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+{"segments": [{"id": 1, "seek": 2593, "start": 4.93, "end": 25.93, "text": "بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة والسلام على سيدنا محمد وعلى آله وصحبه أجمعين هذه المحاضرة رقم عشرين في مساق تحليل حقيقه اتنين لطلاب وطالبات الجامعة الإسلامية كلية العلوم قسم 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, 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, 6225, 46309, 9957, 8978, 47524, 995, 4587, 6055, 5016, 20292, 1211, 11331, 38436, 4587, 3224, 1975, 2655, 1863, 9957, 5296, 9566, 15040, 3555, 4032, 9566, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 28242, 10632, 18863, 1211, 20498, 12174, 38251, 12602, 1829, 46958, 1829, 9307], "avg_logprob": -0.06588041216421586, 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هنستكمل الحديث في ال section الأول اللي وجفنا عند نقطة فيه اللي هو ال section كان تحت عنوان born twice and uniform convergence", "tokens": [3224, 1863, 14851, 24793, 1211, 45595, 20498, 21542, 16254, 12984, 8978, 7187, 1649, 13672, 1829, 31439, 22978, 295, 6828, 20666, 19913, 3555, 9566, 8032, 1863, 14851, 24793, 1211, 21542, 16254, 12984, 8978, 2423, 3541, 16247, 12610, 13672, 1829, 49610, 5172, 8315, 43242, 8717, 47432, 3660, 8978, 3224, 13672, 1829, 31439, 2423, 3541, 25961, 6055, 33753, 18871, 2407, 7649, 4232, 6091, 293, 9452, 32181], "avg_logprob": -0.13195800315588713, "compression_ratio": 1.6022099447513811, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 27.36, "end": 28.4, "word": "هنستكمل", "probability": 0.876171875}, {"start": 28.4, "end": 29.1, "word": " اليوم", "probability": 0.936767578125}, {"start": 29.1, "end": 30.08, "word": " الحديث", "probability": 0.98779296875}, {"start": 30.08, "end": 30.28, "word": " في", "probability": 0.9638671875}, {"start": 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91.77, "word": " 1", "probability": 0.83447265625}, {"start": 91.77, "end": 92.07, "word": " على", "probability": 0.82421875}, {"start": 92.07, "end": 92.37, "word": " n", "probability": 0.60888671875}, {"start": 92.37, "end": 92.99, "word": " sin", "probability": 0.638671875}, {"start": 92.99, "end": 93.31, "word": " n", "probability": 0.87060546875}, {"start": 93.31, "end": 93.63, "word": " x", "probability": 0.7421875}, {"start": 93.63, "end": 93.93, "word": " زائد", "probability": 0.8323567708333334}, {"start": 93.93, "end": 94.09, "word": " n", "probability": 0.84619140625}, {"start": 94.09, "end": 94.41, "word": " قلنا", "probability": 0.8126627604166666}, {"start": 94.41, "end": 94.71, "word": " هذه", "probability": 0.595703125}, {"start": 94.71, "end": 94.85, "word": " ال", "probability": 0.9013671875}, {"start": 94.85, "end": 95.15, "word": " sequence", "probability": 0.75341796875}, {"start": 95.15, "end": 95.37, "word": " of", "probability": 0.9052734375}, {"start": 95.37, 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"probability": 0.732666015625}, {"start": 102.93, "end": 103.41, "word": " آخر", "probability": 0.8701171875}], "temperature": 1.0}, {"id": 5, "seek": 12526, "start": 103.56, "end": 125.26, "text": "على الـ Point Convergence على كل R الآن إيجينا بعد هيك اللي أخدنا لمّا و كيف اللي هو ان ترجم شو معناته Fn Converges Point Twice قولنا الـ K اللي بيلاقيها بتعتمد على Y و X في ال Point Twice لإنه نقطة نقطة ال convergence", "tokens": [3615, 23942, 2423, 39184, 12387, 2656, 331, 15260, 15844, 28242, 497, 6024, 48506, 11933, 1829, 7435, 1829, 8315, 39182, 39896, 4117, 13672, 1829, 5551, 9778, 3215, 8315, 32767, 11703, 995, 4032, 9122, 33911, 13672, 1829, 31439, 16472, 6055, 47341, 2304, 13412, 2407, 20449, 8315, 47395, 479, 77, 2656, 331, 2880, 12387, 46964, 12174, 12610, 8315, 2423, 39184, 591, 13672, 1829, 4724, 1829, 15040, 38436, 11296, 39894, 34268, 2304, 3215, 15844, 398, 4032, 1783, 8978, 2423, 12387, 46964, 5296, 28814, 1863, 3224, 8717, 47432, 3660, 8717, 47432, 3660, 2423, 32181], 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"word": " X", "probability": 0.8095703125}, {"start": 122.22, "end": 122.74, "word": " في", "probability": 0.88623046875}, {"start": 122.74, "end": 122.88, "word": " ال", "probability": 0.8369140625}, {"start": 122.88, "end": 123.24, "word": " Point", "probability": 0.38623046875}, {"start": 123.24, "end": 123.66, "word": " Twice", "probability": 0.88623046875}, {"start": 123.66, "end": 124.04, "word": " لإنه", "probability": 0.82257080078125}, {"start": 124.04, "end": 124.36, "word": " نقطة", "probability": 0.974609375}, {"start": 124.36, "end": 124.72, "word": " نقطة", "probability": 0.97705078125}, {"start": 124.72, "end": 124.8, "word": " ال", "probability": 0.92041015625}, {"start": 124.8, "end": 125.26, "word": " convergence", "probability": 0.5791015625}], "temperature": 1.0}, {"id": 6, "seek": 14591, "start": 126.07, "end": 145.91, "text": "و بعدين اجينا عرفنا شو معناه uniform convergence و قولنا في حالة ال uniform convergence هيكون عندي اللي هو ال K اللي بنلاقيها بس بتعتمد على ال epsilon و الباقي زي ما هو يعني بتنفع ال K هذه لكل ال Xات اللي في ال A note عشان هيك بنسمي uniform convergence", "tokens": [2407, 39182, 9957, 1975, 7435, 1829, 8315, 6225, 28480, 8315, 13412, 2407, 20449, 8315, 3224, 9452, 32181, 4032, 12174, 12610, 8315, 8978, 11331, 6027, 3660, 2423, 9452, 32181, 39896, 30544, 18871, 16254, 13672, 1829, 31439, 2423, 591, 13672, 1829, 44945, 15040, 38436, 11296, 4724, 3794, 39894, 34268, 2304, 3215, 15844, 2423, 17889, 4032, 29739, 995, 38436, 30767, 1829, 19446, 31439, 37495, 22653, 39894, 1863, 5172, 3615, 2423, 591, 29538, 5296, 28820, 2423, 1783, 9307, 13672, 1829, 8978, 2423, 316, 3637, 6225, 8592, 7649, 39896, 4117, 44945, 38251, 1829, 9452, 32181], "avg_logprob": -0.25085852041349305, "compression_ratio": 1.7741935483870968, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 126.07, "end": 126.25, "word": "و", "probability": 0.344482421875}, {"start": 126.25, "end": 126.87, "word": " بعدين", "probability": 0.888916015625}, 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1.0}, {"id": 7, "seek": 16338, "start": 146.57, "end": 163.39, "text": "وقلنا إذا كانت الـ sequence uniformly convergence أكيد هتكون convergence و بعدين أخدنا ال criterion أو اللمّة اللي بننفي فيها أو بنقول شو معناه Fn does not converge uniformly to اللي هو function F", "tokens": [2407, 4587, 1211, 8315, 11933, 15730, 25961, 2655, 2423, 39184, 8310, 48806, 32181, 5551, 4117, 25708, 8032, 2655, 30544, 32181, 4032, 39182, 9957, 5551, 9778, 3215, 8315, 2423, 46691, 34051, 13672, 2304, 11703, 3660, 13672, 1829, 44945, 1863, 5172, 1829, 8978, 11296, 34051, 44945, 39648, 13412, 2407, 20449, 8315, 3224, 479, 77, 775, 406, 41881, 48806, 281, 13672, 1829, 31439, 2445, 479], "avg_logprob": -0.27926588531524416, "compression_ratio": 1.4891304347826086, "no_speech_prob": 0.0, "words": [{"start": 146.57, "end": 147.17, "word": "وقلنا", "probability": 0.61865234375}, {"start": 147.17, "end": 147.43, "word": " إذا", "probability": 0.742431640625}, {"start": 147.43, "end": 147.77, "word": " كانت", 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"probability": 0.7431640625}, {"start": 153.17, "end": 153.49, "word": " أو", "probability": 0.93212890625}, {"start": 153.49, "end": 154.17, "word": " اللمّة", "probability": 0.74993896484375}, {"start": 154.17, "end": 155.07, "word": " اللي", "probability": 0.91552734375}, {"start": 155.07, "end": 155.85, "word": " بننفي", "probability": 0.6617431640625}, {"start": 155.85, "end": 156.23, "word": " فيها", "probability": 0.986572265625}, {"start": 156.23, "end": 156.39, "word": " أو", "probability": 0.85693359375}, {"start": 156.39, "end": 156.87, "word": " بنقول", "probability": 0.958251953125}, {"start": 156.87, "end": 157.23, "word": " شو", "probability": 0.809326171875}, {"start": 157.23, "end": 157.63, "word": " معناه", "probability": 0.7408040364583334}, {"start": 157.63, "end": 158.21, "word": " Fn", "probability": 0.1778564453125}, {"start": 158.21, "end": 158.45, "word": " does", "probability": 0.37939453125}, {"start": 158.45, "end": 158.75, "word": " not", "probability": 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does not converge uniformly to مين؟ to G وهذا مثال عليه اللي هو does not converge uniformly على الـ G مثال على اللي هو توظيف هذه النظرية الجابلة بشوية لإثبات عدم ال uniformly", "tokens": [1863, 4587, 9381, 2423, 39184, 460, 4724, 43042, 3224, 39896, 32887, 5016, 15844, 3714, 9957, 22807, 15844, 25062, 32640, 3660, 36764, 24401, 37495, 22653, 37893, 39896, 32887, 5016, 24976, 3794, 5172, 2288, 37495, 22653, 11933, 15730, 14111, 46411, 775, 406, 41881, 48806, 281, 3714, 9957, 22807, 281, 460, 37037, 15730, 50113, 6027, 47356, 13672, 1829, 31439, 775, 406, 41881, 48806, 15844, 2423, 39184, 460, 50113, 6027, 15844, 13672, 1829, 31439, 33427, 19913, 33911, 29538, 28239, 19913, 2288, 10632, 25724, 16758, 37977, 4724, 8592, 2407, 10632, 5296, 28814, 12984, 3555, 9307, 6225, 40448, 2423, 48806], "avg_logprob": -0.2054276356571599, "compression_ratio": 1.7533632286995515, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 534.83, "end": 535.45, "word": "نقص", "probability": 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{"start": 784.61, "end": 785.37, "word": " شوف", "probability": 0.90869140625}, {"start": 785.37, "end": 785.71, "word": " الآن", "probability": 0.733154296875}, {"start": 785.71, "end": 785.91, "word": " كيف", "probability": 0.92724609375}, {"start": 785.91, "end": 786.17, "word": " بدنا", "probability": 0.95751953125}, {"start": 786.17, "end": 786.89, "word": " نثبت", "probability": 0.9962158203125}, {"start": 786.89, "end": 787.91, "word": " خلصنا", "probability": 0.969482421875}, {"start": 787.91, "end": 788.29, "word": " من", "probability": 0.95166015625}, {"start": 788.29, "end": 788.71, "word": " انه", "probability": 0.40533447265625}, {"start": 788.71, "end": 788.93, "word": " احنا", "probability": 0.9153645833333334}, {"start": 788.93, "end": 789.39, "word": " نثبت", "probability": 0.9947509765625}, {"start": 789.39, "end": 789.77, "word": " fn", "probability": 0.922607421875}, {"start": 789.77, "end": 790.07, "word": " x", "probability": 0.466552734375}, {"start": 790.07, 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ان", "probability": 0.7705078125}, {"start": 796.87, "end": 797.33, "word": " fn", "probability": 0.798583984375}, {"start": 797.33, "end": 797.57, "word": " does", "probability": 0.5400390625}, {"start": 797.57, "end": 797.83, "word": " not", "probability": 0.95751953125}, {"start": 797.83, "end": 798.35, "word": " converge", "probability": 0.9873046875}, {"start": 798.35, "end": 799.01, "word": " uniformly", "probability": 0.97998046875}, {"start": 799.01, "end": 799.67, "word": " لل", "probability": 0.6796875}, {"start": 799.67, "end": 800.07, "word": " function", "probability": 0.56201171875}, {"start": 800.07, "end": 800.55, "word": " f", "probability": 0.89599609375}, {"start": 800.55, "end": 800.93, "word": " on", "probability": 0.912109375}, {"start": 800.93, "end": 801.19, "word": " R", "probability": 0.92529296875}], "temperature": 1.0}, {"id": 36, "seek": 82294, "start": 801.44, "end": 822.94, "text": "اللي هو زي ما قلنا الـ sequence of functions عندي هنا are not bounded functions so we can't use our لمّة اللي قبل بشوية اللي هي normal of a نقص of a converges to zero إذا هنتضرر نروح للتعريف أو للمّة قبلها إذا بتتذكروا اللمّة قلنا of a that does not converge", "tokens": [6027, 20292, 31439, 30767, 1829, 19446, 12174, 1211, 8315, 2423, 39184, 8310, 295, 6828, 18871, 16254, 34105, 366, 406, 37498, 6828, 370, 321, 393, 380, 764, 527, 32767, 11703, 3660, 13672, 1829, 12174, 36150, 4724, 8592, 2407, 10632, 13672, 1829, 39896, 2710, 295, 257, 8717, 4587, 9381, 295, 257, 9652, 2880, 281, 4018, 11933, 15730, 8032, 29399, 11242, 2288, 2288, 8717, 32887, 5016, 24976, 2655, 3615, 16572, 5172, 34051, 5296, 19528, 11703, 3660, 12174, 36150, 11296, 11933, 15730, 39894, 2655, 8848, 37983, 14407, 13672, 2304, 11703, 3660, 12174, 1211, 8315, 295, 257, 300, 775, 406, 41881], "avg_logprob": -0.28785439127499296, "compression_ratio": 1.5384615384615385, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 801.44, "end": 801.72, "word": "اللي", "probability": 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اللي هي اصغر منه بيطلع حد اكبر من الابسلونوت بيكون خلصناه ده نشوف كيف عندي fn of x ايش بالساوي x على n", "tokens": [11622, 1829, 19446, 6225, 42213, 8315, 9673, 25720, 9673, 46958, 10632, 27188, 4117, 25720, 16472, 3224, 2423, 7649, 2423, 283, 77, 74, 295, 2031, 74, 8717, 9778, 20292, 11296, 6225, 3555, 9640, 3660, 18871, 38637, 16758, 2655, 45164, 16490, 1211, 8315, 11296, 38637, 16758, 2655, 37037, 24192, 23032, 3555, 3615, 995, 8608, 5172, 2288, 4724, 1829, 9381, 13546, 6024, 104, 16758, 2655, 5551, 4117, 26890, 4724, 1829, 9566, 1211, 3615, 38637, 16758, 2655, 16490, 2304, 3794, 3660, 8608, 2655, 3660, 8608, 3555, 27884, 36764, 24401, 1975, 2655, 1863, 9957, 44945, 46456, 9640, 1975, 3555, 3794, 1211, 11536, 35473, 13672, 1829, 39896, 1975, 9381, 17082, 2288, 9154, 3224, 4724, 1829, 9566, 1211, 3615, 11331, 3215, 1975, 4117, 26890, 9154, 2423, 16758, 3794, 1211, 11536, 35473, 4724, 1829, 30544, 16490, 1211, 9381, 8315, 3224, 11778, 3224, 8717, 8592, 38688, 9122, 33911, 18871, 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subsequence يعني اللي هي الـ NK اخترناها الـ K بيصير اللي هي FNK اللي هي of X بيساوي FK of X بيصير هذا K X على K طب ال X ايش نختارها عشان نخلي هذا ثابت اختارها", "tokens": [1211, 2407, 10874, 1829, 8315, 1975, 46456, 2288, 8315, 13672, 1829, 31439, 2423, 39184, 426, 42, 2423, 39184, 426, 42, 2423, 39184, 13924, 655, 37495, 22653, 13672, 1829, 39896, 2423, 39184, 426, 42, 1975, 46456, 2288, 8315, 11296, 2423, 39184, 591, 4724, 1829, 9381, 13546, 13672, 1829, 39896, 479, 45, 42, 13672, 1829, 39896, 295, 1783, 4724, 1829, 3794, 995, 45865, 479, 42, 295, 1783, 4724, 1829, 9381, 13546, 23758, 591, 1783, 15844, 591, 23032, 3555, 2423, 1783, 1975, 1829, 8592, 8717, 46456, 9640, 11296, 6225, 8592, 7649, 8717, 9778, 20292, 23758, 38637, 16758, 2655, 1975, 46456, 9640, 11296], "avg_logprob": -0.1793750010430813, "compression_ratio": 1.8994082840236686, "no_speech_prob": 4.827976226806641e-06, "words": [{"start": 901.02, "end": 901.4, "word": "لو", "probability": 0.92333984375}, {"start": 901.4, 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{"start": 913.3, "end": 913.54, "word": " X", "probability": 0.94775390625}, {"start": 913.54, "end": 914.08, "word": " بيساوي", "probability": 0.798828125}, {"start": 914.08, "end": 914.86, "word": " FK", "probability": 0.929443359375}, {"start": 914.86, "end": 915.1, "word": " of", "probability": 0.96484375}, {"start": 915.1, "end": 915.52, "word": " X", "probability": 0.9970703125}, {"start": 915.52, "end": 916.7, "word": " بيصير", "probability": 0.9603271484375}, {"start": 916.7, "end": 916.9, "word": " هذا", "probability": 0.360107421875}, {"start": 916.9, "end": 917.22, "word": " K", "probability": 0.796875}, {"start": 917.22, "end": 917.56, "word": " X", "probability": 0.615234375}, {"start": 917.56, "end": 917.76, "word": " على", "probability": 0.8251953125}, {"start": 917.76, "end": 918.02, "word": " K", "probability": 0.97412109375}, {"start": 918.02, "end": 918.18, "word": " طب", "probability": 0.837158203125}, {"start": 918.18, "end": 918.3, "word": " ال", "probability": 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"probability": 0.904296875}, {"start": 939.24, "end": 939.84, "word": " NK", "probability": 0.55810546875}, {"start": 939.84, "end": 940.26, "word": " هي", "probability": 0.904296875}, {"start": 940.26, "end": 941.12, "word": " let", "probability": 0.81591796875}, {"start": 941.12, "end": 941.72, "word": " NK", "probability": 0.937255859375}, {"start": 941.72, "end": 942.32, "word": " بساوي", "probability": 0.7406005859375}, {"start": 942.32, "end": 942.66, "word": " K", "probability": 0.9375}, {"start": 942.66, "end": 943.38, "word": " يعني", "probability": 0.923583984375}, {"start": 943.38, "end": 943.84, "word": " بمعنى", "probability": 0.99404296875}, {"start": 943.84, "end": 944.36, "word": " اخر", "probability": 0.755859375}, {"start": 944.36, "end": 945.26, "word": " اخد", "probability": 0.8460286458333334}, {"start": 945.26, "end": 945.46, "word": " ال", "probability": 0.927734375}, {"start": 945.46, "end": 945.94, "word": " F", "probability": 0.84033203125}, {"start": 945.94, 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" راح", "probability": 0.4716796875}, {"start": 960.8, "end": 961.4, "word": " نختارها", "probability": 0.9765625}, {"start": 961.4, "end": 962.0, "word": " بتساوي", "probability": 0.8675537109375}, {"start": 962.0, "end": 962.36, "word": " K", "probability": 0.91650390625}, {"start": 962.36, "end": 962.84, "word": " أكيد", "probability": 0.8404947916666666}, {"start": 962.84, "end": 963.06, "word": " وين", "probability": 0.720458984375}, {"start": 963.06, "end": 963.76, "word": " موجودة", "probability": 0.958984375}, {"start": 963.76, "end": 964.18, "word": " في", "probability": 0.8896484375}, {"start": 964.18, "end": 964.48, "word": " R", "probability": 0.9619140625}, {"start": 964.48, "end": 965.3, "word": " then", "probability": 0.3232421875}, {"start": 965.3, "end": 966.66, "word": " FNK", "probability": 0.8885091145833334}, {"start": 966.66, "end": 966.82, "word": " of", "probability": 0.81494140625}, {"start": 966.82, "end": 967.3, "word": " XK", "probability": 0.960205078125}, 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اللي هي Epsilon نص وهذا يعني أن FN does not converge uniformly للF on R", "tokens": [5172, 3555, 9381, 13546, 43242, 7578, 479, 45, 591, 39896, 11296, 479, 42, 4032, 462, 16592, 4724, 3794, 995, 2407, 3660, 8717, 9381, 4032, 1783, 42, 4724, 3794, 995, 2407, 3660, 591, 39896, 1422, 8310, 9154, 2423, 479, 45, 4032, 39896, 45595, 31439, 462, 16592, 8717, 9381, 4032, 39896, 8310, 1783, 42, 294, 497, 4724, 5016, 1829, 12984, 14739, 23758, 2423, 8236, 2158, 5551, 4117, 26890, 9154, 3714, 9957, 22807, 13672, 1829, 31439, 23032, 1211, 3615, 36764, 24401, 13672, 1829, 31439, 5551, 4117, 25708, 5551, 4117, 26890, 9154, 11933, 1829, 8592, 22807, 9154, 8717, 9381, 13672, 1829, 39896, 462, 16592, 8717, 9381, 37037, 15730, 37495, 22653, 14739, 479, 45, 775, 406, 41881, 48806, 24976, 37, 322, 497], "avg_logprob": -0.3053495820801137, "compression_ratio": 1.6857142857142857, "no_speech_prob": 1.4901161193847656e-06, "words": [{"start": 1013.14, "end": 1013.8, "word": "فبصير", "probability": 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"end": 1589.62, "text": "اللي هي converse to zero إذا لكل ي أكبر من صفر there exists K بحيث أنه F أن ناقص F أصغر من ي على اتنين لكل N أكبر أو سوء K of ي على اتنين طيب الآن عندي ال .. ال .. ال F هذه بمقدر نترجمها اللي هو على طول مباشرة إذا اللي هي عندي ال F", "tokens": [6027, 20292, 39896, 9652, 405, 281, 4018, 11933, 15730, 5296, 28820, 7251, 5551, 4117, 26890, 9154, 20328, 5172, 2288, 456, 8198, 591, 4724, 5016, 1829, 12984, 14739, 3224, 479, 14739, 8717, 995, 4587, 9381, 479, 5551, 9381, 17082, 2288, 9154, 7251, 15844, 1975, 2655, 1863, 9957, 5296, 28820, 426, 5551, 4117, 26890, 34051, 8608, 2407, 38207, 591, 295, 7251, 15844, 1975, 2655, 1863, 9957, 23032, 1829, 3555, 6024, 48506, 18871, 16254, 2423, 4386, 2423, 4386, 2423, 479, 29538, 4724, 2304, 28543, 2288, 8717, 2655, 47341, 2304, 11296, 13672, 1829, 31439, 15844, 23032, 12610, 3714, 3555, 33599, 25720, 11933, 15730, 13672, 1829, 39896, 18871, 16254, 2423, 479], "avg_logprob": -0.25321260790958583, "compression_ratio": 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