ
+
+271
+00:18:38,120 --> 00:18:40,360
+Theorem of Invertible Elements اطلع على فوق، شيء
+
+272
+00:18:40,360 --> 00:18:47,200
+بسيط Let A بيكون بلقس بلخ الجيفرة with identity E
+
+273
+00:18:48,110 --> 00:18:52,450
+Then D، The set of all invertible elements of A is
+
+274
+00:18:52,450 --> 00:18:56,690
+an open subset of A يعني الآن لو كانت A كمبلك سبنخ
+
+275
+00:18:56,690 --> 00:19:02,750
+الجيبرا بيصير مجموعة .. مجموعة .. كل ال invertible
+
+276
+00:19:02,750 --> 00:19:07,410
+elements لA هتكون open subset من مين؟ من اللي هي
+
+277
+00:19:07,410 --> 00:19:11,920
+مين؟ من الـAالان بناء على الهنس ده subset M بسوء A
+
+278
+00:19:11,920 --> 00:19:16,040
+-G اللي هي مكملتها هتكون of all non-invertable
+
+279
+00:19:16,040 --> 00:19:20,120
+elements A شمالها is closed إذن the set of all non
+
+280
+00:19:20,120 --> 00:19:24,880
+-invertable elements من الـA closed بينما the set
+
+281
+00:19:24,880 --> 00:19:27,980
+of all of اللي هو ده خلّيني أقول invertable
+
+282
+00:19:27,980 --> 00:19:31,520
+elements A شمالها is an open set وهذا إيه معناه
+
+283
+00:19:31,520 --> 00:19:35,460
+بما يتعلق Pro وLambda مش مشكلة اطلع لفوق خلاص
+
+284
+00:19:35,460 --> 00:19:36,760
+مانعش البرهان اطلع لفوق
+
+285
+00:19:39,650 --> 00:19:44,930
+أطلع لفوق، أطلع لفوق، لأ خلّينا عند النظرية الـ
+
+286
+00:19:44,930 --> 00:19:49,190
+Spectrum اللي هو اللي سمناه اللي هو الطيف لأن let
+
+287
+00:19:49,190 --> 00:19:52,970
+A بيكون Complex بنخ ألجيبرا with identity then for
+
+288
+00:19:52,970 --> 00:19:57,790
+any X element in A هذا إعلان كبير ال Spectrum
+
+289
+00:19:57,790 --> 00:20:02,410
+Sigma of X is compact ال Sigma of X يعني is a
+
+290
+00:20:02,410 --> 00:20:06,860
+bounded closed setالـ sigma of X طبعاً subset من C
+
+291
+00:20:06,860 --> 00:20:10,080
+و الـ compactness بيساوي الـ closed و الـ bounded
+
+292
+00:20:10,080 --> 00:20:13,260
+في الـ C و في الـ R اللي يعني ال spectrum C of X
+
+293
+00:20:13,260 --> 00:20:19,780
+is a compacted و ال spectral radius satisfies اللي
+
+294
+00:20:19,780 --> 00:20:22,320
+هو ال spectral radius، انزلوا خلّيني أعرفكم ال
+
+295
+00:20:22,320 --> 00:20:26,600
+spectral radius على السريع ال spectral radius اللي
+
+296
+00:20:26,600 --> 00:20:30,530
+هو بنسميه R sigma of X ال spectral radius للـ Xهو
+
+297
+00:20:30,530 --> 00:20:33,530
+عبارة عن R Sigma of X بيساوي الـ Supremum لكل الـ
+
+298
+00:20:33,530 --> 00:20:37,010
+Absolute Value لللمضة اللي موجودة في مين في Sigma
+
+299
+00:20:37,010 --> 00:20:41,990
+of X إذا الـ Spectral Radius إلها اللي هو أو
+
+300
+00:20:41,990 --> 00:20:46,170
+خلّيني أقول نصف قطر الطيف اللي هو عبارة عن R Sigma
+
+301
+00:20:46,170 --> 00:20:49,290
+of X بيساوي الـ Supremum للمضة Lambda Element in
+
+302
+00:20:49,290 --> 00:20:53,590
+Sigma of X اللي الآن بيقولني في النظرية إن الـ
+
+303
+00:20:53,590 --> 00:20:59,760
+Sigma of X is compact ومش هيكوالـ Spectral Radius
+
+304
+00:20:59,760 --> 00:21:04,840
+تراحة لن يتجاوز نورمين Normal X لأن أصلا هي كلها
+
+305
+00:21:04,840 --> 00:21:08,600
+محصورة في داخل الصندوق لأنها Closed و Bounded ماشي
+
+306
+00:21:08,600 --> 00:21:11,660
+الحال إذا الـ Spectral Radius إلها R Sigma اللي هو
+
+307
+00:21:11,660 --> 00:21:14,920
+الـ Supermum عليها على كل اللي في الـ Sigma اللي
+
+308
+00:21:14,920 --> 00:21:18,000
+هو R Sigma of X أزاهر سواء Normal X برضه البرنامج
+
+309
+00:21:18,000 --> 00:21:24,310
+ده شيء أطلع لفوق نيجي الآن للإعلان المهم الآخراللي
+
+310
+00:21:24,310 --> 00:21:30,270
+هو الـ Spectrum Sigma of X is a non-empty set هذا
+
+311
+00:21:30,270 --> 00:21:33,690
+إعلان كبير Sigma of X لا تساوي Phi under the
+
+312
+00:21:33,690 --> 00:21:37,450
+assumption of the preceding theorem اللي هو اللي
+
+313
+00:21:37,450 --> 00:21:41,930
+في البنخ الجيبرا Sigma of X لا تساوي Phi و
+
+314
+00:21:41,930 --> 00:21:45,850
+comebackt is non-empty set و comebackت بناء عليه
+
+315
+00:21:45,850 --> 00:21:53,130
+اللي هو الآن فيه كمان الخاصية مزام الـ Sigma of X
+
+316
+00:21:54,070 --> 00:21:58,750
+الـ is closed الـ sigma of X is closed الـ sigma
+
+317
+00:21:58,750 --> 00:22:01,090
+of X is closed الـ sigma of X is closed الـ sigma
+
+318
+00:22:01,090 --> 00:22:01,090
+of X is closed الـ sigma of X is closed الـ sigma
+
+319
+00:22:01,090 --> 00:22:01,490
+of X is closed الـ sigma of X is closed الـ sigma
+
+320
+00:22:01,490 --> 00:22:01,510
+of X is closed الـ sigma of X is closed الـ sigma
+
+321
+00:22:01,510 --> 00:22:01,930
+of X is closed الـ sigma of X is closed الـ sigma
+
+322
+00:22:01,930 --> 00:22:01,930
+of X is closed الـ sigma of X is closed الـ sigma
+
+323
+00:22:01,930 --> 00:22:01,950
+of X is closed الـ sigma of X is closed الـ sigma
+
+324
+00:22:01,950 --> 00:22:01,950
+of X is closed الـ sigma of X is closed الـ sigma
+
+325
+00:22:01,950 --> 00:22:01,950
+of X is closed الـ sigma of X is closed الـ sigma
+
+326
+00:22:01,950 --> 00:22:01,950
+of X is closed الـ sigma of X is closed الـ sigma
+
+327
+00:22:01,950 --> 00:22:01,950
+of X is closed الـ sigma of X is closed الـ sigma
+
+328
+00:22:01,950 --> 00:22:01,990
+of X is closed الـ sigma of X is closed الـ sigma
+
+329
+00:22:01,990 --> 00:22:01,990
+of X is closed الـ sigma of X is closed الـ sigma
+
+330
+00:22:01,990 --> 00:22:04,070
+of X is closed الـ sigma of X is closed الـ sigma
+
+331
+00:22:04,070 --> 00:22:10,770
+of X is closed الـ sigma of X is closed الـ sigma
+
+332
+00:22:18,120 --> 00:22:24,660
+هذا closed و bounded الـ Rovix هو المنطلق برا هو
+
+333
+00:22:24,660 --> 00:22:31,680
+اللي هو unbounded و open set فانجسمت
+
+334
+00:22:31,680 --> 00:22:35,400
+اللي هي ال complex plane إلى جزئين جزء اللي هو
+
+335
+00:22:35,400 --> 00:22:38,040
+sigma rovix اللي هي عناصر الطرف اللي هي closed و
+
+336
+00:22:38,040 --> 00:22:41,880
+bounded و اللي هو اللي فوق اللي هي open set و
+
+337
+00:22:41,880 --> 00:22:47,370
+unbounded setوبارك الله فيكم والسلام عليكم ورحمة
+
+338
+00:22:47,370 --> 00:22:48,270
+الله وبركاته
+
diff --git a/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/5K7ArnEYg-c_raw.json b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/5K7ArnEYg-c_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..53d1d1c759213c6d7478e70e73bcb32cd300471b
--- /dev/null
+++ b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/5K7ArnEYg-c_raw.json
@@ -0,0 +1 @@
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{"id": 37, "seek": 84206, "start": 813.98, "end": 842.06, "text": "و أخ لأب و أخ لأم صح ولا لأ؟ كلهم من الورثة هدول فهيني لحظي زدنا اتنين هالجات لإن هاد موجود من الأول فصاروا اتنين زيادة صح؟ تمام ابن الأخ في عندي ابن أخ شقيق و ابن أخ لأب هدول برضه من الورثة من الورثة ابن الأخ لأم مش من الورثة ابن الأخ الشقيق و ابن الأخ لأب من الورثة العام نفس الشيء في عندي عام شقيق و عام لأب", "tokens": [2407, 5551, 9778, 5296, 10721, 3555, 4032, 5551, 9778, 5296, 10721, 2304, 20328, 5016, 49429, 5296, 10721, 22807, 28242, 16095, 9154, 2423, 13063, 12984, 3660, 8032, 3215, 12610, 6156, 3224, 9957, 1829, 5296, 5016, 19913, 1829, 30767, 3215, 8315, 1975, 2655, 1863, 9957, 8032, 6027, 7435, 9307, 5296, 28814, 1863, 8032, 18513, 3714, 29245, 23328, 9154, 16247, 12610, 6156, 9381, 9640, 14407, 1975, 2655, 1863, 9957, 30767, 1829, 18513, 3660, 20328, 5016, 22807, 46811, 10943, 48127, 1863, 16247, 9778, 8978, 18871, 16254, 48127, 1863, 5551, 9778, 13412, 38436, 4587, 4032, 48127, 1863, 5551, 9778, 5296, 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{"start": 835.18, "end": 835.3, "word": " و", "probability": 0.9931640625}, {"start": 835.3, "end": 835.56, "word": " ابن", "probability": 0.920654296875}, {"start": 835.56, "end": 835.9, "word": " الأخ", "probability": 0.9853515625}, {"start": 835.9, "end": 836.54, "word": " لأب", "probability": 0.9894205729166666}, {"start": 836.54, "end": 836.8, "word": " من", "probability": 0.94970703125}, {"start": 836.8, "end": 837.58, "word": " الورثة", "probability": 0.997802734375}, {"start": 837.58, "end": 838.32, "word": " العام", "probability": 0.7685546875}, {"start": 838.32, "end": 838.62, "word": " نفس", "probability": 0.989013671875}, {"start": 838.62, "end": 839.04, "word": " الشيء", "probability": 0.89453125}, {"start": 839.04, "end": 839.14, "word": " في", "probability": 0.95947265625}, {"start": 839.14, "end": 839.48, "word": " عندي", "probability": 0.965576171875}, {"start": 839.48, "end": 839.7, "word": " عام", "probability": 0.889404296875}, {"start": 839.7, "end": 840.4, "word": 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2905.65, "word": " عصبة", "probability": 0.9650065104166666}, {"start": 2905.65, "end": 2906.09, "word": " بالغير", "probability": 0.9908854166666666}, {"start": 2906.09, "end": 2906.69, "word": " يعرفوا", "probability": 0.7808430989583334}, {"start": 2906.69, "end": 2907.43, "word": " بتطيروه", "probability": 0.6845703125}, {"start": 2907.43, "end": 2907.57, "word": " مش", "probability": 0.9091796875}, {"start": 2907.57, "end": 2907.97, "word": " البنت", "probability": 0.93408203125}, {"start": 2907.97, "end": 2908.89, "word": " صح", "probability": 0.98828125}, {"start": 2908.89, "end": 2909.03, "word": " ولا", "probability": 0.939453125}, {"start": 2909.03, "end": 2909.41, "word": " لأ؟", "probability": 0.6629231770833334}, {"start": 2909.41, "end": 2909.47, "word": " و", "probability": 0.86572265625}, {"start": 2909.47, "end": 2909.73, "word": " البنت", "probability": 0.97998046875}, {"start": 2909.73, "end": 2909.93, "word": " إلها", "probability": 0.6539713541666666}, {"start": 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2913.92, "end": 2914.44, "word": "عادي", "probability": 0.9166666666666666}, {"start": 2914.44, "end": 2915.34, "word": " لكن", "probability": 0.58837890625}, {"start": 2915.34, "end": 2915.72, "word": " إذا", "probability": 0.870849609375}, {"start": 2915.72, "end": 2915.98, "word": " في", "probability": 0.88525390625}, {"start": 2915.98, "end": 2916.46, "word": " إبن", "probability": 0.7798665364583334}, {"start": 2916.46, "end": 2917.34, "word": " بطيرهم", "probability": 0.906982421875}, {"start": 2917.34, "end": 2917.6, "word": " طب", "probability": 0.746826171875}, {"start": 2917.6, "end": 2917.82, "word": " إذا", "probability": 0.982666015625}, {"start": 2917.82, "end": 2918.02, "word": " في", "probability": 0.939453125}, {"start": 2918.02, "end": 2918.36, "word": " أب", "probability": 0.962890625}, {"start": 2918.36, "end": 2918.76, "word": " برضه", "probability": 0.9835611979166666}, {"start": 2918.76, "end": 2919.5, "word": " بطيرهم", "probability": 0.97265625}, {"start": 2919.5, "end": 2920.54, "word": " تمام", "probability": 0.91796875}, {"start": 2920.54, "end": 2922.3, "word": " وصلت؟", "probability": 0.7523193359375}, {"start": 2922.3, "end": 2922.9, "word": " طيب", "probability": 0.9415690104166666}, {"start": 2922.9, "end": 2925.46, "word": " الآن", "probability": 0.6612548828125}, {"start": 2925.46, "end": 2926.34, "word": " نجلأ", "probability": 0.864990234375}, {"start": 2926.34, "end": 2927.5, "word": " بنت", "probability": 0.83740234375}, {"start": 2927.5, "end": 2928.04, "word": " الإبن", "probability": 0.9479166666666666}, {"start": 2928.04, "end": 2928.64, "word": " أو", "probability": 0.88134765625}, {"start": 2928.64, "end": 2929.02, "word": " خلينا", "probability": 0.81787109375}, {"start": 2929.02, "end": 2929.36, "word": " نخليها", "probability": 0.9622802734375}, {"start": 2929.36, "end": 2930.08, "word": " للمحاضرة", "probability": 0.9154296875}, {"start": 2930.08, "end": 2930.74, "word": " القادمة", "probability": 0.9947916666666666}, {"start": 2930.74, "end": 2930.96, "word": " إلى", "probability": 0.91796875}, {"start": 2930.96, "end": 2931.22, "word": " هنا", "probability": 0.98291015625}, {"start": 2931.22, "end": 2931.56, "word": " نكون", "probability": 0.9443359375}, {"start": 2931.56, "end": 2931.8, "word": " قد", "probability": 0.83544921875}, {"start": 2931.8, "end": 2932.22, "word": " انتهينا", "probability": 0.9273681640625}, {"start": 2932.22, "end": 2932.36, "word": " من", "probability": 0.9755859375}, {"start": 2932.36, "end": 2932.7, "word": " موضوع", "probability": 0.9957275390625}, {"start": 2932.7, "end": 2933.44, "word": " محاضرتنا", "probability": 0.95654296875}, {"start": 2933.44, "end": 2933.78, "word": " لهذا", "probability": 0.887451171875}, {"start": 2933.78, "end": 2934.12, "word": " اليوم", "probability": 0.975341796875}, {"start": 2934.12, "end": 2934.98, "word": " أقول", "probability": 0.958740234375}, {"start": 2934.98, "end": 2935.34, "word": " قولي", "probability": 0.9332682291666666}, {"start": 2935.34, "end": 2935.54, "word": " هذا", "probability": 0.96728515625}, {"start": 2935.54, "end": 2936.04, "word": " وأستغفر", "probability": 0.939453125}, {"start": 2936.04, "end": 2936.2, "word": " الله", "probability": 0.9501953125}, {"start": 2936.2, "end": 2936.4, "word": " لي", "probability": 0.970703125}, {"start": 2936.4, "end": 2936.78, "word": " ولكم", "probability": 0.884765625}, {"start": 2936.78, "end": 2937.12, "word": " وصلى", "probability": 0.8232421875}, {"start": 2937.12, "end": 2937.36, "word": " اللهم", "probability": 0.768310546875}, {"start": 2937.36, "end": 2937.8, "word": " وسلم", "probability": 0.6151123046875}, {"start": 2937.8, "end": 2938.16, "word": " وبارك", "probability": 0.8294270833333334}, {"start": 2938.16, "end": 2938.38, "word": " على", "probability": 0.8876953125}, {"start": 2938.38, "end": 2938.86, "word": " سيدنا", "probability": 0.9921875}, {"start": 2938.86, "end": 2939.44, "word": " محمد", "probability": 0.98876953125}, {"start": 2939.44, "end": 2940.18, "word": " والسلام", "probability": 0.9593098958333334}, {"start": 2940.18, "end": 2940.66, "word": " عليكم", "probability": 0.94482421875}, {"start": 2940.66, "end": 2941.04, "word": " ورحمة", "probability": 0.985595703125}, {"start": 2941.04, "end": 2941.2, "word": " الله", "probability": 0.96533203125}, {"start": 2941.2, "end": 2942.46, "word": " وبركاته", "probability": 0.79931640625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2942.6880625, "duration_after_vad": 2863.8412499999886}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/88PynwLnIxQ.srt b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/88PynwLnIxQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1fcd5ef11dbd17cfd197a967dc30bd7f98238485
--- /dev/null
+++ b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/88PynwLnIxQ.srt
@@ -0,0 +1,991 @@
+1
+00:00:04,940 --> 00:00:08,080
+أعوذ بالله من الشيطان الرجيم بسم الله
+
+2
+00:00:08,080 --> 00:00:11,300
+الرحمن الرحيم الحمد لله رب العالمين والصلاة
+
+3
+00:00:11,300 --> 00:00:15,480
+والسلام على أشرف الأنبياء والمرسلين سيدنا محمد بن
+
+4
+00:00:15,480 --> 00:00:18,540
+عبد الله الصادق الأمين ثم عما بعد أحييكم جميعا
+
+5
+00:00:18,540 --> 00:00:22,320
+بتحية الإسلام فالسلام عليكم ورحمة الله تعالى
+
+6
+00:00:22,320 --> 00:00:27,600
+وبركاته كيف حالكم؟ طيبات إن شاء الله؟ تمام إذًا
+
+7
+00:00:27,600 --> 00:00:31,940
+لازلنا نتحدث حول الميراث بالتقدير والاحتياط قلنا
+
+8
+00:00:31,940 --> 00:00:37,280
+إن هناك جملة من الورثة نورثهم ليس على جهة القطع
+
+9
+00:00:37,280 --> 00:00:42,960
+والجزم بل على جهة التقدير والاحتياط فتحدثنا ابتداء
+
+10
+00:00:42,960 --> 00:00:49,200
+عن ميراث الحمل وعرفنا أننا لسنا جازمين من جنس
+
+11
+00:00:49,200 --> 00:00:54,760
+الحمل بالإضافة إلى أننا لسنا جازمين من حياته لذا
+
+12
+00:00:54,760 --> 00:01:00,600
+الأمر اقتضى أن نورثه باعتبارين ثم نوقف له الاعتبار
+
+13
+00:01:00,600 --> 00:01:05,530
+الأفضل على التفصيل الذي ذكرناه سابقا اليوم بإذن
+
+14
+00:01:05,530 --> 00:01:10,970
+الله سنتحدث عن ميراث الخنثى أبدًا خلونا نعرف مع بعض
+
+15
+00:01:10,970 --> 00:01:15,730
+من هو الخنثى يلا نحاول .. مين تحاول تعرفلنا
+
+16
+00:01:15,730 --> 00:01:23,090
+الخنثى؟ الخنثى، من هو الخنثى قبل ما نحكي الإشكال
+
+17
+00:01:23,090 --> 00:01:31,230
+في توريثه؟ يلا يا فادية هو أنه .. هو أن يولد شخص
+
+18
+00:01:31,230 --> 00:01:37,250
+بمشكلة عنده بالتشوه .. بتشوّه جنسي قد يولد بجهاز
+
+19
+00:01:37,250 --> 00:01:41,590
+تناسلي ذكر وأنثوي في نفس الشيء في نفس الوقت أو مثلا
+
+20
+00:01:41,590 --> 00:01:46,420
+بدون أي جهاز .. بدون أي .. بارك الله فيك، إذًا
+
+21
+00:01:46,420 --> 00:01:52,140
+باختصار شديد نقول الخنثى هو من ليس له لا آلة الرجل
+
+22
+00:01:52,140 --> 00:01:56,420
+ولا آلة المرأة بمعنى ما ليش عضو تناسل لا للذكر ولا
+
+23
+00:01:56,420 --> 00:02:03,120
+للأنثى أو من اجتمع فيه في آن واحد آلتي الرجل
+
+24
+00:02:03,120 --> 00:02:10,030
+والمرأة وبالتالي في مظهره لسنا يعني نستطيع أن نحدد
+
+25
+00:02:10,030 --> 00:02:15,150
+جنسه فلديه آلة الرجل وآلة المرأة فهذا هو الخنثى
+
+26
+00:02:15,150 --> 00:02:19,910
+لذلك نستطيع القول بإنه من المشكلات اللي بتواجهنا
+
+27
+00:02:19,910 --> 00:02:25,590
+في موضوع الميراث موضوع التشوه الجنسي فإننا قد نجد
+
+28
+00:02:25,590 --> 00:02:32,350
+إنسان يولد ولديه أكثر من آلتين وقد نجد إنسان يولد وليس
+
+29
+00:02:32,350 --> 00:02:37,620
+لديه أي آلة فبالتأكيد سيكون عندنا إشكال في توريثه
+
+30
+00:02:37,620 --> 00:02:41,720
+باعتبار أنه الميراث كما سبق وأن قلنا بالتأكيد
+
+31
+00:02:41,720 --> 00:02:46,500
+الجنس له دور في التوريث بمعنى الذكر والأنثى في
+
+32
+00:02:46,500 --> 00:02:51,220
+مسائل بسيطة يتساوى ميراث الذكر والأنثى لكن في الكثير
+
+33
+00:02:51,220 --> 00:02:56,450
+من الأحيان هو أن يختلف الميراث في حال الذكورة عن حال
+
+34
+00:02:56,450 --> 00:03:01,370
+الأنوثة مما يوقعنا في إشكال إن كيف لنا أن نوارث
+
+35
+00:03:01,370 --> 00:03:07,950
+مثل هذا الشخص الذي لديه تشوه في جنسه طبعًا لو بدنا
+
+36
+00:03:07,950 --> 00:03:12,050
+نتحدث عن الخنثى كمورّث مافي عنا أي مشكلة إيش
+
+37
+00:03:12,050 --> 00:03:15,390
+يهمّني إن المورّث ذكر أم أنثى؟ صح أم لا؟
+
+38
+00:03:15,390 --> 00:03:20,670
+ما يهمّني إذا الإشكال فيما لو كان وارثًا طيب السؤال
+
+39
+00:03:20,670 --> 00:03:25,290
+الثاني اللي بيترِث نفسه هل يتصور أن يكون الخنثى
+
+40
+00:03:25,290 --> 00:03:32,140
+أبًا؟ هل يتصور أن يكون أمًا؟ هل يتصور أن يكون جدًّا؟
+
+41
+00:03:32,140 --> 00:03:39,260
+جدّة؟ زوجة؟ زوج؟ إذا هؤلاء الستة ما فيش إمكانية أن
+
+42
+00:03:39,260 --> 00:03:44,140
+يكون الخنثى أمًا أو أبًا ما فيش مجال يكون جدًّا أو جدّة
+
+43
+00:03:44,140 --> 00:03:48,360
+ما فيش مجال يكون زوجًا أو زوجة لأن لو بدي أقول زوج
+
+44
+00:03:48,360 --> 00:03:53,120
+معناته هو ذكر زوجة أنثى يعني ما فيش خنثى أم أنثى وهكذا تمام؟ 
+
+45
+00:03:53,120 --> 00:03:58,960
+فإذًا لا يمكن أن يكون الخنثى واحدًا من
+
+46
+00:03:58,960 --> 00:04:02,060
+هؤلاء الستة يعني ما يوجد مجال يكون لا أبًا ولا أمًا ولا
+
+47
+00:04:02,060 --> 00:04:07,220
+جدًّا ولا جدّة ولا زوجًا ولا زوجة لكن في مجال يكون أخًا أو
+
+48
+00:04:07,220 --> 00:04:12,860
+أختًا أو ابنًا أو ابنة وهكذا حينها يحدث لدينا الإشكال
+
+49
+00:04:12,860 --> 00:04:21,100
+بمعنى ما يمكن أن أقول مثلًا ماتت عن أم خنثى كيف أم؟
+
+50
+00:04:21,100 --> 00:04:25,540
+كيف أصلاً أم إذا هي خنثى؟ صح أم لا؟ تمام، حلو، ما 
+
+51
+00:04:25,540 --> 00:04:31,200
+شاء الله عنكم علماء طيب، نأتي الآن لهذا الذي توفرت
+
+52
+00:04:31,200 --> 00:04:37,740
+فيه كلتا الآلتين لا عارفين هو رجل أم هو امرأة طبعًا
+
+53
+00:04:37,740 --> 00:04:44,200
+العلماء حينما جاءوا يعالجون هذا الأمر ابتداءً نظرُوا
+
+54
+00:04:44,200 --> 00:04:49,980
+إلى مَبْول أو من أين يَبُول؟ فإن كان يَبُول من ..
+
+55
+00:04:49,980 --> 00:04:54,320
+باعتبار هذا الشخص لديه الآلتين كما قلنا، فإن كان
+
+56
+00:04:54,320 --> 00:05:00,120
+يَبُول من آلة الرجل فهو ذكر وإن كان يَبُول من آلة
+
+57
+00:05:00,120 --> 00:05:05,290
+الأنثى فهو أنثى، طب ماذا لو بَوَل من كليهما؟ قال لك
+
+58
+00:05:05,290 --> 00:05:10,050
+بدنا نشوف السبق لمن فيهم بمعنى بَوَل ابتداء من أي
+
+59
+00:05:10,050 --> 00:05:14,250
+واحدة فيهم إذا بَوَل من البداية من آلة الأنثى فهو
+
+60
+00:05:14,250 --> 00:05:19,690
+أنثى وهكذا تمام فإذا صار في اجتهادات للعلماء في
+
+61
+00:05:19,690 --> 00:05:26,130
+مثل هذا الأمر هذه إشكالية في إشكالية ثانية وهي أن
+
+62
+00:05:26,130 --> 00:05:33,410
+الخنثى يا جماعة قد يتضح حاله يعني بعد فترة وجيزة من
+
+63
+00:05:33,410 --> 00:05:37,590
+ميلاده بهذا التشوه خلاص عرفنا أنه بعد ما نعود وال
+
+64
+00:05:37,590 --> 00:05:41,750
+ذكورة فإذا عرفت أنه ذكر نروح بعد كده نعمل له
+
+65
+00:05:41,750 --> 00:05:45,350
+معالجة طبية نعمل له عملية جراحية نزيل الآلة الأخرى
+
+66
+00:05:45,350 --> 00:05:50,050
+باعتبار خلاص واضح لنا أنه شو ذكر مثلًا أو العكس 
+
+67
+00:05:50,050 --> 00:05:54,110
+هذه خلاص إذا ما فيها إشكال إذا اتضح حاله وطالما
+
+68
+00:05:54,110 --> 00:05:59,470
+اتضح حاله إذا ما عاد عندي إشكال بمعنى أنني حينما
+
+69
+00:05:59,470 --> 00:06:03,430
+أريد أن أورّثه أورّثه باعتبار ما تبين من حاله
+
+70
+00:06:03,430 --> 00:06:09,290
+ما عندي مشكلة أحيانًا يا جماعة زي ما قلت لكم قبل شويّة
+
+71
+00:06:09,290 --> 00:06:14,710
+بأنه بَوَل من العضوين روحنا قلنا طب من الأسبق لجينا
+
+72
+00:06:14,710 --> 00:06:19,090
+في نفس اللحظة من الاثنين يعني صار عندي إشكال في أني
+
+73
+00:06:19,090 --> 00:06:23,410
+مش قادرة أحدد إيش هو فقال لك العلماء قديماً أنا
+
+74
+00:06:23,410 --> 00:06:27,750
+أتحدث هنا ما عندهم إمكانيات طبية يعرفهم مباشرة
+
+75
+00:06:27,750 --> 00:06:31,890
+يعملوا فحصًا جينيًا أو غير ذلك فكانوا ينتظرون إلى
+
+76
+00:06:31,890 --> 00:06:39,150
+البلوغ بينتظروه لما يبلغ فببلوغه يظهر أنثى صار في من
+
+77
+00:06:39,150 --> 00:06:44,890
+أو كذا ذكر طيب بعدين المفاتن الجسم صار في ظهور
+
+78
+00:06:44,890 --> 00:06:50,650
+أعضاء الأنوثة بشكل واضح أنثى، ظهور الشعر بالوجه
+
+79
+00:06:50,650 --> 00:06:57,310
+وكذا وكذا ذكر الصوت رقيق وناعم ولو كذا فلذلك هذه
+
+80
+00:06:57,310 --> 00:07:02,490
+العلامات تدل على جنسه ببلوغه بالتأكيد يعني اليوم
+
+81
+00:07:02,490 --> 00:07:06,850
+الطفل والطفلة هما صغار صوتهم زي بعض كلهم cute و
+
+82
+00:07:06,850 --> 00:07:10,470
+ناعم وما شاء الله، ببلوغ بتحسي أخوك أول ما يبلغ
+
+83
+00:07:10,470 --> 00:07:13,970
+بيكون طفل صغير وصوته مأحلى، أول ما يبلغ بتحسي خلاص
+
+84
+00:07:13,970 --> 00:07:17,950
+صار صوته رجال، صح غليظ، بخلاف الأنثى هكذا، هذه
+
+85
+00:07:17,950 --> 00:07:23,530
+علامات تدل على الجنس فأي علامة بتدل على الذكورة أو
+
+86
+00:07:23,530 --> 00:07:29,590
+الأنوثة نحكم بها وبالتالي خلاص اتضح جنسه إذا
+
+87
+00:07:29,590 --> 00:07:34,710
+لحظ معايا في عندي خنثى واضح في عندي خنثى مش واضح
+
+88
+00:07:34,710 --> 00:07:39,150
+لكن يرجع يتضح جنسه بالبلوغ زي ما حكينا ومع ذلك
+
+89
+00:07:39,150 --> 00:07:45,880
+يبقى هناك فئة من الخنثى لا يرجع يتضح جنسه بمعنى إن
+
+90
+00:07:45,880 --> 00:07:51,000
+الخلل أصلاً جيني عنده يعني مش بس الفكرة إنه فيه عضو
+
+91
+00:07:51,000 --> 00:07:54,720
+ذكورة وعضو أنوثة لا كمان في التركيبة الداخلية له
+
+92
+00:07:54,720 --> 00:07:58,340
+في ال chromosomes في أي شيء له علاقة بالجينات
+
+93
+00:07:58,340 --> 00:08:05,240
+الجنسية فعنده خلل فيها وبالتالي في عنده كل الأمرين
+
+94
+00:08:05,240 --> 00:08:08,740
+عنده شغلة للأنوثة وشغلة لـ .. في التركيبة الداخلية
+
+95
+00:08:08,740 --> 00:08:17,760
+أتحدث للذكورة فحينها يصعب إيش بيان جنس هذا الخنثى
+
+96
+00:08:17,760 --> 00:08:24,140
+لذلك كان في إشكال لدى علمائنا القدامى وقولنا إن
+
+97
+00:08:24,140 --> 00:08:28,140
+علمائنا القدامى حينما تحدثوا عن هذا الأمر زي ما
+
+98
+00:08:28,140 --> 00:08:32,200
+قلنا قبل شويّة إذا كان عرفوا من أين يبول فهو انسان
+
+99
+00:08:32,200 --> 00:08:38,160
+واتضح حاله وإلّا بدهم ينتظروا للبلوغ وحقيقة ما ذهب
+
+100
+00:08:38,160 --> 00:08:45,190
+إليه القدامى يبرّر في وقتهم، لكن في وقتنا لا يبرّر،
+
+101
+00:08:45,190 --> 00:08:49,330
+لماذا؟ لأنه اليوم بكل بساطة يولد هذا الشخص اللي
+
+102
+00:08:49,330 --> 00:08:55,580
+عنده الآلتين مثلًا، مباشرة أنا بأودّيه لجهة طبية دور
+
+103
+00:08:55,580 --> 00:09:00,080
+هذه الجهة الطبية بتعمل له فحصًا جينيًا واليوم سهل جدًّا
+
+104
+00:09:00,080 --> 00:09:04,160
+تعمل فحوصات جينية بتحدد لأن اليوم الطب يا جماعة
+
+105
+00:09:04,160 --> 00:09:10,280
+بيقف على الأجهزة الداخلية للإنسان سهل جدًّا يعرف
+
+106
+00:09:10,280 --> 00:09:15,660
+التركيبة الداخلية للإنسان بيعرف عدد الكروموسومات و
+
+107
+00:09:15,660 --> 00:09:20,040
+الكروموسومات هذه الـ XX أنثى الـ XY ذكر واو واو الأمور
+
+108
+00:09:20,040 --> 00:09:25,750
+هذه كلها التفصيل بيستطيع العلم إنه يعرفها وبالتالي
+
+109
+00:09:25,750 --> 00:09:30,090
+حتى هذا اللي كان القدامى يقولوا إحنا بدنا نستنى له
+
+110
+00:09:30,090 --> 00:09:35,330
+بلوغه حتى نحكم عليه اليوم في أيام معدودة الطب يقول
+
+111
+00:09:35,330 --> 00:09:39,610
+له هو ذكر أم أنثى مباشرة من خلال نتيجة الفحص اللي
+
+112
+00:09:39,610 --> 00:09:44,230
+بتطلع على أقصى تقدير بعد ثلاثة أسابيع على أقصى تقدير
+
+113
+00:09:44,230 --> 00:09:48,150
+يعني الفحوصات بدها خمسة أيام أسبوع ممكن عشرة ممكن
+
+114
+00:09:48,150 --> 00:09:51,130
+لحد واحد وعشرين يوم في الغالب هيك الطب يقول
+
+115
+00:09:51,130 --> 00:09:56,410
+تقريبًا وبالتالي ما في داعي نقعد نستنى البلوغ
+
+116
+00:09:56,410 --> 00:10:00,820
+خمسة عشر سنة حتى نجزم بالتالي لأنه أنا لما بدي أقول
+
+117
+00:10:00,820 --> 00:10:05,120
+إنه لازم أعرف الجنس حتى أورّث، معناته أنا بدي أستنى
+
+118
+00:10:05,120 --> 00:10:09,820
+حتى يتضح الجنس، فتخيلي إن هذا الشخص بدنا ننتظره
+
+119
+00:10:09,820 --> 00:10:15,970
+للبلوغ هذا يعني أننا سنضرب باقي الورثة وأن نقعد
+
+120
+00:10:15,970 --> 00:10:19,650
+نستنى عشر سنين، إحدى عشرة سنة، خمسة عشر سنة وهكذا
+
+121
+00:10:19,650 --> 00:10:24,890
+فالأمر بالتأكيد ليس منطقيًا وليس عمليًا، بناء على
+
+122
+00:10:24,890 --> 00:10:31,290
+ذلك ما في داعي ننتظر بلوغه حتى نُورّثه، تمام؟ وبناء
+
+123
+00:10:31,290 --> 00:10:35,070
+على ذلك إذا ظهر جنسه مباشرة باعتبار ما قالوا
+
+124
+00:10:35,070 --> 00:10:39,350
+العلماء من أنه من حيث يبول فخلاص إذا ما في داعي
+
+125
+00:10:39,350 --> 00:10:47,240
+للانتظار وبالتالي اتضح حاله ونحن نُورّثه بـ إيش؟ بشو؟ 
+
+126
+00:10:47,240 --> 00:10:52,140
+بالاعتبار الذي بان بالاعتبار الذي بان وتبيّن
+
+127
+00:10:52,140 --> 00:10:56,680
+وبالتالي قسمتنا راح تكون نهائية يعني لا هنستنى ولا
+
+128
+00:10:56,680 --> 00:11:02,200
+أي شيء لأنه خلاص تكشف لنا جنس هذا الخنثى أو هذا
+
+129
+00:11:02,200 --> 00:11:08,120
+المولود طيب لو تأخرت الأمور والكذا الكلام اللي
+
+130
+00:11:08,120 --> 00:11:12,100
+ذكرنا قلنا إنه قديماً كانوا بينتظروا لكن اليوم بدنا
+
+131
+00:11:12,100 --> 00:11:16,800
+نعالج المسألة ونقول بإنه صحيح أن ما ذهب إليه
+
+132
+00:11:16,800 --> 00:11:23,060
+فقهاؤنا القدامى كان بناء على الرؤية الطبية الممكنة 
+
+133
+00:11:24,540 --> 00:11:30,280
+في وقتهم وفي عصرهم أما وقد تطور العلم
+
+134
+00:11:30,280 --> 00:11:36,040
+وتطور الطب فإننا نستطيع القول بأن أو إن العلم
+
+135
+00:11:36,040 --> 00:11:41,920
+المعاصر قد وقف كما قلت قبل قليل على حقيقة الإنسان
+
+136
+00:11:41,920 --> 00:11:49,170
+الداخلية فعرف كل التركيبة وأعضاء الجنسية الداخلية 
+
+137
+00:11:49,170 --> 00:11:53,930
+وتكون بالنسبة للأجهزة الطبية واضحة جدًّا إن كان ذكر
+
+138
+00:11:53,930 --> 00:11:58,930
+أم أنثى بعيدًا عن المظهر
+
+139
+00:11:58,930 --> 00:12:03,570
+الخارجي وبناء على ذلك فإن الحكم عند الفقهاء
+
+140
+00:12:03,570 --> 00:12:08,970
+القدامى مسوّغ ومبرّر في وقتهم لكن في وقتنا لا يمكن
+
+141
+00:12:08,970 --> 00:12:14,410
+أن يقبل بأي حالة من الأحوال للسبب الذي ذكرته قبل
+
+142
+00:12:14,410 --> 00:12:20,370
+بالإضافة إلى ذلك أن موضوع القدامى كانوا كما قلنا
+
+143
+00:12:20,370 --> 00:12:24,590
+يحكمون بالظاهر أنه من وين وبعدين بنستنى البلوغ
+
+144
+00:12:24,590 --> 00:12:29,750
+و دائماً بيقفوا على علامات ظاهرة وقضية الوقوف على
+
+145
+00:12:29,750 --> 00:12:34,110
+العلامات الظاهرة مبدأ معروف في الشريعة الإسلامية
+
+146
+00:12:34,110 --> 00:12:39,320
+ومعتد به ومعتبر في حال إيش غابت الحقيقة يعني أنا مش
+
+147
+00:12:39,320 --> 00:12:44,360
+قادر أقف على الحقيقة حينها يجوز لي أن آخذ بالظاهر
+
+148
+00:12:44,360 --> 00:12:49,310
+ما في أي مشكلة عشان هيك قديمًا العلماء في موضوع القتل
+
+149
+00:12:49,310 --> 00:12:54,810
+حينما تحدثوا أن هذا القتل قتل عمد أو عضوان أو لا طبعا 
+
+150
+00:12:54,810 --> 00:12:58,830
+هذا له علاقة بقصد الجاني صح ولا لا لكن وقفوا على
+
+151
+00:12:58,830 --> 00:13:04,090
+الأداة التي استخدمها القاتل أو الجاني في جنايته
+
+152
+00:13:04,090 --> 00:13:08,730
+فكان ماسك مسدس أو سكين ويجي أسأله يقول لي مثلًا والله 
+
+153
+00:13:08,730 --> 00:13:13,230
+أنا كنت بس بعنّفه مسدس بتعنّفه أو تسجّره أو كذا فاكيد
+
+154
+00:13:13,230 --> 00:13:18,250
+هذه الأداة صارت دلالة ظاهرة على إرادة القتل بقصد 
+
+155
+00:13:18,250 --> 00:13:26,550
+وبعدوان وبعمدية تمام لكن إذا تبينت الحقيقة فليس لي
+
+156
+00:13:26,550 --> 00:13:31,450
+أن آخذ بالظاهر لحظي معي العلماء لجأوا إلى
+
+157
+00:13:31,450 --> 00:13:36,710
+الظاهر متى عند غياب الحقيقة فإذا ما تبينت الحقيقة 
+
+158
+00:13:37,300 --> 00:13:42,640
+فليس لي أن آخذ بالظاهر وهذا الأمر يقال في موضوع
+
+159
+00:13:42,640 --> 00:13:46,840
+الخنثى اليوم الطب وقف على حقيقة الإنسان الداخلية
+
+160
+00:13:46,840 --> 00:13:51,700
+وبالتالي سهل جدًا أن يقول لي جنس هذا الطفل الذي
+
+161
+00:13:51,700 --> 00:13:56,900
+عنده تشوّه جنسي هل هو ذكر أم أنثى طالما تبينت
+
+162
+00:13:56,900 --> 00:14:03,280
+الحقيقة ما الداعي إلى أن نأخذ بالظاهر، صح ولا صح؟
+
+163
+00:14:03,280 --> 00:14:08,440
+تمام، جميل بالإضافة لذلك بنرجع نقول بأنه لو كان
+
+164
+00:14:08,440 --> 00:14:13,340
+هناك خنثى ضمن الورثة التي أنا بدي أورّثها فالأصل
+
+165
+00:14:13,340 --> 00:14:18,940
+مباشرة آخذ هذا الخنثى وأروح لأي جهة طبية حتى تعمل 
+
+166
+00:14:18,940 --> 00:14:22,800
+فحص له عبر فحوصات معينة زي ما قلنا تشوف لي 
+
+167
+00:14:22,800 --> 00:14:26,780
+الكروموسومات التي عنده تشوف لي شغلات التي لها علاقة
+
+168
+00:14:26,780 --> 00:14:31,620
+بالتكوين الداخلي بالجينات بغير ذلك وبتعطيني نتيجة
+
+169
+00:14:31,620 --> 00:14:36,160
+هذا الفحص خلال أيام معدودة وهذه النتيجة بتقول لي إن
+
+170
+00:14:36,160 --> 00:14:42,000
+هو ذكر أم أنثى وهذا يعني لا داعي للانتظار حتى
+
+171
+00:14:42,000 --> 00:14:46,630
+بلوغه وهذا يعني أنه ما في داعي نجسم التركة ما في
+
+172
+00:14:46,630 --> 00:14:51,210
+داعي نقسم التركة باعتبار أنه بس أيام هنستنى بس
+
+173
+00:14:51,210 --> 00:14:56,450
+راح نستنى أيام وبالتالي ما في داعي أنه احنا إيش نجسم 
+
+174
+00:14:56,450 --> 00:14:59,990
+التركة ننتظر نتيجة الفحص وبناء عليها هتكون 
+
+175
+00:14:59,990 --> 00:15:04,910
+جنس حاله هو ذكر أم أنثى وبتكون القسمة وقتها نهائية
+
+176
+00:15:04,910 --> 00:15:11,300
+وما بعمل احتمال الذكورة واحتمال الأنوثة لكن أحيانًا 
+
+177
+00:15:11,300 --> 00:15:15,780
+من نتيجة الفحص بتجي تقول لي إن هذا فعلًا خنثى حقيقي،
+
+178
+00:15:15,780 --> 00:15:20,020
+شو يعني خنثى حقيقي؟ يعني أصلاً في التركيبة الداخلية 
+
+179
+00:15:20,020 --> 00:15:23,700
+له هو ذكر وأنثى، فيه شغلات لا الذكورة ولا
+
+180
+00:15:23,700 --> 00:15:29,090
+الأنوثة في نفس الوقت، وهذا ما فيش مجال لمعالجته عادة 
+
+181
+00:15:29,090 --> 00:15:33,790
+لو كانت الإشكالية خارجية سهل المعالجة، لكن إذا كان
+
+182
+00:15:33,790 --> 00:15:37,430
+الإشكال في الجينات، خلاص، فهذا بنقول عنه خنثى
+
+183
+00:15:37,430 --> 00:15:42,290
+حقيقي، شو يعني خنثى حقيقي؟ يعني ما فيش مجال يصير ما
+
+184
+00:15:42,290 --> 00:15:46,670
+قاله ذكورة أو أنوثة، يعني لن يتضح حاله أبدًا، فهو 
+
+185
+00:15:46,670 --> 00:15:52,210
+يُجمع بين الذكورة والأنوثة فهذا الخنثى الحقيقي ..
+
+186
+00:15:52,210 --> 00:15:57,390
+هذا الخنثى الحقيقي كيف لنا أن نتعامل معه؟ طبعًا 
+
+187
+00:15:57,390 --> 00:16:01,430
+سنتحدث حول الخنثى الحقيقية المحاضرة القادمة بإذن
+
+188
+00:16:01,430 --> 00:16:06,170
+الله باعتباري أنه قليل نادر قليل نادر في موضوع 
+
+189
+00:16:06,170 --> 00:16:12,230
+الخنثى هو أن يكون حقيقيًا إذا الغالب في الخنثى أنه
+
+190
+00:16:12,230 --> 00:16:16,390
+واضح أو يرجع يَفتَضح حاله عبر إجراء فحص جيني معيّن
+
+191
+00:16:16,390 --> 00:16:21,530
+حينها نقف على حقيقته لكن قضية الخنثى الحقيقي هذا
+
+192
+00:16:21,530 --> 00:16:28,190
+مسألة موجودة لكنها نادرة وعلاجها راح يكون وفقًا لما
+
+193
+00:16:28,190 --> 00:16:33,610
+سنعالجه المحاضرة القادمة أو بعد القادمة بإذن الله
+
+194
+00:16:33,610 --> 00:16:38,870
+رب العالمين السلام عليكم وبناء على ذلك نرجع نقول بأن
+
+195
+00:16:38,870 --> 00:16:44,930
+تحديد جنس الخنثى لا يحتاج منّا أن ننتظر بلوغه حتى
+
+196
+00:16:44,930 --> 00:16:52,110
+نحكم عليه بأنه ذكر أم أنثى بل إن هذا سيستغرق معنا 
+
+197
+00:16:52,110 --> 00:16:57,470
+أيام قليلة حينها لا داعي كما قلنا لتقسيم التركة بل
+
+198
+00:16:57,470 --> 00:17:02,630
+ننتظر قليلًا حتى نقسم التركة على الورثة بما فيهم
+
+199
+00:17:02,630 --> 00:17:05,430
+الخنثى الذي اتّضح حاله تمام؟
+
+200
+00:17:08,880 --> 00:17:13,640
+وبناء على ذلك وفق الكلام الذي قدمته قبل قليل
+
+201
+00:17:13,640 --> 00:17:18,900
+نستطيع القول باختصار شديد أن مسائل الخنثى تنحصر بس
+
+202
+00:17:18,900 --> 00:17:23,340
+في مسائل الخنثى الحقيقي الذي لا يرجى اتضاح جنسه
+
+203
+00:17:23,340 --> 00:17:28,060
+أبدًا فهذا الذي يواجهنا أو بيكون فيه إشكال في 
+
+204
+00:17:28,060 --> 00:17:32,190
+توريثه بس هذا القسم وهذا النوع لأن الخنثى الآخر
+
+205
+00:17:32,190 --> 00:17:37,030
+حتى الذي لم تظهر عليه علامات الأنوثة أو الخنوثة أو
+
+206
+00:17:37,030 --> 00:17:41,030
+الذكورة عفوا قلنا الفحص الجيني بيقول لي إيش هو و
+
+207
+00:17:41,030 --> 00:17:44,250
+خلال أيام بتطلع النتيجة إذا ما في عندي مشكلة أبدًا
+
+208
+00:17:44,250 --> 00:17:50,050
+في التوريث صح ولا صح تمام لذلك بنقول بأن الذي
+
+209
+00:17:50,050 --> 00:17:54,290
+يحتاج إلى معالجة هو الخنثى الحقيقي أو مسائل الخنثى 
+
+210
+00:17:54,290 --> 00:18:01,180
+الحقيقي فقط ومع ذلك أحيانًا بقول لك صحيح أن الخناثى
+
+211
+00:18:01,180 --> 00:18:05,600
+الذي يرجى اتضاحه، مش الحقيقي، الذي يرجى اتضاحه 
+
+212
+00:18:05,600 --> 00:18:09,500
+أن الطب قال لي مثلًا بعد عشرة أيام بتطلع النتيجة،
+
+213
+00:18:09,500 --> 00:18:15,070
+فرضًا في ضمن الورثة كان حاجز لعملية وبدها مبلغ 
+
+214
+00:18:15,070 --> 00:18:19,410
+معيّن وبدّه نصيبه من التركة لأنه محتاجها ضروري،
+
+215
+00:18:19,410 --> 00:18:22,910
+أنجله أستنى عشرة؟ طب ما هو مضطر يعني العملية هتروح 
+
+216
+00:18:22,910 --> 00:18:26,090
+عليه هيدخله حد إن بدله بتعرفوا جزء العمليات، بدها
+
+217
+00:18:26,090 --> 00:18:31,270
+حجوزات مسبقة أو أي لغير ذلك فإذا اضطر الورثة 
+
+218
+00:18:31,270 --> 00:18:34,470
+اضطرارًا للتعجيل في القسمة، لحظة يقول التعجيل
+
+219
+00:18:34,470 --> 00:18:37,950
+باعتبار أنه طالما في مجال نعرف الجنس ما في داعي لا 
+
+220
+00:18:37,950 --> 00:18:43,970
+أن نقسم لكن إذا اضطروا اضطرارًا لتعجيل القسمة فإن 
+
+221
+00:18:43,970 --> 00:18:50,010
+هذا جائز وبتكون القسمة مؤقته شو يعني مؤقته؟ بمعنى
+
+222
+00:18:50,010 --> 00:18:54,210
+هأعمل اعتبارين لعند ما يجي نتيجة الفحص وبنعدّل 
+
+223
+00:18:54,210 --> 00:18:59,330
+التوريث الذي عملناه وهذا يعني أنه لازم لازم أثناء
+
+224
+00:18:59,330 --> 00:19:04,990
+التوريث إيش بدي أعمل للخنثى بالتأكيد هأعمل فرضيتين
+
+225
+00:19:04,990 --> 00:19:10,470
+فرض الذكورة وفرض الأنوثة وأورّث الخنثى بالأسوأ 
+
+226
+00:19:11,680 --> 00:19:15,960
+بالأسوأ لحظة في الحال كنا نقول نوقف له هان مش نوقف
+
+227
+00:19:15,960 --> 00:19:19,940
+لأنه أصلاً هو موجود هنعطيه يعني هنعطيه مش نوقف له 
+
+228
+00:19:19,940 --> 00:19:26,580
+نُورّث الخنثى بالأسوأ أي بالأقل وكذلك باقي الورثة 
+
+229
+00:19:26,580 --> 00:19:30,420
+بالأسوأ يعني نُورّث الجميع باليقين شو يعني باليقين
+
+230
+00:19:30,420 --> 00:19:34,220
+بالشيء المتأكدين منه يعني إحنا متأكدين أنه بياخد
+
+231
+00:19:34,220 --> 00:19:38,780
+الألف دينار لكن قضية ممكن ياخذ أكثر من الألف هذه مش
+
+232
+00:19:38,780 --> 00:19:42,900
+عارفين مش متأكدين لكن المتأكدين منه الألف فبنعطي 
+
+233
+00:19:42,900 --> 00:19:47,460
+الجميع الأقل أو الأسوأ ونوقف الفرضية الباقية
+
+234
+00:19:47,460 --> 00:19:53,340
+بنخبيها هنعطي الجميع الأسوأ بمن فيهم الخنسة بمن
+
+235
+00:19:53,340 --> 00:19:57,480
+فيهم الخنسة بنعطي الكل الأسوأ وبنخبي الفرضية لأنه
+
+236
+00:19:57,480 --> 00:20:02,490
+الطبيعي كونه أعطيت الكل الأسوأ معناته فيه فرق نخبيه
+
+237
+00:20:02,490 --> 00:20:07,230
+عندي لما تجي نتيجة الفحص قالت لي ذكر فبدنا نشوف 
+
+238
+00:20:07,230 --> 00:20:12,670
+الذي أخذه هو فعلًا كان الذكر هو الأسوأ مثلًا ولا لأ
+
+239
+00:20:12,670 --> 00:20:16,890
+هو بيستاهل أكثر من كده فإذا بيستاهل أكثر من كده
+
+240
+00:20:16,890 --> 00:20:23,150
+معناته بدي أروح إيش؟ أرد عليه هو الباقي هو بينما لو
+
+241
+00:20:23,150 --> 00:20:28,410
+تبين أن الذي أخذه الأسوأ هو فعلًا الذي أخذه فالباقي
+
+242
+00:20:28,410 --> 00:20:31,330
+بدي أرده على باقي الورثة لأنه تبين أن الورثة
+
+243
+00:20:31,330 --> 00:20:38,380
+بيستحقّه أكثر ممّا وقف إليه هذا ما سنعالجه عمليًا
+
+244
+00:20:38,380 --> 00:20:42,760
+بمسائل إن شاء الله المحاضرة القادمة إلى هنا نكون
+
+245
+00:20:42,760 --> 00:20:46,840
+قد انتهينا من موضوع محاضرتنا لهذا اليوم أقول قولي 
+
+246
+00:20:46,840 --> 00:20:50,460
+هذا وأستغفر الله لي ولكم وصلى اللهم وسلم وبارك
+
+247
+00:20:50,460 --> 00:20:54,120
+على سيدنا محمد والسلام عليكم ورحمة الله تعالى 
+
+248
+00:20:54,120 --> 00:20:54,940
+وبركاته
diff --git a/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/88PynwLnIxQ_postprocess.srt b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/88PynwLnIxQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f59c3a8b9b2988cab07ea169ed6b83d5ad451cb5
--- /dev/null
+++ b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/88PynwLnIxQ_postprocess.srt
@@ -0,0 +1,992 @@
+1
+00:00:04,940 --> 00:00:08,080
+أعوذ بالله السمعي لعليه من الشيطان الرجيم بسم الله
+
+2
+00:00:08,080 --> 00:00:11,300
+الرحمن الرحيم الحمد لله رب العالمين والصلاة
+
+3
+00:00:11,300 --> 00:00:15,480
+والسلام على أشرف الأنبياء والمرسلين سيدنا محمد بن
+
+4
+00:00:15,480 --> 00:00:18,540
+عبد الله الصادق الأمن ثم عما بعد أحييكم جميعا
+
+5
+00:00:18,540 --> 00:00:22,320
+بتحية الإسلام فالسلام عليكم ورحمة الله تعالى
+
+6
+00:00:22,320 --> 00:00:27,600
+وبركاته كيف حالكوا نطيبات ان شاء الله؟تمام إذا
+
+7
+00:00:27,600 --> 00:00:31,940
+لازلنا نتحدث حول الميراث بالتقدير والاحتياط قلنا
+
+8
+00:00:31,940 --> 00:00:37,280
+إن هناك جملة من الورثة نورثهم ليس على جهة القطع
+
+9
+00:00:37,280 --> 00:00:42,960
+والجزم بل على جهة التقدير والاحتياطفتحدثنا ابتداء
+
+10
+00:00:42,960 --> 00:00:49,200
+عن ميراث الحمل وعرفنا أننا لسنا جازمين من جنس
+
+11
+00:00:49,200 --> 00:00:54,760
+الحمل بالإضافة إلى أننا لسنا جازمين من حياته لذا
+
+12
+00:00:54,760 --> 00:01:00,600
+الأمر اقتضى أن نورثه باعتبارين ثم نوقف له الاعتبار
+
+13
+00:01:00,600 --> 00:01:05,530
+الأبضل على التفصيل الذي ذكرناه سابقااليوم بإذن
+
+14
+00:01:05,530 --> 00:01:10,970
+الله سنتحدث عن ميراث الخنسة ابدا خلونا نعرف مع بعض
+
+15
+00:01:10,970 --> 00:01:15,730
+من هو الخنسة يلا نحاول .. مين تحاول تعرفلنا
+
+16
+00:01:15,730 --> 00:01:23,090
+الخنسة؟ الخنسة، من هو الخنسة قبل ما نحكي الإشكال
+
+17
+00:01:23,090 --> 00:01:31,230
+في توريثه؟ يلا يا فادياهو أنه .. هو أن يولد شخص
+
+18
+00:01:31,230 --> 00:01:37,250
+بمشكلة عنده بالتشوّق .. بتشوّق جنسي قد يولد بجهاز
+
+19
+00:01:37,250 --> 00:01:41,590
+بكري وانثوين في نفس الاشي في نفس الوقت أو مثلا
+
+20
+00:01:41,590 --> 00:01:46,420
+بدون أي جهاز .. بدون أي ..بارك الله فيك، إذا
+
+21
+00:01:46,420 --> 00:01:52,140
+باختصار شديد نقول الأنثى هو من ليس له لا آلة الرجل
+
+22
+00:01:52,140 --> 00:01:56,420
+ولا آلة المرأة بمعنى ما ليش عضو تناسل لا للذكر ولا
+
+23
+00:01:56,420 --> 00:02:03,120
+للأنثى أو من اجتمع فيه في آن واحد آلتي الرجل
+
+24
+00:02:03,120 --> 00:02:10,030
+والمرأةوبالتالي في مظهره لسنا يعني نستطيع أن نحدد
+
+25
+00:02:10,030 --> 00:02:15,150
+جنسه فلديه آلة الرجل و آلة المرأة فهذا هو الخنثاء
+
+26
+00:02:15,150 --> 00:02:19,910
+لذلك نستطيع القول بإنه من المشكلات اللي بتواجهنا
+
+27
+00:02:19,910 --> 00:02:25,590
+في موضوع الميراث موضوع التشوه الجنسي فإننا قد نجد
+
+28
+00:02:25,590 --> 00:02:32,350
+إنسان يولد ولديه كتر آلتين وقد نجد إنسان يولد وليس
+
+29
+00:02:32,350 --> 00:02:37,620
+لديه أي آلةفبالتأكيد هيكون عندنا إشكال في توريثه
+
+30
+00:02:37,620 --> 00:02:41,720
+باعتبار أنه الميراث كما سبق و أنقولنا بالتأكيد
+
+31
+00:02:41,720 --> 00:02:46,500
+الجنس له دور في التوريث بمعنى الذكر و الأنثى في
+
+32
+00:02:46,500 --> 00:02:51,220
+مسائل بسيطة يتساوى ميراث الذكر و الأنثى لكن الكثير
+
+33
+00:02:51,220 --> 00:02:56,450
+الغالبهو أن يختلف الميراث في حال الذكورة عن حال
+
+34
+00:02:56,450 --> 00:03:01,370
+الأنوثة مما يوقعنا في إشكال إن كيف لنا أن نوارث
+
+35
+00:03:01,370 --> 00:03:07,950
+مثل هذا الشخص الذي لديه تشوه في جنسه طبعا لو بدنا
+
+36
+00:03:07,950 --> 00:03:12,050
+نتحدث عن الخنثة كموارث مافي عنا أي مشكلة إيش
+
+37
+00:03:12,050 --> 00:03:15,390
+يعنيني إن الموارث ذكر ولا أنثى؟ صح ولا لا؟
+
+38
+00:03:15,390 --> 00:03:20,670
+مابيهمني إذا الإشكال فيما لو كان وارثاطيب السؤال
+
+39
+00:03:20,670 --> 00:03:25,290
+التاني اللي بيترح نفسه هل يتصور أن يكون الخنثا
+
+40
+00:03:25,290 --> 00:03:32,140
+أبان؟هل يتصور أن يكون أمًا؟ هل يتصور أن يكون جدًا؟
+
+41
+00:03:32,140 --> 00:03:39,260
+جدًا؟ زوجة؟ زوجة؟ إذا هذول الستة مافيش إمكانية أن
+
+42
+00:03:39,260 --> 00:03:44,140
+يكون الخنثة أم أو أب مافيش مجال يكون جد أو جدة
+
+43
+00:03:44,140 --> 00:03:48,360
+مافيش مجال يكون زوج أو زوجة لأن لو بدي أقول زوج
+
+44
+00:03:48,360 --> 00:03:53,120
+معناته هو ذكر زوجة أنثى يعني مافيش خنثة أم أنثى و
+
+45
+00:03:53,120 --> 00:03:58,960
+هكذا تمام؟فإذا لا يمكن أن يكون الخنسة واحدا من
+
+46
+00:03:58,960 --> 00:04:02,060
+أولاء الستة يعني مايوجد مجال يكون لا أب ولا أم ولا
+
+47
+00:04:02,060 --> 00:04:07,220
+جد ولا جدة ولا زوج ولا زوجة لكن في مجال يكون أخ أو
+
+48
+00:04:07,220 --> 00:04:12,860
+أخت أو ابن أو ابن و هكذا حينها يحدث لدينا الإشكال
+
+49
+00:04:12,860 --> 00:04:21,100
+بمعنى مايمكن أن أقول مثلا مات عن أم خنسةكيف أم؟
+
+50
+00:04:21,100 --> 00:04:25,540
+كيف أصلا أم إذا هي خنزة؟ صح ولا لا؟ تمام، حلو، ما
+
+51
+00:04:25,540 --> 00:04:31,200
+شاء الله عنكم علماء طيب، نيجي الآن لهذا الذي توفرت
+
+52
+00:04:31,200 --> 00:04:37,740
+فيه كلتل آلتين لا عارفين هو رجل ولا هو امرأة طبعا
+
+53
+00:04:37,740 --> 00:04:44,200
+العلماء حينما جاءوا يعالجوا هذا الأمر ابتداء نظروا
+
+54
+00:04:44,200 --> 00:04:49,980
+إلى مبالغ أو من أين يابولفإن كان يبول من ..
+
+55
+00:04:49,980 --> 00:04:54,320
+باعتبار هذا الشخص لديه الآلتين كما قلنا، فإن كان
+
+56
+00:04:54,320 --> 00:05:00,120
+يبول من آلة الرجل فهو ذكر وإن كان يبول من آلة
+
+57
+00:05:00,120 --> 00:05:05,290
+الأنثى فهو أنثى، طب ماذا لو بال من كليه ما؟قال لك
+
+58
+00:05:05,290 --> 00:05:10,050
+بدنا نشوف السبق لمين فيهم بمعنى بال ابتداء من أي
+
+59
+00:05:10,050 --> 00:05:14,250
+واحدة فيهم إذا بال من البداية من آلة الأنثى فهو
+
+60
+00:05:14,250 --> 00:05:19,690
+أنثى و هكذا تمام فإذا صار في اجتهادات للعلماء في
+
+61
+00:05:19,690 --> 00:05:26,130
+مثل هذا الأمر هذه إشكالية في إشكالية تانية وهي أن
+
+62
+00:05:26,130 --> 00:05:33,410
+الخنسة يا جماعة قد يتضح حالهيعني بعد فترة وجيزة من
+
+63
+00:05:33,410 --> 00:05:37,590
+ميلاده بهذا التشوه خلاص أعرفنا أنه بعد ما نعود و
+
+64
+00:05:37,590 --> 00:05:41,750
+الذكورة فإذا أعرفت أنه ذكر بنروح بعد كده بنعالجه
+
+65
+00:05:41,750 --> 00:05:45,350
+معالجة طبية بنعمله عملية جراحية نزيل الآلة الأخرى
+
+66
+00:05:45,350 --> 00:05:50,050
+باعتبار خلاص واضح لإلنا أنه شو ذكر مثلا أو العكسو
+
+67
+00:05:50,050 --> 00:05:54,110
+هذه خلاص إذا مافيها إشكال إذا اتضحها حاله و طالما
+
+68
+00:05:54,110 --> 00:05:59,470
+اتضح حاله إذا ماعدش عندي إشكال بمعنى أنني حينما
+
+69
+00:05:59,470 --> 00:06:03,430
+أريد أن أورثه أورثه باعتباري ما تبين من حاله
+
+70
+00:06:03,430 --> 00:06:09,290
+ماعندي مشكلة أحيانا يا جماعة زي ما قلتلكم قبل شويه
+
+71
+00:06:09,290 --> 00:06:14,710
+بأنه بال من العضوينروحنا قولنا طب من الأسبق لجينا
+
+72
+00:06:14,710 --> 00:06:19,090
+في نفس اللحظة من التنين يعني صار عندي إشكال في أني
+
+73
+00:06:19,090 --> 00:06:23,410
+مش قادرة أحدد إيش هو فقال لك العلماء قديما أنا
+
+74
+00:06:23,410 --> 00:06:27,750
+أتحدث هنا ما عندهم إمكانيات طبية يعرفهم مباشرة
+
+75
+00:06:27,750 --> 00:06:31,890
+يعملوا فحص جيني أو غير ذلك فكانوا ينتظرون إلى
+
+76
+00:06:31,890 --> 00:06:39,150
+البلغةبينتظروه لما يبلغ فببلغه حاض أنثى صار في من
+
+77
+00:06:39,150 --> 00:06:44,890
+أو كذا ذكر طيب بعدين المفاتن الجسم صار في ظهور
+
+78
+00:06:44,890 --> 00:06:50,650
+أعضاء الأنوثة بشكل واضح أنثى، ظهور الشعر بالوجه
+
+79
+00:06:50,650 --> 00:06:57,310
+وكذا وكذا ذكر الصوت رقيق وناعم ولو كذا فلذلك هذه
+
+80
+00:06:57,310 --> 00:07:02,490
+العلامات تدل على جنسه ببلغه بالتأكيديعني اليوم
+
+81
+00:07:02,490 --> 00:07:06,850
+الطفل و الطفلة هما نصغار صوتهم زي بعت كلهم cute و
+
+82
+00:07:06,850 --> 00:07:10,470
+نوعم و ما شاء الله، بالبلغ بتحسي أخوكي أول ما بلغ
+
+83
+00:07:10,470 --> 00:07:13,970
+بيكون طفل صغير و صوته مأحلى، أول ما بلغ بتحسي خلاص
+
+84
+00:07:13,970 --> 00:07:17,950
+صار صوته رجال، صح غليظ، بخلاف الأنثوا هكذا، هذه
+
+85
+00:07:17,950 --> 00:07:23,530
+علامات تدول على الجنسفأي علامة بتدل على الذكورة أو
+
+86
+00:07:23,530 --> 00:07:29,590
+الأنوثة نحكموا بذلك وبالتالي خلاص اتضاح جنسه إذا
+
+87
+00:07:29,590 --> 00:07:34,710
+لحظي معايا في عندي خنسة واضح في عندي خنسة مش واضح
+
+88
+00:07:34,710 --> 00:07:39,150
+لكن يرجع اتضاح جنسه بالبلغ زي ما حكينا ومع ذلك
+
+89
+00:07:39,150 --> 00:07:45,880
+يبقى هناك فئة من الخنسة لا يرجع اتضاح جنسهبمعنى إن
+
+90
+00:07:45,880 --> 00:07:51,000
+الخلل أصلا جيني عنده يعني مش بس الفكرة إنه فيه عضو
+
+91
+00:07:51,000 --> 00:07:54,720
+ذكورة وعضو أنوثة لأ كمان في التركيبة الداخلية لإله
+
+92
+00:07:54,720 --> 00:07:58,340
+في ال chromosomes في أي شيء له علاقة بالجينات
+
+93
+00:07:58,340 --> 00:08:05,240
+الجنسية فعنده خلل فيها وبالتالي في عنده كل الأمرين
+
+94
+00:08:05,240 --> 00:08:08,740
+عنده شغلة للأنوثة وشغلة ل .. في التركيبة الداخلية
+
+95
+00:08:08,740 --> 00:08:17,760
+أتحدث للذكورة فحينها يصعدإيش بيان جنس هذا الخنسة
+
+96
+00:08:17,760 --> 00:08:24,140
+لذلك كان في إشكال لدى علمائنا القدامى وقولت إن
+
+97
+00:08:24,140 --> 00:08:28,140
+علمائنا القدامى حينما تحدثوا عن هذا الأمر زي ما
+
+98
+00:08:28,140 --> 00:08:32,200
+قلنا قبل شوية إذا كان عرفوا من أين يبور فهو أنسا
+
+99
+00:08:32,200 --> 00:08:38,160
+واتضح حاله وإلا بدهم ينتظروا لالبلوغ وحقيقة ما ذهب
+
+100
+00:08:38,160 --> 00:08:45,190
+إليه القدامىيبرر في وقتهم، لكن في وقتنا لا يبرر،
+
+101
+00:08:45,190 --> 00:08:49,330
+ليش؟ لأنه اليوم بكل بساطة بينولد هذا الشخص اللي
+
+102
+00:08:49,330 --> 00:08:55,580
+عنده الآلتين مثلا، مباشرة أنا بوديه لجهة طبيةدور
+
+103
+00:08:55,580 --> 00:09:00,080
+هذه الجهة الطبية بتعمله فحص جيني و اليوم سهل جدا
+
+104
+00:09:00,080 --> 00:09:04,160
+تعمل فحصات جينية بتحدد لأن اليوم الطب يا جماعة
+
+105
+00:09:04,160 --> 00:09:10,280
+بيقف على الأجهزة الداخلية للإنسان سهل جدا يعرف
+
+106
+00:09:10,280 --> 00:09:15,660
+التركيبة الداخلية للإنسان بيعرف عدد الكرموسومات و
+
+107
+00:09:15,660 --> 00:09:20,040
+الكرموسومات هاي ال XX انثال XY ذكر واو واو الأمور
+
+108
+00:09:20,040 --> 00:09:25,750
+هاي كلهاالتفصيل بيستطيع العلم انه يعرفها وبالتالي
+
+109
+00:09:25,750 --> 00:09:30,090
+حتى هذا اللي كان القدامى يقولوا احنا بدنا نستنى له
+
+110
+00:09:30,090 --> 00:09:35,330
+بلغه حتى نحكم عليه اليوم في أيام معدودة الطب يقول
+
+111
+00:09:35,330 --> 00:09:39,610
+لي هو ذكر او أنثىمباشرة من خلال نتيجة الفحص اللى
+
+112
+00:09:39,610 --> 00:09:44,230
+بتطلع على أقصى تقدير بعد تلت أسابيع على أقصى تقدير
+
+113
+00:09:44,230 --> 00:09:48,150
+يعني الفحصات بدها خمس أيام أسبوع ممكن عشرة ممكن
+
+114
+00:09:48,150 --> 00:09:51,130
+لعند واحد وعشرين يوم في الغالب هيك الطب يقول
+
+115
+00:09:51,130 --> 00:09:56,410
+تقريبا وبالتالي مافي داعي نقعد نستمى البلوغ
+
+116
+00:09:56,410 --> 00:10:00,820
+خمستاشر سنة حتى نجسم التاريخلأنه أنا لما بدي أقول
+
+117
+00:10:00,820 --> 00:10:05,120
+إنه لازم أعرف الجنس حتى أورث، معناته أنا بدي أستنى
+
+118
+00:10:05,120 --> 00:10:09,820
+حتى يتضح الجنس، فتخيلي إن هذا الشخص بدنا ننتظره
+
+119
+00:10:09,820 --> 00:10:15,970
+للبلوغهذا يعني أننا سنضرب باقي الورثة وأن نقعد
+
+120
+00:10:15,970 --> 00:10:19,650
+نستنى عشر سنين، احد عشر سنة، خمس عشر سنة و هكذا
+
+121
+00:10:19,650 --> 00:10:24,890
+فالأمر بالتأكيد ليس منطقيا و ليس عمليا، بناء على
+
+122
+00:10:24,890 --> 00:10:31,290
+ذلك مافي داعي ننتظر بلوغه حتى نورثه، تمام؟وبناء
+
+123
+00:10:31,290 --> 00:10:35,070
+على ذلك إذا ظهر جنسه مباشرة باعتبار ما قالوا
+
+124
+00:10:35,070 --> 00:10:39,350
+العلماء من أنه من حيث يقول فخلاص إذا مافي داعي
+
+125
+00:10:39,350 --> 00:10:47,240
+للانتظار وبالتالي اتضح حاله ونحن نورسه ب إيش؟بشوق
+
+126
+00:10:47,240 --> 00:10:52,140
+بالاعتبار اللذي بان بالاعتبار اللذي بان و تبين
+
+127
+00:10:52,140 --> 00:10:56,680
+وبالتالي قسمتنا راح تكون نهائية يعني لا هنستنى ولا
+
+128
+00:10:56,680 --> 00:11:02,200
+أي شيء لأنه خلاص تكشف لنا جنس هذا الخنثة أو هذا
+
+129
+00:11:02,200 --> 00:11:08,120
+المولودطيب لو اتأخرت الأمرات والكذا الكلام اللي
+
+130
+00:11:08,120 --> 00:11:12,100
+ذكرنا قلنا إنه قديما كانوا بينتظروا لكن اليوم بدنا
+
+131
+00:11:12,100 --> 00:11:16,800
+نعالج المسألة ونقول بإنه صحيح أن ما ذهب إليه
+
+132
+00:11:16,800 --> 00:11:23,060
+فقهائنا القدامى كان بناء على الرؤية الطبية الاش
+
+133
+00:11:24,540 --> 00:11:30,280
+الممكنة في وقتهم وفي عصرهم أما وقد تطور العلم
+
+134
+00:11:30,280 --> 00:11:36,040
+وتطور الطب فإننا نستطيع القول بإن أو إن العلم
+
+135
+00:11:36,040 --> 00:11:41,920
+المعاصر قد وقف كما قلت قبل قليل على حقيقة الإنسان
+
+136
+00:11:41,920 --> 00:11:49,170
+الداخلية فعرف كل التركيبة وأعضاء الجنسية الداخليةو
+
+137
+00:11:49,170 --> 00:11:53,930
+تكون بالنسبة للأجهزة الطبية واضحة جدا إن كان ذكر
+
+138
+00:11:53,930 --> 00:11:58,930
+أو أنثى بعيدا عن المظهر
+
+139
+00:11:58,930 --> 00:12:03,570
+الخارجي وبناء على ذلك فإن الحكم عند الفقهاء
+
+140
+00:12:03,570 --> 00:12:08,970
+القدامى مسوّغ ومبرر في وقتهم لكن في وقتنا لا يمكن
+
+141
+00:12:08,970 --> 00:12:14,410
+أن يقبل بأي حالة من الأحوال للسبب الذي ذكرته قبل
+
+142
+00:12:14,410 --> 00:12:20,370
+قليلإضافة إلى ذلك أن موضوع القدامى كانوا كما قلنا
+
+143
+00:12:20,370 --> 00:12:24,590
+يحكمون بالظاهر أنه من وين بال وبعدين بنستنى البلوغ
+
+144
+00:12:24,590 --> 00:12:29,750
+وواءزا بيقفوا على علامات ظاهرة وقضية الوقوف على
+
+145
+00:12:29,750 --> 00:12:34,110
+العلامات الظاهرة مبدأ معروف في الشريعة الإسلامية
+
+146
+00:12:34,110 --> 00:12:39,320
+ومعتد به ومعتبرفي حال إيش غابت الحقيقة يعني أنا مش
+
+147
+00:12:39,320 --> 00:12:44,360
+قادر أجف على الحقيقة حينها يجوز لي أن أاخد بالظاهر
+
+148
+00:12:44,360 --> 00:12:49,310
+مافي أي مشكلةعشان هيك قديما العلماء في موضوع القتل
+
+149
+00:12:49,310 --> 00:12:54,810
+حينما تحدثوا أن هذا القتل قتل عمض عضوان أو لا طبعا
+
+150
+00:12:54,810 --> 00:12:58,830
+هذا له علاقة بقصد الجاني صح ولا لا لكن وقفوا على
+
+151
+00:12:58,830 --> 00:13:04,090
+الآلة اللى استخدمها القاتل او الجاني في جنايته
+
+152
+00:13:04,090 --> 00:13:08,730
+فكان ماسط مسدس او سكين واجى اسأله يقولى مثلا والله
+
+153
+00:13:08,730 --> 00:13:13,230
+أنا كنت بس بعنفه مسدس بتعنفه او تسجره او كذا فاكيد
+
+154
+00:13:13,230 --> 00:13:18,250
+هذه الآلة صارتدلالة ظاهرة على إيرادة القتل بقصد
+
+155
+00:13:18,250 --> 00:13:26,550
+وبعدوان وبعمدية تمام لكن إذا تبينت الحقيقة فليس لي
+
+156
+00:13:26,550 --> 00:13:31,450
+أن أاخذ بالظاهر لحظي معايا العلماء لجأوا إلى
+
+157
+00:13:31,450 --> 00:13:36,710
+الظاهر إمتى عند غياب الحقيقة فإذا ما تبينت الحقيقة
+
+158
+00:13:37,300 --> 00:13:42,640
+فليس لي أن أاخذ بالظاهر وهذا الأمر يقال في موضوع
+
+159
+00:13:42,640 --> 00:13:46,840
+الخنثة اليوم الطب وقف على حقيقة الإنسان الداخلية
+
+160
+00:13:46,840 --> 00:13:51,700
+وبالتالي سهل جدا أن يقول لي جنس هذا الطفل اللي
+
+161
+00:13:51,700 --> 00:13:56,900
+عنده تشوه جنسي هل هو ذكر أو أنثى طالما تبينت
+
+162
+00:13:56,900 --> 00:14:03,280
+الحقيقة ما الداعي إلى أننأخذ بالظاهر، صح ولا صح؟
+
+163
+00:14:03,280 --> 00:14:08,440
+تمام، جميل بالإضافة لذلك بنرجع نقول بإنه لو كان
+
+164
+00:14:08,440 --> 00:14:13,340
+هناك خنزة ضمن الورثة اللي أنا بدي أورثها فالأصل
+
+165
+00:14:13,340 --> 00:14:18,940
+مباشرة أاخد هذا الخنزة و أروح لأي جهة طبيةحتى تعمل
+
+166
+00:14:18,940 --> 00:14:22,800
+فحص لإله عبر فحصات معينة زي ما قلنا تشوفلي
+
+167
+00:14:22,800 --> 00:14:26,780
+الكرموسومات اللي عنده تشوفلي شغلات اللي لها علاقة
+
+168
+00:14:26,780 --> 00:14:31,620
+بالتكوين الداخلي بالجينات بغير ذلك و بتعطيني نتيجة
+
+169
+00:14:31,620 --> 00:14:36,160
+هذا الفحص خلال أيام معدودة وهذه النتيجة بتقوللي ان
+
+170
+00:14:36,160 --> 00:14:42,000
+هو ذكر او أنثى وهذا يعني لا داعية للانتظار حتى
+
+171
+00:14:42,000 --> 00:14:46,630
+بلوغهوهذا يعني انه مافي داعي نجسم التاريكة مافي
+
+172
+00:14:46,630 --> 00:14:51,210
+داعي نقسم التاريكة باعتبار انه بس أيام هنستنى بس
+
+173
+00:14:51,210 --> 00:14:56,450
+راح نستنى أيام وبالتالي مافي داعي انه احنا اش نجسم
+
+174
+00:14:56,450 --> 00:14:59,990
+التاريكة ننتظر نتيجة الفحص وبناء عليها هتكون
+
+175
+00:14:59,990 --> 00:15:04,910
+جالالي هو ذكر او أنثى وبتكون قسمت وقتها نهائية
+
+176
+00:15:04,910 --> 00:15:11,300
+ومابعمل احتمال الذكورة واحتمال الأنوثةلكن أحيانا
+
+177
+00:15:11,300 --> 00:15:15,780
+من نتيجة الفحص بتجي تقولي إن هذا فعلا خنثة حقيقي،
+
+178
+00:15:15,780 --> 00:15:20,020
+شو يعني خنثة حقيقي؟ يعني أصلا في التركيبة الداخلية
+
+179
+00:15:20,020 --> 00:15:23,700
+لإله هو ذكر و أنثى، فيه شغلات لا الذكورة ولا
+
+180
+00:15:23,700 --> 00:15:29,090
+الأنثى في نفس الوقت، و هذا مافيش مجال لمعالجتهعادة
+
+181
+00:15:29,090 --> 00:15:33,790
+لو كانت الإشكالية خارجية سهل المعالجة، لكن إذا كان
+
+182
+00:15:33,790 --> 00:15:37,430
+الإشكال في الجينات، خلاص، فهذا بنقول عنه خنثة
+
+183
+00:15:37,430 --> 00:15:42,290
+حقيقي، شو يعني خنثة حقيقي؟ يعني فيش مجال يصير ما
+
+184
+00:15:42,290 --> 00:15:46,670
+قاله ذكورة أو أنوثة، يعني لن يتضح حاله أبدا، فهو
+
+185
+00:15:46,670 --> 00:15:52,210
+يجمع بين الذكورة والأنوثةفهذا الخنثة الحقيقي ..
+
+186
+00:15:52,210 --> 00:15:57,390
+هذا الخنثة الحقيقي كيف لنا أن نتعامل معه؟ طبعا
+
+187
+00:15:57,390 --> 00:16:01,430
+سنتحدث حول الخنثة الحقيقية المحاضرة القادمة بإذن
+
+188
+00:16:01,430 --> 00:16:06,170
+الله باعتباري أنه القليل النادرقليل نادر في موضوع
+
+189
+00:16:06,170 --> 00:16:12,230
+الخنثة هو أن يكون حقيقيا إذا الغالب في الخنثة أنه
+
+190
+00:16:12,230 --> 00:16:16,390
+واضح أو يرجع افتضح حاله عبر إجراء فحص جيني معين
+
+191
+00:16:16,390 --> 00:16:21,530
+حينها نقف على حقيقته لكن قضية الخنثة الحقيقي هذا
+
+192
+00:16:21,530 --> 00:16:28,190
+مسألة موجودة لكنها نادرة وعلاجها راح يكون وفقا لما
+
+193
+00:16:28,190 --> 00:16:33,610
+سنعالجه المحاضرة القادمة أو بعد القادمة بإذن الله
+
+194
+00:16:33,610 --> 00:16:38,870
+رب العالمينالسلام عليكموبناء على ذلك نرجع نقول بإن
+
+195
+00:16:38,870 --> 00:16:44,930
+تحديد جنس الخنثة لا يحتاج مننا أن ننتظر بلغه حتى
+
+196
+00:16:44,930 --> 00:16:52,110
+نحكم عليه بأنه ذكر أو أنثى بل إن هذا سيستغرق معنا
+
+197
+00:16:52,110 --> 00:16:57,470
+أيام قليلة حينها لا داعي كما قلنا لتقسيم التركة بل
+
+198
+00:16:57,470 --> 00:17:02,630
+ننتظر قليلا حتى نقسم التركة على الورثة بما فيهم
+
+199
+00:17:02,630 --> 00:17:05,430
+الخنثة الذي اتضح حاله تمام؟
+
+200
+00:17:08,880 --> 00:17:13,640
+وبناء على ذلك وفق الكلام اللي قدمته قبل قليل
+
+201
+00:17:13,640 --> 00:17:18,900
+نستطيع القول باختصار شديد أن مسائل الخنثة تنحصر بس
+
+202
+00:17:18,900 --> 00:17:23,340
+في مسائل الخنثة الحقيقي الذي لا يرجى اتضاح جنسه
+
+203
+00:17:23,340 --> 00:17:28,060
+أبدا فهذا الذي يواجهنا أو بيكون فيه إشكال في
+
+204
+00:17:28,060 --> 00:17:32,190
+توريثه بس هذا القسم و هذا النوعلأن الخنثة الآخر
+
+205
+00:17:32,190 --> 00:17:37,030
+حتى الذي لم تظهر عليه علامات الأنوثة أو الخنوثة أو
+
+206
+00:17:37,030 --> 00:17:41,030
+الذكورة عفوا قلنا الفحص الجيني بيقول لي إيش هو و
+
+207
+00:17:41,030 --> 00:17:44,250
+خلال أيام بتطلع للنتيجة إذا مافي عندي مشكلة أبدا
+
+208
+00:17:44,250 --> 00:17:50,050
+في التوريد صح ولا صح تمام لذلك بنقول بأن الذي
+
+209
+00:17:50,050 --> 00:17:54,290
+يحتاج إلى معالجة هو الخنثة الحقيقي أو مسائل الخنثة
+
+210
+00:17:54,290 --> 00:18:01,180
+الحقيقي فقط ومع ذلكأحيانا بقولك صحيح أن الخنثاء
+
+211
+00:18:01,180 --> 00:18:05,600
+الذي يرجى اتضحّله، مش الحقيقي، الذي يرجى اتضحّله
+
+212
+00:18:05,600 --> 00:18:09,500
+أن الطب قاللي مثلا بعد عشر أيام بتطلع النتيجة،
+
+213
+00:18:09,500 --> 00:18:15,070
+فرضكفي من ضمن الورثة كان حاجز لعملية و بدها مبلغ
+
+214
+00:18:15,070 --> 00:18:19,410
+معين و بده نصيبه من التركة لأنه محتاجه ضرورى،
+
+215
+00:18:19,410 --> 00:18:22,910
+انجله استنى عشرة؟ طب ما هو مضطر يعني العملية هتروح
+
+216
+00:18:22,910 --> 00:18:26,090
+عليه هيدخله حد ان بدله بتعرفه جزء العمليات، بدها
+
+217
+00:18:26,090 --> 00:18:31,270
+حجزات مسبقة و او اي لغير ذلكفإذا اضطر الورثة
+
+218
+00:18:31,270 --> 00:18:34,470
+اضطرارا للتعجيل في القسمة، لحظة يقول التعجيل
+
+219
+00:18:34,470 --> 00:18:37,950
+باعتبار أنه طالما في مجال نعرف الجنس مافي داعي لا
+
+220
+00:18:37,950 --> 00:18:43,970
+أن نقسم لكن إذا اضطروا اضطرارا لتعجيل القسمة فإن
+
+221
+00:18:43,970 --> 00:18:50,010
+هذا جائز وبتكون قسم T مؤقتة شو يعني مؤقتة؟ بمعنى
+
+222
+00:18:50,010 --> 00:18:54,210
+هعمل اعتبارين لعند ما ييجي نتيجة الفحص و بنعدل
+
+223
+00:18:54,210 --> 00:18:59,330
+التوريث اللي عملناهو هذا يعني أنه لازم لازم أثناء
+
+224
+00:18:59,330 --> 00:19:04,990
+التوريط شو بدي أعمل الخنثة بالتأكيد هعمل فرضيتين
+
+225
+00:19:04,990 --> 00:19:10,470
+فرض الذكورة و فرض الأنوثة و أورث الخنثة بالأسواق
+
+226
+00:19:11,680 --> 00:19:15,960
+بالأسوأ لحظة في الحمل كنا نقول نوقف له هان مش نوقف
+
+227
+00:19:15,960 --> 00:19:19,940
+لأنه أصلا هو موجود هنعطيه يعني هنعطيه مش نوقفله
+
+228
+00:19:19,940 --> 00:19:26,580
+نورث الخنثة بالأسوأ أي بالأقل و كذلك باقي الورثة
+
+229
+00:19:26,580 --> 00:19:30,420
+بالأسوأ يعني نورث الجميع باليقين شو يعني باليقين
+
+230
+00:19:30,420 --> 00:19:34,220
+بالشيء المتأكدين منه يعني احنا متأكدين ان هو بياخد
+
+231
+00:19:34,220 --> 00:19:38,780
+الف دينار لكن قضية ممكن ياخد أكترمن الف هذه مش
+
+232
+00:19:38,780 --> 00:19:42,900
+عارفين مش متأكدين لكن المتأكدين منه الألف فبنعطي
+
+233
+00:19:42,900 --> 00:19:47,460
+الجميع الأقل أو الأسوأ ونوقف الفرجية الباجئة
+
+234
+00:19:47,460 --> 00:19:53,340
+بنخبيها هنعطي الجميع الأسوأ بمن فيهم الخنسة بمن
+
+235
+00:19:53,340 --> 00:19:57,480
+فيهم الخنسة بنعطي الكل الأسوأ و بنخبي الفرجية لأنه
+
+236
+00:19:57,480 --> 00:20:02,490
+الطبيعي كونه أعطيت الكل الأسوأ معناته فيه فرقخبيته
+
+237
+00:20:02,490 --> 00:20:07,230
+عندى لما تيجى نتيجة الفحص جالتلى ذكر فبدنا نشوف
+
+238
+00:20:07,230 --> 00:20:12,670
+اللى أخده هو فعلا كان الذكر هو الأسوأ مثلا ولا لأ
+
+239
+00:20:12,670 --> 00:20:16,890
+هو بستاهل أكتر من كده فإذا بستاهل أكتر من كده
+
+240
+00:20:16,890 --> 00:20:23,150
+معناته بدي أروح ايش؟أرد عليه هو الباجي هو بينما لو
+
+241
+00:20:23,150 --> 00:20:28,410
+تبين أن اللي أخده الأسوأ هو فعلا اللي أخده فالباجي
+
+242
+00:20:28,410 --> 00:20:31,330
+بدي أرده على باقي الورثة لأنه تبين أن الورثة
+
+243
+00:20:31,330 --> 00:20:38,380
+بيستحقه أكثر مما وقف إليهمهذا ما سنعالجه عمليًا
+
+244
+00:20:38,380 --> 00:20:42,760
+بمسائل إن شاء الله المحاضرة القادمة إلى هنا نكون
+
+245
+00:20:42,760 --> 00:20:46,840
+قد انتهينا من موضوع محاضرتنا لهذا اليوم أقول قولي
+
+246
+00:20:46,840 --> 00:20:50,460
+هذا وأستغفر الله لي ولكم وصلى اللهم و السلم وبارك
+
+247
+00:20:50,460 --> 00:20:54,120
+على سيدنا محمد والسلام عليكم ورحمة الله تعالى
+
+248
+00:20:54,120 --> 00:20:54,940
+وبركاته
+
diff --git a/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/8d-kAq9zWf4_raw.srt b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/8d-kAq9zWf4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..24df6c5c5dd32bca6918866d70c6bd7e6d99d11d
--- /dev/null
+++ b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/8d-kAq9zWf4_raw.srt
@@ -0,0 +1,1984 @@
+1
+00:00:05,210 --> 00:00:08,130
+أعوذ بالله السميع العليم من الشيطان الرجيم بسم
+
+2
+00:00:08,130 --> 00:00:11,870
+الله الرحمن الرحيم الحمد لله رب العالمين والصلاة
+
+3
+00:00:11,870 --> 00:00:15,390
+والسلام على أشرف الأنبياء والمرسلين سيدنا محمد بن
+
+4
+00:00:15,390 --> 00:00:19,030
+عبد الله الصادق الأمين ثم أما بعد أحييكم جميعا
+
+5
+00:00:19,030 --> 00:00:22,550
+بتحية الإسلام في السلام عليكم ورحمة الله تعالى
+
+6
+00:00:22,550 --> 00:00:27,670
+وبركاته كيف حالكوا نطيبات ان شاء الله؟الحمد لله
+
+7
+00:00:27,670 --> 00:00:32,690
+تحضرنا الجيد ان شاء الله طيب عظيم إذا المحاضرة
+
+8
+00:00:32,690 --> 00:00:37,090
+السابقة كنا قد تحدثنا عن تأصيل المسائل وعرفنا أن
+
+9
+00:00:37,090 --> 00:00:42,650
+تأصيل أي مسألة متوقف على معرفة نوع هذه المسألة فإن
+
+10
+00:00:42,650 --> 00:00:46,830
+كانت المسألة مقتصرة على العصبات فإن أصل المسألة
+
+11
+00:00:46,830 --> 00:00:52,370
+يكون عدد الرؤوس وقضية حساب عدد الرؤوس رح يكون بناء
+
+12
+00:00:52,370 --> 00:00:56,850
+على نوع العصبة إن كانت عصبة بالنفس فبنحسب كل رأسأو
+
+13
+00:00:56,850 --> 00:01:02,350
+كل وارث رأس واحدة أما إن كانت عصبة بالغير فنحسب كل
+
+14
+00:01:02,350 --> 00:01:07,750
+وارث للذكري مثل حظ الأنثين بمعنى إذا كان ذكر راسين
+
+15
+00:01:07,750 --> 00:01:12,150
+وإذا كان أنثى رأس واحدة و هكذا تمام؟ ثم انتقلنا
+
+16
+00:01:12,150 --> 00:01:16,690
+للحديث عن ما لو وجد في المسألة أصحاب فروض و هنا
+
+17
+00:01:16,690 --> 00:01:22,730
+فرقنا بين أمرينالأول منهما أن يكون هناك صاحب فرض
+
+18
+00:01:22,730 --> 00:01:28,730
+واحد وقلنا ما بعنيني موضوع في عصبة أو مافيش مش انه
+
+19
+00:01:28,730 --> 00:01:32,870
+ما بعنيني انه مش هتمني لأ لكن في الحكم هو هو سواء
+
+20
+00:01:32,870 --> 00:01:37,110
+في عصبة أو مافيش وبناء على ذلك لو في عندي صاحب فرض
+
+21
+00:01:37,110 --> 00:01:42,470
+واحد أصل المسألة شويه مقام هذا الفرض طب لو في عندي
+
+22
+00:01:42,470 --> 00:01:49,020
+كذافرض وبالتالي هنا لابد من المقارنة بين مقامات
+
+23
+00:01:49,020 --> 00:01:53,260
+الفروض وحيث إن الفروض عندنا محدودة ومحصورة في ستة
+
+24
+00:01:53,260 --> 00:01:57,620
+فروض فإن المقارنة تكون بين خمسة مقامات فقط
+
+25
+00:01:57,620 --> 00:02:02,120
+وبالمقارنة يتضح أن هناك أربعة احتمالات قد يكونوا
+
+26
+00:02:02,120 --> 00:02:06,600
+بينها تماثلًا حينها أصل المسألة يكون هو أحد هذه
+
+27
+00:02:06,600 --> 00:02:11,940
+المقامات وقد يكون بين هذه المقامات تداخلًا فإن أصل
+
+28
+00:02:11,940 --> 00:02:16,060
+المسألة يكونالمقام الأكبر وقد يكون بين هذه
+
+29
+00:02:16,060 --> 00:02:22,440
+المقامات توافقًا حينها أصل المسألة يكون الحاصل ضرب
+
+30
+00:02:22,440 --> 00:02:25,440
+الأول في التاني على القاسم المشترك بيناتهم
+
+31
+00:02:25,440 --> 00:02:29,400
+والاحتمال الأخير أن يكون بين هذه المقامات تباين
+
+32
+00:02:29,400 --> 00:02:35,580
+فإن أصل المسألة يكون حاصل ضرب الأول في الثانيوبناء
+
+33
+00:02:35,580 --> 00:02:39,460
+على ذلك نخلص إلى التالي سريعا أنه عندي ستة فروض
+
+34
+00:02:39,460 --> 00:02:44,200
+نصف و رجع و تمن تلتين و تلت و سدس عندي خمس مقامات
+
+35
+00:02:44,200 --> 00:02:48,740
+اتنين تلاتة اربع ستة تمانية عندي سبع أصول وهي
+
+36
+00:02:48,740 --> 00:02:54,500
+اتنين تلاتة اربع ستة تمانية اتناش اربع عشرينولمّا
+
+37
+00:02:54,500 --> 00:02:59,300
+بقول عندي سبعة أصول بمعنى لا يمكن أن تكون عندي
+
+38
+00:02:59,300 --> 00:03:03,740
+مسألة أصلها الأصل يخرج عن هذه الأصول السبعة مستحيل
+
+39
+00:03:03,740 --> 00:03:08,880
+ألاجي مسألة أصلها مثلا خمستاش أو أصلها سبعة وعشرين
+
+40
+00:03:08,880 --> 00:03:13,020
+أو كذا كأصل أصلي أنا أتحدث بعيدا عن الأصول الأخرى
+
+41
+00:03:13,020 --> 00:03:17,420
+بمعنىاحيانا بيكون في عندي عول فال 12 بيصير 13 أو
+
+42
+00:03:17,420 --> 00:03:22,620
+بيصير 15 أو بيصير 17 عادي جدا فبصير أصل لكن بيسميه
+
+43
+00:03:22,620 --> 00:03:28,540
+أصل عائل هندرسه أحيانا أصلها 6 بتصير من 5 أصل ردي
+
+44
+00:03:28,540 --> 00:03:33,230
+لحظة الخمسة صار أصل رديأحياناً بيكون في عندى تصحيح
+
+45
+00:03:33,230 --> 00:03:39,130
+في المسألة أنه مثلا مات و ترك مثلا بنت و تلاتة بنت
+
+46
+00:03:39,130 --> 00:03:42,310
+ابن و الأسهم كانوا ستاش .. ستاش و تلاتة بيجسموش
+
+47
+00:03:42,310 --> 00:03:46,150
+على بعض فبنعمل تصحيح فلمّا بنعمل تصحيح الأصل
+
+48
+00:03:46,150 --> 00:03:49,510
+هيتغير، هيصير عندى حاجة اسمها الأصل الجامع
+
+49
+00:03:49,510 --> 00:03:53,370
+وبالتالي فكرة أن يكون الأصل غير الأصول السابعة
+
+50
+00:03:53,370 --> 00:03:58,840
+وارد لكن مش كأصل أصليفأنا أتحدث هنا عن الأصل
+
+51
+00:03:58,840 --> 00:04:04,700
+الأصلي لا يمكن لأي مسألة أصلها الأصل يخرج عن هذه
+
+52
+00:04:04,700 --> 00:04:08,780
+السبعة اللي هي المقامات الخامسة واضفينها 12 و 24
+
+53
+00:04:08,780 --> 00:04:12,580
+والكلام منطقي جدا بناء على الأمثلة اللي أخدناها
+
+54
+00:04:12,580 --> 00:04:17,540
+المحاضرة السابقة وبناء على ما سنطبقه بإذن الله في
+
+55
+00:04:17,540 --> 00:04:21,780
+محاضرة التطبيقات لهذا الموضوع اليوم بإذن الله
+
+56
+00:04:21,780 --> 00:04:29,360
+سنتحدث سويا عن تقسيم التركياتاتفقنا سابقا إن موضوع
+
+57
+00:04:29,360 --> 00:04:33,880
+علم الميراث هو التركة، ألم نقول ذلك في مقدمتنا؟
+
+58
+00:04:33,880 --> 00:04:38,140
+وقلنا الغاية من علم الميراث وثمرة هذا العلم هو
+
+59
+00:04:38,140 --> 00:04:42,080
+إعطاء، قل دي حق حقه، إن التركة هذه كيف؟ أقول فلان
+
+60
+00:04:42,080 --> 00:04:46,180
+إله كذا وفلان إله كذا، فبدنا نقسم هذه التركة على
+
+61
+00:04:46,180 --> 00:04:53,360
+الورثةفمحاضراتنا السابقة كانت بمثابة تمهيد لموضوع
+
+62
+00:04:53,360 --> 00:04:56,980
+تقسيم التريكة عرفت إنه إفلان إمتى بياخد فرضه، إمتى
+
+63
+00:04:56,980 --> 00:05:00,600
+بيكون عصبة وكيف بيرث و .. و .. وكمان اتحدثنا عن
+
+64
+00:05:00,600 --> 00:05:05,500
+تقصيل المسألة فتقصيل المسألة إشي أساسي للحديث عن
+
+65
+00:05:05,500 --> 00:05:10,040
+تقسيم التريكة إذ لا يُتصور أن أقسم تريكة دون أن
+
+66
+00:05:10,040 --> 00:05:14,820
+أعلم أصل هذه المسألةفحين ما انتهينا من التأصيل
+
+67
+00:05:14,820 --> 00:05:21,400
+منطقي أن نتحدث عن تقسيم التريكات تمام؟ بمعنى أن
+
+68
+00:05:21,400 --> 00:05:25,340
+بعد معرفة سهم كل وارث بدي أقول إفلان الوارث
+
+69
+00:05:25,340 --> 00:05:28,640
+بالنسبة لأسهم وجدش هياخد من التريكة اللي تركها
+
+70
+00:05:28,640 --> 00:05:34,210
+الميت الأن يا جماعةالتركة أو ما يتركه الميت قد
+
+71
+00:05:34,210 --> 00:05:38,590
+يترك أموال مثلية و قد يترك أموال قيمية و قد يترك
+
+72
+00:05:38,590 --> 00:05:41,930
+أموال مثلية و أموال قيمية شو يعني أموال مثلية؟ يلا
+
+73
+00:05:41,930 --> 00:05:45,310
+نرجع لمعاملات واحد اللي أخدناها و احنا بمستوى أول
+
+74
+00:05:45,310 --> 00:05:53,330
+الأموال المثلية ع السريع يلا يا سجا تمام
+
+75
+00:05:53,330 --> 00:05:56,130
+إذا باختصار شديد بنقول المال المثل أو الأموال
+
+76
+00:05:56,130 --> 00:06:01,070
+المثلية هي كل ما لها مثل أو نظيريعني أجزاءها
+
+77
+00:06:01,070 --> 00:06:07,470
+متماثلة وإن كان هناك تفاوت يكون تفاوت بسيط، يسير،
+
+78
+00:06:07,470 --> 00:06:11,870
+لا يؤثر زي مثلا الموزونات والمكيلات والعدديات
+
+79
+00:06:11,870 --> 00:06:15,970
+والنقود النقود اليوم أموال مثلية لما أجي أقول ألف
+
+80
+00:06:15,970 --> 00:06:21,030
+شكل و ألف شكلمثلي لما أجي أقول تنقمح و تنقمح برضه
+
+81
+00:06:21,030 --> 00:06:26,170
+مثلي وبالتالي سهل جدا أجسمه بالتساوي بين الشركاء
+
+82
+00:06:26,170 --> 00:06:30,670
+مثلا بينما الأموال القيمية ما ليس له .. اتفضلي يا
+
+83
+00:06:30,670 --> 00:06:37,140
+هيبا او لا مش هيبا امنا اتفضلي امناتمام إذا المال
+
+84
+00:06:37,140 --> 00:06:41,420
+الذي ليس له مثل أو نظير بمعنى لا يوجد تماثل بين
+
+85
+00:06:41,420 --> 00:06:46,400
+أجزائه فصعب أن أجسمه بالتساوي بين الأفراد صعب
+
+86
+00:06:46,400 --> 00:06:50,540
+وبناء على ذلك بدي أقول إذا كانت الأموال التي تركها
+
+87
+00:06:50,540 --> 00:06:54,220
+الميت مثلية كيف بدي أجسمها وإذا كانت الأموال اللي
+
+88
+00:06:54,220 --> 00:06:58,840
+تركها الميت أموال قيمية كيف لي أن أقسمها بين
+
+89
+00:06:58,840 --> 00:07:04,180
+الورثة نبدأ بالأموال المثلية وتقسيم الأموال
+
+90
+00:07:04,180 --> 00:07:09,420
+المثليةالأن يا جماعة في الأموال المثلية زي ما قلنا
+
+91
+00:07:09,420 --> 00:07:14,680
+مثلا عندنا مكيلات يعني شغلات بتنبع بالكيل شغلات
+
+92
+00:07:14,680 --> 00:07:18,480
+بتنبع بالوزن شغلات بتنبع بالعدد هذه كلها أموال
+
+93
+00:07:18,480 --> 00:07:22,900
+مثلية يعني سهل جدا أجسمها وأيضا اليوم النقود يعني
+
+94
+00:07:22,900 --> 00:07:26,760
+هذا هو المثال خليني أقول الحيوي في التقسيم تمام؟
+
+95
+00:07:26,760 --> 00:07:30,380
+لما أقول مات وترجميت ألف دينار مثلا فهيكون سهل
+
+96
+00:07:30,380 --> 00:07:36,690
+عليا أني أقسم بينه الورثة نعم؟تمام حلو فاني اجي
+
+97
+00:07:36,690 --> 00:07:40,370
+نقول بالنسبة لي الأموال المثلية اتفقنا قبل قليل
+
+98
+00:07:40,370 --> 00:07:44,950
+بإنه موضوع تقسيم التاريكة ابتداء مبني على تأصيل
+
+99
+00:07:44,950 --> 00:07:48,810
+المسألة تأصيلا صحيحة لازم أكون مقصلة المسألة بعد
+
+100
+00:07:48,810 --> 00:07:54,890
+ما أصلها بروح أقسم فالان تقسيم التاريكة بدنا نوصل
+
+101
+00:07:54,890 --> 00:07:58,610
+لقيمة السهم مش احنا لما كنا نوزع الأسهم نقول
+
+102
+00:07:58,610 --> 00:08:01,470
+الزوجة إيها تلاتة فلان إله اتنين فلان إله وكذا
+
+103
+00:08:01,470 --> 00:08:08,880
+فهذا اسمه سهمفالان موضوع قيمة السهم بدي أعرف قيمة
+
+104
+00:08:08,880 --> 00:08:12,720
+السهم ع أساس أطلع نصيب الوارث صح ولا لأ؟ لازم أعرف
+
+105
+00:08:12,720 --> 00:08:16,940
+قيمة السهم قيمة السهم بقدر أعرفه من خلال قسمة
+
+106
+00:08:16,940 --> 00:08:23,120
+التريكة على أصل المسألة على أصل المسألة تمام؟
+
+107
+00:08:23,120 --> 00:08:27,540
+وبناء على ذلك طبعا ناخد مثال جابت ومن خلال المثال
+
+108
+00:08:27,540 --> 00:08:33,450
+نيجي نشوف كيف نجسم التريكة نقول مثلا مات عنناخد أي
+
+109
+00:08:33,450 --> 00:08:41,870
+مثال نقول زوجة و اتنين أخت شقيقة و
+
+110
+00:08:41,870 --> 00:08:50,670
+أم مثلا و أخ شقيق و أخي أب عفوا يلا نشوف نحلها على
+
+111
+00:08:50,670 --> 00:08:59,270
+السريع الزوجة ربع و هان تلتين و هان سادس و هاد
+
+112
+00:08:59,270 --> 00:09:04,610
+عصبة المسألة من كام؟مين اللي جالت من ستة؟ في عندي
+
+113
+00:09:04,610 --> 00:09:08,610
+أربعة و تلاتة يا ماما أربعة و تلاتة بناتهم تباين
+
+114
+00:09:08,610 --> 00:09:13,790
+صح نضرب رؤسهم بعيد يعني اتناش و الاتناش و الستة
+
+115
+00:09:13,790 --> 00:09:17,950
+تداخل فبناخد الكبيرة الستناش هى .. هى الحل طيب
+
+116
+00:09:17,950 --> 00:09:22,550
+احنا كمبتدئين ممكن نرجع حاجة تانية الستة و التلاتة
+
+117
+00:09:22,550 --> 00:09:27,770
+تداخل فبناخد الكبير طب ستة و أربعة توافقفبنضرب
+
+118
+00:09:27,770 --> 00:09:32,430
+أربعة في ستة على اتنين تمام؟ فسواء بدأنا من هنا أو
+
+119
+00:09:32,430 --> 00:09:35,350
+من هنا الحال واحد احنا كمبتدئين بنحكي هذا الكلام و
+
+120
+00:09:35,350 --> 00:09:38,870
+لا كمان كم من محاضرة و احنا مغمضين بنكتب اتناش زي
+
+121
+00:09:38,870 --> 00:09:41,990
+ما توه كتبتها و انتوا هتصيروا هيك و أشتر مني بإذن
+
+122
+00:09:41,990 --> 00:09:46,230
+الله تمام؟ طيب نيجي نوزع الأسهم اتناش على أربعة
+
+123
+00:09:46,230 --> 00:09:51,670
+اتناش على تلاتة أربعة في اتنين تمانية اتناش على
+
+124
+00:09:51,670 --> 00:10:00,330
+ستة اتنين و هناصح نجنعد هنحداش وصارت أصلا تلتاشر
+
+125
+00:10:01,370 --> 00:10:04,850
+فالان احنا بنتعامل مع هذا الأصل بننسى هذا لكن هيه
+
+126
+00:10:04,850 --> 00:10:08,730
+الأصل الأصلي هذا واحنا قلنا سبع أصول اللي هم
+
+127
+00:10:08,730 --> 00:10:12,830
+اتنين، تلاتة، أربعة، ستة، اتناش، أربع وعشرين فهيه
+
+128
+00:10:12,830 --> 00:10:16,350
+هذا مش لأن شطبته ماعدش أصل هو أصل أصلي وهذا بنسميه
+
+129
+00:10:16,350 --> 00:10:20,870
+أصل عائل هنحكي عنه لكن الان انا في قضية تقسيم
+
+130
+00:10:20,870 --> 00:10:24,430
+التريكة بدي أتعامل مع الأصل النهائي بمعنى لو كمان
+
+131
+00:10:24,430 --> 00:10:29,190
+فيه تصحيح أو أي شيء بتعامل مع آخر أصل دائما، تمام؟
+
+132
+00:10:30,400 --> 00:10:35,020
+نجي نطلع قيمة السهم، نقول مثلا هذا الإنسان اللي
+
+133
+00:10:35,020 --> 00:10:42,000
+توفي يترك مثلا خلينا نقول 2600 دينار مثلا أو
+
+134
+00:10:42,000 --> 00:10:48,930
+دولار، تمام؟ هى التركة، أموال مثليةفنقول هنا بدي
+
+135
+00:10:48,930 --> 00:10:53,630
+أطلعش قيمة هى اللى هعمله قمر بسيط جدا قيمة السهم
+
+136
+00:10:53,630 --> 00:11:00,790
+قيمة السهم عبارة عن التركة تقسيم شو؟ أصل وطبعا لما
+
+137
+00:11:00,790 --> 00:11:05,110
+أحكي أصل المسألة الأصل النهائي بمعنى لو صار فيه أي
+
+138
+00:11:05,110 --> 00:11:08,950
+شغل على المسألة فباخد أخر أصل مش الأصل الأصلي
+
+139
+00:11:08,950 --> 00:11:13,390
+بينما لو المسألة ماصار عليها أي تعديل فبناخد أكيد
+
+140
+00:11:13,390 --> 00:11:18,150
+الأصل الأصلي، تمام؟ فإذا التركة جاتبش عندناالفين و
+
+141
+00:11:18,150 --> 00:11:24,830
+ستمية على إيش؟ تلتاش، إذا المتان، قيمة الساهم كده؟
+
+142
+00:11:26,520 --> 00:11:30,340
+عرفنا من وين إجت المتان؟ سهلة اللي هي أتركها على
+
+143
+00:11:30,340 --> 00:11:35,080
+أصل المسألة، خلصتها، حلو؟ طيب، لسه ما خلصنا الحل،
+
+144
+00:11:35,080 --> 00:11:40,520
+بدنا نيجي الآن نعرف نصيب الوارث، مش الوارث إله تلت
+
+145
+00:11:40,520 --> 00:11:46,220
+أسهم من التلتاش، إله تلتة من تلتاش، طيب السهم
+
+146
+00:11:46,220 --> 00:11:51,200
+الواحد من التلتة قيمته متين، إذا نصيب الوارث كيف
+
+147
+00:11:51,200 --> 00:11:56,190
+بدنا نطلعه؟أمسح حد يا جماعة بس احفظ المتان امسحوا
+
+148
+00:11:56,190 --> 00:11:59,750
+هذا اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه
+
+149
+00:11:59,750 --> 00:12:00,010
+اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه
+
+150
+00:12:00,010 --> 00:12:00,230
+اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه
+
+151
+00:12:00,230 --> 00:12:02,970
+اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه
+
+152
+00:12:02,970 --> 00:12:03,330
+اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه اه
+
+153
+00:12:03,330 --> 00:12:07,410
+اه اه اه اه اه اه اه اه اه اه اه اه اه
+
+154
+00:12:07,410 --> 00:12:12,410
+اه
+
+155
+00:12:12,410 --> 00:12:25,000
+اه اه اضرب عدد أسهمه .. أسهمين .. الورس اللي أنا
+
+156
+00:12:25,000 --> 00:12:30,720
+بدي أطلع نصيبه قيمة السهم ضرب إيش عدد أسهمه في
+
+157
+00:12:30,720 --> 00:12:35,750
+مسألته؟طب احنا قبل شوية في هذه المثالة طلعنا قيمة
+
+158
+00:12:35,750 --> 00:12:39,530
+السهم وقلنا قيمة السهم عبارة عن التركي على أصل
+
+159
+00:12:39,530 --> 00:12:43,190
+المسألة ففي هذا المثال طلع معنا قيمة السهم 200
+
+160
+00:12:43,190 --> 00:12:47,810
+فبنروح ضربين نيجي ابتداء للزوجة الزوجة جدش نصيبها
+
+161
+00:12:47,810 --> 00:12:56,010
+200 ضرب 3 ويساوي 600 تمام نيجي لأخت الشقيقة
+
+162
+00:12:56,010 --> 00:13:00,050
+الواحدة الواحدة
+
+163
+00:13:01,260 --> 00:13:05,280
+وبالتالي خلّيكم معايا اشرب تاخد نص جماعة بنحكيش عن
+
+164
+00:13:05,280 --> 00:13:09,280
+فرود يا سماح الله يهديكي هل جيت بنحكيش عن فرود
+
+165
+00:13:09,280 --> 00:13:14,000
+بنحكي عن نصيبها في المسألة هذه الواحدة فبنروح نقول
+
+166
+00:13:14,000 --> 00:13:20,560
+200 ضرب 8 على 2 اللي هي من وين جيبنا الاتنين لأن
+
+167
+00:13:20,560 --> 00:13:24,680
+التنتين لهم تمانية معناته الواحدة تمانية على اتنين
+
+168
+00:13:24,680 --> 00:13:29,660
+أربعة صح ولا لأ صح ولا لأ مرة تانية ركزوا معايا في
+
+169
+00:13:29,660 --> 00:13:30,580
+ناس مافهمتش
+
+170
+00:13:33,470 --> 00:13:38,170
+القال الزوجة هان مباشرة قولنا 3 في 200 باعتبار
+
+171
+00:13:38,170 --> 00:13:41,970
+أنها زوجة واحدة خلصنا فطبيعي الزوجة هتاخد التلاتة
+
+172
+00:13:41,970 --> 00:13:48,290
+لحالها صح؟هنا التمن أسهم لمين؟ لأختين مش لأخت ..
+
+173
+00:13:48,290 --> 00:13:53,070
+لأختين معناته الأخت الواحدة أربع أسهم صح ولا لأ؟
+
+174
+00:13:53,070 --> 00:13:59,130
+فنصيب الأخت الواحدة عبارة عن 200 درب 4 من وين جبنا
+
+175
+00:13:59,130 --> 00:14:03,830
+الأربع؟ 8 ع 2 .. حلو؟ اللي هي جداش 800
+
+176
+00:14:06,480 --> 00:14:13,700
+تمام الأم نقول الأم الواحدة تمام اللي هي 2 ضرب 200
+
+177
+00:14:13,700 --> 00:14:18,860
+ويساوي 400 وطبعا هدا كان غالبا zero مالوش ولا حاجة
+
+178
+00:14:18,860 --> 00:14:22,840
+لإنه محجوب بالاستغرق علم ناخد مثال أخير في هذا
+
+179
+00:14:22,840 --> 00:14:26,600
+الموضوع لإن الموضوع مابدوش تطبيق كتير يعني خلاص
+
+180
+00:14:27,270 --> 00:14:30,910
+افهم الفكرة إنه أول شي بدك تعمل تأصيل للمسألة
+
+181
+00:14:30,910 --> 00:14:34,950
+بعدين أول خطوة بدك تعملها في تقسيم التاريخة اتطلع
+
+182
+00:14:34,950 --> 00:14:39,010
+قيمة السهم كيف بدنا نطلع قيمة السهم؟ اتطلع تاريخة
+
+183
+00:14:39,010 --> 00:14:43,090
+على أصل المسألة فالنتيجة هذه بتروح يتطلع نصيب
+
+184
+00:14:43,090 --> 00:14:46,910
+الوارث من خلال تدور بالنتيجة اللي هي قيمة السهم في
+
+185
+00:14:46,910 --> 00:14:51,410
+عدد أسهم الوارث وخلصنا علم؟ ناخد مثال
+
+186
+00:14:54,090 --> 00:14:57,310
+ملونى هدى .. هدى بشبه هدى ولا لا؟ اشى تانى؟ okay
+
+187
+00:14:57,310 --> 00:15:03,530
+ناخد هدى المثال يلا اللى
+
+188
+00:15:03,530 --> 00:15:06,770
+بتسأل تسألني انا اللى جالك ليش قبصرقش ماسمعتش بجيت
+
+189
+00:15:06,770 --> 00:15:13,150
+السؤال ايوة مين عندها سؤال خلاص بطلتوا انتوا احرار
+
+190
+00:15:13,150 --> 00:15:21,490
+انتوا الخسرانى طيب ايوة سلام من اذا
+
+191
+00:15:24,720 --> 00:15:36,820
+أخت شقيقة أخت لأب التاريخة سهل هذا المثال okay
+
+192
+00:15:36,820 --> 00:15:42,520
+يلّا الزوش كده؟ ربع لوجود الفرع الوارث بنت الأبن
+
+193
+00:15:43,340 --> 00:15:48,720
+والشقيقة مع الغير، تقوليش عصبة و تسكت؟ و هاد محجوب
+
+194
+00:15:48,720 --> 00:15:53,160
+لأنه أصبحت في قوتي أخيها فالمسألة من أربع، صح؟
+
+195
+00:15:53,160 --> 00:15:59,580
+تمام هان واحد و هان اتنين و هان جدش بيضل واحد اللي
+
+196
+00:15:59,580 --> 00:16:04,880
+هي أربع ناجس تلاتة واحد تمام؟ و هان طبعا مافيه
+
+197
+00:16:04,880 --> 00:16:08,960
+مافيش نقول zero محجوب الساقط بنقوله zero الساقط
+
+198
+00:16:08,960 --> 00:16:12,260
+بنقوله zero هان بنقولوش ولا حاجة تمام؟ بنعتبره
+
+199
+00:16:12,260 --> 00:16:22,190
+خلاص يعنيفنجي لقى قيمة السهم قيمة السهم قولنا
+
+200
+00:16:22,190 --> 00:16:30,370
+التركة على أصل المسألة يعني جداش 600 على 4 يسوى
+
+201
+00:16:30,370 --> 00:16:40,950
+150 تمام؟ حلو نجي لقى نصيب كل وارث الزوج 1 في
+
+202
+00:16:40,950 --> 00:16:49,970
+150 يعني 150طيب بنت الإبن 300 يعني
+
+203
+00:16:49,970 --> 00:16:54,050
+تلات مية وبيضل
+
+204
+00:16:54,050 --> 00:17:03,250
+عند الشقيقة واحد في مية وخمسين بساوي خلصت بس هذا
+
+205
+00:17:03,250 --> 00:17:06,610
+إذا كانت الأموال مثلية ومافيها أي كلام نيجي
+
+206
+00:17:06,610 --> 00:17:08,010
+للأموال القيمية على السريع
+
+207
+00:17:14,050 --> 00:17:17,870
+الأموال القيمية يا جماعة، بدي أفطر دي فلان، الله
+
+208
+00:17:17,870 --> 00:17:25,510
+يرحمه، ترك لولاده مصنع بطون، مصنع بطون، فبعد موته
+
+209
+00:17:25,510 --> 00:17:30,610
+صار المصنع لمين؟ لأبناءه أو للورثة، ممكن مايكونوش
+
+210
+00:17:30,610 --> 00:17:36,120
+ولاده اللي أخدوا التريكة مثلا، حسب، حلوفالان
+
+211
+00:17:36,120 --> 00:17:41,320
+المصنع هذا لمين لو ورثته فبعد موته أتعامل مع
+
+212
+00:17:41,320 --> 00:17:50,040
+الورثة كأنهم شركاء كأنهم شركاء لأن هذا مال قيمي
+
+213
+00:17:50,040 --> 00:17:54,180
+المال المثل سهل كل واحد باخد نصيبه مع السلامة
+
+214
+00:17:54,180 --> 00:17:59,990
+خلصناخلّصنا، ما بيبقى الـ 600 دينار محططين و
+
+215
+00:17:59,990 --> 00:18:03,830
+بنحطهم و نبقى نطلع عليهم و نطبطب عليهم عشان يكبروا
+
+216
+00:18:03,830 --> 00:18:07,950
+خلاص، كل واحد باخد نصيب و بمشي، خلّصنا و لا حد
+
+217
+00:18:07,950 --> 00:18:11,650
+قيله عند التاني بعد ما أخد حسته، صح ولا لأ؟ ففي
+
+218
+00:18:11,650 --> 00:18:17,710
+المال المثل كل واحد يخرج من التاريخ أو خلّصنا،
+
+219
+00:18:17,710 --> 00:18:23,080
+بينما هنا بدنا نشوف إيش اللي هيصير معنافلان مات و
+
+220
+00:18:23,080 --> 00:18:27,580
+تركشو مثلا مصنع بطون، هذا المصنع هيكون لمن؟
+
+221
+00:18:27,580 --> 00:18:33,590
+للورثة، طب كيف بدنا نجسم عليهم؟طبعاً قضية النقابيع
+
+222
+00:18:33,590 --> 00:18:36,930
+وقيمته نجسمها دي مسألة تانية مش هي اللي بنحكي عنها
+
+223
+00:18:36,930 --> 00:18:40,870
+لإن وجد ما نقول بدنا نبيه أو نجسم ثمنه على الجميع
+
+224
+00:18:40,870 --> 00:18:44,770
+بتصير أموال مثلية وخلصنا فهنرجع على نفس الفكرة على
+
+225
+00:18:44,770 --> 00:18:50,230
+نفس الفكرة لكن أحيانا يا جماعة هدول الورثة بيكون
+
+226
+00:18:50,230 --> 00:18:56,560
+عندهم منطق بيقول هذا المصنع يعنيكل بيطلّعنا
+
+227
+00:18:56,560 --> 00:19:00,400
+للاقتصاد و .. و .. يعني إله .. إله رياح أفضل ما
+
+228
+00:19:00,400 --> 00:19:02,900
+نبيعه كل واحد ياخد جرشين و يصرفهم و بعدين مع
+
+229
+00:19:02,900 --> 00:19:06,940
+السلامة لأ إحنا مصلحتنا إنه المصنع يظل و إحنا
+
+230
+00:19:06,940 --> 00:19:09,780
+نديره فيما بيننا صح ولا لأ؟ و هذا اللي بالغالب
+
+231
+00:19:09,780 --> 00:19:13,120
+بيصير إلا إذا كانوا مشكلة الجيه هدول الورثة فكل
+
+232
+00:19:13,120 --> 00:19:17,050
+يوم و التاني جثة و جتال و بصرشو فبروح يبيعوهوكل
+
+233
+00:19:17,050 --> 00:19:22,670
+واحد بياخد نصيب وخلصنا لكن أنا أتحدث عن ناس حابة
+
+234
+00:19:22,670 --> 00:19:26,730
+المصنع يكون شركة بيناتهم على أساس يستفيدوا أكثر
+
+235
+00:19:26,730 --> 00:19:31,330
+بالتأكيد دائما يا جماعة لما انت تروح تبيع الشغل و
+
+236
+00:19:31,330 --> 00:19:36,740
+تخدي نصيبك من قيمتها مهما كان النصيب كبيرفي
+
+237
+00:19:36,740 --> 00:19:41,080
+النهاية هتاكليه لأن المال قالك دائما مقاله للأكل
+
+238
+00:19:41,080 --> 00:19:44,680
+شو ما عمرتي و شو ما كذا أكلتيه و خلص صح ولا لا؟
+
+239
+00:19:44,680 --> 00:19:48,780
+بينما هنا هتصير تستفيدي كل فترة و تانية بتطلعلك
+
+240
+00:19:48,780 --> 00:19:53,840
+مثلا ريع معين أو دخل معين من هذا المصنع حلو؟ فالان
+
+241
+00:19:53,840 --> 00:19:57,040
+بدنا نفترض أنه هتخلص اه
+
+242
+00:20:10,240 --> 00:20:16,760
+بدنا نفترض أنه قلنا التركة عبارة عن مصنع فقلنا
+
+243
+00:20:16,760 --> 00:20:21,560
+أنا بعامل الورثة على أنهم شركاء شو يعني شركاء؟
+
+244
+00:20:21,560 --> 00:20:27,900
+يعني كل وارث له حصة في كل جزء كل جزء من المصنع كله
+
+245
+00:20:27,900 --> 00:20:31,600
+يتناقل حق فيه كل جزء لأنه بالظبط الله يفتح عليك
+
+246
+00:20:31,600 --> 00:20:36,500
+الشركة هنا على الشيوع مش مفرزة حصاصنا وبالتالي
+
+247
+00:20:36,500 --> 00:20:42,630
+ركزوا معايا شويةهل جيت بدي أفطر دي فلان مات و ترك،
+
+248
+00:20:42,630 --> 00:20:49,170
+ناخد مثلا زوجة و
+
+249
+00:20:49,170 --> 00:20:55,330
+أم، فيها المثل ناخده خلاص، okay أم و بنت و إبن
+
+250
+00:20:55,330 --> 00:21:00,020
+إبن، خليكم معاياالان بنحل المسألة حال طبيعي حتى في
+
+251
+00:21:00,020 --> 00:21:04,400
+الأموال القيمية حتى في الأموال القيمية أو المتقومة
+
+252
+00:21:04,400 --> 00:21:08,860
+بنحل المسألة حال طبيعي عساس نعمل أصل و نطلع أسهم
+
+253
+00:21:08,860 --> 00:21:13,360
+فبنقول الزوجة جداش تمون و الأم سدس لوجود طبعا
+
+254
+00:21:13,360 --> 00:21:17,200
+الفرع الوارث و هالنصف و هالعصبة المسألة من كام؟ من
+
+255
+00:21:17,200 --> 00:21:21,620
+أربع عشرين عرفنا من وين إجت الأربع عشرين؟ تمانية و
+
+256
+00:21:21,620 --> 00:21:24,840
+ستة تمانية و أربعين على اتنين لأنه في توافق بين
+
+257
+00:21:24,840 --> 00:21:31,910
+التمانية و الستة حلو؟وبنجسمهم على اتنين نعم تحكي
+
+258
+00:21:31,910 --> 00:21:38,130
+عادى من اللى حكى ازملتنا
+
+259
+00:21:38,130 --> 00:21:41,770
+بتحكى شوية اه يا قامنة اتفضلى نوحد المقامات كلها
+
+260
+00:21:41,770 --> 00:21:51,370
+مثلا 8×3 يديك 24×4 يديك 22×12 يديك 24كيف ستفتح؟
+
+261
+00:21:51,370 --> 00:21:57,370
+إنه كل قطيطة عنه 24 طيب و إيش بدنا في الغلبة هذه؟
+
+262
+00:21:57,370 --> 00:22:01,090
+مش دائما .. مش دائما الشغلات اللي بتيجي معنا كده
+
+263
+00:22:01,090 --> 00:22:04,090
+في كل المسائل بتظبط يعني مثلا هالجد زبطت معاك
+
+264
+00:22:04,090 --> 00:22:08,190
+فإحنا لأ دائما وفق الأصول العلمية بنطمن إنه مافيش
+
+265
+00:22:08,190 --> 00:22:11,790
+غلط فاهمتي عليا؟ فعشان هيك أنا دائما حريصة إنه
+
+266
+00:22:11,790 --> 00:22:15,620
+المسائل الحسابية إلها ميت ألف طريقةفانا حريصة ناخد
+
+267
+00:22:15,620 --> 00:22:19,840
+طريقة علمية عساس نضمن عدم الخطأ، هاي الهدف، بس
+
+268
+00:22:19,840 --> 00:22:23,740
+فانت خدي أنه هادد كونها داخلة فيهم ضمنها فضال عندي
+
+269
+00:22:23,740 --> 00:22:28,140
+رقمين، تمانية، ستة، شو بنعتهم توافق، يعني في قاسم
+
+270
+00:22:28,140 --> 00:22:31,620
+مشترك، اضربيهم جسمي على هذا القاسم وخلصنا، فتمانية
+
+271
+00:22:31,620 --> 00:22:35,280
+واربعين عتنت، اربع عشرين خلصنا، هان تلاتة، هان
+
+272
+00:22:35,280 --> 00:22:40,520
+أربعة، هان اتناش، وجدش بضال خمس، فالان نرجع
+
+273
+00:22:40,520 --> 00:22:46,480
+لموضوعناقولنا أموال متقومة أو أموال قيمية في هذه
+
+274
+00:22:46,480 --> 00:22:51,680
+الحالة نعامل الورثة كما قلت قبل قليل أنهم شركاء
+
+275
+00:22:51,680 --> 00:22:55,800
+على الشيوع في المصنع شو يعني شركاء على الشيوع؟
+
+276
+00:22:55,800 --> 00:23:00,460
+يعني ولا حدا حصته مفرزة كل واحد له نصيب في كل جزء
+
+277
+00:23:00,460 --> 00:23:06,000
+من هذه الأجزاء فاحنا بنعتبر أن المصنع مجسم لـ 24
+
+278
+00:23:06,000 --> 00:23:15,100
+جزء 24 اللي هو أصل المسألةاربع و عشرين جزء هنعملوا
+
+279
+00:23:15,100 --> 00:23:15,500
+ستة
+
+280
+00:23:21,790 --> 00:23:28,690
+هك 24 ادهم على السريع صح؟ 123 4 123 4 5 6 24 okay
+
+281
+00:23:28,690 --> 00:23:34,710
+فالان بنشوف، بنعتبر و كأنه المصنع عبارة عن ايش؟ 24
+
+282
+00:23:34,710 --> 00:23:40,310
+جزء تلت أجزاء طبعا على الشيوع بمعنى كل جزء هذا
+
+283
+00:23:40,310 --> 00:23:46,130
+الجزء مثلاوكأنه أربع عشرين جزء بمعنى أن الزوجة
+
+284
+00:23:46,130 --> 00:23:48,930
+إلها و الأم إلها و البنت إلها و ابن الإبن إلها و
+
+285
+00:23:48,930 --> 00:23:52,950
+هنا كل واحد إله إله إله تمام لكن هدول الأربع عشرين
+
+286
+00:23:52,950 --> 00:23:56,990
+تلاتة منهم لمين للزوجة لكن على الشيوء مش زي ما أنا
+
+287
+00:23:56,990 --> 00:24:04,130
+محددة بعدين عندك أربع لمين لأم بعدين عندك اتنعاش
+
+288
+00:24:04,130 --> 00:24:04,650
+لمين
+
+289
+00:24:08,400 --> 00:24:12,820
+وهي الاتناش لمين؟ للأم، هدول الاتناش كلهم للأم،
+
+290
+00:24:12,820 --> 00:24:17,580
+والابن بياخد الخمسة هدوللكن مش بهذا الترتيب شيوع
+
+291
+00:24:17,580 --> 00:24:22,040
+فكل جزء هذا الجزء اللي قلنا عنه للزوجة هدول لهم
+
+292
+00:24:22,040 --> 00:24:26,920
+فيه هذا الجزء اللي قلنا عنه لكذا لهم فيه بكل واحد
+
+293
+00:24:26,920 --> 00:24:30,880
+حسب حصته من وان حصته هاي حصته طلعناها بالاسهم اللي
+
+294
+00:24:30,880 --> 00:24:34,620
+هو التأصيل خلانا نطلع الأسهم تمام؟ بس هي اللي
+
+295
+00:24:34,620 --> 00:24:39,480
+بنعمله باعتبار احنا شو ما بدنا نبيع الاش المصنع
+
+296
+00:24:39,480 --> 00:24:43,900
+وبالتالي المصنع جديش بطلع كل شهر اللي بطلعه بدنا
+
+297
+00:24:43,900 --> 00:24:49,730
+نجسمه بنهادي النساءمثلًا بطلّع 1400 شكل في الشهر،
+
+298
+00:24:49,730 --> 00:24:54,890
+الـ 2400 بدنا نجسمها 300 لفلان، 300 شكل لفلان، 400
+
+299
+00:24:54,890 --> 00:24:59,690
+شكل لفلان، 1200 شكل لفلان و 500 شكل لفلان، بنفس
+
+300
+00:24:59,690 --> 00:25:04,050
+الترتيب، حسب جدّش بطلّع في الشهر، علم؟ تمام؟ سهل
+
+301
+00:25:04,050 --> 00:25:08,530
+كتير، فيهاش كلام أصلا، لكن الآن الإشكالية مش هنا،
+
+302
+00:25:08,530 --> 00:25:12,270
+الإشكالية لو واحد كان نحو وقال بدي أطلع، بدي أبيع
+
+303
+00:25:12,270 --> 00:25:18,090
+حصةدي أبيع حصتي، لحظي مش اللي الفكرة كلها انبعت،
+
+304
+00:25:18,090 --> 00:25:22,150
+إذا كل المصنع انبعت المسألة سهلة، صار إيش؟ وكأنه
+
+305
+00:25:22,150 --> 00:25:29,810
+مثلي صار، لكن هنا في حاجة اسمها تخارج، تخارج، يعني
+
+306
+00:25:29,810 --> 00:25:36,190
+واحد بده يخرج لغيره، هذا الغير إما للجميع أو لواحد
+
+307
+00:25:36,190 --> 00:25:40,470
+بعينه أو لأجنبي، إذا عندي تلت احتمالات
+
+308
+00:25:47,670 --> 00:25:56,270
+خلاص لأ شكرا طيب
+
+309
+00:25:56,270 --> 00:25:59,330
+إذا
+
+310
+00:25:59,330 --> 00:26:05,030
+صار واضح هنا فالان موضوع التخرج نعم؟اه اه هنحكي
+
+311
+00:26:05,030 --> 00:26:08,410
+تالتة احتمالات لكن اكيد بالاتفاق كل شعب الاتفاق
+
+312
+00:26:08,410 --> 00:26:12,730
+الآن بنحكي عن موضوع التخارج ما تقولي اللي انت قلت
+
+313
+00:26:12,730 --> 00:26:16,270
+عن التأصيل تخارج لأ هناك ما خارج الحروف مش قولنا
+
+314
+00:26:16,270 --> 00:26:23,070
+في ناس سمت التأصيل ما خارج الحروف الفروضالفروز هنا
+
+315
+00:26:23,070 --> 00:26:27,450
+حاجة اسمها تخارج من اسمها تخارج يعني حد بيخرج لحدا
+
+316
+00:26:27,450 --> 00:26:32,270
+فالان التخارج لا يكون الا في الأموال المتقومة لا
+
+317
+00:26:32,270 --> 00:26:35,790
+يكون في الأموال المثلية لأن علشان نخرج ما كل واحد
+
+318
+00:26:35,790 --> 00:26:39,590
+أخد جبت ومشيت صح ولا لا؟ حلو فالان في الأموال
+
+319
+00:26:39,590 --> 00:26:46,110
+المتقومة أو القيمية قد يخرج أحد الورثة لغيره هنا
+
+320
+00:26:46,110 --> 00:26:50,970
+نفرق بين ثلاثة احتمالاتتمام؟ الاحتمال الاول بس
+
+321
+00:26:50,970 --> 00:26:54,030
+اللى بدنا نركز فيه نونة صغيرة بس والتانى والتالت
+
+322
+00:26:54,030 --> 00:26:59,290
+بحصى الحاصل الاحتمال الاول بنقول ان الوارث اللى
+
+323
+00:26:59,290 --> 00:27:05,370
+اراد ان يخرج لجميع الورثة فهالجيته كأنه بدي احسطه
+
+324
+00:27:05,370 --> 00:27:11,290
+لمن؟ للورثة وفي هذه الحالة كونه بدي احسطه للورثة
+
+325
+00:27:11,290 --> 00:27:18,190
+فكل واحد من الورثة بده يتفعلهمقابل حصته حصته هو
+
+326
+00:27:18,190 --> 00:27:22,070
+يعني ناخد المسألة هذه نفسها مثلا هذه المسألة نفسها
+
+327
+00:27:22,070 --> 00:27:27,840
+خلّيكم معاياالمثال هذا قلنا من 24 صح؟ وهنا رسمنا
+
+328
+00:27:27,840 --> 00:27:32,240
+هنا إنه عبارة عن مصنع 24 جزء كل واحد إله كذا كذا
+
+329
+00:27:32,240 --> 00:27:37,640
+كذا فالآن الزوجة مثلا جالت أنا بدي أطلع بدي أروح
+
+330
+00:27:37,640 --> 00:27:44,140
+عند أهلي اعطوني حجم التلت أسهم قيمة التلت أسهم
+
+331
+00:27:44,140 --> 00:27:50,100
+وانا بدي في التلت أسهم هدول مثلا بدي 4800 دينار
+
+332
+00:27:52,240 --> 00:27:54,800
+طبعاً هي حكت هذا الكلام إنه هي بدها المبلغ
+
+333
+00:27:54,800 --> 00:27:58,840
+بالتأكيد بناء على حد قيمه اللي هجالها إنه حصتك
+
+334
+00:27:58,840 --> 00:28:03,400
+تقريبا مش أقل من 5000 دينار فجالت هيك و بالتأكيد
+
+335
+00:28:03,400 --> 00:28:06,680
+المسألة هتتنحسب مش هتكون على ال .. كده يعني اتفضلي
+
+336
+00:28:06,680 --> 00:28:11,240
+قيمنا كم ستة و طلعناها؟ لسه .. لسه خليكي معاه الآن
+
+337
+00:28:11,240 --> 00:28:17,860
+هي جالت .. هي جالت للورثة أنا بدي أبيعكم .. أنا
+
+338
+00:28:17,860 --> 00:28:23,050
+بدي أبيعكم حصتي بس بـ 4800 ممكن تكون أكترو ممكن
+
+339
+00:28:23,050 --> 00:28:27,890
+تكون أجالي لكن المسألة أنهم راضيوا وبالتأكيد إذا
+
+340
+00:28:27,890 --> 00:28:32,490
+الأمر لمصلحتهم على طول هيوافقوا تمام؟ وبالتأكيد
+
+341
+00:28:34,040 --> 00:28:38,940
+إنه المسألة في الغالب الطرفين هيستفيدوا الطرفين
+
+342
+00:28:38,940 --> 00:28:42,880
+هيستفيدوا لأن حتى الزوجة لما بدها تبيع بدها يمكن
+
+343
+00:28:42,880 --> 00:28:46,260
+محتاجة المبلغ هذا جالت ليك مابديش هالمصنع وأخده
+
+344
+00:28:46,260 --> 00:28:49,200
+وأنا بعملي حاجة معينة مشروع صغير بشتغل على حالي
+
+345
+00:28:49,200 --> 00:28:54,820
+وخلصنا مثلا طبعا انا افتراضا قولت 4800 ممكن المبلغ
+
+346
+00:28:54,820 --> 00:29:00,360
+يكون 20 ألف أصلا مثلا تلت أسهم فهي إشجالت اعطوني
+
+347
+00:29:00,360 --> 00:29:07,970
+4000 أو لحظةخلّينا نقول اضربولي تسعتاش في أربعة ع
+
+348
+00:29:07,970 --> 00:29:11,850
+السريع عشان ناخد أرقام صحيحة تسعتاش في أربعة
+
+349
+00:29:11,850 --> 00:29:17,150
+جدّاه؟
+
+350
+00:29:17,150 --> 00:29:20,250
+ستة و سبعين .. ستة و سبعين .. نقول سبعتلاف و ستمية
+
+351
+00:29:20,250 --> 00:29:30,330
+يلا مثلاجالت أنا بدي أخرج عن أسهمي مقابل جداش
+
+352
+00:29:30,330 --> 00:29:36,130
+سبعتلاف و ستمية جالوا لها موافقين تمام فجيت هي إيش
+
+353
+00:29:36,130 --> 00:29:41,580
+هتطلعهما موافقين، هتطلع لمين؟ لجميع الورثة، لجميع
+
+354
+00:29:41,580 --> 00:29:46,240
+الورثة، هذا الاحتمال الأول فالان الـ 7600 من اللي
+
+355
+00:29:46,240 --> 00:29:53,320
+بدي ادفعهم الورثة كليتهم كلهم بيقاش بنسبة اسهمه،
+
+356
+00:29:53,320 --> 00:29:57,140
+يعني هنجسم هذه على أصل المسألة اللي هو جداش 19
+
+357
+00:29:59,860 --> 00:30:04,960
+أيوة او اكت جسمي على 24 لأن احنا طلعنا الزوجة
+
+358
+00:30:04,960 --> 00:30:09,340
+طلعنا الزوجة صارت المسألة و كأنها من تسعتاش اللي
+
+359
+00:30:09,340 --> 00:30:15,260
+بده يطلع بنشيل أسهمه يا جماعة بنشيل فشيلنا التلاتة
+
+360
+00:30:15,260 --> 00:30:19,200
+من الاربع وعشرين قدش دل .. دل واحد وعشرين او احنا
+
+361
+00:30:19,200 --> 00:30:23,740
+غلطنا اسفة اسفة انا شيلت الخمسة اسفة اذا قوليلي
+
+362
+00:30:23,740 --> 00:30:31,100
+مرة تانية اضرب الواحد وعشرين في تلاتةواحد وعشرين
+
+363
+00:30:31,100 --> 00:30:41,080
+في تلاتة إذا ست آلاف تمام فبتروح المبلغ هذا اللي
+
+364
+00:30:41,080 --> 00:30:47,740
+بدها يامين الزوجة بنجسمه على جداش على واحد وعشرين
+
+365
+00:30:47,740 --> 00:30:55,020
+تمام بنجسمه على واحد وعشرين جداش بيطلع على السريع
+
+366
+00:30:55,020 --> 00:31:01,780
+اللي هو تلاتمية صح؟بطلع تلات مية فالان لأ مش كل
+
+367
+00:31:01,780 --> 00:31:06,480
+واحد تلات مية الأم بضهر تدفع أربع في تلات مية مال
+
+368
+00:31:06,480 --> 00:31:11,760
+نطا و أخدناها و البنت هتدفع اتناش في تلات مية و
+
+369
+00:31:11,760 --> 00:31:17,250
+ابن الإبن هيدفع خمسة في تلات ميةصح ولا لأ مرة
+
+370
+00:31:17,250 --> 00:31:23,230
+أخيرة ركزوا معايا الآن في تقسيم الأموال المتقومة
+
+371
+00:31:23,230 --> 00:31:26,790
+اصحى يا ماما اصحى اصحى اصحى مش بقولها جهوة يا
+
+372
+00:31:26,790 --> 00:31:34,530
+جماعة اسلام جهوة تمام صلوا على رسول الله بنقول
+
+373
+00:31:34,530 --> 00:31:41,070
+أو بنقول حسب القراءات الموجودة بينناإنه ركزوا يا
+
+374
+00:31:41,070 --> 00:31:45,090
+جماعة ركزوا شوية مسألة سهلة صغيرة في تقسيم الأموال
+
+375
+00:31:45,090 --> 00:31:49,750
+المتقومة إذا كلهم بدهم يظلهم سوا مع بعض فإحنا
+
+376
+00:31:49,750 --> 00:31:56,430
+بنعتبر هذا المال المشترك إيش أجزاء بعدد إيش أصل
+
+377
+00:31:56,430 --> 00:32:02,230
+المسألة وكل واحد لهعدد من الأجزاء حسب أسهمه حسب
+
+378
+00:32:02,230 --> 00:32:07,230
+عدد أسهمه خلصنا طب ماذا لو أراد أحد الورثة أن يخرج
+
+379
+00:32:07,230 --> 00:32:12,690
+لباقي الورثة فهنا نفرق بين ثلاثة أمور قد يخرج
+
+380
+00:32:12,690 --> 00:32:18,430
+الوارث لجميع الورثة وقد يخرج لأحد الورثة بعينه وقد
+
+381
+00:32:18,430 --> 00:32:23,560
+يخرج لأجنبيالاحتمال الأول أن يخرج الوارث لمن؟
+
+382
+00:32:23,560 --> 00:32:29,600
+لجميع الورثة قال أنا حصتي بدأ أعطيكم إياها بدل ما
+
+383
+00:32:29,600 --> 00:32:34,560
+أنه المصنع كنتم جسمينه 24 جسمه 21 الزوجة قالت
+
+384
+00:32:34,560 --> 00:32:39,580
+بتطلع هي إلها 3 من 24 إذا المصنع صار وكأنه 21
+
+385
+00:32:39,580 --> 00:32:45,660
+فهتصير الأم إلها 4 من 21 مش 4 من 24 يعني زادت
+
+386
+00:32:45,660 --> 00:32:53,280
+حصتهامش 4 من 21 أكثر من 4 من 24 فزادت حصتها مقابل
+
+387
+00:32:53,280 --> 00:32:57,020
+الزيادة بدأت تدفع لأنها أخدت زيادة بدأت تدفع و نفس
+
+388
+00:32:57,020 --> 00:33:02,360
+ال issue البنت كانت 12 من 24 صارت 12 من 21 زادت
+
+389
+00:33:02,360 --> 00:33:07,000
+حصتها و هكذا ابن الأبن فمقابل هذه الزيادة استفاد
+
+390
+00:33:07,000 --> 00:33:13,770
+هو فبده يدفع فالزوجة طلبت مبلغ و قدره 6300جالت أنا
+
+391
+00:33:13,770 --> 00:33:18,890
+بدي تدفعوا ل 6800 ومش هتشوفي وجهي بعد اليوم قالوا
+
+392
+00:33:18,890 --> 00:33:22,610
+لها ماشي على بركة الله واتفقوا وصاروا بدهم يدفعوا
+
+393
+00:33:22,610 --> 00:33:26,690
+لها على أي أساس بدهم يدفعوا على أساس عدد الأسهم
+
+394
+00:33:28,120 --> 00:33:32,180
+فبدنا نروح نطلع قيمة السهم، كيف بنطلعه؟ هاد بدنا
+
+395
+00:33:32,180 --> 00:33:35,820
+نعملها كإنها تاريكة، تاريكة على إيش؟ على الأصل،
+
+396
+00:33:35,820 --> 00:33:41,120
+الأصل 21، من وين جيبناه؟ إنه احنا استثمنا الزوج،
+
+397
+00:33:41,120 --> 00:33:47,270
+فبطلع 300، فبنروح نقول الأم بدها تتفعلنا 1200البنت
+
+398
+00:33:47,270 --> 00:33:52,770
+بدها تتفعلنا 3600 و ابن الإبن هيتفعلنا 1500 و
+
+399
+00:33:52,770 --> 00:33:57,670
+خلصنا فصار المصنع بس بين .. هتصير المسألة كده
+
+400
+00:33:57,670 --> 00:34:02,230
+بنكتبها مرة تانية أم و بنت و إبن إبن و من 21 و هي
+
+401
+00:34:02,230 --> 00:34:07,630
+الأسهم بالطريقة هذه 4, 12, 5 زي ما هي بتظل لكن 4
+
+402
+00:34:07,630 --> 00:34:13,250
+من إيش؟ من 21 مش من 24، بس شوفتوا ما أسهلها؟ تمام؟
+
+403
+00:34:13,250 --> 00:34:17,010
+سهل جدا، أصلا مافيهاش كلاموبالتالي إذا الاحتمال
+
+404
+00:34:17,010 --> 00:34:20,290
+الأول اللي قلناه بإنه أن يخرج الوارث لجميع الورثة
+
+405
+00:34:20,290 --> 00:34:24,390
+فكل وارث يدفع بنسبة أسهمه من نصيب الخارج زي ما
+
+406
+00:34:24,390 --> 00:34:28,170
+قلنا فيصبح الورثة مالكين من أسهم الوارث من التركة
+
+407
+00:34:28,170 --> 00:34:32,450
+بنسبة أسهمهم، تمام؟ كيف؟
+
+408
+00:34:34,800 --> 00:34:38,580
+هي هذه، شوفتي ما أسهلها؟ سهل كتير، صح يا العنون؟
+
+409
+00:34:38,580 --> 00:34:43,300
+لأ، هي هذه الموضوع كله، موضوع التخارج، تمام؟ وهي
+
+410
+00:34:43,300 --> 00:34:48,920
+مثال تاني، اكتبوا وحلولا حالكم زوجة وشقيقة و أخ لي
+
+411
+00:34:48,920 --> 00:34:53,740
+أم و عم شقيق و أراد العم أن يخرج لجميع الورثة عن
+
+412
+00:34:53,740 --> 00:34:58,860
+مبلغ قدره ألفين و متان، يلا بدنا نمشي عنه بتحلولا
+
+413
+00:34:58,860 --> 00:35:03,020
+حالكم، هذا سهل، لأنه أخدنا الفكرة، صح؟ ولا صح؟ صح
+
+414
+00:35:03,020 --> 00:35:13,390
+تمامجميل نيجي الآن بدكم
+
+415
+00:35:13,390 --> 00:35:16,690
+نحلوا بنحلوا ع السريع يلا ناشط بنحلوا ع السريع
+
+416
+00:35:16,690 --> 00:35:22,010
+حاضر تكرموا بس
+
+417
+00:35:22,010 --> 00:35:27,310
+مش هنطلع غير نخلص اللي بدنا نخلصه فركزوا ع السريع
+
+418
+00:35:27,310 --> 00:35:32,530
+يلا ملوني بسرعة بسرعة همشي بسرعة زوجة شقيقة
+
+419
+00:35:34,890 --> 00:35:42,070
+أخ لأم عم شقيق وطبعا العم هو اللي بدي يخرج مقابل
+
+420
+00:35:42,070 --> 00:35:47,030
+ألفين ومتين لمين؟ لجميع بهم نعرف لمين بدي يخرج
+
+421
+00:35:47,030 --> 00:35:51,510
+لجميع الورثة انحل على السريع الزوجة فش طبعا فرح
+
+422
+00:35:51,510 --> 00:35:56,310
+فإلها الربة الشقيقة نصف والأخ لأم سدس وهد هو
+
+423
+00:35:56,310 --> 00:36:01,800
+العصبة المسألة من اتناشهن تلاتة و هن ستة و هن
+
+424
+00:36:01,800 --> 00:36:07,000
+اتنين جدش بيضل تلاتة صح؟ و لا لأ تسعة .. واحد آسفة
+
+425
+00:36:07,000 --> 00:36:12,540
+بيضل جدش واحد لأنه العم بياخد الباقي فدول الجماعي
+
+426
+00:36:12,540 --> 00:36:16,960
+هتلاقيهم احداش صح؟ فالان اذا العم بده يخرج هتصير
+
+427
+00:36:16,960 --> 00:36:22,980
+المسألة من جداش من احداش حلو؟تمام؟ فبنقول العم
+
+428
+00:36:22,980 --> 00:36:27,020
+بيخرج لجميع الورثة مقابل مبلغ وقدره الفين و متان
+
+429
+00:36:27,020 --> 00:36:32,800
+فبنروح الجسمين الفين و متان على احداش و يساوي جداش
+
+430
+00:36:32,800 --> 00:36:40,160
+متان فبنقول للزوجة ادفعي للعم اعطي العم ستمية وانت
+
+431
+00:36:40,160 --> 00:36:44,740
+يا شقيقة اعطي العم تلت مية .. تلت تلاف و ستمية او
+
+432
+00:36:44,740 --> 00:36:51,800
+عفوا ألف و متين أكتر ألف و متينوانت .. وانت يا أخ
+
+433
+00:36:51,800 --> 00:36:56,740
+اعطي العام جداش 400 و بس و أنتوا تملكوا المصنع
+
+434
+00:36:56,740 --> 00:37:01,420
+لوحدكم فهيصير المصنع بد المكان كأنه 12 جزء صار 11
+
+435
+00:37:01,420 --> 00:37:07,080
+جزء و طلعنا العام فصرت أنا كأخ لي أم كان لي 2 من
+
+436
+00:37:07,080 --> 00:37:12,440
+12 صار 2 من 11 زاد نصيبي و هكذا علم؟تمام؟ نيجي
+
+437
+00:37:12,440 --> 00:37:17,860
+الأن للاحتمال التاني وهو أن يخرج الورثة لأحد
+
+438
+00:37:17,860 --> 00:37:22,900
+الورثة بعينه يعني بدي يطلع من الشركة اللي بيناتهم
+
+439
+00:37:22,900 --> 00:37:26,840
+مش جولنا المال مشترك بدي يطلع لوحد بعينه يعني في
+
+440
+00:37:26,840 --> 00:37:30,960
+هذه المسألة مثلا العم بدي يطلع للزوجة مثلا بدي
+
+441
+00:37:30,960 --> 00:37:34,900
+أعطي أسهمه لمين للزوجة أو بدي أعطي أسهمه للشقيقة
+
+442
+00:37:34,900 --> 00:37:38,980
+أو بدي أعطي أسهمه للأخ لأمه فنقول في هذه الحالة
+
+443
+00:37:39,260 --> 00:37:44,020
+طالما باقي الورثة لم ينازعوا ما جالوشش معنى ليش
+
+444
+00:37:44,020 --> 00:37:47,360
+أنا بدي أبصر إيش لأنه إذا صار في اعتراض لأ لازم
+
+445
+00:37:47,360 --> 00:37:50,960
+يطلع للكل أو ما يطلعش إذا في اعتراض بينما هو جال
+
+446
+00:37:50,960 --> 00:37:54,840
+أنا بدي أعطي أسهمي لفلان هم جالوا مش مشكلة لأنه
+
+447
+00:37:54,840 --> 00:37:58,640
+أصلا مش جادرين يدفعهم هم مش جادرين يدفع يعني هيك
+
+448
+00:37:58,640 --> 00:38:03,080
+هيك إجاهم هذا المال و تركه من اللي مات هم معاهم مش
+
+449
+00:38:03,080 --> 00:38:09,150
+أصلا ولا شك لحتى يدفعوا لحدا مثلا بتصير بينماما هو
+
+450
+00:38:09,150 --> 00:38:13,550
+بالتراضي أنا إجيت أقول أنا حصتي بدي أبيعها للعنود
+
+451
+00:38:13,550 --> 00:38:19,070
+هي من الورثة و طبعا هي موافقة و معاها فلوس كنزة
+
+452
+00:38:19,070 --> 00:38:22,690
+جاية من سعودية و جايبة الخزنة معاها للعنود فجايبة
+
+453
+00:38:22,690 --> 00:38:25,650
+الخزنة كلها فأنا قولت يلا بناخدلنا جورشين منها
+
+454
+00:38:25,650 --> 00:38:31,780
+تمام فبدي أبيع حصتي لمين للعنودأه طبعا .. طبعا ما
+
+455
+00:38:31,780 --> 00:38:34,800
+هي بدها تطلع .. خليكم معاه .. هي بدها تشتري أنا
+
+456
+00:38:34,800 --> 00:38:39,380
+بده أطلع فهي بتعطيني و بتاخد حظتي لحالها فبالتالي
+
+457
+00:38:39,380 --> 00:38:42,920
+المسألة هتظلها من اتناش .. هتظلها من اتناش لكن
+
+458
+00:38:42,920 --> 00:38:48,780
+الواحد بدل ما يطير بدي روح لمين لأ وصلت وبالتالي
+
+459
+00:38:49,410 --> 00:38:57,770
+إذا أراد أحد الوارثة أن يخرج لوارث بعينه فله ذلك
+
+460
+00:38:57,770 --> 00:39:05,410
+بشرط اللي لا ينازعه أحد وحينها فإن هذا الوارث الذي
+
+461
+00:39:05,410 --> 00:39:12,630
+يريد أن يخرج يأخذ قيمةأسهمه، مين اللي بدي أدفعله؟
+
+462
+00:39:12,630 --> 00:39:17,790
+الخارج له، اللي إيش أعطناه، تمام؟ وبالتالي في هذا
+
+463
+00:39:17,790 --> 00:39:21,790
+المثال زي ما قلنا العام أراد أن يخرج مثلا للأخ لأم
+
+464
+00:39:21,790 --> 00:39:28,590
+مثلا للأخ لأم فالأخ لأم هو اللي بدفع المبلغ للعمل
+
+465
+00:39:29,250 --> 00:39:34,230
+والأخ مقابل اللي دفعه هياخد السهم، هيصير له تلاتة،
+
+466
+00:39:34,230 --> 00:39:39,310
+هيصير له تلاتة مش اتنين، وهذا طلع، لكن أصل المسألة
+
+467
+00:39:39,310 --> 00:39:44,970
+ضاله إيش؟ مصلة، فالـ 2200 هدول مين اللي هيدفعهم؟
+
+468
+00:39:44,970 --> 00:39:49,110
+الأخ اللي قام، طب لو هو بده يطلع للشقيقة، نفس
+
+469
+00:39:49,110 --> 00:39:55,800
+الفكرة، فهو اللي هيدفعوبالتالي خلصنا شوفتوا ما
+
+470
+00:39:55,800 --> 00:39:59,840
+أسهلها؟ بتغيرش أصل المسألة هو هو بس الفرق أنه هذا
+
+471
+00:39:59,840 --> 00:40:03,180
+اللي طلع بناخد أسهم و بنضيفهم لللي هيدفع و خلصنا
+
+472
+00:40:03,180 --> 00:40:07,540
+علم؟ الاحتمال التالت نفس التاني مع الفرق التالي ..
+
+473
+00:40:07,540 --> 00:40:13,220
+نفس التاني مع الفرق التالي إذا أراد أحد الورثة أن
+
+474
+00:40:13,220 --> 00:40:20,960
+يخرج لأجنبي حدا من برا الأشالورثة مش من الورثة
+
+475
+00:40:20,960 --> 00:40:23,820
+ممكن من جرايبي لكن مش من ورستي مش فيه جرايب
+
+476
+00:40:23,820 --> 00:40:29,720
+محجوبين مثلا حلو فإذا أنا بدي أخرج لمين؟ أنا كعم
+
+477
+00:40:29,720 --> 00:40:34,520
+شقيق بدي أخرج لمين للعم لأب مثلا هو أصلا مش من
+
+478
+00:40:34,520 --> 00:40:39,980
+الورثة مثلا فالآن أنا بقول بدي أطلع و أنا بدي أبيع
+
+479
+00:40:39,980 --> 00:40:44,620
+حصتي فإنتوا كورثة نفسكم تشتريوها بس معاكم مش فلوس
+
+480
+00:40:45,910 --> 00:40:50,370
+فارضيتوا، إيش بدكم تعملوا؟ مش مشكلة بس بدك تجيبلنا
+
+481
+00:40:50,370 --> 00:40:54,690
+حد يعني بيغلبناش لأنه هيدخل بناتنا، هيصير شريك
+
+482
+00:40:54,690 --> 00:41:00,270
+معنا، بدالة، فإذا مافي مشكلة بشرط زي ما قلت إنه
+
+483
+00:41:00,270 --> 00:41:04,610
+مايكونش فيه منازع من الورثة والورثة بدهم يوافقوا
+
+484
+00:41:04,610 --> 00:41:08,290
+على هذا الشريك الجديد اللي هو الأجنبي وبالتالي إيش
+
+485
+00:41:08,290 --> 00:41:12,890
+الوضع هيصير؟ إنه الأجنبي بديحل محل الخارجمين اللي
+
+486
+00:41:12,890 --> 00:41:15,670
+طلع .. مين اللي طلع في الأجنب دي و قد ما كانوا
+
+487
+00:41:15,670 --> 00:41:21,650
+ياخد أسهمه وبالتالي الأجنب بدي يدفع للي طلع المبلغ
+
+488
+00:41:21,650 --> 00:41:24,990
+كامل ان هو .. و المسألة هتظلها زي ما هي .. المسألة
+
+489
+00:41:24,990 --> 00:41:31,010
+هتظلها زي ما هيلو ما رضيه بدي يسير بدي يبيع للجميع
+
+490
+00:41:31,010 --> 00:41:34,770
+طب الجميع مش راضين يدفعوا أنا مصمم بدي حصته
+
+491
+00:41:34,770 --> 00:41:38,350
+فهيروحوا للقضاء و القضاء هيحكم بناتهم يا بيبيع كل
+
+492
+00:41:38,350 --> 00:41:46,010
+المصنع يا بيراضيهم و خلصنا علم؟ تمام؟ طيب إذا هات
+
+493
+00:41:46,010 --> 00:41:52,260
+بالنسبة لموضوع محاضرتنا لهذا اليومالمحاضرة القادمة
+
+494
+00:41:52,260 --> 00:41:55,840
+بإذن الله نتحدث عن تصحيح المسائل أقول قولي هذا
+
+495
+00:41:55,840 --> 00:41:58,780
+وأستغفر الله لي ولكم وصلى اللهم وسلم وبارك على
+
+496
+00:41:58,780 --> 00:42:02,800
+سيدنا محمد والسلام عليكم ورحمة الله تعالى وبركاته
+
diff --git a/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/9UsB1CkOrEg_postprocess.srt b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/9UsB1CkOrEg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c8c5d29fcf857be3301f052cea8f41465a5a7a9b
--- /dev/null
+++ b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/9UsB1CkOrEg_postprocess.srt
@@ -0,0 +1,836 @@
+1
+00:00:05,150 --> 00:00:08,190
+أعوذ بالله الزميل عليه من الشيطان الرجيم بسم الله
+
+2
+00:00:08,190 --> 00:00:11,250
+الرحمن الرحيم الحمد لله رب العالمين والصلاة
+
+3
+00:00:11,250 --> 00:00:15,330
+والسلام على أشرف الأنبياء والمرسلين سيدنا محمد بن
+
+4
+00:00:15,330 --> 00:00:18,910
+عبدالله الصادق الأمن ثم أما بعد أحييكم جميعا بتحية
+
+5
+00:00:18,910 --> 00:00:23,790
+الإسلام فالسلام عليكم ورحمة الله تعالى وبركاته كيف
+
+6
+00:00:23,790 --> 00:00:29,180
+حالكوا نطيبة ان شاء الله؟الحمد لله إذا اليوم بإذن
+
+7
+00:00:29,180 --> 00:00:34,440
+الله سننهي حديثنا حول ميراث الجد مع الإخوة كنا قد
+
+8
+00:00:34,440 --> 00:00:38,820
+تحدثنا المحاضرة السابقة عنها لو كان الإخوة من أكثر
+
+9
+00:00:38,820 --> 00:00:44,540
+من نوع وقلنا إنه حتى يرث الإخوة لأب مع الإخوة
+
+10
+00:00:44,540 --> 00:00:50,640
+الأشقاء فلابد ابتداء من شرطين أساسيين وهم أن يكون
+
+11
+00:00:50,640 --> 00:00:56,180
+الباقي بعد الجدأكثر من نصف التركة وأيضا أن يكون
+
+12
+00:00:56,180 --> 00:01:00,800
+الأشقاء شقيقة واحدة وهذا الأمر من الناحية العملية
+
+13
+00:01:00,800 --> 00:01:06,520
+حتى يتحقق نفرق بينما إذا كان هناك أصحاب فرود أو لم
+
+14
+00:01:06,520 --> 00:01:11,260
+يكن هناك أصحاب فرود المحاضرة السابقة كنا قد قلنا
+
+15
+00:01:11,260 --> 00:01:17,360
+أنه عند عدم وجود أصحاب فرود فحتى يرث الإخوة لأب
+
+16
+00:01:17,360 --> 00:01:23,710
+لابد من أن يكون الإخوة لأبأكثر من أخوة لأب بمعنى
+
+17
+00:01:23,710 --> 00:01:30,710
+أخ لأب فأكثر حينها يتصور أن يرث الإخوة لأب مع وجود
+
+18
+00:01:30,710 --> 00:01:36,130
+الأشقة طبعا بالشرطين اللذين ذكرتهما قبل قليل اليوم
+
+19
+00:01:36,130 --> 00:01:40,610
+بإذن الله سنتحدث عن ما لو كان هناك أصحاب فرود مع
+
+20
+00:01:40,610 --> 00:01:45,960
+الجدوة الإخوةفي هذه الحالة حتى يرث الإخوة لأب نفس
+
+21
+00:01:45,960 --> 00:01:50,380
+الفكرة اللي ذكرناها قلنا إنه لازم يكون الباقي بعد
+
+22
+00:01:50,380 --> 00:01:55,720
+الجد أكثر من نصف التاريخة والأشقاء شقيقة لأن هدول
+
+23
+00:01:55,720 --> 00:02:00,500
+الشرطين لازم يتوفروا ابتداء بعيدا عن إنه في أصحاب
+
+24
+00:02:00,500 --> 00:02:03,860
+فروض ولا مافيش بشكل أساسي بعدين بنقول إذا مافيش
+
+25
+00:02:03,860 --> 00:02:08,700
+أصحاب فروض ضيف إنه الإخوة لأب أكثر من أخت لأب إذا
+
+26
+00:02:08,700 --> 00:02:13,240
+في أصحاب فروض بدنا نضيفه نقول بإنه مرة تانيةإن عند
+
+27
+00:02:13,240 --> 00:02:18,580
+وجود أصحاب فروض حتى يرث الإخ والي أب لازم يكون
+
+28
+00:02:18,580 --> 00:02:24,360
+الباقي بعد الجد أكثر من نصف التركة الأشقاء لازم
+
+29
+00:02:24,360 --> 00:02:31,080
+يكونوا أخت شقيقة واحدة بعدين لا يتصور ذلك من ناحية
+
+30
+00:02:31,080 --> 00:02:36,180
+العملية عند وجود أصحاب فروض إلا إذا كان صاحب الفرض
+
+31
+00:02:36,180 --> 00:02:43,200
+أم أو جد بسيعني لا يمكن أن يرث الإخوة لأب عند وجود
+
+32
+00:02:43,200 --> 00:02:47,240
+أصحاب فرود مع الأشقاء والجد إلا إذا كان صاحب الفرض
+
+33
+00:02:47,240 --> 00:02:53,260
+أم أو جدة، بس يا أم يا جدة فقط، أي حدا غير الأم
+
+34
+00:02:53,260 --> 00:02:59,060
+والجدة على طول الأشقاء ما بينحشبوا لكن بدنا نعدهم
+
+35
+00:02:59,060 --> 00:03:04,790
+زي ما اتفجنالأن المبدأ العام الذي قررناه أن الإخوة
+
+36
+00:03:04,790 --> 00:03:08,850
+الأشقاء يستفيدون من الإخوة الأبئذ يعضونهم على الجد
+
+37
+00:03:08,850 --> 00:03:16,170
+ثم يحجبونهم بالشرط التي ذكرناها أرجع أقولبإنه عند
+
+38
+00:03:16,170 --> 00:03:21,750
+وجود أصحاب فروض حتى يرث الإخوة لأب مع وجود الأشقاء
+
+39
+00:03:21,750 --> 00:03:27,510
+والجاد فبنقول لازم يكون الباقي بعد الجاد أكثر من
+
+40
+00:03:27,510 --> 00:03:31,370
+نصف التاريخة الأشقاء شقيقة واحدة وهذا من ناحية
+
+41
+00:03:31,370 --> 00:03:35,410
+العملية لا يتصور إلا إذا كان صاحب الفرن أم أو جدة
+
+42
+00:03:35,410 --> 00:03:41,010
+وأيضا لا يتصور ذلك إلا إذا كان الإخوة لأب أكثر من
+
+43
+00:03:41,010 --> 00:03:45,850
+أخ لأبهناك قلنا أكثر من أخوة لأب، يعني أخ لأب هناك
+
+44
+00:03:45,850 --> 00:03:50,550
+بنفع، حان أخ لأب بينفعش، لازم أكثر، شو يعني أكثر؟
+
+45
+00:03:50,550 --> 00:03:54,630
+يعني اتنين أخ لأب أه بينفع، يعني أخ لأب و أخوة لأب
+
+46
+00:03:54,630 --> 00:03:59,170
+أه بينفع، تلاتة أخوة لأب بينفع، اتنين أخوة لأب
+
+47
+00:03:59,170 --> 00:04:03,030
+بينفع طبعا بينفعش، يعني اتنين أخوة بتساوي أخ و
+
+48
+00:04:03,030 --> 00:04:07,830
+احنا بنقول أكثر من أخ، علم؟هذا بشكل عام تقريبا هيك
+
+49
+00:04:07,830 --> 00:04:13,510
+خلصنا لكن بدي أرجع أقرر شغلة و هي أنه عند وجود
+
+50
+00:04:13,510 --> 00:04:18,270
+أصحاب فروض بالتأكيد الجد يرث واحدة من تلت شغلات أو
+
+51
+00:04:18,270 --> 00:04:21,990
+الأفضل من تلت شغلات بدناش ننسى اللي هي سدس التاريخ
+
+52
+00:04:21,990 --> 00:04:27,580
+أو تلت الباقي أو المقاسمة كذكر علم؟تمام؟ و بدى
+
+53
+00:04:27,580 --> 00:04:31,140
+أرجع أقرر كمان الأمر اللى حكيته قبل شوية وكررته
+
+54
+00:04:31,140 --> 00:04:35,080
+كتير أنه دائما دائما الأشقاء بيستفيدوا من الإخوة
+
+55
+00:04:35,080 --> 00:04:38,540
+لقبل إذا يعضونهم على الجد ثم يحجبونهم وهذا يعني
+
+56
+00:04:38,540 --> 00:04:45,040
+أنه كل ما زاد عدد الإخوة قل نصيب الجد وهذا يعني أن
+
+57
+00:04:45,040 --> 00:04:49,220
+الباقي بعد الجد هيزيد الباقي بعد الجد هيزيد صح ولا
+
+58
+00:04:49,220 --> 00:04:51,400
+لا؟ وصلت؟ انشوف
+
+59
+00:04:55,400 --> 00:04:59,680
+القول مثلا يالا مالوني المسألة اللي قدامكم
+
+60
+00:05:13,260 --> 00:05:18,680
+ما تقولي .. بدي أقولك شغلة صغيرة واهية قضية الشروط
+
+61
+00:05:18,680 --> 00:05:22,240
+اللي ذكرناها حابة نقول هدول يارثون بديك تعرفيها
+
+62
+00:05:22,240 --> 00:05:25,340
+على أساس بعد ما تحلي تشوفي حالك صح أو لأ مش من
+
+63
+00:05:25,340 --> 00:05:28,900
+البداية تقولي محجوبين و تحلي، ليش؟ لأنه أنا هدفي
+
+64
+00:05:28,900 --> 00:05:33,000
+أعرف الجد جدش بياخد ومش هعرف إلا إذا حسبت كل إشي،
+
+65
+00:05:33,000 --> 00:05:36,500
+يعني بقولك قوّك تروح تقولي محجوب و تجاوبي على طول
+
+66
+00:05:36,500 --> 00:05:40,480
+بدون هدولإذا جوابتي بدون هدول حلت أكيد هيكون غلط
+
+67
+00:05:40,480 --> 00:05:44,600
+لأن احنا متفجين إن هدول هيستفيدوا من وجود هدول وشو
+
+68
+00:05:44,600 --> 00:05:48,260
+يعني إنك بدك تحلي حال طبيعي لكن قضية الشروط هي
+
+69
+00:05:48,260 --> 00:05:55,220
+بدها تكون زي فلاشة عندك تقولك صح أو غلطوصلت؟ تمام؟
+
+70
+00:05:55,220 --> 00:05:58,400
+يعني هذه المسألة مثلا مباشرة بقول هدول بيرثوا
+
+71
+00:05:58,400 --> 00:06:03,220
+مباشرة لإن الشروط متوفرة إن صاحب الفرض أم الشقيقة
+
+72
+00:06:03,220 --> 00:06:08,660
+واحدة الباقي أكيد هيكون أكثر من النصف لإن الأم ايش
+
+73
+00:06:08,660 --> 00:06:13,920
+صدوس مش ممكنية نعطيها تلت في عدد من الأخوة طبيعي
+
+74
+00:06:13,920 --> 00:06:17,540
+أضعف الإيمان هنا هيكونوا اتنين أخ أضعف الإيمان
+
+75
+00:06:17,540 --> 00:06:22,000
+وبالتالي في كل الأحوال هتكون صدوس هناوصلت؟ تمام
+
+76
+00:06:22,000 --> 00:06:27,600
+خلّيكوا معايا بدنا نشوف انقول الأم جدش بتاخد سدس
+
+77
+00:06:27,600 --> 00:06:33,560
+من ستة الباقي زي ما كنا نحلف المسائل بشكل أساس
+
+78
+00:06:33,560 --> 00:06:42,320
+تعالوا هنا نشوف الخيارات التلاتة هلجيت؟
+
+79
+00:06:42,320 --> 00:06:47,560
+خلاص ماحدش يحكي معاياالأنصف ستة هي كالمسألة من ستة
+
+80
+00:06:47,560 --> 00:06:51,700
+يعني ستة ع ستة اللي هو واحد تلت الباقي خمسة على
+
+81
+00:06:51,700 --> 00:06:58,240
+تلاتة اللي هو واحد و تلتين صح؟ المقاسم تعالوا نعد
+
+82
+00:06:58,240 --> 00:07:03,980
+هي أربعة خمسة ستة سبعة يعني خمسة ع سبعة في اتنين
+
+83
+00:07:03,980 --> 00:07:12,150
+صح؟ صح؟تمام فى اتنى يعنى عشرة على سبعة و العشرة ع
+
+84
+00:07:12,150 --> 00:07:15,590
+سبعة أكيد أجل من خمسة ع تلاتة لأنه العشرة ع سبعة
+
+85
+00:07:15,590 --> 00:07:21,350
+عبارة عن خمسة على تلاتة و نص و خمسة ع تلاتة و نص
+
+86
+00:07:21,350 --> 00:07:26,710
+أجل من خمسة ع تلاتة صح ولا لأ جسمى خمس طفحات ع
+
+87
+00:07:26,710 --> 00:07:28,970
+تلاتة ع شمسة ع تلاتة ماهى سجن مستغربة من الكلام
+
+88
+00:07:28,970 --> 00:07:35,070
+فخدى خمس طفحات كسميها ع تلاتةو جسمي خمس طفحات على
+
+89
+00:07:35,070 --> 00:07:40,810
+تلاتة و نص واحدة فأكيد هتطلع الحصة أقل وصلت فإذا
+
+90
+00:07:40,810 --> 00:07:45,170
+هذا الأفضل تلت الباقي نيجي الأن نعطي الجد ايش
+
+91
+00:07:45,170 --> 00:07:52,350
+بنقول هان تلت الباقي اللي هو خمسة على تلاتة حلو؟
+
+92
+00:07:52,350 --> 00:07:58,950
+تمام و هان واحد طبعا الأن هدول بنقول الباقي بعد
+
+93
+00:07:58,950 --> 00:08:06,840
+الجداللي هو خمسة ناجس خمسة على تلاتة اللي هو بتطلع
+
+94
+00:08:06,840 --> 00:08:11,540
+معايا عشرة على تلاتة، صح؟
+
+95
+00:08:11,540 --> 00:08:16,500
+اللي هو خمستاشر ناجس خمسة كنا بنحل هيك مسائل يعني
+
+96
+00:08:16,500 --> 00:08:21,720
+مش شغلة صعبة، تمام؟ إذا عشرة على تلاتة لحظة معايا
+
+97
+00:08:21,720 --> 00:08:25,300
+هنا بدنا نضرب في شوفي تلاتة حتى نتخلص من الكسر
+
+98
+00:08:26,490 --> 00:08:31,810
+فالست في تلاتة تمانتاش و هنا تلاتة و هنا خمسة و
+
+99
+00:08:31,810 --> 00:08:40,650
+هنا جداش عشرة صح ولا لأ؟ عشرة فالان العشرة من
+
+100
+00:08:40,650 --> 00:08:46,330
+التمنتاش أكثر من الناس صح؟ العشرة من التمنتاش لأن
+
+101
+00:08:46,330 --> 00:08:52,320
+نص التمنتاش تسعةصح ولا لأ؟ فإذا ها الباقي بعد الجد
+
+102
+00:08:52,320 --> 00:08:57,380
+أكثر من النصف الأشقاء شقيقة واحدة صاحب الفرض أم و
+
+103
+00:08:57,380 --> 00:09:02,180
+الإخوة لأب أكثر من أخ لأب فبالتالي سيرثون لكن كيف
+
+104
+00:09:02,180 --> 00:09:09,340
+نورثهم؟ بنقول أن الأخت الشقيقة هتاخد النص اللي هي
+
+105
+00:09:09,340 --> 00:09:16,240
+18 ع 2تمانتاش ع اتنين جداش تسعة و هو أصلا الموجود
+
+106
+00:09:16,240 --> 00:09:22,140
+عشرة فهتاخد تسعة من عشرة هتاخد لحالها تسعة من عشرة
+
+107
+00:09:22,140 --> 00:09:26,760
+و بيضل هنجداش واحد اعرفنا كيف إجت التسعة و الواحد؟
+
+108
+00:09:26,760 --> 00:09:33,460
+الأخت هتاخد النصالاخت هتاخد النصف، نصف التاريكة،
+
+109
+00:09:33,460 --> 00:09:38,500
+التاريكة تمانتاش، نصفها جداش؟ تسعة، بنعطي للاخت
+
+110
+00:09:38,500 --> 00:09:43,720
+تسعة من العشرة فبيضل، لأن العشرة لهدول كلهم سوا،
+
+111
+00:09:43,720 --> 00:09:48,740
+لهدول سوا، الأخت لحالها هتاخد النصف، والباقي أو
+
+112
+00:09:48,740 --> 00:09:51,160
+الأكثر من النصف، اللي بيزيد عن النصف، مين اللي
+
+113
+00:09:51,160 --> 00:09:55,820
+هتاخده؟اللي هياخدوه الإخوة ل up بغض النظر عن عددهم
+
+114
+00:09:55,820 --> 00:10:00,760
+فهيطلعلهم واحد، واحد ع اتنين انكسار فروحي قدر
+
+115
+00:10:00,760 --> 00:10:05,940
+بالمسألة فتنين اللي هو تصحيح تمام ففتنين ستة و
+
+116
+00:10:05,940 --> 00:10:11,860
+تلاتين فتنين ستة فتنين عشرة فتنين تمانتاش فتنين
+
+117
+00:10:11,860 --> 00:10:16,820
+اتنين خلصت بس تمام؟ حلو ناخد مثال آخر
+
+118
+00:10:29,660 --> 00:10:37,700
+ركزوا معايا داخل في ال quiz يلا
+
+119
+00:10:37,700 --> 00:10:53,020
+نشوف بالين المثال اللي قدامكم يلا
+
+120
+00:10:53,020 --> 00:10:58,630
+خليكم معايا نفس المثال 6لأن الطبيعي هتطلع الأرقام
+
+121
+00:10:58,630 --> 00:11:03,470
+متقاربة دائما لأنه محدودين صحاب الفرض اللي جد أو
+
+122
+00:11:03,470 --> 00:11:06,650
+أم بس وبالتالي نفس الفكرة هتكون معانا في الغالب
+
+123
+00:11:06,650 --> 00:11:14,390
+يعني هنا الباقي خمسة على السريع هنا ستة على ستة
+
+124
+00:11:14,390 --> 00:11:19,730
+خمسة على تلاتة والمقاسمة أربعة خمسة ستة سبعة نفس
+
+125
+00:11:19,730 --> 00:11:25,820
+المثال تمامادرب اتنين لأنه في انات عشرة على تلاتة
+
+126
+00:11:25,820 --> 00:11:30,480
+فهذا هو الأفضل فبتروح تقولي هان خمسة على تلاتة و
+
+127
+00:11:30,480 --> 00:11:35,300
+هنا بتقولي اللي هو خمسة ناجس خمسة على تلاتة اللي
+
+128
+00:11:35,300 --> 00:11:40,800
+هو عشرة على تلاتة اضربي في تلاتة هان تمانتاش لحظة
+
+129
+00:11:40,800 --> 00:11:45,720
+سريعة لأن نفس الأرقام هي هي و هنا عشرة فالاخد الها
+
+130
+00:11:45,720 --> 00:11:51,450
+منالتمنتاش تسعة نص التمنتاش يعني تسعة هنا تسعة
+
+131
+00:11:51,450 --> 00:11:55,270
+وهنا واحد الواحد والاربع اضربي في اربع بس اللي هو
+
+132
+00:11:55,270 --> 00:11:59,070
+فقط اختلفة المسألة في التصحيح فقط عدد الرؤوس هو
+
+133
+00:11:59,070 --> 00:12:02,550
+اللي اختلف وغالبا هو اللي هيختلف معاك عدد الرؤوس
+
+134
+00:12:02,550 --> 00:12:07,390
+بس يعني بالغالب هذا اللي هيختلف معاكفقط أما هذا هو
+
+135
+00:12:07,390 --> 00:12:11,430
+هو دائما هذا واحد دائما هذا خمسة على تلاتة ليش
+
+136
+00:12:11,430 --> 00:12:16,230
+دائما؟ ليش؟ لأن صاحب الفرد بس بياخد واحد من ستة
+
+137
+00:12:16,230 --> 00:12:21,470
+فطبيعي الباقي خمسة فإذا تلتل هذا بالظبط فإذا هنروح
+
+138
+00:12:21,470 --> 00:12:26,070
+يقدربي في أربعة هن أربعين و أربع عشرين أربعة و
+
+139
+00:12:26,070 --> 00:12:32,440
+ستينهنا في أربع اتناش في أربع عشرين في أربع ستة و
+
+140
+00:12:32,440 --> 00:12:40,980
+تلاتين و هنا في أربع أربع تمام بس وصلت اتنين و
+
+141
+00:12:40,980 --> 00:12:46,540
+سبعين اه اتنين و سبعين اه لأ اه اتنين و تلاتين صح
+
+142
+00:12:46,540 --> 00:12:52,320
+اتنين و تلاتين انا حسبتها اربع و عشرين تمام ناخد
+
+143
+00:12:52,320 --> 00:12:58,620
+مثال انهناخد مثال انه ايش اختل اي شرط من الشروط
+
+144
+00:12:58,620 --> 00:13:12,340
+اللتي ذكرناه تمام؟ تمام اعملولي
+
+145
+00:13:12,340 --> 00:13:17,100
+المثال اللي قدامكم زوجة
+
+146
+00:13:17,100 --> 00:13:18,880
+جد
+
+147
+00:13:23,860 --> 00:13:28,640
+أخت شقيقة تلاتة
+
+148
+00:13:28,640 --> 00:13:38,580
+أخت لأب يلّا نشوف حل حال طبيعي الزوجة ربع فالمسألة
+
+149
+00:13:38,580 --> 00:13:44,760
+من أربعة الباقي تلاتة فتعالى
+
+150
+00:13:44,760 --> 00:13:50,740
+هان أربعة على ستة تلت الباقي تلاتة على تلاتة
+
+151
+00:13:51,850 --> 00:13:59,210
+المقاسمة تلاتة أربعة خمسة ستة صح؟ ستة يعني تلاتة
+
+152
+00:13:59,210 --> 00:14:05,170
+على ستة عفوا أسفة أه صح تلاتة على ستة ضرب اتنين
+
+153
+00:14:05,170 --> 00:14:08,510
+يعني ستة على ستة يسوا واحد فالان سواء قلت
+
+154
+00:14:08,510 --> 00:14:12,890
+بالمقاسمة او قلت الباقي هو هو النتيجة مختلفتش
+
+155
+00:14:12,890 --> 00:14:18,390
+فالجد يعطي واحد وهدول تلاتة ناقص واحد صح؟ تمام
+
+156
+00:14:20,880 --> 00:14:25,260
+فالان الاتنين .. الاتنين لحظة النص مش أكثر و احنا
+
+157
+00:14:25,260 --> 00:14:29,480
+قلنا هدول حتى يارثوا .. حتى يارثوا لازم الباقي
+
+158
+00:14:29,480 --> 00:14:33,560
+أكثر من النصف و هان الباقي أصلا نصف أختته الأخته
+
+159
+00:14:33,560 --> 00:14:37,780
+خلصت فهذا الاتنين للأخته هدول محجوبين فلا بدها
+
+160
+00:14:37,780 --> 00:14:39,620
+تصحي ولا أي شيء تمام
+
+161
+00:14:43,020 --> 00:14:46,880
+طيب لأنه مافي تطبيقات اليوم باعتبار أنك وز هناخد
+
+162
+00:14:46,880 --> 00:14:50,860
+مثال كمان عساس تثبت معلوماتك و تكون جاهزة ان شاء
+
+163
+00:14:50,860 --> 00:14:54,160
+الله
+
+164
+00:14:54,160 --> 00:15:06,200
+مالوني؟
+
+165
+00:15:06,200 --> 00:15:21,050
+بنت؟ جد؟أخت شقيقة اتنين أخت لأب البنت
+
+166
+00:15:21,050 --> 00:15:28,890
+فالمسألة من واحد هنا الباقي واحد صح ولا لأ نيجي
+
+167
+00:15:28,890 --> 00:15:38,030
+لسدس التاريخ اللي هي اتنين على ستة اللي هو نص طيب
+
+168
+00:15:38,030 --> 00:15:39,870
+طولة الباقي
+
+169
+00:15:44,070 --> 00:15:51,550
+اسفة حصدتني تسنين طيب تلت الباقي واحد على تلاتة
+
+170
+00:15:51,550 --> 00:16:00,790
+طيب المقاسمة اتنين تلاتة اربع خمسة خمسة صح واحد
+
+171
+00:16:00,790 --> 00:16:06,390
+على خمسة ضرب اتنين يعني اتنين على فأكيد اتنين على
+
+172
+00:16:06,390 --> 00:16:13,260
+خمسةأفضل من التلت لأن التلت اتنين على ستة فهذه
+
+173
+00:16:13,260 --> 00:16:18,700
+أفضل اتنين على خمسة أفضل تمام فإذا بناخد اش
+
+174
+00:16:18,700 --> 00:16:24,100
+المقاسمة هنا بتقول الجد يرث بي المقاسمة فبياخد اش
+
+175
+00:16:24,100 --> 00:16:30,470
+اتنين على خمسة هدول هياخدوا واحد ناجس اتنين علىصح
+
+176
+00:16:30,470 --> 00:16:35,330
+ولا لا؟ حلو اللي هو خمسة ناقص اتنين يعني تلاتة على
+
+177
+00:16:35,330 --> 00:16:41,470
+خمسة هنا تلاتة على خمسة بنعرف كيف نحسبها صح؟ جماعة
+
+178
+00:16:41,470 --> 00:16:45,410
+اللي مش فاهمة كيف بتيجي تحكي عندكم quiz أنتوا
+
+179
+00:16:45,410 --> 00:16:47,870
+أحرار، تمام؟
+
+180
+00:16:55,110 --> 00:16:59,310
+من وين خمسة؟ تلاتة على خمسة، احنا بنقول واحد ناجس
+
+181
+00:16:59,310 --> 00:17:04,430
+اتنين على خمسة فبتروحي اتوحدي المقامات، بيصير من
+
+182
+00:17:04,430 --> 00:17:09,570
+خمسة، المقام من خمسة، خمسة في واحد خمسة ناجس، واحد
+
+183
+00:17:09,570 --> 00:17:12,370
+في اتنين اتنين، خمسة ناجس اتنين، تلاتة، تلاتة على
+
+184
+00:17:12,370 --> 00:17:17,200
+خمسة، بستمام يا سماح؟ تمام ان شاء الله يا رب يكون
+
+185
+00:17:17,200 --> 00:17:22,440
+تمام نضرب فيه خمسة عساس نتخلص من المقام فالمسألة
+
+186
+00:17:22,440 --> 00:17:27,680
+من عشرة هنا خمسة هنا اتنين هان جداش تلاتة حلو
+
+187
+00:17:27,680 --> 00:17:36,500
+فالان تلاتة ركزوا معايا الان تلاتة من ايش؟من عشرة،
+
+188
+00:17:36,500 --> 00:17:42,460
+أصلا أجل، يعني هيك هيك نزل نصيب الأخد، والطبيعة هي
+
+189
+00:17:42,460 --> 00:17:45,880
+أصلا مش هتكون صاحبة فرد لإنه في بنت، فهيك هيك هي
+
+190
+00:17:45,880 --> 00:17:51,530
+مش صاحبة فردومع ذلك بنقول طالما أن الباقي بعد الجد
+
+191
+00:17:51,530 --> 00:17:58,030
+أقل من النصف فبالتأكيد الإخوة اللقب لن يريثون لأنه
+
+192
+00:17:58,030 --> 00:18:02,070
+أصلا صاحب الفرض ماكانش لا أم ولا جده، تمام؟ فإذا
+
+193
+00:18:02,070 --> 00:18:07,770
+التلاتة بتاخدها الأخد و هدول محجوبين، تمام؟ بس،
+
+194
+00:18:07,770 --> 00:18:08,450
+وصلت؟
+
+195
+00:18:11,290 --> 00:18:16,550
+هذا ما يتعلق بموضوع محاضراتنا لهذا اليوم بهيك
+
+196
+00:18:16,550 --> 00:18:20,670
+بنكون انتهينا من موضوع ميراث الجد مع الإخوة بكل
+
+197
+00:18:20,670 --> 00:18:26,710
+حالاته و تفصيلاته المحاضرات القادمة بإذن الله
+
+198
+00:18:26,710 --> 00:18:32,170
+سنتحدث عن فكرة جديدة ألا وهي الميراث بالتقدير
+
+199
+00:18:32,170 --> 00:18:36,830
+والاحتياط تتذكروا حينما تحدثنا عن شروط الميراث
+
+200
+00:18:36,830 --> 00:18:43,060
+قلنا أن يكون الوارثأو التيقن من حياة الوارث حقيقة
+
+201
+00:18:43,060 --> 00:18:48,520
+أو حكما أو تقديرا فسنتحدث عن ميراث الحمل وميراث
+
+202
+00:18:48,520 --> 00:18:52,960
+الخنثة بإذن الله باعتبار أن كل من الجنين في رحم
+
+203
+00:18:52,960 --> 00:18:59,020
+أمه والخنثة يرثون بالاحتياط والتقديرلأن الجنن قد
+
+204
+00:18:59,020 --> 00:19:03,520
+يأتي و قد لا يأتي فنحن نحتاط لأمره و الخنثى قد
+
+205
+00:19:03,520 --> 00:19:08,120
+يكون ذكر و قد يكون أنثى فنحن نقدر أنه ذكر أو أنه
+
+206
+00:19:08,120 --> 00:19:12,500
+أنثى و هكذا هذا ما سنتحدث حوله المحاضرات القادمة
+
+207
+00:19:12,500 --> 00:19:16,320
+بإذن الله أقول قولي هذا و أستغفر الله لي و لكم و
+
+208
+00:19:16,320 --> 00:19:19,980
+صلى اللهم و السلم و بارك على سيدنا محمد و السلام
+
+209
+00:19:19,980 --> 00:19:22,480
+عليكم و رحمة الله تعالى وبركاته
+
diff --git a/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/9vKLisOK8-k_raw.srt b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/9vKLisOK8-k_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e7c34bfa819f76e4a184ad7fa8deb56dc652ab7d
--- /dev/null
+++ b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/9vKLisOK8-k_raw.srt
@@ -0,0 +1,884 @@
+1
+00:00:04,930 --> 00:00:07,970
+أعوذ بالله السمعي لعليه من الشيطان الرجيم بسم الله
+
+2
+00:00:07,970 --> 00:00:11,110
+الرحمن الرحيم الحمد لله رب العالمين والصلاة
+
+3
+00:00:11,110 --> 00:00:14,870
+والسلام على أشرف الأنبياء والمرسلين سيدنا محمد بن
+
+4
+00:00:14,870 --> 00:00:18,650
+عبدالله الصادق الأمين ثم أما بعد أحييكم جميعا
+
+5
+00:00:18,650 --> 00:00:21,770
+بتحية الإسلام فالسلام عليكم ورحمة الله تعالى
+
+6
+00:00:21,770 --> 00:00:27,630
+وبركاتك كيف حالك؟ كنا طيبات ان شاء الله؟ طيب
+
+7
+00:00:27,630 --> 00:00:36,120
+تحضرنا جيد ان شاء الله؟ تحضرنا جيد؟إن شاء الله إذا
+
+8
+00:00:36,120 --> 00:00:42,640
+كنا قد شرعنا المحاضرة السابقة في الحالة الثالثة من
+
+9
+00:00:42,640 --> 00:00:48,620
+أحكام البناسخات والتي تحدثنا فيها أن ورثة الميت
+
+10
+00:00:48,620 --> 00:00:54,200
+الثاني هم ورثة الميت الأول مع اختلاف نسبتهم إليه
+
+11
+00:00:54,200 --> 00:00:59,240
+سواء كانوا كلهم وحدهم دون غيرهم أو دون أن يشاركهم
+
+12
+00:00:59,240 --> 00:01:05,540
+الغير أو كانبعضهم يرث من الميت الأول ويضاف إليهم
+
+13
+00:01:05,540 --> 00:01:12,220
+أخرون ليسوا من ورثة الميت الأول وكذلك ما إذا كان
+
+14
+00:01:12,220 --> 00:01:17,600
+بعض الأموات اللاحقين ليسوا أصلا من ورثة الميت
+
+15
+00:01:17,600 --> 00:01:22,000
+الأول فبالتالي لدينا ثلاثة أنواع كنا قد تحدثنا
+
+16
+00:01:22,000 --> 00:01:26,260
+المحاضرة السابقة عن النوع الأول وهو ما إذا كان
+
+17
+00:01:26,260 --> 00:01:32,540
+ورثة الميت الثاني هم بقية ورثة الميت الأولسواء
+
+18
+00:01:32,540 --> 00:01:39,660
+جميعهم يرث أو بعضهم لكن نسبتهم للميت تختلف عن
+
+19
+00:01:39,660 --> 00:01:44,760
+نسبتهم للميت الأول اليوم بإذن الله سنتحدث عن النوع
+
+20
+00:01:44,760 --> 00:01:51,470
+الثاني وهو ما إذا كانورثة الميت الثاني هم كما قلنا
+
+21
+00:01:51,470 --> 00:01:57,130
+ورثة الميت الأول سواء كانوا كلا ان بعضا بمعنى كلهم
+
+22
+00:01:57,130 --> 00:02:02,930
+يارثونا أو بعضهم ويضافوا اليهم أغراب شو يعني أغراب
+
+23
+00:02:02,930 --> 00:02:08,350
+يعني ليسوا من ورثة الميت الأول يا ترى كيف لنا أن
+
+24
+00:02:08,350 --> 00:02:13,650
+نعالج مثل هذا النوع من مسائل المناسخاتنقول إن علاج
+
+25
+00:02:13,650 --> 00:02:19,570
+هذا النوع لا يختلف عن علاج مسائل النوع السابق من
+
+26
+00:02:19,570 --> 00:02:25,630
+مسائل المناسخات بمعنى أننا نقوم بتوريث هؤلاء
+
+27
+00:02:25,630 --> 00:02:29,610
+الورثة في المسألة الأولى ونقوم بحل المسألة حل كامل
+
+28
+00:02:29,610 --> 00:02:35,620
+أيضا المسألة الثانية نحلها حلا كاملا ثم نجمعأسهم
+
+29
+00:02:35,620 --> 00:02:39,740
+الورثة اللي ورثوا من كلا المسألتين أما الورثة
+
+30
+00:02:39,740 --> 00:02:45,380
+الذين لا يرثون من المسألة الأولى فإننا نقتصر على
+
+31
+00:02:45,380 --> 00:02:49,740
+أسهمهم في المسألة الثانية يعني الكلام عامله بعيد
+
+32
+00:02:49,740 --> 00:02:53,660
+بعضه مافي مسألة أو مافي شيء جديد أو حكم جديد في
+
+33
+00:02:53,660 --> 00:03:00,210
+هذا النوع من هذه الحالةو ترجمة هذا الكلام لم تتضح
+
+34
+00:03:00,210 --> 00:03:05,350
+كثيرا إلا بالمثال لذلك دعونا نأخذ مثالا على هذه
+
+35
+00:03:05,350 --> 00:03:11,730
+الحالة وهي كما قلت أن يكون ورثة الميت الثاني هم
+
+36
+00:03:11,730 --> 00:03:21,090
+ورثة الميت الأول ويضاف إليهم أغراب انشوف
+
+37
+00:03:21,090 --> 00:03:33,160
+انقول مثلا مات عن زوجةو بنت و أخ
+
+38
+00:03:33,160 --> 00:03:45,460
+شقيق بعدين مين مات عندنا؟ ثم توفيت البنت عن أم و
+
+39
+00:03:45,460 --> 00:03:55,500
+عم شقيق و زوج و أخ لأم
+
+40
+00:03:56,910 --> 00:04:00,910
+لحظة معايا قبل ما نرتب هذه المسألة، بنقول بإنه،
+
+41
+00:04:00,910 --> 00:04:05,510
+الحالة أو النوى شو بيقول؟ إنه ورثة الميت الثاني،
+
+42
+00:04:05,510 --> 00:04:09,970
+هاي الميت الثاني ورثته، جزء منهم ورثت الميت الأول
+
+43
+00:04:09,970 --> 00:04:15,230
+ويضاف إليهم أغرابراح نلاقي الجزء منهم من الأم و
+
+44
+00:04:15,230 --> 00:04:20,130
+العم الشقيق لأن الأم هي نفسها زوجة الميت الأول و
+
+45
+00:04:20,130 --> 00:04:24,490
+العم الشقيق هو نفسه الأخ بالنسبة للميت الأول
+
+46
+00:04:24,490 --> 00:04:29,690
+فبالتالي ها لحظة معايا إذا نفسهم لكن النسبة بتختلف
+
+47
+00:04:29,690 --> 00:04:32,570
+و يضافوا إليهم أغراب اللي هو الزوج و الأخ لأم
+
+48
+00:04:32,570 --> 00:04:39,570
+الزوج و الأخ لأم بالنسبة للبنت مش من ضمنورثت الميت
+
+49
+00:04:39,570 --> 00:04:43,550
+الأول لأن الأخ لأم لحظة معايا مين اللي ميت هان
+
+50
+00:04:43,550 --> 00:04:48,130
+الأب فهذا مالوش علاقة بالأب بالظبط و هاد بالنسبة
+
+51
+00:04:48,130 --> 00:04:54,230
+ليه الزوج هو مش من ورثته سهره أو نسيبه مش من ورثته
+
+52
+00:04:54,230 --> 00:05:00,930
+صح ولا لا وصلت تمام فدعونا نقوم بحل هذه المسألة
+
+53
+00:05:00,930 --> 00:05:09,810
+كعادتنا بنت و بنت ابن لسه يا سمح و أخشقيق نيجي للي
+
+54
+00:05:09,810 --> 00:05:15,030
+ماتت عندنا اللي هي البنت ماتت عن أم اللي هي هنا أه
+
+55
+00:05:15,030 --> 00:05:20,130
+وهي طبعا لحظة معايا هي مش من ورثة هاي بنت أخوها
+
+56
+00:05:20,130 --> 00:05:24,230
+هتكون فبالتالي مالناش علاقة فيها الأخ الشقيق اللي
+
+57
+00:05:24,230 --> 00:05:29,970
+هو العم عم شقيق و هنا فيه أغراب الأغراب دائما بدنا
+
+58
+00:05:29,970 --> 00:05:33,090
+ننزلهم لتحت ليش؟ لأنهم مش من الورثة وهذه صيرنا
+
+59
+00:05:33,090 --> 00:05:41,330
+متفقين عليها فهنكتب هنا زوج و أخلأم تمام؟ يلّا
+
+60
+00:05:41,330 --> 00:05:43,330
+الحل الزوجة
+
+61
+00:05:44,860 --> 00:05:50,960
+تمن والبنت نصف وبنت الإبن سدس تكملة ليه الثلاثين
+
+62
+00:05:50,960 --> 00:05:56,180
+والأخ هو العصبة فالمسألة من أربع و عشرين تلاتة
+
+63
+00:05:56,180 --> 00:06:02,340
+اتناش اربع بيضل عندنا خمسة للأخ طبعا فش انكسار ولا
+
+64
+00:06:02,340 --> 00:06:06,680
+أي شيء فخلاص ننطق المباشرة ليه المسألة الثانية
+
+65
+00:06:06,680 --> 00:06:12,950
+الأم طبعا لحظة معايا فش لا أخ وبالتالي تلتو طبعا
+
+66
+00:06:12,950 --> 00:06:20,230
+هان نفس الشيء الزوج يأخذ نصف و الأخ لأم سادس
+
+67
+00:06:20,230 --> 00:06:27,760
+فالمسألة من ستة اتنينو هاد هو العصبام هيتطير اكيد
+
+68
+00:06:27,760 --> 00:06:33,640
+لأ هيتطير okay هان تلاتة و هان واحد فإذا هذا محجوب
+
+69
+00:06:33,640 --> 00:06:40,020
+بالاستغراق تمام؟ الآن الخطوة الثانية بنروح نقارن
+
+70
+00:06:40,020 --> 00:06:44,870
+بين أسهم الميت في المسألة الأولى و أصلمسألته صح
+
+71
+00:06:44,870 --> 00:06:49,430
+ولا لا اللي ماتت البنت واصل مسألتها اتناش اتناش
+
+72
+00:06:49,430 --> 00:06:53,390
+وستة التداخل فروحنا ضاربين هاي المسألة في اتنين
+
+73
+00:06:53,390 --> 00:07:01,020
+هتصير المسألة من اتناش هنا اربعهان صفر هان ستة و
+
+74
+00:07:01,020 --> 00:07:07,140
+هان اتنين تمام فهالجيتب نطلع بالمسألة الجامعة و
+
+75
+00:07:07,140 --> 00:07:11,580
+نجعلها أصلا جامعا هو أربع و عشرين الزوجة إلها
+
+76
+00:07:11,580 --> 00:07:15,980
+تلاتة و أربع
+
+77
+00:07:15,980 --> 00:07:18,940
+سبعة
+
+78
+00:07:20,440 --> 00:07:23,780
+البنت صفر لأنه هي اللي ماتت وهنا مافيش إشي يعني
+
+79
+00:07:23,780 --> 00:07:29,800
+كأنه صفر طيب عفوا أسفة هنا هيكون فيه أربع لأنه في
+
+80
+00:07:29,800 --> 00:07:33,700
+المسألة دي مالهاش هنا إلها أربع تمام فهنا أربع
+
+81
+00:07:34,730 --> 00:07:40,270
+العام خمسة و صفر خمسة و بعدين هدول طبعا أغرب طبيعي
+
+82
+00:07:40,270 --> 00:07:45,870
+مش هنظفلهم شاق فهي الجديد في الموضوع أنه لعين دهان
+
+83
+00:07:45,870 --> 00:07:50,230
+بتروح تجمع الأسهم أي أسهم هنا و أسهم هنا بتجمعيها
+
+84
+00:07:50,230 --> 00:07:54,350
+سوا بتطلقيها بالمسألة الجامعة و الأغرب بالتأكيد مش
+
+85
+00:07:54,350 --> 00:07:58,490
+راح نجمعلهم لأن هم ماكانوش هنا أصلا فليس لهم إلا
+
+86
+00:07:58,490 --> 00:08:07,160
+هذه الأسهم ليس إلا تمام؟علم طيب ناخد ايضا مثال اخر
+
+87
+00:08:07,160 --> 00:08:23,700
+يالا
+
+88
+00:08:23,700 --> 00:08:30,670
+في عندها زوجطبعا توفي عن زوج لحظوا معايا توفي عن
+
+89
+00:08:30,670 --> 00:08:43,010
+زوج الله يرحمه كل متزوج زوج طيب ايوة و
+
+90
+00:08:43,010 --> 00:08:57,610
+أخت شقيقة ثم توفي الزوج بنت و أم و أخت أخ شقيقلحظة
+
+91
+00:08:57,610 --> 00:09:01,970
+معايا هنا أن هذه البنت هي بنت التنان، الميت الأول
+
+92
+00:09:01,970 --> 00:09:07,320
+والميت الثاني، صح ولا لأ؟ طيب الأم؟فهي أيوة لكنها
+
+93
+00:09:07,320 --> 00:09:11,240
+مش أمه لهذه فهذه واحدة تانية لأن هاي هتكون كأنها
+
+94
+00:09:11,240 --> 00:09:16,020
+حملة لهذه و هذه حمات التانية حموات بعيد يعني و
+
+95
+00:09:16,020 --> 00:09:19,980
+الأخت الشقيقة نفس الشيء و الأخ الشقيق يعني لحظة
+
+96
+00:09:19,980 --> 00:09:24,600
+أنا أتحدث عن أخت الزوج و أخت الزوجة فهدول لا أحد
+
+97
+00:09:24,600 --> 00:09:30,060
+يرث من الآخر علم؟ تمام؟ طيب فلذلك نيجي نرتب
+
+98
+00:09:30,060 --> 00:09:41,490
+المسألة نقول زوج، بنتو أم و أخت شقيقة الذي توفي هو
+
+99
+00:09:41,490 --> 00:09:47,670
+الزوش توفي عن بنت هو
+
+100
+00:09:47,670 --> 00:09:53,110
+ايه تكتب الام هنا و الأخ هنا مثلا مالهو مش علاقة و
+
+101
+00:09:53,110 --> 00:10:03,410
+أم و أخ شقيق فبنحل طبيعي الزوش ربعوالبنت نصف و
+
+102
+00:10:03,410 --> 00:10:10,550
+الأم سادس و هذه عصبة مع الغين المسألة من اتناش هنا
+
+103
+00:10:10,550 --> 00:10:17,030
+تلاتة هنا ستة اتنين جدش بيظل واحد ومابدهاش تصحيح
+
+104
+00:10:17,030 --> 00:10:22,590
+ولا شيء خلصنا منها بنيجي للمسألة الثانية البنت نصف
+
+105
+00:10:22,590 --> 00:10:30,130
+و الأم سادس و هذه عصبة فالمسألة من ستة هنا تلاتةهن
+
+106
+00:10:30,130 --> 00:10:36,650
+واحد و هن اتنين فنيجي الأن نقارن بين أسهم الزوج
+
+107
+00:10:36,650 --> 00:10:40,930
+اللي هو الميت و أصل مسألته التلاتة و السبتة
+
+108
+00:10:40,930 --> 00:10:45,250
+بيناتهم تداخل ستة ع تلاتة اتنين فحنضرب المسألة
+
+109
+00:10:45,250 --> 00:10:51,920
+هادي في اتنين هتصير المسألة من اربع و عشرينهنا
+
+110
+00:10:51,920 --> 00:10:57,280
+ستة، هنا اتناش، هنا اربع، هنا اتنين فهنروح نطلع
+
+111
+00:10:57,280 --> 00:11:02,500
+الاصل أو المسألة الجامعة و نخرج لها أصلا جامعا من
+
+112
+00:11:02,500 --> 00:11:09,280
+أربع و عشرين فالزوج صفر لأن هو الذي توفي البنت
+
+113
+00:11:09,280 --> 00:11:17,020
+اتناش و تلاتة خمستاش الأم أربع فقط و الأخت الشقيقة
+
+114
+00:11:17,020 --> 00:11:22,850
+فقط اتنينمين اللي بتقول واحد و اتنين؟ اتنين بس
+
+115
+00:11:22,850 --> 00:11:30,510
+okay فالان الأم واحد و الأخ الشقيق اتنين فقط تمام
+
+116
+00:11:30,510 --> 00:11:36,270
+نأخذ مسألة أخيرة و بها نختم تمام عشان نثبت
+
+117
+00:11:36,270 --> 00:11:43,330
+معلوماتنا موضوعنا سهل ان شاء الله جدا نعم
+
+118
+00:11:45,220 --> 00:11:48,760
+طيب عظيم لأ هو لازم ناخده بالاخر لإنه بنكون جمعنا
+
+119
+00:11:48,760 --> 00:11:52,040
+كل شيء طب فرضا المسألة فيها ردف فرضا المسألة فيها
+
+120
+00:11:52,040 --> 00:11:58,000
+كذا مش هنعرف إن حد صحيح طيب نأخذ هذا المثال
+
+121
+00:12:13,270 --> 00:12:18,670
+تلاتة جدة لحظة هنقول من جهة الأب بعيدنا بنعرف ليش
+
+122
+00:12:18,670 --> 00:12:23,850
+من جهة الأب وجدة
+
+123
+00:12:23,850 --> 00:12:36,330
+من جهة الأم وأخت الأم وأخ
+
+124
+00:12:42,010 --> 00:12:55,190
+شقيق سمنة توفية عرفتوا
+
+125
+00:12:55,190 --> 00:12:58,870
+إيش فائدة تقول من جهة الأم ومن جهة الأب لأن هاي
+
+126
+00:12:58,870 --> 00:13:05,890
+مالهاش علاقة بهذا بالأخ عشان كده وصلت تمام وأخت
+
+127
+00:13:05,890 --> 00:13:17,630
+شقيقة وأخ لأمو أخت لأب مسألة حلوة وسهلة حلوة يعني
+
+128
+00:13:17,630 --> 00:13:25,430
+يالا نشوف نرتب المعباد هان هنقول تلاتة جدة من جهة
+
+129
+00:13:25,430 --> 00:13:31,470
+الأب أه و هان جدة ما جمعناهم مش متعمدين على أساس
+
+130
+00:13:31,470 --> 00:13:36,870
+الأن نشوف الموتة من المسألة التانية جدة من جهة
+
+131
+00:13:36,870 --> 00:13:52,300
+الأم في عندنا أختلأم و أخ .. لأم و أخ شقيق خلّيكم
+
+132
+00:13:52,300 --> 00:13:56,850
+معاياعشان تقوليش كيف إجته من وين إجت فركزوا شوية
+
+133
+00:13:56,850 --> 00:14:02,030
+صغيرة بنقول توفي الأخ لأم هذا رحمه الله عليه عن
+
+134
+00:14:02,030 --> 00:14:07,630
+مين؟ عن جدة هتكون هذه بالتأكيد صح ولا لأ؟ بالتأكيد
+
+135
+00:14:07,630 --> 00:14:11,810
+هذه فدول مالهومش علاقة في ورثة الميت الثاني
+
+136
+00:14:11,810 --> 00:14:18,440
+مالهومش علاقة الجدات هدول طيب فالاناخد شقيقة اللي
+
+137
+00:14:18,440 --> 00:14:22,980
+هي هذه صح ولا لأ لأن هو هذا اللي مات فهذه شقيقته
+
+138
+00:14:22,980 --> 00:14:33,340
+اخد لأم اخد شقيقة عفوا طيب
+
+139
+00:14:33,340 --> 00:14:40,020
+و أخ لأم اللي هو هذا هذا شقيق بالنسبة للميت الأول
+
+140
+00:14:40,020 --> 00:14:46,390
+طب بالنسبة لهذامش هاد شقيق لهاد فمعناته هاد أخ لأم
+
+141
+00:14:46,390 --> 00:14:52,490
+بالنسبة لهاد صح ولا لا وصلت الفكرة فإذا هان أخ لأم
+
+142
+00:14:52,490 --> 00:14:59,590
+ومي كمان و أخت لأب هذه هي الغريبة مش قلنا في ورثة
+
+143
+00:14:59,590 --> 00:15:08,070
+أغراب هي هذه الغريبة أخت لأب تمام وصلت هذه يلا نحل
+
+144
+00:15:09,380 --> 00:15:15,700
+الجدات هان مع بعض هما الأربعة صدس، تمام؟ للأربعة
+
+145
+00:15:15,700 --> 00:15:22,300
+الصدس طيب الأخت لأم نقول هان صدس و هان صدس و هاد
+
+146
+00:15:22,300 --> 00:15:30,600
+هو العصبة، صح ولا صح؟ فالمسألة من ستة هان واحد،
+
+147
+00:15:30,600 --> 00:15:37,480
+هان واحد، واحد، كم بيظل؟ تلاتة للشقيق، تمام؟فالان
+
+148
+00:15:37,480 --> 00:15:42,100
+لحظي الواحد والاربعة لأنه هان تلاتة و واحد صح؟
+
+149
+00:15:42,100 --> 00:15:47,800
+فحنلاقي فيه إيش؟ في انكسار فروحنا ضربين المسألة
+
+150
+00:15:47,800 --> 00:15:53,760
+هذه في أربعة فهتصير من أربعة و عشرين هان أربعة،
+
+151
+00:15:53,760 --> 00:15:59,280
+أربعة، أربعة و اتناشر فالأربعة هذه بدي أوزعها
+
+152
+00:15:59,280 --> 00:16:05,170
+تلاتة و واحدتمام؟ تلاتة و هذه واحد اللي هي
+
+153
+00:16:05,170 --> 00:16:09,790
+الأربعة، فبصيرنا فاهمين هذه إيش معناها، حلو طيب
+
+154
+00:16:09,790 --> 00:16:17,210
+نيجي الأن للمسألة الثانية الجدة سدس و الشقيقة نصف
+
+155
+00:16:17,210 --> 00:16:22,750
+و الأخ لأم و الأخت لأب سدس تكمل ليه الثلثين
+
+156
+00:16:22,750 --> 00:16:29,150
+فالمسألة من ستة واحد تلاتة واحد واحد تمام؟حلو فهو
+
+157
+00:16:29,150 --> 00:16:33,550
+ال gate بدنا نقارن بين مين اللي مات عندنا الأخ
+
+158
+00:16:33,550 --> 00:16:39,250
+لأمه هذه اللي مات فبدي أقارن الستة و الأربعة إيش
+
+159
+00:16:39,250 --> 00:16:44,690
+في بيناتهم توافق اتنين في اتنين و اتنين في تلاتة
+
+160
+00:16:44,690 --> 00:16:48,890
+فحنضرب هذه في تلاتة و هذه في اتنين صح ولا لأ؟ في
+
+161
+00:16:48,890 --> 00:16:54,760
+تلاتة هتصير من اتنين و سبعينفى تلاتة تسعة فى تلاتة
+
+162
+00:16:54,760 --> 00:17:00,640
+تلاتة اتناش اتناش و ستة و تلاتين هدى هنضربها فى
+
+163
+00:17:00,640 --> 00:17:07,920
+شو؟ فى اتنين اتناش اتنين ستة اتنين اتنين تمام فهى
+
+164
+00:17:07,920 --> 00:17:11,830
+صارت الأصول مثل بعضهااللي هو الأسهم والأصل تبع
+
+165
+00:17:11,830 --> 00:17:16,770
+الميت فهنطلعش المسألة الجامعة من أصل الجامع الأصل
+
+166
+00:17:16,770 --> 00:17:22,990
+الجامع اللي هو 72 الجدات هدول التلاتة إلهم تسعة
+
+167
+00:17:22,990 --> 00:17:27,770
+فقط هنحنقول كده يا جماعة نسينا نحق أه هي هنفيش إشي
+
+168
+00:17:27,770 --> 00:17:34,030
+تمام هن فقط تسعة بالنسبة لهذه إلها تلاتة زائد إش
+
+169
+00:17:35,410 --> 00:17:43,550
+تلاتة زي اتنين خمسة نيجي لا الأخت لأم اتناش و ستة
+
+170
+00:17:43,550 --> 00:17:51,550
+تمانتاش وهد هو الميت صفر نيجي لا الأخ الشقيق ستة و
+
+171
+00:17:51,550 --> 00:17:57,990
+تلاتين و اتنين تمانية و تلاتين و هد اتنين تمام؟
+
+172
+00:17:57,990 --> 00:18:00,190
+واضح؟
+
+173
+00:18:02,380 --> 00:18:05,940
+احنا قولنا أخر مثال ناخد الأن أخر مثال ماعليش بدنا
+
+174
+00:18:05,940 --> 00:18:23,160
+نثبت معلومتنا و خلاص هلجيت
+
+175
+00:18:23,160 --> 00:18:30,680
+رسمي هذا أخر مثال أه طيب أم و أب و بنت
+
+176
+00:18:33,770 --> 00:18:47,570
+تلاتة ابن ابن ايوة الام توفيت عن بنت ابن تلاتة
+
+177
+00:18:47,570 --> 00:18:56,930
+ابن ابن ابن وزوج طيب
+
+178
+00:19:05,000 --> 00:19:09,300
+نيجي ليش أنا جاي ل .. البنت اللي توفت مش الأم اه
+
+179
+00:19:09,300 --> 00:19:21,760
+اه اه أم صح أم عندي كان بنت ابن معقول اه اه اه
+
+180
+00:19:21,760 --> 00:19:32,680
+اه okay تمام الآن أم أب بنت تلاتة ابن ابن تلاتة
+
+181
+00:19:32,680 --> 00:19:33,440
+ابن ابن
+
+182
+00:19:44,100 --> 00:19:50,300
+فالان اللي توفيت عندنا الأم طبعا هاد مش زوجها، هاد
+
+183
+00:19:50,300 --> 00:19:53,820
+مش زوجها لإنه بنتحدث إنه في أغرب، فهيطلع الغريب
+
+184
+00:19:53,820 --> 00:19:59,980
+عندنا فقط الزوج، تمام؟ و هاد بنت ابن هي هي، و هاد
+
+185
+00:19:59,980 --> 00:20:08,910
+تلاتة ابن ابن ابن، فالزوج هوغريب مقصد الغريب أنه
+
+186
+00:20:08,910 --> 00:20:15,070
+مش من ورثة الميت الأول تمام فاني جنحل الأم سدس وهد
+
+187
+00:20:15,070 --> 00:20:19,190
+سدس أيضا لوجود المذكر وهد نصف وهدول هم العصبة
+
+188
+00:20:19,190 --> 00:20:24,710
+فالمسألة من ستة واحد واحد تلاتة بيضل واحد في
+
+189
+00:20:24,710 --> 00:20:28,350
+انكسار لأن التلاتة بتجسمش على الواحد فروحنا ضربين
+
+190
+00:20:28,350 --> 00:20:33,510
+في تلاتة صارت من تمانتاش هنا تلاتة تلاتة تسعة
+
+191
+00:20:33,510 --> 00:20:41,450
+تلاتة تمام؟طيب نيجي للمسألة الثانية هن نصف و هد
+
+192
+00:20:41,450 --> 00:20:49,050
+ربع و هد عصبة فالمسألة من أربعة هن اتنين و هن واحد
+
+193
+00:20:49,050 --> 00:20:53,770
+واحد طبعا الواحد و التلاتة برضه في انكسار فهنروح
+
+194
+00:20:53,770 --> 00:20:58,230
+ضاربين في ايش؟ في تلاتة هتصير من اتناش هنا ستة
+
+195
+00:20:58,230 --> 00:21:06,240
+تلاتة تلاتة هنيجي للي مات عندنا الأم هي الأمتلاتة
+
+196
+00:21:06,240 --> 00:21:11,240
+و أصل مسألتها اتناش فالتلاتة و الاتناش إيش في
+
+197
+00:21:11,240 --> 00:21:15,280
+بناتهم؟ تداخل، اتناش ع تلاتة أربعة فبنروح ضاربين
+
+198
+00:21:15,280 --> 00:21:19,700
+هذه المسألة فيه؟ أربعة، هاي أربعين و أربعة و
+
+199
+00:21:19,700 --> 00:21:21,100
+عشرين، أربعة و ستين
+
+200
+00:21:24,000 --> 00:21:29,240
+أه اربع اه اتنين و تلاتين صح اتنين و سبعين تمام
+
+201
+00:21:29,240 --> 00:21:37,880
+هنا اتناش اتناش و ستة و تلاتين و اتناش تمام فهذه
+
+202
+00:21:37,880 --> 00:21:42,580
+خلاص هنروح ايش ناخد الأصل النهائي المسألة من اتنين
+
+203
+00:21:42,580 --> 00:21:49,240
+و سبعين فالأم هي اللي ماتت صفر الأب فقط اتناش لأنه
+
+204
+00:21:49,240 --> 00:21:54,880
+هنملش ولا شاقفالبنت ستة و تلاتين و ستة يعني اتنين
+
+205
+00:21:54,880 --> 00:22:00,920
+و اربعين و الأبناء لابن التلاتة مع بعض اتناش و
+
+206
+00:22:00,920 --> 00:22:06,580
+تلاتة خمستاش و لاحظ يعني كل واحد خمسة صح ولا صح؟
+
+207
+00:22:06,580 --> 00:22:11,300
+تمام و الزوج هو اللي هياخد تلاتة لأنه مالوش أسهم
+
+208
+00:22:11,300 --> 00:22:12,960
+في المسألة السابقة
+
+209
+00:22:18,300 --> 00:22:22,980
+كيف؟ خلاص احنا .. انا هكون جاي لالك لو في اشي ..
+
+210
+00:22:22,980 --> 00:22:26,780
+بالظبط .. بالظبط ليش انا ه .. باعتبار اصلا انا
+
+211
+00:22:26,780 --> 00:22:33,220
+اتحدث عن ان هناك من ورثة الميت الثاني أغراب فأكيد
+
+212
+00:22:33,220 --> 00:22:37,060
+مش هتكون هذه الغريبة ولا هذه فتلقائي انا هقول انه
+
+213
+00:22:37,060 --> 00:22:43,400
+الزوج، تمام؟ واضح؟تمام؟ هذا ما يتعلق بموضوع
+
+214
+00:22:43,400 --> 00:22:47,780
+محاضرتنا لهذا اليوم المحاضرة القادمة بإذن الله
+
+215
+00:22:47,780 --> 00:22:53,740
+سنتحدث عن النوع الثالث والأخير من أحكام المناسخات
+
+216
+00:22:53,740 --> 00:23:00,710
+والذي سنتحدث فيه ما إذا كان ورثة الميت الثانيبعضهم
+
+217
+00:23:00,710 --> 00:23:06,010
+من ورثة الميت الأول وهناك أموات أصلا ليسوا من ورثة
+
+218
+00:23:06,010 --> 00:23:11,110
+الميت الأول فعلاج هذا النوع سيكون المحاضرة القادمة
+
+219
+00:23:11,110 --> 00:23:15,590
+بإذن الله أقول قولي هذا وأستغفر الله لي ولكم وصلى
+
+220
+00:23:15,590 --> 00:23:19,530
+اللهم وسلم وبارك على سيدنا محمد والسلام عليكم
+
+221
+00:23:19,530 --> 00:23:21,310
+ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/BNYEjitEWqg.srt b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/BNYEjitEWqg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c29521763bab9b6b74ab8ac8cdb5473afdc2d4ad
--- /dev/null
+++ b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/BNYEjitEWqg.srt
@@ -0,0 +1,903 @@
+1
+00:00:04,990 --> 00:00:07,950
+أعوذ بالله من الشيطان الرجيم بسم الله
+
+2
+00:00:07,950 --> 00:00:10,790
+الرحمن الرحيم الحمد لله رب العالمين والصلاة
+
+3
+00:00:10,790 --> 00:00:14,550
+والسلام على أشرف الأنبياء والمرسلين سيدنا محمد بن
+
+4
+00:00:14,550 --> 00:00:17,310
+عبد الله الصادق الأمين ثم أما بعد أحييكم جميعا
+
+5
+00:00:17,310 --> 00:00:20,830
+بتحية الإسلام السلام عليكم ورحمة الله تعالى
+
+6
+00:00:20,830 --> 00:00:25,590
+وبركاته كيف حالكم؟ طيبين إن شاء الله، تحضيركم جيد
+
+7
+00:00:25,590 --> 00:00:30,880
+إن شاء الله. طبعا إذا كنا قد تحدثنا في المحاضرة السابقة
+
+8
+00:00:30,880 --> 00:00:35,960
+عن موضوع الرد، فقلنا إن فكرة الرد قائمة على أن
+
+9
+00:00:35,960 --> 00:00:40,720
+المسألة لا عصبات فيها، إذ إنه عند وجود العصبات فلا
+
+10
+00:00:40,720 --> 00:00:45,160
+يتصور وجود الرد، كما أنه ينبغي أن يكون أصحاب الفروض
+
+11
+00:00:45,160 --> 00:00:50,240
+أقل من التركة. وبالتالي إذا استغرق أصحاب الفروض جميع
+
+12
+00:00:50,240 --> 00:00:54,260
+التركة، فلن يتصور أيضًا أن يكون هناك رد. قلنا إن
+
+13
+00:00:54,260 --> 00:00:59,460
+هناك خلاف بين العلماء حول الأخذ بالرد أو عدم الأخذ
+
+14
+00:00:59,460 --> 00:01:04,340
+به، فوجدنا أن الإمام مالك والإمام الشافعي خالفوا في
+
+15
+00:01:04,340 --> 00:01:09,720
+موضوع الرد، وقالوا إنه لا يرد على جميع الورثة، بل إن 
+
+16
+00:01:09,720 --> 00:01:14,480
+ما يتبقى من التركة إنما يجعل لبيت مال المسلمين
+
+17
+00:01:14,940 --> 00:01:19,880
+متذرعين بذلك أن الله عز وجل قد أعطى كل ذي حق حقه
+
+18
+00:01:19,880 --> 00:01:25,780
+فلا يستحق شيئًا أكثر مما فرضه له الله تبارك وتعالى.
+
+19
+00:01:25,780 --> 00:01:30,960
+بينما جمهور العلماء ذهبوا إلى أنه يرد إلى الورثة
+
+20
+00:01:31,900 --> 00:01:36,740
+وهؤلاء اختلفوا على ثلاثة أقوال. منهم من رأى أنه يرد
+
+21
+00:01:36,740 --> 00:01:41,280
+على جميع الورثة بمن فيهم الزوجان. وهناك من رأى أنه 
+
+22
+00:01:41,280 --> 00:01:46,320
+يرد على الورثة باستثناء الزوجين والجدات. بينما 
+
+23
+00:01:46,320 --> 00:01:50,860
+الراجح في الموضوع أنه يرد على الورثة باستثناء 
+
+24
+00:01:50,860 --> 00:01:56,280
+الزوجين فقط لأسباب كنا قد تحدثنا عنها تفصيلًا
+
+25
+00:01:56,280 --> 00:02:00,700
+في المحاضرة الماضية. اليوم بإذن الله سنتحدث حول أقسام
+
+26
+00:02:00,700 --> 00:02:06,360
+مسائل الرد. سنجد بأن مسائل الرد عندنا أربع مسائل
+
+27
+00:02:06,360 --> 00:02:12,000
+المسألة الأولى وهي ما لو وجد فريق واحد من الورثة
+
+28
+00:02:12,000 --> 00:02:17,040
+بدون أحد الزوجين. لاحظي معايا، دائما دائما بدك
+
+29
+00:02:17,040 --> 00:02:21,360
+تكوني منتبهة لشغلة وهي إن الفريق هذا بالتأكيد صاحب
+
+30
+00:02:21,360 --> 00:02:26,140
+فرض، مش عصبة. لأنه إذا عصبة مافي رد أصلاً. فدائما طلعي
+
+31
+00:02:26,140 --> 00:02:30,840
+موضوع العصبات من موضوع الرد تمامًا، لأن وجد العصبة
+
+32
+00:02:30,840 --> 00:02:35,770
+إذا خلاص مافي رد أصلاً. فنرجع نقول القسم الأول من
+
+33
+00:02:35,770 --> 00:02:40,910
+أقسام مسائل الرد اللي هو أن يكون هناك فريق واحد من
+
+34
+00:02:40,910 --> 00:02:47,410
+الورثة بدون أحد الزوجين. فالقسم الثاني أن يكون لدي
+
+35
+00:02:47,410 --> 00:02:52,730
+أكثر من فريق من الورثة في المسألة بدون أحد الزوجين
+
+36
+00:02:52,730 --> 00:02:56,770
+والقسم الثالث أنه عندي فريق واحد من الورثة مع أحد
+
+37
+00:02:56,810 --> 00:03:00,090
+مع أحد الزوجين، يعني عندي زوج أو زوجة معهم حدا
+
+38
+00:03:00,090 --> 00:03:06,010
+تمام؟ والأمر الرابع وهو أن يكون هناك أكثر من فريق
+
+39
+00:03:06,010 --> 00:03:09,630
+من الورثة مع أحد الزوجين. وفي كل الأقسام هذه
+
+40
+00:03:09,630 --> 00:03:13,930
+المسألة ردية، يعني في فائدة عندي في التركة، لأن فكرة
+
+41
+00:03:13,930 --> 00:03:19,930
+الرد قلنا بأن أسهم الورثة أقل من أصل مسألتها. وهذا 
+
+42
+00:03:19,930 --> 00:03:24,730
+يعني أن كل وارث يأخذ حقه أكثر من فرضة، باستثناء
+
+43
+00:03:24,730 --> 00:03:28,630
+الزوجين، لأننا اتفقنا أن الزوج لا يرد عليه أو
+
+44
+00:03:28,630 --> 00:03:33,510
+الزوجة لا يرد عليهما، بل يرد على غيرهما من الورثة
+
+45
+00:03:33,510 --> 00:03:41,050
+تمام. نيجي للقسم الأول من أقسام مسائل الرد، خلينا
+
+46
+00:03:41,050 --> 00:03:43,810
+نشيل هذا العنوان اه، بصيرنا عارفين شو بدنا نحكي 
+
+47
+00:03:43,810 --> 00:03:44,090
+اليوم.
+
+48
+00:03:47,070 --> 00:03:50,810
+طبعا مع أن أي إشكالية لا في القسم الأول ولا الثاني
+
+49
+00:03:50,810 --> 00:03:56,150
+ولا حتى الثالث طبعًا، يعني علاج مثل هذه المسائل
+
+50
+00:03:56,150 --> 00:04:05,310
+هيكون يسير جدًا. القسم الأول قلنا وجود فريق واحد من 
+
+51
+00:04:05,310 --> 00:04:10,930
+الورثة طبعًا بدون وجود أحد الزوجين
+
+52
+00:04:14,370 --> 00:04:17,970
+مين تقول لي ليش احنا ميزنا في أحد زوجين أو ما فيش 
+
+53
+00:04:17,970 --> 00:04:22,150
+أحد زوجين؟ مين تقول لي ليش؟ ليش في المسائل مرة
+
+54
+00:04:22,150 --> 00:04:26,330
+بنقول مع أحد الزوجين أو بدون أحد الزوجين؟ معلومته 
+
+55
+00:04:26,330 --> 00:04:31,310
+وحكايتها. اللي هو بالضبط احنا حالنا على فكرة
+
+56
+00:04:31,310 --> 00:04:35,130
+إنه لا يرد للزوجين، صح ولا لأ؟ أو على الزوجين
+
+57
+00:04:35,130 --> 00:04:38,410
+وبالتالي فأنا بدي أشوف مسألة إذا فيها أزواج كيف بدي
+
+58
+00:04:38,410 --> 00:04:42,210
+أتعامل؟ وإذا ما فيهاش أزواج كيف بدي أتعامل؟ بس علم؟
+
+59
+00:04:42,210 --> 00:04:47,850
+فإذا بدي أفترض مات وترك بنت، بس كده، مات وترك بنت
+
+60
+00:04:47,850 --> 00:04:51,550
+فريق واحد. احنا بنقول وهذا الفريق بالتأكيد صاحب 
+
+61
+00:04:51,550 --> 00:04:57,230
+فرض، وإيه؟ بتقول يا عصبة، حلو؟ فاذا بالتأكيد، فاذا
+
+62
+00:04:57,230 --> 00:05:01,170
+مات وترك بنت، إنه فريق واحد بدون أحد الزوجين
+
+63
+00:05:01,170 --> 00:05:06,640
+فالبنت جدًّا هتاخد نصف المسألة من كام؟ من اثنين. واحد
+
+64
+00:05:06,640 --> 00:05:12,340
+طب والباقي فإيش هنقول؟ باختصار شديد، بنقول إذا وجد
+
+65
+00:05:12,340 --> 00:05:18,600
+فريق واحد من الورثة دون أحد الزوجين، فإن هذا الفريق
+
+66
+00:05:18,600 --> 00:05:23,100
+يأخذ جميع التركة فرضا وردا. لازم تقولي فرضا وردا، 
+
+67
+00:05:23,100 --> 00:05:27,280
+ليش؟ لو قلنا جميع التركة كإني بعملها عصبة وهو 
+
+68
+00:05:27,280 --> 00:05:31,860
+مش عصبة أو بتقولي جميع التركة وتسكتي، لأنه لما
+
+69
+00:05:31,860 --> 00:05:35,320
+بدي أحكي جميع التركة وكإني أجعلته عاصب وهو مش
+
+70
+00:05:35,320 --> 00:05:41,680
+عاصب، صح ولا لأ؟ فلذلك نرجع نقول إذا وجد فريق واحد
+
+71
+00:05:41,680 --> 00:05:47,440
+من الورثة فإنه يأخذ جميع التركة بالفرض والرد
+
+72
+00:05:47,440 --> 00:05:52,840
+فرضًا وردًا، فرضًا الأولى ضاد والثانية دالها، فرضًا و
+
+73
+00:05:52,840 --> 00:05:58,140
+ردًا. خفي فيها شوية، فنفس الشيء، مات وترك خمسة إخوة
+
+74
+00:05:58,140 --> 00:06:10,990
+شقيقة، هتقولي ثلثين فرضًا والباقي ردًا وخلصنا، تمام؟ أو 
+
+75
+00:06:10,990 --> 00:06:16,090
+ممكن مباشرة تقولي جميعها، كلاهما صحيح سواء قلت هيك أو
+
+76
+00:06:16,090 --> 00:06:24,550
+هيك، جميع التركة فرضًا وردًا، تمام؟ طب مات وترك أم؟
+
+77
+00:06:25,190 --> 00:06:30,090
+هتقولي ثلث فرضًا والباقي ردًا أو جميع التركة فرضًا و
+
+78
+00:06:30,090 --> 00:06:35,510
+ردًا. مات وترك جدة، هذه الجدة اللي كان سيدنا ابن عباس
+
+79
+00:06:35,510 --> 00:06:39,750
+بدوش يخلي لها ولا شيء من الباقي، هتاخد التركة كلها 
+
+80
+00:06:39,750 --> 00:06:44,210
+سدس بالفرض والباقي بالرد وهكذا. علم بس هي علاج
+
+81
+00:06:44,210 --> 00:06:48,690
+القسم الأول من مسائل الرد. في أي صعوبة؟ بالتأكيد لا.
+
+82
+00:06:48,690 --> 00:06:54,450
+نيجي للقسم الثاني من أقسام مسائل الرد 
+
+83
+00:06:56,930 --> 00:07:02,970
+اللي هو وجود أكثر من فريق بدون أحد الزوجين، إنه 
+
+84
+00:07:02,970 --> 00:07:09,730
+عندي كذا فريق وما فيش إيش معهم؟ لا زوج ولا زوجة، وجود 
+
+85
+00:07:09,730 --> 00:07:24,200
+أكثر من فريق برضه بدون أحد الزوجين، وبدي أرجع أُعيد 
+
+86
+00:07:24,200 --> 00:07:28,960
+نفس الكلام، إن كلا الفريقين هدول أو الثلاثة مش 
+
+87
+00:07:28,960 --> 00:07:34,600
+عصبات بالتأكيد، صار مفروغ منه هذا الكلام. حلو، فمات و
+
+88
+00:07:34,600 --> 00:07:42,880
+ترك مثلًا بنت وبنت ابن، بس
+
+89
+00:07:42,880 --> 00:07:51,840
+مثلًا البنت نصف وبنت الابن، المسألة من كام؟ فهن 
+
+90
+00:07:51,840 --> 00:07:58,460
+ثلاثة، وهن واحد، فإيش المجموع؟ أربعة، يعني أقل من الأصل
+
+91
+00:07:58,460 --> 00:08:04,000
+فكيف بدنا نعالج؟ نفس ما عالجنا عول المسائل في العول،
+
+92
+00:08:04,000 --> 00:08:08,780
+كيف عالجنا الأمور؟ لغينا الأصل الأصلي ووضعنا أصلًا
+
+93
+00:08:08,780 --> 00:08:12,960
+بديلاً عنه يُعرف بالأصل الردّي، هو مجموع سهامها. نفس
+
+94
+00:08:12,960 --> 00:08:19,100
+الفكرة، بنقول إننا نلغي الأصل الأصلي ونضعه أصلًا 
+
+95
+00:08:19,100 --> 00:08:25,620
+بديلاً عنه يُعرف بالأصل الردّي، يُعرف بالأصل الردّي
+
+96
+00:08:25,620 --> 00:08:31,060
+هو مجموع سهام الورثة، يعني معالجة القسم الثاني من
+
+97
+00:08:31,060 --> 00:08:38,320
+أقسام مسائل الرد نفس آلية معالجة مسائل العول تمامًا
+
+98
+00:08:38,320 --> 00:08:44,500
+إلّا إنه إيش بنعمل؟ نلغي الأصل الأصلي ونضعه أصلًا 
+
+99
+00:08:44,500 --> 00:08:50,540
+بديلاً عنه يُعرف بالأصل الردّي، وهو مجموع سهام الورثة
+
+100
+00:08:50,540 --> 00:08:56,460
+تمام فقط، وبالتالي المسألة صارت من أربعة لأنه هدلتها
+
+101
+00:08:56,460 --> 00:09:01,540
+نفس ما كنا نعمل في إيش؟ في العول أيضًا. لو بدي أقول 
+
+102
+00:09:01,540 --> 00:09:08,420
+مثلًا مات وترك أم وثلاثة إخ لأم
+
+103
+00:09:14,060 --> 00:09:24,240
+وإيش كمان؟ خلاص بركة الأم كده؟ سدس، او اهان ثلث،
+
+104
+00:09:24,240 --> 00:09:30,930
+المسألة من كام؟ هن واحد وهن اثنين صارت من ثلاثة
+
+105
+00:09:30,930 --> 00:09:37,010
+فمباشرة لجأت كذا فريق من الورثة ما عندهمش أزواج
+
+106
+00:09:37,010 --> 00:09:43,510
+مباشرة الحل هيكون إنك تلغي الأصل الأصلي وتخلي أصلًا
+
+107
+00:09:43,510 --> 00:09:47,730
+بدلًا عنه يُعرف بالأصل الردّي اللي هو مجموع سهم الورثة
+
+108
+00:09:47,730 --> 00:09:52,970
+وبالتالي أخر مثال، لو قلنا عندنا أخ شقيق وأخ لأب وأخ لأم، فالنص
+
+109
+00:09:52,970 --> 00:10:00,970
+سدس وسدس، فالمسألة من كام؟ من ستة. هن ثلاثة 
+
+110
+00:10:00,970 --> 00:10:07,110
+واحد واحد، فصارت من خمسة بس، لكن طبعًا هدول بدهم
+
+111
+00:10:07,110 --> 00:10:12,050
+يكونوا إيش؟ أجل من الستة صح ولا لأ؟ لأن لو هن في
+
+112
+00:10:12,050 --> 00:10:18,150
+عندي اثنين أخت لأب هتكون عادلة صح ولا لأ؟ هتكون
+
+113
+00:10:18,150 --> 00:10:23,030
+المسألة عادلة، وصلت؟ احنا كيف هنعرف إيش معي الأسهم؟
+
+114
+00:10:23,030 --> 00:10:27,990
+شو فيهم أجل ولا أكتر؟ أكتر عائلة أجل؟ قاصرة، يعني
+
+115
+00:10:27,990 --> 00:10:33,350
+في رد، وطبعًا لما تلاقي أجل يعني قاصرة، بدك تروح
+
+116
+00:10:33,350 --> 00:10:38,150
+تشوف في أنه قسم هذا اه إنه في أزواج ولا لا؟ لأن إذا
+
+117
+00:10:38,150 --> 00:10:43,570
+في أزواج مش هنحل زي كده، مش هنحل زي كده علم؟ إذا لو 
+
+118
+00:10:48,870 --> 00:10:53,050
+في عندي فريق واحد على طول بعطيه كل التركة فرضًا و
+
+119
+00:10:53,050 --> 00:10:57,890
+ردًا وخلصنا. كذا فريق طبعًا ما فيش أزواج، كذا فريق و
+
+120
+00:10:57,890 --> 00:11:01,350
+ما فيش معهم أزواج، الحل هيكون بإني ألغي الأصل 
+
+121
+00:11:01,350 --> 00:11:06,070
+الأصلي وأضعه أصلًا بديلاً عنه يُعرف بالأصل الردّي، مش
+
+122
+00:11:06,070 --> 00:11:11,290
+العقل الردّي تمامًا، وهو مجموع سهام الورثة. نيجي للقسم
+
+123
+00:11:11,290 --> 00:11:15,130
+الثالث، فلاحظي
+
+124
+00:11:15,130 --> 00:11:20,850
+ايه المثال بين ايدك؟ واضح إنه صارت المسألة من
+
+125
+00:11:20,850 --> 00:11:30,470
+خمسة بدل ستة، شايفينه المثال اه، تمام. نيجي الآن للقسم
+
+126
+00:11:30,470 --> 00:11:37,320
+الثالث، إيش القسم الثالث؟ قلنا وجود فريق واحد مع أحد
+
+127
+00:11:37,320 --> 00:11:42,580
+الزوجين، برضه معالجته يسيرة وسهلة، معالجته سهلة و
+
+128
+00:11:42,580 --> 00:11:48,940
+يسيرة، اللي
+
+129
+00:11:48,940 --> 00:11:55,020
+هو عندي فريق واحد من الورثة مع أحد الزوجين، يعني
+
+130
+00:11:55,020 --> 00:12:02,530
+مثلًا مات وترك زوج أو ماتت وتركت زوج وبنت، فريق
+
+131
+00:12:02,530 --> 00:12:09,610
+واحد مع .. ما تقولي نص ونص، هذا أجل، يعني أجل، مات و
+
+132
+00:12:09,610 --> 00:12:16,870
+ترك زوج وأخت شقيقة، بيقولولي اه زوج وأخت شقيقة، مش
+
+133
+00:12:16,870 --> 00:12:22,510
+رد، ما فيها رد، حيكون عادل نص ونص أو اكتجعي أو
+
+134
+00:12:22,510 --> 00:12:29,870
+اكتجعي، حلو؟ طيب، قلت لك هنلو بدي أحلها أنا كطالب 
+
+135
+00:12:29,870 --> 00:12:34,470
+مبتدئ لسه ما عندي علم بمسائل الرد، فبروح أحلها حل
+
+136
+00:12:34,470 --> 00:12:40,130
+طبيعي، هن ربع وهن إيش؟ نصف وهن، المسألة من أربعة
+
+137
+00:12:40,130 --> 00:12:46,390
+هن واحد وهن اثنين، وروح عملتي كده صح؟ لأ هذا
+
+138
+00:12:46,390 --> 00:12:51,630
+حل غلط، تحلي هيك على طول، بحط لك تاخديش ولا ربع درجة.
+
+139
+00:12:53,120 --> 00:12:57,900
+فإيش هنعمل؟ خليكم معايا، ليش؟ خليكم معايا، هذا
+
+141
+00:12:57,900 --> 00:13:00,660
+الكلام غلط، بس بدنا نقول ليش غلط، ركزوا معايا، بدي 
+
+142
+00:13:00,660 --> 00:13:05,260
+أفترض أنا حلته هيك، ليش اعتبرنا غلط؟ لأننا اتفقنا 
+
+143
+00:13:05,260 --> 00:13:09,980
+أننا سنعالج بدون ما نرد على أحد الزوجين، طب هاي
+
+144
+00:13:09,980 --> 00:13:13,220
+المعالجة بتقول إن الزوج كان واحد من أربع أسر وواحد
+
+145
+00:13:13,220 --> 00:13:17,760
+من تلاتة، يعني زاد، يعني ردت عليه، يعني إيش شمله الرد 
+
+146
+00:13:17,760 --> 00:13:22,920
+ونحن اتفقنا إنه راح نستثنيه، فإذا حليه غلط لأن
+
+147
+00:13:22,920 --> 00:13:28,280
+الأزواج لا يرد عليهم، أصبح إيش السبيل؟ السبيل كان
+
+148
+00:13:28,280 --> 00:13:37,180
+التالي، سهل جدا، الآن قال لك طالما أن هناك فريق واحد من
+
+149
+00:13:37,180 --> 00:13:42,120
+الورثة مع أحد الزوجين فإن .. والمسألة بدك تقولي 
+
+150
+00:13:42,120 --> 00:13:46,580
+قاصرة، لأنه ممكن يكون فيه زوج زي ما قلنا أخت شقيقة
+
+151
+00:13:46,580 --> 00:13:51,000
+مش هتكون قاصرة صح ولا لأ؟ حلو، وكانت المسألة قاصرة
+
+152
+00:13:51,000 --> 00:13:59,340
+فإن علاج المسألة يكون بأن نجعل مقام الزوجين سواء
+
+153
+00:13:59,340 --> 00:14:05,840
+زوج أو زوجة هو أصل للمسألة، تمام؟ بدنا نخلي هذا هو 
+
+154
+00:14:05,840 --> 00:14:09,860
+إيش أصل المسألة مية المية، خلصنا، ممكن واحدة ما
+
+155
+00:14:09,860 --> 00:14:13,360
+تقولي، ما هي هي، بقولك لأ، ممكن هذا يكون ستة ولا يكون
+
+156
+00:14:13,360 --> 00:14:17,280
+كذا أو .. الحين هجيبلك مثال ثاني، شو ما كان الرقم 
+
+157
+00:14:17,280 --> 00:14:21,600
+الثاني، دائما خدمين مقام أحد الزوجين، هذا عند وجود 
+
+158
+00:14:21,600 --> 00:14:24,900
+فريق واحد من الورثة مع أحد الزوجين في مسائل الرد
+
+159
+00:14:25,570 --> 00:14:29,890
+فبتاخدي على طول وأنت مغمضة مقام أحد الزوجين، 
+
+160
+00:14:29,890 --> 00:14:35,390
+بتخليه أصل للمسألة، أصل للمسألة، وبتعطيه فرضة زي ما
+
+161
+00:14:35,390 --> 00:14:40,550
+هو، هي أخدت فرضها، خلصنا، صح؟ بعد هيك، بتقولي 
+
+162
+00:14:40,550 --> 00:14:47,780
+والباقي للبنت، فرضا و ردا وبس، يعني كإني بدي أعمل
+
+163
+00:14:47,780 --> 00:14:50,860
+هذا إنه فريق واحد بدون أحد الزوجة، يعني بدي أخد إيش
+
+164
+00:14:50,860 --> 00:14:55,120
+الكل بس هو في حدا أخد من الطريقة كلها فهو هياخد 
+
+165
+00:14:55,120 --> 00:15:00,160
+الباقي لكن بدك تقول الباقي فرضا و ردا زي ما
+
+166
+00:15:00,160 --> 00:15:07,740
+قلنا قبل شوية، ناخد مثل ثاني، مثلًا مات وترك زوجة 
+
+167
+00:15:07,740 --> 00:15:18,800
+وأم زوجة، وأم الزوجة جدة، رجعت، والأم ثلث، فالمسألة أو
+
+168
+00:15:18,800 --> 00:15:23,890
+أُخذت جُولي من اثنا عشر، أو أخذ جولي من 12، احنا على حالنا
+
+169
+00:15:23,890 --> 00:15:27,210
+الأساسي والعادي بنقول 12، لأنه تلاتة وأربعة تباين
+
+170
+00:15:27,210 --> 00:15:30,690
+فبنضربهم بعيد، لكن لا، اتفقنا إنه إذا في فريق واحد
+
+171
+00:15:30,690 --> 00:15:34,790
+من الورثة مع أحد الزوجين، وكانت المسألة قاصرة، ممكن
+
+172
+00:15:34,790 --> 00:15:37,710
+واحدة تقولي، طب أنا لسه مبتدئة أكيد بدي أعرف 
+
+173
+00:15:37,710 --> 00:15:42,250
+لما يكون فريق واحد بالنظر، بس مجرد ما تشوف المسألة
+
+174
+00:15:42,250 --> 00:15:45,810
+هتعرف أنها قاصرة، يعني منطق في ربع وثلت، بالتأكيد 
+
+175
+00:15:45,810 --> 00:15:49,740
+ضايق، الشيء من التركي بالتأكيد بدون ما أروح أحسبه
+
+176
+00:15:49,740 --> 00:15:53,220
+يا ستة، بدي أفطر حالي ميح على الآخر وما بفهمش و
+
+177
+00:15:53,220 --> 00:15:57,620
+بالمرة، يعني معلوماتي zero، فروح اعمل لي أصل مش مشكلة 
+
+178
+00:15:57,620 --> 00:16:02,020
+بعدين، مستحيل هان تلاتة وهان أربعة هتلاقيها سبعة
+
+179
+00:16:02,020 --> 00:16:08,620
+فأنتِ هتحلي كده كمبتدئة، هتطلعي في المسألة أبا غلط
+
+180
+00:16:08,620 --> 00:16:12,820
+حلي أنا، هذا فريق مع أحد الزوجين، بتنحلش كده، أنت
+
+181
+00:16:12,820 --> 00:16:17,800
+بتحاكي حالك، بتنحلش كده، فإيش الحال؟ بدك تجعل مقام 
+
+182
+00:16:17,800 --> 00:16:22,440
+أحد الزوجين هو أصل للمسألة، وبأخد فرضة زي ما هو،
+
+183
+00:16:22,440 --> 00:16:30,040
+لأنه نحن لا نرد عليه، والباقي لمن؟ للأم فرضا و 
+
+184
+00:16:30,040 --> 00:16:36,800
+ردا، بس، خلصت، يعني بتقولي هان تلاتة، بتقولي تلاتة
+
+185
+00:16:36,800 --> 00:16:40,460
+فرضا و ردا بس بدون ما تقولي الباقي تلاتة فرضا و
+
+186
+00:16:40,460 --> 00:16:46,580
+ردا، حلو؟ بس علم؟ تمام؟ هات بالنسبالي الفريق الثالث
+
+187
+00:16:46,580 --> 00:16:50,560
+ناخد فكرة عن أو القسم الثالث عفوا من أقسام مسائل 
+
+188
+00:16:50,560 --> 00:16:54,880
+الرد، ناخد فكرة عن القسم الرابع ونرجع الحديث عنه 
+
+189
+00:16:54,880 --> 00:16:59,900
+للمحاضرة القادمة، بس ناخد فكرة سريعة، بنقول القسم 
+
+190
+00:16:59,900 --> 00:17:06,870
+الرابع معجز شوية، لكن هيزول التعقيد معايا بإذن الله،
+
+191
+00:17:06,870 --> 00:17:12,410
+لا يجتمع التعقيد مع البركة والإيمان، اللهم توفيق، 
+
+192
+00:17:12,410 --> 00:17:19,170
+إذا نرجع نقول، وجود أكثر من فريق من الورثة مع أحد
+
+193
+00:17:19,170 --> 00:17:22,890
+الزوجين، أكثر من فريق مع أحد الزوجين، يعني عندي
+
+194
+00:17:22,890 --> 00:17:24,750
+مثلا زوج وبنت وبنت ابن
+
+195
+00:17:31,950 --> 00:17:35,650
+حتى نتأكد إن هالمسألة ردية أو لأ بنحلها عادي، حلّي
+
+196
+00:17:35,650 --> 00:17:39,170
+دائما حال الطبيعي، عشان تختبري حالك بعدين تمحي حالك
+
+197
+00:17:39,170 --> 00:17:44,390
+فاتزوج ربع وهان نصف وهان سدس، المسألة بتحليها
+
+198
+00:17:44,390 --> 00:17:51,670
+عادي في الأول من إيش؟ من اثنا عشر، هان تلاتة هان ستة و
+
+199
+00:17:51,670 --> 00:17:57,430
+هان اثنين، اجمعيهم هتلاقي أصل من اثنا عشر، صح؟ أصل من
+
+200
+00:17:57,430 --> 00:18:00,050
+اثنا عشر، فعلى طول لما تلاقي هيك
+
+201
+00:18:07,690 --> 00:18:13,110
+بتنحل يا جماعة إنك بتجعلي مسألتين، بتجسميهم كده
+
+202
+00:18:13,110 --> 00:18:17,570
+تجعلي مسألتين، مسألة لأحد الزوجين لحال، والمسألة
+
+203
+00:18:17,570 --> 00:18:23,610
+الثانية لمن؟ للباقي بعد أحد الزوجين، تمام؟ فبالتالي 
+
+204
+00:18:23,610 --> 00:18:27,390
+الآن في مسألة أحد الزوجين، بتحليها حال طبيعي، هذه 
+
+205
+00:18:27,390 --> 00:18:32,150
+مسألة من أربعة بياخد فرضه وهنا بتحطي هامش اسمه 
+
+206
+00:18:32,150 --> 00:18:39,720
+الباقي بعد الزوجين، اللي هو إيش؟ تلاتة، مش أخذ واحد من 
+
+207
+00:18:39,720 --> 00:18:43,180
+أربعة، ضل تلاتة، خلصنا مسألته، بتروح للمسألة
+
+208
+00:18:43,180 --> 00:18:47,100
+الثانية ثانية، تحليها لحالها، على حدة، المسألة
+
+209
+00:18:47,100 --> 00:18:51,520
+الثانية، هتلاقيها من أي قسم من مسائل الرد؟ القسم
+
+210
+00:18:51,520 --> 00:18:55,460
+الثاني، إنه كذا فريق بدون أحد الزوجين، كذا فريق
+
+211
+00:18:55,460 --> 00:18:59,410
+بدون أحد الزوجين، بتحليها لحالها، المسألة من ستة، 
+
+212
+00:18:59,410 --> 00:19:04,570
+صح؟ لحالها، انسيها دي، فمن ستة بتعطي هذا فرضة زي ما
+
+213
+00:19:04,570 --> 00:19:07,970
+هو، وهذا واحد، فبتصير إيش؟ احنا اتفقنا إذا ..
+
+214
+00:19:07,970 --> 00:19:12,130
+إذا كذا فريق بدون أحد الزوجين، العلاج بدي يكون بلغي
+
+215
+00:19:12,130 --> 00:19:17,200
+هذا، وبحط أصل يُعرف بالأصل الردي، صح؟ الخطوة
+
+216
+00:19:17,200 --> 00:19:23,760
+الثانية بتروح تقارن بين هذا الأصل الردي والباقي بعد 
+
+217
+00:19:23,760 --> 00:19:28,200
+أحد الزوجين، ولما بنقارن بين الرقمين بنلاقي
+
+218
+00:19:28,200 --> 00:19:33,940
+احتمالين بس، يا تماثل يا تباين، يا تماثل يا تباين
+
+219
+00:19:33,940 --> 00:19:40,300
+إذا تماثل بنخلّي المسألة من نفس الأصل وبنكمل زي ما
+
+220
+00:19:40,300 --> 00:19:45,920
+هي، حد شرحها احنا، وإذا اختلاف تباين نضرب الأصل
+
+221
+00:19:45,920 --> 00:19:49,880
+الردي في الأصل، أصل مسألة أحد الزوجين، ونجعله أصلا
+
+222
+00:19:49,880 --> 00:19:54,600
+جامعا، ثم يعني شوية شغل هنعمله ونتعرف عليه بإذن 
+
+223
+00:19:54,600 --> 00:19:58,620
+الله بعد الامتحانات النصفية، إلى هنا نكون قد 
+
+224
+00:19:58,620 --> 00:20:02,300
+انتهينا من موضوع محاضرتنا لهذا اليوم، أقول قولي هذا 
+
+225
+00:20:02,300 --> 00:20:05,520
+وأستغفر الله لي ولكم، وصلى اللهم وسلم وبارك
+
+226
+00:20:05,520 --> 00:20:09,600
+على سيدنا محمد، والسلام عليكم ورحمة الله تعالى
+
+227
+00:20:09,600 --> 00:20:10,560
+وبركاته
diff --git a/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/Ci1OyuYc2hs_postprocess.srt b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/Ci1OyuYc2hs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2e1c0c413e2f3426adb7e2b9fa2e7516a7d83371
--- /dev/null
+++ b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/Ci1OyuYc2hs_postprocess.srt
@@ -0,0 +1,1252 @@
+1
+00:00:04,960 --> 00:00:08,160
+أعوذ بالله السميع العلي من الشيطان الرجيم بسم الله
+
+2
+00:00:08,160 --> 00:00:11,300
+الرحمن الرحيم الحمد لله رب العالمين والصلاة
+
+3
+00:00:11,300 --> 00:00:15,100
+والسلام على أشرف الأنبياء والمرسلين سيدنا محمد بن
+
+4
+00:00:15,100 --> 00:00:19,620
+عبدالله الصادق الأمين ثم ثم أما بعد أحييكم جميعا
+
+5
+00:00:19,620 --> 00:00:23,240
+بتحية الإسلام فالسلام عليكم ورحمة الله تعالى
+
+6
+00:00:23,240 --> 00:00:28,180
+وبركاته كيف حالكوا نطيبات ان شاء الله؟إذن بإذن
+
+7
+00:00:28,180 --> 00:00:32,980
+الله سأصحبكم في هذا الفصل مع مساق قانون الأحوال
+
+8
+00:00:32,980 --> 00:00:37,300
+الشخصية ميراث ووصية وهذا الميراث له شقان شق نظري
+
+9
+00:00:37,300 --> 00:00:41,660
+وشق عملي هنبدأ بإذن الله في الجانب النظري وسنتحدث
+
+10
+00:00:41,660 --> 00:00:47,400
+ابتداء قبل الغوص في أعماق هذا المساق حول أهمية
+
+11
+00:00:47,400 --> 00:00:52,780
+دراسة علم الميراث ومصدره وخصائصهإذا سأصحبكم خلال
+
+12
+00:00:52,780 --> 00:00:56,100
+هذا الفصل في مساق قانون الأحوال الشخصية ميراث
+
+13
+00:00:56,100 --> 00:01:01,400
+ووصية وهذا المساق عبارة عن شقين شق نظري وشق عملي
+
+14
+00:01:01,400 --> 00:01:08,340
+سنبدأ بإذن الله بالشق النظري وبعد ذلك سنغوص في
+
+15
+00:01:08,340 --> 00:01:13,460
+غمار هذا المساق الأمر بيتطلب ابتداء كأي مساق أن
+
+16
+00:01:13,460 --> 00:01:18,870
+نتحدث عن أساسيات لدراسة علم المواريثوبالتالي سنبدأ
+
+17
+00:01:18,870 --> 00:01:23,950
+بالحديث عن أهمية دراستنا لعلم الميراث وقبل البدء
+
+18
+00:01:23,950 --> 00:01:29,130
+بالحديث عن أهمية دراسة هذا العلم نعرج قليلا على أن
+
+19
+00:01:29,130 --> 00:01:33,630
+الميراث في الجاهلية كانت المرأة لا ترث فكانت
+
+20
+00:01:33,630 --> 00:01:38,350
+المرأة متهضة وبل إن المرأة كانت من ضمن جملة
+
+21
+00:01:38,350 --> 00:01:44,370
+الميراث فكان إذا توفي الزوج عن زوجته فتترك لإبنه
+
+22
+00:01:44,370 --> 00:01:51,730
+ميراثا وتحدثنا عن أنالشريعة الإسلامية و بمجيئ
+
+23
+00:01:51,730 --> 00:01:57,070
+الإسلام وجدنا أن الميراث أخذ منهج التدرج في
+
+24
+00:01:57,070 --> 00:02:02,520
+التشريع كسائر أحكام الفقه الإسلاميبمعنى أن أول ما
+
+25
+00:02:02,520 --> 00:02:09,260
+فرضت آيات الميراث كانت ابتداء أن المورث ذاته هو من
+
+26
+00:02:09,260 --> 00:02:14,800
+يستطيع أن يقسم التركة لورثته لكن بعد ذلك جاء الحكم
+
+27
+00:02:14,800 --> 00:02:20,280
+النهائي وأصبحت صورة النساء هي الشاملة أو المتضمنة
+
+28
+00:02:20,280 --> 00:02:23,740
+لأحكام المواريث فجاء قول الله تبارك وتعالى يوصيكم
+
+29
+00:02:23,740 --> 00:02:27,600
+الله في أولادكم للذاكر مابمثل حظ الأنسيين ثم اتحدث
+
+30
+00:02:27,600 --> 00:02:31,460
+عن ميراث الأزواج وميراث الإخوة وغير ذلك من الأمور
+
+31
+00:02:31,460 --> 00:02:38,500
+فدعونا نبدأ ونتحدث عن أهمية دراستنا لعلم المواريث
+
+32
+00:02:38,500 --> 00:02:44,800
+فنقول ان هذا العلميعالجوا قضية هي من أخطر القضايا
+
+33
+00:02:44,800 --> 00:02:50,360
+التي تعصف بالحياة الاجتماعية للبشر فإنها قضية
+
+34
+00:02:50,360 --> 00:02:56,380
+مالية وحيث إن البشر مجبولون على حب المال لأن الله
+
+35
+00:02:56,380 --> 00:03:01,620
+عز وجل وصفهم بذلك حينما قالوا تحبون المال حبا جما
+
+36
+00:03:01,940 --> 00:03:06,780
+وأطراف هذه القضية هم أقرب الناس بعضهم لبعض فاقتد
+
+37
+00:03:06,780 --> 00:03:11,720
+الأمر أن يكون لهذا العلم أهمية بالغة وصيانة
+
+38
+00:03:11,720 --> 00:03:16,460
+للأرحام من أن تتقطع فإن الله عز وجل هو الذي تولى
+
+39
+00:03:16,460 --> 00:03:23,400
+هذه القضية بنفسه وعالجها بنفسه فكانت جل أحكام
+
+40
+00:03:23,400 --> 00:03:27,860
+الميراث موجودة في القرآن الكريم على غير ذلك من
+
+41
+00:03:27,860 --> 00:03:33,560
+الأحكامالاخرى لذا فلو نظرنا إلى آيات صورة النساء
+
+42
+00:03:33,560 --> 00:03:39,370
+لوجدنا بأنآيات الميراث فُصّلت تفصيلا دقيقا على
+
+43
+00:03:39,370 --> 00:03:43,530
+خلاف منهج القرآن الكريم في معالجة القضايا الفقهية
+
+44
+00:03:43,530 --> 00:03:48,210
+المتعددة فإن القرآن الكريم حينما يتناول أي قضية
+
+45
+00:03:48,210 --> 00:03:52,910
+فإنه يذكرها بشكل إجمالي ويترك تفصيل هذه القضية
+
+46
+00:03:52,910 --> 00:03:58,350
+للسنة النبوية بخلاف أحكام الميراث فإن الله قد
+
+47
+00:03:58,350 --> 00:04:03,830
+أولاها عناية بالغة للسبب الذي ذكرته قبل قليلإضافة
+
+48
+00:04:03,830 --> 00:04:09,550
+إلى ذلك فإن النبي صلى الله عليه وسلم حث على دراسة
+
+49
+00:04:09,550 --> 00:04:15,550
+علم الميراث وجعل الميراث أو العلماء جعلوا الميراث
+
+50
+00:04:15,550 --> 00:04:20,550
+نصف العلم وأولى العلماء ذلك حينما قالوا إن الميراث
+
+51
+00:04:20,550 --> 00:04:26,550
+نصف العلم لأن أحكام الشريعة الإسلاميةتناولت حياة
+
+52
+00:04:26,550 --> 00:04:30,790
+الإنسان بينما أحكام الميراث تناولت أمر الإنسان بعد
+
+53
+00:04:30,790 --> 00:04:35,230
+وفاته فاقتضى ذلك أن يكون أو أن تكون أحكام الميراث
+
+54
+00:04:35,230 --> 00:04:40,390
+تعالج نصف العلم بتمامه والنبي صلى الله عليه وسلم
+
+55
+00:04:40,390 --> 00:04:44,050
+جعل العلوم في القرآن الكريم والسنة النبوية
+
+56
+00:04:44,050 --> 00:04:49,170
+والفرائض وحث أمته على تعلم هذه العلوم وأن علم
+
+57
+00:04:49,170 --> 00:04:54,930
+الفرائض أي علم المواريث هو أول ما ينسى من القرآنأو
+
+58
+00:04:54,930 --> 00:05:00,950
+من العلومأما بالنسبة لخصائص علم الميراث فنقول إن
+
+59
+00:05:00,950 --> 00:05:06,350
+هذا العلم جاء مسايرا لفترة الإنسان قلت قبل قليل إن
+
+60
+00:05:06,350 --> 00:05:12,230
+الإنسان مجبول على حبي المال وإن الإنسان بطبيعته لا
+
+61
+00:05:12,230 --> 00:05:17,010
+يحب أن يتدخل أحد في أمواله فجاءت أحكام الميراث
+
+62
+00:05:17,010 --> 00:05:21,550
+تلبي هذه الفترة لدى الإنسان فدائما الإنسان يحرص
+
+63
+00:05:21,550 --> 00:05:26,850
+على إن ماله يروح لمين لأبناءه دون الغريبفلذلك فإن
+
+64
+00:05:26,850 --> 00:05:32,310
+الله عز وجل حينما وصف طبيعة المال أو علاقة المال
+
+65
+00:05:32,310 --> 00:05:36,510
+بالإنسان والمال والبنون وزينات الحياة الدنيا
+
+66
+00:05:36,510 --> 00:05:42,550
+فالشريع إذا أثبت للإنسان حق الملك وكذلك أعطى
+
+67
+00:05:42,550 --> 00:05:47,650
+الإنسان الحق في أن يوصي بجزء من ماله لمن يريد
+
+68
+00:05:47,650 --> 00:05:52,490
+وبالتالي وزن بين أمرين في آن واحد وهذا يخالف
+
+69
+00:05:52,490 --> 00:05:57,670
+الأنظماء الأخرى التي ربماأطلقت الحرية للفرد أو
+
+70
+00:05:57,670 --> 00:06:02,730
+قيدت الفرد في حريته بالإضافة إلى ذلك فإن هذا العلم
+
+71
+00:06:02,730 --> 00:06:09,310
+فيه توزيع للثروة وإيجاد للتكافل الاجتماعي قبل وفاة
+
+72
+00:06:09,310 --> 00:06:14,670
+الإنسان المال مقدس في يده وبعد وفاته ينتقل المال
+
+73
+00:06:14,670 --> 00:06:18,030
+إلى ورثته وبالتالي بيصير في إيجاد للتكافل
+
+74
+00:06:18,030 --> 00:06:23,650
+الاجتماعيلأن المال بعد أن كان في يد شخص واحد توزعت
+
+75
+00:06:23,650 --> 00:06:28,730
+هذه الثروة بين كذا شخص بل انه تجاوز الأسرة إلى
+
+76
+00:06:28,730 --> 00:06:35,050
+خارجها فانتفع المجتمع بأكمله من هذا المالإضافة إلى
+
+77
+00:06:35,050 --> 00:06:41,370
+الوسطية التي يحققها نظام الميراث فإن أحكام الميراث
+
+78
+00:06:41,370 --> 00:06:45,870
+بعيدة كل البعد عن الإفراط والتفريط في آن واحد
+
+79
+00:06:45,870 --> 00:06:51,890
+وبالتالي في تشريع هذه المواريث أو أحكام الميراث
+
+80
+00:06:52,200 --> 00:06:57,820
+للعدالة بين الناس فكما قلت فقد راعت حقوق الإنسان
+
+81
+00:06:57,820 --> 00:07:02,700
+ذكرا كان أو أنثى بخلاف الشرائع الأخرى بل أيضا راعت
+
+82
+00:07:02,700 --> 00:07:09,600
+حق الإنسان بكل مراحل حياته شيخا شابا طفلا حتى
+
+83
+00:07:09,600 --> 00:07:16,360
+جنينا في رحم أمه له الميراث فأعطت الحق في أن يوزع
+
+84
+00:07:16,360 --> 00:07:21,040
+الإنسان ميراثه لأبناء وأعطته الحقكما قلت قبل قليل
+
+85
+00:07:21,040 --> 00:07:26,620
+في أن يتصرف بحدود الثلث في ماله لمن أراد حتى لو لم
+
+86
+00:07:26,620 --> 00:07:31,680
+يكونوا من أقربائه أما بالنسبة لمصدر آيات المواريث
+
+87
+00:07:31,680 --> 00:07:37,800
+فقلنا إن آية أو صورة النساء فعالجت أحكام الميراث
+
+88
+00:07:37,800 --> 00:07:42,260
+فنجد أن الله عز وجل يقولفي آية 11 من صورة النساء
+
+89
+00:07:42,260 --> 00:07:47,460
+يوصيكم الله في أولادكم للذكر مثل حظ الأنثيين فإن
+
+90
+00:07:47,460 --> 00:07:51,820
+كنا نساء فوق أثنتين فلهن ثلثاء ما ترك وإن كانت
+
+91
+00:07:51,820 --> 00:07:56,520
+واحدة فلها النصف إلى غير ذلك من الأحكام ثم تحدث
+
+92
+00:07:56,520 --> 00:08:00,700
+الله عز وجل عن ميراث الأزواج حين ما قال الله تبارك
+
+93
+00:08:00,700 --> 00:08:07,040
+وتعالى ولكم نصف ما ترك أزواجكم إن لم يكنلهن ولد
+
+94
+00:08:07,040 --> 00:08:11,600
+فإن كان لهن ولد فلكم الربع مما تركنا من بعد وصية
+
+95
+00:08:11,600 --> 00:08:16,740
+يوصينا بيها أو دين ثم أكمل ذلك حينما تحدث عن
+
+96
+00:08:16,740 --> 00:08:21,740
+الإخوة يستفتون كقول الله يفتيكم في الكلالة إن امرئ
+
+97
+00:08:21,740 --> 00:08:27,060
+هلك ليس له ولد وله أخت ف
+
+98
+00:08:28,580 --> 00:08:33,220
+لها النصف أو لها النصف مما ترك و هو يريثها إن لم
+
+99
+00:08:33,220 --> 00:08:37,200
+يكن لها ولد فلاحظوا معايا أن هذه الآيات شملت أغلب
+
+100
+00:08:37,200 --> 00:08:42,700
+أحكام المواريث صحيح أننا قلنا إن القرآن الكريم قد
+
+101
+00:08:42,700 --> 00:08:46,300
+تناول جل أحكام الميرات لكن هذا لا يعني أن الصنة لم
+
+102
+00:08:46,300 --> 00:08:50,780
+يكن لها دور في تشريع أحكامالحكام الميراث فإن السنة
+
+103
+00:08:50,780 --> 00:08:56,180
+ابتداء فسرت ما ذكره القرآن الكريم وشرحته وبيّنته
+
+104
+00:08:56,180 --> 00:09:01,080
+بالاضافة إلى أنها أنشأت جملة من الأحكام التي سكت
+
+105
+00:09:01,080 --> 00:09:06,940
+عنها القرآن الكريم من ذلك مثلا ميراث الجدةفقد ثبت
+
+106
+00:09:06,940 --> 00:09:12,040
+أنه في عهد أبي بكر رضي الله عنه جاءت جدة تسأله
+
+107
+00:09:12,040 --> 00:09:17,800
+ميراثها وتريد ميراثا من ابن ابنها أو بنت ابنها
+
+108
+00:09:17,800 --> 00:09:23,540
+الذين توفوا فأخبرها سيدنا أبو بكر رضي الله عنه أنه
+
+109
+00:09:23,540 --> 00:09:30,470
+ليس لها شيء في كتاب الله ثم سأل أصحابه هلأعطاها
+
+110
+00:09:30,470 --> 00:09:33,750
+النبي صلى الله عليه وسلم شيئًا فإذ بالمغيرة بن
+
+111
+00:09:33,750 --> 00:09:38,370
+شعبة يقول له بأن النبي صلى الله عليه وسلم جعل لها
+
+112
+00:09:38,370 --> 00:09:45,470
+أسدوس فأراد أبو بكر رضي الله عنه أن يتأكد ويتحرى
+
+113
+00:09:45,470 --> 00:09:50,890
+من هذا التشريع فقال من يشهد معه فإذ بمحمد بن الحسن
+
+114
+00:09:50,890 --> 00:09:58,170
+يشهد معهفمن هنا قرر أبو بكر عملا واعمالا لسنة رسول
+
+115
+00:09:58,170 --> 00:10:04,090
+الله صلى الله عليه وسلم بأن الجددة ترثالسُدُس
+
+116
+00:10:04,090 --> 00:10:09,730
+إضافة إلى ذلك فإن السُنة أيضًا قررت أن بنت الإبن
+
+117
+00:10:09,730 --> 00:10:15,470
+ترف السُدُس عند وجود أنثى أعلى تستحق النصف تكملة
+
+118
+00:10:15,470 --> 00:10:21,310
+للثُرثين فقد ورد أن صحابيا جليلا يدعاه زيل جاء
+
+119
+00:10:21,310 --> 00:10:28,570
+لأبي موسى الأشعري رضي الله عنه يسأله عن نيراث ما
+
+120
+00:10:28,570 --> 00:10:38,750
+لو شخص مات وترك بنت وبنت إبنو بنت و بنت ابن و أخت
+
+121
+00:10:38,750 --> 00:10:44,590
+فما الميراث و كيف يمكن توزيع الميراث حينها قال له
+
+122
+00:10:44,590 --> 00:10:50,370
+أبو موسى سأقضي بما قد رسول الله فقال البنت لها
+
+123
+00:10:50,370 --> 00:10:56,050
+النصف و الأخت لها النصف ولا شيء لبنت الأبنفابو
+
+124
+00:10:56,050 --> 00:11:01,210
+موسى بيحكي له زيل فذهب واتي ابن مسعود فإنه
+
+125
+00:11:01,210 --> 00:11:07,070
+سيوافقني وسيتابعني وحينما ذهب هزيل إلى ابن مسعود
+
+126
+00:11:07,070 --> 00:11:11,930
+رضي الله عنه وذكر إليه ما قاله ابو موسى فقال ابن
+
+127
+00:11:11,930 --> 00:11:17,350
+مسعود رضي الله عنه لقد ضللت وما اهتديت إن حكمت بما
+
+128
+00:11:17,350 --> 00:11:22,840
+حكم فالبنت لها النصفوبنت الإبن لها الصدوس تكمل
+
+129
+00:11:22,840 --> 00:11:28,900
+للثلثين وما تبقى فهو لأخد بمعنى أن الأخد عصب مع
+
+130
+00:11:28,900 --> 00:11:35,600
+الغير فحينما عاد هزيل إلى أبي موسى الأشعري أخبره
+
+131
+00:11:35,600 --> 00:11:42,040
+بفعل إبن مسعود فقال لا تسألني مدام هذا الحبر فيكم
+
+132
+00:11:42,040 --> 00:11:47,970
+فهذا دليل على أن السنة قداستقلت بتقرير أن بنات
+
+133
+00:11:47,970 --> 00:11:52,230
+الإبن يريثنا الصدس عند وجود الفرع المؤنث الأعلى
+
+134
+00:11:52,230 --> 00:11:58,570
+منهم فهذا أيضا يؤكد أن السنة لها دور في تشريع آيات
+
+135
+00:11:58,570 --> 00:12:02,750
+الميراث ليس الأمر إلى هنا انتهى بل إن الاجتهاد
+
+136
+00:12:02,750 --> 00:12:06,730
+أيضا كان حاضرا لكنه كان قليلا بخلاف الاجتهاد في
+
+137
+00:12:06,730 --> 00:12:11,000
+المسائل الأخرىفنجد بأن عمر بن الخطاب رضي الله عنه
+
+138
+00:12:11,000 --> 00:12:17,080
+اجتهد في مسألة وهي أفرادها الأبوين مع أحد الزوجين
+
+139
+00:12:17,080 --> 00:12:22,940
+فلو بده يعطي الأم الثلث باعتبار أن الأم ميراثها يا
+
+140
+00:12:22,940 --> 00:12:27,260
+ثلث يا سدس والثلث عندها عدم وجود فرع وارث للميت
+
+141
+00:12:27,260 --> 00:12:32,760
+وعدم وجود عدد من الإخوة فلو أعطاها الثلث ربماقل
+
+142
+00:12:32,760 --> 00:12:36,600
+نصيب الأب عن نصيب الأم ولا يتصور أن الأم تأخذ
+
+143
+00:12:36,600 --> 00:12:41,420
+وتستحق أكثر من الأب فاجتهد عمر رضي الله عنه في هذه
+
+144
+00:12:41,420 --> 00:12:45,100
+المسألة وعرفت هذه المسألة بالمسألة العمارية
+
+145
+00:12:45,100 --> 00:12:48,580
+وسنتحدث عنها بالتفصيل في وقتها بإذن الله تبارك
+
+146
+00:12:48,580 --> 00:12:52,500
+وتعالى أيضا اجتهد عمر رضي الله عنه في موضوع
+
+147
+00:12:52,500 --> 00:12:59,590
+المسألة المشتركةوهذه المسألة طبعا حينما سُئل عنها
+
+148
+00:12:59,590 --> 00:13:04,670
+رضي الله عنه أيضا عمر فأجاب بأنه لا شيء للإخوة
+
+149
+00:13:04,670 --> 00:13:08,750
+الأشقاء والإخوة لهم يستحقون الثلاثة أفرادها راح
+
+150
+00:13:08,750 --> 00:13:13,590
+ندرسهم بالتفصيل بإذن اللهفجاء إليه الإخوة الأشقاء
+
+151
+00:13:13,590 --> 00:13:18,090
+واعترضوا على حكمه في زمن ما غير الزمن الذي حكم به
+
+152
+00:13:18,090 --> 00:13:23,350
+في أول مسألة عرضت عليه فقالوا له هبقنا أبانا حجرا
+
+153
+00:13:23,350 --> 00:13:28,530
+هبقنا أبانا حمارا هبقنا هبقنا هبقنا فحينها اجتهد
+
+154
+00:13:28,530 --> 00:13:33,570
+رضي الله عنه وقرر أن جميع الإخوة سواء أشقاء أو
+
+155
+00:13:33,570 --> 00:13:40,110
+إخوة لأم شركاء في أثلث يقتسمونه بالتساوي على خلاف
+
+156
+00:13:40,440 --> 00:13:44,240
+القاعدة العامة في الميراث أنه للذكري مثل حظ
+
+157
+00:13:44,240 --> 00:13:50,180
+الأنسيين نأتي الآن ونعرف سويا علم الميراث حينما
+
+158
+00:13:50,180 --> 00:13:54,460
+نريد أن نعرف علم الميراث طبيعي جدا أن نشوف الميراث
+
+159
+00:13:54,460 --> 00:13:58,700
+لوحده شهوه ثم نتحدث عن هذا العلم كمصطلح مركب
+
+160
+00:13:58,950 --> 00:14:03,070
+فالميراث يا جماعة في اللغة انتقال الشيء من شخص
+
+161
+00:14:03,070 --> 00:14:08,990
+لآخر أو انتقال الشيء من قوم لآخر بغض النظر عن كنهي
+
+162
+00:14:08,990 --> 00:14:12,610
+هذا الشيء كان ماديات، معنويات، بغض النظر شهوة
+
+163
+00:14:12,610 --> 00:14:17,670
+فمجرد انتقال شغلة من سين لصاد هذا يعد ميراثا في
+
+164
+00:14:17,670 --> 00:14:25,470
+اللغة أما الفرض أو لأنه احنا بنقول علم ميراث وعلم
+
+165
+00:14:25,470 --> 00:14:31,180
+فرائد نفس الشيء تمام؟فالان الميراث يصير نفهمين شو
+
+166
+00:14:31,180 --> 00:14:36,560
+هو في اللغة اللي هو انتقال الشئ .. الميراث ..
+
+167
+00:14:36,560 --> 00:14:40,280
+انتقال الشئ من شخص لآخر أو من قوم لآخر أما في
+
+168
+00:14:40,280 --> 00:14:45,560
+الاصطلاح فهو انتقال التركة
+
+169
+00:14:45,560 --> 00:14:51,040
+من المورث للوارث
+
+170
+00:14:52,350 --> 00:14:56,570
+وراح نتحدث عنهم هدول في أركان الميراث بإذن الله
+
+171
+00:14:56,570 --> 00:15:03,710
+أما الفرائض الفرض في اللغة هو التقدير مجرد أو مطلق
+
+172
+00:15:03,710 --> 00:15:09,030
+التقدير يعده فرضا أما في الصلاح تعريف ومفهوم الفرض
+
+173
+00:15:09,030 --> 00:15:13,630
+يختلف باختلاف العلم الذي ينتمي إليه فمثلا في علم
+
+174
+00:15:13,630 --> 00:15:19,330
+الأصول إن أردنا أن نعرف الفرض فنقول هوما وجب فعله
+
+175
+00:15:19,330 --> 00:15:23,510
+بدليل انقطع أو ما طلب الشارع فعله طلبا جازما بحيث
+
+176
+00:15:23,510 --> 00:15:28,830
+يثاب فعله ويعاقب تاركه أما بالنسبة لعلم المنطقله
+
+177
+00:15:28,830 --> 00:15:33,230
+التعريف والذي يهمنا هنا هو تعريف الفرض في علم
+
+178
+00:15:33,230 --> 00:15:39,410
+الميراث أو علم المواريث فنقول إن الفرض هو النصيب
+
+179
+00:15:39,410 --> 00:15:46,410
+المقدر شرعا تمام؟ هذا هو تعريف الفرض في الاصطلاح
+
+180
+00:15:47,550 --> 00:15:50,730
+إذا صرنا عارفين شو يعني فرض وشو يعني ميراثه، طب
+
+181
+00:15:50,730 --> 00:15:54,690
+علم الميراث، إن أردنا أن نعرف هذا العلم كمصطلح
+
+182
+00:15:54,690 --> 00:15:56,630
+مركب يا مريم، برك الله فيك
+
+183
+00:16:02,650 --> 00:16:06,730
+وبالتالي نستطيع القول إن علم الفرائض أو علم
+
+184
+00:16:06,730 --> 00:16:10,790
+المواريث مجموعة من الأحكام الفقهية أو القواعد
+
+185
+00:16:10,790 --> 00:16:17,430
+الفقهية والحسابية التي يتوصل من خلالها لمعرفة نصيب
+
+186
+00:16:17,430 --> 00:16:22,750
+كل وارث شرعًا هذا هو علم المواريث أو علم الفرائض
+
+187
+00:16:22,750 --> 00:16:26,810
+لحظة معايا قلت عنه علم مواريث أو علم فرائض ما قلتش
+
+188
+00:16:26,810 --> 00:16:31,080
+علم عصباتمع إن الميراث قد يكون بالفرض كما سنعلم و
+
+189
+00:16:31,080 --> 00:16:35,920
+قد يكون ميراث بالعصابات لكننا أسميناه فرائد أو علم
+
+190
+00:16:35,920 --> 00:16:38,280
+الفرائد دون علم العصابات يا مريم
+
+191
+00:16:41,430 --> 00:16:46,530
+بالضبط لأن أثناء توزيع التريكة نحن نبدأ بالفروض ثم
+
+192
+00:16:46,530 --> 00:16:50,590
+ما تبقى يكون للعصابات من هنا جاءت التسمية بعلم
+
+193
+00:16:50,590 --> 00:16:58,170
+الفرائض ننتقل الآن لنتحدث عن أركان القياس عفوا
+
+194
+00:16:58,170 --> 00:17:02,590
+أركان الميراث لكن قبل ذلك بنقول موضوع علم المواريث
+
+195
+00:17:02,590 --> 00:17:07,750
+هو التريكة وبالنسبة للثمرة من دراسة علم الميراث هي
+
+196
+00:17:08,380 --> 00:17:13,000
+إعطاء كل ذي حق حقه ولمّا بنقول موضوع علم الميراث
+
+197
+00:17:13,000 --> 00:17:17,400
+التركة الأمر بيتطلب مننا نجف شوية عند مفهوم التركة
+
+198
+00:17:17,400 --> 00:17:24,360
+وسنعرف سويا التركة ثم نتحدث عن الحقوق المتعلقة
+
+199
+00:17:24,360 --> 00:17:29,820
+بالتركة التركة يا جماعة ابتداء في اللغة من الترك
+
+200
+00:17:29,820 --> 00:17:36,570
+والترك هو التخليةوفي اللغة نقول بأن التركة هي ما
+
+201
+00:17:36,570 --> 00:17:41,590
+يتركه الميت من الماديات أو معنويات، بغض النظر شو
+
+202
+00:17:41,590 --> 00:17:45,490
+تركه الميت، هذا اسمه تركة في اللغة، فالمعنى اللغوي
+
+203
+00:17:45,490 --> 00:17:49,370
+أكثر عموما من المعنى الاصطلاحي الذي سنقف عنده بعد
+
+204
+00:17:49,370 --> 00:17:54,570
+قليلفأي شيء سمعت الإنسان بعد موته تاريكة، أي شيء
+
+205
+00:17:54,570 --> 00:17:57,630
+يتركه الإنسان من أخلاق، من حسن سمعة و .. و .. إلى
+
+206
+00:17:57,630 --> 00:18:03,470
+غير ذلك يعد تاريكة تمام؟ فخلونا نشوف التاريكة في
+
+207
+00:18:03,470 --> 00:18:07,890
+الاصطلاح قبل قليل قلت إن التاريكة هي موضوع علم
+
+208
+00:18:07,890 --> 00:18:13,790
+المواريثفبتركة هناك خلاف بين الفقاء في تحديد
+
+209
+00:18:13,790 --> 00:18:20,130
+مفهومها والخلاف بينهم مرده إلى الحقوق غير المالية
+
+210
+00:18:20,130 --> 00:18:24,930
+التي لا تتعلق بالمال هل يترى ما يتركه الإنسان من
+
+211
+00:18:24,930 --> 00:18:29,270
+حقوق غير مالية لا تعلق لها بالمال يعدوا تركة أم لا
+
+212
+00:18:29,270 --> 00:18:33,630
+سنجد أن العلماء قد اختلفوا فالحنافية قالوا إن
+
+213
+00:18:33,630 --> 00:18:38,420
+الحقوق غير المالية التي لا علاقة لها بالماللا تعد
+
+214
+00:18:38,420 --> 00:18:43,360
+تاريكة بخلاف جمهور العلماء الذين عدوها من ضمن
+
+215
+00:18:43,360 --> 00:18:48,540
+التاريكة فلذلك نستطيع القول إن الحنفية قالوا إن
+
+216
+00:18:48,540 --> 00:18:58,800
+التاريكة هي ما يتركه الميت تمام فضليا مريم اذا
+
+217
+00:18:58,800 --> 00:19:03,120
+ما يتركه الميت
+
+218
+00:19:03,120 --> 00:19:05,000
+من
+
+219
+00:19:07,010 --> 00:19:19,750
+أموال خالصة عن تعلق حق الغير بعين الأموال
+
+220
+00:19:20,460 --> 00:19:24,320
+شو معنى هذا الكلام؟ معنى الكلام أنه أول ما بيموت
+
+221
+00:19:24,320 --> 00:19:29,940
+الإنسان بروح لأمواله، فيه إشي للغير، فيه أعيان من
+
+222
+00:19:29,940 --> 00:19:34,820
+أمواله للغير ولا لا، فإن وجدته أن من بين أمواله
+
+223
+00:19:34,820 --> 00:19:41,130
+أعيان للغير على طول بعطيها فماتبقى غير متعلق بحقوق
+
+224
+00:19:41,130 --> 00:19:45,610
+الغير فيكونوا تريكة للميت فلاحظوا معايا هنا ان
+
+225
+00:19:45,610 --> 00:19:50,990
+الحنفية اعتبروا ان جميع الأموال التي يتركها الميت
+
+226
+00:19:50,990 --> 00:19:56,310
+والحقوق المالية التي يتركها الميت والحقوق غير
+
+227
+00:19:56,310 --> 00:20:01,000
+المالية التي تتعلق بالمالالحق المروري ونحويه كلها
+
+228
+00:20:01,000 --> 00:20:06,020
+تعد من قبيل التركة بخلاف المنافع لأن المنافع لا
+
+229
+00:20:06,020 --> 00:20:10,220
+تعلق لها بالمال وبالتالي المنافع عندهم ليست من
+
+230
+00:20:10,220 --> 00:20:14,160
+التركة لأنها ليست حقوقا مالية ولا تتعلق بالمال
+
+231
+00:20:14,160 --> 00:20:18,880
+وعندهم فإن الإجارة مثلا تنتهي بالموت ولا يمكن أن
+
+232
+00:20:18,880 --> 00:20:23,360
+تورثبخلاف جمهور الفقهاء من المالكية والشافعية
+
+233
+00:20:23,360 --> 00:20:28,080
+والحنابلة الذين قالوا إن التركة هي كل ما يتركه
+
+234
+00:20:28,080 --> 00:20:33,540
+الميت من بعده من أموال وحقوق مالية أو غير مالية
+
+235
+00:20:33,540 --> 00:20:39,590
+اتعلقت بالمال أو لم تتعلق بالمالوبناء على مفهوم
+
+236
+00:20:39,590 --> 00:20:45,550
+الجمهور للتريكة نقول إن التريكة تشمل الأموال سواء
+
+237
+00:20:45,550 --> 00:20:50,210
+منقولات أو عقارات وبتشمل الحقوق سواء كانت مالية أو
+
+238
+00:20:50,210 --> 00:20:56,590
+غير مالية وبالتالي هذا مفهوم التريكة عند الفقهاء
+
+239
+00:20:56,590 --> 00:21:01,690
+ننتقل الآن للحديث عن آخر نقطة في محاضرتنا لهذا
+
+240
+00:21:01,690 --> 00:21:09,280
+اليوم وهي الحقوق المتعلقة بالتريكةالذي يتبادر إلى
+
+241
+00:21:09,280 --> 00:21:14,780
+أذهان الكثير منكم بأن التركة يعني ميراث وهذا
+
+242
+00:21:14,780 --> 00:21:19,920
+المعنى المعهود لدى الكثيرين ليس صحيحا لأن التركة
+
+243
+00:21:19,920 --> 00:21:26,180
+تتعلق بها جملة من الحقوق أو خمس خمسة حقوق وهذه
+
+244
+00:21:26,180 --> 00:21:33,320
+الحقوق كالتالي باتفاق الفقهاء تجهيز
+
+245
+00:21:33,320 --> 00:21:34,040
+الميت
+
+246
+00:21:40,010 --> 00:21:49,430
+ثم أداء الحقوق العينية ثم
+
+247
+00:21:49,430 --> 00:21:58,810
+أداء الديون ورابعا تنفيذ الوصاية
+
+248
+00:21:58,810 --> 00:22:02,010
+وأخيرا
+
+249
+00:22:02,880 --> 00:22:08,280
+التوريث أو الميراث فلاحظوا معايا أن التوريث هو آخر
+
+250
+00:22:08,280 --> 00:22:13,880
+ما يرجع إليه في موضوع التركة فهذه الحقوق يا جماعة
+
+251
+00:22:13,880 --> 00:22:18,500
+هل هي على الترتيب أو لا سنجد أن العلماء لا خلافة
+
+252
+00:22:18,500 --> 00:22:22,540
+بينهم في موضوع أن أداء الديون قبل تنفيذ الوصاية أو
+
+253
+00:22:22,540 --> 00:22:26,250
+تنفيذ الوصاية قبل التوريثوكمان مافي خلاف إن
+
+254
+00:22:26,250 --> 00:22:30,750
+النقطتين هدول جابل التلت نقاط الأخيرة لكن الخلاف
+
+255
+00:22:30,750 --> 00:22:36,090
+بينهم وقع في أول بندين مين أولى من مين؟ من الذي
+
+256
+00:22:36,090 --> 00:22:40,950
+يقدم على الآخر؟ فنجد مثلا أن الحنافية في غير
+
+257
+00:22:40,950 --> 00:22:46,830
+المشهور والحنابل معهم قالوا أول ما يقدم هو تجهيز
+
+258
+00:22:46,830 --> 00:22:51,520
+الميتولمّا بنقول تجهيز الميت معنا الكلام أن كل ما
+
+259
+00:22:51,520 --> 00:22:57,960
+يتعلق بالميت منذ أن مات إلى أن دفن ووريا التراب،
+
+260
+00:22:57,960 --> 00:23:03,540
+أي شاق، كفن وغير ذلك وغصل وغير ذلك يكون من تركته
+
+261
+00:23:04,610 --> 00:23:09,410
+هذا بناء على رأي الحنافية في غير المشهور والحنابلة
+
+262
+00:23:09,410 --> 00:23:15,750
+وبعد ذلك أداء الحقوق العينية لكن باق الأامة من
+
+263
+00:23:15,750 --> 00:23:19,470
+المالكية والشافعية والحنابلة وحتى الصحابة
+
+264
+00:23:19,470 --> 00:23:24,940
+والتابعين والحنافية في المشهور قالوا لأالذي يقدم
+
+265
+00:23:24,940 --> 00:23:31,100
+أولا هو الحقوق العينية أو أداء الحقوق العينية ثم
+
+266
+00:23:31,100 --> 00:23:36,400
+تجهيز الميت لسبب بسيط وهو أن الحقوق المالية هي
+
+267
+00:23:36,400 --> 00:23:41,630
+أموال الميت أو ليست أموال الميتالحقوق العينية ليست
+
+268
+00:23:41,630 --> 00:23:46,690
+أموال للميت حتى نجعلها من ضمن تركته بحيث نجحز منها
+
+269
+00:23:46,690 --> 00:23:51,310
+الميت، لأ هي ليست للميت وبالتالي أول ما يفعل بنرد
+
+270
+00:23:51,310 --> 00:23:57,920
+الحقوق لأهلها أي شئمتعين لفلان أو علان زي الوديعة
+
+271
+00:23:57,920 --> 00:24:02,000
+زي الرهن زي مثلا جطعة أرض أنا شريها و مش دافعة
+
+272
+00:24:02,000 --> 00:24:06,180
+حاجها هذه الأمور كلها بدها ترجع لاصحابها ثم بعد
+
+273
+00:24:06,180 --> 00:24:11,520
+ذلك بقى أجهز الميت طب لو افترضنا جدلا أنه أنا لما
+
+274
+00:24:11,520 --> 00:24:16,860
+رديت الحقوق لأهلها لم يتبقى شئ لتجهيز الميتفي هذه
+
+275
+00:24:16,860 --> 00:24:22,240
+الحالة يا تورا شو الحل؟ الحل أن تجهيز الميت سيكون
+
+276
+00:24:22,240 --> 00:24:29,950
+على من تجبعليه نفقته يعني مين من ورثة الميت يجب
+
+277
+00:24:29,950 --> 00:24:34,070
+عليه أن ينفق على هذا الميت وبغض النظر ممكن اللي
+
+278
+00:24:34,070 --> 00:24:37,310
+مات هو الأب فبالتالي أولاده ممكن اللي مات هو الإبن
+
+279
+00:24:37,310 --> 00:24:41,550
+فبالتالي أبوها كذا حسب مين هو الميت ومين هو الوارث
+
+280
+00:24:41,550 --> 00:24:47,150
+تمام فنرجع نقول بناء على الرأي الراجح وهو أن أول
+
+281
+00:24:47,150 --> 00:24:52,610
+ما يقسم وما يفعل في التركاء ده الحقوق العينية وهذا
+
+282
+00:24:52,610 --> 00:24:59,180
+هو الراجح ثم تجهيز الميترقم تلاتة أداء الديون أي
+
+283
+00:24:59,180 --> 00:25:04,660
+إنسان له حقوق في ذمته فبدي يرجع لورثته وياخد
+
+284
+00:25:04,660 --> 00:25:10,020
+إحجاجه كاملة ولاحظي الديون ما بتكون الشغلات عينية
+
+285
+00:25:10,020 --> 00:25:14,280
+هي في ذمة الميت مش بأعين ماله وبالتالي لو مافيه
+
+286
+00:25:14,280 --> 00:25:18,680
+سيولة أو مال بعينه فبنروح نبيع سيارة بنبيع أي شيء
+
+287
+00:25:18,680 --> 00:25:24,610
+حتىإن سد الدين ثم رابعا تنفيذ الوصاية إذا في الميت
+
+288
+00:25:24,610 --> 00:25:28,970
+موص بأي شئ بدنا ننفذ هذه الوصاية وأخيرا ننتقل إلى
+
+289
+00:25:28,970 --> 00:25:34,030
+التوريث قبل أن منهي بقى أمر غاية في الأهمية وهو
+
+290
+00:25:35,780 --> 00:25:41,240
+لماذا قلنا إن العلماء قد جعلوا أداء الديون مقدم
+
+291
+00:25:41,240 --> 00:25:45,260
+على تنفيذ الوصاية مع أن الله عز وجل في آيات
+
+292
+00:25:45,260 --> 00:25:50,960
+التوريد دائما دائما يقول من بعد وصية يوصي بها أو
+
+293
+00:25:50,960 --> 00:25:55,480
+دين دائما يقدم الوصية ثم الدين وأنتم هنا تقدمون
+
+294
+00:25:55,480 --> 00:25:58,360
+الديون على الوصاية تفضلي يا مريم
+
+295
+00:26:12,420 --> 00:26:17,120
+بارك الله فيك إذا ما استطيع القول إن العلماء قد
+
+296
+00:26:17,120 --> 00:26:21,000
+قدموا الديون على الوصية مع أن الله عز وجل كان
+
+297
+00:26:21,000 --> 00:26:25,920
+دائما يبدأ بالوصية قبل الدين لأن الدين يا جماعة له
+
+298
+00:26:25,920 --> 00:26:30,970
+مطالب في الدنيافطبيعي جدا بعد ما يموت فلان لو حد
+
+299
+00:26:30,970 --> 00:26:36,190
+بده منه دين بيجي .. بيجي هذا الدائن يطالب ورثة
+
+300
+00:26:36,190 --> 00:26:42,830
+الميت بديونه فربنا عز وجل أخر الدين لأنه فيه مطالب
+
+301
+00:26:42,830 --> 00:26:46,390
+للدين و لن يسقط .. و لن يسقط صاحب الحق عن حقه
+
+302
+00:26:46,390 --> 00:26:52,330
+بخلاص الوصاية مايلها مطالب وبالتالي ربنا جعل هذا
+
+303
+00:26:52,330 --> 00:26:58,360
+راجع إلى الوازع الديني للورثة فالأصلأن يكون الوارث
+
+304
+00:26:58,360 --> 00:27:05,000
+أمينا وينفذ وصية الميت حتى لو لم يطالبه بذلك أحد
+
+305
+00:27:05,000 --> 00:27:09,540
+لذا فإن الله كان دائما يبدأ بالوصية قبل الدين لأن
+
+306
+00:27:09,540 --> 00:27:16,750
+الوصية غالبا لمطالبة لهاوآخر ما يرجع اليه هو تقسيم
+
+307
+00:27:16,750 --> 00:27:20,710
+ما تبقى بعد هذه الحقوق الأربعة أي شيء بضال يقسم
+
+308
+00:27:20,710 --> 00:27:24,610
+بين الورث على النحو الذي سنتحدث عنه بإذن الله
+
+309
+00:27:24,610 --> 00:27:29,350
+حينما نتحدث عن طرق التوريث بالفرض وكذا وغير ذلك
+
+310
+00:27:29,530 --> 00:27:34,850
+المحاضرة القادمة بإذن الله سنتحدث سويا عن أركان
+
+311
+00:27:34,850 --> 00:27:40,570
+الميراث وأسبابه وشروطه وننتهي بموانعه أقول قولي
+
+312
+00:27:40,570 --> 00:27:44,430
+هذا وأستغفر الله لي ولكم وصل اللهم وسلم وبارك على
+
+313
+00:27:44,430 --> 00:27:49,350
+سيدنا محمد والسلام عليكم ورحمة الله تعالى وبركاته
+
diff --git a/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/Qdob7NdamBE_raw.srt b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/Qdob7NdamBE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9ba4727b9dcdc75821b21339d5df5ec0657e94b5
--- /dev/null
+++ b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/Qdob7NdamBE_raw.srt
@@ -0,0 +1,2240 @@
+1
+00:00:05,150 --> 00:00:07,950
+أعوذ بالله السميع العليم من الشيطان الرجيم بسم
+
+2
+00:00:07,950 --> 00:00:11,230
+الله الرحمن الرحيم الحمد لله رب العالمين والصلاة
+
+3
+00:00:11,230 --> 00:00:15,290
+والسلام على أشرف الأنبياء والمرسلين سيدنا محمد بن
+
+4
+00:00:15,290 --> 00:00:18,230
+عبدالله الصادق الأمين ثم أما بعد أحييكم جميعا
+
+5
+00:00:18,230 --> 00:00:21,770
+بتحيات الإسلام فالسلام عليكم ورحمة الله تعالى
+
+6
+00:00:21,770 --> 00:00:27,010
+وبركاته كيف حالكم نطيبات ان شاء الله تحضيرنا جيد
+
+7
+00:00:27,010 --> 00:00:31,980
+ان شاء اللهالحمد لله إذا كنا قد تحدثنا المحاضرة
+
+8
+00:00:31,980 --> 00:00:36,820
+السابقة عن تقسيم التاركة وقلنا إن تقسيم التاركة
+
+9
+00:00:36,820 --> 00:00:42,380
+مبني على تأصيل هذه المسائل وبناء على تأصيلها يسهل
+
+10
+00:00:42,380 --> 00:00:48,420
+علينا أن نعطي كل ذي حق حقه بمعنى كل وارث نصيبه،
+
+11
+00:00:48,420 --> 00:00:54,760
+تمام؟ فقلنا إنتقسيم التاريكة مبني على معرفة قيمة
+
+12
+00:00:54,760 --> 00:00:58,640
+السهم وقيمة السهم بحسبه من خلال قسمة التاريكة على
+
+13
+00:00:58,640 --> 00:01:02,940
+أصل المسألة من هنا كان لابد من معرفة التأصيل كما
+
+14
+00:01:02,940 --> 00:01:07,420
+سبقوا أن تحدثنا قلنا إن الأموال التي يتركها الميت
+
+15
+00:01:07,420 --> 00:01:11,860
+قد تكون أموال مثلية وقد تكون أموال قيمية أو متقومة
+
+16
+00:01:12,090 --> 00:01:15,710
+في الأموال المثلية كما سبق وأنقلنا بقسم هذا المال
+
+17
+00:01:15,710 --> 00:01:20,470
+المثل الذي اتركه الميت على أصل هذه المسألة ثم أخرج
+
+18
+00:01:20,470 --> 00:01:25,270
+نصيبك الوارث بضرب قيمة سهمه أو قيمة السهم في عدد
+
+19
+00:01:25,270 --> 00:01:30,070
+أسهمه في المسألةوالأمر لا يختلف بالنسبة لتقسيم
+
+20
+00:01:30,070 --> 00:01:34,650
+الأموال القيمية فيما لو أراد جميع الورث أن يبقوا
+
+21
+00:01:34,650 --> 00:01:40,450
+على الشيوع في المال الذي ورثوه حينها نفترض أن
+
+22
+00:01:40,450 --> 00:01:44,870
+المال الذي تركه الميت مقسم إلى أجزاء بعدد أصل
+
+23
+00:01:44,870 --> 00:01:51,310
+المسألة كل وارث يستحق نصيبا على الشيوع بعدد أسهمه
+
+24
+00:01:51,310 --> 00:01:57,300
+في مسألتهلكن ماذا لو ترك الميت أموال مثلية و أموال
+
+25
+00:01:57,300 --> 00:02:01,000
+قيمية في ذات الأمر؟ قلنا بنعمل عملية حسابية لكلا
+
+26
+00:02:01,000 --> 00:02:05,900
+الأمرين على حدة و بنعطي الوارث نصيب و خلصنا لكن
+
+27
+00:02:05,900 --> 00:02:11,320
+أحيانا الأموال القيمية التي يتركها الميت يصعب
+
+28
+00:02:11,320 --> 00:02:16,040
+الاشتراك فيهابمعنى أن الميت ترك مثلًا من ضمن
+
+29
+00:02:16,040 --> 00:02:21,940
+أمواله سيارة أو ترك ساعة ثمينة أو تركت الميت خاتم
+
+30
+00:02:21,940 --> 00:02:27,120
+أو أسوارة دهب أو أي شئ من هذا القبيل يعني صعب أنه
+
+31
+00:02:27,120 --> 00:02:31,820
+أنا و أنتي و كلنا كورثة نشترك في هذا المال ماذا
+
+32
+00:02:31,820 --> 00:02:37,120
+نصنع إذاء مثل هذه المسائل؟ نقولفي هذا الأمر
+
+33
+00:02:37,120 --> 00:02:40,620
+بالتأكيد ستباع هذه الأموال لأنه صعب أقول الأسوار
+
+34
+00:02:40,620 --> 00:02:45,580
+هتكون بين سين وصادعين ستباع من الأولى بشراء هذه
+
+35
+00:02:45,580 --> 00:02:50,200
+الأموال بالتأكيد الورثة الورثة أولى بشرائها فإن
+
+36
+00:02:50,200 --> 00:02:56,300
+أراد أحد الورثة أن يشتري هذه الأموال يأخذها وبعد
+
+37
+00:02:56,300 --> 00:03:02,520
+ذلك لما بنحصي كل الأموال الميتفبنروح للنفس الفكرة
+
+38
+00:03:02,520 --> 00:03:05,420
+اللي قلناها، بنجسم هذه الأموال على أصل المسألة
+
+39
+00:03:05,420 --> 00:03:09,500
+عساس نشوف الوارث جداش نصيبه، بدي أفترض جدلا أنه في
+
+40
+00:03:09,500 --> 00:03:15,370
+عندي وارث طلع نصيبه 3000 دينارتمام فانا بقول هذا
+
+41
+00:03:15,370 --> 00:03:20,130
+الوارث ربما كان ماخد أسوارة أو ساعة أو كده باعتبار
+
+42
+00:03:20,130 --> 00:03:24,290
+اشتراها لكن لسه مادفع حاجة باعتبار شو بده ياخد
+
+43
+00:03:24,290 --> 00:03:28,750
+كإرث نصيب من الطريقة فالأسوارة أو الساعة الدهبية
+
+44
+00:03:28,750 --> 00:03:33,750
+اللي أخدها كان قيمتها 5000 دينار مثلا 5000 دينار
+
+45
+00:03:33,750 --> 00:03:39,680
+في هذه الحالةلحظي معايا هو ماخد خمس تلاف و هو أصلا
+
+46
+00:03:39,680 --> 00:03:45,020
+بيستحق تلت تلاف فبدي أدفع من جابه ألفين للورثة
+
+47
+00:03:45,020 --> 00:03:50,480
+تقسم بينهم، تمام؟ و طبعا لو بدي أفترض جدلا مسألة
+
+48
+00:03:50,480 --> 00:03:58,920
+صغيرة، نقول مثلا زوجة و بنت و بنت ابن و أخت شقيقة
+
+49
+00:03:58,920 --> 00:04:11,260
+طبعا الزوجة تمن و هاي نصف، سُدُسعصبة مع الغير بنت
+
+50
+00:04:11,260 --> 00:04:16,460
+الأبن صدس يا سماح طبعا المسألة من 24 لأن في عندي
+
+51
+00:04:16,460 --> 00:04:21,960
+تمانية و ستة فهن تلاتة و هن اتناش و هن اربع ضال
+
+52
+00:04:21,960 --> 00:04:28,360
+عندي خمسة فلو بدى افترض التركة عبارة عن مثلا نقول
+
+53
+00:04:28,360 --> 00:04:33,780
+اربع تلاف و تمانمية زاد اموال
+
+54
+00:04:36,220 --> 00:04:41,700
+قيمية بيعت بـ
+
+55
+00:04:41,700 --> 00:04:50,160
+1200 بـ 1200 دولار مثلا، تمام؟ فلحظي معايا في هذه
+
+56
+00:04:50,160 --> 00:04:53,620
+الحالة بنقول أن الأموال القيمية كانت مثلا عبارة عن
+
+57
+00:04:53,620 --> 00:04:56,300
+ساعة زائد
+
+58
+00:04:57,910 --> 00:05:08,690
+نقول مثلا خاتم و هكذا الساعة كانت قيمتها 800 مثلا
+
+59
+00:05:08,690 --> 00:05:15,950
+وهذه قيمتها 400 انبعوا بقداش فالان لما بدي أحسب و
+
+60
+00:05:15,950 --> 00:05:21,570
+أطلع نصيب كل وارث بدي أجمع ال 1200 مع ال 4800 سواء
+
+61
+00:05:21,570 --> 00:05:26,530
+باعتبرهم كلهم تاريخة واحدة فبإذن قيمة الساهم جداش
+
+62
+00:05:27,880 --> 00:05:36,600
+6000 صح ولا لأ؟ على جداش؟ 24 جداش بيعطيني؟
+
+63
+00:05:36,600 --> 00:05:47,240
+300 اصلا احسبولي 300 كأنه اتأكدي
+
+64
+00:05:47,240 --> 00:05:57,620
+300 اه 250 تمامإذا 250 هدقاش قيمة السهم فالان
+
+65
+00:05:57,620 --> 00:06:06,600
+بنيجي الزوجة تلاتة في قاش 250 يعني سبعمية و
+
+66
+00:06:06,600 --> 00:06:13,200
+خمسين صح احسبولي على السريع تمام okay و هان 250
+
+67
+00:06:13,200 --> 00:06:23,200
+ضرب 12 ألفان و خمسمية ألف و خمسمية تلات تلات و هان
+
+68
+00:06:23,200 --> 00:06:34,690
+ألفصح؟ مش هيك؟ هان ألف و متين و خمسين تمام؟ حلو
+
+69
+00:06:34,690 --> 00:06:42,490
+فالان يا جماعة بدي أفترض أن الشقيقة أخدت الساعة و
+
+70
+00:06:42,490 --> 00:06:48,310
+الخاتم هي اللي أخدتهم جالت هدول من أخويا أنا بدي
+
+71
+00:06:48,310 --> 00:06:56,080
+أخليهم إليكذكرة بدي أخدهم فاشتركتهم جدش حقهم ألف و
+
+72
+00:06:56,080 --> 00:07:00,640
+متين هي بتستحق ألف و متين و خمسين فكأنها أخدت ألف
+
+73
+00:07:00,640 --> 00:07:05,690
+و متين بنديها بس خمسينبنعطيها بس خمسين لإن هي مخدة
+
+74
+00:07:05,690 --> 00:07:10,230
+ألف و متين وهكذا علم هذا تتمت المحاضرة السابقة
+
+75
+00:07:10,230 --> 00:07:14,930
+اليوم بإذن الله سنشرح بالحديث عن موضوع التصحيح
+
+76
+00:07:14,930 --> 00:07:19,550
+جماعة حينما تحدثنا عن تأصيل المسائل شو الهدف من
+
+77
+00:07:19,550 --> 00:07:23,870
+التأصيل قلنا يلا ع السريع مين تقولي إيش الهدف لما
+
+78
+00:07:23,870 --> 00:07:28,930
+تحدثنا عن تأصيل المسألة؟إن أعطي كل وارث عدد صحيح
+
+79
+00:07:28,930 --> 00:07:32,430
+بحيث مايكونش في عندي كسور لإنه مش في عندي نص و ربع
+
+80
+00:07:32,430 --> 00:07:36,250
+و ثم نص و دوس فأنا كيف بدي أوزع التاريخ بينهم
+
+81
+00:07:36,250 --> 00:07:40,510
+فلذلك قلنا لابد من تأصيل المسألة حتى نتحاشى الكسور
+
+82
+00:07:40,510 --> 00:07:46,250
+تمام؟فالان وجهنا في مشكلة تانية بعد ما أصلنا
+
+83
+00:07:46,250 --> 00:07:50,730
+المسألة إجينا بدنا نجسم التاريخ اللي جينا فيه بعض
+
+84
+00:07:50,730 --> 00:07:54,670
+المسائل فيها انكسار يعني مثلا بدي أفطر دهان في
+
+85
+00:07:54,670 --> 00:08:01,290
+مثلا نقول أربع زوجة مثلا فاللحظة التلت أسهم لأربع
+
+86
+00:08:01,290 --> 00:08:06,970
+زوجات الزوجة هيطلعلها كسرهيطلع لها كثر يعني رجعنا
+
+87
+00:08:06,970 --> 00:08:12,250
+لنقطة البداية وكأنه لساته الخلال قائم اللي هو إيش
+
+88
+00:08:12,250 --> 00:08:15,690
+مافيش عدد صحيح بياخدوا الوارث واحنا الهدف من
+
+89
+00:08:15,690 --> 00:08:19,910
+التأصيل أنه نعطي الوارث عدد صحيح بحيث يسهل إعطاء
+
+90
+00:08:19,910 --> 00:08:23,570
+نصيبه من التركة اللي تركها الميت فهنا صار عندي
+
+91
+00:08:23,570 --> 00:08:27,430
+مشكلة جديدة نفس الأمر لو بدي أفطر دهان في تلاتة
+
+92
+00:08:27,430 --> 00:08:32,220
+بنت ابن الأربعة بتكسبش على التلاتةأيضًا الأمر ذاته
+
+93
+00:08:32,220 --> 00:08:36,560
+لو قلنا هان في اتنين أخت شقيقة فالخامسة بتجسمش على
+
+94
+00:08:36,560 --> 00:08:41,360
+اتنين صح ولا لأ؟ إذا الصرفي عند الكسار فلذلك كان
+
+95
+00:08:41,360 --> 00:08:47,780
+لابد من إجراء عملية حسابية لتصحيح هذه المسألة بحيث
+
+96
+00:08:47,780 --> 00:08:54,620
+انعرف التصحيح هو تعديل سهم الوارث بحيث يقبل القسم
+
+97
+00:08:54,620 --> 00:09:01,000
+على عدد الرؤوسفلحظي معايا من خلال المثال هذا نفسه
+
+98
+00:09:01,000 --> 00:09:08,680
+فيها انكسار تصحيح سهم الوارث بحيث إيش يقبل القسم
+
+99
+00:09:08,680 --> 00:09:12,800
+على عدد الرؤوس هان تلاتة وأربعة في انكسار شو
+
+100
+00:09:12,800 --> 00:09:16,860
+انكسار يعني؟ يعني مابيكسمش السهم بيكسمش على عدد
+
+101
+00:09:16,860 --> 00:09:21,730
+الرؤوس وبالتالي كان لابد من معالجة هذه المسألةنفس
+
+102
+00:09:21,730 --> 00:09:25,170
+الأمر هنا في قضية الأربعة والتلاتة في انكسار وفي
+
+103
+00:09:25,170 --> 00:09:29,310
+قضية الخمسة والاتنين في انكسار فلابد إذا من إجراء
+
+104
+00:09:29,310 --> 00:09:36,130
+حسابي بسيط لتعديل هذا السهم بما يحافظ على التوازن
+
+105
+00:09:36,130 --> 00:09:43,630
+بيننسبة حصة كل وارث مع غيره وأيضا للحفاظ على
+
+106
+00:09:43,630 --> 00:09:48,030
+التوازن بين الأسهم وأصل المسألة لأنه أنا لما بتعمل
+
+107
+00:09:48,030 --> 00:09:53,990
+أي إجراء حسابي يجب أن يشمل المسألة كاملة لأنه إذا
+
+108
+00:09:53,990 --> 00:10:00,030
+بدي أعدل مثلا هذا الفريق من الورثةلوحده بعيدا عن
+
+109
+00:10:00,030 --> 00:10:03,550
+غيره حيصير فيه خلل في المسألة أنا مثلا بدي أعالج
+
+110
+00:10:03,550 --> 00:10:08,190
+هذه بطريقة معينة بغض النظر شهية فإذا حيصير التعديل
+
+111
+00:10:08,190 --> 00:10:12,350
+عهد وعهد هيظل زي ما هو أيعقل ذلك؟ حيصير فيه خلل مش
+
+112
+00:10:12,350 --> 00:10:16,330
+حيصير فيه توازن صح ولا لا؟ فلذلك كان ينبغي من
+
+113
+00:10:16,330 --> 00:10:22,610
+إيجاد طريقتين تعادل هذا الانكسار بما يحفظ التوازن
+
+114
+00:10:22,610 --> 00:10:28,330
+بين جميع أسهم الورثة وأيضا يحافظ على أصل المسألة
+
+115
+00:10:28,540 --> 00:10:35,900
+تمام؟ لذلك موضوع تصحيح المسائل لابد إذا من النظر
+
+116
+00:10:35,900 --> 00:10:40,720
+في طبيعة المسألة وسنجد أن هناك احتمالين أن يكون
+
+117
+00:10:40,720 --> 00:10:46,240
+الانكسار مع فريق واحد من الورثة أو مع أكثر من فريق
+
+118
+00:10:46,240 --> 00:10:52,640
+من الورثة خلونا نتحدث عن أول حالة وهي ما لو كان
+
+119
+00:10:52,640 --> 00:10:57,840
+الانكسار مع فريق واحد من الورثة
+
+120
+00:11:07,660 --> 00:11:11,540
+إذا كنا تحدثنا عن تأصيل المسائل زي ما قلنا و تأصيل
+
+121
+00:11:11,540 --> 00:11:17,700
+المسائل بعد ما عملنا وجهنا موضوع الانكسار فكان
+
+122
+00:11:17,700 --> 00:11:21,560
+لابد من تصحيح المسائل على النحو الذي ذكرته قبل
+
+123
+00:11:21,560 --> 00:11:26,680
+قليل فإذا لابد من تعديل سهم الوارث حتى يقبل القسم
+
+124
+00:11:26,680 --> 00:11:30,960
+على عدد الرؤوس فلحظي معايا المسألة اللي قدامك
+
+125
+00:11:30,960 --> 00:11:38,460
+هتلاقي في انكسار بين أسهم البناتمع عدد رؤوسهم لأنه
+
+126
+00:11:38,460 --> 00:11:44,740
+16 و7 في انكسار 16 مابتكسمش على 7 كمان في عندك زي
+
+127
+00:11:44,740 --> 00:11:49,740
+ما انت ملاحظة انكسار في قضية أسهم الشقيقات اللي
+
+128
+00:11:49,740 --> 00:11:54,450
+لهم سهم 1 وعددهم 5لكن موضوع الزوجات مافي انكسار
+
+129
+00:11:54,450 --> 00:11:58,190
+لأن مع التلاتة مافي اي مشكلة عادي فكل واحدة هتاخد
+
+130
+00:11:58,190 --> 00:12:02,250
+سهم مع أنها اي مشكلة بمعنى مافي انكسار وموضوع
+
+131
+00:12:02,250 --> 00:12:07,110
+الجدات برضه مافي مشكلة لأن هم جدتين لهم أربع أسهم
+
+132
+00:12:07,110 --> 00:12:10,350
+وبالتالي طبيعي كل جدة لها سهمين إذا مافي عندنا اي
+
+133
+00:12:10,350 --> 00:12:14,890
+مشكلة المشكلة انحصرت فقطفي قضية نصيب البنات ونصيب
+
+134
+00:12:14,890 --> 00:12:19,530
+الخوات الشقيقات هذا بشكل عام الآن زي ما قلت أننا
+
+135
+00:12:19,530 --> 00:12:24,470
+نعالج الطريقة الأولى من المسائل أو القسم الأول من
+
+136
+00:12:24,470 --> 00:12:30,490
+المسائل وهي ما إذا وجد الانكسار مع فريق واحد من
+
+137
+00:12:30,490 --> 00:12:36,360
+الورثةبدنا نروح احنا نعالج هذه المسألة بالنظر في
+
+138
+00:12:36,360 --> 00:12:40,880
+عدد الأسهم و عدد الرؤوس دائما المقارنة هتكون بين
+
+139
+00:12:40,880 --> 00:12:45,820
+شو شو يعني أول خطوة بعملها بحل حال طبيعي بعدين
+
+140
+00:12:45,820 --> 00:12:49,640
+بوصل للأسهم بروح أقارن بين السهم و عدد الرؤوس
+
+141
+00:12:49,640 --> 00:12:54,920
+مستحقه فانا لما بقارن بقالاجي ممكن في انكسار و
+
+142
+00:12:54,920 --> 00:12:59,200
+ممكن مافيش انكسار فدائما دائما إذا عدد الرؤوس كان
+
+143
+00:12:59,200 --> 00:13:04,430
+واحد مستحيل يكون في عندي انكسارصح ولا صح؟ صح منطقي
+
+144
+00:13:04,430 --> 00:13:08,470
+وضمني هذا المفهوم أنه إذا عدد الرؤوس واحد طبيعي
+
+145
+00:13:08,470 --> 00:13:11,590
+مافي انكسار لأنه شو ما كان الأسهم بيكسب على الواحد
+
+146
+00:13:11,590 --> 00:13:16,970
+لكن الإشكال هي إذا تعددت الرؤوس وبالتالي صار في
+
+147
+00:13:16,970 --> 00:13:22,410
+انكسار بين عدد الأسهم وعدد الرؤوس لذلكبدنا نشوف
+
+148
+00:13:22,410 --> 00:13:26,730
+إنه القسم الأول كما قلت إنه كان فيه انكسار مع فريق
+
+149
+00:13:26,730 --> 00:13:31,650
+واحد من الورثة، فإيش بده أعمل حتى أعالج المسألة؟
+
+150
+00:13:31,650 --> 00:13:37,760
+بدي أقارن بين شوعدد الأسهم دائما المقارنة من تحت
+
+151
+00:13:37,760 --> 00:13:43,100
+لفُج و هقولك ليش مش من فُج لتحت، من تحت لفُج يعني
+
+152
+00:13:43,100 --> 00:13:46,820
+أسهم مع الرؤوس مش الرؤوس مع الأسهم لسبب بسيط،
+
+153
+00:13:46,820 --> 00:13:50,760
+أقولك إياها الجد، بدي أفترض عدد الرؤوس عندي أربعة
+
+154
+00:13:50,760 --> 00:13:55,060
+أو عفوان، عدد الرؤوس مثلا اتنين و الأسهم أربعة
+
+155
+00:13:56,260 --> 00:13:58,820
+الاربعة بتكسب مع اتنين، اذا مافيش عندي مشكلة، صح
+
+156
+00:13:58,820 --> 00:14:02,360
+ولا لأ؟ فانا لو روحت اعملت من فوق لتحت، هلاجي انه
+
+157
+00:14:02,360 --> 00:14:06,700
+في انكسار، مع انه مافيش انكسار، صح ولا لأ؟ فدائما
+
+158
+00:14:06,700 --> 00:14:12,780
+انا بقارن بين الأسهم والرؤوس، من تحت لفوق، تمام؟
+
+159
+00:14:12,840 --> 00:14:17,260
+هذه داخليا ناخدها عساس تسهل علينا ان اعرف فين كسار
+
+160
+00:14:17,260 --> 00:14:20,380
+او لا احنا في البداية ممكن نتغلب شويه بس كمان
+
+161
+00:14:20,380 --> 00:14:24,220
+محاضرة هنلاقي حالنا صيرنا علماء يعني الإمام زيد
+
+162
+00:14:24,220 --> 00:14:29,120
+هيحسدنا على الشطارة الموجودة عندنا تمام؟نجي الأن
+
+163
+00:14:29,120 --> 00:14:35,340
+إذا كان هناك انكسار مع فريق واحد من الورثة فإن
+
+164
+00:14:35,340 --> 00:14:40,740
+معالجة المسألة تكون بالمقارنة بين عدد أسهم الوارث
+
+165
+00:14:40,740 --> 00:14:47,640
+وعدد رؤوسه و بالمقارنة سأجد أن هناك ثلاثة احتمالات
+
+166
+00:14:47,640 --> 00:14:52,700
+اوعى تقولي أربع؟ مين تقولي ليش استثننا واحد منهم؟
+
+167
+00:14:53,060 --> 00:14:55,680
+الاحتمالات اللي كنا حكيناها في موضوع التأصيل، شو
+
+168
+00:14:55,680 --> 00:14:58,740
+هي الاحتمالات الأساسية اللي قلناها، تماثل، تداخل،
+
+169
+00:14:58,740 --> 00:15:02,540
+توافق، تباين، صح؟ هان بنقول الاحتمالات بس تلاتة
+
+170
+00:15:02,540 --> 00:15:04,120
+بدون التماثل، ليش؟
+
+171
+00:15:06,760 --> 00:15:10,980
+لأنه إذا تماثل فيش انكسار يا جماعة إذا تماثل فيش
+
+172
+00:15:10,980 --> 00:15:15,300
+انكسار لما أقول زي ما تول مثال تلاتة زوجة إلهم
+
+173
+00:15:15,300 --> 00:15:20,240
+تلات أسهم هي تماثل إذا مافيش انكسار يعني فيش مشكلة
+
+174
+00:15:20,240 --> 00:15:24,440
+أصبح المشكلة منحصرة فيما لو كان هناك تداخل أو
+
+175
+00:15:24,440 --> 00:15:29,160
+توافق أو تباين تمام؟ إذا نرجع نقول إذا وجد
+
+176
+00:15:29,160 --> 00:15:37,090
+الإنكسارمع فريق واحد من الورثة فإن علاج المسألة
+
+177
+00:15:37,090 --> 00:15:43,330
+يكون بشو بالمقارنة بين عدد أسهم الوارث وعدد رؤوسه
+
+178
+00:15:43,330 --> 00:15:49,210
+وبالمقارنة يتضح أن هناك ثلاثة احتمالات الاحتمال
+
+179
+00:15:49,210 --> 00:15:52,790
+الأول أن يكون .. هحكي سريعا بعدين ناخدهم واحد واحد
+
+180
+00:15:52,790 --> 00:15:58,520
+تمام؟الاحتمال الأول أن يكون هناك تداخل بين عدد
+
+181
+00:15:58,520 --> 00:16:05,200
+الأسهم وعدد الرؤوس فحينها نخرجه مصححا هذا المصحح
+
+182
+00:16:05,200 --> 00:16:11,420
+هو عدد الرؤوس على عدد الأسهم فالنتج بنضربه في كامل
+
+183
+00:16:11,420 --> 00:16:17,570
+المسألةأما إذا كان هناك توافق بين عدد الأسهم وعدد
+
+184
+00:16:17,570 --> 00:16:23,550
+الرؤوس فإن المصحح هو عدد الرؤوس على القاسم المشترك
+
+185
+00:16:23,550 --> 00:16:29,550
+بين الرقمين فهذا النتيجة اسمها الوفق بنضربها في
+
+186
+00:16:29,550 --> 00:16:33,750
+كامل المسألة اسمه المصحح بصير الاحتمال التالت أن
+
+187
+00:16:33,750 --> 00:16:41,070
+يكون هناك تباين بين عدد الأسهم مع عدد الرؤوسوإذا
+
+188
+00:16:41,070 --> 00:16:45,470
+كان هناك تباين فإن المصحح هو عدد الرؤوس بناخد عدد
+
+189
+00:16:45,470 --> 00:16:49,390
+الرؤوس و بنضربه في كامل المسألة و هيك بنكون علجنا
+
+190
+00:16:49,390 --> 00:16:52,890
+هذا الانكسار يلّا نشوف أول احتمال من هذه
+
+191
+00:16:52,890 --> 00:16:57,770
+الاحتمالات إذا قلنا بالمقارنة بينهم عدد الأسهم و
+
+192
+00:16:57,770 --> 00:17:01,910
+عدد الرؤوس يتضح أن هناك ثلاثة احتمالات الاحتمال
+
+193
+00:17:01,910 --> 00:17:08,550
+الأول من هذه الاحتمالات أن يكون هناك تداخل
+
+194
+00:17:09,960 --> 00:17:21,100
+ملوني المسألة زوجة و أربع بنت و عشرة أخشقيق و
+
+195
+00:17:21,100 --> 00:17:26,100
+خلصنا ركزوا معايا شوية بنحل حال طبيعي الزوجة جدش
+
+196
+00:17:26,100 --> 00:17:31,220
+إلها الثمن لوجود الفرق الوارث و هان طولتين و هان
+
+197
+00:17:31,220 --> 00:17:37,120
+عصبة المسألة من؟ قلت عصبة بالغير يا سمح؟ الله
+
+198
+00:17:37,120 --> 00:17:41,180
+يهديك يا رب عصبة بالنفس أخوة شقاء هدول معهم
+
+199
+00:17:41,180 --> 00:17:46,800
+الشقيقاتتمام؟ جماعة من هالجيت بدأ أحكيلك أنا في
+
+200
+00:17:46,800 --> 00:17:50,780
+قضية عشرة أخ كذا ممكن أحطلك ستة و تلاتين الفكرة
+
+201
+00:17:50,780 --> 00:17:54,740
+افتراضية عساس موضوع التصحيح بس عساس انطبق يعني أنا
+
+202
+00:17:54,740 --> 00:17:58,700
+بجيب أرقام عساس بس توضحلنا إيه اللي بنشرح فيه يعني
+
+203
+00:17:58,700 --> 00:18:05,410
+مش ضروري يكون الموضوع جد يعني تمام؟ تمامالمسألة من
+
+204
+00:18:05,410 --> 00:18:13,410
+24 الزوجة لها 3 أسهم البنات لهم 16 و الإخوة لهم 5
+
+205
+00:18:13,410 --> 00:18:22,250
+خلّيكم معايالحظة معايا أتحدث عن الانكسار بين فريق
+
+206
+00:18:22,250 --> 00:18:26,490
+واحد من الورثة نيجي واحد واحد تركزوا معايا الزوجة
+
+207
+00:18:26,490 --> 00:18:30,650
+في انكسار مش اي مشكلة لأنه من تحت لفوق مش من فوق
+
+208
+00:18:30,650 --> 00:18:34,670
+لتحت التلاتة والواحد في بناته منكسار لأ لأن
+
+209
+00:18:34,670 --> 00:18:39,170
+التلاتة بتكسب على الواحد تمام؟ بينما لو بدي افترض
+
+210
+00:18:39,170 --> 00:18:42,750
+هان واحد و هان تلاتة في انكسار مش موضوعنا ..حلو
+
+211
+00:18:42,750 --> 00:18:47,800
+الاربعتاش ..أفوان الستاش والاربعة مافيش انكسارلأن
+
+212
+00:18:47,800 --> 00:18:51,820
+ال 16 بتكسب على الأربعة، كل بنت إلها أربعة أسهم،
+
+213
+00:18:51,820 --> 00:18:55,440
+مافي عندنا مشكلة، مافي عندي مشكلة هنا، إذا هان فاش
+
+214
+00:18:55,440 --> 00:19:00,500
+مشكلة و هان فاش مشكلة نيجي للفريقة ده سنجد أن هناك
+
+215
+00:19:00,500 --> 00:19:05,400
+مشكلة، الخمسة بتكسب على العشرة؟ بتكسبش، أوقك
+
+216
+00:19:05,400 --> 00:19:08,680
+تقارني من فوق لتحت، لأنك لو بتجيولي عشرة و خمسة أه
+
+217
+00:19:08,680 --> 00:19:13,470
+بتكسب، فاش مشكلة، لأ، دائما من تحت لفوقمن تحت
+
+218
+00:19:13,470 --> 00:19:18,790
+لفوق، خمسة على عشرة، مش عشرة على خمسة، خمسة على
+
+219
+00:19:18,790 --> 00:19:22,490
+عشرة، هنلاقي فين كيصار لأن الخمسة ما بتجسم على
+
+220
+00:19:22,490 --> 00:19:25,930
+العشرة وبالتالي نيجي نقارن الخمسة والعشرة إيش في
+
+221
+00:19:25,930 --> 00:19:30,310
+بناتهم؟ تداخل، وصيرنا فاهمين شو يعني تداخل؟ لصغير؟
+
+222
+00:19:30,730 --> 00:19:34,830
+بيدخل في الكبير، الكبير من المضاعفات لصغير، الكبير
+
+223
+00:19:34,830 --> 00:19:38,370
+بيكسب على الصغير، هيك معناه التداخل، أخدناه، فإذا
+
+224
+00:19:38,370 --> 00:19:42,890
+الخمسة داخلة في العشرة، صح؟ تداخل، طيب، إذا وجد
+
+225
+00:19:42,890 --> 00:19:49,550
+هناك تداخلا بينعدد الأسهم وعدد الرؤوس فإنه لابد من
+
+226
+00:19:49,550 --> 00:19:55,550
+إيجاد مصحح حتى إيش انعالج المسألة والمصحح هنا هو
+
+227
+00:19:55,550 --> 00:20:00,250
+عدد الرؤوس على عدد الأسهم عدد الرؤوس لكبير على
+
+228
+00:20:00,250 --> 00:20:05,290
+صغير يعني عدد الرؤوس على عدد الأسهم إيش النتيجة؟
+
+229
+00:20:05,290 --> 00:20:08,630
+بنضربها في كامل المسألة إذا نيجي الأن بدنا نطلع
+
+230
+00:20:08,630 --> 00:20:14,140
+مصححو لحظة قلت قبل قليل بإن المعالجة بدها تكون
+
+231
+00:20:14,140 --> 00:20:18,040
+لكامل المسألة أنا لما بعالج هذا الفريق بدي أطلع
+
+232
+00:20:18,040 --> 00:20:23,380
+رقم أضربه في كامل المسألة حتى إيش؟ أحافظ على
+
+233
+00:20:23,380 --> 00:20:28,140
+التوازن لأن أنا لو بدي أضرب بس هذا الفريق معناته
+
+234
+00:20:28,140 --> 00:20:32,380
+هذا هيصير مثلا عشرة و هيظلهم زي ما هم طب جمعيهم
+
+235
+00:20:32,380 --> 00:20:36,590
+هتلاقيهم أكتر من 24 يعني صار في خللصار فيه خلط
+
+236
+00:20:36,590 --> 00:20:42,110
+فإذا أنا دائما في التصحيح بحاول أن أحافظ على
+
+237
+00:20:42,110 --> 00:20:48,330
+التوازن بين أسهم الورثة وبين أصل مسألتهم لذلك
+
+238
+00:20:48,330 --> 00:20:53,230
+المعالجة ينبغي أن تعالج المسألة كاملا بشكل كامل
+
+239
+00:20:53,230 --> 00:20:57,450
+حلو؟ وبالتالي نرجع نقول إذا في هذه المسألة المصححة
+
+240
+00:20:59,900 --> 00:21:03,360
+عند التداخل، أه هي الاحتمال الأول التداخل عند
+
+241
+00:21:03,360 --> 00:21:09,360
+التداخل بين الأسهم والرؤوس فلابد من إيجاد مصحح
+
+242
+00:21:09,360 --> 00:21:21,040
+بقسمة عدد الرؤوس على عدد الأسهميعني أنا بالمقارنة
+
+243
+00:21:21,040 --> 00:21:27,020
+أسهم رؤوس، بالجسم رؤوس أسهم، حلو؟ فإذا نيجي نجسم
+
+244
+00:21:27,020 --> 00:21:30,960
+عدد الرؤوس عشرة على خمسة ويساوي اتنين، إذا المصحح
+
+245
+00:21:30,960 --> 00:21:35,440
+عندي اتنين فبروح ضرب المسألة كل ياتها في اتنين،
+
+246
+00:21:35,440 --> 00:21:39,500
+فالمسألة هتصير من جداش؟ من تمانية وأربعين، لحظي
+
+247
+00:21:39,500 --> 00:21:45,060
+معايا صار عندي أصل جديد، هذا بنسميه الأصل الجامع،
+
+248
+00:21:45,060 --> 00:21:51,960
+تمام؟ الأصل الجامع، طيبفنضرب الأتنين في التلاتة
+
+249
+00:21:51,960 --> 00:21:56,500
+ستة الأتنين في الستاشر اتنين و تلاتين و هان عشرة
+
+250
+00:21:56,500 --> 00:22:00,780
+فلحظي معايا العشرة توزعت على الإخوة كل أخ صارله
+
+251
+00:22:00,780 --> 00:22:05,400
+ساهم فلحظي عساسي تتأكدي أنه ما صار في عندي خلال في
+
+252
+00:22:05,400 --> 00:22:11,640
+المسألة الآن الواحد من التمانية و أربعين هو نفسه
+
+253
+00:22:11,640 --> 00:22:16,360
+اللي هو النص من الأربعة و عشرين مش كان كل أخ له نص
+
+254
+00:22:17,190 --> 00:22:20,610
+صح ولا لأ؟ لأنه خمسة للعشرة، يعني الواحد إله نص،
+
+255
+00:22:20,610 --> 00:22:25,330
+كسر، فكان نص من أربع وعشرين، هلجيت واحد من تمانية
+
+256
+00:22:25,330 --> 00:22:28,830
+واربعين هي هي، نفس النسبة، نفس الأمر لما بدي أجي
+
+257
+00:22:28,830 --> 00:22:33,910
+أقول البنت الواحدة إلها تمانية من تمانية واربعين،
+
+258
+00:22:33,910 --> 00:22:38,360
+بعادل الأربع من أربع وعشرين، هو هويعني حفظت على
+
+259
+00:22:38,360 --> 00:22:44,180
+التوازن هنا الزوجة كان لها 3 من 24 صار لها 6 من 48
+
+260
+00:22:44,180 --> 00:22:49,640
+هي هي نفس النتيجة انا مالعبتش في المسألة فقط مسألة
+
+261
+00:22:49,640 --> 00:22:55,620
+حسابية الهدف منها ان اعدل سهم الوارث بحيث يقبل
+
+262
+00:22:55,620 --> 00:22:59,950
+القسم على عدد الرؤوسفلحظي معايا ما أصبح في خلل أنا
+
+263
+00:22:59,950 --> 00:23:05,390
+صحيح أنني يعني صححت المسألة عدّلت سهم الوارث لكن
+
+264
+00:23:05,390 --> 00:23:11,530
+تعديلي كان بما لا يخرج المسألة عن أصلها بمعنى أنني
+
+265
+00:23:11,530 --> 00:23:18,650
+حافظت على أسهم الورثة وأيضا على أصل مسألتهم علم؟
+
+266
+00:23:18,650 --> 00:23:23,730
+تمام؟ يارحمكم الله في أي سؤال يا جماعة قبل ما نروح
+
+267
+00:23:23,730 --> 00:23:29,290
+لاحتمال التاني؟مالناس كتير أنا مش فاهمة سكوتكم طب
+
+268
+00:23:29,290 --> 00:23:32,270
+رجيتك دكتورة بس في المسائل لما بيقولنا مثلا أول
+
+269
+00:23:32,270 --> 00:23:35,190
+حاجة هم نطلع زي هيك بعدين بنحلنا تقصيل المسألة
+
+270
+00:23:35,190 --> 00:23:39,790
+تقسيم التاريكة ده لو جبتنا مسألة تقسيم مش تقصيل
+
+271
+00:23:39,790 --> 00:23:44,450
+تقسيم التاريكة مش تقصيلين بالظبط ما هي الخطوات
+
+272
+00:23:44,450 --> 00:23:48,310
+كانت تالي هتصيرعشان هيك إذا لاحظتي لما كانت TGM
+
+273
+00:23:48,310 --> 00:23:52,950
+أمثلة فيها إشي بيكسمش فروح تغير الرقم، صح ولا لا؟
+
+274
+00:23:52,950 --> 00:23:56,530
+عشان بديش أوجعكوا في هذه الجثة، فأول خطوة بتعمليها
+
+275
+00:23:56,530 --> 00:24:00,070
+دائما في أي مسألة، بتوزع الفروض، بعدين الأصابات،
+
+276
+00:24:00,070 --> 00:24:04,290
+بعدين التقصيل، بعدين التصحيح، بعدين التقسيم، تقسيم
+
+277
+00:24:04,290 --> 00:24:04,570
+التريك
+
+278
+00:24:08,160 --> 00:24:11,580
+دائما اي مسألة بتمر عليها اول شي بعمل فيها الشو و
+
+279
+00:24:11,580 --> 00:24:14,840
+بوزع الفروض بعد الفروض العصابات لان الفرض قبل
+
+280
+00:24:14,840 --> 00:24:19,520
+العصابة فروض عصابات بعدين تأصيل المسألة بعد تأصيل
+
+281
+00:24:19,520 --> 00:24:23,560
+المسألة بشوف اذا في انكسار بصحح تصحيح بعدين بتجسم
+
+282
+00:24:23,560 --> 00:24:28,180
+تقسيم الترك لو معطيكي مبلغ المبلغ بتخليه على جمب
+
+283
+00:24:28,180 --> 00:24:33,200
+بتروحي اتصحح لو في تصحيح ثم بتقسمي علم؟ وبالتالي
+
+284
+00:24:33,200 --> 00:24:36,560
+انا لما بدي كون في عندي تركة بقسمها على 48 مش على
+
+285
+00:24:36,560 --> 00:24:43,210
+24 علم؟إذا نرجع نقول إذا وجد الإنكسار مع فريق واحد
+
+286
+00:24:43,210 --> 00:24:49,810
+من الورثة فإن معالجة المسألة يكون بالمقارنة بين
+
+287
+00:24:49,810 --> 00:24:56,270
+عدد أسهم الوارث مع عدد رؤوسه وبالمقارنة يتضح أن
+
+288
+00:24:56,270 --> 00:25:00,370
+هناك ثلاثة احتمالات الأول منها أن يكون بينهما
+
+289
+00:25:00,370 --> 00:25:08,010
+تداخلاوحينها فإن المصحح فإن
+
+290
+00:25:08,010 --> 00:25:15,530
+المصحح هوقسمة عدد الرؤوس على عدد الأسهم فالنتيجة
+
+291
+00:25:15,530 --> 00:25:19,150
+اسمها مصحح فبنضربها في المسألة كاملة الاحتمال
+
+292
+00:25:19,150 --> 00:25:25,050
+الثاني أن يكون بين المسائل أو عفوا بين الأسهم
+
+293
+00:25:25,050 --> 00:25:29,010
+والرؤوس توافق وصيرنا فاهمين شو يعني توافق يعني في
+
+294
+00:25:29,010 --> 00:25:33,970
+عامل مشترك بين الرقمين إذا كان بينهما توافقان
+
+295
+00:25:33,970 --> 00:25:40,940
+فإننا لابد من أن نخرج الوفق اللي هوالمصحح قسم
+
+296
+00:25:40,940 --> 00:25:46,380
+مشترك بعدين بنطلق الوفق اللي هو المصحح ويكون ذلك
+
+297
+00:25:46,380 --> 00:25:51,440
+كالتالي بعد ما طلق القسم المشترك بروح أجسم عدد
+
+298
+00:25:51,440 --> 00:25:55,380
+الرؤوس على القسم المشترك عدد الرؤوس على القسم
+
+299
+00:25:55,380 --> 00:25:59,940
+المشترك النتيجة مش القسم المشترك، النتيجة هي
+
+300
+00:25:59,940 --> 00:26:05,450
+المصححوليس القاسم المشترك هو المصحح النتيجة نتيجة
+
+301
+00:26:05,450 --> 00:26:09,990
+قسم الرؤوس على القاسم المشترك هي المصحح أو بنسميه
+
+302
+00:26:09,990 --> 00:26:14,450
+الوفق الوفق أو المصحح بنروح ضربين المسألة كاملا
+
+303
+00:26:14,450 --> 00:26:23,590
+فيه وبيانوا ذلك على النحو التالي يلا
+
+304
+00:26:23,590 --> 00:26:30,350
+نشوف هتخلصنا منه المثال ملوني
+
+305
+00:26:30,350 --> 00:26:30,870
+المسألة
+
+306
+00:26:35,590 --> 00:26:45,190
+زوجة، اتناشر بنت ابن واخد شقيقة وبس تمام، الآن
+
+307
+00:26:45,190 --> 00:26:51,290
+نيجي نحل الزوجة طمون لوجود الفرع الوارث وهدول
+
+308
+00:26:51,290 --> 00:26:58,140
+تلتين والشقيقة عصباء مع الغيرتمام جميل المسألة من
+
+309
+00:26:58,140 --> 00:27:03,720
+24 بمعنى لحد الآن حلنا عادي نفس الخطوات السابقة مش
+
+310
+00:27:03,720 --> 00:27:08,000
+إشي جديد وحتى موضوع التصحيح مش هالإشي يعني حاجة
+
+311
+00:27:08,000 --> 00:27:13,540
+بسيطة ان شاء الله تمام الآن تلاتة و هان ستاشر و
+
+312
+00:27:13,540 --> 00:27:19,660
+هان جداشر الباقي اللي هو خمسة فالآن لحظة معايا لأ
+
+313
+00:27:19,660 --> 00:27:24,740
+في خطأOkay، أه صحيح، الآن لحظة معايا الزوجة في
+
+314
+00:27:24,740 --> 00:27:28,680
+انكسار بين أسهمها؟ مافيش مشكلة، طيب الأخت الشقيقة
+
+315
+00:27:28,680 --> 00:27:33,180
+في مشكلة؟ لأ، دائما إذا عدد الرؤوس واحد مافيش أي
+
+316
+00:27:33,180 --> 00:27:35,700
+مشكلة، دائما إذا عدد الرؤوس واحد مافيش عندنا
+
+317
+00:27:35,700 --> 00:27:43,920
+مشاكل، نيجي الآن للاتناش والستاشيا ترى ال 16 بتجسم
+
+318
+00:27:43,920 --> 00:27:48,980
+على ال 12؟ لأ طيب ال 16 و ال 12 بيجربوا لبعض؟ أه
+
+319
+00:27:48,980 --> 00:27:53,680
+بيجربوا لبعض يعني في قاسم مشترك بينهم ال 12 عبارة
+
+320
+00:27:53,680 --> 00:27:59,200
+عن أربعة في تلاتة ال 16 أربعة في أربعة صح ولا لأ
+
+321
+00:27:59,200 --> 00:28:02,560
+أربعة في أربعة أربعة في تلاتة إذا القاسم المشترك
+
+322
+00:28:02,560 --> 00:28:07,520
+بينهما أربعة صح ولا لأ القاسم المشترك بين ال 16 و
+
+323
+00:28:07,520 --> 00:28:15,380
+ال 12 أربعةفإذا المصحح عبارة عن عدد الرؤوس على
+
+324
+00:28:15,380 --> 00:28:22,990
+القاسم المشتركعدد الرؤوس 12 هنا على القاسم المشترك
+
+325
+00:28:22,990 --> 00:28:28,610
+يعني على 4 ويساوي 3 فلحظي معايا ما تقول المصحح هو
+
+326
+00:28:28,610 --> 00:28:33,910
+القاسم المشترك اقعك اقعك تقول المصحح حينما يكون
+
+327
+00:28:33,910 --> 00:28:37,850
+التوافق هو القاسم المشترك لأ المصحح هو عدد الرؤوس
+
+328
+00:28:37,850 --> 00:28:42,930
+تقسيم القاسم المشترك فالنتيجة هي المصحح أو بنسميها
+
+329
+00:28:42,930 --> 00:28:47,920
+الوفقتمام؟ وبالتالي نيجي نجولهان المصحح في الحالة
+
+330
+00:28:47,920 --> 00:28:52,680
+التانية وهي التداخل عفوا التوافق
+
+331
+00:28:55,070 --> 00:29:00,590
+إذا كان هناك توافق فإن المصحح أو بنسميه الوفق
+
+332
+00:29:00,590 --> 00:29:06,270
+عبارة عن عدد الرؤوس على القاسم المشترك، تمام؟ عدد
+
+333
+00:29:06,270 --> 00:29:12,730
+الرؤوس على القاسم المشترك عدد الرؤوس كم هنا؟ اتناش
+
+334
+00:29:12,730 --> 00:29:17,000
+على القاسم المشتركو يساوي تلاتة فبنروح ضربين
+
+335
+00:29:17,000 --> 00:29:21,860
+المسألة كلها يتها في جداش في تلاتة نضرب المسألة
+
+336
+00:29:21,860 --> 00:29:26,680
+كلها ماتنساش تضرب الاصل كل حاجة بنضربه فهن عندنا
+
+337
+00:29:26,680 --> 00:29:32,620
+ستة اتنين و سبعين و هن تسعة و هن تمانتاش و تلاتين
+
+338
+00:29:32,620 --> 00:29:38,100
+تمانية و أربعين و هن خمستاش فنيجي نرجع الآن
+
+339
+00:29:38,100 --> 00:29:41,940
+التمانية و أربعين بتجسم على الأتناش؟ أه أربع بتجسم
+
+340
+00:29:42,720 --> 00:29:47,740
+تجسم وبالتالي خلصنا علجنا المسألة حلو؟ وبناء على
+
+341
+00:29:47,740 --> 00:29:52,060
+ذلك لو في عندي تاريخة بجسمها على شو؟ على الاتنين
+
+342
+00:29:52,060 --> 00:29:56,560
+فعلى هذا الأصل ولا هذا التغة تمام؟ لكن ما بنشطبه
+
+343
+00:29:56,560 --> 00:29:59,780
+بيضلوا لأن هو الأصل الأصلي سابق وانقلنا في عندي
+
+344
+00:29:59,780 --> 00:30:03,300
+أصل أصلي وفي أصول استثنائية حسب التعديل اللي صار
+
+345
+00:30:03,300 --> 00:30:09,340
+على المسألة كما قلنا سابقا تمام؟ حلو؟ إذا نرجع
+
+346
+00:30:09,340 --> 00:30:15,390
+نقولفي موضوع الانكسار مع فريق واحد من الورثة فلابد
+
+347
+00:30:15,390 --> 00:30:19,290
+من معالجة المسألة والمعالجة تكون بالنظر بينها
+
+348
+00:30:19,290 --> 00:30:23,990
+والمقارنة بينها عدد أسهم الوارث وعدد رؤوسه
+
+349
+00:30:23,990 --> 00:30:29,330
+وبالمقارنة يتضح أن هناك ثلاثة احتمالات الأول منها
+
+350
+00:30:29,330 --> 00:30:34,690
+أن يكون بينهما تداخلا حينها فإن المصحح هو عدد
+
+351
+00:30:34,690 --> 00:30:38,240
+الرؤوس على عدد الأسهموبنضربه بكامل المسألة
+
+352
+00:30:38,240 --> 00:30:43,700
+الاحتمال الثاني أن يكون بينهما توافقا وحينها فإن
+
+353
+00:30:43,700 --> 00:30:48,100
+المصحح هو عدد الرؤوس على القاسم المشترك بين
+
+354
+00:30:48,100 --> 00:30:53,790
+الرقمين تمام؟والاحتمال الثالث أن يكون بينهما
+
+355
+00:30:53,790 --> 00:30:59,670
+تباينا تباين شو يعني تباين؟ اختلاف يعني بيجربوش
+
+356
+00:30:59,670 --> 00:31:05,810
+لبعض، تمام؟ فإذا كان بينه عدد الأسهم وعدد الرؤوس
+
+357
+00:31:05,810 --> 00:31:11,970
+تباين فإن المصحح هو عدد الرؤوس بس المصحح هو عدد
+
+358
+00:31:11,970 --> 00:31:16,410
+الرؤوس بتاخد عدد الرؤوس بتضربيه في المسألة تمام؟
+
+359
+00:31:16,410 --> 00:31:26,810
+يلا نشوف مثال على ذلكإذا كان إذا فيه تباين مالوني
+
+360
+00:31:26,810 --> 00:31:35,950
+إذا
+
+361
+00:31:35,950 --> 00:31:40,910
+إذا كان فيه تباين فإن المصحح هو عدد الرؤوس يلا
+
+362
+00:31:40,910 --> 00:31:48,770
+نشوف اتنين زوجة اتنين بنت ابن
+
+363
+00:31:50,600 --> 00:32:03,780
+ابن أخ شقيق يالا انجب طمان طولتين و هاد هو العصب
+
+364
+00:32:03,780 --> 00:32:12,280
+المسألة من 24فهن تلاتة و هن ستاش و هن خمسة صح؟ هن
+
+365
+00:32:12,280 --> 00:32:16,860
+في انكسار؟ لأ هن في انكسار؟ برضه لأ طب هن في
+
+366
+00:32:16,860 --> 00:32:22,490
+انكسار؟ نعم بين التلاتة والاتنين في تباينبين
+
+367
+00:32:22,490 --> 00:32:26,690
+التلاتة والاتنين تباين إيش الحل إذا كان فيه تباين
+
+368
+00:32:26,690 --> 00:32:31,030
+بنضرب المسألة في عدد الرؤوس يعني ع السريع وانت
+
+369
+00:32:31,030 --> 00:32:35,630
+مغمضة أضرب المسألة في اتنين تمام فتعالى أضرب إيه
+
+370
+00:32:35,630 --> 00:32:40,590
+هان 48 و هان 6 لأنه هتصير ال 6 بتكسب على ال 2
+
+371
+00:32:40,590 --> 00:32:47,170
+مافيش مشاكل بعدين هان 32 و هان 10 فلحظة معايا حتى
+
+372
+00:32:47,170 --> 00:32:51,590
+لما عملنا تعديل على المسألةحافظنا على التوازن لأن
+
+373
+00:32:51,590 --> 00:32:57,150
+هذه اللي كان بياخد 5 من 24 صار بياخد 10 من 48 يعني
+
+374
+00:32:57,150 --> 00:33:01,910
+هي هي و هذا اللي لازم يصير لأنه ما بيصير أنا أعمل
+
+375
+00:33:01,910 --> 00:33:06,230
+معالجة و أتغير النسب المعالجة اللي بدي أعملها لازم
+
+376
+00:33:06,230 --> 00:33:09,950
+تحافظ على النسب تظلها زي ما هي كيف أنا بدي أحافظ
+
+377
+00:33:09,950 --> 00:33:13,730
+على النسب تظلها زي ما هي بعالج المسألة كاملا و ليس
+
+378
+00:33:13,730 --> 00:33:21,190
+فريقا واحدا علم؟ تمام؟نجي الآن للموضوع الثاني، في
+
+379
+00:33:21,190 --> 00:33:25,990
+أي سؤال قبل ما نروح للقسم الثاني؟ عالسريع بدي أجمل
+
+380
+00:33:25,990 --> 00:33:30,390
+و راح أكون سريعة أنه إذا وجد انكسار مع فريق واحد
+
+381
+00:33:30,390 --> 00:33:35,830
+من الورثة فإن معالجة المسألة يكون بتصحيحها وذلك
+
+382
+00:33:35,830 --> 00:33:40,130
+بالمقارنة بين عدد أسهم الوارث وعدد رؤوسه
+
+383
+00:33:40,130 --> 00:33:44,430
+وبالمقارنة يتضح أن هناك ثلاثة احتمالات الأول منها
+
+384
+00:33:44,430 --> 00:33:49,940
+أن يكون بينهما تداخلا فحينها فإنالمصحح هو عدد
+
+385
+00:33:49,940 --> 00:33:53,380
+الرؤوس على عدد الأسهم واحتمال أن يكون بينهما
+
+386
+00:33:53,380 --> 00:33:56,720
+توافقًا فإن المصحح يكون عدد الرؤوس على القاسم
+
+387
+00:33:56,720 --> 00:34:01,500
+المشترك واحتمال أن يكون بينهما تباينًا فإن المصحح
+
+388
+00:34:01,500 --> 00:34:07,300
+هو عدد الرؤوس أما إذا قسم الثاني إذا وجد الانكسار
+
+389
+00:34:07,300 --> 00:34:14,160
+بينأكثر من فريق من الورثة أو مع أكثر من فريق من
+
+390
+00:34:14,160 --> 00:34:18,580
+الورثة يعني كذا فريق حينها يا جماعة كده بتعالج
+
+391
+00:34:18,580 --> 00:34:22,400
+أكتر من فريقها مش فريق واحد المعالجة بتكون على
+
+392
+00:34:22,400 --> 00:34:26,600
+خطوتين على خطوتين ركزوا معايا بتحكي كلام نظري بحت
+
+393
+00:34:26,600 --> 00:34:29,900
+بعدين نرجع ناخد واحدة واحدة ركزوا سيبي الجلم من
+
+394
+00:34:29,900 --> 00:34:35,620
+إيدكالأن إذا كان في عندي انكسار مع أكتر من فريق،
+
+395
+00:34:35,620 --> 00:34:40,240
+بتعمل خطوة تانية، الخطوة الأولى اللى هى ما تحدثنا
+
+396
+00:34:40,240 --> 00:34:44,340
+عنه في القسم الأول بمعنى أنى بروح أعالج كل فريق
+
+397
+00:34:44,340 --> 00:34:48,620
+على حدا، بعالج هذا و بطلّعله مصحح بدون ماعمل إشي،
+
+398
+00:34:48,620 --> 00:34:51,760
+بدروفش في المسألة ولا شيء، بعدين بعالج الفريق
+
+399
+00:34:51,760 --> 00:34:55,160
+التاني و بطلّعله مصحححسب المقارن مش قولنا تالت
+
+400
+00:34:55,160 --> 00:34:59,000
+احتمالات و نفس الشيء لو في فريق تالت كمان بعالجه و
+
+401
+00:34:59,000 --> 00:35:02,460
+بطلعله مصحح هذه ايش الخطوة الأولى، اذا أنا الخطوة
+
+402
+00:35:02,460 --> 00:35:06,780
+الأولى بروح عالج كل فريق على حدا فلما علجت كل فريق
+
+403
+00:35:06,780 --> 00:35:11,000
+على حدا شوفر عندي كذا مصحح صار صح ولا لأ صار عندي
+
+404
+00:35:11,000 --> 00:35:15,740
+كذا مصحح فبروح للخطوة التانية و هي أن أقارن بين
+
+405
+00:35:15,740 --> 00:35:21,540
+المصححاتالخطوة التانية بقارن بين شو؟ بين المصححات
+
+406
+00:35:21,540 --> 00:35:25,740
+مش أنا لما روحت علاجة كل فريق على حدا طلعت لكل
+
+407
+00:35:25,740 --> 00:35:30,720
+فريق مصحح فصار عندي كذا مصحح صح ولا لا؟ فأنا لما
+
+408
+00:35:30,720 --> 00:35:35,780
+خلصت أطلع مصحح لكل فريق على حدا بنتقل للخطوة
+
+409
+00:35:35,780 --> 00:35:41,820
+الثانية وهي المقارنة بين المصححات وبالمقارنة بين
+
+410
+00:35:41,820 --> 00:35:47,910
+المصححات يتضح أن هناك أربعة احتمالات أربعةوهي أن
+
+411
+00:35:47,910 --> 00:35:53,150
+يكون بينها تماثلًا أو تداخلًا أو توافقًا أو
+
+412
+00:35:53,150 --> 00:35:58,370
+تباينًا فإذا كان بين المصححات تماثلًا فإن المصحح
+
+413
+00:35:58,370 --> 00:36:02,870
+العام لحظة قلنا قائد عام للقوات المسلحة مصحح عام
+
+414
+00:36:02,870 --> 00:36:06,710
+ليش قلنا مصحح عام؟ لأنه فيه مصححات صغيرة فأنا ما
+
+415
+00:36:06,710 --> 00:36:10,570
+بتعمل بيها بعد كده باخد مش مصحح عام على أي أساس
+
+416
+00:36:10,570 --> 00:36:13,950
+بدي أطلع هذا المصحح العام؟ وعلى أي أساس أنا بدي
+
+417
+00:36:13,950 --> 00:36:18,160
+أنتخبه و أجعله هو القائد؟على أساس المقارنة بين هذه
+
+418
+00:36:18,160 --> 00:36:22,520
+المصححات وبالمقارنة بينها يتضح أن هناك أربعة
+
+419
+00:36:22,520 --> 00:36:27,020
+احتمالات أن يكون تماثل فإن المصحح العام هو أحد هذه
+
+420
+00:36:27,020 --> 00:36:32,360
+المصححات خلصنا أن يكون بين المصححات تداخلا يعني في
+
+421
+00:36:32,360 --> 00:36:37,890
+إش كبير وإش صغير فبالتأكيد هناخد كبيرأو أن يكون
+
+422
+00:36:37,890 --> 00:36:41,370
+بين المصحيحات التوافق فبنضرب الأول في التاني على
+
+423
+00:36:41,370 --> 00:36:45,670
+العامل المشترك بينهما أو أن يكون بينها تباين
+
+424
+00:36:45,670 --> 00:36:49,230
+بنضربهم بعيد وخلصنا هاي موضوع التصحيح شوفته ما
+
+425
+00:36:49,230 --> 00:36:54,370
+أسهله؟ خلاص؟ نعتبر حالنا خلصنا؟ طيب يالا ع السريع
+
+426
+00:36:54,370 --> 00:36:59,290
+نشوف ترجمة الكلام اللي ذكرته وإن كان أظن أنه صار
+
+427
+00:36:59,290 --> 00:37:04,080
+مفهوم بالنسبة للعلمأذا إذا كان الانكسار ووجد
+
+428
+00:37:04,080 --> 00:37:09,100
+الانكسار مع أكثر من فريق من الورثة قلنا التصحيح
+
+429
+00:37:09,100 --> 00:37:13,440
+بدي يكون بإجراء خطوتين الخطوة الأولى أني بعالج كل
+
+430
+00:37:13,440 --> 00:37:17,460
+فريق على حدة خلصنا الخطوة التانية بروح أش أعمل
+
+431
+00:37:17,460 --> 00:37:22,480
+أقارن بين المصححات اللي طلعناها فنجي نشوف مسألة
+
+432
+00:37:22,480 --> 00:37:24,180
+ملوني هذه المسألة
+
+433
+00:37:30,580 --> 00:37:36,920
+في اي سؤال يا جماعة؟ طيب، غير مكانك، يالا، اه،
+
+434
+00:37:36,920 --> 00:37:40,500
+عسّر يالا،
+
+435
+00:37:40,500 --> 00:37:45,140
+هيك امشي، ايوة، كده، عسّر يالا، وين ما بدك، المهم
+
+436
+00:37:45,140 --> 00:37:52,400
+غير مكانك، اذا
+
+437
+00:37:52,400 --> 00:38:01,900
+زوجة، ستة أختلأنها لما جلت ست أخوة شقيقة يعني أخوة
+
+438
+00:38:01,900 --> 00:38:08,180
+شقيقة ست هيك مادام مرتبة لأ تمام ست خوات شقيقات
+
+439
+00:38:08,180 --> 00:38:12,520
+تمام حلو تلاتة عم شقيق
+
+440
+00:38:15,150 --> 00:38:20,350
+نجي الآن نحل المسألة حال طبيعي هذه ربع و هدول
+
+441
+00:38:20,350 --> 00:38:28,110
+تلتين و هد هو العصبة المسألة من اتناش تنسوش صح ولا
+
+442
+00:38:28,110 --> 00:38:34,890
+لأ؟ حلو فهن تلاتة هن تمانية و هن بيضل واحد نجي
+
+443
+00:38:34,890 --> 00:38:39,690
+نشوف هل جيت بالنسبة للزوجة فيش مشاكل؟ فيش مشاكل
+
+444
+00:38:39,690 --> 00:38:45,710
+هنلاقي المشاكل مع الخواتو مع العام، الأعمام مش
+
+445
+00:38:45,710 --> 00:38:49,310
+العام، تمام؟ لأن لو عام مافيش مشاكل أصلا، طبيعي
+
+446
+00:38:49,310 --> 00:38:53,530
+دائما لما يكون واحد مافيش مشاكل فحنلاجي المشاكل
+
+447
+00:38:53,530 --> 00:38:57,130
+بين فريقين فإيش قلنا الحل؟ هيكون كالتالي يا جماعة،
+
+448
+00:38:57,130 --> 00:39:01,610
+بروح أعالج كل فريق على حدة، بعالج كل فريق على حدة،
+
+449
+00:39:01,610 --> 00:39:05,610
+نيجي لهذا الفريق، التمانية والستة إيش في بناتهم؟
+
+450
+00:39:06,210 --> 00:39:12,490
+توافق، تمام، فإذا كان هناك توافق فإن المصحح هو عدد
+
+451
+00:39:12,490 --> 00:39:16,110
+الرؤوس على القاسم المشترك، إيش القاسم المشترك بين
+
+452
+00:39:16,110 --> 00:39:19,910
+أتهم؟ اتنين، لأن الست تلتة في اتنين والتمانية
+
+453
+00:39:19,910 --> 00:39:24,420
+أربعة في اتنين، فبنروح مجسمين الست على اتنينإذا
+
+454
+00:39:24,420 --> 00:39:28,580
+بتحطي هنا فوق لحالك تلاتة، بتحطي في دايرة، شو
+
+455
+00:39:28,580 --> 00:39:32,200
+يعني؟ أن المصحح تبع هذا الفريق، تحطي التلاتة هنا
+
+456
+00:39:32,200 --> 00:39:36,520
+فوق، تحطيهاش على الجانب، لأن هنحط المصحح العام،
+
+457
+00:39:36,520 --> 00:39:41,540
+القائد العام، تمام؟ حلونجي للفريق التاني، علاجنا
+
+458
+00:39:41,540 --> 00:39:46,660
+هذا خلصنا، بس لحظة لما بنعالجه، بنجف، بنروحش نضرب،
+
+459
+00:39:46,660 --> 00:39:51,140
+تجفي لأنه في خطوة تانية، تجفي، ماتضربيش، تمام؟
+
+460
+00:39:51,140 --> 00:39:55,280
+طيب، نجي للفريق التاني، بقارن بين الأسهم والرؤوس،
+
+461
+00:39:55,280 --> 00:39:59,640
+إيش بلاقي؟ تباين، الواحد والتلاتة تباين، فإذا
+
+462
+00:39:59,640 --> 00:40:03,260
+بناخد عدد الرؤوس، مش بقولنا لما يكون تباين، باخد
+
+463
+00:40:03,260 --> 00:40:09,810
+عدد الرؤوس، نجي للخطوة التانية، نقارن بيننقارن بين
+
+464
+00:40:09,810 --> 00:40:16,420
+إيش؟تمام فإذا هلجيت أنا بقارن بين المصححات بلاقي
+
+465
+00:40:16,420 --> 00:40:22,300
+في تماثل بين المصححات فإذا كان هناك تماثل بين
+
+466
+00:40:22,300 --> 00:40:27,960
+المصححات فإن .. فإننا نختار مصححا عاما هو أحد هذه
+
+467
+00:40:27,960 --> 00:40:32,280
+المصححات واحد فبنروح ضربين المسألة كل يدها في
+
+468
+00:40:32,280 --> 00:40:37,220
+تلاتة فالمسألة من ستة و تلاتين و هن تسعة و هن أربع
+
+469
+00:40:37,220 --> 00:40:43,680
+و عشرين و هنتلاتة فاللحظة معايا اتعالجت الانكسار
+
+470
+00:40:43,680 --> 00:40:47,560
+اللي هنا و هنتعالج الانكسار فما .. ماعدش عندي
+
+471
+00:40:47,560 --> 00:40:54,560
+انكسار علم؟ لأ حاضر تمام
+
+472
+00:40:54,560 --> 00:41:00,660
+حلو، الان التمانية والستة إيش في بناتهم؟ توافق، في
+
+473
+00:41:00,660 --> 00:41:03,460
+شو توافق؟ متوافقين في شو هما الإتنين؟ إيش العامل
+
+474
+00:41:03,460 --> 00:41:07,730
+المشترك بناتهم؟تلاتة في اتنين لأن ستة عبارة عن
+
+475
+00:41:07,730 --> 00:41:10,970
+تلاتة في اتنين والتمانية ايش اربع في اتنين حلو
+
+476
+00:41:10,970 --> 00:41:16,730
+فقلنا في القسم الأول من مسائل الانكسار انه اذا كان
+
+477
+00:41:16,730 --> 00:41:21,330
+في توافق المصحح اشهد عدد الرؤوف على القاسم المشترك
+
+478
+00:41:21,330 --> 00:41:25,370
+يعني ستة على اتنين تلاتةوهن في التباين و بناخد عدد
+
+479
+00:41:25,370 --> 00:41:28,810
+الرؤوس فالخطوة التانية بروح أقارن بين المصححات
+
+480
+00:41:28,810 --> 00:41:31,950
+تلاتة و تلاتة تماثل فبناخد واحد فبنروح ضربين
+
+481
+00:41:31,950 --> 00:41:36,310
+المسألة كلها في هذا المصحح تمام الاحتمال الأول
+
+482
+00:41:36,310 --> 00:41:40,770
+الاحتمال التاني أنه نفس الفكرة أنه انكسار مع كذا
+
+483
+00:41:40,770 --> 00:41:44,490
+فريق بنروح نعمل مصحح لكل واحد بنقارن لما بنقارن
+
+484
+00:41:44,490 --> 00:41:50,530
+بنلاقي تداخلوإذا كان هناك تداخلا بين المصححات فإن
+
+485
+00:41:50,530 --> 00:41:56,010
+المصحح العام هو المصحح الأكبر تمام؟ انشوف مثال
+
+486
+00:41:56,010 --> 00:42:02,750
+يالا
+
+487
+00:42:02,750 --> 00:42:11,710
+مالوني المسألة اتنين
+
+488
+00:42:11,710 --> 00:42:25,250
+زوجة اتنين زوجة تلاتين دولة32 بنت 16 جدة و جد تمام
+
+489
+00:42:25,250 --> 00:42:30,110
+خلّيكم معايا إذا الزوجتين مع بعض إلهم الطمون و
+
+490
+00:42:30,110 --> 00:42:35,090
+البنات إلهم طولتين و الجدات إلهم السدس و الجد إله
+
+491
+00:42:35,090 --> 00:42:42,870
+سدس زائد عصبة انحل المسألة أصلها من 24 فهان تلاتة
+
+492
+00:42:42,870 --> 00:42:51,970
+و هانست عشر و هان أربعة و هان أربعة زائد سين صح؟
+
+493
+00:42:52,980 --> 00:42:56,680
+حلو لأن أصل المسألة عائلة لأ سبعة وعشرين المسألة
+
+494
+00:42:56,680 --> 00:43:02,080
+صارت من سبعة وعشرين تعالوا نعدهم هي تسعة عشر واربع
+
+495
+00:43:02,080 --> 00:43:06,720
+تلاتة وعشرين واربع سبعة وعشرين فالمسألة عائلة أصلا
+
+496
+00:43:06,720 --> 00:43:11,740
+عالت فإذا صار عندي الأصل بنسمي الأصل العائل هذا
+
+497
+00:43:11,740 --> 00:43:15,820
+أصل أصلي و أصل عائل وعدي هشوف أصل كمان حاجة تانية
+
+498
+00:43:15,820 --> 00:43:19,760
+هذا أصل عائل تمام نيجي نشوف الآن ونعالج هاي
+
+499
+00:43:19,760 --> 00:43:30,590
+المسائل هان هنلاقي فانتصار صح؟حلو طيب
+
+500
+00:43:30,590 --> 00:43:35,670
+انشوف ال 16 وال 32 برضه فينكي صار؟طيب الأربع
+
+501
+00:43:35,670 --> 00:43:39,050
+والستاش برضه في انكسار مش ستاش و أربعة هه و مش
+
+502
+00:43:39,050 --> 00:43:41,390
+اتنين و تلاتين لو بدنا ناخد من فوق لتحت مافي
+
+503
+00:43:41,390 --> 00:43:45,470
+انكسار لأ بناخد من تحت لفوق عشان نتأكد فهن برضه في
+
+504
+00:43:45,470 --> 00:43:49,110
+انكسار فإذا في .. هن طبعا مافيش مشكلة لأنه واحد
+
+505
+00:43:49,110 --> 00:43:52,950
+طالما واحد دائما مافيش مشكلة نيجي نشوف و نعالج كل
+
+506
+00:43:52,950 --> 00:43:57,970
+فريق على حدة الفريق الأول تلاتة و اتنين تباين إذا
+
+507
+00:43:57,970 --> 00:44:04,290
+المصحح إيش هو؟ عدد الرؤوس عدد الرؤوسعدد الرؤوس
+
+508
+00:44:04,290 --> 00:44:09,770
+اللي جالت ستة نضربهم مش في بعض مع الفريق الواحد
+
+509
+00:44:09,770 --> 00:44:12,950
+بنضربش في بعض بناخد عدد الرؤوس لما يكون فيه تباين
+
+510
+00:44:14,330 --> 00:44:23,290
+الـ 16 و 32 تداخل لأنه 16 داخلة في ال 32 32 ع 16 2
+
+511
+00:44:23,290 --> 00:44:28,230
+صح ولا لأ فإذا كان هناك تداخل بنجسم 32 ع 16 مش
+
+512
+00:44:28,230 --> 00:44:34,610
+قولنا عدد الرؤوس على عدد الأسهم 32 ع 16 يعني 2 صح
+
+513
+00:44:34,610 --> 00:44:41,810
+ولا لأ طيب نشوف الفريق التالتالاربع والستاش برضه
+
+514
+00:44:41,810 --> 00:44:47,590
+تداخل .. تداخل فبنروح مجسمين ستاش على اربع .. اربع
+
+515
+00:44:48,320 --> 00:44:53,060
+صح ولا لأ؟ تمام الخطوة التانية بروح أقارن بين
+
+516
+00:44:53,060 --> 00:44:58,700
+المصححات و بالمقارنة يتضح أن هناك تداخل اتنين و
+
+517
+00:44:58,700 --> 00:45:01,800
+اتنين تماثل بناخد واحد، الأتنين و الأربع تداخل
+
+518
+00:45:01,800 --> 00:45:07,160
+فبناخد الكبير، إذا المصحح الأعم هو أربع فبنروح
+
+519
+00:45:07,160 --> 00:45:11,340
+ضربين المسألة كل ياتها في أربعفبتضرب السابع وعشرين
+
+520
+00:45:11,340 --> 00:45:14,700
+مش الاربع وعشرين ها السابع وعشرين سبع وعشرين في
+
+521
+00:45:14,700 --> 00:45:20,920
+أربعة تمانين و تمانية وعشرين تمانية وتسعين صح او
+
+522
+00:45:20,920 --> 00:45:29,140
+واحد وعشرين صحمية و تمانية و هان اتناش و هان
+
+523
+00:45:29,140 --> 00:45:36,060
+اربعين و اربع و عشرين اربع و ستين و هان ستاش و هان
+
+524
+00:45:36,060 --> 00:45:40,780
+ستاش فاللحظة معايا ماعدش فيه انكسار هان ماعدش فيه
+
+525
+00:45:40,780 --> 00:45:45,340
+انكسار و هان ماعدش فيه انكسار هذا بالنسبة لموضوع
+
+526
+00:45:45,340 --> 00:45:50,220
+التداخل او الاحتمال التاني ناخد الاحتمال التالت
+
+527
+00:45:50,220 --> 00:45:56,860
+وبه نختم تمام الاحتمال التالتإنه يكون بين المصححات
+
+528
+00:45:56,860 --> 00:46:02,180
+توافق يكون بين المصححات توافق فإذا كان بين
+
+529
+00:46:02,180 --> 00:46:07,500
+المصححات توافق فإن المصحح العام هو حاصل ضرب الأول
+
+530
+00:46:07,500 --> 00:46:16,060
+في التاني على القاسم المشترك بينهما تمام؟ حلو؟ يلا
+
+531
+00:46:16,060 --> 00:46:20,180
+نشوف ملوني
+
+532
+00:46:20,180 --> 00:46:27,830
+المثال الأخير وبه نختم ان شاء اللهع السريع يالا
+
+533
+00:46:27,830 --> 00:46:35,570
+زوجة
+
+534
+00:46:35,570 --> 00:46:38,830
+خمس
+
+535
+00:46:38,830 --> 00:46:41,870
+عشر يناير عشرة أكشر
+
+536
+00:46:46,750 --> 00:46:52,230
+و بعدين خلاص كده؟ الزوجة تمن لوجود الفرع الوارث و
+
+537
+00:46:52,230 --> 00:46:59,130
+هان تلتان و هان عصباء من أربع عشرين، تلاتة، ستاشر،
+
+538
+00:46:59,130 --> 00:47:02,570
+خمسة، تمام؟ يلّا تعالوا نشوف، طبعا الزوجة مافي
+
+539
+00:47:02,570 --> 00:47:08,380
+انكسار، مافي مشكلةفي تباين و هنا في انكسار، انكسار
+
+540
+00:47:08,380 --> 00:47:12,600
+و انكسار، حلو؟ فالان هان في تباين إذا بناخد عدد
+
+541
+00:47:12,600 --> 00:47:16,880
+الرؤوس، هان برضه في تباين بناخد عدد الرؤوس، صح ولا
+
+542
+00:47:16,880 --> 00:47:21,500
+لأ؟ لأن نقطة ستاش و خمستاش بيجربوش لبعد، و الخمسة
+
+543
+00:47:21,500 --> 00:47:23,920
+و الأتناش بيجربوش لبعد، فبناخد هان عدد الرؤوس و
+
+544
+00:47:23,920 --> 00:47:27,370
+هان عدد الرؤوسفبنلاقي الخمستاش و الأتناش إيش في
+
+545
+00:47:27,370 --> 00:47:32,450
+بناتهم؟ توافق، إذا كان هناك توافق بين المصححات فإن
+
+546
+00:47:32,450 --> 00:47:36,370
+المصحح الأعم هو حاصل ضرب الأول في التاني على
+
+547
+00:47:36,370 --> 00:47:40,130
+القاسم المشترك بينهما، شهو القاسم المشترك بينهم؟
+
+548
+00:47:40,130 --> 00:47:44,750
+تلاتة، الخمستاش عبارة عن شو؟خمسة في تلاتة و هان
+
+549
+00:47:44,750 --> 00:47:48,370
+أربعة في تلاتة فبنروح ضربين خمستاشف اتناش على
+
+550
+00:47:48,370 --> 00:47:54,250
+تلاتة يعني ستين تمام لأنه لما اتجسمي على تلاتة هان
+
+551
+00:47:54,250 --> 00:47:57,690
+أربعة أربعة في خمستاشف ستين تمام إذا تضربي خمستاشف
+
+552
+00:47:57,690 --> 00:48:04,550
+ضرب اتناش على تلاتة فإذا المصحح العام هنا إيش
+
+553
+00:48:04,550 --> 00:48:13,610
+المصحح الأول ضرب الثانيعلى القاسم المشترك بينهما
+
+554
+00:48:13,610 --> 00:48:17,270
+تمام وبالتالي روحنا نضرب المسألة في ايش؟ في ستين
+
+555
+00:48:17,270 --> 00:48:21,970
+اضرب المسألة في ستين وخلصنا تمام هذا ما يتعلق
+
+556
+00:48:21,970 --> 00:48:25,710
+بموضوع محاضرتنا لهذا اليوم المحاضرة القادمة بإذن
+
+557
+00:48:25,710 --> 00:48:30,620
+الله نكمل حديثنا حول التصحيحثم نتحدث عن أقسام
+
+558
+00:48:30,620 --> 00:48:34,760
+المسائل أقول قولي هذا وأستغفر الله لي ولكم وصلى
+
+559
+00:48:34,760 --> 00:48:38,500
+اللهم وسلم وبارك على سيدنا محمد والسلام عليكم
+
+560
+00:48:38,500 --> 00:48:40,300
+ورحمة الله تعالى وبركاته
+
diff --git a/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/QvNoIgEvgbk_raw.json b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/QvNoIgEvgbk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..16feb8130f4681636e8fe53307013c6bdfd3b349
--- /dev/null
+++ b/PL9fwy3NUQKwa4Cbi5tmhrHaJlOXc6GmAK/QvNoIgEvgbk_raw.json
@@ -0,0 +1 @@
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