diff --git "a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Lc2K-uxXK74_raw.json" "b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Lc2K-uxXK74_raw.json"
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+{"segments": [{"id": 1, "seek": 4591, "start": 20.75, "end": 45.91, "text": "Okay اذا اليوم ان شاء الله هنكمل موضوع ال limit theorems او نظريات النهايات و من النظريات المهمة هذه هي نظرية 12 بتقول لو في عندي sequence x in و ال sequence هذي convergent ل x فال sequence of absolute values", "tokens": [8297, 1975, 15730, 45595, 20498, 16472, 13412, 16606, 21984, 8032, 1863, 24793, 1211, 3714, 2407, 11242, 45367, 2423, 4948, 10299, 2592, 1975, 2407, 8717, 19913, 16572, 9307, 28239, 11296, 1829, 9307, 4032, 9154, 28239, 19913, 16572, 9307, 9673, 16095, 3660, 29538, 39896, 8717, 19913, 2288, 10632, 2272, 39894, 39648, 45164, 8978, 18871, 16254, 8310, 2031, 294, 4032, 2423, 8310, 8032, 8848, 1829, 9652, 6930, 5296, 2031, 6156, 6027, 8310, 295, 8236, 4190], "avg_logprob": -0.20879708250908002, "compression_ratio": 1.5226130653266332, "no_speech_prob": 0.0, "words": [{"start": 20.75, "end": 21.25, "word": "Okay", "probability": 0.396240234375}, {"start": 21.25, "end": 21.61, "word": " اذا", 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0.560791015625}, {"start": 148.06, "end": 148.36, "word": " الهدف", "probability": 0.7447509765625}, {"start": 148.36, "end": 148.82, "word": " بيطلع", "probability": 0.7927734375}, {"start": 148.82, "end": 149.42, "word": " أصغر", "probability": 0.9814453125}, {"start": 149.42, "end": 149.72, "word": " من", "probability": 0.99560546875}, {"start": 149.72, "end": 150.3, "word": " epsilon", "probability": 0.283935546875}, {"start": 150.3, "end": 154.26, "word": " لكل", "probability": 0.949951171875}, {"start": 154.26, "end": 154.76, "word": " n", "probability": 0.52734375}, {"start": 154.76, "end": 155.48, "word": " أكبر", "probability": 0.9630533854166666}, {"start": 155.48, "end": 155.78, "word": " من", "probability": 0.990234375}, {"start": 155.78, "end": 156.0, "word": " أو", "probability": 0.98193359375}, {"start": 156.0, "end": 156.58, "word": " ساوي", "probability": 0.94580078125}, {"start": 156.58, "end": 157.02, "word": " capital", "probability": 0.658203125}, {"start": 157.02, "end": 157.32, "word": " N", "probability": 0.79541015625}, {"start": 157.32, "end": 161.18, "word": " إذا", "probability": 0.81982421875}, {"start": 161.18, "end": 161.38, "word": " أنا", "probability": 0.7822265625}, {"start": 161.38, "end": 161.6, "word": " هيك", "probability": 0.932861328125}, {"start": 161.6, "end": 161.9, "word": " بكون", "probability": 0.930908203125}, {"start": 161.9, "end": 162.46, "word": " أثبتت", "probability": 0.9763671875}, {"start": 162.46, "end": 162.8, "word": " إنه", "probability": 0.586181640625}, {"start": 162.8, "end": 163.16, "word": " لأي", "probability": 0.9708658854166666}, {"start": 163.16, "end": 163.68, "word": " epsilon", "probability": 0.94189453125}, {"start": 163.68, "end": 164.08, "word": " أكبر", "probability": 0.98291015625}, {"start": 164.08, "end": 164.32, "word": " من", "probability": 0.99560546875}, {"start": 164.32, "end": 164.8, "word": " سفر", "probability": 0.7361653645833334}, {"start": 164.8, "end": 166.46, "word": " يوجد", "probability": 0.9651692708333334}, {"start": 166.46, "end": 166.9, "word": " capital", "probability": 0.810546875}, {"start": 166.9, "end": 167.2, "word": " N", "probability": 0.95263671875}, {"start": 167.2, "end": 167.72, "word": " يعتمد", "probability": 0.9483642578125}, {"start": 167.72, "end": 167.9, "word": " على", "probability": 0.9013671875}, {"start": 167.9, "end": 168.32, "word": " epsilon", "probability": 0.90869140625}, {"start": 168.32, "end": 168.74, "word": " عدد", "probability": 0.9812825520833334}, {"start": 168.74, "end": 169.4, "word": " طبيعي", "probability": 0.985107421875}, {"start": 169.4, "end": 170.76, "word": " بحيث", "probability": 0.973876953125}, {"start": 170.76, "end": 171.28, "word": " لكل", "probability": 0.987548828125}, {"start": 171.28, "end": 171.58, "word": " n", "probability": 0.72265625}, {"start": 171.58, "end": 172.1, "word": " أكبر", "probability": 0.9822591145833334}, {"start": 172.1, "end": 172.34, "word": " من", "probability": 0.99560546875}, {"start": 172.34, "end": 172.52, "word": " أو", "probability": 0.9970703125}, {"start": 172.52, "end": 173.02, "word": " ساوي", "probability": 0.97509765625}, {"start": 173.02, "end": 173.44, "word": " capital", "probability": 0.83349609375}, {"start": 173.44, "end": 173.76, "word": " N", "probability": 0.98681640625}], "temperature": 1.0}, {"id": 7, "seek": 19814, "start": 174.96, "end": 198.14, "text": "القيمة المطلقة ل absolute xn minus absolute x أصغر من epsilon إذا حسب تعريف epsilon capital N for limits هذا معناه بالظبط أن limit absolute xn as n tends to infinity بساوي absolute x وهو المطلوب", "tokens": [6027, 4587, 32640, 3660, 9673, 9566, 1211, 28671, 5296, 8236, 2031, 77, 3175, 8236, 2031, 5551, 9381, 17082, 2288, 9154, 17889, 11933, 15730, 11331, 35457, 37279, 16572, 5172, 17889, 4238, 426, 337, 10406, 23758, 20449, 8315, 3224, 20666, 19913, 3555, 9566, 14739, 4948, 8236, 2031, 77, 382, 297, 12258, 281, 13202, 4724, 3794, 995, 45865, 8236, 2031, 37037, 2407, 9673, 9566, 1211, 37746], "avg_logprob": -0.18774414318613708, "compression_ratio": 1.4545454545454546, "no_speech_prob": 0.0, "words": [{"start": 174.96, "end": 175.66, "word": "القيمة", "probability": 0.8858642578125}, {"start": 175.66, "end": 176.32, "word": " المطلقة", "probability": 0.9852294921875}, {"start": 176.32, "end": 177.04, "word": " ل", "probability": 0.951171875}, {"start": 177.04, "end": 177.4, "word": " absolute", "probability": 0.320556640625}, {"start": 177.4, "end": 178.16, "word": " xn", "probability": 0.6007080078125}, {"start": 178.16, "end": 178.48, "word": " minus", "probability": 0.68310546875}, {"start": 178.48, "end": 178.96, "word": " absolute", "probability": 0.89501953125}, {"start": 178.96, "end": 179.52, "word": " x", "probability": 0.982421875}, {"start": 179.52, "end": 180.1, "word": " أصغر", "probability": 0.9620361328125}, {"start": 180.1, "end": 180.3, "word": " من", "probability": 0.99169921875}, {"start": 180.3, "end": 180.72, "word": " epsilon", "probability": 0.24560546875}, {"start": 180.72, "end": 182.48, "word": " إذا", "probability": 0.45294189453125}, {"start": 182.48, "end": 182.96, "word": " حسب", "probability": 0.96435546875}, {"start": 182.96, "end": 183.56, "word": " تعريف", "probability": 0.9884440104166666}, {"start": 183.56, "end": 184.08, "word": " epsilon", "probability": 0.74853515625}, {"start": 184.08, "end": 184.54, "word": " capital", "probability": 0.70703125}, {"start": 184.54, "end": 184.98, "word": " N", "probability": 0.73828125}, {"start": 184.98, "end": 186.16, "word": " for", "probability": 0.90869140625}, {"start": 186.16, "end": 186.78, "word": " limits", "probability": 0.96923828125}, {"start": 186.78, "end": 187.34, "word": " هذا", "probability": 0.5615234375}, {"start": 187.34, "end": 187.9, "word": " معناه", "probability": 0.9816080729166666}, {"start": 187.9, "end": 188.5, "word": " بالظبط", "probability": 0.943115234375}, {"start": 188.5, "end": 188.78, "word": " أن", 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{"start": 197.58, "end": 198.14, "word": " المطلوب", "probability": 0.835693359375}], "temperature": 1.0}, {"id": 8, "seek": 22821, "start": 200.03, "end": 228.21, "text": "Okay تمام اذا هذا بيكمل برهان نظرية اتناش تمام واضح النظرية اللي بعدها نظرية تلاتاش بتقول لو انا فيها اندي sequence حدودها كلها غير سالبة حدود ال sequence xm كلها غير سالبة اعداد غير سالبة", "tokens": [8297, 46811, 10943, 1975, 15730, 23758, 4724, 1829, 24793, 1211, 4724, 2288, 3224, 7649, 8717, 19913, 2288, 10632, 1975, 2655, 1863, 33599, 46811, 10943, 4032, 46958, 5016, 28239, 19913, 2288, 10632, 13672, 1829, 39182, 11296, 8717, 19913, 2288, 10632, 6055, 1211, 9307, 33599, 39894, 39648, 45164, 1975, 8315, 8978, 11296, 16472, 16254, 8310, 11331, 3215, 23328, 11296, 28242, 11296, 32771, 13546, 8608, 6027, 49401, 11331, 3215, 23328, 2423, 8310, 2031, 76, 28242, 11296, 32771, 13546, 8608, 6027, 49401, 1975, 22488, 18513, 32771, 13546, 8608, 6027, 49401], "avg_logprob": -0.15077227388305225, "compression_ratio": 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اللي", "probability": 0.856201171875}, {"start": 213.03, "end": 213.99, "word": " بعدها", "probability": 0.916015625}, {"start": 213.99, "end": 216.21, "word": " نظرية", "probability": 0.952880859375}, {"start": 216.21, "end": 217.03, "word": " تلاتاش", "probability": 0.857666015625}, {"start": 217.03, "end": 218.33, "word": " بتقول", "probability": 0.86328125}, {"start": 218.33, "end": 218.53, "word": " لو", "probability": 0.89794921875}, {"start": 218.53, "end": 218.71, "word": " انا", "probability": 0.837646484375}, {"start": 218.71, "end": 218.97, "word": " فيها", "probability": 0.94384765625}, {"start": 218.97, "end": 219.27, "word": " اندي", "probability": 0.797119140625}, {"start": 219.27, "end": 220.07, "word": " sequence", "probability": 0.87451171875}, {"start": 220.07, "end": 220.79, "word": " حدودها", "probability": 0.9888916015625}, {"start": 220.79, "end": 221.21, "word": " كلها", "probability": 0.9873046875}, {"start": 221.21, "end": 221.57, "word": " غير", "probability": 0.99658203125}, {"start": 221.57, "end": 222.13, "word": " سالبة", "probability": 0.7566731770833334}, {"start": 222.13, "end": 224.49, "word": " حدود", "probability": 0.982421875}, {"start": 224.49, "end": 224.63, "word": " ال", "probability": 0.900390625}, {"start": 224.63, "end": 224.99, "word": " sequence", "probability": 0.98291015625}, {"start": 224.99, "end": 225.49, "word": " xm", "probability": 0.580810546875}, {"start": 225.49, "end": 225.99, "word": " كلها", "probability": 0.990966796875}, {"start": 225.99, "end": 226.47, "word": " غير", "probability": 0.980224609375}, {"start": 226.47, "end": 226.99, "word": " سالبة", "probability": 0.97900390625}, {"start": 226.99, "end": 227.45, "word": " اعداد", "probability": 0.81640625}, {"start": 227.45, "end": 227.73, "word": " غير", "probability": 0.99755859375}, {"start": 227.73, "end": 228.21, "word": " سالبة", "probability": 0.9783528645833334}], "temperature": 1.0}, {"id": 9, "seek": 24989, "start": 229.41, "end": 249.89, "text": "والـ sequence لو كانت الـ sequence Xn convergent to some X فالـ limit للـ sequence of square roots لـ Xn تطلع convergent والـ limit تبعتها بساول square root للـ limit للـ sequence Xn", "tokens": [2407, 6027, 39184, 8310, 45164, 25961, 2655, 2423, 39184, 8310, 1783, 77, 9652, 6930, 281, 512, 1783, 6156, 6027, 39184, 4948, 24976, 39184, 8310, 295, 3732, 10669, 5296, 39184, 1783, 77, 6055, 9566, 1211, 3615, 9652, 6930, 16070, 39184, 4948, 6055, 3555, 34268, 11296, 4724, 3794, 995, 12610, 3732, 5593, 24976, 39184, 4948, 24976, 39184, 8310, 1783, 77], "avg_logprob": -0.2510593230441465, "compression_ratio": 1.7218045112781954, "no_speech_prob": 0.0, "words": [{"start": 229.41, "end": 230.05, "word": "والـ", "probability": 0.599853515625}, {"start": 230.05, "end": 230.53, "word": " sequence", "probability": 0.751953125}, {"start": 230.53, "end": 230.75, "word": " لو", "probability": 0.85302734375}, {"start": 230.75, "end": 231.09, "word": " كانت", "probability": 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{"start": 239.31, "end": 239.85, "word": " square", "probability": 0.63623046875}, {"start": 239.85, "end": 240.49, "word": " roots", "probability": 0.85546875}, {"start": 240.49, "end": 241.05, "word": " لـ", "probability": 0.83447265625}, {"start": 241.05, "end": 241.57, "word": " Xn", "probability": 0.947265625}, {"start": 241.57, "end": 242.73, "word": " تطلع", "probability": 0.9422607421875}, {"start": 242.73, "end": 243.65, "word": " convergent", "probability": 0.915771484375}, {"start": 243.65, "end": 244.69, "word": " والـ", "probability": 0.631591796875}, {"start": 244.69, "end": 244.93, "word": " limit", "probability": 0.98193359375}, {"start": 244.93, "end": 245.63, "word": " تبعتها", "probability": 0.9183349609375}, {"start": 245.63, "end": 246.23, "word": " بساول", "probability": 0.6248779296875}, {"start": 246.23, "end": 246.67, "word": " square", "probability": 0.759765625}, {"start": 246.67, "end": 247.33, "word": " root", "probability": 0.9052734375}, {"start": 247.33, 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{"start": 599.53, "end": 599.77, "word": " square", "probability": 0.56298828125}, {"start": 599.77, "end": 600.03, "word": " root", "probability": 0.83154296875}, {"start": 600.03, "end": 600.21, "word": " of", "probability": 0.978515625}, {"start": 600.21, "end": 600.71, "word": " xn", "probability": 0.617919921875}, {"start": 600.71, "end": 601.83, "word": " وفي", "probability": 0.836669921875}, {"start": 601.83, "end": 602.15, "word": " عندي", "probability": 0.96533203125}, {"start": 602.15, "end": 602.51, "word": " عدد", "probability": 0.98291015625}, {"start": 602.51, "end": 602.81, "word": " square", "probability": 0.88623046875}, {"start": 602.81, "end": 603.05, "word": " root", "probability": 0.9169921875}, {"start": 603.05, "end": 603.23, "word": " of", "probability": 0.98291015625}, {"start": 603.23, "end": 603.45, "word": " x", "probability": 0.978515625}, {"start": 603.45, "end": 604.19, "word": " المسافة", "probability": 0.9627685546875}, {"start": 604.19, "end": 605.35, 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"probability": 0.8231201171875}, {"start": 614.39, "end": 614.99, "word": " واحد", "probability": 0.895263671875}, {"start": 614.99, "end": 615.23, "word": " على", "probability": 0.437744140625}, {"start": 615.23, "end": 615.61, "word": " square", "probability": 0.87939453125}, {"start": 615.61, "end": 615.95, "word": " root", "probability": 0.9296875}, {"start": 615.95, "end": 616.11, "word": " of", "probability": 0.56103515625}, {"start": 616.11, "end": 616.55, "word": " xn", "probability": 0.971435546875}, {"start": 616.55, "end": 616.81, "word": " زي", "probability": 0.805908203125}, {"start": 616.81, "end": 617.15, "word": " square", "probability": 0.8115234375}, {"start": 617.15, "end": 617.39, "word": " root", "probability": 0.90869140625}, {"start": 617.39, "end": 617.55, "word": " of", "probability": 0.93115234375}, {"start": 617.55, "end": 617.81, "word": " x", "probability": 0.9873046875}, {"start": 617.81, "end": 620.33, "word": " والكسر", "probability": 0.710107421875}, {"start": 620.33, "end": 620.81, "word": " هذا", "probability": 0.919921875}, {"start": 620.81, "end": 621.87, "word": " من", "probability": 0.94921875}, {"start": 621.87, "end": 623.11, "word": " المتباينة", "probability": 0.8717447916666666}, {"start": 623.11, "end": 623.53, "word": " تسعة", "probability": 0.8665364583333334}], "temperature": 1.0}, {"id": 26, "seek": 64989, "start": 624.29, "end": 649.89, "text": "هذا الكثير أصغر من أو يساوي واحد على square root of x ضرب absolute x in سالب x الآن ارجعوا لنظرية اتنين اربعة with c عدد موجب ساوي واحد على جدر ال x هذا عدد موجب", "tokens": [3224, 15730, 33251, 12984, 13546, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 36764, 24401, 15844, 3732, 5593, 295, 2031, 48812, 25513, 8236, 2031, 294, 8608, 6027, 3555, 2031, 6024, 48506, 1975, 47341, 3615, 14407, 5296, 1863, 19913, 2288, 10632, 1975, 2655, 1863, 9957, 1975, 25513, 27884, 365, 269, 6225, 3215, 3215, 3714, 29245, 3555, 8608, 995, 45865, 36764, 24401, 15844, 10874, 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628.67, "end": 628.85, "word": " of", "probability": 0.9716796875}, {"start": 628.85, "end": 629.09, "word": " x", "probability": 0.513671875}, {"start": 629.09, "end": 629.83, "word": " ضرب", "probability": 0.930908203125}, {"start": 629.83, "end": 630.17, "word": " absolute", "probability": 0.90966796875}, {"start": 630.17, "end": 630.59, "word": " x", "probability": 0.90234375}, {"start": 630.59, "end": 630.85, "word": " in", "probability": 0.1656494140625}, {"start": 630.85, "end": 631.27, "word": " سالب", "probability": 0.7400716145833334}, {"start": 631.27, "end": 631.55, "word": " x", "probability": 0.96533203125}, {"start": 631.55, "end": 632.61, "word": " الآن", "probability": 0.6800537109375}, {"start": 632.61, "end": 633.65, "word": " ارجعوا", "probability": 0.7545166015625}, {"start": 633.65, "end": 635.75, "word": " لنظرية", "probability": 0.9708984375}, {"start": 635.75, "end": 636.37, "word": " اتنين", "probability": 0.788299560546875}, {"start": 636.37, "end": 636.99, "word": " اربعة", "probability": 0.8740234375}, {"start": 636.99, "end": 643.83, "word": " with", "probability": 0.7509765625}, {"start": 643.83, "end": 646.11, "word": " c", "probability": 0.70849609375}, {"start": 646.11, "end": 646.55, "word": " عدد", "probability": 0.97900390625}, {"start": 646.55, "end": 647.05, "word": " موجب", "probability": 0.9842122395833334}, {"start": 647.05, "end": 647.49, "word": " ساوي", "probability": 0.7599283854166666}, {"start": 647.49, "end": 647.93, "word": " واحد", "probability": 0.9794921875}, {"start": 647.93, "end": 648.07, "word": " على", "probability": 0.58984375}, {"start": 648.07, "end": 648.39, "word": " جدر", "probability": 0.9715169270833334}, {"start": 648.39, "end": 648.53, "word": " ال", "probability": 0.9482421875}, {"start": 648.53, "end": 648.73, "word": " x", "probability": 0.755859375}, {"start": 648.73, "end": 649.03, "word": " هذا", "probability": 0.67822265625}, {"start": 649.03, "end": 649.37, "word": " عدد", "probability": 0.9912109375}, {"start": 649.37, "end": 649.89, "word": " موجب", "probability": 0.99365234375}], "temperature": 1.0}, {"id": 27, "seek": 67514, "start": 651.22, "end": 675.14, "text": "و a n بساوي x n minus x إذن هى يوجد c عدد موجب اللى هو واحد على جدر ال X و هى فى عندي sequence a n الحد العام تبعها x n سالد x و ال sequence هذه تقول إلى سفر as n tends to infinity", "tokens": [2407, 257, 297, 4724, 3794, 995, 45865, 2031, 297, 3175, 2031, 11933, 8848, 1863, 8032, 7578, 7251, 29245, 3215, 269, 6225, 3215, 3215, 3714, 29245, 3555, 13672, 7578, 31439, 36764, 24401, 15844, 10874, 3215, 2288, 2423, 1783, 4032, 8032, 7578, 6156, 7578, 18871, 16254, 8310, 257, 297, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 2031, 297, 8608, 6027, 3215, 2031, 4032, 2423, 8310, 29538, 6055, 39648, 30731, 8608, 5172, 2288, 382, 297, 12258, 281, 13202], "avg_logprob": -0.33603897342434175, "compression_ratio": 1.4692737430167597, "no_speech_prob": 0.0, "words": [{"start": 651.22, "end": 651.68, "word": 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{"start": 661.0, "end": 661.42, "word": " موجب", "probability": 0.9451497395833334}, {"start": 661.42, "end": 661.58, "word": " اللى", "probability": 0.78369140625}, {"start": 661.58, "end": 661.7, "word": " هو", "probability": 0.77734375}, {"start": 661.7, "end": 662.0, "word": " واحد", "probability": 0.973876953125}, {"start": 662.0, "end": 662.16, "word": " على", "probability": 0.51123046875}, {"start": 662.16, "end": 662.48, "word": " جدر", "probability": 0.731201171875}, {"start": 662.48, "end": 662.62, "word": " ال", "probability": 0.9091796875}, {"start": 662.62, "end": 662.88, "word": " X", "probability": 0.51611328125}, {"start": 662.88, "end": 663.8, "word": " و", "probability": 0.42333984375}, {"start": 663.8, "end": 663.94, "word": " هى", "probability": 0.767822265625}, {"start": 663.94, "end": 664.08, "word": " فى", "probability": 0.6611328125}, {"start": 664.08, "end": 664.3, "word": " عندي", "probability": 0.63525390625}, {"start": 664.3, "end": 664.86, "word": " sequence", "probability": 0.7490234375}, {"start": 664.86, "end": 665.2, "word": " a", "probability": 0.91259765625}, {"start": 665.2, "end": 665.46, "word": " n", "probability": 0.96533203125}, {"start": 665.46, "end": 665.88, "word": " الحد", "probability": 0.805908203125}, {"start": 665.88, "end": 666.14, "word": " العام", "probability": 0.83544921875}, {"start": 666.14, "end": 666.62, "word": " تبعها", "probability": 0.9281005859375}, {"start": 666.62, "end": 666.88, "word": " x", "probability": 0.60546875}, {"start": 666.88, "end": 667.12, "word": " n", "probability": 0.62255859375}, {"start": 667.12, "end": 667.56, "word": " سالد", "probability": 0.6827799479166666}, {"start": 667.56, "end": 667.86, "word": " x", "probability": 0.6572265625}, {"start": 667.86, "end": 668.82, "word": " و", "probability": 0.391357421875}, {"start": 668.82, "end": 668.94, "word": " ال", "probability": 0.7060546875}, {"start": 668.94, "end": 669.38, "word": " sequence", "probability": 0.9482421875}, {"start": 669.38, "end": 669.86, "word": " هذه", "probability": 0.40966796875}, {"start": 669.86, "end": 670.54, "word": " تقول", "probability": 0.938232421875}, {"start": 670.54, "end": 670.86, "word": " إلى", "probability": 0.7001953125}, {"start": 670.86, "end": 671.32, "word": " سفر", "probability": 0.8546549479166666}, {"start": 671.32, "end": 671.96, "word": " as", "probability": 0.9052734375}, {"start": 671.96, "end": 674.18, "word": " n", "probability": 0.76025390625}, {"start": 674.18, "end": 674.52, "word": " tends", "probability": 0.73681640625}, {"start": 674.52, "end": 674.68, "word": " to", "probability": 0.9716796875}, {"start": 674.68, "end": 675.14, "word": " infinity", "probability": 0.87841796875}], "temperature": 1.0}, {"id": 28, "seek": 69921, "start": 676.57, "end": 699.21, "text": "لأن انا من المعطيات عندي xn تقول x أو limit xn بساوي x، لذلك limit الفرق بساوي سفر، لذلك حسب نظرية 2.4، كل شروطة متحققة، وبالتالي، لذلك حسب النظرية هذه، by theorem 2.4، بيطلع عندي 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88223, "start": 861.47, "end": 882.23, "text": "Discurses ل Convergence يعني بين هل ال sequence هذي Convergent ولا Divergent وده كانت Convergent عايزين نجيب ال limit تبعتها طيب تعالوا أول شي احنا طبعا هنطبق ال ratio test نظرية 2.14 اللي هو الرسم منها ال ratio test", "tokens": [35, 5606, 2156, 279, 5296, 2656, 331, 15260, 37495, 22653, 4724, 1829, 1863, 8032, 1211, 2423, 8310, 8032, 8848, 1829, 2656, 331, 6930, 49429, 413, 1837, 6930, 4032, 3215, 3224, 25961, 2655, 2656, 331, 6930, 6225, 47302, 11622, 9957, 8717, 7435, 1829, 3555, 2423, 4948, 6055, 3555, 34268, 11296, 23032, 1829, 3555, 37279, 6027, 14407, 5551, 12610, 44049, 1975, 5016, 8315, 23032, 3555, 3615, 995, 8032, 1863, 9566, 3555, 4587, 2423, 8509, 1500, 8717, 19913, 2288, 10632, 568, 13, 7271, 13672, 1829, 31439, 34892, 38251, 9154, 11296, 2423, 8509, 1500], "avg_logprob": -0.30511674972680897, "compression_ratio": 1.5422885572139304, "no_speech_prob": 0.0, "words": [{"start": 861.47, "end": 862.13, "word": "Discurses", 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وده", "probability": 0.67529296875}, {"start": 866.79, "end": 867.13, "word": " كانت", "probability": 0.869384765625}, {"start": 867.13, "end": 867.85, "word": " Convergent", "probability": 0.9659830729166666}, {"start": 867.85, "end": 868.91, "word": " عايزين", "probability": 0.91796875}, {"start": 868.91, "end": 869.29, "word": " نجيب", "probability": 0.9700927734375}, {"start": 869.29, "end": 869.41, "word": " ال", "probability": 0.8525390625}, {"start": 869.41, "end": 869.67, "word": " limit", "probability": 0.9326171875}, {"start": 869.67, "end": 870.55, "word": " تبعتها", "probability": 0.96435546875}, {"start": 870.55, "end": 872.83, "word": " طيب", "probability": 0.8165690104166666}, {"start": 872.83, "end": 873.75, "word": " تعالوا", "probability": 0.8478190104166666}, {"start": 873.75, "end": 874.49, "word": " أول", "probability": 0.7470703125}, {"start": 874.49, "end": 874.77, "word": " شي", "probability": 0.6005859375}, {"start": 874.77, "end": 875.79, "word": " احنا", 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{"start": 886.35, "end": 886.67, "word": " ال", "probability": 0.5361328125}, {"start": 886.67, "end": 887.15, "word": " sequence", "probability": 0.943359375}, {"start": 887.15, "end": 887.69, "word": " xn", "probability": 0.63916015625}, {"start": 887.69, "end": 888.27, "word": " حدودها", "probability": 0.988525390625}, {"start": 888.27, "end": 888.77, "word": " موجبة", "probability": 0.92822265625}, {"start": 888.77, "end": 889.89, "word": " وهذا", "probability": 0.74951171875}, {"start": 889.89, "end": 890.41, "word": " صحيح", "probability": 0.9949951171875}, {"start": 890.41, "end": 890.69, "word": " لان", "probability": 0.7333984375}, {"start": 890.69, "end": 890.85, "word": " ال", "probability": 0.5625}, {"start": 890.85, "end": 891.03, "word": " bus", "probability": 0.213623046875}, {"start": 891.03, "end": 891.37, "word": " b", "probability": 0.344970703125}, {"start": 891.37, "end": 891.61, "word": " اكبر", "probability": 0.6665852864583334}, {"start": 891.61, "end": 891.79, 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"end": 911.47, "word": " بn", "probability": 0.464111328125}, {"start": 911.47, "end": 911.79, "word": " زياد", "probability": 0.9459635416666666}, {"start": 911.79, "end": 912.23, "word": " واحد", "probability": 0.985107421875}], "temperature": 1.0}, {"id": 37, "seek": 93764, "start": 913.16, "end": 937.64, "text": "وضربها في مقلوب xn هي مقلوب xn وطبعا احنا عارفين ان n plus one factorial بتساوي n plus one في n factorial هذا بنفك حاصل ضرب زي هذا n factorial بتروح مع n factorial وb to n بتروح مع b to n بضل b", "tokens": [2407, 11242, 25513, 11296, 8978, 3714, 4587, 1211, 37746, 2031, 77, 39896, 3714, 4587, 1211, 37746, 2031, 77, 4032, 9566, 3555, 3615, 995, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 16472, 297, 1804, 472, 36916, 39894, 3794, 995, 45865, 297, 1804, 472, 8978, 297, 36916, 23758, 44945, 5172, 4117, 11331, 33546, 1211, 48812, 25513, 30767, 1829, 23758, 297, 36916, 39894, 32887, 5016, 20449, 297, 36916, 4032, 65, 281, 297, 39894, 32887, 5016, 20449, 272, 281, 297, 4724, 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واحد", "probability": 0.9951171875}, {"start": 961.33, "end": 961.89, "word": " اللي", "probability": 0.889892578125}, {"start": 961.89, "end": 962.11, "word": " هي", "probability": 0.87841796875}, {"start": 962.11, "end": 962.57, "word": " سفر", "probability": 0.9855143229166666}, {"start": 962.57, "end": 963.21, "word": " بي", "probability": 0.9306640625}, {"start": 963.21, "end": 963.29, "word": " في", "probability": 0.95361328125}, {"start": 963.29, "end": 963.63, "word": " سفر", "probability": 0.9884440104166666}, {"start": 963.63, "end": 964.01, "word": " بساوي", "probability": 0.8333740234375}, {"start": 964.01, "end": 964.49, "word": " سفر", "probability": 0.98681640625}, {"start": 964.49, "end": 966.31, "word": " تمام؟", "probability": 0.8976236979166666}], "temperature": 1.0}, {"id": 39, "seek": 99551, "start": 966.55, "end": 995.51, "text": "إذا أنا عندي L اللي هو بمثل limit ال ratio هذا طلع بساوي سفر عدد حقيقي أصغر من واحد إذا حسب ال ratio test limit لل sequence xn بساوي 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1018.23, "end": 1021.93, "word": " two", "probability": 0.865234375}, {"start": 1021.93, "end": 1023.39, "word": " divergent", "probability": 0.94091796875}, {"start": 1023.39, "end": 1024.09, "word": " sequences", "probability": 0.97314453125}], "temperature": 1.0}, {"id": 41, "seek": 105109, "start": 1026.94, "end": 1051.1, "text": "such that there are some مجموعهم there are some converges نعطي مثال ل two divergent sequences تنتهي from two divergent لكن مجموعهم convergent فأسهل مثال هو مثل هذا الحل", "tokens": [39974, 300, 456, 366, 512, 3714, 7435, 2304, 45367, 16095, 456, 366, 512, 9652, 2880, 8717, 3615, 9566, 1829, 50113, 6027, 5296, 732, 18558, 6930, 22978, 6055, 29399, 3224, 1829, 490, 732, 18558, 6930, 44381, 3714, 7435, 2304, 45367, 16095, 9652, 6930, 6156, 10721, 3794, 3224, 1211, 50113, 6027, 31439, 50113, 1211, 23758, 21542, 1211], "avg_logprob": -0.3674665040203503, "compression_ratio": 1.5172413793103448, "no_speech_prob": 0.0, "words": [{"start": 1026.94, "end": 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1040.84, "word": " ل", "probability": 0.95556640625}, {"start": 1040.84, "end": 1041.14, "word": " two", "probability": 0.63330078125}, {"start": 1041.14, "end": 1041.84, "word": " divergent", "probability": 0.695068359375}, {"start": 1041.84, "end": 1042.72, "word": " sequences", "probability": 0.9560546875}, {"start": 1042.72, "end": 1043.66, "word": " تنتهي", "probability": 0.4776611328125}, {"start": 1043.66, "end": 1043.76, "word": " from", "probability": 0.1173095703125}, {"start": 1043.76, "end": 1044.06, "word": " two", "probability": 0.324951171875}, {"start": 1044.06, "end": 1044.44, "word": " divergent", "probability": 0.845703125}, {"start": 1044.44, "end": 1044.68, "word": " لكن", "probability": 0.6220703125}, {"start": 1044.68, "end": 1045.34, "word": " مجموعهم", "probability": 0.9033203125}, {"start": 1045.34, "end": 1046.08, "word": " convergent", "probability": 0.6280517578125}, {"start": 1046.08, "end": 1047.86, "word": " فأسهل", "probability": 0.96767578125}, {"start": 1047.86, "end": 1048.38, "word": " مثال", "probability": 0.81103515625}, {"start": 1048.38, "end": 1048.6, "word": " هو", "probability": 0.91455078125}, {"start": 1048.6, "end": 1049.14, "word": " مثل", "probability": 0.62744140625}, {"start": 1049.14, "end": 1049.5, "word": " هذا", "probability": 0.88671875}, {"start": 1049.5, "end": 1051.1, "word": " الحل", "probability": 0.864013671875}], "temperature": 1.0}, {"id": 42, "seek": 107636, "start": 1052.21, "end": 1076.37, "text": "ناخد الـ sequence xn للحد العام تبعها سالب واحد to n و n بتبدأ من واحد إلى ملا نهاية طبعا ال sequence هذه لو بيننا انفرفتها فحدودها هتكون هكذا أول حد سالب واحد، تاني واحد، تالت سالب واحد، الرابع واحد، و هكذا", "tokens": [1863, 47283, 3215, 2423, 39184, 8310, 2031, 77, 24976, 24401, 18863, 10943, 6055, 3555, 3615, 11296, 8608, 6027, 3555, 36764, 24401, 281, 297, 4032, 297, 39894, 44510, 10721, 9154, 36764, 24401, 30731, 3714, 15040, 8717, 11296, 10632, 23032, 3555, 3615, 995, 2423, 8310, 29538, 45164, 49374, 8315, 16472, 5172, 28480, 2655, 11296, 6156, 24401, 23328, 11296, 8032, 2655, 30544, 8032, 4117, 15730, 5551, 12610, 11331, 3215, 8608, 6027, 3555, 36764, 24401, 12399, 6055, 7649, 1829, 36764, 24401, 12399, 6055, 6027, 2655, 8608, 6027, 3555, 36764, 24401, 12399, 34892, 16758, 3615, 36764, 24401, 12399, 4032, 8032, 4117, 15730], "avg_logprob": -0.1924426070585543, "compression_ratio": 1.8670212765957446, "no_speech_prob": 0.0, "words": [{"start": 1052.21, "end": 1052.79, "word": "ناخد", "probability": 0.7713216145833334}, {"start": 1052.79, "end": 1052.99, "word": " الـ", "probability": 0.617919921875}, {"start": 1052.99, "end": 1053.37, "word": " sequence", "probability": 0.75732421875}, {"start": 1053.37, "end": 1054.07, "word": " xn", "probability": 0.44049072265625}, {"start": 1054.07, "end": 1054.55, "word": " للحد", "probability": 0.8623046875}, {"start": 1054.55, "end": 1054.91, "word": " العام", "probability": 0.903564453125}, {"start": 1054.91, "end": 1055.57, "word": " تبعها", "probability": 0.89453125}, {"start": 1055.57, "end": 1056.27, "word": " سالب", "probability": 0.7081705729166666}, {"start": 1056.27, "end": 1056.69, "word": " واحد", "probability": 0.97802734375}, {"start": 1056.69, "end": 1056.89, "word": " to", "probability": 0.6708984375}, {"start": 1056.89, "end": 1057.23, "word": " n", "probability": 0.88720703125}, {"start": 1057.23, "end": 1058.47, "word": " و", "probability": 0.7119140625}, {"start": 1058.47, "end": 1058.65, "word": " n", "probability": 0.312744140625}, {"start": 1058.65, "end": 1059.15, "word": " بتبدأ", "probability": 0.8336588541666666}, {"start": 1059.15, "end": 1059.33, "word": " من", "probability": 0.99072265625}, {"start": 1059.33, "end": 1059.83, "word": " واحد", "probability": 0.981201171875}, {"start": 1059.83, "end": 1060.11, "word": " إلى", "probability": 0.814453125}, {"start": 1060.11, "end": 1060.49, "word": " ملا", "probability": 0.6070556640625}, {"start": 1060.49, "end": 1061.07, "word": " نهاية", "probability": 0.9259440104166666}, {"start": 1061.07, "end": 1062.31, "word": " طبعا", "probability": 0.8970947265625}, {"start": 1062.31, "end": 1062.43, "word": " ال", "probability": 0.85009765625}, {"start": 1062.43, "end": 1062.75, "word": " sequence", "probability": 0.70068359375}, {"start": 1062.75, "end": 1063.09, "word": " هذه", "probability": 0.53857421875}, {"start": 1063.09, "end": 1063.25, "word": " لو", "probability": 0.931640625}, {"start": 1063.25, "end": 1063.69, "word": " بيننا", "probability": 0.568603515625}, {"start": 1063.69, "end": 1064.75, "word": " انفرفتها", "probability": 0.82548828125}, {"start": 1064.75, "end": 1066.85, "word": " فحدودها", "probability": 0.9769287109375}, {"start": 1066.85, "end": 1067.49, "word": " هتكون", "probability": 0.97216796875}, {"start": 1067.49, "end": 1068.21, "word": " هكذا", "probability": 0.970703125}, {"start": 1068.21, "end": 1069.11, "word": " أول", "probability": 0.77587890625}, {"start": 1069.11, "end": 1069.53, "word": " حد", "probability": 0.982177734375}, {"start": 1069.53, "end": 1070.11, "word": " سالب", "probability": 0.9755859375}, {"start": 1070.11, "end": 1071.31, "word": " واحد،", "probability": 0.775634765625}, {"start": 1071.31, "end": 1071.57, "word": " تاني", "probability": 0.86767578125}, {"start": 1071.57, "end": 1072.37, "word": " واحد،", "probability": 0.98681640625}, {"start": 1072.37, "end": 1072.75, "word": " تالت", "probability": 0.9098307291666666}, {"start": 1072.75, "end": 1073.17, "word": " سالب", "probability": 0.9832356770833334}, {"start": 1073.17, "end": 1073.67, "word": " واحد،", "probability": 0.9866536458333334}, {"start": 1073.67, "end": 1074.07, "word": " الرابع", "probability": 0.74462890625}, {"start": 1074.07, "end": 1075.19, "word": " واحد،", "probability": 0.8226725260416666}, {"start": 1075.19, "end": 1075.83, "word": " و", "probability": 0.82421875}, {"start": 1075.83, "end": 1076.37, "word": " هكذا", "probability": 0.9093424479166666}], "temperature": 1.0}, {"id": 43, "seek": 109761, "start": 1077.38, "end": 1097.62, "text": "وناخد ال sequence yn الحد العام تبعها سالب واحد قص ان زاد واحد وان طبعا تبدأ من واحد فهذه ال sequence حدودها هتكون أول حد واحد، التاني سالب واحد، التالت واحد، الرابع سالب واحد و هكذا", "tokens": [2407, 1863, 47283, 3215, 2423, 8310, 17861, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 8608, 6027, 3555, 36764, 24401, 12174, 9381, 16472, 30767, 18513, 36764, 24401, 4032, 7649, 23032, 3555, 3615, 995, 6055, 44510, 10721, 9154, 36764, 24401, 6156, 3224, 24192, 2423, 8310, 11331, 3215, 23328, 11296, 8032, 2655, 30544, 5551, 12610, 11331, 3215, 36764, 24401, 12399, 16712, 7649, 1829, 8608, 6027, 3555, 36764, 24401, 12399, 16712, 6027, 2655, 36764, 24401, 12399, 34892, 16758, 3615, 8608, 6027, 3555, 36764, 24401, 4032, 8032, 4117, 15730], "avg_logprob": -0.1697856118512708, "compression_ratio": 1.94375, "no_speech_prob": 0.0, "words": [{"start": 1077.38, "end": 1078.0, "word": "وناخد", "probability": 0.7315673828125}, {"start": 1078.0, "end": 1078.14, "word": " ال", "probability": 0.8759765625}, {"start": 1078.14, "end": 1078.56, "word": " sequence", "probability": 0.544921875}, {"start": 1078.56, "end": 1079.04, "word": " yn", "probability": 0.71533203125}, {"start": 1079.04, "end": 1079.76, "word": " الحد", "probability": 0.87890625}, {"start": 1079.76, "end": 1080.04, "word": " العام", "probability": 0.78564453125}, {"start": 1080.04, "end": 1080.68, "word": " تبعها", "probability": 0.79638671875}, {"start": 1080.68, "end": 1081.86, "word": " سالب", "probability": 0.677001953125}, {"start": 1081.86, "end": 1082.26, "word": " واحد", "probability": 0.9873046875}, {"start": 1082.26, "end": 1082.56, "word": " قص", "probability": 0.70166015625}, {"start": 1082.56, "end": 1082.78, "word": " ان", "probability": 0.464599609375}, {"start": 1082.78, "end": 1083.22, "word": " زاد", "probability": 0.818603515625}, {"start": 1083.22, "end": 1083.64, "word": " واحد", "probability": 0.981201171875}, {"start": 1083.64, "end": 1083.9, "word": " وان", "probability": 0.58837890625}, {"start": 1083.9, "end": 1084.24, "word": " طبعا", "probability": 0.9556884765625}, {"start": 1084.24, "end": 1084.62, "word": " تبدأ", "probability": 0.8712565104166666}, {"start": 1084.62, "end": 1084.76, "word": " من", "probability": 0.9853515625}, {"start": 1084.76, "end": 1085.22, "word": " واحد", "probability": 0.98974609375}, {"start": 1085.22, "end": 1086.84, "word": " فهذه", "probability": 0.8680013020833334}, {"start": 1086.84, "end": 1087.18, "word": " ال", "probability": 0.93896484375}, {"start": 1087.18, "end": 1087.92, "word": " sequence", "probability": 0.96044921875}, {"start": 1087.92, "end": 1089.72, "word": " حدودها", "probability": 0.900390625}, {"start": 1089.72, "end": 1090.26, "word": " هتكون", "probability": 0.9519856770833334}, {"start": 1090.26, "end": 1091.08, "word": " أول", "probability": 0.75146484375}, {"start": 1091.08, "end": 1091.46, "word": " حد", "probability": 0.9921875}, {"start": 1091.46, "end": 1092.08, "word": " واحد،", "probability": 0.7787272135416666}, {"start": 1092.08, "end": 1092.58, "word": " التاني", "probability": 0.9386393229166666}, {"start": 1092.58, "end": 1093.06, "word": " سالب", "probability": 0.9856770833333334}, {"start": 1093.06, "end": 1093.6, "word": " واحد،", "probability": 0.9812825520833334}, {"start": 1093.6, "end": 1094.1, "word": " التالت", "probability": 0.85107421875}, {"start": 1094.1, "end": 1095.34, "word": " واحد،", "probability": 0.9832356770833334}, {"start": 1095.34, "end": 1095.88, "word": " الرابع", "probability": 0.9850260416666666}, {"start": 1095.88, "end": 1096.44, "word": " سالب", "probability": 0.9879557291666666}, {"start": 1096.44, "end": 1096.98, "word": " واحد", "probability": 0.9921875}, {"start": 1096.98, "end": 1097.16, "word": " و", "probability": 0.6220703125}, {"start": 1097.16, "end": 1097.62, "word": " هكذا", "probability": 0.7611490885416666}], "temperature": 1.0}, {"id": 44, "seek": 112120, "start": 1100.3, "end": 1121.2, "text": "تمام احنا اثبتنا بالتفصيل ان ال sequence xn هذي divergent by contradiction فرضنا انها convergent وصلنا الى تناغم صح؟ طب ما هذي هي هذي هي ال sequence ال sequence yn هي سالب ال sequence xn", "tokens": [2655, 15042, 2304, 1975, 5016, 8315, 1975, 12984, 3555, 2655, 8315, 20666, 2655, 5172, 9381, 26895, 16472, 2423, 8310, 2031, 77, 8032, 8848, 1829, 18558, 6930, 538, 34937, 6156, 43042, 8315, 16472, 11296, 9652, 6930, 4032, 36520, 8315, 2423, 7578, 6055, 1863, 5718, 118, 2304, 20328, 5016, 22807, 23032, 3555, 19446, 8032, 8848, 1829, 39896, 8032, 8848, 1829, 39896, 2423, 8310, 2423, 8310, 17861, 39896, 8608, 6027, 3555, 2423, 8310, 2031, 77], "avg_logprob": -0.24272260273972604, "compression_ratio": 1.6419753086419753, "no_speech_prob": 0.0, "words": [{"start": 1100.3, "end": 1101.18, "word": "تمام", "probability": 0.5717366536458334}, {"start": 1101.18, "end": 1101.88, "word": " احنا", "probability": 0.748291015625}, {"start": 1101.88, "end": 1102.38, "word": " اثبتنا", "probability": 0.92548828125}, {"start": 1102.38, "end": 1103.24, "word": " بالتفصيل", "probability": 0.98359375}, {"start": 1103.24, "end": 1103.84, "word": " ان", "probability": 0.84521484375}, {"start": 1103.84, "end": 1104.04, "word": " ال", "probability": 0.8662109375}, {"start": 1104.04, "end": 1104.46, "word": " sequence", "probability": 0.8271484375}, {"start": 1104.46, "end": 1105.14, "word": " xn", "probability": 0.5482177734375}, {"start": 1105.14, "end": 1105.72, "word": " هذي", "probability": 0.48876953125}, {"start": 1105.72, "end": 1107.16, "word": " divergent", "probability": 0.59002685546875}, {"start": 1107.16, "end": 1107.42, "word": " by", "probability": 0.5771484375}, {"start": 1107.42, "end": 1108.14, "word": " contradiction", "probability": 0.90625}, {"start": 1108.14, "end": 1108.68, "word": " فرضنا", "probability": 0.9148763020833334}, {"start": 1108.68, "end": 1108.9, "word": " انها", "probability": 0.918701171875}, {"start": 1108.9, "end": 1109.66, "word": " convergent", "probability": 0.87939453125}, {"start": 1109.66, "end": 1110.76, "word": " وصلنا", "probability": 0.8919270833333334}, {"start": 1110.76, "end": 1110.98, "word": " الى", "probability": 0.773193359375}, {"start": 1110.98, "end": 1111.44, "word": " تناغم", "probability": 0.917578125}, {"start": 1111.44, "end": 1114.22, "word": " صح؟", "probability": 0.7623697916666666}, {"start": 1114.22, "end": 1114.48, "word": " طب", "probability": 0.961181640625}, {"start": 1114.48, "end": 1114.62, "word": " ما", "probability": 0.53564453125}, {"start": 1114.62, "end": 1115.0, "word": " هذي", "probability": 0.6892903645833334}, {"start": 1115.0, "end": 1115.2, "word": " هي", "probability": 0.57861328125}, {"start": 1115.2, "end": 1115.6, "word": " هذي", "probability": 0.81005859375}, {"start": 1115.6, "end": 1115.78, "word": " هي", "probability": 0.791015625}, {"start": 1115.78, "end": 1115.96, "word": " ال", "probability": 0.8271484375}, {"start": 1115.96, "end": 1116.48, "word": " sequence", "probability": 0.9833984375}, {"start": 1116.48, "end": 1116.86, "word": " ال", "probability": 0.67724609375}, {"start": 1116.86, "end": 1117.36, "word": " sequence", "probability": 0.90771484375}, {"start": 1117.36, "end": 1117.98, "word": " yn", "probability": 0.82666015625}, {"start": 1117.98, "end": 1118.4, "word": " هي", "probability": 0.92041015625}, {"start": 1118.4, "end": 1119.2, "word": " سالب", "probability": 0.9456380208333334}, {"start": 1119.2, "end": 1120.12, "word": " ال", "probability": 0.93994140625}, {"start": 1120.12, "end": 1120.56, "word": " sequence", "probability": 0.99462890625}, {"start": 1120.56, "end": 1121.2, "word": " xn", "probability": 0.9853515625}], "temperature": 1.0}, {"id": 45, "seek": 115213, "start": 1122.93, "end": 1152.13, "text": "و Xn is divergent و Yn is divergent او بنفس البرهان ممكن نعمل نفس البرهان اذا هي عندي مثال على two sequences كلاهما both are divergent لكن لما نيجي نجمعهم لو أخدت ال sequence جديدة ال inf term تبعها او الحد العام تبعها هو مجموعة ال inf term زي Xn وYn هذه sequence تالتة جديدة", "tokens": [2407, 1783, 77, 307, 18558, 6930, 4032, 398, 77, 307, 18558, 6930, 1975, 2407, 44945, 36178, 2423, 26890, 3224, 7649, 3714, 43020, 8717, 25957, 1211, 8717, 36178, 2423, 26890, 3224, 7649, 1975, 15730, 39896, 18871, 16254, 50113, 6027, 15844, 732, 22978, 9122, 15040, 3224, 15042, 1293, 366, 18558, 6930, 44381, 5296, 15042, 8717, 1829, 7435, 1829, 8717, 7435, 2304, 3615, 16095, 45164, 5551, 9778, 3215, 2655, 2423, 8310, 10874, 16254, 41891, 2423, 1536, 1433, 6055, 3555, 3615, 11296, 1975, 2407, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 31439, 3714, 7435, 2304, 2407, 27884, 2423, 1536, 1433, 30767, 1829, 1783, 77, 4032, 56, 77, 29538, 8310, 6055, 6027, 2655, 3660, 10874, 16254, 41891], "avg_logprob": -0.2583607398627097, "compression_ratio": 1.7739130434782608, "no_speech_prob": 0.0, "words": [{"start": 1122.93, "end": 1123.25, "word": "و", "probability": 0.51953125}, {"start": 1123.25, "end": 1123.75, "word": " Xn", "probability": 0.3841552734375}, {"start": 1123.75, "end": 1123.83, "word": " is", "probability": 0.206298828125}, {"start": 1123.83, "end": 1124.41, "word": " divergent", "probability": 0.884521484375}, {"start": 1124.41, "end": 1124.93, "word": " و", "probability": 0.5029296875}, {"start": 1124.93, "end": 1125.45, "word": " Yn", "probability": 0.780029296875}, {"start": 1125.45, "end": 1125.51, "word": " is", "probability": 0.85400390625}, {"start": 1125.51, "end": 1126.23, "word": " divergent", "probability": 0.9208984375}, {"start": 1126.23, "end": 1126.81, "word": " او", "probability": 0.750244140625}, {"start": 1126.81, "end": 1127.17, "word": " بنفس", "probability": 0.903564453125}, {"start": 1127.17, "end": 1127.71, "word": " البرهان", "probability": 0.7864990234375}, {"start": 1127.71, "end": 1127.91, "word": " ممكن", "probability": 0.572509765625}, {"start": 1127.91, "end": 1128.19, "word": " 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{"start": 1173.56, "end": 1173.8, "word": " أي", "probability": 0.76904296875}, {"start": 1173.8, "end": 1174.36, "word": " sequence", "probability": 0.9677734375}, {"start": 1174.36, "end": 1175.48, "word": " ثابتة", "probability": 0.918701171875}, {"start": 1175.48, "end": 1176.68, "word": " بتكون", "probability": 0.825927734375}, {"start": 1176.68, "end": 1177.56, "word": " convergent", "probability": 0.7548828125}, {"start": 1177.56, "end": 1177.72, "word": " و", "probability": 0.67431640625}, {"start": 1177.72, "end": 1178.02, "word": " limit", "probability": 0.64208984375}, {"start": 1178.02, "end": 1178.76, "word": " تبعتها", "probability": 0.9158935546875}, {"start": 1178.76, "end": 1179.0, "word": " هي", "probability": 0.9375}, {"start": 1179.0, "end": 1179.36, "word": " الحد", "probability": 0.98388671875}, {"start": 1179.36, "end": 1179.88, "word": " الثابت", "probability": 0.94873046875}, {"start": 1179.88, "end": 1180.42, "word": " نفسه،", "probability": 0.8392333984375}, 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"word": " هذا", "probability": 0.853515625}, {"start": 1229.44, "end": 1229.8, "word": " عبارة", "probability": 0.9962158203125}, {"start": 1229.8, "end": 1229.98, "word": " عن", "probability": 0.99560546875}, {"start": 1229.98, "end": 1230.38, "word": " exercise", "probability": 0.90966796875}, {"start": 1230.38, "end": 1231.08, "word": " أربعة", "probability": 0.6424967447916666}, {"start": 1231.08, "end": 1231.48, "word": " عشر", "probability": 0.658447265625}, {"start": 1231.48, "end": 1231.66, "word": " في", "probability": 0.459716796875}, {"start": 1231.66, "end": 1231.98, "word": " section", "probability": 0.90283203125}, {"start": 1231.98, "end": 1232.46, "word": " تلاتة", "probability": 0.9425048828125}, {"start": 1232.46, "end": 1232.9, "word": " اتنين", "probability": 0.9539794921875}], "temperature": 1.0}, {"id": 49, "seek": 126285, "start": 1235.1, "end": 1262.86, "text": "بقول خد zn بساوي a to n plus b to n to the power one over n where a و b are positive numbers and a 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1345.27, "end": 1345.85, "word": " دمجت", "probability": 0.9832763671875}, {"start": 1345.85, "end": 1347.09, "word": " المتباينتين", "probability": 0.9434988839285714}, {"start": 1347.09, "end": 1347.67, "word": " عشرة", "probability": 0.8642578125}, {"start": 1347.67, "end": 1347.79, "word": " و", "probability": 0.8623046875}, {"start": 1347.79, "end": 1348.31, "word": " أحداشر", "probability": 0.737060546875}, {"start": 1348.31, "end": 1348.47, "word": " مع", "probability": 0.9912109375}, {"start": 1348.47, "end": 1348.95, "word": " بعض", "probability": 0.994140625}, {"start": 1348.95, "end": 1350.99, "word": " فبطلع", "probability": 0.9728515625}, {"start": 1350.99, "end": 1351.39, "word": " عندي", "probability": 0.93798828125}, {"start": 1351.39, "end": 1351.71, "word": " b", "probability": 0.732421875}], "temperature": 1.0}, {"id": 53, "seek": 137449, "start": 1352.21, "end": 1374.49, "text": "من المتباينة عشرة الـ B هدا هي أصغر من ال ZN ومن المتباينة أحداشر ال ZN أصغر من two to one over N times B for every N natural number احنا اتوصلنا لالمتباينة هذه صحيحة لكل N", "tokens": [27842, 9673, 2655, 3555, 995, 9957, 3660, 6225, 8592, 25720, 2423, 39184, 363, 8032, 28259, 39896, 5551, 9381, 17082, 2288, 9154, 2423, 1176, 45, 4032, 27842, 9673, 2655, 3555, 995, 9957, 3660, 5551, 24401, 33599, 2288, 2423, 1176, 45, 5551, 9381, 17082, 2288, 9154, 732, 281, 472, 670, 426, 1413, 363, 337, 633, 426, 3303, 1230, 1975, 5016, 8315, 1975, 2655, 2407, 36520, 8315, 5296, 45340, 2655, 3555, 995, 9957, 3660, 29538, 20328, 5016, 1829, 5016, 3660, 5296, 28820, 426], "avg_logprob": -0.22260802763479728, "compression_ratio": 1.535294117647059, "no_speech_prob": 0.0, "words": [{"start": 1352.21, "end": 1352.71, "word": "من", "probability": 0.7861328125}, {"start": 1352.71, "end": 1353.67, "word": " المتباينة", "probability": 0.9475911458333334}, {"start": 1353.67, "end": 1354.09, "word": " عشرة", "probability": 0.8792317708333334}, {"start": 1354.09, "end": 1355.11, "word": " الـ", 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تنتين هاي متتالية وهاي متتالية المتتالية هذه الحد العام تبعها ثابت بيه", "tokens": [7649, 995, 5296, 7649, 18871, 16254, 2423, 39184, 8310, 1176, 45, 29538, 13672, 1829, 1975, 8315, 6225, 47302, 11622, 1975, 12984, 3555, 2655, 16472, 2423, 4948, 6055, 3555, 34268, 11296, 20666, 3794, 995, 45865, 4724, 1829, 3224, 307, 39470, 1296, 732, 22978, 3714, 5016, 9381, 13063, 3660, 9154, 44650, 2655, 6027, 36081, 9957, 6055, 29399, 9957, 8032, 47302, 44650, 2655, 6027, 10632, 37037, 47302, 44650, 2655, 6027, 10632, 9673, 2655, 2655, 6027, 10632, 29538, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 38637, 16758, 2655, 4724, 1829, 3224], "avg_logprob": -0.23683285847138824, "compression_ratio": 1.7395833333333333, "no_speech_prob": 0.0, "words": [{"start": 1376.42, "end": 1376.78, "word": "انا", "probability": 0.5595703125}, {"start": 1376.78, "end": 1377.08, "word": " لان", "probability": 0.477783203125}, {"start": 1377.08, "end": 1377.58, "word": " عندي", "probability": 0.7802734375}, 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بي و limit ال sequence هذي two to واحد على n limit two to واحد على n بتساوي واحد اثبتنا احنا قبل هيك ان لو n دي c عدد موجب ف limit", "tokens": [37746, 6027, 2655, 6027, 1829, 2423, 4948, 6055, 3555, 34268, 4724, 1829, 5296, 15042, 4724, 1829, 6055, 4587, 2407, 1211, 5296, 13202, 39894, 3794, 995, 45865, 4724, 1829, 4032, 4948, 2423, 8310, 8032, 8848, 1829, 732, 281, 36764, 24401, 15844, 297, 4948, 732, 281, 36764, 24401, 15844, 297, 39894, 3794, 995, 45865, 36764, 24401, 1975, 12984, 3555, 2655, 8315, 1975, 5016, 8315, 12174, 36150, 39896, 4117, 16472, 45164, 297, 11778, 1829, 269, 6225, 3215, 3215, 3714, 29245, 3555, 6156, 4948], "avg_logprob": -0.3115354938271605, "compression_ratio": 1.6568047337278107, "no_speech_prob": 0.0, "words": [{"start": 1404.16, "end": 1404.96, "word": "وبالتالي", "probability": 0.882470703125}, {"start": 1404.96, "end": 1405.76, "word": " ال", "probability": 0.1939697265625}, {"start": 1405.76, "end": 1406.0, "word": " limit", "probability": 0.7236328125}, 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"probability": 0.9891357421875}, {"start": 1499.48, "end": 1499.6, "word": " في", "probability": 0.98388671875}, {"start": 1499.6, "end": 1500.14, "word": " المناجم", "probability": 0.8570556640625}], "temperature": 1.0}, {"id": 59, "seek": 152231, "start": 1501.49, "end": 1522.31, "text": "إذا ما يكون إلا من شطرتكم تحاولوا تحلوا باقي التمرين اللي في ال section هذا طبعا هنا لهنا الامتحان .. الامتحان داخل لحد التمرين هذه الجزء اللي بعد هيك مش داخل في الامتحان النصف الأول", "tokens": [28814, 15730, 19446, 7251, 30544, 11933, 15040, 9154, 13412, 9566, 43500, 24793, 6055, 5016, 995, 12610, 14407, 6055, 5016, 1211, 14407, 4724, 995, 38436, 16712, 29973, 9957, 13672, 1829, 8978, 2423, 3541, 23758, 23032, 3555, 3615, 995, 34105, 5296, 3224, 8315, 2423, 10943, 2655, 5016, 7649, 4386, 2423, 10943, 2655, 5016, 7649, 11778, 47283, 1211, 5296, 24401, 16712, 29973, 9957, 29538, 25724, 11622, 38207, 13672, 1829, 39182, 39896, 4117, 37893, 11778, 47283, 1211, 8978, 2423, 10943, 2655, 5016, 7649, 28239, 9381, 5172, 16247, 12610], "avg_logprob": -0.11691176786142236, "compression_ratio": 1.8135593220338984, "no_speech_prob": 0.0, "words": [{"start": 1501.49, "end": 1501.83, "word": "إذا", "probability": 0.792724609375}, {"start": 1501.83, "end": 1502.01, "word": " ما", "probability": 0.9921875}, {"start": 1502.01, "end": 1502.53, "word": " يكون", "probability": 0.761962890625}, {"start": 1502.53, "end": 1503.05, "word": " إلا", "probability": 0.933349609375}, {"start": 1503.05, "end": 1503.43, "word": " من", "probability": 0.94140625}, {"start": 1503.43, "end": 1505.27, "word": " شطرتكم", "probability": 0.88037109375}, {"start": 1505.27, "end": 1505.81, "word": " تحاولوا", "probability": 0.91201171875}, {"start": 1505.81, "end": 1506.37, "word": " تحلوا", "probability": 0.920654296875}, {"start": 1506.37, "end": 1507.39, "word": " باقي", "probability": 0.87841796875}, {"start": 1507.39, "end": 1508.13, "word": " التمرين", "probability": 0.8551432291666666}, {"start": 1508.13, "end": 1509.09, "word": " اللي", "probability": 0.916259765625}, {"start": 1509.09, "end": 1509.23, "word": " في", "probability": 0.91796875}, {"start": 1509.23, "end": 1509.35, "word": " ال", "probability": 0.86865234375}, {"start": 1509.35, "end": 1509.75, "word": " section", "probability": 0.93408203125}, {"start": 1509.75, "end": 1510.21, "word": " هذا", "probability": 0.6396484375}, {"start": 1510.21, "end": 1511.61, "word": " طبعا", "probability": 0.963134765625}, {"start": 1511.61, "end": 1511.95, "word": " هنا", "probability": 0.95166015625}, {"start": 1511.95, "end": 1512.73, "word": " لهنا", "probability": 0.6879069010416666}, {"start": 1512.73, "end": 1513.49, "word": " الامتحان", "probability": 0.923828125}, {"start": 1513.49, "end": 1513.63, "word": " ..", "probability": 0.411376953125}, {"start": 1513.63, "end": 1514.51, "word": " الامتحان", "probability": 0.9767578125}, {"start": 1514.51, "end": 1515.11, "word": " داخل", "probability": 0.9910481770833334}, {"start": 1515.11, "end": 1515.55, "word": " لحد", "probability": 0.97998046875}, {"start": 1515.55, "end": 1517.05, "word": " التمرين", "probability": 0.9814453125}, {"start": 1517.05, "end": 1517.51, "word": " هذه", "probability": 0.62109375}, {"start": 1517.51, "end": 1519.85, "word": " الجزء", "probability": 0.9446614583333334}, {"start": 1519.85, "end": 1519.97, "word": " اللي", "probability": 0.742431640625}, {"start": 1519.97, "end": 1520.21, "word": " بعد", "probability": 0.9150390625}, {"start": 1520.21, "end": 1520.55, "word": " هيك", "probability": 0.96826171875}, {"start": 1520.55, "end": 1520.73, "word": " مش", "probability": 0.98486328125}, {"start": 1520.73, "end": 1521.03, "word": " داخل", "probability": 0.9876302083333334}, {"start": 1521.03, "end": 1521.15, "word": " في", "probability": 0.9013671875}, {"start": 1521.15, "end": 1521.59, "word": " الامتحان", "probability": 0.98818359375}, {"start": 1521.59, "end": 1521.97, "word": " النصف", "probability": 0.85009765625}, {"start": 1521.97, "end": 1522.31, "word": " الأول", "probability": 0.976806640625}], "temperature": 1.0}, {"id": 60, "seek": 155574, "start": 1526.22, "end": 1555.74, "text": "تمام فإذا هنا ال section جديد أو أنوان جديد ال monotone sequences المتتاليات اللي بيسموها الواتيرية المتتاليات الواتيرية ال monotone sequence يعني متتالية واتيرية يعني إما متزايدة أو متلاقصة فناخد تعريف let x in be a sequence of real numbers", "tokens": [2655, 15042, 2304, 6156, 28814, 15730, 34105, 2423, 3541, 10874, 16254, 3215, 34051, 14739, 2407, 7649, 10874, 16254, 3215, 2423, 1108, 310, 546, 22978, 9673, 2655, 2655, 6027, 1829, 9307, 13672, 1829, 4724, 1829, 38251, 2407, 11296, 2423, 2407, 9307, 13546, 10632, 9673, 2655, 2655, 6027, 1829, 9307, 2423, 2407, 9307, 13546, 10632, 2423, 1108, 310, 546, 8310, 37495, 22653, 44650, 2655, 6027, 10632, 4032, 9307, 13546, 10632, 37495, 22653, 11933, 15042, 44650, 11622, 995, 25708, 3660, 34051, 44650, 15040, 4587, 9381, 3660, 6156, 1863, 47283, 3215, 37279, 16572, 5172, 718, 2031, 294, 312, 257, 8310, 295, 957, 3547], "avg_logprob": -0.14765625670552254, "compression_ratio": 1.8743718592964824, "no_speech_prob": 0.0, "words": [{"start": 1526.22, "end": 1527.02, "word": "تمام", "probability": 0.5777180989583334}, {"start": 1527.02, "end": 1528.12, "word": " فإذا", "probability": 0.6771647135416666}, {"start": 1528.12, "end": 1528.46, "word": " هنا", "probability": 0.92578125}, {"start": 1528.46, "end": 1528.86, "word": " ال", "probability": 0.5947265625}, {"start": 1528.86, "end": 1529.92, "word": " section", "probability": 0.802734375}, {"start": 1529.92, "end": 1530.54, "word": " جديد", "probability": 0.9695638020833334}, {"start": 1530.54, "end": 1530.74, "word": " أو", "probability": 0.7822265625}, {"start": 1530.74, "end": 1531.16, "word": " أنوان", "probability": 0.7998046875}, {"start": 1531.16, "end": 1532.22, "word": " جديد", "probability": 0.9931640625}, {"start": 1532.22, "end": 1532.64, "word": " ال", "probability": 0.8896484375}, {"start": 1532.64, "end": 1533.22, "word": " monotone", "probability": 0.8045247395833334}, {"start": 1533.22, "end": 1534.08, "word": " sequences", "probability": 0.90625}, {"start": 1534.08, "end": 1536.96, "word": " المتتاليات", "probability": 0.9554850260416666}, {"start": 1536.96, "end": 1537.58, "word": " اللي", "probability": 0.706298828125}, {"start": 1537.58, "end": 1538.16, "word": " بيسموها", "probability": 0.96142578125}, {"start": 1538.16, "end": 1539.06, "word": " الواتيرية", "probability": 0.8109375}, {"start": 1539.06, "end": 1541.22, "word": " المتتاليات", "probability": 0.9835611979166666}, {"start": 1541.22, "end": 1541.88, "word": " الواتيرية", "probability": 0.97685546875}, {"start": 1541.88, "end": 1542.02, "word": " ال", "probability": 0.3916015625}, {"start": 1542.02, "end": 1542.38, "word": " monotone", "probability": 0.92626953125}, {"start": 1542.38, "end": 1542.9, "word": " sequence", "probability": 0.7890625}, {"start": 1542.9, "end": 1543.2, "word": " يعني", "probability": 0.936767578125}, {"start": 1543.2, "end": 1544.2, "word": " متتالية", "probability": 0.891357421875}, {"start": 1544.2, "end": 1544.9, "word": " واتيرية", "probability": 0.9852294921875}, {"start": 1544.9, "end": 1545.76, "word": " يعني", "probability": 0.9462890625}, {"start": 1545.76, "end": 1546.0, "word": " إما", "probability": 0.847412109375}, {"start": 1546.0, "end": 1546.82, "word": " متزايدة", "probability": 0.97919921875}, {"start": 1546.82, "end": 1546.96, "word": " أو", "probability": 0.90625}, {"start": 1546.96, "end": 1547.9, "word": " متلاقصة", "probability": 0.777587890625}, {"start": 1547.9, "end": 1549.8, "word": " فناخد", "probability": 0.9512939453125}, {"start": 1549.8, "end": 1550.58, "word": " تعريف", "probability": 0.9786783854166666}, {"start": 1550.58, "end": 1553.4, "word": " let", "probability": 0.87255859375}, {"start": 1553.4, "end": 1553.78, "word": " x", "probability": 0.748046875}, {"start": 1553.78, "end": 1553.98, "word": " in", "probability": 0.5830078125}, {"start": 1553.98, "end": 1554.14, "word": " be", "probability": 0.91259765625}, {"start": 1554.14, "end": 1554.24, "word": " a", "probability": 0.728515625}, {"start": 1554.24, "end": 1554.72, "word": " sequence", "probability": 0.97412109375}, {"start": 1554.72, "end": 1554.98, "word": " of", "probability": 0.98193359375}, {"start": 1554.98, "end": 1555.2, "word": " real", "probability": 0.96435546875}, {"start": 1555.2, "end": 1555.74, "word": " numbers", "probability": 0.90283203125}], "temperature": 1.0}, {"id": 61, "seek": 158056, "start": 1557.04, "end": 1580.56, "text": "سنقول إن سيكوينس Xn increasing متزايدة إذا كان Xn less than or equal to Xn plus one for every n لو كان كل حد أصغر من أول ساول لبعده فالسيكوينس في الحالة دي بنسميها increasing و بنسميها decreasing", "tokens": [3794, 1863, 39648, 36145, 8608, 1829, 4117, 2407, 9957, 3794, 1783, 77, 5662, 44650, 11622, 995, 25708, 3660, 11933, 15730, 25961, 1783, 77, 1570, 813, 420, 2681, 281, 1783, 77, 1804, 472, 337, 633, 297, 45164, 25961, 28242, 11331, 3215, 5551, 9381, 17082, 2288, 9154, 5551, 12610, 8608, 995, 12610, 5296, 3555, 22488, 3224, 6156, 6027, 3794, 1829, 4117, 2407, 9957, 3794, 8978, 21542, 6027, 3660, 11778, 1829, 44945, 38251, 1829, 11296, 5662, 4032, 44945, 38251, 1829, 11296, 23223], "avg_logprob": -0.2900390598922968, "compression_ratio": 1.486910994764398, "no_speech_prob": 0.0, "words": [{"start": 1557.04, "end": 1557.64, "word": "سنقول", "probability": 0.54266357421875}, {"start": 1557.64, "end": 1557.9, "word": " إن", "probability": 0.40673828125}, {"start": 1557.9, "end": 1558.44, "word": " سيكوينس", "probability": 0.6485188802083334}, {"start": 1558.44, "end": 1558.98, "word": " Xn", "probability": 0.4586181640625}, {"start": 1558.98, "end": 1559.64, "word": " increasing", "probability": 0.2132568359375}, {"start": 1559.64, "end": 1561.6, "word": " متزايدة", "probability": 0.90693359375}, {"start": 1561.6, "end": 1562.88, "word": " إذا", "probability": 0.935791015625}, {"start": 1562.88, "end": 1563.36, "word": " كان", "probability": 0.9541015625}, {"start": 1563.36, "end": 1564.36, "word": " Xn", "probability": 0.927734375}, {"start": 1564.36, "end": 1567.4, "word": " less", "probability": 0.1802978515625}, {"start": 1567.4, "end": 1567.66, "word": " than", "probability": 0.96044921875}, {"start": 1567.66, "end": 1567.8, "word": " or", "probability": 0.392333984375}, {"start": 1567.8, "end": 1568.04, "word": " equal", "probability": 0.9326171875}, {"start": 1568.04, "end": 1568.3, "word": " to", "probability": 0.53564453125}, {"start": 1568.3, "end": 1568.82, "word": " Xn", "probability": 0.94287109375}, {"start": 1568.82, "end": 1569.18, "word": " plus", "probability": 0.64697265625}, {"start": 1569.18, "end": 1569.44, "word": " one", "probability": 0.8505859375}, {"start": 1569.44, "end": 1569.7, "word": " for", "probability": 0.927734375}, {"start": 1569.7, "end": 1570.04, "word": " every", "probability": 0.77587890625}, {"start": 1570.04, "end": 1570.36, "word": " n", "probability": 0.71337890625}, {"start": 1570.36, "end": 1571.18, "word": " لو", "probability": 0.280029296875}, {"start": 1571.18, "end": 1571.5, "word": " كان", "probability": 0.97412109375}, {"start": 1571.5, "end": 1571.8, "word": " كل", "probability": 0.94775390625}, {"start": 1571.8, "end": 1572.18, "word": " حد", "probability": 0.9833984375}, {"start": 1572.18, "end": 1572.6, "word": " أصغر", "probability": 0.9866943359375}, {"start": 1572.6, "end": 1572.76, "word": " من", "probability": 0.9833984375}, {"start": 1572.76, "end": 1572.98, "word": " أول", "probability": 0.74853515625}, {"start": 1572.98, "end": 1573.28, "word": " ساول", "probability": 0.7091471354166666}, {"start": 1573.28, "end": 1574.1, "word": " لبعده", "probability": 0.9091796875}, {"start": 1574.1, "end": 1576.84, "word": " فالسيكوينس", "probability": 0.847900390625}, {"start": 1576.84, "end": 1576.92, "word": " في", "probability": 0.68408203125}, {"start": 1576.92, "end": 1577.18, "word": " الحالة", "probability": 0.8186848958333334}, {"start": 1577.18, "end": 1577.26, "word": " دي", "probability": 0.964111328125}, {"start": 1577.26, "end": 1577.76, "word": " بنسميها", "probability": 0.8797607421875}, {"start": 1577.76, "end": 1578.32, "word": " increasing", "probability": 0.955078125}, {"start": 1578.32, "end": 1579.28, "word": " و", "probability": 0.62744140625}, {"start": 1579.28, "end": 1579.96, "word": " بنسميها", "probability": 0.8477783203125}, {"start": 1579.96, "end": 1580.56, "word": " decreasing", "probability": 0.97119140625}], "temperature": 1.0}, {"id": 62, "seek": 160604, "start": 1582.76, "end": 1606.04, "text": "إذا كان كل حد أكبر من أو يساوي اللي بعده تمام؟ طيب بنسمي ال sequence monotone ال sequence بنسميها monotone أو واتيرية if it is either increasing or decreasing", "tokens": [28814, 15730, 25961, 28242, 11331, 3215, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 13672, 1829, 39182, 3224, 46811, 10943, 22807, 23032, 1829, 3555, 44945, 38251, 1829, 2423, 8310, 1108, 310, 546, 2423, 8310, 44945, 38251, 1829, 11296, 1108, 310, 546, 34051, 4032, 9307, 13546, 10632, 498, 309, 307, 2139, 5662, 420, 23223], "avg_logprob": -0.153693180734461, "compression_ratio": 1.4415584415584415, "no_speech_prob": 0.0, "words": [{"start": 1582.76, "end": 1583.1, "word": "إذا", "probability": 0.77392578125}, {"start": 1583.1, "end": 1583.48, "word": " كان", "probability": 0.97265625}, {"start": 1583.48, "end": 1583.86, "word": " كل", "probability": 0.87353515625}, {"start": 1583.86, "end": 1584.48, "word": " حد", "probability": 0.951171875}, {"start": 1584.48, "end": 1585.88, "word": " أكبر", "probability": 0.9288736979166666}, {"start": 1585.88, "end": 1586.14, "word": " من", "probability": 0.95166015625}, {"start": 1586.14, "end": 1586.36, "word": " أو", "probability": 0.95361328125}, {"start": 1586.36, "end": 1586.86, "word": " يساوي", "probability": 0.9451904296875}, {"start": 1586.86, "end": 1587.02, "word": " اللي", "probability": 0.931396484375}, {"start": 1587.02, "end": 1587.56, "word": " بعده", "probability": 0.9111328125}, {"start": 1587.56, "end": 1592.76, "word": " تمام؟", "probability": 0.6607259114583334}, {"start": 1592.76, "end": 1593.74, "word": " طيب", "probability": 0.8580729166666666}, {"start": 1593.74, "end": 1594.4, "word": " بنسمي", "probability": 0.8948567708333334}, {"start": 1594.4, "end": 1594.48, "word": " ال", "probability": 0.86767578125}, {"start": 1594.48, "end": 1594.84, "word": " sequence", "probability": 0.8466796875}, {"start": 1594.84, "end": 1595.84, "word": " monotone", "probability": 0.7692057291666666}, {"start": 1595.84, "end": 1598.48, "word": " ال", "probability": 0.6044921875}, {"start": 1598.48, "end": 1599.36, "word": " sequence", "probability": 0.875}, {"start": 1599.36, "end": 1600.0, "word": " بنسميها", "probability": 0.958251953125}, {"start": 1600.0, "end": 1600.6, "word": " monotone", "probability": 0.9392903645833334}, {"start": 1600.6, "end": 1600.82, "word": " أو", "probability": 0.76611328125}, {"start": 1600.82, "end": 1601.54, "word": " واتيرية", "probability": 0.737548828125}, {"start": 1601.54, "end": 1602.92, "word": " if", "probability": 0.8125}, {"start": 1602.92, "end": 1603.16, "word": " it", "probability": 0.97705078125}, {"start": 1603.16, "end": 1603.44, "word": " is", "probability": 0.91259765625}, {"start": 1603.44, "end": 1604.02, "word": " either", "probability": 0.94091796875}, {"start": 1604.02, "end": 1604.74, "word": " increasing", "probability": 0.96630859375}, {"start": 1604.74, "end": 1605.46, "word": " or", "probability": 0.96826171875}, {"start": 1605.46, "end": 1606.04, "word": " decreasing", "probability": 0.95166015625}], "temperature": 1.0}, {"id": 63, "seek": 163705, "start": 1608.95, "end": 1637.05, "text": "إن المتتالي الوطرية هي متتالية إما increasing أو decreasing معنى آخر كل increasing sequence is monotone sequence and every decreasing sequence is monotone sequence طب هاي أمثلة على monotone sequences فاندي هنا sequence n of natural numbers", "tokens": [28814, 1863, 9673, 2655, 2655, 6027, 1829, 2423, 2407, 9566, 2288, 10632, 39896, 44650, 2655, 6027, 10632, 11933, 15042, 5662, 34051, 23223, 20449, 1863, 7578, 19753, 34740, 28242, 5662, 8310, 307, 1108, 310, 546, 8310, 293, 633, 23223, 8310, 307, 1108, 310, 546, 8310, 23032, 3555, 8032, 47302, 5551, 2304, 12984, 37977, 15844, 1108, 310, 546, 22978, 6156, 7649, 16254, 34105, 8310, 297, 295, 3303, 3547], "avg_logprob": -0.22971081466817145, "compression_ratio": 1.7142857142857142, "no_speech_prob": 0.0, "words": [{"start": 1608.95, "end": 1609.25, "word": "إن", "probability": 0.5556640625}, {"start": 1609.25, "end": 1609.97, "word": " المتتالي", "probability": 0.91982421875}, {"start": 1609.97, "end": 1610.61, "word": " الوطرية", "probability": 0.714453125}, {"start": 1610.61, "end": 1610.97, "word": " هي", "probability": 0.5625}, {"start": 1610.97, "end": 1611.81, "word": " متتالية", "probability": 0.8819580078125}, {"start": 1611.81, "end": 1612.11, "word": " إما", "probability": 0.777099609375}, {"start": 1612.11, "end": 1612.65, "word": " increasing", "probability": 0.81494140625}, {"start": 1612.65, "end": 1613.17, "word": " أو", "probability": 0.955078125}, {"start": 1613.17, "end": 1613.69, "word": " decreasing", "probability": 0.982421875}, {"start": 1613.69, "end": 1618.25, "word": " معنى", "probability": 0.71435546875}, {"start": 1618.25, "end": 1618.61, "word": " آخر", "probability": 0.959228515625}, {"start": 1618.61, "end": 1618.95, "word": " كل", "probability": 0.900390625}, {"start": 1618.95, "end": 1619.53, "word": " increasing", "probability": 0.5693359375}, {"start": 1619.53, "end": 1620.09, "word": " sequence", "probability": 0.97265625}, {"start": 1620.09, "end": 1620.37, "word": " is", "probability": 0.837890625}, {"start": 1620.37, "end": 1620.87, "word": " monotone", "probability": 0.880859375}, {"start": 1620.87, "end": 1621.49, "word": " sequence", "probability": 0.91064453125}, {"start": 1621.49, "end": 1622.33, "word": " and", "probability": 0.67236328125}, {"start": 1622.33, "end": 1622.83, "word": " every", "probability": 0.72412109375}, {"start": 1622.83, "end": 1623.65, "word": " decreasing", "probability": 0.95458984375}, {"start": 1623.65, "end": 1624.39, "word": " sequence", "probability": 0.94775390625}, {"start": 1624.39, "end": 1624.69, "word": " is", "probability": 0.93603515625}, {"start": 1624.69, "end": 1625.35, "word": " monotone", "probability": 0.9803059895833334}, {"start": 1625.35, "end": 1626.09, "word": " sequence", "probability": 0.72900390625}, {"start": 1626.09, "end": 1628.95, "word": " طب", "probability": 0.800537109375}, {"start": 1628.95, "end": 1629.13, "word": " هاي", "probability": 0.6610107421875}, {"start": 1629.13, "end": 1629.67, "word": " أمثلة", "probability": 0.985595703125}, {"start": 1629.67, "end": 1630.07, "word": " على", "probability": 0.75390625}, {"start": 1630.07, "end": 1630.91, "word": " monotone", "probability": 0.9581705729166666}, {"start": 1630.91, "end": 1631.71, "word": " sequences", "probability": 0.87060546875}, {"start": 1631.71, "end": 1634.11, "word": " فاندي", "probability": 0.6166178385416666}, {"start": 1634.11, "end": 1634.37, "word": " هنا", "probability": 0.98876953125}, {"start": 1634.37, "end": 1634.91, "word": " sequence", "probability": 0.76513671875}, {"start": 1634.91, "end": 1635.69, "word": " n", "probability": 0.4658203125}, {"start": 1635.69, "end": 1635.95, "word": " of", "probability": 0.947265625}, {"start": 1635.95, "end": 1636.45, "word": " natural", "probability": 0.8935546875}, {"start": 1636.45, "end": 1637.05, "word": " numbers", "probability": 0.88232421875}], "temperature": 1.0}, {"id": 64, "seek": 166784, "start": 1638.24, "end": 1667.84, "text": "is increasing واضح ان xn بساوي n أصغر من او ساوي xn plus one اللي هو n زاد واحد لان هذا increasing وهذا increasing ال sequence اللي ال inf term تبعها two to n اللي هي هذه is increasing بينما ال sequence one over n decreasing هي كل حد أكبر من أو ساوي لبعده", "tokens": [271, 5662, 4032, 46958, 5016, 16472, 2031, 77, 4724, 3794, 995, 45865, 297, 5551, 9381, 17082, 2288, 9154, 1975, 2407, 8608, 995, 45865, 2031, 77, 1804, 472, 13672, 1829, 31439, 297, 30767, 18513, 36764, 24401, 5296, 7649, 23758, 5662, 37037, 15730, 5662, 2423, 8310, 13672, 1829, 2423, 1536, 1433, 6055, 3555, 3615, 11296, 732, 281, 297, 13672, 1829, 39896, 29538, 307, 5662, 49374, 15042, 2423, 8310, 472, 670, 297, 23223, 39896, 28242, 11331, 3215, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 5296, 3555, 22488, 3224], "avg_logprob": -0.24694683531235004, "compression_ratio": 1.7828282828282829, "no_speech_prob": 0.0, "words": [{"start": 1638.24, "end": 1638.6, "word": "is", "probability": 0.275634765625}, {"start": 1638.6, "end": 1639.22, "word": " increasing", "probability": 0.9423828125}, {"start": 1639.22, "end": 1641.38, "word": " واضح", "probability": 0.94580078125}, {"start": 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1646.22, "word": " هو", "probability": 0.92333984375}, {"start": 1646.22, "end": 1646.44, "word": " n", "probability": 0.6572265625}, {"start": 1646.44, "end": 1646.74, "word": " زاد", "probability": 0.780029296875}, {"start": 1646.74, "end": 1647.08, "word": " واحد", "probability": 0.9423828125}, {"start": 1647.08, "end": 1648.34, "word": " لان", "probability": 0.3653564453125}, {"start": 1648.34, "end": 1648.56, "word": " هذا", "probability": 0.320556640625}, {"start": 1648.56, "end": 1649.14, "word": " increasing", "probability": 0.85693359375}, {"start": 1649.14, "end": 1650.28, "word": " وهذا", "probability": 0.757568359375}, {"start": 1650.28, "end": 1650.86, "word": " increasing", "probability": 0.9423828125}, {"start": 1650.86, "end": 1651.44, "word": " ال", "probability": 0.336181640625}, {"start": 1651.44, "end": 1651.86, "word": " sequence", "probability": 0.90478515625}, {"start": 1651.86, "end": 1652.14, "word": " اللي", "probability": 0.91943359375}, {"start": 1652.14, "end": 1652.88, "word": " ال", "probability": 0.56298828125}, {"start": 1652.88, "end": 1653.2, "word": " inf", "probability": 0.11181640625}, {"start": 1653.2, "end": 1653.68, "word": " term", "probability": 0.96044921875}, {"start": 1653.68, "end": 1654.32, "word": " تبعها", "probability": 0.9095458984375}, {"start": 1654.32, "end": 1654.54, "word": " two", "probability": 0.837890625}, {"start": 1654.54, "end": 1654.72, "word": " to", "probability": 0.87353515625}, {"start": 1654.72, "end": 1655.02, "word": " n", "probability": 0.7978515625}, {"start": 1655.02, "end": 1655.8, "word": " اللي", "probability": 0.94189453125}, {"start": 1655.8, "end": 1656.04, "word": " هي", "probability": 0.6923828125}, {"start": 1656.04, "end": 1656.5, "word": " هذه", "probability": 0.6103515625}, {"start": 1656.5, "end": 1657.62, "word": " is", "probability": 0.87548828125}, {"start": 1657.62, "end": 1658.26, "word": " increasing", "probability": 0.9794921875}, {"start": 1658.26, "end": 1661.44, "word": " بينما", "probability": 0.97412109375}, {"start": 1661.44, "end": 1661.76, "word": " ال", "probability": 0.92822265625}, {"start": 1661.76, "end": 1662.18, "word": " sequence", "probability": 0.98876953125}, {"start": 1662.18, "end": 1662.52, "word": " one", "probability": 0.9404296875}, {"start": 1662.52, "end": 1662.88, "word": " over", "probability": 0.94140625}, {"start": 1662.88, "end": 1663.28, "word": " n", "probability": 0.9150390625}, {"start": 1663.28, "end": 1664.14, "word": " decreasing", "probability": 0.61279296875}, {"start": 1664.14, "end": 1665.34, "word": " هي", "probability": 0.58837890625}, {"start": 1665.34, "end": 1665.8, "word": " كل", "probability": 0.92333984375}, {"start": 1665.8, "end": 1666.16, "word": " حد", "probability": 0.991455078125}, {"start": 1666.16, "end": 1666.56, "word": " أكبر", "probability": 0.88525390625}, {"start": 1666.56, "end": 1666.72, "word": " من", "probability": 0.99365234375}, {"start": 1666.72, "end": 1666.92, "word": " أو", "probability": 0.85205078125}, {"start": 1666.92, "end": 1667.24, "word": " ساوي", "probability": 0.923828125}, {"start": 1667.24, "end": 1667.84, "word": " لبعده", "probability": 0.8734130859375}], "temperature": 1.0}, {"id": 65, "seek": 169454, "start": 1669.34, "end": 1694.54, "text": "و كذلك ال sequence one over two to n طيب، في سؤال هنا بطلح نفسه، هل كل sequence لازم تكون monotone sequence؟ لأ، مو لأ، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط", "tokens": [2407, 9122, 8848, 23275, 2423, 8310, 472, 670, 732, 281, 297, 23032, 1829, 3555, 12399, 8978, 8608, 33604, 6027, 34105, 4724, 9566, 1211, 5016, 8717, 36178, 3224, 12399, 8032, 1211, 28242, 8310, 5296, 31377, 2304, 6055, 30544, 1108, 310, 546, 8310, 22807, 5296, 10721, 12399, 3714, 2407, 5296, 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0.9864501953125}, {"start": 1690.78, "end": 1690.96, "word": " مش", "probability": 0.98828125}, {"start": 1690.96, "end": 1690.98, "word": " شرط،", "probability": 0.9869384765625}, {"start": 1690.98, "end": 1690.98, "word": " مش", "probability": 0.98779296875}, {"start": 1690.98, "end": 1690.98, "word": " شرط،", "probability": 0.9874267578125}, {"start": 1690.98, "end": 1690.98, "word": " مش", "probability": 0.98779296875}, {"start": 1690.98, "end": 1690.98, "word": " شرط،", "probability": 0.9876708984375}, {"start": 1690.98, "end": 1691.36, "word": " مش", "probability": 0.98779296875}, {"start": 1691.36, "end": 1692.58, "word": " شرط،", "probability": 0.9879150390625}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.9873046875}, {"start": 1692.58, "end": 1692.58, "word": " شرط،", "probability": 0.9884033203125}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.98681640625}, {"start": 1692.58, "end": 1692.58, "word": " شرط،", "probability": 0.9886474609375}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.98681640625}, {"start": 1692.58, "end": 1692.58, "word": " شرط،", "probability": 0.989013671875}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.986328125}, {"start": 1692.58, "end": 1692.58, "word": " شرط،", "probability": 0.989013671875}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.98583984375}, {"start": 1692.58, "end": 1692.58, "word": " شرط،", "probability": 0.9888916015625}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.9853515625}, {"start": 1692.58, "end": 1692.58, "word": " شرط،", "probability": 0.9893798828125}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.984375}, {"start": 1692.58, "end": 1692.58, "word": " شرط،", "probability": 0.9893798828125}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.98388671875}, {"start": 1692.58, "end": 1692.6, "word": " شرط،", "probability": 0.9888916015625}, {"start": 1692.6, "end": 1693.66, "word": " مش", "probability": 0.98193359375}, {"start": 1693.66, "end": 1694.54, "word": " شرط", "probability": 0.9952799479166666}], "temperature": 1.0}, {"id": 66, "seek": 172443, "start": 1695.75, "end": 1724.43, "text": "the following sequence is sequence اللي الحد اللي عام تبعها negative one to n أو n زيادة واحد اللي هي ال alternated sequence ال sequence هذه المتدبدبة alternating يعني المتدبدبة في الإشارة واحد سالب واحد واحد سالب واحد هذه ليست conversion ليست monotone is not increasing and it is not decreasing", "tokens": [3322, 3480, 8310, 307, 8310, 13672, 1829, 21542, 3215, 13672, 1829, 6225, 10943, 6055, 3555, 3615, 11296, 3671, 472, 281, 297, 34051, 297, 30767, 1829, 18513, 3660, 36764, 24401, 13672, 1829, 39896, 2423, 5400, 770, 8310, 2423, 8310, 29538, 9673, 2655, 3215, 44510, 49401, 40062, 37495, 22653, 9673, 2655, 3215, 44510, 49401, 8978, 33688, 8592, 9640, 3660, 36764, 24401, 8608, 6027, 3555, 36764, 24401, 36764, 24401, 8608, 6027, 3555, 36764, 24401, 29538, 32239, 14851, 416, 29153, 32239, 14851, 1108, 310, 546, 307, 406, 5662, 293, 309, 307, 406, 23223], "avg_logprob": -0.26684027678436706, "compression_ratio": 1.9471153846153846, "no_speech_prob": 0.0, "words": [{"start": 1695.75, "end": 1696.01, "word": "the", "probability": 0.168701171875}, {"start": 1696.01, "end": 1696.37, "word": " following", "probability": 0.78564453125}, {"start": 1696.37, "end": 1696.97, "word": " sequence", "probability": 0.91259765625}, {"start": 1696.97, "end": 1697.15, "word": " is", "probability": 0.2027587890625}, {"start": 1697.15, "end": 1697.69, "word": " sequence", "probability": 0.6455078125}, {"start": 1697.69, "end": 1698.09, "word": " اللي", "probability": 0.724365234375}, {"start": 1698.09, "end": 1698.43, "word": " الحد", "probability": 0.83740234375}, {"start": 1698.43, "end": 1698.53, "word": " اللي", "probability": 0.614990234375}, {"start": 1698.53, "end": 1698.67, "word": " عام", "probability": 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{"start": 1702.85, "end": 1704.05, "word": " alternated", "probability": 0.65869140625}, {"start": 1704.05, "end": 1704.83, "word": " sequence", "probability": 0.97509765625}, {"start": 1704.83, "end": 1706.83, "word": " ال", "probability": 0.59716796875}, {"start": 1706.83, "end": 1707.21, "word": " sequence", "probability": 0.85009765625}, {"start": 1707.21, "end": 1707.49, "word": " هذه", "probability": 0.39990234375}, {"start": 1707.49, "end": 1708.47, "word": " المتدبدبة", "probability": 0.84306640625}, {"start": 1708.47, "end": 1709.27, "word": " alternating", "probability": 0.48779296875}, {"start": 1709.27, "end": 1709.75, "word": " يعني", "probability": 0.862060546875}, {"start": 1709.75, "end": 1710.47, "word": " المتدبدبة", "probability": 0.89580078125}, {"start": 1710.47, "end": 1710.61, "word": " في", "probability": 0.94482421875}, {"start": 1710.61, "end": 1711.63, "word": " الإشارة", "probability": 0.984375}, {"start": 1711.63, "end": 1712.79, "word": " واحد", "probability": 0.956787109375}, {"start": 1712.79, "end": 1713.27, "word": " سالب", "probability": 0.7762044270833334}, {"start": 1713.27, "end": 1713.69, "word": " واحد", "probability": 0.949462890625}, {"start": 1713.69, "end": 1714.11, "word": " واحد", "probability": 0.96875}, {"start": 1714.11, "end": 1714.57, "word": " سالب", "probability": 0.9500325520833334}, {"start": 1714.57, "end": 1714.93, "word": " واحد", "probability": 0.951416015625}, {"start": 1714.93, "end": 1715.35, "word": " هذه", "probability": 0.3779296875}, {"start": 1715.35, "end": 1715.75, "word": " ليست", "probability": 0.9833984375}, {"start": 1715.75, "end": 1716.33, "word": " conversion", "probability": 0.452056884765625}, {"start": 1716.33, "end": 1717.01, "word": " ليست", "probability": 0.8076171875}, {"start": 1717.01, "end": 1717.85, "word": " monotone", "probability": 0.7628580729166666}, {"start": 1717.85, "end": 1720.15, "word": " is", "probability": 0.6572265625}, {"start": 1720.15, "end": 1720.45, "word": " not", "probability": 0.96728515625}, {"start": 1720.45, "end": 1721.07, "word": " increasing", "probability": 0.96240234375}, {"start": 1721.07, "end": 1722.61, "word": " and", "probability": 0.56396484375}, {"start": 1722.61, "end": 1723.07, "word": " it", "probability": 0.97021484375}, {"start": 1723.07, "end": 1723.35, "word": " is", "probability": 0.94384765625}, {"start": 1723.35, "end": 1723.63, "word": " not", "probability": 0.96044921875}, {"start": 1723.63, "end": 1724.43, "word": " decreasing", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 67, "seek": 174308, "start": 1726.04, "end": 1743.08, "text": "نفس الشيء ال sequence اللي حد اللي عم تبعها سالب one to n اللي هي سالب واحد موجة بتنين سالب تلاتة و هكذا ال sequence هذه is not monotone لا increasing ولا decreasing تمام واضح", "tokens": [1863, 36178, 25124, 1829, 38207, 2423, 8310, 13672, 1829, 11331, 3215, 13672, 1829, 6225, 2304, 6055, 3555, 3615, 11296, 8608, 6027, 3555, 472, 281, 297, 13672, 1829, 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"probability": 0.62451171875}, {"start": 1728.06, "end": 1728.46, "word": " تبعها", "probability": 0.811279296875}, {"start": 1728.46, "end": 1728.82, "word": " سالب", "probability": 0.7060546875}, {"start": 1728.82, "end": 1729.04, "word": " one", "probability": 0.8408203125}, {"start": 1729.04, "end": 1729.22, "word": " to", "probability": 0.84033203125}, {"start": 1729.22, "end": 1729.54, "word": " n", "probability": 0.70947265625}, {"start": 1729.54, "end": 1731.18, "word": " اللي", "probability": 0.6280517578125}, {"start": 1731.18, "end": 1731.42, "word": " هي", "probability": 0.88916015625}, {"start": 1731.42, "end": 1731.9, "word": " سالب", "probability": 0.9591471354166666}, {"start": 1731.9, "end": 1732.28, "word": " واحد", "probability": 0.968994140625}, {"start": 1732.28, "end": 1732.68, "word": " موجة", "probability": 0.8719075520833334}, {"start": 1732.68, "end": 1733.18, "word": " بتنين", "probability": 0.78125}, {"start": 1733.18, "end": 1733.62, "word": " سالب", "probability": 0.9417317708333334}, {"start": 1733.62, "end": 1734.08, "word": " تلاتة", "probability": 0.951416015625}, {"start": 1734.08, "end": 1734.2, "word": " و", "probability": 0.580078125}, {"start": 1734.2, "end": 1734.74, "word": " هكذا", "probability": 0.8395182291666666}, {"start": 1734.74, "end": 1736.04, "word": " ال", "probability": 0.8740234375}, {"start": 1736.04, "end": 1736.48, "word": " sequence", "probability": 0.982421875}, {"start": 1736.48, "end": 1736.82, "word": " هذه", "probability": 0.44140625}, {"start": 1736.82, "end": 1737.34, "word": " is", "probability": 0.8447265625}, {"start": 1737.34, "end": 1737.64, "word": " not", "probability": 0.9658203125}, {"start": 1737.64, "end": 1738.52, "word": " monotone", "probability": 0.8024088541666666}, {"start": 1738.52, "end": 1739.54, "word": " لا", "probability": 0.7568359375}, {"start": 1739.54, "end": 1740.02, "word": " increasing", "probability": 0.8720703125}, {"start": 1740.02, "end": 1740.56, "word": " ولا", "probability": 0.94873046875}, {"start": 1740.56, "end": 1741.82, "word": " decreasing", "probability": 0.974609375}, {"start": 1741.82, "end": 1742.62, "word": " تمام", "probability": 0.8642578125}, {"start": 1742.62, "end": 1743.08, "word": " واضح", "probability": 0.8948567708333334}], "temperature": 1.0}, {"id": 68, "seek": 176687, "start": 1743.93, "end": 1766.87, "text": "إذا ال sequence .. أي .. لو أخدنا أي sequence عشوائية فممكن تكون increasing، ممكن تكون decreasing، ممكن تكون neither، neither increasing nor decreasing زي ال function ممكن تكون odd أو even أو neither، لا odd ولا even، أه؟ تمام؟ طيب ال .. في نظرية مهمة هنا في هذا السياق", "tokens": [28814, 15730, 2423, 8310, 4386, 36632, 4386, 45164, 5551, 9778, 3215, 8315, 36632, 8310, 6225, 8592, 2407, 16373, 10632, 6156, 2304, 43020, 6055, 30544, 5662, 12399, 3714, 43020, 6055, 30544, 23223, 12399, 3714, 43020, 6055, 30544, 9662, 12399, 9662, 5662, 6051, 23223, 30767, 1829, 2423, 2445, 3714, 43020, 6055, 30544, 7401, 34051, 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"probability": 0.97900390625}], "temperature": 1.0}, {"id": 70, "seek": 182517, "start": 1796.49, "end": 1825.17, "text": "الان هذه الـ monotone sequence بتكون convergent if and only if it is bounded تمام؟ moreover إضافة إلى ذلك لو كانت ال sequence x in هذه bounded and increasing فأكيد طبعا convergent و ال limit تبعتها بساوي ال supremum إلها ك set كذلك لو كانت ال sequence x in bounded و decreasing", "tokens": [6027, 7649, 29538, 2423, 39184, 1108, 310, 546, 8310, 39894, 30544, 9652, 6930, 498, 293, 787, 498, 309, 307, 37498, 46811, 10943, 22807, 544, 3570, 11933, 11242, 31845, 3660, 30731, 29910, 23275, 45164, 25961, 2655, 2423, 8310, 2031, 294, 29538, 37498, 293, 5662, 6156, 10721, 4117, 25708, 23032, 3555, 3615, 995, 9652, 6930, 4032, 2423, 4948, 6055, 3555, 34268, 11296, 4724, 3794, 995, 45865, 2423, 23710, 449, 11933, 1211, 11296, 9122, 992, 9122, 8848, 23275, 45164, 25961, 2655, 2423, 8310, 2031, 294, 37498, 4032, 23223], "avg_logprob": -0.18050508703603302, "compression_ratio": 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"word": " تبعتها", "probability": 0.9014892578125}, {"start": 1817.87, "end": 1818.43, "word": " بساوي", "probability": 0.839111328125}, {"start": 1818.43, "end": 1818.63, "word": " ال", "probability": 0.365966796875}, {"start": 1818.63, "end": 1819.17, "word": " supremum", "probability": 0.8212890625}, {"start": 1819.17, "end": 1819.43, "word": " إلها", "probability": 0.685546875}, {"start": 1819.43, "end": 1819.65, "word": " ك", "probability": 0.91357421875}, {"start": 1819.65, "end": 1819.97, "word": " set", "probability": 0.78955078125}, {"start": 1819.97, "end": 1822.37, "word": " كذلك", "probability": 0.9840494791666666}, {"start": 1822.37, "end": 1822.59, "word": " لو", "probability": 0.955078125}, {"start": 1822.59, "end": 1822.93, "word": " كانت", "probability": 0.994384765625}, {"start": 1822.93, "end": 1823.05, "word": " ال", "probability": 0.9501953125}, {"start": 1823.05, "end": 1823.31, "word": " sequence", "probability": 0.9931640625}, {"start": 1823.31, "end": 1823.65, "word": " x", "probability": 0.970703125}, {"start": 1823.65, "end": 1823.89, "word": " in", "probability": 0.92236328125}, {"start": 1823.89, "end": 1824.31, "word": " bounded", "probability": 0.92333984375}, {"start": 1824.31, "end": 1824.65, "word": " و", "probability": 0.98681640625}, {"start": 1824.65, "end": 1825.17, "word": " decreasing", "probability": 0.9775390625}], "temperature": 1.0}, {"id": 71, "seek": 185469, "start": 1827.59, "end": 1854.69, "text": "فبتكون طبعا convergent و ال limit بتبعتها بساوة ال inform اللي لها ك set طيب احنا عندي انا عندي هنا two statements او تلاتة statements انا عندي العبارة هذه انا عندي بتثبت العبارة هذه و العبارتين هدون فكيف البرهان بتتم", "tokens": [5172, 3555, 2655, 30544, 23032, 3555, 3615, 995, 9652, 6930, 4032, 2423, 4948, 39894, 3555, 34268, 11296, 4724, 3794, 995, 2407, 3660, 2423, 1356, 13672, 1829, 5296, 11296, 9122, 992, 23032, 1829, 3555, 1975, 5016, 8315, 18871, 16254, 1975, 8315, 18871, 16254, 34105, 732, 12363, 1975, 2407, 6055, 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يعنى", "tokens": [10721, 12610, 44049, 18863, 3555, 9640, 3660, 16247, 12610, 7578, 13672, 7578, 6156, 7578, 2423, 26890, 2407, 31377, 29538, 498, 293, 787, 498, 5629, 20328, 5016, 6156, 5172, 7578, 732, 3166, 36764, 24401, 23758, 2423, 644, 2423, 787, 498, 644, 4032, 2423, 498, 644, 8717, 8592, 38688, 2423, 787, 498, 644, 37495, 1863, 7578], "avg_logprob": -0.18991477977145801, "compression_ratio": 1.5571428571428572, "no_speech_prob": 0.0, "words": [{"start": 1856.77, "end": 1857.23, "word": "أول", "probability": 0.91845703125}, {"start": 1857.23, "end": 1857.49, "word": " شي", "probability": 0.79736328125}, {"start": 1857.49, "end": 1858.89, "word": " العبارة", "probability": 0.87744140625}, {"start": 1858.89, "end": 1859.29, "word": " الأولى", "probability": 0.9796549479166666}, {"start": 1859.29, "end": 1859.39, "word": " اللى", "probability": 0.876953125}, {"start": 1859.39, "end": 1859.51, "word": " فى", "probability": 0.753173828125}, {"start": 1859.51, "end": 1860.15, "word": 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0.98095703125}, {"start": 1875.75, "end": 1876.17, "word": " only", "probability": 0.8994140625}, {"start": 1876.17, "end": 1876.55, "word": " if", "probability": 0.98095703125}, {"start": 1876.55, "end": 1877.01, "word": " part", "probability": 0.94873046875}, {"start": 1877.01, "end": 1877.47, "word": " يعنى", "probability": 0.8458658854166666}], "temperature": 1.0}, {"id": 73, "seek": 190770, "start": 1878.34, "end": 1907.7, "text": "لو كانت x in convergent بينا نثبت إنها it is bounded وهذا أثبتناه في نظرية سابقة أثبتنا إن كل تجارب convergent is bounded اختبار الدم فاكرين؟ إذا هذا was proved proved earlier تم إثباته سابقا في نظرية سابقة", "tokens": [1211, 2407, 25961, 2655, 2031, 294, 9652, 6930, 4724, 1829, 8315, 8717, 12984, 3555, 2655, 36145, 11296, 309, 307, 37498, 37037, 15730, 5551, 12984, 3555, 2655, 8315, 3224, 8978, 8717, 19913, 2288, 10632, 8608, 16758, 28671, 5551, 12984, 3555, 2655, 8315, 36145, 28242, 6055, 7435, 9640, 3555, 9652, 6930, 307, 37498, 1975, 46456, 3555, 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1881.58, "end": 1881.74, "word": " it", "probability": 0.59814453125}, {"start": 1881.74, "end": 1881.94, "word": " is", "probability": 0.935546875}, {"start": 1881.94, "end": 1882.34, "word": " bounded", "probability": 0.93310546875}, {"start": 1882.34, "end": 1883.18, "word": " وهذا", "probability": 0.68798828125}, {"start": 1883.18, "end": 1883.98, "word": " أثبتناه", "probability": 0.9722493489583334}, {"start": 1883.98, "end": 1884.56, "word": " في", "probability": 0.95263671875}, {"start": 1884.56, "end": 1885.1, "word": " نظرية", "probability": 0.974853515625}, {"start": 1885.1, "end": 1885.68, "word": " سابقة", "probability": 0.98046875}, {"start": 1885.68, "end": 1887.16, "word": " أثبتنا", "probability": 0.9041015625}, {"start": 1887.16, "end": 1887.46, "word": " إن", "probability": 0.62353515625}, {"start": 1887.46, "end": 1887.96, "word": " كل", "probability": 0.66064453125}, {"start": 1887.96, "end": 1888.18, "word": " تجارب", "probability": 0.57147216796875}, {"start": 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1929.67, "end": 1930.21, "word": " bounded", "probability": 0.9609375}, {"start": 1930.21, "end": 1932.97, "word": " السيكوانس", "probability": 0.92236328125}, {"start": 1932.97, "end": 1933.19, "word": " لو", "probability": 0.9892578125}, {"start": 1933.19, "end": 1933.61, "word": " كانت", "probability": 0.98583984375}, {"start": 1933.61, "end": 1934.11, "word": " bounded", "probability": 0.9619140625}, {"start": 1934.11, "end": 1937.73, "word": " و", "probability": 0.982421875}, {"start": 1937.73, "end": 1938.51, "word": " monotone", "probability": 0.88330078125}], "temperature": 1.0}, {"id": 75, "seek": 197026, "start": 1941.42, "end": 1970.26, "text": "طبعا احنا فرضين انها monotone اه من البداية x in is monotone فالان عشان نكمل برهان العبارة هذه ال if and only if او ال by conditional statement هذا فبدنا نثبت ان لو كانت ال sequence bounded و monotone فبتطلع convergent طيب monotone", "tokens": [9566, 3555, 3615, 995, 1975, 5016, 8315, 6156, 43042, 9957, 16472, 11296, 1108, 310, 546, 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"word": " فبدنا", "probability": 0.82275390625}, {"start": 1956.68, "end": 1957.78, "word": " نثبت", "probability": 0.994140625}, {"start": 1957.78, "end": 1958.0, "word": " ان", "probability": 0.8544921875}, {"start": 1958.0, "end": 1958.24, "word": " لو", "probability": 0.765625}, {"start": 1958.24, "end": 1958.62, "word": " كانت", "probability": 0.98095703125}, {"start": 1958.62, "end": 1958.74, "word": " ال", "probability": 0.83984375}, {"start": 1958.74, "end": 1959.2, "word": " sequence", "probability": 0.9658203125}, {"start": 1959.2, "end": 1959.84, "word": " bounded", "probability": 0.9306640625}, {"start": 1959.84, "end": 1960.92, "word": " و", "probability": 0.9912109375}, {"start": 1960.92, "end": 1961.62, "word": " monotone", "probability": 0.9446614583333334}, {"start": 1961.62, "end": 1963.52, "word": " فبتطلع", "probability": 0.9628092447916666}, {"start": 1963.52, "end": 1964.32, "word": " convergent", "probability": 0.88525390625}, {"start": 1964.32, "end": 1969.52, "word": " طيب", "probability": 0.86328125}, {"start": 1969.52, "end": 1970.26, "word": " monotone", "probability": 0.78515625}], "temperature": 1.0}, {"id": 76, "seek": 200030, "start": 1970.68, "end": 2000.3, "text": "مونوتون لما ال sequence تكون مونوتون معناها اما increasing او decreasing او decreasing اذا عشان اثبت الجزء هذا بده اثبت a و b هذا الجزء هذا لبرهانه بده برهين a و b", "tokens": [2304, 11536, 35473, 11536, 5296, 15042, 2423, 8310, 6055, 30544, 3714, 11536, 35473, 11536, 20449, 8315, 11296, 1975, 15042, 5662, 1975, 2407, 23223, 1975, 2407, 23223, 1975, 15730, 6225, 8592, 7649, 1975, 12984, 3555, 2655, 25724, 11622, 38207, 23758, 47525, 3224, 1975, 12984, 3555, 2655, 257, 4032, 272, 23758, 25724, 11622, 38207, 23758, 5296, 26890, 3224, 7649, 3224, 47525, 3224, 4724, 2288, 3224, 9957, 257, 4032, 272], "avg_logprob": -0.1843979718054042, "compression_ratio": 1.7692307692307692, "no_speech_prob": 0.0, "words": [{"start": 1970.68, "end": 1971.5, "word": "مونوتون", "probability": 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"word": " صحيح", "probability": 0.990966796875}, {"start": 2344.59, "end": 2345.05, "word": " لكل", "probability": 0.962646484375}, {"start": 2345.05, "end": 2345.53, "word": " إبسلون", "probability": 0.9888671875}, {"start": 2345.53, "end": 2345.85, "word": " أكبر", "probability": 0.9762369791666666}, {"start": 2345.85, "end": 2346.07, "word": " من", "probability": 0.9970703125}, {"start": 2346.07, "end": 2346.47, "word": " سفر", "probability": 0.81201171875}, {"start": 2346.47, "end": 2347.69, "word": " إذن", "probability": 0.7986653645833334}, {"start": 2347.69, "end": 2347.97, "word": " هذا", "probability": 0.94580078125}, {"start": 2347.97, "end": 2348.47, "word": " معناه", "probability": 0.9825846354166666}, {"start": 2348.47, "end": 2348.81, "word": " حسب", "probability": 0.94677734375}, {"start": 2348.81, "end": 2349.43, "word": " التعريف", "probability": 0.9942626953125}, {"start": 2349.43, "end": 2349.65, "word": " إن", "probability": 0.454345703125}, {"start": 2349.65, "end": 2349.93, "word": " limit", "probability": 0.921875}, {"start": 2349.93, "end": 2350.61, "word": " xn", "probability": 0.949462890625}, {"start": 2350.61, "end": 2351.45, "word": " بساوي", "probability": 0.8616943359375}, {"start": 2351.45, "end": 2352.47, "word": " x", "probability": 0.89794921875}, {"start": 2352.47, "end": 2353.19, "word": " star", "probability": 0.890625}], "temperature": 1.0}, {"id": 90, "seek": 237530, "start": 2358.78, "end": 2375.3, "text": "إذا هذا بثبت ال claim وبالتالي هكذا نكون أثبتنا الجزء A من النظرية فالجزء التاني B ممكن نستخدم A في برهان ال B", "tokens": [28814, 15730, 23758, 4724, 12984, 3555, 2655, 2423, 3932, 46599, 6027, 2655, 6027, 1829, 8032, 4117, 15730, 8717, 30544, 5551, 12984, 3555, 2655, 8315, 25724, 11622, 38207, 316, 9154, 28239, 19913, 2288, 10632, 6156, 6027, 7435, 11622, 38207, 16712, 7649, 1829, 363, 3714, 43020, 8717, 14851, 9778, 40448, 316, 8978, 4724, 2288, 3224, 7649, 2423, 363], "avg_logprob": -0.2946820133610776, 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"temperature": 1.0}, {"id": 91, "seek": 240603, "start": 2378.51, "end": 2406.03, "text": "ففي الجزء B الان انا عندي ال sequence تبعتي bounded و decreasing اذا ا assume x in is bounded and decreasing فاش عمل هعرف sequence جديدة yn اللي هي negative الحد العام تبعها negative x in تمام؟ الان بما ان x in decreasing اذا ال sequence سالب x in تطلع increasing", "tokens": [5172, 41185, 25724, 11622, 38207, 363, 2423, 7649, 1975, 8315, 18871, 16254, 2423, 8310, 6055, 3555, 3615, 31371, 37498, 4032, 23223, 1975, 15730, 1975, 6552, 2031, 294, 307, 37498, 293, 23223, 6156, 33599, 6225, 42213, 8032, 3615, 28480, 8310, 10874, 16254, 41891, 17861, 13672, 1829, 39896, 3671, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 3671, 2031, 294, 46811, 10943, 22807, 2423, 7649, 4724, 15042, 16472, 2031, 294, 23223, 1975, 15730, 2423, 8310, 8608, 6027, 3555, 2031, 294, 6055, 9566, 1211, 3615, 5662], "avg_logprob": -0.28106397958028884, "compression_ratio": 1.7450980392156863, "no_speech_prob": 0.0, 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0.805908203125}, {"start": 2391.77, "end": 2392.31, "word": " sequence", "probability": 0.525390625}, {"start": 2392.31, "end": 2392.87, "word": " جديدة", "probability": 0.9352213541666666}, {"start": 2392.87, "end": 2393.53, "word": " yn", "probability": 0.50732421875}, {"start": 2393.53, "end": 2394.45, "word": " اللي", "probability": 0.8671875}, {"start": 2394.45, "end": 2394.77, "word": " هي", "probability": 0.9482421875}, {"start": 2394.77, "end": 2395.25, "word": " negative", "probability": 0.7421875}, {"start": 2395.25, "end": 2395.69, "word": " الحد", "probability": 0.8203125}, {"start": 2395.69, "end": 2395.93, "word": " العام", "probability": 0.9130859375}, {"start": 2395.93, "end": 2396.37, "word": " تبعها", "probability": 0.95458984375}, {"start": 2396.37, "end": 2396.75, "word": " negative", "probability": 0.826171875}, {"start": 2396.75, "end": 2397.23, "word": " x", "probability": 0.98095703125}, {"start": 2397.23, "end": 2397.99, "word": " in", "probability": 0.8046875}, {"start": 2397.99, "end": 2399.93, "word": " تمام؟", "probability": 0.5948893229166666}, {"start": 2399.93, "end": 2400.39, "word": " الان", "probability": 0.817626953125}, {"start": 2400.39, "end": 2400.77, "word": " بما", "probability": 0.979736328125}, {"start": 2400.77, "end": 2400.91, "word": " ان", "probability": 0.85009765625}, {"start": 2400.91, "end": 2401.25, "word": " x", "probability": 0.43701171875}, {"start": 2401.25, "end": 2401.53, "word": " in", "probability": 0.8720703125}, {"start": 2401.53, "end": 2402.11, "word": " decreasing", "probability": 0.859375}, {"start": 2402.11, "end": 2402.97, "word": " اذا", "probability": 0.6639404296875}, {"start": 2402.97, "end": 2403.17, "word": " ال", "probability": 0.91064453125}, {"start": 2403.17, "end": 2403.51, "word": " sequence", "probability": 0.98388671875}, {"start": 2403.51, "end": 2404.15, "word": " سالب", "probability": 0.77392578125}, {"start": 2404.15, "end": 2404.43, "word": " x", "probability": 0.96923828125}, {"start": 2404.43, "end": 2404.65, "word": " in", "probability": 0.90625}, {"start": 2404.65, "end": 2405.17, "word": " تطلع", "probability": 0.95556640625}, {"start": 2405.17, "end": 2406.03, "word": " increasing", "probability": 0.9580078125}], "temperature": 1.0}, {"id": 92, "seek": 242905, "start": 2407.47, "end": 2429.05, "text": "وطبعا بما أن ال sequence x in bounded إذا ال sequence سالب x in أيضا bounded إذا الأن أنا في عندي sequence جديد اللي هي sequence yn bounded وin crazy إذا حسب الجزء a by part a limit ال sequence yn تطلع exist", "tokens": [2407, 9566, 3555, 3615, 995, 4724, 15042, 14739, 2423, 8310, 2031, 294, 37498, 11933, 15730, 2423, 8310, 8608, 6027, 3555, 2031, 294, 36632, 11242, 995, 37498, 11933, 15730, 16247, 1863, 41850, 8978, 18871, 16254, 8310, 10874, 16254, 3215, 13672, 1829, 39896, 8310, 17861, 37498, 4032, 259, 3219, 11933, 15730, 11331, 35457, 25724, 11622, 38207, 257, 538, 644, 257, 4948, 2423, 8310, 17861, 6055, 9566, 1211, 3615, 2514], 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"probability": 0.97509765625}, {"start": 2412.25, "end": 2412.77, "word": " سالب", "probability": 0.8133138020833334}, {"start": 2412.77, "end": 2412.99, "word": " x", "probability": 0.951171875}, {"start": 2412.99, "end": 2413.23, "word": " in", "probability": 0.90625}, {"start": 2413.23, "end": 2413.63, "word": " أيضا", "probability": 0.9420572916666666}, {"start": 2413.63, "end": 2414.07, "word": " bounded", "probability": 0.8955078125}, {"start": 2414.07, "end": 2415.29, "word": " إذا", "probability": 0.8505859375}, {"start": 2415.29, "end": 2415.67, "word": " الأن", "probability": 0.59326171875}, {"start": 2415.67, "end": 2415.87, "word": " أنا", "probability": 0.625}, {"start": 2415.87, "end": 2415.97, "word": " في", "probability": 0.7978515625}, {"start": 2415.97, "end": 2416.29, "word": " عندي", "probability": 0.82861328125}, {"start": 2416.29, "end": 2416.79, "word": " sequence", "probability": 0.90478515625}, {"start": 2416.79, "end": 2417.25, "word": " جديد", "probability": 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" xn", "probability": 0.917236328125}, {"start": 2493.76, "end": 2494.46, "word": " convergent", "probability": 0.6536865234375}, {"start": 2494.46, "end": 2495.36, "word": " وال", "probability": 0.316650390625}, {"start": 2495.36, "end": 2495.62, "word": " limit", "probability": 0.9169921875}, {"start": 2495.62, "end": 2496.26, "word": " تبعتها", "probability": 0.898681640625}, {"start": 2496.26, "end": 2497.08, "word": " بساوي", "probability": 0.9420166015625}, {"start": 2497.08, "end": 2497.36, "word": " ال", "probability": 0.94140625}, {"start": 2497.36, "end": 2497.64, "word": " inform", "probability": 0.7412109375}], "temperature": 1.0}, {"id": 96, "seek": 251844, "start": 2500.76, "end": 2518.44, "text": "بنكمل برهان الـ monotone convergence theorem طبعا الأمثلة هذه اللي هنا كلها أمثلة تطبيق على الـ monotone convergence theorem فارجو أنكم تحاولوا تخرجوا الأمثلة هذه و تشوفوا كيف نستخدم الـ monotone convergence theorem في", "tokens": [3555, 1863, 24793, 1211, 4724, 2288, 3224, 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\ No newline at end of file